Properties

Label 320.6.l.a.81.11
Level 320
Weight 6
Character 320.81
Analytic conductor 51.323
Analytic rank 0
Dimension 80
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 320.l (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(51.3228223402\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(40\) over \(\Q(i)\)
Twist minimal: no (minimal twist has level 80)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 81.11
Character \(\chi\) \(=\) 320.81
Dual form 320.6.l.a.241.11

$q$-expansion

\(f(q)\) \(=\) \(q+(-9.88924 - 9.88924i) q^{3} +(-17.6777 + 17.6777i) q^{5} +122.335i q^{7} -47.4058i q^{9} +O(q^{10})\) \(q+(-9.88924 - 9.88924i) q^{3} +(-17.6777 + 17.6777i) q^{5} +122.335i q^{7} -47.4058i q^{9} +(301.232 - 301.232i) q^{11} +(-384.386 - 384.386i) q^{13} +349.637 q^{15} -1558.08 q^{17} +(2096.85 + 2096.85i) q^{19} +(1209.80 - 1209.80i) q^{21} -4768.93i q^{23} -625.000i q^{25} +(-2871.89 + 2871.89i) q^{27} +(-1907.21 - 1907.21i) q^{29} -1152.69 q^{31} -5957.91 q^{33} +(-2162.60 - 2162.60i) q^{35} +(-7429.66 + 7429.66i) q^{37} +7602.58i q^{39} +4115.54i q^{41} +(-8400.86 + 8400.86i) q^{43} +(838.025 + 838.025i) q^{45} +8941.71 q^{47} +1841.08 q^{49} +(15408.3 + 15408.3i) q^{51} +(24969.5 - 24969.5i) q^{53} +10650.2i q^{55} -41472.4i q^{57} +(-23257.6 + 23257.6i) q^{59} +(14305.9 + 14305.9i) q^{61} +5799.41 q^{63} +13590.1 q^{65} +(38864.6 + 38864.6i) q^{67} +(-47161.1 + 47161.1i) q^{69} -12843.7i q^{71} +28584.7i q^{73} +(-6180.78 + 6180.78i) q^{75} +(36851.3 + 36851.3i) q^{77} +50757.6 q^{79} +45282.1 q^{81} +(39493.3 + 39493.3i) q^{83} +(27543.3 - 27543.3i) q^{85} +37721.7i q^{87} +97259.4i q^{89} +(47024.0 - 47024.0i) q^{91} +(11399.2 + 11399.2i) q^{93} -74134.7 q^{95} -46757.9 q^{97} +(-14280.1 - 14280.1i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q + O(q^{10}) \) \( 80q - 1208q^{11} + 1800q^{15} - 2360q^{19} + 7464q^{27} - 8144q^{29} + 21296q^{37} - 32072q^{43} + 88360q^{47} - 192080q^{49} + 5920q^{51} - 49456q^{53} - 44984q^{59} + 48080q^{61} - 158760q^{63} - 61160q^{67} - 22320q^{69} - 14896q^{77} - 177680q^{79} - 524880q^{81} + 329240q^{83} + 132400q^{85} - 364832q^{91} - 362352q^{93} - 288800q^{95} - 659000q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/320\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(257\) \(261\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{3}{4}\right)\)

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
\(3\) −9.88924 9.88924i −0.634395 0.634395i 0.314772 0.949167i \(-0.398072\pi\)
−0.949167 + 0.314772i \(0.898072\pi\)
\(4\) 0 0
\(5\) −17.6777 + 17.6777i −0.316228 + 0.316228i
\(6\) 0 0
\(7\) 122.335i 0.943641i 0.881695 + 0.471820i \(0.156403\pi\)
−0.881695 + 0.471820i \(0.843597\pi\)
\(8\) 0 0
\(9\) 47.4058i 0.195086i
\(10\) 0 0
\(11\) 301.232 301.232i 0.750618 0.750618i −0.223976 0.974595i \(-0.571904\pi\)
0.974595 + 0.223976i \(0.0719039\pi\)
\(12\) 0 0
\(13\) −384.386 384.386i −0.630826 0.630826i 0.317449 0.948275i \(-0.397174\pi\)
−0.948275 + 0.317449i \(0.897174\pi\)
\(14\) 0 0
\(15\) 349.637 0.401227
\(16\) 0 0
\(17\) −1558.08 −1.30758 −0.653791 0.756676i \(-0.726822\pi\)
−0.653791 + 0.756676i \(0.726822\pi\)
\(18\) 0 0
\(19\) 2096.85 + 2096.85i 1.33255 + 1.33255i 0.903085 + 0.429462i \(0.141297\pi\)
0.429462 + 0.903085i \(0.358703\pi\)
\(20\) 0 0
\(21\) 1209.80 1209.80i 0.598641 0.598641i
\(22\) 0 0
\(23\) 4768.93i 1.87975i −0.341513 0.939877i \(-0.610939\pi\)
0.341513 0.939877i \(-0.389061\pi\)
\(24\) 0 0
\(25\) 625.000i 0.200000i
\(26\) 0 0
\(27\) −2871.89 + 2871.89i −0.758157 + 0.758157i
\(28\) 0 0
\(29\) −1907.21 1907.21i −0.421117 0.421117i 0.464471 0.885588i \(-0.346244\pi\)
−0.885588 + 0.464471i \(0.846244\pi\)
\(30\) 0 0
\(31\) −1152.69 −0.215431 −0.107715 0.994182i \(-0.534354\pi\)
−0.107715 + 0.994182i \(0.534354\pi\)
\(32\) 0 0
\(33\) −5957.91 −0.952377
\(34\) 0 0
\(35\) −2162.60 2162.60i −0.298405 0.298405i
\(36\) 0 0
\(37\) −7429.66 + 7429.66i −0.892205 + 0.892205i −0.994730 0.102525i \(-0.967308\pi\)
0.102525 + 0.994730i \(0.467308\pi\)
