Properties

Label 507.2.e.k.484.1
Level $507$
Weight $2$
Character 507.484
Analytic conductor $4.048$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(4.04841538248\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.64827.1
Defining polynomial: \(x^{6} - x^{5} + 3 x^{4} + 5 x^{2} - 2 x + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 484.1
Root \(-0.623490 - 1.07992i\) of defining polynomial
Character \(\chi\) \(=\) 507.484
Dual form 507.2.e.k.22.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.623490 - 1.07992i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.222521 - 0.385418i) q^{4} -2.80194 q^{5} +(-0.623490 + 1.07992i) q^{6} +(2.40097 - 4.15860i) q^{7} -3.04892 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.623490 - 1.07992i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.222521 - 0.385418i) q^{4} -2.80194 q^{5} +(-0.623490 + 1.07992i) q^{6} +(2.40097 - 4.15860i) q^{7} -3.04892 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.74698 + 3.02586i) q^{10} +(-0.733406 - 1.27030i) q^{11} -0.445042 q^{12} -5.98792 q^{14} +(1.40097 + 2.42655i) q^{15} +(1.45593 + 2.52174i) q^{16} +(1.22252 - 2.11747i) q^{17} +1.24698 q^{18} +(-1.27144 + 2.20220i) q^{19} +(-0.623490 + 1.07992i) q^{20} -4.80194 q^{21} +(-0.914542 + 1.58403i) q^{22} +(1.75786 + 3.04471i) q^{23} +(1.52446 + 2.64044i) q^{24} +2.85086 q^{25} +1.00000 q^{27} +(-1.06853 - 1.85075i) q^{28} +(-0.925428 - 1.60289i) q^{29} +(1.74698 - 3.02586i) q^{30} -7.63102 q^{31} +(-1.23341 + 2.13632i) q^{32} +(-0.733406 + 1.27030i) q^{33} -3.04892 q^{34} +(-6.72737 + 11.6521i) q^{35} +(0.222521 + 0.385418i) q^{36} +(2.27748 + 3.94471i) q^{37} +3.17092 q^{38} +8.54288 q^{40} +(-0.623490 - 1.07992i) q^{41} +(2.99396 + 5.18569i) q^{42} +(-1.19202 + 2.06464i) q^{43} -0.652793 q^{44} +(1.40097 - 2.42655i) q^{45} +(2.19202 - 3.79669i) q^{46} +12.8170 q^{47} +(1.45593 - 2.52174i) q^{48} +(-8.02930 - 13.9072i) q^{49} +(-1.77748 - 3.07868i) q^{50} -2.44504 q^{51} -8.85086 q^{53} +(-0.623490 - 1.07992i) q^{54} +(2.05496 + 3.55929i) q^{55} +(-7.32036 + 12.6792i) q^{56} +2.54288 q^{57} +(-1.15399 + 1.99877i) q^{58} +(-1.08815 + 1.88472i) q^{59} +1.24698 q^{60} +(3.91454 - 6.78019i) q^{61} +(4.75786 + 8.24086i) q^{62} +(2.40097 + 4.15860i) q^{63} +8.89977 q^{64} +1.82908 q^{66} +(1.79105 + 3.10219i) q^{67} +(-0.544073 - 0.942362i) q^{68} +(1.75786 - 3.04471i) q^{69} +16.7778 q^{70} +(4.41939 - 7.65460i) q^{71} +(1.52446 - 2.64044i) q^{72} -7.69202 q^{73} +(2.83997 - 4.91897i) q^{74} +(-1.42543 - 2.46891i) q^{75} +(0.565843 + 0.980069i) q^{76} -7.04354 q^{77} -4.02177 q^{79} +(-4.07942 - 7.06576i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.777479 + 1.34663i) q^{82} -0.652793 q^{83} +(-1.06853 + 1.85075i) q^{84} +(-3.42543 + 5.93301i) q^{85} +2.97285 q^{86} +(-0.925428 + 1.60289i) q^{87} +(2.23609 + 3.87303i) q^{88} +(-3.14795 - 5.45241i) q^{89} -3.49396 q^{90} +1.56465 q^{92} +(3.81551 + 6.60866i) q^{93} +(-7.99127 - 13.8413i) q^{94} +(3.56249 - 6.17042i) q^{95} +2.46681 q^{96} +(5.01573 - 8.68750i) q^{97} +(-10.0124 + 17.3419i) q^{98} +1.46681 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + q^{2} - 3q^{3} + q^{4} - 8q^{5} + q^{6} + 10q^{7} - 3q^{9} + O(q^{10}) \) \( 6q + q^{2} - 3q^{3} + q^{4} - 8q^{5} + q^{6} + 10q^{7} - 3q^{9} + q^{10} - q^{11} - 2q^{12} + 2q^{14} + 4q^{15} + 5q^{16} + 7q^{17} - 2q^{18} + 11q^{19} + q^{20} - 20q^{21} + 5q^{22} - 2q^{23} - 10q^{25} + 6q^{27} - q^{28} + 8q^{29} + q^{30} - 16q^{31} - 4q^{32} - q^{33} - 18q^{35} + q^{36} + 14q^{37} + 40q^{38} + 14q^{40} + q^{41} - q^{42} + 3q^{43} + 32q^{44} + 4q^{45} + 3q^{46} + 18q^{47} + 5q^{48} - 17q^{49} - 11q^{50} - 14q^{51} - 26q^{53} + q^{54} + 13q^{55} - 7q^{56} - 22q^{57} - 12q^{58} - 14q^{59} - 2q^{60} + 13q^{61} + 16q^{62} + 10q^{63} + 8q^{64} - 10q^{66} + 5q^{67} - 7q^{68} - 2q^{69} + 16q^{70} - 6q^{71} - 36q^{73} - 7q^{74} + 5q^{75} + q^{76} - 30q^{77} - 18q^{79} - 16q^{80} - 3q^{81} - 5q^{82} + 32q^{83} - q^{84} - 7q^{85} + 30q^{86} + 8q^{87} + 7q^{88} - 5q^{89} - 2q^{90} - 34q^{92} + 8q^{93} - 32q^{94} - 3q^{95} + 8q^{96} + 5q^{97} - 13q^{98} + 2q^{99} + O(q^{100}) \)

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.623490 1.07992i −0.440874 0.763616i 0.556881 0.830593i \(-0.311998\pi\)
−0.997755 + 0.0669766i \(0.978665\pi\)
\(3\) −0.500000 0.866025i −0.288675 0.500000i
\(4\) 0.222521 0.385418i 0.111260 0.192709i
\(5\) −2.80194 −1.25306 −0.626532 0.779395i \(-0.715526\pi\)
−0.626532 + 0.779395i \(0.715526\pi\)
\(6\) −0.623490 + 1.07992i −0.254539 + 0.440874i
\(7\) 2.40097 4.15860i 0.907481 1.57180i 0.0899290 0.995948i \(-0.471336\pi\)
0.817552 0.575855i \(-0.195331\pi\)
\(8\) −3.04892 −1.07796
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 1.74698 + 3.02586i 0.552443 + 0.956860i
\(11\) −0.733406 1.27030i −0.221130 0.383009i 0.734021 0.679127i \(-0.237641\pi\)
−0.955151 + 0.296118i \(0.904308\pi\)
\(12\) −0.445042 −0.128473
\(13\) 0 0
\(14\) −5.98792 −1.60034
\(15\) 1.40097 + 2.42655i 0.361729 + 0.626532i
\(16\) 1.45593 + 2.52174i 0.363982 + 0.630435i
\(17\) 1.22252 2.11747i 0.296505 0.513562i −0.678829 0.734296i \(-0.737512\pi\)
0.975334 + 0.220735i \(0.0708456\pi\)
\(18\) 1.24698 0.293916
