Properties

Label 1040.2.dh.a.289.6
Level $1040$
Weight $2$
Character 1040.289
Analytic conductor $8.304$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1040 = 2^{4} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1040.dh (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.30444181021\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - 8 x^{10} + 54 x^{8} - 78 x^{6} + 92 x^{4} - 10 x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 65)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 289.6
Root \(-0.286513 - 0.165418i\) of defining polynomial
Character \(\chi\) \(=\) 1040.289
Dual form 1040.2.dh.a.529.6

$q$-expansion

\(f(q)\) \(=\) \(q+(2.33117 - 1.34590i) q^{3} +(-2.12291 - 0.702335i) q^{5} +(-2.90420 - 1.67674i) q^{7} +(2.12291 - 3.67698i) q^{9} +O(q^{10})\) \(q+(2.33117 - 1.34590i) q^{3} +(-2.12291 - 0.702335i) q^{5} +(-2.90420 - 1.67674i) q^{7} +(2.12291 - 3.67698i) q^{9} +(-1.62291 - 2.81095i) q^{11} +(-1.21648 + 3.39414i) q^{13} +(-5.89413 + 1.21996i) q^{15} +(-1.68772 - 0.974404i) q^{17} +(0.622905 - 1.07890i) q^{19} -9.02690 q^{21} +(-2.33117 + 1.34590i) q^{23} +(4.01345 + 2.98198i) q^{25} -3.35348i q^{27} +(1.50000 + 2.59808i) q^{29} -3.78109 q^{31} +(-7.56654 - 4.36854i) q^{33} +(4.98770 + 5.59927i) q^{35} +(-1.68772 + 0.974404i) q^{37} +(1.73236 + 9.54958i) q^{39} +(-1.39055 - 2.40850i) q^{41} +(-7.56654 - 4.36854i) q^{43} +(-7.08920 + 6.31489i) q^{45} -6.86960i q^{47} +(2.12291 + 3.67698i) q^{49} -5.24581 q^{51} -12.8336i q^{53} +(1.47104 + 7.10721i) q^{55} -3.35348i q^{57} +(1.26764 - 2.19562i) q^{59} +(3.74581 - 6.48793i) q^{61} +(-12.3307 + 7.11911i) q^{63} +(4.96629 - 6.35106i) q^{65} +(-3.47722 + 2.00758i) q^{67} +(-3.62291 + 6.27506i) q^{69} +(2.62291 - 4.54300i) q^{71} -5.46493i q^{73} +(13.3695 + 1.54979i) q^{75} +10.8848i q^{77} +13.7811 q^{79} +(1.85526 + 3.21341i) q^{81} -8.61955i q^{83} +(2.89851 + 3.25391i) q^{85} +(6.99351 + 4.03771i) q^{87} +(5.15819 + 8.93425i) q^{89} +(9.22398 - 7.81753i) q^{91} +(-8.81438 + 5.08898i) q^{93} +(-2.08012 + 1.85292i) q^{95} +(-4.56055 - 2.63304i) q^{97} -13.7811 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 6 q^{5} + 6 q^{9} + O(q^{10}) \) \( 12 q - 6 q^{5} + 6 q^{9} + 4 q^{15} - 12 q^{19} - 8 q^{21} - 2 q^{25} + 18 q^{29} + 16 q^{31} - 10 q^{35} + 32 q^{39} + 14 q^{41} - 29 q^{45} + 6 q^{49} - 24 q^{51} + 26 q^{55} + 4 q^{59} + 6 q^{61} + 23 q^{65} - 24 q^{69} + 12 q^{71} - 2 q^{75} + 104 q^{79} + 14 q^{81} + 21 q^{85} + 20 q^{89} + 44 q^{91} - 20 q^{95} - 104 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1040\mathbb{Z}\right)^\times\).

\(n\) \(261\) \(417\) \(561\) \(911\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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
\(3\) 2.33117 1.34590i 1.34590 0.777057i 0.358236 0.933631i \(-0.383378\pi\)
0.987666 + 0.156574i \(0.0500450\pi\)
\(4\) 0 0
\(5\) −2.12291 0.702335i −0.949392 0.314094i
\(6\) 0 0
\(7\) −2.90420 1.67674i −1.09768 0.633748i −0.162072 0.986779i \(-0.551818\pi\)
−0.935611 + 0.353031i \(0.885151\pi\)
\(8\) 0 0
\(9\) 2.12291 3.67698i 0.707635 1.22566i
\(10\) 0 0
\(11\) −1.62291 2.81095i −0.489324 0.847535i 0.510600 0.859818i \(-0.329423\pi\)
−0.999925 + 0.0122837i \(0.996090\pi\)
\(12\) 0 0
\(13\) −1.21648 + 3.39414i −0.337391 + 0.941365i
\(14\) 0 0
\(15\) −5.89413 + 1.21996i −1.52186 + 0.314992i
\(16\) 0 0
\(17\) −1.68772 0.974404i −0.409332 0.236328i 0.281171 0.959658i \(-0.409277\pi\)
−0.690503 + 0.723330i \(0.742611\pi\)
\(18\) 0 0
\(19\) 0.622905 1.07890i 0.142904 0.247517i −0.785685 0.618627i \(-0.787689\pi\)
0.928589 + 0.371110i \(0.121023\pi\)
\(20\) 0 0
\(21\) −9.02690 −1.96983
\(22\) 0 0
\(23\) −2.33117 + 1.34590i −0.486083 + 0.280640i −0.722948 0.690903i \(-0.757213\pi\)
0.236865 + 0.971543i \(0.423880\pi\)
\(24\) 0 0
\(25\) 4.01345 + 2.98198i 0.802690 + 0.596396i
\(26\) 0 0
\(27\) 3.35348i 0.645377i
\(28\) 0 0
\(29\) 1.50000 + 2.59808i 0.278543 + 0.482451i 0.971023 0.238987i \(-0.0768152\pi\)
−0.692480 + 0.721437i \(0.743482\pi\)
\(30\) 0 0
\(31\) −3.78109 −0.679105 −0.339552 0.940587i \(-0.610276\pi\)
−0.339552 + 0.940587i \(0.610276\pi\)
\(32\) 0 0
\(33\) −7.56654 4.36854i −1.31717 0.760466i
\(34\) 0 0
\(35\) 4.98770 + 5.59927i 0.843076 + 0.946450i
\(36\) 0 0
