Properties

Label 384.2.n.a.49.3
Level $384$
Weight $2$
Character 384.49
Analytic conductor $3.066$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 384 = 2^{7} \cdot 3 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 384.n (of order \(8\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.06625543762\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 96)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 49.3
Character \(\chi\) \(=\) 384.49
Dual form 384.2.n.a.337.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.923880 + 0.382683i) q^{3} +(-0.00259461 + 0.00626394i) q^{5} +(2.41880 + 2.41880i) q^{7} +(0.707107 - 0.707107i) q^{9} +O(q^{10})\) \(q+(-0.923880 + 0.382683i) q^{3} +(-0.00259461 + 0.00626394i) q^{5} +(2.41880 + 2.41880i) q^{7} +(0.707107 - 0.707107i) q^{9} +(-1.29952 - 0.538278i) q^{11} +(-0.559497 - 1.35074i) q^{13} -0.00678004i q^{15} +5.82199i q^{17} +(2.67819 + 6.46573i) q^{19} +(-3.16031 - 1.30904i) q^{21} +(-0.178878 + 0.178878i) q^{23} +(3.53550 + 3.53550i) q^{25} +(-0.382683 + 0.923880i) q^{27} +(5.72901 - 2.37303i) q^{29} +6.19719 q^{31} +1.40659 q^{33} +(-0.0214270 + 0.00887537i) q^{35} +(-2.02932 + 4.89922i) q^{37} +(1.03381 + 1.03381i) q^{39} +(-3.36712 + 3.36712i) q^{41} +(-9.37558 - 3.88349i) q^{43} +(0.00259461 + 0.00626394i) q^{45} -12.5050i q^{47} +4.70117i q^{49} +(-2.22798 - 5.37882i) q^{51} +(-8.36811 - 3.46618i) q^{53} +(0.00674348 - 0.00674348i) q^{55} +(-4.94866 - 4.94866i) q^{57} +(-1.59507 + 3.85084i) q^{59} +(7.27395 - 3.01297i) q^{61} +3.42070 q^{63} +0.00991266 q^{65} +(4.38775 - 1.81747i) q^{67} +(0.0968082 - 0.233716i) q^{69} +(-5.95188 - 5.95188i) q^{71} +(7.85539 - 7.85539i) q^{73} +(-4.61936 - 1.91340i) q^{75} +(-1.84128 - 4.44525i) q^{77} +1.42456i q^{79} -1.00000i q^{81} +(3.03596 + 7.32946i) q^{83} +(-0.0364686 - 0.0151058i) q^{85} +(-4.38479 + 4.38479i) q^{87} +(-9.96127 - 9.96127i) q^{89} +(1.91387 - 4.62049i) q^{91} +(-5.72545 + 2.37156i) q^{93} -0.0474498 q^{95} -1.24058 q^{97} +(-1.29952 + 0.538278i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + O(q^{10}) \) \( 32q + 16q^{23} + 48q^{31} + 48q^{35} + 16q^{43} - 16q^{51} - 32q^{53} - 32q^{55} - 64q^{59} - 32q^{61} - 16q^{63} - 16q^{67} - 32q^{69} - 64q^{71} - 32q^{75} - 32q^{77} + 48q^{91} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(133\) \(257\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{8}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.923880 + 0.382683i −0.533402 + 0.220942i
\(4\) 0 0
\(5\) −0.00259461 + 0.00626394i −0.00116034 + 0.00280132i −0.924459 0.381282i \(-0.875483\pi\)
0.923298 + 0.384084i \(0.125483\pi\)
\(6\) 0 0
\(7\) 2.41880 + 2.41880i 0.914220 + 0.914220i 0.996601 0.0823812i \(-0.0262525\pi\)
−0.0823812 + 0.996601i \(0.526253\pi\)
\(8\) 0 0
\(9\) 0.707107 0.707107i 0.235702 0.235702i
\(10\) 0 0
\(11\) −1.29952 0.538278i −0.391819 0.162297i 0.178071 0.984018i \(-0.443014\pi\)
−0.569890 + 0.821721i \(0.693014\pi\)
\(12\) 0 0
\(13\) −0.559497 1.35074i −0.155176 0.374629i 0.827103 0.562050i \(-0.189987\pi\)
−0.982280 + 0.187421i \(0.939987\pi\)
\(14\) 0 0
\(15\) 0.00678004i 0.00175060i
\(16\) 0 0
\(17\) 5.82199i 1.41204i 0.708192 + 0.706020i \(0.249511\pi\)
−0.708192 + 0.706020i \(0.750489\pi\)
\(18\) 0 0
\(19\) 2.67819 + 6.46573i 0.614420 + 1.48334i 0.858099 + 0.513484i \(0.171646\pi\)
−0.243679 + 0.969856i \(0.578354\pi\)
\(20\) 0 0
\(21\) −3.16031 1.30904i −0.689637 0.285657i
\(22\) 0 0
\(23\) −0.178878 + 0.178878i −0.0372987 + 0.0372987i −0.725510 0.688211i \(-0.758396\pi\)
0.688211 + 0.725510i \(0.258396\pi\)
\(24\) 0 0
\(25\) 3.53550 + 3.53550i 0.707100 + 0.707100i
\(26\) 0 0
\(27\) −0.382683 + 0.923880i −0.0736475 + 0.177801i
\(28\) 0 0
\(29\) 5.72901 2.37303i 1.06385 0.440661i 0.219034 0.975717i \(-0.429710\pi\)
0.844817 + 0.535056i \(0.179710\pi\)
\(30\) 0 0
\(31\) 6.19719 1.11305 0.556524 0.830832i \(-0.312135\pi\)
0.556524 + 0.830832i \(0.312135\pi\)
\(32\) 0 0
\(33\) 1.40659 0.244855
\(34\) 0 0
\(35\) −0.0214270 + 0.00887537i −0.00362183 + 0.00150021i
\(36\) 0 0
\(37\) −2.02932 + 4.89922i −0.333619 + 0.805427i 0.664680 + 0.747128i \(0.268568\pi\)
−0.998299 + 0.0582992i \(0.981432\pi\)
\(38\) 0 0
\(39\) 1.03381 + 1.03381i 0.165543 + 0.165543i
\(40\) 0 0
\(41\) −3.36712 + 3.36712i −0.525856 + 0.525856i −0.919334 0.393478i \(-0.871272\pi\)
0.393478 + 0.919334i \(0.371272\pi\)
