Properties

Label 507.2.j.h.361.2
Level $507$
Weight $2$
Character 507.361
Analytic conductor $4.048$
Analytic rank $0$
Dimension $12$
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: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: 12.0.17213603549184.1
Defining polynomial: \(x^{12} - 5 x^{10} + 19 x^{8} - 28 x^{6} + 31 x^{4} - 6 x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 361.2
Root \(-1.07992 + 0.623490i\) of defining polynomial
Character \(\chi\) \(=\) 507.361
Dual form 507.2.j.h.316.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.07992 + 0.623490i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.222521 + 0.385418i) q^{4} +2.80194i q^{5} +(1.07992 + 0.623490i) q^{6} +(4.15860 + 2.40097i) q^{7} -3.04892i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-1.07992 + 0.623490i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.222521 + 0.385418i) q^{4} +2.80194i q^{5} +(1.07992 + 0.623490i) q^{6} +(4.15860 + 2.40097i) q^{7} -3.04892i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.74698 - 3.02586i) q^{10} +(1.27030 - 0.733406i) q^{11} +0.445042 q^{12} -5.98792 q^{14} +(2.42655 - 1.40097i) q^{15} +(1.45593 + 2.52174i) q^{16} +(-1.22252 + 2.11747i) q^{17} -1.24698i q^{18} +(2.20220 + 1.27144i) q^{19} +(-1.07992 - 0.623490i) q^{20} -4.80194i q^{21} +(-0.914542 + 1.58403i) q^{22} +(-1.75786 - 3.04471i) q^{23} +(-2.64044 + 1.52446i) q^{24} -2.85086 q^{25} +1.00000 q^{27} +(-1.85075 + 1.06853i) q^{28} +(-0.925428 - 1.60289i) q^{29} +(-1.74698 + 3.02586i) q^{30} +7.63102i q^{31} +(2.13632 + 1.23341i) q^{32} +(-1.27030 - 0.733406i) q^{33} -3.04892i q^{34} +(-6.72737 + 11.6521i) q^{35} +(-0.222521 - 0.385418i) q^{36} +(-3.94471 + 2.27748i) q^{37} -3.17092 q^{38} +8.54288 q^{40} +(-1.07992 + 0.623490i) q^{41} +(2.99396 + 5.18569i) q^{42} +(1.19202 - 2.06464i) q^{43} +0.652793i q^{44} +(-2.42655 - 1.40097i) q^{45} +(3.79669 + 2.19202i) q^{46} +12.8170i q^{47} +(1.45593 - 2.52174i) q^{48} +(8.02930 + 13.9072i) q^{49} +(3.07868 - 1.77748i) q^{50} +2.44504 q^{51} -8.85086 q^{53} +(-1.07992 + 0.623490i) q^{54} +(2.05496 + 3.55929i) q^{55} +(7.32036 - 12.6792i) q^{56} -2.54288i q^{57} +(1.99877 + 1.15399i) q^{58} +(-1.88472 - 1.08815i) q^{59} +1.24698i q^{60} +(3.91454 - 6.78019i) q^{61} +(-4.75786 - 8.24086i) q^{62} +(-4.15860 + 2.40097i) q^{63} -8.89977 q^{64} +1.82908 q^{66} +(3.10219 - 1.79105i) q^{67} +(-0.544073 - 0.942362i) q^{68} +(-1.75786 + 3.04471i) q^{69} -16.7778i q^{70} +(-7.65460 - 4.41939i) q^{71} +(2.64044 + 1.52446i) q^{72} -7.69202i q^{73} +(2.83997 - 4.91897i) q^{74} +(1.42543 + 2.46891i) q^{75} +(-0.980069 + 0.565843i) q^{76} +7.04354 q^{77} -4.02177 q^{79} +(-7.06576 + 4.07942i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.777479 - 1.34663i) q^{82} +0.652793i q^{83} +(1.85075 + 1.06853i) q^{84} +(-5.93301 - 3.42543i) q^{85} +2.97285i q^{86} +(-0.925428 + 1.60289i) q^{87} +(-2.23609 - 3.87303i) q^{88} +(5.45241 - 3.14795i) q^{89} +3.49396 q^{90} +1.56465 q^{92} +(6.60866 - 3.81551i) q^{93} +(-7.99127 - 13.8413i) q^{94} +(-3.56249 + 6.17042i) q^{95} -2.46681i q^{96} +(-8.68750 - 5.01573i) q^{97} +(-17.3419 - 10.0124i) q^{98} +1.46681i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 6q^{3} - 2q^{4} - 6q^{9} + O(q^{10}) \) \( 12q - 6q^{3} - 2q^{4} - 6q^{9} - 2q^{10} + 4q^{12} + 4q^{14} + 10q^{16} - 14q^{17} + 10q^{22} + 4q^{23} + 20q^{25} + 12q^{27} + 16q^{29} - 2q^{30} - 36q^{35} - 2q^{36} - 80q^{38} + 28q^{40} - 2q^{42} - 6q^{43} + 10q^{48} + 34q^{49} + 28q^{51} - 52q^{53} + 26q^{55} + 14q^{56} + 26q^{61} - 32q^{62} - 16q^{64} - 20q^{66} - 14q^{68} + 4q^{69} - 14q^{74} - 10q^{75} + 60q^{77} - 36q^{79} - 6q^{81} + 10q^{82} + 16q^{87} - 14q^{88} + 4q^{90} - 68q^{92} - 64q^{94} + 6q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.07992 + 0.623490i −0.763616 + 0.440874i −0.830593 0.556881i \(-0.811998\pi\)
0.0669766 + 0.997755i \(0.478665\pi\)
\(3\) −0.500000 0.866025i −0.288675 0.500000i
\(4\) −0.222521 + 0.385418i −0.111260 + 0.192709i
\(5\) 2.80194i 1.25306i 0.779395 + 0.626532i \(0.215526\pi\)
−0.779395 + 0.626532i \(0.784474\pi\)
\(6\) 1.07992 + 0.623490i 0.440874 + 0.254539i
\(7\) 4.15860 + 2.40097i 1.57180 + 0.907481i 0.995948 + 0.0899290i \(0.0286640\pi\)
0.575855 + 0.817552i \(0.304669\pi\)
\(8\) 3.04892i 1.07796i
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) −1.74698 3.02586i −0.552443 0.956860i
\(11\) 1.27030 0.733406i 0.383009 0.221130i −0.296118 0.955151i \(-0.595692\pi\)
0.679127 + 0.734021i \(0.262359\pi\)
\(12\) 0.445042 0.128473
\(13\) 0 0
\(14\) −5.98792 −1.60034
\(15\) 2.42655 1.40097i 0.626532 0.361729i
\(16\) 1.45593 + 2.52174i 0.363982 + 0.630435i
\(17\) −1.22252 + 2.11747i −0.296505 + 0.513562i −0.975334 0.220735i \(-0.929154\pi\)
0.678829 + 0.734296i \(0.262488\pi\)
\(18\) 1.24698i 0.293916i
\(19\) 2.20220 + 1.27144i 0.505218 + 0.291688i 0.730866 0.682521i \(-0.239116\pi\)
−0.225648 + 0.974209i \(0.572450\pi\)
\(20\) −1.07992 0.623490i −0.241477 0.139417i
\(21\) 4.80194i 1.04787i
\(22\) −0.914542 + 1.58403i −0.194981 + 0.337717i
\(23\) −1.75786 3.04471i −0.366540 0.634866i 0.622482 0.782634i \(-0.286124\pi\)
−0.989022 + 0.147768i \(0.952791\pi\)
\(24\) −2.64044 + 1.52446i −0.538978 + 0.311179i
\(25\) −2.85086 −0.570171
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) −1.85075 + 1.06853i −0.349759 + 0.201934i
\(29\) −0.925428 1.60289i −0.171848 0.297649i 0.767218 0.641386i \(-0.221640\pi\)
−0.939066 + 0.343737i \(0.888307\pi\)
