Properties

Label 1710.2.d.g.1369.4
Level $1710$
Weight $2$
Character 1710.1369
Analytic conductor $13.654$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1710.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.6544187456\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\Q(\zeta_{24})\)
Defining polynomial: \(x^{8} - x^{4} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1369.4
Root \(0.965926 - 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 1710.1369
Dual form 1710.2.d.g.1369.7

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} -1.00000 q^{4} +(1.41421 + 1.73205i) q^{5} -3.86370i q^{7} +1.00000i q^{8} +O(q^{10})\) \(q-1.00000i q^{2} -1.00000 q^{4} +(1.41421 + 1.73205i) q^{5} -3.86370i q^{7} +1.00000i q^{8} +(1.73205 - 1.41421i) q^{10} -1.03528 q^{11} -3.86370i q^{13} -3.86370 q^{14} +1.00000 q^{16} +0.535898i q^{17} +1.00000 q^{19} +(-1.41421 - 1.73205i) q^{20} +1.03528i q^{22} -5.46410i q^{23} +(-1.00000 + 4.89898i) q^{25} -3.86370 q^{26} +3.86370i q^{28} +4.62158 q^{29} -10.9282 q^{31} -1.00000i q^{32} +0.535898 q^{34} +(6.69213 - 5.46410i) q^{35} +1.79315i q^{37} -1.00000i q^{38} +(-1.73205 + 1.41421i) q^{40} -1.79315 q^{41} -6.69213i q^{43} +1.03528 q^{44} -5.46410 q^{46} +2.53590i q^{47} -7.92820 q^{49} +(4.89898 + 1.00000i) q^{50} +3.86370i q^{52} -6.00000i q^{53} +(-1.46410 - 1.79315i) q^{55} +3.86370 q^{56} -4.62158i q^{58} +6.96953 q^{59} -2.00000 q^{61} +10.9282i q^{62} -1.00000 q^{64} +(6.69213 - 5.46410i) q^{65} -13.3843i q^{67} -0.535898i q^{68} +(-5.46410 - 6.69213i) q^{70} -4.14110 q^{71} -3.58630i q^{73} +1.79315 q^{74} -1.00000 q^{76} +4.00000i q^{77} +4.00000 q^{79} +(1.41421 + 1.73205i) q^{80} +1.79315i q^{82} -16.3923i q^{83} +(-0.928203 + 0.757875i) q^{85} -6.69213 q^{86} -1.03528i q^{88} -3.86370 q^{89} -14.9282 q^{91} +5.46410i q^{92} +2.53590 q^{94} +(1.41421 + 1.73205i) q^{95} -2.55103i q^{97} +7.92820i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 8 q^{4} + O(q^{10}) \) \( 8 q - 8 q^{4} + 8 q^{16} + 8 q^{19} - 8 q^{25} - 32 q^{31} + 32 q^{34} - 16 q^{46} - 8 q^{49} + 16 q^{55} - 16 q^{61} - 8 q^{64} - 16 q^{70} - 8 q^{76} + 32 q^{79} + 48 q^{85} - 64 q^{91} + 48 q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(1027\) \(1351\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 0 0
\(4\) −1.00000 −0.500000
\(5\) 1.41421 + 1.73205i 0.632456 + 0.774597i
\(6\) 0 0
\(7\) 3.86370i 1.46034i −0.683264 0.730171i \(-0.739440\pi\)
0.683264 0.730171i \(-0.260560\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 1.73205 1.41421i 0.547723 0.447214i
\(11\) −1.03528 −0.312148 −0.156074 0.987745i \(-0.549884\pi\)
−0.156074 + 0.987745i \(0.549884\pi\)
\(12\) 0 0
\(13\) 3.86370i 1.07160i −0.844345 0.535799i \(-0.820010\pi\)
0.844345 0.535799i \(-0.179990\pi\)
\(14\) −3.86370 −1.03262
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 0.535898i 0.129974i 0.997886 + 0.0649872i \(0.0207007\pi\)
−0.997886 + 0.0649872i \(0.979299\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) −1.41421 1.73205i −0.316228 0.387298i
\(21\) 0 0
\(22\) 1.03528i 0.220722i
\(23\) 5.46410i 1.13934i −0.821872 0.569672i \(-0.807070\pi\)
0.821872 0.569672i \(-0.192930\pi\)
\(24\) 0 0
\(25\) −1.00000 + 4.89898i −0.200000 + 0.979796i
\(26\) −3.86370 −0.757735
\(27\) 0 0
\(28\) 3.86370i 0.730171i
\(29\) 4.62158 0.858206 0.429103 0.903256i \(-0.358830\pi\)
0.429103 + 0.903256i \(0.358830\pi\)
\(30\) 0 0
\(31\) −10.9282 −1.96276 −0.981382 0.192068i \(-0.938481\pi\)
−0.981382 + 0.192068i \(0.938481\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0 0
\(34\) 0.535898 0.0919058
\(35\) 6.69213 5.46410i 1.13118 0.923602i
\(36\) 0 0
\(37\) 1.79315i 0.294792i 0.989078 + 0.147396i \(0.0470892\pi\)
−0.989078 + 0.147396i \(0.952911\pi\)
\(38\) 1.00000i 0.162221i
\(39\) 0 0
\(40\) −1.73205 + 1.41421i −0.273861 + 0.223607i
\(41\) −1.79315 −0.280043 −0.140022 0.990148i \(-0.544717\pi\)
−0.140022 + 0.990148i \(0.544717\pi\)
\(42\) 0 0
\(43\) 6.69213i 1.02054i −0.860014 0.510270i \(-0.829545\pi\)
