Properties

Label 252.12.k.d.37.2
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 37.2
Root \(-10168.9 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 252.37
Dual form 252.12.k.d.109.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-4949.72 + 8573.16i) q^{5} +(29163.1 + 33568.4i) q^{7} +O(q^{10})\) \(q+(-4949.72 + 8573.16i) q^{5} +(29163.1 + 33568.4i) q^{7} +(-25007.0 - 43313.5i) q^{11} +1.46252e6 q^{13} +(-3.16934e6 - 5.48946e6i) q^{17} +(-1.02494e7 + 1.77525e7i) q^{19} +(2.36024e7 - 4.08806e7i) q^{23} +(-2.45854e7 - 4.25831e7i) q^{25} +9.10208e7 q^{29} +(-4.83443e7 - 8.37349e7i) q^{31} +(-4.32137e8 + 8.38657e7i) q^{35} +(-7.14098e7 + 1.23685e8i) q^{37} -8.44357e8 q^{41} -1.55607e9 q^{43} +(4.22680e8 - 7.32103e8i) q^{47} +(-2.76354e8 + 1.95792e9i) q^{49} +(-1.26817e9 - 2.19654e9i) q^{53} +4.95111e8 q^{55} +(-2.80141e9 - 4.85219e9i) q^{59} +(-5.98273e8 + 1.03624e9i) q^{61} +(-7.23904e9 + 1.25384e10i) q^{65} +(-2.73114e9 - 4.73048e9i) q^{67} -1.81232e10 q^{71} +(9.87533e9 + 1.71046e10i) q^{73} +(7.24683e8 - 2.10260e9i) q^{77} +(-2.14642e10 + 3.71770e10i) q^{79} +5.21192e10 q^{83} +6.27494e10 q^{85} +(1.39910e10 - 2.42332e10i) q^{89} +(4.26515e10 + 4.90944e10i) q^{91} +(-1.01464e11 - 1.75740e11i) q^{95} +5.42003e10 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 2156q^{5} + 50512q^{7} + O(q^{10}) \) \( 16q + 2156q^{5} + 50512q^{7} + 222796q^{11} + 2703176q^{13} - 5114600q^{17} + 6910556q^{19} + 51387712q^{23} - 191456372q^{25} - 118854616q^{29} + 164659160q^{31} - 55239344q^{35} + 75658364q^{37} + 1815568608q^{41} + 10754408q^{43} + 1034359464q^{47} + 4123496848q^{49} + 665159988q^{53} - 1264543896q^{55} - 1040514580q^{59} - 14391208024q^{61} + 20938150200q^{65} - 33307097284q^{67} - 65848902896q^{71} + 17709749204q^{73} - 8594484604q^{77} - 26626784032q^{79} + 210306955048q^{83} - 25867402032q^{85} + 55951560072q^{89} + 66078280292q^{91} - 106810047392q^{95} - 156216030712q^{97} + O(q^{100}) \)

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
\(5\) −4949.72 + 8573.16i −0.708346 + 1.22689i 0.257124 + 0.966378i \(0.417225\pi\)
−0.965470 + 0.260513i \(0.916108\pi\)
\(6\) 0 0
\(7\) 29163.1 + 33568.4i 0.655835 + 0.754904i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −25007.0 43313.5i −0.0468169 0.0810892i 0.841667 0.539996i \(-0.181574\pi\)
−0.888484 + 0.458907i \(0.848241\pi\)
\(12\) 0 0
\(13\) 1.46252e6 1.09248 0.546238 0.837630i \(-0.316059\pi\)
0.546238 + 0.837630i \(0.316059\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −3.16934e6 5.48946e6i −0.541378 0.937693i −0.998825 0.0484569i \(-0.984570\pi\)
0.457448 0.889237i \(-0.348764\pi\)
\(18\) 0 0
\(19\) −1.02494e7 + 1.77525e7i −0.949632 + 1.64481i −0.203431 + 0.979089i \(0.565209\pi\)
−0.746201 + 0.665721i \(0.768124\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 2.36024e7 4.08806e7i 0.764634 1.32438i −0.175806 0.984425i \(-0.556253\pi\)
0.940440 0.339960i \(-0.110414\pi\)
\(24\) 0 0
\(25\) −2.45854e7 4.25831e7i −0.503508 0.872102i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 9.10208e7 0.824046 0.412023 0.911173i \(-0.364822\pi\)
0.412023 + 0.911173i \(0.364822\pi\)
\(30\) 0 0
\(31\) −4.83443e7 8.37349e7i −0.303289 0.525312i 0.673590 0.739105i \(-0.264751\pi\)
−0.976879 + 0.213794i \(0.931418\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −4.32137e8 + 8.38657e7i −1.39074 + 0.269904i
\(36\) 0 0
\(37\) −7.14098e7 + 1.23685e8i −0.169297 + 0.293230i −0.938173 0.346167i \(-0.887483\pi\)
0.768876 + 0.639398i \(0.220816\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −8.44357e8 −1.13819 −0.569095 0.822272i \(-0.692706\pi\)
−0.569095 + 0.822272i \(0.692706\pi\)
\(42\) 0 0
\(43\) −1.55607e9 −1.61418 −0.807089 0.590430i \(-0.798958\pi\)
−0.807089 + 0.590430i \(0.798958\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 4.22680e8 7.32103e8i 0.268827 0.465623i −0.699732 0.714405i \(-0.746697\pi\)
