Properties

Label 462.2.c.b.197.10
Level $462$
Weight $2$
Character 462.197
Analytic conductor $3.689$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 462.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.68908857338\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
Defining polynomial: \(x^{12} + 16 x^{10} + 94 x^{8} + 246 x^{6} + 277 x^{4} + 114 x^{2} + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 197.10
Root \(0.319443i\) of defining polynomial
Character \(\chi\) \(=\) 462.197
Dual form 462.2.c.b.197.9

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +(1.37401 + 1.05456i) q^{3} +1.00000 q^{4} -3.92876i q^{5} +(1.37401 + 1.05456i) q^{6} +1.00000i q^{7} +1.00000 q^{8} +(0.775791 + 2.89796i) q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +(1.37401 + 1.05456i) q^{3} +1.00000 q^{4} -3.92876i q^{5} +(1.37401 + 1.05456i) q^{6} +1.00000i q^{7} +1.00000 q^{8} +(0.775791 + 2.89796i) q^{9} -3.92876i q^{10} +(-1.42857 - 2.99319i) q^{11} +(1.37401 + 1.05456i) q^{12} -0.109128i q^{13} +1.00000i q^{14} +(4.14313 - 5.39815i) q^{15} +1.00000 q^{16} +6.97666 q^{17} +(0.775791 + 2.89796i) q^{18} +5.78023i q^{19} -3.92876i q^{20} +(-1.05456 + 1.37401i) q^{21} +(-1.42857 - 2.99319i) q^{22} -0.938770i q^{23} +(1.37401 + 1.05456i) q^{24} -10.4352 q^{25} -0.109128i q^{26} +(-1.99014 + 4.79993i) q^{27} +1.00000i q^{28} -10.3479 q^{29} +(4.14313 - 5.39815i) q^{30} -2.61516 q^{31} +1.00000 q^{32} +(1.19364 - 5.61918i) q^{33} +6.97666 q^{34} +3.92876 q^{35} +(0.775791 + 2.89796i) q^{36} +7.21864 q^{37} +5.78023i q^{38} +(0.115082 - 0.149942i) q^{39} -3.92876i q^{40} -8.95059 q^{41} +(-1.05456 + 1.37401i) q^{42} +1.44880i q^{43} +(-1.42857 - 2.99319i) q^{44} +(11.3854 - 3.04790i) q^{45} -0.938770i q^{46} +11.4115i q^{47} +(1.37401 + 1.05456i) q^{48} -1.00000 q^{49} -10.4352 q^{50} +(9.58598 + 7.35733i) q^{51} -0.109128i q^{52} -5.55158i q^{53} +(-1.99014 + 4.79993i) q^{54} +(-11.7595 + 5.61252i) q^{55} +1.00000i q^{56} +(-6.09562 + 7.94207i) q^{57} -10.3479 q^{58} +7.60516i q^{59} +(4.14313 - 5.39815i) q^{60} -6.35346i q^{61} -2.61516 q^{62} +(-2.89796 + 0.775791i) q^{63} +1.00000 q^{64} -0.428736 q^{65} +(1.19364 - 5.61918i) q^{66} +5.60544 q^{67} +6.97666 q^{68} +(0.989993 - 1.28988i) q^{69} +3.92876 q^{70} -4.39287i q^{71} +(0.775791 + 2.89796i) q^{72} +3.31566i q^{73} +7.21864 q^{74} +(-14.3380 - 11.0046i) q^{75} +5.78023i q^{76} +(2.99319 - 1.42857i) q^{77} +(0.115082 - 0.149942i) q^{78} -0.361499i q^{79} -3.92876i q^{80} +(-7.79630 + 4.49641i) q^{81} -8.95059 q^{82} +1.48034 q^{83} +(-1.05456 + 1.37401i) q^{84} -27.4097i q^{85} +1.44880i q^{86} +(-14.2181 - 10.9125i) q^{87} +(-1.42857 - 2.99319i) q^{88} -0.722227i q^{89} +(11.3854 - 3.04790i) q^{90} +0.109128 q^{91} -0.938770i q^{92} +(-3.59325 - 2.75786i) q^{93} +11.4115i q^{94} +22.7092 q^{95} +(1.37401 + 1.05456i) q^{96} -3.48997 q^{97} -1.00000 q^{98} +(7.56586 - 6.46202i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 12 q^{2} + 4 q^{3} + 12 q^{4} + 4 q^{6} + 12 q^{8} + O(q^{10}) \) \( 12 q + 12 q^{2} + 4 q^{3} + 12 q^{4} + 4 q^{6} + 12 q^{8} + 8 q^{11} + 4 q^{12} + 4 q^{15} + 12 q^{16} + 4 q^{17} + 8 q^{22} + 4 q^{24} - 28 q^{25} - 8 q^{27} - 8 q^{29} + 4 q^{30} + 12 q^{31} + 12 q^{32} - 16 q^{33} + 4 q^{34} + 4 q^{35} + 36 q^{39} - 20 q^{41} + 8 q^{44} - 12 q^{45} + 4 q^{48} - 12 q^{49} - 28 q^{50} - 8 q^{51} - 8 q^{54} + 4 q^{55} - 28 q^{57} - 8 q^{58} + 4 q^{60} + 12 q^{62} - 4 q^{63} + 12 q^{64} - 16 q^{66} + 24 q^{67} + 4 q^{68} - 20 q^{69} + 4 q^{70} - 40 q^{75} - 4 q^{77} + 36 q^{78} + 4 q^{81} - 20 q^{82} - 44 q^{83} - 8 q^{87} + 8 q^{88} - 12 q^{90} - 24 q^{91} - 24 q^{93} + 4 q^{96} - 48 q^{97} - 12 q^{98} + 20 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(211\)
\(\chi(n)\) \(-1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 1.37401 + 1.05456i 0.793283 + 0.608853i
\(4\) 1.00000 0.500000
\(5\) 3.92876i 1.75700i −0.477746 0.878498i \(-0.658546\pi\)
0.477746 0.878498i \(-0.341454\pi\)
\(6\) 1.37401 + 1.05456i 0.560936 + 0.430524i
\(7\) 1.00000i 0.377964i
\(8\) 1.00000 0.353553
\(9\) 0.775791 + 2.89796i 0.258597 + 0.965985i
\(10\) 3.92876i 1.24238i
\(11\) −1.42857 2.99319i −0.430730 0.902481i
\(12\) 1.37401 + 1.05456i 0.396642 + 0.304426i
\(13\) 0.109128i 0.0302665i −0.999885 0.0151333i \(-0.995183\pi\)
0.999885 0.0151333i \(-0.00481725\pi\)
\(14\) 1.00000i 0.267261i
\(15\) 4.14313 5.39815i 1.06975 1.39380i
\(16\) 1.00000 0.250000
\(17\) 6.97666 1.69209 0.846045 0.533112i \(-0.178978\pi\)
0.846045 + 0.533112i \(0.178978\pi\)
\(18\) 0.775791 + 2.89796i 0.182856 + 0.683055i
\(19\) 5.78023i 1.32608i 0.748586 + 0.663038i \(0.230733\pi\)
−0.748586 + 0.663038i \(0.769267\pi\)
\(20\) 3.92876i 0.878498i
\(21\) −1.05456 + 1.37401i −0.230125 + 0.299833i
\(22\) −1.42857 2.99319i −0.304572 0.638150i
\(23\) 0.938770i 0.195747i −0.995199 0.0978736i \(-0.968796\pi\)
0.995199 0.0978736i \(-0.0312041\pi\)
\(24\) 1.37401 + 1.05456i 0.280468 + 0.215262i
\(25\) −10.4352 −2.08704
\(26\) 0.109128i 0.0214017i
\(27\) −1.99014 + 4.79993i −0.383002 + 0.923747i
\(28\) 1.00000i 0.188982i
\(29\) −10.3479 −1.92155 −0.960776 0.277324i \(-0.910552\pi\)
