Properties

Label 2268.2.i.n.2053.4
Level $2268$
Weight $2$
Character 2268.2053
Analytic conductor $18.110$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2268.i (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.1100711784\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 9 x^{14} + 31 x^{12} - 282 x^{10} + 1695 x^{8} - 3318 x^{6} + 4606 x^{4} - 4116 x^{2} + 2401\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 3^{7} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 2053.4
Root \(1.30887 + 2.01944i\) of defining polynomial
Character \(\chi\) \(=\) 2268.2053
Dual form 2268.2.i.n.865.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.171869 - 0.297685i) q^{5} +(0.271847 + 2.63175i) q^{7} +O(q^{10})\) \(q+(-0.171869 - 0.297685i) q^{5} +(0.271847 + 2.63175i) q^{7} +(-2.45988 + 4.26064i) q^{11} +(0.974162 - 1.68730i) q^{13} +(2.07359 + 3.59156i) q^{17} +(0.202315 - 0.350420i) q^{19} +(-1.37943 - 2.38925i) q^{23} +(2.44092 - 4.22780i) q^{25} +(1.63861 + 2.83815i) q^{29} -3.28647 q^{31} +(0.736710 - 0.533240i) q^{35} +(-3.38925 + 5.87035i) q^{37} +(-2.81250 + 4.87139i) q^{41} +(-4.96295 - 8.59608i) q^{43} -13.2008 q^{47} +(-6.85220 + 1.43087i) q^{49} +(1.38163 + 2.39306i) q^{53} +1.69110 q^{55} -8.45121 q^{59} +10.7561 q^{61} -0.669711 q^{65} -8.42554 q^{67} -5.08888 q^{71} +(4.58416 + 7.94000i) q^{73} +(-11.8816 - 5.31554i) q^{77} +4.49202 q^{79} +(4.62966 + 8.01880i) q^{83} +(0.712770 - 1.23455i) q^{85} +(3.54253 - 6.13584i) q^{89} +(4.70537 + 2.10506i) q^{91} -0.139086 q^{95} +(-1.31231 - 2.27299i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 6 q^{7} + O(q^{10}) \) \( 16 q - 6 q^{7} + 10 q^{13} + 8 q^{19} + 16 q^{31} - 4 q^{37} - 10 q^{43} + 10 q^{49} - 32 q^{55} - 56 q^{61} - 36 q^{67} + 40 q^{79} - 38 q^{85} - 2 q^{91} + 42 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(1135\) \(1541\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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 0
\(4\) 0 0
\(5\) −0.171869 0.297685i −0.0768620 0.133129i 0.825032 0.565085i \(-0.191157\pi\)
−0.901894 + 0.431956i \(0.857823\pi\)
\(6\) 0 0
\(7\) 0.271847 + 2.63175i 0.102749 + 0.994707i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −2.45988 + 4.26064i −0.741682 + 1.28463i 0.210048 + 0.977691i \(0.432638\pi\)
−0.951729 + 0.306939i \(0.900695\pi\)
\(12\) 0 0
\(13\) 0.974162 1.68730i 0.270184 0.467972i −0.698725 0.715391i \(-0.746249\pi\)
0.968909 + 0.247418i \(0.0795821\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.07359 + 3.59156i 0.502919 + 0.871082i 0.999994 + 0.00337409i \(0.00107401\pi\)
−0.497075 + 0.867708i \(0.665593\pi\)
\(18\) 0 0
\(19\) 0.202315 0.350420i 0.0464142 0.0803918i −0.841885 0.539657i \(-0.818554\pi\)
0.888299 + 0.459265i \(0.151887\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −1.37943 2.38925i −0.287631 0.498192i 0.685612 0.727967i \(-0.259535\pi\)
−0.973244 + 0.229774i \(0.926201\pi\)
\(24\) 0 0
\(25\) 2.44092 4.22780i 0.488184 0.845560i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 1.63861 + 2.83815i 0.304282 + 0.527031i 0.977101 0.212775i \(-0.0682503\pi\)
−0.672819 + 0.739807i \(0.734917\pi\)
\(30\) 0 0
\(31\) −3.28647 −0.590268 −0.295134 0.955456i \(-0.595364\pi\)
−0.295134 + 0.955456i \(0.595364\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0.736710 0.533240i 0.124527 0.0901340i
\(36\) 0 0
\(37\) −3.38925 + 5.87035i −0.557189 + 0.965079i 0.440541 + 0.897733i \(0.354787\pi\)
−0.997730 + 0.0673466i \(0.978547\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −2.81250 + 4.87139i −0.439238 + 0.760783i −0.997631 0.0687936i \(-0.978085\pi\)
0.558392 + 0.829577i \(0.311418\pi\)
\(42\) 0 0
\(43\) −4.96295 8.59608i −0.756843 1.31089i −0.944453 0.328647i \(-0.893407\pi\)
0.187610 0.982244i \(-0.439926\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −13.2008 −1.92553 −0.962764 0.270344i \(-0.912862\pi\)
