Properties

Label 252.12.k.d.37.3
Level $252$
Weight $12$
Character 252.37
Analytic conductor $193.622$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

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 37.3
Root \(-6748.51 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 252.37
Dual form 252.12.k.d.109.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-3239.51 + 5610.99i) q^{5} +(-44011.6 + 6348.37i) q^{7} +O(q^{10})\) \(q+(-3239.51 + 5610.99i) q^{5} +(-44011.6 + 6348.37i) q^{7} +(-153860. - 266493. i) q^{11} +584277. q^{13} +(-4.72018e6 - 8.17558e6i) q^{17} +(8.44479e6 - 1.46268e7i) q^{19} +(-1.59358e7 + 2.76016e7i) q^{23} +(3.42527e6 + 5.93275e6i) q^{25} +1.08011e8 q^{29} +(1.25482e8 + 2.17341e8i) q^{31} +(1.06955e8 - 2.67514e8i) q^{35} +(8.03798e7 - 1.39222e8i) q^{37} +5.43424e8 q^{41} +2.35306e8 q^{43} +(-4.31156e8 + 7.46784e8i) q^{47} +(1.89672e9 - 5.58805e8i) q^{49} +(1.83924e9 + 3.18566e9i) q^{53} +1.99372e9 q^{55} +(1.91162e9 + 3.31102e9i) q^{59} +(-2.30312e9 + 3.98912e9i) q^{61} +(-1.89277e9 + 3.27837e9i) q^{65} +(9.21035e8 + 1.59528e9i) q^{67} -1.51591e10 q^{71} +(-1.51263e10 - 2.61995e10i) q^{73} +(8.46341e9 + 1.07520e10i) q^{77} +(1.74865e10 - 3.02876e10i) q^{79} -2.03419e10 q^{83} +6.11641e10 q^{85} +(-4.42219e10 + 7.65945e10i) q^{89} +(-2.57150e10 + 3.70921e9i) q^{91} +(5.47139e10 + 9.47672e10i) q^{95} -9.58828e10 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 2156q^{5} + 50512q^{7} + O(q^{10}) \) \( 16q + 2156q^{5} + 50512q^{7} + 222796q^{11} + 2703176q^{13} - 5114600q^{17} + 6910556q^{19} + 51387712q^{23} - 191456372q^{25} - 118854616q^{29} + 164659160q^{31} - 55239344q^{35} + 75658364q^{37} + 1815568608q^{41} + 10754408q^{43} + 1034359464q^{47} + 4123496848q^{49} + 665159988q^{53} - 1264543896q^{55} - 1040514580q^{59} - 14391208024q^{61} + 20938150200q^{65} - 33307097284q^{67} - 65848902896q^{71} + 17709749204q^{73} - 8594484604q^{77} - 26626784032q^{79} + 210306955048q^{83} - 25867402032q^{85} + 55951560072q^{89} + 66078280292q^{91} - 106810047392q^{95} - 156216030712q^{97} + O(q^{100}) \)

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
\(5\) −3239.51 + 5610.99i −0.463600 + 0.802979i −0.999137 0.0415326i \(-0.986776\pi\)
0.535537 + 0.844512i \(0.320109\pi\)
\(6\) 0 0
\(7\) −44011.6 + 6348.37i −0.989757 + 0.142766i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −153860. 266493.i −0.288048 0.498914i 0.685296 0.728265i \(-0.259673\pi\)
−0.973344 + 0.229351i \(0.926340\pi\)
\(12\) 0 0
\(13\) 584277. 0.436446 0.218223 0.975899i \(-0.429974\pi\)
0.218223 + 0.975899i \(0.429974\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −4.72018e6 8.17558e6i −0.806286 1.39653i −0.915419 0.402501i \(-0.868141\pi\)
0.109134 0.994027i \(-0.465192\pi\)
\(18\) 0 0
\(19\) 8.44479e6 1.46268e7i 0.782427 1.35520i −0.148097 0.988973i \(-0.547315\pi\)
0.930524 0.366231i \(-0.119352\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −1.59358e7 + 2.76016e7i −0.516262 + 0.894193i 0.483559 + 0.875312i \(0.339344\pi\)
−0.999822 + 0.0188811i \(0.993990\pi\)
\(24\) 0 0
\(25\) 3.42527e6 + 5.93275e6i 0.0701496 + 0.121503i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 1.08011e8 0.977864 0.488932 0.872322i \(-0.337387\pi\)
0.488932 + 0.872322i \(0.337387\pi\)
\(30\) 0 0
\(31\) 1.25482e8 + 2.17341e8i 0.787210 + 1.36349i 0.927670 + 0.373402i \(0.121809\pi\)
−0.140459 + 0.990086i \(0.544858\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 1.06955e8 2.67514e8i 0.344214 0.860940i
\(36\) 0 0
\(37\) 8.03798e7 1.39222e8i 0.190563 0.330064i −0.754874 0.655870i \(-0.772302\pi\)
0.945437 + 0.325805i \(0.105635\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 5.43424e8 0.732534 0.366267 0.930510i \(-0.380636\pi\)
0.366267 + 0.930510i \(0.380636\pi\)
\(42\) 0 0
\(43\) 2.35306e8 0.244094 0.122047 0.992524i \(-0.461054\pi\)
