Properties

Label 147.2.e.d.79.1
Level $147$
Weight $2$
Character 147.79
Analytic conductor $1.174$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 147 = 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 147.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.17380090971\)
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: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 79.1
Root \(-0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 147.79
Dual form 147.2.e.d.67.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.207107 + 0.358719i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.914214 + 1.58346i) q^{4} +(-1.70711 + 2.95680i) q^{5} +0.414214 q^{6} -1.58579 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.207107 + 0.358719i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.914214 + 1.58346i) q^{4} +(-1.70711 + 2.95680i) q^{5} +0.414214 q^{6} -1.58579 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.707107 - 1.22474i) q^{10} +(1.00000 + 1.73205i) q^{11} +(0.914214 - 1.58346i) q^{12} +2.58579 q^{13} +3.41421 q^{15} +(-1.50000 + 2.59808i) q^{16} +(1.12132 + 1.94218i) q^{17} +(-0.207107 - 0.358719i) q^{18} +(1.41421 - 2.44949i) q^{19} -6.24264 q^{20} -0.828427 q^{22} +(3.82843 - 6.63103i) q^{23} +(0.792893 + 1.37333i) q^{24} +(-3.32843 - 5.76500i) q^{25} +(-0.535534 + 0.927572i) q^{26} +1.00000 q^{27} -6.82843 q^{29} +(-0.707107 + 1.22474i) q^{30} +(0.585786 + 1.01461i) q^{31} +(-2.20711 - 3.82282i) q^{32} +(1.00000 - 1.73205i) q^{33} -0.928932 q^{34} -1.82843 q^{36} +(2.00000 - 3.46410i) q^{37} +(0.585786 + 1.01461i) q^{38} +(-1.29289 - 2.23936i) q^{39} +(2.70711 - 4.68885i) q^{40} +6.24264 q^{41} +5.65685 q^{43} +(-1.82843 + 3.16693i) q^{44} +(-1.70711 - 2.95680i) q^{45} +(1.58579 + 2.74666i) q^{46} +(1.41421 - 2.44949i) q^{47} +3.00000 q^{48} +2.75736 q^{50} +(1.12132 - 1.94218i) q^{51} +(2.36396 + 4.09450i) q^{52} +(1.00000 + 1.73205i) q^{53} +(-0.207107 + 0.358719i) q^{54} -6.82843 q^{55} -2.82843 q^{57} +(1.41421 - 2.44949i) q^{58} +(0.585786 + 1.01461i) q^{59} +(3.12132 + 5.40629i) q^{60} +(-6.12132 + 10.6024i) q^{61} -0.485281 q^{62} -4.17157 q^{64} +(-4.41421 + 7.64564i) q^{65} +(0.414214 + 0.717439i) q^{66} +(2.82843 + 4.89898i) q^{67} +(-2.05025 + 3.55114i) q^{68} -7.65685 q^{69} +9.31371 q^{71} +(0.792893 - 1.37333i) q^{72} +(-6.94975 - 12.0373i) q^{73} +(0.828427 + 1.43488i) q^{74} +(-3.32843 + 5.76500i) q^{75} +5.17157 q^{76} +1.07107 q^{78} +(-6.82843 + 11.8272i) q^{79} +(-5.12132 - 8.87039i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.29289 + 2.23936i) q^{82} +7.31371 q^{83} -7.65685 q^{85} +(-1.17157 + 2.02922i) q^{86} +(3.41421 + 5.91359i) q^{87} +(-1.58579 - 2.74666i) q^{88} +(7.12132 - 12.3345i) q^{89} +1.41421 q^{90} +14.0000 q^{92} +(0.585786 - 1.01461i) q^{93} +(0.585786 + 1.01461i) q^{94} +(4.82843 + 8.36308i) q^{95} +(-2.20711 + 3.82282i) q^{96} +2.58579 q^{97} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{2} - 2q^{3} - 2q^{4} - 4q^{5} - 4q^{6} - 12q^{8} - 2q^{9} + O(q^{10}) \) \( 4q + 2q^{2} - 2q^{3} - 2q^{4} - 4q^{5} - 4q^{6} - 12q^{8} - 2q^{9} + 4q^{11} - 2q^{12} + 16q^{13} + 8q^{15} - 6q^{16} - 4q^{17} + 2q^{18} - 8q^{20} + 8q^{22} + 4q^{23} + 6q^{24} - 2q^{25} + 12q^{26} + 4q^{27} - 16q^{29} + 8q^{31} - 6q^{32} + 4q^{33} - 32q^{34} + 4q^{36} + 8q^{37} + 8q^{38} - 8q^{39} + 8q^{40} + 8q^{41} + 4q^{44} - 4q^{45} + 12q^{46} + 12q^{48} + 28q^{50} - 4q^{51} - 16q^{52} + 4q^{53} + 2q^{54} - 16q^{55} + 8q^{59} + 4q^{60} - 16q^{61} + 32q^{62} - 28q^{64} - 12q^{65} - 4q^{66} - 28q^{68} - 8q^{69} - 8q^{71} + 6q^{72} - 8q^{73} - 8q^{74} - 2q^{75} + 32q^{76} - 24q^{78} - 16q^{79} - 12q^{80} - 2q^{81} - 8q^{82} - 16q^{83} - 8q^{85} - 16q^{86} + 8q^{87} - 12q^{88} + 20q^{89} + 56q^{92} + 8q^{93} + 8q^{94} + 8q^{95} - 6q^{96} + 16q^{97} - 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).

\(n\) \(50\) \(52\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.207107 + 0.358719i −0.146447 + 0.253653i −0.929912 0.367783i \(-0.880117\pi\)
0.783465 + 0.621436i \(0.213450\pi\)
\(3\) −0.500000 0.866025i −0.288675 0.500000i
\(4\) 0.914214 + 1.58346i 0.457107 + 0.791732i
\(5\) −1.70711 + 2.95680i −0.763441 + 1.32232i 0.177625 + 0.984098i \(0.443158\pi\)
−0.941067 + 0.338221i \(0.890175\pi\)
\(6\) 0.414214 0.169102
\(7\) 0 0
\(8\) −1.58579 −0.560660
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) −0.707107 1.22474i −0.223607 0.387298i
\(11\) 1.00000 + 1.73205i 0.301511 + 0.522233i 0.976478 0.215615i \(-0.0691756\pi\)
−0.674967 + 0.737848i \(0.735842\pi\)
\(12\) 0.914214 1.58346i 0.263911 0.457107i
\(13\) 2.58579 0.717168 0.358584 0.933497i \(-0.383260\pi\)
0.358584 + 0.933497i \(0.383260\pi\)
\(14\) 0 0
\(15\) 3.41421 0.881546
\(16\) −1.50000 + 2.59808i −0.375000 + 0.649519i
\(17\) 1.12132 + 1.94218i 0.271960 + 0.471049i 0.969364 0.245630i \(-0.0789948\pi\)
−0.697404 + 0.716679i \(0.745661\pi\)
\(18\) −0.207107 0.358719i −0.0488155 0.0845510i
\(19\) 1.41421 2.44949i 0.324443 0.561951i −0.656957 0.753928i \(-0.728157\pi\)
0.981399 + 0.191977i \(0.0614899\pi\)
\(20\) −6.24264 −1.39590
\(21\) 0 0
\(22\) −0.828427 −0.176621
\(23\) 3.82843 6.63103i 0.798282 1.38267i −0.122452 0.992474i \(-0.539076\pi\)
0.920734 0.390191i \(-0.127591\pi\)
\(24\) 0.792893 + 1.37333i 0.161849 + 0.280330i
\(25\) −3.32843 5.76500i −0.665685 1.15300i
