Properties

Label 2268.2.l.n.109.4
Level $2268$
Weight $2$
Character 2268.109
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.l (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: \( x^{16} - 9x^{14} + 31x^{12} - 282x^{10} + 1695x^{8} - 3318x^{6} + 4606x^{4} - 4116x^{2} + 2401 \) Copy content Toggle raw display
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 109.4
Root \(-2.40332 - 0.123797i\) of defining polynomial
Character \(\chi\) \(=\) 2268.109
Dual form 2268.2.l.n.541.4

$q$-expansion

\(f(q)\) \(=\) \(q-0.343737 q^{5} +(2.14324 + 1.55130i) q^{7} +O(q^{10})\) \(q-0.343737 q^{5} +(2.14324 + 1.55130i) q^{7} -4.91976 q^{11} +(0.974162 - 1.68730i) q^{13} +(-2.07359 + 3.59156i) q^{17} +(0.202315 + 0.350420i) q^{19} -2.75886 q^{23} -4.88184 q^{25} +(-1.63861 - 2.83815i) q^{29} +(1.64324 + 2.84617i) q^{31} +(-0.736710 - 0.533240i) q^{35} +(-3.38925 - 5.87035i) q^{37} +(2.81250 - 4.87139i) q^{41} +(-4.96295 - 8.59608i) q^{43} +(-6.60038 + 11.4322i) q^{47} +(2.18693 + 6.64961i) q^{49} +(-1.38163 + 2.39306i) q^{53} +1.69110 q^{55} +(-4.22560 - 7.31896i) q^{59} +(-5.37804 + 9.31503i) q^{61} +(-0.334856 + 0.579987i) q^{65} +(4.21277 + 7.29673i) q^{67} +5.08888 q^{71} +(4.58416 - 7.94000i) q^{73} +(-10.5442 - 7.63203i) q^{77} +(-2.24601 + 3.89020i) q^{79} +(-4.62966 - 8.01880i) q^{83} +(0.712770 - 1.23455i) q^{85} +(-3.54253 - 6.13584i) q^{89} +(4.70537 - 2.10506i) q^{91} +(-0.0695431 - 0.120452i) q^{95} +(-1.31231 - 2.27299i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 10 q^{13} + 8 q^{19} - 8 q^{31} - 4 q^{37} - 10 q^{43} - 20 q^{49} - 32 q^{55} + 28 q^{61} + 18 q^{67} - 20 q^{79} - 38 q^{85} - 2 q^{91} + 42 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(325\) \(1135\) \(1541\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(5\) −0.343737 −0.153724 −0.0768620 0.997042i \(-0.524490\pi\)
−0.0768620 + 0.997042i \(0.524490\pi\)
\(6\) 0 0
\(7\) 2.14324 + 1.55130i 0.810068 + 0.586337i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −4.91976 −1.48336 −0.741682 0.670752i \(-0.765971\pi\)
−0.741682 + 0.670752i \(0.765971\pi\)
\(12\) 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 0.497075 + 0.867708i \(0.334407\pi\)
−0.999994 + 0.00337409i \(0.998926\pi\)
\(18\) 0 0
\(19\) 0.202315 + 0.350420i 0.0464142 + 0.0803918i 0.888299 0.459265i \(-0.151887\pi\)
−0.841885 + 0.539657i \(0.818554\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −2.75886 −0.575263 −0.287631 0.957741i \(-0.592868\pi\)
−0.287631 + 0.957741i \(0.592868\pi\)
\(24\) 0 0
\(25\) −4.88184 −0.976369
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −1.63861 2.83815i −0.304282 0.527031i 0.672819 0.739807i \(-0.265083\pi\)
−0.977101 + 0.212775i \(0.931750\pi\)
\(30\) 0 0
\(31\) 1.64324 + 2.84617i 0.295134 + 0.511187i 0.975016 0.222134i \(-0.0713023\pi\)
−0.679882 + 0.733322i \(0.737969\pi\)
\(32\) 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 −0.997730 0.0673466i \(-0.978547\pi\)
0.440541 0.897733i \(-0.354787\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 2.81250 4.87139i 0.439238 0.760783i −0.558392 0.829577i \(-0.688582\pi\)
0.997631 + 0.0687936i \(0.0219150\pi\)
\(42\) 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
\(47\) −6.60038 + 11.4322i −0.962764 + 1.66756i −0.247257 + 0.968950i \(0.579529\pi\)
−0.715507 + 0.698606i \(0.753804\pi\)
\(48\) 0 0
\(49\) 2.18693 + 6.64961i 0.312419 + 0.949944i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −1.38163 + 2.39306i −0.189782 + 0.328711i −0.945177 0.326557i \(-0.894111\pi\)
