Properties

Label 1620.3.t.d.1349.2
Level $1620$
Weight $3$
Character 1620.1349
Analytic conductor $44.142$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1620.t (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(44.1418028264\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.154550410641.1
Defining polynomial: \( x^{8} - 15x^{6} + 221x^{4} - 60x^{2} + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: no (minimal twist has level 540)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1349.2
Root \(-3.32360 + 1.91888i\) of defining polynomial
Character \(\chi\) \(=\) 1620.1349
Dual form 1620.3.t.d.269.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.0689865 - 4.99952i) q^{5} +(-2.42096 + 1.39774i) q^{7} +O(q^{10})\) \(q+(0.0689865 - 4.99952i) q^{5} +(-2.42096 + 1.39774i) q^{7} +(-15.7154 + 9.07327i) q^{11} +(-19.9416 - 11.5133i) q^{13} +5.72842 q^{17} +23.1852 q^{19} +(-0.135792 + 0.235199i) q^{23} +(-24.9905 - 0.689799i) q^{25} +(34.4674 - 19.8997i) q^{29} +(-23.6852 + 41.0241i) q^{31} +(6.82104 + 12.2001i) q^{35} +34.8712i q^{37} +(-11.4891 - 6.63325i) q^{41} +(40.4571 - 23.3579i) q^{43} +(20.4568 + 35.4323i) q^{47} +(-20.5926 + 35.6675i) q^{49} +91.3705 q^{53} +(44.2779 + 79.1953i) q^{55} +(68.2773 + 39.4199i) q^{59} +(-15.5926 - 27.0072i) q^{61} +(-58.9366 + 98.9042i) q^{65} +(-5.98970 - 3.45816i) q^{67} +81.5870i q^{71} -106.084i q^{73} +(25.3642 - 43.9321i) q^{77} +(-31.7779 - 55.0409i) q^{79} +(0.142081 + 0.246091i) q^{83} +(0.395183 - 28.6394i) q^{85} +28.5210i q^{89} +64.3705 q^{91} +(1.59947 - 115.915i) q^{95} +(80.4657 - 46.4569i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 3 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 3 q^{5} - 12 q^{17} + 12 q^{19} - 30 q^{23} - 9 q^{25} - 16 q^{31} - 90 q^{35} + 48 q^{47} - 78 q^{49} + 384 q^{53} + 94 q^{55} - 38 q^{61} + 138 q^{65} + 174 q^{77} + 6 q^{79} - 288 q^{83} + 100 q^{85} + 168 q^{91} + 318 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times\).

\(n\) \(811\) \(1297\) \(1541\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{5}{6}\right)\)

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
\(3\) 0 0
\(4\) 0 0
\(5\) 0.0689865 4.99952i 0.0137973 0.999905i
\(6\) 0 0
\(7\) −2.42096 + 1.39774i −0.345852 + 0.199678i −0.662857 0.748746i \(-0.730656\pi\)
0.317005 + 0.948424i \(0.397323\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −15.7154 + 9.07327i −1.42867 + 0.824843i −0.997016 0.0771971i \(-0.975403\pi\)
−0.431653 + 0.902040i \(0.642070\pi\)
\(12\) 0 0
\(13\) −19.9416 11.5133i −1.53397 0.885637i −0.999173 0.0406560i \(-0.987055\pi\)
−0.534796 0.844981i \(-0.679611\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 5.72842 0.336966 0.168483 0.985705i \(-0.446113\pi\)
0.168483 + 0.985705i \(0.446113\pi\)
\(18\) 0 0
\(19\) 23.1852 1.22028 0.610138 0.792295i \(-0.291114\pi\)
0.610138 + 0.792295i \(0.291114\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −0.135792 + 0.235199i −0.00590400 + 0.0102260i −0.868962 0.494878i \(-0.835213\pi\)
0.863058 + 0.505104i \(0.168546\pi\)
\(24\) 0 0
\(25\) −24.9905 0.689799i −0.999619 0.0275920i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 34.4674 19.8997i 1.18853 0.686198i 0.230558 0.973059i \(-0.425945\pi\)
0.957972 + 0.286860i \(0.0926116\pi\)
\(30\) 0 0
\(31\) −23.6852 + 41.0241i −0.764040 + 1.32336i 0.176712 + 0.984263i \(0.443454\pi\)
−0.940752 + 0.339094i \(0.889880\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 6.82104 + 12.2001i 0.194887 + 0.348574i
\(36\) 0 0
\(37\) 34.8712i 0.942465i 0.882009 + 0.471232i \(0.156191\pi\)
−0.882009 + 0.471232i \(0.843809\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −11.4891 6.63325i −0.280223 0.161787i 0.353302 0.935509i \(-0.385059\pi\)
−0.633524 + 0.773723i \(0.718392\pi\)
\(42\) 0 0
\(43\) 40.4571 23.3579i 0.940862 0.543207i 0.0506318 0.998717i \(-0.483877\pi\)
