Properties

Label 128.4.g.a.17.11
Level $128$
Weight $4$
Character 128.17
Analytic conductor $7.552$
Analytic rank $0$
Dimension $44$
CM no
Inner twists $2$

Related objects

Downloads

Learn more about

Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 17.11
Character \(\chi\) \(=\) 128.17
Dual form 128.4.g.a.113.11

$q$-expansion

\(f(q)\) \(=\) \(q+(3.28810 - 7.93817i) q^{3} +(11.2895 - 4.67626i) q^{5} +(11.8490 - 11.8490i) q^{7} +(-33.1111 - 33.1111i) q^{9} +O(q^{10})\) \(q+(3.28810 - 7.93817i) q^{3} +(11.2895 - 4.67626i) q^{5} +(11.8490 - 11.8490i) q^{7} +(-33.1111 - 33.1111i) q^{9} +(23.5791 + 56.9250i) q^{11} +(-13.6580 - 5.65734i) q^{13} -104.994i q^{15} +44.1663i q^{17} +(-66.5184 - 27.5528i) q^{19} +(-55.0988 - 133.020i) q^{21} +(-60.0240 - 60.0240i) q^{23} +(17.1966 - 17.1966i) q^{25} +(-157.383 + 65.1901i) q^{27} +(-14.3335 + 34.6041i) q^{29} +174.518 q^{31} +529.411 q^{33} +(78.3602 - 189.178i) q^{35} +(-118.428 + 49.0545i) q^{37} +(-89.8179 + 89.8179i) q^{39} +(15.5284 + 15.5284i) q^{41} +(87.3822 + 210.959i) q^{43} +(-528.642 - 218.971i) q^{45} -228.677i q^{47} +62.2017i q^{49} +(350.600 + 145.223i) q^{51} +(258.652 + 624.440i) q^{53} +(532.392 + 532.392i) q^{55} +(-437.438 + 437.438i) q^{57} +(-456.272 + 188.994i) q^{59} +(242.128 - 584.548i) q^{61} -784.667 q^{63} -180.647 q^{65} +(-332.601 + 802.971i) q^{67} +(-673.845 + 279.116i) q^{69} +(550.460 - 550.460i) q^{71} +(69.2096 + 69.2096i) q^{73} +(-79.9655 - 193.054i) q^{75} +(953.895 + 395.116i) q^{77} -518.934i q^{79} +199.379i q^{81} +(595.241 + 246.557i) q^{83} +(206.533 + 498.615i) q^{85} +(227.563 + 227.563i) q^{87} +(656.135 - 656.135i) q^{89} +(-228.868 + 94.8003i) q^{91} +(573.832 - 1385.35i) q^{93} -879.802 q^{95} -388.503 q^{97} +(1104.12 - 2665.58i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + O(q^{10}) \) \( 44q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + 4q^{11} - 4q^{13} + 4q^{19} - 4q^{21} - 324q^{23} - 4q^{25} + 268q^{27} - 4q^{29} + 752q^{31} - 8q^{33} + 460q^{35} - 4q^{37} - 596q^{39} - 4q^{41} - 804q^{43} + 104q^{45} + 1384q^{51} + 748q^{53} + 292q^{55} - 4q^{57} - 1372q^{59} - 1828q^{61} - 2512q^{63} - 8q^{65} - 2036q^{67} - 1060q^{69} - 220q^{71} - 4q^{73} + 1712q^{75} + 1900q^{77} - 2436q^{83} + 496q^{85} + 1292q^{87} - 4q^{89} + 3604q^{91} - 112q^{93} + 6088q^{95} - 8q^{97} + 5424q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(5\) \(127\)
\(\chi(n)\) \(e\left(\frac{7}{8}\right)\) \(1\)

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
\(3\) 3.28810 7.93817i 0.632795 1.52770i −0.203300 0.979116i \(-0.565167\pi\)
0.836095 0.548585i \(-0.184833\pi\)
\(4\) 0 0
\(5\) 11.2895 4.67626i 1.00976 0.418257i 0.184394 0.982852i \(-0.440968\pi\)
0.825368 + 0.564595i \(0.190968\pi\)
\(6\) 0 0
\(7\) 11.8490 11.8490i 0.639787 0.639787i −0.310716 0.950503i \(-0.600569\pi\)
0.950503 + 0.310716i \(0.100569\pi\)
\(8\) 0 0
\(9\) −33.1111 33.1111i −1.22634 1.22634i
\(10\) 0 0
\(11\) 23.5791 + 56.9250i 0.646306 + 1.56032i 0.818029 + 0.575176i \(0.195067\pi\)
−0.171723 + 0.985145i \(0.554933\pi\)
\(12\) 0 0
\(13\) −13.6580 5.65734i −0.291389 0.120697i 0.232200 0.972668i \(-0.425407\pi\)
−0.523590 + 0.851971i \(0.675407\pi\)
\(14\) 0 0
\(15\) 104.994i 1.80728i
\(16\) 0 0
\(17\) 44.1663i 0.630112i 0.949073 + 0.315056i \(0.102023\pi\)
−0.949073 + 0.315056i \(0.897977\pi\)
\(18\) 0 0
\(19\) −66.5184 27.5528i −0.803177 0.332687i −0.0569490 0.998377i \(-0.518137\pi\)
−0.746228 + 0.665690i \(0.768137\pi\)
\(20\) 0 0
\(21\) −55.0988 133.020i −0.572549 1.38226i
\(22\) 0 0
\(23\) −60.0240 60.0240i −0.544168 0.544168i 0.380580 0.924748i \(-0.375724\pi\)
−0.924748 + 0.380580i \(0.875724\pi\)
\(24\) 0 0
\(25\) 17.1966 17.1966i 0.137573 0.137573i
\(26\) 0 0
\(27\) −157.383 + 65.1901i −1.12179 + 0.464661i
\(28\) 0 0
\(29\) −14.3335 + 34.6041i −0.0917813 + 0.221580i −0.963103 0.269132i \(-0.913263\pi\)
0.871322 + 0.490712i \(0.163263\pi\)
\(30\) 0 0
\(31\) 174.518 1.01111 0.505554 0.862795i \(-0.331288\pi\)
0.505554 + 0.862795i \(0.331288\pi\)
\(32\) 0 0
\(33\) 529.411 2.79268
\(34\) 0 0
\(35\) 78.3602 189.178i 0.378437 0.913627i
\(36\) 0 0
\(37\) −118.428 + 49.0545i −0.526201 + 0.217960i −0.629938 0.776645i \(-0.716920\pi\)
