Properties

Label 252.12.k.d.37.6
Level $252$
Weight $12$
Character 252.37
Analytic conductor $193.622$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 252.k (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(193.622481501\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 581500324 x^{14} - 481772282104 x^{13} + 132272376701859942 x^{12} + \)\(18\!\cdots\!08\)\( x^{11} - \)\(14\!\cdots\!08\)\( x^{10} - \)\(25\!\cdots\!56\)\( x^{9} + \)\(80\!\cdots\!79\)\( x^{8} + \)\(11\!\cdots\!68\)\( x^{7} - \)\(19\!\cdots\!68\)\( x^{6} + \)\(59\!\cdots\!08\)\( x^{5} + \)\(21\!\cdots\!06\)\( x^{4} - \)\(37\!\cdots\!04\)\( x^{3} - \)\(31\!\cdots\!28\)\( x^{2} + \)\(25\!\cdots\!24\)\( x + \)\(79\!\cdots\!77\)\(\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{42}\cdot 3^{15}\cdot 7^{9} \)
Twist minimal: no (minimal twist has level 84)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 37.6
Root \(2410.13 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 252.37
Dual form 252.12.k.d.109.6

$q$-expansion

\(f(q)\) \(=\) \(q+(1339.81 - 2320.63i) q^{5} +(-28039.7 + 34512.4i) q^{7} +O(q^{10})\) \(q+(1339.81 - 2320.63i) q^{5} +(-28039.7 + 34512.4i) q^{7} +(239334. + 414539. i) q^{11} -1.17059e6 q^{13} +(2.40839e6 + 4.17145e6i) q^{17} +(-4.55281e6 + 7.88570e6i) q^{19} +(4.21644e6 - 7.30309e6i) q^{23} +(2.08239e7 + 3.60680e7i) q^{25} -3.65821e7 q^{29} +(-1.20947e7 - 2.09487e7i) q^{31} +(4.25223e7 + 1.11310e8i) q^{35} +(-1.66789e8 + 2.88888e8i) q^{37} -5.86887e7 q^{41} +8.57155e8 q^{43} +(-4.75883e8 + 8.24254e8i) q^{47} +(-4.04880e8 - 1.93543e9i) q^{49} +(9.09651e8 + 1.57556e9i) q^{53} +1.28265e9 q^{55} +(-8.43761e8 - 1.46144e9i) q^{59} +(3.82941e9 - 6.63273e9i) q^{61} +(-1.56837e9 + 2.71649e9i) q^{65} +(-2.92346e9 - 5.06358e9i) q^{67} -1.03360e10 q^{71} +(4.61314e9 + 7.99018e9i) q^{73} +(-2.10176e10 - 3.36355e9i) q^{77} +(9.94865e9 - 1.72316e10i) q^{79} -4.78020e10 q^{83} +1.29072e10 q^{85} +(9.70762e9 - 1.68141e10i) q^{89} +(3.28229e10 - 4.03997e10i) q^{91} +(1.21998e10 + 2.11307e10i) q^{95} +8.32856e10 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 2156q^{5} + 50512q^{7} + O(q^{10}) \) \( 16q + 2156q^{5} + 50512q^{7} + 222796q^{11} + 2703176q^{13} - 5114600q^{17} + 6910556q^{19} + 51387712q^{23} - 191456372q^{25} - 118854616q^{29} + 164659160q^{31} - 55239344q^{35} + 75658364q^{37} + 1815568608q^{41} + 10754408q^{43} + 1034359464q^{47} + 4123496848q^{49} + 665159988q^{53} - 1264543896q^{55} - 1040514580q^{59} - 14391208024q^{61} + 20938150200q^{65} - 33307097284q^{67} - 65848902896q^{71} + 17709749204q^{73} - 8594484604q^{77} - 26626784032q^{79} + 210306955048q^{83} - 25867402032q^{85} + 55951560072q^{89} + 66078280292q^{91} - 106810047392q^{95} - 156216030712q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) 1339.81 2320.63i 0.191739 0.332101i −0.754088 0.656773i \(-0.771921\pi\)
0.945826 + 0.324673i \(0.105254\pi\)
\(6\) 0 0
\(7\) −28039.7 + 34512.4i −0.630571 + 0.776132i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 239334. + 414539.i 0.448069 + 0.776079i 0.998260 0.0589601i \(-0.0187785\pi\)
−0.550191 + 0.835039i \(0.685445\pi\)
\(12\) 0 0
\(13\) −1.17059e6 −0.874410 −0.437205 0.899362i \(-0.644032\pi\)
−0.437205 + 0.899362i \(0.644032\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.40839e6 + 4.17145e6i 0.411394 + 0.712555i 0.995042 0.0994514i \(-0.0317088\pi\)
−0.583649 + 0.812006i \(0.698375\pi\)
\(18\) 0 0
\(19\) −4.55281e6 + 7.88570e6i −0.421827 + 0.730626i −0.996118 0.0880250i \(-0.971944\pi\)
0.574291 + 0.818651i \(0.305278\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 4.21644e6 7.30309e6i 0.136598 0.236594i −0.789609 0.613610i \(-0.789717\pi\)
0.926207 + 0.377016i \(0.123050\pi\)
\(24\) 0 0
\(25\) 2.08239e7 + 3.60680e7i 0.426473 + 0.738672i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −3.65821e7 −0.331192 −0.165596 0.986194i \(-0.552955\pi\)
−0.165596 + 0.986194i \(0.552955\pi\)
\(30\) 0 0
\(31\) −1.20947e7 2.09487e7i −0.0758765 0.131422i 0.825591 0.564270i \(-0.190842\pi\)