\(38\) 0 0
\(39\) 7602.58i 0.800386i
\(40\) 0 0
\(41\) 4115.54i 0.382356i 0.981555 + 0.191178i \(0.0612307\pi\)
−0.981555 + 0.191178i \(0.938769\pi\)
\(42\) 0 0
\(43\) −8400.86 + 8400.86i −0.692871 + 0.692871i −0.962863 0.269992i \(-0.912979\pi\)
0.269992 + 0.962863i \(0.412979\pi\)
\(44\) 0 0
\(45\) 838.025 + 838.025i 0.0616915 + 0.0616915i
\(46\) 0 0
\(47\) 8941.71 0.590441 0.295220 0.955429i \(-0.404607\pi\)
0.295220 + 0.955429i \(0.404607\pi\)
\(48\) 0 0
\(49\) 1841.08 0.109543
\(50\) 0 0
\(51\) 15408.3 + 15408.3i 0.829523 + 0.829523i
\(52\) 0 0
\(53\) 24969.5 24969.5i 1.22101 1.22101i 0.253738 0.967273i \(-0.418340\pi\)
0.967273 0.253738i \(-0.0816601\pi\)
\(54\) 0 0
\(55\) 10650.2i 0.474733i
\(56\) 0 0
\(57\) 41472.4i 1.69072i
\(58\) 0 0
\(59\) −23257.6 + 23257.6i −0.869831 + 0.869831i −0.992453 0.122622i \(-0.960870\pi\)
0.122622 + 0.992453i \(0.460870\pi\)
\(60\) 0 0
\(61\) 14305.9 + 14305.9i 0.492257 + 0.492257i 0.909017 0.416760i \(-0.136834\pi\)
−0.416760 + 0.909017i \(0.636834\pi\)
\(62\) 0 0
\(63\) 5799.41 0.184091
\(64\) 0 0
\(65\) 13590.1 0.398970
\(66\) 0 0
\(67\) 38864.6 + 38864.6i 1.05771 + 1.05771i 0.998229 + 0.0594820i \(0.0189449\pi\)
0.0594820 + 0.998229i \(0.481055\pi\)
\(68\) 0 0
\(69\) −47161.1 + 47161.1i −1.19251 + 1.19251i
\(70\) 0 0
\(71\) 12843.7i 0.302373i −0.988505 0.151187i \(-0.951691\pi\)
0.988505 0.151187i \(-0.0483094\pi\)
\(72\) 0 0
\(73\) 28584.7i 0.627807i 0.949455 + 0.313904i \(0.101637\pi\)
−0.949455 + 0.313904i \(0.898363\pi\)
\(74\) 0 0
\(75\) −6180.78 + 6180.78i −0.126879 + 0.126879i
\(76\) 0 0
\(77\) 36851.3 + 36851.3i 0.708314 + 0.708314i
\(78\) 0 0
\(79\) 50757.6 0.915025 0.457513 0.889203i \(-0.348740\pi\)
0.457513 + 0.889203i \(0.348740\pi\)
\(80\) 0 0
\(81\) 45282.1 0.766856
\(82\) 0 0
\(83\) 39493.3 + 39493.3i 0.629257 + 0.629257i 0.947881 0.318624i \(-0.103221\pi\)
−0.318624 + 0.947881i \(0.603221\pi\)
\(84\) 0 0
\(85\) 27543.3 27543.3i 0.413493 0.413493i
\(86\) 0 0
\(87\) 37721.7i 0.534309i
\(88\) 0 0
\(89\) 97259.4i 1.30154i 0.759276 + 0.650768i \(0.225553\pi\)
−0.759276 + 0.650768i \(0.774447\pi\)
\(90\) 0 0
\(91\) 47024.0 47024.0i 0.595273 0.595273i
\(92\) 0 0
\(93\) 11399.2 + 11399.2i 0.136668 + 0.136668i
\(94\) 0 0
\(95\) −74134.7 −0.842777
\(96\) 0 0
\(97\) −46757.9 −0.504575 −0.252287 0.967652i \(-0.581183\pi\)
−0.252287 + 0.967652i \(0.581183\pi\)
\(98\) 0 0
\(99\) −14280.1 14280.1i −0.146435 0.146435i
\(100\) 0 0
\(101\) −62869.3 + 62869.3i −0.613247 + 0.613247i −0.943791 0.330544i \(-0.892768\pi\)
0.330544 + 0.943791i \(0.392768\pi\)
\(102\) 0 0
\(103\) 8850.12i 0.0821971i 0.999155 + 0.0410985i \(0.0130858\pi\)
−0.999155 + 0.0410985i \(0.986914\pi\)
\(104\) 0 0
\(105\) 42773.0i 0.378614i
\(106\) 0 0
\(107\) −119180. + 119180.i −1.00634 + 1.00634i −0.00636140 + 0.999980i \(0.502025\pi\)
−0.999980 + 0.00636140i \(0.997975\pi\)
\(108\) 0 0
\(109\) 118189. + 118189.i 0.952819 + 0.952819i 0.998936 0.0461173i \(-0.0146848\pi\)
−0.0461173 + 0.998936i \(0.514685\pi\)
\(110\) 0 0
\(111\) 146947. 1.13202
\(112\) 0 0
\(113\) 72392.2 0.533329 0.266665 0.963789i \(-0.414078\pi\)
0.266665 + 0.963789i \(0.414078\pi\)
\(114\) 0 0
\(115\) 84303.5 + 84303.5i 0.594430 + 0.594430i
\(116\) 0 0
\(117\) −18222.2 + 18222.2i −0.123065 + 0.123065i
\(118\) 0 0
\(119\) 190609.i 1.23389i
\(120\) 0 0
\(121\) 20430.2i 0.126855i
\(122\) 0 0
\(123\) 40699.6 40699.6i 0.242565 0.242565i
\(124\) 0 0
\(125\) 11048.5 + 11048.5i 0.0632456 + 0.0632456i
\(126\) 0 0
\(127\) −122901. −0.676153 −0.338076 0.941119i \(-0.609776\pi\)
−0.338076 + 0.941119i \(0.609776\pi\)
\(128\) 0 0
\(129\) 166156. 0.879108
\(130\) 0 0
\(131\) 75109.1 + 75109.1i 0.382397 + 0.382397i 0.871965 0.489568i \(-0.162846\pi\)
−0.489568 + 0.871965i \(0.662846\pi\)
\(132\) 0 0
\(133\) −256518. + 256518.i −1.25745 + 1.25745i
\(134\) 0 0
\(135\) 101537.i 0.479500i
\(136\) 0 0
\(137\) 73685.1i 0.335412i 0.985837 + 0.167706i \(0.0536359\pi\)
−0.985837 + 0.167706i \(0.946364\pi\)
\(138\) 0 0
\(139\) −18908.2 + 18908.2i −0.0830067 + 0.0830067i −0.747391 0.664384i \(-0.768694\pi\)
