Properties

Label 1728.2.bc.d.721.1
Level $1728$
Weight $2$
Character 1728.721
Analytic conductor $13.798$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1728 = 2^{6} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1728.bc (of order \(12\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.7981494693\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 144)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 721.1
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1728.721
Dual form 1728.2.bc.d.1009.1

$q$-expansion

\(f(q)\) \(=\) \(q+(3.73205 + 1.00000i) q^{5} +(0.633975 + 0.366025i) q^{7} +O(q^{10})\) \(q+(3.73205 + 1.00000i) q^{5} +(0.633975 + 0.366025i) q^{7} +(-0.767949 - 2.86603i) q^{11} +(-1.63397 + 6.09808i) q^{13} +2.26795 q^{17} +(0.633975 + 0.633975i) q^{19} +(-1.09808 + 0.633975i) q^{23} +(8.59808 + 4.96410i) q^{25} +(2.36603 - 0.633975i) q^{29} +(3.73205 + 6.46410i) q^{31} +(2.00000 + 2.00000i) q^{35} +(1.26795 - 1.26795i) q^{37} +(2.59808 - 1.50000i) q^{41} +(-0.330127 - 1.23205i) q^{43} +(-4.83013 + 8.36603i) q^{47} +(-3.23205 - 5.59808i) q^{49} +(0.535898 - 0.535898i) q^{53} -11.4641i q^{55} +(4.96410 + 1.33013i) q^{59} +(-3.00000 + 0.803848i) q^{61} +(-12.1962 + 21.1244i) q^{65} +(-1.40192 + 5.23205i) q^{67} -10.9282i q^{71} -9.73205i q^{73} +(0.562178 - 2.09808i) q^{77} +(6.00000 - 10.3923i) q^{79} +(-1.36603 + 0.366025i) q^{83} +(8.46410 + 2.26795i) q^{85} +2.00000i q^{89} +(-3.26795 + 3.26795i) q^{91} +(1.73205 + 3.00000i) q^{95} +(-4.13397 + 7.16025i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 8q^{5} + 6q^{7} + O(q^{10}) \) \( 4q + 8q^{5} + 6q^{7} - 10q^{11} - 10q^{13} + 16q^{17} + 6q^{19} + 6q^{23} + 24q^{25} + 6q^{29} + 8q^{31} + 8q^{35} + 12q^{37} + 16q^{43} - 2q^{47} - 6q^{49} + 16q^{53} + 6q^{59} - 12q^{61} - 28q^{65} - 16q^{67} - 22q^{77} + 24q^{79} - 2q^{83} + 20q^{85} - 20q^{91} - 20q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(703\) \(1217\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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 0
\(4\) 0 0
\(5\) 3.73205 + 1.00000i 1.66902 + 0.447214i 0.964847 0.262811i \(-0.0846497\pi\)
0.704177 + 0.710025i \(0.251316\pi\)
\(6\) 0 0
\(7\) 0.633975 + 0.366025i 0.239620 + 0.138345i 0.615002 0.788526i \(-0.289155\pi\)
−0.375382 + 0.926870i \(0.622489\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −0.767949 2.86603i −0.231545 0.864139i −0.979676 0.200587i \(-0.935715\pi\)
0.748130 0.663552i \(-0.230952\pi\)
\(12\) 0 0
\(13\) −1.63397 + 6.09808i −0.453183 + 1.69130i 0.240192 + 0.970725i \(0.422790\pi\)
−0.693375 + 0.720577i \(0.743877\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.26795 0.550058 0.275029 0.961436i \(-0.411312\pi\)
0.275029 + 0.961436i \(0.411312\pi\)
\(18\) 0 0
\(19\) 0.633975 + 0.633975i 0.145444 + 0.145444i 0.776079 0.630635i \(-0.217206\pi\)
−0.630635 + 0.776079i \(0.717206\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −1.09808 + 0.633975i −0.228965 + 0.132193i −0.610094 0.792329i \(-0.708868\pi\)
0.381130 + 0.924522i \(0.375535\pi\)
\(24\) 0 0
\(25\) 8.59808 + 4.96410i 1.71962 + 0.992820i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 2.36603 0.633975i 0.439360 0.117726i −0.0323566 0.999476i \(-0.510301\pi\)
0.471717 + 0.881750i \(0.343635\pi\)
\(30\) 0 0
\(31\) 3.73205 + 6.46410i 0.670296 + 1.16099i 0.977820 + 0.209447i \(0.0671662\pi\)
−0.307524 + 0.951540i \(0.599500\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 2.00000 + 2.00000i 0.338062 + 0.338062i
\(36\) 0 0
\(37\) 1.26795 1.26795i 0.208450 0.208450i −0.595159 0.803608i \(-0.702911\pi\)
0.803608 + 0.595159i \(0.202911\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 2.59808 1.50000i 0.405751 0.234261i −0.283211 0.959058i \(-0.591400\pi\)
0.688963 + 0.724797i \(0.258066\pi\)
\(42\) 0 0
\(43\) −0.330127 1.23205i −0.0503439 0.187886i 0.936175 0.351535i \(-0.114340\pi\)