\(42\) 0 0
\(43\) −9.37558 3.88349i −1.42976 0.592227i −0.472470 0.881347i \(-0.656637\pi\)
−0.957293 + 0.289120i \(0.906637\pi\)
\(44\) 0 0
\(45\) 0.00259461 + 0.00626394i 0.000386782 + 0.000933773i
\(46\) 0 0
\(47\) 12.5050i 1.82405i −0.410137 0.912024i \(-0.634519\pi\)
0.410137 0.912024i \(-0.365481\pi\)
\(48\) 0 0
\(49\) 4.70117i 0.671595i
\(50\) 0 0
\(51\) −2.22798 5.37882i −0.311979 0.753185i
\(52\) 0 0
\(53\) −8.36811 3.46618i −1.14945 0.476117i −0.275100 0.961416i \(-0.588711\pi\)
−0.874348 + 0.485299i \(0.838711\pi\)
\(54\) 0 0
\(55\) 0.00674348 0.00674348i 0.000909291 0.000909291i
\(56\) 0 0
\(57\) −4.94866 4.94866i −0.655465 0.655465i
\(58\) 0 0
\(59\) −1.59507 + 3.85084i −0.207661 + 0.501337i −0.993054 0.117660i \(-0.962461\pi\)
0.785393 + 0.618997i \(0.212461\pi\)
\(60\) 0 0
\(61\) 7.27395 3.01297i 0.931333 0.385771i 0.135149 0.990825i \(-0.456849\pi\)
0.796184 + 0.605054i \(0.206849\pi\)
\(62\) 0 0
\(63\) 3.42070 0.430967
\(64\) 0 0
\(65\) 0.00991266 0.00122951
\(66\) 0 0
\(67\) 4.38775 1.81747i 0.536049 0.222039i −0.0982011 0.995167i \(-0.531309\pi\)
0.634250 + 0.773128i \(0.281309\pi\)
\(68\) 0 0
\(69\) 0.0968082 0.233716i 0.0116543 0.0281361i
\(70\) 0 0
\(71\) −5.95188 5.95188i −0.706358 0.706358i 0.259409 0.965768i \(-0.416472\pi\)
−0.965768 + 0.259409i \(0.916472\pi\)
\(72\) 0 0
\(73\) 7.85539 7.85539i 0.919404 0.919404i −0.0775823 0.996986i \(-0.524720\pi\)
0.996986 + 0.0775823i \(0.0247201\pi\)
\(74\) 0 0
\(75\) −4.61936 1.91340i −0.533397 0.220940i
\(76\) 0 0
\(77\) −1.84128 4.44525i −0.209834 0.506584i
\(78\) 0 0
\(79\) 1.42456i 0.160276i 0.996784 + 0.0801378i \(0.0255360\pi\)
−0.996784 + 0.0801378i \(0.974464\pi\)
\(80\) 0 0
\(81\) 1.00000i 0.111111i
\(82\) 0 0
\(83\) 3.03596 + 7.32946i 0.333240 + 0.804513i 0.998331 + 0.0577507i \(0.0183929\pi\)
−0.665091 + 0.746763i \(0.731607\pi\)
\(84\) 0 0
\(85\) −0.0364686 0.0151058i −0.00395557 0.00163845i
\(86\) 0 0
\(87\) −4.38479 + 4.38479i −0.470099 + 0.470099i
\(88\) 0 0
\(89\) −9.96127 9.96127i −1.05589 1.05589i −0.998343 0.0575498i \(-0.981671\pi\)
−0.0575498 0.998343i \(-0.518329\pi\)
\(90\) 0 0
\(91\) 1.91387 4.62049i 0.200628 0.484359i
\(92\) 0 0
\(93\) −5.72545 + 2.37156i −0.593702 + 0.245919i
\(94\) 0 0
\(95\) −0.0474498 −0.00486825
\(96\) 0 0
\(97\) −1.24058 −0.125961 −0.0629807 0.998015i \(-0.520061\pi\)
−0.0629807 + 0.998015i \(0.520061\pi\)
\(98\) 0 0
\(99\) −1.29952 + 0.538278i −0.130606 + 0.0540989i
\(100\) 0 0
\(101\) 6.15953 14.8704i 0.612896 1.47966i −0.246908 0.969039i \(-0.579415\pi\)
0.859804 0.510624i \(-0.170585\pi\)
\(102\) 0 0
\(103\) 5.60558 + 5.60558i 0.552334 + 0.552334i 0.927114 0.374779i \(-0.122282\pi\)
−0.374779 + 0.927114i \(0.622282\pi\)
\(104\) 0 0
\(105\) 0.0163995 0.0163995i 0.00160043 0.00160043i
\(106\) 0 0
\(107\) 5.46375 + 2.26316i 0.528201 + 0.218788i 0.630815 0.775933i \(-0.282721\pi\)
−0.102614 + 0.994721i \(0.532721\pi\)
\(108\) 0 0
\(109\) −0.982918 2.37297i −0.0941464 0.227290i 0.869790 0.493422i \(-0.164254\pi\)
−0.963936 + 0.266132i \(0.914254\pi\)
\(110\) 0 0
\(111\) 5.30288i 0.503327i
\(112\) 0 0
\(113\) 4.42809i 0.416560i 0.978069 + 0.208280i \(0.0667865\pi\)
−0.978069 + 0.208280i \(0.933213\pi\)
\(114\) 0 0
\(115\) −0.000656364 0.00158460i −6.12062e−5 0.000147765i
\(116\) 0 0
\(117\) −1.35074 0.559497i −0.124876 0.0517255i
\(118\) 0 0
\(119\) −14.0822 + 14.0822i −1.29091 + 1.29091i
\(120\) 0 0
\(121\) −6.37917 6.37917i −0.579925 0.579925i
\(122\) 0 0
\(123\) 1.82227 4.39936i 0.164309 0.396677i
\(124\) 0 0
\(125\) −0.0626391 + 0.0259460i −0.00560261 + 0.00232068i
\(126\) 0 0
\(127\) −14.5930 −1.29492 −0.647458 0.762101i \(-0.724168\pi\)
−0.647458 + 0.762101i \(0.724168\pi\)
\(128\) 0 0
\(129\) 10.1481 0.893487
\(130\) 0 0
\(131\) 8.62727 3.57353i 0.753768 0.312221i 0.0274902 0.999622i \(-0.491248\pi\)
0.726278 + 0.687401i \(0.241248\pi\)
\(132\) 0 0
\(133\) −9.16129 + 22.1173i −0.794384 + 1.91781i
\(134\) 0 0
\(135\) −0.00479421 0.00479421i −0.000412620 0.000412620i
\(136\) 0 0
\(137\) −0.109126 + 0.109126i −0.00932323 + 0.00932323i −0.711753 0.702430i \(-0.752098\pi\)
0.702430 + 0.711753i \(0.252098\pi\)
\(138\) 0 0
\(139\) −5.80724 2.40544i −0.492564 0.204027i 0.122554 0.992462i \(-0.460892\pi\)
−0.615118 + 0.788435i \(0.710892\pi\)
\(140\) 0 0
\(141\) 4.78547 + 11.5532i 0.403009 + 0.972951i
\(142\) 0 0