\(37\) −1.68772 + 0.974404i −0.277459 + 0.160191i −0.632273 0.774746i \(-0.717878\pi\)
0.354813 + 0.934937i \(0.384544\pi\)
\(38\) 0 0
\(39\) 1.73236 + 9.54958i 0.277399 + 1.52916i
\(40\) 0 0
\(41\) −1.39055 2.40850i −0.217167 0.376144i 0.736774 0.676139i \(-0.236348\pi\)
−0.953941 + 0.299995i \(0.903015\pi\)
\(42\) 0 0
\(43\) −7.56654 4.36854i −1.15389 0.666197i −0.204055 0.978959i \(-0.565412\pi\)
−0.949831 + 0.312763i \(0.898745\pi\)
\(44\) 0 0
\(45\) −7.08920 + 6.31489i −1.05679 + 0.941368i
\(46\) 0 0
\(47\) 6.86960i 1.00203i −0.865437 0.501017i \(-0.832959\pi\)
0.865437 0.501017i \(-0.167041\pi\)
\(48\) 0 0
\(49\) 2.12291 + 3.67698i 0.303272 + 0.525283i
\(50\) 0 0
\(51\) −5.24581 −0.734560
\(52\) 0 0
\(53\) 12.8336i 1.76282i −0.472347 0.881412i \(-0.656593\pi\)
0.472347 0.881412i \(-0.343407\pi\)
\(54\) 0 0
\(55\) 1.47104 + 7.10721i 0.198355 + 0.958336i
\(56\) 0 0
\(57\) 3.35348i 0.444179i
\(58\) 0 0
\(59\) 1.26764 2.19562i 0.165033 0.285845i −0.771634 0.636067i \(-0.780560\pi\)
0.936667 + 0.350221i \(0.113894\pi\)
\(60\) 0 0
\(61\) 3.74581 6.48793i 0.479602 0.830695i −0.520124 0.854090i \(-0.674114\pi\)
0.999726 + 0.0233957i \(0.00744777\pi\)
\(62\) 0 0
\(63\) −12.3307 + 7.11911i −1.55352 + 0.896924i
\(64\) 0 0
\(65\) 4.96629 6.35106i 0.615993 0.787752i
\(66\) 0 0
\(67\) −3.47722 + 2.00758i −0.424810 + 0.245264i −0.697133 0.716942i \(-0.745541\pi\)
0.272323 + 0.962206i \(0.412208\pi\)
\(68\) 0 0
\(69\) −3.62291 + 6.27506i −0.436147 + 0.755428i
\(70\) 0 0
\(71\) 2.62291 4.54300i 0.311282 0.539155i −0.667359 0.744737i \(-0.732575\pi\)
0.978640 + 0.205581i \(0.0659084\pi\)
\(72\) 0 0
\(73\) 5.46493i 0.639622i −0.947481 0.319811i \(-0.896381\pi\)
0.947481 0.319811i \(-0.103619\pi\)
\(74\) 0 0
\(75\) 13.3695 + 1.54979i 1.54378 + 0.178954i
\(76\) 0 0
\(77\) 10.8848i 1.24043i
\(78\) 0 0
\(79\) 13.7811 1.55049 0.775247 0.631658i \(-0.217625\pi\)
0.775247 + 0.631658i \(0.217625\pi\)
\(80\) 0 0
\(81\) 1.85526 + 3.21341i 0.206140 + 0.357046i
\(82\) 0 0
\(83\) 8.61955i 0.946119i −0.881031 0.473059i \(-0.843150\pi\)
0.881031 0.473059i \(-0.156850\pi\)
\(84\) 0 0
\(85\) 2.89851 + 3.25391i 0.314387 + 0.352936i
\(86\) 0 0
\(87\) 6.99351 + 4.03771i 0.749783 + 0.432888i
\(88\) 0 0
\(89\) 5.15819 + 8.93425i 0.546767 + 0.947028i 0.998493 + 0.0548717i \(0.0174750\pi\)
−0.451726 + 0.892156i \(0.649192\pi\)
\(90\) 0 0
\(91\) 9.22398 7.81753i 0.966936 0.819500i
\(92\) 0 0
\(93\) −8.81438 + 5.08898i −0.914008 + 0.527703i
\(94\) 0 0
\(95\) −2.08012 + 1.85292i −0.213416 + 0.190106i
\(96\) 0 0
\(97\) −4.56055 2.63304i −0.463054 0.267344i 0.250273 0.968175i \(-0.419479\pi\)
−0.713328 + 0.700831i \(0.752813\pi\)
\(98\) 0 0
\(99\) −13.7811 −1.38505
\(100\) 0 0
\(101\) −2.85526 4.94546i −0.284109 0.492092i 0.688283 0.725442i \(-0.258365\pi\)
−0.972393 + 0.233350i \(0.925031\pi\)
\(102\) 0 0
\(103\) 7.36863i 0.726052i 0.931779 + 0.363026i \(0.118256\pi\)
−0.931779 + 0.363026i \(0.881744\pi\)
\(104\) 0 0
\(105\) 19.1633 + 6.33991i 1.87014 + 0.618712i
\(106\) 0 0
\(107\) 7.42568 4.28722i 0.717868 0.414461i −0.0960996 0.995372i \(-0.530637\pi\)
0.813967 + 0.580911i \(0.197303\pi\)
\(108\) 0 0
\(109\) 8.49162 0.813350 0.406675 0.913573i \(-0.366688\pi\)
0.406675 + 0.913573i \(0.366688\pi\)
\(110\) 0 0
\(111\) −2.62291 + 4.54300i −0.248955 + 0.431203i
\(112\) 0 0
\(113\) 6.35006 + 3.66621i 0.597363 + 0.344888i 0.768004 0.640446i \(-0.221250\pi\)
−0.170640 + 0.985333i \(0.554584\pi\)
\(114\) 0 0
\(115\) 5.89413 1.21996i 0.549630 0.113762i
\(116\) 0 0
\(117\) 9.89771 + 11.6784i 0.915044 + 1.07967i
\(118\) 0 0
\(119\) 3.26764 + 5.65972i 0.299544 + 0.518826i
\(120\) 0 0
\(121\) 0.232358 0.402456i 0.0211234 0.0365869i
\(122\) 0 0
\(123\) −6.48321 3.74308i −0.584571 0.337502i
\(124\) 0 0
\(125\) −6.42583 9.14925i −0.574744 0.818333i
\(126\) 0 0
\(127\) −7.93599 + 4.58185i −0.704205 + 0.406573i −0.808912 0.587930i \(-0.799943\pi\)
0.104707 + 0.994503i \(0.466610\pi\)
\(128\) 0 0
\(129\) −23.5185 −2.07069
\(130\) 0 0
\(131\) −10.0000 −0.873704 −0.436852 0.899533i \(-0.643907\pi\)
−0.436852 + 0.899533i \(0.643907\pi\)
\(132\) 0 0
\(133\) −3.61808 + 2.08890i −0.313727 + 0.181130i
\(134\) 0 0
\(135\) −2.35526 + 7.11911i −0.202709 + 0.612716i
\(136\) 0 0
\(137\) 14.5914 + 8.42435i 1.24663 + 0.719741i 0.970435 0.241361i \(-0.0775938\pi\)
0.276193 + 0.961102i \(0.410927\pi\)
