Properties

Label 756.2.ck.a.5.10
Level 756
Weight 2
Character 756.5
Analytic conductor 6.037
Analytic rank 0
Dimension 144
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 756.ck (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.03669039281\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(24\) over \(\Q(\zeta_{18})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 5.10
Character \(\chi\) = 756.5
Dual form 756.2.ck.a.605.10

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.538039 + 1.64636i) q^{3} +(-0.430811 + 2.44325i) q^{5} +(-0.571962 + 2.58319i) q^{7} +(-2.42103 - 1.77162i) q^{9} +O(q^{10})\) \(q+(-0.538039 + 1.64636i) q^{3} +(-0.430811 + 2.44325i) q^{5} +(-0.571962 + 2.58319i) q^{7} +(-2.42103 - 1.77162i) q^{9} +(-0.859257 + 0.151510i) q^{11} +(-0.741685 + 0.883906i) q^{13} +(-3.79069 - 2.02384i) q^{15} -1.65187 q^{17} +1.94001i q^{19} +(-3.94513 - 2.33151i) q^{21} +(3.26024 - 3.88540i) q^{23} +(-1.08542 - 0.395060i) q^{25} +(4.21933 - 3.03270i) q^{27} +(-2.90948 - 3.46738i) q^{29} +(1.64570 + 4.52151i) q^{31} +(0.212873 - 1.49617i) q^{33} +(-6.06497 - 2.51031i) q^{35} +(-2.87361 - 4.97723i) q^{37} +(-1.05618 - 1.69666i) q^{39} +(-1.42301 - 1.19405i) q^{41} +(4.32294 + 1.57342i) q^{43} +(5.37151 - 5.15195i) q^{45} +(-6.51094 - 2.36979i) q^{47} +(-6.34572 - 2.95497i) q^{49} +(0.888769 - 2.71958i) q^{51} +(-5.19487 + 2.99926i) q^{53} -2.16465i q^{55} +(-3.19396 - 1.04380i) q^{57} +(8.36733 + 7.02103i) q^{59} +(-2.06159 + 5.66419i) q^{61} +(5.96115 - 5.24068i) q^{63} +(-1.84008 - 2.19292i) q^{65} +(-2.01145 + 11.4075i) q^{67} +(4.64265 + 7.45803i) q^{69} +(-14.0958 - 8.13823i) q^{71} +(1.46473 + 0.845663i) q^{73} +(1.23441 - 1.57443i) q^{75} +(0.100083 - 2.30628i) q^{77} +(0.801174 + 4.54368i) q^{79} +(2.72276 + 8.57826i) q^{81} +(0.417251 - 0.350116i) q^{83} +(0.711644 - 4.03593i) q^{85} +(7.27398 - 2.92448i) q^{87} -9.52231 q^{89} +(-1.85908 - 2.42147i) q^{91} +(-8.32950 + 0.276666i) q^{93} +(-4.73993 - 0.835777i) q^{95} +(1.27535 - 3.50400i) q^{97} +(2.34870 + 1.15546i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144q + 6q^{9} + O(q^{10}) \) \( 144q + 6q^{9} - 6q^{11} + 12q^{15} + 33q^{21} + 21q^{23} - 6q^{29} + 27q^{35} + 39q^{39} - 54q^{47} + 18q^{49} - 9q^{51} - 45q^{53} + 3q^{57} + 45q^{59} + 39q^{63} + 24q^{65} - 36q^{69} + 36q^{71} + 45q^{75} + 21q^{77} - 18q^{79} + 18q^{81} + 36q^{85} - 45q^{87} + 9q^{91} - 48q^{93} - 66q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\) \(379\)
\(\chi(n)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\)

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
\(3\) −0.538039 + 1.64636i −0.310637 + 0.950529i
\(4\) 0 0
\(5\) −0.430811 + 2.44325i −0.192665 + 1.09266i 0.723041 + 0.690805i \(0.242744\pi\)
−0.915705 + 0.401850i \(0.868367\pi\)
\(6\) 0 0
\(7\) −0.571962 + 2.58319i −0.216181 + 0.976353i
\(8\) 0 0
\(9\) −2.42103 1.77162i −0.807010 0.590538i
\(10\) 0 0
\(11\) −0.859257 + 0.151510i −0.259076 + 0.0456820i −0.301677 0.953410i \(-0.597547\pi\)
0.0426015 + 0.999092i \(0.486435\pi\)
\(12\) 0 0
\(13\) −0.741685 + 0.883906i −0.205706 + 0.245151i −0.859027 0.511930i \(-0.828931\pi\)
0.653321 + 0.757081i \(0.273375\pi\)
\(14\) 0 0
\(15\) −3.79069 2.02384i −0.978752 0.522552i
\(16\) 0 0
\(17\) −1.65187 −0.400637 −0.200319 0.979731i \(-0.564198\pi\)
−0.200319 + 0.979731i \(0.564198\pi\)
\(18\) 0 0
\(19\) 1.94001i 0.445068i 0.974925 + 0.222534i \(0.0714329\pi\)
−0.974925 + 0.222534i \(0.928567\pi\)
\(20\) 0 0
\(21\) −3.94513 2.33151i −0.860898 0.508778i
\(22\) 0 0
\(23\) 3.26024 3.88540i 0.679807 0.810162i −0.310276 0.950646i \(-0.600422\pi\)
0.990083 + 0.140485i \(0.0448660\pi\)
\(24\) 0 0
\(25\) −1.08542 0.395060i −0.217083 0.0790119i
\(26\) 0 0
\(27\) 4.21933 3.03270i 0.812010 0.583643i
\(28\) 0 0
\(29\) −2.90948 3.46738i −0.540277 0.643877i 0.424973 0.905206i \(-0.360284\pi\)
−0.965250 + 0.261329i \(0.915839\pi\)
\(30\) 0 0
\(31\) 1.64570 + 4.52151i 0.295576 + 0.812087i 0.995226 + 0.0976014i \(0.0311170\pi\)
−0.699650 + 0.714486i \(0.746661\pi\)
\(32\) 0 0
\(33\) 0.212873 1.49617i 0.0370564 0.260449i
\(34\) 0 0
\(35\) −6.06497 2.51031i −1.02517 0.424320i
\(36\) 0 0
\(37\) −2.87361 4.97723i −0.472418 0.818252i 0.527084 0.849813i \(-0.323285\pi\)
−0.999502 + 0.0315615i \(0.989952\pi\)
\(38\) 0 0
\(39\) −1.05618 1.69666i −0.169123 0.271683i
\(40\) 0 0
\(41\) −1.42301 1.19405i −0.222237 0.186479i 0.524871 0.851182i \(-0.324114\pi\)
