Properties

Label 507.2.e.k.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 \(0.900969 - 1.56052i\) of defining polynomial
Character \(\chi\) \(=\) 507.22
Dual form 507.2.e.k.484.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.900969 - 1.56052i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.623490 - 1.07992i) q^{4} -1.44504 q^{5} +(0.900969 + 1.56052i) q^{6} +(1.72252 + 2.98349i) q^{7} +1.35690 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.900969 - 1.56052i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.623490 - 1.07992i) q^{4} -1.44504 q^{5} +(0.900969 + 1.56052i) q^{6} +(1.72252 + 2.98349i) q^{7} +1.35690 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.30194 + 2.25502i) q^{10} +(-2.59299 + 4.49119i) q^{11} +1.24698 q^{12} +6.20775 q^{14} +(0.722521 - 1.25144i) q^{15} +(2.46950 - 4.27730i) q^{16} +(0.376510 + 0.652135i) q^{17} -1.80194 q^{18} +(3.98039 + 6.89423i) q^{19} +(0.900969 + 1.56052i) q^{20} -3.44504 q^{21} +(4.67241 + 8.09285i) q^{22} +(1.41454 - 2.45006i) q^{23} +(-0.678448 + 1.17511i) q^{24} -2.91185 q^{25} +1.00000 q^{27} +(2.14795 - 3.72036i) q^{28} +(1.95593 - 3.38776i) q^{29} +(-1.30194 - 2.25502i) q^{30} +4.89977 q^{31} +(-3.09299 - 5.35722i) q^{32} +(-2.59299 - 4.49119i) q^{33} +1.35690 q^{34} +(-2.48911 - 4.31127i) q^{35} +(-0.623490 + 1.07992i) q^{36} +(3.12349 - 5.41004i) q^{37} +14.3448 q^{38} -1.96077 q^{40} +(0.900969 - 1.56052i) q^{41} +(-3.10388 + 5.37607i) q^{42} +(3.54892 + 6.14691i) q^{43} +6.46681 q^{44} +(0.722521 + 1.25144i) q^{45} +(-2.54892 - 4.41485i) q^{46} -10.5526 q^{47} +(2.46950 + 4.27730i) q^{48} +(-2.43416 + 4.21608i) q^{49} +(-2.62349 + 4.54402i) q^{50} -0.753020 q^{51} -3.08815 q^{53} +(0.900969 - 1.56052i) q^{54} +(3.74698 - 6.48996i) q^{55} +(2.33728 + 4.04829i) q^{56} -7.96077 q^{57} +(-3.52446 - 6.10454i) q^{58} +(0.939001 + 1.62640i) q^{59} -1.80194 q^{60} +(-1.67241 - 2.89669i) q^{61} +(4.41454 - 7.64621i) q^{62} +(1.72252 - 2.98349i) q^{63} -1.26875 q^{64} -9.34481 q^{66} +(-2.27144 + 3.93425i) q^{67} +(0.469501 - 0.813199i) q^{68} +(1.41454 + 2.45006i) q^{69} -8.97046 q^{70} +(-4.55980 - 7.89781i) q^{71} +(-0.678448 - 1.17511i) q^{72} -2.95108 q^{73} +(-5.62833 - 9.74856i) q^{74} +(1.45593 - 2.52174i) q^{75} +(4.96346 - 8.59696i) q^{76} -17.8659 q^{77} -9.43296 q^{79} +(-3.56853 + 6.18088i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.62349 - 2.81197i) q^{82} +6.46681 q^{83} +(2.14795 + 3.72036i) q^{84} +(-0.544073 - 0.942362i) q^{85} +12.7899 q^{86} +(1.95593 + 3.38776i) q^{87} +(-3.51842 + 6.09408i) q^{88} +(0.579417 - 1.00358i) q^{89} +2.60388 q^{90} -3.52781 q^{92} +(-2.44989 + 4.24333i) q^{93} +(-9.50753 + 16.4675i) q^{94} +(-5.75182 - 9.96245i) q^{95} +6.18598 q^{96} +(4.32908 + 7.49819i) q^{97} +(4.38620 + 7.59712i) q^{98} +5.18598 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:
<
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.900969 1.56052i 0.637081 1.10346i −0.348989 0.937127i \(-0.613475\pi\)
0.986070 0.166330i \(-0.0531917\pi\)
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i
\(4\) −0.623490 1.07992i −0.311745 0.539958i
\(5\) −1.44504 −0.646242 −0.323121 0.946358i \(-0.604732\pi\)
−0.323121 + 0.946358i \(0.604732\pi\)
\(6\) 0.900969 + 1.56052i 0.367819 + 0.637081i
\(7\) 1.72252 + 2.98349i 0.651052 + 1.12765i 0.982868 + 0.184311i \(0.0590052\pi\)
−0.331816 + 0.943344i \(0.607661\pi\)
\(8\) 1.35690 0.479735
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) −1.30194 + 2.25502i −0.411709 + 0.713101i
\(11\) −2.59299 + 4.49119i −0.781816 + 1.35415i 0.149067 + 0.988827i \(0.452373\pi\)
−0.930883 + 0.365318i \(0.880960\pi\)
\(12\) 1.24698 0.359972
\(13\) 0 0
\(14\) 6.20775 1.65909
\(15\) 0.722521 1.25144i 0.186554 0.323121i
\(16\) 2.46950 4.27730i 0.617375 1.06933i
\(17\) 0.376510 + 0.652135i 0.0913171 + 0.158166i 0.908066 0.418828i \(-0.137559\pi\)
−0.816748 + 0.576994i \(0.804226\pi\)
\(18\) −1.80194 −0.424721
\(19\) 3.98039 + 6.89423i 0.913163 + 1.58164i 0.809569 + 0.587025i \(0.199701\pi\)
0.103594 + 0.994620i \(0.466966\pi\)
\(20\) 0.900969 + 1.56052i 0.201463 + 0.348944i
\(21\) −3.44504 −0.751770
\(22\) 4.67241 + 8.09285i 0.996161 + 1.72540i
\(23\) 1.41454 2.45006i 0.294952 0.510873i −0.680021 0.733192i \(-0.738030\pi\)
0.974974 + 0.222320i \(0.0713628\pi\)
\(24\) −0.678448 + 1.17511i −0.138488 + 0.239868i
\(25\) −2.91185 −0.582371
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 2.14795 3.72036i 0.405924 0.703081i
\(29\) 1.95593 3.38776i 0.363207 0.629092i −0.625280 0.780400i \(-0.715015\pi\)
0.988487 + 0.151308i \(0.0483486\pi\)
\(30\) −1.30194 2.25502i −0.237700 0.411709i
\(31\) 4.89977 0.880025 0.440013 0.897992i \(-0.354974\pi\)
0.440013 + 0.897992i \(0.354974\pi\)
\(32\) −3.09299 5.35722i −0.546769 0.947031i
\(33\) −2.59299 4.49119i −0.451382 0.781816i
\(34\) 1.35690 0.232706
\(35\) −2.48911 4.31127i −0.420737 0.728738i
\(36\) −0.623490 + 1.07992i −0.103915 + 0.179986i
\(37\) 3.12349 5.41004i 0.513499 0.889406i −0.486379 0.873748i \(-0.661683\pi\)
0.999877 0.0156576i \(-0.00498416\pi\)
\(38\) 14.3448 2.32704
\(39\) 0 0
\(40\) −1.96077 −0.310025
\(41\) 0.900969 1.56052i 0.140708 0.243713i −0.787056 0.616882i \(-0.788396\pi\)
0.927763 + 0.373169i \(0.121729\pi\)
\(42\) −3.10388 + 5.37607i −0.478938 + 0.829546i
\(43\) 3.54892 + 6.14691i 0.541205 + 0.937394i 0.998835 + 0.0482517i \(0.0153650\pi\)
