Properties

Label 1728.2.bc.a.1585.1
Level $1728$
Weight $2$
Character 1728.1585
Analytic conductor $13.798$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

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 1585.1
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1728.1585
Dual form 1728.2.bc.a.145.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 + 3.73205i) q^{5} +(-0.633975 - 0.366025i) q^{7} +O(q^{10})\) \(q+(-1.00000 + 3.73205i) q^{5} +(-0.633975 - 0.366025i) q^{7} +(2.86603 - 0.767949i) q^{11} +(6.09808 + 1.63397i) q^{13} +2.26795 q^{17} +(0.633975 - 0.633975i) q^{19} +(1.09808 - 0.633975i) q^{23} +(-8.59808 - 4.96410i) q^{25} +(-0.633975 - 2.36603i) q^{29} +(3.73205 + 6.46410i) q^{31} +(2.00000 - 2.00000i) q^{35} +(1.26795 + 1.26795i) q^{37} +(-2.59808 + 1.50000i) q^{41} +(1.23205 - 0.330127i) q^{43} +(-4.83013 + 8.36603i) q^{47} +(-3.23205 - 5.59808i) q^{49} +(0.535898 + 0.535898i) q^{53} +11.4641i q^{55} +(-1.33013 + 4.96410i) q^{59} +(0.803848 + 3.00000i) q^{61} +(-12.1962 + 21.1244i) q^{65} +(5.23205 + 1.40192i) q^{67} +10.9282i q^{71} +9.73205i q^{73} +(-2.09808 - 0.562178i) q^{77} +(6.00000 - 10.3923i) q^{79} +(0.366025 + 1.36603i) q^{83} +(-2.26795 + 8.46410i) q^{85} -2.00000i q^{89} +(-3.26795 - 3.26795i) q^{91} +(1.73205 + 3.00000i) q^{95} +(-4.13397 + 7.16025i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 4q^{5} - 6q^{7} + O(q^{10}) \) \( 4q - 4q^{5} - 6q^{7} + 8q^{11} + 14q^{13} + 16q^{17} + 6q^{19} - 6q^{23} - 24q^{25} - 6q^{29} + 8q^{31} + 8q^{35} + 12q^{37} - 2q^{43} - 2q^{47} - 6q^{49} + 16q^{53} + 12q^{59} + 24q^{61} - 28q^{65} + 14q^{67} + 2q^{77} + 24q^{79} - 2q^{83} - 16q^{85} - 20q^{91} - 20q^{97} + O(q^{100}) \)

Character values

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

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

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
\(5\) −1.00000 + 3.73205i −0.447214 + 1.66902i 0.262811 + 0.964847i \(0.415350\pi\)
−0.710025 + 0.704177i \(0.751316\pi\)
\(6\) 0 0
\(7\) −0.633975 0.366025i −0.239620 0.138345i 0.375382 0.926870i \(-0.377511\pi\)
−0.615002 + 0.788526i \(0.710845\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 2.86603 0.767949i 0.864139 0.231545i 0.200587 0.979676i \(-0.435715\pi\)
0.663552 + 0.748130i \(0.269048\pi\)
\(12\) 0 0
\(13\) 6.09808 + 1.63397i 1.69130 + 0.453183i 0.970725 0.240192i \(-0.0772105\pi\)
0.720577 + 0.693375i \(0.243877\pi\)
\(14\) 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 −0.630635 0.776079i \(-0.717206\pi\)
0.776079 + 0.630635i \(0.217206\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 1.09808 0.633975i 0.228965 0.132193i −0.381130 0.924522i \(-0.624465\pi\)
0.610094 + 0.792329i \(0.291132\pi\)
\(24\) 0 0
\(25\) −8.59808 4.96410i −1.71962 0.992820i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −0.633975 2.36603i −0.117726 0.439360i 0.881750 0.471717i \(-0.156365\pi\)
−0.999476 + 0.0323566i \(0.989699\pi\)
\(30\) 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 0.803608 0.595159i \(-0.202911\pi\)
−0.595159 + 0.803608i \(0.702911\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −2.59808 + 1.50000i −0.405751 + 0.234261i −0.688963 0.724797i \(-0.741934\pi\)