−0.747108 + 0.664703i \(0.768558\pi\)
\(42\) 0 0
\(43\) 4.32294 + 1.57342i 0.659243 + 0.239945i 0.649909 0.760012i \(-0.274807\pi\)
0.00933336 + 0.999956i \(0.497029\pi\)
\(44\) 0 0
\(45\) 5.37151 5.15195i 0.800737 0.768007i
\(46\) 0 0
\(47\) −6.51094 2.36979i −0.949719 0.345669i −0.179722 0.983717i \(-0.557520\pi\)
−0.769996 + 0.638048i \(0.779742\pi\)
\(48\) 0 0
\(49\) −6.34572 2.95497i −0.906531 0.422139i
\(50\) 0 0
\(51\) 0.888769 2.71958i 0.124453 0.380817i
\(52\) 0 0
\(53\) −5.19487 + 2.99926i −0.713570 + 0.411980i −0.812381 0.583127i \(-0.801829\pi\)
0.0988117 + 0.995106i \(0.468496\pi\)
\(54\) 0 0
\(55\) 2.16465i 0.291882i
\(56\) 0 0
\(57\) −3.19396 1.04380i −0.423050 0.138255i
\(58\) 0 0
\(59\) 8.36733 + 7.02103i 1.08933 + 0.914060i 0.996662 0.0816371i \(-0.0260148\pi\)
0.0926717 + 0.995697i \(0.470459\pi\)
\(60\) 0 0
\(61\) −2.06159 + 5.66419i −0.263960 + 0.725225i 0.734931 + 0.678142i \(0.237215\pi\)
−0.998891 + 0.0470825i \(0.985008\pi\)
\(62\) 0 0
\(63\) 5.96115 5.24068i 0.751034 0.660263i
\(64\) 0 0
\(65\) −1.84008 2.19292i −0.228234 0.271998i
\(66\) 0 0
\(67\) −2.01145 + 11.4075i −0.245738 + 1.39365i 0.573035 + 0.819531i \(0.305766\pi\)
−0.818773 + 0.574118i \(0.805345\pi\)
\(68\) 0 0
\(69\) 4.64265 + 7.45803i 0.558909 + 0.897842i
\(70\) 0 0
\(71\) −14.0958 8.13823i −1.67287 0.965830i −0.966021 0.258463i \(-0.916784\pi\)
−0.706846 0.707367i \(-0.749883\pi\)
\(72\) 0 0
\(73\) 1.46473 + 0.845663i 0.171434 + 0.0989774i 0.583262 0.812284i \(-0.301776\pi\)
−0.411828 + 0.911262i \(0.635110\pi\)
\(74\) 0 0
\(75\) 1.23441 1.57443i 0.142537 0.181800i
\(76\) 0 0
\(77\) 0.100083 2.30628i 0.0114055 0.262825i
\(78\) 0 0
\(79\) 0.801174 + 4.54368i 0.0901391 + 0.511204i 0.996129 + 0.0879048i \(0.0280171\pi\)
−0.905990 + 0.423300i \(0.860872\pi\)
\(80\) 0 0
\(81\) 2.72276 + 8.57826i 0.302529 + 0.953140i
\(82\) 0 0
\(83\) 0.417251 0.350116i 0.0457993 0.0384302i −0.619601 0.784917i \(-0.712705\pi\)
0.665400 + 0.746487i \(0.268261\pi\)
\(84\) 0 0
\(85\) 0.711644 4.03593i 0.0771886 0.437758i
\(86\) 0 0
\(87\) 7.27398 2.92448i 0.779853 0.313537i
\(88\) 0 0
\(89\) −9.52231 −1.00936 −0.504681 0.863306i \(-0.668390\pi\)
−0.504681 + 0.863306i \(0.668390\pi\)
\(90\) 0 0
\(91\) −1.85908 2.42147i −0.194885 0.253839i
\(92\) 0 0
\(93\) −8.32950 + 0.276666i −0.863729 + 0.0286889i
\(94\) 0 0
\(95\) −4.73993 0.835777i −0.486306 0.0857489i
\(96\) 0 0
\(97\) 1.27535 3.50400i 0.129492 0.355778i −0.857955 0.513725i \(-0.828265\pi\)
0.987448 + 0.157947i \(0.0504875\pi\)
\(98\) 0 0
\(99\) 2.34870 + 1.15546i 0.236054 + 0.116128i
\(100\) 0 0
\(101\) −8.08175 + 6.78139i −0.804164 + 0.674773i −0.949207 0.314652i \(-0.898112\pi\)
0.145043 + 0.989425i \(0.453668\pi\)
\(102\) 0 0
\(103\) 16.9540 + 2.98944i 1.67052 + 0.294559i 0.927254 0.374433i \(-0.122163\pi\)
0.743270 + 0.668991i \(0.233274\pi\)
\(104\) 0 0
\(105\) 7.39608 8.63450i 0.721783 0.842641i
\(106\) 0 0
\(107\) 10.5700 + 6.10258i 1.02184 + 0.589958i 0.914636 0.404279i \(-0.132478\pi\)
0.107202 + 0.994237i \(0.465811\pi\)
\(108\) 0 0
\(109\) 3.72917 + 6.45912i 0.357190 + 0.618672i 0.987490 0.157680i \(-0.0504015\pi\)
−0.630300 + 0.776352i \(0.717068\pi\)
\(110\) 0 0
\(111\) 9.74044 2.05306i 0.924522 0.194868i
\(112\) 0 0
\(113\) −1.24798 3.42880i −0.117400 0.322555i 0.867049 0.498223i \(-0.166014\pi\)
−0.984449 + 0.175668i \(0.943792\pi\)
\(114\) 0 0
\(115\) 8.08846 + 9.63945i 0.754253 + 0.898884i
\(116\) 0 0
\(117\) 3.36158 0.825981i 0.310778 0.0763620i
\(118\) 0 0
\(119\) 0.944806 4.26709i 0.0866102 0.391163i
\(120\) 0 0
\(121\) −9.62125 + 3.50185i −0.874659 + 0.318350i
\(122\) 0 0
\(123\) 2.73147 1.70035i 0.246288 0.153315i
\(124\) 0 0
\(125\) −4.76952 + 8.26105i −0.426599 + 0.738890i
\(126\) 0 0
\(127\) −7.18742 12.4490i −0.637780 1.10467i −0.985919 0.167225i \(-0.946520\pi\)
0.348139 0.937443i \(-0.386814\pi\)
\(128\) 0 0
\(129\) −4.91634 + 6.27058i −0.432859 + 0.552093i
\(130\) 0 0
\(131\) 6.22200 + 5.22088i 0.543618 + 0.456150i 0.872773 0.488126i \(-0.162319\pi\)
−0.329155 + 0.944276i \(0.606764\pi\)
\(132\) 0 0
\(133\) −5.01141 1.10961i −0.434544 0.0962155i
\(134\) 0 0
\(135\) 5.59191 + 11.6154i 0.481275 + 0.999695i
\(136\) 0 0
\(137\) 1.07791 2.96154i 0.0920922 0.253021i −0.885092 0.465417i \(-0.845904\pi\)
0.977184 + 0.212396i \(0.0681266\pi\)
\(138\) 0 0
\(139\) 12.5717 + 2.21673i 1.06632 + 0.188021i 0.679158 0.733992i \(-0.262345\pi\)