0.755396 + 0.655269i \(0.227445\pi\)
\(54\) 0 0
\(55\) 1.69110 0.228028
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −4.22560 7.31896i −0.550127 0.952847i −0.998265 0.0588830i \(-0.981246\pi\)
0.448138 0.893964i \(-0.352087\pi\)
\(60\) 0 0
\(61\) −5.37804 + 9.31503i −0.688587 + 1.19267i 0.283708 + 0.958911i \(0.408435\pi\)
−0.972295 + 0.233757i \(0.924898\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −0.334856 + 0.579987i −0.0415337 + 0.0719386i
\(66\) 0 0
\(67\) 4.21277 + 7.29673i 0.514672 + 0.891438i 0.999855 + 0.0170251i \(0.00541953\pi\)
−0.485183 + 0.874412i \(0.661247\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 5.08888 0.603939 0.301970 0.953318i \(-0.402356\pi\)
0.301970 + 0.953318i \(0.402356\pi\)
\(72\) 0 0
\(73\) 4.58416 7.94000i 0.536535 0.929306i −0.462552 0.886592i \(-0.653066\pi\)
0.999087 0.0427143i \(-0.0136005\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −10.5442 7.63203i −1.20162 0.869750i
\(78\) 0 0
\(79\) −2.24601 + 3.89020i −0.252696 + 0.437682i −0.964267 0.264932i \(-0.914651\pi\)
0.711571 + 0.702614i \(0.247984\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −4.62966 8.01880i −0.508171 0.880178i −0.999955 0.00946064i \(-0.996989\pi\)
0.491784 0.870717i \(-0.336345\pi\)
\(84\) 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 \(-0.289198\pi\)
−0.990403 + 0.138211i \(0.955865\pi\)
\(90\) 0 0
\(91\) 4.70537 2.10506i 0.493257 0.220670i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −0.0695431 0.120452i −0.00713498 0.0123581i
\(96\) 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
\(101\) −15.7054 −1.56274 −0.781372 0.624066i \(-0.785480\pi\)
−0.781372 + 0.624066i \(0.785480\pi\)
\(102\) 0 0
\(103\) −7.74278 −0.762919 −0.381459 0.924386i \(-0.624578\pi\)
−0.381459 + 0.924386i \(0.624578\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 6.12952 + 10.6166i 0.592563 + 1.02635i 0.993886 + 0.110413i \(0.0352173\pi\)
−0.401323 + 0.915937i \(0.631449\pi\)
\(108\) 0 0
\(109\) 4.89342 8.47565i 0.468705 0.811820i −0.530656 0.847588i \(-0.678054\pi\)
0.999360 + 0.0357675i \(0.0113876\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −2.54664 + 4.41091i −0.239568 + 0.414944i −0.960590 0.277968i \(-0.910339\pi\)
0.721022 + 0.692912i \(0.243672\pi\)
\(114\) 0 0
\(115\) 0.948324 0.0884317
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −10.0158 + 4.48081i −0.918146 + 0.410755i
\(120\) 0 0
\(121\) 13.2040 1.20037
\(122\) 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
\(131\) −7.45443 −0.651297 −0.325648 0.945491i \(-0.605583\pi\)
−0.325648 + 0.945491i \(0.605583\pi\)
\(132\) 0 0
\(133\) −0.109997 + 1.06488i −0.00953799 + 0.0923371i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −8.44681 −0.721659 −0.360830 0.932632i \(-0.617506\pi\)
−0.360830 + 0.932632i \(0.617506\pi\)
\(138\) 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
\(149\) 0.294156 0.0240982 0.0120491 0.999927i \(-0.496165\pi\)
0.0120491 + 0.999927i \(0.496165\pi\)
\(150\) 0 0
\(151\) −19.2040 −1.56280 −0.781401 0.624029i \(-0.785495\pi\)
−0.781401 + 0.624029i \(0.785495\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −0.564842 0.978335i −0.0453692 0.0785817i
\(156\) 0 0
\(157\) 6.55832 + 11.3593i 0.523411 + 0.906575i 0.999629 + 0.0272471i \(0.00867410\pi\)
−0.476218 + 0.879327i \(0.657993\pi\)
