Properties

Label 349.2.e.a.123.16
Level 349
Weight 2
Character 349.123
Analytic conductor 2.787
Analytic rank 0
Dimension 58
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 349 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 349.e (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.78677903054\)
Analytic rank: \(0\)
Dimension: \(58\)
Relative dimension: \(29\) over \(\Q(\zeta_{6})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 123.16
Character \(\chi\) = 349.123
Dual form 349.2.e.a.227.16

$q$-expansion

\(f(q)\) \(=\) \(q+(0.228167 - 0.131732i) q^{2} +(0.150552 - 0.260763i) q^{3} +(-0.965293 + 1.67194i) q^{4} +(0.807178 - 1.39807i) q^{5} -0.0793300i q^{6} +(1.23534 - 0.713223i) q^{7} +1.03557i q^{8} +(1.45467 + 2.51956i) q^{9} +O(q^{10})\) \(q+(0.228167 - 0.131732i) q^{2} +(0.150552 - 0.260763i) q^{3} +(-0.965293 + 1.67194i) q^{4} +(0.807178 - 1.39807i) q^{5} -0.0793300i q^{6} +(1.23534 - 0.713223i) q^{7} +1.03557i q^{8} +(1.45467 + 2.51956i) q^{9} -0.425325i q^{10} +2.29478i q^{11} +(0.290653 + 0.503426i) q^{12} +(0.932614 - 0.538445i) q^{13} +(0.187909 - 0.325468i) q^{14} +(-0.243044 - 0.420964i) q^{15} +(-1.79417 - 3.10759i) q^{16} +6.95728 q^{17} +(0.663814 + 0.383253i) q^{18} +(0.461520 - 0.799377i) q^{19} +(1.55833 + 2.69910i) q^{20} -0.429508i q^{21} +(0.302296 + 0.523593i) q^{22} +(-2.46875 - 4.27600i) q^{23} +(0.270038 + 0.155907i) q^{24} +(1.19693 + 2.07314i) q^{25} +(0.141861 - 0.245710i) q^{26} +1.77932 q^{27} +2.75388i q^{28} +(-4.87947 + 8.45149i) q^{29} +(-0.110909 - 0.0640334i) q^{30} +10.1669 q^{31} +(-2.61240 - 1.50827i) q^{32} +(0.598395 + 0.345483i) q^{33} +(1.58742 - 0.916497i) q^{34} -2.30279i q^{35} -5.61673 q^{36} -0.988427 q^{37} -0.243188i q^{38} -0.324255i q^{39} +(1.44780 + 0.835888i) q^{40} -9.20028 q^{41} +(-0.0565800 - 0.0979994i) q^{42} +(-3.45983 - 1.99754i) q^{43} +(-3.83673 - 2.21514i) q^{44} +4.69670 q^{45} +(-1.12657 - 0.650427i) q^{46} -7.91493i q^{47} -1.08046 q^{48} +(-2.48262 + 4.30003i) q^{49} +(0.546199 + 0.315348i) q^{50} +(1.04743 - 1.81420i) q^{51} +2.07903i q^{52} -11.3001i q^{53} +(0.405982 - 0.234394i) q^{54} +(3.20827 + 1.85230i) q^{55} +(0.738592 + 1.27928i) q^{56} +(-0.138965 - 0.240695i) q^{57} +2.57113i q^{58} +(-7.66776 - 4.42698i) q^{59} +0.938434 q^{60} -7.83978i q^{61} +(2.31975 - 1.33931i) q^{62} +(3.59402 + 2.07501i) q^{63} +6.38193 q^{64} -1.73848i q^{65} +0.182045 q^{66} -15.4898 q^{67} +(-6.71582 + 11.6321i) q^{68} -1.48670 q^{69} +(-0.303352 - 0.525420i) q^{70} +(-0.457735 + 0.264273i) q^{71} +(-2.60918 + 1.50641i) q^{72} +(-0.909516 + 1.57533i) q^{73} +(-0.225526 + 0.130208i) q^{74} +0.720799 q^{75} +(0.891005 + 1.54327i) q^{76} +(1.63669 + 2.83483i) q^{77} +(-0.0427148 - 0.0739842i) q^{78} +0.588986i q^{79} -5.79285 q^{80} +(-4.09613 + 7.09470i) q^{81} +(-2.09920 + 1.21197i) q^{82} +(3.82294 + 6.62153i) q^{83} +(0.718110 + 0.414601i) q^{84} +(5.61576 - 9.72678i) q^{85} -1.05256 q^{86} +(1.46922 + 2.54477i) q^{87} -2.37640 q^{88} +(-14.4224 - 8.32678i) q^{89} +(1.07163 - 0.618706i) q^{90} +(0.768063 - 1.33032i) q^{91} +9.53226 q^{92} +(1.53065 - 2.65116i) q^{93} +(-1.04265 - 1.80592i) q^{94} +(-0.745058 - 1.29048i) q^{95} +(-0.786601 + 0.454145i) q^{96} +(10.7513 - 6.20729i) q^{97} +1.30817i q^{98} +(-5.78184 + 3.33815i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 58q - 3q^{2} + 27q^{4} + 2q^{5} - 29q^{9} + O(q^{10}) \) \( 58q - 3q^{2} + 27q^{4} + 2q^{5} - 29q^{9} - q^{12} - 3q^{13} - 10q^{14} + q^{15} - 29q^{16} - 10q^{17} + 15q^{18} - 9q^{19} - 3q^{22} - 17q^{23} - 48q^{24} - 29q^{25} - 4q^{26} + 18q^{27} - 2q^{29} + 9q^{30} + 32q^{31} + 9q^{32} - 12q^{33} - 63q^{34} + 24q^{36} - 16q^{37} + 54q^{40} - 10q^{41} - 15q^{42} - 45q^{43} + 18q^{44} - 2q^{45} + 27q^{46} + 6q^{48} + 35q^{49} + 6q^{50} - 14q^{51} + 27q^{54} + 24q^{55} + 11q^{56} - 29q^{57} - 18q^{59} + 116q^{60} - 9q^{62} - 21q^{63} - 132q^{64} + 130q^{66} + 58q^{67} + 42q^{69} + 40q^{70} - 24q^{71} + 72q^{72} - 6q^{73} + 30q^{74} - 58q^{75} + 37q^{76} - 4q^{77} - 33q^{78} - 40q^{80} - 81q^{81} + 21q^{82} + 12q^{83} + 18q^{84} - 11q^{85} - 126q^{86} - 42q^{87} - 50q^{88} + 3q^{89} - 12q^{90} - 28q^{91} - 120q^{92} + 31q^{93} + 29q^{94} + 60q^{95} - 120q^{96} - 15q^{97} + 39q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/349\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.228167 0.131732i 0.161338 0.0931487i −0.417157 0.908834i \(-0.636973\pi\)
0.578495 + 0.815686i \(0.303640\pi\)
\(3\) 0.150552 0.260763i 0.0869211 0.150552i −0.819287 0.573383i \(-0.805631\pi\)
0.906208 + 0.422832i \(0.138964\pi\)
\(4\) −0.965293 + 1.67194i −0.482647 + 0.835969i
\(5\) 0.807178 1.39807i 0.360981 0.625237i −0.627142 0.778905i \(-0.715775\pi\)
0.988123 + 0.153668i \(0.0491087\pi\)
\(6\) 0.0793300i 0.0323863i
\(7\) 1.23534 0.713223i 0.466914 0.269573i −0.248033 0.968752i \(-0.579784\pi\)
0.714947 + 0.699179i \(0.246451\pi\)
\(8\) 1.03557i 0.366129i
\(9\) 1.45467 + 2.51956i 0.484889 + 0.839853i
\(10\) 0.425325i 0.134499i
\(11\) 2.29478i 0.691903i 0.938252 + 0.345951i \(0.112444\pi\)
−0.938252 + 0.345951i \(0.887556\pi\)
\(12\) 0.290653 + 0.503426i 0.0839043 + 0.145327i
\(13\) 0.932614 0.538445i 0.258661 0.149338i −0.365063 0.930983i \(-0.618953\pi\)
0.623723 + 0.781645i \(0.285619\pi\)
\(14\) 0.187909 0.325468i 0.0502207 0.0869849i
\(15\) −0.243044 0.420964i −0.0627537 0.108693i
\(16\) −1.79417 3.10759i −0.448542 0.776898i
\(17\) 6.95728 1.68739 0.843694 0.536824i \(-0.180376\pi\)
0.843694 + 0.536824i \(0.180376\pi\)
\(18\) 0.663814 + 0.383253i 0.156462 + 0.0903336i
\(19\) 0.461520 0.799377i 0.105880 0.183390i −0.808217 0.588884i \(-0.799567\pi\)
0.914097 + 0.405495i \(0.132901\pi\)
\(20\) 1.55833 + 2.69910i 0.348452 + 0.603537i
