Properties

Label 1800.2.k.m.901.4
Level $1800$
Weight $2$
Character 1800.901
Analytic conductor $14.373$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1800.k (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(14.3730723638\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{-3})\)
Defining polynomial: \( x^{4} - 2x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 40)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 901.4
Root \(-1.22474 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 1800.901
Dual form 1800.2.k.m.901.3

$q$-expansion

\(f(q)\) \(=\) \(q+(1.22474 + 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +2.44949 q^{7} +2.82843i q^{8} +O(q^{10})\) \(q+(1.22474 + 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +2.44949 q^{7} +2.82843i q^{8} +3.46410i q^{11} +(3.00000 + 1.73205i) q^{14} +(-2.00000 + 3.46410i) q^{16} +4.89898 q^{17} -3.46410i q^{19} +(-2.44949 + 4.24264i) q^{22} -2.44949 q^{23} +(2.44949 + 4.24264i) q^{28} +4.00000 q^{31} +(-4.89898 + 2.82843i) q^{32} +(6.00000 + 3.46410i) q^{34} +8.48528i q^{37} +(2.44949 - 4.24264i) q^{38} +4.24264i q^{43} +(-6.00000 + 3.46410i) q^{44} +(-3.00000 - 1.73205i) q^{46} -7.34847 q^{47} -1.00000 q^{49} -5.65685i q^{53} +6.92820i q^{56} -10.3923i q^{59} +3.46410i q^{61} +(4.89898 + 2.82843i) q^{62} -8.00000 q^{64} +4.24264i q^{67} +(4.89898 + 8.48528i) q^{68} +12.0000 q^{71} +4.89898 q^{73} +(-6.00000 + 10.3923i) q^{74} +(6.00000 - 3.46410i) q^{76} +8.48528i q^{77} +4.00000 q^{79} +9.89949i q^{83} +(-3.00000 + 5.19615i) q^{86} -9.79796 q^{88} +6.00000 q^{89} +(-2.44949 - 4.24264i) q^{92} +(-9.00000 - 5.19615i) q^{94} +4.89898 q^{97} +(-1.22474 - 0.707107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 4 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 4 q^{4} + 12 q^{14} - 8 q^{16} + 16 q^{31} + 24 q^{34} - 24 q^{44} - 12 q^{46} - 4 q^{49} - 32 q^{64} + 48 q^{71} - 24 q^{74} + 24 q^{76} + 16 q^{79} - 12 q^{86} + 24 q^{89} - 36 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1800\mathbb{Z}\right)^\times\).

\(n\) \(577\) \(901\) \(1001\) \(1351\)
\(\chi(n)\) \(1\) \(-1\) \(1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.22474 + 0.707107i 0.866025 + 0.500000i
\(3\) 0 0
\(4\) 1.00000 + 1.73205i 0.500000 + 0.866025i
\(5\) 0 0
\(6\) 0 0
\(7\) 2.44949 0.925820 0.462910 0.886405i \(-0.346805\pi\)
0.462910 + 0.886405i \(0.346805\pi\)
\(8\) 2.82843i 1.00000i
\(9\) 0 0
\(10\) 0 0
\(11\) 3.46410i 1.04447i 0.852803 + 0.522233i \(0.174901\pi\)
−0.852803 + 0.522233i \(0.825099\pi\)
\(12\) 0 0
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 3.00000 + 1.73205i 0.801784 + 0.462910i
\(15\) 0 0
\(16\) −2.00000 + 3.46410i −0.500000 + 0.866025i
\(17\) 4.89898 1.18818 0.594089 0.804400i \(-0.297513\pi\)
0.594089 + 0.804400i \(0.297513\pi\)
\(18\) 0 0
\(19\) 3.46410i 0.794719i −0.917663 0.397360i \(-0.869927\pi\)
0.917663 0.397360i \(-0.130073\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −2.44949 + 4.24264i −0.522233 + 0.904534i
\(23\) −2.44949 −0.510754 −0.255377 0.966842i \(-0.582200\pi\)
−0.255377 + 0.966842i \(0.582200\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 0 0
\(28\) 2.44949 + 4.24264i 0.462910 + 0.801784i
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) 4.00000 0.718421 0.359211 0.933257i \(-0.383046\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(32\) −4.89898 + 2.82843i −0.866025 + 0.500000i
\(33\) 0 0
\(34\) 6.00000 + 3.46410i 1.02899 + 0.594089i
\(35\) 0 0
\(36\) 0 0
\(37\) 8.48528i 1.39497i 0.716599 + 0.697486i \(0.245698\pi\)
−0.716599 + 0.697486i \(0.754302\pi\)
\(38\) 2.44949 4.24264i 0.397360 0.688247i
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) 0 0
\(43\) 4.24264i 0.646997i 0.946229 + 0.323498i \(0.104859\pi\)
−0.946229 + 0.323498i \(0.895141\pi\)
\(44\) −6.00000 + 3.46410i −0.904534 + 0.522233i