−0.986519 + 0.163649i \(0.947674\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −4.83013 + 8.36603i −0.704546 + 1.22031i 0.262309 + 0.964984i \(0.415516\pi\)
−0.966855 + 0.255326i \(0.917817\pi\)
\(48\) 0 0
\(49\) −3.23205 5.59808i −0.461722 0.799725i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 0.535898 0.535898i 0.0736113 0.0736113i −0.669343 0.742954i \(-0.733424\pi\)
0.742954 + 0.669343i \(0.233424\pi\)
\(54\) 0 0
\(55\) 11.4641i 1.54582i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 4.96410 + 1.33013i 0.646271 + 0.173168i 0.567042 0.823689i \(-0.308088\pi\)
0.0792287 + 0.996856i \(0.474754\pi\)
\(60\) 0 0
\(61\) −3.00000 + 0.803848i −0.384111 + 0.102922i −0.445707 0.895179i \(-0.647048\pi\)
0.0615961 + 0.998101i \(0.480381\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −12.1962 + 21.1244i −1.51275 + 2.62015i
\(66\) 0 0
\(67\) −1.40192 + 5.23205i −0.171272 + 0.639197i 0.825884 + 0.563840i \(0.190676\pi\)
−0.997157 + 0.0753572i \(0.975990\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 10.9282i 1.29694i −0.761241 0.648470i \(-0.775409\pi\)
0.761241 0.648470i \(-0.224591\pi\)
\(72\) 0 0
\(73\) 9.73205i 1.13905i −0.821974 0.569525i \(-0.807127\pi\)
0.821974 0.569525i \(-0.192873\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0.562178 2.09808i 0.0640661 0.239098i
\(78\) 0 0
\(79\) 6.00000 10.3923i 0.675053 1.16923i −0.301401 0.953498i \(-0.597454\pi\)
0.976453 0.215728i \(-0.0692125\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −1.36603 + 0.366025i −0.149941 + 0.0401765i −0.333009 0.942924i \(-0.608064\pi\)
0.183068 + 0.983100i \(0.441397\pi\)
\(84\) 0 0
\(85\) 8.46410 + 2.26795i 0.918061 + 0.245994i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 2.00000i 0.212000i 0.994366 + 0.106000i \(0.0338043\pi\)
−0.994366 + 0.106000i \(0.966196\pi\)
\(90\) 0 0
\(91\) −3.26795 + 3.26795i −0.342574 + 0.342574i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 1.73205 + 3.00000i 0.177705 + 0.307794i
\(96\) 0 0
\(97\) −4.13397 + 7.16025i −0.419742 + 0.727014i −0.995913 0.0903150i \(-0.971213\pi\)
0.576172 + 0.817329i \(0.304546\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 2.00000 + 7.46410i 0.199007 + 0.742706i 0.991193 + 0.132426i \(0.0422765\pi\)
−0.792186 + 0.610280i \(0.791057\pi\)
\(102\) 0 0
\(103\) 7.90192 4.56218i 0.778600 0.449525i −0.0573341 0.998355i \(-0.518260\pi\)
0.835934 + 0.548830i \(0.184927\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −13.4904 + 13.4904i −1.30416 + 1.30416i −0.378607 + 0.925558i \(0.623597\pi\)
−0.925558 + 0.378607i \(0.876403\pi\)
\(108\) 0 0
\(109\) 7.26795 + 7.26795i 0.696143 + 0.696143i 0.963576 0.267433i \(-0.0861754\pi\)
−0.267433 + 0.963576i \(0.586175\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −6.92820 12.0000i −0.651751 1.12887i −0.982698 0.185216i \(-0.940702\pi\)
0.330947 0.943649i \(-0.392632\pi\)
\(114\) 0 0
\(115\) −4.73205 + 1.26795i −0.441266 + 0.118237i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 1.43782 + 0.830127i 0.131805 + 0.0760976i
\(120\) 0 0
\(121\) 1.90192 1.09808i 0.172902 0.0998251i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 13.4641 + 13.4641i 1.20427 + 1.20427i
\(126\) 0 0
\(127\) 6.19615 0.549820 0.274910 0.961470i \(-0.411352\pi\)
0.274910 + 0.961470i \(0.411352\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 0.830127 3.09808i 0.0725285 0.270680i −0.920133 0.391606i \(-0.871920\pi\)
0.992662 + 0.120926i \(0.0385863\pi\)
\(132\) 0 0
\(133\) 0.169873 + 0.633975i 0.0147299 + 0.0549726i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −14.2583 8.23205i −1.21817 0.703312i −0.253645 0.967297i \(-0.581629\pi\)
−0.964527 + 0.263986i \(0.914963\pi\)
\(138\) 0 0
\(139\) 9.06218 + 2.42820i 0.768644 + 0.205958i 0.621772 0.783198i \(-0.286413\pi\)
0.146872 + 0.989156i \(0.453080\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 18.7321 1.56645
\(144\) 0 0
\(145\) 9.46410 0.785951
