Properties

Label 507.2.j.f.361.3
Level $507$
Weight $2$
Character 507.361
Analytic conductor $4.048$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 507 = 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 507.j (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.04841538248\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
Defining polynomial: \(x^{8} - x^{4} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: no (minimal twist has level 39)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 361.3
Root \(0.965926 + 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 507.361
Dual form 507.2.j.f.316.3

$q$-expansion

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

Character values

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

\(n\) \(170\) \(340\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.358719 0.207107i 0.253653 0.146447i −0.367783 0.929912i \(-0.619883\pi\)
0.621436 + 0.783465i \(0.286550\pi\)
\(3\) −0.500000 0.866025i −0.288675 0.500000i
\(4\) −0.914214 + 1.58346i −0.457107 + 0.791732i
\(5\) 2.82843i 1.26491i −0.774597 0.632456i \(-0.782047\pi\)
0.774597 0.632456i \(-0.217953\pi\)
\(6\) −0.358719 0.207107i −0.146447 0.0845510i
\(7\) 2.44949 + 1.41421i 0.925820 + 0.534522i 0.885487 0.464664i \(-0.153825\pi\)
0.0403329 + 0.999186i \(0.487158\pi\)
\(8\) 1.58579i 0.560660i
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) −0.585786 1.01461i −0.185242 0.320848i
\(11\) 1.73205 1.00000i 0.522233 0.301511i −0.215615 0.976478i \(-0.569176\pi\)
0.737848 + 0.674967i \(0.235842\pi\)
\(12\) 1.82843 0.527821
\(13\) 0 0
\(14\) 1.17157 0.313116
\(15\) −2.44949 + 1.41421i −0.632456 + 0.365148i
\(16\) −1.50000 2.59808i −0.375000 0.649519i
\(17\) 3.82843 6.63103i 0.928530 1.60826i 0.142747 0.989759i \(-0.454407\pi\)
0.785783 0.618502i \(-0.212260\pi\)
\(18\) 0.414214i 0.0976311i
\(19\) 2.44949 + 1.41421i 0.561951 + 0.324443i 0.753928 0.656957i \(-0.228157\pi\)
−0.191977 + 0.981399i \(0.561490\pi\)
\(20\) 4.47871 + 2.58579i 1.00147 + 0.578199i
\(21\) 2.82843i 0.617213i
\(22\) 0.414214 0.717439i 0.0883106 0.152958i
\(23\) −2.00000 3.46410i −0.417029 0.722315i 0.578610 0.815604i \(-0.303595\pi\)
−0.995639 + 0.0932891i \(0.970262\pi\)
\(24\) 1.37333 0.792893i 0.280330 0.161849i
\(25\) −3.00000 −0.600000
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) −4.47871 + 2.58579i −0.846397 + 0.488668i
\(29\) −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
\(31\) 1.17157i 0.210421i −0.994450 0.105210i \(-0.966448\pi\)
0.994450 0.105210i \(-0.0335516\pi\)
\(32\) −3.82282 2.20711i −0.675786 0.390165i
\(33\) −1.73205 1.00000i −0.301511 0.174078i
\(34\) 3.17157i 0.543920i
\(35\) 4.00000 6.92820i 0.676123 1.17108i
\(36\) −0.914214 1.58346i −0.152369 0.263911i
\(37\) 6.63103 3.82843i 1.09013 0.629390i 0.156522 0.987674i \(-0.449972\pi\)
0.933612 + 0.358285i \(0.116638\pi\)
\(38\) 1.17157 0.190054
\(39\) 0 0
\(40\) 4.48528 0.709185
\(41\) 4.47871 2.58579i 0.699458 0.403832i −0.107688 0.994185i \(-0.534345\pi\)
0.807145 + 0.590353i \(0.201011\pi\)
\(42\) −0.585786 1.01461i −0.0903888 0.156558i
\(43\) −0.828427 + 1.43488i −0.126334 + 0.218817i −0.922254 0.386585i \(-0.873654\pi\)
0.795920 + 0.605402i \(0.206988\pi\)
\(44\) 3.65685i 0.551292i
\(45\) 2.44949 + 1.41421i 0.365148 + 0.210819i
\(46\) −1.43488 0.828427i −0.211561 0.122145i
\(47\) 11.6569i 1.70033i 0.526519 + 0.850163i \(0.323497\pi\)
−0.526519 + 0.850163i \(0.676503\pi\)
\(48\) −1.50000 + 2.59808i −0.216506 + 0.375000i
\(49\) 0.500000 + 0.866025i 0.0714286 + 0.123718i
\(50\) −1.07616 + 0.621320i −0.152192 + 0.0878680i
\(51\) −7.65685 −1.07217
\(52\) 0 0
\(53\) −2.00000 −0.274721 −0.137361 0.990521i \(-0.543862\pi\)
−0.137361 + 0.990521i \(0.543862\pi\)
\(54\) 0.358719 0.207107i 0.0488155 0.0281837i
\(55\) −2.82843 4.89898i −0.381385 0.660578i
\(56\) −2.24264 + 3.88437i −0.299685 + 0.519070i
\(57\) 2.82843i 0.374634i
\(58\) −0.717439 0.414214i −0.0942043 0.0543889i
\(59\) 6.63103 + 3.82843i 0.863287 + 0.498419i 0.865112 0.501580i \(-0.167248\pi\)
−0.00182490 + 0.999998i \(0.500581\pi\)
\(60\) 5.17157i 0.667647i
\(61\) −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
\(63\) −2.44949 + 1.41421i −0.308607 + 0.178174i
\(64\) 4.17157 0.521447
\(65\) 0 0
\(66\) −0.828427 −0.101972
\(67\) 5.91359 3.41421i 0.722460 0.417113i −0.0931973 0.995648i \(-0.529709\pi\)
0.815657 + 0.578535i \(0.196375\pi\)
\(68\) 7.00000 + 12.1244i 0.848875 + 1.47029i
\(69\) −2.00000 + 3.46410i −0.240772 + 0.417029i
\(70\) 3.31371i 0.396064i
\(71\) −1.73205 1.00000i −0.205557 0.118678i 0.393688 0.919244i \(-0.371199\pi\)
−0.599245 + 0.800566i \(0.704532\pi\)
\(72\) −1.37333 0.792893i −0.161849 0.0934434i
\(73\) 0.343146i 0.0401622i −0.999798 0.0200811i \(-0.993608\pi\)
0.999798 0.0200811i \(-0.00639244\pi\)
\(74\) 1.58579 2.74666i 0.184344 0.319293i
