Properties

Label 384.2.k.b.287.6
Level $384$
Weight $2$
Character 384.287
Analytic conductor $3.066$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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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 287.6
Root \(-0.204810 + 1.39930i\) of defining polynomial
Character \(\chi\) \(=\) 384.287
Dual form 384.2.k.b.95.6

$q$-expansion

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

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
\(3\) 1.52878 + 0.814141i 0.882643 + 0.470045i
\(4\) 0 0
\(5\) 2.08397 2.08397i 0.931979 0.931979i −0.0658506 0.997829i \(-0.520976\pi\)
0.997829 + 0.0658506i \(0.0209761\pi\)
\(6\) 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 0.912937 0.408102i \(-0.133809\pi\)
−0.408102 + 0.912937i \(0.633809\pi\)
\(12\) 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 \(-0.762517\pi\)
0.734358 0.678762i \(-0.237483\pi\)
\(18\) 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
\(21\) −1.75254 0.933303i −0.382436 0.203663i
\(22\) 0 0
\(23\) 3.34870i 0.698252i 0.937076 + 0.349126i \(0.113521\pi\)
−0.937076 + 0.349126i \(0.886479\pi\)
\(24\) 0 0
\(25\) 3.68585i 0.737169i
\(26\) 0 0
\(27\) 0.533081 + 5.16874i 0.102592 + 0.994724i
\(28\) 0 0
\(29\) −3.51325 3.51325i −0.652394 0.652394i 0.301175 0.953569i \(-0.402621\pi\)
−0.953569 + 0.301175i \(0.902621\pi\)
\(30\) 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 \(-0.515169\pi\)
−0.0476363 + 0.998865i \(0.515169\pi\)
\(42\) 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
\(45\) 8.67689 + 1.69831i 1.29347 + 0.253169i
\(46\) 0 0
\(47\) −6.41646 −0.935936 −0.467968 0.883745i \(-0.655014\pi\)
−0.467968 + 0.883745i \(0.655014\pi\)
\(48\) 0 0
\(49\) −5.68585 −0.812264
\(50\) 0 0
\(51\) 4.55693 8.55693i 0.638097 1.19821i
\(52\) 0 0
\(53\) 0.164553 0.164553i 0.0226031 0.0226031i −0.695715 0.718318i \(-0.744912\pi\)
0.718318 + 0.695715i \(0.244912\pi\)
\(54\) 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 \(-0.936525\pi\)
−0.198093 0.980183i \(-0.563475\pi\)
\(60\) 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
\(69\) −2.72631 + 5.11943i −0.328209 + 0.616307i
\(70\) 0 0
\(71\) 6.90659i 0.819662i −0.912162 0.409831i \(-0.865588\pi\)
0.912162 0.409831i \(-0.134412\pi\)
\(72\) 0 0
\(73\) 7.07896i 0.828530i 0.910156 + 0.414265i \(0.135961\pi\)
−0.910156 + 0.414265i \(0.864039\pi\)
\(74\) 0 0
\(75\) 3.00080 5.63485i 0.346502 0.650657i
\(76\) 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 −0.994339 0.106257i \(-0.966113\pi\)
0.106257 + 0.994339i \(0.466113\pi\)
\(84\) 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 \(-0.508270\pi\)
−0.0259770 + 0.999663i \(0.508270\pi\)
\(90\) 0 0
\(91\) 0.167788 0.167788i 0.0175890 0.0175890i
\(92\) 0 0
\(93\) −4.74824 + 8.91618i −0.492370 + 0.924565i
\(94\) 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
\(99\) −1.36449 + 6.97138i −0.137137 + 0.700650i
\(100\) 0 0
\(101\) −8.29123 + 8.29123i −0.825008 + 0.825008i −0.986821 0.161813i \(-0.948266\pi\)
0.161813 + 0.986821i \(0.448266\pi\)
\(102\) 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 0.671719 0.740806i \(-0.265556\pi\)
−0.740806 + 0.671719i \(0.765556\pi\)
\(108\) 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 \(0.0829419\pi\)
−0.966243 + 0.257631i \(0.917058\pi\)
\(114\) 0 0
\(115\) 6.97858 + 6.97858i 0.650756 + 0.650756i
\(116\) 0 0