\(138\) 0 0
\(139\) 0.513452 0.889325i 0.0435505 0.0754316i −0.843429 0.537241i \(-0.819466\pi\)
0.886979 + 0.461810i \(0.152800\pi\)
\(140\) 0 0
\(141\) −9.24581 16.0142i −0.778638 1.34864i
\(142\) 0 0
\(143\) 11.5150 2.08890i 0.962933 0.174682i
\(144\) 0 0
\(145\) −1.35964 6.56897i −0.112912 0.545523i
\(146\) 0 0
\(147\) 9.89771 + 5.71445i 0.816349 + 0.471319i
\(148\) 0 0
\(149\) 7.92583 13.7279i 0.649309 1.12464i −0.333979 0.942581i \(-0.608391\pi\)
0.983288 0.182056i \(-0.0582753\pi\)
\(150\) 0 0
\(151\) −14.5454 −1.18369 −0.591845 0.806052i \(-0.701600\pi\)
−0.591845 + 0.806052i \(0.701600\pi\)
\(152\) 0 0
\(153\) −7.16573 + 4.13713i −0.579315 + 0.334468i
\(154\) 0 0
\(155\) 8.02690 + 2.65559i 0.644736 + 0.213302i
\(156\) 0 0
\(157\) 10.9210i 0.871588i −0.900047 0.435794i \(-0.856468\pi\)
0.900047 0.435794i \(-0.143532\pi\)
\(158\) 0 0
\(159\) −17.2727 29.9172i −1.36982 2.37259i
\(160\) 0 0
\(161\) 9.02690 0.711420
\(162\) 0 0
\(163\) −3.61808 2.08890i −0.283390 0.163615i 0.351567 0.936163i \(-0.385649\pi\)
−0.634957 + 0.772547i \(0.718982\pi\)
\(164\) 0 0
\(165\) 12.9949 + 14.5882i 1.01165 + 1.13569i
\(166\) 0 0
\(167\) −2.90420 + 1.67674i −0.224733 + 0.129750i −0.608140 0.793830i \(-0.708084\pi\)
0.383407 + 0.923580i \(0.374751\pi\)
\(168\) 0 0
\(169\) −10.0404 8.25780i −0.772335 0.635215i
\(170\) 0 0
\(171\) −2.64474 4.58082i −0.202248 0.350304i
\(172\) 0 0
\(173\) −7.56654 4.36854i −0.575273 0.332134i 0.183979 0.982930i \(-0.441102\pi\)
−0.759253 + 0.650796i \(0.774435\pi\)
\(174\) 0 0
\(175\) −6.65585 15.3898i −0.503135 1.16336i
\(176\) 0 0
\(177\) 6.82449i 0.512960i
\(178\) 0 0
\(179\) 9.00507 + 15.5972i 0.673071 + 1.16579i 0.977029 + 0.213107i \(0.0683584\pi\)
−0.303958 + 0.952685i \(0.598308\pi\)
\(180\) 0 0
\(181\) 1.04366 0.0775749 0.0387875 0.999247i \(-0.487650\pi\)
0.0387875 + 0.999247i \(0.487650\pi\)
\(182\) 0 0
\(183\) 20.1660i 1.49071i
\(184\) 0 0
\(185\) 4.26722 0.883225i 0.313732 0.0649360i
\(186\) 0 0
\(187\) 6.32546i 0.462564i
\(188\) 0 0
\(189\) −5.62291 + 9.73916i −0.409006 + 0.708419i
\(190\) 0 0
\(191\) 12.7593 22.0997i 0.923228 1.59908i 0.128841 0.991665i \(-0.458874\pi\)
0.794387 0.607412i \(-0.207792\pi\)
\(192\) 0 0
\(193\) −17.1652 + 9.91035i −1.23558 + 0.713362i −0.968188 0.250225i \(-0.919495\pi\)
−0.267392 + 0.963588i \(0.586162\pi\)
\(194\) 0 0
\(195\) 3.02937 21.4895i 0.216938 1.53890i
\(196\) 0 0
\(197\) −18.7512 + 10.8260i −1.33596 + 0.771319i −0.986206 0.165521i \(-0.947070\pi\)
−0.349758 + 0.936840i \(0.613736\pi\)
\(198\) 0 0
\(199\) −9.11453 + 15.7868i −0.646112 + 1.11910i 0.337932 + 0.941171i \(0.390273\pi\)
−0.984044 + 0.177928i \(0.943061\pi\)
\(200\) 0 0
\(201\) −5.40400 + 9.36000i −0.381169 + 0.660204i
\(202\) 0 0
\(203\) 10.0604i 0.706104i
\(204\) 0 0
\(205\) 1.26043 + 6.08964i 0.0880321 + 0.425319i
\(206\) 0 0
\(207\) 11.4289i 0.794363i
\(208\) 0 0
\(209\) −4.04366 −0.279706
\(210\) 0 0
\(211\) 9.64981 + 16.7140i 0.664320 + 1.15064i 0.979469 + 0.201594i \(0.0646122\pi\)
−0.315149 + 0.949042i \(0.602054\pi\)
\(212\) 0 0
\(213\) 14.1207i 0.967534i
\(214\) 0 0
\(215\) 12.9949 + 14.5882i 0.886242 + 0.994910i
\(216\) 0 0
\(217\) 10.9810 + 6.33991i 0.745442 + 0.430381i
\(218\) 0 0
\(219\) −7.35526 12.7397i −0.497023 0.860868i
\(220\) 0 0
\(221\) 5.36034 4.54300i 0.360575 0.305596i
\(222\) 0 0
\(223\) −10.7134 + 6.18537i −0.717421 + 0.414203i −0.813803 0.581141i \(-0.802606\pi\)
0.0963818 + 0.995344i \(0.469273\pi\)
\(224\) 0 0
\(225\) 19.4849 8.42692i 1.29899 0.561795i
\(226\) 0 0
\(227\) 5.33715 + 3.08141i 0.354239 + 0.204520i 0.666551 0.745460i \(-0.267770\pi\)
−0.312311 + 0.949980i \(0.601103\pi\)
\(228\) 0 0
\(229\) 26.9832 1.78310 0.891551 0.452920i \(-0.149618\pi\)
0.891551 + 0.452920i \(0.149618\pi\)
\(230\) 0 0
\(231\) 14.6498 + 25.3742i 0.963887 + 1.66950i
\(232\) 0 0
\(233\) 0.824319i 0.0540029i 0.999635 + 0.0270015i \(0.00859588\pi\)
−0.999635 + 0.0270015i \(0.991404\pi\)
\(234\) 0 0
\(235\) −4.82476 + 14.5835i −0.314733 + 0.951323i
\(236\) 0 0
\(237\) 32.1261 18.5480i 2.08681 1.20482i
\(238\) 0 0
\(239\) 4.00000 0.258738 0.129369 0.991596i \(-0.458705\pi\)
0.129369 + 0.991596i \(0.458705\pi\)
\(240\) 0 0
\(241\) −11.3469 + 19.6534i −0.730917 + 1.26599i 0.225575 + 0.974226i \(0.427574\pi\)
−0.956492 + 0.291760i \(0.905759\pi\)