−0.457630 + 0.889143i \(0.651302\pi\)
\(44\) 6.46681 0.974909
\(45\) 0.722521 + 1.25144i 0.107707 + 0.186554i
\(46\) −2.54892 4.41485i −0.375817 0.650935i
\(47\) −10.5526 −1.53925 −0.769625 0.638496i \(-0.779557\pi\)
−0.769625 + 0.638496i \(0.779557\pi\)
\(48\) 2.46950 + 4.27730i 0.356442 + 0.617375i
\(49\) −2.43416 + 4.21608i −0.347737 + 0.602298i
\(50\) −2.62349 + 4.54402i −0.371017 + 0.642621i
\(51\) −0.753020 −0.105444
\(52\) 0 0
\(53\) −3.08815 −0.424189 −0.212095 0.977249i \(-0.568029\pi\)
−0.212095 + 0.977249i \(0.568029\pi\)
\(54\) 0.900969 1.56052i 0.122606 0.212360i
\(55\) 3.74698 6.48996i 0.505243 0.875106i
\(56\) 2.33728 + 4.04829i 0.312332 + 0.540976i
\(57\) −7.96077 −1.05443
\(58\) −3.52446 6.10454i −0.462784 0.801566i
\(59\) 0.939001 + 1.62640i 0.122248 + 0.211739i 0.920654 0.390380i \(-0.127656\pi\)
−0.798406 + 0.602119i \(0.794323\pi\)
\(60\) −1.80194 −0.232629
\(61\) −1.67241 2.89669i −0.214130 0.370884i 0.738873 0.673844i \(-0.235358\pi\)
−0.953003 + 0.302961i \(0.902025\pi\)
\(62\) 4.41454 7.64621i 0.560647 0.971070i
\(63\) 1.72252 2.98349i 0.217017 0.375885i
\(64\) −1.26875 −0.158594
\(65\) 0 0
\(66\) −9.34481 −1.15027
\(67\) −2.27144 + 3.93425i −0.277500 + 0.480645i −0.970763 0.240040i \(-0.922839\pi\)
0.693263 + 0.720685i \(0.256173\pi\)
\(68\) 0.469501 0.813199i 0.0569353 0.0986148i
\(69\) 1.41454 + 2.45006i 0.170291 + 0.294952i
\(70\) −8.97046 −1.07218
\(71\) −4.55980 7.89781i −0.541149 0.937298i −0.998838 0.0481854i \(-0.984656\pi\)
0.457689 0.889112i \(-0.348677\pi\)
\(72\) −0.678448 1.17511i −0.0799559 0.138488i
\(73\) −2.95108 −0.345398 −0.172699 0.984975i \(-0.555249\pi\)
−0.172699 + 0.984975i \(0.555249\pi\)
\(74\) −5.62833 9.74856i −0.654281 1.13325i
\(75\) 1.45593 2.52174i 0.168116 0.291185i
\(76\) 4.96346 8.59696i 0.569348 0.986139i
\(77\) −17.8659 −2.03601
\(78\) 0 0
\(79\) −9.43296 −1.06129 −0.530645 0.847594i \(-0.678050\pi\)
−0.530645 + 0.847594i \(0.678050\pi\)
\(80\) −3.56853 + 6.18088i −0.398974 + 0.691043i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −1.62349 2.81197i −0.179284 0.310530i
\(83\) 6.46681 0.709825 0.354912 0.934900i \(-0.384511\pi\)
0.354912 + 0.934900i \(0.384511\pi\)
\(84\) 2.14795 + 3.72036i 0.234360 + 0.405924i
\(85\) −0.544073 0.942362i −0.0590130 0.102214i
\(86\) 12.7899 1.37917
\(87\) 1.95593 + 3.38776i 0.209697 + 0.363207i
\(88\) −3.51842 + 6.09408i −0.375065 + 0.649631i
\(89\) 0.579417 1.00358i 0.0614181 0.106379i −0.833681 0.552246i \(-0.813771\pi\)
0.895099 + 0.445866i \(0.147104\pi\)
\(90\) 2.60388 0.274473
\(91\) 0 0
\(92\) −3.52781 −0.367800
\(93\) −2.44989 + 4.24333i −0.254041 + 0.440013i
\(94\) −9.50753 + 16.4675i −0.980627 + 1.69850i
\(95\) −5.75182 9.96245i −0.590125 1.02213i
\(96\) 6.18598 0.631354
\(97\) 4.32908 + 7.49819i 0.439552 + 0.761326i 0.997655 0.0684454i \(-0.0218039\pi\)
−0.558103 + 0.829772i \(0.688471\pi\)
\(98\) 4.38620 + 7.59712i 0.443073 + 0.767425i
\(99\) 5.18598 0.521211
\(100\) 1.81551 + 3.14456i 0.181551 + 0.314456i
\(101\) 4.23825 7.34087i 0.421722 0.730443i −0.574386 0.818584i \(-0.694759\pi\)
0.996108 + 0.0881410i \(0.0280926\pi\)
\(102\) −0.678448 + 1.17511i −0.0671764 + 0.116353i
\(103\) 5.64742 0.556456 0.278228 0.960515i \(-0.410253\pi\)
0.278228 + 0.960515i \(0.410253\pi\)
\(104\) 0 0
\(105\) 4.97823 0.485825
\(106\) −2.78232 + 4.81913i −0.270243 + 0.468075i
\(107\) 3.36778 5.83317i 0.325576 0.563914i −0.656053 0.754715i \(-0.727775\pi\)
0.981629 + 0.190801i \(0.0611086\pi\)
\(108\) −0.623490 1.07992i −0.0599953 0.103915i
\(109\) 2.07606 0.198851 0.0994255 0.995045i \(-0.468300\pi\)
0.0994255 + 0.995045i \(0.468300\pi\)
\(110\) −6.75182 11.6945i −0.643761 1.11503i
\(111\) 3.12349 + 5.41004i 0.296469 + 0.513499i
\(112\) 17.0151 1.60777
\(113\) −3.08426 5.34210i −0.290143 0.502542i 0.683700 0.729763i \(-0.260370\pi\)
−0.973843 + 0.227221i \(0.927036\pi\)
\(114\) −7.17241 + 12.4230i −0.671757 + 1.16352i
\(115\) −2.04407 + 3.54044i −0.190611 + 0.330148i
\(116\) −4.87800 −0.452911
\(117\) 0 0
\(118\) 3.38404 0.311526
\(119\) −1.29709 + 2.24663i −0.118904 + 0.205948i
\(120\) 0.980386 1.69808i 0.0894966 0.155013i
\(121\) −7.94720 13.7650i −0.722473 1.25136i
\(122\) −6.02715 −0.545672
\(123\) 0.900969 + 1.56052i 0.0812376 + 0.140708i
\(124\) −3.05496 5.29134i −0.274343 0.475177i
\(125\) 11.4330 1.02260
\(126\) −3.10388 5.37607i −0.276515 0.478938i
\(127\) 7.13102 12.3513i 0.632776 1.09600i −0.354206 0.935168i \(-0.615249\pi\)
0.986982 0.160833i \(-0.0514179\pi\)
\(128\) 5.04288 8.73452i 0.445732 0.772030i
\(129\) −7.09783 −0.624929
\(130\) 0 0
\(131\) 22.6015 1.97470 0.987350 0.158554i \(-0.0506831\pi\)
0.987350 + 0.158554i \(0.0506831\pi\)
\(132\) −3.23341 + 5.60042i −0.281432 + 0.487454i
\(133\) −13.7126 + 23.7509i −1.18903 + 2.05947i
\(134\) 4.09299 + 7.08927i 0.353581 + 0.612419i
\(135\) −1.44504 −0.124369
\(136\) 0.510885 + 0.884879i 0.0438080 + 0.0758777i
\(137\) −6.81767 11.8085i −0.582473 1.00887i −0.995185 0.0980109i \(-0.968752\pi\)
0.412713 0.910861i \(-0.364581\pi\)
\(138\) 5.09783 0.433957
\(139\) −8.80074 15.2433i −0.746469 1.29292i −0.949505 0.313751i \(-0.898414\pi\)
0.203036 0.979171i \(-0.434919\pi\)
\(140\) −3.10388 + 5.37607i −0.262325 + 0.454361i
\(141\) 5.27628 9.13879i 0.444343 0.769625i
\(142\) −16.4330 −1.37902
\(143\) 0 0
\(144\) −4.93900 −0.411583