0.283211 + 0.959058i \(0.408600\pi\)
\(42\) 0 0
\(43\) 1.23205 0.330127i 0.187886 0.0503439i −0.163649 0.986519i \(-0.552326\pi\)
0.351535 + 0.936175i \(0.385660\pi\)
\(44\) 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 0.742954 0.669343i \(-0.233424\pi\)
−0.669343 + 0.742954i \(0.733424\pi\)
\(54\) 0 0
\(55\) 11.4641i 1.54582i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −1.33013 + 4.96410i −0.173168 + 0.646271i 0.823689 + 0.567042i \(0.191912\pi\)
−0.996856 + 0.0792287i \(0.974754\pi\)
\(60\) 0 0
\(61\) 0.803848 + 3.00000i 0.102922 + 0.384111i 0.998101 0.0615961i \(-0.0196191\pi\)
−0.895179 + 0.445707i \(0.852952\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −12.1962 + 21.1244i −1.51275 + 2.62015i
\(66\) 0 0
\(67\) 5.23205 + 1.40192i 0.639197 + 0.171272i 0.563840 0.825884i \(-0.309324\pi\)
0.0753572 + 0.997157i \(0.475990\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 10.9282i 1.29694i 0.761241 + 0.648470i \(0.224591\pi\)
−0.761241 + 0.648470i \(0.775409\pi\)
\(72\) 0 0
\(73\) 9.73205i 1.13905i 0.821974 + 0.569525i \(0.192873\pi\)
−0.821974 + 0.569525i \(0.807127\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −2.09808 0.562178i −0.239098 0.0640661i
\(78\) 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
\(83\) 0.366025 + 1.36603i 0.0401765 + 0.149941i 0.983100 0.183068i \(-0.0586028\pi\)
−0.942924 + 0.333009i \(0.891936\pi\)
\(84\) 0 0
\(85\) −2.26795 + 8.46410i −0.245994 + 0.918061i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 2.00000i 0.212000i −0.994366 0.106000i \(-0.966196\pi\)
0.994366 0.106000i \(-0.0338043\pi\)
\(90\) 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
\(101\) −7.46410 + 2.00000i −0.742706 + 0.199007i −0.610280 0.792186i \(-0.708943\pi\)
−0.132426 + 0.991193i \(0.542277\pi\)
\(102\) 0 0
\(103\) −7.90192 + 4.56218i −0.778600 + 0.449525i −0.835934 0.548830i \(-0.815073\pi\)
0.0573341 + 0.998355i \(0.481740\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −13.4904 13.4904i −1.30416 1.30416i −0.925558 0.378607i \(-0.876403\pi\)
−0.378607 0.925558i \(-0.623597\pi\)
\(108\) 0 0
\(109\) 7.26795 7.26795i 0.696143 0.696143i −0.267433 0.963576i \(-0.586175\pi\)
0.963576 + 0.267433i \(0.0861754\pi\)
\(110\) 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
\(115\) 1.26795 + 4.73205i 0.118237 + 0.441266i
\(116\) 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
\(131\) −3.09808 0.830127i −0.270680 0.0725285i 0.120926 0.992662i \(-0.461414\pi\)
−0.391606 + 0.920133i \(0.628080\pi\)
\(132\) 0 0
\(133\) −0.633975 + 0.169873i −0.0549726 + 0.0147299i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 14.2583 + 8.23205i 1.21817 + 0.703312i 0.964527 0.263986i \(-0.0850372\pi\)
0.253645 + 0.967297i \(0.418371\pi\)
\(138\) 0 0
\(139\) −2.42820 + 9.06218i −0.205958 + 0.768644i 0.783198 + 0.621772i \(0.213587\pi\)
−0.989156 + 0.146872i \(0.953080\pi\)
\(140\) 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
\(149\) 0.830127 3.09808i 0.0680067 0.253804i −0.923550 0.383478i \(-0.874726\pi\)
0.991557 + 0.129674i \(0.0413929\pi\)
\(150\) 0 0
\(151\) −2.36603 1.36603i −0.192544 0.111166i 0.400629 0.916240i \(-0.368792\pi\)
