Properties

Label 546.2.p.c.281.3
Level $546$
Weight $2$
Character 546.281
Analytic conductor $4.360$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.p (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.35983195036\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
Defining polynomial: \(x^{20} - 4 x^{19} + 8 x^{18} - 20 x^{17} + 56 x^{16} - 140 x^{15} + 288 x^{14} - 532 x^{13} + 1065 x^{12} - 2080 x^{11} + 3712 x^{10} - 6240 x^{9} + 9585 x^{8} - 14364 x^{7} + 23328 x^{6} - 34020 x^{5} + 40824 x^{4} - 43740 x^{3} + 52488 x^{2} - 78732 x + 59049\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 281.3
Root \(-1.01577 + 1.40293i\) of defining polynomial
Character \(\chi\) \(=\) 546.281
Dual form 546.2.p.c.239.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(0.273767 + 1.71028i) q^{3} -1.00000i q^{4} +(-1.75112 + 1.75112i) q^{5} +(-1.40293 - 1.01577i) q^{6} +(0.707107 - 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.85010 + 0.936434i) q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(0.273767 + 1.71028i) q^{3} -1.00000i q^{4} +(-1.75112 + 1.75112i) q^{5} +(-1.40293 - 1.01577i) q^{6} +(0.707107 - 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.85010 + 0.936434i) q^{9} -2.47645i q^{10} +(-2.12300 - 2.12300i) q^{11} +(1.71028 - 0.273767i) q^{12} +(-3.47808 - 0.950237i) q^{13} +1.00000i q^{14} +(-3.47430 - 2.51550i) q^{15} -1.00000 q^{16} -3.03575 q^{17} +(1.35317 - 2.67749i) q^{18} +(2.63603 + 2.63603i) q^{19} +(1.75112 + 1.75112i) q^{20} +(1.40293 + 1.01577i) q^{21} +3.00237 q^{22} -0.478247 q^{23} +(-1.01577 + 1.40293i) q^{24} -1.13282i q^{25} +(3.13129 - 1.78746i) q^{26} +(-2.38183 - 4.61811i) q^{27} +(-0.707107 - 0.707107i) q^{28} -6.03691i q^{29} +(4.23543 - 0.677971i) q^{30} +(-2.07156 - 2.07156i) q^{31} +(0.707107 - 0.707107i) q^{32} +(3.04971 - 4.21213i) q^{33} +(2.14660 - 2.14660i) q^{34} +2.47645i q^{35} +(0.936434 + 2.85010i) q^{36} +(-4.21400 + 4.21400i) q^{37} -3.72791 q^{38} +(0.672986 - 6.20863i) q^{39} -2.47645 q^{40} +(-4.84049 + 4.84049i) q^{41} +(-1.71028 + 0.273767i) q^{42} -4.59522i q^{43} +(-2.12300 + 2.12300i) q^{44} +(3.35106 - 6.63067i) q^{45} +(0.338172 - 0.338172i) q^{46} +(6.97225 + 6.97225i) q^{47} +(-0.273767 - 1.71028i) q^{48} -1.00000i q^{49} +(0.801028 + 0.801028i) q^{50} +(-0.831086 - 5.19197i) q^{51} +(-0.950237 + 3.47808i) q^{52} -5.90009i q^{53} +(4.94970 + 1.58129i) q^{54} +7.43524 q^{55} +1.00000 q^{56} +(-3.78669 + 5.23000i) q^{57} +(4.26874 + 4.26874i) q^{58} +(-3.76763 - 3.76763i) q^{59} +(-2.51550 + 3.47430i) q^{60} +13.2619 q^{61} +2.92963 q^{62} +(-1.35317 + 2.67749i) q^{63} +1.00000i q^{64} +(7.75451 - 4.42655i) q^{65} +(0.821950 + 5.13490i) q^{66} +(-6.61080 - 6.61080i) q^{67} +3.03575i q^{68} +(-0.130928 - 0.817936i) q^{69} +(-1.75112 - 1.75112i) q^{70} +(-7.36537 + 7.36537i) q^{71} +(-2.67749 - 1.35317i) q^{72} +(-8.06119 + 8.06119i) q^{73} -5.95950i q^{74} +(1.93745 - 0.310130i) q^{75} +(2.63603 - 2.63603i) q^{76} -3.00237 q^{77} +(3.91429 + 4.86604i) q^{78} -11.6022 q^{79} +(1.75112 - 1.75112i) q^{80} +(7.24618 - 5.33787i) q^{81} -6.84548i q^{82} +(-9.96904 + 9.96904i) q^{83} +(1.01577 - 1.40293i) q^{84} +(5.31595 - 5.31595i) q^{85} +(3.24931 + 3.24931i) q^{86} +(10.3248 - 1.65271i) q^{87} -3.00237i q^{88} +(-10.9270 - 10.9270i) q^{89} +(2.31904 + 7.05815i) q^{90} +(-3.13129 + 1.78746i) q^{91} +0.478247i q^{92} +(2.97582 - 4.11007i) q^{93} -9.86025 q^{94} -9.23199 q^{95} +(1.40293 + 1.01577i) q^{96} +(10.7186 + 10.7186i) q^{97} +(0.707107 + 0.707107i) q^{98} +(8.03882 + 4.06272i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 4q^{5} - 4q^{6} - 8q^{9} + O(q^{10}) \) \( 20q - 4q^{5} - 4q^{6} - 8q^{9} - 16q^{11} - 8q^{12} + 4q^{13} - 4q^{15} - 20q^{16} + 12q^{17} - 8q^{18} + 12q^{19} + 4q^{20} + 4q^{21} - 12q^{22} - 4q^{23} + 4q^{24} + 24q^{27} + 12q^{30} - 8q^{31} - 48q^{33} - 4q^{34} + 32q^{37} - 4q^{38} - 16q^{39} - 4q^{40} + 8q^{41} + 8q^{42} - 16q^{44} + 16q^{45} - 8q^{46} + 32q^{50} - 8q^{51} - 8q^{52} + 28q^{54} + 28q^{55} + 20q^{56} + 36q^{57} - 4q^{58} + 20q^{59} - 4q^{60} - 4q^{61} + 48q^{62} + 8q^{63} + 52q^{65} - 36q^{67} + 68q^{69} - 4q^{70} - 28q^{71} - 16q^{72} - 24q^{73} - 76q^{75} + 12q^{76} + 12q^{77} + 40q^{78} - 64q^{79} + 4q^{80} + 32q^{81} - 24q^{83} - 4q^{84} + 24q^{85} + 4q^{86} + 4q^{87} - 4q^{89} - 8q^{90} - 32q^{93} - 40q^{94} - 76q^{95} + 4q^{96} + 32q^{97} - 4q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 + 0.707107i −0.500000 + 0.500000i
\(3\) 0.273767 + 1.71028i 0.158059 + 0.987430i
\(4\) 1.00000i 0.500000i
\(5\) −1.75112 + 1.75112i −0.783124 + 0.783124i −0.980357 0.197233i \(-0.936804\pi\)
0.197233 + 0.980357i \(0.436804\pi\)
\(6\) −1.40293 1.01577i −0.572744 0.414685i
\(7\) 0.707107 0.707107i 0.267261 0.267261i
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) −2.85010 + 0.936434i −0.950035 + 0.312145i
\(10\) 2.47645i 0.783124i
\(11\) −2.12300 2.12300i −0.640108 0.640108i 0.310474 0.950582i \(-0.399512\pi\)
−0.950582 + 0.310474i \(0.899512\pi\)
\(12\) 1.71028 0.273767i 0.493715 0.0790296i
\(13\) −3.47808 0.950237i −0.964646 0.263548i
\(14\) 1.00000i 0.267261i
\(15\) −3.47430 2.51550i −0.897059 0.649499i
\(16\) −1.00000 −0.250000
\(17\) −3.03575 −0.736277 −0.368138 0.929771i \(-0.620005\pi\)
−0.368138 + 0.929771i \(0.620005\pi\)
\(18\) 1.35317 2.67749i 0.318945 0.631090i
\(19\) 2.63603 + 2.63603i 0.604747 + 0.604747i 0.941568 0.336822i \(-0.109352\pi\)
−0.336822 + 0.941568i \(0.609352\pi\)
\(20\) 1.75112 + 1.75112i 0.391562 + 0.391562i
\(21\) 1.40293 + 1.01577i 0.306145 + 0.221659i
\(22\) 3.00237 0.640108
\(23\) −0.478247 −0.0997215 −0.0498607 0.998756i \(-0.515878\pi\)
−0.0498607 + 0.998756i \(0.515878\pi\)
\(24\) −1.01577 + 1.40293i −0.207343 + 0.286372i
\(25\) 1.13282i 0.226565i
\(26\) 3.13129 1.78746i 0.614097 0.350549i
