Properties

Label 507.2.j.h.361.1
Level $507$
Weight $2$
Character 507.361
Analytic conductor $4.048$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 507 = 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 507.j (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.04841538248\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: 12.0.17213603549184.1
Defining polynomial: \(x^{12} - 5 x^{10} + 19 x^{8} - 28 x^{6} + 31 x^{4} - 6 x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 361.1
Root \(-1.56052 + 0.900969i\) of defining polynomial
Character \(\chi\) \(=\) 507.361
Dual form 507.2.j.h.316.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.56052 + 0.900969i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.623490 - 1.07992i) q^{4} -1.44504i q^{5} +(1.56052 + 0.900969i) q^{6} +(-2.98349 - 1.72252i) q^{7} -1.35690i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-1.56052 + 0.900969i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.623490 - 1.07992i) q^{4} -1.44504i q^{5} +(1.56052 + 0.900969i) q^{6} +(-2.98349 - 1.72252i) q^{7} -1.35690i q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.30194 + 2.25502i) q^{10} +(-4.49119 + 2.59299i) q^{11} -1.24698 q^{12} +6.20775 q^{14} +(-1.25144 + 0.722521i) q^{15} +(2.46950 + 4.27730i) q^{16} +(-0.376510 + 0.652135i) q^{17} -1.80194i q^{18} +(6.89423 + 3.98039i) q^{19} +(-1.56052 - 0.900969i) q^{20} +3.44504i q^{21} +(4.67241 - 8.09285i) q^{22} +(-1.41454 - 2.45006i) q^{23} +(-1.17511 + 0.678448i) q^{24} +2.91185 q^{25} +1.00000 q^{27} +(-3.72036 + 2.14795i) q^{28} +(1.95593 + 3.38776i) q^{29} +(1.30194 - 2.25502i) q^{30} +4.89977i q^{31} +(-5.35722 - 3.09299i) q^{32} +(4.49119 + 2.59299i) q^{33} -1.35690i q^{34} +(-2.48911 + 4.31127i) q^{35} +(0.623490 + 1.07992i) q^{36} +(5.41004 - 3.12349i) q^{37} -14.3448 q^{38} -1.96077 q^{40} +(-1.56052 + 0.900969i) q^{41} +(-3.10388 - 5.37607i) q^{42} +(-3.54892 + 6.14691i) q^{43} +6.46681i q^{44} +(1.25144 + 0.722521i) q^{45} +(4.41485 + 2.54892i) q^{46} +10.5526i q^{47} +(2.46950 - 4.27730i) q^{48} +(2.43416 + 4.21608i) q^{49} +(-4.54402 + 2.62349i) q^{50} +0.753020 q^{51} -3.08815 q^{53} +(-1.56052 + 0.900969i) q^{54} +(3.74698 + 6.48996i) q^{55} +(-2.33728 + 4.04829i) q^{56} -7.96077i q^{57} +(-6.10454 - 3.52446i) q^{58} +(-1.62640 - 0.939001i) q^{59} +1.80194i q^{60} +(-1.67241 + 2.89669i) q^{61} +(-4.41454 - 7.64621i) q^{62} +(2.98349 - 1.72252i) q^{63} +1.26875 q^{64} -9.34481 q^{66} +(3.93425 - 2.27144i) q^{67} +(0.469501 + 0.813199i) q^{68} +(-1.41454 + 2.45006i) q^{69} -8.97046i q^{70} +(-7.89781 - 4.55980i) q^{71} +(1.17511 + 0.678448i) q^{72} +2.95108i q^{73} +(-5.62833 + 9.74856i) q^{74} +(-1.45593 - 2.52174i) q^{75} +(8.59696 - 4.96346i) q^{76} +17.8659 q^{77} -9.43296 q^{79} +(6.18088 - 3.56853i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.62349 - 2.81197i) q^{82} +6.46681i q^{83} +(3.72036 + 2.14795i) q^{84} +(0.942362 + 0.544073i) q^{85} -12.7899i q^{86} +(1.95593 - 3.38776i) q^{87} +(3.51842 + 6.09408i) q^{88} +(1.00358 - 0.579417i) q^{89} -2.60388 q^{90} -3.52781 q^{92} +(4.24333 - 2.44989i) q^{93} +(-9.50753 - 16.4675i) q^{94} +(5.75182 - 9.96245i) q^{95} +6.18598i q^{96} +(7.49819 + 4.32908i) q^{97} +(-7.59712 - 4.38620i) q^{98} -5.18598i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 6q^{3} - 2q^{4} - 6q^{9} + O(q^{10}) \) \( 12q - 6q^{3} - 2q^{4} - 6q^{9} - 2q^{10} + 4q^{12} + 4q^{14} + 10q^{16} - 14q^{17} + 10q^{22} + 4q^{23} + 20q^{25} + 12q^{27} + 16q^{29} - 2q^{30} - 36q^{35} - 2q^{36} - 80q^{38} + 28q^{40} - 2q^{42} - 6q^{43} + 10q^{48} + 34q^{49} + 28q^{51} - 52q^{53} + 26q^{55} + 14q^{56} + 26q^{61} - 32q^{62} - 16q^{64} - 20q^{66} - 14q^{68} + 4q^{69} - 14q^{74} - 10q^{75} + 60q^{77} - 36q^{79} - 6q^{81} + 10q^{82} + 16q^{87} - 14q^{88} + 4q^{90} - 68q^{92} - 64q^{94} + 6q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).

\(n\) \(170\) \(340\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.56052 + 0.900969i −1.10346 + 0.637081i −0.937127 0.348989i \(-0.886525\pi\)
−0.166330 + 0.986070i \(0.553192\pi\)
\(3\) −0.500000 0.866025i −0.288675 0.500000i
\(4\) 0.623490 1.07992i 0.311745 0.539958i
\(5\) 1.44504i 0.646242i −0.946358 0.323121i \(-0.895268\pi\)
0.946358 0.323121i \(-0.104732\pi\)
\(6\) 1.56052 + 0.900969i 0.637081 + 0.367819i
\(7\) −2.98349 1.72252i −1.12765 0.651052i −0.184311 0.982868i \(-0.559005\pi\)
−0.943344 + 0.331816i \(0.892339\pi\)
\(8\) 1.35690i 0.479735i
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 1.30194 + 2.25502i 0.411709 + 0.713101i
\(11\) −4.49119 + 2.59299i −1.35415 + 0.781816i −0.988827 0.149067i \(-0.952373\pi\)
−0.365318 + 0.930883i \(0.619040\pi\)
\(12\) −1.24698 −0.359972
\(13\) 0 0
\(14\) 6.20775 1.65909
\(15\) −1.25144 + 0.722521i −0.323121 + 0.186554i
\(16\) 2.46950 + 4.27730i 0.617375 + 1.06933i
\(17\) −0.376510 + 0.652135i −0.0913171 + 0.158166i −0.908066 0.418828i \(-0.862441\pi\)
0.816748 + 0.576994i \(0.195774\pi\)
\(18\) 1.80194i 0.424721i
\(19\) 6.89423 + 3.98039i 1.58164 + 0.913163i 0.994620 + 0.103594i \(0.0330344\pi\)
0.587025 + 0.809569i \(0.300299\pi\)
\(20\) −1.56052 0.900969i −0.348944 0.201463i
\(21\) 3.44504i 0.751770i
\(22\) 4.67241 8.09285i 0.996161 1.72540i
\(23\) −1.41454 2.45006i −0.294952 0.510873i 0.680021 0.733192i \(-0.261970\pi\)
−0.974974 + 0.222320i \(0.928637\pi\)
\(24\) −1.17511 + 0.678448i −0.239868 + 0.138488i
\(25\) 2.91185 0.582371
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) −3.72036 + 2.14795i −0.703081 + 0.405924i