\(45\) 0 0
\(46\) −3.00000 1.73205i −0.442326 0.255377i
\(47\) −7.34847 −1.07188 −0.535942 0.844255i \(-0.680044\pi\)
−0.535942 + 0.844255i \(0.680044\pi\)
\(48\) 0 0
\(49\) −1.00000 −0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 5.65685i 0.777029i −0.921443 0.388514i \(-0.872988\pi\)
0.921443 0.388514i \(-0.127012\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 6.92820i 0.925820i
\(57\) 0 0
\(58\) 0 0
\(59\) 10.3923i 1.35296i −0.736460 0.676481i \(-0.763504\pi\)
0.736460 0.676481i \(-0.236496\pi\)
\(60\) 0 0
\(61\) 3.46410i 0.443533i 0.975100 + 0.221766i \(0.0711822\pi\)
−0.975100 + 0.221766i \(0.928818\pi\)
\(62\) 4.89898 + 2.82843i 0.622171 + 0.359211i
\(63\) 0 0
\(64\) −8.00000 −1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) 4.24264i 0.518321i 0.965834 + 0.259161i \(0.0834459\pi\)
−0.965834 + 0.259161i \(0.916554\pi\)
\(68\) 4.89898 + 8.48528i 0.594089 + 1.02899i
\(69\) 0 0
\(70\) 0 0
\(71\) 12.0000 1.42414 0.712069 0.702109i \(-0.247758\pi\)
0.712069 + 0.702109i \(0.247758\pi\)
\(72\) 0 0
\(73\) 4.89898 0.573382 0.286691 0.958023i \(-0.407445\pi\)
0.286691 + 0.958023i \(0.407445\pi\)
\(74\) −6.00000 + 10.3923i −0.697486 + 1.20808i
\(75\) 0 0
\(76\) 6.00000 3.46410i 0.688247 0.397360i
\(77\) 8.48528i 0.966988i
\(78\) 0 0
\(79\) 4.00000 0.450035 0.225018 0.974355i \(-0.427756\pi\)
0.225018 + 0.974355i \(0.427756\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 9.89949i 1.08661i 0.839535 + 0.543305i \(0.182827\pi\)
−0.839535 + 0.543305i \(0.817173\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −3.00000 + 5.19615i −0.323498 + 0.560316i
\(87\) 0 0
\(88\) −9.79796 −1.04447
\(89\) 6.00000 0.635999 0.317999 0.948091i \(-0.396989\pi\)
0.317999 + 0.948091i \(0.396989\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −2.44949 4.24264i −0.255377 0.442326i
\(93\) 0 0
\(94\) −9.00000 5.19615i −0.928279 0.535942i
\(95\) 0 0
\(96\) 0 0
\(97\) 4.89898 0.497416 0.248708 0.968579i \(-0.419994\pi\)
0.248708 + 0.968579i \(0.419994\pi\)
\(98\) −1.22474 0.707107i −0.123718 0.0714286i
\(99\) 0 0
\(100\) 0 0
\(101\) 13.8564i 1.37876i −0.724398 0.689382i \(-0.757882\pi\)
0.724398 0.689382i \(-0.242118\pi\)
\(102\) 0 0
\(103\) −7.34847 −0.724066 −0.362033 0.932165i \(-0.617917\pi\)
−0.362033 + 0.932165i \(0.617917\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 4.00000 6.92820i 0.388514 0.672927i
\(107\) 1.41421i 0.136717i 0.997661 + 0.0683586i \(0.0217762\pi\)
−0.997661 + 0.0683586i \(0.978224\pi\)
\(108\) 0 0
\(109\) 3.46410i 0.331801i 0.986143 + 0.165900i \(0.0530530\pi\)
−0.986143 + 0.165900i \(0.946947\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −4.89898 + 8.48528i −0.462910 + 0.801784i
\(113\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 7.34847 12.7279i 0.676481 1.17170i
\(119\) 12.0000 1.10004
\(120\) 0 0
\(121\) −1.00000 −0.0909091
\(122\) −2.44949 + 4.24264i −0.221766 + 0.384111i
\(123\) 0 0
\(124\) 4.00000 + 6.92820i 0.359211 + 0.622171i
\(125\) 0 0
\(126\) 0 0
\(127\) −17.1464 −1.52150 −0.760750 0.649045i \(-0.775169\pi\)
−0.760750 + 0.649045i \(0.775169\pi\)
\(128\) −9.79796 5.65685i −0.866025 0.500000i
\(129\) 0 0
\(130\) 0 0
\(131\) 3.46410i 0.302660i −0.988483 0.151330i \(-0.951644\pi\)
0.988483 0.151330i \(-0.0483556\pi\)
\(132\) 0 0
\(133\) 8.48528i 0.735767i
\(134\) −3.00000 + 5.19615i −0.259161 + 0.448879i
\(135\) 0 0
\(136\) 13.8564i 1.18818i
\(137\) −9.79796 −0.837096 −0.418548 0.908195i \(-0.637461\pi\)
−0.418548 + 0.908195i \(0.637461\pi\)
\(138\) 0 0
\(139\) 10.3923i 0.881464i −0.897639 0.440732i \(-0.854719\pi\)
0.897639 0.440732i \(-0.145281\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 14.6969 + 8.48528i 1.23334 + 0.712069i
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) 6.00000 + 3.46410i 0.496564 + 0.286691i
\(147\) 0 0
\(148\) −14.6969 + 8.48528i −1.20808 + 0.697486i