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −3.09808 0.830127i −0.253804 0.0680067i 0.129674 0.991557i \(-0.458607\pi\)
−0.383478 + 0.923550i \(0.625274\pi\)
\(150\) 0 0
\(151\) 2.36603 + 1.36603i 0.192544 + 0.111166i 0.593173 0.805075i \(-0.297875\pi\)
−0.400629 + 0.916240i \(0.631208\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 7.46410 + 27.8564i 0.599531 + 2.23748i
\(156\) 0 0
\(157\) −1.26795 + 4.73205i −0.101193 + 0.377659i −0.997886 0.0649959i \(-0.979297\pi\)
0.896692 + 0.442655i \(0.145963\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −0.928203 −0.0731527
\(162\) 0 0
\(163\) 7.00000 + 7.00000i 0.548282 + 0.548282i 0.925944 0.377661i \(-0.123272\pi\)
−0.377661 + 0.925944i \(0.623272\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0.464102 0.267949i 0.0359133 0.0207345i −0.481936 0.876206i \(-0.660066\pi\)
0.517849 + 0.855472i \(0.326733\pi\)
\(168\) 0 0
\(169\) −23.2583 13.4282i −1.78910 1.03294i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 12.5622 3.36603i 0.955085 0.255914i 0.252566 0.967580i \(-0.418725\pi\)
0.702519 + 0.711665i \(0.252059\pi\)
\(174\) 0 0
\(175\) 3.63397 + 6.29423i 0.274703 + 0.475799i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 11.9282 + 11.9282i 0.891556 + 0.891556i 0.994670 0.103114i \(-0.0328806\pi\)
−0.103114 + 0.994670i \(0.532881\pi\)
\(180\) 0 0
\(181\) 13.3923 13.3923i 0.995442 0.995442i −0.00454748 0.999990i \(-0.501448\pi\)
0.999990 + 0.00454748i \(0.00144751\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 6.00000 3.46410i 0.441129 0.254686i
\(186\) 0 0
\(187\) −1.74167 6.50000i −0.127364 0.475327i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 7.02628 12.1699i 0.508404 0.880581i −0.491549 0.870850i \(-0.663569\pi\)
0.999953 0.00973114i \(-0.00309757\pi\)
\(192\) 0 0
\(193\) −9.13397 15.8205i −0.657478 1.13879i −0.981266 0.192656i \(-0.938290\pi\)
0.323789 0.946129i \(-0.395043\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 3.66025 3.66025i 0.260782 0.260782i −0.564590 0.825372i \(-0.690966\pi\)
0.825372 + 0.564590i \(0.190966\pi\)
\(198\) 0 0
\(199\) 0.875644i 0.0620728i −0.999518 0.0310364i \(-0.990119\pi\)
0.999518 0.0310364i \(-0.00988078\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 1.73205 + 0.464102i 0.121566 + 0.0325735i
\(204\) 0 0
\(205\) 11.1962 3.00000i 0.781973 0.209529i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 1.33013 2.30385i 0.0920068 0.159360i
\(210\) 0 0
\(211\) 1.09808 4.09808i 0.0755947 0.282123i −0.917773 0.397106i \(-0.870015\pi\)
0.993367 + 0.114983i \(0.0366812\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 4.92820i 0.336101i
\(216\) 0 0
\(217\) 5.46410i 0.370927i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −3.70577 + 13.8301i −0.249277 + 0.930315i
\(222\) 0 0
\(223\) −11.0263 + 19.0981i −0.738374 + 1.27890i 0.214853 + 0.976646i \(0.431073\pi\)
−0.953227 + 0.302255i \(0.902260\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −14.4282 + 3.86603i −0.957633 + 0.256597i −0.703598 0.710598i \(-0.748425\pi\)
−0.254035 + 0.967195i \(0.581758\pi\)
\(228\) 0 0
\(229\) 6.83013 + 1.83013i 0.451347 + 0.120938i 0.477330 0.878724i \(-0.341605\pi\)
−0.0259823 + 0.999662i \(0.508271\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 7.19615i 0.471436i −0.971822 0.235718i \(-0.924256\pi\)
0.971822 0.235718i \(-0.0757441\pi\)
\(234\) 0 0
\(235\) −26.3923 + 26.3923i −1.72164 + 1.72164i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −13.0981 22.6865i −0.847244 1.46747i −0.883658 0.468133i \(-0.844927\pi\)
0.0364139 0.999337i \(-0.488407\pi\)
\(240\) 0 0
\(241\) −6.40192 + 11.0885i −0.412384 + 0.714270i −0.995150 0.0983699i \(-0.968637\pi\)
0.582766 + 0.812640i \(0.301971\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −6.46410 24.1244i −0.412976 1.54125i
\(246\) 0 0
\(247\) −4.90192 + 2.83013i −0.311902 + 0.180077i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 2.83013 2.83013i 0.178636 0.178636i −0.612125 0.790761i \(-0.709685\pi\)
