Properties

Label 392.6.i.e.177.1
Level $392$
Weight $6$
Character 392.177
Analytic conductor $62.870$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 392 = 2^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 392.i (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(62.8704573667\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 8)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 177.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 392.177
Dual form 392.6.i.e.361.1

$q$-expansion

\(f(q)\) \(=\) \(q+(10.0000 + 17.3205i) q^{3} +(-37.0000 + 64.0859i) q^{5} +(-78.5000 + 135.966i) q^{9} +O(q^{10})\) \(q+(10.0000 + 17.3205i) q^{3} +(-37.0000 + 64.0859i) q^{5} +(-78.5000 + 135.966i) q^{9} +(-62.0000 - 107.387i) q^{11} -478.000 q^{13} -1480.00 q^{15} +(-599.000 - 1037.50i) q^{17} +(1522.00 - 2636.18i) q^{19} +(-92.0000 + 159.349i) q^{23} +(-1175.50 - 2036.03i) q^{25} +1720.00 q^{27} -3282.00 q^{29} +(-2864.00 - 4960.59i) q^{31} +(1240.00 - 2147.74i) q^{33} +(-5163.00 + 8942.58i) q^{37} +(-4780.00 - 8279.20i) q^{39} +8886.00 q^{41} -9188.00 q^{43} +(-5809.00 - 10061.5i) q^{45} +(11832.0 - 20493.6i) q^{47} +(11980.0 - 20750.0i) q^{51} +(-5843.00 - 10120.4i) q^{53} +9176.00 q^{55} +60880.0 q^{57} +(8438.00 + 14615.0i) q^{59} +(-9241.00 + 16005.9i) q^{61} +(17686.0 - 30633.1i) q^{65} +(7766.00 + 13451.1i) q^{67} -3680.00 q^{69} -31960.0 q^{71} +(-2443.00 - 4231.40i) q^{73} +(23510.0 - 40720.5i) q^{75} +(-22280.0 + 38590.1i) q^{79} +(36275.5 + 62831.0i) q^{81} -67364.0 q^{83} +88652.0 q^{85} +(-32820.0 - 56845.9i) q^{87} +(35997.0 - 62348.6i) q^{89} +(57280.0 - 99211.9i) q^{93} +(112628. + 195077. i) q^{95} -48866.0 q^{97} +19468.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 20 q^{3} - 74 q^{5} - 157 q^{9} + O(q^{10}) \) \( 2 q + 20 q^{3} - 74 q^{5} - 157 q^{9} - 124 q^{11} - 956 q^{13} - 2960 q^{15} - 1198 q^{17} + 3044 q^{19} - 184 q^{23} - 2351 q^{25} + 3440 q^{27} - 6564 q^{29} - 5728 q^{31} + 2480 q^{33} - 10326 q^{37} - 9560 q^{39} + 17772 q^{41} - 18376 q^{43} - 11618 q^{45} + 23664 q^{47} + 23960 q^{51} - 11686 q^{53} + 18352 q^{55} + 121760 q^{57} + 16876 q^{59} - 18482 q^{61} + 35372 q^{65} + 15532 q^{67} - 7360 q^{69} - 63920 q^{71} - 4886 q^{73} + 47020 q^{75} - 44560 q^{79} + 72551 q^{81} - 134728 q^{83} + 177304 q^{85} - 65640 q^{87} + 71994 q^{89} + 114560 q^{93} + 225256 q^{95} - 97732 q^{97} + 38936 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/392\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(295\) \(297\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(3\) 10.0000 + 17.3205i 0.641500 + 1.11111i 0.985098 + 0.171994i \(0.0550210\pi\)
−0.343598 + 0.939117i \(0.611646\pi\)
\(4\) 0 0
\(5\) −37.0000 + 64.0859i −0.661876 + 1.14640i 0.318246 + 0.948008i \(0.396906\pi\)
−0.980122 + 0.198395i \(0.936427\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −78.5000 + 135.966i −0.323045 + 0.559531i
\(10\) 0 0
\(11\) −62.0000 107.387i −0.154493 0.267590i 0.778381 0.627792i \(-0.216041\pi\)
−0.932874 + 0.360202i \(0.882708\pi\)
\(12\) 0 0
\(13\) −478.000 −0.784458 −0.392229 0.919868i \(-0.628296\pi\)
−0.392229 + 0.919868i \(0.628296\pi\)
\(14\) 0 0
\(15\) −1480.00 −1.69837
\(16\) 0 0
\(17\) −599.000 1037.50i −0.502695 0.870693i −0.999995 0.00311466i \(-0.999009\pi\)
0.497300 0.867579i \(-0.334325\pi\)
\(18\) 0 0
\(19\) 1522.00 2636.18i 0.967232 1.67529i 0.263737 0.964595i \(-0.415045\pi\)
0.703495 0.710700i \(-0.251622\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −92.0000 + 159.349i −0.0362634 + 0.0628100i −0.883587 0.468266i \(-0.844879\pi\)
0.847324 + 0.531076i \(0.178212\pi\)
\(24\) 0 0
\(25\) −1175.50 2036.03i −0.376160 0.651528i
\(26\) 0 0
\(27\) 1720.00 0.454066
\(28\) 0 0
\(29\) −3282.00 −0.724676 −0.362338 0.932047i \(-0.618021\pi\)
−0.362338 + 0.932047i \(0.618021\pi\)
\(30\) 0 0
\(31\) −2864.00 4960.59i −0.535265 0.927106i −0.999150 0.0412109i \(-0.986878\pi\)
0.463886 0.885895i \(-0.346455\pi\)
\(32\) 0 0
\(33\) 1240.00 2147.74i 0.198215 0.343319i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −5163.00 + 8942.58i −0.620009 + 1.07389i 0.369475 + 0.929241i \(0.379538\pi\)