\(21\) 0.429508i 0.0937263i
\(22\) 0.302296 + 0.523593i 0.0644498 + 0.111630i
\(23\) −2.46875 4.27600i −0.514769 0.891607i −0.999853 0.0171390i \(-0.994544\pi\)
0.485084 0.874468i \(-0.338789\pi\)
\(24\) 0.270038 + 0.155907i 0.0551213 + 0.0318243i
\(25\) 1.19693 + 2.07314i 0.239386 + 0.414628i
\(26\) 0.141861 0.245710i 0.0278212 0.0481878i
\(27\) 1.77932 0.342431
\(28\) 2.75388i 0.520434i
\(29\) −4.87947 + 8.45149i −0.906095 + 1.56940i −0.0866541 + 0.996238i \(0.527618\pi\)
−0.819441 + 0.573164i \(0.805716\pi\)
\(30\) −0.110909 0.0640334i −0.0202491 0.0116908i
\(31\) 10.1669 1.82603 0.913016 0.407924i \(-0.133747\pi\)
0.913016 + 0.407924i \(0.133747\pi\)
\(32\) −2.61240 1.50827i −0.461811 0.266627i
\(33\) 0.598395 + 0.345483i 0.104167 + 0.0601409i
\(34\) 1.58742 0.916497i 0.272240 0.157178i
\(35\) 2.30279i 0.389243i
\(36\) −5.61673 −0.936121
\(37\) −0.988427 −0.162496 −0.0812482 0.996694i \(-0.525891\pi\)
−0.0812482 + 0.996694i \(0.525891\pi\)
\(38\) 0.243188i 0.0394503i
\(39\) 0.324255i 0.0519224i
\(40\) 1.44780 + 0.835888i 0.228917 + 0.132165i
\(41\) −9.20028 −1.43684 −0.718421 0.695608i \(-0.755135\pi\)
−0.718421 + 0.695608i \(0.755135\pi\)
\(42\) −0.0565800 0.0979994i −0.00873048 0.0151216i
\(43\) −3.45983 1.99754i −0.527620 0.304621i 0.212427 0.977177i \(-0.431863\pi\)
−0.740047 + 0.672556i \(0.765197\pi\)
\(44\) −3.83673 2.21514i −0.578409 0.333945i
\(45\) 4.69670 0.700143
\(46\) −1.12657 0.650427i −0.166104 0.0959002i
\(47\) 7.91493i 1.15451i −0.816563 0.577256i \(-0.804124\pi\)
0.816563 0.577256i \(-0.195876\pi\)
\(48\) −1.08046 −0.155951
\(49\) −2.48262 + 4.30003i −0.354661 + 0.614290i
\(50\) 0.546199 + 0.315348i 0.0772441 + 0.0445969i
\(51\) 1.04743 1.81420i 0.146670 0.254039i
\(52\) 2.07903i 0.288309i
\(53\) 11.3001i 1.55218i −0.630620 0.776092i \(-0.717199\pi\)
0.630620 0.776092i \(-0.282801\pi\)
\(54\) 0.405982 0.234394i 0.0552471 0.0318969i
\(55\) 3.20827 + 1.85230i 0.432603 + 0.249764i
\(56\) 0.738592 + 1.27928i 0.0986985 + 0.170951i
\(57\) −0.138965 0.240695i −0.0184064 0.0318808i
\(58\) 2.57113i 0.337606i
\(59\) −7.66776 4.42698i −0.998258 0.576344i −0.0905253 0.995894i \(-0.528855\pi\)
−0.907732 + 0.419550i \(0.862188\pi\)
\(60\) 0.938434 0.121151
\(61\) 7.83978i 1.00378i −0.864931 0.501890i \(-0.832638\pi\)
0.864931 0.501890i \(-0.167362\pi\)
\(62\) 2.31975 1.33931i 0.294609 0.170092i
\(63\) 3.59402 + 2.07501i 0.452804 + 0.261426i
\(64\) 6.38193 0.797741
\(65\) 1.73848i 0.215632i
\(66\) 0.182045 0.0224082
\(67\) −15.4898 −1.89238 −0.946192 0.323607i \(-0.895105\pi\)
−0.946192 + 0.323607i \(0.895105\pi\)
\(68\) −6.71582 + 11.6321i −0.814413 + 1.41060i
\(69\) −1.48670 −0.178977
\(70\) −0.303352 0.525420i −0.0362574 0.0627997i
\(71\) −0.457735 + 0.264273i −0.0543231 + 0.0313635i −0.526916 0.849918i \(-0.676652\pi\)
0.472592 + 0.881281i \(0.343318\pi\)
\(72\) −2.60918 + 1.50641i −0.307494 + 0.177532i
\(73\) −0.909516 + 1.57533i −0.106451 + 0.184378i −0.914330 0.404970i \(-0.867282\pi\)
0.807879 + 0.589348i \(0.200615\pi\)
\(74\) −0.225526 + 0.130208i −0.0262169 + 0.0151363i
\(75\) 0.720799 0.0832306
\(76\) 0.891005 + 1.54327i 0.102205 + 0.177025i
\(77\) 1.63669 + 2.83483i 0.186518 + 0.323059i
\(78\) −0.0427148 0.0739842i −0.00483650 0.00837706i
\(79\) 0.588986i 0.0662661i 0.999451 + 0.0331330i \(0.0105485\pi\)
−0.999451 + 0.0331330i \(0.989451\pi\)
\(80\) −5.79285 −0.647661
\(81\) −4.09613 + 7.09470i −0.455125 + 0.788300i
\(82\) −2.09920 + 1.21197i −0.231818 + 0.133840i
\(83\) 3.82294 + 6.62153i 0.419622 + 0.726807i 0.995901 0.0904459i \(-0.0288292\pi\)
−0.576279 + 0.817253i \(0.695496\pi\)
\(84\) 0.718110 + 0.414601i 0.0783522 + 0.0452367i
\(85\) 5.61576 9.72678i 0.609115 1.05502i
\(86\) −1.05256 −0.113500
\(87\) 1.46922 + 2.54477i 0.157517 + 0.272828i
\(88\) −2.37640 −0.253326
\(89\) −14.4224 8.32678i −1.52877 0.882637i −0.999414 0.0342383i \(-0.989099\pi\)
−0.529358 0.848398i \(-0.677567\pi\)
\(90\) 1.07163 0.618706i 0.112960 0.0652174i
\(91\) 0.768063 1.33032i 0.0805149 0.139456i
\(92\) 9.53226 0.993807
\(93\) 1.53065 2.65116i 0.158721 0.274912i
\(94\) −1.04265 1.80592i −0.107541 0.186267i
\(95\) −0.745058 1.29048i −0.0764413 0.132400i
\(96\) −0.786601 + 0.454145i −0.0802822 + 0.0463509i
\(97\) 10.7513 6.20729i 1.09163 0.630255i 0.157623 0.987499i \(-0.449617\pi\)
0.934011 + 0.357245i \(0.116284\pi\)
\(98\) 1.30817i 0.132145i
\(99\) −5.78184 + 3.33815i −0.581097 + 0.335496i
\(100\) −4.62155 −0.462155
\(101\) 12.6666i 1.26037i 0.776445 + 0.630185i \(0.217021\pi\)
−0.776445 + 0.630185i \(0.782979\pi\)
\(102\) 0.551921i 0.0546483i
\(103\) 9.75770i 0.961455i 0.876870 + 0.480727i \(0.159627\pi\)
−0.876870 + 0.480727i \(0.840373\pi\)
\(104\) 0.557597 + 0.965786i 0.0546769 + 0.0947031i
\(105\) −0.600483 0.346689i −0.0586012 0.0338334i
\(106\) −1.48858 2.57830i −0.144584 0.250427i
\(107\) 4.95963 2.86344i 0.479465 0.276819i −0.240728 0.970593i \(-0.577386\pi\)
0.720194 + 0.693773i \(0.244053\pi\)
\(108\) −1.71757 + 2.97491i −0.165273 + 0.286261i
\(109\) −3.74145 + 6.48038i −0.358366 + 0.620708i −0.987688 0.156437i \(-0.949999\pi\)
0.629322 + 0.777145i \(0.283333\pi\)
\(110\) 0.976028 0.0930606
\(111\) −0.148809 + 0.257745i −0.0141244 + 0.0244641i
\(112\) −4.43281 2.55929i −0.418862 0.241830i
\(113\) 5.48746 3.16819i 0.516217 0.298038i −0.219168 0.975687i \(-0.570334\pi\)
0.735386 + 0.677649i \(0.237001\pi\)
\(114\) −0.0634145 0.0366124i −0.00593931 0.00342906i
\(115\) −7.97087 −0.743287
\(116\) −9.42024 16.3163i −0.874647 1.51493i
\(117\) 2.71329 + 1.56652i 0.250844 + 0.144825i
\(118\) −2.33270 −0.214743
\(119\) 8.59460 4.96210i 0.787866 0.454875i
\(120\) 0.435938 0.251689i 0.0397955 0.0229759i
\(121\) 5.73397 0.521270
\(122\) −1.03275 1.78878i −0.0935008 0.161948i