−0.962764 + 0.270344i \(0.912862\pi\)
\(48\) 0 0
\(49\) −6.85220 + 1.43087i −0.978885 + 0.204410i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 1.38163 + 2.39306i 0.189782 + 0.328711i 0.945177 0.326557i \(-0.105889\pi\)
−0.755396 + 0.655269i \(0.772555\pi\)
\(54\) 0 0
\(55\) 1.69110 0.228028
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −8.45121 −1.10025 −0.550127 0.835081i \(-0.685421\pi\)
−0.550127 + 0.835081i \(0.685421\pi\)
\(60\) 0 0
\(61\) 10.7561 1.37717 0.688587 0.725154i \(-0.258231\pi\)
0.688587 + 0.725154i \(0.258231\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −0.669711 −0.0830675
\(66\) 0 0
\(67\) −8.42554 −1.02934 −0.514672 0.857387i \(-0.672086\pi\)
−0.514672 + 0.857387i \(0.672086\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −5.08888 −0.603939 −0.301970 0.953318i \(-0.597644\pi\)
−0.301970 + 0.953318i \(0.597644\pi\)
\(72\) 0 0
\(73\) 4.58416 + 7.94000i 0.536535 + 0.929306i 0.999087 + 0.0427143i \(0.0136005\pi\)
−0.462552 + 0.886592i \(0.653066\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −11.8816 5.31554i −1.35404 0.605762i
\(78\) 0 0
\(79\) 4.49202 0.505392 0.252696 0.967546i \(-0.418683\pi\)
0.252696 + 0.967546i \(0.418683\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 4.62966 + 8.01880i 0.508171 + 0.880178i 0.999955 + 0.00946064i \(0.00301146\pi\)
−0.491784 + 0.870717i \(0.663655\pi\)
\(84\) 0 0
\(85\) 0.712770 1.23455i 0.0773107 0.133906i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 3.54253 6.13584i 0.375507 0.650397i −0.614896 0.788608i \(-0.710802\pi\)
0.990403 + 0.138211i \(0.0441353\pi\)
\(90\) 0 0
\(91\) 4.70537 + 2.10506i 0.493257 + 0.220670i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −0.139086 −0.0142700
\(96\) 0 0
\(97\) −1.31231 2.27299i −0.133245 0.230787i 0.791681 0.610935i \(-0.209206\pi\)
−0.924926 + 0.380148i \(0.875873\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −7.85269 + 13.6013i −0.781372 + 1.35338i 0.149771 + 0.988721i \(0.452146\pi\)
−0.931143 + 0.364655i \(0.881187\pi\)
\(102\) 0 0
\(103\) 3.87139 + 6.70544i 0.381459 + 0.660707i 0.991271 0.131839i \(-0.0420883\pi\)
−0.609812 + 0.792546i \(0.708755\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −6.12952 + 10.6166i −0.592563 + 1.02635i 0.401323 + 0.915937i \(0.368551\pi\)
−0.993886 + 0.110413i \(0.964783\pi\)
\(108\) 0 0
\(109\) 4.89342 + 8.47565i 0.468705 + 0.811820i 0.999360 0.0357675i \(-0.0113876\pi\)
−0.530656 + 0.847588i \(0.678054\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 2.54664 4.41091i 0.239568 0.414944i −0.721022 0.692912i \(-0.756328\pi\)
0.960590 + 0.277968i \(0.0896609\pi\)
\(114\) 0 0
\(115\) −0.474162 + 0.821273i −0.0442158 + 0.0765841i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −8.88839 + 6.43352i −0.814797 + 0.589760i
\(120\) 0 0
\(121\) −6.60202 11.4350i −0.600183 1.03955i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −3.39676 −0.303815
\(126\) 0 0
\(127\) 2.24242 0.198982 0.0994911 0.995038i \(-0.468279\pi\)
0.0994911 + 0.995038i \(0.468279\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −3.72722 6.45573i −0.325648 0.564039i 0.655995 0.754765i \(-0.272249\pi\)
−0.981643 + 0.190726i \(0.938916\pi\)
\(132\) 0 0
\(133\) 0.977215 + 0.437181i 0.0847353 + 0.0379084i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −4.22340 + 7.31515i −0.360830 + 0.624975i −0.988098 0.153828i \(-0.950840\pi\)
0.627268 + 0.778804i \(0.284173\pi\)
\(138\) 0 0
\(139\) 1.82352 3.15843i 0.154669 0.267895i −0.778269 0.627931i \(-0.783902\pi\)
0.932939 + 0.360036i \(0.117235\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 4.79264 + 8.30110i 0.400781 + 0.694173i
\(144\) 0 0
\(145\) 0.563250 0.975578i 0.0467754 0.0810173i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 0.147078 + 0.254746i 0.0120491 + 0.0208696i 0.871987 0.489529i \(-0.162831\pi\)
