Properties

Label 507.2.j.h.316.5
Level $507$
Weight $2$
Character 507.316
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 316.5
Root \(1.07992 + 0.623490i\) of defining polynomial
Character \(\chi\) \(=\) 507.316
Dual form 507.2.j.h.361.5

$q$-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 \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).

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

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 \(-0.188002\pi\)
−0.0669766 + 0.997755i \(0.521335\pi\)
\(3\) −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 −0.575855 + 0.817552i \(0.695331\pi\)
−0.995948 + 0.0899290i \(0.971336\pi\)
\(8\) 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 \(-0.404308\pi\)
−0.679127 + 0.734021i \(0.737641\pi\)
\(12\) 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 0.678829 0.734296i \(-0.262488\pi\)
−0.975334 + 0.220735i \(0.929154\pi\)
\(18\) 1.24698i 0.293916i
\(19\) −2.20220 + 1.27144i −0.505218 + 0.291688i −0.730866 0.682521i \(-0.760884\pi\)
0.225648 + 0.974209i \(0.427550\pi\)
\(20\) 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 −0.989022 0.147768i \(-0.952791\pi\)
0.622482 + 0.782634i \(0.286124\pi\)
\(24\) 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 −0.939066 0.343737i \(-0.888307\pi\)
0.767218 + 0.641386i \(0.221640\pi\)
\(30\) −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 \(-0.211177\pi\)
−0.139377 + 0.990239i \(0.544510\pi\)
\(38\) −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 \(-0.302289\pi\)
−0.413297 + 0.910596i \(0.635623\pi\)
\(42\) 2.99396 5.18569i 0.461978 0.800169i
\(43\) 1.19202 + 2.06464i 0.181782 + 0.314855i 0.942487 0.334242i \(-0.108480\pi\)
−0.760706 + 0.649097i \(0.775147\pi\)
\(44\) 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 \(-0.621421\pi\)
0.617642 + 0.786459i \(0.288088\pi\)
\(60\) 1.24698i 0.160984i
\(61\) 3.91454 + 6.78019i 0.501206 + 0.868114i 0.999999 + 0.00139289i \(0.000443372\pi\)
−0.498793 + 0.866721i \(0.666223\pi\)
\(62\) −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 \(-0.403551\pi\)
−0.677380 + 0.735633i \(0.736885\pi\)
\(68\) −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 \(-0.490925\pi\)
0.879927 + 0.475109i \(0.157591\pi\)
\(72\) −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 \(-0.441624\pi\)
−0.760320 + 0.649549i \(0.774958\pi\)
\(90\) 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 \(-0.496582\pi\)
0.871344 + 0.490672i \(0.163249\pi\)
\(98\) 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 −0.280592 0.959827i \(-0.590531\pi\)
0.971531 0.236913i \(-0.0761358\pi\)
\(102\) 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 0.489854 + 0.871804i \(0.337050\pi\)
−0.999932 + 0.0116758i \(0.996283\pi\)
\(108\) −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 0.933354 + 0.358957i \(0.116868\pi\)
−0.155811 + 0.987787i \(0.549799\pi\)
\(114\) 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 −0.996246 0.0865622i \(-0.972412\pi\)
0.573088 + 0.819494i \(0.305745\pi\)
\(128\) −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 \(-0.909641\pi\)
−0.237438 + 0.971403i \(0.576308\pi\)
\(138\) 4.38404i 0.373195i
\(139\) 5.25451 + 9.10108i 0.445682 + 0.771944i 0.998099 0.0616238i \(-0.0196279\pi\)
−0.552418 + 0.833568i \(0.686295\pi\)
\(140\) −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 \(-0.866675\pi\)
−0.104555 + 0.994519i \(0.533342\pi\)
\(150\) 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 \(-0.617861\pi\)
0.626400 + 0.779502i \(0.284528\pi\)
\(164\) 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 \(-0.635645\pi\)
−0.995255 + 0.0973035i \(0.968978\pi\)
\(168\) −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 0.999994 + 0.00360102i \(0.00114624\pi\)
−0.496878 + 0.867820i \(0.665520\pi\)
\(174\) 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 −0.661518 0.749930i \(-0.730087\pi\)
0.980217 + 0.197926i \(0.0634207\pi\)
\(180\) −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 −0.935600 0.353062i \(-0.885140\pi\)
0.162039 0.986784i \(-0.448193\pi\)
\(192\) 4.44989 7.70743i 0.321143 0.556236i
\(193\) 7.29850 + 4.21379i 0.525358 + 0.303315i 0.739124 0.673569i \(-0.235240\pi\)
−0.213766 + 0.976885i \(0.568573\pi\)
\(194\) 12.5090 0.898096
\(195\) 0 0
\(196\) −7.14675 −0.510482
