Properties

Label 441.2.w.a.251.13
Level $441$
Weight $2$
Character 441.251
Analytic conductor $3.521$
Analytic rank $0$
Dimension $120$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.w (of order \(14\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(120\)
Relative dimension: \(20\) over \(\Q(\zeta_{14})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label 251.13
Character \(\chi\) \(=\) 441.251
Dual form 441.2.w.a.188.13

$q$-expansion

\(f(q)\) \(=\) \(q+(0.920203 + 0.733838i) q^{2} +(-0.136785 - 0.599296i) q^{4} +(-1.46088 - 0.703524i) q^{5} +(-2.01956 - 1.70920i) q^{7} +(1.33526 - 2.77270i) q^{8} +O(q^{10})\) \(q+(0.920203 + 0.733838i) q^{2} +(-0.136785 - 0.599296i) q^{4} +(-1.46088 - 0.703524i) q^{5} +(-2.01956 - 1.70920i) q^{7} +(1.33526 - 2.77270i) q^{8} +(-0.828037 - 1.71944i) q^{10} +(2.35512 + 1.87814i) q^{11} +(-2.44072 - 1.94641i) q^{13} +(-0.604130 - 3.05484i) q^{14} +(2.15577 - 1.03816i) q^{16} +(0.882993 - 3.86864i) q^{17} -6.34682i q^{19} +(-0.221792 + 0.971733i) q^{20} +(0.788935 + 3.45655i) q^{22} +(-1.23051 + 0.280855i) q^{23} +(-1.47822 - 1.85362i) q^{25} +(-0.817612 - 3.58219i) q^{26} +(-0.748071 + 1.44411i) q^{28} +(7.25165 + 1.65514i) q^{29} +1.49304i q^{31} +(-3.25504 - 0.742941i) q^{32} +(3.65149 - 2.91197i) q^{34} +(1.74788 + 3.91776i) q^{35} +(-1.72116 + 7.54089i) q^{37} +(4.65754 - 5.84036i) q^{38} +(-3.90133 + 3.11121i) q^{40} +(9.09214 + 4.37855i) q^{41} +(-0.978095 + 0.471026i) q^{43} +(0.803418 - 1.66832i) q^{44} +(-1.33842 - 0.644549i) q^{46} +(-5.44608 + 6.82916i) q^{47} +(1.15725 + 6.90368i) q^{49} -2.79048i q^{50} +(-0.832622 + 1.72896i) q^{52} +(0.104261 - 0.0237970i) q^{53} +(-2.11923 - 4.40063i) q^{55} +(-7.43576 + 3.31741i) q^{56} +(5.45839 + 6.84461i) q^{58} +(1.54958 - 0.746240i) q^{59} +(-10.5852 - 2.41600i) q^{61} +(-1.09565 + 1.37390i) q^{62} +(-5.43377 - 6.81373i) q^{64} +(2.19626 + 4.56059i) q^{65} +11.0005 q^{67} -2.43924 q^{68} +(-1.26659 + 4.88779i) q^{70} +(3.29503 - 0.752069i) q^{71} +(8.80135 - 7.01884i) q^{73} +(-7.11761 + 5.67610i) q^{74} +(-3.80362 + 0.868152i) q^{76} +(-1.54618 - 7.81840i) q^{77} +14.5682 q^{79} -3.87969 q^{80} +(5.15348 + 10.7013i) q^{82} +(2.15744 + 2.70535i) q^{83} +(-4.01163 + 5.03043i) q^{85} +(-1.24570 - 0.284324i) q^{86} +(8.35225 - 4.02223i) q^{88} +(-7.65264 - 9.59610i) q^{89} +(1.60238 + 8.10259i) q^{91} +(0.336631 + 0.699021i) q^{92} +(-10.0230 + 2.28768i) q^{94} +(-4.46514 + 9.27196i) q^{95} -6.40900i q^{97} +(-4.00127 + 7.20202i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 120q + 24q^{4} + O(q^{10}) \) \( 120q + 24q^{4} - 32q^{16} - 44q^{22} - 4q^{25} - 56q^{28} + 112q^{34} - 76q^{37} + 28q^{40} + 8q^{43} - 40q^{46} - 84q^{49} - 140q^{52} + 12q^{58} - 84q^{61} + 24q^{64} + 16q^{67} + 112q^{70} - 84q^{76} - 24q^{79} + 140q^{82} - 96q^{85} - 24q^{88} - 112q^{91} - 112q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{9}{14}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.920203 + 0.733838i 0.650682 + 0.518902i 0.892284 0.451474i \(-0.149102\pi\)
−0.241602 + 0.970375i \(0.577673\pi\)
\(3\) 0 0
\(4\) −0.136785 0.599296i −0.0683927 0.299648i
\(5\) −1.46088 0.703524i −0.653327 0.314626i 0.0776976 0.996977i \(-0.475243\pi\)
−0.731024 + 0.682351i \(0.760957\pi\)
\(6\) 0 0
\(7\) −2.01956 1.70920i −0.763322 0.646018i
\(8\) 1.33526 2.77270i 0.472087 0.980299i
\(9\) 0 0
\(10\) −0.828037 1.71944i −0.261848 0.543734i
\(11\) 2.35512 + 1.87814i 0.710095 + 0.566282i 0.910539 0.413423i \(-0.135667\pi\)
−0.200444 + 0.979705i \(0.564238\pi\)
\(12\) 0 0
\(13\) −2.44072 1.94641i −0.676935 0.539838i 0.223567 0.974688i \(-0.428230\pi\)
−0.900503 + 0.434851i \(0.856801\pi\)
\(14\) −0.604130 3.05484i −0.161460 0.816441i
\(15\) 0 0
\(16\) 2.15577 1.03816i 0.538941 0.259540i
\(17\) 0.882993 3.86864i 0.214157 0.938284i −0.747550 0.664205i \(-0.768770\pi\)
0.961707 0.274079i \(-0.0883729\pi\)
\(18\) 0 0
\(19\) 6.34682i 1.45606i −0.685545 0.728030i \(-0.740436\pi\)
0.685545 0.728030i \(-0.259564\pi\)
\(20\) −0.221792 + 0.971733i −0.0495941 + 0.217286i
\(21\) 0 0
\(22\) 0.788935 + 3.45655i 0.168202 + 0.736939i
\(23\) −1.23051 + 0.280855i −0.256579 + 0.0585624i −0.348875 0.937169i \(-0.613436\pi\)
0.0922967 + 0.995732i \(0.470579\pi\)
\(24\) 0 0
\(25\) −1.47822 1.85362i −0.295643 0.370725i
\(26\) −0.817612 3.58219i −0.160347 0.702526i
\(27\) 0 0
\(28\) −0.748071 + 1.44411i −0.141372 + 0.272911i
\(29\) 7.25165 + 1.65514i 1.34660 + 0.307352i 0.834232 0.551414i \(-0.185912\pi\)
0.512367 + 0.858767i \(0.328769\pi\)
\(30\) 0 0
\(31\) 1.49304i 0.268158i 0.990971 + 0.134079i \(0.0428076\pi\)
−0.990971 + 0.134079i \(0.957192\pi\)
\(32\) −3.25504 0.742941i −0.575415 0.131335i
\(33\) 0 0
\(34\) 3.65149 2.91197i 0.626225 0.499398i
\(35\) 1.74788 + 3.91776i 0.295445 + 0.662221i
\(36\) 0 0
\(37\) −1.72116 + 7.54089i −0.282957 + 1.23971i 0.611025 + 0.791611i \(0.290757\pi\)
−0.893982 + 0.448103i \(0.852100\pi\)
\(38\) 4.65754 5.84036i 0.755552 0.947432i
\(39\) 0 0
\(40\) −3.90133 + 3.11121i −0.616854 + 0.491925i