\(26\) −0.535534 + 0.927572i −0.105027 + 0.181912i
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −6.82843 −1.26801 −0.634004 0.773330i \(-0.718590\pi\)
−0.634004 + 0.773330i \(0.718590\pi\)
\(30\) −0.707107 + 1.22474i −0.129099 + 0.223607i
\(31\) 0.585786 + 1.01461i 0.105210 + 0.182230i 0.913824 0.406110i \(-0.133115\pi\)
−0.808614 + 0.588340i \(0.799782\pi\)
\(32\) −2.20711 3.82282i −0.390165 0.675786i
\(33\) 1.00000 1.73205i 0.174078 0.301511i
\(34\) −0.928932 −0.159311
\(35\) 0 0
\(36\) −1.82843 −0.304738
\(37\) 2.00000 3.46410i 0.328798 0.569495i −0.653476 0.756948i \(-0.726690\pi\)
0.982274 + 0.187453i \(0.0600231\pi\)
\(38\) 0.585786 + 1.01461i 0.0950271 + 0.164592i
\(39\) −1.29289 2.23936i −0.207029 0.358584i
\(40\) 2.70711 4.68885i 0.428031 0.741372i
\(41\) 6.24264 0.974937 0.487468 0.873141i \(-0.337920\pi\)
0.487468 + 0.873141i \(0.337920\pi\)
\(42\) 0 0
\(43\) 5.65685 0.862662 0.431331 0.902194i \(-0.358044\pi\)
0.431331 + 0.902194i \(0.358044\pi\)
\(44\) −1.82843 + 3.16693i −0.275646 + 0.477432i
\(45\) −1.70711 2.95680i −0.254480 0.440773i
\(46\) 1.58579 + 2.74666i 0.233811 + 0.404973i
\(47\) 1.41421 2.44949i 0.206284 0.357295i −0.744257 0.667893i \(-0.767196\pi\)
0.950541 + 0.310599i \(0.100530\pi\)
\(48\) 3.00000 0.433013
\(49\) 0 0
\(50\) 2.75736 0.389949
\(51\) 1.12132 1.94218i 0.157016 0.271960i
\(52\) 2.36396 + 4.09450i 0.327822 + 0.567805i
\(53\) 1.00000 + 1.73205i 0.137361 + 0.237915i 0.926497 0.376303i \(-0.122805\pi\)
−0.789136 + 0.614218i \(0.789471\pi\)
\(54\) −0.207107 + 0.358719i −0.0281837 + 0.0488155i
\(55\) −6.82843 −0.920745
\(56\) 0 0
\(57\) −2.82843 −0.374634
\(58\) 1.41421 2.44949i 0.185695 0.321634i
\(59\) 0.585786 + 1.01461i 0.0762629 + 0.132091i 0.901635 0.432498i \(-0.142368\pi\)
−0.825372 + 0.564589i \(0.809035\pi\)
\(60\) 3.12132 + 5.40629i 0.402961 + 0.697948i
\(61\) −6.12132 + 10.6024i −0.783755 + 1.35750i 0.145985 + 0.989287i \(0.453365\pi\)
−0.929740 + 0.368216i \(0.879969\pi\)
\(62\) −0.485281 −0.0616308
\(63\) 0 0
\(64\) −4.17157 −0.521447
\(65\) −4.41421 + 7.64564i −0.547516 + 0.948325i
\(66\) 0.414214 + 0.717439i 0.0509862 + 0.0883106i
\(67\) 2.82843 + 4.89898i 0.345547 + 0.598506i 0.985453 0.169948i \(-0.0543599\pi\)
−0.639906 + 0.768453i \(0.721027\pi\)
\(68\) −2.05025 + 3.55114i −0.248630 + 0.430639i
\(69\) −7.65685 −0.921777
\(70\) 0 0
\(71\) 9.31371 1.10533 0.552667 0.833402i \(-0.313610\pi\)
0.552667 + 0.833402i \(0.313610\pi\)
\(72\) 0.792893 1.37333i 0.0934434 0.161849i
\(73\) −6.94975 12.0373i −0.813406 1.40886i −0.910467 0.413583i \(-0.864277\pi\)
0.0970601 0.995279i \(-0.469056\pi\)
\(74\) 0.828427 + 1.43488i 0.0963027 + 0.166801i
\(75\) −3.32843 + 5.76500i −0.384334 + 0.665685i
\(76\) 5.17157 0.593220
\(77\) 0 0
\(78\) 1.07107 0.121275
\(79\) −6.82843 + 11.8272i −0.768258 + 1.33066i 0.170249 + 0.985401i \(0.445543\pi\)
−0.938507 + 0.345261i \(0.887790\pi\)
\(80\) −5.12132 8.87039i −0.572581 0.991739i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −1.29289 + 2.23936i −0.142776 + 0.247296i
\(83\) 7.31371 0.802784 0.401392 0.915906i \(-0.368527\pi\)
0.401392 + 0.915906i \(0.368527\pi\)
\(84\) 0 0
\(85\) −7.65685 −0.830502
\(86\) −1.17157 + 2.02922i −0.126334 + 0.218817i
\(87\) 3.41421 + 5.91359i 0.366042 + 0.634004i
\(88\) −1.58579 2.74666i −0.169045 0.292795i
\(89\) 7.12132 12.3345i 0.754858 1.30745i −0.190586 0.981670i \(-0.561039\pi\)
0.945445 0.325783i \(-0.105628\pi\)
\(90\) 1.41421 0.149071
\(91\) 0 0
\(92\) 14.0000 1.45960
\(93\) 0.585786 1.01461i 0.0607432 0.105210i
\(94\) 0.585786 + 1.01461i 0.0604193 + 0.104649i
\(95\) 4.82843 + 8.36308i 0.495386 + 0.858034i
\(96\) −2.20711 + 3.82282i −0.225262 + 0.390165i
\(97\) 2.58579 0.262547 0.131273 0.991346i \(-0.458093\pi\)
0.131273 + 0.991346i \(0.458093\pi\)
\(98\) 0 0
\(99\) −2.00000 −0.201008
\(100\) 6.08579 10.5409i 0.608579 1.05409i
\(101\) −1.46447 2.53653i −0.145720 0.252394i 0.783921 0.620860i \(-0.213216\pi\)
−0.929641 + 0.368466i \(0.879883\pi\)
\(102\) 0.464466 + 0.804479i 0.0459890 + 0.0796553i
\(103\) −2.24264 + 3.88437i −0.220974 + 0.382738i −0.955104 0.296271i \(-0.904257\pi\)
0.734130 + 0.679009i \(0.237590\pi\)
\(104\) −4.10051 −0.402088
\(105\) 0 0
\(106\) −0.828427 −0.0804640
\(107\) 0.171573 0.297173i 0.0165866 0.0287288i −0.857613 0.514296i \(-0.828053\pi\)
0.874200 + 0.485567i \(0.161387\pi\)
\(108\) 0.914214 + 1.58346i 0.0879702 + 0.152369i
\(109\) 2.82843 + 4.89898i 0.270914 + 0.469237i 0.969096 0.246683i \(-0.0793407\pi\)
−0.698182 + 0.715920i \(0.746007\pi\)
\(110\) 1.41421 2.44949i 0.134840 0.233550i
\(111\) −4.00000 −0.379663
\(112\) 0 0
\(113\) −5.31371 −0.499872 −0.249936 0.968262i \(-0.580410\pi\)
−0.249936 + 0.968262i \(0.580410\pi\)
\(114\) 0.585786 1.01461i 0.0548639 0.0950271i
\(115\) 13.0711 + 22.6398i 1.21888 + 2.11117i
\(116\) −6.24264 10.8126i −0.579615 1.00392i
\(117\) −1.29289 + 2.23936i −0.119528 + 0.207029i
\(118\) −0.485281 −0.0446738
\(119\) 0 0
\(120\) −5.41421 −0.494248
\(121\) 3.50000 6.06218i 0.318182 0.551107i
\(122\) −2.53553 4.39167i −0.229556 0.397603i
\(123\) −3.12132 5.40629i −0.281440 0.487468i
\(124\) −1.07107 + 1.85514i −0.0961847 + 0.166597i
\(125\) 5.65685 0.505964
\(126\) 0 0
\(127\) −1.65685 −0.147022 −0.0735110 0.997294i \(-0.523420\pi\)
−0.0735110 + 0.997294i \(0.523420\pi\)
