Properties

Label 384.2.k.b.287.4
Level $384$
Weight $2$
Character 384.287
Analytic conductor $3.066$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(3.06625543762\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(i)\)
Coefficient field: 12.0.163368480538624.2
Defining polynomial: \(x^{12} - 2 x^{10} - 2 x^{8} + 16 x^{6} - 8 x^{4} - 32 x^{2} + 64\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{7} \)
Twist minimal: no (minimal twist has level 48)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 287.4
Root \(0.204810 - 1.39930i\) of defining polynomial
Character \(\chi\) \(=\) 384.287
Dual form 384.2.k.b.95.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.814141 + 1.52878i) q^{3} +(-2.08397 + 2.08397i) q^{5} -1.14637 q^{7} +(-1.67435 + 2.48929i) q^{9} +O(q^{10})\) \(q+(0.814141 + 1.52878i) q^{3} +(-2.08397 + 2.08397i) q^{5} -1.14637 q^{7} +(-1.67435 + 2.48929i) q^{9} +(-1.67435 - 1.67435i) q^{11} +(-0.146365 + 0.146365i) q^{13} +(-4.88258 - 1.48929i) q^{15} +5.59722i q^{17} +(-1.48929 - 1.48929i) q^{19} +(-0.933303 - 1.75254i) q^{21} -3.34870i q^{23} -3.68585i q^{25} +(-5.16874 - 0.533081i) q^{27} +(3.51325 + 3.51325i) q^{29} +5.83221i q^{31} +(1.19656 - 3.92287i) q^{33} +(2.38899 - 2.38899i) q^{35} +(4.83221 + 4.83221i) q^{37} +(-0.342923 - 0.104599i) q^{39} +0.610042 q^{41} +(1.48929 - 1.48929i) q^{43} +(-1.69831 - 8.67689i) q^{45} +6.41646 q^{47} -5.68585 q^{49} +(-8.55693 + 4.55693i) q^{51} +(-0.164553 + 0.164553i) q^{53} +6.97858 q^{55} +(1.06431 - 3.48929i) q^{57} +(9.05051 + 9.05051i) q^{59} +(-4.53948 + 4.53948i) q^{61} +(1.91942 - 2.85363i) q^{63} -0.610042i q^{65} +(0.635654 + 0.635654i) q^{67} +(5.11943 - 2.72631i) q^{69} +6.90659i q^{71} +7.07896i q^{73} +(5.63485 - 3.00080i) q^{75} +(1.91942 + 1.91942i) q^{77} -9.83221i q^{79} +(-3.39312 - 8.33587i) q^{81} +(8.09081 - 8.09081i) q^{83} +(-11.6644 - 11.6644i) q^{85} +(-2.51071 + 8.23127i) q^{87} +0.490134 q^{89} +(0.167788 - 0.167788i) q^{91} +(-8.91618 + 4.74824i) q^{93} +6.20726 q^{95} +12.3503 q^{97} +(6.97138 - 1.36449i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 2 q^{3} - 8 q^{7} + O(q^{10}) \) \( 12 q + 2 q^{3} - 8 q^{7} + 4 q^{13} + 12 q^{19} + 8 q^{21} - 10 q^{27} - 4 q^{33} + 4 q^{37} + 20 q^{39} - 12 q^{43} + 12 q^{45} - 20 q^{49} - 24 q^{51} + 24 q^{55} - 12 q^{61} - 28 q^{67} - 4 q^{69} + 34 q^{75} - 4 q^{81} - 32 q^{85} - 60 q^{87} + 56 q^{91} - 28 q^{93} - 8 q^{97} + 52 q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(127\) \(133\) \(257\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\) \(-1\)

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
\(3\) 0.814141 + 1.52878i 0.470045 + 0.882643i
\(4\) 0 0
\(5\) −2.08397 + 2.08397i −0.931979 + 0.931979i −0.997829 0.0658506i \(-0.979024\pi\)
0.0658506 + 0.997829i \(0.479024\pi\)
\(6\) 0 0
\(7\) −1.14637 −0.433285 −0.216643 0.976251i \(-0.569511\pi\)
−0.216643 + 0.976251i \(0.569511\pi\)
\(8\) 0 0
\(9\) −1.67435 + 2.48929i −0.558116 + 0.829763i
\(10\) 0 0
\(11\) −1.67435 1.67435i −0.504835 0.504835i 0.408102 0.912937i \(-0.366191\pi\)
−0.912937 + 0.408102i \(0.866191\pi\)
\(12\) 0 0
\(13\) −0.146365 + 0.146365i −0.0405945 + 0.0405945i −0.727113 0.686518i \(-0.759138\pi\)
0.686518 + 0.727113i \(0.259138\pi\)
\(14\) 0 0
\(15\) −4.88258 1.48929i −1.26068 0.384533i
\(16\) 0 0
\(17\) 5.59722i 1.35752i 0.734358 + 0.678762i \(0.237483\pi\)
−0.734358 + 0.678762i \(0.762517\pi\)
\(18\) 0 0
\(19\) −1.48929 1.48929i −0.341666 0.341666i 0.515327 0.856993i \(-0.327670\pi\)
−0.856993 + 0.515327i \(0.827670\pi\)
\(20\) 0 0
\(21\) −0.933303 1.75254i −0.203663 0.382436i
\(22\) 0 0
\(23\) 3.34870i 0.698252i −0.937076 0.349126i \(-0.886479\pi\)
0.937076 0.349126i \(-0.113521\pi\)
\(24\) 0 0
\(25\) 3.68585i 0.737169i
\(26\) 0 0
\(27\) −5.16874 0.533081i −0.994724 0.102592i
\(28\) 0 0
\(29\) 3.51325 + 3.51325i 0.652394 + 0.652394i 0.953569 0.301175i \(-0.0973788\pi\)
−0.301175 + 0.953569i \(0.597379\pi\)
\(30\) 0 0
\(31\) 5.83221i 1.04750i 0.851873 + 0.523748i \(0.175467\pi\)
−0.851873 + 0.523748i \(0.824533\pi\)
\(32\) 0 0
\(33\) 1.19656 3.92287i 0.208294 0.682884i
\(34\) 0 0
\(35\) 2.38899 2.38899i 0.403813 0.403813i
\(36\) 0 0