\(242\) 0 0
\(243\) 17.3625 + 10.0242i 1.11380 + 0.643054i
\(244\) 0 0
\(245\) −1.92426 9.29687i −0.122936 0.593955i
\(246\) 0 0
\(247\) 2.90420 + 3.42669i 0.184790 + 0.218035i
\(248\) 0 0
\(249\) −11.6011 20.0936i −0.735188 1.27338i
\(250\) 0 0
\(251\) 9.51345 16.4778i 0.600484 1.04007i −0.392264 0.919853i \(-0.628308\pi\)
0.992748 0.120216i \(-0.0383586\pi\)
\(252\) 0 0
\(253\) 7.56654 + 4.36854i 0.475704 + 0.274648i
\(254\) 0 0
\(255\) 11.1364 + 3.68431i 0.697386 + 0.230721i
\(256\) 0 0
\(257\) 1.82857 1.05573i 0.114063 0.0658544i −0.441883 0.897073i \(-0.645689\pi\)
0.555946 + 0.831218i \(0.312356\pi\)
\(258\) 0 0
\(259\) 6.53528 0.406083
\(260\) 0 0
\(261\) 12.7374 0.788427
\(262\) 0 0
\(263\) −25.9092 + 14.9587i −1.59763 + 0.922391i −0.605685 + 0.795704i \(0.707101\pi\)
−0.991943 + 0.126687i \(0.959566\pi\)
\(264\) 0 0
\(265\) −9.01345 + 27.2444i −0.553692 + 1.67361i
\(266\) 0 0
\(267\) 24.0492 + 13.8848i 1.47179 + 0.849738i
\(268\) 0 0
\(269\) 9.29455 16.0986i 0.566699 0.981551i −0.430191 0.902738i \(-0.641554\pi\)
0.996889 0.0788127i \(-0.0251129\pi\)
\(270\) 0 0
\(271\) 2.91238 + 5.04439i 0.176914 + 0.306425i 0.940822 0.338901i \(-0.110055\pi\)
−0.763908 + 0.645326i \(0.776722\pi\)
\(272\) 0 0
\(273\) 10.9810 30.6386i 0.664603 1.85433i
\(274\) 0 0
\(275\) 1.86875 16.1211i 0.112690 0.972139i
\(276\) 0 0
\(277\) −11.7263 6.77017i −0.704564 0.406780i 0.104481 0.994527i \(-0.466682\pi\)
−0.809045 + 0.587747i \(0.800015\pi\)
\(278\) 0 0
\(279\) −8.02690 + 13.9030i −0.480558 + 0.832351i
\(280\) 0 0
\(281\) −0.464716 −0.0277226 −0.0138613 0.999904i \(-0.504412\pi\)
−0.0138613 + 0.999904i \(0.504412\pi\)
\(282\) 0 0
\(283\) 8.71259 5.03022i 0.517910 0.299015i −0.218169 0.975911i \(-0.570009\pi\)
0.736079 + 0.676896i \(0.236675\pi\)
\(284\) 0 0
\(285\) −2.35526 + 7.11911i −0.139514 + 0.421700i
\(286\) 0 0
\(287\) 9.32634i 0.550516i
\(288\) 0 0
\(289\) −6.60107 11.4334i −0.388298 0.672553i
\(290\) 0 0
\(291\) −14.1752 −0.830967
\(292\) 0 0
\(293\) 11.6481 + 6.72506i 0.680492 + 0.392882i 0.800040 0.599946i \(-0.204811\pi\)
−0.119548 + 0.992828i \(0.538145\pi\)
\(294\) 0 0
\(295\) −4.23314 + 3.77079i −0.246463 + 0.219544i
\(296\) 0 0
\(297\) −9.42647 + 5.44238i −0.546979 + 0.315799i
\(298\) 0 0
\(299\) −1.73236 9.54958i −0.100185 0.552266i
\(300\) 0 0
\(301\) 14.6498 + 25.3742i 0.844401 + 1.46255i
\(302\) 0 0
\(303\) −13.3122 7.68581i −0.764767 0.441538i
\(304\) 0 0
\(305\) −12.5087 + 11.1425i −0.716246 + 0.638015i
\(306\) 0 0
\(307\) 24.6077i 1.40444i −0.711961 0.702219i \(-0.752193\pi\)
0.711961 0.702219i \(-0.247807\pi\)
\(308\) 0 0
\(309\) 9.91745 + 17.1775i 0.564184 + 0.977196i
\(310\) 0 0
\(311\) −2.43781 −0.138236 −0.0691178 0.997609i \(-0.522018\pi\)
−0.0691178 + 0.997609i \(0.522018\pi\)
\(312\) 0 0
\(313\) 19.2965i 1.09071i 0.838207 + 0.545353i \(0.183604\pi\)
−0.838207 + 0.545353i \(0.816396\pi\)
\(314\) 0 0
\(315\) 31.1768 6.45295i 1.75662 0.363583i
\(316\) 0 0
\(317\) 28.8217i 1.61879i −0.587265 0.809395i \(-0.699795\pi\)
0.587265 0.809395i \(-0.300205\pi\)
\(318\) 0 0
\(319\) 4.86872 8.43286i 0.272596 0.472150i
\(320\) 0 0
\(321\) 11.5404 19.9885i 0.644120 1.11565i
\(322\) 0 0
\(323\) −2.10258 + 1.21392i −0.116990 + 0.0675445i
\(324\) 0 0
\(325\) −15.0035 + 9.99470i −0.832246 + 0.554406i
\(326\) 0 0
\(327\) 19.7954 11.4289i 1.09469 0.632019i
\(328\) 0 0
\(329\) −11.5185 + 19.9507i −0.635037 + 1.09992i
\(330\) 0 0
\(331\) −1.48655 + 2.57478i −0.0817081 + 0.141522i −0.903984 0.427567i \(-0.859371\pi\)
0.822276 + 0.569089i \(0.192704\pi\)
\(332\) 0 0
\(333\) 8.27427i 0.453427i
\(334\) 0 0
\(335\) 8.79180 1.81972i 0.480347 0.0994218i
\(336\) 0 0
\(337\) 1.90370i 0.103701i 0.998655 + 0.0518505i \(0.0165119\pi\)
−0.998655 + 0.0518505i \(0.983488\pi\)
\(338\) 0 0
\(339\) 19.7374 1.07199
\(340\) 0 0
\(341\) 6.13636 + 10.6285i 0.332302 + 0.575565i
\(342\) 0 0
\(343\) 9.23611i 0.498703i
\(344\) 0 0
\(345\) 12.0983 10.7769i 0.651349 0.580206i
\(346\) 0 0
\(347\) −10.9420 6.31735i −0.587396 0.339133i 0.176671 0.984270i \(-0.443467\pi\)
−0.764067 + 0.645137i \(0.776800\pi\)
\(348\) 0 0
\(349\) 4.48655 + 7.77093i 0.240159 + 0.415968i 0.960760 0.277383i \(-0.0894670\pi\)
−0.720600 + 0.693351i \(0.756134\pi\)
\(350\) 0 0
\(351\) 11.3822 + 4.07944i 0.607535 + 0.217744i
\(352\) 0 0