\(128\) 5.27817 9.14207i 0.466529 0.808052i
\(129\) −2.82843 4.89898i −0.249029 0.431331i
\(130\) −1.82843 3.16693i −0.160364 0.277758i
\(131\) 7.65685 13.2621i 0.668982 1.15871i −0.309207 0.950995i \(-0.600063\pi\)
0.978189 0.207717i \(-0.0666032\pi\)
\(132\) 3.65685 0.318288
\(133\) 0 0
\(134\) −2.34315 −0.202417
\(135\) −1.70711 + 2.95680i −0.146924 + 0.254480i
\(136\) −1.77817 3.07989i −0.152477 0.264098i
\(137\) −7.07107 12.2474i −0.604122 1.04637i −0.992190 0.124739i \(-0.960191\pi\)
0.388067 0.921631i \(-0.373143\pi\)
\(138\) 1.58579 2.74666i 0.134991 0.233811i
\(139\) −17.6569 −1.49763 −0.748817 0.662776i \(-0.769378\pi\)
−0.748817 + 0.662776i \(0.769378\pi\)
\(140\) 0 0
\(141\) −2.82843 −0.238197
\(142\) −1.92893 + 3.34101i −0.161872 + 0.280371i
\(143\) 2.58579 + 4.47871i 0.216234 + 0.374529i
\(144\) −1.50000 2.59808i −0.125000 0.216506i
\(145\) 11.6569 20.1903i 0.968049 1.67671i
\(146\) 5.75736 0.476482
\(147\) 0 0
\(148\) 7.31371 0.601183
\(149\) −8.65685 + 14.9941i −0.709197 + 1.22837i 0.255958 + 0.966688i \(0.417609\pi\)
−0.965155 + 0.261678i \(0.915724\pi\)
\(150\) −1.37868 2.38794i −0.112569 0.194975i
\(151\) −6.00000 10.3923i −0.488273 0.845714i 0.511636 0.859202i \(-0.329040\pi\)
−0.999909 + 0.0134886i \(0.995706\pi\)
\(152\) −2.24264 + 3.88437i −0.181902 + 0.315064i
\(153\) −2.24264 −0.181307
\(154\) 0 0
\(155\) −4.00000 −0.321288
\(156\) 2.36396 4.09450i 0.189268 0.327822i
\(157\) −5.87868 10.1822i −0.469170 0.812626i 0.530209 0.847867i \(-0.322113\pi\)
−0.999379 + 0.0352411i \(0.988780\pi\)
\(158\) −2.82843 4.89898i −0.225018 0.389742i
\(159\) 1.00000 1.73205i 0.0793052 0.137361i
\(160\) 15.0711 1.19147
\(161\) 0 0
\(162\) 0.414214 0.0325437
\(163\) 5.65685 9.79796i 0.443079 0.767435i −0.554837 0.831959i \(-0.687219\pi\)
0.997916 + 0.0645236i \(0.0205528\pi\)
\(164\) 5.70711 + 9.88500i 0.445650 + 0.771889i
\(165\) 3.41421 + 5.91359i 0.265796 + 0.460372i
\(166\) −1.51472 + 2.62357i −0.117565 + 0.203628i
\(167\) −19.7990 −1.53209 −0.766046 0.642786i \(-0.777779\pi\)
−0.766046 + 0.642786i \(0.777779\pi\)
\(168\) 0 0
\(169\) −6.31371 −0.485670
\(170\) 1.58579 2.74666i 0.121624 0.210659i
\(171\) 1.41421 + 2.44949i 0.108148 + 0.187317i
\(172\) 5.17157 + 8.95743i 0.394329 + 0.682997i
\(173\) −10.5355 + 18.2481i −0.801002 + 1.38738i 0.117956 + 0.993019i \(0.462366\pi\)
−0.918957 + 0.394357i \(0.870967\pi\)
\(174\) −2.82843 −0.214423
\(175\) 0 0
\(176\) −6.00000 −0.452267
\(177\) 0.585786 1.01461i 0.0440304 0.0762629i
\(178\) 2.94975 + 5.10911i 0.221093 + 0.382944i
\(179\) 9.82843 + 17.0233i 0.734611 + 1.27238i 0.954894 + 0.296948i \(0.0959687\pi\)
−0.220283 + 0.975436i \(0.570698\pi\)
\(180\) 3.12132 5.40629i 0.232649 0.402961i
\(181\) −2.58579 −0.192200 −0.0961000 0.995372i \(-0.530637\pi\)
−0.0961000 + 0.995372i \(0.530637\pi\)
\(182\) 0 0
\(183\) 12.2426 0.905002
\(184\) −6.07107 + 10.5154i −0.447565 + 0.775205i
\(185\) 6.82843 + 11.8272i 0.502036 + 0.869552i
\(186\) 0.242641 + 0.420266i 0.0177913 + 0.0308154i
\(187\) −2.24264 + 3.88437i −0.163998 + 0.284053i
\(188\) 5.17157 0.377176
\(189\) 0 0
\(190\) −4.00000 −0.290191
\(191\) 9.00000 15.5885i 0.651217 1.12794i −0.331611 0.943416i \(-0.607592\pi\)
0.982828 0.184525i \(-0.0590746\pi\)
\(192\) 2.08579 + 3.61269i 0.150529 + 0.260723i
\(193\) −2.65685 4.60181i −0.191245 0.331245i 0.754418 0.656394i \(-0.227919\pi\)
−0.945663 + 0.325149i \(0.894586\pi\)
\(194\) −0.535534 + 0.927572i −0.0384491 + 0.0665958i
\(195\) 8.82843 0.632217
\(196\) 0 0
\(197\) 2.00000 0.142494 0.0712470 0.997459i \(-0.477302\pi\)
0.0712470 + 0.997459i \(0.477302\pi\)
\(198\) 0.414214 0.717439i 0.0294369 0.0509862i
\(199\) −10.8284 18.7554i −0.767607 1.32953i −0.938857 0.344307i \(-0.888114\pi\)
0.171250 0.985228i \(-0.445219\pi\)
\(200\) 5.27817 + 9.14207i 0.373223 + 0.646442i
\(201\) 2.82843 4.89898i 0.199502 0.345547i
\(202\) 1.21320 0.0853607
\(203\) 0 0
\(204\) 4.10051 0.287093
\(205\) −10.6569 + 18.4582i −0.744307 + 1.28918i
\(206\) −0.928932 1.60896i −0.0647218 0.112101i
\(207\) 3.82843 + 6.63103i 0.266094 + 0.460888i
\(208\) −3.87868 + 6.71807i −0.268938 + 0.465814i
\(209\) 5.65685 0.391293
\(210\) 0 0
\(211\) 12.9706 0.892930 0.446465 0.894801i \(-0.352683\pi\)
0.446465 + 0.894801i \(0.352683\pi\)
\(212\) −1.82843 + 3.16693i −0.125577 + 0.217506i
\(213\) −4.65685 8.06591i −0.319082 0.552667i
\(214\) 0.0710678 + 0.123093i 0.00485810 + 0.00841447i
\(215\) −9.65685 + 16.7262i −0.658592 + 1.14071i
\(216\) −1.58579 −0.107899
\(217\) 0 0
\(218\) −2.34315 −0.158698
\(219\) −6.94975 + 12.0373i −0.469620 + 0.813406i
\(220\) −6.24264 10.8126i −0.420879 0.728983i
\(221\) 2.89949 + 5.02207i 0.195041 + 0.337821i
\(222\) 0.828427 1.43488i 0.0556004 0.0963027i
\(223\) 24.9706 1.67215 0.836076 0.548613i \(-0.184844\pi\)
0.836076 + 0.548613i \(0.184844\pi\)
\(224\) 0 0
\(225\) 6.65685 0.443790
\(226\) 1.10051 1.90613i 0.0732045 0.126794i
\(227\) −11.8995 20.6105i −0.789797 1.36797i −0.926091 0.377300i \(-0.876852\pi\)
0.136294 0.990668i \(-0.456481\pi\)
\(228\) −2.58579 4.47871i −0.171248 0.296610i
\(229\) 0.121320 0.210133i 0.00801707 0.0138860i −0.861989 0.506927i \(-0.830781\pi\)
0.870006 + 0.493041i \(0.164115\pi\)
\(230\) −10.8284 −0.714005
\(231\) 0 0
\(232\) 10.8284 0.710921
\(233\) 3.07107 5.31925i 0.201192 0.348475i −0.747721 0.664014i \(-0.768852\pi\)
