Properties

Label 252.9.z.d.73.1
Level $252$
Weight $9$
Character 252.73
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: \( x^{12} - 3 x^{11} + 148097 x^{10} + 46071824 x^{9} + 21578502553 x^{8} + 3561445462121 x^{7} + 576413321817541 x^{6} + \cdots + 45\!\cdots\!96 \) Copy content Toggle raw display
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 73.1
Root \(-41.5970 + 72.0480i\) of defining polynomial
Character \(\chi\) \(=\) 252.73
Dual form 252.9.z.d.145.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1011.88 + 584.207i) q^{5} +(-1829.74 + 1554.62i) q^{7} +O(q^{10})\) \(q+(-1011.88 + 584.207i) q^{5} +(-1829.74 + 1554.62i) q^{7} +(13077.9 - 22651.7i) q^{11} +28593.8i q^{13} +(18015.1 + 10401.0i) q^{17} +(42991.6 - 24821.2i) q^{19} +(-170925. - 296051. i) q^{23} +(487282. - 843998. i) q^{25} +1.12659e6 q^{29} +(1.47519e6 + 851702. i) q^{31} +(943251. - 2.64203e6i) q^{35} +(320285. + 554750. i) q^{37} -1.34661e6i q^{41} -1.80008e6 q^{43} +(-7.88787e6 + 4.55406e6i) q^{47} +(931110. - 5.68911e6i) q^{49} +(1.82943e6 - 3.16867e6i) q^{53} +3.05609e7i q^{55} +(-9.97907e6 - 5.76142e6i) q^{59} +(-8.77419e6 + 5.06578e6i) q^{61} +(-1.67047e7 - 2.89334e7i) q^{65} +(-8.86768e6 + 1.53593e7i) q^{67} +3.79392e7 q^{71} +(2.94841e7 + 1.70227e7i) q^{73} +(1.12855e7 + 6.17779e7i) q^{77} +(-9.66395e6 - 1.67384e7i) q^{79} -960779. i q^{83} -2.43053e7 q^{85} +(-5.62273e7 + 3.24629e7i) q^{89} +(-4.44525e7 - 5.23193e7i) q^{91} +(-2.90015e7 + 5.02320e7i) q^{95} -2.66661e7i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 285 q^{5} + 198 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 285 q^{5} + 198 q^{7} + 17919 q^{11} + 205782 q^{17} + 74313 q^{19} + 62832 q^{23} + 878679 q^{25} + 575454 q^{29} + 1442952 q^{31} + 3989514 q^{35} - 2058621 q^{37} + 7721322 q^{43} - 12088194 q^{47} - 16964694 q^{49} + 5506743 q^{53} - 7511901 q^{59} - 37215576 q^{61} - 5047122 q^{65} - 36824553 q^{67} + 30011556 q^{71} + 95080185 q^{73} + 38333727 q^{77} + 8514456 q^{79} + 20121540 q^{85} - 83038554 q^{89} - 198538635 q^{91} + 221605224 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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
\(5\) −1011.88 + 584.207i −1.61900 + 0.934731i −0.631822 + 0.775114i \(0.717693\pi\)
−0.987179 + 0.159617i \(0.948974\pi\)
\(6\) 0 0
\(7\) −1829.74 + 1554.62i −0.762075 + 0.647489i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 13077.9 22651.7i 0.893241 1.54714i 0.0572739 0.998359i \(-0.481759\pi\)
0.835967 0.548780i \(-0.184907\pi\)
\(12\) 0 0
\(13\) 28593.8i 1.00115i 0.865694 + 0.500574i \(0.166878\pi\)
−0.865694 + 0.500574i \(0.833122\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 18015.1 + 10401.0i 0.215695 + 0.124532i 0.603955 0.797018i \(-0.293591\pi\)
−0.388260 + 0.921550i \(0.626924\pi\)
\(18\) 0 0
\(19\) 42991.6 24821.2i 0.329890 0.190462i −0.325902 0.945404i \(-0.605668\pi\)
0.655792 + 0.754941i \(0.272335\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −170925. 296051.i −0.610794 1.05793i −0.991107 0.133068i \(-0.957517\pi\)
0.380313 0.924858i \(-0.375816\pi\)
\(24\) 0 0
\(25\) 487282. 843998.i 1.24744 2.16063i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 1.12659e6 1.59284 0.796422 0.604741i \(-0.206723\pi\)
0.796422 + 0.604741i \(0.206723\pi\)
\(30\) 0 0
\(31\) 1.47519e6 + 851702.i 1.59735 + 0.922233i 0.991994 + 0.126282i \(0.0403044\pi\)
0.605360 + 0.795951i \(0.293029\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 943251. 2.64203e6i 0.628572 1.76062i
\(36\) 0 0
\(37\) 320285. + 554750.i 0.170895 + 0.295999i 0.938733 0.344645i \(-0.112001\pi\)
−0.767838 + 0.640644i \(0.778667\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 1.34661e6i 0.476549i −0.971198 0.238275i \(-0.923418\pi\)
0.971198 0.238275i \(-0.0765818\pi\)
\(42\) 0 0
\(43\) −1.80008e6 −0.526524 −0.263262 0.964724i \(-0.584798\pi\)