−0.960776 + 0.277324i \(0.910552\pi\)
\(30\) 4.14313 5.39815i 0.756429 0.985563i
\(31\) −2.61516 −0.469697 −0.234849 0.972032i \(-0.575459\pi\)
−0.234849 + 0.972032i \(0.575459\pi\)
\(32\) 1.00000 0.176777
\(33\) 1.19364 5.61918i 0.207787 0.978174i
\(34\) 6.97666 1.19649
\(35\) 3.92876 0.664082
\(36\) 0.775791 + 2.89796i 0.129298 + 0.482993i
\(37\) 7.21864 1.18674 0.593369 0.804931i \(-0.297798\pi\)
0.593369 + 0.804931i \(0.297798\pi\)
\(38\) 5.78023i 0.937677i
\(39\) 0.115082 0.149942i 0.0184279 0.0240099i
\(40\) 3.92876i 0.621192i
\(41\) −8.95059 −1.39785 −0.698923 0.715197i \(-0.746337\pi\)
−0.698923 + 0.715197i \(0.746337\pi\)
\(42\) −1.05456 + 1.37401i −0.162723 + 0.212014i
\(43\) 1.44880i 0.220941i 0.993879 + 0.110470i \(0.0352357\pi\)
−0.993879 + 0.110470i \(0.964764\pi\)
\(44\) −1.42857 2.99319i −0.215365 0.451240i
\(45\) 11.3854 3.04790i 1.69723 0.454354i
\(46\) 0.938770i 0.138414i
\(47\) 11.4115i 1.66453i 0.554376 + 0.832266i \(0.312957\pi\)
−0.554376 + 0.832266i \(0.687043\pi\)
\(48\) 1.37401 + 1.05456i 0.198321 + 0.152213i
\(49\) −1.00000 −0.142857
\(50\) −10.4352 −1.47576
\(51\) 9.58598 + 7.35733i 1.34231 + 1.03023i
\(52\) 0.109128i 0.0151333i
\(53\) 5.55158i 0.762568i −0.924458 0.381284i \(-0.875482\pi\)
0.924458 0.381284i \(-0.124518\pi\)
\(54\) −1.99014 + 4.79993i −0.270823 + 0.653188i
\(55\) −11.7595 + 5.61252i −1.58566 + 0.756792i
\(56\) 1.00000i 0.133631i
\(57\) −6.09562 + 7.94207i −0.807385 + 1.05195i
\(58\) −10.3479 −1.35874
\(59\) 7.60516i 0.990107i 0.868863 + 0.495053i \(0.164852\pi\)
−0.868863 + 0.495053i \(0.835148\pi\)
\(60\) 4.14313 5.39815i 0.534876 0.696898i
\(61\) 6.35346i 0.813477i −0.913545 0.406738i \(-0.866666\pi\)
0.913545 0.406738i \(-0.133334\pi\)
\(62\) −2.61516 −0.332126
\(63\) −2.89796 + 0.775791i −0.365108 + 0.0977404i
\(64\) 1.00000 0.125000
\(65\) −0.428736 −0.0531782
\(66\) 1.19364 5.61918i 0.146927 0.691674i
\(67\) 5.60544 0.684814 0.342407 0.939552i \(-0.388758\pi\)
0.342407 + 0.939552i \(0.388758\pi\)
\(68\) 6.97666 0.846045
\(69\) 0.989993 1.28988i 0.119181 0.155283i
\(70\) 3.92876 0.469577
\(71\) 4.39287i 0.521337i −0.965428 0.260669i \(-0.916057\pi\)
0.965428 0.260669i \(-0.0839430\pi\)
\(72\) 0.775791 + 2.89796i 0.0914278 + 0.341527i
\(73\) 3.31566i 0.388069i 0.980995 + 0.194035i \(0.0621574\pi\)
−0.980995 + 0.194035i \(0.937843\pi\)
\(74\) 7.21864 0.839150
\(75\) −14.3380 11.0046i −1.65561 1.27070i
\(76\) 5.78023i 0.663038i
\(77\) 2.99319 1.42857i 0.341106 0.162801i
\(78\) 0.115082 0.149942i 0.0130305 0.0169776i
\(79\) 0.361499i 0.0406719i −0.999793 0.0203359i \(-0.993526\pi\)
0.999793 0.0203359i \(-0.00647357\pi\)
\(80\) 3.92876i 0.439249i
\(81\) −7.79630 + 4.49641i −0.866255 + 0.499602i
\(82\) −8.95059 −0.988427
\(83\) 1.48034 0.162489 0.0812445 0.996694i \(-0.474111\pi\)
0.0812445 + 0.996694i \(0.474111\pi\)
\(84\) −1.05456 + 1.37401i −0.115062 + 0.149916i
\(85\) 27.4097i 2.97299i
\(86\) 1.44880i 0.156229i
\(87\) −14.2181 10.9125i −1.52434 1.16994i
\(88\) −1.42857 2.99319i −0.152286 0.319075i
\(89\) 0.722227i 0.0765559i −0.999267 0.0382779i \(-0.987813\pi\)
0.999267 0.0382779i \(-0.0121872\pi\)
\(90\) 11.3854 3.04790i 1.20012 0.321277i
\(91\) 0.109128 0.0114397
\(92\) 0.938770i 0.0978736i
\(93\) −3.59325 2.75786i −0.372603 0.285976i
\(94\) 11.4115i 1.17700i
\(95\) 22.7092 2.32991
\(96\) 1.37401 + 1.05456i 0.140234 + 0.107631i
\(97\) −3.48997 −0.354352 −0.177176 0.984179i \(-0.556696\pi\)
−0.177176 + 0.984179i \(0.556696\pi\)
\(98\) −1.00000 −0.101015
\(99\) 7.56586 6.46202i 0.760398 0.649458i
\(100\) −10.4352 −1.04352
\(101\) −10.2648 −1.02139 −0.510694 0.859762i \(-0.670612\pi\)
−0.510694 + 0.859762i \(0.670612\pi\)
\(102\) 9.58598 + 7.35733i 0.949154 + 0.728485i
\(103\) −3.64331 −0.358986 −0.179493 0.983759i \(-0.557446\pi\)
−0.179493 + 0.983759i \(0.557446\pi\)
\(104\) 0.109128i 0.0107008i
\(105\) 5.39815 + 4.14313i 0.526805 + 0.404328i
\(106\) 5.55158i 0.539217i
\(107\) −10.3337 −0.999000 −0.499500 0.866314i \(-0.666483\pi\)
−0.499500 + 0.866314i \(0.666483\pi\)
\(108\) −1.99014 + 4.79993i −0.191501 + 0.461874i
\(109\) 13.7090i 1.31308i −0.754290 0.656542i \(-0.772019\pi\)
0.754290 0.656542i \(-0.227981\pi\)
\(110\) −11.7595 + 5.61252i −1.12123 + 0.535133i
\(111\) 9.91846 + 7.61252i 0.941419 + 0.722548i
\(112\) 1.00000i 0.0944911i
\(113\) 0.803856i 0.0756204i −0.999285 0.0378102i \(-0.987962\pi\)
0.999285 0.0378102i \(-0.0120382\pi\)
\(114\) −6.09562 + 7.94207i −0.570907 + 0.743843i
\(115\) −3.68821 −0.343927
\(116\) −10.3479 −0.960776
\(117\) 0.316247 0.0846601i 0.0292370 0.00782683i
\(118\) 7.60516i 0.700111i
\(119\) 6.97666i 0.639550i
\(120\) 4.14313 5.39815i 0.378214 0.492781i
\(121\) −6.91837 + 8.55197i −0.628943 + 0.777452i
\(122\) 6.35346i 0.575215i
\(123\) −12.2982 9.43896i −1.10889 0.851083i
\(124\) −2.61516 −0.234849
\(125\) 21.3536i 1.90992i
\(126\) −2.89796 + 0.775791i −0.258170 + 0.0691129i
\(127\) 14.3201i 1.27070i −0.772223 0.635351i \(-0.780855\pi\)
0.772223 0.635351i \(-0.219145\pi\)
\(128\) 1.00000 0.0883883
\(129\) −1.52786 + 1.99067i −0.134520 + 0.175269i
\(130\) −0.428736 −0.0376026
\(131\) 17.8346 1.55822 0.779109 0.626889i \(-0.215672\pi\)