0.790761 + 0.612125i \(0.209685\pi\)
\(252\) 0 0
\(253\) 2.66025 + 2.66025i 0.167249 + 0.167249i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 4.42820 + 7.66987i 0.276224 + 0.478434i 0.970443 0.241330i \(-0.0775836\pi\)
−0.694219 + 0.719763i \(0.744250\pi\)
\(258\) 0 0
\(259\) 1.26795 0.339746i 0.0787865 0.0211108i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −23.4904 13.5622i −1.44848 0.836280i −0.450088 0.892984i \(-0.648607\pi\)
−0.998391 + 0.0567045i \(0.981941\pi\)
\(264\) 0 0
\(265\) 2.53590 1.46410i 0.155779 0.0899390i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −4.73205 4.73205i −0.288518 0.288518i 0.547976 0.836494i \(-0.315399\pi\)
−0.836494 + 0.547976i \(0.815399\pi\)
\(270\) 0 0
\(271\) −20.3923 −1.23874 −0.619372 0.785098i \(-0.712613\pi\)
−0.619372 + 0.785098i \(0.712613\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 7.62436 28.4545i 0.459766 1.71587i
\(276\) 0 0
\(277\) −4.22243 15.7583i −0.253701 0.946826i −0.968808 0.247811i \(-0.920289\pi\)
0.715107 0.699015i \(-0.246378\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 8.66025 + 5.00000i 0.516627 + 0.298275i 0.735554 0.677466i \(-0.236922\pi\)
−0.218926 + 0.975741i \(0.570255\pi\)
\(282\) 0 0
\(283\) −27.7583 7.43782i −1.65006 0.442133i −0.690431 0.723398i \(-0.742579\pi\)
−0.959630 + 0.281265i \(0.909246\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 2.19615 0.129635
\(288\) 0 0
\(289\) −11.8564 −0.697436
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −13.5622 3.63397i −0.792311 0.212299i −0.160106 0.987100i \(-0.551183\pi\)
−0.632205 + 0.774801i \(0.717850\pi\)
\(294\) 0 0
\(295\) 17.1962 + 9.92820i 1.00120 + 0.578042i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −2.07180 7.73205i −0.119815 0.447156i
\(300\) 0 0
\(301\) 0.241670 0.901924i 0.0139296 0.0519860i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −12.0000 −0.687118
\(306\) 0 0
\(307\) 16.0263 + 16.0263i 0.914668 + 0.914668i 0.996635 0.0819670i \(-0.0261202\pi\)
−0.0819670 + 0.996635i \(0.526120\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 13.9019 8.02628i 0.788306 0.455129i −0.0510600 0.998696i \(-0.516260\pi\)
0.839366 + 0.543567i \(0.182927\pi\)
\(312\) 0 0
\(313\) 24.6506 + 14.2321i 1.39334 + 0.804443i 0.993683 0.112223i \(-0.0357972\pi\)
0.399653 + 0.916666i \(0.369131\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −31.4904 + 8.43782i −1.76868 + 0.473915i −0.988445 0.151577i \(-0.951565\pi\)
−0.780231 + 0.625492i \(0.784898\pi\)
\(318\) 0 0
\(319\) −3.63397 6.29423i −0.203464 0.352409i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 1.43782 + 1.43782i 0.0800026 + 0.0800026i
\(324\) 0 0
\(325\) −44.3205 + 44.3205i −2.45846 + 2.45846i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −6.12436 + 3.53590i −0.337647 + 0.194940i
\(330\) 0 0
\(331\) −5.09808 19.0263i −0.280216 1.04578i −0.952265 0.305273i \(-0.901252\pi\)
0.672049 0.740506i \(-0.265414\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −10.4641 + 18.1244i −0.571715 + 0.990239i
\(336\) 0 0
\(337\) −11.8923 20.5981i −0.647815 1.12205i −0.983644 0.180126i \(-0.942350\pi\)
0.335829 0.941923i \(-0.390984\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 15.6603 15.6603i 0.848050 0.848050i
\(342\) 0 0
\(343\) 9.85641i 0.532196i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −24.7224 6.62436i −1.32717 0.355614i −0.475510 0.879710i \(-0.657737\pi\)
−0.851659 + 0.524096i \(0.824403\pi\)
\(348\) 0 0
\(349\) −7.73205 + 2.07180i −0.413887 + 0.110901i −0.459753 0.888047i \(-0.652062\pi\)
0.0458657 + 0.998948i \(0.485395\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 10.1603 17.5981i 0.540776 0.936651i −0.458084 0.888909i \(-0.651464\pi\)
0.998860 0.0477421i \(-0.0152026\pi\)
\(354\) 0 0
\(355\) 10.9282 40.7846i 0.580009 2.16462i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 14.7321i 0.777528i 0.921337 + 0.388764i \(0.127098\pi\)
