Properties

Label 1386.2.r.a.89.4
Level $1386$
Weight $2$
Character 1386.89
Analytic conductor $11.067$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1386.r (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.0672657201\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
Defining polynomial: \(x^{8} - x^{4} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 89.4
Root \(0.258819 - 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 1386.89
Dual form 1386.2.r.a.1277.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.0340742 + 0.0590182i) q^{5} +(-2.19067 - 1.48356i) q^{7} +1.00000i q^{8} +O(q^{10})\) \(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.0340742 + 0.0590182i) q^{5} +(-2.19067 - 1.48356i) q^{7} +1.00000i q^{8} +(-0.0590182 + 0.0340742i) q^{10} +(0.866025 - 0.500000i) q^{11} +2.44949i q^{13} +(-1.15539 - 2.38014i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(0.817837 + 1.41654i) q^{17} +(6.28497 + 3.62863i) q^{19} -0.0681483 q^{20} +1.00000 q^{22} +(0.405083 + 0.233875i) q^{23} +(2.49768 + 4.32611i) q^{25} +(-1.22474 + 2.12132i) q^{26} +(0.189469 - 2.63896i) q^{28} +7.23143i q^{29} +(-0.201501 + 0.116337i) q^{31} +(-0.866025 + 0.500000i) q^{32} +1.63567i q^{34} +(0.162203 - 0.0787382i) q^{35} +(2.74496 - 4.75442i) q^{37} +(3.62863 + 6.28497i) q^{38} +(-0.0590182 - 0.0340742i) q^{40} +5.38891 q^{41} +9.64100 q^{43} +(0.866025 + 0.500000i) q^{44} +(0.233875 + 0.405083i) q^{46} +(-4.31199 + 7.46859i) q^{47} +(2.59808 + 6.50000i) q^{49} +4.99536i q^{50} +(-2.12132 + 1.22474i) q^{52} +(-7.34278 + 4.23936i) q^{53} +0.0681483i q^{55} +(1.48356 - 2.19067i) q^{56} +(-3.61571 + 6.26260i) q^{58} +(0.439158 + 0.760643i) q^{59} +(-8.63223 - 4.98382i) q^{61} -0.232673 q^{62} -1.00000 q^{64} +(-0.144564 - 0.0834643i) q^{65} +(1.52993 + 2.64991i) q^{67} +(-0.817837 + 1.41654i) q^{68} +(0.179841 + 0.0129120i) q^{70} -15.8771i q^{71} +(6.76696 - 3.90691i) q^{73} +(4.75442 - 2.74496i) q^{74} +7.25725i q^{76} +(-2.63896 - 0.189469i) q^{77} +(5.76612 - 9.98722i) q^{79} +(-0.0340742 - 0.0590182i) q^{80} +(4.66693 + 2.69445i) q^{82} -17.1270 q^{83} -0.111469 q^{85} +(8.34935 + 4.82050i) q^{86} +(0.500000 + 0.866025i) q^{88} +(-5.33814 + 9.24592i) q^{89} +(3.63397 - 5.36603i) q^{91} +0.467750i q^{92} +(-7.46859 + 4.31199i) q^{94} +(-0.428310 + 0.247285i) q^{95} +9.99876i q^{97} +(-1.00000 + 6.92820i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 4q^{4} - 8q^{5} + O(q^{10}) \) \( 8q + 4q^{4} - 8q^{5} - 4q^{16} + 4q^{17} + 24q^{19} - 16q^{20} + 8q^{22} - 24q^{23} - 4q^{25} + 12q^{31} - 16q^{35} + 12q^{37} + 8q^{38} - 16q^{41} - 32q^{43} + 8q^{46} - 48q^{53} - 4q^{58} - 16q^{59} - 24q^{62} - 8q^{64} + 12q^{65} - 24q^{67} - 4q^{68} - 20q^{70} - 24q^{73} + 12q^{74} + 40q^{79} - 8q^{80} + 12q^{82} - 72q^{83} - 32q^{85} + 24q^{86} + 4q^{88} + 16q^{89} + 36q^{91} - 24q^{95} - 8q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(1135\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 + 0.500000i 0.612372 + 0.353553i
\(3\) 0 0
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) −0.0340742 + 0.0590182i −0.0152384 + 0.0263937i −0.873544 0.486745i \(-0.838184\pi\)
0.858306 + 0.513139i \(0.171517\pi\)
\(6\) 0 0
\(7\) −2.19067 1.48356i −0.827996 0.560734i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) −0.0590182 + 0.0340742i −0.0186632 + 0.0107752i
\(11\) 0.866025 0.500000i 0.261116 0.150756i
\(12\) 0 0
\(13\) 2.44949i 0.679366i 0.940540 + 0.339683i \(0.110320\pi\)
−0.940540 + 0.339683i \(0.889680\pi\)
\(14\) −1.15539 2.38014i −0.308792 0.636119i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 0.817837 + 1.41654i 0.198355 + 0.343560i 0.947995 0.318285i \(-0.103107\pi\)
−0.749640 + 0.661845i \(0.769774\pi\)
\(18\) 0 0
\(19\) 6.28497 + 3.62863i 1.44187 + 0.832464i 0.997975 0.0636147i \(-0.0202629\pi\)
0.443895 + 0.896079i \(0.353596\pi\)
\(20\) −0.0681483 −0.0152384
\(21\) 0 0
\(22\) 1.00000 0.213201
\(23\) 0.405083 + 0.233875i 0.0844657 + 0.0487663i 0.541638 0.840612i \(-0.317804\pi\)
−0.457172 + 0.889378i \(0.651138\pi\)
\(24\) 0 0
\(25\) 2.49768 + 4.32611i 0.499536 + 0.865221i
\(26\) −1.22474 + 2.12132i −0.240192 + 0.416025i
\(27\) 0 0
\(28\) 0.189469 2.63896i 0.0358062 0.498716i
\(29\) 7.23143i 1.34284i 0.741076 + 0.671421i \(0.234316\pi\)
−0.741076 + 0.671421i \(0.765684\pi\)
\(30\) 0 0
\(31\) −0.201501 + 0.116337i −0.0361906 + 0.0208947i −0.517986 0.855389i \(-0.673318\pi\)
0.481796 + 0.876284i \(0.339985\pi\)
\(32\) −0.866025 + 0.500000i −0.153093 + 0.0883883i
\(33\) 0 0
\(34\) 1.63567i 0.280516i
\(35\) 0.162203 0.0787382i 0.0274172 0.0133092i
\(36\) 0 0
\(37\) 2.74496 4.75442i 0.451269 0.781621i −0.547196 0.837004i \(-0.684305\pi\)
0.998465 + 0.0553835i \(0.0176381\pi\)
\(38\) 3.62863 + 6.28497i 0.588641 + 1.01956i
\(39\) 0 0
\(40\) −0.0590182 0.0340742i −0.00933160 0.00538760i