0.122047 + 0.992524i \(0.461054\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −4.31156e8 + 7.46784e8i −0.274218 + 0.474960i −0.969938 0.243354i \(-0.921752\pi\)
0.695719 + 0.718314i \(0.255086\pi\)
\(48\) 0 0
\(49\) 1.89672e9 5.58805e8i 0.959236 0.282606i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 1.83924e9 + 3.18566e9i 0.604117 + 1.04636i 0.992190 + 0.124733i \(0.0398075\pi\)
−0.388073 + 0.921629i \(0.626859\pi\)
\(54\) 0 0
\(55\) 1.99372e9 0.534156
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 1.91162e9 + 3.31102e9i 0.348109 + 0.602943i 0.985914 0.167255i \(-0.0534905\pi\)
−0.637804 + 0.770198i \(0.720157\pi\)
\(60\) 0 0
\(61\) −2.30312e9 + 3.98912e9i −0.349142 + 0.604732i −0.986097 0.166169i \(-0.946860\pi\)
0.636955 + 0.770901i \(0.280194\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −1.89277e9 + 3.27837e9i −0.202336 + 0.350457i
\(66\) 0 0
\(67\) 9.21035e8 + 1.59528e9i 0.0833422 + 0.144353i 0.904684 0.426084i \(-0.140107\pi\)
−0.821341 + 0.570437i \(0.806774\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −1.51591e10 −0.997131 −0.498566 0.866852i \(-0.666140\pi\)
−0.498566 + 0.866852i \(0.666140\pi\)
\(72\) 0 0
\(73\) −1.51263e10 2.61995e10i −0.853997 1.47917i −0.877573 0.479444i \(-0.840838\pi\)
0.0235759 0.999722i \(-0.492495\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 8.46341e9 + 1.07520e10i 0.356325 + 0.452680i
\(78\) 0 0
\(79\) 1.74865e10 3.02876e10i 0.639374 1.10743i −0.346197 0.938162i \(-0.612527\pi\)
0.985570 0.169266i \(-0.0541396\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −2.03419e10 −0.566842 −0.283421 0.958996i \(-0.591469\pi\)
−0.283421 + 0.958996i \(0.591469\pi\)
\(84\) 0 0
\(85\) 6.11641e10 1.49518
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −4.42219e10 + 7.65945e10i −0.839444 + 1.45396i 0.0509155 + 0.998703i \(0.483786\pi\)
−0.890360 + 0.455257i \(0.849547\pi\)
\(90\) 0 0
\(91\) −2.57150e10 + 3.70921e9i −0.431975 + 0.0623094i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 5.47139e10 + 9.47672e10i 0.725467 + 1.25655i
\(96\) 0 0
\(97\) −9.58828e10 −1.13370 −0.566848 0.823823i \(-0.691837\pi\)
−0.566848 + 0.823823i \(0.691837\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −8.02124e10 1.38932e11i −0.759406 1.31533i −0.943154 0.332357i \(-0.892156\pi\)
0.183748 0.982973i \(-0.441177\pi\)
\(102\) 0 0
\(103\) 6.76095e10 1.17103e11i 0.574650 0.995322i −0.421430 0.906861i \(-0.638472\pi\)
0.996080 0.0884613i \(-0.0281950\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −4.11930e10 + 7.13484e10i −0.283931 + 0.491783i −0.972349 0.233531i \(-0.924972\pi\)
0.688418 + 0.725314i \(0.258305\pi\)
\(108\) 0 0
\(109\) −1.13457e11 1.96514e11i −0.706295 1.22334i −0.966222 0.257711i \(-0.917032\pi\)
0.259927 0.965628i \(-0.416301\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 1.73656e11 0.886661 0.443331 0.896358i \(-0.353797\pi\)
0.443331 + 0.896358i \(0.353797\pi\)
\(114\) 0 0
\(115\) −1.03248e11 1.78831e11i −0.478679 0.829096i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 2.59644e11 + 3.29855e11i 0.997403 + 1.26711i
\(120\) 0 0
\(121\) 9.53103e10 1.65082e11i 0.334057 0.578603i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −3.60743e11 −1.05729
\(126\) 0 0
\(127\) 5.34602e11 1.43585 0.717926 0.696119i \(-0.245091\pi\)
0.717926 + 0.696119i \(0.245091\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −2.15277e9 + 3.72871e9i −0.00487535 + 0.00844435i −0.868453 0.495772i \(-0.834885\pi\)
0.863577 + 0.504216i \(0.168219\pi\)
\(132\) 0 0
\(133\) −2.78813e11 + 6.97360e11i −0.580936 + 1.45303i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −2.72967e11 4.72793e11i −0.483222 0.836966i 0.516592 0.856232i \(-0.327200\pi\)
−0.999814 + 0.0192659i \(0.993867\pi\)
\(138\) 0 0
\(139\) −1.98706e11 −0.324811 −0.162405 0.986724i \(-0.551925\pi\)
−0.162405 + 0.986724i \(0.551925\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −8.98965e10 1.55705e11i −0.125717 0.217749i
\(144\) 0 0
