Properties

Label 260.2.x.a.101.3
Level $260$
Weight $2$
Character 260.101
Analytic conductor $2.076$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 260.x (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.07611045255\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.22581504.2
Defining polynomial: \( x^{8} - 4x^{7} + 5x^{6} + 2x^{5} - 11x^{4} + 4x^{3} + 20x^{2} - 32x + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 101.3
Root \(0.665665 - 1.24775i\) of defining polynomial
Character \(\chi\) \(=\) 260.101
Dual form 260.2.x.a.121.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.0473938 + 0.0820885i) q^{3} -1.00000i q^{5} +(0.716063 + 0.413419i) q^{7} +(1.49551 - 2.59030i) q^{9} +O(q^{10})\) \(q+(0.0473938 + 0.0820885i) q^{3} -1.00000i q^{5} +(0.716063 + 0.413419i) q^{7} +(1.49551 - 2.59030i) q^{9} +(1.50000 - 0.866025i) q^{11} +(3.32235 + 1.40072i) q^{13} +(0.0820885 - 0.0473938i) q^{15} +(0.716063 - 1.24026i) q^{17} +(-0.926118 - 0.534695i) q^{19} +0.0783740i q^{21} +(1.54290 + 2.67238i) q^{23} -1.00000 q^{25} +0.567874 q^{27} +(-3.72756 - 6.45632i) q^{29} +5.84325i q^{31} +(0.142181 + 0.0820885i) q^{33} +(0.413419 - 0.716063i) q^{35} +(0.851811 - 0.491793i) q^{37} +(0.0424756 + 0.339112i) q^{39} +(-3.69615 + 2.13397i) q^{41} +(-4.77046 + 8.26268i) q^{43} +(-2.59030 - 1.49551i) q^{45} +3.46410i q^{47} +(-3.15817 - 5.47011i) q^{49} +0.135748 q^{51} +0.334308 q^{53} +(-0.866025 - 1.50000i) q^{55} -0.101365i q^{57} +(-9.98052 - 5.76225i) q^{59} +(-1.35824 + 2.35255i) q^{61} +(2.14176 - 1.23654i) q^{63} +(1.40072 - 3.32235i) q^{65} +(-11.9122 + 6.87752i) q^{67} +(-0.146248 + 0.253309i) q^{69} +(8.46704 + 4.88845i) q^{71} +11.1806i q^{73} +(-0.0473938 - 0.0820885i) q^{75} +1.43213 q^{77} -0.252387 q^{79} +(-4.45961 - 7.72427i) q^{81} +5.67165i q^{83} +(-1.24026 - 0.716063i) q^{85} +(0.353326 - 0.611979i) q^{87} +(3.98052 - 2.29815i) q^{89} +(1.79992 + 2.37653i) q^{91} +(-0.479664 + 0.276934i) q^{93} +(-0.534695 + 0.926118i) q^{95} +(8.25698 + 4.76717i) q^{97} -5.18059i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 2 q^{3} + 6 q^{7} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 2 q^{3} + 6 q^{7} - 4 q^{9} + 12 q^{11} - 8 q^{13} - 6 q^{15} + 6 q^{17} - 6 q^{23} - 8 q^{25} + 4 q^{27} - 6 q^{33} - 6 q^{35} + 6 q^{37} - 4 q^{39} + 12 q^{41} + 10 q^{43} - 4 q^{49} + 24 q^{53} - 24 q^{59} - 4 q^{61} + 24 q^{63} - 54 q^{67} - 24 q^{69} - 36 q^{71} + 2 q^{75} + 12 q^{77} - 16 q^{79} + 8 q^{81} + 18 q^{85} - 6 q^{87} - 24 q^{89} + 24 q^{93} - 30 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/260\mathbb{Z}\right)^\times\).

\(n\) \(41\) \(131\) \(157\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.0473938 + 0.0820885i 0.0273628 + 0.0473938i 0.879383 0.476116i \(-0.157956\pi\)
−0.852020 + 0.523510i \(0.824622\pi\)
\(4\) 0 0
\(5\) 1.00000i 0.447214i
\(6\) 0 0
\(7\) 0.716063 + 0.413419i 0.270646 + 0.156258i 0.629181 0.777259i \(-0.283390\pi\)
−0.358535 + 0.933516i \(0.616724\pi\)
\(8\) 0 0
\(9\) 1.49551 2.59030i 0.498503 0.863432i
\(10\) 0 0
\(11\) 1.50000 0.866025i 0.452267 0.261116i −0.256520 0.966539i \(-0.582576\pi\)
0.708787 + 0.705422i \(0.249243\pi\)
\(12\) 0 0
\(13\) 3.32235 + 1.40072i 0.921453 + 0.388490i
\(14\) 0 0
\(15\) 0.0820885 0.0473938i 0.0211951 0.0122370i
\(16\) 0 0
\(17\) 0.716063 1.24026i 0.173671 0.300807i −0.766030 0.642805i \(-0.777770\pi\)
0.939700 + 0.341999i \(0.111104\pi\)
\(18\) 0 0
\(19\) −0.926118 0.534695i −0.212466 0.122667i 0.389991 0.920819i \(-0.372478\pi\)
−0.602457 + 0.798151i \(0.705811\pi\)
\(20\) 0 0
\(21\) 0.0783740i 0.0171026i
\(22\) 0 0
\(23\) 1.54290 + 2.67238i 0.321717 + 0.557231i 0.980842 0.194803i \(-0.0624066\pi\)
−0.659125 + 0.752033i \(0.729073\pi\)
\(24\) 0 0
\(25\) −1.00000 −0.200000
\(26\) 0 0
\(27\) 0.567874 0.109287
\(28\) 0 0
\(29\) −3.72756 6.45632i −0.692190 1.19891i −0.971119 0.238597i \(-0.923313\pi\)
0.278928 0.960312i \(-0.410021\pi\)
\(30\) 0 0
\(31\) 5.84325i 1.04948i 0.851263 + 0.524740i \(0.175837\pi\)
−0.851263 + 0.524740i \(0.824163\pi\)
\(32\) 0 0
\(33\) 0.142181 + 0.0820885i 0.0247506 + 0.0142898i
\(34\) 0 0
\(35\) 0.413419 0.716063i 0.0698806 0.121037i
\(36\) 0 0
\(37\) 0.851811 0.491793i 0.140037 0.0808503i −0.428345 0.903615i \(-0.640903\pi\)
0.568382 + 0.822765i \(0.307570\pi\)