\(41\) 5.38891 0.841606 0.420803 0.907152i \(-0.361748\pi\)
0.420803 + 0.907152i \(0.361748\pi\)
\(42\) 0 0
\(43\) 9.64100 1.47024 0.735119 0.677938i \(-0.237126\pi\)
0.735119 + 0.677938i \(0.237126\pi\)
\(44\) 0.866025 + 0.500000i 0.130558 + 0.0753778i
\(45\) 0 0
\(46\) 0.233875 + 0.405083i 0.0344830 + 0.0597263i
\(47\) −4.31199 + 7.46859i −0.628969 + 1.08941i 0.358791 + 0.933418i \(0.383189\pi\)
−0.987759 + 0.155987i \(0.950144\pi\)
\(48\) 0 0
\(49\) 2.59808 + 6.50000i 0.371154 + 0.928571i
\(50\) 4.99536i 0.706450i
\(51\) 0 0
\(52\) −2.12132 + 1.22474i −0.294174 + 0.169842i
\(53\) −7.34278 + 4.23936i −1.00861 + 0.582320i −0.910784 0.412883i \(-0.864522\pi\)
−0.0978246 + 0.995204i \(0.531188\pi\)
\(54\) 0 0
\(55\) 0.0681483i 0.00918912i
\(56\) 1.48356 2.19067i 0.198250 0.292741i
\(57\) 0 0
\(58\) −3.61571 + 6.26260i −0.474767 + 0.822320i
\(59\) 0.439158 + 0.760643i 0.0571734 + 0.0990273i 0.893196 0.449668i \(-0.148458\pi\)
−0.836022 + 0.548696i \(0.815125\pi\)
\(60\) 0 0
\(61\) −8.63223 4.98382i −1.10524 0.638113i −0.167651 0.985846i \(-0.553618\pi\)
−0.937593 + 0.347733i \(0.886951\pi\)
\(62\) −0.232673 −0.0295495
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) −0.144564 0.0834643i −0.0179310 0.0103525i
\(66\) 0 0
\(67\) 1.52993 + 2.64991i 0.186910 + 0.323738i 0.944219 0.329319i \(-0.106819\pi\)
−0.757308 + 0.653058i \(0.773486\pi\)
\(68\) −0.817837 + 1.41654i −0.0991773 + 0.171780i
\(69\) 0 0
\(70\) 0.179841 + 0.0129120i 0.0214951 + 0.00154328i
\(71\) 15.8771i 1.88426i −0.335245 0.942131i \(-0.608819\pi\)
0.335245 0.942131i \(-0.391181\pi\)
\(72\) 0 0
\(73\) 6.76696 3.90691i 0.792013 0.457269i −0.0486577 0.998816i \(-0.515494\pi\)
0.840671 + 0.541547i \(0.182161\pi\)
\(74\) 4.75442 2.74496i 0.552690 0.319095i
\(75\) 0 0
\(76\) 7.25725i 0.832464i
\(77\) −2.63896 0.189469i −0.300737 0.0215920i
\(78\) 0 0
\(79\) 5.76612 9.98722i 0.648740 1.12365i −0.334684 0.942330i \(-0.608630\pi\)
0.983424 0.181320i \(-0.0580370\pi\)
\(80\) −0.0340742 0.0590182i −0.00380961 0.00659844i
\(81\) 0 0
\(82\) 4.66693 + 2.69445i 0.515376 + 0.297553i
\(83\) −17.1270 −1.87993 −0.939967 0.341266i \(-0.889144\pi\)
−0.939967 + 0.341266i \(0.889144\pi\)
\(84\) 0 0
\(85\) −0.111469 −0.0120905
\(86\) 8.34935 + 4.82050i 0.900333 + 0.519808i
\(87\) 0 0
\(88\) 0.500000 + 0.866025i 0.0533002 + 0.0923186i
\(89\) −5.33814 + 9.24592i −0.565841 + 0.980066i 0.431129 + 0.902290i \(0.358115\pi\)
−0.996971 + 0.0777760i \(0.975218\pi\)
\(90\) 0 0
\(91\) 3.63397 5.36603i 0.380944 0.562512i
\(92\) 0.467750i 0.0487663i
\(93\) 0 0
\(94\) −7.46859 + 4.31199i −0.770326 + 0.444748i
\(95\) −0.428310 + 0.247285i −0.0439437 + 0.0253709i
\(96\) 0 0
\(97\) 9.99876i 1.01522i 0.861587 + 0.507610i \(0.169471\pi\)
−0.861587 + 0.507610i \(0.830529\pi\)
\(98\) −1.00000 + 6.92820i −0.101015 + 0.699854i
\(99\) 0 0
\(100\) −2.49768 + 4.32611i −0.249768 + 0.432611i
\(101\) −1.76028 3.04889i −0.175154 0.303376i 0.765060 0.643959i \(-0.222709\pi\)
−0.940215 + 0.340582i \(0.889376\pi\)
\(102\) 0 0
\(103\) 13.8471 + 7.99465i 1.36440 + 0.787736i 0.990206 0.139614i \(-0.0445862\pi\)
0.374194 + 0.927351i \(0.377920\pi\)
\(104\) −2.44949 −0.240192
\(105\) 0 0
\(106\) −8.47871 −0.823525
\(107\) 5.25201 + 3.03225i 0.507731 + 0.293139i 0.731901 0.681412i \(-0.238634\pi\)
−0.224169 + 0.974550i \(0.571967\pi\)
\(108\) 0 0
\(109\) −9.00877 15.6036i −0.862883 1.49456i −0.869134 0.494577i \(-0.835323\pi\)
0.00625046 0.999980i \(-0.498010\pi\)
\(110\) −0.0340742 + 0.0590182i −0.00324884 + 0.00562716i
\(111\) 0 0
\(112\) 2.38014 1.15539i 0.224902 0.109175i
\(113\) 7.05521i 0.663698i −0.943332 0.331849i \(-0.892327\pi\)
0.943332 0.331849i \(-0.107673\pi\)
\(114\) 0 0
\(115\) −0.0276058 + 0.0159382i −0.00257425 + 0.00148624i
\(116\) −6.26260 + 3.61571i −0.581468 + 0.335711i
\(117\) 0 0
\(118\) 0.878315i 0.0808555i
\(119\) 0.309909 4.31648i 0.0284093 0.395691i
\(120\) 0 0
\(121\) 0.500000 0.866025i 0.0454545 0.0787296i
\(122\) −4.98382 8.63223i −0.451214 0.781526i
\(123\) 0 0
\(124\) −0.201501 0.116337i −0.0180953 0.0104473i
\(125\) −0.681167 −0.0609254
\(126\) 0 0
\(127\) 6.83939 0.606898 0.303449 0.952848i \(-0.401862\pi\)
0.303449 + 0.952848i \(0.401862\pi\)
\(128\) −0.866025 0.500000i −0.0765466 0.0441942i
\(129\) 0 0
\(130\) −0.0834643 0.144564i −0.00732031 0.0126791i
\(131\) −0.757359 + 1.31178i −0.0661708 + 0.114611i −0.897213 0.441599i \(-0.854412\pi\)
0.831042 + 0.556210i \(0.187745\pi\)
\(132\) 0 0
\(133\) −8.38499 17.2733i −0.727071 1.49778i
\(134\) 3.05986i 0.264331i
\(135\) 0 0
\(136\) −1.41654 + 0.817837i −0.121467 + 0.0701290i
\(137\) −4.27427 + 2.46775i −0.365175 + 0.210834i −0.671349 0.741142i \(-0.734285\pi\)
0.306173 + 0.951976i \(0.400951\pi\)
\(138\) 0 0
\(139\) 1.10583i 0.0937952i 0.998900 + 0.0468976i \(0.0149334\pi\)
−0.998900 + 0.0468976i \(0.985067\pi\)
