Properties

Label 1078.2.e.m.67.2
Level $1078$
Weight $2$
Character 1078.67
Analytic conductor $8.608$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1078.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.60787333789\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} + 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 154)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 67.2
Root \(0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 1078.67
Dual form 1078.2.e.m.177.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(0.207107 - 0.358719i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.70711 - 2.95680i) q^{5} -0.414214 q^{6} +1.00000 q^{8} +(1.41421 + 2.44949i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(0.207107 - 0.358719i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.70711 - 2.95680i) q^{5} -0.414214 q^{6} +1.00000 q^{8} +(1.41421 + 2.44949i) q^{9} +(-1.70711 + 2.95680i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(0.207107 + 0.358719i) q^{12} -1.82843 q^{13} -1.41421 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.82843 + 6.63103i) q^{17} +(1.41421 - 2.44949i) q^{18} +(-1.70711 - 2.95680i) q^{19} +3.41421 q^{20} +1.00000 q^{22} +(-1.12132 - 1.94218i) q^{23} +(0.207107 - 0.358719i) q^{24} +(-3.32843 + 5.76500i) q^{25} +(0.914214 + 1.58346i) q^{26} +2.41421 q^{27} -8.65685 q^{29} +(0.707107 + 1.22474i) q^{30} +(-2.00000 + 3.46410i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.207107 + 0.358719i) q^{33} +7.65685 q^{34} -2.82843 q^{36} +(3.29289 + 5.70346i) q^{37} +(-1.70711 + 2.95680i) q^{38} +(-0.378680 + 0.655892i) q^{39} +(-1.70711 - 2.95680i) q^{40} +2.58579 q^{41} +5.65685 q^{43} +(-0.500000 - 0.866025i) q^{44} +(4.82843 - 8.36308i) q^{45} +(-1.12132 + 1.94218i) q^{46} +(3.24264 + 5.61642i) q^{47} -0.414214 q^{48} +6.65685 q^{50} +(1.58579 + 2.74666i) q^{51} +(0.914214 - 1.58346i) q^{52} +(5.94975 - 10.3053i) q^{53} +(-1.20711 - 2.09077i) q^{54} +3.41421 q^{55} -1.41421 q^{57} +(4.32843 + 7.49706i) q^{58} +(-4.20711 + 7.28692i) q^{59} +(0.707107 - 1.22474i) q^{60} +(3.08579 + 5.34474i) q^{61} +4.00000 q^{62} +1.00000 q^{64} +(3.12132 + 5.40629i) q^{65} +(0.207107 - 0.358719i) q^{66} +(-5.62132 + 9.73641i) q^{67} +(-3.82843 - 6.63103i) q^{68} -0.928932 q^{69} +3.07107 q^{71} +(1.41421 + 2.44949i) q^{72} +(-3.29289 + 5.70346i) q^{73} +(3.29289 - 5.70346i) q^{74} +(1.37868 + 2.38794i) q^{75} +3.41421 q^{76} +0.757359 q^{78} +(2.37868 + 4.11999i) q^{79} +(-1.70711 + 2.95680i) q^{80} +(-3.74264 + 6.48244i) q^{81} +(-1.29289 - 2.23936i) q^{82} -16.1421 q^{83} +26.1421 q^{85} +(-2.82843 - 4.89898i) q^{86} +(-1.79289 + 3.10538i) q^{87} +(-0.500000 + 0.866025i) q^{88} +(-2.24264 - 3.88437i) q^{89} -9.65685 q^{90} +2.24264 q^{92} +(0.828427 + 1.43488i) q^{93} +(3.24264 - 5.61642i) q^{94} +(-5.82843 + 10.0951i) q^{95} +(0.207107 + 0.358719i) q^{96} -1.82843 q^{97} -2.82843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{2} - 2q^{3} - 2q^{4} - 4q^{5} + 4q^{6} + 4q^{8} + O(q^{10}) \) \( 4q - 2q^{2} - 2q^{3} - 2q^{4} - 4q^{5} + 4q^{6} + 4q^{8} - 4q^{10} - 2q^{11} - 2q^{12} + 4q^{13} - 2q^{16} - 4q^{17} - 4q^{19} + 8q^{20} + 4q^{22} + 4q^{23} - 2q^{24} - 2q^{25} - 2q^{26} + 4q^{27} - 12q^{29} - 8q^{31} - 2q^{32} - 2q^{33} + 8q^{34} + 16q^{37} - 4q^{38} - 10q^{39} - 4q^{40} + 16q^{41} - 2q^{44} + 8q^{45} + 4q^{46} - 4q^{47} + 4q^{48} + 4q^{50} + 12q^{51} - 2q^{52} + 4q^{53} - 2q^{54} + 8q^{55} + 6q^{58} - 14q^{59} + 18q^{61} + 16q^{62} + 4q^{64} + 4q^{65} - 2q^{66} - 14q^{67} - 4q^{68} - 32q^{69} - 16q^{71} - 16q^{73} + 16q^{74} + 14q^{75} + 8q^{76} + 20q^{78} + 18q^{79} - 4q^{80} + 2q^{81} - 8q^{82} - 8q^{83} + 48q^{85} - 10q^{87} - 2q^{88} + 8q^{89} - 16q^{90} - 8q^{92} - 8q^{93} - 4q^{94} - 12q^{95} - 2q^{96} + 4q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(981\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) 0.207107 0.358719i 0.119573 0.207107i −0.800025 0.599966i \(-0.795181\pi\)
0.919599 + 0.392859i \(0.128514\pi\)
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −1.70711 2.95680i −0.763441 1.32232i −0.941067 0.338221i \(-0.890175\pi\)
0.177625 0.984098i \(-0.443158\pi\)
\(6\) −0.414214 −0.169102
\(7\) 0 0
\(8\) 1.00000 0.353553
\(9\) 1.41421 + 2.44949i 0.471405 + 0.816497i
\(10\) −1.70711 + 2.95680i −0.539835 + 0.935021i
\(11\) −0.500000 + 0.866025i −0.150756 + 0.261116i
\(12\) 0.207107 + 0.358719i 0.0597866 + 0.103553i
\(13\) −1.82843 −0.507114 −0.253557 0.967320i \(-0.581601\pi\)
−0.253557 + 0.967320i \(0.581601\pi\)
\(14\) 0 0
\(15\) −1.41421 −0.365148
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −3.82843 + 6.63103i −0.928530 + 1.60826i −0.142747 + 0.989759i \(0.545593\pi\)
−0.785783 + 0.618502i \(0.787740\pi\)
\(18\) 1.41421 2.44949i 0.333333 0.577350i
\(19\) −1.70711 2.95680i −0.391637 0.678335i 0.601028 0.799228i \(-0.294758\pi\)
−0.992666 + 0.120892i \(0.961424\pi\)
\(20\) 3.41421 0.763441
\(21\) 0 0
\(22\) 1.00000 0.213201
\(23\) −1.12132 1.94218i −0.233811 0.404973i 0.725115 0.688628i \(-0.241787\pi\)
−0.958927 + 0.283654i \(0.908453\pi\)
\(24\) 0.207107 0.358719i 0.0422755 0.0732233i
\(25\) −3.32843 + 5.76500i −0.665685 + 1.15300i
\(26\) 0.914214 + 1.58346i 0.179292 + 0.310543i
\(27\) 2.41421 0.464616
\(28\) 0 0
