Properties

Label 128.4.g.a.113.3
Level $128$
Weight $4$
Character 128.113
Analytic conductor $7.552$
Analytic rank $0$
Dimension $44$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 113.3
Character \(\chi\) \(=\) 128.113
Dual form 128.4.g.a.17.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.94138 - 4.68690i) q^{3} +(4.93338 + 2.04347i) q^{5} +(-14.0755 - 14.0755i) q^{7} +(0.893826 - 0.893826i) q^{9} +O(q^{10})\) \(q+(-1.94138 - 4.68690i) q^{3} +(4.93338 + 2.04347i) q^{5} +(-14.0755 - 14.0755i) q^{7} +(0.893826 - 0.893826i) q^{9} +(3.78733 - 9.14343i) q^{11} +(-64.7407 + 26.8165i) q^{13} -27.0894i q^{15} -79.3923i q^{17} +(-94.7756 + 39.2573i) q^{19} +(-38.6445 + 93.2961i) q^{21} +(-71.6801 + 71.6801i) q^{23} +(-68.2259 - 68.2259i) q^{25} +(-132.471 - 54.8712i) q^{27} +(-53.0409 - 128.052i) q^{29} +267.650 q^{31} -50.2070 q^{33} +(-40.6768 - 98.2026i) q^{35} +(205.678 + 85.1946i) q^{37} +(251.372 + 251.372i) q^{39} +(210.468 - 210.468i) q^{41} +(56.9749 - 137.550i) q^{43} +(6.23610 - 2.58308i) q^{45} -173.739i q^{47} +53.2384i q^{49} +(-372.103 + 154.130i) q^{51} +(-188.605 + 455.333i) q^{53} +(37.3687 - 37.3687i) q^{55} +(367.990 + 367.990i) q^{57} +(627.964 + 260.111i) q^{59} +(66.5782 + 160.734i) q^{61} -25.1621 q^{63} -374.189 q^{65} +(-211.710 - 511.113i) q^{67} +(475.115 + 196.799i) q^{69} +(226.201 + 226.201i) q^{71} +(802.290 - 802.290i) q^{73} +(-187.316 + 452.220i) q^{75} +(-182.007 + 75.3897i) q^{77} -552.368i q^{79} +693.272i q^{81} +(137.983 - 57.1544i) q^{83} +(162.236 - 391.672i) q^{85} +(-497.195 + 497.195i) q^{87} +(-579.803 - 579.803i) q^{89} +(1288.71 + 533.802i) q^{91} +(-519.610 - 1254.45i) q^{93} -547.785 q^{95} -912.077 q^{97} +(-4.78742 - 11.5579i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + O(q^{10}) \) \( 44q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + 4q^{11} - 4q^{13} + 4q^{19} - 4q^{21} - 324q^{23} - 4q^{25} + 268q^{27} - 4q^{29} + 752q^{31} - 8q^{33} + 460q^{35} - 4q^{37} - 596q^{39} - 4q^{41} - 804q^{43} + 104q^{45} + 1384q^{51} + 748q^{53} + 292q^{55} - 4q^{57} - 1372q^{59} - 1828q^{61} - 2512q^{63} - 8q^{65} - 2036q^{67} - 1060q^{69} - 220q^{71} - 4q^{73} + 1712q^{75} + 1900q^{77} - 2436q^{83} + 496q^{85} + 1292q^{87} - 4q^{89} + 3604q^{91} - 112q^{93} + 6088q^{95} - 8q^{97} + 5424q^{99} + O(q^{100}) \)

Character values

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

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.94138 4.68690i −0.373618 0.901994i −0.993131 0.117007i \(-0.962670\pi\)
0.619513 0.784986i \(-0.287330\pi\)
\(4\) 0 0
\(5\) 4.93338 + 2.04347i 0.441255 + 0.182774i 0.592239 0.805762i \(-0.298244\pi\)
−0.150984 + 0.988536i \(0.548244\pi\)
\(6\) 0 0
\(7\) −14.0755 14.0755i −0.760005 0.760005i 0.216318 0.976323i \(-0.430595\pi\)
−0.976323 + 0.216318i \(0.930595\pi\)
\(8\) 0 0
\(9\) 0.893826 0.893826i 0.0331047 0.0331047i
\(10\) 0 0
\(11\) 3.78733 9.14343i 0.103811 0.250623i −0.863436 0.504458i \(-0.831692\pi\)
0.967247 + 0.253836i \(0.0816922\pi\)
\(12\) 0 0
\(13\) −64.7407 + 26.8165i −1.38122 + 0.572120i −0.944807 0.327627i \(-0.893751\pi\)
−0.436412 + 0.899747i \(0.643751\pi\)
\(14\) 0 0
\(15\) 27.0894i 0.466297i
\(16\) 0 0
\(17\) 79.3923i 1.13267i −0.824174 0.566337i \(-0.808360\pi\)
0.824174 0.566337i \(-0.191640\pi\)
\(18\) 0 0
\(19\) −94.7756 + 39.2573i −1.14437 + 0.474013i −0.872642 0.488361i \(-0.837595\pi\)
−0.271727 + 0.962374i \(0.587595\pi\)
\(20\) 0 0
\(21\) −38.6445 + 93.2961i −0.401568 + 0.969471i
\(22\) 0 0
\(23\) −71.6801 + 71.6801i −0.649841 + 0.649841i −0.952954 0.303114i \(-0.901974\pi\)
0.303114 + 0.952954i \(0.401974\pi\)
\(24\) 0 0
\(25\) −68.2259 68.2259i −0.545807 0.545807i
\(26\) 0 0
\(27\) −132.471 54.8712i −0.944222 0.391110i
\(28\) 0 0
\(29\) −53.0409 128.052i −0.339636 0.819955i −0.997751 0.0670366i \(-0.978646\pi\)
0.658114 0.752918i \(-0.271354\pi\)
\(30\) 0 0
\(31\) 267.650 1.55069 0.775346 0.631537i \(-0.217576\pi\)
0.775346 + 0.631537i \(0.217576\pi\)
\(32\) 0 0
\(33\) −50.2070 −0.264846
\(34\) 0 0
\(35\) −40.6768 98.2026i −0.196447 0.474265i
\(36\) 0 0
\(37\) 205.678 + 85.1946i 0.913872 + 0.378538i 0.789537 0.613702i \(-0.210321\pi\)
0.124334 + 0.992240i \(0.460321\pi\)
\(38\) 0 0
\(39\) 251.372 + 251.372i 1.03210 + 1.03210i
\(40\) 0 0