\(29\) 1.95593 + 3.38776i 0.363207 + 0.629092i 0.988487 0.151308i \(-0.0483486\pi\)
−0.625280 + 0.780400i \(0.715015\pi\)
\(30\) 1.30194 2.25502i 0.237700 0.411709i
\(31\) 4.89977i 0.880025i 0.897992 + 0.440013i \(0.145026\pi\)
−0.897992 + 0.440013i \(0.854974\pi\)
\(32\) −5.35722 3.09299i −0.947031 0.546769i
\(33\) 4.49119 + 2.59299i 0.781816 + 0.451382i
\(34\) 1.35690i 0.232706i
\(35\) −2.48911 + 4.31127i −0.420737 + 0.728738i
\(36\) 0.623490 + 1.07992i 0.103915 + 0.179986i
\(37\) 5.41004 3.12349i 0.889406 0.513499i 0.0156576 0.999877i \(-0.495016\pi\)
0.873748 + 0.486379i \(0.161683\pi\)
\(38\) −14.3448 −2.32704
\(39\) 0 0
\(40\) −1.96077 −0.310025
\(41\) −1.56052 + 0.900969i −0.243713 + 0.140708i −0.616882 0.787056i \(-0.711604\pi\)
0.373169 + 0.927763i \(0.378271\pi\)
\(42\) −3.10388 5.37607i −0.478938 0.829546i
\(43\) −3.54892 + 6.14691i −0.541205 + 0.937394i 0.457630 + 0.889143i \(0.348698\pi\)
−0.998835 + 0.0482517i \(0.984635\pi\)
\(44\) 6.46681i 0.974909i
\(45\) 1.25144 + 0.722521i 0.186554 + 0.107707i
\(46\) 4.41485 + 2.54892i 0.650935 + 0.375817i
\(47\) 10.5526i 1.53925i 0.638496 + 0.769625i \(0.279557\pi\)
−0.638496 + 0.769625i \(0.720443\pi\)
\(48\) 2.46950 4.27730i 0.356442 0.617375i
\(49\) 2.43416 + 4.21608i 0.347737 + 0.602298i
\(50\) −4.54402 + 2.62349i −0.642621 + 0.371017i
\(51\) 0.753020 0.105444
\(52\) 0 0
\(53\) −3.08815 −0.424189 −0.212095 0.977249i \(-0.568029\pi\)
−0.212095 + 0.977249i \(0.568029\pi\)
\(54\) −1.56052 + 0.900969i −0.212360 + 0.122606i
\(55\) 3.74698 + 6.48996i 0.505243 + 0.875106i
\(56\) −2.33728 + 4.04829i −0.312332 + 0.540976i
\(57\) 7.96077i 1.05443i
\(58\) −6.10454 3.52446i −0.801566 0.462784i
\(59\) −1.62640 0.939001i −0.211739 0.122248i 0.390380 0.920654i \(-0.372344\pi\)
−0.602119 + 0.798406i \(0.705677\pi\)
\(60\) 1.80194i 0.232629i
\(61\) −1.67241 + 2.89669i −0.214130 + 0.370884i −0.953003 0.302961i \(-0.902025\pi\)
0.738873 + 0.673844i \(0.235358\pi\)
\(62\) −4.41454 7.64621i −0.560647 0.971070i
\(63\) 2.98349 1.72252i 0.375885 0.217017i
\(64\) 1.26875 0.158594
\(65\) 0 0
\(66\) −9.34481 −1.15027
\(67\) 3.93425 2.27144i 0.480645 0.277500i −0.240040 0.970763i \(-0.577161\pi\)
0.720685 + 0.693263i \(0.243827\pi\)
\(68\) 0.469501 + 0.813199i 0.0569353 + 0.0986148i
\(69\) −1.41454 + 2.45006i −0.170291 + 0.294952i
\(70\) 8.97046i 1.07218i
\(71\) −7.89781 4.55980i −0.937298 0.541149i −0.0481854 0.998838i \(-0.515344\pi\)
−0.889112 + 0.457689i \(0.848677\pi\)
\(72\) 1.17511 + 0.678448i 0.138488 + 0.0799559i
\(73\) 2.95108i 0.345398i 0.984975 + 0.172699i \(0.0552488\pi\)
−0.984975 + 0.172699i \(0.944751\pi\)
\(74\) −5.62833 + 9.74856i −0.654281 + 1.13325i
\(75\) −1.45593 2.52174i −0.168116 0.291185i
\(76\) 8.59696 4.96346i 0.986139 0.569348i
\(77\) 17.8659 2.03601
\(78\) 0 0
\(79\) −9.43296 −1.06129 −0.530645 0.847594i \(-0.678050\pi\)
−0.530645 + 0.847594i \(0.678050\pi\)
\(80\) 6.18088 3.56853i 0.691043 0.398974i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 1.62349 2.81197i 0.179284 0.310530i
\(83\) 6.46681i 0.709825i 0.934900 + 0.354912i \(0.115489\pi\)
−0.934900 + 0.354912i \(0.884511\pi\)
\(84\) 3.72036 + 2.14795i 0.405924 + 0.234360i
\(85\) 0.942362 + 0.544073i 0.102214 + 0.0590130i
\(86\) 12.7899i 1.37917i
\(87\) 1.95593 3.38776i 0.209697 0.363207i
\(88\) 3.51842 + 6.09408i 0.375065 + 0.649631i
\(89\) 1.00358 0.579417i 0.106379 0.0614181i −0.445866 0.895099i \(-0.647104\pi\)
0.552246 + 0.833681i \(0.313771\pi\)
\(90\) −2.60388 −0.274473
\(91\) 0 0
\(92\) −3.52781 −0.367800
\(93\) 4.24333 2.44989i 0.440013 0.254041i
\(94\) −9.50753 16.4675i −0.980627 1.69850i
\(95\) 5.75182 9.96245i 0.590125 1.02213i
\(96\) 6.18598i 0.631354i
\(97\) 7.49819 + 4.32908i 0.761326 + 0.439552i 0.829772 0.558103i \(-0.188471\pi\)
−0.0684454 + 0.997655i \(0.521804\pi\)
\(98\) −7.59712 4.38620i −0.767425 0.443073i
\(99\) 5.18598i 0.521211i
\(100\) 1.81551 3.14456i 0.181551 0.314456i
\(101\) −4.23825 7.34087i −0.421722 0.730443i 0.574386 0.818584i \(-0.305241\pi\)
−0.996108 + 0.0881410i \(0.971907\pi\)
\(102\) −1.17511 + 0.678448i −0.116353 + 0.0671764i
\(103\) −5.64742 −0.556456 −0.278228 0.960515i \(-0.589747\pi\)
−0.278228 + 0.960515i \(0.589747\pi\)
\(104\) 0 0
\(105\) 4.97823 0.485825
\(106\) 4.81913 2.78232i 0.468075 0.270243i
\(107\) 3.36778 + 5.83317i 0.325576 + 0.563914i 0.981629 0.190801i \(-0.0611086\pi\)
−0.656053 + 0.754715i \(0.727775\pi\)
\(108\) 0.623490 1.07992i 0.0599953 0.103915i
\(109\) 2.07606i 0.198851i 0.995045 + 0.0994255i \(0.0317005\pi\)
−0.995045 + 0.0994255i \(0.968300\pi\)
\(110\) −11.6945 6.75182i −1.11503 0.643761i
\(111\) −5.41004 3.12349i −0.513499 0.296469i
\(112\) 17.0151i 1.60777i
\(113\) −3.08426 + 5.34210i −0.290143 + 0.502542i −0.973843 0.227221i \(-0.927036\pi\)
0.683700 + 0.729763i \(0.260370\pi\)
\(114\) 7.17241 + 12.4230i 0.671757 + 1.16352i
\(115\) −3.54044 + 2.04407i −0.330148 + 0.190611i
\(116\) 4.87800 0.452911
\(117\) 0 0
\(118\) 3.38404 0.311526
\(119\) 2.24663 1.29709i 0.205948 0.118904i
\(120\) 0.980386 + 1.69808i 0.0894966 + 0.155013i
\(121\) 7.94720 13.7650i 0.722473 1.25136i
\(122\) 6.02715i 0.545672i
\(123\) 1.56052 + 0.900969i 0.140708 + 0.0812376i
\(124\) 5.29134 + 3.05496i 0.475177 + 0.274343i
\(125\) 11.4330i 1.02260i
\(126\) −3.10388 + 5.37607i −0.276515 + 0.478938i
\(127\) −7.13102 12.3513i −0.632776 1.09600i −0.986982 0.160833i \(-0.948582\pi\)
0.354206 0.935168i \(-0.384751\pi\)
\(128\) 8.73452 5.04288i 0.772030 0.445732i