\(353\) 29.6618 17.1252i 1.57874 0.911484i 0.583701 0.811969i \(-0.301604\pi\)
0.995036 0.0995150i \(-0.0317291\pi\)
\(354\) 0 0
\(355\) −8.75889 + 7.80221i −0.464874 + 0.414098i
\(356\) 0 0
\(357\) 15.2349 + 8.79585i 0.806315 + 0.465526i
\(358\) 0 0
\(359\) 22.4043 1.18245 0.591227 0.806505i \(-0.298644\pi\)
0.591227 + 0.806505i \(0.298644\pi\)
\(360\) 0 0
\(361\) 8.72398 + 15.1104i 0.459157 + 0.795283i
\(362\) 0 0
\(363\) 1.25092i 0.0656565i
\(364\) 0 0
\(365\) −3.83821 + 11.6015i −0.200901 + 0.607252i
\(366\) 0 0
\(367\) 11.4273 6.59753i 0.596498 0.344388i −0.171165 0.985242i \(-0.554753\pi\)
0.767663 + 0.640854i \(0.221420\pi\)
\(368\) 0 0
\(369\) −11.8080 −0.614700
\(370\) 0 0
\(371\) −21.5185 + 37.2712i −1.11719 + 1.93502i
\(372\) 0 0
\(373\) −13.2168 7.63070i −0.684338 0.395103i 0.117149 0.993114i \(-0.462624\pi\)
−0.801488 + 0.598012i \(0.795958\pi\)
\(374\) 0 0
\(375\) −27.2937 12.6799i −1.40944 0.654788i
\(376\) 0 0
\(377\) −10.6430 + 1.93070i −0.548140 + 0.0994362i
\(378\) 0 0
\(379\) −9.11453 15.7868i −0.468182 0.810915i 0.531157 0.847273i \(-0.321757\pi\)
−0.999339 + 0.0363588i \(0.988424\pi\)
\(380\) 0 0
\(381\) −12.3334 + 21.3621i −0.631861 + 1.09442i
\(382\) 0 0
\(383\) −1.24784 0.720440i −0.0637616 0.0368128i 0.467780 0.883845i \(-0.345054\pi\)
−0.531542 + 0.847032i \(0.678387\pi\)
\(384\) 0 0
\(385\) 7.64474 23.1073i 0.389612 1.17766i
\(386\) 0 0
\(387\) −32.1261 + 18.5480i −1.63306 + 0.942848i
\(388\) 0 0
\(389\) 18.7912 0.952754 0.476377 0.879241i \(-0.341950\pi\)
0.476377 + 0.879241i \(0.341950\pi\)
\(390\) 0 0
\(391\) 5.24581 0.265292
\(392\) 0 0
\(393\) −23.3117 + 13.4590i −1.17592 + 0.678918i
\(394\) 0 0
\(395\) −29.2560 9.67894i −1.47203 0.487000i
\(396\) 0 0
\(397\) 14.8027 + 8.54634i 0.742926 + 0.428928i 0.823132 0.567850i \(-0.192225\pi\)
−0.0802063 + 0.996778i \(0.525558\pi\)
\(398\) 0 0
\(399\) −5.62291 + 9.73916i −0.281497 + 0.487568i
\(400\) 0 0
\(401\) −11.1011 19.2276i −0.554361 0.960182i −0.997953 0.0639527i \(-0.979629\pi\)
0.443592 0.896229i \(-0.353704\pi\)
\(402\) 0 0
\(403\) 4.59962 12.8336i 0.229124 0.639285i
\(404\) 0 0
\(405\) −1.68166 8.12478i −0.0835623 0.403724i
\(406\) 0 0
\(407\) 5.47801 + 3.16273i 0.271535 + 0.156771i
\(408\) 0 0
\(409\) −4.81638 + 8.34221i −0.238155 + 0.412496i −0.960185 0.279366i \(-0.909876\pi\)
0.722030 + 0.691862i \(0.243209\pi\)
\(410\) 0 0
\(411\) 45.3534 2.23712
\(412\) 0 0
\(413\) −7.36296 + 4.25101i −0.362308 + 0.209178i
\(414\) 0 0
\(415\) −6.05381 + 18.2985i −0.297170 + 0.898238i
\(416\) 0 0
\(417\) 2.76423i 0.135365i
\(418\) 0 0
\(419\) 0.978168 + 1.69424i 0.0477866 + 0.0827689i 0.888929 0.458044i \(-0.151450\pi\)
−0.841143 + 0.540813i \(0.818117\pi\)
\(420\) 0 0
\(421\) −12.0807 −0.588778 −0.294389 0.955686i \(-0.595116\pi\)
−0.294389 + 0.955686i \(0.595116\pi\)
\(422\) 0 0
\(423\) −25.2594 14.5835i −1.22815 0.709075i
\(424\) 0 0
\(425\) −3.86792 8.94346i −0.187622 0.433822i
\(426\) 0 0
\(427\) −21.7571 + 12.5615i −1.05290 + 0.607893i
\(428\) 0 0
\(429\) 24.0320 20.3676i 1.16027 0.983359i
\(430\) 0 0
\(431\) 12.2945 + 21.2948i 0.592207 + 1.02573i 0.993934 + 0.109974i \(0.0350767\pi\)
−0.401727 + 0.915759i \(0.631590\pi\)
\(432\) 0 0
\(433\) −31.2400 18.0364i −1.50130 0.866775i −0.999999 0.00150085i \(-0.999522\pi\)
−0.501299 0.865274i \(-0.667144\pi\)
\(434\) 0 0
\(435\) −12.0107 13.4835i −0.575871 0.646482i
\(436\) 0 0
\(437\) 3.35348i 0.160419i
\(438\) 0 0
\(439\) −1.26764 2.19562i −0.0605013 0.104791i 0.834188 0.551480i \(-0.185937\pi\)
−0.894690 + 0.446688i \(0.852603\pi\)
\(440\) 0 0
\(441\) 18.0269 0.858424
\(442\) 0 0
\(443\) 19.3579i 0.919721i −0.887991 0.459860i \(-0.847899\pi\)
0.887991 0.459860i \(-0.152101\pi\)
\(444\) 0 0
\(445\) −4.67552 22.5893i −0.221641 1.07084i
\(446\) 0 0
\(447\) 42.6696i 2.01820i
\(448\) 0 0
\(449\) −12.4040 + 21.4844i −0.585381 + 1.01391i 0.409447 + 0.912334i \(0.365722\pi\)
−0.994828 + 0.101576i \(0.967612\pi\)
\(450\) 0 0
\(451\) −4.51345 + 7.81753i −0.212530 + 0.368113i
\(452\) 0 0
\(453\) −33.9079 + 19.5767i −1.59313 + 0.919795i
\(454\) 0 0
\(455\) −25.0722 + 10.1176i −1.17540 + 0.474318i
\(456\) 0 0
\(457\) 6.55363 3.78374i 0.306566 0.176996i −0.338823 0.940850i \(-0.610029\pi\)
0.645389 + 0.763854i \(0.276695\pi\)
\(458\) 0 0
\(459\) −3.26764 + 5.65972i −0.152520 + 0.264173i