\(19\) −1.27144 + 2.20220i −0.291688 + 0.505218i −0.974209 0.225648i \(-0.927550\pi\)
0.682521 + 0.730866i \(0.260884\pi\)
\(20\) −0.623490 + 1.07992i −0.139417 + 0.241477i
\(21\) −4.80194 −1.04787
\(22\) −0.914542 + 1.58403i −0.194981 + 0.337717i
\(23\) 1.75786 + 3.04471i 0.366540 + 0.634866i 0.989022 0.147768i \(-0.0472089\pi\)
−0.622482 + 0.782634i \(0.713876\pi\)
\(24\) 1.52446 + 2.64044i 0.311179 + 0.538978i
\(25\) 2.85086 0.570171
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) −1.06853 1.85075i −0.201934 0.349759i
\(29\) −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
\(31\) −7.63102 −1.37057 −0.685286 0.728274i \(-0.740323\pi\)
−0.685286 + 0.728274i \(0.740323\pi\)
\(32\) −1.23341 + 2.13632i −0.218037 + 0.377652i
\(33\) −0.733406 + 1.27030i −0.127670 + 0.221130i
\(34\) −3.04892 −0.522885
\(35\) −6.72737 + 11.6521i −1.13713 + 1.96957i
\(36\) 0.222521 + 0.385418i 0.0370868 + 0.0642363i
\(37\) 2.27748 + 3.94471i 0.374415 + 0.648506i 0.990239 0.139377i \(-0.0445101\pi\)
−0.615824 + 0.787884i \(0.711177\pi\)
\(38\) 3.17092 0.514390
\(39\) 0 0
\(40\) 8.54288 1.35075
\(41\) −0.623490 1.07992i −0.0973727 0.168655i 0.813224 0.581951i \(-0.197711\pi\)
−0.910596 + 0.413297i \(0.864377\pi\)
\(42\) 2.99396 + 5.18569i 0.461978 + 0.800169i
\(43\) −1.19202 + 2.06464i −0.181782 + 0.314855i −0.942487 0.334242i \(-0.891520\pi\)
0.760706 + 0.649097i \(0.224853\pi\)
\(44\) −0.652793 −0.0984122
\(45\) 1.40097 2.42655i 0.208844 0.361729i
\(46\) 2.19202 3.79669i 0.323196 0.559792i
\(47\) 12.8170 1.86955 0.934776 0.355238i \(-0.115600\pi\)
0.934776 + 0.355238i \(0.115600\pi\)
\(48\) 1.45593 2.52174i 0.210145 0.363982i
\(49\) −8.02930 13.9072i −1.14704 1.98674i
\(50\) −1.77748 3.07868i −0.251374 0.435392i
\(51\) −2.44504 −0.342374
\(52\) 0 0
\(53\) −8.85086 −1.21576 −0.607879 0.794030i \(-0.707980\pi\)
−0.607879 + 0.794030i \(0.707980\pi\)
\(54\) −0.623490 1.07992i −0.0848462 0.146958i
\(55\) 2.05496 + 3.55929i 0.277090 + 0.479935i
\(56\) −7.32036 + 12.6792i −0.978224 + 1.69433i
\(57\) 2.54288 0.336812
\(58\) −1.15399 + 1.99877i −0.151526 + 0.262451i
\(59\) −1.08815 + 1.88472i −0.141665 + 0.245370i −0.928124 0.372272i \(-0.878579\pi\)
0.786459 + 0.617642i \(0.211912\pi\)
\(60\) 1.24698 0.160984
\(61\) 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
\(63\) 2.40097 + 4.15860i 0.302494 + 0.523934i
\(64\) 8.89977 1.11247
\(65\) 0 0
\(66\) 1.82908 0.225145
\(67\) 1.79105 + 3.10219i 0.218812 + 0.378993i 0.954445 0.298387i \(-0.0964486\pi\)
−0.735633 + 0.677380i \(0.763115\pi\)
\(68\) −0.544073 0.942362i −0.0659785 0.114278i
\(69\) 1.75786 3.04471i 0.211622 0.366540i
\(70\) 16.7778 2.00533
\(71\) 4.41939 7.65460i 0.524485 0.908434i −0.475109 0.879927i \(-0.657591\pi\)
0.999594 0.0285072i \(-0.00907534\pi\)
\(72\) 1.52446 2.64044i 0.179659 0.311179i
\(73\) −7.69202 −0.900283 −0.450142 0.892957i \(-0.648626\pi\)
−0.450142 + 0.892957i \(0.648626\pi\)
\(74\) 2.83997 4.91897i 0.330140 0.571819i
\(75\) −1.42543 2.46891i −0.164594 0.285086i
\(76\) 0.565843 + 0.980069i 0.0649067 + 0.112422i
\(77\) −7.04354 −0.802686
\(78\) 0 0
\(79\) −4.02177 −0.452485 −0.226242 0.974071i \(-0.572644\pi\)
−0.226242 + 0.974071i \(0.572644\pi\)
\(80\) −4.07942 7.06576i −0.456093 0.789976i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −0.777479 + 1.34663i −0.0858582 + 0.148711i
\(83\) −0.652793 −0.0716533 −0.0358267 0.999358i \(-0.511406\pi\)
−0.0358267 + 0.999358i \(0.511406\pi\)
\(84\) −1.06853 + 1.85075i −0.116586 + 0.201934i
\(85\) −3.42543 + 5.93301i −0.371540 + 0.643526i
\(86\) 2.97285 0.320571
\(87\) −0.925428 + 1.60289i −0.0992162 + 0.171848i
\(88\) 2.23609 + 3.87303i 0.238368 + 0.412866i
\(89\) −3.14795 5.45241i −0.333682 0.577954i 0.649549 0.760320i \(-0.274958\pi\)
−0.983231 + 0.182366i \(0.941624\pi\)
\(90\) −3.49396 −0.368296
\(91\) 0 0
\(92\) 1.56465 0.163126
\(93\) 3.81551 + 6.60866i 0.395650 + 0.685286i
\(94\) −7.99127 13.8413i −0.824237 1.42762i
\(95\) 3.56249 6.17042i 0.365504 0.633071i
\(96\) 2.46681 0.251768
\(97\) 5.01573 8.68750i 0.509270 0.882082i −0.490672 0.871344i \(-0.663249\pi\)
0.999942 0.0107376i \(-0.00341793\pi\)
\(98\) −10.0124 + 17.3419i −1.01140 + 1.75180i
\(99\) 1.46681 0.147420
\(100\) 0.634375 1.09877i 0.0634375 0.109877i
\(101\) −6.94385 12.0271i −0.690938 1.19674i −0.971531 0.236913i \(-0.923864\pi\)
0.280592 0.959827i \(-0.409469\pi\)
\(102\) 1.52446 + 2.64044i 0.150944 + 0.261443i
\(103\) −17.4034 −1.71481 −0.857405 0.514642i \(-0.827925\pi\)
−0.857405 + 0.514642i \(0.827925\pi\)
\(104\) 0 0
\(105\) 13.4547 1.31305
\(106\) 5.51842 + 9.55818i 0.535996 + 0.928373i
\(107\) −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
\(109\) 1.07069 0.102553 0.0512766 0.998684i \(-0.483671\pi\)
0.0512766 + 0.998684i \(0.483671\pi\)
\(110\) 2.56249 4.43836i 0.244324 0.423181i
\(111\) 2.27748 3.94471i 0.216169 0.374415i
\(112\) 13.9825 1.32123
\(113\) 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
\(115\) −4.92543 8.53109i −0.459298 0.795528i
\(116\) −0.823708 −0.0764794
\(117\) 0 0
\(118\) 2.71379 0.249825
\(119\) −5.87047 10.1680i −0.538145 0.932095i
\(120\) −4.27144 7.39835i −0.389927 0.675374i
\(121\) 4.42423 7.66299i 0.402203 0.696636i
\(122\) −9.76271 −0.883874
\(123\) −0.623490 + 1.07992i −0.0562182 + 0.0973727i