\(41\) 210.468 210.468i 0.801697 0.801697i −0.181664 0.983361i \(-0.558148\pi\)
0.983361 + 0.181664i \(0.0581482\pi\)
\(42\) 0 0
\(43\) 56.9749 137.550i 0.202060 0.487817i −0.790072 0.613015i \(-0.789957\pi\)
0.992132 + 0.125198i \(0.0399566\pi\)
\(44\) 0 0
\(45\) 6.23610 2.58308i 0.0206583 0.00855694i
\(46\) 0 0
\(47\) 173.739i 0.539201i −0.962972 0.269600i \(-0.913108\pi\)
0.962972 0.269600i \(-0.0868916\pi\)
\(48\) 0 0
\(49\) 53.2384i 0.155214i
\(50\) 0 0
\(51\) −372.103 + 154.130i −1.02166 + 0.423187i
\(52\) 0 0
\(53\) −188.605 + 455.333i −0.488810 + 1.18009i 0.466510 + 0.884516i \(0.345511\pi\)
−0.955319 + 0.295575i \(0.904489\pi\)
\(54\) 0 0
\(55\) 37.3687 37.3687i 0.0916145 0.0916145i
\(56\) 0 0
\(57\) 367.990 + 367.990i 0.855113 + 0.855113i
\(58\) 0 0
\(59\) 627.964 + 260.111i 1.38566 + 0.573959i 0.945989 0.324199i \(-0.105095\pi\)
0.439671 + 0.898159i \(0.355095\pi\)
\(60\) 0 0
\(61\) 66.5782 + 160.734i 0.139745 + 0.337375i 0.978222 0.207563i \(-0.0665532\pi\)
−0.838476 + 0.544938i \(0.816553\pi\)
\(62\) 0 0
\(63\) −25.1621 −0.0503194
\(64\) 0 0
\(65\) −374.189 −0.714038
\(66\) 0 0
\(67\) −211.710 511.113i −0.386037 0.931975i −0.990771 0.135548i \(-0.956721\pi\)
0.604734 0.796428i \(-0.293279\pi\)
\(68\) 0 0
\(69\) 475.115 + 196.799i 0.828945 + 0.343360i
\(70\) 0 0
\(71\) 226.201 + 226.201i 0.378100 + 0.378100i 0.870416 0.492316i \(-0.163850\pi\)
−0.492316 + 0.870416i \(0.663850\pi\)
\(72\) 0 0
\(73\) 802.290 802.290i 1.28631 1.28631i 0.349305 0.937009i \(-0.386418\pi\)
0.937009 0.349305i \(-0.113582\pi\)
\(74\) 0 0
\(75\) −187.316 + 452.220i −0.288391 + 0.696238i
\(76\) 0 0
\(77\) −182.007 + 75.3897i −0.269371 + 0.111577i
\(78\) 0 0
\(79\) 552.368i 0.786662i −0.919397 0.393331i \(-0.871323\pi\)
0.919397 0.393331i \(-0.128677\pi\)
\(80\) 0 0
\(81\) 693.272i 0.950991i
\(82\) 0 0
\(83\) 137.983 57.1544i 0.182477 0.0755845i −0.289574 0.957156i \(-0.593514\pi\)
0.472051 + 0.881571i \(0.343514\pi\)
\(84\) 0 0
\(85\) 162.236 391.672i 0.207023 0.499798i
\(86\) 0 0
\(87\) −497.195 + 497.195i −0.612700 + 0.612700i
\(88\) 0 0
\(89\) −579.803 579.803i −0.690550 0.690550i 0.271803 0.962353i \(-0.412380\pi\)
−0.962353 + 0.271803i \(0.912380\pi\)
\(90\) 0 0
\(91\) 1288.71 + 533.802i 1.48455 + 0.614919i
\(92\) 0 0
\(93\) −519.610 1254.45i −0.579366 1.39871i
\(94\) 0 0
\(95\) −547.785 −0.591595
\(96\) 0 0
\(97\) −912.077 −0.954716 −0.477358 0.878709i \(-0.658405\pi\)
−0.477358 + 0.878709i \(0.658405\pi\)
\(98\) 0 0
\(99\) −4.78742 11.5579i −0.00486014 0.0117334i
\(100\) 0 0
\(101\) −968.800 401.290i −0.954447 0.395345i −0.149547 0.988755i \(-0.547781\pi\)
−0.804901 + 0.593410i \(0.797781\pi\)
\(102\) 0 0
\(103\) −351.683 351.683i −0.336430 0.336430i 0.518592 0.855022i \(-0.326457\pi\)
−0.855022 + 0.518592i \(0.826457\pi\)
\(104\) 0 0
\(105\) −381.296 + 381.296i −0.354388 + 0.354388i
\(106\) 0 0
\(107\) 95.4774 230.503i 0.0862631 0.208257i −0.874861 0.484374i \(-0.839047\pi\)
0.961124 + 0.276116i \(0.0890475\pi\)
\(108\) 0 0
\(109\) 858.330 355.532i 0.754249 0.312420i 0.0277749 0.999614i \(-0.491158\pi\)
0.726474 + 0.687194i \(0.241158\pi\)
\(110\) 0 0
\(111\) 1129.39i 0.965735i
\(112\) 0 0
\(113\) 1154.63i 0.961222i 0.876934 + 0.480611i \(0.159585\pi\)
−0.876934 + 0.480611i \(0.840415\pi\)
\(114\) 0 0
\(115\) −500.102 + 207.149i −0.405519 + 0.167972i
\(116\) 0 0
\(117\) −33.8977 + 81.8362i −0.0267850 + 0.0646646i
\(118\) 0 0
\(119\) −1117.48 + 1117.48i −0.860838 + 0.860838i
\(120\) 0 0
\(121\) 871.901 + 871.901i 0.655072 + 0.655072i
\(122\) 0 0
\(123\) −1395.04 577.844i −1.02265 0.423597i
\(124\) 0 0
\(125\) −452.601 1092.67i −0.323855 0.781854i
\(126\) 0 0
\(127\) −953.091 −0.665930 −0.332965 0.942939i \(-0.608049\pi\)
−0.332965 + 0.942939i \(0.608049\pi\)
\(128\) 0 0
\(129\) −755.290 −0.515501
\(130\) 0 0
\(131\) −26.3943 63.7216i −0.0176037 0.0424991i 0.914833 0.403832i \(-0.132322\pi\)
−0.932437 + 0.361333i \(0.882322\pi\)
\(132\) 0 0
\(133\) 1886.58 + 781.446i 1.22998 + 0.509473i
\(134\) 0 0
\(135\) −541.401 541.401i −0.345158 0.345158i
\(136\) 0 0
\(137\) −1910.45 + 1910.45i −1.19139 + 1.19139i −0.214713 + 0.976677i \(0.568882\pi\)
−0.976677 + 0.214713i \(0.931118\pi\)
\(138\) 0 0
\(139\) 525.552 1268.79i 0.320696 0.774228i −0.678518 0.734584i \(-0.737377\pi\)