−0.901467 + 0.432848i \(0.857509\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 4.25223e7 + 1.11310e8i 0.136849 + 0.358227i
\(36\) 0 0
\(37\) −1.66789e8 + 2.88888e8i −0.395420 + 0.684888i −0.993155 0.116806i \(-0.962734\pi\)
0.597734 + 0.801694i \(0.296068\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −5.86887e7 −0.0791122 −0.0395561 0.999217i \(-0.512594\pi\)
−0.0395561 + 0.999217i \(0.512594\pi\)
\(42\) 0 0
\(43\) 8.57155e8 0.889166 0.444583 0.895738i \(-0.353352\pi\)
0.444583 + 0.895738i \(0.353352\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −4.75883e8 + 8.24254e8i −0.302665 + 0.524231i −0.976739 0.214433i \(-0.931210\pi\)
0.674074 + 0.738664i \(0.264543\pi\)
\(48\) 0 0
\(49\) −4.04880e8 1.93543e9i −0.204761 0.978812i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 9.09651e8 + 1.57556e9i 0.298784 + 0.517509i 0.975858 0.218406i \(-0.0700857\pi\)
−0.677074 + 0.735915i \(0.736752\pi\)
\(54\) 0 0
\(55\) 1.28265e9 0.343649
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −8.43761e8 1.46144e9i −0.153650 0.266130i 0.778916 0.627128i \(-0.215770\pi\)
−0.932567 + 0.360998i \(0.882436\pi\)
\(60\) 0 0
\(61\) 3.82941e9 6.63273e9i 0.580521 1.00549i −0.414897 0.909868i \(-0.636182\pi\)
0.995418 0.0956231i \(-0.0304843\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −1.56837e9 + 2.71649e9i −0.167658 + 0.290392i
\(66\) 0 0
\(67\) −2.92346e9 5.06358e9i −0.264537 0.458191i 0.702906 0.711283i \(-0.251886\pi\)
−0.967442 + 0.253093i \(0.918552\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −1.03360e10 −0.679877 −0.339939 0.940448i \(-0.610406\pi\)
−0.339939 + 0.940448i \(0.610406\pi\)
\(72\) 0 0
\(73\) 4.61314e9 + 7.99018e9i 0.260448 + 0.451109i 0.966361 0.257190i \(-0.0827965\pi\)
−0.705913 + 0.708298i \(0.749463\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −2.10176e10 3.36355e9i −0.884879 0.141612i
\(78\) 0 0
\(79\) 9.94865e9 1.72316e10i 0.363760 0.630051i −0.624816 0.780772i \(-0.714826\pi\)
0.988576 + 0.150721i \(0.0481594\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −4.78020e10 −1.33204 −0.666018 0.745935i \(-0.732003\pi\)
−0.666018 + 0.745935i \(0.732003\pi\)
\(84\) 0 0
\(85\) 1.29072e10 0.315520
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 9.70762e9 1.68141e10i 0.184276 0.319175i −0.759057 0.651025i \(-0.774339\pi\)
0.943332 + 0.331850i \(0.107673\pi\)
\(90\) 0 0
\(91\) 3.28229e10 4.03997e10i 0.551377 0.678657i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 1.21998e10 + 2.11307e10i 0.161761 + 0.280178i
\(96\) 0 0
\(97\) 8.32856e10 0.984749 0.492374 0.870383i \(-0.336129\pi\)
0.492374 + 0.870383i \(0.336129\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 7.46928e10 + 1.29372e11i 0.707149 + 1.22482i 0.965910 + 0.258877i \(0.0833523\pi\)
−0.258761 + 0.965941i \(0.583314\pi\)
\(102\) 0 0
\(103\) 3.62922e10 6.28600e10i 0.308467 0.534281i −0.669560 0.742758i \(-0.733517\pi\)
0.978027 + 0.208477i \(0.0668507\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1.26123e11 + 2.18451e11i −0.869326 + 1.50572i −0.00663879 + 0.999978i \(0.502113\pi\)
−0.862687 + 0.505738i \(0.831220\pi\)
\(108\) 0 0
\(109\) 6.84739e10 + 1.18600e11i 0.426265 + 0.738312i 0.996538 0.0831430i \(-0.0264958\pi\)
−0.570273 + 0.821455i \(0.693162\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −2.33958e11 −1.19456 −0.597279 0.802034i \(-0.703751\pi\)
−0.597279 + 0.802034i \(0.703751\pi\)
\(114\) 0 0
\(115\) −1.12985e10 1.95696e10i −0.0523821 0.0907284i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −2.11497e11 3.38470e10i −0.812449 0.130020i
\(120\) 0 0
\(121\) 2.80940e10 4.86603e10i 0.0984679 0.170551i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 2.42442e11 0.710562
\(126\) 0 0
\(127\) −2.05552e11 −0.552078 −0.276039 0.961146i \(-0.589022\pi\)
−0.276039 + 0.961146i \(0.589022\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 1.71371e10 2.96824e10i 0.0388102 0.0672213i −0.845968 0.533234i \(-0.820977\pi\)
0.884778 + 0.466013i \(0.154310\pi\)