0.664384 + 0.747391i \(0.268694\pi\)
\(140\) 0 0
\(141\) −88426.8 88426.8i −0.374573 0.374573i
\(142\) 0 0
\(143\) −231579. −0.947019
\(144\) 0 0
\(145\) 67430.0 0.266338
\(146\) 0 0
\(147\) −18206.9 18206.9i −0.0694932 0.0694932i
\(148\) 0 0
\(149\) −147704. + 147704.i −0.545039 + 0.545039i −0.925002 0.379963i \(-0.875937\pi\)
0.379963 + 0.925002i \(0.375937\pi\)
\(150\) 0 0
\(151\) 86096.9i 0.307288i 0.988126 + 0.153644i \(0.0491008\pi\)
−0.988126 + 0.153644i \(0.950899\pi\)
\(152\) 0 0
\(153\) 73862.3i 0.255090i
\(154\) 0 0
\(155\) 20376.8 20376.8i 0.0681251 0.0681251i
\(156\) 0 0
\(157\) −141259. 141259.i −0.457370 0.457370i 0.440421 0.897791i \(-0.354829\pi\)
−0.897791 + 0.440421i \(0.854829\pi\)
\(158\) 0 0
\(159\) −493858. −1.54921
\(160\) 0 0
\(161\) 583408. 1.77381
\(162\) 0 0
\(163\) 283813. + 283813.i 0.836687 + 0.836687i 0.988421 0.151734i \(-0.0484858\pi\)
−0.151734 + 0.988421i \(0.548486\pi\)
\(164\) 0 0
\(165\) 105322. 105322.i 0.301168 0.301168i
\(166\) 0 0
\(167\) 15467.8i 0.0429178i −0.999770 0.0214589i \(-0.993169\pi\)
0.999770 0.0214589i \(-0.00683110\pi\)
\(168\) 0 0
\(169\) 75787.0i 0.204117i
\(170\) 0 0
\(171\) 99402.7 99402.7i 0.259961 0.259961i
\(172\) 0 0
\(173\) −433381. 433381.i −1.10092 1.10092i −0.994300 0.106617i \(-0.965998\pi\)
−0.106617 0.994300i \(-0.534002\pi\)
\(174\) 0 0
\(175\) 76459.5 0.188728
\(176\) 0 0
\(177\) 460000. 1.10363
\(178\) 0 0
\(179\) −197142. 197142.i −0.459883 0.459883i 0.438734 0.898617i \(-0.355427\pi\)
−0.898617 + 0.438734i \(0.855427\pi\)
\(180\) 0 0
\(181\) −86411.6 + 86411.6i −0.196054 + 0.196054i −0.798306 0.602252i \(-0.794270\pi\)
0.602252 + 0.798306i \(0.294270\pi\)
\(182\) 0 0
\(183\) 282950.i 0.624570i
\(184\) 0 0
\(185\) 262678.i 0.564280i
\(186\) 0 0
\(187\) −469344. + 469344.i −0.981494 + 0.981494i
\(188\) 0 0
\(189\) −351334. 351334.i −0.715427 0.715427i
\(190\) 0 0
\(191\) 697785. 1.38401 0.692003 0.721895i \(-0.256729\pi\)
0.692003 + 0.721895i \(0.256729\pi\)
\(192\) 0 0
\(193\) −573139. −1.10756 −0.553779 0.832663i \(-0.686815\pi\)
−0.553779 + 0.832663i \(0.686815\pi\)
\(194\) 0 0
\(195\) −134396. 134396.i −0.253104 0.253104i
\(196\) 0 0
\(197\) −259965. + 259965.i −0.477254 + 0.477254i −0.904252 0.426999i \(-0.859571\pi\)
0.426999 + 0.904252i \(0.359571\pi\)
\(198\) 0 0
\(199\) 80858.1i 0.144741i 0.997378 + 0.0723704i \(0.0230564\pi\)
−0.997378 + 0.0723704i \(0.976944\pi\)
\(200\) 0 0
\(201\) 768683.i 1.34201i
\(202\) 0 0
\(203\) 233319. 233319.i 0.397383 0.397383i
\(204\) 0 0
\(205\) −72753.2 72753.2i −0.120912 0.120912i
\(206\) 0 0
\(207\) −226075. −0.366713
\(208\) 0 0
\(209\) 1.26327e6 2.00047
\(210\) 0 0
\(211\) 520212. + 520212.i 0.804404 + 0.804404i 0.983780 0.179377i \(-0.0574082\pi\)
−0.179377 + 0.983780i \(0.557408\pi\)
\(212\) 0 0
\(213\) −127014. + 127014.i −0.191824 + 0.191824i
\(214\) 0 0
\(215\) 297015.i 0.438210i
\(216\) 0 0
\(217\) 141014.i 0.203289i
\(218\) 0 0
\(219\) 282681. 282681.i 0.398278 0.398278i
\(220\) 0 0
\(221\) 598907. + 598907.i 0.824856 + 0.824856i
\(222\) 0 0
\(223\) 126355. 0.170150 0.0850749 0.996375i \(-0.472887\pi\)
0.0850749 + 0.996375i \(0.472887\pi\)
\(224\) 0 0
\(225\) −29628.7 −0.0390172
\(226\) 0 0
\(227\) 918677. + 918677.i 1.18331 + 1.18331i 0.978882 + 0.204427i \(0.0655332\pi\)
0.204427 + 0.978882i \(0.434467\pi\)
\(228\) 0 0
\(229\) −347876. + 347876.i −0.438365 + 0.438365i −0.891461 0.453097i \(-0.850319\pi\)
0.453097 + 0.891461i \(0.350319\pi\)
\(230\) 0 0
\(231\) 728862.i 0.898702i
\(232\) 0 0
\(233\) 728178.i 0.878714i −0.898313 0.439357i \(-0.855206\pi\)
0.898313 0.439357i \(-0.144794\pi\)
\(234\) 0 0
\(235\) −158069. + 158069.i −0.186714 + 0.186714i
\(236\) 0 0
\(237\) −501954. 501954.i −0.580488 0.580488i
\(238\) 0 0
\(239\) −203434. −0.230372 −0.115186 0.993344i \(-0.536746\pi\)
−0.115186 + 0.993344i \(0.536746\pi\)
\(240\) 0 0
\(241\) −131370. −0.145698 −0.0728490 0.997343i \(-0.523209\pi\)
−0.0728490 + 0.997343i \(0.523209\pi\)
\(242\) 0 0
\(243\) 250065. + 250065.i 0.271667 + 0.271667i