−0.263262 + 0.964724i \(0.584798\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −7.88787e6 + 4.55406e6i −1.61647 + 0.933270i −0.628648 + 0.777690i \(0.716392\pi\)
−0.987823 + 0.155581i \(0.950275\pi\)
\(48\) 0 0
\(49\) 931110. 5.68911e6i 0.161516 0.986870i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 1.82943e6 3.16867e6i 0.231853 0.401582i −0.726500 0.687166i \(-0.758854\pi\)
0.958354 + 0.285584i \(0.0921877\pi\)
\(54\) 0 0
\(55\) 3.05609e7i 3.33976i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −9.97907e6 5.76142e6i −0.823535 0.475468i 0.0280988 0.999605i \(-0.491055\pi\)
−0.851634 + 0.524137i \(0.824388\pi\)
\(60\) 0 0
\(61\) −8.77419e6 + 5.06578e6i −0.633706 + 0.365870i −0.782186 0.623045i \(-0.785895\pi\)
0.148480 + 0.988915i \(0.452562\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −1.67047e7 2.89334e7i −0.935804 1.62086i
\(66\) 0 0
\(67\) −8.86768e6 + 1.53593e7i −0.440059 + 0.762205i −0.997693 0.0678821i \(-0.978376\pi\)
0.557634 + 0.830087i \(0.311709\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 3.79392e7 1.49298 0.746491 0.665396i \(-0.231737\pi\)
0.746491 + 0.665396i \(0.231737\pi\)
\(72\) 0 0
\(73\) 2.94841e7 + 1.70227e7i 1.03824 + 0.599426i 0.919333 0.393480i \(-0.128729\pi\)
0.118903 + 0.992906i \(0.462062\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 1.12855e7 + 6.17779e7i 0.321038 + 1.75740i
\(78\) 0 0
\(79\) −9.66395e6 1.67384e7i −0.248111 0.429741i 0.714891 0.699236i \(-0.246476\pi\)
−0.963002 + 0.269495i \(0.913143\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 960779.i 0.0202447i −0.999949 0.0101223i \(-0.996778\pi\)
0.999949 0.0101223i \(-0.00322210\pi\)
\(84\) 0 0
\(85\) −2.43053e7 −0.465614
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −5.62273e7 + 3.24629e7i −0.896164 + 0.517400i −0.875954 0.482395i \(-0.839767\pi\)
−0.0202100 + 0.999796i \(0.506433\pi\)
\(90\) 0 0
\(91\) −4.44525e7 5.23193e7i −0.648233 0.762950i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −2.90015e7 + 5.02320e7i −0.356062 + 0.616717i
\(96\) 0 0
\(97\) 2.66661e7i 0.301213i −0.988594 0.150606i \(-0.951877\pi\)
0.988594 0.150606i \(-0.0481226\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −6.33466e6 3.65732e6i −0.0608749 0.0351461i 0.469254 0.883063i \(-0.344523\pi\)
−0.530129 + 0.847917i \(0.677856\pi\)
\(102\) 0 0
\(103\) 2.35283e7 1.35841e7i 0.209046 0.120693i −0.391822 0.920041i \(-0.628155\pi\)
0.600868 + 0.799348i \(0.294822\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 6.81604e7 + 1.18057e8i 0.519992 + 0.900653i 0.999730 + 0.0232412i \(0.00739857\pi\)
−0.479737 + 0.877412i \(0.659268\pi\)
\(108\) 0 0
\(109\) 4.81540e7 8.34051e7i 0.341135 0.590863i −0.643509 0.765439i \(-0.722522\pi\)
0.984644 + 0.174576i \(0.0558554\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 8.83287e7 0.541737 0.270868 0.962616i \(-0.412689\pi\)
0.270868 + 0.962616i \(0.412689\pi\)
\(114\) 0 0
\(115\) 3.45910e8 + 1.99711e8i 1.97775 + 1.14185i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −4.91325e7 + 8.97544e6i −0.245009 + 0.0447577i
\(120\) 0 0
\(121\) −2.34885e8 4.06834e8i −1.09576 1.89791i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 6.82283e8i 2.79463i
\(126\) 0 0
\(127\) −3.88706e7 −0.149419 −0.0747097 0.997205i \(-0.523803\pi\)
−0.0747097 + 0.997205i \(0.523803\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −3.31013e8 + 1.91111e8i −1.12398 + 0.648933i −0.942415 0.334445i \(-0.891451\pi\)
−0.181570 + 0.983378i \(0.558118\pi\)
\(132\) 0 0
\(133\) −4.00760e7 + 1.12252e8i −0.128079 + 0.358747i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 2.14124e7 3.70873e7i 0.0607831 0.105279i −0.834033 0.551715i \(-0.813974\pi\)
0.894816 + 0.446436i \(0.147307\pi\)
\(138\) 0 0
\(139\) 1.51148e8i 0.404896i 0.979293 + 0.202448i \(0.0648897\pi\)
−0.979293 + 0.202448i \(0.935110\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 6.47697e8 + 3.73948e8i 1.54892 + 0.894267i
\(144\) 0 0
