Properties

Label 784.2.i.m.753.1
Level $784$
Weight $2$
Character 784.753
Analytic conductor $6.260$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 784 = 2^{4} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 784.i (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.26027151847\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \( x^{4} + 2x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 98)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 753.1
Root \(-0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 784.753
Dual form 784.2.i.m.177.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 1.22474i) q^{3} +(-1.41421 - 2.44949i) q^{5} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.707107 + 1.22474i) q^{3} +(-1.41421 - 2.44949i) q^{5} +(0.500000 + 0.866025i) q^{9} +(-1.00000 + 1.73205i) q^{11} +4.00000 q^{15} +(0.707107 - 1.22474i) q^{17} +(-3.53553 - 6.12372i) q^{19} +(-2.00000 - 3.46410i) q^{23} +(-1.50000 + 2.59808i) q^{25} -5.65685 q^{27} +2.00000 q^{29} +(4.24264 - 7.34847i) q^{31} +(-1.41421 - 2.44949i) q^{33} +(-5.00000 - 8.66025i) q^{37} -9.89949 q^{41} -2.00000 q^{43} +(1.41421 - 2.44949i) q^{45} +(1.41421 + 2.44949i) q^{47} +(1.00000 + 1.73205i) q^{51} +(1.00000 - 1.73205i) q^{53} +5.65685 q^{55} +10.0000 q^{57} +(-0.707107 + 1.22474i) q^{59} +(-1.41421 - 2.44949i) q^{61} +(6.00000 - 10.3923i) q^{67} +5.65685 q^{69} +12.0000 q^{71} +(0.707107 - 1.22474i) q^{73} +(-2.12132 - 3.67423i) q^{75} +(-2.00000 - 3.46410i) q^{79} +(2.50000 - 4.33013i) q^{81} -9.89949 q^{83} -4.00000 q^{85} +(-1.41421 + 2.44949i) q^{87} +(3.53553 + 6.12372i) q^{89} +(6.00000 + 10.3923i) q^{93} +(-10.0000 + 17.3205i) q^{95} +9.89949 q^{97} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{9} - 4 q^{11} + 16 q^{15} - 8 q^{23} - 6 q^{25} + 8 q^{29} - 20 q^{37} - 8 q^{43} + 4 q^{51} + 4 q^{53} + 40 q^{57} + 24 q^{67} + 48 q^{71} - 8 q^{79} + 10 q^{81} - 16 q^{85} + 24 q^{93} - 40 q^{95} - 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(687\) \(689\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.707107 + 1.22474i −0.408248 + 0.707107i −0.994694 0.102882i \(-0.967194\pi\)
0.586445 + 0.809989i \(0.300527\pi\)
\(4\) 0 0
\(5\) −1.41421 2.44949i −0.632456 1.09545i −0.987048 0.160424i \(-0.948714\pi\)
0.354593 0.935021i \(-0.384620\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 0.500000 + 0.866025i 0.166667 + 0.288675i
\(10\) 0 0
\(11\) −1.00000 + 1.73205i −0.301511 + 0.522233i −0.976478 0.215615i \(-0.930824\pi\)
0.674967 + 0.737848i \(0.264158\pi\)
\(12\) 0 0
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) 0 0
\(15\) 4.00000 1.03280
\(16\) 0 0
\(17\) 0.707107 1.22474i 0.171499 0.297044i −0.767445 0.641114i \(-0.778472\pi\)
0.938944 + 0.344070i \(0.111806\pi\)
\(18\) 0 0
\(19\) −3.53553 6.12372i −0.811107 1.40488i −0.912090 0.409991i \(-0.865532\pi\)
0.100983 0.994888i \(-0.467801\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −2.00000 3.46410i −0.417029 0.722315i 0.578610 0.815604i \(-0.303595\pi\)
−0.995639 + 0.0932891i \(0.970262\pi\)
\(24\) 0 0
\(25\) −1.50000 + 2.59808i −0.300000 + 0.519615i
\(26\) 0 0
\(27\) −5.65685 −1.08866
\(28\) 0 0
\(29\) 2.00000 0.371391 0.185695 0.982607i \(-0.440546\pi\)
0.185695 + 0.982607i \(0.440546\pi\)
\(30\) 0 0
\(31\) 4.24264 7.34847i 0.762001 1.31982i −0.179817 0.983700i \(-0.557551\pi\)
0.941818 0.336124i \(-0.109116\pi\)
\(32\) 0 0
\(33\) −1.41421 2.44949i −0.246183 0.426401i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −5.00000 8.66025i −0.821995 1.42374i −0.904194 0.427121i \(-0.859528\pi\)
0.0821995 0.996616i \(-0.473806\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −9.89949 −1.54604 −0.773021 0.634381i \(-0.781255\pi\)
−0.773021 + 0.634381i \(0.781255\pi\)
\(42\) 0 0
\(43\) −2.00000 −0.304997 −0.152499 0.988304i \(-0.548732\pi\)
