Properties

Label 507.2.e.j.22.3
Level $507$
Weight $2$
Character 507.22
Analytic conductor $4.048$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(4.04841538248\)
Analytic rank: \(0\)
Dimension: \(6\)
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 22.3
Root \(-0.623490 + 1.07992i\) of defining polynomial
Character \(\chi\) \(=\) 507.22
Dual form 507.2.e.j.484.3

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

\(n\) \(170\) \(340\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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 \(-0.688002\pi\)
0.997755 + 0.0669766i \(0.0213353\pi\)
\(3\) −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 \(-0.284474\pi\)
0.626532 + 0.779395i \(0.284474\pi\)
\(6\) 0.623490 + 1.07992i 0.254539 + 0.440874i
\(7\) −2.40097 4.15860i −0.907481 1.57180i −0.817552 0.575855i \(-0.804669\pi\)
−0.0899290 0.995948i \(-0.528664\pi\)
\(8\) 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 \(-0.762359\pi\)
0.955151 + 0.296118i \(0.0956921\pi\)
\(12\) −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 0.975334 0.220735i \(-0.0708456\pi\)
−0.678829 + 0.734296i \(0.737512\pi\)
\(18\) −1.24698 −0.293916
\(19\) 1.27144 + 2.20220i 0.291688 + 0.505218i 0.974209 0.225648i \(-0.0724498\pi\)
−0.682521 + 0.730866i \(0.739116\pi\)
\(20\) 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 −0.622482 0.782634i \(-0.713876\pi\)
0.989022 + 0.147768i \(0.0472089\pi\)
\(24\) −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 −0.939066 0.343737i \(-0.888307\pi\)
0.767218 + 0.641386i \(0.221640\pi\)
\(30\) 1.74698 + 3.02586i 0.318953 + 0.552443i
\(31\) 7.63102 1.37057 0.685286 0.728274i \(-0.259677\pi\)
0.685286 + 0.728274i \(0.259677\pi\)
\(32\) 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 \(-0.955490\pi\)
0.615824 + 0.787884i \(0.288823\pi\)
\(38\) 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 \(-0.802289\pi\)
0.910596 + 0.413297i \(0.135623\pi\)
\(42\) 2.99396 5.18569i 0.461978 0.800169i
\(43\) −1.19202 2.06464i −0.181782 0.314855i 0.760706 0.649097i \(-0.224853\pi\)
−0.942487 + 0.334242i \(0.891520\pi\)
\(44\) 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 \(-0.884400\pi\)
−0.934776 + 0.355238i \(0.884400\pi\)
\(48\) 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 \(-0.121421\pi\)
−0.786459 + 0.617642i \(0.788088\pi\)
\(60\) −1.24698 −0.160984
\(61\) 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
\(63\) −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 \(-0.903551\pi\)
0.735633 + 0.677380i \(0.236885\pi\)
\(68\) −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 −0.999594 0.0285072i \(-0.990925\pi\)
0.475109 0.879927i \(-0.342409\pi\)
\(72\) −1.52446 2.64044i −0.179659 0.311179i
\(73\) 7.69202 0.900283 0.450142 0.892957i \(-0.351374\pi\)
0.450142 + 0.892957i \(0.351374\pi\)
\(74\) 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 \(-0.488594\pi\)
0.0358267 + 0.999358i \(0.488594\pi\)
\(84\) 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 \(-0.725042\pi\)
0.983231 + 0.182366i \(0.0583755\pi\)
\(90\) −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 −0.999942 0.0107376i \(-0.996582\pi\)
0.490672 0.871344i \(-0.336751\pi\)
\(98\) 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 0.280592 + 0.959827i \(0.409469\pi\)
−0.971531 + 0.236913i \(0.923864\pi\)
\(102\) −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 0.489854 + 0.871804i \(0.337050\pi\)
−0.999932 + 0.0116758i \(0.996283\pi\)
\(108\) 0.222521 + 0.385418i 0.0214121 + 0.0370868i
\(109\) −1.07069 −0.102553 −0.0512766 0.998684i \(-0.516329\pi\)
−0.0512766 + 0.998684i \(0.516329\pi\)
\(110\) −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 0.933354 + 0.358957i \(0.116868\pi\)
−0.155811 + 0.987787i \(0.549799\pi\)
\(114\) −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 −0.573088 0.819494i \(-0.694255\pi\)
0.996246 + 0.0865622i \(0.0275881\pi\)
\(128\) 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 −0.971403 0.237438i \(-0.923692\pi\)