0.890231 + 0.455510i \(0.150543\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 20.4568 + 35.4323i 0.435252 + 0.753878i 0.997316 0.0732153i \(-0.0233260\pi\)
−0.562064 + 0.827093i \(0.689993\pi\)
\(48\) 0 0
\(49\) −20.5926 + 35.6675i −0.420258 + 0.727908i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 91.3705 1.72397 0.861986 0.506932i \(-0.169221\pi\)
0.861986 + 0.506932i \(0.169221\pi\)
\(54\) 0 0
\(55\) 44.2779 + 79.1953i 0.805052 + 1.43991i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 68.2773 + 39.4199i 1.15724 + 0.668134i 0.950641 0.310292i \(-0.100427\pi\)
0.206600 + 0.978425i \(0.433760\pi\)
\(60\) 0 0
\(61\) −15.5926 27.0072i −0.255617 0.442741i 0.709446 0.704760i \(-0.248945\pi\)
−0.965063 + 0.262018i \(0.915612\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −58.9366 + 98.9042i −0.906718 + 1.52160i
\(66\) 0 0
\(67\) −5.98970 3.45816i −0.0893986 0.0516143i 0.454634 0.890678i \(-0.349770\pi\)
−0.544033 + 0.839064i \(0.683103\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 81.5870i 1.14911i 0.818465 + 0.574556i \(0.194825\pi\)
−0.818465 + 0.574556i \(0.805175\pi\)
\(72\) 0 0
\(73\) 106.084i 1.45320i −0.687060 0.726601i \(-0.741099\pi\)
0.687060 0.726601i \(-0.258901\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 25.3642 43.9321i 0.329405 0.570547i
\(78\) 0 0
\(79\) −31.7779 55.0409i −0.402252 0.696720i 0.591746 0.806125i \(-0.298439\pi\)
−0.993997 + 0.109405i \(0.965106\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 0.142081 + 0.246091i 0.00171182 + 0.00296495i 0.866880 0.498517i \(-0.166122\pi\)
−0.865168 + 0.501482i \(0.832788\pi\)
\(84\) 0 0
\(85\) 0.395183 28.6394i 0.00464921 0.336934i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 28.5210i 0.320461i 0.987080 + 0.160230i \(0.0512237\pi\)
−0.987080 + 0.160230i \(0.948776\pi\)
\(90\) 0 0
\(91\) 64.3705 0.707368
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 1.59947 115.915i 0.0168365 1.22016i
\(96\) 0 0
\(97\) 80.4657 46.4569i 0.829543 0.478937i −0.0241531 0.999708i \(-0.507689\pi\)
0.853696 + 0.520771i \(0.174356\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −40.4153 + 23.3338i −0.400151 + 0.231027i −0.686549 0.727083i \(-0.740875\pi\)
0.286398 + 0.958111i \(0.407542\pi\)
\(102\) 0 0
\(103\) 9.68385 + 5.59098i 0.0940180 + 0.0542813i 0.546272 0.837608i \(-0.316047\pi\)
−0.452254 + 0.891889i \(0.649380\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 147.297 1.37661 0.688303 0.725424i \(-0.258356\pi\)
0.688303 + 0.725424i \(0.258356\pi\)
\(108\) 0 0
\(109\) −121.556 −1.11519 −0.557595 0.830113i \(-0.688276\pi\)
−0.557595 + 0.830113i \(0.688276\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −48.8148 + 84.5496i −0.431989 + 0.748227i −0.997045 0.0768260i \(-0.975521\pi\)
0.565056 + 0.825053i \(0.308855\pi\)
\(114\) 0 0
\(115\) 1.16651 + 0.695121i 0.0101436 + 0.00604453i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −13.8683 + 8.00686i −0.116540 + 0.0672845i
\(120\) 0 0
\(121\) 104.148 180.390i 0.860730 1.49083i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −5.17267 + 124.893i −0.0413814 + 0.999143i
\(126\) 0 0
\(127\) 88.6481i 0.698017i −0.937120 0.349008i \(-0.886518\pi\)
0.937120 0.349008i \(-0.113482\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 77.9193 + 44.9867i 0.594804 + 0.343410i 0.766995 0.641653i \(-0.221751\pi\)
−0.172191 + 0.985064i \(0.555085\pi\)
\(132\) 0 0
\(133\) −56.1306 + 32.4070i −0.422035 + 0.243662i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 114.963 + 199.122i 0.839147 + 1.45345i 0.890609 + 0.454770i \(0.150279\pi\)
−0.0514620 + 0.998675i \(0.516388\pi\)
\(138\) 0 0
\(139\) −28.8148 + 49.9086i −0.207300 + 0.359055i −0.950863 0.309611i \(-0.899801\pi\)
0.743563 + 0.668666i \(0.233134\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 417.852 2.92205