\(75\) 1.50000 + 2.59808i 0.173205 + 0.300000i
\(76\) −4.47871 + 2.58579i −0.513744 + 0.296610i
\(77\) 5.65685 0.644658
\(78\) 0 0
\(79\) −11.3137 −1.27289 −0.636446 0.771321i \(-0.719596\pi\)
−0.636446 + 0.771321i \(0.719596\pi\)
\(80\) −7.34847 + 4.24264i −0.821584 + 0.474342i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 1.07107 1.85514i 0.118280 0.204866i
\(83\) 3.65685i 0.401392i 0.979654 + 0.200696i \(0.0643203\pi\)
−0.979654 + 0.200696i \(0.935680\pi\)
\(84\) 4.47871 + 2.58579i 0.488668 + 0.282132i
\(85\) −18.7554 10.8284i −2.03431 1.17451i
\(86\) 0.686292i 0.0740047i
\(87\) −1.00000 + 1.73205i −0.107211 + 0.185695i
\(88\) 1.58579 + 2.74666i 0.169045 + 0.292795i
\(89\) −12.8418 + 7.41421i −1.36123 + 0.785905i −0.989787 0.142552i \(-0.954469\pi\)
−0.371440 + 0.928457i \(0.621136\pi\)
\(90\) 1.17157 0.123495
\(91\) 0 0
\(92\) 7.31371 0.762507
\(93\) −1.01461 + 0.585786i −0.105210 + 0.0607432i
\(94\) 2.41421 + 4.18154i 0.249007 + 0.431293i
\(95\) 4.00000 6.92820i 0.410391 0.710819i
\(96\) 4.41421i 0.450524i
\(97\) −3.16693 1.82843i −0.321553 0.185649i 0.330532 0.943795i \(-0.392772\pi\)
−0.652085 + 0.758146i \(0.726105\pi\)
\(98\) 0.358719 + 0.207107i 0.0362361 + 0.0209209i
\(99\) 2.00000i 0.201008i
\(100\) 2.74264 4.75039i 0.274264 0.475039i
\(101\) 3.82843 + 6.63103i 0.380943 + 0.659812i 0.991197 0.132393i \(-0.0422662\pi\)
−0.610255 + 0.792205i \(0.708933\pi\)
\(102\) −2.74666 + 1.58579i −0.271960 + 0.157016i
\(103\) −2.34315 −0.230877 −0.115439 0.993315i \(-0.536827\pi\)
−0.115439 + 0.993315i \(0.536827\pi\)
\(104\) 0 0
\(105\) −8.00000 −0.780720
\(106\) −0.717439 + 0.414214i −0.0696838 + 0.0402320i
\(107\) 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
\(109\) 5.31371i 0.508961i 0.967078 + 0.254480i \(0.0819045\pi\)
−0.967078 + 0.254480i \(0.918096\pi\)
\(110\) −2.02922 1.17157i −0.193479 0.111705i
\(111\) −6.63103 3.82843i −0.629390 0.363378i
\(112\) 8.48528i 0.801784i
\(113\) 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
\(115\) −9.79796 + 5.65685i −0.913664 + 0.527504i
\(116\) 3.65685 0.339530
\(117\) 0 0
\(118\) 3.17157 0.291967
\(119\) 18.7554 10.8284i 1.71930 0.992640i
\(120\) −2.24264 3.88437i −0.204724 0.354593i
\(121\) −3.50000 + 6.06218i −0.318182 + 0.551107i
\(122\) 5.51472i 0.499279i
\(123\) −4.47871 2.58579i −0.403832 0.233153i
\(124\) 1.85514 + 1.07107i 0.166597 + 0.0961847i
\(125\) 5.65685i 0.505964i
\(126\) −0.585786 + 1.01461i −0.0521860 + 0.0903888i
\(127\) 2.82843 + 4.89898i 0.250982 + 0.434714i 0.963797 0.266639i \(-0.0859131\pi\)
−0.712814 + 0.701353i \(0.752580\pi\)
\(128\) 9.14207 5.27817i 0.808052 0.466529i
\(129\) 1.65685 0.145878
\(130\) 0 0
\(131\) −8.00000 −0.698963 −0.349482 0.936943i \(-0.613642\pi\)
−0.349482 + 0.936943i \(0.613642\pi\)
\(132\) 3.16693 1.82843i 0.275646 0.159144i
\(133\) 4.00000 + 6.92820i 0.346844 + 0.600751i
\(134\) 1.41421 2.44949i 0.122169 0.211604i
\(135\) 2.82843i 0.243432i
\(136\) 10.5154 + 6.07107i 0.901688 + 0.520590i
\(137\) −9.37769 5.41421i −0.801190 0.462567i 0.0426968 0.999088i \(-0.486405\pi\)
−0.843887 + 0.536521i \(0.819738\pi\)
\(138\) 1.65685i 0.141041i
\(139\) 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
\(141\) 10.0951 5.82843i 0.850163 0.490842i
\(142\) −0.828427 −0.0695201
\(143\) 0 0
\(144\) 3.00000 0.250000
\(145\) −4.89898 + 2.82843i −0.406838 + 0.234888i
\(146\) −0.0710678 0.123093i −0.00588161 0.0101873i
\(147\) 0.500000 0.866025i 0.0412393 0.0714286i
\(148\) 14.0000i 1.15079i
\(149\) 7.94282 + 4.58579i 0.650701 + 0.375682i 0.788725 0.614747i \(-0.210742\pi\)
−0.138024 + 0.990429i \(0.544075\pi\)
\(150\) 1.07616 + 0.621320i 0.0878680 + 0.0507306i
\(151\) 3.51472i 0.286024i 0.989721 + 0.143012i \(0.0456787\pi\)
−0.989721 + 0.143012i \(0.954321\pi\)
\(152\) −2.24264 + 3.88437i −0.181902 + 0.315064i
\(153\) 3.82843 + 6.63103i 0.309510 + 0.536087i
\(154\) 2.02922 1.17157i 0.163520 0.0944080i
\(155\) −3.31371 −0.266163
\(156\) 0 0
\(157\) −10.0000 −0.798087 −0.399043 0.916932i \(-0.630658\pi\)
−0.399043 + 0.916932i \(0.630658\pi\)
\(158\) −4.05845 + 2.34315i −0.322873 + 0.186411i
\(159\) 1.00000 + 1.73205i 0.0793052 + 0.137361i
\(160\) −6.24264 + 10.8126i −0.493524 + 0.854809i
\(161\) 11.3137i 0.891645i
\(162\) −0.358719 0.207107i −0.0281837 0.0162718i
\(163\) 16.3059 + 9.41421i 1.27718 + 0.737378i 0.976328 0.216294i \(-0.0693970\pi\)
0.300848 + 0.953672i \(0.402730\pi\)
\(164\) 9.45584i 0.738377i
\(165\) −2.82843 + 4.89898i −0.220193 + 0.381385i
\(166\) 0.757359 + 1.31178i 0.0587825 + 0.101814i
\(167\) 3.16693 1.82843i 0.245064 0.141488i −0.372438 0.928057i \(-0.621478\pi\)
0.617502 + 0.786569i \(0.288145\pi\)
\(168\) 4.48528 0.346047
\(169\) 0 0
\(170\) −8.97056 −0.688011
\(171\) −2.44949 + 1.41421i −0.187317 + 0.108148i
\(172\) −1.51472 2.62357i −0.115496 0.200045i