0.387160 + 0.922013i \(0.373456\pi\)
\(140\) 0 0
\(141\) 7.40467 9.44434i 0.623586 0.795357i
\(142\) 0 0
\(143\) 0.503377 0.871875i 0.0420945 0.0729099i
\(144\) 0 0
\(145\) 9.72512 5.61480i 0.807627 0.466284i
\(146\) 0 0
\(147\) 8.27920 8.85747i 0.682857 0.730552i
\(148\) 0 0
\(149\) 1.93083 + 5.30491i 0.158180 + 0.434595i 0.993313 0.115452i \(-0.0368318\pi\)
−0.835133 + 0.550048i \(0.814610\pi\)
\(150\) 0 0
\(151\) 3.79794 + 21.5392i 0.309072 + 1.75283i 0.603691 + 0.797218i \(0.293696\pi\)
−0.294619 + 0.955615i \(0.595193\pi\)
\(152\) 0 0
\(153\) 3.99922 + 2.92648i 0.323318 + 0.236592i
\(154\) 0 0
\(155\) −11.7562 + 2.07293i −0.944278 + 0.166502i
\(156\) 0 0
\(157\) 14.7707 17.6030i 1.17883 1.40487i 0.283789 0.958887i \(-0.408409\pi\)
0.895040 0.445986i \(-0.147147\pi\)
\(158\) 0 0
\(159\) −2.14283 10.1664i −0.169937 0.806244i
\(160\) 0 0
\(161\) 8.17199 + 10.6441i 0.644043 + 0.838873i
\(162\) 0 0
\(163\) −3.61108 + 6.25457i −0.282841 + 0.489896i −0.972083 0.234635i \(-0.924610\pi\)
0.689242 + 0.724531i \(0.257944\pi\)
\(164\) 0 0
\(165\) 3.56381 + 1.16467i 0.277442 + 0.0906692i
\(166\) 0 0
\(167\) −11.2129 + 4.08117i −0.867681 + 0.315810i −0.737228 0.675644i \(-0.763866\pi\)
−0.130454 + 0.991454i \(0.541643\pi\)
\(168\) 0 0
\(169\) 2.02623 + 11.4913i 0.155864 + 0.883949i
\(170\) 0 0
\(171\) 3.43695 4.69682i 0.262830 0.359174i
\(172\) 0 0
\(173\) 6.01812 5.04980i 0.457549 0.383929i −0.384679 0.923050i \(-0.625688\pi\)
0.842228 + 0.539121i \(0.181243\pi\)
\(174\) 0 0
\(175\) 1.64133 2.57788i 0.124073 0.194869i
\(176\) 0 0
\(177\) −16.0611 + 9.99809i −1.20723 + 0.751503i
\(178\) 0 0
\(179\) 6.27958i 0.469358i 0.972073 + 0.234679i \(0.0754039\pi\)
−0.972073 + 0.234679i \(0.924596\pi\)
\(180\) 0 0
\(181\) −11.7793 + 6.80080i −0.875551 + 0.505499i −0.869189 0.494480i \(-0.835358\pi\)
−0.00636187 + 0.999980i \(0.502025\pi\)
\(182\) 0 0
\(183\) −8.21609 6.44169i −0.607351 0.476183i
\(184\) 0 0
\(185\) 13.3986 4.87669i 0.985085 0.358542i
\(186\) 0 0
\(187\) 1.41938 0.250275i 0.103795 0.0183019i
\(188\) 0 0
\(189\) 5.42073 + 12.6339i 0.394300 + 0.918982i
\(190\) 0 0
\(191\) 3.77976 0.666474i 0.273494 0.0482243i −0.0352191 0.999380i \(-0.511213\pi\)
0.308713 + 0.951155i \(0.400102\pi\)
\(192\) 0 0
\(193\) −2.56697 + 0.934299i −0.184774 + 0.0672523i −0.432750 0.901514i \(-0.642457\pi\)
0.247976 + 0.968766i \(0.420235\pi\)
\(194\) 0 0
\(195\) 4.60038 1.84956i 0.329440 0.132450i
\(196\) 0 0
\(197\) −3.32357 + 1.91886i −0.236795 + 0.136713i −0.613703 0.789537i \(-0.710321\pi\)
0.376908 + 0.926251i \(0.376987\pi\)
\(198\) 0 0
\(199\) 23.7659i 1.68472i 0.538915 + 0.842360i \(0.318834\pi\)
−0.538915 + 0.842360i \(0.681166\pi\)
\(200\) 0 0
\(201\) −17.6987 9.44926i −1.24837 0.666500i
\(202\) 0 0
\(203\) 10.6210 5.53252i 0.745449 0.388307i
\(204\) 0 0
\(205\) 3.53041 2.96236i 0.246574 0.206900i
\(206\) 0 0
\(207\) −14.7766 + 3.63078i −1.02704 + 0.252357i
\(208\) 0 0
\(209\) −0.293931 1.66697i −0.0203316 0.115306i
\(210\) 0 0
\(211\) 26.2398 9.55051i 1.80642 0.657484i 0.808837 0.588033i \(-0.200098\pi\)
0.997585 0.0694506i \(-0.0221246\pi\)
\(212\) 0 0
\(213\) 20.9826 18.8282i 1.43770 1.29009i
\(214\) 0 0
\(215\) −5.70664 + 9.88419i −0.389190 + 0.674096i
\(216\) 0 0
\(217\) −12.6212 + 1.66501i −0.856782 + 0.113028i
\(218\) 0 0
\(219\) −2.18035 + 1.95648i −0.147335 + 0.132207i
\(220\) 0 0
\(221\) 1.22517 1.46010i 0.0824136 0.0982168i
\(222\) 0 0
\(223\) 7.03311 1.24013i 0.470972 0.0830451i 0.0668753 0.997761i \(-0.478697\pi\)
0.404097 + 0.914716i \(0.367586\pi\)
\(224\) 0 0
\(225\) 1.92793 + 2.87939i 0.128529 + 0.191959i
\(226\) 0 0
\(227\) −3.57871 20.2959i −0.237527 1.34708i −0.837226 0.546857i \(-0.815824\pi\)
0.599699 0.800226i \(-0.295287\pi\)
\(228\) 0 0
\(229\) 1.79601 + 4.93449i 0.118684 + 0.326080i 0.984782 0.173793i \(-0.0556022\pi\)
−0.866099 + 0.499873i \(0.833380\pi\)
\(230\) 0 0
\(231\) 3.74313 + 1.40564i 0.246280 + 0.0924844i
\(232\) 0 0
\(233\) 13.3287 7.69531i 0.873190 0.504137i 0.00478320 0.999989i \(-0.498477\pi\)
0.868407 + 0.495852i \(0.165144\pi\)
\(234\) 0 0
\(235\) 8.59498 14.8869i 0.560675 0.971117i
\(236\) 0 0
\(237\) −7.91162 1.12565i −0.513915 0.0731191i
\(238\) 0 0
\(239\) −7.55229 1.33167i −0.488517 0.0861388i −0.0760364 0.997105i \(-0.524227\pi\)
−0.412481 + 0.910966i \(0.635338\pi\)
\(240\) 0 0
\(241\) −3.60552 + 9.90608i −0.232252 + 0.638107i −0.999996 0.00264928i \(-0.999157\pi\)