\(144\) 0 0
\(145\) −97.1115 173.693i −0.669734 1.19788i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −9.64205 5.56684i −0.0647117 0.0373613i 0.467295 0.884101i \(-0.345229\pi\)
−0.532007 + 0.846740i \(0.678562\pi\)
\(150\) 0 0
\(151\) 11.0926 + 19.2130i 0.0734611 + 0.127238i 0.900416 0.435030i \(-0.143262\pi\)
−0.826955 + 0.562268i \(0.809929\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 203.467 + 121.245i 1.31269 + 0.782226i
\(156\) 0 0
\(157\) 195.148 + 112.669i 1.24298 + 0.717635i 0.969700 0.244299i \(-0.0785579\pi\)
0.273281 + 0.961934i \(0.411891\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0.759209i 0.00471559i
\(162\) 0 0
\(163\) 302.948i 1.85858i 0.369352 + 0.929290i \(0.379580\pi\)
−0.369352 + 0.929290i \(0.620420\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 119.334 206.692i 0.714573 1.23768i −0.248552 0.968619i \(-0.579955\pi\)
0.963124 0.269057i \(-0.0867121\pi\)
\(168\) 0 0
\(169\) 180.611 + 312.828i 1.06871 + 1.85105i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −54.4011 94.2254i −0.314457 0.544656i 0.664865 0.746964i \(-0.268489\pi\)
−0.979322 + 0.202308i \(0.935156\pi\)
\(174\) 0 0
\(175\) 61.4652 33.2603i 0.351230 0.190059i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 168.054i 0.938849i 0.882973 + 0.469425i \(0.155539\pi\)
−0.882973 + 0.469425i \(0.844461\pi\)
\(180\) 0 0
\(181\) −154.297 −0.852468 −0.426234 0.904613i \(-0.640160\pi\)
−0.426234 + 0.904613i \(0.640160\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 174.339 + 2.40564i 0.942375 + 0.0130035i
\(186\) 0 0
\(187\) −90.0241 + 51.9755i −0.481412 + 0.277944i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −134.175 + 77.4662i −0.702489 + 0.405582i −0.808274 0.588807i \(-0.799598\pi\)
0.105785 + 0.994389i \(0.466264\pi\)
\(192\) 0 0
\(193\) 55.4313 + 32.0033i 0.287209 + 0.165820i 0.636683 0.771126i \(-0.280306\pi\)
−0.349473 + 0.936946i \(0.613640\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 9.56832 0.0485702 0.0242851 0.999705i \(-0.492269\pi\)
0.0242851 + 0.999705i \(0.492269\pi\)
\(198\) 0 0
\(199\) −117.815 −0.592034 −0.296017 0.955183i \(-0.595658\pi\)
−0.296017 + 0.955183i \(0.595658\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −55.6295 + 96.3531i −0.274037 + 0.474646i
\(204\) 0 0
\(205\) −33.9557 + 56.9826i −0.165637 + 0.277964i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −364.365 + 210.366i −1.74337 + 1.00654i
\(210\) 0 0
\(211\) 24.4074 42.2748i 0.115675 0.200355i −0.802375 0.596821i \(-0.796430\pi\)
0.918049 + 0.396466i \(0.129764\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −113.987 203.878i −0.530174 0.948268i
\(216\) 0 0
\(217\) 132.424i 0.610247i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −114.234 65.9529i −0.516895 0.298429i
\(222\) 0 0
\(223\) −276.887 + 159.861i −1.24164 + 0.716864i −0.969429 0.245372i \(-0.921090\pi\)
−0.272216 + 0.962236i \(0.587756\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 9.13579 + 15.8237i 0.0402458 + 0.0697077i 0.885447 0.464741i \(-0.153853\pi\)
−0.845201 + 0.534449i \(0.820519\pi\)
\(228\) 0 0
\(229\) −67.0369 + 116.111i −0.292737 + 0.507036i −0.974456 0.224578i \(-0.927900\pi\)
0.681719 + 0.731615i \(0.261233\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 284.173 1.21963 0.609813 0.792546i \(-0.291245\pi\)
0.609813 + 0.792546i \(0.291245\pi\)
\(234\) 0 0
\(235\) 178.556 99.8301i 0.759812 0.424809i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −179.068 103.385i −0.749237 0.432572i 0.0761810 0.997094i \(-0.475727\pi\)
−0.825418 + 0.564522i \(0.809061\pi\)
\(240\) 0 0
\(241\) 81.3336 + 140.874i 0.337484 + 0.584539i 0.983959 0.178396i \(-0.0570908\pi\)
−0.646475 + 0.762935i \(0.723757\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 176.900 + 105.414i 0.722040 + 0.430261i
\(246\) 0 0