\(117\) −0.609413 0.119279i −0.0563402 0.0110274i
\(118\) 0 0
\(119\) 6.41646i 0.588196i
\(120\) 0 0
\(121\) 5.39312i 0.490283i
\(122\) 0 0
\(123\) −0.932621 0.496660i −0.0840916 0.0447824i
\(124\) 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 −0.190869 0.981616i \(-0.561130\pi\)
0.981616 + 0.190869i \(0.0611304\pi\)
\(132\) 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 \(-0.694708\pi\)
−0.574255 + 0.818677i \(0.694708\pi\)
\(138\) 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
\(141\) −9.80936 5.22390i −0.826097 0.439932i
\(142\) 0 0
\(143\) −0.490134 −0.0409870
\(144\) 0 0
\(145\) −14.6430 −1.21603
\(146\) 0 0
\(147\) −8.69242 4.62908i −0.716939 0.381800i
\(148\) 0 0
\(149\) 11.6399 11.6399i 0.953580 0.953580i −0.0453896 0.998969i \(-0.514453\pi\)
0.998969 + 0.0453896i \(0.0144529\pi\)
\(150\) 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
\(165\) 10.6687 + 5.68155i 0.830559 + 0.442308i
\(166\) 0 0
\(167\) 2.36843i 0.183275i −0.995792 0.0916373i \(-0.970790\pi\)
0.995792 0.0916373i \(-0.0292100\pi\)
\(168\) 0 0
\(169\) 12.9572i 0.996704i
\(170\) 0 0
\(171\) 1.21368 6.20086i 0.0928125 0.474191i
\(172\) 0 0
\(173\) 5.22347 + 5.22347i 0.397133 + 0.397133i 0.877221 0.480088i \(-0.159395\pi\)
−0.480088 + 0.877221i \(0.659395\pi\)
\(174\) 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 −0.388462 0.921465i \(-0.626993\pi\)
0.921465 + 0.388462i \(0.126993\pi\)
\(180\) 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
\(189\) −0.611106 5.92526i −0.0444514 0.430999i
\(190\) 0 0
\(191\) 25.5284 1.84717 0.923584 0.383396i \(-0.125246\pi\)
0.923584 + 0.383396i \(0.125246\pi\)
\(192\) 0 0
\(193\) 9.07896 0.653518 0.326759 0.945108i \(-0.394043\pi\)
0.326759 + 0.945108i \(0.394043\pi\)
\(194\) 0 0
\(195\) −0.496660 + 0.932621i −0.0355666 + 0.0667864i
\(196\) 0 0
\(197\) 3.18414 3.18414i 0.226861 0.226861i −0.584519 0.811380i \(-0.698717\pi\)
0.811380 + 0.584519i \(0.198717\pi\)
\(198\) 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
\(213\) 5.62294 10.5587i 0.385277 0.723468i
\(214\) 0 0
\(215\) 6.20726i 0.423332i
\(216\) 0 0
\(217\) 6.68585i 0.453865i
\(218\) 0 0
\(219\) −5.76327 + 10.8222i −0.389446 + 0.731296i
\(220\) 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 −0.656810 0.754056i \(-0.728095\pi\)
0.754056 + 0.656810i \(0.228095\pi\)
\(228\) 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 \(-0.294322\pi\)
0.602121 + 0.798405i \(0.294322\pi\)
\(234\) 0 0
\(235\) −13.3717 + 13.3717i −0.872273 + 0.872273i
\(236\) 0 0
\(237\) 8.00481 15.0313i 0.519968 0.976388i
\(238\) 0 0
\(239\) 13.5322 0.875328 0.437664 0.899139i \(-0.355806\pi\)
0.437664 + 0.899139i \(0.355806\pi\)
\(240\) 0 0
\(241\) 4.87819 0.314232 0.157116 0.987580i \(-0.449780\pi\)
0.157116 + 0.987580i \(0.449780\pi\)
\(242\) 0 0
\(243\) −11.9739 + 9.98126i −0.768127 + 0.640298i
\(244\) 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 0.852684 0.522427i \(-0.174973\pi\)
−0.522427 + 0.852684i \(0.674973\pi\)
\(252\) 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 \(0.131076\pi\)
−0.916407 + 0.400248i \(0.868924\pi\)
\(258\) 0 0
\(259\) −5.53948 5.53948i −0.344207 0.344207i
\(260\) 0 0
\(261\) 2.86309 14.6279i 0.177221 0.905444i
\(262\) 0 0
\(263\) 28.3152i 1.74599i 0.487729 + 0.872995i \(0.337825\pi\)
−0.487729 + 0.872995i \(0.662175\pi\)
\(264\) 0 0
\(265\) 0.685846i 0.0421312i
\(266\) 0 0
\(267\) −0.749307 0.399038i −0.0458569 0.0244207i
