Properties

Label 784.2.i.m.753.2
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: \(x^{4} + 2 x^{2} + 4\)
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 753.2
Root \(0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 784.753
Dual form 784.2.i.m.177.2

$q$-expansion

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

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 −0.586445 0.809989i \(-0.699473\pi\)
0.994694 + 0.102882i \(0.0328064\pi\)
\(4\) 0 0
\(5\) 1.41421 + 2.44949i 0.632456 + 1.09545i 0.987048 + 0.160424i \(0.0512862\pi\)
−0.354593 + 0.935021i \(0.615380\pi\)
\(6\) 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 −0.938944 0.344070i \(-0.888194\pi\)
0.767445 + 0.641114i \(0.221528\pi\)
\(18\) 0 0
\(19\) 3.53553 + 6.12372i 0.811107 + 1.40488i 0.912090 + 0.409991i \(0.134468\pi\)
−0.100983 + 0.994888i \(0.532199\pi\)
\(20\) 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 \(0.442449\pi\)
−0.941818 + 0.336124i \(0.890884\pi\)
\(32\) 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 \(-0.218745\pi\)
0.773021 + 0.634381i \(0.218745\pi\)
\(42\) 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 0.744257 0.667893i \(-0.232804\pi\)
−0.950541 + 0.310599i \(0.899470\pi\)
\(48\) 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 −0.816319 0.577601i \(-0.803989\pi\)
0.908377 + 0.418153i \(0.137322\pi\)
\(60\) 0 0
\(61\) 1.41421 + 2.44949i 0.181071 + 0.313625i 0.942246 0.334922i \(-0.108710\pi\)
−0.761174 + 0.648547i \(0.775377\pi\)
\(62\) 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 −0.904435 0.426612i \(-0.859707\pi\)
0.821674 + 0.569958i \(0.193040\pi\)
\(74\) 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 \(-0.317173\pi\)
0.543305 + 0.839535i \(0.317173\pi\)
\(84\) 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 0.615526 0.788116i \(-0.288944\pi\)
−0.990292 + 0.139003i \(0.955610\pi\)
\(90\) 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 \(-0.667612\pi\)
−0.502571 + 0.864536i \(0.667612\pi\)
\(98\) 0 0
\(99\) −2.00000 −0.201008
\(100\) 0 0
\(101\) 4.24264 7.34847i 0.422159 0.731200i −0.573992 0.818861i \(-0.694606\pi\)
0.996150 + 0.0876610i \(0.0279392\pi\)
\(102\) 0 0
\(103\) −1.41421 2.44949i −0.139347 0.241355i 0.787903 0.615800i \(-0.211167\pi\)
−0.927249 + 0.374444i \(0.877834\pi\)
\(104\) 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 \(-0.978994\pi\)
0.441801 0.897113i \(-0.354340\pi\)
\(132\) 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 \(-0.362089\pi\)
0.419832 + 0.907602i \(0.362089\pi\)
\(140\) 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 −0.998477 0.0551630i \(-0.982432\pi\)
0.547011 + 0.837125i \(0.315765\pi\)
\(158\) 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 \(-0.777779\pi\)
−0.766046 + 0.642786i \(0.777779\pi\)
\(168\) 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 \(-0.943472\pi\)
0.339149 0.940733i \(-0.389861\pi\)
\(174\) 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 −0.976307 0.216391i \(-0.930571\pi\)
0.675554 + 0.737311i \(0.263905\pi\)
\(200\) 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 \(-0.584736\pi\)
0.967057 0.254561i \(-0.0819311\pi\)
\(228\) 0 0
\(229\) −8.48528 14.6969i −0.560723 0.971201i −0.997434 0.0715988i \(-0.977190\pi\)
0.436710 0.899602i \(-0.356143\pi\)
\(230\) 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 \(0.406093\pi\)
−0.973989 + 0.226595i \(0.927241\pi\)
\(242\) 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 \(-0.398859\pi\)
0.312425 + 0.949942i \(0.398859\pi\)
\(252\) 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 0.993351 0.115126i \(-0.0367273\pi\)
−0.596378 + 0.802704i \(0.703394\pi\)
\(258\) 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 −0.985336 0.170623i \(-0.945422\pi\)
0.640432 + 0.768015i \(0.278755\pi\)
\(270\) 0 0
\(271\) −11.3137 19.5959i −0.687259 1.19037i −0.972721 0.231977i \(-0.925480\pi\)
0.285462 0.958390i \(-0.407853\pi\)
\(272\) 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 −0.844243 0.535960i \(-0.819950\pi\)
0.886277 + 0.463156i \(0.153283\pi\)
\(284\) 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 \(-0.303703\pi\)
0.578335 + 0.815800i \(0.303703\pi\)
\(294\) 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 \(-0.591163\pi\)
−0.282497 + 0.959268i \(0.591163\pi\)
\(308\) 0 0
\(309\) −4.00000 −0.227552
\(310\) 0 0
\(311\) 5.65685 9.79796i 0.320771 0.555591i −0.659877 0.751374i \(-0.729391\pi\)
0.980647 + 0.195783i \(0.0627248\pi\)
\(312\) 0 0
\(313\) 6.36396 + 11.0227i 0.359712 + 0.623040i 0.987913 0.155012i \(-0.0495415\pi\)