−0.152499 + 0.988304i \(0.548732\pi\)
\(44\) 0 0
\(45\) 1.41421 2.44949i 0.210819 0.365148i
\(46\) 0 0
\(47\) 1.41421 + 2.44949i 0.206284 + 0.357295i 0.950541 0.310599i \(-0.100530\pi\)
−0.744257 + 0.667893i \(0.767196\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 1.00000 + 1.73205i 0.140028 + 0.242536i
\(52\) 0 0
\(53\) 1.00000 1.73205i 0.137361 0.237915i −0.789136 0.614218i \(-0.789471\pi\)
0.926497 + 0.376303i \(0.122805\pi\)
\(54\) 0 0
\(55\) 5.65685 0.762770
\(56\) 0 0
\(57\) 10.0000 1.32453
\(58\) 0 0
\(59\) −0.707107 + 1.22474i −0.0920575 + 0.159448i −0.908377 0.418153i \(-0.862678\pi\)
0.816319 + 0.577601i \(0.196011\pi\)
\(60\) 0 0
\(61\) −1.41421 2.44949i −0.181071 0.313625i 0.761174 0.648547i \(-0.224623\pi\)
−0.942246 + 0.334922i \(0.891290\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 6.00000 10.3923i 0.733017 1.26962i −0.222571 0.974916i \(-0.571445\pi\)
0.955588 0.294706i \(-0.0952216\pi\)
\(68\) 0 0
\(69\) 5.65685 0.681005
\(70\) 0 0
\(71\) 12.0000 1.42414 0.712069 0.702109i \(-0.247758\pi\)
0.712069 + 0.702109i \(0.247758\pi\)
\(72\) 0 0
\(73\) 0.707107 1.22474i 0.0827606 0.143346i −0.821674 0.569958i \(-0.806960\pi\)
0.904435 + 0.426612i \(0.140293\pi\)
\(74\) 0 0
\(75\) −2.12132 3.67423i −0.244949 0.424264i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −2.00000 3.46410i −0.225018 0.389742i 0.731307 0.682048i \(-0.238911\pi\)
−0.956325 + 0.292306i \(0.905577\pi\)
\(80\) 0 0
\(81\) 2.50000 4.33013i 0.277778 0.481125i
\(82\) 0 0
\(83\) −9.89949 −1.08661 −0.543305 0.839535i \(-0.682827\pi\)
−0.543305 + 0.839535i \(0.682827\pi\)
\(84\) 0 0
\(85\) −4.00000 −0.433861
\(86\) 0 0
\(87\) −1.41421 + 2.44949i −0.151620 + 0.262613i
\(88\) 0 0
\(89\) 3.53553 + 6.12372i 0.374766 + 0.649113i 0.990292 0.139003i \(-0.0443898\pi\)
−0.615526 + 0.788116i \(0.711056\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 6.00000 + 10.3923i 0.622171 + 1.07763i
\(94\) 0 0
\(95\) −10.0000 + 17.3205i −1.02598 + 1.77705i
\(96\) 0 0
\(97\) 9.89949 1.00514 0.502571 0.864536i \(-0.332388\pi\)
0.502571 + 0.864536i \(0.332388\pi\)
\(98\) 0 0
\(99\) −2.00000 −0.201008
\(100\) 0 0
\(101\) −4.24264 + 7.34847i −0.422159 + 0.731200i −0.996150 0.0876610i \(-0.972061\pi\)
0.573992 + 0.818861i \(0.305394\pi\)
\(102\) 0 0
\(103\) 1.41421 + 2.44949i 0.139347 + 0.241355i 0.927249 0.374444i \(-0.122166\pi\)
−0.787903 + 0.615800i \(0.788833\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −2.00000 3.46410i −0.193347 0.334887i 0.753010 0.658009i \(-0.228601\pi\)
−0.946357 + 0.323122i \(0.895268\pi\)
\(108\) 0 0
\(109\) 1.00000 1.73205i 0.0957826 0.165900i −0.814152 0.580651i \(-0.802798\pi\)
0.909935 + 0.414751i \(0.136131\pi\)
\(110\) 0 0
\(111\) 14.1421 1.34231
\(112\) 0 0
\(113\) −12.0000 −1.12887 −0.564433 0.825479i \(-0.690905\pi\)
−0.564433 + 0.825479i \(0.690905\pi\)
\(114\) 0 0
\(115\) −5.65685 + 9.79796i −0.527504 + 0.913664i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 3.50000 + 6.06218i 0.318182 + 0.551107i
\(122\) 0 0
\(123\) 7.00000 12.1244i 0.631169 1.09322i
\(124\) 0 0
\(125\) −5.65685 −0.505964
\(126\) 0 0
\(127\) −16.0000 −1.41977 −0.709885 0.704317i \(-0.751253\pi\)
−0.709885 + 0.704317i \(0.751253\pi\)
\(128\) 0 0
\(129\) 1.41421 2.44949i 0.124515 0.215666i
\(130\) 0 0
\(131\) 6.36396 + 11.0227i 0.556022 + 0.963058i 0.997823 + 0.0659452i \(0.0210063\pi\)
−0.441801 + 0.897113i \(0.645660\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 8.00000 + 13.8564i 0.688530 + 1.19257i
\(136\) 0 0
\(137\) −6.00000 + 10.3923i −0.512615 + 0.887875i 0.487278 + 0.873247i \(0.337990\pi\)
−0.999893 + 0.0146279i \(0.995344\pi\)
\(138\) 0 0
\(139\) −9.89949 −0.839664 −0.419832 0.907602i \(-0.637911\pi\)
−0.419832 + 0.907602i \(0.637911\pi\)
\(140\) 0 0
\(141\) −4.00000 −0.336861