\(268\) 0 0
\(269\) 6.58101 + 6.58101i 0.401251 + 0.401251i 0.878674 0.477423i \(-0.158429\pi\)
−0.477423 + 0.878674i \(0.658429\pi\)
\(270\) 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 \(-0.784866\pi\)
−0.780167 + 0.625571i \(0.784866\pi\)
\(282\) 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
\(285\) −9.48955 5.05359i −0.562112 0.299349i
\(286\) 0 0
\(287\) 0.699331 0.0412802
\(288\) 0 0
\(289\) −14.3288 −0.842873
\(290\) 0 0
\(291\) 18.8809 + 10.0549i 1.10682 + 0.589426i
\(292\) 0 0
\(293\) −0.654687 + 0.654687i −0.0382472 + 0.0382472i −0.725972 0.687725i \(-0.758610\pi\)
0.687725 + 0.725972i \(0.258610\pi\)
\(294\) 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
\(309\) −18.6899 9.95314i −1.06323 0.566214i
\(310\) 0 0
\(311\) 33.1343i 1.87887i −0.342723 0.939437i \(-0.611349\pi\)
0.342723 0.939437i \(-0.388651\pi\)
\(312\) 0 0
\(313\) 13.2285i 0.747717i −0.927486 0.373858i \(-0.878035\pi\)
0.927486 0.373858i \(-0.121965\pi\)
\(314\) 0 0
\(315\) −9.94688 1.94688i −0.560443 0.109694i
\(316\) 0 0
\(317\) −7.89038 7.89038i −0.443168 0.443168i 0.449907 0.893075i \(-0.351457\pi\)
−0.893075 + 0.449907i \(0.851457\pi\)
\(318\) 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
\(333\) −3.93796 + 20.1196i −0.215799 + 1.10255i
\(334\) 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
\(339\) −4.45930 + 8.37361i −0.242196 + 0.454792i
\(340\) 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 0.121938 0.992538i \(-0.461089\pi\)
−0.992538 + 0.121938i \(0.961089\pi\)
\(348\) 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 \(0.209141\pi\)
−0.791806 + 0.610772i \(0.790859\pi\)
\(354\) 0 0
\(355\) −14.3931 14.3931i −0.763907 0.763907i
\(356\) 0 0
\(357\) −5.22390 + 9.80936i −0.276478 + 0.519167i
\(358\) 0 0
\(359\) 18.3408i 0.967993i −0.875070 0.483996i \(-0.839185\pi\)
0.875070 0.483996i \(-0.160815\pi\)
\(360\) 0 0
\(361\) 14.5640i 0.766528i
\(362\) 0 0
\(363\) 4.39076 8.24490i 0.230455 0.432745i
\(364\) 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
\(381\) 5.86499 11.0132i 0.300473 0.564223i
\(382\) 0 0
\(383\) −30.7659 −1.57206 −0.786031 0.618187i \(-0.787867\pi\)
−0.786031 + 0.618187i \(0.787867\pi\)
\(384\) 0 0
\(385\) −8.00000 −0.407718
\(386\) 0 0
\(387\) 6.20086 + 1.21368i 0.315207 + 0.0616949i
\(388\) 0 0
\(389\) −11.0299 + 11.0299i −0.559237 + 0.559237i −0.929090 0.369853i \(-0.879408\pi\)
0.369853 + 0.929090i \(0.379408\pi\)
\(390\) 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 \(-0.790780\pi\)
0.791654 0.610970i \(-0.209220\pi\)
\(402\) 0 0
\(403\) −0.853635 0.853635i −0.0425226 0.0425226i
\(404\) 0 0
\(405\) 10.3005 + 24.4428i 0.511838 + 1.21457i
\(406\) 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
\(411\) −20.5513 10.9445i −1.01372 0.539851i
\(412\) 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 −0.615823 0.787885i \(-0.711176\pi\)
0.787885 + 0.615823i \(0.211176\pi\)
\(420\) 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
\(429\) −0.749307 0.399038i −0.0361769 0.0192657i
\(430\) 0 0
\(431\) −12.1336 −0.584454 −0.292227 0.956349i \(-0.594396\pi\)
−0.292227 + 0.956349i \(0.594396\pi\)
\(432\) 0 0
\(433\) −12.1495 −0.583868 −0.291934 0.956439i \(-0.594299\pi\)
−0.291934 + 0.956439i \(0.594299\pi\)
\(434\) 0 0
\(435\) −22.3860 11.9215i −1.07332 0.571591i
\(436\) 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 \(0.170457\pi\)