\(132\) 0 0
\(133\) −1.44495e11 3.78241e11i −0.301070 0.788105i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −7.70171e10 1.33397e11i −0.136340 0.236148i 0.789768 0.613405i \(-0.210201\pi\)
−0.926109 + 0.377257i \(0.876867\pi\)
\(138\) 0 0
\(139\) −1.11480e11 −0.182228 −0.0911138 0.995840i \(-0.529043\pi\)
−0.0911138 + 0.995840i \(0.529043\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −2.80161e11 4.85254e11i −0.391796 0.678611i
\(144\) 0 0
\(145\) −4.90132e10 + 8.48933e10i −0.0635022 + 0.109989i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 8.33795e11 1.44418e12i 0.930112 1.61100i 0.146985 0.989139i \(-0.453043\pi\)
0.783127 0.621862i \(-0.213623\pi\)
\(150\) 0 0
\(151\) 3.71218e11 + 6.42968e11i 0.384818 + 0.666524i 0.991744 0.128234i \(-0.0409309\pi\)
−0.606926 + 0.794758i \(0.707598\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −6.48188e10 −0.0581938
\(156\) 0 0
\(157\) −4.37190e11 7.57235e11i −0.365782 0.633552i 0.623120 0.782126i \(-0.285865\pi\)
−0.988901 + 0.148574i \(0.952532\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 1.33819e11 + 3.50296e11i 0.0974937 + 0.255207i
\(162\) 0 0
\(163\) −5.70121e11 + 9.87478e11i −0.388092 + 0.672196i −0.992193 0.124712i \(-0.960199\pi\)
0.604101 + 0.796908i \(0.293533\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −1.67533e12 −0.998068 −0.499034 0.866582i \(-0.666312\pi\)
−0.499034 + 0.866582i \(0.666312\pi\)
\(168\) 0 0
\(169\) −4.21888e11 −0.235408
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 1.84651e12 3.19825e12i 0.905937 1.56913i 0.0862817 0.996271i \(-0.472502\pi\)
0.819655 0.572858i \(-0.194165\pi\)
\(174\) 0 0
\(175\) −1.82869e12 2.92654e11i −0.842228 0.134786i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 8.10662e11 + 1.40411e12i 0.329722 + 0.571096i 0.982457 0.186491i \(-0.0597115\pi\)
−0.652734 + 0.757587i \(0.726378\pi\)
\(180\) 0 0
\(181\) −3.72161e12 −1.42396 −0.711982 0.702198i \(-0.752202\pi\)
−0.711982 + 0.702198i \(0.752202\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 4.46934e11 + 7.74112e11i 0.151635 + 0.262639i
\(186\) 0 0
\(187\) −1.15282e12 + 1.99674e12i −0.368666 + 0.638548i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −1.15479e12 + 2.00015e12i −0.328714 + 0.569349i −0.982257 0.187540i \(-0.939948\pi\)
0.653543 + 0.756889i \(0.273282\pi\)
\(192\) 0 0
\(193\) 6.67031e11 + 1.15533e12i 0.179300 + 0.310557i 0.941641 0.336619i \(-0.109283\pi\)
−0.762341 + 0.647176i \(0.775950\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −3.95053e12 −0.948618 −0.474309 0.880359i \(-0.657302\pi\)
−0.474309 + 0.880359i \(0.657302\pi\)
\(198\) 0 0
\(199\) −5.18976e11 8.98893e11i −0.117884 0.204181i 0.801045 0.598604i \(-0.204278\pi\)
−0.918929 + 0.394423i \(0.870944\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 1.02575e12 1.26253e12i 0.208840 0.257048i
\(204\) 0 0
\(205\) −7.86320e10 + 1.36195e11i −0.0151689 + 0.0262732i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −4.35857e12 −0.756031
\(210\) 0 0
\(211\) 4.91335e12 0.808769 0.404385 0.914589i \(-0.367486\pi\)
0.404385 + 0.914589i \(0.367486\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 1.14843e12 1.98914e12i 0.170487 0.295293i
\(216\) 0 0
\(217\) 1.06212e12 + 1.69977e11i 0.149846 + 0.0239807i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −2.81923e12 4.88305e12i −0.359727 0.623065i
\(222\) 0 0
\(223\) −8.25284e12 −1.00214 −0.501068 0.865408i \(-0.667059\pi\)
−0.501068 + 0.865408i \(0.667059\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −6.55247e12 1.13492e13i −0.721544 1.24975i −0.960381 0.278691i \(-0.910099\pi\)
0.238837 0.971060i \(-0.423234\pi\)
\(228\) 0 0
\(229\) 3.18856e12 5.52274e12i 0.334579 0.579508i −0.648825 0.760938i \(-0.724739\pi\)
0.983404 + 0.181430i \(0.0580724\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −3.04721e12 + 5.27793e12i −0.290700 + 0.503507i −0.973975 0.226653i \(-0.927222\pi\)
0.683275 + 0.730161i \(0.260555\pi\)
\(234\) 0 0