\(158\) 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 0.884803 0.465964i \(-0.154293\pi\)
−0.845939 + 0.533280i \(0.820959\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 6.93040 12.0038i 0.536291 0.928883i −0.462809 0.886458i \(-0.653158\pi\)
0.999100 0.0424246i \(-0.0135082\pi\)
\(168\) 0 0
\(169\) 4.60202 + 7.97093i 0.354001 + 0.613148i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 2.50243 4.33434i 0.190256 0.329534i −0.755079 0.655634i \(-0.772401\pi\)
0.945335 + 0.326100i \(0.105735\pi\)
\(174\) 0 0
\(175\) −10.4630 7.57321i −0.790925 0.572481i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −10.8101 + 18.7236i −0.807982 + 1.39947i 0.106277 + 0.994337i \(0.466107\pi\)
−0.914259 + 0.405130i \(0.867226\pi\)
\(180\) 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
\(185\) 1.16501 + 2.01786i 0.0856532 + 0.148356i
\(186\) 0 0
\(187\) 10.2016 17.6696i 0.746012 1.29213i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −8.85252 + 15.3330i −0.640546 + 1.10946i 0.344766 + 0.938689i \(0.387958\pi\)
−0.985311 + 0.170769i \(0.945375\pi\)
\(192\) 0 0
\(193\) 1.48214 + 2.56715i 0.106687 + 0.184787i 0.914426 0.404753i \(-0.132642\pi\)
−0.807739 + 0.589540i \(0.799309\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −18.2357 −1.29924 −0.649618 0.760260i \(-0.725071\pi\)
−0.649618 + 0.760260i \(0.725071\pi\)
\(198\) 0 0
\(199\) 1.61323 2.79419i 0.114359 0.198075i −0.803165 0.595757i \(-0.796852\pi\)
0.917523 + 0.397682i \(0.130185\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0.890902 8.62480i 0.0625290 0.605342i
\(204\) 0 0
\(205\) −0.966760 + 1.67448i −0.0675215 + 0.116951i
\(206\) 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
\(221\) 4.04002 + 6.99753i 0.271761 + 0.470705i
\(222\) 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
\(227\) 2.17757 0.144530 0.0722652 0.997385i \(-0.476977\pi\)
0.0722652 + 0.997385i \(0.476977\pi\)
\(228\) 0 0
\(229\) 6.21238 0.410525 0.205263 0.978707i \(-0.434195\pi\)
0.205263 + 0.978707i \(0.434195\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −6.76391 11.7154i −0.443118 0.767503i 0.554801 0.831983i \(-0.312794\pi\)
−0.997919 + 0.0644799i \(0.979461\pi\)
\(234\) 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 −0.928704 0.370822i \(-0.879076\pi\)
0.785493 + 0.618870i \(0.212409\pi\)
\(240\) 0 0
\(241\) −22.1090 −1.42417 −0.712084 0.702095i \(-0.752248\pi\)
−0.712084 + 0.702095i \(0.752248\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −0.751730 2.28572i −0.0480263 0.146029i
\(246\) 0 0
\(247\) 0.788350 0.0501615
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 29.4679 1.86000 0.929998 0.367564i \(-0.119808\pi\)
0.929998 + 0.367564i \(0.119808\pi\)
\(252\) 0 0
\(253\) 13.5729 0.853324
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −31.2054 −1.94654 −0.973270 0.229662i \(-0.926238\pi\)
−0.973270 + 0.229662i \(0.926238\pi\)
\(258\) 0 0
\(259\) 1.84271 17.8393i 0.114501 1.10848i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 22.8117 1.40663 0.703314 0.710879i \(-0.251703\pi\)
0.703314 + 0.710879i \(0.251703\pi\)
\(264\) 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 −0.243135 0.969992i \(-0.578176\pi\)
0.961606 0.274435i \(-0.0884908\pi\)
\(270\) 0 0
\(271\) 0.0112106 + 0.0194174i 0.000680998 + 0.00117952i 0.866366 0.499410i \(-0.166450\pi\)
−0.865685 + 0.500590i \(0.833117\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 24.0175 1.44831
\(276\) 0 0
