Properties

Label 507.2.e.d.484.2
Level $507$
Weight $2$
Character 507.484
Analytic conductor $4.048$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 507 = 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 507.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.04841538248\)
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 39)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 484.2
Root \(0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 507.484
Dual form 507.2.e.d.22.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.207107 + 0.358719i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.914214 - 1.58346i) q^{4} +2.82843 q^{5} +(0.207107 - 0.358719i) q^{6} +(1.41421 - 2.44949i) q^{7} +1.58579 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.207107 + 0.358719i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.914214 - 1.58346i) q^{4} +2.82843 q^{5} +(0.207107 - 0.358719i) q^{6} +(1.41421 - 2.44949i) q^{7} +1.58579 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.585786 + 1.01461i) q^{10} +(-1.00000 - 1.73205i) q^{11} -1.82843 q^{12} +1.17157 q^{14} +(-1.41421 - 2.44949i) q^{15} +(-1.50000 - 2.59808i) q^{16} +(-3.82843 + 6.63103i) q^{17} -0.414214 q^{18} +(-1.41421 + 2.44949i) q^{19} +(2.58579 - 4.47871i) q^{20} -2.82843 q^{21} +(0.414214 - 0.717439i) q^{22} +(2.00000 + 3.46410i) q^{23} +(-0.792893 - 1.37333i) q^{24} +3.00000 q^{25} +1.00000 q^{27} +(-2.58579 - 4.47871i) q^{28} +(-1.00000 - 1.73205i) q^{29} +(0.585786 - 1.01461i) q^{30} +1.17157 q^{31} +(2.20711 - 3.82282i) q^{32} +(-1.00000 + 1.73205i) q^{33} -3.17157 q^{34} +(4.00000 - 6.92820i) q^{35} +(0.914214 + 1.58346i) q^{36} +(-3.82843 - 6.63103i) q^{37} -1.17157 q^{38} +4.48528 q^{40} +(2.58579 + 4.47871i) q^{41} +(-0.585786 - 1.01461i) q^{42} +(0.828427 - 1.43488i) q^{43} -3.65685 q^{44} +(-1.41421 + 2.44949i) q^{45} +(-0.828427 + 1.43488i) q^{46} +11.6569 q^{47} +(-1.50000 + 2.59808i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(0.621320 + 1.07616i) q^{50} +7.65685 q^{51} -2.00000 q^{53} +(0.207107 + 0.358719i) q^{54} +(-2.82843 - 4.89898i) q^{55} +(2.24264 - 3.88437i) q^{56} +2.82843 q^{57} +(0.414214 - 0.717439i) q^{58} +(3.82843 - 6.63103i) q^{59} -5.17157 q^{60} +(-6.65685 + 11.5300i) q^{61} +(0.242641 + 0.420266i) q^{62} +(1.41421 + 2.44949i) q^{63} -4.17157 q^{64} -0.828427 q^{66} +(3.41421 + 5.91359i) q^{67} +(7.00000 + 12.1244i) q^{68} +(2.00000 - 3.46410i) q^{69} +3.31371 q^{70} +(1.00000 - 1.73205i) q^{71} +(-0.792893 + 1.37333i) q^{72} -0.343146 q^{73} +(1.58579 - 2.74666i) q^{74} +(-1.50000 - 2.59808i) q^{75} +(2.58579 + 4.47871i) q^{76} -5.65685 q^{77} -11.3137 q^{79} +(-4.24264 - 7.34847i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.07107 + 1.85514i) q^{82} -3.65685 q^{83} +(-2.58579 + 4.47871i) q^{84} +(-10.8284 + 18.7554i) q^{85} +0.686292 q^{86} +(-1.00000 + 1.73205i) q^{87} +(-1.58579 - 2.74666i) q^{88} +(7.41421 + 12.8418i) q^{89} -1.17157 q^{90} +7.31371 q^{92} +(-0.585786 - 1.01461i) q^{93} +(2.41421 + 4.18154i) q^{94} +(-4.00000 + 6.92820i) q^{95} -4.41421 q^{96} +(1.82843 - 3.16693i) q^{97} +(0.207107 - 0.358719i) q^{98} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{2} - 2q^{3} - 2q^{4} - 2q^{6} + 12q^{8} - 2q^{9} + O(q^{10}) \) \( 4q - 2q^{2} - 2q^{3} - 2q^{4} - 2q^{6} + 12q^{8} - 2q^{9} + 8q^{10} - 4q^{11} + 4q^{12} + 16q^{14} - 6q^{16} - 4q^{17} + 4q^{18} + 16q^{20} - 4q^{22} + 8q^{23} - 6q^{24} + 12q^{25} + 4q^{27} - 16q^{28} - 4q^{29} + 8q^{30} + 16q^{31} + 6q^{32} - 4q^{33} - 24q^{34} + 16q^{35} - 2q^{36} - 4q^{37} - 16q^{38} - 16q^{40} + 16q^{41} - 8q^{42} - 8q^{43} + 8q^{44} + 8q^{46} + 24q^{47} - 6q^{48} - 2q^{49} - 6q^{50} + 8q^{51} - 8q^{53} - 2q^{54} - 8q^{56} - 4q^{58} + 4q^{59} - 32q^{60} - 4q^{61} - 16q^{62} - 28q^{64} + 8q^{66} + 8q^{67} + 28q^{68} + 8q^{69} - 32q^{70} + 4q^{71} - 6q^{72} - 24q^{73} + 12q^{74} - 6q^{75} + 16q^{76} - 2q^{81} + 24q^{82} + 8q^{83} - 16q^{84} - 32q^{85} + 48q^{86} - 4q^{87} - 12q^{88} + 24q^{89} - 16q^{90} - 16q^{92} - 8q^{93} + 4q^{94} - 16q^{95} - 12q^{96} - 4q^{97} - 2q^{98} + 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).

\(n\) \(170\) \(340\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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 \(-0.119883\pi\)
−0.783465 + 0.621436i \(0.786550\pi\)
\(3\) −0.500000 0.866025i −0.288675 0.500000i
\(4\) 0.914214 1.58346i 0.457107 0.791732i
\(5\) 2.82843 1.26491 0.632456 0.774597i \(-0.282047\pi\)
0.632456 + 0.774597i \(0.282047\pi\)
\(6\) 0.207107 0.358719i 0.0845510 0.146447i
\(7\) 1.41421 2.44949i 0.534522 0.925820i −0.464664 0.885487i \(-0.653825\pi\)
0.999186 0.0403329i \(-0.0128419\pi\)
\(8\) 1.58579 0.560660
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0.585786 + 1.01461i 0.185242 + 0.320848i
\(11\) −1.00000 1.73205i −0.301511 0.522233i 0.674967 0.737848i \(-0.264158\pi\)
−0.976478 + 0.215615i \(0.930824\pi\)
\(12\) −1.82843 −0.527821
\(13\) 0 0
\(14\) 1.17157 0.313116
\(15\) −1.41421 2.44949i −0.365148 0.632456i
\(16\) −1.50000 2.59808i −0.375000 0.649519i
\(17\) −3.82843 + 6.63103i −0.928530 + 1.60826i −0.142747 + 0.989759i \(0.545593\pi\)
−0.785783 + 0.618502i \(0.787740\pi\)
\(18\) −0.414214 −0.0976311
\(19\) −1.41421 + 2.44949i −0.324443 + 0.561951i −0.981399 0.191977i \(-0.938510\pi\)
0.656957 + 0.753928i \(0.271843\pi\)
\(20\) 2.58579 4.47871i 0.578199 1.00147i
\(21\) −2.82843 −0.617213
\(22\) 0.414214 0.717439i 0.0883106 0.152958i
\(23\) 2.00000 + 3.46410i 0.417029 + 0.722315i 0.995639 0.0932891i \(-0.0297381\pi\)