\(27\) −2.38183 4.61811i −0.458383 0.888755i
\(28\) −0.707107 0.707107i −0.133631 0.133631i
\(29\) 6.03691i 1.12103i −0.828145 0.560513i \(-0.810604\pi\)
0.828145 0.560513i \(-0.189396\pi\)
\(30\) 4.23543 0.677971i 0.773279 0.123780i
\(31\) −2.07156 2.07156i −0.372064 0.372064i 0.496165 0.868228i \(-0.334741\pi\)
−0.868228 + 0.496165i \(0.834741\pi\)
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) 3.04971 4.21213i 0.530887 0.733237i
\(34\) 2.14660 2.14660i 0.368138 0.368138i
\(35\) 2.47645i 0.418597i
\(36\) 0.936434 + 2.85010i 0.156072 + 0.475017i
\(37\) −4.21400 + 4.21400i −0.692778 + 0.692778i −0.962842 0.270064i \(-0.912955\pi\)
0.270064 + 0.962842i \(0.412955\pi\)
\(38\) −3.72791 −0.604747
\(39\) 0.672986 6.20863i 0.107764 0.994176i
\(40\) −2.47645 −0.391562
\(41\) −4.84049 + 4.84049i −0.755957 + 0.755957i −0.975584 0.219627i \(-0.929516\pi\)
0.219627 + 0.975584i \(0.429516\pi\)
\(42\) −1.71028 + 0.273767i −0.263902 + 0.0422431i
\(43\) 4.59522i 0.700764i −0.936607 0.350382i \(-0.886052\pi\)
0.936607 0.350382i \(-0.113948\pi\)
\(44\) −2.12300 + 2.12300i −0.320054 + 0.320054i
\(45\) 3.35106 6.63067i 0.499546 0.988442i
\(46\) 0.338172 0.338172i 0.0498607 0.0498607i
\(47\) 6.97225 + 6.97225i 1.01701 + 1.01701i 0.999853 + 0.0171544i \(0.00546067\pi\)
0.0171544 + 0.999853i \(0.494539\pi\)
\(48\) −0.273767 1.71028i −0.0395148 0.246857i
\(49\) 1.00000i 0.142857i
\(50\) 0.801028 + 0.801028i 0.113282 + 0.113282i
\(51\) −0.831086 5.19197i −0.116375 0.727021i
\(52\) −0.950237 + 3.47808i −0.131774 + 0.482323i
\(53\) 5.90009i 0.810440i −0.914219 0.405220i \(-0.867195\pi\)
0.914219 0.405220i \(-0.132805\pi\)
\(54\) 4.94970 + 1.58129i 0.673569 + 0.215186i
\(55\) 7.43524 1.00257
\(56\) 1.00000 0.133631
\(57\) −3.78669 + 5.23000i −0.501559 + 0.692730i
\(58\) 4.26874 + 4.26874i 0.560513 + 0.560513i
\(59\) −3.76763 3.76763i −0.490504 0.490504i 0.417961 0.908465i \(-0.362745\pi\)
−0.908465 + 0.417961i \(0.862745\pi\)
\(60\) −2.51550 + 3.47430i −0.324750 + 0.448530i
\(61\) 13.2619 1.69801 0.849007 0.528382i \(-0.177201\pi\)
0.849007 + 0.528382i \(0.177201\pi\)
\(62\) 2.92963 0.372064
\(63\) −1.35317 + 2.67749i −0.170483 + 0.337332i
\(64\) 1.00000i 0.125000i
\(65\) 7.75451 4.42655i 0.961828 0.549046i
\(66\) 0.821950 + 5.13490i 0.101175 + 0.632062i
\(67\) −6.61080 6.61080i −0.807638 0.807638i 0.176638 0.984276i \(-0.443478\pi\)
−0.984276 + 0.176638i \(0.943478\pi\)
\(68\) 3.03575i 0.368138i
\(69\) −0.130928 0.817936i −0.0157619 0.0984680i
\(70\) −1.75112 1.75112i −0.209299 0.209299i
\(71\) −7.36537 + 7.36537i −0.874109 + 0.874109i −0.992917 0.118808i \(-0.962093\pi\)
0.118808 + 0.992917i \(0.462093\pi\)
\(72\) −2.67749 1.35317i −0.315545 0.159472i
\(73\) −8.06119 + 8.06119i −0.943491 + 0.943491i −0.998487 0.0549955i \(-0.982486\pi\)
0.0549955 + 0.998487i \(0.482486\pi\)
\(74\) 5.95950i 0.692778i
\(75\) 1.93745 0.310130i 0.223717 0.0358107i
\(76\) 2.63603 2.63603i 0.302373 0.302373i
\(77\) −3.00237 −0.342152
\(78\) 3.91429 + 4.86604i 0.443206 + 0.550970i
\(79\) −11.6022 −1.30535 −0.652673 0.757640i \(-0.726353\pi\)
−0.652673 + 0.757640i \(0.726353\pi\)
\(80\) 1.75112 1.75112i 0.195781 0.195781i
\(81\) 7.24618 5.33787i 0.805131 0.593097i
\(82\) 6.84548i 0.755957i
\(83\) −9.96904 + 9.96904i −1.09424 + 1.09424i −0.0991748 + 0.995070i \(0.531620\pi\)
−0.995070 + 0.0991748i \(0.968380\pi\)
\(84\) 1.01577 1.40293i 0.110829 0.153072i
\(85\) 5.31595 5.31595i 0.576596 0.576596i
\(86\) 3.24931 + 3.24931i 0.350382 + 0.350382i
\(87\) 10.3248 1.65271i 1.10694 0.177189i
\(88\) 3.00237i 0.320054i
\(89\) −10.9270 10.9270i −1.15826 1.15826i −0.984849 0.173415i \(-0.944520\pi\)
−0.173415 0.984849i \(-0.555480\pi\)
\(90\) 2.31904 + 7.05815i 0.244448 + 0.743994i
\(91\) −3.13129 + 1.78746i −0.328249 + 0.187376i
\(92\) 0.478247i 0.0498607i
\(93\) 2.97582 4.11007i 0.308579 0.426195i
\(94\) −9.86025 −1.01701
\(95\) −9.23199 −0.947182
\(96\) 1.40293 + 1.01577i 0.143186 + 0.103671i
\(97\) 10.7186 + 10.7186i 1.08831 + 1.08831i 0.995703 + 0.0926043i \(0.0295192\pi\)
0.0926043 + 0.995703i \(0.470481\pi\)
\(98\) 0.707107 + 0.707107i 0.0714286 + 0.0714286i
\(99\) 8.03882 + 4.06272i 0.807932 + 0.408319i
\(100\) −1.13282 −0.113282
\(101\) 5.04608 0.502103 0.251052 0.967974i \(-0.419224\pi\)
0.251052 + 0.967974i \(0.419224\pi\)
\(102\) 4.25894 + 3.08361i 0.421698 + 0.305323i
\(103\) 17.3260i 1.70718i 0.520944 + 0.853591i \(0.325580\pi\)
−0.520944 + 0.853591i \(0.674420\pi\)
\(104\) −1.78746 3.13129i −0.175274 0.307049i
\(105\) −4.23543 + 0.677971i −0.413335 + 0.0661632i
\(106\) 4.17199 + 4.17199i 0.405220 + 0.405220i
\(107\) 7.64785i 0.739345i 0.929162 + 0.369673i \(0.120530\pi\)
−0.929162 + 0.369673i \(0.879470\pi\)
\(108\) −4.61811 + 2.38183i −0.444377 + 0.229191i
\(109\) 2.94969 + 2.94969i 0.282529 + 0.282529i 0.834117 0.551588i \(-0.185978\pi\)
−0.551588 + 0.834117i \(0.685978\pi\)
\(110\) −5.25751 + 5.25751i −0.501284 + 0.501284i
\(111\) −8.36077 6.05346i −0.793569 0.574569i
\(112\) −0.707107 + 0.707107i −0.0668153 + 0.0668153i
\(113\) 4.99755i 0.470130i 0.971980 + 0.235065i \(0.0755303\pi\)
−0.971980 + 0.235065i \(0.924470\pi\)
\(114\) −1.02058 6.37576i −0.0955858 0.597145i
\(115\) 0.837467 0.837467i 0.0780942 0.0780942i
\(116\) −6.03691 −0.560513
\(117\) 10.8027 0.548722i 0.998712 0.0507294i
\(118\) 5.32824 0.490504
\(119\) −2.14660 + 2.14660i −0.196778 + 0.196778i
\(120\) −0.677971 4.23543i −0.0618900 0.386640i
\(121\) 1.98575i 0.180522i
\(122\) −9.37758 + 9.37758i −0.849007 + 0.849007i
\(123\) −9.60374 6.95342i −0.865940 0.626968i
\(124\) −2.07156 + 2.07156i −0.186032 + 0.186032i
\(125\) −6.77188 6.77188i −0.605695 0.605695i
\(126\) −0.936434 2.85010i −0.0834242 0.253907i
\(127\) 0.521751i 0.0462979i −0.999732 0.0231490i \(-0.992631\pi\)
0.999732 0.0231490i \(-0.00736920\pi\)
