Properties

Label 950.2.e.n.201.5
Level $950$
Weight $2$
Character 950.201
Analytic conductor $7.586$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.58578819202\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} + \cdots)\)
Defining polynomial: \(x^{10} + 10 x^{8} - 12 x^{7} + 85 x^{6} - 70 x^{5} + 186 x^{4} - 110 x^{3} + 285 x^{2} - 150 x + 100\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 190)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 201.5
Root \(1.17030 - 2.02701i\) of defining polynomial
Character \(\chi\) \(=\) 950.201
Dual form 950.2.e.n.501.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(1.17030 - 2.02701i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.17030 + 2.02701i) q^{6} +1.34059 q^{7} +1.00000 q^{8} +(-1.23919 - 2.14634i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(1.17030 - 2.02701i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.17030 + 2.02701i) q^{6} +1.34059 q^{7} +1.00000 q^{8} +(-1.23919 - 2.14634i) q^{9} +3.25749 q^{11} -2.34059 q^{12} +(0.745938 + 1.29200i) q^{13} +(-0.670297 + 1.16099i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(3.29230 - 5.70242i) q^{17} +2.47838 q^{18} +(-1.25821 + 4.17336i) q^{19} +(1.56889 - 2.71740i) q^{21} +(-1.62875 + 2.82107i) q^{22} +(1.07564 + 1.86306i) q^{23} +(1.17030 - 2.02701i) q^{24} -1.49188 q^{26} +1.22089 q^{27} +(-0.670297 - 1.16099i) q^{28} +(-2.65543 - 4.59933i) q^{29} -2.76561 q^{31} +(-0.500000 - 0.866025i) q^{32} +(3.81223 - 6.60298i) q^{33} +(3.29230 + 5.70242i) q^{34} +(-1.23919 + 2.14634i) q^{36} +5.27098 q^{37} +(-2.98513 - 3.17632i) q^{38} +3.49188 q^{39} +(-2.79230 + 4.83640i) q^{41} +(1.56889 + 2.71740i) q^{42} +(3.81898 - 6.61466i) q^{43} +(-1.62875 - 2.82107i) q^{44} -2.15128 q^{46} +(-0.465912 - 0.806983i) q^{47} +(1.17030 + 2.02701i) q^{48} -5.20281 q^{49} +(-7.70593 - 13.3471i) q^{51} +(0.745938 - 1.29200i) q^{52} +(4.54498 + 7.87214i) q^{53} +(-0.610447 + 1.05732i) q^{54} +1.34059 q^{56} +(6.98698 + 7.43448i) q^{57} +5.31085 q^{58} +(0.0837650 - 0.145085i) q^{59} +(-5.84474 - 10.1234i) q^{61} +(1.38281 - 2.39509i) q^{62} +(-1.66125 - 2.87738i) q^{63} +1.00000 q^{64} +(3.81223 + 6.60298i) q^{66} +(-6.53563 - 11.3201i) q^{67} -6.58459 q^{68} +5.03528 q^{69} +(-3.59466 + 6.22613i) q^{71} +(-1.23919 - 2.14634i) q^{72} +(7.62615 - 13.2089i) q^{73} +(-2.63549 + 4.56480i) q^{74} +(4.24334 - 0.997038i) q^{76} +4.36697 q^{77} +(-1.74594 + 3.02405i) q^{78} +(7.75423 - 13.4307i) q^{79} +(5.14638 - 8.91380i) q^{81} +(-2.79230 - 4.83640i) q^{82} -0.313611 q^{83} -3.13779 q^{84} +(3.81898 + 6.61466i) q^{86} -12.4306 q^{87} +3.25749 q^{88} +(4.90689 + 8.49898i) q^{89} +(1.00000 + 1.73205i) q^{91} +(1.07564 - 1.86306i) q^{92} +(-3.23659 + 5.60594i) q^{93} +0.931824 q^{94} -2.34059 q^{96} +(-6.01504 + 10.4184i) q^{97} +(2.60140 - 4.50576i) q^{98} +(-4.03665 - 6.99169i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 5q^{2} - 5q^{4} - 10q^{7} + 10q^{8} - 5q^{9} + O(q^{10}) \) \( 10q - 5q^{2} - 5q^{4} - 10q^{7} + 10q^{8} - 5q^{9} - 6q^{11} - 2q^{13} + 5q^{14} - 5q^{16} + 4q^{17} + 10q^{18} + 11q^{19} + 20q^{21} + 3q^{22} + 13q^{23} + 4q^{26} + 36q^{27} + 5q^{28} + 2q^{29} - 8q^{31} - 5q^{32} + 2q^{33} + 4q^{34} - 5q^{36} + 10q^{37} - 13q^{38} + 16q^{39} + q^{41} + 20q^{42} + 3q^{44} - 26q^{46} - 10q^{47} - 20q^{49} + 4q^{51} - 2q^{52} + 5q^{53} - 18q^{54} - 10q^{56} - 10q^{57} - 4q^{58} + 22q^{59} - 2q^{61} + 4q^{62} + 23q^{63} + 10q^{64} + 2q^{66} + 4q^{67} - 8q^{68} - 24q^{69} - 22q^{71} - 5q^{72} + 26q^{73} - 5q^{74} + 2q^{76} + 10q^{77} - 8q^{78} + 2q^{79} - 5q^{81} + q^{82} + 12q^{83} - 40q^{84} - 20q^{87} - 6q^{88} - q^{89} + 10q^{91} + 13q^{92} + 6q^{93} + 20q^{94} + 8q^{97} + 10q^{98} + 13q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) 1.17030 2.02701i 0.675671 1.17030i −0.300601 0.953750i \(-0.597187\pi\)
0.976272 0.216547i \(-0.0694795\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0 0
\(6\) 1.17030 + 2.02701i 0.477772 + 0.827525i
\(7\) 1.34059 0.506697 0.253349 0.967375i \(-0.418468\pi\)
0.253349 + 0.967375i \(0.418468\pi\)
\(8\) 1.00000 0.353553
\(9\) −1.23919 2.14634i −0.413064 0.715448i
\(10\) 0 0
\(11\) 3.25749 0.982170 0.491085 0.871112i \(-0.336600\pi\)
0.491085 + 0.871112i \(0.336600\pi\)
\(12\) −2.34059 −0.675671
\(13\) 0.745938 + 1.29200i 0.206886 + 0.358337i 0.950732 0.310014i \(-0.100334\pi\)
−0.743846 + 0.668351i \(0.767000\pi\)
\(14\) −0.670297 + 1.16099i −0.179144 + 0.310287i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 3.29230 5.70242i 0.798499 1.38304i −0.122094 0.992519i \(-0.538961\pi\)
0.920593 0.390523i \(-0.127706\pi\)
\(18\) 2.47838 0.584161
\(19\) −1.25821 + 4.17336i −0.288653 + 0.957434i
\(20\) 0 0
\(21\) 1.56889 2.71740i 0.342361 0.592986i
\(22\) −1.62875 + 2.82107i −0.347250 + 0.601454i
\(23\) 1.07564 + 1.86306i 0.224287 + 0.388476i 0.956105 0.293024i \(-0.0946615\pi\)
−0.731819 + 0.681499i \(0.761328\pi\)
\(24\) 1.17030 2.02701i 0.238886 0.413763i
\(25\) 0 0
\(26\) −1.49188 −0.292581
\(27\) 1.22089 0.234961
\(28\) −0.670297 1.16099i −0.126674 0.219406i
\(29\) −2.65543 4.59933i −0.493100 0.854075i 0.506868 0.862024i \(-0.330803\pi\)
