Properties

Label 252.9.z.d.145.6
Level $252$
Weight $9$
Character 252.145
Analytic conductor $102.659$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 252.z (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(102.659409735\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - 3 x^{11} + 148097 x^{10} + 46071824 x^{9} + 21578502553 x^{8} + 3561445462121 x^{7} + 576413321817541 x^{6} + 47217566733462528 x^{5} + 5214056955297543333 x^{4} + 358752845334081085965 x^{3} + 30962072851910211245661 x^{2} + 1221542968331193193318500 x + 45396580558961892385326096\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{20}\cdot 3^{10}\cdot 7^{4} \)
Twist minimal: no (minimal twist has level 84)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 145.6
Root \(44.6586 + 77.3509i\) of defining polynomial
Character \(\chi\) \(=\) 252.145
Dual form 252.9.z.d.73.6

$q$-expansion

\(f(q)\) \(=\) \(q+(939.615 + 542.487i) q^{5} +(1451.57 + 1912.52i) q^{7} +O(q^{10})\) \(q+(939.615 + 542.487i) q^{5} +(1451.57 + 1912.52i) q^{7} +(8435.48 + 14610.7i) q^{11} -9958.41i q^{13} +(91736.7 - 52964.2i) q^{17} +(147650. + 85245.9i) q^{19} +(105694. - 183067. i) q^{23} +(393272. + 681166. i) q^{25} +567529. q^{29} +(549248. - 317108. i) q^{31} +(326400. + 2.58449e6i) q^{35} +(-1.07740e6 + 1.86611e6i) q^{37} -5.45428e6i q^{41} +5.56726e6 q^{43} +(-2.76739e6 - 1.59775e6i) q^{47} +(-1.55068e6 + 5.55233e6i) q^{49} +(-4.38272e6 - 7.59109e6i) q^{53} +1.83046e7i q^{55} +(8.08566e6 - 4.66826e6i) q^{59} +(-2.13748e7 - 1.23407e7i) q^{61} +(5.40231e6 - 9.35707e6i) q^{65} +(-6.91779e6 - 1.19820e7i) q^{67} -1.19189e7 q^{71} +(-1.83300e7 + 1.05828e7i) q^{73} +(-1.56985e7 + 3.73415e7i) q^{77} +(-8.61190e6 + 1.49162e7i) q^{79} -6.82663e7i q^{83} +1.14930e8 q^{85} +(7.87155e7 + 4.54464e7i) q^{89} +(1.90457e7 - 1.44553e7i) q^{91} +(9.24895e7 + 1.60197e8i) q^{95} +3.95376e7i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 285 q^{5} + 198 q^{7} + O(q^{10}) \) \( 12 q - 285 q^{5} + 198 q^{7} + 17919 q^{11} + 205782 q^{17} + 74313 q^{19} + 62832 q^{23} + 878679 q^{25} + 575454 q^{29} + 1442952 q^{31} + 3989514 q^{35} - 2058621 q^{37} + 7721322 q^{43} - 12088194 q^{47} - 16964694 q^{49} + 5506743 q^{53} - 7511901 q^{59} - 37215576 q^{61} - 5047122 q^{65} - 36824553 q^{67} + 30011556 q^{71} + 95080185 q^{73} + 38333727 q^{77} + 8514456 q^{79} + 20121540 q^{85} - 83038554 q^{89} - 198538635 q^{91} + 221605224 q^{95} + O(q^{100}) \)

Character values

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

\(n\) \(29\) \(73\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(1\)

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
\(5\) 939.615 + 542.487i 1.50338 + 0.867979i 0.999992 + 0.00392070i \(0.00124800\pi\)
0.503392 + 0.864058i \(0.332085\pi\)
\(6\) 0 0
\(7\) 1451.57 + 1912.52i 0.604570 + 0.796552i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 8435.48 + 14610.7i 0.576155 + 0.997929i 0.995915 + 0.0902942i \(0.0287807\pi\)
−0.419760 + 0.907635i \(0.637886\pi\)
\(12\) 0 0
\(13\) 9958.41i 0.348672i −0.984686 0.174336i \(-0.944222\pi\)
0.984686 0.174336i \(-0.0557778\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 91736.7 52964.2i 1.09837 0.634142i 0.162575 0.986696i \(-0.448020\pi\)
0.935792 + 0.352554i \(0.114687\pi\)
\(18\) 0 0
\(19\) 147650. + 85245.9i 1.13297 + 0.654122i 0.944681 0.327991i \(-0.106372\pi\)
0.188292 + 0.982113i \(0.439705\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 105694. 183067.i 0.377692 0.654183i −0.613034 0.790057i \(-0.710051\pi\)
0.990726 + 0.135874i \(0.0433843\pi\)
\(24\) 0 0
\(25\) 393272. + 681166.i 1.00678 + 1.74379i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 567529. 0.802409 0.401205 0.915989i \(-0.368592\pi\)
0.401205 + 0.915989i \(0.368592\pi\)
\(30\) 0 0
\(31\) 549248. 317108.i 0.594732 0.343369i −0.172234 0.985056i \(-0.555099\pi\)
0.766967 + 0.641687i \(0.221765\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 326400. + 2.58449e6i 0.217510 + 1.72228i