\(145\) −1.13997e9 + 6.58161e8i −2.57882 + 1.48888i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −1.30228e8 2.25561e8i −0.264215 0.457634i 0.703143 0.711049i \(-0.251780\pi\)
−0.967358 + 0.253415i \(0.918446\pi\)
\(150\) 0 0
\(151\) −2.43650e8 + 4.22014e8i −0.468661 + 0.811744i −0.999358 0.0358171i \(-0.988597\pi\)
0.530698 + 0.847561i \(0.321930\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −1.99028e9 −3.44816
\(156\) 0 0
\(157\) 2.17705e8 + 1.25692e8i 0.358318 + 0.206875i 0.668343 0.743853i \(-0.267004\pi\)
−0.310024 + 0.950729i \(0.600337\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 7.72996e8 + 2.75973e8i 1.15047 + 0.410736i
\(162\) 0 0
\(163\) 4.84569e8 + 8.39298e8i 0.686444 + 1.18896i 0.972981 + 0.230887i \(0.0741627\pi\)
−0.286536 + 0.958069i \(0.592504\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 4.87973e8i 0.627378i 0.949526 + 0.313689i \(0.101565\pi\)
−0.949526 + 0.313689i \(0.898435\pi\)
\(168\) 0 0
\(169\) −1.87509e6 −0.00229867
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 6.43728e7 3.71657e7i 0.0718651 0.0414914i −0.463637 0.886025i \(-0.653456\pi\)
0.535502 + 0.844534i \(0.320122\pi\)
\(174\) 0 0
\(175\) 4.20496e8 + 2.30184e9i 0.448342 + 2.45427i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −2.17987e8 + 3.77565e8i −0.212334 + 0.367773i −0.952444 0.304712i \(-0.901440\pi\)
0.740111 + 0.672485i \(0.234773\pi\)
\(180\) 0 0
\(181\) 1.22472e9i 1.14110i −0.821264 0.570548i \(-0.806731\pi\)
0.821264 0.570548i \(-0.193269\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −6.48177e8 3.74225e8i −0.553359 0.319482i
\(186\) 0 0
\(187\) 4.71200e8 2.72047e8i 0.385335 0.222473i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 3.18497e8 + 5.51652e8i 0.239316 + 0.414507i 0.960518 0.278217i \(-0.0897436\pi\)
−0.721202 + 0.692724i \(0.756410\pi\)
\(192\) 0 0
\(193\) 8.35413e8 1.44698e9i 0.602105 1.04288i −0.390397 0.920646i \(-0.627662\pi\)
0.992502 0.122229i \(-0.0390043\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 4.97108e8 0.330055 0.165027 0.986289i \(-0.447229\pi\)
0.165027 + 0.986289i \(0.447229\pi\)
\(198\) 0 0
\(199\) 1.42581e9 + 8.23189e8i 0.909176 + 0.524913i 0.880166 0.474666i \(-0.157431\pi\)
0.0290099 + 0.999579i \(0.490765\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −2.06137e9 + 1.75142e9i −1.21387 + 1.03135i
\(204\) 0 0
\(205\) 7.86701e8 + 1.36261e9i 0.445445 + 0.771533i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 1.29844e9i 0.680515i
\(210\) 0 0
\(211\) −3.49413e9 −1.76283 −0.881413 0.472347i \(-0.843407\pi\)
−0.881413 + 0.472347i \(0.843407\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 1.82146e9 1.05162e9i 0.852442 0.492158i
\(216\) 0 0
\(217\) −4.02329e9 + 7.34968e8i −1.81444 + 0.331459i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −2.97404e8 + 5.15119e8i −0.124675 + 0.215943i
\(222\) 0 0
\(223\) 2.69455e8i 0.108960i −0.998515 0.0544799i \(-0.982650\pi\)
0.998515 0.0544799i \(-0.0173501\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 1.25301e9 + 7.23427e8i 0.471902 + 0.272453i 0.717036 0.697037i \(-0.245499\pi\)
−0.245134 + 0.969489i \(0.578832\pi\)
\(228\) 0 0
\(229\) 1.59604e8 9.21477e7i 0.0580367 0.0335075i −0.470701 0.882293i \(-0.655999\pi\)
0.528738 + 0.848785i \(0.322666\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 2.09346e9 + 3.62598e9i 0.710299 + 1.23027i 0.964745 + 0.263186i \(0.0847734\pi\)
−0.254446 + 0.967087i \(0.581893\pi\)
\(234\) 0 0
\(235\) 5.32103e9 9.21629e9i 1.74471 3.02193i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −2.19326e9 −0.672201 −0.336101 0.941826i \(-0.609108\pi\)
−0.336101 + 0.941826i \(0.609108\pi\)
\(240\) 0 0
\(241\) 4.71562e9 + 2.72256e9i 1.39788 + 0.807067i 0.994171 0.107819i \(-0.0343868\pi\)
0.403711 + 0.914887i \(0.367720\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 2.38145e9 + 6.30063e9i 0.660963 + 1.74872i
\(246\) 0 0