0.999214 0.0396445i \(-0.0126225\pi\)
\(140\) 0 0
\(141\) −814.297 + 337.293i −0.486356 + 0.201455i
\(142\) 0 0
\(143\) 693.516i 0.405557i
\(144\) 0 0
\(145\) 740.118i 0.423886i
\(146\) 0 0
\(147\) 249.523 103.356i 0.140002 0.0579908i
\(148\) 0 0
\(149\) 477.450 1152.67i 0.262512 0.633759i −0.736581 0.676349i \(-0.763561\pi\)
0.999093 + 0.0425902i \(0.0135610\pi\)
\(150\) 0 0
\(151\) 1185.23 1185.23i 0.638757 0.638757i −0.311492 0.950249i \(-0.600829\pi\)
0.950249 + 0.311492i \(0.100829\pi\)
\(152\) 0 0
\(153\) −70.9629 70.9629i −0.0374968 0.0374968i
\(154\) 0 0
\(155\) 1320.42 + 546.937i 0.684250 + 0.283426i
\(156\) 0 0
\(157\) 187.368 + 452.347i 0.0952460 + 0.229944i 0.964321 0.264737i \(-0.0852850\pi\)
−0.869075 + 0.494681i \(0.835285\pi\)
\(158\) 0 0
\(159\) 2500.25 1.24706
\(160\) 0 0
\(161\) 2017.87 0.987764
\(162\) 0 0
\(163\) 926.026 + 2235.62i 0.444981 + 1.07428i 0.974178 + 0.225781i \(0.0724933\pi\)
−0.529197 + 0.848499i \(0.677507\pi\)
\(164\) 0 0
\(165\) −247.690 102.597i −0.116865 0.0484069i
\(166\) 0 0
\(167\) −753.289 753.289i −0.349049 0.349049i 0.510706 0.859755i \(-0.329384\pi\)
−0.859755 + 0.510706i \(0.829384\pi\)
\(168\) 0 0
\(169\) 1918.72 1918.72i 0.873338 0.873338i
\(170\) 0 0
\(171\) −49.6237 + 119.802i −0.0221919 + 0.0535760i
\(172\) 0 0
\(173\) −186.646 + 77.3114i −0.0820257 + 0.0339762i −0.423319 0.905981i \(-0.639135\pi\)
0.341293 + 0.939957i \(0.389135\pi\)
\(174\) 0 0
\(175\) 1920.62i 0.829632i
\(176\) 0 0
\(177\) 3448.18i 1.46430i
\(178\) 0 0
\(179\) 1509.31 625.176i 0.630229 0.261049i −0.0446216 0.999004i \(-0.514208\pi\)
0.674850 + 0.737955i \(0.264208\pi\)
\(180\) 0 0
\(181\) −772.420 + 1864.79i −0.317202 + 0.765793i 0.682199 + 0.731167i \(0.261024\pi\)
−0.999400 + 0.0346258i \(0.988976\pi\)
\(182\) 0 0
\(183\) 624.090 624.090i 0.252099 0.252099i
\(184\) 0 0
\(185\) 840.595 + 840.595i 0.334064 + 0.334064i
\(186\) 0 0
\(187\) −725.918 300.685i −0.283874 0.117584i
\(188\) 0 0
\(189\) 1092.25 + 2636.93i 0.420368 + 1.01486i
\(190\) 0 0
\(191\) −1509.32 −0.571784 −0.285892 0.958262i \(-0.592290\pi\)
−0.285892 + 0.958262i \(0.592290\pi\)
\(192\) 0 0
\(193\) 3625.68 1.35224 0.676120 0.736791i \(-0.263660\pi\)
0.676120 + 0.736791i \(0.263660\pi\)
\(194\) 0 0
\(195\) 726.442 + 1753.79i 0.266778 + 0.644058i
\(196\) 0 0
\(197\) −1764.33 730.811i −0.638090 0.264305i 0.0400962 0.999196i \(-0.487234\pi\)
−0.678186 + 0.734890i \(0.737234\pi\)
\(198\) 0 0
\(199\) 2008.70 + 2008.70i 0.715544 + 0.715544i 0.967689 0.252146i \(-0.0811362\pi\)
−0.252146 + 0.967689i \(0.581136\pi\)
\(200\) 0 0
\(201\) −1984.52 + 1984.52i −0.696406 + 0.696406i
\(202\) 0 0
\(203\) −1055.82 + 2548.97i −0.365044 + 0.881295i
\(204\) 0 0
\(205\) 1468.40 608.233i 0.500282 0.207224i
\(206\) 0 0
\(207\) 128.139i 0.0430255i
\(208\) 0 0
\(209\) 1015.25i 0.336013i
\(210\) 0 0
\(211\) 1133.08 469.337i 0.369689 0.153130i −0.190101 0.981764i \(-0.560882\pi\)
0.559790 + 0.828634i \(0.310882\pi\)
\(212\) 0 0
\(213\) 621.039 1499.32i 0.199779 0.482309i
\(214\) 0 0
\(215\) 562.158 562.158i 0.178320 0.178320i
\(216\) 0 0
\(217\) −3767.31 3767.31i −1.17853 1.17853i
\(218\) 0 0
\(219\) −5317.80 2202.70i −1.64084 0.679657i
\(220\) 0 0
\(221\) 2129.02 + 5139.91i 0.648025 + 1.56447i
\(222\) 0 0
\(223\) 3100.74 0.931125 0.465562 0.885015i \(-0.345852\pi\)
0.465562 + 0.885015i \(0.345852\pi\)
\(224\) 0 0
\(225\) −121.964 −0.0361375
\(226\) 0 0
\(227\) −1661.15 4010.36i −0.485701 1.17259i −0.956863 0.290539i \(-0.906165\pi\)
0.471162 0.882047i \(-0.343835\pi\)
\(228\) 0 0
\(229\) −2972.95 1231.44i −0.857895 0.355352i −0.0900110 0.995941i \(-0.528690\pi\)
−0.767884 + 0.640589i \(0.778690\pi\)
\(230\) 0 0
\(231\) 706.687 + 706.687i 0.201284 + 0.201284i
\(232\) 0 0
\(233\) 1590.35 1590.35i 0.447155 0.447155i −0.447253 0.894408i \(-0.647597\pi\)
0.894408 + 0.447253i \(0.147597\pi\)
\(234\) 0 0
\(235\) 355.031 857.121i 0.0985518 0.237925i
\(236\) 0 0
\(237\) −2588.89 + 1072.35i −0.709564 + 0.293911i
\(238\) 0 0
\(239\) 6173.19i 1.67076i 0.549676 + 0.835378i \(0.314751\pi\)
−0.549676 + 0.835378i \(0.685249\pi\)
\(240\) 0 0
\(241\) 1436.00i 0.383822i 0.981412 + 0.191911i \(0.0614685\pi\)
−0.981412 + 0.191911i \(0.938531\pi\)
\(242\) 0 0
\(243\) −327.413 + 135.619i −0.0864344 + 0.0358023i
\(244\) 0 0