0.948913 + 0.315538i \(0.102185\pi\)
\(234\) −0.535534 0.927572i −0.0350089 0.0606373i
\(235\) 4.82843 + 8.36308i 0.314972 + 0.545547i
\(236\) −1.07107 + 1.85514i −0.0697206 + 0.120760i
\(237\) 13.6569 0.887108
\(238\) 0 0
\(239\) −15.6569 −1.01276 −0.506379 0.862311i \(-0.669016\pi\)
−0.506379 + 0.862311i \(0.669016\pi\)
\(240\) −5.12132 + 8.87039i −0.330580 + 0.572581i
\(241\) 8.12132 + 14.0665i 0.523140 + 0.906105i 0.999637 + 0.0269294i \(0.00857294\pi\)
−0.476497 + 0.879176i \(0.658094\pi\)
\(242\) 1.44975 + 2.51104i 0.0931933 + 0.161416i
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) −22.3848 −1.43304
\(245\) 0 0
\(246\) 2.58579 0.164864
\(247\) 3.65685 6.33386i 0.232680 0.403014i
\(248\) −0.928932 1.60896i −0.0589873 0.102169i
\(249\) −3.65685 6.33386i −0.231744 0.401392i
\(250\) −1.17157 + 2.02922i −0.0740968 + 0.128339i
\(251\) −12.4853 −0.788064 −0.394032 0.919097i \(-0.628920\pi\)
−0.394032 + 0.919097i \(0.628920\pi\)
\(252\) 0 0
\(253\) 15.3137 0.962765
\(254\) 0.343146 0.594346i 0.0215309 0.0372926i
\(255\) 3.82843 + 6.63103i 0.239745 + 0.415251i
\(256\) −1.98528 3.43861i −0.124080 0.214913i
\(257\) −11.6066 + 20.1032i −0.724000 + 1.25400i 0.235384 + 0.971902i \(0.424365\pi\)
−0.959384 + 0.282102i \(0.908968\pi\)
\(258\) 2.34315 0.145878
\(259\) 0 0
\(260\) −16.1421 −1.00109
\(261\) 3.41421 5.91359i 0.211335 0.366042i
\(262\) 3.17157 + 5.49333i 0.195940 + 0.339379i
\(263\) −2.65685 4.60181i −0.163829 0.283760i 0.772410 0.635124i \(-0.219051\pi\)
−0.936239 + 0.351365i \(0.885718\pi\)
\(264\) −1.58579 + 2.74666i −0.0975984 + 0.169045i
\(265\) −6.82843 −0.419467
\(266\) 0 0
\(267\) −14.2426 −0.871635
\(268\) −5.17157 + 8.95743i −0.315904 + 0.547162i
\(269\) 7.36396 + 12.7548i 0.448989 + 0.777671i 0.998320 0.0579332i \(-0.0184510\pi\)
−0.549332 + 0.835604i \(0.685118\pi\)
\(270\) −0.707107 1.22474i −0.0430331 0.0745356i
\(271\) 5.07107 8.78335i 0.308045 0.533550i −0.669889 0.742461i \(-0.733658\pi\)
0.977935 + 0.208911i \(0.0669918\pi\)
\(272\) −6.72792 −0.407940
\(273\) 0 0
\(274\) 5.85786 0.353887
\(275\) 6.65685 11.5300i 0.401423 0.695286i
\(276\) −7.00000 12.1244i −0.421350 0.729800i
\(277\) 4.65685 + 8.06591i 0.279803 + 0.484633i 0.971336 0.237712i \(-0.0763974\pi\)
−0.691532 + 0.722345i \(0.743064\pi\)
\(278\) 3.65685 6.33386i 0.219324 0.379880i
\(279\) −1.17157 −0.0701402
\(280\) 0 0
\(281\) 0.485281 0.0289495 0.0144747 0.999895i \(-0.495392\pi\)
0.0144747 + 0.999895i \(0.495392\pi\)
\(282\) 0.585786 1.01461i 0.0348831 0.0604193i
\(283\) 4.24264 + 7.34847i 0.252199 + 0.436821i 0.964131 0.265427i \(-0.0855130\pi\)
−0.711932 + 0.702248i \(0.752180\pi\)
\(284\) 8.51472 + 14.7479i 0.505256 + 0.875128i
\(285\) 4.82843 8.36308i 0.286011 0.495386i
\(286\) −2.14214 −0.126667
\(287\) 0 0
\(288\) 4.41421 0.260110
\(289\) 5.98528 10.3668i 0.352075 0.609812i
\(290\) 4.82843 + 8.36308i 0.283535 + 0.491097i
\(291\) −1.29289 2.23936i −0.0757907 0.131273i
\(292\) 12.7071 22.0094i 0.743627 1.28800i
\(293\) 16.5858 0.968952 0.484476 0.874805i \(-0.339010\pi\)
0.484476 + 0.874805i \(0.339010\pi\)
\(294\) 0 0
\(295\) −4.00000 −0.232889
\(296\) −3.17157 + 5.49333i −0.184344 + 0.319293i
\(297\) 1.00000 + 1.73205i 0.0580259 + 0.100504i
\(298\) −3.58579 6.21076i −0.207719 0.359780i
\(299\) 9.89949 17.1464i 0.572503 0.991604i
\(300\) −12.1716 −0.702726
\(301\) 0 0
\(302\) 4.97056 0.286024
\(303\) −1.46447 + 2.53653i −0.0841314 + 0.145720i
\(304\) 4.24264 + 7.34847i 0.243332 + 0.421464i
\(305\) −20.8995 36.1990i −1.19670 2.07275i
\(306\) 0.464466 0.804479i 0.0265518 0.0459890i
\(307\) 30.1421 1.72030 0.860151 0.510039i \(-0.170369\pi\)
0.860151 + 0.510039i \(0.170369\pi\)
\(308\) 0 0
\(309\) 4.48528 0.255159
\(310\) 0.828427 1.43488i 0.0470515 0.0814956i
\(311\) −3.07107 5.31925i −0.174144 0.301627i 0.765721 0.643173i \(-0.222383\pi\)
−0.939865 + 0.341547i \(0.889049\pi\)
\(312\) 2.05025 + 3.55114i 0.116073 + 0.201044i
\(313\) −0.949747 + 1.64501i −0.0536829 + 0.0929815i −0.891618 0.452788i \(-0.850429\pi\)
0.837935 + 0.545770i \(0.183763\pi\)
\(314\) 4.87006 0.274833
\(315\) 0 0
\(316\) −24.9706 −1.40470
\(317\) −5.00000 + 8.66025i −0.280828 + 0.486408i −0.971589 0.236675i \(-0.923942\pi\)
0.690761 + 0.723083i \(0.257276\pi\)
\(318\) 0.414214 + 0.717439i 0.0232279 + 0.0402320i
\(319\) −6.82843 11.8272i −0.382319 0.662195i
\(320\) 7.12132 12.3345i 0.398094 0.689519i
\(321\) −0.343146 −0.0191525
\(322\) 0 0
\(323\) 6.34315 0.352942
\(324\) 0.914214 1.58346i 0.0507896 0.0879702i
\(325\) −8.60660 14.9071i −0.477408 0.826896i
\(326\) 2.34315 + 4.05845i 0.129775 + 0.224777i
\(327\) 2.82843 4.89898i 0.156412 0.270914i
\(328\) −9.89949 −0.546608
\(329\) 0 0
\(330\) −2.82843 −0.155700
\(331\) 2.00000 3.46410i 0.109930 0.190404i −0.805812 0.592172i \(-0.798271\pi\)
0.915742 + 0.401768i \(0.131604\pi\)
\(332\) 6.68629 + 11.5810i 0.366958 + 0.635590i
\(333\) 2.00000 + 3.46410i 0.109599 + 0.189832i
\(334\) 4.10051 7.10228i 0.224370 0.388620i
\(335\) −19.3137 −1.05522
\(336\) 0 0
\(337\) −29.6569 −1.61551 −0.807756 0.589517i \(-0.799318\pi\)
−0.807756 + 0.589517i \(0.799318\pi\)
\(338\) 1.30761 2.26485i 0.0711247 0.123192i
\(339\) 2.65685 + 4.60181i 0.144301 + 0.249936i
\(340\) −7.00000 12.1244i −0.379628 0.657536i
\(341\) −1.17157 + 2.02922i −0.0634442 + 0.109889i
\(342\) −1.17157 −0.0633514
