Properties

Label 1900.2.i.e.201.4
Level $1900$
Weight $2$
Character 1900.201
Analytic conductor $15.172$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1900.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.1715763840\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - 3 x^{11} + 15 x^{10} - 16 x^{9} + 79 x^{8} - 65 x^{7} + 298 x^{6} + 13 x^{5} + 233 x^{4} + 14 x^{3} + 145 x^{2} + 33 x + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 201.4
Root \(0.430479 - 0.745611i\) of defining polynomial
Character \(\chi\) \(=\) 1900.201
Dual form 1900.2.i.e.501.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.0695210 + 0.120414i) q^{3} -3.40785 q^{7} +(1.49033 + 2.58133i) q^{9} +O(q^{10})\) \(q+(-0.0695210 + 0.120414i) q^{3} -3.40785 q^{7} +(1.49033 + 2.58133i) q^{9} +0.185690 q^{11} +(-1.17736 - 2.03925i) q^{13} +(3.35663 - 5.81385i) q^{17} +(-2.14437 + 3.79495i) q^{19} +(0.236918 - 0.410353i) q^{21} +(-0.463767 - 0.803267i) q^{23} -0.831564 q^{27} +(0.677360 + 1.17322i) q^{29} -9.46158 q^{31} +(-0.0129094 + 0.0223597i) q^{33} -1.62862 q^{37} +0.327405 q^{39} +(4.29573 - 7.44043i) q^{41} +(3.80076 - 6.58312i) q^{43} +(4.09639 + 7.09515i) q^{47} +4.61347 q^{49} +(0.466712 + 0.808369i) q^{51} +(-6.70168 - 11.6077i) q^{53} +(-0.307887 - 0.522041i) q^{57} +(2.02981 - 3.51573i) q^{59} +(-6.31247 - 10.9335i) q^{61} +(-5.07884 - 8.79681i) q^{63} +(-1.62613 - 2.81654i) q^{67} +0.128966 q^{69} +(6.59887 - 11.4296i) q^{71} +(2.45260 - 4.24802i) q^{73} -0.632805 q^{77} +(-2.98245 + 5.16576i) q^{79} +(-4.41319 + 7.64387i) q^{81} +1.30480 q^{83} -0.188363 q^{87} +(1.95584 + 3.38761i) q^{89} +(4.01227 + 6.94946i) q^{91} +(0.657779 - 1.13931i) q^{93} +(7.25291 - 12.5624i) q^{97} +(0.276740 + 0.479328i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 3 q^{3} - 3 q^{9} + O(q^{10}) \) \( 12 q - 3 q^{3} - 3 q^{9} + 2 q^{11} - 7 q^{13} + q^{17} + q^{21} + 2 q^{23} + 24 q^{27} + q^{29} + 2 q^{31} - 10 q^{33} - 20 q^{37} + 36 q^{39} - 7 q^{41} - 19 q^{43} + 14 q^{47} + 8 q^{49} + 11 q^{51} - 6 q^{53} + 28 q^{57} - 5 q^{61} + 11 q^{63} - 14 q^{67} - 14 q^{69} + 8 q^{71} + 9 q^{73} - 2 q^{77} + q^{79} + 2 q^{81} + 26 q^{83} - 30 q^{87} - 8 q^{89} + 3 q^{91} - 9 q^{93} + 11 q^{97} - 18 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\) \(951\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.0695210 + 0.120414i −0.0401380 + 0.0695210i −0.885397 0.464837i \(-0.846113\pi\)
0.845259 + 0.534358i \(0.179446\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −3.40785 −1.28805 −0.644024 0.765005i \(-0.722736\pi\)
−0.644024 + 0.765005i \(0.722736\pi\)
\(8\) 0 0
\(9\) 1.49033 + 2.58133i 0.496778 + 0.860445i
\(10\) 0 0
\(11\) 0.185690 0.0559876 0.0279938 0.999608i \(-0.491088\pi\)
0.0279938 + 0.999608i \(0.491088\pi\)
\(12\) 0 0
\(13\) −1.17736 2.03925i −0.326541 0.565586i 0.655282 0.755384i \(-0.272550\pi\)
−0.981823 + 0.189799i \(0.939216\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 3.35663 5.81385i 0.814102 1.41007i −0.0958696 0.995394i \(-0.530563\pi\)
0.909971 0.414671i \(-0.136103\pi\)
\(18\) 0 0
\(19\) −2.14437 + 3.79495i −0.491952 + 0.870622i
\(20\) 0 0
\(21\) 0.236918 0.410353i 0.0516996 0.0895464i
\(22\) 0 0
\(23\) −0.463767 0.803267i −0.0967020 0.167493i 0.813616 0.581403i \(-0.197496\pi\)
−0.910318 + 0.413910i \(0.864163\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −0.831564 −0.160035
\(28\) 0 0
\(29\) 0.677360 + 1.17322i 0.125783 + 0.217862i 0.922039 0.387098i \(-0.126522\pi\)
−0.796256 + 0.604960i \(0.793189\pi\)
\(30\) 0 0
\(31\) −9.46158 −1.69935 −0.849675 0.527306i \(-0.823202\pi\)
−0.849675 + 0.527306i \(0.823202\pi\)
\(32\) 0 0
\(33\) −0.0129094 + 0.0223597i −0.00224723 + 0.00389232i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −1.62862 −0.267743 −0.133872 0.990999i \(-0.542741\pi\)
−0.133872 + 0.990999i \(0.542741\pi\)
\(38\) 0 0
\(39\) 0.327405 0.0524268
\(40\) 0 0
\(41\) 4.29573 7.44043i 0.670881 1.16200i −0.306774 0.951782i \(-0.599250\pi\)
0.977655 0.210217i \(-0.0674171\pi\)