\(149\) 17.3205i 1.41895i −0.704730 0.709476i \(-0.748932\pi\)
0.704730 0.709476i \(-0.251068\pi\)
\(150\) 0 0
\(151\) −16.0000 −1.30206 −0.651031 0.759051i \(-0.725663\pi\)
−0.651031 + 0.759051i \(0.725663\pi\)
\(152\) 9.79796 0.794719
\(153\) 0 0
\(154\) −6.00000 + 10.3923i −0.483494 + 0.837436i
\(155\) 0 0
\(156\) 0 0
\(157\) 8.48528i 0.677199i −0.940931 0.338600i \(-0.890047\pi\)
0.940931 0.338600i \(-0.109953\pi\)
\(158\) 4.89898 + 2.82843i 0.389742 + 0.225018i
\(159\) 0 0
\(160\) 0 0
\(161\) −6.00000 −0.472866
\(162\) 0 0
\(163\) 21.2132i 1.66155i 0.556611 + 0.830773i \(0.312101\pi\)
−0.556611 + 0.830773i \(0.687899\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) −7.00000 + 12.1244i −0.543305 + 0.941033i
\(167\) 12.2474 0.947736 0.473868 0.880596i \(-0.342857\pi\)
0.473868 + 0.880596i \(0.342857\pi\)
\(168\) 0 0
\(169\) 13.0000 1.00000
\(170\) 0 0
\(171\) 0 0
\(172\) −7.34847 + 4.24264i −0.560316 + 0.323498i
\(173\) 2.82843i 0.215041i −0.994203 0.107521i \(-0.965709\pi\)
0.994203 0.107521i \(-0.0342912\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −12.0000 6.92820i −0.904534 0.522233i
\(177\) 0 0
\(178\) 7.34847 + 4.24264i 0.550791 + 0.317999i
\(179\) 3.46410i 0.258919i −0.991585 0.129460i \(-0.958676\pi\)
0.991585 0.129460i \(-0.0413242\pi\)
\(180\) 0 0
\(181\) 13.8564i 1.02994i −0.857209 0.514969i \(-0.827803\pi\)
0.857209 0.514969i \(-0.172197\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 6.92820i 0.510754i
\(185\) 0 0
\(186\) 0 0
\(187\) 16.9706i 1.24101i
\(188\) −7.34847 12.7279i −0.535942 0.928279i
\(189\) 0 0
\(190\) 0 0
\(191\) −24.0000 −1.73658 −0.868290 0.496058i \(-0.834780\pi\)
−0.868290 + 0.496058i \(0.834780\pi\)
\(192\) 0 0
\(193\) 24.4949 1.76318 0.881591 0.472015i \(-0.156473\pi\)
0.881591 + 0.472015i \(0.156473\pi\)
\(194\) 6.00000 + 3.46410i 0.430775 + 0.248708i
\(195\) 0 0
\(196\) −1.00000 1.73205i −0.0714286 0.123718i
\(197\) 5.65685i 0.403034i −0.979485 0.201517i \(-0.935413\pi\)
0.979485 0.201517i \(-0.0645872\pi\)
\(198\) 0 0
\(199\) −4.00000 −0.283552 −0.141776 0.989899i \(-0.545281\pi\)
−0.141776 + 0.989899i \(0.545281\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 9.79796 16.9706i 0.689382 1.19404i
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) −9.00000 5.19615i −0.627060 0.362033i
\(207\) 0 0
\(208\) 0 0
\(209\) 12.0000 0.830057
\(210\) 0 0
\(211\) 24.2487i 1.66935i −0.550743 0.834675i \(-0.685655\pi\)
0.550743 0.834675i \(-0.314345\pi\)
\(212\) 9.79796 5.65685i 0.672927 0.388514i
\(213\) 0 0
\(214\) −1.00000 + 1.73205i −0.0683586 + 0.118401i
\(215\) 0 0
\(216\) 0 0
\(217\) 9.79796 0.665129
\(218\) −2.44949 + 4.24264i −0.165900 + 0.287348i
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −22.0454 −1.47627 −0.738135 0.674653i \(-0.764293\pi\)
−0.738135 + 0.674653i \(0.764293\pi\)
\(224\) −12.0000 + 6.92820i −0.801784 + 0.462910i
\(225\) 0 0
\(226\) 0 0
\(227\) 1.41421i 0.0938647i −0.998898 0.0469323i \(-0.985055\pi\)
0.998898 0.0469323i \(-0.0149445\pi\)
\(228\) 0 0
\(229\) 27.7128i 1.83131i −0.401960 0.915657i \(-0.631671\pi\)
0.401960 0.915657i \(-0.368329\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 14.6969 0.962828 0.481414 0.876493i \(-0.340123\pi\)
0.481414 + 0.876493i \(0.340123\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 18.0000 10.3923i 1.17170 0.676481i
\(237\) 0 0
\(238\) 14.6969 + 8.48528i 0.952661 + 0.550019i
\(239\) −12.0000 −0.776215 −0.388108 0.921614i \(-0.626871\pi\)
−0.388108 + 0.921614i \(0.626871\pi\)
\(240\) 0 0
\(241\) 4.00000 0.257663 0.128831 0.991667i \(-0.458877\pi\)
0.128831 + 0.991667i \(0.458877\pi\)
\(242\) −1.22474 0.707107i −0.0787296 0.0454545i
\(243\) 0 0
\(244\) −6.00000 + 3.46410i −0.384111 + 0.221766i
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 11.3137i 0.718421i
\(249\) 0 0
\(250\) 0 0