0.860014 0.510270i \(-0.170455\pi\)
\(44\) 1.03528 0.156074
\(45\) 0 0
\(46\) −5.46410 −0.805638
\(47\) 2.53590i 0.369899i 0.982748 + 0.184949i \(0.0592121\pi\)
−0.982748 + 0.184949i \(0.940788\pi\)
\(48\) 0 0
\(49\) −7.92820 −1.13260
\(50\) 4.89898 + 1.00000i 0.692820 + 0.141421i
\(51\) 0 0
\(52\) 3.86370i 0.535799i
\(53\) 6.00000i 0.824163i −0.911147 0.412082i \(-0.864802\pi\)
0.911147 0.412082i \(-0.135198\pi\)
\(54\) 0 0
\(55\) −1.46410 1.79315i −0.197419 0.241788i
\(56\) 3.86370 0.516309
\(57\) 0 0
\(58\) 4.62158i 0.606843i
\(59\) 6.96953 0.907356 0.453678 0.891166i \(-0.350112\pi\)
0.453678 + 0.891166i \(0.350112\pi\)
\(60\) 0 0
\(61\) −2.00000 −0.256074 −0.128037 0.991769i \(-0.540868\pi\)
−0.128037 + 0.991769i \(0.540868\pi\)
\(62\) 10.9282i 1.38788i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 6.69213 5.46410i 0.830057 0.677738i
\(66\) 0 0
\(67\) 13.3843i 1.63515i −0.575824 0.817574i \(-0.695319\pi\)
0.575824 0.817574i \(-0.304681\pi\)
\(68\) 0.535898i 0.0649872i
\(69\) 0 0
\(70\) −5.46410 6.69213i −0.653085 0.799863i
\(71\) −4.14110 −0.491459 −0.245729 0.969338i \(-0.579027\pi\)
−0.245729 + 0.969338i \(0.579027\pi\)
\(72\) 0 0
\(73\) 3.58630i 0.419745i −0.977729 0.209872i \(-0.932695\pi\)
0.977729 0.209872i \(-0.0673049\pi\)
\(74\) 1.79315 0.208450
\(75\) 0 0
\(76\) −1.00000 −0.114708
\(77\) 4.00000i 0.455842i
\(78\) 0 0
\(79\) 4.00000 0.450035 0.225018 0.974355i \(-0.427756\pi\)
0.225018 + 0.974355i \(0.427756\pi\)
\(80\) 1.41421 + 1.73205i 0.158114 + 0.193649i
\(81\) 0 0
\(82\) 1.79315i 0.198020i
\(83\) 16.3923i 1.79929i −0.436623 0.899645i \(-0.643826\pi\)
0.436623 0.899645i \(-0.356174\pi\)
\(84\) 0 0
\(85\) −0.928203 + 0.757875i −0.100678 + 0.0822031i
\(86\) −6.69213 −0.721631
\(87\) 0 0
\(88\) 1.03528i 0.110361i
\(89\) −3.86370 −0.409552 −0.204776 0.978809i \(-0.565647\pi\)
−0.204776 + 0.978809i \(0.565647\pi\)
\(90\) 0 0
\(91\) −14.9282 −1.56490
\(92\) 5.46410i 0.569672i
\(93\) 0 0
\(94\) 2.53590 0.261558
\(95\) 1.41421 + 1.73205i 0.145095 + 0.177705i
\(96\) 0 0
\(97\) 2.55103i 0.259017i −0.991578 0.129509i \(-0.958660\pi\)
0.991578 0.129509i \(-0.0413400\pi\)
\(98\) 7.92820i 0.800869i
\(99\) 0 0
\(100\) 1.00000 4.89898i 0.100000 0.489898i
\(101\) 10.5558 1.05034 0.525172 0.850996i \(-0.324001\pi\)
0.525172 + 0.850996i \(0.324001\pi\)
\(102\) 0 0
\(103\) 4.89898i 0.482711i 0.970437 + 0.241355i \(0.0775919\pi\)
−0.970437 + 0.241355i \(0.922408\pi\)
\(104\) 3.86370 0.378867
\(105\) 0 0
\(106\) −6.00000 −0.582772
\(107\) 2.92820i 0.283080i −0.989933 0.141540i \(-0.954795\pi\)
0.989933 0.141540i \(-0.0452054\pi\)
\(108\) 0 0
\(109\) −8.92820 −0.855167 −0.427583 0.903976i \(-0.640635\pi\)
−0.427583 + 0.903976i \(0.640635\pi\)
\(110\) −1.79315 + 1.46410i −0.170970 + 0.139597i
\(111\) 0 0
\(112\) 3.86370i 0.365086i
\(113\) 6.00000i 0.564433i −0.959351 0.282216i \(-0.908930\pi\)
0.959351 0.282216i \(-0.0910696\pi\)
\(114\) 0 0
\(115\) 9.46410 7.72741i 0.882532 0.720584i
\(116\) −4.62158 −0.429103
\(117\) 0 0
\(118\) 6.96953i 0.641597i
\(119\) 2.07055 0.189807
\(120\) 0 0
\(121\) −9.92820 −0.902564
\(122\) 2.00000i 0.181071i
\(123\) 0 0
\(124\) 10.9282 0.981382
\(125\) −9.89949 + 5.19615i −0.885438 + 0.464758i
\(126\) 0 0
\(127\) 8.48528i 0.752947i −0.926427 0.376473i \(-0.877137\pi\)
0.926427 0.376473i \(-0.122863\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 0 0
\(130\) −5.46410 6.69213i −0.479233 0.586939i
\(131\) −3.10583 −0.271357 −0.135679 0.990753i \(-0.543322\pi\)
−0.135679 + 0.990753i \(0.543322\pi\)
\(132\) 0 0
\(133\) 3.86370i 0.335026i
\(134\) −13.3843 −1.15622
\(135\) 0 0
\(136\) −0.535898 −0.0459529
\(137\) 0.535898i 0.0457849i 0.999738 + 0.0228924i \(0.00728753\pi\)
−0.999738 + 0.0228924i \(0.992712\pi\)
\(138\) 0 0
\(139\) −6.92820 −0.587643 −0.293821 0.955860i \(-0.594927\pi\)
−0.293821 + 0.955860i \(0.594927\pi\)
\(140\) −6.69213 + 5.46410i −0.565588 + 0.461801i
\(141\) 0 0
\(142\) 4.14110i 0.347514i
\(143\) 4.00000i 0.334497i
