Properties

Label 2352.2.q.ba.1537.2
Level $2352$
Weight $2$
Character 2352.1537
Analytic conductor $18.781$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2352.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.7808145554\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} + 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1176)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 1537.2
Root \(0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 2352.1537
Dual form 2352.2.q.ba.961.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{3} +(-0.292893 - 0.507306i) q^{5} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{3} +(-0.292893 - 0.507306i) q^{5} +(-0.500000 - 0.866025i) q^{9} +(-2.41421 + 4.18154i) q^{11} +4.24264 q^{13} +0.585786 q^{15} +(-2.29289 + 3.97141i) q^{17} +(0.585786 + 1.01461i) q^{19} +(0.414214 + 0.717439i) q^{23} +(2.32843 - 4.03295i) q^{25} +1.00000 q^{27} -2.82843 q^{29} +(1.41421 - 2.44949i) q^{31} +(-2.41421 - 4.18154i) q^{33} +(-4.82843 - 8.36308i) q^{37} +(-2.12132 + 3.67423i) q^{39} +1.75736 q^{41} -11.3137 q^{43} +(-0.292893 + 0.507306i) q^{45} +(6.24264 + 10.8126i) q^{47} +(-2.29289 - 3.97141i) q^{51} +(1.00000 - 1.73205i) q^{53} +2.82843 q^{55} -1.17157 q^{57} +(-4.24264 + 7.34847i) q^{59} +(1.53553 + 2.65962i) q^{61} +(-1.24264 - 2.15232i) q^{65} +(-5.65685 + 9.79796i) q^{67} -0.828427 q^{69} -6.48528 q^{71} +(-8.12132 + 14.0665i) q^{73} +(2.32843 + 4.03295i) q^{75} +(1.17157 + 2.02922i) q^{79} +(-0.500000 + 0.866025i) q^{81} +4.00000 q^{83} +2.68629 q^{85} +(1.41421 - 2.44949i) q^{87} +(-7.12132 - 12.3345i) q^{89} +(1.41421 + 2.44949i) q^{93} +(0.343146 - 0.594346i) q^{95} +8.24264 q^{97} +4.82843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{3} - 4q^{5} - 2q^{9} + O(q^{10}) \) \( 4q - 2q^{3} - 4q^{5} - 2q^{9} - 4q^{11} + 8q^{15} - 12q^{17} + 8q^{19} - 4q^{23} - 2q^{25} + 4q^{27} - 4q^{33} - 8q^{37} + 24q^{41} - 4q^{45} + 8q^{47} - 12q^{51} + 4q^{53} - 16q^{57} - 8q^{61} + 12q^{65} + 8q^{69} + 8q^{71} - 24q^{73} - 2q^{75} + 16q^{79} - 2q^{81} + 16q^{83} + 56q^{85} - 20q^{89} + 24q^{95} + 16q^{97} + 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2352\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1471\) \(1765\) \(2257\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i
\(4\) 0 0
\(5\) −0.292893 0.507306i −0.130986 0.226874i 0.793071 0.609129i \(-0.208481\pi\)
−0.924057 + 0.382255i \(0.875148\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0 0
\(11\) −2.41421 + 4.18154i −0.727913 + 1.26078i 0.229851 + 0.973226i \(0.426176\pi\)
−0.957764 + 0.287556i \(0.907157\pi\)
\(12\) 0 0
\(13\) 4.24264 1.17670 0.588348 0.808608i \(-0.299778\pi\)
0.588348 + 0.808608i \(0.299778\pi\)
\(14\) 0 0
\(15\) 0.585786 0.151249
\(16\) 0 0
\(17\) −2.29289 + 3.97141i −0.556108 + 0.963208i 0.441708 + 0.897159i \(0.354373\pi\)
−0.997816 + 0.0660490i \(0.978961\pi\)
\(18\) 0 0
\(19\) 0.585786 + 1.01461i 0.134389 + 0.232768i 0.925364 0.379080i \(-0.123760\pi\)
−0.790975 + 0.611848i \(0.790426\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0.414214 + 0.717439i 0.0863695 + 0.149596i 0.905974 0.423333i \(-0.139140\pi\)
−0.819604 + 0.572930i \(0.805807\pi\)
\(24\) 0 0
\(25\) 2.32843 4.03295i 0.465685 0.806591i
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −2.82843 −0.525226 −0.262613 0.964901i \(-0.584584\pi\)
−0.262613 + 0.964901i \(0.584584\pi\)
\(30\) 0 0
\(31\) 1.41421 2.44949i 0.254000 0.439941i −0.710623 0.703573i \(-0.751587\pi\)
0.964623 + 0.263631i \(0.0849203\pi\)
\(32\) 0 0
\(33\) −2.41421 4.18154i −0.420261 0.727913i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −4.82843 8.36308i −0.793789 1.37488i −0.923606 0.383344i \(-0.874772\pi\)
0.129817 0.991538i \(-0.458561\pi\)
\(38\) 0 0
\(39\) −2.12132 + 3.67423i −0.339683 + 0.588348i
\(40\) 0 0
\(41\) 1.75736 0.274453 0.137227 0.990540i \(-0.456181\pi\)
0.137227 + 0.990540i \(0.456181\pi\)
\(42\) 0 0
\(43\) −11.3137 −1.72532 −0.862662 0.505781i \(-0.831205\pi\)