−0.859938 + 0.510399i \(0.829498\pi\)
\(150\) 0 0
\(151\) 9.60202 16.6312i 0.781401 1.35343i −0.149725 0.988728i \(-0.547839\pi\)
0.931126 0.364699i \(-0.118828\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0.564842 + 0.978335i 0.0453692 + 0.0785817i
\(156\) 0 0
\(157\) −13.1166 −1.04682 −0.523411 0.852080i \(-0.675341\pi\)
−0.523411 + 0.852080i \(0.675341\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 5.91290 4.27983i 0.466002 0.337298i
\(162\) 0 0
\(163\) 0.496191 0.859428i 0.0388647 0.0673156i −0.845939 0.533280i \(-0.820959\pi\)
0.884803 + 0.465964i \(0.154293\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −6.93040 + 12.0038i −0.536291 + 0.928883i 0.462809 + 0.886458i \(0.346842\pi\)
−0.999100 + 0.0424246i \(0.986492\pi\)
\(168\) 0 0
\(169\) 4.60202 + 7.97093i 0.354001 + 0.613148i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 5.00487 0.380513 0.190256 0.981734i \(-0.439068\pi\)
0.190256 + 0.981734i \(0.439068\pi\)
\(174\) 0 0
\(175\) 11.7901 + 5.27458i 0.891245 + 0.398721i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 10.8101 + 18.7236i 0.807982 + 1.39947i 0.914259 + 0.405130i \(0.132774\pi\)
−0.106277 + 0.994337i \(0.533893\pi\)
\(180\) 0 0
\(181\) −26.0342 −1.93511 −0.967553 0.252666i \(-0.918693\pi\)
−0.967553 + 0.252666i \(0.918693\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 2.33002 0.171306
\(186\) 0 0
\(187\) −20.4031 −1.49202
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −17.7050 −1.28109 −0.640546 0.767920i \(-0.721292\pi\)
−0.640546 + 0.767920i \(0.721292\pi\)
\(192\) 0 0
\(193\) −2.96429 −0.213374 −0.106687 0.994293i \(-0.534024\pi\)
−0.106687 + 0.994293i \(0.534024\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 18.2357 1.29924 0.649618 0.760260i \(-0.274929\pi\)
0.649618 + 0.760260i \(0.274929\pi\)
\(198\) 0 0
\(199\) 1.61323 + 2.79419i 0.114359 + 0.198075i 0.917523 0.397682i \(-0.130185\pi\)
−0.803165 + 0.595757i \(0.796852\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −7.02385 + 5.08394i −0.492977 + 0.356823i
\(204\) 0 0
\(205\) 1.93352 0.135043
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0.995340 + 1.72398i 0.0688491 + 0.119250i
\(210\) 0 0
\(211\) −4.72740 + 8.18809i −0.325447 + 0.563691i −0.981603 0.190934i \(-0.938848\pi\)
0.656155 + 0.754626i \(0.272182\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −1.70595 + 2.95479i −0.116345 + 0.201515i
\(216\) 0 0
\(217\) −0.893419 8.64917i −0.0606492 0.587144i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 8.08005 0.543523
\(222\) 0 0
\(223\) 9.63203 + 16.6832i 0.645008 + 1.11719i 0.984300 + 0.176506i \(0.0564794\pi\)
−0.339291 + 0.940681i \(0.610187\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 1.08878 1.88583i 0.0722652 0.125167i −0.827629 0.561276i \(-0.810311\pi\)
0.899894 + 0.436109i \(0.143644\pi\)
\(228\) 0 0
\(229\) −3.10619 5.38008i −0.205263 0.355525i 0.744954 0.667116i \(-0.232472\pi\)
−0.950216 + 0.311591i \(0.899138\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 6.76391 11.7154i 0.443118 0.767503i −0.554801 0.831983i \(-0.687206\pi\)
0.997919 + 0.0644799i \(0.0205388\pi\)
\(234\) 0 0
\(235\) 2.26879 + 3.92967i 0.148000 + 0.256343i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 2.21398 3.83473i 0.143211 0.248048i −0.785493 0.618870i \(-0.787591\pi\)
0.928704 + 0.370822i \(0.120924\pi\)
\(240\) 0 0
\(241\) 11.0545 19.1470i 0.712084 1.23337i −0.251990 0.967730i \(-0.581085\pi\)
0.964074 0.265635i \(-0.0855817\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 1.60363 + 1.79388i 0.102452 + 0.114607i
\(246\) 0 0
\(247\) −0.394175 0.682731i −0.0250808 0.0434411i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −29.4679 −1.86000 −0.929998 0.367564i \(-0.880192\pi\)