0.510276 + 0.860011i \(0.329543\pi\)
\(444\) 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 \(-0.926678\pi\)
0.973587 0.228316i \(-0.0733220\pi\)
\(450\) 0 0
\(451\) −1.02142 1.02142i −0.0480969 0.0480969i
\(452\) 0 0
\(453\) −1.23952 0.660097i −0.0582377 0.0310140i
\(454\) 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
\(459\) 28.9305 2.98377i 1.35036 0.139271i
\(460\) 0 0
\(461\) −27.5406 27.5406i −1.28269 1.28269i −0.939129 0.343565i \(-0.888366\pi\)
−0.343565 0.939129i \(-0.611634\pi\)
\(462\) 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 −0.197489 0.980305i \(-0.563279\pi\)
0.980305 + 0.197489i \(0.0632785\pi\)
\(468\) 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
\(477\) 0.685139 + 0.134101i 0.0313703 + 0.00614005i
\(478\) 0 0
\(479\) −18.5500 −0.847573 −0.423786 0.905762i \(-0.639299\pi\)
−0.423786 + 0.905762i \(0.639299\pi\)
\(480\) 0 0
\(481\) −1.41454 −0.0644974
\(482\) 0 0
\(483\) 3.12535 5.86873i 0.142208 0.267037i
\(484\) 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 0.811696 0.584081i \(-0.198545\pi\)
−0.584081 + 0.811696i \(0.698545\pi\)
\(492\) 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
\(501\) 1.92824 3.62081i 0.0861472 0.161766i
\(502\) 0 0
\(503\) 32.7159i 1.45873i 0.684125 + 0.729365i \(0.260184\pi\)
−0.684125 + 0.729365i \(0.739816\pi\)
\(504\) 0 0
\(505\) 34.5573i 1.53778i
\(506\) 0 0
\(507\) −10.5490 + 19.8087i −0.468495 + 0.879734i
\(508\) 0 0
\(509\) 10.1389 + 10.1389i 0.449399 + 0.449399i 0.895155 0.445756i \(-0.147065\pi\)
−0.445756 + 0.895155i \(0.647065\pi\)
\(510\) 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 \(-0.542572\pi\)
−0.133346 + 0.991070i \(0.542572\pi\)
\(522\) 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
\(525\) −3.44001 + 6.45960i −0.150134 + 0.281920i
\(526\) 0 0
\(527\) 32.6442 1.42200
\(528\) 0 0
\(529\) 11.7862 0.512445
\(530\) 0 0
\(531\) 7.37563 37.6831i 0.320075 1.63531i
\(532\) 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
\(549\) −18.9007 3.69941i −0.806664 0.157887i
\(550\) 0 0
\(551\) 10.4645i 0.445802i
\(552\) 0 0
\(553\) 11.2713i 0.479305i
\(554\) 0 0
\(555\) 30.7902 + 16.3971i 1.30697 + 0.696018i
\(556\) 0 0
\(557\) −26.1831 26.1831i −1.10941 1.10941i −0.993228 0.116184i \(-0.962934\pi\)
−0.116184 0.993228i \(-0.537066\pi\)
\(558\) 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 \(0.518182\pi\)
−0.998369 + 0.0570880i \(0.981818\pi\)
\(564\) 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 \(-0.415303\pi\)
0.262955 + 0.964808i \(0.415303\pi\)
\(570\) 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
\(573\) 39.0273 + 20.7837i 1.63039 + 0.868251i
\(574\) 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
\(579\) 13.8798 + 7.39156i 0.576823 + 0.307183i
\(580\) 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 0.909721 0.415220i \(-0.136295\pi\)
−0.415220 + 0.909721i \(0.636295\pi\)
\(588\) 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 \(-0.978567\pi\)
0.997734 0.0672843i \(-0.0214334\pi\)
\(594\) 0 0
\(595\) 13.3717 + 13.3717i 0.548186 + 0.548186i
\(596\) 0 0
\(597\) 29.8941 + 15.9199i 1.22348 + 0.651556i
\(598\) 0 0
\(599\) 38.9889i 1.59304i −0.604611 0.796521i \(-0.706671\pi\)
0.604611 0.796521i \(-0.293329\pi\)
\(600\) 0 0
\(601\) 23.5787i 0.961797i 0.876776 + 0.480898i \(0.159689\pi\)
−0.876776 + 0.480898i \(0.840311\pi\)
\(602\) 0 0
\(603\) −0.518020 + 2.64663i −0.0210954 + 0.107779i