\(247\) 7.09734e8 + 1.22929e9i 0.190681 + 0.330269i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 1.90950e9i 0.481089i −0.970638 0.240544i \(-0.922674\pi\)
0.970638 0.240544i \(-0.0773260\pi\)
\(252\) 0 0
\(253\) −8.94139e9 −2.18234
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −3.63082e9 + 2.09626e9i −0.832286 + 0.480521i −0.854635 0.519230i \(-0.826219\pi\)
0.0223487 + 0.999750i \(0.492886\pi\)
\(258\) 0 0
\(259\) −1.44846e9 5.17127e8i −0.321891 0.114921i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −2.08663e9 + 3.61415e9i −0.436136 + 0.755410i −0.997388 0.0722352i \(-0.976987\pi\)
0.561251 + 0.827645i \(0.310320\pi\)
\(264\) 0 0
\(265\) 4.27507e9i 0.866882i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 6.02865e9 + 3.48064e9i 1.15136 + 0.664737i 0.949218 0.314619i \(-0.101877\pi\)
0.202141 + 0.979356i \(0.435210\pi\)
\(270\) 0 0
\(271\) −5.31995e9 + 3.07148e9i −0.986349 + 0.569469i −0.904181 0.427150i \(-0.859518\pi\)
−0.0821681 + 0.996618i \(0.526184\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1.27453e10 2.20755e10i −2.22853 3.85993i
\(276\) 0 0
\(277\) −2.03712e8 + 3.52839e8i −0.0346016 + 0.0599318i −0.882808 0.469735i \(-0.844350\pi\)
0.848206 + 0.529666i \(0.177683\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 1.61123e9 0.258423 0.129212 0.991617i \(-0.458755\pi\)
0.129212 + 0.991617i \(0.458755\pi\)
\(282\) 0 0
\(283\) −5.30872e9 3.06499e9i −0.827645 0.477841i 0.0254009 0.999677i \(-0.491914\pi\)
−0.853046 + 0.521836i \(0.825247\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 2.09347e9 + 2.46396e9i 0.308560 + 0.363166i
\(288\) 0 0
\(289\) −3.27152e9 5.66643e9i −0.468984 0.812304i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 8.04420e9i 1.09147i 0.837957 + 0.545736i \(0.183750\pi\)
−0.837957 + 0.545736i \(0.816250\pi\)
\(294\) 0 0
\(295\) 1.34634e10 1.77774
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 8.46522e9 4.88740e9i 1.05914 0.611495i
\(300\) 0 0
\(301\) 3.29368e9 2.79844e9i 0.401250 0.340918i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 5.91893e9 1.02519e10i 0.683981 1.18469i
\(306\) 0 0
\(307\) 5.92170e9i 0.666642i −0.942813 0.333321i \(-0.891831\pi\)
0.942813 0.333321i \(-0.108169\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −3.70737e8 2.14045e8i −0.0396300 0.0228804i 0.480054 0.877239i \(-0.340617\pi\)
−0.519684 + 0.854358i \(0.673950\pi\)
\(312\) 0 0
\(313\) −7.31975e9 + 4.22606e9i −0.762639 + 0.440310i −0.830242 0.557402i \(-0.811798\pi\)
0.0676034 + 0.997712i \(0.478465\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −3.10216e9 5.37310e9i −0.307204 0.532094i 0.670545 0.741869i \(-0.266060\pi\)
−0.977750 + 0.209775i \(0.932727\pi\)
\(318\) 0 0
\(319\) 1.47335e10 2.55191e10i 1.42279 2.46435i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 1.03266e9 0.0948743
\(324\) 0 0
\(325\) 2.41331e10 + 1.39333e10i 2.16312 + 1.24888i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 7.35292e9 2.05954e10i 0.627590 1.75787i
\(330\) 0 0
\(331\) 4.74528e8 + 8.21906e8i 0.0395321 + 0.0684716i 0.885114 0.465373i \(-0.154080\pi\)
−0.845582 + 0.533845i \(0.820747\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 2.07222e10i 1.64535i
\(336\) 0 0
\(337\) 1.18629e10 0.919752 0.459876 0.887983i \(-0.347894\pi\)
0.459876 + 0.887983i \(0.347894\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 3.85849e10 2.22770e10i 2.85364 1.64755i
\(342\) 0 0
\(343\) 7.14072e9 + 1.18571e10i 0.515900 + 0.856649i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 1.59847e9 2.76864e9i 0.110252 0.190963i −0.805620 0.592433i \(-0.798167\pi\)
0.915872 + 0.401471i \(0.131501\pi\)
\(348\) 0 0
\(349\) 1.85896e10i 1.25305i −0.779401 0.626525i \(-0.784477\pi\)
0.779401 0.626525i \(-0.215523\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −2.29612e10 1.32566e10i −1.47875 0.853758i −0.479041 0.877793i \(-0.659015\pi\)
−0.999711 + 0.0240347i \(0.992349\pi\)
\(354\) 0 0