\(38\) 0 0
\(39\) 0.0424756 + 0.339112i 0.00680154 + 0.0543013i
\(40\) 0 0
\(41\) −3.69615 + 2.13397i −0.577242 + 0.333271i −0.760037 0.649880i \(-0.774819\pi\)
0.182795 + 0.983151i \(0.441486\pi\)
\(42\) 0 0
\(43\) −4.77046 + 8.26268i −0.727488 + 1.26005i 0.230453 + 0.973083i \(0.425979\pi\)
−0.957942 + 0.286963i \(0.907354\pi\)
\(44\) 0 0
\(45\) −2.59030 1.49551i −0.386138 0.222937i
\(46\) 0 0
\(47\) 3.46410i 0.505291i 0.967559 + 0.252646i \(0.0813007\pi\)
−0.967559 + 0.252646i \(0.918699\pi\)
\(48\) 0 0
\(49\) −3.15817 5.47011i −0.451167 0.781444i
\(50\) 0 0
\(51\) 0.135748 0.0190085
\(52\) 0 0
\(53\) 0.334308 0.0459207 0.0229603 0.999736i \(-0.492691\pi\)
0.0229603 + 0.999736i \(0.492691\pi\)
\(54\) 0 0
\(55\) −0.866025 1.50000i −0.116775 0.202260i
\(56\) 0 0
\(57\) 0.101365i 0.0134261i
\(58\) 0 0
\(59\) −9.98052 5.76225i −1.29935 0.750181i −0.319060 0.947734i \(-0.603367\pi\)
−0.980292 + 0.197553i \(0.936701\pi\)
\(60\) 0 0
\(61\) −1.35824 + 2.35255i −0.173905 + 0.301213i −0.939782 0.341775i \(-0.888972\pi\)
0.765877 + 0.642988i \(0.222305\pi\)
\(62\) 0 0
\(63\) 2.14176 1.23654i 0.269836 0.155790i
\(64\) 0 0
\(65\) 1.40072 3.32235i 0.173738 0.412086i
\(66\) 0 0
\(67\) −11.9122 + 6.87752i −1.45531 + 0.840223i −0.998775 0.0494832i \(-0.984243\pi\)
−0.456534 + 0.889706i \(0.650909\pi\)
\(68\) 0 0
\(69\) −0.146248 + 0.253309i −0.0176062 + 0.0304948i
\(70\) 0 0
\(71\) 8.46704 + 4.88845i 1.00485 + 0.580152i 0.909680 0.415309i \(-0.136327\pi\)
0.0951721 + 0.995461i \(0.469660\pi\)
\(72\) 0 0
\(73\) 11.1806i 1.30859i 0.756240 + 0.654295i \(0.227034\pi\)
−0.756240 + 0.654295i \(0.772966\pi\)
\(74\) 0 0
\(75\) −0.0473938 0.0820885i −0.00547256 0.00947876i
\(76\) 0 0
\(77\) 1.43213 0.163206
\(78\) 0 0
\(79\) −0.252387 −0.0283958 −0.0141979 0.999899i \(-0.504519\pi\)
−0.0141979 + 0.999899i \(0.504519\pi\)
\(80\) 0 0
\(81\) −4.45961 7.72427i −0.495512 0.858252i
\(82\) 0 0
\(83\) 5.67165i 0.622544i 0.950321 + 0.311272i \(0.100755\pi\)
−0.950321 + 0.311272i \(0.899245\pi\)
\(84\) 0 0
\(85\) −1.24026 0.716063i −0.134525 0.0776679i
\(86\) 0 0
\(87\) 0.353326 0.611979i 0.0378806 0.0656110i
\(88\) 0 0
\(89\) 3.98052 2.29815i 0.421934 0.243604i −0.273971 0.961738i \(-0.588337\pi\)
0.695904 + 0.718135i \(0.255004\pi\)
\(90\) 0 0
\(91\) 1.79992 + 2.37653i 0.188683 + 0.249128i
\(92\) 0 0
\(93\) −0.479664 + 0.276934i −0.0497388 + 0.0287167i
\(94\) 0 0
\(95\) −0.534695 + 0.926118i −0.0548585 + 0.0950177i
\(96\) 0 0
\(97\) 8.25698 + 4.76717i 0.838370 + 0.484033i 0.856710 0.515799i \(-0.172505\pi\)
−0.0183401 + 0.999832i \(0.505838\pi\)
\(98\) 0 0
\(99\) 5.18059i 0.520669i
\(100\) 0 0
\(101\) −2.90072 5.02419i −0.288632 0.499926i 0.684851 0.728683i \(-0.259867\pi\)
−0.973484 + 0.228757i \(0.926534\pi\)
\(102\) 0 0
\(103\) 10.0760 0.992814 0.496407 0.868090i \(-0.334652\pi\)
0.496407 + 0.868090i \(0.334652\pi\)
\(104\) 0 0
\(105\) 0.0783740 0.00764852
\(106\) 0 0
\(107\) −8.13977 14.0985i −0.786902 1.36295i −0.927856 0.372938i \(-0.878351\pi\)
0.140955 0.990016i \(-0.454983\pi\)
\(108\) 0 0
\(109\) 3.12979i 0.299780i 0.988703 + 0.149890i \(0.0478919\pi\)
−0.988703 + 0.149890i \(0.952108\pi\)
\(110\) 0 0
\(111\) 0.0807411 + 0.0466159i 0.00766361 + 0.00442458i
\(112\) 0 0
\(113\) 5.08538 8.80813i 0.478392 0.828599i −0.521301 0.853373i \(-0.674553\pi\)
0.999693 + 0.0247735i \(0.00788647\pi\)
\(114\) 0 0
\(115\) 2.67238 1.54290i 0.249201 0.143876i
\(116\) 0 0
\(117\) 8.59687 6.51107i 0.794781 0.601949i
\(118\) 0 0
\(119\) 1.02549 0.592068i 0.0940068 0.0542748i
\(120\) 0 0
\(121\) −4.00000 + 6.92820i −0.363636 + 0.629837i
\(122\) 0 0
\(123\) −0.350349 0.202274i −0.0315899 0.0182385i
\(124\) 0 0
\(125\) 1.00000i 0.0894427i
\(126\) 0 0
\(127\) 2.98401 + 5.16846i 0.264788 + 0.458627i 0.967508 0.252840i \(-0.0813646\pi\)
−0.702720 + 0.711467i \(0.748031\pi\)
\(128\) 0 0
\(129\) −0.904361 −0.0796245
\(130\) 0 0
\(131\) 16.6267 1.45268 0.726342 0.687334i \(-0.241219\pi\)
0.726342 + 0.687334i \(0.241219\pi\)
\(132\) 0 0
\(133\) −0.442106 0.765750i −0.0383355 0.0663990i
\(134\) 0 0
\(135\) 0.567874i 0.0488748i
\(136\) 0 0
\(137\) −0.350349 0.202274i −0.0299324 0.0172815i 0.484959 0.874537i \(-0.338834\pi\)
−0.514892 + 0.857255i \(0.672168\pi\)
\(138\) 0 0