\(244\) 0 0
\(245\) −32546.0 + 32546.0i −0.0346404 + 0.0346404i
\(246\) 0 0
\(247\) 1.61200e6i 1.68121i
\(248\) 0 0
\(249\) 781117.i 0.798395i
\(250\) 0 0
\(251\) −487551. + 487551.i −0.488467 + 0.488467i −0.907822 0.419355i \(-0.862256\pi\)
0.419355 + 0.907822i \(0.362256\pi\)
\(252\) 0 0
\(253\) −1.43655e6 1.43655e6i −1.41098 1.41098i
\(254\) 0 0
\(255\) −544765. −0.524636
\(256\) 0 0
\(257\) −1.90822e6 −1.80217 −0.901084 0.433645i \(-0.857227\pi\)
−0.901084 + 0.433645i \(0.857227\pi\)
\(258\) 0 0
\(259\) −908910. 908910.i −0.841921 0.841921i
\(260\) 0 0
\(261\) −90412.8 + 90412.8i −0.0821540 + 0.0821540i
\(262\) 0 0
\(263\) 484503.i 0.431924i −0.976402 0.215962i \(-0.930711\pi\)
0.976402 0.215962i \(-0.0692887\pi\)
\(264\) 0 0
\(265\) 882804.i 0.772235i
\(266\) 0 0
\(267\) 961821. 961821.i 0.825689 0.825689i
\(268\) 0 0
\(269\) 986492. + 986492.i 0.831214 + 0.831214i 0.987683 0.156469i \(-0.0500110\pi\)
−0.156469 + 0.987683i \(0.550011\pi\)
\(270\) 0 0
\(271\) −1.22694e6 −1.01484 −0.507422 0.861698i \(-0.669401\pi\)
−0.507422 + 0.861698i \(0.669401\pi\)
\(272\) 0 0
\(273\) −930064. −0.755277
\(274\) 0 0
\(275\) −188270. 188270.i −0.150124 0.150124i
\(276\) 0 0
\(277\) 1.69007e6 1.69007e6i 1.32344 1.32344i 0.412473 0.910970i \(-0.364665\pi\)
0.910970 0.412473i \(-0.135335\pi\)
\(278\) 0 0
\(279\) 54644.1i 0.0420275i
\(280\) 0 0
\(281\) 1.34620e6i 1.01705i −0.861046 0.508527i \(-0.830190\pi\)
0.861046 0.508527i \(-0.169810\pi\)
\(282\) 0 0
\(283\) −944602. + 944602.i −0.701104 + 0.701104i −0.964648 0.263543i \(-0.915109\pi\)
0.263543 + 0.964648i \(0.415109\pi\)
\(284\) 0 0
\(285\) 733136. + 733136.i 0.534653 + 0.534653i
\(286\) 0 0
\(287\) −503476. −0.360806
\(288\) 0 0
\(289\) 1.00777e6 0.709768
\(290\) 0 0
\(291\) 462400. + 462400.i 0.320100 + 0.320100i
\(292\) 0 0
\(293\) −838880. + 838880.i −0.570862 + 0.570862i −0.932369 0.361508i \(-0.882262\pi\)
0.361508 + 0.932369i \(0.382262\pi\)
\(294\) 0 0
\(295\) 822281.i 0.550130i
\(296\) 0 0
\(297\) 1.73021e6i 1.13817i
\(298\) 0 0
\(299\) −1.83311e6 + 1.83311e6i −1.18580 + 1.18580i
\(300\) 0 0
\(301\) −1.02772e6 1.02772e6i −0.653821 0.653821i
\(302\) 0 0
\(303\) 1.24346e6 0.778082
\(304\) 0 0
\(305\) −505791. −0.311330
\(306\) 0 0
\(307\) 521897. + 521897.i 0.316038 + 0.316038i 0.847243 0.531205i \(-0.178261\pi\)
−0.531205 + 0.847243i \(0.678261\pi\)
\(308\) 0 0
\(309\) 87521.0 87521.0i 0.0521454 0.0521454i
\(310\) 0 0
\(311\) 1.29428e6i 0.758798i −0.925233 0.379399i \(-0.876131\pi\)
0.925233 0.379399i \(-0.123869\pi\)
\(312\) 0 0
\(313\) 2.45861e6i 1.41850i −0.704957 0.709251i \(-0.749034\pi\)
0.704957 0.709251i \(-0.250966\pi\)
\(314\) 0 0
\(315\) −102520. + 102520.i −0.0582146 + 0.0582146i
\(316\) 0 0
\(317\) 1.88035e6 + 1.88035e6i 1.05097 + 1.05097i 0.998629 + 0.0523414i \(0.0166684\pi\)
0.0523414 + 0.998629i \(0.483332\pi\)
\(318\) 0 0
\(319\) −1.14902e6 −0.632197
\(320\) 0 0
\(321\) 2.35721e6 1.27684
\(322\) 0 0
\(323\) −3.26706e6 3.26706e6i −1.74241 1.74241i
\(324\) 0 0
\(325\) −240242. + 240242.i −0.126165 + 0.126165i
\(326\) 0 0
\(327\) 2.33760e6i 1.20893i
\(328\) 0 0
\(329\) 1.09389e6i 0.557164i
\(330\) 0 0
\(331\) 2.05885e6 2.05885e6i 1.03289 1.03289i 0.0334519 0.999440i \(-0.489350\pi\)
0.999440 0.0334519i \(-0.0106500\pi\)
\(332\) 0 0
\(333\) 352209. + 352209.i 0.174057 + 0.174057i
\(334\) 0 0
\(335\) −1.37407e6 −0.668955
\(336\) 0 0
\(337\) −256497. −0.123029 −0.0615145 0.998106i \(-0.519593\pi\)
−0.0615145 + 0.998106i \(0.519593\pi\)
\(338\) 0 0
\(339\) −715904. 715904.i −0.338342 0.338342i
\(340\) 0 0
\(341\) −347226. + 347226.i −0.161706 + 0.161706i
\(342\) 0 0
\(343\) 2.28132e6i 1.04701i
\(344\) 0 0
\(345\) 1.66740e6i 0.754207i
\(346\) 0 0
\(347\) 297841. 297841.i 0.132789 0.132789i −0.637589 0.770377i \(-0.720068\pi\)
0.770377 + 0.637589i \(0.220068\pi\)
\(348\) 0 0
\(349\) −1.06398e6 1.06398e6i −0.467597 0.467597i 0.433538 0.901135i \(-0.357265\pi\)
−0.901135 + 0.433538i \(0.857265\pi\)
\(350\) 0 0
\(351\) 2.20783e6 0.956530
\(352\) 0 0