−0.989483 + 0.144646i \(0.953796\pi\)
\(38\) 0 0
\(39\) −4780.00 8279.20i −0.503230 0.871620i
\(40\) 0 0
\(41\) 8886.00 0.825556 0.412778 0.910832i \(-0.364558\pi\)
0.412778 + 0.910832i \(0.364558\pi\)
\(42\) 0 0
\(43\) −9188.00 −0.757792 −0.378896 0.925439i \(-0.623696\pi\)
−0.378896 + 0.925439i \(0.623696\pi\)
\(44\) 0 0
\(45\) −5809.00 10061.5i −0.427632 0.740680i
\(46\) 0 0
\(47\) 11832.0 20493.6i 0.781292 1.35324i −0.149897 0.988702i \(-0.547894\pi\)
0.931189 0.364536i \(-0.118772\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 11980.0 20750.0i 0.644958 1.11710i
\(52\) 0 0
\(53\) −5843.00 10120.4i −0.285724 0.494888i 0.687061 0.726600i \(-0.258901\pi\)
−0.972784 + 0.231712i \(0.925567\pi\)
\(54\) 0 0
\(55\) 9176.00 0.409022
\(56\) 0 0
\(57\) 60880.0 2.48192
\(58\) 0 0
\(59\) 8438.00 + 14615.0i 0.315580 + 0.546601i 0.979561 0.201149i \(-0.0644676\pi\)
−0.663981 + 0.747750i \(0.731134\pi\)
\(60\) 0 0
\(61\) −9241.00 + 16005.9i −0.317976 + 0.550751i −0.980066 0.198674i \(-0.936336\pi\)
0.662090 + 0.749425i \(0.269670\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 17686.0 30633.1i 0.519214 0.899305i
\(66\) 0 0
\(67\) 7766.00 + 13451.1i 0.211354 + 0.366076i 0.952139 0.305667i \(-0.0988794\pi\)
−0.740785 + 0.671743i \(0.765546\pi\)
\(68\) 0 0
\(69\) −3680.00 −0.0930519
\(70\) 0 0
\(71\) −31960.0 −0.752421 −0.376210 0.926534i \(-0.622773\pi\)
−0.376210 + 0.926534i \(0.622773\pi\)
\(72\) 0 0
\(73\) −2443.00 4231.40i −0.0536558 0.0929345i 0.837950 0.545747i \(-0.183754\pi\)
−0.891606 + 0.452812i \(0.850421\pi\)
\(74\) 0 0
\(75\) 23510.0 40720.5i 0.482614 0.835911i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −22280.0 + 38590.1i −0.401650 + 0.695678i −0.993925 0.110058i \(-0.964896\pi\)
0.592275 + 0.805736i \(0.298230\pi\)
\(80\) 0 0
\(81\) 36275.5 + 62831.0i 0.614329 + 1.06405i
\(82\) 0 0
\(83\) −67364.0 −1.07333 −0.536664 0.843796i \(-0.680316\pi\)
−0.536664 + 0.843796i \(0.680316\pi\)
\(84\) 0 0
\(85\) 88652.0 1.33089
\(86\) 0 0
\(87\) −32820.0 56845.9i −0.464880 0.805195i
\(88\) 0 0
\(89\) 35997.0 62348.6i 0.481716 0.834357i −0.518064 0.855342i \(-0.673347\pi\)
0.999780 + 0.0209851i \(0.00668026\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 57280.0 99211.9i 0.686745 1.18948i
\(94\) 0 0
\(95\) 112628. + 195077.i 1.28038 + 2.21768i
\(96\) 0 0
\(97\) −48866.0 −0.527324 −0.263662 0.964615i \(-0.584930\pi\)
−0.263662 + 0.964615i \(0.584930\pi\)
\(98\) 0 0
\(99\) 19468.0 0.199633
\(100\) 0 0
\(101\) 25803.0 + 44692.1i 0.251690 + 0.435941i 0.963991 0.265934i \(-0.0856802\pi\)
−0.712301 + 0.701874i \(0.752347\pi\)
\(102\) 0 0
\(103\) 90212.0 156252.i 0.837860 1.45122i −0.0538212 0.998551i \(-0.517140\pi\)
0.891681 0.452665i \(-0.149527\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 32850.0 56897.9i 0.277381 0.480437i −0.693352 0.720599i \(-0.743867\pi\)
0.970733 + 0.240162i \(0.0772004\pi\)
\(108\) 0 0
\(109\) 56353.0 + 97606.3i 0.454308 + 0.786885i 0.998648 0.0519796i \(-0.0165531\pi\)
−0.544340 + 0.838865i \(0.683220\pi\)
\(110\) 0 0
\(111\) −206520. −1.59094
\(112\) 0 0
\(113\) −23502.0 −0.173145 −0.0865723 0.996246i \(-0.527591\pi\)
−0.0865723 + 0.996246i \(0.527591\pi\)
\(114\) 0 0
\(115\) −6808.00 11791.8i −0.0480037 0.0831449i
\(116\) 0 0
\(117\) 37523.0 64991.7i 0.253415 0.438928i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 72837.5 126158.i 0.452264 0.783343i
\(122\) 0 0
\(123\) 88860.0 + 153910.i 0.529595 + 0.917285i
\(124\) 0 0
\(125\) −57276.0 −0.327867
\(126\) 0 0
\(127\) −94592.0 −0.520409 −0.260205 0.965553i \(-0.583790\pi\)
−0.260205 + 0.965553i \(0.583790\pi\)
\(128\) 0 0
\(129\) −91880.0 159141.i −0.486124 0.841991i
\(130\) 0 0
\(131\) 35146.0 60874.7i 0.178936 0.309926i −0.762580 0.646893i \(-0.776068\pi\)
0.941516 + 0.336967i \(0.109401\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −63640.0 + 110228.i −0.300535 + 0.520543i
\(136\) 0 0
\(137\) −138645. 240140.i −0.631107 1.09311i −0.987326 0.158706i \(-0.949268\pi\)
0.356219 0.934402i \(-0.384066\pi\)
\(138\) 0 0