\(29\) −8.65685 −1.60754 −0.803769 0.594942i \(-0.797175\pi\)
−0.803769 + 0.594942i \(0.797175\pi\)
\(30\) 0.707107 + 1.22474i 0.129099 + 0.223607i
\(31\) −2.00000 + 3.46410i −0.359211 + 0.622171i −0.987829 0.155543i \(-0.950287\pi\)
0.628619 + 0.777714i \(0.283621\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 0.207107 + 0.358719i 0.0360527 + 0.0624450i
\(34\) 7.65685 1.31314
\(35\) 0 0
\(36\) −2.82843 −0.471405
\(37\) 3.29289 + 5.70346i 0.541348 + 0.937643i 0.998827 + 0.0484222i \(0.0154193\pi\)
−0.457479 + 0.889221i \(0.651247\pi\)
\(38\) −1.70711 + 2.95680i −0.276929 + 0.479656i
\(39\) −0.378680 + 0.655892i −0.0606373 + 0.105027i
\(40\) −1.70711 2.95680i −0.269917 0.467510i
\(41\) 2.58579 0.403832 0.201916 0.979403i \(-0.435283\pi\)
0.201916 + 0.979403i \(0.435283\pi\)
\(42\) 0 0
\(43\) 5.65685 0.862662 0.431331 0.902194i \(-0.358044\pi\)
0.431331 + 0.902194i \(0.358044\pi\)
\(44\) −0.500000 0.866025i −0.0753778 0.130558i
\(45\) 4.82843 8.36308i 0.719779 1.24669i
\(46\) −1.12132 + 1.94218i −0.165330 + 0.286359i
\(47\) 3.24264 + 5.61642i 0.472988 + 0.819239i 0.999522 0.0309151i \(-0.00984215\pi\)
−0.526534 + 0.850154i \(0.676509\pi\)
\(48\) −0.414214 −0.0597866
\(49\) 0 0
\(50\) 6.65685 0.941421
\(51\) 1.58579 + 2.74666i 0.222055 + 0.384610i
\(52\) 0.914214 1.58346i 0.126779 0.219587i
\(53\) 5.94975 10.3053i 0.817261 1.41554i −0.0904325 0.995903i \(-0.528825\pi\)
0.907693 0.419634i \(-0.137842\pi\)
\(54\) −1.20711 2.09077i −0.164266 0.284518i
\(55\) 3.41421 0.460372
\(56\) 0 0
\(57\) −1.41421 −0.187317
\(58\) 4.32843 + 7.49706i 0.568350 + 0.984412i
\(59\) −4.20711 + 7.28692i −0.547719 + 0.948677i 0.450712 + 0.892670i \(0.351170\pi\)
−0.998430 + 0.0560070i \(0.982163\pi\)
\(60\) 0.707107 1.22474i 0.0912871 0.158114i
\(61\) 3.08579 + 5.34474i 0.395094 + 0.684324i 0.993113 0.117158i \(-0.0373785\pi\)
−0.598019 + 0.801482i \(0.704045\pi\)
\(62\) 4.00000 0.508001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 3.12132 + 5.40629i 0.387152 + 0.670567i
\(66\) 0.207107 0.358719i 0.0254931 0.0441553i
\(67\) −5.62132 + 9.73641i −0.686754 + 1.18949i 0.286129 + 0.958191i \(0.407632\pi\)
−0.972882 + 0.231301i \(0.925702\pi\)
\(68\) −3.82843 6.63103i −0.464265 0.804131i
\(69\) −0.928932 −0.111830
\(70\) 0 0
\(71\) 3.07107 0.364469 0.182234 0.983255i \(-0.441667\pi\)
0.182234 + 0.983255i \(0.441667\pi\)
\(72\) 1.41421 + 2.44949i 0.166667 + 0.288675i
\(73\) −3.29289 + 5.70346i −0.385404 + 0.667539i −0.991825 0.127604i \(-0.959271\pi\)
0.606421 + 0.795144i \(0.292605\pi\)
\(74\) 3.29289 5.70346i 0.382791 0.663014i
\(75\) 1.37868 + 2.38794i 0.159196 + 0.275736i
\(76\) 3.41421 0.391637
\(77\) 0 0
\(78\) 0.757359 0.0857541
\(79\) 2.37868 + 4.11999i 0.267622 + 0.463536i 0.968247 0.249994i \(-0.0804287\pi\)
−0.700625 + 0.713530i \(0.747095\pi\)
\(80\) −1.70711 + 2.95680i −0.190860 + 0.330580i
\(81\) −3.74264 + 6.48244i −0.415849 + 0.720272i
\(82\) −1.29289 2.23936i −0.142776 0.247296i
\(83\) −16.1421 −1.77183 −0.885915 0.463848i \(-0.846468\pi\)
−0.885915 + 0.463848i \(0.846468\pi\)
\(84\) 0 0
\(85\) 26.1421 2.83551
\(86\) −2.82843 4.89898i −0.304997 0.528271i
\(87\) −1.79289 + 3.10538i −0.192218 + 0.332932i
\(88\) −0.500000 + 0.866025i −0.0533002 + 0.0923186i
\(89\) −2.24264 3.88437i −0.237719 0.411742i 0.722340 0.691538i \(-0.243067\pi\)
−0.960060 + 0.279796i \(0.909733\pi\)
\(90\) −9.65685 −1.01792
\(91\) 0 0
\(92\) 2.24264 0.233811
\(93\) 0.828427 + 1.43488i 0.0859039 + 0.148790i
\(94\) 3.24264 5.61642i 0.334453 0.579289i
\(95\) −5.82843 + 10.0951i −0.597984 + 1.03574i
\(96\) 0.207107 + 0.358719i 0.0211377 + 0.0366117i
\(97\) −1.82843 −0.185649 −0.0928243 0.995683i \(-0.529589\pi\)
−0.0928243 + 0.995683i \(0.529589\pi\)
\(98\) 0 0
\(99\) −2.82843 −0.284268
\(100\) −3.32843 5.76500i −0.332843 0.576500i
\(101\) 5.91421 10.2437i 0.588486 1.01929i −0.405945 0.913898i \(-0.633057\pi\)
0.994431 0.105390i \(-0.0336092\pi\)
\(102\) 1.58579 2.74666i 0.157016 0.271960i
\(103\) 5.29289 + 9.16756i 0.521524 + 0.903307i 0.999687 + 0.0250350i \(0.00796973\pi\)
−0.478162 + 0.878271i \(0.658697\pi\)
\(104\) −1.82843 −0.179292
\(105\) 0 0
\(106\) −11.8995 −1.15578
\(107\) −5.53553 9.58783i −0.535140 0.926890i −0.999157 0.0410635i \(-0.986925\pi\)
0.464016 0.885827i \(-0.346408\pi\)
\(108\) −1.20711 + 2.09077i −0.116154 + 0.201184i
\(109\) 0.242641 0.420266i 0.0232408 0.0402542i −0.854171 0.519992i \(-0.825935\pi\)
0.877412 + 0.479738i \(0.159268\pi\)
\(110\) −1.70711 2.95680i −0.162766 0.281919i
\(111\) 2.72792 0.258923
\(112\) 0 0
\(113\) −13.8284 −1.30087 −0.650434 0.759562i \(-0.725413\pi\)
−0.650434 + 0.759562i \(0.725413\pi\)
\(114\) 0.707107 + 1.22474i 0.0662266 + 0.114708i
\(115\) −3.82843 + 6.63103i −0.357003 + 0.618347i
\(116\) 4.32843 7.49706i 0.401884 0.696084i
\(117\) −2.58579 4.47871i −0.239056 0.414057i
\(118\) 8.41421 0.774591
\(119\) 0 0
\(120\) −1.41421 −0.129099
\(121\) −0.500000 0.866025i −0.0454545 0.0787296i
\(122\) 3.08579 5.34474i 0.279374 0.483890i
\(123\) 0.535534 0.927572i 0.0482875 0.0836363i
\(124\) −2.00000 3.46410i −0.179605 0.311086i
\(125\) 5.65685 0.505964
\(126\) 0 0
\(127\) −9.72792 −0.863213 −0.431607 0.902062i \(-0.642053\pi\)
−0.431607 + 0.902062i \(0.642053\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 1.17157 2.02922i 0.103151 0.178663i