−0.862662 + 0.505781i \(0.831205\pi\)
\(44\) 0 0
\(45\) −0.292893 + 0.507306i −0.0436619 + 0.0756247i
\(46\) 0 0
\(47\) 6.24264 + 10.8126i 0.910583 + 1.57718i 0.813243 + 0.581924i \(0.197700\pi\)
0.0973398 + 0.995251i \(0.468967\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −2.29289 3.97141i −0.321069 0.556108i
\(52\) 0 0
\(53\) 1.00000 1.73205i 0.137361 0.237915i −0.789136 0.614218i \(-0.789471\pi\)
0.926497 + 0.376303i \(0.122805\pi\)
\(54\) 0 0
\(55\) 2.82843 0.381385
\(56\) 0 0
\(57\) −1.17157 −0.155179
\(58\) 0 0
\(59\) −4.24264 + 7.34847i −0.552345 + 0.956689i 0.445760 + 0.895152i \(0.352933\pi\)
−0.998105 + 0.0615367i \(0.980400\pi\)
\(60\) 0 0
\(61\) 1.53553 + 2.65962i 0.196605 + 0.340530i 0.947425 0.319976i \(-0.103675\pi\)
−0.750821 + 0.660506i \(0.770342\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −1.24264 2.15232i −0.154131 0.266962i
\(66\) 0 0
\(67\) −5.65685 + 9.79796i −0.691095 + 1.19701i 0.280385 + 0.959888i \(0.409538\pi\)
−0.971480 + 0.237124i \(0.923795\pi\)
\(68\) 0 0
\(69\) −0.828427 −0.0997309
\(70\) 0 0
\(71\) −6.48528 −0.769661 −0.384831 0.922987i \(-0.625740\pi\)
−0.384831 + 0.922987i \(0.625740\pi\)
\(72\) 0 0
\(73\) −8.12132 + 14.0665i −0.950529 + 1.64636i −0.206245 + 0.978500i \(0.566124\pi\)
−0.744284 + 0.667864i \(0.767209\pi\)
\(74\) 0 0
\(75\) 2.32843 + 4.03295i 0.268864 + 0.465685i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 1.17157 + 2.02922i 0.131812 + 0.228306i 0.924375 0.381485i \(-0.124587\pi\)
−0.792563 + 0.609790i \(0.791254\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) 4.00000 0.439057 0.219529 0.975606i \(-0.429548\pi\)
0.219529 + 0.975606i \(0.429548\pi\)
\(84\) 0 0
\(85\) 2.68629 0.291369
\(86\) 0 0
\(87\) 1.41421 2.44949i 0.151620 0.262613i
\(88\) 0 0
\(89\) −7.12132 12.3345i −0.754858 1.30745i −0.945445 0.325783i \(-0.894372\pi\)
0.190586 0.981670i \(-0.438961\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 1.41421 + 2.44949i 0.146647 + 0.254000i
\(94\) 0 0
\(95\) 0.343146 0.594346i 0.0352060 0.0609786i
\(96\) 0 0
\(97\) 8.24264 0.836913 0.418457 0.908237i \(-0.362571\pi\)
0.418457 + 0.908237i \(0.362571\pi\)
\(98\) 0 0
\(99\) 4.82843 0.485275
\(100\) 0 0
\(101\) −7.36396 + 12.7548i −0.732742 + 1.26915i 0.222966 + 0.974826i \(0.428426\pi\)
−0.955707 + 0.294319i \(0.904907\pi\)
\(102\) 0 0
\(103\) −7.07107 12.2474i −0.696733 1.20678i −0.969593 0.244723i \(-0.921303\pi\)
0.272860 0.962054i \(-0.412030\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 3.58579 + 6.21076i 0.346651 + 0.600417i 0.985652 0.168788i \(-0.0539855\pi\)
−0.639001 + 0.769206i \(0.720652\pi\)
\(108\) 0 0
\(109\) −9.65685 + 16.7262i −0.924959 + 1.60208i −0.133332 + 0.991071i \(0.542568\pi\)
−0.791627 + 0.611004i \(0.790766\pi\)
\(110\) 0 0
\(111\) 9.65685 0.916588
\(112\) 0 0
\(113\) −10.0000 −0.940721 −0.470360 0.882474i \(-0.655876\pi\)
−0.470360 + 0.882474i \(0.655876\pi\)
\(114\) 0 0
\(115\) 0.242641 0.420266i 0.0226264 0.0391900i
\(116\) 0 0
\(117\) −2.12132 3.67423i −0.196116 0.339683i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −6.15685 10.6640i −0.559714 0.969453i
\(122\) 0 0
\(123\) −0.878680 + 1.52192i −0.0792279 + 0.137227i
\(124\) 0 0
\(125\) −5.65685 −0.505964
\(126\) 0 0
\(127\) −20.0000 −1.77471 −0.887357 0.461084i \(-0.847461\pi\)
−0.887357 + 0.461084i \(0.847461\pi\)
\(128\) 0 0
\(129\) 5.65685 9.79796i 0.498058 0.862662i
\(130\) 0 0
\(131\) −2.00000 3.46410i −0.174741 0.302660i 0.765331 0.643637i \(-0.222575\pi\)
−0.940072 + 0.340977i \(0.889242\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −0.292893 0.507306i −0.0252082 0.0436619i
\(136\) 0 0
\(137\) 7.41421 12.8418i 0.633439 1.09715i −0.353405 0.935471i \(-0.614976\pi\)
0.986844 0.161678i \(-0.0516906\pi\)
\(138\) 0 0
\(139\) −12.9706 −1.10015 −0.550074 0.835116i \(-0.685401\pi\)
−0.550074 + 0.835116i \(0.685401\pi\)
\(140\) 0 0
\(141\) −12.4853 −1.05145
\(142\) 0 0
\(143\) −10.2426 + 17.7408i −0.856533 + 1.48356i
\(144\) 0 0