−0.578610 + 0.815604i \(0.696405\pi\)
\(24\) −0.792893 1.37333i −0.161849 0.280330i
\(25\) 3.00000 0.600000
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) −2.58579 4.47871i −0.488668 0.846397i
\(29\) −1.00000 1.73205i −0.185695 0.321634i 0.758115 0.652121i \(-0.226120\pi\)
−0.943811 + 0.330487i \(0.892787\pi\)
\(30\) 0.585786 1.01461i 0.106949 0.185242i
\(31\) 1.17157 0.210421 0.105210 0.994450i \(-0.466448\pi\)
0.105210 + 0.994450i \(0.466448\pi\)
\(32\) 2.20711 3.82282i 0.390165 0.675786i
\(33\) −1.00000 + 1.73205i −0.174078 + 0.301511i
\(34\) −3.17157 −0.543920
\(35\) 4.00000 6.92820i 0.676123 1.17108i
\(36\) 0.914214 + 1.58346i 0.152369 + 0.263911i
\(37\) −3.82843 6.63103i −0.629390 1.09013i −0.987674 0.156522i \(-0.949972\pi\)
0.358285 0.933612i \(-0.383362\pi\)
\(38\) −1.17157 −0.190054
\(39\) 0 0
\(40\) 4.48528 0.709185
\(41\) 2.58579 + 4.47871i 0.403832 + 0.699458i 0.994185 0.107688i \(-0.0343447\pi\)
−0.590353 + 0.807145i \(0.701011\pi\)
\(42\) −0.585786 1.01461i −0.0903888 0.156558i
\(43\) 0.828427 1.43488i 0.126334 0.218817i −0.795920 0.605402i \(-0.793012\pi\)
0.922254 + 0.386585i \(0.126346\pi\)
\(44\) −3.65685 −0.551292
\(45\) −1.41421 + 2.44949i −0.210819 + 0.365148i
\(46\) −0.828427 + 1.43488i −0.122145 + 0.211561i
\(47\) 11.6569 1.70033 0.850163 0.526519i \(-0.176503\pi\)
0.850163 + 0.526519i \(0.176503\pi\)
\(48\) −1.50000 + 2.59808i −0.216506 + 0.375000i
\(49\) −0.500000 0.866025i −0.0714286 0.123718i
\(50\) 0.621320 + 1.07616i 0.0878680 + 0.152192i
\(51\) 7.65685 1.07217
\(52\) 0 0
\(53\) −2.00000 −0.274721 −0.137361 0.990521i \(-0.543862\pi\)
−0.137361 + 0.990521i \(0.543862\pi\)
\(54\) 0.207107 + 0.358719i 0.0281837 + 0.0488155i
\(55\) −2.82843 4.89898i −0.381385 0.660578i
\(56\) 2.24264 3.88437i 0.299685 0.519070i
\(57\) 2.82843 0.374634
\(58\) 0.414214 0.717439i 0.0543889 0.0942043i
\(59\) 3.82843 6.63103i 0.498419 0.863287i −0.501580 0.865112i \(-0.667248\pi\)
0.999998 + 0.00182490i \(0.000580884\pi\)
\(60\) −5.17157 −0.667647
\(61\) −6.65685 + 11.5300i −0.852323 + 1.47627i 0.0267837 + 0.999641i \(0.491473\pi\)
−0.879107 + 0.476625i \(0.841860\pi\)
\(62\) 0.242641 + 0.420266i 0.0308154 + 0.0533738i
\(63\) 1.41421 + 2.44949i 0.178174 + 0.308607i
\(64\) −4.17157 −0.521447
\(65\) 0 0
\(66\) −0.828427 −0.101972
\(67\) 3.41421 + 5.91359i 0.417113 + 0.722460i 0.995648 0.0931973i \(-0.0297087\pi\)
−0.578535 + 0.815657i \(0.696375\pi\)
\(68\) 7.00000 + 12.1244i 0.848875 + 1.47029i
\(69\) 2.00000 3.46410i 0.240772 0.417029i
\(70\) 3.31371 0.396064
\(71\) 1.00000 1.73205i 0.118678 0.205557i −0.800566 0.599245i \(-0.795468\pi\)
0.919244 + 0.393688i \(0.128801\pi\)
\(72\) −0.792893 + 1.37333i −0.0934434 + 0.161849i
\(73\) −0.343146 −0.0401622 −0.0200811 0.999798i \(-0.506392\pi\)
−0.0200811 + 0.999798i \(0.506392\pi\)
\(74\) 1.58579 2.74666i 0.184344 0.319293i
\(75\) −1.50000 2.59808i −0.173205 0.300000i
\(76\) 2.58579 + 4.47871i 0.296610 + 0.513744i
\(77\) −5.65685 −0.644658
\(78\) 0 0
\(79\) −11.3137 −1.27289 −0.636446 0.771321i \(-0.719596\pi\)
−0.636446 + 0.771321i \(0.719596\pi\)
\(80\) −4.24264 7.34847i −0.474342 0.821584i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −1.07107 + 1.85514i −0.118280 + 0.204866i
\(83\) −3.65685 −0.401392 −0.200696 0.979654i \(-0.564320\pi\)
−0.200696 + 0.979654i \(0.564320\pi\)
\(84\) −2.58579 + 4.47871i −0.282132 + 0.488668i
\(85\) −10.8284 + 18.7554i −1.17451 + 2.03431i
\(86\) 0.686292 0.0740047
\(87\) −1.00000 + 1.73205i −0.107211 + 0.185695i
\(88\) −1.58579 2.74666i −0.169045 0.292795i
\(89\) 7.41421 + 12.8418i 0.785905 + 1.36123i 0.928457 + 0.371440i \(0.121136\pi\)
−0.142552 + 0.989787i \(0.545531\pi\)
\(90\) −1.17157 −0.123495
\(91\) 0 0
\(92\) 7.31371 0.762507
\(93\) −0.585786 1.01461i −0.0607432 0.105210i
\(94\) 2.41421 + 4.18154i 0.249007 + 0.431293i
\(95\) −4.00000 + 6.92820i −0.410391 + 0.710819i
\(96\) −4.41421 −0.450524
\(97\) 1.82843 3.16693i 0.185649 0.321553i −0.758146 0.652085i \(-0.773895\pi\)
0.943795 + 0.330532i \(0.107228\pi\)
\(98\) 0.207107 0.358719i 0.0209209 0.0362361i
\(99\) 2.00000 0.201008
\(100\) 2.74264 4.75039i 0.274264 0.475039i
\(101\) −3.82843 6.63103i −0.380943 0.659812i 0.610255 0.792205i \(-0.291067\pi\)
−0.991197 + 0.132393i \(0.957734\pi\)
\(102\) 1.58579 + 2.74666i 0.157016 + 0.271960i
\(103\) 2.34315 0.230877 0.115439 0.993315i \(-0.463173\pi\)
0.115439 + 0.993315i \(0.463173\pi\)
\(104\) 0 0
\(105\) −8.00000 −0.780720
\(106\) −0.414214 0.717439i −0.0402320 0.0696838i
\(107\) 5.65685 + 9.79796i 0.546869 + 0.947204i 0.998487 + 0.0549930i \(0.0175137\pi\)
−0.451618 + 0.892211i \(0.649153\pi\)
\(108\) 0.914214 1.58346i 0.0879702 0.152369i
\(109\) −5.31371 −0.508961 −0.254480 0.967078i \(-0.581904\pi\)
−0.254480 + 0.967078i \(0.581904\pi\)
\(110\) 1.17157 2.02922i 0.111705 0.193479i
\(111\) −3.82843 + 6.63103i −0.363378 + 0.629390i
\(112\) −8.48528 −0.801784
\(113\) 2.65685 4.60181i 0.249936 0.432902i −0.713572 0.700582i \(-0.752924\pi\)
0.963508 + 0.267680i \(0.0862571\pi\)
\(114\) 0.585786 + 1.01461i 0.0548639 + 0.0950271i
\(115\) 5.65685 + 9.79796i 0.527504 + 0.913664i
\(116\) −3.65685 −0.339530
\(117\) 0 0
\(118\) 3.17157 0.291967
\(119\) 10.8284 + 18.7554i 0.992640 + 1.71930i
\(120\) −2.24264 3.88437i −0.204724 0.354593i
\(121\) 3.50000 6.06218i 0.318182 0.551107i
\(122\) −5.51472 −0.499279
\(123\) 2.58579 4.47871i 0.233153 0.403832i
\(124\) 1.07107 1.85514i 0.0961847 0.166597i
\(125\) −5.65685 −0.505964
\(126\) −0.585786 + 1.01461i −0.0521860 + 0.0903888i