\(145\) −2.82640 + 4.89546i −0.234719 + 0.406546i
\(146\) −2.65883 + 4.60523i −0.220047 + 0.381132i
\(147\) −2.43416 4.21608i −0.200766 0.347737i
\(148\) −7.78986 −0.640322
\(149\) 6.36927 + 11.0319i 0.521791 + 0.903769i 0.999679 + 0.0253478i \(0.00806931\pi\)
−0.477888 + 0.878421i \(0.658597\pi\)
\(150\) −2.62349 4.54402i −0.214207 0.371017i
\(151\) −15.6407 −1.27282 −0.636412 0.771350i \(-0.719582\pi\)
−0.636412 + 0.771350i \(0.719582\pi\)
\(152\) 5.40097 + 9.35475i 0.438076 + 0.758771i
\(153\) 0.376510 0.652135i 0.0304390 0.0527220i
\(154\) −16.0966 + 27.8802i −1.29710 + 2.24665i
\(155\) −7.08038 −0.568710
\(156\) 0 0
\(157\) −0.823708 −0.0657391 −0.0328695 0.999460i \(-0.510465\pi\)
−0.0328695 + 0.999460i \(0.510465\pi\)
\(158\) −8.49880 + 14.7204i −0.676129 + 1.17109i
\(159\) 1.54407 2.67441i 0.122453 0.212095i
\(160\) 4.46950 + 7.74140i 0.353345 + 0.612012i
\(161\) 9.74632 0.768117
\(162\) 0.900969 + 1.56052i 0.0707868 + 0.122606i
\(163\) 3.13437 + 5.42890i 0.245503 + 0.425224i 0.962273 0.272086i \(-0.0877135\pi\)
−0.716770 + 0.697310i \(0.754380\pi\)
\(164\) −2.24698 −0.175460
\(165\) 3.74698 + 6.48996i 0.291702 + 0.505243i
\(166\) 5.82640 10.0916i 0.452216 0.783261i
\(167\) −3.72521 + 6.45225i −0.288265 + 0.499290i −0.973396 0.229130i \(-0.926412\pi\)
0.685130 + 0.728420i \(0.259745\pi\)
\(168\) −4.67456 −0.360650
\(169\) 0 0
\(170\) −1.96077 −0.150384
\(171\) 3.98039 6.89423i 0.304388 0.527215i
\(172\) 4.42543 7.66507i 0.337436 0.584456i
\(173\) 1.00484 + 1.74044i 0.0763969 + 0.132323i 0.901693 0.432377i \(-0.142325\pi\)
−0.825296 + 0.564700i \(0.808992\pi\)
\(174\) 7.04892 0.534377
\(175\) −5.01573 8.68750i −0.379154 0.656713i
\(176\) 12.8068 + 22.1820i 0.965348 + 1.67203i
\(177\) −1.87800 −0.141159
\(178\) −1.04407 1.80839i −0.0782566 0.135544i
\(179\) −10.0184 + 17.3524i −0.748812 + 1.29698i 0.199581 + 0.979881i \(0.436042\pi\)
−0.948393 + 0.317099i \(0.897291\pi\)
\(180\) 0.900969 1.56052i 0.0671543 0.116315i
\(181\) 24.1226 1.79302 0.896509 0.443026i \(-0.146095\pi\)
0.896509 + 0.443026i \(0.146095\pi\)
\(182\) 0 0
\(183\) 3.34481 0.247256
\(184\) 1.91939 3.32448i 0.141499 0.245084i
\(185\) −4.51357 + 7.81774i −0.331845 + 0.574772i
\(186\) 4.41454 + 7.64621i 0.323690 + 0.560647i
\(187\) −3.90515 −0.285573
\(188\) 6.57942 + 11.3959i 0.479853 + 0.831130i
\(189\) 1.72252 + 2.98349i 0.125295 + 0.217017i
\(190\) −20.7289 −1.50383
\(191\) 3.54019 + 6.13179i 0.256159 + 0.443680i 0.965210 0.261477i \(-0.0842096\pi\)
−0.709051 + 0.705158i \(0.750876\pi\)
\(192\) 0.634375 1.09877i 0.0457821 0.0792969i
\(193\) 4.88404 8.45941i 0.351561 0.608922i −0.634962 0.772543i \(-0.718984\pi\)
0.986523 + 0.163622i \(0.0523176\pi\)
\(194\) 15.6015 1.12012
\(195\) 0 0
\(196\) 6.07069 0.433621
\(197\) 11.7056 20.2747i 0.833989 1.44451i −0.0608617 0.998146i \(-0.519385\pi\)
0.894851 0.446365i \(-0.147282\pi\)
\(198\) 4.67241 8.09285i 0.332054 0.575134i
\(199\) −2.01238 3.48554i −0.142654 0.247083i 0.785841 0.618428i \(-0.212230\pi\)
−0.928495 + 0.371345i \(0.878897\pi\)
\(200\) −3.95108 −0.279384
\(201\) −2.27144 3.93425i −0.160215 0.277500i
\(202\) −7.63706 13.2278i −0.537342 0.930703i
\(203\) 13.4765 0.945865
\(204\) 0.469501 + 0.813199i 0.0328716 + 0.0569353i
\(205\) −1.30194 + 2.25502i −0.0909313 + 0.157498i
\(206\) 5.08815 8.81293i 0.354508 0.614026i
\(207\) −2.82908 −0.196635
\(208\) 0 0
\(209\) −41.2844 −2.85570
\(210\) 4.48523 7.76865i 0.309510 0.536088i
\(211\) 1.95593 3.38776i 0.134652 0.233223i −0.790813 0.612058i \(-0.790342\pi\)
0.925464 + 0.378835i \(0.123675\pi\)
\(212\) 1.92543 + 3.33494i 0.132239 + 0.229045i
\(213\) 9.11960 0.624865
\(214\) −6.06853 10.5110i −0.414836 0.718518i
\(215\) −5.12833 8.88254i −0.349749 0.605784i
\(216\) 1.35690 0.0923251
\(217\) 8.43996 + 14.6184i 0.572942 + 0.992364i
\(218\) 1.87047 3.23975i 0.126684 0.219423i
\(219\) 1.47554 2.55571i 0.0997078 0.172699i
\(220\) −9.34481 −0.630027
\(221\) 0 0
\(222\) 11.2567 0.755498
\(223\) 3.72468 6.45133i 0.249423 0.432013i −0.713943 0.700204i \(-0.753092\pi\)
0.963366 + 0.268191i \(0.0864258\pi\)
\(224\) 10.6555 18.4558i 0.711949 1.23313i
\(225\) 1.45593 + 2.52174i 0.0970618 + 0.168116i
\(226\) −11.1153 −0.739378
\(227\) −10.6250 18.4030i −0.705205 1.22145i −0.966618 0.256223i \(-0.917522\pi\)
0.261413 0.965227i \(-0.415812\pi\)
\(228\) 4.96346 + 8.59696i 0.328713 + 0.569348i
\(229\) −9.29590 −0.614290 −0.307145 0.951663i \(-0.599374\pi\)
−0.307145 + 0.951663i \(0.599374\pi\)
\(230\) 3.68329 + 6.37965i 0.242869 + 0.420662i
\(231\) 8.93296 15.4723i 0.587746 1.01801i
\(232\) 2.65399 4.59684i 0.174243 0.301798i
\(233\) 16.2107 1.06200 0.531000 0.847372i \(-0.321816\pi\)
0.531000 + 0.847372i \(0.321816\pi\)
\(234\) 0 0
\(235\) 15.2489 0.994728
\(236\) 1.17092 2.02808i 0.0762201 0.132017i
\(237\) 4.71648 8.16918i 0.306368 0.530645i
\(238\) 2.33728 + 4.04829i 0.151503 + 0.262412i
\(239\) 13.5090 0.873826 0.436913 0.899504i \(-0.356072\pi\)
0.436913 + 0.899504i \(0.356072\pi\)
\(240\) −3.56853 6.18088i −0.230348 0.398974i
\(241\) 3.13437 + 5.42890i 0.201903 + 0.349706i 0.949142 0.314850i \(-0.101954\pi\)
−0.747239 + 0.664556i \(0.768621\pi\)
\(242\) −28.6407 −1.84109
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) −2.08546 + 3.61212i −0.133508 + 0.231242i
\(245\) 3.51746 6.09242i 0.224722 0.389230i
\(246\) 3.24698 0.207020
\(247\) 0 0
