Properties

Label 825.2.k.f.518.2
Level $825$
Weight $2$
Character 825.518
Analytic conductor $6.588$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 825.k (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.58765816676\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(\zeta_{8})\)
Defining polynomial: \(x^{4} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 165)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 518.2
Root \(0.707107 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 825.518
Dual form 825.2.k.f.782.2

$q$-expansion

\(f(q)\) \(=\) \(q+(1.70711 + 1.70711i) q^{2} +(1.00000 + 1.41421i) q^{3} +3.82843i q^{4} +(-0.707107 + 4.12132i) q^{6} +(0.585786 - 0.585786i) q^{7} +(-3.12132 + 3.12132i) q^{8} +(-1.00000 + 2.82843i) q^{9} +O(q^{10})\) \(q+(1.70711 + 1.70711i) q^{2} +(1.00000 + 1.41421i) q^{3} +3.82843i q^{4} +(-0.707107 + 4.12132i) q^{6} +(0.585786 - 0.585786i) q^{7} +(-3.12132 + 3.12132i) q^{8} +(-1.00000 + 2.82843i) q^{9} +1.00000i q^{11} +(-5.41421 + 3.82843i) q^{12} +(2.00000 + 2.00000i) q^{13} +2.00000 q^{14} -3.00000 q^{16} +(-2.82843 - 2.82843i) q^{17} +(-6.53553 + 3.12132i) q^{18} -2.82843i q^{19} +(1.41421 + 0.242641i) q^{21} +(-1.70711 + 1.70711i) q^{22} +(5.24264 - 5.24264i) q^{23} +(-7.53553 - 1.29289i) q^{24} +6.82843i q^{26} +(-5.00000 + 1.41421i) q^{27} +(2.24264 + 2.24264i) q^{28} -4.82843 q^{29} -8.82843 q^{31} +(1.12132 + 1.12132i) q^{32} +(-1.41421 + 1.00000i) q^{33} -9.65685i q^{34} +(-10.8284 - 3.82843i) q^{36} +(5.82843 - 5.82843i) q^{37} +(4.82843 - 4.82843i) q^{38} +(-0.828427 + 4.82843i) q^{39} -3.65685i q^{41} +(2.00000 + 2.82843i) q^{42} +(8.24264 + 8.24264i) q^{43} -3.82843 q^{44} +17.8995 q^{46} +(-1.24264 - 1.24264i) q^{47} +(-3.00000 - 4.24264i) q^{48} +6.31371i q^{49} +(1.17157 - 6.82843i) q^{51} +(-7.65685 + 7.65685i) q^{52} +(-1.00000 + 1.00000i) q^{53} +(-10.9497 - 6.12132i) q^{54} +3.65685i q^{56} +(4.00000 - 2.82843i) q^{57} +(-8.24264 - 8.24264i) q^{58} -4.00000 q^{59} +10.4853 q^{61} +(-15.0711 - 15.0711i) q^{62} +(1.07107 + 2.24264i) q^{63} +9.82843i q^{64} +(-4.12132 - 0.707107i) q^{66} +(3.58579 - 3.58579i) q^{67} +(10.8284 - 10.8284i) q^{68} +(12.6569 + 2.17157i) q^{69} -14.4853i q^{71} +(-5.70711 - 11.9497i) q^{72} +19.8995 q^{74} +10.8284 q^{76} +(0.585786 + 0.585786i) q^{77} +(-9.65685 + 6.82843i) q^{78} -5.17157i q^{79} +(-7.00000 - 5.65685i) q^{81} +(6.24264 - 6.24264i) q^{82} +(-5.07107 + 5.07107i) q^{83} +(-0.928932 + 5.41421i) q^{84} +28.1421i q^{86} +(-4.82843 - 6.82843i) q^{87} +(-3.12132 - 3.12132i) q^{88} +1.65685 q^{89} +2.34315 q^{91} +(20.0711 + 20.0711i) q^{92} +(-8.82843 - 12.4853i) q^{93} -4.24264i q^{94} +(-0.464466 + 2.70711i) q^{96} +(0.656854 - 0.656854i) q^{97} +(-10.7782 + 10.7782i) q^{98} +(-2.82843 - 1.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 4q^{2} + 4q^{3} + 8q^{7} - 4q^{8} - 4q^{9} + O(q^{10}) \) \( 4q + 4q^{2} + 4q^{3} + 8q^{7} - 4q^{8} - 4q^{9} - 16q^{12} + 8q^{13} + 8q^{14} - 12q^{16} - 12q^{18} - 4q^{22} + 4q^{23} - 16q^{24} - 20q^{27} - 8q^{28} - 8q^{29} - 24q^{31} - 4q^{32} - 32q^{36} + 12q^{37} + 8q^{38} + 8q^{39} + 8q^{42} + 16q^{43} - 4q^{44} + 32q^{46} + 12q^{47} - 12q^{48} + 16q^{51} - 8q^{52} - 4q^{53} - 24q^{54} + 16q^{57} - 16q^{58} - 16q^{59} + 8q^{61} - 32q^{62} - 24q^{63} - 8q^{66} + 20q^{67} + 32q^{68} + 28q^{69} - 20q^{72} + 40q^{74} + 32q^{76} + 8q^{77} - 16q^{78} - 28q^{81} + 8q^{82} + 8q^{83} - 32q^{84} - 8q^{87} - 4q^{88} - 16q^{89} + 32q^{91} + 52q^{92} - 24q^{93} - 16q^{96} - 20q^{97} - 12q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).

\(n\) \(376\) \(551\) \(727\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.70711 + 1.70711i 1.20711 + 1.20711i 0.971960 + 0.235147i \(0.0755571\pi\)
0.235147 + 0.971960i \(0.424443\pi\)
\(3\) 1.00000 + 1.41421i 0.577350 + 0.816497i
\(4\) 3.82843i 1.91421i
\(5\) 0 0
\(6\) −0.707107 + 4.12132i −0.288675 + 1.68252i
\(7\) 0.585786 0.585786i 0.221406 0.221406i −0.587684 0.809091i \(-0.699960\pi\)
0.809091 + 0.587684i \(0.199960\pi\)
\(8\) −3.12132 + 3.12132i −1.10355 + 1.10355i
\(9\) −1.00000 + 2.82843i −0.333333 + 0.942809i
\(10\) 0 0
\(11\) 1.00000i 0.301511i
\(12\) −5.41421 + 3.82843i −1.56295 + 1.10517i
\(13\) 2.00000 + 2.00000i 0.554700 + 0.554700i 0.927794 0.373094i \(-0.121703\pi\)
−0.373094 + 0.927794i \(0.621703\pi\)
\(14\) 2.00000 0.534522
\(15\) 0 0
\(16\) −3.00000 −0.750000
\(17\) −2.82843 2.82843i −0.685994 0.685994i 0.275350 0.961344i \(-0.411206\pi\)
−0.961344 + 0.275350i \(0.911206\pi\)
\(18\) −6.53553 + 3.12132i −1.54044 + 0.735702i
\(19\) 2.82843i 0.648886i −0.945905 0.324443i \(-0.894823\pi\)
0.945905 0.324443i \(-0.105177\pi\)
\(20\) 0 0
\(21\) 1.41421 + 0.242641i 0.308607 + 0.0529485i
\(22\) −1.70711 + 1.70711i −0.363956 + 0.363956i
\(23\) 5.24264 5.24264i 1.09317 1.09317i 0.0979775 0.995189i \(-0.468763\pi\)
0.995189 0.0979775i \(-0.0312373\pi\)
\(24\) −7.53553 1.29289i −1.53818 0.263911i
\(25\) 0 0
\(26\) 6.82843i 1.33916i
\(27\) −5.00000 + 1.41421i −0.962250 + 0.272166i
\(28\) 2.24264 + 2.24264i 0.423819 + 0.423819i