0.767745 + 0.640756i \(0.221379\pi\)
\(242\) 0 0
\(243\) −15.5879 0.132782i −0.999964 0.00851796i
\(244\) 0 0
\(245\) 9.95354 14.2312i 0.635909 0.909195i
\(246\) 0 0
\(247\) −1.71478 1.43888i −0.109109 0.0915535i
\(248\) 0 0
\(249\) 0.351920 + 0.875323i 0.0223020 + 0.0554714i
\(250\) 0 0
\(251\) −1.84579 3.19700i −0.116505 0.201793i 0.801875 0.597491i \(-0.203836\pi\)
−0.918380 + 0.395699i \(0.870502\pi\)
\(252\) 0 0
\(253\) −2.21270 + 3.83252i −0.139112 + 0.240948i
\(254\) 0 0
\(255\) 6.26172 + 3.34311i 0.392124 + 0.209354i
\(256\) 0 0
\(257\) −2.35880 + 0.858533i −0.147138 + 0.0535538i −0.414539 0.910031i \(-0.636057\pi\)
0.267401 + 0.963585i \(0.413835\pi\)
\(258\) 0 0
\(259\) 14.5007 4.57628i 0.901031 0.284356i
\(260\) 0 0
\(261\) 0.901066 + 13.5491i 0.0557746 + 0.838669i
\(262\) 0 0
\(263\) 12.1095 + 14.4315i 0.746701 + 0.889883i 0.996930 0.0783034i \(-0.0249503\pi\)
−0.250229 + 0.968187i \(0.580506\pi\)
\(264\) 0 0
\(265\) −5.08993 13.9845i −0.312672 0.859060i
\(266\) 0 0
\(267\) 5.12337 15.6772i 0.313545 0.959428i
\(268\) 0 0
\(269\) 4.49619 + 7.78763i 0.274138 + 0.474820i 0.969917 0.243435i \(-0.0782743\pi\)
−0.695779 + 0.718255i \(0.744941\pi\)
\(270\) 0 0
\(271\) −23.0777 13.3239i −1.40187 0.809369i −0.407283 0.913302i \(-0.633524\pi\)
−0.994584 + 0.103933i \(0.966857\pi\)
\(272\) 0 0
\(273\) 4.98688 1.75788i 0.301820 0.106391i
\(274\) 0 0
\(275\) 0.992508 + 0.175006i 0.0598505 + 0.0105533i
\(276\) 0 0
\(277\) −12.4231 + 10.4242i −0.746430 + 0.626329i −0.934556 0.355816i \(-0.884203\pi\)
0.188126 + 0.982145i \(0.439759\pi\)
\(278\) 0 0
\(279\) 4.02610 13.8622i 0.241036 0.829911i
\(280\) 0 0
\(281\) 10.2506 28.1634i 0.611501 1.68009i −0.115380 0.993321i \(-0.536809\pi\)
0.726881 0.686764i \(-0.240969\pi\)
\(282\) 0 0
\(283\) 11.7175 + 2.06611i 0.696534 + 0.122818i 0.510694 0.859762i \(-0.329388\pi\)
0.185840 + 0.982580i \(0.440499\pi\)
\(284\) 0 0
\(285\) 3.92626 7.35397i 0.232571 0.435611i
\(286\) 0 0
\(287\) 3.89836 2.99295i 0.230113 0.176668i
\(288\) 0 0
\(289\) −14.2713 −0.839490
\(290\) 0 0
\(291\) 5.08268 + 3.98498i 0.297952 + 0.233604i
\(292\) 0 0
\(293\) −4.63962 + 26.3126i −0.271049 + 1.53720i 0.480189 + 0.877165i \(0.340568\pi\)
−0.751238 + 0.660032i \(0.770543\pi\)
\(294\) 0 0
\(295\) −20.7589 + 17.4188i −1.20863 + 1.01416i
\(296\) 0 0
\(297\) −3.16600 + 3.24514i −0.183710 + 0.188302i
\(298\) 0 0
\(299\) 1.01626 + 5.76349i 0.0587717 + 0.333311i
\(300\) 0 0
\(301\) −6.53701 + 10.2670i −0.376787 + 0.591782i
\(302\) 0 0
\(303\) −6.81634 16.9541i −0.391589 0.973990i
\(304\) 0 0
\(305\) −12.9509 7.47719i −0.741565 0.428143i
\(306\) 0 0
\(307\) −12.1594 7.02025i −0.693975 0.400667i 0.111124 0.993807i \(-0.464555\pi\)
−0.805099 + 0.593140i \(0.797888\pi\)
\(308\) 0 0
\(309\) −14.0436 + 26.3040i −0.798913 + 1.49638i
\(310\) 0 0
\(311\) 3.89641 22.0977i 0.220945 1.25304i −0.649341 0.760497i \(-0.724955\pi\)
0.870287 0.492546i \(-0.163934\pi\)
\(312\) 0 0
\(313\) −11.7304 13.9798i −0.663044 0.790185i 0.324775 0.945791i \(-0.394711\pi\)
−0.987819 + 0.155607i \(0.950267\pi\)
\(314\) 0 0
\(315\) 10.2362 + 16.8223i 0.576742 + 0.947831i
\(316\) 0 0
\(317\) −3.78845 + 10.4087i −0.212780 + 0.584609i −0.999464 0.0327476i \(-0.989574\pi\)
0.786683 + 0.617357i \(0.211796\pi\)
\(318\) 0 0
\(319\) 3.02533 + 2.53856i 0.169386 + 0.142132i
\(320\) 0 0
\(321\) −15.7341 + 14.1186i −0.878193 + 0.788023i
\(322\) 0 0
\(323\) 3.20464i 0.178311i
\(324\) 0 0
\(325\) 1.15423 0.666397i 0.0640254 0.0369651i
\(326\) 0 0
\(327\) −12.6405 + 2.66432i −0.699021 + 0.147337i
\(328\) 0 0
\(329\) 9.84562 15.4636i 0.542807 0.852534i
\(330\) 0 0
\(331\) −19.1638 6.97506i −1.05334 0.383384i −0.243417 0.969922i \(-0.578268\pi\)
−0.809922 + 0.586538i \(0.800491\pi\)
\(332\) 0 0
\(333\) −1.86066 + 17.1409i −0.101963 + 0.939318i
\(334\) 0 0
\(335\) −27.0049 9.82897i −1.47543 0.537014i
\(336\) 0 0
\(337\) 3.48238 + 2.92206i 0.189697 + 0.159175i 0.732690 0.680562i \(-0.238264\pi\)
−0.542993 + 0.839737i \(0.682709\pi\)
\(338\) 0 0
\(339\) 6.31652 0.209804i 0.343066 0.0113950i
\(340\) 0 0
\(341\) −2.09913 3.63580i −0.113674 0.196890i
\(342\) 0 0
\(343\) 11.2628 14.7021i 0.608132 0.793836i
\(344\) 0 0
\(345\) −20.2220 + 8.13015i −1.08871 + 0.437713i
\(346\) 0 0
\(347\) 4.44853 + 12.2222i 0.238810 + 0.656124i 0.999971 + 0.00756190i \(0.00240705\pi\)
−0.761162 + 0.648562i \(0.775371\pi\)
\(348\) 0 0