\(37\) 4.83221 + 4.83221i 0.794411 + 0.794411i 0.982208 0.187797i \(-0.0601348\pi\)
−0.187797 + 0.982208i \(0.560135\pi\)
\(38\) 0 0
\(39\) −0.342923 0.104599i −0.0549116 0.0167492i
\(40\) 0 0
\(41\) 0.610042 0.0952726 0.0476363 0.998865i \(-0.484831\pi\)
0.0476363 + 0.998865i \(0.484831\pi\)
\(42\) 0 0
\(43\) 1.48929 1.48929i 0.227114 0.227114i −0.584372 0.811486i \(-0.698659\pi\)
0.811486 + 0.584372i \(0.198659\pi\)
\(44\) 0 0
\(45\) −1.69831 8.67689i −0.253169 1.29347i
\(46\) 0 0
\(47\) 6.41646 0.935936 0.467968 0.883745i \(-0.344986\pi\)
0.467968 + 0.883745i \(0.344986\pi\)
\(48\) 0 0
\(49\) −5.68585 −0.812264
\(50\) 0 0
\(51\) −8.55693 + 4.55693i −1.19821 + 0.638097i
\(52\) 0 0
\(53\) −0.164553 + 0.164553i −0.0226031 + 0.0226031i −0.718318 0.695715i \(-0.755088\pi\)
0.695715 + 0.718318i \(0.255088\pi\)
\(54\) 0 0
\(55\) 6.97858 0.940991
\(56\) 0 0
\(57\) 1.06431 3.48929i 0.140971 0.462168i
\(58\) 0 0
\(59\) 9.05051 + 9.05051i 1.17828 + 1.17828i 0.980183 + 0.198093i \(0.0634749\pi\)
0.198093 + 0.980183i \(0.436525\pi\)
\(60\) 0 0
\(61\) −4.53948 + 4.53948i −0.581221 + 0.581221i −0.935239 0.354018i \(-0.884815\pi\)
0.354018 + 0.935239i \(0.384815\pi\)
\(62\) 0 0
\(63\) 1.91942 2.85363i 0.241824 0.359524i
\(64\) 0 0
\(65\) 0.610042i 0.0756664i
\(66\) 0 0
\(67\) 0.635654 + 0.635654i 0.0776575 + 0.0776575i 0.744869 0.667211i \(-0.232512\pi\)
−0.667211 + 0.744869i \(0.732512\pi\)
\(68\) 0 0
\(69\) 5.11943 2.72631i 0.616307 0.328209i
\(70\) 0 0
\(71\) 6.90659i 0.819662i 0.912162 + 0.409831i \(0.134412\pi\)
−0.912162 + 0.409831i \(0.865588\pi\)
\(72\) 0 0
\(73\) 7.07896i 0.828530i 0.910156 + 0.414265i \(0.135961\pi\)
−0.910156 + 0.414265i \(0.864039\pi\)
\(74\) 0 0
\(75\) 5.63485 3.00080i 0.650657 0.346502i
\(76\) 0 0
\(77\) 1.91942 + 1.91942i 0.218738 + 0.218738i
\(78\) 0 0
\(79\) 9.83221i 1.10621i −0.833111 0.553105i \(-0.813443\pi\)
0.833111 0.553105i \(-0.186557\pi\)
\(80\) 0 0
\(81\) −3.39312 8.33587i −0.377013 0.926208i
\(82\) 0 0
\(83\) 8.09081 8.09081i 0.888081 0.888081i −0.106257 0.994339i \(-0.533887\pi\)
0.994339 + 0.106257i \(0.0338867\pi\)
\(84\) 0 0
\(85\) −11.6644 11.6644i −1.26518 1.26518i
\(86\) 0 0
\(87\) −2.51071 + 8.23127i −0.269177 + 0.882485i
\(88\) 0 0
\(89\) 0.490134 0.0519541 0.0259770 0.999663i \(-0.491730\pi\)
0.0259770 + 0.999663i \(0.491730\pi\)
\(90\) 0 0
\(91\) 0.167788 0.167788i 0.0175890 0.0175890i
\(92\) 0 0
\(93\) −8.91618 + 4.74824i −0.924565 + 0.492370i
\(94\) 0 0
\(95\) 6.20726 0.636851
\(96\) 0 0
\(97\) 12.3503 1.25398 0.626990 0.779027i \(-0.284287\pi\)
0.626990 + 0.779027i \(0.284287\pi\)
\(98\) 0 0
\(99\) 6.97138 1.36449i 0.700650 0.137137i
\(100\) 0 0
\(101\) 8.29123 8.29123i 0.825008 0.825008i −0.161813 0.986821i \(-0.551734\pi\)
0.986821 + 0.161813i \(0.0517343\pi\)
\(102\) 0 0
\(103\) −12.2253 −1.20460 −0.602299 0.798271i \(-0.705748\pi\)
−0.602299 + 0.798271i \(0.705748\pi\)
\(104\) 0 0
\(105\) 5.59722 + 1.70727i 0.546233 + 0.166612i
\(106\) 0 0
\(107\) 0.714641 + 0.714641i 0.0690869 + 0.0690869i 0.740806 0.671719i \(-0.234444\pi\)
−0.671719 + 0.740806i \(0.734444\pi\)
\(108\) 0 0
\(109\) 12.4966 12.4966i 1.19696 1.19696i 0.221888 0.975072i \(-0.428778\pi\)
0.975072 0.221888i \(-0.0712221\pi\)
\(110\) 0 0
\(111\) −3.45330 + 11.3215i −0.327772 + 1.07459i
\(112\) 0 0
\(113\) 5.47731i 0.515262i −0.966243 0.257631i \(-0.917058\pi\)
0.966243 0.257631i \(-0.0829419\pi\)
\(114\) 0 0
\(115\) 6.97858 + 6.97858i 0.650756 + 0.650756i
\(116\) 0 0
\(117\) −0.119279 0.609413i −0.0110274 0.0563402i
\(118\) 0 0
\(119\) 6.41646i 0.588196i
\(120\) 0 0
\(121\) 5.39312i 0.490283i
\(122\) 0 0
\(123\) 0.496660 + 0.932621i 0.0447824 + 0.0840916i
\(124\) 0 0
\(125\) −2.73865 2.73865i −0.244953 0.244953i
\(126\) 0 0
\(127\) 7.20390i 0.639243i −0.947545 0.319622i \(-0.896444\pi\)
0.947545 0.319622i \(-0.103556\pi\)
\(128\) 0 0
\(129\) 3.48929 + 1.06431i 0.307215 + 0.0937069i
\(130\) 0 0
\(131\) −9.05051 + 9.05051i −0.790747 + 0.790747i −0.981616 0.190869i \(-0.938870\pi\)
0.190869 + 0.981616i \(0.438870\pi\)
\(132\) 0 0
\(133\) 1.70727 + 1.70727i 0.148039 + 0.148039i
\(134\) 0 0
\(135\) 11.8824 9.66056i 1.02267 0.831448i
\(136\) 0 0
\(137\) 13.4430 1.14851 0.574255 0.818677i \(-0.305292\pi\)
0.574255 + 0.818677i \(0.305292\pi\)
\(138\) 0 0