\(139\) 4.65817 8.06819i 0.395101 0.684335i −0.598013 0.801486i \(-0.704043\pi\)
0.993114 + 0.117152i \(0.0373763\pi\)
\(140\) 0 0
\(141\) −0.284363 + 0.164177i −0.0239477 + 0.0138262i
\(142\) 0 0
\(143\) 6.19658 0.776156i 0.518184 0.0649054i
\(144\) 0 0
\(145\) −6.45632 + 3.72756i −0.536168 + 0.309557i
\(146\) 0 0
\(147\) 0.299355 0.518498i 0.0246904 0.0427650i
\(148\) 0 0
\(149\) 9.41179 + 5.43390i 0.771044 + 0.445162i 0.833247 0.552901i \(-0.186479\pi\)
−0.0622030 + 0.998064i \(0.519813\pi\)
\(150\) 0 0
\(151\) 0.991015i 0.0806477i −0.999187 0.0403238i \(-0.987161\pi\)
0.999187 0.0403238i \(-0.0128390\pi\)
\(152\) 0 0
\(153\) −2.14176 3.70963i −0.173151 0.299906i
\(154\) 0 0
\(155\) 5.84325 0.469341
\(156\) 0 0
\(157\) 17.5729 1.40247 0.701235 0.712930i \(-0.252632\pi\)
0.701235 + 0.712930i \(0.252632\pi\)
\(158\) 0 0
\(159\) 0.0158441 + 0.0274428i 0.00125652 + 0.00217636i
\(160\) 0 0
\(161\) 2.55146i 0.201083i
\(162\) 0 0
\(163\) −14.9666 8.64098i −1.17228 0.676814i −0.218061 0.975935i \(-0.569973\pi\)
−0.954215 + 0.299122i \(0.903306\pi\)
\(164\) 0 0
\(165\) 0.0820885 0.142181i 0.00639058 0.0110688i
\(166\) 0 0
\(167\) −2.64965 + 1.52978i −0.205036 + 0.118378i −0.599002 0.800747i \(-0.704436\pi\)
0.393966 + 0.919125i \(0.371103\pi\)
\(168\) 0 0
\(169\) 9.07597 + 9.30735i 0.698151 + 0.715950i
\(170\) 0 0
\(171\) −2.77003 + 1.59928i −0.211830 + 0.122300i
\(172\) 0 0
\(173\) −1.71006 + 2.96190i −0.130013 + 0.225189i −0.923681 0.383161i \(-0.874835\pi\)
0.793668 + 0.608351i \(0.208169\pi\)
\(174\) 0 0
\(175\) −0.716063 0.413419i −0.0541293 0.0312516i
\(176\) 0 0
\(177\) 1.09238i 0.0821083i
\(178\) 0 0
\(179\) −5.19109 8.99123i −0.388000 0.672036i 0.604180 0.796848i \(-0.293501\pi\)
−0.992180 + 0.124811i \(0.960167\pi\)
\(180\) 0 0
\(181\) −10.3492 −0.769247 −0.384624 0.923073i \(-0.625669\pi\)
−0.384624 + 0.923073i \(0.625669\pi\)
\(182\) 0 0
\(183\) −0.257489 −0.0190342
\(184\) 0 0
\(185\) −0.491793 0.851811i −0.0361574 0.0626264i
\(186\) 0 0
\(187\) 2.48052i 0.181393i
\(188\) 0 0
\(189\) 0.406634 + 0.234770i 0.0295782 + 0.0170770i
\(190\) 0 0
\(191\) 7.75296 13.4285i 0.560984 0.971653i −0.436427 0.899740i \(-0.643756\pi\)
0.997411 0.0719134i \(-0.0229105\pi\)
\(192\) 0 0
\(193\) 4.82401 2.78514i 0.347239 0.200479i −0.316229 0.948683i \(-0.602417\pi\)
0.663469 + 0.748204i \(0.269084\pi\)
\(194\) 0 0
\(195\) 0.339112 0.0424756i 0.0242843 0.00304174i
\(196\) 0 0
\(197\) −21.5405 + 12.4364i −1.53470 + 0.886058i −0.535561 + 0.844497i \(0.679900\pi\)
−0.999136 + 0.0415608i \(0.986767\pi\)
\(198\) 0 0
\(199\) −9.32443 + 16.1504i −0.660991 + 1.14487i 0.319364 + 0.947632i \(0.396531\pi\)
−0.980356 + 0.197239i \(0.936803\pi\)
\(200\) 0 0
\(201\) −1.12913 0.651904i −0.0796427 0.0459817i
\(202\) 0 0
\(203\) 6.16418i 0.432640i
\(204\) 0 0
\(205\) 2.13397 + 3.69615i 0.149043 + 0.258150i
\(206\) 0 0
\(207\) 9.22968 0.641507
\(208\) 0 0
\(209\) −1.85224 −0.128122
\(210\) 0 0
\(211\) −4.82235 8.35255i −0.331984 0.575013i 0.650917 0.759149i \(-0.274385\pi\)
−0.982901 + 0.184136i \(0.941051\pi\)
\(212\) 0 0
\(213\) 0.926728i 0.0634984i
\(214\) 0 0
\(215\) 8.26268 + 4.77046i 0.563510 + 0.325343i
\(216\) 0 0
\(217\) −2.41571 + 4.18414i −0.163989 + 0.284038i
\(218\) 0 0
\(219\) −0.917797 + 0.529891i −0.0620190 + 0.0358067i
\(220\) 0 0
\(221\) 4.11626 3.11756i 0.276890 0.209710i
\(222\) 0 0
\(223\) −1.00558 + 0.580573i −0.0673387 + 0.0388780i −0.533291 0.845932i \(-0.679045\pi\)
0.465953 + 0.884810i \(0.345712\pi\)
\(224\) 0 0
\(225\) −1.49551 + 2.59030i −0.0997005 + 0.172686i
\(226\) 0 0
\(227\) −23.5957 13.6230i −1.56610 0.904191i −0.996617 0.0821911i \(-0.973808\pi\)
−0.569488 0.822000i \(-0.692858\pi\)
\(228\) 0 0
\(229\) 24.3432i 1.60864i 0.594193 + 0.804322i \(0.297471\pi\)
−0.594193 + 0.804322i \(0.702529\pi\)
\(230\) 0 0
\(231\) 0.0678739 + 0.117561i 0.00446577 + 0.00773495i
\(232\) 0 0
\(233\) −23.0238 −1.50834 −0.754171 0.656678i \(-0.771961\pi\)
−0.754171 + 0.656678i \(0.771961\pi\)
\(234\) 0 0
\(235\) 3.46410 0.225973
\(236\) 0 0
\(237\) −0.0119616 0.0207181i −0.000776989 0.00134578i
\(238\) 0 0
\(239\) 23.7057i 1.53340i 0.642008 + 0.766698i \(0.278102\pi\)
−0.642008 + 0.766698i \(0.721898\pi\)
\(240\) 0 0
\(241\) −9.37968 5.41536i −0.604198 0.348834i 0.166493 0.986043i \(-0.446756\pi\)
−0.770691 + 0.637209i \(0.780089\pi\)