\(30\) −1.74698 + 3.02586i −0.318953 + 0.552443i
\(31\) 7.63102i 1.37057i 0.728274 + 0.685286i \(0.240323\pi\)
−0.728274 + 0.685286i \(0.759677\pi\)
\(32\) 2.13632 + 1.23341i 0.377652 + 0.218037i
\(33\) −1.27030 0.733406i −0.221130 0.127670i
\(34\) 3.04892i 0.522885i
\(35\) −6.72737 + 11.6521i −1.13713 + 1.96957i
\(36\) −0.222521 0.385418i −0.0370868 0.0642363i
\(37\) −3.94471 + 2.27748i −0.648506 + 0.374415i −0.787884 0.615824i \(-0.788823\pi\)
0.139377 + 0.990239i \(0.455490\pi\)
\(38\) −3.17092 −0.514390
\(39\) 0 0
\(40\) 8.54288 1.35075
\(41\) −1.07992 + 0.623490i −0.168655 + 0.0973727i −0.581951 0.813224i \(-0.697711\pi\)
0.413297 + 0.910596i \(0.364377\pi\)
\(42\) 2.99396 + 5.18569i 0.461978 + 0.800169i
\(43\) 1.19202 2.06464i 0.181782 0.314855i −0.760706 0.649097i \(-0.775147\pi\)
0.942487 + 0.334242i \(0.108480\pi\)
\(44\) 0.652793i 0.0984122i
\(45\) −2.42655 1.40097i −0.361729 0.208844i
\(46\) 3.79669 + 2.19202i 0.559792 + 0.323196i
\(47\) 12.8170i 1.86955i 0.355238 + 0.934776i \(0.384400\pi\)
−0.355238 + 0.934776i \(0.615600\pi\)
\(48\) 1.45593 2.52174i 0.210145 0.363982i
\(49\) 8.02930 + 13.9072i 1.14704 + 1.98674i
\(50\) 3.07868 1.77748i 0.435392 0.251374i
\(51\) 2.44504 0.342374
\(52\) 0 0
\(53\) −8.85086 −1.21576 −0.607879 0.794030i \(-0.707980\pi\)
−0.607879 + 0.794030i \(0.707980\pi\)
\(54\) −1.07992 + 0.623490i −0.146958 + 0.0848462i
\(55\) 2.05496 + 3.55929i 0.277090 + 0.479935i
\(56\) 7.32036 12.6792i 0.978224 1.69433i
\(57\) 2.54288i 0.336812i
\(58\) 1.99877 + 1.15399i 0.262451 + 0.151526i
\(59\) −1.88472 1.08815i −0.245370 0.141665i 0.372272 0.928124i \(-0.378579\pi\)
−0.617642 + 0.786459i \(0.711912\pi\)
\(60\) 1.24698i 0.160984i
\(61\) 3.91454 6.78019i 0.501206 0.868114i −0.498793 0.866721i \(-0.666223\pi\)
0.999999 0.00139289i \(-0.000443372\pi\)
\(62\) −4.75786 8.24086i −0.604249 1.04659i
\(63\) −4.15860 + 2.40097i −0.523934 + 0.302494i
\(64\) −8.89977 −1.11247
\(65\) 0 0
\(66\) 1.82908 0.225145
\(67\) 3.10219 1.79105i 0.378993 0.218812i −0.298387 0.954445i \(-0.596449\pi\)
0.677380 + 0.735633i \(0.263115\pi\)
\(68\) −0.544073 0.942362i −0.0659785 0.114278i
\(69\) −1.75786 + 3.04471i −0.211622 + 0.366540i
\(70\) 16.7778i 2.00533i
\(71\) −7.65460 4.41939i −0.908434 0.524485i −0.0285072 0.999594i \(-0.509075\pi\)
−0.879927 + 0.475109i \(0.842409\pi\)
\(72\) 2.64044 + 1.52446i 0.311179 + 0.179659i
\(73\) 7.69202i 0.900283i −0.892957 0.450142i \(-0.851374\pi\)
0.892957 0.450142i \(-0.148626\pi\)
\(74\) 2.83997 4.91897i 0.330140 0.571819i
\(75\) 1.42543 + 2.46891i 0.164594 + 0.285086i
\(76\) −0.980069 + 0.565843i −0.112422 + 0.0649067i
\(77\) 7.04354 0.802686
\(78\) 0 0
\(79\) −4.02177 −0.452485 −0.226242 0.974071i \(-0.572644\pi\)
−0.226242 + 0.974071i \(0.572644\pi\)
\(80\) −7.06576 + 4.07942i −0.789976 + 0.456093i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 0.777479 1.34663i 0.0858582 0.148711i
\(83\) 0.652793i 0.0716533i 0.999358 + 0.0358267i \(0.0114064\pi\)
−0.999358 + 0.0358267i \(0.988594\pi\)
\(84\) 1.85075 + 1.06853i 0.201934 + 0.116586i
\(85\) −5.93301 3.42543i −0.643526 0.371540i
\(86\) 2.97285i 0.320571i
\(87\) −0.925428 + 1.60289i −0.0992162 + 0.171848i
\(88\) −2.23609 3.87303i −0.238368 0.412866i
\(89\) 5.45241 3.14795i 0.577954 0.333682i −0.182366 0.983231i \(-0.558376\pi\)
0.760320 + 0.649549i \(0.225042\pi\)
\(90\) 3.49396 0.368296
\(91\) 0 0
\(92\) 1.56465 0.163126
\(93\) 6.60866 3.81551i 0.685286 0.395650i
\(94\) −7.99127 13.8413i −0.824237 1.42762i
\(95\) −3.56249 + 6.17042i −0.365504 + 0.633071i
\(96\) 2.46681i 0.251768i
\(97\) −8.68750 5.01573i −0.882082 0.509270i −0.0107376 0.999942i \(-0.503418\pi\)
−0.871344 + 0.490672i \(0.836751\pi\)
\(98\) −17.3419 10.0124i −1.75180 1.01140i
\(99\) 1.46681i 0.147420i
\(100\) 0.634375 1.09877i 0.0634375 0.109877i
\(101\) 6.94385 + 12.0271i 0.690938 + 1.19674i 0.971531 + 0.236913i \(0.0761358\pi\)
−0.280592 + 0.959827i \(0.590531\pi\)
\(102\) −2.64044 + 1.52446i −0.261443 + 0.150944i
\(103\) 17.4034 1.71481 0.857405 0.514642i \(-0.172075\pi\)
0.857405 + 0.514642i \(0.172075\pi\)
\(104\) 0 0
\(105\) 13.4547 1.31305
\(106\) 9.55818 5.51842i 0.928373 0.535996i
\(107\) −5.27628 9.13879i −0.510077 0.883480i −0.999932 0.0116758i \(-0.996283\pi\)
0.489854 0.871804i \(-0.337050\pi\)
\(108\) −0.222521 + 0.385418i −0.0214121 + 0.0370868i
\(109\) 1.07069i 0.102553i −0.998684 0.0512766i \(-0.983671\pi\)
0.998684 0.0512766i \(-0.0163290\pi\)
\(110\) −4.43836 2.56249i −0.423181 0.244324i
\(111\) 3.94471 + 2.27748i 0.374415 + 0.216169i
\(112\) 13.9825i 1.32123i
\(113\) 8.26540 14.3161i 0.777543 1.34674i −0.155811 0.987787i \(-0.549799\pi\)
0.933354 0.358957i \(-0.116868\pi\)
\(114\) 1.58546 + 2.74609i 0.148492 + 0.257195i
\(115\) 8.53109 4.92543i 0.795528 0.459298i
\(116\) 0.823708 0.0764794
\(117\) 0 0
\(118\) 2.71379 0.249825
\(119\) −10.1680 + 5.87047i −0.932095 + 0.538145i
\(120\) −4.27144 7.39835i −0.389927 0.675374i
\(121\) −4.42423 + 7.66299i −0.402203 + 0.696636i
\(122\) 9.76271i 0.883874i
\(123\) 1.07992 + 0.623490i 0.0973727 + 0.0562182i
\(124\) −2.94113 1.69806i −0.264121 0.152490i
\(125\) 6.02177i 0.538604i
\(126\) 2.99396 5.18569i 0.266723 0.461978i
\(127\) −4.76875 8.25972i −0.423158 0.732931i 0.573088 0.819494i \(-0.305745\pi\)
−0.996246 + 0.0865622i \(0.972412\pi\)
\(128\) 5.33836 3.08211i 0.471849 0.272422i
\(129\) −2.38404 −0.209903
\(130\) 0 0
\(131\) −5.50902 −0.481326 −0.240663 0.970609i \(-0.577365\pi\)
−0.240663 + 0.970609i \(0.577365\pi\)
