Properties

Label 128.4.g.a.17.3
Level $128$
Weight $4$
Character 128.17
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 17.3
Character \(\chi\) \(=\) 128.17
Dual form 128.4.g.a.113.3

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

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

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
\(3\) −1.94138 + 4.68690i −0.373618 + 0.901994i 0.619513 + 0.784986i \(0.287330\pi\)
−0.993131 + 0.117007i \(0.962670\pi\)
\(4\) 0 0
\(5\) 4.93338 2.04347i 0.441255 0.182774i −0.150984 0.988536i \(-0.548244\pi\)
0.592239 + 0.805762i \(0.298244\pi\)
\(6\) 0 0
\(7\) −14.0755 + 14.0755i −0.760005 + 0.760005i −0.976323 0.216318i \(-0.930595\pi\)
0.216318 + 0.976323i \(0.430595\pi\)
\(8\) 0 0
\(9\) 0.893826 + 0.893826i 0.0331047 + 0.0331047i
\(10\) 0 0
\(11\) 3.78733 + 9.14343i 0.103811 + 0.250623i 0.967247 0.253836i \(-0.0816922\pi\)
−0.863436 + 0.504458i \(0.831692\pi\)
\(12\) 0 0
\(13\) −64.7407 26.8165i −1.38122 0.572120i −0.436412 0.899747i \(-0.643751\pi\)
−0.944807 + 0.327627i \(0.893751\pi\)
\(14\) 0 0
\(15\) 27.0894i 0.466297i
\(16\) 0 0
\(17\) 79.3923i 1.13267i 0.824174 + 0.566337i \(0.191640\pi\)
−0.824174 + 0.566337i \(0.808360\pi\)
\(18\) 0 0
\(19\) −94.7756 39.2573i −1.14437 0.474013i −0.271727 0.962374i \(-0.587595\pi\)
−0.872642 + 0.488361i \(0.837595\pi\)
\(20\) 0 0
\(21\) −38.6445 93.2961i −0.401568 0.969471i
\(22\) 0 0
\(23\) −71.6801 71.6801i −0.649841 0.649841i 0.303114 0.952954i \(-0.401974\pi\)
−0.952954 + 0.303114i \(0.901974\pi\)
\(24\) 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 0.658114 + 0.752918i \(0.271354\pi\)
−0.997751 + 0.0670366i \(0.978646\pi\)
\(30\) 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 0.124334 0.992240i \(-0.460321\pi\)
0.789537 + 0.613702i \(0.210321\pi\)
\(38\) 0 0
\(39\) 251.372 251.372i 1.03210 1.03210i
\(40\) 0 0
\(41\) 210.468 + 210.468i 0.801697 + 0.801697i 0.983361 0.181664i \(-0.0581482\pi\)
−0.181664 + 0.983361i \(0.558148\pi\)
\(42\) 0 0
\(43\) 56.9749 + 137.550i 0.202060 + 0.487817i 0.992132 0.125198i \(-0.0399566\pi\)
−0.790072 + 0.613015i \(0.789957\pi\)
\(44\) 0 0
\(45\) 6.23610 + 2.58308i 0.0206583 + 0.00855694i
\(46\) 0 0
\(47\) 173.739i 0.539201i 0.962972 + 0.269600i \(0.0868916\pi\)
−0.962972 + 0.269600i \(0.913108\pi\)
\(48\) 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 −0.955319 0.295575i \(-0.904489\pi\)
0.466510 0.884516i \(-0.345511\pi\)
\(54\) 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 0.439671 0.898159i \(-0.355095\pi\)
0.945989 + 0.324199i \(0.105095\pi\)
\(60\) 0 0
\(61\) 66.5782 160.734i 0.139745 0.337375i −0.838476 0.544938i \(-0.816553\pi\)
0.978222 + 0.207563i \(0.0665532\pi\)
\(62\) 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 0.604734 + 0.796428i \(0.293279\pi\)
−0.990771 + 0.135548i \(0.956721\pi\)
\(68\) 0 0
\(69\) 475.115 196.799i 0.828945 0.343360i
\(70\) 0 0
\(71\) 226.201 226.201i 0.378100 0.378100i −0.492316 0.870416i \(-0.663850\pi\)