\(242\) 0 0
\(243\) 1.27453 2.20754i 0.0817609 0.141614i
\(244\) 0 0
\(245\) −5.47011 + 3.15817i −0.349472 + 0.201768i
\(246\) 0 0
\(247\) −2.32793 3.07367i −0.148123 0.195573i
\(248\) 0 0
\(249\) −0.465577 + 0.268801i −0.0295047 + 0.0170346i
\(250\) 0 0
\(251\) −0.560405 + 0.970649i −0.0353724 + 0.0612668i −0.883170 0.469054i \(-0.844595\pi\)
0.847797 + 0.530321i \(0.177928\pi\)
\(252\) 0 0
\(253\) 4.62870 + 2.67238i 0.291004 + 0.168011i
\(254\) 0 0
\(255\) 0.135748i 0.00850086i
\(256\) 0 0
\(257\) 8.31534 + 14.4026i 0.518697 + 0.898409i 0.999764 + 0.0217255i \(0.00691599\pi\)
−0.481067 + 0.876684i \(0.659751\pi\)
\(258\) 0 0
\(259\) 0.813267 0.0505340
\(260\) 0 0
\(261\) −22.2984 −1.38023
\(262\) 0 0
\(263\) −12.2510 21.2193i −0.755427 1.30844i −0.945162 0.326603i \(-0.894096\pi\)
0.189734 0.981836i \(-0.439237\pi\)
\(264\) 0 0
\(265\) 0.334308i 0.0205364i
\(266\) 0 0
\(267\) 0.377303 + 0.217836i 0.0230906 + 0.0133314i
\(268\) 0 0
\(269\) 3.26643 5.65763i 0.199158 0.344952i −0.749098 0.662460i \(-0.769513\pi\)
0.948256 + 0.317508i \(0.102846\pi\)
\(270\) 0 0
\(271\) 4.89831 2.82804i 0.297551 0.171791i −0.343791 0.939046i \(-0.611711\pi\)
0.641342 + 0.767255i \(0.278378\pi\)
\(272\) 0 0
\(273\) −0.109780 + 0.260386i −0.00664419 + 0.0157593i
\(274\) 0 0
\(275\) −1.50000 + 0.866025i −0.0904534 + 0.0522233i
\(276\) 0 0
\(277\) 1.85782 3.21784i 0.111626 0.193341i −0.804800 0.593546i \(-0.797728\pi\)
0.916426 + 0.400205i \(0.131061\pi\)
\(278\) 0 0
\(279\) 15.1357 + 8.73863i 0.906154 + 0.523168i
\(280\) 0 0
\(281\) 9.70447i 0.578920i 0.957190 + 0.289460i \(0.0934758\pi\)
−0.957190 + 0.289460i \(0.906524\pi\)
\(282\) 0 0
\(283\) −12.0988 20.9558i −0.719200 1.24569i −0.961317 0.275444i \(-0.911175\pi\)
0.242117 0.970247i \(-0.422158\pi\)
\(284\) 0 0
\(285\) −0.101365 −0.00600433
\(286\) 0 0
\(287\) −3.52890 −0.208305
\(288\) 0 0
\(289\) 7.47451 + 12.9462i 0.439677 + 0.761543i
\(290\) 0 0
\(291\) 0.903737i 0.0529780i
\(292\) 0 0
\(293\) −3.14218 1.81414i −0.183568 0.105983i 0.405400 0.914139i \(-0.367132\pi\)
−0.588968 + 0.808156i \(0.700466\pi\)
\(294\) 0 0
\(295\) −5.76225 + 9.98052i −0.335491 + 0.581088i
\(296\) 0 0
\(297\) 0.851811 0.491793i 0.0494271 0.0285367i
\(298\) 0 0
\(299\) 1.38279 + 11.0398i 0.0799689 + 0.638446i
\(300\) 0 0
\(301\) −6.83190 + 3.94440i −0.393784 + 0.227351i
\(302\) 0 0
\(303\) 0.274952 0.476231i 0.0157956 0.0273588i
\(304\) 0 0
\(305\) 2.35255 + 1.35824i 0.134707 + 0.0777729i
\(306\) 0 0
\(307\) 9.40129i 0.536560i −0.963341 0.268280i \(-0.913545\pi\)
0.963341 0.268280i \(-0.0864552\pi\)
\(308\) 0 0
\(309\) 0.477538 + 0.827121i 0.0271662 + 0.0470532i
\(310\) 0 0
\(311\) 25.5370 1.44807 0.724034 0.689764i \(-0.242286\pi\)
0.724034 + 0.689764i \(0.242286\pi\)
\(312\) 0 0
\(313\) 5.25656 0.297118 0.148559 0.988904i \(-0.452536\pi\)
0.148559 + 0.988904i \(0.452536\pi\)
\(314\) 0 0
\(315\) −1.23654 2.14176i −0.0696713 0.120674i
\(316\) 0 0
\(317\) 14.1536i 0.794947i −0.917614 0.397474i \(-0.869887\pi\)
0.917614 0.397474i \(-0.130113\pi\)
\(318\) 0 0
\(319\) −11.1827 6.45632i −0.626110 0.361485i
\(320\) 0 0
\(321\) 0.771550 1.33636i 0.0430637 0.0745885i
\(322\) 0 0
\(323\) −1.32632 + 0.765750i −0.0737983 + 0.0426075i
\(324\) 0 0
\(325\) −3.32235 1.40072i −0.184291 0.0776980i
\(326\) 0 0
\(327\) −0.256920 + 0.148333i −0.0142077 + 0.00820282i
\(328\) 0 0
\(329\) −1.43213 + 2.48052i −0.0789557 + 0.136755i
\(330\) 0 0
\(331\) −16.0945 9.29214i −0.884632 0.510742i −0.0124490 0.999923i \(-0.503963\pi\)
−0.872183 + 0.489180i \(0.837296\pi\)
\(332\) 0 0
\(333\) 2.94192i 0.161216i
\(334\) 0 0
\(335\) 6.87752 + 11.9122i 0.375759 + 0.650834i
\(336\) 0 0
\(337\) 22.4060 1.22053 0.610267 0.792196i \(-0.291062\pi\)
0.610267 + 0.792196i \(0.291062\pi\)
\(338\) 0 0
\(339\) 0.964061 0.0523606
\(340\) 0 0
\(341\) 5.06040 + 8.76488i 0.274036 + 0.474645i
\(342\) 0 0
\(343\) 11.0105i 0.594509i
\(344\) 0 0
\(345\) 0.253309 + 0.146248i 0.0136377 + 0.00787372i
\(346\) 0 0
\(347\) −10.0862 + 17.4699i −0.541457 + 0.937831i 0.457364 + 0.889280i \(0.348794\pi\)
−0.998821 + 0.0485514i \(0.984540\pi\)
\(348\) 0 0
\(349\) 24.7634 14.2972i 1.32556 0.765310i 0.340947 0.940083i \(-0.389252\pi\)
0.984609 + 0.174773i \(0.0559192\pi\)
\(350\) 0 0
\(351\) 1.88667 + 0.795432i 0.100703 + 0.0424570i