\(129\) 7.09783 0.624929
\(130\) 0 0
\(131\) 22.6015 1.97470 0.987350 0.158554i \(-0.0506831\pi\)
0.987350 + 0.158554i \(0.0506831\pi\)
\(132\) 5.60042 3.23341i 0.487454 0.281432i
\(133\) −13.7126 23.7509i −1.18903 2.05947i
\(134\) −4.09299 + 7.08927i −0.353581 + 0.612419i
\(135\) 1.44504i 0.124369i
\(136\) 0.884879 + 0.510885i 0.0758777 + 0.0438080i
\(137\) 11.8085 + 6.81767i 1.00887 + 0.582473i 0.910861 0.412713i \(-0.135419\pi\)
0.0980109 + 0.995185i \(0.468752\pi\)
\(138\) 5.09783i 0.433957i
\(139\) −8.80074 + 15.2433i −0.746469 + 1.29292i 0.203036 + 0.979171i \(0.434919\pi\)
−0.949505 + 0.313751i \(0.898414\pi\)
\(140\) 3.10388 + 5.37607i 0.262325 + 0.454361i
\(141\) 9.13879 5.27628i 0.769625 0.444343i
\(142\) 16.4330 1.37902
\(143\) 0 0
\(144\) −4.93900 −0.411583
\(145\) 4.89546 2.82640i 0.406546 0.234719i
\(146\) −2.65883 4.60523i −0.220047 0.381132i
\(147\) 2.43416 4.21608i 0.200766 0.347737i
\(148\) 7.78986i 0.640322i
\(149\) 11.0319 + 6.36927i 0.903769 + 0.521791i 0.878421 0.477888i \(-0.158597\pi\)
0.0253478 + 0.999679i \(0.491931\pi\)
\(150\) 4.54402 + 2.62349i 0.371017 + 0.214207i
\(151\) 15.6407i 1.27282i 0.771350 + 0.636412i \(0.219582\pi\)
−0.771350 + 0.636412i \(0.780418\pi\)
\(152\) 5.40097 9.35475i 0.438076 0.758771i
\(153\) −0.376510 0.652135i −0.0304390 0.0527220i
\(154\) −27.8802 + 16.0966i −2.24665 + 1.29710i
\(155\) 7.08038 0.568710
\(156\) 0 0
\(157\) −0.823708 −0.0657391 −0.0328695 0.999460i \(-0.510465\pi\)
−0.0328695 + 0.999460i \(0.510465\pi\)
\(158\) 14.7204 8.49880i 1.17109 0.676129i
\(159\) 1.54407 + 2.67441i 0.122453 + 0.212095i
\(160\) −4.46950 + 7.74140i −0.353345 + 0.612012i
\(161\) 9.74632i 0.768117i
\(162\) 1.56052 + 0.900969i 0.122606 + 0.0707868i
\(163\) −5.42890 3.13437i −0.425224 0.245503i 0.272086 0.962273i \(-0.412287\pi\)
−0.697310 + 0.716770i \(0.745620\pi\)
\(164\) 2.24698i 0.175460i
\(165\) 3.74698 6.48996i 0.291702 0.505243i
\(166\) −5.82640 10.0916i −0.452216 0.783261i
\(167\) −6.45225 + 3.72521i −0.499290 + 0.288265i −0.728420 0.685130i \(-0.759745\pi\)
0.229130 + 0.973396i \(0.426412\pi\)
\(168\) 4.67456 0.360650
\(169\) 0 0
\(170\) −1.96077 −0.150384
\(171\) −6.89423 + 3.98039i −0.527215 + 0.304388i
\(172\) 4.42543 + 7.66507i 0.337436 + 0.584456i
\(173\) −1.00484 + 1.74044i −0.0763969 + 0.132323i −0.901693 0.432377i \(-0.857675\pi\)
0.825296 + 0.564700i \(0.191008\pi\)
\(174\) 7.04892i 0.534377i
\(175\) −8.68750 5.01573i −0.656713 0.379154i
\(176\) −22.1820 12.8068i −1.67203 0.965348i
\(177\) 1.87800i 0.141159i
\(178\) −1.04407 + 1.80839i −0.0782566 + 0.135544i
\(179\) 10.0184 + 17.3524i 0.748812 + 1.29698i 0.948393 + 0.317099i \(0.102709\pi\)
−0.199581 + 0.979881i \(0.563958\pi\)
\(180\) 1.56052 0.900969i 0.116315 0.0671543i
\(181\) −24.1226 −1.79302 −0.896509 0.443026i \(-0.853905\pi\)
−0.896509 + 0.443026i \(0.853905\pi\)
\(182\) 0 0
\(183\) 3.34481 0.247256
\(184\) −3.32448 + 1.91939i −0.245084 + 0.141499i
\(185\) −4.51357 7.81774i −0.331845 0.574772i
\(186\) −4.41454 + 7.64621i −0.323690 + 0.560647i
\(187\) 3.90515i 0.285573i
\(188\) 11.3959 + 6.57942i 0.831130 + 0.479853i
\(189\) −2.98349 1.72252i −0.217017 0.125295i
\(190\) 20.7289i 1.50383i
\(191\) 3.54019 6.13179i 0.256159 0.443680i −0.709051 0.705158i \(-0.750876\pi\)
0.965210 + 0.261477i \(0.0842096\pi\)
\(192\) −0.634375 1.09877i −0.0457821 0.0792969i
\(193\) 8.45941 4.88404i 0.608922 0.351561i −0.163622 0.986523i \(-0.552318\pi\)
0.772543 + 0.634962i \(0.218984\pi\)
\(194\) −15.6015 −1.12012
\(195\) 0 0
\(196\) 6.07069 0.433621
\(197\) −20.2747 + 11.7056i −1.44451 + 0.833989i −0.998146 0.0608617i \(-0.980615\pi\)
−0.446365 + 0.894851i \(0.647282\pi\)
\(198\) 4.67241 + 8.09285i 0.332054 + 0.575134i
\(199\) 2.01238 3.48554i 0.142654 0.247083i −0.785841 0.618428i \(-0.787770\pi\)
0.928495 + 0.371345i \(0.121103\pi\)
\(200\) 3.95108i 0.279384i
\(201\) −3.93425 2.27144i −0.277500 0.160215i
\(202\) 13.2278 + 7.63706i 0.930703 + 0.537342i
\(203\) 13.4765i 0.945865i
\(204\) 0.469501 0.813199i 0.0328716 0.0569353i
\(205\) 1.30194 + 2.25502i 0.0909313 + 0.157498i
\(206\) 8.81293 5.08815i 0.614026 0.354508i
\(207\) 2.82908 0.196635
\(208\) 0 0
\(209\) −41.2844 −2.85570
\(210\) −7.76865 + 4.48523i −0.536088 + 0.309510i
\(211\) 1.95593 + 3.38776i 0.134652 + 0.233223i 0.925464 0.378835i \(-0.123675\pi\)
−0.790813 + 0.612058i \(0.790342\pi\)
\(212\) −1.92543 + 3.33494i −0.132239 + 0.229045i
\(213\) 9.11960i 0.624865i
\(214\) −10.5110 6.06853i −0.718518 0.414836i
\(215\) 8.88254 + 5.12833i 0.605784 + 0.349749i
\(216\) 1.35690i 0.0923251i
\(217\) 8.43996 14.6184i 0.572942 0.992364i
\(218\) −1.87047 3.23975i −0.126684 0.219423i
\(219\) 2.55571 1.47554i 0.172699 0.0997078i
\(220\) 9.34481 0.630027
\(221\) 0 0
\(222\) 11.2567 0.755498
\(223\) −6.45133 + 3.72468i −0.432013 + 0.249423i −0.700204 0.713943i \(-0.746908\pi\)
0.268191 + 0.963366i \(0.413574\pi\)
\(224\) 10.6555 + 18.4558i 0.711949 + 1.23313i
\(225\) −1.45593 + 2.52174i −0.0970618 + 0.168116i
\(226\) 11.1153i 0.739378i
\(227\) −18.4030 10.6250i −1.22145 0.705205i −0.256223 0.966618i \(-0.582478\pi\)
−0.965227 + 0.261413i \(0.915812\pi\)
\(228\) −8.59696 4.96346i −0.569348 0.328713i
\(229\) 9.29590i 0.614290i 0.951663 + 0.307145i \(0.0993737\pi\)
−0.951663 + 0.307145i \(0.900626\pi\)
\(230\) 3.68329 6.37965i 0.242869 0.420662i
\(231\) −8.93296 15.4723i −0.587746 1.01801i
\(232\) 4.59684 2.65399i 0.301798 0.174243i
\(233\) −16.2107 −1.06200 −0.531000 0.847372i \(-0.678184\pi\)