\(124\) −1.69806 + 2.94113i −0.152490 + 0.264121i
\(125\) 6.02177 0.538604
\(126\) 2.99396 5.18569i 0.266723 0.461978i
\(127\) 4.76875 + 8.25972i 0.423158 + 0.732931i 0.996246 0.0865622i \(-0.0275881\pi\)
−0.573088 + 0.819494i \(0.694255\pi\)
\(128\) −3.08211 5.33836i −0.272422 0.471849i
\(129\) 2.38404 0.209903
\(130\) 0 0
\(131\) −5.50902 −0.481326 −0.240663 0.970609i \(-0.577365\pi\)
−0.240663 + 0.970609i \(0.577365\pi\)
\(132\) 0.326396 + 0.565335i 0.0284092 + 0.0492061i
\(133\) 6.10537 + 10.5748i 0.529402 + 0.916952i
\(134\) 2.23341 3.86837i 0.192937 0.334177i
\(135\) −2.80194 −0.241152
\(136\) −3.72737 + 6.45599i −0.319619 + 0.553596i
\(137\) 8.09179 14.0154i 0.691329 1.19742i −0.280074 0.959978i \(-0.590359\pi\)
0.971403 0.237438i \(-0.0763076\pi\)
\(138\) −4.38404 −0.373195
\(139\) 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
\(141\) −6.40850 11.0999i −0.539693 0.934776i
\(142\) −11.0218 −0.924926
\(143\) 0 0
\(144\) −2.91185 −0.242654
\(145\) 2.59299 + 4.49119i 0.215336 + 0.372973i
\(146\) 4.79590 + 8.30674i 0.396911 + 0.687470i
\(147\) −8.02930 + 13.9072i −0.662246 + 1.14704i
\(148\) 2.02715 0.166630
\(149\) −7.17510 + 12.4276i −0.587807 + 1.01811i 0.406712 + 0.913556i \(0.366675\pi\)
−0.994519 + 0.104555i \(0.966658\pi\)
\(150\) −1.77748 + 3.07868i −0.145131 + 0.251374i
\(151\) 1.96615 0.160003 0.0800014 0.996795i \(-0.474508\pi\)
0.0800014 + 0.996795i \(0.474508\pi\)
\(152\) 3.87651 6.71431i 0.314426 0.544603i
\(153\) 1.22252 + 2.11747i 0.0988350 + 0.171187i
\(154\) 4.39158 + 7.60643i 0.353883 + 0.612944i
\(155\) 21.3817 1.71742
\(156\) 0 0
\(157\) 10.7017 0.854089 0.427045 0.904231i \(-0.359555\pi\)
0.427045 + 0.904231i \(0.359555\pi\)
\(158\) 2.50753 + 4.34317i 0.199489 + 0.345524i
\(159\) 4.42543 + 7.66507i 0.350959 + 0.607879i
\(160\) 3.45593 5.98584i 0.273215 0.473222i
\(161\) 16.8823 1.33051
\(162\) −0.623490 + 1.07992i −0.0489860 + 0.0848462i
\(163\) −1.94989 + 3.37730i −0.152727 + 0.264531i −0.932229 0.361869i \(-0.882139\pi\)
0.779502 + 0.626400i \(0.215472\pi\)
\(164\) −0.554958 −0.0433349
\(165\) 2.05496 3.55929i 0.159978 0.277090i
\(166\) 0.407010 + 0.704961i 0.0315901 + 0.0547156i
\(167\) −10.5097 18.2033i −0.813264 1.40861i −0.910568 0.413360i \(-0.864355\pi\)
0.0973035 0.995255i \(-0.468978\pi\)
\(168\) 14.6407 1.12956
\(169\) 0 0
\(170\) 8.54288 0.655209
\(171\) −1.27144 2.20220i −0.0972293 0.168406i
\(172\) 0.530499 + 0.918852i 0.0404502 + 0.0700618i
\(173\) −6.61745 + 11.4618i −0.503115 + 0.871421i 0.496878 + 0.867820i \(0.334480\pi\)
−0.999994 + 0.00360102i \(0.998854\pi\)
\(174\) 2.30798 0.174967
\(175\) 6.84481 11.8556i 0.517419 0.896197i
\(176\) 2.13557 3.69892i 0.160975 0.278816i
\(177\) 2.17629 0.163580
\(178\) −3.92543 + 6.79904i −0.294223 + 0.509610i
\(179\) −4.26391 7.38530i −0.318699 0.552003i 0.661518 0.749930i \(-0.269913\pi\)
−0.980217 + 0.197926i \(0.936579\pi\)
\(180\) −0.623490 1.07992i −0.0464722 0.0804922i
\(181\) −3.63640 −0.270291 −0.135146 0.990826i \(-0.543150\pi\)
−0.135146 + 0.990826i \(0.543150\pi\)
\(182\) 0 0
\(183\) −7.82908 −0.578743
\(184\) −5.35958 9.28307i −0.395114 0.684357i
\(185\) −6.38135 11.0528i −0.469167 0.812620i
\(186\) 4.75786 8.24086i 0.348864 0.604249i
\(187\) −3.58642 −0.262265
\(188\) 2.85205 4.93990i 0.208007 0.360279i
\(189\) 2.40097 4.15860i 0.174645 0.302494i
\(190\) −8.88471 −0.644564
\(191\) −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
\(193\) 4.21379 + 7.29850i 0.303315 + 0.525358i 0.976885 0.213766i \(-0.0685731\pi\)
−0.673569 + 0.739124i \(0.735240\pi\)
\(194\) −12.5090 −0.898096
\(195\) 0 0
\(196\) −7.14675 −0.510482
\(197\) 13.2383 + 22.9293i 0.943186 + 1.63365i 0.759343 + 0.650691i \(0.225521\pi\)
0.183844 + 0.982955i \(0.441146\pi\)
\(198\) −0.914542 1.58403i −0.0649937 0.112572i
\(199\) 7.12618 12.3429i 0.505161 0.874965i −0.494821 0.868995i \(-0.664766\pi\)
0.999982 0.00597014i \(-0.00190036\pi\)
\(200\) −8.69202 −0.614619
\(201\) 1.79105 3.10219i 0.126331 0.218812i
\(202\) −8.65883 + 14.9975i −0.609233 + 1.05522i
\(203\) −8.88769 −0.623794
\(204\) −0.544073 + 0.942362i −0.0380927 + 0.0659785i
\(205\) 1.74698 + 3.02586i 0.122014 + 0.211335i
\(206\) 10.8509 + 18.7942i 0.756015 + 1.30946i
\(207\) −3.51573 −0.244360
\(208\) 0 0
\(209\) 3.72992 0.258004
\(210\) −8.38889 14.5300i −0.578888 1.00266i
\(211\) −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
\(213\) −8.83877 −0.605623
\(214\) −6.57942 + 11.3959i −0.449760 + 0.779007i
\(215\) 3.33997 5.78500i 0.227784 0.394534i
\(216\) −3.04892 −0.207453
\(217\) −18.3218 + 31.7344i −1.24377 + 2.15427i
\(218\) −0.667563 1.15625i −0.0452131 0.0783113i
\(219\) 3.84601 + 6.66149i 0.259889 + 0.450142i
\(220\) 1.82908 0.123317
\(221\) 0 0
\(222\) −5.67994 −0.381213
\(223\) −9.32520 16.1517i −0.624462 1.08160i −0.988645 0.150272i \(-0.951985\pi\)
0.364183 0.931327i \(-0.381348\pi\)
\(224\) 5.92274 + 10.2585i 0.395730 + 0.685424i
\(225\) −1.42543 + 2.46891i −0.0950285 + 0.164594i
\(226\) −20.6136 −1.37119
\(227\) −4.87867 + 8.45010i −0.323808 + 0.560853i −0.981270 0.192635i \(-0.938297\pi\)
0.657462 + 0.753488i \(0.271630\pi\)
\(228\) 0.565843 0.980069i 0.0374739 0.0649067i
\(229\) −2.86294 −0.189188 −0.0945941 0.995516i \(-0.530155\pi\)
−0.0945941 + 0.995516i \(0.530155\pi\)
