Properties

Label 128.3.h.a.79.2
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 79.2
Character \(\chi\) \(=\) 128.79
Dual form 128.3.h.a.47.2

$q$-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 \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).

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

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
\(3\) −0.936461 2.26082i −0.312154 0.753605i −0.999625 0.0273938i \(-0.991279\pi\)
0.687471 0.726212i \(-0.258721\pi\)
\(4\) 0 0
\(5\) −3.18221 + 7.68254i −0.636442 + 1.53651i 0.194945 + 0.980814i \(0.437547\pi\)
−0.831387 + 0.555693i \(0.812453\pi\)
\(6\) 0 0
\(7\) −3.67370 + 3.67370i −0.524814 + 0.524814i −0.919021 0.394208i \(-0.871019\pi\)
0.394208 + 0.919021i \(0.371019\pi\)
\(8\) 0 0
\(9\) 2.12963 2.12963i 0.236625 0.236625i
\(10\) 0 0
\(11\) −6.10089 + 14.7288i −0.554626 + 1.33899i 0.359345 + 0.933205i \(0.383000\pi\)
−0.913971 + 0.405781i \(0.867000\pi\)
\(12\) 0 0
\(13\) 2.82075 + 6.80990i 0.216981 + 0.523839i 0.994466 0.105063i \(-0.0335046\pi\)
−0.777484 + 0.628902i \(0.783505\pi\)
\(14\) 0 0
\(15\) 20.3488 1.35659
\(16\) 0 0
\(17\) 3.67152i 0.215972i 0.994152 + 0.107986i \(0.0344401\pi\)
−0.994152 + 0.107986i \(0.965560\pi\)
\(18\) 0 0
\(19\) 1.65751 0.686564i 0.0872375 0.0361349i −0.338638 0.940917i \(-0.609966\pi\)
0.425875 + 0.904782i \(0.359966\pi\)
\(20\) 0 0
\(21\) 11.7458 + 4.86528i 0.559325 + 0.231680i
\(22\) 0 0
\(23\) 8.31529 + 8.31529i 0.361534 + 0.361534i 0.864378 0.502843i \(-0.167713\pi\)
−0.502843 + 0.864378i \(0.667713\pi\)
\(24\) 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 −0.933483 0.358621i \(-0.883247\pi\)
−0.406489 + 0.913656i \(0.633247\pi\)
\(30\) 0 0
\(31\) 4.11293i 0.132675i 0.997797 + 0.0663376i \(0.0211314\pi\)
−0.997797 + 0.0663376i \(0.978869\pi\)
\(32\) 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 −0.389493 0.921030i \(-0.627350\pi\)
0.926679 0.375853i \(-0.122650\pi\)
\(38\) 0 0
\(39\) 12.7544 12.7544i 0.327036 0.327036i
\(40\) 0 0
\(41\) 21.1187 21.1187i 0.515091 0.515091i −0.400991 0.916082i \(-0.631334\pi\)
0.916082 + 0.400991i \(0.131334\pi\)
\(42\) 0 0
\(43\) 0.102495 0.247444i 0.00238360 0.00575451i −0.922683 0.385559i \(-0.874009\pi\)
0.925067 + 0.379804i \(0.124009\pi\)
\(44\) 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 0.585692 0.810534i \(-0.300823\pi\)
−0.158987 + 0.987281i \(0.550823\pi\)
\(54\) 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 0.999869 + 0.0161592i \(0.00514387\pi\)
0.718441 + 0.695588i \(0.244856\pi\)
\(60\) 0 0
\(61\) −14.0475 + 5.81867i −0.230287 + 0.0953880i −0.494843 0.868982i \(-0.664775\pi\)
0.264556 + 0.964370i \(0.414775\pi\)
\(62\) 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 0.894083 0.447901i \(-0.147828\pi\)
−0.948926 + 0.315498i \(0.897828\pi\)
\(68\) 0 0
\(69\) 11.0124 26.5863i 0.159600 0.385309i
\(70\) 0 0
\(71\) −75.7712 + 75.7712i −1.06720 + 1.06720i −0.0696271 + 0.997573i \(0.522181\pi\)
−0.997573 + 0.0696271i \(0.977819\pi\)
\(72\) 0 0
\(73\) −29.0378 + 29.0378i −0.397779 + 0.397779i −0.877449 0.479670i \(-0.840756\pi\)
0.479670 + 0.877449i \(0.340756\pi\)
\(74\) 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 0.149381 0.988780i \(-0.452272\pi\)
0.804801 + 0.593544i \(0.202272\pi\)
\(84\) 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 0.985188 0.171480i \(-0.0548548\pi\)
−0.171480 + 0.985188i \(0.554855\pi\)
\(90\) 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 −0.956694 0.291095i \(-0.905981\pi\)