\(247\) −462.351 266.938i −1.87187 1.08072i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 347.387i 1.38401i 0.721893 + 0.692005i \(0.243272\pi\)
−0.721893 + 0.692005i \(0.756728\pi\)
\(252\) 0 0
\(253\) 4.92831i 0.0194795i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −10.5189 + 18.2192i −0.0409294 + 0.0708919i −0.885764 0.464135i \(-0.846365\pi\)
0.844835 + 0.535027i \(0.179699\pi\)
\(258\) 0 0
\(259\) −48.7410 84.4219i −0.188189 0.325953i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −107.728 186.591i −0.409614 0.709472i 0.585233 0.810865i \(-0.301003\pi\)
−0.994846 + 0.101394i \(0.967670\pi\)
\(264\) 0 0
\(265\) 6.30333 456.809i 0.0237861 1.72381i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 180.237i 0.670024i 0.942214 + 0.335012i \(0.108740\pi\)
−0.942214 + 0.335012i \(0.891260\pi\)
\(270\) 0 0
\(271\) 231.741 0.855133 0.427566 0.903984i \(-0.359371\pi\)
0.427566 + 0.903984i \(0.359371\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 398.993 215.905i 1.45088 0.785109i
\(276\) 0 0
\(277\) −91.4227 + 52.7829i −0.330046 + 0.190552i −0.655862 0.754881i \(-0.727694\pi\)
0.325816 + 0.945433i \(0.394361\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 436.993 252.298i 1.55514 0.897859i 0.557426 0.830226i \(-0.311789\pi\)
0.997710 0.0676323i \(-0.0215445\pi\)
\(282\) 0 0
\(283\) 131.306 + 75.8095i 0.463978 + 0.267878i 0.713716 0.700436i \(-0.247011\pi\)
−0.249737 + 0.968314i \(0.580344\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 37.0863 0.129221
\(288\) 0 0
\(289\) −256.185 −0.886454
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −274.519 + 475.481i −0.936924 + 1.62280i −0.165759 + 0.986166i \(0.553007\pi\)
−0.771166 + 0.636634i \(0.780326\pi\)
\(294\) 0 0
\(295\) 201.791 338.634i 0.684037 1.14791i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 5.41582 3.12682i 0.0181131 0.0104576i
\(300\) 0 0
\(301\) −65.2967 + 113.097i −0.216933 + 0.375738i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −136.099 + 76.0926i −0.446226 + 0.249484i
\(306\) 0 0
\(307\) 146.401i 0.476876i 0.971158 + 0.238438i \(0.0766355\pi\)
−0.971158 + 0.238438i \(0.923365\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 422.468 + 243.912i 1.35842 + 0.784282i 0.989410 0.145144i \(-0.0463647\pi\)
0.369006 + 0.929427i \(0.379698\pi\)
\(312\) 0 0
\(313\) 94.9915 54.8433i 0.303487 0.175218i −0.340521 0.940237i \(-0.610604\pi\)
0.644008 + 0.765018i \(0.277270\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 181.784 + 314.859i 0.573452 + 0.993247i 0.996208 + 0.0870039i \(0.0277293\pi\)
−0.422756 + 0.906243i \(0.638937\pi\)
\(318\) 0 0
\(319\) −361.111 + 625.463i −1.13201 + 1.96070i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 132.815 0.411191
\(324\) 0 0
\(325\) 490.408 + 301.478i 1.50895 + 0.927625i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −99.0505 57.1868i −0.301065 0.173820i
\(330\) 0 0
\(331\) −150.111 260.001i −0.453509 0.785501i 0.545092 0.838376i \(-0.316495\pi\)
−0.998601 + 0.0528755i \(0.983161\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −17.7023 + 29.7071i −0.0528428 + 0.0886779i
\(336\) 0 0
\(337\) 323.334 + 186.677i 0.959447 + 0.553937i 0.896003 0.444049i \(-0.146458\pi\)
0.0634441 + 0.997985i \(0.479792\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 859.610i 2.52085i
\(342\) 0 0
\(343\) 252.112i 0.735020i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −8.72213 + 15.1072i −0.0251358 + 0.0435365i −0.878320 0.478074i \(-0.841335\pi\)
0.853184 + 0.521610i \(0.174668\pi\)
\(348\) 0 0
\(349\) −117.075 202.779i −0.335457 0.581029i 0.648115 0.761542i \(-0.275558\pi\)
−0.983573 + 0.180513i \(0.942224\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −190.642 330.202i −0.540063 0.935416i −0.998900 0.0468954i \(-0.985067\pi\)
0.458837 0.888520i \(-0.348266\pi\)
\(354\) 0 0