\(29\) −4.82843 −0.896616 −0.448308 0.893879i \(-0.647973\pi\)
−0.448308 + 0.893879i \(0.647973\pi\)
\(30\) 0 0
\(31\) −8.82843 −1.58563 −0.792816 0.609461i \(-0.791386\pi\)
−0.792816 + 0.609461i \(0.791386\pi\)
\(32\) 1.12132 + 1.12132i 0.198223 + 0.198223i
\(33\) −1.41421 + 1.00000i −0.246183 + 0.174078i
\(34\) 9.65685i 1.65614i
\(35\) 0 0
\(36\) −10.8284 3.82843i −1.80474 0.638071i
\(37\) 5.82843 5.82843i 0.958188 0.958188i −0.0409727 0.999160i \(-0.513046\pi\)
0.999160 + 0.0409727i \(0.0130457\pi\)
\(38\) 4.82843 4.82843i 0.783274 0.783274i
\(39\) −0.828427 + 4.82843i −0.132655 + 0.773167i
\(40\) 0 0
\(41\) 3.65685i 0.571105i −0.958363 0.285552i \(-0.907823\pi\)
0.958363 0.285552i \(-0.0921770\pi\)
\(42\) 2.00000 + 2.82843i 0.308607 + 0.436436i
\(43\) 8.24264 + 8.24264i 1.25699 + 1.25699i 0.952522 + 0.304469i \(0.0984788\pi\)
0.304469 + 0.952522i \(0.401521\pi\)
\(44\) −3.82843 −0.577157
\(45\) 0 0
\(46\) 17.8995 2.63914
\(47\) −1.24264 1.24264i −0.181258 0.181258i 0.610646 0.791904i \(-0.290910\pi\)
−0.791904 + 0.610646i \(0.790910\pi\)
\(48\) −3.00000 4.24264i −0.433013 0.612372i
\(49\) 6.31371i 0.901958i
\(50\) 0 0
\(51\) 1.17157 6.82843i 0.164053 0.956171i
\(52\) −7.65685 + 7.65685i −1.06181 + 1.06181i
\(53\) −1.00000 + 1.00000i −0.137361 + 0.137361i −0.772444 0.635083i \(-0.780966\pi\)
0.635083 + 0.772444i \(0.280966\pi\)
\(54\) −10.9497 6.12132i −1.49007 0.833006i
\(55\) 0 0
\(56\) 3.65685i 0.488668i
\(57\) 4.00000 2.82843i 0.529813 0.374634i
\(58\) −8.24264 8.24264i −1.08231 1.08231i
\(59\) −4.00000 −0.520756 −0.260378 0.965507i \(-0.583847\pi\)
−0.260378 + 0.965507i \(0.583847\pi\)
\(60\) 0 0
\(61\) 10.4853 1.34250 0.671251 0.741230i \(-0.265757\pi\)
0.671251 + 0.741230i \(0.265757\pi\)
\(62\) −15.0711 15.0711i −1.91403 1.91403i
\(63\) 1.07107 + 2.24264i 0.134942 + 0.282546i
\(64\) 9.82843i 1.22855i
\(65\) 0 0
\(66\) −4.12132 0.707107i −0.507299 0.0870388i
\(67\) 3.58579 3.58579i 0.438074 0.438074i −0.453290 0.891363i \(-0.649750\pi\)
0.891363 + 0.453290i \(0.149750\pi\)
\(68\) 10.8284 10.8284i 1.31314 1.31314i
\(69\) 12.6569 + 2.17157i 1.52371 + 0.261427i
\(70\) 0 0
\(71\) 14.4853i 1.71909i −0.511063 0.859543i \(-0.670748\pi\)
0.511063 0.859543i \(-0.329252\pi\)
\(72\) −5.70711 11.9497i −0.672589 1.40829i
\(73\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(74\) 19.8995 2.31327
\(75\) 0 0
\(76\) 10.8284 1.24211
\(77\) 0.585786 + 0.585786i 0.0667566 + 0.0667566i
\(78\) −9.65685 + 6.82843i −1.09342 + 0.773167i
\(79\) 5.17157i 0.581847i −0.956746 0.290924i \(-0.906037\pi\)
0.956746 0.290924i \(-0.0939626\pi\)
\(80\) 0 0
\(81\) −7.00000 5.65685i −0.777778 0.628539i
\(82\) 6.24264 6.24264i 0.689384 0.689384i
\(83\) −5.07107 + 5.07107i −0.556622 + 0.556622i −0.928344 0.371722i \(-0.878767\pi\)
0.371722 + 0.928344i \(0.378767\pi\)
\(84\) −0.928932 + 5.41421i −0.101355 + 0.590739i
\(85\) 0 0
\(86\) 28.1421i 3.03464i
\(87\) −4.82843 6.82843i −0.517662 0.732084i
\(88\) −3.12132 3.12132i −0.332734 0.332734i
\(89\) 1.65685 0.175626 0.0878131 0.996137i \(-0.472012\pi\)
0.0878131 + 0.996137i \(0.472012\pi\)
\(90\) 0 0
\(91\) 2.34315 0.245628
\(92\) 20.0711 + 20.0711i 2.09255 + 2.09255i
\(93\) −8.82843 12.4853i −0.915465 1.29466i
\(94\) 4.24264i 0.437595i
\(95\) 0 0
\(96\) −0.464466 + 2.70711i −0.0474044 + 0.276293i
\(97\) 0.656854 0.656854i 0.0666934 0.0666934i −0.672973 0.739667i \(-0.734983\pi\)
0.739667 + 0.672973i \(0.234983\pi\)
\(98\) −10.7782 + 10.7782i −1.08876 + 1.08876i
\(99\) −2.82843 1.00000i −0.284268 0.100504i
\(100\) 0 0
\(101\) 12.8284i 1.27648i 0.769839 + 0.638238i \(0.220336\pi\)
−0.769839 + 0.638238i \(0.779664\pi\)
\(102\) 13.6569 9.65685i 1.35223 0.956171i
\(103\) 3.58579 + 3.58579i 0.353318 + 0.353318i 0.861343 0.508025i \(-0.169624\pi\)
−0.508025 + 0.861343i \(0.669624\pi\)
\(104\) −12.4853 −1.22428
\(105\) 0 0
\(106\) −3.41421 −0.331618
\(107\) 8.24264 + 8.24264i 0.796846 + 0.796846i 0.982597 0.185751i \(-0.0594717\pi\)
−0.185751 + 0.982597i \(0.559472\pi\)
\(108\) −5.41421 19.1421i −0.520983 1.84195i
\(109\) 8.82843i 0.845610i −0.906221 0.422805i \(-0.861046\pi\)
0.906221 0.422805i \(-0.138954\pi\)
\(110\) 0 0
\(111\) 14.0711 + 2.41421i 1.33557 + 0.229147i
\(112\) −1.75736 + 1.75736i −0.166055 + 0.166055i
\(113\) 0.171573 0.171573i 0.0161402 0.0161402i −0.698991 0.715131i \(-0.746367\pi\)
0.715131 + 0.698991i \(0.246367\pi\)
\(114\) 11.6569 + 2.00000i 1.09176 + 0.187317i
\(115\) 0 0
\(116\) 18.4853i 1.71632i
\(117\) −7.65685 + 3.65685i −0.707876 + 0.338076i
\(118\) −6.82843 6.82843i −0.628608 0.628608i
\(119\) −3.31371 −0.303767
\(120\) 0 0
\(121\) −1.00000 −0.0909091
\(122\) 17.8995 + 17.8995i 1.62054 + 1.62054i
\(123\) 5.17157 3.65685i 0.466305 0.329727i
\(124\) 33.7990i 3.03524i
\(125\) 0 0
\(126\) −2.00000 + 5.65685i −0.178174 + 0.503953i
\(127\) 1.41421 1.41421i 0.125491 0.125491i −0.641572 0.767063i \(-0.721717\pi\)
0.767063 + 0.641572i \(0.221717\pi\)
\(128\) −14.5355 + 14.5355i −1.28477 + 1.28477i
\(129\) −3.41421 + 19.8995i −0.300605 + 1.75205i
\(130\) 0 0
\(131\) 1.17157i 0.102361i −0.998689 0.0511804i \(-0.983702\pi\)