\(128\) −0.707107 0.707107i −0.0625000 0.0625000i
\(129\) 7.85910 1.25802i 0.691956 0.110762i
\(130\) −2.35322 + 8.61331i −0.206391 + 0.755437i
\(131\) 10.1350i 0.885497i 0.896646 + 0.442748i \(0.145997\pi\)
−0.896646 + 0.442748i \(0.854003\pi\)
\(132\) −4.21213 3.04971i −0.366619 0.265443i
\(133\) 3.72791 0.323251
\(134\) 9.34908 0.807638
\(135\) 12.2577 + 3.91599i 1.05498 + 0.337034i
\(136\) −2.14660 2.14660i −0.184069 0.184069i
\(137\) 4.06995 + 4.06995i 0.347720 + 0.347720i 0.859259 0.511540i \(-0.170925\pi\)
−0.511540 + 0.859259i \(0.670925\pi\)
\(138\) 0.670949 + 0.485788i 0.0571149 + 0.0413530i
\(139\) 0.173766 0.0147387 0.00736933 0.999973i \(-0.497654\pi\)
0.00736933 + 0.999973i \(0.497654\pi\)
\(140\) 2.47645 0.209299
\(141\) −10.0157 + 13.8333i −0.843476 + 1.16497i
\(142\) 10.4162i 0.874109i
\(143\) 5.36661 + 9.40132i 0.448779 + 0.786178i
\(144\) 2.85010 0.936434i 0.237509 0.0780362i
\(145\) 10.5713 + 10.5713i 0.877903 + 0.877903i
\(146\) 11.4002i 0.943491i
\(147\) 1.71028 0.273767i 0.141061 0.0225799i
\(148\) 4.21400 + 4.21400i 0.346389 + 0.346389i
\(149\) −4.13899 + 4.13899i −0.339079 + 0.339079i −0.856021 0.516941i \(-0.827071\pi\)
0.516941 + 0.856021i \(0.327071\pi\)
\(150\) −1.15069 + 1.58928i −0.0939531 + 0.129764i
\(151\) −6.75083 + 6.75083i −0.549375 + 0.549375i −0.926260 0.376885i \(-0.876995\pi\)
0.376885 + 0.926260i \(0.376995\pi\)
\(152\) 3.72791i 0.302373i
\(153\) 8.65219 2.84278i 0.699488 0.229825i
\(154\) 2.12300 2.12300i 0.171076 0.171076i
\(155\) 7.25510 0.582744
\(156\) −6.20863 0.672986i −0.497088 0.0538820i
\(157\) −4.14765 −0.331018 −0.165509 0.986208i \(-0.552927\pi\)
−0.165509 + 0.986208i \(0.552927\pi\)
\(158\) 8.20397 8.20397i 0.652673 0.652673i
\(159\) 10.0908 1.61525i 0.800252 0.128098i
\(160\) 2.47645i 0.195781i
\(161\) −0.338172 + 0.338172i −0.0266517 + 0.0266517i
\(162\) −1.34938 + 8.89827i −0.106017 + 0.699114i
\(163\) −13.3414 + 13.3414i −1.04498 + 1.04498i −0.0460395 + 0.998940i \(0.514660\pi\)
−0.998940 + 0.0460395i \(0.985340\pi\)
\(164\) 4.84049 + 4.84049i 0.377979 + 0.377979i
\(165\) 2.03552 + 12.7163i 0.158465 + 0.989965i
\(166\) 14.0984i 1.09424i
\(167\) 6.44717 + 6.44717i 0.498897 + 0.498897i 0.911095 0.412197i \(-0.135239\pi\)
−0.412197 + 0.911095i \(0.635239\pi\)
\(168\) 0.273767 + 1.71028i 0.0211216 + 0.131951i
\(169\) 11.1941 + 6.61000i 0.861085 + 0.508462i
\(170\) 7.51789i 0.576596i
\(171\) −9.98142 5.04449i −0.763299 0.385762i
\(172\) −4.59522 −0.350382
\(173\) −2.65682 −0.201994 −0.100997 0.994887i \(-0.532203\pi\)
−0.100997 + 0.994887i \(0.532203\pi\)
\(174\) −6.13210 + 8.46938i −0.464873 + 0.642062i
\(175\) −0.801028 0.801028i −0.0605520 0.0605520i
\(176\) 2.12300 + 2.12300i 0.160027 + 0.160027i
\(177\) 5.41225 7.47515i 0.406809 0.561867i
\(178\) 15.4532 1.15826
\(179\) −3.64878 −0.272723 −0.136361 0.990659i \(-0.543541\pi\)
−0.136361 + 0.990659i \(0.543541\pi\)
\(180\) −6.63067 3.35106i −0.494221 0.249773i
\(181\) 19.5037i 1.44970i −0.688909 0.724848i \(-0.741910\pi\)
0.688909 0.724848i \(-0.258090\pi\)
\(182\) 0.950237 3.47808i 0.0704362 0.257813i
\(183\) 3.63067 + 22.6815i 0.268387 + 1.67667i
\(184\) −0.338172 0.338172i −0.0249304 0.0249304i
\(185\) 14.7584i 1.08506i
\(186\) 0.802036 + 5.01049i 0.0588081 + 0.367387i
\(187\) 6.44489 + 6.44489i 0.471297 + 0.471297i
\(188\) 6.97225 6.97225i 0.508504 0.508504i
\(189\) −4.94970 1.58129i −0.360038 0.115022i
\(190\) 6.52800 6.52800i 0.473591 0.473591i
\(191\) 0.854794i 0.0618508i −0.999522 0.0309254i \(-0.990155\pi\)
0.999522 0.0309254i \(-0.00984542\pi\)
\(192\) −1.71028 + 0.273767i −0.123429 + 0.0197574i
\(193\) −16.3246 + 16.3246i −1.17507 + 1.17507i −0.194083 + 0.980985i \(0.562173\pi\)
−0.980985 + 0.194083i \(0.937827\pi\)
\(194\) −15.1584 −1.08831
\(195\) 9.69356 + 12.0505i 0.694170 + 0.862956i
\(196\) −1.00000 −0.0714286
\(197\) 7.45721 7.45721i 0.531304 0.531304i −0.389656 0.920960i \(-0.627406\pi\)
0.920960 + 0.389656i \(0.127406\pi\)
\(198\) −8.55708 + 2.81153i −0.608125 + 0.199807i
\(199\) 0.778109i 0.0551587i 0.999620 + 0.0275793i \(0.00877989\pi\)
−0.999620 + 0.0275793i \(0.991220\pi\)
\(200\) 0.801028 0.801028i 0.0566412 0.0566412i
\(201\) 9.49649 13.1161i 0.669831 0.925140i
\(202\) −3.56811 + 3.56811i −0.251052 + 0.251052i
\(203\) −4.26874 4.26874i −0.299607 0.299607i
\(204\) −5.19197 + 0.831086i −0.363511 + 0.0581877i
\(205\) 16.9525i 1.18402i
\(206\) −12.2513 12.2513i −0.853591 0.853591i
\(207\) 1.36305 0.447847i 0.0947389 0.0311275i
\(208\) 3.47808 + 0.950237i 0.241162 + 0.0658871i
\(209\) 11.1926i 0.774207i
\(210\) 2.51550 3.47430i 0.173586 0.239749i
\(211\) −4.51239 −0.310646 −0.155323 0.987864i \(-0.549642\pi\)
−0.155323 + 0.987864i \(0.549642\pi\)
\(212\) −5.90009 −0.405220
\(213\) −14.6132 10.5804i −1.00128 0.724960i
\(214\) −5.40784 5.40784i −0.369673 0.369673i
\(215\) 8.04677 + 8.04677i 0.548785 + 0.548785i
\(216\) 1.58129 4.94970i 0.107593 0.336784i
\(217\) −2.92963 −0.198876
\(218\) −4.17149 −0.282529
\(219\) −15.9938 11.5800i −1.08076 0.782504i
\(220\) 7.43524i 0.501284i
\(221\) 10.5586 + 2.88468i 0.710246 + 0.194044i
\(222\) 10.1924 1.63151i 0.684069 0.109500i
\(223\) −3.08394 3.08394i −0.206516 0.206516i 0.596269 0.802785i \(-0.296649\pi\)
−0.802785 + 0.596269i \(0.796649\pi\)
\(224\) 1.00000i 0.0668153i
\(225\) 1.06082 + 3.22867i 0.0707211 + 0.215245i
\(226\) −3.53380 3.53380i −0.235065 0.235065i
\(227\) 18.9348 18.9348i 1.25675 1.25675i 0.304109 0.952637i \(-0.401641\pi\)
0.952637 0.304109i \(-0.0983588\pi\)
\(228\) 5.23000 + 3.78669i 0.346365 + 0.250779i
\(229\) 12.2479 12.2479i 0.809366 0.809366i −0.175172 0.984538i \(-0.556048\pi\)
0.984538 + 0.175172i \(0.0560482\pi\)
\(230\) 1.18436i 0.0780942i
\(231\) −0.821950 5.13490i −0.0540804 0.337851i
\(232\) 4.26874 4.26874i 0.280257 0.280257i
\(233\) 15.4793 1.01408 0.507041 0.861922i \(-0.330739\pi\)