−0.999968 + 0.00794880i \(0.997470\pi\)
\(30\) 0 0
\(31\) −2.76561 −0.496719 −0.248360 0.968668i \(-0.579891\pi\)
−0.248360 + 0.968668i \(0.579891\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 3.81223 6.60298i 0.663624 1.14943i
\(34\) 3.29230 + 5.70242i 0.564624 + 0.977958i
\(35\) 0 0
\(36\) −1.23919 + 2.14634i −0.206532 + 0.357724i
\(37\) 5.27098 0.866544 0.433272 0.901263i \(-0.357359\pi\)
0.433272 + 0.901263i \(0.357359\pi\)
\(38\) −2.98513 3.17632i −0.484252 0.515267i
\(39\) 3.49188 0.559148
\(40\) 0 0
\(41\) −2.79230 + 4.83640i −0.436083 + 0.755319i −0.997383 0.0722938i \(-0.976968\pi\)
0.561300 + 0.827612i \(0.310301\pi\)
\(42\) 1.56889 + 2.71740i 0.242086 + 0.419305i
\(43\) 3.81898 6.61466i 0.582389 1.00873i −0.412807 0.910819i \(-0.635452\pi\)
0.995195 0.0979082i \(-0.0312151\pi\)
\(44\) −1.62875 2.82107i −0.245543 0.425292i
\(45\) 0 0
\(46\) −2.15128 −0.317189
\(47\) −0.465912 0.806983i −0.0679602 0.117711i 0.830043 0.557699i \(-0.188316\pi\)
−0.898003 + 0.439989i \(0.854982\pi\)
\(48\) 1.17030 + 2.02701i 0.168918 + 0.292574i
\(49\) −5.20281 −0.743258
\(50\) 0 0
\(51\) −7.70593 13.3471i −1.07905 1.86896i
\(52\) 0.745938 1.29200i 0.103443 0.179168i
\(53\) 4.54498 + 7.87214i 0.624301 + 1.08132i 0.988676 + 0.150069i \(0.0479495\pi\)
−0.364375 + 0.931252i \(0.618717\pi\)
\(54\) −0.610447 + 1.05732i −0.0830713 + 0.143884i
\(55\) 0 0
\(56\) 1.34059 0.179144
\(57\) 6.98698 + 7.43448i 0.925448 + 0.984720i
\(58\) 5.31085 0.697349
\(59\) 0.0837650 0.145085i 0.0109053 0.0188885i −0.860521 0.509415i \(-0.829862\pi\)
0.871427 + 0.490526i \(0.163195\pi\)
\(60\) 0 0
\(61\) −5.84474 10.1234i −0.748342 1.29617i −0.948617 0.316427i \(-0.897517\pi\)
0.200274 0.979740i \(-0.435817\pi\)
\(62\) 1.38281 2.39509i 0.175617 0.304177i
\(63\) −1.66125 2.87738i −0.209298 0.362515i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 3.81223 + 6.60298i 0.469253 + 0.812771i
\(67\) −6.53563 11.3201i −0.798455 1.38296i −0.920622 0.390455i \(-0.872318\pi\)
0.122167 0.992510i \(-0.461016\pi\)
\(68\) −6.58459 −0.798499
\(69\) 5.03528 0.606176
\(70\) 0 0
\(71\) −3.59466 + 6.22613i −0.426607 + 0.738906i −0.996569 0.0827657i \(-0.973625\pi\)
0.569962 + 0.821671i \(0.306958\pi\)
\(72\) −1.23919 2.14634i −0.146040 0.252949i
\(73\) 7.62615 13.2089i 0.892573 1.54598i 0.0557926 0.998442i \(-0.482231\pi\)
0.836780 0.547539i \(-0.184435\pi\)
\(74\) −2.63549 + 4.56480i −0.306370 + 0.530648i
\(75\) 0 0
\(76\) 4.24334 0.997038i 0.486744 0.114368i
\(77\) 4.36697 0.497663
\(78\) −1.74594 + 3.02405i −0.197689 + 0.342407i
\(79\) 7.75423 13.4307i 0.872419 1.51107i 0.0129320 0.999916i \(-0.495883\pi\)
0.859487 0.511158i \(-0.170783\pi\)
\(80\) 0 0
\(81\) 5.14638 8.91380i 0.571820 0.990422i
\(82\) −2.79230 4.83640i −0.308358 0.534091i
\(83\) −0.313611 −0.0344233 −0.0172116 0.999852i \(-0.505479\pi\)
−0.0172116 + 0.999852i \(0.505479\pi\)
\(84\) −3.13779 −0.342361
\(85\) 0 0
\(86\) 3.81898 + 6.61466i 0.411811 + 0.713278i
\(87\) −12.4306 −1.33270
\(88\) 3.25749 0.347250
\(89\) 4.90689 + 8.49898i 0.520129 + 0.900890i 0.999726 + 0.0234013i \(0.00744955\pi\)
−0.479597 + 0.877489i \(0.659217\pi\)
\(90\) 0 0
\(91\) 1.00000 + 1.73205i 0.104828 + 0.181568i
\(92\) 1.07564 1.86306i 0.112143 0.194238i
\(93\) −3.23659 + 5.60594i −0.335619 + 0.581309i
\(94\) 0.931824 0.0961103
\(95\) 0 0
\(96\) −2.34059 −0.238886
\(97\) −6.01504 + 10.4184i −0.610735 + 1.05782i 0.380382 + 0.924829i \(0.375792\pi\)
−0.991117 + 0.132994i \(0.957541\pi\)
\(98\) 2.60140 4.50576i 0.262781 0.455151i
\(99\) −4.03665 6.99169i −0.405699 0.702691i
\(100\) 0 0
\(101\) 6.25008 + 10.8255i 0.621907 + 1.07717i 0.989130 + 0.147041i \(0.0469750\pi\)
−0.367224 + 0.930133i \(0.619692\pi\)
\(102\) 15.4119 1.52600
\(103\) −8.78740 −0.865848 −0.432924 0.901430i \(-0.642518\pi\)
−0.432924 + 0.901430i \(0.642518\pi\)
\(104\) 0.745938 + 1.29200i 0.0731452 + 0.126691i
\(105\) 0 0
\(106\) −9.08996 −0.882895
\(107\) −10.0000 −0.966736 −0.483368 0.875417i \(-0.660587\pi\)
−0.483368 + 0.875417i \(0.660587\pi\)
\(108\) −0.610447 1.05732i −0.0587403 0.101741i
\(109\) −8.17306 + 14.1562i −0.782838 + 1.35591i 0.147445 + 0.989070i \(0.452895\pi\)
−0.930282 + 0.366844i \(0.880438\pi\)
\(110\) 0 0
\(111\) 6.16862 10.6844i 0.585499 1.01411i
\(112\) −0.670297 + 1.16099i −0.0633371 + 0.109703i
\(113\) 6.36514 0.598782 0.299391 0.954131i \(-0.403217\pi\)
0.299391 + 0.954131i \(0.403217\pi\)
\(114\) −9.93193 + 2.33366i −0.930211 + 0.218568i
\(115\) 0 0
\(116\) −2.65543 + 4.59933i −0.246550 + 0.427037i
\(117\) 1.84872 3.20208i 0.170914 0.296032i
\(118\) 0.0837650 + 0.145085i 0.00771120 + 0.0133562i
\(119\) 4.41364 7.64464i 0.404597 0.700783i
\(120\) 0 0
\(121\) −0.388758 −0.0353416
\(122\) 11.6895 1.05832
\(123\) 6.53563 + 11.3201i 0.589298 + 1.02069i
\(124\) 1.38281 + 2.39509i 0.124180 + 0.215086i
\(125\) 0 0
\(126\) 3.32251 0.295992
\(127\) 0.220635 + 0.382151i 0.0195782 + 0.0339104i 0.875649 0.482949i \(-0.160434\pi\)
−0.856070 + 0.516859i \(0.827101\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) −8.93868 15.4822i −0.787007 1.36314i
\(130\) 0 0
\(131\) −3.56077 + 6.16743i −0.311106 + 0.538851i −0.978602 0.205762i \(-0.934033\pi\)