−0.921337 + 0.388764i \(0.872902\pi\)
\(360\) 0 0
\(361\) 18.1962i 0.957692i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 9.73205 36.3205i 0.509399 1.90110i
\(366\) 0 0
\(367\) 10.1244 17.5359i 0.528487 0.915366i −0.470961 0.882154i \(-0.656093\pi\)
0.999448 0.0332125i \(-0.0105738\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0.535898 0.143594i 0.0278225 0.00745501i
\(372\) 0 0
\(373\) −5.63397 1.50962i −0.291716 0.0781651i 0.109993 0.993932i \(-0.464917\pi\)
−0.401709 + 0.915767i \(0.631584\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 15.4641i 0.796442i
\(378\) 0 0
\(379\) 18.7583 18.7583i 0.963551 0.963551i −0.0358080 0.999359i \(-0.511400\pi\)
0.999359 + 0.0358080i \(0.0114005\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −3.26795 5.66025i −0.166984 0.289225i 0.770374 0.637593i \(-0.220070\pi\)
−0.937358 + 0.348367i \(0.886736\pi\)
\(384\) 0 0
\(385\) 4.19615 7.26795i 0.213856 0.370409i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 2.75833 + 10.2942i 0.139853 + 0.521938i 0.999931 + 0.0117752i \(0.00374824\pi\)
−0.860078 + 0.510163i \(0.829585\pi\)
\(390\) 0 0
\(391\) −2.49038 + 1.43782i −0.125944 + 0.0727138i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 32.7846 32.7846i 1.64957 1.64957i
\(396\) 0 0
\(397\) −12.7321 12.7321i −0.639003 0.639003i 0.311306 0.950310i \(-0.399233\pi\)
−0.950310 + 0.311306i \(0.899233\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −13.7942 23.8923i −0.688851 1.19312i −0.972210 0.234111i \(-0.924782\pi\)
0.283359 0.959014i \(-0.408551\pi\)
\(402\) 0 0
\(403\) −45.5167 + 12.1962i −2.26735 + 0.607534i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −4.60770 2.66025i −0.228395 0.131864i
\(408\) 0 0
\(409\) −26.1340 + 15.0885i −1.29224 + 0.746076i −0.979051 0.203614i \(-0.934731\pi\)
−0.313191 + 0.949690i \(0.601398\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 2.66025 + 2.66025i 0.130903 + 0.130903i
\(414\) 0 0
\(415\) −5.46410 −0.268222
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −8.36603 + 31.2224i −0.408707 + 1.52532i 0.388408 + 0.921488i \(0.373025\pi\)
−0.797115 + 0.603828i \(0.793641\pi\)
\(420\) 0 0
\(421\) 0.588457 + 2.19615i 0.0286797 + 0.107034i 0.978782 0.204905i \(-0.0656884\pi\)
−0.950102 + 0.311938i \(0.899022\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 19.5000 + 11.2583i 0.945889 + 0.546109i
\(426\) 0 0
\(427\) −2.19615 0.588457i −0.106279 0.0284774i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −5.80385 −0.279562 −0.139781 0.990182i \(-0.544640\pi\)
−0.139781 + 0.990182i \(0.544640\pi\)
\(432\) 0 0
\(433\) −2.26795 −0.108991 −0.0544953 0.998514i \(-0.517355\pi\)
−0.0544953 + 0.998514i \(0.517355\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −1.09808 0.294229i −0.0525281 0.0140749i
\(438\) 0 0
\(439\) 4.85641 + 2.80385i 0.231784 + 0.133820i 0.611395 0.791326i \(-0.290609\pi\)
−0.379611 + 0.925146i \(0.623942\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −5.25833 19.6244i −0.249831 0.932381i −0.970894 0.239511i \(-0.923013\pi\)
0.721063 0.692870i \(-0.243654\pi\)
\(444\) 0 0
\(445\) −2.00000 + 7.46410i −0.0948091 + 0.353832i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 20.6603 0.975018 0.487509 0.873118i \(-0.337906\pi\)
0.487509 + 0.873118i \(0.337906\pi\)
\(450\) 0 0
\(451\) −6.29423 6.29423i −0.296384 0.296384i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −15.4641 + 8.92820i −0.724968 + 0.418561i
\(456\) 0 0
\(457\) 20.2583 + 11.6962i 0.947645 + 0.547123i 0.892348 0.451347i \(-0.149056\pi\)
0.0552962 + 0.998470i \(0.482390\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −2.56218 + 0.686533i −0.119333 + 0.0319751i −0.317991 0.948094i \(-0.603008\pi\)
0.198659 + 0.980069i \(0.436342\pi\)
\(462\) 0 0
\(463\) 9.19615 + 15.9282i 0.427381 + 0.740246i 0.996640 0.0819125i \(-0.0261028\pi\)