\(145\) 0.828427 + 1.43488i 0.0687971 + 0.119160i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 10.6569 + 18.4582i 0.873044 + 1.51216i 0.858832 + 0.512257i \(0.171190\pi\)
0.0142111 + 0.999899i \(0.495476\pi\)
\(150\) 0 0
\(151\) 0.828427 1.43488i 0.0674164 0.116769i −0.830347 0.557247i \(-0.811858\pi\)
0.897763 + 0.440478i \(0.145191\pi\)
\(152\) 0 0
\(153\) 4.58579 0.370739
\(154\) 0 0
\(155\) −1.65685 −0.133082
\(156\) 0 0
\(157\) 4.12132 7.13834i 0.328917 0.569701i −0.653380 0.757030i \(-0.726650\pi\)
0.982297 + 0.187329i \(0.0599830\pi\)
\(158\) 0 0
\(159\) 1.00000 + 1.73205i 0.0793052 + 0.137361i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −2.82843 4.89898i −0.221540 0.383718i 0.733736 0.679435i \(-0.237775\pi\)
−0.955276 + 0.295717i \(0.904442\pi\)
\(164\) 0 0
\(165\) −1.41421 + 2.44949i −0.110096 + 0.190693i
\(166\) 0 0
\(167\) 9.17157 0.709718 0.354859 0.934920i \(-0.384529\pi\)
0.354859 + 0.934920i \(0.384529\pi\)
\(168\) 0 0
\(169\) 5.00000 0.384615
\(170\) 0 0
\(171\) 0.585786 1.01461i 0.0447962 0.0775893i
\(172\) 0 0
\(173\) 9.70711 + 16.8132i 0.738018 + 1.27828i 0.953387 + 0.301751i \(0.0975712\pi\)
−0.215369 + 0.976533i \(0.569095\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −4.24264 7.34847i −0.318896 0.552345i
\(178\) 0 0
\(179\) 5.24264 9.08052i 0.391853 0.678710i −0.600841 0.799369i \(-0.705167\pi\)
0.992694 + 0.120659i \(0.0385007\pi\)
\(180\) 0 0
\(181\) 7.07107 0.525588 0.262794 0.964852i \(-0.415356\pi\)
0.262794 + 0.964852i \(0.415356\pi\)
\(182\) 0 0
\(183\) −3.07107 −0.227020
\(184\) 0 0
\(185\) −2.82843 + 4.89898i −0.207950 + 0.360180i
\(186\) 0 0
\(187\) −11.0711 19.1757i −0.809597 1.40226i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −8.07107 13.9795i −0.584002 1.01152i −0.994999 0.0998844i \(-0.968153\pi\)
0.410997 0.911637i \(-0.365181\pi\)
\(192\) 0 0
\(193\) −1.00000 + 1.73205i −0.0719816 + 0.124676i −0.899770 0.436365i \(-0.856266\pi\)
0.827788 + 0.561041i \(0.189599\pi\)
\(194\) 0 0
\(195\) 2.48528 0.177975
\(196\) 0 0
\(197\) −25.3137 −1.80353 −0.901764 0.432230i \(-0.857727\pi\)
−0.901764 + 0.432230i \(0.857727\pi\)
\(198\) 0 0
\(199\) 2.82843 4.89898i 0.200502 0.347279i −0.748188 0.663486i \(-0.769076\pi\)
0.948690 + 0.316207i \(0.102409\pi\)
\(200\) 0 0
\(201\) −5.65685 9.79796i −0.399004 0.691095i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −0.514719 0.891519i −0.0359495 0.0622664i
\(206\) 0 0
\(207\) 0.414214 0.717439i 0.0287898 0.0498655i
\(208\) 0 0
\(209\) −5.65685 −0.391293
\(210\) 0 0
\(211\) 9.65685 0.664805 0.332403 0.943138i \(-0.392141\pi\)
0.332403 + 0.943138i \(0.392141\pi\)
\(212\) 0 0
\(213\) 3.24264 5.61642i 0.222182 0.384831i
\(214\) 0 0
\(215\) 3.31371 + 5.73951i 0.225993 + 0.391431i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −8.12132 14.0665i −0.548788 0.950529i
\(220\) 0 0
\(221\) −9.72792 + 16.8493i −0.654371 + 1.13340i
\(222\) 0 0
\(223\) −2.34315 −0.156909 −0.0784543 0.996918i \(-0.524998\pi\)
−0.0784543 + 0.996918i \(0.524998\pi\)
\(224\) 0 0
\(225\) −4.65685 −0.310457
\(226\) 0 0
\(227\) −5.41421 + 9.37769i −0.359354 + 0.622419i −0.987853 0.155391i \(-0.950336\pi\)
0.628499 + 0.777810i \(0.283670\pi\)
\(228\) 0 0
\(229\) 11.2929 + 19.5599i 0.746255 + 1.29255i 0.949606 + 0.313446i \(0.101484\pi\)
−0.203351 + 0.979106i \(0.565183\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 4.58579 + 7.94282i 0.300425 + 0.520351i 0.976232 0.216727i \(-0.0695382\pi\)
−0.675807 + 0.737078i \(0.736205\pi\)
\(234\) 0 0
\(235\) 3.65685 6.33386i 0.238547 0.413175i
\(236\) 0 0
\(237\) −2.34315 −0.152204
\(238\) 0 0
\(239\) 7.17157 0.463890 0.231945 0.972729i \(-0.425491\pi\)
0.231945 + 0.972729i \(0.425491\pi\)
\(240\) 0 0
\(241\) 2.94975 5.10911i 0.190010 0.329107i −0.755243 0.655445i \(-0.772481\pi\)
0.945253 + 0.326338i \(0.105815\pi\)
\(242\) 0 0
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 2.48528 + 4.30463i 0.158135 + 0.273897i
\(248\) 0 0
\(249\) −2.00000 + 3.46410i −0.126745 + 0.219529i
\(250\) 0 0
\(251\) −22.1421 −1.39760 −0.698800 0.715317i \(-0.746282\pi\)