\(235\) 1.27519e12 + 2.20869e12i 0.116065 + 0.201031i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −1.63982e13 −1.36022 −0.680108 0.733112i \(-0.738067\pi\)
−0.680108 + 0.733112i \(0.738067\pi\)
\(240\) 0 0
\(241\) −7.93321e12 1.37407e13i −0.628573 1.08872i −0.987838 0.155484i \(-0.950306\pi\)
0.359266 0.933235i \(-0.383027\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −5.03387e12 1.65354e12i −0.364325 0.119675i
\(246\) 0 0
\(247\) 5.32946e12 9.23089e12i 0.368850 0.638867i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −2.61416e13 −1.65625 −0.828125 0.560544i \(-0.810592\pi\)
−0.828125 + 0.560544i \(0.810592\pi\)
\(252\) 0 0
\(253\) 4.03656e12 0.244821
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −9.97426e12 + 1.72759e13i −0.554943 + 0.961190i 0.442965 + 0.896539i \(0.353927\pi\)
−0.997908 + 0.0646509i \(0.979407\pi\)
\(258\) 0 0
\(259\) −5.29348e12 1.38566e13i −0.282223 0.738769i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −1.90133e13 3.29321e13i −0.931755 1.61385i −0.780321 0.625379i \(-0.784944\pi\)
−0.151434 0.988467i \(-0.548389\pi\)
\(264\) 0 0
\(265\) 4.87505e12 0.229154
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 6.11726e12 + 1.05954e13i 0.264801 + 0.458649i 0.967511 0.252827i \(-0.0813604\pi\)
−0.702710 + 0.711476i \(0.748027\pi\)
\(270\) 0 0
\(271\) −4.65635e12 + 8.06503e12i −0.193515 + 0.335177i −0.946413 0.322960i \(-0.895322\pi\)
0.752898 + 0.658137i \(0.228655\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −9.96773e12 + 1.72646e13i −0.382179 + 0.661953i
\(276\) 0 0
\(277\) −1.90071e13 3.29212e13i −0.700288 1.21293i −0.968365 0.249537i \(-0.919722\pi\)
0.268077 0.963397i \(-0.413612\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −3.06527e13 −1.04372 −0.521860 0.853031i \(-0.674762\pi\)
−0.521860 + 0.853031i \(0.674762\pi\)
\(282\) 0 0
\(283\) 3.55669e12 + 6.16037e12i 0.116472 + 0.201735i 0.918367 0.395729i \(-0.129508\pi\)
−0.801895 + 0.597465i \(0.796175\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 1.64561e12 2.02549e12i 0.0498859 0.0614015i
\(288\) 0 0
\(289\) 5.53527e12 9.58736e12i 0.161510 0.279744i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −4.95279e12 −0.133992 −0.0669959 0.997753i \(-0.521341\pi\)
−0.0669959 + 0.997753i \(0.521341\pi\)
\(294\) 0 0
\(295\) −4.52193e12 −0.117843
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −4.93571e12 + 8.54890e12i −0.119442 + 0.206880i
\(300\) 0 0
\(301\) −2.40343e13 + 2.95824e13i −0.560682 + 0.690110i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −1.02614e13 1.77733e13i −0.222616 0.385583i
\(306\) 0 0
\(307\) 2.23542e13 0.467842 0.233921 0.972256i \(-0.424844\pi\)
0.233921 + 0.972256i \(0.424844\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −2.65812e13 4.60399e13i −0.518074 0.897330i −0.999780 0.0209972i \(-0.993316\pi\)
0.481706 0.876333i \(-0.340017\pi\)
\(312\) 0 0
\(313\) −2.79998e13 + 4.84971e13i −0.526819 + 0.912476i 0.472693 + 0.881227i \(0.343282\pi\)
−0.999512 + 0.0312493i \(0.990051\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 3.41827e13 5.92062e13i 0.599764 1.03882i −0.393092 0.919499i \(-0.628594\pi\)
0.992856 0.119322i \(-0.0380722\pi\)
\(318\) 0 0
\(319\) −8.75535e12 1.51647e13i −0.148397 0.257031i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −4.38598e13 −0.694148
\(324\) 0 0
\(325\) −2.43761e13 4.22207e13i −0.372912 0.645902i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −1.51033e13 3.95357e13i −0.216021 0.565473i
\(330\) 0 0
\(331\) −1.92107e13 + 3.32739e13i −0.265759 + 0.460309i −0.967762 0.251865i \(-0.918956\pi\)
0.702003 + 0.712174i \(0.252289\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −1.56676e13 −0.202887
\(336\) 0 0
\(337\) −1.59403e14 −1.99771 −0.998855 0.0478440i \(-0.984765\pi\)
−0.998855 + 0.0478440i \(0.984765\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 5.78938e12 1.00275e13i 0.0679959 0.117772i
\(342\) 0 0
\(343\) 7.81490e13 + 4.02955e13i 0.888803 + 0.458289i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −3.76248e13 6.51680e13i −0.401478 0.695380i 0.592426 0.805625i \(-0.298170\pi\)