0.998689 0.0511804i \(-0.0162983\pi\)
\(132\) −3.82843 5.41421i −0.333222 0.471247i
\(133\) −1.65685 1.65685i −0.143667 0.143667i
\(134\) 12.2426 1.05760
\(135\) 0 0
\(136\) 17.6569 1.51406
\(137\) −5.82843 5.82843i −0.497956 0.497956i 0.412845 0.910801i \(-0.364535\pi\)
−0.910801 + 0.412845i \(0.864535\pi\)
\(138\) 17.8995 + 25.3137i 1.52371 + 2.15485i
\(139\) 6.34315i 0.538019i 0.963138 + 0.269009i \(0.0866962\pi\)
−0.963138 + 0.269009i \(0.913304\pi\)
\(140\) 0 0
\(141\) 0.514719 3.00000i 0.0433471 0.252646i
\(142\) 24.7279 24.7279i 2.07512 2.07512i
\(143\) −2.00000 + 2.00000i −0.167248 + 0.167248i
\(144\) 3.00000 8.48528i 0.250000 0.707107i
\(145\) 0 0
\(146\) 0 0
\(147\) −8.92893 + 6.31371i −0.736446 + 0.520746i
\(148\) 22.3137 + 22.3137i 1.83418 + 1.83418i
\(149\) −10.0000 −0.819232 −0.409616 0.912258i \(-0.634337\pi\)
−0.409616 + 0.912258i \(0.634337\pi\)
\(150\) 0 0
\(151\) −18.1421 −1.47639 −0.738193 0.674590i \(-0.764321\pi\)
−0.738193 + 0.674590i \(0.764321\pi\)
\(152\) 8.82843 + 8.82843i 0.716080 + 0.716080i
\(153\) 10.8284 5.17157i 0.875426 0.418097i
\(154\) 2.00000i 0.161165i
\(155\) 0 0
\(156\) −18.4853 3.17157i −1.48001 0.253929i
\(157\) −7.48528 + 7.48528i −0.597390 + 0.597390i −0.939617 0.342227i \(-0.888819\pi\)
0.342227 + 0.939617i \(0.388819\pi\)
\(158\) 8.82843 8.82843i 0.702352 0.702352i
\(159\) −2.41421 0.414214i −0.191460 0.0328493i
\(160\) 0 0
\(161\) 6.14214i 0.484068i
\(162\) −2.29289 21.6066i −0.180147 1.69757i
\(163\) −6.41421 6.41421i −0.502400 0.502400i 0.409783 0.912183i \(-0.365604\pi\)
−0.912183 + 0.409783i \(0.865604\pi\)
\(164\) 14.0000 1.09322
\(165\) 0 0
\(166\) −17.3137 −1.34380
\(167\) 10.7279 + 10.7279i 0.830152 + 0.830152i 0.987537 0.157386i \(-0.0503066\pi\)
−0.157386 + 0.987537i \(0.550307\pi\)
\(168\) −5.17157 + 3.65685i −0.398996 + 0.282132i
\(169\) 5.00000i 0.384615i
\(170\) 0 0
\(171\) 8.00000 + 2.82843i 0.611775 + 0.216295i
\(172\) −31.5563 + 31.5563i −2.40615 + 2.40615i
\(173\) 8.48528 8.48528i 0.645124 0.645124i −0.306687 0.951811i \(-0.599220\pi\)
0.951811 + 0.306687i \(0.0992203\pi\)
\(174\) 3.41421 19.8995i 0.258831 1.50858i
\(175\) 0 0
\(176\) 3.00000i 0.226134i
\(177\) −4.00000 5.65685i −0.300658 0.425195i
\(178\) 2.82843 + 2.82843i 0.212000 + 0.212000i
\(179\) −4.14214 −0.309598 −0.154799 0.987946i \(-0.549473\pi\)
−0.154799 + 0.987946i \(0.549473\pi\)
\(180\) 0 0
\(181\) −5.65685 −0.420471 −0.210235 0.977651i \(-0.567423\pi\)
−0.210235 + 0.977651i \(0.567423\pi\)
\(182\) 4.00000 + 4.00000i 0.296500 + 0.296500i
\(183\) 10.4853 + 14.8284i 0.775094 + 1.09615i
\(184\) 32.7279i 2.41273i
\(185\) 0 0
\(186\) 6.24264 36.3848i 0.457733 2.66786i
\(187\) 2.82843 2.82843i 0.206835 0.206835i
\(188\) 4.75736 4.75736i 0.346966 0.346966i
\(189\) −2.10051 + 3.75736i −0.152789 + 0.273308i
\(190\) 0 0
\(191\) 11.3137i 0.818631i 0.912393 + 0.409316i \(0.134232\pi\)
−0.912393 + 0.409316i \(0.865768\pi\)
\(192\) −13.8995 + 9.82843i −1.00311 + 0.709306i
\(193\) −8.00000 8.00000i −0.575853 0.575853i 0.357905 0.933758i \(-0.383491\pi\)
−0.933758 + 0.357905i \(0.883491\pi\)
\(194\) 2.24264 0.161012
\(195\) 0 0
\(196\) −24.1716 −1.72654
\(197\) −14.1421 14.1421i −1.00759 1.00759i −0.999971 0.00761443i \(-0.997576\pi\)
−0.00761443 0.999971i \(-0.502424\pi\)
\(198\) −3.12132 6.53553i −0.221823 0.464460i
\(199\) 2.48528i 0.176177i −0.996113 0.0880885i \(-0.971924\pi\)
0.996113 0.0880885i \(-0.0280758\pi\)
\(200\) 0 0
\(201\) 8.65685 + 1.48528i 0.610607 + 0.104764i
\(202\) −21.8995 + 21.8995i −1.54084 + 1.54084i
\(203\) −2.82843 + 2.82843i −0.198517 + 0.198517i
\(204\) 26.1421 + 4.48528i 1.83032 + 0.314033i
\(205\) 0 0
\(206\) 12.2426i 0.852985i
\(207\) 9.58579 + 20.0711i 0.666258 + 1.39504i
\(208\) −6.00000 6.00000i −0.416025 0.416025i
\(209\) 2.82843 0.195646
\(210\) 0 0
\(211\) 12.4853 0.859522 0.429761 0.902943i \(-0.358598\pi\)
0.429761 + 0.902943i \(0.358598\pi\)
\(212\) −3.82843 3.82843i −0.262937 0.262937i
\(213\) 20.4853 14.4853i 1.40363 0.992515i
\(214\) 28.1421i 1.92376i
\(215\) 0 0
\(216\) 11.1924 20.0208i 0.761546 1.36224i
\(217\) −5.17157 + 5.17157i −0.351069 + 0.351069i
\(218\) 15.0711 15.0711i 1.02074 1.02074i
\(219\) 0 0
\(220\) 0 0
\(221\) 11.3137i 0.761042i
\(222\) 19.8995 + 28.1421i 1.33557 + 1.88878i
\(223\) −14.5563 14.5563i −0.974765 0.974765i 0.0249241 0.999689i \(-0.492066\pi\)
−0.999689 + 0.0249241i \(0.992066\pi\)
\(224\) 1.31371 0.0877758
\(225\) 0 0
\(226\) 0.585786 0.0389659
\(227\) −1.75736 1.75736i −0.116640 0.116640i 0.646378 0.763018i \(-0.276283\pi\)
−0.763018 + 0.646378i \(0.776283\pi\)
\(228\) 10.8284 + 15.3137i 0.717130 + 1.01418i
\(229\) 1.65685i 0.109488i −0.998500 0.0547440i \(-0.982566\pi\)
0.998500 0.0547440i \(-0.0174343\pi\)
\(230\) 0 0
\(231\) −0.242641 + 1.41421i −0.0159646 + 0.0930484i
\(232\) 15.0711 15.0711i 0.989464 0.989464i
\(233\) −8.34315 + 8.34315i −0.546578 + 0.546578i −0.925449 0.378872i \(-0.876312\pi\)
0.378872 + 0.925449i \(0.376312\pi\)
\(234\) −19.3137 6.82843i −1.26258 0.446388i
\(235\) 0 0
\(236\) 15.3137i 0.996838i