0.667496 + 0.744613i \(0.267366\pi\)
\(132\) −7.62446 −0.663624
\(133\) −1.68675 + 5.59478i −0.146260 + 0.485129i
\(134\) 13.0713 1.12919
\(135\) 0 0
\(136\) 3.29230 5.70242i 0.282312 0.488979i
\(137\) 1.51487 + 2.62383i 0.129424 + 0.224169i 0.923454 0.383710i \(-0.125354\pi\)
−0.794029 + 0.607879i \(0.792020\pi\)
\(138\) −2.51764 + 4.36068i −0.214316 + 0.371205i
\(139\) 6.69534 + 11.5967i 0.567891 + 0.983617i 0.996774 + 0.0802567i \(0.0255740\pi\)
−0.428883 + 0.903360i \(0.641093\pi\)
\(140\) 0 0
\(141\) −2.18102 −0.183675
\(142\) −3.59466 6.22613i −0.301657 0.522485i
\(143\) 2.42988 + 4.20868i 0.203197 + 0.351948i
\(144\) 2.47838 0.206532
\(145\) 0 0
\(146\) 7.62615 + 13.2089i 0.631144 + 1.09317i
\(147\) −6.08883 + 10.5462i −0.502198 + 0.869833i
\(148\) −2.63549 4.56480i −0.216636 0.375225i
\(149\) −10.9212 + 18.9161i −0.894700 + 1.54967i −0.0605252 + 0.998167i \(0.519278\pi\)
−0.834175 + 0.551500i \(0.814056\pi\)
\(150\) 0 0
\(151\) 18.3441 1.49282 0.746410 0.665486i \(-0.231776\pi\)
0.746410 + 0.665486i \(0.231776\pi\)
\(152\) −1.25821 + 4.17336i −0.102054 + 0.338504i
\(153\) −16.3191 −1.31932
\(154\) −2.18349 + 3.78191i −0.175950 + 0.304755i
\(155\) 0 0
\(156\) −1.74594 3.02405i −0.139787 0.242118i
\(157\) −3.72080 + 6.44462i −0.296952 + 0.514337i −0.975437 0.220278i \(-0.929304\pi\)
0.678485 + 0.734614i \(0.262637\pi\)
\(158\) 7.75423 + 13.4307i 0.616893 + 1.06849i
\(159\) 21.2759 1.68729
\(160\) 0 0
\(161\) 1.44200 + 2.49761i 0.113645 + 0.196839i
\(162\) 5.14638 + 8.91380i 0.404338 + 0.700334i
\(163\) −15.5400 −1.21719 −0.608595 0.793481i \(-0.708267\pi\)
−0.608595 + 0.793481i \(0.708267\pi\)
\(164\) 5.58459 0.436083
\(165\) 0 0
\(166\) 0.156805 0.271595i 0.0121705 0.0210799i
\(167\) 11.0317 + 19.1074i 0.853655 + 1.47857i 0.877887 + 0.478868i \(0.158953\pi\)
−0.0242320 + 0.999706i \(0.507714\pi\)
\(168\) 1.56889 2.71740i 0.121043 0.209652i
\(169\) 5.38715 9.33082i 0.414396 0.717756i
\(170\) 0 0
\(171\) 10.5166 2.47104i 0.804226 0.188965i
\(172\) −7.63796 −0.582389
\(173\) 0.190893 0.330637i 0.0145134 0.0251379i −0.858678 0.512516i \(-0.828713\pi\)
0.873191 + 0.487378i \(0.162047\pi\)
\(174\) 6.21528 10.7652i 0.471179 0.816106i
\(175\) 0 0
\(176\) −1.62875 + 2.82107i −0.122771 + 0.212646i
\(177\) −0.196060 0.339586i −0.0147368 0.0255248i
\(178\) −9.81378 −0.735574
\(179\) 12.1814 0.910477 0.455239 0.890369i \(-0.349554\pi\)
0.455239 + 0.890369i \(0.349554\pi\)
\(180\) 0 0
\(181\) 0.996021 + 1.72516i 0.0740337 + 0.128230i 0.900666 0.434513i \(-0.143079\pi\)
−0.826632 + 0.562743i \(0.809746\pi\)
\(182\) −2.00000 −0.148250
\(183\) −27.3603 −2.02253
\(184\) 1.07564 + 1.86306i 0.0792973 + 0.137347i
\(185\) 0 0
\(186\) −3.23659 5.60594i −0.237318 0.411048i
\(187\) 10.7246 18.5756i 0.784262 1.35838i
\(188\) −0.465912 + 0.806983i −0.0339801 + 0.0588553i
\(189\) 1.63672 0.119054
\(190\) 0 0
\(191\) −10.6217 −0.768560 −0.384280 0.923217i \(-0.625550\pi\)
−0.384280 + 0.923217i \(0.625550\pi\)
\(192\) 1.17030 2.02701i 0.0844589 0.146287i
\(193\) −7.64118 + 13.2349i −0.550024 + 0.952670i 0.448248 + 0.893909i \(0.352048\pi\)
−0.998272 + 0.0587608i \(0.981285\pi\)
\(194\) −6.01504 10.4184i −0.431855 0.747994i
\(195\) 0 0
\(196\) 2.60140 + 4.50576i 0.185814 + 0.321840i
\(197\) −4.10865 −0.292729 −0.146365 0.989231i \(-0.546757\pi\)
−0.146365 + 0.989231i \(0.546757\pi\)
\(198\) 8.07331 0.573745
\(199\) 5.20281 + 9.01152i 0.368817 + 0.638810i 0.989381 0.145346i \(-0.0464295\pi\)
−0.620564 + 0.784156i \(0.713096\pi\)
\(200\) 0 0
\(201\) −30.5945 −2.15797
\(202\) −12.5002 −0.879509
\(203\) −3.55985 6.16584i −0.249853 0.432757i
\(204\) −7.70593 + 13.3471i −0.539523 + 0.934481i
\(205\) 0 0
\(206\) 4.39370 7.61011i 0.306124 0.530222i
\(207\) 2.66585 4.61739i 0.185289 0.320931i
\(208\) −1.49188 −0.103443
\(209\) −4.09860 + 13.5947i −0.283506 + 0.940363i
\(210\) 0 0
\(211\) 6.98513 12.0986i 0.480876 0.832902i −0.518883 0.854845i \(-0.673652\pi\)
0.999759 + 0.0219433i \(0.00698534\pi\)
\(212\) 4.54498 7.87214i 0.312151 0.540661i
\(213\) 8.41364 + 14.5728i 0.576493 + 0.998515i
\(214\) 5.00000 8.66025i 0.341793 0.592003i
\(215\) 0 0
\(216\) 1.22089 0.0830713
\(217\) −3.70757 −0.251686
\(218\) −8.17306 14.1562i −0.553550 0.958776i
\(219\) −17.8497 30.9166i −1.20617 2.08915i
\(220\) 0 0
\(221\) 9.82339 0.660793
\(222\) 6.16862 + 10.6844i 0.414010 + 0.717087i
\(223\) −2.32970 + 4.03516i −0.156008 + 0.270215i −0.933426 0.358771i \(-0.883196\pi\)
0.777417 + 0.628985i \(0.216529\pi\)
\(224\) −0.670297 1.16099i −0.0447861 0.0775718i
\(225\) 0 0
\(226\) −3.18257 + 5.51237i −0.211701 + 0.366677i
\(227\) −4.14740 −0.275273 −0.137636 0.990483i \(-0.543951\pi\)
−0.137636 + 0.990483i \(0.543951\pi\)
\(228\) 2.94496 9.76814i 0.195034 0.646911i
\(229\) −20.8071 −1.37497 −0.687487 0.726196i \(-0.741286\pi\)
−0.687487 + 0.726196i \(0.741286\pi\)
\(230\) 0 0
\(231\) 5.11066 8.85192i 0.336257 0.582414i
\(232\) −2.65543 4.59933i −0.174337 0.301961i
\(233\) −0.506444 + 0.877186i −0.0331782 + 0.0574664i −0.882138 0.470992i \(-0.843896\pi\)
0.848960 + 0.528458i \(0.177230\pi\)
\(234\) 1.84872 + 3.20208i 0.120855 + 0.209326i
\(235\) 0 0
\(236\) −0.167530 −0.0109053