−0.593173 + 0.805075i \(0.702125\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −27.8564 + 7.46410i −2.23748 + 0.599531i
\(156\) 0 0
\(157\) 4.73205 + 1.26795i 0.377659 + 0.101193i 0.442655 0.896692i \(-0.354037\pi\)
−0.0649959 + 0.997886i \(0.520703\pi\)
\(158\) 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 −0.377661 0.925944i \(-0.623272\pi\)
0.925944 + 0.377661i \(0.123272\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −0.464102 + 0.267949i −0.0359133 + 0.0207345i −0.517849 0.855472i \(-0.673267\pi\)
0.481936 + 0.876206i \(0.339934\pi\)
\(168\) 0 0
\(169\) 23.2583 + 13.4282i 1.78910 + 1.03294i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −3.36603 12.5622i −0.255914 0.955085i −0.967580 0.252566i \(-0.918725\pi\)
0.711665 0.702519i \(-0.247941\pi\)
\(174\) 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 −0.103114 0.994670i \(-0.532881\pi\)
0.994670 + 0.103114i \(0.0328806\pi\)
\(180\) 0 0
\(181\) 13.3923 + 13.3923i 0.995442 + 0.995442i 0.999990 0.00454748i \(-0.00144751\pi\)
−0.00454748 + 0.999990i \(0.501448\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −6.00000 + 3.46410i −0.441129 + 0.254686i
\(186\) 0 0
\(187\) 6.50000 1.74167i 0.475327 0.127364i
\(188\) 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 0.825372 0.564590i \(-0.190966\pi\)
−0.564590 + 0.825372i \(0.690966\pi\)
\(198\) 0 0
\(199\) 0.875644i 0.0620728i 0.999518 + 0.0310364i \(0.00988078\pi\)
−0.999518 + 0.0310364i \(0.990119\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −0.464102 + 1.73205i −0.0325735 + 0.121566i
\(204\) 0 0
\(205\) −3.00000 11.1962i −0.209529 0.781973i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 1.33013 2.30385i 0.0920068 0.159360i
\(210\) 0 0
\(211\) −4.09808 1.09808i −0.282123 0.0755947i 0.114983 0.993367i \(-0.463319\pi\)
−0.397106 + 0.917773i \(0.629985\pi\)
\(212\) 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
\(221\) 13.8301 + 3.70577i 0.930315 + 0.249277i
\(222\) 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
\(227\) 3.86603 + 14.4282i 0.256597 + 0.957633i 0.967195 + 0.254035i \(0.0817579\pi\)
−0.710598 + 0.703598i \(0.751575\pi\)
\(228\) 0 0
\(229\) −1.83013 + 6.83013i −0.120938 + 0.451347i −0.999662 0.0259823i \(-0.991729\pi\)
0.878724 + 0.477330i \(0.158395\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 7.19615i 0.471436i 0.971822 + 0.235718i \(0.0757441\pi\)
−0.971822 + 0.235718i \(0.924256\pi\)
\(234\) 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
\(245\) 24.1244 6.46410i 1.54125 0.412976i
\(246\) 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 0.790761 0.612125i \(-0.209685\pi\)
−0.612125 + 0.790761i \(0.709685\pi\)
\(252\) 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
\(259\) −0.339746 1.26795i −0.0211108 0.0787865i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 23.4904 + 13.5622i 1.44848 + 0.836280i 0.998391 0.0567045i \(-0.0180593\pi\)
0.450088 + 0.892984i \(0.351393\pi\)
\(264\) 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 −0.836494 0.547976i \(-0.815399\pi\)
0.547976 + 0.836494i \(0.315399\pi\)
\(270\) 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
\(275\) −28.4545 7.62436i −1.71587 0.459766i
\(276\) 0 0