0.779109 + 0.626889i \(0.215672\pi\)
\(132\) 1.19364 5.61918i 0.103893 0.489087i
\(133\) −5.78023 −0.501209
\(134\) 5.60544 0.484237
\(135\) 18.8578 + 7.81878i 1.62302 + 0.672933i
\(136\) 6.97666 0.598244
\(137\) 6.72300i 0.574385i 0.957873 + 0.287192i \(0.0927219\pi\)
−0.957873 + 0.287192i \(0.907278\pi\)
\(138\) 0.989993 1.28988i 0.0842738 0.109802i
\(139\) 6.05064i 0.513208i −0.966517 0.256604i \(-0.917396\pi\)
0.966517 0.256604i \(-0.0826036\pi\)
\(140\) 3.92876 0.332041
\(141\) −12.0341 + 15.6794i −1.01346 + 1.32045i
\(142\) 4.39287i 0.368641i
\(143\) −0.326639 + 0.155896i −0.0273150 + 0.0130367i
\(144\) 0.775791 + 2.89796i 0.0646492 + 0.241496i
\(145\) 40.6544i 3.37616i
\(146\) 3.31566i 0.274406i
\(147\) −1.37401 1.05456i −0.113326 0.0869790i
\(148\) 7.21864 0.593369
\(149\) 6.65134 0.544899 0.272450 0.962170i \(-0.412166\pi\)
0.272450 + 0.962170i \(0.412166\pi\)
\(150\) −14.3380 11.0046i −1.17069 0.898519i
\(151\) 0.977889i 0.0795795i −0.999208 0.0397897i \(-0.987331\pi\)
0.999208 0.0397897i \(-0.0126688\pi\)
\(152\) 5.78023i 0.468838i
\(153\) 5.41243 + 20.2181i 0.437569 + 1.63453i
\(154\) 2.99319 1.42857i 0.241198 0.115118i
\(155\) 10.2744i 0.825256i
\(156\) 0.115082 0.149942i 0.00921393 0.0120050i
\(157\) −1.12491 −0.0897774 −0.0448887 0.998992i \(-0.514293\pi\)
−0.0448887 + 0.998992i \(0.514293\pi\)
\(158\) 0.361499i 0.0287593i
\(159\) 5.85450 7.62791i 0.464292 0.604933i
\(160\) 3.92876i 0.310596i
\(161\) 0.938770 0.0739855
\(162\) −7.79630 + 4.49641i −0.612535 + 0.353272i
\(163\) −2.94048 −0.230316 −0.115158 0.993347i \(-0.536737\pi\)
−0.115158 + 0.993347i \(0.536737\pi\)
\(164\) −8.95059 −0.698923
\(165\) −22.0764 4.68954i −1.71865 0.365080i
\(166\) 1.48034 0.114897
\(167\) 21.5860 1.67037 0.835186 0.549968i \(-0.185360\pi\)
0.835186 + 0.549968i \(0.185360\pi\)
\(168\) −1.05456 + 1.37401i −0.0813614 + 0.106007i
\(169\) 12.9881 0.999084
\(170\) 27.4097i 2.10222i
\(171\) −16.7508 + 4.48425i −1.28097 + 0.342919i
\(172\) 1.44880i 0.110470i
\(173\) 5.10422 0.388067 0.194033 0.980995i \(-0.437843\pi\)
0.194033 + 0.980995i \(0.437843\pi\)
\(174\) −14.2181 10.9125i −1.07787 0.827274i
\(175\) 10.4352i 0.788826i
\(176\) −1.42857 2.99319i −0.107683 0.225620i
\(177\) −8.02012 + 10.4495i −0.602829 + 0.785435i
\(178\) 0.722227i 0.0541332i
\(179\) 17.2258i 1.28752i −0.765229 0.643759i \(-0.777374\pi\)
0.765229 0.643759i \(-0.222626\pi\)
\(180\) 11.3854 3.04790i 0.848616 0.227177i
\(181\) 11.9832 0.890701 0.445350 0.895356i \(-0.353079\pi\)
0.445350 + 0.895356i \(0.353079\pi\)
\(182\) 0.109128 0.00808907
\(183\) 6.70013 8.72970i 0.495288 0.645318i
\(184\) 0.938770i 0.0692071i
\(185\) 28.3603i 2.08509i
\(186\) −3.59325 2.75786i −0.263470 0.202216i
\(187\) −9.96665 20.8825i −0.728834 1.52708i
\(188\) 11.4115i 0.832266i
\(189\) −4.79993 1.99014i −0.349144 0.144761i
\(190\) 22.7092 1.64750
\(191\) 13.1345i 0.950381i 0.879883 + 0.475191i \(0.157621\pi\)
−0.879883 + 0.475191i \(0.842379\pi\)
\(192\) 1.37401 + 1.05456i 0.0991604 + 0.0761066i
\(193\) 7.13624i 0.513678i −0.966454 0.256839i \(-0.917319\pi\)
0.966454 0.256839i \(-0.0826810\pi\)
\(194\) −3.48997 −0.250565
\(195\) −0.589087 0.452130i −0.0421854 0.0323777i
\(196\) −1.00000 −0.0714286
\(197\) 1.57331 0.112093 0.0560467 0.998428i \(-0.482150\pi\)
0.0560467 + 0.998428i \(0.482150\pi\)
\(198\) 7.56586 6.46202i 0.537682 0.459236i
\(199\) −4.38353 −0.310740 −0.155370 0.987856i \(-0.549657\pi\)
−0.155370 + 0.987856i \(0.549657\pi\)
\(200\) −10.4352 −0.737879
\(201\) 7.70192 + 5.91130i 0.543252 + 0.416951i
\(202\) −10.2648 −0.722231
\(203\) 10.3479i 0.726279i
\(204\) 9.58598 + 7.35733i 0.671153 + 0.515116i
\(205\) 35.1647i 2.45601i
\(206\) −3.64331 −0.253842
\(207\) 2.72052 0.728289i 0.189089 0.0506196i
\(208\) 0.109128i 0.00756663i
\(209\) 17.3013 8.25747i 1.19676 0.571181i
\(210\) 5.39815 + 4.14313i 0.372508 + 0.285903i
\(211\) 5.34526i 0.367983i 0.982928 + 0.183991i \(0.0589018\pi\)
−0.982928 + 0.183991i \(0.941098\pi\)
\(212\) 5.55158i 0.381284i
\(213\) 4.63256 6.03583i 0.317418 0.413568i
\(214\) −10.3337 −0.706399
\(215\) 5.69201 0.388192
\(216\) −1.99014 + 4.79993i −0.135412 + 0.326594i
\(217\) 2.61516i 0.177529i
\(218\) 13.7090i 0.928490i
\(219\) −3.49658 + 4.55575i −0.236277 + 0.307849i
\(220\) −11.7595 + 5.61252i −0.792828 + 0.378396i
\(221\) 0.761346i 0.0512137i
\(222\) 9.91846 + 7.61252i 0.665684 + 0.510919i
\(223\) 19.0577 1.27620 0.638100 0.769953i \(-0.279721\pi\)
0.638100 + 0.769953i \(0.279721\pi\)
\(224\) 1.00000i 0.0668153i
\(225\) −8.09552 30.2407i −0.539701 2.01605i
\(226\) 0.803856i 0.0534717i
\(227\) 17.2146 1.14258 0.571288 0.820750i \(-0.306444\pi\)
0.571288 + 0.820750i \(0.306444\pi\)
\(228\) −6.09562 + 7.94207i −0.403692 + 0.525977i
\(229\) 20.4671 1.35250 0.676252 0.736670i \(-0.263603\pi\)
0.676252 + 0.736670i \(0.263603\pi\)
\(230\) −3.68821 −0.243193
\(231\) 5.61918 + 1.19364i 0.369715 + 0.0785360i
\(232\) −10.3479 −0.679372
\(233\) −17.1712 −1.12492 −0.562460 0.826824i \(-0.690145\pi\)
−0.562460 + 0.826824i \(0.690145\pi\)
\(234\) 0.316247 0.0846601i 0.0206737 0.00553440i
\(235\) 44.8329 2.92458