\(123\) −1.38512 + 2.39909i −0.124892 + 0.216319i
\(124\) −9.81405 + 16.9984i −0.881328 + 1.52650i
\(125\) 11.9363 1.06762
\(126\) 1.09338 0.0974060
\(127\) 21.7667i 1.93148i −0.259504 0.965742i \(-0.583559\pi\)
0.259504 0.965742i \(-0.416441\pi\)
\(128\) 6.68094 3.85724i 0.590517 0.340935i
\(129\) −1.04177 + 0.601465i −0.0917225 + 0.0529560i
\(130\) −0.229014 0.396664i −0.0200859 0.0347897i
\(131\) 18.3057i 1.59938i −0.600416 0.799688i \(-0.704998\pi\)
0.600416 0.799688i \(-0.295002\pi\)
\(132\) −1.15525 + 0.666985i −0.100552 + 0.0580536i
\(133\) 1.31667i 0.114170i
\(134\) −3.53426 + 2.04051i −0.305314 + 0.176273i
\(135\) 1.43623 2.48762i 0.123611 0.214100i
\(136\) 7.20474i 0.617802i
\(137\) −0.994485 0.574166i −0.0849646 0.0490543i 0.456916 0.889510i \(-0.348954\pi\)
−0.541880 + 0.840456i \(0.682287\pi\)
\(138\) −0.339215 + 0.195846i −0.0288759 + 0.0166715i
\(139\) 3.10135 0.263053 0.131526 0.991313i \(-0.458012\pi\)
0.131526 + 0.991313i \(0.458012\pi\)
\(140\) 3.85012 + 2.22287i 0.325395 + 0.187867i
\(141\) −2.06392 1.19161i −0.173814 0.100351i
\(142\) −0.0696266 + 0.120597i −0.00584293 + 0.0101203i
\(143\) 1.23561 + 2.14015i 0.103327 + 0.178968i
\(144\) 5.21984 9.04103i 0.434987 0.753419i
\(145\) 7.87720 + 13.6437i 0.654166 + 1.13305i
\(146\) 0.479250i 0.0396630i
\(147\) 0.747527 + 1.29475i 0.0616550 + 0.106790i
\(148\) 0.954122 1.65259i 0.0784283 0.135842i
\(149\) 2.08586 1.20427i 0.170880 0.0986576i −0.412121 0.911129i \(-0.635212\pi\)
0.583001 + 0.812472i \(0.301878\pi\)
\(150\) 0.164462 0.0949523i 0.0134283 0.00775282i
\(151\) −1.38393 + 2.39704i −0.112623 + 0.195068i −0.916827 0.399285i \(-0.869258\pi\)
0.804204 + 0.594353i \(0.202592\pi\)
\(152\) 0.827810 + 0.477936i 0.0671442 + 0.0387657i
\(153\) 10.1205 + 17.5293i 0.818197 + 1.41716i
\(154\) 0.746877 + 0.431210i 0.0601851 + 0.0347479i
\(155\) 8.20650 14.2141i 0.659162 1.14170i
\(156\) 0.542134 + 0.313001i 0.0434055 + 0.0250602i
\(157\) −7.99617 + 13.8498i −0.638164 + 1.10533i 0.347671 + 0.937617i \(0.386973\pi\)
−0.985835 + 0.167716i \(0.946361\pi\)
\(158\) 0.0775883 + 0.134387i 0.00617259 + 0.0106912i
\(159\) −2.94664 1.70124i −0.233684 0.134917i
\(160\) −4.21734 + 2.43488i −0.333410 + 0.192494i
\(161\) −6.09948 3.52154i −0.480706 0.277536i
\(162\) 2.15836i 0.169577i
\(163\) 16.5453i 1.29593i 0.761671 + 0.647965i \(0.224380\pi\)
−0.761671 + 0.647965i \(0.775620\pi\)
\(164\) 8.88097 15.3823i 0.693487 1.20115i
\(165\) 0.966021 0.557733i 0.0752047 0.0434194i
\(166\) 1.74454 + 1.00721i 0.135402 + 0.0781745i
\(167\) 21.7742i 1.68493i −0.538747 0.842467i \(-0.681102\pi\)
0.538747 0.842467i \(-0.318898\pi\)
\(168\) 0.444785 0.0343159
\(169\) −5.92015 + 10.2540i −0.455396 + 0.788770i
\(170\) 2.95910i 0.226953i
\(171\) 2.68544 0.205360
\(172\) 6.67951 3.85642i 0.509308 0.294049i
\(173\) −13.3729 + 7.72082i −1.01672 + 0.587003i −0.913152 0.407619i \(-0.866359\pi\)
−0.103567 + 0.994622i \(0.533026\pi\)
\(174\) 0.670456 + 0.387088i 0.0508272 + 0.0293451i
\(175\) 2.95723 + 1.70736i 0.223545 + 0.129064i
\(176\) 7.13125 4.11723i 0.537538 0.310348i
\(177\) −2.30879 + 1.33298i −0.173539 + 0.100193i
\(178\) −4.38762 −0.328866
\(179\) 15.3849i 1.14992i 0.818181 + 0.574961i \(0.194983\pi\)
−0.818181 + 0.574961i \(0.805017\pi\)
\(180\) −4.53370 + 7.85259i −0.337922 + 0.585298i
\(181\) 16.8627 1.25340 0.626699 0.779262i \(-0.284406\pi\)
0.626699 + 0.779262i \(0.284406\pi\)
\(182\) 0.404714i 0.0299994i
\(183\) −2.04432 1.18029i −0.151121 0.0872497i
\(184\) 4.42809 2.55656i 0.326443 0.188472i
\(185\) −0.797836 + 1.38189i −0.0586581 + 0.101599i
\(186\) 0.806541i 0.0591384i
\(187\) 15.9654i 1.16751i
\(188\) 13.2333 + 7.64023i 0.965135 + 0.557221i
\(189\) 2.19806 1.26905i 0.159886 0.0923101i
\(190\) −0.339995 0.196296i −0.0246658 0.0142408i
\(191\) −6.88001 11.9165i −0.497820 0.862250i 0.502176 0.864765i \(-0.332533\pi\)
−0.999997 + 0.00251495i \(0.999199\pi\)
\(192\) 0.960810 1.66417i 0.0693405 0.120101i
\(193\) 18.4964 + 10.6789i 1.33140 + 0.768684i 0.985514 0.169593i \(-0.0542453\pi\)
0.345885 + 0.938277i \(0.387579\pi\)
\(194\) 1.63540 2.83259i 0.117415 0.203368i
\(195\) −0.453332 0.261731i −0.0324638 0.0187430i
\(196\) −4.79292 8.30158i −0.342352 0.592970i
\(197\) −2.28052 1.31666i −0.162480 0.0938079i 0.416555 0.909110i \(-0.363237\pi\)
−0.579035 + 0.815303i \(0.696571\pi\)
\(198\) −0.879482 + 1.52331i −0.0625021 + 0.108257i
\(199\) 19.5884 11.3094i 1.38859 0.801700i 0.395429 0.918496i \(-0.370596\pi\)
0.993156 + 0.116796i \(0.0372624\pi\)
\(200\) −2.14688 + 1.23950i −0.151807 + 0.0876460i
\(201\) −2.33202 + 4.03918i −0.164488 + 0.284901i
\(202\) 1.66859 + 2.89009i 0.117402 + 0.203346i
\(203\) 13.9206i 0.977035i
\(204\) 2.02216 + 3.50248i 0.141579 + 0.245222i
\(205\) −7.42626 + 12.8627i −0.518672 + 0.898367i
\(206\) 1.28540 + 2.22638i 0.0895582 + 0.155119i
\(207\) 7.18242 12.4403i 0.499213 0.864661i
\(208\) −3.34653 1.93212i −0.232040 0.133969i
\(209\) 1.83440 + 1.05909i 0.126888 + 0.0732587i
\(210\) −0.182680 −0.0126061
\(211\) 1.31819 0.761056i 0.0907477 0.0523932i −0.453939 0.891033i \(-0.649982\pi\)
0.544687 + 0.838639i \(0.316648\pi\)
\(212\) 18.8930 + 10.9079i 1.29758 + 0.749156i
\(213\) 0.159147i 0.0109046i
\(214\) 0.754414 1.30668i 0.0515707 0.0893231i
\(215\) −5.58540 + 3.22473i −0.380921 + 0.219925i
\(216\) 1.84261i 0.125374i
\(217\) 12.5596 7.25128i 0.852600 0.492249i
\(218\) 1.97148i 0.133525i
\(219\) 0.273858 + 0.474337i 0.0185056 + 0.0320527i
\(220\) −6.19385 + 3.57602i −0.417589 + 0.241095i
\(221\) 6.48846 3.74611i 0.436461 0.251991i
\(222\) 0.0784119i 0.00526266i
\(223\) −15.1017 −1.01128 −0.505642 0.862744i \(-0.668744\pi\)
−0.505642 + 0.862744i \(0.668744\pi\)
\(224\) −4.30293 −0.287501
\(225\) −3.48227 + 6.03147i −0.232151 + 0.402098i