0.280074 0.959978i \(-0.409641\pi\)
\(138\) 4.38404 0.373195
\(139\) 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
\(141\) 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 0.994519 + 0.104555i \(0.0333418\pi\)
−0.406712 + 0.913556i \(0.633325\pi\)
\(150\) 1.77748 + 3.07868i 0.145131 + 0.251374i
\(151\) −1.96615 −0.160003 −0.0800014 0.996795i \(-0.525492\pi\)
−0.0800014 + 0.996795i \(0.525492\pi\)
\(152\) 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 \(-0.117861\pi\)
−0.779502 + 0.626400i \(0.784528\pi\)
\(164\) 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 −0.0973035 0.995255i \(-0.531022\pi\)
0.910568 0.413360i \(-0.135645\pi\)
\(168\) 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 −0.999994 0.00360102i \(-0.998854\pi\)
0.496878 0.867820i \(-0.334480\pi\)
\(174\) −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 −0.980217 0.197926i \(-0.936579\pi\)
0.661518 + 0.749930i \(0.269913\pi\)
\(180\) 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 −0.935600 0.353062i \(-0.885140\pi\)
0.162039 0.986784i \(-0.448193\pi\)
\(192\) −4.44989 + 7.70743i −0.321143 + 0.556236i
\(193\) −4.21379 + 7.29850i −0.303315 + 0.525358i −0.976885 0.213766i \(-0.931427\pi\)
0.673569 + 0.739124i \(0.264760\pi\)
\(194\) −12.5090 −0.898096
\(195\) 0 0
\(196\) −7.14675 −0.510482
\(197\) −13.2383 + 22.9293i −0.943186 + 1.63365i −0.183844 + 0.982955i \(0.558854\pi\)
−0.759343 + 0.650691i \(0.774479\pi\)
\(198\) −0.914542 + 1.58403i −0.0649937 + 0.112572i
\(199\) 7.12618 + 12.3429i 0.505161 + 0.874965i 0.999982 + 0.00597014i \(0.00190036\pi\)
−0.494821 + 0.868995i \(0.664766\pi\)
\(200\) 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 −0.896121 0.443811i \(-0.853626\pi\)
0.832412 + 0.554158i \(0.186960\pi\)
\(212\) −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 −0.364183 0.931327i \(-0.618652\pi\)
0.988645 0.150272i \(-0.0480149\pi\)
\(224\) 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 \(-0.0617033\pi\)
−0.657462 + 0.753488i \(0.728370\pi\)
\(228\) −0.565843 0.980069i −0.0374739 0.0649067i
\(229\) 2.86294 0.189188 0.0945941 0.995516i \(-0.469845\pi\)
0.0945941 + 0.995516i \(0.469845\pi\)
\(230\) −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 \(-0.573672\pi\)
−0.229386 + 0.973335i \(0.573672\pi\)
\(240\) 4.07942 + 7.06576i 0.263325 + 0.456093i
\(241\) 1.94989 + 3.37730i 0.125603 + 0.217551i 0.921969 0.387265i \(-0.126580\pi\)
−0.796365 + 0.604816i \(0.793247\pi\)
\(242\) 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 0.902026 0.431682i \(-0.142080\pi\)
−0.824861 + 0.565336i \(0.808747\pi\)
\(252\) −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 −0.557029 0.830493i \(-0.688059\pi\)
0.997743 + 0.0671545i \(0.0213920\pi\)
\(258\) 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 −0.224847 0.974394i \(-0.572188\pi\)
0.956274 0.292473i \(-0.0944783\pi\)
\(264\) 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 0.942002 0.335606i \(-0.108941\pi\)
−0.761645 + 0.647995i \(0.775608\pi\)
\(270\) 1.74698 3.02586i 0.106318 0.184148i
\(271\) 1.59515 2.76287i 0.0968982 0.167833i −0.813501 0.581563i \(-0.802441\pi\)
0.910399 + 0.413731i \(0.135775\pi\)
\(272\) 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 −0.980869 0.194667i \(-0.937637\pi\)
0.321848 0.946791i \(-0.395696\pi\)
\(278\) 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 \(-0.383581\pi\)
0.357641 + 0.933859i \(0.383581\pi\)
\(282\) −7.99127 13.8413i −0.475873 0.824237i
\(283\) 7.18329 12.4418i 0.427002 0.739590i −0.569603 0.821920i \(-0.692903\pi\)
0.996605 + 0.0823303i \(0.0262362\pi\)
\(284\) 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 −0.998416 0.0562695i \(-0.982079\pi\)
0.450477 0.892788i \(-0.351254\pi\)
\(294\) −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 \(-0.238922\pi\)
0.731283 + 0.682074i \(0.238922\pi\)
\(308\) −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 \(-0.602408\pi\)
−0.316203 + 0.948692i \(0.602408\pi\)