−0.569258 + 0.822159i \(0.692769\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 4.36603 + 4.36603i 0.202036 + 0.202036i 0.800872 0.598836i \(-0.204370\pi\)
−0.598836 + 0.800872i \(0.704370\pi\)
\(468\) 0 0
\(469\) −2.80385 + 2.80385i −0.129470 + 0.129470i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −3.27757 + 1.89230i −0.150703 + 0.0870083i
\(474\) 0 0
\(475\) 2.30385 + 8.59808i 0.105708 + 0.394507i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 12.8301 22.2224i 0.586223 1.01537i −0.408498 0.912759i \(-0.633947\pi\)
0.994722 0.102610i \(-0.0327193\pi\)
\(480\) 0 0
\(481\) 5.66025 + 9.80385i 0.258085 + 0.447017i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −22.5885 + 22.5885i −1.02569 + 1.02569i
\(486\) 0 0
\(487\) 16.1962i 0.733918i −0.930237 0.366959i \(-0.880399\pi\)
0.930237 0.366959i \(-0.119601\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −25.7224 6.89230i −1.16084 0.311045i −0.373537 0.927615i \(-0.621855\pi\)
−0.787300 + 0.616570i \(0.788522\pi\)
\(492\) 0 0
\(493\) 5.36603 1.43782i 0.241674 0.0647563i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 4.00000 6.92820i 0.179425 0.310772i
\(498\) 0 0
\(499\) 1.69615 6.33013i 0.0759302 0.283375i −0.917512 0.397707i \(-0.869806\pi\)
0.993443 + 0.114332i \(0.0364727\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 27.7128i 1.23565i 0.786314 + 0.617827i \(0.211987\pi\)
−0.786314 + 0.617827i \(0.788013\pi\)
\(504\) 0 0
\(505\) 29.8564i 1.32859i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 4.53590 16.9282i 0.201050 0.750329i −0.789567 0.613664i \(-0.789695\pi\)
0.990617 0.136665i \(-0.0436385\pi\)
\(510\) 0 0
\(511\) 3.56218 6.16987i 0.157581 0.272939i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 34.0526 9.12436i 1.50054 0.402067i
\(516\) 0 0
\(517\) 27.6865 + 7.41858i 1.21765 + 0.326269i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 13.0000i 0.569540i −0.958596 0.284770i \(-0.908083\pi\)
0.958596 0.284770i \(-0.0919173\pi\)
\(522\) 0 0
\(523\) 14.4641 14.4641i 0.632471 0.632471i −0.316216 0.948687i \(-0.602412\pi\)
0.948687 + 0.316216i \(0.102412\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 8.46410 + 14.6603i 0.368702 + 0.638611i
\(528\) 0 0
\(529\) −10.6962 + 18.5263i −0.465050 + 0.805490i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 4.90192 + 18.2942i 0.212326 + 0.792411i
\(534\) 0 0
\(535\) −63.8372 + 36.8564i −2.75992 + 1.59344i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −13.5622 + 13.5622i −0.584164 + 0.584164i
\(540\) 0 0
\(541\) −8.19615 8.19615i −0.352380 0.352380i 0.508614 0.860994i \(-0.330158\pi\)
−0.860994 + 0.508614i \(0.830158\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 19.8564 + 34.3923i 0.850555 + 1.47320i
\(546\) 0 0
\(547\) 31.2583 8.37564i 1.33651 0.358117i 0.481371 0.876517i \(-0.340139\pi\)
0.855138 + 0.518400i \(0.173472\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 1.90192 + 1.09808i 0.0810247 + 0.0467796i
\(552\) 0 0
\(553\) 7.60770 4.39230i 0.323512 0.186780i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 25.1962 + 25.1962i 1.06760 + 1.06760i 0.997543 + 0.0700519i \(0.0223165\pi\)
0.0700519 + 0.997543i \(0.477684\pi\)
\(558\) 0 0
\(559\) 8.05256 0.340587
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 1.00962 3.76795i 0.0425504 0.158800i −0.941382 0.337343i \(-0.890472\pi\)
0.983932 + 0.178543i \(0.0571384\pi\)
\(564\) 0 0
\(565\) −13.8564 51.7128i −0.582943 2.17557i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −23.5981 13.6244i −0.989283 0.571163i −0.0842230 0.996447i \(-0.526841\pi\)
−0.905060 + 0.425284i \(0.860174\pi\)
\(570\) 0 0
\(571\) 19.8923 + 5.33013i 0.832467 + 0.223059i 0.649790 0.760114i \(-0.274857\pi\)
0.182677 + 0.983173i \(0.441524\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −12.5885 −0.524975
\(576\) 0 0
\(577\) 35.7846 1.48973 0.744866 0.667214i \(-0.232513\pi\)