\(349\) 5.68358 + 6.77342i 0.304235 + 0.362573i 0.896402 0.443242i \(-0.146172\pi\)
−0.592167 + 0.805815i \(0.701727\pi\)
\(350\) 0 0
\(351\) −0.448796 + 5.97880i −0.0239549 + 0.319125i
\(352\) 0 0
\(353\) −3.69612 1.34528i −0.196725 0.0716019i 0.241779 0.970331i \(-0.422269\pi\)
−0.438504 + 0.898729i \(0.644491\pi\)
\(354\) 0 0
\(355\) 25.9564 30.9336i 1.37762 1.64179i
\(356\) 0 0
\(357\) 6.51684 + 3.85135i 0.344908 + 0.203835i
\(358\) 0 0
\(359\) 27.5239i 1.45266i 0.687347 + 0.726329i \(0.258775\pi\)
−0.687347 + 0.726329i \(0.741225\pi\)
\(360\) 0 0
\(361\) 15.2364 0.801914
\(362\) 0 0
\(363\) −0.588713 17.7242i −0.0308994 0.930280i
\(364\) 0 0
\(365\) −2.69719 + 3.21439i −0.141177 + 0.168249i
\(366\) 0 0
\(367\) −12.7848 + 2.25431i −0.667362 + 0.117674i −0.497058 0.867718i \(-0.665586\pi\)
−0.170304 + 0.985391i \(0.554475\pi\)
\(368\) 0 0
\(369\) 1.32976 + 5.41185i 0.0692243 + 0.281730i
\(370\) 0 0
\(371\) −4.77638 15.1348i −0.247977 0.785758i
\(372\) 0 0
\(373\) 2.20575 12.5094i 0.114209 0.647714i −0.872929 0.487847i \(-0.837782\pi\)
0.987139 0.159867i \(-0.0511066\pi\)
\(374\) 0 0
\(375\) −11.0345 12.2971i −0.569819 0.635021i
\(376\) 0 0
\(377\) 5.22276 0.268986
\(378\) 0 0
\(379\) −28.2292 −1.45004 −0.725018 0.688730i \(-0.758169\pi\)
−0.725018 + 0.688730i \(0.758169\pi\)
\(380\) 0 0
\(381\) 24.3626 5.13508i 1.24814 0.263078i
\(382\) 0 0
\(383\) −4.99450 + 28.3252i −0.255207 + 1.44735i 0.540333 + 0.841451i \(0.318298\pi\)
−0.795540 + 0.605901i \(0.792813\pi\)
\(384\) 0 0
\(385\) 5.59171 + 1.23810i 0.284980 + 0.0630994i
\(386\) 0 0
\(387\) −7.67847 11.4679i −0.390319 0.582946i
\(388\) 0 0
\(389\) 20.1396 3.55115i 1.02112 0.180051i 0.362069 0.932151i \(-0.382070\pi\)
0.659048 + 0.752101i \(0.270959\pi\)
\(390\) 0 0
\(391\) −5.38548 + 6.41817i −0.272356 + 0.324581i
\(392\) 0 0
\(393\) −11.9431 + 7.43464i −0.602451 + 0.375028i
\(394\) 0 0
\(395\) −11.4465 −0.575937
\(396\) 0 0
\(397\) 0.558097i 0.0280101i 0.999902 + 0.0140050i \(0.00445809\pi\)
−0.999902 + 0.0140050i \(0.995542\pi\)
\(398\) 0 0
\(399\) 4.52315 7.65358i 0.226441 0.383158i
\(400\) 0 0
\(401\) 19.2013 22.8832i 0.958868 1.14273i −0.0308249 0.999525i \(-0.509813\pi\)
0.989692 0.143209i \(-0.0457421\pi\)
\(402\) 0 0
\(403\) −5.21718 1.89890i −0.259886 0.0945908i
\(404\) 0 0
\(405\) −22.1318 + 2.95678i −1.09974 + 0.146923i
\(406\) 0 0
\(407\) 3.22327 + 3.84134i 0.159771 + 0.190408i
\(408\) 0 0
\(409\) −3.24389 8.91252i −0.160400 0.440696i 0.833293 0.552832i \(-0.186453\pi\)
−0.993693 + 0.112136i \(0.964231\pi\)
\(410\) 0 0
\(411\) 4.29581 + 3.36806i 0.211897 + 0.166134i
\(412\) 0 0
\(413\) −22.9224 + 17.5986i −1.12794 + 0.865972i
\(414\) 0 0
\(415\) 0.675664 + 1.17028i 0.0331670 + 0.0574470i
\(416\) 0 0
\(417\) −10.4136 + 19.5049i −0.509956 + 0.955159i
\(418\) 0 0
\(419\) 11.1641 + 9.36783i 0.545404 + 0.457648i 0.873381 0.487037i \(-0.161922\pi\)
−0.327977 + 0.944686i \(0.606367\pi\)
\(420\) 0 0
\(421\) −16.4485 5.98678i −0.801653 0.291778i −0.0914815 0.995807i \(-0.529160\pi\)
−0.710171 + 0.704029i \(0.751382\pi\)
\(422\) 0 0
\(423\) 11.5648 + 17.2722i 0.562301 + 0.839804i
\(424\) 0 0
\(425\) 1.79297 + 0.652587i 0.0869717 + 0.0316551i
\(426\) 0 0
\(427\) −13.4525 8.56519i −0.651012 0.414498i
\(428\) 0 0
\(429\) 1.16459 + 1.29785i 0.0562268 + 0.0626606i
\(430\) 0 0
\(431\) −26.8638 + 15.5098i −1.29398 + 0.747082i −0.979358 0.202134i \(-0.935212\pi\)
−0.314626 + 0.949216i \(0.601879\pi\)
\(432\) 0 0
\(433\) 17.1170i 0.822593i 0.911502 + 0.411296i \(0.134924\pi\)
−0.911502 + 0.411296i \(0.865076\pi\)
\(434\) 0 0
\(435\) 4.01152 + 19.0321i 0.192337 + 0.912518i
\(436\) 0 0
\(437\) 7.53771 + 6.32489i 0.360577 + 0.302560i
\(438\) 0 0
\(439\) 6.38198 17.5343i 0.304595 0.836869i −0.689091 0.724675i \(-0.741990\pi\)
0.993686 0.112194i \(-0.0357878\pi\)
\(440\) 0 0
\(441\) 10.1281 + 18.3962i 0.482290 + 0.876011i
\(442\) 0 0
\(443\) −19.3405 23.0491i −0.918896 1.09510i −0.995185 0.0980121i \(-0.968752\pi\)
0.0762890 0.997086i \(-0.475693\pi\)
\(444\) 0 0
\(445\) 4.10232 23.2654i 0.194468 1.10289i
\(446\) 0 0
\(447\) −9.77267 + 0.324601i −0.462232 + 0.0153531i
\(448\) 0 0
\(449\) 12.9905 + 7.50006i 0.613059 + 0.353950i 0.774162 0.632988i \(-0.218172\pi\)
−0.161103 + 0.986938i \(0.551505\pi\)
\(450\) 0 0
\(451\) 1.40364 + 0.810393i 0.0660949 + 0.0381599i
\(452\) 0 0
\(453\) −37.5048 5.33612i −1.76213 0.250713i
\(454\) 0 0
\(455\) 6.71718 3.49900i 0.314906 0.164036i