−0.698800 + 0.715317i \(0.746282\pi\)
\(252\) 0 0
\(253\) −4.00000 −0.251478
\(254\) 0 0
\(255\) −1.34315 + 2.32640i −0.0841110 + 0.145685i
\(256\) 0 0
\(257\) 0.292893 + 0.507306i 0.0182702 + 0.0316449i 0.875016 0.484094i \(-0.160851\pi\)
−0.856746 + 0.515739i \(0.827517\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 1.41421 + 2.44949i 0.0875376 + 0.151620i
\(262\) 0 0
\(263\) 4.07107 7.05130i 0.251033 0.434802i −0.712778 0.701390i \(-0.752563\pi\)
0.963810 + 0.266589i \(0.0858965\pi\)
\(264\) 0 0
\(265\) −1.17157 −0.0719691
\(266\) 0 0
\(267\) 14.2426 0.871635
\(268\) 0 0
\(269\) 9.94975 17.2335i 0.606647 1.05074i −0.385142 0.922857i \(-0.625848\pi\)
0.991789 0.127886i \(-0.0408191\pi\)
\(270\) 0 0
\(271\) −11.0711 19.1757i −0.672519 1.16484i −0.977187 0.212379i \(-0.931879\pi\)
0.304668 0.952459i \(-0.401455\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 11.2426 + 19.4728i 0.677957 + 1.17426i
\(276\) 0 0
\(277\) −8.31371 + 14.3998i −0.499522 + 0.865198i −1.00000 0.000551476i \(-0.999824\pi\)
0.500478 + 0.865750i \(0.333158\pi\)
\(278\) 0 0
\(279\) −2.82843 −0.169334
\(280\) 0 0
\(281\) 6.82843 0.407350 0.203675 0.979039i \(-0.434711\pi\)
0.203675 + 0.979039i \(0.434711\pi\)
\(282\) 0 0
\(283\) 1.07107 1.85514i 0.0636684 0.110277i −0.832434 0.554124i \(-0.813053\pi\)
0.896103 + 0.443847i \(0.146387\pi\)
\(284\) 0 0
\(285\) 0.343146 + 0.594346i 0.0203262 + 0.0352060i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −2.01472 3.48960i −0.118513 0.205270i
\(290\) 0 0
\(291\) −4.12132 + 7.13834i −0.241596 + 0.418457i
\(292\) 0 0
\(293\) −10.2426 −0.598381 −0.299191 0.954193i \(-0.596717\pi\)
−0.299191 + 0.954193i \(0.596717\pi\)
\(294\) 0 0
\(295\) 4.97056 0.289397
\(296\) 0 0
\(297\) −2.41421 + 4.18154i −0.140087 + 0.242638i
\(298\) 0 0
\(299\) 1.75736 + 3.04384i 0.101631 + 0.176030i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −7.36396 12.7548i −0.423049 0.732742i
\(304\) 0 0
\(305\) 0.899495 1.55797i 0.0515049 0.0892092i
\(306\) 0 0
\(307\) 28.4853 1.62574 0.812870 0.582445i \(-0.197904\pi\)
0.812870 + 0.582445i \(0.197904\pi\)
\(308\) 0 0
\(309\) 14.1421 0.804518
\(310\) 0 0
\(311\) −7.89949 + 13.6823i −0.447939 + 0.775854i −0.998252 0.0591052i \(-0.981175\pi\)
0.550312 + 0.834959i \(0.314509\pi\)
\(312\) 0 0
\(313\) −1.63604 2.83370i −0.0924744 0.160170i 0.816077 0.577943i \(-0.196144\pi\)
−0.908552 + 0.417772i \(0.862811\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 11.0000 + 19.0526i 0.617822 + 1.07010i 0.989882 + 0.141890i \(0.0453179\pi\)
−0.372061 + 0.928208i \(0.621349\pi\)
\(318\) 0 0
\(319\) 6.82843 11.8272i 0.382319 0.662195i
\(320\) 0 0
\(321\) −7.17157 −0.400278
\(322\) 0 0
\(323\) −5.37258 −0.298939
\(324\) 0 0
\(325\) 9.87868 17.1104i 0.547971 0.949113i
\(326\) 0 0
\(327\) −9.65685 16.7262i −0.534025 0.924959i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −7.65685 13.2621i −0.420859 0.728949i 0.575165 0.818037i \(-0.304938\pi\)
−0.996024 + 0.0890887i \(0.971605\pi\)
\(332\) 0 0
\(333\) −4.82843 + 8.36308i −0.264596 + 0.458294i
\(334\) 0 0
\(335\) 6.62742 0.362094
\(336\) 0 0
\(337\) 21.6569 1.17972 0.589862 0.807504i \(-0.299182\pi\)
0.589862 + 0.807504i \(0.299182\pi\)
\(338\) 0 0
\(339\) 5.00000 8.66025i 0.271563 0.470360i
\(340\) 0 0
\(341\) 6.82843 + 11.8272i 0.369780 + 0.640478i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0.242641 + 0.420266i 0.0130633 + 0.0226264i
\(346\) 0 0
\(347\) 7.24264 12.5446i 0.388805 0.673431i −0.603484 0.797375i \(-0.706221\pi\)
0.992289 + 0.123945i \(0.0395545\pi\)
\(348\) 0 0
\(349\) 13.4142 0.718046 0.359023 0.933329i \(-0.383110\pi\)
0.359023 + 0.933329i \(0.383110\pi\)
\(350\) 0 0
\(351\) 4.24264 0.226455
\(352\) 0 0
\(353\) −15.8492 + 27.4517i −0.843570 + 1.46111i 0.0432872 + 0.999063i \(0.486217\pi\)
−0.886857 + 0.462044i \(0.847116\pi\)
\(354\) 0 0
\(355\) 1.89949 + 3.29002i 0.100815 + 0.174616i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 11.5858 + 20.0672i 0.611474 + 1.05910i 0.990992 + 0.133920i \(0.0427566\pi\)