\(130\) 3.12132 5.40629i 0.273758 0.474163i
\(131\) −1.70711 2.95680i −0.149151 0.258336i 0.781763 0.623575i \(-0.214321\pi\)
−0.930914 + 0.365239i \(0.880987\pi\)
\(132\) −0.414214 −0.0360527
\(133\) 0 0
\(134\) 11.2426 0.971216
\(135\) −4.12132 7.13834i −0.354707 0.614370i
\(136\) −3.82843 + 6.63103i −0.328285 + 0.568606i
\(137\) 2.67157 4.62730i 0.228248 0.395337i −0.729041 0.684470i \(-0.760034\pi\)
0.957289 + 0.289133i \(0.0933670\pi\)
\(138\) 0.464466 + 0.804479i 0.0395380 + 0.0684818i
\(139\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(140\) 0 0
\(141\) 2.68629 0.226227
\(142\) −1.53553 2.65962i −0.128859 0.223191i
\(143\) 0.914214 1.58346i 0.0764504 0.132416i
\(144\) 1.41421 2.44949i 0.117851 0.204124i
\(145\) 14.7782 + 25.5965i 1.22726 + 2.12568i
\(146\) 6.58579 0.545044
\(147\) 0 0
\(148\) −6.58579 −0.541348
\(149\) −3.17157 5.49333i −0.259825 0.450031i 0.706370 0.707843i \(-0.250332\pi\)
−0.966195 + 0.257812i \(0.916998\pi\)
\(150\) 1.37868 2.38794i 0.112569 0.194975i
\(151\) −4.86396 + 8.42463i −0.395824 + 0.685586i −0.993206 0.116370i \(-0.962874\pi\)
0.597382 + 0.801957i \(0.296207\pi\)
\(152\) −1.70711 2.95680i −0.138465 0.239828i
\(153\) −21.6569 −1.75085
\(154\) 0 0
\(155\) 13.6569 1.09694
\(156\) −0.378680 0.655892i −0.0303186 0.0525134i
\(157\) 3.17157 5.49333i 0.253119 0.438415i −0.711264 0.702925i \(-0.751877\pi\)
0.964383 + 0.264510i \(0.0852102\pi\)
\(158\) 2.37868 4.11999i 0.189238 0.327769i
\(159\) −2.46447 4.26858i −0.195445 0.338520i
\(160\) 3.41421 0.269917
\(161\) 0 0
\(162\) 7.48528 0.588099
\(163\) 7.86396 + 13.6208i 0.615953 + 1.06686i 0.990217 + 0.139539i \(0.0445622\pi\)
−0.374264 + 0.927322i \(0.622104\pi\)
\(164\) −1.29289 + 2.23936i −0.100958 + 0.174864i
\(165\) 0.707107 1.22474i 0.0550482 0.0953463i
\(166\) 8.07107 + 13.9795i 0.626436 + 1.08502i
\(167\) 11.7279 0.907534 0.453767 0.891120i \(-0.350080\pi\)
0.453767 + 0.891120i \(0.350080\pi\)
\(168\) 0 0
\(169\) −9.65685 −0.742835
\(170\) −13.0711 22.6398i −1.00251 1.73639i
\(171\) 4.82843 8.36308i 0.369239 0.639541i
\(172\) −2.82843 + 4.89898i −0.215666 + 0.373544i
\(173\) −2.08579 3.61269i −0.158579 0.274668i 0.775777 0.631007i \(-0.217358\pi\)
−0.934357 + 0.356339i \(0.884025\pi\)
\(174\) 3.58579 0.271838
\(175\) 0 0
\(176\) 1.00000 0.0753778
\(177\) 1.74264 + 3.01834i 0.130985 + 0.226872i
\(178\) −2.24264 + 3.88437i −0.168093 + 0.291146i
\(179\) 9.44975 16.3674i 0.706307 1.22336i −0.259910 0.965633i \(-0.583693\pi\)
0.966218 0.257727i \(-0.0829736\pi\)
\(180\) 4.82843 + 8.36308i 0.359890 + 0.623347i
\(181\) −3.65685 −0.271812 −0.135906 0.990722i \(-0.543394\pi\)
−0.135906 + 0.990722i \(0.543394\pi\)
\(182\) 0 0
\(183\) 2.55635 0.188971
\(184\) −1.12132 1.94218i −0.0826648 0.143180i
\(185\) 11.2426 19.4728i 0.826575 1.43167i
\(186\) 0.828427 1.43488i 0.0607432 0.105210i
\(187\) −3.82843 6.63103i −0.279962 0.484909i
\(188\) −6.48528 −0.472988
\(189\) 0 0
\(190\) 11.6569 0.845677
\(191\) 6.41421 + 11.1097i 0.464116 + 0.803873i 0.999161 0.0409507i \(-0.0130387\pi\)
−0.535045 + 0.844824i \(0.679705\pi\)
\(192\) 0.207107 0.358719i 0.0149466 0.0258883i
\(193\) −1.05025 + 1.81909i −0.0755988 + 0.130941i −0.901347 0.433099i \(-0.857420\pi\)
0.825748 + 0.564040i \(0.190754\pi\)
\(194\) 0.914214 + 1.58346i 0.0656367 + 0.113686i
\(195\) 2.58579 0.185172
\(196\) 0 0
\(197\) −17.4853 −1.24577 −0.622887 0.782312i \(-0.714041\pi\)
−0.622887 + 0.782312i \(0.714041\pi\)
\(198\) 1.41421 + 2.44949i 0.100504 + 0.174078i
\(199\) 9.94975 17.2335i 0.705319 1.22165i −0.261257 0.965269i \(-0.584137\pi\)
0.966576 0.256379i \(-0.0825295\pi\)
\(200\) −3.32843 + 5.76500i −0.235355 + 0.407647i
\(201\) 2.32843 + 4.03295i 0.164235 + 0.284463i
\(202\) −11.8284 −0.832245
\(203\) 0 0
\(204\) −3.17157 −0.222055
\(205\) −4.41421 7.64564i −0.308302 0.533995i
\(206\) 5.29289 9.16756i 0.368773 0.638734i
\(207\) 3.17157 5.49333i 0.220440 0.381813i
\(208\) 0.914214 + 1.58346i 0.0633893 + 0.109793i
\(209\) 3.41421 0.236166
\(210\) 0 0
\(211\) 4.58579 0.315699 0.157849 0.987463i \(-0.449544\pi\)
0.157849 + 0.987463i \(0.449544\pi\)
\(212\) 5.94975 + 10.3053i 0.408630 + 0.707768i
\(213\) 0.636039 1.10165i 0.0435807 0.0754839i
\(214\) −5.53553 + 9.58783i −0.378401 + 0.655410i
\(215\) −9.65685 16.7262i −0.658592 1.14071i
\(216\) 2.41421 0.164266
\(217\) 0 0
\(218\) −0.485281 −0.0328674
\(219\) 1.36396 + 2.36245i 0.0921679 + 0.159640i
\(220\) −1.70711 + 2.95680i −0.115093 + 0.199347i
\(221\) 7.00000 12.1244i 0.470871 0.815572i
\(222\) −1.36396 2.36245i −0.0915431 0.158557i
\(223\) −11.4142 −0.764352 −0.382176 0.924089i \(-0.624825\pi\)
−0.382176 + 0.924089i \(0.624825\pi\)
\(224\) 0 0
\(225\) −18.8284 −1.25523
\(226\) 6.91421 + 11.9758i 0.459927 + 0.796616i
\(227\) −11.5858 + 20.0672i −0.768976 + 1.33190i 0.169143 + 0.985591i \(0.445900\pi\)
−0.938119 + 0.346313i \(0.887433\pi\)
\(228\) 0.707107 1.22474i 0.0468293 0.0811107i
\(229\) 0.343146 + 0.594346i 0.0226757 + 0.0392755i 0.877141 0.480234i \(-0.159448\pi\)
−0.854465 + 0.519509i \(0.826115\pi\)
\(230\) 7.65685 0.504878
\(231\) 0 0
\(232\) −8.65685 −0.568350
\(233\) 0.707107 + 1.22474i 0.0463241 + 0.0802357i 0.888258 0.459345i \(-0.151916\pi\)
−0.841934 + 0.539581i \(0.818583\pi\)
\(234\) −2.58579 + 4.47871i −0.169038 + 0.292783i