\(140\) 0.149291 + 0.101102i 0.0126174 + 0.00854471i
\(141\) 0 0
\(142\) 7.93854 13.7499i 0.666187 1.15387i
\(143\) 1.22474 + 2.12132i 0.102418 + 0.177394i
\(144\) 0 0
\(145\) −0.426786 0.246405i −0.0354426 0.0204628i
\(146\) 7.81382 0.646676
\(147\) 0 0
\(148\) 5.48993 0.451269
\(149\) 0.275702 + 0.159176i 0.0225863 + 0.0130402i 0.511251 0.859432i \(-0.329182\pi\)
−0.488664 + 0.872472i \(0.662516\pi\)
\(150\) 0 0
\(151\) −1.76941 3.06471i −0.143992 0.249402i 0.785004 0.619491i \(-0.212661\pi\)
−0.928997 + 0.370088i \(0.879327\pi\)
\(152\) −3.62863 + 6.28497i −0.294320 + 0.509778i
\(153\) 0 0
\(154\) −2.19067 1.48356i −0.176529 0.119549i
\(155\) 0.0158563i 0.00127361i
\(156\) 0 0
\(157\) −5.64589 + 3.25966i −0.450591 + 0.260149i −0.708080 0.706132i \(-0.750438\pi\)
0.257489 + 0.966281i \(0.417105\pi\)
\(158\) 9.98722 5.76612i 0.794541 0.458728i
\(159\) 0 0
\(160\) 0.0681483i 0.00538760i
\(161\) −0.540436 1.11331i −0.0425923 0.0877411i
\(162\) 0 0
\(163\) 0.553536 0.958753i 0.0433563 0.0750954i −0.843533 0.537078i \(-0.819528\pi\)
0.886889 + 0.461982i \(0.152862\pi\)
\(164\) 2.69445 + 4.66693i 0.210401 + 0.364426i
\(165\) 0 0
\(166\) −14.8324 8.56350i −1.15122 0.664657i
\(167\) −9.93426 −0.768736 −0.384368 0.923180i \(-0.625581\pi\)
−0.384368 + 0.923180i \(0.625581\pi\)
\(168\) 0 0
\(169\) 7.00000 0.538462
\(170\) −0.0965346 0.0557343i −0.00740386 0.00427462i
\(171\) 0 0
\(172\) 4.82050 + 8.34935i 0.367560 + 0.636632i
\(173\) −6.61107 + 11.4507i −0.502630 + 0.870581i 0.497365 + 0.867541i \(0.334301\pi\)
−0.999995 + 0.00303994i \(0.999032\pi\)
\(174\) 0 0
\(175\) 0.946464 13.1825i 0.0715459 0.996506i
\(176\) 1.00000i 0.0753778i
\(177\) 0 0
\(178\) −9.24592 + 5.33814i −0.693011 + 0.400110i
\(179\) 9.79227 5.65357i 0.731909 0.422568i −0.0872113 0.996190i \(-0.527796\pi\)
0.819120 + 0.573622i \(0.194462\pi\)
\(180\) 0 0
\(181\) 8.26670i 0.614459i 0.951635 + 0.307230i \(0.0994020\pi\)
−0.951635 + 0.307230i \(0.900598\pi\)
\(182\) 5.83013 2.83013i 0.432158 0.209783i
\(183\) 0 0
\(184\) −0.233875 + 0.405083i −0.0172415 + 0.0298631i
\(185\) 0.187065 + 0.324006i 0.0137533 + 0.0238214i
\(186\) 0 0
\(187\) 1.41654 + 0.817837i 0.103587 + 0.0598062i
\(188\) −8.62398 −0.628969
\(189\) 0 0
\(190\) −0.494570 −0.0358799
\(191\) 10.3133 + 5.95439i 0.746245 + 0.430845i 0.824335 0.566102i \(-0.191549\pi\)
−0.0780906 + 0.996946i \(0.524882\pi\)
\(192\) 0 0
\(193\) −12.7134 22.0203i −0.915132 1.58506i −0.806707 0.590951i \(-0.798753\pi\)
−0.108425 0.994105i \(-0.534581\pi\)
\(194\) −4.99938 + 8.65918i −0.358934 + 0.621693i
\(195\) 0 0
\(196\) −4.33013 + 5.50000i −0.309295 + 0.392857i
\(197\) 8.37821i 0.596923i 0.954422 + 0.298461i \(0.0964734\pi\)
−0.954422 + 0.298461i \(0.903527\pi\)
\(198\) 0 0
\(199\) 17.3736 10.0306i 1.23158 0.711053i 0.264220 0.964462i \(-0.414885\pi\)
0.967359 + 0.253410i \(0.0815521\pi\)
\(200\) −4.32611 + 2.49768i −0.305902 + 0.176612i
\(201\) 0 0
\(202\) 3.52056i 0.247706i
\(203\) 10.7283 15.8417i 0.752978 1.11187i
\(204\) 0 0
\(205\) −0.183622 + 0.318043i −0.0128248 + 0.0222131i
\(206\) 7.99465 + 13.8471i 0.557014 + 0.964776i
\(207\) 0 0
\(208\) −2.12132 1.22474i −0.147087 0.0849208i
\(209\) 7.25725 0.501995
\(210\) 0 0
\(211\) 2.96399 0.204050 0.102025 0.994782i \(-0.467468\pi\)
0.102025 + 0.994782i \(0.467468\pi\)
\(212\) −7.34278 4.23936i −0.504304 0.291160i
\(213\) 0 0
\(214\) 3.03225 + 5.25201i 0.207280 + 0.359020i
\(215\) −0.328509 + 0.568994i −0.0224041 + 0.0388051i
\(216\) 0 0
\(217\) 0.614014 + 0.0440843i 0.0416820 + 0.00299263i
\(218\) 18.0175i 1.22030i
\(219\) 0 0
\(220\) −0.0590182 + 0.0340742i −0.00397901 + 0.00229728i
\(221\) −3.46979 + 2.00328i −0.233403 + 0.134755i
\(222\) 0 0
\(223\) 13.8238i 0.925709i 0.886434 + 0.462854i \(0.153175\pi\)
−0.886434 + 0.462854i \(0.846825\pi\)
\(224\) 2.63896 + 0.189469i 0.176323 + 0.0126594i
\(225\) 0 0
\(226\) 3.52761 6.10999i 0.234653 0.406431i
\(227\) −11.1257 19.2702i −0.738437 1.27901i −0.953199 0.302345i \(-0.902231\pi\)
0.214761 0.976667i \(-0.431103\pi\)
\(228\) 0 0
\(229\) 12.3195 + 7.11269i 0.814098 + 0.470020i 0.848377 0.529393i \(-0.177580\pi\)
−0.0342790 + 0.999412i \(0.510913\pi\)
\(230\) −0.0318764 −0.00210187
\(231\) 0 0
\(232\) −7.23143 −0.474767
\(233\) −0.445759 0.257359i −0.0292027 0.0168602i 0.485328 0.874332i \(-0.338700\pi\)
−0.514530 + 0.857472i \(0.672034\pi\)
\(234\) 0 0
\(235\) −0.293855 0.508972i −0.0191690 0.0332017i
\(236\) −0.439158 + 0.760643i −0.0285867 + 0.0495137i
\(237\) 0 0
\(238\) 2.42663 3.58322i 0.157295 0.232266i
\(239\) 21.8238i 1.41166i −0.708380 0.705832i \(-0.750574\pi\)
0.708380 0.705832i \(-0.249426\pi\)
\(240\) 0 0
\(241\) −7.95439 + 4.59247i −0.512387 + 0.295827i −0.733814 0.679350i \(-0.762262\pi\)
0.221427 + 0.975177i \(0.428929\pi\)
\(242\) 0.866025 0.500000i 0.0556702 0.0321412i
\(243\) 0 0