\(139\) −8.63565 + 8.63565i −0.732467 + 0.732467i −0.971108 0.238641i \(-0.923298\pi\)
0.238641 + 0.971108i \(0.423298\pi\)
\(140\) 0 0
\(141\) 5.22390 + 9.80936i 0.439932 + 0.826097i
\(142\) 0 0
\(143\) 0.490134 0.0409870
\(144\) 0 0
\(145\) −14.6430 −1.21603
\(146\) 0 0
\(147\) −4.62908 8.69242i −0.381800 0.716939i
\(148\) 0 0
\(149\) −11.6399 + 11.6399i −0.953580 + 0.953580i −0.998969 0.0453896i \(-0.985547\pi\)
0.0453896 + 0.998969i \(0.485547\pi\)
\(150\) 0 0
\(151\) −0.810789 −0.0659811 −0.0329905 0.999456i \(-0.510503\pi\)
−0.0329905 + 0.999456i \(0.510503\pi\)
\(152\) 0 0
\(153\) −13.9331 9.37169i −1.12642 0.757656i
\(154\) 0 0
\(155\) −12.1541 12.1541i −0.976244 0.976244i
\(156\) 0 0
\(157\) −5.51806 + 5.51806i −0.440389 + 0.440389i −0.892143 0.451754i \(-0.850799\pi\)
0.451754 + 0.892143i \(0.350799\pi\)
\(158\) 0 0
\(159\) −0.385535 0.117596i −0.0305749 0.00932599i
\(160\) 0 0
\(161\) 3.83883i 0.302542i
\(162\) 0 0
\(163\) −10.0748 10.0748i −0.789115 0.789115i 0.192234 0.981349i \(-0.438427\pi\)
−0.981349 + 0.192234i \(0.938427\pi\)
\(164\) 0 0
\(165\) 5.68155 + 10.6687i 0.442308 + 0.830559i
\(166\) 0 0
\(167\) 2.36843i 0.183275i 0.995792 + 0.0916373i \(0.0292100\pi\)
−0.995792 + 0.0916373i \(0.970790\pi\)
\(168\) 0 0
\(169\) 12.9572i 0.996704i
\(170\) 0 0
\(171\) 6.20086 1.21368i 0.474191 0.0928125i
\(172\) 0 0
\(173\) −5.22347 5.22347i −0.397133 0.397133i 0.480088 0.877221i \(-0.340605\pi\)
−0.877221 + 0.480088i \(0.840605\pi\)
\(174\) 0 0
\(175\) 4.22533i 0.319405i
\(176\) 0 0
\(177\) −6.46787 + 21.2047i −0.486155 + 1.59384i
\(178\) 0 0
\(179\) −7.13110 + 7.13110i −0.533003 + 0.533003i −0.921465 0.388462i \(-0.873007\pi\)
0.388462 + 0.921465i \(0.373007\pi\)
\(180\) 0 0
\(181\) 6.73183 + 6.73183i 0.500373 + 0.500373i 0.911554 0.411181i \(-0.134884\pi\)
−0.411181 + 0.911554i \(0.634884\pi\)
\(182\) 0 0
\(183\) −10.6357 3.24410i −0.786210 0.239811i
\(184\) 0 0
\(185\) −20.1403 −1.48075
\(186\) 0 0
\(187\) 9.37169 9.37169i 0.685326 0.685326i
\(188\) 0 0
\(189\) 5.92526 + 0.611106i 0.430999 + 0.0444514i
\(190\) 0 0
\(191\) −25.5284 −1.84717 −0.923584 0.383396i \(-0.874754\pi\)
−0.923584 + 0.383396i \(0.874754\pi\)
\(192\) 0 0
\(193\) 9.07896 0.653518 0.326759 0.945108i \(-0.394043\pi\)
0.326759 + 0.945108i \(0.394043\pi\)
\(194\) 0 0
\(195\) 0.932621 0.496660i 0.0667864 0.0355666i
\(196\) 0 0
\(197\) −3.18414 + 3.18414i −0.226861 + 0.226861i −0.811380 0.584519i \(-0.801283\pi\)
0.584519 + 0.811380i \(0.301283\pi\)
\(198\) 0 0
\(199\) 19.5542 1.38616 0.693079 0.720861i \(-0.256254\pi\)
0.693079 + 0.720861i \(0.256254\pi\)
\(200\) 0 0
\(201\) −0.454264 + 1.48929i −0.0320413 + 0.105046i
\(202\) 0 0
\(203\) −4.02747 4.02747i −0.282673 0.282673i
\(204\) 0 0
\(205\) −1.27131 + 1.27131i −0.0887920 + 0.0887920i
\(206\) 0 0
\(207\) 8.33587 + 5.60688i 0.579383 + 0.389705i
\(208\) 0 0
\(209\) 4.98718i 0.344970i
\(210\) 0 0
\(211\) 10.3429 + 10.3429i 0.712036 + 0.712036i 0.966961 0.254925i \(-0.0820507\pi\)
−0.254925 + 0.966961i \(0.582051\pi\)
\(212\) 0 0
\(213\) −10.5587 + 5.62294i −0.723468 + 0.385277i
\(214\) 0 0
\(215\) 6.20726i 0.423332i
\(216\) 0 0
\(217\) 6.68585i 0.453865i
\(218\) 0 0
\(219\) −10.8222 + 5.76327i −0.731296 + 0.389446i
\(220\) 0 0
\(221\) −0.819240 0.819240i −0.0551080 0.0551080i
\(222\) 0 0
\(223\) 22.6184i 1.51464i 0.653042 + 0.757321i \(0.273492\pi\)
−0.653042 + 0.757321i \(0.726508\pi\)
\(224\) 0 0
\(225\) 9.17513 + 6.17139i 0.611676 + 0.411426i
\(226\) 0 0
\(227\) −1.46515 + 1.46515i −0.0972455 + 0.0972455i −0.754056 0.656810i \(-0.771905\pi\)
0.656810 + 0.754056i \(0.271905\pi\)
\(228\) 0 0
\(229\) 7.51806 + 7.51806i 0.496807 + 0.496807i 0.910443 0.413635i \(-0.135741\pi\)
−0.413635 + 0.910443i \(0.635741\pi\)
\(230\) 0 0
\(231\) −1.37169 + 4.49704i −0.0902507 + 0.295884i
\(232\) 0 0
\(233\) −18.3820 −1.20424 −0.602121 0.798405i \(-0.705678\pi\)
−0.602121 + 0.798405i \(0.705678\pi\)
\(234\) 0 0
\(235\) −13.3717 + 13.3717i −0.872273 + 0.872273i
\(236\) 0 0
\(237\) 15.0313 8.00481i 0.976388 0.519968i
\(238\) 0 0
\(239\) −13.5322 −0.875328 −0.437664 0.899139i \(-0.644194\pi\)
−0.437664 + 0.899139i \(0.644194\pi\)
\(240\) 0 0
\(241\) 4.87819 0.314232 0.157116 0.987580i \(-0.449780\pi\)