\(139\) 130308. 0.572050 0.286025 0.958222i \(-0.407666\pi\)
0.286025 + 0.958222i \(0.407666\pi\)
\(140\) 0 0
\(141\) 473280. 2.00480
\(142\) 0 0
\(143\) 29636.0 + 51331.1i 0.121194 + 0.209913i
\(144\) 0 0
\(145\) 121434. 210330.i 0.479645 0.830770i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 200765. 347735.i 0.740836 1.28317i −0.211278 0.977426i \(-0.567763\pi\)
0.952115 0.305740i \(-0.0989040\pi\)
\(150\) 0 0
\(151\) 37988.0 + 65797.1i 0.135583 + 0.234836i 0.925820 0.377965i \(-0.123376\pi\)
−0.790237 + 0.612801i \(0.790043\pi\)
\(152\) 0 0
\(153\) 188086. 0.649573
\(154\) 0 0
\(155\) 423872. 1.41712
\(156\) 0 0
\(157\) −197161. 341493.i −0.638369 1.10569i −0.985791 0.167979i \(-0.946276\pi\)
0.347421 0.937709i \(-0.387057\pi\)
\(158\) 0 0
\(159\) 116860. 202407.i 0.366584 0.634941i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 5862.00 10153.3i 0.0172813 0.0299321i −0.857255 0.514891i \(-0.827832\pi\)
0.874537 + 0.484959i \(0.161166\pi\)
\(164\) 0 0
\(165\) 91760.0 + 158933.i 0.262388 + 0.454469i
\(166\) 0 0
\(167\) 551928. 1.53141 0.765705 0.643192i \(-0.222390\pi\)
0.765705 + 0.643192i \(0.222390\pi\)
\(168\) 0 0
\(169\) −142809. −0.384626
\(170\) 0 0
\(171\) 238954. + 413880.i 0.624919 + 1.08239i
\(172\) 0 0
\(173\) 216447. 374897.i 0.549840 0.952351i −0.448445 0.893810i \(-0.648022\pi\)
0.998285 0.0585404i \(-0.0186446\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −168760. + 292301.i −0.404889 + 0.701289i
\(178\) 0 0
\(179\) −279810. 484645.i −0.652726 1.13055i −0.982459 0.186480i \(-0.940292\pi\)
0.329733 0.944074i \(-0.393041\pi\)
\(180\) 0 0
\(181\) −604710. −1.37199 −0.685995 0.727607i \(-0.740633\pi\)
−0.685995 + 0.727607i \(0.740633\pi\)
\(182\) 0 0
\(183\) −369640. −0.815927
\(184\) 0 0
\(185\) −382062. 661751.i −0.820738 1.42156i
\(186\) 0 0
\(187\) −74276.0 + 128650.i −0.155326 + 0.269033i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 204576. 354336.i 0.405762 0.702800i −0.588648 0.808390i \(-0.700340\pi\)
0.994410 + 0.105589i \(0.0336729\pi\)
\(192\) 0 0
\(193\) −270433. 468404.i −0.522596 0.905164i −0.999654 0.0262917i \(-0.991630\pi\)
0.477058 0.878872i \(-0.341703\pi\)
\(194\) 0 0
\(195\) 707440. 1.33230
\(196\) 0 0
\(197\) −629898. −1.15639 −0.578195 0.815898i \(-0.696243\pi\)
−0.578195 + 0.815898i \(0.696243\pi\)
\(198\) 0 0
\(199\) 141524. + 245127.i 0.253336 + 0.438791i 0.964442 0.264293i \(-0.0851388\pi\)
−0.711106 + 0.703085i \(0.751805\pi\)
\(200\) 0 0
\(201\) −155320. + 269022.i −0.271167 + 0.469675i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −328782. + 569467.i −0.546416 + 0.946420i
\(206\) 0 0
\(207\) −14444.0 25017.7i −0.0234294 0.0405810i
\(208\) 0 0
\(209\) −377456. −0.597724
\(210\) 0 0
\(211\) 142756. 0.220744 0.110372 0.993890i \(-0.464796\pi\)
0.110372 + 0.993890i \(0.464796\pi\)
\(212\) 0 0
\(213\) −319600. 553563.i −0.482678 0.836023i
\(214\) 0 0
\(215\) 339956. 588821.i 0.501564 0.868735i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 48860.0 84628.0i 0.0688404 0.119235i
\(220\) 0 0
\(221\) 286322. + 495924.i 0.394343 + 0.683022i
\(222\) 0 0
\(223\) −889696. −1.19806 −0.599031 0.800726i \(-0.704447\pi\)
−0.599031 + 0.800726i \(0.704447\pi\)
\(224\) 0 0
\(225\) 369107. 0.486067
\(226\) 0 0
\(227\) 571578. + 990002.i 0.736226 + 1.27518i 0.954184 + 0.299222i \(0.0967271\pi\)
−0.217958 + 0.975958i \(0.569940\pi\)
\(228\) 0 0
\(229\) −347893. + 602568.i −0.438386 + 0.759307i −0.997565 0.0697396i \(-0.977783\pi\)
0.559179 + 0.829047i \(0.311116\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 173563. 300620.i 0.209444 0.362767i −0.742096 0.670294i \(-0.766168\pi\)
0.951539 + 0.307527i \(0.0995014\pi\)
\(234\) 0 0
\(235\) 875568. + 1.51653e6i 1.03424 + 1.79135i
\(236\) 0 0
\(237\) −891200. −1.03063
\(238\) 0 0
\(239\) −1.64296e6 −1.86051 −0.930255 0.366912i \(-0.880415\pi\)
−0.930255 + 0.366912i \(0.880415\pi\)
\(240\) 0 0
\(241\) −583719. 1.01103e6i −0.647383 1.12130i −0.983746 0.179568i \(-0.942530\pi\)
0.336363 0.941733i \(-0.390803\pi\)
\(242\) 0 0