\(173\) −5.82843 + 10.0951i −0.443127 + 0.767519i −0.997920 0.0644701i \(-0.979464\pi\)
0.554793 + 0.831989i \(0.312798\pi\)
\(174\) 0.828427i 0.0628029i
\(175\) −7.34847 4.24264i −0.555492 0.320713i
\(176\) −5.19615 3.00000i −0.391675 0.226134i
\(177\) 7.65685i 0.575524i
\(178\) −3.07107 + 5.31925i −0.230186 + 0.398694i
\(179\) −11.6569 20.1903i −0.871274 1.50909i −0.860679 0.509147i \(-0.829961\pi\)
−0.0105948 0.999944i \(-0.503372\pi\)
\(180\) −4.47871 + 2.58579i −0.333824 + 0.192733i
\(181\) −14.0000 −1.04061 −0.520306 0.853980i \(-0.674182\pi\)
−0.520306 + 0.853980i \(0.674182\pi\)
\(182\) 0 0
\(183\) 13.3137 0.984178
\(184\) 5.49333 3.17157i 0.404973 0.233811i
\(185\) −10.8284 18.7554i −0.796122 1.37892i
\(186\) −0.242641 + 0.420266i −0.0177913 + 0.0308154i
\(187\) 15.3137i 1.11985i
\(188\) −18.4582 10.6569i −1.34620 0.777231i
\(189\) 2.44949 + 1.41421i 0.178174 + 0.102869i
\(190\) 3.31371i 0.240402i
\(191\) −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
\(193\) −4.60181 + 2.65685i −0.331245 + 0.191245i −0.656394 0.754418i \(-0.727919\pi\)
0.325149 + 0.945663i \(0.394586\pi\)
\(194\) −1.51472 −0.108750
\(195\) 0 0
\(196\) −1.82843 −0.130602
\(197\) 0.420266 0.242641i 0.0299427 0.0172874i −0.484954 0.874540i \(-0.661164\pi\)
0.514897 + 0.857252i \(0.327830\pi\)
\(198\) 0.414214 + 0.717439i 0.0294369 + 0.0509862i
\(199\) 10.8284 18.7554i 0.767607 1.32953i −0.171250 0.985228i \(-0.554781\pi\)
0.938857 0.344307i \(-0.111886\pi\)
\(200\) 4.75736i 0.336396i
\(201\) −5.91359 3.41421i −0.417113 0.240820i
\(202\) 2.74666 + 1.58579i 0.193255 + 0.111576i
\(203\) 5.65685i 0.397033i
\(204\) 7.00000 12.1244i 0.490098 0.848875i
\(205\) −7.31371 12.6677i −0.510812 0.884752i
\(206\) −0.840532 + 0.485281i −0.0585626 + 0.0338112i
\(207\) 4.00000 0.278019
\(208\) 0 0
\(209\) 5.65685 0.391293
\(210\) −2.86976 + 1.65685i −0.198032 + 0.114334i
\(211\) 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
\(213\) 2.00000i 0.137038i
\(214\) 4.05845 + 2.34315i 0.277430 + 0.160174i
\(215\) 4.05845 + 2.34315i 0.276784 + 0.159801i
\(216\) 1.58579i 0.107899i
\(217\) 1.65685 2.86976i 0.112475 0.194812i
\(218\) 1.10051 + 1.90613i 0.0745356 + 0.129099i
\(219\) −0.297173 + 0.171573i −0.0200811 + 0.0115938i
\(220\) 10.3431 0.697335
\(221\) 0 0
\(222\) −3.17157 −0.212862
\(223\) −10.8126 + 6.24264i −0.724063 + 0.418038i −0.816246 0.577704i \(-0.803949\pi\)
0.0921831 + 0.995742i \(0.470615\pi\)
\(224\) −6.24264 10.8126i −0.417104 0.722445i
\(225\) 1.50000 2.59808i 0.100000 0.173205i
\(226\) 2.20101i 0.146409i
\(227\) 14.9941 + 8.65685i 0.995194 + 0.574576i 0.906823 0.421512i \(-0.138500\pi\)
0.0883713 + 0.996088i \(0.471834\pi\)
\(228\) 4.47871 + 2.58579i 0.296610 + 0.171248i
\(229\) 1.31371i 0.0868123i 0.999058 + 0.0434062i \(0.0138209\pi\)
−0.999058 + 0.0434062i \(0.986179\pi\)
\(230\) −2.34315 + 4.05845i −0.154502 + 0.267606i
\(231\) −2.82843 4.89898i −0.186097 0.322329i
\(232\) 2.74666 1.58579i 0.180327 0.104112i
\(233\) −6.97056 −0.456657 −0.228328 0.973584i \(-0.573326\pi\)
−0.228328 + 0.973584i \(0.573326\pi\)
\(234\) 0 0
\(235\) 32.9706 2.15076
\(236\) −12.1244 + 7.00000i −0.789228 + 0.455661i
\(237\) 5.65685 + 9.79796i 0.367452 + 0.636446i
\(238\) 4.48528 7.76874i 0.290738 0.503572i
\(239\) 2.00000i 0.129369i 0.997906 + 0.0646846i \(0.0206041\pi\)
−0.997906 + 0.0646846i \(0.979396\pi\)
\(240\) 7.34847 + 4.24264i 0.474342 + 0.273861i
\(241\) 0.297173 + 0.171573i 0.0191426 + 0.0110520i 0.509541 0.860447i \(-0.329815\pi\)
−0.490398 + 0.871499i \(0.663149\pi\)
\(242\) 2.89949i 0.186387i
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) −12.1716 21.0818i −0.779205 1.34962i
\(245\) 2.44949 1.41421i 0.156492 0.0903508i
\(246\) −2.14214 −0.136578
\(247\) 0 0
\(248\) 1.85786 0.117975
\(249\) 3.16693 1.82843i 0.200696 0.115872i
\(250\) −1.17157 2.02922i −0.0740968 0.128339i
\(251\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(252\) 5.17157i 0.325778i
\(253\) −6.92820 4.00000i −0.435572 0.251478i
\(254\) 2.02922 + 1.17157i 0.127325 + 0.0735110i
\(255\) 21.6569i 1.35620i
\(256\) −1.98528 + 3.43861i −0.124080 + 0.214913i
\(257\) −2.17157 3.76127i −0.135459 0.234622i 0.790314 0.612702i \(-0.209918\pi\)
−0.925773 + 0.378081i \(0.876584\pi\)
\(258\) 0.594346 0.343146i 0.0370024 0.0213633i
\(259\) 21.6569 1.34569
\(260\) 0 0
\(261\) 2.00000 0.123797
\(262\) −2.86976 + 1.65685i −0.177294 + 0.102361i
\(263\) −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
\(265\) 5.65685i 0.347498i
\(266\) 2.86976 + 1.65685i 0.175956 + 0.101588i
\(267\) 12.8418 + 7.41421i 0.785905 + 0.453743i
\(268\) 12.4853i 0.762660i
\(269\) −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
\(271\) 24.0746 13.8995i 1.46243 0.844334i 0.463306 0.886198i \(-0.346663\pi\)
0.999123 + 0.0418640i \(0.0133296\pi\)
\(272\) −22.9706 −1.39279
\(273\) 0 0
\(274\) −4.48528 −0.270966