\(236\) 7.60516i 0.495053i
\(237\) 0.381224 0.496703i 0.0247632 0.0322643i
\(238\) 6.97666i 0.452230i
\(239\) −9.38967 −0.607367 −0.303684 0.952773i \(-0.598217\pi\)
−0.303684 + 0.952773i \(0.598217\pi\)
\(240\) 4.14313 5.39815i 0.267438 0.348449i
\(241\) 10.3774i 0.668470i 0.942490 + 0.334235i \(0.108478\pi\)
−0.942490 + 0.334235i \(0.891522\pi\)
\(242\) −6.91837 + 8.55197i −0.444730 + 0.549741i
\(243\) −15.4539 2.04359i −0.991370 0.131096i
\(244\) 6.35346i 0.406738i
\(245\) 3.92876i 0.251000i
\(246\) −12.2982 9.43896i −0.784103 0.601806i
\(247\) 0.630782 0.0401357
\(248\) −2.61516 −0.166063
\(249\) 2.03400 + 1.56112i 0.128900 + 0.0989318i
\(250\) 21.3536i 1.35052i
\(251\) 7.75369i 0.489409i −0.969598 0.244704i \(-0.921309\pi\)
0.969598 0.244704i \(-0.0786909\pi\)
\(252\) −2.89796 + 0.775791i −0.182554 + 0.0488702i
\(253\) −2.80992 + 1.34110i −0.176658 + 0.0843142i
\(254\) 14.3201i 0.898522i
\(255\) 28.9052 37.6611i 1.81012 2.35843i
\(256\) 1.00000 0.0625000
\(257\) 22.2224i 1.38619i 0.720844 + 0.693097i \(0.243754\pi\)
−0.720844 + 0.693097i \(0.756246\pi\)
\(258\) −1.52786 + 1.99067i −0.0951202 + 0.123934i
\(259\) 7.21864i 0.448545i
\(260\) −0.428736 −0.0265891
\(261\) −8.02779 29.9877i −0.496908 1.85619i
\(262\) 17.8346 1.10183
\(263\) −18.9287 −1.16720 −0.583598 0.812043i \(-0.698356\pi\)
−0.583598 + 0.812043i \(0.698356\pi\)
\(264\) 1.19364 5.61918i 0.0734637 0.345837i
\(265\) −21.8109 −1.33983
\(266\) −5.78023 −0.354409
\(267\) 0.761634 0.992345i 0.0466113 0.0607305i
\(268\) 5.60544 0.342407
\(269\) 17.4450i 1.06364i −0.846857 0.531820i \(-0.821508\pi\)
0.846857 0.531820i \(-0.178492\pi\)
\(270\) 18.8578 + 7.81878i 1.14765 + 0.475836i
\(271\) 8.89232i 0.540170i −0.962836 0.270085i \(-0.912948\pi\)
0.962836 0.270085i \(-0.0870518\pi\)
\(272\) 6.97666 0.423022
\(273\) 0.149942 + 0.115082i 0.00907490 + 0.00696507i
\(274\) 6.72300i 0.406151i
\(275\) 14.9074 + 31.2345i 0.898950 + 1.88351i
\(276\) 0.989993 1.28988i 0.0595906 0.0776415i
\(277\) 11.6381i 0.699266i −0.936887 0.349633i \(-0.886306\pi\)
0.936887 0.349633i \(-0.113694\pi\)
\(278\) 6.05064i 0.362893i
\(279\) −2.02882 7.57863i −0.121462 0.453720i
\(280\) 3.92876 0.234789
\(281\) −16.8968 −1.00798 −0.503989 0.863710i \(-0.668135\pi\)
−0.503989 + 0.863710i \(0.668135\pi\)
\(282\) −12.0341 + 15.6794i −0.716621 + 0.933696i
\(283\) 6.18032i 0.367382i −0.982984 0.183691i \(-0.941195\pi\)
0.982984 0.183691i \(-0.0588046\pi\)
\(284\) 4.39287i 0.260669i
\(285\) 31.2025 + 23.9482i 1.84828 + 1.41857i
\(286\) −0.326639 + 0.155896i −0.0193146 + 0.00921834i
\(287\) 8.95059i 0.528336i
\(288\) 0.775791 + 2.89796i 0.0457139 + 0.170764i
\(289\) 31.6738 1.86317
\(290\) 40.6544i 2.38731i
\(291\) −4.79524 3.68039i −0.281102 0.215748i
\(292\) 3.31566i 0.194035i
\(293\) −13.0184 −0.760544 −0.380272 0.924875i \(-0.624170\pi\)
−0.380272 + 0.924875i \(0.624170\pi\)
\(294\) −1.37401 1.05456i −0.0801337 0.0615034i
\(295\) 29.8789 1.73961
\(296\) 7.21864 0.419575
\(297\) 17.2102 0.900184i 0.998635 0.0522339i
\(298\) 6.65134 0.385302
\(299\) −0.102446 −0.00592459
\(300\) −14.3380 11.0046i −0.827806 0.635349i
\(301\) −1.44880 −0.0835077
\(302\) 0.977889i 0.0562712i
\(303\) −14.1039 10.8249i −0.810250 0.621875i
\(304\) 5.78023i 0.331519i
\(305\) −24.9612 −1.42928
\(306\) 5.41243 + 20.2181i 0.309408 + 1.15579i
\(307\) 14.2481i 0.813182i 0.913610 + 0.406591i \(0.133283\pi\)
−0.913610 + 0.406591i \(0.866717\pi\)
\(308\) 2.99319 1.42857i 0.170553 0.0814004i
\(309\) −5.00594 3.84211i −0.284778 0.218570i
\(310\) 10.2744i 0.583544i
\(311\) 19.9015i 1.12851i 0.825601 + 0.564255i \(0.190836\pi\)
−0.825601 + 0.564255i \(0.809164\pi\)
\(312\) 0.115082 0.149942i 0.00651523 0.00848879i
\(313\) −30.6797 −1.73412 −0.867059 0.498206i \(-0.833992\pi\)
−0.867059 + 0.498206i \(0.833992\pi\)
\(314\) −1.12491 −0.0634822
\(315\) 3.04790 + 11.3854i 0.171730 + 0.641494i
\(316\) 0.361499i 0.0203359i
\(317\) 15.9925i 0.898226i −0.893475 0.449113i \(-0.851740\pi\)
0.893475 0.449113i \(-0.148260\pi\)
\(318\) 5.85450 7.62791i 0.328304 0.427752i
\(319\) 14.7827 + 30.9732i 0.827671 + 1.73416i
\(320\) 3.92876i 0.219625i
\(321\) −14.1986 10.8976i −0.792490 0.608244i
\(322\) 0.938770 0.0523156
\(323\) 40.3267i 2.24384i
\(324\) −7.79630 + 4.49641i −0.433128 + 0.249801i
\(325\) 1.13877i 0.0631673i
\(326\) −2.94048 −0.162858
\(327\) 14.4570 18.8363i 0.799474 1.04165i
\(328\) −8.95059 −0.494213
\(329\) −11.4115 −0.629134
\(330\) −22.0764 4.68954i −1.21527 0.258151i
\(331\) −0.500933 −0.0275338 −0.0137669 0.999905i \(-0.504382\pi\)
−0.0137669 + 0.999905i \(0.504382\pi\)
\(332\) 1.48034 0.0812445
\(333\) 5.60015 + 20.9193i 0.306887 + 1.14637i
\(334\) 21.5860 1.18113
\(335\) 22.0225i 1.20322i
\(336\) −1.05456 + 1.37401i −0.0575312 + 0.0749582i
\(337\) 11.7562i 0.640402i −0.947350 0.320201i \(-0.896250\pi\)
0.947350 0.320201i \(-0.103750\pi\)
\(338\) 12.9881 0.706459
\(339\) 0.847717 1.10450i 0.0460417 0.0599884i
\(340\) 27.4097i 1.48650i
\(341\) 3.73594 + 7.82768i 0.202313 + 0.423892i
\(342\) −16.7508 + 4.48425i −0.905782 + 0.242480i
\(343\) 1.00000i 0.0539949i
\(344\) 1.44880i 0.0781143i
\(345\) −5.06762 3.88945i −0.272832 0.209401i