\(127\) −2.82843 4.89898i −0.250982 0.434714i 0.712814 0.701353i \(-0.247420\pi\)
−0.963797 + 0.266639i \(0.914087\pi\)
\(128\) −5.27817 9.14207i −0.466529 0.808052i
\(129\) −1.65685 −0.145878
\(130\) 0 0
\(131\) −8.00000 −0.698963 −0.349482 0.936943i \(-0.613642\pi\)
−0.349482 + 0.936943i \(0.613642\pi\)
\(132\) 1.82843 + 3.16693i 0.159144 + 0.275646i
\(133\) 4.00000 + 6.92820i 0.346844 + 0.600751i
\(134\) −1.41421 + 2.44949i −0.122169 + 0.211604i
\(135\) 2.82843 0.243432
\(136\) −6.07107 + 10.5154i −0.520590 + 0.901688i
\(137\) −5.41421 + 9.37769i −0.462567 + 0.801190i −0.999088 0.0426968i \(-0.986405\pi\)
0.536521 + 0.843887i \(0.319738\pi\)
\(138\) 1.65685 0.141041
\(139\) 3.65685 6.33386i 0.310170 0.537231i −0.668229 0.743956i \(-0.732947\pi\)
0.978399 + 0.206725i \(0.0662806\pi\)
\(140\) −7.31371 12.6677i −0.618121 1.07062i
\(141\) −5.82843 10.0951i −0.490842 0.850163i
\(142\) 0.828427 0.0695201
\(143\) 0 0
\(144\) 3.00000 0.250000
\(145\) −2.82843 4.89898i −0.234888 0.406838i
\(146\) −0.0710678 0.123093i −0.00588161 0.0101873i
\(147\) −0.500000 + 0.866025i −0.0412393 + 0.0714286i
\(148\) −14.0000 −1.15079
\(149\) −4.58579 + 7.94282i −0.375682 + 0.650701i −0.990429 0.138024i \(-0.955925\pi\)
0.614747 + 0.788725i \(0.289258\pi\)
\(150\) 0.621320 1.07616i 0.0507306 0.0878680i
\(151\) 3.51472 0.286024 0.143012 0.989721i \(-0.454321\pi\)
0.143012 + 0.989721i \(0.454321\pi\)
\(152\) −2.24264 + 3.88437i −0.181902 + 0.315064i
\(153\) −3.82843 6.63103i −0.309510 0.536087i
\(154\) −1.17157 2.02922i −0.0944080 0.163520i
\(155\) 3.31371 0.266163
\(156\) 0 0
\(157\) −10.0000 −0.798087 −0.399043 0.916932i \(-0.630658\pi\)
−0.399043 + 0.916932i \(0.630658\pi\)
\(158\) −2.34315 4.05845i −0.186411 0.322873i
\(159\) 1.00000 + 1.73205i 0.0793052 + 0.137361i
\(160\) 6.24264 10.8126i 0.493524 0.854809i
\(161\) 11.3137 0.891645
\(162\) 0.207107 0.358719i 0.0162718 0.0281837i
\(163\) 9.41421 16.3059i 0.737378 1.27718i −0.216294 0.976328i \(-0.569397\pi\)
0.953672 0.300848i \(-0.0972697\pi\)
\(164\) 9.45584 0.738377
\(165\) −2.82843 + 4.89898i −0.220193 + 0.381385i
\(166\) −0.757359 1.31178i −0.0587825 0.101814i
\(167\) −1.82843 3.16693i −0.141488 0.245064i 0.786569 0.617502i \(-0.211855\pi\)
−0.928057 + 0.372438i \(0.878522\pi\)
\(168\) −4.48528 −0.346047
\(169\) 0 0
\(170\) −8.97056 −0.688011
\(171\) −1.41421 2.44949i −0.108148 0.187317i
\(172\) −1.51472 2.62357i −0.115496 0.200045i
\(173\) 5.82843 10.0951i 0.443127 0.767519i −0.554793 0.831989i \(-0.687202\pi\)
0.997920 + 0.0644701i \(0.0205357\pi\)
\(174\) −0.828427 −0.0628029
\(175\) 4.24264 7.34847i 0.320713 0.555492i
\(176\) −3.00000 + 5.19615i −0.226134 + 0.391675i
\(177\) −7.65685 −0.575524
\(178\) −3.07107 + 5.31925i −0.230186 + 0.398694i
\(179\) 11.6569 + 20.1903i 0.871274 + 1.50909i 0.860679 + 0.509147i \(0.170039\pi\)
0.0105948 + 0.999944i \(0.496628\pi\)
\(180\) 2.58579 + 4.47871i 0.192733 + 0.333824i
\(181\) 14.0000 1.04061 0.520306 0.853980i \(-0.325818\pi\)
0.520306 + 0.853980i \(0.325818\pi\)
\(182\) 0 0
\(183\) 13.3137 0.984178
\(184\) 3.17157 + 5.49333i 0.233811 + 0.404973i
\(185\) −10.8284 18.7554i −0.796122 1.37892i
\(186\) 0.242641 0.420266i 0.0177913 0.0308154i
\(187\) 15.3137 1.11985
\(188\) 10.6569 18.4582i 0.777231 1.34620i
\(189\) 1.41421 2.44949i 0.102869 0.178174i
\(190\) −3.31371 −0.240402
\(191\) −1.65685 + 2.86976i −0.119886 + 0.207648i −0.919722 0.392570i \(-0.871586\pi\)
0.799836 + 0.600218i \(0.204919\pi\)
\(192\) 2.08579 + 3.61269i 0.150529 + 0.260723i
\(193\) 2.65685 + 4.60181i 0.191245 + 0.331245i 0.945663 0.325149i \(-0.105414\pi\)
−0.754418 + 0.656394i \(0.772081\pi\)
\(194\) 1.51472 0.108750
\(195\) 0 0
\(196\) −1.82843 −0.130602
\(197\) 0.242641 + 0.420266i 0.0172874 + 0.0299427i 0.874540 0.484954i \(-0.161164\pi\)
−0.857252 + 0.514897i \(0.827830\pi\)
\(198\) 0.414214 + 0.717439i 0.0294369 + 0.0509862i
\(199\) −10.8284 + 18.7554i −0.767607 + 1.32953i 0.171250 + 0.985228i \(0.445219\pi\)
−0.938857 + 0.344307i \(0.888114\pi\)
\(200\) 4.75736 0.336396
\(201\) 3.41421 5.91359i 0.240820 0.417113i
\(202\) 1.58579 2.74666i 0.111576 0.193255i
\(203\) −5.65685 −0.397033
\(204\) 7.00000 12.1244i 0.490098 0.848875i
\(205\) 7.31371 + 12.6677i 0.510812 + 0.884752i
\(206\) 0.485281 + 0.840532i 0.0338112 + 0.0585626i
\(207\) −4.00000 −0.278019
\(208\) 0 0
\(209\) 5.65685 0.391293
\(210\) −1.65685 2.86976i −0.114334 0.198032i
\(211\) 6.00000 + 10.3923i 0.413057 + 0.715436i 0.995222 0.0976347i \(-0.0311277\pi\)
−0.582165 + 0.813070i \(0.697794\pi\)
\(212\) −1.82843 + 3.16693i −0.125577 + 0.217506i
\(213\) −2.00000 −0.137038
\(214\) −2.34315 + 4.05845i −0.160174 + 0.277430i
\(215\) 2.34315 4.05845i 0.159801 0.276784i
\(216\) 1.58579 0.107899
\(217\) 1.65685 2.86976i 0.112475 0.194812i
\(218\) −1.10051 1.90613i −0.0745356 0.129099i
\(219\) 0.171573 + 0.297173i 0.0115938 + 0.0200811i
\(220\) −10.3431 −0.697335
\(221\) 0 0
\(222\) −3.17157 −0.212862
\(223\) −6.24264 10.8126i −0.418038 0.724063i 0.577704 0.816246i \(-0.303949\pi\)
−0.995742 + 0.0921831i \(0.970615\pi\)
\(224\) −6.24264 10.8126i −0.417104 0.722445i
\(225\) −1.50000 + 2.59808i −0.100000 + 0.173205i
\(226\) 2.20101 0.146409
\(227\) −8.65685 + 14.9941i −0.574576 + 0.995194i 0.421512 + 0.906823i \(0.361500\pi\)
−0.996088 + 0.0883713i \(0.971834\pi\)
\(228\) 2.58579 4.47871i 0.171248 0.296610i
\(229\) 1.31371 0.0868123 0.0434062 0.999058i \(-0.486179\pi\)
0.0434062 + 0.999058i \(0.486179\pi\)
\(230\) −2.34315 + 4.05845i −0.154502 + 0.267606i