\(275\) −5.19615 + 3.00000i −0.313340 + 0.180907i
\(276\) −3.65685 6.33386i −0.220117 0.381253i
\(277\) −1.00000 + 1.73205i −0.0600842 + 0.104069i −0.894503 0.447062i \(-0.852470\pi\)
0.834419 + 0.551131i \(0.185804\pi\)
\(278\) 3.02944i 0.181694i
\(279\) 1.01461 + 0.585786i 0.0607432 + 0.0350701i
\(280\) 10.9867 + 6.34315i 0.656578 + 0.379075i
\(281\) 21.1716i 1.26299i −0.775380 0.631495i \(-0.782442\pi\)
0.775380 0.631495i \(-0.217558\pi\)
\(282\) 2.41421 4.18154i 0.143764 0.249007i
\(283\) 14.4853 + 25.0892i 0.861061 + 1.49140i 0.870906 + 0.491449i \(0.163533\pi\)
−0.00984565 + 0.999952i \(0.503134\pi\)
\(284\) 3.16693 1.82843i 0.187923 0.108497i
\(285\) −8.00000 −0.473879
\(286\) 0 0
\(287\) 14.6274 0.863429
\(288\) 3.82282 2.20711i 0.225262 0.130055i
\(289\) −20.8137 36.0504i −1.22434 2.12061i
\(290\) −1.17157 + 2.02922i −0.0687971 + 0.119160i
\(291\) 3.65685i 0.214369i
\(292\) 0.543359 + 0.313708i 0.0317977 + 0.0183584i
\(293\) 1.85514 + 1.07107i 0.108379 + 0.0625724i 0.553210 0.833042i \(-0.313403\pi\)
−0.444831 + 0.895615i \(0.646736\pi\)
\(294\) 0.414214i 0.0241574i
\(295\) 10.8284 18.7554i 0.630455 1.09198i
\(296\) 6.07107 + 10.5154i 0.352874 + 0.611195i
\(297\) 1.73205 1.00000i 0.100504 0.0580259i
\(298\) 3.79899 0.220070
\(299\) 0 0
\(300\) −5.48528 −0.316693
\(301\) −4.05845 + 2.34315i −0.233925 + 0.135057i
\(302\) 0.727922 + 1.26080i 0.0418872 + 0.0725508i
\(303\) 3.82843 6.63103i 0.219937 0.380943i
\(304\) 8.48528i 0.486664i
\(305\) 32.6118 + 18.8284i 1.86735 + 1.07811i
\(306\) 2.74666 + 1.58579i 0.157016 + 0.0906534i
\(307\) 22.8284i 1.30289i 0.758697 + 0.651444i \(0.225836\pi\)
−0.758697 + 0.651444i \(0.774164\pi\)
\(308\) −5.17157 + 8.95743i −0.294678 + 0.510397i
\(309\) 1.17157 + 2.02922i 0.0666485 + 0.115439i
\(310\) −1.18869 + 0.686292i −0.0675132 + 0.0389787i
\(311\) 10.6274 0.602626 0.301313 0.953525i \(-0.402575\pi\)
0.301313 + 0.953525i \(0.402575\pi\)
\(312\) 0 0
\(313\) 6.00000 0.339140 0.169570 0.985518i \(-0.445762\pi\)
0.169570 + 0.985518i \(0.445762\pi\)
\(314\) −3.58719 + 2.07107i −0.202437 + 0.116877i
\(315\) 4.00000 + 6.92820i 0.225374 + 0.390360i
\(316\) 10.3431 17.9149i 0.581847 1.00779i
\(317\) 8.48528i 0.476581i 0.971194 + 0.238290i \(0.0765870\pi\)
−0.971194 + 0.238290i \(0.923413\pi\)
\(318\) 0.717439 + 0.414214i 0.0402320 + 0.0232279i
\(319\) −3.46410 2.00000i −0.193952 0.111979i
\(320\) 11.7990i 0.659584i
\(321\) 5.65685 9.79796i 0.315735 0.546869i
\(322\) −2.34315 4.05845i −0.130578 0.226168i
\(323\) 18.7554 10.8284i 1.04358 0.602510i
\(324\) 1.82843 0.101579
\(325\) 0 0
\(326\) 7.79899 0.431946
\(327\) 4.60181 2.65685i 0.254480 0.146924i
\(328\) 4.10051 + 7.10228i 0.226413 + 0.392158i
\(329\) −16.4853 + 28.5533i −0.908863 + 1.57420i
\(330\) 2.34315i 0.128986i
\(331\) −22.6398 13.0711i −1.24439 0.718451i −0.274408 0.961613i \(-0.588482\pi\)
−0.969986 + 0.243163i \(0.921815\pi\)
\(332\) −5.79050 3.34315i −0.317795 0.183479i
\(333\) 7.65685i 0.419593i
\(334\) 0.757359 1.31178i 0.0414409 0.0717777i
\(335\) −9.65685 16.7262i −0.527610 0.913848i
\(336\) −7.34847 + 4.24264i −0.400892 + 0.231455i
\(337\) −9.31371 −0.507350 −0.253675 0.967290i \(-0.581639\pi\)
−0.253675 + 0.967290i \(0.581639\pi\)
\(338\) 0 0
\(339\) −5.31371 −0.288601
\(340\) 34.2929 19.7990i 1.85979 1.07375i
\(341\) −1.17157 2.02922i −0.0634442 0.109889i
\(342\) −0.585786 + 1.01461i −0.0316757 + 0.0548639i
\(343\) 16.9706i 0.916324i
\(344\) −2.27541 1.31371i −0.122682 0.0708304i
\(345\) 9.79796 + 5.65685i 0.527504 + 0.304555i
\(346\) 4.82843i 0.259578i
\(347\) 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
\(349\) −3.16693 + 1.82843i −0.169522 + 0.0978735i −0.582360 0.812931i \(-0.697871\pi\)
0.412839 + 0.910804i \(0.364537\pi\)
\(350\) −3.51472 −0.187870
\(351\) 0 0
\(352\) −8.82843 −0.470557
\(353\) −28.9736 + 16.7279i −1.54211 + 0.890337i −0.543404 + 0.839471i \(0.682865\pi\)
−0.998705 + 0.0508663i \(0.983802\pi\)
\(354\) −1.58579 2.74666i −0.0842836 0.145983i
\(355\) −2.82843 + 4.89898i −0.150117 + 0.260011i
\(356\) 27.1127i 1.43697i
\(357\) −18.7554 10.8284i −0.992640 0.573101i
\(358\) −8.36308 4.82843i −0.442003 0.255190i
\(359\) 34.9706i 1.84568i −0.385189 0.922838i \(-0.625864\pi\)
0.385189 0.922838i \(-0.374136\pi\)
\(360\) −2.24264 + 3.88437i −0.118198 + 0.204724i
\(361\) −5.50000 9.52628i −0.289474 0.501383i
\(362\) −5.02207 + 2.89949i −0.263954 + 0.152394i
\(363\) 7.00000 0.367405
\(364\) 0 0
\(365\) −0.970563 −0.0508016
\(366\) 4.77589 2.75736i 0.249640 0.144129i
\(367\) 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
\(369\) 5.17157i 0.269221i
\(370\) −7.76874 4.48528i −0.403877 0.233179i
\(371\) −4.89898 2.82843i −0.254342 0.146845i
\(372\) 2.14214i 0.111065i
\(373\) −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
\(375\) −4.89898 + 2.82843i −0.252982 + 0.146059i
\(376\) −18.4853 −0.953306