\(277\) 11.0783 0.665628 0.332814 0.942992i \(-0.392002\pi\)
0.332814 + 0.942992i \(0.392002\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 0.136542 + 0.236498i 0.00814541 + 0.0141083i 0.870069 0.492929i \(-0.164074\pi\)
−0.861924 + 0.507038i \(0.830741\pi\)
\(282\) 0 0
\(283\) −5.57676 9.65923i −0.331504 0.574181i 0.651303 0.758818i \(-0.274223\pi\)
−0.982807 + 0.184636i \(0.940889\pi\)
\(284\) 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 \(-0.526538\pi\)
0.904655 0.426144i \(-0.140128\pi\)
\(294\) 0 0
\(295\) 1.45250 + 2.51580i 0.0845676 + 0.146475i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −2.68758 + 4.65503i −0.155427 + 0.269207i
\(300\) 0 0
\(301\) 2.69833 26.1225i 0.155529 1.50567i
\(302\) 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
\(311\) 13.9513 + 24.1643i 0.791105 + 1.37023i 0.925283 + 0.379277i \(0.123827\pi\)
−0.134179 + 0.990957i \(0.542840\pi\)
\(312\) 0 0
\(313\) 6.15786 10.6657i 0.348063 0.602863i −0.637842 0.770167i \(-0.720173\pi\)
0.985905 + 0.167304i \(0.0535062\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 13.7767 23.8619i 0.773775 1.34022i −0.161705 0.986839i \(-0.551699\pi\)
0.935480 0.353379i \(-0.114967\pi\)
\(318\) 0 0
\(319\) 8.06155 + 13.9630i 0.451360 + 0.781779i
\(320\) 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
\(329\) −31.8809 + 14.2627i −1.75765 + 0.786329i
\(330\) 0 0
\(331\) −5.05585 + 8.75699i −0.277895 + 0.481327i −0.970861 0.239642i \(-0.922970\pi\)
0.692967 + 0.720970i \(0.256303\pi\)
\(332\) 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
\(347\) 14.2249 + 24.6383i 0.763634 + 1.32265i 0.940966 + 0.338502i \(0.109920\pi\)
−0.177331 + 0.984151i \(0.556746\pi\)
\(348\) 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
\(353\) 27.5145 1.46445 0.732225 0.681063i \(-0.238482\pi\)
0.732225 + 0.681063i \(0.238482\pi\)
\(354\) 0 0
\(355\) −1.74924 −0.0928400
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 9.73182 + 16.8560i 0.513626 + 0.889626i 0.999875 + 0.0158059i \(0.00503137\pi\)
−0.486249 + 0.873820i \(0.661635\pi\)
\(360\) 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
\(367\) 6.96429 0.363533 0.181766 0.983342i \(-0.441819\pi\)
0.181766 + 0.983342i \(0.441819\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −6.67351 + 2.98556i −0.346471 + 0.155003i
\(372\) 0 0
\(373\) −13.8149 −0.715310 −0.357655 0.933854i \(-0.616424\pi\)
−0.357655 + 0.933854i \(0.616424\pi\)
\(374\) 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
\(383\) −4.46789 −0.228299 −0.114149 0.993464i \(-0.536414\pi\)
−0.114149 + 0.993464i \(0.536414\pi\)
\(384\) 0 0
\(385\) 3.62444 + 2.62341i 0.184718 + 0.133701i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 28.2463 1.43214 0.716072 0.698026i \(-0.245938\pi\)
0.716072 + 0.698026i \(0.245938\pi\)
\(390\) 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 0.873297 0.487188i \(-0.161977\pi\)
−0.858566 + 0.512703i \(0.828644\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 29.0301 1.44969 0.724846 0.688911i \(-0.241911\pi\)
0.724846 + 0.688911i \(0.241911\pi\)
\(402\) 0 0
\(403\) 6.40312 0.318962
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 16.6743 + 28.8807i 0.826513 + 1.43156i
\(408\) 0 0
\(409\) −11.0021 19.0562i −0.544018 0.942267i −0.998668 0.0515965i \(-0.983569\pi\)
0.454650 0.890670i \(-0.349764\pi\)
\(410\) 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 \(-0.623025\pi\)
0.990616 0.136674i \(-0.0436413\pi\)