\(245\) −108.791 + 262.646i −0.0283691 + 0.0684890i
\(246\) 0 0
\(247\) 5083.09 5083.09i 1.30943 1.30943i
\(248\) 0 0
\(249\) −535.754 535.754i −0.136354 0.136354i
\(250\) 0 0
\(251\) −4781.23 1980.45i −1.20235 0.498028i −0.310589 0.950544i \(-0.600526\pi\)
−0.891756 + 0.452516i \(0.850526\pi\)
\(252\) 0 0
\(253\) 383.926 + 926.879i 0.0954040 + 0.230326i
\(254\) 0 0
\(255\) −2150.69 −0.528162
\(256\) 0 0
\(257\) −246.466 −0.0598215 −0.0299107 0.999553i \(-0.509522\pi\)
−0.0299107 + 0.999553i \(0.509522\pi\)
\(258\) 0 0
\(259\) −1695.86 4094.17i −0.406856 0.982237i
\(260\) 0 0
\(261\) −161.866 67.0470i −0.0383879 0.0159008i
\(262\) 0 0
\(263\) −3454.60 3454.60i −0.809960 0.809960i 0.174667 0.984628i \(-0.444115\pi\)
−0.984628 + 0.174667i \(0.944115\pi\)
\(264\) 0 0
\(265\) −1860.92 + 1860.92i −0.431380 + 0.431380i
\(266\) 0 0
\(267\) −1591.86 + 3843.09i −0.364870 + 0.880874i
\(268\) 0 0
\(269\) 2611.67 1081.79i 0.591958 0.245197i −0.0665350 0.997784i \(-0.521194\pi\)
0.658493 + 0.752587i \(0.271194\pi\)
\(270\) 0 0
\(271\) 3464.52i 0.776585i −0.921536 0.388292i \(-0.873065\pi\)
0.921536 0.388292i \(-0.126935\pi\)
\(272\) 0 0
\(273\) 7076.37i 1.56880i
\(274\) 0 0
\(275\) −882.213 + 365.425i −0.193453 + 0.0801307i
\(276\) 0 0
\(277\) 1186.33 2864.06i 0.257328 0.621245i −0.741432 0.671028i \(-0.765853\pi\)
0.998760 + 0.0497833i \(0.0158531\pi\)
\(278\) 0 0
\(279\) 239.233 239.233i 0.0513352 0.0513352i
\(280\) 0 0
\(281\) 3210.39 + 3210.39i 0.681552 + 0.681552i 0.960350 0.278798i \(-0.0899360\pi\)
−0.278798 + 0.960350i \(0.589936\pi\)
\(282\) 0 0
\(283\) 2512.41 + 1040.67i 0.527729 + 0.218593i 0.630608 0.776101i \(-0.282806\pi\)
−0.102879 + 0.994694i \(0.532806\pi\)
\(284\) 0 0
\(285\) 1063.46 + 2567.41i 0.221031 + 0.533615i
\(286\) 0 0
\(287\) −5924.88 −1.21859
\(288\) 0 0
\(289\) −1390.14 −0.282950
\(290\) 0 0
\(291\) 1770.68 + 4274.81i 0.356699 + 0.861147i
\(292\) 0 0
\(293\) −7264.11 3008.89i −1.44838 0.599937i −0.486563 0.873646i \(-0.661749\pi\)
−0.961812 + 0.273709i \(0.911749\pi\)
\(294\) 0 0
\(295\) 2566.46 + 2566.46i 0.506525 + 0.506525i
\(296\) 0 0
\(297\) −1003.42 + 1003.42i −0.196042 + 0.196042i
\(298\) 0 0
\(299\) 2718.41 6562.83i 0.525786 1.26936i
\(300\) 0 0
\(301\) −2738.03 + 1134.13i −0.524310 + 0.217176i
\(302\) 0 0
\(303\) 5319.72i 1.00861i
\(304\) 0 0
\(305\) 929.012i 0.174410i
\(306\) 0 0
\(307\) −1055.79 + 437.322i −0.196277 + 0.0813006i −0.478657 0.878002i \(-0.658876\pi\)
0.282380 + 0.959303i \(0.408876\pi\)
\(308\) 0 0
\(309\) −965.552 + 2331.05i −0.177762 + 0.429155i
\(310\) 0 0
\(311\) −2154.35 + 2154.35i −0.392804 + 0.392804i −0.875686 0.482882i \(-0.839590\pi\)
0.482882 + 0.875686i \(0.339590\pi\)
\(312\) 0 0
\(313\) −3659.65 3659.65i −0.660881 0.660881i 0.294706 0.955588i \(-0.404778\pi\)
−0.955588 + 0.294706i \(0.904778\pi\)
\(314\) 0 0
\(315\) −124.134 51.4180i −0.0222037 0.00919707i
\(316\) 0 0
\(317\) −3106.88 7500.68i −0.550473 1.32896i −0.917125 0.398601i \(-0.869496\pi\)
0.366652 0.930358i \(-0.380504\pi\)
\(318\) 0 0
\(319\) −1371.72 −0.240757
\(320\) 0 0
\(321\) −1265.70 −0.220076
\(322\) 0 0
\(323\) 3116.73 + 7524.45i 0.536902 + 1.29620i
\(324\) 0 0
\(325\) 6246.57 + 2587.41i 1.06615 + 0.441612i
\(326\) 0 0
\(327\) −3332.68 3332.68i −0.563602 0.563602i
\(328\) 0 0
\(329\) −2445.46 + 2445.46i −0.409795 + 0.409795i
\(330\) 0 0
\(331\) −2372.98 + 5728.87i −0.394050 + 0.951321i 0.594998 + 0.803727i \(0.297153\pi\)
−0.989048 + 0.147594i \(0.952847\pi\)
\(332\) 0 0
\(333\) 259.990 107.691i 0.0427848 0.0177220i
\(334\) 0 0
\(335\) 2954.14i 0.481796i
\(336\) 0 0
\(337\) 5514.75i 0.891418i 0.895178 + 0.445709i \(0.147048\pi\)
−0.895178 + 0.445709i \(0.852952\pi\)
\(338\) 0 0
\(339\) 5411.61 2241.56i 0.867016 0.359130i
\(340\) 0 0
\(341\) 1013.68 2447.24i 0.160979 0.388638i
\(342\) 0 0
\(343\) −4078.53 + 4078.53i −0.642041 + 0.642041i
\(344\) 0 0
\(345\) 1941.77 + 1941.77i 0.303019 + 0.303019i
\(346\) 0 0
\(347\) 9323.05 + 3861.74i 1.44233 + 0.597432i 0.960361 0.278758i \(-0.0899227\pi\)
0.481966 + 0.876190i \(0.339923\pi\)
\(348\) 0 0
\(349\) −1844.20 4452.29i −0.282859 0.682882i 0.717041 0.697031i \(-0.245496\pi\)
−0.999900 + 0.0141493i \(0.995496\pi\)
\(350\) 0 0
\(351\) 10047.7 1.52794
\(352\) 0 0
\(353\) 7343.73 1.10727 0.553636 0.832759i \(-0.313240\pi\)