\(226\) 0.834704 1.44575i 0.0555237 0.0961699i
\(227\) −4.68430 8.11345i −0.310908 0.538509i 0.667651 0.744474i \(-0.267300\pi\)
−0.978559 + 0.205966i \(0.933966\pi\)
\(228\) 0.536569 0.0355352
\(229\) −11.0112 + 6.35729i −0.727638 + 0.420102i −0.817557 0.575847i \(-0.804672\pi\)
0.0899196 + 0.995949i \(0.471339\pi\)
\(230\) −1.81869 + 1.05002i −0.119921 + 0.0692362i
\(231\) 0.985627 0.0648495
\(232\) −8.75210 5.05303i −0.574604 0.331747i
\(233\) −11.9504 20.6987i −0.782896 1.35602i −0.930248 0.366931i \(-0.880408\pi\)
0.147352 0.989084i \(-0.452925\pi\)
\(234\) 0.825442 0.0539609
\(235\) −11.0656 6.38875i −0.721843 0.416756i
\(236\) 14.8033 8.54668i 0.963611 0.556341i
\(237\) 0.153586 + 0.0886728i 0.00997647 + 0.00575992i
\(238\) 1.30733 2.26437i 0.0847419 0.146777i
\(239\) 6.62978 0.428845 0.214422 0.976741i \(-0.431213\pi\)
0.214422 + 0.976741i \(0.431213\pi\)
\(240\) −0.872124 + 1.51056i −0.0562953 + 0.0975064i
\(241\) −0.372777 + 0.645668i −0.0240127 + 0.0415911i −0.877782 0.479060i \(-0.840978\pi\)
0.853769 + 0.520651i \(0.174311\pi\)
\(242\) 1.30830 0.755348i 0.0841008 0.0485556i
\(243\) 3.90234 + 6.75905i 0.250335 + 0.433593i
\(244\) 13.1076 + 7.56768i 0.839129 + 0.484471i
\(245\) 4.00784 + 6.94178i 0.256051 + 0.443494i
\(246\) 0.729858i 0.0465340i
\(247\) 0.994013i 0.0632475i
\(248\) 10.5285i 0.668563i
\(249\) 2.30220 0.145896
\(250\) 2.72347 1.57240i 0.172247 0.0994470i
\(251\) 9.84495i 0.621408i −0.950507 0.310704i \(-0.899435\pi\)
0.950507 0.310704i \(-0.100565\pi\)
\(252\) −6.93856 + 4.00598i −0.437088 + 0.252353i
\(253\) 9.81248 5.66524i 0.616905 0.356170i
\(254\) −2.86738 4.96644i −0.179915 0.311622i
\(255\) −1.69092 2.92877i −0.105890 0.183407i
\(256\) −5.36568 + 9.29363i −0.335355 + 0.580852i
\(257\) 9.77861 0.609973 0.304986 0.952357i \(-0.401348\pi\)
0.304986 + 0.952357i \(0.401348\pi\)
\(258\) −0.158464 + 0.274468i −0.00986557 + 0.0170877i
\(259\) −1.22104 + 0.704969i −0.0758719 + 0.0438047i
\(260\) 2.90663 + 1.67815i 0.180262 + 0.104074i
\(261\) −28.3920 −1.75742
\(262\) −2.41145 4.17675i −0.148980 0.258040i
\(263\) −11.9681 −0.737986 −0.368993 0.929432i \(-0.620297\pi\)
−0.368993 + 0.929432i \(0.620297\pi\)
\(264\) −0.357772 + 0.619679i −0.0220193 + 0.0381386i
\(265\) −15.7983 9.12116i −0.970483 0.560308i
\(266\) −0.173448 0.300420i −0.0106347 0.0184199i
\(267\) −4.34263 + 2.50722i −0.265765 + 0.153439i
\(268\) 14.9522 25.8980i 0.913352 1.58197i
\(269\) 4.76791 0.290705 0.145352 0.989380i \(-0.453568\pi\)
0.145352 + 0.989380i \(0.453568\pi\)
\(270\) 0.756789i 0.0460567i
\(271\) −10.7221 18.5713i −0.651324 1.12813i −0.982802 0.184663i \(-0.940881\pi\)
0.331478 0.943463i \(-0.392453\pi\)
\(272\) −12.4825 21.6204i −0.756865 1.31093i
\(273\) −0.231266 0.400565i −0.0139969 0.0242433i
\(274\) −0.302545 −0.0182774
\(275\) −4.75741 + 2.74669i −0.286883 + 0.165632i
\(276\) 1.43510 2.48566i 0.0863827 0.149619i
\(277\) −11.7762 + 6.79900i −0.707564 + 0.408512i −0.810158 0.586211i \(-0.800619\pi\)
0.102595 + 0.994723i \(0.467286\pi\)
\(278\) 0.707624 0.408547i 0.0424405 0.0245030i
\(279\) 14.7895 + 25.6161i 0.885423 + 1.53360i
\(280\) 2.38470 0.142513
\(281\) −3.25545 + 5.63860i −0.194204 + 0.336371i −0.946639 0.322295i \(-0.895546\pi\)
0.752435 + 0.658666i \(0.228879\pi\)
\(282\) −0.627891 −0.0373904
\(283\) 16.5940 0.986409 0.493205 0.869913i \(-0.335825\pi\)
0.493205 + 0.869913i \(0.335825\pi\)
\(284\) 1.02041i 0.0605499i
\(285\) −0.448679 −0.0265774
\(286\) 0.563852 + 0.325540i 0.0333413 + 0.0192496i
\(287\) −11.3655 + 6.56185i −0.670882 + 0.387334i
\(288\) 8.77612i 0.517138i
\(289\) 31.4038 1.84728
\(290\) 3.59463 + 2.07536i 0.211084 + 0.121869i
\(291\) 3.73807i 0.219130i
\(292\) −1.75590 3.04131i −0.102756 0.177979i
\(293\) −2.72794 4.72494i −0.159368 0.276034i 0.775273 0.631627i \(-0.217612\pi\)
−0.934641 + 0.355593i \(0.884279\pi\)
\(294\) 0.341121 + 0.196947i 0.0198946 + 0.0114862i
\(295\) −12.3785 + 7.14673i −0.720704 + 0.416098i
\(296\) 1.02358i 0.0594946i
\(297\) 4.08315i 0.236929i
\(298\) 0.317282 0.549549i 0.0183797 0.0318345i
\(299\) −4.60478 2.65857i −0.266301 0.153749i
\(300\) −0.695782 + 1.20513i −0.0401710 + 0.0695782i
\(301\) −5.69876 −0.328471
\(302\) 0.729232i 0.0419626i
\(303\) 3.30297 + 1.90697i 0.189751 + 0.109553i
\(304\) −3.31218 −0.189967
\(305\) −10.9606 6.32809i −0.627601 0.362345i
\(306\) 4.61834 + 2.66640i 0.264013 + 0.152428i
\(307\) −1.40390 2.43162i −0.0801246 0.138780i 0.823179 0.567782i \(-0.192198\pi\)
−0.903303 + 0.429002i \(0.858865\pi\)
\(308\) −6.31955 −0.360090
\(309\) 2.54445 + 1.46904i 0.144749 + 0.0835706i
\(310\) 4.32424i 0.245600i
\(311\) 13.6304i 0.772909i 0.922309 + 0.386454i \(0.126300\pi\)
−0.922309 + 0.386454i \(0.873700\pi\)
\(312\) 0.335788 0.0190103
\(313\) −17.7039 −1.00068 −0.500341 0.865829i \(-0.666792\pi\)
−0.500341 + 0.865829i \(0.666792\pi\)
\(314\) 4.21341i 0.237777i
\(315\) 5.80202 3.34980i 0.326907 0.188740i
\(316\) −0.984747 0.568544i −0.0553963 0.0319831i
\(317\) −5.14241 2.96897i −0.288826 0.166754i 0.348586 0.937277i \(-0.386662\pi\)
−0.637412 + 0.770523i \(0.719995\pi\)
\(318\) −0.896434 −0.0502695
\(319\) −19.3943 11.1973i −1.08587 0.626930i
\(320\) 5.15135 8.92240i 0.287969 0.498777i
\(321\) 1.72438i 0.0962457i
\(322\) −1.85560 −0.103408
\(323\) 3.21093 5.56149i 0.178661 0.309450i
\(324\) −7.90792 13.6969i −0.439329 0.760940i
\(325\) 2.23254 + 1.28896i 0.123839 + 0.0714987i
\(326\) 2.17955 + 3.77509i 0.120714 + 0.209083i
\(327\) 1.12656 + 1.95126i 0.0622991 + 0.107905i
\(328\) 9.52752i 0.526069i
\(329\) −5.64511 9.77762i −0.311225 0.539058i
\(330\) 0.146943 0.254512i 0.00808892 0.0140104i
\(331\) −17.4079 10.0504i −0.956824 0.552422i −0.0616297 0.998099i \(-0.519630\pi\)
−0.895194 + 0.445677i \(0.852963\pi\)