−0.993905 + 0.110244i \(0.964837\pi\)
\(348\) 0 0
\(349\) −1.81299e14 −1.87437 −0.937187 0.348828i \(-0.886580\pi\)
−0.937187 + 0.348828i \(0.886580\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 6.08571e12 + 1.05408e13i 0.0590949 + 0.102355i 0.894059 0.447948i \(-0.147845\pi\)
−0.834964 + 0.550304i \(0.814512\pi\)
\(354\) 0 0
\(355\) −1.38483e13 + 2.39859e13i −0.130359 + 0.225788i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 4.61043e13 7.98551e13i 0.408058 0.706778i −0.586614 0.809867i \(-0.699539\pi\)
0.994672 + 0.103089i \(0.0328726\pi\)
\(360\) 0 0
\(361\) 1.67890e13 + 2.90794e13i 0.144123 + 0.249629i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 2.47230e13 0.199751
\(366\) 0 0
\(367\) −3.47460e13 6.01818e13i −0.272421 0.471847i 0.697060 0.717013i \(-0.254491\pi\)
−0.969481 + 0.245165i \(0.921158\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −7.98826e13 1.27840e13i −0.590060 0.0944303i
\(372\) 0 0
\(373\) 2.75190e13 4.76643e13i 0.197349 0.341818i −0.750319 0.661076i \(-0.770100\pi\)
0.947668 + 0.319258i \(0.103434\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 4.28225e13 0.289597
\(378\) 0 0
\(379\) 1.64609e14 1.08128 0.540640 0.841254i \(-0.318182\pi\)
0.540640 + 0.841254i \(0.318182\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −2.37086e13 + 4.10645e13i −0.146998 + 0.254609i −0.930117 0.367264i \(-0.880295\pi\)
0.783118 + 0.621873i \(0.213628\pi\)
\(384\) 0 0
\(385\) −3.59652e13 + 4.42674e13i −0.216695 + 0.266717i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 1.47659e14 + 2.55752e14i 0.840496 + 1.45578i 0.889476 + 0.456982i \(0.151070\pi\)
−0.0489795 + 0.998800i \(0.515597\pi\)
\(390\) 0 0
\(391\) 4.06194e13 0.224782
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −2.66587e13 4.61742e13i −0.139494 0.241610i
\(396\) 0 0
\(397\) 1.02252e14 1.77106e14i 0.520386 0.901335i −0.479333 0.877633i \(-0.659121\pi\)
0.999719 0.0237017i \(-0.00754518\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 7.18349e13 1.24422e14i 0.345972 0.599242i −0.639558 0.768743i \(-0.720882\pi\)
0.985530 + 0.169502i \(0.0542158\pi\)
\(402\) 0 0
\(403\) 1.41579e13 + 2.45223e13i 0.0663472 + 0.114917i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −1.59674e14 −0.708703
\(408\) 0 0
\(409\) −5.12511e13 8.87695e13i −0.221424 0.383518i 0.733816 0.679348i \(-0.237737\pi\)
−0.955241 + 0.295830i \(0.904404\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 7.40964e13 + 1.18580e13i 0.303439 + 0.0485610i
\(414\) 0 0
\(415\) −6.40457e13 + 1.10930e14i −0.255403 + 0.442371i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −2.06951e14 −0.782871 −0.391436 0.920206i \(-0.628021\pi\)
−0.391436 + 0.920206i \(0.628021\pi\)
\(420\) 0 0
\(421\) −2.28895e13 −0.0843498 −0.0421749 0.999110i \(-0.513429\pi\)
−0.0421749 + 0.999110i \(0.513429\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −1.00304e14 + 1.73732e14i −0.350896 + 0.607770i
\(426\) 0 0
\(427\) 1.21536e14 + 3.18142e14i 0.414335 + 1.08459i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 6.89096e13 + 1.19355e14i 0.223180 + 0.386559i 0.955772 0.294109i \(-0.0950230\pi\)
−0.732592 + 0.680668i \(0.761690\pi\)
\(432\) 0 0
\(433\) 1.37606e14 0.434463 0.217231 0.976120i \(-0.430297\pi\)
0.217231 + 0.976120i \(0.430297\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 3.83933e13 + 6.64992e13i 0.115241 + 0.199604i
\(438\) 0 0
\(439\) 2.24449e14 3.88757e14i 0.656996 1.13795i −0.324393 0.945922i \(-0.605160\pi\)
0.981389 0.192028i \(-0.0615066\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −9.09994e13 + 1.57616e14i −0.253407 + 0.438913i −0.964462 0.264223i \(-0.914884\pi\)
0.711055 + 0.703137i \(0.248218\pi\)
\(444\) 0 0
\(445\) −2.60128e13 4.50555e13i −0.0706654 0.122396i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −7.82493e13 −0.202360 −0.101180 0.994868i \(-0.532262\pi\)
−0.101180 + 0.994868i \(0.532262\pi\)
\(450\) 0 0