−0.531000 + 0.847372i \(0.678184\pi\)
\(234\) 0 0
\(235\) 15.2489 0.994728
\(236\) −2.02808 + 1.17092i −0.132017 + 0.0762201i
\(237\) 4.71648 + 8.16918i 0.306368 + 0.530645i
\(238\) −2.33728 + 4.04829i −0.151503 + 0.262412i
\(239\) 13.5090i 0.873826i 0.899504 + 0.436913i \(0.143928\pi\)
−0.899504 + 0.436913i \(0.856072\pi\)
\(240\) −6.18088 3.56853i −0.398974 0.230348i
\(241\) −5.42890 3.13437i −0.349706 0.201903i 0.314850 0.949142i \(-0.398046\pi\)
−0.664556 + 0.747239i \(0.731379\pi\)
\(242\) 28.6407i 1.84109i
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) 2.08546 + 3.61212i 0.133508 + 0.231242i
\(245\) 6.09242 3.51746i 0.389230 0.224722i
\(246\) −3.24698 −0.207020
\(247\) 0 0
\(248\) 6.64848 0.422179
\(249\) 5.60042 3.23341i 0.354912 0.204909i
\(250\) 10.3007 + 17.8414i 0.651476 + 1.12839i
\(251\) −0.376510 + 0.652135i −0.0237651 + 0.0411624i −0.877663 0.479278i \(-0.840899\pi\)
0.853898 + 0.520440i \(0.174232\pi\)
\(252\) 4.29590i 0.270616i
\(253\) 12.7060 + 7.33579i 0.798817 + 0.461197i
\(254\) 22.2563 + 12.8497i 1.39648 + 0.806259i
\(255\) 1.08815i 0.0681423i
\(256\) −10.3557 + 17.9366i −0.647231 + 1.12104i
\(257\) 9.86323 + 17.0836i 0.615252 + 1.06565i 0.990340 + 0.138658i \(0.0442789\pi\)
−0.375089 + 0.926989i \(0.622388\pi\)
\(258\) −11.0763 + 6.39493i −0.689583 + 0.398131i
\(259\) −21.5211 −1.33726
\(260\) 0 0
\(261\) −3.91185 −0.242138
\(262\) −35.2702 + 20.3632i −2.17900 + 1.25804i
\(263\) 8.80463 + 15.2501i 0.542917 + 0.940359i 0.998735 + 0.0502861i \(0.0160133\pi\)
−0.455818 + 0.890073i \(0.650653\pi\)
\(264\) 3.51842 6.09408i 0.216544 0.375065i
\(265\) 4.46250i 0.274129i
\(266\) 42.7977 + 24.7092i 2.62409 + 1.51502i
\(267\) −1.00358 0.579417i −0.0614181 0.0354597i
\(268\) 5.66487i 0.346037i
\(269\) 8.19351 14.1916i 0.499567 0.865276i −0.500433 0.865776i \(-0.666826\pi\)
1.00000 0.000499532i \(0.000159006\pi\)
\(270\) 1.30194 + 2.25502i 0.0792334 + 0.137236i
\(271\) −0.688692 + 0.397616i −0.0418351 + 0.0241535i −0.520772 0.853696i \(-0.674356\pi\)
0.478937 + 0.877849i \(0.341022\pi\)
\(272\) −3.71917 −0.225508
\(273\) 0 0
\(274\) −24.5700 −1.48433
\(275\) −13.0777 + 7.55041i −0.788615 + 0.455307i
\(276\) 1.76391 + 3.05517i 0.106175 + 0.183900i
\(277\) −2.41670 + 4.18584i −0.145205 + 0.251503i −0.929450 0.368949i \(-0.879718\pi\)
0.784244 + 0.620452i \(0.213051\pi\)
\(278\) 31.7168i 1.90225i
\(279\) −4.24333 2.44989i −0.254041 0.146671i
\(280\) 5.84995 + 3.37747i 0.349601 + 0.201842i
\(281\) 18.7748i 1.12001i 0.828489 + 0.560005i \(0.189201\pi\)
−0.828489 + 0.560005i \(0.810799\pi\)
\(282\) −9.50753 + 16.4675i −0.566165 + 0.980627i
\(283\) −3.95862 6.85652i −0.235315 0.407578i 0.724049 0.689749i \(-0.242279\pi\)
−0.959364 + 0.282171i \(0.908946\pi\)
\(284\) −9.84841 + 5.68598i −0.584395 + 0.337401i
\(285\) −11.5036 −0.681417
\(286\) 0 0
\(287\) 6.20775 0.366432
\(288\) 5.35722 3.09299i 0.315677 0.182256i
\(289\) 8.21648 + 14.2314i 0.483322 + 0.837139i
\(290\) −5.09299 + 8.82132i −0.299071 + 0.518006i
\(291\) 8.65817i 0.507551i
\(292\) 3.18692 + 1.83997i 0.186500 + 0.107676i
\(293\) −5.69769 3.28956i −0.332862 0.192178i 0.324249 0.945972i \(-0.394888\pi\)
−0.657111 + 0.753794i \(0.728222\pi\)
\(294\) 8.77240i 0.511617i
\(295\) −1.35690 + 2.35021i −0.0790015 + 0.136835i
\(296\) −4.23825 7.34087i −0.246343 0.426679i
\(297\) −4.49119 + 2.59299i −0.260605 + 0.150461i
\(298\) −22.9541 −1.32969
\(299\) 0 0
\(300\) −3.63102 −0.209637
\(301\) 21.1763 12.2262i 1.22058 0.704705i
\(302\) −14.0918 24.4077i −0.810892 1.40451i
\(303\) −4.23825 + 7.34087i −0.243481 + 0.421722i
\(304\) 39.3183i 2.25506i
\(305\) 4.18584 + 2.41670i 0.239681 + 0.138380i
\(306\) 1.17511 + 0.678448i 0.0671764 + 0.0387843i
\(307\) 24.8649i 1.41911i −0.704649 0.709556i \(-0.748895\pi\)
0.704649 0.709556i \(-0.251105\pi\)
\(308\) 11.1392 19.2937i 0.634716 1.09936i
\(309\) 2.82371 + 4.89081i 0.160635 + 0.278228i
\(310\) −11.0491 + 6.37920i −0.627546 + 0.362314i
\(311\) 17.0804 0.968539 0.484270 0.874919i \(-0.339085\pi\)
0.484270 + 0.874919i \(0.339085\pi\)
\(312\) 0 0
\(313\) 15.6974 0.887269 0.443635 0.896208i \(-0.353689\pi\)
0.443635 + 0.896208i \(0.353689\pi\)
\(314\) 1.28542 0.742135i 0.0725402 0.0418811i
\(315\) −2.48911 4.31127i −0.140246 0.242913i
\(316\) −5.88135 + 10.1868i −0.330852 + 0.573053i
\(317\) 32.7821i 1.84123i −0.390477 0.920613i \(-0.627690\pi\)
0.390477 0.920613i \(-0.372310\pi\)
\(318\) −4.81913 2.78232i −0.270243 0.156025i
\(319\) −17.5689 10.1434i −0.983669 0.567921i
\(320\) 1.83340i 0.102490i
\(321\) 3.36778 5.83317i 0.187971 0.325576i
\(322\) −8.78113 15.2094i −0.489353 0.847584i
\(323\) −5.19150 + 2.99731i −0.288863 + 0.166775i
\(324\) −1.24698 −0.0692766
\(325\) 0 0
\(326\) 11.2959 0.625622
\(327\) 1.79792 1.03803i 0.0994255 0.0574033i
\(328\) 1.22252 + 2.11747i 0.0675024 + 0.116918i
\(329\) 18.1770 31.4835i 1.00213 1.73574i
\(330\) 13.5036i 0.743351i
\(331\) −25.2549 14.5809i −1.38813 0.801439i −0.395029 0.918669i \(-0.629265\pi\)
−0.993105 + 0.117230i \(0.962599\pi\)
\(332\) 6.98361 + 4.03199i 0.383276 + 0.221284i
\(333\) 6.24698i 0.342332i
\(334\) 6.71260 11.6266i 0.367297 0.636177i
\(335\) −3.28232 5.68515i −0.179332 0.310613i
\(336\) −14.7355 + 8.50753i −0.803886 + 0.464124i
\(337\) 33.2911 1.81348 0.906741 0.421688i \(-0.138562\pi\)
0.906741 + 0.421688i \(0.138562\pi\)
\(338\) 0 0
\(339\) 6.16852 0.335028
\(340\) 1.17511 0.678448i 0.0637291 0.0367940i
\(341\) −12.7051 22.0058i −0.688018 1.19168i
\(342\) 7.17241 12.4230i 0.387839 0.671757i