\(42\) 0 0
\(43\) 3.80076 6.58312i 0.579611 1.00392i −0.415913 0.909405i \(-0.636538\pi\)
0.995524 0.0945112i \(-0.0301288\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 4.09639 + 7.09515i 0.597519 + 1.03493i 0.993186 + 0.116540i \(0.0371802\pi\)
−0.395667 + 0.918394i \(0.629486\pi\)
\(48\) 0 0
\(49\) 4.61347 0.659067
\(50\) 0 0
\(51\) 0.466712 + 0.808369i 0.0653528 + 0.113194i
\(52\) 0 0
\(53\) −6.70168 11.6077i −0.920547 1.59443i −0.798571 0.601901i \(-0.794410\pi\)
−0.121976 0.992533i \(-0.538923\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −0.307887 0.522041i −0.0407806 0.0691460i
\(58\) 0 0
\(59\) 2.02981 3.51573i 0.264259 0.457710i −0.703110 0.711081i \(-0.748206\pi\)
0.967369 + 0.253371i \(0.0815394\pi\)
\(60\) 0 0
\(61\) −6.31247 10.9335i −0.808228 1.39989i −0.914090 0.405512i \(-0.867093\pi\)
0.105861 0.994381i \(-0.466240\pi\)
\(62\) 0 0
\(63\) −5.07884 8.79681i −0.639874 1.10829i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −1.62613 2.81654i −0.198664 0.344096i 0.749432 0.662082i \(-0.230327\pi\)
−0.948095 + 0.317986i \(0.896993\pi\)
\(68\) 0 0
\(69\) 0.128966 0.0155257
\(70\) 0 0
\(71\) 6.59887 11.4296i 0.783142 1.35644i −0.146961 0.989142i \(-0.546949\pi\)
0.930103 0.367300i \(-0.119718\pi\)
\(72\) 0 0
\(73\) 2.45260 4.24802i 0.287055 0.497193i −0.686051 0.727554i \(-0.740657\pi\)
0.973105 + 0.230360i \(0.0739905\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −0.632805 −0.0721148
\(78\) 0 0
\(79\) −2.98245 + 5.16576i −0.335552 + 0.581194i −0.983591 0.180414i \(-0.942256\pi\)
0.648038 + 0.761608i \(0.275590\pi\)
\(80\) 0 0
\(81\) −4.41319 + 7.64387i −0.490354 + 0.849319i
\(82\) 0 0
\(83\) 1.30480 0.143221 0.0716105 0.997433i \(-0.477186\pi\)
0.0716105 + 0.997433i \(0.477186\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −0.188363 −0.0201946
\(88\) 0 0
\(89\) 1.95584 + 3.38761i 0.207319 + 0.359086i 0.950869 0.309594i \(-0.100193\pi\)
−0.743550 + 0.668680i \(0.766860\pi\)
\(90\) 0 0
\(91\) 4.01227 + 6.94946i 0.420600 + 0.728501i
\(92\) 0 0
\(93\) 0.657779 1.13931i 0.0682085 0.118141i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 7.25291 12.5624i 0.736421 1.27552i −0.217676 0.976021i \(-0.569848\pi\)
0.954097 0.299498i \(-0.0968192\pi\)
\(98\) 0 0
\(99\) 0.276740 + 0.479328i 0.0278134 + 0.0481743i
\(100\) 0 0
\(101\) −0.348049 0.602838i −0.0346321 0.0599846i 0.848190 0.529692i \(-0.177693\pi\)
−0.882822 + 0.469708i \(0.844359\pi\)
\(102\) 0 0
\(103\) −10.5016 −1.03476 −0.517378 0.855757i \(-0.673092\pi\)
−0.517378 + 0.855757i \(0.673092\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −15.1627 −1.46583 −0.732915 0.680320i \(-0.761841\pi\)
−0.732915 + 0.680320i \(0.761841\pi\)
\(108\) 0 0
\(109\) −0.0595573 + 0.103156i −0.00570456 + 0.00988058i −0.868864 0.495052i \(-0.835149\pi\)
0.863159 + 0.504932i \(0.168482\pi\)
\(110\) 0 0
\(111\) 0.113223 0.196109i 0.0107467 0.0186138i
\(112\) 0 0
\(113\) −10.1268 −0.952648 −0.476324 0.879270i \(-0.658031\pi\)
−0.476324 + 0.879270i \(0.658031\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 3.50932 6.07832i 0.324437 0.561941i
\(118\) 0 0
\(119\) −11.4389 + 19.8127i −1.04860 + 1.81623i
\(120\) 0 0
\(121\) −10.9655 −0.996865
\(122\) 0 0
\(123\) 0.597288 + 1.03453i 0.0538556 + 0.0932806i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −1.85268 3.20894i −0.164399 0.284748i 0.772043 0.635571i \(-0.219235\pi\)
−0.936442 + 0.350823i \(0.885902\pi\)
\(128\) 0 0
\(129\) 0.528466 + 0.915330i 0.0465288 + 0.0805903i
\(130\) 0 0
\(131\) 10.7555 18.6291i 0.939713 1.62763i 0.173707 0.984797i \(-0.444425\pi\)
0.766006 0.642833i \(-0.222241\pi\)
\(132\) 0 0
\(133\) 7.30770 12.9327i 0.633658 1.12140i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −6.88852 11.9313i −0.588526 1.01936i −0.994426 0.105439i \(-0.966375\pi\)
0.405900 0.913918i \(-0.366958\pi\)
\(138\) 0 0
\(139\) 9.25188 + 16.0247i 0.784734 + 1.35920i 0.929158 + 0.369683i \(0.120534\pi\)
−0.144424 + 0.989516i \(0.546133\pi\)
\(140\) 0 0