\(332\) −14.7610 −0.810117
\(333\) −1.43783 2.49040i −0.0787928 0.136473i
\(334\) −2.86835 4.96814i −0.156949 0.271844i
\(335\) −12.5030 + 21.6559i −0.683114 + 1.18319i
\(336\) −1.33474 + 0.770610i −0.0728158 + 0.0420402i
\(337\) 12.8702 + 22.2918i 0.701082 + 1.21431i 0.968087 + 0.250615i \(0.0806327\pi\)
−0.267005 + 0.963695i \(0.586034\pi\)
\(338\) 3.11950i 0.169678i
\(339\) 1.90790i 0.103623i
\(340\) 10.8417 + 18.7784i 0.587975 + 1.01840i
\(341\) 23.3309i 1.26344i
\(342\) 0.612727 0.353758i 0.0331325 0.0191291i
\(343\) 17.0678i 0.921574i
\(344\) 2.06859 3.58290i 0.111531 0.193177i
\(345\) −1.20003 + 2.07851i −0.0646073 + 0.111903i
\(346\) −2.03416 + 3.52327i −0.109357 + 0.189412i
\(347\) −23.9913 + 13.8514i −1.28792 + 0.743582i −0.978283 0.207272i \(-0.933542\pi\)
−0.309639 + 0.950854i \(0.600208\pi\)
\(348\) −5.67293 −0.304101
\(349\) 2.39700 18.5271i 0.128309 0.991734i
\(350\) 0.899654 0.0480885
\(351\) 1.65942 0.958066i 0.0885733 0.0511378i
\(352\) 3.46115 5.99488i 0.184480 0.319528i
\(353\) −5.73692 + 9.93664i −0.305346 + 0.528874i −0.977338 0.211684i \(-0.932105\pi\)
0.671993 + 0.740558i \(0.265439\pi\)
\(354\) −0.351192 + 0.608283i −0.0186657 + 0.0323299i
\(355\) 0.853262i 0.0452865i
\(356\) 27.8437 16.0756i 1.47571 0.852003i
\(357\) 2.98821i 0.158153i
\(358\) 2.02669 + 3.51032i 0.107114 + 0.185526i
\(359\) 12.4405i 0.656585i 0.944576 + 0.328292i \(0.106473\pi\)
−0.944576 + 0.328292i \(0.893527\pi\)
\(360\) 4.86376i 0.256343i
\(361\) 9.07400 + 15.7166i 0.477579 + 0.827191i
\(362\) 3.84751 2.22136i 0.202221 0.116752i
\(363\) 0.863259 1.49521i 0.0453094 0.0784781i
\(364\) 1.48281 + 2.56831i 0.0777205 + 0.134616i
\(365\) 1.46828 + 2.54314i 0.0768534 + 0.133114i
\(366\) −0.621929 −0.0325088
\(367\) 1.12969 + 0.652228i 0.0589695 + 0.0340460i 0.529195 0.848500i \(-0.322494\pi\)
−0.470225 + 0.882546i \(0.655827\pi\)
\(368\) −8.85870 + 15.3437i −0.461792 + 0.799847i
\(369\) −13.3834 23.1807i −0.696710 1.20674i
\(370\) 0.420402i 0.0218557i
\(371\) −8.05947 13.9594i −0.418427 0.724737i
\(372\) 2.95504 + 5.11829i 0.153212 + 0.265371i
\(373\) 31.8980 + 18.4163i 1.65161 + 0.953560i 0.976409 + 0.215931i \(0.0692785\pi\)
0.675206 + 0.737629i \(0.264055\pi\)
\(374\) 2.10316 + 3.64278i 0.108752 + 0.188364i
\(375\) 1.79703 3.11255i 0.0927983 0.160731i
\(376\) 8.19646 0.422700
\(377\) 10.5093i 0.541257i
\(378\) 0.334350 0.579111i 0.0171971 0.0297863i
\(379\) −14.8281 8.56103i −0.761670 0.439750i 0.0682250 0.997670i \(-0.478266\pi\)
−0.829895 + 0.557920i \(0.811600\pi\)
\(380\) 2.87680 0.147577
\(381\) −5.67596 3.27702i −0.290788 0.167887i
\(382\) −3.13958 1.81264i −0.160635 0.0927426i
\(383\) −14.5715 + 8.41285i −0.744568 + 0.429876i −0.823728 0.566986i \(-0.808110\pi\)
0.0791601 + 0.996862i \(0.474776\pi\)
\(384\) 2.32286i 0.118538i
\(385\) 5.28441 0.269318
\(386\) 5.62701 0.286407
\(387\) 11.6230i 0.590831i
\(388\) 23.9674i 1.21676i
\(389\) 7.64661 + 4.41477i 0.387698 + 0.223838i 0.681162 0.732132i \(-0.261475\pi\)
−0.293464 + 0.955970i \(0.594808\pi\)
\(390\) −0.137914 −0.00698353
\(391\) −17.1758 29.7493i −0.868616 1.50449i
\(392\) −4.45298 2.57093i −0.224909 0.129852i
\(393\) −4.77345 2.75595i −0.240789 0.139019i
\(394\) −0.693784 −0.0349523
\(395\) 0.823445 + 0.475416i 0.0414320 + 0.0239208i
\(396\) 12.8892i 0.647705i
\(397\) −8.74650 −0.438974 −0.219487 0.975615i \(-0.570438\pi\)
−0.219487 + 0.975615i \(0.570438\pi\)
\(398\) 2.97961 5.16084i 0.149355 0.258690i
\(399\) −0.343339 0.198227i −0.0171884 0.00992375i
\(400\) 4.29498 7.43913i 0.214749 0.371957i
\(401\) 14.0713i 0.702688i −0.936246 0.351344i \(-0.885725\pi\)
0.936246 0.351344i \(-0.114275\pi\)
\(402\) 1.22881i 0.0612873i
\(403\) 9.48180 5.47432i 0.472322 0.272695i
\(404\) −21.1777 12.2269i −1.05363 0.608313i
\(405\) 6.61260 + 11.4534i 0.328583 + 0.569122i
\(406\) 1.83379 + 3.17622i 0.0910095 + 0.157633i
\(407\) 2.26822i 0.112432i
\(408\) 1.87873 + 1.08469i 0.0930111 + 0.0537000i
\(409\) −14.1651 −0.700419 −0.350209 0.936671i \(-0.613890\pi\)
−0.350209 + 0.936671i \(0.613890\pi\)
\(410\) 3.91311i 0.193255i
\(411\) −0.299443 + 0.172883i −0.0147704 + 0.00852771i
\(412\) −16.3143 9.41904i −0.803746 0.464043i
\(413\) −12.6297 −0.621468
\(414\) 3.78462i 0.186004i
\(415\) 12.3432 0.605902
\(416\) −3.24848 −0.159270
\(417\) 0.466913 0.808717i 0.0228648 0.0396030i
\(418\) 0.558064 0.0272958
\(419\) −14.8950 25.7990i −0.727670 1.26036i −0.957866 0.287217i \(-0.907270\pi\)
0.230196 0.973144i \(-0.426063\pi\)
\(420\) 1.15928 0.669313i 0.0565673 0.0326592i
\(421\) 19.7861 11.4235i 0.964315 0.556748i 0.0668167 0.997765i \(-0.478716\pi\)
0.897498 + 0.441018i \(0.145382\pi\)
\(422\) 0.200511 0.347295i 0.00976072 0.0169061i
\(423\) 19.9421 11.5136i 0.969620 0.559810i
\(424\) 11.7020 0.568299
\(425\) 8.32737 + 14.4234i 0.403937 + 0.699639i
\(426\) 0.0209648 + 0.0363121i 0.00101575 + 0.00175933i
\(427\) −5.59151 9.68478i −0.270592 0.468679i
\(428\) 11.0562i 0.534424i
\(429\) 0.744095 0.0359252
\(430\) −0.849602 + 1.47155i −0.0409714 + 0.0709646i
\(431\) −1.46490 + 0.845761i −0.0705618 + 0.0407389i −0.534866 0.844937i \(-0.679638\pi\)
0.464304 + 0.885676i \(0.346305\pi\)
\(432\) −3.19240 5.52940i −0.153595 0.266034i
\(433\) 5.38392 + 3.10841i 0.258735 + 0.149381i 0.623757 0.781618i \(-0.285605\pi\)
−0.365023 + 0.930999i \(0.618939\pi\)
\(434\) 1.91045 3.30900i 0.0917047 0.158837i
\(435\) 4.74370 0.227443
\(436\) −7.22319 12.5109i −0.345928 0.599165i
\(437\) −4.55751 −0.218015
\(438\) 0.124971 + 0.0721519i 0.00597133 + 0.00344755i
\(439\) 25.4833 14.7128i 1.21625 0.702203i 0.252137 0.967692i \(-0.418867\pi\)
0.964114 + 0.265489i \(0.0855334\pi\)
\(440\) −1.91818 + 3.32239i −0.0914457 + 0.158389i
\(441\) −14.4456 −0.687885
