Properties

Label 570.2.f.b.341.2
Level $570$
Weight $2$
Character 570.341
Analytic conductor $4.551$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 570.f (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.55147291521\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{8})\)
Defining polynomial: \(x^{4} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 341.2
Root \(-0.707107 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 570.341
Dual form 570.2.f.b.341.3

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +(1.00000 - 1.41421i) q^{3} +1.00000 q^{4} +1.00000i q^{5} +(1.00000 - 1.41421i) q^{6} +0.585786 q^{7} +1.00000 q^{8} +(-1.00000 - 2.82843i) q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +(1.00000 - 1.41421i) q^{3} +1.00000 q^{4} +1.00000i q^{5} +(1.00000 - 1.41421i) q^{6} +0.585786 q^{7} +1.00000 q^{8} +(-1.00000 - 2.82843i) q^{9} +1.00000i q^{10} -5.41421i q^{11} +(1.00000 - 1.41421i) q^{12} +2.24264i q^{13} +0.585786 q^{14} +(1.41421 + 1.00000i) q^{15} +1.00000 q^{16} -2.82843i q^{17} +(-1.00000 - 2.82843i) q^{18} +(4.24264 + 1.00000i) q^{19} +1.00000i q^{20} +(0.585786 - 0.828427i) q^{21} -5.41421i q^{22} +6.00000i q^{23} +(1.00000 - 1.41421i) q^{24} -1.00000 q^{25} +2.24264i q^{26} +(-5.00000 - 1.41421i) q^{27} +0.585786 q^{28} +5.07107 q^{29} +(1.41421 + 1.00000i) q^{30} +6.82843i q^{31} +1.00000 q^{32} +(-7.65685 - 5.41421i) q^{33} -2.82843i q^{34} +0.585786i q^{35} +(-1.00000 - 2.82843i) q^{36} +2.24264i q^{37} +(4.24264 + 1.00000i) q^{38} +(3.17157 + 2.24264i) q^{39} +1.00000i q^{40} -11.0711 q^{41} +(0.585786 - 0.828427i) q^{42} +6.58579 q^{43} -5.41421i q^{44} +(2.82843 - 1.00000i) q^{45} +6.00000i q^{46} -3.17157i q^{47} +(1.00000 - 1.41421i) q^{48} -6.65685 q^{49} -1.00000 q^{50} +(-4.00000 - 2.82843i) q^{51} +2.24264i q^{52} -3.17157 q^{53} +(-5.00000 - 1.41421i) q^{54} +5.41421 q^{55} +0.585786 q^{56} +(5.65685 - 5.00000i) q^{57} +5.07107 q^{58} -12.8284 q^{59} +(1.41421 + 1.00000i) q^{60} -4.48528 q^{61} +6.82843i q^{62} +(-0.585786 - 1.65685i) q^{63} +1.00000 q^{64} -2.24264 q^{65} +(-7.65685 - 5.41421i) q^{66} -2.82843i q^{68} +(8.48528 + 6.00000i) q^{69} +0.585786i q^{70} -2.82843 q^{71} +(-1.00000 - 2.82843i) q^{72} +2.48528 q^{73} +2.24264i q^{74} +(-1.00000 + 1.41421i) q^{75} +(4.24264 + 1.00000i) q^{76} -3.17157i q^{77} +(3.17157 + 2.24264i) q^{78} +13.3137i q^{79} +1.00000i q^{80} +(-7.00000 + 5.65685i) q^{81} -11.0711 q^{82} +12.8284i q^{83} +(0.585786 - 0.828427i) q^{84} +2.82843 q^{85} +6.58579 q^{86} +(5.07107 - 7.17157i) q^{87} -5.41421i q^{88} +10.5858 q^{89} +(2.82843 - 1.00000i) q^{90} +1.31371i q^{91} +6.00000i q^{92} +(9.65685 + 6.82843i) q^{93} -3.17157i q^{94} +(-1.00000 + 4.24264i) q^{95} +(1.00000 - 1.41421i) q^{96} +6.58579i q^{97} -6.65685 q^{98} +(-15.3137 + 5.41421i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 4q^{2} + 4q^{3} + 4q^{4} + 4q^{6} + 8q^{7} + 4q^{8} - 4q^{9} + O(q^{10}) \) \( 4q + 4q^{2} + 4q^{3} + 4q^{4} + 4q^{6} + 8q^{7} + 4q^{8} - 4q^{9} + 4q^{12} + 8q^{14} + 4q^{16} - 4q^{18} + 8q^{21} + 4q^{24} - 4q^{25} - 20q^{27} + 8q^{28} - 8q^{29} + 4q^{32} - 8q^{33} - 4q^{36} + 24q^{39} - 16q^{41} + 8q^{42} + 32q^{43} + 4q^{48} - 4q^{49} - 4q^{50} - 16q^{51} - 24q^{53} - 20q^{54} + 16q^{55} + 8q^{56} - 8q^{58} - 40q^{59} + 16q^{61} - 8q^{63} + 4q^{64} + 8q^{65} - 8q^{66} - 4q^{72} - 24q^{73} - 4q^{75} + 24q^{78} - 28q^{81} - 16q^{82} + 8q^{84} + 32q^{86} - 8q^{87} + 48q^{89} + 16q^{93} - 4q^{95} + 4q^{96} - 4q^{98} - 16q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(211\) \(457\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 1.00000 1.41421i 0.577350 0.816497i
\(4\) 1.00000 0.500000
\(5\) 1.00000i 0.447214i
\(6\) 1.00000 1.41421i 0.408248 0.577350i
\(7\) 0.585786 0.221406 0.110703 0.993854i \(-0.464690\pi\)
0.110703 + 0.993854i \(0.464690\pi\)
\(8\) 1.00000 0.353553
\(9\) −1.00000 2.82843i −0.333333 0.942809i
\(10\) 1.00000i 0.316228i
\(11\) 5.41421i 1.63245i −0.577736 0.816223i \(-0.696064\pi\)
0.577736 0.816223i \(-0.303936\pi\)
\(12\) 1.00000 1.41421i 0.288675 0.408248i
\(13\) 2.24264i 0.621997i 0.950410 + 0.310998i \(0.100663\pi\)
−0.950410 + 0.310998i \(0.899337\pi\)
\(14\) 0.585786 0.156558
\(15\) 1.41421 + 1.00000i 0.365148 + 0.258199i
\(16\) 1.00000 0.250000
\(17\) 2.82843i 0.685994i −0.939336 0.342997i \(-0.888558\pi\)
0.939336 0.342997i \(-0.111442\pi\)
\(18\) −1.00000 2.82843i −0.235702 0.666667i
\(19\) 4.24264 + 1.00000i 0.973329 + 0.229416i
\(20\) 1.00000i 0.223607i
\(21\) 0.585786 0.828427i 0.127829 0.180778i
\(22\) 5.41421i 1.15431i
\(23\) 6.00000i 1.25109i 0.780189 + 0.625543i \(0.215123\pi\)
−0.780189 + 0.625543i \(0.784877\pi\)
\(24\) 1.00000 1.41421i 0.204124 0.288675i
\(25\) −1.00000 −0.200000
\(26\) 2.24264i 0.439818i
\(27\) −5.00000 1.41421i −0.962250 0.272166i
\(28\) 0.585786 0.110703
\(29\) 5.07107 0.941674 0.470837 0.882220i \(-0.343952\pi\)
0.470837 + 0.882220i \(0.343952\pi\)
\(30\) 1.41421 + 1.00000i 0.258199 + 0.182574i