\(235\) 11.0711 19.1757i 0.722197 1.25088i
\(236\) −4.20711 7.28692i −0.273859 0.474338i
\(237\) 1.97056 0.128002
\(238\) 0 0
\(239\) −22.2132 −1.43685 −0.718426 0.695603i \(-0.755137\pi\)
−0.718426 + 0.695603i \(0.755137\pi\)
\(240\) 0.707107 + 1.22474i 0.0456435 + 0.0790569i
\(241\) 1.87868 3.25397i 0.121016 0.209607i −0.799152 0.601129i \(-0.794718\pi\)
0.920169 + 0.391522i \(0.128051\pi\)
\(242\) −0.500000 + 0.866025i −0.0321412 + 0.0556702i
\(243\) 5.17157 + 8.95743i 0.331757 + 0.574619i
\(244\) −6.17157 −0.395094
\(245\) 0 0
\(246\) −1.07107 −0.0682888
\(247\) 3.12132 + 5.40629i 0.198605 + 0.343994i
\(248\) −2.00000 + 3.46410i −0.127000 + 0.219971i
\(249\) −3.34315 + 5.79050i −0.211863 + 0.366958i
\(250\) −2.82843 4.89898i −0.178885 0.309839i
\(251\) −2.14214 −0.135210 −0.0676052 0.997712i \(-0.521536\pi\)
−0.0676052 + 0.997712i \(0.521536\pi\)
\(252\) 0 0
\(253\) 2.24264 0.140994
\(254\) 4.86396 + 8.42463i 0.305192 + 0.528608i
\(255\) 5.41421 9.37769i 0.339051 0.587254i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 1.57107 + 2.72117i 0.0980005 + 0.169742i 0.910857 0.412722i \(-0.135422\pi\)
−0.812856 + 0.582464i \(0.802089\pi\)
\(258\) −2.34315 −0.145878
\(259\) 0 0
\(260\) −6.24264 −0.387152
\(261\) −12.2426 21.2049i −0.757800 1.31255i
\(262\) −1.70711 + 2.95680i −0.105465 + 0.182671i
\(263\) −15.5208 + 26.8828i −0.957054 + 1.65767i −0.227459 + 0.973788i \(0.573042\pi\)
−0.729595 + 0.683879i \(0.760291\pi\)
\(264\) 0.207107 + 0.358719i 0.0127465 + 0.0220777i
\(265\) −40.6274 −2.49572
\(266\) 0 0
\(267\) −1.85786 −0.113699
\(268\) −5.62132 9.73641i −0.343377 0.594746i
\(269\) 6.82843 11.8272i 0.416337 0.721116i −0.579231 0.815163i \(-0.696647\pi\)
0.995568 + 0.0940473i \(0.0299805\pi\)
\(270\) −4.12132 + 7.13834i −0.250816 + 0.434425i
\(271\) −13.2782 22.9985i −0.806592 1.39706i −0.915211 0.402974i \(-0.867976\pi\)
0.108620 0.994083i \(-0.465357\pi\)
\(272\) 7.65685 0.464265
\(273\) 0 0
\(274\) −5.34315 −0.322791
\(275\) −3.32843 5.76500i −0.200712 0.347643i
\(276\) 0.464466 0.804479i 0.0279576 0.0484239i
\(277\) 1.91421 3.31552i 0.115014 0.199210i −0.802771 0.596287i \(-0.796642\pi\)
0.917785 + 0.397077i \(0.129975\pi\)
\(278\) 0 0
\(279\) −11.3137 −0.677334
\(280\) 0 0
\(281\) −16.7279 −0.997904 −0.498952 0.866630i \(-0.666282\pi\)
−0.498952 + 0.866630i \(0.666282\pi\)
\(282\) −1.34315 2.32640i −0.0799832 0.138535i
\(283\) −10.2929 + 17.8278i −0.611849 + 1.05975i 0.379080 + 0.925364i \(0.376241\pi\)
−0.990929 + 0.134389i \(0.957093\pi\)
\(284\) −1.53553 + 2.65962i −0.0911172 + 0.157820i
\(285\) 2.41421 + 4.18154i 0.143006 + 0.247693i
\(286\) −1.82843 −0.108117
\(287\) 0 0
\(288\) −2.82843 −0.166667
\(289\) −20.8137 36.0504i −1.22434 2.12061i
\(290\) 14.7782 25.5965i 0.867804 1.50308i
\(291\) −0.378680 + 0.655892i −0.0221986 + 0.0384491i
\(292\) −3.29289 5.70346i −0.192702 0.333770i
\(293\) 5.17157 0.302127 0.151063 0.988524i \(-0.451730\pi\)
0.151063 + 0.988524i \(0.451730\pi\)
\(294\) 0 0
\(295\) 28.7279 1.67260
\(296\) 3.29289 + 5.70346i 0.191396 + 0.331507i
\(297\) −1.20711 + 2.09077i −0.0700434 + 0.121319i
\(298\) −3.17157 + 5.49333i −0.183724 + 0.318220i
\(299\) 2.05025 + 3.55114i 0.118569 + 0.205368i
\(300\) −2.75736 −0.159196
\(301\) 0 0
\(302\) 9.72792 0.559779
\(303\) −2.44975 4.24309i −0.140734 0.243759i
\(304\) −1.70711 + 2.95680i −0.0979093 + 0.169584i
\(305\) 10.5355 18.2481i 0.603263 1.04488i
\(306\) 10.8284 + 18.7554i 0.619020 + 1.07217i
\(307\) 9.89949 0.564994 0.282497 0.959268i \(-0.408837\pi\)
0.282497 + 0.959268i \(0.408837\pi\)
\(308\) 0 0
\(309\) 4.38478 0.249441
\(310\) −6.82843 11.8272i −0.387829 0.671739i
\(311\) −4.36396 + 7.55860i −0.247458 + 0.428609i −0.962820 0.270145i \(-0.912928\pi\)
0.715362 + 0.698754i \(0.246262\pi\)
\(312\) −0.378680 + 0.655892i −0.0214385 + 0.0371326i
\(313\) −4.67157 8.09140i −0.264053 0.457353i 0.703262 0.710931i \(-0.251726\pi\)
−0.967315 + 0.253578i \(0.918393\pi\)
\(314\) −6.34315 −0.357964
\(315\) 0 0
\(316\) −4.75736 −0.267622
\(317\) −15.6569 27.1185i −0.879377 1.52312i −0.852026 0.523499i \(-0.824626\pi\)
−0.0273502 0.999626i \(-0.508707\pi\)
\(318\) −2.46447 + 4.26858i −0.138200 + 0.239370i
\(319\) 4.32843 7.49706i 0.242345 0.419755i
\(320\) −1.70711 2.95680i −0.0954302 0.165290i
\(321\) −4.58579 −0.255954
\(322\) 0 0
\(323\) 26.1421 1.45459
\(324\) −3.74264 6.48244i −0.207924 0.360136i
\(325\) 6.08579 10.5409i 0.337579 0.584703i
\(326\) 7.86396 13.6208i 0.435545 0.754385i
\(327\) −0.100505 0.174080i −0.00555794 0.00962664i
\(328\) 2.58579 0.142776
\(329\) 0 0
\(330\) −1.41421 −0.0778499
\(331\) 4.96447 + 8.59871i 0.272872 + 0.472628i 0.969596 0.244711i \(-0.0786932\pi\)
−0.696724 + 0.717339i \(0.745360\pi\)
\(332\) 8.07107 13.9795i 0.442957 0.767225i
\(333\) −9.31371 + 16.1318i −0.510388 + 0.884018i
\(334\) −5.86396 10.1567i −0.320862 0.555749i
\(335\) 38.3848 2.09718
\(336\) 0 0
\(337\) −19.7574 −1.07625 −0.538126 0.842864i \(-0.680868\pi\)
−0.538126 + 0.842864i \(0.680868\pi\)
\(338\) 4.82843 + 8.36308i 0.262632 + 0.454892i
\(339\) −2.86396 + 4.96053i −0.155549 + 0.269419i
\(340\) −13.0711 + 22.6398i −0.708878 + 1.22781i
\(341\) −2.00000 3.46410i −0.108306 0.187592i
\(342\) −9.65685 −0.522183
\(343\) 0 0
\(344\) 5.65685 0.304997
\(345\) 1.58579 + 2.74666i 0.0853759 + 0.147875i