\(41\) 9.09214 + 4.37855i 1.41995 + 0.683814i 0.977100 0.212780i \(-0.0682516\pi\)
0.442854 + 0.896594i \(0.353966\pi\)
\(42\) 0 0
\(43\) −0.978095 + 0.471026i −0.149158 + 0.0718308i −0.506974 0.861961i \(-0.669236\pi\)
0.357816 + 0.933792i \(0.383522\pi\)
\(44\) 0.803418 1.66832i 0.121120 0.251508i
\(45\) 0 0
\(46\) −1.33842 0.644549i −0.197339 0.0950336i
\(47\) −5.44608 + 6.82916i −0.794392 + 0.996136i 0.205455 + 0.978666i \(0.434132\pi\)
−0.999847 + 0.0174695i \(0.994439\pi\)
\(48\) 0 0
\(49\) 1.15725 + 6.90368i 0.165322 + 0.986240i
\(50\) 2.79048i 0.394634i
\(51\) 0 0
\(52\) −0.832622 + 1.72896i −0.115464 + 0.239763i
\(53\) 0.104261 0.0237970i 0.0143214 0.00326877i −0.215354 0.976536i \(-0.569091\pi\)
0.229676 + 0.973267i \(0.426233\pi\)
\(54\) 0 0
\(55\) −2.11923 4.40063i −0.285757 0.593381i
\(56\) −7.43576 + 3.31741i −0.993645 + 0.443308i
\(57\) 0 0
\(58\) 5.45839 + 6.84461i 0.716722 + 0.898741i
\(59\) 1.54958 0.746240i 0.201739 0.0971522i −0.330287 0.943881i \(-0.607145\pi\)
0.532025 + 0.846728i \(0.321431\pi\)
\(60\) 0 0
\(61\) −10.5852 2.41600i −1.35529 0.309337i −0.517668 0.855581i \(-0.673200\pi\)
−0.837626 + 0.546244i \(0.816057\pi\)
\(62\) −1.09565 + 1.37390i −0.139148 + 0.174486i
\(63\) 0 0
\(64\) −5.43377 6.81373i −0.679221 0.851717i
\(65\) 2.19626 + 4.56059i 0.272413 + 0.565672i
\(66\) 0 0
\(67\) 11.0005 1.34392 0.671961 0.740587i \(-0.265452\pi\)
0.671961 + 0.740587i \(0.265452\pi\)
\(68\) −2.43924 −0.295802
\(69\) 0 0
\(70\) −1.26659 + 4.88779i −0.151387 + 0.584203i
\(71\) 3.29503 0.752069i 0.391048 0.0892542i −0.0224758 0.999747i \(-0.507155\pi\)
0.413524 + 0.910493i \(0.364298\pi\)
\(72\) 0 0
\(73\) 8.80135 7.01884i 1.03012 0.821493i 0.0459897 0.998942i \(-0.485356\pi\)
0.984130 + 0.177449i \(0.0567844\pi\)
\(74\) −7.11761 + 5.67610i −0.827405 + 0.659833i
\(75\) 0 0
\(76\) −3.80362 + 0.868152i −0.436305 + 0.0995838i
\(77\) −1.54618 7.81840i −0.176203 0.890990i
\(78\) 0 0
\(79\) 14.5682 1.63905 0.819525 0.573044i \(-0.194238\pi\)
0.819525 + 0.573044i \(0.194238\pi\)
\(80\) −3.87969 −0.433763
\(81\) 0 0
\(82\) 5.15348 + 10.7013i 0.569107 + 1.18176i
\(83\) 2.15744 + 2.70535i 0.236810 + 0.296950i 0.886009 0.463668i \(-0.153467\pi\)
−0.649199 + 0.760619i \(0.724896\pi\)
\(84\) 0 0
\(85\) −4.01163 + 5.03043i −0.435123 + 0.545627i
\(86\) −1.24570 0.284324i −0.134328 0.0306594i
\(87\) 0 0
\(88\) 8.35225 4.02223i 0.890352 0.428771i
\(89\) −7.65264 9.59610i −0.811178 1.01718i −0.999385 0.0350556i \(-0.988839\pi\)
0.188207 0.982129i \(-0.439732\pi\)
\(90\) 0 0
\(91\) 1.60238 + 8.10259i 0.167975 + 0.849382i
\(92\) 0.336631 + 0.699021i 0.0350962 + 0.0728780i
\(93\) 0 0
\(94\) −10.0230 + 2.28768i −1.03379 + 0.235957i
\(95\) −4.46514 + 9.27196i −0.458114 + 0.951283i
\(96\) 0 0
\(97\) 6.40900i 0.650736i −0.945587 0.325368i \(-0.894512\pi\)
0.945587 0.325368i \(-0.105488\pi\)
\(98\) −4.00127 + 7.20202i −0.404189 + 0.727514i
\(99\) 0 0
\(100\) −0.908671 + 1.13944i −0.0908671 + 0.113944i
\(101\) 0.402455 + 0.193812i 0.0400458 + 0.0192850i 0.453799 0.891104i \(-0.350068\pi\)
−0.413754 + 0.910389i \(0.635783\pi\)
\(102\) 0 0
\(103\) −1.04038 + 2.16038i −0.102512 + 0.212869i −0.945916 0.324411i \(-0.894834\pi\)
0.843404 + 0.537280i \(0.180548\pi\)
\(104\) −8.65584 + 4.16843i −0.848775 + 0.408749i
\(105\) 0 0
\(106\) 0.113405 + 0.0546129i 0.0110149 + 0.00530447i
\(107\) −12.7985 + 10.2065i −1.23728 + 0.986698i −0.237397 + 0.971413i \(0.576294\pi\)
−0.999883 + 0.0152850i \(0.995134\pi\)
\(108\) 0 0
\(109\) 12.8699 16.1383i 1.23271 1.54577i 0.498419 0.866936i \(-0.333914\pi\)
0.734292 0.678834i \(-0.237515\pi\)
\(110\) 1.27923 5.60465i 0.121969 0.534383i
\(111\) 0 0
\(112\) −6.12813 1.58801i −0.579054 0.150053i
\(113\) 0.0806342 0.0643036i 0.00758543 0.00604918i −0.619690 0.784847i \(-0.712742\pi\)
0.627275 + 0.778798i \(0.284170\pi\)
\(114\) 0 0
\(115\) 1.99522 + 0.455395i 0.186055 + 0.0424658i
\(116\) 4.57228i 0.424526i
\(117\) 0 0
\(118\) 1.97355 + 0.450450i 0.181680 + 0.0414673i
\(119\) −8.39555 + 6.30375i −0.769619 + 0.577864i
\(120\) 0 0
\(121\) −0.428573 1.87770i −0.0389612 0.170700i
\(122\) −7.96757 9.99102i −0.721350 0.904544i
\(123\) 0 0
\(124\) 0.894772 0.204226i 0.0803529 0.0183400i
\(125\) 2.65947 + 11.6519i 0.237870 + 1.04218i
\(126\) 0 0
\(127\) 2.10534 9.22408i 0.186818 0.818504i −0.791462 0.611218i \(-0.790680\pi\)
0.978280 0.207286i \(-0.0664631\pi\)
\(128\) 3.58003i 0.316433i
\(129\) 0 0
\(130\) −1.32572 + 5.80837i −0.116274 + 0.509428i
\(131\) 9.38963 4.52181i 0.820376 0.395072i 0.0238790 0.999715i \(-0.492398\pi\)
0.796497 + 0.604643i \(0.206684\pi\)
\(132\) 0 0
\(133\) −10.8480 + 12.8178i −0.940641 + 1.11144i
\(134\) 10.1227 + 8.07256i 0.874466 + 0.697363i
\(135\) 0 0
\(136\) −9.54758 7.61394i −0.818698 0.652890i
\(137\) −0.174028 0.361374i −0.0148682 0.0308742i 0.893402 0.449257i \(-0.148311\pi\)
−0.908271 + 0.418383i \(0.862597\pi\)
\(138\) 0 0
\(139\) −0.906271 + 1.88189i −0.0768689 + 0.159620i −0.935861 0.352368i \(-0.885377\pi\)