\(237\) −18.1495 31.4359i −1.17894 2.04198i
\(238\) 4.41364 + 7.64464i 0.286093 + 0.495528i
\(239\) −22.7248 −1.46994 −0.734971 0.678098i \(-0.762804\pi\)
−0.734971 + 0.678098i \(0.762804\pi\)
\(240\) 0 0
\(241\) 7.36702 + 12.7600i 0.474551 + 0.821947i 0.999575 0.0291404i \(-0.00927699\pi\)
−0.525024 + 0.851087i \(0.675944\pi\)
\(242\) 0.194379 0.336674i 0.0124952 0.0216422i
\(243\) −10.2143 17.6916i −0.655245 1.13492i
\(244\) −5.84474 + 10.1234i −0.374171 + 0.648083i
\(245\) 0 0
\(246\) −13.0713 −0.833394
\(247\) −6.33053 + 1.48746i −0.402802 + 0.0946446i
\(248\) −2.76561 −0.175617
\(249\) −0.367018 + 0.635694i −0.0232588 + 0.0402854i
\(250\) 0 0
\(251\) −9.81668 17.0030i −0.619623 1.07322i −0.989554 0.144160i \(-0.953952\pi\)
0.369931 0.929059i \(-0.379381\pi\)
\(252\) −1.66125 + 2.87738i −0.104649 + 0.181258i
\(253\) 3.50389 + 6.06891i 0.220288 + 0.381549i
\(254\) −0.441270 −0.0276877
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 1.29075 + 2.23565i 0.0805148 + 0.139456i 0.903471 0.428649i \(-0.141010\pi\)
−0.822956 + 0.568105i \(0.807677\pi\)
\(258\) 17.8774 1.11300
\(259\) 7.06625 0.439075
\(260\) 0 0
\(261\) −6.58117 + 11.3989i −0.407364 + 0.705575i
\(262\) −3.56077 6.16743i −0.219985 0.381025i
\(263\) −3.93122 + 6.80906i −0.242409 + 0.419865i −0.961400 0.275155i \(-0.911271\pi\)
0.718991 + 0.695020i \(0.244604\pi\)
\(264\) 3.81223 6.60298i 0.234627 0.406385i
\(265\) 0 0
\(266\) −4.00185 4.25816i −0.245369 0.261084i
\(267\) 22.9701 1.40575
\(268\) −6.53563 + 11.3201i −0.399227 + 0.691482i
\(269\) −1.04119 + 1.80340i −0.0634826 + 0.109955i −0.896020 0.444014i \(-0.853554\pi\)
0.832537 + 0.553969i \(0.186887\pi\)
\(270\) 0 0
\(271\) −5.38624 + 9.32923i −0.327190 + 0.566711i −0.981953 0.189124i \(-0.939435\pi\)
0.654763 + 0.755834i \(0.272769\pi\)
\(272\) 3.29230 + 5.70242i 0.199625 + 0.345760i
\(273\) 4.68119 0.283318
\(274\) −3.02974 −0.183033
\(275\) 0 0
\(276\) −2.51764 4.36068i −0.151544 0.262482i
\(277\) −8.52030 −0.511935 −0.255967 0.966685i \(-0.582394\pi\)
−0.255967 + 0.966685i \(0.582394\pi\)
\(278\) −13.3907 −0.803120
\(279\) 3.42713 + 5.93596i 0.205177 + 0.355377i
\(280\) 0 0
\(281\) −3.29766 5.71172i −0.196722 0.340733i 0.750742 0.660596i \(-0.229696\pi\)
−0.947464 + 0.319863i \(0.896363\pi\)
\(282\) 1.09051 1.88882i 0.0649390 0.112478i
\(283\) 3.36481 5.82802i 0.200017 0.346440i −0.748516 0.663116i \(-0.769234\pi\)
0.948534 + 0.316676i \(0.102567\pi\)
\(284\) 7.18931 0.426607
\(285\) 0 0
\(286\) −4.85977 −0.287364
\(287\) −3.74334 + 6.48365i −0.220962 + 0.382718i
\(288\) −1.23919 + 2.14634i −0.0730201 + 0.126474i
\(289\) −13.1784 22.8257i −0.775202 1.34269i
\(290\) 0 0
\(291\) 14.0788 + 24.3851i 0.825312 + 1.42948i
\(292\) −15.2523 −0.892573
\(293\) −1.06829 −0.0624103 −0.0312051 0.999513i \(-0.509935\pi\)
−0.0312051 + 0.999513i \(0.509935\pi\)
\(294\) −6.08883 10.5462i −0.355108 0.615065i
\(295\) 0 0
\(296\) 5.27098 0.306370
\(297\) 3.97705 0.230772
\(298\) −10.9212 18.9161i −0.632649 1.09578i
\(299\) −1.60472 + 2.77946i −0.0928034 + 0.160740i
\(300\) 0 0
\(301\) 5.11970 8.86758i 0.295095 0.511119i
\(302\) −9.17204 + 15.8864i −0.527792 + 0.914162i
\(303\) 29.2578 1.68082
\(304\) −2.98513 3.17632i −0.171209 0.182174i
\(305\) 0 0
\(306\) 8.15957 14.1328i 0.466452 0.807918i
\(307\) 1.67862 2.90746i 0.0958041 0.165937i −0.814140 0.580669i \(-0.802791\pi\)
0.909944 + 0.414731i \(0.136124\pi\)
\(308\) −2.18349 3.78191i −0.124416 0.215494i
\(309\) −10.2839 + 17.8122i −0.585029 + 1.01330i
\(310\) 0 0
\(311\) −7.70225 −0.436755 −0.218377 0.975864i \(-0.570076\pi\)
−0.218377 + 0.975864i \(0.570076\pi\)
\(312\) 3.49188 0.197689
\(313\) −2.87534 4.98024i −0.162524 0.281500i 0.773249 0.634102i \(-0.218630\pi\)
−0.935773 + 0.352602i \(0.885297\pi\)
\(314\) −3.72080 6.44462i −0.209977 0.363691i
\(315\) 0 0
\(316\) −15.5085 −0.872419
\(317\) 8.71462 + 15.0942i 0.489462 + 0.847772i 0.999926 0.0121262i \(-0.00385998\pi\)
−0.510465 + 0.859899i \(0.670527\pi\)
\(318\) −10.6380 + 18.4255i −0.596547 + 1.03325i
\(319\) −8.65003 14.9823i −0.484308 0.838847i
\(320\) 0 0
\(321\) −11.7030 + 20.2701i −0.653196 + 1.13137i
\(322\) −2.88400 −0.160719
\(323\) 19.6559 + 20.9148i 1.09368 + 1.16373i
\(324\) −10.2928 −0.571820
\(325\) 0 0
\(326\) 7.77002 13.4581i 0.430342 0.745373i
\(327\) 19.1298 + 33.1338i 1.05788 + 1.83231i
\(328\) −2.79230 + 4.83640i −0.154179 + 0.267045i
\(329\) −0.624599 1.08184i −0.0344353 0.0596436i
\(330\) 0 0
\(331\) −12.1108 −0.665670 −0.332835 0.942985i \(-0.608005\pi\)
−0.332835 + 0.942985i \(0.608005\pi\)
\(332\) 0.156805 + 0.271595i 0.00860581 + 0.0149057i
\(333\) −6.53176 11.3133i −0.357938 0.619967i
\(334\) −22.0633 −1.20725
\(335\) 0 0
\(336\) 1.56889 + 2.71740i 0.0855902 + 0.148247i
\(337\) −16.1078 + 27.8995i −0.877445 + 1.51978i −0.0233106 + 0.999728i \(0.507421\pi\)
−0.854135 + 0.520052i \(0.825913\pi\)
\(338\) 5.38715 + 9.33082i 0.293023 + 0.507530i
\(339\) 7.44910 12.9022i 0.404580 0.700753i
\(340\) 0 0
\(341\) −9.00896 −0.487863
\(342\) −3.11832 + 10.3432i −0.168620 + 0.559295i
\(343\) −16.3590 −0.883304
\(344\) 3.81898 6.61466i 0.205905 0.356639i
\(345\) 0 0
\(346\) 0.190893 + 0.330637i 0.0102625 + 0.0177752i