\(343\) 0 0
\(344\) −8.97056 −0.483660
\(345\) 13.0711 22.6398i 0.703723 1.21888i
\(346\) −4.36396 7.55860i −0.234608 0.406353i
\(347\) −16.6569 28.8505i −0.894187 1.54878i −0.834808 0.550541i \(-0.814421\pi\)
−0.0593789 0.998236i \(-0.518912\pi\)
\(348\) −6.24264 + 10.8126i −0.334641 + 0.579615i
\(349\) −9.89949 −0.529908 −0.264954 0.964261i \(-0.585357\pi\)
−0.264954 + 0.964261i \(0.585357\pi\)
\(350\) 0 0
\(351\) 2.58579 0.138019
\(352\) 4.41421 7.64564i 0.235278 0.407514i
\(353\) 7.36396 + 12.7548i 0.391944 + 0.678867i 0.992706 0.120561i \(-0.0384693\pi\)
−0.600762 + 0.799428i \(0.705136\pi\)
\(354\) 0.242641 + 0.420266i 0.0128962 + 0.0223369i
\(355\) −15.8995 + 27.5387i −0.843858 + 1.46160i
\(356\) 26.0416 1.38020
\(357\) 0 0
\(358\) −8.14214 −0.430325
\(359\) 0.171573 0.297173i 0.00905527 0.0156842i −0.861462 0.507822i \(-0.830451\pi\)
0.870518 + 0.492137i \(0.163784\pi\)
\(360\) 2.70711 + 4.68885i 0.142677 + 0.247124i
\(361\) 5.50000 + 9.52628i 0.289474 + 0.501383i
\(362\) 0.535534 0.927572i 0.0281470 0.0487521i
\(363\) −7.00000 −0.367405
\(364\) 0 0
\(365\) 47.4558 2.48395
\(366\) −2.53553 + 4.39167i −0.132534 + 0.229556i
\(367\) 1.65685 + 2.86976i 0.0864871 + 0.149800i 0.906024 0.423226i \(-0.139103\pi\)
−0.819537 + 0.573027i \(0.805769\pi\)
\(368\) 11.4853 + 19.8931i 0.598712 + 1.03700i
\(369\) −3.12132 + 5.40629i −0.162489 + 0.281440i
\(370\) −5.65685 −0.294086
\(371\) 0 0
\(372\) 2.14214 0.111065
\(373\) 5.34315 9.25460i 0.276658 0.479185i −0.693894 0.720077i \(-0.744107\pi\)
0.970552 + 0.240892i \(0.0774399\pi\)
\(374\) −0.928932 1.60896i −0.0480339 0.0831972i
\(375\) −2.82843 4.89898i −0.146059 0.252982i
\(376\) −2.24264 + 3.88437i −0.115655 + 0.200321i
\(377\) −17.6569 −0.909374
\(378\) 0 0
\(379\) 8.68629 0.446185 0.223092 0.974797i \(-0.428385\pi\)
0.223092 + 0.974797i \(0.428385\pi\)
\(380\) −8.82843 + 15.2913i −0.452889 + 0.784426i
\(381\) 0.828427 + 1.43488i 0.0424416 + 0.0735110i
\(382\) 3.72792 + 6.45695i 0.190737 + 0.330366i
\(383\) 9.17157 15.8856i 0.468645 0.811718i −0.530712 0.847552i \(-0.678076\pi\)
0.999358 + 0.0358343i \(0.0114088\pi\)
\(384\) −10.5563 −0.538701
\(385\) 0 0
\(386\) 2.20101 0.112028
\(387\) −2.82843 + 4.89898i −0.143777 + 0.249029i
\(388\) 2.36396 + 4.09450i 0.120012 + 0.207867i
\(389\) 9.07107 + 15.7116i 0.459921 + 0.796607i 0.998956 0.0456762i \(-0.0145442\pi\)
−0.539035 + 0.842283i \(0.681211\pi\)
\(390\) −1.82843 + 3.16693i −0.0925860 + 0.160364i
\(391\) 17.1716 0.868404
\(392\) 0 0
\(393\) −15.3137 −0.772474
\(394\) −0.414214 + 0.717439i −0.0208678 + 0.0361441i
\(395\) −23.3137 40.3805i −1.17304 2.03176i
\(396\) −1.82843 3.16693i −0.0918819 0.159144i
\(397\) 1.19239 2.06528i 0.0598442 0.103653i −0.834551 0.550931i \(-0.814273\pi\)
0.894395 + 0.447277i \(0.147606\pi\)
\(398\) 8.97056 0.449654
\(399\) 0 0
\(400\) 19.9706 0.998528
\(401\) 3.07107 5.31925i 0.153362 0.265630i −0.779100 0.626900i \(-0.784323\pi\)
0.932461 + 0.361270i \(0.117657\pi\)
\(402\) 1.17157 + 2.02922i 0.0584327 + 0.101208i
\(403\) 1.51472 + 2.62357i 0.0754535 + 0.130689i
\(404\) 2.67767 4.63786i 0.133219 0.230742i
\(405\) 3.41421 0.169654
\(406\) 0 0
\(407\) 8.00000 0.396545
\(408\) −1.77817 + 3.07989i −0.0880328 + 0.152477i
\(409\) 10.7071 + 18.5453i 0.529432 + 0.917004i 0.999411 + 0.0343258i \(0.0109284\pi\)
−0.469978 + 0.882678i \(0.655738\pi\)
\(410\) −4.41421 7.64564i −0.218002 0.377591i
\(411\) −7.07107 + 12.2474i −0.348790 + 0.604122i
\(412\) −8.20101 −0.404035
\(413\) 0 0
\(414\) −3.17157 −0.155874
\(415\) −12.4853 + 21.6251i −0.612878 + 1.06154i
\(416\) −5.70711 9.88500i −0.279814 0.484652i
\(417\) 8.82843 + 15.2913i 0.432330 + 0.748817i
\(418\) −1.17157 + 2.02922i −0.0573035 + 0.0992526i
\(419\) 33.1716 1.62054 0.810269 0.586059i \(-0.199321\pi\)
0.810269 + 0.586059i \(0.199321\pi\)
\(420\) 0 0
\(421\) 16.6274 0.810371 0.405185 0.914235i \(-0.367207\pi\)
0.405185 + 0.914235i \(0.367207\pi\)
\(422\) −2.68629 + 4.65279i −0.130767 + 0.226494i
\(423\) 1.41421 + 2.44949i 0.0687614 + 0.119098i
\(424\) −1.58579 2.74666i −0.0770126 0.133390i
\(425\) 7.46447 12.9288i 0.362080 0.627141i
\(426\) 3.85786 0.186914
\(427\) 0 0
\(428\) 0.627417 0.0303273
\(429\) 2.58579 4.47871i 0.124843 0.216234i
\(430\) −4.00000 6.92820i −0.192897 0.334108i
\(431\) 13.4853 + 23.3572i 0.649563 + 1.12508i 0.983227 + 0.182384i \(0.0583815\pi\)
−0.333664 + 0.942692i \(0.608285\pi\)
\(432\) −1.50000 + 2.59808i −0.0721688 + 0.125000i
\(433\) −20.2426 −0.972799 −0.486400 0.873736i \(-0.661690\pi\)
−0.486400 + 0.873736i \(0.661690\pi\)
\(434\) 0 0
\(435\) −23.3137 −1.11781
\(436\) −5.17157 + 8.95743i −0.247673 + 0.428983i
\(437\) −10.8284 18.7554i −0.517994 0.897192i
\(438\) −2.87868 4.98602i −0.137549 0.238241i
\(439\) −6.34315 + 10.9867i −0.302742 + 0.524364i −0.976756 0.214354i \(-0.931235\pi\)
0.674014 + 0.738718i \(0.264569\pi\)
\(440\) 10.8284 0.516225
\(441\) 0 0
\(442\) −2.40202 −0.114252
\(443\) −17.4853 + 30.2854i −0.830751 + 1.43890i 0.0666929 + 0.997774i \(0.478755\pi\)
−0.897444 + 0.441129i \(0.854578\pi\)
\(444\) −3.65685 6.33386i −0.173547 0.300592i
\(445\) 24.3137 + 42.1126i 1.15258 + 1.99633i
\(446\) −5.17157 + 8.95743i −0.244881 + 0.424146i
\(447\) 17.3137 0.818910
\(448\) 0 0
\(449\) −5.31371 −0.250769 −0.125385 0.992108i \(-0.540017\pi\)
−0.125385 + 0.992108i \(0.540017\pi\)