−0.929998 + 0.367564i \(0.880192\pi\)
\(252\) 0 0
\(253\) 13.5729 0.853324
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −15.6027 27.0247i −0.973270 1.68575i −0.685528 0.728046i \(-0.740429\pi\)
−0.287742 0.957708i \(-0.592905\pi\)
\(258\) 0 0
\(259\) −16.3706 7.32381i −1.01722 0.455079i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 11.4058 19.7555i 0.703314 1.21818i −0.263982 0.964528i \(-0.585036\pi\)
0.967296 0.253648i \(-0.0816306\pi\)
\(264\) 0 0
\(265\) 0.474918 0.822582i 0.0291740 0.0505308i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −11.7838 20.4101i −0.718471 1.24443i −0.961606 0.274435i \(-0.911509\pi\)
0.243135 0.969992i \(-0.421824\pi\)
\(270\) 0 0
\(271\) 0.0112106 0.0194174i 0.000680998 0.00117952i −0.865685 0.500590i \(-0.833117\pi\)
0.866366 + 0.499410i \(0.166450\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 12.0088 + 20.7998i 0.724155 + 1.25427i
\(276\) 0 0
\(277\) −5.53913 + 9.59405i −0.332814 + 0.576451i −0.983062 0.183271i \(-0.941331\pi\)
0.650248 + 0.759722i \(0.274665\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −0.136542 0.236498i −0.00814541 0.0141083i 0.861924 0.507038i \(-0.169259\pi\)
−0.870069 + 0.492929i \(0.835926\pi\)
\(282\) 0 0
\(283\) 11.1535 0.663008 0.331504 0.943454i \(-0.392444\pi\)
0.331504 + 0.943454i \(0.392444\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −13.5848 6.07751i −0.801888 0.358744i
\(288\) 0 0
\(289\) −0.0995427 + 0.172413i −0.00585545 + 0.0101419i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −14.0597 + 24.3522i −0.821379 + 1.42267i 0.0832760 + 0.996527i \(0.473462\pi\)
−0.904655 + 0.426144i \(0.859872\pi\)
\(294\) 0 0
\(295\) 1.45250 + 2.51580i 0.0845676 + 0.146475i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −5.37516 −0.310854
\(300\) 0 0
\(301\) 21.2736 15.3981i 1.22619 0.887529i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −1.84863 3.20192i −0.105852 0.183342i
\(306\) 0 0
\(307\) 22.3340 1.27467 0.637333 0.770588i \(-0.280037\pi\)
0.637333 + 0.770588i \(0.280037\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 27.9026 1.58221 0.791105 0.611681i \(-0.209506\pi\)
0.791105 + 0.611681i \(0.209506\pi\)
\(312\) 0 0
\(313\) −12.3157 −0.696126 −0.348063 0.937471i \(-0.613161\pi\)
−0.348063 + 0.937471i \(0.613161\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 27.5533 1.54755 0.773775 0.633461i \(-0.218366\pi\)
0.773775 + 0.633461i \(0.218366\pi\)
\(318\) 0 0
\(319\) −16.1231 −0.902720
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 1.67807 0.0933704
\(324\) 0 0
\(325\) −4.75571 8.23713i −0.263799 0.456914i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −3.58859 34.7411i −0.197845 1.91534i
\(330\) 0 0
\(331\) 10.1117 0.555789 0.277895 0.960612i \(-0.410363\pi\)
0.277895 + 0.960612i \(0.410363\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 1.44809 + 2.50816i 0.0791174 + 0.137035i
\(336\) 0 0
\(337\) −5.91508 + 10.2452i −0.322215 + 0.558093i −0.980945 0.194287i \(-0.937761\pi\)
0.658730 + 0.752380i \(0.271094\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 8.08433 14.0025i 0.437791 0.758276i
\(342\) 0 0
\(343\) −5.62843 17.6443i −0.303907 0.952702i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 28.4499 1.52727 0.763634 0.645649i \(-0.223413\pi\)
0.763634 + 0.645649i \(0.223413\pi\)
\(348\) 0 0
\(349\) 8.79028 + 15.2252i 0.470533 + 0.814987i 0.999432 0.0336976i \(-0.0107283\pi\)
−0.528899 + 0.848685i \(0.677395\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 13.7573 23.8283i 0.732225 1.26825i −0.223705 0.974657i \(-0.571815\pi\)
0.955930 0.293594i \(-0.0948513\pi\)
\(354\) 0 0
\(355\) 0.874619 + 1.51489i 0.0464200 + 0.0804018i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −9.73182 + 16.8560i −0.513626 + 0.889626i 0.486249 + 0.873820i \(0.338365\pi\)
−0.999875 + 0.0158059i \(0.994969\pi\)
