Properties

Label 441.2.w.a.251.8
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 251.8
Character \(\chi\) \(=\) 441.251
Dual form 441.2.w.a.188.8

$q$-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 0.241602 0.970375i \(-0.422327\pi\)
−0.892284 + 0.451474i \(0.850898\pi\)
\(3\) 0 0
\(4\) −0.136785 0.599296i −0.0683927 0.299648i
\(5\) 1.46088 + 0.703524i 0.653327 + 0.314626i 0.731024 0.682351i \(-0.239043\pi\)
−0.0776976 + 0.996977i \(0.524757\pi\)
\(6\) 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 0.200444 0.979705i \(-0.435762\pi\)
−0.910539 + 0.413423i \(0.864333\pi\)
\(12\) 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 \(0.231230\pi\)
−0.961707 + 0.274079i \(0.911627\pi\)
\(18\) 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 −0.0922967 0.995732i \(-0.529421\pi\)
0.348875 + 0.937169i \(0.386564\pi\)
\(24\) 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 −0.512367 0.858767i \(-0.671231\pi\)
−0.834232 + 0.551414i \(0.814088\pi\)
\(30\) 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 −0.442854 0.896594i \(-0.646034\pi\)
−0.977100 + 0.212780i \(0.931748\pi\)
\(42\) 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 \(-0.565868\pi\)
0.999847 0.0174695i \(-0.00556100\pi\)
\(48\) 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 −0.229676 0.973267i \(-0.573767\pi\)
0.215354 + 0.976536i \(0.430909\pi\)
\(54\) 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 −0.532025 0.846728i \(-0.678569\pi\)
0.330287 + 0.943881i \(0.392855\pi\)
\(60\) 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 −0.413524 0.910493i \(-0.635702\pi\)
0.0224758 + 0.999747i \(0.492845\pi\)
\(72\) 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 0.649199 0.760619i \(-0.275104\pi\)
−0.886009 + 0.463668i \(0.846533\pi\)
\(84\) 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 \(0.0111608\pi\)
−0.188207 + 0.982129i \(0.560268\pi\)
\(90\) 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 0.413754 0.910389i \(-0.364217\pi\)
−0.453799 + 0.891104i \(0.649932\pi\)
\(102\) 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 \(-0.423706\pi\)
0.999883 0.0152850i \(-0.00486557\pi\)
\(108\) 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 −0.627275 0.778798i \(-0.715830\pi\)
0.619690 + 0.784847i \(0.287258\pi\)
\(114\) 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 −0.796497 0.604643i \(-0.793316\pi\)
−0.0238790 + 0.999715i \(0.507602\pi\)
\(132\) 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 0.908271 0.418383i \(-0.137403\pi\)
−0.893402 + 0.449257i \(0.851689\pi\)
\(138\) 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 0.846938 0.531692i \(-0.178443\pi\)
−0.329900 + 0.944016i \(0.607015\pi\)
\(150\) 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 −0.988644 0.150273i \(-0.951985\pi\)
0.955939 + 0.293565i \(0.0948418\pi\)
\(168\) 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 \(-0.980537\pi\)
0.872771 0.488129i \(-0.162321\pi\)
\(174\) 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 −0.749885 0.661568i \(-0.769891\pi\)
−0.962667 + 0.270689i \(0.912749\pi\)
\(180\) 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 \(-0.593073\pi\)
0.928368 0.371663i \(-0.121212\pi\)
\(192\) 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 \(0.295766\pi\)
−0.598495 + 0.801127i \(0.704234\pi\)
\(198\) 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 \(-0.610112\pi\)
−0.339068 + 0.940762i \(0.610112\pi\)
\(228\) 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 −0.234893 0.972021i \(-0.575474\pi\)
−0.633376 + 0.773845i \(0.718331\pi\)
\(234\) 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 0.677987 0.735073i \(-0.262852\pi\)
−0.997422 + 0.0717611i \(0.977138\pi\)
\(240\) 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 −0.687434 0.726246i \(-0.741263\pi\)
0.139194 + 0.990265i \(0.455549\pi\)
\(252\) 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 \(0.291368\pi\)
−0.893121 + 0.449817i \(0.851489\pi\)
\(258\) 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 \(0.0209283\pi\)
−0.997839 + 0.0657008i \(0.979072\pi\)
\(264\) 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 0.250784 0.968043i \(-0.419312\pi\)
−0.999577 + 0.0290862i \(0.990740\pi\)
\(270\) 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 0.996510 0.0834696i \(-0.0266002\pi\)
0.140368 + 0.990099i \(0.455172\pi\)
\(282\) 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 \(-0.557162\pi\)
−0.178616 + 0.983919i \(0.557162\pi\)
\(294\) 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 \(-0.579300\pi\)
0.642632 0.766175i \(-0.277843\pi\)
\(312\) 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 0.684913 0.728625i \(-0.259840\pi\)