\(450\) −1.37868 + 2.38794i −0.0649916 + 0.112569i
\(451\) 6.24264 + 10.8126i 0.293954 + 0.509144i
\(452\) −4.85786 8.41407i −0.228495 0.395764i
\(453\) −6.00000 + 10.3923i −0.281905 + 0.488273i
\(454\) 9.85786 0.462652
\(455\) 0 0
\(456\) 4.48528 0.210043
\(457\) 9.00000 15.5885i 0.421002 0.729197i −0.575036 0.818128i \(-0.695012\pi\)
0.996038 + 0.0889312i \(0.0283451\pi\)
\(458\) 0.0502525 + 0.0870399i 0.00234815 + 0.00406711i
\(459\) 1.12132 + 1.94218i 0.0523388 + 0.0906534i
\(460\) −23.8995 + 41.3951i −1.11432 + 1.93006i
\(461\) −16.5858 −0.772477 −0.386239 0.922399i \(-0.626226\pi\)
−0.386239 + 0.922399i \(0.626226\pi\)
\(462\) 0 0
\(463\) −26.6274 −1.23748 −0.618741 0.785595i \(-0.712357\pi\)
−0.618741 + 0.785595i \(0.712357\pi\)
\(464\) 10.2426 17.7408i 0.475503 0.823595i
\(465\) 2.00000 + 3.46410i 0.0927478 + 0.160644i
\(466\) 1.27208 + 2.20330i 0.0589279 + 0.102066i
\(467\) −0.100505 + 0.174080i −0.00465082 + 0.00805546i −0.868341 0.495967i \(-0.834814\pi\)
0.863691 + 0.504022i \(0.168147\pi\)
\(468\) −4.72792 −0.218548
\(469\) 0 0
\(470\) −4.00000 −0.184506
\(471\) −5.87868 + 10.1822i −0.270875 + 0.469170i
\(472\) −0.928932 1.60896i −0.0427576 0.0740583i
\(473\) 5.65685 + 9.79796i 0.260102 + 0.450511i
\(474\) −2.82843 + 4.89898i −0.129914 + 0.225018i
\(475\) −18.8284 −0.863907
\(476\) 0 0
\(477\) −2.00000 −0.0915737
\(478\) 3.24264 5.61642i 0.148315 0.256889i
\(479\) −0.928932 1.60896i −0.0424440 0.0735152i 0.844023 0.536307i \(-0.180181\pi\)
−0.886467 + 0.462792i \(0.846848\pi\)
\(480\) −7.53553 13.0519i −0.343948 0.595736i
\(481\) 5.17157 8.95743i 0.235803 0.408424i
\(482\) −6.72792 −0.306448
\(483\) 0 0
\(484\) 12.7990 0.581772
\(485\) −4.41421 + 7.64564i −0.200439 + 0.347171i
\(486\) −0.207107 0.358719i −0.00939455 0.0162718i
\(487\) −13.3137 23.0600i −0.603302 1.04495i −0.992317 0.123718i \(-0.960518\pi\)
0.389016 0.921231i \(-0.372815\pi\)
\(488\) 9.70711 16.8132i 0.439420 0.761098i
\(489\) −11.3137 −0.511624
\(490\) 0 0
\(491\) 5.02944 0.226975 0.113488 0.993539i \(-0.463798\pi\)
0.113488 + 0.993539i \(0.463798\pi\)
\(492\) 5.70711 9.88500i 0.257296 0.445650i
\(493\) −7.65685 13.2621i −0.344847 0.597293i
\(494\) 1.51472 + 2.62357i 0.0681504 + 0.118040i
\(495\) 3.41421 5.91359i 0.153457 0.265796i
\(496\) −3.51472 −0.157816
\(497\) 0 0
\(498\) 3.02944 0.135752
\(499\) −1.65685 + 2.86976i −0.0741710 + 0.128468i −0.900725 0.434389i \(-0.856964\pi\)
0.826554 + 0.562857i \(0.190298\pi\)
\(500\) 5.17157 + 8.95743i 0.231280 + 0.400588i
\(501\) 9.89949 + 17.1464i 0.442277 + 0.766046i
\(502\) 2.58579 4.47871i 0.115409 0.199895i
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) 10.0000 0.444994
\(506\) −3.17157 + 5.49333i −0.140994 + 0.244208i
\(507\) 3.15685 + 5.46783i 0.140201 + 0.242835i
\(508\) −1.51472 2.62357i −0.0672048 0.116402i
\(509\) −2.77817 + 4.81194i −0.123140 + 0.213285i −0.921005 0.389552i \(-0.872630\pi\)
0.797864 + 0.602837i \(0.205963\pi\)
\(510\) −3.17157 −0.140440
\(511\) 0 0
\(512\) 22.7574 1.00574
\(513\) 1.41421 2.44949i 0.0624391 0.108148i
\(514\) −4.80761 8.32703i −0.212055 0.367289i
\(515\) −7.65685 13.2621i −0.337401 0.584396i
\(516\) 5.17157 8.95743i 0.227666 0.394329i
\(517\) 5.65685 0.248788
\(518\) 0 0
\(519\) 21.0711 0.924917
\(520\) 7.00000 12.1244i 0.306970 0.531688i
\(521\) 17.7071 + 30.6696i 0.775762 + 1.34366i 0.934365 + 0.356317i \(0.115968\pi\)
−0.158603 + 0.987343i \(0.550699\pi\)
\(522\) 1.41421 + 2.44949i 0.0618984 + 0.107211i
\(523\) 12.8284 22.2195i 0.560948 0.971590i −0.436466 0.899721i \(-0.643770\pi\)
0.997414 0.0718696i \(-0.0228966\pi\)
\(524\) 28.0000 1.22319
\(525\) 0 0
\(526\) 2.20101 0.0959686
\(527\) −1.31371 + 2.27541i −0.0572260 + 0.0991184i
\(528\) 3.00000 + 5.19615i 0.130558 + 0.226134i
\(529\) −17.8137 30.8542i −0.774509 1.34149i
\(530\) 1.41421 2.44949i 0.0614295 0.106399i
\(531\) −1.17157 −0.0508419
\(532\) 0 0
\(533\) 16.1421 0.699194
\(534\) 2.94975 5.10911i 0.127648 0.221093i
\(535\) 0.585786 + 1.01461i 0.0253258 + 0.0438655i
\(536\) −4.48528 7.76874i −0.193735 0.335558i
\(537\) 9.82843 17.0233i 0.424128 0.734611i
\(538\) −6.10051 −0.263011
\(539\) 0 0
\(540\) −6.24264 −0.268640
\(541\) −8.65685 + 14.9941i −0.372187 + 0.644647i −0.989902 0.141755i \(-0.954725\pi\)
0.617715 + 0.786402i \(0.288059\pi\)
\(542\) 2.10051 + 3.63818i 0.0902244 + 0.156273i
\(543\) 1.29289 + 2.23936i 0.0554834 + 0.0961000i
\(544\) 4.94975 8.57321i 0.212219 0.367574i
\(545\) −19.3137 −0.827308
\(546\) 0 0
\(547\) −36.9706 −1.58075 −0.790374 0.612625i \(-0.790114\pi\)
−0.790374 + 0.612625i \(0.790114\pi\)
\(548\) 12.9289 22.3936i 0.552297 0.956606i
\(549\) −6.12132 10.6024i −0.261252 0.452501i
\(550\) 2.75736 + 4.77589i 0.117574 + 0.203644i
\(551\) −9.65685 + 16.7262i −0.411396 + 0.712558i
\(552\) 12.1421 0.516804
\(553\) 0 0
\(554\) −3.85786 −0.163905
\(555\) 6.82843 11.8272i 0.289851 0.502036i
\(556\) −16.1421 27.9590i −0.684579 1.18573i
\(557\) −13.0000 22.5167i −0.550828 0.954062i −0.998215 0.0597213i \(-0.980979\pi\)
0.447387 0.894340i \(-0.352355\pi\)
\(558\) 0.242641 0.420266i 0.0102718 0.0177913i
\(559\) 14.6274 0.618674
\(560\) 0 0
\(561\) 4.48528 0.189369
\(562\) −0.100505 + 0.174080i −0.00423955 + 0.00734312i
\(563\) 0.585786 + 1.01461i 0.0246880 + 0.0427608i 0.878105 0.478467i \(-0.158807\pi\)