\(31\) 6.82843i 1.22642i 0.789919 + 0.613211i \(0.210122\pi\)
−0.789919 + 0.613211i \(0.789878\pi\)
\(32\) 1.00000 0.176777
\(33\) −7.65685 5.41421i −1.33289 0.942494i
\(34\) 2.82843i 0.485071i
\(35\) 0.585786i 0.0990160i
\(36\) −1.00000 2.82843i −0.166667 0.471405i
\(37\) 2.24264i 0.368688i 0.982862 + 0.184344i \(0.0590160\pi\)
−0.982862 + 0.184344i \(0.940984\pi\)
\(38\) 4.24264 + 1.00000i 0.688247 + 0.162221i
\(39\) 3.17157 + 2.24264i 0.507858 + 0.359110i
\(40\) 1.00000i 0.158114i
\(41\) −11.0711 −1.72901 −0.864505 0.502624i \(-0.832368\pi\)
−0.864505 + 0.502624i \(0.832368\pi\)
\(42\) 0.585786 0.828427i 0.0903888 0.127829i
\(43\) 6.58579 1.00432 0.502162 0.864774i \(-0.332538\pi\)
0.502162 + 0.864774i \(0.332538\pi\)
\(44\) 5.41421i 0.816223i
\(45\) 2.82843 1.00000i 0.421637 0.149071i
\(46\) 6.00000i 0.884652i
\(47\) 3.17157i 0.462621i −0.972880 0.231311i \(-0.925699\pi\)
0.972880 0.231311i \(-0.0743014\pi\)
\(48\) 1.00000 1.41421i 0.144338 0.204124i
\(49\) −6.65685 −0.950979
\(50\) −1.00000 −0.141421
\(51\) −4.00000 2.82843i −0.560112 0.396059i
\(52\) 2.24264i 0.310998i
\(53\) −3.17157 −0.435649 −0.217825 0.975988i \(-0.569896\pi\)
−0.217825 + 0.975988i \(0.569896\pi\)
\(54\) −5.00000 1.41421i −0.680414 0.192450i
\(55\) 5.41421 0.730052
\(56\) 0.585786 0.0782790
\(57\) 5.65685 5.00000i 0.749269 0.662266i
\(58\) 5.07107 0.665864
\(59\) −12.8284 −1.67012 −0.835059 0.550160i \(-0.814567\pi\)
−0.835059 + 0.550160i \(0.814567\pi\)
\(60\) 1.41421 + 1.00000i 0.182574 + 0.129099i
\(61\) −4.48528 −0.574281 −0.287141 0.957888i \(-0.592705\pi\)
−0.287141 + 0.957888i \(0.592705\pi\)
\(62\) 6.82843i 0.867211i
\(63\) −0.585786 1.65685i −0.0738022 0.208744i
\(64\) 1.00000 0.125000
\(65\) −2.24264 −0.278165
\(66\) −7.65685 5.41421i −0.942494 0.666444i
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) 2.82843i 0.342997i
\(69\) 8.48528 + 6.00000i 1.02151 + 0.722315i
\(70\) 0.585786i 0.0700149i
\(71\) −2.82843 −0.335673 −0.167836 0.985815i \(-0.553678\pi\)
−0.167836 + 0.985815i \(0.553678\pi\)
\(72\) −1.00000 2.82843i −0.117851 0.333333i
\(73\) 2.48528 0.290880 0.145440 0.989367i \(-0.453540\pi\)
0.145440 + 0.989367i \(0.453540\pi\)
\(74\) 2.24264i 0.260702i
\(75\) −1.00000 + 1.41421i −0.115470 + 0.163299i
\(76\) 4.24264 + 1.00000i 0.486664 + 0.114708i
\(77\) 3.17157i 0.361434i
\(78\) 3.17157 + 2.24264i 0.359110 + 0.253929i
\(79\) 13.3137i 1.49791i 0.662621 + 0.748955i \(0.269444\pi\)
−0.662621 + 0.748955i \(0.730556\pi\)
\(80\) 1.00000i 0.111803i
\(81\) −7.00000 + 5.65685i −0.777778 + 0.628539i
\(82\) −11.0711 −1.22259
\(83\) 12.8284i 1.40810i 0.710149 + 0.704051i \(0.248628\pi\)
−0.710149 + 0.704051i \(0.751372\pi\)
\(84\) 0.585786 0.828427i 0.0639145 0.0903888i
\(85\) 2.82843 0.306786
\(86\) 6.58579 0.710164
\(87\) 5.07107 7.17157i 0.543676 0.768873i
\(88\) 5.41421i 0.577157i
\(89\) 10.5858 1.12209 0.561046 0.827785i \(-0.310399\pi\)
0.561046 + 0.827785i \(0.310399\pi\)
\(90\) 2.82843 1.00000i 0.298142 0.105409i
\(91\) 1.31371i 0.137714i
\(92\) 6.00000i 0.625543i
\(93\) 9.65685 + 6.82843i 1.00137 + 0.708075i
\(94\) 3.17157i 0.327123i
\(95\) −1.00000 + 4.24264i −0.102598 + 0.435286i
\(96\) 1.00000 1.41421i 0.102062 0.144338i
\(97\) 6.58579i 0.668685i 0.942452 + 0.334343i \(0.108514\pi\)
−0.942452 + 0.334343i \(0.891486\pi\)
\(98\) −6.65685 −0.672444
\(99\) −15.3137 + 5.41421i −1.53909 + 0.544149i
\(100\) −1.00000 −0.100000
\(101\) 7.65685i 0.761885i −0.924599 0.380943i \(-0.875599\pi\)
0.924599 0.380943i \(-0.124401\pi\)
\(102\) −4.00000 2.82843i −0.396059 0.280056i
\(103\) 4.34315i 0.427943i −0.976840 0.213971i \(-0.931360\pi\)
0.976840 0.213971i \(-0.0686399\pi\)
\(104\) 2.24264i 0.219909i
\(105\) 0.828427 + 0.585786i 0.0808462 + 0.0571669i
\(106\) −3.17157 −0.308050
\(107\) 3.65685 0.353521 0.176761 0.984254i \(-0.443438\pi\)
0.176761 + 0.984254i \(0.443438\pi\)
\(108\) −5.00000 1.41421i −0.481125 0.136083i
\(109\) 2.34315i 0.224433i 0.993684 + 0.112216i \(0.0357950\pi\)
−0.993684 + 0.112216i \(0.964205\pi\)
\(110\) 5.41421 0.516225
\(111\) 3.17157 + 2.24264i 0.301032 + 0.212862i
\(112\) 0.585786 0.0553516
\(113\) 12.8284 1.20680 0.603398 0.797440i \(-0.293813\pi\)
0.603398 + 0.797440i \(0.293813\pi\)
\(114\) 5.65685 5.00000i 0.529813 0.468293i
\(115\) −6.00000 −0.559503
\(116\) 5.07107 0.470837
\(117\) 6.34315 2.24264i 0.586424 0.207332i
\(118\) −12.8284 −1.18095
\(119\) 1.65685i 0.151884i
\(120\) 1.41421 + 1.00000i 0.129099 + 0.0912871i
\(121\) −18.3137 −1.66488
\(122\) −4.48528 −0.406078
\(123\) −11.0711 + 15.6569i −0.998245 + 1.41173i
\(124\) 6.82843i 0.613211i
\(125\) 1.00000i 0.0894427i
\(126\) −0.585786 1.65685i −0.0521860 0.147604i
\(127\) 12.8284i 1.13834i 0.822220 + 0.569169i \(0.192735\pi\)
−0.822220 + 0.569169i \(0.807265\pi\)
\(128\) 1.00000 0.0883883
\(129\) 6.58579 9.31371i 0.579846 0.820026i
\(130\) −2.24264 −0.196693
\(131\) 4.92893i 0.430643i −0.976543 0.215321i \(-0.930920\pi\)
0.976543 0.215321i \(-0.0690799\pi\)
\(132\) −7.65685 5.41421i −0.666444 0.471247i
\(133\) 2.48528 + 0.585786i 0.215501 + 0.0507941i