\(244\) 9.96764i 0.638113i
\(245\) −0.472146 0.0681483i −0.0301643 0.00435384i
\(246\) 0 0
\(247\) −8.88828 + 15.3950i −0.565548 + 0.979558i
\(248\) −0.116337 0.201501i −0.00738738 0.0127953i
\(249\) 0 0
\(250\) −0.589908 0.340583i −0.0373091 0.0215404i
\(251\) 31.3044 1.97592 0.987959 0.154718i \(-0.0494468\pi\)
0.987959 + 0.154718i \(0.0494468\pi\)
\(252\) 0 0
\(253\) 0.467750 0.0294072
\(254\) 5.92309 + 3.41970i 0.371647 + 0.214571i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −2.01033 + 3.48200i −0.125401 + 0.217201i −0.921890 0.387453i \(-0.873355\pi\)
0.796489 + 0.604654i \(0.206688\pi\)
\(258\) 0 0
\(259\) −13.0668 + 6.34303i −0.811931 + 0.394137i
\(260\) 0.166929i 0.0103525i
\(261\) 0 0
\(262\) −1.31178 + 0.757359i −0.0810423 + 0.0467898i
\(263\) −11.6746 + 6.74032i −0.719885 + 0.415626i −0.814710 0.579868i \(-0.803104\pi\)
0.0948253 + 0.995494i \(0.469771\pi\)
\(264\) 0 0
\(265\) 0.577810i 0.0354946i
\(266\) 1.37502 19.1516i 0.0843080 1.17426i
\(267\) 0 0
\(268\) −1.52993 + 2.64991i −0.0934552 + 0.161869i
\(269\) −15.7399 27.2624i −0.959681 1.66222i −0.723273 0.690562i \(-0.757363\pi\)
−0.236408 0.971654i \(-0.575970\pi\)
\(270\) 0 0
\(271\) −4.89157 2.82415i −0.297142 0.171555i 0.344017 0.938964i \(-0.388212\pi\)
−0.641158 + 0.767409i \(0.721546\pi\)
\(272\) −1.63567 −0.0991773
\(273\) 0 0
\(274\) −4.93550 −0.298164
\(275\) 4.32611 + 2.49768i 0.260874 + 0.150616i
\(276\) 0 0
\(277\) −3.45982 5.99259i −0.207881 0.360060i 0.743166 0.669107i \(-0.233323\pi\)
−0.951047 + 0.309047i \(0.899990\pi\)
\(278\) −0.552914 + 0.957676i −0.0331616 + 0.0574376i
\(279\) 0 0
\(280\) 0.0787382 + 0.162203i 0.00470551 + 0.00969346i
\(281\) 30.4582i 1.81698i −0.417902 0.908492i \(-0.637234\pi\)
0.417902 0.908492i \(-0.362766\pi\)
\(282\) 0 0
\(283\) −22.8490 + 13.1919i −1.35823 + 0.784175i −0.989385 0.145315i \(-0.953580\pi\)
−0.368846 + 0.929490i \(0.620247\pi\)
\(284\) 13.7499 7.93854i 0.815909 0.471065i
\(285\) 0 0
\(286\) 2.44949i 0.144841i
\(287\) −11.8053 7.99479i −0.696846 0.471917i
\(288\) 0 0
\(289\) 7.16228 12.4054i 0.421311 0.729732i
\(290\) −0.246405 0.426786i −0.0144694 0.0250617i
\(291\) 0 0
\(292\) 6.76696 + 3.90691i 0.396007 + 0.228634i
\(293\) 15.0095 0.876862 0.438431 0.898765i \(-0.355534\pi\)
0.438431 + 0.898765i \(0.355534\pi\)
\(294\) 0 0
\(295\) −0.0598557 −0.00348494
\(296\) 4.75442 + 2.74496i 0.276345 + 0.159548i
\(297\) 0 0
\(298\) 0.159176 + 0.275702i 0.00922084 + 0.0159710i
\(299\) −0.572874 + 0.992248i −0.0331302 + 0.0573832i
\(300\) 0 0
\(301\) −21.1203 14.3030i −1.21735 0.824413i
\(302\) 3.53882i 0.203636i
\(303\) 0 0
\(304\) −6.28497 + 3.62863i −0.360467 + 0.208116i
\(305\) 0.588272 0.339639i 0.0336844 0.0194477i
\(306\) 0 0
\(307\) 15.0711i 0.860151i −0.902793 0.430076i \(-0.858487\pi\)
0.902793 0.430076i \(-0.141513\pi\)
\(308\) −1.15539 2.38014i −0.0658347 0.135621i
\(309\) 0 0
\(310\) 0.00792814 0.0137319i 0.000450288 0.000779922i
\(311\) −9.93645 17.2104i −0.563445 0.975915i −0.997193 0.0748804i \(-0.976143\pi\)
0.433748 0.901034i \(-0.357191\pi\)
\(312\) 0 0
\(313\) −7.81257 4.51059i −0.441593 0.254954i 0.262680 0.964883i \(-0.415394\pi\)
−0.704273 + 0.709929i \(0.748727\pi\)
\(314\) −6.51931 −0.367906
\(315\) 0 0
\(316\) 11.5322 0.648740
\(317\) 10.2958 + 5.94427i 0.578268 + 0.333863i 0.760445 0.649403i \(-0.224981\pi\)
−0.182177 + 0.983266i \(0.558314\pi\)
\(318\) 0 0
\(319\) 3.61571 + 6.26260i 0.202441 + 0.350638i
\(320\) 0.0340742 0.0590182i 0.00190480 0.00329922i
\(321\) 0 0
\(322\) 0.0886240 1.23437i 0.00493882 0.0687889i
\(323\) 11.8705i 0.660492i
\(324\) 0 0
\(325\) −10.5967 + 6.11804i −0.587802 + 0.339368i
\(326\) 0.958753 0.553536i 0.0531004 0.0306575i
\(327\) 0 0
\(328\) 5.38891i 0.297553i
\(329\) 20.5263 9.96410i 1.13165 0.549339i
\(330\) 0 0
\(331\) −11.5175 + 19.9489i −0.633061 + 1.09649i 0.353862 + 0.935298i \(0.384868\pi\)
−0.986922 + 0.161196i \(0.948465\pi\)
\(332\) −8.56350 14.8324i −0.469983 0.814035i
\(333\) 0 0
\(334\) −8.60332 4.96713i −0.470753 0.271789i
\(335\) −0.208524 −0.0113929
\(336\) 0 0
\(337\) −20.8191 −1.13409 −0.567045 0.823687i \(-0.691914\pi\)
−0.567045 + 0.823687i \(0.691914\pi\)
\(338\) 6.06218 + 3.50000i 0.329739 + 0.190375i
\(339\) 0 0
\(340\) −0.0557343 0.0965346i −0.00302261 0.00523532i
\(341\) −0.116337 + 0.201501i −0.00629998 + 0.0109119i
\(342\) 0 0
\(343\) 3.95164 18.0938i 0.213368 0.976972i
\(344\) 9.64100i 0.519808i
\(345\) 0 0
\(346\) −11.4507 + 6.61107i −0.615594 + 0.355413i
\(347\) −6.30751 + 3.64165i −0.338605 + 0.195494i −0.659655 0.751569i \(-0.729298\pi\)
0.321050 + 0.947062i \(0.395964\pi\)
\(348\) 0 0
\(349\) 33.7366i 1.80588i 0.429767 + 0.902940i \(0.358596\pi\)
−0.429767 + 0.902940i \(0.641404\pi\)
\(350\) 7.41093 10.9432i 0.396131 0.584938i
\(351\) 0 0
\(352\) −0.500000 + 0.866025i −0.0266501 + 0.0461593i