0.553636 + 0.832759i \(0.313240\pi\)
\(354\) 0 0
\(355\) 653.700 + 1578.17i 0.0977317 + 0.235945i
\(356\) 0 0
\(357\) 7406.99 + 3068.08i 1.09809 + 0.454846i
\(358\) 0 0
\(359\) −4187.33 4187.33i −0.615596 0.615596i 0.328802 0.944399i \(-0.393355\pi\)
−0.944399 + 0.328802i \(0.893355\pi\)
\(360\) 0 0
\(361\) 2591.22 2591.22i 0.377784 0.377784i
\(362\) 0 0
\(363\) 2393.82 5779.20i 0.346124 0.835617i
\(364\) 0 0
\(365\) 5597.46 2318.54i 0.802697 0.332488i
\(366\) 0 0
\(367\) 9231.47i 1.31302i −0.754317 0.656510i \(-0.772032\pi\)
0.754317 0.656510i \(-0.227968\pi\)
\(368\) 0 0
\(369\) 376.244i 0.0530798i
\(370\) 0 0
\(371\) 9063.75 3754.33i 1.26837 0.525377i
\(372\) 0 0
\(373\) −117.113 + 282.737i −0.0162571 + 0.0392481i −0.931800 0.362973i \(-0.881762\pi\)
0.915543 + 0.402221i \(0.131762\pi\)
\(374\) 0 0
\(375\) −4242.58 + 4242.58i −0.584230 + 0.584230i
\(376\) 0 0
\(377\) 6867.82 + 6867.82i 0.938224 + 0.938224i
\(378\) 0 0
\(379\) −3068.05 1270.83i −0.415819 0.172238i 0.164958 0.986301i \(-0.447251\pi\)
−0.580777 + 0.814063i \(0.697251\pi\)
\(380\) 0 0
\(381\) 1850.31 + 4467.04i 0.248804 + 0.600665i
\(382\) 0 0
\(383\) −1379.97 −0.184107 −0.0920537 0.995754i \(-0.529343\pi\)
−0.0920537 + 0.995754i \(0.529343\pi\)
\(384\) 0 0
\(385\) −1051.97 −0.139255
\(386\) 0 0
\(387\) −72.0198 173.871i −0.00945987 0.0228381i
\(388\) 0 0
\(389\) 1279.89 + 530.148i 0.166820 + 0.0690992i 0.464531 0.885557i \(-0.346223\pi\)
−0.297711 + 0.954656i \(0.596223\pi\)
\(390\) 0 0
\(391\) 5690.85 + 5690.85i 0.736058 + 0.736058i
\(392\) 0 0
\(393\) −247.415 + 247.415i −0.0317568 + 0.0317568i
\(394\) 0 0
\(395\) 1128.75 2725.04i 0.143781 0.347118i
\(396\) 0 0
\(397\) −706.615 + 292.690i −0.0893300 + 0.0370017i −0.426901 0.904298i \(-0.640395\pi\)
0.337571 + 0.941300i \(0.390395\pi\)
\(398\) 0 0
\(399\) 10359.3i 1.29978i
\(400\) 0 0
\(401\) 9680.79i 1.20557i 0.797902 + 0.602787i \(0.205943\pi\)
−0.797902 + 0.602787i \(0.794057\pi\)
\(402\) 0 0
\(403\) −17327.9 + 7177.45i −2.14184 + 0.887181i
\(404\) 0 0
\(405\) −1416.68 + 3420.18i −0.173816 + 0.419630i
\(406\) 0 0
\(407\) 1557.94 1557.94i 0.189740 0.189740i
\(408\) 0 0
\(409\) −1231.14 1231.14i −0.148841 0.148841i 0.628759 0.777600i \(-0.283563\pi\)
−0.777600 + 0.628759i \(0.783563\pi\)
\(410\) 0 0
\(411\) 12663.0 + 5245.17i 1.51975 + 0.629502i
\(412\) 0 0
\(413\) −5177.71 12500.1i −0.616896 1.48932i
\(414\) 0 0
\(415\) 797.516 0.0943338
\(416\) 0 0
\(417\) −6967.00 −0.818167
\(418\) 0 0
\(419\) −3904.87 9427.19i −0.455287 1.09916i −0.970284 0.241968i \(-0.922207\pi\)
0.514997 0.857192i \(-0.327793\pi\)
\(420\) 0 0
\(421\) 10566.0 + 4376.59i 1.22318 + 0.506656i 0.898418 0.439141i \(-0.144717\pi\)
0.324758 + 0.945797i \(0.394717\pi\)
\(422\) 0 0
\(423\) −155.292 155.292i −0.0178501 0.0178501i
\(424\) 0 0
\(425\) −5416.61 + 5416.61i −0.618222 + 0.618222i
\(426\) 0 0
\(427\) 1325.29 3199.53i 0.150199 0.362614i
\(428\) 0 0
\(429\) 3250.44 1346.37i 0.365810 0.151523i
\(430\) 0 0
\(431\) 16965.2i 1.89602i 0.318242 + 0.948010i \(0.396908\pi\)
−0.318242 + 0.948010i \(0.603092\pi\)
\(432\) 0 0
\(433\) 5628.82i 0.624720i 0.949964 + 0.312360i \(0.101120\pi\)
−0.949964 + 0.312360i \(0.898880\pi\)
\(434\) 0 0
\(435\) −3468.86 + 1436.85i −0.382342 + 0.158371i
\(436\) 0 0
\(437\) 3979.55 9607.49i 0.435625 1.05169i
\(438\) 0 0
\(439\) −6003.38 + 6003.38i −0.652678 + 0.652678i −0.953637 0.300959i \(-0.902693\pi\)
0.300959 + 0.953637i \(0.402693\pi\)
\(440\) 0 0
\(441\) 47.5859 + 47.5859i 0.00513831 + 0.00513831i
\(442\) 0 0
\(443\) −1448.22 599.872i −0.155321 0.0643359i 0.303669 0.952778i \(-0.401788\pi\)
−0.458989 + 0.888442i \(0.651788\pi\)
\(444\) 0 0
\(445\) −1675.58 4045.20i −0.178494 0.430923i
\(446\) 0 0
\(447\) −6329.34 −0.669726
\(448\) 0 0
\(449\) −12533.6 −1.31737 −0.658683 0.752421i \(-0.728886\pi\)
−0.658683 + 0.752421i \(0.728886\pi\)
\(450\) 0 0
\(451\) −1127.29 2721.51i −0.117698 0.284149i
\(452\) 0 0
\(453\) −7856.00 3254.06i −0.814806 0.337504i
\(454\) 0 0
\(455\) 5266.90 + 5266.90i 0.542672 + 0.542672i
\(456\) 0 0
\(457\) 11661.6 11661.6i 1.19367 1.19367i 0.217641 0.976029i \(-0.430164\pi\)
0.976029 0.217641i \(-0.0698361\pi\)
\(458\) 0 0
\(459\) −4356.35 + 10517.2i −0.443000 + 1.06950i
\(460\) 0 0