\(36\) 0 0
\(37\) −1.07740e6 + 1.86611e6i −0.574870 + 0.995703i 0.421186 + 0.906974i \(0.361614\pi\)
−0.996056 + 0.0887291i \(0.971719\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 5.45428e6i 1.93020i −0.261884 0.965099i \(-0.584344\pi\)
0.261884 0.965099i \(-0.415656\pi\)
\(42\) 0 0
\(43\) 5.56726e6 1.62842 0.814212 0.580568i \(-0.197169\pi\)
0.814212 + 0.580568i \(0.197169\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −2.76739e6 1.59775e6i −0.567125 0.327430i 0.188876 0.982001i \(-0.439516\pi\)
−0.756000 + 0.654572i \(0.772849\pi\)
\(48\) 0 0
\(49\) −1.55068e6 + 5.55233e6i −0.268991 + 0.963143i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −4.38272e6 7.59109e6i −0.555443 0.962056i −0.997869 0.0652510i \(-0.979215\pi\)
0.442425 0.896805i \(-0.354118\pi\)
\(54\) 0 0
\(55\) 1.83046e7i 2.00036i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 8.08566e6 4.66826e6i 0.667279 0.385254i −0.127766 0.991804i \(-0.540781\pi\)
0.795045 + 0.606551i \(0.207447\pi\)
\(60\) 0 0
\(61\) −2.13748e7 1.23407e7i −1.54377 0.891296i −0.998596 0.0529726i \(-0.983130\pi\)
−0.545174 0.838323i \(-0.683536\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 5.40231e6 9.35707e6i 0.302640 0.524187i
\(66\) 0 0
\(67\) −6.91779e6 1.19820e7i −0.343295 0.594605i 0.641747 0.766916i \(-0.278210\pi\)
−0.985043 + 0.172311i \(0.944877\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −1.19189e7 −0.469031 −0.234515 0.972112i \(-0.575350\pi\)
−0.234515 + 0.972112i \(0.575350\pi\)
\(72\) 0 0
\(73\) −1.83300e7 + 1.05828e7i −0.645463 + 0.372658i −0.786716 0.617315i \(-0.788220\pi\)
0.141253 + 0.989974i \(0.454887\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −1.56985e7 + 3.73415e7i −0.446577 + 1.06226i
\(78\) 0 0
\(79\) −8.61190e6 + 1.49162e7i −0.221101 + 0.382958i −0.955143 0.296147i \(-0.904298\pi\)
0.734042 + 0.679104i \(0.237632\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 6.82663e7i 1.43845i −0.694779 0.719223i \(-0.744498\pi\)
0.694779 0.719223i \(-0.255502\pi\)
\(84\) 0 0
\(85\) 1.14930e8 2.20169
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 7.87155e7 + 4.54464e7i 1.25459 + 0.724335i 0.972017 0.234912i \(-0.0754802\pi\)
0.282569 + 0.959247i \(0.408814\pi\)
\(90\) 0 0
\(91\) 1.90457e7 1.44553e7i 0.277735 0.210796i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 9.24895e7 + 1.60197e8i 1.13553 + 1.96679i
\(96\) 0 0
\(97\) 3.95376e7i 0.446605i 0.974749 + 0.223302i \(0.0716837\pi\)
−0.974749 + 0.223302i \(0.928316\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −1.01453e8 + 5.85738e7i −0.974941 + 0.562882i −0.900739 0.434361i \(-0.856974\pi\)
−0.0742019 + 0.997243i \(0.523641\pi\)
\(102\) 0 0
\(103\) −4.22305e7 2.43818e7i −0.375212 0.216629i 0.300521 0.953775i \(-0.402839\pi\)
−0.675733 + 0.737146i \(0.736173\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −5.90508e7 + 1.02279e8i −0.450496 + 0.780282i −0.998417 0.0562482i \(-0.982086\pi\)
0.547921 + 0.836530i \(0.315420\pi\)
\(108\) 0 0
\(109\) −7.54688e6 1.30716e7i −0.0534640 0.0926024i 0.838055 0.545586i \(-0.183693\pi\)
−0.891519 + 0.452984i \(0.850360\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 6.94293e7 0.425823 0.212911 0.977072i \(-0.431705\pi\)
0.212911 + 0.977072i \(0.431705\pi\)
\(114\) 0 0
\(115\) 1.98623e8 1.14675e8i 1.13563 0.655658i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 2.34458e8 + 9.85671e7i 1.16917 + 0.491523i
\(120\) 0 0
\(121\) −3.51352e7 + 6.08560e7i −0.163908 + 0.283898i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 4.29561e8i 1.75948i
\(126\) 0 0
\(127\) −1.00139e8 −0.384934 −0.192467 0.981303i \(-0.561649\pi\)
−0.192467 + 0.981303i \(0.561649\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 6.73342e6 + 3.88754e6i 0.0228639 + 0.0132005i 0.511388 0.859350i \(-0.329131\pi\)
−0.488524 + 0.872550i \(0.662465\pi\)
\(132\) 0 0
\(133\) 5.12902e7 + 4.06125e8i 0.163919 + 1.29793i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 5.53803e7 + 9.59215e7i 0.157207 + 0.272291i 0.933861 0.357637i \(-0.116418\pi\)