\(451\) −1.40462e13 2.43288e13i −0.0354478 0.0613973i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −4.97760e13 1.30298e14i −0.119662 0.313238i
\(456\) 0 0
\(457\) 6.37712e12 1.10455e13i 0.0149653 0.0259206i −0.858446 0.512904i \(-0.828570\pi\)
0.873411 + 0.486984i \(0.161903\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 4.11130e14 0.919653 0.459826 0.888009i \(-0.347912\pi\)
0.459826 + 0.888009i \(0.347912\pi\)
\(462\) 0 0
\(463\) 8.91432e14 1.94712 0.973560 0.228430i \(-0.0733593\pi\)
0.973560 + 0.228430i \(0.0733593\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −9.36710e13 + 1.62243e14i −0.195147 + 0.338005i −0.946949 0.321384i \(-0.895852\pi\)
0.751802 + 0.659389i \(0.229185\pi\)
\(468\) 0 0
\(469\) 2.56729e14 + 4.10857e13i 0.522425 + 0.0836064i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 2.05147e14 + 3.55324e14i 0.398408 + 0.690063i
\(474\) 0 0
\(475\) −3.79228e14 −0.719591
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 3.54805e14 + 6.14540e14i 0.642901 + 1.11354i 0.984782 + 0.173794i \(0.0556028\pi\)
−0.341881 + 0.939743i \(0.611064\pi\)
\(480\) 0 0
\(481\) 1.95241e14 3.38168e14i 0.345759 0.598873i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 1.11587e14 1.93275e14i 0.188814 0.327036i
\(486\) 0 0
\(487\) 1.72334e14 + 2.98491e14i 0.285077 + 0.493768i 0.972628 0.232368i \(-0.0746475\pi\)
−0.687551 + 0.726136i \(0.741314\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −2.50906e12 −0.00396791 −0.00198396 0.999998i \(-0.500632\pi\)
−0.00198396 + 0.999998i \(0.500632\pi\)
\(492\) 0 0
\(493\) −8.81039e13 1.52601e14i −0.136250 0.235992i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 2.89817e14 3.56719e14i 0.428711 0.527674i
\(498\) 0 0
\(499\) 3.62370e12 6.27644e12i 0.00524324 0.00908155i −0.863392 0.504534i \(-0.831664\pi\)
0.868635 + 0.495452i \(0.164998\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 1.22748e15 1.69977 0.849887 0.526965i \(-0.176670\pi\)
0.849887 + 0.526965i \(0.176670\pi\)
\(504\) 0 0
\(505\) 4.00297e14 0.542351
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 1.64697e13 2.85263e13i 0.0213667 0.0370082i −0.855144 0.518390i \(-0.826532\pi\)
0.876511 + 0.481382i \(0.159865\pi\)
\(510\) 0 0
\(511\) −4.05111e14 6.48320e13i −0.514350 0.0823142i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −9.72497e13 1.68441e14i −0.118290 0.204884i
\(516\) 0 0
\(517\) −4.55581e14 −0.542459
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 4.69615e14 + 8.13397e14i 0.535962 + 0.928314i 0.999116 + 0.0420361i \(0.0133844\pi\)
−0.463154 + 0.886278i \(0.653282\pi\)
\(522\) 0 0
\(523\) −4.77717e14 + 8.27430e14i −0.533840 + 0.924639i 0.465378 + 0.885112i \(0.345918\pi\)
−0.999219 + 0.0395267i \(0.987415\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 5.82577e13 1.00905e14i 0.0624303 0.108132i
\(528\) 0 0
\(529\) 4.40848e14 + 7.63571e14i 0.462682 + 0.801389i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 6.87002e13 0.0691765
\(534\) 0 0
\(535\) 3.37962e14 + 5.85367e14i 0.333366 + 0.577408i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 7.05410e14 6.31053e14i 0.667888 0.597486i
\(540\) 0 0
\(541\) −5.37113e14 + 9.30307e14i −0.498289 + 0.863061i −0.999998 0.00197505i \(-0.999371\pi\)
0.501709 + 0.865036i \(0.332705\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 3.66969e14 0.326926
\(546\) 0 0
\(547\) 1.38381e15 1.20822 0.604111 0.796900i \(-0.293528\pi\)
0.604111 + 0.796900i \(0.293528\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 1.66551e14 2.88475e14i 0.139706 0.241977i
\(552\) 0 0
\(553\) 3.15745e14 + 8.26519e14i 0.259626 + 0.679618i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 7.14824e14 + 1.23811e15i 0.564931 + 0.978490i 0.997056 + 0.0766761i \(0.0244307\pi\)
−0.432125 + 0.901814i \(0.642236\pi\)
\(558\) 0 0
\(559\) −1.00337e15 −0.777495
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 1.27988e15 + 2.21682e15i 0.953615 + 1.65171i 0.737507 + 0.675340i \(0.236003\pi\)
0.216108 + 0.976370i \(0.430664\pi\)
\(564\) 0 0