\(460\) 0 0
\(461\) 6.17164 10.6896i 0.287442 0.497864i −0.685756 0.727831i \(-0.740528\pi\)
0.973198 + 0.229967i \(0.0738618\pi\)
\(462\) 0 0
\(463\) 22.8578i 1.06229i 0.847281 + 0.531146i \(0.178238\pi\)
−0.847281 + 0.531146i \(0.821762\pi\)
\(464\) 0 0
\(465\) 22.2863 4.61279i 1.03350 0.213913i
\(466\) 0 0
\(467\) 15.2976i 0.707889i 0.935266 + 0.353945i \(0.115160\pi\)
−0.935266 + 0.353945i \(0.884840\pi\)
\(468\) 0 0
\(469\) 13.4647 0.621743
\(470\) 0 0
\(471\) −14.6985 25.4586i −0.677273 1.17307i
\(472\) 0 0
\(473\) 28.3589i 1.30394i
\(474\) 0 0
\(475\) 5.71727 2.47264i 0.262326 0.113452i
\(476\) 0 0
\(477\) −47.1887 27.2444i −2.16062 1.24744i
\(478\) 0 0
\(479\) −12.1414 21.0296i −0.554756 0.960866i −0.997922 0.0644264i \(-0.979478\pi\)
0.443166 0.896439i \(-0.353855\pi\)
\(480\) 0 0
\(481\) −1.25419 6.91369i −0.0571861 0.315237i
\(482\) 0 0
\(483\) 21.0433 12.1493i 0.957501 0.552814i
\(484\) 0 0
\(485\) 7.83235 + 8.79272i 0.355649 + 0.399257i
\(486\) 0 0
\(487\) 31.9462 + 18.4441i 1.44762 + 0.835783i 0.998339 0.0576081i \(-0.0183474\pi\)
0.449280 + 0.893391i \(0.351681\pi\)
\(488\) 0 0
\(489\) −11.2458 −0.508553
\(490\) 0 0
\(491\) −17.6767 30.6170i −0.797739 1.38172i −0.921085 0.389361i \(-0.872696\pi\)
0.123346 0.992364i \(-0.460637\pi\)
\(492\) 0 0
\(493\) 5.84642i 0.263310i
\(494\) 0 0
\(495\) 29.2560 + 9.67894i 1.31496 + 0.435036i
\(496\) 0 0
\(497\) −15.2349 + 8.79585i −0.683377 + 0.394548i
\(498\) 0 0
\(499\) 16.2189 0.726058 0.363029 0.931778i \(-0.381743\pi\)
0.363029 + 0.931778i \(0.381743\pi\)
\(500\) 0 0
\(501\) −4.51345 + 7.81753i −0.201646 + 0.349261i
\(502\) 0 0
\(503\) −17.5270 10.1192i −0.781489 0.451193i 0.0554688 0.998460i \(-0.482335\pi\)
−0.836958 + 0.547268i \(0.815668\pi\)
\(504\) 0 0
\(505\) 2.58808 + 12.5041i 0.115168 + 0.556425i
\(506\) 0 0
\(507\) −34.5200 5.73700i −1.53309 0.254789i
\(508\) 0 0
\(509\) −10.0185 17.3526i −0.444063 0.769140i 0.553923 0.832568i \(-0.313130\pi\)
−0.997986 + 0.0634276i \(0.979797\pi\)
\(510\) 0 0
\(511\) −9.16326 + 15.8712i −0.405359 + 0.702102i
\(512\) 0 0
\(513\) −3.61808 2.08890i −0.159742 0.0922271i
\(514\) 0 0
\(515\) 5.17524 15.6429i 0.228048 0.689308i
\(516\) 0 0
\(517\) −19.3101 + 11.1487i −0.849259 + 0.490320i
\(518\) 0 0
\(519\) −23.5185 −1.03235
\(520\) 0 0
\(521\) 16.0269 0.702151 0.351076 0.936347i \(-0.385816\pi\)
0.351076 + 0.936347i \(0.385816\pi\)
\(522\) 0 0
\(523\) −10.1654 + 5.86898i −0.444501 + 0.256633i −0.705505 0.708705i \(-0.749280\pi\)
0.261004 + 0.965338i \(0.415946\pi\)
\(524\) 0 0
\(525\) −36.2291 26.9180i −1.58117 1.17480i
\(526\) 0 0
\(527\) 6.38142 + 3.68431i 0.277979 + 0.160491i
\(528\) 0 0
\(529\) −7.87709 + 13.6435i −0.342482 + 0.593197i
\(530\) 0 0
\(531\) −5.38217 9.32219i −0.233566 0.404548i
\(532\) 0 0
\(533\) 9.86635 1.78982i 0.427359 0.0775258i
\(534\) 0 0
\(535\) −18.7751 + 3.88605i −0.811718 + 0.168008i
\(536\) 0 0
\(537\) 41.9847 + 24.2399i 1.81177 + 1.04603i
\(538\) 0 0
\(539\) 6.89055 11.9348i 0.296797 0.514067i
\(540\) 0 0
\(541\) −21.8080 −0.937599 −0.468800 0.883305i \(-0.655313\pi\)
−0.468800 + 0.883305i \(0.655313\pi\)
\(542\) 0 0
\(543\) 2.43296 1.40467i 0.104408 0.0602801i
\(544\) 0 0
\(545\) −18.0269 5.96396i −0.772188 0.255468i
\(546\) 0 0
\(547\) 6.30924i 0.269764i 0.990862 + 0.134882i \(0.0430655\pi\)
−0.990862 + 0.134882i \(0.956935\pi\)
\(548\) 0 0
\(549\) −15.9040 27.5465i −0.678766 1.17566i
\(550\) 0 0
\(551\) 3.73743 0.159220
\(552\) 0 0
\(553\) −40.0230 23.1073i −1.70195 0.982622i
\(554\) 0 0
\(555\) 8.75889 7.80221i 0.371794 0.331185i
\(556\) 0 0
\(557\) 31.0364 17.9189i 1.31506 0.759247i 0.332126 0.943235i \(-0.392234\pi\)
0.982929 + 0.183987i \(0.0589006\pi\)
\(558\) 0 0
\(559\) 24.0320 20.3676i 1.01644 0.861459i
\(560\) 0 0
\(561\) 8.51345 + 14.7457i 0.359438 + 0.622565i
\(562\) 0 0
\(563\) −4.33196 2.50106i −0.182570 0.105407i 0.405929 0.913904i \(-0.366948\pi\)
−0.588500 + 0.808497i \(0.700281\pi\)
\(564\) 0 0
\(565\) −10.9057 12.2429i −0.458805 0.515062i
\(566\) 0 0
\(567\) 12.4432i 0.522564i
\(568\) 0 0
\(569\) −6.58402 11.4039i −0.276017 0.478075i 0.694375 0.719614i \(-0.255681\pi\)
−0.970391 + 0.241539i \(0.922348\pi\)
\(570\) 0 0
\(571\) −19.8349 −0.830065 −0.415032 0.909807i \(-0.636230\pi\)
−0.415032 + 0.909807i \(0.636230\pi\)