0.858993 + 0.511988i \(0.171091\pi\)
\(140\) 2.10881 1.58339i 0.178227 0.133821i
\(141\) 0 0
\(142\) 3.58400 + 1.72596i 0.300762 + 0.144839i
\(143\) −2.09255 9.16807i −0.174988 0.766672i
\(144\) 0 0
\(145\) −9.42939 7.51968i −0.783068 0.624476i
\(146\) 13.2497 1.09655
\(147\) 0 0
\(148\) 4.75465 0.390830
\(149\) −6.31126 5.03306i −0.517038 0.412324i 0.329900 0.944016i \(-0.392985\pi\)
−0.846938 + 0.531692i \(0.821557\pi\)
\(150\) 0 0
\(151\) 3.42041 + 14.9858i 0.278349 + 1.21953i 0.899880 + 0.436137i \(0.143654\pi\)
−0.621532 + 0.783389i \(0.713489\pi\)
\(152\) −17.5979 8.47468i −1.42737 0.687387i
\(153\) 0 0
\(154\) 4.31464 8.32916i 0.347684 0.671183i
\(155\) 1.05039 2.18116i 0.0843693 0.175195i
\(156\) 0 0
\(157\) 4.33471 + 9.00113i 0.345948 + 0.718368i 0.999250 0.0387294i \(-0.0123311\pi\)
−0.653302 + 0.757097i \(0.726617\pi\)
\(158\) 13.4057 + 10.6907i 1.06650 + 0.850505i
\(159\) 0 0
\(160\) 4.23255 + 3.37535i 0.334613 + 0.266845i
\(161\) 2.96513 + 1.53598i 0.233685 + 0.121052i
\(162\) 0 0
\(163\) 0.815328 0.392641i 0.0638614 0.0307540i −0.401680 0.915780i \(-0.631574\pi\)
0.465542 + 0.885026i \(0.345859\pi\)
\(164\) 1.38037 6.04780i 0.107789 0.472254i
\(165\) 0 0
\(166\) 4.07268i 0.316101i
\(167\) 0.422648 1.85174i 0.0327055 0.143292i −0.955939 0.293565i \(-0.905158\pi\)
0.988644 + 0.150273i \(0.0480154\pi\)
\(168\) 0 0
\(169\) −0.724159 3.17275i −0.0557045 0.244057i
\(170\) −7.38304 + 1.68513i −0.566253 + 0.129244i
\(171\) 0 0
\(172\) 0.416073 + 0.521739i 0.0317253 + 0.0397822i
\(173\) 1.64885 + 7.22409i 0.125360 + 0.549237i 0.998131 + 0.0611080i \(0.0194634\pi\)
−0.872771 + 0.488129i \(0.837679\pi\)
\(174\) 0 0
\(175\) −0.182871 + 6.27008i −0.0138238 + 0.473973i
\(176\) 7.02690 + 1.60384i 0.529673 + 0.120894i
\(177\) 0 0
\(178\) 14.4462i 1.08279i
\(179\) 22.9124 + 5.22960i 1.71255 + 0.390879i 0.962667 0.270689i \(-0.0872514\pi\)
0.749885 + 0.661568i \(0.230109\pi\)
\(180\) 0 0
\(181\) 10.1147 8.06617i 0.751817 0.599554i −0.170785 0.985308i \(-0.554630\pi\)
0.922601 + 0.385755i \(0.126059\pi\)
\(182\) −4.47147 + 8.63192i −0.331448 + 0.639840i
\(183\) 0 0
\(184\) −0.864324 + 3.78685i −0.0637188 + 0.279170i
\(185\) 7.81961 9.80548i 0.574909 0.720913i
\(186\) 0 0
\(187\) 9.34543 7.45273i 0.683405 0.544998i
\(188\) 4.83763 + 2.32968i 0.352821 + 0.169909i
\(189\) 0 0
\(190\) −10.9130 + 5.25540i −0.791709 + 0.381267i
\(191\) −8.84660 + 18.3702i −0.640118 + 1.32922i 0.288250 + 0.957555i \(0.406927\pi\)
−0.928368 + 0.371663i \(0.878788\pi\)
\(192\) 0 0
\(193\) −3.34801 1.61232i −0.240995 0.116057i 0.309488 0.950903i \(-0.399842\pi\)
−0.550483 + 0.834846i \(0.685557\pi\)
\(194\) 4.70317 5.89759i 0.337668 0.423422i
\(195\) 0 0
\(196\) 3.97905 1.63786i 0.284218 0.116990i
\(197\) 22.4887i 1.60225i −0.598495 0.801127i \(-0.704234\pi\)
0.598495 0.801127i \(-0.295766\pi\)
\(198\) 0 0
\(199\) −3.52589 + 7.32159i −0.249944 + 0.519014i −0.987759 0.155989i \(-0.950143\pi\)
0.737815 + 0.675003i \(0.235858\pi\)
\(200\) −7.11336 + 1.62358i −0.502991 + 0.114804i
\(201\) 0 0
\(202\) 0.228114 + 0.473683i 0.0160500 + 0.0333282i
\(203\) −11.8162 15.7372i −0.829334 1.10454i
\(204\) 0 0
\(205\) −10.2021 12.7931i −0.712549 0.893508i
\(206\) −2.54274 + 1.22452i −0.177161 + 0.0853161i
\(207\) 0 0
\(208\) −7.28232 1.66214i −0.504938 0.115249i
\(209\) 11.9202 14.9475i 0.824540 1.03394i
\(210\) 0 0
\(211\) −7.04725 8.83697i −0.485153 0.608362i 0.477656 0.878547i \(-0.341487\pi\)
−0.962808 + 0.270185i \(0.912915\pi\)
\(212\) −0.0285229 0.0592283i −0.00195896 0.00406782i
\(213\) 0 0
\(214\) −19.2671 −1.31708
\(215\) 1.76026 0.120049
\(216\) 0 0
\(217\) 2.55191 3.01528i 0.173235 0.204691i
\(218\) 23.6858 5.40613i 1.60421 0.366149i
\(219\) 0 0
\(220\) −2.34740 + 1.87199i −0.158262 + 0.126209i
\(221\) −9.68512 + 7.72363i −0.651492 + 0.519547i
\(222\) 0 0
\(223\) −14.7674 + 3.37056i −0.988899 + 0.225710i −0.686229 0.727386i \(-0.740735\pi\)
−0.302670 + 0.953095i \(0.597878\pi\)
\(224\) 5.30391 + 7.06393i 0.354382 + 0.471979i
\(225\) 0 0
\(226\) 0.121388 0.00807463
\(227\) 10.2172 0.678137 0.339068 0.940762i \(-0.389888\pi\)
0.339068 + 0.940762i \(0.389888\pi\)
\(228\) 0 0
\(229\) 8.72661 + 18.1210i 0.576670 + 1.19747i 0.961583 + 0.274515i \(0.0885173\pi\)
−0.384912 + 0.922953i \(0.625768\pi\)
\(230\) 1.50182 + 1.88322i 0.0990270 + 0.124176i
\(231\) 0 0
\(232\) 14.2721 17.8966i 0.937009 1.17497i
\(233\) 13.2535 + 3.02504i 0.868269 + 0.198177i 0.633376 0.773845i \(-0.281669\pi\)
0.234893 + 0.972021i \(0.424526\pi\)
\(234\) 0 0
\(235\) 12.7606 6.14516i 0.832407 0.400866i
\(236\) −0.659179 0.826584i −0.0429089 0.0538060i
\(237\) 0 0
\(238\) −12.3515 0.360242i −0.800632 0.0233510i
\(239\) 4.93834 + 10.2546i 0.319434 + 0.663312i 0.997422 0.0717611i \(-0.0228619\pi\)
−0.677987 + 0.735073i \(0.737148\pi\)
\(240\) 0 0
\(241\) −10.7608 + 2.45609i −0.693166 + 0.158211i −0.554569 0.832138i \(-0.687117\pi\)
−0.138598 + 0.990349i \(0.544260\pi\)
\(242\) 0.983553 2.04237i 0.0632252 0.131288i
\(243\) 0 0
\(244\) 6.67413i 0.427267i