−0.379518 + 0.925184i \(0.623910\pi\)
\(360\) 0 0
\(361\) 8.81371 15.2658i 0.463879 0.803463i
\(362\) 0 0
\(363\) 12.3137 0.646302
\(364\) 0 0
\(365\) 9.51472 0.498023
\(366\) 0 0
\(367\) 13.6569 23.6544i 0.712882 1.23475i −0.250889 0.968016i \(-0.580723\pi\)
0.963771 0.266732i \(-0.0859438\pi\)
\(368\) 0 0
\(369\) −0.878680 1.52192i −0.0457422 0.0792279i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 8.65685 + 14.9941i 0.448235 + 0.776366i 0.998271 0.0587751i \(-0.0187195\pi\)
−0.550036 + 0.835141i \(0.685386\pi\)
\(374\) 0 0
\(375\) 2.82843 4.89898i 0.146059 0.252982i
\(376\) 0 0
\(377\) −12.0000 −0.618031
\(378\) 0 0
\(379\) 0.686292 0.0352524 0.0176262 0.999845i \(-0.494389\pi\)
0.0176262 + 0.999845i \(0.494389\pi\)
\(380\) 0 0
\(381\) 10.0000 17.3205i 0.512316 0.887357i
\(382\) 0 0
\(383\) 12.4853 + 21.6251i 0.637968 + 1.10499i 0.985878 + 0.167465i \(0.0535582\pi\)
−0.347910 + 0.937528i \(0.613108\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 5.65685 + 9.79796i 0.287554 + 0.498058i
\(388\) 0 0
\(389\) −1.89949 + 3.29002i −0.0963082 + 0.166811i −0.910154 0.414270i \(-0.864037\pi\)
0.813846 + 0.581081i \(0.197370\pi\)
\(390\) 0 0
\(391\) −3.79899 −0.192123
\(392\) 0 0
\(393\) 4.00000 0.201773
\(394\) 0 0
\(395\) 0.686292 1.18869i 0.0345311 0.0598096i
\(396\) 0 0
\(397\) 3.87868 + 6.71807i 0.194665 + 0.337170i 0.946791 0.321850i \(-0.104305\pi\)
−0.752125 + 0.659020i \(0.770971\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −3.41421 5.91359i −0.170498 0.295311i 0.768096 0.640334i \(-0.221204\pi\)
−0.938594 + 0.345024i \(0.887871\pi\)
\(402\) 0 0
\(403\) 6.00000 10.3923i 0.298881 0.517678i
\(404\) 0 0
\(405\) 0.585786 0.0291080
\(406\) 0 0
\(407\) 46.6274 2.31124
\(408\) 0 0
\(409\) −0.121320 + 0.210133i −0.00599890 + 0.0103904i −0.869009 0.494796i \(-0.835243\pi\)
0.863010 + 0.505186i \(0.168576\pi\)
\(410\) 0 0
\(411\) 7.41421 + 12.8418i 0.365716 + 0.633439i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −1.17157 2.02922i −0.0575103 0.0996107i
\(416\) 0 0
\(417\) 6.48528 11.2328i 0.317586 0.550074i
\(418\) 0 0
\(419\) −24.4853 −1.19618 −0.598092 0.801427i \(-0.704074\pi\)
−0.598092 + 0.801427i \(0.704074\pi\)
\(420\) 0 0
\(421\) −2.68629 −0.130922 −0.0654609 0.997855i \(-0.520852\pi\)
−0.0654609 + 0.997855i \(0.520852\pi\)
\(422\) 0 0
\(423\) 6.24264 10.8126i 0.303528 0.525725i
\(424\) 0 0
\(425\) 10.6777 + 18.4943i 0.517943 + 0.897104i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −10.2426 17.7408i −0.494519 0.856533i
\(430\) 0 0
\(431\) 10.0711 17.4436i 0.485106 0.840229i −0.514747 0.857342i \(-0.672114\pi\)
0.999854 + 0.0171133i \(0.00544758\pi\)
\(432\) 0 0
\(433\) 15.0711 0.724269 0.362135 0.932126i \(-0.382048\pi\)
0.362135 + 0.932126i \(0.382048\pi\)
\(434\) 0 0
\(435\) −1.65685 −0.0794401
\(436\) 0 0
\(437\) −0.485281 + 0.840532i −0.0232142 + 0.0402081i
\(438\) 0 0
\(439\) 17.6569 + 30.5826i 0.842716 + 1.45963i 0.887590 + 0.460634i \(0.152378\pi\)
−0.0448746 + 0.998993i \(0.514289\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −8.41421 14.5738i −0.399771 0.692424i 0.593926 0.804520i \(-0.297577\pi\)
−0.993697 + 0.112095i \(0.964244\pi\)
\(444\) 0 0
\(445\) −4.17157 + 7.22538i −0.197752 + 0.342516i
\(446\) 0 0
\(447\) −21.3137 −1.00810
\(448\) 0 0
\(449\) 28.6274 1.35101 0.675506 0.737355i \(-0.263925\pi\)
0.675506 + 0.737355i \(0.263925\pi\)
\(450\) 0 0
\(451\) −4.24264 + 7.34847i −0.199778 + 0.346026i
\(452\) 0 0
\(453\) 0.828427 + 1.43488i 0.0389229 + 0.0674164i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −10.3137 17.8639i −0.482455 0.835636i 0.517342 0.855779i \(-0.326921\pi\)
−0.999797 + 0.0201422i \(0.993588\pi\)
\(458\) 0 0
\(459\) −2.29289 + 3.97141i −0.107023 + 0.185369i
\(460\) 0 0
\(461\) −20.3848 −0.949414 −0.474707 0.880144i \(-0.657446\pi\)
−0.474707 + 0.880144i \(0.657446\pi\)
\(462\) 0 0
\(463\) 9.65685 0.448792 0.224396 0.974498i \(-0.427959\pi\)
0.224396 + 0.974498i \(0.427959\pi\)