\(360\) 0 0
\(361\) 9.41814 + 16.3127i 0.495691 + 0.858563i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 1.57575 2.72927i 0.0824783 0.142857i
\(366\) 0 0
\(367\) −3.48214 + 6.03125i −0.181766 + 0.314829i −0.942482 0.334257i \(-0.891515\pi\)
0.760716 + 0.649085i \(0.224848\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −5.92233 + 4.28665i −0.307472 + 0.222552i
\(372\) 0 0
\(373\) 6.90747 + 11.9641i 0.357655 + 0.619477i 0.987569 0.157188i \(-0.0502430\pi\)
−0.629914 + 0.776665i \(0.716910\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 6.38507 0.328848
\(378\) 0 0
\(379\) −13.3822 −0.687398 −0.343699 0.939080i \(-0.611680\pi\)
−0.343699 + 0.939080i \(0.611680\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −2.23395 3.86931i −0.114149 0.197712i 0.803290 0.595588i \(-0.203081\pi\)
−0.917439 + 0.397876i \(0.869748\pi\)
\(384\) 0 0
\(385\) 0.459722 + 4.45056i 0.0234296 + 0.226822i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 14.1232 24.4620i 0.716072 1.24027i −0.246472 0.969150i \(-0.579271\pi\)
0.962545 0.271124i \(-0.0873953\pi\)
\(390\) 0 0
\(391\) 5.72075 9.90863i 0.289311 0.501101i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −0.772037 1.33721i −0.0388454 0.0672822i
\(396\) 0 0
\(397\) 0.293513 0.508379i 0.0147310 0.0255148i −0.858566 0.512703i \(-0.828644\pi\)
0.873297 + 0.487188i \(0.161977\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 14.5150 + 25.1408i 0.724846 + 1.25547i 0.959037 + 0.283280i \(0.0914226\pi\)
−0.234191 + 0.972191i \(0.575244\pi\)
\(402\) 0 0
\(403\) −3.20156 + 5.54526i −0.159481 + 0.276229i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −16.6743 28.8807i −0.826513 1.43156i
\(408\) 0 0
\(409\) 22.0042 1.08804 0.544018 0.839074i \(-0.316902\pi\)
0.544018 + 0.839074i \(0.316902\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −2.29744 22.2414i −0.113049 1.09443i
\(414\) 0 0
\(415\) 1.59138 2.75636i 0.0781180 0.135304i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −12.5615 + 21.7572i −0.613671 + 1.06291i 0.376945 + 0.926236i \(0.376975\pi\)
−0.990616 + 0.136674i \(0.956359\pi\)
\(420\) 0 0
\(421\) −0.0961261 0.166495i −0.00468490 0.00811449i 0.863673 0.504052i \(-0.168158\pi\)
−0.868358 + 0.495937i \(0.834825\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 20.2459 0.982069
\(426\) 0 0
\(427\) 2.92401 + 28.3073i 0.141503 + 1.36989i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 10.7344 + 18.5925i 0.517057 + 0.895569i 0.999804 + 0.0198093i \(0.00630591\pi\)
−0.482747 + 0.875760i \(0.660361\pi\)
\(432\) 0 0
\(433\) −40.3807 −1.94057 −0.970286 0.241960i \(-0.922210\pi\)
−0.970286 + 0.241960i \(0.922210\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −1.11632 −0.0534008
\(438\) 0 0
\(439\) −33.6577 −1.60639 −0.803196 0.595714i \(-0.796869\pi\)
−0.803196 + 0.595714i \(0.796869\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 11.5483 0.548677 0.274339 0.961633i \(-0.411541\pi\)
0.274339 + 0.961633i \(0.411541\pi\)
\(444\) 0 0
\(445\) −2.43540 −0.115449
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 22.6025 1.06668 0.533338 0.845902i \(-0.320937\pi\)
0.533338 + 0.845902i \(0.320937\pi\)
\(450\) 0 0
\(451\) −13.8368 23.9661i −0.651550 1.12852i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −0.182059 1.76251i −0.00853507 0.0826278i
\(456\) 0 0
\(457\) 2.08128 0.0973583 0.0486792 0.998814i \(-0.484499\pi\)
0.0486792 + 0.998814i \(0.484499\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 4.21838 + 7.30644i 0.196469 + 0.340295i 0.947381 0.320108i \(-0.103719\pi\)
−0.750912 + 0.660402i \(0.770386\pi\)
\(462\) 0 0
\(463\) 2.92231 5.06159i 0.135811 0.235232i −0.790096 0.612983i \(-0.789969\pi\)
0.925907 + 0.377751i \(0.123303\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 1.04009 1.80149i 0.0481298 0.0833632i −0.840957 0.541102i \(-0.818007\pi\)