0.507041 + 0.861922i \(0.330739\pi\)
\(234\) −7.25068 + 8.02669i −0.473992 + 0.524721i
\(235\) −24.4185 −1.59288
\(236\) −3.76763 + 3.76763i −0.245252 + 0.245252i
\(237\) −3.17629 19.8429i −0.206322 1.28894i
\(238\) 3.03575i 0.196778i
\(239\) 11.2898 11.2898i 0.730278 0.730278i −0.240397 0.970675i \(-0.577278\pi\)
0.970675 + 0.240397i \(0.0772776\pi\)
\(240\) 3.47430 + 2.51550i 0.224265 + 0.162375i
\(241\) −3.14172 + 3.14172i −0.202376 + 0.202376i −0.801017 0.598641i \(-0.795707\pi\)
0.598641 + 0.801017i \(0.295707\pi\)
\(242\) 1.40413 + 1.40413i 0.0902612 + 0.0902612i
\(243\) 11.1130 + 10.9317i 0.712900 + 0.701266i
\(244\) 13.2619i 0.849007i
\(245\) 1.75112 + 1.75112i 0.111875 + 0.111875i
\(246\) 11.7077 1.87406i 0.746454 0.119486i
\(247\) −6.66347 11.6732i −0.423987 0.742746i
\(248\) 2.92963i 0.186032i
\(249\) −19.7790 14.3206i −1.25345 0.907534i
\(250\) 9.57688 0.605695
\(251\) −18.4294 −1.16326 −0.581628 0.813455i \(-0.697584\pi\)
−0.581628 + 0.813455i \(0.697584\pi\)
\(252\) 2.67749 + 1.35317i 0.168666 + 0.0852416i
\(253\) 1.01532 + 1.01532i 0.0638326 + 0.0638326i
\(254\) 0.368934 + 0.368934i 0.0231490 + 0.0231490i
\(255\) 10.5471 + 7.63642i 0.660484 + 0.478211i
\(256\) 1.00000 0.0625000
\(257\) 4.35687 0.271774 0.135887 0.990724i \(-0.456612\pi\)
0.135887 + 0.990724i \(0.456612\pi\)
\(258\) −4.66767 + 6.44678i −0.290597 + 0.401359i
\(259\) 5.95950i 0.370305i
\(260\) −4.42655 7.75451i −0.274523 0.480914i
\(261\) 5.65317 + 17.2058i 0.349923 + 1.06501i
\(262\) −7.16651 7.16651i −0.442748 0.442748i
\(263\) 1.49647i 0.0922762i −0.998935 0.0461381i \(-0.985309\pi\)
0.998935 0.0461381i \(-0.0146914\pi\)
\(264\) 5.13490 0.821950i 0.316031 0.0505875i
\(265\) 10.3318 + 10.3318i 0.634674 + 0.634674i
\(266\) −2.63603 + 2.63603i −0.161625 + 0.161625i
\(267\) 15.6968 21.6797i 0.960630 1.32678i
\(268\) −6.61080 + 6.61080i −0.403819 + 0.403819i
\(269\) 11.0765i 0.675349i −0.941263 0.337674i \(-0.890360\pi\)
0.941263 0.337674i \(-0.109640\pi\)
\(270\) −11.4365 + 5.89849i −0.696005 + 0.358970i
\(271\) −9.41699 + 9.41699i −0.572042 + 0.572042i −0.932699 0.360657i \(-0.882553\pi\)
0.360657 + 0.932699i \(0.382553\pi\)
\(272\) 3.03575 0.184069
\(273\) −3.91429 4.86604i −0.236904 0.294506i
\(274\) −5.75578 −0.347720
\(275\) −2.40499 + 2.40499i −0.145026 + 0.145026i
\(276\) −0.817936 + 0.130928i −0.0492340 + 0.00788095i
\(277\) 20.3743i 1.22417i −0.790792 0.612085i \(-0.790331\pi\)
0.790792 0.612085i \(-0.209669\pi\)
\(278\) −0.122871 + 0.122871i −0.00736933 + 0.00736933i
\(279\) 7.84405 + 3.96429i 0.469611 + 0.237336i
\(280\) −1.75112 + 1.75112i −0.104649 + 0.104649i
\(281\) −14.5729 14.5729i −0.869346 0.869346i 0.123054 0.992400i \(-0.460731\pi\)
−0.992400 + 0.123054i \(0.960731\pi\)
\(282\) −2.69941 16.8638i −0.160747 1.00422i
\(283\) 17.5244i 1.04171i −0.853644 0.520857i \(-0.825612\pi\)
0.853644 0.520857i \(-0.174388\pi\)
\(284\) 7.36537 + 7.36537i 0.437055 + 0.437055i
\(285\) −2.52741 15.7893i −0.149711 0.935276i
\(286\) −10.4425 2.85297i −0.617478 0.168699i
\(287\) 6.84548i 0.404076i
\(288\) −1.35317 + 2.67749i −0.0797362 + 0.157772i
\(289\) −7.78425 −0.457897
\(290\) −14.9501 −0.877903
\(291\) −15.3974 + 21.2662i −0.902610 + 1.24664i
\(292\) 8.06119 + 8.06119i 0.471746 + 0.471746i
\(293\) 22.5588 + 22.5588i 1.31790 + 1.31790i 0.915435 + 0.402466i \(0.131847\pi\)
0.402466 + 0.915435i \(0.368153\pi\)
\(294\) −1.01577 + 1.40293i −0.0592407 + 0.0818206i
\(295\) 13.1951 0.768250
\(296\) −5.95950 −0.346389
\(297\) −4.74762 + 14.8609i −0.275485 + 0.862314i
\(298\) 5.85342i 0.339079i
\(299\) 1.66338 + 0.454448i 0.0961960 + 0.0262814i
\(300\) −0.310130 1.93745i −0.0179053 0.111858i
\(301\) −3.24931 3.24931i −0.187287 0.187287i
\(302\) 9.54712i 0.549375i
\(303\) 1.38145 + 8.63019i 0.0793621 + 0.495792i
\(304\) −2.63603 2.63603i −0.151187 0.151187i
\(305\) −23.2232 + 23.2232i −1.32975 + 1.32975i
\(306\) −4.10788 + 8.12817i −0.234832 + 0.464657i
\(307\) 15.0145 15.0145i 0.856921 0.856921i −0.134053 0.990974i \(-0.542799\pi\)
0.990974 + 0.134053i \(0.0427992\pi\)
\(308\) 3.00237i 0.171076i
\(309\) −29.6323 + 4.74328i −1.68572 + 0.269836i
\(310\) −5.13013 + 5.13013i −0.291372 + 0.291372i
\(311\) 10.7272 0.608283 0.304142 0.952627i \(-0.401630\pi\)
0.304142 + 0.952627i \(0.401630\pi\)
\(312\) 4.86604 3.91429i 0.275485 0.221603i
\(313\) −17.3350 −0.979834 −0.489917 0.871769i \(-0.662973\pi\)
−0.489917 + 0.871769i \(0.662973\pi\)
\(314\) 2.93283 2.93283i 0.165509 0.165509i
\(315\) −2.31904 7.05815i −0.130663 0.397682i
\(316\) 11.6022i 0.652673i
\(317\) 19.6716 19.6716i 1.10487 1.10487i 0.111055 0.993814i \(-0.464577\pi\)
0.993814 0.111055i \(-0.0354229\pi\)
\(318\) −5.99312 + 8.27742i −0.336077 + 0.464175i
\(319\) −12.8164 + 12.8164i −0.717579 + 0.717579i
\(320\) −1.75112 1.75112i −0.0978904 0.0978904i
\(321\) −13.0799 + 2.09373i −0.730051 + 0.116860i
\(322\) 0.478247i 0.0266517i
\(323\) −8.00231 8.00231i −0.445261 0.445261i
\(324\) −5.33787 7.24618i −0.296548 0.402566i
\(325\) −1.07645 + 3.94006i −0.0597108 + 0.218555i
\(326\) 18.8676i 1.04498i
\(327\) −4.23726 + 5.85232i −0.234321 + 0.323634i
\(328\) −6.84548 −0.377979
\(329\) 9.86025 0.543613
\(330\) −10.4311 7.55248i −0.574215 0.415750i
\(331\) 4.17896 + 4.17896i 0.229697 + 0.229697i 0.812566 0.582869i \(-0.198070\pi\)
−0.582869 + 0.812566i \(0.698070\pi\)
\(332\) 9.96904 + 9.96904i 0.547122 + 0.547122i
\(333\) 8.06421 15.9565i 0.441916 0.874410i
\(334\) −9.11768 −0.498897
\(335\) 23.1526 1.26496
\(336\) −1.40293 1.01577i −0.0765362 0.0554146i
\(337\) 7.79284i 0.424503i 0.977215 + 0.212251i \(0.0680796\pi\)
−0.977215 + 0.212251i \(0.931920\pi\)
\(338\) −12.5894 + 3.24145i −0.684773 + 0.176311i
\(339\) −8.54720 + 1.36816i −0.464220 + 0.0743084i
\(340\) −5.31595 5.31595i −0.288298 0.288298i