\(461\) −8424.31 + 3489.46i −0.851104 + 0.352539i −0.765222 0.643766i \(-0.777371\pi\)
−0.0858823 + 0.996305i \(0.527371\pi\)
\(462\) 0 0
\(463\) 11549.8i 1.15932i −0.814860 0.579658i \(-0.803186\pi\)
0.814860 0.579658i \(-0.196814\pi\)
\(464\) 0 0
\(465\) 7250.49i 0.723083i
\(466\) 0 0
\(467\) 6314.42 2615.52i 0.625689 0.259169i −0.0472314 0.998884i \(-0.515040\pi\)
0.672920 + 0.739715i \(0.265040\pi\)
\(468\) 0 0
\(469\) −4214.24 + 10174.1i −0.414916 + 1.00170i
\(470\) 0 0
\(471\) 1756.35 1756.35i 0.171823 0.171823i
\(472\) 0 0
\(473\) −1041.89 1041.89i −0.101282 0.101282i
\(474\) 0 0
\(475\) 9144.51 + 3787.78i 0.883324 + 0.365885i
\(476\) 0 0
\(477\) 238.409 + 575.569i 0.0228847 + 0.0552484i
\(478\) 0 0
\(479\) 10874.6 1.03731 0.518655 0.854983i \(-0.326433\pi\)
0.518655 + 0.854983i \(0.326433\pi\)
\(480\) 0 0
\(481\) −15600.4 −1.47883
\(482\) 0 0
\(483\) −3917.43 9457.52i −0.369046 0.890957i
\(484\) 0 0
\(485\) −4499.62 1863.81i −0.421273 0.174497i
\(486\) 0 0
\(487\) −538.006 538.006i −0.0500603 0.0500603i 0.681633 0.731694i \(-0.261270\pi\)
−0.731694 + 0.681633i \(0.761270\pi\)
\(488\) 0 0
\(489\) 8680.37 8680.37i 0.802741 0.802741i
\(490\) 0 0
\(491\) −1701.48 + 4107.75i −0.156389 + 0.377556i −0.982582 0.185831i \(-0.940502\pi\)
0.826193 + 0.563387i \(0.190502\pi\)
\(492\) 0 0
\(493\) −10166.4 + 4211.04i −0.928742 + 0.384697i
\(494\) 0 0
\(495\) 66.8023i 0.00606574i
\(496\) 0 0
\(497\) 6367.77i 0.574716i
\(498\) 0 0
\(499\) −19571.5 + 8106.78i −1.75579 + 0.727273i −0.758669 + 0.651476i \(0.774150\pi\)
−0.997123 + 0.0757967i \(0.975850\pi\)
\(500\) 0 0
\(501\) −2068.17 + 4993.00i −0.184429 + 0.445251i
\(502\) 0 0
\(503\) 373.535 373.535i 0.0331115 0.0331115i −0.690357 0.723469i \(-0.742547\pi\)
0.723469 + 0.690357i \(0.242547\pi\)
\(504\) 0 0
\(505\) −3959.43 3959.43i −0.348896 0.348896i
\(506\) 0 0
\(507\) −12717.8 5267.90i −1.11404 0.461451i
\(508\) 0 0
\(509\) 874.883 + 2112.15i 0.0761857 + 0.183928i 0.957384 0.288819i \(-0.0932624\pi\)
−0.881198 + 0.472747i \(0.843262\pi\)
\(510\) 0 0
\(511\) −22585.2 −1.95521
\(512\) 0 0
\(513\) 14709.1 1.26593
\(514\) 0 0
\(515\) −1016.33 2453.64i −0.0869609 0.209942i
\(516\) 0 0
\(517\) −1588.57 658.008i −0.135136 0.0559751i
\(518\) 0 0
\(519\) 724.701 + 724.701i 0.0612926 + 0.0612926i
\(520\) 0 0
\(521\) 15352.0 15352.0i 1.29095 1.29095i 0.356743 0.934203i \(-0.383887\pi\)
0.934203 0.356743i \(-0.116113\pi\)
\(522\) 0 0
\(523\) 2376.45 5737.26i 0.198690 0.479680i −0.792860 0.609404i \(-0.791409\pi\)
0.991550 + 0.129723i \(0.0414089\pi\)
\(524\) 0 0
\(525\) 9001.77 3728.65i 0.748323 0.309965i
\(526\) 0 0
\(527\) 21249.4i 1.75643i
\(528\) 0 0
\(529\) 1890.92i 0.155414i
\(530\) 0 0
\(531\) 793.785 328.796i 0.0648726 0.0268711i
\(532\) 0 0
\(533\) −7981.84 + 19269.9i −0.648653 + 1.56599i
\(534\) 0 0
\(535\) 942.053 942.053i 0.0761280 0.0761280i
\(536\) 0 0
\(537\) −5860.27 5860.27i −0.470930 0.470930i
\(538\) 0 0
\(539\) 486.782 + 201.632i 0.0389002 + 0.0161130i
\(540\) 0 0
\(541\) 2381.59 + 5749.66i 0.189265 + 0.456926i 0.989819 0.142335i \(-0.0454610\pi\)
−0.800553 + 0.599261i \(0.795461\pi\)
\(542\) 0 0
\(543\) 10239.6 0.809252
\(544\) 0 0
\(545\) 4960.99 0.389918
\(546\) 0 0
\(547\) 2560.31 + 6181.14i 0.200130 + 0.483156i 0.991801 0.127791i \(-0.0407887\pi\)
−0.791671 + 0.610947i \(0.790789\pi\)
\(548\) 0 0
\(549\) 203.178 + 84.1589i 0.0157949 + 0.00654247i
\(550\) 0 0
\(551\) 10054.0 + 10054.0i 0.777338 + 0.777338i
\(552\) 0 0
\(553\) −7774.85 + 7774.85i −0.597866 + 0.597866i
\(554\) 0 0
\(555\) 2307.87 5571.69i 0.176511 0.426135i
\(556\) 0 0
\(557\) 10306.9 4269.27i 0.784055 0.324766i 0.0455041 0.998964i \(-0.485511\pi\)
0.738551 + 0.674198i \(0.235511\pi\)
\(558\) 0 0
\(559\) 10432.9i 0.789384i
\(560\) 0 0
\(561\) 3986.05i 0.299984i
\(562\) 0 0
\(563\) 8478.56 3511.93i 0.634687 0.262896i −0.0420563 0.999115i \(-0.513391\pi\)
0.676743 + 0.736219i \(0.263391\pi\)
\(564\) 0 0
\(565\) −2359.45 + 5696.21i −0.175686 + 0.424144i
\(566\) 0 0
\(567\) 9758.15 9758.15i 0.722758 0.722758i
\(568\) 0 0
\(569\) 304.321 + 304.321i 0.0224214 + 0.0224214i 0.718229 0.695807i \(-0.244953\pi\)
−0.695807 + 0.718229i \(0.744953\pi\)
\(570\) 0 0
\(571\) −7459.96 3090.02i −0.546742 0.226468i 0.0921763 0.995743i \(-0.470618\pi\)
−0.638918 + 0.769275i \(0.720618\pi\)