\(565\) −3.13461e14 + 5.42930e14i −0.229043 + 0.396714i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 1.13256e15 1.96165e15i 0.796056 1.37881i −0.126110 0.992016i \(-0.540249\pi\)
0.922166 0.386794i \(-0.126417\pi\)
\(570\) 0 0
\(571\) −5.49376e14 9.51547e14i −0.378766 0.656042i 0.612117 0.790767i \(-0.290318\pi\)
−0.990883 + 0.134725i \(0.956985\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 3.51211e14 0.233021
\(576\) 0 0
\(577\) −1.22669e15 2.12470e15i −0.798490 1.38303i −0.920599 0.390509i \(-0.872299\pi\)
0.122109 0.992517i \(-0.461034\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 1.34035e15 1.64976e15i 0.839943 1.03384i
\(582\) 0 0
\(583\) −4.35421e14 + 7.54172e14i −0.267752 + 0.463760i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 3.57451e14 0.211693 0.105847 0.994382i \(-0.466245\pi\)
0.105847 + 0.994382i \(0.466245\pi\)
\(588\) 0 0
\(589\) 2.20260e14 0.128027
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −3.47719e14 + 6.02267e14i −0.194728 + 0.337278i −0.946811 0.321790i \(-0.895716\pi\)
0.752084 + 0.659068i \(0.229049\pi\)
\(594\) 0 0
\(595\) −3.61913e14 + 4.45457e14i −0.198958 + 0.244885i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −1.18753e14 2.05685e14i −0.0629210 0.108982i 0.832849 0.553500i \(-0.186708\pi\)
−0.895770 + 0.444518i \(0.853375\pi\)
\(600\) 0 0
\(601\) 2.93732e15 1.52806 0.764032 0.645178i \(-0.223217\pi\)
0.764032 + 0.645178i \(0.223217\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −7.52816e13 1.30391e14i −0.0377602 0.0654026i
\(606\) 0 0
\(607\) 8.62651e14 1.49416e15i 0.424910 0.735966i −0.571502 0.820601i \(-0.693639\pi\)
0.996412 + 0.0846345i \(0.0269723\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 5.57062e14 9.64860e14i 0.264653 0.458393i
\(612\) 0 0
\(613\) −5.07686e14 8.79338e14i −0.236899 0.410320i 0.722924 0.690927i \(-0.242798\pi\)
−0.959823 + 0.280607i \(0.909464\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −4.29465e15 −1.93357 −0.966784 0.255595i \(-0.917729\pi\)
−0.966784 + 0.255595i \(0.917729\pi\)
\(618\) 0 0
\(619\) −8.18875e14 1.41833e15i −0.362175 0.627306i 0.626143 0.779708i \(-0.284633\pi\)
−0.988319 + 0.152402i \(0.951299\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 3.08095e14 + 8.06495e14i 0.131523 + 0.344284i
\(624\) 0 0
\(625\) −6.91964e14 + 1.19852e15i −0.290231 + 0.502694i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −1.60678e15 −0.650694
\(630\) 0 0
\(631\) 2.24346e15 0.892804 0.446402 0.894832i \(-0.352705\pi\)
0.446402 + 0.894832i \(0.352705\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −2.75401e14 + 4.77008e14i −0.105855 + 0.183346i
\(636\) 0 0
\(637\) 4.73946e14 + 2.26559e15i 0.179045 + 0.855883i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −9.60927e14 1.66437e15i −0.350729 0.607480i 0.635649 0.771978i \(-0.280733\pi\)
−0.986377 + 0.164499i \(0.947399\pi\)
\(642\) 0 0
\(643\) −8.48487e14 −0.304428 −0.152214 0.988348i \(-0.548640\pi\)
−0.152214 + 0.988348i \(0.548640\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1.54367e15 + 2.67372e15i 0.535280 + 0.927132i 0.999150 + 0.0412287i \(0.0131272\pi\)
−0.463870 + 0.885903i \(0.653539\pi\)
\(648\) 0 0
\(649\) 4.03882e14 6.99544e14i 0.137692 0.238489i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −4.33958e14 + 7.51637e14i −0.143029 + 0.247734i −0.928636 0.370992i \(-0.879018\pi\)
0.785607 + 0.618726i \(0.212351\pi\)
\(654\) 0 0
\(655\) −4.59211e13 7.95378e13i −0.0148828 0.0257778i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −3.99805e15 −1.25308 −0.626540 0.779389i \(-0.715529\pi\)
−0.626540 + 0.779389i \(0.715529\pi\)
\(660\) 0 0
\(661\) −1.60004e15 2.77135e15i −0.493200 0.854247i 0.506770 0.862081i \(-0.330839\pi\)
−0.999969 + 0.00783472i \(0.997506\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −1.07135e15 1.71454e14i −0.319457 0.0511244i
\(666\) 0 0
\(667\) −1.54246e14 + 2.67163e14i −0.0452400 + 0.0783580i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 3.66604e15 1.04045