0.889087 + 0.457739i \(0.151341\pi\)
\(468\) 0 0
\(469\) −2.29046 22.1739i −0.105764 1.02390i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 48.8331 2.24535
\(474\) 0 0
\(475\) −0.987670 1.71069i −0.0453174 0.0784920i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 8.51538 14.7491i 0.389077 0.673902i −0.603248 0.797553i \(-0.706127\pi\)
0.992326 + 0.123652i \(0.0394605\pi\)
\(480\) 0 0
\(481\) 6.60335 + 11.4373i 0.301087 + 0.521498i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −0.451091 + 0.781312i −0.0204830 + 0.0354775i
\(486\) 0 0
\(487\) −11.0758 19.1838i −0.501892 0.869302i −0.999998 0.00218582i \(-0.999304\pi\)
0.498106 0.867116i \(-0.334029\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 2.88390 4.99505i 0.130148 0.225424i −0.793585 0.608459i \(-0.791788\pi\)
0.923734 + 0.383035i \(0.125121\pi\)
\(492\) 0 0
\(493\) −6.79559 + 11.7703i −0.306058 + 0.530108i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −1.38340 13.3927i −0.0620539 0.600743i
\(498\) 0 0
\(499\) 5.16034 + 8.93797i 0.231008 + 0.400118i 0.958105 0.286417i \(-0.0924642\pi\)
−0.727097 + 0.686535i \(0.759131\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −29.4644 −1.31375 −0.656876 0.753998i \(-0.728123\pi\)
−0.656876 + 0.753998i \(0.728123\pi\)
\(504\) 0 0
\(505\) 5.39852 0.240231
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −1.87465 3.24698i −0.0830922 0.143920i 0.821484 0.570231i \(-0.193146\pi\)
−0.904577 + 0.426311i \(0.859813\pi\)
\(510\) 0 0
\(511\) −19.6499 + 14.2228i −0.869260 + 0.629181i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 1.33074 2.30491i 0.0586394 0.101566i
\(516\) 0 0
\(517\) 32.4723 56.2436i 1.42813 2.47359i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 13.9592 + 24.1780i 0.611562 + 1.05926i 0.990977 + 0.134030i \(0.0427919\pi\)
−0.379415 + 0.925226i \(0.623875\pi\)
\(522\) 0 0
\(523\) 21.0680 36.4909i 0.921240 1.59563i 0.123741 0.992315i \(-0.460511\pi\)
0.797499 0.603320i \(-0.206156\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −6.81480 11.8036i −0.296857 0.514172i
\(528\) 0 0
\(529\) 7.69433 13.3270i 0.334536 0.579434i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 5.47966 + 9.49105i 0.237350 + 0.411103i
\(534\) 0 0
\(535\) 4.21389 0.182182
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 10.7592 32.7145i 0.463431 1.40911i
\(540\) 0 0
\(541\) −14.5992 + 25.2865i −0.627667 + 1.08715i 0.360352 + 0.932816i \(0.382657\pi\)
−0.988019 + 0.154334i \(0.950677\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 1.68205 2.91340i 0.0720511 0.124796i
\(546\) 0 0
\(547\) 5.76122 + 9.97872i 0.246332 + 0.426659i 0.962505 0.271263i \(-0.0874414\pi\)
−0.716173 + 0.697922i \(0.754108\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 1.32606 0.0564920
\(552\) 0 0
\(553\) 1.22114 + 11.8219i 0.0519283 + 0.502717i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −5.97631 10.3513i −0.253224 0.438597i 0.711187 0.703002i \(-0.248158\pi\)
−0.964412 + 0.264405i \(0.914824\pi\)
\(558\) 0 0
\(559\) −19.3389 −0.817947
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 23.6198 0.995455 0.497728 0.867333i \(-0.334168\pi\)
0.497728 + 0.867333i \(0.334168\pi\)
\(564\) 0 0
\(565\) −1.75075 −0.0736546
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 23.9491 1.00400 0.501999 0.864868i \(-0.332598\pi\)
0.501999 + 0.864868i \(0.332598\pi\)
\(570\) 0 0
\(571\) 10.0992 0.422637 0.211319 0.977417i \(-0.432224\pi\)
0.211319 + 0.977417i \(0.432224\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −13.4683 −0.561669
\(576\) 0 0
\(577\) 16.1744 + 28.0149i 0.673348 + 1.16627i 0.976949 + 0.213474i \(0.0684780\pi\)
−0.303600 + 0.952800i \(0.598189\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −19.8449 + 14.3640i −0.823305 + 0.595918i
\(582\) 0 0