\(420\) 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
\(425\) 10.1229 17.5334i 0.491035 0.850497i
\(426\) 0 0
\(427\) −25.9768 + 11.6214i −1.25711 + 0.562398i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −10.7344 + 18.5925i −0.517057 + 0.895569i 0.482747 + 0.875760i \(0.339639\pi\)
−0.999804 + 0.0198093i \(0.993694\pi\)
\(432\) 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
\(437\) −0.558159 0.966760i −0.0267004 0.0462464i
\(438\) 0 0
\(439\) 16.8288 29.1484i 0.803196 1.39118i −0.114306 0.993446i \(-0.536464\pi\)
0.917502 0.397731i \(-0.130202\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 5.77416 10.0011i 0.274339 0.475168i −0.695629 0.718401i \(-0.744874\pi\)
0.969968 + 0.243232i \(0.0782078\pi\)
\(444\) 0 0
\(445\) 1.21770 + 2.10911i 0.0577244 + 0.0999816i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −22.6025 −1.06668 −0.533338 0.845902i \(-0.679063\pi\)
−0.533338 + 0.845902i \(0.679063\pi\)
\(450\) 0 0
\(451\) −13.8368 + 23.9661i −0.651550 + 1.12852i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −1.61741 + 0.723588i −0.0758253 + 0.0339223i
\(456\) 0 0
\(457\) −1.04064 + 1.80244i −0.0486792 + 0.0843148i −0.889338 0.457250i \(-0.848835\pi\)
0.840659 + 0.541565i \(0.182168\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −4.21838 7.30644i −0.196469 0.340295i 0.750912 0.660402i \(-0.229614\pi\)
−0.947381 + 0.320108i \(0.896281\pi\)
\(462\) 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 \(-0.181993\pi\)
−0.889087 + 0.457739i \(0.848659\pi\)
\(468\) 0 0
\(469\) −2.29046 + 22.1739i −0.105764 + 1.02390i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 24.4165 + 42.2907i 1.12267 + 1.94453i
\(474\) 0 0
\(475\) −0.987670 1.71069i −0.0453174 0.0784920i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 17.0308 0.778155 0.389077 0.921205i \(-0.372794\pi\)
0.389077 + 0.921205i \(0.372794\pi\)
\(480\) 0 0
\(481\) −13.2067 −0.602174
\(482\) 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 0.498106 + 0.867116i \(0.334029\pi\)
−0.999998 + 0.00218582i \(0.999304\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −2.88390 + 4.99505i −0.130148 + 0.225424i −0.923734 0.383035i \(-0.874879\pi\)
0.793585 + 0.608459i \(0.208212\pi\)
\(492\) 0 0
\(493\) 13.5912 0.612116
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 10.9067 + 7.89439i 0.489232 + 0.354112i
\(498\) 0 0
\(499\) −10.3207 −0.462017 −0.231008 0.972952i \(-0.574203\pi\)
−0.231008 + 0.972952i \(0.574203\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 29.4644 1.31375 0.656876 0.753998i \(-0.271877\pi\)
0.656876 + 0.753998i \(0.271877\pi\)
\(504\) 0 0
\(505\) 5.39852 0.240231
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −3.74929 −0.166184 −0.0830922 0.996542i \(-0.526480\pi\)
−0.0830922 + 0.996542i \(0.526480\pi\)
\(510\) 0 0
\(511\) 22.1423 9.90589i 0.979516 0.438211i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 2.66148 0.117279
\(516\) 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 0.379415 + 0.925226i \(0.376125\pi\)
−0.990977 + 0.134030i \(0.957208\pi\)
\(522\) 0 0
\(523\) 21.0680 + 36.4909i 0.921240 + 1.59563i 0.797499 + 0.603320i \(0.206156\pi\)
0.123741 + 0.992315i \(0.460511\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −13.6296 −0.593714
\(528\) 0 0
\(529\) −15.3887 −0.669072
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −5.47966 9.49105i −0.237350 0.411103i
\(534\) 0 0
\(535\) −2.10694 3.64934i −0.0910912 0.157775i
