Properties

Label 950.2.e.o.201.1
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 201.1
Root \(1.17030 - 2.02701i\) of defining polynomial
Character \(\chi\) \(=\) 950.201
Dual form 950.2.e.o.501.1

$q$-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 \(0.402813\pi\)
−0.976272 + 0.216547i \(0.930520\pi\)
\(4\) −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 \(-0.581532\pi\)
−0.253349 + 0.967375i \(0.581532\pi\)
\(8\) −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 0.743846 0.668351i \(-0.233000\pi\)
−0.950732 + 0.310014i \(0.899666\pi\)
\(14\) −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 \(0.461039\pi\)
−0.920593 + 0.390523i \(0.872294\pi\)
\(18\) −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 0.731819 0.681499i \(-0.238672\pi\)
−0.956105 + 0.293024i \(0.905338\pi\)
\(24\) 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 \(-0.642641\pi\)
−0.433272 + 0.901263i \(0.642641\pi\)
\(38\) 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 \(0.364548\pi\)
−0.995195 + 0.0979082i \(0.968785\pi\)
\(44\) −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 0.898003 0.439989i \(-0.145018\pi\)
−0.830043 + 0.557699i \(0.811684\pi\)
\(48\) −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 \(-0.952051\pi\)
0.364375 0.931252i \(-0.381283\pi\)
\(54\) −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 \(0.127682\pi\)
−0.122167 + 0.992510i \(0.538984\pi\)
\(68\) 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 \(0.517769\pi\)
−0.836780 + 0.547539i \(0.815565\pi\)
\(74\) −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 \(-0.494521\pi\)
0.0172116 + 0.999852i \(0.494521\pi\)
\(84\) −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 \(-0.624208\pi\)
0.991117 0.132994i \(-0.0424591\pi\)
\(98\) −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 \(-0.357482\pi\)
0.432924 + 0.901430i \(0.357482\pi\)
\(104\) 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 \(-0.339413\pi\)
0.483368 + 0.875417i \(0.339413\pi\)
\(108\) 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 \(-0.596783\pi\)
−0.299391 + 0.954131i \(0.596783\pi\)
\(114\) −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 0.856070 0.516859i \(-0.172899\pi\)
−0.875649 + 0.482949i \(0.839566\pi\)
\(128\) 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 0.794029 0.607879i \(-0.207980\pi\)
−0.923454 + 0.383710i \(0.874646\pi\)
\(138\) 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 −0.678485 0.734614i \(-0.737363\pi\)
0.975437 + 0.220278i \(0.0706964\pi\)
\(158\) −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 \(-0.291733\pi\)
0.608595 + 0.793481i \(0.291733\pi\)
\(164\) 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 \(-0.841047\pi\)
0.0242320 0.999706i \(-0.492286\pi\)
\(168\) −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 −0.873191 0.487378i \(-0.837953\pi\)
0.858678 + 0.512516i \(0.171287\pi\)
\(174\) 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 \(-0.647952\pi\)
0.998272 0.0587608i \(-0.0187149\pi\)
\(194\) −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 \(-0.453243\pi\)
0.146365 + 0.989231i \(0.453243\pi\)
\(198\) −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 −0.777417 0.628985i \(-0.783471\pi\)
0.933426 + 0.358771i \(0.116804\pi\)
\(224\) −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 \(-0.456049\pi\)
0.137636 + 0.990483i \(0.456049\pi\)
\(228\) −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 −0.848960 0.528458i \(-0.822770\pi\)
0.882138 + 0.470992i \(0.156104\pi\)
\(234\) 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 0.822956 0.568105i \(-0.192323\pi\)
−0.903471 + 0.428649i \(0.858990\pi\)
\(258\) −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 −0.718991 0.695020i \(-0.755396\pi\)
0.961400 + 0.275155i \(0.0887290\pi\)
\(264\) 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 \(-0.417606\pi\)
0.255967 + 0.966685i \(0.417606\pi\)
\(278\) 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 −0.948534 0.316676i \(-0.897433\pi\)
0.748516 + 0.663116i \(0.230766\pi\)
\(284\) 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 \(-0.490065\pi\)
0.0312051 + 0.999513i \(0.490065\pi\)
\(294\) −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 −0.909944 0.414731i \(-0.863876\pi\)
0.814140 + 0.580669i \(0.197209\pi\)
\(308\) 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 0.935773 0.352602i \(-0.114703\pi\)
−0.773249 + 0.634102i \(0.781370\pi\)
\(314\) −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 0.510465 0.859899i \(-0.329473\pi\)