0.103737 + 0.994605i \(0.466920\pi\)
\(38\) 0 0
\(39\) −89.8179 + 89.8179i −0.368779 + 0.368779i
\(40\) 0 0
\(41\) 15.5284 + 15.5284i 0.0591494 + 0.0591494i 0.736063 0.676913i \(-0.236683\pi\)
−0.676913 + 0.736063i \(0.736683\pi\)
\(42\) 0 0
\(43\) 87.3822 + 210.959i 0.309899 + 0.748163i 0.999708 + 0.0241712i \(0.00769467\pi\)
−0.689809 + 0.723992i \(0.742305\pi\)
\(44\) 0 0
\(45\) −528.642 218.971i −1.75123 0.725383i
\(46\) 0 0
\(47\) 228.677i 0.709703i −0.934923 0.354851i \(-0.884531\pi\)
0.934923 0.354851i \(-0.115469\pi\)
\(48\) 0 0
\(49\) 62.2017i 0.181346i
\(50\) 0 0
\(51\) 350.600 + 145.223i 0.962623 + 0.398731i
\(52\) 0 0
\(53\) 258.652 + 624.440i 0.670349 + 1.61837i 0.781017 + 0.624509i \(0.214701\pi\)
−0.110668 + 0.993857i \(0.535299\pi\)
\(54\) 0 0
\(55\) 532.392 + 532.392i 1.30523 + 1.30523i
\(56\) 0 0
\(57\) −437.438 + 437.438i −1.01649 + 1.01649i
\(58\) 0 0
\(59\) −456.272 + 188.994i −1.00681 + 0.417033i −0.824289 0.566169i \(-0.808425\pi\)
−0.182518 + 0.983203i \(0.558425\pi\)
\(60\) 0 0
\(61\) 242.128 584.548i 0.508218 1.22695i −0.436690 0.899612i \(-0.643849\pi\)
0.944908 0.327335i \(-0.106151\pi\)
\(62\) 0 0
\(63\) −784.667 −1.56919
\(64\) 0 0
\(65\) −180.647 −0.344716
\(66\) 0 0
\(67\) −332.601 + 802.971i −0.606473 + 1.46416i 0.260337 + 0.965518i \(0.416166\pi\)
−0.866810 + 0.498639i \(0.833834\pi\)
\(68\) 0 0
\(69\) −673.845 + 279.116i −1.17567 + 0.486980i
\(70\) 0 0
\(71\) 550.460 550.460i 0.920107 0.920107i −0.0769293 0.997037i \(-0.524512\pi\)
0.997037 + 0.0769293i \(0.0245116\pi\)
\(72\) 0 0
\(73\) 69.2096 + 69.2096i 0.110964 + 0.110964i 0.760409 0.649445i \(-0.224999\pi\)
−0.649445 + 0.760409i \(0.724999\pi\)
\(74\) 0 0
\(75\) −79.9655 193.054i −0.123115 0.297226i
\(76\) 0 0
\(77\) 953.895 + 395.116i 1.41177 + 0.584775i
\(78\) 0 0
\(79\) 518.934i 0.739046i −0.929222 0.369523i \(-0.879521\pi\)
0.929222 0.369523i \(-0.120479\pi\)
\(80\) 0 0
\(81\) 199.379i 0.273496i
\(82\) 0 0
\(83\) 595.241 + 246.557i 0.787183 + 0.326062i 0.739810 0.672815i \(-0.234915\pi\)
0.0473726 + 0.998877i \(0.484915\pi\)
\(84\) 0 0
\(85\) 206.533 + 498.615i 0.263549 + 0.636263i
\(86\) 0 0
\(87\) 227.563 + 227.563i 0.280429 + 0.280429i
\(88\) 0 0
\(89\) 656.135 656.135i 0.781462 0.781462i −0.198615 0.980078i \(-0.563644\pi\)
0.980078 + 0.198615i \(0.0636445\pi\)
\(90\) 0 0
\(91\) −228.868 + 94.8003i −0.263647 + 0.109206i
\(92\) 0 0
\(93\) 573.832 1385.35i 0.639823 1.54467i
\(94\) 0 0
\(95\) −879.802 −0.950166
\(96\) 0 0
\(97\) −388.503 −0.406665 −0.203333 0.979110i \(-0.565177\pi\)
−0.203333 + 0.979110i \(0.565177\pi\)
\(98\) 0 0
\(99\) 1104.12 2665.58i 1.12089 2.70607i
\(100\) 0 0
\(101\) 658.558 272.784i 0.648802 0.268742i −0.0339161 0.999425i \(-0.510798\pi\)
0.682718 + 0.730682i \(0.260798\pi\)
\(102\) 0 0
\(103\) −467.607 + 467.607i −0.447327 + 0.447327i −0.894465 0.447138i \(-0.852443\pi\)
0.447138 + 0.894465i \(0.352443\pi\)
\(104\) 0 0
\(105\) −1244.07 1244.07i −1.15628 1.15628i
\(106\) 0 0
\(107\) −237.456 573.269i −0.214539 0.517944i 0.779571 0.626314i \(-0.215437\pi\)
−0.994111 + 0.108369i \(0.965437\pi\)
\(108\) 0 0
\(109\) −117.568 48.6982i −0.103311 0.0427930i 0.330429 0.943831i \(-0.392807\pi\)
−0.433741 + 0.901038i \(0.642807\pi\)
\(110\) 0 0
\(111\) 1101.40i 0.941802i
\(112\) 0 0
\(113\) 1440.10i 1.19887i −0.800422 0.599437i \(-0.795391\pi\)
0.800422 0.599437i \(-0.204609\pi\)
\(114\) 0 0
\(115\) −958.327 396.952i −0.777083 0.321878i
\(116\) 0 0
\(117\) 264.911 + 639.553i 0.209325 + 0.505356i
\(118\) 0 0
\(119\) 523.327 + 523.327i 0.403137 + 0.403137i
\(120\) 0 0
\(121\) −1743.32 + 1743.32i −1.30978 + 1.30978i
\(122\) 0 0
\(123\) 174.326 72.2081i 0.127792 0.0529332i
\(124\) 0 0
\(125\) −470.807 + 1136.63i −0.336882 + 0.813305i
\(126\) 0 0
\(127\) −340.683 −0.238037 −0.119019 0.992892i \(-0.537975\pi\)
−0.119019 + 0.992892i \(0.537975\pi\)
\(128\) 0 0
\(129\) 1961.95 1.33907
\(130\) 0 0
\(131\) 460.465 1111.66i 0.307107 0.741421i −0.692689 0.721236i \(-0.743574\pi\)
0.999796 0.0201855i \(-0.00642567\pi\)
\(132\) 0 0
\(133\) −1114.65 + 461.704i −0.726711 + 0.301013i
\(134\) 0 0
\(135\) −1471.93 + 1471.93i −0.938394 + 0.938394i
\(136\) 0 0
\(137\) −109.800 109.800i −0.0684732 0.0684732i 0.672041 0.740514i \(-0.265418\pi\)