\(237\) 7.31371 5.17157i 0.475076 0.335930i
\(238\) −5.65685 5.65685i −0.366679 0.366679i
\(239\) 15.7990 1.02195 0.510976 0.859595i \(-0.329284\pi\)
0.510976 + 0.859595i \(0.329284\pi\)
\(240\) 0 0
\(241\) −28.1421 −1.81279 −0.906397 0.422427i \(-0.861178\pi\)
−0.906397 + 0.422427i \(0.861178\pi\)
\(242\) −1.70711 1.70711i −0.109737 0.109737i
\(243\) 1.00000 15.5563i 0.0641500 0.997940i
\(244\) 40.1421i 2.56984i
\(245\) 0 0
\(246\) 15.0711 + 2.58579i 0.960896 + 0.164864i
\(247\) 5.65685 5.65685i 0.359937 0.359937i
\(248\) 27.5563 27.5563i 1.74983 1.74983i
\(249\) −12.2426 2.10051i −0.775846 0.133114i
\(250\) 0 0
\(251\) 12.1421i 0.766405i −0.923664 0.383202i \(-0.874821\pi\)
0.923664 0.383202i \(-0.125179\pi\)
\(252\) −8.58579 + 4.10051i −0.540854 + 0.258308i
\(253\) 5.24264 + 5.24264i 0.329602 + 0.329602i
\(254\) 4.82843 0.302962
\(255\) 0 0
\(256\) −29.9706 −1.87316
\(257\) −3.82843 3.82843i −0.238811 0.238811i 0.577547 0.816358i \(-0.304010\pi\)
−0.816358 + 0.577547i \(0.804010\pi\)
\(258\) −39.7990 + 28.1421i −2.47778 + 1.75205i
\(259\) 6.82843i 0.424298i
\(260\) 0 0
\(261\) 4.82843 13.6569i 0.298872 0.845338i
\(262\) 2.00000 2.00000i 0.123560 0.123560i
\(263\) 10.2426 10.2426i 0.631588 0.631588i −0.316878 0.948466i \(-0.602635\pi\)
0.948466 + 0.316878i \(0.102635\pi\)
\(264\) 1.29289 7.53553i 0.0795721 0.463780i
\(265\) 0 0
\(266\) 5.65685i 0.346844i
\(267\) 1.65685 + 2.34315i 0.101398 + 0.143398i
\(268\) 13.7279 + 13.7279i 0.838566 + 0.838566i
\(269\) −14.0000 −0.853595 −0.426798 0.904347i \(-0.640358\pi\)
−0.426798 + 0.904347i \(0.640358\pi\)
\(270\) 0 0
\(271\) −8.48528 −0.515444 −0.257722 0.966219i \(-0.582972\pi\)
−0.257722 + 0.966219i \(0.582972\pi\)
\(272\) 8.48528 + 8.48528i 0.514496 + 0.514496i
\(273\) 2.34315 + 3.31371i 0.141814 + 0.200555i
\(274\) 19.8995i 1.20217i
\(275\) 0 0
\(276\) −8.31371 + 48.4558i −0.500426 + 2.91670i
\(277\) 1.51472 1.51472i 0.0910106 0.0910106i −0.660136 0.751146i \(-0.729501\pi\)
0.751146 + 0.660136i \(0.229501\pi\)
\(278\) −10.8284 + 10.8284i −0.649446 + 0.649446i
\(279\) 8.82843 24.9706i 0.528544 1.49495i
\(280\) 0 0
\(281\) 16.6274i 0.991909i 0.868349 + 0.495954i \(0.165182\pi\)
−0.868349 + 0.495954i \(0.834818\pi\)
\(282\) 6.00000 4.24264i 0.357295 0.252646i
\(283\) 0.928932 + 0.928932i 0.0552193 + 0.0552193i 0.734177 0.678958i \(-0.237568\pi\)
−0.678958 + 0.734177i \(0.737568\pi\)
\(284\) 55.4558 3.29070
\(285\) 0 0
\(286\) −6.82843 −0.403773
\(287\) −2.14214 2.14214i −0.126446 0.126446i
\(288\) −4.29289 + 2.05025i −0.252961 + 0.120812i
\(289\) 1.00000i 0.0588235i
\(290\) 0 0
\(291\) 1.58579 + 0.272078i 0.0929604 + 0.0159495i
\(292\) 0 0
\(293\) −7.65685 + 7.65685i −0.447318 + 0.447318i −0.894462 0.447144i \(-0.852441\pi\)
0.447144 + 0.894462i \(0.352441\pi\)
\(294\) −26.0208 4.46447i −1.51756 0.260373i
\(295\) 0 0
\(296\) 36.3848i 2.11482i
\(297\) −1.41421 5.00000i −0.0820610 0.290129i
\(298\) −17.0711 17.0711i −0.988900 0.988900i
\(299\) 20.9706 1.21276
\(300\) 0 0
\(301\) 9.65685 0.556612
\(302\) −30.9706 30.9706i −1.78216 1.78216i
\(303\) −18.1421 + 12.8284i −1.04224 + 0.736974i
\(304\) 8.48528i 0.486664i
\(305\) 0 0
\(306\) 27.3137 + 9.65685i 1.56142 + 0.552046i
\(307\) −7.89949 + 7.89949i −0.450848 + 0.450848i −0.895636 0.444788i \(-0.853279\pi\)
0.444788 + 0.895636i \(0.353279\pi\)
\(308\) −2.24264 + 2.24264i −0.127786 + 0.127786i
\(309\) −1.48528 + 8.65685i −0.0844947 + 0.492471i
\(310\) 0 0
\(311\) 0.142136i 0.00805977i 0.999992 + 0.00402989i \(0.00128276\pi\)
−0.999992 + 0.00402989i \(0.998717\pi\)
\(312\) −12.4853 17.6569i −0.706840 0.999623i
\(313\) −1.34315 1.34315i −0.0759191 0.0759191i 0.668128 0.744047i \(-0.267096\pi\)
−0.744047 + 0.668128i \(0.767096\pi\)
\(314\) −25.5563 −1.44223
\(315\) 0 0
\(316\) 19.7990 1.11378
\(317\) 20.3137 + 20.3137i 1.14093 + 1.14093i 0.988280 + 0.152651i \(0.0487812\pi\)
0.152651 + 0.988280i \(0.451219\pi\)
\(318\) −3.41421 4.82843i −0.191460 0.270765i
\(319\) 4.82843i 0.270340i
\(320\) 0 0
\(321\) −3.41421 + 19.8995i −0.190563 + 1.11068i
\(322\) 10.4853 10.4853i 0.584322 0.584322i
\(323\) −8.00000 + 8.00000i −0.445132 + 0.445132i
\(324\) 21.6569 26.7990i 1.20316 1.48883i
\(325\) 0 0
\(326\) 21.8995i 1.21290i
\(327\) 12.4853 8.82843i 0.690438 0.488213i
\(328\) 11.4142 + 11.4142i 0.630245 + 0.630245i
\(329\) −1.45584 −0.0802633
\(330\) 0 0
\(331\) 10.4853 0.576323 0.288162 0.957582i \(-0.406956\pi\)
0.288162 + 0.957582i \(0.406956\pi\)
\(332\) −19.4142 19.4142i −1.06549 1.06549i
\(333\) 10.6569 + 22.3137i 0.583992 + 1.22278i
\(334\) 36.6274i 2.00416i
\(335\) 0 0
\(336\) −4.24264 0.727922i −0.231455 0.0397114i
\(337\) 5.17157 5.17157i 0.281714 0.281714i −0.552079 0.833792i \(-0.686165\pi\)
0.833792 + 0.552079i \(0.186165\pi\)
\(338\) 8.53553 8.53553i 0.464272 0.464272i
\(339\) 0.414214 + 0.0710678i 0.0224970 + 0.00385987i
\(340\) 0 0
\(341\) 8.82843i 0.478086i
\(342\) 8.82843 + 18.4853i 0.477387 + 0.999570i
\(343\) 7.79899 + 7.79899i 0.421106 + 0.421106i
\(344\) −51.4558 −2.77431
\(345\) 0 0
\(346\) 28.9706 1.55747