\(277\) 15.7583 4.22243i 0.946826 0.253701i 0.247811 0.968808i \(-0.420289\pi\)
0.699015 + 0.715107i \(0.253622\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −8.66025 5.00000i −0.516627 0.298275i 0.218926 0.975741i \(-0.429745\pi\)
−0.735554 + 0.677466i \(0.763078\pi\)
\(282\) 0 0
\(283\) 7.43782 27.7583i 0.442133 1.65006i −0.281265 0.959630i \(-0.590754\pi\)
0.723398 0.690431i \(-0.242579\pi\)
\(284\) 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
\(293\) 3.63397 13.5622i 0.212299 0.792311i −0.774801 0.632205i \(-0.782150\pi\)
0.987100 0.160106i \(-0.0511834\pi\)
\(294\) 0 0
\(295\) −17.1962 9.92820i −1.00120 0.578042i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 7.73205 2.07180i 0.447156 0.119815i
\(300\) 0 0
\(301\) −0.901924 0.241670i −0.0519860 0.0139296i
\(302\) 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 −0.0819670 0.996635i \(-0.526120\pi\)
0.996635 + 0.0819670i \(0.0261202\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −13.9019 + 8.02628i −0.788306 + 0.455129i −0.839366 0.543567i \(-0.817073\pi\)
0.0510600 + 0.998696i \(0.483740\pi\)
\(312\) 0 0
\(313\) −24.6506 14.2321i −1.39334 0.804443i −0.399653 0.916666i \(-0.630869\pi\)
−0.993683 + 0.112223i \(0.964203\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 8.43782 + 31.4904i 0.473915 + 1.76868i 0.625492 + 0.780231i \(0.284898\pi\)
−0.151577 + 0.988445i \(0.548435\pi\)
\(318\) 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
\(331\) 19.0263 5.09808i 1.04578 0.280216i 0.305273 0.952265i \(-0.401252\pi\)
0.740506 + 0.672049i \(0.234586\pi\)
\(332\) 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
\(347\) 6.62436 24.7224i 0.355614 1.32717i −0.524096 0.851659i \(-0.675597\pi\)
0.879710 0.475510i \(-0.157737\pi\)
\(348\) 0 0
\(349\) 2.07180 + 7.73205i 0.110901 + 0.413887i 0.998948 0.0458657i \(-0.0146046\pi\)
−0.888047 + 0.459753i \(0.847938\pi\)
\(350\) 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
\(355\) −40.7846 10.9282i −2.16462 0.580009i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 14.7321i 0.777528i −0.921337 0.388764i \(-0.872902\pi\)
0.921337 0.388764i \(-0.127098\pi\)
\(360\) 0 0
\(361\) 18.1962i 0.957692i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −36.3205 9.73205i −1.90110 0.509399i
\(366\) 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
\(371\) −0.143594 0.535898i −0.00745501 0.0278225i
\(372\) 0 0
\(373\) 1.50962 5.63397i 0.0781651 0.291716i −0.915767 0.401709i \(-0.868416\pi\)
0.993932 + 0.109993i \(0.0350829\pi\)
\(374\) 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 0.999359 0.0358080i \(-0.0114005\pi\)
−0.0358080 + 0.999359i \(0.511400\pi\)
\(380\) 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
\(389\) −10.2942 + 2.75833i −0.521938 + 0.139853i −0.510163 0.860078i \(-0.670415\pi\)
−0.0117752 + 0.999931i \(0.503748\pi\)
\(390\) 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 −0.950310 0.311306i \(-0.899233\pi\)
0.311306 + 0.950310i \(0.399233\pi\)
\(398\) 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
\(403\) 12.1962 + 45.5167i 0.607534 + 2.26735i
\(404\) 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 0.313191 0.949690i \(-0.398602\pi\)