\(230\) −6.14191 + 10.6381i −0.404985 + 0.701455i
\(231\) 3.52177 + 6.09989i 0.231715 + 0.401343i
\(232\) 2.82155 + 4.88707i 0.185244 + 0.320852i
\(233\) −5.78554 −0.379024 −0.189512 0.981878i \(-0.560691\pi\)
−0.189512 + 0.981878i \(0.560691\pi\)
\(234\) 0 0
\(235\) −35.9124 −2.34267
\(236\) 0.484271 + 0.838781i 0.0315233 + 0.0546000i
\(237\) 2.01089 + 3.48296i 0.130621 + 0.226242i
\(238\) −7.32036 + 12.6792i −0.474508 + 0.821872i
\(239\) 7.09246 0.458773 0.229386 0.973335i \(-0.426328\pi\)
0.229386 + 0.973335i \(0.426328\pi\)
\(240\) −4.07942 + 7.06576i −0.263325 + 0.456093i
\(241\) −1.94989 + 3.37730i −0.125603 + 0.217551i −0.921969 0.387265i \(-0.873420\pi\)
0.796365 + 0.604816i \(0.206753\pi\)
\(242\) −11.0339 −0.709283
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) −1.74214 3.01747i −0.111529 0.193174i
\(245\) 22.4976 + 38.9670i 1.43732 + 2.48951i
\(246\) 1.55496 0.0991405
\(247\) 0 0
\(248\) 23.2664 1.47742
\(249\) 0.326396 + 0.565335i 0.0206845 + 0.0358267i
\(250\) −3.75451 6.50301i −0.237456 0.411286i
\(251\) 1.22252 2.11747i 0.0771648 0.133653i −0.824861 0.565336i \(-0.808747\pi\)
0.902026 + 0.431682i \(0.142080\pi\)
\(252\) 2.13706 0.134622
\(253\) 2.57846 4.46602i 0.162106 0.280776i
\(254\) 5.94653 10.2997i 0.373119 0.646261i
\(255\) 6.85086 0.429017
\(256\) 5.05645 8.75803i 0.316028 0.547377i
\(257\) 7.06518 + 12.2372i 0.440714 + 0.763339i 0.997743 0.0671545i \(-0.0213920\pi\)
−0.557029 + 0.830493i \(0.688059\pi\)
\(258\) −1.48643 2.57457i −0.0925409 0.160285i
\(259\) 21.8726 1.35910
\(260\) 0 0
\(261\) 1.85086 0.114565
\(262\) 3.43482 + 5.94928i 0.212204 + 0.367548i
\(263\) 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
\(265\) 24.7995 1.52342
\(266\) 7.61327 13.1866i 0.466799 0.808520i
\(267\) −3.14795 + 5.45241i −0.192651 + 0.333682i
\(268\) 1.59419 0.0973805
\(269\) 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
\(271\) −1.59515 2.76287i −0.0968982 0.167833i 0.813501 0.581563i \(-0.197559\pi\)
−0.910399 + 0.413731i \(0.864225\pi\)
\(272\) 7.11960 0.431689
\(273\) 0 0
\(274\) −20.1806 −1.21915
\(275\) −2.09083 3.62143i −0.126082 0.218381i
\(276\) −0.782323 1.35502i −0.0470903 0.0815629i
\(277\) −10.9683 + 18.9977i −0.659022 + 1.14146i 0.321848 + 0.946791i \(0.395696\pi\)
−0.980869 + 0.194667i \(0.937637\pi\)
\(278\) −13.1045 −0.785958
\(279\) 3.81551 6.60866i 0.228429 0.395650i
\(280\) 20.5112 35.5264i 1.22578 2.12311i
\(281\) −11.9903 −0.715282 −0.357641 0.933859i \(-0.616419\pi\)
−0.357641 + 0.933859i \(0.616419\pi\)
\(282\) −7.99127 + 13.8413i −0.475873 + 0.824237i
\(283\) 7.18329 + 12.4418i 0.427002 + 0.739590i 0.996605 0.0823303i \(-0.0262362\pi\)
−0.569603 + 0.821920i \(0.692903\pi\)
\(284\) −1.96681 3.40662i −0.116709 0.202146i
\(285\) −7.12498 −0.422047
\(286\) 0 0
\(287\) −5.98792 −0.353456
\(288\) −1.23341 2.13632i −0.0726791 0.125884i
\(289\) 5.51089 + 9.54513i 0.324170 + 0.561478i
\(290\) 3.23341 5.60042i 0.189872 0.328868i
\(291\) −10.0315 −0.588055
\(292\) −1.71164 + 2.96464i −0.100166 + 0.173492i
\(293\) 9.37920 16.2452i 0.547939 0.949058i −0.450477 0.892788i \(-0.648746\pi\)
0.998416 0.0562695i \(-0.0179206\pi\)
\(294\) 20.0248 1.16787
\(295\) 3.04892 5.28088i 0.177515 0.307465i
\(296\) −6.94385 12.0271i −0.403603 0.699061i
\(297\) −0.733406 1.27030i −0.0425565 0.0737101i
\(298\) 17.8944 1.03659
\(299\) 0 0
\(300\) −1.26875 −0.0732513
\(301\) 5.72401 + 9.91428i 0.329927 + 0.571450i
\(302\) −1.22587 2.12327i −0.0705411 0.122181i
\(303\) −6.94385 + 12.0271i −0.398913 + 0.690938i
\(304\) −7.40449 −0.424676
\(305\) −10.9683 + 18.9977i −0.628043 + 1.08780i
\(306\) 1.52446 2.64044i 0.0871475 0.150944i
\(307\) −25.6262 −1.46257 −0.731283 0.682074i \(-0.761078\pi\)
−0.731283 + 0.682074i \(0.761078\pi\)
\(308\) −1.56734 + 2.71470i −0.0893072 + 0.154685i
\(309\) 8.70171 + 15.0718i 0.495023 + 0.857405i
\(310\) −13.3312 23.0904i −0.757164 1.31145i
\(311\) 11.3817 0.645394 0.322697 0.946502i \(-0.395410\pi\)
0.322697 + 0.946502i \(0.395410\pi\)
\(312\) 0 0
\(313\) 27.5743 1.55859 0.779297 0.626655i \(-0.215576\pi\)
0.779297 + 0.626655i \(0.215576\pi\)
\(314\) −6.67241 11.5569i −0.376546 0.652196i
\(315\) −6.72737 11.6521i −0.379044 0.656524i
\(316\) −0.894928 + 1.55006i −0.0503436 + 0.0871977i
\(317\) 11.2597 0.632405 0.316203 0.948692i \(-0.397592\pi\)
0.316203 + 0.948692i \(0.397592\pi\)
\(318\) 5.51842 9.55818i 0.309458 0.535996i
\(319\) −1.35743 + 2.35113i −0.0760014 + 0.131638i
\(320\) −24.9366 −1.39400
\(321\) −5.27628 + 9.13879i −0.294493 + 0.510077i
\(322\) −10.5260 18.2315i −0.586588 1.01600i
\(323\) 3.10872 + 5.38446i 0.172974 + 0.299599i
\(324\) −0.445042 −0.0247245
\(325\) 0 0
\(326\) 4.86294 0.269333
\(327\) −0.535344 0.927243i −0.0296046 0.0512766i
\(328\) 1.90097 + 3.29257i 0.104963 + 0.181802i
\(329\) 30.7732 53.3008i 1.69658 2.93857i
\(330\) −5.12498 −0.282121
\(331\) −5.95324 + 10.3113i −0.327220 + 0.566761i −0.981959 0.189094i \(-0.939445\pi\)
0.654739 + 0.755855i \(0.272778\pi\)
\(332\) −0.145260 + 0.251598i −0.00797218 + 0.0138082i
\(333\) −4.55496 −0.249610
\(334\) −13.1054 + 22.6992i −0.717094 + 1.24204i
\(335\) −5.01842 8.69215i −0.274185 0.474903i
\(336\) −6.99127 12.1092i −0.381405 0.660613i
\(337\) 17.1672 0.935157 0.467578 0.883952i \(-0.345127\pi\)