\(197\) −22.9293 13.2383i −1.63365 0.943186i −0.982955 0.183844i \(-0.941146\pi\)
−0.650691 0.759343i \(-0.725521\pi\)
\(198\) −0.914542 + 1.58403i −0.0649937 + 0.112572i
\(199\) −7.12618 12.3429i −0.505161 0.874965i −0.999982 0.00597014i \(-0.998100\pi\)
0.494821 0.868995i \(-0.335234\pi\)
\(200\) 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 −0.896121 0.443811i \(-0.853626\pi\)
0.832412 + 0.554158i \(0.186960\pi\)
\(212\) 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 \(-0.118652\pi\)
0.150272 + 0.988645i \(0.451985\pi\)
\(224\) 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 \(-0.771630\pi\)
0.192635 + 0.981270i \(0.438297\pi\)
\(228\) −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 \(-0.626580\pi\)
0.604816 + 0.796365i \(0.293247\pi\)
\(242\) 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 0.824861 0.565336i \(-0.191253\pi\)
−0.902026 + 0.431682i \(0.857920\pi\)
\(252\) 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 −0.997743 0.0671545i \(-0.978608\pi\)
0.557029 + 0.830493i \(0.311941\pi\)
\(258\) −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 −0.224847 0.974394i \(-0.572188\pi\)
0.956274 0.292473i \(-0.0944783\pi\)
\(264\) −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 0.942002 0.335606i \(-0.108941\pi\)
−0.761645 + 0.647995i \(0.775608\pi\)
\(270\) −1.74698 + 3.02586i −0.106318 + 0.184148i
\(271\) −2.76287 1.59515i −0.167833 0.0968982i 0.413731 0.910399i \(-0.364225\pi\)
−0.581563 + 0.813501i \(0.697559\pi\)
\(272\) −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 0.980869 + 0.194667i \(0.0623627\pi\)
−0.321848 + 0.946791i \(0.604304\pi\)
\(278\) 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 −0.996605 0.0823303i \(-0.973764\pi\)
0.569603 + 0.821920i \(0.307097\pi\)
\(284\) −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 \(-0.851254\pi\)
−0.0562695 + 0.998416i \(0.517921\pi\)
\(294\) 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 \(-0.772778\pi\)
0.189094 + 0.981959i \(0.439445\pi\)
\(332\) 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 0.982734 + 0.185025i \(0.0592366\pi\)
−0.331131 + 0.943585i \(0.607430\pi\)
\(348\) −0.411854 + 0.713352i −0.0220777 + 0.0382397i
\(349\) −3.95983 2.28621i −0.211965 0.122378i 0.390259 0.920705i \(-0.372385\pi\)
−0.602224 + 0.798327i \(0.705719\pi\)
\(350\) 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 \(-0.281636\pi\)
−0.353385 + 0.935478i \(0.614970\pi\)
\(354\) −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 −0.266164 + 0.963928i \(0.585756\pi\)
−0.701704 + 0.712468i \(0.747577\pi\)
\(368\) 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 0.755385 + 0.655282i \(0.227450\pi\)
0.189798 + 0.981823i \(0.439217\pi\)
\(374\) −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 \(-0.0940988\pi\)
0.226009 + 0.974125i \(0.427432\pi\)
\(380\) −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 \(-0.786155\pi\)
0.147672 + 0.989036i \(0.452822\pi\)
\(384\) 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 \(-0.730252\pi\)
0.318208 + 0.948021i \(0.396919\pi\)
\(398\) 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 \(-0.309973\pi\)
−0.435154 + 0.900356i \(0.643306\pi\)
\(402\) 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 \(-0.572804\pi\)
0.730105 + 0.683335i \(0.239471\pi\)
\(410\) −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 −0.941653 0.336584i \(-0.890728\pi\)
0.762317 + 0.647203i \(0.224062\pi\)
\(420\) −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 \(-0.402426\pi\)
−0.674775 + 0.738024i \(0.735759\pi\)
\(432\) 1.45593 2.52174i 0.0700483 0.121327i
\(433\) 1.45742 + 2.52432i 0.0700391 + 0.121311i 0.898918 0.438116i \(-0.144354\pi\)
−0.828879 + 0.559428i \(0.811021\pi\)
\(434\) 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 −0.737463 0.675388i \(-0.763976\pi\)
0.953634 + 0.300967i \(0.0973095\pi\)
\(440\) −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 \(-0.904073\pi\)
−0.220411 + 0.975407i \(0.570740\pi\)
\(450\) 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 \(-0.186121\pi\)
−0.0610792 + 0.998133i \(0.519454\pi\)
\(458\) 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 \(-0.401974\pi\)
0.976839 + 0.213974i \(0.0686409\pi\)
\(462\) −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 \(-0.292377\pi\)