\(231\) 2.82843 + 4.89898i 0.186097 + 0.322329i
\(232\) −1.58579 2.74666i −0.104112 0.180327i
\(233\) 6.97056 0.456657 0.228328 0.973584i \(-0.426674\pi\)
0.228328 + 0.973584i \(0.426674\pi\)
\(234\) 0 0
\(235\) 32.9706 2.15076
\(236\) −7.00000 12.1244i −0.455661 0.789228i
\(237\) 5.65685 + 9.79796i 0.367452 + 0.636446i
\(238\) −4.48528 + 7.76874i −0.290738 + 0.503572i
\(239\) −2.00000 −0.129369 −0.0646846 0.997906i \(-0.520604\pi\)
−0.0646846 + 0.997906i \(0.520604\pi\)
\(240\) −4.24264 + 7.34847i −0.273861 + 0.474342i
\(241\) 0.171573 0.297173i 0.0110520 0.0191426i −0.860447 0.509541i \(-0.829815\pi\)
0.871499 + 0.490398i \(0.163149\pi\)
\(242\) 2.89949 0.186387
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) 12.1716 + 21.0818i 0.779205 + 1.34962i
\(245\) −1.41421 2.44949i −0.0903508 0.156492i
\(246\) 2.14214 0.136578
\(247\) 0 0
\(248\) 1.85786 0.117975
\(249\) 1.82843 + 3.16693i 0.115872 + 0.200696i
\(250\) −1.17157 2.02922i −0.0740968 0.128339i
\(251\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(252\) 5.17157 0.325778
\(253\) 4.00000 6.92820i 0.251478 0.435572i
\(254\) 1.17157 2.02922i 0.0735110 0.127325i
\(255\) 21.6569 1.35620
\(256\) −1.98528 + 3.43861i −0.124080 + 0.214913i
\(257\) 2.17157 + 3.76127i 0.135459 + 0.234622i 0.925773 0.378081i \(-0.123416\pi\)
−0.790314 + 0.612702i \(0.790082\pi\)
\(258\) −0.343146 0.594346i −0.0213633 0.0370024i
\(259\) −21.6569 −1.34569
\(260\) 0 0
\(261\) 2.00000 0.123797
\(262\) −1.65685 2.86976i −0.102361 0.177294i
\(263\) −6.00000 10.3923i −0.369976 0.640817i 0.619586 0.784929i \(-0.287301\pi\)
−0.989561 + 0.144112i \(0.953967\pi\)
\(264\) −1.58579 + 2.74666i −0.0975984 + 0.169045i
\(265\) −5.65685 −0.347498
\(266\) −1.65685 + 2.86976i −0.101588 + 0.175956i
\(267\) 7.41421 12.8418i 0.453743 0.785905i
\(268\) 12.4853 0.762660
\(269\) −9.00000 + 15.5885i −0.548740 + 0.950445i 0.449622 + 0.893219i \(0.351559\pi\)
−0.998361 + 0.0572259i \(0.981774\pi\)
\(270\) 0.585786 + 1.01461i 0.0356498 + 0.0617473i
\(271\) −13.8995 24.0746i −0.844334 1.46243i −0.886198 0.463306i \(-0.846663\pi\)
0.0418640 0.999123i \(-0.486670\pi\)
\(272\) 22.9706 1.39279
\(273\) 0 0
\(274\) −4.48528 −0.270966
\(275\) −3.00000 5.19615i −0.180907 0.313340i
\(276\) −3.65685 6.33386i −0.220117 0.381253i
\(277\) 1.00000 1.73205i 0.0600842 0.104069i −0.834419 0.551131i \(-0.814196\pi\)
0.894503 + 0.447062i \(0.147530\pi\)
\(278\) 3.02944 0.181694
\(279\) −0.585786 + 1.01461i −0.0350701 + 0.0607432i
\(280\) 6.34315 10.9867i 0.379075 0.656578i
\(281\) −21.1716 −1.26299 −0.631495 0.775380i \(-0.717558\pi\)
−0.631495 + 0.775380i \(0.717558\pi\)
\(282\) 2.41421 4.18154i 0.143764 0.249007i
\(283\) −14.4853 25.0892i −0.861061 1.49140i −0.870906 0.491449i \(-0.836467\pi\)
0.00984565 0.999952i \(-0.496866\pi\)
\(284\) −1.82843 3.16693i −0.108497 0.187923i
\(285\) 8.00000 0.473879
\(286\) 0 0
\(287\) 14.6274 0.863429
\(288\) 2.20711 + 3.82282i 0.130055 + 0.225262i
\(289\) −20.8137 36.0504i −1.22434 2.12061i
\(290\) 1.17157 2.02922i 0.0687971 0.119160i
\(291\) −3.65685 −0.214369
\(292\) −0.313708 + 0.543359i −0.0183584 + 0.0317977i
\(293\) 1.07107 1.85514i 0.0625724 0.108379i −0.833042 0.553210i \(-0.813403\pi\)
0.895615 + 0.444831i \(0.146736\pi\)
\(294\) −0.414214 −0.0241574
\(295\) 10.8284 18.7554i 0.630455 1.09198i
\(296\) −6.07107 10.5154i −0.352874 0.611195i
\(297\) −1.00000 1.73205i −0.0580259 0.100504i
\(298\) −3.79899 −0.220070
\(299\) 0 0
\(300\) −5.48528 −0.316693
\(301\) −2.34315 4.05845i −0.135057 0.233925i
\(302\) 0.727922 + 1.26080i 0.0418872 + 0.0725508i
\(303\) −3.82843 + 6.63103i −0.219937 + 0.380943i
\(304\) 8.48528 0.486664
\(305\) −18.8284 + 32.6118i −1.07811 + 1.86735i
\(306\) 1.58579 2.74666i 0.0906534 0.157016i
\(307\) 22.8284 1.30289 0.651444 0.758697i \(-0.274164\pi\)
0.651444 + 0.758697i \(0.274164\pi\)
\(308\) −5.17157 + 8.95743i −0.294678 + 0.510397i
\(309\) −1.17157 2.02922i −0.0666485 0.115439i
\(310\) 0.686292 + 1.18869i 0.0389787 + 0.0675132i
\(311\) −10.6274 −0.602626 −0.301313 0.953525i \(-0.597425\pi\)
−0.301313 + 0.953525i \(0.597425\pi\)
\(312\) 0 0
\(313\) 6.00000 0.339140 0.169570 0.985518i \(-0.445762\pi\)
0.169570 + 0.985518i \(0.445762\pi\)
\(314\) −2.07107 3.58719i −0.116877 0.202437i
\(315\) 4.00000 + 6.92820i 0.225374 + 0.390360i
\(316\) −10.3431 + 17.9149i −0.581847 + 1.00779i
\(317\) −8.48528 −0.476581 −0.238290 0.971194i \(-0.576587\pi\)
−0.238290 + 0.971194i \(0.576587\pi\)
\(318\) −0.414214 + 0.717439i −0.0232279 + 0.0402320i
\(319\) −2.00000 + 3.46410i −0.111979 + 0.193952i
\(320\) −11.7990 −0.659584
\(321\) 5.65685 9.79796i 0.315735 0.546869i
\(322\) 2.34315 + 4.05845i 0.130578 + 0.226168i
\(323\) −10.8284 18.7554i −0.602510 1.04358i
\(324\) −1.82843 −0.101579
\(325\) 0 0
\(326\) 7.79899 0.431946
\(327\) 2.65685 + 4.60181i 0.146924 + 0.254480i
\(328\) 4.10051 + 7.10228i 0.226413 + 0.392158i
\(329\) 16.4853 28.5533i 0.908863 1.57420i
\(330\) −2.34315 −0.128986
\(331\) 13.0711 22.6398i 0.718451 1.24439i −0.243163 0.969986i \(-0.578185\pi\)
0.961613 0.274408i \(-0.0884818\pi\)
\(332\) −3.34315 + 5.79050i −0.183479 + 0.317795i
\(333\) 7.65685 0.419593
\(334\) 0.757359 1.31178i 0.0414409 0.0717777i
\(335\) 9.65685 + 16.7262i 0.527610 + 0.913848i
\(336\) 4.24264 + 7.34847i 0.231455 + 0.400892i
\(337\) 9.31371 0.507350 0.253675 0.967290i \(-0.418361\pi\)
0.253675 + 0.967290i \(0.418361\pi\)
\(338\) 0 0
\(339\) −5.31371 −0.288601
\(340\) 19.7990 + 34.2929i 1.07375 + 1.85979i
\(341\) −1.17157 2.02922i −0.0634442 0.109889i