−0.740514 + 0.672041i \(0.765418\pi\)
\(138\) 0 0
\(139\) −199.529 481.706i −0.121754 0.293941i 0.851238 0.524781i \(-0.175853\pi\)
−0.972992 + 0.230840i \(0.925853\pi\)
\(140\) 0 0
\(141\) −1815.28 751.914i −1.08421 0.449096i
\(142\) 0 0
\(143\) 910.879i 0.532668i
\(144\) 0 0
\(145\) 457.689i 0.262131i
\(146\) 0 0
\(147\) 493.767 + 204.525i 0.277042 + 0.114755i
\(148\) 0 0
\(149\) −917.500 2215.04i −0.504460 1.21787i −0.947031 0.321141i \(-0.895934\pi\)
0.442572 0.896733i \(-0.354066\pi\)
\(150\) 0 0
\(151\) −191.904 191.904i −0.103423 0.103423i 0.653502 0.756925i \(-0.273299\pi\)
−0.756925 + 0.653502i \(0.773299\pi\)
\(152\) 0 0
\(153\) 1462.39 1462.39i 0.772729 0.772729i
\(154\) 0 0
\(155\) 1970.22 816.090i 1.02098 0.422903i
\(156\) 0 0
\(157\) −572.497 + 1382.13i −0.291021 + 0.702586i −0.999996 0.00264665i \(-0.999158\pi\)
0.708976 + 0.705233i \(0.249158\pi\)
\(158\) 0 0
\(159\) 5807.38 2.89657
\(160\) 0 0
\(161\) −1422.45 −0.696303
\(162\) 0 0
\(163\) −1331.47 + 3214.44i −0.639807 + 1.54463i 0.187130 + 0.982335i \(0.440081\pi\)
−0.826937 + 0.562295i \(0.809919\pi\)
\(164\) 0 0
\(165\) 5976.77 2475.66i 2.81995 1.16806i
\(166\) 0 0
\(167\) −214.549 + 214.549i −0.0994149 + 0.0994149i −0.755065 0.655650i \(-0.772395\pi\)
0.655650 + 0.755065i \(0.272395\pi\)
\(168\) 0 0
\(169\) −1398.98 1398.98i −0.636767 0.636767i
\(170\) 0 0
\(171\) 1290.19 + 3114.80i 0.576979 + 1.39295i
\(172\) 0 0
\(173\) 3387.83 + 1403.29i 1.48886 + 0.616705i 0.971068 0.238804i \(-0.0767553\pi\)
0.517789 + 0.855509i \(0.326755\pi\)
\(174\) 0 0
\(175\) 407.526i 0.176035i
\(176\) 0 0
\(177\) 4243.40i 1.80200i
\(178\) 0 0
\(179\) −1642.06 680.162i −0.685659 0.284009i 0.0125313 0.999921i \(-0.496011\pi\)
−0.698190 + 0.715912i \(0.746011\pi\)
\(180\) 0 0
\(181\) 1072.59 + 2589.47i 0.440471 + 1.06339i 0.975784 + 0.218736i \(0.0701935\pi\)
−0.535313 + 0.844653i \(0.679807\pi\)
\(182\) 0 0
\(183\) −3844.10 3844.10i −1.55281 1.55281i
\(184\) 0 0
\(185\) −1107.60 + 1107.60i −0.440175 + 0.440175i
\(186\) 0 0
\(187\) −2514.17 + 1041.40i −0.983177 + 0.407245i
\(188\) 0 0
\(189\) −1092.39 + 2637.27i −0.420423 + 1.01499i
\(190\) 0 0
\(191\) −3774.95 −1.43008 −0.715042 0.699082i \(-0.753592\pi\)
−0.715042 + 0.699082i \(0.753592\pi\)
\(192\) 0 0
\(193\) −1118.54 −0.417172 −0.208586 0.978004i \(-0.566886\pi\)
−0.208586 + 0.978004i \(0.566886\pi\)
\(194\) 0 0
\(195\) −593.986 + 1434.01i −0.218134 + 0.526623i
\(196\) 0 0
\(197\) −4025.41 + 1667.38i −1.45583 + 0.603024i −0.963578 0.267429i \(-0.913826\pi\)
−0.492252 + 0.870453i \(0.663826\pi\)
\(198\) 0 0
\(199\) 776.416 776.416i 0.276576 0.276576i −0.555165 0.831741i \(-0.687345\pi\)
0.831741 + 0.555165i \(0.187345\pi\)
\(200\) 0 0
\(201\) 5280.49 + 5280.49i 1.85302 + 1.85302i
\(202\) 0 0
\(203\) 240.186 + 579.861i 0.0830433 + 0.200484i
\(204\) 0 0
\(205\) 247.922 + 102.693i 0.0844665 + 0.0349872i
\(206\) 0 0
\(207\) 3974.92i 1.33467i
\(208\) 0 0
\(209\) 4436.23i 1.46823i
\(210\) 0 0
\(211\) 1455.68 + 602.962i 0.474944 + 0.196728i 0.607298 0.794474i \(-0.292254\pi\)
−0.132354 + 0.991203i \(0.542254\pi\)
\(212\) 0 0
\(213\) −2559.68 6179.61i −0.823410 1.98789i
\(214\) 0 0
\(215\) 1973.00 + 1973.00i 0.625849 + 0.625849i
\(216\) 0 0
\(217\) 2067.86 2067.86i 0.646893 0.646893i
\(218\) 0 0
\(219\) 776.966 321.830i 0.239737 0.0993025i
\(220\) 0 0
\(221\) 249.864 603.225i 0.0760528 0.183608i
\(222\) 0 0
\(223\) −1454.48 −0.436768 −0.218384 0.975863i \(-0.570079\pi\)
−0.218384 + 0.975863i \(0.570079\pi\)
\(224\) 0 0
\(225\) −1138.80 −0.337421
\(226\) 0 0
\(227\) −1309.75 + 3162.03i −0.382958 + 0.924542i 0.608433 + 0.793605i \(0.291798\pi\)
−0.991391 + 0.130937i \(0.958202\pi\)
\(228\) 0 0
\(229\) −5746.77 + 2380.39i −1.65833 + 0.686903i −0.997948 0.0640278i \(-0.979605\pi\)
−0.660381 + 0.750930i \(0.729605\pi\)
\(230\) 0 0
\(231\) 6273.00 6273.00i 1.78672 1.78672i
\(232\) 0 0
\(233\) 1497.10 + 1497.10i 0.420938 + 0.420938i 0.885526 0.464589i \(-0.153798\pi\)
−0.464589 + 0.885526i \(0.653798\pi\)
\(234\) 0 0
\(235\) −1069.35 2581.65i −0.296838 0.716631i
\(236\) 0 0
\(237\) −4119.39 1706.31i −1.12904 0.467665i
\(238\) 0 0
\(239\) 1039.75i 0.281404i −0.990052 0.140702i \(-0.955064\pi\)
0.990052 0.140702i \(-0.0449360\pi\)