\(134\) 0 0
\(135\) 1.41421 5.00000i 0.121716 0.430331i
\(136\) 2.82843i 0.242536i
\(137\) 14.4853i 1.23756i −0.785564 0.618781i \(-0.787627\pi\)
0.785564 0.618781i \(-0.212373\pi\)
\(138\) 8.48528 + 6.00000i 0.722315 + 0.510754i
\(139\) 18.1421 1.53880 0.769398 0.638770i \(-0.220556\pi\)
0.769398 + 0.638770i \(0.220556\pi\)
\(140\) 0.585786i 0.0495080i
\(141\) −4.48528 3.17157i −0.377729 0.267095i
\(142\) −2.82843 −0.237356
\(143\) 12.1421 1.01538
\(144\) −1.00000 2.82843i −0.0833333 0.235702i
\(145\) 5.07107i 0.421129i
\(146\) 2.48528 0.205683
\(147\) −6.65685 + 9.41421i −0.549048 + 0.776471i
\(148\) 2.24264i 0.184344i
\(149\) 14.4853i 1.18668i 0.804952 + 0.593340i \(0.202191\pi\)
−0.804952 + 0.593340i \(0.797809\pi\)
\(150\) −1.00000 + 1.41421i −0.0816497 + 0.115470i
\(151\) 20.4853i 1.66707i −0.552468 0.833534i \(-0.686314\pi\)
0.552468 0.833534i \(-0.313686\pi\)
\(152\) 4.24264 + 1.00000i 0.344124 + 0.0811107i
\(153\) −8.00000 + 2.82843i −0.646762 + 0.228665i
\(154\) 3.17157i 0.255573i
\(155\) −6.82843 −0.548472
\(156\) 3.17157 + 2.24264i 0.253929 + 0.179555i
\(157\) −23.7990 −1.89937 −0.949683 0.313212i \(-0.898595\pi\)
−0.949683 + 0.313212i \(0.898595\pi\)
\(158\) 13.3137i 1.05918i
\(159\) −3.17157 + 4.48528i −0.251522 + 0.355706i
\(160\) 1.00000i 0.0790569i
\(161\) 3.51472i 0.276999i
\(162\) −7.00000 + 5.65685i −0.549972 + 0.444444i
\(163\) 12.7279 0.996928 0.498464 0.866910i \(-0.333898\pi\)
0.498464 + 0.866910i \(0.333898\pi\)
\(164\) −11.0711 −0.864505
\(165\) 5.41421 7.65685i 0.421496 0.596085i
\(166\) 12.8284i 0.995679i
\(167\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) 0.585786 0.828427i 0.0451944 0.0639145i
\(169\) 7.97056 0.613120
\(170\) 2.82843 0.216930
\(171\) −1.41421 13.0000i −0.108148 0.994135i
\(172\) 6.58579 0.502162
\(173\) 6.00000 0.456172 0.228086 0.973641i \(-0.426753\pi\)
0.228086 + 0.973641i \(0.426753\pi\)
\(174\) 5.07107 7.17157i 0.384437 0.543676i
\(175\) −0.585786 −0.0442813
\(176\) 5.41421i 0.408112i
\(177\) −12.8284 + 18.1421i −0.964244 + 1.36365i
\(178\) 10.5858 0.793438
\(179\) −21.7990 −1.62933 −0.814667 0.579930i \(-0.803080\pi\)
−0.814667 + 0.579930i \(0.803080\pi\)
\(180\) 2.82843 1.00000i 0.210819 0.0745356i
\(181\) 10.8284i 0.804871i −0.915448 0.402435i \(-0.868164\pi\)
0.915448 0.402435i \(-0.131836\pi\)
\(182\) 1.31371i 0.0973786i
\(183\) −4.48528 + 6.34315i −0.331562 + 0.468899i
\(184\) 6.00000i 0.442326i
\(185\) −2.24264 −0.164882
\(186\) 9.65685 + 6.82843i 0.708075 + 0.500685i
\(187\) −15.3137 −1.11985
\(188\) 3.17157i 0.231311i
\(189\) −2.92893 0.828427i −0.213048 0.0602592i
\(190\) −1.00000 + 4.24264i −0.0725476 + 0.307794i
\(191\) 10.2426i 0.741131i −0.928806 0.370566i \(-0.879164\pi\)
0.928806 0.370566i \(-0.120836\pi\)
\(192\) 1.00000 1.41421i 0.0721688 0.102062i
\(193\) 19.5563i 1.40770i −0.710350 0.703848i \(-0.751463\pi\)
0.710350 0.703848i \(-0.248537\pi\)
\(194\) 6.58579i 0.472832i
\(195\) −2.24264 + 3.17157i −0.160599 + 0.227121i
\(196\) −6.65685 −0.475490
\(197\) 18.1421i 1.29257i −0.763095 0.646287i \(-0.776321\pi\)
0.763095 0.646287i \(-0.223679\pi\)
\(198\) −15.3137 + 5.41421i −1.08830 + 0.384771i
\(199\) −16.9706 −1.20301 −0.601506 0.798869i \(-0.705432\pi\)
−0.601506 + 0.798869i \(0.705432\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 0 0
\(202\) 7.65685i 0.538734i
\(203\) 2.97056 0.208493
\(204\) −4.00000 2.82843i −0.280056 0.198030i
\(205\) 11.0711i 0.773237i
\(206\) 4.34315i 0.302601i
\(207\) 16.9706 6.00000i 1.17954 0.417029i
\(208\) 2.24264i 0.155499i
\(209\) 5.41421 22.9706i 0.374509 1.58891i
\(210\) 0.828427 + 0.585786i 0.0571669 + 0.0404231i
\(211\) 2.00000i 0.137686i 0.997628 + 0.0688428i \(0.0219307\pi\)
−0.997628 + 0.0688428i \(0.978069\pi\)
\(212\) −3.17157 −0.217825
\(213\) −2.82843 + 4.00000i −0.193801 + 0.274075i
\(214\) 3.65685 0.249977
\(215\) 6.58579i 0.449147i
\(216\) −5.00000 1.41421i −0.340207 0.0962250i
\(217\) 4.00000i 0.271538i
\(218\) 2.34315i 0.158698i
\(219\) 2.48528 3.51472i 0.167940 0.237503i
\(220\) 5.41421 0.365026
\(221\) 6.34315 0.426686
\(222\) 3.17157 + 2.24264i 0.212862 + 0.150516i
\(223\) 18.0000i 1.20537i 0.797980 + 0.602685i \(0.205902\pi\)
−0.797980 + 0.602685i \(0.794098\pi\)
\(224\) 0.585786 0.0391395
\(225\) 1.00000 + 2.82843i 0.0666667 + 0.188562i
\(226\) 12.8284 0.853334
\(227\) −2.34315 −0.155520 −0.0777600 0.996972i \(-0.524777\pi\)
−0.0777600 + 0.996972i \(0.524777\pi\)
\(228\) 5.65685 5.00000i 0.374634 0.331133i
\(229\) 8.48528 0.560723 0.280362 0.959894i \(-0.409546\pi\)
0.280362 + 0.959894i \(0.409546\pi\)
\(230\) −6.00000 −0.395628
\(231\) −4.48528 3.17157i −0.295110 0.208674i
\(232\) 5.07107 0.332932
\(233\) 17.7990i 1.16605i −0.812454 0.583025i \(-0.801869\pi\)
0.812454 0.583025i \(-0.198131\pi\)
\(234\) 6.34315 2.24264i 0.414664 0.146606i
\(235\) 3.17157 0.206891
\(236\) −12.8284 −0.835059
\(237\) 18.8284 + 13.3137i 1.22304 + 0.864818i
\(238\) 1.65685i 0.107398i
\(239\) 0.100505i 0.00650113i 0.999995 + 0.00325057i \(0.00103469\pi\)