0.979051 + 0.203614i \(0.0652688\pi\)
\(410\) 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
\(419\) 31.2224 + 8.36603i 1.52532 + 0.408707i 0.921488 0.388408i \(-0.126975\pi\)
0.603828 + 0.797115i \(0.293641\pi\)
\(420\) 0 0
\(421\) −2.19615 + 0.588457i −0.107034 + 0.0286797i −0.311938 0.950102i \(-0.600978\pi\)
0.204905 + 0.978782i \(0.434312\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −19.5000 11.2583i −0.945889 0.546109i
\(426\) 0 0
\(427\) 0.588457 2.19615i 0.0284774 0.106279i
\(428\) 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
\(437\) 0.294229 1.09808i 0.0140749 0.0525281i
\(438\) 0 0
\(439\) −4.85641 2.80385i −0.231784 0.133820i 0.379611 0.925146i \(-0.376058\pi\)
−0.611395 + 0.791326i \(0.709391\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 19.6244 5.25833i 0.932381 0.249831i 0.239511 0.970894i \(-0.423013\pi\)
0.692870 + 0.721063i \(0.256346\pi\)
\(444\) 0 0
\(445\) 7.46410 + 2.00000i 0.353832 + 0.0948091i
\(446\) 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 −0.0552962 0.998470i \(-0.517610\pi\)
−0.892348 + 0.451347i \(0.850944\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0.686533 + 2.56218i 0.0319751 + 0.119333i 0.980069 0.198659i \(-0.0636585\pi\)
−0.948094 + 0.317991i \(0.896992\pi\)
\(462\) 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 −0.598836 0.800872i \(-0.704370\pi\)
0.800872 + 0.598836i \(0.204370\pi\)
\(468\) 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
\(475\) −8.59808 + 2.30385i −0.394507 + 0.105708i
\(476\) 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 \(0.119601\pi\)
−0.930237 + 0.366959i \(0.880399\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 6.89230 25.7224i 0.311045 1.16084i −0.616570 0.787300i \(-0.711478\pi\)
0.927615 0.373537i \(-0.121855\pi\)
\(492\) 0 0
\(493\) −1.43782 5.36603i −0.0647563 0.241674i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 4.00000 6.92820i 0.179425 0.310772i
\(498\) 0 0
\(499\) −6.33013 1.69615i −0.283375 0.0759302i 0.114332 0.993443i \(-0.463527\pi\)
−0.397707 + 0.917512i \(0.630194\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 27.7128i 1.23565i −0.786314 0.617827i \(-0.788013\pi\)
0.786314 0.617827i \(-0.211987\pi\)
\(504\) 0 0
\(505\) 29.8564i 1.32859i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −16.9282 4.53590i −0.750329 0.201050i −0.136665 0.990617i \(-0.543638\pi\)
−0.613664 + 0.789567i \(0.710305\pi\)
\(510\) 0 0
\(511\) 3.56218 6.16987i 0.157581 0.272939i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −9.12436 34.0526i −0.402067 1.50054i
\(516\) 0 0
\(517\) −7.41858 + 27.6865i −0.326269 + 1.21765i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 13.0000i 0.569540i 0.958596 + 0.284770i \(0.0919173\pi\)
−0.958596 + 0.284770i \(0.908083\pi\)
\(522\) 0 0
\(523\) 14.4641 + 14.4641i 0.632471 + 0.632471i 0.948687 0.316216i \(-0.102412\pi\)
−0.316216 + 0.948687i \(0.602412\pi\)
\(524\) 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
\(533\) −18.2942 + 4.90192i −0.792411 + 0.212326i
\(534\) 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 −0.860994 0.508614i \(-0.830158\pi\)
0.508614 + 0.860994i \(0.330158\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 19.8564 + 34.3923i 0.850555 + 1.47320i