\(355\) −3.83897e10 + 2.21643e10i −2.41714 + 1.39554i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −4.13582e9 7.16345e9i −0.248991 0.431265i 0.714255 0.699886i \(-0.246766\pi\)
−0.963246 + 0.268620i \(0.913432\pi\)
\(360\) 0 0
\(361\) −7.25959e9 + 1.25740e10i −0.427448 + 0.740362i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −3.97790e10 −2.24121
\(366\) 0 0
\(367\) −9.87269e9 5.70000e9i −0.544216 0.314203i 0.202570 0.979268i \(-0.435071\pi\)
−0.746786 + 0.665065i \(0.768404\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 1.57869e9 + 8.64193e9i 0.0833301 + 0.456158i
\(372\) 0 0
\(373\) 1.55738e10 + 2.69746e10i 0.804562 + 1.39354i 0.916587 + 0.399836i \(0.130933\pi\)
−0.112025 + 0.993705i \(0.535734\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 3.22135e10i 1.59467i
\(378\) 0 0
\(379\) 7.55220e9 0.366030 0.183015 0.983110i \(-0.441414\pi\)
0.183015 + 0.983110i \(0.441414\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −6.02966e9 + 3.48123e9i −0.280219 + 0.161785i −0.633523 0.773724i \(-0.718392\pi\)
0.353303 + 0.935509i \(0.385058\pi\)
\(384\) 0 0
\(385\) −4.75106e10 5.59185e10i −2.16246 2.54515i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −8.85548e9 + 1.53381e10i −0.386735 + 0.669845i −0.992008 0.126173i \(-0.959731\pi\)
0.605273 + 0.796018i \(0.293064\pi\)
\(390\) 0 0
\(391\) 7.11117e9i 0.304252i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 1.95574e10 + 1.12915e10i 0.803384 + 0.463834i
\(396\) 0 0
\(397\) 2.62194e10 1.51378e10i 1.05551 0.609396i 0.131320 0.991340i \(-0.458078\pi\)
0.924186 + 0.381944i \(0.124745\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 1.80548e9 + 3.12718e9i 0.0698257 + 0.120942i 0.898824 0.438309i \(-0.144422\pi\)
−0.828999 + 0.559250i \(0.811089\pi\)
\(402\) 0 0
\(403\) −2.43534e10 + 4.21813e10i −0.923293 + 1.59919i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 1.67547e10 0.610602
\(408\) 0 0
\(409\) −2.41617e10 1.39498e10i −0.863446 0.498511i 0.00171879 0.999999i \(-0.499453\pi\)
−0.865165 + 0.501488i \(0.832786\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 2.72160e10 4.97176e9i 0.935456 0.170887i
\(414\) 0 0
\(415\) 5.61293e8 + 9.72188e8i 0.0189233 + 0.0327762i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 5.41022e8i 0.0175533i −0.999961 0.00877665i \(-0.997206\pi\)
0.999961 0.00877665i \(-0.00279373\pi\)
\(420\) 0 0
\(421\) 3.09569e10 0.985437 0.492718 0.870189i \(-0.336003\pi\)
0.492718 + 0.870189i \(0.336003\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 1.75568e10 1.01364e10i 0.538134 0.310692i
\(426\) 0 0
\(427\) 8.17914e9 2.29096e10i 0.246035 0.689138i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −2.75045e10 + 4.76391e10i −0.797066 + 1.38056i 0.124453 + 0.992225i \(0.460282\pi\)
−0.921519 + 0.388333i \(0.873051\pi\)
\(432\) 0 0
\(433\) 9.42119e9i 0.268012i 0.990981 + 0.134006i \(0.0427842\pi\)
−0.990981 + 0.134006i \(0.957216\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −1.46967e10 8.48514e9i −0.402990 0.232666i
\(438\) 0 0
\(439\) 2.49773e10 1.44206e10i 0.672492 0.388263i −0.124529 0.992216i \(-0.539742\pi\)
0.797020 + 0.603953i \(0.206408\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −1.66156e10 2.87791e10i −0.431422 0.747245i 0.565574 0.824697i \(-0.308655\pi\)
−0.996996 + 0.0774529i \(0.975321\pi\)
\(444\) 0 0
\(445\) 3.79300e10 6.56967e10i 0.967260 1.67534i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 5.22184e9 0.128481 0.0642404 0.997934i \(-0.479538\pi\)
0.0642404 + 0.997934i \(0.479538\pi\)
\(450\) 0 0
\(451\) −3.05030e10 1.76109e10i −0.737287 0.425673i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 7.55457e10 + 2.69711e10i 1.76264 + 0.629294i
\(456\) 0 0
\(457\) 4.00779e10 + 6.94170e10i 0.918841 + 1.59148i 0.801178 + 0.598426i \(0.204207\pi\)
0.117664 + 0.993054i \(0.462460\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 5.16689e9i 0.114400i 0.998363 + 0.0571999i \(0.0182173\pi\)
−0.998363 + 0.0571999i \(0.981783\pi\)