\(342\) 0.585786 1.01461i 0.0316757 0.0548639i
\(343\) 16.9706 0.916324
\(344\) 1.31371 2.27541i 0.0708304 0.122682i
\(345\) 5.65685 9.79796i 0.304555 0.527504i
\(346\) 4.82843 0.259578
\(347\) 4.34315 7.52255i 0.233152 0.403832i −0.725582 0.688136i \(-0.758429\pi\)
0.958734 + 0.284304i \(0.0917626\pi\)
\(348\) 1.82843 + 3.16693i 0.0980140 + 0.169765i
\(349\) 1.82843 + 3.16693i 0.0978735 + 0.169522i 0.910804 0.412839i \(-0.135463\pi\)
−0.812931 + 0.582360i \(0.802129\pi\)
\(350\) 3.51472 0.187870
\(351\) 0 0
\(352\) −8.82843 −0.470557
\(353\) −16.7279 28.9736i −0.890337 1.54211i −0.839471 0.543404i \(-0.817135\pi\)
−0.0508663 0.998705i \(-0.516198\pi\)
\(354\) −1.58579 2.74666i −0.0842836 0.145983i
\(355\) 2.82843 4.89898i 0.150117 0.260011i
\(356\) 27.1127 1.43697
\(357\) 10.8284 18.7554i 0.573101 0.992640i
\(358\) −4.82843 + 8.36308i −0.255190 + 0.442003i
\(359\) −34.9706 −1.84568 −0.922838 0.385189i \(-0.874136\pi\)
−0.922838 + 0.385189i \(0.874136\pi\)
\(360\) −2.24264 + 3.88437i −0.118198 + 0.204724i
\(361\) 5.50000 + 9.52628i 0.289474 + 0.501383i
\(362\) 2.89949 + 5.02207i 0.152394 + 0.263954i
\(363\) −7.00000 −0.367405
\(364\) 0 0
\(365\) −0.970563 −0.0508016
\(366\) 2.75736 + 4.77589i 0.144129 + 0.249640i
\(367\) 12.0000 + 20.7846i 0.626395 + 1.08495i 0.988269 + 0.152721i \(0.0488036\pi\)
−0.361874 + 0.932227i \(0.617863\pi\)
\(368\) 6.00000 10.3923i 0.312772 0.541736i
\(369\) −5.17157 −0.269221
\(370\) 4.48528 7.76874i 0.233179 0.403877i
\(371\) −2.82843 + 4.89898i −0.146845 + 0.254342i
\(372\) −2.14214 −0.111065
\(373\) −5.00000 + 8.66025i −0.258890 + 0.448411i −0.965945 0.258748i \(-0.916690\pi\)
0.707055 + 0.707159i \(0.250023\pi\)
\(374\) 3.17157 + 5.49333i 0.163998 + 0.284053i
\(375\) 2.82843 + 4.89898i 0.146059 + 0.252982i
\(376\) 18.4853 0.953306
\(377\) 0 0
\(378\) 1.17157 0.0602592
\(379\) 0.242641 + 0.420266i 0.0124636 + 0.0215876i 0.872190 0.489167i \(-0.162699\pi\)
−0.859726 + 0.510755i \(0.829366\pi\)
\(380\) 7.31371 + 12.6677i 0.375185 + 0.649840i
\(381\) −2.82843 + 4.89898i −0.144905 + 0.250982i
\(382\) −1.37258 −0.0702275
\(383\) 15.4853 26.8213i 0.791261 1.37050i −0.133926 0.990991i \(-0.542758\pi\)
0.925187 0.379513i \(-0.123908\pi\)
\(384\) −5.27817 + 9.14207i −0.269351 + 0.466529i
\(385\) −16.0000 −0.815436
\(386\) −1.10051 + 1.90613i −0.0560142 + 0.0970195i
\(387\) 0.828427 + 1.43488i 0.0421113 + 0.0729389i
\(388\) −3.34315 5.79050i −0.169723 0.293968i
\(389\) −26.9706 −1.36746 −0.683731 0.729734i \(-0.739644\pi\)
−0.683731 + 0.729734i \(0.739644\pi\)
\(390\) 0 0
\(391\) −30.6274 −1.54890
\(392\) −0.792893 1.37333i −0.0400472 0.0693637i
\(393\) 4.00000 + 6.92820i 0.201773 + 0.349482i
\(394\) −0.100505 + 0.174080i −0.00506337 + 0.00877002i
\(395\) −32.0000 −1.61009
\(396\) 1.82843 3.16693i 0.0918819 0.159144i
\(397\) 15.4853 26.8213i 0.777184 1.34612i −0.156375 0.987698i \(-0.549981\pi\)
0.933559 0.358424i \(-0.116686\pi\)
\(398\) −8.97056 −0.449654
\(399\) 4.00000 6.92820i 0.200250 0.346844i
\(400\) −4.50000 7.79423i −0.225000 0.389711i
\(401\) 13.0711 + 22.6398i 0.652738 + 1.13058i 0.982456 + 0.186496i \(0.0597131\pi\)
−0.329718 + 0.944080i \(0.606954\pi\)
\(402\) 2.82843 0.141069
\(403\) 0 0
\(404\) −14.0000 −0.696526
\(405\) −1.41421 2.44949i −0.0702728 0.121716i
\(406\) −1.17157 2.02922i −0.0581442 0.100709i
\(407\) −7.65685 + 13.2621i −0.379536 + 0.657376i
\(408\) 12.1421 0.601125
\(409\) −17.4853 + 30.2854i −0.864592 + 1.49752i 0.00286068 + 0.999996i \(0.499089\pi\)
−0.867452 + 0.497521i \(0.834244\pi\)
\(410\) −3.02944 + 5.24714i −0.149613 + 0.259138i
\(411\) 10.8284 0.534127
\(412\) 2.14214 3.71029i 0.105535 0.182793i
\(413\) −10.8284 18.7554i −0.532832 0.922892i
\(414\) −0.828427 1.43488i −0.0407150 0.0705204i
\(415\) −10.3431 −0.507725
\(416\) 0 0
\(417\) −7.31371 −0.358154
\(418\) 1.17157 + 2.02922i 0.0573035 + 0.0992526i
\(419\) −7.31371 12.6677i −0.357298 0.618858i 0.630210 0.776424i \(-0.282969\pi\)
−0.987508 + 0.157566i \(0.949635\pi\)
\(420\) −7.31371 + 12.6677i −0.356872 + 0.618121i
\(421\) −37.3137 −1.81856 −0.909279 0.416186i \(-0.863366\pi\)
−0.909279 + 0.416186i \(0.863366\pi\)
\(422\) −2.48528 + 4.30463i −0.120982 + 0.209546i
\(423\) −5.82843 + 10.0951i −0.283388 + 0.490842i
\(424\) −3.17157 −0.154025
\(425\) −11.4853 + 19.8931i −0.557118 + 0.964957i
\(426\) −0.414214 0.717439i −0.0200687 0.0347600i
\(427\) 18.8284 + 32.6118i 0.911171 + 1.57820i
\(428\) 20.6863 0.999910
\(429\) 0 0
\(430\) 1.94113 0.0936094
\(431\) 4.17157 + 7.22538i 0.200938 + 0.348034i 0.948831 0.315785i \(-0.102268\pi\)
−0.747893 + 0.663819i \(0.768934\pi\)
\(432\) −1.50000 2.59808i −0.0721688 0.125000i
\(433\) 10.6569 18.4582i 0.512136 0.887045i −0.487765 0.872975i \(-0.662188\pi\)
0.999901 0.0140703i \(-0.00447886\pi\)
\(434\) 1.37258 0.0658861
\(435\) −2.82843 + 4.89898i −0.135613 + 0.234888i
\(436\) −4.85786 + 8.41407i −0.232650 + 0.402961i
\(437\) −11.3137 −0.541208
\(438\) −0.0710678 + 0.123093i −0.00339575 + 0.00588161i
\(439\) −8.48528 14.6969i −0.404980 0.701447i 0.589339 0.807886i \(-0.299388\pi\)
−0.994319 + 0.106439i \(0.966055\pi\)
\(440\) −4.48528 7.76874i −0.213827 0.370360i
\(441\) 1.00000 0.0476190
\(442\) 0 0
\(443\) −25.9411 −1.23250 −0.616250 0.787551i \(-0.711349\pi\)
−0.616250 + 0.787551i \(0.711349\pi\)
\(444\) 7.00000 + 12.1244i 0.332205 + 0.575396i
\(445\) 20.9706 + 36.3221i 0.994100 + 1.72183i
\(446\) 2.58579 4.47871i 0.122441 0.212073i
\(447\) 9.17157 0.433801
\(448\) −5.89949 + 10.2182i −0.278725 + 0.482766i