\(346\) −2.08579 + 3.61269i −0.112133 + 0.194219i
\(347\) −7.29289 + 12.6317i −0.391503 + 0.678103i −0.992648 0.121037i \(-0.961378\pi\)
0.601145 + 0.799140i \(0.294711\pi\)
\(348\) −1.79289 3.10538i −0.0961092 0.166466i
\(349\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(350\) 0 0
\(351\) −4.41421 −0.235613
\(352\) −0.500000 0.866025i −0.0266501 0.0461593i
\(353\) −12.6569 + 21.9223i −0.673656 + 1.16681i 0.303203 + 0.952926i \(0.401944\pi\)
−0.976860 + 0.213881i \(0.931389\pi\)
\(354\) 1.74264 3.01834i 0.0926203 0.160423i
\(355\) −5.24264 9.08052i −0.278250 0.481944i
\(356\) 4.48528 0.237719
\(357\) 0 0
\(358\) −18.8995 −0.998869
\(359\) −5.37868 9.31615i −0.283876 0.491687i 0.688460 0.725274i \(-0.258287\pi\)
−0.972336 + 0.233587i \(0.924954\pi\)
\(360\) 4.82843 8.36308i 0.254480 0.440773i
\(361\) 3.67157 6.35935i 0.193241 0.334703i
\(362\) 1.82843 + 3.16693i 0.0961000 + 0.166450i
\(363\) −0.414214 −0.0217406
\(364\) 0 0
\(365\) 22.4853 1.17693
\(366\) −1.27817 2.21386i −0.0668113 0.115720i
\(367\) 7.36396 12.7548i 0.384396 0.665793i −0.607290 0.794481i \(-0.707743\pi\)
0.991685 + 0.128688i \(0.0410765\pi\)
\(368\) −1.12132 + 1.94218i −0.0584529 + 0.101243i
\(369\) 3.65685 + 6.33386i 0.190368 + 0.329727i
\(370\) −22.4853 −1.16895
\(371\) 0 0
\(372\) −1.65685 −0.0859039
\(373\) −6.98528 12.0989i −0.361684 0.626455i 0.626554 0.779378i \(-0.284465\pi\)
−0.988238 + 0.152923i \(0.951131\pi\)
\(374\) −3.82843 + 6.63103i −0.197963 + 0.342882i
\(375\) 1.17157 2.02922i 0.0604998 0.104789i
\(376\) 3.24264 + 5.61642i 0.167226 + 0.289645i
\(377\) 15.8284 0.815205
\(378\) 0 0
\(379\) −25.8701 −1.32886 −0.664428 0.747352i \(-0.731325\pi\)
−0.664428 + 0.747352i \(0.731325\pi\)
\(380\) −5.82843 10.0951i −0.298992 0.517869i
\(381\) −2.01472 + 3.48960i −0.103217 + 0.178777i
\(382\) 6.41421 11.1097i 0.328180 0.568424i
\(383\) 15.1924 + 26.3140i 0.776295 + 1.34458i 0.934064 + 0.357106i \(0.116236\pi\)
−0.157769 + 0.987476i \(0.550430\pi\)
\(384\) −0.414214 −0.0211377
\(385\) 0 0
\(386\) 2.10051 0.106913
\(387\) 8.00000 + 13.8564i 0.406663 + 0.704361i
\(388\) 0.914214 1.58346i 0.0464122 0.0803882i
\(389\) −1.36396 + 2.36245i −0.0691556 + 0.119781i −0.898530 0.438912i \(-0.855364\pi\)
0.829374 + 0.558693i \(0.188697\pi\)
\(390\) −1.29289 2.23936i −0.0654682 0.113394i
\(391\) 17.1716 0.868404
\(392\) 0 0
\(393\) −1.41421 −0.0713376
\(394\) 8.74264 + 15.1427i 0.440448 + 0.762878i
\(395\) 8.12132 14.0665i 0.408628 0.707764i
\(396\) 1.41421 2.44949i 0.0710669 0.123091i
\(397\) 11.0000 + 19.0526i 0.552074 + 0.956221i 0.998125 + 0.0612128i \(0.0194968\pi\)
−0.446051 + 0.895008i \(0.647170\pi\)
\(398\) −19.8995 −0.997472
\(399\) 0 0
\(400\) 6.65685 0.332843
\(401\) 2.15685 + 3.73578i 0.107708 + 0.186556i 0.914841 0.403813i \(-0.132315\pi\)
−0.807133 + 0.590369i \(0.798982\pi\)
\(402\) 2.32843 4.03295i 0.116131 0.201145i
\(403\) 3.65685 6.33386i 0.182161 0.315512i
\(404\) 5.91421 + 10.2437i 0.294243 + 0.509644i
\(405\) 25.5563 1.26991
\(406\) 0 0
\(407\) −6.58579 −0.326445
\(408\) 1.58579 + 2.74666i 0.0785081 + 0.135980i
\(409\) −11.3640 + 19.6830i −0.561912 + 0.973260i 0.435418 + 0.900228i \(0.356601\pi\)
−0.997330 + 0.0730312i \(0.976733\pi\)
\(410\) −4.41421 + 7.64564i −0.218002 + 0.377591i
\(411\) −1.10660 1.91669i −0.0545846 0.0945434i
\(412\) −10.5858 −0.521524
\(413\) 0 0
\(414\) −6.34315 −0.311749
\(415\) 27.5563 + 47.7290i 1.35269 + 2.34292i
\(416\) 0.914214 1.58346i 0.0448230 0.0776357i
\(417\) 0 0
\(418\) −1.70711 2.95680i −0.0834973 0.144622i
\(419\) −2.14214 −0.104650 −0.0523251 0.998630i \(-0.516663\pi\)
−0.0523251 + 0.998630i \(0.516663\pi\)
\(420\) 0 0
\(421\) 23.3137 1.13624 0.568120 0.822946i \(-0.307671\pi\)
0.568120 + 0.822946i \(0.307671\pi\)
\(422\) −2.29289 3.97141i −0.111616 0.193325i
\(423\) −9.17157 + 15.8856i −0.445937 + 0.772386i
\(424\) 5.94975 10.3053i 0.288945 0.500468i
\(425\) −25.4853 44.1418i −1.23622 2.14119i
\(426\) −1.27208 −0.0616324
\(427\) 0 0
\(428\) 11.0711 0.535140
\(429\) −0.378680 0.655892i −0.0182828 0.0316668i
\(430\) −9.65685 + 16.7262i −0.465695 + 0.806607i
\(431\) 10.2071 17.6792i 0.491659 0.851578i −0.508295 0.861183i \(-0.669724\pi\)
0.999954 + 0.00960469i \(0.00305731\pi\)
\(432\) −1.20711 2.09077i −0.0580770 0.100592i
\(433\) 2.14214 0.102944 0.0514722 0.998674i \(-0.483609\pi\)
0.0514722 + 0.998674i \(0.483609\pi\)
\(434\) 0 0
\(435\) 12.2426 0.586990
\(436\) 0.242641 + 0.420266i 0.0116204 + 0.0201271i
\(437\) −3.82843 + 6.63103i −0.183139 + 0.317205i
\(438\) 1.36396 2.36245i 0.0651726 0.112882i
\(439\) 4.69239 + 8.12745i 0.223955 + 0.387902i 0.956006 0.293349i \(-0.0947696\pi\)
−0.732050 + 0.681251i \(0.761436\pi\)
\(440\) 3.41421 0.162766
\(441\) 0 0
\(442\) −14.0000 −0.665912
\(443\) 16.3137 + 28.2562i 0.775088 + 1.34249i 0.934745 + 0.355319i \(0.115628\pi\)
−0.159658 + 0.987172i \(0.551039\pi\)
\(444\) −1.36396 + 2.36245i −0.0647307 + 0.112117i
\(445\) −7.65685 + 13.2621i −0.362970 + 0.628682i
\(446\) 5.70711 + 9.88500i 0.270239 + 0.468068i
\(447\) −2.62742 −0.124273
\(448\) 0 0
\(449\) 33.6569 1.58837 0.794183 0.607679i \(-0.207899\pi\)
0.794183 + 0.607679i \(0.207899\pi\)
\(450\) 9.41421 + 16.3059i 0.443790 + 0.768667i
\(451\) −1.29289 + 2.23936i −0.0608800 + 0.105447i