\(143\) 2.05648i 0.171971i
\(144\) 0 0
\(145\) 0.0420433i 0.00349150i
\(146\) 0 0
\(147\) −1.79906 4.34331i −0.148384 0.358230i
\(148\) 0 0
\(149\) 15.4722 + 6.40879i 1.26753 + 0.525028i 0.912213 0.409717i \(-0.134373\pi\)
0.355318 + 0.934745i \(0.384373\pi\)
\(150\) 0 0
\(151\) 9.38822 9.38822i 0.764003 0.764003i −0.213041 0.977043i \(-0.568337\pi\)
0.977043 + 0.213041i \(0.0683367\pi\)
\(152\) 0 0
\(153\) 4.11677 + 4.11677i 0.332821 + 0.332821i
\(154\) 0 0
\(155\) −0.0160793 + 0.0388188i −0.00129152 + 0.00311800i
\(156\) 0 0
\(157\) −0.959615 + 0.397486i −0.0765856 + 0.0317228i −0.420647 0.907224i \(-0.638197\pi\)
0.344062 + 0.938947i \(0.388197\pi\)
\(158\) 0 0
\(159\) 9.05757 0.718312
\(160\) 0 0
\(161\) −0.865341 −0.0681984
\(162\) 0 0
\(163\) 7.39543 3.06329i 0.579255 0.239935i −0.0737655 0.997276i \(-0.523502\pi\)
0.653020 + 0.757340i \(0.273502\pi\)
\(164\) 0 0
\(165\) −0.00364954 + 0.00881078i −0.000284117 + 0.000685918i
\(166\) 0 0
\(167\) −0.697073 0.697073i −0.0539412 0.0539412i 0.679622 0.733563i \(-0.262144\pi\)
−0.733563 + 0.679622i \(0.762144\pi\)
\(168\) 0 0
\(169\) 7.68091 7.68091i 0.590840 0.590840i
\(170\) 0 0
\(171\) 6.46573 + 2.67819i 0.494447 + 0.204807i
\(172\) 0 0
\(173\) 6.61178 + 15.9623i 0.502685 + 1.21359i 0.948016 + 0.318222i \(0.103086\pi\)
−0.445331 + 0.895366i \(0.646914\pi\)
\(174\) 0 0
\(175\) 17.1033i 1.29289i
\(176\) 0 0
\(177\) 4.16812i 0.313295i
\(178\) 0 0
\(179\) −1.14101 2.75465i −0.0852832 0.205892i 0.875484 0.483246i \(-0.160542\pi\)
−0.960768 + 0.277354i \(0.910542\pi\)
\(180\) 0 0
\(181\) −6.23325 2.58190i −0.463314 0.191911i 0.138801 0.990320i \(-0.455675\pi\)
−0.602115 + 0.798409i \(0.705675\pi\)
\(182\) 0 0
\(183\) −5.56724 + 5.56724i −0.411542 + 0.411542i
\(184\) 0 0
\(185\) −0.0254231 0.0254231i −0.00186915 0.00186915i
\(186\) 0 0
\(187\) 3.13385 7.56577i 0.229170 0.553264i
\(188\) 0 0
\(189\) −3.16031 + 1.30904i −0.229879 + 0.0952189i
\(190\) 0 0
\(191\) 5.12197 0.370613 0.185306 0.982681i \(-0.440672\pi\)
0.185306 + 0.982681i \(0.440672\pi\)
\(192\) 0 0
\(193\) −20.7951 −1.49686 −0.748431 0.663213i \(-0.769192\pi\)
−0.748431 + 0.663213i \(0.769192\pi\)
\(194\) 0 0
\(195\) −0.00915810 + 0.00379341i −0.000655825 + 0.000271652i
\(196\) 0 0
\(197\) −3.47339 + 8.38550i −0.247469 + 0.597442i −0.997988 0.0634065i \(-0.979804\pi\)
0.750519 + 0.660849i \(0.229804\pi\)
\(198\) 0 0
\(199\) −9.79652 9.79652i −0.694457 0.694457i 0.268753 0.963209i \(-0.413389\pi\)
−0.963209 + 0.268753i \(0.913389\pi\)
\(200\) 0 0
\(201\) −3.35824 + 3.35824i −0.236872 + 0.236872i
\(202\) 0 0
\(203\) 19.5972 + 8.11743i 1.37545 + 0.569732i
\(204\) 0 0
\(205\) −0.0123551 0.0298278i −0.000862917 0.00208326i
\(206\) 0 0
\(207\) 0.252972i 0.0175828i
\(208\) 0 0
\(209\) 9.84394i 0.680919i
\(210\) 0 0
\(211\) 2.59646 + 6.26841i 0.178748 + 0.431535i 0.987704 0.156333i \(-0.0499673\pi\)
−0.808957 + 0.587868i \(0.799967\pi\)
\(212\) 0 0
\(213\) 7.77651 + 3.22114i 0.532838 + 0.220709i
\(214\) 0 0
\(215\) 0.0486519 0.0486519i 0.00331804 0.00331804i
\(216\) 0 0
\(217\) 14.9897 + 14.9897i 1.01757 + 1.01757i
\(218\) 0 0
\(219\) −4.25131 + 10.2636i −0.287277 + 0.693547i
\(220\) 0 0
\(221\) 7.86402 3.25738i 0.528991 0.219115i
\(222\) 0 0
\(223\) −14.6051 −0.978032 −0.489016 0.872275i \(-0.662644\pi\)
−0.489016 + 0.872275i \(0.662644\pi\)
\(224\) 0 0
\(225\) 4.99995 0.333330
\(226\) 0 0
\(227\) 3.75119 1.55379i 0.248975 0.103129i −0.254706 0.967019i \(-0.581979\pi\)
0.503681 + 0.863890i \(0.331979\pi\)
\(228\) 0 0
\(229\) 2.06540 4.98631i 0.136485 0.329505i −0.840828 0.541302i \(-0.817932\pi\)
0.977314 + 0.211797i \(0.0679316\pi\)
\(230\) 0 0
\(231\) 3.40225 + 3.40225i 0.223852 + 0.223852i
\(232\) 0 0
\(233\) −20.5003 + 20.5003i −1.34302 + 1.34302i −0.449987 + 0.893035i \(0.648572\pi\)
−0.893035 + 0.449987i \(0.851428\pi\)
\(234\) 0 0
\(235\) 0.0783308 + 0.0324457i 0.00510974 + 0.00211652i
\(236\) 0 0
\(237\) −0.545156 1.31612i −0.0354117 0.0854913i
\(238\) 0 0
\(239\) 2.23671i 0.144680i 0.997380 + 0.0723402i \(0.0230467\pi\)
−0.997380 + 0.0723402i \(0.976953\pi\)
\(240\) 0 0
\(241\) 19.6755i 1.26741i −0.773575 0.633704i \(-0.781534\pi\)
0.773575 0.633704i \(-0.218466\pi\)
\(242\) 0 0
\(243\) 0.382683 + 0.923880i 0.0245492 + 0.0592669i
\(244\) 0 0
\(245\) −0.0294478 0.0121977i −0.00188135 0.000779282i
\(246\) 0 0
\(247\) 7.23511 7.23511i 0.460359 0.460359i