\(248\) 6.64848 0.422179
\(249\) −3.23341 + 5.60042i −0.204909 + 0.354912i
\(250\) 10.3007 17.8414i 0.651476 1.12839i
\(251\) 0.376510 + 0.652135i 0.0237651 + 0.0411624i 0.877663 0.479278i \(-0.159101\pi\)
−0.853898 + 0.520440i \(0.825768\pi\)
\(252\) −4.29590 −0.270616
\(253\) 7.33579 + 12.7060i 0.461197 + 0.798817i
\(254\) −12.8497 22.2563i −0.806259 1.39648i
\(255\) 1.08815 0.0681423
\(256\) −10.3557 17.9366i −0.647231 1.12104i
\(257\) −9.86323 + 17.0836i −0.615252 + 1.06565i 0.375089 + 0.926989i \(0.377612\pi\)
−0.990340 + 0.138658i \(0.955721\pi\)
\(258\) −6.39493 + 11.0763i −0.398131 + 0.689583i
\(259\) 21.5211 1.33726
\(260\) 0 0
\(261\) −3.91185 −0.242138
\(262\) 20.3632 35.2702i 1.25804 2.17900i
\(263\) 8.80463 15.2501i 0.542917 0.940359i −0.455818 0.890073i \(-0.650653\pi\)
0.998735 0.0502861i \(-0.0160133\pi\)
\(264\) −3.51842 6.09408i −0.216544 0.375065i
\(265\) 4.46250 0.274129
\(266\) 24.7092 + 42.7977i 1.51502 + 2.62409i
\(267\) 0.579417 + 1.00358i 0.0354597 + 0.0614181i
\(268\) 5.66487 0.346037
\(269\) 8.19351 + 14.1916i 0.499567 + 0.865276i 1.00000 0.000499532i \(-0.000159006\pi\)
−0.500433 + 0.865776i \(0.666826\pi\)
\(270\) −1.30194 + 2.25502i −0.0792334 + 0.137236i
\(271\) −0.397616 + 0.688692i −0.0241535 + 0.0418351i −0.877849 0.478937i \(-0.841022\pi\)
0.853696 + 0.520772i \(0.174356\pi\)
\(272\) 3.71917 0.225508
\(273\) 0 0
\(274\) −24.5700 −1.48433
\(275\) 7.55041 13.0777i 0.455307 0.788615i
\(276\) 1.76391 3.05517i 0.106175 0.183900i
\(277\) 2.41670 + 4.18584i 0.145205 + 0.251503i 0.929450 0.368949i \(-0.120282\pi\)
−0.784244 + 0.620452i \(0.786949\pi\)
\(278\) −31.7168 −1.90225
\(279\) −2.44989 4.24333i −0.146671 0.254041i
\(280\) −3.37747 5.84995i −0.201842 0.349601i
\(281\) −18.7748 −1.12001 −0.560005 0.828489i \(-0.689201\pi\)
−0.560005 + 0.828489i \(0.689201\pi\)
\(282\) −9.50753 16.4675i −0.566165 0.980627i
\(283\) 3.95862 6.85652i 0.235315 0.407578i −0.724049 0.689749i \(-0.757721\pi\)
0.959364 + 0.282171i \(0.0910544\pi\)
\(284\) −5.68598 + 9.84841i −0.337401 + 0.584395i
\(285\) 11.5036 0.681417
\(286\) 0 0
\(287\) 6.20775 0.366432
\(288\) −3.09299 + 5.35722i −0.182256 + 0.315677i
\(289\) 8.21648 14.2314i 0.483322 0.837139i
\(290\) 5.09299 + 8.82132i 0.299071 + 0.518006i
\(291\) −8.65817 −0.507551
\(292\) 1.83997 + 3.18692i 0.107676 + 0.186500i
\(293\) 3.28956 + 5.69769i 0.192178 + 0.332862i 0.945972 0.324249i \(-0.105112\pi\)
−0.753794 + 0.657111i \(0.771778\pi\)
\(294\) −8.77240 −0.511617
\(295\) −1.35690 2.35021i −0.0790015 0.136835i
\(296\) 4.23825 7.34087i 0.246343 0.426679i
\(297\) −2.59299 + 4.49119i −0.150461 + 0.260605i
\(298\) 22.9541 1.32969
\(299\) 0 0
\(300\) −3.63102 −0.209637
\(301\) −12.2262 + 21.1763i −0.704705 + 1.22058i
\(302\) −14.0918 + 24.4077i −0.810892 + 1.40451i
\(303\) 4.23825 + 7.34087i 0.243481 + 0.421722i
\(304\) 39.3183 2.25506
\(305\) 2.41670 + 4.18584i 0.138380 + 0.239681i
\(306\) −0.678448 1.17511i −0.0387843 0.0671764i
\(307\) 24.8649 1.41911 0.709556 0.704649i \(-0.248895\pi\)
0.709556 + 0.704649i \(0.248895\pi\)
\(308\) 11.1392 + 19.2937i 0.634716 + 1.09936i
\(309\) −2.82371 + 4.89081i −0.160635 + 0.278228i
\(310\) −6.37920 + 11.0491i −0.362314 + 0.627546i
\(311\) −17.0804 −0.968539 −0.484270 0.874919i \(-0.660915\pi\)
−0.484270 + 0.874919i \(0.660915\pi\)
\(312\) 0 0
\(313\) 15.6974 0.887269 0.443635 0.896208i \(-0.353689\pi\)
0.443635 + 0.896208i \(0.353689\pi\)
\(314\) −0.742135 + 1.28542i −0.0418811 + 0.0725402i
\(315\) −2.48911 + 4.31127i −0.140246 + 0.242913i
\(316\) 5.88135 + 10.1868i 0.330852 + 0.573053i
\(317\) −32.7821 −1.84123 −0.920613 0.390477i \(-0.872310\pi\)
−0.920613 + 0.390477i \(0.872310\pi\)
\(318\) −2.78232 4.81913i −0.156025 0.270243i
\(319\) 10.1434 + 17.5689i 0.567921 + 0.983669i
\(320\) 1.83340 0.102490
\(321\) 3.36778 + 5.83317i 0.187971 + 0.325576i
\(322\) 8.78113 15.2094i 0.489353 0.847584i
\(323\) −2.99731 + 5.19150i −0.166775 + 0.288863i
\(324\) 1.24698 0.0692766
\(325\) 0 0
\(326\) 11.2959 0.625622
\(327\) −1.03803 + 1.79792i −0.0574033 + 0.0994255i
\(328\) 1.22252 2.11747i 0.0675024 0.116918i
\(329\) −18.1770 31.4835i −1.00213 1.73574i
\(330\) 13.5036 0.743351
\(331\) −14.5809 25.2549i −0.801439 1.38813i −0.918669 0.395029i \(-0.870735\pi\)
0.117230 0.993105i \(-0.462599\pi\)
\(332\) −4.03199 6.98361i −0.221284 0.383276i
\(333\) −6.24698 −0.342332
\(334\) 6.71260 + 11.6266i 0.367297 + 0.636177i
\(335\) 3.28232 5.68515i 0.179332 0.310613i
\(336\) −8.50753 + 14.7355i −0.464124 + 0.803886i
\(337\) −33.2911 −1.81348 −0.906741 0.421688i \(-0.861438\pi\)
−0.906741 + 0.421688i \(0.861438\pi\)
\(338\) 0 0
\(339\) 6.16852 0.335028
\(340\) −0.678448 + 1.17511i −0.0367940 + 0.0637291i
\(341\) −12.7051 + 22.0058i −0.688018 + 1.19168i
\(342\) −7.17241 12.4230i −0.387839 0.671757i
\(343\) 7.34375 0.396525
\(344\) 4.81551 + 8.34071i 0.259635 + 0.449701i
\(345\) −2.04407 3.54044i −0.110049 0.190611i
\(346\) 3.62133 0.194684
\(347\) 0.436845 + 0.756638i 0.0234511 + 0.0406185i 0.877513 0.479553i \(-0.159201\pi\)
−0.854062 + 0.520172i \(0.825868\pi\)
\(348\) 2.43900 4.22447i 0.130744 0.226456i
\(349\) −1.61596 + 2.79892i −0.0865002 + 0.149823i −0.906029 0.423215i \(-0.860902\pi\)
0.819529 + 0.573037i \(0.194235\pi\)
\(350\) −18.0761 −0.966206
\(351\) 0 0
\(352\) 32.0804 1.70989
\(353\) 4.07338 7.05529i 0.216804 0.375515i −0.737025 0.675865i \(-0.763770\pi\)