\(245\) 3.16629 10.8996i 0.202287 0.696351i
\(246\) 0 0
\(247\) −12.3535 + 15.4908i −0.786036 + 0.985658i
\(248\) 4.13976 + 1.99360i 0.262875 + 0.126594i
\(249\) 0 0
\(250\) −6.10336 + 12.6738i −0.386010 + 0.801558i
\(251\) 8.68576 4.18284i 0.548240 0.264019i −0.139194 0.990265i \(-0.544451\pi\)
0.687434 + 0.726246i \(0.258737\pi\)
\(252\) 0 0
\(253\) −3.42548 1.64962i −0.215358 0.103711i
\(254\) 8.70631 6.94305i 0.546283 0.435646i
\(255\) 0 0
\(256\) −8.24038 + 10.3331i −0.515024 + 0.645819i
\(257\) 4.54669 19.9204i 0.283615 1.24260i −0.609506 0.792781i \(-0.708632\pi\)
0.893121 0.449817i \(-0.148511\pi\)
\(258\) 0 0
\(259\) 16.3649 12.2875i 1.01686 0.763507i
\(260\) 2.43273 1.94003i 0.150871 0.120316i
\(261\) 0 0
\(262\) 11.9586 + 2.72948i 0.738807 + 0.168628i
\(263\) 2.13098i 0.131402i −0.997839 0.0657008i \(-0.979072\pi\)
0.997839 0.0657008i \(-0.0209283\pi\)
\(264\) 0 0
\(265\) −0.169055 0.0385858i −0.0103850 0.00237031i
\(266\) −19.3885 + 3.83430i −1.18879 + 0.235096i
\(267\) 0 0
\(268\) −1.50470 6.59254i −0.0919144 0.402703i
\(269\) 12.2811 + 15.4000i 0.748793 + 0.938957i 0.999577 0.0290862i \(-0.00925973\pi\)
−0.250784 + 0.968043i \(0.580688\pi\)
\(270\) 0 0
\(271\) −9.93868 + 2.26844i −0.603732 + 0.137798i −0.513452 0.858119i \(-0.671633\pi\)
−0.0902801 + 0.995916i \(0.528776\pi\)
\(272\) −2.11275 9.25658i −0.128105 0.561263i
\(273\) 0 0
\(274\) 0.105048 0.460246i 0.00634619 0.0278045i
\(275\) 7.14181i 0.430667i
\(276\) 0 0
\(277\) 1.55911 6.83089i 0.0936776 0.410428i −0.906247 0.422750i \(-0.861065\pi\)
0.999924 + 0.0123214i \(0.00392213\pi\)
\(278\) −2.21496 + 1.06667i −0.132844 + 0.0639744i
\(279\) 0 0
\(280\) 13.1967 + 0.384890i 0.788651 + 0.0230016i
\(281\) −19.0575 15.1979i −1.13688 0.906630i −0.140368 0.990099i \(-0.544828\pi\)
−0.996510 + 0.0834696i \(0.973400\pi\)
\(282\) 0 0
\(283\) −11.2353 8.95982i −0.667867 0.532606i 0.229824 0.973232i \(-0.426185\pi\)
−0.897691 + 0.440626i \(0.854756\pi\)
\(284\) −0.901424 1.87183i −0.0534897 0.111072i
\(285\) 0 0
\(286\) 4.80230 9.97208i 0.283966 0.589661i
\(287\) −10.8783 24.3831i −0.642127 1.43929i
\(288\) 0 0
\(289\) 1.12974 + 0.544053i 0.0664552 + 0.0320031i
\(290\) −3.15873 13.8393i −0.185487 0.812671i
\(291\) 0 0
\(292\) −5.41026 4.31453i −0.316611 0.252489i
\(293\) 6.11482 0.357232 0.178616 0.983919i \(-0.442838\pi\)
0.178616 + 0.983919i \(0.442838\pi\)
\(294\) 0 0
\(295\) −2.78876 −0.162368
\(296\) 18.6105 + 14.8413i 1.08171 + 0.862636i
\(297\) 0 0
\(298\) −2.11419 9.26288i −0.122472 0.536584i
\(299\) 3.54999 + 1.70959i 0.205301 + 0.0988679i
\(300\) 0 0
\(301\) 2.78040 + 0.720497i 0.160260 + 0.0415288i
\(302\) −7.84966 + 16.3000i −0.451697 + 0.937959i
\(303\) 0 0
\(304\) −6.58903 13.6823i −0.377907 0.784731i
\(305\) 13.7640 + 10.9764i 0.788125 + 0.628508i
\(306\) 0 0
\(307\) 19.0106 + 15.1604i 1.08499 + 0.865253i 0.991466 0.130364i \(-0.0416147\pi\)
0.0935262 + 0.995617i \(0.470186\pi\)
\(308\) −4.47404 + 1.99606i −0.254932 + 0.113736i
\(309\) 0 0
\(310\) 2.56719 1.23629i 0.145806 0.0702167i
\(311\) −6.98480 + 30.6024i −0.396072 + 1.73530i 0.246560 + 0.969128i \(0.420700\pi\)
−0.642632 + 0.766175i \(0.722157\pi\)
\(312\) 0 0
\(313\) 23.8964i 1.35070i −0.737496 0.675351i \(-0.763992\pi\)
0.737496 0.675351i \(-0.236008\pi\)
\(314\) −2.61655 + 11.4638i −0.147660 + 0.646942i
\(315\) 0 0
\(316\) −1.99271 8.73065i −0.112099 0.491138i
\(317\) −28.8101 + 6.57572i −1.61814 + 0.369329i −0.933224 0.359296i \(-0.883017\pi\)
−0.684913 + 0.728625i \(0.740160\pi\)
\(318\) 0 0
\(319\) 13.9699 + 17.5177i 0.782165 + 0.980804i
\(320\) 3.14448 + 13.7769i 0.175782 + 0.770150i
\(321\) 0 0
\(322\) 1.60136 + 3.58934i 0.0892401 + 0.200026i
\(323\) −24.5536 5.60420i −1.36620 0.311826i
\(324\) 0 0
\(325\) 7.40140i 0.410556i
\(326\) 1.03840 + 0.237009i 0.0575118 + 0.0131267i
\(327\) 0 0
\(328\) 24.2808 19.3633i 1.34068 1.06916i
\(329\) 22.6711 4.48347i 1.24990 0.247182i
\(330\) 0 0
\(331\) −2.23262 + 9.78176i −0.122716 + 0.537654i 0.875774 + 0.482721i \(0.160352\pi\)
−0.998490 + 0.0549329i \(0.982506\pi\)
\(332\) 1.32620 1.66300i 0.0727845 0.0912688i
\(333\) 0 0
\(334\) 1.74780 1.39382i 0.0956353 0.0762666i
\(335\) −16.0704 7.73910i −0.878020 0.422832i
\(336\) 0 0
\(337\) 2.17525 1.04754i 0.118493 0.0570633i −0.373698 0.927550i \(-0.621910\pi\)
0.492191 + 0.870487i \(0.336196\pi\)
\(338\) 1.66191 3.45099i 0.0903959 0.187709i
\(339\) 0 0
\(340\) 3.56345 + 1.71607i 0.193255 + 0.0930668i
\(341\) −2.80414 + 3.51629i −0.151853 + 0.190418i
\(342\) 0 0
\(343\) 9.46264 15.9204i 0.510934 0.859620i
\(344\) 3.34091i 0.180130i
\(345\) 0 0
\(346\) −3.78403 + 7.85762i −0.203431 + 0.422428i
\(347\) −21.6209 + 4.93483i −1.16067 + 0.264916i −0.759139 0.650929i \(-0.774380\pi\)
−0.401533 + 0.915845i \(0.631522\pi\)
\(348\) 0 0
\(349\) −12.3332 25.6101i −0.660180 1.37088i −0.914828 0.403844i \(-0.867674\pi\)
0.254648 0.967034i \(-0.418040\pi\)
\(350\) −4.76950 + 5.63555i −0.254940 + 0.301233i
\(351\) 0 0
\(352\) −6.27065 7.86315i −0.334227 0.419107i