\(341\) 8.79586i 0.476322i
\(342\) 10.6249 3.49094i 0.574530 0.188768i
\(343\) −0.707107 0.707107i −0.0381802 0.0381802i
\(344\) 3.24931 3.24931i 0.175191 0.175191i
\(345\) 1.66157 + 1.20303i 0.0894561 + 0.0647691i
\(346\) 1.87865 1.87865i 0.100997 0.100997i
\(347\) 10.9288i 0.586690i 0.956007 + 0.293345i \(0.0947684\pi\)
−0.956007 + 0.293345i \(0.905232\pi\)
\(348\) −1.65271 10.3248i −0.0885944 0.553468i
\(349\) −23.3039 + 23.3039i −1.24743 + 1.24743i −0.290581 + 0.956850i \(0.593849\pi\)
−0.956850 + 0.290581i \(0.906151\pi\)
\(350\) 1.13282 0.0605520
\(351\) 3.89589 + 18.3254i 0.207947 + 0.978140i
\(352\) −3.00237 −0.160027
\(353\) 17.4264 17.4264i 0.927516 0.927516i −0.0700290 0.997545i \(-0.522309\pi\)
0.997545 + 0.0700290i \(0.0223092\pi\)
\(354\) 1.45869 + 9.11277i 0.0775287 + 0.484338i
\(355\) 25.7953i 1.36907i
\(356\) −10.9270 + 10.9270i −0.579132 + 0.579132i
\(357\) −4.25894 3.08361i −0.225407 0.163202i
\(358\) 2.58008 2.58008i 0.136361 0.136361i
\(359\) 13.3523 + 13.3523i 0.704707 + 0.704707i 0.965417 0.260710i \(-0.0839568\pi\)
−0.260710 + 0.965417i \(0.583957\pi\)
\(360\) 7.05815 2.31904i 0.371997 0.122224i
\(361\) 5.10270i 0.268563i
\(362\) 13.7912 + 13.7912i 0.724848 + 0.724848i
\(363\) 3.39618 0.543631i 0.178253 0.0285332i
\(364\) 1.78746 + 3.13129i 0.0936882 + 0.164124i
\(365\) 28.2322i 1.47774i
\(366\) −18.6055 13.4710i −0.972528 0.704141i
\(367\) 23.3338 1.21801 0.609006 0.793165i \(-0.291568\pi\)
0.609006 + 0.793165i \(0.291568\pi\)
\(368\) 0.478247 0.0249304
\(369\) 9.26309 18.3287i 0.482217 0.954153i
\(370\) 10.4358 + 10.4358i 0.542531 + 0.542531i
\(371\) −4.17199 4.17199i −0.216599 0.216599i
\(372\) −4.11007 2.97582i −0.213097 0.154289i
\(373\) 6.26271 0.324271 0.162135 0.986769i \(-0.448162\pi\)
0.162135 + 0.986769i \(0.448162\pi\)
\(374\) −9.11445 −0.471297
\(375\) 9.72788 13.4357i 0.502346 0.693817i
\(376\) 9.86025i 0.508504i
\(377\) −5.73650 + 20.9969i −0.295445 + 1.08139i
\(378\) 4.61811 2.38183i 0.237530 0.122508i
\(379\) −23.9024 23.9024i −1.22779 1.22779i −0.964800 0.262986i \(-0.915293\pi\)
−0.262986 0.964800i \(-0.584707\pi\)
\(380\) 9.23199i 0.473591i
\(381\) 0.892340 0.142838i 0.0457160 0.00731782i
\(382\) 0.604431 + 0.604431i 0.0309254 + 0.0309254i
\(383\) −6.96614 + 6.96614i −0.355953 + 0.355953i −0.862319 0.506366i \(-0.830989\pi\)
0.506366 + 0.862319i \(0.330989\pi\)
\(384\) 1.01577 1.40293i 0.0518356 0.0715931i
\(385\) 5.25751 5.25751i 0.267948 0.267948i
\(386\) 23.0864i 1.17507i
\(387\) 4.30312 + 13.0969i 0.218740 + 0.665750i
\(388\) 10.7186 10.7186i 0.544154 0.544154i
\(389\) 33.8785 1.71771 0.858854 0.512220i \(-0.171177\pi\)
0.858854 + 0.512220i \(0.171177\pi\)
\(390\) −15.3754 1.66662i −0.778563 0.0843926i
\(391\) 1.45184 0.0734226
\(392\) 0.707107 0.707107i 0.0357143 0.0357143i
\(393\) −17.3336 + 2.77462i −0.874366 + 0.139961i
\(394\) 10.5461i 0.531304i
\(395\) 20.3168 20.3168i 1.02225 1.02225i
\(396\) 4.06272 8.03882i 0.204159 0.403966i
\(397\) 1.28835 1.28835i 0.0646606 0.0646606i −0.674037 0.738698i \(-0.735441\pi\)
0.738698 + 0.674037i \(0.235441\pi\)
\(398\) −0.550206 0.550206i −0.0275793 0.0275793i
\(399\) 1.02058 + 6.37576i 0.0510928 + 0.319187i
\(400\) 1.13282i 0.0566412i
\(401\) −17.5817 17.5817i −0.877988 0.877988i 0.115339 0.993326i \(-0.463205\pi\)
−0.993326 + 0.115339i \(0.963205\pi\)
\(402\) 2.55947 + 15.9895i 0.127655 + 0.797486i
\(403\) 5.23659 + 9.17354i 0.260853 + 0.456967i
\(404\) 5.04608i 0.251052i
\(405\) −3.34168 + 22.0362i −0.166049 + 1.09499i
\(406\) 6.03691 0.299607
\(407\) 17.8927 0.886906
\(408\) 3.08361 4.25894i 0.152661 0.210849i
\(409\) 21.1765 + 21.1765i 1.04711 + 1.04711i 0.998834 + 0.0482783i \(0.0153735\pi\)
0.0482783 + 0.998834i \(0.484627\pi\)
\(410\) 11.9872 + 11.9872i 0.592008 + 0.592008i
\(411\) −5.84653 + 8.07497i −0.288388 + 0.398309i
\(412\) 17.3260 0.853591
\(413\) −5.32824 −0.262185
\(414\) −0.647149 + 1.28050i −0.0318057 + 0.0629332i
\(415\) 34.9139i 1.71386i
\(416\) −3.13129 + 1.78746i −0.153524 + 0.0876372i
\(417\) 0.0475714 + 0.297189i 0.00232958 + 0.0145534i
\(418\) 7.91435 + 7.91435i 0.387103 + 0.387103i
\(419\) 31.9709i 1.56188i 0.624607 + 0.780939i \(0.285259\pi\)
−0.624607 + 0.780939i \(0.714741\pi\)
\(420\) 0.677971 + 4.23543i 0.0330816 + 0.206668i
\(421\) 11.0977 + 11.0977i 0.540869 + 0.540869i 0.923784 0.382915i \(-0.125080\pi\)
−0.382915 + 0.923784i \(0.625080\pi\)
\(422\) 3.19074 3.19074i 0.155323 0.155323i
\(423\) −26.4007 13.3426i −1.28365 0.648738i
\(424\) 4.17199 4.17199i 0.202610 0.202610i
\(425\) 3.43897i 0.166814i
\(426\) 17.8146 2.85161i 0.863121 0.138161i
\(427\) 9.37758 9.37758i 0.453813 0.453813i
\(428\) 7.64785 0.369673
\(429\) −14.6097 + 11.7522i −0.705361 + 0.567400i
\(430\) −11.3798 −0.548785
\(431\) −0.127561 + 0.127561i −0.00614442 + 0.00614442i −0.710172 0.704028i \(-0.751383\pi\)
0.704028 + 0.710172i \(0.251383\pi\)
\(432\) 2.38183 + 4.61811i 0.114596 + 0.222189i
\(433\) 10.1128i 0.485988i −0.970028 0.242994i \(-0.921870\pi\)
0.970028 0.242994i \(-0.0781296\pi\)
\(434\) 2.07156 2.07156i 0.0994382 0.0994382i
\(435\) −15.1859 + 20.9740i −0.728106 + 1.00563i
\(436\) 2.94969 2.94969i 0.141265 0.141265i
\(437\) −1.26067 1.26067i −0.0603062 0.0603062i
\(438\) 19.4976 3.12101i 0.931631 0.149128i
\(439\) 22.8399i 1.09009i 0.838408 + 0.545043i \(0.183487\pi\)
−0.838408 + 0.545043i \(0.816513\pi\)
\(440\) 5.25751 + 5.25751i 0.250642 + 0.250642i
\(441\) 0.936434 + 2.85010i 0.0445921 + 0.135719i
\(442\) −9.50581 + 5.42626i −0.452145 + 0.258101i
\(443\) 8.91535i 0.423581i −0.977315 0.211791i \(-0.932071\pi\)
0.977315 0.211791i \(-0.0679295\pi\)
\(444\) −6.05346 + 8.36077i −0.287285 + 0.396785i
\(445\) 38.2691 1.81413
\(446\) 4.36135 0.206516
\(447\) −8.21195 5.94571i −0.388412 0.281222i
\(448\) 0.707107 + 0.707107i 0.0334077 + 0.0334077i