\(377\) 0 0
\(378\) 1.17157 0.0602592
\(379\) 0.420266 0.242641i 0.0215876 0.0124636i −0.489167 0.872190i \(-0.662699\pi\)
0.510755 + 0.859726i \(0.329366\pi\)
\(380\) 7.31371 + 12.6677i 0.375185 + 0.649840i
\(381\) 2.82843 4.89898i 0.144905 0.250982i
\(382\) 1.37258i 0.0702275i
\(383\) −26.8213 15.4853i −1.37050 0.791261i −0.379513 0.925187i \(-0.623908\pi\)
−0.990991 + 0.133926i \(0.957242\pi\)
\(384\) −9.14207 5.27817i −0.466529 0.269351i
\(385\) 16.0000i 0.815436i
\(386\) −1.10051 + 1.90613i −0.0560142 + 0.0970195i
\(387\) −0.828427 1.43488i −0.0421113 0.0729389i
\(388\) 5.79050 3.34315i 0.293968 0.169723i
\(389\) 26.9706 1.36746 0.683731 0.729734i \(-0.260356\pi\)
0.683731 + 0.729734i \(0.260356\pi\)
\(390\) 0 0
\(391\) −30.6274 −1.54890
\(392\) −1.37333 + 0.792893i −0.0693637 + 0.0400472i
\(393\) 4.00000 + 6.92820i 0.201773 + 0.349482i
\(394\) 0.100505 0.174080i 0.00506337 0.00877002i
\(395\) 32.0000i 1.61009i
\(396\) −3.16693 1.82843i −0.159144 0.0918819i
\(397\) 26.8213 + 15.4853i 1.34612 + 0.777184i 0.987698 0.156375i \(-0.0499808\pi\)
0.358424 + 0.933559i \(0.383314\pi\)
\(398\) 8.97056i 0.449654i
\(399\) 4.00000 6.92820i 0.200250 0.346844i
\(400\) 4.50000 + 7.79423i 0.225000 + 0.389711i
\(401\) −22.6398 + 13.0711i −1.13058 + 0.652738i −0.944080 0.329718i \(-0.893046\pi\)
−0.186496 + 0.982456i \(0.559713\pi\)
\(402\) −2.82843 −0.141069
\(403\) 0 0
\(404\) −14.0000 −0.696526
\(405\) −2.44949 + 1.41421i −0.121716 + 0.0702728i
\(406\) −1.17157 2.02922i −0.0581442 0.100709i
\(407\) 7.65685 13.2621i 0.379536 0.657376i
\(408\) 12.1421i 0.601125i
\(409\) 30.2854 + 17.4853i 1.49752 + 0.864592i 0.999996 0.00286068i \(-0.000910584\pi\)
0.497521 + 0.867452i \(0.334244\pi\)
\(410\) −5.24714 3.02944i −0.259138 0.149613i
\(411\) 10.8284i 0.534127i
\(412\) 2.14214 3.71029i 0.105535 0.182793i
\(413\) 10.8284 + 18.7554i 0.532832 + 0.922892i
\(414\) 1.43488 0.828427i 0.0705204 0.0407150i
\(415\) 10.3431 0.507725
\(416\) 0 0
\(417\) −7.31371 −0.358154
\(418\) 2.02922 1.17157i 0.0992526 0.0573035i
\(419\) −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
\(421\) 37.3137i 1.81856i 0.416186 + 0.909279i \(0.363366\pi\)
−0.416186 + 0.909279i \(0.636634\pi\)
\(422\) 4.30463 + 2.48528i 0.209546 + 0.120982i
\(423\) −10.0951 5.82843i −0.490842 0.283388i
\(424\) 3.17157i 0.154025i
\(425\) −11.4853 + 19.8931i −0.557118 + 0.964957i
\(426\) 0.414214 + 0.717439i 0.0200687 + 0.0347600i
\(427\) −32.6118 + 18.8284i −1.57820 + 0.911171i
\(428\) −20.6863 −0.999910
\(429\) 0 0
\(430\) 1.94113 0.0936094
\(431\) 7.22538 4.17157i 0.348034 0.200938i −0.315785 0.948831i \(-0.602268\pi\)
0.663819 + 0.747893i \(0.268934\pi\)
\(432\) −1.50000 2.59808i −0.0721688 0.125000i
\(433\) −10.6569 + 18.4582i −0.512136 + 0.887045i 0.487765 + 0.872975i \(0.337812\pi\)
−0.999901 + 0.0140703i \(0.995521\pi\)
\(434\) 1.37258i 0.0658861i
\(435\) 4.89898 + 2.82843i 0.234888 + 0.135613i
\(436\) −8.41407 4.85786i −0.402961 0.232650i
\(437\) 11.3137i 0.541208i
\(438\) −0.0710678 + 0.123093i −0.00339575 + 0.00588161i
\(439\) 8.48528 + 14.6969i 0.404980 + 0.701447i 0.994319 0.106439i \(-0.0339450\pi\)
−0.589339 + 0.807886i \(0.700612\pi\)
\(440\) 7.76874 4.48528i 0.370360 0.213827i
\(441\) −1.00000 −0.0476190
\(442\) 0 0
\(443\) −25.9411 −1.23250 −0.616250 0.787551i \(-0.711349\pi\)
−0.616250 + 0.787551i \(0.711349\pi\)
\(444\) 12.1244 7.00000i 0.575396 0.332205i
\(445\) 20.9706 + 36.3221i 0.994100 + 1.72183i
\(446\) −2.58579 + 4.47871i −0.122441 + 0.212073i
\(447\) 9.17157i 0.433801i
\(448\) 10.2182 + 5.89949i 0.482766 + 0.278725i
\(449\) −27.5387 15.8995i −1.29963 0.750344i −0.319293 0.947656i \(-0.603445\pi\)
−0.980341 + 0.197313i \(0.936779\pi\)
\(450\) 1.24264i 0.0585786i
\(451\) 5.17157 8.95743i 0.243520 0.421789i
\(452\) 4.85786 + 8.41407i 0.228495 + 0.395764i
\(453\) 3.04384 1.75736i 0.143012 0.0825679i
\(454\) 7.17157 0.336579
\(455\) 0 0
\(456\) 4.48528 0.210043
\(457\) −6.63103 + 3.82843i −0.310187 + 0.179086i −0.647010 0.762482i \(-0.723981\pi\)
0.336823 + 0.941568i \(0.390647\pi\)
\(458\) 0.272078 + 0.471253i 0.0127134 + 0.0220202i
\(459\) 3.82843 6.63103i 0.178696 0.309510i
\(460\) 20.6863i 0.964503i
\(461\) −4.47871 2.58579i −0.208594 0.120432i 0.392064 0.919938i \(-0.371761\pi\)
−0.600658 + 0.799506i \(0.705095\pi\)
\(462\) −2.02922 1.17157i −0.0944080 0.0545065i
\(463\) 24.4853i 1.13793i 0.822363 + 0.568964i \(0.192656\pi\)
−0.822363 + 0.568964i \(0.807344\pi\)
\(464\) −3.00000 + 5.19615i −0.139272 + 0.241225i
\(465\) 1.65685 + 2.86976i 0.0768348 + 0.133082i
\(466\) −2.50048 + 1.44365i −0.115832 + 0.0668758i
\(467\) 8.00000 0.370196 0.185098 0.982720i \(-0.440740\pi\)
0.185098 + 0.982720i \(0.440740\pi\)
\(468\) 0 0
\(469\) 19.3137 0.891824
\(470\) 11.8272 6.82843i 0.545547 0.314972i
\(471\) 5.00000 + 8.66025i 0.230388 + 0.399043i