\(145\) −3.49902e11 + 6.06048e11i −0.453338 + 0.785205i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −4.06132e11 + 7.03441e11i −0.453047 + 0.784700i −0.998574 0.0533936i \(-0.982996\pi\)
0.545527 + 0.838093i \(0.316330\pi\)
\(150\) 0 0
\(151\) 7.00195e10 + 1.21277e11i 0.0725848 + 0.125721i 0.900033 0.435821i \(-0.143542\pi\)
−0.827449 + 0.561541i \(0.810209\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −1.62599e12 −1.45980
\(156\) 0 0
\(157\) 8.58436e11 + 1.48686e12i 0.718224 + 1.24400i 0.961703 + 0.274094i \(0.0883780\pi\)
−0.243479 + 0.969906i \(0.578289\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 5.26135e11 1.31596e12i 0.383314 0.958737i
\(162\) 0 0
\(163\) −4.32301e11 + 7.48767e11i −0.294276 + 0.509701i −0.974816 0.223010i \(-0.928412\pi\)
0.680540 + 0.732711i \(0.261745\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 2.19947e12 1.31032 0.655160 0.755490i \(-0.272601\pi\)
0.655160 + 0.755490i \(0.272601\pi\)
\(168\) 0 0
\(169\) −1.45078e12 −0.809515
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 4.03725e11 6.99272e11i 0.198076 0.343078i −0.749828 0.661632i \(-0.769864\pi\)
0.947905 + 0.318554i \(0.103197\pi\)
\(174\) 0 0
\(175\) −1.88415e11 2.39365e11i −0.0867774 0.110243i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −1.33293e12 2.30870e12i −0.542145 0.939022i −0.998781 0.0493684i \(-0.984279\pi\)
0.456636 0.889654i \(-0.349054\pi\)
\(180\) 0 0
\(181\) 9.78597e11 0.374431 0.187216 0.982319i \(-0.440054\pi\)
0.187216 + 0.982319i \(0.440054\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 5.20782e11 + 9.02021e11i 0.176690 + 0.306036i
\(186\) 0 0
\(187\) −1.45249e12 + 2.51578e12i −0.464498 + 0.804534i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −3.05977e10 + 5.29968e10i −0.00870975 + 0.0150857i −0.870347 0.492438i \(-0.836106\pi\)
0.861638 + 0.507524i \(0.169439\pi\)
\(192\) 0 0
\(193\) −4.45854e11 7.72242e11i −0.119847 0.207581i 0.799860 0.600187i \(-0.204907\pi\)
−0.919707 + 0.392605i \(0.871574\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −1.84992e12 −0.444211 −0.222105 0.975023i \(-0.571293\pi\)
−0.222105 + 0.975023i \(0.571293\pi\)
\(198\) 0 0
\(199\) −1.14607e12 1.98506e12i −0.260328 0.450901i 0.706001 0.708210i \(-0.250497\pi\)
−0.966329 + 0.257310i \(0.917164\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −4.75374e12 + 6.85693e11i −0.967847 + 0.139605i
\(204\) 0 0
\(205\) −1.76043e12 + 3.04915e12i −0.339603 + 0.588210i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −5.19725e12 −0.901506
\(210\) 0 0
\(211\) −3.84826e12 −0.633449 −0.316724 0.948518i \(-0.602583\pi\)
−0.316724 + 0.948518i \(0.602583\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −7.62276e11 + 1.32030e12i −0.113162 + 0.196002i
\(216\) 0 0
\(217\) −6.90241e12 8.76891e12i −0.973806 1.23714i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −2.75789e12 4.77680e12i −0.351900 0.609509i
\(222\) 0 0
\(223\) 1.00191e13 1.21661 0.608303 0.793705i \(-0.291850\pi\)
0.608303 + 0.793705i \(0.291850\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 3.22157e12 + 5.57992e12i 0.354752 + 0.614449i 0.987075 0.160256i \(-0.0512320\pi\)
−0.632323 + 0.774704i \(0.717899\pi\)
\(228\) 0 0
\(229\) −8.43324e12 + 1.46068e13i −0.884911 + 1.53271i −0.0390952 + 0.999235i \(0.512448\pi\)
−0.845816 + 0.533475i \(0.820886\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −7.37785e12 + 1.27788e13i −0.703837 + 1.21908i 0.263273 + 0.964721i \(0.415198\pi\)
−0.967110 + 0.254360i \(0.918135\pi\)
\(234\) 0 0
\(235\) −2.79346e12 4.83842e12i −0.254255 0.440383i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −2.22602e13 −1.84646 −0.923231 0.384247i \(-0.874461\pi\)
−0.923231 + 0.384247i \(0.874461\pi\)
\(240\) 0 0
\(241\) −5.59484e12 9.69055e12i −0.443296 0.767812i 0.554636 0.832093i \(-0.312858\pi\)
−0.997932 + 0.0642818i \(0.979524\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −3.00900e12 + 1.24527e13i −0.217775 + 0.901263i