\(132\) 0.565335 0.326396i 0.0492061 0.0284092i
\(133\) 6.10537 + 10.5748i 0.529402 + 0.916952i
\(134\) −2.23341 + 3.86837i −0.192937 + 0.334177i
\(135\) 2.80194i 0.241152i
\(136\) 6.45599 + 3.72737i 0.553596 + 0.319619i
\(137\) 14.0154 + 8.09179i 1.19742 + 0.691329i 0.959978 0.280074i \(-0.0903590\pi\)
0.237438 + 0.971403i \(0.423692\pi\)
\(138\) 4.38404i 0.373195i
\(139\) 5.25451 9.10108i 0.445682 0.771944i −0.552418 0.833568i \(-0.686295\pi\)
0.998099 + 0.0616238i \(0.0196279\pi\)
\(140\) −2.99396 5.18569i −0.253036 0.438271i
\(141\) 11.0999 6.40850i 0.934776 0.539693i
\(142\) 11.0218 0.924926
\(143\) 0 0
\(144\) −2.91185 −0.242654
\(145\) 4.49119 2.59299i 0.372973 0.215336i
\(146\) 4.79590 + 8.30674i 0.396911 + 0.687470i
\(147\) 8.02930 13.9072i 0.662246 1.14704i
\(148\) 2.02715i 0.166630i
\(149\) 12.4276 + 7.17510i 1.01811 + 0.587807i 0.913556 0.406712i \(-0.133325\pi\)
0.104555 + 0.994519i \(0.466658\pi\)
\(150\) −3.07868 1.77748i −0.251374 0.145131i
\(151\) 1.96615i 0.160003i 0.996795 + 0.0800014i \(0.0254925\pi\)
−0.996795 + 0.0800014i \(0.974508\pi\)
\(152\) 3.87651 6.71431i 0.314426 0.544603i
\(153\) −1.22252 2.11747i −0.0988350 0.171187i
\(154\) −7.60643 + 4.39158i −0.612944 + 0.353883i
\(155\) −21.3817 −1.71742
\(156\) 0 0
\(157\) 10.7017 0.854089 0.427045 0.904231i \(-0.359555\pi\)
0.427045 + 0.904231i \(0.359555\pi\)
\(158\) 4.34317 2.50753i 0.345524 0.199489i
\(159\) 4.42543 + 7.66507i 0.350959 + 0.607879i
\(160\) −3.45593 + 5.98584i −0.273215 + 0.473222i
\(161\) 16.8823i 1.33051i
\(162\) 1.07992 + 0.623490i 0.0848462 + 0.0489860i
\(163\) −3.37730 1.94989i −0.264531 0.152727i 0.361869 0.932229i \(-0.382139\pi\)
−0.626400 + 0.779502i \(0.715472\pi\)
\(164\) 0.554958i 0.0433349i
\(165\) 2.05496 3.55929i 0.159978 0.277090i
\(166\) −0.407010 0.704961i −0.0315901 0.0547156i
\(167\) 18.2033 10.5097i 1.40861 0.813264i 0.413360 0.910568i \(-0.364355\pi\)
0.995255 + 0.0973035i \(0.0310218\pi\)
\(168\) −14.6407 −1.12956
\(169\) 0 0
\(170\) 8.54288 0.655209
\(171\) −2.20220 + 1.27144i −0.168406 + 0.0972293i
\(172\) 0.530499 + 0.918852i 0.0404502 + 0.0700618i
\(173\) 6.61745 11.4618i 0.503115 0.871421i −0.496878 0.867820i \(-0.665520\pi\)
0.999994 0.00360102i \(-0.00114624\pi\)
\(174\) 2.30798i 0.174967i
\(175\) −11.8556 6.84481i −0.896197 0.517419i
\(176\) 3.69892 + 2.13557i 0.278816 + 0.160975i
\(177\) 2.17629i 0.163580i
\(178\) −3.92543 + 6.79904i −0.294223 + 0.509610i
\(179\) 4.26391 + 7.38530i 0.318699 + 0.552003i 0.980217 0.197926i \(-0.0634207\pi\)
−0.661518 + 0.749930i \(0.730087\pi\)
\(180\) 1.07992 0.623490i 0.0804922 0.0464722i
\(181\) 3.63640 0.270291 0.135146 0.990826i \(-0.456850\pi\)
0.135146 + 0.990826i \(0.456850\pi\)
\(182\) 0 0
\(183\) −7.82908 −0.578743
\(184\) −9.28307 + 5.35958i −0.684357 + 0.395114i
\(185\) −6.38135 11.0528i −0.469167 0.812620i
\(186\) −4.75786 + 8.24086i −0.348864 + 0.604249i
\(187\) 3.58642i 0.262265i
\(188\) −4.93990 2.85205i −0.360279 0.208007i
\(189\) 4.15860 + 2.40097i 0.302494 + 0.174645i
\(190\) 8.88471i 0.644564i
\(191\) −10.6908 + 18.5171i −0.773561 + 1.33985i 0.162039 + 0.986784i \(0.448193\pi\)
−0.935600 + 0.353062i \(0.885140\pi\)
\(192\) 4.44989 + 7.70743i 0.321143 + 0.556236i
\(193\) −7.29850 + 4.21379i −0.525358 + 0.303315i −0.739124 0.673569i \(-0.764760\pi\)
0.213766 + 0.976885i \(0.431427\pi\)
\(194\) 12.5090 0.898096
\(195\) 0 0
\(196\) −7.14675 −0.510482
\(197\) 22.9293 13.2383i 1.63365 0.943186i 0.650691 0.759343i \(-0.274479\pi\)
0.982955 0.183844i \(-0.0588540\pi\)
\(198\) −0.914542 1.58403i −0.0649937 0.112572i
\(199\) −7.12618 + 12.3429i −0.505161 + 0.874965i 0.494821 + 0.868995i \(0.335234\pi\)
−0.999982 + 0.00597014i \(0.998100\pi\)
\(200\) 8.69202i 0.614619i
\(201\) −3.10219 1.79105i −0.218812 0.126331i
\(202\) −14.9975 8.65883i −1.05522 0.609233i
\(203\) 8.88769i 0.623794i
\(204\) −0.544073 + 0.942362i −0.0380927 + 0.0659785i
\(205\) −1.74698 3.02586i −0.122014 0.211335i
\(206\) −18.7942 + 10.8509i −1.30946 + 0.756015i
\(207\) 3.51573 0.244360
\(208\) 0 0
\(209\) 3.72992 0.258004
\(210\) −14.5300 + 8.38889i −1.00266 + 0.578888i
\(211\) −0.925428 1.60289i −0.0637091 0.110347i 0.832412 0.554158i \(-0.186960\pi\)
−0.896121 + 0.443811i \(0.853626\pi\)
\(212\) 1.96950 3.41127i 0.135266 0.234287i
\(213\) 8.83877i 0.605623i
\(214\) 11.3959 + 6.57942i 0.779007 + 0.449760i
\(215\) 5.78500 + 3.33997i 0.394534 + 0.227784i
\(216\) 3.04892i 0.207453i
\(217\) −18.3218 + 31.7344i −1.24377 + 2.15427i
\(218\) 0.667563 + 1.15625i 0.0452131 + 0.0783113i
\(219\) −6.66149 + 3.84601i −0.450142 + 0.259889i
\(220\) −1.82908 −0.123317
\(221\) 0 0
\(222\) −5.67994 −0.381213
\(223\) −16.1517 + 9.32520i −1.08160 + 0.624462i −0.931327 0.364183i \(-0.881348\pi\)
−0.150272 + 0.988645i \(0.548015\pi\)
\(224\) 5.92274 + 10.2585i 0.395730 + 0.685424i
\(225\) 1.42543 2.46891i 0.0950285 0.164594i
\(226\) 20.6136i 1.37119i
\(227\) 8.45010 + 4.87867i 0.560853 + 0.323808i 0.753488 0.657462i \(-0.228370\pi\)
−0.192635 + 0.981270i \(0.561703\pi\)
\(228\) 0.980069 + 0.565843i 0.0649067 + 0.0374739i
\(229\) 2.86294i 0.189188i −0.995516 0.0945941i \(-0.969845\pi\)
0.995516 0.0945941i \(-0.0301553\pi\)
\(230\) −6.14191 + 10.6381i −0.404985 + 0.701455i
\(231\) −3.52177 6.09989i −0.231715 0.401343i
\(232\) −4.88707 + 2.82155i −0.320852 + 0.185244i
\(233\) 5.78554 0.379024 0.189512 0.981878i \(-0.439309\pi\)
0.189512 + 0.981878i \(0.439309\pi\)
\(234\) 0 0
\(235\) −35.9124 −2.34267