0.968559 + 0.248783i \(0.0800306\pi\)
\(48\) 0 0
\(49\) −2.76354e8 + 1.95792e9i −0.139762 + 0.990185i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −1.26817e9 2.19654e9i −0.416544 0.721476i 0.579045 0.815296i \(-0.303426\pi\)
−0.995589 + 0.0938196i \(0.970092\pi\)
\(54\) 0 0
\(55\) 4.95111e8 0.132650
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −2.80141e9 4.85219e9i −0.510142 0.883592i −0.999931 0.0117512i \(-0.996259\pi\)
0.489789 0.871841i \(-0.337074\pi\)
\(60\) 0 0
\(61\) −5.98273e8 + 1.03624e9i −0.0906955 + 0.157089i −0.907804 0.419395i \(-0.862242\pi\)
0.817108 + 0.576484i \(0.195576\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −7.23904e9 + 1.25384e10i −0.773851 + 1.34035i
\(66\) 0 0
\(67\) −2.73114e9 4.73048e9i −0.247134 0.428049i 0.715595 0.698515i \(-0.246156\pi\)
−0.962730 + 0.270466i \(0.912822\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −1.81232e10 −1.19210 −0.596051 0.802947i \(-0.703264\pi\)
−0.596051 + 0.802947i \(0.703264\pi\)
\(72\) 0 0
\(73\) 9.87533e9 + 1.71046e10i 0.557540 + 0.965687i 0.997701 + 0.0677684i \(0.0215879\pi\)
−0.440161 + 0.897919i \(0.645079\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 7.24683e8 2.10260e9i 0.0305105 0.0885234i
\(78\) 0 0
\(79\) −2.14642e10 + 3.71770e10i −0.784811 + 1.35933i 0.144301 + 0.989534i \(0.453907\pi\)
−0.929112 + 0.369799i \(0.879427\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 5.21192e10 1.45234 0.726170 0.687515i \(-0.241299\pi\)
0.726170 + 0.687515i \(0.241299\pi\)
\(84\) 0 0
\(85\) 6.27494e10 1.53393
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 1.39910e10 2.42332e10i 0.265586 0.460008i −0.702131 0.712048i \(-0.747768\pi\)
0.967717 + 0.252039i \(0.0811013\pi\)
\(90\) 0 0
\(91\) 4.26515e10 + 4.90944e10i 0.716484 + 0.824715i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −1.01464e11 1.75740e11i −1.34534 2.33019i
\(96\) 0 0
\(97\) 5.42003e10 0.640851 0.320426 0.947274i \(-0.396174\pi\)
0.320426 + 0.947274i \(0.396174\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −6.07024e10 1.05140e11i −0.574696 0.995403i −0.996075 0.0885179i \(-0.971787\pi\)
0.421379 0.906885i \(-0.361546\pi\)
\(102\) 0 0
\(103\) 8.26479e10 1.43150e11i 0.702469 1.21671i −0.265128 0.964213i \(-0.585414\pi\)
0.967597 0.252499i \(-0.0812525\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1.05098e11 + 1.82035e11i −0.724410 + 1.25472i 0.234806 + 0.972042i \(0.424554\pi\)
−0.959216 + 0.282673i \(0.908779\pi\)
\(108\) 0 0
\(109\) −4.57197e10 7.91888e10i −0.284615 0.492967i 0.687901 0.725805i \(-0.258532\pi\)
−0.972516 + 0.232837i \(0.925199\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 3.60006e9 0.0183814 0.00919068 0.999958i \(-0.497074\pi\)
0.00919068 + 0.999958i \(0.497074\pi\)
\(114\) 0 0
\(115\) 2.33651e11 + 4.04695e11i 1.08325 + 1.87625i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 9.18449e10 2.66480e11i 0.352815 1.02366i
\(120\) 0 0
\(121\) 1.41405e11 2.44921e11i 0.495616 0.858433i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 3.39174e9 0.00994071
\(126\) 0 0
\(127\) 6.33083e11 1.70036 0.850179 0.526494i \(-0.176494\pi\)
0.850179 + 0.526494i \(0.176494\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 4.80539e10 8.32318e10i 0.108827 0.188494i −0.806468 0.591277i \(-0.798624\pi\)
0.915295 + 0.402783i \(0.131957\pi\)
\(132\) 0 0
\(133\) −8.94831e11 + 1.73662e11i −1.86448 + 0.361843i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 1.83227e10 + 3.17359e10i 0.0324360 + 0.0561808i 0.881788 0.471647i \(-0.156340\pi\)
−0.849352 + 0.527827i \(0.823007\pi\)
\(138\) 0 0
\(139\) −7.27117e11 −1.18856 −0.594282 0.804257i \(-0.702564\pi\)
−0.594282 + 0.804257i \(0.702564\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −3.65732e10 6.33466e10i −0.0511463 0.0885880i
\(144\) 0 0
\(145\) −4.50527e11 + 7.80336e11i −0.583710 + 1.01102i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −5.76995e11 + 9.99385e11i −0.643647 + 1.11483i 0.340965 + 0.940076i \(0.389246\pi\)