\(462\) 0 0
\(463\) −1.17425e10 −0.255527 −0.127764 0.991805i \(-0.540780\pi\)
−0.127764 + 0.991805i \(0.540780\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −6.41407e7 + 3.70316e7i −0.00134855 + 0.000778584i −0.500674 0.865636i \(-0.666914\pi\)
0.499326 + 0.866414i \(0.333581\pi\)
\(468\) 0 0
\(469\) −7.65228e9 4.18894e10i −0.158161 0.865790i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −2.35413e10 + 4.07748e10i −0.470312 + 0.814605i
\(474\) 0 0
\(475\) 4.83798e10i 0.950363i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −6.21346e10 3.58735e10i −1.18030 0.681445i −0.224215 0.974540i \(-0.571982\pi\)
−0.956084 + 0.293094i \(0.905315\pi\)
\(480\) 0 0
\(481\) −1.58624e10 + 9.15816e9i −0.296339 + 0.171091i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 1.55785e10 + 2.69828e10i 0.281553 + 0.487663i
\(486\) 0 0
\(487\) −2.48075e10 + 4.29679e10i −0.441029 + 0.763885i −0.997766 0.0668039i \(-0.978720\pi\)
0.556737 + 0.830689i \(0.312053\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 2.92296e10 0.502917 0.251458 0.967868i \(-0.419090\pi\)
0.251458 + 0.967868i \(0.419090\pi\)
\(492\) 0 0
\(493\) 2.02956e10 + 1.17177e10i 0.343569 + 0.198359i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −6.94189e10 + 5.89810e10i −1.13776 + 0.966689i
\(498\) 0 0
\(499\) 3.45740e10 + 5.98840e10i 0.557632 + 0.965847i 0.997694 + 0.0678795i \(0.0216233\pi\)
−0.440061 + 0.897968i \(0.645043\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 4.21850e10i 0.659001i 0.944155 + 0.329501i \(0.106880\pi\)
−0.944155 + 0.329501i \(0.893120\pi\)
\(504\) 0 0
\(505\) 8.54652e9 0.131409
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 3.01952e10 1.74332e10i 0.449849 0.259721i −0.257917 0.966167i \(-0.583036\pi\)
0.707766 + 0.706446i \(0.249703\pi\)
\(510\) 0 0
\(511\) −8.04120e10 + 1.46895e10i −1.17934 + 0.215439i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −1.58718e10 + 2.74908e10i −0.225630 + 0.390803i
\(516\) 0 0
\(517\) 2.38231e11i 3.33454i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −6.86868e10 3.96564e10i −0.932229 0.538223i −0.0447131 0.999000i \(-0.514237\pi\)
−0.887516 + 0.460777i \(0.847571\pi\)
\(522\) 0 0
\(523\) 1.49357e10 8.62310e9i 0.199626 0.115254i −0.396855 0.917881i \(-0.629898\pi\)
0.596481 + 0.802627i \(0.296565\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 1.77171e10 + 3.06869e10i 0.229694 + 0.397842i
\(528\) 0 0
\(529\) −1.92753e10 + 3.33858e10i −0.246138 + 0.426323i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 3.85048e10 0.477096
\(534\) 0 0
\(535\) −1.37940e11 7.96395e10i −1.68374 0.972106i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −1.16691e11 9.54930e10i −1.38255 1.13140i
\(540\) 0 0
\(541\) 8.22880e10 + 1.42527e11i 0.960611 + 1.66383i 0.720970 + 0.692966i \(0.243696\pi\)
0.239641 + 0.970862i \(0.422970\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 1.12527e11i 1.27548i
\(546\) 0 0
\(547\) 2.02743e10 0.226462 0.113231 0.993569i \(-0.463880\pi\)
0.113231 + 0.993569i \(0.463880\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 4.84339e10 2.79633e10i 0.525464 0.303377i
\(552\) 0 0
\(553\) 4.37045e10 + 1.56033e10i 0.467332 + 0.166846i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −4.16250e10 + 7.20966e10i −0.432448 + 0.749021i −0.997083 0.0763188i \(-0.975683\pi\)
0.564636 + 0.825340i \(0.309017\pi\)
\(558\) 0 0
\(559\) 5.14711e10i 0.527128i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 1.59377e10 + 9.20165e9i 0.158633 + 0.0915867i 0.577215 0.816592i \(-0.304139\pi\)
−0.418582 + 0.908179i \(0.637473\pi\)
\(564\) 0 0
\(565\) −8.93777e10 + 5.16022e10i −0.877072 + 0.506378i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 4.00051e10 + 6.92908e10i 0.381651 + 0.661038i 0.991298 0.131634i \(-0.0420225\pi\)
−0.609648 + 0.792672i \(0.708689\pi\)
\(570\) 0 0
\(571\) −9.17409e10 + 1.58900e11i −0.863015 + 1.49479i 0.00598894 + 0.999982i \(0.498094\pi\)