\(240\) 0 0
\(241\) 120.503i 0.0322087i −0.999870 0.0161043i \(-0.994874\pi\)
0.999870 0.0161043i \(-0.00512639\pi\)
\(242\) 0 0
\(243\) −2666.64 1104.56i −0.703970 0.291594i
\(244\) 0 0
\(245\) 290.871 + 702.224i 0.0758492 + 0.183116i
\(246\) 0 0
\(247\) 752.635 + 752.635i 0.193883 + 0.193883i
\(248\) 0 0
\(249\) 3914.42 3914.42i 0.996250 0.996250i
\(250\) 0 0
\(251\) 5865.74 2429.67i 1.47507 0.610994i 0.507061 0.861910i \(-0.330732\pi\)
0.968009 + 0.250916i \(0.0807319\pi\)
\(252\) 0 0
\(253\) 2001.55 4832.18i 0.497378 1.20078i
\(254\) 0 0
\(255\) 4637.19 1.13879
\(256\) 0 0
\(257\) −4520.96 −1.09731 −0.548657 0.836048i \(-0.684861\pi\)
−0.548657 + 0.836048i \(0.684861\pi\)
\(258\) 0 0
\(259\) −822.008 + 1984.50i −0.197209 + 0.476104i
\(260\) 0 0
\(261\) 1620.37 671.180i 0.384286 0.159176i
\(262\) 0 0
\(263\) −449.651 + 449.651i −0.105425 + 0.105425i −0.757852 0.652427i \(-0.773751\pi\)
0.652427 + 0.757852i \(0.273751\pi\)
\(264\) 0 0
\(265\) 5840.08 + 5840.08i 1.35379 + 1.35379i
\(266\) 0 0
\(267\) −3051.07 7365.94i −0.699336 1.68835i
\(268\) 0 0
\(269\) −2436.90 1009.40i −0.552343 0.228788i 0.0890145 0.996030i \(-0.471628\pi\)
−0.641357 + 0.767243i \(0.721628\pi\)
\(270\) 0 0
\(271\) 1662.12i 0.372570i 0.982496 + 0.186285i \(0.0596448\pi\)
−0.982496 + 0.186285i \(0.940355\pi\)
\(272\) 0 0
\(273\) 2128.51i 0.471880i
\(274\) 0 0
\(275\) 1384.40 + 573.437i 0.303572 + 0.125744i
\(276\) 0 0
\(277\) −2447.54 5908.88i −0.530897 1.28170i −0.930930 0.365198i \(-0.881001\pi\)
0.400033 0.916501i \(-0.368999\pi\)
\(278\) 0 0
\(279\) −5778.47 5778.47i −1.23996 1.23996i
\(280\) 0 0
\(281\) 3546.76 3546.76i 0.752960 0.752960i −0.222070 0.975031i \(-0.571281\pi\)
0.975031 + 0.222070i \(0.0712814\pi\)
\(282\) 0 0
\(283\) 2136.81 885.094i 0.448834 0.185913i −0.146805 0.989165i \(-0.546899\pi\)
0.595639 + 0.803252i \(0.296899\pi\)
\(284\) 0 0
\(285\) −2892.87 + 6984.02i −0.601260 + 1.45157i
\(286\) 0 0
\(287\) 367.992 0.0756860
\(288\) 0 0
\(289\) 2962.34 0.602959
\(290\) 0 0
\(291\) −1277.44 + 3084.00i −0.257336 + 0.621263i
\(292\) 0 0
\(293\) 7533.04 3120.29i 1.50200 0.622147i 0.528109 0.849177i \(-0.322901\pi\)
0.973888 + 0.227029i \(0.0729014\pi\)
\(294\) 0 0
\(295\) −4267.29 + 4267.29i −0.842208 + 0.842208i
\(296\) 0 0
\(297\) −7421.90 7421.90i −1.45004 1.45004i
\(298\) 0 0
\(299\) 480.234 + 1159.39i 0.0928851 + 0.224244i
\(300\) 0 0
\(301\) 3535.05 + 1464.27i 0.676934 + 0.280395i
\(302\) 0 0
\(303\) 6124.68i 1.16123i
\(304\) 0 0
\(305\) 7731.50i 1.45149i
\(306\) 0 0
\(307\) 3320.22 + 1375.28i 0.617247 + 0.255672i 0.669324 0.742971i \(-0.266584\pi\)
−0.0520765 + 0.998643i \(0.516584\pi\)
\(308\) 0 0
\(309\) 2174.41 + 5249.49i 0.400316 + 0.966449i
\(310\) 0 0
\(311\) −2136.23 2136.23i −0.389499 0.389499i 0.485010 0.874509i \(-0.338816\pi\)
−0.874509 + 0.485010i \(0.838816\pi\)
\(312\) 0 0
\(313\) −7352.03 + 7352.03i −1.32767 + 1.32767i −0.420274 + 0.907397i \(0.638066\pi\)
−0.907397 + 0.420274i \(0.861934\pi\)
\(314\) 0 0
\(315\) −8858.48 + 3669.30i −1.58450 + 0.656323i
\(316\) 0 0
\(317\) 321.560 776.314i 0.0569735 0.137546i −0.892829 0.450395i \(-0.851283\pi\)
0.949803 + 0.312849i \(0.101283\pi\)
\(318\) 0 0
\(319\) −2307.81 −0.405054
\(320\) 0 0
\(321\) −5331.49 −0.927023
\(322\) 0 0
\(323\) 1216.91 2937.87i 0.209630 0.506092i
\(324\) 0 0
\(325\) −332.159 + 137.585i −0.0566920 + 0.0234826i
\(326\) 0 0
\(327\) −773.148 + 773.148i −0.130750 + 0.130750i
\(328\) 0 0
\(329\) −2709.60 2709.60i −0.454058 0.454058i
\(330\) 0 0
\(331\) 383.476 + 925.792i 0.0636789 + 0.153735i 0.952516 0.304489i \(-0.0984858\pi\)
−0.888837 + 0.458224i \(0.848486\pi\)
\(332\) 0 0
\(333\) 5545.52 + 2297.03i 0.912590 + 0.378007i
\(334\) 0 0
\(335\) 10620.4i 1.73211i
\(336\) 0 0
\(337\) 6360.72i 1.02816i 0.857742 + 0.514081i \(0.171867\pi\)
−0.857742 + 0.514081i \(0.828133\pi\)
\(338\) 0 0
\(339\) −11431.7 4735.17i −1.83152 0.758641i
\(340\) 0 0
\(341\) 4114.98 + 9934.43i 0.653485 + 1.57765i
\(342\) 0 0
\(343\) 4801.24 + 4801.24i 0.755809 + 0.755809i
\(344\) 0 0
\(345\) −6302.15 + 6302.15i −0.983467 + 0.983467i
\(346\) 0 0
\(347\) 10094.1 4181.11i 1.56161 0.646840i 0.576242 0.817279i \(-0.304518\pi\)
0.985368 + 0.170438i \(0.0545184\pi\)