\(355\) 407.896 + 5.62840i 1.14900 + 0.0158546i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 222.024i 0.618451i −0.950989 0.309226i \(-0.899930\pi\)
0.950989 0.309226i \(-0.100070\pi\)
\(360\) 0 0
\(361\) 176.556 0.489074
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −530.368 7.31834i −1.45306 0.0200502i
\(366\) 0 0
\(367\) 389.023 224.602i 1.06001 0.611995i 0.134573 0.990904i \(-0.457034\pi\)
0.925434 + 0.378908i \(0.123700\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −221.205 + 127.713i −0.596239 + 0.344239i
\(372\) 0 0
\(373\) −278.932 161.041i −0.747806 0.431746i 0.0770948 0.997024i \(-0.475436\pi\)
−0.824901 + 0.565278i \(0.808769\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −916.446 −2.43089
\(378\) 0 0
\(379\) −216.074 −0.570115 −0.285058 0.958510i \(-0.592013\pi\)
−0.285058 + 0.958510i \(0.592013\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 186.988 323.873i 0.488220 0.845622i −0.511688 0.859171i \(-0.670980\pi\)
0.999908 + 0.0135493i \(0.00431302\pi\)
\(384\) 0 0
\(385\) −217.890 129.840i −0.565948 0.337246i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 193.217 111.554i 0.496702 0.286771i −0.230648 0.973037i \(-0.574085\pi\)
0.727351 + 0.686266i \(0.240751\pi\)
\(390\) 0 0
\(391\) −0.777873 + 1.34731i −0.00198944 + 0.00344582i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −277.370 + 155.077i −0.702204 + 0.392600i
\(396\) 0 0
\(397\) 610.535i 1.53787i 0.639325 + 0.768936i \(0.279214\pi\)
−0.639325 + 0.768936i \(0.720786\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −356.319 205.721i −0.888575 0.513019i −0.0150992 0.999886i \(-0.504806\pi\)
−0.873476 + 0.486867i \(0.838140\pi\)
\(402\) 0 0
\(403\) 944.643 545.390i 2.34403 1.35333i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −316.396 548.013i −0.777385 1.34647i
\(408\) 0 0
\(409\) −295.315 + 511.500i −0.722041 + 1.25061i 0.238139 + 0.971231i \(0.423462\pi\)
−0.960180 + 0.279381i \(0.909871\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −220.396 −0.533646
\(414\) 0 0
\(415\) 1.24014 0.693359i 0.00298829 0.00167074i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 207.462 + 119.778i 0.495135 + 0.285867i 0.726702 0.686952i \(-0.241052\pi\)
−0.231567 + 0.972819i \(0.574385\pi\)
\(420\) 0 0
\(421\) −296.704 513.907i −0.704760 1.22068i −0.966778 0.255618i \(-0.917721\pi\)
0.262018 0.965063i \(-0.415612\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −143.156 3.95146i −0.336837 0.00929754i
\(426\) 0 0
\(427\) 75.4983 + 43.5890i 0.176811 + 0.102082i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 436.566i 1.01291i 0.862265 + 0.506457i \(0.169045\pi\)
−0.862265 + 0.506457i \(0.830955\pi\)
\(432\) 0 0
\(433\) 231.736i 0.535187i −0.963532 0.267593i \(-0.913772\pi\)
0.963532 0.267593i \(-0.0862284\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −3.14837 + 5.45314i −0.00720451 + 0.0124786i
\(438\) 0 0
\(439\) 209.611 + 363.058i 0.477475 + 0.827011i 0.999667 0.0258173i \(-0.00821881\pi\)
−0.522192 + 0.852828i \(0.674885\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −223.260 386.697i −0.503973 0.872906i −0.999989 0.00459325i \(-0.998538\pi\)
0.496017 0.868313i \(-0.334795\pi\)
\(444\) 0 0
\(445\) 142.591 + 1.96756i 0.320430 + 0.00442149i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 495.776i 1.10418i −0.833785 0.552089i \(-0.813831\pi\)
0.833785 0.552089i \(-0.186169\pi\)
\(450\) 0 0
\(451\) 240.741 0.533794
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 4.44069 321.822i 0.00975976 0.707301i
\(456\) 0 0
\(457\) −591.810 + 341.681i −1.29499 + 0.747662i −0.979534 0.201279i \(-0.935490\pi\)
−0.315454 + 0.948941i \(0.602157\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −346.521 + 200.064i −0.751672 + 0.433978i −0.826298 0.563234i \(-0.809557\pi\)
0.0746257 + 0.997212i \(0.476224\pi\)
\(462\) 0 0