\(251\) 10.3923i 0.655956i −0.944685 0.327978i \(-0.893633\pi\)
0.944685 0.327978i \(-0.106367\pi\)
\(252\) 0 0
\(253\) 8.48528i 0.533465i
\(254\) −21.0000 12.1244i −1.31766 0.760750i
\(255\) 0 0
\(256\) −8.00000 13.8564i −0.500000 0.866025i
\(257\) 9.79796 0.611180 0.305590 0.952163i \(-0.401146\pi\)
0.305590 + 0.952163i \(0.401146\pi\)
\(258\) 0 0
\(259\) 20.7846i 1.29149i
\(260\) 0 0
\(261\) 0 0
\(262\) 2.44949 4.24264i 0.151330 0.262111i
\(263\) −7.34847 −0.453126 −0.226563 0.973997i \(-0.572749\pi\)
−0.226563 + 0.973997i \(0.572749\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 6.00000 10.3923i 0.367884 0.637193i
\(267\) 0 0
\(268\) −7.34847 + 4.24264i −0.448879 + 0.259161i
\(269\) 10.3923i 0.633630i −0.948487 0.316815i \(-0.897387\pi\)
0.948487 0.316815i \(-0.102613\pi\)
\(270\) 0 0
\(271\) 20.0000 1.21491 0.607457 0.794353i \(-0.292190\pi\)
0.607457 + 0.794353i \(0.292190\pi\)
\(272\) −9.79796 + 16.9706i −0.594089 + 1.02899i
\(273\) 0 0
\(274\) −12.0000 6.92820i −0.724947 0.418548i
\(275\) 0 0
\(276\) 0 0
\(277\) 25.4558i 1.52949i −0.644331 0.764747i \(-0.722864\pi\)
0.644331 0.764747i \(-0.277136\pi\)
\(278\) 7.34847 12.7279i 0.440732 0.763370i
\(279\) 0 0
\(280\) 0 0
\(281\) 12.0000 0.715860 0.357930 0.933748i \(-0.383483\pi\)
0.357930 + 0.933748i \(0.383483\pi\)
\(282\) 0 0
\(283\) 21.2132i 1.26099i −0.776192 0.630497i \(-0.782851\pi\)
0.776192 0.630497i \(-0.217149\pi\)
\(284\) 12.0000 + 20.7846i 0.712069 + 1.23334i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 7.00000 0.411765
\(290\) 0 0
\(291\) 0 0
\(292\) 4.89898 + 8.48528i 0.286691 + 0.496564i
\(293\) 19.7990i 1.15667i 0.815800 + 0.578335i \(0.196297\pi\)
−0.815800 + 0.578335i \(0.803703\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −24.0000 −1.39497
\(297\) 0 0
\(298\) 12.2474 21.2132i 0.709476 1.22885i
\(299\) 0 0
\(300\) 0 0
\(301\) 10.3923i 0.599002i
\(302\) −19.5959 11.3137i −1.12762 0.651031i
\(303\) 0 0
\(304\) 12.0000 + 6.92820i 0.688247 + 0.397360i
\(305\) 0 0
\(306\) 0 0
\(307\) 29.6985i 1.69498i −0.530810 0.847491i \(-0.678112\pi\)
0.530810 0.847491i \(-0.321888\pi\)
\(308\) −14.6969 + 8.48528i −0.837436 + 0.483494i
\(309\) 0 0
\(310\) 0 0
\(311\) 24.0000 1.36092 0.680458 0.732787i \(-0.261781\pi\)
0.680458 + 0.732787i \(0.261781\pi\)
\(312\) 0 0
\(313\) 9.79796 0.553813 0.276907 0.960897i \(-0.410691\pi\)
0.276907 + 0.960897i \(0.410691\pi\)
\(314\) 6.00000 10.3923i 0.338600 0.586472i
\(315\) 0 0
\(316\) 4.00000 + 6.92820i 0.225018 + 0.389742i
\(317\) 28.2843i 1.58860i −0.607524 0.794301i \(-0.707837\pi\)
0.607524 0.794301i \(-0.292163\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) −7.34847 4.24264i −0.409514 0.236433i
\(323\) 16.9706i 0.944267i
\(324\) 0 0
\(325\) 0 0
\(326\) −15.0000 + 25.9808i −0.830773 + 1.43894i
\(327\) 0 0
\(328\) 0 0
\(329\) −18.0000 −0.992372
\(330\) 0 0
\(331\) 31.1769i 1.71364i 0.515617 + 0.856819i \(0.327563\pi\)
−0.515617 + 0.856819i \(0.672437\pi\)
\(332\) −17.1464 + 9.89949i −0.941033 + 0.543305i
\(333\) 0 0
\(334\) 15.0000 + 8.66025i 0.820763 + 0.473868i
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(338\) 15.9217 + 9.19239i 0.866025 + 0.500000i
\(339\) 0 0
\(340\) 0 0
\(341\) 13.8564i 0.750366i
\(342\) 0 0
\(343\) −19.5959 −1.05808
\(344\) −12.0000 −0.646997
\(345\) 0 0
\(346\) 2.00000 3.46410i 0.107521 0.186231i
\(347\) 15.5563i 0.835109i 0.908652 + 0.417554i \(0.137113\pi\)
−0.908652 + 0.417554i \(0.862887\pi\)
\(348\) 0 0
\(349\) 13.8564i 0.741716i 0.928689 + 0.370858i \(0.120936\pi\)
−0.928689 + 0.370858i \(0.879064\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −9.79796 16.9706i −0.522233 0.904534i
\(353\) 29.3939 1.56448 0.782239 0.622978i \(-0.214078\pi\)
0.782239 + 0.622978i \(0.214078\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 6.00000 + 10.3923i 0.317999 + 0.550791i
\(357\) 0 0