−0.776653 + 0.629928i \(0.783084\pi\)
\(138\) 0 0
\(139\) 3.31664e8i 0.888464i −0.895912 0.444232i \(-0.853477\pi\)
0.895912 0.444232i \(-0.146523\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 1.45499e8 8.40040e7i 0.347949 0.200889i
\(144\) 0 0
\(145\) 5.33258e8 + 3.07877e8i 1.20633 + 0.696474i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −3.47265e8 + 6.01481e8i −0.704557 + 1.22033i 0.262294 + 0.964988i \(0.415521\pi\)
−0.966851 + 0.255341i \(0.917812\pi\)
\(150\) 0 0
\(151\) −4.10896e8 7.11694e8i −0.790359 1.36894i −0.925745 0.378150i \(-0.876561\pi\)
0.135385 0.990793i \(-0.456773\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 6.88109e8 1.19215
\(156\) 0 0
\(157\) −4.16332e8 + 2.40369e8i −0.685238 + 0.395622i −0.801825 0.597558i \(-0.796138\pi\)
0.116588 + 0.993180i \(0.462804\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 5.03542e8 6.35933e7i 0.749432 0.0946472i
\(162\) 0 0
\(163\) −3.04664e8 + 5.27694e8i −0.431590 + 0.747536i −0.997010 0.0772671i \(-0.975381\pi\)
0.565420 + 0.824803i \(0.308714\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 1.84576e8i 0.237307i −0.992936 0.118653i \(-0.962142\pi\)
0.992936 0.118653i \(-0.0378577\pi\)
\(168\) 0 0
\(169\) 7.16561e8 0.878428
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 2.92420e8 + 1.68829e8i 0.326454 + 0.188478i 0.654266 0.756265i \(-0.272978\pi\)
−0.327812 + 0.944743i \(0.606311\pi\)
\(174\) 0 0
\(175\) −7.31884e8 + 1.74090e9i −0.780351 + 1.85619i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −2.92703e8 5.06977e8i −0.285112 0.493828i 0.687524 0.726161i \(-0.258697\pi\)
−0.972636 + 0.232333i \(0.925364\pi\)
\(180\) 0 0
\(181\) 1.29407e9i 1.20571i 0.797850 + 0.602856i \(0.205971\pi\)
−0.797850 + 0.602856i \(0.794029\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −2.02468e9 + 1.16895e9i −1.72850 + 0.997950i
\(186\) 0 0
\(187\) 1.54769e9 + 8.93557e8i 1.26566 + 0.730728i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 7.80043e8 1.35107e9i 0.586118 1.01519i −0.408617 0.912706i \(-0.633989\pi\)
0.994735 0.102480i \(-0.0326777\pi\)
\(192\) 0 0
\(193\) 8.76806e8 + 1.51867e9i 0.631937 + 1.09455i 0.987155 + 0.159764i \(0.0510734\pi\)
−0.355218 + 0.934784i \(0.615593\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 1.78624e9 1.18598 0.592988 0.805212i \(-0.297948\pi\)
0.592988 + 0.805212i \(0.297948\pi\)
\(198\) 0 0
\(199\) −2.60521e9 + 1.50412e9i −1.66123 + 0.959114i −0.689107 + 0.724660i \(0.741997\pi\)
−0.972127 + 0.234454i \(0.924670\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 8.23809e8 + 1.08541e9i 0.485112 + 0.639161i
\(204\) 0 0
\(205\) 2.95888e9 5.12492e9i 1.67537 2.90183i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 2.87636e9i 1.50750i
\(210\) 0 0
\(211\) 3.33988e9 1.68501 0.842503 0.538692i \(-0.181081\pi\)
0.842503 + 0.538692i \(0.181081\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 5.23108e9 + 3.02016e9i 2.44815 + 1.41344i
\(216\) 0 0
\(217\) 1.40375e9 + 5.90143e8i 0.633069 + 0.266145i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −5.27439e8 9.13552e8i −0.221107 0.382969i
\(222\) 0 0
\(223\) 1.94513e9i 0.786556i 0.919420 + 0.393278i \(0.128659\pi\)
−0.919420 + 0.393278i \(0.871341\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −1.17894e9 + 6.80660e8i −0.444004 + 0.256346i −0.705295 0.708914i \(-0.749185\pi\)
0.261290 + 0.965260i \(0.415852\pi\)
\(228\) 0 0
\(229\) −3.23205e9 1.86603e9i −1.17527 0.678541i −0.220352 0.975420i \(-0.570721\pi\)
−0.954915 + 0.296880i \(0.904054\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 1.72263e8 2.98368e8i 0.0584477 0.101234i −0.835321 0.549762i \(-0.814718\pi\)
0.893769 + 0.448528i \(0.148052\pi\)
\(234\) 0 0
\(235\) −1.73352e9 3.00254e9i −0.568404 0.984505i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −3.17982e9 −0.974565 −0.487283 0.873244i \(-0.662012\pi\)
−0.487283 + 0.873244i \(0.662012\pi\)
\(240\) 0 0