−0.999995 + 0.00325057i \(0.998965\pi\)
\(240\) 1.41421 + 1.00000i 0.0912871 + 0.0645497i
\(241\) 8.48528i 0.546585i −0.961931 0.273293i \(-0.911887\pi\)
0.961931 0.273293i \(-0.0881127\pi\)
\(242\) −18.3137 −1.17725
\(243\) 1.00000 + 15.5563i 0.0641500 + 0.997940i
\(244\) −4.48528 −0.287141
\(245\) 6.65685i 0.425291i
\(246\) −11.0711 + 15.6569i −0.705866 + 0.998245i
\(247\) −2.24264 + 9.51472i −0.142696 + 0.605407i
\(248\) 6.82843i 0.433606i
\(249\) 18.1421 + 12.8284i 1.14971 + 0.812969i
\(250\) 1.00000i 0.0632456i
\(251\) 4.92893i 0.311111i −0.987827 0.155556i \(-0.950283\pi\)
0.987827 0.155556i \(-0.0497168\pi\)
\(252\) −0.585786 1.65685i −0.0369011 0.104372i
\(253\) 32.4853 2.04233
\(254\) 12.8284i 0.804927i
\(255\) 2.82843 4.00000i 0.177123 0.250490i
\(256\) 1.00000 0.0625000
\(257\) 28.1421 1.75546 0.877729 0.479157i \(-0.159058\pi\)
0.877729 + 0.479157i \(0.159058\pi\)
\(258\) 6.58579 9.31371i 0.410013 0.579846i
\(259\) 1.31371i 0.0816299i
\(260\) −2.24264 −0.139083
\(261\) −5.07107 14.3431i −0.313891 0.887818i
\(262\) 4.92893i 0.304510i
\(263\) 11.1716i 0.688869i 0.938810 + 0.344434i \(0.111929\pi\)
−0.938810 + 0.344434i \(0.888071\pi\)
\(264\) −7.65685 5.41421i −0.471247 0.333222i
\(265\) 3.17157i 0.194828i
\(266\) 2.48528 + 0.585786i 0.152382 + 0.0359169i
\(267\) 10.5858 14.9706i 0.647840 0.916184i
\(268\) 0 0
\(269\) −24.3848 −1.48677 −0.743383 0.668866i \(-0.766780\pi\)
−0.743383 + 0.668866i \(0.766780\pi\)
\(270\) 1.41421 5.00000i 0.0860663 0.304290i
\(271\) −28.9706 −1.75984 −0.879918 0.475125i \(-0.842403\pi\)
−0.879918 + 0.475125i \(0.842403\pi\)
\(272\) 2.82843i 0.171499i
\(273\) 1.85786 + 1.31371i 0.112443 + 0.0795093i
\(274\) 14.4853i 0.875088i
\(275\) 5.41421i 0.326489i
\(276\) 8.48528 + 6.00000i 0.510754 + 0.361158i
\(277\) 24.9706 1.50034 0.750168 0.661247i \(-0.229973\pi\)
0.750168 + 0.661247i \(0.229973\pi\)
\(278\) 18.1421 1.08809
\(279\) 19.3137 6.82843i 1.15628 0.408807i
\(280\) 0.585786i 0.0350074i
\(281\) −0.928932 −0.0554154 −0.0277077 0.999616i \(-0.508821\pi\)
−0.0277077 + 0.999616i \(0.508821\pi\)
\(282\) −4.48528 3.17157i −0.267095 0.188864i
\(283\) 12.7279 0.756596 0.378298 0.925684i \(-0.376509\pi\)
0.378298 + 0.925684i \(0.376509\pi\)
\(284\) −2.82843 −0.167836
\(285\) 5.00000 + 5.65685i 0.296174 + 0.335083i
\(286\) 12.1421 0.717980
\(287\) −6.48528 −0.382814
\(288\) −1.00000 2.82843i −0.0589256 0.166667i
\(289\) 9.00000 0.529412
\(290\) 5.07107i 0.297783i
\(291\) 9.31371 + 6.58579i 0.545979 + 0.386066i
\(292\) 2.48528 0.145440
\(293\) 3.17157 0.185285 0.0926426 0.995699i \(-0.470469\pi\)
0.0926426 + 0.995699i \(0.470469\pi\)
\(294\) −6.65685 + 9.41421i −0.388236 + 0.549048i
\(295\) 12.8284i 0.746900i
\(296\) 2.24264i 0.130351i
\(297\) −7.65685 + 27.0711i −0.444296 + 1.57082i
\(298\) 14.4853i 0.839110i
\(299\) −13.4558 −0.778172
\(300\) −1.00000 + 1.41421i −0.0577350 + 0.0816497i
\(301\) 3.85786 0.222364
\(302\) 20.4853i 1.17880i
\(303\) −10.8284 7.65685i −0.622077 0.439875i
\(304\) 4.24264 + 1.00000i 0.243332 + 0.0573539i
\(305\) 4.48528i 0.256826i
\(306\) −8.00000 + 2.82843i −0.457330 + 0.161690i
\(307\) 18.1421i 1.03543i 0.855554 + 0.517713i \(0.173217\pi\)
−0.855554 + 0.517713i \(0.826783\pi\)
\(308\) 3.17157i 0.180717i
\(309\) −6.14214 4.34315i −0.349414 0.247073i
\(310\) −6.82843 −0.387829
\(311\) 5.07107i 0.287554i −0.989610 0.143777i \(-0.954075\pi\)
0.989610 0.143777i \(-0.0459248\pi\)
\(312\) 3.17157 + 2.24264i 0.179555 + 0.126965i
\(313\) −16.8284 −0.951199 −0.475599 0.879662i \(-0.657769\pi\)
−0.475599 + 0.879662i \(0.657769\pi\)
\(314\) −23.7990 −1.34305
\(315\) 1.65685 0.585786i 0.0933532 0.0330053i
\(316\) 13.3137i 0.748955i
\(317\) −0.343146 −0.0192730 −0.00963649 0.999954i \(-0.503067\pi\)
−0.00963649 + 0.999954i \(0.503067\pi\)
\(318\) −3.17157 + 4.48528i −0.177853 + 0.251522i
\(319\) 27.4558i 1.53723i
\(320\) 1.00000i 0.0559017i
\(321\) 3.65685 5.17157i 0.204106 0.288649i
\(322\) 3.51472i 0.195868i
\(323\) 2.82843 12.0000i 0.157378 0.667698i
\(324\) −7.00000 + 5.65685i −0.388889 + 0.314270i
\(325\) 2.24264i 0.124399i
\(326\) 12.7279 0.704934
\(327\) 3.31371 + 2.34315i 0.183248 + 0.129576i
\(328\) −11.0711 −0.611297
\(329\) 1.85786i 0.102427i
\(330\) 5.41421 7.65685i 0.298043 0.421496i
\(331\) 16.9706i 0.932786i −0.884577 0.466393i \(-0.845553\pi\)
0.884577 0.466393i \(-0.154447\pi\)
\(332\) 12.8284i 0.704051i
\(333\) 6.34315 2.24264i 0.347602 0.122896i
\(334\) 0 0
\(335\) 0 0
\(336\) 0.585786 0.828427i 0.0319573 0.0451944i
\(337\) 29.2132i 1.59134i −0.605727 0.795672i \(-0.707118\pi\)
0.605727 0.795672i \(-0.292882\pi\)
\(338\) 7.97056 0.433541
\(339\) 12.8284 18.1421i 0.696745 0.985346i
\(340\) 2.82843 0.153393
\(341\) 36.9706 2.00207
\(342\) −1.41421 13.0000i −0.0764719 0.702959i
\(343\) −8.00000 −0.431959
\(344\) 6.58579 0.355082
\(345\) −6.00000 + 8.48528i −0.323029 + 0.456832i
\(346\) 6.00000 0.322562
\(347\) 30.2843i 1.62574i 0.582442 + 0.812872i \(0.302097\pi\)
−0.582442 + 0.812872i \(0.697903\pi\)