\(347\) 17.8995 + 17.8995i 0.960895 + 0.960895i 0.999264 0.0383684i \(-0.0122160\pi\)
−0.0383684 + 0.999264i \(0.512216\pi\)
\(348\) 26.1421 18.4853i 1.40137 0.990915i
\(349\) 30.0000i 1.60586i −0.596071 0.802932i \(-0.703272\pi\)
0.596071 0.802932i \(-0.296728\pi\)
\(350\) 0 0
\(351\) −12.8284 7.17157i −0.684731 0.382790i
\(352\) −1.12132 + 1.12132i −0.0597666 + 0.0597666i
\(353\) −2.17157 + 2.17157i −0.115581 + 0.115581i −0.762532 0.646951i \(-0.776044\pi\)
0.646951 + 0.762532i \(0.276044\pi\)
\(354\) 2.82843 16.4853i 0.150329 0.876183i
\(355\) 0 0
\(356\) 6.34315i 0.336186i
\(357\) −3.31371 4.68629i −0.175380 0.248025i
\(358\) −7.07107 7.07107i −0.373718 0.373718i
\(359\) 6.14214 0.324170 0.162085 0.986777i \(-0.448178\pi\)
0.162085 + 0.986777i \(0.448178\pi\)
\(360\) 0 0
\(361\) 11.0000 0.578947
\(362\) −9.65685 9.65685i −0.507553 0.507553i
\(363\) −1.00000 1.41421i −0.0524864 0.0742270i
\(364\) 8.97056i 0.470185i
\(365\) 0 0
\(366\) −7.41421 + 43.2132i −0.387547 + 2.25879i
\(367\) 20.8995 20.8995i 1.09094 1.09094i 0.0955170 0.995428i \(-0.469550\pi\)
0.995428 0.0955170i \(-0.0304504\pi\)
\(368\) −15.7279 + 15.7279i −0.819875 + 0.819875i
\(369\) 10.3431 + 3.65685i 0.538443 + 0.190368i
\(370\) 0 0
\(371\) 1.17157i 0.0608250i
\(372\) 47.7990 33.7990i 2.47826 1.75240i
\(373\) −20.4853 20.4853i −1.06069 1.06069i −0.998035 0.0626522i \(-0.980044\pi\)
−0.0626522 0.998035i \(-0.519956\pi\)
\(374\) 9.65685 0.499344
\(375\) 0 0
\(376\) 7.75736 0.400055
\(377\) −9.65685 9.65685i −0.497353 0.497353i
\(378\) −10.0000 + 2.82843i −0.514344 + 0.145479i
\(379\) 0.142136i 0.00730102i −0.999993 0.00365051i \(-0.998838\pi\)
0.999993 0.00365051i \(-0.00116200\pi\)
\(380\) 0 0
\(381\) 3.41421 + 0.585786i 0.174915 + 0.0300107i
\(382\) −19.3137 + 19.3137i −0.988175 + 0.988175i
\(383\) −8.07107 + 8.07107i −0.412412 + 0.412412i −0.882578 0.470166i \(-0.844194\pi\)
0.470166 + 0.882578i \(0.344194\pi\)
\(384\) −35.0919 6.02082i −1.79078 0.307248i
\(385\) 0 0
\(386\) 27.3137i 1.39023i
\(387\) −31.5563 + 15.0711i −1.60410 + 0.766105i
\(388\) 2.51472 + 2.51472i 0.127665 + 0.127665i
\(389\) 5.31371 0.269416 0.134708 0.990885i \(-0.456990\pi\)
0.134708 + 0.990885i \(0.456990\pi\)
\(390\) 0 0
\(391\) −29.6569 −1.49981
\(392\) −19.7071 19.7071i −0.995359 0.995359i
\(393\) 1.65685 1.17157i 0.0835772 0.0590980i
\(394\) 48.2843i 2.43253i
\(395\) 0 0
\(396\) 3.82843 10.8284i 0.192386 0.544149i
\(397\) −11.8284 + 11.8284i −0.593652 + 0.593652i −0.938616 0.344964i \(-0.887891\pi\)
0.344964 + 0.938616i \(0.387891\pi\)
\(398\) 4.24264 4.24264i 0.212664 0.212664i
\(399\) 0.686292 4.00000i 0.0343575 0.200250i
\(400\) 0 0
\(401\) 24.3431i 1.21564i −0.794075 0.607819i \(-0.792044\pi\)
0.794075 0.607819i \(-0.207956\pi\)
\(402\) 12.2426 + 17.3137i 0.610607 + 0.863529i
\(403\) −17.6569 17.6569i −0.879551 0.879551i
\(404\) −49.1127 −2.44345
\(405\) 0 0
\(406\) −9.65685 −0.479262
\(407\) 5.82843 + 5.82843i 0.288904 + 0.288904i
\(408\) 17.6569 + 24.9706i 0.874145 + 1.23623i
\(409\) 1.51472i 0.0748980i −0.999299 0.0374490i \(-0.988077\pi\)
0.999299 0.0374490i \(-0.0119232\pi\)
\(410\) 0 0
\(411\) 2.41421 14.0711i 0.119084 0.694075i
\(412\) −13.7279 + 13.7279i −0.676326 + 0.676326i
\(413\) −2.34315 + 2.34315i −0.115299 + 0.115299i
\(414\) −17.8995 + 50.6274i −0.879712 + 2.48820i
\(415\) 0 0
\(416\) 4.48528i 0.219909i
\(417\) −8.97056 + 6.34315i −0.439290 + 0.310625i
\(418\) 4.82843 + 4.82843i 0.236166 + 0.236166i
\(419\) −35.4558 −1.73213 −0.866066 0.499930i \(-0.833359\pi\)
−0.866066 + 0.499930i \(0.833359\pi\)
\(420\) 0 0
\(421\) −4.00000 −0.194948 −0.0974740 0.995238i \(-0.531076\pi\)
−0.0974740 + 0.995238i \(0.531076\pi\)
\(422\) 21.3137 + 21.3137i 1.03754 + 1.03754i
\(423\) 4.75736 2.27208i 0.231311 0.110472i
\(424\) 6.24264i 0.303169i
\(425\) 0 0
\(426\) 59.6985 + 10.2426i 2.89240 + 0.496258i
\(427\) 6.14214 6.14214i 0.297239 0.297239i
\(428\) −31.5563 + 31.5563i −1.52533 + 1.52533i
\(429\) −4.82843 0.828427i −0.233119 0.0399968i
\(430\) 0 0
\(431\) 17.6569i 0.850501i 0.905076 + 0.425250i \(0.139814\pi\)
−0.905076 + 0.425250i \(0.860186\pi\)
\(432\) 15.0000 4.24264i 0.721688 0.204124i
\(433\) −22.3137 22.3137i −1.07233 1.07233i −0.997172 0.0751567i \(-0.976054\pi\)
−0.0751567 0.997172i \(-0.523946\pi\)
\(434\) −17.6569 −0.847556
\(435\) 0 0
\(436\) 33.7990 1.61868
\(437\) −14.8284 14.8284i −0.709340 0.709340i
\(438\) 0 0
\(439\) 15.3137i 0.730883i 0.930834 + 0.365442i \(0.119082\pi\)
−0.930834 + 0.365442i \(0.880918\pi\)
\(440\) 0 0
\(441\) −17.8579 6.31371i −0.850374 0.300653i
\(442\) 19.3137 19.3137i 0.918659 0.918659i
\(443\) 29.2426 29.2426i 1.38936 1.38936i 0.562696 0.826664i \(-0.309764\pi\)
0.826664 0.562696i \(-0.190236\pi\)
\(444\) −9.24264 + 53.8701i −0.438636 + 2.55656i
\(445\) 0 0
\(446\) 49.6985i 2.35329i
\(447\) −10.0000 14.1421i −0.472984 0.668900i
\(448\) 5.75736 + 5.75736i 0.272010 + 0.272010i
\(449\) −36.9706 −1.74475 −0.872374 0.488838i \(-0.837421\pi\)
−0.872374 + 0.488838i \(0.837421\pi\)
\(450\) 0 0
\(451\) 3.65685 0.172195
\(452\) 0.656854 + 0.656854i 0.0308958 + 0.0308958i