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) −2.82843 4.89898i −0.234888 0.406838i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −5.00000 8.66025i −0.409616 0.709476i 0.585231 0.810867i \(-0.301004\pi\)
−0.994847 + 0.101391i \(0.967671\pi\)
\(150\) 0 0
\(151\) −8.00000 + 13.8564i −0.651031 + 1.12762i 0.331842 + 0.943335i \(0.392330\pi\)
−0.982873 + 0.184284i \(0.941004\pi\)
\(152\) 0 0
\(153\) 1.41421 0.114332
\(154\) 0 0
\(155\) −24.0000 −1.92773
\(156\) 0 0
\(157\) 5.65685 9.79796i 0.451466 0.781962i −0.547011 0.837125i \(-0.684235\pi\)
0.998477 + 0.0551630i \(0.0175678\pi\)
\(158\) 0 0
\(159\) 1.41421 + 2.44949i 0.112154 + 0.194257i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 5.00000 + 8.66025i 0.391630 + 0.678323i 0.992665 0.120900i \(-0.0385779\pi\)
−0.601035 + 0.799223i \(0.705245\pi\)
\(164\) 0 0
\(165\) −4.00000 + 6.92820i −0.311400 + 0.539360i
\(166\) 0 0
\(167\) 19.7990 1.53209 0.766046 0.642786i \(-0.222221\pi\)
0.766046 + 0.642786i \(0.222221\pi\)
\(168\) 0 0
\(169\) −13.0000 −1.00000
\(170\) 0 0
\(171\) 3.53553 6.12372i 0.270369 0.468293i
\(172\) 0 0
\(173\) 8.48528 + 14.6969i 0.645124 + 1.11739i 0.984273 + 0.176655i \(0.0565276\pi\)
−0.339149 + 0.940733i \(0.610139\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −1.00000 1.73205i −0.0751646 0.130189i
\(178\) 0 0
\(179\) 6.00000 10.3923i 0.448461 0.776757i −0.549825 0.835280i \(-0.685306\pi\)
0.998286 + 0.0585225i \(0.0186389\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(182\) 0 0
\(183\) 4.00000 0.295689
\(184\) 0 0
\(185\) −14.1421 + 24.4949i −1.03975 + 1.80090i
\(186\) 0 0
\(187\) 1.41421 + 2.44949i 0.103418 + 0.179124i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −2.00000 3.46410i −0.144715 0.250654i 0.784552 0.620063i \(-0.212893\pi\)
−0.929267 + 0.369410i \(0.879560\pi\)
\(192\) 0 0
\(193\) 8.00000 13.8564i 0.575853 0.997406i −0.420096 0.907480i \(-0.638004\pi\)
0.995948 0.0899262i \(-0.0286631\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 2.00000 0.142494 0.0712470 0.997459i \(-0.477302\pi\)
0.0712470 + 0.997459i \(0.477302\pi\)
\(198\) 0 0
\(199\) 4.24264 7.34847i 0.300753 0.520919i −0.675554 0.737311i \(-0.736095\pi\)
0.976307 + 0.216391i \(0.0694287\pi\)
\(200\) 0 0
\(201\) 8.48528 + 14.6969i 0.598506 + 1.03664i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 14.0000 + 24.2487i 0.977802 + 1.69360i
\(206\) 0 0
\(207\) 2.00000 3.46410i 0.139010 0.240772i
\(208\) 0 0
\(209\) 14.1421 0.978232
\(210\) 0 0
\(211\) 12.0000 0.826114 0.413057 0.910705i \(-0.364461\pi\)
0.413057 + 0.910705i \(0.364461\pi\)
\(212\) 0 0
\(213\) −8.48528 + 14.6969i −0.581402 + 1.00702i
\(214\) 0 0
\(215\) 2.82843 + 4.89898i 0.192897 + 0.334108i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 1.00000 + 1.73205i 0.0675737 + 0.117041i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(224\) 0 0
\(225\) −3.00000 −0.200000
\(226\) 0 0
\(227\) −10.6066 + 18.3712i −0.703985 + 1.21934i 0.263072 + 0.964776i \(0.415264\pi\)
−0.967057 + 0.254561i \(0.918069\pi\)
\(228\) 0 0
\(229\) 8.48528 + 14.6969i 0.560723 + 0.971201i 0.997434 + 0.0715988i \(0.0228101\pi\)
−0.436710 + 0.899602i \(0.643857\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −12.0000 20.7846i −0.786146 1.36165i −0.928312 0.371802i \(-0.878740\pi\)
0.142166 0.989843i \(-0.454593\pi\)
\(234\) 0 0
\(235\) 4.00000 6.92820i 0.260931 0.451946i
\(236\) 0 0
\(237\) 5.65685 0.367452
\(238\) 0 0
\(239\) 12.0000 0.776215 0.388108 0.921614i \(-0.373129\pi\)
0.388108 + 0.921614i \(0.373129\pi\)
\(240\) 0 0
\(241\) 10.6066 18.3712i 0.683231 1.18339i −0.290758 0.956797i \(-0.593907\pi\)
0.973989 0.226595i \(-0.0727593\pi\)
\(242\) 0 0
\(243\) −4.94975 8.57321i −0.317526 0.549972i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 7.00000 12.1244i 0.443607 0.768350i
\(250\) 0 0
\(251\) −9.89949 −0.624851 −0.312425 0.949942i \(-0.601141\pi\)