\(449\) −19.3368 19.3368i −0.912558 0.912558i 0.0839148 0.996473i \(-0.473258\pi\)
−0.996473 + 0.0839148i \(0.973258\pi\)
\(450\) −3.03312 1.53290i −0.142983 0.0722617i
\(451\) 20.5527 0.967789
\(452\) 4.99755 0.235065
\(453\) −13.3940 9.69765i −0.629303 0.455635i
\(454\) 26.7778i 1.25675i
\(455\) 2.35322 8.61331i 0.110321 0.403798i
\(456\) −6.37576 + 1.02058i −0.298572 + 0.0477929i
\(457\) 6.87890 + 6.87890i 0.321781 + 0.321781i 0.849450 0.527669i \(-0.176934\pi\)
−0.527669 + 0.849450i \(0.676934\pi\)
\(458\) 17.3212i 0.809366i
\(459\) 7.23062 + 14.0194i 0.337497 + 0.654369i
\(460\) −0.837467 0.837467i −0.0390471 0.0390471i
\(461\) 5.37847 5.37847i 0.250500 0.250500i −0.570675 0.821176i \(-0.693319\pi\)
0.821176 + 0.570675i \(0.193319\pi\)
\(462\) 4.21213 + 3.04971i 0.195966 + 0.141886i
\(463\) −1.71052 + 1.71052i −0.0794944 + 0.0794944i −0.745736 0.666242i \(-0.767902\pi\)
0.666242 + 0.745736i \(0.267902\pi\)
\(464\) 6.03691i 0.280257i
\(465\) 1.98621 + 12.4082i 0.0921081 + 0.575418i
\(466\) −10.9455 + 10.9455i −0.507041 + 0.507041i
\(467\) −12.1098 −0.560375 −0.280188 0.959945i \(-0.590397\pi\)
−0.280188 + 0.959945i \(0.590397\pi\)
\(468\) −0.548722 10.8027i −0.0253647 0.499356i
\(469\) −9.34908 −0.431701
\(470\) 17.2665 17.2665i 0.796442 0.796442i
\(471\) −1.13549 7.09363i −0.0523205 0.326857i
\(472\) 5.32824i 0.245252i
\(473\) −9.75565 + 9.75565i −0.448565 + 0.448565i
\(474\) 16.2771 + 11.7851i 0.747630 + 0.541308i
\(475\) 2.98616 2.98616i 0.137014 0.137014i
\(476\) 2.14660 + 2.14660i 0.0983891 + 0.0983891i
\(477\) 5.52505 + 16.8159i 0.252975 + 0.769946i
\(478\) 15.9662i 0.730278i
\(479\) −0.535810 0.535810i −0.0244818 0.0244818i 0.694760 0.719242i \(-0.255511\pi\)
−0.719242 + 0.694760i \(0.755511\pi\)
\(480\) −4.23543 + 0.677971i −0.193320 + 0.0309450i
\(481\) 18.6609 10.6523i 0.850866 0.485705i
\(482\) 4.44306i 0.202376i
\(483\) −0.670949 0.485788i −0.0305292 0.0221041i
\(484\) −1.98575 −0.0902612
\(485\) −37.5390 −1.70456
\(486\) −15.5879 + 0.128235i −0.707083 + 0.00581687i
\(487\) 5.52429 + 5.52429i 0.250329 + 0.250329i 0.821106 0.570776i \(-0.193358\pi\)
−0.570776 + 0.821106i \(0.693358\pi\)
\(488\) 9.37758 + 9.37758i 0.424503 + 0.424503i
\(489\) −26.4699 19.1651i −1.19701 0.866675i
\(490\) −2.47645 −0.111875
\(491\) −32.2992 −1.45764 −0.728821 0.684704i \(-0.759932\pi\)
−0.728821 + 0.684704i \(0.759932\pi\)
\(492\) −6.95342 + 9.60374i −0.313484 + 0.432970i
\(493\) 18.3265i 0.825386i
\(494\) 12.9660 + 3.54240i 0.583366 + 0.159380i
\(495\) −21.1912 + 6.96262i −0.952474 + 0.312946i
\(496\) 2.07156 + 2.07156i 0.0930159 + 0.0930159i
\(497\) 10.4162i 0.467231i
\(498\) 24.1121 3.85966i 1.08049 0.172956i
\(499\) 24.5090 + 24.5090i 1.09717 + 1.09717i 0.994740 + 0.102433i \(0.0326627\pi\)
0.102433 + 0.994740i \(0.467337\pi\)
\(500\) −6.77188 + 6.77188i −0.302848 + 0.302848i
\(501\) −9.26144 + 12.7915i −0.413771 + 0.571481i
\(502\) 13.0316 13.0316i 0.581628 0.581628i
\(503\) 22.3557i 0.996792i 0.866949 + 0.498396i \(0.166077\pi\)
−0.866949 + 0.498396i \(0.833923\pi\)
\(504\) −2.85010 + 0.936434i −0.126954 + 0.0417121i
\(505\) −8.83627 + 8.83627i −0.393209 + 0.393209i
\(506\) −1.43588 −0.0638326
\(507\) −8.24037 + 20.9546i −0.365968 + 0.930628i
\(508\) −0.521751 −0.0231490
\(509\) 2.91721 2.91721i 0.129303 0.129303i −0.639493 0.768797i \(-0.720856\pi\)
0.768797 + 0.639493i \(0.220856\pi\)
\(510\) −12.8577 + 2.05815i −0.569347 + 0.0911363i
\(511\) 11.4002i 0.504317i
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) 5.89490 18.4520i 0.260266 0.814677i
\(514\) −3.08077 + 3.08077i −0.135887 + 0.135887i
\(515\) −30.3399 30.3399i −1.33693 1.33693i
\(516\) −1.25802 7.85910i −0.0553812 0.345978i
\(517\) 29.6042i 1.30199i
\(518\) −4.21400 4.21400i −0.185153 0.185153i
\(519\) −0.727347 4.54389i −0.0319270 0.199455i
\(520\) 8.61331 + 2.35322i 0.377719 + 0.103195i
\(521\) 20.6947i 0.906651i 0.891345 + 0.453325i \(0.149762\pi\)
−0.891345 + 0.453325i \(0.850238\pi\)
\(522\) −16.1638 8.16896i −0.707469 0.357546i
\(523\) −22.5537 −0.986202 −0.493101 0.869972i \(-0.664137\pi\)
−0.493101 + 0.869972i \(0.664137\pi\)
\(524\) 10.1350 0.442748
\(525\) 1.15069 1.58928i 0.0502201 0.0693617i
\(526\) 1.05816 + 1.05816i 0.0461381 + 0.0461381i
\(527\) 6.28874 + 6.28874i 0.273942 + 0.273942i
\(528\) −3.04971 + 4.21213i −0.132722 + 0.183309i
\(529\) −22.7713 −0.990056
\(530\) −14.6113 −0.634674
\(531\) 14.2663 + 7.21000i 0.619104 + 0.312887i
\(532\) 3.72791i 0.161625i
\(533\) 21.4352 12.2360i 0.928462 0.530000i
\(534\) 4.23056 + 26.4292i 0.183074 + 1.14370i
\(535\) −13.3923 13.3923i −0.578999 0.578999i
\(536\) 9.34908i 0.403819i
\(537\) −0.998915 6.24043i −0.0431063 0.269294i
\(538\) 7.83230 + 7.83230i 0.337674 + 0.337674i
\(539\) −2.12300 + 2.12300i −0.0914441 + 0.0914441i
\(540\) 3.91599 12.2577i 0.168517 0.527488i
\(541\) −0.860954 + 0.860954i −0.0370153 + 0.0370153i −0.725372 0.688357i \(-0.758332\pi\)
0.688357 + 0.725372i \(0.258332\pi\)
\(542\) 13.3176i 0.572042i
\(543\) 33.3567 5.33945i 1.43147 0.229138i
\(544\) −2.14660 + 2.14660i −0.0920346 + 0.0920346i
\(545\) −10.3305 −0.442510
\(546\) 6.20863 + 0.672986i 0.265705 + 0.0288012i
\(547\) 38.4468 1.64387 0.821934 0.569582i \(-0.192895\pi\)
0.821934 + 0.569582i \(0.192895\pi\)
\(548\) 4.06995 4.06995i 0.173860 0.173860i
\(549\) −37.7978 + 12.4189i −1.61317 + 0.530026i
\(550\) 3.40116i 0.145026i
\(551\) 15.9135 15.9135i 0.677937 0.677937i
\(552\) 0.485788 0.670949i 0.0206765 0.0285575i
\(553\) −8.20397 + 8.20397i −0.348868 + 0.348868i
\(554\) 14.4068 + 14.4068i 0.612085 + 0.612085i
\(555\) 25.2410 4.04037i 1.07142 0.171504i
\(556\) 0.173766i 0.00736933i
\(557\) −0.845111 0.845111i −0.0358085 0.0358085i 0.688976 0.724784i \(-0.258061\pi\)
−0.724784 + 0.688976i \(0.758061\pi\)
\(558\) −8.34976 + 2.74341i −0.353473 + 0.116138i