\(353\) −8.71467 15.0943i −0.463835 0.803386i 0.535313 0.844654i \(-0.320194\pi\)
−0.999148 + 0.0412678i \(0.986860\pi\)
\(354\) 0 0
\(355\) 0.937036 + 0.540998i 0.0497327 + 0.0287132i
\(356\) −10.6763 −0.565841
\(357\) 0 0
\(358\) 11.3071 0.597601
\(359\) 22.6722 + 13.0898i 1.19659 + 0.690852i 0.959794 0.280707i \(-0.0905688\pi\)
0.236798 + 0.971559i \(0.423902\pi\)
\(360\) 0 0
\(361\) 16.8339 + 29.1571i 0.885992 + 1.53458i
\(362\) −4.13335 + 7.15918i −0.217244 + 0.376278i
\(363\) 0 0
\(364\) 6.46410 + 0.464102i 0.338811 + 0.0243255i
\(365\) 0.532499i 0.0278723i
\(366\) 0 0
\(367\) 9.91510 5.72449i 0.517564 0.298816i −0.218373 0.975865i \(-0.570075\pi\)
0.735937 + 0.677050i \(0.236742\pi\)
\(368\) −0.405083 + 0.233875i −0.0211164 + 0.0121916i
\(369\) 0 0
\(370\) 0.374129i 0.0194501i
\(371\) 22.3750 + 1.60645i 1.16165 + 0.0834028i
\(372\) 0 0
\(373\) 14.1189 24.4546i 0.731048 1.26621i −0.225388 0.974269i \(-0.572365\pi\)
0.956436 0.291943i \(-0.0943016\pi\)
\(374\) 0.817837 + 1.41654i 0.0422894 + 0.0732473i
\(375\) 0 0
\(376\) −7.46859 4.31199i −0.385163 0.222374i
\(377\) −17.7133 −0.912282
\(378\) 0 0
\(379\) 9.93550 0.510352 0.255176 0.966895i \(-0.417867\pi\)
0.255176 + 0.966895i \(0.417867\pi\)
\(380\) −0.428310 0.247285i −0.0219718 0.0126854i
\(381\) 0 0
\(382\) 5.95439 + 10.3133i 0.304653 + 0.527675i
\(383\) 6.97381 12.0790i 0.356345 0.617208i −0.631002 0.775781i \(-0.717356\pi\)
0.987347 + 0.158573i \(0.0506894\pi\)
\(384\) 0 0
\(385\) 0.101102 0.149291i 0.00515266 0.00760855i
\(386\) 25.4269i 1.29419i
\(387\) 0 0
\(388\) −8.65918 + 4.99938i −0.439603 + 0.253805i
\(389\) −1.53141 + 0.884161i −0.0776457 + 0.0448288i −0.538320 0.842740i \(-0.680941\pi\)
0.460674 + 0.887569i \(0.347608\pi\)
\(390\) 0 0
\(391\) 0.765087i 0.0386921i
\(392\) −6.50000 + 2.59808i −0.328300 + 0.131223i
\(393\) 0 0
\(394\) −4.18910 + 7.25574i −0.211044 + 0.365539i
\(395\) 0.392952 + 0.680613i 0.0197716 + 0.0342453i
\(396\) 0 0
\(397\) −1.04114 0.601102i −0.0522533 0.0301685i 0.473646 0.880715i \(-0.342938\pi\)
−0.525899 + 0.850547i \(0.676271\pi\)
\(398\) 20.0613 1.00558
\(399\) 0 0
\(400\) −4.99536 −0.249768
\(401\) 15.4934 + 8.94510i 0.773702 + 0.446697i 0.834194 0.551472i \(-0.185933\pi\)
−0.0604915 + 0.998169i \(0.519267\pi\)
\(402\) 0 0
\(403\) −0.284965 0.493574i −0.0141951 0.0245867i
\(404\) 1.76028 3.04889i 0.0875771 0.151688i
\(405\) 0 0
\(406\) 17.2118 8.35515i 0.854208 0.414659i
\(407\) 5.48993i 0.272126i
\(408\) 0 0
\(409\) −1.35436 + 0.781939i −0.0669687 + 0.0386644i −0.533110 0.846046i \(-0.678977\pi\)
0.466142 + 0.884710i \(0.345644\pi\)
\(410\) −0.318043 + 0.183622i −0.0157070 + 0.00906847i
\(411\) 0 0
\(412\) 15.9893i 0.787736i
\(413\) 0.166413 2.31784i 0.00818866 0.114053i
\(414\) 0 0
\(415\) 0.583589 1.01081i 0.0286472 0.0496185i
\(416\) −1.22474 2.12132i −0.0600481 0.104006i
\(417\) 0 0
\(418\) 6.28497 + 3.62863i 0.307408 + 0.177482i
\(419\) −4.99020 −0.243787 −0.121894 0.992543i \(-0.538897\pi\)
−0.121894 + 0.992543i \(0.538897\pi\)
\(420\) 0 0
\(421\) −37.0235 −1.80441 −0.902207 0.431302i \(-0.858054\pi\)
−0.902207 + 0.431302i \(0.858054\pi\)
\(422\) 2.56689 + 1.48200i 0.124954 + 0.0721425i
\(423\) 0 0
\(424\) −4.23936 7.34278i −0.205881 0.356597i
\(425\) −4.08539 + 7.07610i −0.198170 + 0.343241i
\(426\) 0 0
\(427\) 11.5166 + 23.7244i 0.557325 + 1.14810i
\(428\) 6.06450i 0.293139i
\(429\) 0 0
\(430\) −0.568994 + 0.328509i −0.0274393 + 0.0158421i
\(431\) −11.4567 + 6.61453i −0.551850 + 0.318611i −0.749868 0.661588i \(-0.769883\pi\)
0.198018 + 0.980198i \(0.436550\pi\)
\(432\) 0 0
\(433\) 12.5794i 0.604527i −0.953224 0.302263i \(-0.902258\pi\)
0.953224 0.302263i \(-0.0977422\pi\)
\(434\) 0.509710 + 0.345185i 0.0244669 + 0.0165694i
\(435\) 0 0
\(436\) 9.00877 15.6036i 0.431442 0.747279i
\(437\) 1.69729 + 2.93979i 0.0811924 + 0.140629i
\(438\) 0 0
\(439\) −15.2358 8.79639i −0.727165 0.419829i 0.0902191 0.995922i \(-0.471243\pi\)
−0.817384 + 0.576093i \(0.804577\pi\)
\(440\) −0.0681483 −0.00324884
\(441\) 0 0
\(442\) −4.00657 −0.190573
\(443\) 23.4746 + 13.5531i 1.11531 + 0.643926i 0.940200 0.340623i \(-0.110638\pi\)
0.175112 + 0.984549i \(0.443971\pi\)
\(444\) 0 0
\(445\) −0.363785 0.630094i −0.0172451 0.0298693i
\(446\) −6.91189 + 11.9717i −0.327288 + 0.566879i
\(447\) 0 0
\(448\) 2.19067 + 1.48356i 0.103499 + 0.0700918i
\(449\) 14.9950i 0.707658i 0.935310 + 0.353829i \(0.115121\pi\)
−0.935310 + 0.353829i \(0.884879\pi\)
\(450\) 0 0
\(451\) 4.66693 2.69445i 0.219757 0.126877i
\(452\) 6.10999 3.52761i 0.287390 0.165925i
\(453\) 0 0
\(454\) 22.2514i 1.04431i
\(455\) 0.192868 + 0.397314i 0.00904181 + 0.0186263i
\(456\) 0 0
\(457\) 0.475430 0.823468i 0.0222397 0.0385202i −0.854691 0.519136i \(-0.826254\pi\)
0.876931 + 0.480616i \(0.159587\pi\)
\(458\) 7.11269 + 12.3195i 0.332354 + 0.575654i
\(459\) 0 0