\(347\) 15.2549 26.4222i 0.818924 1.41842i −0.0875523 0.996160i \(-0.527905\pi\)
0.906476 0.422257i \(-0.138762\pi\)
\(348\) 6.21528 + 10.7652i 0.333174 + 0.577074i
\(349\) 26.3315 1.40949 0.704747 0.709459i \(-0.251061\pi\)
0.704747 + 0.709459i \(0.251061\pi\)
\(350\) 0 0
\(351\) 0.910710 + 1.57740i 0.0486101 + 0.0841952i
\(352\) −1.62875 2.82107i −0.0868124 0.150363i
\(353\) 0.368812 0.0196299 0.00981493 0.999952i \(-0.496876\pi\)
0.00981493 + 0.999952i \(0.496876\pi\)
\(354\) 0.392120 0.0208409
\(355\) 0 0
\(356\) 4.90689 8.49898i 0.260065 0.450445i
\(357\) −10.3305 17.8930i −0.546750 0.946998i
\(358\) −6.09068 + 10.5494i −0.321902 + 0.557551i
\(359\) −14.7532 + 25.5533i −0.778645 + 1.34865i 0.154079 + 0.988059i \(0.450759\pi\)
−0.932723 + 0.360593i \(0.882574\pi\)
\(360\) 0 0
\(361\) −15.8338 10.5019i −0.833359 0.552732i
\(362\) −1.99204 −0.104699
\(363\) −0.454962 + 0.788018i −0.0238793 + 0.0413602i
\(364\) 1.00000 1.73205i 0.0524142 0.0907841i
\(365\) 0 0
\(366\) 13.6802 23.6947i 0.715074 1.23854i
\(367\) −9.16862 15.8805i −0.478598 0.828956i 0.521101 0.853495i \(-0.325521\pi\)
−0.999699 + 0.0245392i \(0.992188\pi\)
\(368\) −2.15128 −0.112143
\(369\) 13.8408 0.720521
\(370\) 0 0
\(371\) 6.09298 + 10.5533i 0.316332 + 0.547902i
\(372\) 6.47318 0.335619
\(373\) 20.1928 1.04554 0.522772 0.852473i \(-0.324898\pi\)
0.522772 + 0.852473i \(0.324898\pi\)
\(374\) 10.7246 + 18.5756i 0.554557 + 0.960521i
\(375\) 0 0
\(376\) −0.465912 0.806983i −0.0240276 0.0416170i
\(377\) 3.96157 6.86163i 0.204031 0.353392i
\(378\) −0.818361 + 1.41744i −0.0420920 + 0.0729054i
\(379\) 15.2700 0.784367 0.392183 0.919887i \(-0.371720\pi\)
0.392183 + 0.919887i \(0.371720\pi\)
\(380\) 0 0
\(381\) 1.03283 0.0529137
\(382\) 5.31085 9.19867i 0.271727 0.470645i
\(383\) 13.4026 23.2139i 0.684838 1.18617i −0.288649 0.957435i \(-0.593206\pi\)
0.973488 0.228740i \(-0.0734605\pi\)
\(384\) 1.17030 + 2.02701i 0.0597215 + 0.103441i
\(385\) 0 0
\(386\) −7.64118 13.2349i −0.388926 0.673640i
\(387\) −18.9298 −0.962255
\(388\) 12.0301 0.610735
\(389\) 12.1644 + 21.0694i 0.616761 + 1.06826i 0.990073 + 0.140556i \(0.0448890\pi\)
−0.373311 + 0.927706i \(0.621778\pi\)
\(390\) 0 0
\(391\) 14.1653 0.716370
\(392\) −5.20281 −0.262781
\(393\) 8.33432 + 14.4355i 0.420411 + 0.728173i
\(394\) 2.05433 3.55820i 0.103495 0.179259i
\(395\) 0 0
\(396\) −4.03665 + 6.99169i −0.202850 + 0.351346i
\(397\) 9.53415 16.5136i 0.478505 0.828795i −0.521191 0.853440i \(-0.674512\pi\)
0.999696 + 0.0246449i \(0.00784550\pi\)
\(398\) −10.4056 −0.521586
\(399\) 9.36670 + 9.96662i 0.468922 + 0.498955i
\(400\) 0 0
\(401\) 4.80098 8.31554i 0.239750 0.415258i −0.720893 0.693047i \(-0.756268\pi\)
0.960642 + 0.277788i \(0.0896013\pi\)
\(402\) 15.2973 26.4956i 0.762958 1.32148i
\(403\) −2.06298 3.57318i −0.102764 0.177993i
\(404\) 6.25008 10.8255i 0.310953 0.538587i
\(405\) 0 0
\(406\) 7.11970 0.353345
\(407\) 17.1702 0.851094
\(408\) −7.70593 13.3471i −0.381500 0.660778i
\(409\) 11.3689 + 19.6916i 0.562158 + 0.973685i 0.997308 + 0.0733276i \(0.0233619\pi\)
−0.435150 + 0.900358i \(0.643305\pi\)
\(410\) 0 0
\(411\) 7.09140 0.349793
\(412\) 4.39370 + 7.61011i 0.216462 + 0.374923i
\(413\) 0.112295 0.194501i 0.00552567 0.00957075i
\(414\) 2.66585 + 4.61739i 0.131019 + 0.226932i
\(415\) 0 0
\(416\) 0.745938 1.29200i 0.0365726 0.0633456i
\(417\) 31.3422 1.53483
\(418\) −9.72403 10.3468i −0.475618 0.506080i
\(419\) 36.5783 1.78697 0.893483 0.449097i \(-0.148254\pi\)
0.893483 + 0.449097i \(0.148254\pi\)
\(420\) 0 0
\(421\) −5.51620 + 9.55434i −0.268843 + 0.465650i −0.968563 0.248767i \(-0.919975\pi\)
0.699720 + 0.714417i \(0.253308\pi\)
\(422\) 6.98513 + 12.0986i 0.340031 + 0.588951i
\(423\) −1.15471 + 2.00001i −0.0561438 + 0.0972440i
\(424\) 4.54498 + 7.87214i 0.220724 + 0.382305i
\(425\) 0 0
\(426\) −16.8273 −0.815284
\(427\) −7.83543 13.5714i −0.379183 0.656764i
\(428\) 5.00000 + 8.66025i 0.241684 + 0.418609i
\(429\) 11.3747 0.549178
\(430\) 0 0
\(431\) 10.4489 + 18.0980i 0.503306 + 0.871752i 0.999993 + 0.00382204i \(0.00121659\pi\)
−0.496686 + 0.867930i \(0.665450\pi\)
\(432\) −0.610447 + 1.05732i −0.0293701 + 0.0508705i
\(433\) −7.12477 12.3405i −0.342394 0.593045i 0.642482 0.766300i \(-0.277905\pi\)
−0.984877 + 0.173256i \(0.944571\pi\)
\(434\) 1.85378 3.21085i 0.0889845 0.154126i
\(435\) 0 0
\(436\) 16.3461 0.782838
\(437\) −9.12861 + 2.14491i −0.436681 + 0.102605i
\(438\) 35.6994 1.70578
\(439\) 5.25331 9.09900i 0.250727 0.434272i −0.712999 0.701165i \(-0.752664\pi\)
0.963726 + 0.266893i \(0.0859971\pi\)
\(440\) 0 0
\(441\) 6.44727 + 11.1670i 0.307013 + 0.531762i
\(442\) −4.91170 + 8.50731i −0.233626 + 0.404651i
\(443\) −19.2281 33.3040i −0.913553 1.58232i −0.809006 0.587801i \(-0.799994\pi\)
−0.104548 0.994520i \(-0.533340\pi\)
\(444\) −12.3372 −0.585499
\(445\) 0 0
\(446\) −2.32970 4.03516i −0.110315 0.191071i
\(447\) 25.5621 + 44.2749i 1.20905 + 2.09413i
\(448\) 1.34059 0.0633371
\(449\) −26.9402 −1.27139 −0.635694 0.771941i \(-0.719286\pi\)
−0.635694 + 0.771941i \(0.719286\pi\)
\(450\) 0 0
\(451\) −9.09588 + 15.7545i −0.428308 + 0.741852i
\(452\) −3.18257 5.51237i −0.149695 0.259280i