\(572\) 0 0
\(573\) 2930.16 + 7074.04i 0.213629 + 0.515746i
\(574\) 0 0
\(575\) 9780.88 0.709376
\(576\) 0 0
\(577\) −11616.3 −0.838118 −0.419059 0.907959i \(-0.637640\pi\)
−0.419059 + 0.907959i \(0.637640\pi\)
\(578\) 0 0
\(579\) −7038.82 16993.2i −0.505221 1.21971i
\(580\) 0 0
\(581\) −2746.65 1137.70i −0.196128 0.0812389i
\(582\) 0 0
\(583\) 3449.00 + 3449.00i 0.245014 + 0.245014i
\(584\) 0 0
\(585\) −334.460 + 334.460i −0.0236380 + 0.0236380i
\(586\) 0 0
\(587\) −6654.96 + 16066.5i −0.467938 + 1.12970i 0.497123 + 0.867680i \(0.334390\pi\)
−0.965062 + 0.262023i \(0.915610\pi\)
\(588\) 0 0
\(589\) −25366.7 + 10507.2i −1.77456 + 0.735048i
\(590\) 0 0
\(591\) 9688.04i 0.674302i
\(592\) 0 0
\(593\) 9365.10i 0.648530i −0.945966 0.324265i \(-0.894883\pi\)
0.945966 0.324265i \(-0.105117\pi\)
\(594\) 0 0
\(595\) −7796.53 + 3229.43i −0.537187 + 0.222510i
\(596\) 0 0
\(597\) 5514.93 13314.2i 0.378076 0.912756i
\(598\) 0 0
\(599\) −12280.1 + 12280.1i −0.837647 + 0.837647i −0.988549 0.150902i \(-0.951782\pi\)
0.150902 + 0.988549i \(0.451782\pi\)
\(600\) 0 0
\(601\) 11681.6 + 11681.6i 0.792852 + 0.792852i 0.981957 0.189105i \(-0.0605587\pi\)
−0.189105 + 0.981957i \(0.560559\pi\)
\(602\) 0 0
\(603\) −646.078 267.614i −0.0436324 0.0180731i
\(604\) 0 0
\(605\) 2519.71 + 6083.12i 0.169324 + 0.408784i
\(606\) 0 0
\(607\) 20354.6 1.36107 0.680535 0.732716i \(-0.261747\pi\)
0.680535 + 0.732716i \(0.261747\pi\)
\(608\) 0 0
\(609\) 13996.5 0.931309
\(610\) 0 0
\(611\) 4659.07 + 11248.0i 0.308487 + 0.744754i
\(612\) 0 0
\(613\) 23946.8 + 9919.08i 1.57782 + 0.653553i 0.988066 0.154032i \(-0.0492260\pi\)
0.589751 + 0.807585i \(0.299226\pi\)
\(614\) 0 0
\(615\) −5701.45 5701.45i −0.373829 0.373829i
\(616\) 0 0
\(617\) −17139.4 + 17139.4i −1.11833 + 1.11833i −0.126340 + 0.991987i \(0.540323\pi\)
−0.991987 + 0.126340i \(0.959677\pi\)
\(618\) 0 0
\(619\) 9612.31 23206.2i 0.624154 1.50684i −0.222629 0.974903i \(-0.571464\pi\)
0.846783 0.531938i \(-0.178536\pi\)
\(620\) 0 0
\(621\) 13428.7 5562.35i 0.867753 0.359435i
\(622\) 0 0
\(623\) 16322.0i 1.04964i
\(624\) 0 0
\(625\) 5745.29i 0.367699i
\(626\) 0 0
\(627\) 4758.39 1970.99i 0.303081 0.125540i
\(628\) 0 0
\(629\) 6763.80 16329.2i 0.428760 1.03512i
\(630\) 0 0
\(631\) −2243.98 + 2243.98i −0.141571 + 0.141571i −0.774340 0.632769i \(-0.781918\pi\)
0.632769 + 0.774340i \(0.281918\pi\)
\(632\) 0 0
\(633\) −4399.46 4399.46i −0.276245 0.276245i
\(634\) 0 0
\(635\) −4701.96 1947.62i −0.293845 0.121715i
\(636\) 0 0
\(637\) −1427.67 3446.70i −0.0888010 0.214385i
\(638\) 0 0
\(639\) 404.369 0.0250338
\(640\) 0 0
\(641\) 19815.9 1.22103 0.610515 0.792005i \(-0.290963\pi\)
0.610515 + 0.792005i \(0.290963\pi\)
\(642\) 0 0
\(643\) 5189.74 + 12529.1i 0.318295 + 0.768431i 0.999345 + 0.0361945i \(0.0115236\pi\)
−0.681050 + 0.732237i \(0.738476\pi\)
\(644\) 0 0
\(645\) −3726.13 1543.42i −0.227467 0.0942200i
\(646\) 0 0
\(647\) −18031.1 18031.1i −1.09563 1.09563i −0.994915 0.100717i \(-0.967886\pi\)
−0.100717 0.994915i \(-0.532114\pi\)
\(648\) 0 0
\(649\) 4756.62 4756.62i 0.287694 0.287694i
\(650\) 0 0
\(651\) −10343.2 + 24970.8i −0.622708 + 1.50335i
\(652\) 0 0
\(653\) 4031.36 1669.85i 0.241592 0.100071i −0.258602 0.965984i \(-0.583262\pi\)
0.500194 + 0.865913i \(0.333262\pi\)
\(654\) 0 0
\(655\) 368.299i 0.0219704i
\(656\) 0 0
\(657\) 1434.22i 0.0851660i
\(658\) 0 0
\(659\) 16047.0 6646.88i 0.948561 0.392907i 0.145871 0.989304i \(-0.453401\pi\)
0.802690 + 0.596397i \(0.203401\pi\)
\(660\) 0 0
\(661\) 6313.25 15241.5i 0.371493 0.896864i −0.622005 0.783014i \(-0.713682\pi\)
0.993498 0.113850i \(-0.0363185\pi\)
\(662\) 0 0
\(663\) 19957.0 19957.0i 1.16903 1.16903i
\(664\) 0 0
\(665\) 7710.34 + 7710.34i 0.449615 + 0.449615i
\(666\) 0 0
\(667\) 12980.8 + 5376.81i 0.753550 + 0.312131i
\(668\) 0 0
\(669\) −6019.70 14532.8i −0.347885 0.839869i
\(670\) 0 0
\(671\) 1721.81 0.0990609
\(672\) 0 0
\(673\) 9059.04 0.518871 0.259436 0.965760i \(-0.416463\pi\)
0.259436 + 0.965760i \(0.416463\pi\)
\(674\) 0 0
\(675\) 5294.30 + 12781.6i 0.301893 + 0.728834i
\(676\) 0 0
\(677\) 1398.12 + 579.121i 0.0793710 + 0.0328765i 0.422016 0.906589i \(-0.361323\pi\)
−0.342645 + 0.939465i \(0.611323\pi\)
\(678\) 0 0
\(679\) 12837.9 + 12837.9i 0.725588 + 0.725588i
\(680\) 0 0