\(472\) −6.07107 + 10.5154i −0.279444 + 0.484010i
\(473\) 3.31371i 0.152364i
\(474\) 4.05845 + 2.34315i 0.186411 + 0.107624i
\(475\) −7.34847 4.24264i −0.337171 0.194666i
\(476\) 39.5980i 1.81497i
\(477\) 1.00000 1.73205i 0.0457869 0.0793052i
\(478\) 0.414214 + 0.717439i 0.0189457 + 0.0328149i
\(479\) −21.9223 + 12.6569i −1.00166 + 0.578306i −0.908738 0.417367i \(-0.862953\pi\)
−0.0929182 + 0.995674i \(0.529620\pi\)
\(480\) 12.4853 0.569873
\(481\) 0 0
\(482\) 0.142136 0.00647410
\(483\) −9.79796 + 5.65685i −0.445823 + 0.257396i
\(484\) −6.39949 11.0843i −0.290886 0.503830i
\(485\) −5.17157 + 8.95743i −0.234829 + 0.406736i
\(486\) 0.414214i 0.0187891i
\(487\) 6.75412 + 3.89949i 0.306059 + 0.176703i 0.645161 0.764046i \(-0.276790\pi\)
−0.339103 + 0.940749i \(0.610123\pi\)
\(488\) −18.2841 10.5563i −0.827684 0.477863i
\(489\) 18.8284i 0.851451i
\(490\) 0.585786 1.01461i 0.0264631 0.0458355i
\(491\) 15.3137 + 26.5241i 0.691098 + 1.19702i 0.971478 + 0.237128i \(0.0762060\pi\)
−0.280380 + 0.959889i \(0.590461\pi\)
\(492\) 8.18900 4.72792i 0.369189 0.213151i
\(493\) −15.3137 −0.689695
\(494\) 0 0
\(495\) 5.65685 0.254257
\(496\) −3.04384 + 1.75736i −0.136672 + 0.0789078i
\(497\) −2.82843 4.89898i −0.126872 0.219749i
\(498\) 0.757359 1.31178i 0.0339381 0.0587825i
\(499\) 26.1421i 1.17028i 0.810931 + 0.585141i \(0.198961\pi\)
−0.810931 + 0.585141i \(0.801039\pi\)
\(500\) 8.95743 + 5.17157i 0.400588 + 0.231280i
\(501\) −3.16693 1.82843i −0.141488 0.0816881i
\(502\) 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
\(505\) 18.7554 10.8284i 0.834604 0.481859i
\(506\) −3.31371 −0.147312
\(507\) 0 0
\(508\) −10.3431 −0.458903
\(509\) 10.2182 5.89949i 0.452915 0.261491i −0.256146 0.966638i \(-0.582453\pi\)
0.709060 + 0.705148i \(0.249119\pi\)
\(510\) 4.48528 + 7.76874i 0.198612 + 0.344005i
\(511\) 0.485281 0.840532i 0.0214676 0.0371829i
\(512\) 22.7574i 1.00574i
\(513\) 2.44949 + 1.41421i 0.108148 + 0.0624391i
\(514\) −1.55797 0.899495i −0.0687192 0.0396750i
\(515\) 6.62742i 0.292039i
\(516\) −1.51472 + 2.62357i −0.0666818 + 0.115496i
\(517\) 11.6569 + 20.1903i 0.512668 + 0.887967i
\(518\) 7.76874 4.48528i 0.341339 0.197072i
\(519\) 11.6569 0.511679
\(520\) 0 0
\(521\) 25.3137 1.10901 0.554507 0.832179i \(-0.312907\pi\)
0.554507 + 0.832179i \(0.312907\pi\)
\(522\) 0.717439 0.414214i 0.0314014 0.0181296i
\(523\) 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
\(525\) 8.48528i 0.370328i
\(526\) −4.30463 2.48528i −0.187691 0.108363i
\(527\) −7.76874 4.48528i −0.338411 0.195382i
\(528\) 6.00000i 0.261116i
\(529\) 3.50000 6.06218i 0.152174 0.263573i
\(530\) 1.17157 + 2.02922i 0.0508899 + 0.0881438i
\(531\) −6.63103 + 3.82843i −0.287762 + 0.166140i
\(532\) −14.6274 −0.634179
\(533\) 0 0
\(534\) 6.14214 0.265796
\(535\) 27.7128 16.0000i 1.19813 0.691740i
\(536\) 5.41421 + 9.37769i 0.233858 + 0.405055i
\(537\) −11.6569 + 20.1903i −0.503030 + 0.871274i
\(538\) 7.45584i 0.321444i
\(539\) 1.73205 + 1.00000i 0.0746047 + 0.0430730i
\(540\) 4.47871 + 2.58579i 0.192733 + 0.111275i
\(541\) 10.0000i 0.429934i −0.976621 0.214967i \(-0.931036\pi\)
0.976621 0.214967i \(-0.0689643\pi\)
\(542\) 5.75736 9.97204i 0.247300 0.428336i
\(543\) 7.00000 + 12.1244i 0.300399 + 0.520306i
\(544\) −29.2708 + 16.8995i −1.25497 + 0.724560i
\(545\) 15.0294 0.643790
\(546\) 0 0
\(547\) 23.3137 0.996822 0.498411 0.866941i \(-0.333917\pi\)
0.498411 + 0.866941i \(0.333917\pi\)
\(548\) 17.1464 9.89949i 0.732459 0.422885i
\(549\) −6.65685 11.5300i −0.284108 0.492089i
\(550\) −1.24264 + 2.15232i −0.0529864 + 0.0917751i
\(551\) 5.65685i 0.240990i
\(552\) −5.49333 3.17157i −0.233811 0.134991i
\(553\) −27.7128 16.0000i −1.17847 0.680389i
\(554\) 0.828427i 0.0351965i
\(555\) −10.8284 + 18.7554i −0.459641 + 0.796122i
\(556\) 6.68629 + 11.5810i 0.283562 + 0.491144i
\(557\) 6.75412 3.89949i 0.286181 0.165227i −0.350037 0.936736i \(-0.613831\pi\)
0.636218 + 0.771509i \(0.280498\pi\)
\(558\) 0.485281 0.0205436
\(559\) 0 0
\(560\) −24.0000 −1.01419
\(561\) −13.2621 + 7.65685i −0.559925 + 0.323273i
\(562\) −4.38478 7.59466i −0.184961 0.320361i
\(563\) 2.00000 3.46410i 0.0842900 0.145994i −0.820798 0.571218i \(-0.806471\pi\)
0.905088 + 0.425223i \(0.139804\pi\)
\(564\) 21.3137i 0.897469i
\(565\) −13.0159 7.51472i −0.547582 0.316147i
\(566\) 10.3923 + 6.00000i 0.436821 + 0.252199i
\(567\) 2.82843i 0.118783i
\(568\) 1.58579 2.74666i 0.0665381 0.115247i
\(569\) −21.4853 37.2136i −0.900710 1.56008i −0.826575 0.562827i \(-0.809714\pi\)
−0.0741351 0.997248i \(-0.523620\pi\)
\(570\) −2.86976 + 1.65685i −0.120201 + 0.0693980i
\(571\) 12.9706 0.542801 0.271401 0.962466i \(-0.412513\pi\)
0.271401 + 0.962466i \(0.412513\pi\)
\(572\) 0 0
\(573\) 3.31371 0.138432
\(574\) 5.24714 3.02944i 0.219011 0.126446i
\(575\) 6.00000 + 10.3923i 0.250217 + 0.433389i
\(576\) −2.08579 + 3.61269i −0.0869078 + 0.150529i