\(241\) −4.09977e9 + 2.36701e9i −1.21532 + 0.701667i −0.963914 0.266214i \(-0.914227\pi\)
−0.251409 + 0.967881i \(0.580894\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −4.46911e9 + 4.37583e9i −1.24038 + 1.21449i
\(246\) 0 0
\(247\) 8.48913e8 1.47036e9i 0.228074 0.395035i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 7.03152e9i 1.77155i −0.464112 0.885776i \(-0.653627\pi\)
0.464112 0.885776i \(-0.346373\pi\)
\(252\) 0 0
\(253\) 3.56631e9 0.870437
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 1.10931e9 + 6.40462e8i 0.254286 + 0.146812i 0.621725 0.783236i \(-0.286432\pi\)
−0.367439 + 0.930047i \(0.619765\pi\)
\(258\) 0 0
\(259\) −5.13289e9 + 6.48243e8i −1.14068 + 0.144058i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −2.37972e8 4.12179e8i −0.0497396 0.0861516i 0.840084 0.542457i \(-0.182506\pi\)
−0.889823 + 0.456305i \(0.849172\pi\)
\(264\) 0 0
\(265\) 9.51027e9i 1.92845i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 4.95417e9 2.86029e9i 0.946154 0.546262i 0.0542696 0.998526i \(-0.482717\pi\)
0.891884 + 0.452264i \(0.149384\pi\)
\(270\) 0 0
\(271\) −5.53293e9 3.19444e9i −1.02584 0.592267i −0.110048 0.993926i \(-0.535100\pi\)
−0.915789 + 0.401659i \(0.868434\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −6.63487e9 + 1.14919e10i −1.16012 + 2.00938i
\(276\) 0 0
\(277\) −2.63656e9 4.56666e9i −0.447836 0.775675i 0.550409 0.834895i \(-0.314472\pi\)
−0.998245 + 0.0592204i \(0.981139\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −7.48748e9 −1.20091 −0.600455 0.799658i \(-0.705014\pi\)
−0.600455 + 0.799658i \(0.705014\pi\)
\(282\) 0 0
\(283\) −3.62475e9 + 2.09275e9i −0.565109 + 0.326266i −0.755193 0.655502i \(-0.772457\pi\)
0.190085 + 0.981768i \(0.439124\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 1.04314e10 7.91728e9i 1.53750 1.16694i
\(288\) 0 0
\(289\) 2.12254e9 3.67634e9i 0.304273 0.527017i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 1.12022e9i 0.151997i −0.997108 0.0759983i \(-0.975786\pi\)
0.997108 0.0759983i \(-0.0242143\pi\)
\(294\) 0 0
\(295\) 1.01299e10 1.33757
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −1.82306e9 1.05254e9i −0.228095 0.131691i
\(300\) 0 0
\(301\) 8.08127e9 + 1.06475e10i 0.984496 + 1.29712i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −1.33894e10 2.31911e10i −1.54725 2.67992i
\(306\) 0 0
\(307\) 1.02340e10i 1.15210i 0.817413 + 0.576051i \(0.195407\pi\)
−0.817413 + 0.576051i \(0.804593\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −5.99552e9 + 3.46151e9i −0.640892 + 0.370019i −0.784958 0.619549i \(-0.787316\pi\)
0.144066 + 0.989568i \(0.453982\pi\)
\(312\) 0 0
\(313\) 4.79188e8 + 2.76659e8i 0.0499262 + 0.0288249i 0.524755 0.851253i \(-0.324157\pi\)
−0.474829 + 0.880078i \(0.657490\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 6.72093e8 1.16410e9i 0.0665568 0.115280i −0.830827 0.556531i \(-0.812132\pi\)
0.897384 + 0.441251i \(0.145465\pi\)
\(318\) 0 0
\(319\) 4.78738e9 + 8.29198e9i 0.462312 + 0.800747i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 1.80599e10 1.65923
\(324\) 0 0
\(325\) 6.78333e9 3.91636e9i 0.608009 0.351034i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −9.61326e8 7.61194e9i −0.0820516 0.649698i
\(330\) 0 0
\(331\) 3.38567e8 5.86414e8i 0.0282054 0.0488532i −0.851578 0.524228i \(-0.824354\pi\)
0.879784 + 0.475374i \(0.157687\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 1.50112e10i 1.19189i
\(336\) 0 0
\(337\) −1.73692e10 −1.34667 −0.673333 0.739340i \(-0.735138\pi\)
−0.673333 + 0.739340i \(0.735138\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 9.26634e9 + 5.34992e9i 0.685316 + 0.395667i
\(342\) 0 0
\(343\) −1.28699e10 + 5.09389e9i −0.929817 + 0.368022i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −8.82405e9 1.52837e10i −0.608626 1.05417i −0.991467 0.130356i \(-0.958388\pi\)
0.382842 0.923814i \(-0.374946\pi\)
\(348\) 0 0
\(349\) 9.49559e9i 0.640059i −0.947408 0.320030i \(-0.896307\pi\)