\(583\) −13.5946 −0.563030
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −5.02746 8.70781i −0.207505 0.359410i 0.743423 0.668822i \(-0.233201\pi\)
−0.950928 + 0.309412i \(0.899868\pi\)
\(588\) 0 0
\(589\) −0.664903 + 1.15165i −0.0273968 + 0.0474527i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 17.0673 29.5613i 0.700868 1.21394i −0.267294 0.963615i \(-0.586130\pi\)
0.968162 0.250324i \(-0.0805371\pi\)
\(594\) 0 0
\(595\) 3.44280 + 1.54022i 0.141141 + 0.0631429i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 30.4283 1.24327 0.621633 0.783309i \(-0.286470\pi\)
0.621633 + 0.783309i \(0.286470\pi\)
\(600\) 0 0
\(601\) 23.6966 + 41.0438i 0.966606 + 1.67421i 0.705238 + 0.708971i \(0.250840\pi\)
0.261368 + 0.965239i \(0.415826\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −2.26936 + 3.93064i −0.0922625 + 0.159803i
\(606\) 0 0
\(607\) 21.9060 + 37.9422i 0.889135 + 1.54003i 0.840899 + 0.541192i \(0.182027\pi\)
0.0482359 + 0.998836i \(0.484640\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −12.8597 + 22.2736i −0.520247 + 0.901094i
\(612\) 0 0
\(613\) 0.997163 + 1.72714i 0.0402750 + 0.0697584i 0.885460 0.464715i \(-0.153843\pi\)
−0.845185 + 0.534474i \(0.820510\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 21.0562 36.4704i 0.847690 1.46824i −0.0355743 0.999367i \(-0.511326\pi\)
0.883264 0.468875i \(-0.155341\pi\)
\(618\) 0 0
\(619\) −5.88221 + 10.1883i −0.236426 + 0.409502i −0.959686 0.281074i \(-0.909309\pi\)
0.723260 + 0.690576i \(0.242643\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 17.1110 + 7.65503i 0.685538 + 0.306692i
\(624\) 0 0
\(625\) −11.6208 20.1278i −0.464833 0.805114i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −28.1116 −1.12088
\(630\) 0 0
\(631\) 37.3202 1.48570 0.742848 0.669460i \(-0.233475\pi\)
0.742848 + 0.669460i \(0.233475\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −0.385401 0.667534i −0.0152942 0.0264903i
\(636\) 0 0
\(637\) −4.26085 + 12.9556i −0.168821 + 0.513320i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 20.2296 35.0387i 0.799022 1.38395i −0.121231 0.992624i \(-0.538684\pi\)
0.920254 0.391323i \(-0.127982\pi\)
\(642\) 0 0
\(643\) 1.43445 2.48455i 0.0565693 0.0979809i −0.836354 0.548190i \(-0.815317\pi\)
0.892923 + 0.450209i \(0.148650\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −1.71712 2.97413i −0.0675068 0.116925i 0.830296 0.557322i \(-0.188171\pi\)
−0.897803 + 0.440397i \(0.854838\pi\)
\(648\) 0 0
\(649\) 20.7889 36.0075i 0.816038 1.41342i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 12.2475 + 21.2133i 0.479283 + 0.830142i 0.999718 0.0237590i \(-0.00756342\pi\)
−0.520435 + 0.853901i \(0.674230\pi\)
\(654\) 0 0
\(655\) −1.28118 + 2.21907i −0.0500599 + 0.0867064i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −11.6375 20.1567i −0.453332 0.785194i 0.545259 0.838268i \(-0.316431\pi\)
−0.998591 + 0.0530740i \(0.983098\pi\)
\(660\) 0 0
\(661\) −33.5798 −1.30610 −0.653051 0.757314i \(-0.726511\pi\)
−0.653051 + 0.757314i \(0.726511\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −0.0378102 0.366040i −0.00146622 0.0141944i
\(666\) 0 0
\(667\) 4.52069 7.83007i 0.175042 0.303182i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −26.4586 + 45.8277i −1.02142 + 1.76916i
\(672\) 0 0
\(673\) −23.3581 40.4574i −0.900388 1.55952i −0.826991 0.562215i \(-0.809949\pi\)
−0.0733972 0.997303i \(-0.523384\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −3.47307 −0.133481 −0.0667404 0.997770i \(-0.521260\pi\)
−0.0667404 + 0.997770i \(0.521260\pi\)
\(678\) 0 0
\(679\) 5.62519 4.07158i 0.215875 0.156253i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 3.49075 + 6.04615i 0.133570 + 0.231349i 0.925050 0.379845i \(-0.124023\pi\)
−0.791480 + 0.611194i \(0.790689\pi\)
\(684\) 0 0
\(685\) 2.90348 0.110936