0.157116 + 0.987580i \(0.449780\pi\)
\(242\) 0 0
\(243\) 9.98126 11.9739i 0.640298 0.768127i
\(244\) 0 0
\(245\) 11.8491 11.8491i 0.757013 0.757013i
\(246\) 0 0
\(247\) 0.435961 0.0277395
\(248\) 0 0
\(249\) 18.9561 + 5.78202i 1.20130 + 0.366421i
\(250\) 0 0
\(251\) −5.23224 5.23224i −0.330256 0.330256i 0.522427 0.852684i \(-0.325027\pi\)
−0.852684 + 0.522427i \(0.825027\pi\)
\(252\) 0 0
\(253\) −5.60688 + 5.60688i −0.352502 + 0.352502i
\(254\) 0 0
\(255\) 8.33587 27.3288i 0.522013 1.71140i
\(256\) 0 0
\(257\) 12.8329i 0.800495i −0.916407 0.400248i \(-0.868924\pi\)
0.916407 0.400248i \(-0.131076\pi\)
\(258\) 0 0
\(259\) −5.53948 5.53948i −0.344207 0.344207i
\(260\) 0 0
\(261\) −14.6279 + 2.86309i −0.905444 + 0.177221i
\(262\) 0 0
\(263\) 28.3152i 1.74599i −0.487729 0.872995i \(-0.662175\pi\)
0.487729 0.872995i \(-0.337825\pi\)
\(264\) 0 0
\(265\) 0.685846i 0.0421312i
\(266\) 0 0
\(267\) 0.399038 + 0.749307i 0.0244207 + 0.0458569i
\(268\) 0 0
\(269\) −6.58101 6.58101i −0.401251 0.401251i 0.477423 0.878674i \(-0.341571\pi\)
−0.878674 + 0.477423i \(0.841571\pi\)
\(270\) 0 0
\(271\) 8.66129i 0.526136i −0.964777 0.263068i \(-0.915266\pi\)
0.964777 0.263068i \(-0.0847343\pi\)
\(272\) 0 0
\(273\) 0.393115 + 0.119908i 0.0237924 + 0.00725719i
\(274\) 0 0
\(275\) −6.17139 + 6.17139i −0.372149 + 0.372149i
\(276\) 0 0
\(277\) −13.1249 13.1249i −0.788601 0.788601i 0.192664 0.981265i \(-0.438287\pi\)
−0.981265 + 0.192664i \(0.938287\pi\)
\(278\) 0 0
\(279\) −14.5181 9.76515i −0.869173 0.584624i
\(280\) 0 0
\(281\) 26.1560 1.56033 0.780167 0.625571i \(-0.215134\pi\)
0.780167 + 0.625571i \(0.215134\pi\)
\(282\) 0 0
\(283\) 17.9070 17.9070i 1.06446 1.06446i 0.0666843 0.997774i \(-0.478758\pi\)
0.997774 0.0666843i \(-0.0212420\pi\)
\(284\) 0 0
\(285\) 5.05359 + 9.48955i 0.299349 + 0.562112i
\(286\) 0 0
\(287\) −0.699331 −0.0412802
\(288\) 0 0
\(289\) −14.3288 −0.842873
\(290\) 0 0
\(291\) 10.0549 + 18.8809i 0.589426 + 1.10682i
\(292\) 0 0
\(293\) 0.654687 0.654687i 0.0382472 0.0382472i −0.687725 0.725972i \(-0.741390\pi\)
0.725972 + 0.687725i \(0.241390\pi\)
\(294\) 0 0
\(295\) −37.7220 −2.19626
\(296\) 0 0
\(297\) 7.76170 + 9.54683i 0.450379 + 0.553963i
\(298\) 0 0
\(299\) 0.490134 + 0.490134i 0.0283452 + 0.0283452i
\(300\) 0 0
\(301\) −1.70727 + 1.70727i −0.0984054 + 0.0984054i
\(302\) 0 0
\(303\) 19.4257 + 5.92525i 1.11598 + 0.340397i
\(304\) 0 0
\(305\) 18.9203i 1.08337i
\(306\) 0 0
\(307\) 0.971231 + 0.971231i 0.0554311 + 0.0554311i 0.734279 0.678848i \(-0.237520\pi\)
−0.678848 + 0.734279i \(0.737520\pi\)
\(308\) 0 0
\(309\) −9.95314 18.6899i −0.566214 1.06323i
\(310\) 0 0
\(311\) 33.1343i 1.87887i 0.342723 + 0.939437i \(0.388651\pi\)
−0.342723 + 0.939437i \(0.611349\pi\)
\(312\) 0 0
\(313\) 13.2285i 0.747717i −0.927486 0.373858i \(-0.878035\pi\)
0.927486 0.373858i \(-0.121965\pi\)
\(314\) 0 0
\(315\) 1.94688 + 9.94688i 0.109694 + 0.560443i
\(316\) 0 0
\(317\) 7.89038 + 7.89038i 0.443168 + 0.443168i 0.893075 0.449907i \(-0.148543\pi\)
−0.449907 + 0.893075i \(0.648543\pi\)
\(318\) 0 0
\(319\) 11.7648i 0.658703i
\(320\) 0 0
\(321\) −0.510711 + 1.67435i −0.0285051 + 0.0934530i
\(322\) 0 0
\(323\) 8.33587 8.33587i 0.463820 0.463820i
\(324\) 0 0
\(325\) 0.539481 + 0.539481i 0.0299250 + 0.0299250i
\(326\) 0 0
\(327\) 29.2787 + 8.93060i 1.61911 + 0.493864i
\(328\) 0 0
\(329\) −7.35561 −0.405528
\(330\) 0 0
\(331\) 3.02877 3.02877i 0.166476 0.166476i −0.618952 0.785429i \(-0.712443\pi\)
0.785429 + 0.618952i \(0.212443\pi\)
\(332\) 0 0
\(333\) −20.1196 + 3.93796i −1.10255 + 0.215799i
\(334\) 0 0
\(335\) −2.64937 −0.144750
\(336\) 0 0
\(337\) 15.2285 0.829547 0.414774 0.909925i \(-0.363861\pi\)
0.414774 + 0.909925i \(0.363861\pi\)
\(338\) 0 0
\(339\) 8.37361 4.45930i 0.454792 0.242196i
\(340\) 0 0
\(341\) 9.76515 9.76515i 0.528813 0.528813i
\(342\) 0 0
\(343\) 14.5426 0.785227
\(344\) 0 0
\(345\) −4.98718 + 16.3503i −0.268501 + 0.880269i
\(346\) 0 0
\(347\) 16.2175 + 16.2175i 0.870600 + 0.870600i 0.992538 0.121938i \(-0.0389108\pi\)
−0.121938 + 0.992538i \(0.538911\pi\)
\(348\) 0 0
\(349\) 6.14637 6.14637i 0.329007 0.329007i −0.523202 0.852209i \(-0.675263\pi\)
0.852209 + 0.523202i \(0.175263\pi\)
\(350\) 0 0