\(348\) 0 0
\(349\) 697.242 1683.29i 0.106941 0.258179i −0.861346 0.508019i \(-0.830378\pi\)
0.968287 + 0.249840i \(0.0803780\pi\)
\(350\) 0 0
\(351\) 2518.34 0.382961
\(352\) 0 0
\(353\) 3236.30 0.487963 0.243982 0.969780i \(-0.421546\pi\)
0.243982 + 0.969780i \(0.421546\pi\)
\(354\) 0 0
\(355\) 3640.32 8788.50i 0.544248 1.31393i
\(356\) 0 0
\(357\) 5875.01 2433.51i 0.870976 0.360770i
\(358\) 0 0
\(359\) −5424.53 + 5424.53i −0.797482 + 0.797482i −0.982698 0.185216i \(-0.940701\pi\)
0.185216 + 0.982698i \(0.440701\pi\)
\(360\) 0 0
\(361\) −1184.51 1184.51i −0.172694 0.172694i
\(362\) 0 0
\(363\) 8106.58 + 19571.0i 1.17214 + 2.82978i
\(364\) 0 0
\(365\) 1104.98 + 457.699i 0.158459 + 0.0656358i
\(366\) 0 0
\(367\) 10914.3i 1.55237i −0.630503 0.776187i \(-0.717151\pi\)
0.630503 0.776187i \(-0.282849\pi\)
\(368\) 0 0
\(369\) 1028.32i 0.145074i
\(370\) 0 0
\(371\) 10463.8 + 4334.23i 1.46429 + 0.606529i
\(372\) 0 0
\(373\) −3921.61 9467.61i −0.544379 1.31425i −0.921606 0.388127i \(-0.873122\pi\)
0.377227 0.926121i \(-0.376878\pi\)
\(374\) 0 0
\(375\) 7474.69 + 7474.69i 1.02931 + 1.02931i
\(376\) 0 0
\(377\) 391.534 391.534i 0.0534881 0.0534881i
\(378\) 0 0
\(379\) −10042.4 + 4159.68i −1.36106 + 0.563769i −0.939349 0.342962i \(-0.888570\pi\)
−0.421710 + 0.906731i \(0.638570\pi\)
\(380\) 0 0
\(381\) −1120.20 + 2704.40i −0.150629 + 0.363650i
\(382\) 0 0
\(383\) −1609.29 −0.214702 −0.107351 0.994221i \(-0.534237\pi\)
−0.107351 + 0.994221i \(0.534237\pi\)
\(384\) 0 0
\(385\) 12616.6 1.67014
\(386\) 0 0
\(387\) 4091.77 9878.41i 0.537458 1.29754i
\(388\) 0 0
\(389\) −3941.97 + 1632.82i −0.513793 + 0.212820i −0.624488 0.781034i \(-0.714692\pi\)
0.110695 + 0.993854i \(0.464692\pi\)
\(390\) 0 0
\(391\) 2651.04 2651.04i 0.342887 0.342887i
\(392\) 0 0
\(393\) −7310.49 7310.49i −0.938335 0.938335i
\(394\) 0 0
\(395\) −2426.67 5858.50i −0.309111 0.746261i
\(396\) 0 0
\(397\) 2995.05 + 1240.59i 0.378632 + 0.156835i 0.563879 0.825857i \(-0.309308\pi\)
−0.185247 + 0.982692i \(0.559308\pi\)
\(398\) 0 0
\(399\) 10366.4i 1.30068i
\(400\) 0 0
\(401\) 8084.70i 1.00681i 0.864051 + 0.503405i \(0.167919\pi\)
−0.864051 + 0.503405i \(0.832081\pi\)
\(402\) 0 0
\(403\) −2383.57 987.308i −0.294626 0.122038i
\(404\) 0 0
\(405\) 932.346 + 2250.88i 0.114392 + 0.276166i
\(406\) 0 0
\(407\) −5584.85 5584.85i −0.680174 0.680174i
\(408\) 0 0
\(409\) 4621.85 4621.85i 0.558767 0.558767i −0.370189 0.928956i \(-0.620707\pi\)
0.928956 + 0.370189i \(0.120707\pi\)
\(410\) 0 0
\(411\) −1232.64 + 510.577i −0.147936 + 0.0612771i
\(412\) 0 0
\(413\) −3166.98 + 7645.77i −0.377329 + 0.910954i
\(414\) 0 0
\(415\) 7872.92 0.931245
\(416\) 0 0
\(417\) −4479.93 −0.526099
\(418\) 0 0
\(419\) 2131.19 5145.14i 0.248485 0.599897i −0.749590 0.661902i \(-0.769750\pi\)
0.998076 + 0.0620052i \(0.0197495\pi\)
\(420\) 0 0
\(421\) −8558.20 + 3544.92i −0.990739 + 0.410378i −0.818393 0.574659i \(-0.805135\pi\)
−0.172346 + 0.985036i \(0.555135\pi\)
\(422\) 0 0
\(423\) −7571.75 + 7571.75i −0.870334 + 0.870334i
\(424\) 0 0
\(425\) 759.512 + 759.512i 0.0866864 + 0.0866864i
\(426\) 0 0
\(427\) −4057.35 9795.30i −0.459833 1.11014i
\(428\) 0 0
\(429\) −7230.71 2995.06i −0.813758 0.337069i
\(430\) 0 0
\(431\) 6610.79i 0.738818i 0.929267 + 0.369409i \(0.120440\pi\)
−0.929267 + 0.369409i \(0.879560\pi\)
\(432\) 0 0
\(433\) 8705.35i 0.966172i 0.875573 + 0.483086i \(0.160484\pi\)
−0.875573 + 0.483086i \(0.839516\pi\)
\(434\) 0 0
\(435\) 3633.21 + 1504.92i 0.400458 + 0.165875i
\(436\) 0 0
\(437\) 2338.87 + 5646.53i 0.256026 + 0.618101i
\(438\) 0 0
\(439\) 11344.9 + 11344.9i 1.23341 + 1.23341i 0.962648 + 0.270757i \(0.0872741\pi\)
0.270757 + 0.962648i \(0.412726\pi\)
\(440\) 0 0
\(441\) 2059.56 2059.56i 0.222391 0.222391i
\(442\) 0 0
\(443\) 1931.24 799.946i 0.207124 0.0857936i −0.276709 0.960954i \(-0.589244\pi\)
0.483834 + 0.875160i \(0.339244\pi\)
\(444\) 0 0
\(445\) 4339.16 10475.7i 0.462239 1.11594i
\(446\) 0 0
\(447\) −20600.2 −2.17977
\(448\) 0 0
\(449\) 1770.44 0.186085 0.0930426 0.995662i \(-0.470341\pi\)
0.0930426 + 0.995662i \(0.470341\pi\)
\(450\) 0 0
\(451\) −517.808 + 1250.10i −0.0540635 + 0.130521i
\(452\) 0 0
\(453\) −2154.36 + 892.366i −0.223445 + 0.0925541i
\(454\) 0 0