\(144\) 0 0
\(145\) 6.53590 + 8.00481i 0.542777 + 0.664763i
\(146\) −3.58630 −0.296804
\(147\) 0 0
\(148\) 1.79315i 0.147396i
\(149\) 20.3538 1.66745 0.833724 0.552182i \(-0.186205\pi\)
0.833724 + 0.552182i \(0.186205\pi\)
\(150\) 0 0
\(151\) 5.85641 0.476588 0.238294 0.971193i \(-0.423412\pi\)
0.238294 + 0.971193i \(0.423412\pi\)
\(152\) 1.00000i 0.0811107i
\(153\) 0 0
\(154\) 4.00000 0.322329
\(155\) −15.4548 18.9282i −1.24136 1.52035i
\(156\) 0 0
\(157\) 14.1421i 1.12867i −0.825547 0.564333i \(-0.809134\pi\)
0.825547 0.564333i \(-0.190866\pi\)
\(158\) 4.00000i 0.318223i
\(159\) 0 0
\(160\) 1.73205 1.41421i 0.136931 0.111803i
\(161\) −21.1117 −1.66383
\(162\) 0 0
\(163\) 23.6627i 1.85341i 0.375796 + 0.926703i \(0.377369\pi\)
−0.375796 + 0.926703i \(0.622631\pi\)
\(164\) 1.79315 0.140022
\(165\) 0 0
\(166\) −16.3923 −1.27229
\(167\) 10.9282i 0.845650i 0.906211 + 0.422825i \(0.138961\pi\)
−0.906211 + 0.422825i \(0.861039\pi\)
\(168\) 0 0
\(169\) −1.92820 −0.148323
\(170\) 0.757875 + 0.928203i 0.0581263 + 0.0711899i
\(171\) 0 0
\(172\) 6.69213i 0.510270i
\(173\) 22.7846i 1.73228i 0.499800 + 0.866141i \(0.333407\pi\)
−0.499800 + 0.866141i \(0.666593\pi\)
\(174\) 0 0
\(175\) 18.9282 + 3.86370i 1.43084 + 0.292069i
\(176\) −1.03528 −0.0780369
\(177\) 0 0
\(178\) 3.86370i 0.289597i
\(179\) −16.7675 −1.25326 −0.626631 0.779316i \(-0.715566\pi\)
−0.626631 + 0.779316i \(0.715566\pi\)
\(180\) 0 0
\(181\) 19.8564 1.47592 0.737958 0.674847i \(-0.235790\pi\)
0.737958 + 0.674847i \(0.235790\pi\)
\(182\) 14.9282i 1.10655i
\(183\) 0 0
\(184\) 5.46410 0.402819
\(185\) −3.10583 + 2.53590i −0.228345 + 0.186443i
\(186\) 0 0
\(187\) 0.554803i 0.0405712i
\(188\) 2.53590i 0.184949i
\(189\) 0 0
\(190\) 1.73205 1.41421i 0.125656 0.102598i
\(191\) 17.2480 1.24802 0.624009 0.781417i \(-0.285503\pi\)
0.624009 + 0.781417i \(0.285503\pi\)
\(192\) 0 0
\(193\) 8.76268i 0.630752i 0.948967 + 0.315376i \(0.102131\pi\)
−0.948967 + 0.315376i \(0.897869\pi\)
\(194\) −2.55103 −0.183153
\(195\) 0 0
\(196\) 7.92820 0.566300
\(197\) 23.4641i 1.67175i 0.548921 + 0.835874i \(0.315039\pi\)
−0.548921 + 0.835874i \(0.684961\pi\)
\(198\) 0 0
\(199\) −13.0718 −0.926635 −0.463318 0.886192i \(-0.653341\pi\)
−0.463318 + 0.886192i \(0.653341\pi\)
\(200\) −4.89898 1.00000i −0.346410 0.0707107i
\(201\) 0 0
\(202\) 10.5558i 0.742706i
\(203\) 17.8564i 1.25327i
\(204\) 0 0
\(205\) −2.53590 3.10583i −0.177115 0.216920i
\(206\) 4.89898 0.341328
\(207\) 0 0
\(208\) 3.86370i 0.267900i
\(209\) −1.03528 −0.0716116
\(210\) 0 0
\(211\) −17.8564 −1.22929 −0.614643 0.788806i \(-0.710700\pi\)
−0.614643 + 0.788806i \(0.710700\pi\)
\(212\) 6.00000i 0.412082i
\(213\) 0 0
\(214\) −2.92820 −0.200168
\(215\) 11.5911 9.46410i 0.790507 0.645446i
\(216\) 0 0
\(217\) 42.2233i 2.86631i
\(218\) 8.92820i 0.604694i
\(219\) 0 0
\(220\) 1.46410 + 1.79315i 0.0987097 + 0.120894i
\(221\) 2.07055 0.139280
\(222\) 0 0
\(223\) 10.5558i 0.706871i −0.935459 0.353435i \(-0.885013\pi\)
0.935459 0.353435i \(-0.114987\pi\)
\(224\) −3.86370 −0.258155
\(225\) 0 0
\(226\) −6.00000 −0.399114
\(227\) 1.85641i 0.123214i −0.998100 0.0616070i \(-0.980377\pi\)
0.998100 0.0616070i \(-0.0196225\pi\)
\(228\) 0 0
\(229\) 3.85641 0.254839 0.127419 0.991849i \(-0.459331\pi\)
0.127419 + 0.991849i \(0.459331\pi\)
\(230\) −7.72741 9.46410i −0.509530 0.624044i
\(231\) 0 0
\(232\) 4.62158i 0.303421i
\(233\) 12.5359i 0.821254i −0.911803 0.410627i \(-0.865310\pi\)
0.911803 0.410627i \(-0.134690\pi\)
\(234\) 0 0
\(235\) −4.39230 + 3.58630i −0.286522 + 0.233945i
\(236\) −6.96953 −0.453678
\(237\) 0 0
\(238\) 2.07055i 0.134214i
\(239\) 13.1069 0.847812 0.423906 0.905706i \(-0.360659\pi\)
0.423906 + 0.905706i \(0.360659\pi\)
\(240\) 0 0
\(241\) 10.0000 0.644157 0.322078 0.946713i \(-0.395619\pi\)
0.322078 + 0.946713i \(0.395619\pi\)
\(242\) 9.92820i 0.638209i
\(243\) 0 0
\(244\) 2.00000 0.128037
\(245\) −11.2122 13.7321i −0.716319 0.877309i
\(246\) 0 0
\(247\) 3.86370i 0.245842i
\(248\) 10.9282i 0.693942i