\(351\) 0.834549 0.678500i 0.0445449 0.0362156i
\(352\) 0 0
\(353\) 22.9507i 1.22154i −0.791806 0.610772i \(-0.790859\pi\)
0.791806 0.610772i \(-0.209141\pi\)
\(354\) 0 0
\(355\) −14.3931 14.3931i −0.763907 0.763907i
\(356\) 0 0
\(357\) 9.80936 5.22390i 0.519167 0.276478i
\(358\) 0 0
\(359\) 18.3408i 0.967993i 0.875070 + 0.483996i \(0.160815\pi\)
−0.875070 + 0.483996i \(0.839185\pi\)
\(360\) 0 0
\(361\) 14.5640i 0.766528i
\(362\) 0 0
\(363\) 8.24490 4.39076i 0.432745 0.230455i
\(364\) 0 0
\(365\) −14.7523 14.7523i −0.772172 0.772172i
\(366\) 0 0
\(367\) 2.86833i 0.149725i 0.997194 + 0.0748627i \(0.0238519\pi\)
−0.997194 + 0.0748627i \(0.976148\pi\)
\(368\) 0 0
\(369\) −1.02142 + 1.51857i −0.0531731 + 0.0790536i
\(370\) 0 0
\(371\) 0.188638 0.188638i 0.00979359 0.00979359i
\(372\) 0 0
\(373\) 17.2253 + 17.2253i 0.891894 + 0.891894i 0.994701 0.102808i \(-0.0327826\pi\)
−0.102808 + 0.994701i \(0.532783\pi\)
\(374\) 0 0
\(375\) 1.95715 6.41646i 0.101067 0.331344i
\(376\) 0 0
\(377\) −1.02844 −0.0529672
\(378\) 0 0
\(379\) −5.83956 + 5.83956i −0.299958 + 0.299958i −0.840997 0.541039i \(-0.818031\pi\)
0.541039 + 0.840997i \(0.318031\pi\)
\(380\) 0 0
\(381\) 11.0132 5.86499i 0.564223 0.300473i
\(382\) 0 0
\(383\) 30.7659 1.57206 0.786031 0.618187i \(-0.212133\pi\)
0.786031 + 0.618187i \(0.212133\pi\)
\(384\) 0 0
\(385\) −8.00000 −0.407718
\(386\) 0 0
\(387\) 1.21368 + 6.20086i 0.0616949 + 0.315207i
\(388\) 0 0
\(389\) 11.0299 11.0299i 0.559237 0.559237i −0.369853 0.929090i \(-0.620592\pi\)
0.929090 + 0.369853i \(0.120592\pi\)
\(390\) 0 0
\(391\) 18.7434 0.947894
\(392\) 0 0
\(393\) −21.2047 6.46787i −1.06963 0.326261i
\(394\) 0 0
\(395\) 20.4900 + 20.4900i 1.03096 + 1.03096i
\(396\) 0 0
\(397\) 1.75325 1.75325i 0.0879931 0.0879931i −0.661740 0.749733i \(-0.730182\pi\)
0.749733 + 0.661740i \(0.230182\pi\)
\(398\) 0 0
\(399\) −1.22008 + 4.00000i −0.0610806 + 0.200250i
\(400\) 0 0
\(401\) 24.4693i 1.22194i 0.791654 + 0.610970i \(0.209220\pi\)
−0.791654 + 0.610970i \(0.790780\pi\)
\(402\) 0 0
\(403\) −0.853635 0.853635i −0.0425226 0.0425226i
\(404\) 0 0
\(405\) 24.4428 + 10.3005i 1.21457 + 0.511838i
\(406\) 0 0
\(407\) 16.1816i 0.802093i
\(408\) 0 0
\(409\) 8.78623i 0.434451i 0.976121 + 0.217226i \(0.0697007\pi\)
−0.976121 + 0.217226i \(0.930299\pi\)
\(410\) 0 0
\(411\) 10.9445 + 20.5513i 0.539851 + 1.01372i
\(412\) 0 0
\(413\) −10.3752 10.3752i −0.510530 0.510530i
\(414\) 0 0
\(415\) 33.7220i 1.65535i
\(416\) 0 0
\(417\) −20.2327 6.17139i −0.990798 0.302214i
\(418\) 0 0
\(419\) −3.52202 + 3.52202i −0.172062 + 0.172062i −0.787885 0.615823i \(-0.788824\pi\)
0.615823 + 0.787885i \(0.288824\pi\)
\(420\) 0 0
\(421\) −11.2253 11.2253i −0.547089 0.547089i 0.378509 0.925598i \(-0.376437\pi\)
−0.925598 + 0.378509i \(0.876437\pi\)
\(422\) 0 0
\(423\) −10.7434 + 15.9724i −0.522361 + 0.776605i
\(424\) 0 0
\(425\) 20.6305 1.00073
\(426\) 0 0
\(427\) 5.20390 5.20390i 0.251835 0.251835i
\(428\) 0 0
\(429\) 0.399038 + 0.749307i 0.0192657 + 0.0361769i
\(430\) 0 0
\(431\) 12.1336 0.584454 0.292227 0.956349i \(-0.405604\pi\)
0.292227 + 0.956349i \(0.405604\pi\)
\(432\) 0 0
\(433\) −12.1495 −0.583868 −0.291934 0.956439i \(-0.594299\pi\)
−0.291934 + 0.956439i \(0.594299\pi\)
\(434\) 0 0
\(435\) −11.9215 22.3860i −0.571591 1.07332i
\(436\) 0 0
\(437\) −4.98718 + 4.98718i −0.238569 + 0.238569i
\(438\) 0 0
\(439\) 27.1035 1.29358 0.646790 0.762668i \(-0.276111\pi\)
0.646790 + 0.762668i \(0.276111\pi\)
\(440\) 0 0
\(441\) 9.52009 14.1537i 0.453337 0.673986i
\(442\) 0 0
\(443\) −28.8412 28.8412i −1.37029 1.37029i −0.860011 0.510276i \(-0.829543\pi\)
−0.510276 0.860011i \(-0.670457\pi\)
\(444\) 0 0
\(445\) −1.02142 + 1.02142i −0.0484201 + 0.0484201i
\(446\) 0 0
\(447\) −27.2714 8.31836i −1.28990 0.393445i
\(448\) 0 0
\(449\) 9.67586i 0.456632i 0.973587 + 0.228316i \(0.0733220\pi\)
−0.973587 + 0.228316i \(0.926678\pi\)
\(450\) 0 0
\(451\) −1.02142 1.02142i −0.0480969 0.0480969i
\(452\) 0 0
\(453\) −0.660097 1.23952i −0.0310140 0.0582377i
\(454\) 0 0
\(455\) 0.699331i 0.0327851i
\(456\) 0 0
\(457\) 4.20077i 0.196504i −0.995162 0.0982518i \(-0.968675\pi\)
0.995162 0.0982518i \(-0.0313251\pi\)
\(458\) 0 0
\(459\) 2.98377 28.9305i 0.139271 1.35036i
\(460\) 0 0