\(141\) −1.13914 −0.0959329
\(142\) 0 0
\(143\) −0.218624 0.378668i −0.0182823 0.0316658i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −0.320733 + 0.555526i −0.0264536 + 0.0458190i
\(148\) 0 0
\(149\) 3.40386 5.89565i 0.278855 0.482991i −0.692246 0.721662i \(-0.743379\pi\)
0.971100 + 0.238671i \(0.0767119\pi\)
\(150\) 0 0
\(151\) 3.67527 0.299089 0.149545 0.988755i \(-0.452219\pi\)
0.149545 + 0.988755i \(0.452219\pi\)
\(152\) 0 0
\(153\) 20.0100 1.61771
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −7.05638 + 12.2220i −0.563160 + 0.975422i 0.434058 + 0.900885i \(0.357081\pi\)
−0.997218 + 0.0745372i \(0.976252\pi\)
\(158\) 0 0
\(159\) 1.86363 0.147796
\(160\) 0 0
\(161\) 1.58045 + 2.73742i 0.124557 + 0.215739i
\(162\) 0 0
\(163\) −5.63660 −0.441493 −0.220746 0.975331i \(-0.570849\pi\)
−0.220746 + 0.975331i \(0.570849\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 3.73880 + 6.47579i 0.289317 + 0.501112i 0.973647 0.228061i \(-0.0732385\pi\)
−0.684330 + 0.729173i \(0.739905\pi\)
\(168\) 0 0
\(169\) 3.72765 6.45647i 0.286742 0.496652i
\(170\) 0 0
\(171\) −12.9919 + 0.120414i −0.993513 + 0.00920829i
\(172\) 0 0
\(173\) −11.6888 + 20.2457i −0.888686 + 1.53925i −0.0472554 + 0.998883i \(0.515047\pi\)
−0.841430 + 0.540366i \(0.818286\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0.282229 + 0.488835i 0.0212136 + 0.0367431i
\(178\) 0 0
\(179\) 10.0035 0.747698 0.373849 0.927490i \(-0.378038\pi\)
0.373849 + 0.927490i \(0.378038\pi\)
\(180\) 0 0
\(181\) 7.13969 + 12.3663i 0.530689 + 0.919180i 0.999359 + 0.0358064i \(0.0114000\pi\)
−0.468670 + 0.883373i \(0.655267\pi\)
\(182\) 0 0
\(183\) 1.75540 0.129763
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0.623292 1.07957i 0.0455796 0.0789462i
\(188\) 0 0
\(189\) 2.83385 0.206132
\(190\) 0 0
\(191\) −5.36977 −0.388543 −0.194271 0.980948i \(-0.562234\pi\)
−0.194271 + 0.980948i \(0.562234\pi\)
\(192\) 0 0
\(193\) 7.54615 13.0703i 0.543184 0.940822i −0.455535 0.890218i \(-0.650552\pi\)
0.998719 0.0506044i \(-0.0161148\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 10.4610 0.745315 0.372657 0.927969i \(-0.378447\pi\)
0.372657 + 0.927969i \(0.378447\pi\)
\(198\) 0 0
\(199\) −8.36446 14.4877i −0.592941 1.02700i −0.993834 0.110879i \(-0.964633\pi\)
0.400893 0.916125i \(-0.368700\pi\)
\(200\) 0 0
\(201\) 0.452202 0.0318958
\(202\) 0 0
\(203\) −2.30835 3.99817i −0.162014 0.280617i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 1.38233 2.39427i 0.0960789 0.166413i
\(208\) 0 0
\(209\) −0.398188 + 0.704685i −0.0275432 + 0.0487441i
\(210\) 0 0
\(211\) 9.00494 15.5970i 0.619926 1.07374i −0.369573 0.929202i \(-0.620496\pi\)
0.989499 0.144541i \(-0.0461706\pi\)
\(212\) 0 0
\(213\) 0.917521 + 1.58919i 0.0628675 + 0.108890i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 32.2437 2.18884
\(218\) 0 0
\(219\) 0.341014 + 0.590654i 0.0230436 + 0.0399127i
\(220\) 0 0
\(221\) −15.8078 −1.06335
\(222\) 0 0
\(223\) −3.96313 + 6.86434i −0.265391 + 0.459670i −0.967666 0.252235i \(-0.918834\pi\)
0.702275 + 0.711906i \(0.252168\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −14.4260 −0.957487 −0.478743 0.877955i \(-0.658908\pi\)
−0.478743 + 0.877955i \(0.658908\pi\)
\(228\) 0 0
\(229\) 1.27578 0.0843061 0.0421530 0.999111i \(-0.486578\pi\)
0.0421530 + 0.999111i \(0.486578\pi\)
\(230\) 0 0
\(231\) 0.0439932 0.0761985i 0.00289454 0.00501349i
\(232\) 0 0
\(233\) 1.59603 2.76441i 0.104560 0.181102i −0.808999 0.587811i \(-0.799990\pi\)
0.913558 + 0.406708i \(0.133323\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −0.414687 0.718258i −0.0269368 0.0466559i
\(238\) 0 0
\(239\) −11.9921 −0.775705 −0.387853 0.921721i \(-0.626783\pi\)
−0.387853 + 0.921721i \(0.626783\pi\)
\(240\) 0 0
\(241\) 12.9988 + 22.5145i 0.837323 + 1.45029i 0.892125 + 0.451789i \(0.149214\pi\)
−0.0548017 + 0.998497i \(0.517453\pi\)
\(242\) 0 0
\(243\) −1.86097 3.22329i −0.119381 0.206774i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 10.2635 0.0951268i 0.653054 0.00605277i
\(248\) 0 0