\(243\) −516530. + 894656.i −0.561151 + 0.971942i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −727516. + 1.26009e6i −0.758753 + 1.31420i
\(248\) 0 0
\(249\) −673640. 1.16678e6i −0.688541 1.19259i
\(250\) 0 0
\(251\) 790612. 0.792098 0.396049 0.918229i \(-0.370381\pi\)
0.396049 + 0.918229i \(0.370381\pi\)
\(252\) 0 0
\(253\) 22816.0 0.0224098
\(254\) 0 0
\(255\) 886520. + 1.53550e6i 0.853764 + 1.47876i
\(256\) 0 0
\(257\) −64895.0 + 112401.i −0.0612884 + 0.106155i −0.895042 0.445983i \(-0.852854\pi\)
0.833753 + 0.552137i \(0.186188\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 257637. 446240.i 0.234103 0.405478i
\(262\) 0 0
\(263\) −35444.0 61390.8i −0.0315975 0.0547286i 0.849794 0.527115i \(-0.176726\pi\)
−0.881392 + 0.472386i \(0.843393\pi\)
\(264\) 0 0
\(265\) 864764. 0.756455
\(266\) 0 0
\(267\) 1.43988e6 1.23608
\(268\) 0 0
\(269\) 895087. + 1.55034e6i 0.754197 + 1.30631i 0.945773 + 0.324829i \(0.105307\pi\)
−0.191576 + 0.981478i \(0.561360\pi\)
\(270\) 0 0
\(271\) −886808. + 1.53600e6i −0.733511 + 1.27048i 0.221863 + 0.975078i \(0.428786\pi\)
−0.955374 + 0.295400i \(0.904547\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −145762. + 252467.i −0.116228 + 0.201314i
\(276\) 0 0
\(277\) 137725. + 238547.i 0.107848 + 0.186799i 0.914898 0.403684i \(-0.132271\pi\)
−0.807050 + 0.590483i \(0.798937\pi\)
\(278\) 0 0
\(279\) 899296. 0.691659
\(280\) 0 0
\(281\) 594170. 0.448895 0.224448 0.974486i \(-0.427942\pi\)
0.224448 + 0.974486i \(0.427942\pi\)
\(282\) 0 0
\(283\) 546214. + 946070.i 0.405412 + 0.702194i 0.994369 0.105970i \(-0.0337947\pi\)
−0.588957 + 0.808164i \(0.700461\pi\)
\(284\) 0 0
\(285\) −2.25256e6 + 3.90155e6i −1.64272 + 2.84528i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −7673.50 + 13290.9i −0.00540442 + 0.00936073i
\(290\) 0 0
\(291\) −488660. 846384.i −0.338278 0.585915i
\(292\) 0 0
\(293\) −333654. −0.227053 −0.113527 0.993535i \(-0.536215\pi\)
−0.113527 + 0.993535i \(0.536215\pi\)
\(294\) 0 0
\(295\) −1.24882e6 −0.835500
\(296\) 0 0
\(297\) −106640. 184706.i −0.0701502 0.121504i
\(298\) 0 0
\(299\) 43976.0 76168.7i 0.0284471 0.0492718i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −516060. + 893842.i −0.322919 + 0.559312i
\(304\) 0 0
\(305\) −683834. 1.18444e6i −0.420921 0.729057i
\(306\) 0 0
\(307\) −1.05997e6 −0.641872 −0.320936 0.947101i \(-0.603997\pi\)
−0.320936 + 0.947101i \(0.603997\pi\)
\(308\) 0 0
\(309\) 3.60848e6 2.14995
\(310\) 0 0
\(311\) −668244. 1.15743e6i −0.391773 0.678570i 0.600911 0.799316i \(-0.294805\pi\)
−0.992683 + 0.120746i \(0.961471\pi\)
\(312\) 0 0
\(313\) 822093. 1.42391e6i 0.474308 0.821525i −0.525260 0.850942i \(-0.676032\pi\)
0.999567 + 0.0294171i \(0.00936512\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 861849. 1.49277e6i 0.481707 0.834341i −0.518072 0.855337i \(-0.673350\pi\)
0.999780 + 0.0209956i \(0.00668359\pi\)
\(318\) 0 0
\(319\) 203484. + 352445.i 0.111958 + 0.193916i
\(320\) 0 0
\(321\) 1.31400e6 0.711759
\(322\) 0 0
\(323\) −3.64671e6 −1.94489
\(324\) 0 0
\(325\) 561889. + 973220.i 0.295082 + 0.511096i
\(326\) 0 0
\(327\) −1.12706e6 + 1.95213e6i −0.582878 + 1.00957i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −1.37481e6 + 2.38125e6i −0.689722 + 1.19463i 0.282206 + 0.959354i \(0.408934\pi\)
−0.971928 + 0.235279i \(0.924399\pi\)
\(332\) 0 0
\(333\) −810591. 1.40398e6i −0.400582 0.693828i
\(334\) 0 0
\(335\) −1.14937e6 −0.559561
\(336\) 0 0
\(337\) −3.41489e6 −1.63796 −0.818978 0.573824i \(-0.805459\pi\)
−0.818978 + 0.573824i \(0.805459\pi\)
\(338\) 0 0
\(339\) −235020. 407067.i −0.111072 0.192383i
\(340\) 0 0
\(341\) −355136. + 615114.i −0.165390 + 0.286464i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 136160. 235836.i 0.0615888 0.106675i
\(346\) 0 0
\(347\) −365382. 632860.i −0.162901 0.282153i 0.773007 0.634398i \(-0.218752\pi\)
−0.935908 + 0.352245i \(0.885418\pi\)
\(348\) 0 0
\(349\) 2.29749e6 1.00969 0.504847 0.863209i \(-0.331549\pi\)
0.504847 + 0.863209i \(0.331549\pi\)
\(350\) 0 0
\(351\) −822160. −0.356196
\(352\) 0 0
\(353\) −585359. 1.01387e6i −0.250026 0.433058i 0.713507 0.700649i \(-0.247106\pi\)