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 5.38373 0.205104
\(690\) 0 0
\(691\) 33.0832 1.25854 0.629272 0.777185i \(-0.283353\pi\)
0.629272 + 0.777185i \(0.283353\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −1.25363 −0.0475527
\(696\) 0 0
\(697\) −23.3279 −0.883606
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −39.4243 −1.48904 −0.744518 0.667602i \(-0.767321\pi\)
−0.744518 + 0.667602i \(0.767321\pi\)
\(702\) 0 0
\(703\) 1.37139 + 2.37532i 0.0517230 + 0.0895868i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −37.9298 16.9688i −1.42650 0.638179i
\(708\) 0 0
\(709\) 21.1542 0.794464 0.397232 0.917718i \(-0.369971\pi\)
0.397232 + 0.917718i \(0.369971\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 4.53347 + 7.85220i 0.169780 + 0.294067i
\(714\) 0 0
\(715\) 1.64741 2.85340i 0.0616096 0.106711i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 13.7586 23.8305i 0.513108 0.888729i −0.486777 0.873527i \(-0.661827\pi\)
0.999884 0.0152024i \(-0.00483926\pi\)
\(720\) 0 0
\(721\) −16.5946 + 12.0114i −0.618016 + 0.447327i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 15.9988 0.594182
\(726\) 0 0
\(727\) −10.5095 18.2030i −0.389775 0.675110i 0.602644 0.798010i \(-0.294114\pi\)
−0.992419 + 0.122900i \(0.960781\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 20.5822 35.6495i 0.761262 1.31854i
\(732\) 0 0
\(733\) 3.21219 + 5.56368i 0.118645 + 0.205499i 0.919231 0.393719i \(-0.128812\pi\)
−0.800586 + 0.599218i \(0.795478\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 20.7258 35.8982i 0.763445 1.32233i
\(738\) 0 0
\(739\) 19.2219 + 33.2933i 0.707089 + 1.22471i 0.965932 + 0.258794i \(0.0833252\pi\)
−0.258844 + 0.965919i \(0.583342\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 9.85728 17.0733i 0.361629 0.626359i −0.626600 0.779341i \(-0.715554\pi\)
0.988229 + 0.152982i \(0.0488875\pi\)
\(744\) 0 0
\(745\) 0.0505562 0.0875658i 0.00185223 0.00320816i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −29.6066 13.2453i −1.08180 0.483971i
\(750\) 0 0
\(751\) −11.4624 19.8534i −0.418268 0.724461i 0.577497 0.816392i \(-0.304029\pi\)
−0.995765 + 0.0919312i \(0.970696\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −6.60114 −0.240240
\(756\) 0 0
\(757\) −52.3408 −1.90236 −0.951179 0.308639i \(-0.900127\pi\)
−0.951179 + 0.308639i \(0.900127\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −0.939077 1.62653i −0.0340415 0.0589616i 0.848503 0.529191i \(-0.177505\pi\)
−0.882544 + 0.470229i \(0.844171\pi\)
\(762\) 0 0
\(763\) −20.9755 + 15.1823i −0.759365 + 0.549637i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −8.23284 + 14.2597i −0.297271 + 0.514888i
\(768\) 0 0
\(769\) −13.4060 + 23.2198i −0.483431 + 0.837327i −0.999819 0.0190276i \(-0.993943\pi\)
0.516388 + 0.856355i \(0.327276\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 4.67835 + 8.10314i 0.168268 + 0.291450i 0.937811 0.347146i \(-0.112849\pi\)
−0.769543 + 0.638595i \(0.779516\pi\)
\(774\) 0 0
\(775\) −8.02203 + 13.8946i −0.288160 + 0.499107i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 1.13802 + 1.97111i 0.0407738 + 0.0706223i
\(780\) 0 0
\(781\) 12.5180 21.6819i 0.447931 0.775839i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 2.25434 + 3.90463i 0.0804608 + 0.139362i
\(786\) 0 0
\(787\) 18.8735 0.672768 0.336384 0.941725i \(-0.390796\pi\)
0.336384 + 0.941725i \(0.390796\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 12.3007 + 5.50302i 0.437363 + 0.195665i
\(792\) 0 0
\(793\) 10.4782 18.1487i 0.372090 0.644479i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −17.9023 + 31.0078i −0.634134 + 1.09835i 0.352564 + 0.935788i \(0.385310\pi\)
−0.986698 + 0.162564i \(0.948024\pi\)
\(798\) 0 0
\(799\) −27.3729 47.4113i −0.968385 1.67729i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −45.1059 −1.59175
\(804\) 0 0