\(343\) 7.34375i 0.396525i
\(344\) 8.34071 + 4.81551i 0.449701 + 0.259635i
\(345\) 3.54044 + 2.04407i 0.190611 + 0.110049i
\(346\) 3.62133i 0.194684i
\(347\) 0.436845 0.756638i 0.0234511 0.0406185i −0.854062 0.520172i \(-0.825868\pi\)
0.877513 + 0.479553i \(0.159201\pi\)
\(348\) −2.43900 4.22447i −0.130744 0.226456i
\(349\) −2.79892 + 1.61596i −0.149823 + 0.0865002i −0.573037 0.819529i \(-0.694235\pi\)
0.423215 + 0.906029i \(0.360902\pi\)
\(350\) 18.0761 0.966206
\(351\) 0 0
\(352\) 32.0804 1.70989
\(353\) −7.05529 + 4.07338i −0.375515 + 0.216804i −0.675865 0.737025i \(-0.736230\pi\)
0.300350 + 0.953829i \(0.402897\pi\)
\(354\) −1.69202 2.93067i −0.0899299 0.155763i
\(355\) −6.58911 + 11.4127i −0.349713 + 0.605721i
\(356\) 1.44504i 0.0765871i
\(357\) −2.24663 1.29709i −0.118904 0.0686495i
\(358\) −31.2680 18.0526i −1.65256 0.954108i
\(359\) 2.64071i 0.139371i 0.997569 + 0.0696857i \(0.0221996\pi\)
−0.997569 + 0.0696857i \(0.977800\pi\)
\(360\) 0.980386 1.69808i 0.0516709 0.0894966i
\(361\) 22.1869 + 38.4289i 1.16773 + 2.02257i
\(362\) 37.6439 21.7337i 1.97852 1.14230i
\(363\) −15.8944 −0.834239
\(364\) 0 0
\(365\) 4.26444 0.223211
\(366\) −5.21966 + 3.01357i −0.272836 + 0.157522i
\(367\) 1.45204 + 2.51501i 0.0757960 + 0.131282i 0.901432 0.432920i \(-0.142517\pi\)
−0.825636 + 0.564203i \(0.809184\pi\)
\(368\) 6.98643 12.1008i 0.364193 0.630800i
\(369\) 1.80194i 0.0938051i
\(370\) 14.0871 + 8.13318i 0.732352 + 0.422824i
\(371\) 9.21346 + 5.31940i 0.478339 + 0.276169i
\(372\) 6.10992i 0.316784i
\(373\) 4.19926 7.27333i 0.217429 0.376599i −0.736592 0.676337i \(-0.763566\pi\)
0.954021 + 0.299739i \(0.0968995\pi\)
\(374\) 3.51842 + 6.09408i 0.181933 + 0.315117i
\(375\) −9.90123 + 5.71648i −0.511298 + 0.295198i
\(376\) 14.3187 0.738432
\(377\) 0 0
\(378\) 6.20775 0.319292
\(379\) −13.6384 + 7.87412i −0.700556 + 0.404466i −0.807555 0.589793i \(-0.799209\pi\)
0.106998 + 0.994259i \(0.465876\pi\)
\(380\) −7.17241 12.4230i −0.367937 0.637285i
\(381\) −7.13102 + 12.3513i −0.365333 + 0.632776i
\(382\) 12.7584i 0.652776i
\(383\) 11.0319 + 6.36927i 0.563704 + 0.325455i 0.754631 0.656150i \(-0.227816\pi\)
−0.190927 + 0.981604i \(0.561149\pi\)
\(384\) −8.73452 5.04288i −0.445732 0.257343i
\(385\) 25.8170i 1.31576i
\(386\) −8.80074 + 15.2433i −0.447946 + 0.775865i
\(387\) −3.54892 6.14691i −0.180402 0.312465i
\(388\) 9.35010 5.39828i 0.474679 0.274056i
\(389\) 0.310371 0.0157365 0.00786823 0.999969i \(-0.497495\pi\)
0.00786823 + 0.999969i \(0.497495\pi\)
\(390\) 0 0
\(391\) 2.13036 0.107737
\(392\) 5.72079 3.30290i 0.288943 0.166822i
\(393\) −11.3007 19.5735i −0.570047 0.987350i
\(394\) 21.0928 36.5337i 1.06264 1.84054i
\(395\) 13.6310i 0.685851i
\(396\) −5.60042 3.23341i −0.281432 0.162485i
\(397\) −1.29122 0.745488i −0.0648046 0.0374150i 0.467248 0.884127i \(-0.345246\pi\)
−0.532052 + 0.846712i \(0.678579\pi\)
\(398\) 7.25236i 0.363528i
\(399\) −13.7126 + 23.7509i −0.686488 + 1.18903i
\(400\) 7.19083 + 12.4549i 0.359541 + 0.622744i
\(401\) −20.6403 + 11.9167i −1.03073 + 0.595092i −0.917193 0.398442i \(-0.869551\pi\)
−0.113535 + 0.993534i \(0.536218\pi\)
\(402\) 8.18598 0.408280
\(403\) 0 0
\(404\) −10.5700 −0.525878
\(405\) −1.25144 + 0.722521i −0.0621847 + 0.0359024i
\(406\) 12.1419 + 21.0304i 0.602593 + 1.04372i
\(407\) −16.1984 + 28.0564i −0.802923 + 1.39070i
\(408\) 1.02177i 0.0505852i
\(409\) 3.69570 + 2.13371i 0.182740 + 0.105505i 0.588580 0.808439i \(-0.299687\pi\)
−0.405839 + 0.913945i \(0.633021\pi\)
\(410\) −4.06341 2.34601i −0.200678 0.115861i
\(411\) 13.6353i 0.672581i
\(412\) −3.52111 + 6.09873i −0.173472 + 0.300463i
\(413\) 3.23490 + 5.60301i 0.159179 + 0.275706i
\(414\) −4.41485 + 2.54892i −0.216978 + 0.125272i
\(415\) 9.34481 0.458719
\(416\) 0 0
\(417\) 17.6015 0.861948
\(418\) 64.4253 37.1960i 3.15114 1.81931i
\(419\) −14.8448 25.7120i −0.725217 1.25611i −0.958885 0.283796i \(-0.908406\pi\)
0.233668 0.972316i \(-0.424927\pi\)
\(420\) 3.10388 5.37607i 0.151454 0.262325i
\(421\) 29.3991i 1.43282i −0.697677 0.716412i \(-0.745783\pi\)
0.697677 0.716412i \(-0.254217\pi\)
\(422\) −6.10454 3.52446i −0.297164 0.171568i
\(423\) −9.13879 5.27628i −0.444343 0.256542i
\(424\) 4.19029i 0.203499i
\(425\) −1.09634 + 1.89892i −0.0531804 + 0.0921112i
\(426\) −8.21648 14.2314i −0.398090 0.689512i
\(427\) 9.97923 5.76151i 0.482929 0.278819i
\(428\) 8.39911 0.405986
\(429\) 0 0
\(430\) −18.4819 −0.891275
\(431\) 28.6275 16.5281i 1.37894 0.796131i 0.386907 0.922119i \(-0.373543\pi\)
0.992032 + 0.125988i \(0.0402100\pi\)
\(432\) 2.46950 + 4.27730i 0.118814 + 0.205792i
\(433\) −14.6332 + 25.3454i −0.703226 + 1.21802i 0.264102 + 0.964495i \(0.414924\pi\)
−0.967328 + 0.253528i \(0.918409\pi\)
\(434\) 30.4166i 1.46004i
\(435\) −4.89546 2.82640i −0.234719 0.135515i
\(436\) 2.24198 + 1.29440i 0.107371 + 0.0619908i
\(437\) 22.5217i 1.07736i
\(438\) −2.65883 + 4.60523i −0.127044 + 0.220047i
\(439\) −1.06584 1.84609i −0.0508699 0.0881093i 0.839469 0.543407i \(-0.182866\pi\)
−0.890339 + 0.455298i \(0.849533\pi\)
\(440\) 8.80620 5.08426i 0.419819 0.242383i
\(441\) −4.86831 −0.231824
\(442\) 0 0
\(443\) −22.9922 −1.09239 −0.546197 0.837657i \(-0.683925\pi\)
−0.546197 + 0.837657i \(0.683925\pi\)
\(444\) −6.74621 + 3.89493i −0.320161 + 0.184845i
\(445\) −0.837282 1.45021i −0.0396910 0.0687467i
\(446\) 6.71164 11.6249i 0.317805 0.550455i
\(447\) 12.7385i 0.602513i
\(448\) −3.78531 2.18545i −0.178839 0.103253i
\(449\) 11.2046 + 6.46897i 0.528777 + 0.305289i 0.740518 0.672036i \(-0.234580\pi\)