−0.984612 + 0.174754i \(0.944087\pi\)
\(150\) 0 0
\(151\) −3.74264e11 6.48245e11i −0.387976 0.671995i 0.604201 0.796832i \(-0.293492\pi\)
−0.992177 + 0.124837i \(0.960159\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 9.57164e11 0.859334
\(156\) 0 0
\(157\) −1.07175e12 1.85633e12i −0.896697 1.55312i −0.831691 0.555239i \(-0.812627\pi\)
−0.0650059 0.997885i \(-0.520707\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 2.06062e12 3.99908e11i 1.50126 0.291352i
\(162\) 0 0
\(163\) 1.02063e10 1.76779e10i 0.00694765 0.0120337i −0.862531 0.506005i \(-0.831122\pi\)
0.869478 + 0.493971i \(0.164455\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 2.47826e11 0.147641 0.0738204 0.997272i \(-0.476481\pi\)
0.0738204 + 0.997272i \(0.476481\pi\)
\(168\) 0 0
\(169\) 3.46792e11 0.193505
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −9.53660e11 + 1.65179e12i −0.467886 + 0.810402i −0.999327 0.0366932i \(-0.988318\pi\)
0.531441 + 0.847096i \(0.321651\pi\)
\(174\) 0 0
\(175\) 7.12463e11 2.06715e12i 0.328136 0.952056i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −2.54501e11 4.40808e11i −0.103514 0.179291i 0.809616 0.586959i \(-0.199675\pi\)
−0.913130 + 0.407669i \(0.866342\pi\)
\(180\) 0 0
\(181\) −1.05292e12 −0.402869 −0.201434 0.979502i \(-0.564560\pi\)
−0.201434 + 0.979502i \(0.564560\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −7.06917e11 1.22442e12i −0.239841 0.415417i
\(186\) 0 0
\(187\) −1.58512e11 + 2.74550e11i −0.0506912 + 0.0877997i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 3.42442e12 5.93127e12i 0.974773 1.68836i 0.294092 0.955777i \(-0.404983\pi\)
0.680681 0.732580i \(-0.261684\pi\)
\(192\) 0 0
\(193\) −1.13876e12 1.97240e12i −0.306104 0.530187i 0.671403 0.741093i \(-0.265692\pi\)
−0.977506 + 0.210906i \(0.932359\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −2.51939e12 −0.604966 −0.302483 0.953155i \(-0.597816\pi\)
−0.302483 + 0.953155i \(0.597816\pi\)
\(198\) 0 0
\(199\) 5.73459e11 + 9.93260e11i 0.130260 + 0.225617i 0.923777 0.382932i \(-0.125086\pi\)
−0.793517 + 0.608548i \(0.791752\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 2.65445e12 + 3.05543e12i 0.540438 + 0.622076i
\(204\) 0 0
\(205\) 4.17933e12 7.23881e12i 0.806233 1.39644i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 1.02523e12 0.177835
\(210\) 0 0
\(211\) −1.08695e12 −0.178919 −0.0894593 0.995990i \(-0.528514\pi\)
−0.0894593 + 0.995990i \(0.528514\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 7.70209e12 1.33404e13i 1.14340 1.98042i
\(216\) 0 0
\(217\) 1.40098e12 4.06481e12i 0.197653 0.573472i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −4.63521e12 8.02843e12i −0.591442 1.02441i
\(222\) 0 0
\(223\) 1.60167e13 1.94489 0.972447 0.233124i \(-0.0748949\pi\)
0.972447 + 0.233124i \(0.0748949\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 5.82492e12 + 1.00891e13i 0.641428 + 1.11099i 0.985114 + 0.171901i \(0.0549910\pi\)
−0.343686 + 0.939085i \(0.611676\pi\)
\(228\) 0 0
\(229\) 4.67803e11 8.10258e11i 0.0490871 0.0850214i −0.840438 0.541908i \(-0.817702\pi\)
0.889525 + 0.456887i \(0.151035\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 6.06338e12 1.05021e13i 0.578438 1.00188i −0.417220 0.908805i \(-0.636996\pi\)
0.995659 0.0930793i \(-0.0296710\pi\)
\(234\) 0 0
\(235\) 4.18429e12 + 7.24741e12i 0.380846 + 0.659644i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −2.98561e12 −0.247654 −0.123827 0.992304i \(-0.539517\pi\)
−0.123827 + 0.992304i \(0.539517\pi\)
\(240\) 0 0
\(241\) −4.35089e12 7.53596e12i −0.344734 0.597097i 0.640571 0.767899i \(-0.278698\pi\)
−0.985305 + 0.170802i \(0.945364\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −1.54177e13 1.20604e13i −1.11585 0.872866i
\(246\) 0 0