−0.869004 + 0.494804i \(0.835240\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −3.33155e11 −3.04772
\(576\) 0 0
\(577\) −2.30693e10 1.33190e10i −0.208128 0.120163i 0.392313 0.919832i \(-0.371675\pi\)
−0.600441 + 0.799669i \(0.705008\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 1.49365e9 + 1.75798e9i 0.0131082 + 0.0154280i
\(582\) 0 0
\(583\) −4.78505e10 8.28794e10i −0.414202 0.717419i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 9.04647e10i 0.761950i 0.924585 + 0.380975i \(0.124412\pi\)
−0.924585 + 0.380975i \(0.875588\pi\)
\(588\) 0 0
\(589\) 8.45612e10 0.702603
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 2.90780e10 1.67882e10i 0.235151 0.135764i −0.377795 0.925889i \(-0.623318\pi\)
0.612946 + 0.790125i \(0.289984\pi\)
\(594\) 0 0
\(595\) 4.44725e10 3.77856e10i 0.354833 0.301480i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 7.46968e10 1.29379e11i 0.580223 1.00498i −0.415230 0.909717i \(-0.636299\pi\)
0.995453 0.0952587i \(-0.0303678\pi\)
\(600\) 0 0
\(601\) 3.12742e10i 0.239711i −0.992791 0.119856i \(-0.961757\pi\)
0.992791 0.119856i \(-0.0382431\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 4.75350e11 + 2.74443e11i 3.54807 + 2.04848i
\(606\) 0 0
\(607\) 1.03866e11 5.99669e10i 0.765099 0.441730i −0.0660244 0.997818i \(-0.521032\pi\)
0.831124 + 0.556088i \(0.187698\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −1.30218e11 2.25544e11i −0.934342 1.61833i
\(612\) 0 0
\(613\) 3.95362e10 6.84787e10i 0.279997 0.484968i −0.691387 0.722485i \(-0.743000\pi\)
0.971384 + 0.237516i \(0.0763333\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 7.35075e10 0.507214 0.253607 0.967307i \(-0.418383\pi\)
0.253607 + 0.967307i \(0.418383\pi\)
\(618\) 0 0
\(619\) 2.19835e11 + 1.26922e11i 1.49739 + 0.864517i 0.999995 0.00300805i \(-0.000957493\pi\)
0.497393 + 0.867526i \(0.334291\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 5.24140e10 1.46811e11i 0.347933 0.974554i
\(624\) 0 0
\(625\) −2.08250e11 3.60699e11i −1.36478 2.36388i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 1.33251e10i 0.0851273i
\(630\) 0 0
\(631\) 6.11257e9 0.0385573 0.0192786 0.999814i \(-0.493863\pi\)
0.0192786 + 0.999814i \(0.493863\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 3.93322e10 2.27085e10i 0.241910 0.139667i
\(636\) 0 0
\(637\) 1.62673e11 + 2.66240e10i 0.988004 + 0.161702i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −9.48169e10 + 1.64228e11i −0.561634 + 0.972779i 0.435720 + 0.900082i \(0.356494\pi\)
−0.997354 + 0.0726969i \(0.976839\pi\)
\(642\) 0 0
\(643\) 1.50630e11i 0.881188i −0.897706 0.440594i \(-0.854768\pi\)
0.897706 0.440594i \(-0.145232\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −1.86275e11 1.07546e11i −1.06301 0.613729i −0.136747 0.990606i \(-0.543665\pi\)
−0.926264 + 0.376876i \(0.876998\pi\)
\(648\) 0 0
\(649\) −2.61011e11 + 1.50695e11i −1.47123 + 0.849415i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 1.66655e11 + 2.88654e11i 0.916567 + 1.58754i 0.804590 + 0.593831i \(0.202385\pi\)
0.111977 + 0.993711i \(0.464282\pi\)
\(654\) 0 0
\(655\) 2.23296e11 3.86761e11i 1.21316 2.10125i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 6.54805e10 0.347193 0.173596 0.984817i \(-0.444461\pi\)
0.173596 + 0.984817i \(0.444461\pi\)
\(660\) 0 0
\(661\) 1.46661e11 + 8.46750e10i 0.768263 + 0.443557i 0.832255 0.554394i \(-0.187050\pi\)
−0.0639915 + 0.997950i \(0.520383\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −2.50265e10 1.36998e11i −0.127972 0.700531i
\(666\) 0 0
\(667\) −1.92562e11 3.33528e11i −0.972899 1.68511i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 2.65000e11i 1.30724i
\(672\) 0 0
\(673\) −1.23724e11 −0.603105 −0.301552 0.953450i \(-0.597505\pi\)
−0.301552 + 0.953450i \(0.597505\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −2.80203e11 + 1.61775e11i −1.33389 + 0.770119i −0.985893 0.167378i \(-0.946470\pi\)