−0.211741 + 0.977326i \(0.567913\pi\)
\(450\) 5.24698i 0.247345i
\(451\) 4.67241 8.09285i 0.220015 0.381077i
\(452\) 3.84601 + 6.66149i 0.180901 + 0.313330i
\(453\) 13.5453 7.82036i 0.636412 0.367432i
\(454\) 38.2911 1.79709
\(455\) 0 0
\(456\) −10.8019 −0.505847
\(457\) 4.20304 2.42662i 0.196610 0.113513i −0.398463 0.917184i \(-0.630456\pi\)
0.595073 + 0.803672i \(0.297123\pi\)
\(458\) −8.37531 14.5065i −0.391353 0.677843i
\(459\) −0.376510 + 0.652135i −0.0175740 + 0.0304390i
\(460\) 5.09783i 0.237688i
\(461\) 16.3111 + 9.41723i 0.759685 + 0.438604i 0.829183 0.558978i \(-0.188806\pi\)
−0.0694978 + 0.997582i \(0.522140\pi\)
\(462\) 27.8802 + 16.0966i 1.29710 + 0.748883i
\(463\) 22.8767i 1.06317i −0.847005 0.531585i \(-0.821597\pi\)
0.847005 0.531585i \(-0.178403\pi\)
\(464\) −9.66033 + 16.7322i −0.448469 + 0.776772i
\(465\) −3.54019 6.13179i −0.164172 0.284355i
\(466\) 25.2972 14.6054i 1.17187 0.676581i
\(467\) −13.0000 −0.601568 −0.300784 0.953692i \(-0.597248\pi\)
−0.300784 + 0.953692i \(0.597248\pi\)
\(468\) 0 0
\(469\) −15.6504 −0.722668
\(470\) −23.7963 + 13.7388i −1.09764 + 0.633723i
\(471\) 0.411854 + 0.713352i 0.0189772 + 0.0328695i
\(472\) −1.27413 + 2.20685i −0.0586464 + 0.101579i
\(473\) 36.8092i 1.69249i
\(474\) −14.7204 8.49880i −0.676129 0.390363i
\(475\) 20.0750 + 11.5903i 0.921104 + 0.531800i
\(476\) 3.23490i 0.148271i
\(477\) 1.54407 2.67441i 0.0706982 0.122453i
\(478\) −12.1712 21.0812i −0.556698 0.964230i
\(479\) −32.9870 + 19.0450i −1.50721 + 0.870190i −0.507248 + 0.861800i \(0.669337\pi\)
−0.999965 + 0.00838964i \(0.997329\pi\)
\(480\) 8.93900 0.408008
\(481\) 0 0
\(482\) 11.2959 0.514514
\(483\) 8.44056 4.87316i 0.384059 0.221736i
\(484\) −9.90999 17.1646i −0.450454 0.780210i
\(485\) 6.25571 10.8352i 0.284057 0.492001i
\(486\) 1.80194i 0.0817376i
\(487\) −18.4030 10.6250i −0.833920 0.481464i 0.0212730 0.999774i \(-0.493228\pi\)
−0.855193 + 0.518310i \(0.826561\pi\)
\(488\) 3.93051 + 2.26928i 0.177926 + 0.102726i
\(489\) 6.26875i 0.283483i
\(490\) −6.33824 + 10.9782i −0.286333 + 0.495943i
\(491\) −3.17510 5.49943i −0.143290 0.248186i 0.785444 0.618933i \(-0.212435\pi\)
−0.928734 + 0.370748i \(0.879102\pi\)
\(492\) 1.94594 1.12349i 0.0877298 0.0506508i
\(493\) −2.94571 −0.132668
\(494\) 0 0
\(495\) −7.49396 −0.336828
\(496\) −20.9578 + 12.1000i −0.941033 + 0.543306i
\(497\) 15.7087 + 27.2083i 0.704632 + 1.22046i
\(498\) −5.82640 + 10.0916i −0.261087 + 0.452216i
\(499\) 4.65087i 0.208202i 0.994567 + 0.104101i \(0.0331965\pi\)
−0.994567 + 0.104101i \(0.966804\pi\)
\(500\) −12.3466 7.12833i −0.552158 0.318789i
\(501\) 6.45225 + 3.72521i 0.288265 + 0.166430i
\(502\) 1.35690i 0.0605612i
\(503\) −7.73759 + 13.4019i −0.345002 + 0.597561i −0.985354 0.170521i \(-0.945455\pi\)
0.640352 + 0.768081i \(0.278788\pi\)
\(504\) −2.33728 4.04829i −0.104111 0.180325i
\(505\) −10.6079 + 6.12445i −0.472043 + 0.272534i
\(506\) −26.4373 −1.17528
\(507\) 0 0
\(508\) −17.7845 −0.789059
\(509\) 17.7576 10.2524i 0.787092 0.454428i −0.0518459 0.998655i \(-0.516510\pi\)
0.838938 + 0.544227i \(0.183177\pi\)
\(510\) 0.980386 + 1.69808i 0.0434122 + 0.0751921i
\(511\) 5.08330 8.80454i 0.224872 0.389490i
\(512\) 17.1491i 0.757892i
\(513\) 6.89423 + 3.98039i 0.304388 + 0.175738i
\(514\) −30.7836 17.7729i −1.35781 0.783930i
\(515\) 8.16075i 0.359606i
\(516\) 4.42543 7.66507i 0.194819 0.337436i
\(517\) −27.3627 47.3936i −1.20341 2.08437i
\(518\) 33.5842 19.3898i 1.47561 0.851941i
\(519\) 2.00969 0.0882155
\(520\) 0 0
\(521\) −42.0267 −1.84122 −0.920611 0.390481i \(-0.872309\pi\)
−0.920611 + 0.390481i \(0.872309\pi\)
\(522\) 6.10454 3.52446i 0.267189 0.154261i
\(523\) 14.9943 + 25.9708i 0.655653 + 1.13562i 0.981730 + 0.190281i \(0.0609399\pi\)
−0.326077 + 0.945343i \(0.605727\pi\)
\(524\) 14.0918 24.4077i 0.615603 1.06626i
\(525\) 10.0315i 0.437809i
\(526\) −27.4797 15.8654i −1.19817 0.691764i
\(527\) −3.19531 1.84481i −0.139190 0.0803614i
\(528\) 25.6136i 1.11469i
\(529\) 7.49814 12.9872i 0.326006 0.564659i
\(530\) −4.02057 6.96384i −0.174643 0.302490i
\(531\) 1.62640 0.939001i 0.0705796 0.0407492i
\(532\) −34.1987 −1.48270
\(533\) 0 0
\(534\) 2.08815 0.0903629
\(535\) 8.42917 4.86658i 0.364425 0.210401i
\(536\) −3.08211 5.33836i −0.133127 0.230582i
\(537\) 10.0184 17.3524i 0.432327 0.748812i
\(538\) 29.5284i 1.27306i
\(539\) −21.8645 12.6235i −0.941772 0.543732i
\(540\) −1.56052 0.900969i −0.0671543 0.0387715i
\(541\) 36.3803i 1.56411i 0.623208 + 0.782056i \(0.285829\pi\)
−0.623208 + 0.782056i \(0.714171\pi\)
\(542\) 0.716480 1.24098i 0.0307755 0.0533047i
\(543\) 12.0613 + 20.8908i 0.517600 + 0.896509i
\(544\) 4.03409 2.32908i 0.172960 0.0998587i
\(545\) 3.00000 0.128506
\(546\) 0 0
\(547\) −25.8159 −1.10381 −0.551905 0.833907i \(-0.686099\pi\)
−0.551905 + 0.833907i \(0.686099\pi\)
\(548\) 14.7250 8.50149i 0.629022 0.363166i
\(549\) −1.67241 2.89669i −0.0713766 0.123628i
\(550\) 13.6054 23.5652i 0.580135 1.00482i
\(551\) 31.1414i 1.32667i
\(552\) 3.32448 + 1.91939i 0.141499 + 0.0816945i
\(553\) 28.1432 + 16.2485i 1.19677 + 0.690955i
\(554\) 8.70948i 0.370030i
\(555\) −4.51357 + 7.81774i −0.191591 + 0.331845i
\(556\) 10.9743 + 19.0081i 0.465416 + 0.806124i
\(557\) 15.5801 8.99516i 0.660149 0.381137i −0.132185 0.991225i \(-0.542199\pi\)
0.792334 + 0.610088i \(0.208866\pi\)
\(558\) 8.82908 0.373765
\(559\) 0 0
\(560\) −24.5875 −1.03901
\(561\) −3.38196 + 1.95257i −0.142786 + 0.0824378i
\(562\) −16.9155 29.2985i −0.713537 1.23588i