\(442\) 0.986967 1.70948i 0.0469452 0.0813115i
\(443\) 1.79917 + 3.11626i 0.0854812 + 0.148058i 0.905596 0.424141i \(-0.139424\pi\)
−0.820115 + 0.572199i \(0.806091\pi\)
\(444\) −0.287289 0.497600i −0.0136341 0.0236150i
\(445\) −23.2829 + 13.4424i −1.10371 + 0.637230i
\(446\) −3.44570 + 1.98938i −0.163159 + 0.0941997i
\(447\) 0.725219i 0.0343017i
\(448\) 7.88384 4.55174i 0.372477 0.215049i
\(449\) −6.85482 −0.323499 −0.161750 0.986832i \(-0.551714\pi\)
−0.161750 + 0.986832i \(0.551714\pi\)
\(450\) 1.83491i 0.0864983i
\(451\) 21.1126i 0.994155i
\(452\) 12.2329i 0.575388i
\(453\) 0.416706 + 0.721756i 0.0195785 + 0.0339110i
\(454\) −2.13760 1.23415i −0.100323 0.0579213i
\(455\) −1.23993 2.14762i −0.0581286 0.100682i
\(456\) 0.249256 0.143908i 0.0116725 0.00673912i
\(457\) 10.1856 17.6420i 0.476464 0.825260i −0.523173 0.852227i \(-0.675252\pi\)
0.999636 + 0.0269673i \(0.00858499\pi\)
\(458\) −1.67492 + 2.90105i −0.0782638 + 0.135557i
\(459\) 12.3792 0.577813
\(460\) 7.69423 13.3268i 0.358745 0.621365i
\(461\) 16.3078 + 9.41533i 0.759532 + 0.438516i 0.829128 0.559060i \(-0.188838\pi\)
−0.0695960 + 0.997575i \(0.522171\pi\)
\(462\) 0.224887 0.129839i 0.0104627 0.00604064i
\(463\) 22.0626 + 12.7379i 1.02534 + 0.591978i 0.915645 0.401988i \(-0.131680\pi\)
0.109691 + 0.993966i \(0.465014\pi\)
\(464\) 35.0184 1.62569
\(465\) −2.47101 4.27991i −0.114590 0.198476i
\(466\) −5.45336 3.14850i −0.252622 0.145851i
\(467\) 1.95622 0.0905229 0.0452614 0.998975i \(-0.485588\pi\)
0.0452614 + 0.998975i \(0.485588\pi\)
\(468\) −5.23824 + 3.02430i −0.242138 + 0.139798i
\(469\) −19.1352 + 11.0477i −0.883581 + 0.510136i
\(470\) −3.36642 −0.155281
\(471\) 2.40767 + 4.17022i 0.110940 + 0.192153i
\(472\) 4.58445 7.94050i 0.211016 0.365491i
\(473\) 4.58391 7.93957i 0.210768 0.365062i
\(474\) 0.0467242 0.00214611
\(475\) 2.20963 0.101385
\(476\) 19.1595i 0.878175i
\(477\) 28.4712 16.4379i 1.30361 0.752637i
\(478\) 1.51269 0.873355i 0.0691890 0.0399463i
\(479\) 6.34681 + 10.9930i 0.289993 + 0.502282i 0.973808 0.227373i \(-0.0730137\pi\)
−0.683815 + 0.729656i \(0.739680\pi\)
\(480\) 1.46630i 0.0669272i
\(481\) −0.921821 + 0.532213i −0.0420314 + 0.0242668i
\(482\) 0.196427i 0.00894699i
\(483\) −1.83657 + 1.06035i −0.0835670 + 0.0482474i
\(484\) −5.53497 + 9.58684i −0.251589 + 0.435766i
\(485\) 20.0415i 0.910040i
\(486\) 1.78077 + 1.02813i 0.0807772 + 0.0466368i
\(487\) −12.2172 + 7.05357i −0.553612 + 0.319628i −0.750578 0.660782i \(-0.770225\pi\)
0.196966 + 0.980410i \(0.436891\pi\)
\(488\) 8.11863 0.367513
\(489\) 4.31441 + 2.49092i 0.195104 + 0.112644i
\(490\) 1.82891 + 1.05592i 0.0826217 + 0.0477017i
\(491\) −12.2865 + 21.2809i −0.554483 + 0.960392i 0.443461 + 0.896294i \(0.353750\pi\)
−0.997944 + 0.0640984i \(0.979583\pi\)
\(492\) −2.67409 4.63166i −0.120557 0.208811i
\(493\) −33.9478 + 58.7994i −1.52893 + 2.64819i
\(494\) −0.130943 0.226801i −0.00589142 0.0102042i
\(495\) 10.7779i 0.484431i
\(496\) −18.2412 31.5946i −0.819052 1.41864i
\(497\) −0.376972 + 0.652935i −0.0169095 + 0.0292881i
\(498\) 0.525285 0.303274i 0.0235386 0.0135900i
\(499\) −20.6915 + 11.9463i −0.926280 + 0.534788i −0.885633 0.464386i \(-0.846275\pi\)
−0.0406467 + 0.999174i \(0.512942\pi\)
\(500\) −11.5220 + 19.9568i −0.515281 + 0.892494i
\(501\) −5.67790 3.27814i −0.253670 0.146456i
\(502\) −1.29690 2.24629i −0.0578833 0.100257i
\(503\) 28.7114 + 16.5765i 1.28018 + 0.739110i 0.976880 0.213786i \(-0.0685796\pi\)
0.303296 + 0.952896i \(0.401913\pi\)
\(504\) −2.14881 + 3.72185i −0.0957157 + 0.165784i
\(505\) 17.7088 + 10.2242i 0.788030 + 0.454969i
\(506\) 1.49259 2.58524i 0.0663536 0.114928i
\(507\) 1.78258 + 3.08752i 0.0791671 + 0.137121i
\(508\) 36.3926 + 21.0113i 1.61466 + 0.932224i
\(509\) −13.6609 + 7.88715i −0.605510 + 0.349592i −0.771206 0.636585i \(-0.780346\pi\)
0.165696 + 0.986177i \(0.447013\pi\)
\(510\) −0.771625 0.445498i −0.0341681 0.0197270i
\(511\) 2.59475i 0.114785i
\(512\) 18.2563i 0.806822i
\(513\) 0.821193 1.42235i 0.0362566 0.0627982i
\(514\) 2.23115 1.28816i 0.0984119 0.0568181i
\(515\) 13.6420 + 7.87619i 0.601137 + 0.347067i
\(516\) 2.32236i 0.102236i
\(517\) 18.1630 0.798810
\(518\) −0.185734 + 0.321701i −0.00816069 + 0.0141347i
\(519\) 4.64953i 0.204092i
\(520\) 1.80032 0.0789492
\(521\) 5.70170 3.29188i 0.249796 0.144220i −0.369875 0.929082i \(-0.620599\pi\)
0.619671 + 0.784862i \(0.287266\pi\)
\(522\) −6.47812 + 3.74014i −0.283540 + 0.163702i
\(523\) 4.25033 + 2.45393i 0.185854 + 0.107303i 0.590040 0.807374i \(-0.299112\pi\)
−0.404186 + 0.914677i \(0.632445\pi\)
\(524\) 30.6060 + 17.6704i 1.33703 + 0.771933i
\(525\) 0.890431 0.514090i 0.0388616 0.0224367i
\(526\) −2.73073 + 1.57658i −0.119065 + 0.0687424i
\(527\) 70.7341 3.08123
\(528\) 2.47942i 0.107903i
\(529\) −0.689427 + 1.19412i −0.0299751 + 0.0519183i
\(530\) −4.80620 −0.208768
\(531\) 25.7592i 1.11785i
\(532\) 2.20139 + 1.27097i 0.0954422 + 0.0551036i
\(533\) −8.58031 + 4.95384i −0.371654 + 0.214575i
\(534\) −0.660563 + 1.14413i −0.0285854 + 0.0495113i
\(535\) 9.24522i 0.399706i
\(536\) 16.0408i 0.692856i
\(537\) 4.01182 + 2.31622i 0.173123 + 0.0999524i
\(538\) 1.08788 0.628087i 0.0469017 0.0270787i
\(539\) −9.86764 5.69708i −0.425029 0.245391i
\(540\) 2.77276 + 4.80257i 0.119321 + 0.206670i
\(541\) 10.0677 17.4377i 0.432843 0.749706i −0.564274 0.825587i \(-0.690844\pi\)
0.997117 + 0.0758820i \(0.0241772\pi\)
\(542\) −4.89287 2.82490i −0.210167 0.121340i
\(543\) 2.53871 4.39718i 0.108947 0.188701i
\(544\) −18.1752 10.4934i −0.779254 0.449903i
\(545\) 6.04003 + 10.4616i 0.258726 + 0.448127i
\(546\) −0.105535 0.0609304i −0.00451646 0.00260758i
\(547\) −6.43133 + 11.1394i −0.274984 + 0.476286i −0.970131 0.242581i \(-0.922006\pi\)
0.695147 + 0.718867i \(0.255339\pi\)