\(248\) 0 0
\(249\) −5.60973 5.60973i −0.355502 0.355502i
\(250\) 0 0
\(251\) −2.41942 + 5.84100i −0.152712 + 0.368680i −0.981658 0.190648i \(-0.938941\pi\)
0.828946 + 0.559329i \(0.188941\pi\)
\(252\) 0 0
\(253\) 0.328742 0.136169i 0.0206678 0.00856088i
\(254\) 0 0
\(255\) 0.0394733 0.00247191
\(256\) 0 0
\(257\) 9.46013 0.590106 0.295053 0.955481i \(-0.404663\pi\)
0.295053 + 0.955481i \(0.404663\pi\)
\(258\) 0 0
\(259\) −16.7588 + 6.94170i −1.04134 + 0.431336i
\(260\) 0 0
\(261\) 2.37303 5.72901i 0.146887 0.354617i
\(262\) 0 0
\(263\) 7.01762 + 7.01762i 0.432725 + 0.432725i 0.889554 0.456829i \(-0.151015\pi\)
−0.456829 + 0.889554i \(0.651015\pi\)
\(264\) 0 0
\(265\) 0.0434239 0.0434239i 0.00266751 0.00266751i
\(266\) 0 0
\(267\) 13.0150 + 5.39100i 0.796507 + 0.329924i
\(268\) 0 0
\(269\) 0.579856 + 1.39990i 0.0353545 + 0.0853532i 0.940571 0.339598i \(-0.110291\pi\)
−0.905216 + 0.424952i \(0.860291\pi\)
\(270\) 0 0
\(271\) 2.19594i 0.133394i 0.997773 + 0.0666969i \(0.0212460\pi\)
−0.997773 + 0.0666969i \(0.978754\pi\)
\(272\) 0 0
\(273\) 5.00118i 0.302685i
\(274\) 0 0
\(275\) −2.69136 6.49753i −0.162295 0.391816i
\(276\) 0 0
\(277\) 24.0612 + 9.96649i 1.44570 + 0.598829i 0.961173 0.275948i \(-0.0889916\pi\)
0.484527 + 0.874776i \(0.338992\pi\)
\(278\) 0 0
\(279\) 4.38207 4.38207i 0.262348 0.262348i
\(280\) 0 0
\(281\) 18.0180 + 18.0180i 1.07487 + 1.07487i 0.996961 + 0.0779048i \(0.0248230\pi\)
0.0779048 + 0.996961i \(0.475177\pi\)
\(282\) 0 0
\(283\) 1.15856 2.79702i 0.0688695 0.166266i −0.885697 0.464264i \(-0.846319\pi\)
0.954566 + 0.297998i \(0.0963189\pi\)
\(284\) 0 0
\(285\) 0.0438379 0.0181583i 0.00259673 0.00107560i
\(286\) 0 0
\(287\) −16.2888 −0.961496
\(288\) 0 0
\(289\) −16.8955 −0.993855
\(290\) 0 0
\(291\) 1.14614 0.474748i 0.0671881 0.0278302i
\(292\) 0 0
\(293\) 3.52001 8.49805i 0.205641 0.496461i −0.787087 0.616842i \(-0.788412\pi\)
0.992728 + 0.120381i \(0.0384116\pi\)
\(294\) 0 0
\(295\) −0.0199829 0.0199829i −0.00116345 0.00116345i
\(296\) 0 0
\(297\) 0.994607 0.994607i 0.0577130 0.0577130i
\(298\) 0 0
\(299\) 0.341700 + 0.141537i 0.0197610 + 0.00818529i
\(300\) 0 0
\(301\) −13.2843 32.0710i −0.765692 1.84854i
\(302\) 0 0
\(303\) 16.0956i 0.924670i
\(304\) 0 0
\(305\) 0.0533810i 0.00305659i
\(306\) 0 0
\(307\) 1.41754 + 3.42224i 0.0809032 + 0.195318i 0.959155 0.282881i \(-0.0912900\pi\)
−0.878252 + 0.478198i \(0.841290\pi\)
\(308\) 0 0
\(309\) −7.32405 3.03372i −0.416650 0.172582i
\(310\) 0 0
\(311\) 22.4396 22.4396i 1.27243 1.27243i 0.327622 0.944809i \(-0.393753\pi\)
0.944809 0.327622i \(-0.106247\pi\)
\(312\) 0 0
\(313\) −2.24961 2.24961i −0.127155 0.127155i 0.640665 0.767821i \(-0.278659\pi\)
−0.767821 + 0.640665i \(0.778659\pi\)
\(314\) 0 0
\(315\) −0.00887537 + 0.0214270i −0.000500071 + 0.00120728i
\(316\) 0 0
\(317\) −31.4340 + 13.0204i −1.76551 + 0.731298i −0.769852 + 0.638223i \(0.779670\pi\)
−0.995659 + 0.0930756i \(0.970330\pi\)
\(318\) 0 0
\(319\) −8.72230 −0.488355
\(320\) 0 0
\(321\) −5.91392 −0.330083
\(322\) 0 0
\(323\) −37.6434 + 15.5924i −2.09453 + 0.867585i
\(324\) 0 0
\(325\) 2.79746 6.75366i 0.155175 0.374626i
\(326\) 0 0
\(327\) 1.81620 + 1.81620i 0.100436 + 0.100436i
\(328\) 0 0
\(329\) 30.2472 30.2472i 1.66758 1.66758i
\(330\) 0 0
\(331\) −24.6043 10.1914i −1.35237 0.560172i −0.415422 0.909629i \(-0.636366\pi\)
−0.936952 + 0.349457i \(0.886366\pi\)
\(332\) 0 0
\(333\) 2.02932 + 4.89922i 0.111206 + 0.268476i
\(334\) 0 0
\(335\) 0.0322002i 0.00175929i
\(336\) 0 0
\(337\) 20.1009i 1.09497i −0.836817 0.547483i \(-0.815586\pi\)
0.836817 0.547483i \(-0.184414\pi\)
\(338\) 0 0
\(339\) −1.69456 4.09103i −0.0920358 0.222194i
\(340\) 0 0
\(341\) −8.05335 3.33581i −0.436113 0.180644i
\(342\) 0 0
\(343\) 5.56041 5.56041i 0.300234 0.300234i
\(344\) 0 0
\(345\) 0.00121280 + 0.00121280i 6.52950e−5 + 6.52950e-5i
\(346\) 0 0
\(347\) 5.23707 12.6434i 0.281141 0.678734i −0.718722 0.695297i \(-0.755273\pi\)
0.999863 + 0.0165638i \(0.00527266\pi\)
\(348\) 0 0
\(349\) −16.5877 + 6.87085i −0.887920 + 0.367788i −0.779563 0.626324i \(-0.784559\pi\)
−0.108357 + 0.994112i \(0.534559\pi\)
\(350\) 0 0
\(351\) 1.46203 0.0780377
\(352\) 0 0
\(353\) 10.8817 0.579174 0.289587 0.957152i \(-0.406482\pi\)
0.289587 + 0.957152i \(0.406482\pi\)
\(354\) 0 0
\(355\) 0.0527250 0.0218394i 0.00279835 0.00115912i
\(356\) 0 0