\(456\) 0 0
\(457\) −7.24635 41.0961i −0.338970 1.92239i −0.383836 0.923401i \(-0.625397\pi\)
0.0448656 0.998993i \(-0.485714\pi\)
\(458\) 0 0
\(459\) −6.96978 + 5.00962i −0.325321 + 0.233829i
\(460\) 0 0
\(461\) 18.5581 15.5721i 0.864339 0.725267i −0.0985592 0.995131i \(-0.531423\pi\)
0.962898 + 0.269865i \(0.0869789\pi\)
\(462\) 0 0
\(463\) −0.385388 + 2.18564i −0.0179105 + 0.101575i −0.992453 0.122629i \(-0.960867\pi\)
0.974542 + 0.224205i \(0.0719785\pi\)
\(464\) 0 0
\(465\) 2.91248 20.4703i 0.135063 0.949285i
\(466\) 0 0
\(467\) 21.4644 0.993252 0.496626 0.867965i \(-0.334572\pi\)
0.496626 + 0.867965i \(0.334572\pi\)
\(468\) 0 0
\(469\) −28.3173 11.7206i −1.30757 0.541208i
\(470\) 0 0
\(471\) 21.0338 + 33.7890i 0.969185 + 1.55692i
\(472\) 0 0
\(473\) −3.95291 0.697005i −0.181755 0.0320483i
\(474\) 0 0
\(475\) 0.766419 2.10572i 0.0351657 0.0966170i
\(476\) 0 0
\(477\) 17.8904 + 1.94201i 0.819147 + 0.0889187i
\(478\) 0 0
\(479\) −30.1070 + 25.2628i −1.37563 + 1.15429i −0.404826 + 0.914394i \(0.632668\pi\)
−0.970799 + 0.239893i \(0.922888\pi\)
\(480\) 0 0
\(481\) 6.53072 + 1.15154i 0.297775 + 0.0525058i
\(482\) 0 0
\(483\) −21.9209 + 7.72712i −0.997436 + 0.351596i
\(484\) 0 0
\(485\) 8.01173 + 4.62557i 0.363794 + 0.210036i
\(486\) 0 0
\(487\) −6.65268 11.5228i −0.301462 0.522147i 0.675006 0.737813i \(-0.264141\pi\)
−0.976467 + 0.215666i \(0.930808\pi\)
\(488\) 0 0
\(489\) −8.35440 9.31035i −0.377799 0.421029i
\(490\) 0 0
\(491\) 6.40724 + 17.6037i 0.289155 + 0.794446i 0.996185 + 0.0872628i \(0.0278120\pi\)
−0.707031 + 0.707183i \(0.749966\pi\)
\(492\) 0 0
\(493\) 4.80608 + 5.72766i 0.216455 + 0.257961i
\(494\) 0 0
\(495\) −3.83493 + 5.24069i −0.172367 + 0.235551i
\(496\) 0 0
\(497\) 29.0849 31.7574i 1.30463 1.42452i
\(498\) 0 0
\(499\) −0.586888 + 0.213610i −0.0262727 + 0.00956249i −0.355123 0.934820i \(-0.615561\pi\)
0.328850 + 0.944382i \(0.393339\pi\)
\(500\) 0 0
\(501\) −0.686105 20.6564i −0.0306529 0.922858i
\(502\) 0 0
\(503\) −4.62878 + 8.01728i −0.206387 + 0.357473i −0.950574 0.310499i \(-0.899504\pi\)
0.744187 + 0.667972i \(0.232837\pi\)
\(504\) 0 0
\(505\) −13.0869 22.6672i −0.582361 1.00868i
\(506\) 0 0
\(507\) −20.0091 2.84687i −0.888636 0.126434i
\(508\) 0 0
\(509\) 20.3411 + 17.0682i 0.901604 + 0.756535i 0.970503 0.241088i \(-0.0775043\pi\)
−0.0688994 + 0.997624i \(0.521949\pi\)
\(510\) 0 0
\(511\) −3.02228 + 3.29999i −0.133698 + 0.145983i
\(512\) 0 0
\(513\) 5.88346 + 8.18553i 0.259761 + 0.361400i
\(514\) 0 0
\(515\) −14.6079 + 40.1349i −0.643702 + 1.76856i
\(516\) 0 0
\(517\) 5.95362 + 1.04978i 0.261840 + 0.0461694i
\(518\) 0 0
\(519\) 5.07583 + 12.6250i 0.222804 + 0.554176i
\(520\) 0 0
\(521\) −2.72391 + 4.71794i −0.119336 + 0.206697i −0.919505 0.393079i \(-0.871410\pi\)
0.800168 + 0.599775i \(0.204743\pi\)
\(522\) 0 0
\(523\) 37.6388 21.7308i 1.64583 0.950221i 0.667128 0.744943i \(-0.267523\pi\)
0.978704 0.205279i \(-0.0658100\pi\)
\(524\) 0 0
\(525\) 3.36103 + 4.08922i 0.146687 + 0.178468i
\(526\) 0 0
\(527\) −2.71847 7.46894i −0.118419 0.325352i
\(528\) 0 0
\(529\) −0.473275 2.68407i −0.0205772 0.116699i
\(530\) 0 0
\(531\) −7.81900 31.8218i −0.339316 1.38095i
\(532\) 0 0
\(533\) 2.11085 0.372200i 0.0914311 0.0161218i
\(534\) 0 0
\(535\) −19.4638 + 23.1960i −0.841493 + 1.00285i
\(536\) 0 0
\(537\) −10.3385 3.37866i −0.446138 0.145800i
\(538\) 0 0
\(539\) 5.90031 + 1.57764i 0.254144 + 0.0679537i
\(540\) 0 0
\(541\) 19.8445 34.3717i 0.853181 1.47775i −0.0251413 0.999684i \(-0.508004\pi\)
0.878322 0.478069i \(-0.158663\pi\)
\(542\) 0 0
\(543\) −4.85886 23.0522i −0.208513 0.989263i
\(544\) 0 0
\(545\) −17.3878 + 6.32865i −0.744813 + 0.271090i
\(546\) 0 0
\(547\) 2.15543 + 12.2240i 0.0921594 + 0.522662i 0.995581 + 0.0939084i \(0.0299361\pi\)
−0.903421 + 0.428754i \(0.858953\pi\)
\(548\) 0 0
\(549\) 15.0259 10.0608i 0.641291 0.429385i
\(550\) 0 0
\(551\) 6.72675 5.64441i 0.286569 0.240460i
\(552\) 0 0
\(553\) −12.1954 0.529232i −0.518603 0.0225052i
\(554\) 0 0
\(555\) 0.819845 + 24.6828i 0.0348005 + 1.04773i
\(556\) 0 0
\(557\) 12.2620i 0.519556i −0.965668 0.259778i \(-0.916351\pi\)
0.965668 0.259778i \(-0.0836494\pi\)
\(558\) 0 0
\(559\) −4.59702 + 2.65409i −0.194433 + 0.112256i
\(560\) 0 0
\(561\) −0.351638 + 2.47147i −0.0148461 + 0.104346i
\(562\) 0 0
\(563\) 9.24373 3.36444i 0.389577 0.141794i −0.139803 0.990179i \(-0.544647\pi\)
0.529380 + 0.848385i \(0.322425\pi\)