\(453\) −18.1421 25.6569i −0.852392 1.20546i
\(454\) 6.00000i 0.281594i
\(455\) 0 0
\(456\) −3.65685 + 21.3137i −0.171248 + 0.998106i
\(457\) −10.4853 + 10.4853i −0.490481 + 0.490481i −0.908458 0.417977i \(-0.862739\pi\)
0.417977 + 0.908458i \(0.362739\pi\)
\(458\) 2.82843 2.82843i 0.132164 0.132164i
\(459\) 18.1421 + 10.1421i 0.846802 + 0.473394i
\(460\) 0 0
\(461\) 30.4853i 1.41984i 0.704282 + 0.709921i \(0.251269\pi\)
−0.704282 + 0.709921i \(0.748731\pi\)
\(462\) −2.82843 + 2.00000i −0.131590 + 0.0930484i
\(463\) 13.7279 + 13.7279i 0.637991 + 0.637991i 0.950059 0.312069i \(-0.101022\pi\)
−0.312069 + 0.950059i \(0.601022\pi\)
\(464\) 14.4853 0.672462
\(465\) 0 0
\(466\) −28.4853 −1.31956
\(467\) −2.41421 2.41421i −0.111716 0.111716i 0.649039 0.760755i \(-0.275171\pi\)
−0.760755 + 0.649039i \(0.775171\pi\)
\(468\) −14.0000 29.3137i −0.647150 1.35503i
\(469\) 4.20101i 0.193985i
\(470\) 0 0
\(471\) −18.0711 3.10051i −0.832671 0.142864i
\(472\) 12.4853 12.4853i 0.574682 0.574682i
\(473\) −8.24264 + 8.24264i −0.378997 + 0.378997i
\(474\) 21.3137 + 3.65685i 0.978971 + 0.167965i
\(475\) 0 0
\(476\) 12.6863i 0.581475i
\(477\) −1.82843 3.82843i −0.0837179 0.175292i
\(478\) 26.9706 + 26.9706i 1.23360 + 1.23360i
\(479\) −1.85786 −0.0848880 −0.0424440 0.999099i \(-0.513514\pi\)
−0.0424440 + 0.999099i \(0.513514\pi\)
\(480\) 0 0
\(481\) 23.3137 1.06301
\(482\) −48.0416 48.0416i −2.18824 2.18824i
\(483\) 8.68629 6.14214i 0.395240 0.279477i
\(484\) 3.82843i 0.174019i
\(485\) 0 0
\(486\) 28.2635 24.8492i 1.28206 1.12718i
\(487\) 13.7279 13.7279i 0.622072 0.622072i −0.323989 0.946061i \(-0.605024\pi\)
0.946061 + 0.323989i \(0.105024\pi\)
\(488\) −32.7279 + 32.7279i −1.48152 + 1.48152i
\(489\) 2.65685 15.4853i 0.120147 0.700269i
\(490\) 0 0
\(491\) 20.0000i 0.902587i 0.892375 + 0.451294i \(0.149037\pi\)
−0.892375 + 0.451294i \(0.850963\pi\)
\(492\) 14.0000 + 19.7990i 0.631169 + 0.892607i
\(493\) 13.6569 + 13.6569i 0.615074 + 0.615074i
\(494\) 19.3137 0.868965
\(495\) 0 0
\(496\) 26.4853 1.18922
\(497\) −8.48528 8.48528i −0.380617 0.380617i
\(498\) −17.3137 24.4853i −0.775846 1.09721i
\(499\) 19.1716i 0.858237i 0.903248 + 0.429119i \(0.141176\pi\)
−0.903248 + 0.429119i \(0.858824\pi\)
\(500\) 0 0
\(501\) −4.44365 + 25.8995i −0.198528 + 1.15710i
\(502\) 20.7279 20.7279i 0.925132 0.925132i
\(503\) −15.0711 + 15.0711i −0.671986 + 0.671986i −0.958174 0.286188i \(-0.907612\pi\)
0.286188 + 0.958174i \(0.407612\pi\)
\(504\) −10.3431 3.65685i −0.460720 0.162889i
\(505\) 0 0
\(506\) 17.8995i 0.795730i
\(507\) 7.07107 5.00000i 0.314037 0.222058i
\(508\) 5.41421 + 5.41421i 0.240217 + 0.240217i
\(509\) 24.3431 1.07899 0.539495 0.841988i \(-0.318615\pi\)
0.539495 + 0.841988i \(0.318615\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −22.0919 22.0919i −0.976333 0.976333i
\(513\) 4.00000 + 14.1421i 0.176604 + 0.624391i
\(514\) 13.0711i 0.576540i
\(515\) 0 0
\(516\) −76.1838 13.0711i −3.35380 0.575422i
\(517\) 1.24264 1.24264i 0.0546513 0.0546513i
\(518\) 11.6569 11.6569i 0.512173 0.512173i
\(519\) 20.4853 + 3.51472i 0.899204 + 0.154279i
\(520\) 0 0
\(521\) 16.3431i 0.716006i 0.933720 + 0.358003i \(0.116542\pi\)
−0.933720 + 0.358003i \(0.883458\pi\)
\(522\) 31.5563 15.0711i 1.38118 0.659643i
\(523\) −15.2132 15.2132i −0.665227 0.665227i 0.291380 0.956607i \(-0.405885\pi\)
−0.956607 + 0.291380i \(0.905885\pi\)
\(524\) 4.48528 0.195940
\(525\) 0 0
\(526\) 34.9706 1.52479
\(527\) 24.9706 + 24.9706i 1.08773 + 1.08773i
\(528\) 4.24264 3.00000i 0.184637 0.130558i
\(529\) 31.9706i 1.39002i
\(530\) 0 0
\(531\) 4.00000 11.3137i 0.173585 0.490973i
\(532\) 6.34315 6.34315i 0.275010 0.275010i
\(533\) 7.31371 7.31371i 0.316792 0.316792i
\(534\) −1.17157 + 6.82843i −0.0506989 + 0.295495i
\(535\) 0 0
\(536\) 22.3848i 0.966875i
\(537\) −4.14214 5.85786i −0.178746 0.252786i
\(538\) −23.8995 23.8995i −1.03038 1.03038i
\(539\) −6.31371 −0.271951
\(540\) 0 0
\(541\) −33.3137 −1.43227 −0.716134 0.697963i \(-0.754090\pi\)
−0.716134 + 0.697963i \(0.754090\pi\)
\(542\) −14.4853 14.4853i −0.622196 0.622196i
\(543\) −5.65685 8.00000i −0.242759 0.343313i
\(544\) 6.34315i 0.271960i
\(545\) 0 0
\(546\) −1.65685 + 9.65685i −0.0709068 + 0.413275i
\(547\) −21.8995 + 21.8995i −0.936355 + 0.936355i −0.998092 0.0617376i \(-0.980336\pi\)
0.0617376 + 0.998092i \(0.480336\pi\)
\(548\) 22.3137 22.3137i 0.953194 0.953194i
\(549\) −10.4853 + 29.6569i −0.447501 + 1.26572i
\(550\) 0 0
\(551\) 13.6569i 0.581802i
\(552\) −46.2843 + 32.7279i −1.96999 + 1.39299i
\(553\) −3.02944 3.02944i −0.128825 0.128825i
\(554\) 5.17157 0.219719
\(555\) 0 0
\(556\) −24.2843 −1.02988
\(557\) 24.9706 + 24.9706i 1.05804 + 1.05804i 0.998209 + 0.0598280i \(0.0190552\pi\)
0.0598280 + 0.998209i \(0.480945\pi\)
\(558\) 57.6985 27.5563i 2.44257 1.16655i
\(559\) 32.9706i 1.39451i
\(560\) 0 0
\(561\) 6.82843 + 1.17157i 0.288296 + 0.0494638i
\(562\) −28.3848 + 28.3848i −1.19734 + 1.19734i
\(563\) −9.89949 + 9.89949i −0.417214 + 0.417214i −0.884242 0.467028i \(-0.845325\pi\)
0.467028 + 0.884242i \(0.345325\pi\)
\(564\) 11.4853 + 1.97056i 0.483618 + 0.0829757i