\(249\) 0 0
\(250\) 5.19615 + 9.89949i 0.328634 + 0.626099i
\(251\) 28.3586 1.78998 0.894990 0.446087i \(-0.147183\pi\)
0.894990 + 0.446087i \(0.147183\pi\)
\(252\) 0 0
\(253\) 5.65685i 0.355643i
\(254\) −8.48528 −0.532414
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 22.7846i 1.42126i 0.703563 + 0.710632i \(0.251591\pi\)
−0.703563 + 0.710632i \(0.748409\pi\)
\(258\) 0 0
\(259\) 6.92820 0.430498
\(260\) −6.69213 + 5.46410i −0.415028 + 0.338869i
\(261\) 0 0
\(262\) 3.10583i 0.191879i
\(263\) 19.3205i 1.19135i −0.803224 0.595677i \(-0.796884\pi\)
0.803224 0.595677i \(-0.203116\pi\)
\(264\) 0 0
\(265\) 10.3923 8.48528i 0.638394 0.521247i
\(266\) −3.86370 −0.236899
\(267\) 0 0
\(268\) 13.3843i 0.817574i
\(269\) −31.9449 −1.94772 −0.973858 0.227160i \(-0.927056\pi\)
−0.973858 + 0.227160i \(0.927056\pi\)
\(270\) 0 0
\(271\) 10.9282 0.663841 0.331921 0.943307i \(-0.392303\pi\)
0.331921 + 0.943307i \(0.392303\pi\)
\(272\) 0.535898i 0.0324936i
\(273\) 0 0
\(274\) 0.535898 0.0323748
\(275\) 1.03528 5.07180i 0.0624295 0.305841i
\(276\) 0 0
\(277\) 18.2832i 1.09853i 0.835647 + 0.549267i \(0.185093\pi\)
−0.835647 + 0.549267i \(0.814907\pi\)
\(278\) 6.92820i 0.415526i
\(279\) 0 0
\(280\) 5.46410 + 6.69213i 0.326543 + 0.399931i
\(281\) 31.1870 1.86046 0.930231 0.366974i \(-0.119606\pi\)
0.930231 + 0.366974i \(0.119606\pi\)
\(282\) 0 0
\(283\) 5.17638i 0.307704i 0.988094 + 0.153852i \(0.0491679\pi\)
−0.988094 + 0.153852i \(0.950832\pi\)
\(284\) 4.14110 0.245729
\(285\) 0 0
\(286\) 4.00000 0.236525
\(287\) 6.92820i 0.408959i
\(288\) 0 0
\(289\) 16.7128 0.983107
\(290\) 8.00481 6.53590i 0.470059 0.383801i
\(291\) 0 0
\(292\) 3.58630i 0.209872i
\(293\) 19.8564i 1.16002i 0.814608 + 0.580012i \(0.196952\pi\)
−0.814608 + 0.580012i \(0.803048\pi\)
\(294\) 0 0
\(295\) 9.85641 + 12.0716i 0.573862 + 0.702835i
\(296\) −1.79315 −0.104225
\(297\) 0 0
\(298\) 20.3538i 1.17906i
\(299\) −21.1117 −1.22092
\(300\) 0 0
\(301\) −25.8564 −1.49034
\(302\) 5.85641i 0.336998i
\(303\) 0 0
\(304\) 1.00000 0.0573539
\(305\) −2.82843 3.46410i −0.161955 0.198354i
\(306\) 0 0
\(307\) 17.5254i 1.00023i −0.865960 0.500113i \(-0.833292\pi\)
0.865960 0.500113i \(-0.166708\pi\)
\(308\) 4.00000i 0.227921i
\(309\) 0 0
\(310\) −18.9282 + 15.4548i −1.07505 + 0.877774i
\(311\) 1.79315 0.101680 0.0508401 0.998707i \(-0.483810\pi\)
0.0508401 + 0.998707i \(0.483810\pi\)
\(312\) 0 0
\(313\) 19.5959i 1.10763i −0.832641 0.553813i \(-0.813172\pi\)
0.832641 0.553813i \(-0.186828\pi\)
\(314\) −14.1421 −0.798087
\(315\) 0 0
\(316\) −4.00000 −0.225018
\(317\) 14.0000i 0.786318i 0.919470 + 0.393159i \(0.128618\pi\)
−0.919470 + 0.393159i \(0.871382\pi\)
\(318\) 0 0
\(319\) −4.78461 −0.267887
\(320\) −1.41421 1.73205i −0.0790569 0.0968246i
\(321\) 0 0
\(322\) 21.1117i 1.17651i
\(323\) 0.535898i 0.0298182i
\(324\) 0 0
\(325\) 18.9282 + 3.86370i 1.04995 + 0.214320i
\(326\) 23.6627 1.31056
\(327\) 0 0
\(328\) 1.79315i 0.0990102i
\(329\) 9.79796 0.540179
\(330\) 0 0
\(331\) 13.8564 0.761617 0.380808 0.924654i \(-0.375646\pi\)
0.380808 + 0.924654i \(0.375646\pi\)
\(332\) 16.3923i 0.899645i
\(333\) 0 0
\(334\) 10.9282 0.597965
\(335\) 23.1822 18.9282i 1.26658 1.03416i
\(336\) 0 0
\(337\) 1.03528i 0.0563951i −0.999602 0.0281975i \(-0.991023\pi\)
0.999602 0.0281975i \(-0.00897675\pi\)
\(338\) 1.92820i 0.104880i
\(339\) 0 0
\(340\) 0.928203 0.757875i 0.0503389 0.0411015i
\(341\) 11.3137 0.612672
\(342\) 0 0
\(343\) 3.58630i 0.193642i
\(344\) 6.69213 0.360815
\(345\) 0 0
\(346\) 22.7846 1.22491
\(347\) 18.5359i 0.995059i 0.867447 + 0.497530i \(0.165759\pi\)
−0.867447 + 0.497530i \(0.834241\pi\)
\(348\) 0 0
\(349\) −4.14359 −0.221801 −0.110901 0.993831i \(-0.535374\pi\)
−0.110901 + 0.993831i \(0.535374\pi\)
\(350\) 3.86370 18.9282i 0.206524 1.01176i
\(351\) 0 0
\(352\) 1.03528i 0.0551804i
\(353\) 21.3205i 1.13478i −0.823451 0.567388i \(-0.807954\pi\)
0.823451 0.567388i \(-0.192046\pi\)
\(354\) 0 0
\(355\) −5.85641 7.17260i −0.310826 0.380682i