\(353\) −8.75844 + 4.21784i −0.466165 + 0.224493i −0.652195 0.758051i \(-0.726152\pi\)
0.186031 + 0.982544i \(0.440438\pi\)
\(354\) 0 0
\(355\) −5.34276 1.21945i −0.283564 0.0647216i
\(356\) −4.70413 + 5.89880i −0.249319 + 0.312636i
\(357\) 0 0
\(358\) 17.2464 + 21.6263i 0.911500 + 1.14298i
\(359\) −5.14678 10.6874i −0.271637 0.564059i 0.719871 0.694108i \(-0.244201\pi\)
−0.991508 + 0.130049i \(0.958487\pi\)
\(360\) 0 0
\(361\) −21.2821 −1.12011
\(362\) 15.2268 0.800303
\(363\) 0 0
\(364\) 4.63667 2.06861i 0.243027 0.108425i
\(365\) −17.7957 + 4.06174i −0.931468 + 0.212601i
\(366\) 0 0
\(367\) −24.7126 + 19.7076i −1.28999 + 1.02873i −0.292618 + 0.956230i \(0.594526\pi\)
−0.997368 + 0.0725000i \(0.976902\pi\)
\(368\) −2.36111 + 1.88292i −0.123082 + 0.0981543i
\(369\) 0 0
\(370\) 14.3913 3.28471i 0.748166 0.170764i
\(371\) −0.251236 0.130144i −0.0130435 0.00675676i
\(372\) 0 0
\(373\) 21.5782 1.11728 0.558638 0.829411i \(-0.311324\pi\)
0.558638 + 0.829411i \(0.311324\pi\)
\(374\) 14.0688 0.727480
\(375\) 0 0
\(376\) 11.6633 + 24.2191i 0.601489 + 1.24900i
\(377\) −14.4777 18.1545i −0.745639 0.935002i
\(378\) 0 0
\(379\) 5.85961 7.34772i 0.300988 0.377427i −0.608221 0.793768i \(-0.708116\pi\)
0.909208 + 0.416341i \(0.136688\pi\)
\(380\) 6.16741 + 1.40767i 0.316382 + 0.0722120i
\(381\) 0 0
\(382\) −21.6214 + 10.4123i −1.10625 + 0.532740i
\(383\) 0.146422 + 0.183607i 0.00748181 + 0.00938190i 0.785558 0.618788i \(-0.212376\pi\)
−0.778077 + 0.628170i \(0.783804\pi\)
\(384\) 0 0
\(385\) −3.24165 + 12.5095i −0.165210 + 0.637545i
\(386\) −1.89767 3.94056i −0.0965890 0.200569i
\(387\) 0 0
\(388\) −3.84089 + 0.876658i −0.194992 + 0.0445056i
\(389\) 10.9367 22.7103i 0.554513 1.15146i −0.415766 0.909472i \(-0.636486\pi\)
0.970279 0.241987i \(-0.0777992\pi\)
\(390\) 0 0
\(391\) 5.00839i 0.253285i
\(392\) 20.6871 + 6.00951i 1.04486 + 0.303526i
\(393\) 0 0
\(394\) 16.5031 20.6942i 0.831412 1.04256i
\(395\) −21.2824 10.2491i −1.07083 0.515687i
\(396\) 0 0
\(397\) −10.6086 + 22.0291i −0.532432 + 1.10561i 0.445229 + 0.895417i \(0.353122\pi\)
−0.977661 + 0.210190i \(0.932592\pi\)
\(398\) −8.61740 + 4.14992i −0.431951 + 0.208017i
\(399\) 0 0
\(400\) −5.11105 2.46135i −0.255552 0.123068i
\(401\) −13.1606 + 10.4952i −0.657209 + 0.524107i −0.894350 0.447369i \(-0.852361\pi\)
0.237141 + 0.971475i \(0.423790\pi\)
\(402\) 0 0
\(403\) 2.90607 3.64410i 0.144762 0.181525i
\(404\) 0.0611008 0.267700i 0.00303988 0.0133186i
\(405\) 0 0
\(406\) 0.675262 23.1526i 0.0335127 1.14904i
\(407\) −18.2164 + 14.5271i −0.902954 + 0.720082i
\(408\) 0 0
\(409\) −8.16130 1.86276i −0.403550 0.0921077i 0.0159278 0.999873i \(-0.494930\pi\)
−0.419478 + 0.907765i \(0.637787\pi\)
\(410\) 19.2590i 0.951132i
\(411\) 0 0
\(412\) 1.43702 + 0.327990i 0.0707967 + 0.0161589i
\(413\) −4.40495 1.14147i −0.216754 0.0561683i
\(414\) 0 0
\(415\) −1.24849 5.47001i −0.0612861 0.268512i
\(416\) 6.49858 + 8.14896i 0.318619 + 0.399536i
\(417\) 0 0
\(418\) 21.9381 5.00723i 1.07303 0.244912i
\(419\) 5.69223 + 24.9393i 0.278084 + 1.21836i 0.900213 + 0.435450i \(0.143411\pi\)
−0.622129 + 0.782915i \(0.713732\pi\)
\(420\) 0 0
\(421\) 0.390341 1.71019i 0.0190240 0.0833497i −0.964525 0.263992i \(-0.914961\pi\)
0.983549 + 0.180643i \(0.0578178\pi\)
\(422\) 13.3034i 0.647597i
\(423\) 0 0
\(424\) 0.0732345 0.320861i 0.00355658 0.0155824i
\(425\) −8.47627 + 4.08195i −0.411159 + 0.198004i
\(426\) 0 0
\(427\) 17.2480 + 22.9715i 0.834689 + 1.11167i
\(428\) 7.86735 + 6.27400i 0.380283 + 0.303265i
\(429\) 0 0
\(430\) 1.61980 + 1.29175i 0.0781136 + 0.0622935i
\(431\) 11.7556 + 24.4108i 0.566248 + 1.17583i 0.965841 + 0.259134i \(0.0834372\pi\)
−0.399593 + 0.916693i \(0.630849\pi\)
\(432\) 0 0
\(433\) −13.8451 + 28.7496i −0.665351 + 1.38162i 0.245709 + 0.969344i \(0.420979\pi\)
−0.911061 + 0.412273i \(0.864735\pi\)
\(434\) 4.56100 0.901990i 0.218935 0.0432969i
\(435\) 0 0
\(436\) −11.4320 5.50538i −0.547495 0.263660i
\(437\) 1.78254 + 7.80981i 0.0852704 + 0.373594i
\(438\) 0 0
\(439\) 23.1323 + 18.4474i 1.10405 + 0.880448i 0.993546 0.113429i \(-0.0361833\pi\)
0.110500 + 0.993876i \(0.464755\pi\)
\(440\) −15.0314 −0.716594
\(441\) 0 0
\(442\) −14.5802 −0.693508
\(443\) 2.08603 + 1.66356i 0.0991105 + 0.0790380i 0.671791 0.740740i \(-0.265525\pi\)
−0.572681 + 0.819778i \(0.694097\pi\)
\(444\) 0 0
\(445\) 4.42852 + 19.4026i 0.209932 + 0.919771i
\(446\) −16.0625 7.73528i −0.760580 0.366276i
\(447\) 0 0
\(448\) −0.672217 + 23.0482i −0.0317593 + 1.08892i
\(449\) 7.81973 16.2378i 0.369036 0.766310i −0.630919 0.775849i \(-0.717322\pi\)
0.999955 + 0.00953840i \(0.00303621\pi\)
\(450\) 0 0
\(451\) 13.1895 + 27.3884i 0.621071 + 1.28967i
\(452\) −0.0495665 0.0395279i −0.00233141 0.00185924i
\(453\) 0 0
\(454\) 9.40186 + 7.49774i 0.441251 + 0.351886i
\(455\) 3.35948 12.9643i 0.157495 0.607774i
\(456\) 0 0
\(457\) −17.2758 + 8.31958i −0.808127 + 0.389173i −0.791866 0.610694i \(-0.790890\pi\)
−0.0162604 + 0.999868i \(0.505176\pi\)
\(458\) −5.26761 + 23.0789i −0.246139 + 1.07841i