\(449\) −15.8995 + 27.5387i −0.750344 + 1.29963i 0.197313 + 0.980341i \(0.436779\pi\)
−0.947656 + 0.319293i \(0.896555\pi\)
\(450\) −1.24264 −0.0585786
\(451\) 5.17157 8.95743i 0.243520 0.421789i
\(452\) −4.85786 8.41407i −0.228495 0.395764i
\(453\) −1.75736 3.04384i −0.0825679 0.143012i
\(454\) −7.17157 −0.336579
\(455\) 0 0
\(456\) 4.48528 0.210043
\(457\) −3.82843 6.63103i −0.179086 0.310187i 0.762482 0.647010i \(-0.223981\pi\)
−0.941568 + 0.336823i \(0.890647\pi\)
\(458\) 0.272078 + 0.471253i 0.0127134 + 0.0220202i
\(459\) −3.82843 + 6.63103i −0.178696 + 0.309510i
\(460\) 20.6863 0.964503
\(461\) 2.58579 4.47871i 0.120432 0.208594i −0.799506 0.600658i \(-0.794905\pi\)
0.919938 + 0.392064i \(0.128239\pi\)
\(462\) −1.17157 + 2.02922i −0.0545065 + 0.0944080i
\(463\) 24.4853 1.13793 0.568964 0.822363i \(-0.307344\pi\)
0.568964 + 0.822363i \(0.307344\pi\)
\(464\) −3.00000 + 5.19615i −0.139272 + 0.241225i
\(465\) −1.65685 2.86976i −0.0768348 0.133082i
\(466\) 1.44365 + 2.50048i 0.0668758 + 0.115832i
\(467\) −8.00000 −0.370196 −0.185098 0.982720i \(-0.559260\pi\)
−0.185098 + 0.982720i \(0.559260\pi\)
\(468\) 0 0
\(469\) 19.3137 0.891824
\(470\) 6.82843 + 11.8272i 0.314972 + 0.545547i
\(471\) 5.00000 + 8.66025i 0.230388 + 0.399043i
\(472\) 6.07107 10.5154i 0.279444 0.484010i
\(473\) −3.31371 −0.152364
\(474\) −2.34315 + 4.05845i −0.107624 + 0.186411i
\(475\) −4.24264 + 7.34847i −0.194666 + 0.337171i
\(476\) 39.5980 1.81497
\(477\) 1.00000 1.73205i 0.0457869 0.0793052i
\(478\) −0.414214 0.717439i −0.0189457 0.0328149i
\(479\) 12.6569 + 21.9223i 0.578306 + 1.00166i 0.995674 + 0.0929182i \(0.0296195\pi\)
−0.417367 + 0.908738i \(0.637047\pi\)
\(480\) −12.4853 −0.569873
\(481\) 0 0
\(482\) 0.142136 0.00647410
\(483\) −5.65685 9.79796i −0.257396 0.445823i
\(484\) −6.39949 11.0843i −0.290886 0.503830i
\(485\) 5.17157 8.95743i 0.234829 0.406736i
\(486\) −0.414214 −0.0187891
\(487\) −3.89949 + 6.75412i −0.176703 + 0.306059i −0.940749 0.339103i \(-0.889877\pi\)
0.764046 + 0.645161i \(0.223210\pi\)
\(488\) −10.5563 + 18.2841i −0.477863 + 0.827684i
\(489\) −18.8284 −0.851451
\(490\) 0.585786 1.01461i 0.0264631 0.0458355i
\(491\) −15.3137 26.5241i −0.691098 1.19702i −0.971478 0.237128i \(-0.923794\pi\)
0.280380 0.959889i \(-0.409539\pi\)
\(492\) −4.72792 8.18900i −0.213151 0.369189i
\(493\) 15.3137 0.689695
\(494\) 0 0
\(495\) 5.65685 0.254257
\(496\) −1.75736 3.04384i −0.0789078 0.136672i
\(497\) −2.82843 4.89898i −0.126872 0.219749i
\(498\) −0.757359 + 1.31178i −0.0339381 + 0.0587825i
\(499\) −26.1421 −1.17028 −0.585141 0.810931i \(-0.698961\pi\)
−0.585141 + 0.810931i \(0.698961\pi\)
\(500\) −5.17157 + 8.95743i −0.231280 + 0.400588i
\(501\) −1.82843 + 3.16693i −0.0816881 + 0.141488i
\(502\) 0 0
\(503\) 3.65685 6.33386i 0.163051 0.282413i −0.772910 0.634515i \(-0.781200\pi\)
0.935961 + 0.352102i \(0.114533\pi\)
\(504\) 2.24264 + 3.88437i 0.0998952 + 0.173023i
\(505\) −10.8284 18.7554i −0.481859 0.834604i
\(506\) 3.31371 0.147312
\(507\) 0 0
\(508\) −10.3431 −0.458903
\(509\) 5.89949 + 10.2182i 0.261491 + 0.452915i 0.966638 0.256146i \(-0.0824527\pi\)
−0.705148 + 0.709060i \(0.749119\pi\)
\(510\) 4.48528 + 7.76874i 0.198612 + 0.344005i
\(511\) −0.485281 + 0.840532i −0.0214676 + 0.0371829i
\(512\) −22.7574 −1.00574
\(513\) −1.41421 + 2.44949i −0.0624391 + 0.108148i
\(514\) −0.899495 + 1.55797i −0.0396750 + 0.0687192i
\(515\) 6.62742 0.292039
\(516\) −1.51472 + 2.62357i −0.0666818 + 0.115496i
\(517\) −11.6569 20.1903i −0.512668 0.887967i
\(518\) −4.48528 7.76874i −0.197072 0.341339i
\(519\) −11.6569 −0.511679
\(520\) 0 0
\(521\) 25.3137 1.10901 0.554507 0.832179i \(-0.312907\pi\)
0.554507 + 0.832179i \(0.312907\pi\)
\(522\) 0.414214 + 0.717439i 0.0181296 + 0.0314014i
\(523\) 7.65685 + 13.2621i 0.334811 + 0.579909i 0.983448 0.181188i \(-0.0579942\pi\)
−0.648638 + 0.761097i \(0.724661\pi\)
\(524\) −7.31371 + 12.6677i −0.319501 + 0.553392i
\(525\) −8.48528 −0.370328
\(526\) 2.48528 4.30463i 0.108363 0.187691i
\(527\) −4.48528 + 7.76874i −0.195382 + 0.338411i
\(528\) 6.00000 0.261116
\(529\) 3.50000 6.06218i 0.152174 0.263573i
\(530\) −1.17157 2.02922i −0.0508899 0.0881438i
\(531\) 3.82843 + 6.63103i 0.166140 + 0.287762i
\(532\) 14.6274 0.634179
\(533\) 0 0
\(534\) 6.14214 0.265796
\(535\) 16.0000 + 27.7128i 0.691740 + 1.19813i
\(536\) 5.41421 + 9.37769i 0.233858 + 0.405055i
\(537\) 11.6569 20.1903i 0.503030 0.871274i
\(538\) −7.45584 −0.321444
\(539\) −1.00000 + 1.73205i −0.0430730 + 0.0746047i
\(540\) 2.58579 4.47871i 0.111275 0.192733i
\(541\) −10.0000 −0.429934 −0.214967 0.976621i \(-0.568964\pi\)
−0.214967 + 0.976621i \(0.568964\pi\)
\(542\) 5.75736 9.97204i 0.247300 0.428336i
\(543\) −7.00000 12.1244i −0.300399 0.520306i
\(544\) 16.8995 + 29.2708i 0.724560 + 1.25497i
\(545\) −15.0294 −0.643790
\(546\) 0 0
\(547\) 23.3137 0.996822 0.498411 0.866941i \(-0.333917\pi\)
0.498411 + 0.866941i \(0.333917\pi\)
\(548\) 9.89949 + 17.1464i 0.422885 + 0.732459i
\(549\) −6.65685 11.5300i −0.284108 0.492089i
\(550\) 1.24264 2.15232i 0.0529864 0.0917751i
\(551\) 5.65685 0.240990
\(552\) 3.17157 5.49333i 0.134991 0.233811i
\(553\) −16.0000 + 27.7128i −0.680389 + 1.17847i
\(554\) 0.828427 0.0351965
\(555\) −10.8284 + 18.7554i −0.459641 + 0.796122i
\(556\) −6.68629 11.5810i −0.283562 0.491144i
\(557\) −3.89949 6.75412i −0.165227 0.286181i 0.771509 0.636218i \(-0.219502\pi\)
−0.936736 + 0.350037i \(0.886169\pi\)
\(558\) −0.485281 −0.0205436
\(559\) 0 0
\(560\) −24.0000 −1.01419
\(561\) −7.65685 13.2621i −0.323273 0.559925i