\(455\) −2140.49 + 2140.49i −0.220545 + 0.220545i
\(456\) 0 0
\(457\) −7694.10 7694.10i −0.787560 0.787560i 0.193534 0.981094i \(-0.438005\pi\)
−0.981094 + 0.193534i \(0.938005\pi\)
\(458\) 0 0
\(459\) −2879.21 6951.02i −0.292788 0.706854i
\(460\) 0 0
\(461\) −5291.40 2191.77i −0.534588 0.221433i 0.0990235 0.995085i \(-0.468428\pi\)
−0.633611 + 0.773652i \(0.718428\pi\)
\(462\) 0 0
\(463\) 13153.5i 1.32029i −0.751138 0.660145i \(-0.770495\pi\)
0.751138 0.660145i \(-0.229505\pi\)
\(464\) 0 0
\(465\) 18323.3i 1.82736i
\(466\) 0 0
\(467\) −7862.87 3256.91i −0.779122 0.322723i −0.0425611 0.999094i \(-0.513552\pi\)
−0.736561 + 0.676371i \(0.763552\pi\)
\(468\) 0 0
\(469\) 5573.41 + 13455.4i 0.548734 + 1.32476i
\(470\) 0 0
\(471\) 9089.16 + 9089.16i 0.889185 + 0.889185i
\(472\) 0 0
\(473\) −9948.47 + 9948.47i −0.967085 + 0.967085i
\(474\) 0 0
\(475\) −1617.71 + 670.076i −0.156264 + 0.0647268i
\(476\) 0 0
\(477\) 12111.6 29240.1i 1.16259 2.80673i
\(478\) 0 0
\(479\) −15687.9 −1.49645 −0.748224 0.663446i \(-0.769093\pi\)
−0.748224 + 0.663446i \(0.769093\pi\)
\(480\) 0 0
\(481\) 1895.01 0.179636
\(482\) 0 0
\(483\) −4677.16 + 11291.7i −0.440617 + 1.06374i
\(484\) 0 0
\(485\) −4386.00 + 1816.74i −0.410635 + 0.170091i
\(486\) 0 0
\(487\) 13515.4 13515.4i 1.25758 1.25758i 0.305330 0.952247i \(-0.401233\pi\)
0.952247 0.305330i \(-0.0987668\pi\)
\(488\) 0 0
\(489\) 21138.8 + 21138.8i 1.95487 + 1.95487i
\(490\) 0 0
\(491\) 1348.48 + 3255.53i 0.123943 + 0.299226i 0.973657 0.228019i \(-0.0732249\pi\)
−0.849713 + 0.527245i \(0.823225\pi\)
\(492\) 0 0
\(493\) −1528.33 633.056i −0.139620 0.0578325i
\(494\) 0 0
\(495\) 35256.1i 3.20130i
\(496\) 0 0
\(497\) 13044.8i 1.17734i
\(498\) 0 0
\(499\) 13952.2 + 5779.20i 1.25168 + 0.518462i 0.907345 0.420386i \(-0.138105\pi\)
0.344332 + 0.938848i \(0.388105\pi\)
\(500\) 0 0
\(501\) 997.667 + 2408.58i 0.0889671 + 0.214785i
\(502\) 0 0
\(503\) −12832.8 12832.8i −1.13755 1.13755i −0.988889 0.148658i \(-0.952505\pi\)
−0.148658 0.988889i \(-0.547495\pi\)
\(504\) 0 0
\(505\) 6159.17 6159.17i 0.542732 0.542732i
\(506\) 0 0
\(507\) −15705.3 + 6505.34i −1.37573 + 0.569847i
\(508\) 0 0
\(509\) −294.015 + 709.814i −0.0256031 + 0.0618113i −0.936164 0.351564i \(-0.885650\pi\)
0.910561 + 0.413375i \(0.135650\pi\)
\(510\) 0 0
\(511\) 1640.13 0.141987
\(512\) 0 0
\(513\) 12265.0 1.05558
\(514\) 0 0
\(515\) −3092.39 + 7465.70i −0.264596 + 0.638792i
\(516\) 0 0
\(517\) 13017.5 5392.01i 1.10736 0.458685i
\(518\) 0 0
\(519\) 22279.0 22279.0i 1.88428 1.88428i
\(520\) 0 0
\(521\) −4736.98 4736.98i −0.398332 0.398332i 0.479312 0.877644i \(-0.340886\pi\)
−0.877644 + 0.479312i \(0.840886\pi\)
\(522\) 0 0
\(523\) −881.013 2126.95i −0.0736597 0.177830i 0.882761 0.469822i \(-0.155682\pi\)
−0.956421 + 0.291992i \(0.905682\pi\)
\(524\) 0 0
\(525\) −3235.01 1339.99i −0.268929 0.111394i
\(526\) 0 0
\(527\) 7707.81i 0.637111i
\(528\) 0 0
\(529\) 4961.24i 0.407762i
\(530\) 0 0
\(531\) 21365.5 + 8849.86i 1.74611 + 0.723260i
\(532\) 0 0
\(533\) −124.238 299.937i −0.0100963 0.0243747i
\(534\) 0 0
\(535\) −5361.51 5361.51i −0.433268 0.433268i
\(536\) 0 0
\(537\) −10798.5 + 10798.5i −0.867763 + 0.867763i
\(538\) 0 0
\(539\) −3540.83 + 1466.66i −0.282958 + 0.117205i
\(540\) 0 0
\(541\) 8550.73 20643.3i 0.679528 1.64053i −0.0853508 0.996351i \(-0.527201\pi\)
0.764879 0.644174i \(-0.222799\pi\)
\(542\) 0 0
\(543\) 24082.4 1.90327
\(544\) 0 0
\(545\) −1555.00 −0.122218
\(546\) 0 0
\(547\) 2552.53 6162.34i 0.199521 0.481687i −0.792174 0.610295i \(-0.791051\pi\)
0.991696 + 0.128608i \(0.0410509\pi\)
\(548\) 0 0
\(549\) −27372.1 + 11337.9i −2.12789 + 0.881403i
\(550\) 0 0
\(551\) 1906.88 1906.88i 0.147433 0.147433i
\(552\) 0 0
\(553\) −6148.86 6148.86i −0.472832 0.472832i
\(554\) 0 0
\(555\) 5150.41 + 12434.2i 0.393915 + 0.950995i
\(556\) 0 0
\(557\) −2494.05 1033.07i −0.189724 0.0785863i 0.285799 0.958290i \(-0.407741\pi\)
−0.475523 + 0.879703i \(0.657741\pi\)
\(558\) 0 0
\(559\) 3375.64i 0.255411i
\(560\) 0 0
\(561\) 23382.1i 1.75970i
\(562\) 0 0
\(563\) −19457.5 8059.54i −1.45654 0.603320i −0.492798 0.870144i \(-0.664026\pi\)
−0.963745 + 0.266823i \(0.914026\pi\)
\(564\) 0 0
\(565\) −6734.26 16257.9i −0.501438 1.21058i
\(566\) 0 0