\(247\) −1.49900e13 + 2.59634e13i −1.03745 + 1.79692i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −1.10571e13 −0.700544 −0.350272 0.936648i \(-0.613911\pi\)
−0.350272 + 0.936648i \(0.613911\pi\)
\(252\) 0 0
\(253\) −2.36091e12 −0.143191
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 1.27142e13 2.20217e13i 0.707387 1.22523i −0.258436 0.966028i \(-0.583207\pi\)
0.965823 0.259202i \(-0.0834596\pi\)
\(258\) 0 0
\(259\) −6.23446e12 + 1.20993e12i −0.332392 + 0.0645079i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −1.68147e13 2.91239e13i −0.824011 1.42723i −0.902673 0.430327i \(-0.858398\pi\)
0.0786626 0.996901i \(-0.474935\pi\)
\(264\) 0 0
\(265\) 2.51084e13 1.18023
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −7.46102e12 1.29229e13i −0.322969 0.559398i 0.658130 0.752904i \(-0.271348\pi\)
−0.981099 + 0.193506i \(0.938014\pi\)
\(270\) 0 0
\(271\) 1.07841e13 1.86786e13i 0.448179 0.776269i −0.550089 0.835106i \(-0.685406\pi\)
0.998268 + 0.0588375i \(0.0187394\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1.22961e12 + 2.12975e12i −0.0471454 + 0.0816582i
\(276\) 0 0
\(277\) −1.45333e13 2.51724e13i −0.535457 0.927439i −0.999141 0.0414380i \(-0.986806\pi\)
0.463684 0.886001i \(-0.346527\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −2.02171e13 −0.688390 −0.344195 0.938898i \(-0.611848\pi\)
−0.344195 + 0.938898i \(0.611848\pi\)
\(282\) 0 0
\(283\) −2.44690e11 4.23815e11i −0.00801291 0.0138788i 0.861991 0.506923i \(-0.169217\pi\)
−0.870004 + 0.493045i \(0.835884\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −2.46241e13 2.83438e13i −0.746465 0.859225i
\(288\) 0 0
\(289\) −2.95353e12 + 5.11566e12i −0.0861794 + 0.149267i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 6.82921e13 1.84756 0.923780 0.382924i \(-0.125083\pi\)
0.923780 + 0.382924i \(0.125083\pi\)
\(294\) 0 0
\(295\) 5.54649e13 1.44543
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 3.45189e13 5.97885e13i 0.835345 1.44686i
\(300\) 0 0
\(301\) −4.53797e13 5.22347e13i −1.05863 1.21855i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −5.92257e12 1.02582e13i −0.128488 0.222547i
\(306\) 0 0
\(307\) −2.82225e13 −0.590655 −0.295328 0.955396i \(-0.595429\pi\)
−0.295328 + 0.955396i \(0.595429\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −3.53006e13 6.11425e13i −0.688019 1.19168i −0.972478 0.232996i \(-0.925147\pi\)
0.284459 0.958688i \(-0.408186\pi\)
\(312\) 0 0
\(313\) 1.75608e13 3.04162e13i 0.330408 0.572283i −0.652184 0.758061i \(-0.726147\pi\)
0.982592 + 0.185778i \(0.0594804\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1.54610e13 + 2.67792e13i −0.271275 + 0.469863i −0.969189 0.246319i \(-0.920779\pi\)
0.697913 + 0.716182i \(0.254112\pi\)
\(318\) 0 0
\(319\) −2.27616e12 3.94242e12i −0.0385793 0.0668212i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 1.29936e14 2.05644
\(324\) 0 0
\(325\) −3.59565e13 6.22785e13i −0.550071 0.952751i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 3.69022e13 7.16169e12i 0.527807 0.102433i
\(330\) 0 0
\(331\) −1.86187e13 + 3.22486e13i −0.257571 + 0.446125i −0.965591 0.260067i \(-0.916255\pi\)
0.708020 + 0.706192i \(0.249589\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 5.40736e13 0.700227
\(336\) 0 0
\(337\) 9.01286e13 1.12953 0.564766 0.825251i \(-0.308967\pi\)
0.564766 + 0.825251i \(0.308967\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −2.41790e12 + 4.18792e12i −0.0283981 + 0.0491869i
\(342\) 0 0
\(343\) −7.37837e13 + 4.78222e13i −0.839156 + 0.543891i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 4.20561e13 + 7.28433e13i 0.448763 + 0.777280i 0.998306 0.0581855i \(-0.0185315\pi\)
−0.549543 + 0.835465i \(0.685198\pi\)
\(348\) 0 0
\(349\) 1.62557e14 1.68061 0.840305 0.542114i \(-0.182376\pi\)
0.840305 + 0.542114i \(0.182376\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 7.77383e13 + 1.34647e14i 0.754873 + 1.30748i 0.945437 + 0.325804i \(0.105635\pi\)
−0.190564 + 0.981675i \(0.561032\pi\)