−0.628200 + 0.778052i \(0.716208\pi\)
\(314\) 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 −0.884230 0.467052i \(-0.845316\pi\)
0.846594 + 0.532239i \(0.178649\pi\)
\(354\) 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 \(0.430997\pi\)
−0.953299 + 0.302028i \(0.902336\pi\)
\(368\) 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 \(0.221967\pi\)
0.172859 + 0.984947i \(0.444700\pi\)
\(384\) 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 \(0.0255459\pi\)
−0.428963 + 0.903322i \(0.641121\pi\)
\(398\) 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 \(-0.440332\pi\)
0.757676 0.652631i \(-0.226335\pi\)
\(410\) 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 \(-0.577741\pi\)
−0.241811 + 0.970323i \(0.577741\pi\)
\(420\) 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 \(-0.247059\pi\)
0.713609 + 0.700544i \(0.247059\pi\)
\(434\) 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 0.994319 0.106439i \(-0.0339450\pi\)
−0.589339 + 0.807886i \(0.700612\pi\)
\(440\) 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 \(-0.873553\pi\)
−0.922131 + 0.386878i \(0.873553\pi\)
\(462\) 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 \(-0.895474\pi\)
0.193984 0.981005i \(-0.437859\pi\)
\(468\) 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 \(-0.581672\pi\)
0.964562 0.263857i \(-0.0849947\pi\)
\(480\) 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 \(-0.155660\pi\)
0.882793 + 0.469762i \(0.155660\pi\)
\(504\) 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 \(0.000541051\pi\)
−0.498527 + 0.866874i \(0.666126\pi\)
\(510\) 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 −0.881099 0.472931i \(-0.843196\pi\)
0.850120 + 0.526589i \(0.176529\pi\)
\(522\) 0 0
\(523\) −6.36396 11.0227i −0.278277 0.481989i 0.692680 0.721245i \(-0.256430\pi\)
−0.970957 + 0.239256i \(0.923097\pi\)
\(524\) 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 −0.850740 0.525586i \(-0.823846\pi\)
0.880541 + 0.473970i \(0.157179\pi\)
\(564\) 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 −0.997805 0.0662152i \(-0.978908\pi\)
0.556247 + 0.831017i \(0.312241\pi\)
\(578\) 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 \(-0.709995\pi\)
−0.612894 + 0.790165i \(0.709995\pi\)
\(588\) 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 0.784256 0.620438i \(-0.213045\pi\)
−0.929443 + 0.368967i \(0.879712\pi\)
\(594\) 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 \(-0.707112\pi\)
−0.605713 + 0.795683i \(0.707112\pi\)
\(602\) 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 0.985246 0.171145i \(-0.0547467\pi\)
−0.640839 + 0.767675i \(0.721413\pi\)
\(608\) 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 −0.989483 0.144647i \(-0.953795\pi\)
0.620010 + 0.784594i \(0.287129\pi\)
\(620\) 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 \(-0.437465\pi\)
0.195199 + 0.980764i \(0.437465\pi\)
\(644\) 0 0
\(645\) −8.00000 −0.315000
\(646\) 0 0
\(647\) −4.24264 + 7.34847i −0.166795 + 0.288898i −0.937291 0.348547i \(-0.886675\pi\)
0.770496 + 0.637445i \(0.220009\pi\)
\(648\) 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 −0.771643 0.636056i \(-0.780565\pi\)
0.936662 + 0.350234i \(0.113898\pi\)
\(662\) 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 0.655622 0.755090i \(-0.272407\pi\)
−0.981738 + 0.190240i \(0.939073\pi\)
\(678\) 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 0.719215 0.694788i \(-0.244502\pi\)
−0.961311 + 0.275464i \(0.911168\pi\)
\(692\) 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 0.838449 0.544979i \(-0.183463\pi\)
−0.891191 + 0.453629i \(0.850129\pi\)
\(720\) 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 \(-0.619667\pi\)
−0.367152 + 0.930161i \(0.619667\pi\)
\(728\) 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 \(0.119915\pi\)
−0.146347 + 0.989233i \(0.546752\pi\)
\(734\) 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 0.794802 0.606869i \(-0.207575\pi\)
−0.922965 + 0.384884i \(0.874241\pi\)
\(762\) 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 \(-0.679868\pi\)
−0.535477 + 0.844550i \(0.679868\pi\)
\(770\) 0 0
\(771\) 18.0000 0.648254
\(772\) 0 0
\(773\) 24.0416 41.6413i 0.864717 1.49773i −0.00261021 0.999997i \(-0.500831\pi\)
0.867328 0.497738i \(-0.165836\pi\)
\(774\) 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 −0.853147 0.521670i \(-0.825309\pi\)
0.878353 + 0.478012i \(0.158643\pi\)
\(788\) 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 0
\(801\) 3.53553 6.12372i 0.124922