\(559\) −4.36655 + 15.9825i −0.184685 + 0.675990i
\(560\) 2.47645i 0.104649i
\(561\) −9.25816 + 12.7869i −0.390880 + 0.539865i
\(562\) 20.6092 0.869346
\(563\) −42.4619 −1.78955 −0.894777 0.446513i \(-0.852666\pi\)
−0.894777 + 0.446513i \(0.852666\pi\)
\(564\) 13.8333 + 10.0157i 0.582485 + 0.421738i
\(565\) −8.75130 8.75130i −0.368170 0.368170i
\(566\) 12.3916 + 12.3916i 0.520857 + 0.520857i
\(567\) 1.34938 8.89827i 0.0566686 0.373692i
\(568\) −10.4162 −0.437055
\(569\) 13.1702 0.552122 0.276061 0.961140i \(-0.410971\pi\)
0.276061 + 0.961140i \(0.410971\pi\)
\(570\) 12.9519 + 9.37755i 0.542493 + 0.392783i
\(571\) 22.7843i 0.953494i 0.879041 + 0.476747i \(0.158184\pi\)
−0.879041 + 0.476747i \(0.841816\pi\)
\(572\) 9.40132 5.36661i 0.393089 0.224389i
\(573\) 1.46194 0.234014i 0.0610733 0.00977609i
\(574\) −4.84049 4.84049i −0.202038 0.202038i
\(575\) 0.541771i 0.0225934i
\(576\) −0.936434 2.85010i −0.0390181 0.118754i
\(577\) 17.2984 + 17.2984i 0.720142 + 0.720142i 0.968634 0.248492i \(-0.0799350\pi\)
−0.248492 + 0.968634i \(0.579935\pi\)
\(578\) 5.50429 5.50429i 0.228948 0.228948i
\(579\) −32.3887 23.4504i −1.34603 0.974567i
\(580\) 10.5713 10.5713i 0.438951 0.438951i
\(581\) 14.0984i 0.584898i
\(582\) −4.14986 25.9250i −0.172017 1.07463i
\(583\) −12.5259 + 12.5259i −0.518769 + 0.518769i
\(584\) −11.4002 −0.471746
\(585\) −17.9560 + 19.8777i −0.742388 + 0.821843i
\(586\) −31.9030 −1.31790
\(587\) −21.3846 + 21.3846i −0.882638 + 0.882638i −0.993802 0.111164i \(-0.964542\pi\)
0.111164 + 0.993802i \(0.464542\pi\)
\(588\) −0.273767 1.71028i −0.0112899 0.0705307i
\(589\) 10.9214i 0.450009i
\(590\) −9.33037 + 9.33037i −0.384125 + 0.384125i
\(591\) 14.7954 + 10.7124i 0.608603 + 0.440648i
\(592\) 4.21400 4.21400i 0.173194 0.173194i
\(593\) −0.343278 0.343278i −0.0140968 0.0140968i 0.700023 0.714120i \(-0.253173\pi\)
−0.714120 + 0.700023i \(0.753173\pi\)
\(594\) −7.15114 13.8653i −0.293415 0.568900i
\(595\) 7.51789i 0.308203i
\(596\) 4.13899 + 4.13899i 0.169540 + 0.169540i
\(597\) −1.33078 + 0.213020i −0.0544653 + 0.00871834i
\(598\) −1.49753 + 0.854846i −0.0612387 + 0.0349573i
\(599\) 36.3142i 1.48376i −0.670534 0.741879i \(-0.733935\pi\)
0.670534 0.741879i \(-0.266065\pi\)
\(600\) 1.58928 + 1.15069i 0.0648819 + 0.0469766i
\(601\) −21.1337 −0.862061 −0.431031 0.902337i \(-0.641850\pi\)
−0.431031 + 0.902337i \(0.641850\pi\)
\(602\) 4.59522 0.187287
\(603\) 25.0320 + 12.6509i 1.01938 + 0.515184i
\(604\) 6.75083 + 6.75083i 0.274687 + 0.274687i
\(605\) 3.47727 + 3.47727i 0.141371 + 0.141371i
\(606\) −7.07930 5.12564i −0.287577 0.208215i
\(607\) −5.09736 −0.206896 −0.103448 0.994635i \(-0.532987\pi\)
−0.103448 + 0.994635i \(0.532987\pi\)
\(608\) 3.72791 0.151187
\(609\) 6.13210 8.46938i 0.248485 0.343197i
\(610\) 32.8425i 1.32975i
\(611\) −17.6248 30.8753i −0.713022 1.24908i
\(612\) −2.84278 8.65219i −0.114912 0.349744i
\(613\) 28.8407 + 28.8407i 1.16486 + 1.16486i 0.983397 + 0.181467i \(0.0580845\pi\)
0.181467 + 0.983397i \(0.441915\pi\)
\(614\) 21.2337i 0.856921i
\(615\) 28.9935 4.64104i 1.16913 0.187145i
\(616\) −2.12300 2.12300i −0.0855381 0.0855381i
\(617\) −29.3917 + 29.3917i −1.18327 + 1.18327i −0.204373 + 0.978893i \(0.565515\pi\)
−0.978893 + 0.204373i \(0.934485\pi\)
\(618\) 17.5992 24.3072i 0.707943 0.977779i
\(619\) −2.81364 + 2.81364i −0.113090 + 0.113090i −0.761387 0.648298i \(-0.775481\pi\)
0.648298 + 0.761387i \(0.275481\pi\)
\(620\) 7.25510i 0.291372i
\(621\) 1.13910 + 2.20860i 0.0457106 + 0.0886280i
\(622\) −7.58527 + 7.58527i −0.304142 + 0.304142i
\(623\) −15.4532 −0.619118
\(624\) −0.672986 + 6.20863i −0.0269410 + 0.248544i
\(625\) 29.3808 1.17523
\(626\) 12.2577 12.2577i 0.489917 0.489917i
\(627\) 19.1424 3.06415i 0.764475 0.122371i
\(628\) 4.14765i 0.165509i
\(629\) 12.7926 12.7926i 0.510076 0.510076i
\(630\) 6.63067 + 3.35106i 0.264172 + 0.133509i
\(631\) −22.1341 + 22.1341i −0.881143 + 0.881143i −0.993651 0.112507i \(-0.964112\pi\)
0.112507 + 0.993651i \(0.464112\pi\)
\(632\) −8.20397 8.20397i −0.326337 0.326337i
\(633\) −1.23534 7.71744i −0.0491004 0.306741i
\(634\) 27.8199i 1.10487i
\(635\) 0.913648 + 0.913648i 0.0362570 + 0.0362570i
\(636\) −1.61525 10.0908i −0.0640488 0.400126i
\(637\) −0.950237 + 3.47808i −0.0376498 + 0.137807i
\(638\) 18.1251i 0.717579i
\(639\) 14.0949 27.8893i 0.557585 1.10328i
\(640\) 2.47645 0.0978904
\(641\) 22.5807 0.891885 0.445943 0.895062i \(-0.352869\pi\)
0.445943 + 0.895062i \(0.352869\pi\)
\(642\) 7.76843 10.7294i 0.306595 0.423456i
\(643\) −11.9697 11.9697i −0.472039 0.472039i 0.430535 0.902574i \(-0.358325\pi\)
−0.902574 + 0.430535i \(0.858325\pi\)
\(644\) 0.338172 + 0.338172i 0.0133258 + 0.0133258i
\(645\) −11.5593 + 15.9652i −0.455146 + 0.628627i
\(646\) 11.3170 0.445261
\(647\) 49.1692 1.93304 0.966521 0.256586i \(-0.0825978\pi\)
0.966521 + 0.256586i \(0.0825978\pi\)
\(648\) 8.89827 + 1.34938i 0.349557 + 0.0530086i
\(649\) 15.9974i 0.627951i
\(650\) −2.02487 3.54721i −0.0794221 0.139133i
\(651\) −0.802036 5.01049i −0.0314343 0.196376i
\(652\) 13.3414 + 13.3414i 0.522490 + 0.522490i
\(653\) 34.8066i 1.36209i 0.732242 + 0.681044i \(0.238474\pi\)
−0.732242 + 0.681044i \(0.761526\pi\)
\(654\) −1.14202 7.13441i −0.0446563 0.278978i
\(655\) −17.7475 17.7475i −0.693453 0.693453i
\(656\) 4.84049 4.84049i 0.188989 0.188989i
\(657\) 15.4265 30.5240i 0.601843 1.19085i
\(658\) −6.97225 + 6.97225i −0.271807 + 0.271807i
\(659\) 12.0404i 0.469029i −0.972113 0.234514i \(-0.924650\pi\)
0.972113 0.234514i \(-0.0753500\pi\)
\(660\) 12.7163 2.03552i 0.494983 0.0792326i
\(661\) 27.1053 27.1053i 1.05427 1.05427i 0.0558331 0.998440i \(-0.482219\pi\)
0.998440 0.0558331i \(-0.0177815\pi\)
\(662\) −5.90994 −0.229697
\(663\) −2.04302 + 18.8478i −0.0793442 + 0.731989i
\(664\) −14.0984 −0.547122
\(665\) −6.52800 + 6.52800i −0.253145 + 0.253145i