\(346\) 5.10422 0.274405
\(347\) 31.2589 1.67806 0.839032 0.544083i \(-0.183122\pi\)
0.839032 + 0.544083i \(0.183122\pi\)
\(348\) −14.2181 10.9125i −0.762168 0.584971i
\(349\) 26.8168i 1.43547i 0.696316 + 0.717736i \(0.254821\pi\)
−0.696316 + 0.717736i \(0.745179\pi\)
\(350\) 10.4352i 0.557784i
\(351\) 0.523805 + 0.217179i 0.0279586 + 0.0115921i
\(352\) −1.42857 2.99319i −0.0761431 0.159538i
\(353\) 30.7700i 1.63772i −0.573992 0.818861i \(-0.694606\pi\)
0.573992 0.818861i \(-0.305394\pi\)
\(354\) −8.02012 + 10.4495i −0.426265 + 0.555387i
\(355\) −17.2585 −0.915988
\(356\) 0.722227i 0.0382779i
\(357\) −7.35733 + 9.58598i −0.389391 + 0.507344i
\(358\) 17.2258i 0.910412i
\(359\) 14.7885 0.780510 0.390255 0.920707i \(-0.372387\pi\)
0.390255 + 0.920707i \(0.372387\pi\)
\(360\) 11.3854 3.04790i 0.600062 0.160638i
\(361\) −14.4110 −0.758476
\(362\) 11.9832 0.629820
\(363\) −18.5245 + 4.45460i −0.972283 + 0.233806i
\(364\) 0.109128 0.00571984
\(365\) 13.0265 0.681836
\(366\) 6.70013 8.72970i 0.350221 0.456309i
\(367\) −16.5826 −0.865606 −0.432803 0.901488i \(-0.642475\pi\)
−0.432803 + 0.901488i \(0.642475\pi\)
\(368\) 0.938770i 0.0489368i
\(369\) −6.94378 25.9384i −0.361479 1.35030i
\(370\) 28.3603i 1.47438i
\(371\) 5.55158 0.288224
\(372\) −3.59325 2.75786i −0.186301 0.142988i
\(373\) 18.1538i 0.939970i −0.882674 0.469985i \(-0.844259\pi\)
0.882674 0.469985i \(-0.155741\pi\)
\(374\) −9.96665 20.8825i −0.515363 1.07981i
\(375\) −22.5187 + 29.3399i −1.16286 + 1.51511i
\(376\) 11.4115i 0.588501i
\(377\) 1.12924i 0.0581587i
\(378\) −4.79993 1.99014i −0.246882 0.102362i
\(379\) −12.5603 −0.645180 −0.322590 0.946539i \(-0.604554\pi\)
−0.322590 + 0.946539i \(0.604554\pi\)
\(380\) 22.7092 1.16495
\(381\) 15.1014 19.6759i 0.773671 1.00803i
\(382\) 13.1345i 0.672021i
\(383\) 3.12388i 0.159623i −0.996810 0.0798114i \(-0.974568\pi\)
0.996810 0.0798114i \(-0.0254318\pi\)
\(384\) 1.37401 + 1.05456i 0.0701170 + 0.0538155i
\(385\) −5.61252 11.7595i −0.286040 0.599321i
\(386\) 7.13624i 0.363225i
\(387\) −4.19857 + 1.12397i −0.213425 + 0.0571346i
\(388\) −3.48997 −0.177176
\(389\) 25.8114i 1.30869i −0.756196 0.654345i \(-0.772944\pi\)
0.756196 0.654345i \(-0.227056\pi\)
\(390\) −0.589087 0.452130i −0.0298296 0.0228945i
\(391\) 6.54948i 0.331222i
\(392\) −1.00000 −0.0505076
\(393\) 24.5049 + 18.8077i 1.23611 + 0.948725i
\(394\) 1.57331 0.0792620
\(395\) −1.42025 −0.0714603
\(396\) 7.56586 6.46202i 0.380199 0.324729i
\(397\) 26.4518 1.32758 0.663789 0.747920i \(-0.268947\pi\)
0.663789 + 0.747920i \(0.268947\pi\)
\(398\) −4.38353 −0.219727
\(399\) −7.94207 6.09562i −0.397601 0.305163i
\(400\) −10.4352 −0.521759
\(401\) 28.0552i 1.40101i 0.713649 + 0.700504i \(0.247041\pi\)
−0.713649 + 0.700504i \(0.752959\pi\)
\(402\) 7.70192 + 5.91130i 0.384137 + 0.294829i
\(403\) 0.285386i 0.0142161i
\(404\) −10.2648 −0.510694
\(405\) 17.6653 + 30.6298i 0.877798 + 1.52201i
\(406\) 10.3479i 0.513557i
\(407\) −10.3123 21.6068i −0.511164 1.07101i
\(408\) 9.58598 + 7.35733i 0.474577 + 0.364242i
\(409\) 1.22795i 0.0607183i 0.999539 + 0.0303591i \(0.00966510\pi\)
−0.999539 + 0.0303591i \(0.990335\pi\)
\(410\) 35.1647i 1.73666i
\(411\) −7.08983 + 9.23745i −0.349716 + 0.455650i
\(412\) −3.64331 −0.179493
\(413\) −7.60516 −0.374225
\(414\) 2.72052 0.728289i 0.133706 0.0357935i
\(415\) 5.81593i 0.285493i
\(416\) 0.109128i 0.00535042i
\(417\) 6.38078 8.31362i 0.312468 0.407120i
\(418\) 17.3013 8.25747i 0.846235 0.403886i
\(419\) 10.5048i 0.513192i −0.966519 0.256596i \(-0.917399\pi\)
0.966519 0.256596i \(-0.0826010\pi\)
\(420\) 5.39815 + 4.14313i 0.263403 + 0.202164i
\(421\) −14.6003 −0.711575 −0.355787 0.934567i \(-0.615787\pi\)
−0.355787 + 0.934567i \(0.615787\pi\)
\(422\) 5.34526i 0.260203i
\(423\) −33.0699 + 8.85290i −1.60791 + 0.430443i
\(424\) 5.55158i 0.269609i
\(425\) −72.8028 −3.53145
\(426\) 4.63256 6.03583i 0.224448 0.292437i
\(427\) 6.35346 0.307465
\(428\) −10.3337 −0.499500
\(429\) −0.613207 0.130259i −0.0296059 0.00628898i
\(430\) 5.69201 0.274493
\(431\) −15.1801 −0.731198 −0.365599 0.930772i \(-0.619136\pi\)
−0.365599 + 0.930772i \(0.619136\pi\)
\(432\) −1.99014 + 4.79993i −0.0957505 + 0.230937i
\(433\) 17.1583 0.824577 0.412289 0.911053i \(-0.364730\pi\)
0.412289 + 0.911053i \(0.364730\pi\)
\(434\) 2.61516i 0.125532i
\(435\) −42.8726 + 55.8594i −2.05559 + 2.67825i
\(436\) 13.7090i 0.656542i
\(437\) 5.42631 0.259576
\(438\) −3.49658 + 4.55575i −0.167073 + 0.217682i
\(439\) 17.7286i 0.846141i 0.906097 + 0.423070i \(0.139048\pi\)
−0.906097 + 0.423070i \(0.860952\pi\)
\(440\) −11.7595 + 5.61252i −0.560614 + 0.267566i
\(441\) −0.775791 2.89796i −0.0369424 0.137998i
\(442\) 0.761346i 0.0362135i
\(443\) 6.70808i 0.318711i −0.987221 0.159355i \(-0.949058\pi\)
0.987221 0.159355i \(-0.0509415\pi\)
\(444\) 9.91846 + 7.61252i 0.470709 + 0.361274i
\(445\) −2.83746 −0.134508
\(446\) 19.0577 0.902410
\(447\) 9.13899 + 7.01426i 0.432259 + 0.331763i
\(448\) 1.00000i 0.0472456i
\(449\) 2.86960i 0.135425i 0.997705 + 0.0677123i \(0.0215700\pi\)
−0.997705 + 0.0677123i \(0.978430\pi\)
\(450\) −8.09552 30.2407i −0.381626 1.42556i
