Properties

Label 507.2.e.k.22.1
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 22.1
Root \(-0.623490 + 1.07992i\) of defining polynomial
Character \(\chi\) \(=\) 507.22
Dual form 507.2.e.k.484.1

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

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

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 −0.997755 0.0669766i \(-0.978665\pi\)
0.556881 + 0.830593i \(0.311998\pi\)
\(3\) −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 0.817552 + 0.575855i \(0.195331\pi\)
0.0899290 + 0.995948i \(0.471336\pi\)
\(8\) −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 −0.955151 0.296118i \(-0.904308\pi\)
0.734021 + 0.679127i \(0.237641\pi\)
\(12\) −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 0.682521 0.730866i \(-0.260884\pi\)
−0.974209 + 0.225648i \(0.927550\pi\)
\(20\) −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 \(-0.740323\pi\)
−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 −0.615824 0.787884i \(-0.711177\pi\)
0.990239 + 0.139377i \(0.0445101\pi\)
\(38\) 3.17092 0.514390
\(39\) 0 0
\(40\) 8.54288 1.35075
\(41\) −0.623490 + 1.07992i −0.0973727 + 0.168655i −0.910596 0.413297i \(-0.864377\pi\)
0.813224 + 0.581951i \(0.197711\pi\)
\(42\) 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 \(-0.115600\pi\)
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 0.786459 0.617642i \(-0.211912\pi\)
−0.928124 + 0.372272i \(0.878579\pi\)
\(60\) 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 −0.735633 0.677380i \(-0.763115\pi\)
0.954445 + 0.298387i \(0.0964486\pi\)
\(68\) −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 \(0.00907534\pi\)
−0.475109 + 0.879927i \(0.657591\pi\)
\(72\) 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 −0.983231 0.182366i \(-0.941624\pi\)
0.649549 + 0.760320i \(0.274958\pi\)
\(90\) −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 \(0.00341793\pi\)
−0.490672 + 0.871344i \(0.663249\pi\)
\(98\) −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 \(-0.483671\pi\)
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 0.933354 + 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 \(0.0763076\pi\)
−0.280074 + 0.959978i \(0.590359\pi\)
\(138\) −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 \(-0.966658\pi\)
0.406712 0.913556i \(-0.366675\pi\)
\(150\) −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 0.779502 0.626400i \(-0.215472\pi\)
−0.932229 + 0.361869i \(0.882139\pi\)
\(164\) −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 \(0.468978\pi\)
−0.910568 + 0.413360i \(0.864355\pi\)
\(168\) 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 −0.673569 0.739124i \(-0.735240\pi\)
0.976885 + 0.213766i \(0.0685731\pi\)
\(194\) −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 \(-0.441146\pi\)
0.759343 0.650691i \(-0.225521\pi\)
\(198\) −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 \(0.381348\pi\)
−0.988645 + 0.150272i \(0.951985\pi\)
\(224\) 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 0.657462 0.753488i \(-0.271630\pi\)
−0.981270 + 0.192635i \(0.938297\pi\)
\(228\) 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 0.796365 0.604816i \(-0.206753\pi\)
−0.921969 + 0.387265i \(0.873420\pi\)
\(242\) −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 −0.910399 0.413731i \(-0.864225\pi\)
0.813501 + 0.581563i \(0.197559\pi\)
\(272\) 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 \(-0.616419\pi\)
−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 −0.569603 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 \(0.0179206\pi\)
−0.450477 + 0.892788i \(0.648746\pi\)
\(294\) 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 0.654739 0.755855i \(-0.272778\pi\)
−0.981959 + 0.189094i \(0.939445\pi\)
\(332\) −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 −0.920705 0.390259i \(-0.872385\pi\)
0.798327 + 0.602224i \(0.205719\pi\)
\(350\) −17.0707 −0.912467
\(351\) 0 0
\(352\) 3.61835 0.192859
\(353\) −3.03803 + 5.26203i −0.161698 + 0.280069i −0.935478 0.353385i \(-0.885030\pi\)
0.773780 + 0.633455i \(0.218364\pi\)