\(357\) 7.62124 18.3993i 0.403359 0.973794i
\(358\) 0 0
\(359\) −5.54201 5.54201i −0.292496 0.292496i 0.545570 0.838066i \(-0.316313\pi\)
−0.838066 + 0.545570i \(0.816313\pi\)
\(360\) 0 0
\(361\) −21.1979 + 21.1979i −1.11568 + 1.11568i
\(362\) 0 0
\(363\) 8.33479 + 3.45238i 0.437463 + 0.181203i
\(364\) 0 0
\(365\) 0.0288240 + 0.0695874i 0.00150872 + 0.00364237i
\(366\) 0 0
\(367\) 2.99994i 0.156596i −0.996930 0.0782979i \(-0.975051\pi\)
0.996930 0.0782979i \(-0.0249485\pi\)
\(368\) 0 0
\(369\) 4.76183i 0.247891i
\(370\) 0 0
\(371\) −11.8568 28.6248i −0.615572 1.48612i
\(372\) 0 0
\(373\) −15.3503 6.35832i −0.794811 0.329221i −0.0519347 0.998650i \(-0.516539\pi\)
−0.742876 + 0.669429i \(0.766539\pi\)
\(374\) 0 0
\(375\) 0.0479419 0.0479419i 0.00247571 0.00247571i
\(376\) 0 0
\(377\) −6.41072 6.41072i −0.330169 0.330169i
\(378\) 0 0
\(379\) 2.50517 6.04801i 0.128682 0.310665i −0.846387 0.532568i \(-0.821227\pi\)
0.975069 + 0.221903i \(0.0712269\pi\)
\(380\) 0 0
\(381\) 13.4821 5.58448i 0.690711 0.286102i
\(382\) 0 0
\(383\) 32.1450 1.64253 0.821266 0.570545i \(-0.193268\pi\)
0.821266 + 0.570545i \(0.193268\pi\)
\(384\) 0 0
\(385\) 0.0326222 0.00166258
\(386\) 0 0
\(387\) −9.37558 + 3.88349i −0.476588 + 0.197409i
\(388\) 0 0
\(389\) 2.48310 5.99473i 0.125898 0.303945i −0.848346 0.529443i \(-0.822401\pi\)
0.974244 + 0.225498i \(0.0724010\pi\)
\(390\) 0 0
\(391\) −1.04143 1.04143i −0.0526672 0.0526672i
\(392\) 0 0
\(393\) −6.60303 + 6.60303i −0.333079 + 0.333079i
\(394\) 0 0
\(395\) −0.00892336 0.00369618i −0.000448983 0.000185975i
\(396\) 0 0
\(397\) −9.62118 23.2276i −0.482873 1.16576i −0.958238 0.285970i \(-0.907684\pi\)
0.475365 0.879788i \(-0.342316\pi\)
\(398\) 0 0
\(399\) 23.9396i 1.19848i
\(400\) 0 0
\(401\) 4.48158i 0.223800i 0.993719 + 0.111900i \(0.0356936\pi\)
−0.993719 + 0.111900i \(0.964306\pi\)
\(402\) 0 0
\(403\) −3.46730 8.37081i −0.172719 0.416980i
\(404\) 0 0
\(405\) 0.00626394 + 0.00259461i 0.000311258 + 0.000128927i
\(406\) 0 0
\(407\) 5.27428 5.27428i 0.261437 0.261437i
\(408\) 0 0
\(409\) 22.1171 + 22.1171i 1.09362 + 1.09362i 0.995139 + 0.0984792i \(0.0313978\pi\)
0.0984792 + 0.995139i \(0.468602\pi\)
\(410\) 0 0
\(411\) 0.0590584 0.142579i 0.00291313 0.00703293i
\(412\) 0 0
\(413\) −13.1726 + 5.45626i −0.648180 + 0.268485i
\(414\) 0 0
\(415\) −0.0537885 −0.00264037
\(416\) 0 0
\(417\) 6.28571 0.307813
\(418\) 0 0
\(419\) 8.59414 3.55981i 0.419851 0.173908i −0.162748 0.986668i \(-0.552036\pi\)
0.582599 + 0.812760i \(0.302036\pi\)
\(420\) 0 0
\(421\) 7.82429 18.8895i 0.381333 0.920619i −0.610376 0.792112i \(-0.708982\pi\)
0.991709 0.128507i \(-0.0410184\pi\)
\(422\) 0 0
\(423\) −8.84240 8.84240i −0.429932 0.429932i
\(424\) 0 0
\(425\) −20.5836 + 20.5836i −0.998453 + 0.998453i
\(426\) 0 0
\(427\) 24.8820 + 10.3064i 1.20412 + 0.498764i
\(428\) 0 0
\(429\) −0.786981 1.89994i −0.0379958 0.0917300i
\(430\) 0 0
\(431\) 17.2386i 0.830353i 0.909741 + 0.415177i \(0.136280\pi\)
−0.909741 + 0.415177i \(0.863720\pi\)
\(432\) 0 0
\(433\) 20.8456i 1.00177i 0.865513 + 0.500887i \(0.166993\pi\)
−0.865513 + 0.500887i \(0.833007\pi\)
\(434\) 0 0
\(435\) −0.0160893 0.0388429i −0.000771421 0.00186238i
\(436\) 0 0
\(437\) −1.63565 0.677508i −0.0782437 0.0324096i
\(438\) 0 0
\(439\) 11.5583 11.5583i 0.551648 0.551648i −0.375269 0.926916i \(-0.622450\pi\)
0.926916 + 0.375269i \(0.122450\pi\)
\(440\) 0 0
\(441\) 3.32423 + 3.32423i 0.158297 + 0.158297i
\(442\) 0 0
\(443\) −7.86432 + 18.9861i −0.373645 + 0.902059i 0.619481 + 0.785011i \(0.287343\pi\)
−0.993126 + 0.117047i \(0.962657\pi\)
\(444\) 0 0
\(445\) 0.0882424 0.0365512i 0.00418309 0.00173269i
\(446\) 0 0
\(447\) −16.7470 −0.792105
\(448\) 0 0
\(449\) −2.11825 −0.0999665 −0.0499832 0.998750i \(-0.515917\pi\)
−0.0499832 + 0.998750i \(0.515917\pi\)
\(450\) 0 0
\(451\) 6.18808 2.56319i 0.291385 0.120696i
\(452\) 0 0
\(453\) −5.08087 + 12.2663i −0.238720 + 0.576321i
\(454\) 0 0
\(455\) 0.0239767 + 0.0239767i 0.00112405 + 0.00112405i
\(456\) 0 0
\(457\) 7.54089 7.54089i 0.352748 0.352748i −0.508383 0.861131i \(-0.669757\pi\)
0.861131 + 0.508383i \(0.169757\pi\)
\(458\) 0 0
\(459\) −5.37882 2.22798i −0.251062 0.103993i
\(460\) 0 0
\(461\) −1.56851 3.78672i −0.0730529 0.176365i 0.883135 0.469119i \(-0.155428\pi\)
−0.956188 + 0.292754i \(0.905428\pi\)
\(462\) 0 0
\(463\) 8.35374i 0.388231i −0.980979 0.194116i \(-0.937816\pi\)
