Properties

Label 507.2.e.j.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 \(0.900969 - 1.56052i\) of defining polynomial
Character \(\chi\) \(=\) 507.22
Dual form 507.2.e.j.484.1

$q$-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 \(0.386525\pi\)
−0.986070 + 0.166330i \(0.946808\pi\)
\(3\) −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 \(-0.395268\pi\)
0.323121 + 0.946358i \(0.395268\pi\)
\(6\) −0.900969 1.56052i −0.367819 0.637081i
\(7\) −1.72252 2.98349i −0.651052 1.12765i −0.982868 0.184311i \(-0.940995\pi\)
0.331816 0.943344i \(-0.392339\pi\)
\(8\) −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 \(-0.547627\pi\)
0.930883 0.365318i \(-0.119040\pi\)
\(12\) 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 \(-0.800299\pi\)
−0.103594 0.994620i \(-0.533034\pi\)
\(20\) −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 \(-0.645026\pi\)
−0.440013 + 0.897992i \(0.645026\pi\)
\(32\) 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 \(0.338317\pi\)
−0.999877 + 0.0156576i \(0.995016\pi\)
\(38\) 14.3448 2.32704
\(39\) 0 0
\(40\) −1.96077 −0.310025
\(41\) −0.900969 + 1.56052i −0.140708 + 0.243713i −0.927763 0.373169i \(-0.878271\pi\)
0.787056 + 0.616882i \(0.211604\pi\)
\(42\) −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 \(-0.220443\pi\)
0.769625 + 0.638496i \(0.220443\pi\)
\(48\) 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 0.798406 0.602119i \(-0.205677\pi\)
−0.920654 + 0.390380i \(0.872344\pi\)
\(60\) 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 −0.693263 0.720685i \(-0.743827\pi\)
0.970763 + 0.240040i \(0.0771607\pi\)
\(68\) 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 \(0.0153438\pi\)
−0.457689 + 0.889112i \(0.651323\pi\)
\(72\) 0.678448 + 1.17511i 0.0799559 + 0.138488i
\(73\) 2.95108 0.345398 0.172699 0.984975i \(-0.444751\pi\)
0.172699 + 0.984975i \(0.444751\pi\)
\(74\) −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 \(-0.615489\pi\)
−0.354912 + 0.934900i \(0.615489\pi\)
\(84\) −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 −0.895099 0.445866i \(-0.852896\pi\)
0.833681 + 0.552246i \(0.186229\pi\)
\(90\) 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 0.558103 0.829772i \(-0.311529\pi\)
−0.997655 + 0.0684454i \(0.978196\pi\)
\(98\) −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 \(-0.531700\pi\)
−0.0994255 + 0.995045i \(0.531700\pi\)
\(110\) 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 \(0.0312480\pi\)
−0.412713 + 0.910861i \(0.635419\pi\)
\(138\) −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 \(-0.991931\pi\)
0.477888 0.878421i \(-0.341403\pi\)
\(150\) 2.62349 + 4.54402i 0.214207 + 0.371017i
\(151\) 15.6407 1.27282 0.636412 0.771350i \(-0.280418\pi\)
0.636412 + 0.771350i \(0.280418\pi\)
\(152\) 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 0.716770 0.697310i \(-0.245620\pi\)
−0.962273 + 0.272086i \(0.912287\pi\)
\(164\) 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 −0.685130 0.728420i \(-0.740255\pi\)
0.973396 + 0.229130i \(0.0735881\pi\)
\(168\) −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 −0.986523 0.163622i \(-0.947682\pi\)
0.634962 + 0.772543i \(0.281016\pi\)
\(194\) 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 \(0.480615\pi\)
−0.894851 + 0.446365i \(0.852718\pi\)
\(198\) 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 −0.963366 0.268191i \(-0.913574\pi\)
0.713943 + 0.700204i \(0.246908\pi\)
\(224\) 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 \(0.0824783\pi\)
−0.261413 + 0.965227i \(0.584188\pi\)
\(228\) −4.96346 8.59696i −0.328713 0.569348i
\(229\) 9.29590 0.614290 0.307145 0.951663i \(-0.400626\pi\)
0.307145 + 0.951663i \(0.400626\pi\)
\(230\) 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 \(-0.643928\pi\)
−0.436913 + 0.899504i \(0.643928\pi\)
\(240\) 3.56853 + 6.18088i 0.230348 + 0.398974i
\(241\) −3.13437 5.42890i −0.201903 0.349706i 0.747239 0.664556i \(-0.231379\pi\)
−0.949142 + 0.314850i \(0.898046\pi\)
\(242\) 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 −0.853696 0.520772i \(-0.825644\pi\)
0.877849 + 0.478937i \(0.158978\pi\)
\(272\) 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 \(-0.310799\pi\)
0.560005 + 0.828489i \(0.310799\pi\)
\(282\) −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 0.753794 0.657111i \(-0.228222\pi\)
−0.945972 + 0.324249i \(0.894888\pi\)
\(294\) 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 \(-0.751105\pi\)
−0.709556 + 0.704649i \(0.751105\pi\)
\(308\) 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 \(-0.127690\pi\)
0.920613 + 0.390477i \(0.127690\pi\)
\(318\) 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 \(0.129265\pi\)
−0.117230 + 0.993105i \(0.537401\pi\)
\(332\) 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 −0.819529 0.573037i \(-0.805765\pi\)
0.906029 + 0.423215i \(0.139098\pi\)
\(350\) −18.0761 −0.966206
\(351\) 0 0