\(236\) 0.838781 0.484271i 0.0546000 0.0315233i
\(237\) 2.01089 + 3.48296i 0.130621 + 0.226242i
\(238\) 7.32036 12.6792i 0.474508 0.821872i
\(239\) 7.09246i 0.458773i −0.973335 0.229386i \(-0.926328\pi\)
0.973335 0.229386i \(-0.0736720\pi\)
\(240\) 7.06576 + 4.07942i 0.456093 + 0.263325i
\(241\) −3.37730 1.94989i −0.217551 0.125603i 0.387265 0.921969i \(-0.373420\pi\)
−0.604816 + 0.796365i \(0.706753\pi\)
\(242\) 11.0339i 0.709283i
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) 1.74214 + 3.01747i 0.111529 + 0.193174i
\(245\) −38.9670 + 22.4976i −2.48951 + 1.43732i
\(246\) −1.55496 −0.0991405
\(247\) 0 0
\(248\) 23.2664 1.47742
\(249\) 0.565335 0.326396i 0.0358267 0.0206845i
\(250\) −3.75451 6.50301i −0.237456 0.411286i
\(251\) −1.22252 + 2.11747i −0.0771648 + 0.133653i −0.902026 0.431682i \(-0.857920\pi\)
0.824861 + 0.565336i \(0.191253\pi\)
\(252\) 2.13706i 0.134622i
\(253\) −4.46602 2.57846i −0.280776 0.162106i
\(254\) 10.2997 + 5.94653i 0.646261 + 0.373119i
\(255\) 6.85086i 0.429017i
\(256\) 5.05645 8.75803i 0.316028 0.547377i
\(257\) −7.06518 12.2372i −0.440714 0.763339i 0.557029 0.830493i \(-0.311941\pi\)
−0.997743 + 0.0671545i \(0.978608\pi\)
\(258\) 2.57457 1.48643i 0.160285 0.0925409i
\(259\) −21.8726 −1.35910
\(260\) 0 0
\(261\) 1.85086 0.114565
\(262\) 5.94928 3.43482i 0.367548 0.212204i
\(263\) 11.8617 + 20.5451i 0.731426 + 1.26687i 0.956274 + 0.292473i \(0.0944783\pi\)
−0.224847 + 0.974394i \(0.572188\pi\)
\(264\) −2.23609 + 3.87303i −0.137622 + 0.238368i
\(265\) 24.7995i 1.52342i
\(266\) −13.1866 7.61327i −0.808520 0.466799i
\(267\) −5.45241 3.14795i −0.333682 0.192651i
\(268\) 1.59419i 0.0973805i
\(269\) 2.95808 5.12355i 0.180357 0.312388i −0.761645 0.647995i \(-0.775608\pi\)
0.942002 + 0.335606i \(0.108941\pi\)
\(270\) −1.74698 3.02586i −0.106318 0.184148i
\(271\) 2.76287 1.59515i 0.167833 0.0968982i −0.413731 0.910399i \(-0.635775\pi\)
0.581563 + 0.813501i \(0.302441\pi\)
\(272\) −7.11960 −0.431689
\(273\) 0 0
\(274\) −20.1806 −1.21915
\(275\) −3.62143 + 2.09083i −0.218381 + 0.126082i
\(276\) −0.782323 1.35502i −0.0470903 0.0815629i
\(277\) 10.9683 18.9977i 0.659022 1.14146i −0.321848 0.946791i \(-0.604304\pi\)
0.980869 0.194667i \(-0.0623627\pi\)
\(278\) 13.1045i 0.785958i
\(279\) −6.60866 3.81551i −0.395650 0.228429i
\(280\) 35.5264 + 20.5112i 2.12311 + 1.22578i
\(281\) 11.9903i 0.715282i −0.933859 0.357641i \(-0.883581\pi\)
0.933859 0.357641i \(-0.116419\pi\)
\(282\) −7.99127 + 13.8413i −0.475873 + 0.824237i
\(283\) −7.18329 12.4418i −0.427002 0.739590i 0.569603 0.821920i \(-0.307097\pi\)
−0.996605 + 0.0823303i \(0.973764\pi\)
\(284\) 3.40662 1.96681i 0.202146 0.116709i
\(285\) 7.12498 0.422047
\(286\) 0 0
\(287\) −5.98792 −0.353456
\(288\) −2.13632 + 1.23341i −0.125884 + 0.0726791i
\(289\) 5.51089 + 9.54513i 0.324170 + 0.561478i
\(290\) −3.23341 + 5.60042i −0.189872 + 0.328868i
\(291\) 10.0315i 0.588055i
\(292\) 2.96464 + 1.71164i 0.173492 + 0.100166i
\(293\) 16.2452 + 9.37920i 0.949058 + 0.547939i 0.892788 0.450477i \(-0.148746\pi\)
0.0562695 + 0.998416i \(0.482079\pi\)
\(294\) 20.0248i 1.16787i
\(295\) 3.04892 5.28088i 0.177515 0.307465i
\(296\) 6.94385 + 12.0271i 0.403603 + 0.699061i
\(297\) 1.27030 0.733406i 0.0737101 0.0425565i
\(298\) −17.8944 −1.03659
\(299\) 0 0
\(300\) −1.26875 −0.0732513
\(301\) 9.91428 5.72401i 0.571450 0.329927i
\(302\) −1.22587 2.12327i −0.0705411 0.122181i
\(303\) 6.94385 12.0271i 0.398913 0.690938i
\(304\) 7.40449i 0.424676i
\(305\) 18.9977 + 10.9683i 1.08780 + 0.628043i
\(306\) 2.64044 + 1.52446i 0.150944 + 0.0871475i
\(307\) 25.6262i 1.46257i −0.682074 0.731283i \(-0.738922\pi\)
0.682074 0.731283i \(-0.261078\pi\)
\(308\) −1.56734 + 2.71470i −0.0893072 + 0.154685i
\(309\) −8.70171 15.0718i −0.495023 0.857405i
\(310\) 23.0904 13.3312i 1.31145 0.757164i
\(311\) −11.3817 −0.645394 −0.322697 0.946502i \(-0.604590\pi\)
−0.322697 + 0.946502i \(0.604590\pi\)
\(312\) 0 0
\(313\) 27.5743 1.55859 0.779297 0.626655i \(-0.215576\pi\)
0.779297 + 0.626655i \(0.215576\pi\)
\(314\) −11.5569 + 6.67241i −0.652196 + 0.376546i
\(315\) −6.72737 11.6521i −0.379044 0.656524i
\(316\) 0.894928 1.55006i 0.0503436 0.0871977i
\(317\) 11.2597i 0.632405i −0.948692 0.316203i \(-0.897592\pi\)
0.948692 0.316203i \(-0.102408\pi\)
\(318\) −9.55818 5.51842i −0.535996 0.309458i
\(319\) −2.35113 1.35743i −0.131638 0.0760014i
\(320\) 24.9366i 1.39400i
\(321\) −5.27628 + 9.13879i −0.294493 + 0.510077i
\(322\) 10.5260 + 18.2315i 0.586588 + 1.01600i
\(323\) −5.38446 + 3.10872i −0.299599 + 0.172974i
\(324\) 0.445042 0.0247245
\(325\) 0 0
\(326\) 4.86294 0.269333
\(327\) −0.927243 + 0.535344i −0.0512766 + 0.0296046i
\(328\) 1.90097 + 3.29257i 0.104963 + 0.181802i
\(329\) −30.7732 + 53.3008i −1.69658 + 2.93857i
\(330\) 5.12498i 0.282121i
\(331\) 10.3113 + 5.95324i 0.566761 + 0.327220i 0.755855 0.654739i \(-0.227222\pi\)
−0.189094 + 0.981959i \(0.560555\pi\)
\(332\) −0.251598 0.145260i −0.0138082 0.00797218i
\(333\) 4.55496i 0.249610i
\(334\) −13.1054 + 22.6992i −0.717094 + 1.24204i
\(335\) 5.01842 + 8.69215i 0.274185 + 0.474903i
\(336\) 12.1092 6.99127i 0.660613 0.381405i
\(337\) −17.1672 −0.935157 −0.467578 0.883952i \(-0.654873\pi\)
−0.467578 + 0.883952i \(0.654873\pi\)
\(338\) 0 0
\(339\) −16.5308 −0.897830
\(340\) 2.64044 1.52446i 0.143198 0.0826754i
\(341\) 5.59664 + 9.69366i 0.303075 + 0.524941i
\(342\) 1.58546 2.74609i 0.0857317 0.148492i
\(343\) 43.4989i 2.34872i
\(344\) −6.29492 3.63437i −0.339399 0.195952i