\(358\) 2.44949 4.24264i 0.129460 0.224231i
\(359\) 24.0000 1.26667 0.633336 0.773877i \(-0.281685\pi\)
0.633336 + 0.773877i \(0.281685\pi\)
\(360\) 0 0
\(361\) 7.00000 0.368421
\(362\) 9.79796 16.9706i 0.514969 0.891953i
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 12.2474 0.639312 0.319656 0.947534i \(-0.396433\pi\)
0.319656 + 0.947534i \(0.396433\pi\)
\(368\) 4.89898 8.48528i 0.255377 0.442326i
\(369\) 0 0
\(370\) 0 0
\(371\) 13.8564i 0.719389i
\(372\) 0 0
\(373\) 8.48528i 0.439351i −0.975573 0.219676i \(-0.929500\pi\)
0.975573 0.219676i \(-0.0704999\pi\)
\(374\) −12.0000 + 20.7846i −0.620505 + 1.07475i
\(375\) 0 0
\(376\) 20.7846i 1.07188i
\(377\) 0 0
\(378\) 0 0
\(379\) 24.2487i 1.24557i −0.782392 0.622786i \(-0.786001\pi\)
0.782392 0.622786i \(-0.213999\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −29.3939 16.9706i −1.50392 0.868290i
\(383\) −26.9444 −1.37679 −0.688397 0.725334i \(-0.741685\pi\)
−0.688397 + 0.725334i \(0.741685\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 30.0000 + 17.3205i 1.52696 + 0.881591i
\(387\) 0 0
\(388\) 4.89898 + 8.48528i 0.248708 + 0.430775i
\(389\) 3.46410i 0.175637i −0.996136 0.0878185i \(-0.972010\pi\)
0.996136 0.0878185i \(-0.0279895\pi\)
\(390\) 0 0
\(391\) −12.0000 −0.606866
\(392\) 2.82843i 0.142857i
\(393\) 0 0
\(394\) 4.00000 6.92820i 0.201517 0.349038i
\(395\) 0 0
\(396\) 0 0
\(397\) 16.9706i 0.851728i 0.904787 + 0.425864i \(0.140030\pi\)
−0.904787 + 0.425864i \(0.859970\pi\)
\(398\) −4.89898 2.82843i −0.245564 0.141776i
\(399\) 0 0
\(400\) 0 0
\(401\) 18.0000 0.898877 0.449439 0.893311i \(-0.351624\pi\)
0.449439 + 0.893311i \(0.351624\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 24.0000 13.8564i 1.19404 0.689382i
\(405\) 0 0
\(406\) 0 0
\(407\) −29.3939 −1.45700
\(408\) 0 0
\(409\) −32.0000 −1.58230 −0.791149 0.611623i \(-0.790517\pi\)
−0.791149 + 0.611623i \(0.790517\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −7.34847 12.7279i −0.362033 0.627060i
\(413\) 25.4558i 1.25260i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 14.6969 + 8.48528i 0.718851 + 0.415029i
\(419\) 10.3923i 0.507697i 0.967244 + 0.253849i \(0.0816965\pi\)
−0.967244 + 0.253849i \(0.918303\pi\)
\(420\) 0 0
\(421\) 24.2487i 1.18181i 0.806741 + 0.590905i \(0.201229\pi\)
−0.806741 + 0.590905i \(0.798771\pi\)
\(422\) 17.1464 29.6985i 0.834675 1.44570i
\(423\) 0 0
\(424\) 16.0000 0.777029
\(425\) 0 0
\(426\) 0 0
\(427\) 8.48528i 0.410632i
\(428\) −2.44949 + 1.41421i −0.118401 + 0.0683586i
\(429\) 0 0
\(430\) 0 0
\(431\) −12.0000 −0.578020 −0.289010 0.957326i \(-0.593326\pi\)
−0.289010 + 0.957326i \(0.593326\pi\)
\(432\) 0 0
\(433\) −4.89898 −0.235430 −0.117715 0.993047i \(-0.537557\pi\)
−0.117715 + 0.993047i \(0.537557\pi\)
\(434\) 12.0000 + 6.92820i 0.576018 + 0.332564i
\(435\) 0 0
\(436\) −6.00000 + 3.46410i −0.287348 + 0.165900i
\(437\) 8.48528i 0.405906i
\(438\) 0 0
\(439\) 8.00000 0.381819 0.190910 0.981608i \(-0.438856\pi\)
0.190910 + 0.981608i \(0.438856\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 1.41421i 0.0671913i −0.999436 0.0335957i \(-0.989304\pi\)
0.999436 0.0335957i \(-0.0106958\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −27.0000 15.5885i −1.27849 0.738135i
\(447\) 0 0
\(448\) −19.5959 −0.925820
\(449\) −12.0000 −0.566315 −0.283158 0.959073i \(-0.591382\pi\)
−0.283158 + 0.959073i \(0.591382\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 1.00000 1.73205i 0.0469323 0.0812892i
\(455\) 0 0
\(456\) 0 0
\(457\) −19.5959 −0.916658 −0.458329 0.888783i \(-0.651552\pi\)
−0.458329 + 0.888783i \(0.651552\pi\)
\(458\) 19.5959 33.9411i 0.915657 1.58596i
\(459\) 0 0
\(460\) 0 0
\(461\) 13.8564i 0.645357i 0.946509 + 0.322679i \(0.104583\pi\)
−0.946509 + 0.322679i \(0.895417\pi\)
\(462\) 0 0
\(463\) −17.1464 −0.796862 −0.398431 0.917198i \(-0.630445\pi\)