\(246\) 0 0
\(247\) 4.93409e12 8.54610e12i 0.341487 0.591473i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −2.65870e13 −1.68447 −0.842237 0.539107i \(-0.818762\pi\)
−0.842237 + 0.539107i \(0.818762\pi\)
\(252\) 0 0
\(253\) 9.80749e12 0.594833
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −8.80530e12 + 1.52512e13i −0.489905 + 0.848541i −0.999933 0.0116173i \(-0.996302\pi\)
0.510027 + 0.860158i \(0.329635\pi\)
\(258\) 0 0
\(259\) −2.65382e12 + 6.63767e12i −0.141489 + 0.353889i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 9.38995e12 + 1.62639e13i 0.460158 + 0.797016i 0.998968 0.0454104i \(-0.0144596\pi\)
−0.538811 + 0.842427i \(0.681126\pi\)
\(264\) 0 0
\(265\) −2.38329e13 −1.12028
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 1.02550e13 + 1.77621e13i 0.443912 + 0.768878i 0.997976 0.0635960i \(-0.0202569\pi\)
−0.554064 + 0.832474i \(0.686924\pi\)
\(270\) 0 0
\(271\) 1.99679e13 3.45854e13i 0.829853 1.43735i −0.0683002 0.997665i \(-0.521758\pi\)
0.898153 0.439683i \(-0.144909\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 1.05402e12 1.82562e12i 0.0404129 0.0699972i
\(276\) 0 0
\(277\) 8.57932e12 + 1.48598e13i 0.316092 + 0.547488i 0.979669 0.200620i \(-0.0642957\pi\)
−0.663577 + 0.748108i \(0.730962\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 2.74808e12 0.0935718 0.0467859 0.998905i \(-0.485102\pi\)
0.0467859 + 0.998905i \(0.485102\pi\)
\(282\) 0 0
\(283\) −6.50503e12 1.12670e13i −0.213022 0.368965i 0.739637 0.673006i \(-0.234997\pi\)
−0.952659 + 0.304041i \(0.901664\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −2.39170e13 + 3.44986e12i −0.725030 + 0.104581i
\(288\) 0 0
\(289\) −2.74242e13 + 4.75001e13i −0.800194 + 1.38598i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −1.21317e13 −0.328208 −0.164104 0.986443i \(-0.552473\pi\)
−0.164104 + 0.986443i \(0.552473\pi\)
\(294\) 0 0
\(295\) −2.47708e13 −0.645534
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −9.31091e12 + 1.61270e13i −0.225320 + 0.390266i
\(300\) 0 0
\(301\) −1.03562e13 + 1.49381e12i −0.241594 + 0.0348482i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −1.49219e13 2.58455e13i −0.323725 0.560708i
\(306\) 0 0
\(307\) 2.49166e13 0.521467 0.260734 0.965411i \(-0.416036\pi\)
0.260734 + 0.965411i \(0.416036\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −2.40293e13 4.16199e13i −0.468337 0.811184i 0.531008 0.847367i \(-0.321813\pi\)
−0.999345 + 0.0361830i \(0.988480\pi\)
\(312\) 0 0
\(313\) −2.23518e13 + 3.87144e13i −0.420550 + 0.728415i −0.995993 0.0894273i \(-0.971496\pi\)
0.575443 + 0.817842i \(0.304830\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −2.52513e13 + 4.37365e13i −0.443055 + 0.767394i −0.997914 0.0645502i \(-0.979439\pi\)
0.554859 + 0.831944i \(0.312772\pi\)
\(318\) 0 0
\(319\) −1.66185e13 2.87841e13i −0.281672 0.487870i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −1.59444e14 −2.52344
\(324\) 0 0
\(325\) 2.00131e12 + 3.46637e12i 0.0306165 + 0.0530293i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 1.42350e13 3.56043e13i 0.203601 0.509243i
\(330\) 0 0
\(331\) −5.47976e13 + 9.49122e13i −0.758067 + 1.31301i 0.185769 + 0.982594i \(0.440523\pi\)
−0.943835 + 0.330416i \(0.892811\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −1.19348e13 −0.154550
\(336\) 0 0
\(337\) 6.51104e13 0.815992 0.407996 0.912984i \(-0.366228\pi\)
0.407996 + 0.912984i \(0.366228\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 3.86131e13 6.68799e13i 0.453509 0.785500i
\(342\) 0 0
\(343\) −7.99304e13 + 3.66350e13i −0.909064 + 0.416657i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −1.58107e13 2.73849e13i −0.168709 0.292212i 0.769257 0.638939i \(-0.220626\pi\)
−0.937966 + 0.346727i \(0.887293\pi\)
\(348\) 0 0
\(349\) −1.82337e14 −1.88510 −0.942549 0.334068i \(-0.891578\pi\)
−0.942549 + 0.334068i \(0.891578\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −5.26328e13 9.11627e13i −0.511088 0.885230i −0.999917 0.0128510i \(-0.995909\pi\)