0.947408 0.320030i \(-0.103693\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −6.12231e9 + 3.53472e9i −0.394290 + 0.227644i −0.684017 0.729466i \(-0.739769\pi\)
0.289727 + 0.957109i \(0.406435\pi\)
\(354\) 0 0
\(355\) −1.11991e10 6.46583e9i −0.705134 0.407109i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 6.55145e9 1.13474e10i 0.394421 0.683157i −0.598606 0.801043i \(-0.704279\pi\)
0.993027 + 0.117887i \(0.0376119\pi\)
\(360\) 0 0
\(361\) 6.04193e9 + 1.04649e10i 0.355752 + 0.616180i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −2.29642e10 −1.29384
\(366\) 0 0
\(367\) 2.12630e10 1.22762e10i 1.17209 0.676707i 0.217919 0.975967i \(-0.430073\pi\)
0.954172 + 0.299260i \(0.0967399\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 8.15629e9 1.94011e10i 0.430524 1.02407i
\(372\) 0 0
\(373\) 5.64618e9 9.77947e9i 0.291689 0.505219i −0.682521 0.730866i \(-0.739116\pi\)
0.974209 + 0.225647i \(0.0724496\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 5.65168e9i 0.279777i
\(378\) 0 0
\(379\) −3.52545e9 −0.170867 −0.0854335 0.996344i \(-0.527228\pi\)
−0.0854335 + 0.996344i \(0.527228\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −2.74394e10 1.58422e10i −1.27521 0.736240i −0.299243 0.954177i \(-0.596734\pi\)
−0.975963 + 0.217937i \(0.930067\pi\)
\(384\) 0 0
\(385\) −3.50079e10 + 2.65704e10i −1.59339 + 1.20936i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −2.01146e9 3.48396e9i −0.0878443 0.152151i 0.818755 0.574143i \(-0.194664\pi\)
−0.906600 + 0.421992i \(0.861331\pi\)
\(390\) 0 0
\(391\) 2.23920e10i 0.958043i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −1.61837e10 + 9.34368e9i −0.664799 + 0.383822i
\(396\) 0 0
\(397\) −3.37145e10 1.94651e10i −1.35724 0.783600i −0.367985 0.929832i \(-0.619952\pi\)
−0.989250 + 0.146232i \(0.953286\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −2.03692e10 + 3.52804e10i −0.787764 + 1.36445i 0.139571 + 0.990212i \(0.455428\pi\)
−0.927334 + 0.374234i \(0.877906\pi\)
\(402\) 0 0
\(403\) −3.15790e9 5.46963e9i −0.119723 0.207366i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −3.63535e10 −1.32486
\(408\) 0 0
\(409\) −1.08712e10 + 6.27648e9i −0.388493 + 0.224297i −0.681507 0.731812i \(-0.738675\pi\)
0.293014 + 0.956108i \(0.405342\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 2.06651e10 + 8.68769e9i 0.710291 + 0.298610i
\(414\) 0 0
\(415\) 3.70336e10 6.41440e10i 1.24854 2.16254i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 1.94158e9i 0.0629941i −0.999504 0.0314970i \(-0.989973\pi\)
0.999504 0.0314970i \(-0.0100275\pi\)
\(420\) 0 0
\(421\) 1.38803e9 0.0441846 0.0220923 0.999756i \(-0.492967\pi\)
0.0220923 + 0.999756i \(0.492967\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 7.21549e10 + 4.16586e10i 2.21162 + 1.27688i
\(426\) 0 0
\(427\) −7.42511e9 5.87932e10i −0.223353 1.76854i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 1.62135e10 + 2.80826e10i 0.469860 + 0.813821i 0.999406 0.0344602i \(-0.0109712\pi\)
−0.529546 + 0.848281i \(0.677638\pi\)
\(432\) 0 0
\(433\) 4.65333e10i 1.32377i 0.749606 + 0.661884i \(0.230243\pi\)
−0.749606 + 0.661884i \(0.769757\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 3.12114e10 1.80199e10i 0.855831 0.494114i
\(438\) 0 0
\(439\) −4.44106e10 2.56404e10i −1.19572 0.690347i −0.236119 0.971724i \(-0.575876\pi\)
−0.959597 + 0.281377i \(0.909209\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −2.09215e10 + 3.62371e10i −0.543223 + 0.940891i 0.455493 + 0.890239i \(0.349463\pi\)
−0.998716 + 0.0506512i \(0.983870\pi\)
\(444\) 0 0
\(445\) 4.93082e10 + 8.54042e10i 1.25742 + 2.17791i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −2.89337e10 −0.711900 −0.355950 0.934505i \(-0.615843\pi\)
−0.355950 + 0.934505i \(0.615843\pi\)
\(450\) 0 0
\(451\) 7.96907e10 4.60095e10i 1.92620 1.11209i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 2.57374e10 3.25043e9i 0.600509 0.0758394i
\(456\) 0 0
\(457\) −3.38299e10 + 5.85951e10i −0.775597 + 1.34337i 0.158862 + 0.987301i \(0.449218\pi\)