0.744866 + 0.667214i \(0.232513\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −1.00000 0.267949i −0.0414870 0.0111164i
\(582\) 0 0
\(583\) −1.94744 1.12436i −0.0806548 0.0465661i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −1.00962 3.76795i −0.0416714 0.155520i 0.941955 0.335739i \(-0.108986\pi\)
−0.983626 + 0.180219i \(0.942319\pi\)
\(588\) 0 0
\(589\) −1.73205 + 6.46410i −0.0713679 + 0.266349i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −10.5359 −0.432657 −0.216329 0.976321i \(-0.569408\pi\)
−0.216329 + 0.976321i \(0.569408\pi\)
\(594\) 0 0
\(595\) 4.53590 + 4.53590i 0.185954 + 0.185954i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 23.3205 13.4641i 0.952850 0.550128i 0.0588850 0.998265i \(-0.481245\pi\)
0.893965 + 0.448136i \(0.147912\pi\)
\(600\) 0 0
\(601\) −17.5526 10.1340i −0.715984 0.413373i 0.0972889 0.995256i \(-0.468983\pi\)
−0.813273 + 0.581883i \(0.802316\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 8.19615 2.19615i 0.333221 0.0892863i
\(606\) 0 0
\(607\) −22.5885 39.1244i −0.916837 1.58801i −0.804189 0.594374i \(-0.797400\pi\)
−0.112648 0.993635i \(-0.535933\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −43.1244 43.1244i −1.74462 1.74462i
\(612\) 0 0
\(613\) 1.66025 1.66025i 0.0670570 0.0670570i −0.672783 0.739840i \(-0.734901\pi\)
0.739840 + 0.672783i \(0.234901\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −3.91154 + 2.25833i −0.157473 + 0.0909170i −0.576666 0.816980i \(-0.695646\pi\)
0.419193 + 0.907897i \(0.362313\pi\)
\(618\) 0 0
\(619\) 10.4019 + 38.8205i 0.418089 + 1.56033i 0.778568 + 0.627561i \(0.215947\pi\)
−0.360479 + 0.932767i \(0.617387\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −0.732051 + 1.26795i −0.0293290 + 0.0507993i
\(624\) 0 0
\(625\) 11.9641 + 20.7224i 0.478564 + 0.828897i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 2.87564 2.87564i 0.114659 0.114659i
\(630\) 0 0
\(631\) 38.3923i 1.52837i −0.644995 0.764187i \(-0.723141\pi\)
0.644995 0.764187i \(-0.276859\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 23.1244 + 6.19615i 0.917662 + 0.245887i
\(636\) 0 0
\(637\) 39.4186 10.5622i 1.56182 0.418489i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 4.20577 7.28461i 0.166118 0.287725i −0.770934 0.636915i \(-0.780210\pi\)
0.937052 + 0.349191i \(0.113543\pi\)
\(642\) 0 0
\(643\) −12.2321 + 45.6506i −0.482385 + 1.80029i 0.109173 + 0.994023i \(0.465180\pi\)
−0.591558 + 0.806263i \(0.701487\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 13.2679i 0.521617i 0.965391 + 0.260808i \(0.0839891\pi\)
−0.965391 + 0.260808i \(0.916011\pi\)
\(648\) 0 0
\(649\) 15.2487i 0.598564i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 1.50962 5.63397i 0.0590760 0.220474i −0.930077 0.367365i \(-0.880260\pi\)
0.989153 + 0.146891i \(0.0469266\pi\)
\(654\) 0 0
\(655\) 6.19615 10.7321i 0.242104 0.419336i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −15.0263 + 4.02628i −0.585341 + 0.156842i −0.539323 0.842099i \(-0.681320\pi\)
−0.0460178 + 0.998941i \(0.514653\pi\)
\(660\) 0 0
\(661\) −8.19615 2.19615i −0.318793 0.0854204i 0.0958740 0.995393i \(-0.469435\pi\)
−0.414667 + 0.909973i \(0.636102\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 2.53590i 0.0983379i
\(666\) 0 0
\(667\) −2.19615 + 2.19615i −0.0850354 + 0.0850354i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 4.60770 + 7.98076i 0.177878 + 0.308094i
\(672\) 0 0
\(673\) 8.80385 15.2487i 0.339363 0.587795i −0.644950 0.764225i \(-0.723122\pi\)
0.984313 + 0.176430i \(0.0564550\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 1.26795 + 4.73205i 0.0487312 + 0.181867i 0.986002 0.166736i \(-0.0533227\pi\)
−0.937270 + 0.348603i \(0.886656\pi\)
\(678\) 0 0
\(679\) −5.24167 + 3.02628i −0.201157 + 0.116138i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −4.70577 + 4.70577i −0.180061 + 0.180061i −0.791383 0.611321i \(-0.790638\pi\)
0.611321 + 0.791383i \(0.290638\pi\)
\(684\) 0 0