\(460\) −0.0276058 0.0159382i −0.00128713 0.000743122i
\(461\) −17.7698 −0.827621 −0.413810 0.910363i \(-0.635802\pi\)
−0.413810 + 0.910363i \(0.635802\pi\)
\(462\) 0 0
\(463\) 1.21592 0.0565088 0.0282544 0.999601i \(-0.491005\pi\)
0.0282544 + 0.999601i \(0.491005\pi\)
\(464\) −6.26260 3.61571i −0.290734 0.167855i
\(465\) 0 0
\(466\) −0.257359 0.445759i −0.0119219 0.0206494i
\(467\) 4.45982 7.72464i 0.206376 0.357454i −0.744194 0.667963i \(-0.767166\pi\)
0.950570 + 0.310510i \(0.100500\pi\)
\(468\) 0 0
\(469\) 0.579747 8.07483i 0.0267702 0.372861i
\(470\) 0.587710i 0.0271090i
\(471\) 0 0
\(472\) −0.760643 + 0.439158i −0.0350114 + 0.0202139i
\(473\) 8.34935 4.82050i 0.383903 0.221647i
\(474\) 0 0
\(475\) 36.2526i 1.66338i
\(476\) 3.89313 1.88985i 0.178441 0.0866211i
\(477\) 0 0
\(478\) 10.9119 18.9000i 0.499098 0.864464i
\(479\) −10.3161 17.8680i −0.471355 0.816411i 0.528108 0.849177i \(-0.322902\pi\)
−0.999463 + 0.0327661i \(0.989568\pi\)
\(480\) 0 0
\(481\) 11.6459 + 6.72376i 0.531007 + 0.306577i
\(482\) −9.18494 −0.418363
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) −0.590109 0.340699i −0.0267954 0.0154704i
\(486\) 0 0
\(487\) −0.0189644 0.0328473i −0.000859360 0.00148845i 0.865595 0.500744i \(-0.166940\pi\)
−0.866455 + 0.499256i \(0.833607\pi\)
\(488\) 4.98382 8.63223i 0.225607 0.390763i
\(489\) 0 0
\(490\) −0.374816 0.295091i −0.0169325 0.0133309i
\(491\) 34.6919i 1.56562i −0.622258 0.782812i \(-0.713785\pi\)
0.622258 0.782812i \(-0.286215\pi\)
\(492\) 0 0
\(493\) −10.2436 + 5.91413i −0.461347 + 0.266359i
\(494\) −15.3950 + 8.88828i −0.692652 + 0.399903i
\(495\) 0 0
\(496\) 0.232673i 0.0104473i
\(497\) −23.5546 + 34.7814i −1.05657 + 1.56016i
\(498\) 0 0
\(499\) 10.2268 17.7133i 0.457814 0.792957i −0.541031 0.841002i \(-0.681966\pi\)
0.998845 + 0.0480457i \(0.0152993\pi\)
\(500\) −0.340583 0.589908i −0.0152314 0.0263815i
\(501\) 0 0
\(502\) 27.1104 + 15.6522i 1.21000 + 0.698592i
\(503\) 31.4660 1.40300 0.701501 0.712669i \(-0.252514\pi\)
0.701501 + 0.712669i \(0.252514\pi\)
\(504\) 0 0
\(505\) 0.239920 0.0106763
\(506\) 0.405083 + 0.233875i 0.0180082 + 0.0103970i
\(507\) 0 0
\(508\) 3.41970 + 5.92309i 0.151724 + 0.262794i
\(509\) 4.97798 8.62211i 0.220645 0.382168i −0.734359 0.678761i \(-0.762517\pi\)
0.955004 + 0.296593i \(0.0958505\pi\)
\(510\) 0 0
\(511\) −20.6203 1.48047i −0.912190 0.0654923i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) −3.48200 + 2.01033i −0.153584 + 0.0886720i
\(515\) −0.943660 + 0.544822i −0.0415826 + 0.0240077i
\(516\) 0 0
\(517\) 8.62398i 0.379282i
\(518\) −14.4877 1.04017i −0.636552 0.0457024i
\(519\) 0 0
\(520\) 0.0834643 0.144564i 0.00366015 0.00633957i
\(521\) 20.4947 + 35.4979i 0.897891 + 1.55519i 0.830186 + 0.557487i \(0.188234\pi\)
0.0677047 + 0.997705i \(0.478432\pi\)
\(522\) 0 0
\(523\) 32.0347 + 18.4952i 1.40078 + 0.808741i 0.994473 0.104996i \(-0.0334829\pi\)
0.406307 + 0.913736i \(0.366816\pi\)
\(524\) −1.51472 −0.0661708
\(525\) 0 0
\(526\) −13.4806 −0.587784
\(527\) −0.329590 0.190289i −0.0143571 0.00828910i
\(528\) 0 0
\(529\) −11.3906 19.7291i −0.495244 0.857787i
\(530\) 0.288905 0.500398i 0.0125492 0.0217359i
\(531\) 0 0
\(532\) 10.7666 15.8983i 0.466791 0.689277i
\(533\) 13.2001i 0.571758i
\(534\) 0 0
\(535\) −0.357916 + 0.206643i −0.0154741 + 0.00893395i
\(536\) −2.64991 + 1.52993i −0.114459 + 0.0660828i
\(537\) 0 0
\(538\) 31.4799i 1.35719i
\(539\) 5.50000 + 4.33013i 0.236902 + 0.186512i
\(540\) 0 0
\(541\) 17.7301 30.7095i 0.762277 1.32030i −0.179397 0.983777i \(-0.557415\pi\)
0.941674 0.336526i \(-0.109252\pi\)
\(542\) −2.82415 4.89157i −0.121308 0.210111i
\(543\) 0 0
\(544\) −1.41654 0.817837i −0.0607335 0.0350645i
\(545\) 1.22786 0.0525960
\(546\) 0 0
\(547\) 33.2066 1.41981 0.709907 0.704296i \(-0.248737\pi\)
0.709907 + 0.704296i \(0.248737\pi\)
\(548\) −4.27427 2.46775i −0.182588 0.105417i
\(549\) 0 0
\(550\) 2.49768 + 4.32611i 0.106501 + 0.184466i
\(551\) −26.2402 + 45.4493i −1.11787 + 1.93620i
\(552\) 0 0
\(553\) −27.4484 + 13.3243i −1.16722 + 0.566607i
\(554\) 6.91964i 0.293987i
\(555\) 0 0
\(556\) −0.957676 + 0.552914i −0.0406145 + 0.0234488i
\(557\) −1.95592 + 1.12925i −0.0828748 + 0.0478478i −0.540865 0.841110i \(-0.681903\pi\)
0.457990 + 0.888957i \(0.348570\pi\)
\(558\) 0 0
\(559\) 23.6155i 0.998830i
\(560\) −0.0129120 + 0.179841i −0.000545631 + 0.00759965i
\(561\) 0 0
\(562\) 15.2291 26.3776i 0.642401 1.11267i
\(563\) −4.02066 6.96399i −0.169451 0.293497i 0.768776 0.639518i \(-0.220866\pi\)
−0.938227 + 0.346021i \(0.887533\pi\)
\(564\) 0 0
\(565\) 0.416386 + 0.240401i 0.0175175 + 0.0101137i
\(566\) −26.3837 −1.10899
\(567\) 0 0
\(568\) 15.8771 0.666187
\(569\) 15.6841 + 9.05521i 0.657511 + 0.379614i 0.791328 0.611392i \(-0.209390\pi\)
−0.133817 + 0.991006i \(0.542723\pi\)
\(570\) 0 0
\(571\) −7.15006 12.3843i −0.299221 0.518266i 0.676737 0.736225i \(-0.263393\pi\)