0.980979 0.194116i \(-0.0621837\pi\)
\(464\) 0 0
\(465\) 0.0420172i 0.00194850i
\(466\) 0 0
\(467\) −11.8505 28.6097i −0.548377 1.32390i −0.918685 0.394990i \(-0.870748\pi\)
0.370308 0.928909i \(-0.379252\pi\)
\(468\) 0 0
\(469\) 15.0092 + 6.21700i 0.693059 + 0.287075i
\(470\) 0 0
\(471\) 0.734458 0.734458i 0.0338420 0.0338420i
\(472\) 0 0
\(473\) 10.0933 + 10.0933i 0.464092 + 0.464092i
\(474\) 0 0
\(475\) −13.3908 + 32.3283i −0.614414 + 1.48333i
\(476\) 0 0
\(477\) −8.36811 + 3.46618i −0.383149 + 0.158706i
\(478\) 0 0
\(479\) 4.36086 0.199253 0.0996264 0.995025i \(-0.468235\pi\)
0.0996264 + 0.995025i \(0.468235\pi\)
\(480\) 0 0
\(481\) 7.75299 0.353506
\(482\) 0 0
\(483\) 0.799470 0.331151i 0.0363772 0.0150679i
\(484\) 0 0
\(485\) 0.00321881 0.00777090i 0.000146159 0.000352858i
\(486\) 0 0
\(487\) −7.91861 7.91861i −0.358827 0.358827i 0.504554 0.863380i \(-0.331657\pi\)
−0.863380 + 0.504554i \(0.831657\pi\)
\(488\) 0 0
\(489\) −5.66022 + 5.66022i −0.255964 + 0.255964i
\(490\) 0 0
\(491\) −37.8921 15.6954i −1.71005 0.708324i −0.999991 0.00417652i \(-0.998671\pi\)
−0.710054 0.704147i \(-0.751329\pi\)
\(492\) 0 0
\(493\) 13.8158 + 33.3542i 0.622231 + 1.50220i
\(494\) 0 0
\(495\) 0.00953672i 0.000428644i
\(496\) 0 0
\(497\) 28.7928i 1.29153i
\(498\) 0 0
\(499\) 9.18191 + 22.1671i 0.411039 + 0.992336i 0.984859 + 0.173355i \(0.0554607\pi\)
−0.573821 + 0.818981i \(0.694539\pi\)
\(500\) 0 0
\(501\) 0.910770 + 0.377253i 0.0406902 + 0.0168544i
\(502\) 0 0
\(503\) −16.5963 + 16.5963i −0.739995 + 0.739995i −0.972577 0.232582i \(-0.925283\pi\)
0.232582 + 0.972577i \(0.425283\pi\)
\(504\) 0 0
\(505\) 0.0771659 + 0.0771659i 0.00343384 + 0.00343384i
\(506\) 0 0
\(507\) −4.15688 + 10.0356i −0.184614 + 0.445697i
\(508\) 0 0
\(509\) 5.26058 2.17900i 0.233171 0.0965826i −0.263039 0.964785i \(-0.584725\pi\)
0.496210 + 0.868203i \(0.334725\pi\)
\(510\) 0 0
\(511\) 38.0012 1.68107
\(512\) 0 0
\(513\) −6.99846 −0.308989
\(514\) 0 0
\(515\) −0.0496573 + 0.0205687i −0.00218816 + 0.000906367i
\(516\) 0 0
\(517\) −6.73118 + 16.2505i −0.296037 + 0.714697i
\(518\) 0 0
\(519\) −12.2170 12.2170i −0.536266 0.536266i
\(520\) 0 0
\(521\) 13.8290 13.8290i 0.605861 0.605861i −0.336001 0.941862i \(-0.609074\pi\)
0.941862 + 0.336001i \(0.109074\pi\)
\(522\) 0 0
\(523\) 20.8657 + 8.64286i 0.912393 + 0.377926i 0.788972 0.614429i \(-0.210613\pi\)
0.123421 + 0.992354i \(0.460613\pi\)
\(524\) 0 0
\(525\) −6.54516 15.8014i −0.285654 0.689630i
\(526\) 0 0
\(527\) 36.0799i 1.57167i
\(528\) 0 0
\(529\) 22.9360i 0.997218i
\(530\) 0 0
\(531\) 1.59507 + 3.85084i 0.0692202 + 0.167112i
\(532\) 0 0
\(533\) 6.43201 + 2.66423i 0.278601 + 0.115400i
\(534\) 0 0
\(535\) −0.0283526 + 0.0283526i −0.00122579 + 0.00122579i
\(536\) 0 0
\(537\) 2.10832 + 2.10832i 0.0909805 + 0.0909805i
\(538\) 0 0
\(539\) 2.53053 6.10925i 0.108998 0.263144i
\(540\) 0 0
\(541\) 24.5863 10.1840i 1.05705 0.437843i 0.214645 0.976692i \(-0.431141\pi\)
0.842402 + 0.538849i \(0.181141\pi\)
\(542\) 0 0
\(543\) 6.74682 0.289534
\(544\) 0 0
\(545\) 0.0174145 0.000745953
\(546\) 0 0
\(547\) −9.15022 + 3.79015i −0.391235 + 0.162055i −0.569625 0.821905i \(-0.692911\pi\)
0.178389 + 0.983960i \(0.442911\pi\)
\(548\) 0 0
\(549\) 3.01297 7.27395i 0.128590 0.310444i
\(550\) 0 0
\(551\) 30.6868 + 30.6868i 1.30730 + 1.30730i
\(552\) 0 0
\(553\) −3.44572 + 3.44572i −0.146527 + 0.146527i
\(554\) 0 0
\(555\) 0.0332169 + 0.0137589i 0.00140998 + 0.000584033i
\(556\) 0 0
\(557\) −2.57099 6.20693i −0.108936 0.262996i 0.860005 0.510285i \(-0.170460\pi\)
−0.968942 + 0.247289i \(0.920460\pi\)
\(558\) 0 0
\(559\) 14.8368i 0.627530i
\(560\) 0 0
\(561\) 8.18913i 0.345746i
\(562\) 0 0
\(563\) 16.2626 + 39.2615i 0.685388 + 1.65467i 0.753872 + 0.657021i \(0.228184\pi\)
−0.0684842 + 0.997652i \(0.521816\pi\)
\(564\) 0 0
\(565\) −0.0277373 0.0114892i −0.00116692 0.000483353i
\(566\) 0 0
\(567\) 2.41880 2.41880i 0.101580 0.101580i
\(568\) 0 0
\(569\) −23.1230 23.1230i −0.969368 0.969368i 0.0301764 0.999545i \(-0.490393\pi\)
−0.999545 + 0.0301764i \(0.990393\pi\)
\(570\) 0 0
\(571\) 3.47053 8.37861i 0.145237 0.350634i −0.834474 0.551047i \(-0.814228\pi\)
0.979711 + 0.200413i \(0.0642285\pi\)
\(572\) 0 0
\(573\) −4.73208 + 1.96009i −0.197686 + 0.0818841i
\(574\) 0 0
\(575\) −1.26485 −0.0527478
\(576\) 0 0
\(577\) 18.7910 0.782278 0.391139 0.920332i \(-0.372081\pi\)