−0.963533 + 0.267590i \(0.913773\pi\)
\(354\) 0 0
\(355\) 1.18252e6 2.04818e6i 0.498009 0.862578i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −1.94327e6 + 3.36584e6i −0.795787 + 1.37834i 0.126552 + 0.991960i \(0.459609\pi\)
−0.922339 + 0.386383i \(0.873724\pi\)
\(360\) 0 0
\(361\) −3.39492e6 5.88017e6i −1.37108 2.37477i
\(362\) 0 0
\(363\) 2.91350e6 1.16051
\(364\) 0 0
\(365\) 361564. 0.142054
\(366\) 0 0
\(367\) 466520. + 808036.i 0.180803 + 0.313160i 0.942154 0.335180i \(-0.108797\pi\)
−0.761351 + 0.648339i \(0.775464\pi\)
\(368\) 0 0
\(369\) −697551. + 1.20819e6i −0.266692 + 0.461924i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 196109. 339671.i 0.0729836 0.126411i −0.827224 0.561872i \(-0.810081\pi\)
0.900208 + 0.435461i \(0.143415\pi\)
\(374\) 0 0
\(375\) −572760. 992049.i −0.210327 0.364297i
\(376\) 0 0
\(377\) 1.56880e6 0.568477
\(378\) 0 0
\(379\) −4.72930e6 −1.69122 −0.845608 0.533805i \(-0.820762\pi\)
−0.845608 + 0.533805i \(0.820762\pi\)
\(380\) 0 0
\(381\) −945920. 1.63838e6i −0.333843 0.578233i
\(382\) 0 0
\(383\) 948672. 1.64315e6i 0.330460 0.572374i −0.652142 0.758097i \(-0.726129\pi\)
0.982602 + 0.185723i \(0.0594627\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 721258. 1.24926e6i 0.244801 0.424008i
\(388\) 0 0
\(389\) 1.86148e6 + 3.22417e6i 0.623711 + 1.08030i 0.988789 + 0.149323i \(0.0477093\pi\)
−0.365077 + 0.930977i \(0.618957\pi\)
\(390\) 0 0
\(391\) 220432. 0.0729177
\(392\) 0 0
\(393\) 1.40584e6 0.459150
\(394\) 0 0
\(395\) −1.64872e6 2.85567e6i −0.531685 0.920905i
\(396\) 0 0
\(397\) 1.66904e6 2.89086e6i 0.531484 0.920557i −0.467841 0.883813i \(-0.654968\pi\)
0.999325 0.0367445i \(-0.0116988\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −2.13745e6 + 3.70217e6i −0.663796 + 1.14973i 0.315814 + 0.948821i \(0.397722\pi\)
−0.979610 + 0.200908i \(0.935611\pi\)
\(402\) 0 0
\(403\) 1.36899e6 + 2.37116e6i 0.419893 + 0.727275i
\(404\) 0 0
\(405\) −5.36877e6 −1.62644
\(406\) 0 0
\(407\) 1.28042e6 0.383149
\(408\) 0 0
\(409\) −1.28660e6 2.22845e6i −0.380306 0.658710i 0.610800 0.791785i \(-0.290848\pi\)
−0.991106 + 0.133075i \(0.957515\pi\)
\(410\) 0 0
\(411\) 2.77290e6 4.80280e6i 0.809710 1.40246i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 2.49247e6 4.31708e6i 0.710410 1.23047i
\(416\) 0 0
\(417\) 1.30308e6 + 2.25700e6i 0.366970 + 0.635611i
\(418\) 0 0
\(419\) −5.26828e6 −1.46600 −0.732999 0.680230i \(-0.761880\pi\)
−0.732999 + 0.680230i \(0.761880\pi\)
\(420\) 0 0
\(421\) −973354. −0.267649 −0.133824 0.991005i \(-0.542726\pi\)
−0.133824 + 0.991005i \(0.542726\pi\)
\(422\) 0 0
\(423\) 1.85762e6 + 3.21750e6i 0.504786 + 0.874314i
\(424\) 0 0
\(425\) −1.40825e6 + 2.43916e6i −0.378187 + 0.655040i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −592720. + 1.02662e6i −0.155491 + 0.269319i
\(430\) 0 0
\(431\) −1.77868e6 3.08076e6i −0.461216 0.798850i 0.537806 0.843069i \(-0.319253\pi\)
−0.999022 + 0.0442188i \(0.985920\pi\)
\(432\) 0 0
\(433\) 1.95496e6 0.501092 0.250546 0.968105i \(-0.419390\pi\)
0.250546 + 0.968105i \(0.419390\pi\)
\(434\) 0 0
\(435\) 4.85736e6 1.23077
\(436\) 0 0
\(437\) 280048. + 485057.i 0.0701502 + 0.121504i
\(438\) 0 0
\(439\) −1.64840e6 + 2.85512e6i −0.408228 + 0.707071i −0.994691 0.102905i \(-0.967186\pi\)
0.586464 + 0.809976i \(0.300520\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 2.52910e6 4.38053e6i 0.612289 1.06052i −0.378565 0.925575i \(-0.623582\pi\)
0.990854 0.134941i \(-0.0430844\pi\)
\(444\) 0 0
\(445\) 2.66378e6 + 4.61380e6i 0.637673 + 1.10448i
\(446\) 0 0
\(447\) 8.03060e6 1.90099
\(448\) 0 0
\(449\) 2.12730e6 0.497981 0.248990 0.968506i \(-0.419901\pi\)
0.248990 + 0.968506i \(0.419901\pi\)
\(450\) 0 0
\(451\) −550932. 954242.i −0.127543 0.220911i
\(452\) 0 0
\(453\) −759760. + 1.31594e6i −0.173953 + 0.301295i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −144565. + 250394.i −0.0323797 + 0.0560833i −0.881761 0.471696i \(-0.843642\pi\)
0.849381 + 0.527779i \(0.176975\pi\)
\(458\) 0 0
\(459\) −1.03028e6 1.78450e6i −0.228257 0.395352i
\(460\) 0 0
\(461\) −2.66870e6 −0.584854 −0.292427 0.956288i \(-0.594463\pi\)