0.953829 + 0.300350i \(0.0971034\pi\)
\(354\) −1.69202 + 2.93067i −0.0899299 + 0.155763i
\(355\) 6.58911 + 11.4127i 0.349713 + 0.605721i
\(356\) −1.44504 −0.0765871
\(357\) −1.29709 2.24663i −0.0686495 0.118904i
\(358\) 18.0526 + 31.2680i 0.954108 + 1.65256i
\(359\) −2.64071 −0.139371 −0.0696857 0.997569i \(-0.522200\pi\)
−0.0696857 + 0.997569i \(0.522200\pi\)
\(360\) 0.980386 + 1.69808i 0.0516709 + 0.0894966i
\(361\) −22.1869 + 38.4289i −1.16773 + 2.02257i
\(362\) 21.7337 37.6439i 1.14230 1.97852i
\(363\) 15.8944 0.834239
\(364\) 0 0
\(365\) 4.26444 0.223211
\(366\) 3.01357 5.21966i 0.157522 0.272836i
\(367\) 1.45204 2.51501i 0.0757960 0.131282i −0.825636 0.564203i \(-0.809184\pi\)
0.901432 + 0.432920i \(0.142517\pi\)
\(368\) −6.98643 12.1008i −0.364193 0.630800i
\(369\) −1.80194 −0.0938051
\(370\) 8.13318 + 14.0871i 0.422824 + 0.732352i
\(371\) −5.31940 9.21346i −0.276169 0.478339i
\(372\) 6.10992 0.316784
\(373\) 4.19926 + 7.27333i 0.217429 + 0.376599i 0.954021 0.299739i \(-0.0968995\pi\)
−0.736592 + 0.676337i \(0.763566\pi\)
\(374\) −3.51842 + 6.09408i −0.181933 + 0.315117i
\(375\) −5.71648 + 9.90123i −0.295198 + 0.511298i
\(376\) −14.3187 −0.738432
\(377\) 0 0
\(378\) 6.20775 0.319292
\(379\) 7.87412 13.6384i 0.404466 0.700556i −0.589793 0.807555i \(-0.700791\pi\)
0.994259 + 0.106998i \(0.0341240\pi\)
\(380\) −7.17241 + 12.4230i −0.367937 + 0.637285i
\(381\) 7.13102 + 12.3513i 0.365333 + 0.632776i
\(382\) 12.7584 0.652776
\(383\) 6.36927 + 11.0319i 0.325455 + 0.563704i 0.981604 0.190927i \(-0.0611493\pi\)
−0.656150 + 0.754631i \(0.727816\pi\)
\(384\) 5.04288 + 8.73452i 0.257343 + 0.445732i
\(385\) 25.8170 1.31576
\(386\) −8.80074 15.2433i −0.447946 0.775865i
\(387\) 3.54892 6.14691i 0.180402 0.312465i
\(388\) 5.39828 9.35010i 0.274056 0.474679i
\(389\) −0.310371 −0.0157365 −0.00786823 0.999969i \(-0.502505\pi\)
−0.00786823 + 0.999969i \(0.502505\pi\)
\(390\) 0 0
\(391\) 2.13036 0.107737
\(392\) −3.30290 + 5.72079i −0.166822 + 0.288943i
\(393\) −11.3007 + 19.5735i −0.570047 + 0.987350i
\(394\) −21.0928 36.5337i −1.06264 1.84054i
\(395\) 13.6310 0.685851
\(396\) −3.23341 5.60042i −0.162485 0.281432i
\(397\) 0.745488 + 1.29122i 0.0374150 + 0.0648046i 0.884127 0.467248i \(-0.154754\pi\)
−0.846712 + 0.532052i \(0.821421\pi\)
\(398\) −7.25236 −0.363528
\(399\) −13.7126 23.7509i −0.686488 1.18903i
\(400\) −7.19083 + 12.4549i −0.359541 + 0.622744i
\(401\) −11.9167 + 20.6403i −0.595092 + 1.03073i 0.398442 + 0.917193i \(0.369551\pi\)
−0.993534 + 0.113535i \(0.963782\pi\)
\(402\) −8.18598 −0.408280
\(403\) 0 0
\(404\) −10.5700 −0.525878
\(405\) 0.722521 1.25144i 0.0359024 0.0621847i
\(406\) 12.1419 21.0304i 0.602593 1.04372i
\(407\) 16.1984 + 28.0564i 0.802923 + 1.39070i
\(408\) −1.02177 −0.0505852
\(409\) 2.13371 + 3.69570i 0.105505 + 0.182740i 0.913945 0.405839i \(-0.133021\pi\)
−0.808439 + 0.588580i \(0.799687\pi\)
\(410\) 2.34601 + 4.06341i 0.115861 + 0.200678i
\(411\) 13.6353 0.672581
\(412\) −3.52111 6.09873i −0.173472 0.300463i
\(413\) −3.23490 + 5.60301i −0.159179 + 0.275706i
\(414\) −2.54892 + 4.41485i −0.125272 + 0.216978i
\(415\) −9.34481 −0.458719
\(416\) 0 0
\(417\) 17.6015 0.861948
\(418\) −37.1960 + 64.4253i −1.81931 + 3.15114i
\(419\) −14.8448 + 25.7120i −0.725217 + 1.25611i 0.233668 + 0.972316i \(0.424927\pi\)
−0.958885 + 0.283796i \(0.908406\pi\)
\(420\) −3.10388 5.37607i −0.151454 0.262325i
\(421\) −29.3991 −1.43282 −0.716412 0.697677i \(-0.754217\pi\)
−0.716412 + 0.697677i \(0.754217\pi\)
\(422\) −3.52446 6.10454i −0.171568 0.297164i
\(423\) 5.27628 + 9.13879i 0.256542 + 0.444343i
\(424\) −4.19029 −0.203499
\(425\) −1.09634 1.89892i −0.0531804 0.0921112i
\(426\) 8.21648 14.2314i 0.398090 0.689512i
\(427\) 5.76151 9.97923i 0.278819 0.482929i
\(428\) −8.39911 −0.405986
\(429\) 0 0
\(430\) −18.4819 −0.891275
\(431\) −16.5281 + 28.6275i −0.796131 + 1.37894i 0.125988 + 0.992032i \(0.459790\pi\)
−0.922119 + 0.386907i \(0.873543\pi\)
\(432\) 2.46950 4.27730i 0.118814 0.205792i
\(433\) 14.6332 + 25.3454i 0.703226 + 1.21802i 0.967328 + 0.253528i \(0.0815910\pi\)
−0.264102 + 0.964495i \(0.585076\pi\)
\(434\) 30.4166 1.46004
\(435\) −2.82640 4.89546i −0.135515 0.234719i
\(436\) −1.29440 2.24198i −0.0619908 0.107371i
\(437\) 22.5217 1.07736
\(438\) −2.65883 4.60523i −0.127044 0.220047i
\(439\) 1.06584 1.84609i 0.0508699 0.0881093i −0.839469 0.543407i \(-0.817134\pi\)
0.890339 + 0.455298i \(0.150467\pi\)
\(440\) 5.08426 8.80620i 0.242383 0.419819i
\(441\) 4.86831 0.231824
\(442\) 0 0
\(443\) −22.9922 −1.09239 −0.546197 0.837657i \(-0.683925\pi\)
−0.546197 + 0.837657i \(0.683925\pi\)
\(444\) 3.89493 6.74621i 0.184845 0.320161i
\(445\) −0.837282 + 1.45021i −0.0396910 + 0.0687467i
\(446\) −6.71164 11.6249i −0.317805 0.550455i
\(447\) −12.7385 −0.602513
\(448\) −2.18545 3.78531i −0.103253 0.178839i
\(449\) −6.46897 11.2046i −0.305289 0.528777i 0.672036 0.740518i \(-0.265420\pi\)
−0.977326 + 0.211741i \(0.932087\pi\)
\(450\) 5.24698 0.247345
\(451\) 4.67241 + 8.09285i 0.220015 + 0.381077i
\(452\) −3.84601 + 6.66149i −0.180901 + 0.313330i
\(453\) 7.82036 13.5453i 0.367432 0.636412i
\(454\) −38.2911 −1.79709
\(455\) 0 0
\(456\) −10.8019 −0.505847
\(457\) −2.42662 + 4.20304i −0.113513 + 0.196610i −0.917184 0.398463i \(-0.869544\pi\)
0.803672 + 0.595073i \(0.202877\pi\)