−0.312425 + 0.949942i \(0.601141\pi\)
\(252\) 0 0
\(253\) 8.00000 0.502956
\(254\) 0 0
\(255\) 2.82843 4.89898i 0.177123 0.306786i
\(256\) 0 0
\(257\) −6.36396 11.0227i −0.396973 0.687577i 0.596378 0.802704i \(-0.296606\pi\)
−0.993351 + 0.115126i \(0.963273\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 1.00000 + 1.73205i 0.0618984 + 0.107211i
\(262\) 0 0
\(263\) 6.00000 10.3923i 0.369976 0.640817i −0.619586 0.784929i \(-0.712699\pi\)
0.989561 + 0.144112i \(0.0460326\pi\)
\(264\) 0 0
\(265\) −5.65685 −0.347498
\(266\) 0 0
\(267\) −10.0000 −0.611990
\(268\) 0 0
\(269\) 5.65685 9.79796i 0.344904 0.597392i −0.640432 0.768015i \(-0.721245\pi\)
0.985336 + 0.170623i \(0.0545780\pi\)
\(270\) 0 0
\(271\) 11.3137 + 19.5959i 0.687259 + 1.19037i 0.972721 + 0.231977i \(0.0745195\pi\)
−0.285462 + 0.958390i \(0.592147\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −3.00000 5.19615i −0.180907 0.313340i
\(276\) 0 0
\(277\) 1.00000 1.73205i 0.0600842 0.104069i −0.834419 0.551131i \(-0.814196\pi\)
0.894503 + 0.447062i \(0.147530\pi\)
\(278\) 0 0
\(279\) 8.48528 0.508001
\(280\) 0 0
\(281\) 16.0000 0.954480 0.477240 0.878773i \(-0.341637\pi\)
0.477240 + 0.878773i \(0.341637\pi\)
\(282\) 0 0
\(283\) −0.707107 + 1.22474i −0.0420331 + 0.0728035i −0.886277 0.463156i \(-0.846717\pi\)
0.844243 + 0.535960i \(0.180050\pi\)
\(284\) 0 0
\(285\) −14.1421 24.4949i −0.837708 1.45095i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 7.50000 + 12.9904i 0.441176 + 0.764140i
\(290\) 0 0
\(291\) −7.00000 + 12.1244i −0.410347 + 0.710742i
\(292\) 0 0
\(293\) −19.7990 −1.15667 −0.578335 0.815800i \(-0.696297\pi\)
−0.578335 + 0.815800i \(0.696297\pi\)
\(294\) 0 0
\(295\) 4.00000 0.232889
\(296\) 0 0
\(297\) 5.65685 9.79796i 0.328244 0.568535i
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −6.00000 10.3923i −0.344691 0.597022i
\(304\) 0 0
\(305\) −4.00000 + 6.92820i −0.229039 + 0.396708i
\(306\) 0 0
\(307\) 9.89949 0.564994 0.282497 0.959268i \(-0.408837\pi\)
0.282497 + 0.959268i \(0.408837\pi\)
\(308\) 0 0
\(309\) −4.00000 −0.227552
\(310\) 0 0
\(311\) −5.65685 + 9.79796i −0.320771 + 0.555591i −0.980647 0.195783i \(-0.937275\pi\)
0.659877 + 0.751374i \(0.270609\pi\)
\(312\) 0 0
\(313\) −6.36396 11.0227i −0.359712 0.623040i 0.628200 0.778052i \(-0.283792\pi\)
−0.987913 + 0.155012i \(0.950459\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −5.00000 8.66025i −0.280828 0.486408i 0.690761 0.723083i \(-0.257276\pi\)
−0.971589 + 0.236675i \(0.923942\pi\)
\(318\) 0 0
\(319\) −2.00000 + 3.46410i −0.111979 + 0.193952i
\(320\) 0 0
\(321\) 5.65685 0.315735
\(322\) 0 0
\(323\) −10.0000 −0.556415
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 1.41421 + 2.44949i 0.0782062 + 0.135457i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 5.00000 + 8.66025i 0.274825 + 0.476011i 0.970091 0.242742i \(-0.0780468\pi\)
−0.695266 + 0.718752i \(0.744713\pi\)
\(332\) 0 0
\(333\) 5.00000 8.66025i 0.273998 0.474579i
\(334\) 0 0
\(335\) −33.9411 −1.85440
\(336\) 0 0
\(337\) 2.00000 0.108947 0.0544735 0.998515i \(-0.482652\pi\)
0.0544735 + 0.998515i \(0.482652\pi\)
\(338\) 0 0
\(339\) 8.48528 14.6969i 0.460857 0.798228i
\(340\) 0 0
\(341\) 8.48528 + 14.6969i 0.459504 + 0.795884i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −8.00000 13.8564i −0.430706 0.746004i
\(346\) 0 0
\(347\) −15.0000 + 25.9808i −0.805242 + 1.39472i 0.110885 + 0.993833i \(0.464631\pi\)
−0.916127 + 0.400887i \(0.868702\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 0.707107 1.22474i 0.0376355 0.0651866i −0.846594 0.532239i \(-0.821351\pi\)
0.884230 + 0.467052i \(0.154684\pi\)
\(354\) 0 0
\(355\) −16.9706 29.3939i −0.900704 1.56007i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −16.0000 27.7128i −0.844448 1.46263i −0.886100 0.463494i \(-0.846596\pi\)
0.0416523 0.999132i \(-0.486738\pi\)