0.870416 + 0.492316i \(0.163850\pi\)
\(72\) 0 0
\(73\) 802.290 + 802.290i 1.28631 + 1.28631i 0.937009 + 0.349305i \(0.113582\pi\)
0.349305 + 0.937009i \(0.386418\pi\)
\(74\) 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 \(0.128677\pi\)
−0.919397 + 0.393331i \(0.871323\pi\)
\(80\) 0 0
\(81\) 693.272i 0.950991i
\(82\) 0 0
\(83\) 137.983 + 57.1544i 0.182477 + 0.0755845i 0.472051 0.881571i \(-0.343514\pi\)
−0.289574 + 0.957156i \(0.593514\pi\)
\(84\) 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 −0.962353 0.271803i \(-0.912380\pi\)
0.271803 + 0.962353i \(0.412380\pi\)
\(90\) 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 −0.804901 0.593410i \(-0.797781\pi\)
−0.149547 + 0.988755i \(0.547781\pi\)
\(102\) 0 0
\(103\) −351.683 + 351.683i −0.336430 + 0.336430i −0.855022 0.518592i \(-0.826457\pi\)
0.518592 + 0.855022i \(0.326457\pi\)
\(104\) 0 0
\(105\) −381.296 381.296i −0.354388 0.354388i
\(106\) 0 0
\(107\) 95.4774 + 230.503i 0.0862631 + 0.208257i 0.961124 0.276116i \(-0.0890475\pi\)
−0.874861 + 0.484374i \(0.839047\pi\)
\(108\) 0 0
\(109\) 858.330 + 355.532i 0.754249 + 0.312420i 0.726474 0.687194i \(-0.241158\pi\)
0.0277749 + 0.999614i \(0.491158\pi\)
\(110\) 0 0
\(111\) 1129.39i 0.965735i
\(112\) 0 0
\(113\) 1154.63i 0.961222i −0.876934 0.480611i \(-0.840415\pi\)
0.876934 0.480611i \(-0.159585\pi\)
\(114\) 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 −0.932437 0.361333i \(-0.882322\pi\)
0.914833 + 0.403832i \(0.132322\pi\)
\(132\) 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 −0.976677 0.214713i \(-0.931118\pi\)
−0.214713 0.976677i \(-0.568882\pi\)
\(138\) 0 0
\(139\) 525.552 + 1268.79i 0.320696 + 0.774228i 0.999214 + 0.0396445i \(0.0126225\pi\)
−0.678518 + 0.734584i \(0.737377\pi\)
\(140\) 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 0.999093 0.0425902i \(-0.0135610\pi\)
−0.736581 + 0.676349i \(0.763561\pi\)
\(150\) 0 0
\(151\) 1185.23 + 1185.23i 0.638757 + 0.638757i 0.950249 0.311492i \(-0.100829\pi\)
−0.311492 + 0.950249i \(0.600829\pi\)
\(152\) 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 −0.869075 0.494681i \(-0.835285\pi\)
0.964321 + 0.264737i \(0.0852850\pi\)
\(158\) 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 −0.529197 0.848499i \(-0.677507\pi\)
0.974178 0.225781i \(-0.0724933\pi\)
\(164\) 0 0
\(165\) −247.690 + 102.597i −0.116865 + 0.0484069i
\(166\) 0 0
\(167\) −753.289 + 753.289i −0.349049 + 0.349049i −0.859755 0.510706i \(-0.829384\pi\)
0.510706 + 0.859755i \(0.329384\pi\)
\(168\) 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 0.341293 0.939957i \(-0.389135\pi\)
−0.423319 + 0.905981i \(0.639135\pi\)
\(174\) 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 0.674850 0.737955i \(-0.264208\pi\)
−0.0446216 + 0.999004i \(0.514208\pi\)
\(180\) 0 0
\(181\) −772.420 1864.79i −0.317202 0.765793i −0.999400 0.0346258i \(-0.988976\pi\)
0.682199 0.731167i \(-0.261024\pi\)