\(461\) 27.5406 + 27.5406i 1.28269 + 1.28269i 0.939129 + 0.343565i \(0.111634\pi\)
0.343565 + 0.939129i \(0.388366\pi\)
\(462\) 0 0
\(463\) 37.4109i 1.73863i −0.494255 0.869317i \(-0.664559\pi\)
0.494255 0.869317i \(-0.335441\pi\)
\(464\) 0 0
\(465\) 8.68585 28.4762i 0.402796 1.32055i
\(466\) 0 0
\(467\) −16.9168 + 16.9168i −0.782817 + 0.782817i −0.980305 0.197489i \(-0.936721\pi\)
0.197489 + 0.980305i \(0.436721\pi\)
\(468\) 0 0
\(469\) −0.728692 0.728692i −0.0336479 0.0336479i
\(470\) 0 0
\(471\) −12.9284 3.94343i −0.595709 0.181704i
\(472\) 0 0
\(473\) −4.98718 −0.229311
\(474\) 0 0
\(475\) −5.48929 + 5.48929i −0.251866 + 0.251866i
\(476\) 0 0
\(477\) −0.134101 0.685139i −0.00614005 0.0313703i
\(478\) 0 0
\(479\) 18.5500 0.847573 0.423786 0.905762i \(-0.360701\pi\)
0.423786 + 0.905762i \(0.360701\pi\)
\(480\) 0 0
\(481\) −1.41454 −0.0644974
\(482\) 0 0
\(483\) −5.86873 + 3.12535i −0.267037 + 0.142208i
\(484\) 0 0
\(485\) −25.7376 + 25.7376i −1.16868 + 1.16868i
\(486\) 0 0
\(487\) −40.9259 −1.85453 −0.927264 0.374408i \(-0.877846\pi\)
−0.927264 + 0.374408i \(0.877846\pi\)
\(488\) 0 0
\(489\) 7.19983 23.6044i 0.325587 1.06743i
\(490\) 0 0
\(491\) −5.04360 5.04360i −0.227615 0.227615i 0.584081 0.811696i \(-0.301455\pi\)
−0.811696 + 0.584081i \(0.801455\pi\)
\(492\) 0 0
\(493\) −19.6644 + 19.6644i −0.885641 + 0.885641i
\(494\) 0 0
\(495\) −11.6846 + 17.3717i −0.525182 + 0.780800i
\(496\) 0 0
\(497\) 7.91748i 0.355147i
\(498\) 0 0
\(499\) 11.4647 + 11.4647i 0.513232 + 0.513232i 0.915515 0.402283i \(-0.131783\pi\)
−0.402283 + 0.915515i \(0.631783\pi\)
\(500\) 0 0
\(501\) −3.62081 + 1.92824i −0.161766 + 0.0861472i
\(502\) 0 0
\(503\) 32.7159i 1.45873i −0.684125 0.729365i \(-0.739816\pi\)
0.684125 0.729365i \(-0.260184\pi\)
\(504\) 0 0
\(505\) 34.5573i 1.53778i
\(506\) 0 0
\(507\) −19.8087 + 10.5490i −0.879734 + 0.468495i
\(508\) 0 0
\(509\) −10.1389 10.1389i −0.449399 0.449399i 0.445756 0.895155i \(-0.352935\pi\)
−0.895155 + 0.445756i \(0.852935\pi\)
\(510\) 0 0
\(511\) 8.11508i 0.358990i
\(512\) 0 0
\(513\) 6.90383 + 8.49165i 0.304811 + 0.374916i
\(514\) 0 0
\(515\) 25.4772 25.4772i 1.12266 1.12266i
\(516\) 0 0
\(517\) −10.7434 10.7434i −0.472494 0.472494i
\(518\) 0 0
\(519\) 3.73290 12.2382i 0.163856 0.537197i
\(520\) 0 0
\(521\) 6.08735 0.266692 0.133346 0.991070i \(-0.457428\pi\)
0.133346 + 0.991070i \(0.457428\pi\)
\(522\) 0 0
\(523\) −15.8824 + 15.8824i −0.694489 + 0.694489i −0.963216 0.268727i \(-0.913397\pi\)
0.268727 + 0.963216i \(0.413397\pi\)
\(524\) 0 0
\(525\) −6.45960 + 3.44001i −0.281920 + 0.150134i
\(526\) 0 0
\(527\) −32.6442 −1.42200
\(528\) 0 0
\(529\) 11.7862 0.512445
\(530\) 0 0
\(531\) −37.6831 + 7.37563i −1.63531 + 0.320075i
\(532\) 0 0
\(533\) −0.0892891 + 0.0892891i −0.00386754 + 0.00386754i
\(534\) 0 0
\(535\) −2.97858 −0.128775
\(536\) 0 0
\(537\) −16.7076 5.09617i −0.720987 0.219916i
\(538\) 0 0
\(539\) 9.52009 + 9.52009i 0.410059 + 0.410059i
\(540\) 0 0
\(541\) 25.6184 25.6184i 1.10142 1.10142i 0.107184 0.994239i \(-0.465817\pi\)
0.994239 0.107184i \(-0.0341833\pi\)
\(542\) 0 0
\(543\) −4.81084 + 15.7722i −0.206453 + 0.676848i
\(544\) 0 0
\(545\) 52.0852i 2.23108i
\(546\) 0 0
\(547\) 27.2113 + 27.2113i 1.16347 + 1.16347i 0.983711 + 0.179758i \(0.0575315\pi\)
0.179758 + 0.983711i \(0.442468\pi\)
\(548\) 0 0
\(549\) −3.69941 18.9007i −0.157887 0.806664i
\(550\) 0 0
\(551\) 10.4645i 0.445802i
\(552\) 0 0
\(553\) 11.2713i 0.479305i
\(554\) 0 0
\(555\) −16.3971 30.7902i −0.696018 1.30697i
\(556\) 0 0
\(557\) 26.1831 + 26.1831i 1.10941 + 1.10941i 0.993228 + 0.116184i \(0.0370662\pi\)
0.116184 + 0.993228i \(0.462934\pi\)
\(558\) 0 0
\(559\) 0.435961i 0.0184392i
\(560\) 0 0
\(561\) 21.9572 + 6.69739i 0.927032 + 0.282764i
\(562\) 0 0
\(563\) 25.0435 25.0435i 1.05546 1.05546i 0.0570880 0.998369i \(-0.481818\pi\)
0.998369 0.0570880i \(-0.0181816\pi\)
\(564\) 0 0
\(565\) 11.4145 + 11.4145i 0.480213 + 0.480213i
\(566\) 0 0
\(567\) 3.88975 + 9.55596i 0.163354 + 0.401312i
\(568\) 0 0
\(569\) −12.5449 −0.525911 −0.262955 0.964808i \(-0.584697\pi\)
−0.262955 + 0.964808i \(0.584697\pi\)
\(570\) 0 0
\(571\) 4.48615 4.48615i 0.187740 0.187740i −0.606979 0.794718i \(-0.707619\pi\)
0.794718 + 0.606979i \(0.207619\pi\)