0.488829 0.872379i \(-0.337424\pi\)
\(354\) 0 0
\(355\) 4.91080e13 8.50575e13i 0.462270 0.800676i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −6.42748e13 + 1.11327e14i −0.568881 + 0.985330i 0.427796 + 0.903875i \(0.359290\pi\)
−0.996677 + 0.0814552i \(0.974043\pi\)
\(360\) 0 0
\(361\) −8.43838e13 1.46157e14i −0.724385 1.25467i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 1.96007e14 1.58365
\(366\) 0 0
\(367\) 9.45396e13 + 1.63747e14i 0.741225 + 1.28384i 0.951938 + 0.306292i \(0.0990884\pi\)
−0.210712 + 0.977548i \(0.567578\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −1.01172e14 1.28530e14i −0.747313 0.949396i
\(372\) 0 0
\(373\) −1.09656e14 + 1.89929e14i −0.786381 + 1.36205i 0.141790 + 0.989897i \(0.454714\pi\)
−0.928171 + 0.372155i \(0.878619\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 6.31082e13 0.426784
\(378\) 0 0
\(379\) 4.98932e13 0.327737 0.163869 0.986482i \(-0.447603\pi\)
0.163869 + 0.986482i \(0.447603\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −1.22245e14 + 2.11734e14i −0.757945 + 1.31280i 0.185952 + 0.982559i \(0.440463\pi\)
−0.943897 + 0.330240i \(0.892870\pi\)
\(384\) 0 0
\(385\) −8.77467e13 + 1.26569e13i −0.528685 + 0.0762591i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −1.42290e13 2.46453e13i −0.0809937 0.140285i 0.822683 0.568500i \(-0.192476\pi\)
−0.903677 + 0.428215i \(0.859143\pi\)
\(390\) 0 0
\(391\) 3.00879e14 1.66502
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 1.13295e14 + 1.96233e14i 0.592828 + 1.02681i
\(396\) 0 0
\(397\) 5.53607e13 9.58875e13i 0.281743 0.487994i −0.690071 0.723742i \(-0.742421\pi\)
0.971814 + 0.235748i \(0.0757540\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 2.25564e13 3.90688e13i 0.108636 0.188164i −0.806582 0.591123i \(-0.798685\pi\)
0.915218 + 0.402959i \(0.132018\pi\)
\(402\) 0 0
\(403\) 7.33160e13 + 1.26987e14i 0.343574 + 0.595088i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −4.94688e13 −0.219565
\(408\) 0 0
\(409\) 1.07447e13 + 1.86104e13i 0.0464213 + 0.0804041i 0.888302 0.459259i \(-0.151885\pi\)
−0.841881 + 0.539663i \(0.818552\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −1.05153e14 1.33588e14i −0.430623 0.547069i
\(414\) 0 0
\(415\) 6.58977e13 1.14138e14i 0.262788 0.455163i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 4.15127e14 1.57038 0.785189 0.619256i \(-0.212566\pi\)
0.785189 + 0.619256i \(0.212566\pi\)
\(420\) 0 0
\(421\) 1.01947e14 0.375683 0.187842 0.982199i \(-0.439851\pi\)
0.187842 + 0.982199i \(0.439851\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 3.23358e13 5.60072e13i 0.113121 0.195932i
\(426\) 0 0
\(427\) 7.60396e13 1.90189e14i 0.259231 0.648383i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 4.54120e13 + 7.86560e13i 0.147077 + 0.254746i 0.930146 0.367190i \(-0.119680\pi\)
−0.783069 + 0.621935i \(0.786347\pi\)
\(432\) 0 0
\(433\) 2.65109e14 0.837029 0.418515 0.908210i \(-0.362551\pi\)
0.418515 + 0.908210i \(0.362551\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 2.69149e14 + 4.66179e14i 0.807875 + 1.39928i
\(438\) 0 0
\(439\) 9.01623e13 1.56166e14i 0.263919 0.457121i −0.703361 0.710833i \(-0.748318\pi\)
0.967280 + 0.253712i \(0.0816516\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 1.03229e14 1.78798e14i 0.287463 0.497901i −0.685740 0.727846i \(-0.740521\pi\)
0.973203 + 0.229946i \(0.0738548\pi\)
\(444\) 0 0
\(445\) −2.86514e14 4.96257e14i −0.778333 1.34811i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −2.98661e14 −0.772366 −0.386183 0.922422i \(-0.626207\pi\)
−0.386183 + 0.922422i \(0.626207\pi\)
\(450\) 0 0
\(451\) −8.36110e13 1.44819e14i −0.211005 0.365471i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 6.24915e13 1.56302e14i 0.150231 0.375753i
\(456\) 0 0
\(457\) 3.32118e13 5.75245e13i 0.0779386 0.134994i −0.824422 0.565976i \(-0.808500\pi\)