\(249\) −0.0907114 + 0.157117i −0.00574860 + 0.00995687i
\(250\) 0 0
\(251\) −5.22437 9.04887i −0.329759 0.571160i 0.652705 0.757612i \(-0.273634\pi\)
−0.982464 + 0.186453i \(0.940301\pi\)
\(252\) 0 0
\(253\) −0.0861168 0.149159i −0.00541412 0.00937753i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 6.28137 + 10.8797i 0.391821 + 0.678655i 0.992690 0.120693i \(-0.0385118\pi\)
−0.600868 + 0.799348i \(0.705178\pi\)
\(258\) 0 0
\(259\) 5.55010 0.344866
\(260\) 0 0
\(261\) −2.01899 + 3.49699i −0.124972 + 0.216458i
\(262\) 0 0
\(263\) −1.47801 + 2.55999i −0.0911381 + 0.157856i −0.907990 0.418991i \(-0.862384\pi\)
0.816852 + 0.576847i \(0.195717\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −0.543888 −0.0332854
\(268\) 0 0
\(269\) −1.93417 + 3.35007i −0.117928 + 0.204258i −0.918946 0.394382i \(-0.870959\pi\)
0.801018 + 0.598640i \(0.204292\pi\)
\(270\) 0 0
\(271\) 3.47998 6.02749i 0.211393 0.366144i −0.740757 0.671773i \(-0.765533\pi\)
0.952151 + 0.305628i \(0.0988665\pi\)
\(272\) 0 0
\(273\) −1.11575 −0.0675282
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −18.1698 −1.09172 −0.545858 0.837878i \(-0.683796\pi\)
−0.545858 + 0.837878i \(0.683796\pi\)
\(278\) 0 0
\(279\) −14.1009 24.4235i −0.844200 1.46220i
\(280\) 0 0
\(281\) 1.08306 + 1.87591i 0.0646099 + 0.111908i 0.896521 0.443001i \(-0.146086\pi\)
−0.831911 + 0.554909i \(0.812753\pi\)
\(282\) 0 0
\(283\) −9.13750 + 15.8266i −0.543168 + 0.940794i 0.455552 + 0.890209i \(0.349442\pi\)
−0.998720 + 0.0505849i \(0.983891\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −14.6392 + 25.3559i −0.864127 + 1.49671i
\(288\) 0 0
\(289\) −14.0339 24.3074i −0.825523 1.42985i
\(290\) 0 0
\(291\) 1.00846 + 1.74670i 0.0591169 + 0.102394i
\(292\) 0 0
\(293\) 4.01486 0.234550 0.117275 0.993099i \(-0.462584\pi\)
0.117275 + 0.993099i \(0.462584\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −0.154413 −0.00895996
\(298\) 0 0
\(299\) −1.09204 + 1.89147i −0.0631544 + 0.109387i
\(300\) 0 0
\(301\) −12.9524 + 22.4343i −0.746567 + 1.29309i
\(302\) 0 0
\(303\) 0.0967868 0.00556026
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −6.91354 + 11.9746i −0.394577 + 0.683427i −0.993047 0.117718i \(-0.962442\pi\)
0.598470 + 0.801145i \(0.295775\pi\)
\(308\) 0 0
\(309\) 0.730084 1.26454i 0.0415330 0.0719373i
\(310\) 0 0
\(311\) 22.4425 1.27260 0.636299 0.771443i \(-0.280464\pi\)
0.636299 + 0.771443i \(0.280464\pi\)
\(312\) 0 0
\(313\) 10.4976 + 18.1823i 0.593357 + 1.02772i 0.993776 + 0.111393i \(0.0355312\pi\)
−0.400419 + 0.916332i \(0.631136\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −5.40192 9.35641i −0.303402 0.525508i 0.673502 0.739185i \(-0.264789\pi\)
−0.976904 + 0.213677i \(0.931456\pi\)
\(318\) 0 0
\(319\) 0.125779 + 0.217856i 0.00704227 + 0.0121976i
\(320\) 0 0
\(321\) 1.05412 1.82580i 0.0588355 0.101906i
\(322\) 0 0
\(323\) 14.8654 + 25.2053i 0.827135 + 1.40246i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −0.00828097 0.0143431i −0.000457939 0.000793173i
\(328\) 0 0
\(329\) −13.9599 24.1792i −0.769633 1.33304i
\(330\) 0 0
\(331\) 7.71526 0.424069 0.212035 0.977262i \(-0.431991\pi\)
0.212035 + 0.977262i \(0.431991\pi\)
\(332\) 0 0
\(333\) −2.42719 4.20401i −0.133009 0.230378i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 3.29656 5.70981i 0.179575 0.311033i −0.762160 0.647389i \(-0.775861\pi\)
0.941735 + 0.336355i \(0.109194\pi\)
\(338\) 0 0
\(339\) 0.704025 1.21941i 0.0382374 0.0662291i
\(340\) 0 0
\(341\) −1.75692 −0.0951426
\(342\) 0 0
\(343\) 8.13294 0.439138
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −12.4385 + 21.5441i −0.667732 + 1.15655i 0.310805 + 0.950474i \(0.399402\pi\)
−0.978537 + 0.206072i \(0.933932\pi\)
\(348\) 0 0
\(349\) 20.9351 1.12063 0.560316 0.828279i \(-0.310680\pi\)
0.560316 + 0.828279i \(0.310680\pi\)
\(350\) 0 0
\(351\) 0.979051 + 1.69577i 0.0522579 + 0.0905133i
\(352\) 0 0
\(353\) 18.6926 0.994907 0.497454 0.867491i \(-0.334268\pi\)