\(458\) −8.37531 + 14.5065i −0.391353 + 0.677843i
\(459\) 0.376510 + 0.652135i 0.0175740 + 0.0304390i
\(460\) 5.09783 0.237688
\(461\) 9.41723 + 16.3111i 0.438604 + 0.759685i 0.997582 0.0694978i \(-0.0221397\pi\)
−0.558978 + 0.829183i \(0.688806\pi\)
\(462\) −16.0966 27.8802i −0.748883 1.29710i
\(463\) 22.8767 1.06317 0.531585 0.847005i \(-0.321597\pi\)
0.531585 + 0.847005i \(0.321597\pi\)
\(464\) −9.66033 16.7322i −0.448469 0.776772i
\(465\) 3.54019 6.13179i 0.164172 0.284355i
\(466\) 14.6054 25.2972i 0.676581 1.17187i
\(467\) 13.0000 0.601568 0.300784 0.953692i \(-0.402752\pi\)
0.300784 + 0.953692i \(0.402752\pi\)
\(468\) 0 0
\(469\) −15.6504 −0.722668
\(470\) 13.7388 23.7963i 0.633723 1.09764i
\(471\) 0.411854 0.713352i 0.0189772 0.0328695i
\(472\) 1.27413 + 2.20685i 0.0586464 + 0.101579i
\(473\) −36.8092 −1.69249
\(474\) −8.49880 14.7204i −0.390363 0.676129i
\(475\) −11.5903 20.0750i −0.531800 0.921104i
\(476\) 3.23490 0.148271
\(477\) 1.54407 + 2.67441i 0.0706982 + 0.122453i
\(478\) 12.1712 21.0812i 0.556698 0.964230i
\(479\) −19.0450 + 32.9870i −0.870190 + 1.50721i −0.00838964 + 0.999965i \(0.502671\pi\)
−0.861800 + 0.507248i \(0.830663\pi\)
\(480\) −8.93900 −0.408008
\(481\) 0 0
\(482\) 11.2959 0.514514
\(483\) −4.87316 + 8.44056i −0.221736 + 0.384059i
\(484\) −9.90999 + 17.1646i −0.450454 + 0.780210i
\(485\) −6.25571 10.8352i −0.284057 0.492001i
\(486\) −1.80194 −0.0817376
\(487\) −10.6250 18.4030i −0.481464 0.833920i 0.518310 0.855193i \(-0.326561\pi\)
−0.999774 + 0.0212730i \(0.993228\pi\)
\(488\) −2.26928 3.93051i −0.102726 0.177926i
\(489\) −6.26875 −0.283483
\(490\) −6.33824 10.9782i −0.286333 0.495943i
\(491\) 3.17510 5.49943i 0.143290 0.248186i −0.785444 0.618933i \(-0.787565\pi\)
0.928734 + 0.370748i \(0.120898\pi\)
\(492\) 1.12349 1.94594i 0.0506508 0.0877298i
\(493\) 2.94571 0.132668
\(494\) 0 0
\(495\) −7.49396 −0.336828
\(496\) 12.1000 20.9578i 0.543306 0.941033i
\(497\) 15.7087 27.2083i 0.704632 1.22046i
\(498\) 5.82640 + 10.0916i 0.261087 + 0.452216i
\(499\) 4.65087 0.208202 0.104101 0.994567i \(-0.466804\pi\)
0.104101 + 0.994567i \(0.466804\pi\)
\(500\) −7.12833 12.3466i −0.318789 0.552158i
\(501\) −3.72521 6.45225i −0.166430 0.288265i
\(502\) 1.35690 0.0605612
\(503\) −7.73759 13.4019i −0.345002 0.597561i 0.640352 0.768081i \(-0.278788\pi\)
−0.985354 + 0.170521i \(0.945455\pi\)
\(504\) 2.33728 4.04829i 0.104111 0.180325i
\(505\) −6.12445 + 10.6079i −0.272534 + 0.472043i
\(506\) 26.4373 1.17528
\(507\) 0 0
\(508\) −17.7845 −0.789059
\(509\) −10.2524 + 17.7576i −0.454428 + 0.787092i −0.998655 0.0518459i \(-0.983490\pi\)
0.544227 + 0.838938i \(0.316823\pi\)
\(510\) 0.980386 1.69808i 0.0434122 0.0751921i
\(511\) −5.08330 8.80454i −0.224872 0.389490i
\(512\) −17.1491 −0.757892
\(513\) 3.98039 + 6.89423i 0.175738 + 0.304388i
\(514\) 17.7729 + 30.7836i 0.783930 + 1.35781i
\(515\) −8.16075 −0.359606
\(516\) 4.42543 + 7.66507i 0.194819 + 0.337436i
\(517\) 27.3627 47.3936i 1.20341 2.08437i
\(518\) 19.3898 33.5842i 0.851941 1.47561i
\(519\) −2.00969 −0.0882155
\(520\) 0 0
\(521\) −42.0267 −1.84122 −0.920611 0.390481i \(-0.872309\pi\)
−0.920611 + 0.390481i \(0.872309\pi\)
\(522\) −3.52446 + 6.10454i −0.154261 + 0.267189i
\(523\) 14.9943 25.9708i 0.655653 1.13562i −0.326077 0.945343i \(-0.605727\pi\)
0.981730 0.190281i \(-0.0609399\pi\)
\(524\) −14.0918 24.4077i −0.615603 1.06626i
\(525\) 10.0315 0.437809
\(526\) −15.8654 27.4797i −0.691764 1.19817i
\(527\) 1.84481 + 3.19531i 0.0803614 + 0.139190i
\(528\) −25.6136 −1.11469
\(529\) 7.49814 + 12.9872i 0.326006 + 0.564659i
\(530\) 4.02057 6.96384i 0.174643 0.302490i
\(531\) 0.939001 1.62640i 0.0407492 0.0705796i
\(532\) 34.1987 1.48270
\(533\) 0 0
\(534\) 2.08815 0.0903629
\(535\) −4.86658 + 8.42917i −0.210401 + 0.364425i
\(536\) −3.08211 + 5.33836i −0.133127 + 0.230582i
\(537\) −10.0184 17.3524i −0.432327 0.748812i
\(538\) 29.5284 1.27306
\(539\) −12.6235 21.8645i −0.543732 0.941772i
\(540\) 0.900969 + 1.56052i 0.0387715 + 0.0671543i
\(541\) −36.3803 −1.56411 −0.782056 0.623208i \(-0.785829\pi\)
−0.782056 + 0.623208i \(0.785829\pi\)
\(542\) 0.716480 + 1.24098i 0.0307755 + 0.0533047i
\(543\) −12.0613 + 20.8908i −0.517600 + 0.896509i
\(544\) 2.32908 4.03409i 0.0998587 0.172960i
\(545\) −3.00000 −0.128506
\(546\) 0 0
\(547\) −25.8159 −1.10381 −0.551905 0.833907i \(-0.686099\pi\)
−0.551905 + 0.833907i \(0.686099\pi\)
\(548\) −8.50149 + 14.7250i −0.363166 + 0.629022i
\(549\) −1.67241 + 2.89669i −0.0713766 + 0.123628i
\(550\) −13.6054 23.5652i −0.580135 1.00482i
\(551\) 31.1414 1.32667
\(552\) 1.91939 + 3.32448i 0.0816945 + 0.141499i
\(553\) −16.2485 28.1432i −0.690955 1.19677i
\(554\) 8.70948 0.370030
\(555\) −4.51357 7.81774i −0.191591 0.331845i
\(556\) −10.9743 + 19.0081i −0.465416 + 0.806124i
\(557\) 8.99516 15.5801i 0.381137 0.660149i −0.610088 0.792334i \(-0.708866\pi\)
0.991225 + 0.132185i \(0.0421993\pi\)
\(558\) −8.82908 −0.373765
\(559\) 0 0
\(560\) −24.5875 −1.03901
\(561\) 1.95257 3.38196i 0.0824378 0.142786i
\(562\) −16.9155 + 29.2985i −0.713537 + 1.23588i
\(563\) 19.5661 + 33.8895i 0.824614 + 1.42827i 0.902214 + 0.431289i \(0.141941\pi\)
−0.0775992 + 0.996985i \(0.524725\pi\)
\(564\) −13.1588 −0.554087
\(565\) 4.45689 + 7.71955i 0.187503 + 0.324764i
\(566\) −7.13318 12.3550i −0.299830 0.519321i
\(567\) −3.44504 −0.144678