\(352\) 0 0
\(353\) 9.66167 5.57817i 0.514239 0.296896i −0.220336 0.975424i \(-0.570715\pi\)
0.734574 + 0.678528i \(0.237382\pi\)
\(354\) 0 0
\(355\) 4.88845 8.46704i 0.259452 0.449384i
\(356\) 0 0
\(357\) 0.0972040 + 0.0561207i 0.00514458 + 0.00297022i
\(358\) 0 0
\(359\) 11.0490i 0.583145i 0.956549 + 0.291572i \(0.0941784\pi\)
−0.956549 + 0.291572i \(0.905822\pi\)
\(360\) 0 0
\(361\) −8.92820 15.4641i −0.469905 0.813900i
\(362\) 0 0
\(363\) −0.758301 −0.0398005
\(364\) 0 0
\(365\) 11.1806 0.585219
\(366\) 0 0
\(367\) −12.2026 21.1355i −0.636970 1.10326i −0.986094 0.166188i \(-0.946854\pi\)
0.349124 0.937076i \(-0.386479\pi\)
\(368\) 0 0
\(369\) 12.7655i 0.664545i
\(370\) 0 0
\(371\) 0.239385 + 0.138209i 0.0124283 + 0.00717546i
\(372\) 0 0
\(373\) 2.65566 4.59974i 0.137505 0.238165i −0.789047 0.614333i \(-0.789425\pi\)
0.926552 + 0.376168i \(0.122758\pi\)
\(374\) 0 0
\(375\) −0.0820885 + 0.0473938i −0.00423903 + 0.00244740i
\(376\) 0 0
\(377\) −3.34074 26.6714i −0.172057 1.37365i
\(378\) 0 0
\(379\) 29.0469 16.7703i 1.49204 0.861430i 0.492082 0.870549i \(-0.336236\pi\)
0.999958 + 0.00911888i \(0.00290267\pi\)
\(380\) 0 0
\(381\) −0.282847 + 0.489906i −0.0144907 + 0.0250986i
\(382\) 0 0
\(383\) 20.6138 + 11.9014i 1.05331 + 0.608131i 0.923575 0.383417i \(-0.125253\pi\)
0.129739 + 0.991548i \(0.458586\pi\)
\(384\) 0 0
\(385\) 1.43213i 0.0729879i
\(386\) 0 0
\(387\) 14.2685 + 24.7138i 0.725310 + 1.25627i
\(388\) 0 0
\(389\) −26.2787 −1.33238 −0.666191 0.745781i \(-0.732077\pi\)
−0.666191 + 0.745781i \(0.732077\pi\)
\(390\) 0 0
\(391\) 4.41926 0.223492
\(392\) 0 0
\(393\) 0.788003 + 1.36486i 0.0397495 + 0.0688482i
\(394\) 0 0
\(395\) 0.252387i 0.0126990i
\(396\) 0 0
\(397\) 28.8317 + 16.6460i 1.44702 + 0.835439i 0.998303 0.0582340i \(-0.0185469\pi\)
0.448719 + 0.893673i \(0.351880\pi\)
\(398\) 0 0
\(399\) 0.0419062 0.0725836i 0.00209793 0.00363373i
\(400\) 0 0
\(401\) 12.2709 7.08460i 0.612779 0.353788i −0.161273 0.986910i \(-0.551560\pi\)
0.774052 + 0.633122i \(0.218227\pi\)
\(402\) 0 0
\(403\) −8.18476 + 19.4133i −0.407712 + 0.967046i
\(404\) 0 0
\(405\) −7.72427 + 4.45961i −0.383822 + 0.221600i
\(406\) 0 0
\(407\) 0.851811 1.47538i 0.0422227 0.0731319i
\(408\) 0 0
\(409\) 5.93213 + 3.42491i 0.293325 + 0.169351i 0.639440 0.768841i \(-0.279166\pi\)
−0.346116 + 0.938192i \(0.612499\pi\)
\(410\) 0 0
\(411\) 0.0383462i 0.00189148i
\(412\) 0 0
\(413\) −4.76445 8.25227i −0.234443 0.406068i
\(414\) 0 0
\(415\) 5.67165 0.278410
\(416\) 0 0
\(417\) 0.883073 0.0432443
\(418\) 0 0
\(419\) 8.19109 + 14.1874i 0.400161 + 0.693099i 0.993745 0.111673i \(-0.0356209\pi\)
−0.593584 + 0.804772i \(0.702288\pi\)
\(420\) 0 0
\(421\) 21.7045i 1.05781i −0.848681 0.528906i \(-0.822603\pi\)
0.848681 0.528906i \(-0.177397\pi\)
\(422\) 0 0
\(423\) 8.97305 + 5.18059i 0.436284 + 0.251889i
\(424\) 0 0
\(425\) −0.716063 + 1.24026i −0.0347342 + 0.0601613i
\(426\) 0 0
\(427\) −1.94518 + 1.12305i −0.0941337 + 0.0543481i
\(428\) 0 0
\(429\) 0.357393 + 0.471883i 0.0172551 + 0.0227827i
\(430\) 0 0
\(431\) 28.0495 16.1944i 1.35110 0.780056i 0.362693 0.931909i \(-0.381857\pi\)
0.988403 + 0.151853i \(0.0485240\pi\)
\(432\) 0 0
\(433\) 14.3987 24.9393i 0.691959 1.19851i −0.279236 0.960223i \(-0.590081\pi\)
0.971195 0.238286i \(-0.0765855\pi\)
\(434\) 0 0
\(435\) −0.611979 0.353326i −0.0293422 0.0169407i
\(436\) 0 0
\(437\) 3.29992i 0.157857i
\(438\) 0 0
\(439\) −8.79992 15.2419i −0.419997 0.727457i 0.575941 0.817491i \(-0.304636\pi\)
−0.995939 + 0.0900341i \(0.971302\pi\)
\(440\) 0 0
\(441\) −18.8923 −0.899632
\(442\) 0 0
\(443\) −14.4043 −0.684370 −0.342185 0.939633i \(-0.611167\pi\)
−0.342185 + 0.939633i \(0.611167\pi\)
\(444\) 0 0
\(445\) −2.29815 3.98052i −0.108943 0.188695i
\(446\) 0 0
\(447\) 1.03013i 0.0487236i
\(448\) 0 0
\(449\) −2.58821 1.49430i −0.122145 0.0705206i 0.437683 0.899130i \(-0.355799\pi\)
−0.559828 + 0.828609i \(0.689133\pi\)
\(450\) 0 0
\(451\) −3.69615 + 6.40192i −0.174045 + 0.301455i
\(452\) 0 0
\(453\) 0.0813509 0.0469680i 0.00382220 0.00220675i
\(454\) 0 0
\(455\) 2.37653 1.79992i 0.111413 0.0843818i
\(456\) 0 0
\(457\) −23.0540 + 13.3102i −1.07842 + 0.622626i −0.930470 0.366369i \(-0.880601\pi\)
−0.147950 + 0.988995i \(0.547267\pi\)
\(458\) 0 0