\(345\) −8.53109 4.92543i −0.459298 0.265176i
\(346\) 16.5036i 0.887242i
\(347\) 12.1380 21.0237i 0.651603 1.12861i −0.331131 0.943585i \(-0.607430\pi\)
0.982734 0.185025i \(-0.0592366\pi\)
\(348\) −0.411854 0.713352i −0.0220777 0.0382397i
\(349\) 3.95983 2.28621i 0.211965 0.122378i −0.390259 0.920705i \(-0.627615\pi\)
0.602224 + 0.798327i \(0.294281\pi\)
\(350\) 17.0707 0.912467
\(351\) 0 0
\(352\) 3.61835 0.192859
\(353\) −5.26203 + 3.03803i −0.280069 + 0.161698i −0.633455 0.773780i \(-0.718364\pi\)
0.353385 + 0.935478i \(0.385030\pi\)
\(354\) −1.35690 2.35021i −0.0721182 0.124912i
\(355\) 12.3828 21.4477i 0.657213 1.13833i
\(356\) 2.80194i 0.148502i
\(357\) 10.1680 + 5.87047i 0.538145 + 0.310698i
\(358\) −9.20932 5.31700i −0.486728 0.281012i
\(359\) 14.9661i 0.789883i 0.918706 + 0.394942i \(0.129235\pi\)
−0.918706 + 0.394942i \(0.870765\pi\)
\(360\) −4.27144 + 7.39835i −0.225125 + 0.389927i
\(361\) −6.26689 10.8546i −0.329836 0.571293i
\(362\) −3.92701 + 2.26726i −0.206399 + 0.119164i
\(363\) 8.84846 0.464424
\(364\) 0 0
\(365\) 21.5526 1.12811
\(366\) 8.45475 4.88135i 0.441937 0.255152i
\(367\) −18.5417 32.1151i −0.967868 1.67640i −0.701704 0.712468i \(-0.747577\pi\)
−0.266164 0.963928i \(-0.585756\pi\)
\(368\) 5.11865 8.86575i 0.266828 0.462159i
\(369\) 1.24698i 0.0649152i
\(370\) 13.7827 + 7.95742i 0.716526 + 0.413687i
\(371\) −36.8072 21.2506i −1.91093 1.10328i
\(372\) 3.39612i 0.176081i
\(373\) 18.2545 31.6177i 0.945183 1.63710i 0.189798 0.981823i \(-0.439217\pi\)
0.755385 0.655282i \(-0.227450\pi\)
\(374\) −2.23609 3.87303i −0.115626 0.200270i
\(375\) 5.21501 3.01089i 0.269302 0.155481i
\(376\) 39.0780 2.01529
\(377\) 0 0
\(378\) −5.98792 −0.307985
\(379\) −23.0234 + 13.2925i −1.18263 + 0.682792i −0.956622 0.291333i \(-0.905901\pi\)
−0.226009 + 0.974125i \(0.572568\pi\)
\(380\) −1.58546 2.74609i −0.0813323 0.140872i
\(381\) −4.76875 + 8.25972i −0.244310 + 0.423158i
\(382\) 26.6625i 1.36417i
\(383\) 12.4276 + 7.17510i 0.635022 + 0.366630i 0.782694 0.622406i \(-0.213845\pi\)
−0.147672 + 0.989036i \(0.547178\pi\)
\(384\) −5.33836 3.08211i −0.272422 0.157283i
\(385\) 19.7356i 1.00582i
\(386\) 5.25451 9.10108i 0.267448 0.463233i
\(387\) 1.19202 + 2.06464i 0.0605939 + 0.104952i
\(388\) 3.86630 2.23221i 0.196282 0.113323i
\(389\) 22.6582 1.14881 0.574407 0.818570i \(-0.305233\pi\)
0.574407 + 0.818570i \(0.305233\pi\)
\(390\) 0 0
\(391\) 8.59611 0.434724
\(392\) 42.4018 24.4807i 2.14161 1.23646i
\(393\) 2.75451 + 4.77096i 0.138947 + 0.240663i
\(394\) −16.5078 + 28.5924i −0.831652 + 1.44046i
\(395\) 11.2687i 0.566992i
\(396\) −0.565335 0.326396i −0.0284092 0.0164020i
\(397\) 6.84813 + 3.95377i 0.343698 + 0.198434i 0.661906 0.749587i \(-0.269748\pi\)
−0.318208 + 0.948021i \(0.603081\pi\)
\(398\) 17.7724i 0.890850i
\(399\) 6.10537 10.5748i 0.305651 0.529402i
\(400\) −4.15064 7.18911i −0.207532 0.359456i
\(401\) −2.54318 + 1.46830i −0.127000 + 0.0733236i −0.562154 0.827032i \(-0.690027\pi\)
0.435154 + 0.900356i \(0.356694\pi\)
\(402\) 4.46681 0.222784
\(403\) 0 0
\(404\) −6.18060 −0.307497
\(405\) 2.42655 1.40097i 0.120576 0.0696147i
\(406\) 5.54138 + 9.59796i 0.275014 + 0.476339i
\(407\) −3.34063 + 5.78615i −0.165589 + 0.286809i
\(408\) 7.45473i 0.369064i
\(409\) −10.1801 5.87747i −0.503372 0.290622i 0.226733 0.973957i \(-0.427196\pi\)
−0.730105 + 0.683335i \(0.760529\pi\)
\(410\) 3.77318 + 2.17845i 0.186344 + 0.107586i
\(411\) 16.1836i 0.798278i
\(412\) −3.87263 + 6.70758i −0.190791 + 0.330459i
\(413\) −5.22521 9.05033i −0.257116 0.445338i
\(414\) −3.79669 + 2.19202i −0.186597 + 0.107732i
\(415\) −1.82908 −0.0897862
\(416\) 0 0
\(417\) −10.5090 −0.514629
\(418\) −4.02800 + 2.32557i −0.197016 + 0.113747i
\(419\) −3.67092 6.35821i −0.179336 0.310619i 0.762317 0.647203i \(-0.224062\pi\)
−0.941653 + 0.336584i \(0.890728\pi\)
\(420\) −2.99396 + 5.18569i −0.146090 + 0.253036i
\(421\) 25.6963i 1.25236i 0.779677 + 0.626181i \(0.215383\pi\)
−0.779677 + 0.626181i \(0.784617\pi\)
\(422\) 1.99877 + 1.15399i 0.0972985 + 0.0561753i
\(423\) −11.0999 6.40850i −0.539693 0.311592i
\(424\) 26.9855i 1.31053i
\(425\) 3.48523 6.03660i 0.169058 0.292818i
\(426\) −5.51089 9.54513i −0.267003 0.462463i
\(427\) 32.5580 18.7974i 1.57559 0.909669i
\(428\) 4.69633 0.227006
\(429\) 0 0
\(430\) −8.32975 −0.401696
\(431\) 7.74399 4.47099i 0.373015 0.215360i −0.301760 0.953384i \(-0.597574\pi\)
0.674775 + 0.738024i \(0.264241\pi\)
\(432\) 1.45593 + 2.52174i 0.0700483 + 0.121327i
\(433\) 1.45742 2.52432i 0.0700391 0.121311i −0.828879 0.559428i \(-0.811021\pi\)
0.898918 + 0.438116i \(0.144354\pi\)
\(434\) 45.6939i 2.19338i
\(435\) −4.49119 2.59299i −0.215336 0.124324i
\(436\) 0.412662 + 0.238250i 0.0197629 + 0.0114101i
\(437\) 8.94007i 0.427661i
\(438\) 4.79590 8.30674i 0.229157 0.396911i
\(439\) 4.52930 + 7.84498i 0.216172 + 0.374421i 0.953634 0.300967i \(-0.0973095\pi\)
−0.737463 + 0.675388i \(0.763976\pi\)
\(440\) 10.8520 6.26540i 0.517348 0.298691i
\(441\) −16.0586 −0.764696
\(442\) 0 0
\(443\) 11.2325 0.533672 0.266836 0.963742i \(-0.414022\pi\)
0.266836 + 0.963742i \(0.414022\pi\)
\(444\) −1.75556 + 1.01357i −0.0833152 + 0.0481021i
\(445\) 8.82036 + 15.2773i 0.418125 + 0.724214i
\(446\) 11.6283 20.1409i 0.550618 0.953698i
\(447\) 14.3502i 0.678741i
\(448\) −37.0106 21.3681i −1.74859 1.00955i
\(449\) 24.9051 + 14.3790i 1.17534 + 0.678585i 0.954933 0.296822i \(-0.0959268\pi\)
0.220411 + 0.975407i \(0.429260\pi\)
\(450\) 3.55496i 0.167582i
\(451\) −0.914542 + 1.58403i −0.0430641 + 0.0745892i