\(182\) 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 −0.678186 0.734890i \(-0.737234\pi\)
0.0400962 + 0.999196i \(0.487234\pi\)
\(198\) 0 0
\(199\) 2008.70 2008.70i 0.715544 0.715544i −0.252146 0.967689i \(-0.581136\pi\)
0.967689 + 0.252146i \(0.0811362\pi\)
\(200\) 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 0.559790 0.828634i \(-0.310882\pi\)
−0.190101 + 0.981764i \(0.560882\pi\)
\(212\) 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 0.471162 + 0.882047i \(0.343835\pi\)
−0.956863 + 0.290539i \(0.906165\pi\)
\(228\) 0 0
\(229\) −2972.95 + 1231.44i −0.857895 + 0.355352i −0.767884 0.640589i \(-0.778690\pi\)
−0.0900110 + 0.995941i \(0.528690\pi\)
\(230\) 0 0
\(231\) 706.687 706.687i 0.201284 0.201284i
\(232\) 0 0
\(233\) 1590.35 + 1590.35i 0.447155 + 0.447155i 0.894408 0.447253i \(-0.147597\pi\)
−0.447253 + 0.894408i \(0.647597\pi\)
\(234\) 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 \(-0.685249\pi\)
0.549676 0.835378i \(-0.314751\pi\)
\(240\) 0 0
\(241\) 1436.00i 0.383822i −0.981412 0.191911i \(-0.938531\pi\)
0.981412 0.191911i \(-0.0614685\pi\)
\(242\) 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 −0.891756 0.452516i \(-0.850526\pi\)
−0.310589 + 0.950544i \(0.600526\pi\)
\(252\) 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 −0.984628 0.174667i \(-0.944115\pi\)
0.174667 + 0.984628i \(0.444115\pi\)
\(264\) 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 0.658493 0.752587i \(-0.271194\pi\)
−0.0665350 + 0.997784i \(0.521194\pi\)
\(270\) 0 0
\(271\) 3464.52i 0.776585i 0.921536 + 0.388292i \(0.126935\pi\)
−0.921536 + 0.388292i \(0.873065\pi\)
\(272\) 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 0.998760 0.0497833i \(-0.0158531\pi\)
−0.741432 + 0.671028i \(0.765853\pi\)
\(278\) 0 0
\(279\) 239.233 + 239.233i 0.0513352 + 0.0513352i
\(280\) 0 0
\(281\) 3210.39 3210.39i 0.681552 0.681552i −0.278798 0.960350i \(-0.589936\pi\)
0.960350 + 0.278798i \(0.0899360\pi\)
\(282\) 0 0
\(283\) 2512.41 1040.67i 0.527729 0.218593i −0.102879 0.994694i \(-0.532806\pi\)
0.630608 + 0.776101i \(0.282806\pi\)
\(284\) 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 −0.961812 0.273709i \(-0.911749\pi\)
−0.486563 + 0.873646i \(0.661749\pi\)
\(294\) 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 0.282380 0.959303i \(-0.408876\pi\)
−0.478657 + 0.878002i \(0.658876\pi\)
\(308\) 0 0
\(309\) −965.552 2331.05i −0.177762 0.429155i
\(310\) 0 0
\(311\) −2154.35 2154.35i −0.392804 0.392804i 0.482882 0.875686i \(-0.339590\pi\)
−0.875686 + 0.482882i \(0.839590\pi\)
\(312\) 0 0
\(313\) −3659.65 + 3659.65i −0.660881 + 0.660881i −0.955588 0.294706i \(-0.904778\pi\)
0.294706 + 0.955588i \(0.404778\pi\)
\(314\) 0 0
\(315\) −124.134 + 51.4180i −0.0222037 + 0.00919707i
\(316\) 0 0
\(317\) −3106.88 + 7500.68i −0.550473 + 1.32896i 0.366652 + 0.930358i \(0.380504\pi\)
−0.917125 + 0.398601i \(0.869496\pi\)
\(318\) 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 −0.989048 0.147594i \(-0.952847\pi\)