−0.398431 + 0.917198i \(0.630445\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 18.0000 + 10.3923i 0.833834 + 0.481414i
\(467\) 7.07107i 0.327210i −0.986526 0.163605i \(-0.947688\pi\)
0.986526 0.163605i \(-0.0523123\pi\)
\(468\) 0 0
\(469\) 10.3923i 0.479872i
\(470\) 0 0
\(471\) 0 0
\(472\) 29.3939 1.35296
\(473\) −14.6969 −0.675766
\(474\) 0 0
\(475\) 0 0
\(476\) 12.0000 + 20.7846i 0.550019 + 0.952661i
\(477\) 0 0
\(478\) −14.6969 8.48528i −0.672222 0.388108i
\(479\) −24.0000 −1.09659 −0.548294 0.836286i \(-0.684723\pi\)
−0.548294 + 0.836286i \(0.684723\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 4.89898 + 2.82843i 0.223142 + 0.128831i
\(483\) 0 0
\(484\) −1.00000 1.73205i −0.0454545 0.0787296i
\(485\) 0 0
\(486\) 0 0
\(487\) −7.34847 −0.332991 −0.166495 0.986042i \(-0.553245\pi\)
−0.166495 + 0.986042i \(0.553245\pi\)
\(488\) −9.79796 −0.443533
\(489\) 0 0
\(490\) 0 0
\(491\) 24.2487i 1.09433i 0.837025 + 0.547165i \(0.184293\pi\)
−0.837025 + 0.547165i \(0.815707\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) −8.00000 + 13.8564i −0.359211 + 0.622171i
\(497\) 29.3939 1.31850
\(498\) 0 0
\(499\) 17.3205i 0.775372i 0.921791 + 0.387686i \(0.126726\pi\)
−0.921791 + 0.387686i \(0.873274\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 7.34847 12.7279i 0.327978 0.568075i
\(503\) −12.2474 −0.546087 −0.273043 0.962002i \(-0.588030\pi\)
−0.273043 + 0.962002i \(0.588030\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 6.00000 10.3923i 0.266733 0.461994i
\(507\) 0 0
\(508\) −17.1464 29.6985i −0.760750 1.31766i
\(509\) 27.7128i 1.22835i 0.789170 + 0.614174i \(0.210511\pi\)
−0.789170 + 0.614174i \(0.789489\pi\)
\(510\) 0 0
\(511\) 12.0000 0.530849
\(512\) 22.6274i 1.00000i
\(513\) 0 0
\(514\) 12.0000 + 6.92820i 0.529297 + 0.305590i
\(515\) 0 0
\(516\) 0 0
\(517\) 25.4558i 1.11955i
\(518\) −14.6969 + 25.4558i −0.645746 + 1.11847i
\(519\) 0 0
\(520\) 0 0
\(521\) −18.0000 −0.788594 −0.394297 0.918983i \(-0.629012\pi\)
−0.394297 + 0.918983i \(0.629012\pi\)
\(522\) 0 0
\(523\) 12.7279i 0.556553i 0.960501 + 0.278277i \(0.0897632\pi\)
−0.960501 + 0.278277i \(0.910237\pi\)
\(524\) 6.00000 3.46410i 0.262111 0.151330i
\(525\) 0 0
\(526\) −9.00000 5.19615i −0.392419 0.226563i
\(527\) 19.5959 0.853612
\(528\) 0 0
\(529\) −17.0000 −0.739130
\(530\) 0 0
\(531\) 0 0
\(532\) 14.6969 8.48528i 0.637193 0.367884i
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) −12.0000 −0.518321
\(537\) 0 0
\(538\) 7.34847 12.7279i 0.316815 0.548740i
\(539\) 3.46410i 0.149209i
\(540\) 0 0
\(541\) 41.5692i 1.78720i −0.448864 0.893600i \(-0.648171\pi\)
0.448864 0.893600i \(-0.351829\pi\)
\(542\) 24.4949 + 14.1421i 1.05215 + 0.607457i
\(543\) 0 0
\(544\) −24.0000 + 13.8564i −1.02899 + 0.594089i
\(545\) 0 0
\(546\) 0 0
\(547\) 4.24264i 0.181402i −0.995878 0.0907011i \(-0.971089\pi\)
0.995878 0.0907011i \(-0.0289108\pi\)
\(548\) −9.79796 16.9706i −0.418548 0.724947i
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 9.79796 0.416652
\(554\) 18.0000 31.1769i 0.764747 1.32458i
\(555\) 0 0
\(556\) 18.0000 10.3923i 0.763370 0.440732i
\(557\) 14.1421i 0.599222i −0.954062 0.299611i \(-0.903143\pi\)
0.954062 0.299611i \(-0.0968568\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 14.6969 + 8.48528i 0.619953 + 0.357930i
\(563\) 41.0122i 1.72846i 0.503099 + 0.864229i \(0.332193\pi\)
−0.503099 + 0.864229i \(0.667807\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 15.0000 25.9808i 0.630497 1.09205i
\(567\) 0 0
\(568\) 33.9411i 1.42414i
\(569\) 24.0000 1.00613 0.503066 0.864248i \(-0.332205\pi\)
0.503066 + 0.864248i \(0.332205\pi\)
\(570\) 0 0
\(571\) 3.46410i 0.144968i −0.997370 0.0724841i \(-0.976907\pi\)
0.997370 0.0724841i \(-0.0230926\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 29.3939 1.22368 0.611842 0.790980i \(-0.290429\pi\)
0.611842 + 0.790980i \(0.290429\pi\)