\(360\) 0 0
\(361\) −15.5000 + 26.8468i −0.815789 + 1.41299i
\(362\) 0 0
\(363\) −9.89949 −0.519589
\(364\) 0 0
\(365\) −4.00000 −0.209370
\(366\) 0 0
\(367\) 14.1421 24.4949i 0.738213 1.27862i −0.215086 0.976595i \(-0.569003\pi\)
0.953299 0.302028i \(-0.0976636\pi\)
\(368\) 0 0
\(369\) −4.94975 8.57321i −0.257674 0.446304i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −5.00000 8.66025i −0.258890 0.448411i 0.707055 0.707159i \(-0.250023\pi\)
−0.965945 + 0.258748i \(0.916690\pi\)
\(374\) 0 0
\(375\) 4.00000 6.92820i 0.206559 0.357771i
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 26.0000 1.33553 0.667765 0.744372i \(-0.267251\pi\)
0.667765 + 0.744372i \(0.267251\pi\)
\(380\) 0 0
\(381\) 11.3137 19.5959i 0.579619 1.00393i
\(382\) 0 0
\(383\) −18.3848 31.8434i −0.939418 1.62712i −0.766559 0.642173i \(-0.778033\pi\)
−0.172859 0.984947i \(-0.555300\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −1.00000 1.73205i −0.0508329 0.0880451i
\(388\) 0 0
\(389\) −13.0000 + 22.5167i −0.659126 + 1.14164i 0.321716 + 0.946836i \(0.395740\pi\)
−0.980842 + 0.194804i \(0.937593\pi\)
\(390\) 0 0
\(391\) −5.65685 −0.286079
\(392\) 0 0
\(393\) −18.0000 −0.907980
\(394\) 0 0
\(395\) −5.65685 + 9.79796i −0.284627 + 0.492989i
\(396\) 0 0
\(397\) −11.3137 19.5959i −0.567819 0.983491i −0.996781 0.0801687i \(-0.974454\pi\)
0.428963 0.903322i \(-0.358879\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 9.00000 + 15.5885i 0.449439 + 0.778450i 0.998350 0.0574304i \(-0.0182907\pi\)
−0.548911 + 0.835881i \(0.684957\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) −14.1421 −0.702728
\(406\) 0 0
\(407\) 20.0000 0.991363
\(408\) 0 0
\(409\) −19.0919 + 33.0681i −0.944033 + 1.63511i −0.186357 + 0.982482i \(0.559668\pi\)
−0.757676 + 0.652631i \(0.773665\pi\)
\(410\) 0 0
\(411\) −8.48528 14.6969i −0.418548 0.724947i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 14.0000 + 24.2487i 0.687233 + 1.19032i
\(416\) 0 0
\(417\) 7.00000 12.1244i 0.342791 0.593732i
\(418\) 0 0
\(419\) 9.89949 0.483622 0.241811 0.970323i \(-0.422259\pi\)
0.241811 + 0.970323i \(0.422259\pi\)
\(420\) 0 0
\(421\) 30.0000 1.46211 0.731055 0.682318i \(-0.239028\pi\)
0.731055 + 0.682318i \(0.239028\pi\)
\(422\) 0 0
\(423\) −1.41421 + 2.44949i −0.0687614 + 0.119098i
\(424\) 0 0
\(425\) 2.12132 + 3.67423i 0.102899 + 0.178227i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 6.00000 10.3923i 0.289010 0.500580i −0.684564 0.728953i \(-0.740007\pi\)
0.973574 + 0.228373i \(0.0733406\pi\)
\(432\) 0 0
\(433\) −29.6985 −1.42722 −0.713609 0.700544i \(-0.752941\pi\)
−0.713609 + 0.700544i \(0.752941\pi\)
\(434\) 0 0
\(435\) 8.00000 0.383571
\(436\) 0 0
\(437\) −14.1421 + 24.4949i −0.676510 + 1.17175i
\(438\) 0 0
\(439\) −8.48528 14.6969i −0.404980 0.701447i 0.589339 0.807886i \(-0.299388\pi\)
−0.994319 + 0.106439i \(0.966055\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −2.00000 3.46410i −0.0950229 0.164584i 0.814595 0.580030i \(-0.196959\pi\)
−0.909618 + 0.415445i \(0.863626\pi\)
\(444\) 0 0
\(445\) 10.0000 17.3205i 0.474045 0.821071i
\(446\) 0 0
\(447\) 14.1421 0.668900
\(448\) 0 0
\(449\) 30.0000 1.41579 0.707894 0.706319i \(-0.249646\pi\)
0.707894 + 0.706319i \(0.249646\pi\)
\(450\) 0 0
\(451\) 9.89949 17.1464i 0.466149 0.807394i
\(452\) 0 0
\(453\) −11.3137 19.5959i −0.531564 0.920697i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −12.0000 20.7846i −0.561336 0.972263i −0.997380 0.0723376i \(-0.976954\pi\)
0.436044 0.899925i \(-0.356379\pi\)
\(458\) 0 0
\(459\) −4.00000 + 6.92820i −0.186704 + 0.323381i
\(460\) 0 0
\(461\) 39.5980 1.84426 0.922131 0.386878i \(-0.126447\pi\)
0.922131 + 0.386878i \(0.126447\pi\)
\(462\) 0 0
\(463\) −16.0000 −0.743583 −0.371792 0.928316i \(-0.621256\pi\)
−0.371792 + 0.928316i \(0.621256\pi\)
\(464\) 0 0