−0.934458 + 0.356072i \(0.884116\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 2.13195e10i 0.472035i −0.971749 0.236017i \(-0.924158\pi\)
0.971749 0.236017i \(-0.0758422\pi\)
\(462\) 0 0
\(463\) 5.73662e10 1.24834 0.624168 0.781290i \(-0.285438\pi\)
0.624168 + 0.781290i \(0.285438\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 1.40331e10 + 8.10202e9i 0.295044 + 0.170343i 0.640214 0.768196i \(-0.278846\pi\)
−0.345171 + 0.938540i \(0.612179\pi\)
\(468\) 0 0
\(469\) 1.28741e10 3.06231e10i 0.266088 0.632933i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 4.69625e10 + 8.13414e10i 0.938224 + 1.62505i
\(474\) 0 0
\(475\) 1.34099e11i 2.63422i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 8.47162e10 4.89109e10i 1.60925 0.929103i 0.619716 0.784826i \(-0.287248\pi\)
0.989537 0.144276i \(-0.0460854\pi\)
\(480\) 0 0
\(481\) 1.85835e10 + 1.07292e10i 0.347173 + 0.200441i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −2.14486e10 + 3.71501e10i −0.387644 + 0.671418i
\(486\) 0 0
\(487\) 2.47120e10 + 4.28025e10i 0.439332 + 0.760945i 0.997638 0.0686896i \(-0.0218818\pi\)
−0.558306 + 0.829635i \(0.688548\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −4.36304e10 −0.750695 −0.375348 0.926884i \(-0.622477\pi\)
−0.375348 + 0.926884i \(0.622477\pi\)
\(492\) 0 0
\(493\) 5.20632e10 3.00587e10i 0.881340 0.508842i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −1.73011e10 2.27951e10i −0.283562 0.373608i
\(498\) 0 0
\(499\) 1.70928e10 2.96057e10i 0.275684 0.477499i −0.694623 0.719374i \(-0.744429\pi\)
0.970308 + 0.241874i \(0.0777622\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 1.10624e10i 0.172813i 0.996260 + 0.0864063i \(0.0275383\pi\)
−0.996260 + 0.0864063i \(0.972462\pi\)
\(504\) 0 0
\(505\) −1.27102e11 −1.95428
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 9.58080e10 + 5.53148e10i 1.42735 + 0.824081i 0.996911 0.0785379i \(-0.0250252\pi\)
0.430440 + 0.902619i \(0.358358\pi\)
\(510\) 0 0
\(511\) −4.68473e10 1.96948e10i −0.687069 0.288847i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −2.64536e10 4.58189e10i −0.376059 0.651353i
\(516\) 0 0
\(517\) 5.39112e10i 0.754600i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −1.11862e11 + 6.45834e10i −1.51820 + 0.876536i −0.518434 + 0.855118i \(0.673485\pi\)
−0.999771 + 0.0214183i \(0.993182\pi\)
\(522\) 0 0
\(523\) 4.41818e10 + 2.55084e10i 0.590523 + 0.340939i 0.765304 0.643669i \(-0.222588\pi\)
−0.174781 + 0.984607i \(0.555922\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 3.35908e10 5.81810e10i 0.435490 0.754290i
\(528\) 0 0
\(529\) 1.68131e10 + 2.91212e10i 0.214697 + 0.371866i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −5.43159e10 −0.673005
\(534\) 0 0
\(535\) −1.10970e11 + 6.40686e10i −1.35454 + 0.782042i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −9.42040e10 + 2.41801e10i −1.11613 + 0.286485i
\(540\) 0 0
\(541\) −5.42593e10 + 9.39799e10i −0.633410 + 1.09710i 0.353439 + 0.935457i \(0.385012\pi\)
−0.986850 + 0.161641i \(0.948321\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 1.63763e10i 0.185623i
\(546\) 0 0
\(547\) −6.18018e10 −0.690322 −0.345161 0.938544i \(-0.612176\pi\)
−0.345161 + 0.938544i \(0.612176\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 8.37957e10 + 4.83795e10i 0.909108 + 0.524874i
\(552\) 0 0
\(553\) −4.10284e10 + 5.18156e9i −0.438717 + 0.0554064i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −2.68485e10 4.65029e10i −0.278932 0.483125i 0.692188 0.721718i \(-0.256647\pi\)
−0.971120 + 0.238593i \(0.923314\pi\)
\(558\) 0 0
\(559\) 5.54410e10i 0.567785i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 1.24343e11 7.17894e10i 1.23762 0.714540i 0.269013 0.963137i \(-0.413303\pi\)
0.968607 + 0.248596i \(0.0799693\pi\)
\(564\) 0 0
\(565\) 6.52368e10 + 3.76645e10i 0.640175 + 0.369605i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −4.80492e10 + 8.32237e10i −0.458392 + 0.793958i −0.998876 0.0473959i \(-0.984908\pi\)
0.540484 + 0.841354i \(0.318241\pi\)