−0.292427 + 0.956288i \(0.594463\pi\)
\(462\) 0 0
\(463\) 7.58619e6 1.64464 0.822321 0.569024i \(-0.192679\pi\)
0.822321 + 0.569024i \(0.192679\pi\)
\(464\) 0 0
\(465\) 4.23872e6 + 7.34168e6i 0.909081 + 1.57457i
\(466\) 0 0
\(467\) −709806. + 1.22942e6i −0.150608 + 0.260860i −0.931451 0.363867i \(-0.881456\pi\)
0.780843 + 0.624727i \(0.214790\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 3.94322e6 6.82986e6i 0.819028 1.41860i
\(472\) 0 0
\(473\) 569656. + 986673.i 0.117074 + 0.202778i
\(474\) 0 0
\(475\) −7.15644e6 −1.45534
\(476\) 0 0
\(477\) 1.83470e6 0.369207
\(478\) 0 0
\(479\) −942032. 1.63165e6i −0.187597 0.324928i 0.756851 0.653587i \(-0.226737\pi\)
−0.944449 + 0.328659i \(0.893403\pi\)
\(480\) 0 0
\(481\) 2.46791e6 4.27455e6i 0.486371 0.842419i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 1.80804e6 3.13162e6i 0.349023 0.604526i
\(486\) 0 0
\(487\) 3.00694e6 + 5.20817e6i 0.574516 + 0.995091i 0.996094 + 0.0882991i \(0.0281431\pi\)
−0.421578 + 0.906792i \(0.638524\pi\)
\(488\) 0 0
\(489\) 234480. 0.0443439
\(490\) 0 0
\(491\) 4.29232e6 0.803504 0.401752 0.915749i \(-0.368401\pi\)
0.401752 + 0.915749i \(0.368401\pi\)
\(492\) 0 0
\(493\) 1.96592e6 + 3.40507e6i 0.364291 + 0.630970i
\(494\) 0 0
\(495\) −720316. + 1.24762e6i −0.132133 + 0.228860i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −672546. + 1.16488e6i −0.120912 + 0.209426i −0.920128 0.391618i \(-0.871915\pi\)
0.799215 + 0.601045i \(0.205249\pi\)
\(500\) 0 0
\(501\) 5.51928e6 + 9.55967e6i 0.982399 + 1.70157i
\(502\) 0 0
\(503\) −202008. −0.0355999 −0.0177999 0.999842i \(-0.505666\pi\)
−0.0177999 + 0.999842i \(0.505666\pi\)
\(504\) 0 0
\(505\) −3.81884e6 −0.666352
\(506\) 0 0
\(507\) −1.42809e6 2.47352e6i −0.246738 0.427362i
\(508\) 0 0
\(509\) 4.89172e6 8.47271e6i 0.836887 1.44953i −0.0555970 0.998453i \(-0.517706\pi\)
0.892484 0.451078i \(-0.148960\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 2.61784e6 4.53423e6i 0.439187 0.760695i
\(514\) 0 0
\(515\) 6.67569e6 + 1.15626e7i 1.10912 + 1.92105i
\(516\) 0 0
\(517\) −2.93434e6 −0.482818
\(518\) 0 0
\(519\) 8.65788e6 1.41089
\(520\) 0 0
\(521\) −5.24152e6 9.07857e6i −0.845985 1.46529i −0.884763 0.466041i \(-0.845680\pi\)
0.0387785 0.999248i \(-0.487653\pi\)
\(522\) 0 0
\(523\) 3.10509e6 5.37817e6i 0.496386 0.859766i −0.503605 0.863934i \(-0.667993\pi\)
0.999991 + 0.00416822i \(0.00132679\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −3.43107e6 + 5.94279e6i −0.538150 + 0.932103i
\(528\) 0 0
\(529\) 3.20124e6 + 5.54472e6i 0.497370 + 0.861470i
\(530\) 0 0
\(531\) −2.64953e6 −0.407787
\(532\) 0 0
\(533\) −4.24751e6 −0.647614
\(534\) 0 0
\(535\) 2.43090e6 + 4.21044e6i 0.367183 + 0.635980i
\(536\) 0 0
\(537\) 5.59620e6 9.69290e6i 0.837447 1.45050i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −2.54044e6 + 4.40017e6i −0.373178 + 0.646363i −0.990052 0.140699i \(-0.955065\pi\)
0.616875 + 0.787061i \(0.288398\pi\)
\(542\) 0 0
\(543\) −6.04710e6 1.04739e7i −0.880132 1.52443i
\(544\) 0 0
\(545\) −8.34024e6 −1.20278
\(546\) 0 0
\(547\) 3.34687e6 0.478267 0.239133 0.970987i \(-0.423137\pi\)
0.239133 + 0.970987i \(0.423137\pi\)
\(548\) 0 0
\(549\) −1.45084e6 2.51292e6i −0.205441 0.355835i
\(550\) 0 0
\(551\) −4.99520e6 + 8.65195e6i −0.700929 + 1.21405i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 7.64124e6 1.32350e7i 1.05301 1.82386i
\(556\) 0 0
\(557\) −3.50189e6 6.06545e6i −0.478260 0.828371i 0.521429 0.853295i \(-0.325399\pi\)
−0.999689 + 0.0249237i \(0.992066\pi\)
\(558\) 0 0
\(559\) 4.39186e6 0.594456
\(560\) 0 0
\(561\) −2.97104e6 −0.398567
\(562\) 0 0
\(563\) −6.49094e6 1.12426e7i −0.863052 1.49485i −0.868969 0.494867i \(-0.835217\pi\)
0.00591737 0.999982i \(-0.498116\pi\)
\(564\) 0 0
\(565\) 869574. 1.50615e6i 0.114600 0.198493i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −949709. + 1.64494e6i −0.122973 + 0.212996i −0.920939 0.389707i \(-0.872576\pi\)
0.797966 + 0.602703i \(0.205910\pi\)
\(570\) 0 0
\(571\) 831498. + 1.44020e6i 0.106726 + 0.184855i 0.914442 0.404717i \(-0.132630\pi\)
−0.807716 + 0.589572i \(0.799297\pi\)