\(354\) 0 0
\(355\) 8.97046e13 1.55373e14i 0.844421 1.46258i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 6.44669e13 1.11660e14i 0.570581 0.988275i −0.425925 0.904758i \(-0.640051\pi\)
0.996506 0.0835170i \(-0.0266153\pi\)
\(360\) 0 0
\(361\) −1.51857e14 2.63024e14i −1.30360 2.25790i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −1.95520e14 −1.57972
\(366\) 0 0
\(367\) 8.09211e13 + 1.40159e14i 0.634452 + 1.09890i 0.986631 + 0.162970i \(0.0521074\pi\)
−0.352179 + 0.935933i \(0.614559\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 3.67506e13 1.06629e14i 0.271461 0.787620i
\(372\) 0 0
\(373\) 7.49137e12 1.29754e13i 0.0537233 0.0930515i −0.837913 0.545804i \(-0.816224\pi\)
0.891636 + 0.452752i \(0.149558\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 1.33119e14 0.900251
\(378\) 0 0
\(379\) −1.46414e14 −0.961758 −0.480879 0.876787i \(-0.659682\pi\)
−0.480879 + 0.876787i \(0.659682\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −1.03039e14 + 1.78468e14i −0.638861 + 1.10654i 0.346822 + 0.937931i \(0.387261\pi\)
−0.985683 + 0.168609i \(0.946072\pi\)
\(384\) 0 0
\(385\) 1.44390e13 + 1.66201e13i 0.0869966 + 0.100138i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −4.28674e13 7.42485e13i −0.244008 0.422634i 0.717844 0.696204i \(-0.245129\pi\)
−0.961852 + 0.273569i \(0.911796\pi\)
\(390\) 0 0
\(391\) −2.99217e14 −1.65582
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −2.12483e14 3.68032e14i −1.11184 1.92576i
\(396\) 0 0
\(397\) −5.18685e13 + 8.98388e13i −0.263971 + 0.457210i −0.967293 0.253660i \(-0.918366\pi\)
0.703323 + 0.710871i \(0.251699\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −8.92898e13 + 1.54655e14i −0.430039 + 0.744850i −0.996876 0.0789803i \(-0.974834\pi\)
0.566837 + 0.823830i \(0.308167\pi\)
\(402\) 0 0
\(403\) −7.07044e13 1.22464e14i −0.331336 0.573891i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 7.14299e12 0.0317038
\(408\) 0 0
\(409\) 1.39715e14 + 2.41994e14i 0.603622 + 1.04550i 0.992268 + 0.124117i \(0.0396099\pi\)
−0.388645 + 0.921388i \(0.627057\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 8.11826e13 2.35544e14i 0.332459 0.964599i
\(414\) 0 0
\(415\) −2.57975e14 + 4.46827e14i −1.02876 + 1.78186i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −1.47340e14 −0.557370 −0.278685 0.960383i \(-0.589898\pi\)
−0.278685 + 0.960383i \(0.589898\pi\)
\(420\) 0 0
\(421\) 1.13118e14 0.416852 0.208426 0.978038i \(-0.433166\pi\)
0.208426 + 0.978038i \(0.433166\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −1.55839e14 + 2.69921e14i −0.545176 + 0.944273i
\(426\) 0 0
\(427\) −5.22325e13 + 1.01369e13i −0.178069 + 0.0345581i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −2.21901e14 3.84344e14i −0.718678 1.24479i −0.961524 0.274722i \(-0.911414\pi\)
0.242845 0.970065i \(-0.421919\pi\)
\(432\) 0 0
\(433\) 3.99750e14 1.26213 0.631067 0.775729i \(-0.282617\pi\)
0.631067 + 0.775729i \(0.282617\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 4.83823e14 + 8.38006e14i 1.45224 + 2.51536i
\(438\) 0 0
\(439\) 2.14931e14 3.72271e14i 0.629134 1.08969i −0.358591 0.933495i \(-0.616743\pi\)
0.987726 0.156198i \(-0.0499239\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 6.77263e13 1.17305e14i 0.188598 0.326661i −0.756185 0.654358i \(-0.772939\pi\)
0.944783 + 0.327697i \(0.106272\pi\)
\(444\) 0 0
\(445\) 1.38503e14 + 2.39895e14i 0.376254 + 0.651690i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −9.79795e13 −0.253385 −0.126692 0.991942i \(-0.540436\pi\)
−0.126692 + 0.991942i \(0.540436\pi\)
\(450\) 0 0
\(451\) 2.11149e13 + 3.65720e13i 0.0532865 + 0.0922949i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −6.32007e14 + 1.22655e14i −1.51935 + 0.294864i
\(456\) 0 0
\(457\) −3.69842e14 + 6.40586e14i −0.867916 + 1.50327i −0.00379321 + 0.999993i \(0.501207\pi\)
−0.864123 + 0.503281i \(0.832126\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −2.05197e14 −0.459003 −0.229501 0.973308i \(-0.573710\pi\)