\(459\) 0.406634 0.704310i 0.0189800 0.0328744i
\(460\) 0 0
\(461\) 7.26488 + 4.19438i 0.338359 + 0.195352i 0.659546 0.751664i \(-0.270748\pi\)
−0.321187 + 0.947016i \(0.604082\pi\)
\(462\) 0 0
\(463\) 21.3014i 0.989960i −0.868904 0.494980i \(-0.835175\pi\)
0.868904 0.494980i \(-0.164825\pi\)
\(464\) 0 0
\(465\) 0.276934 + 0.479664i 0.0128425 + 0.0222439i
\(466\) 0 0
\(467\) 2.12392 0.0982833 0.0491417 0.998792i \(-0.484351\pi\)
0.0491417 + 0.998792i \(0.484351\pi\)
\(468\) 0 0
\(469\) −11.3732 −0.525165
\(470\) 0 0
\(471\) 0.832846 + 1.44253i 0.0383755 + 0.0664684i
\(472\) 0 0
\(473\) 16.5254i 0.759837i
\(474\) 0 0
\(475\) 0.926118 + 0.534695i 0.0424932 + 0.0245335i
\(476\) 0 0
\(477\) 0.499960 0.865955i 0.0228916 0.0396494i
\(478\) 0 0
\(479\) −25.1617 + 14.5271i −1.14967 + 0.663762i −0.948806 0.315858i \(-0.897708\pi\)
−0.200862 + 0.979619i \(0.564374\pi\)
\(480\) 0 0
\(481\) 3.51887 0.440759i 0.160447 0.0200969i
\(482\) 0 0
\(483\) −0.209445 + 0.120923i −0.00953010 + 0.00550220i
\(484\) 0 0
\(485\) 4.76717 8.25698i 0.216466 0.374930i
\(486\) 0 0
\(487\) −26.2570 15.1595i −1.18982 0.686941i −0.231552 0.972822i \(-0.574380\pi\)
−0.958265 + 0.285881i \(0.907714\pi\)
\(488\) 0 0
\(489\) 1.63811i 0.0740781i
\(490\) 0 0
\(491\) 19.0759 + 33.0405i 0.860884 + 1.49110i 0.871076 + 0.491148i \(0.163422\pi\)
−0.0101919 + 0.999948i \(0.503244\pi\)
\(492\) 0 0
\(493\) −10.6767 −0.480853
\(494\) 0 0
\(495\) −5.18059 −0.232850
\(496\) 0 0
\(497\) 4.04196 + 7.00087i 0.181306 + 0.314032i
\(498\) 0 0
\(499\) 16.5179i 0.739444i −0.929142 0.369722i \(-0.879453\pi\)
0.929142 0.369722i \(-0.120547\pi\)
\(500\) 0 0
\(501\) −0.251154 0.145004i −0.0112207 0.00647829i
\(502\) 0 0
\(503\) −5.88081 + 10.1859i −0.262212 + 0.454165i −0.966830 0.255423i \(-0.917785\pi\)
0.704617 + 0.709588i \(0.251119\pi\)
\(504\) 0 0
\(505\) −5.02419 + 2.90072i −0.223574 + 0.129080i
\(506\) 0 0
\(507\) −0.333882 + 1.18614i −0.0148282 + 0.0526785i
\(508\) 0 0
\(509\) 27.5930 15.9308i 1.22304 0.706122i 0.257474 0.966285i \(-0.417110\pi\)
0.965565 + 0.260164i \(0.0837765\pi\)
\(510\) 0 0
\(511\) −4.62227 + 8.00601i −0.204477 + 0.354165i
\(512\) 0 0
\(513\) −0.525918 0.303639i −0.0232199 0.0134060i
\(514\) 0 0
\(515\) 10.0760i 0.444000i
\(516\) 0 0
\(517\) 3.00000 + 5.19615i 0.131940 + 0.228527i
\(518\) 0 0
\(519\) −0.324184 −0.0142301
\(520\) 0 0
\(521\) −19.5013 −0.854367 −0.427183 0.904165i \(-0.640494\pi\)
−0.427183 + 0.904165i \(0.640494\pi\)
\(522\) 0 0
\(523\) 22.2830 + 38.5952i 0.974365 + 1.68765i 0.682014 + 0.731340i \(0.261105\pi\)
0.292352 + 0.956311i \(0.405562\pi\)
\(524\) 0 0
\(525\) 0.0783740i 0.00342052i
\(526\) 0 0
\(527\) 7.24714 + 4.18414i 0.315690 + 0.182264i
\(528\) 0 0
\(529\) 6.73891 11.6721i 0.292996 0.507484i
\(530\) 0 0
\(531\) −29.8519 + 17.2350i −1.29546 + 0.747935i
\(532\) 0 0
\(533\) −15.2690 + 1.91253i −0.661374 + 0.0828407i
\(534\) 0 0
\(535\) −14.0985 + 8.13977i −0.609531 + 0.351913i
\(536\) 0 0
\(537\) 0.492051 0.852257i 0.0212336 0.0367776i
\(538\) 0 0
\(539\) −9.47451 5.47011i −0.408096 0.235614i
\(540\) 0 0
\(541\) 3.74450i 0.160989i −0.996755 0.0804943i \(-0.974350\pi\)
0.996755 0.0804943i \(-0.0256499\pi\)
\(542\) 0 0
\(543\) −0.490486 0.849547i −0.0210488 0.0364576i
\(544\) 0 0
\(545\) 3.12979 0.134066
\(546\) 0 0
\(547\) 38.3803 1.64102 0.820511 0.571630i \(-0.193689\pi\)
0.820511 + 0.571630i \(0.193689\pi\)
\(548\) 0 0
\(549\) 4.06253 + 7.03651i 0.173385 + 0.300311i
\(550\) 0 0
\(551\) 7.97242i 0.339637i
\(552\) 0 0
\(553\) −0.180725 0.104342i −0.00768522 0.00443706i
\(554\) 0 0
\(555\) 0.0466159 0.0807411i 0.00197873 0.00342727i
\(556\) 0 0
\(557\) −23.0763 + 13.3231i −0.977772 + 0.564517i −0.901597 0.432577i \(-0.857604\pi\)
−0.0761755 + 0.997094i \(0.524271\pi\)
\(558\) 0 0
\(559\) −27.4228 + 20.7694i −1.15986 + 0.878452i
\(560\) 0 0
\(561\) 0.203622 0.117561i 0.00859691 0.00496343i
\(562\) 0 0
\(563\) −8.34675 + 14.4570i −0.351774 + 0.609290i −0.986560 0.163398i \(-0.947755\pi\)
0.634787 + 0.772687i \(0.281088\pi\)
\(564\) 0 0
\(565\) −8.80813 5.08538i −0.370561 0.213943i
\(566\) 0 0
\(567\) 7.37475i 0.309710i
\(568\) 0 0
\(569\) −21.9620 38.0393i −0.920694 1.59469i −0.798344 0.602202i \(-0.794290\pi\)
−0.122350 0.992487i \(-0.539043\pi\)
\(570\) 0 0
\(571\) −11.4641 −0.479758 −0.239879 0.970803i \(-0.577108\pi\)