0.882320 + 0.470650i \(0.155981\pi\)
\(102\) 0 0
\(103\) −0.589180 + 0.589180i −0.00572020 + 0.00572020i −0.709961 0.704241i \(-0.751288\pi\)
0.704241 + 0.709961i \(0.251288\pi\)
\(104\) 0 0
\(105\) −74.7554 + 74.7554i −0.711956 + 0.711956i
\(106\) 0 0
\(107\) 55.4567 133.884i 0.518287 1.25126i −0.420668 0.907215i \(-0.638204\pi\)
0.938955 0.344041i \(-0.111796\pi\)
\(108\) 0 0
\(109\) 29.4015 + 70.9815i 0.269739 + 0.651207i 0.999471 0.0325264i \(-0.0103553\pi\)
−0.729732 + 0.683733i \(0.760355\pi\)
\(110\) 0 0
\(111\) −127.098 −1.14502
\(112\) 0 0
\(113\) 134.274i 1.18826i 0.804368 + 0.594131i \(0.202504\pi\)
−0.804368 + 0.594131i \(0.797496\pi\)
\(114\) 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 \(-0.877301\pi\)
0.926621 0.375996i \(-0.122699\pi\)
\(128\) 0 0
\(129\) −0.655407 −0.00508068
\(130\) 0 0
\(131\) 67.1188 + 162.039i 0.512357 + 1.23694i 0.942508 + 0.334183i \(0.108460\pi\)
−0.430151 + 0.902757i \(0.641540\pi\)
\(132\) 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 −0.304794 0.952418i \(-0.598588\pi\)
0.952418 + 0.304794i \(0.0985878\pi\)
\(138\) 0 0
\(139\) 27.6838 66.8346i 0.199164 0.480824i −0.792469 0.609912i \(-0.791205\pi\)
0.991633 + 0.129087i \(0.0412048\pi\)
\(140\) 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 0.0188878 0.999822i \(-0.493987\pi\)
−0.693625 + 0.720336i \(0.743987\pi\)
\(150\) 0 0
\(151\) 134.706 + 134.706i 0.892096 + 0.892096i 0.994720 0.102624i \(-0.0327239\pi\)
−0.102624 + 0.994720i \(0.532724\pi\)
\(152\) 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 −0.553976 0.832533i \(-0.686890\pi\)
0.196969 + 0.980410i \(0.436890\pi\)
\(158\) 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 −0.934029 0.357198i \(-0.883732\pi\)
0.407881 0.913035i \(-0.366268\pi\)
\(164\) 0 0
\(165\) −124.146 + 299.715i −0.752399 + 1.81645i
\(166\) 0 0
\(167\) −72.6395 + 72.6395i −0.434967 + 0.434967i −0.890314 0.455347i \(-0.849515\pi\)
0.455347 + 0.890314i \(0.349515\pi\)
\(168\) 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 0.911727 0.410796i \(-0.134749\pi\)
−0.935165 + 0.354212i \(0.884749\pi\)
\(174\) 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 −0.889817 0.456317i \(-0.849168\pi\)
−0.306531 + 0.951861i \(0.599168\pi\)
\(180\) 0 0
\(181\) −98.2125 40.6810i −0.542611 0.224757i 0.0945057 0.995524i \(-0.469873\pi\)
−0.637116 + 0.770768i \(0.719873\pi\)
\(182\) 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 \(0.157923\pi\)
−0.879431 + 0.476026i \(0.842077\pi\)
\(192\) 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 −0.958203 0.286089i \(-0.907645\pi\)
0.879847 + 0.475256i \(0.157645\pi\)
\(198\) 0 0
\(199\) 135.618 135.618i 0.681498 0.681498i −0.278840 0.960338i \(-0.589950\pi\)
0.960338 + 0.278840i \(0.0899498\pi\)
\(200\) 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 −0.684954 0.728587i \(-0.740178\pi\)
0.0308532 + 0.999524i \(0.490178\pi\)
\(212\) 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 \(-0.978127\pi\)
0.997640 0.0686609i \(-0.0218727\pi\)
\(224\) 0 0
\(225\) −132.962 −0.590944
\(226\) 0 0
\(227\) −8.41171 20.3077i −0.0370560 0.0894611i 0.904268 0.426965i \(-0.140417\pi\)
−0.941324 + 0.337504i \(0.890417\pi\)
\(228\) 0 0
\(229\) 76.6532 185.057i 0.334730 0.808110i −0.663474 0.748199i \(-0.730919\pi\)
0.998204 0.0599101i \(-0.0190814\pi\)
\(230\) 0 0
\(231\) −143.320 + 143.320i −0.620432 + 0.620432i
\(232\) 0 0
\(233\) −127.558 + 127.558i −0.547461 + 0.547461i −0.925706 0.378245i \(-0.876528\pi\)
0.378245 + 0.925706i \(0.376528\pi\)