\(565\) 0 0
\(566\) 3.17157i 0.133311i
\(567\) −7.41421 + 0.786797i −0.311368 + 0.0330423i
\(568\) 45.2132 + 45.2132i 1.89710 + 1.89710i
\(569\) −39.6569 −1.66250 −0.831251 0.555897i \(-0.812375\pi\)
−0.831251 + 0.555897i \(0.812375\pi\)
\(570\) 0 0
\(571\) 18.3431 0.767637 0.383818 0.923409i \(-0.374609\pi\)
0.383818 + 0.923409i \(0.374609\pi\)
\(572\) −7.65685 7.65685i −0.320149 0.320149i
\(573\) −16.0000 + 11.3137i −0.668410 + 0.472637i
\(574\) 7.31371i 0.305268i
\(575\) 0 0
\(576\) −27.7990 9.82843i −1.15829 0.409518i
\(577\) −17.0000 + 17.0000i −0.707719 + 0.707719i −0.966055 0.258336i \(-0.916826\pi\)
0.258336 + 0.966055i \(0.416826\pi\)
\(578\) 1.70711 1.70711i 0.0710063 0.0710063i
\(579\) 3.31371 19.3137i 0.137713 0.802650i
\(580\) 0 0
\(581\) 5.94113i 0.246479i
\(582\) 2.24264 + 3.17157i 0.0929604 + 0.131466i
\(583\) −1.00000 1.00000i −0.0414158 0.0414158i
\(584\) 0 0
\(585\) 0 0
\(586\) −26.1421 −1.07992
\(587\) −2.41421 2.41421i −0.0996453 0.0996453i 0.655527 0.755172i \(-0.272447\pi\)
−0.755172 + 0.655527i \(0.772447\pi\)
\(588\) −24.1716 34.1838i −0.996819 1.40971i
\(589\) 24.9706i 1.02889i
\(590\) 0 0
\(591\) 5.85786 34.1421i 0.240960 1.40442i
\(592\) −17.4853 + 17.4853i −0.718641 + 0.718641i
\(593\) −34.1421 + 34.1421i −1.40205 + 1.40205i −0.608481 + 0.793568i \(0.708221\pi\)
−0.793568 + 0.608481i \(0.791779\pi\)
\(594\) 6.12132 10.9497i 0.251161 0.449274i
\(595\) 0 0
\(596\) 38.2843i 1.56818i
\(597\) 3.51472 2.48528i 0.143848 0.101716i
\(598\) 35.7990 + 35.7990i 1.46393 + 1.46393i
\(599\) 47.4558 1.93899 0.969497 0.245105i \(-0.0788223\pi\)
0.969497 + 0.245105i \(0.0788223\pi\)
\(600\) 0 0
\(601\) 23.4558 0.956784 0.478392 0.878146i \(-0.341220\pi\)
0.478392 + 0.878146i \(0.341220\pi\)
\(602\) 16.4853 + 16.4853i 0.671890 + 0.671890i
\(603\) 6.55635 + 13.7279i 0.266995 + 0.559044i
\(604\) 69.4558i 2.82612i
\(605\) 0 0
\(606\) −52.8701 9.07107i −2.14770 0.368487i
\(607\) 2.10051 2.10051i 0.0852569 0.0852569i −0.663192 0.748449i \(-0.730799\pi\)
0.748449 + 0.663192i \(0.230799\pi\)
\(608\) 3.17157 3.17157i 0.128624 0.128624i
\(609\) −6.82843 1.17157i −0.276702 0.0474745i
\(610\) 0 0
\(611\) 4.97056i 0.201087i
\(612\) 19.7990 + 41.4558i 0.800327 + 1.67575i
\(613\) 16.0000 + 16.0000i 0.646234 + 0.646234i 0.952081 0.305847i \(-0.0989395\pi\)
−0.305847 + 0.952081i \(0.598940\pi\)
\(614\) −26.9706 −1.08844
\(615\) 0 0
\(616\) −3.65685 −0.147339
\(617\) −24.1716 24.1716i −0.973111 0.973111i 0.0265370 0.999648i \(-0.491552\pi\)
−0.999648 + 0.0265370i \(0.991552\pi\)
\(618\) −17.3137 + 12.2426i −0.696459 + 0.492471i
\(619\) 23.3137i 0.937057i −0.883448 0.468529i \(-0.844784\pi\)
0.883448 0.468529i \(-0.155216\pi\)
\(620\) 0 0
\(621\) −18.7990 + 33.6274i −0.754377 + 1.34942i
\(622\) −0.242641 + 0.242641i −0.00972901 + 0.00972901i
\(623\) 0.970563 0.970563i 0.0388848 0.0388848i
\(624\) 2.48528 14.4853i 0.0994909 0.579875i
\(625\) 0 0
\(626\) 4.58579i 0.183285i
\(627\) 2.82843 + 4.00000i 0.112956 + 0.159745i
\(628\) −28.6569 28.6569i −1.14353 1.14353i
\(629\) −32.9706 −1.31462
\(630\) 0 0
\(631\) 16.9706 0.675587 0.337794 0.941220i \(-0.390319\pi\)
0.337794 + 0.941220i \(0.390319\pi\)
\(632\) 16.1421 + 16.1421i 0.642100 + 0.642100i
\(633\) 12.4853 + 17.6569i 0.496245 + 0.701797i
\(634\) 69.3553i 2.75445i
\(635\) 0 0
\(636\) 1.58579 9.24264i 0.0628805 0.366495i
\(637\) −12.6274 + 12.6274i −0.500316 + 0.500316i
\(638\) 8.24264 8.24264i 0.326329 0.326329i
\(639\) 40.9706 + 14.4853i 1.62077 + 0.573029i
\(640\) 0 0
\(641\) 12.6274i 0.498753i −0.968407 0.249376i \(-0.919774\pi\)
0.968407 0.249376i \(-0.0802257\pi\)
\(642\) −39.7990 + 28.1421i −1.57074 + 1.11068i
\(643\) 0.757359 + 0.757359i 0.0298673 + 0.0298673i 0.721883 0.692015i \(-0.243277\pi\)
−0.692015 + 0.721883i \(0.743277\pi\)
\(644\) 23.5147 0.926610
\(645\) 0 0
\(646\) −27.3137 −1.07464
\(647\) 13.7279 + 13.7279i 0.539700 + 0.539700i 0.923441 0.383741i \(-0.125364\pi\)
−0.383741 + 0.923441i \(0.625364\pi\)
\(648\) 39.5061 4.19239i 1.55195 0.164693i
\(649\) 4.00000i 0.157014i
\(650\) 0 0
\(651\) −12.4853 2.14214i −0.489337 0.0839569i
\(652\) 24.5563 24.5563i 0.961701 0.961701i
\(653\) 2.65685 2.65685i 0.103971 0.103971i −0.653208 0.757179i \(-0.726577\pi\)
0.757179 + 0.653208i \(0.226577\pi\)
\(654\) 36.3848 + 6.24264i 1.42276 + 0.244107i
\(655\) 0 0
\(656\) 10.9706i 0.428329i
\(657\) 0 0
\(658\) −2.48528 2.48528i −0.0968864 0.0968864i
\(659\) 8.97056 0.349444 0.174722 0.984618i \(-0.444097\pi\)
0.174722 + 0.984618i \(0.444097\pi\)
\(660\) 0 0
\(661\) 14.0000 0.544537 0.272268 0.962221i \(-0.412226\pi\)
0.272268 + 0.962221i \(0.412226\pi\)
\(662\) 17.8995 + 17.8995i 0.695684 + 0.695684i
\(663\) 16.0000 11.3137i 0.621389 0.439388i
\(664\) 31.6569i 1.22852i
\(665\) 0 0
\(666\) −19.8995 + 56.2843i −0.771090 + 2.18097i
\(667\) −25.3137 + 25.3137i −0.980151 + 0.980151i
\(668\) −41.0711 + 41.0711i −1.58909 + 1.58909i
\(669\) 6.02944 35.1421i 0.233112 1.35867i
\(670\) 0 0
\(671\) 10.4853i 0.404780i
\(672\) 1.31371 + 1.85786i 0.0506774 + 0.0716687i