−0.239879 + 0.970803i \(0.577108\pi\)
\(572\) 0 0
\(573\) 1.46977 0.0614004
\(574\) 0 0
\(575\) −1.54290 2.67238i −0.0643434 0.111446i
\(576\) 0 0
\(577\) 44.9354i 1.87069i −0.353743 0.935343i \(-0.615091\pi\)
0.353743 0.935343i \(-0.384909\pi\)
\(578\) 0 0
\(579\) 0.457256 + 0.263997i 0.0190029 + 0.0109713i
\(580\) 0 0
\(581\) −2.34477 + 4.06126i −0.0972773 + 0.168489i
\(582\) 0 0
\(583\) 0.501461 0.289519i 0.0207684 0.0119906i
\(584\) 0 0
\(585\) −6.51107 8.59687i −0.269200 0.355437i
\(586\) 0 0
\(587\) −21.2364 + 12.2608i −0.876520 + 0.506059i −0.869509 0.493916i \(-0.835565\pi\)
−0.00701059 + 0.999975i \(0.502232\pi\)
\(588\) 0 0
\(589\) 3.12436 5.41154i 0.128737 0.222979i
\(590\) 0 0
\(591\) −2.04177 1.17882i −0.0839873 0.0484901i
\(592\) 0 0
\(593\) 18.7655i 0.770607i 0.922790 + 0.385303i \(0.125903\pi\)
−0.922790 + 0.385303i \(0.874097\pi\)
\(594\) 0 0
\(595\) −0.592068 1.02549i −0.0242724 0.0420411i
\(596\) 0 0
\(597\) −1.76768 −0.0723464
\(598\) 0 0
\(599\) −35.9293 −1.46803 −0.734015 0.679133i \(-0.762356\pi\)
−0.734015 + 0.679133i \(0.762356\pi\)
\(600\) 0 0
\(601\) 19.8863 + 34.4441i 0.811179 + 1.40500i 0.912039 + 0.410103i \(0.134507\pi\)
−0.100860 + 0.994901i \(0.532160\pi\)
\(602\) 0 0
\(603\) 41.1415i 1.67541i
\(604\) 0 0
\(605\) 6.92820 + 4.00000i 0.281672 + 0.162623i
\(606\) 0 0
\(607\) −16.7306 + 28.9783i −0.679076 + 1.17619i 0.296184 + 0.955131i \(0.404286\pi\)
−0.975260 + 0.221063i \(0.929047\pi\)
\(608\) 0 0
\(609\) 0.506008 0.292144i 0.0205045 0.0118383i
\(610\) 0 0
\(611\) −4.85224 + 11.5089i −0.196300 + 0.465602i
\(612\) 0 0
\(613\) 17.1212 9.88495i 0.691520 0.399249i −0.112661 0.993633i \(-0.535937\pi\)
0.804181 + 0.594384i \(0.202604\pi\)
\(614\) 0 0
\(615\) −0.202274 + 0.350349i −0.00815649 + 0.0141275i
\(616\) 0 0
\(617\) −16.8950 9.75436i −0.680169 0.392696i 0.119750 0.992804i \(-0.461791\pi\)
−0.799919 + 0.600108i \(0.795124\pi\)
\(618\) 0 0
\(619\) 40.4640i 1.62639i −0.581994 0.813193i \(-0.697727\pi\)
0.581994 0.813193i \(-0.302273\pi\)
\(620\) 0 0
\(621\) 0.876173 + 1.51758i 0.0351596 + 0.0608983i
\(622\) 0 0
\(623\) 3.80040 0.152260
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −0.0877845 0.152047i −0.00350578 0.00607218i
\(628\) 0 0
\(629\) 1.40862i 0.0561653i
\(630\) 0 0
\(631\) −16.9707 9.79806i −0.675594 0.390054i 0.122599 0.992456i \(-0.460877\pi\)
−0.798193 + 0.602402i \(0.794211\pi\)
\(632\) 0 0
\(633\) 0.457099 0.791718i 0.0181680 0.0314680i
\(634\) 0 0
\(635\) 5.16846 2.98401i 0.205104 0.118417i
\(636\) 0 0
\(637\) −2.83044 22.5973i −0.112146 0.895338i
\(638\) 0 0
\(639\) 25.3250 14.6214i 1.00184 0.578414i
\(640\) 0 0
\(641\) 15.5238 26.8881i 0.613155 1.06202i −0.377550 0.925989i \(-0.623233\pi\)
0.990705 0.136026i \(-0.0434332\pi\)
\(642\) 0 0
\(643\) −5.14990 2.97329i −0.203092 0.117255i 0.395005 0.918679i \(-0.370743\pi\)
−0.598097 + 0.801424i \(0.704076\pi\)
\(644\) 0 0
\(645\) 0.904361i 0.0356092i
\(646\) 0 0
\(647\) 21.2510 + 36.8078i 0.835462 + 1.44706i 0.893654 + 0.448757i \(0.148133\pi\)
−0.0581916 + 0.998305i \(0.518533\pi\)
\(648\) 0 0
\(649\) −19.9610 −0.783539
\(650\) 0 0
\(651\) −0.457959 −0.0179488
\(652\) 0 0
\(653\) 15.3054 + 26.5097i 0.598945 + 1.03740i 0.992977 + 0.118307i \(0.0377467\pi\)
−0.394032 + 0.919097i \(0.628920\pi\)
\(654\) 0 0
\(655\) 16.6267i 0.649660i
\(656\) 0 0
\(657\) 28.9610 + 16.7207i 1.12988 + 0.652335i
\(658\) 0 0
\(659\) 12.7191 22.0302i 0.495467 0.858175i −0.504519 0.863401i \(-0.668330\pi\)
0.999986 + 0.00522582i \(0.00166344\pi\)
\(660\) 0 0
\(661\) −0.288909 + 0.166802i −0.0112373 + 0.00648784i −0.505608 0.862763i \(-0.668732\pi\)
0.494371 + 0.869251i \(0.335398\pi\)
\(662\) 0 0
\(663\) 0.451001 + 0.190145i 0.0175154 + 0.00738461i
\(664\) 0 0
\(665\) −0.765750 + 0.442106i −0.0296945 + 0.0171441i
\(666\) 0 0
\(667\) 11.5025 19.9229i 0.445379 0.771419i
\(668\) 0 0
\(669\) −0.0953167 0.0550311i −0.00368516 0.00212763i
\(670\) 0 0
\(671\) 4.70510i 0.181638i
\(672\) 0 0
\(673\) 4.90706 + 8.49928i 0.189153 + 0.327623i 0.944968 0.327162i \(-0.106092\pi\)
−0.755815 + 0.654785i \(0.772759\pi\)
\(674\) 0 0
\(675\) −0.567874 −0.0218575
\(676\) 0 0
\(677\) −23.2414 −0.893241 −0.446620 0.894724i \(-0.647373\pi\)
−0.446620 + 0.894724i \(0.647373\pi\)
\(678\) 0 0