\(452\) 6.91421 11.9758i 0.325217 0.563293i
\(453\) 2.01472 + 3.48960i 0.0946597 + 0.163955i
\(454\) 23.1716 1.08750
\(455\) 0 0
\(456\) −1.41421 −0.0662266
\(457\) 0.171573 + 0.297173i 0.00802584 + 0.0139012i 0.870010 0.493033i \(-0.164112\pi\)
−0.861985 + 0.506934i \(0.830779\pi\)
\(458\) 0.343146 0.594346i 0.0160341 0.0277720i
\(459\) −9.24264 + 16.0087i −0.431410 + 0.747223i
\(460\) −3.82843 6.63103i −0.178501 0.309173i
\(461\) −14.3137 −0.666656 −0.333328 0.942811i \(-0.608172\pi\)
−0.333328 + 0.942811i \(0.608172\pi\)
\(462\) 0 0
\(463\) 7.17157 0.333291 0.166646 0.986017i \(-0.446706\pi\)
0.166646 + 0.986017i \(0.446706\pi\)
\(464\) 4.32843 + 7.49706i 0.200942 + 0.348042i
\(465\) 2.82843 4.89898i 0.131165 0.227185i
\(466\) 0.707107 1.22474i 0.0327561 0.0567352i
\(467\) −17.0000 29.4449i −0.786666 1.36255i −0.927999 0.372584i \(-0.878472\pi\)
0.141332 0.989962i \(-0.454861\pi\)
\(468\) 5.17157 0.239056
\(469\) 0 0
\(470\) −22.1421 −1.02134
\(471\) −1.31371 2.27541i −0.0605325 0.104845i
\(472\) −4.20711 + 7.28692i −0.193648 + 0.335408i
\(473\) −2.82843 + 4.89898i −0.130051 + 0.225255i
\(474\) −0.985281 1.70656i −0.0452555 0.0783848i
\(475\) 22.7279 1.04283
\(476\) 0 0
\(477\) 33.6569 1.54104
\(478\) 11.1066 + 19.2372i 0.508004 + 0.879889i
\(479\) −13.0355 + 22.5782i −0.595609 + 1.03162i 0.397852 + 0.917450i \(0.369756\pi\)
−0.993461 + 0.114175i \(0.963578\pi\)
\(480\) 0.707107 1.22474i 0.0322749 0.0559017i
\(481\) −6.02082 10.4284i −0.274526 0.475492i
\(482\) −3.75736 −0.171143
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) 3.12132 + 5.40629i 0.141732 + 0.245487i
\(486\) 5.17157 8.95743i 0.234587 0.406317i
\(487\) −0.828427 + 1.43488i −0.0375396 + 0.0650205i −0.884185 0.467137i \(-0.845285\pi\)
0.846645 + 0.532158i \(0.178619\pi\)
\(488\) 3.08579 + 5.34474i 0.139687 + 0.241945i
\(489\) 6.51472 0.294606
\(490\) 0 0
\(491\) 24.8284 1.12049 0.560246 0.828327i \(-0.310707\pi\)
0.560246 + 0.828327i \(0.310707\pi\)
\(492\) 0.535534 + 0.927572i 0.0241437 + 0.0418182i
\(493\) 33.1421 57.4039i 1.49265 2.58534i
\(494\) 3.12132 5.40629i 0.140435 0.243240i
\(495\) 4.82843 + 8.36308i 0.217022 + 0.375893i
\(496\) 4.00000 0.179605
\(497\) 0 0
\(498\) 6.68629 0.299620
\(499\) 3.07107 + 5.31925i 0.137480 + 0.238122i 0.926542 0.376191i \(-0.122766\pi\)
−0.789062 + 0.614313i \(0.789433\pi\)
\(500\) −2.82843 + 4.89898i −0.126491 + 0.219089i
\(501\) 2.42893 4.20703i 0.108517 0.187956i
\(502\) 1.07107 + 1.85514i 0.0478041 + 0.0827991i
\(503\) 38.2132 1.70384 0.851921 0.523670i \(-0.175437\pi\)
0.851921 + 0.523670i \(0.175437\pi\)
\(504\) 0 0
\(505\) −40.3848 −1.79710
\(506\) −1.12132 1.94218i −0.0498488 0.0863406i
\(507\) −2.00000 + 3.46410i −0.0888231 + 0.153846i
\(508\) 4.86396 8.42463i 0.215803 0.373782i
\(509\) −6.65685 11.5300i −0.295060 0.511059i 0.679939 0.733269i \(-0.262006\pi\)
−0.974999 + 0.222210i \(0.928673\pi\)
\(510\) −10.8284 −0.479491
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) −4.12132 7.13834i −0.181961 0.315165i
\(514\) 1.57107 2.72117i 0.0692968 0.120026i
\(515\) 18.0711 31.3000i 0.796306 1.37924i
\(516\) 1.17157 + 2.02922i 0.0515756 + 0.0893316i
\(517\) −6.48528 −0.285222
\(518\) 0 0
\(519\) −1.72792 −0.0758474
\(520\) 3.12132 + 5.40629i 0.136879 + 0.237081i
\(521\) 14.1421 24.4949i 0.619578 1.07314i −0.369984 0.929038i \(-0.620637\pi\)
0.989563 0.144103i \(-0.0460297\pi\)
\(522\) −12.2426 + 21.2049i −0.535846 + 0.928112i
\(523\) 6.36396 + 11.0227i 0.278277 + 0.481989i 0.970957 0.239256i \(-0.0769035\pi\)
−0.692680 + 0.721245i \(0.743570\pi\)
\(524\) 3.41421 0.149151
\(525\) 0 0
\(526\) 31.0416 1.35348
\(527\) −15.3137 26.5241i −0.667076 1.15541i
\(528\) 0.207107 0.358719i 0.00901317 0.0156113i
\(529\) 8.98528 15.5630i 0.390664 0.676651i
\(530\) 20.3137 + 35.1844i 0.882371 + 1.52831i
\(531\) −23.7990 −1.03279
\(532\) 0 0
\(533\) −4.72792 −0.204789
\(534\) 0.928932 + 1.60896i 0.0401988 + 0.0696264i
\(535\) −18.8995 + 32.7349i −0.817096 + 1.41525i
\(536\) −5.62132 + 9.73641i −0.242804 + 0.420549i
\(537\) −3.91421 6.77962i −0.168911 0.292562i
\(538\) −13.6569 −0.588789
\(539\) 0 0
\(540\) 8.24264 0.354707
\(541\) 20.5711 + 35.6301i 0.884419 + 1.53186i 0.846378 + 0.532583i \(0.178779\pi\)
0.0380415 + 0.999276i \(0.487888\pi\)
\(542\) −13.2782 + 22.9985i −0.570346 + 0.987869i
\(543\) −0.757359 + 1.31178i −0.0325014 + 0.0562941i
\(544\) −3.82843 6.63103i −0.164142 0.284303i
\(545\) −1.65685 −0.0709718
\(546\) 0 0
\(547\) −18.8701 −0.806825 −0.403413 0.915018i \(-0.632176\pi\)
−0.403413 + 0.915018i \(0.632176\pi\)
\(548\) 2.67157 + 4.62730i 0.114124 + 0.197668i
\(549\) −8.72792 + 15.1172i −0.372499 + 0.645187i
\(550\) −3.32843 + 5.76500i −0.141925 + 0.245821i
\(551\) 14.7782 + 25.5965i 0.629571 + 1.09045i
\(552\) −0.928932 −0.0395380
\(553\) 0 0
\(554\) −3.82843 −0.162654
\(555\) −4.65685 8.06591i −0.197672 0.342379i
\(556\) 0 0
\(557\) −12.2426 + 21.2049i −0.518737 + 0.898479i 0.481026 + 0.876707i \(0.340264\pi\)
−0.999763 + 0.0217729i \(0.993069\pi\)
\(558\) 5.65685 + 9.79796i 0.239474 + 0.414781i
\(559\) −10.3431 −0.437468
\(560\) 0 0
\(561\) −3.17157 −0.133904
\(562\) 8.36396 + 14.4868i 0.352812 + 0.611089i
\(563\) −2.53553 + 4.39167i −0.106860 + 0.185087i −0.914497 0.404594i \(-0.867413\pi\)
0.807637 + 0.589681i \(0.200746\pi\)