\(546\) 0 0
\(547\) −8.37564 31.2583i −0.358117 1.33651i −0.876517 0.481371i \(-0.840139\pi\)
0.518400 0.855138i \(-0.326528\pi\)
\(548\) 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 0.0700519 0.997543i \(-0.477684\pi\)
0.997543 0.0700519i \(-0.0223165\pi\)
\(558\) 0 0
\(559\) 8.05256 0.340587
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −3.76795 1.00962i −0.158800 0.0425504i 0.178543 0.983932i \(-0.442862\pi\)
−0.337343 + 0.941382i \(0.609528\pi\)
\(564\) 0 0
\(565\) 51.7128 13.8564i 2.17557 0.582943i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 23.5981 + 13.6244i 0.989283 + 0.571163i 0.905060 0.425284i \(-0.139826\pi\)
0.0842230 + 0.996447i \(0.473159\pi\)
\(570\) 0 0
\(571\) −5.33013 + 19.8923i −0.223059 + 0.832467i 0.760114 + 0.649790i \(0.225143\pi\)
−0.983173 + 0.182677i \(0.941524\pi\)
\(572\) 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
\(581\) 0.267949 1.00000i 0.0111164 0.0414870i
\(582\) 0 0
\(583\) 1.94744 + 1.12436i 0.0806548 + 0.0465661i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 3.76795 1.00962i 0.155520 0.0416714i −0.180219 0.983626i \(-0.557681\pi\)
0.335739 + 0.941955i \(0.391014\pi\)
\(588\) 0 0
\(589\) 6.46410 + 1.73205i 0.266349 + 0.0713679i
\(590\) 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 −0.893965 0.448136i \(-0.852088\pi\)
−0.0588850 + 0.998265i \(0.518755\pi\)
\(600\) 0 0
\(601\) 17.5526 + 10.1340i 0.715984 + 0.413373i 0.813273 0.581883i \(-0.197684\pi\)
−0.0972889 + 0.995256i \(0.531017\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −2.19615 8.19615i −0.0892863 0.333221i
\(606\) 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 0.739840 0.672783i \(-0.234901\pi\)
−0.672783 + 0.739840i \(0.734901\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 3.91154 2.25833i 0.157473 0.0909170i −0.419193 0.907897i \(-0.637687\pi\)
0.576666 + 0.816980i \(0.304354\pi\)
\(618\) 0 0
\(619\) −38.8205 + 10.4019i −1.56033 + 0.418089i −0.932767 0.360479i \(-0.882613\pi\)
−0.627561 + 0.778568i \(0.715947\pi\)
\(620\) 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 \(0.276859\pi\)
−0.644995 + 0.764187i \(0.723141\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −6.19615 + 23.1244i −0.245887 + 0.917662i
\(636\) 0 0
\(637\) −10.5622 39.4186i −0.418489 1.56182i
\(638\) 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
\(643\) 45.6506 + 12.2321i 1.80029 + 0.482385i 0.994023 0.109173i \(-0.0348202\pi\)
0.806263 + 0.591558i \(0.201487\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 13.2679i 0.521617i −0.965391 0.260808i \(-0.916011\pi\)
0.965391 0.260808i \(-0.0839891\pi\)
\(648\) 0 0
\(649\) 15.2487i 0.598564i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −5.63397 1.50962i −0.220474 0.0590760i 0.146891 0.989153i \(-0.453073\pi\)
−0.367365 + 0.930077i \(0.619740\pi\)
\(654\) 0 0
\(655\) 6.19615 10.7321i 0.242104 0.419336i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 4.02628 + 15.0263i 0.156842 + 0.585341i 0.998941 + 0.0460178i \(0.0146531\pi\)
−0.842099 + 0.539323i \(0.818680\pi\)
\(660\) 0 0
\(661\) 2.19615 8.19615i 0.0854204 0.318793i −0.909973 0.414667i \(-0.863898\pi\)