\(604\) 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 \(-0.326648\pi\)
0.518078 + 0.855334i \(0.326648\pi\)
\(618\) 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
\(621\) −17.3085 + 1.78513i −0.694567 + 0.0716347i
\(622\) 0 0
\(623\) 0.561872 0.0225109
\(624\) 0 0
\(625\) 29.8438 1.19375
\(626\) 0 0
\(627\) 4.06027 7.62430i 0.162151 0.304485i
\(628\) 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 \(-0.870283\pi\)
0.918108 0.396331i \(-0.129717\pi\)
\(642\) 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
\(645\) 5.05359 9.48955i 0.198985 0.373651i
\(646\) 0 0
\(647\) 1.95003i 0.0766638i 0.999265 + 0.0383319i \(0.0122044\pi\)
−0.999265 + 0.0383319i \(0.987796\pi\)
\(648\) 0 0
\(649\) 30.3074i 1.18967i
\(650\) 0 0
\(651\) 5.44322 10.2212i 0.213337 0.400600i
\(652\) 0 0
\(653\) 5.80289 + 5.80289i 0.227085 + 0.227085i 0.811474 0.584389i \(-0.198666\pi\)
−0.584389 + 0.811474i \(0.698666\pi\)
\(654\) 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 −0.591986 0.805948i \(-0.701656\pi\)
0.805948 + 0.591986i \(0.201656\pi\)
\(660\) 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
\(669\) −18.4146 + 34.5787i −0.711950 + 1.33689i
\(670\) 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
\(675\) 19.0512 1.96486i 0.733280 0.0756273i
\(676\) 0 0
\(677\) −13.7685 + 13.7685i −0.529168 + 0.529168i −0.920324 0.391156i \(-0.872075\pi\)
0.391156 + 0.920324i \(0.372075\pi\)
\(678\) 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 0.589100 0.808060i \(-0.299483\pi\)
−0.808060 + 0.589100i \(0.799483\pi\)
\(684\) 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
\(693\) 1.56421 7.99175i 0.0594194 0.303581i
\(694\) 0 0
\(695\) 35.9929i 1.36529i
\(696\) 0 0
\(697\) 3.41454i 0.129335i
\(698\) 0 0
\(699\) 28.1020 + 14.9655i 1.06292 + 0.566048i
\(700\) 0 0
\(701\) −10.9100 10.9100i −0.412064 0.412064i 0.470393 0.882457i \(-0.344112\pi\)
−0.882457 + 0.470393i \(0.844112\pi\)
\(702\) 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
\(717\) 20.6879 + 11.0172i 0.772602 + 0.411443i
\(718\) 0 0
\(719\) −30.0665 −1.12129 −0.560646 0.828055i \(-0.689447\pi\)
−0.560646 + 0.828055i \(0.689447\pi\)
\(720\) 0 0
\(721\) 14.0147 0.521934
\(722\) 0 0
\(723\) 7.45769 + 3.97154i 0.277355 + 0.147703i
\(724\) 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
\(741\) 0.666489 + 0.354934i 0.0244841 + 0.0130388i
\(742\) 0 0
\(743\) 0.908529i 0.0333307i 0.999861 + 0.0166653i \(0.00530499\pi\)
−0.999861 + 0.0166653i \(0.994695\pi\)
\(744\) 0 0
\(745\) 48.5145i 1.77743i
\(746\) 0 0
\(747\) −33.6872 6.59352i −1.23255 0.241244i
\(748\) 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 \(-0.687669\pi\)
−0.556012 + 0.831174i \(0.687669\pi\)
\(762\) 0 0
\(763\) −14.3257 + 14.3257i −0.518626 + 0.518626i
\(764\) 0 0
\(765\) 9.50581 48.5664i 0.343683 1.75592i
\(766\) 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
\(771\) −10.4478 + 19.6187i −0.376268 + 0.706551i
\(772\) 0 0
\(773\) −17.6074 + 17.6074i −0.633293 + 0.633293i −0.948892 0.315599i \(-0.897794\pi\)
0.315599 + 0.948892i \(0.397794\pi\)
\(774\) 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
\(789\) −23.0526 + 43.2878i −0.820693 + 1.54108i
\(790\) 0 0
\(791\) 6.27900i 0.223255i
\(792\) 0 0
\(793\) 1.32885i 0.0471887i
\(794\) 0 0
\(795\) 0.558376 1.04851i 0.0198035 0.0371868i
\(796\) 0 0
\(797\) 5.76177 + 5.76177i 0.204092 + 0.204092i 0.801751