\(451\) 12.7865 + 26.7908i 0.602095 + 1.26153i
\(452\) 0.803856i 0.0378102i
\(453\) 1.03125 1.34363i 0.0484522 0.0631291i
\(454\) 17.2146 0.807923
\(455\) 0.428736i 0.0200995i
\(456\) −6.09562 + 7.94207i −0.285454 + 0.371922i
\(457\) 10.7141i 0.501183i 0.968093 + 0.250591i \(0.0806250\pi\)
−0.968093 + 0.250591i \(0.919375\pi\)
\(458\) 20.4671 0.956365
\(459\) −13.8845 + 33.4875i −0.648074 + 1.56306i
\(460\) −3.68821 −0.171964
\(461\) −5.60949 −0.261260 −0.130630 0.991431i \(-0.541700\pi\)
−0.130630 + 0.991431i \(0.541700\pi\)
\(462\) 5.61918 + 1.19364i 0.261428 + 0.0555333i
\(463\) −3.97144 −0.184569 −0.0922843 0.995733i \(-0.529417\pi\)
−0.0922843 + 0.995733i \(0.529417\pi\)
\(464\) −10.3479 −0.480388
\(465\) −10.8350 + 14.1170i −0.502459 + 0.654662i
\(466\) −17.1712 −0.795439
\(467\) 6.98066i 0.323026i 0.986871 + 0.161513i \(0.0516374\pi\)
−0.986871 + 0.161513i \(0.948363\pi\)
\(468\) 0.316247 0.0846601i 0.0146185 0.00391341i
\(469\) 5.60544i 0.258835i
\(470\) 44.8329 2.06799
\(471\) −1.54563 1.18629i −0.0712189 0.0546612i
\(472\) 7.60516i 0.350056i
\(473\) 4.33655 2.06972i 0.199395 0.0951658i
\(474\) 0.381224 0.496703i 0.0175102 0.0228143i
\(475\) 60.3178i 2.76757i
\(476\) 6.97666i 0.319775i
\(477\) 16.0882 4.30686i 0.736630 0.197198i
\(478\) −9.38967 −0.429474
\(479\) −22.5631 −1.03093 −0.515467 0.856909i \(-0.672382\pi\)
−0.515467 + 0.856909i \(0.672382\pi\)
\(480\) 4.14313 5.39815i 0.189107 0.246391i
\(481\) 0.787752i 0.0359184i
\(482\) 10.3774i 0.472679i
\(483\) 1.28988 + 0.989993i 0.0586914 + 0.0450463i
\(484\) −6.91837 + 8.55197i −0.314471 + 0.388726i
\(485\) 13.7113i 0.622596i
\(486\) −15.4539 2.04359i −0.701004 0.0926991i
\(487\) −9.83009 −0.445444 −0.222722 0.974882i \(-0.571494\pi\)
−0.222722 + 0.974882i \(0.571494\pi\)
\(488\) 6.35346i 0.287608i
\(489\) −4.04024 3.10093i −0.182706 0.140229i
\(490\) 3.92876i 0.177483i
\(491\) 7.60395 0.343161 0.171581 0.985170i \(-0.445113\pi\)
0.171581 + 0.985170i \(0.445113\pi\)
\(492\) −12.2982 9.43896i −0.554444 0.425541i
\(493\) −72.1937 −3.25144
\(494\) 0.630782 0.0283802
\(495\) −25.3878 29.7245i −1.14110 1.33602i
\(496\) −2.61516 −0.117424
\(497\) 4.39287 0.197047
\(498\) 2.03400 + 1.56112i 0.0911459 + 0.0699554i
\(499\) −40.0276 −1.79188 −0.895941 0.444173i \(-0.853498\pi\)
−0.895941 + 0.444173i \(0.853498\pi\)
\(500\) 21.3536i 0.954960i
\(501\) 29.6593 + 22.7638i 1.32508 + 1.01701i
\(502\) 7.75369i 0.346064i
\(503\) 15.7056 0.700279 0.350139 0.936698i \(-0.386134\pi\)
0.350139 + 0.936698i \(0.386134\pi\)
\(504\) −2.89796 + 0.775791i −0.129085 + 0.0345565i
\(505\) 40.3281i 1.79458i
\(506\) −2.80992 + 1.34110i −0.124916 + 0.0596192i
\(507\) 17.8457 + 13.6968i 0.792557 + 0.608295i
\(508\) 14.3201i 0.635351i
\(509\) 3.26942i 0.144915i 0.997372 + 0.0724573i \(0.0230841\pi\)
−0.997372 + 0.0724573i \(0.976916\pi\)
\(510\) 28.9052 37.6611i 1.27995 1.66766i
\(511\) −3.31566 −0.146676
\(512\) 1.00000 0.0441942
\(513\) −27.7447 11.5035i −1.22496 0.507890i
\(514\) 22.2224i 0.980187i
\(515\) 14.3137i 0.630738i
\(516\) −1.52786 + 1.99067i −0.0672602 + 0.0876343i
\(517\) 34.1567 16.3021i 1.50221 0.716965i
\(518\) 7.21864i 0.317169i
\(519\) 7.01324 + 5.38273i 0.307847 + 0.236276i
\(520\) −0.428736 −0.0188013
\(521\) 31.6143i 1.38505i −0.721395 0.692524i \(-0.756499\pi\)
0.721395 0.692524i \(-0.243501\pi\)
\(522\) −8.02779 29.9877i −0.351367 1.31253i
\(523\) 13.1081i 0.573177i −0.958054 0.286589i \(-0.907479\pi\)
0.958054 0.286589i \(-0.0925213\pi\)
\(524\) 17.8346 0.779109
\(525\) 11.0046 14.3380i 0.480279 0.625762i
\(526\) −18.9287 −0.825332
\(527\) −18.2451 −0.794769
\(528\) 1.19364 5.61918i 0.0519467 0.244544i
\(529\) 22.1187 0.961683
\(530\) −21.8109 −0.947403
\(531\) −22.0394 + 5.90001i −0.956429 + 0.256039i
\(532\) −5.78023 −0.250605
\(533\) 0.976755i 0.0423080i
\(534\) 0.761634 0.992345i 0.0329591 0.0429430i
\(535\) 40.5988i 1.75524i
\(536\) 5.60544 0.242118
\(537\) 18.1657 23.6684i 0.783908 1.02137i
\(538\) 17.4450i 0.752107i
\(539\) 1.42857 + 2.99319i 0.0615329 + 0.128926i
\(540\) 18.8578 + 7.81878i 0.811511 + 0.336467i
\(541\) 22.4743i 0.966244i 0.875553 + 0.483122i \(0.160497\pi\)
−0.875553 + 0.483122i \(0.839503\pi\)
\(542\) 8.89232i 0.381958i
\(543\) 16.4649 + 12.6370i 0.706578 + 0.542305i
\(544\) 6.97666 0.299122
\(545\) −53.8594 −2.30708
\(546\) 0.149942 + 0.115082i 0.00641692 + 0.00492505i
\(547\) 42.0607i 1.79839i −0.437553 0.899193i \(-0.644155\pi\)
0.437553 0.899193i \(-0.355845\pi\)
\(548\) 6.72300i 0.287192i
\(549\) 18.4120 4.92895i 0.785807 0.210363i
\(550\) 14.9074 + 31.2345i 0.635654 + 1.33184i
\(551\) 59.8131i 2.54812i
\(552\) 0.989993 1.28988i 0.0421369 0.0549008i
\(553\) 0.361499 0.0153725
\(554\) 11.6381i 0.494456i
\(555\) 29.9078 38.9673i 1.26951 1.65407i
\(556\) 6.05064i 0.256604i
\(557\) −19.4913 −0.825873 −0.412937 0.910760i \(-0.635497\pi\)
−0.412937 + 0.910760i \(0.635497\pi\)
\(558\) −2.02882 7.57863i −0.0858867 0.320829i
\(559\) 0.158104 0.00668711
\(560\) 3.92876 0.166021
\(561\) 8.32765 39.2031i 0.351593 1.65516i
\(562\) −16.8968 −0.712749
\(563\) −15.9611 −0.672679 −0.336340 0.941741i \(-0.609189\pi\)
−0.336340 + 0.941741i \(0.609189\pi\)