\(672\) 0 0
\(673\) 6.83323e15 1.90785 0.953923 0.300052i \(-0.0970041\pi\)
0.953923 + 0.300052i \(0.0970041\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −1.59834e15 + 2.76841e15i −0.431949 + 0.748158i −0.997041 0.0768700i \(-0.975507\pi\)
0.565092 + 0.825028i \(0.308841\pi\)
\(678\) 0 0
\(679\) −2.33530e15 + 2.87438e15i −0.620954 + 0.764295i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 1.63286e14 + 2.82819e14i 0.0420372 + 0.0728106i 0.886278 0.463153i \(-0.153282\pi\)
−0.844241 + 0.535963i \(0.819949\pi\)
\(684\) 0 0
\(685\) −4.12754e14 −0.104567
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −1.06482e15 1.84433e15i −0.261260 0.452515i
\(690\) 0 0
\(691\) −1.77293e12 + 3.07081e12i −0.000428117 + 0.000741521i −0.866239 0.499629i \(-0.833470\pi\)
0.865811 + 0.500371i \(0.166803\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −1.49362e14 + 2.58703e14i −0.0349401 + 0.0605180i
\(696\) 0 0
\(697\) −1.41345e14 2.44817e14i −0.0325463 0.0563718i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −6.37107e15 −1.42155 −0.710777 0.703418i \(-0.751656\pi\)
−0.710777 + 0.703418i \(0.751656\pi\)
\(702\) 0 0
\(703\) −1.51872e15 2.63050e15i −0.333598 0.577809i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −6.55928e15 1.04972e15i −1.39653 0.223494i
\(708\) 0 0
\(709\) 3.87624e13 6.71385e13i 0.00812562 0.0140740i −0.861934 0.507020i \(-0.830747\pi\)
0.870060 + 0.492946i \(0.164080\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −2.03987e14 −0.0414582
\(714\) 0 0
\(715\) −1.50146e15 −0.300490
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −2.30995e15 + 4.00095e15i −0.448326 + 0.776523i −0.998277 0.0586734i \(-0.981313\pi\)
0.549951 + 0.835197i \(0.314646\pi\)
\(720\) 0 0
\(721\) 1.15182e15 + 3.01511e15i 0.220162 + 0.576313i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −7.61781e14 1.31944e15i −0.141244 0.244642i
\(726\) 0 0
\(727\) −2.05407e14 −0.0375124 −0.0187562 0.999824i \(-0.505971\pi\)
−0.0187562 + 0.999824i \(0.505971\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 2.06436e15 + 3.57558e15i 0.365797 + 0.633579i
\(732\) 0 0
\(733\) 4.30318e15 7.45332e15i 0.751134 1.30100i −0.196140 0.980576i \(-0.562841\pi\)
0.947274 0.320426i \(-0.103826\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 1.39937e15 2.42378e15i 0.237061 0.410602i
\(738\) 0 0
\(739\) −4.84230e15 8.38712e15i −0.808179 1.39981i −0.914124 0.405435i \(-0.867120\pi\)
0.105945 0.994372i \(-0.466213\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −4.55474e15 −0.737947 −0.368974 0.929440i \(-0.620291\pi\)
−0.368974 + 0.929440i \(0.620291\pi\)
\(744\) 0 0
\(745\) −2.23426e15 3.86985e15i −0.356676 0.617782i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −4.00282e15 1.04781e16i −0.620463 1.62417i
\(750\) 0 0
\(751\) −4.98893e15 + 8.64108e15i −0.762058 + 1.31992i 0.179731 + 0.983716i \(0.442477\pi\)
−0.941788 + 0.336206i \(0.890856\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 1.98945e15 0.295138
\(756\) 0 0
\(757\) 2.16914e15 0.317146 0.158573 0.987347i \(-0.449311\pi\)
0.158573 + 0.987347i \(0.449311\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 4.02973e15 6.97970e15i 0.572349 0.991337i −0.423976 0.905674i \(-0.639366\pi\)
0.996324 0.0856631i \(-0.0273009\pi\)
\(762\) 0 0
\(763\) −6.01316e15 9.62318e14i −0.841818 0.134720i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 9.87695e14 + 1.71074e15i 0.134353 + 0.232707i
\(768\) 0 0
\(769\) −2.54259e15 −0.340943 −0.170472 0.985363i \(-0.554529\pi\)
−0.170472 + 0.985363i \(0.554529\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −6.44824e15 1.11687e16i −0.840338 1.45551i −0.889609 0.456723i \(-0.849023\pi\)
0.0492707 0.998785i \(-0.484310\pi\)
\(774\) 0 0
\(775\) 5.03719e14 8.72466e14i 0.0647185 0.112096i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 2.67199e14 4.62802e14i 0.0333717 0.0578015i
\(780\) 0 0
\(781\) −2.47375e15 4.28467e15i −0.304632 0.527638i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −2.34301e15