\(572\) 0 0
\(573\) 68.6909i 2.86960i
\(574\) 0 0
\(575\) −13.3695 1.54979i −0.557547 0.0646307i
\(576\) 0 0
\(577\) 10.9210i 0.454646i 0.973819 + 0.227323i \(0.0729972\pi\)
−0.973819 + 0.227323i \(0.927003\pi\)
\(578\) 0 0
\(579\) −26.6767 + 46.2054i −1.10865 + 1.92023i
\(580\) 0 0
\(581\) −14.4527 + 25.0329i −0.599601 + 1.03854i
\(582\) 0 0
\(583\) −36.0745 + 20.8276i −1.49406 + 0.862593i
\(584\) 0 0
\(585\) −12.8098 31.7436i −0.529618 1.31244i
\(586\) 0 0
\(587\) −35.0303 + 20.2247i −1.44585 + 0.834764i −0.998231 0.0594576i \(-0.981063\pi\)
−0.447624 + 0.894222i \(0.647730\pi\)
\(588\) 0 0
\(589\) −2.35526 + 4.07944i −0.0970469 + 0.168090i
\(590\) 0 0
\(591\) −29.1414 + 50.4744i −1.19872 + 2.07624i
\(592\) 0 0
\(593\) 1.47709i 0.0606569i −0.999540 0.0303284i \(-0.990345\pi\)
0.999540 0.0303284i \(-0.00965532\pi\)
\(594\) 0 0
\(595\) −2.96188 14.3100i −0.121425 0.586654i
\(596\) 0 0
\(597\) 49.0690i 2.00826i
\(598\) 0 0
\(599\) 2.27271 0.0928606 0.0464303 0.998922i \(-0.485215\pi\)
0.0464303 + 0.998922i \(0.485215\pi\)
\(600\) 0 0
\(601\) −3.70215 6.41231i −0.151014 0.261563i 0.780587 0.625048i \(-0.214920\pi\)
−0.931600 + 0.363484i \(0.881587\pi\)
\(602\) 0 0
\(603\) 17.0476i 0.694231i
\(604\) 0 0
\(605\) −0.775932 + 0.691182i −0.0315461 + 0.0281006i
\(606\) 0 0
\(607\) −9.26059 5.34661i −0.375876 0.217012i 0.300146 0.953893i \(-0.402964\pi\)
−0.676022 + 0.736881i \(0.736298\pi\)
\(608\) 0 0
\(609\) −13.5404 23.4526i −0.548683 0.950347i
\(610\) 0 0
\(611\) 23.3164 + 8.35673i 0.943280 + 0.338077i
\(612\) 0 0
\(613\) −5.26673 + 3.04075i −0.212721 + 0.122815i −0.602575 0.798062i \(-0.705859\pi\)
0.389854 + 0.920877i \(0.372525\pi\)
\(614\) 0 0
\(615\) 11.1343 + 12.4996i 0.448980 + 0.504032i
\(616\) 0 0
\(617\) −27.5732 15.9194i −1.11006 0.640892i −0.171213 0.985234i \(-0.554769\pi\)
−0.938844 + 0.344342i \(0.888102\pi\)
\(618\) 0 0
\(619\) −26.4043 −1.06128 −0.530639 0.847598i \(-0.678048\pi\)
−0.530639 + 0.847598i \(0.678048\pi\)
\(620\) 0 0
\(621\) 4.51345 + 7.81753i 0.181119 + 0.313707i
\(622\) 0 0
\(623\) 34.5957i 1.38605i
\(624\) 0 0
\(625\) 7.21560 + 23.9361i 0.288624 + 0.957443i
\(626\) 0 0
\(627\) −9.42647 + 5.44238i −0.376457 + 0.217348i
\(628\) 0 0
\(629\) 3.79785 0.151430
\(630\) 0 0
\(631\) 17.5840 30.4564i 0.700009 1.21245i −0.268454 0.963293i \(-0.586513\pi\)
0.968463 0.249158i \(-0.0801539\pi\)
\(632\) 0 0
\(633\) 44.9907 + 25.9754i 1.78822 + 1.03243i
\(634\) 0 0
\(635\) 20.0653 4.15310i 0.796269 0.164811i
\(636\) 0 0
\(637\) −15.0626 + 2.73247i −0.596804 + 0.108264i
\(638\) 0 0
\(639\) −11.1364 19.2887i −0.440547 0.763051i
\(640\) 0 0
\(641\) −2.76257 + 4.78491i −0.109115 + 0.188993i −0.915412 0.402518i \(-0.868135\pi\)
0.806297 + 0.591511i \(0.201468\pi\)
\(642\) 0 0
\(643\) 27.8472 + 16.0776i 1.09819 + 0.634039i 0.935744 0.352679i \(-0.114729\pi\)
0.162444 + 0.986718i \(0.448062\pi\)
\(644\) 0 0
\(645\) 49.9276 + 16.5179i 1.96590 + 0.650391i
\(646\) 0 0
\(647\) 11.9376 6.89216i 0.469314 0.270959i −0.246638 0.969108i \(-0.579326\pi\)
0.715953 + 0.698149i \(0.245993\pi\)
\(648\) 0 0
\(649\) −8.22905 −0.323019
\(650\) 0 0
\(651\) 34.1316 1.33772
\(652\) 0 0
\(653\) −7.36296 + 4.25101i −0.288135 + 0.166355i −0.637100 0.770781i \(-0.719866\pi\)
0.348965 + 0.937136i \(0.386533\pi\)
\(654\) 0 0
\(655\) 21.2291 + 7.02335i 0.829488 + 0.274425i
\(656\) 0 0
\(657\) −20.0944 11.6015i −0.783959 0.452619i
\(658\) 0 0
\(659\) −2.02183 + 3.50192i −0.0787594 + 0.136415i −0.902715 0.430239i \(-0.858429\pi\)
0.823956 + 0.566654i \(0.191763\pi\)
\(660\) 0 0
\(661\) −15.6364 27.0830i −0.608184 1.05341i −0.991540 0.129805i \(-0.958565\pi\)
0.383356 0.923601i \(-0.374768\pi\)
\(662\) 0 0
\(663\) 6.38142 17.8050i 0.247834 0.691489i
\(664\) 0 0
\(665\) 9.14794 1.89343i 0.354742 0.0734241i
\(666\) 0 0
\(667\) −6.99351 4.03771i −0.270790 0.156341i
\(668\) 0 0
\(669\) −16.6498 + 28.8383i −0.643719 + 1.11495i
\(670\) 0 0
\(671\) −24.3164 −0.938723
\(672\) 0 0
\(673\) 27.7768 16.0370i 1.07072 0.618179i 0.142340 0.989818i \(-0.454537\pi\)
0.928377 + 0.371639i \(0.121204\pi\)
\(674\) 0 0
\(675\) 10.0000 13.4590i 0.384900 0.518038i
\(676\) 0 0
\(677\) 14.2382i 0.547220i 0.961841 + 0.273610i \(0.0882177\pi\)
−0.961841 + 0.273610i \(0.911782\pi\)
\(678\) 0 0
\(679\) 8.82983 + 15.2937i 0.338858 + 0.586919i