\(548\) 1.91994 1.10848i 0.0820158 0.0473518i
\(549\) 19.7528 11.4043i 0.843028 0.486723i
\(550\) −0.723655 + 1.25341i −0.0308567 + 0.0534454i
\(551\) 4.50395 + 7.80107i 0.191875 + 0.332337i
\(552\) 1.53958i 0.0655287i
\(553\) 0.420078 + 0.727597i 0.0178635 + 0.0309406i
\(554\) −1.79129 + 3.10261i −0.0761047 + 0.131817i
\(555\) 0.240231 + 0.416093i 0.0101972 + 0.0176621i
\(556\) −2.99371 + 5.18526i −0.126962 + 0.219904i
\(557\) 16.1028 + 9.29695i 0.682297 + 0.393924i 0.800720 0.599039i \(-0.204451\pi\)
−0.118423 + 0.992963i \(0.537784\pi\)
\(558\) 6.74894 + 3.89650i 0.285705 + 0.164952i
\(559\) −4.30225 −0.181966
\(560\) −7.15614 + 4.13160i −0.302402 + 0.174592i
\(561\) 4.16320 + 2.40362i 0.175770 + 0.101481i
\(562\) 1.71539i 0.0723593i
\(563\) 7.07944 12.2620i 0.298363 0.516780i −0.677399 0.735616i \(-0.736893\pi\)
0.975762 + 0.218836i \(0.0702261\pi\)
\(564\) 3.98458 2.30050i 0.167781 0.0968685i
\(565\) 10.2292i 0.430344i
\(566\) 3.78619 2.18596i 0.159146 0.0918827i
\(567\) 11.6858i 0.490758i
\(568\) −0.273673 0.474016i −0.0114831 0.0198893i
\(569\) 15.2521 8.80581i 0.639402 0.369159i −0.144982 0.989434i \(-0.546313\pi\)
0.784384 + 0.620275i \(0.212979\pi\)
\(570\) −0.102374 + 0.0591054i −0.00428796 + 0.00247565i
\(571\) 18.5509i 0.776332i 0.921590 + 0.388166i \(0.126891\pi\)
−0.921590 + 0.388166i \(0.873109\pi\)
\(572\) −4.77092 −0.199482
\(573\) −4.14319 −0.173084
\(574\) −1.72881 + 2.99439i −0.0721593 + 0.124984i
\(575\) 5.90983 10.2361i 0.246457 0.426876i
\(576\) 9.28359 + 16.0796i 0.386816 + 0.669985i
\(577\) −12.8099 −0.533283 −0.266642 0.963796i \(-0.585914\pi\)
−0.266642 + 0.963796i \(0.585914\pi\)
\(578\) 7.16529 4.13688i 0.298037 0.172072i
\(579\) 5.56933 3.21545i 0.231453 0.133630i
\(580\) −30.4152 −1.26292
\(581\) 9.44526 + 5.45322i 0.391855 + 0.226238i
\(582\) −0.492424 0.852904i −0.0204116 0.0353540i
\(583\) 25.9312 1.07396
\(584\) −1.63136 0.941867i −0.0675062 0.0389747i
\(585\) 4.38021 2.52892i 0.181099 0.104558i
\(586\) −1.24485 0.718716i −0.0514244 0.0296899i
\(587\) −16.5620 + 28.6863i −0.683589 + 1.18401i 0.290290 + 0.956939i \(0.406248\pi\)
−0.973878 + 0.227071i \(0.927085\pi\)
\(588\) −2.88633 −0.119030
\(589\) 4.69224 8.12720i 0.193340 0.334875i
\(590\) −1.88291 + 3.26129i −0.0775180 + 0.134265i
\(591\) −0.686671 + 0.396450i −0.0282459 + 0.0163078i
\(592\) 1.77341 + 3.07163i 0.0728865 + 0.126243i
\(593\) −4.07226 2.35112i −0.167228 0.0965489i 0.414050 0.910254i \(-0.364114\pi\)
−0.581278 + 0.813705i \(0.697447\pi\)
\(594\) 0.537882 + 0.931640i 0.0220696 + 0.0382256i
\(595\) 16.0212i 0.656804i
\(596\) 4.64989i 0.190467i
\(597\) 6.81058i 0.278738i
\(598\) −1.40088 −0.0572860
\(599\) −6.82546 + 3.94068i −0.278881 + 0.161012i −0.632917 0.774220i \(-0.718142\pi\)
0.354036 + 0.935232i \(0.384809\pi\)
\(600\) 0.746436i 0.0304731i
\(601\) −6.88820 + 3.97690i −0.280975 + 0.162221i −0.633865 0.773444i \(-0.718532\pi\)
0.352889 + 0.935665i \(0.385199\pi\)
\(602\) −1.30027 + 0.750709i −0.0529949 + 0.0305966i
\(603\) −22.5326 39.0275i −0.917597 1.58932i
\(604\) −2.67180 4.62769i −0.108714 0.188298i
\(605\) 4.62834 8.01651i 0.188169 0.325918i
\(606\) 1.00484 0.0408187
\(607\) −10.2194 + 17.7005i −0.414793 + 0.718443i −0.995407 0.0957364i \(-0.969479\pi\)
0.580613 + 0.814179i \(0.302813\pi\)
\(608\) −2.41135 + 1.39219i −0.0977931 + 0.0564609i
\(609\) 3.62998 + 2.09577i 0.147094 + 0.0849249i
\(610\) −3.33445 −0.135008
\(611\) −4.26175 7.38157i −0.172412 0.298627i
\(612\) −39.0772 −1.57960
\(613\) 8.65475 14.9905i 0.349562 0.605459i −0.636610 0.771186i \(-0.719664\pi\)
0.986172 + 0.165727i \(0.0529970\pi\)
\(614\) −0.640645 0.369876i −0.0258543 0.0149270i
\(615\) 2.23607 + 3.87299i 0.0901671 + 0.156174i
\(616\) −2.93567 + 1.69491i −0.118281 + 0.0682898i
\(617\) −16.7959 + 29.0913i −0.676175 + 1.17117i 0.299948 + 0.953955i \(0.403031\pi\)
−0.976124 + 0.217215i \(0.930303\pi\)
\(618\) 0.774078 0.0311380
\(619\) 17.3770i 0.698442i −0.937040 0.349221i \(-0.886446\pi\)
0.937040 0.349221i \(-0.113554\pi\)
\(620\) 15.8434 + 27.4415i 0.636285 + 1.10208i
\(621\) −4.39269 7.60837i −0.176273 0.305313i
\(622\) 1.79556 + 3.11000i 0.0719954 + 0.124700i
\(623\) −23.7554 −0.951741
\(624\) −1.00765 + 0.581768i −0.0403384 + 0.0232894i
\(625\) 3.65008 6.32212i 0.146003 0.252885i
\(626\) −4.03943 + 2.33217i −0.161448 + 0.0932121i
\(627\) 0.552343 0.318895i 0.0220584 0.0127354i
\(628\) −15.4373 26.7382i −0.616016 1.06697i
\(629\) −6.87677 −0.274195
\(630\) 0.882552 1.52862i 0.0351617 0.0609019i
\(631\) 49.3236 1.96354 0.981770 0.190070i \(-0.0608716\pi\)
0.981770 + 0.190070i \(0.0608716\pi\)
\(632\) −0.609935 −0.0242619
\(633\) 0.458313i 0.0182163i
\(634\) −1.56443 −0.0621316
\(635\) −30.4315 17.5696i −1.20764 0.697229i
\(636\) 5.68875 3.28440i 0.225573 0.130235i
\(637\) 5.34703i 0.211857i
\(638\) −5.90019 −0.233591
\(639\) −1.33171 0.768860i −0.0526814 0.0304156i
\(640\) 12.4539i 0.492284i
\(641\) −24.8742 43.0833i −0.982471 1.70169i −0.652676 0.757637i \(-0.726354\pi\)
−0.329795 0.944053i \(-0.606980\pi\)
\(642\) −0.227157 0.393447i −0.00896516 0.0155281i
\(643\) 2.35775 + 1.36125i 0.0929806 + 0.0536824i 0.545769 0.837935i \(-0.316237\pi\)
−0.452789 + 0.891618i \(0.649571\pi\)
\(644\) 11.7756 6.79863i 0.464023 0.267904i
\(645\) 1.94196i 0.0764644i
\(646\) 1.69193i 0.0665681i
\(647\) 13.9952 24.2404i 0.550207 0.952987i −0.448052 0.894008i \(-0.647882\pi\)
0.998259 0.0589796i \(-0.0187847\pi\)
\(648\) −7.34705 4.24182i −0.288619 0.166634i
\(649\) 10.1590 17.5958i 0.398774 0.690697i
\(650\) 0.679190 0.0266400
\(651\) 4.36677i 0.171147i
\(652\) −27.6627 15.9711i −1.08336 0.625476i
\(653\) −4.23861 −0.165870 −0.0829348 0.996555i \(-0.526429\pi\)
−0.0829348 + 0.996555i \(0.526429\pi\)