\(318\) −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 \(-0.0605550\pi\)
−0.654739 + 0.755855i \(0.727222\pi\)
\(332\) 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 0.982734 + 0.185025i \(0.0592366\pi\)
−0.331131 + 0.943585i \(0.607430\pi\)
\(348\) 0.411854 0.713352i 0.0220777 0.0382397i
\(349\) 2.28621 3.95983i 0.122378 0.211965i −0.798327 0.602224i \(-0.794281\pi\)
0.920705 + 0.390259i \(0.127615\pi\)
\(350\) −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 \(-0.781636\pi\)
0.935478 + 0.353385i \(0.114970\pi\)
\(354\) −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 \(-0.629235\pi\)
−0.394942 + 0.918706i \(0.629235\pi\)
\(360\) −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 −0.266164 + 0.963928i \(0.585756\pi\)
−0.701704 + 0.712468i \(0.747577\pi\)
\(368\) −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 0.755385 + 0.655282i \(0.227450\pi\)
0.189798 + 0.981823i \(0.439217\pi\)
\(374\) 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 −0.291333 0.956622i \(-0.594099\pi\)
0.974125 0.226009i \(-0.0725679\pi\)
\(380\) −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 \(-0.0471781\pi\)
−0.622406 + 0.782694i \(0.713845\pi\)
\(384\) 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 \(-0.230252\pi\)
−0.948021 + 0.318208i \(0.896919\pi\)
\(398\) 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 \(-0.856694\pi\)
0.827032 + 0.562154i \(0.190027\pi\)
\(402\) −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 \(-0.260529\pi\)
−0.973957 + 0.226733i \(0.927196\pi\)
\(410\) −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 −0.941653 0.336584i \(-0.890728\pi\)
0.762317 + 0.647203i \(0.224062\pi\)
\(420\) 2.99396 + 5.18569i 0.146090 + 0.253036i
\(421\) 25.6963 1.25236 0.626181 0.779677i \(-0.284617\pi\)
0.626181 + 0.779677i \(0.284617\pi\)
\(422\) 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 \(-0.902426\pi\)
0.738024 + 0.674775i \(0.235759\pi\)
\(432\) 1.45593 2.52174i 0.0700483 0.121327i
\(433\) −1.45742 2.52432i −0.0700391 0.121311i 0.828879 0.559428i \(-0.188979\pi\)
−0.898918 + 0.438116i \(0.855646\pi\)
\(434\) −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 −0.953634 0.300967i \(-0.902690\pi\)
0.737463 + 0.675388i \(0.236024\pi\)
\(440\) 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 −0.975407 0.220411i \(-0.929260\pi\)
0.296822 0.954933i \(-0.404073\pi\)
\(450\) −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 \(-0.686121\pi\)
0.998133 + 0.0610792i \(0.0194542\pi\)
\(458\) 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 −0.952955 0.303113i \(-0.901974\pi\)
0.213974 0.976839i \(-0.431359\pi\)
\(462\) −4.39158 7.60643i −0.204315 0.353883i
\(463\) −36.4784 −1.69530 −0.847648 0.530559i \(-0.821982\pi\)
−0.847648 + 0.530559i \(0.821982\pi\)
\(464\) 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 \(-0.874290\pi\)
0.794710 + 0.606989i \(0.207623\pi\)
\(480\) −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 \(-0.0957106\pi\)
−0.734061 + 0.679084i \(0.762377\pi\)
\(488\) 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 −0.770547 0.637383i \(-0.780017\pi\)
0.937263 + 0.348622i \(0.113350\pi\)
\(492\) −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 \(-0.920241\pi\)
−0.968771 + 0.247956i \(0.920241\pi\)
\(500\) −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 0.720686 0.693261i \(-0.243827\pi\)
−0.960725 + 0.277502i \(0.910494\pi\)
\(504\) −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 0.122417 0.992479i \(-0.460935\pi\)
0.798303 0.602256i \(-0.205731\pi\)
\(510\) −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 −0.944540 0.328397i \(-0.893492\pi\)
0.756670 + 0.653797i \(0.226825\pi\)
\(524\) −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 \(-0.264577\pi\)
0.673995 + 0.738736i \(0.264577\pi\)
\(542\) −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 0.262910 + 0.964820i \(0.415318\pi\)
−0.967014 + 0.254723i \(0.918016\pi\)
\(558\) −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 0.822350 0.568982i \(-0.192663\pi\)