\(562\) −4.38478 7.59466i −0.184961 0.320361i
\(563\) −2.00000 + 3.46410i −0.0842900 + 0.145994i −0.905088 0.425223i \(-0.860196\pi\)
0.820798 + 0.571218i \(0.193529\pi\)
\(564\) −21.3137 −0.897469
\(565\) 7.51472 13.0159i 0.316147 0.547582i
\(566\) 6.00000 10.3923i 0.252199 0.436821i
\(567\) −2.82843 −0.118783
\(568\) 1.58579 2.74666i 0.0665381 0.115247i
\(569\) 21.4853 + 37.2136i 0.900710 + 1.56008i 0.826575 + 0.562827i \(0.190286\pi\)
0.0741351 + 0.997248i \(0.476380\pi\)
\(570\) 1.65685 + 2.86976i 0.0693980 + 0.120201i
\(571\) −12.9706 −0.542801 −0.271401 0.962466i \(-0.587487\pi\)
−0.271401 + 0.962466i \(0.587487\pi\)
\(572\) 0 0
\(573\) 3.31371 0.138432
\(574\) 3.02944 + 5.24714i 0.126446 + 0.219011i
\(575\) 6.00000 + 10.3923i 0.250217 + 0.433389i
\(576\) 2.08579 3.61269i 0.0869078 0.150529i
\(577\) 31.9411 1.32973 0.664863 0.746965i \(-0.268490\pi\)
0.664863 + 0.746965i \(0.268490\pi\)
\(578\) 8.62132 14.9326i 0.358600 0.621113i
\(579\) 2.65685 4.60181i 0.110415 0.191245i
\(580\) −10.3431 −0.429476
\(581\) −5.17157 + 8.95743i −0.214553 + 0.371617i
\(582\) −0.757359 1.31178i −0.0313936 0.0543752i
\(583\) 2.00000 + 3.46410i 0.0828315 + 0.143468i
\(584\) −0.544156 −0.0225173
\(585\) 0 0
\(586\) 0.887302 0.0366541
\(587\) −5.48528 9.50079i −0.226402 0.392139i 0.730337 0.683087i \(-0.239363\pi\)
−0.956739 + 0.290947i \(0.906030\pi\)
\(588\) 0.914214 + 1.58346i 0.0377015 + 0.0653010i
\(589\) −1.65685 + 2.86976i −0.0682695 + 0.118246i
\(590\) 8.97056 0.369312
\(591\) 0.242641 0.420266i 0.00998090 0.0172874i
\(592\) −11.4853 + 19.8931i −0.472042 + 0.817601i
\(593\) 20.4853 0.841230 0.420615 0.907239i \(-0.361814\pi\)
0.420615 + 0.907239i \(0.361814\pi\)
\(594\) 0.414214 0.717439i 0.0169954 0.0294369i
\(595\) 30.6274 + 53.0482i 1.25560 + 2.17477i
\(596\) 8.38478 + 14.5229i 0.343454 + 0.594879i
\(597\) 21.6569 0.886356
\(598\) 0 0
\(599\) −23.3137 −0.952572 −0.476286 0.879290i \(-0.658017\pi\)
−0.476286 + 0.879290i \(0.658017\pi\)
\(600\) −2.37868 4.11999i −0.0971092 0.168198i
\(601\) 0.313708 + 0.543359i 0.0127964 + 0.0221641i 0.872353 0.488877i \(-0.162593\pi\)
−0.859556 + 0.511041i \(0.829260\pi\)
\(602\) 0.970563 1.68106i 0.0395572 0.0685151i
\(603\) −6.82843 −0.278075
\(604\) 3.21320 5.56543i 0.130743 0.226454i
\(605\) 9.89949 17.1464i 0.402472 0.697101i
\(606\) −3.17157 −0.128836
\(607\) −20.9706 + 36.3221i −0.851169 + 1.47427i 0.0289853 + 0.999580i \(0.490772\pi\)
−0.880154 + 0.474688i \(0.842561\pi\)
\(608\) 6.24264 + 10.8126i 0.253173 + 0.438508i
\(609\) 2.82843 + 4.89898i 0.114614 + 0.198517i
\(610\) −15.5980 −0.631544
\(611\) 0 0
\(612\) −14.0000 −0.565916
\(613\) −23.8284 41.2720i −0.962421 1.66696i −0.716390 0.697700i \(-0.754207\pi\)
−0.246031 0.969262i \(-0.579127\pi\)
\(614\) 4.72792 + 8.18900i 0.190803 + 0.330481i
\(615\) 7.31371 12.6677i 0.294917 0.510812i
\(616\) −8.97056 −0.361434
\(617\) −17.4142 + 30.1623i −0.701070 + 1.21429i 0.267021 + 0.963691i \(0.413961\pi\)
−0.968091 + 0.250598i \(0.919373\pi\)
\(618\) 0.485281 0.840532i 0.0195209 0.0338112i
\(619\) −23.7990 −0.956562 −0.478281 0.878207i \(-0.658740\pi\)
−0.478281 + 0.878207i \(0.658740\pi\)
\(620\) 3.02944 5.24714i 0.121665 0.210730i
\(621\) 2.00000 + 3.46410i 0.0802572 + 0.139010i
\(622\) −2.20101 3.81226i −0.0882525 0.152858i
\(623\) 41.9411 1.68034
\(624\) 0 0
\(625\) −31.0000 −1.24000
\(626\) 1.24264 + 2.15232i 0.0496659 + 0.0860239i
\(627\) −2.82843 4.89898i −0.112956 0.195646i
\(628\) −9.14214 + 15.8346i −0.364811 + 0.631871i
\(629\) 58.6274 2.33763
\(630\) −1.65685 + 2.86976i −0.0660107 + 0.114334i
\(631\) 21.5563 37.3367i 0.858145 1.48635i −0.0155519 0.999879i \(-0.504951\pi\)
0.873697 0.486471i \(-0.161716\pi\)
\(632\) −17.9411 −0.713660
\(633\) 6.00000 10.3923i 0.238479 0.413057i
\(634\) −1.75736 3.04384i −0.0697937 0.120886i
\(635\) −8.00000 13.8564i −0.317470 0.549875i
\(636\) 3.65685 0.145004
\(637\) 0 0
\(638\) −1.65685 −0.0655955
\(639\) 1.00000 + 1.73205i 0.0395594 + 0.0685189i
\(640\) −14.9289 25.8577i −0.590118 1.02211i
\(641\) −15.1421 + 26.2269i −0.598078 + 1.03590i 0.395026 + 0.918670i \(0.370736\pi\)
−0.993105 + 0.117232i \(0.962598\pi\)
\(642\) 4.68629 0.184953
\(643\) 11.4142 19.7700i 0.450133 0.779653i −0.548261 0.836307i \(-0.684710\pi\)
0.998394 + 0.0566545i \(0.0180434\pi\)
\(644\) 10.3431 17.9149i 0.407577 0.705944i
\(645\) −4.68629 −0.184523
\(646\) 4.48528 7.76874i 0.176471 0.305657i
\(647\) −5.65685 9.79796i −0.222394 0.385198i 0.733140 0.680077i \(-0.238054\pi\)
−0.955534 + 0.294880i \(0.904720\pi\)
\(648\) −0.792893 1.37333i −0.0311478 0.0539496i
\(649\) −15.3137 −0.601116
\(650\) 0 0
\(651\) −3.31371 −0.129874
\(652\) −17.2132 29.8141i −0.674121 1.16761i
\(653\) 12.6569 + 21.9223i 0.495301 + 0.857886i 0.999985 0.00541749i \(-0.00172445\pi\)
−0.504684 + 0.863304i \(0.668391\pi\)
\(654\) −1.10051 + 1.90613i −0.0430332 + 0.0745356i
\(655\) −22.6274 −0.884126
\(656\) 7.75736 13.4361i 0.302874 0.524593i
\(657\) 0.171573 0.297173i 0.00669370 0.0115938i
\(658\) 13.6569 0.532400
\(659\) 23.6569 40.9749i 0.921540 1.59615i 0.124507 0.992219i \(-0.460265\pi\)
0.797033 0.603936i \(-0.206402\pi\)
\(660\) 5.17157 + 8.95743i 0.201303 + 0.348667i
\(661\) −17.4853 30.2854i −0.680099 1.17797i −0.974950 0.222422i \(-0.928604\pi\)
0.294852 0.955543i \(-0.404730\pi\)
\(662\) 10.8284 0.420859
\(663\) 0 0
\(664\) −5.79899 −0.225044
\(665\) 11.3137 + 19.5959i 0.438727 + 0.759897i
\(666\) 1.58579 + 2.74666i 0.0614480 + 0.106431i
\(667\) 4.00000 6.92820i 0.154881 0.268261i