−0.229501 + 0.973308i \(0.573710\pi\)
\(462\) 0 0
\(463\) 3.01270e14 0.658052 0.329026 0.944321i \(-0.393280\pi\)
0.329026 + 0.944321i \(0.393280\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 1.92054e14 3.32648e14i 0.400111 0.693013i −0.593628 0.804740i \(-0.702305\pi\)
0.993739 + 0.111727i \(0.0356381\pi\)
\(468\) 0 0
\(469\) 7.91463e13 2.29636e14i 0.161057 0.467293i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 3.89126e13 + 6.73986e13i 0.0755707 + 0.130892i
\(474\) 0 0
\(475\) 1.00794e15 1.91259
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 3.73993e14 + 6.47776e14i 0.677671 + 1.17376i 0.975681 + 0.219197i \(0.0703438\pi\)
−0.298010 + 0.954563i \(0.596323\pi\)
\(480\) 0 0
\(481\) −1.04438e14 + 1.80892e14i −0.184953 + 0.320347i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −2.68276e14 + 4.64668e14i −0.453945 + 0.786255i
\(486\) 0 0
\(487\) 6.99482e13 + 1.21154e14i 0.115709 + 0.200414i 0.918063 0.396435i \(-0.129753\pi\)
−0.802354 + 0.596848i \(0.796419\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −2.86402e13 −0.0452926 −0.0226463 0.999744i \(-0.507209\pi\)
−0.0226463 + 0.999744i \(0.507209\pi\)
\(492\) 0 0
\(493\) −2.88476e14 4.99655e14i −0.446120 0.772703i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −5.28528e14 6.08367e14i −0.781822 0.899923i
\(498\) 0 0
\(499\) −5.75867e14 + 9.97430e14i −0.833238 + 1.44321i 0.0622193 + 0.998063i \(0.480182\pi\)
−0.895457 + 0.445148i \(0.853151\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 9.85521e14 1.36472 0.682358 0.731019i \(-0.260955\pi\)
0.682358 + 0.731019i \(0.260955\pi\)
\(504\) 0 0
\(505\) 1.20184e15 1.62833
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −3.82938e14 + 6.63268e14i −0.496799 + 0.860481i −0.999993 0.00369203i \(-0.998825\pi\)
0.503194 + 0.864173i \(0.332158\pi\)
\(510\) 0 0
\(511\) −2.86179e14 + 8.30322e14i −0.363348 + 1.05422i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 8.18168e14 + 1.41711e15i 0.995183 + 1.72371i
\(516\) 0 0
\(517\) −4.22799e13 −0.0503426
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 3.90199e14 + 6.75845e14i 0.445327 + 0.771329i 0.998075 0.0620194i \(-0.0197541\pi\)
−0.552748 + 0.833349i \(0.686421\pi\)
\(522\) 0 0
\(523\) −1.32813e14 + 2.30039e14i −0.148416 + 0.257064i −0.930642 0.365930i \(-0.880751\pi\)
0.782226 + 0.622995i \(0.214084\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −3.06440e14 + 5.30769e14i −0.328388 + 0.568784i
\(528\) 0 0
\(529\) −6.37744e14 1.10461e15i −0.669330 1.15931i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −1.23489e15 −1.24345
\(534\) 0 0
\(535\) −1.04041e15 1.80205e15i −1.02627 1.77755i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 9.17151e13 3.69919e13i 0.0868365 0.0350242i
\(540\) 0 0
\(541\) −2.32642e14 + 4.02947e14i −0.215825 + 0.373820i −0.953528 0.301306i \(-0.902577\pi\)
0.737702 + 0.675126i \(0.235911\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 9.05198e14 0.806423
\(546\) 0 0
\(547\) −4.31654e14 −0.376882 −0.188441 0.982084i \(-0.560343\pi\)
−0.188441 + 0.982084i \(0.560343\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −9.32912e14 + 1.61585e15i −0.782540 + 1.35540i
\(552\) 0 0
\(553\) −1.87394e15 + 3.63679e14i −1.54087 + 0.299040i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −1.93906e13 3.35855e13i −0.0153246 0.0265429i 0.858261 0.513213i \(-0.171545\pi\)
−0.873586 + 0.486670i \(0.838211\pi\)
\(558\) 0 0
\(559\) −2.27577e15 −1.76345
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 2.67759e14 + 4.63772e14i 0.199502 + 0.345548i 0.948367 0.317175i \(-0.102734\pi\)
−0.748865 + 0.662723i \(0.769401\pi\)
\(564\) 0 0
\(565\) −1.78193e13 + 3.08639e13i −0.0130204 + 0.0225519i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 4.33929e14 7.51587e14i 0.305001 0.528277i −0.672261 0.740314i \(-0.734677\pi\)