0.467578 + 0.883952i \(0.345127\pi\)
\(338\) 0 0
\(339\) −16.5308 −0.897830
\(340\) 1.52446 + 2.64044i 0.0826754 + 0.143198i
\(341\) 5.59664 + 9.69366i 0.303075 + 0.524941i
\(342\) −1.58546 + 2.74609i −0.0857317 + 0.148492i
\(343\) −43.4989 −2.34872
\(344\) 3.63437 6.29492i 0.195952 0.339399i
\(345\) −4.92543 + 8.53109i −0.265176 + 0.459298i
\(346\) 16.5036 0.887242
\(347\) 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
\(349\) −2.28621 3.95983i −0.122378 0.211965i 0.798327 0.602224i \(-0.205719\pi\)
−0.920705 + 0.390259i \(0.872385\pi\)
\(350\) −17.0707 −0.912467
\(351\) 0 0
\(352\) 3.61835 0.192859
\(353\) −3.03803 5.26203i −0.161698 0.280069i 0.773780 0.633455i \(-0.218364\pi\)
−0.935478 + 0.353385i \(0.885030\pi\)
\(354\) −1.35690 2.35021i −0.0721182 0.124912i
\(355\) −12.3828 + 21.4477i −0.657213 + 1.13833i
\(356\) −2.80194 −0.148502
\(357\) −5.87047 + 10.1680i −0.310698 + 0.538145i
\(358\) −5.31700 + 9.20932i −0.281012 + 0.486728i
\(359\) 14.9661 0.789883 0.394942 0.918706i \(-0.370765\pi\)
0.394942 + 0.918706i \(0.370765\pi\)
\(360\) −4.27144 + 7.39835i −0.225125 + 0.389927i
\(361\) 6.26689 + 10.8546i 0.329836 + 0.571293i
\(362\) 2.26726 + 3.92701i 0.119164 + 0.206399i
\(363\) −8.84846 −0.464424
\(364\) 0 0
\(365\) 21.5526 1.12811
\(366\) 4.88135 + 8.45475i 0.255152 + 0.441937i
\(367\) −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
\(369\) 1.24698 0.0649152
\(370\) −7.95742 + 13.7827i −0.413687 + 0.716526i
\(371\) −21.2506 + 36.8072i −1.10328 + 1.91093i
\(372\) 3.39612 0.176081
\(373\) 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
\(375\) −3.01089 5.21501i −0.155481 0.269302i
\(376\) −39.0780 −2.01529
\(377\) 0 0
\(378\) −5.98792 −0.307985
\(379\) −13.2925 23.0234i −0.682792 1.18263i −0.974125 0.226009i \(-0.927432\pi\)
0.291333 0.956622i \(-0.405901\pi\)
\(380\) −1.58546 2.74609i −0.0813323 0.140872i
\(381\) 4.76875 8.25972i 0.244310 0.423158i
\(382\) 26.6625 1.36417
\(383\) −7.17510 + 12.4276i −0.366630 + 0.635022i −0.989036 0.147672i \(-0.952822\pi\)
0.622406 + 0.782694i \(0.286155\pi\)
\(384\) −3.08211 + 5.33836i −0.157283 + 0.272422i
\(385\) 19.7356 1.00582
\(386\) 5.25451 9.10108i 0.267448 0.463233i
\(387\) −1.19202 2.06464i −0.0605939 0.104952i
\(388\) −2.23221 3.86630i −0.113323 0.196282i
\(389\) −22.6582 −1.14881 −0.574407 0.818570i \(-0.694767\pi\)
−0.574407 + 0.818570i \(0.694767\pi\)
\(390\) 0 0
\(391\) 8.59611 0.434724
\(392\) 24.4807 + 42.4018i 1.23646 + 2.14161i
\(393\) 2.75451 + 4.77096i 0.138947 + 0.240663i
\(394\) 16.5078 28.5924i 0.831652 1.44046i
\(395\) 11.2687 0.566992
\(396\) 0.326396 0.565335i 0.0164020 0.0284092i
\(397\) 3.95377 6.84813i 0.198434 0.343698i −0.749587 0.661906i \(-0.769748\pi\)
0.948021 + 0.318208i \(0.103081\pi\)
\(398\) −17.7724 −0.890850
\(399\) 6.10537 10.5748i 0.305651 0.529402i
\(400\) 4.15064 + 7.18911i 0.207532 + 0.359456i
\(401\) 1.46830 + 2.54318i 0.0733236 + 0.127000i 0.900356 0.435154i \(-0.143306\pi\)
−0.827032 + 0.562154i \(0.809973\pi\)
\(402\) −4.46681 −0.222784
\(403\) 0 0
\(404\) −6.18060 −0.307497
\(405\) 1.40097 + 2.42655i 0.0696147 + 0.120576i
\(406\) 5.54138 + 9.59796i 0.275014 + 0.476339i
\(407\) 3.34063 5.78615i 0.165589 0.286809i
\(408\) 7.45473 0.369064
\(409\) 5.87747 10.1801i 0.290622 0.503372i −0.683335 0.730105i \(-0.739471\pi\)
0.973957 + 0.226733i \(0.0728044\pi\)
\(410\) 2.17845 3.77318i 0.107586 0.186344i
\(411\) −16.1836 −0.798278
\(412\) −3.87263 + 6.70758i −0.190791 + 0.330459i
\(413\) 5.22521 + 9.05033i 0.257116 + 0.445338i
\(414\) 2.19202 + 3.79669i 0.107732 + 0.186597i
\(415\) 1.82908 0.0897862
\(416\) 0 0
\(417\) −10.5090 −0.514629
\(418\) −2.32557 4.02800i −0.113747 0.197016i
\(419\) −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
\(421\) −25.6963 −1.25236 −0.626181 0.779677i \(-0.715383\pi\)
−0.626181 + 0.779677i \(0.715383\pi\)
\(422\) −1.15399 + 1.99877i −0.0561753 + 0.0972985i
\(423\) −6.40850 + 11.0999i −0.311592 + 0.539693i
\(424\) 26.9855 1.31053
\(425\) 3.48523 6.03660i 0.169058 0.292818i
\(426\) 5.51089 + 9.54513i 0.267003 + 0.462463i
\(427\) −18.7974 32.5580i −0.909669 1.57559i
\(428\) −4.69633 −0.227006
\(429\) 0 0
\(430\) −8.32975 −0.401696
\(431\) 4.47099 + 7.74399i 0.215360 + 0.373015i 0.953384 0.301760i \(-0.0975741\pi\)
−0.738024 + 0.674775i \(0.764241\pi\)
\(432\) 1.45593 + 2.52174i 0.0700483 + 0.121327i
\(433\) −1.45742 + 2.52432i −0.0700391 + 0.121311i −0.898918 0.438116i \(-0.855646\pi\)
0.828879 + 0.559428i \(0.188979\pi\)
\(434\) 45.6939 2.19338
\(435\) 2.59299 4.49119i 0.124324 0.215336i
\(436\) 0.238250 0.412662i 0.0114101 0.0197629i
\(437\) −8.94007 −0.427661
\(438\) 4.79590 8.30674i 0.229157 0.396911i
\(439\) −4.52930 7.84498i −0.216172 0.374421i 0.737463 0.675388i \(-0.236024\pi\)
−0.953634 + 0.300967i \(0.902690\pi\)
\(440\) −6.26540 10.8520i −0.298691 0.517348i
\(441\) 16.0586 0.764696
\(442\) 0 0
\(443\) 11.2325 0.533672 0.266836 0.963742i \(-0.414022\pi\)
0.266836 + 0.963742i \(0.414022\pi\)
\(444\) −1.01357 1.75556i −0.0481021 0.0833152i
\(445\) 8.82036 + 15.2773i 0.418125 + 0.724214i
\(446\) −11.6283 + 20.1409i −0.550618 + 0.953698i
\(447\) 14.3502 0.678741
\(448\) 21.3681 37.0106i 1.00955 1.74859i