\(666\) 5.58068 + 16.9852i 0.216247 + 0.658163i
\(667\) 2.88714i 0.111790i
\(668\) 6.44717 6.44717i 0.249449 0.249449i
\(669\) 4.43011 6.11867i 0.171278 0.236561i
\(670\) −16.3713 + 16.3713i −0.632480 + 0.632480i
\(671\) −28.1550 28.1550i −1.08691 1.08691i
\(672\) 1.71028 0.273767i 0.0659754 0.0105608i
\(673\) 17.0132i 0.655809i −0.944711 0.327905i \(-0.893658\pi\)
0.944711 0.327905i \(-0.106342\pi\)
\(674\) −5.51037 5.51037i −0.212251 0.212251i
\(675\) −5.23150 + 2.69819i −0.201361 + 0.103853i
\(676\) 6.61000 11.1941i 0.254231 0.430542i
\(677\) 2.58605i 0.0993901i −0.998764 0.0496950i \(-0.984175\pi\)
0.998764 0.0496950i \(-0.0158249\pi\)
\(678\) 5.07635 7.01122i 0.194956 0.269264i
\(679\) 15.1584 0.581725
\(680\) 7.51789 0.288298
\(681\) 37.5675 + 27.2001i 1.43959 + 1.04231i
\(682\) −6.21961 6.21961i −0.238161 0.238161i
\(683\) −25.9379 25.9379i −0.992486 0.992486i 0.00748557 0.999972i \(-0.497617\pi\)
−0.999972 + 0.00748557i \(0.997617\pi\)
\(684\) −5.04449 + 9.98142i −0.192881 + 0.381649i
\(685\) −14.2539 −0.544615
\(686\) 1.00000 0.0381802
\(687\) 24.3004 + 17.5943i 0.927119 + 0.671264i
\(688\) 4.59522i 0.175191i
\(689\) −5.60648 + 20.5210i −0.213590 + 0.781788i
\(690\) −2.02558 + 0.324238i −0.0771126 + 0.0123435i
\(691\) −35.6892 35.6892i −1.35768 1.35768i −0.876768 0.480914i \(-0.840305\pi\)
−0.480914 0.876768i \(-0.659695\pi\)
\(692\) 2.65682i 0.100997i
\(693\) 8.55708 2.81153i 0.325057 0.106801i
\(694\) −7.72784 7.72784i −0.293345 0.293345i
\(695\) −0.304285 + 0.304285i −0.0115422 + 0.0115422i
\(696\) 8.46938 + 6.13210i 0.321031 + 0.232437i
\(697\) 14.6945 14.6945i 0.556593 0.556593i
\(698\) 32.9568i 1.24743i
\(699\) 4.23771 + 26.4739i 0.160285 + 1.00133i
\(700\) −0.801028 + 0.801028i −0.0302760 + 0.0302760i
\(701\) 28.4715 1.07535 0.537676 0.843151i \(-0.319302\pi\)
0.537676 + 0.843151i \(0.319302\pi\)
\(702\) −15.7129 10.2032i −0.593044 0.385096i
\(703\) −22.2165 −0.837910
\(704\) 2.12300 2.12300i 0.0800136 0.0800136i
\(705\) −6.68496 41.7624i −0.251770 1.57286i
\(706\) 24.6447i 0.927516i
\(707\) 3.56811 3.56811i 0.134193 0.134193i
\(708\) −7.47515 5.41225i −0.280933 0.203405i
\(709\) 34.7099 34.7099i 1.30356 1.30356i 0.377584 0.925975i \(-0.376755\pi\)
0.925975 0.377584i \(-0.123245\pi\)
\(710\) 18.2400 + 18.2400i 0.684535 + 0.684535i
\(711\) 33.0674 10.8647i 1.24012 0.407457i
\(712\) 15.4532i 0.579132i
\(713\) 0.990720 + 0.990720i 0.0371028 + 0.0371028i
\(714\) 5.19197 0.831086i 0.194305 0.0311026i
\(715\) −25.8604 7.06524i −0.967123 0.264225i
\(716\) 3.64878i 0.136361i
\(717\) 22.3995 + 16.2180i 0.836525 + 0.605671i
\(718\) −18.8830 −0.704707
\(719\) 3.99422 0.148959 0.0744797 0.997223i \(-0.476270\pi\)
0.0744797 + 0.997223i \(0.476270\pi\)
\(720\) −3.35106 + 6.63067i −0.124887 + 0.247111i
\(721\) 12.2513 + 12.2513i 0.456263 + 0.456263i
\(722\) 3.60816 + 3.60816i 0.134282 + 0.134282i
\(723\) −6.23331 4.51311i −0.231819 0.167844i
\(724\) −19.5037 −0.724848
\(725\) −6.83877 −0.253985
\(726\) −2.01705 + 2.78587i −0.0748599 + 0.103393i
\(727\) 31.5807i 1.17126i −0.810577 0.585632i \(-0.800846\pi\)
0.810577 0.585632i \(-0.199154\pi\)
\(728\) −3.47808 0.950237i −0.128906 0.0352181i
\(729\) −15.6538 + 21.9991i −0.579770 + 0.814780i
\(730\) 19.9632 + 19.9632i 0.738870 + 0.738870i
\(731\) 13.9499i 0.515956i
\(732\) 22.6815 3.63067i 0.838334 0.134193i
\(733\) −3.05349 3.05349i −0.112783 0.112783i 0.648463 0.761246i \(-0.275412\pi\)
−0.761246 + 0.648463i \(0.775412\pi\)
\(734\) −16.4995 + 16.4995i −0.609006 + 0.609006i
\(735\) −2.51550 + 3.47430i −0.0927856 + 0.128151i
\(736\) −0.338172 + 0.338172i −0.0124652 + 0.0124652i
\(737\) 28.0695i 1.03395i
\(738\) 6.41035 + 19.5103i 0.235968 + 0.718185i
\(739\) 5.30152 5.30152i 0.195020 0.195020i −0.602841 0.797861i \(-0.705965\pi\)
0.797861 + 0.602841i \(0.205965\pi\)
\(740\) −14.7584 −0.542531
\(741\) 18.1401 14.5921i 0.666395 0.536055i
\(742\) 5.90009 0.216599
\(743\) −21.0757 + 21.0757i −0.773191 + 0.773191i −0.978663 0.205472i \(-0.934127\pi\)
0.205472 + 0.978663i \(0.434127\pi\)
\(744\) 5.01049 0.802036i 0.183693 0.0294041i
\(745\) 14.4957i 0.531082i
\(746\) −4.42841 + 4.42841i −0.162135 + 0.162135i
\(747\) 19.0775 37.7482i 0.698007 1.38113i
\(748\) 6.44489 6.44489i 0.235648 0.235648i
\(749\) 5.40784 + 5.40784i 0.197598 + 0.197598i
\(750\) 2.62183 + 16.3791i 0.0957357 + 0.598081i
\(751\) 52.4292i 1.91317i −0.291454 0.956585i \(-0.594139\pi\)
0.291454 0.956585i \(-0.405861\pi\)
\(752\) −6.97225 6.97225i −0.254252 0.254252i
\(753\) −5.04536 31.5195i −0.183863 1.14863i
\(754\) −10.7907 18.9034i −0.392975 0.688420i
\(755\) 23.6430i 0.860457i
\(756\) −1.58129 + 4.94970i −0.0575109 + 0.180019i
\(757\) −37.6352 −1.36787 −0.683937 0.729541i \(-0.739734\pi\)
−0.683937 + 0.729541i \(0.739734\pi\)
\(758\) 33.8031 1.22779
\(759\) −1.45852 + 2.01444i −0.0529408 + 0.0731195i
\(760\) −6.52800 6.52800i −0.236796 0.236796i
\(761\) −4.70073 4.70073i −0.170401 0.170401i 0.616754 0.787156i \(-0.288447\pi\)
−0.787156 + 0.616754i \(0.788447\pi\)
\(762\) −0.529978 + 0.731981i −0.0191991 + 0.0265169i
\(763\) 4.17149 0.151018
\(764\) −0.854794 −0.0309254
\(765\) −10.1730 + 20.1290i −0.367804 + 0.727767i
\(766\) 9.85161i 0.355953i
\(767\) 9.52399 + 16.6843i 0.343891 + 0.602434i
\(768\) 0.273767 + 1.71028i 0.00987870 + 0.0617144i
\(769\) −11.5981 11.5981i −0.418239 0.418239i 0.466358 0.884596i \(-0.345566\pi\)
−0.884596 + 0.466358i \(0.845566\pi\)
\(770\) 7.43524i 0.267948i
\(771\) 1.19277 + 7.45146i 0.0429564 + 0.268358i
\(772\) 16.3246 + 16.3246i 0.587534 + 0.587534i
\(773\) −21.5154 + 21.5154i −0.773854 + 0.773854i −0.978778 0.204924i \(-0.934305\pi\)
0.204924 + 0.978778i \(0.434305\pi\)
\(774\) −12.3036 6.21811i −0.442245 0.223505i
\(775\) −2.34672 + 2.34672i −0.0842966 + 0.0842966i
\(776\) 15.1584i 0.544154i