\(356\) 3.86370 0.204776
\(357\) 0 0
\(358\) 16.7675i 0.886189i
\(359\) 34.7733 1.83527 0.917633 0.397429i \(-0.130097\pi\)
0.917633 + 0.397429i \(0.130097\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 19.8564i 1.04363i
\(363\) 0 0
\(364\) 14.9282 0.782450
\(365\) 6.21166 5.07180i 0.325133 0.265470i
\(366\) 0 0
\(367\) 5.37945i 0.280805i 0.990094 + 0.140403i \(0.0448397\pi\)
−0.990094 + 0.140403i \(0.955160\pi\)
\(368\) 5.46410i 0.284836i
\(369\) 0 0
\(370\) 2.53590 + 3.10583i 0.131835 + 0.161464i
\(371\) −23.1822 −1.20356
\(372\) 0 0
\(373\) 24.9754i 1.29318i −0.762840 0.646588i \(-0.776195\pi\)
0.762840 0.646588i \(-0.223805\pi\)
\(374\) −0.554803 −0.0286882
\(375\) 0 0
\(376\) −2.53590 −0.130779
\(377\) 17.8564i 0.919652i
\(378\) 0 0
\(379\) 35.7128 1.83444 0.917222 0.398376i \(-0.130426\pi\)
0.917222 + 0.398376i \(0.130426\pi\)
\(380\) −1.41421 1.73205i −0.0725476 0.0888523i
\(381\) 0 0
\(382\) 17.2480i 0.882483i
\(383\) 22.9282i 1.17158i 0.810464 + 0.585788i \(0.199215\pi\)
−0.810464 + 0.585788i \(0.800785\pi\)
\(384\) 0 0
\(385\) −6.92820 + 5.65685i −0.353094 + 0.288300i
\(386\) 8.76268 0.446009
\(387\) 0 0
\(388\) 2.55103i 0.129509i
\(389\) −19.7990 −1.00385 −0.501924 0.864912i \(-0.667374\pi\)
−0.501924 + 0.864912i \(0.667374\pi\)
\(390\) 0 0
\(391\) 2.92820 0.148086
\(392\) 7.92820i 0.400435i
\(393\) 0 0
\(394\) 23.4641 1.18210
\(395\) 5.65685 + 6.92820i 0.284627 + 0.348596i
\(396\) 0 0
\(397\) 18.2832i 0.917610i −0.888537 0.458805i \(-0.848278\pi\)
0.888537 0.458805i \(-0.151722\pi\)
\(398\) 13.0718i 0.655230i
\(399\) 0 0
\(400\) −1.00000 + 4.89898i −0.0500000 + 0.244949i
\(401\) −9.52056 −0.475434 −0.237717 0.971334i \(-0.576399\pi\)
−0.237717 + 0.971334i \(0.576399\pi\)
\(402\) 0 0
\(403\) 42.2233i 2.10329i
\(404\) −10.5558 −0.525172
\(405\) 0 0
\(406\) −17.8564 −0.886199
\(407\) 1.85641i 0.0920187i
\(408\) 0 0
\(409\) 20.9282 1.03483 0.517417 0.855734i \(-0.326894\pi\)
0.517417 + 0.855734i \(0.326894\pi\)
\(410\) −3.10583 + 2.53590i −0.153386 + 0.125239i
\(411\) 0 0
\(412\) 4.89898i 0.241355i
\(413\) 26.9282i 1.32505i
\(414\) 0 0
\(415\) 28.3923 23.1822i 1.39372 1.13797i
\(416\) −3.86370 −0.189434
\(417\) 0 0
\(418\) 1.03528i 0.0506370i
\(419\) 29.3195 1.43235 0.716177 0.697919i \(-0.245890\pi\)
0.716177 + 0.697919i \(0.245890\pi\)
\(420\) 0 0
\(421\) 29.7128 1.44811 0.724057 0.689740i \(-0.242275\pi\)
0.724057 + 0.689740i \(0.242275\pi\)
\(422\) 17.8564i 0.869236i
\(423\) 0 0
\(424\) 6.00000 0.291386
\(425\) −2.62536 0.535898i −0.127348 0.0259949i
\(426\) 0 0
\(427\) 7.72741i 0.373955i
\(428\) 2.92820i 0.141540i
\(429\) 0 0
\(430\) −9.46410 11.5911i −0.456400 0.558973i
\(431\) 26.2137 1.26267 0.631335 0.775510i \(-0.282507\pi\)
0.631335 + 0.775510i \(0.282507\pi\)
\(432\) 0 0
\(433\) 10.8332i 0.520612i −0.965526 0.260306i \(-0.916177\pi\)
0.965526 0.260306i \(-0.0838235\pi\)
\(434\) 42.2233 2.02678
\(435\) 0 0
\(436\) 8.92820 0.427583
\(437\) 5.46410i 0.261383i
\(438\) 0 0
\(439\) −20.0000 −0.954548 −0.477274 0.878755i \(-0.658375\pi\)
−0.477274 + 0.878755i \(0.658375\pi\)
\(440\) 1.79315 1.46410i 0.0854851 0.0697983i
\(441\) 0 0
\(442\) 2.07055i 0.0984861i
\(443\) 16.3923i 0.778822i −0.921064 0.389411i \(-0.872679\pi\)
0.921064 0.389411i \(-0.127321\pi\)
\(444\) 0 0
\(445\) −5.46410 6.69213i −0.259023 0.317237i
\(446\) −10.5558 −0.499833
\(447\) 0 0
\(448\) 3.86370i 0.182543i
\(449\) −40.4302 −1.90802 −0.954009 0.299777i \(-0.903088\pi\)
−0.954009 + 0.299777i \(0.903088\pi\)
\(450\) 0 0
\(451\) 1.85641 0.0874148
\(452\) 6.00000i 0.282216i
\(453\) 0 0
\(454\) −1.85641 −0.0871255
\(455\) −21.1117 25.8564i −0.989730 1.21217i
\(456\) 0 0
\(457\) 33.9411i 1.58770i 0.608114 + 0.793849i \(0.291926\pi\)
−0.608114 + 0.793849i \(0.708074\pi\)
\(458\) 3.85641i 0.180198i
\(459\) 0 0
\(460\) −9.46410 + 7.72741i −0.441266 + 0.360292i
\(461\) −27.5264 −1.28203 −0.641016 0.767527i \(-0.721487\pi\)
−0.641016 + 0.767527i \(0.721487\pi\)
\(462\) 0 0