\(449\) 14.3790 24.9051i 0.678585 1.17534i −0.296822 0.954933i \(-0.595927\pi\)
0.975407 0.220411i \(-0.0707399\pi\)
\(450\) 3.55496 0.167582
\(451\) −0.914542 + 1.58403i −0.0430641 + 0.0745892i
\(452\) −3.67845 6.37126i −0.173020 0.299679i
\(453\) −0.983074 1.70273i −0.0461888 0.0800014i
\(454\) 12.1672 0.571035
\(455\) 0 0
\(456\) −7.75302 −0.363068
\(457\) −9.53803 16.5204i −0.446170 0.772790i 0.551963 0.833869i \(-0.313879\pi\)
−0.998133 + 0.0610792i \(0.980546\pi\)
\(458\) 1.78501 + 3.09173i 0.0834081 + 0.144467i
\(459\) 1.22252 2.11747i 0.0570624 0.0988350i
\(460\) −4.38404 −0.204407
\(461\) 15.8666 27.4817i 0.738981 1.27995i −0.213974 0.976839i \(-0.568641\pi\)
0.952955 0.303113i \(-0.0980258\pi\)
\(462\) 4.39158 7.60643i 0.204315 0.353883i
\(463\) 36.4784 1.69530 0.847648 0.530559i \(-0.178018\pi\)
0.847648 + 0.530559i \(0.178018\pi\)
\(464\) 2.69471 4.66737i 0.125099 0.216677i
\(465\) −10.6908 18.5171i −0.495775 0.858708i
\(466\) 3.60723 + 6.24790i 0.167102 + 0.289428i
\(467\) 13.0000 0.601568 0.300784 0.953692i \(-0.402752\pi\)
0.300784 + 0.953692i \(0.402752\pi\)
\(468\) 0 0
\(469\) 17.2010 0.794271
\(470\) 22.3910 + 38.7824i 1.03282 + 1.78890i
\(471\) −5.35086 9.26795i −0.246554 0.427045i
\(472\) 3.31767 5.74637i 0.152708 0.264498i
\(473\) 3.49694 0.160790
\(474\) 2.50753 4.34317i 0.115175 0.199489i
\(475\) −3.62469 + 6.27814i −0.166312 + 0.288061i
\(476\) −5.22521 −0.239497
\(477\) 4.42543 7.66507i 0.202626 0.350959i
\(478\) −4.42208 7.65926i −0.202261 0.350326i
\(479\) 2.80827 + 4.86407i 0.128313 + 0.222245i 0.923023 0.384744i \(-0.125710\pi\)
−0.794710 + 0.606989i \(0.792377\pi\)
\(480\) −6.91185 −0.315482
\(481\) 0 0
\(482\) 4.86294 0.221501
\(483\) −8.44116 14.6205i −0.384086 0.665256i
\(484\) −1.96897 3.41035i −0.0894985 0.155016i
\(485\) −14.0538 + 24.3418i −0.638148 + 1.10531i
\(486\) 1.24698 0.0565641
\(487\) −4.87867 + 8.45010i −0.221073 + 0.382910i −0.955134 0.296173i \(-0.904289\pi\)
0.734061 + 0.679084i \(0.237623\pi\)
\(488\) −11.9351 + 20.6722i −0.540277 + 0.935788i
\(489\) 3.89977 0.176354
\(490\) 28.0541 48.5911i 1.26735 2.19512i
\(491\) 3.69418 + 6.39850i 0.166716 + 0.288760i 0.937263 0.348622i \(-0.113350\pi\)
−0.770547 + 0.637383i \(0.780017\pi\)
\(492\) 0.277479 + 0.480608i 0.0125097 + 0.0216675i
\(493\) −4.52542 −0.203815
\(494\) 0 0
\(495\) −4.10992 −0.184727
\(496\) −11.1102 19.2435i −0.498863 0.864056i
\(497\) −21.2216 36.7569i −0.951920 1.64877i
\(498\) 0.407010 0.704961i 0.0182385 0.0315901i
\(499\) 43.2814 1.93754 0.968771 0.247956i \(-0.0797589\pi\)
0.968771 + 0.247956i \(0.0797589\pi\)
\(500\) 1.33997 2.32090i 0.0599253 0.103794i
\(501\) −10.5097 + 18.2033i −0.469538 + 0.813264i
\(502\) −3.04892 −0.136080
\(503\) −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
\(505\) 19.4562 + 33.6992i 0.865791 + 1.49959i
\(506\) −6.43057 −0.285874
\(507\) 0 0
\(508\) 4.24459 0.188323
\(509\) −20.7724 35.9788i −0.920720 1.59473i −0.798303 0.602256i \(-0.794269\pi\)
−0.122417 0.992479i \(-0.539065\pi\)
\(510\) −4.27144 7.39835i −0.189142 0.327604i
\(511\) −18.4683 + 31.9880i −0.816990 + 1.41507i
\(512\) −24.9390 −1.10216
\(513\) −1.27144 + 2.20220i −0.0561354 + 0.0972293i
\(514\) 8.81013 15.2596i 0.388598 0.673072i
\(515\) 48.7633 2.14877
\(516\) 0.530499 0.918852i 0.0233539 0.0404502i
\(517\) −9.40007 16.2814i −0.413415 0.716055i
\(518\) −13.6374 23.6206i −0.599191 1.03783i
\(519\) 13.2349 0.580948
\(520\) 0 0
\(521\) 25.7198 1.12680 0.563402 0.826183i \(-0.309492\pi\)
0.563402 + 0.826183i \(0.309492\pi\)
\(522\) −1.15399 1.99877i −0.0505087 0.0874837i
\(523\) −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
\(525\) −13.6896 −0.597464
\(526\) 14.7913 25.6194i 0.644933 1.11706i
\(527\) −9.32908 + 16.1584i −0.406381 + 0.703873i
\(528\) −4.27114 −0.185878
\(529\) 5.31982 9.21420i 0.231297 0.400618i
\(530\) −15.4623 26.7814i −0.671638 1.16331i
\(531\) −1.08815 1.88472i −0.0472215 0.0817901i
\(532\) 5.43429 0.235606
\(533\) 0 0
\(534\) 7.85086 0.339740
\(535\) 14.7838 + 25.6063i 0.639160 + 1.10706i
\(536\) −5.46077 9.45833i −0.235869 0.408538i
\(537\) −4.26391 + 7.38530i −0.184001 + 0.318699i
\(538\) −7.37734 −0.318060
\(539\) −11.7775 + 20.3992i −0.507292 + 0.878655i
\(540\) −0.623490 + 1.07992i −0.0268307 + 0.0464722i
\(541\) −31.3534 −1.34799 −0.673995 0.738736i \(-0.735423\pi\)
−0.673995 + 0.738736i \(0.735423\pi\)
\(542\) −1.98911 + 3.44525i −0.0854398 + 0.147986i
\(543\) 1.81820 + 3.14921i 0.0780264 + 0.135146i
\(544\) 3.01573 + 5.22340i 0.129298 + 0.223951i
\(545\) −3.00000 −0.128506
\(546\) 0 0
\(547\) 19.9342 0.852325 0.426163 0.904647i \(-0.359865\pi\)
0.426163 + 0.904647i \(0.359865\pi\)
\(548\) −3.60119 6.23744i −0.153835 0.266450i
\(549\) 3.91454 + 6.78019i 0.167069 + 0.289371i
\(550\) −2.60723 + 4.51585i −0.111173 + 0.192557i
\(551\) 4.70650 0.200503
\(552\) −5.35958 + 9.28307i −0.228119 + 0.395114i
\(553\) −9.65615 + 16.7249i −0.410621 + 0.711217i
\(554\) 27.3545 1.16218
\(555\) −6.38135 + 11.0528i −0.270873 + 0.469167i
\(556\) −2.33848 4.05036i −0.0991736 0.171774i
\(557\) 16.6174 + 28.7823i 0.704104 + 1.21954i 0.967014 + 0.254723i \(0.0819844\pi\)
−0.262910 + 0.964820i \(0.584682\pi\)
\(558\) −9.51573 −0.402833
\(559\) 0 0
\(560\) −39.1782 −1.65558
\(561\) 1.79321 + 3.10593i 0.0757093 + 0.131132i