\(353\) 2.71943e6 1.16156 0.580780 0.814060i \(-0.302748\pi\)
0.580780 + 0.814060i \(0.302748\pi\)
\(354\) 0 0
\(355\) 227046. + 227046.i 0.0956187 + 0.0956187i
\(356\) 0 0
\(357\) −1.88497e6 + 1.88497e6i −0.782771 + 0.782771i
\(358\) 0 0
\(359\) 1.93088e6i 0.790714i 0.918528 + 0.395357i \(0.129379\pi\)
−0.918528 + 0.395357i \(0.870621\pi\)
\(360\) 0 0
\(361\) 6.31742e6i 2.55136i
\(362\) 0 0
\(363\) −202039. + 202039.i −0.0804764 + 0.0804764i
\(364\) 0 0
\(365\) −505311. 505311.i −0.198530 0.198530i
\(366\) 0 0
\(367\) 4.26731e6 1.65382 0.826911 0.562332i \(-0.190096\pi\)
0.826911 + 0.562332i \(0.190096\pi\)
\(368\) 0 0
\(369\) 195101. 0.0745922
\(370\) 0 0
\(371\) 3.05465e6 + 3.05465e6i 1.15220 + 1.15220i
\(372\) 0 0
\(373\) −1.60230e6 + 1.60230e6i −0.596311 + 0.596311i −0.939329 0.343018i \(-0.888551\pi\)
0.343018 + 0.939329i \(0.388551\pi\)
\(374\) 0 0
\(375\) 218523.i 0.0802453i
\(376\) 0 0
\(377\) 1.46621e6i 0.531304i
\(378\) 0 0
\(379\) 1.32305e6 1.32305e6i 0.473127 0.473127i −0.429798 0.902925i \(-0.641415\pi\)
0.902925 + 0.429798i \(0.141415\pi\)
\(380\) 0 0
\(381\) 1.21539e6 + 1.21539e6i 0.428948 + 0.428948i
\(382\) 0 0
\(383\) −2.69607e6 −0.939149 −0.469574 0.882893i \(-0.655593\pi\)
−0.469574 + 0.882893i \(0.655593\pi\)
\(384\) 0 0
\(385\) −1.30289e6 −0.447977
\(386\) 0 0
\(387\) 398250. + 398250.i 0.135169 + 0.135169i
\(388\) 0 0
\(389\) 2.79493e6 2.79493e6i 0.936475 0.936475i −0.0616242 0.998099i \(-0.519628\pi\)
0.998099 + 0.0616242i \(0.0196280\pi\)
\(390\) 0 0
\(391\) 7.43039e6i 2.45793i
\(392\) 0 0
\(393\) 1.48554e6i 0.485181i
\(394\) 0 0
\(395\) −897276. + 897276.i −0.289356 + 0.289356i
\(396\) 0 0
\(397\) 2.49038e6 + 2.49038e6i 0.793030 + 0.793030i 0.981986 0.188956i \(-0.0605103\pi\)
−0.188956 + 0.981986i \(0.560510\pi\)
\(398\) 0 0
\(399\) 5.07354e6 1.59543
\(400\) 0 0
\(401\) −4.48252e6 −1.39207 −0.696036 0.718007i \(-0.745054\pi\)
−0.696036 + 0.718007i \(0.745054\pi\)
\(402\) 0 0
\(403\) 443078. + 443078.i 0.135899 + 0.135899i
\(404\) 0 0
\(405\) −800481. + 800481.i −0.242501 + 0.242501i
\(406\) 0 0
\(407\) 4.47610e6i 1.33941i
\(408\) 0 0
\(409\) 2.36608e6i 0.699393i 0.936863 + 0.349696i \(0.113715\pi\)
−0.936863 + 0.349696i \(0.886285\pi\)
\(410\) 0 0
\(411\) 728690. 728690.i 0.212784 0.212784i
\(412\) 0 0
\(413\) −2.84523e6 2.84523e6i −0.820808 0.820808i
\(414\) 0 0
\(415\) −1.39630e6 −0.397977
\(416\) 0 0
\(417\) 373975. 0.105318
\(418\) 0 0
\(419\) 1.04928e6 + 1.04928e6i 0.291983 + 0.291983i 0.837863 0.545880i \(-0.183805\pi\)
−0.545880 + 0.837863i \(0.683805\pi\)
\(420\) 0 0
\(421\) −83315.8 + 83315.8i −0.0229099 + 0.0229099i −0.718469 0.695559i \(-0.755157\pi\)
0.695559 + 0.718469i \(0.255157\pi\)
\(422\) 0 0
\(423\) 423890.i 0.115187i
\(424\) 0 0
\(425\) 973803.i 0.261516i
\(426\) 0 0
\(427\) −1.75012e6 + 1.75012e6i −0.464513 + 0.464513i
\(428\) 0 0
\(429\) 2.29014e6 + 2.29014e6i 0.600784 + 0.600784i
\(430\) 0 0
\(431\) −1.89615e6 −0.491676 −0.245838 0.969311i \(-0.579063\pi\)
−0.245838 + 0.969311i \(0.579063\pi\)
\(432\) 0 0
\(433\) −6.49433e6 −1.66462 −0.832309 0.554312i \(-0.812982\pi\)
−0.832309 + 0.554312i \(0.812982\pi\)
\(434\) 0 0
\(435\) −666831. 666831.i −0.168963 0.168963i
\(436\) 0 0
\(437\) 9.99970e6 9.99970e6i 2.50486 2.50486i
\(438\) 0 0
\(439\) 2.58577e6i 0.640365i 0.947356 + 0.320183i \(0.103744\pi\)
−0.947356 + 0.320183i \(0.896256\pi\)
\(440\) 0 0
\(441\) 87278.0i 0.0213702i
\(442\) 0 0
\(443\) 562901. 562901.i 0.136277 0.136277i −0.635678 0.771955i \(-0.719279\pi\)
0.771955 + 0.635678i \(0.219279\pi\)
\(444\) 0 0
\(445\) −1.71932e6 1.71932e6i −0.411582 0.411582i
\(446\) 0 0
\(447\) 2.92137e6 0.691540
\(448\) 0 0
\(449\) 6.62708e6 1.55134 0.775669 0.631141i \(-0.217413\pi\)
0.775669 + 0.631141i \(0.217413\pi\)
\(450\) 0 0
\(451\) 1.23973e6 + 1.23973e6i 0.287003 + 0.287003i
\(452\) 0 0
\(453\) 851433. 851433.i 0.194942 0.194942i
\(454\) 0 0
\(455\) 1.66255e6i 0.376484i
\(456\) 0 0
\(457\) 2.47813e6i 0.555052i 0.960718 + 0.277526i \(0.0895145\pi\)
−0.960718 + 0.277526i \(0.910485\pi\)
\(458\) 0 0