−0.903928 + 0.427685i \(0.859329\pi\)
\(564\) 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 −0.996162 0.0875324i \(-0.972102\pi\)
0.573886 + 0.818935i \(0.305435\pi\)
\(570\) −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 \(-0.613366\pi\)
−0.348669 + 0.937246i \(0.613366\pi\)
\(578\) −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 \(-0.788928\pi\)
0.927138 + 0.374719i \(0.122261\pi\)
\(588\) 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 \(-0.378675\pi\)
0.371992 + 0.928236i \(0.378675\pi\)
\(594\) −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 −0.814088 0.580742i \(-0.802763\pi\)
0.909981 + 0.414650i \(0.136096\pi\)
\(602\) 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 −0.997416 0.0718472i \(-0.977111\pi\)
0.436486 0.899711i \(-0.356223\pi\)
\(608\) −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 −0.286409 + 0.958108i \(0.592461\pi\)
−0.686541 + 0.727091i \(0.740872\pi\)
\(614\) 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 −0.991239 0.132077i \(-0.957835\pi\)
0.381238 0.924477i \(-0.375498\pi\)
\(618\) −10.8509 18.7942i −0.436485 0.756015i
\(619\) −10.9041 −0.438272 −0.219136 0.975694i \(-0.570324\pi\)
−0.219136 + 0.975694i \(0.570324\pi\)
\(620\) 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 \(-0.0999548\pi\)
−0.743050 + 0.669236i \(0.766621\pi\)
\(632\) −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 0.985798 0.167934i \(-0.0537095\pi\)
−0.638334 + 0.769760i \(0.720376\pi\)
\(642\) −13.1588 −0.519338
\(643\) −11.3029 19.5772i −0.445743 0.772049i 0.552361 0.833605i \(-0.313727\pi\)
−0.998104 + 0.0615560i \(0.980394\pi\)
\(644\) −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 −0.512561 0.858651i \(-0.671303\pi\)
0.999894 + 0.0145658i \(0.00463659\pi\)
\(648\) −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 −0.569826 0.821765i \(-0.692989\pi\)
0.996583 + 0.0826012i \(0.0263228\pi\)
\(654\) −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 0.658584 0.752507i \(-0.271156\pi\)
−0.980982 + 0.194097i \(0.937822\pi\)
\(660\) −0.914542 + 1.58403i −0.0355985 + 0.0616584i
\(661\) 7.97703 13.8166i 0.310271 0.537405i −0.668150 0.744026i \(-0.732914\pi\)
0.978421 + 0.206622i \(0.0662470\pi\)
\(662\) 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 −0.786000 0.618227i \(-0.787851\pi\)
0.928400 + 0.371583i \(0.121185\pi\)
\(674\) 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 \(-0.222370\pi\)
−0.939851 + 0.341584i \(0.889037\pi\)
\(684\) 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 \(-0.917695\pi\)
0.704819 + 0.709387i \(0.251028\pi\)
\(692\) 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 \(-0.210110\pi\)
−0.926001 + 0.377521i \(0.876777\pi\)
\(710\) −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 0.523846 0.851813i \(-0.324497\pi\)
−0.999615 + 0.0277580i \(0.991163\pi\)
\(720\) −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 \(-0.256459\pi\)
0.692614 + 0.721308i \(0.256459\pi\)
\(734\) 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 0.128915 + 0.991656i \(0.458851\pi\)
−0.923257 + 0.384184i \(0.874483\pi\)
\(740\) −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 \(-0.912845\pi\)
0.715546 + 0.698566i \(0.246178\pi\)
\(744\) −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 0.333943 + 0.942593i \(0.391621\pi\)
−0.983281 + 0.182093i \(0.941713\pi\)
\(752\) −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 −0.733483 0.679708i \(-0.762106\pi\)
0.955386 + 0.295360i \(0.0954397\pi\)
\(758\) −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 −0.997479 0.0709569i \(-0.977395\pi\)
0.437289 0.899321i \(-0.355939\pi\)
\(762\) 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 \(-0.902690\pi\)
0.737463 + 0.675388i \(0.236024\pi\)
\(770\) −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 −0.925549 0.378628i \(-0.876396\pi\)
0.134873 0.990863i \(-0.456938\pi\)
\(774\) 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
\(781\) −12.9648 −0.463918