\(563\) −19.5661 + 33.8895i −0.824614 + 1.42827i 0.0775992 + 0.996985i \(0.475275\pi\)
−0.902214 + 0.431289i \(0.858059\pi\)
\(564\) 13.1588i 0.554087i
\(565\) 7.71955 + 4.45689i 0.324764 + 0.187503i
\(566\) 12.3550 + 7.13318i 0.519321 + 0.299830i
\(567\) 3.44504i 0.144678i
\(568\) −6.18718 + 10.7165i −0.259608 + 0.449655i
\(569\) 15.3001 + 26.5005i 0.641413 + 1.11096i 0.985118 + 0.171882i \(0.0549846\pi\)
−0.343705 + 0.939078i \(0.611682\pi\)
\(570\) 17.9517 10.3644i 0.751915 0.434118i
\(571\) 2.96184 0.123949 0.0619745 0.998078i \(-0.480260\pi\)
0.0619745 + 0.998078i \(0.480260\pi\)
\(572\) 0 0
\(573\) −7.08038 −0.295787
\(574\) −9.68734 + 5.59299i −0.404342 + 0.233447i
\(575\) −4.11894 7.13422i −0.171772 0.297517i
\(576\) −0.634375 + 1.09877i −0.0264323 + 0.0457821i
\(577\) 0.819396i 0.0341119i 0.999855 + 0.0170560i \(0.00542934\pi\)
−0.999855 + 0.0170560i \(0.994571\pi\)
\(578\) −25.6440 14.8056i −1.06665 0.615831i
\(579\) −8.45941 4.88404i −0.351561 0.202974i
\(580\) 7.04892i 0.292690i
\(581\) 11.1392 19.2937i 0.462133 0.800437i
\(582\) 7.80074 + 13.5113i 0.323351 + 0.560061i
\(583\) 13.8695 8.00753i 0.574414 0.331638i
\(584\) 4.00431 0.165700
\(585\) 0 0
\(586\) 11.8552 0.489732
\(587\) 27.5392 15.8998i 1.13666 0.656254i 0.191062 0.981578i \(-0.438807\pi\)
0.945603 + 0.325324i \(0.105473\pi\)
\(588\) −3.03534 5.25737i −0.125175 0.216810i
\(589\) −19.5030 + 33.7802i −0.803606 + 1.39189i
\(590\) 4.89008i 0.201322i
\(591\) 20.2747 + 11.7056i 0.833989 + 0.481504i
\(592\) 26.7202 + 15.4269i 1.09819 + 0.634042i
\(593\) 4.26337i 0.175076i −0.996161 0.0875379i \(-0.972100\pi\)
0.996161 0.0875379i \(-0.0278999\pi\)
\(594\) 4.67241 8.09285i 0.191711 0.332054i
\(595\) −1.87435 3.24648i −0.0768410 0.133093i
\(596\) 13.7566 7.94235i 0.563491 0.325331i
\(597\) −4.02475 −0.164722
\(598\) 0 0
\(599\) 24.7278 1.01035 0.505175 0.863017i \(-0.331428\pi\)
0.505175 + 0.863017i \(0.331428\pi\)
\(600\) −3.42174 + 1.97554i −0.139692 + 0.0806511i
\(601\) −3.41185 5.90950i −0.139172 0.241054i 0.788011 0.615661i \(-0.211111\pi\)
−0.927184 + 0.374607i \(0.877778\pi\)
\(602\) −22.0308 + 38.1585i −0.897908 + 1.55522i
\(603\) 4.54288i 0.185000i
\(604\) 16.8907 + 9.75182i 0.687271 + 0.396796i
\(605\) −19.8909 11.4840i −0.808681 0.466892i
\(606\) 15.2741i 0.620469i
\(607\) −15.9981 + 27.7096i −0.649344 + 1.12470i 0.333935 + 0.942596i \(0.391623\pi\)
−0.983280 + 0.182102i \(0.941710\pi\)
\(608\) −24.6226 42.6476i −0.998578 1.72959i
\(609\) −11.6710 + 6.73825i −0.472932 + 0.273048i
\(610\) −8.70948 −0.352637
\(611\) 0 0
\(612\) −0.939001 −0.0379569
\(613\) −29.0876 + 16.7937i −1.17484 + 0.678293i −0.954815 0.297202i \(-0.903947\pi\)
−0.220023 + 0.975495i \(0.570613\pi\)
\(614\) 22.4025 + 38.8022i 0.904090 + 1.56593i
\(615\) 1.30194 2.25502i 0.0524992 0.0909313i
\(616\) 24.2422i 0.976746i
\(617\) −23.0250 13.2935i −0.926953 0.535176i −0.0411061 0.999155i \(-0.513088\pi\)
−0.885846 + 0.463978i \(0.846421\pi\)
\(618\) −8.81293 5.08815i −0.354508 0.204675i
\(619\) 9.17928i 0.368946i −0.982838 0.184473i \(-0.940942\pi\)
0.982838 0.184473i \(-0.0590579\pi\)
\(620\) 4.41454 7.64621i 0.177292 0.307079i
\(621\) −1.41454 2.45006i −0.0567636 0.0983175i
\(622\) −26.6543 + 15.3889i −1.06874 + 0.617038i
\(623\) −3.99223 −0.159945
\(624\) 0 0
\(625\) −1.96184 −0.0784735
\(626\) −24.4962 + 14.1429i −0.979064 + 0.565263i
\(627\) 20.6422 + 35.7533i 0.824370 + 1.42785i
\(628\) −0.513574 + 0.889535i −0.0204938 + 0.0354963i
\(629\) 4.70410i 0.187565i
\(630\) 7.76865 + 4.48523i 0.309510 + 0.178696i
\(631\) −14.7262 8.50216i −0.586239 0.338465i 0.177370 0.984144i \(-0.443241\pi\)
−0.763609 + 0.645679i \(0.776575\pi\)
\(632\) 12.7995i 0.509139i
\(633\) 1.95593 3.38776i 0.0777411 0.134652i
\(634\) 29.5356 + 51.1572i 1.17301 + 2.03171i
\(635\) −17.8481 + 10.3046i −0.708282 + 0.408927i
\(636\) 3.85086 0.152696
\(637\) 0 0
\(638\) 36.5555 1.44725
\(639\) 7.89781 4.55980i 0.312433 0.180383i
\(640\) −7.28717 12.6217i −0.288051 0.498918i
\(641\) −10.8324 + 18.7623i −0.427856 + 0.741068i −0.996682 0.0813898i \(-0.974064\pi\)
0.568827 + 0.822457i \(0.307397\pi\)
\(642\) 12.1371i 0.479012i
\(643\) 8.10216 + 4.67778i 0.319518 + 0.184474i 0.651178 0.758925i \(-0.274275\pi\)
−0.331660 + 0.943399i \(0.607609\pi\)
\(644\) 10.5252 + 6.07673i 0.414751 + 0.239457i
\(645\) 10.2567i 0.403856i
\(646\) 5.40097 9.35475i 0.212498 0.368058i
\(647\) −0.351388 0.608621i −0.0138145 0.0239274i 0.859036 0.511916i \(-0.171064\pi\)
−0.872850 + 0.487989i \(0.837731\pi\)
\(648\) −1.17511 + 0.678448i −0.0461625 + 0.0266520i
\(649\) 9.73928 0.382300
\(650\) 0 0
\(651\) −16.8799 −0.661576
\(652\) −6.76972 + 3.90850i −0.265123 + 0.153069i
\(653\) 18.6705 + 32.3383i 0.730635 + 1.26550i 0.956612 + 0.291364i \(0.0941092\pi\)
−0.225977 + 0.974133i \(0.572557\pi\)
\(654\) −1.87047 + 3.23975i −0.0731411 + 0.126684i
\(655\) 32.6601i 1.27614i
\(656\) −7.70743 4.44989i −0.300925 0.173739i
\(657\) −2.55571 1.47554i −0.0997078 0.0575664i
\(658\) 65.5077i 2.55376i
\(659\) 0.367781 0.637015i 0.0143267 0.0248146i −0.858773 0.512356i \(-0.828773\pi\)
0.873100 + 0.487541i \(0.162106\pi\)
\(660\) −4.67241 8.09285i −0.181873 0.315014i
\(661\) 11.9931 6.92423i 0.466478 0.269321i −0.248286 0.968687i \(-0.579867\pi\)
0.714764 + 0.699365i \(0.246534\pi\)
\(662\) 52.5478 2.04233
\(663\) 0 0
\(664\) 8.77479 0.340528
\(665\) −34.3211 + 19.8153i −1.33091 + 0.768403i
\(666\) −5.62833 9.74856i −0.218094 0.377749i
\(667\) 5.53348 9.58427i 0.214257 0.371105i
\(668\) 9.29052i 0.359461i