\(459\) 4.47465e6 4.47465e6i 0.991351 0.991351i
\(460\) 0 0
\(461\) 2.88325e6 + 2.88325e6i 0.631872 + 0.631872i 0.948537 0.316665i \(-0.102563\pi\)
−0.316665 + 0.948537i \(0.602563\pi\)
\(462\) 0 0
\(463\) −4.18992e6 −0.908351 −0.454175 0.890912i \(-0.650066\pi\)
−0.454175 + 0.890912i \(0.650066\pi\)
\(464\) 0 0
\(465\) −403023. −0.0864365
\(466\) 0 0
\(467\) 1.38927e6 + 1.38927e6i 0.294777 + 0.294777i 0.838964 0.544187i \(-0.183162\pi\)
−0.544187 + 0.838964i \(0.683162\pi\)
\(468\) 0 0
\(469\) −4.75451e6 + 4.75451e6i −0.998099 + 0.998099i
\(470\) 0 0
\(471\) 2.79389e6i 0.580306i
\(472\) 0 0
\(473\) 5.06121e6i 1.04016i
\(474\) 0 0
\(475\) 1.31053e6 1.31053e6i 0.266509 0.266509i
\(476\) 0 0
\(477\) −1.18370e6 1.18370e6i −0.238202 0.238202i
\(478\) 0 0
\(479\) 3.01097e6 0.599609 0.299804 0.954001i \(-0.403079\pi\)
0.299804 + 0.954001i \(0.403079\pi\)
\(480\) 0 0
\(481\) 5.71172e6 1.12565
\(482\) 0 0
\(483\) −5.76946e6 5.76946e6i −1.12530 1.12530i
\(484\) 0 0
\(485\) 826570. 826570.i 0.159561 0.159561i
\(486\) 0 0
\(487\) 1.73420e6i 0.331341i 0.986181 + 0.165671i \(0.0529789\pi\)
−0.986181 + 0.165671i \(0.947021\pi\)
\(488\) 0 0
\(489\) 5.61339e6i 1.06158i
\(490\) 0 0
\(491\) −2.65718e6 + 2.65718e6i −0.497414 + 0.497414i −0.910632 0.413218i \(-0.864405\pi\)
0.413218 + 0.910632i \(0.364405\pi\)
\(492\) 0 0
\(493\) 2.97159e6 + 2.97159e6i 0.550645 + 0.550645i
\(494\) 0 0
\(495\) 504879. 0.0926136
\(496\) 0 0
\(497\) 1.57123e6 0.285331
\(498\) 0 0
\(499\) −7.30951e6 7.30951e6i −1.31413 1.31413i −0.918345 0.395781i \(-0.870474\pi\)
−0.395781 0.918345i \(-0.629526\pi\)
\(500\) 0 0
\(501\) −152965. + 152965.i −0.0272268 + 0.0272268i
\(502\) 0 0
\(503\) 5.49766e6i 0.968853i 0.874832 + 0.484426i \(0.160972\pi\)
−0.874832 + 0.484426i \(0.839028\pi\)
\(504\) 0 0
\(505\) 2.22277e6i 0.387851i
\(506\) 0 0
\(507\) −749476. + 749476.i −0.129491 + 0.129491i
\(508\) 0 0
\(509\) −2.60875e6 2.60875e6i −0.446311 0.446311i 0.447815 0.894126i \(-0.352202\pi\)
−0.894126 + 0.447815i \(0.852202\pi\)
\(510\) 0 0
\(511\) −3.49692e6 −0.592424
\(512\) 0 0
\(513\) −1.20438e7 −2.02056
\(514\) 0 0
\(515\) −156450. 156450.i −0.0259930 0.0259930i
\(516\) 0 0
\(517\) 2.69353e6 2.69353e6i 0.443195 0.443195i
\(518\) 0 0
\(519\) 8.57162e6i 1.39683i
\(520\) 0 0
\(521\) 9.50774e6i 1.53456i −0.641314 0.767279i \(-0.721610\pi\)
0.641314 0.767279i \(-0.278390\pi\)
\(522\) 0 0
\(523\) −2.12191e6 + 2.12191e6i −0.339213 + 0.339213i −0.856071 0.516858i \(-0.827102\pi\)
0.516858 + 0.856071i \(0.327102\pi\)
\(524\) 0 0
\(525\) −756127. 756127.i −0.119728 0.119728i
\(526\) 0 0
\(527\) 1.79598e6 0.281693
\(528\) 0 0
\(529\) −1.63063e7 −2.53348
\(530\) 0 0
\(531\) 1.10255e6 + 1.10255e6i 0.169692 + 0.169692i
\(532\) 0 0
\(533\) 1.58196e6 1.58196e6i 0.241200 0.241200i
\(534\) 0 0
\(535\) 4.21366e6i 0.636466i
\(536\) 0 0
\(537\) 3.89918e6i 0.583495i
\(538\) 0 0
\(539\) 554592. 554592.i 0.0822246 0.0822246i
\(540\) 0 0
\(541\) 7.92767e6 + 7.92767e6i 1.16454 + 1.16454i 0.983471 + 0.181064i \(0.0579541\pi\)
0.181064 + 0.983471i \(0.442046\pi\)
\(542\) 0 0
\(543\) 1.70909e6 0.248751
\(544\) 0 0
\(545\) −4.17861e6 −0.602615
\(546\) 0 0
\(547\) −2.38242e6 2.38242e6i −0.340447 0.340447i 0.516088 0.856535i \(-0.327388\pi\)
−0.856535 + 0.516088i \(0.827388\pi\)
\(548\) 0 0
\(549\) 678185. 678185.i 0.0960323 0.0960323i
\(550\) 0 0
\(551\) 7.99824e6i 1.12232i
\(552\) 0 0
\(553\) 6.20944e6i 0.863455i
\(554\) 0 0
\(555\) −2.59769e6 + 2.59769e6i −0.357976 + 0.357976i
\(556\) 0 0
\(557\) −2.36995e6 2.36995e6i −0.323669 0.323669i 0.526504 0.850173i \(-0.323503\pi\)
−0.850173 + 0.526504i \(0.823503\pi\)
\(558\) 0 0
\(559\) 6.45835e6 0.874162
\(560\) 0 0
\(561\) 9.28292e6 1.24531
\(562\) 0 0
\(563\) −6.69440e6 6.69440e6i −0.890104 0.890104i 0.104429 0.994532i \(-0.466699\pi\)
−0.994532 + 0.104429i \(0.966699\pi\)
\(564\) 0 0
\(565\) −1.27973e6 + 1.27973e6i −0.168654 + 0.168654i
\(566\) 0 0
\(567\) 5.53959e6i 0.723636i
\(568\) 0 0
\(569\) 6.90268e6i 0.893793i 0.894586 + 0.446897i \(0.147471\pi\)
−0.894586 + 0.446897i \(0.852529\pi\)