0.391139 + 0.920332i \(0.372081\pi\)
\(578\) 0 0
\(579\) 19.2121 7.95793i 0.798429 0.330720i
\(580\) 0 0
\(581\) −10.3851 + 25.0719i −0.430847 + 1.04016i
\(582\) 0 0
\(583\) 9.00873 + 9.00873i 0.373104 + 0.373104i
\(584\) 0 0
\(585\) 0.00700931 0.00700931i 0.000289799 0.000289799i
\(586\) 0 0
\(587\) 28.1601 + 11.6643i 1.16229 + 0.481436i 0.878637 0.477490i \(-0.158453\pi\)
0.283653 + 0.958927i \(0.408453\pi\)
\(588\) 0 0
\(589\) 16.5973 + 40.0693i 0.683878 + 1.65103i
\(590\) 0 0
\(591\) 9.07640i 0.373353i
\(592\) 0 0
\(593\) 12.2535i 0.503189i −0.967833 0.251594i \(-0.919045\pi\)
0.967833 0.251594i \(-0.0809549\pi\)
\(594\) 0 0
\(595\) −0.0516723 0.124748i −0.00211836 0.00511417i
\(596\) 0 0
\(597\) 12.7998 + 5.30184i 0.523859 + 0.216990i
\(598\) 0 0
\(599\) −8.63937 + 8.63937i −0.352995 + 0.352995i −0.861223 0.508228i \(-0.830301\pi\)
0.508228 + 0.861223i \(0.330301\pi\)
\(600\) 0 0
\(601\) −14.3695 14.3695i −0.586143 0.586143i 0.350441 0.936585i \(-0.386032\pi\)
−0.936585 + 0.350441i \(0.886032\pi\)
\(602\) 0 0
\(603\) 1.81747 4.38775i 0.0740130 0.178683i
\(604\) 0 0
\(605\) 0.0565102 0.0234073i 0.00229747 0.000951642i
\(606\) 0 0
\(607\) −21.4916 −0.872319 −0.436159 0.899869i \(-0.643662\pi\)
−0.436159 + 0.899869i \(0.643662\pi\)
\(608\) 0 0
\(609\) −21.2119 −0.859548
\(610\) 0 0
\(611\) −16.8911 + 6.99653i −0.683341 + 0.283049i
\(612\) 0 0
\(613\) 12.3921 29.9172i 0.500513 1.20834i −0.448693 0.893686i \(-0.648110\pi\)
0.949205 0.314658i \(-0.101890\pi\)
\(614\) 0 0
\(615\) 0.0228292 + 0.0228292i 0.000920563 + 0.000920563i
\(616\) 0 0
\(617\) 17.5651 17.5651i 0.707143 0.707143i −0.258790 0.965933i \(-0.583324\pi\)
0.965933 + 0.258790i \(0.0833239\pi\)
\(618\) 0 0
\(619\) 16.3569 + 6.77526i 0.657440 + 0.272321i 0.686361 0.727261i \(-0.259207\pi\)
−0.0289208 + 0.999582i \(0.509207\pi\)
\(620\) 0 0
\(621\) −0.0968082 0.233716i −0.00388478 0.00937869i
\(622\) 0 0
\(623\) 48.1886i 1.93064i
\(624\) 0 0
\(625\) 24.9993i 0.999972i
\(626\) 0 0
\(627\) 3.76711 + 9.09461i 0.150444 + 0.363204i
\(628\) 0 0
\(629\) −28.5232 11.8147i −1.13729 0.471083i
\(630\) 0 0
\(631\) −23.6874 + 23.6874i −0.942982 + 0.942982i −0.998460 0.0554784i \(-0.982332\pi\)
0.0554784 + 0.998460i \(0.482332\pi\)
\(632\) 0 0
\(633\) −4.79763 4.79763i −0.190689 0.190689i
\(634\) 0 0
\(635\) 0.0378630 0.0914094i 0.00150255 0.00362747i
\(636\) 0 0
\(637\) 6.35007 2.63029i 0.251599 0.104216i
\(638\) 0 0
\(639\) −8.41723 −0.332981
\(640\) 0 0
\(641\) 6.79529 0.268398 0.134199 0.990954i \(-0.457154\pi\)
0.134199 + 0.990954i \(0.457154\pi\)
\(642\) 0 0
\(643\) 18.4729 7.65173i 0.728500 0.301755i 0.0125646 0.999921i \(-0.496000\pi\)
0.715935 + 0.698166i \(0.246000\pi\)
\(644\) 0 0
\(645\) −0.0263302 + 0.0635668i −0.00103675 + 0.00250294i
\(646\) 0 0
\(647\) 5.34732 + 5.34732i 0.210225 + 0.210225i 0.804363 0.594138i \(-0.202507\pi\)
−0.594138 + 0.804363i \(0.702507\pi\)
\(648\) 0 0
\(649\) 4.14565 4.14565i 0.162731 0.162731i
\(650\) 0 0
\(651\) −19.5850 8.11239i −0.767598 0.317950i
\(652\) 0 0
\(653\) −1.51225 3.65091i −0.0591791 0.142871i 0.891524 0.452973i \(-0.149637\pi\)
−0.950703 + 0.310102i \(0.899637\pi\)
\(654\) 0 0
\(655\) 0.0633126i 0.00247383i
\(656\) 0 0
\(657\) 11.1092i 0.433411i
\(658\) 0 0
\(659\) 7.07771 + 17.0871i 0.275708 + 0.665619i 0.999708 0.0241818i \(-0.00769807\pi\)
−0.723999 + 0.689801i \(0.757698\pi\)
\(660\) 0 0
\(661\) 15.2261 + 6.30685i 0.592226 + 0.245308i 0.658608 0.752486i \(-0.271146\pi\)
−0.0663821 + 0.997794i \(0.521146\pi\)
\(662\) 0 0
\(663\) −6.01886 + 6.01886i −0.233753 + 0.233753i
\(664\) 0 0
\(665\) −0.114772 0.114772i −0.00445065 0.00445065i
\(666\) 0 0
\(667\) −0.600311 + 1.44928i −0.0232441 + 0.0561163i
\(668\) 0 0
\(669\) 13.4934 5.58914i 0.521684 0.216089i
\(670\) 0 0
\(671\) −11.0744 −0.427524
\(672\) 0 0
\(673\) 5.46222 0.210553 0.105276 0.994443i \(-0.466427\pi\)
0.105276 + 0.994443i \(0.466427\pi\)
\(674\) 0 0
\(675\) −4.61936 + 1.91340i −0.177799 + 0.0736468i
\(676\) 0 0
\(677\) −4.02477 + 9.71665i −0.154684 + 0.373441i −0.982156 0.188066i \(-0.939778\pi\)
0.827472 + 0.561507i \(0.189778\pi\)
\(678\) 0 0
\(679\) −3.00070 3.00070i −0.115156 0.115156i
\(680\) 0 0
\(681\) −2.87104 + 2.87104i −0.110018 + 0.110018i
\(682\) 0 0
\(683\) −39.7212 16.4530i −1.51989 0.629558i −0.542319 0.840173i \(-0.682453\pi\)