\(463\) −273.892 158.132i −0.591559 0.341537i 0.174155 0.984718i \(-0.444281\pi\)
−0.765714 + 0.643181i \(0.777614\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 419.741 0.898803 0.449401 0.893330i \(-0.351637\pi\)
0.449401 + 0.893330i \(0.351637\pi\)
\(468\) 0 0
\(469\) 19.3345 0.0412249
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −423.865 + 734.156i −0.896121 + 1.55213i
\(474\) 0 0
\(475\) −579.411 15.9932i −1.21981 0.0336698i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 731.766 422.485i 1.52769 0.882015i 0.528237 0.849097i \(-0.322853\pi\)
0.999458 0.0329177i \(-0.0104799\pi\)
\(480\) 0 0
\(481\) 401.482 695.387i 0.834682 1.44571i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −226.711 405.495i −0.467446 0.836072i
\(486\) 0 0
\(487\) 546.384i 1.12194i −0.827837 0.560969i \(-0.810429\pi\)
0.827837 0.560969i \(-0.189571\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −560.713 323.728i −1.14198 0.659324i −0.195062 0.980791i \(-0.562491\pi\)
−0.946921 + 0.321467i \(0.895824\pi\)
\(492\) 0 0
\(493\) 197.443 113.994i 0.400494 0.231225i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −114.038 197.519i −0.229452 0.397423i
\(498\) 0 0
\(499\) −291.407 + 504.732i −0.583983 + 1.01149i 0.411019 + 0.911627i \(0.365173\pi\)
−0.995001 + 0.0998608i \(0.968160\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −752.520 −1.49606 −0.748032 0.663663i \(-0.769001\pi\)
−0.748032 + 0.663663i \(0.769001\pi\)
\(504\) 0 0
\(505\) 113.870 + 203.667i 0.225484 + 0.403301i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 252.479 + 145.769i 0.496030 + 0.286383i 0.727073 0.686560i \(-0.240880\pi\)
−0.231042 + 0.972944i \(0.574214\pi\)
\(510\) 0 0
\(511\) 148.278 + 256.825i 0.290172 + 0.502593i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 28.6203 48.0290i 0.0555733 0.0932601i
\(516\) 0 0
\(517\) −642.973 371.221i −1.24366 0.718028i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 137.690i 0.264280i 0.991231 + 0.132140i \(0.0421848\pi\)
−0.991231 + 0.132140i \(0.957815\pi\)
\(522\) 0 0
\(523\) 330.987i 0.632862i −0.948616 0.316431i \(-0.897515\pi\)
0.948616 0.316431i \(-0.102485\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −135.679 + 235.003i −0.257455 + 0.445926i
\(528\) 0 0
\(529\) 264.463 + 458.064i 0.499930 + 0.865905i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 152.741 + 264.555i 0.286568 + 0.496351i
\(534\) 0 0
\(535\) 10.1615 736.414i 0.0189934 1.37647i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 747.370i 1.38659i
\(540\) 0 0
\(541\) 556.593 1.02882 0.514412 0.857543i \(-0.328010\pi\)
0.514412 + 0.857543i \(0.328010\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −8.38570 + 607.721i −0.0153866 + 1.11508i
\(546\) 0 0
\(547\) −402.849 + 232.585i −0.736470 + 0.425201i −0.820784 0.571238i \(-0.806463\pi\)
0.0843144 + 0.996439i \(0.473130\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 799.135 461.381i 1.45034 0.837351i
\(552\) 0 0
\(553\) 153.866 + 88.8347i 0.278239 + 0.160641i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −1059.37 −1.90192 −0.950962 0.309306i \(-0.899903\pi\)
−0.950962 + 0.309306i \(0.899903\pi\)
\(558\) 0 0
\(559\) −1075.70 −1.92434
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 193.080 334.424i 0.342949 0.594004i −0.642030 0.766679i \(-0.721908\pi\)
0.984979 + 0.172675i \(0.0552410\pi\)
\(564\) 0 0
\(565\) 419.340 + 249.883i 0.742195 + 0.442271i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 594.147 343.031i 1.04420 0.602866i 0.123176 0.992385i \(-0.460692\pi\)
0.921019 + 0.389518i \(0.127359\pi\)
\(570\) 0 0
\(571\) 410.816 711.554i 0.719467 1.24615i −0.241744 0.970340i \(-0.577720\pi\)
0.961211 0.275813i \(-0.0889471\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 3.55575 5.78406i 0.00618390 0.0100592i
\(576\) 0 0
\(577\) 183.840i 0.318613i 0.987229 + 0.159306i \(0.0509258\pi\)