\(570\) 0 0
\(571\) 6.09499e6 6.09499e6i 0.782317 0.782317i −0.197904 0.980221i \(-0.563414\pi\)
0.980221 + 0.197904i \(0.0634135\pi\)
\(572\) 0 0
\(573\) −6.90056e6 6.90056e6i −0.878006 0.878006i
\(574\) 0 0
\(575\) −2.98058e6 −0.375951
\(576\) 0 0
\(577\) −6.40682e6 −0.801130 −0.400565 0.916268i \(-0.631186\pi\)
−0.400565 + 0.916268i \(0.631186\pi\)
\(578\) 0 0
\(579\) 5.66791e6 + 5.66791e6i 0.702630 + 0.702630i
\(580\) 0 0
\(581\) −4.83142e6 + 4.83142e6i −0.593792 + 0.593792i
\(582\) 0 0
\(583\) 1.50432e7i 1.83303i
\(584\) 0 0
\(585\) 644251.i 0.0778333i
\(586\) 0 0
\(587\) 3.17862e6 3.17862e6i 0.380754 0.380754i −0.490620 0.871374i \(-0.663230\pi\)
0.871374 + 0.490620i \(0.163230\pi\)
\(588\) 0 0
\(589\) −2.41701e6 2.41701e6i −0.287071 0.287071i
\(590\) 0 0
\(591\) 5.14171e6 0.605535
\(592\) 0 0
\(593\) 6.93794e6 0.810203 0.405102 0.914272i \(-0.367236\pi\)
0.405102 + 0.914272i \(0.367236\pi\)
\(594\) 0 0
\(595\) 3.36952e6 + 3.36952e6i 0.390189 + 0.390189i
\(596\) 0 0
\(597\) 799625. 799625.i 0.0918228 0.0918228i
\(598\) 0 0
\(599\) 1.29586e7i 1.47568i −0.674978 0.737838i \(-0.735847\pi\)
0.674978 0.737838i \(-0.264153\pi\)
\(600\) 0 0
\(601\) 3.22149e6i 0.363806i −0.983316 0.181903i \(-0.941774\pi\)
0.983316 0.181903i \(-0.0582257\pi\)
\(602\) 0 0
\(603\) 1.84241e6 1.84241e6i 0.206344 0.206344i
\(604\) 0 0
\(605\) 361158. + 361158.i 0.0401152 + 0.0401152i
\(606\) 0 0
\(607\) 2.77321e6 0.305500 0.152750 0.988265i \(-0.451187\pi\)
0.152750 + 0.988265i \(0.451187\pi\)
\(608\) 0 0
\(609\) −4.61469e6 −0.504196
\(610\) 0 0
\(611\) −3.43707e6 3.43707e6i −0.372465 0.372465i
\(612\) 0 0
\(613\) 3.18104e6 3.18104e6i 0.341915 0.341915i −0.515172 0.857087i \(-0.672272\pi\)
0.857087 + 0.515172i \(0.172272\pi\)
\(614\) 0 0
\(615\) 1.43895e6i 0.153411i
\(616\) 0 0
\(617\) 2.69222e6i 0.284707i 0.989816 + 0.142353i \(0.0454669\pi\)
−0.989816 + 0.142353i \(0.954533\pi\)
\(618\) 0 0
\(619\) −1.97397e6 + 1.97397e6i −0.207069 + 0.207069i −0.803020 0.595952i \(-0.796775\pi\)
0.595952 + 0.803020i \(0.296775\pi\)
\(620\) 0 0
\(621\) 1.36958e7 + 1.36958e7i 1.42515 + 1.42515i
\(622\) 0 0
\(623\) −1.18983e7 −1.22818
\(624\) 0 0
\(625\) −390625. −0.0400000
\(626\) 0 0
\(627\) −1.24928e7 1.24928e7i −1.26909 1.26909i
\(628\) 0 0
\(629\) 1.15760e7 1.15760e7i 1.16663 1.16663i
\(630\) 0 0
\(631\) 7.74739e6i 0.774608i −0.921952 0.387304i \(-0.873406\pi\)
0.921952 0.387304i \(-0.126594\pi\)
\(632\) 0 0
\(633\) 1.02890e7i 1.02062i
\(634\) 0 0
\(635\) 2.17260e6 2.17260e6i 0.213818 0.213818i
\(636\) 0 0
\(637\) −707687. 707687.i −0.0691023 0.0691023i
\(638\) 0 0
\(639\) −608865. −0.0589887
\(640\) 0 0
\(641\) 1.28304e7 1.23337 0.616687 0.787209i \(-0.288475\pi\)
0.616687 + 0.787209i \(0.288475\pi\)
\(642\) 0 0
\(643\) −4.34386e6 4.34386e6i −0.414332 0.414332i 0.468912 0.883245i \(-0.344646\pi\)
−0.883245 + 0.468912i \(0.844646\pi\)
\(644\) 0 0
\(645\) −2.93725e6 + 2.93725e6i −0.277998 + 0.277998i
\(646\) 0 0
\(647\) 4.82724e6i 0.453355i 0.973970 + 0.226678i \(0.0727863\pi\)
−0.973970 + 0.226678i \(0.927214\pi\)
\(648\) 0 0
\(649\) 1.40119e7i 1.30582i
\(650\) 0 0
\(651\) −1.39453e6 + 1.39453e6i −0.128966 + 0.128966i
\(652\) 0 0
\(653\) 4.17503e6 + 4.17503e6i 0.383157 + 0.383157i 0.872238 0.489081i \(-0.162668\pi\)
−0.489081 + 0.872238i \(0.662668\pi\)
\(654\) 0 0
\(655\) −2.65551e6 −0.241849
\(656\) 0 0
\(657\) 1.35508e6 0.122476
\(658\) 0 0
\(659\) 1.12655e7 + 1.12655e7i 1.01051 + 1.01051i 0.999944 + 0.0105615i \(0.00336189\pi\)
0.0105615 + 0.999944i \(0.496638\pi\)
\(660\) 0 0
\(661\) 6.22807e6 6.22807e6i 0.554434 0.554434i −0.373284 0.927717i \(-0.621768\pi\)
0.927717 + 0.373284i \(0.121768\pi\)
\(662\) 0 0
\(663\) 1.18455e7i 1.04657i
\(664\) 0 0
\(665\) 9.06929e6i 0.795278i
\(666\) 0 0
\(667\) −9.09533e6 + 9.09533e6i −0.791597 + 0.791597i
\(668\) 0 0
\(669\) −1.24956e6 1.24956e6i −0.107942 0.107942i
\(670\) 0 0
\(671\) 8.61880e6 0.738994
\(672\) 0 0
\(673\) −5.79021e6 −0.492784 −0.246392 0.969170i \(-0.579245\pi\)
−0.246392 + 0.969170i \(0.579245\pi\)