\(577\) 31.9411i 1.32973i −0.746965 0.664863i \(-0.768490\pi\)
0.746965 0.664863i \(-0.231510\pi\)
\(578\) −14.9326 8.62132i −0.621113 0.358600i
\(579\) 4.60181 + 2.65685i 0.191245 + 0.110415i
\(580\) 10.3431i 0.429476i
\(581\) −5.17157 + 8.95743i −0.214553 + 0.371617i
\(582\) 0.757359 + 1.31178i 0.0313936 + 0.0543752i
\(583\) −3.46410 + 2.00000i −0.143468 + 0.0828315i
\(584\) 0.544156 0.0225173
\(585\) 0 0
\(586\) 0.887302 0.0366541
\(587\) −9.50079 + 5.48528i −0.392139 + 0.226402i −0.683087 0.730337i \(-0.739363\pi\)
0.290947 + 0.956739i \(0.406030\pi\)
\(588\) 0.914214 + 1.58346i 0.0377015 + 0.0653010i
\(589\) 1.65685 2.86976i 0.0682695 0.118246i
\(590\) 8.97056i 0.369312i
\(591\) −0.420266 0.242641i −0.0172874 0.00998090i
\(592\) −19.8931 11.4853i −0.817601 0.472042i
\(593\) 20.4853i 0.841230i 0.907239 + 0.420615i \(0.138186\pi\)
−0.907239 + 0.420615i \(0.861814\pi\)
\(594\) 0.414214 0.717439i 0.0169954 0.0294369i
\(595\) −30.6274 53.0482i −1.25560 2.17477i
\(596\) −14.5229 + 8.38478i −0.594879 + 0.343454i
\(597\) −21.6569 −0.886356
\(598\) 0 0
\(599\) −23.3137 −0.952572 −0.476286 0.879290i \(-0.658017\pi\)
−0.476286 + 0.879290i \(0.658017\pi\)
\(600\) −4.11999 + 2.37868i −0.168198 + 0.0971092i
\(601\) 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
\(603\) 6.82843i 0.278075i
\(604\) −5.56543 3.21320i −0.226454 0.130743i
\(605\) 17.1464 + 9.89949i 0.697101 + 0.402472i
\(606\) 3.17157i 0.128836i
\(607\) −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
\(609\) −4.89898 + 2.82843i −0.198517 + 0.114614i
\(610\) 15.5980 0.631544
\(611\) 0 0
\(612\) −14.0000 −0.565916
\(613\) −41.2720 + 23.8284i −1.66696 + 0.962421i −0.697700 + 0.716390i \(0.745793\pi\)
−0.969262 + 0.246031i \(0.920873\pi\)
\(614\) 4.72792 + 8.18900i 0.190803 + 0.330481i
\(615\) −7.31371 + 12.6677i −0.294917 + 0.510812i
\(616\) 8.97056i 0.361434i
\(617\) 30.1623 + 17.4142i 1.21429 + 0.701070i 0.963691 0.267021i \(-0.0860394\pi\)
0.250598 + 0.968091i \(0.419373\pi\)
\(618\) 0.840532 + 0.485281i 0.0338112 + 0.0195209i
\(619\) 23.7990i 0.956562i −0.878207 0.478281i \(-0.841260\pi\)
0.878207 0.478281i \(-0.158740\pi\)
\(620\) 3.02944 5.24714i 0.121665 0.210730i
\(621\) −2.00000 3.46410i −0.0802572 0.139010i
\(622\) 3.81226 2.20101i 0.152858 0.0882525i
\(623\) −41.9411 −1.68034
\(624\) 0 0
\(625\) −31.0000 −1.24000
\(626\) 2.15232 1.24264i 0.0860239 0.0496659i
\(627\) −2.82843 4.89898i −0.112956 0.195646i
\(628\) 9.14214 15.8346i 0.364811 0.631871i
\(629\) 58.6274i 2.33763i
\(630\) 2.86976 + 1.65685i 0.114334 + 0.0660107i
\(631\) 37.3367 + 21.5563i 1.48635 + 0.858145i 0.999879 0.0155519i \(-0.00495053\pi\)
0.486471 + 0.873697i \(0.338284\pi\)
\(632\) 17.9411i 0.713660i
\(633\) 6.00000 10.3923i 0.238479 0.413057i
\(634\) 1.75736 + 3.04384i 0.0697937 + 0.120886i
\(635\) 13.8564 8.00000i 0.549875 0.317470i
\(636\) −3.65685 −0.145004
\(637\) 0 0
\(638\) −1.65685 −0.0655955
\(639\) 1.73205 1.00000i 0.0685189 0.0395594i
\(640\) −14.9289 25.8577i −0.590118 1.02211i
\(641\) 15.1421 26.2269i 0.598078 1.03590i −0.395026 0.918670i \(-0.629264\pi\)
0.993105 0.117232i \(-0.0374022\pi\)
\(642\) 4.68629i 0.184953i
\(643\) −19.7700 11.4142i −0.779653 0.450133i 0.0566545 0.998394i \(-0.481957\pi\)
−0.836307 + 0.548261i \(0.815290\pi\)
\(644\) 17.9149 + 10.3431i 0.705944 + 0.407577i
\(645\) 4.68629i 0.184523i
\(646\) 4.48528 7.76874i 0.176471 0.305657i
\(647\) 5.65685 + 9.79796i 0.222394 + 0.385198i 0.955534 0.294880i \(-0.0952796\pi\)
−0.733140 + 0.680077i \(0.761946\pi\)
\(648\) 1.37333 0.792893i 0.0539496 0.0311478i
\(649\) 15.3137 0.601116
\(650\) 0 0
\(651\) −3.31371 −0.129874
\(652\) −29.8141 + 17.2132i −1.16761 + 0.674121i
\(653\) 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
\(655\) 22.6274i 0.884126i
\(656\) −13.4361 7.75736i −0.524593 0.302874i
\(657\) 0.297173 + 0.171573i 0.0115938 + 0.00669370i
\(658\) 13.6569i 0.532400i
\(659\) 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
\(661\) 30.2854 17.4853i 1.17797 0.680099i 0.222422 0.974950i \(-0.428604\pi\)
0.955543 + 0.294852i \(0.0952703\pi\)
\(662\) −10.8284 −0.420859
\(663\) 0 0
\(664\) −5.79899 −0.225044
\(665\) 19.5959 11.3137i 0.759897 0.438727i
\(666\) 1.58579 + 2.74666i 0.0614480 + 0.106431i
\(667\) −4.00000 + 6.92820i −0.154881 + 0.268261i
\(668\) 6.68629i 0.258700i
\(669\) 10.8126 + 6.24264i 0.418038 + 0.241354i
\(670\) −6.92820 4.00000i −0.267660 0.154533i
\(671\) 26.6274i 1.02794i
\(672\) −6.24264 + 10.8126i −0.240815 + 0.417104i
\(673\) 8.31371 + 14.3998i 0.320470 + 0.555070i 0.980585 0.196094i \(-0.0628259\pi\)
−0.660115 + 0.751164i \(0.729493\pi\)
\(674\) −3.34101 + 1.92893i −0.128691 + 0.0742997i
\(675\) −3.00000 −0.115470
\(676\) 0 0
\(677\) 26.6863 1.02564 0.512819 0.858497i \(-0.328601\pi\)
0.512819 + 0.858497i \(0.328601\pi\)