\(452\) 3.67845 + 6.37126i 0.173020 + 0.299679i
\(453\) 1.70273 0.983074i 0.0800014 0.0461888i
\(454\) −12.1672 −0.571035
\(455\) 0 0
\(456\) −7.75302 −0.363068
\(457\) −16.5204 + 9.53803i −0.772790 + 0.446170i −0.833869 0.551963i \(-0.813879\pi\)
0.0610792 + 0.998133i \(0.480546\pi\)
\(458\) 1.78501 + 3.09173i 0.0834081 + 0.144467i
\(459\) −1.22252 + 2.11747i −0.0570624 + 0.0988350i
\(460\) 4.38404i 0.204407i
\(461\) −27.4817 15.8666i −1.27995 0.738981i −0.303113 0.952955i \(-0.598026\pi\)
−0.976839 + 0.213974i \(0.931359\pi\)
\(462\) 7.60643 + 4.39158i 0.353883 + 0.204315i
\(463\) 36.4784i 1.69530i 0.530559 + 0.847648i \(0.321982\pi\)
−0.530559 + 0.847648i \(0.678018\pi\)
\(464\) 2.69471 4.66737i 0.125099 0.216677i
\(465\) 10.6908 + 18.5171i 0.495775 + 0.858708i
\(466\) −6.24790 + 3.60723i −0.289428 + 0.167102i
\(467\) −13.0000 −0.601568 −0.300784 0.953692i \(-0.597248\pi\)
−0.300784 + 0.953692i \(0.597248\pi\)
\(468\) 0 0
\(469\) 17.2010 0.794271
\(470\) 38.7824 22.3910i 1.78890 1.03282i
\(471\) −5.35086 9.26795i −0.246554 0.427045i
\(472\) −3.31767 + 5.74637i −0.152708 + 0.264498i
\(473\) 3.49694i 0.160790i
\(474\) −4.34317 2.50753i −0.199489 0.115175i
\(475\) −6.27814 3.62469i −0.288061 0.166312i
\(476\) 5.22521i 0.239497i
\(477\) 4.42543 7.66507i 0.202626 0.350959i
\(478\) 4.42208 + 7.65926i 0.202261 + 0.350326i
\(479\) −4.86407 + 2.80827i −0.222245 + 0.128313i −0.606989 0.794710i \(-0.707623\pi\)
0.384744 + 0.923023i \(0.374290\pi\)
\(480\) 6.91185 0.315482
\(481\) 0 0
\(482\) 4.86294 0.221501
\(483\) −14.6205 + 8.44116i −0.665256 + 0.384086i
\(484\) −1.96897 3.41035i −0.0894985 0.155016i
\(485\) 14.0538 24.3418i 0.638148 1.10531i
\(486\) 1.24698i 0.0565641i
\(487\) 8.45010 + 4.87867i 0.382910 + 0.221073i 0.679084 0.734061i \(-0.262377\pi\)
−0.296173 + 0.955134i \(0.595711\pi\)
\(488\) −20.6722 11.9351i −0.935788 0.540277i
\(489\) 3.89977i 0.176354i
\(490\) 28.0541 48.5911i 1.26735 2.19512i
\(491\) −3.69418 6.39850i −0.166716 0.288760i 0.770547 0.637383i \(-0.219983\pi\)
−0.937263 + 0.348622i \(0.886650\pi\)
\(492\) −0.480608 + 0.277479i −0.0216675 + 0.0125097i
\(493\) 4.52542 0.203815
\(494\) 0 0
\(495\) −4.10992 −0.184727
\(496\) −19.2435 + 11.1102i −0.864056 + 0.498863i
\(497\) −21.2216 36.7569i −0.951920 1.64877i
\(498\) −0.407010 + 0.704961i −0.0182385 + 0.0315901i
\(499\) 43.2814i 1.93754i −0.247956 0.968771i \(-0.579759\pi\)
0.247956 0.968771i \(-0.420241\pi\)
\(500\) −2.32090 1.33997i −0.103794 0.0599253i
\(501\) −18.2033 10.5097i −0.813264 0.469538i
\(502\) 3.04892i 0.136080i
\(503\) −5.38351 + 9.32451i −0.240039 + 0.415760i −0.960725 0.277502i \(-0.910494\pi\)
0.720686 + 0.693261i \(0.243827\pi\)
\(504\) 7.32036 + 12.6792i 0.326075 + 0.564778i
\(505\) −33.6992 + 19.4562i −1.49959 + 0.865791i
\(506\) 6.43057 0.285874
\(507\) 0 0
\(508\) 4.24459 0.188323
\(509\) −35.9788 + 20.7724i −1.59473 + 0.920720i −0.602256 + 0.798303i \(0.705731\pi\)
−0.992479 + 0.122417i \(0.960935\pi\)
\(510\) −4.27144 7.39835i −0.189142 0.327604i
\(511\) 18.4683 31.9880i 0.816990 1.41507i
\(512\) 24.9390i 1.10216i
\(513\) 2.20220 + 1.27144i 0.0972293 + 0.0561354i
\(514\) 15.2596 + 8.81013i 0.673072 + 0.388598i
\(515\) 48.7633i 2.14877i
\(516\) 0.530499 0.918852i 0.0233539 0.0404502i
\(517\) 9.40007 + 16.2814i 0.413415 + 0.716055i
\(518\) 23.6206 13.6374i 1.03783 0.599191i
\(519\) −13.2349 −0.580948
\(520\) 0 0
\(521\) 25.7198 1.12680 0.563402 0.826183i \(-0.309492\pi\)
0.563402 + 0.826183i \(0.309492\pi\)
\(522\) −1.99877 + 1.15399i −0.0874837 + 0.0505087i
\(523\) −4.29643 7.44163i −0.187870 0.325400i 0.756670 0.653797i \(-0.226825\pi\)
−0.944540 + 0.328397i \(0.893492\pi\)
\(524\) 1.22587 2.12327i 0.0535525 0.0927557i
\(525\) 13.6896i 0.597464i
\(526\) −25.6194 14.7913i −1.11706 0.644933i
\(527\) −16.1584 9.32908i −0.703873 0.406381i
\(528\) 4.27114i 0.185878i
\(529\) 5.31982 9.21420i 0.231297 0.400618i
\(530\) 15.4623 + 26.7814i 0.671638 + 1.16331i
\(531\) 1.88472 1.08815i 0.0817901 0.0472215i
\(532\) −5.43429 −0.235606
\(533\) 0 0
\(534\) 7.85086 0.339740
\(535\) 25.6063 14.7838i 1.10706 0.639160i
\(536\) −5.46077 9.45833i −0.235869 0.408538i
\(537\) 4.26391 7.38530i 0.184001 0.318699i
\(538\) 7.37734i 0.318060i
\(539\) 20.3992 + 11.7775i 0.878655 + 0.507292i
\(540\) −1.07992 0.623490i −0.0464722 0.0268307i
\(541\) 31.3534i 1.34799i −0.738736 0.673995i \(-0.764577\pi\)
0.738736 0.673995i \(-0.235423\pi\)
\(542\) −1.98911 + 3.44525i −0.0854398 + 0.147986i
\(543\) −1.81820 3.14921i −0.0780264 0.135146i
\(544\) −5.22340 + 3.01573i −0.223951 + 0.129298i
\(545\) 3.00000 0.128506
\(546\) 0 0
\(547\) 19.9342 0.852325 0.426163 0.904647i \(-0.359865\pi\)
0.426163 + 0.904647i \(0.359865\pi\)
\(548\) −6.23744 + 3.60119i −0.266450 + 0.153835i
\(549\) 3.91454 + 6.78019i 0.167069 + 0.289371i
\(550\) 2.60723 4.51585i 0.111173 0.192557i
\(551\) 4.70650i 0.200503i
\(552\) 9.28307 + 5.35958i 0.395114 + 0.228119i
\(553\) −16.7249 9.65615i −0.711217 0.410621i
\(554\) 27.3545i 1.16218i
\(555\) −6.38135 + 11.0528i −0.270873 + 0.469167i
\(556\) 2.33848 + 4.05036i 0.0991736 + 0.171774i
\(557\) −28.7823 + 16.6174i −1.21954 + 0.704104i −0.964820 0.262910i \(-0.915318\pi\)
−0.254723 + 0.967014i \(0.581984\pi\)
\(558\) 9.51573 0.402833
\(559\) 0 0
\(560\) −39.1782 −1.65558
\(561\) 3.10593 1.79321i 0.131132 0.0757093i
\(562\) 7.47584 + 12.9485i 0.315349 + 0.546201i
\(563\) 1.93565 3.35264i 0.0815779 0.141297i −0.822350 0.568982i \(-0.807337\pi\)