\(564\) −1.34315 + 2.32640i −0.0565566 + 0.0979590i
\(565\) 23.6066 + 40.8878i 0.993137 + 1.72016i
\(566\) 20.5858 0.865285
\(567\) 0 0
\(568\) 3.07107 0.128859
\(569\) 2.00000 + 3.46410i 0.0838444 + 0.145223i 0.904898 0.425628i \(-0.139947\pi\)
−0.821054 + 0.570851i \(0.806613\pi\)
\(570\) 2.41421 4.18154i 0.101120 0.175145i
\(571\) 5.19239 8.99348i 0.217295 0.376365i −0.736685 0.676236i \(-0.763610\pi\)
0.953980 + 0.299870i \(0.0969434\pi\)
\(572\) 0.914214 + 1.58346i 0.0382252 + 0.0662080i
\(573\) 5.31371 0.221983
\(574\) 0 0
\(575\) 14.9289 0.622580
\(576\) 1.41421 + 2.44949i 0.0589256 + 0.102062i
\(577\) −16.1569 + 27.9845i −0.672619 + 1.16501i 0.304540 + 0.952499i \(0.401497\pi\)
−0.977159 + 0.212510i \(0.931836\pi\)
\(578\) −20.8137 + 36.0504i −0.865736 + 1.49950i
\(579\) 0.435029 + 0.753492i 0.0180792 + 0.0313141i
\(580\) −29.5563 −1.22726
\(581\) 0 0
\(582\) 0.757359 0.0313936
\(583\) 5.94975 + 10.3053i 0.246413 + 0.426800i
\(584\) −3.29289 + 5.70346i −0.136261 + 0.236011i
\(585\) −8.82843 + 15.2913i −0.365011 + 0.632217i
\(586\) −2.58579 4.47871i −0.106818 0.185014i
\(587\) 44.8995 1.85320 0.926600 0.376048i \(-0.122717\pi\)
0.926600 + 0.376048i \(0.122717\pi\)
\(588\) 0 0
\(589\) 13.6569 0.562721
\(590\) −14.3640 24.8791i −0.591355 1.02426i
\(591\) −3.62132 + 6.27231i −0.148961 + 0.258008i
\(592\) 3.29289 5.70346i 0.135337 0.234411i
\(593\) −17.8492 30.9158i −0.732981 1.26956i −0.955604 0.294655i \(-0.904795\pi\)
0.222623 0.974905i \(-0.428538\pi\)
\(594\) 2.41421 0.0990564
\(595\) 0 0
\(596\) 6.34315 0.259825
\(597\) −4.12132 7.13834i −0.168674 0.292153i
\(598\) 2.05025 3.55114i 0.0838411 0.145217i
\(599\) 1.31371 2.27541i 0.0536767 0.0929707i −0.837939 0.545765i \(-0.816239\pi\)
0.891615 + 0.452794i \(0.149573\pi\)
\(600\) 1.37868 + 2.38794i 0.0562844 + 0.0974874i
\(601\) 35.9411 1.46607 0.733035 0.680191i \(-0.238103\pi\)
0.733035 + 0.680191i \(0.238103\pi\)
\(602\) 0 0
\(603\) −31.7990 −1.29495
\(604\) −4.86396 8.42463i −0.197912 0.342793i
\(605\) −1.70711 + 2.95680i −0.0694038 + 0.120211i
\(606\) −2.44975 + 4.24309i −0.0995142 + 0.172364i
\(607\) −4.51472 7.81972i −0.183247 0.317393i 0.759738 0.650230i \(-0.225327\pi\)
−0.942984 + 0.332837i \(0.891994\pi\)
\(608\) 3.41421 0.138465
\(609\) 0 0
\(610\) −21.0711 −0.853143
\(611\) −5.92893 10.2692i −0.239859 0.415448i
\(612\) 10.8284 18.7554i 0.437713 0.758142i
\(613\) 8.31371 14.3998i 0.335788 0.581601i −0.647848 0.761769i \(-0.724331\pi\)
0.983636 + 0.180168i \(0.0576643\pi\)
\(614\) −4.94975 8.57321i −0.199756 0.345987i
\(615\) −3.65685 −0.147459
\(616\) 0 0
\(617\) −8.02944 −0.323253 −0.161626 0.986852i \(-0.551674\pi\)
−0.161626 + 0.986852i \(0.551674\pi\)
\(618\) −2.19239 3.79733i −0.0881908 0.152751i
\(619\) 22.9706 39.7862i 0.923265 1.59914i 0.128937 0.991653i \(-0.458844\pi\)
0.794328 0.607489i \(-0.207823\pi\)
\(620\) −6.82843 + 11.8272i −0.274236 + 0.474991i
\(621\) −2.70711 4.68885i −0.108632 0.188157i
\(622\) 8.72792 0.349958
\(623\) 0 0
\(624\) 0.757359 0.0303186
\(625\) 6.98528 + 12.0989i 0.279411 + 0.483954i
\(626\) −4.67157 + 8.09140i −0.186714 + 0.323397i
\(627\) 0.707107 1.22474i 0.0282391 0.0489116i
\(628\) 3.17157 + 5.49333i 0.126560 + 0.219208i
\(629\) −50.4264 −2.01063
\(630\) 0 0
\(631\) 48.7279 1.93983 0.969914 0.243448i \(-0.0782785\pi\)
0.969914 + 0.243448i \(0.0782785\pi\)
\(632\) 2.37868 + 4.11999i 0.0946188 + 0.163885i
\(633\) 0.949747 1.64501i 0.0377491 0.0653833i
\(634\) −15.6569 + 27.1185i −0.621813 + 1.07701i
\(635\) 16.6066 + 28.7635i 0.659013 + 1.14144i
\(636\) 4.92893 0.195445
\(637\) 0 0
\(638\) −8.65685 −0.342728
\(639\) 4.34315 + 7.52255i 0.171812 + 0.297587i
\(640\) −1.70711 + 2.95680i −0.0674793 + 0.116878i
\(641\) 20.6421 35.7532i 0.815315 1.41217i −0.0937859 0.995592i \(-0.529897\pi\)
0.909101 0.416575i \(-0.136770\pi\)
\(642\) 2.29289 + 3.97141i 0.0904933 + 0.156739i
\(643\) −4.41421 −0.174080 −0.0870398 0.996205i \(-0.527741\pi\)
−0.0870398 + 0.996205i \(0.527741\pi\)
\(644\) 0 0
\(645\) −8.00000 −0.315000
\(646\) −13.0711 22.6398i −0.514274 0.890749i
\(647\) −23.0919 + 39.9963i −0.907836 + 1.57242i −0.0907706 + 0.995872i \(0.528933\pi\)
−0.817065 + 0.576546i \(0.804400\pi\)
\(648\) −3.74264 + 6.48244i −0.147025 + 0.254654i
\(649\) −4.20711 7.28692i −0.165143 0.286037i
\(650\) −12.1716 −0.477408
\(651\) 0 0
\(652\) −15.7279 −0.615953
\(653\) −9.19239 15.9217i −0.359726 0.623064i 0.628189 0.778061i \(-0.283796\pi\)
−0.987915 + 0.154997i \(0.950463\pi\)
\(654\) −0.100505 + 0.174080i −0.00393006 + 0.00680706i
\(655\) −5.82843 + 10.0951i −0.227735 + 0.394449i
\(656\) −1.29289 2.23936i −0.0504790 0.0874322i
\(657\) −18.6274 −0.726725
\(658\) 0 0
\(659\) −12.0000 −0.467454 −0.233727 0.972302i \(-0.575092\pi\)
−0.233727 + 0.972302i \(0.575092\pi\)
\(660\) 0.707107 + 1.22474i 0.0275241 + 0.0476731i
\(661\) −7.48528 + 12.9649i −0.291144 + 0.504276i −0.974080 0.226202i \(-0.927369\pi\)
0.682937 + 0.730478i \(0.260702\pi\)
\(662\) 4.96447 8.59871i 0.192949 0.334198i
\(663\) −2.89949 5.02207i −0.112607 0.195041i
\(664\) −16.1421 −0.626436
\(665\) 0 0
\(666\) 18.6274 0.721798
\(667\) 9.70711 + 16.8132i 0.375861 + 0.651010i
\(668\) −5.86396 + 10.1567i −0.226883 + 0.392974i
\(669\) −2.36396 + 4.09450i −0.0913960 + 0.158303i
\(670\) −19.1924 33.2422i −0.741467 1.28426i