\(564\) −12.0341 + 15.6794i −0.506728 + 0.660223i
\(565\) −3.15816 −0.132865
\(566\) 6.18032i 0.259778i
\(567\) −4.49641 7.79630i −0.188832 0.327414i
\(568\) 4.39287i 0.184321i
\(569\) 13.4452 0.563653 0.281827 0.959465i \(-0.409060\pi\)
0.281827 + 0.959465i \(0.409060\pi\)
\(570\) 31.2025 + 23.9482i 1.30693 + 1.00308i
\(571\) 7.63852i 0.319662i −0.987144 0.159831i \(-0.948905\pi\)
0.987144 0.159831i \(-0.0510950\pi\)
\(572\) −0.326639 + 0.155896i −0.0136575 + 0.00651835i
\(573\) −13.8512 + 18.0469i −0.578642 + 0.753922i
\(574\) 8.95059i 0.373590i
\(575\) 9.79624i 0.408532i
\(576\) 0.775791 + 2.89796i 0.0323246 + 0.120748i
\(577\) −34.2239 −1.42476 −0.712380 0.701794i \(-0.752383\pi\)
−0.712380 + 0.701794i \(0.752383\pi\)
\(578\) 31.6738 1.31746
\(579\) 7.52562 9.80524i 0.312754 0.407492i
\(580\) 40.6544i 1.68808i
\(581\) 1.48034i 0.0614151i
\(582\) −4.79524 3.68039i −0.198769 0.152557i
\(583\) −16.6169 + 7.93083i −0.688203 + 0.328461i
\(584\) 3.31566i 0.137203i
\(585\) −0.332609 1.24246i −0.0137517 0.0513693i
\(586\) −13.0184 −0.537786
\(587\) 6.57288i 0.271292i 0.990757 + 0.135646i \(0.0433109\pi\)
−0.990757 + 0.135646i \(0.956689\pi\)
\(588\) −1.37401 1.05456i −0.0566631 0.0434895i
\(589\) 15.1162i 0.622854i
\(590\) 29.8789 1.23009
\(591\) 2.16173 + 1.65915i 0.0889218 + 0.0682484i
\(592\) 7.21864 0.296684
\(593\) −9.78733 −0.401917 −0.200959 0.979600i \(-0.564406\pi\)
−0.200959 + 0.979600i \(0.564406\pi\)
\(594\) 17.2102 0.900184i 0.706141 0.0369350i
\(595\) 27.4097 1.12369
\(596\) 6.65134 0.272450
\(597\) −6.02301 4.62272i −0.246505 0.189195i
\(598\) −0.102446 −0.00418932
\(599\) 34.2466i 1.39928i 0.714497 + 0.699639i \(0.246656\pi\)
−0.714497 + 0.699639i \(0.753344\pi\)
\(600\) −14.3380 11.0046i −0.585347 0.449260i
\(601\) 41.4594i 1.69117i −0.533845 0.845583i \(-0.679253\pi\)
0.533845 0.845583i \(-0.320747\pi\)
\(602\) −1.44880 −0.0590489
\(603\) 4.34865 + 16.2443i 0.177091 + 0.661520i
\(604\) 0.977889i 0.0397897i
\(605\) 33.5987 + 27.1806i 1.36598 + 1.10505i
\(606\) −14.1039 10.8249i −0.572934 0.439732i
\(607\) 2.09167i 0.0848983i 0.999099 + 0.0424491i \(0.0135160\pi\)
−0.999099 + 0.0424491i \(0.986484\pi\)
\(608\) 5.78023i 0.234419i
\(609\) 10.9125 14.2181i 0.442197 0.576145i
\(610\) −24.9612 −1.01065
\(611\) 1.24530 0.0503796
\(612\) 5.41243 + 20.2181i 0.218784 + 0.817267i
\(613\) 9.03532i 0.364933i −0.983212 0.182467i \(-0.941592\pi\)
0.983212 0.182467i \(-0.0584081\pi\)
\(614\) 14.2481i 0.575007i
\(615\) −37.0835 + 48.3166i −1.49535 + 1.94831i
\(616\) 2.99319 1.42857i 0.120599 0.0575588i
\(617\) 2.52949i 0.101834i 0.998703 + 0.0509168i \(0.0162143\pi\)
−0.998703 + 0.0509168i \(0.983786\pi\)
\(618\) −5.00594 3.84211i −0.201368 0.154552i
\(619\) 23.8636 0.959161 0.479580 0.877498i \(-0.340789\pi\)
0.479580 + 0.877498i \(0.340789\pi\)
\(620\) 10.2744i 0.412628i
\(621\) 4.50603 + 1.86828i 0.180821 + 0.0749716i
\(622\) 19.9015i 0.797977i
\(623\) 0.722227 0.0289354
\(624\) 0.115082 0.149942i 0.00460696 0.00600248i
\(625\) 31.7172 1.26869
\(626\) −30.6797 −1.22621
\(627\) 32.4802 + 6.89953i 1.29713 + 0.275541i
\(628\) −1.12491 −0.0448887
\(629\) 50.3620 2.00807
\(630\) 3.04790 + 11.3854i 0.121431 + 0.453605i
\(631\) 5.50038 0.218967 0.109483 0.993989i \(-0.465080\pi\)
0.109483 + 0.993989i \(0.465080\pi\)
\(632\) 0.361499i 0.0143797i
\(633\) −5.63691 + 7.34442i −0.224047 + 0.291914i
\(634\) 15.9925i 0.635142i
\(635\) −56.2603 −2.23262
\(636\) 5.85450 7.62791i 0.232146 0.302466i
\(637\) 0.109128i 0.00432379i
\(638\) 14.7827 + 30.9732i 0.585252 + 1.22624i
\(639\) 12.7303 3.40794i 0.503604 0.134816i
\(640\) 3.92876i 0.155298i
\(641\) 19.8911i 0.785652i −0.919613 0.392826i \(-0.871497\pi\)
0.919613 0.392826i \(-0.128503\pi\)
\(642\) −14.1986 10.8976i −0.560375 0.430093i
\(643\) −5.96699 −0.235315 −0.117657 0.993054i \(-0.537538\pi\)
−0.117657 + 0.993054i \(0.537538\pi\)
\(644\) 0.938770 0.0369927
\(645\) 7.82086 + 6.00259i 0.307946 + 0.236352i
\(646\) 40.3267i 1.58663i
\(647\) 2.10535i 0.0827700i −0.999143 0.0413850i \(-0.986823\pi\)
0.999143 0.0413850i \(-0.0131770\pi\)
\(648\) −7.79630 + 4.49641i −0.306268 + 0.176636i
\(649\) 22.7637 10.8645i 0.893552 0.426469i
\(650\) 1.13877i 0.0446661i
\(651\) 2.75786 3.59325i 0.108089 0.140831i
\(652\) −2.94048 −0.115158
\(653\) 28.1561i 1.10183i 0.834561 + 0.550916i \(0.185722\pi\)
−0.834561 + 0.550916i \(0.814278\pi\)
\(654\) 14.4570 18.8363i 0.565314 0.736556i
\(655\) 70.0680i 2.73778i
\(656\) −8.95059 −0.349462
\(657\) −9.60865 + 2.57226i −0.374869 + 0.100353i
\(658\) −11.4115 −0.444865
\(659\) 49.3012 1.92050 0.960251 0.279138i \(-0.0900487\pi\)
0.960251 + 0.279138i \(0.0900487\pi\)
\(660\) −22.0764 4.68954i −0.859324 0.182540i
\(661\) 4.68898 0.182380 0.0911900 0.995834i \(-0.470933\pi\)
0.0911900 + 0.995834i \(0.470933\pi\)
\(662\) −0.500933 −0.0194693
\(663\) 0.802888 1.04609i 0.0311816 0.0406269i
\(664\) 1.48034 0.0574485
\(665\) 22.7092i 0.880623i
\(666\) 5.60015 + 20.9193i 0.217002 + 0.810607i
\(667\) 9.71428i 0.376139i
\(668\) 21.5860 0.835186
\(669\) 26.1855 + 20.0976i 1.01239 + 0.777018i
\(670\) 22.0225i 0.850802i
\(671\) −19.0171 + 9.07636i −0.734147 + 0.350389i