0.903928 + 0.427685i \(0.140671\pi\)
\(564\) 5.70410i 0.240186i
\(565\) 40.1128 + 23.1591i 1.68756 + 0.974312i
\(566\) 15.5147 + 8.95742i 0.652132 + 0.376508i
\(567\) 4.80194i 0.201662i
\(568\) −13.4743 + 23.3382i −0.565371 + 0.979251i
\(569\) 10.0728 + 17.4467i 0.422276 + 0.731403i 0.996162 0.0875324i \(-0.0278981\pi\)
−0.573886 + 0.818935i \(0.694565\pi\)
\(570\) −7.69438 + 4.44235i −0.322282 + 0.186070i
\(571\) 32.1269 1.34447 0.672234 0.740338i \(-0.265335\pi\)
0.672234 + 0.740338i \(0.265335\pi\)
\(572\) 0 0
\(573\) 21.3817 0.893231
\(574\) 6.46645 3.73341i 0.269904 0.155829i
\(575\) 5.01142 + 8.68003i 0.208991 + 0.361982i
\(576\) 4.44989 7.70743i 0.185412 0.321143i
\(577\) 16.7506i 0.697338i −0.937246 0.348669i \(-0.886634\pi\)
0.937246 0.348669i \(-0.113366\pi\)
\(578\) −11.9026 6.87196i −0.495082 0.285836i
\(579\) 7.29850 + 4.21379i 0.303315 + 0.175119i
\(580\) 2.30798i 0.0958336i
\(581\) −1.56734 + 2.71470i −0.0650240 + 0.112625i
\(582\) −6.25451 10.8331i −0.259258 0.449048i
\(583\) −11.2432 + 6.49127i −0.465646 + 0.268841i
\(584\) −23.4523 −0.970465
\(585\) 0 0
\(586\) −23.3913 −0.966287
\(587\) −5.83524 + 3.36898i −0.240846 + 0.139053i −0.615566 0.788086i \(-0.711072\pi\)
0.374719 + 0.927138i \(0.377739\pi\)
\(588\) 3.57338 + 6.18927i 0.147364 + 0.255241i
\(589\) −9.70237 + 16.8050i −0.399779 + 0.692438i
\(590\) 7.60388i 0.313047i
\(591\) −22.9293 13.2383i −0.943186 0.544549i
\(592\) −11.4864 6.63169i −0.472089 0.272561i
\(593\) 18.1172i 0.743985i −0.928236 0.371992i \(-0.878675\pi\)
0.928236 0.371992i \(-0.121325\pi\)
\(594\) −0.914542 + 1.58403i −0.0375241 + 0.0649937i
\(595\) −16.4487 28.4900i −0.674331 1.16797i
\(596\) −5.53082 + 3.19322i −0.226551 + 0.130799i
\(597\) 14.2524 0.583310
\(598\) 0 0
\(599\) −26.7851 −1.09441 −0.547204 0.836999i \(-0.684308\pi\)
−0.547204 + 0.836999i \(0.684308\pi\)
\(600\) 7.52751 4.34601i 0.307309 0.177425i
\(601\) 2.35086 + 4.07180i 0.0958934 + 0.166092i 0.909981 0.414650i \(-0.136096\pi\)
−0.814088 + 0.580742i \(0.802763\pi\)
\(602\) −7.13773 + 12.3629i −0.290912 + 0.503874i
\(603\) 3.58211i 0.145875i
\(604\) −0.757788 0.437509i −0.0308340 0.0178020i
\(605\) −21.4712 12.3964i −0.872930 0.503986i
\(606\) 17.3177i 0.703482i
\(607\) −13.8198 + 23.9366i −0.560929 + 0.971558i 0.436486 + 0.899711i \(0.356223\pi\)
−0.997416 + 0.0718472i \(0.977111\pi\)
\(608\) 3.13640 + 5.43240i 0.127198 + 0.220313i
\(609\) −7.69697 + 4.44385i −0.311897 + 0.180074i
\(610\) −27.3545 −1.10755
\(611\) 0 0
\(612\) 1.08815 0.0439857
\(613\) 41.7236 24.0891i 1.68520 0.972950i 0.727091 0.686541i \(-0.240872\pi\)
0.958108 0.286409i \(-0.0924615\pi\)
\(614\) 15.9777 + 27.6742i 0.644807 + 1.11684i
\(615\) −1.74698 + 3.02586i −0.0704450 + 0.122014i
\(616\) 21.4752i 0.865259i
\(617\) −26.2443 15.1521i −1.05655 0.610002i −0.132077 0.991239i \(-0.542165\pi\)
−0.924477 + 0.381238i \(0.875498\pi\)
\(618\) 18.7942 + 10.8509i 0.756015 + 0.436485i
\(619\) 10.9041i 0.438272i 0.975694 + 0.219136i \(0.0703239\pi\)
−0.975694 + 0.219136i \(0.929676\pi\)
\(620\) 4.75786 8.24086i 0.191080 0.330961i
\(621\) −1.75786 3.04471i −0.0705407 0.122180i
\(622\) 12.2912 7.09634i 0.492833 0.284537i
\(623\) 30.2325 1.21124
\(624\) 0 0
\(625\) −31.1269 −1.24508
\(626\) −29.7780 + 17.1923i −1.19017 + 0.687143i
\(627\) −1.86496 3.23021i −0.0744794 0.129002i
\(628\) −2.38135 + 4.12463i −0.0950264 + 0.164591i
\(629\) 11.1371i 0.444064i
\(630\) 14.5300 + 8.38889i 0.578888 + 0.334221i
\(631\) −9.05199 5.22617i −0.360354 0.208050i 0.308882 0.951100i \(-0.400045\pi\)
−0.669236 + 0.743050i \(0.733379\pi\)
\(632\) 12.2620i 0.487758i
\(633\) −0.925428 + 1.60289i −0.0367824 + 0.0637091i
\(634\) 7.02028 + 12.1595i 0.278811 + 0.482915i
\(635\) 23.1432 13.3617i 0.918410 0.530244i
\(636\) −3.93900 −0.156192
\(637\) 0 0
\(638\) 3.38537 0.134028
\(639\) 7.65460 4.41939i 0.302811 0.174828i
\(640\) 8.63587 + 14.9578i 0.341363 + 0.591257i
\(641\) −8.79709 + 15.2370i −0.347464 + 0.601826i −0.985798 0.167934i \(-0.946291\pi\)
0.638334 + 0.769760i \(0.279624\pi\)
\(642\) 13.1588i 0.519338i
\(643\) −19.5772 11.3029i −0.772049 0.445743i 0.0615560 0.998104i \(-0.480394\pi\)
−0.833605 + 0.552361i \(0.813727\pi\)
\(644\) 6.50674 + 3.75667i 0.256401 + 0.148033i
\(645\) 6.67994i 0.263022i
\(646\) 3.87651 6.71431i 0.152519 0.264171i
\(647\) −12.3959 21.4703i −0.487333 0.844085i 0.512561 0.858651i \(-0.328697\pi\)
−0.999894 + 0.0145658i \(0.995363\pi\)
\(648\) −2.64044 + 1.52446i −0.103726 + 0.0598864i
\(649\) −3.19221 −0.125305
\(650\) 0 0
\(651\) 36.6437 1.43618
\(652\) 1.50304 0.867781i 0.0588636 0.0339849i
\(653\) 10.9053 + 18.8885i 0.426757 + 0.739164i 0.996583 0.0826012i \(-0.0263228\pi\)
−0.569826 + 0.821765i \(0.692989\pi\)
\(654\) 0.667563 1.15625i 0.0261038 0.0452131i
\(655\) 15.4359i 0.603132i
\(656\) −3.14456 1.81551i −0.122774 0.0708838i
\(657\) 6.66149 + 3.84601i 0.259889 + 0.150047i
\(658\) 76.7472i 2.99192i
\(659\) −8.27628 + 14.3349i −0.322398 + 0.558410i −0.980982 0.194097i \(-0.937822\pi\)
0.658584 + 0.752507i \(0.271156\pi\)
\(660\) 0.914542 + 1.58403i 0.0355985 + 0.0616584i
\(661\) 13.8166 7.97703i 0.537405 0.310271i −0.206622 0.978421i \(-0.566247\pi\)
0.744026 + 0.668150i \(0.232914\pi\)
\(662\) −14.8471 −0.577050
\(663\) 0 0
\(664\) 1.99031 0.0772391
\(665\) −29.6299 + 17.1069i −1.14900 + 0.663376i
\(666\) 2.83997 + 4.91897i 0.110047 + 0.190606i
\(667\) −3.25355 + 5.63532i −0.125978 + 0.218200i
\(668\) 9.35450i 0.361937i
\(669\) 16.1517 + 9.32520i 0.624462 + 0.360533i