\(674\) 0 0
\(675\) 1.79493e6 + 1.79493e6i 0.151631 + 0.151631i
\(676\) 0 0
\(677\) −1.96617e6 + 1.96617e6i −0.164873 + 0.164873i −0.784721 0.619849i \(-0.787194\pi\)
0.619849 + 0.784721i \(0.287194\pi\)
\(678\) 0 0
\(679\) 5.72014e6i 0.476137i
\(680\) 0 0
\(681\) 1.81700e7i 1.50137i
\(682\) 0 0
\(683\) 554999. 554999.i 0.0455240 0.0455240i −0.683978 0.729502i \(-0.739752\pi\)
0.729502 + 0.683978i \(0.239752\pi\)
\(684\) 0 0
\(685\) −1.30258e6 1.30258e6i −0.106067 0.106067i
\(686\) 0 0
\(687\) 6.88046e6 0.556193
\(688\) 0 0
\(689\) −1.91959e7 −1.54049
\(690\) 0 0
\(691\) 1.32042e7 + 1.32042e7i 1.05200 + 1.05200i 0.998572 + 0.0534279i \(0.0170147\pi\)
0.0534279 + 0.998572i \(0.482985\pi\)
\(692\) 0 0
\(693\) 1.74697e6 1.74697e6i 0.138182 0.138182i
\(694\) 0 0
\(695\) 668506.i 0.0524980i
\(696\) 0 0
\(697\) 6.41236e6i 0.499961i
\(698\) 0 0
\(699\) −7.20112e6 + 7.20112e6i −0.557452 + 0.557452i
\(700\) 0 0
\(701\) −1.03528e7 1.03528e7i −0.795723 0.795723i 0.186695 0.982418i \(-0.440222\pi\)
−0.982418 + 0.186695i \(0.940222\pi\)
\(702\) 0 0
\(703\) −3.11577e7 −2.37781
\(704\) 0 0
\(705\) 3.12636e6 0.236900
\(706\) 0 0
\(707\) −7.69114e6 7.69114e6i −0.578685 0.578685i
\(708\) 0 0
\(709\) −2.20601e6 + 2.20601e6i −0.164813 + 0.164813i −0.784695 0.619882i \(-0.787181\pi\)
0.619882 + 0.784695i \(0.287181\pi\)
\(710\) 0 0
\(711\) 2.40621e6i 0.178508i
\(712\) 0 0
\(713\) 5.49708e6i 0.404957i
\(714\) 0 0
\(715\) 4.09377e6 4.09377e6i 0.299474 0.299474i
\(716\) 0 0
\(717\) 2.01181e6 + 2.01181e6i 0.146147 + 0.146147i
\(718\) 0 0
\(719\) 7.60007e6 0.548271 0.274136 0.961691i \(-0.411608\pi\)
0.274136 + 0.961691i \(0.411608\pi\)
\(720\) 0 0
\(721\) −1.08268e6 −0.0775645
\(722\) 0 0
\(723\) 1.29915e6 + 1.29915e6i 0.0924301 + 0.0924301i
\(724\) 0 0
\(725\) −1.19200e6 + 1.19200e6i −0.0842235 + 0.0842235i
\(726\) 0 0
\(727\) 1.18770e7i 0.833432i 0.909037 + 0.416716i \(0.136819\pi\)
−0.909037 + 0.416716i \(0.863181\pi\)
\(728\) 0 0
\(729\) 1.59494e7i 1.11154i
\(730\) 0 0
\(731\) 1.30892e7 1.30892e7i 0.905985 0.905985i
\(732\) 0 0
\(733\) −1.72162e7 1.72162e7i −1.18352 1.18352i −0.978825 0.204698i \(-0.934379\pi\)
−0.204698 0.978825i \(-0.565621\pi\)
\(734\) 0 0
\(735\) 643711. 0.0439514
\(736\) 0 0
\(737\) 2.34145e7 1.58787
\(738\) 0 0
\(739\) −7.02153e6 7.02153e6i −0.472956 0.472956i 0.429914 0.902870i \(-0.358544\pi\)
−0.902870 + 0.429914i \(0.858544\pi\)
\(740\) 0 0
\(741\) −1.59414e7 + 1.59414e7i −1.06655 + 1.06655i
\(742\) 0 0
\(743\) 3.78191e6i 0.251327i −0.992073 0.125664i \(-0.959894\pi\)
0.992073 0.125664i \(-0.0401060\pi\)
\(744\) 0 0
\(745\) 5.22214e6i 0.344713i
\(746\) 0 0
\(747\) 1.87221e6 1.87221e6i 0.122759 0.122759i
\(748\) 0 0
\(749\) −1.45800e7 1.45800e7i −0.949624 0.949624i
\(750\) 0 0
\(751\) −1.35554e7 −0.877027 −0.438514 0.898725i \(-0.644495\pi\)
−0.438514 + 0.898725i \(0.644495\pi\)
\(752\) 0 0
\(753\) 9.64301e6 0.619762
\(754\) 0 0
\(755\) −1.52199e6 1.52199e6i −0.0971729 0.0971729i
\(756\) 0 0
\(757\) −1.42526e7 + 1.42526e7i −0.903974 + 0.903974i −0.995777 0.0918036i \(-0.970737\pi\)
0.0918036 + 0.995777i \(0.470737\pi\)
\(758\) 0 0
\(759\) 2.84128e7i 1.79023i
\(760\) 0 0
\(761\) 5.64585e6i 0.353401i 0.984265 + 0.176701i \(0.0565424\pi\)
−0.984265 + 0.176701i \(0.943458\pi\)
\(762\) 0 0
\(763\) −1.44587e7 + 1.44587e7i −0.899118 + 0.899118i
\(764\) 0 0
\(765\) −1.30571e6 1.30571e6i −0.0806667 0.0806667i
\(766\) 0 0
\(767\) 1.78798e7 1.09743
\(768\) 0 0
\(769\) 1.87425e7 1.14291 0.571455 0.820633i \(-0.306379\pi\)
0.571455 + 0.820633i \(0.306379\pi\)
\(770\) 0 0
\(771\) 1.88708e7 + 1.88708e7i 1.14329 + 1.14329i
\(772\) 0 0
\(773\) 5.14466e6 5.14466e6i 0.309676 0.309676i −0.535108 0.844784i \(-0.679729\pi\)
0.844784 + 0.535108i \(0.179729\pi\)
\(774\) 0 0
\(775\) 720430.i 0.0430861i
\(776\) 0 0
\(777\) 1.79769e7i 1.06822i
\(778\) 0 0
\(779\) −8.62966e6 + 8.62966e6i −0.509507 + 0.509507i
\(780\) 0 0
\(781\) −3.86892e6 3.86892e6i −0.226967 0.226967i
\(782\) 0 0
\(783\) 1.09546e7 0.638546
\(784\) 0 0
\(785\) 4.99426e6 0.289266
\(786\) 0 0