\(672\) −1.05456 + 1.37401i −0.0406807 + 0.0530035i
\(673\) 40.7322i 1.57011i 0.619426 + 0.785055i \(0.287365\pi\)
−0.619426 + 0.785055i \(0.712635\pi\)
\(674\) 11.7562i 0.452833i
\(675\) 20.7675 50.0882i 0.799340 1.92789i
\(676\) 12.9881 0.499542
\(677\) 16.1261 0.619776 0.309888 0.950773i \(-0.399708\pi\)
0.309888 + 0.950773i \(0.399708\pi\)
\(678\) 0.847717 1.10450i 0.0325564 0.0424182i
\(679\) 3.48997i 0.133933i
\(680\) 27.4097i 1.05111i
\(681\) 23.6530 + 18.1539i 0.906386 + 0.695660i
\(682\) 3.73594 + 7.82768i 0.143057 + 0.299737i
\(683\) 35.6615i 1.36455i −0.731095 0.682276i \(-0.760990\pi\)
0.731095 0.682276i \(-0.239010\pi\)
\(684\) −16.7508 + 4.48425i −0.640485 + 0.171459i
\(685\) 26.4131 1.00919
\(686\) 1.00000i 0.0381802i
\(687\) 28.1220 + 21.5839i 1.07292 + 0.823476i
\(688\) 1.44880i 0.0552352i
\(689\) −0.605830 −0.0230803
\(690\) −5.06762 3.88945i −0.192921 0.148069i
\(691\) −35.8799 −1.36494 −0.682468 0.730916i \(-0.739093\pi\)
−0.682468 + 0.730916i \(0.739093\pi\)
\(692\) 5.10422 0.194033
\(693\) 6.46202 + 7.56586i 0.245472 + 0.287403i
\(694\) 31.2589 1.18657
\(695\) −23.7715 −0.901705
\(696\) −14.2181 10.9125i −0.538934 0.413637i
\(697\) −62.4452 −2.36528
\(698\) 26.8168i 1.01503i
\(699\) −23.5933 18.1081i −0.892381 0.684911i
\(700\) 10.4352i 0.394413i
\(701\) 22.3303 0.843405 0.421702 0.906734i \(-0.361433\pi\)
0.421702 + 0.906734i \(0.361433\pi\)
\(702\) 0.523805 + 0.217179i 0.0197697 + 0.00819688i
\(703\) 41.7254i 1.57370i
\(704\) −1.42857 2.99319i −0.0538413 0.112810i
\(705\) 61.6008 + 47.2792i 2.32002 + 1.78064i
\(706\) 30.7700i 1.15804i
\(707\) 10.2648i 0.386049i
\(708\) −8.02012 + 10.4495i −0.301415 + 0.392718i
\(709\) 22.2230 0.834601 0.417300 0.908769i \(-0.362976\pi\)
0.417300 + 0.908769i \(0.362976\pi\)
\(710\) −17.2585 −0.647701
\(711\) 1.04761 0.280448i 0.0392884 0.0105176i
\(712\) 0.722227i 0.0270666i
\(713\) 2.45504i 0.0919419i
\(714\) −7.35733 + 9.58598i −0.275341 + 0.358746i
\(715\) 0.612480 + 1.28329i 0.0229055 + 0.0479923i
\(716\) 17.2258i 0.643759i
\(717\) −12.9015 9.90201i −0.481814 0.369797i
\(718\) 14.7885 0.551904
\(719\) 14.2388i 0.531017i −0.964109 0.265508i \(-0.914460\pi\)
0.964109 0.265508i \(-0.0855398\pi\)
\(720\) 11.3854 3.04790i 0.424308 0.113588i
\(721\) 3.64331i 0.135684i
\(722\) −14.4110 −0.536324
\(723\) −10.9437 + 14.2587i −0.407000 + 0.530286i
\(724\) 11.9832 0.445350
\(725\) 107.982 4.01035
\(726\) −18.5245 + 4.45460i −0.687508 + 0.165326i
\(727\) −0.772552 −0.0286524 −0.0143262 0.999897i \(-0.504560\pi\)
−0.0143262 + 0.999897i \(0.504560\pi\)
\(728\) 0.109128 0.00404453
\(729\) −19.0787 19.1051i −0.706619 0.707595i
\(730\) 13.0265 0.482131
\(731\) 10.1078i 0.373851i
\(732\) 6.70013 8.72970i 0.247644 0.322659i
\(733\) 20.9468i 0.773687i −0.922145 0.386844i \(-0.873565\pi\)
0.922145 0.386844i \(-0.126435\pi\)
\(734\) −16.5826 −0.612076
\(735\) −4.14313 + 5.39815i −0.152822 + 0.199114i
\(736\) 0.938770i 0.0346035i
\(737\) −8.00777 16.7782i −0.294970 0.618031i
\(738\) −6.94378 25.9384i −0.255604 0.954806i
\(739\) 31.8490i 1.17159i 0.810461 + 0.585793i \(0.199217\pi\)
−0.810461 + 0.585793i \(0.800783\pi\)
\(740\) 28.3603i 1.04255i
\(741\) 0.866699 + 0.665200i 0.0318390 + 0.0244367i
\(742\) 5.55158 0.203805
\(743\) 2.95393 0.108369 0.0541847 0.998531i \(-0.482744\pi\)
0.0541847 + 0.998531i \(0.482744\pi\)
\(744\) −3.59325 2.75786i −0.131735 0.101108i
\(745\) 26.1316i 0.957386i
\(746\) 18.1538i 0.664659i
\(747\) 1.14844 + 4.28997i 0.0420191 + 0.156962i
\(748\) −9.96665 20.8825i −0.364417 0.763539i
\(749\) 10.3337i 0.377586i
\(750\) −22.5187 + 29.3399i −0.822266 + 1.07134i
\(751\) −7.94197 −0.289807 −0.144903 0.989446i \(-0.546287\pi\)
−0.144903 + 0.989446i \(0.546287\pi\)
\(752\) 11.4115i 0.416133i
\(753\) 8.17676 10.6536i 0.297978 0.388240i
\(754\) 1.12924i 0.0411244i
\(755\) −3.84190 −0.139821
\(756\) −4.79993 1.99014i −0.174572 0.0723806i
\(757\) −22.0057 −0.799810 −0.399905 0.916557i \(-0.630957\pi\)
−0.399905 + 0.916557i \(0.630957\pi\)
\(758\) −12.5603 −0.456211
\(759\) −5.27512 1.12056i −0.191475 0.0406736i
\(760\) 22.7092 0.823748
\(761\) 32.8592 1.19114 0.595572 0.803302i \(-0.296925\pi\)
0.595572 + 0.803302i \(0.296925\pi\)
\(762\) 15.1014 19.6759i 0.547068 0.712783i
\(763\) 13.7090 0.496299
\(764\) 13.1345i 0.475191i
\(765\) 79.4320 21.2642i 2.87187 0.768807i
\(766\) 3.12388i 0.112870i
\(767\) 0.829932 0.0299671
\(768\) 1.37401 + 1.05456i 0.0495802 + 0.0380533i
\(769\) 8.41547i 0.303470i −0.988421 0.151735i \(-0.951514\pi\)
0.988421 0.151735i \(-0.0484860\pi\)
\(770\) −5.61252 11.7595i −0.202261 0.423784i
\(771\) −23.4349 + 30.5337i −0.843988 + 1.09964i
\(772\) 7.13624i 0.256839i
\(773\) 38.4899i 1.38438i 0.721713 + 0.692192i \(0.243355\pi\)
−0.721713 + 0.692192i \(0.756645\pi\)
\(774\) −4.19857 + 1.12397i −0.150915 + 0.0404002i
\(775\) 27.2897 0.980275
\(776\) −3.48997 −0.125282
\(777\) −7.61252 + 9.91846i −0.273098 + 0.355823i
\(778\) 25.8114i 0.925383i
\(779\) 51.7364i 1.85365i
\(780\) −0.589087 0.452130i −0.0210927 0.0161888i
\(781\) −13.1487 + 6.27552i −0.470497 + 0.224556i
\(782\) 6.54948i 0.234209i
\(783\) 20.5937 49.6691i 0.735959