\(578\) 8.57321 + 4.94975i 0.356599 + 0.205882i
\(579\) 0 0
\(580\) 0 0
\(581\) 24.2487i 1.00601i
\(582\) 0 0
\(583\) 19.5959 0.811580
\(584\) 13.8564i 0.573382i
\(585\) 0 0
\(586\) −14.0000 + 24.2487i −0.578335 + 1.00171i
\(587\) 9.89949i 0.408596i 0.978909 + 0.204298i \(0.0654911\pi\)
−0.978909 + 0.204298i \(0.934509\pi\)
\(588\) 0 0
\(589\) 13.8564i 0.570943i
\(590\) 0 0
\(591\) 0 0
\(592\) −29.3939 16.9706i −1.20808 0.697486i
\(593\) −9.79796 −0.402354 −0.201177 0.979555i \(-0.564477\pi\)
−0.201177 + 0.979555i \(0.564477\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 30.0000 17.3205i 1.22885 0.709476i
\(597\) 0 0
\(598\) 0 0
\(599\) 12.0000 0.490307 0.245153 0.969484i \(-0.421162\pi\)
0.245153 + 0.969484i \(0.421162\pi\)
\(600\) 0 0
\(601\) −28.0000 −1.14214 −0.571072 0.820900i \(-0.693472\pi\)
−0.571072 + 0.820900i \(0.693472\pi\)
\(602\) −7.34847 + 12.7279i −0.299501 + 0.518751i
\(603\) 0 0
\(604\) −16.0000 27.7128i −0.651031 1.12762i
\(605\) 0 0
\(606\) 0 0
\(607\) 7.34847 0.298265 0.149133 0.988817i \(-0.452352\pi\)
0.149133 + 0.988817i \(0.452352\pi\)
\(608\) 9.79796 + 16.9706i 0.397360 + 0.688247i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 33.9411i 1.37087i −0.728134 0.685435i \(-0.759612\pi\)
0.728134 0.685435i \(-0.240388\pi\)
\(614\) 21.0000 36.3731i 0.847491 1.46790i
\(615\) 0 0
\(616\) −24.0000 −0.966988
\(617\) −34.2929 −1.38058 −0.690289 0.723534i \(-0.742517\pi\)
−0.690289 + 0.723534i \(0.742517\pi\)
\(618\) 0 0
\(619\) 10.3923i 0.417702i 0.977947 + 0.208851i \(0.0669724\pi\)
−0.977947 + 0.208851i \(0.933028\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 29.3939 + 16.9706i 1.17859 + 0.680458i
\(623\) 14.6969 0.588820
\(624\) 0 0
\(625\) 0 0
\(626\) 12.0000 + 6.92820i 0.479616 + 0.276907i
\(627\) 0 0
\(628\) 14.6969 8.48528i 0.586472 0.338600i
\(629\) 41.5692i 1.65747i
\(630\) 0 0
\(631\) 16.0000 0.636950 0.318475 0.947931i \(-0.396829\pi\)
0.318475 + 0.947931i \(0.396829\pi\)
\(632\) 11.3137i 0.450035i
\(633\) 0 0
\(634\) 20.0000 34.6410i 0.794301 1.37577i
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −12.0000 −0.473972 −0.236986 0.971513i \(-0.576159\pi\)
−0.236986 + 0.971513i \(0.576159\pi\)
\(642\) 0 0
\(643\) 29.6985i 1.17119i 0.810602 + 0.585597i \(0.199140\pi\)
−0.810602 + 0.585597i \(0.800860\pi\)
\(644\) −6.00000 10.3923i −0.236433 0.409514i
\(645\) 0 0
\(646\) 12.0000 20.7846i 0.472134 0.817760i
\(647\) −12.2474 −0.481497 −0.240748 0.970588i \(-0.577393\pi\)
−0.240748 + 0.970588i \(0.577393\pi\)
\(648\) 0 0
\(649\) 36.0000 1.41312
\(650\) 0 0
\(651\) 0 0
\(652\) −36.7423 + 21.2132i −1.43894 + 0.830773i
\(653\) 11.3137i 0.442740i −0.975190 0.221370i \(-0.928947\pi\)
0.975190 0.221370i \(-0.0710528\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) −22.0454 12.7279i −0.859419 0.496186i
\(659\) 24.2487i 0.944596i 0.881439 + 0.472298i \(0.156575\pi\)
−0.881439 + 0.472298i \(0.843425\pi\)
\(660\) 0 0
\(661\) 10.3923i 0.404214i −0.979363 0.202107i \(-0.935221\pi\)
0.979363 0.202107i \(-0.0647788\pi\)
\(662\) −22.0454 + 38.1838i −0.856819 + 1.48405i
\(663\) 0 0
\(664\) −28.0000 −1.08661
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 12.2474 + 21.2132i 0.473868 + 0.820763i
\(669\) 0 0
\(670\) 0 0
\(671\) −12.0000 −0.463255
\(672\) 0 0
\(673\) 34.2929 1.32189 0.660946 0.750433i \(-0.270155\pi\)
0.660946 + 0.750433i \(0.270155\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 13.0000 + 22.5167i 0.500000 + 0.866025i
\(677\) 22.6274i 0.869642i 0.900517 + 0.434821i \(0.143188\pi\)
−0.900517 + 0.434821i \(0.856812\pi\)
\(678\) 0 0
\(679\) 12.0000 0.460518
\(680\) 0 0
\(681\) 0 0
\(682\) −9.79796 + 16.9706i −0.375183 + 0.649836i
\(683\) 15.5563i 0.595247i −0.954683 0.297624i \(-0.903806\pi\)
0.954683 0.297624i \(-0.0961940\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −24.0000 13.8564i −0.916324 0.529040i