\(654\) 0.514088 + 0.296809i 0.0201024 + 0.0116062i
\(655\) −25.5927 14.7759i −0.999989 0.577344i
\(656\) 16.5069 + 28.5907i 0.644484 + 1.11628i
\(657\) −5.29218 −0.206468
\(658\) −2.57605 1.48729i −0.100425 0.0579804i
\(659\) 6.43426i 0.250643i 0.992116 + 0.125322i \(0.0399963\pi\)
−0.992116 + 0.125322i \(0.960004\pi\)
\(660\) 2.15350i 0.0838250i
\(661\) −3.71144 −0.144358 −0.0721792 0.997392i \(-0.522995\pi\)
−0.0721792 + 0.997392i \(0.522995\pi\)
\(662\) −5.29586 −0.205830
\(663\) 2.25593i 0.0876132i
\(664\) −6.85705 + 3.95892i −0.266105 + 0.153636i
\(665\) −1.84080 1.06279i −0.0713831 0.0412130i
\(666\) −0.656131 0.378818i −0.0254246 0.0146789i
\(667\) 48.1847 1.86572
\(668\) 36.4050 + 21.0184i 1.40855 + 0.813228i
\(669\) −2.27358 + 3.93796i −0.0879018 + 0.152250i
\(670\) 6.58821i 0.254525i
\(671\) 17.9906 0.694519
\(672\) −0.647813 + 1.12205i −0.0249899 + 0.0432838i
\(673\) 10.9305 + 18.9321i 0.421338 + 0.729779i 0.996071 0.0885620i \(-0.0282271\pi\)
−0.574732 + 0.818341i \(0.694894\pi\)
\(674\) 5.87308 + 3.39082i 0.226223 + 0.130610i
\(675\) 2.12972 + 3.68878i 0.0819730 + 0.141981i
\(676\) −11.4294 19.7963i −0.439591 0.761394i
\(677\) 30.3095i 1.16489i 0.812871 + 0.582444i \(0.197903\pi\)
−0.812871 + 0.582444i \(0.802097\pi\)
\(678\) −0.251332 0.435320i −0.00965236 0.0167184i
\(679\) 8.85437 15.3362i 0.339800 0.588550i
\(680\) 10.0728 + 5.81551i 0.386273 + 0.223015i
\(681\) −2.82092 −0.108098
\(682\) 3.07342 + 5.32332i 0.117687 + 0.203841i
\(683\) −6.11410 10.5899i −0.233949 0.405212i 0.725017 0.688731i \(-0.241832\pi\)
−0.958967 + 0.283518i \(0.908498\pi\)
\(684\) −2.59223 + 4.48988i −0.0991165 + 0.171675i
\(685\) −1.60545 + 0.926908i −0.0613412 + 0.0354154i
\(686\) 2.24838 + 3.89430i 0.0858434 + 0.148685i
\(687\) 3.82841i 0.146063i
\(688\) 14.3357i 0.546542i
\(689\) −6.08446 10.5386i −0.231800 0.401489i
\(690\) 0.632329i 0.0240723i
\(691\) −1.58963 + 0.917771i −0.0604722 + 0.0349136i −0.529931 0.848041i \(-0.677782\pi\)
0.469459 + 0.882954i \(0.344449\pi\)
\(692\) 29.8114i 1.13326i
\(693\) −4.76169 + 8.24749i −0.180882 + 0.313296i
\(694\) −3.64935 + 6.32086i −0.138527 + 0.239936i
\(695\) 2.50334 4.33591i 0.0949570 0.164470i
\(696\) −2.63529 + 1.52148i −0.0998903 + 0.0576717i
\(697\) −64.0089 −2.42451
\(698\) −1.89370 4.54304i −0.0716776 0.171956i
\(699\) −7.19660 −0.272201
\(700\) −5.70918 + 3.29620i −0.215787 + 0.124585i
\(701\) 19.0609 33.0144i 0.719919 1.24694i −0.241112 0.970497i \(-0.577512\pi\)
0.961031 0.276440i \(-0.0891546\pi\)
\(702\) 0.252416 0.437198i 0.00952683 0.0165010i
\(703\) −0.456179 + 0.790126i −0.0172051 + 0.0298002i
\(704\) 14.6451i 0.551959i
\(705\) −3.33190 + 1.92368i −0.125487 + 0.0724498i
\(706\) 3.02295i 0.113770i
\(707\) 9.03409 + 15.6475i 0.339762 + 0.588485i
\(708\) 5.14687i 0.193431i
\(709\) 17.0720i 0.641153i 0.947223 + 0.320576i \(0.103877\pi\)
−0.947223 + 0.320576i \(0.896123\pi\)
\(710\) 0.112402 + 0.194686i 0.00421837 + 0.00730644i
\(711\) −1.48398 + 0.856779i −0.0556538 + 0.0321317i
\(712\) 8.62295 14.9354i 0.323159 0.559727i
\(713\) −25.0995 43.4737i −0.939985 1.62810i
\(714\) −0.393643 0.681809i −0.0147317 0.0255161i
\(715\) 3.98944 0.149197
\(716\) −25.7226 14.8509i −0.961298 0.555006i
\(717\) 0.998124 1.72880i 0.0372756 0.0645633i
\(718\) 1.63881 + 2.83851i 0.0611600 + 0.105932i
\(719\) 30.1437i 1.12417i 0.827079 + 0.562086i \(0.190001\pi\)
−0.827079 + 0.562086i \(0.809999\pi\)
\(720\) −8.42668 14.5954i −0.314044 0.543940i
\(721\) 6.95942 + 12.0541i 0.259182 + 0.448917i
\(722\) 4.14077 + 2.39067i 0.154103 + 0.0889717i
\(723\) 0.112244 + 0.194413i 0.00417441 + 0.00723029i
\(724\) −16.2775 + 28.1934i −0.604948 + 1.04780i
\(725\) −23.3615 −0.867625
\(726\) 0.454876i 0.0168820i
\(727\) 10.6416 18.4318i 0.394675 0.683597i −0.598385 0.801209i \(-0.704191\pi\)
0.993060 + 0.117612i \(0.0375240\pi\)
\(728\) 1.37764 + 0.795382i 0.0510588 + 0.0294788i
\(729\) −22.2267 −0.823213
\(730\) 0.670026 + 0.386840i 0.0247988 + 0.0143176i
\(731\) −24.0710 13.8974i −0.890300 0.514015i
\(732\) 3.94675 2.27865i 0.145876 0.0842215i
\(733\) 10.3040i 0.380588i 0.981727 + 0.190294i \(0.0609441\pi\)
−0.981727 + 0.190294i \(0.939056\pi\)
\(734\) 0.343677 0.0126854
\(735\) 2.41355 0.0890250
\(736\) 14.8941i 0.549005i
\(737\) 35.5458i 1.30935i
\(738\) −6.10727 3.52603i −0.224812 0.129795i
\(739\) 30.1693 1.10980 0.554898 0.831919i \(-0.312757\pi\)
0.554898 + 0.831919i \(0.312757\pi\)
\(740\) −1.54029 2.66786i −0.0566222 0.0980726i
\(741\) −0.259202 0.149650i −0.00952202 0.00549754i
\(742\) −3.67781 2.12338i −0.135017 0.0779518i
\(743\) −29.1395 −1.06902 −0.534512 0.845161i \(-0.679505\pi\)
−0.534512 + 0.845161i \(0.679505\pi\)
\(744\) 2.74545 + 1.58509i 0.100653 + 0.0581122i
\(745\) 3.88824i 0.142454i
\(746\) 9.70407 0.355291
\(747\) −11.1222 + 19.2643i −0.406941 + 0.704842i
\(748\) −26.6932 15.4113i −0.976001 0.563494i
\(749\) 4.08455 7.07464i 0.149246 0.258502i
\(750\) 0.946907i 0.0345762i
\(751\) 13.9733i 0.509892i 0.966955 + 0.254946i \(0.0820577\pi\)
−0.966955 + 0.254946i \(0.917942\pi\)
\(752\) −24.5964 + 14.2007i −0.896937 + 0.517847i
\(753\) −2.56720 1.48217i −0.0935539 0.0540134i
\(754\) 1.38441 + 2.39787i 0.0504173 + 0.0873254i
\(755\) 2.23415 + 3.86967i 0.0813092 + 0.140832i
\(756\) 4.90004i 0.178213i
\(757\) 5.39746 + 3.11623i 0.196174 + 0.113261i 0.594870 0.803822i \(-0.297204\pi\)
−0.398696 + 0.917083i \(0.630537\pi\)
\(758\) −4.51105 −0.163849
\(759\) 3.41164i 0.123835i
\(760\) 1.33638 0.771559i 0.0484756 0.0279874i
\(761\) 36.0638 + 20.8214i 1.30731 + 0.754776i 0.981647 0.190710i \(-0.0610789\pi\)
0.325664 + 0.945486i \(0.394412\pi\)
\(762\) −1.72675 −0.0625537
\(763\) 10.6740i 0.386423i
\(764\) 26.5649 0.961085
\(765\) 32.6763 1.18141
\(766\) −2.21648 + 3.83906i −0.0800848