\(678\) −1.90613 + 1.10051i −0.0732045 + 0.0422646i
\(679\) −5.17157 8.95743i −0.198467 0.343754i
\(680\) 17.1716 29.7420i 0.658500 1.14056i
\(681\) 17.3137i 0.663463i
\(682\) −0.840532 0.485281i −0.0321856 0.0185824i
\(683\) 41.5182 + 23.9706i 1.58865 + 0.917208i 0.993530 + 0.113572i \(0.0362293\pi\)
0.595121 + 0.803636i \(0.297104\pi\)
\(684\) 5.17157i 0.197740i
\(685\) −15.3137 + 26.5241i −0.585107 + 1.01343i
\(686\) −3.51472 6.08767i −0.134193 0.232428i
\(687\) 1.13770 0.656854i 0.0434062 0.0250606i
\(688\) 4.97056 0.189501
\(689\) 0 0
\(690\) 4.68629 0.178404
\(691\) −5.07306 + 2.92893i −0.192988 + 0.111422i −0.593381 0.804922i \(-0.702207\pi\)
0.400392 + 0.916344i \(0.368874\pi\)
\(692\) −10.6569 18.4582i −0.405113 0.701676i
\(693\) −2.82843 + 4.89898i −0.107443 + 0.186097i
\(694\) 3.59798i 0.136577i
\(695\) −17.9149 10.3431i −0.679549 0.392338i
\(696\) −2.74666 1.58579i −0.104112 0.0601091i
\(697\) 39.5980i 1.49988i
\(698\) −0.757359 + 1.31178i −0.0286665 + 0.0496518i
\(699\) 3.48528 + 6.03668i 0.131825 + 0.228328i
\(700\) 13.4361 7.75736i 0.507838 0.293201i
\(701\) −5.02944 −0.189959 −0.0949796 0.995479i \(-0.530279\pi\)
−0.0949796 + 0.995479i \(0.530279\pi\)
\(702\) 0 0
\(703\) 21.6569 0.816804
\(704\) 7.22538 4.17157i 0.272317 0.157222i
\(705\) −16.4853 28.5533i −0.620872 1.07538i
\(706\) −6.92893 + 12.0013i −0.260774 + 0.451673i
\(707\) 21.6569i 0.814490i
\(708\) 12.1244 + 7.00000i 0.455661 + 0.263076i
\(709\) −4.00746 2.31371i −0.150503 0.0868931i 0.422857 0.906196i \(-0.361027\pi\)
−0.573360 + 0.819303i \(0.694361\pi\)
\(710\) 2.34315i 0.0879367i
\(711\) 5.65685 9.79796i 0.212149 0.367452i
\(712\) −11.7574 20.3643i −0.440626 0.763186i
\(713\) −4.05845 + 2.34315i −0.151990 + 0.0877515i
\(714\) −8.97056 −0.335715
\(715\) 0 0
\(716\) 42.6274 1.59306
\(717\) 1.73205 1.00000i 0.0646846 0.0373457i
\(718\) −7.24264 12.5446i −0.270293 0.468161i
\(719\) −14.9706 + 25.9298i −0.558308 + 0.967017i 0.439330 + 0.898326i \(0.355216\pi\)
−0.997638 + 0.0686918i \(0.978117\pi\)
\(720\) 8.48528i 0.316228i
\(721\) −5.73951 3.31371i −0.213751 0.123409i
\(722\) −3.94591 2.27817i −0.146852 0.0847849i
\(723\) 0.343146i 0.0127617i
\(724\) 12.7990 22.1685i 0.475671 0.823886i
\(725\) 3.00000 + 5.19615i 0.111417 + 0.192980i
\(726\) 2.51104 1.44975i 0.0931933 0.0538052i
\(727\) 10.3431 0.383606 0.191803 0.981433i \(-0.438567\pi\)
0.191803 + 0.981433i \(0.438567\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −0.348160 + 0.201010i −0.0128860 + 0.00743972i
\(731\) 6.34315 + 10.9867i 0.234610 + 0.406356i
\(732\) −12.1716 + 21.0818i −0.449874 + 0.779205i
\(733\) 36.6274i 1.35286i −0.736505 0.676432i \(-0.763525\pi\)
0.736505 0.676432i \(-0.236475\pi\)
\(734\) 8.60927 + 4.97056i 0.317774 + 0.183467i
\(735\) −2.44949 1.41421i −0.0903508 0.0521641i
\(736\) 17.6569i 0.650840i
\(737\) 6.82843 11.8272i 0.251528 0.435660i
\(738\) 1.07107 + 1.85514i 0.0394266 + 0.0682888i
\(739\) 15.7116 9.07107i 0.577959 0.333685i −0.182363 0.983231i \(-0.558375\pi\)
0.760322 + 0.649547i \(0.225041\pi\)
\(740\) 39.5980 1.45565
\(741\) 0 0
\(742\) −2.34315 −0.0860196
\(743\) 1.73205 1.00000i 0.0635428 0.0366864i −0.467892 0.883786i \(-0.654986\pi\)
0.531435 + 0.847099i \(0.321653\pi\)
\(744\) −0.928932 1.60896i −0.0340563 0.0589873i
\(745\) 12.9706 22.4657i 0.475205 0.823079i
\(746\) 4.14214i 0.151654i
\(747\) −3.16693 1.82843i −0.115872 0.0668987i
\(748\) 24.2487 + 14.0000i 0.886621 + 0.511891i
\(749\) 32.0000i 1.16925i
\(750\) −1.17157 + 2.02922i −0.0427798 + 0.0740968i
\(751\) −0.485281 0.840532i −0.0177082 0.0306714i 0.857036 0.515257i \(-0.172304\pi\)
−0.874744 + 0.484586i \(0.838970\pi\)
\(752\) 30.2854 17.4853i 1.10439 0.637623i
\(753\) 0 0
\(754\) 0 0
\(755\) 9.94113 0.361795
\(756\) −4.47871 + 2.58579i −0.162889 + 0.0940441i
\(757\) −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
\(759\) 8.00000i 0.290382i
\(760\) 10.9867 + 6.34315i 0.398528 + 0.230090i
\(761\) 28.1331 + 16.2426i 1.01982 + 0.588795i 0.914053 0.405595i \(-0.132936\pi\)
0.105771 + 0.994391i \(0.466269\pi\)
\(762\) 2.34315i 0.0848832i
\(763\) −7.51472 + 13.0159i −0.272051 + 0.471206i
\(764\) −3.02944 5.24714i −0.109601 0.189835i
\(765\) 18.7554 10.8284i 0.678102 0.391503i
\(766\) −12.8284 −0.463510
\(767\) 0 0
\(768\) 3.97056 0.143275
\(769\) 36.3731 21.0000i 1.31165 0.757279i 0.329278 0.944233i \(-0.393195\pi\)
0.982369 + 0.186954i \(0.0598615\pi\)
\(770\) −3.31371 5.73951i −0.119418 0.206838i
\(771\) −2.17157 + 3.76127i −0.0782073 + 0.135459i
\(772\) 9.71573i 0.349677i
\(773\) −29.5680 17.0711i −1.06349 0.614004i −0.137091 0.990558i \(-0.543775\pi\)
−0.926394 + 0.376555i \(0.877109\pi\)
\(774\) −0.594346 0.343146i −0.0213633 0.0123341i
\(775\) 3.51472i 0.126252i
\(776\) 2.89949 5.02207i 0.104086 0.180282i
\(777\) −10.8284 18.7554i −0.388468 0.672846i
\(778\) 9.67487 5.58579i 0.346861 0.200260i