−0.987229 + 0.159306i \(0.949074\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −0.687945 0.397185i −0.00118407 0.000683623i
\(582\) 0 0
\(583\) −1435.92 + 829.029i −2.46299 + 1.42201i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −160.203 277.480i −0.272919 0.472709i 0.696689 0.717373i \(-0.254656\pi\)
−0.969608 + 0.244664i \(0.921322\pi\)
\(588\) 0 0
\(589\) −549.148 + 951.153i −0.932340 + 1.61486i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −1061.34 −1.78977 −0.894887 0.446292i \(-0.852744\pi\)
−0.894887 + 0.446292i \(0.852744\pi\)
\(594\) 0 0
\(595\) 39.0738 + 69.8872i 0.0656702 + 0.117457i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 846.155 + 488.528i 1.41261 + 0.815573i 0.995634 0.0933433i \(-0.0297554\pi\)
0.416979 + 0.908916i \(0.363089\pi\)
\(600\) 0 0
\(601\) 130.908 + 226.740i 0.217817 + 0.377271i 0.954140 0.299359i \(-0.0967730\pi\)
−0.736323 + 0.676630i \(0.763440\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −894.681 533.137i −1.47881 0.881218i
\(606\) 0 0
\(607\) 579.203 + 334.403i 0.954206 + 0.550911i 0.894385 0.447298i \(-0.147614\pi\)
0.0598212 + 0.998209i \(0.480947\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 942.101i 1.54190i
\(612\) 0 0
\(613\) 220.119i 0.359086i 0.983750 + 0.179543i \(0.0574618\pi\)
−0.983750 + 0.179543i \(0.942538\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −160.531 + 278.049i −0.260181 + 0.450646i −0.966290 0.257457i \(-0.917115\pi\)
0.706109 + 0.708103i \(0.250449\pi\)
\(618\) 0 0
\(619\) 445.593 + 771.791i 0.719860 + 1.24683i 0.961055 + 0.276358i \(0.0891275\pi\)
−0.241195 + 0.970477i \(0.577539\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −39.8651 69.0483i −0.0639889 0.110832i
\(624\) 0 0
\(625\) 624.048 + 34.4768i 0.998477 + 0.0551629i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 199.757i 0.317578i
\(630\) 0 0
\(631\) −583.669 −0.924990 −0.462495 0.886622i \(-0.653046\pi\)
−0.462495 + 0.886622i \(0.653046\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −443.198 6.11552i −0.697950 0.00963074i
\(636\) 0 0
\(637\) 821.300 474.178i 1.28932 0.744392i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −603.006 + 348.146i −0.940727 + 0.543129i −0.890188 0.455593i \(-0.849427\pi\)
−0.0505391 + 0.998722i \(0.516094\pi\)
\(642\) 0 0
\(643\) 694.262 + 400.832i 1.07972 + 0.623378i 0.930822 0.365474i \(-0.119093\pi\)
0.148901 + 0.988852i \(0.452426\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 216.221 0.334191 0.167095 0.985941i \(-0.446561\pi\)
0.167095 + 0.985941i \(0.446561\pi\)
\(648\) 0 0
\(649\) −1430.67 −2.20442
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 219.401 380.014i 0.335989 0.581951i −0.647685 0.761908i \(-0.724263\pi\)
0.983674 + 0.179958i \(0.0575960\pi\)
\(654\) 0 0
\(655\) 230.288 386.456i 0.351584 0.590009i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −317.063 + 183.056i −0.481127 + 0.277779i −0.720886 0.693054i \(-0.756265\pi\)
0.239759 + 0.970832i \(0.422932\pi\)
\(660\) 0 0
\(661\) −79.0377 + 136.897i −0.119573 + 0.207106i −0.919599 0.392859i \(-0.871486\pi\)
0.800026 + 0.599966i \(0.204819\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 158.148 + 282.862i 0.237816 + 0.425357i
\(666\) 0 0
\(667\) 10.8089i 0.0162052i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 490.087 + 282.952i 0.730384 + 0.421687i
\(672\) 0 0
\(673\) −561.683 + 324.288i −0.834595 + 0.481854i −0.855423 0.517929i \(-0.826703\pi\)
0.0208282 + 0.999783i \(0.493370\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 101.173 + 175.236i 0.149443 + 0.258842i 0.931022 0.364964i \(-0.118919\pi\)
−0.781579 + 0.623806i \(0.785585\pi\)
\(678\) 0 0
\(679\) −129.870 + 224.941i −0.191266 + 0.331283i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 173.829 0.254508 0.127254 0.991870i \(-0.459384\pi\)
0.127254 + 0.991870i \(0.459384\pi\)