\(572\) 0 0
\(573\) −20.7837 39.0273i −0.868251 1.63039i
\(574\) 0 0
\(575\) −12.3428 −0.514730
\(576\) 0 0
\(577\) 4.48508 0.186716 0.0933581 0.995633i \(-0.470240\pi\)
0.0933581 + 0.995633i \(0.470240\pi\)
\(578\) 0 0
\(579\) 7.39156 + 13.8798i 0.307183 + 0.576823i
\(580\) 0 0
\(581\) −9.27502 + 9.27502i −0.384793 + 0.384793i
\(582\) 0 0
\(583\) 0.551038 0.0228217
\(584\) 0 0
\(585\) 1.51857 + 1.02142i 0.0627852 + 0.0422306i
\(586\) 0 0
\(587\) −11.9808 11.9808i −0.494501 0.494501i 0.415220 0.909721i \(-0.363705\pi\)
−0.909721 + 0.415220i \(0.863705\pi\)
\(588\) 0 0
\(589\) 8.68585 8.68585i 0.357894 0.357894i
\(590\) 0 0
\(591\) −7.46020 2.27552i −0.306872 0.0936023i
\(592\) 0 0
\(593\) 3.27696i 0.134569i 0.997734 + 0.0672843i \(0.0214334\pi\)
−0.997734 + 0.0672843i \(0.978567\pi\)
\(594\) 0 0
\(595\) 13.3717 + 13.3717i 0.548186 + 0.548186i
\(596\) 0 0
\(597\) 15.9199 + 29.8941i 0.651556 + 1.22348i
\(598\) 0 0
\(599\) 38.9889i 1.59304i 0.604611 + 0.796521i \(0.293329\pi\)
−0.604611 + 0.796521i \(0.706671\pi\)
\(600\) 0 0
\(601\) 23.5787i 0.961797i 0.876776 + 0.480898i \(0.159689\pi\)
−0.876776 + 0.480898i \(0.840311\pi\)
\(602\) 0 0
\(603\) −2.64663 + 0.518020i −0.107779 + 0.0210954i
\(604\) 0 0
\(605\) 11.2391 + 11.2391i 0.456934 + 0.456934i
\(606\) 0 0
\(607\) 22.2829i 0.904434i 0.891908 + 0.452217i \(0.149367\pi\)
−0.891908 + 0.452217i \(0.850633\pi\)
\(608\) 0 0
\(609\) 2.87819 9.43605i 0.116630 0.382368i
\(610\) 0 0
\(611\) −0.939148 + 0.939148i −0.0379939 + 0.0379939i
\(612\) 0 0
\(613\) −22.1611 22.1611i −0.895077 0.895077i 0.0999189 0.994996i \(-0.468142\pi\)
−0.994996 + 0.0999189i \(0.968142\pi\)
\(614\) 0 0
\(615\) −2.97858 0.908529i −0.120108 0.0366354i
\(616\) 0 0
\(617\) −25.7376 −1.03616 −0.518078 0.855334i \(-0.673352\pi\)
−0.518078 + 0.855334i \(0.673352\pi\)
\(618\) 0 0
\(619\) −7.71462 + 7.71462i −0.310077 + 0.310077i −0.844939 0.534863i \(-0.820363\pi\)
0.534863 + 0.844939i \(0.320363\pi\)
\(620\) 0 0
\(621\) −1.78513 + 17.3085i −0.0716347 + 0.694567i
\(622\) 0 0
\(623\) −0.561872 −0.0225109
\(624\) 0 0
\(625\) 29.8438 1.19375
\(626\) 0 0
\(627\) −7.62430 + 4.06027i −0.304485 + 0.162151i
\(628\) 0 0
\(629\) −27.0469 + 27.0469i −1.07843 + 1.07843i
\(630\) 0 0
\(631\) 2.26817 0.0902945 0.0451473 0.998980i \(-0.485624\pi\)
0.0451473 + 0.998980i \(0.485624\pi\)
\(632\) 0 0
\(633\) −7.39147 + 24.2327i −0.293785 + 0.963162i
\(634\) 0 0
\(635\) 15.0127 + 15.0127i 0.595761 + 0.595761i
\(636\) 0 0
\(637\) 0.832212 0.832212i 0.0329734 0.0329734i
\(638\) 0 0
\(639\) −17.1925 11.5640i −0.680125 0.457466i
\(640\) 0 0
\(641\) 20.0686i 0.792662i 0.918108 + 0.396331i \(0.129717\pi\)
−0.918108 + 0.396331i \(0.870283\pi\)
\(642\) 0 0
\(643\) −14.0748 14.0748i −0.555054 0.555054i 0.372841 0.927895i \(-0.378384\pi\)
−0.927895 + 0.372841i \(0.878384\pi\)
\(644\) 0 0
\(645\) −9.48955 + 5.05359i −0.373651 + 0.198985i
\(646\) 0 0
\(647\) 1.95003i 0.0766638i −0.999265 0.0383319i \(-0.987796\pi\)
0.999265 0.0383319i \(-0.0122044\pi\)
\(648\) 0 0
\(649\) 30.3074i 1.18967i
\(650\) 0 0
\(651\) 10.2212 5.44322i 0.400600 0.213337i
\(652\) 0 0
\(653\) −5.80289 5.80289i −0.227085 0.227085i 0.584389 0.811474i \(-0.301334\pi\)
−0.811474 + 0.584389i \(0.801334\pi\)
\(654\) 0 0
\(655\) 37.7220i 1.47392i
\(656\) 0 0
\(657\) −17.6216 11.8526i −0.687483 0.462416i
\(658\) 0 0
\(659\) −5.49262 + 5.49262i −0.213962 + 0.213962i −0.805948 0.591986i \(-0.798344\pi\)
0.591986 + 0.805948i \(0.298344\pi\)
\(660\) 0 0
\(661\) 5.86833 + 5.86833i 0.228251 + 0.228251i 0.811962 0.583710i \(-0.198400\pi\)
−0.583710 + 0.811962i \(0.698400\pi\)
\(662\) 0 0
\(663\) 0.585462 1.91942i 0.0227375 0.0745439i
\(664\) 0 0
\(665\) −7.11579 −0.275938
\(666\) 0 0
\(667\) 11.7648 11.7648i 0.455535 0.455535i
\(668\) 0 0
\(669\) −34.5787 + 18.4146i −1.33689 + 0.711950i
\(670\) 0 0
\(671\) 15.2013 0.586841
\(672\) 0 0
\(673\) −22.8929 −0.882456 −0.441228 0.897395i \(-0.645457\pi\)
−0.441228 + 0.897395i \(0.645457\pi\)
\(674\) 0 0
\(675\) −1.96486 + 19.0512i −0.0756273 + 0.733280i
\(676\) 0 0
\(677\) 13.7685 13.7685i 0.529168 0.529168i −0.391156 0.920324i \(-0.627925\pi\)
0.920324 + 0.391156i \(0.127925\pi\)
\(678\) 0 0
\(679\) −14.1579 −0.543331
\(680\) 0 0