\(234\) 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 \(0.312928\pi\)
−0.554451 + 0.832216i \(0.687072\pi\)
\(242\) 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 −0.101829 0.994802i \(-0.532469\pi\)
−0.775435 + 0.631427i \(0.782469\pi\)
\(252\) 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 0.272219 0.962235i \(-0.412242\pi\)
0.962235 0.272219i \(-0.0877576\pi\)
\(264\) 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 −0.994193 0.107612i \(-0.965680\pi\)
0.626907 0.779094i \(-0.284320\pi\)
\(270\) 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 0.458556 0.888666i \(-0.348367\pi\)
−0.304134 + 0.952629i \(0.598367\pi\)
\(278\) 0 0
\(279\) 8.75902 + 8.75902i 0.0313943 + 0.0313943i
\(280\) 0 0
\(281\) −167.424 167.424i −0.595813 0.595813i 0.343382 0.939196i \(-0.388427\pi\)
−0.939196 + 0.343382i \(0.888427\pi\)
\(282\) 0 0
\(283\) 494.380 + 204.779i 1.74693 + 0.723601i 0.998151 + 0.0607762i \(0.0193576\pi\)
0.748775 + 0.662824i \(0.230642\pi\)
\(284\) 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 −0.448075 0.893996i \(-0.647890\pi\)
0.948987 0.315314i \(-0.102110\pi\)
\(294\) 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 −0.293962 0.955817i \(-0.594974\pi\)
0.468003 + 0.883727i \(0.344974\pi\)
\(308\) 0 0
\(309\) 1.88377 + 0.780284i 0.00609635 + 0.00252519i
\(310\) 0 0
\(311\) −274.515 274.515i −0.882685 0.882685i 0.111122 0.993807i \(-0.464556\pi\)
−0.993807 + 0.111122i \(0.964556\pi\)
\(312\) 0 0
\(313\) −78.4013 78.4013i −0.250483 0.250483i 0.570685 0.821169i \(-0.306678\pi\)
−0.821169 + 0.570685i \(0.806678\pi\)
\(314\) 0 0
\(315\) −120.210 49.7928i −0.381620 0.158072i
\(316\) 0 0
\(317\) −136.520 + 56.5483i −0.430661 + 0.178386i −0.587475 0.809243i \(-0.699878\pi\)
0.156814 + 0.987628i \(0.449878\pi\)
\(318\) 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 0.543841 + 0.839189i \(0.316970\pi\)
−0.977949 + 0.208843i \(0.933030\pi\)
\(332\) 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 \(0.251705\pi\)
−0.703310 + 0.710884i \(0.748295\pi\)
\(338\) 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 0.120585 0.992703i \(-0.461523\pi\)
−0.616680 + 0.787214i \(0.711523\pi\)
\(348\) 0 0
\(349\) 388.120 160.765i 1.11209 0.460644i 0.250434 0.968134i \(-0.419427\pi\)
0.861658 + 0.507490i \(0.169427\pi\)
\(350\) 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 −0.833610 0.552353i \(-0.813730\pi\)
0.552353 + 0.833610i \(0.313730\pi\)
\(360\) 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 0.994593 0.103845i \(-0.0331146\pi\)
0.629854 + 0.776713i \(0.283115\pi\)
\(374\) 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 0.870750 0.491725i \(-0.163634\pi\)
0.268011 + 0.963416i \(0.413634\pi\)
\(380\) 0 0
\(381\) −215.915 + 89.4348i −0.566705 + 0.234737i
\(382\) 0 0
\(383\) 583.987i 1.52477i 0.647124 + 0.762385i \(0.275972\pi\)
−0.647124 + 0.762385i \(0.724028\pi\)
\(384\) 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 −0.980667 0.195684i \(-0.937307\pi\)
0.831806 + 0.555067i \(0.187307\pi\)
\(390\) 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 0.920944 + 0.389696i \(0.127420\pi\)
−0.375649 + 0.926762i \(0.622580\pi\)
\(398\) 0 0
\(399\) 22.8092 0.0571658
\(400\) 0 0
\(401\) 271.900i 0.678055i 0.940776 + 0.339028i \(0.110098\pi\)
−0.940776 + 0.339028i \(0.889902\pi\)
\(402\) 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 0.449147 0.893458i \(-0.351728\pi\)
−0.893458 + 0.449147i \(0.851728\pi\)
\(410\) 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 0.992084 0.125575i \(-0.0400775\pi\)