\(459\) 0 0
\(460\) 1.25802i 0.0586553i
\(461\) 3.12162 13.6767i 0.145389 0.636989i −0.848743 0.528806i \(-0.822640\pi\)
0.994131 0.108182i \(-0.0345031\pi\)
\(462\) 0 0
\(463\) 4.48852 + 19.6655i 0.208599 + 0.913932i 0.965500 + 0.260403i \(0.0838553\pi\)
−0.756901 + 0.653529i \(0.773288\pi\)
\(464\) 17.3512 3.96029i 0.805508 0.183852i
\(465\) 0 0
\(466\) 9.97607 + 12.5096i 0.462133 + 0.579496i
\(467\) 8.78197 + 38.4763i 0.406381 + 1.78047i 0.600638 + 0.799521i \(0.294913\pi\)
−0.194257 + 0.980951i \(0.562229\pi\)
\(468\) 0 0
\(469\) −22.2161 18.8020i −1.02585 0.868197i
\(470\) 16.2519 + 3.70938i 0.749643 + 0.171101i
\(471\) 0 0
\(472\) 5.29296i 0.243628i
\(473\) −3.18819 0.727683i −0.146593 0.0334589i
\(474\) 0 0
\(475\) −11.7646 + 9.38197i −0.539798 + 0.430474i
\(476\) 4.92620 + 4.16916i 0.225792 + 0.191093i
\(477\) 0 0
\(478\) −2.98091 + 13.0602i −0.136344 + 0.597360i
\(479\) −15.8455 + 19.8697i −0.724001 + 0.907869i −0.998557 0.0537025i \(-0.982898\pi\)
0.274556 + 0.961571i \(0.411469\pi\)
\(480\) 0 0
\(481\) 18.8786 15.0551i 0.860788 0.686456i
\(482\) −11.7045 5.63660i −0.533127 0.256740i
\(483\) 0 0
\(484\) −1.06667 + 0.513684i −0.0484852 + 0.0233493i
\(485\) −4.50889 + 9.36281i −0.204738 + 0.425143i
\(486\) 0 0
\(487\) −4.73926 2.28231i −0.214757 0.103421i 0.323413 0.946258i \(-0.395170\pi\)
−0.538170 + 0.842837i \(0.680884\pi\)
\(488\) −20.8329 + 26.1236i −0.943060 + 1.18256i
\(489\) 0 0
\(490\) 10.9122 7.70633i 0.492962 0.348136i
\(491\) 32.1882i 1.45263i 0.687361 + 0.726316i \(0.258769\pi\)
−0.687361 + 0.726316i \(0.741231\pi\)
\(492\) 0 0
\(493\) 12.8063 26.5926i 0.576768 1.19767i
\(494\) −22.7355 + 5.18923i −1.02292 + 0.233475i
\(495\) 0 0
\(496\) 1.55002 + 3.21864i 0.0695978 + 0.144521i
\(497\) −7.93996 4.11303i −0.356156 0.184494i
\(498\) 0 0
\(499\) −16.9252 21.2236i −0.757677 0.950097i 0.242120 0.970246i \(-0.422157\pi\)
−0.999797 + 0.0201497i \(0.993586\pi\)
\(500\) 6.61916 3.18762i 0.296018 0.142555i
\(501\) 0 0
\(502\) 11.0622 + 2.52487i 0.493730 + 0.112691i
\(503\) 24.4642 30.6772i 1.09081 1.36783i 0.166559 0.986031i \(-0.446734\pi\)
0.924247 0.381796i \(-0.124694\pi\)
\(504\) 0 0
\(505\) −0.451588 0.566274i −0.0200954 0.0251988i
\(506\) −1.94158 4.03174i −0.0863138 0.179233i
\(507\) 0 0
\(508\) −5.81593 −0.258040
\(509\) 43.5926 1.93221 0.966104 0.258153i \(-0.0831139\pi\)
0.966104 + 0.258153i \(0.0831139\pi\)
\(510\) 0 0
\(511\) −29.7715 0.868307i −1.31701 0.0384116i
\(512\) −22.1462 + 5.05472i −0.978733 + 0.223389i
\(513\) 0 0
\(514\) 18.8022 14.9943i 0.829329 0.661368i
\(515\) 3.03976 2.42413i 0.133948 0.106820i
\(516\) 0 0
\(517\) −25.6523 + 5.85497i −1.12819 + 0.257501i
\(518\) 24.0760 + 0.702196i 1.05784 + 0.0308527i
\(519\) 0 0
\(520\) 15.5778 0.683130
\(521\) 8.32018 0.364514 0.182257 0.983251i \(-0.441660\pi\)
0.182257 + 0.983251i \(0.441660\pi\)
\(522\) 0 0
\(523\) −12.8076 26.5953i −0.560039 1.16293i −0.968236 0.250039i \(-0.919557\pi\)
0.408197 0.912894i \(-0.366158\pi\)
\(524\) −3.99426 5.00865i −0.174490 0.218804i
\(525\) 0 0
\(526\) 1.56379 1.96093i 0.0681845 0.0855007i
\(527\) 5.77604 + 1.31834i 0.251608 + 0.0574279i
\(528\) 0 0
\(529\) −19.2870 + 9.28814i −0.838566 + 0.403832i
\(530\) −0.127250 0.159566i −0.00552737 0.00693111i
\(531\) 0 0
\(532\) 9.16549 + 4.74787i 0.397375 + 0.205846i
\(533\) −13.6690 28.3839i −0.592068 1.22944i
\(534\) 0 0
\(535\) 25.8777 5.90641i 1.11879 0.255356i
\(536\) 14.6885 30.5011i 0.634448 1.31745i
\(537\) 0 0
\(538\) 23.1835i 0.999513i
\(539\) −10.2406 + 18.4325i −0.441095 + 0.793943i
\(540\) 0 0
\(541\) −26.2932 + 32.9706i −1.13043 + 1.41752i −0.235182 + 0.971951i \(0.575569\pi\)
−0.895250 + 0.445565i \(0.853003\pi\)
\(542\) −10.8103 5.20595i −0.464341 0.223615i
\(543\) 0 0
\(544\) −5.74835 + 11.9366i −0.246458 + 0.511776i
\(545\) −30.1551 + 14.5219i −1.29170 + 0.622051i
\(546\) 0 0
\(547\) 22.5823 + 10.8751i 0.965549 + 0.464984i 0.849111 0.528214i \(-0.177138\pi\)
0.116438 + 0.993198i \(0.462852\pi\)
\(548\) −0.192765 + 0.153725i −0.00823452 + 0.00656681i
\(549\) 0 0
\(550\) 5.24093 6.57192i 0.223474 0.280227i
\(551\) 10.5049 46.0249i 0.447523 1.96073i
\(552\) 0 0
\(553\) −29.4213 24.9000i −1.25112 1.05885i
\(554\) 6.44746 5.14168i 0.273926 0.218449i
\(555\) 0 0
\(556\) 1.25177 + 0.285709i 0.0530870 + 0.0121168i
\(557\) 38.6766i 1.63878i −0.573237 0.819389i \(-0.694313\pi\)
0.573237 0.819389i \(-0.305687\pi\)
\(558\) 0 0
\(559\) 3.30407 + 0.754133i 0.139747 + 0.0318964i
\(560\) 7.83528 + 6.63118i 0.331101 + 0.280219i
\(561\) 0 0
\(562\) −6.38404 27.9703i −0.269294 1.17986i
\(563\) 16.3519 + 20.5046i 0.689150 + 0.864167i 0.996161 0.0875387i \(-0.0279001\pi\)
−0.307011 + 0.951706i \(0.599329\pi\)
\(564\) 0 0
\(565\) −0.163036 + 0.0372120i −0.00685899 + 0.00156552i
\(566\) −3.76367 16.4897i −0.158199 0.693114i
\(567\) 0 0
\(568\) 2.31447 10.1404i 0.0971131 0.425480i
\(569\) 0.617863i 0.0259022i −0.999916 0.0129511i \(-0.995877\pi\)
0.999916 0.0129511i \(-0.00412257\pi\)
\(570\) 0 0