\(465\) 16.9706 29.3939i 0.786991 1.36311i
\(466\) 0 0
\(467\) 16.2635 + 28.1691i 0.752583 + 1.30351i 0.946567 + 0.322507i \(0.104526\pi\)
−0.193984 + 0.981005i \(0.562141\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 8.00000 + 13.8564i 0.368621 + 0.638470i
\(472\) 0 0
\(473\) 2.00000 3.46410i 0.0919601 0.159280i
\(474\) 0 0
\(475\) 21.2132 0.973329
\(476\) 0 0
\(477\) 2.00000 0.0915737
\(478\) 0 0
\(479\) −15.5563 + 26.9444i −0.710788 + 1.23112i 0.253774 + 0.967264i \(0.418328\pi\)
−0.964562 + 0.263857i \(0.915005\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −14.0000 24.2487i −0.635707 1.10108i
\(486\) 0 0
\(487\) 6.00000 10.3923i 0.271886 0.470920i −0.697459 0.716625i \(-0.745686\pi\)
0.969345 + 0.245705i \(0.0790193\pi\)
\(488\) 0 0
\(489\) −14.1421 −0.639529
\(490\) 0 0
\(491\) 12.0000 0.541552 0.270776 0.962642i \(-0.412720\pi\)
0.270776 + 0.962642i \(0.412720\pi\)
\(492\) 0 0
\(493\) 1.41421 2.44949i 0.0636930 0.110319i
\(494\) 0 0
\(495\) 2.82843 + 4.89898i 0.127128 + 0.220193i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −2.00000 3.46410i −0.0895323 0.155074i 0.817781 0.575529i \(-0.195204\pi\)
−0.907314 + 0.420455i \(0.861871\pi\)
\(500\) 0 0
\(501\) −14.0000 + 24.2487i −0.625474 + 1.08335i
\(502\) 0 0
\(503\) −39.5980 −1.76559 −0.882793 0.469762i \(-0.844340\pi\)
−0.882793 + 0.469762i \(0.844340\pi\)
\(504\) 0 0
\(505\) 24.0000 1.06799
\(506\) 0 0
\(507\) 9.19239 15.9217i 0.408248 0.707107i
\(508\) 0 0
\(509\) −11.3137 19.5959i −0.501471 0.868574i −0.999999 0.00169976i \(-0.999459\pi\)
0.498527 0.866874i \(-0.333874\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 20.0000 + 34.6410i 0.883022 + 1.52944i
\(514\) 0 0
\(515\) 4.00000 6.92820i 0.176261 0.305293i
\(516\) 0 0
\(517\) −5.65685 −0.248788
\(518\) 0 0
\(519\) −24.0000 −1.05348
\(520\) 0 0
\(521\) 0.707107 1.22474i 0.0309789 0.0536570i −0.850120 0.526589i \(-0.823471\pi\)
0.881099 + 0.472931i \(0.156804\pi\)
\(522\) 0 0
\(523\) 6.36396 + 11.0227i 0.278277 + 0.481989i 0.970957 0.239256i \(-0.0769035\pi\)
−0.692680 + 0.721245i \(0.743570\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −6.00000 10.3923i −0.261364 0.452696i
\(528\) 0 0
\(529\) 3.50000 6.06218i 0.152174 0.263573i
\(530\) 0 0
\(531\) −1.41421 −0.0613716
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) −5.65685 + 9.79796i −0.244567 + 0.423603i
\(536\) 0 0
\(537\) 8.48528 + 14.6969i 0.366167 + 0.634220i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −5.00000 8.66025i −0.214967 0.372333i 0.738296 0.674477i \(-0.235631\pi\)
−0.953262 + 0.302144i \(0.902298\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −5.65685 −0.242313
\(546\) 0 0
\(547\) 26.0000 1.11168 0.555840 0.831289i \(-0.312397\pi\)
0.555840 + 0.831289i \(0.312397\pi\)
\(548\) 0 0
\(549\) 1.41421 2.44949i 0.0603572 0.104542i
\(550\) 0 0
\(551\) −7.07107 12.2474i −0.301238 0.521759i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −20.0000 34.6410i −0.848953 1.47043i
\(556\) 0 0
\(557\) 15.0000 25.9808i 0.635570 1.10084i −0.350824 0.936442i \(-0.614098\pi\)
0.986394 0.164399i \(-0.0525683\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) −4.00000 −0.168880
\(562\) 0 0
\(563\) −0.707107 + 1.22474i −0.0298010 + 0.0516168i −0.880541 0.473970i \(-0.842821\pi\)
0.850740 + 0.525586i \(0.176154\pi\)
\(564\) 0 0
\(565\) 16.9706 + 29.3939i 0.713957 + 1.23661i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −5.00000 8.66025i −0.209611 0.363057i 0.741981 0.670421i \(-0.233886\pi\)
−0.951592 + 0.307364i \(0.900553\pi\)
\(570\) 0 0
\(571\) −1.00000 + 1.73205i −0.0418487 + 0.0724841i −0.886191 0.463320i \(-0.846658\pi\)
0.844342 + 0.535804i \(0.179991\pi\)
\(572\) 0 0
\(573\) 5.65685 0.236318
\(574\) 0 0
\(575\) 12.0000 0.500435
\(576\) 0 0
\(577\) 10.6066 18.3712i 0.441559 0.764802i −0.556247 0.831017i \(-0.687759\pi\)