−0.975958 + 0.217959i \(0.930060\pi\)
\(572\) −1.22474 + 2.12132i −0.0512092 + 0.0886969i
\(573\) 0 0
\(574\) −6.22631 12.8263i −0.259881 0.535361i
\(575\) 2.33658i 0.0974420i
\(576\) 0 0
\(577\) −27.3960 + 15.8171i −1.14051 + 0.658475i −0.946557 0.322536i \(-0.895465\pi\)
−0.193955 + 0.981011i \(0.562131\pi\)
\(578\) 12.4054 7.16228i 0.515998 0.297912i
\(579\) 0 0
\(580\) 0.492810i 0.0204628i
\(581\) 37.5196 + 25.4090i 1.55658 + 1.05414i
\(582\) 0 0
\(583\) −4.23936 + 7.34278i −0.175576 + 0.304107i
\(584\) 3.90691 + 6.76696i 0.161669 + 0.280019i
\(585\) 0 0
\(586\) 12.9986 + 7.50473i 0.536966 + 0.310017i
\(587\) −25.9909 −1.07276 −0.536381 0.843976i \(-0.680209\pi\)
−0.536381 + 0.843976i \(0.680209\pi\)
\(588\) 0 0
\(589\) −1.68857 −0.0695762
\(590\) −0.0518366 0.0299279i −0.00213408 0.00123211i
\(591\) 0 0
\(592\) 2.74496 + 4.75442i 0.112817 + 0.195405i
\(593\) −15.0260 + 26.0258i −0.617043 + 1.06875i 0.372979 + 0.927840i \(0.378336\pi\)
−0.990022 + 0.140911i \(0.954997\pi\)
\(594\) 0 0
\(595\) 0.244191 + 0.165371i 0.0100108 + 0.00677954i
\(596\) 0.318353i 0.0130402i
\(597\) 0 0
\(598\) −0.992248 + 0.572874i −0.0405760 + 0.0234266i
\(599\) 8.18991 4.72844i 0.334631 0.193199i −0.323265 0.946309i \(-0.604780\pi\)
0.657895 + 0.753110i \(0.271447\pi\)
\(600\) 0 0
\(601\) 2.30182i 0.0938931i 0.998897 + 0.0469465i \(0.0149490\pi\)
−0.998897 + 0.0469465i \(0.985051\pi\)
\(602\) −11.1392 22.9469i −0.453998 0.935247i
\(603\) 0 0
\(604\) 1.76941 3.06471i 0.0719962 0.124701i
\(605\) 0.0340742 + 0.0590182i 0.00138531 + 0.00239943i
\(606\) 0 0
\(607\) −3.13710 1.81121i −0.127331 0.0735145i 0.434982 0.900439i \(-0.356755\pi\)
−0.562313 + 0.826925i \(0.690088\pi\)
\(608\) −7.25725 −0.294320
\(609\) 0 0
\(610\) 0.679278 0.0275032
\(611\) −18.2942 10.5622i −0.740105 0.427300i
\(612\) 0 0
\(613\) 4.97209 + 8.61192i 0.200821 + 0.347832i 0.948793 0.315898i \(-0.102306\pi\)
−0.747972 + 0.663730i \(0.768972\pi\)
\(614\) 7.53553 13.0519i 0.304109 0.526733i
\(615\) 0 0
\(616\) 0.189469 2.63896i 0.00763391 0.106327i
\(617\) 5.20936i 0.209721i 0.994487 + 0.104860i \(0.0334396\pi\)
−0.994487 + 0.104860i \(0.966560\pi\)
\(618\) 0 0
\(619\) 10.6324 6.13859i 0.427350 0.246731i −0.270867 0.962617i \(-0.587310\pi\)
0.698217 + 0.715886i \(0.253977\pi\)
\(620\) 0.0137319 0.00792814i 0.000551488 0.000318402i
\(621\) 0 0
\(622\) 19.8729i 0.796831i
\(623\) 25.4110 12.3353i 1.01807 0.494204i
\(624\) 0 0
\(625\) −12.4652 + 21.5903i −0.498607 + 0.863613i
\(626\) −4.51059 7.81257i −0.180279 0.312253i
\(627\) 0 0
\(628\) −5.64589 3.25966i −0.225296 0.130074i
\(629\) 8.97973 0.358045
\(630\) 0 0
\(631\) 1.18708 0.0472568 0.0236284 0.999721i \(-0.492478\pi\)
0.0236284 + 0.999721i \(0.492478\pi\)
\(632\) 9.98722 + 5.76612i 0.397270 + 0.229364i
\(633\) 0 0
\(634\) 5.94427 + 10.2958i 0.236077 + 0.408897i
\(635\) −0.233047 + 0.403649i −0.00924817 + 0.0160183i
\(636\) 0 0
\(637\) −15.9217 + 6.36396i −0.630840 + 0.252149i
\(638\) 7.23143i 0.286295i
\(639\) 0 0
\(640\) 0.0590182 0.0340742i 0.00233290 0.00134690i
\(641\) −32.2791 + 18.6364i −1.27495 + 0.736092i −0.975915 0.218151i \(-0.929997\pi\)
−0.299033 + 0.954243i \(0.596664\pi\)
\(642\) 0 0
\(643\) 2.75684i 0.108719i 0.998521 + 0.0543597i \(0.0173117\pi\)
−0.998521 + 0.0543597i \(0.982688\pi\)
\(644\) 0.693937 1.02469i 0.0273450 0.0403783i
\(645\) 0 0
\(646\) −5.93525 + 10.2802i −0.233519 + 0.404467i
\(647\) −15.2508 26.4151i −0.599570 1.03849i −0.992884 0.119081i \(-0.962005\pi\)
0.393315 0.919404i \(-0.371328\pi\)
\(648\) 0 0
\(649\) 0.760643 + 0.439158i 0.0298579 + 0.0172384i
\(650\) −12.2361 −0.479938
\(651\) 0 0
\(652\) 1.10707 0.0433563
\(653\) 9.77473 + 5.64344i 0.382515 + 0.220845i 0.678912 0.734220i \(-0.262452\pi\)
−0.296397 + 0.955065i \(0.595785\pi\)
\(654\) 0 0
\(655\) −0.0516128 0.0893960i −0.00201668 0.00349299i
\(656\) −2.69445 + 4.66693i −0.105201 + 0.182213i
\(657\) 0 0
\(658\) 22.7583 + 1.63397i 0.887212 + 0.0636990i
\(659\) 10.2338i 0.398652i −0.979933 0.199326i \(-0.936125\pi\)
0.979933 0.199326i \(-0.0638753\pi\)
\(660\) 0 0
\(661\) −19.6739 + 11.3587i −0.765226 + 0.441803i −0.831169 0.556020i \(-0.812328\pi\)
0.0659431 + 0.997823i \(0.478994\pi\)
\(662\) −19.9489 + 11.5175i −0.775338 + 0.447642i
\(663\) 0 0
\(664\) 17.1270i 0.664657i
\(665\) 1.30515 + 0.0937055i 0.0506115 + 0.00363374i
\(666\) 0 0
\(667\) −1.69125 + 2.92933i −0.0654855 + 0.113424i
\(668\) −4.96713 8.60332i −0.192184 0.332872i
\(669\) 0 0
\(670\) −0.180587 0.104262i −0.00697669 0.00402799i
\(671\) −9.96764 −0.384797
\(672\) 0 0
\(673\) −28.2268 −1.08806 −0.544031 0.839065i \(-0.683103\pi\)
−0.544031 + 0.839065i \(0.683103\pi\)
\(674\) −18.0299 10.4096i −0.694486 0.400962i
\(675\) 0 0
\(676\) 3.50000 + 6.06218i 0.134615 + 0.233161i