0.933224 + 0.359296i \(0.116983\pi\)
\(318\) 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 0.401533 0.915845i \(-0.368478\pi\)
0.759139 + 0.650929i \(0.225620\pi\)
\(348\) 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 −0.186031 0.982544i \(-0.559562\pi\)
0.652195 + 0.758051i \(0.273848\pi\)
\(354\) 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 0.991508 0.130049i \(-0.0415134\pi\)
−0.719871 + 0.694108i \(0.755799\pi\)
\(360\) 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 0.778077 0.628170i \(-0.216196\pi\)
−0.785558 + 0.618788i \(0.787624\pi\)
\(384\) 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 \(0.363514\pi\)
−0.970279 + 0.241987i \(0.922201\pi\)
\(390\) 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 −0.237141 0.971475i \(-0.576210\pi\)
0.894350 + 0.447369i \(0.147639\pi\)
\(402\) 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 \(-0.856589\pi\)
0.622129 0.782915i \(-0.286268\pi\)
\(420\) 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 \(-0.916563\pi\)
0.399593 0.916693i \(-0.369151\pi\)
\(432\) 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 0.572681 0.819778i \(-0.305903\pi\)
−0.671791 + 0.740740i \(0.734475\pi\)
\(444\) 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 −0.999955 0.00953840i \(-0.996964\pi\)
0.630919 + 0.775849i \(0.282678\pi\)
\(450\) 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 \(0.177360\pi\)
−0.994131 + 0.108182i \(0.965497\pi\)
\(462\) 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 \(-0.705087\pi\)
0.194257 0.980951i \(-0.437771\pi\)
\(468\) 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 −0.274556 0.961571i \(-0.588531\pi\)
0.998557 + 0.0537025i \(0.0171023\pi\)
\(480\) 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 \(-0.741231\pi\)
0.687361 0.726316i \(-0.258769\pi\)
\(492\) 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 \(0.553266\pi\)
−0.924247 + 0.381796i \(0.875306\pi\)
\(504\) 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 \(-0.916886\pi\)
−0.966104 + 0.258153i \(0.916886\pi\)
\(510\) 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 \(-0.558340\pi\)
−0.182257 + 0.983251i \(0.558340\pi\)
\(522\) 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 \(0.305687\pi\)
−0.573237 + 0.819389i \(0.694313\pi\)
\(558\) 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 0.307011 0.951706i \(-0.400671\pi\)
−0.996161 + 0.0875387i \(0.972100\pi\)
\(564\) 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 \(0.00412257\pi\)
−0.999916 + 0.0129511i \(0.995877\pi\)
\(570\) 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 \(-0.699850\pi\)
−0.587405 + 0.809293i \(0.699850\pi\)
\(588\) 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 −0.0239281 0.999714i \(-0.507617\pi\)
−0.796527 + 0.604604i \(0.793332\pi\)
\(594\) 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 0.826427 0.563043i \(-0.190370\pi\)
−0.365029 + 0.930996i \(0.618941\pi\)
\(600\) 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 0.719338 0.694660i \(-0.244445\pi\)
0.346699 + 0.937976i \(0.387302\pi\)
\(618\) 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 −0.291921 0.956443i \(-0.594294\pi\)
0.151973 + 0.988385i \(0.451437\pi\)
\(642\) 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 0.567695 0.823239i \(-0.307835\pi\)
0.997586 + 0.0694398i \(0.0221212\pi\)
\(648\) 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 \(0.00798639\pi\)
−0.603679 + 0.797227i \(0.706299\pi\)
\(654\) 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 −0.254281 0.967130i \(-0.581839\pi\)
0.190523 + 0.981683i \(0.438982\pi\)
\(660\) 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 0.973245 0.229770i \(-0.0737973\pi\)
−0.440576 + 0.897715i \(0.645226\pi\)
\(678\) 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 −0.985096 0.172005i \(-0.944976\pi\)
0.748676 + 0.662936i \(0.230690\pi\)
\(684\) 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 −0.489054 0.872253i \(-0.662658\pi\)
0.741559 + 0.670887i \(0.234087\pi\)
\(702\) 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 0.0859072 0.996303i \(-0.472621\pi\)
0.832503 + 0.554020i \(0.186907\pi\)
\(720\) 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 −0.968932 0.247327i \(-0.920448\pi\)
0.797488 + 0.603335i \(0.206162\pi\)
\(744\) 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 \(-0.752486\pi\)
0.337641 0.941275i \(-0.390371\pi\)
\(762\) 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 −0.947475 0.319831i \(-0.896374\pi\)
0.522645 + 0.852550i \(0.324945\pi\)
\(774\) 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 0