0.997805 + 0.0662152i \(0.0210924\pi\)
\(578\) 0 0
\(579\) 11.3137 + 19.5959i 0.470182 + 0.814379i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 2.00000 + 3.46410i 0.0828315 + 0.143468i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 29.6985 1.22579 0.612894 0.790165i \(-0.290005\pi\)
0.612894 + 0.790165i \(0.290005\pi\)
\(588\) 0 0
\(589\) −60.0000 −2.47226
\(590\) 0 0
\(591\) −1.41421 + 2.44949i −0.0581730 + 0.100759i
\(592\) 0 0
\(593\) 3.53553 + 6.12372i 0.145187 + 0.251471i 0.929443 0.368967i \(-0.120288\pi\)
−0.784256 + 0.620438i \(0.786955\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 6.00000 + 10.3923i 0.245564 + 0.425329i
\(598\) 0 0
\(599\) −8.00000 + 13.8564i −0.326871 + 0.566157i −0.981889 0.189456i \(-0.939328\pi\)
0.655018 + 0.755613i \(0.272661\pi\)
\(600\) 0 0
\(601\) 29.6985 1.21143 0.605713 0.795683i \(-0.292888\pi\)
0.605713 + 0.795683i \(0.292888\pi\)
\(602\) 0 0
\(603\) 12.0000 0.488678
\(604\) 0 0
\(605\) 9.89949 17.1464i 0.402472 0.697101i
\(606\) 0 0
\(607\) −8.48528 14.6969i −0.344407 0.596530i 0.640839 0.767675i \(-0.278587\pi\)
−0.985246 + 0.171145i \(0.945253\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 15.0000 25.9808i 0.605844 1.04935i −0.386073 0.922468i \(-0.626169\pi\)
0.991917 0.126885i \(-0.0404979\pi\)
\(614\) 0 0
\(615\) −39.5980 −1.59674
\(616\) 0 0
\(617\) −26.0000 −1.04672 −0.523360 0.852111i \(-0.675322\pi\)
−0.523360 + 0.852111i \(0.675322\pi\)
\(618\) 0 0
\(619\) 9.19239 15.9217i 0.369473 0.639946i −0.620010 0.784594i \(-0.712871\pi\)
0.989483 + 0.144647i \(0.0462048\pi\)
\(620\) 0 0
\(621\) 11.3137 + 19.5959i 0.454003 + 0.786357i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 15.5000 + 26.8468i 0.620000 + 1.07387i
\(626\) 0 0
\(627\) −10.0000 + 17.3205i −0.399362 + 0.691714i
\(628\) 0 0
\(629\) −14.1421 −0.563884
\(630\) 0 0
\(631\) −44.0000 −1.75161 −0.875806 0.482663i \(-0.839670\pi\)
−0.875806 + 0.482663i \(0.839670\pi\)
\(632\) 0 0
\(633\) −8.48528 + 14.6969i −0.337260 + 0.584151i
\(634\) 0 0
\(635\) 22.6274 + 39.1918i 0.897942 + 1.55528i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 6.00000 + 10.3923i 0.237356 + 0.411113i
\(640\) 0 0
\(641\) −13.0000 + 22.5167i −0.513469 + 0.889355i 0.486409 + 0.873731i \(0.338307\pi\)
−0.999878 + 0.0156233i \(0.995027\pi\)
\(642\) 0 0
\(643\) −9.89949 −0.390398 −0.195199 0.980764i \(-0.562535\pi\)
−0.195199 + 0.980764i \(0.562535\pi\)
\(644\) 0 0
\(645\) −8.00000 −0.315000
\(646\) 0 0
\(647\) 4.24264 7.34847i 0.166795 0.288898i −0.770496 0.637445i \(-0.779991\pi\)
0.937291 + 0.348547i \(0.113325\pi\)
\(648\) 0 0
\(649\) −1.41421 2.44949i −0.0555127 0.0961509i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 9.00000 + 15.5885i 0.352197 + 0.610023i 0.986634 0.162951i \(-0.0521013\pi\)
−0.634437 + 0.772975i \(0.718768\pi\)
\(654\) 0 0
\(655\) 18.0000 31.1769i 0.703318 1.21818i
\(656\) 0 0
\(657\) 1.41421 0.0551737
\(658\) 0 0
\(659\) −30.0000 −1.16863 −0.584317 0.811525i \(-0.698638\pi\)
−0.584317 + 0.811525i \(0.698638\pi\)
\(660\) 0 0
\(661\) −4.24264 + 7.34847i −0.165020 + 0.285822i −0.936662 0.350234i \(-0.886102\pi\)
0.771643 + 0.636056i \(0.219435\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −4.00000 6.92820i −0.154881 0.268261i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 5.65685 0.218380
\(672\) 0 0
\(673\) −12.0000 −0.462566 −0.231283 0.972887i \(-0.574292\pi\)
−0.231283 + 0.972887i \(0.574292\pi\)
\(674\) 0 0
\(675\) 8.48528 14.6969i 0.326599 0.565685i
\(676\) 0 0
\(677\) 8.48528 + 14.6969i 0.326116 + 0.564849i 0.981738 0.190240i \(-0.0609267\pi\)
−0.655622 + 0.755090i \(0.727593\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −15.0000 25.9808i −0.574801 0.995585i
\(682\) 0 0
\(683\) 6.00000 10.3923i 0.229584 0.397650i −0.728101 0.685470i \(-0.759597\pi\)
0.957685 + 0.287819i \(0.0929302\pi\)