\(464\) 0 0
\(465\) 0.828427 1.43488i 0.0384174 0.0665409i
\(466\) 0 0
\(467\) −6.58579 11.4069i −0.304754 0.527849i 0.672453 0.740140i \(-0.265241\pi\)
−0.977206 + 0.212291i \(0.931908\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 4.12132 + 7.13834i 0.189900 + 0.328917i
\(472\) 0 0
\(473\) 27.3137 47.3087i 1.25589 2.17526i
\(474\) 0 0
\(475\) 5.45584 0.250331
\(476\) 0 0
\(477\) −2.00000 −0.0915737
\(478\) 0 0
\(479\) 8.58579 14.8710i 0.392295 0.679474i −0.600457 0.799657i \(-0.705015\pi\)
0.992752 + 0.120183i \(0.0383480\pi\)
\(480\) 0 0
\(481\) −20.4853 35.4815i −0.934048 1.61782i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −2.41421 4.18154i −0.109624 0.189874i
\(486\) 0 0
\(487\) −14.4853 + 25.0892i −0.656391 + 1.13690i 0.325152 + 0.945662i \(0.394584\pi\)
−0.981543 + 0.191241i \(0.938749\pi\)
\(488\) 0 0
\(489\) 5.65685 0.255812
\(490\) 0 0
\(491\) −24.8284 −1.12049 −0.560246 0.828327i \(-0.689293\pi\)
−0.560246 + 0.828327i \(0.689293\pi\)
\(492\) 0 0
\(493\) 6.48528 11.2328i 0.292082 0.505902i
\(494\) 0 0
\(495\) −1.41421 2.44949i −0.0635642 0.110096i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 4.48528 + 7.76874i 0.200789 + 0.347776i 0.948783 0.315929i \(-0.102316\pi\)
−0.747994 + 0.663705i \(0.768983\pi\)
\(500\) 0 0
\(501\) −4.58579 + 7.94282i −0.204878 + 0.354859i
\(502\) 0 0
\(503\) −3.31371 −0.147751 −0.0738755 0.997267i \(-0.523537\pi\)
−0.0738755 + 0.997267i \(0.523537\pi\)
\(504\) 0 0
\(505\) 8.62742 0.383915
\(506\) 0 0
\(507\) −2.50000 + 4.33013i −0.111029 + 0.192308i
\(508\) 0 0
\(509\) −0.192388 0.333226i −0.00852746 0.0147700i 0.861730 0.507367i \(-0.169381\pi\)
−0.870258 + 0.492597i \(0.836048\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0.585786 + 1.01461i 0.0258631 + 0.0447962i
\(514\) 0 0
\(515\) −4.14214 + 7.17439i −0.182524 + 0.316141i
\(516\) 0 0
\(517\) −60.2843 −2.65130
\(518\) 0 0
\(519\) −19.4142 −0.852189
\(520\) 0 0
\(521\) −2.87868 + 4.98602i −0.126117 + 0.218441i −0.922169 0.386787i \(-0.873585\pi\)
0.796052 + 0.605228i \(0.206918\pi\)
\(522\) 0 0
\(523\) 14.4853 + 25.0892i 0.633397 + 1.09708i 0.986852 + 0.161625i \(0.0516734\pi\)
−0.353455 + 0.935451i \(0.614993\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 6.48528 + 11.2328i 0.282503 + 0.489310i
\(528\) 0 0
\(529\) 11.1569 19.3242i 0.485081 0.840184i
\(530\) 0 0
\(531\) 8.48528 0.368230
\(532\) 0 0
\(533\) 7.45584 0.322948
\(534\) 0 0
\(535\) 2.10051 3.63818i 0.0908128 0.157292i
\(536\) 0 0
\(537\) 5.24264 + 9.08052i 0.226237 + 0.391853i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 9.00000 + 15.5885i 0.386940 + 0.670200i 0.992036 0.125952i \(-0.0401986\pi\)
−0.605096 + 0.796152i \(0.706865\pi\)
\(542\) 0 0
\(543\) −3.53553 + 6.12372i −0.151724 + 0.262794i
\(544\) 0 0
\(545\) 11.3137 0.484626
\(546\) 0 0
\(547\) 36.9706 1.58075 0.790374 0.612625i \(-0.209886\pi\)
0.790374 + 0.612625i \(0.209886\pi\)
\(548\) 0 0
\(549\) 1.53553 2.65962i 0.0655350 0.113510i
\(550\) 0 0
\(551\) −1.65685 2.86976i −0.0705844 0.122256i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −2.82843 4.89898i −0.120060 0.207950i
\(556\) 0 0
\(557\) 6.31371 10.9357i 0.267520 0.463359i −0.700700 0.713456i \(-0.747129\pi\)
0.968221 + 0.250097i \(0.0804624\pi\)
\(558\) 0 0
\(559\) −48.0000 −2.03018
\(560\) 0 0
\(561\) 22.1421 0.934842
\(562\) 0 0
\(563\) 15.0711 26.1039i 0.635170 1.10015i −0.351309 0.936259i \(-0.614263\pi\)
0.986479 0.163887i \(-0.0524032\pi\)
\(564\) 0 0
\(565\) 2.92893 + 5.07306i 0.123221 + 0.213425i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 17.0711 + 29.5680i 0.715656 + 1.23955i 0.962706 + 0.270550i \(0.0872057\pi\)
−0.247049 + 0.969003i \(0.579461\pi\)
\(570\) 0 0
\(571\) −15.1716 + 26.2779i −0.634911 + 1.09970i 0.351624 + 0.936141i \(0.385630\pi\)
−0.986534 + 0.163556i \(0.947704\pi\)
\(572\) 0 0
\(573\) 16.1421 0.674347
\(574\) 0 0
\(575\) 3.85786 0.160884
\(576\) 0 0
\(577\) 14.6066 25.2994i 0.608081 1.05323i −0.383476 0.923551i \(-0.625273\pi\)