\(673\) 33.6569 + 33.6569i 1.29738 + 1.29738i 0.930120 + 0.367257i \(0.119703\pi\)
0.367257 + 0.930120i \(0.380297\pi\)
\(674\) 17.6569 0.680117
\(675\) 0 0
\(676\) 19.1421 0.736236
\(677\) −8.34315 8.34315i −0.320653 0.320653i 0.528365 0.849018i \(-0.322805\pi\)
−0.849018 + 0.528365i \(0.822805\pi\)
\(678\) 0.585786 + 0.828427i 0.0224970 + 0.0318156i
\(679\) 0.769553i 0.0295327i
\(680\) 0 0
\(681\) 0.727922 4.24264i 0.0278940 0.162578i
\(682\) 15.0711 15.0711i 0.577101 0.577101i
\(683\) 17.7279 17.7279i 0.678340 0.678340i −0.281284 0.959624i \(-0.590760\pi\)
0.959624 + 0.281284i \(0.0907604\pi\)
\(684\) −10.8284 + 30.6274i −0.414035 + 1.17107i
\(685\) 0 0
\(686\) 26.6274i 1.01664i
\(687\) 2.34315 1.65685i 0.0893966 0.0632129i
\(688\) −24.7279 24.7279i −0.942743 0.942743i
\(689\) −4.00000 −0.152388
\(690\) 0 0
\(691\) 20.0000 0.760836 0.380418 0.924815i \(-0.375780\pi\)
0.380418 + 0.924815i \(0.375780\pi\)
\(692\) 32.4853 + 32.4853i 1.23491 + 1.23491i
\(693\) −2.24264 + 1.07107i −0.0851909 + 0.0406865i
\(694\) 61.1127i 2.31981i
\(695\) 0 0
\(696\) 36.3848 + 6.24264i 1.37916 + 0.236627i
\(697\) −10.3431 + 10.3431i −0.391775 + 0.391775i
\(698\) 51.2132 51.2132i 1.93845 1.93845i
\(699\) −20.1421 3.45584i −0.761846 0.130712i
\(700\) 0 0
\(701\) 21.3137i 0.805008i 0.915418 + 0.402504i \(0.131860\pi\)
−0.915418 + 0.402504i \(0.868140\pi\)
\(702\) −9.65685 34.1421i −0.364474 1.28861i
\(703\) −16.4853 16.4853i −0.621754 0.621754i
\(704\) −9.82843 −0.370423
\(705\) 0 0
\(706\) −7.41421 −0.279038
\(707\) 7.51472 + 7.51472i 0.282620 + 0.282620i
\(708\) 21.6569 15.3137i 0.813914 0.575524i
\(709\) 6.68629i 0.251109i 0.992087 + 0.125554i \(0.0400710\pi\)
−0.992087 + 0.125554i \(0.959929\pi\)
\(710\) 0 0
\(711\) 14.6274 + 5.17157i 0.548571 + 0.193949i
\(712\) −5.17157 + 5.17157i −0.193813 + 0.193813i
\(713\) −46.2843 + 46.2843i −1.73336 + 1.73336i
\(714\) 2.34315 13.6569i 0.0876900 0.511095i
\(715\) 0 0
\(716\) 15.8579i 0.592636i
\(717\) 15.7990 + 22.3431i 0.590024 + 0.834420i
\(718\) 10.4853 + 10.4853i 0.391307 + 0.391307i
\(719\) 50.7696 1.89338 0.946692 0.322139i \(-0.104402\pi\)
0.946692 + 0.322139i \(0.104402\pi\)
\(720\) 0 0
\(721\) 4.20101 0.156454
\(722\) 18.7782 + 18.7782i 0.698851 + 0.698851i
\(723\) −28.1421 39.7990i −1.04662 1.48014i
\(724\) 21.6569i 0.804871i
\(725\) 0 0
\(726\) 0.707107 4.12132i 0.0262432 0.152957i
\(727\) 22.2132 22.2132i 0.823842 0.823842i −0.162815 0.986657i \(-0.552057\pi\)
0.986657 + 0.162815i \(0.0520572\pi\)
\(728\) −7.31371 + 7.31371i −0.271064 + 0.271064i
\(729\) 23.0000 14.1421i 0.851852 0.523783i
\(730\) 0 0
\(731\) 46.6274i 1.72458i
\(732\) −56.7696 + 40.1421i −2.09826 + 1.48370i
\(733\) 35.7990 + 35.7990i 1.32227 + 1.32227i 0.911938 + 0.410328i \(0.134586\pi\)
0.410328 + 0.911938i \(0.365414\pi\)
\(734\) 71.3553 2.63377
\(735\) 0 0
\(736\) 11.7574 0.433382
\(737\) 3.58579 + 3.58579i 0.132084 + 0.132084i
\(738\) 11.4142 + 23.8995i 0.420163 + 0.879753i
\(739\) 30.6274i 1.12665i 0.826236 + 0.563324i \(0.190478\pi\)
−0.826236 + 0.563324i \(0.809522\pi\)
\(740\) 0 0
\(741\) 13.6569 + 2.34315i 0.501697 + 0.0860776i
\(742\) −2.00000 + 2.00000i −0.0734223 + 0.0734223i
\(743\) −22.0416 + 22.0416i −0.808629 + 0.808629i −0.984426 0.175797i \(-0.943750\pi\)
0.175797 + 0.984426i \(0.443750\pi\)
\(744\) 66.5269 + 11.4142i 2.43899 + 0.418465i
\(745\) 0 0
\(746\) 69.9411i 2.56073i
\(747\) −9.27208 19.4142i −0.339248 0.710329i
\(748\) 10.8284 + 10.8284i 0.395927 + 0.395927i
\(749\) 9.65685 0.352854
\(750\) 0 0
\(751\) −1.37258 −0.0500863 −0.0250431 0.999686i \(-0.507972\pi\)
−0.0250431 + 0.999686i \(0.507972\pi\)
\(752\) 3.72792 + 3.72792i 0.135943 + 0.135943i
\(753\) 17.1716 12.1421i 0.625767 0.442484i
\(754\) 32.9706i 1.20072i
\(755\) 0 0
\(756\) −14.3848 8.04163i −0.523169 0.292471i
\(757\) −5.82843 + 5.82843i −0.211838 + 0.211838i −0.805048 0.593210i \(-0.797860\pi\)
0.593210 + 0.805048i \(0.297860\pi\)
\(758\) 0.242641 0.242641i 0.00881311 0.00881311i
\(759\) −2.17157 + 12.6569i −0.0788231 + 0.459415i
\(760\) 0 0
\(761\) 18.4853i 0.670091i −0.942202 0.335045i \(-0.891248\pi\)
0.942202 0.335045i \(-0.108752\pi\)
\(762\) 4.82843 + 6.82843i 0.174915 + 0.247368i
\(763\) −5.17157 5.17157i −0.187224 0.187224i
\(764\) −43.3137 −1.56703
\(765\) 0 0
\(766\) −27.5563 −0.995651
\(767\) −8.00000 8.00000i −0.288863 0.288863i
\(768\) −29.9706 42.3848i −1.08147 1.52943i
\(769\) 7.37258i 0.265862i 0.991125 + 0.132931i \(0.0424389\pi\)
−0.991125 + 0.132931i \(0.957561\pi\)
\(770\) 0 0
\(771\) 1.58579 9.24264i 0.0571107 0.332866i
\(772\) 30.6274 30.6274i 1.10230 1.10230i
\(773\) 0.656854 0.656854i 0.0236254 0.0236254i −0.695195 0.718821i \(-0.744682\pi\)
0.718821 + 0.695195i \(0.244682\pi\)
\(774\) −79.5980 28.1421i −2.86109 1.01155i
\(775\) 0 0
\(776\) 4.10051i 0.147200i
\(777\) 9.65685 6.82843i 0.346438 0.244968i
\(778\) 9.07107 + 9.07107i 0.325214 + 0.325214i
\(779\) −10.3431 −0.370582
\(780\) 0 0
\(781\) 14.4853 0.518324
\(782\) −50.6274 50.6274i −1.81043 1.81043i
\(783\) 24.1421 6.82843i 0.862770 0.244028i
\(784\) 18.9411i 0.676469i
\(785\)