−0.347993 + 0.937497i \(0.613137\pi\)
\(678\) 0 0
\(679\) 4.14557e10 + 4.87921e10i 0.195032 + 0.229547i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 9.35871e10 1.62098e11i 0.430064 0.744893i −0.566814 0.823846i \(-0.691824\pi\)
0.996878 + 0.0789529i \(0.0251577\pi\)
\(684\) 0 0
\(685\) 5.00370e10i 0.227263i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 9.06045e10 + 5.23105e10i 0.402043 + 0.232120i
\(690\) 0 0
\(691\) 1.13839e11 6.57249e10i 0.499319 0.288282i −0.229113 0.973400i \(-0.573583\pi\)
0.728432 + 0.685118i \(0.240249\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −8.83017e10 1.52943e11i −0.378469 0.655527i
\(696\) 0 0
\(697\) 1.40061e10 2.42593e10i 0.0593454 0.102789i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 1.13631e10 0.0470569 0.0235285 0.999723i \(-0.492510\pi\)
0.0235285 + 0.999723i \(0.492510\pi\)
\(702\) 0 0
\(703\) 2.75391e10 + 1.58997e10i 0.112753 + 0.0650981i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 1.72765e10 3.15605e9i 0.0691479 0.0126318i
\(708\) 0 0
\(709\) 1.67229e11 + 2.89649e11i 0.661801 + 1.14627i 0.980142 + 0.198296i \(0.0635408\pi\)
−0.318341 + 0.947976i \(0.603126\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 5.82309e11i 2.25318i
\(714\) 0 0
\(715\) −8.73852e11 −3.34359
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −2.41998e11 + 1.39717e11i −0.905515 + 0.522800i −0.878985 0.476849i \(-0.841779\pi\)
−0.0265298 + 0.999648i \(0.508446\pi\)
\(720\) 0 0
\(721\) −2.19326e10 + 6.14329e10i −0.0811614 + 0.227332i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 5.48967e11 9.50839e11i 1.98698 3.44156i
\(726\) 0 0
\(727\) 4.98526e11i 1.78464i 0.451407 + 0.892318i \(0.350922\pi\)
−0.451407 + 0.892318i \(0.649078\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −3.24286e10 1.87226e10i −0.113569 0.0655688i
\(732\) 0 0
\(733\) 2.34185e11 1.35207e11i 0.811229 0.468363i −0.0361535 0.999346i \(-0.511511\pi\)
0.847383 + 0.530983i \(0.178177\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 2.31942e11 + 4.01735e11i 0.786157 + 1.36166i
\(738\) 0 0
\(739\) −2.38418e11 + 4.12953e11i −0.799396 + 1.38459i 0.120615 + 0.992699i \(0.461513\pi\)
−0.920010 + 0.391894i \(0.871820\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −4.19326e11 −1.37593 −0.687966 0.725743i \(-0.741496\pi\)
−0.687966 + 0.725743i \(0.741496\pi\)
\(744\) 0 0
\(745\) 2.63548e11 + 1.52160e11i 0.855529 + 0.493940i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −3.08250e11 1.10051e11i −0.979436 0.349676i
\(750\) 0 0
\(751\) 1.18803e10 + 2.05772e10i 0.0373479 + 0.0646885i 0.884095 0.467307i \(-0.154776\pi\)
−0.846747 + 0.531995i \(0.821442\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 5.69368e11i 1.75229i
\(756\) 0 0
\(757\) −4.90289e11 −1.49303 −0.746516 0.665368i \(-0.768275\pi\)
−0.746516 + 0.665368i \(0.768275\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 2.40688e11 1.38961e11i 0.717656 0.414339i −0.0962332 0.995359i \(-0.530679\pi\)
0.813889 + 0.581020i \(0.197346\pi\)
\(762\) 0 0
\(763\) 4.15540e10 + 2.27471e11i 0.122607 + 0.671163i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 1.64741e11 2.85340e11i 0.476014 0.824481i
\(768\) 0 0
\(769\) 1.97929e11i 0.565984i −0.959122 0.282992i \(-0.908673\pi\)
0.959122 0.282992i \(-0.0913270\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 4.68415e11 + 2.70439e11i 1.31194 + 0.757447i 0.982417 0.186702i \(-0.0597799\pi\)
0.329520 + 0.944149i \(0.393113\pi\)
\(774\) 0 0
\(775\) 1.43767e12 8.30038e11i 3.98522 2.30087i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −3.34246e10 5.78931e10i −0.0907646 0.157209i
\(780\) 0 0
\(781\) 4.96166e11 8.59385e11i 1.33359 2.30985i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −2.93720e11 −0.773490
\(786\) 0 0
\(787\) 3.58532e11 + 2.06999e11i 0.934607 + 0.539596i 0.888266 0.459330i \(-0.151910\pi\)
0.0463413 + 0.998926i \(0.485244\pi\)
\(788\) 0 0
\(789\) 0