\(568\) −6.18718 10.7165i −0.259608 0.449655i
\(569\) −15.3001 + 26.5005i −0.641413 + 1.11096i 0.343705 + 0.939078i \(0.388318\pi\)
−0.985118 + 0.171882i \(0.945015\pi\)
\(570\) 10.3644 17.9517i 0.434118 0.751915i
\(571\) −2.96184 −0.123949 −0.0619745 0.998078i \(-0.519740\pi\)
−0.0619745 + 0.998078i \(0.519740\pi\)
\(572\) 0 0
\(573\) −7.08038 −0.295787
\(574\) 5.59299 9.68734i 0.233447 0.404342i
\(575\) −4.11894 + 7.13422i −0.171772 + 0.297517i
\(576\) 0.634375 + 1.09877i 0.0264323 + 0.0457821i
\(577\) 0.819396 0.0341119 0.0170560 0.999855i \(-0.494571\pi\)
0.0170560 + 0.999855i \(0.494571\pi\)
\(578\) −14.8056 25.6440i −0.615831 1.06665i
\(579\) 4.88404 + 8.45941i 0.202974 + 0.351561i
\(580\) 7.04892 0.292690
\(581\) 11.1392 + 19.2937i 0.462133 + 0.800437i
\(582\) −7.80074 + 13.5113i −0.323351 + 0.560061i
\(583\) 8.00753 13.8695i 0.331638 0.574414i
\(584\) −4.00431 −0.165700
\(585\) 0 0
\(586\) 11.8552 0.489732
\(587\) −15.8998 + 27.5392i −0.656254 + 1.13666i 0.325324 + 0.945603i \(0.394527\pi\)
−0.981578 + 0.191062i \(0.938807\pi\)
\(588\) −3.03534 + 5.25737i −0.125175 + 0.216810i
\(589\) 19.5030 + 33.7802i 0.803606 + 1.39189i
\(590\) −4.89008 −0.201322
\(591\) 11.7056 + 20.2747i 0.481504 + 0.833989i
\(592\) −15.4269 26.7202i −0.634042 1.09819i
\(593\) 4.26337 0.175076 0.0875379 0.996161i \(-0.472100\pi\)
0.0875379 + 0.996161i \(0.472100\pi\)
\(594\) 4.67241 + 8.09285i 0.191711 + 0.332054i
\(595\) 1.87435 3.24648i 0.0768410 0.133093i
\(596\) 7.94235 13.7566i 0.325331 0.563491i
\(597\) 4.02475 0.164722
\(598\) 0 0
\(599\) 24.7278 1.01035 0.505175 0.863017i \(-0.331428\pi\)
0.505175 + 0.863017i \(0.331428\pi\)
\(600\) 1.97554 3.42174i 0.0806511 0.139692i
\(601\) −3.41185 + 5.90950i −0.139172 + 0.241054i −0.927184 0.374607i \(-0.877778\pi\)
0.788011 + 0.615661i \(0.211111\pi\)
\(602\) 22.0308 + 38.1585i 0.897908 + 1.55522i
\(603\) 4.54288 0.185000
\(604\) 9.75182 + 16.8907i 0.396796 + 0.687271i
\(605\) 11.4840 + 19.8909i 0.466892 + 0.808681i
\(606\) 15.2741 0.620469
\(607\) −15.9981 27.7096i −0.649344 1.12470i −0.983280 0.182102i \(-0.941710\pi\)
0.333935 0.942596i \(-0.391623\pi\)
\(608\) 24.6226 42.6476i 0.998578 1.72959i
\(609\) −6.73825 + 11.6710i −0.273048 + 0.472932i
\(610\) 8.70948 0.352637
\(611\) 0 0
\(612\) −0.939001 −0.0379569
\(613\) 16.7937 29.0876i 0.678293 1.17484i −0.297202 0.954815i \(-0.596053\pi\)
0.975495 0.220023i \(-0.0706132\pi\)
\(614\) 22.4025 38.8022i 0.904090 1.56593i
\(615\) −1.30194 2.25502i −0.0524992 0.0909313i
\(616\) −24.2422 −0.976746
\(617\) −13.2935 23.0250i −0.535176 0.926953i −0.999155 0.0411061i \(-0.986912\pi\)
0.463978 0.885846i \(-0.346421\pi\)
\(618\) 5.08815 + 8.81293i 0.204675 + 0.354508i
\(619\) 9.17928 0.368946 0.184473 0.982838i \(-0.440942\pi\)
0.184473 + 0.982838i \(0.440942\pi\)
\(620\) 4.41454 + 7.64621i 0.177292 + 0.307079i
\(621\) 1.41454 2.45006i 0.0567636 0.0983175i
\(622\) −15.3889 + 26.6543i −0.617038 + 1.06874i
\(623\) 3.99223 0.159945
\(624\) 0 0
\(625\) −1.96184 −0.0784735
\(626\) 14.1429 24.4962i 0.565263 0.979064i
\(627\) 20.6422 35.7533i 0.824370 1.42785i
\(628\) 0.513574 + 0.889535i 0.0204938 + 0.0354963i
\(629\) 4.70410 0.187565
\(630\) 4.48523 + 7.76865i 0.178696 + 0.309510i
\(631\) 8.50216 + 14.7262i 0.338465 + 0.586239i 0.984144 0.177370i \(-0.0567588\pi\)
−0.645679 + 0.763609i \(0.723425\pi\)
\(632\) −12.7995 −0.509139
\(633\) 1.95593 + 3.38776i 0.0777411 + 0.134652i
\(634\) −29.5356 + 51.1572i −1.17301 + 2.03171i
\(635\) −10.3046 + 17.8481i −0.408927 + 0.708282i
\(636\) −3.85086 −0.152696
\(637\) 0 0
\(638\) 36.5555 1.44725
\(639\) −4.55980 + 7.89781i −0.180383 + 0.312433i
\(640\) −7.28717 + 12.6217i −0.288051 + 0.498918i
\(641\) 10.8324 + 18.7623i 0.427856 + 0.741068i 0.996682 0.0813898i \(-0.0259359\pi\)
−0.568827 + 0.822457i \(0.692603\pi\)
\(642\) 12.1371 0.479012
\(643\) 4.67778 + 8.10216i 0.184474 + 0.319518i 0.943399 0.331660i \(-0.107609\pi\)
−0.758925 + 0.651178i \(0.774275\pi\)
\(644\) −6.07673 10.5252i −0.239457 0.414751i
\(645\) 10.2567 0.403856
\(646\) 5.40097 + 9.35475i 0.212498 + 0.368058i
\(647\) 0.351388 0.608621i 0.0138145 0.0239274i −0.859036 0.511916i \(-0.828936\pi\)
0.872850 + 0.487989i \(0.162269\pi\)
\(648\) −0.678448 + 1.17511i −0.0266520 + 0.0461625i
\(649\) −9.73928 −0.382300
\(650\) 0 0
\(651\) −16.8799 −0.661576
\(652\) 3.90850 6.76972i 0.153069 0.265123i
\(653\) 18.6705 32.3383i 0.730635 1.26550i −0.225977 0.974133i \(-0.572557\pi\)
0.956612 0.291364i \(-0.0941092\pi\)
\(654\) 1.87047 + 3.23975i 0.0731411 + 0.126684i
\(655\) −32.6601 −1.27614
\(656\) −4.44989 7.70743i −0.173739 0.300925i
\(657\) 1.47554 + 2.55571i 0.0575664 + 0.0997078i
\(658\) −65.5077 −2.55376
\(659\) 0.367781 + 0.637015i 0.0143267 + 0.0248146i 0.873100 0.487541i \(-0.162106\pi\)
−0.858773 + 0.512356i \(0.828773\pi\)
\(660\) 4.67241 8.09285i 0.181873 0.315014i
\(661\) 6.92423 11.9931i 0.269321 0.466478i −0.699365 0.714764i \(-0.746534\pi\)
0.968687 + 0.248286i \(0.0798673\pi\)
\(662\) −52.5478 −2.04233
\(663\) 0 0
\(664\) 8.77479 0.340528
\(665\) 19.8153 34.3211i 0.768403 1.33091i
\(666\) −5.62833 + 9.74856i −0.218094 + 0.377749i
\(667\) −5.53348 9.58427i −0.214257 0.371105i
\(668\) 9.29052 0.359461
\(669\) 3.72468 + 6.45133i 0.144004 + 0.249423i
\(670\) −5.91454 10.2443i −0.228499 0.395771i
\(671\) 17.3461 0.669640
\(672\) 10.6555 + 18.4558i 0.411044 + 0.711949i