\(354\) −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 −0.266164 + 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 \(0.405901\pi\)
−0.974125 + 0.226009i \(0.927432\pi\)
\(380\) −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 0.622406 0.782694i \(-0.286155\pi\)
−0.989036 + 0.147672i \(0.952822\pi\)
\(384\) −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 0.948021 0.318208i \(-0.103081\pi\)
−0.749587 + 0.661906i \(0.769748\pi\)
\(398\) −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 −0.827032 0.562154i \(-0.809973\pi\)
0.900356 + 0.435154i \(0.143306\pi\)
\(402\) −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 0.973957 0.226733i \(-0.0728044\pi\)
−0.683335 + 0.730105i \(0.739471\pi\)
\(410\) 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 \(-0.715383\pi\)
−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 −0.738024 0.674775i \(-0.764241\pi\)
0.953384 + 0.301760i \(0.0975741\pi\)
\(432\) 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 \(0.0707399\pi\)
−0.296822 + 0.954933i \(0.595927\pi\)
\(450\) 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 −0.998133 0.0610792i \(-0.980546\pi\)
0.551963 + 0.833869i \(0.313879\pi\)
\(458\) 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 \(0.0980258\pi\)
−0.213974 + 0.976839i \(0.568641\pi\)
\(462\) 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 −0.794710 0.606989i \(-0.792377\pi\)
0.923023 + 0.384744i \(0.125710\pi\)
\(480\) −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 0.734061 0.679084i \(-0.237623\pi\)
−0.955134 + 0.296173i \(0.904289\pi\)
\(488\) −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 \(-0.0797589\pi\)
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 0.720686 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 \(0.539065\pi\)
−0.798303 + 0.602256i \(0.794269\pi\)
\(510\) −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 \(-0.735423\pi\)
−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 −0.262910 0.964820i \(-0.584682\pi\)
0.967014 0.254723i \(-0.0819844\pi\)
\(558\) −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 \(-0.386634\pi\)
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 −0.927138 0.374719i \(-0.877739\pi\)
0.788086 + 0.615566i \(0.211072\pi\)
\(588\) 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 −0.814088 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 \(-0.407539\pi\)
0.686541 0.727091i \(-0.259128\pi\)
\(614\) 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 \(0.0421646\pi\)
−0.381238 + 0.924477i \(0.624502\pi\)
\(618\) 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 0.743050 0.669236i \(-0.233379\pi\)
−0.951100 + 0.308882i \(0.900045\pi\)
\(632\) 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 0.998104 0.0615560i \(-0.0196063\pi\)
−0.552361 + 0.833605i \(0.686273\pi\)
\(644\) 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 −0.978421 0.206622i \(-0.933753\pi\)
0.668150 + 0.744026i \(0.267086\pi\)
\(662\) 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 0.939851 0.341584i \(-0.110963\pi\)
−0.765746 + 0.643143i \(0.777630\pi\)
\(684\) −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 −0.704819 0.709387i \(-0.748972\pi\)
0.966757 + 0.255697i \(0.0823050\pi\)
\(692\) 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 0.926001 0.377521i \(-0.123223\pi\)
−0.789943 + 0.613180i \(0.789890\pi\)
\(710\) 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 \(-0.743541\pi\)
−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 −0.128915 0.991656i \(-0.541149\pi\)
0.923257 0.384184i \(-0.125517\pi\)
\(740\) −5.67994 −0.208799
\(741\) 0 0
\(742\) 52.9982 1.94563
\(743\) 6.73825 11.6710i 0.247202 0.428167i −0.715546 0.698566i \(-0.753822\pi\)
0.962749 + 0.270398i \(0.0871554\pi\)
\(744\) −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 \(0.0226053\pi\)
−0.437289 + 0.899321i \(0.644061\pi\)
\(762\) −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 −0.737463 0.675388i \(-0.763976\pi\)
0.953634 + 0.300968i \(0.0973096\pi\)
\(770\) −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 \(0.123604\pi\)
−0.134873 + 0.990863i \(0.543062\pi\)
\(774\) −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