0.991556 0.129676i \(-0.0413937\pi\)
\(578\) 0 0
\(579\) −1.00000 1.73205i −0.0415586 0.0719816i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 4.82843 + 8.36308i 0.199973 + 0.346363i
\(584\) 0 0
\(585\) −1.24264 + 2.15232i −0.0513769 + 0.0889873i
\(586\) 0 0
\(587\) −3.79899 −0.156801 −0.0784005 0.996922i \(-0.524981\pi\)
−0.0784005 + 0.996922i \(0.524981\pi\)
\(588\) 0 0
\(589\) 3.31371 0.136539
\(590\) 0 0
\(591\) 12.6569 21.9223i 0.520633 0.901764i
\(592\) 0 0
\(593\) −22.2929 38.6124i −0.915459 1.58562i −0.806227 0.591606i \(-0.798494\pi\)
−0.109232 0.994016i \(-0.534839\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 2.82843 + 4.89898i 0.115760 + 0.200502i
\(598\) 0 0
\(599\) −13.7279 + 23.7775i −0.560908 + 0.971521i 0.436510 + 0.899699i \(0.356214\pi\)
−0.997418 + 0.0718211i \(0.977119\pi\)
\(600\) 0 0
\(601\) −3.75736 −0.153266 −0.0766329 0.997059i \(-0.524417\pi\)
−0.0766329 + 0.997059i \(0.524417\pi\)
\(602\) 0 0
\(603\) 11.3137 0.460730
\(604\) 0 0
\(605\) −3.60660 + 6.24682i −0.146629 + 0.253969i
\(606\) 0 0
\(607\) −4.48528 7.76874i −0.182052 0.315323i 0.760527 0.649306i \(-0.224941\pi\)
−0.942579 + 0.333983i \(0.891607\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 26.4853 + 45.8739i 1.07148 + 1.85586i
\(612\) 0 0
\(613\) 10.8284 18.7554i 0.437356 0.757523i −0.560129 0.828406i \(-0.689248\pi\)
0.997485 + 0.0708828i \(0.0225816\pi\)
\(614\) 0 0
\(615\) 1.02944 0.0415109
\(616\) 0 0
\(617\) 12.4853 0.502639 0.251319 0.967904i \(-0.419136\pi\)
0.251319 + 0.967904i \(0.419136\pi\)
\(618\) 0 0
\(619\) 11.1716 19.3497i 0.449023 0.777731i −0.549299 0.835626i \(-0.685105\pi\)
0.998323 + 0.0578943i \(0.0184386\pi\)
\(620\) 0 0
\(621\) 0.414214 + 0.717439i 0.0166218 + 0.0287898i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −9.98528 17.2950i −0.399411 0.691801i
\(626\) 0 0
\(627\) 2.82843 4.89898i 0.112956 0.195646i
\(628\) 0 0
\(629\) 44.2843 1.76573
\(630\) 0 0
\(631\) 36.9706 1.47177 0.735887 0.677104i \(-0.236765\pi\)
0.735887 + 0.677104i \(0.236765\pi\)
\(632\) 0 0
\(633\) −4.82843 + 8.36308i −0.191913 + 0.332403i
\(634\) 0 0
\(635\) 5.85786 + 10.1461i 0.232462 + 0.402636i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 3.24264 + 5.61642i 0.128277 + 0.222182i
\(640\) 0 0
\(641\) 13.5563 23.4803i 0.535444 0.927416i −0.463698 0.885993i \(-0.653478\pi\)
0.999142 0.0414223i \(-0.0131889\pi\)
\(642\) 0 0
\(643\) 7.79899 0.307562 0.153781 0.988105i \(-0.450855\pi\)
0.153781 + 0.988105i \(0.450855\pi\)
\(644\) 0 0
\(645\) −6.62742 −0.260954
\(646\) 0 0
\(647\) −19.8995 + 34.4669i −0.782330 + 1.35504i 0.148251 + 0.988950i \(0.452636\pi\)
−0.930581 + 0.366085i \(0.880698\pi\)
\(648\) 0 0
\(649\) −20.4853 35.4815i −0.804118 1.39277i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −8.92893 15.4654i −0.349416 0.605206i 0.636730 0.771087i \(-0.280287\pi\)
−0.986146 + 0.165881i \(0.946953\pi\)
\(654\) 0 0
\(655\) −1.17157 + 2.02922i −0.0457771 + 0.0792883i
\(656\) 0 0
\(657\) 16.2426 0.633686
\(658\) 0 0
\(659\) −38.4853 −1.49917 −0.749587 0.661906i \(-0.769748\pi\)
−0.749587 + 0.661906i \(0.769748\pi\)
\(660\) 0 0
\(661\) −9.53553 + 16.5160i −0.370889 + 0.642399i −0.989703 0.143139i \(-0.954280\pi\)
0.618813 + 0.785538i \(0.287614\pi\)
\(662\) 0 0
\(663\) −9.72792 16.8493i −0.377801 0.654371i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −1.17157 2.02922i −0.0453635 0.0785719i
\(668\) 0 0
\(669\) 1.17157 2.02922i 0.0452956 0.0784543i
\(670\) 0 0
\(671\) −14.8284 −0.572445
\(672\) 0 0
\(673\) −0.686292 −0.0264546 −0.0132273 0.999913i \(-0.504211\pi\)
−0.0132273 + 0.999913i \(0.504211\pi\)
\(674\) 0 0
\(675\) 2.32843 4.03295i 0.0896212 0.155228i
\(676\) 0 0
\(677\) 15.8492 + 27.4517i 0.609136 + 1.05505i 0.991383 + 0.130994i \(0.0418169\pi\)
−0.382247 + 0.924060i \(0.624850\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −5.41421 9.37769i −0.207473 0.359354i
\(682\) 0 0
\(683\) 18.8995 32.7349i 0.723169 1.25257i −0.236554 0.971618i \(-0.576018\pi\)