\(567\) 2362.44 + 2362.44i 0.174979 + 0.174979i
\(568\) 0 0
\(569\) 1740.16 1740.16i 0.128209 0.128209i −0.640090 0.768300i \(-0.721103\pi\)
0.768300 + 0.640090i \(0.221103\pi\)
\(570\) 0 0
\(571\) −16395.2 + 6791.10i −1.20160 + 0.497721i −0.891517 0.452987i \(-0.850358\pi\)
−0.310088 + 0.950708i \(0.600358\pi\)
\(572\) 0 0
\(573\) −12412.4 + 29966.2i −0.904949 + 2.18474i
\(574\) 0 0
\(575\) −2064.42 −0.149726
\(576\) 0 0
\(577\) −13473.2 −0.972091 −0.486046 0.873933i \(-0.661561\pi\)
−0.486046 + 0.873933i \(0.661561\pi\)
\(578\) 0 0
\(579\) −3677.87 + 8879.15i −0.263984 + 0.637314i
\(580\) 0 0
\(581\) 9974.48 4131.56i 0.712239 0.295019i
\(582\) 0 0
\(583\) −29447.5 + 29447.5i −2.09192 + 2.09192i
\(584\) 0 0
\(585\) 5981.42 + 5981.42i 0.422737 + 0.422737i
\(586\) 0 0
\(587\) −873.151 2107.97i −0.0613949 0.148220i 0.890205 0.455560i \(-0.150561\pi\)
−0.951600 + 0.307340i \(0.900561\pi\)
\(588\) 0 0
\(589\) −11608.6 4808.46i −0.812098 0.336382i
\(590\) 0 0
\(591\) 37436.9i 2.60566i
\(592\) 0 0
\(593\) 4205.87i 0.291255i 0.989339 + 0.145628i \(0.0465201\pi\)
−0.989339 + 0.145628i \(0.953480\pi\)
\(594\) 0 0
\(595\) 8355.30 + 3460.88i 0.575688 + 0.238458i
\(596\) 0 0
\(597\) −3610.39 8716.25i −0.247510 0.597541i
\(598\) 0 0
\(599\) 9771.17 + 9771.17i 0.666510 + 0.666510i 0.956906 0.290397i \(-0.0937872\pi\)
−0.290397 + 0.956906i \(0.593787\pi\)
\(600\) 0 0
\(601\) 15649.6 15649.6i 1.06216 1.06216i 0.0642295 0.997935i \(-0.479541\pi\)
0.997935 0.0642295i \(-0.0204590\pi\)
\(602\) 0 0
\(603\) 37600.0 15574.4i 2.53929 1.05181i
\(604\) 0 0
\(605\) −11529.0 + 27833.4i −0.774744 + 1.87040i
\(606\) 0 0
\(607\) 12239.3 0.818417 0.409209 0.912441i \(-0.365805\pi\)
0.409209 + 0.912441i \(0.365805\pi\)
\(608\) 0 0
\(609\) 5392.79 0.358829
\(610\) 0 0
\(611\) −1293.71 + 3123.29i −0.0856592 + 0.206800i
\(612\) 0 0
\(613\) −17070.1 + 7070.67i −1.12472 + 0.465876i −0.865984 0.500072i \(-0.833307\pi\)
−0.258739 + 0.965947i \(0.583307\pi\)
\(614\) 0 0
\(615\) 1630.38 1630.38i 0.106900 0.106900i
\(616\) 0 0
\(617\) 11602.2 + 11602.2i 0.757031 + 0.757031i 0.975781 0.218750i \(-0.0701978\pi\)
−0.218750 + 0.975781i \(0.570198\pi\)
\(618\) 0 0
\(619\) 8701.45 + 21007.2i 0.565009 + 1.36405i 0.905717 + 0.423884i \(0.139333\pi\)
−0.340707 + 0.940169i \(0.610667\pi\)
\(620\) 0 0
\(621\) 13359.7 + 5533.78i 0.863297 + 0.357589i
\(622\) 0 0
\(623\) 15549.1i 0.999938i
\(624\) 0 0
\(625\) 18073.5i 1.15670i
\(626\) 0 0
\(627\) −35215.6 14586.8i −2.24302 0.929089i
\(628\) 0 0
\(629\) −2166.56 5230.53i −0.137339 0.331566i
\(630\) 0 0
\(631\) −6552.95 6552.95i −0.413421 0.413421i 0.469508 0.882928i \(-0.344431\pi\)
−0.882928 + 0.469508i \(0.844431\pi\)
\(632\) 0 0
\(633\) 9572.83 9572.83i 0.601084 0.601084i
\(634\) 0 0
\(635\) −3846.14 + 1593.12i −0.240361 + 0.0995608i
\(636\) 0 0
\(637\) 351.896 849.553i 0.0218880 0.0528422i
\(638\) 0 0
\(639\) −36452.6 −2.25672
\(640\) 0 0
\(641\) 7331.07 0.451731 0.225866 0.974158i \(-0.427479\pi\)
0.225866 + 0.974158i \(0.427479\pi\)
\(642\) 0 0
\(643\) 6386.47 15418.3i 0.391692 0.945628i −0.597879 0.801586i \(-0.703990\pi\)
0.989572 0.144042i \(-0.0460101\pi\)
\(644\) 0 0
\(645\) 22149.4 9174.59i 1.35214 0.560076i
\(646\) 0 0
\(647\) 2351.92 2351.92i 0.142911 0.142911i −0.632031 0.774943i \(-0.717779\pi\)
0.774943 + 0.632031i \(0.217779\pi\)
\(648\) 0 0
\(649\) −21517.0 21517.0i −1.30141 1.30141i
\(650\) 0 0
\(651\) −9615.72 23214.4i −0.578909 1.39761i
\(652\) 0 0
\(653\) 18790.1 + 7783.11i 1.12605 + 0.466427i 0.866438 0.499285i \(-0.166404\pi\)
0.259616 + 0.965712i \(0.416404\pi\)
\(654\) 0 0
\(655\) 14703.3i 0.877109i
\(656\) 0 0
\(657\) 4583.21i 0.272158i
\(658\) 0 0
\(659\) −438.021 181.434i −0.0258921 0.0107248i 0.369700 0.929151i \(-0.379461\pi\)
−0.395592 + 0.918426i \(0.629461\pi\)
\(660\) 0 0
\(661\) 10971.1 + 26486.6i 0.645577 + 1.55856i 0.819050 + 0.573722i \(0.194501\pi\)
−0.173473 + 0.984839i \(0.555499\pi\)
\(662\) 0 0
\(663\) −3966.93 3966.93i −0.232372 0.232372i
\(664\) 0 0
\(665\) −10424.8 + 10424.8i −0.607904 + 0.607904i
\(666\) 0 0
\(667\) 2937.43 1216.72i 0.170521 0.0706322i
\(668\) 0 0
\(669\) −4782.48 + 11545.9i −0.276385 + 0.667251i
\(670\) 0 0
\(671\) 38984.6 2.24290
\(672\) 0 0
\(673\) 27506.8 1.57550 0.787749 0.615996i \(-0.211246\pi\)