\(348\) 5.07107 7.17157i 0.271838 0.384437i
\(349\) −10.9706 −0.587241 −0.293620 0.955922i \(-0.594860\pi\)
−0.293620 + 0.955922i \(0.594860\pi\)
\(350\) −0.585786 −0.0313116
\(351\) 3.17157 11.2132i 0.169286 0.598517i
\(352\) 5.41421i 0.288579i
\(353\) 8.82843i 0.469890i −0.972009 0.234945i \(-0.924509\pi\)
0.972009 0.234945i \(-0.0754910\pi\)
\(354\) −12.8284 + 18.1421i −0.681823 + 0.964244i
\(355\) 2.82843i 0.150117i
\(356\) 10.5858 0.561046
\(357\) −2.34315 1.65685i −0.124012 0.0876900i
\(358\) −21.7990 −1.15211
\(359\) 19.4142i 1.02464i −0.858794 0.512322i \(-0.828786\pi\)
0.858794 0.512322i \(-0.171214\pi\)
\(360\) 2.82843 1.00000i 0.149071 0.0527046i
\(361\) 17.0000 + 8.48528i 0.894737 + 0.446594i
\(362\) 10.8284i 0.569129i
\(363\) −18.3137 + 25.8995i −0.961220 + 1.35937i
\(364\) 1.31371i 0.0688570i
\(365\) 2.48528i 0.130086i
\(366\) −4.48528 + 6.34315i −0.234449 + 0.331562i
\(367\) −14.2426 −0.743460 −0.371730 0.928341i \(-0.621235\pi\)
−0.371730 + 0.928341i \(0.621235\pi\)
\(368\) 6.00000i 0.312772i
\(369\) 11.0711 + 31.3137i 0.576337 + 1.63013i
\(370\) −2.24264 −0.116589
\(371\) −1.85786 −0.0964555
\(372\) 9.65685 + 6.82843i 0.500685 + 0.354037i
\(373\) 14.0416i 0.727048i −0.931585 0.363524i \(-0.881573\pi\)
0.931585 0.363524i \(-0.118427\pi\)
\(374\) −15.3137 −0.791853
\(375\) −1.41421 1.00000i −0.0730297 0.0516398i
\(376\) 3.17157i 0.163561i
\(377\) 11.3726i 0.585718i
\(378\) −2.92893 0.828427i −0.150648 0.0426097i
\(379\) 8.00000i 0.410932i −0.978664 0.205466i \(-0.934129\pi\)
0.978664 0.205466i \(-0.0658711\pi\)
\(380\) −1.00000 + 4.24264i −0.0512989 + 0.217643i
\(381\) 18.1421 + 12.8284i 0.929450 + 0.657220i
\(382\) 10.2426i 0.524059i
\(383\) 32.1421 1.64239 0.821193 0.570650i \(-0.193309\pi\)
0.821193 + 0.570650i \(0.193309\pi\)
\(384\) 1.00000 1.41421i 0.0510310 0.0721688i
\(385\) 3.17157 0.161638
\(386\) 19.5563i 0.995392i
\(387\) −6.58579 18.6274i −0.334774 0.946885i
\(388\) 6.58579i 0.334343i
\(389\) 20.3431i 1.03144i 0.856758 + 0.515719i \(0.172475\pi\)
−0.856758 + 0.515719i \(0.827525\pi\)
\(390\) −2.24264 + 3.17157i −0.113561 + 0.160599i
\(391\) 16.9706 0.858238
\(392\) −6.65685 −0.336222
\(393\) −6.97056 4.92893i −0.351618 0.248632i
\(394\) 18.1421i 0.913988i
\(395\) −13.3137 −0.669885
\(396\) −15.3137 + 5.41421i −0.769543 + 0.272074i
\(397\) 16.9706 0.851728 0.425864 0.904787i \(-0.359970\pi\)
0.425864 + 0.904787i \(0.359970\pi\)
\(398\) −16.9706 −0.850657
\(399\) 3.31371 2.92893i 0.165893 0.146630i
\(400\) −1.00000 −0.0500000
\(401\) −18.3848 −0.918092 −0.459046 0.888413i \(-0.651809\pi\)
−0.459046 + 0.888413i \(0.651809\pi\)
\(402\) 0 0
\(403\) −15.3137 −0.762830
\(404\) 7.65685i 0.380943i
\(405\) −5.65685 7.00000i −0.281091 0.347833i
\(406\) 2.97056 0.147427
\(407\) 12.1421 0.601863
\(408\) −4.00000 2.82843i −0.198030 0.140028i
\(409\) 4.48528i 0.221783i −0.993833 0.110891i \(-0.964629\pi\)
0.993833 0.110891i \(-0.0353706\pi\)
\(410\) 11.0711i 0.546761i
\(411\) −20.4853 14.4853i −1.01046 0.714506i
\(412\) 4.34315i 0.213971i
\(413\) −7.51472 −0.369775
\(414\) 16.9706 6.00000i 0.834058 0.294884i
\(415\) −12.8284 −0.629723
\(416\) 2.24264i 0.109955i
\(417\) 18.1421 25.6569i 0.888424 1.25642i
\(418\) 5.41421 22.9706i 0.264818 1.12353i
\(419\) 6.38478i 0.311917i 0.987764 + 0.155958i \(0.0498466\pi\)
−0.987764 + 0.155958i \(0.950153\pi\)
\(420\) 0.828427 + 0.585786i 0.0404231 + 0.0285835i
\(421\) 24.2843i 1.18354i −0.806106 0.591771i \(-0.798429\pi\)
0.806106 0.591771i \(-0.201571\pi\)
\(422\) 2.00000i 0.0973585i
\(423\) −8.97056 + 3.17157i −0.436164 + 0.154207i
\(424\) −3.17157 −0.154025
\(425\) 2.82843i 0.137199i
\(426\) −2.82843 + 4.00000i −0.137038 + 0.193801i
\(427\) −2.62742 −0.127150
\(428\) 3.65685 0.176761
\(429\) 12.1421 17.1716i 0.586228 0.829051i
\(430\) 6.58579i 0.317595i
\(431\) −19.3137 −0.930309 −0.465154 0.885230i \(-0.654001\pi\)
−0.465154 + 0.885230i \(0.654001\pi\)
\(432\) −5.00000 1.41421i −0.240563 0.0680414i
\(433\) 14.3848i 0.691288i 0.938366 + 0.345644i \(0.112340\pi\)
−0.938366 + 0.345644i \(0.887660\pi\)
\(434\) 4.00000i 0.192006i
\(435\) 7.17157 + 5.07107i 0.343851 + 0.243139i
\(436\) 2.34315i 0.112216i
\(437\) −6.00000 + 25.4558i −0.287019 + 1.21772i
\(438\) 2.48528 3.51472i 0.118751 0.167940i
\(439\) 39.9411i 1.90629i −0.302520 0.953143i \(-0.597828\pi\)
0.302520 0.953143i \(-0.402172\pi\)
\(440\) 5.41421 0.258113
\(441\) 6.65685 + 18.8284i 0.316993 + 0.896592i
\(442\) 6.34315 0.301713
\(443\) 18.0000i 0.855206i −0.903967 0.427603i \(-0.859358\pi\)
0.903967 0.427603i \(-0.140642\pi\)
\(444\) 3.17157 + 2.24264i 0.150516 + 0.106431i
\(445\) 10.5858i 0.501814i
\(446\) 18.0000i 0.852325i
\(447\) 20.4853 + 14.4853i 0.968921 + 0.685130i
\(448\) 0.585786 0.0276758
\(449\) −16.2426 −0.766538 −0.383269 0.923637i \(-0.625202\pi\)
−0.383269 + 0.923637i \(0.625202\pi\)
\(450\) 1.00000 + 2.82843i 0.0471405 + 0.133333i
\(451\) 59.9411i 2.82252i
\(452\) 12.8284 0.603398
\(453\) −28.9706 20.4853i −1.36116 0.962482i
\(454\) −2.34315 −0.109969