0.497454 + 0.867491i \(0.334268\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −1.59049 2.75481i −0.0841775 0.145800i
\(358\) 0 0
\(359\) −6.92376 + 11.9923i −0.365422 + 0.632929i −0.988844 0.148956i \(-0.952409\pi\)
0.623422 + 0.781886i \(0.285742\pi\)
\(360\) 0 0
\(361\) −9.80336 16.2756i −0.515966 0.856609i
\(362\) 0 0
\(363\) 0.762334 1.32040i 0.0400122 0.0693031i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −9.15058 15.8493i −0.477656 0.827325i 0.522016 0.852936i \(-0.325180\pi\)
−0.999672 + 0.0256108i \(0.991847\pi\)
\(368\) 0 0
\(369\) 25.6083 1.33311
\(370\) 0 0
\(371\) 22.8384 + 39.5572i 1.18571 + 2.05371i
\(372\) 0 0
\(373\) −12.9735 −0.671743 −0.335872 0.941908i \(-0.609031\pi\)
−0.335872 + 0.941908i \(0.609031\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 1.59499 2.76261i 0.0821464 0.142282i
\(378\) 0 0
\(379\) −17.4091 −0.894243 −0.447122 0.894473i \(-0.647551\pi\)
−0.447122 + 0.894473i \(0.647551\pi\)
\(380\) 0 0
\(381\) 0.515202 0.0263946
\(382\) 0 0
\(383\) −6.66235 + 11.5395i −0.340430 + 0.589642i −0.984513 0.175314i \(-0.943906\pi\)
0.644082 + 0.764956i \(0.277239\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 22.6576 1.15175
\(388\) 0 0
\(389\) 13.9471 + 24.1572i 0.707148 + 1.22482i 0.965911 + 0.258875i \(0.0833519\pi\)
−0.258763 + 0.965941i \(0.583315\pi\)
\(390\) 0 0
\(391\) −6.22677 −0.314901
\(392\) 0 0
\(393\) 1.49547 + 2.59023i 0.0754364 + 0.130660i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 14.7453 25.5397i 0.740048 1.28180i −0.212425 0.977177i \(-0.568136\pi\)
0.952473 0.304623i \(-0.0985305\pi\)
\(398\) 0 0
\(399\) 1.04923 + 1.77904i 0.0525273 + 0.0890634i
\(400\) 0 0
\(401\) −14.8616 + 25.7411i −0.742154 + 1.28545i 0.209359 + 0.977839i \(0.432862\pi\)
−0.951513 + 0.307609i \(0.900471\pi\)
\(402\) 0 0
\(403\) 11.1397 + 19.2945i 0.554908 + 0.961128i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −0.302418 −0.0149903
\(408\) 0 0
\(409\) −3.66752 6.35233i −0.181347 0.314102i 0.760992 0.648761i \(-0.224712\pi\)
−0.942340 + 0.334658i \(0.891379\pi\)
\(410\) 0 0
\(411\) 1.91559 0.0944890
\(412\) 0 0
\(413\) −6.91730 + 11.9811i −0.340378 + 0.589552i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −2.57280 −0.125991
\(418\) 0 0
\(419\) −13.9330 −0.680671 −0.340336 0.940304i \(-0.610541\pi\)
−0.340336 + 0.940304i \(0.610541\pi\)
\(420\) 0 0
\(421\) −11.7615 + 20.3715i −0.573219 + 0.992845i 0.423014 + 0.906123i \(0.360972\pi\)
−0.996233 + 0.0867212i \(0.972361\pi\)
\(422\) 0 0
\(423\) −12.2100 + 21.1483i −0.593669 + 1.02826i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 21.5120 + 37.2598i 1.04104 + 1.80313i
\(428\) 0 0
\(429\) 0.0607959 0.00293525
\(430\) 0 0
\(431\) 6.02358 + 10.4331i 0.290146 + 0.502547i 0.973844 0.227218i \(-0.0729629\pi\)
−0.683698 + 0.729765i \(0.739630\pi\)
\(432\) 0 0
\(433\) 15.4837 + 26.8186i 0.744101 + 1.28882i 0.950613 + 0.310377i \(0.100455\pi\)
−0.206512 + 0.978444i \(0.566211\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 4.04285 0.0374708i 0.193396 0.00179247i
\(438\) 0 0
\(439\) 14.4121 24.9625i 0.687852 1.19139i −0.284680 0.958623i \(-0.591887\pi\)
0.972531 0.232771i \(-0.0747794\pi\)
\(440\) 0 0
\(441\) 6.87561 + 11.9089i 0.327410 + 0.567091i
\(442\) 0 0
\(443\) 10.6001 + 18.3599i 0.503624 + 0.872303i 0.999991 + 0.00419027i \(0.00133381\pi\)
−0.496367 + 0.868113i \(0.665333\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0.473279 + 0.819743i 0.0223853 + 0.0387725i
\(448\) 0 0
\(449\) −27.5158 −1.29855 −0.649275 0.760553i \(-0.724928\pi\)
−0.649275 + 0.760553i \(0.724928\pi\)
\(450\) 0 0
\(451\) 0.797675 1.38161i 0.0375610 0.0650576i
\(452\) 0 0
\(453\) −0.255508 + 0.442554i −0.0120048 + 0.0207930i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 17.5615 0.821492 0.410746 0.911750i \(-0.365268\pi\)
0.410746 + 0.911750i \(0.365268\pi\)
\(458\) 0 0
\(459\) −2.79125 + 4.83459i −0.130284 + 0.225659i
\(460\) 0 0
\(461\) 17.9075 31.0167i 0.834036 1.44459i −0.0607773 0.998151i \(-0.519358\pi\)
0.894813 0.446441i \(-0.147309\pi\)
\(462\) 0 0