\(572\) 0 0
\(573\) 8.18304e6 1.04119
\(574\) 0 0
\(575\) 432584. 0.0545633
\(576\) 0 0
\(577\) 4.38672e6 + 7.59802e6i 0.548530 + 0.950082i 0.998376 + 0.0569756i \(0.0181457\pi\)
−0.449845 + 0.893106i \(0.648521\pi\)
\(578\) 0 0
\(579\) 5.40866e6 9.36807e6i 0.670491 1.16133i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −724532. + 1.25493e6i −0.0882849 + 0.152914i
\(584\) 0 0
\(585\) 2.77670e6 + 4.80939e6i 0.335459 + 0.581032i
\(586\) 0 0
\(587\) −5.18393e6 −0.620961 −0.310480 0.950580i \(-0.600490\pi\)
−0.310480 + 0.950580i \(0.600490\pi\)
\(588\) 0 0
\(589\) −1.74360e7 −2.07090
\(590\) 0 0
\(591\) −6.29898e6 1.09102e7i −0.741825 1.28488i
\(592\) 0 0
\(593\) 4.24929e6 7.35998e6i 0.496226 0.859489i −0.503765 0.863841i \(-0.668052\pi\)
0.999991 + 0.00435235i \(0.00138540\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −2.83048e6 + 4.90254e6i −0.325031 + 0.562970i
\(598\) 0 0
\(599\) −5.62355e6 9.74027e6i −0.640388 1.10918i −0.985346 0.170567i \(-0.945440\pi\)
0.344958 0.938618i \(-0.387893\pi\)
\(600\) 0 0
\(601\) 3.46439e6 0.391238 0.195619 0.980680i \(-0.437328\pi\)
0.195619 + 0.980680i \(0.437328\pi\)
\(602\) 0 0
\(603\) −2.43852e6 −0.273108
\(604\) 0 0
\(605\) 5.38997e6 + 9.33571e6i 0.598685 + 1.03695i
\(606\) 0 0
\(607\) −499856. + 865776.i −0.0550647 + 0.0953748i −0.892244 0.451554i \(-0.850870\pi\)
0.837179 + 0.546929i \(0.184203\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −5.65570e6 + 9.79595e6i −0.612891 + 1.06156i
\(612\) 0 0
\(613\) −4.90670e6 8.49865e6i −0.527398 0.913480i −0.999490 0.0319305i \(-0.989834\pi\)
0.472092 0.881549i \(-0.343499\pi\)
\(614\) 0 0
\(615\) −1.31513e7 −1.40210
\(616\) 0 0
\(617\) −5.34745e6 −0.565501 −0.282751 0.959193i \(-0.591247\pi\)
−0.282751 + 0.959193i \(0.591247\pi\)
\(618\) 0 0
\(619\) −3.41384e6 5.91295e6i −0.358110 0.620265i 0.629535 0.776972i \(-0.283245\pi\)
−0.987645 + 0.156707i \(0.949912\pi\)
\(620\) 0 0
\(621\) −158240. + 274080.i −0.0164660 + 0.0285199i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 5.79265e6 1.00332e7i 0.593167 1.02740i
\(626\) 0 0
\(627\) −3.77456e6 6.53773e6i −0.383440 0.664138i
\(628\) 0 0
\(629\) 1.23705e7 1.24670
\(630\) 0 0
\(631\) −3.60970e6 −0.360909 −0.180455 0.983583i \(-0.557757\pi\)
−0.180455 + 0.983583i \(0.557757\pi\)
\(632\) 0 0
\(633\) 1.42756e6 + 2.47261e6i 0.141607 + 0.245271i
\(634\) 0 0
\(635\) 3.49990e6 6.06201e6i 0.344447 0.596599i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 2.50886e6 4.34547e6i 0.243066 0.421003i
\(640\) 0 0
\(641\) 6.69267e6 + 1.15920e7i 0.643361 + 1.11433i 0.984678 + 0.174385i \(0.0557937\pi\)
−0.341317 + 0.939948i \(0.610873\pi\)
\(642\) 0 0
\(643\) 9.91115e6 0.945358 0.472679 0.881235i \(-0.343287\pi\)
0.472679 + 0.881235i \(0.343287\pi\)
\(644\) 0 0
\(645\) 1.35982e7 1.28701
\(646\) 0 0
\(647\) −8.91796e6 1.54464e7i −0.837539 1.45066i −0.891946 0.452141i \(-0.850660\pi\)
0.0544074 0.998519i \(-0.482673\pi\)
\(648\) 0 0
\(649\) 1.04631e6 1.81227e6i 0.0975101 0.168892i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 2.16162e6 3.74403e6i 0.198379 0.343603i −0.749624 0.661864i \(-0.769766\pi\)
0.948003 + 0.318261i \(0.103099\pi\)
\(654\) 0 0
\(655\) 2.60080e6 + 4.50472e6i 0.236867 + 0.410266i
\(656\) 0 0
\(657\) 767102. 0.0693330
\(658\) 0 0
\(659\) 1.97858e7 1.77476 0.887382 0.461035i \(-0.152522\pi\)
0.887382 + 0.461035i \(0.152522\pi\)
\(660\) 0 0
\(661\) 7.88858e6 + 1.36634e7i 0.702255 + 1.21634i 0.967673 + 0.252209i \(0.0811569\pi\)
−0.265417 + 0.964134i \(0.585510\pi\)
\(662\) 0 0
\(663\) −5.72644e6 + 9.91849e6i −0.505942 + 0.876318i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 301944. 522982.i 0.0262792 0.0455169i
\(668\) 0 0
\(669\) −8.89696e6 1.54100e7i −0.768557 1.33118i
\(670\) 0 0
\(671\) 2.29177e6 0.196501
\(672\) 0 0
\(673\) 6.78762e6 0.577670 0.288835 0.957379i \(-0.406732\pi\)
0.288835 + 0.957379i \(0.406732\pi\)
\(674\) 0 0
\(675\) −2.02186e6 3.50196e6i −0.170801 0.295837i
\(676\) 0 0
\(677\) −7.49711e6 + 1.29854e7i −0.628669 + 1.08889i 0.359150 + 0.933280i \(0.383067\pi\)