\(455\) −1.31371 −0.0615876
\(456\) 5.65685 5.00000i 0.264906 0.234146i
\(457\) −0.828427 −0.0387522 −0.0193761 0.999812i \(-0.506168\pi\)
−0.0193761 + 0.999812i \(0.506168\pi\)
\(458\) 8.48528 0.396491
\(459\) −4.00000 + 14.1421i −0.186704 + 0.660098i
\(460\) −6.00000 −0.279751
\(461\) 28.1421i 1.31071i 0.755321 + 0.655355i \(0.227481\pi\)
−0.755321 + 0.655355i \(0.772519\pi\)
\(462\) −4.48528 3.17157i −0.208674 0.147555i
\(463\) 19.2132 0.892913 0.446457 0.894805i \(-0.352686\pi\)
0.446457 + 0.894805i \(0.352686\pi\)
\(464\) 5.07107 0.235418
\(465\) −6.82843 + 9.65685i −0.316661 + 0.447826i
\(466\) 17.7990i 0.824522i
\(467\) 25.7990i 1.19383i 0.802303 + 0.596917i \(0.203608\pi\)
−0.802303 + 0.596917i \(0.796392\pi\)
\(468\) 6.34315 2.24264i 0.293212 0.103666i
\(469\) 0 0
\(470\) 3.17157 0.146294
\(471\) −23.7990 + 33.6569i −1.09660 + 1.55083i
\(472\) −12.8284 −0.590476
\(473\) 35.6569i 1.63950i
\(474\) 18.8284 + 13.3137i 0.864818 + 0.611519i
\(475\) −4.24264 1.00000i −0.194666 0.0458831i
\(476\) 1.65685i 0.0759418i
\(477\) 3.17157 + 8.97056i 0.145216 + 0.410734i
\(478\) 0.100505i 0.00459699i
\(479\) 3.41421i 0.155999i 0.996953 + 0.0779997i \(0.0248533\pi\)
−0.996953 + 0.0779997i \(0.975147\pi\)
\(480\) 1.41421 + 1.00000i 0.0645497 + 0.0456435i
\(481\) −5.02944 −0.229323
\(482\) 8.48528i 0.386494i
\(483\) 4.97056 + 3.51472i 0.226168 + 0.159925i
\(484\) −18.3137 −0.832441
\(485\) −6.58579 −0.299045
\(486\) 1.00000 + 15.5563i 0.0453609 + 0.705650i
\(487\) 36.1421i 1.63776i −0.573967 0.818878i \(-0.694596\pi\)
0.573967 0.818878i \(-0.305404\pi\)
\(488\) −4.48528 −0.203039
\(489\) 12.7279 18.0000i 0.575577 0.813988i
\(490\) 6.65685i 0.300726i
\(491\) 43.5563i 1.96567i 0.184485 + 0.982835i \(0.440938\pi\)
−0.184485 + 0.982835i \(0.559062\pi\)
\(492\) −11.0711 + 15.6569i −0.499122 + 0.705866i
\(493\) 14.3431i 0.645983i
\(494\) −2.24264 + 9.51472i −0.100901 + 0.428087i
\(495\) −5.41421 15.3137i −0.243351 0.688300i
\(496\) 6.82843i 0.306605i
\(497\) −1.65685 −0.0743201
\(498\) 18.1421 + 12.8284i 0.812969 + 0.574856i
\(499\) −25.6569 −1.14856 −0.574279 0.818659i \(-0.694718\pi\)
−0.574279 + 0.818659i \(0.694718\pi\)
\(500\) 1.00000i 0.0447214i
\(501\) 0 0
\(502\) 4.92893i 0.219989i
\(503\) 14.2843i 0.636904i 0.947939 + 0.318452i \(0.103163\pi\)
−0.947939 + 0.318452i \(0.896837\pi\)
\(504\) −0.585786 1.65685i −0.0260930 0.0738022i
\(505\) 7.65685 0.340726
\(506\) 32.4853 1.44415
\(507\) 7.97056 11.2721i 0.353985 0.500611i
\(508\) 12.8284i 0.569169i
\(509\) 4.10051 0.181752 0.0908758 0.995862i \(-0.471033\pi\)
0.0908758 + 0.995862i \(0.471033\pi\)
\(510\) 2.82843 4.00000i 0.125245 0.177123i
\(511\) 1.45584 0.0644028
\(512\) 1.00000 0.0441942
\(513\) −19.7990 11.0000i −0.874147 0.485662i
\(514\) 28.1421 1.24130
\(515\) 4.34315 0.191382
\(516\) 6.58579 9.31371i 0.289923 0.410013i
\(517\) −17.1716 −0.755205
\(518\) 1.31371i 0.0577210i
\(519\) 6.00000 8.48528i 0.263371 0.372463i
\(520\) −2.24264 −0.0983463
\(521\) 14.3848 0.630208 0.315104 0.949057i \(-0.397961\pi\)
0.315104 + 0.949057i \(0.397961\pi\)
\(522\) −5.07107 14.3431i −0.221955 0.627782i
\(523\) 8.97056i 0.392255i 0.980578 + 0.196128i \(0.0628367\pi\)
−0.980578 + 0.196128i \(0.937163\pi\)
\(524\) 4.92893i 0.215321i
\(525\) −0.585786 + 0.828427i −0.0255658 + 0.0361555i
\(526\) 11.1716i 0.487104i
\(527\) 19.3137 0.841318
\(528\) −7.65685 5.41421i −0.333222 0.235623i
\(529\) −13.0000 −0.565217
\(530\) 3.17157i 0.137764i
\(531\) 12.8284 + 36.2843i 0.556706 + 1.57460i
\(532\) 2.48528 + 0.585786i 0.107751 + 0.0253971i
\(533\) 24.8284i 1.07544i
\(534\) 10.5858 14.9706i 0.458092 0.647840i
\(535\) 3.65685i 0.158100i
\(536\) 0 0
\(537\) −21.7990 + 30.8284i −0.940696 + 1.33034i
\(538\) −24.3848 −1.05130
\(539\) 36.0416i 1.55242i
\(540\) 1.41421 5.00000i 0.0608581 0.215166i
\(541\) −42.9706 −1.84745 −0.923724 0.383058i \(-0.874871\pi\)
−0.923724 + 0.383058i \(0.874871\pi\)
\(542\) −28.9706 −1.24439
\(543\) −15.3137 10.8284i −0.657174 0.464692i
\(544\) 2.82843i 0.121268i
\(545\) −2.34315 −0.100369
\(546\) 1.85786 + 1.31371i 0.0795093 + 0.0562215i
\(547\) 13.1716i 0.563176i 0.959535 + 0.281588i \(0.0908611\pi\)
−0.959535 + 0.281588i \(0.909139\pi\)
\(548\) 14.4853i 0.618781i
\(549\) 4.48528 + 12.6863i 0.191427 + 0.541438i
\(550\) 5.41421i 0.230863i
\(551\) 21.5147 + 5.07107i 0.916558 + 0.216035i
\(552\) 8.48528 + 6.00000i 0.361158 + 0.255377i
\(553\) 7.79899i 0.331647i
\(554\) 24.9706 1.06090
\(555\) −2.24264 + 3.17157i −0.0951948 + 0.134626i
\(556\) 18.1421 0.769398
\(557\) 28.6274i 1.21298i −0.795090 0.606491i \(-0.792576\pi\)
0.795090 0.606491i \(-0.207424\pi\)
\(558\) 19.3137 6.82843i 0.817614 0.289070i
\(559\) 14.7696i 0.624686i
\(560\) 0.585786i 0.0247540i
\(561\) −15.3137 + 21.6569i −0.646545 + 0.914353i
\(562\) −0.928932 −0.0391846
\(563\) −13.6569 −0.575568 −0.287784 0.957695i \(-0.592918\pi\)
−0.287784 + 0.957695i \(0.592918\pi\)
\(564\) −4.48528 3.17157i −0.188864 0.133547i
\(565\) 12.8284i 0.539696i
\(566\) 12.7279 0.534994