\(352\) 32.0804 1.70989
\(353\) −4.07338 + 7.05529i −0.216804 + 0.375515i −0.953829 0.300350i \(-0.902897\pi\)
0.737025 + 0.675865i \(0.236230\pi\)
\(354\) −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 \(-0.477800\pi\)
0.0696857 + 0.997569i \(0.477800\pi\)
\(360\) 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 −0.994259 0.106998i \(-0.965876\pi\)
0.589793 + 0.807555i \(0.299209\pi\)
\(380\) −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 0.656150 0.754631i \(-0.272184\pi\)
−0.981604 + 0.190927i \(0.938851\pi\)
\(384\) −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 0.846712 0.532052i \(-0.178579\pi\)
−0.884127 + 0.467248i \(0.845246\pi\)
\(398\) 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 \(-0.630449\pi\)
0.993534 0.113535i \(-0.0362175\pi\)
\(402\) −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 0.808439 0.588580i \(-0.200313\pi\)
−0.913945 + 0.405839i \(0.866979\pi\)
\(410\) −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 \(-0.245783\pi\)
0.716412 + 0.697677i \(0.245783\pi\)
\(422\) 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 \(-0.540210\pi\)
0.922119 0.386907i \(-0.126457\pi\)
\(432\) 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 0.977326 0.211741i \(-0.0679134\pi\)
−0.672036 + 0.740518i \(0.734580\pi\)
\(450\) −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 −0.803672 0.595073i \(-0.797123\pi\)
0.917184 + 0.398463i \(0.130456\pi\)
\(458\) −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 0.558978 0.829183i \(-0.311194\pi\)
−0.997582 + 0.0694978i \(0.977860\pi\)
\(462\) 16.0966 + 27.8802i 0.748883 + 1.29710i
\(463\) −22.8767 −1.06317 −0.531585 0.847005i \(-0.678403\pi\)
−0.531585 + 0.847005i \(0.678403\pi\)
\(464\) −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 \(-0.497329\pi\)
0.861800 0.507248i \(-0.169337\pi\)
\(480\) −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 0.999774 0.0212730i \(-0.00677192\pi\)
−0.518310 + 0.855193i \(0.673439\pi\)
\(488\) 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 \(-0.533196\pi\)
−0.104101 + 0.994567i \(0.533196\pi\)
\(500\) 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 −0.544227 0.838938i \(-0.683177\pi\)
0.998655 + 0.0518459i \(0.0165105\pi\)
\(510\) 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 \(-0.214171\pi\)
0.782056 + 0.623208i \(0.214171\pi\)
\(542\) 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 −0.991225 0.132185i \(-0.957801\pi\)
0.610088 + 0.792334i \(0.291134\pi\)
\(558\) −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 \(-0.505429\pi\)
−0.0170560 + 0.999855i \(0.505429\pi\)
\(578\) 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 \(-0.605473\pi\)
0.981578 0.191062i \(-0.0611933\pi\)
\(588\) −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 \(-0.527900\pi\)
−0.0875379 + 0.996161i \(0.527900\pi\)
\(594\) 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 \(0.403947\pi\)
−0.975495 + 0.220023i \(0.929387\pi\)
\(614\) 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 \(0.0130882\pi\)
−0.463978 + 0.885846i \(0.653579\pi\)
\(618\) −5.08815 8.81293i −0.204675 0.354508i
\(619\) −9.17928 −0.368946 −0.184473 0.982838i \(-0.559058\pi\)
−0.184473 + 0.982838i \(0.559058\pi\)
\(620\) 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 0.645679 0.763609i \(-0.276575\pi\)
−0.984144 + 0.177370i \(0.943241\pi\)
\(632\) 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 0.758925 0.651178i \(-0.225725\pi\)
−0.943399 + 0.331660i \(0.892391\pi\)
\(644\) 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 −0.968687 0.248286i \(-0.920133\pi\)
0.699365 + 0.714764i \(0.253466\pi\)
\(662\) −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 0.620705 0.784044i \(-0.286846\pi\)
−0.989355 + 0.145525i \(0.953513\pi\)
\(684\) 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 \(-0.563655\pi\)
0.948090 0.318002i \(-0.103012\pi\)
\(692\) 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 \(0.0901609\pi\)
−0.238043 + 0.971255i \(0.576506\pi\)
\(710\) −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 \(-0.349745\pi\)
0.454705 + 0.890642i \(0.349745\pi\)
\(734\) 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 \(-0.528033\pi\)
0.906647 0.421891i \(-0.138634\pi\)
\(740\) 11.2567 0.413803
\(741\) 0 0
\(742\) −19.1704 −0.703769
\(743\) −5.20560 + 9.01636i −0.190975 + 0.330778i −0.945574 0.325408i \(-0.894498\pi\)
0.754599 + 0.656186i \(0.227832\pi\)
\(744\) −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 0.907973 0.419028i \(-0.137629\pi\)
−0.816876 + 0.576814i \(0.804296\pi\)
\(762\) −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 \(0.444083\pi\)
−0.940080 + 0.340953i \(0.889250\pi\)
\(770\) 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 0.525519 0.850782i \(-0.323871\pi\)
−0.999558 + 0.0297223i \(0.990538\pi\)
\(774\) 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
\(781\) 47.2941 1.69232