−0.790304 + 0.612715i \(0.790077\pi\)
\(420\) 0 0
\(421\) 13.1417 31.7269i 0.0312155 0.0753608i −0.907503 0.420045i \(-0.862014\pi\)
0.938719 + 0.344685i \(0.112014\pi\)
\(422\) 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 \(-0.859361\pi\)
0.903970 0.427595i \(-0.140639\pi\)
\(434\) 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 0.708780 0.705429i \(-0.249246\pi\)
−0.705429 + 0.708780i \(0.749246\pi\)
\(440\) 0 0
\(441\) 46.8687 + 46.8687i 0.106278 + 0.106278i
\(442\) 0 0
\(443\) −15.4970 6.41908i −0.0349820 0.0144900i 0.365124 0.930959i \(-0.381027\pi\)
−0.400106 + 0.916469i \(0.631027\pi\)
\(444\) 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 −0.499767 0.866160i \(-0.666581\pi\)
0.866160 + 0.499767i \(0.166581\pi\)
\(458\) 0 0
\(459\) 41.2992 99.7051i 0.0899764 0.217222i
\(460\) 0 0
\(461\) 299.864 + 723.935i 0.650463 + 1.57036i 0.812107 + 0.583508i \(0.198320\pi\)
−0.161644 + 0.986849i \(0.551680\pi\)
\(462\) 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 −0.284416 0.958701i \(-0.591800\pi\)
0.476791 + 0.879017i \(0.341800\pi\)
\(468\) 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 \(-0.610800\pi\)
0.341101 0.940027i \(-0.389200\pi\)
\(480\) 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 −0.503623 0.863924i \(-0.668000\pi\)
0.863924 + 0.503623i \(0.168000\pi\)
\(488\) 0 0
\(489\) −387.785 + 387.785i −0.793015 + 0.793015i
\(490\) 0 0
\(491\) 111.990 270.368i 0.228086 0.550648i −0.767858 0.640620i \(-0.778678\pi\)
0.995944 + 0.0899713i \(0.0286775\pi\)
\(492\) 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 −0.477192 0.878799i \(-0.658345\pi\)
0.283980 + 0.958830i \(0.408345\pi\)
\(500\) 0 0
\(501\) 232.249 + 96.2005i 0.463570 + 0.192017i
\(502\) 0 0
\(503\) −491.151 491.151i −0.976442 0.976442i 0.0232864 0.999729i \(-0.492587\pi\)
−0.999729 + 0.0232864i \(0.992587\pi\)
\(504\) 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 0.753457 0.657498i \(-0.228385\pi\)
0.997695 0.0678534i \(-0.0216150\pi\)
\(510\) 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 −0.377569 0.925982i \(-0.623240\pi\)
0.925982 + 0.377569i \(0.123240\pi\)
\(522\) 0 0
\(523\) −260.696 + 629.375i −0.498462 + 1.20339i 0.451849 + 0.892094i \(0.350764\pi\)
−0.950312 + 0.311300i \(0.899236\pi\)
\(524\) 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 −0.0295603 0.999563i \(-0.509411\pi\)
0.685895 + 0.727700i \(0.259411\pi\)
\(542\) 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 −0.605010 0.796218i \(-0.706831\pi\)
−0.135204 0.990818i \(-0.543169\pi\)
\(548\) 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 −0.929441 0.368970i \(-0.879711\pi\)
0.396313 0.918115i \(-0.370289\pi\)
\(558\) 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 −0.342644 0.939465i \(-0.611322\pi\)
0.422017 + 0.906588i \(0.361322\pi\)
\(564\) 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 0.990870 0.134818i \(-0.0430449\pi\)
−0.134818 + 0.990870i \(0.543045\pi\)
\(570\) 0 0
\(571\) 252.561 + 104.614i 0.442313 + 0.183212i 0.592714 0.805413i \(-0.298056\pi\)
−0.150401 + 0.988625i \(0.548056\pi\)
\(572\) 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 −0.971319 0.237780i \(-0.923580\pi\)
0.854962 + 0.518690i \(0.173580\pi\)
\(588\) 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 \(-0.954882\pi\)
0.989971 0.141269i \(-0.0451182\pi\)
\(594\) 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 0.920338 0.391125i \(-0.127914\pi\)