\(564\) 0 0
\(565\) 8.91507 1.57197i 0.375060 0.0661332i
\(566\) 0 0
\(567\) −23.7166 + 2.12696i −0.996003 + 0.0893240i
\(568\) 0 0
\(569\) 24.3413 4.29203i 1.02044 0.179931i 0.361695 0.932296i \(-0.382198\pi\)
0.658747 + 0.752365i \(0.271087\pi\)
\(570\) 0 0
\(571\) −2.97933 + 1.08439i −0.124681 + 0.0453801i −0.403607 0.914932i \(-0.632244\pi\)
0.278926 + 0.960313i \(0.410022\pi\)
\(572\) 0 0
\(573\) −0.936399 + 6.58145i −0.0391186 + 0.274944i
\(574\) 0 0
\(575\) −5.07368 + 2.92929i −0.211587 + 0.122160i
\(576\) 0 0
\(577\) 14.0177i 0.583565i 0.956485 + 0.291782i \(0.0942483\pi\)
−0.956485 + 0.291782i \(0.905752\pi\)
\(578\) 0 0
\(579\) −0.157070 4.72885i −0.00652759 0.196524i
\(580\) 0 0
\(581\) 0.665762 + 1.27809i 0.0276205 + 0.0530242i
\(582\) 0 0
\(583\) 4.00931 3.36421i 0.166049 0.139331i
\(584\) 0 0
\(585\) 0.569873 + 8.56903i 0.0235613 + 0.354286i
\(586\) 0 0
\(587\) −1.43178 8.12004i −0.0590960 0.335150i 0.940898 0.338691i \(-0.109984\pi\)
−0.999994 + 0.00354081i \(0.998873\pi\)
\(588\) 0 0
\(589\) −8.77177 + 3.19266i −0.361434 + 0.131551i
\(590\) 0 0
\(591\) −1.37094 6.50423i −0.0563929 0.267548i
\(592\) 0 0
\(593\) 4.01055 6.94647i 0.164693 0.285258i −0.771853 0.635801i \(-0.780670\pi\)
0.936546 + 0.350544i \(0.114003\pi\)
\(594\) 0 0
\(595\) 10.0185 + 4.14671i 0.410720 + 0.169998i
\(596\) 0 0
\(597\) −39.1273 12.7870i −1.60137 0.523336i
\(598\) 0 0
\(599\) 23.0074 27.4192i 0.940059 1.12032i −0.0525086 0.998620i \(-0.516722\pi\)
0.992567 0.121698i \(-0.0388339\pi\)
\(600\) 0 0
\(601\) 39.9932 7.05187i 1.63136 0.287652i 0.718375 0.695656i \(-0.244886\pi\)
0.912980 + 0.408004i \(0.133775\pi\)
\(602\) 0 0
\(603\) 25.0795 24.0544i 1.02132 0.979571i
\(604\) 0 0
\(605\) −4.41096 25.0158i −0.179331 1.01704i
\(606\) 0 0
\(607\) −1.77126 4.86649i −0.0718931 0.197525i 0.898542 0.438888i \(-0.144628\pi\)
−0.970435 + 0.241364i \(0.922405\pi\)
\(608\) 0 0
\(609\) 3.39403 + 20.4628i 0.137533 + 0.829193i
\(610\) 0 0
\(611\) 6.92374 3.99742i 0.280105 0.161718i
\(612\) 0 0
\(613\) 21.5022 37.2430i 0.868468 1.50423i 0.00490505 0.999988i \(-0.498439\pi\)
0.863562 0.504242i \(-0.168228\pi\)
\(614\) 0 0
\(615\) 2.97763 + 7.40620i 0.120070 + 0.298647i
\(616\) 0 0
\(617\) 24.8905 + 4.38886i 1.00205 + 0.176689i 0.650522 0.759487i \(-0.274550\pi\)
0.351531 + 0.936176i \(0.385661\pi\)
\(618\) 0 0
\(619\) −7.20390 + 19.7925i −0.289549 + 0.795529i 0.706581 + 0.707633i \(0.250237\pi\)
−0.996130 + 0.0878968i \(0.971985\pi\)
\(620\) 0 0
\(621\) 1.97278 26.2811i 0.0791649 1.05462i
\(622\) 0 0
\(623\) 5.44640 24.5979i 0.218205 0.985494i
\(624\) 0 0
\(625\) −22.5533 18.9244i −0.902130 0.756977i
\(626\) 0 0
\(627\) 2.90258 + 0.412975i 0.115918 + 0.0164926i
\(628\) 0 0
\(629\) 4.74682 + 8.22173i 0.189268 + 0.327822i
\(630\) 0 0
\(631\) −5.23606 + 9.06912i −0.208444 + 0.361036i −0.951225 0.308499i \(-0.900173\pi\)
0.742780 + 0.669535i \(0.233507\pi\)
\(632\) 0 0
\(633\) 1.60558 + 48.3388i 0.0638162 + 1.92129i
\(634\) 0 0
\(635\) 33.5124 12.1975i 1.32990 0.484044i
\(636\) 0 0
\(637\) 7.31844 3.41736i 0.289967 0.135401i
\(638\) 0 0
\(639\) 19.7086 + 44.6753i 0.779660 + 1.76733i
\(640\) 0 0
\(641\) 16.3459 + 19.4803i 0.645624 + 0.769424i 0.985247 0.171137i \(-0.0547441\pi\)
−0.339623 + 0.940561i \(0.610300\pi\)
\(642\) 0 0
\(643\) 10.1011 + 27.7526i 0.398349 + 1.09446i 0.963088 + 0.269186i \(0.0867547\pi\)
−0.564739 + 0.825270i \(0.691023\pi\)
\(644\) 0 0
\(645\) −13.2026 14.7133i −0.519851 0.579335i
\(646\) 0 0
\(647\) −20.7854 36.0013i −0.817157 1.41536i −0.907769 0.419471i \(-0.862215\pi\)
0.0906115 0.995886i \(-0.471118\pi\)
\(648\) 0 0
\(649\) −8.25345 4.76513i −0.323976 0.187048i
\(650\) 0 0
\(651\) 4.04948 21.6749i 0.158712 0.849506i
\(652\) 0 0
\(653\) 15.0553 + 2.65466i 0.589160 + 0.103885i 0.460278 0.887775i \(-0.347750\pi\)
0.128883 + 0.991660i \(0.458861\pi\)
\(654\) 0 0
\(655\) −15.4364 + 12.9527i −0.603151 + 0.506104i
\(656\) 0 0
\(657\) −2.04797 4.64232i −0.0798988 0.181114i
\(658\) 0 0
\(659\) 0.375700 1.03223i 0.0146352 0.0402099i −0.932160 0.362047i \(-0.882078\pi\)
0.946795 + 0.321837i \(0.104300\pi\)
\(660\) 0 0
\(661\) 7.04002 + 1.24135i 0.273825 + 0.0482827i 0.308874 0.951103i \(-0.400048\pi\)
−0.0350493 + 0.999386i \(0.511159\pi\)
\(662\) 0 0
\(663\) 1.74466 + 2.80266i 0.0677571 + 0.108846i
\(664\) 0 0
\(665\) 4.87003 11.7661i 0.188852 0.456269i
\(666\) 0 0
\(667\) −22.9578 −0.888928