\(681\) −3.43274 1.04706i −0.131543 0.0401233i
\(682\) 0 0
\(683\) 5.72238 + 5.72238i 0.218961 + 0.218961i 0.808060 0.589100i \(-0.200517\pi\)
−0.589100 + 0.808060i \(0.700517\pi\)
\(684\) 0 0
\(685\) −28.0147 + 28.0147i −1.07039 + 1.07039i
\(686\) 0 0
\(687\) −5.37271 + 17.6142i −0.204982 + 0.672025i
\(688\) 0 0
\(689\) 0.0481697i 0.00183512i
\(690\) 0 0
\(691\) −24.2327 24.2327i −0.921854 0.921854i 0.0753061 0.997160i \(-0.476007\pi\)
−0.997160 + 0.0753061i \(0.976007\pi\)
\(692\) 0 0
\(693\) −7.99175 + 1.56421i −0.303581 + 0.0594194i
\(694\) 0 0
\(695\) 35.9929i 1.36529i
\(696\) 0 0
\(697\) 3.41454i 0.129335i
\(698\) 0 0
\(699\) −14.9655 28.1020i −0.566048 1.06292i
\(700\) 0 0
\(701\) 10.9100 + 10.9100i 0.412064 + 0.412064i 0.882457 0.470393i \(-0.155888\pi\)
−0.470393 + 0.882457i \(0.655888\pi\)
\(702\) 0 0
\(703\) 14.3931i 0.542847i
\(704\) 0 0
\(705\) −31.3288 9.55596i −1.17991 0.359898i
\(706\) 0 0
\(707\) −9.50478 + 9.50478i −0.357464 + 0.357464i
\(708\) 0 0
\(709\) 14.0031 + 14.0031i 0.525899 + 0.525899i 0.919347 0.393448i \(-0.128718\pi\)
−0.393448 + 0.919347i \(0.628718\pi\)
\(710\) 0 0
\(711\) 24.4752 + 16.4625i 0.917892 + 0.617394i
\(712\) 0 0
\(713\) 19.5303 0.731416
\(714\) 0 0
\(715\) −1.02142 + 1.02142i −0.0381990 + 0.0381990i
\(716\) 0 0
\(717\) −11.0172 20.6879i −0.411443 0.772602i
\(718\) 0 0
\(719\) 30.0665 1.12129 0.560646 0.828055i \(-0.310553\pi\)
0.560646 + 0.828055i \(0.310553\pi\)
\(720\) 0 0
\(721\) 14.0147 0.521934
\(722\) 0 0
\(723\) 3.97154 + 7.45769i 0.147703 + 0.277355i
\(724\) 0 0
\(725\) 12.9493 12.9493i 0.480925 0.480925i
\(726\) 0 0
\(727\) 9.48194 0.351666 0.175833 0.984420i \(-0.443738\pi\)
0.175833 + 0.984420i \(0.443738\pi\)
\(728\) 0 0
\(729\) 26.4316 + 5.51071i 0.978950 + 0.204100i
\(730\) 0 0
\(731\) 8.33587 + 8.33587i 0.308313 + 0.308313i
\(732\) 0 0
\(733\) 29.4752 29.4752i 1.08869 1.08869i 0.0930283 0.995663i \(-0.470345\pi\)
0.995663 0.0930283i \(-0.0296547\pi\)
\(734\) 0 0
\(735\) 27.7616 + 8.46787i 1.02400 + 0.312342i
\(736\) 0 0
\(737\) 2.12861i 0.0784085i
\(738\) 0 0
\(739\) −22.1077 22.1077i −0.813246 0.813246i 0.171873 0.985119i \(-0.445018\pi\)
−0.985119 + 0.171873i \(0.945018\pi\)
\(740\) 0 0
\(741\) 0.354934 + 0.666489i 0.0130388 + 0.0244841i
\(742\) 0 0
\(743\) 0.908529i 0.0333307i −0.999861 0.0166653i \(-0.994695\pi\)
0.999861 0.0166653i \(-0.00530499\pi\)
\(744\) 0 0
\(745\) 48.5145i 1.77743i
\(746\) 0 0
\(747\) 6.59352 + 33.6872i 0.241244 + 1.23255i
\(748\) 0 0
\(749\) −0.819240 0.819240i −0.0299344 0.0299344i
\(750\) 0 0
\(751\) 39.1182i 1.42744i 0.700429 + 0.713722i \(0.252992\pi\)
−0.700429 + 0.713722i \(0.747008\pi\)
\(752\) 0 0
\(753\) 3.73917 12.2587i 0.136263 0.446733i
\(754\) 0 0
\(755\) 1.68966 1.68966i 0.0614930 0.0614930i
\(756\) 0 0
\(757\) 8.97544 + 8.97544i 0.326218 + 0.326218i 0.851146 0.524928i \(-0.175908\pi\)
−0.524928 + 0.851146i \(0.675908\pi\)
\(758\) 0 0
\(759\) −13.1365 4.00691i −0.476825 0.145442i
\(760\) 0 0
\(761\) 30.6766 1.11202 0.556012 0.831174i \(-0.312331\pi\)
0.556012 + 0.831174i \(0.312331\pi\)
\(762\) 0 0
\(763\) −14.3257 + 14.3257i −0.518626 + 0.518626i
\(764\) 0 0
\(765\) 48.5664 9.50581i 1.75592 0.343683i
\(766\) 0 0
\(767\) −2.64937 −0.0956630
\(768\) 0 0
\(769\) −41.7795 −1.50661 −0.753304 0.657673i \(-0.771541\pi\)
−0.753304 + 0.657673i \(0.771541\pi\)
\(770\) 0 0
\(771\) 19.6187 10.4478i 0.706551 0.376268i
\(772\) 0 0
\(773\) 17.6074 17.6074i 0.633293 0.633293i −0.315599 0.948892i \(-0.602206\pi\)
0.948892 + 0.315599i \(0.102206\pi\)
\(774\) 0 0
\(775\) 21.4966 0.772182
\(776\) 0 0
\(777\) 3.95874 12.9786i 0.142019 0.465604i
\(778\) 0 0
\(779\) −0.908529 0.908529i −0.0325514 0.0325514i
\(780\) 0 0
\(781\) 11.5640 11.5640i 0.413794 0.413794i
\(782\) 0 0
\(783\) −16.2862 20.0319i −0.582022 0.715882i
\(784\) 0 0
\(785\) 22.9989i 0.820866i
\(786\) 0 0
\(787\) −1.69006 1.69006i −0.0602440 0.0602440i 0.676343 0.736587i \(-0.263564\pi\)
−0.736587 + 0.676343i \(0.763564\pi\)
\(788\) 0 0
\(789\) 43.2878 23.0526i 1.54108 0.820693i
\(790\) 0 0
\(791\) 6.27900i 0.223255i
\(792\) 0 0
\(793\) 1.32885i 0.0471887i
\(794\) 0 0
\(795\) 1.04851 0.558376i 0.0371868 0.0198035i
\(796\) 0 0
\(797\) −5.76177 5.76177i −0.204092 0.204092i 0.597658