0.902360 + 0.430982i \(0.141833\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 6.90622e13 0.154485 0.0772424 0.997012i \(-0.475388\pi\)
0.0772424 + 0.997012i \(0.475388\pi\)
\(462\) 0 0
\(463\) −2.06831e14 −0.451772 −0.225886 0.974154i \(-0.572528\pi\)
−0.225886 + 0.974154i \(0.572528\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −3.93370e14 + 6.81337e14i −0.819518 + 1.41945i 0.0865201 + 0.996250i \(0.472425\pi\)
−0.906038 + 0.423196i \(0.860908\pi\)
\(468\) 0 0
\(469\) −5.06637e13 6.43638e13i −0.103097 0.130976i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −3.62041e13 6.27074e13i −0.0703108 0.121782i
\(474\) 0 0
\(475\) 1.15703e14 0.219548
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 6.50604e13 + 1.12688e14i 0.117889 + 0.204189i 0.918931 0.394419i \(-0.129054\pi\)
−0.801042 + 0.598608i \(0.795721\pi\)
\(480\) 0 0
\(481\) 4.69641e13 8.13441e13i 0.0831702 0.144055i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 3.10613e14 5.37997e14i 0.525581 0.910334i
\(486\) 0 0
\(487\) −3.32294e13 5.75550e13i −0.0549684 0.0952081i 0.837232 0.546848i \(-0.184172\pi\)
−0.892200 + 0.451640i \(0.850839\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 2.37328e13 0.0375320 0.0187660 0.999824i \(-0.494026\pi\)
0.0187660 + 0.999824i \(0.494026\pi\)
\(492\) 0 0
\(493\) −5.09830e14 8.83052e14i −0.788438 1.36561i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 6.67177e14 9.62356e13i 0.986917 0.142356i
\(498\) 0 0
\(499\) −4.56733e14 + 7.91084e14i −0.660859 + 1.14464i 0.319531 + 0.947576i \(0.396475\pi\)
−0.980390 + 0.197066i \(0.936859\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 4.77391e12 0.00661075 0.00330537 0.999995i \(-0.498948\pi\)
0.00330537 + 0.999995i \(0.498948\pi\)
\(504\) 0 0
\(505\) 1.03939e15 1.40824
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 6.48244e14 1.12279e15i 0.840990 1.45664i −0.0480692 0.998844i \(-0.515307\pi\)
0.889059 0.457793i \(-0.151360\pi\)
\(510\) 0 0
\(511\) 8.32056e14 + 1.05705e15i 1.05642 + 1.34209i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 4.38043e14 + 7.58712e14i 0.532815 + 0.922863i
\(516\) 0 0
\(517\) 2.65350e14 0.315952
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 2.33019e14 + 4.03600e14i 0.265940 + 0.460621i 0.967809 0.251684i \(-0.0809844\pi\)
−0.701870 + 0.712305i \(0.747651\pi\)
\(522\) 0 0
\(523\) 6.61957e14 1.14654e15i 0.739725 1.28124i −0.212894 0.977075i \(-0.568289\pi\)
0.952619 0.304166i \(-0.0983777\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 1.18459e15 2.05177e15i 1.26943 2.19872i
\(528\) 0 0
\(529\) −3.14938e13 5.45489e13i −0.0330536 0.0572505i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 3.17510e14 0.319711
\(534\) 0 0
\(535\) −2.66890e14 4.62267e14i −0.263261 0.455982i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −4.40746e14 4.19485e14i −0.417302 0.397172i
\(540\) 0 0
\(541\) −8.67334e14 + 1.50227e15i −0.804639 + 1.39368i 0.111895 + 0.993720i \(0.464308\pi\)
−0.916534 + 0.399956i \(0.869025\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 1.47018e15 1.30975
\(546\) 0 0
\(547\) 1.77536e15 1.55009 0.775043 0.631908i \(-0.217728\pi\)
0.775043 + 0.631908i \(0.217728\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 9.12129e14 1.57985e15i 0.765108 1.32521i
\(552\) 0 0
\(553\) −5.77334e14 + 1.44402e15i −0.474722 + 1.18736i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −5.78568e14 1.00211e15i −0.457247 0.791975i 0.541567 0.840657i \(-0.317831\pi\)
−0.998814 + 0.0486825i \(0.984498\pi\)
\(558\) 0 0
\(559\) 1.37484e14 0.106534
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 3.74197e13 + 6.48129e13i 0.0278808 + 0.0482909i 0.879629 0.475660i \(-0.157791\pi\)
−0.851748 + 0.523951i \(0.824457\pi\)
\(564\) 0 0
\(565\) −5.62559e14 + 9.74380e14i −0.411056 + 0.711971i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −7.17284e14 + 1.24237e15i −0.504166 + 0.873242i 0.495822 + 0.868424i \(0.334867\pi\)