\(571\) 7.72061 33.8262i 0.323098 1.41558i −0.508911 0.860819i \(-0.669952\pi\)
0.832008 0.554763i \(-0.187191\pi\)
\(572\) −5.20815 + 2.50811i −0.217764 + 0.104870i
\(573\) 0 0
\(574\) 7.88294 30.4203i 0.329028 1.26972i
\(575\) 2.33956 + 1.86573i 0.0975663 + 0.0778065i
\(576\) 0 0
\(577\) 20.0054 + 15.9538i 0.832837 + 0.664165i 0.944112 0.329624i \(-0.106922\pi\)
−0.111275 + 0.993790i \(0.535494\pi\)
\(578\) 0.640342 + 1.32968i 0.0266347 + 0.0553076i
\(579\) 0 0
\(580\) −3.21671 + 6.67957i −0.133567 + 0.277354i
\(581\) 0.266899 9.15112i 0.0110728 0.379652i
\(582\) 0 0
\(583\) 0.290242 + 0.139773i 0.0120206 + 0.00578882i
\(584\) −7.70905 33.7755i −0.319003 1.39764i
\(585\) 0 0
\(586\) 5.62688 + 4.48729i 0.232444 + 0.185368i
\(587\) 28.4634 1.17481 0.587405 0.809293i \(-0.300150\pi\)
0.587405 + 0.809293i \(0.300150\pi\)
\(588\) 0 0
\(589\) 9.47605 0.390454
\(590\) −2.56622 2.04650i −0.105650 0.0842529i
\(591\) 0 0
\(592\) 4.11825 + 18.0432i 0.169259 + 0.741572i
\(593\) 19.9794 + 9.62156i 0.820455 + 0.395110i 0.796527 0.604604i \(-0.206668\pi\)
0.0239281 + 0.999714i \(0.492383\pi\)
\(594\) 0 0
\(595\) 16.6998 3.30257i 0.684624 0.135392i
\(596\) −2.15300 + 4.47076i −0.0881905 + 0.183129i
\(597\) 0 0
\(598\) 2.01216 + 4.17829i 0.0822832 + 0.170863i
\(599\) −11.2925 9.00546i −0.461398 0.367953i 0.365029 0.930996i \(-0.381059\pi\)
−0.826427 + 0.563043i \(0.809630\pi\)
\(600\) 0 0
\(601\) 3.05140 + 2.43341i 0.124469 + 0.0992610i 0.683746 0.729720i \(-0.260350\pi\)
−0.559277 + 0.828981i \(0.688921\pi\)
\(602\) 2.02981 + 2.70337i 0.0827288 + 0.110181i
\(603\) 0 0
\(604\) 8.51305 4.09967i 0.346391 0.166813i
\(605\) −0.694913 + 3.04461i −0.0282522 + 0.123781i
\(606\) 0 0
\(607\) 40.6191i 1.64868i −0.566097 0.824338i \(-0.691547\pi\)
0.566097 0.824338i \(-0.308453\pi\)
\(608\) −4.71531 + 20.6591i −0.191231 + 0.837839i
\(609\) 0 0
\(610\) 4.61077 + 20.2011i 0.186685 + 0.817918i
\(611\) 26.5847 6.06779i 1.07550 0.245477i
\(612\) 0 0
\(613\) −6.96530 8.73421i −0.281326 0.352771i 0.621012 0.783801i \(-0.286722\pi\)
−0.902338 + 0.431030i \(0.858150\pi\)
\(614\) 6.36831 + 27.9014i 0.257004 + 1.12601i
\(615\) 0 0
\(616\) −23.7427 6.15254i −0.956620 0.247893i
\(617\) −26.4798 6.04385i −1.06604 0.243316i −0.346699 0.937976i \(-0.612698\pi\)
−0.719338 + 0.694660i \(0.755555\pi\)
\(618\) 0 0
\(619\) 13.0186i 0.523262i −0.965168 0.261631i \(-0.915740\pi\)
0.965168 0.261631i \(-0.0842603\pi\)
\(620\) −1.45084 0.331144i −0.0582670 0.0132991i
\(621\) 0 0
\(622\) −28.8846 + 23.0347i −1.15817 + 0.923608i
\(623\) −0.946715 + 32.4598i −0.0379293 + 1.30048i
\(624\) 0 0
\(625\) 1.67438 7.33593i 0.0669751 0.293437i
\(626\) 17.5361 21.9895i 0.700882 0.878878i
\(627\) 0 0
\(628\) 4.80141 3.82900i 0.191597 0.152794i
\(629\) 27.6532 + 13.3171i 1.10261 + 0.530988i
\(630\) 0 0
\(631\) −13.3941 + 6.45024i −0.533209 + 0.256780i −0.681057 0.732230i \(-0.738480\pi\)
0.147848 + 0.989010i \(0.452765\pi\)
\(632\) 19.4524 40.3933i 0.773774 1.60676i
\(633\) 0 0
\(634\) −31.3367 15.0909i −1.24454 0.599338i
\(635\) −9.56501 + 11.9941i −0.379576 + 0.475973i
\(636\) 0 0
\(637\) 10.6129 19.1025i 0.420497 0.756867i
\(638\) 26.3715i 1.04406i
\(639\) 0 0
\(640\) −2.51864 + 5.23001i −0.0995580 + 0.206734i
\(641\) 3.54318 0.808708i 0.139947 0.0319420i −0.151973 0.988385i \(-0.548563\pi\)
0.291921 + 0.956443i \(0.405706\pi\)
\(642\) 0 0
\(643\) −9.21696 19.1392i −0.363482 0.754777i 0.636381 0.771375i \(-0.280431\pi\)
−0.999862 + 0.0165979i \(0.994716\pi\)
\(644\) 0.514922 1.98709i 0.0202908 0.0783022i
\(645\) 0 0
\(646\) −18.4817 23.1753i −0.727154 0.911822i
\(647\) −39.8148 + 19.1738i −1.56528 + 0.753799i −0.997586 0.0694398i \(-0.977879\pi\)
−0.567695 + 0.823239i \(0.692165\pi\)
\(648\) 0 0
\(649\) 5.05100 + 1.15286i 0.198269 + 0.0452536i
\(650\) −5.43143 + 6.81080i −0.213038 + 0.267141i
\(651\) 0 0
\(652\) −0.346833 0.434915i −0.0135830 0.0170326i
\(653\) −10.1195 21.0133i −0.396006 0.822314i −0.999685 0.0250873i \(-0.992014\pi\)
0.603679 0.797227i \(-0.293701\pi\)
\(654\) 0 0
\(655\) −16.8984 −0.660273
\(656\) 24.1462 0.942750
\(657\) 0 0
\(658\) 24.1522 + 12.5112i 0.941550 + 0.487738i
\(659\) 1.63674 0.373574i 0.0637582 0.0145524i −0.190523 0.981683i \(-0.561018\pi\)
0.254281 + 0.967130i \(0.418161\pi\)
\(660\) 0 0
\(661\) 19.4053 15.4752i 0.754778 0.601915i −0.168655 0.985675i \(-0.553942\pi\)
0.923433 + 0.383760i \(0.125371\pi\)
\(662\) −9.23270 + 7.36283i −0.358839 + 0.286164i
\(663\) 0 0
\(664\) 10.3819 2.36960i 0.402895 0.0919582i
\(665\) 24.8653 11.0935i 0.964234 0.430186i
\(666\) 0 0
\(667\) −9.38807 −0.363508
\(668\) −1.16755 −0.0451739
\(669\) 0 0
\(670\) −9.10880 18.9146i −0.351904 0.730736i
\(671\) −20.3918 25.5705i −0.787216 0.987137i
\(672\) 0 0
\(673\) −28.7486 + 36.0496i −1.10818 + 1.38961i −0.195612 + 0.980681i \(0.562669\pi\)
−0.912566 + 0.408930i \(0.865902\pi\)
\(674\) 2.77040 + 0.632325i 0.106712 + 0.0243562i
\(675\) 0 0
\(676\) −1.80236 + 0.867971i −0.0693215 + 0.0333835i
\(677\) −13.8596 17.3794i −0.532669 0.667945i 0.440576 0.897715i \(-0.354774\pi\)