0.977262 + 0.212038i \(0.0680099\pi\)
\(570\) 0 0
\(571\) 5.01450e14 + 8.68538e14i 0.345724 + 0.598811i 0.985485 0.169762i \(-0.0543000\pi\)
−0.639761 + 0.768574i \(0.720967\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −2.32110e15 −1.54000
\(576\) 0 0
\(577\) −1.70850e14 2.95920e14i −0.111211 0.192623i 0.805048 0.593210i \(-0.202140\pi\)
−0.916259 + 0.400587i \(0.868806\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 1.51996e15 + 1.74956e15i 0.952495 + 1.09638i
\(582\) 0 0
\(583\) −6.34265e13 + 1.09858e14i −0.0390026 + 0.0675545i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −1.31315e15 −0.777689 −0.388845 0.921303i \(-0.627126\pi\)
−0.388845 + 0.921303i \(0.627126\pi\)
\(588\) 0 0
\(589\) 1.98201e15 1.15205
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 1.42951e15 2.47598e15i 0.800543 1.38658i −0.118715 0.992928i \(-0.537878\pi\)
0.919259 0.393654i \(-0.128789\pi\)
\(594\) 0 0
\(595\) 1.82997e15 + 2.10640e15i 1.00601 + 1.15797i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 1.07552e15 + 1.86285e15i 0.569862 + 0.987030i 0.996579 + 0.0826451i \(0.0263368\pi\)
−0.426717 + 0.904385i \(0.640330\pi\)
\(600\) 0 0
\(601\) −3.46561e15 −1.80289 −0.901447 0.432889i \(-0.857494\pi\)
−0.901447 + 0.432889i \(0.857494\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 1.39983e15 + 2.42458e15i 0.702136 + 1.21613i
\(606\) 0 0
\(607\) 8.39119e14 1.45340e15i 0.413319 0.715890i −0.581931 0.813238i \(-0.697703\pi\)
0.995250 + 0.0973481i \(0.0310360\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 6.18176e14 1.07071e15i 0.293688 0.508682i
\(612\) 0 0
\(613\) 2.51033e14 + 4.34802e14i 0.117138 + 0.202889i 0.918632 0.395113i \(-0.129295\pi\)
−0.801494 + 0.598002i \(0.795961\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −3.06387e15 −1.37944 −0.689719 0.724077i \(-0.742266\pi\)
−0.689719 + 0.724077i \(0.742266\pi\)
\(618\) 0 0
\(619\) 6.07837e14 + 1.05280e15i 0.268837 + 0.465639i 0.968562 0.248773i \(-0.0800275\pi\)
−0.699725 + 0.714412i \(0.746694\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 1.22149e15 2.37058e14i 0.521443 0.101197i
\(624\) 0 0
\(625\) 1.18367e15 2.05018e15i 0.496467 0.859906i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 9.05289e14 0.366614
\(630\) 0 0
\(631\) 2.29369e15 0.912794 0.456397 0.889776i \(-0.349140\pi\)
0.456397 + 0.889776i \(0.349140\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −3.13358e15 + 5.42753e15i −1.20444 + 2.08615i
\(636\) 0 0
\(637\) −4.04173e14 + 2.86349e15i −0.152686 + 1.08175i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −9.49382e13 1.64438e14i −0.0346515 0.0600181i 0.848180 0.529709i \(-0.177699\pi\)
−0.882831 + 0.469691i \(0.844365\pi\)
\(642\) 0 0
\(643\) 1.75159e15 0.628452 0.314226 0.949348i \(-0.398255\pi\)
0.314226 + 0.949348i \(0.398255\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −1.59994e15 2.77118e15i −0.554793 0.960930i −0.997920 0.0644710i \(-0.979464\pi\)
0.443126 0.896459i \(-0.353869\pi\)
\(648\) 0 0
\(649\) −1.40110e14 + 2.42678e14i −0.0477665 + 0.0827341i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 1.12815e15 1.95401e15i 0.371829 0.644026i −0.618018 0.786164i \(-0.712064\pi\)
0.989847 + 0.142138i \(0.0453976\pi\)
\(654\) 0 0
\(655\) 4.75706e14 + 8.23948e14i 0.154174 + 0.267038i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −3.01218e15 −0.944084 −0.472042 0.881576i \(-0.656483\pi\)
−0.472042 + 0.881576i \(0.656483\pi\)
\(660\) 0 0
\(661\) −1.47975e15 2.56300e15i −0.456121 0.790024i 0.542631 0.839971i \(-0.317428\pi\)
−0.998752 + 0.0499469i \(0.984095\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 2.94033e15 8.53111e15i 0.876753 2.54382i
\(666\) 0 0
\(667\) 2.14831e15 3.72098e15i 0.630094 1.09135i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 5.98442e13 0.0169843
\(672\) 0 0
\(673\) 4.01157e15 1.12004 0.560018 0.828481i \(-0.310794\pi\)