\(681\) −15571.2 + 15571.2i −0.876199 + 0.876199i
\(682\) 0 0
\(683\) 11645.5 28114.8i 0.652422 1.57509i −0.156830 0.987626i \(-0.550127\pi\)
0.809252 0.587462i \(-0.199873\pi\)
\(684\) 0 0
\(685\) −13328.9 + 5521.01i −0.743462 + 0.307952i
\(686\) 0 0
\(687\) 16324.6i 0.906582i
\(688\) 0 0
\(689\) 34536.3i 1.90962i
\(690\) 0 0
\(691\) 4362.78 1807.12i 0.240185 0.0994879i −0.259344 0.965785i \(-0.583506\pi\)
0.499529 + 0.866297i \(0.333506\pi\)
\(692\) 0 0
\(693\) −95.2972 + 230.068i −0.00522372 + 0.0126112i
\(694\) 0 0
\(695\) 5185.49 5185.49i 0.283017 0.283017i
\(696\) 0 0
\(697\) −16709.5 16709.5i −0.908061 0.908061i
\(698\) 0 0
\(699\) −10541.3 4366.33i −0.570396 0.236266i
\(700\) 0 0
\(701\) 6417.56 + 15493.3i 0.345774 + 0.834773i 0.997109 + 0.0759825i \(0.0242093\pi\)
−0.651335 + 0.758790i \(0.725791\pi\)
\(702\) 0 0
\(703\) −22837.8 −1.22524
\(704\) 0 0
\(705\) −4706.48 −0.251428
\(706\) 0 0
\(707\) 7987.97 + 19284.7i 0.424920 + 1.02585i
\(708\) 0 0
\(709\) −17513.4 7254.29i −0.927686 0.384260i −0.132886 0.991131i \(-0.542424\pi\)
−0.794800 + 0.606871i \(0.792424\pi\)
\(710\) 0 0
\(711\) −493.721 493.721i −0.0260422 0.0260422i
\(712\) 0 0
\(713\) −19185.2 + 19185.2i −1.00770 + 1.00770i
\(714\) 0 0
\(715\) −1417.18 + 3421.38i −0.0741252 + 0.178954i
\(716\) 0 0
\(717\) 28933.1 11984.5i 1.50701 0.624224i
\(718\) 0 0
\(719\) 4682.98i 0.242901i −0.992598 0.121450i \(-0.961245\pi\)
0.992598 0.121450i \(-0.0387545\pi\)
\(720\) 0 0
\(721\) 9900.21i 0.511377i
\(722\) 0 0
\(723\) 6730.40 2787.82i 0.346205 0.143403i
\(724\) 0 0
\(725\) −5117.71 + 12355.2i −0.262161 + 0.632913i
\(726\) 0 0
\(727\) −20269.6 + 20269.6i −1.03405 + 1.03405i −0.0346553 + 0.999399i \(0.511033\pi\)
−0.999399 + 0.0346553i \(0.988967\pi\)
\(728\) 0 0
\(729\) 14507.1 + 14507.1i 0.737039 + 0.737039i
\(730\) 0 0
\(731\) −10920.4 4523.37i −0.552537 0.228868i
\(732\) 0 0
\(733\) 1705.29 + 4116.94i 0.0859297 + 0.207453i 0.961003 0.276538i \(-0.0891870\pi\)
−0.875073 + 0.483990i \(0.839187\pi\)
\(734\) 0 0
\(735\) 1442.20 0.0723758
\(736\) 0 0
\(737\) −5475.14 −0.273649
\(738\) 0 0
\(739\) 467.052 + 1127.56i 0.0232487 + 0.0561273i 0.935078 0.354443i \(-0.115330\pi\)
−0.911829 + 0.410570i \(0.865330\pi\)
\(740\) 0 0
\(741\) −33692.1 13955.7i −1.67033 0.691872i
\(742\) 0 0
\(743\) −27671.7 27671.7i −1.36632 1.36632i −0.865620 0.500701i \(-0.833076\pi\)
−0.500701 0.865620i \(-0.666924\pi\)
\(744\) 0 0
\(745\) 4710.89 4710.89i 0.231669 0.231669i
\(746\) 0 0
\(747\) 72.2467 174.419i 0.00353865 0.00854305i
\(748\) 0 0
\(749\) −4588.33 + 1900.55i −0.223837 + 0.0927163i
\(750\) 0 0
\(751\) 22288.5i 1.08298i −0.840707 0.541490i \(-0.817860\pi\)
0.840707 0.541490i \(-0.182140\pi\)
\(752\) 0 0
\(753\) 26253.9i 1.27058i
\(754\) 0 0
\(755\) 8269.15 3425.19i 0.398603 0.165107i
\(756\) 0 0
\(757\) 10902.9 26321.9i 0.523478 1.26379i −0.412252 0.911070i \(-0.635258\pi\)
0.935730 0.352718i \(-0.114742\pi\)
\(758\) 0 0
\(759\) 3598.84 3598.84i 0.172108 0.172108i
\(760\) 0 0
\(761\) −6249.83 6249.83i −0.297709 0.297709i 0.542407 0.840116i \(-0.317513\pi\)
−0.840116 + 0.542407i \(0.817513\pi\)
\(762\) 0 0
\(763\) −17085.7 7077.13i −0.810673 0.335792i
\(764\) 0 0
\(765\) −205.076 495.098i −0.00969222 0.0233991i
\(766\) 0 0
\(767\) −47630.1 −2.24227
\(768\) 0 0
\(769\) 5109.01 0.239578 0.119789 0.992799i \(-0.461778\pi\)
0.119789 + 0.992799i \(0.461778\pi\)
\(770\) 0 0
\(771\) 478.483 + 1155.16i 0.0223504 + 0.0539586i
\(772\) 0 0
\(773\) 119.699 + 49.5811i 0.00556958 + 0.00230699i 0.385466 0.922722i \(-0.374041\pi\)
−0.379897 + 0.925029i \(0.624041\pi\)
\(774\) 0 0
\(775\) −18260.7 18260.7i −0.846379 0.846379i
\(776\) 0 0
\(777\) −15896.7 + 15896.7i −0.733963 + 0.733963i
\(778\) 0 0
\(779\) −11684.8 + 28209.6i −0.537422 + 1.29745i
\(780\) 0 0
\(781\) 2924.95 1211.55i 0.134011 0.0555094i
\(782\) 0 0
\(783\) 19873.6i 0.907055i
\(784\) 0 0
\(785\) 2614.48i 0.118872i
\(786\) 0 0
\(787\) 24341.3 10082.5i 1.10251 0.456674i 0.244157 0.969736i \(-0.421489\pi\)
0.858352 + 0.513062i \(0.171489\pi\)
\(788\) 0 0
\(789\) −9484.67 + 22898.0i −0.427963 + 1.03319i
\(790\) 0 0
\(791\) 16251.9 16251.9i 0.730533 0.730533i
\(792\) 0 0
\(793\) −8620.64 8620.64i −0.386038 0.386038i
\(794\) 0 0
\(795\) 12334.7 + 5109.20i 0.550273 + 0.227930i
\(796\) 0 0