\(670\) −10.8389 6.25786i −0.418745 0.241762i
\(671\) 11.4838i 0.443327i
\(672\) 5.92274 10.2585i 0.228475 0.395730i
\(673\) −3.69418 6.39850i −0.142400 0.246644i 0.786000 0.618227i \(-0.212149\pi\)
−0.928400 + 0.371583i \(0.878815\pi\)
\(674\) 18.5391 10.7036i 0.714101 0.412286i
\(675\) −2.85086 −0.109729
\(676\) 0 0
\(677\) −22.1454 −0.851118 −0.425559 0.904931i \(-0.639922\pi\)
−0.425559 + 0.904931i \(0.639922\pi\)
\(678\) 17.8519 10.3068i 0.685597 0.395830i
\(679\) −24.0852 41.7168i −0.924306 1.60094i
\(680\) −10.4438 + 18.0893i −0.400503 + 0.693692i
\(681\) 9.75733i 0.373902i
\(682\) −12.0878 6.97889i −0.462866 0.267236i
\(683\) 7.88103 + 4.55011i 0.301559 + 0.174105i 0.643143 0.765746i \(-0.277630\pi\)
−0.341584 + 0.939851i \(0.610963\pi\)
\(684\) 1.13169i 0.0432711i
\(685\) −22.6727 + 39.2703i −0.866279 + 1.50044i
\(686\) −27.1211 46.9751i −1.03549 1.79352i
\(687\) −2.47938 + 1.43147i −0.0945941 + 0.0546139i
\(688\) 6.94198 0.264661
\(689\) 0 0
\(690\) 12.2838 0.467637
\(691\) 11.9261 6.88553i 0.453690 0.261938i −0.255697 0.966757i \(-0.582305\pi\)
0.709387 + 0.704819i \(0.248972\pi\)
\(692\) 2.94504 + 5.10096i 0.111954 + 0.193909i
\(693\) −3.52177 + 6.09989i −0.133781 + 0.231715i
\(694\) 30.2717i 1.14910i
\(695\) 25.5007 + 14.7228i 0.967295 + 0.558468i
\(696\) 4.88707 + 2.82155i 0.185244 + 0.106951i
\(697\) 3.04892i 0.115486i
\(698\) −2.85086 + 4.93783i −0.107906 + 0.186899i
\(699\) −2.89277 5.01043i −0.109415 0.189512i
\(700\) 5.27622 3.04623i 0.199422 0.115137i
\(701\) −46.5090 −1.75662 −0.878311 0.478090i \(-0.841329\pi\)
−0.878311 + 0.478090i \(0.841329\pi\)
\(702\) 0 0
\(703\) −11.5827 −0.436850
\(704\) −11.3054 + 6.52715i −0.426086 + 0.246001i
\(705\) 17.9562 + 31.1011i 0.676270 + 1.17133i
\(706\) 3.78836 6.56164i 0.142577 0.246951i
\(707\) 66.6878i 2.50805i
\(708\) −0.838781 0.484271i −0.0315233 0.0182000i
\(709\) 6.27492 + 3.62283i 0.235660 + 0.136058i 0.613180 0.789943i \(-0.289890\pi\)
−0.377521 + 0.926001i \(0.623223\pi\)
\(710\) 30.8823i 1.15899i
\(711\) 2.01089 3.48296i 0.0754141 0.130621i
\(712\) −9.59783 16.6239i −0.359694 0.623008i
\(713\) 23.2343 13.4143i 0.870130 0.502370i
\(714\) −14.6407 −0.547915
\(715\) 0 0
\(716\) −3.79523 −0.141835
\(717\) −6.14225 + 3.54623i −0.229386 + 0.132436i
\(718\) −9.33124 16.1622i −0.348239 0.603167i
\(719\) 12.7573 22.0963i 0.475768 0.824055i −0.523846 0.851813i \(-0.675503\pi\)
0.999615 + 0.0277580i \(0.00883678\pi\)
\(720\) 8.15883i 0.304062i
\(721\) 72.3739 + 41.7851i 2.69534 + 1.55616i
\(722\) 13.5354 + 7.81468i 0.503736 + 0.290832i
\(723\) 3.89977i 0.145034i
\(724\) −0.809175 + 1.40153i −0.0300728 + 0.0520875i
\(725\) 2.63826 + 4.56960i 0.0979825 + 0.169711i
\(726\) −9.55560 + 5.51693i −0.354641 + 0.204752i
\(727\) 14.4873 0.537303 0.268651 0.963238i \(-0.413422\pi\)
0.268651 + 0.963238i \(0.413422\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −23.2750 + 13.4378i −0.861445 + 0.497355i
\(731\) 2.91454 + 5.04814i 0.107798 + 0.186712i
\(732\) 1.74214 3.01747i 0.0643912 0.111529i
\(733\) 37.5036i 1.38523i 0.721308 + 0.692614i \(0.243541\pi\)
−0.721308 + 0.692614i \(0.756459\pi\)
\(734\) 40.0469 + 23.1211i 1.47816 + 0.853415i
\(735\) 38.9670 + 22.4976i 1.43732 + 0.829837i
\(736\) 8.67264i 0.319678i
\(737\) 2.62714 4.55034i 0.0967719 0.167614i
\(738\) 0.777479 + 1.34663i 0.0286194 + 0.0495703i
\(739\) −37.4016 + 21.5938i −1.37584 + 0.794341i −0.991656 0.128915i \(-0.958851\pi\)
−0.384184 + 0.923257i \(0.625517\pi\)
\(740\) 5.67994 0.208799
\(741\) 0 0
\(742\) 52.9982 1.94563
\(743\) 11.6710 6.73825i 0.428167 0.247202i −0.270398 0.962749i \(-0.587155\pi\)
0.698566 + 0.715546i \(0.253822\pi\)
\(744\) −11.6332 20.1493i −0.426493 0.738708i
\(745\) −20.1042 + 34.8214i −0.736560 + 1.27576i
\(746\) 45.5260i 1.66683i
\(747\) −0.565335 0.326396i −0.0206845 0.0119422i
\(748\) −1.38227 0.798053i −0.0505407 0.0291797i
\(749\) 50.6728i 1.85154i
\(750\) −3.75451 + 6.50301i −0.137095 + 0.237456i
\(751\) 17.7947 + 30.8213i 0.649338 + 1.12469i 0.983281 + 0.182093i \(0.0582872\pi\)
−0.333943 + 0.942593i \(0.608379\pi\)
\(752\) −32.3211 + 18.6606i −1.17863 + 0.680483i
\(753\) 2.44504 0.0891023
\(754\) 0 0
\(755\) −5.50902 −0.200494
\(756\) −1.85075 + 1.06853i −0.0673112 + 0.0388621i
\(757\) 6.10537 + 10.5748i 0.221903 + 0.384348i 0.955386 0.295360i \(-0.0954397\pi\)
−0.733483 + 0.679708i \(0.762106\pi\)
\(758\) 16.5755 28.7097i 0.602050 1.04278i
\(759\) 5.15691i 0.187184i
\(760\) 18.8131 + 10.8617i 0.682422 + 0.393997i
\(761\) 26.7663 + 15.4535i 0.970278 + 0.560190i 0.899321 0.437289i \(-0.144061\pi\)
0.0709569 + 0.997479i \(0.477395\pi\)
\(762\) 11.8931i 0.430840i
\(763\) 2.57069 4.45256i 0.0930651 0.161194i
\(764\) −4.75786 8.24086i −0.172134 0.298144i
\(765\) 5.93301 3.42543i 0.214509 0.123847i
\(766\) −17.8944 −0.646551
\(767\) 0 0
\(768\) −10.1129 −0.364918
\(769\) 10.3830 5.99462i 0.374420 0.216172i −0.300968 0.953634i \(-0.597310\pi\)
0.675388 + 0.737463i \(0.263976\pi\)
\(770\) −12.3049 21.3127i −0.443439 0.768058i
\(771\) −7.06518 + 12.2372i −0.254446 + 0.440714i
\(772\) 3.75063i 0.134988i
\(773\) −38.0758 21.9831i −1.36949 0.790676i −0.378628 0.925549i \(-0.623604\pi\)
−0.990863 + 0.134873i \(0.956938\pi\)
\(774\) −2.57457 1.48643i −0.0925409 0.0534285i
\(775\) 21.7549i 0.781460i
\(776\) −15.2925 + 26.4875i −0.548970 + 0.950845i
\(777\) 10.9363 + 18.9422i 0.392338 + 0.679549i
\(778\) −24.4689 + 14.1271i −0.877253 + 0.506482i
\(779\) −3.17092 −0.113610
\(780\) 0 0 <