−0.853417 + 0.521228i \(0.825474\pi\)
\(564\) −2.58579 4.47871i −0.108881 0.188588i
\(565\) 9.07107 15.7116i 0.381623 0.660990i
\(566\) −3.51472 −0.147735
\(567\) 0 0
\(568\) −14.7696 −0.619717
\(569\) 8.24264 14.2767i 0.345549 0.598509i −0.639904 0.768455i \(-0.721026\pi\)
0.985453 + 0.169946i \(0.0543592\pi\)
\(570\) 2.00000 + 3.46410i 0.0837708 + 0.145095i
\(571\) −11.1716 19.3497i −0.467516 0.809761i 0.531795 0.846873i \(-0.321518\pi\)
−0.999311 + 0.0371118i \(0.988184\pi\)
\(572\) −4.72792 + 8.18900i −0.197684 + 0.342399i
\(573\) −18.0000 −0.751961
\(574\) 0 0
\(575\) −50.9706 −2.12562
\(576\) 2.08579 3.61269i 0.0869078 0.150529i
\(577\) 16.9497 + 29.3578i 0.705627 + 1.22218i 0.966465 + 0.256799i \(0.0826680\pi\)
−0.260837 + 0.965383i \(0.583999\pi\)
\(578\) 2.47918 + 4.29407i 0.103120 + 0.178610i
\(579\) −2.65685 + 4.60181i −0.110415 + 0.191245i
\(580\) 42.6274 1.77001
\(581\) 0 0
\(582\) 1.07107 0.0443972
\(583\) −2.00000 + 3.46410i −0.0828315 + 0.143468i
\(584\) 11.0208 + 19.0886i 0.456045 + 0.789892i
\(585\) −4.41421 7.64564i −0.182505 0.316108i
\(586\) −3.43503 + 5.94964i −0.141900 + 0.245778i
\(587\) −22.8284 −0.942230 −0.471115 0.882072i \(-0.656148\pi\)
−0.471115 + 0.882072i \(0.656148\pi\)
\(588\) 0 0
\(589\) 3.31371 0.136539
\(590\) 0.828427 1.43488i 0.0341058 0.0590730i
\(591\) −1.00000 1.73205i −0.0411345 0.0712470i
\(592\) 6.00000 + 10.3923i 0.246598 + 0.427121i
\(593\) 3.46447 6.00063i 0.142269 0.246416i −0.786082 0.618122i \(-0.787894\pi\)
0.928351 + 0.371706i \(0.121227\pi\)
\(594\) −0.828427 −0.0339908
\(595\) 0 0
\(596\) −31.6569 −1.29672
\(597\) −10.8284 + 18.7554i −0.443178 + 0.767607i
\(598\) 4.10051 + 7.10228i 0.167682 + 0.290434i
\(599\) 1.00000 + 1.73205i 0.0408589 + 0.0707697i 0.885732 0.464198i \(-0.153657\pi\)
−0.844873 + 0.534967i \(0.820324\pi\)
\(600\) 5.27817 9.14207i 0.215481 0.373223i
\(601\) −15.0711 −0.614762 −0.307381 0.951587i \(-0.599453\pi\)
−0.307381 + 0.951587i \(0.599453\pi\)
\(602\) 0 0
\(603\) −5.65685 −0.230365
\(604\) 10.9706 19.0016i 0.446386 0.773163i
\(605\) 11.9497 + 20.6976i 0.485826 + 0.841476i
\(606\) −0.606602 1.05066i −0.0246415 0.0426803i
\(607\) 9.17157 15.8856i 0.372263 0.644778i −0.617651 0.786453i \(-0.711915\pi\)
0.989913 + 0.141675i \(0.0452487\pi\)
\(608\) −12.4853 −0.506345
\(609\) 0 0
\(610\) 17.3137 0.701012
\(611\) 3.65685 6.33386i 0.147940 0.256240i
\(612\) −2.05025 3.55114i −0.0828765 0.143546i
\(613\) −2.34315 4.05845i −0.0946388 0.163919i 0.814819 0.579715i \(-0.196836\pi\)
−0.909458 + 0.415796i \(0.863503\pi\)
\(614\) −6.24264 + 10.8126i −0.251932 + 0.436360i
\(615\) 21.3137 0.859452
\(616\) 0 0
\(617\) −24.4853 −0.985740 −0.492870 0.870103i \(-0.664052\pi\)
−0.492870 + 0.870103i \(0.664052\pi\)
\(618\) −0.928932 + 1.60896i −0.0373671 + 0.0647218i
\(619\) −14.4853 25.0892i −0.582213 1.00842i −0.995217 0.0976926i \(-0.968854\pi\)
0.413004 0.910729i \(-0.364480\pi\)
\(620\) −3.65685 6.33386i −0.146863 0.254374i
\(621\) 3.82843 6.63103i 0.153629 0.266094i
\(622\) 2.54416 0.102011
\(623\) 0 0
\(624\) 7.75736 0.310543
\(625\) 6.98528 12.0989i 0.279411 0.483954i
\(626\) −0.393398 0.681386i −0.0157234 0.0272337i
\(627\) −2.82843 4.89898i −0.112956 0.195646i
\(628\) 10.7487 18.6174i 0.428921 0.742914i
\(629\) 8.97056 0.357680
\(630\) 0 0
\(631\) 23.3137 0.928104 0.464052 0.885808i \(-0.346395\pi\)
0.464052 + 0.885808i \(0.346395\pi\)
\(632\) 10.8284 18.7554i 0.430732 0.746049i
\(633\) −6.48528 11.2328i −0.257767 0.446465i
\(634\) −2.07107 3.58719i −0.0822526 0.142466i
\(635\) 2.82843 4.89898i 0.112243 0.194410i
\(636\) 3.65685 0.145004
\(637\) 0 0
\(638\) 5.65685 0.223957
\(639\) −4.65685 + 8.06591i −0.184222 + 0.319082i
\(640\) 18.0208 + 31.2130i 0.712335 + 1.23380i
\(641\) 5.41421 + 9.37769i 0.213849 + 0.370397i 0.952916 0.303235i \(-0.0980668\pi\)
−0.739067 + 0.673632i \(0.764733\pi\)
\(642\) 0.0710678 0.123093i 0.00280482 0.00485810i
\(643\) −34.4264 −1.35764 −0.678822 0.734302i \(-0.737509\pi\)
−0.678822 + 0.734302i \(0.737509\pi\)
\(644\) 0 0
\(645\) 19.3137 0.760477
\(646\) −1.31371 + 2.27541i −0.0516872 + 0.0895248i
\(647\) −13.4142 23.2341i −0.527367 0.913427i −0.999491 0.0318946i \(-0.989846\pi\)
0.472124 0.881532i \(-0.343487\pi\)
\(648\) 0.792893 + 1.37333i 0.0311478 + 0.0539496i
\(649\) −1.17157 + 2.02922i −0.0459883 + 0.0796540i
\(650\) 7.12994 0.279659
\(651\) 0 0
\(652\) 20.6863 0.810138
\(653\) −18.2426 + 31.5972i −0.713890 + 1.23649i 0.249497 + 0.968376i \(0.419735\pi\)
−0.963386 + 0.268118i \(0.913598\pi\)
\(654\) 1.17157 + 2.02922i 0.0458121 + 0.0793489i
\(655\) 26.1421 + 45.2795i 1.02146 + 1.76922i
\(656\) −9.36396 + 16.2189i −0.365601 + 0.633240i
\(657\) 13.8995 0.542271
\(658\) 0 0
\(659\) 9.31371 0.362811 0.181405 0.983408i \(-0.441935\pi\)
0.181405 + 0.983408i \(0.441935\pi\)
\(660\) −6.24264 + 10.8126i −0.242994 + 0.420879i
\(661\) 11.7782 + 20.4004i 0.458118 + 0.793483i 0.998862 0.0477040i \(-0.0151904\pi\)
−0.540744 + 0.841187i \(0.681857\pi\)
\(662\) 0.828427 + 1.43488i 0.0321977 + 0.0557681i
\(663\) 2.89949 5.02207i 0.112607 0.195041i
\(664\) −11.5980 −0.450089
\(665\) 0 0
\(666\) −1.65685 −0.0642018
\(667\) −26.1421 + 45.2795i −1.01223 + 1.75323i
\(668\) −18.1005 31.3510i −0.700330 1.21301i
\(669\) −12.4853 21.6251i −0.482709 0.836076i
\(670\) 4.00000 6.92820i 0.154533 0.267660i
\(671\) −24.4853 −0.945244