\(536\) 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 −0.988019 0.154334i \(-0.950677\pi\)
0.360352 0.932816i \(-0.382657\pi\)
\(542\) 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
\(551\) 0.663029 1.14840i 0.0282460 0.0489235i
\(552\) 0 0
\(553\) −10.8486 + 4.85339i −0.461330 + 0.206387i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 5.97631 10.3513i 0.253224 0.438597i −0.711187 0.703002i \(-0.751842\pi\)
0.964412 + 0.264405i \(0.0851756\pi\)
\(558\) 0 0
\(559\) −19.3389 −0.817947
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 11.8099 + 20.4553i 0.497728 + 0.862090i 0.999997 0.00262192i \(-0.000834585\pi\)
−0.502269 + 0.864711i \(0.667501\pi\)
\(564\) 0 0
\(565\) 0.875375 1.51619i 0.0368273 0.0637868i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 11.9745 20.7405i 0.501999 0.869487i −0.497999 0.867178i \(-0.665932\pi\)
0.999997 0.00230931i \(-0.000735078\pi\)
\(570\) 0 0
\(571\) −5.04958 8.74614i −0.211319 0.366014i 0.740809 0.671716i \(-0.234442\pi\)
−0.952127 + 0.305701i \(0.901109\pi\)
\(572\) 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 −0.303600 0.952800i \(-0.598189\pi\)
0.976949 0.213474i \(-0.0684780\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 2.51712 24.3682i 0.104428 1.01096i
\(582\) 0 0
\(583\) 6.79729 11.7733i 0.281515 0.487598i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 5.02746 + 8.70781i 0.207505 + 0.359410i 0.950928 0.309412i \(-0.100132\pi\)
−0.743423 + 0.668822i \(0.766799\pi\)
\(588\) 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 −0.968162 0.250324i \(-0.919463\pi\)
0.267294 0.963615i \(-0.413870\pi\)
\(594\) 0 0
\(595\) 3.44280 1.54022i 0.141141 0.0631429i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 15.2141 + 26.3517i 0.621633 + 1.07670i 0.989182 + 0.146695i \(0.0468637\pi\)
−0.367549 + 0.930004i \(0.619803\pi\)
\(600\) 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
\(605\) −4.53872 −0.184525
\(606\) 0 0
\(607\) −43.8119 −1.77827 −0.889135 0.457644i \(-0.848693\pi\)
−0.889135 + 0.457644i \(0.848693\pi\)
\(608\) 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 −0.845185 0.534474i \(-0.820510\pi\)
0.885460 + 0.464715i \(0.153843\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −21.0562 + 36.4704i −0.847690 + 1.46824i 0.0355743 + 0.999367i \(0.488674\pi\)
−0.883264 + 0.468875i \(0.844659\pi\)
\(618\) 0 0
\(619\) 11.7644 0.472852 0.236426 0.971650i \(-0.424024\pi\)
0.236426 + 0.971650i \(0.424024\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 1.92605 18.6461i 0.0771656 0.747039i
\(624\) 0 0
\(625\) 23.2416 0.929665
\(626\) 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
\(635\) −0.770802 −0.0305883
\(636\) 0 0
\(637\) 13.3503 + 2.78779i 0.528958 + 0.110456i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 40.4592 1.59804 0.799022 0.601302i \(-0.205351\pi\)
0.799022 + 0.601302i \(0.205351\pi\)
\(642\) 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 \(-0.811829\pi\)
0.897803 + 0.440397i \(0.145162\pi\)
\(648\) 0 0
\(649\) 20.7889 + 36.0075i 0.816038 + 1.41342i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 24.4951 0.958566 0.479283 0.877660i \(-0.340897\pi\)
0.479283 + 0.877660i \(0.340897\pi\)
\(654\) 0 0
\(655\) 2.56236 0.100120
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 11.6375 + 20.1567i 0.453332 + 0.785194i 0.998591 0.0530740i \(-0.0169019\pi\)
−0.545259 + 0.838268i \(0.683569\pi\)
\(660\) 0 0