0.995393 + 0.0958740i \(0.0305646\pi\)
\(662\) 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
\(677\) −4.73205 + 1.26795i −0.181867 + 0.0487312i −0.348603 0.937270i \(-0.613344\pi\)
0.166736 + 0.986002i \(0.446677\pi\)
\(678\) 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 0.611321 0.791383i \(-0.290638\pi\)
−0.791383 + 0.611321i \(0.790638\pi\)
\(684\) 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
\(691\) 6.29423 + 23.4904i 0.239444 + 0.893616i 0.976095 + 0.217344i \(0.0697392\pi\)
−0.736651 + 0.676273i \(0.763594\pi\)
\(692\) 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 −0.879160 0.476527i \(-0.841895\pi\)
0.476527 + 0.879160i \(0.341895\pi\)
\(702\) 0 0
\(703\) 1.60770 0.0606354
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 5.46410 + 1.46410i 0.205499 + 0.0550632i
\(708\) 0 0
\(709\) −20.1962 + 5.41154i −0.758482 + 0.203235i −0.617277 0.786746i \(-0.711764\pi\)
−0.141205 + 0.989980i \(0.545098\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 8.19615 + 4.73205i 0.306948 + 0.177217i
\(714\) 0 0
\(715\) −18.7321 + 69.9090i −0.700539 + 2.61445i
\(716\) 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
\(725\) −6.29423 + 23.4904i −0.233762 + 0.872411i
\(726\) 0 0
\(727\) −31.8109 18.3660i −1.17980 0.681158i −0.223832 0.974628i \(-0.571857\pi\)
−0.955968 + 0.293470i \(0.905190\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 2.79423 0.748711i 0.103348 0.0276921i
\(732\) 0 0
\(733\) −29.9545 8.02628i −1.10639 0.296457i −0.341028 0.940053i \(-0.610775\pi\)
−0.765366 + 0.643596i \(0.777442\pi\)
\(734\) 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 −0.979945 0.199266i \(-0.936144\pi\)
0.199266 + 0.979945i \(0.436144\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 2.24167 1.29423i 0.0822389 0.0474806i −0.458317 0.888789i \(-0.651547\pi\)
0.540556 + 0.841308i \(0.318214\pi\)
\(744\) 0 0
\(745\) 10.7321 + 6.19615i 0.393192 + 0.227009i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 3.61474 + 13.4904i 0.132080 + 0.492928i
\(750\) 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 0.588103 0.808786i \(-0.299875\pi\)
−0.808786 + 0.588103i \(0.799875\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 27.3731 15.8038i 0.992273 0.572889i 0.0863200 0.996267i \(-0.472489\pi\)
0.905953 + 0.423378i \(0.139156\pi\)
\(762\) 0 0
\(763\) −7.26795 + 1.94744i −0.263117 + 0.0705021i
\(764\) 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 0.623306 0.781978i \(-0.285789\pi\)
−0.781978 + 0.623306i \(0.785789\pi\)
\(774\) 0 0
\(775\) 74.1051i 2.66193i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −0.696152 + 2.59808i −0.0249422 + 0.0930857i
\(780\) 0 0
\(781\) 8.39230 + 31.3205i 0.300300 + 1.12074i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −9.46410 + 16.3923i −0.337788 + 0.585066i
\(786\) 0 0
\(787\) −49.8109 13.3468i −1.77557 0.475762i −0.785803 0.618477i \(-0.787750\pi\)
−0.989764 + 0.142716i \(0.954417\pi\)
\(788\) 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
\(797\) 54.1769 + 14.5167i 1.91904 + 0.514206i 0.989275 + 0.146065i \(0.0466609\pi\)
0.929770 + 0.368142i \(0.120006\pi\)
\(798\) 0 0
\(799\) −10.9545 + 18.9737i −0.387542 + 0.671242i
\(800\) 0 0