−0.999926 + 0.0121262i \(0.996140\pi\)
\(318\) 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 \(-0.492579\pi\)
0.854135 0.520052i \(-0.174087\pi\)
\(338\) −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 \(0.472095\pi\)
−0.906476 + 0.422257i \(0.861238\pi\)
\(348\) −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 \(-0.503124\pi\)
−0.00981493 + 0.999952i \(0.503124\pi\)
\(354\) 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 0.999699 0.0245392i \(-0.00781185\pi\)
−0.521101 + 0.853495i \(0.674479\pi\)
\(368\) 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 \(-0.675102\pi\)
−0.522772 + 0.852473i \(0.675102\pi\)
\(374\) 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 \(0.406794\pi\)
−0.973488 + 0.228740i \(0.926539\pi\)
\(384\) 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 −0.999696 0.0246449i \(-0.992155\pi\)
0.521191 + 0.853440i \(0.325488\pi\)
\(398\) 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 0.984877 0.173256i \(-0.0554288\pi\)
−0.642482 + 0.766300i \(0.722095\pi\)
\(434\) 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 \(0.200006\pi\)
0.104548 + 0.994520i \(0.466660\pi\)
\(444\) −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 \(-0.388698\pi\)
0.342583 + 0.939488i \(0.388698\pi\)
\(458\) −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 \(-0.694212\pi\)
−0.572978 + 0.819571i \(0.694212\pi\)
\(464\) 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 \(-0.673668\pi\)
−0.518925 + 0.854820i \(0.673668\pi\)
\(468\) 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 \(-0.124823\pi\)
0.924093 + 0.382168i \(0.124823\pi\)
\(488\) 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 \(-0.985762\pi\)
0.460776 0.887517i \(-0.347571\pi\)
\(504\) −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 \(-0.998751\pi\)
0.496598 0.867981i \(-0.334582\pi\)
\(524\) 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 0.972216 0.234084i \(-0.0752091\pi\)
−0.688831 + 0.724922i \(0.741876\pi\)
\(548\) −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 \(-0.995082\pi\)
0.486562 0.873646i \(-0.338251\pi\)
\(558\) 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 \(-0.693995\pi\)
−0.572420 + 0.819961i \(0.693995\pi\)
\(564\) 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 \(-0.175064\pi\)
0.852536 + 0.522669i \(0.175064\pi\)
\(578\) −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 −0.988686 0.149998i \(-0.952073\pi\)
0.624245 + 0.781229i \(0.285407\pi\)
\(588\) −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 0.567294 0.823515i \(-0.307990\pi\)
−0.996832 + 0.0795335i \(0.974657\pi\)
\(594\) −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 \(-0.493933\pi\)
0.0190604 + 0.999818i \(0.493933\pi\)
\(608\) −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 −0.936264 0.351297i \(-0.885741\pi\)
0.772364 + 0.635180i \(0.219074\pi\)
\(614\) 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 0.757395 0.652957i \(-0.226472\pi\)
−0.944175 + 0.329445i \(0.893138\pi\)
\(618\) 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 −0.982889 0.184199i \(-0.941031\pi\)
0.650965 + 0.759108i \(0.274364\pi\)
\(644\) 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 \(-0.550956\pi\)
−0.159400 + 0.987214i \(0.550956\pi\)
\(648\) −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 \(-0.271017\pi\)
0.658912 + 0.752220i \(0.271017\pi\)
\(654\) −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 \(-0.366910\pi\)
0.406038 + 0.913856i \(0.366910\pi\)
\(674\) −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 \(-0.468352\pi\)
0.0992604 + 0.995061i \(0.468352\pi\)
\(678\) −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 \(-0.393464\pi\)
0.328480 + 0.944511i \(0.393464\pi\)
\(684\) −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 −0.988743 0.149627i \(-0.952193\pi\)
0.623952 + 0.781463i \(0.285526\pi\)
\(728\) −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 \(-0.320317\pi\)
0.534987 + 0.844861i \(0.320317\pi\)
\(734\) 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 −0.910440 0.413641i \(-0.864257\pi\)
0.813444 + 0.581643i \(0.197590\pi\)
\(744\) −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 \(0.353496\pi\)
−0.997994 + 0.0633020i \(0.979837\pi\)
\(758\) 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 0.533248 0.845959i \(-0.320971\pi\)
−0.999246 + 0.0388273i \(0.987638\pi\)
\(774\) 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 −0.594551