\(687\) 0 0
\(688\) −14.6969 8.48528i −0.560316 0.323498i
\(689\) 0 0
\(690\) 0 0
\(691\) 3.46410i 0.131781i 0.997827 + 0.0658903i \(0.0209887\pi\)
−0.997827 + 0.0658903i \(0.979011\pi\)
\(692\) 4.89898 2.82843i 0.186231 0.107521i
\(693\) 0 0
\(694\) −11.0000 + 19.0526i −0.417554 + 0.723225i
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) −9.79796 + 16.9706i −0.370858 + 0.642345i
\(699\) 0 0
\(700\) 0 0
\(701\) 24.2487i 0.915861i −0.888988 0.457931i \(-0.848591\pi\)
0.888988 0.457931i \(-0.151409\pi\)
\(702\) 0 0
\(703\) 29.3939 1.10861
\(704\) 27.7128i 1.04447i
\(705\) 0 0
\(706\) 36.0000 + 20.7846i 1.35488 + 0.782239i
\(707\) 33.9411i 1.27649i
\(708\) 0 0
\(709\) 41.5692i 1.56116i 0.625053 + 0.780582i \(0.285077\pi\)
−0.625053 + 0.780582i \(0.714923\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 16.9706i 0.635999i
\(713\) −9.79796 −0.366936
\(714\) 0 0
\(715\) 0 0
\(716\) 6.00000 3.46410i 0.224231 0.129460i
\(717\) 0 0
\(718\) 29.3939 + 16.9706i 1.09697 + 0.633336i
\(719\) −36.0000 −1.34257 −0.671287 0.741198i \(-0.734258\pi\)
−0.671287 + 0.741198i \(0.734258\pi\)
\(720\) 0 0
\(721\) −18.0000 −0.670355
\(722\) 8.57321 + 4.94975i 0.319062 + 0.184211i
\(723\) 0 0
\(724\) 24.0000 13.8564i 0.891953 0.514969i
\(725\) 0 0
\(726\) 0 0
\(727\) −46.5403 −1.72608 −0.863042 0.505132i \(-0.831444\pi\)
−0.863042 + 0.505132i \(0.831444\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 20.7846i 0.768747i
\(732\) 0 0
\(733\) 42.4264i 1.56706i 0.621357 + 0.783528i \(0.286582\pi\)
−0.621357 + 0.783528i \(0.713418\pi\)
\(734\) 15.0000 + 8.66025i 0.553660 + 0.319656i
\(735\) 0 0
\(736\) 12.0000 6.92820i 0.442326 0.255377i
\(737\) −14.6969 −0.541369
\(738\) 0 0
\(739\) 3.46410i 0.127429i 0.997968 + 0.0637145i \(0.0202947\pi\)
−0.997968 + 0.0637145i \(0.979705\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 9.79796 16.9706i 0.359694 0.623009i
\(743\) 51.4393 1.88712 0.943562 0.331195i \(-0.107452\pi\)
0.943562 + 0.331195i \(0.107452\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 6.00000 10.3923i 0.219676 0.380489i
\(747\) 0 0
\(748\) −29.3939 + 16.9706i −1.07475 + 0.620505i
\(749\) 3.46410i 0.126576i
\(750\) 0 0
\(751\) −32.0000 −1.16770 −0.583848 0.811863i \(-0.698454\pi\)
−0.583848 + 0.811863i \(0.698454\pi\)
\(752\) 14.6969 25.4558i 0.535942 0.928279i
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 25.4558i 0.925208i 0.886565 + 0.462604i \(0.153085\pi\)
−0.886565 + 0.462604i \(0.846915\pi\)
\(758\) 17.1464 29.6985i 0.622786 1.07870i
\(759\) 0 0
\(760\) 0 0
\(761\) −6.00000 −0.217500 −0.108750 0.994069i \(-0.534685\pi\)
−0.108750 + 0.994069i \(0.534685\pi\)
\(762\) 0 0
\(763\) 8.48528i 0.307188i
\(764\) −24.0000 41.5692i −0.868290 1.50392i
\(765\) 0 0
\(766\) −33.0000 19.0526i −1.19234 0.688397i
\(767\) 0 0
\(768\) 0 0
\(769\) 14.0000 0.504853 0.252426 0.967616i \(-0.418771\pi\)
0.252426 + 0.967616i \(0.418771\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 24.4949 + 42.4264i 0.881591 + 1.52696i
\(773\) 28.2843i 1.01731i −0.860969 0.508657i \(-0.830142\pi\)
0.860969 0.508657i \(-0.169858\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 13.8564i 0.497416i
\(777\) 0 0
\(778\) 2.44949 4.24264i 0.0878185 0.152106i
\(779\) 0 0
\(780\) 0 0
\(781\) 41.5692i 1.48746i
\(782\) −14.6969 8.48528i −0.525561 0.303433i
\(783\) 0 0
\(784\) 2.00000 3.46410i 0.0714286 0.123718i
\(785\) 0 0
\(786\) 0 0
\(787\) 21.2132i 0.756169i 0.925771 + 0.378085i \(0.123417\pi\)
−0.925771 + 0.378085i \(0.876583\pi\)
\(788\) 9.79796 5.65685i 0.349038 0.201517i
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) −12.0000 + 20.7846i −0.425864 + 0.737618i
\(795\) 0 0
\(796\) −4.00000 6.92820i −0.141776 0.245564i
\(797\) 39.5980i 1.40263i 0.712850 + 0.701316i \(0.247404\pi\)
−0.712850 + 0.701316i \(0.752596\pi\)
\(798\) 0 0
\(799\)