\(685\) −44.9808 44.9808i −1.71863 1.71863i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 2.39230 + 4.14359i 0.0911396 + 0.157858i
\(690\) 0 0
\(691\) −23.4904 + 6.29423i −0.893616 + 0.239444i −0.676273 0.736651i \(-0.736406\pi\)
−0.217344 + 0.976095i \(0.569739\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 31.3923 + 18.1244i 1.19078 + 0.687496i
\(696\) 0 0
\(697\) 5.89230 3.40192i 0.223187 0.128857i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −10.6603 10.6603i −0.402632 0.402632i 0.476527 0.879160i \(-0.341895\pi\)
−0.879160 + 0.476527i \(0.841895\pi\)
\(702\) 0 0
\(703\) 1.60770 0.0606354
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −1.46410 + 5.46410i −0.0550632 + 0.205499i
\(708\) 0 0
\(709\) 5.41154 + 20.1962i 0.203235 + 0.758482i 0.989980 + 0.141205i \(0.0450977\pi\)
−0.786746 + 0.617277i \(0.788236\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −8.19615 4.73205i −0.306948 0.177217i
\(714\) 0 0
\(715\) 69.9090 + 18.7321i 2.61445 + 0.700539i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −16.3923 −0.611330 −0.305665 0.952139i \(-0.598879\pi\)
−0.305665 + 0.952139i \(0.598879\pi\)
\(720\) 0 0
\(721\) 6.67949 0.248757
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 23.4904 + 6.29423i 0.872411 + 0.233762i
\(726\) 0 0
\(727\) 31.8109 + 18.3660i 1.17980 + 0.681158i 0.955968 0.293470i \(-0.0948099\pi\)
0.223832 + 0.974628i \(0.428143\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −0.748711 2.79423i −0.0276921 0.103348i
\(732\) 0 0
\(733\) 8.02628 29.9545i 0.296457 1.10639i −0.643596 0.765366i \(-0.722558\pi\)
0.940053 0.341028i \(-0.110775\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 16.0718 0.592012
\(738\) 0 0
\(739\) −21.2224 21.2224i −0.780680 0.780680i 0.199266 0.979945i \(-0.436144\pi\)
−0.979945 + 0.199266i \(0.936144\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −2.24167 + 1.29423i −0.0822389 + 0.0474806i −0.540556 0.841308i \(-0.681786\pi\)
0.458317 + 0.888789i \(0.348453\pi\)
\(744\) 0 0
\(745\) −10.7321 6.19615i −0.393192 0.227009i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −13.4904 + 3.61474i −0.492928 + 0.132080i
\(750\) 0 0
\(751\) −18.8564 32.6603i −0.688080 1.19179i −0.972458 0.233077i \(-0.925120\pi\)
0.284378 0.958712i \(-0.408213\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 7.46410 + 7.46410i 0.271646 + 0.271646i
\(756\) 0 0
\(757\) −6.07180 + 6.07180i −0.220683 + 0.220683i −0.808786 0.588103i \(-0.799875\pi\)
0.588103 + 0.808786i \(0.299875\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −27.3731 + 15.8038i −0.992273 + 0.572889i −0.905953 0.423378i \(-0.860844\pi\)
−0.0863200 + 0.996267i \(0.527511\pi\)
\(762\) 0 0
\(763\) 1.94744 + 7.26795i 0.0705021 + 0.263117i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −16.2224 + 28.0981i −0.585758 + 1.01456i
\(768\) 0 0
\(769\) 10.1244 + 17.5359i 0.365094 + 0.632361i 0.988791 0.149305i \(-0.0477036\pi\)
−0.623698 + 0.781666i \(0.714370\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −4.41154 + 4.41154i −0.158672 + 0.158672i −0.781978 0.623306i \(-0.785789\pi\)
0.623306 + 0.781978i \(0.285789\pi\)
\(774\) 0 0
\(775\) 74.1051i 2.66193i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 2.59808 + 0.696152i 0.0930857 + 0.0249422i
\(780\) 0 0
\(781\) −31.3205 + 8.39230i −1.12074 + 0.300300i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −9.46410 + 16.3923i −0.337788 + 0.585066i
\(786\) 0 0
\(787\) 13.3468 49.8109i 0.475762 1.77557i −0.142716 0.989764i \(-0.545583\pi\)
0.618477 0.785803i \(-0.287750\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 10.1436i 0.360665i
\(792\) 0 0
\(793\) 19.6077i 0.696290i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −14.5167 + 54.1769i −0.514206 + 1.91904i −0.146065 + 0.989275i \(0.546661\pi\)
−0.368142 + 0.929770i \(0.620006\pi\)
\(798\) 0 0
\(799\) −10.9545 + 18.9737i −0.387542 + 0.671242i
\(800\) 0 0
\(801\)