\(567\) −4.10051 + 3.31371i −0.172205 + 0.139163i
\(568\) −2.82843 −0.118678
\(569\) −28.9289 −1.21276 −0.606382 0.795174i \(-0.707380\pi\)
−0.606382 + 0.795174i \(0.707380\pi\)
\(570\) 5.00000 + 5.65685i 0.209427 + 0.236940i
\(571\) −1.65685 −0.0693372 −0.0346686 0.999399i \(-0.511038\pi\)
−0.0346686 + 0.999399i \(0.511038\pi\)
\(572\) 12.1421 0.507688
\(573\) −14.4853 10.2426i −0.605131 0.427892i
\(574\) −6.48528 −0.270690
\(575\) 6.00000i 0.250217i
\(576\) −1.00000 2.82843i −0.0416667 0.117851i
\(577\) −19.1716 −0.798123 −0.399062 0.916924i \(-0.630664\pi\)
−0.399062 + 0.916924i \(0.630664\pi\)
\(578\) 9.00000 0.374351
\(579\) −27.6569 19.5563i −1.14938 0.812734i
\(580\) 5.07107i 0.210565i
\(581\) 7.51472i 0.311763i
\(582\) 9.31371 + 6.58579i 0.386066 + 0.272990i
\(583\) 17.1716i 0.711174i
\(584\) 2.48528 0.102842
\(585\) 2.24264 + 6.34315i 0.0927218 + 0.262257i
\(586\) 3.17157 0.131016
\(587\) 3.17157i 0.130905i 0.997856 + 0.0654524i \(0.0208491\pi\)
−0.997856 + 0.0654524i \(0.979151\pi\)
\(588\) −6.65685 + 9.41421i −0.274524 + 0.388236i
\(589\) −6.82843 + 28.9706i −0.281360 + 1.19371i
\(590\) 12.8284i 0.528138i
\(591\) −25.6569 18.1421i −1.05538 0.746268i
\(592\) 2.24264i 0.0921720i
\(593\) 12.1421i 0.498618i 0.968424 + 0.249309i \(0.0802034\pi\)
−0.968424 + 0.249309i \(0.919797\pi\)
\(594\) −7.65685 + 27.0711i −0.314165 + 1.11074i
\(595\) 1.65685 0.0679244
\(596\) 14.4853i 0.593340i
\(597\) −16.9706 + 24.0000i −0.694559 + 0.982255i
\(598\) −13.4558 −0.550250
\(599\) 21.1716 0.865047 0.432524 0.901623i \(-0.357623\pi\)
0.432524 + 0.901623i \(0.357623\pi\)
\(600\) −1.00000 + 1.41421i −0.0408248 + 0.0577350i
\(601\) 4.00000i 0.163163i −0.996667 0.0815817i \(-0.974003\pi\)
0.996667 0.0815817i \(-0.0259972\pi\)
\(602\) 3.85786 0.157235
\(603\) 0 0
\(604\) 20.4853i 0.833534i
\(605\) 18.3137i 0.744558i
\(606\) −10.8284 7.65685i −0.439875 0.311038i
\(607\) 1.51472i 0.0614805i 0.999527 + 0.0307403i \(0.00978647\pi\)
−0.999527 + 0.0307403i \(0.990214\pi\)
\(608\) 4.24264 + 1.00000i 0.172062 + 0.0405554i
\(609\) 2.97056 4.20101i 0.120373 0.170234i
\(610\) 4.48528i 0.181604i
\(611\) 7.11270 0.287749
\(612\) −8.00000 + 2.82843i −0.323381 + 0.114332i
\(613\) −23.1127 −0.933513 −0.466757 0.884386i \(-0.654578\pi\)
−0.466757 + 0.884386i \(0.654578\pi\)
\(614\) 18.1421i 0.732157i
\(615\) −15.6569 11.0711i −0.631345 0.446429i
\(616\) 3.17157i 0.127786i
\(617\) 18.8284i 0.758004i 0.925396 + 0.379002i \(0.123733\pi\)
−0.925396 + 0.379002i \(0.876267\pi\)
\(618\) −6.14214 4.34315i −0.247073 0.174707i
\(619\) 41.4558 1.66625 0.833126 0.553084i \(-0.186549\pi\)
0.833126 + 0.553084i \(0.186549\pi\)
\(620\) −6.82843 −0.274236
\(621\) 8.48528 30.0000i 0.340503 1.20386i
\(622\) 5.07107i 0.203331i
\(623\) 6.20101 0.248438
\(624\) 3.17157 + 2.24264i 0.126965 + 0.0897775i
\(625\) 1.00000 0.0400000
\(626\) −16.8284 −0.672599
\(627\) −27.0711 30.6274i −1.08111 1.22314i
\(628\) −23.7990 −0.949683
\(629\) 6.34315 0.252918
\(630\) 1.65685 0.585786i 0.0660107 0.0233383i
\(631\) 23.5147 0.936106 0.468053 0.883700i \(-0.344956\pi\)
0.468053 + 0.883700i \(0.344956\pi\)
\(632\) 13.3137i 0.529591i
\(633\) 2.82843 + 2.00000i 0.112420 + 0.0794929i
\(634\) −0.343146 −0.0136281
\(635\) −12.8284 −0.509081
\(636\) −3.17157 + 4.48528i −0.125761 + 0.177853i
\(637\) 14.9289i 0.591506i
\(638\) 27.4558i 1.08699i
\(639\) 2.82843 + 8.00000i 0.111891 + 0.316475i
\(640\) 1.00000i 0.0395285i
\(641\) −11.2721 −0.445220 −0.222610 0.974908i \(-0.571458\pi\)
−0.222610 + 0.974908i \(0.571458\pi\)
\(642\) 3.65685 5.17157i 0.144325 0.204106i
\(643\) −20.7279 −0.817429 −0.408715 0.912662i \(-0.634023\pi\)
−0.408715 + 0.912662i \(0.634023\pi\)
\(644\) 3.51472i 0.138499i
\(645\) 9.31371 + 6.58579i 0.366727 + 0.259315i
\(646\) 2.82843 12.0000i 0.111283 0.472134i
\(647\) 2.68629i 0.105609i −0.998605 0.0528045i \(-0.983184\pi\)
0.998605 0.0528045i \(-0.0168160\pi\)
\(648\) −7.00000 + 5.65685i −0.274986 + 0.222222i
\(649\) 69.4558i 2.72638i
\(650\) 2.24264i 0.0879636i
\(651\) 5.65685 + 4.00000i 0.221710 + 0.156772i
\(652\) 12.7279 0.498464
\(653\) 15.1127i 0.591406i 0.955280 + 0.295703i \(0.0955538\pi\)
−0.955280 + 0.295703i \(0.904446\pi\)
\(654\) 3.31371 + 2.34315i 0.129576 + 0.0916242i
\(655\) 4.92893 0.192589
\(656\) −11.0711 −0.432253
\(657\) −2.48528 7.02944i −0.0969601 0.274244i
\(658\) 1.85786i 0.0724271i
\(659\) −8.82843 −0.343907 −0.171953 0.985105i \(-0.555008\pi\)
−0.171953 + 0.985105i \(0.555008\pi\)
\(660\) 5.41421 7.65685i 0.210748 0.298043i
\(661\) 3.51472i 0.136707i −0.997661 0.0683534i \(-0.978225\pi\)
0.997661 0.0683534i \(-0.0217745\pi\)
\(662\) 16.9706i 0.659580i
\(663\) 6.34315 8.97056i 0.246347 0.348388i
\(664\) 12.8284i 0.497840i
\(665\) −0.585786 + 2.48528i −0.0227158 + 0.0963751i
\(666\) 6.34315 2.24264i 0.245792 0.0869006i
\(667\) 30.4264i 1.17812i
\(668\) 0 0
\(669\) 25.4558 + 18.0000i 0.984180 + 0.695920i
\(670\) 0 0
\(671\) 24.2843i 0.937484i
\(672\) 0.585786 0.828427i 0.0225972 0.0319573i