\(463\) 2.10186 0.0976817 0.0488409 0.998807i \(-0.484447\pi\)
0.0488409 + 0.998807i \(0.484447\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −17.3019 −0.800637 −0.400319 0.916376i \(-0.631101\pi\)
−0.400319 + 0.916376i \(0.631101\pi\)
\(468\) 0 0
\(469\) 5.54162 + 9.59837i 0.255888 + 0.443212i
\(470\) 0 0
\(471\) −0.981133 1.69937i −0.0452082 0.0783030i
\(472\) 0 0
\(473\) 0.705764 1.22242i 0.0324511 0.0562069i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 19.9755 34.5985i 0.914614 1.58416i
\(478\) 0 0
\(479\) 14.5267 + 25.1610i 0.663743 + 1.14964i 0.979625 + 0.200837i \(0.0643663\pi\)
−0.315882 + 0.948799i \(0.602300\pi\)
\(480\) 0 0
\(481\) 1.91747 + 3.32116i 0.0874292 + 0.151432i
\(482\) 0 0
\(483\) −0.439498 −0.0199978
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 13.0964 0.593456 0.296728 0.954962i \(-0.404105\pi\)
0.296728 + 0.954962i \(0.404105\pi\)
\(488\) 0 0
\(489\) 0.391862 0.678726i 0.0177206 0.0306930i
\(490\) 0 0
\(491\) −3.11779 + 5.40016i −0.140704 + 0.243706i −0.927762 0.373173i \(-0.878270\pi\)
0.787058 + 0.616879i \(0.211603\pi\)
\(492\) 0 0
\(493\) 9.09458 0.409599
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −22.4880 + 38.9504i −1.00872 + 1.74716i
\(498\) 0 0
\(499\) 5.67610 9.83130i 0.254097 0.440109i −0.710553 0.703644i \(-0.751555\pi\)
0.964650 + 0.263535i \(0.0848883\pi\)
\(500\) 0 0
\(501\) −1.03970 −0.0464504
\(502\) 0 0
\(503\) 8.99758 + 15.5843i 0.401182 + 0.694868i 0.993869 0.110565i \(-0.0352661\pi\)
−0.592687 + 0.805433i \(0.701933\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0.518300 + 0.897721i 0.0230185 + 0.0398692i
\(508\) 0 0
\(509\) −12.8639 22.2810i −0.570184 0.987587i −0.996547 0.0830350i \(-0.973539\pi\)
0.426363 0.904552i \(-0.359795\pi\)
\(510\) 0 0
\(511\) −8.35809 + 14.4766i −0.369740 + 0.640409i
\(512\) 0 0
\(513\) 1.78318 3.15575i 0.0787294 0.139330i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0.760658 + 1.31750i 0.0334537 + 0.0579435i
\(518\) 0 0
\(519\) −1.62524 2.81500i −0.0713401 0.123565i
\(520\) 0 0
\(521\) 13.7913 0.604206 0.302103 0.953275i \(-0.402311\pi\)
0.302103 + 0.953275i \(0.402311\pi\)
\(522\) 0 0
\(523\) −11.0625 19.1607i −0.483728 0.837841i 0.516098 0.856530i \(-0.327384\pi\)
−0.999825 + 0.0186889i \(0.994051\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −31.7590 + 55.0082i −1.38344 + 2.39620i
\(528\) 0 0
\(529\) 11.0698 19.1735i 0.481297 0.833632i
\(530\) 0 0
\(531\) 12.1004 0.525112
\(532\) 0 0
\(533\) −20.2305 −0.876280
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −0.695455 + 1.20456i −0.0300111 + 0.0519808i
\(538\) 0 0
\(539\) 0.856676 0.0368996
\(540\) 0 0
\(541\) −14.7284 25.5104i −0.633224 1.09678i −0.986888 0.161404i \(-0.948398\pi\)
0.353664 0.935372i \(-0.384936\pi\)
\(542\) 0 0
\(543\) −1.98543 −0.0852031
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −20.2421 35.0604i −0.865491 1.49908i −0.866558 0.499076i \(-0.833673\pi\)
0.00106707 0.999999i \(-0.499660\pi\)
\(548\) 0 0
\(549\) 18.8154 32.5892i 0.803020 1.39087i
\(550\) 0 0
\(551\) −5.90484 + 0.0547284i −0.251554 + 0.00233151i
\(552\) 0 0
\(553\) 10.1638 17.6042i 0.432208 0.748605i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 10.1035 + 17.4998i 0.428099 + 0.741490i 0.996704 0.0811209i \(-0.0258500\pi\)
−0.568605 + 0.822611i \(0.692517\pi\)
\(558\) 0 0
\(559\) −17.8995 −0.757067
\(560\) 0 0
\(561\) 0.0866638 + 0.150106i 0.00365895 + 0.00633749i
\(562\) 0 0
\(563\) 25.1900 1.06163 0.530816 0.847487i \(-0.321885\pi\)
0.530816 + 0.847487i \(0.321885\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 15.0395 26.0492i 0.631600 1.09396i
\(568\) 0 0
\(569\) −32.6378 −1.36825 −0.684124 0.729366i \(-0.739815\pi\)
−0.684124 + 0.729366i \(0.739815\pi\)
\(570\) 0 0
\(571\) −30.4795 −1.27553 −0.637764 0.770232i \(-0.720141\pi\)
−0.637764 + 0.770232i \(0.720141\pi\)
\(572\) 0 0
\(573\) 0.373312 0.646595i 0.0155953 0.0270119i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 18.3407 0.763533 0.381766 0.924259i \(-0.375316\pi\)