\(562\) 7.47584 + 12.9485i 0.315349 + 0.546201i
\(563\) −1.93565 + 3.35264i −0.0815779 + 0.141297i −0.903928 0.427685i \(-0.859329\pi\)
0.822350 + 0.568982i \(0.192663\pi\)
\(564\) −5.70410 −0.240186
\(565\) −23.1591 + 40.1128i −0.974312 + 1.68756i
\(566\) 8.95742 15.5147i 0.376508 0.652132i
\(567\) −4.80194 −0.201662
\(568\) −13.4743 + 23.3382i −0.565371 + 0.979251i
\(569\) −10.0728 17.4467i −0.422276 0.731403i 0.573886 0.818935i \(-0.305435\pi\)
−0.996162 + 0.0875324i \(0.972102\pi\)
\(570\) 4.44235 + 7.69438i 0.186070 + 0.322282i
\(571\) −32.1269 −1.34447 −0.672234 0.740338i \(-0.734665\pi\)
−0.672234 + 0.740338i \(0.734665\pi\)
\(572\) 0 0
\(573\) 21.3817 0.893231
\(574\) 3.73341 + 6.46645i 0.155829 + 0.269904i
\(575\) 5.01142 + 8.68003i 0.208991 + 0.361982i
\(576\) −4.44989 + 7.70743i −0.185412 + 0.321143i
\(577\) 16.7506 0.697338 0.348669 0.937246i \(-0.386634\pi\)
0.348669 + 0.937246i \(0.386634\pi\)
\(578\) 6.87196 11.9026i 0.285836 0.495082i
\(579\) 4.21379 7.29850i 0.175119 0.303315i
\(580\) 2.30798 0.0958336
\(581\) −1.56734 + 2.71470i −0.0650240 + 0.112625i
\(582\) 6.25451 + 10.8331i 0.259258 + 0.449048i
\(583\) 6.49127 + 11.2432i 0.268841 + 0.465646i
\(584\) 23.4523 0.970465
\(585\) 0 0
\(586\) −23.3913 −0.966287
\(587\) −3.36898 5.83524i −0.139053 0.240846i 0.788086 0.615566i \(-0.211072\pi\)
−0.927138 + 0.374719i \(0.877739\pi\)
\(588\) 3.57338 + 6.18927i 0.147364 + 0.255241i
\(589\) 9.70237 16.8050i 0.399779 0.692438i
\(590\) −7.60388 −0.313047
\(591\) 13.2383 22.9293i 0.544549 0.943186i
\(592\) −6.63169 + 11.4864i −0.272561 + 0.472089i
\(593\) −18.1172 −0.743985 −0.371992 0.928236i \(-0.621325\pi\)
−0.371992 + 0.928236i \(0.621325\pi\)
\(594\) −0.914542 + 1.58403i −0.0375241 + 0.0649937i
\(595\) 16.4487 + 28.4900i 0.674331 + 1.16797i
\(596\) 3.19322 + 5.53082i 0.130799 + 0.226551i
\(597\) −14.2524 −0.583310
\(598\) 0 0
\(599\) −26.7851 −1.09441 −0.547204 0.836999i \(-0.684308\pi\)
−0.547204 + 0.836999i \(0.684308\pi\)
\(600\) 4.34601 + 7.52751i 0.177425 + 0.307309i
\(601\) 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
\(603\) −3.58211 −0.145875
\(604\) 0.437509 0.757788i 0.0178020 0.0308340i
\(605\) −12.3964 + 21.4712i −0.503986 + 0.872930i
\(606\) 17.3177 0.703482
\(607\) −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
\(609\) 4.44385 + 7.69697i 0.180074 + 0.311897i
\(610\) 27.3545 1.10755
\(611\) 0 0
\(612\) 1.08815 0.0439857
\(613\) 24.0891 + 41.7236i 0.972950 + 1.68520i 0.686541 + 0.727091i \(0.259128\pi\)
0.286409 + 0.958108i \(0.407539\pi\)
\(614\) 15.9777 + 27.6742i 0.644807 + 1.11684i
\(615\) 1.74698 3.02586i 0.0704450 0.122014i
\(616\) 21.4752 0.865259
\(617\) 15.1521 26.2443i 0.610002 1.05655i −0.381238 0.924477i \(-0.624502\pi\)
0.991239 0.132077i \(-0.0421646\pi\)
\(618\) 10.8509 18.7942i 0.436485 0.756015i
\(619\) 10.9041 0.438272 0.219136 0.975694i \(-0.429676\pi\)
0.219136 + 0.975694i \(0.429676\pi\)
\(620\) 4.75786 8.24086i 0.191080 0.330961i
\(621\) 1.75786 + 3.04471i 0.0705407 + 0.122180i
\(622\) −7.09634 12.2912i −0.284537 0.492833i
\(623\) −30.2325 −1.21124
\(624\) 0 0
\(625\) −31.1269 −1.24508
\(626\) −17.1923 29.7780i −0.687143 1.19017i
\(627\) −1.86496 3.23021i −0.0744794 0.129002i
\(628\) 2.38135 4.12463i 0.0950264 0.164591i
\(629\) 11.1371 0.444064
\(630\) −8.38889 + 14.5300i −0.334221 + 0.578888i
\(631\) −5.22617 + 9.05199i −0.208050 + 0.360354i −0.951100 0.308882i \(-0.900045\pi\)
0.743050 + 0.669236i \(0.233379\pi\)
\(632\) 12.2620 0.487758
\(633\) −0.925428 + 1.60289i −0.0367824 + 0.0637091i
\(634\) −7.02028 12.1595i −0.278811 0.482915i
\(635\) −13.3617 23.1432i −0.530244 0.918410i
\(636\) 3.93900 0.156192
\(637\) 0 0
\(638\) 3.38537 0.134028
\(639\) 4.41939 + 7.65460i 0.174828 + 0.302811i
\(640\) 8.63587 + 14.9578i 0.341363 + 0.591257i
\(641\) 8.79709 15.2370i 0.347464 0.601826i −0.638334 0.769760i \(-0.720376\pi\)
0.985798 + 0.167934i \(0.0537095\pi\)
\(642\) 13.1588 0.519338
\(643\) 11.3029 19.5772i 0.445743 0.772049i −0.552361 0.833605i \(-0.686273\pi\)
0.998104 + 0.0615560i \(0.0196063\pi\)
\(644\) 3.75667 6.50674i 0.148033 0.256401i
\(645\) −6.67994 −0.263022
\(646\) 3.87651 6.71431i 0.152519 0.264171i
\(647\) 12.3959 + 21.4703i 0.487333 + 0.844085i 0.999894 0.0145658i \(-0.00463659\pi\)
−0.512561 + 0.858651i \(0.671303\pi\)
\(648\) 1.52446 + 2.64044i 0.0598864 + 0.103726i
\(649\) 3.19221 0.125305
\(650\) 0 0
\(651\) 36.6437 1.43618
\(652\) 0.867781 + 1.50304i 0.0339849 + 0.0588636i
\(653\) 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
\(655\) 15.4359 0.603132
\(656\) 1.81551 3.14456i 0.0708838 0.122774i
\(657\) 3.84601 6.66149i 0.150047 0.259889i
\(658\) −76.7472 −2.99192
\(659\) −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
\(661\) −7.97703 13.8166i −0.310271 0.537405i 0.668150 0.744026i \(-0.267086\pi\)
−0.978421 + 0.206622i \(0.933753\pi\)
\(662\) 14.8471 0.577050
\(663\) 0 0
\(664\) 1.99031 0.0772391
\(665\) −17.1069 29.6299i −0.663376 1.14900i
\(666\) 2.83997 + 4.91897i 0.110047 + 0.190606i
\(667\) 3.25355 5.63532i 0.125978 0.218200i
\(668\) −9.35450 −0.361937
\(669\) −9.32520 + 16.1517i −0.360533 + 0.624462i
\(670\) −6.25786 + 10.8389i −0.241762 + 0.418745i
\(671\) −11.4838 −0.443327