\(669\) 6.45133 + 3.72468i 0.249423 + 0.144004i
\(670\) 10.2443 + 5.91454i 0.395771 + 0.228499i
\(671\) 17.3461i 0.669640i
\(672\) 10.6555 18.4558i 0.411044 0.711949i
\(673\) −3.17510 5.49943i −0.122391 0.211987i 0.798319 0.602235i \(-0.205723\pi\)
−0.920710 + 0.390247i \(0.872390\pi\)
\(674\) −51.9516 + 29.9943i −2.00110 + 1.15534i
\(675\) 2.91185 0.112077
\(676\) 0 0
\(677\) 33.7241 1.29612 0.648061 0.761589i \(-0.275580\pi\)
0.648061 + 0.761589i \(0.275580\pi\)
\(678\) −9.62613 + 5.55765i −0.369689 + 0.213440i
\(679\) −14.9139 25.8316i −0.572342 0.991326i
\(680\) 0.738250 1.27869i 0.0283106 0.0490354i
\(681\) 21.2500i 0.814300i
\(682\) 39.6531 + 22.8937i 1.51840 + 0.876646i
\(683\) −16.6872 9.63437i −0.638519 0.368649i 0.145525 0.989355i \(-0.453513\pi\)
−0.784044 + 0.620705i \(0.786846\pi\)
\(684\) 9.92692i 0.379565i
\(685\) 9.85181 17.0638i 0.376418 0.651976i
\(686\) −6.61649 11.4601i −0.252619 0.437548i
\(687\) 8.05048 4.64795i 0.307145 0.177330i
\(688\) −35.0562 −1.33651
\(689\) 0 0
\(690\) −7.36658 −0.280441
\(691\) 34.1223 19.7005i 1.29807 0.749443i 0.318002 0.948090i \(-0.396988\pi\)
0.980071 + 0.198647i \(0.0636548\pi\)
\(692\) 1.25302 + 2.17029i 0.0476327 + 0.0825022i
\(693\) −8.93296 + 15.4723i −0.339335 + 0.587746i
\(694\) 1.57434i 0.0597610i
\(695\) 22.0273 + 12.7174i 0.835541 + 0.482400i
\(696\) −4.59684 2.65399i −0.174243 0.100599i
\(697\) 1.35690i 0.0513961i
\(698\) 2.91185 5.04348i 0.110215 0.190898i
\(699\) 8.10537 + 14.0389i 0.306573 + 0.531000i
\(700\) −10.8331 + 6.25451i −0.409454 + 0.236398i
\(701\) −18.3985 −0.694902 −0.347451 0.937698i \(-0.612953\pi\)
−0.347451 + 0.937698i \(0.612953\pi\)
\(702\) 0 0
\(703\) 49.7308 1.87563
\(704\) −5.69820 + 3.28986i −0.214759 + 0.123991i
\(705\) −7.62445 13.2059i −0.287153 0.497364i
\(706\) 7.33997 12.7132i 0.276243 0.478468i
\(707\) 29.2019i 1.09825i
\(708\) 2.02808 + 1.17092i 0.0762201 + 0.0440057i
\(709\) 33.3033 + 19.2277i 1.25073 + 0.722110i 0.971255 0.238043i \(-0.0765058\pi\)
0.279476 + 0.960153i \(0.409839\pi\)
\(710\) 23.7463i 0.891183i
\(711\) 4.71648 8.16918i 0.176882 0.306368i
\(712\) −0.786208 1.36175i −0.0294644 0.0510338i
\(713\) 12.0047 6.93094i 0.449581 0.259566i
\(714\) 4.67456 0.174941
\(715\) 0 0
\(716\) 24.9855 0.933753
\(717\) 11.6992 6.75451i 0.436913 0.252252i
\(718\) −2.37920 4.12089i −0.0887909 0.153790i
\(719\) 24.2500 42.0022i 0.904371 1.56642i 0.0826117 0.996582i \(-0.473674\pi\)
0.821759 0.569835i \(-0.192993\pi\)
\(720\) 7.13706i 0.265983i
\(721\) 16.8490 + 9.72779i 0.627491 + 0.362282i
\(722\) −69.2465 39.9795i −2.57709 1.48788i
\(723\) 6.26875i 0.233137i
\(724\) −15.0402 + 26.0504i −0.558964 + 0.968154i
\(725\) 5.69537 + 9.86468i 0.211521 + 0.366365i
\(726\) 24.8036 14.3204i 0.920547 0.531478i
\(727\) −19.0344 −0.705948 −0.352974 0.935633i \(-0.614830\pi\)
−0.352974 + 0.935633i \(0.614830\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −6.65476 + 3.84213i −0.246304 + 0.142203i
\(731\) −2.67241 4.62874i −0.0988425 0.171200i
\(732\) 2.08546 3.61212i 0.0770807 0.133508i
\(733\) 24.6213i 0.909410i −0.890642 0.454705i \(-0.849745\pi\)
0.890642 0.454705i \(-0.150255\pi\)
\(734\) −4.53189 2.61649i −0.167275 0.0965764i
\(735\) −6.09242 3.51746i −0.224722 0.129743i
\(736\) 17.5007i 0.645083i
\(737\) −11.7796 + 20.4029i −0.433908 + 0.751551i
\(738\) 1.62349 + 2.81197i 0.0597615 + 0.103510i
\(739\) −38.5481 + 22.2558i −1.41802 + 0.818692i −0.996124 0.0879549i \(-0.971967\pi\)
−0.421891 + 0.906647i \(0.638634\pi\)
\(740\) −11.2567 −0.413803
\(741\) 0 0
\(742\) −19.1704 −0.703769
\(743\) −9.01636 + 5.20560i −0.330778 + 0.190975i −0.656186 0.754599i \(-0.727832\pi\)
0.325408 + 0.945574i \(0.394498\pi\)
\(744\) −3.32424 5.75775i −0.121873 0.211089i
\(745\) 9.20387 15.9416i 0.337204 0.584054i
\(746\) 15.1336i 0.554081i
\(747\) −5.60042 3.23341i −0.204909 0.118304i
\(748\) −4.21723 2.43482i −0.154197 0.0890259i
\(749\) 23.2043i 0.847866i
\(750\) 10.3007 17.8414i 0.376130 0.651476i
\(751\) 0.849896 + 1.47206i 0.0310131 + 0.0537163i 0.881115 0.472901i \(-0.156793\pi\)
−0.850102 + 0.526618i \(0.823460\pi\)
\(752\) −45.1365 + 26.0596i −1.64596 + 0.950295i
\(753\) 0.753020 0.0274416
\(754\) 0 0
\(755\) 22.6015 0.822552
\(756\) −3.72036 + 2.14795i −0.135308 + 0.0781201i
\(757\) −13.7126 23.7509i −0.498393 0.863242i 0.501606 0.865096i \(-0.332743\pi\)
−0.999998 + 0.00185490i \(0.999410\pi\)
\(758\) 14.1887 24.5755i 0.515356 0.892622i
\(759\) 14.6716i 0.532545i
\(760\) −13.5180 7.80463i −0.490350 0.283104i
\(761\) 4.35271 + 2.51304i 0.157786 + 0.0910977i 0.576814 0.816876i \(-0.304296\pi\)
−0.419028 + 0.907973i \(0.637629\pi\)
\(762\) 25.6993i 0.930988i
\(763\) 3.57606 6.19393i 0.129462 0.224235i
\(764\) −4.41454 7.64621i −0.159713 0.276630i
\(765\) −0.942362 + 0.544073i −0.0340712 + 0.0196710i
\(766\) −22.9541 −0.829364
\(767\) 0 0
\(768\) 20.7114 0.747358
\(769\) −36.7590 + 21.2228i −1.32556 + 0.765314i −0.984610 0.174766i \(-0.944083\pi\)
−0.340953 + 0.940080i \(0.610750\pi\)
\(770\) 23.2603 + 40.2880i 0.838244 + 1.45188i
\(771\) 9.86323 17.0836i 0.355216 0.615252i
\(772\) 12.1806i 0.438390i
\(773\) 22.8278 + 13.1796i 0.821059 + 0.474039i 0.850782 0.525519i \(-0.176129\pi\)
−0.0297223 + 0.999558i \(0.509462\pi\)
\(774\) 11.0763 + 6.39493i 0.398131 + 0.229861i
\(775\) 14.2674i 0.512501i
\(776\) 5.87412 10.1743i 0.210869 0.365235i
\(777\) 10.7606 + 18.6378i 0.386033 + 0.668628i
\(778\) −0.484342 + 0.279635i −0.0173645 + 0.0100254i
\(779\) −14.3448 −0.513956
\(780\) 0 0