\(453\) 21.4680 37.1837i 1.00866 1.74704i
\(454\) 2.07370 3.59176i 0.0973236 0.168569i
\(455\) 0 0
\(456\) 6.98698 + 7.43448i 0.327195 + 0.348151i
\(457\) −14.6472 −0.685166 −0.342583 0.939488i \(-0.611302\pi\)
−0.342583 + 0.939488i \(0.611302\pi\)
\(458\) 10.4036 18.0195i 0.486127 0.841997i
\(459\) 4.01954 6.96205i 0.187616 0.324961i
\(460\) 0 0
\(461\) 0.104103 0.180311i 0.00484855 0.00839794i −0.863591 0.504193i \(-0.831790\pi\)
0.868440 + 0.495795i \(0.165123\pi\)
\(462\) 5.11066 + 8.85192i 0.237769 + 0.411829i
\(463\) 24.6580 1.14596 0.572978 0.819571i \(-0.305788\pi\)
0.572978 + 0.819571i \(0.305788\pi\)
\(464\) 5.31085 0.246550
\(465\) 0 0
\(466\) −0.506444 0.877186i −0.0234605 0.0406349i
\(467\) 22.4281 1.03785 0.518925 0.854820i \(-0.326332\pi\)
0.518925 + 0.854820i \(0.326332\pi\)
\(468\) −3.69744 −0.170914
\(469\) −8.76164 15.1756i −0.404575 0.700744i
\(470\) 0 0
\(471\) 8.70889 + 15.0842i 0.401284 + 0.695045i
\(472\) 0.0837650 0.145085i 0.00385560 0.00667809i
\(473\) 12.4403 21.5472i 0.572005 0.990741i
\(474\) 36.2990 1.66727
\(475\) 0 0
\(476\) −8.82727 −0.404597
\(477\) 11.2642 19.5102i 0.515752 0.893309i
\(478\) 11.3624 19.6802i 0.519703 0.900152i
\(479\) −8.17582 14.1609i −0.373563 0.647030i 0.616548 0.787317i \(-0.288531\pi\)
−0.990111 + 0.140288i \(0.955197\pi\)
\(480\) 0 0
\(481\) 3.93182 + 6.81012i 0.179276 + 0.310515i
\(482\) −14.7340 −0.671117
\(483\) 6.75026 0.307148
\(484\) 0.194379 + 0.336674i 0.00883541 + 0.0153034i
\(485\) 0 0
\(486\) 20.4285 0.926656
\(487\) −40.7859 −1.84819 −0.924093 0.382168i \(-0.875177\pi\)
−0.924093 + 0.382168i \(0.875177\pi\)
\(488\) −5.84474 10.1234i −0.264579 0.458264i
\(489\) −18.1865 + 31.4999i −0.822420 + 1.42447i
\(490\) 0 0
\(491\) −11.1912 + 19.3838i −0.505053 + 0.874778i 0.494930 + 0.868933i \(0.335194\pi\)
−0.999983 + 0.00584462i \(0.998140\pi\)
\(492\) 6.53563 11.3201i 0.294649 0.510347i
\(493\) −34.9698 −1.57496
\(494\) 1.87709 6.22613i 0.0844543 0.280127i
\(495\) 0 0
\(496\) 1.38281 2.39509i 0.0620899 0.107543i
\(497\) −4.81898 + 8.34671i −0.216161 + 0.374401i
\(498\) −0.367018 0.635694i −0.0164465 0.0284861i
\(499\) 4.07719 7.06189i 0.182520 0.316134i −0.760218 0.649668i \(-0.774908\pi\)
0.942738 + 0.333534i \(0.108241\pi\)
\(500\) 0 0
\(501\) 51.6413 2.30716
\(502\) 19.6334 0.876280
\(503\) 12.0711 + 20.9078i 0.538224 + 0.932232i 0.999000 + 0.0447150i \(0.0142380\pi\)
−0.460776 + 0.887517i \(0.652429\pi\)
\(504\) −1.66125 2.87738i −0.0739981 0.128169i
\(505\) 0 0
\(506\) −7.00778 −0.311534
\(507\) −12.6091 21.8397i −0.559992 0.969934i
\(508\) 0.220635 0.382151i 0.00978909 0.0169552i
\(509\) 7.16576 + 12.4115i 0.317617 + 0.550128i 0.979990 0.199046i \(-0.0637842\pi\)
−0.662374 + 0.749174i \(0.730451\pi\)
\(510\) 0 0
\(511\) 10.2236 17.7077i 0.452264 0.783344i
\(512\) 1.00000 0.0441942
\(513\) −1.53614 + 5.09522i −0.0678222 + 0.224960i
\(514\) −2.58150 −0.113865
\(515\) 0 0
\(516\) −8.93868 + 15.4822i −0.393503 + 0.681568i
\(517\) −1.51770 2.62874i −0.0667485 0.115612i
\(518\) −3.53313 + 6.11955i −0.155237 + 0.268878i
\(519\) −0.446804 0.773888i −0.0196125 0.0339699i
\(520\) 0 0
\(521\) 3.10621 0.136086 0.0680428 0.997682i \(-0.478325\pi\)
0.0680428 + 0.997682i \(0.478325\pi\)
\(522\) −6.58117 11.3989i −0.288050 0.498917i
\(523\) 11.5122 + 19.9398i 0.503394 + 0.871905i 0.999992 + 0.00392391i \(0.00124902\pi\)
−0.496598 + 0.867981i \(0.665418\pi\)
\(524\) 7.12154 0.311106
\(525\) 0 0
\(526\) −3.93122 6.80906i −0.171409 0.296889i
\(527\) −9.10522 + 15.7707i −0.396630 + 0.686983i
\(528\) 3.81223 + 6.60298i 0.165906 + 0.287358i
\(529\) 9.18600 15.9106i 0.399391 0.691766i
\(530\) 0 0
\(531\) −0.415204 −0.0180183
\(532\) 5.68860 1.33662i 0.246632 0.0579500i
\(533\) −8.33152 −0.360878
\(534\) −11.4850 + 19.8927i −0.497006 + 0.860840i
\(535\) 0 0
\(536\) −6.53563 11.3201i −0.282296 0.488952i
\(537\) 14.2558 24.6918i 0.615184 1.06553i
\(538\) −1.04119 1.80340i −0.0448890 0.0777500i
\(539\) −16.9481 −0.730006
\(540\) 0 0
\(541\) 10.2489 + 17.7516i 0.440633 + 0.763199i 0.997737 0.0672443i \(-0.0214207\pi\)
−0.557104 + 0.830443i \(0.688087\pi\)
\(542\) −5.38624 9.32923i −0.231359 0.400725i
\(543\) 4.66256 0.200090
\(544\) −6.58459 −0.282312
\(545\) 0 0
\(546\) −2.34059 + 4.05403i −0.100168 + 0.173496i
\(547\) −6.62783 11.4797i −0.283385 0.490838i 0.688831 0.724922i \(-0.258124\pi\)
−0.972216 + 0.234084i \(0.924791\pi\)
\(548\) 1.51487 2.62383i 0.0647121 0.112085i
\(549\) −14.4855 + 25.0896i −0.618226 + 1.07080i
\(550\) 0 0
\(551\) 22.5357 5.29512i 0.960055 0.225580i
\(552\) 5.03528 0.214316
\(553\) 10.3953 18.0052i 0.442052 0.765657i
\(554\) 4.26015 7.37879i 0.180996 0.313495i
\(555\) 0 0
\(556\) 6.69534 11.5967i 0.283946 0.491808i
\(557\) 12.1148 + 20.9834i 0.513319 + 0.889094i 0.999881 + 0.0154482i \(0.00491750\pi\)
−0.486562 + 0.873646i \(0.661749\pi\)
\(558\) −6.85425 −0.290164
\(559\) 11.3949 0.481952
\(560\) 0 0
\(561\) −25.1020 43.4779i −1.05981 1.83564i
\(562\) 6.59533 0.278207
\(563\) 27.1643 1.14484 0.572420 0.819961i \(-0.306005\pi\)
0.572420 + 0.819961i \(0.306005\pi\)
\(564\) 1.09051 + 1.88882i 0.0459188 + 0.0795337i
\(565\) 0 0