\(679\) 3.94168 + 6.82719i 0.151268 + 0.262004i
\(680\) 0 0
\(681\) 2.58258i 0.0989648i
\(682\) 0 0
\(683\) 4.56144 + 2.63355i 0.174539 + 0.100770i 0.584724 0.811232i \(-0.301203\pi\)
−0.410186 + 0.912002i \(0.634536\pi\)
\(684\) 0 0
\(685\) −0.202274 + 0.350349i −0.00772850 + 0.0133862i
\(686\) 0 0
\(687\) −1.99830 + 1.15372i −0.0762398 + 0.0440171i
\(688\) 0 0
\(689\) 1.11069 + 0.468271i 0.0423138 + 0.0178397i
\(690\) 0 0
\(691\) 17.1334 9.89199i 0.651787 0.376309i −0.137354 0.990522i \(-0.543860\pi\)
0.789140 + 0.614213i \(0.210526\pi\)
\(692\) 0 0
\(693\) 2.14176 3.70963i 0.0813586 0.140917i
\(694\) 0 0
\(695\) −8.06819 4.65817i −0.306044 0.176694i
\(696\) 0 0
\(697\) 6.11224i 0.231518i
\(698\) 0 0
\(699\) −1.09119 1.88999i −0.0412725 0.0714861i
\(700\) 0 0
\(701\) 18.1256 0.684595 0.342298 0.939592i \(-0.388795\pi\)
0.342298 + 0.939592i \(0.388795\pi\)
\(702\) 0 0
\(703\) −1.05184 −0.0396708
\(704\) 0 0
\(705\) 0.164177 + 0.284363i 0.00618326 + 0.0107097i
\(706\) 0 0
\(707\) 4.79685i 0.180404i
\(708\) 0 0
\(709\) −22.3514 12.9046i −0.839424 0.484642i 0.0176445 0.999844i \(-0.494383\pi\)
−0.857068 + 0.515203i \(0.827717\pi\)
\(710\) 0 0
\(711\) −0.377447 + 0.653758i −0.0141554 + 0.0245178i
\(712\) 0 0
\(713\) −15.6154 + 9.01556i −0.584802 + 0.337635i
\(714\) 0 0
\(715\) −0.776156 6.19658i −0.0290266 0.231739i
\(716\) 0 0
\(717\) −1.94597 + 1.12350i −0.0726734 + 0.0419580i
\(718\) 0 0
\(719\) −4.51338 + 7.81741i −0.168321 + 0.291540i −0.937830 0.347096i \(-0.887168\pi\)
0.769509 + 0.638636i \(0.220501\pi\)
\(720\) 0 0
\(721\) 7.21503 + 4.16560i 0.268702 + 0.155135i
\(722\) 0 0
\(723\) 1.02662i 0.0381803i
\(724\) 0 0
\(725\) 3.72756 + 6.45632i 0.138438 + 0.239782i
\(726\) 0 0
\(727\) 24.8934 0.923245 0.461623 0.887076i \(-0.347267\pi\)
0.461623 + 0.887076i \(0.347267\pi\)
\(728\) 0 0
\(729\) −26.5160 −0.982075
\(730\) 0 0
\(731\) 6.83190 + 11.8332i 0.252687 + 0.437667i
\(732\) 0 0
\(733\) 13.2793i 0.490484i −0.969462 0.245242i \(-0.921133\pi\)
0.969462 0.245242i \(-0.0788674\pi\)
\(734\) 0 0
\(735\) −0.518498 0.299355i −0.0191251 0.0110419i
\(736\) 0 0
\(737\) −11.9122 + 20.6326i −0.438792 + 0.760010i
\(738\) 0 0
\(739\) 16.9656 9.79508i 0.624089 0.360318i −0.154370 0.988013i \(-0.549335\pi\)
0.778459 + 0.627695i \(0.216002\pi\)
\(740\) 0 0
\(741\) 0.141984 0.336769i 0.00521590 0.0123715i
\(742\) 0 0
\(743\) 44.3804 25.6230i 1.62816 0.940017i 0.643515 0.765434i \(-0.277475\pi\)
0.984642 0.174583i \(-0.0558578\pi\)
\(744\) 0 0
\(745\) 5.43390 9.41179i 0.199083 0.344821i
\(746\) 0 0
\(747\) 14.6912 + 8.48199i 0.537524 + 0.310340i
\(748\) 0 0
\(749\) 13.4606i 0.491838i
\(750\) 0 0
\(751\) −10.5992 18.3584i −0.386772 0.669908i 0.605242 0.796042i \(-0.293077\pi\)
−0.992013 + 0.126134i \(0.959743\pi\)
\(752\) 0 0
\(753\) −0.106239 −0.00387156
\(754\) 0 0
\(755\) −0.991015 −0.0360667
\(756\) 0 0
\(757\) 16.4747 + 28.5350i 0.598783 + 1.03712i 0.993001 + 0.118106i \(0.0376823\pi\)
−0.394218 + 0.919017i \(0.628984\pi\)
\(758\) 0 0
\(759\) 0.506618i 0.0183891i
\(760\) 0 0
\(761\) 45.2367 + 26.1174i 1.63983 + 0.946756i 0.980891 + 0.194559i \(0.0623277\pi\)
0.658939 + 0.752197i \(0.271006\pi\)
\(762\) 0 0
\(763\) −1.29392 + 2.24113i −0.0468429 + 0.0811343i
\(764\) 0 0
\(765\) −3.70963 + 2.14176i −0.134122 + 0.0774353i
\(766\) 0 0
\(767\) −25.0874 33.1241i −0.905854 1.19604i
\(768\) 0 0
\(769\) 23.2717 13.4359i 0.839200 0.484513i −0.0177920 0.999842i \(-0.505664\pi\)
0.856992 + 0.515329i \(0.172330\pi\)
\(770\) 0 0
\(771\) −0.788191 + 1.36519i −0.0283860 + 0.0491660i
\(772\) 0 0
\(773\) 10.3533 + 5.97746i 0.372381 + 0.214994i 0.674498 0.738276i \(-0.264360\pi\)
−0.302117 + 0.953271i \(0.597693\pi\)
\(774\) 0 0
\(775\) 5.84325i 0.209896i
\(776\) 0 0
\(777\) 0.0385438 + 0.0667598i 0.00138275 + 0.00239500i
\(778\) 0 0
\(779\) 4.56410 0.163526
\(780\) 0 0
\(781\) 16.9341 0.605949
\(782\) 0 0
\(783\) −2.11678 3.66638i −0.0756477 0.131026i
\(784\) 0 0
\(785\) 17.5729i 0.627204i
\(786\) 0 0
\(787\) 29.8724 + 17.2468i 1.06484 + 0.614783i 0.926766 0.375639i \(-0.122577\pi\)
0.138070 + 0.990422i \(0.455910\pi\)
\(788\) 0 0
\(789\) 1.16124 2.01133i 0.0413413 0.0716051i
\(790\) 0 0
\(791\) 7.28290 4.20479i 0.258950 0.149505i
\(792\) 0 0
\(793\) −7.80782 + 5.91346i −0.277264 + 0.209993i
\(794\) 0 0