0.787749 + 0.615996i \(0.211246\pi\)
\(674\) 0 0
\(675\) −1585.40 + 3827.51i −0.0904034 + 0.218253i
\(676\) 0 0
\(677\) 21591.8 8943.62i 1.22576 0.507727i 0.326524 0.945189i \(-0.394122\pi\)
0.899237 + 0.437462i \(0.144122\pi\)
\(678\) 0 0
\(679\) −4603.38 + 4603.38i −0.260179 + 0.260179i
\(680\) 0 0
\(681\) 20794.1 + 20794.1i 1.17009 + 1.17009i
\(682\) 0 0
\(683\) 11875.5 + 28670.1i 0.665308 + 1.60619i 0.789368 + 0.613920i \(0.210408\pi\)
−0.124060 + 0.992275i \(0.539592\pi\)
\(684\) 0 0
\(685\) −1753.03 726.130i −0.0977810 0.0405022i
\(686\) 0 0
\(687\) 53445.8i 2.96810i
\(688\) 0 0
\(689\) 9991.91i 0.552484i
\(690\) 0 0
\(691\) 2996.03 + 1241.00i 0.164941 + 0.0683209i 0.463626 0.886031i \(-0.346548\pi\)
−0.298685 + 0.954352i \(0.596548\pi\)
\(692\) 0 0
\(693\) −18501.7 44667.2i −1.01417 2.44843i
\(694\) 0 0
\(695\) −4505.16 4505.16i −0.245886 0.245886i
\(696\) 0 0
\(697\) −685.832 + 685.832i −0.0372708 + 0.0372708i
\(698\) 0 0
\(699\) 16806.9 6961.63i 0.909434 0.376700i
\(700\) 0 0
\(701\) 1477.30 3566.51i 0.0795959 0.192162i −0.879072 0.476689i \(-0.841837\pi\)
0.958668 + 0.284528i \(0.0918367\pi\)
\(702\) 0 0
\(703\) 9229.23 0.495145
\(704\) 0 0
\(705\) −24009.7 −1.28264
\(706\) 0 0
\(707\) 4571.05 11035.5i 0.243157 0.587032i
\(708\) 0 0
\(709\) 15754.7 6525.83i 0.834530 0.345674i 0.0758356 0.997120i \(-0.475838\pi\)
0.758694 + 0.651447i \(0.225838\pi\)
\(710\) 0 0
\(711\) −17182.5 + 17182.5i −0.906319 + 0.906319i
\(712\) 0 0
\(713\) −10475.3 10475.3i −0.550213 0.550213i
\(714\) 0 0
\(715\) −4259.50 10283.4i −0.222792 0.537868i
\(716\) 0 0
\(717\) −8253.69 3418.79i −0.429902 0.178071i
\(718\) 0 0
\(719\) 1013.44i 0.0525657i −0.999655 0.0262829i \(-0.991633\pi\)
0.999655 0.0262829i \(-0.00836706\pi\)
\(720\) 0 0
\(721\) 11081.4i 0.572388i
\(722\) 0 0
\(723\) −956.575 396.226i −0.0492053 0.0203815i
\(724\) 0 0
\(725\) 348.586 + 841.560i 0.0178568 + 0.0431100i
\(726\) 0 0
\(727\) −3353.13 3353.13i −0.171060 0.171060i 0.616385 0.787445i \(-0.288597\pi\)
−0.787445 + 0.616385i \(0.788597\pi\)
\(728\) 0 0
\(729\) −21342.8 + 21342.8i −1.08433 + 1.08433i
\(730\) 0 0
\(731\) −9317.30 + 3859.35i −0.471426 + 0.195271i
\(732\) 0 0
\(733\) −12032.3 + 29048.5i −0.606307 + 1.46375i 0.260681 + 0.965425i \(0.416053\pi\)
−0.866988 + 0.498329i \(0.833947\pi\)
\(734\) 0 0
\(735\) 6530.79 0.327744
\(736\) 0 0
\(737\) −53551.6 −2.67652
\(738\) 0 0
\(739\) −827.863 + 1998.64i −0.0412090 + 0.0994873i −0.943144 0.332385i \(-0.892147\pi\)
0.901935 + 0.431872i \(0.142147\pi\)
\(740\) 0 0
\(741\) 8449.28 3499.81i 0.418883 0.173507i
\(742\) 0 0
\(743\) 15379.7 15379.7i 0.759391 0.759391i −0.216821 0.976211i \(-0.569569\pi\)
0.976211 + 0.216821i \(0.0695688\pi\)
\(744\) 0 0
\(745\) −20716.2 20716.2i −1.01877 1.01877i
\(746\) 0 0
\(747\) −11545.3 27872.8i −0.565489 1.36521i
\(748\) 0 0
\(749\) −9606.29 3979.06i −0.468633 0.194114i
\(750\) 0 0
\(751\) 23971.2i 1.16474i −0.812923 0.582371i \(-0.802125\pi\)
0.812923 0.582371i \(-0.197875\pi\)
\(752\) 0 0
\(753\) 54552.3i 2.64010i
\(754\) 0 0
\(755\) −3063.88 1269.10i −0.147690 0.0611753i
\(756\) 0 0
\(757\) 9946.89 + 24013.9i 0.477577 + 1.15297i 0.960742 + 0.277443i \(0.0894871\pi\)
−0.483165 + 0.875529i \(0.660513\pi\)
\(758\) 0 0
\(759\) −31777.4 31777.4i −1.51969 1.51969i
\(760\) 0 0
\(761\) 26392.4 26392.4i 1.25719 1.25719i 0.304763 0.952428i \(-0.401423\pi\)
0.952428 0.304763i \(-0.0985771\pi\)
\(762\) 0 0
\(763\) −1970.09 + 816.037i −0.0934757 + 0.0387189i
\(764\) 0 0
\(765\) 9671.13 23348.2i 0.457073 1.10347i
\(766\) 0 0
\(767\) 7300.99 0.343707
\(768\) 0 0
\(769\) −13563.7 −0.636046 −0.318023 0.948083i \(-0.603019\pi\)
−0.318023 + 0.948083i \(0.603019\pi\)
\(770\) 0 0
\(771\) −14865.3 + 35888.1i −0.694374 + 1.67637i
\(772\) 0 0
\(773\) 3266.20 1352.90i 0.151975 0.0629502i −0.305399 0.952224i \(-0.598790\pi\)
0.457374 + 0.889274i \(0.348790\pi\)
\(774\) 0 0
\(775\) 3001.12 3001.12i 0.139101 0.139101i
\(776\) 0 0
\(777\) 13050.5 + 13050.5i 0.602552 + 0.602552i
\(778\) 0 0
\(779\) −605.073 1460.77i −0.0278292 0.0671857i
\(780\) 0 0
\(781\) 44314.3 + 18355.6i 2.03033 + 0.840992i
\(782\) 0 0
\(783\) 6380.49i 0.291213i
\(784\) 0 0
\(785\) 18280.7i 0.831166i
\(786\) 0 0