\(680\) 0 0
\(681\) 16.5891 0.635695
\(682\) 0 0
\(683\) 22.3302 + 12.8923i 0.854440 + 0.493311i 0.862146 0.506659i \(-0.169120\pi\)
−0.00770647 + 0.999970i \(0.502453\pi\)
\(684\) 0 0
\(685\) −25.0595 28.1322i −0.957473 1.07487i
\(686\) 0 0
\(687\) 62.9025 36.3168i 2.39988 1.38557i
\(688\) 0 0
\(689\) 43.5589 + 15.6118i 1.65946 + 0.594761i
\(690\) 0 0
\(691\) −0.0218318 0.0378138i −0.000830522 0.00143851i 0.865610 0.500719i \(-0.166931\pi\)
−0.866440 + 0.499281i \(0.833598\pi\)
\(692\) 0 0
\(693\) 40.0230 + 23.1073i 1.52035 + 0.877774i
\(694\) 0 0
\(695\) −1.71461 + 1.52734i −0.0650390 + 0.0579352i
\(696\) 0 0
\(697\) 5.41982i 0.205290i
\(698\) 0 0
\(699\) 1.10945 + 1.92163i 0.0419634 + 0.0726827i
\(700\) 0 0
\(701\) −14.5454 −0.549373 −0.274687 0.961534i \(-0.588574\pi\)
−0.274687 + 0.961534i \(0.588574\pi\)
\(702\) 0 0
\(703\) 2.42785i 0.0915679i
\(704\) 0 0
\(705\) 8.38064 + 40.4903i 0.315633 + 1.52495i
\(706\) 0 0
\(707\) 19.1501i 0.720214i
\(708\) 0 0
\(709\) 9.81638 17.0025i 0.368662 0.638541i −0.620695 0.784052i \(-0.713149\pi\)
0.989357 + 0.145511i \(0.0464827\pi\)
\(710\) 0 0
\(711\) 29.2560 50.6728i 1.09718 1.90038i
\(712\) 0 0
\(713\) 8.81438 5.08898i 0.330101 0.190584i
\(714\) 0 0
\(715\) −25.9124 3.65285i −0.969067 0.136609i
\(716\) 0 0
\(717\) 9.32468 5.38361i 0.348237 0.201055i
\(718\) 0 0
\(719\) −23.7156 + 41.0766i −0.884443 + 1.53190i −0.0380914 + 0.999274i \(0.512128\pi\)
−0.846351 + 0.532625i \(0.821206\pi\)
\(720\) 0 0
\(721\) 12.3553 21.3999i 0.460134 0.796976i
\(722\) 0 0
\(723\) 61.0872i 2.27186i
\(724\) 0 0
\(725\) −1.72723 + 14.9002i −0.0641477 + 0.553380i
\(726\) 0 0
\(727\) 34.0951i 1.26452i −0.774757 0.632259i \(-0.782128\pi\)
0.774757 0.632259i \(-0.217872\pi\)
\(728\) 0 0
\(729\) 42.8349 1.58648
\(730\) 0 0
\(731\) 8.51345 + 14.7457i 0.314881 + 0.545391i
\(732\) 0 0
\(733\) 14.3920i 0.531580i 0.964031 + 0.265790i \(0.0856327\pi\)
−0.964031 + 0.265790i \(0.914367\pi\)
\(734\) 0 0
\(735\) −16.9984 19.0827i −0.626997 0.703877i
\(736\) 0 0
\(737\) 11.2864 + 6.51621i 0.415740 + 0.240028i
\(738\) 0 0
\(739\) 17.2240 + 29.8328i 0.633594 + 1.09742i 0.986811 + 0.161876i \(0.0517545\pi\)
−0.353217 + 0.935541i \(0.614912\pi\)
\(740\) 0 0
\(741\) 11.3822 + 4.07944i 0.418134 + 0.149862i
\(742\) 0 0
\(743\) 35.2589 20.3567i 1.29352 0.746816i 0.314246 0.949342i \(-0.398248\pi\)
0.979277 + 0.202526i \(0.0649150\pi\)
\(744\) 0 0
\(745\) −26.4674 + 23.5765i −0.969690 + 0.863777i
\(746\) 0 0
\(747\) −31.6939 18.2985i −1.15962 0.669507i
\(748\) 0 0
\(749\) −28.7542 −1.05066
\(750\) 0 0
\(751\) 16.2509 + 28.1474i 0.593003 + 1.02711i 0.993825 + 0.110956i \(0.0353912\pi\)
−0.400822 + 0.916156i \(0.631275\pi\)
\(752\) 0 0
\(753\) 51.2167i 1.86644i
\(754\) 0 0
\(755\) 30.8786 + 10.2158i 1.12379 + 0.371790i
\(756\) 0 0
\(757\) −11.2864 + 6.51621i −0.410211 + 0.236836i −0.690881 0.722969i \(-0.742777\pi\)
0.280669 + 0.959805i \(0.409444\pi\)
\(758\) 0 0
\(759\) 23.5185 0.853668
\(760\) 0 0
\(761\) 1.99493 3.45532i 0.0723161 0.125255i −0.827600 0.561318i \(-0.810294\pi\)
0.899916 + 0.436063i \(0.143628\pi\)
\(762\) 0 0
\(763\) −24.6613 14.2382i −0.892800 0.515458i
\(764\) 0 0
\(765\) 18.1178 3.75001i 0.655051 0.135582i
\(766\) 0 0
\(767\) 5.91018 + 6.97348i 0.213404 + 0.251798i
\(768\) 0 0
\(769\) 3.33343 + 5.77367i 0.120207 + 0.208204i 0.919849 0.392272i \(-0.128311\pi\)
−0.799642 + 0.600476i \(0.794978\pi\)
\(770\) 0 0
\(771\) 2.84181 4.92216i 0.102345 0.177267i
\(772\) 0 0
\(773\) 41.8593 + 24.1675i 1.50557 + 0.869244i 0.999979 + 0.00647254i \(0.00206029\pi\)
0.505595 + 0.862771i \(0.331273\pi\)
\(774\) 0 0
\(775\) −15.1752 11.2751i −0.545111 0.405015i
\(776\) 0 0
\(777\) 15.2349 8.79585i 0.546548 0.315549i
\(778\) 0 0
\(779\) −3.46472 −0.124136
\(780\) 0 0
\(781\) −17.0269 −0.609271
\(782\) 0 0
\(783\) 8.71259 5.03022i 0.311363 0.179765i
\(784\) 0 0
\(785\) −7.67017 + 23.1842i −0.273760 + 0.827478i
\(786\) 0 0
\(787\) −24.2151 13.9806i −0.863176 0.498355i 0.00189876 0.999998i \(-0.499396\pi\)
−0.865074 + 0.501643i \(0.832729\pi\)
\(788\) 0 0
\(789\) −40.2658 + 69.7424i −1.43350 + 2.48290i
\(790\) 0 0
\(791\) −12.2945 21.2948i −0.437144 0.757155i
\(792\) 0 0
\(793\) 17.4642 + 20.6062i 0.620174 + 0.731749i
\(794\) 0 0
\(795\) 15.6564 + 75.6426i 0.555277 + 2.68277i
\(796\) 0