0.381766 + 0.924259i \(0.375316\pi\)
\(578\) 0 0
\(579\) 1.04923 + 1.81732i 0.0436046 + 0.0755254i
\(580\) 0 0
\(581\) −4.44658 −0.184475
\(582\) 0 0
\(583\) −1.24444 2.15543i −0.0515392 0.0892686i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −8.16010 + 14.1337i −0.336804 + 0.583361i −0.983830 0.179107i \(-0.942679\pi\)
0.647026 + 0.762468i \(0.276012\pi\)
\(588\) 0 0
\(589\) 20.2891 35.9063i 0.835999 1.47949i
\(590\) 0 0
\(591\) −0.727259 + 1.25965i −0.0299154 + 0.0518150i
\(592\) 0 0
\(593\) −4.27547 7.40534i −0.175573 0.304101i 0.764787 0.644284i \(-0.222844\pi\)
−0.940359 + 0.340183i \(0.889511\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 2.32602 0.0951978
\(598\) 0 0
\(599\) −7.09169 12.2832i −0.289758 0.501876i 0.683994 0.729488i \(-0.260242\pi\)
−0.973752 + 0.227612i \(0.926908\pi\)
\(600\) 0 0
\(601\) 21.3129 0.869370 0.434685 0.900583i \(-0.356860\pi\)
0.434685 + 0.900583i \(0.356860\pi\)
\(602\) 0 0
\(603\) 4.84696 8.39518i 0.197383 0.341878i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −28.4812 −1.15602 −0.578009 0.816031i \(-0.696170\pi\)
−0.578009 + 0.816031i \(0.696170\pi\)
\(608\) 0 0
\(609\) 0.641914 0.0260117
\(610\) 0 0
\(611\) 9.64584 16.7071i 0.390229 0.675896i
\(612\) 0 0
\(613\) −12.9742 + 22.4720i −0.524025 + 0.907638i 0.475584 + 0.879670i \(0.342237\pi\)
−0.999609 + 0.0279673i \(0.991097\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 6.71585 + 11.6322i 0.270370 + 0.468295i 0.968957 0.247231i \(-0.0795206\pi\)
−0.698587 + 0.715526i \(0.746187\pi\)
\(618\) 0 0
\(619\) −23.9017 −0.960690 −0.480345 0.877080i \(-0.659489\pi\)
−0.480345 + 0.877080i \(0.659489\pi\)
\(620\) 0 0
\(621\) 0.385652 + 0.667968i 0.0154757 + 0.0268047i
\(622\) 0 0
\(623\) −6.66521 11.5445i −0.267036 0.462520i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −0.0571715 0.0969378i −0.00228321 0.00387132i
\(628\) 0 0
\(629\) −5.46667 + 9.46855i −0.217970 + 0.377536i
\(630\) 0 0
\(631\) 12.0962 + 20.9512i 0.481541 + 0.834054i 0.999776 0.0211849i \(-0.00674387\pi\)
−0.518234 + 0.855239i \(0.673411\pi\)
\(632\) 0 0
\(633\) 1.25207 + 2.16864i 0.0497651 + 0.0861957i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −5.43172 9.40801i −0.215213 0.372759i
\(638\) 0 0
\(639\) 39.3381 1.55619
\(640\) 0 0
\(641\) 11.7338 20.3235i 0.463456 0.802729i −0.535675 0.844424i \(-0.679943\pi\)
0.999130 + 0.0416956i \(0.0132760\pi\)
\(642\) 0 0
\(643\) 0.497264 0.861287i 0.0196102 0.0339658i −0.856054 0.516887i \(-0.827091\pi\)
0.875664 + 0.482921i \(0.160424\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 2.24679 0.0883306 0.0441653 0.999024i \(-0.485937\pi\)
0.0441653 + 0.999024i \(0.485937\pi\)
\(648\) 0 0
\(649\) 0.376915 0.652837i 0.0147952 0.0256261i
\(650\) 0 0
\(651\) −2.24162 + 3.88259i −0.0878558 + 0.152171i
\(652\) 0 0
\(653\) −16.9500 −0.663307 −0.331653 0.943401i \(-0.607606\pi\)
−0.331653 + 0.943401i \(0.607606\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 14.6207 0.570410
\(658\) 0 0
\(659\) −16.1670 28.0020i −0.629775 1.09080i −0.987597 0.157013i \(-0.949814\pi\)
0.357821 0.933790i \(-0.383520\pi\)
\(660\) 0 0
\(661\) 9.67075 + 16.7502i 0.376149 + 0.651509i 0.990498 0.137525i \(-0.0439149\pi\)
−0.614350 + 0.789034i \(0.710582\pi\)
\(662\) 0 0
\(663\) 1.09898 1.90348i 0.0426807 0.0739252i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0.628274 1.08820i 0.0243269 0.0421354i
\(668\) 0 0
\(669\) −0.551042 0.954432i −0.0213045 0.0369005i
\(670\) 0 0
\(671\) −1.17216 2.03024i −0.0452508 0.0783767i
\(672\) 0 0
\(673\) 22.4887 0.866875 0.433438 0.901184i \(-0.357300\pi\)
0.433438 + 0.901184i \(0.357300\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 18.8477 0.724377 0.362188 0.932105i \(-0.382030\pi\)
0.362188 + 0.932105i \(0.382030\pi\)
\(678\) 0 0
\(679\) −24.7169 + 42.8109i −0.948546 + 1.64293i
\(680\) 0 0
\(681\) 1.00291 1.73709i 0.0384316 0.0665655i
\(682\) 0 0
\(683\) −44.8197 −1.71498 −0.857489 0.514502i \(-0.827977\pi\)