\(684\) 0 0
\(685\) 33.9411 1.29682
\(686\) 0 0
\(687\) −24.0000 −0.915657
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 6.36396 + 11.0227i 0.242096 + 0.419323i 0.961311 0.275464i \(-0.0888316\pi\)
−0.719215 + 0.694788i \(0.755498\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 14.0000 + 24.2487i 0.531050 + 0.919806i
\(696\) 0 0
\(697\) −7.00000 + 12.1244i −0.265144 + 0.459243i
\(698\) 0 0
\(699\) 33.9411 1.28377
\(700\) 0 0
\(701\) 30.0000 1.13308 0.566542 0.824033i \(-0.308281\pi\)
0.566542 + 0.824033i \(0.308281\pi\)
\(702\) 0 0
\(703\) −35.3553 + 61.2372i −1.33345 + 2.30961i
\(704\) 0 0
\(705\) 5.65685 + 9.79796i 0.213049 + 0.369012i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −5.00000 8.66025i −0.187779 0.325243i 0.756730 0.653727i \(-0.226796\pi\)
−0.944509 + 0.328484i \(0.893462\pi\)
\(710\) 0 0
\(711\) 2.00000 3.46410i 0.0750059 0.129914i
\(712\) 0 0
\(713\) −33.9411 −1.27111
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −8.48528 + 14.6969i −0.316889 + 0.548867i
\(718\) 0 0
\(719\) 1.41421 + 2.44949i 0.0527413 + 0.0913506i 0.891191 0.453629i \(-0.149871\pi\)
−0.838449 + 0.544979i \(0.816537\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 15.0000 + 25.9808i 0.557856 + 0.966235i
\(724\) 0 0
\(725\) −3.00000 + 5.19615i −0.111417 + 0.192980i
\(726\) 0 0
\(727\) 19.7990 0.734304 0.367152 0.930161i \(-0.380333\pi\)
0.367152 + 0.930161i \(0.380333\pi\)
\(728\) 0 0
\(729\) 29.0000 1.07407
\(730\) 0 0
\(731\) −1.41421 + 2.44949i −0.0523066 + 0.0905977i
\(732\) 0 0
\(733\) −21.2132 36.7423i −0.783528 1.35711i −0.929875 0.367876i \(-0.880085\pi\)
0.146347 0.989233i \(-0.453248\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 12.0000 + 20.7846i 0.442026 + 0.765611i
\(738\) 0 0
\(739\) −15.0000 + 25.9808i −0.551784 + 0.955718i 0.446362 + 0.894852i \(0.352719\pi\)
−0.998146 + 0.0608653i \(0.980614\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −16.0000 −0.586983 −0.293492 0.955962i \(-0.594817\pi\)
−0.293492 + 0.955962i \(0.594817\pi\)
\(744\) 0 0
\(745\) −14.1421 + 24.4949i −0.518128 + 0.897424i
\(746\) 0 0
\(747\) −4.94975 8.57321i −0.181102 0.313678i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −2.00000 3.46410i −0.0729810 0.126407i 0.827225 0.561870i \(-0.189918\pi\)
−0.900207 + 0.435463i \(0.856585\pi\)
\(752\) 0 0
\(753\) 7.00000 12.1244i 0.255094 0.441836i
\(754\) 0 0
\(755\) 45.2548 1.64699
\(756\) 0 0
\(757\) 2.00000 0.0726912 0.0363456 0.999339i \(-0.488428\pi\)
0.0363456 + 0.999339i \(0.488428\pi\)
\(758\) 0 0
\(759\) −5.65685 + 9.79796i −0.205331 + 0.355643i
\(760\) 0 0
\(761\) 3.53553 + 6.12372i 0.128163 + 0.221985i 0.922965 0.384884i \(-0.125759\pi\)
−0.794802 + 0.606869i \(0.792425\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −2.00000 3.46410i −0.0723102 0.125245i
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 29.6985 1.07095 0.535477 0.844550i \(-0.320132\pi\)
0.535477 + 0.844550i \(0.320132\pi\)
\(770\) 0 0
\(771\) 18.0000 0.648254
\(772\) 0 0
\(773\) −24.0416 + 41.6413i −0.864717 + 1.49773i 0.00261021 + 0.999997i \(0.499169\pi\)
−0.867328 + 0.497738i \(0.834164\pi\)
\(774\) 0 0
\(775\) 12.7279 + 22.0454i 0.457200 + 0.791894i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 35.0000 + 60.6218i 1.25401 + 2.17200i
\(780\) 0 0
\(781\) −12.0000 + 20.7846i −0.429394 + 0.743732i
\(782\) 0 0
\(783\) −11.3137 −0.404319
\(784\) 0 0
\(785\) −32.0000 −1.14213
\(786\) 0 0
\(787\) −0.707107 + 1.22474i −0.0252056 + 0.0436574i −0.878353 0.478012i \(-0.841357\pi\)
0.853147 + 0.521670i \(0.174691\pi\)
\(788\) 0 0
\(789\) 8.48528 + 14.6969i 0.302084 + 0.523225i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 4.00000 6.92820i 0.141865 0.245718i
\(796\) 0 0
\(797\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(798\) 0 0
\(799\) 4.00000 0.141510
\(800\) 0