\(671\) −6.17157 −0.238251
\(672\) 0 0
\(673\) −25.5563 −0.985125 −0.492562 0.870277i \(-0.663940\pi\)
−0.492562 + 0.870277i \(0.663940\pi\)
\(674\) 9.87868 + 17.1104i 0.380513 + 0.659067i
\(675\) −8.03553 + 13.9180i −0.309288 + 0.535702i
\(676\) 4.82843 8.36308i 0.185709 0.321657i
\(677\) −6.34315 10.9867i −0.243787 0.422251i 0.718003 0.696040i \(-0.245056\pi\)
−0.961790 + 0.273789i \(0.911723\pi\)
\(678\) 5.72792 0.219980
\(679\) 0 0
\(680\) 26.1421 1.00251
\(681\) 4.79899 + 8.31209i 0.183898 + 0.318520i
\(682\) −2.00000 + 3.46410i −0.0765840 + 0.132647i
\(683\) −8.20711 + 14.2151i −0.314036 + 0.543927i −0.979232 0.202742i \(-0.935015\pi\)
0.665196 + 0.746669i \(0.268348\pi\)
\(684\) 4.82843 + 8.36308i 0.184620 + 0.319770i
\(685\) −18.2426 −0.697015
\(686\) 0 0
\(687\) 0.284271 0.0108456
\(688\) −2.82843 4.89898i −0.107833 0.186772i
\(689\) −10.8787 + 18.8424i −0.414445 + 0.717839i
\(690\) 1.58579 2.74666i 0.0603699 0.104564i
\(691\) 6.96447 + 12.0628i 0.264941 + 0.458891i 0.967548 0.252687i \(-0.0813143\pi\)
−0.702607 + 0.711578i \(0.747981\pi\)
\(692\) 4.17157 0.158579
\(693\) 0 0
\(694\) 14.5858 0.553669
\(695\) 0 0
\(696\) −1.79289 + 3.10538i −0.0679594 + 0.117709i
\(697\) −9.89949 + 17.1464i −0.374970 + 0.649467i
\(698\) 0 0
\(699\) 0.585786 0.0221565
\(700\) 0 0
\(701\) 36.1127 1.36396 0.681979 0.731372i \(-0.261120\pi\)
0.681979 + 0.731372i \(0.261120\pi\)
\(702\) 2.20711 + 3.82282i 0.0833019 + 0.144283i
\(703\) 11.2426 19.4728i 0.424024 0.734432i
\(704\) −0.500000 + 0.866025i −0.0188445 + 0.0326396i
\(705\) −4.58579 7.94282i −0.172711 0.299144i
\(706\) 25.3137 0.952694
\(707\) 0 0
\(708\) −3.48528 −0.130985
\(709\) −18.0208 31.2130i −0.676786 1.17223i −0.975943 0.218024i \(-0.930039\pi\)
0.299158 0.954204i \(-0.403294\pi\)
\(710\) −5.24264 + 9.08052i −0.196753 + 0.340786i
\(711\) −6.72792 + 11.6531i −0.252317 + 0.437026i
\(712\) −2.24264 3.88437i −0.0840465 0.145573i
\(713\) 8.97056 0.335950
\(714\) 0 0
\(715\) −6.24264 −0.233462
\(716\) 9.44975 + 16.3674i 0.353154 + 0.611680i
\(717\) −4.60051 + 7.96831i −0.171809 + 0.297582i
\(718\) −5.37868 + 9.31615i −0.200731 + 0.347675i
\(719\) −9.24264 16.0087i −0.344692 0.597025i 0.640605 0.767870i \(-0.278683\pi\)
−0.985298 + 0.170846i \(0.945350\pi\)
\(720\) −9.65685 −0.359890
\(721\) 0 0
\(722\) −7.34315 −0.273284
\(723\) −0.778175 1.34784i −0.0289406 0.0501266i
\(724\) 1.82843 3.16693i 0.0679530 0.117698i
\(725\) 28.8137 49.9068i 1.07011 1.85349i
\(726\) 0.207107 + 0.358719i 0.00768645 + 0.0133133i
\(727\) 48.4264 1.79604 0.898018 0.439959i \(-0.145007\pi\)
0.898018 + 0.439959i \(0.145007\pi\)
\(728\) 0 0
\(729\) −18.1716 −0.673021
\(730\) −11.2426 19.4728i −0.416109 0.720722i
\(731\) −21.6569 + 37.5108i −0.801008 + 1.38739i
\(732\) −1.27817 + 2.21386i −0.0472427 + 0.0818267i
\(733\) −6.50000 11.2583i −0.240083 0.415836i 0.720655 0.693294i \(-0.243841\pi\)
−0.960738 + 0.277458i \(0.910508\pi\)
\(734\) −14.7279 −0.543618
\(735\) 0 0
\(736\) 2.24264 0.0826648
\(737\) −5.62132 9.73641i −0.207064 0.358645i
\(738\) 3.65685 6.33386i 0.134611 0.233153i
\(739\) −16.2132 + 28.0821i −0.596412 + 1.03302i 0.396934 + 0.917847i \(0.370074\pi\)
−0.993346 + 0.115169i \(0.963259\pi\)
\(740\) 11.2426 + 19.4728i 0.413288 + 0.715835i
\(741\) 2.58579 0.0949912
\(742\) 0 0
\(743\) 9.31371 0.341687 0.170843 0.985298i \(-0.445351\pi\)
0.170843 + 0.985298i \(0.445351\pi\)
\(744\) 0.828427 + 1.43488i 0.0303716 + 0.0526052i
\(745\) −10.8284 + 18.7554i −0.396723 + 0.687144i
\(746\) −6.98528 + 12.0989i −0.255749 + 0.442971i
\(747\) −22.8284 39.5400i −0.835248 1.44669i
\(748\) 7.65685 0.279962
\(749\) 0 0
\(750\) −2.34315 −0.0855596
\(751\) −17.1716 29.7420i −0.626600 1.08530i −0.988229 0.152980i \(-0.951113\pi\)
0.361630 0.932322i \(-0.382220\pi\)
\(752\) 3.24264 5.61642i 0.118247 0.204810i
\(753\) −0.443651 + 0.768426i −0.0161675 + 0.0280030i
\(754\) −7.91421 13.7078i −0.288219 0.499209i
\(755\) 33.2132 1.20875
\(756\) 0 0
\(757\) 19.6569 0.714441 0.357220 0.934020i \(-0.383725\pi\)
0.357220 + 0.934020i \(0.383725\pi\)
\(758\) 12.9350 + 22.4041i 0.469821 + 0.813755i
\(759\) 0.464466 0.804479i 0.0168591 0.0292007i
\(760\) −5.82843 + 10.0951i −0.211419 + 0.366189i
\(761\) −1.48528 2.57258i −0.0538414 0.0932561i 0.837849 0.545903i \(-0.183813\pi\)
−0.891690 + 0.452647i \(0.850480\pi\)
\(762\) 4.02944 0.145971
\(763\) 0 0
\(764\) −12.8284 −0.464116
\(765\) 36.9706 + 64.0349i 1.33667 + 2.31519i
\(766\) 15.1924 26.3140i 0.548923 0.950763i
\(767\) 7.69239 13.3236i 0.277756 0.481088i
\(768\) 0.207107 + 0.358719i 0.00747332 + 0.0129442i
\(769\) 10.9706 0.395609 0.197804 0.980242i \(-0.436619\pi\)
0.197804 + 0.980242i \(0.436619\pi\)
\(770\) 0 0
\(771\) 1.30152 0.0468729
\(772\) −1.05025 1.81909i −0.0377994 0.0654705i
\(773\) 22.9706 39.7862i 0.826194 1.43101i −0.0748099 0.997198i \(-0.523835\pi\)
0.901004 0.433812i \(-0.142832\pi\)
\(774\) 8.00000 13.8564i 0.287554 0.498058i
\(775\) −13.3137 23.0600i −0.478243 0.828340i
\(776\) −1.82843 −0.0656367
\(777\) 0 0
\(778\) 2.72792 0.0978007
\(779\) −4.41421 7.64564i −0.158156 0.273934i
\(780\) −1.29289 + 2.23936i −0.0462930 + 0.0801818i
\(781\) −1.53553 + 2.65962i −0.0549457 + 0.0951688i
\(782\) −8.58579 14.8710i −0.307027 0.531787i
\(783\) −20.8995 −0.746887
\(784\) 0