\(566\) 3.36481 + 5.82802i 0.141434 + 0.244970i
\(567\) 6.89921 11.9498i 0.289740 0.501844i
\(568\) −3.59466 + 6.22613i −0.150828 + 0.261243i
\(569\) −43.8600 −1.83871 −0.919353 0.393433i \(-0.871287\pi\)
−0.919353 + 0.393433i \(0.871287\pi\)
\(570\) 0 0
\(571\) 30.5834 1.27988 0.639938 0.768427i \(-0.278960\pi\)
0.639938 + 0.768427i \(0.278960\pi\)
\(572\) 2.42988 4.20868i 0.101599 0.175974i
\(573\) −12.4306 + 21.5304i −0.519294 + 0.899443i
\(574\) −3.74334 6.48365i −0.156244 0.270622i
\(575\) 0 0
\(576\) −1.23919 2.14634i −0.0516330 0.0894310i
\(577\) −40.9572 −1.70507 −0.852536 0.522669i \(-0.824936\pi\)
−0.852536 + 0.522669i \(0.824936\pi\)
\(578\) 26.3569 1.09630
\(579\) 17.8849 + 30.9776i 0.743272 + 1.28738i
\(580\) 0 0
\(581\) −0.420425 −0.0174422
\(582\) −28.1575 −1.16717
\(583\) 14.8052 + 25.6434i 0.613170 + 1.06204i
\(584\) 7.62615 13.2089i 0.315572 0.546587i
\(585\) 0 0
\(586\) 0.534146 0.925168i 0.0220654 0.0382183i
\(587\) 8.82971 15.2935i 0.364441 0.631231i −0.624245 0.781229i \(-0.714593\pi\)
0.988686 + 0.149998i \(0.0479267\pi\)
\(588\) 12.1777 0.502198
\(589\) 3.47972 11.5419i 0.143379 0.475576i
\(590\) 0 0
\(591\) −4.80834 + 8.32830i −0.197789 + 0.342580i
\(592\) −2.63549 + 4.56480i −0.108318 + 0.187612i
\(593\) 10.4599 + 18.1171i 0.429538 + 0.743982i 0.996832 0.0795335i \(-0.0253431\pi\)
−0.567294 + 0.823515i \(0.692010\pi\)
\(594\) −1.98852 + 3.44422i −0.0815901 + 0.141318i
\(595\) 0 0
\(596\) 21.8424 0.894700
\(597\) 24.3553 0.996797
\(598\) −1.60472 2.77946i −0.0656219 0.113661i
\(599\) −6.31990 10.9464i −0.258224 0.447257i 0.707542 0.706671i \(-0.249804\pi\)
−0.965766 + 0.259414i \(0.916471\pi\)
\(600\) 0 0
\(601\) −43.8933 −1.79045 −0.895223 0.445618i \(-0.852984\pi\)
−0.895223 + 0.445618i \(0.852984\pi\)
\(602\) 5.11970 + 8.86758i 0.208663 + 0.361416i
\(603\) −16.1978 + 28.0554i −0.659626 + 1.14251i
\(604\) −9.17204 15.8864i −0.373205 0.646410i
\(605\) 0 0
\(606\) −14.6289 + 25.3380i −0.594259 + 1.02929i
\(607\) −0.939196 −0.0381208 −0.0190604 0.999818i \(-0.506067\pi\)
−0.0190604 + 0.999818i \(0.506067\pi\)
\(608\) 4.24334 0.997038i 0.172090 0.0404352i
\(609\) −16.6643 −0.675273
\(610\) 0 0
\(611\) 0.695083 1.20392i 0.0281200 0.0487053i
\(612\) 8.15957 + 14.1328i 0.329831 + 0.571284i
\(613\) 4.05797 7.02861i 0.163900 0.283883i −0.772364 0.635180i \(-0.780926\pi\)
0.936264 + 0.351297i \(0.114259\pi\)
\(614\) 1.67862 + 2.90746i 0.0677437 + 0.117336i
\(615\) 0 0
\(616\) 4.36697 0.175950
\(617\) 4.63950 + 8.03585i 0.186779 + 0.323511i 0.944175 0.329445i \(-0.106862\pi\)
−0.757395 + 0.652957i \(0.773528\pi\)
\(618\) −10.2839 17.8122i −0.413678 0.716511i
\(619\) −1.87972 −0.0755521 −0.0377761 0.999286i \(-0.512027\pi\)
−0.0377761 + 0.999286i \(0.512027\pi\)
\(620\) 0 0
\(621\) 1.31324 + 2.27460i 0.0526986 + 0.0912766i
\(622\) 3.85113 6.67035i 0.154416 0.267457i
\(623\) 6.57815 + 11.3937i 0.263548 + 0.456478i
\(624\) −1.74594 + 3.02405i −0.0698934 + 0.121059i
\(625\) 0 0
\(626\) 5.75069 0.229844
\(627\) 22.7600 + 24.2177i 0.908947 + 0.967163i
\(628\) 7.44160 0.296952
\(629\) 17.3536 30.0574i 0.691935 1.19847i
\(630\) 0 0
\(631\) −7.83481 13.5703i −0.311899 0.540225i 0.666875 0.745170i \(-0.267632\pi\)
−0.978773 + 0.204945i \(0.934298\pi\)
\(632\) 7.75423 13.4307i 0.308447 0.534245i
\(633\) −16.3494 28.3179i −0.649829 1.12554i
\(634\) −17.4292 −0.692203
\(635\) 0 0
\(636\) −10.6380 18.4255i −0.421822 0.730618i
\(637\) −3.88097 6.72204i −0.153770 0.266337i
\(638\) 17.3001 0.684916
\(639\) 17.8179 0.704864
\(640\) 0 0
\(641\) −14.3585 + 24.8696i −0.567125 + 0.982289i 0.429724 + 0.902960i \(0.358611\pi\)
−0.996849 + 0.0793287i \(0.974722\pi\)
\(642\) −11.7030 20.2701i −0.461880 0.799999i
\(643\) 8.41674 14.5782i 0.331924 0.574909i −0.650965 0.759108i \(-0.725636\pi\)
0.982889 + 0.184199i \(0.0589690\pi\)
\(644\) 1.44200 2.49761i 0.0568227 0.0984197i
\(645\) 0 0
\(646\) −27.9407 + 6.56509i −1.09931 + 0.258300i
\(647\) 8.10908 0.318801 0.159400 0.987214i \(-0.449044\pi\)
0.159400 + 0.987214i \(0.449044\pi\)
\(648\) 5.14638 8.91380i 0.202169 0.350167i
\(649\) 0.272864 0.472614i 0.0107108 0.0185517i
\(650\) 0 0
\(651\) −4.33896 + 7.51529i −0.170057 + 0.294548i
\(652\) 7.77002 + 13.4581i 0.304297 + 0.527059i
\(653\) −33.6755 −1.31782 −0.658912 0.752220i \(-0.728983\pi\)
−0.658912 + 0.752220i \(0.728983\pi\)
\(654\) −38.2597 −1.49607
\(655\) 0 0
\(656\) −2.79230 4.83640i −0.109021 0.188830i
\(657\) −37.8010 −1.47476
\(658\) 1.24920 0.0486988
\(659\) −10.2712 17.7903i −0.400111 0.693012i 0.593628 0.804739i \(-0.297695\pi\)
−0.993739 + 0.111727i \(0.964362\pi\)
\(660\) 0 0
\(661\) 2.11413 + 3.66179i 0.0822302 + 0.142427i 0.904208 0.427093i \(-0.140462\pi\)
−0.821977 + 0.569520i \(0.807129\pi\)
\(662\) 6.05540 10.4883i 0.235350 0.407638i
\(663\) 11.4963 19.9122i 0.446479 0.773324i
\(664\) −0.313611 −0.0121705
\(665\) 0 0
\(666\) 13.0635 0.506201
\(667\) 5.71257 9.89446i 0.221192 0.383115i
\(668\) 11.0317 19.1074i 0.426828 0.739287i
\(669\) 5.45289 + 9.44468i 0.210821 + 0.365152i
\(670\) 0 0
\(671\) −19.0392 32.9768i −0.735000 1.27306i
\(672\) −3.13779 −0.121043
\(673\) −21.0671 −0.812076 −0.406038 0.913856i \(-0.633090\pi\)