\(570\) 0 0
\(571\) 1.02075e11 + 1.76799e11i 0.960231 + 1.66317i 0.721915 + 0.691981i \(0.243262\pi\)
0.238316 + 0.971188i \(0.423405\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 1.66266e11 1.52101
\(576\) 0 0
\(577\) −1.23039e10 + 7.10368e9i −0.111005 + 0.0640885i −0.554474 0.832201i \(-0.687081\pi\)
0.443470 + 0.896289i \(0.353747\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 1.30561e11 9.90934e10i 1.14580 0.869641i
\(582\) 0 0
\(583\) 7.39406e10 1.28069e11i 0.640043 1.10859i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 6.63318e10i 0.558688i 0.960191 + 0.279344i \(0.0901170\pi\)
−0.960191 + 0.279344i \(0.909883\pi\)
\(588\) 0 0
\(589\) 1.08129e11 0.898421
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −9.13541e10 5.27433e10i −0.738770 0.426529i 0.0828520 0.996562i \(-0.473597\pi\)
−0.821622 + 0.570033i \(0.806930\pi\)
\(594\) 0 0
\(595\) 1.66829e11 + 2.19805e11i 1.33107 + 1.75376i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 7.35115e10 + 1.27326e11i 0.571016 + 0.989028i 0.996462 + 0.0840447i \(0.0267839\pi\)
−0.425446 + 0.904984i \(0.639883\pi\)
\(600\) 0 0
\(601\) 1.86033e11i 1.42591i −0.701210 0.712954i \(-0.747357\pi\)
0.701210 0.712954i \(-0.252643\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −6.60272e10 + 3.81208e10i −0.492834 + 0.284538i
\(606\) 0 0
\(607\) −5.85799e10 3.38211e10i −0.431513 0.249134i 0.268478 0.963286i \(-0.413479\pi\)
−0.699991 + 0.714152i \(0.746813\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −1.59111e10 + 2.75588e10i −0.114165 + 0.197740i
\(612\) 0 0
\(613\) −1.19635e11 2.07214e11i −0.847261 1.46750i −0.883643 0.468161i \(-0.844917\pi\)
0.0363824 0.999338i \(-0.488417\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 3.40881e10 0.235214 0.117607 0.993060i \(-0.462478\pi\)
0.117607 + 0.993060i \(0.462478\pi\)
\(618\) 0 0
\(619\) 8.42286e10 4.86294e10i 0.573716 0.331235i −0.184916 0.982754i \(-0.559201\pi\)
0.758632 + 0.651519i \(0.225868\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 2.73439e10 + 2.16514e11i 0.181513 + 1.43725i
\(624\) 0 0
\(625\) −7.94095e10 + 1.37541e11i −0.520418 + 0.901391i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 2.28254e11i 1.45820i
\(630\) 0 0
\(631\) −1.63168e11 −1.02924 −0.514621 0.857418i \(-0.672067\pi\)
−0.514621 + 0.857418i \(0.672067\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −9.40916e10 5.43238e10i −0.578704 0.334115i
\(636\) 0 0
\(637\) 5.52923e10 + 1.54423e10i 0.335820 + 0.0937895i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 2.04255e10 + 3.53779e10i 0.120987 + 0.209556i 0.920157 0.391549i \(-0.128061\pi\)
−0.799170 + 0.601105i \(0.794727\pi\)
\(642\) 0 0
\(643\) 1.66499e11i 0.974022i −0.873396 0.487011i \(-0.838087\pi\)
0.873396 0.487011i \(-0.161913\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 4.33764e10 2.50434e10i 0.247535 0.142914i −0.371100 0.928593i \(-0.621019\pi\)
0.618635 + 0.785678i \(0.287686\pi\)
\(648\) 0 0
\(649\) 1.36413e11 + 7.87580e10i 0.768912 + 0.443931i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 2.99393e10 5.18564e10i 0.164660 0.285200i −0.771874 0.635775i \(-0.780681\pi\)
0.936535 + 0.350575i \(0.114014\pi\)
\(654\) 0 0
\(655\) 4.21788e9 + 7.30558e9i 0.0229155 + 0.0396908i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 5.62292e10 0.298140 0.149070 0.988827i \(-0.452372\pi\)
0.149070 + 0.988827i \(0.452372\pi\)
\(660\) 0 0
\(661\) 1.99084e11 1.14941e11i 1.04287 0.602102i 0.122226 0.992502i \(-0.460997\pi\)
0.920645 + 0.390400i \(0.127663\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −1.72124e11 + 4.09425e11i −0.880147 + 2.09357i
\(666\) 0 0
\(667\) 5.99843e10 1.03896e11i 0.303064 0.524922i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 4.16400e11i 2.05410i
\(672\) 0 0
\(673\) 9.84906e10 0.480103 0.240052 0.970760i \(-0.422836\pi\)
0.240052 + 0.970760i \(0.422836\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −1.28763e11 7.43413e10i −0.612965 0.353896i 0.161160 0.986928i \(-0.448477\pi\)