0.560018 + 0.828481i \(0.310794\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 3.58231e15 6.20474e15i 0.968111 1.67682i 0.267096 0.963670i \(-0.413936\pi\)
0.701015 0.713147i \(-0.252731\pi\)
\(678\) 0 0
\(679\) 1.58065e15 + 1.81942e15i 0.420293 + 0.483782i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −7.37708e13 1.27775e14i −0.0189920 0.0328951i 0.856373 0.516357i \(-0.172712\pi\)
−0.875365 + 0.483462i \(0.839379\pi\)
\(684\) 0 0
\(685\) −3.62770e14 −0.0919037
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −1.85472e15 3.21248e15i −0.455065 0.788196i
\(690\) 0 0
\(691\) 1.43011e15 2.47703e15i 0.345335 0.598138i −0.640079 0.768309i \(-0.721099\pi\)
0.985415 + 0.170171i \(0.0544319\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 3.59902e15 6.23369e15i 0.841915 1.45824i
\(696\) 0 0
\(697\) 2.67606e15 + 4.63507e15i 0.616191 + 1.06727i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −3.67571e14 −0.0820147 −0.0410073 0.999159i \(-0.513057\pi\)
−0.0410073 + 0.999159i \(0.513057\pi\)
\(702\) 0 0
\(703\) −1.46382e15 2.53541e15i −0.321539 0.556922i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 1.75910e15 5.10388e15i 0.374528 1.08666i
\(708\) 0 0
\(709\) −3.52656e15 + 6.10818e15i −0.739259 + 1.28043i 0.213570 + 0.976928i \(0.431491\pi\)
−0.952829 + 0.303507i \(0.901842\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −4.56418e15 −0.927620
\(714\) 0 0
\(715\) 7.24108e14 0.144917
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −3.63237e15 + 6.29146e15i −0.704988 + 1.22108i 0.261708 + 0.965147i \(0.415714\pi\)
−0.966696 + 0.255928i \(0.917619\pi\)
\(720\) 0 0
\(721\) 7.21561e15 1.40035e15i 1.37921 0.267665i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −2.23778e15 3.87595e15i −0.414914 0.718652i
\(726\) 0 0
\(727\) −8.82541e15 −1.61174 −0.805871 0.592091i \(-0.798302\pi\)
−0.805871 + 0.592091i \(0.798302\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 4.93171e15 + 8.54196e15i 0.873880 + 1.51360i
\(732\) 0 0
\(733\) −3.25078e15 + 5.63051e15i −0.567434 + 0.982825i 0.429384 + 0.903122i \(0.358731\pi\)
−0.996819 + 0.0797030i \(0.974603\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −1.36596e14 + 2.36591e14i −0.0231401 + 0.0400799i
\(738\) 0 0
\(739\) −4.66487e15 8.07979e15i −0.778565 1.34851i −0.932769 0.360475i \(-0.882615\pi\)
0.154204 0.988039i \(-0.450719\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −7.14846e15 −1.15817 −0.579087 0.815266i \(-0.696591\pi\)
−0.579087 + 0.815266i \(0.696591\pi\)
\(744\) 0 0
\(745\) −5.71193e15 9.89335e15i −0.911850 1.57937i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −9.17564e15 + 1.78073e15i −1.42228 + 0.276025i
\(750\) 0 0
\(751\) 2.33373e15 4.04213e15i 0.356476 0.617434i −0.630893 0.775869i \(-0.717312\pi\)
0.987369 + 0.158435i \(0.0506448\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 7.41001e15 1.09929
\(756\) 0 0
\(757\) 4.72097e15 0.690246 0.345123 0.938557i \(-0.387837\pi\)
0.345123 + 0.938557i \(0.387837\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −6.09532e14 + 1.05574e15i −0.0865727 + 0.149948i −0.906060 0.423149i \(-0.860925\pi\)
0.819488 + 0.573097i \(0.194258\pi\)
\(762\) 0 0
\(763\) 1.32492e15 3.84413e15i 0.185483 0.538162i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −4.09711e15 7.09641e15i −0.557318 0.965304i
\(768\) 0 0
\(769\) 4.52570e15 0.606864 0.303432 0.952853i \(-0.401867\pi\)
0.303432 + 0.952853i \(0.401867\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 2.34216e15 + 4.05675e15i 0.305232 + 0.528677i 0.977313 0.211800i \(-0.0679327\pi\)
−0.672081 + 0.740478i \(0.734599\pi\)
\(774\) 0 0
\(775\) −2.37713e15 + 4.11731e15i −0.305417 + 0.528998i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 8.65418e15 1.49895e16i 1.08086 1.87211i
\(780\) 0 0
\(781\) 4.53207e14 + 7.84977e14i 0.0558105 + 0.0966666i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 2.12195e16 2.54069