−0.406038 + 0.913856i \(0.633090\pi\)
\(674\) −16.1078 27.8995i −0.620448 1.07465i
\(675\) 0 0
\(676\) −10.7743 −0.414396
\(677\) −5.16536 −0.198521 −0.0992604 0.995061i \(-0.531648\pi\)
−0.0992604 + 0.995061i \(0.531648\pi\)
\(678\) 7.44910 + 12.9022i 0.286081 + 0.495507i
\(679\) −8.06373 + 13.9668i −0.309457 + 0.535996i
\(680\) 0 0
\(681\) −4.85369 + 8.40684i −0.185994 + 0.322151i
\(682\) 4.50448 7.80199i 0.172486 0.298754i
\(683\) −17.1692 −0.656961 −0.328480 0.944511i \(-0.606536\pi\)
−0.328480 + 0.944511i \(0.606536\pi\)
\(684\) −7.39829 7.87214i −0.282881 0.300999i
\(685\) 0 0
\(686\) 8.17951 14.1673i 0.312295 0.540911i
\(687\) −24.3505 + 42.1764i −0.929031 + 1.60913i
\(688\) 3.81898 + 6.61466i 0.145597 + 0.252182i
\(689\) −6.78054 + 11.7442i −0.258318 + 0.447420i
\(690\) 0 0
\(691\) −2.98323 −0.113488 −0.0567438 0.998389i \(-0.518072\pi\)
−0.0567438 + 0.998389i \(0.518072\pi\)
\(692\) −0.381787 −0.0145134
\(693\) −5.41152 9.37302i −0.205567 0.356052i
\(694\) 15.2549 + 26.4222i 0.579066 + 1.00297i
\(695\) 0 0
\(696\) −12.4306 −0.471179
\(697\) 18.3861 + 31.8457i 0.696425 + 1.20624i
\(698\) −13.1658 + 22.8038i −0.498331 + 0.863135i
\(699\) 1.18538 + 2.05314i 0.0448352 + 0.0776568i
\(700\) 0 0
\(701\) 11.6523 20.1824i 0.440103 0.762280i −0.557594 0.830114i \(-0.688275\pi\)
0.997697 + 0.0678338i \(0.0216087\pi\)
\(702\) −1.82142 −0.0687451
\(703\) −6.63199 + 21.9977i −0.250130 + 0.829659i
\(704\) 3.25749 0.122771
\(705\) 0 0
\(706\) −0.184406 + 0.319400i −0.00694020 + 0.0120208i
\(707\) 8.37883 + 14.5126i 0.315118 + 0.545801i
\(708\) −0.196060 + 0.339586i −0.00736839 + 0.0127624i
\(709\) −12.7003 21.9976i −0.476970 0.826137i 0.522681 0.852528i \(-0.324932\pi\)
−0.999652 + 0.0263912i \(0.991598\pi\)
\(710\) 0 0
\(711\) −38.4359 −1.44146
\(712\) 4.90689 + 8.49898i 0.183893 + 0.318513i
\(713\) −2.97481 5.15252i −0.111407 0.192963i
\(714\) 20.6611 0.773221
\(715\) 0 0
\(716\) −6.09068 10.5494i −0.227619 0.394248i
\(717\) −26.5947 + 46.0634i −0.993198 + 1.72027i
\(718\) −14.7532 25.5533i −0.550585 0.953641i
\(719\) 20.8709 36.1495i 0.778353 1.34815i −0.154537 0.987987i \(-0.549389\pi\)
0.932890 0.360161i \(-0.117278\pi\)
\(720\) 0 0
\(721\) −11.7803 −0.438723
\(722\) 17.0118 8.46154i 0.633115 0.314906i
\(723\) 34.4864 1.28256
\(724\) 0.996021 1.72516i 0.0370168 0.0641150i
\(725\) 0 0
\(726\) −0.454962 0.788018i −0.0168852 0.0292461i
\(727\) 9.83583 17.0362i 0.364791 0.631836i −0.623952 0.781463i \(-0.714474\pi\)
0.988743 + 0.149627i \(0.0478072\pi\)
\(728\) 1.00000 + 1.73205i 0.0370625 + 0.0641941i
\(729\) −16.9366 −0.627280
\(730\) 0 0
\(731\) −25.1464 43.5549i −0.930074 1.61094i
\(732\) 13.6802 + 23.6947i 0.505634 + 0.875783i
\(733\) −28.9684 −1.06997 −0.534987 0.844861i \(-0.679683\pi\)
−0.534987 + 0.844861i \(0.679683\pi\)
\(734\) 18.3372 0.676840
\(735\) 0 0
\(736\) 1.07564 1.86306i 0.0396486 0.0686734i
\(737\) −21.2898 36.8750i −0.784219 1.35831i
\(738\) −6.92038 + 11.9865i −0.254743 + 0.441227i
\(739\) −3.07219 + 5.32118i −0.113012 + 0.195743i −0.916983 0.398925i \(-0.869383\pi\)
0.803971 + 0.594668i \(0.202717\pi\)
\(740\) 0 0
\(741\) −4.39351 + 14.5728i −0.161400 + 0.535347i
\(742\) −12.1860 −0.447360
\(743\) 2.64392 4.57940i 0.0969959 0.168002i −0.813444 0.581643i \(-0.802410\pi\)
0.910440 + 0.413641i \(0.135743\pi\)
\(744\) −3.23659 + 5.60594i −0.118659 + 0.205524i
\(745\) 0 0
\(746\) −10.0964 + 17.4875i −0.369656 + 0.640262i
\(747\) 0.388624 + 0.673116i 0.0142190 + 0.0246280i
\(748\) −21.4492 −0.784262
\(749\) −13.4059 −0.489843
\(750\) 0 0
\(751\) −18.1097 31.3669i −0.660832 1.14460i −0.980397 0.197031i \(-0.936870\pi\)
0.319565 0.947564i \(-0.396463\pi\)
\(752\) 0.931824 0.0339801
\(753\) −45.9537 −1.67465
\(754\) 3.96157 + 6.86163i 0.144272 + 0.249886i
\(755\) 0 0
\(756\) −0.818361 1.41744i −0.0297635 0.0515519i
\(757\) 15.2376 26.3922i 0.553818 0.959242i −0.444176 0.895940i \(-0.646504\pi\)
0.997994 0.0633020i \(-0.0201631\pi\)
\(758\) −7.63500 + 13.2242i −0.277316 + 0.480325i
\(759\) 16.4024 0.595368
\(760\) 0 0
\(761\) 1.54196 0.0558962 0.0279481 0.999609i \(-0.491103\pi\)
0.0279481 + 0.999609i \(0.491103\pi\)
\(762\) −0.516417 + 0.894460i −0.0187078 + 0.0324029i
\(763\) −10.9568 + 18.9777i −0.396662 + 0.687038i
\(764\) 5.31085 + 9.19867i 0.192140 + 0.332796i
\(765\) 0 0
\(766\) 13.4026 + 23.2139i 0.484254 + 0.838752i
\(767\) 0.249934 0.00902459
\(768\) −2.34059 −0.0844589
\(769\) 3.58197 + 6.20415i 0.129169 + 0.223728i 0.923355 0.383948i \(-0.125436\pi\)
−0.794186 + 0.607675i \(0.792102\pi\)
\(770\) 0 0
\(771\) 6.04225 0.217606
\(772\) 15.2824 0.550024
\(773\) 12.9561 + 22.4406i 0.465998 + 0.807131i 0.999246 0.0388273i \(-0.0123622\pi\)
−0.533248 + 0.845959i \(0.679029\pi\)
\(774\) 9.46489 16.3937i 0.340208 0.589258i
\(775\) 0 0
\(776\) −6.01504 + 10.4184i −0.215927 + 0.373997i
\(777\) 8.26961 14.3234i 0.296671 0.513849i
\(778\) −24.3289 −0.872232
\(779\) −16.6707 17.7384i −0.597291 0.635546i
\(780\) 0 0
\(781\) −11.7096 + 20.2816i −0.419001 + 0.725731i
\(782\) −7.08265 + 12.2675i −0.253275 + 0.438685i
\(783\) −3.24199 5.61530i −0.115859 0.200674i
\(784\) 2.60140 4.50576i 0.0929072 0.160920i
\(785\) 0 0
\(786\) −16.6686