\(668\) −6.68629 −0.258700
\(669\) −6.24264 + 10.8126i −0.241354 + 0.418038i
\(670\) −4.00000 + 6.92820i −0.154533 + 0.267660i
\(671\) 26.6274 1.02794
\(672\) −6.24264 + 10.8126i −0.240815 + 0.417104i
\(673\) −8.31371 14.3998i −0.320470 0.555070i 0.660115 0.751164i \(-0.270507\pi\)
−0.980585 + 0.196094i \(0.937174\pi\)
\(674\) 1.92893 + 3.34101i 0.0742997 + 0.128691i
\(675\) 3.00000 0.115470
\(676\) 0 0
\(677\) 26.6863 1.02564 0.512819 0.858497i \(-0.328601\pi\)
0.512819 + 0.858497i \(0.328601\pi\)
\(678\) −1.10051 1.90613i −0.0422646 0.0732045i
\(679\) −5.17157 8.95743i −0.198467 0.343754i
\(680\) −17.1716 + 29.7420i −0.658500 + 1.14056i
\(681\) 17.3137 0.663463
\(682\) 0.485281 0.840532i 0.0185824 0.0321856i
\(683\) 23.9706 41.5182i 0.917208 1.58865i 0.113572 0.993530i \(-0.463771\pi\)
0.803636 0.595121i \(-0.202896\pi\)
\(684\) −5.17157 −0.197740
\(685\) −15.3137 + 26.5241i −0.585107 + 1.01343i
\(686\) 3.51472 + 6.08767i 0.134193 + 0.232428i
\(687\) −0.656854 1.13770i −0.0250606 0.0434062i
\(688\) −4.97056 −0.189501
\(689\) 0 0
\(690\) 4.68629 0.178404
\(691\) −2.92893 5.07306i −0.111422 0.192988i 0.804922 0.593381i \(-0.202207\pi\)
−0.916344 + 0.400392i \(0.868874\pi\)
\(692\) −10.6569 18.4582i −0.405113 0.701676i
\(693\) 2.82843 4.89898i 0.107443 0.186097i
\(694\) 3.59798 0.136577
\(695\) 10.3431 17.9149i 0.392338 0.679549i
\(696\) −1.58579 + 2.74666i −0.0601091 + 0.104112i
\(697\) −39.5980 −1.49988
\(698\) −0.757359 + 1.31178i −0.0286665 + 0.0496518i
\(699\) −3.48528 6.03668i −0.131825 0.228328i
\(700\) −7.75736 13.4361i −0.293201 0.507838i
\(701\) 5.02944 0.189959 0.0949796 0.995479i \(-0.469721\pi\)
0.0949796 + 0.995479i \(0.469721\pi\)
\(702\) 0 0
\(703\) 21.6569 0.816804
\(704\) 4.17157 + 7.22538i 0.157222 + 0.272317i
\(705\) −16.4853 28.5533i −0.620872 1.07538i
\(706\) 6.92893 12.0013i 0.260774 0.451673i
\(707\) −21.6569 −0.814490
\(708\) −7.00000 + 12.1244i −0.263076 + 0.455661i
\(709\) −2.31371 + 4.00746i −0.0868931 + 0.150503i −0.906196 0.422857i \(-0.861027\pi\)
0.819303 + 0.573360i \(0.194361\pi\)
\(710\) 2.34315 0.0879367
\(711\) 5.65685 9.79796i 0.212149 0.367452i
\(712\) 11.7574 + 20.3643i 0.440626 + 0.763186i
\(713\) 2.34315 + 4.05845i 0.0877515 + 0.151990i
\(714\) 8.97056 0.335715
\(715\) 0 0
\(716\) 42.6274 1.59306
\(717\) 1.00000 + 1.73205i 0.0373457 + 0.0646846i
\(718\) −7.24264 12.5446i −0.270293 0.468161i
\(719\) 14.9706 25.9298i 0.558308 0.967017i −0.439330 0.898326i \(-0.644784\pi\)
0.997638 0.0686918i \(-0.0218825\pi\)
\(720\) 8.48528 0.316228
\(721\) 3.31371 5.73951i 0.123409 0.213751i
\(722\) −2.27817 + 3.94591i −0.0847849 + 0.146852i
\(723\) −0.343146 −0.0127617
\(724\) 12.7990 22.1685i 0.475671 0.823886i
\(725\) −3.00000 5.19615i −0.111417 0.192980i
\(726\) −1.44975 2.51104i −0.0538052 0.0931933i
\(727\) −10.3431 −0.383606 −0.191803 0.981433i \(-0.561433\pi\)
−0.191803 + 0.981433i \(0.561433\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −0.201010 0.348160i −0.00743972 0.0128860i
\(731\) 6.34315 + 10.9867i 0.234610 + 0.406356i
\(732\) 12.1716 21.0818i 0.449874 0.779205i
\(733\) 36.6274 1.35286 0.676432 0.736505i \(-0.263525\pi\)
0.676432 + 0.736505i \(0.263525\pi\)
\(734\) −4.97056 + 8.60927i −0.183467 + 0.317774i
\(735\) −1.41421 + 2.44949i −0.0521641 + 0.0903508i
\(736\) 17.6569 0.650840
\(737\) 6.82843 11.8272i 0.251528 0.435660i
\(738\) −1.07107 1.85514i −0.0394266 0.0682888i
\(739\) −9.07107 15.7116i −0.333685 0.577959i 0.649547 0.760322i \(-0.274959\pi\)
−0.983231 + 0.182363i \(0.941625\pi\)
\(740\) −39.5980 −1.45565
\(741\) 0 0
\(742\) −2.34315 −0.0860196
\(743\) 1.00000 + 1.73205i 0.0366864 + 0.0635428i 0.883786 0.467892i \(-0.154986\pi\)
−0.847099 + 0.531435i \(0.821653\pi\)
\(744\) −0.928932 1.60896i −0.0340563 0.0589873i
\(745\) −12.9706 + 22.4657i −0.475205 + 0.823079i
\(746\) −4.14214 −0.151654
\(747\) 1.82843 3.16693i 0.0668987 0.115872i
\(748\) 14.0000 24.2487i 0.511891 0.886621i
\(749\) 32.0000 1.16925
\(750\) −1.17157 + 2.02922i −0.0427798 + 0.0740968i
\(751\) 0.485281 + 0.840532i 0.0177082 + 0.0306714i 0.874744 0.484586i \(-0.161030\pi\)
−0.857036 + 0.515257i \(0.827696\pi\)
\(752\) −17.4853 30.2854i −0.637623 1.10439i
\(753\) 0 0
\(754\) 0 0
\(755\) 9.94113 0.361795
\(756\) −2.58579 4.47871i −0.0940441 0.162889i
\(757\) −25.9706 44.9823i −0.943916 1.63491i −0.757907 0.652363i \(-0.773778\pi\)
−0.186009 0.982548i \(-0.559555\pi\)
\(758\) −0.100505 + 0.174080i −0.00365051 + 0.00632287i
\(759\) −8.00000 −0.290382
\(760\) −6.34315 + 10.9867i −0.230090 + 0.398528i
\(761\) 16.2426 28.1331i 0.588795 1.01982i −0.405595 0.914053i \(-0.632936\pi\)
0.994391 0.105771i \(-0.0337309\pi\)
\(762\) −2.34315 −0.0848832
\(763\) −7.51472 + 13.0159i −0.272051 + 0.471206i
\(764\) 3.02944 + 5.24714i 0.109601 + 0.189835i
\(765\) −10.8284 18.7554i −0.391503 0.678102i
\(766\) 12.8284 0.463510
\(767\) 0 0
\(768\) 3.97056 0.143275
\(769\) 21.0000 + 36.3731i 0.757279 + 1.31165i 0.944233 + 0.329278i \(0.106805\pi\)
−0.186954 + 0.982369i \(0.559861\pi\)
\(770\) −3.31371 5.73951i −0.119418 0.206838i
\(771\) 2.17157 3.76127i 0.0782073 0.135459i
\(772\) 9.71573 0.349677
\(773\) 17.0711 29.5680i 0.614004 1.06349i −0.376555 0.926394i \(-0.622891\pi\)
0.990558 0.137091i \(-0.0437753\pi\)
\(774\) −0.343146 + 0.594346i −0.0123341 + 0.0213633i
\(775\) 3.51472 0.126252
\(776\) 2.89949 5.02207i 0.104086 0.180282i
\(777\) 10.8284 + 18.7554i 0.388468 + 0.672846i
\(778\) −5.58579 9.67487i −0.200260 0.346861i
\(779\) −14.6274 −0.524082
\(780\) 0