−0.973245 + 0.229770i \(0.926203\pi\)
\(678\) 0 0
\(679\) −10.9543 + 12.9434i −0.420387 + 0.496721i
\(680\) 8.59131 + 17.8400i 0.329462 + 0.684134i
\(681\) 0 0
\(682\) −5.16077 + 1.17791i −0.197616 + 0.0451046i
\(683\) 6.17866 12.8301i 0.236420 0.490931i −0.748676 0.662936i \(-0.769310\pi\)
0.985096 + 0.172005i \(0.0550245\pi\)
\(684\) 0 0
\(685\) 0.650358i 0.0248489i
\(686\) 20.3905 7.70595i 0.778514 0.294215i
\(687\) 0 0
\(688\) −1.61954 + 2.03084i −0.0617445 + 0.0774252i
\(689\) −0.300792 0.144854i −0.0114593 0.00551849i
\(690\) 0 0
\(691\) 11.3856 23.6425i 0.433130 0.899404i −0.564148 0.825674i \(-0.690795\pi\)
0.997278 0.0737304i \(-0.0234904\pi\)
\(692\) 4.10383 1.97630i 0.156004 0.0751276i
\(693\) 0 0
\(694\) −23.5170 11.3252i −0.892693 0.429898i
\(695\) 2.64791 2.11164i 0.100441 0.0800990i
\(696\) 0 0
\(697\) 24.9673 31.3080i 0.945705 1.18588i
\(698\) 7.44463 32.6171i 0.281784 1.23457i
\(699\) 0 0
\(700\) 3.78264 0.748061i 0.142971 0.0282740i
\(701\) −6.68543 + 5.33145i −0.252505 + 0.201366i −0.741559 0.670887i \(-0.765913\pi\)
0.489054 + 0.872253i \(0.337342\pi\)
\(702\) 0 0
\(703\) 47.8607 + 10.9239i 1.80510 + 0.412002i
\(704\) 26.2526i 0.989431i
\(705\) 0 0
\(706\) −11.1548 2.54600i −0.419815 0.0958200i
\(707\) −0.481518 1.07929i −0.0181094 0.0405910i
\(708\) 0 0
\(709\) −2.32873 10.2028i −0.0874573 0.383176i 0.912189 0.409770i \(-0.134391\pi\)
−0.999646 + 0.0265942i \(0.991534\pi\)
\(710\) −4.02154 5.04286i −0.150926 0.189255i
\(711\) 0 0
\(712\) −36.8255 + 8.40517i −1.38009 + 0.314997i
\(713\) −0.419328 1.83720i −0.0157040 0.0688036i
\(714\) 0 0
\(715\) −3.39298 + 14.8656i −0.126890 + 0.555943i
\(716\) 14.4466i 0.539896i
\(717\) 0 0
\(718\) 3.10673 13.6115i 0.115942 0.507976i
\(719\) −24.6264 + 11.8595i −0.918411 + 0.442283i −0.832503 0.554020i \(-0.813093\pi\)
−0.0859072 + 0.996303i \(0.527379\pi\)
\(720\) 0 0
\(721\) 5.79365 2.58479i 0.215767 0.0962628i
\(722\) −19.5839 15.6176i −0.728836 0.581228i
\(723\) 0 0
\(724\) −6.21756 4.95834i −0.231074 0.184275i
\(725\) −7.65150 15.8885i −0.284169 0.590084i
\(726\) 0 0
\(727\) −8.59104 + 17.8395i −0.318624 + 0.661629i −0.997349 0.0727629i \(-0.976818\pi\)
0.678725 + 0.734392i \(0.262533\pi\)
\(728\) 24.6057 + 6.37618i 0.911948 + 0.236317i
\(729\) 0 0
\(730\) −19.3563 9.32150i −0.716408 0.345004i
\(731\) 0.958581 + 4.19982i 0.0354544 + 0.155336i
\(732\) 0 0
\(733\) 4.46629 + 3.56175i 0.164966 + 0.131556i 0.702493 0.711690i \(-0.252070\pi\)
−0.537527 + 0.843246i \(0.680641\pi\)
\(734\) −37.2028 −1.37318
\(735\) 0 0
\(736\) 4.21401 0.155330
\(737\) 25.9074 + 20.6605i 0.954312 + 0.761039i
\(738\) 0 0
\(739\) 1.07259 + 4.69931i 0.0394558 + 0.172867i 0.990817 0.135211i \(-0.0431713\pi\)
−0.951361 + 0.308078i \(0.900314\pi\)
\(740\) −6.94599 3.34501i −0.255340 0.122965i
\(741\) 0 0
\(742\) −0.135684 0.304126i −0.00498110 0.0111648i
\(743\) 4.67324 9.70408i 0.171444 0.356008i −0.797488 0.603335i \(-0.793838\pi\)
0.968932 + 0.247327i \(0.0795523\pi\)
\(744\) 0 0
\(745\) 5.67913 + 11.7928i 0.208067 + 0.432056i
\(746\) 19.8563 + 15.8349i 0.726992 + 0.579757i
\(747\) 0 0
\(748\) −5.74471 4.58125i −0.210047 0.167507i
\(749\) 43.2923 + 1.26265i 1.58187 + 0.0461363i
\(750\) 0 0
\(751\) 41.2195 19.8503i 1.50412 0.724346i 0.513134 0.858308i \(-0.328484\pi\)
0.990986 + 0.133962i \(0.0427700\pi\)
\(752\) −4.65069 + 20.3760i −0.169593 + 0.743036i
\(753\) 0 0
\(754\) 27.3301i 0.995303i
\(755\) 5.54605 24.2988i 0.201841 0.884324i
\(756\) 0 0
\(757\) −4.65249 20.3839i −0.169098 0.740866i −0.986360 0.164600i \(-0.947367\pi\)
0.817263 0.576265i \(-0.195491\pi\)
\(758\) 10.7841 2.46139i 0.391695 0.0894018i
\(759\) 0 0
\(760\) 19.7463 + 24.7610i 0.716272 + 0.898177i
\(761\) 10.3439 + 45.3197i 0.374967 + 1.64284i 0.712608 + 0.701562i \(0.247514\pi\)
−0.337641 + 0.941275i \(0.609629\pi\)
\(762\) 0 0
\(763\) −53.5752 + 10.5951i −1.93955 + 0.383568i
\(764\) 12.2192 + 2.78896i 0.442077 + 0.100901i
\(765\) 0 0
\(766\) 0.276406i 0.00998696i
\(767\) −5.23460 1.19476i −0.189010 0.0431404i
\(768\) 0 0
\(769\) 33.0698 26.3723i 1.19253 0.951009i 0.192984 0.981202i \(-0.438183\pi\)
0.999544 + 0.0301926i \(0.00961206\pi\)
\(770\) −12.1630 + 9.13248i −0.438323 + 0.329112i
\(771\) 0 0
\(772\) −0.508296 + 2.22699i −0.0182940 + 0.0801511i
\(773\) 11.8115 14.8111i 0.424829 0.532719i −0.522645 0.852550i \(-0.675055\pi\)
0.947475 + 0.319831i \(0.103626\pi\)
\(774\) 0 0
\(775\) 2.76753 2.20703i 0.0994128 0.0792790i
\(776\) −17.7703 8.55772i −0.637916 0.307204i
\(777\) 0 0
\(778\) 26.7297 12.8723i 0.958306 0.461496i
\(779\) 27.7898 57.7062i 0.995674 2.06754i
\(780\) 0 0
\(781\) 9.17269 + 4.41733i 0.328225 + 0.158065i
\(782\) −3.67535 + 4.60874i −0.131430 + 0.164808i
\(783\) 0 0
\(784\) 9.66190 + 13.6813i 0.345068 + 0.488618i
\(785\) 16.1992i 0.578173i
\(786\) 0 0
\(787\) −8.74293 + 18.1549i −0.311652 + 0.647152i −0.996685 0.0813603i \(-0.974074\pi\)
0.685033 + 0.728512i \(0.259788\pi\)
\(788\) −13.4774 + 3.07612i −0.480112 + 0.109582i
\(789\) 0