0.594998 0.803727i \(-0.297153\pi\)
\(332\) 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 \(-0.852952\pi\)
0.895178 0.445709i \(-0.147048\pi\)
\(338\) 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 0.481966 0.876190i \(-0.339923\pi\)
0.960361 + 0.278758i \(0.0899227\pi\)
\(348\) 0 0
\(349\) −1844.20 + 4452.29i −0.282859 + 0.682882i −0.999900 0.0141493i \(-0.995496\pi\)
0.717041 + 0.697031i \(0.245496\pi\)
\(350\) 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 −0.944399 0.328802i \(-0.893355\pi\)
0.328802 + 0.944399i \(0.393355\pi\)
\(360\) 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 \(0.227968\pi\)
−0.754317 + 0.656510i \(0.772032\pi\)
\(368\) 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 0.915543 0.402221i \(-0.131762\pi\)
−0.931800 + 0.362973i \(0.881762\pi\)
\(374\) 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 −0.580777 0.814063i \(-0.697251\pi\)
0.164958 + 0.986301i \(0.447251\pi\)
\(380\) 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 −0.297711 0.954656i \(-0.596223\pi\)
0.464531 + 0.885557i \(0.346223\pi\)
\(390\) 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 0.337571 0.941300i \(-0.390395\pi\)
−0.426901 + 0.904298i \(0.640395\pi\)
\(398\) 0 0
\(399\) 10359.3i 1.29978i
\(400\) 0 0
\(401\) 9680.79i 1.20557i −0.797902 0.602787i \(-0.794057\pi\)
0.797902 0.602787i \(-0.205943\pi\)
\(402\) 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 −0.777600 0.628759i \(-0.783563\pi\)
0.628759 + 0.777600i \(0.283563\pi\)
\(410\) 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 0.514997 + 0.857192i \(0.327793\pi\)
−0.970284 + 0.241968i \(0.922207\pi\)
\(420\) 0 0
\(421\) 10566.0 4376.59i 1.22318 0.506656i 0.324758 0.945797i \(-0.394717\pi\)
0.898418 + 0.439141i \(0.144717\pi\)
\(422\) 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 \(-0.603092\pi\)
0.318242 0.948010i \(-0.396908\pi\)
\(432\) 0 0
\(433\) 5628.82i 0.624720i −0.949964 0.312360i \(-0.898880\pi\)
0.949964 0.312360i \(-0.101120\pi\)
\(434\) 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 0.300959 0.953637i \(-0.402693\pi\)
−0.953637 + 0.300959i \(0.902693\pi\)
\(440\) 0 0
\(441\) 47.5859 47.5859i 0.00513831 0.00513831i
\(442\) 0 0
\(443\) −1448.22 + 599.872i −0.155321 + 0.0643359i −0.458989 0.888442i \(-0.651788\pi\)
0.303669 + 0.952778i \(0.401788\pi\)
\(444\) 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 0.976029 + 0.217641i \(0.0698361\pi\)
0.217641 + 0.976029i \(0.430164\pi\)
\(458\) 0 0
\(459\) −4356.35 10517.2i −0.443000 1.06950i
\(460\) 0 0
\(461\) −8424.31 3489.46i −0.851104 0.352539i −0.0858823 0.996305i \(-0.527371\pi\)
−0.765222 + 0.643766i \(0.777371\pi\)
\(462\) 0 0
\(463\) 11549.8i 1.15932i 0.814860 + 0.579658i \(0.196814\pi\)
−0.814860 + 0.579658i \(0.803186\pi\)
\(464\) 0 0
\(465\) 7250.49i 0.723083i
\(466\) 0 0
\(467\) 6314.42 + 2615.52i 0.625689 + 0.259169i 0.672920 0.739715i \(-0.265040\pi\)