\(463\) 19.8733i 0.923591i 0.886986 + 0.461796i \(0.152795\pi\)
−0.886986 + 0.461796i \(0.847205\pi\)
\(464\) 4.62158 0.214551
\(465\) 0 0
\(466\) −12.5359 −0.580714
\(467\) 2.53590i 0.117347i 0.998277 + 0.0586737i \(0.0186871\pi\)
−0.998277 + 0.0586737i \(0.981313\pi\)
\(468\) 0 0
\(469\) −51.7128 −2.38788
\(470\) 3.58630 + 4.39230i 0.165424 + 0.202602i
\(471\) 0 0
\(472\) 6.96953i 0.320799i
\(473\) 6.92820i 0.318559i
\(474\) 0 0
\(475\) −1.00000 + 4.89898i −0.0458831 + 0.224781i
\(476\) −2.07055 −0.0949036
\(477\) 0 0
\(478\) 13.1069i 0.599494i
\(479\) 16.6932 0.762730 0.381365 0.924425i \(-0.375454\pi\)
0.381365 + 0.924425i \(0.375454\pi\)
\(480\) 0 0
\(481\) 6.92820 0.315899
\(482\) 10.0000i 0.455488i
\(483\) 0 0
\(484\) 9.92820 0.451282
\(485\) 4.41851 3.60770i 0.200634 0.163817i
\(486\) 0 0
\(487\) 3.38323i 0.153309i 0.997058 + 0.0766544i \(0.0244238\pi\)
−0.997058 + 0.0766544i \(0.975576\pi\)
\(488\) 2.00000i 0.0905357i
\(489\) 0 0
\(490\) −13.7321 + 11.2122i −0.620351 + 0.506514i
\(491\) −18.5606 −0.837630 −0.418815 0.908072i \(-0.637554\pi\)
−0.418815 + 0.908072i \(0.637554\pi\)
\(492\) 0 0
\(493\) 2.47670i 0.111545i
\(494\) −3.86370 −0.173836
\(495\) 0 0
\(496\) −10.9282 −0.490691
\(497\) 16.0000i 0.717698i
\(498\) 0 0
\(499\) −25.8564 −1.15749 −0.578746 0.815508i \(-0.696458\pi\)
−0.578746 + 0.815508i \(0.696458\pi\)
\(500\) 9.89949 5.19615i 0.442719 0.232379i
\(501\) 0 0
\(502\) 28.3586i 1.26571i
\(503\) 11.3205i 0.504757i 0.967629 + 0.252378i \(0.0812127\pi\)
−0.967629 + 0.252378i \(0.918787\pi\)
\(504\) 0 0
\(505\) 14.9282 + 18.2832i 0.664296 + 0.813594i
\(506\) 5.65685 0.251478
\(507\) 0 0
\(508\) 8.48528i 0.376473i
\(509\) −37.0470 −1.64208 −0.821039 0.570873i \(-0.806605\pi\)
−0.821039 + 0.570873i \(0.806605\pi\)
\(510\) 0 0
\(511\) −13.8564 −0.612971
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 22.7846 1.00499
\(515\) −8.48528 + 6.92820i −0.373906 + 0.305293i
\(516\) 0 0
\(517\) 2.62536i 0.115463i
\(518\) 6.92820i 0.304408i
\(519\) 0 0
\(520\) 5.46410 + 6.69213i 0.239617 + 0.293469i
\(521\) −9.52056 −0.417103 −0.208552 0.978011i \(-0.566875\pi\)
−0.208552 + 0.978011i \(0.566875\pi\)
\(522\) 0 0
\(523\) 26.7685i 1.17051i 0.810851 + 0.585253i \(0.199005\pi\)
−0.810851 + 0.585253i \(0.800995\pi\)
\(524\) 3.10583 0.135679
\(525\) 0 0
\(526\) −19.3205 −0.842414
\(527\) 5.85641i 0.255109i
\(528\) 0 0
\(529\) −6.85641 −0.298105
\(530\) −8.48528 10.3923i −0.368577 0.451413i
\(531\) 0 0
\(532\) 3.86370i 0.167513i
\(533\) 6.92820i 0.300094i
\(534\) 0 0
\(535\) 5.07180 4.14110i 0.219273 0.179036i
\(536\) 13.3843 0.578112
\(537\) 0 0
\(538\) 31.9449i 1.37724i
\(539\) 8.20788 0.353538
\(540\) 0 0
\(541\) 26.0000 1.11783 0.558914 0.829226i \(-0.311218\pi\)
0.558914 + 0.829226i \(0.311218\pi\)
\(542\) 10.9282i 0.469407i
\(543\) 0 0
\(544\) 0.535898 0.0229765
\(545\) −12.6264 15.4641i −0.540855 0.662409i
\(546\) 0 0
\(547\) 10.3528i 0.442652i 0.975200 + 0.221326i \(0.0710385\pi\)
−0.975200 + 0.221326i \(0.928961\pi\)
\(548\) 0.535898i 0.0228924i
\(549\) 0 0
\(550\) −5.07180 1.03528i −0.216262 0.0441443i
\(551\) 4.62158 0.196886
\(552\) 0 0
\(553\) 15.4548i 0.657206i
\(554\) 18.2832 0.776780
\(555\) 0 0
\(556\) 6.92820 0.293821
\(557\) 31.4641i 1.33318i 0.745426 + 0.666588i \(0.232246\pi\)
−0.745426 + 0.666588i \(0.767754\pi\)
\(558\) 0 0
\(559\) −25.8564 −1.09361
\(560\) 6.69213 5.46410i 0.282794 0.230900i
\(561\) 0 0
\(562\) 31.1870i 1.31555i
\(563\) 25.8564i 1.08972i −0.838528 0.544859i \(-0.816583\pi\)
0.838528 0.544859i \(-0.183417\pi\)
\(564\) 0 0
\(565\) 10.3923 8.48528i 0.437208 0.356978i
\(566\) 5.17638 0.217580
\(567\) 0 0
\(568\) 4.14110i 0.173757i
\(569\) 44.0165 1.84527 0.922634 0.385678i \(-0.126032\pi\)
0.922634 + 0.385678i \(0.126032\pi\)
\(570\) 0 0
\(571\) 14.9282 0.624726 0.312363 0.949963i \(-0.398880\pi\)
0.312363 + 0.949963i \(0.398880\pi\)
\(572\) 4.00000i 0.167248i
\(573\) 0 0
\(574\) 6.92820 0.289178
\(575\) 26.7685 + 5.46410i 1.11632 + 0.227869i
\(576\) 0 0