−0.999988 + 0.00481770i \(0.998466\pi\)
\(570\) 0 0
\(571\) 5.10440e14 + 8.84108e14i 0.351922 + 0.609546i 0.986586 0.163242i \(-0.0521950\pi\)
−0.634665 + 0.772788i \(0.718862\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −2.18338e14 −0.144862
\(576\) 0 0
\(577\) 3.42848e14 + 5.93830e14i 0.223169 + 0.386540i 0.955769 0.294120i \(-0.0950264\pi\)
−0.732599 + 0.680660i \(0.761693\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 8.95281e14 1.29138e14i 0.561036 0.0809255i
\(582\) 0 0
\(583\) 5.65970e14 9.80288e14i 0.348029 0.602805i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 2.45428e15 1.45350 0.726749 0.686903i \(-0.241030\pi\)
0.726749 + 0.686903i \(0.241030\pi\)
\(588\) 0 0
\(589\) 4.23866e15 2.46374
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −1.66959e14 + 2.89182e14i −0.0934995 + 0.161946i −0.908981 0.416837i \(-0.863139\pi\)
0.815482 + 0.578783i \(0.196472\pi\)
\(594\) 0 0
\(595\) −2.69193e15 + 3.88293e14i −1.47986 + 0.213460i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 1.76178e14 + 3.05148e14i 0.0933476 + 0.161683i 0.908918 0.416975i \(-0.136910\pi\)
−0.815570 + 0.578658i \(0.803577\pi\)
\(600\) 0 0
\(601\) −1.86713e15 −0.971327 −0.485663 0.874146i \(-0.661422\pi\)
−0.485663 + 0.874146i \(0.661422\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 6.17516e14 + 1.06957e15i 0.309738 + 0.536481i
\(606\) 0 0
\(607\) 1.87189e14 3.24221e14i 0.0922025 0.159699i −0.816235 0.577720i \(-0.803943\pi\)
0.908438 + 0.418020i \(0.137276\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −2.51914e14 + 4.36328e14i −0.119681 + 0.207294i
\(612\) 0 0
\(613\) 1.64601e14 + 2.85097e14i 0.0768067 + 0.133033i 0.901871 0.432006i \(-0.142194\pi\)
−0.825064 + 0.565040i \(0.808861\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −4.23369e15 −1.90612 −0.953061 0.302777i \(-0.902086\pi\)
−0.953061 + 0.302777i \(0.902086\pi\)
\(618\) 0 0
\(619\) −1.66928e15 2.89129e15i −0.738298 1.27877i −0.953261 0.302148i \(-0.902296\pi\)
0.214963 0.976622i \(-0.431037\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 1.46003e15 3.65179e15i 0.623270 1.55891i
\(624\) 0 0
\(625\) 1.00138e15 1.73444e15i 0.420008 0.727476i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −1.51763e15 −0.614592
\(630\) 0 0
\(631\) −7.53088e14 −0.299698 −0.149849 0.988709i \(-0.547879\pi\)
−0.149849 + 0.988709i \(0.547879\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −1.73185e15 + 2.99964e15i −0.665662 + 1.15296i
\(636\) 0 0
\(637\) 1.10821e15 3.26497e14i 0.418654 0.123342i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 7.70022e14 + 1.33372e15i 0.281050 + 0.486793i 0.971644 0.236450i \(-0.0759840\pi\)
−0.690594 + 0.723243i \(0.742651\pi\)
\(642\) 0 0
\(643\) −4.35931e15 −1.56407 −0.782037 0.623232i \(-0.785819\pi\)
−0.782037 + 0.623232i \(0.785819\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1.90014e15 + 3.29114e15i 0.658890 + 1.14123i 0.980903 + 0.194496i \(0.0623070\pi\)
−0.322014 + 0.946735i \(0.604360\pi\)
\(648\) 0 0
\(649\) 5.88242e14 1.01887e15i 0.200544 0.347353i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 1.23183e15 2.13359e15i 0.406001 0.703215i −0.588436 0.808544i \(-0.700256\pi\)
0.994437 + 0.105329i \(0.0335896\pi\)
\(654\) 0 0
\(655\) −1.39478e13 2.41583e13i −0.00452043 0.00782961i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −4.32943e15 −1.35694 −0.678471 0.734627i \(-0.737357\pi\)
−0.678471 + 0.734627i \(0.737357\pi\)
\(660\) 0 0
\(661\) −1.08449e15 1.87839e15i −0.334284 0.578998i 0.649063 0.760735i \(-0.275161\pi\)
−0.983347 + 0.181737i \(0.941828\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −3.00967e15 3.82352e15i −0.897427 1.14010i
\(666\) 0 0
\(667\) −1.72124e15 + 2.98127e15i −0.504834 + 0.874399i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 1.41743e15 0.402279
\(672\) 0 0
\(673\) 8.47908e13 0.0236737 0.0118368 0.999930i \(-0.496232\pi\)