\(673\) 37.6985i 1.45317i −0.687077 0.726585i \(-0.741106\pi\)
0.687077 0.726585i \(-0.258894\pi\)
\(674\) 29.2132i 1.12525i
\(675\) 5.00000 + 1.41421i 0.192450 + 0.0544331i
\(676\) 7.97056 0.306560
\(677\) −37.5980 −1.44501 −0.722504 0.691367i \(-0.757009\pi\)
−0.722504 + 0.691367i \(0.757009\pi\)
\(678\) 12.8284 18.1421i 0.492673 0.696745i
\(679\) 3.85786i 0.148051i
\(680\) 2.82843 0.108465
\(681\) −2.34315 + 3.31371i −0.0897895 + 0.126982i
\(682\) 36.9706 1.41568
\(683\) 39.2548 1.50204 0.751022 0.660277i \(-0.229561\pi\)
0.751022 + 0.660277i \(0.229561\pi\)
\(684\) −1.41421 13.0000i −0.0540738 0.497067i
\(685\) 14.4853 0.553454
\(686\) −8.00000 −0.305441
\(687\) 8.48528 12.0000i 0.323734 0.457829i
\(688\) 6.58579 0.251081
\(689\) 7.11270i 0.270972i
\(690\) −6.00000 + 8.48528i −0.228416 + 0.323029i
\(691\) 36.9706 1.40643 0.703213 0.710979i \(-0.251748\pi\)
0.703213 + 0.710979i \(0.251748\pi\)
\(692\) 6.00000 0.228086
\(693\) −8.97056 + 3.17157i −0.340764 + 0.120478i
\(694\) 30.2843i 1.14958i
\(695\) 18.1421i 0.688170i
\(696\) 5.07107 7.17157i 0.192218 0.271838i
\(697\) 31.3137i 1.18609i
\(698\) −10.9706 −0.415242
\(699\) −25.1716 17.7990i −0.952076 0.673220i
\(700\) −0.585786 −0.0221406
\(701\) 2.48528i 0.0938678i −0.998898 0.0469339i \(-0.985055\pi\)
0.998898 0.0469339i \(-0.0149450\pi\)
\(702\) 3.17157 11.2132i 0.119703 0.423215i
\(703\) −2.24264 + 9.51472i −0.0845828 + 0.358854i
\(704\) 5.41421i 0.204056i
\(705\) 3.17157 4.48528i 0.119448 0.168925i
\(706\) 8.82843i 0.332262i
\(707\) 4.48528i 0.168686i
\(708\) −12.8284 + 18.1421i −0.482122 + 0.681823i
\(709\) 19.5147 0.732891 0.366445 0.930440i \(-0.380575\pi\)
0.366445 + 0.930440i \(0.380575\pi\)
\(710\) 2.82843i 0.106149i
\(711\) 37.6569 13.3137i 1.41224 0.499303i
\(712\) 10.5858 0.396719
\(713\) −40.9706 −1.53436
\(714\) −2.34315 1.65685i −0.0876900 0.0620062i
\(715\) 12.1421i 0.454090i
\(716\) −21.7990 −0.814667
\(717\) 0.142136 + 0.100505i 0.00530815 + 0.00375343i
\(718\) 19.4142i 0.724532i
\(719\) 30.7279i 1.14596i 0.819570 + 0.572979i \(0.194212\pi\)
−0.819570 + 0.572979i \(0.805788\pi\)
\(720\) 2.82843 1.00000i 0.105409 0.0372678i
\(721\) 2.54416i 0.0947493i
\(722\) 17.0000 + 8.48528i 0.632674 + 0.315789i
\(723\) −12.0000 8.48528i −0.446285 0.315571i
\(724\) 10.8284i 0.402435i
\(725\) −5.07107 −0.188335
\(726\) −18.3137 + 25.8995i −0.679685 + 0.961220i
\(727\) 25.5563 0.947833 0.473916 0.880570i \(-0.342840\pi\)
0.473916 + 0.880570i \(0.342840\pi\)
\(728\) 1.31371i 0.0486893i
\(729\) 23.0000 + 14.1421i 0.851852 + 0.523783i
\(730\) 2.48528i 0.0919844i
\(731\) 18.6274i 0.688960i
\(732\) −4.48528 + 6.34315i −0.165781 + 0.234449i
\(733\) −15.5147 −0.573049 −0.286525 0.958073i \(-0.592500\pi\)
−0.286525 + 0.958073i \(0.592500\pi\)
\(734\) −14.2426 −0.525705
\(735\) −9.41421 6.65685i −0.347248 0.245542i
\(736\) 6.00000i 0.221163i
\(737\) 0 0
\(738\) 11.0711 + 31.3137i 0.407532 + 1.15267i
\(739\) −20.4853 −0.753563 −0.376782 0.926302i \(-0.622969\pi\)
−0.376782 + 0.926302i \(0.622969\pi\)
\(740\) −2.24264 −0.0824411
\(741\) 11.2132 + 12.6863i 0.411927 + 0.466043i
\(742\) −1.85786 −0.0682043
\(743\) −43.1716 −1.58381 −0.791906 0.610643i \(-0.790911\pi\)
−0.791906 + 0.610643i \(0.790911\pi\)
\(744\) 9.65685 + 6.82843i 0.354037 + 0.250342i
\(745\) −14.4853 −0.530700
\(746\) 14.0416i 0.514101i
\(747\) 36.2843 12.8284i 1.32757 0.469368i
\(748\) −15.3137 −0.559925
\(749\) 2.14214 0.0782719
\(750\) −1.41421 1.00000i −0.0516398 0.0365148i
\(751\) 48.4853i 1.76925i −0.466300 0.884627i \(-0.654413\pi\)
0.466300 0.884627i \(-0.345587\pi\)
\(752\) 3.17157i 0.115655i
\(753\) −6.97056 4.92893i −0.254021 0.179620i
\(754\) 11.3726i 0.414165i
\(755\) 20.4853 0.745536
\(756\) −2.92893 0.828427i −0.106524 0.0301296i
\(757\) 49.6569 1.80481 0.902405 0.430890i \(-0.141800\pi\)
0.902405 + 0.430890i \(0.141800\pi\)
\(758\) 8.00000i 0.290573i
\(759\) 32.4853 45.9411i 1.17914 1.66756i
\(760\) −1.00000 + 4.24264i −0.0362738 + 0.153897i
\(761\) 1.17157i 0.0424695i 0.999775 + 0.0212347i \(0.00675974\pi\)
−0.999775 + 0.0212347i \(0.993240\pi\)
\(762\) 18.1421 + 12.8284i 0.657220 + 0.464725i
\(763\) 1.37258i 0.0496908i
\(764\) 10.2426i 0.370566i
\(765\) −2.82843 8.00000i −0.102262 0.289241i
\(766\) 32.1421 1.16134
\(767\) 28.7696i 1.03881i
\(768\) 1.00000 1.41421i 0.0360844 0.0510310i
\(769\) −13.3137 −0.480105 −0.240052 0.970760i \(-0.577165\pi\)
−0.240052 + 0.970760i \(0.577165\pi\)
\(770\) 3.17157 0.114296
\(771\) 28.1421 39.7990i 1.01351 1.43333i
\(772\) 19.5563i 0.703848i
\(773\) 0.343146 0.0123421 0.00617105 0.999981i \(-0.498036\pi\)
0.00617105 + 0.999981i \(0.498036\pi\)
\(774\) −6.58579 18.6274i −0.236721 0.669549i
\(775\) 6.82843i 0.245284i
\(776\) 6.58579i 0.236416i
\(777\) 1.85786 + 1.31371i 0.0666505 + 0.0471290i
\(778\) 20.3431i 0.729337i
\(779\) −46.9706 11.0711i −1.68290 0.396662i
\(780\) −2.24264 + 3.17157i −0.0802994 + 0.113561i
\(781\) 15.3137i 0.547968i
\(782\) 16.9706 0.606866
\(783\) −25.3553 7.17157i −0.906126 0.256291i
\(784\) −6.65685 −0.237745