\(577\) 5.65685i 0.235498i −0.993043 0.117749i \(-0.962432\pi\)
0.993043 0.117749i \(-0.0375678\pi\)
\(578\) 16.7128i 0.695161i
\(579\) 0 0
\(580\) −6.53590 8.00481i −0.271388 0.332382i
\(581\) −63.3350 −2.62758
\(582\) 0 0
\(583\) 6.21166i 0.257261i
\(584\) 3.58630 0.148402
\(585\) 0 0
\(586\) 19.8564 0.820261
\(587\) 24.3923i 1.00678i 0.864060 + 0.503389i \(0.167914\pi\)
−0.864060 + 0.503389i \(0.832086\pi\)
\(588\) 0 0
\(589\) −10.9282 −0.450289
\(590\) 12.0716 9.85641i 0.496979 0.405782i
\(591\) 0 0
\(592\) 1.79315i 0.0736980i
\(593\) 4.53590i 0.186267i 0.995654 + 0.0931335i \(0.0296883\pi\)
−0.995654 + 0.0931335i \(0.970312\pi\)
\(594\) 0 0
\(595\) 2.92820 + 3.58630i 0.120045 + 0.147024i
\(596\) −20.3538 −0.833724
\(597\) 0 0
\(598\) 21.1117i 0.863320i
\(599\) −20.5569 −0.839931 −0.419965 0.907540i \(-0.637958\pi\)
−0.419965 + 0.907540i \(0.637958\pi\)
\(600\) 0 0
\(601\) −18.7846 −0.766240 −0.383120 0.923699i \(-0.625150\pi\)
−0.383120 + 0.923699i \(0.625150\pi\)
\(602\) 25.8564i 1.05383i
\(603\) 0 0
\(604\) −5.85641 −0.238294
\(605\) −14.0406 17.1962i −0.570832 0.699123i
\(606\) 0 0
\(607\) 45.6066i 1.85111i 0.378609 + 0.925557i \(0.376402\pi\)
−0.378609 + 0.925557i \(0.623598\pi\)
\(608\) 1.00000i 0.0405554i
\(609\) 0 0
\(610\) −3.46410 + 2.82843i −0.140257 + 0.114520i
\(611\) 9.79796 0.396383
\(612\) 0 0
\(613\) 5.85993i 0.236680i −0.992973 0.118340i \(-0.962243\pi\)
0.992973 0.118340i \(-0.0377573\pi\)
\(614\) −17.5254 −0.707266
\(615\) 0 0
\(616\) −4.00000 −0.161165
\(617\) 28.2487i 1.13725i 0.822597 + 0.568625i \(0.192524\pi\)
−0.822597 + 0.568625i \(0.807476\pi\)
\(618\) 0 0
\(619\) 34.6410 1.39234 0.696170 0.717877i \(-0.254886\pi\)
0.696170 + 0.717877i \(0.254886\pi\)
\(620\) 15.4548 + 18.9282i 0.620680 + 0.760175i
\(621\) 0 0
\(622\) 1.79315i 0.0718988i
\(623\) 14.9282i 0.598086i
\(624\) 0 0
\(625\) −23.0000 9.79796i −0.920000 0.391918i
\(626\) −19.5959 −0.783210
\(627\) 0 0
\(628\) 14.1421i 0.564333i
\(629\) −0.960947 −0.0383155
\(630\) 0 0
\(631\) 21.8564 0.870090 0.435045 0.900409i \(-0.356732\pi\)
0.435045 + 0.900409i \(0.356732\pi\)
\(632\) 4.00000i 0.159111i
\(633\) 0 0
\(634\) 14.0000 0.556011
\(635\) 14.6969 12.0000i 0.583230 0.476205i
\(636\) 0 0
\(637\) 30.6322i 1.21369i
\(638\) 4.78461i 0.189425i
\(639\) 0 0
\(640\) −1.73205 + 1.41421i −0.0684653 + 0.0559017i
\(641\) −17.2480 −0.681254 −0.340627 0.940199i \(-0.610639\pi\)
−0.340627 + 0.940199i \(0.610639\pi\)
\(642\) 0 0
\(643\) 37.0470i 1.46099i −0.682918 0.730495i \(-0.739290\pi\)
0.682918 0.730495i \(-0.260710\pi\)
\(644\) 21.1117 0.831916
\(645\) 0 0
\(646\) 0.535898 0.0210846
\(647\) 13.4641i 0.529328i 0.964341 + 0.264664i \(0.0852611\pi\)
−0.964341 + 0.264664i \(0.914739\pi\)
\(648\) 0 0
\(649\) −7.21539 −0.283229
\(650\) 3.86370 18.9282i 0.151547 0.742425i
\(651\) 0 0
\(652\) 23.6627i 0.926703i
\(653\) 24.2487i 0.948925i 0.880276 + 0.474463i \(0.157358\pi\)
−0.880276 + 0.474463i \(0.842642\pi\)
\(654\) 0 0
\(655\) −4.39230 5.37945i −0.171622 0.210193i
\(656\) −1.79315 −0.0700108
\(657\) 0 0
\(658\) 9.79796i 0.381964i
\(659\) 20.3538 0.792871 0.396436 0.918063i \(-0.370247\pi\)
0.396436 + 0.918063i \(0.370247\pi\)
\(660\) 0 0
\(661\) −10.7846 −0.419473 −0.209736 0.977758i \(-0.567261\pi\)
−0.209736 + 0.977758i \(0.567261\pi\)
\(662\) 13.8564i 0.538545i
\(663\) 0 0
\(664\) 16.3923 0.636145
\(665\) 6.69213 5.46410i 0.259510 0.211889i
\(666\) 0 0
\(667\) 25.2528i 0.977791i
\(668\) 10.9282i 0.422825i
\(669\) 0 0
\(670\) −18.9282 23.1822i −0.731260 0.895607i
\(671\) 2.07055 0.0799328
\(672\) 0 0
\(673\) 27.2490i 1.05037i −0.850988 0.525186i \(-0.823996\pi\)
0.850988 0.525186i \(-0.176004\pi\)
\(674\) −1.03528 −0.0398773
\(675\) 0 0
\(676\) 1.92820 0.0741617
\(677\) 36.6410i 1.40823i 0.710087 + 0.704114i \(0.248656\pi\)
−0.710087 + 0.704114i \(0.751344\pi\)
\(678\) 0 0
\(679\) −9.85641 −0.378254
\(680\) −0.757875 0.928203i −0.0290632 0.0355950i
\(681\) 0 0
\(682\) 11.3137i 0.433224i
\(683\) 18.9282i 0.724268i −0.932126 0.362134i \(-0.882048\pi\)