0.0118368 + 0.999930i \(0.496232\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −2.98941e15 + 5.17782e15i −0.807883 + 1.39929i 0.106445 + 0.994319i \(0.466053\pi\)
−0.914328 + 0.404976i \(0.867280\pi\)
\(678\) 0 0
\(679\) 4.21996e15 6.08700e14i 1.12208 0.161853i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 1.50741e15 + 2.61091e15i 0.388077 + 0.672169i 0.992191 0.124729i \(-0.0398062\pi\)
−0.604114 + 0.796898i \(0.706473\pi\)
\(684\) 0 0
\(685\) 3.53711e15 0.896088
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 1.07463e15 + 1.86131e15i 0.263664 + 0.456680i
\(690\) 0 0
\(691\) 1.26172e15 2.18537e15i 0.304673 0.527710i −0.672515 0.740083i \(-0.734786\pi\)
0.977189 + 0.212374i \(0.0681194\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 6.43710e14 1.11494e15i 0.150582 0.260816i
\(696\) 0 0
\(697\) −2.56506e15 4.44281e15i −0.590632 1.02300i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −6.09678e15 −1.36035 −0.680176 0.733049i \(-0.738097\pi\)
−0.680176 + 0.733049i \(0.738097\pi\)
\(702\) 0 0
\(703\) −1.35758e15 2.35140e15i −0.298203 0.516502i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 4.41227e15 + 5.60541e15i 0.939411 + 1.19344i
\(708\) 0 0
\(709\) 3.01210e15 5.21711e15i 0.631415 1.09364i −0.355848 0.934544i \(-0.615808\pi\)
0.987263 0.159099i \(-0.0508589\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −7.99860e15 −1.62563
\(714\) 0 0
\(715\) 1.16488e15 0.233130
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 7.19170e13 1.24564e14i 0.0139580 0.0241759i −0.858962 0.512039i \(-0.828890\pi\)
0.872920 + 0.487863i \(0.162224\pi\)
\(720\) 0 0
\(721\) −2.23219e15 + 5.58311e15i −0.426665 + 1.06717i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 3.69967e14 + 6.40801e14i 0.0685968 + 0.118813i
\(726\) 0 0
\(727\) −8.32629e15 −1.52059 −0.760295 0.649578i \(-0.774946\pi\)
−0.760295 + 0.649578i \(0.774946\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −1.11069e15 1.92377e15i −0.196810 0.340884i
\(732\) 0 0
\(733\) −1.34131e15 + 2.32322e15i −0.234131 + 0.405526i −0.959020 0.283339i \(-0.908558\pi\)
0.724889 + 0.688866i \(0.241891\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 2.83420e14 4.90898e14i 0.0480131 0.0831611i
\(738\) 0 0
\(739\) 4.12901e15 + 7.15166e15i 0.689131 + 1.19361i 0.972119 + 0.234486i \(0.0753408\pi\)
−0.282989 + 0.959123i \(0.591326\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −2.41601e15 −0.391435 −0.195718 0.980660i \(-0.562704\pi\)
−0.195718 + 0.980660i \(0.562704\pi\)
\(744\) 0 0
\(745\) −2.63133e15 4.55760e15i −0.420065 0.727574i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 1.36003e15 3.40167e15i 0.210813 0.527281i
\(750\) 0 0
\(751\) −5.49081e15 + 9.51036e15i −0.838719 + 1.45270i 0.0522466 + 0.998634i \(0.483362\pi\)
−0.890966 + 0.454070i \(0.849972\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −9.07314e14 −0.134601
\(756\) 0 0
\(757\) −3.46816e15 −0.507075 −0.253537 0.967326i \(-0.581594\pi\)
−0.253537 + 0.967326i \(0.581594\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −3.37973e15 + 5.85386e15i −0.480028 + 0.831432i −0.999738 0.0229104i \(-0.992707\pi\)
0.519710 + 0.854343i \(0.326040\pi\)
\(762\) 0 0
\(763\) 6.24098e15 + 7.92862e15i 0.873711 + 1.10997i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 1.11692e15 + 1.93455e15i 0.151931 + 0.263152i
\(768\) 0 0
\(769\) −8.71762e15 −1.16897 −0.584485 0.811405i \(-0.698703\pi\)
−0.584485 + 0.811405i \(0.698703\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 1.98343e15 + 3.43541e15i 0.258482 + 0.447704i 0.965835 0.259156i \(-0.0834444\pi\)
−0.707354 + 0.706860i \(0.750111\pi\)
\(774\) 0 0
\(775\) −8.59618e14 + 1.48890e15i −0.110445 + 0.191296i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 4.58910e15 7.94856e15i 0.573155 0.992733i
\(780\) 0 0
\(781\) 2.33237e15 + 4.03979e15i 0.287222 + 0.497482i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −1.11236e16 −1.33188