−0.857489 + 0.514502i \(0.827977\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −0.0886937 + 0.153622i −0.00338388 + 0.00586105i
\(688\) 0 0
\(689\) −15.7806 + 27.3328i −0.601192 + 1.04130i
\(690\) 0 0
\(691\) 1.57873 0.0600578 0.0300289 0.999549i \(-0.490440\pi\)
0.0300289 + 0.999549i \(0.490440\pi\)
\(692\) 0 0
\(693\) −0.943090 1.63348i −0.0358250 0.0620508i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −28.8383 49.9495i −1.09233 1.89197i
\(698\) 0 0
\(699\) 0.221916 + 0.384369i 0.00839362 + 0.0145382i
\(700\) 0 0
\(701\) −17.2140 + 29.8155i −0.650163 + 1.12611i 0.332920 + 0.942955i \(0.391966\pi\)
−0.983083 + 0.183160i \(0.941367\pi\)
\(702\) 0 0
\(703\) 3.49236 6.18054i 0.131717 0.233103i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 1.18610 + 2.05438i 0.0446078 + 0.0772630i
\(708\) 0 0
\(709\) 11.3751 + 19.7023i 0.427202 + 0.739936i 0.996623 0.0821102i \(-0.0261659\pi\)
−0.569421 + 0.822046i \(0.692833\pi\)
\(710\) 0 0
\(711\) −17.7794 −0.666780
\(712\) 0 0
\(713\) 4.38797 + 7.60018i 0.164331 + 0.284629i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0.833704 1.44402i 0.0311352 0.0539278i
\(718\) 0 0
\(719\) −15.0042 + 25.9880i −0.559561 + 0.969188i 0.437972 + 0.898989i \(0.355697\pi\)
−0.997533 + 0.0701994i \(0.977636\pi\)
\(720\) 0 0
\(721\) 35.7880 1.33282
\(722\) 0 0
\(723\) −3.61475 −0.134434
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −12.0504 + 20.8719i −0.446924 + 0.774096i −0.998184 0.0602381i \(-0.980814\pi\)
0.551260 + 0.834334i \(0.314147\pi\)
\(728\) 0 0
\(729\) −25.9616 −0.961542
\(730\) 0 0
\(731\) −25.5155 44.1941i −0.943724 1.63458i
\(732\) 0 0
\(733\) −12.5801 −0.464657 −0.232329 0.972637i \(-0.574635\pi\)
−0.232329 + 0.972637i \(0.574635\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −0.301957 0.523004i −0.0111227 0.0192651i
\(738\) 0 0
\(739\) 3.54647 6.14266i 0.130459 0.225961i −0.793395 0.608708i \(-0.791688\pi\)
0.923854 + 0.382746i \(0.125022\pi\)
\(740\) 0 0
\(741\) −0.702078 + 1.24249i −0.0257915 + 0.0456439i
\(742\) 0 0
\(743\) 17.1507 29.7060i 0.629200 1.08981i −0.358513 0.933525i \(-0.616716\pi\)
0.987713 0.156281i \(-0.0499506\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 1.94459 + 3.36814i 0.0711490 + 0.123234i
\(748\) 0 0
\(749\) 51.6722 1.88806
\(750\) 0 0
\(751\) −19.0760 33.0406i −0.696094 1.20567i −0.969811 0.243860i \(-0.921586\pi\)
0.273717 0.961810i \(-0.411747\pi\)
\(752\) 0 0
\(753\) 1.45281 0.0529435
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 14.2143 24.6200i 0.516629 0.894828i −0.483185 0.875519i \(-0.660520\pi\)
0.999814 0.0193092i \(-0.00614669\pi\)
\(758\) 0 0
\(759\) 0.0239477 0.000869247
\(760\) 0 0
\(761\) −3.88441 −0.140810 −0.0704048 0.997519i \(-0.522429\pi\)
−0.0704048 + 0.997519i \(0.522429\pi\)
\(762\) 0 0
\(763\) 0.202963 0.351542i 0.00734774 0.0127267i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −9.55927 −0.345165
\(768\) 0 0
\(769\) 17.8289 + 30.8806i 0.642928 + 1.11358i 0.984776 + 0.173829i \(0.0556140\pi\)
−0.341847 + 0.939755i \(0.611053\pi\)
\(770\) 0 0
\(771\) −1.74675 −0.0629077
\(772\) 0 0
\(773\) −15.0060 25.9912i −0.539729 0.934839i −0.998918 0.0465000i \(-0.985193\pi\)
0.459189 0.888339i \(-0.348140\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −0.385849 + 0.668309i −0.0138422 + 0.0239755i
\(778\) 0 0
\(779\) 19.0244 + 32.2571i 0.681621 + 1.15573i
\(780\) 0 0
\(781\) 1.22534 2.12236i 0.0438463 0.0759440i
\(782\) 0 0
\(783\) −0.563269 0.975610i −0.0201296 0.0348654i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 40.9891 1.46110 0.730552 0.682857i \(-0.239263\pi\)
0.730552 + 0.682857i \(0.239263\pi\)
\(788\) 0 0
\(789\) −0.205506 0.355947i −0.00731620 0.0126720i
\(790\) 0 0
\(791\) 34.5106 1.22706
\(792\) 0 0
\(793\) −14.8641 + 25.7454i −0.527839 + 0.914245i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −46.6104 −1.65103 −0.825513 0.564383i \(-0.809114\pi\)
−0.825513 + 0.564383i \(0.809114\pi\)
\(798\) 0 0
\(799\) 55.0001 1.94577
\(800\) 0 0
\(801\) −5.82971 + 10.0973i −0.205983 + 0.356772i