\(672\) 5.92274 10.2585i 0.228475 0.395730i
\(673\) 3.69418 + 6.39850i 0.142400 + 0.246644i 0.928400 0.371583i \(-0.121185\pi\)
−0.786000 + 0.618227i \(0.787851\pi\)
\(674\) −10.7036 18.5391i −0.412286 0.714101i
\(675\) 2.85086 0.109729
\(676\) 0 0
\(677\) −22.1454 −0.851118 −0.425559 0.904931i \(-0.639922\pi\)
−0.425559 + 0.904931i \(0.639922\pi\)
\(678\) 10.3068 + 17.8519i 0.395830 + 0.685597i
\(679\) −24.0852 41.7168i −0.924306 1.60094i
\(680\) 10.4438 18.0893i 0.400503 0.693692i
\(681\) 9.75733 0.373902
\(682\) 6.97889 12.0878i 0.267236 0.462866i
\(683\) 4.55011 7.88103i 0.174105 0.301559i −0.765746 0.643143i \(-0.777630\pi\)
0.939851 + 0.341584i \(0.110963\pi\)
\(684\) −1.13169 −0.0432711
\(685\) −22.6727 + 39.2703i −0.866279 + 1.50044i
\(686\) 27.1211 + 46.9751i 1.03549 + 1.79352i
\(687\) 1.43147 + 2.47938i 0.0546139 + 0.0945941i
\(688\) −6.94198 −0.264661
\(689\) 0 0
\(690\) 12.2838 0.467637
\(691\) 6.88553 + 11.9261i 0.261938 + 0.453690i 0.966757 0.255697i \(-0.0823050\pi\)
−0.704819 + 0.709387i \(0.748972\pi\)
\(692\) 2.94504 + 5.10096i 0.111954 + 0.193909i
\(693\) 3.52177 6.09989i 0.133781 0.231715i
\(694\) −30.2717 −1.14910
\(695\) −14.7228 + 25.5007i −0.558468 + 0.967295i
\(696\) 2.82155 4.88707i 0.106951 0.185244i
\(697\) −3.04892 −0.115486
\(698\) −2.85086 + 4.93783i −0.107906 + 0.186899i
\(699\) 2.89277 + 5.01043i 0.109415 + 0.189512i
\(700\) −3.04623 5.27622i −0.115137 0.199422i
\(701\) 46.5090 1.75662 0.878311 0.478090i \(-0.158671\pi\)
0.878311 + 0.478090i \(0.158671\pi\)
\(702\) 0 0
\(703\) −11.5827 −0.436850
\(704\) −6.52715 11.3054i −0.246001 0.426086i
\(705\) 17.9562 + 31.1011i 0.676270 + 1.17133i
\(706\) −3.78836 + 6.56164i −0.142577 + 0.246951i
\(707\) −66.6878 −2.50805
\(708\) 0.484271 0.838781i 0.0182000 0.0315233i
\(709\) 3.62283 6.27492i 0.136058 0.235660i −0.789943 0.613180i \(-0.789890\pi\)
0.926001 + 0.377521i \(0.123223\pi\)
\(710\) 30.8823 1.15899
\(711\) 2.01089 3.48296i 0.0754141 0.130621i
\(712\) 9.59783 + 16.6239i 0.359694 + 0.623008i
\(713\) −13.4143 23.2343i −0.502370 0.870130i
\(714\) 14.6407 0.547915
\(715\) 0 0
\(716\) −3.79523 −0.141835
\(717\) −3.54623 6.14225i −0.132436 0.229386i
\(718\) −9.33124 16.1622i −0.348239 0.603167i
\(719\) −12.7573 + 22.0963i −0.475768 + 0.824055i −0.999615 0.0277580i \(-0.991163\pi\)
0.523846 + 0.851813i \(0.324497\pi\)
\(720\) 8.15883 0.304062
\(721\) −41.7851 + 72.3739i −1.55616 + 2.69534i
\(722\) 7.81468 13.5354i 0.290832 0.503736i
\(723\) 3.89977 0.145034
\(724\) −0.809175 + 1.40153i −0.0300728 + 0.0520875i
\(725\) −2.63826 4.56960i −0.0979825 0.169711i
\(726\) 5.51693 + 9.55560i 0.204752 + 0.354641i
\(727\) −14.4873 −0.537303 −0.268651 0.963238i \(-0.586578\pi\)
−0.268651 + 0.963238i \(0.586578\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −13.4378 23.2750i −0.497355 0.861445i
\(731\) 2.91454 + 5.04814i 0.107798 + 0.186712i
\(732\) −1.74214 + 3.01747i −0.0643912 + 0.111529i
\(733\) −37.5036 −1.38523 −0.692614 0.721308i \(-0.743541\pi\)
−0.692614 + 0.721308i \(0.743541\pi\)
\(734\) −23.1211 + 40.0469i −0.853415 + 1.47816i
\(735\) 22.4976 38.9670i 0.829837 1.43732i
\(736\) −8.67264 −0.319678
\(737\) 2.62714 4.55034i 0.0967719 0.167614i
\(738\) −0.777479 1.34663i −0.0286194 0.0495703i
\(739\) 21.5938 + 37.4016i 0.794341 + 1.37584i 0.923257 + 0.384184i \(0.125517\pi\)
−0.128915 + 0.991656i \(0.541149\pi\)
\(740\) −5.67994 −0.208799
\(741\) 0 0
\(742\) 52.9982 1.94563
\(743\) 6.73825 + 11.6710i 0.247202 + 0.428167i 0.962749 0.270398i \(-0.0871554\pi\)
−0.715546 + 0.698566i \(0.753822\pi\)
\(744\) −11.6332 20.1493i −0.426493 0.738708i
\(745\) 20.1042 34.8214i 0.736560 1.27576i
\(746\) −45.5260 −1.66683
\(747\) 0.326396 0.565335i 0.0119422 0.0206845i
\(748\) −0.798053 + 1.38227i −0.0291797 + 0.0505407i
\(749\) −50.6728 −1.85154
\(750\) −3.75451 + 6.50301i −0.137095 + 0.237456i
\(751\) −17.7947 30.8213i −0.649338 1.12469i −0.983281 0.182093i \(-0.941713\pi\)
0.333943 0.942593i \(-0.391621\pi\)
\(752\) 18.6606 + 32.3211i 0.680483 + 1.17863i
\(753\) −2.44504 −0.0891023
\(754\) 0 0
\(755\) −5.50902 −0.200494
\(756\) −1.06853 1.85075i −0.0388621 0.0673112i
\(757\) 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
\(759\) −5.15691 −0.187184
\(760\) −10.8617 + 18.8131i −0.393997 + 0.682422i
\(761\) 15.4535 26.7663i 0.560190 0.970278i −0.437289 0.899321i \(-0.644061\pi\)
0.997479 0.0709569i \(-0.0226053\pi\)
\(762\) −11.8931 −0.430840
\(763\) 2.57069 4.45256i 0.0930651 0.161194i
\(764\) 4.75786 + 8.24086i 0.172134 + 0.298144i
\(765\) −3.42543 5.93301i −0.123847 0.214509i
\(766\) 17.8944 0.646551
\(767\) 0 0
\(768\) −10.1129 −0.364918
\(769\) 5.99462 + 10.3830i 0.216172 + 0.374420i 0.953634 0.300968i \(-0.0973096\pi\)
−0.737463 + 0.675388i \(0.763976\pi\)
\(770\) −12.3049 21.3127i −0.443439 0.768058i
\(771\) 7.06518 12.2372i 0.254446 0.440714i
\(772\) 3.75063 0.134988
\(773\) 21.9831 38.0758i 0.790676 1.36949i −0.134873 0.990863i \(-0.543062\pi\)
0.925549 0.378628i \(-0.123604\pi\)
\(774\) −1.48643 + 2.57457i −0.0534285 + 0.0925409i
\(775\) −21.7549 −0.781460
\(776\) −15.2925 + 26.4875i −0.548970 + 0.950845i
\(777\) −10.9363 18.9422i −0.392338 0.679549i
\(778\) 14.1271 + 24.4689i 0.506482 + 0.877253i
\(779\) 3.17092 0.113610
\(780\) 0 0