−0.384744 + 0.923023i \(0.625710\pi\)
\(480\) 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 \(-0.737623\pi\)
0.296173 + 0.955134i \(0.404289\pi\)
\(488\) 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 −0.937263 0.348622i \(-0.886650\pi\)
0.770547 + 0.637383i \(0.219983\pi\)
\(492\) 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 0.720686 0.693261i \(-0.243827\pi\)
−0.960725 + 0.277502i \(0.910494\pi\)
\(504\) 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 0.992479 + 0.122417i \(0.0390646\pi\)
0.602256 + 0.798303i \(0.294269\pi\)
\(510\) −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 −0.944540 0.328397i \(-0.893492\pi\)
0.756670 + 0.653797i \(0.226825\pi\)
\(524\) 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 \(-0.0846822\pi\)
0.254723 + 0.967014i \(0.418016\pi\)
\(558\) 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 0.903928 0.427685i \(-0.140671\pi\)
−0.822350 + 0.568982i \(0.807337\pi\)
\(564\) 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 −0.573886 0.818935i \(-0.694565\pi\)
0.996162 + 0.0875324i \(0.0278981\pi\)
\(570\) 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 \(-0.288928\pi\)
−0.374719 + 0.927138i \(0.622261\pi\)
\(588\) 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 −0.814088 0.580742i \(-0.802763\pi\)
0.909981 + 0.414650i \(0.136096\pi\)
\(602\) −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 −0.997416 0.0718472i \(-0.977111\pi\)
0.436486 0.899711i \(-0.356223\pi\)
\(608\) 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 −0.958108 0.286409i \(-0.907539\pi\)
−0.727091 0.686541i \(-0.759128\pi\)
\(614\) 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 \(-0.457835\pi\)
0.924477 + 0.381238i \(0.124502\pi\)
\(618\) −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 \(-0.599955\pi\)
0.669236 + 0.743050i \(0.266621\pi\)
\(632\) 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 0.638334 0.769760i \(-0.279624\pi\)
−0.985798 + 0.167934i \(0.946291\pi\)
\(642\) 13.1588i 0.519338i
\(643\) 19.5772 11.3029i 0.772049 0.445743i −0.0615560 0.998104i \(-0.519606\pi\)
0.833605 + 0.552361i \(0.186273\pi\)
\(644\) −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 −0.999894 0.0145658i \(-0.995363\pi\)
0.512561 + 0.858651i \(0.328697\pi\)
\(648\) 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 −0.569826 0.821765i \(-0.692989\pi\)
0.996583 + 0.0826012i \(0.0263228\pi\)
\(654\) 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 0.658584 0.752507i \(-0.271156\pi\)
−0.980982 + 0.194097i \(0.937822\pi\)
\(660\) 0.914542 1.58403i 0.0355985 0.0616584i
\(661\) −13.8166 7.97703i −0.537405 0.310271i 0.206622 0.978421i \(-0.433753\pi\)
−0.744026 + 0.668150i \(0.767086\pi\)
\(662\) −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 −0.928400 0.371583i \(-0.878815\pi\)
0.786000 + 0.618227i \(0.212149\pi\)
\(674\) −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 \(-0.722370\pi\)
0.341584 + 0.939851i \(0.389037\pi\)
\(684\) 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 \(-0.417695\pi\)
−0.709387 + 0.704819i \(0.751028\pi\)
\(692\) 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 \(-0.710110\pi\)
0.377521 + 0.926001i \(0.376777\pi\)
\(710\) 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 0.999615 0.0277580i \(-0.00883678\pi\)
−0.523846 + 0.851813i \(0.675503\pi\)
\(720\) 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 \(-0.0411495\pi\)
0.384184 + 0.923257i \(0.374483\pi\)
\(740\) 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 \(-0.412845\pi\)
−0.698566 + 0.715546i \(0.746178\pi\)
\(744\) −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 −0.333943 0.942593i \(-0.608379\pi\)
0.983281 0.182093i \(-0.0582872\pi\)
\(752\) 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 −0.733483 0.679708i \(-0.762106\pi\)
0.955386 + 0.295360i \(0.0954397\pi\)
\(758\) 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 \(-0.855939\pi\)
−0.0709569 + 0.997479i \(0.522605\pi\)
\(762\) 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 \(-0.402690\pi\)
−0.675388 + 0.737463i \(0.736024\pi\)
\(770\) −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 \(-0.376396\pi\)
0.990863 + 0.134873i \(0.0430625\pi\)
\(774\) 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