−0.977569 + 0.210615i \(0.932453\pi\)
\(684\) 0 0
\(685\) −0.000400418 0 0.000966695i −1.52992e−5 0 3.69355e-5i
\(686\) 0 0
\(687\) 5.39714i 0.205914i
\(688\) 0 0
\(689\) 13.2425i 0.504499i
\(690\) 0 0
\(691\) −7.36888 17.7900i −0.280325 0.676765i 0.719518 0.694474i \(-0.244363\pi\)
−0.999843 + 0.0177088i \(0.994363\pi\)
\(692\) 0 0
\(693\) −4.44525 1.84128i −0.168861 0.0699446i
\(694\) 0 0
\(695\) 0.0301350 0.0301350i 0.00114309 0.00114309i
\(696\) 0 0
\(697\) −19.6033 19.6033i −0.742529 0.742529i
\(698\) 0 0
\(699\) 11.0947 26.7850i 0.419640 1.01310i
\(700\) 0 0
\(701\) 0.759834 0.314734i 0.0286985 0.0118873i −0.368288 0.929712i \(-0.620056\pi\)
0.396987 + 0.917824i \(0.370056\pi\)
\(702\) 0 0
\(703\) −37.1120 −1.39970
\(704\) 0 0
\(705\) −0.0847847 −0.00319318
\(706\) 0 0
\(707\) 50.8672 21.0699i 1.91306 0.792415i
\(708\) 0 0
\(709\) −18.3991 + 44.4194i −0.690994 + 1.66821i 0.0517745 + 0.998659i \(0.483512\pi\)
−0.742768 + 0.669548i \(0.766488\pi\)
\(710\) 0 0
\(711\) 1.00732 + 1.00732i 0.0377773 + 0.0377773i
\(712\) 0 0
\(713\) −1.10854 + 1.10854i −0.0415152 + 0.0415152i
\(714\) 0 0
\(715\) −0.0128817 0.00533576i −0.000481747 0.000199546i
\(716\) 0 0
\(717\) −0.855950 2.06645i −0.0319660 0.0771729i
\(718\) 0 0
\(719\) 0.494401i 0.0184380i −0.999958 0.00921901i \(-0.997065\pi\)
0.999958 0.00921901i \(-0.00293455\pi\)
\(720\) 0 0
\(721\) 27.1175i 1.00991i
\(722\) 0 0
\(723\) 7.52948 + 18.1778i 0.280024 + 0.676039i
\(724\) 0 0
\(725\) 28.6448 + 11.8651i 1.06384 + 0.440657i
\(726\) 0 0
\(727\) −13.9621 + 13.9621i −0.517826 + 0.517826i −0.916913 0.399087i \(-0.869327\pi\)
0.399087 + 0.916913i \(0.369327\pi\)
\(728\) 0 0
\(729\) −0.707107 0.707107i −0.0261891 0.0261891i
\(730\) 0 0
\(731\) 22.6097 54.5845i 0.836248 2.01888i
\(732\) 0 0
\(733\) 21.0117 8.70335i 0.776087 0.321466i 0.0407515 0.999169i \(-0.487025\pi\)
0.735335 + 0.677704i \(0.237025\pi\)
\(734\) 0 0
\(735\) 0.0318741 0.00117569
\(736\) 0 0
\(737\) −6.68026 −0.246071
\(738\) 0 0
\(739\) 23.9176 9.90698i 0.879822 0.364434i 0.103394 0.994640i \(-0.467030\pi\)
0.776428 + 0.630206i \(0.217030\pi\)
\(740\) 0 0
\(741\) −3.91561 + 9.45312i −0.143844 + 0.347269i
\(742\) 0 0
\(743\) −22.7644 22.7644i −0.835144 0.835144i 0.153071 0.988215i \(-0.451084\pi\)
−0.988215 + 0.153071i \(0.951084\pi\)
\(744\) 0 0
\(745\) −0.0802886 + 0.0802886i −0.00294155 + 0.00294155i
\(746\) 0 0
\(747\) 7.32946 + 3.03596i 0.268171 + 0.111080i
\(748\) 0 0
\(749\) 7.74158 + 18.6898i 0.282871 + 0.682912i
\(750\) 0 0
\(751\) 31.4436i 1.14739i −0.819068 0.573697i \(-0.805509\pi\)
0.819068 0.573697i \(-0.194491\pi\)
\(752\) 0 0
\(753\) 6.32225i 0.230396i
\(754\) 0 0
\(755\) 0.0344485 + 0.0831660i 0.00125371 + 0.00302672i
\(756\) 0 0
\(757\) −23.6692 9.80412i −0.860273 0.356337i −0.0914586 0.995809i \(-0.529153\pi\)
−0.768814 + 0.639472i \(0.779153\pi\)
\(758\) 0 0
\(759\) −0.251608 + 0.251608i −0.00913279 + 0.00913279i
\(760\) 0 0
\(761\) −5.35154 5.35154i −0.193993 0.193993i 0.603426 0.797419i \(-0.293802\pi\)
−0.797419 + 0.603426i \(0.793802\pi\)
\(762\) 0 0
\(763\) 3.36226 8.11722i 0.121722 0.293863i
\(764\) 0 0
\(765\) −0.0364686 + 0.0151058i −0.00131852 + 0.000546151i
\(766\) 0 0
\(767\) 6.09394 0.220040
\(768\) 0 0
\(769\) 16.9993 0.613011 0.306505 0.951869i \(-0.400840\pi\)
0.306505 + 0.951869i \(0.400840\pi\)
\(770\) 0 0
\(771\) −8.74002 + 3.62023i −0.314764 + 0.130380i
\(772\) 0 0
\(773\) −16.2444 + 39.2174i −0.584269 + 1.41055i 0.304640 + 0.952467i \(0.401464\pi\)
−0.888910 + 0.458083i \(0.848536\pi\)
\(774\) 0 0
\(775\) 21.9102 + 21.9102i 0.787036 + 0.787036i
\(776\) 0 0
\(777\) 12.8266 12.8266i 0.460151 0.460151i
\(778\) 0 0
\(779\) −30.7887 12.7531i −1.10312 0.456927i
\(780\) 0 0
\(781\) 4.53081 + 10.9383i 0.162125 + 0.391405i
\(782\) 0 0
\(783\) 6.20104i 0.221607i
\(784\) 0 0
\(785\) 0.00704229i 0.000251350i
\(786\) 0 0
\(787\) −1.91880 4.63239i −0.0683978 0.165127i 0.885984 0.463716i \(-0.153484\pi\)
−0.954382 + 0.298589i \(0.903484\pi\)
\(788\) 0 0
\(789\) −9.16896 3.79791i −0.326424 0.135209i
\(790\) 0 0
\(791\) −10.7107 + 10.7107i −0.380827 + 0.380827i
\(792\) 0 0
\(793\) −8.13949 8.13949i −0.289042 0.289042i
\(794\) 0 0
\(795\) −0.0235009 + 0.0567361i −0.000833490 + 0.00201222i
\(796\) 0 0
\(797\) −8.85578 + 3.66818i −0.313688 + 0.129934i −0.533972 0.845502i \(-0.679301\pi\)
0.220285 + 0.975436i \(0.429301\pi\)