0.932126 0.362134i \(-0.117952\pi\)
\(684\) 0 0
\(685\) −0.928203 + 0.757875i −0.0354648 + 0.0289569i
\(686\) 3.58630 0.136926
\(687\) 0 0
\(688\) 6.69213i 0.255135i
\(689\) −23.1822 −0.883172
\(690\) 0 0
\(691\) 38.9282 1.48090 0.740449 0.672112i \(-0.234613\pi\)
0.740449 + 0.672112i \(0.234613\pi\)
\(692\) 22.7846i 0.866141i
\(693\) 0 0
\(694\) 18.5359 0.703613
\(695\) −9.79796 12.0000i −0.371658 0.455186i
\(696\) 0 0
\(697\) 0.960947i 0.0363985i
\(698\) 4.14359i 0.156837i
\(699\) 0 0
\(700\) −18.9282 3.86370i −0.715419 0.146034i
\(701\) 7.52433 0.284190 0.142095 0.989853i \(-0.454616\pi\)
0.142095 + 0.989853i \(0.454616\pi\)
\(702\) 0 0
\(703\) 1.79315i 0.0676300i
\(704\) 1.03528 0.0390184
\(705\) 0 0
\(706\) −21.3205 −0.802408
\(707\) 40.7846i 1.53386i
\(708\) 0 0
\(709\) 11.8564 0.445277 0.222638 0.974901i \(-0.428533\pi\)
0.222638 + 0.974901i \(0.428533\pi\)
\(710\) −7.17260 + 5.85641i −0.269183 + 0.219787i
\(711\) 0 0
\(712\) 3.86370i 0.144798i
\(713\) 59.7128i 2.23626i
\(714\) 0 0
\(715\) −6.92820 + 5.65685i −0.259100 + 0.211554i
\(716\) 16.7675 0.626631
\(717\) 0 0
\(718\) 34.7733i 1.29773i
\(719\) 46.6418 1.73945 0.869724 0.493539i \(-0.164297\pi\)
0.869724 + 0.493539i \(0.164297\pi\)
\(720\) 0 0
\(721\) 18.9282 0.704923
\(722\) 1.00000i 0.0372161i
\(723\) 0 0
\(724\) −19.8564 −0.737958
\(725\) −4.62158 + 22.6410i −0.171641 + 0.840866i
\(726\) 0 0
\(727\) 15.1774i 0.562899i 0.959576 + 0.281450i \(0.0908152\pi\)
−0.959576 + 0.281450i \(0.909185\pi\)
\(728\) 14.9282i 0.553276i
\(729\) 0 0
\(730\) −5.07180 6.21166i −0.187716 0.229904i
\(731\) 3.58630 0.132644
\(732\) 0 0
\(733\) 21.8695i 0.807770i −0.914810 0.403885i \(-0.867660\pi\)
0.914810 0.403885i \(-0.132340\pi\)
\(734\) 5.37945 0.198559
\(735\) 0 0
\(736\) −5.46410 −0.201409
\(737\) 13.8564i 0.510407i
\(738\) 0 0
\(739\) −23.7128 −0.872290 −0.436145 0.899876i \(-0.643657\pi\)
−0.436145 + 0.899876i \(0.643657\pi\)
\(740\) 3.10583 2.53590i 0.114173 0.0932215i
\(741\) 0 0
\(742\) 23.1822i 0.851046i
\(743\) 34.6410i 1.27086i 0.772160 + 0.635428i \(0.219176\pi\)
−0.772160 + 0.635428i \(0.780824\pi\)
\(744\) 0 0
\(745\) 28.7846 + 35.2538i 1.05459 + 1.29160i
\(746\) −24.9754 −0.914413
\(747\) 0 0
\(748\) 0.554803i 0.0202856i
\(749\) −11.3137 −0.413394
\(750\) 0 0
\(751\) 5.85641 0.213703 0.106852 0.994275i \(-0.465923\pi\)
0.106852 + 0.994275i \(0.465923\pi\)
\(752\) 2.53590i 0.0924747i
\(753\) 0 0
\(754\) −17.8564 −0.650292
\(755\) 8.28221 + 10.1436i 0.301420 + 0.369163i
\(756\) 0 0
\(757\) 40.3559i 1.46676i −0.679820 0.733379i \(-0.737942\pi\)
0.679820 0.733379i \(-0.262058\pi\)
\(758\) 35.7128i 1.29715i
\(759\) 0 0
\(760\) −1.73205 + 1.41421i −0.0628281 + 0.0512989i
\(761\) −23.1822 −0.840355 −0.420177 0.907442i \(-0.638032\pi\)
−0.420177 + 0.907442i \(0.638032\pi\)
\(762\) 0 0
\(763\) 34.4959i 1.24884i
\(764\) −17.2480 −0.624009
\(765\) 0 0
\(766\) 22.9282 0.828430
\(767\) 26.9282i 0.972321i
\(768\) 0 0
\(769\) −35.8564 −1.29302 −0.646508 0.762908i \(-0.723771\pi\)
−0.646508 + 0.762908i \(0.723771\pi\)
\(770\) 5.65685 + 6.92820i 0.203859 + 0.249675i
\(771\) 0 0
\(772\) 8.76268i 0.315376i
\(773\) 7.85641i 0.282575i 0.989969 + 0.141288i \(0.0451242\pi\)
−0.989969 + 0.141288i \(0.954876\pi\)
\(774\) 0 0
\(775\) 10.9282 53.5370i 0.392553 1.92311i
\(776\) 2.55103 0.0915765
\(777\) 0 0
\(778\) 19.7990i 0.709828i
\(779\) −1.79315 −0.0642463
\(780\) 0 0
\(781\) 4.28719 0.153408
\(782\) 2.92820i 0.104712i
\(783\) 0 0
\(784\) −7.92820 −0.283150
\(785\) 24.4949 20.0000i 0.874260 0.713831i
\(786\) 0 0
\(787\) 7.17260i 0.255676i −0.991795 0.127838i \(-0.959196\pi\)
0.991795 0.127838i \(-0.0408037\pi\)
\(788\) 23.4641i 0.835874i
\(789\) 0 0
\(790\) 6.92820 5.65685i 0.246494 0.201262i
\(791\) −23.1822 −0.824265
\(792\) 0 0
\(793\) 7.72741i 0.274408i
\(794\) −18.2832 −0.648848
\(795\) 0 0
\(796\) 13.0718 0.463318
\(797\) 40.6410i 1.43958i 0.694193 + 0.719789i \(0.255762\pi\)
−0.694193 + 0.719789i \(0.744238\pi\)
\(798\) 0