\(684\) 0 0
\(685\) 1003.45 561.024i 1.46488 0.819013i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −1822.07 1051.97i −2.64452 1.52681i
\(690\) 0 0
\(691\) 423.371 + 733.301i 0.612694 + 1.06122i 0.990784 + 0.135448i \(0.0432474\pi\)
−0.378091 + 0.925769i \(0.623419\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 247.531 + 147.503i 0.356160 + 0.212235i
\(696\) 0 0
\(697\) −65.8145 37.9980i −0.0944254 0.0545165i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 72.2614i 0.103083i 0.998671 + 0.0515416i \(0.0164135\pi\)
−0.998671 + 0.0515416i \(0.983587\pi\)
\(702\) 0 0
\(703\) 808.497i 1.15007i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 65.2293 112.980i 0.0922621 0.159803i
\(708\) 0 0
\(709\) −143.779 249.032i −0.202791 0.351244i 0.746636 0.665233i \(-0.231668\pi\)
−0.949427 + 0.313989i \(0.898334\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −6.43253 11.1415i −0.00902178 0.0156262i
\(714\) 0 0
\(715\) 28.8262 2089.06i 0.0403163 2.92177i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 1015.27i 1.41205i 0.708185 + 0.706027i \(0.249514\pi\)
−0.708185 + 0.706027i \(0.750486\pi\)
\(720\) 0 0
\(721\) −31.2590 −0.0433551
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −875.083 + 473.529i −1.20701 + 0.653143i
\(726\) 0 0
\(727\) −269.696 + 155.709i −0.370971 + 0.214180i −0.673883 0.738838i \(-0.735375\pi\)
0.302911 + 0.953019i \(0.402041\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 231.755 133.804i 0.317038 0.183042i
\(732\) 0 0
\(733\) 278.035 + 160.523i 0.379310 + 0.218995i 0.677518 0.735506i \(-0.263055\pi\)
−0.298208 + 0.954501i \(0.596389\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 125.507 0.170295
\(738\) 0 0
\(739\) −657.185 −0.889290 −0.444645 0.895707i \(-0.646670\pi\)
−0.444645 + 0.895707i \(0.646670\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 512.482 887.645i 0.689747 1.19468i −0.282173 0.959364i \(-0.591055\pi\)
0.971920 0.235313i \(-0.0756116\pi\)
\(744\) 0 0
\(745\) −28.4967 + 47.8216i −0.0382506 + 0.0641901i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −356.600 + 205.883i −0.476101 + 0.274877i
\(750\) 0 0
\(751\) 31.5738 54.6874i 0.0420423 0.0728194i −0.844239 0.535968i \(-0.819947\pi\)
0.886281 + 0.463148i \(0.153280\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 96.8210 54.1324i 0.128240 0.0716986i
\(756\) 0 0
\(757\) 1452.21i 1.91837i −0.282781 0.959185i \(-0.591257\pi\)
0.282781 0.959185i \(-0.408743\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 422.468 + 243.912i 0.555148 + 0.320515i 0.751196 0.660079i \(-0.229477\pi\)
−0.196048 + 0.980594i \(0.562811\pi\)
\(762\) 0 0
\(763\) 294.282 169.904i 0.385691 0.222679i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −907.705 1572.19i −1.18345 2.04979i
\(768\) 0 0
\(769\) −338.574 + 586.427i −0.440278 + 0.762584i −0.997710 0.0676389i \(-0.978453\pi\)
0.557432 + 0.830223i \(0.311787\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −949.926 −1.22888 −0.614441 0.788963i \(-0.710619\pi\)
−0.614441 + 0.788963i \(0.710619\pi\)
\(774\) 0 0
\(775\) 620.204 1008.87i 0.800263 1.30177i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −266.378 153.794i −0.341949 0.197424i
\(780\) 0 0
\(781\) −740.261 1282.17i −0.947837 1.64170i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 576.752 967.874i 0.734717 1.23296i
\(786\) 0 0
\(787\) 991.018 + 572.164i 1.25923 + 0.727020i 0.972926 0.231118i \(-0.0742383\pi\)
0.286309 + 0.958137i \(0.407572\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 272.922i 0.345034i
\(792\) 0 0
\(793\) 718.089i 0.905535i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −325.550 + 563.870i −0.408470 + 0.707490i −0.994718 0.102641i \(-0.967271\pi\)
0.586249 + 0.810131i \(0.300604\pi\)
\(798\) 0 0
\(799\) 117.185 + 202.971i 0.146665 + 0.254031i
\(800\) 0 0
\(801\) 0 0