−0.987819 + 0.155607i \(0.950267\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −1.14316e7 + 1.98000e7i −0.944578 + 1.63606i
\(682\) 0 0
\(683\) −5.77902e6 1.00096e7i −0.474026 0.821038i 0.525531 0.850774i \(-0.323867\pi\)
−0.999558 + 0.0297363i \(0.990533\pi\)
\(684\) 0 0
\(685\) 2.05195e7 1.67086
\(686\) 0 0
\(687\) −1.39157e7 −1.12490
\(688\) 0 0
\(689\) 2.79295e6 + 4.83754e6i 0.224138 + 0.388219i
\(690\) 0 0
\(691\) −110078. + 190661.i −0.00877012 + 0.0151903i −0.870377 0.492386i \(-0.836125\pi\)
0.861607 + 0.507576i \(0.169458\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −4.82140e6 + 8.35090e6i −0.378626 + 0.655800i
\(696\) 0 0
\(697\) −5.32271e6 9.21921e6i −0.415003 0.718806i
\(698\) 0 0
\(699\) 6.94252e6 0.537433
\(700\) 0 0
\(701\) 4.78933e6 0.368111 0.184056 0.982916i \(-0.441077\pi\)
0.184056 + 0.982916i \(0.441077\pi\)
\(702\) 0 0
\(703\) 1.57162e7 + 2.72212e7i 1.19938 + 2.07740i
\(704\) 0 0
\(705\) −1.75114e7 + 3.03306e7i −1.32693 + 2.29831i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −2.13446e6 + 3.69699e6i −0.159468 + 0.276206i −0.934677 0.355499i \(-0.884311\pi\)
0.775209 + 0.631705i \(0.217644\pi\)
\(710\) 0 0
\(711\) −3.49796e6 6.05864e6i −0.259502 0.449471i
\(712\) 0 0
\(713\) 1.05395e6 0.0776421
\(714\) 0 0
\(715\) −4.38613e6 −0.320860
\(716\) 0 0
\(717\) −1.64296e7 2.84569e7i −1.19352 2.06723i
\(718\) 0 0
\(719\) −8.09798e6 + 1.40261e7i −0.584190 + 1.01185i 0.410786 + 0.911732i \(0.365254\pi\)
−0.994976 + 0.100115i \(0.968079\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 1.16744e7 2.02206e7i 0.830593 1.43863i
\(724\) 0 0
\(725\) 3.85799e6 + 6.68224e6i 0.272594 + 0.472147i
\(726\) 0 0
\(727\) −6.53426e6 −0.458522 −0.229261 0.973365i \(-0.573631\pi\)
−0.229261 + 0.973365i \(0.573631\pi\)
\(728\) 0 0
\(729\) −3.03131e6 −0.211257
\(730\) 0 0
\(731\) 5.50361e6 + 9.53254e6i 0.380938 + 0.659804i
\(732\) 0 0
\(733\) 6.58086e6 1.13984e7i 0.452400 0.783579i −0.546135 0.837697i \(-0.683901\pi\)
0.998535 + 0.0541179i \(0.0172347\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 962984. 1.66794e6i 0.0653056 0.113113i
\(738\) 0 0
\(739\) 7.11738e6 + 1.23277e7i 0.479412 + 0.830366i 0.999721 0.0236117i \(-0.00751652\pi\)
−0.520309 + 0.853978i \(0.674183\pi\)
\(740\) 0 0
\(741\) −2.91006e7 −1.94696
\(742\) 0 0
\(743\) −2.15835e7 −1.43434 −0.717168 0.696901i \(-0.754562\pi\)
−0.717168 + 0.696901i \(0.754562\pi\)
\(744\) 0 0
\(745\) 1.48566e7 + 2.57324e7i 0.980684 + 1.69859i
\(746\) 0 0
\(747\) 5.28807e6 9.15921e6i 0.346734 0.600560i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −9.32969e6 + 1.61595e7i −0.603625 + 1.04551i 0.388642 + 0.921389i \(0.372944\pi\)
−0.992267 + 0.124121i \(0.960389\pi\)
\(752\) 0 0
\(753\) 7.90612e6 + 1.36938e7i 0.508131 + 0.880109i
\(754\) 0 0
\(755\) −5.62222e6 −0.358956
\(756\) 0 0
\(757\) −2.56681e6 −0.162800 −0.0813999 0.996682i \(-0.525939\pi\)
−0.0813999 + 0.996682i \(0.525939\pi\)
\(758\) 0 0
\(759\) 228160. + 395185.i 0.0143759 + 0.0248998i
\(760\) 0 0
\(761\) −1.29793e7 + 2.24808e7i −0.812436 + 1.40718i 0.0987188 + 0.995115i \(0.468526\pi\)
−0.911155 + 0.412065i \(0.864808\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −6.95918e6 + 1.20537e7i −0.429937 + 0.744672i
\(766\) 0 0
\(767\) −4.03336e6 6.98599e6i −0.247559 0.428785i
\(768\) 0 0
\(769\) −5.53267e6 −0.337380 −0.168690 0.985669i \(-0.553954\pi\)
−0.168690 + 0.985669i \(0.553954\pi\)
\(770\) 0 0
\(771\) −2.59580e6 −0.157266
\(772\) 0 0
\(773\) 4.16470e6 + 7.21347e6i 0.250689 + 0.434206i 0.963716 0.266931i \(-0.0860096\pi\)
−0.713027 + 0.701137i \(0.752676\pi\)
\(774\) 0 0
\(775\) −6.73326e6 + 1.16624e7i −0.402691 + 0.697480i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 1.35245e7 2.34251e7i 0.798504 1.38305i
\(780\) 0 0
\(781\) 1.98152e6 + 3.43209e6i 0.116244 + 0.201341i
\(782\) 0 0
\(783\) −5.64504e6 −0.329051
\(784\) 0 0
\(785\) 2.91798e7 1.69009
\(786\) 0 0
\(787\) −6.82613e6 1.18232e7i −0.392860 0.680453i 0.599966 0.800026i \(-0.295181\pi\)
−0.992825 + 0.119573i \(0.961848\pi\)
\(788\) 0 0
\(789\) 708880. 1.22782e6i 0.0405397 0.0702168i
\(790\) 0 0
\(791\) 0 0
\(792\)