−0.0472314 + 0.998884i \(0.515040\pi\)
\(468\) 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 −0.731694 0.681633i \(-0.761270\pi\)
0.681633 + 0.731694i \(0.261270\pi\)
\(488\) 0 0
\(489\) 8680.37 + 8680.37i 0.802741 + 0.802741i
\(490\) 0 0
\(491\) −1701.48 4107.75i −0.156389 0.377556i 0.826193 0.563387i \(-0.190502\pi\)
−0.982582 + 0.185831i \(0.940502\pi\)
\(492\) 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 −0.997123 0.0757967i \(-0.975850\pi\)
−0.758669 0.651476i \(-0.774150\pi\)
\(500\) 0 0
\(501\) −2068.17 4993.00i −0.184429 0.445251i
\(502\) 0 0
\(503\) 373.535 + 373.535i 0.0331115 + 0.0331115i 0.723469 0.690357i \(-0.242547\pi\)
−0.690357 + 0.723469i \(0.742547\pi\)
\(504\) 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 −0.881198 0.472747i \(-0.843262\pi\)
0.957384 + 0.288819i \(0.0932624\pi\)
\(510\) 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 0.934203 + 0.356743i \(0.116113\pi\)
0.356743 + 0.934203i \(0.383887\pi\)
\(522\) 0 0
\(523\) 2376.45 + 5737.26i 0.198690 + 0.479680i 0.991550 0.129723i \(-0.0414089\pi\)
−0.792860 + 0.609404i \(0.791409\pi\)
\(524\) 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 −0.800553 0.599261i \(-0.795461\pi\)
0.989819 + 0.142335i \(0.0454610\pi\)
\(542\) 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 −0.791671 0.610947i \(-0.790789\pi\)
0.991801 + 0.127791i \(0.0407887\pi\)
\(548\) 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 0.738551 0.674198i \(-0.235511\pi\)
0.0455041 + 0.998964i \(0.485511\pi\)
\(558\) 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 0.676743 0.736219i \(-0.263391\pi\)
−0.0420563 + 0.999115i \(0.513391\pi\)
\(564\) 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 −0.695807 0.718229i \(-0.744953\pi\)
0.718229 + 0.695807i \(0.244953\pi\)
\(570\) 0 0
\(571\) −7459.96 + 3090.02i −0.546742 + 0.226468i −0.638918 0.769275i \(-0.720618\pi\)
0.0921763 + 0.995743i \(0.470618\pi\)
\(572\) 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 −0.965062 0.262023i \(-0.915610\pi\)
0.497123 0.867680i \(-0.334390\pi\)
\(588\) 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 \(0.105117\pi\)
−0.945966 + 0.324265i \(0.894883\pi\)
\(594\) 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 0.150902 0.988549i \(-0.451782\pi\)
−0.988549 + 0.150902i \(0.951782\pi\)
\(600\) 0 0
\(601\) 11681.6 11681.6i 0.792852 0.792852i −0.189105 0.981957i \(-0.560559\pi\)
0.981957 + 0.189105i \(0.0605587\pi\)
\(602\) 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 0.589751 0.807585i \(-0.299226\pi\)
0.988066 + 0.154032i \(0.0492260\pi\)
\(614\) 0 0
\(615\) −5701.45 + 5701.45i −0.373829 + 0.373829i
\(616\) 0 0
\(617\) −17139.4 17139.4i −1.11833 1.11833i −0.991987 0.126340i \(-0.959677\pi\)
−0.126340 0.991987i \(-0.540323\pi\)
\(618\) 0 0
\(619\) 9612.31 + 23206.2i 0.624154 + 1.50684i 0.846783 + 0.531938i \(0.178536\pi\)
−0.222629 + 0.974903i \(0.571464\pi\)