\(661\) 16.7899 + 29.0809i 0.653051 + 1.13112i 0.982379 + 0.186902i \(0.0598446\pi\)
−0.329328 + 0.944216i \(0.606822\pi\)
\(662\) 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
\(677\) −1.73653 + 3.00777i −0.0667404 + 0.115598i −0.897465 0.441086i \(-0.854593\pi\)
0.830724 + 0.556684i \(0.187927\pi\)
\(678\) 0 0
\(679\) 0.713497 6.90735i 0.0273815 0.265080i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −3.49075 + 6.04615i −0.133570 + 0.231349i −0.925050 0.379845i \(-0.875977\pi\)
0.791480 + 0.611194i \(0.209311\pi\)
\(684\) 0 0
\(685\) 2.90348 0.110936
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 2.69187 + 4.66245i 0.102552 + 0.177625i
\(690\) 0 0
\(691\) −16.5416 + 28.6509i −0.629272 + 1.08993i 0.358426 + 0.933558i \(0.383314\pi\)
−0.987698 + 0.156373i \(0.950020\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −0.626813 + 1.08567i −0.0237764 + 0.0411819i
\(696\) 0 0
\(697\) 11.6639 + 20.2025i 0.441803 + 0.765225i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 39.4243 1.48904 0.744518 0.667602i \(-0.232679\pi\)
0.744518 + 0.667602i \(0.232679\pi\)
\(702\) 0 0
\(703\) 1.37139 2.37532i 0.0517230 0.0895868i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −33.6604 24.3638i −1.26593 0.916294i
\(708\) 0 0
\(709\) −10.5771 + 18.3201i −0.397232 + 0.688026i −0.993383 0.114846i \(-0.963363\pi\)
0.596151 + 0.802872i \(0.296696\pi\)
\(710\) 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 −0.999884 0.0152024i \(-0.995161\pi\)
0.486777 0.873527i \(-0.338173\pi\)
\(720\) 0 0
\(721\) −16.5946 12.0114i −0.618016 0.447327i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 7.99942 + 13.8554i 0.297091 + 0.514577i
\(726\) 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
\(731\) 41.1645 1.52252
\(732\) 0 0
\(733\) −6.42438 −0.237290 −0.118645 0.992937i \(-0.537855\pi\)
−0.118645 + 0.992937i \(0.537855\pi\)
\(734\) 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 −0.258844 0.965919i \(-0.583342\pi\)
0.965932 0.258794i \(-0.0833252\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −9.85728 + 17.0733i −0.361629 + 0.626359i −0.988229 0.152982i \(-0.951112\pi\)
0.626600 + 0.779341i \(0.284446\pi\)
\(744\) 0 0
\(745\) −0.101112 −0.00370447
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −3.33259 + 32.2627i −0.121770 + 1.17885i
\(750\) 0 0
\(751\) 22.9247 0.836536 0.418268 0.908324i \(-0.362637\pi\)
0.418268 + 0.908324i \(0.362637\pi\)
\(752\) 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
\(761\) −1.87815 −0.0680830 −0.0340415 0.999420i \(-0.510838\pi\)
−0.0340415 + 0.999420i \(0.510838\pi\)
\(762\) 0 0
\(763\) 23.6360 10.5742i 0.855682 0.382810i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −16.4657 −0.594542
\(768\) 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 \(-0.887151\pi\)
0.769543 + 0.638595i \(0.220484\pi\)
\(774\) 0 0
\(775\) −8.02203 13.8946i −0.288160 0.499107i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 2.27604 0.0815476
\(780\) 0 0
\(781\) −25.0361 −0.895862
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −2.25434 3.90463i −0.0804608 0.139362i
\(786\) 0 0
\(787\) −9.43675 16.3449i −0.336384 0.582634i 0.647366 0.762179i \(-0.275871\pi\)
−0.983750 + 0.179546i \(0.942537\pi\)
\(788\) 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 \(-0.614690\pi\)
0.986698 0.162564i \(-0.0519765\pi\)
\(798\) 0 0
\(799\) −27.3729 47.4113i −0.968385 1.67729i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\)