0.959723 0.280947i \(-0.0906486\pi\)
\(684\) 0 0
\(685\) −8.68629 −0.331886
\(686\) 0 0
\(687\) −22.5858 −0.861701
\(688\) 0 0
\(689\) 4.24264 7.34847i 0.161632 0.279954i
\(690\) 0 0
\(691\) 15.6569 + 27.1185i 0.595615 + 1.03164i 0.993460 + 0.114182i \(0.0364248\pi\)
−0.397845 + 0.917453i \(0.630242\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 3.79899 + 6.58004i 0.144104 + 0.249595i
\(696\) 0 0
\(697\) −4.02944 + 6.97919i −0.152626 + 0.264356i
\(698\) 0 0
\(699\) −9.17157 −0.346901
\(700\) 0 0
\(701\) 22.1421 0.836297 0.418148 0.908379i \(-0.362679\pi\)
0.418148 + 0.908379i \(0.362679\pi\)
\(702\) 0 0
\(703\) 5.65685 9.79796i 0.213352 0.369537i
\(704\) 0 0
\(705\) 3.65685 + 6.33386i 0.137725 + 0.238547i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 19.3137 + 33.4523i 0.725342 + 1.25633i 0.958833 + 0.283970i \(0.0916515\pi\)
−0.233492 + 0.972359i \(0.575015\pi\)
\(710\) 0 0
\(711\) 1.17157 2.02922i 0.0439374 0.0761018i
\(712\) 0 0
\(713\) 2.34315 0.0877515
\(714\) 0 0
\(715\) 12.0000 0.448775
\(716\) 0 0
\(717\) −3.58579 + 6.21076i −0.133914 + 0.231945i
\(718\) 0 0
\(719\) 19.3137 + 33.4523i 0.720280 + 1.24756i 0.960888 + 0.276939i \(0.0893199\pi\)
−0.240608 + 0.970622i \(0.577347\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 2.94975 + 5.10911i 0.109702 + 0.190010i
\(724\) 0 0
\(725\) −6.58579 + 11.4069i −0.244590 + 0.423642i
\(726\) 0 0
\(727\) 38.1421 1.41461 0.707307 0.706907i \(-0.249910\pi\)
0.707307 + 0.706907i \(0.249910\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 25.9411 44.9313i 0.959467 1.66185i
\(732\) 0 0
\(733\) −20.0208 34.6771i −0.739486 1.28083i −0.952727 0.303827i \(-0.901735\pi\)
0.213241 0.977000i \(-0.431598\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −27.3137 47.3087i −1.00611 1.74264i
\(738\) 0 0
\(739\) −0.485281 + 0.840532i −0.0178514 + 0.0309195i −0.874813 0.484461i \(-0.839016\pi\)
0.856962 + 0.515380i \(0.172349\pi\)
\(740\) 0 0
\(741\) −4.97056 −0.182598
\(742\) 0 0
\(743\) −0.828427 −0.0303920 −0.0151960 0.999885i \(-0.504837\pi\)
−0.0151960 + 0.999885i \(0.504837\pi\)
\(744\) 0 0
\(745\) 6.24264 10.8126i 0.228713 0.396142i
\(746\) 0 0
\(747\) −2.00000 3.46410i −0.0731762 0.126745i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −18.1421 31.4231i −0.662016 1.14665i −0.980085 0.198578i \(-0.936368\pi\)
0.318069 0.948067i \(-0.396966\pi\)
\(752\) 0 0
\(753\) 11.0711 19.1757i 0.403452 0.698800i
\(754\) 0 0
\(755\) −0.970563 −0.0353224
\(756\) 0 0
\(757\) −25.9411 −0.942846 −0.471423 0.881907i \(-0.656260\pi\)
−0.471423 + 0.881907i \(0.656260\pi\)
\(758\) 0 0
\(759\) 2.00000 3.46410i 0.0725954 0.125739i
\(760\) 0 0
\(761\) 6.05025 + 10.4793i 0.219321 + 0.379876i 0.954601 0.297888i \(-0.0962823\pi\)
−0.735279 + 0.677764i \(0.762949\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −1.34315 2.32640i −0.0485615 0.0841110i
\(766\) 0 0
\(767\) −18.0000 + 31.1769i −0.649942 + 1.12573i
\(768\) 0 0
\(769\) −18.8701 −0.680472 −0.340236 0.940340i \(-0.610507\pi\)
−0.340236 + 0.940340i \(0.610507\pi\)
\(770\) 0 0
\(771\) −0.585786 −0.0210966
\(772\) 0 0
\(773\) 18.6777 32.3507i 0.671789 1.16357i −0.305607 0.952158i \(-0.598859\pi\)
0.977396 0.211415i \(-0.0678072\pi\)
\(774\) 0 0
\(775\) −6.58579 11.4069i −0.236568 0.409749i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 1.02944 + 1.78304i 0.0368834 + 0.0638840i
\(780\) 0 0
\(781\) 15.6569 27.1185i 0.560246 0.970375i
\(782\) 0 0
\(783\) −2.82843 −0.101080
\(784\) 0 0
\(785\) −4.82843 −0.172334
\(786\) 0 0
\(787\) −3.65685 + 6.33386i −0.130353 + 0.225778i −0.923813 0.382845i \(-0.874944\pi\)
0.793460 + 0.608623i \(0.208278\pi\)
\(788\) 0 0
\(789\) 4.07107 + 7.05130i 0.144934 + 0.251033i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 6.51472 + 11.2838i 0.231344 + 0.400700i
\(794\) 0 0
\(795\) 0.585786 1.01461i 0.0207757 0.0359846i
\(796\) 0 0
\(797\) −36.5858 −1.29594 −0.647968 0.761668i \(-0.724381\pi\)
−0.647968 + 0.761668i \(0.724381\pi\)
\(798\) 0 0
\(799\) −57.2548 −2.02553