\(668\) 0 0
\(669\) −1.74239 + 12.2463i −0.0673645 + 0.473469i
\(670\) 0 0
\(671\) 0.913258 5.17934i 0.0352559 0.199946i
\(672\) 0 0
\(673\) −15.6316 + 13.1164i −0.602552 + 0.505601i −0.892265 0.451512i \(-0.850885\pi\)
0.289713 + 0.957114i \(0.406440\pi\)
\(674\) 0 0
\(675\) −5.77783 + 1.62485i −0.222389 + 0.0625407i
\(676\) 0 0
\(677\) 4.06771 + 23.0691i 0.156335 + 0.886619i 0.957555 + 0.288250i \(0.0930734\pi\)
−0.801220 + 0.598369i \(0.795815\pi\)
\(678\) 0 0
\(679\) 8.32205 + 5.29863i 0.319371 + 0.203343i
\(680\) 0 0
\(681\) 35.3399 + 5.02810i 1.35423 + 0.192677i
\(682\) 0 0
\(683\) 33.2323 + 19.1867i 1.27160 + 0.734157i 0.975289 0.220935i \(-0.0709108\pi\)
0.296309 + 0.955092i \(0.404244\pi\)
\(684\) 0 0
\(685\) 6.77141 + 3.90947i 0.258722 + 0.149373i
\(686\) 0 0
\(687\) −9.09029 + 0.301936i −0.346816 + 0.0115196i
\(688\) 0 0
\(689\) 1.20189 6.81628i 0.0457885 0.259680i
\(690\) 0 0
\(691\) 12.7844 + 15.2358i 0.486341 + 0.579599i 0.952283 0.305217i \(-0.0987289\pi\)
−0.465942 + 0.884815i \(0.654284\pi\)
\(692\) 0 0
\(693\) −4.32814 + 5.40626i −0.164413 + 0.205367i
\(694\) 0 0
\(695\) −10.8321 + 29.7608i −0.410883 + 1.12889i
\(696\) 0 0
\(697\) 2.35063 + 1.97241i 0.0890363 + 0.0747103i
\(698\) 0 0
\(699\) 5.49794 + 26.0842i 0.207951 + 0.986596i
\(700\) 0 0
\(701\) 51.2062i 1.93403i −0.254720 0.967015i \(-0.581983\pi\)
0.254720 0.967015i \(-0.418017\pi\)
\(702\) 0 0
\(703\) 9.65587 5.57482i 0.364178 0.210258i
\(704\) 0 0
\(705\) 19.8849 + 22.1602i 0.748908 + 0.834602i
\(706\) 0 0
\(707\) −12.8952 24.7554i −0.484972 0.931021i
\(708\) 0 0
\(709\) 16.9304 + 6.16216i 0.635834 + 0.231425i 0.639769 0.768568i \(-0.279030\pi\)
−0.00393462 + 0.999992i \(0.501252\pi\)
\(710\) 0 0
\(711\) 6.10999 12.4198i 0.229143 0.465778i
\(712\) 0 0
\(713\) 22.9332 + 8.34701i 0.858856 + 0.312598i
\(714\) 0 0
\(715\) 1.91335 + 1.60549i 0.0715552 + 0.0600420i
\(716\) 0 0
\(717\) 6.25584 11.7173i 0.233629 0.437592i
\(718\) 0 0
\(719\) 18.8025 + 32.5670i 0.701216 + 1.21454i 0.968040 + 0.250797i \(0.0806926\pi\)
−0.266823 + 0.963745i \(0.585974\pi\)
\(720\) 0 0
\(721\) −17.4193 + 42.0854i −0.648729 + 1.56734i
\(722\) 0 0
\(723\) −14.3691 11.2658i −0.534393 0.418981i
\(724\) 0 0
\(725\) 1.78818 + 4.91297i 0.0664112 + 0.182463i
\(726\) 0 0
\(727\) 20.7271 + 24.7016i 0.768725 + 0.916131i 0.998366 0.0571448i \(-0.0181997\pi\)
−0.229641 + 0.973275i \(0.573755\pi\)
\(728\) 0 0
\(729\) 8.60550 25.5919i 0.318722 0.947848i
\(730\) 0 0
\(731\) −7.14094 2.59909i −0.264117 0.0961307i
\(732\) 0 0
\(733\) −10.3675 + 12.3555i −0.382932 + 0.456361i −0.922737 0.385429i \(-0.874053\pi\)
0.539805 + 0.841790i \(0.318498\pi\)
\(734\) 0 0
\(735\) 18.0743 + 24.0441i 0.666679 + 0.886879i
\(736\) 0 0
\(737\) 10.1067i 0.372287i
\(738\) 0 0
\(739\) −7.26540 −0.267262 −0.133631 0.991031i \(-0.542664\pi\)
−0.133631 + 0.991031i \(0.542664\pi\)
\(740\) 0 0
\(741\) 3.29153 2.04899i 0.120917 0.0752715i
\(742\) 0 0
\(743\) −5.70028 + 6.79333i −0.209123 + 0.249223i −0.860403 0.509615i \(-0.829788\pi\)
0.651280 + 0.758838i \(0.274232\pi\)
\(744\) 0 0
\(745\) −13.7931 + 2.43209i −0.505338 + 0.0891048i
\(746\) 0 0
\(747\) −1.63045 + 0.108431i −0.0596550 + 0.00396728i
\(748\) 0 0
\(749\) −21.8097 + 23.8138i −0.796910 + 0.870137i
\(750\) 0 0
\(751\) −5.42070 + 30.7423i −0.197804 + 1.12180i 0.710564 + 0.703632i \(0.248440\pi\)
−0.908369 + 0.418171i \(0.862671\pi\)
\(752\) 0 0
\(753\) 6.25653 1.31873i 0.228001 0.0480572i
\(754\) 0 0
\(755\) −54.2618 −1.97479
\(756\) 0 0
\(757\) −1.50694 −0.0547708 −0.0273854 0.999625i \(-0.508718\pi\)
−0.0273854 + 0.999625i \(0.508718\pi\)
\(758\) 0 0
\(759\) −5.11920 5.70496i −0.185815 0.207077i
\(760\) 0 0
\(761\) −6.65857 + 37.7626i −0.241373 + 1.36889i 0.587395 + 0.809301i \(0.300154\pi\)
−0.828768 + 0.559593i \(0.810957\pi\)
\(762\) 0 0
\(763\) −18.8181 + 5.93879i −0.681260 + 0.214999i
\(764\) 0 0
\(765\) −8.87303 + 8.51035i −0.320805 + 0.307692i
\(766\) 0 0
\(767\) −12.4119 + 2.18854i −0.448166 + 0.0790238i
\(768\) 0 0
\(769\) 26.9964 32.1731i 0.973516 1.16019i −0.0135556 0.999908i \(-0.504315\pi\)
0.987071 0.160283i \(-0.0512405\pi\)
\(770\) 0 0
\(771\) −0.144332 4.34537i −0.00519800 0.156495i
\(772\) 0 0
\(773\) −11.6630 −0.419490 −0.209745 0.977756i \(-0.567263\pi\)
−0.209745 + 0.977756i \(0.567263\pi\)
\(774\) 0 0
\(775\) 5.55787i 0.199645i
\(776\) 0 0
\(777\) −0.267730 + 26.3357i −0.00960475 + 0.944787i
\(778\)