\(677\) −8.40665 + 14.5607i −0.323094 + 0.559615i −0.981125 0.193376i \(-0.938056\pi\)
0.658031 + 0.752991i \(0.271390\pi\)
\(678\) 0 0
\(679\) 14.8338 21.9040i 0.569269 0.840598i
\(680\) 0.111469i 0.00427462i
\(681\) 0 0
\(682\) −0.201501 + 0.116337i −0.00771586 + 0.00445476i
\(683\) −17.9178 + 10.3448i −0.685604 + 0.395834i −0.801963 0.597374i \(-0.796211\pi\)
0.116359 + 0.993207i \(0.462878\pi\)
\(684\) 0 0
\(685\) 0.336346i 0.0128511i
\(686\) 12.4691 13.6938i 0.476073 0.522834i
\(687\) 0 0
\(688\) −4.82050 + 8.34935i −0.183780 + 0.318316i
\(689\) −10.3843 17.9861i −0.395609 0.685215i
\(690\) 0 0
\(691\) 40.3537 + 23.2982i 1.53513 + 0.886306i 0.999114 + 0.0420972i \(0.0134039\pi\)
0.536014 + 0.844209i \(0.319929\pi\)
\(692\) −13.2221 −0.502630
\(693\) 0 0
\(694\) −7.28329 −0.276470
\(695\) −0.0652640 0.0376802i −0.00247561 0.00142929i
\(696\) 0 0
\(697\) 4.40725 + 7.63358i 0.166936 + 0.289142i
\(698\) −16.8683 + 29.2168i −0.638475 + 1.10587i
\(699\) 0 0
\(700\) 11.8896 5.77161i 0.449386 0.218146i
\(701\) 25.8612i 0.976765i 0.872630 + 0.488382i \(0.162413\pi\)
−0.872630 + 0.488382i \(0.837587\pi\)
\(702\) 0 0
\(703\) 34.5040 19.9209i 1.30134 0.751331i
\(704\) −0.866025 + 0.500000i −0.0326396 + 0.0188445i
\(705\) 0 0
\(706\) 17.4293i 0.655962i
\(707\) −0.667035 + 9.29061i −0.0250864 + 0.349409i
\(708\) 0 0
\(709\) −10.3750 + 17.9700i −0.389641 + 0.674878i −0.992401 0.123044i \(-0.960734\pi\)
0.602760 + 0.797923i \(0.294068\pi\)
\(710\) 0.540998 + 0.937036i 0.0203033 + 0.0351663i
\(711\) 0 0
\(712\) −9.24592 5.33814i −0.346506 0.200055i
\(713\) −0.108833 −0.00407582
\(714\) 0 0
\(715\) −0.166929 −0.00624278
\(716\) 9.79227 + 5.65357i 0.365954 + 0.211284i
\(717\) 0 0
\(718\) 13.0898 + 22.6722i 0.488506 + 0.846118i
\(719\) −12.4722 + 21.6025i −0.465136 + 0.805639i −0.999208 0.0398001i \(-0.987328\pi\)
0.534072 + 0.845439i \(0.320661\pi\)
\(720\) 0 0
\(721\) −18.4740 38.0568i −0.688006 1.41731i
\(722\) 33.6677i 1.25298i
\(723\) 0 0
\(724\) −7.15918 + 4.13335i −0.266069 + 0.153615i
\(725\) −31.2839 + 18.0618i −1.16186 + 0.670798i
\(726\) 0 0
\(727\) 19.4534i 0.721487i −0.932665 0.360743i \(-0.882523\pi\)
0.932665 0.360743i \(-0.117477\pi\)
\(728\) 5.36603 + 3.63397i 0.198878 + 0.134684i
\(729\) 0 0
\(730\) −0.266249 + 0.461157i −0.00985433 + 0.0170682i
\(731\) 7.88477 + 13.6568i 0.291629 + 0.505116i
\(732\) 0 0
\(733\) 2.02326 + 1.16813i 0.0747309 + 0.0431459i 0.536900 0.843646i \(-0.319595\pi\)
−0.462169 + 0.886792i \(0.652929\pi\)
\(734\) 11.4490 0.422589
\(735\) 0 0
\(736\) −0.467750 −0.0172415
\(737\) 2.64991 + 1.52993i 0.0976108 + 0.0563556i
\(738\) 0 0
\(739\) −18.2066 31.5348i −0.669742 1.16003i −0.977976 0.208717i \(-0.933071\pi\)
0.308234 0.951310i \(-0.400262\pi\)
\(740\) −0.187065 + 0.324006i −0.00687663 + 0.0119107i
\(741\) 0 0
\(742\) 18.5741 + 12.5787i 0.681876 + 0.461779i
\(743\) 52.1166i 1.91197i 0.293409 + 0.955987i \(0.405210\pi\)
−0.293409 + 0.955987i \(0.594790\pi\)
\(744\) 0 0
\(745\) −0.0187886 + 0.0108476i −0.000688361 + 0.000397425i
\(746\) 24.4546 14.1189i 0.895347 0.516929i
\(747\) 0 0
\(748\) 1.63567i 0.0598062i
\(749\) −7.00689 14.4344i −0.256026 0.527420i
\(750\) 0 0
\(751\) 4.88661 8.46385i 0.178315 0.308850i −0.762989 0.646412i \(-0.776269\pi\)
0.941303 + 0.337562i \(0.109602\pi\)
\(752\) −4.31199 7.46859i −0.157242 0.272351i
\(753\) 0 0
\(754\) −15.3402 8.85666i −0.558656 0.322540i
\(755\) 0.241165 0.00877688
\(756\) 0 0
\(757\) 27.6251 1.00405 0.502026 0.864852i \(-0.332588\pi\)
0.502026 + 0.864852i \(0.332588\pi\)
\(758\) 8.60440 + 4.96775i 0.312526 + 0.180437i
\(759\) 0 0
\(760\) −0.247285 0.428310i −0.00896997 0.0155364i
\(761\) −10.0318 + 17.3755i −0.363651 + 0.629863i −0.988559 0.150836i \(-0.951803\pi\)
0.624907 + 0.780699i \(0.285137\pi\)
\(762\) 0 0
\(763\) −3.41376 + 47.5475i −0.123586 + 1.72134i
\(764\) 11.9088i 0.430845i
\(765\) 0 0
\(766\) 12.0790 6.97381i 0.436432 0.251974i
\(767\) −1.86319 + 1.07571i −0.0672758 + 0.0388417i
\(768\) 0 0
\(769\) 31.4568i 1.13436i −0.823593 0.567181i \(-0.808034\pi\)
0.823593 0.567181i \(-0.191966\pi\)
\(770\) 0.162203 0.0787382i 0.00584537 0.00283753i
\(771\) 0 0
\(772\) 12.7134 22.0203i 0.457566 0.792528i
\(773\) 3.56548 + 6.17559i 0.128241 + 0.222121i 0.922995 0.384811i \(-0.125733\pi\)
−0.794754 + 0.606932i \(0.792400\pi\)
\(774\) 0 0
\(775\) −1.00657 0.581142i −0.0361570 0.0208752i
\(776\) −9.99876 −0.358934
\(777\) 0 0
\(778\) −1.76832 −0.0633974
\(779\) 33.8691 + 19.5543i 1.21349 + 0.700606i
\(780\) 0 0
\(781\) −7.93854 13.7499i −0.284063 0.492012i
\(782\) −0.382543 + 0.662585i −0.0136797 + 0.0236940i
\(783\) 0 0
\(784\) −6.92820 1.00000i −0.247436 0.0357143i
\(785\) 0.444280i 0.0158570i
\(786\) 0 0
\(787\) 20.7613 11.9865i 0.740061 0.427274i −0.0820306 0.996630i \(-0.526141\pi\)
0.822091 + 0.569356i \(0.192807\pi\)
\(788\) −7.25574 + 4.18910i −0.258475 + 0.149231i