\(673\) 3.17510 5.49943i 0.122391 0.211987i −0.798319 0.602235i \(-0.794277\pi\)
0.920710 + 0.390247i \(0.127610\pi\)
\(674\) −29.9943 + 51.9516i −1.15534 + 2.00110i
\(675\) −2.91185 −0.112077
\(676\) 0 0
\(677\) 33.7241 1.29612 0.648061 0.761589i \(-0.275580\pi\)
0.648061 + 0.761589i \(0.275580\pi\)
\(678\) 5.55765 9.62613i 0.213440 0.369689i
\(679\) −14.9139 + 25.8316i −0.572342 + 0.991326i
\(680\) −0.738250 1.27869i −0.0283106 0.0490354i
\(681\) 21.2500 0.814300
\(682\) 22.8937 + 39.6531i 0.876646 + 1.51840i
\(683\) 9.63437 + 16.6872i 0.368649 + 0.638519i 0.989355 0.145525i \(-0.0464871\pi\)
−0.620705 + 0.784044i \(0.713154\pi\)
\(684\) −9.92692 −0.379565
\(685\) 9.85181 + 17.0638i 0.376418 + 0.651976i
\(686\) 6.61649 11.4601i 0.252619 0.437548i
\(687\) 4.64795 8.05048i 0.177330 0.307145i
\(688\) 35.0562 1.33651
\(689\) 0 0
\(690\) −7.36658 −0.280441
\(691\) −19.7005 + 34.1223i −0.749443 + 1.29807i 0.198647 + 0.980071i \(0.436345\pi\)
−0.948090 + 0.318002i \(0.896988\pi\)
\(692\) 1.25302 2.17029i 0.0476327 0.0825022i
\(693\) 8.93296 + 15.4723i 0.339335 + 0.587746i
\(694\) 1.57434 0.0597610
\(695\) 12.7174 + 22.0273i 0.482400 + 0.835541i
\(696\) 2.65399 + 4.59684i 0.100599 + 0.174243i
\(697\) 1.35690 0.0513961
\(698\) 2.91185 + 5.04348i 0.110215 + 0.190898i
\(699\) −8.10537 + 14.0389i −0.306573 + 0.531000i
\(700\) −6.25451 + 10.8331i −0.236398 + 0.409454i
\(701\) 18.3985 0.694902 0.347451 0.937698i \(-0.387047\pi\)
0.347451 + 0.937698i \(0.387047\pi\)
\(702\) 0 0
\(703\) 49.7308 1.87563
\(704\) 3.28986 5.69820i 0.123991 0.214759i
\(705\) −7.62445 + 13.2059i −0.287153 + 0.497364i
\(706\) −7.33997 12.7132i −0.276243 0.478468i
\(707\) 29.2019 1.09825
\(708\) 1.17092 + 2.02808i 0.0440057 + 0.0762201i
\(709\) −19.2277 33.3033i −0.722110 1.25073i −0.960153 0.279476i \(-0.909839\pi\)
0.238043 0.971255i \(-0.423494\pi\)
\(710\) 23.7463 0.891183
\(711\) 4.71648 + 8.16918i 0.176882 + 0.306368i
\(712\) 0.786208 1.36175i 0.0294644 0.0510338i
\(713\) 6.93094 12.0047i 0.259566 0.449581i
\(714\) −4.67456 −0.174941
\(715\) 0 0
\(716\) 24.9855 0.933753
\(717\) −6.75451 + 11.6992i −0.252252 + 0.436913i
\(718\) −2.37920 + 4.12089i −0.0887909 + 0.153790i
\(719\) −24.2500 42.0022i −0.904371 1.56642i −0.821759 0.569835i \(-0.807007\pi\)
−0.0826117 0.996582i \(-0.526326\pi\)
\(720\) 7.13706 0.265983
\(721\) 9.72779 + 16.8490i 0.362282 + 0.627491i
\(722\) 39.9795 + 69.2465i 1.48788 + 2.57709i
\(723\) −6.26875 −0.233137
\(724\) −15.0402 26.0504i −0.558964 0.968154i
\(725\) −5.69537 + 9.86468i −0.211521 + 0.366365i
\(726\) 14.3204 24.8036i 0.531478 0.920547i
\(727\) 19.0344 0.705948 0.352974 0.935633i \(-0.385170\pi\)
0.352974 + 0.935633i \(0.385170\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 3.84213 6.65476i 0.142203 0.246304i
\(731\) −2.67241 + 4.62874i −0.0988425 + 0.171200i
\(732\) −2.08546 3.61212i −0.0770807 0.133508i
\(733\) −24.6213 −0.909410 −0.454705 0.890642i \(-0.650255\pi\)
−0.454705 + 0.890642i \(0.650255\pi\)
\(734\) −2.61649 4.53189i −0.0965764 0.167275i
\(735\) 3.51746 + 6.09242i 0.129743 + 0.224722i
\(736\) −17.5007 −0.645083
\(737\) −11.7796 20.4029i −0.433908 0.751551i
\(738\) −1.62349 + 2.81197i −0.0597615 + 0.103510i
\(739\) −22.2558 + 38.5481i −0.818692 + 1.41802i 0.0879549 + 0.996124i \(0.471967\pi\)
−0.906647 + 0.421891i \(0.861366\pi\)
\(740\) 11.2567 0.413803
\(741\) 0 0
\(742\) −19.1704 −0.703769
\(743\) 5.20560 9.01636i 0.190975 0.330778i −0.754599 0.656186i \(-0.772168\pi\)
0.945574 + 0.325408i \(0.105502\pi\)
\(744\) −3.32424 + 5.75775i −0.121873 + 0.211089i
\(745\) −9.20387 15.9416i −0.337204 0.584054i
\(746\) 15.1336 0.554081
\(747\) −3.23341 5.60042i −0.118304 0.204909i
\(748\) 2.43482 + 4.21723i 0.0890259 + 0.154197i
\(749\) 23.2043 0.847866
\(750\) 10.3007 + 17.8414i 0.376130 + 0.651476i
\(751\) −0.849896 + 1.47206i −0.0310131 + 0.0537163i −0.881115 0.472901i \(-0.843207\pi\)
0.850102 + 0.526618i \(0.176540\pi\)
\(752\) −26.0596 + 45.1365i −0.950295 + 1.64596i
\(753\) −0.753020 −0.0274416
\(754\) 0 0
\(755\) 22.6015 0.822552
\(756\) 2.14795 3.72036i 0.0781201 0.135308i
\(757\) −13.7126 + 23.7509i −0.498393 + 0.863242i −0.999998 0.00185490i \(-0.999410\pi\)
0.501606 + 0.865096i \(0.332743\pi\)
\(758\) −14.1887 24.5755i −0.515356 0.892622i
\(759\) −14.6716 −0.532545
\(760\) −7.80463 13.5180i −0.283104 0.490350i
\(761\) −2.51304 4.35271i −0.0910977 0.157786i 0.816876 0.576814i \(-0.195704\pi\)
−0.907973 + 0.419028i \(0.862371\pi\)
\(762\) 25.6993 0.930988
\(763\) 3.57606 + 6.19393i 0.129462 + 0.224235i
\(764\) 4.41454 7.64621i 0.159713 0.276630i
\(765\) −0.544073 + 0.942362i −0.0196710 + 0.0340712i
\(766\) 22.9541 0.829364
\(767\) 0 0
\(768\) 20.7114 0.747358
\(769\) 21.2228 36.7590i 0.765314 1.32556i −0.174766 0.984610i \(-0.555917\pi\)
0.940080 0.340953i \(-0.110750\pi\)
\(770\) 23.2603 40.2880i 0.838244 1.45188i
\(771\) −9.86323 17.0836i −0.355216 0.615252i
\(772\) −12.1806 −0.438390
\(773\) 13.1796 + 22.8278i 0.474039 + 0.821059i 0.999558 0.0297223i \(-0.00946228\pi\)
−0.525519 + 0.850782i \(0.676129\pi\)
\(774\) −6.39493 11.0763i −0.229861 0.398131i
\(775\) −14.2674 −0.512501
\(776\) 5.87412 + 10.1743i 0.210869 + 0.365235i
\(777\) −10.7606 + 18.6378i −0.386033 + 0.668628i
\(778\) −0.279635 + 0.484342i −0.0100254 + 0.0173645i
\(779\) 14.3448 0.513956
\(780\) 0 0
\(781\)