−0.391125 + 0.920338i \(0.627914\pi\)
\(600\) 0 0
\(601\) −224.198 224.198i −0.373042 0.373042i 0.495542 0.868584i \(-0.334970\pi\)
−0.868584 + 0.495542i \(0.834970\pi\)
\(602\) 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 \(-0.976578\pi\)
0.997294 0.0735146i \(-0.0234216\pi\)
\(608\) 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 −0.668865 0.743384i \(-0.733220\pi\)
0.998611 0.0526926i \(-0.0167803\pi\)
\(614\) 0 0
\(615\) 429.741 429.741i 0.698766 0.698766i
\(616\) 0 0
\(617\) 380.984 380.984i 0.617479 0.617479i −0.327405 0.944884i \(-0.606174\pi\)
0.944884 + 0.327405i \(0.106174\pi\)
\(618\) 0 0
\(619\) 371.320 896.447i 0.599871 1.44822i −0.273841 0.961775i \(-0.588294\pi\)
0.873712 0.486443i \(-0.161706\pi\)
\(620\) 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 0.333162 0.942870i \(-0.391885\pi\)
−0.942870 + 0.333162i \(0.891885\pi\)
\(632\) 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 0.951313 + 0.308226i \(0.0997352\pi\)
−0.454732 + 0.890629i \(0.650265\pi\)
\(644\) 0 0
\(645\) 2.08564 5.03519i 0.00323356 0.00780650i
\(646\) 0 0
\(647\) 48.6565 48.6565i 0.0752033 0.0752033i −0.668505 0.743708i \(-0.733065\pi\)
0.743708 + 0.668505i \(0.233065\pi\)
\(648\) 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 −0.974436 0.224663i \(-0.927872\pi\)
0.530170 0.847892i \(-0.322128\pi\)
\(654\) 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 −0.904134 0.427248i \(-0.859483\pi\)
−0.337209 + 0.941430i \(0.609483\pi\)
\(660\) 0 0
\(661\) −35.2123 14.5854i −0.0532712 0.0220657i 0.355889 0.934528i \(-0.384178\pi\)
−0.409160 + 0.912463i \(0.634178\pi\)
\(662\) 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 0.685310 + 0.728252i \(0.259667\pi\)
−0.999539 + 0.0303647i \(0.990333\pi\)
\(678\) 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 0.397959 + 0.917403i \(0.369719\pi\)
−0.930102 + 0.367302i \(0.880281\pi\)
\(684\) 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 0.170249 0.985401i \(-0.445543\pi\)
0.817168 + 0.576399i \(0.195543\pi\)
\(692\) 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 −0.747708 0.664028i \(-0.768846\pi\)
−0.0591703 + 0.998248i \(0.518846\pi\)
\(702\) 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 −0.206360 0.978476i \(-0.566162\pi\)
0.837806 0.545968i \(-0.183838\pi\)
\(710\) 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 0.338301 0.941038i \(-0.390148\pi\)
−0.941038 + 0.338301i \(0.890148\pi\)
\(728\) 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 −0.768099 0.640331i \(-0.778797\pi\)
−0.0903463 + 0.995910i \(0.528797\pi\)
\(734\) 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 0.881795 0.471633i \(-0.156335\pi\)
−0.957018 + 0.290028i \(0.906335\pi\)
\(740\) 0 0
\(741\) 12.3839 29.8973i 0.0167124 0.0403473i
\(742\) 0 0
\(743\) 180.295 180.295i 0.242658 0.242658i −0.575291 0.817949i \(-0.695111\pi\)
0.817949 + 0.575291i \(0.195111\pi\)
\(744\) 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 −0.123761 0.992312i \(-0.539496\pi\)
−0.789183 + 0.614158i \(0.789496\pi\)
\(758\) 0 0
\(759\) 324.400 + 324.400i 0.427404 + 0.427404i
\(760\) 0 0
\(761\) 287.342 + 287.342i 0.377585 + 0.377585i 0.870230 0.492645i \(-0.163970\pi\)
−0.492645 + 0.870230i \(0.663970\pi\)
\(762\) 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 0.572342 + 0.820015i \(0.306035\pi\)
−0.984545 + 0.175131i \(0.943965\pi\)
\(774\) 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 −0.721842 0.692058i \(-0.756704\pi\)
−0.0210600 + 0.999778i \(0.506704\pi\)
\(788\) 0 0