\(620\) 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 0.632769 0.774340i \(-0.281918\pi\)
−0.774340 + 0.632769i \(0.781918\pi\)
\(632\) 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 −0.681050 0.732237i \(-0.738476\pi\)
0.999345 0.0361945i \(-0.0115236\pi\)
\(644\) 0 0
\(645\) −3726.13 + 1543.42i −0.227467 + 0.0942200i
\(646\) 0 0
\(647\) −18031.1 + 18031.1i −1.09563 + 1.09563i −0.100717 + 0.994915i \(0.532114\pi\)
−0.994915 + 0.100717i \(0.967886\pi\)
\(648\) 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 0.500194 0.865913i \(-0.333262\pi\)
−0.258602 + 0.965984i \(0.583262\pi\)
\(654\) 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 0.802690 0.596397i \(-0.203401\pi\)
0.145871 + 0.989304i \(0.453401\pi\)
\(660\) 0 0
\(661\) 6313.25 + 15241.5i 0.371493 + 0.896864i 0.993498 + 0.113850i \(0.0363185\pi\)
−0.622005 + 0.783014i \(0.713682\pi\)
\(662\) 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 −0.342645 0.939465i \(-0.611323\pi\)
0.422016 + 0.906589i \(0.361323\pi\)
\(678\) 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 0.809252 + 0.587462i \(0.199873\pi\)
−0.156830 + 0.987626i \(0.550127\pi\)
\(684\) 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 0.499529 0.866297i \(-0.333506\pi\)
−0.259344 + 0.965785i \(0.583506\pi\)
\(692\) 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 −0.651335 0.758790i \(-0.725791\pi\)
0.997109 0.0759825i \(-0.0242093\pi\)
\(702\) 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 −0.794800 0.606871i \(-0.792424\pi\)
−0.132886 + 0.991131i \(0.542424\pi\)
\(710\) 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 \(0.0387545\pi\)
−0.992598 + 0.121450i \(0.961245\pi\)
\(720\) 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 −0.999399 0.0346553i \(-0.988967\pi\)
−0.0346553 0.999399i \(-0.511033\pi\)
\(728\) 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 −0.875073 0.483990i \(-0.839187\pi\)
0.961003 + 0.276538i \(0.0891870\pi\)
\(734\) 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 −0.911829 0.410570i \(-0.865330\pi\)
0.935078 + 0.354443i \(0.115330\pi\)
\(740\) 0 0
\(741\) −33692.1 + 13955.7i −1.67033 + 0.691872i
\(742\) 0 0
\(743\) −27671.7 + 27671.7i −1.36632 + 1.36632i −0.500701 + 0.865620i \(0.666924\pi\)
−0.865620 + 0.500701i \(0.833076\pi\)
\(744\) 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 \(0.182140\pi\)
−0.840707 + 0.541490i \(0.817860\pi\)
\(752\) 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 0.935730 + 0.352718i \(0.114742\pi\)
−0.412252 + 0.911070i \(0.635258\pi\)
\(758\) 0 0
\(759\) 3598.84 + 3598.84i 0.172108 + 0.172108i
\(760\) 0 0
\(761\) −6249.83 + 6249.83i −0.297709 + 0.297709i −0.840116 0.542407i \(-0.817513\pi\)
0.542407 + 0.840116i \(0.317513\pi\)
\(762\) 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 −0.379897 0.925029i \(-0.624041\pi\)
0.385466 + 0.922722i \(0.374041\pi\)
\(774\) 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