−0.774125 + 0.633033i \(0.781810\pi\)
\(678\) 0 0
\(679\) −7.56165e10 + 5.73917e10i −0.355744 + 0.270004i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −1.76448e11 3.05616e11i −0.810836 1.40441i −0.912280 0.409568i \(-0.865680\pi\)
0.101444 0.994841i \(-0.467654\pi\)
\(684\) 0 0
\(685\) 1.20172e11i 0.545811i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −7.55951e10 + 4.36449e10i −0.335442 + 0.193667i
\(690\) 0 0
\(691\) −2.91147e11 1.68094e11i −1.27703 0.737291i −0.300725 0.953711i \(-0.597229\pi\)
−0.976300 + 0.216420i \(0.930562\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 1.79924e11 3.11637e11i 0.771168 1.33570i
\(696\) 0 0
\(697\) −2.88882e11 5.00358e11i −1.22402 2.12007i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −4.11369e11 −1.70357 −0.851784 0.523893i \(-0.824479\pi\)
−0.851784 + 0.523893i \(0.824479\pi\)
\(702\) 0 0
\(703\) −3.18156e11 + 1.83687e11i −1.30262 + 0.752070i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −2.59290e11 1.09007e11i −1.03778 0.436290i
\(708\) 0 0
\(709\) −6.95122e10 + 1.20399e11i −0.275091 + 0.476472i −0.970158 0.242473i \(-0.922041\pi\)
0.695067 + 0.718945i \(0.255375\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 1.34066e11i 0.518751i
\(714\) 0 0
\(715\) 1.82284e11 0.697469
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 1.01094e11 + 5.83667e10i 0.378277 + 0.218398i 0.677068 0.735920i \(-0.263250\pi\)
−0.298791 + 0.954318i \(0.596583\pi\)
\(720\) 0 0
\(721\) −1.46699e10 1.16159e11i −0.0542857 0.429843i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 2.23193e11 + 3.86581e11i 0.807846 + 1.39923i
\(726\) 0 0
\(727\) 2.43338e11i 0.871109i −0.900162 0.435555i \(-0.856552\pi\)
0.900162 0.435555i \(-0.143448\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 5.10722e11 2.94865e11i 1.78861 1.03265i
\(732\) 0 0
\(733\) 4.20029e11 + 2.42504e11i 1.45500 + 0.840046i 0.998759 0.0498097i \(-0.0158615\pi\)
0.456243 + 0.889855i \(0.349195\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 1.16710e11 2.02147e11i 0.395582 0.685169i
\(738\) 0 0
\(739\) −1.98657e11 3.44083e11i −0.666078 1.15368i −0.978992 0.203900i \(-0.934638\pi\)
0.312913 0.949782i \(-0.398695\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −2.20639e11 −0.723980 −0.361990 0.932182i \(-0.617903\pi\)
−0.361990 + 0.932182i \(0.617903\pi\)
\(744\) 0 0
\(745\) −6.52591e11 + 3.76774e11i −2.11844 + 1.22308i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −2.81327e11 + 3.55294e10i −0.893892 + 0.112891i
\(750\) 0 0
\(751\) 2.44854e8 4.24099e8i 0.000769745 0.00133324i −0.865640 0.500666i \(-0.833088\pi\)
0.866410 + 0.499333i \(0.166422\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 8.91624e11i 2.74406i
\(756\) 0 0
\(757\) −6.35724e10 −0.193591 −0.0967955 0.995304i \(-0.530859\pi\)
−0.0967955 + 0.995304i \(0.530859\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −5.15892e10 2.97850e10i −0.153823 0.0888095i 0.421113 0.907008i \(-0.361640\pi\)
−0.574936 + 0.818199i \(0.694973\pi\)
\(762\) 0 0
\(763\) 1.40449e10 3.34079e10i 0.0414399 0.0985715i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −4.64884e10 8.05203e10i −0.134327 0.232661i
\(768\) 0 0
\(769\) 3.28466e11i 0.939259i 0.882864 + 0.469629i \(0.155612\pi\)
−0.882864 + 0.469629i \(0.844388\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −4.19975e11 + 2.42473e11i −1.17627 + 0.679117i −0.955148 0.296130i \(-0.904304\pi\)
−0.221118 + 0.975247i \(0.570970\pi\)
\(774\) 0 0
\(775\) 4.32007e11 + 2.49420e11i 1.19752 + 0.691391i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 4.64955e11 8.05325e11i 1.26259 2.18686i
\(780\) 0 0
\(781\) −1.00541e11 1.74143e11i −0.270234 0.468060i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −5.21589e11 −1.37357
\(786\) 0 0
\(787\) 2.48776e11 1.43631e11i 0.648500 0.374412i −0.139381 0.990239i \(-0.544511\pi\)
0.787881 + 0.615827i \(0.211178\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0