\(672\) 0 0
\(673\) 23.3137 0.898677 0.449339 0.893361i \(-0.351660\pi\)
0.449339 + 0.893361i \(0.351660\pi\)
\(674\) 6.14214 10.6385i 0.236586 0.409779i
\(675\) −3.32843 5.76500i −0.128111 0.221895i
\(676\) −5.77208 9.99753i −0.222003 0.384520i
\(677\) −15.7071 + 27.2055i −0.603673 + 1.04559i 0.388587 + 0.921412i \(0.372963\pi\)
−0.992260 + 0.124180i \(0.960370\pi\)
\(678\) −2.20101 −0.0845293
\(679\) 0 0
\(680\) 12.1421 0.465630
\(681\) −11.8995 + 20.6105i −0.455990 + 0.789797i
\(682\) −0.485281 0.840532i −0.0185824 0.0321856i
\(683\) 9.82843 + 17.0233i 0.376074 + 0.651380i 0.990487 0.137605i \(-0.0439404\pi\)
−0.614413 + 0.788985i \(0.710607\pi\)
\(684\) −2.58579 + 4.47871i −0.0988700 + 0.171248i
\(685\) 48.2843 1.84485
\(686\) 0 0
\(687\) −0.242641 −0.00925732
\(688\) −8.48528 + 14.6969i −0.323498 + 0.560316i
\(689\) 2.58579 + 4.47871i 0.0985106 + 0.170625i
\(690\) 5.41421 + 9.37769i 0.206116 + 0.357003i
\(691\) 0.343146 0.594346i 0.0130539 0.0226100i −0.859425 0.511262i \(-0.829178\pi\)
0.872479 + 0.488652i \(0.162511\pi\)
\(692\) −38.5269 −1.46457
\(693\) 0 0
\(694\) 13.7990 0.523802
\(695\) 30.1421 52.2077i 1.14336 1.98035i
\(696\) −5.41421 9.37769i −0.205225 0.355461i
\(697\) 7.00000 + 12.1244i 0.265144 + 0.459243i
\(698\) 2.05025 3.55114i 0.0776032 0.134413i
\(699\) −6.14214 −0.232317
\(700\) 0 0
\(701\) −17.1716 −0.648561 −0.324281 0.945961i \(-0.605122\pi\)
−0.324281 + 0.945961i \(0.605122\pi\)
\(702\) −0.535534 + 0.927572i −0.0202124 + 0.0350089i
\(703\) −5.65685 9.79796i −0.213352 0.369537i
\(704\) −4.17157 7.22538i −0.157222 0.272317i
\(705\) 4.82843 8.36308i 0.181849 0.314972i
\(706\) −6.10051 −0.229596
\(707\) 0 0
\(708\) 2.14214 0.0805064
\(709\) 18.1421 31.4231i 0.681342 1.18012i −0.293229 0.956042i \(-0.594730\pi\)
0.974571 0.224077i \(-0.0719368\pi\)
\(710\) −6.58579 11.4069i −0.247160 0.428094i
\(711\) −6.82843 11.8272i −0.256086 0.443554i
\(712\) −11.2929 + 19.5599i −0.423219 + 0.733037i
\(713\) 8.97056 0.335950
\(714\) 0 0
\(715\) −17.6569 −0.660329
\(716\) −17.9706 + 31.1259i −0.671591 + 1.16323i
\(717\) 7.82843 + 13.5592i 0.292358 + 0.506379i
\(718\) 0.0710678 + 0.123093i 0.00265223 + 0.00459379i
\(719\) −20.9706 + 36.3221i −0.782070 + 1.35459i 0.148664 + 0.988888i \(0.452503\pi\)
−0.930734 + 0.365697i \(0.880831\pi\)
\(720\) 10.2426 0.381721
\(721\) 0 0
\(722\) −4.55635 −0.169570
\(723\) 8.12132 14.0665i 0.302035 0.523140i
\(724\) −2.36396 4.09450i −0.0878559 0.152171i
\(725\) 22.7279 + 39.3659i 0.844094 + 1.46201i
\(726\) 1.44975 2.51104i 0.0538052 0.0931933i
\(727\) 12.4853 0.463053 0.231527 0.972829i \(-0.425628\pi\)
0.231527 + 0.972829i \(0.425628\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −9.82843 + 17.0233i −0.363766 + 0.630062i
\(731\) 6.34315 + 10.9867i 0.234610 + 0.406356i
\(732\) 11.1924 + 19.3858i 0.413683 + 0.716519i
\(733\) −24.8492 + 43.0402i −0.917828 + 1.58972i −0.115120 + 0.993352i \(0.536725\pi\)
−0.802708 + 0.596373i \(0.796608\pi\)
\(734\) −1.37258 −0.0506630
\(735\) 0 0
\(736\) −33.7990 −1.24585
\(737\) −5.65685 + 9.79796i −0.208373 + 0.360912i
\(738\) −1.29289 2.23936i −0.0475921 0.0824319i
\(739\) −2.34315 4.05845i −0.0861940 0.149292i 0.819705 0.572785i \(-0.194137\pi\)
−0.905899 + 0.423493i \(0.860804\pi\)
\(740\) −12.4853 + 21.6251i −0.458968 + 0.794956i
\(741\) −7.31371 −0.268676
\(742\) 0 0
\(743\) −50.9706 −1.86993 −0.934964 0.354742i \(-0.884569\pi\)
−0.934964 + 0.354742i \(0.884569\pi\)
\(744\) −0.928932 + 1.60896i −0.0340563 + 0.0589873i
\(745\) −29.5563 51.1931i −1.08286 1.87557i
\(746\) 2.21320 + 3.83338i 0.0810311 + 0.140350i
\(747\) −3.65685 + 6.33386i −0.133797 + 0.231744i
\(748\) −8.20101 −0.299859
\(749\) 0 0
\(750\) 2.34315 0.0855596
\(751\) −6.82843 + 11.8272i −0.249173 + 0.431580i −0.963297 0.268440i \(-0.913492\pi\)
0.714124 + 0.700020i \(0.246825\pi\)
\(752\) 4.24264 + 7.34847i 0.154713 + 0.267971i
\(753\) 6.24264 + 10.8126i 0.227494 + 0.394032i
\(754\) 3.65685 6.33386i 0.133175 0.230665i
\(755\) 40.9706 1.49107
\(756\) 0 0
\(757\) 26.3431 0.957458 0.478729 0.877963i \(-0.341098\pi\)
0.478729 + 0.877963i \(0.341098\pi\)
\(758\) −1.79899 + 3.11594i −0.0653423 + 0.113176i
\(759\) −7.65685 13.2621i −0.277926 0.481382i
\(760\) −7.65685 13.2621i −0.277743 0.481065i
\(761\) 9.26346 16.0448i 0.335800 0.581623i −0.647838 0.761778i \(-0.724327\pi\)
0.983638 + 0.180155i \(0.0576600\pi\)
\(762\) −0.686292 −0.0248617
\(763\) 0 0
\(764\) 32.9117 1.19070
\(765\) 3.82843 6.63103i 0.138417 0.239745i
\(766\) 3.79899 + 6.58004i 0.137263 + 0.237747i
\(767\) 1.51472 + 2.62357i 0.0546933 + 0.0947316i
\(768\) −1.98528 + 3.43861i −0.0716377 + 0.124080i
\(769\) 29.6985 1.07095 0.535477 0.844550i \(-0.320132\pi\)
0.535477 + 0.844550i \(0.320132\pi\)
\(770\) 0 0
\(771\) 23.2132 0.836003
\(772\) 4.85786 8.41407i 0.174838 0.302829i
\(773\) 4.77817 + 8.27604i 0.171859 + 0.297669i 0.939070 0.343727i \(-0.111689\pi\)
−0.767211 + 0.641395i \(0.778356\pi\)
\(774\) −1.17157 2.02922i −0.0421113 0.0729389i
\(775\) 3.89949 6.75412i 0.140074 0.242615i
\(776\) −4.10051 −0.147200
\(777\) 0 0
\(778\) −7.51472 −0.269416
\(779\) 8.82843 15.2913i 0.316311 0.547867i
\(780\) 8.07107 + 13.9795i 0.288991 + 0.500546i
\(781\) 9.31371 + 16.1318i 0.333271 + 0.577242i
\(782\) −3.55635 + 6.15978i −0.127175 + 0.220273i
\(783\) −6.82843 −0.244028