Properties

Label 144.3.m.c.19.8
Level $144$
Weight $3$
Character 144.19
Analytic conductor $3.924$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 144.m (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.92371580679\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 6 x^{14} - 4 x^{13} + 10 x^{12} + 56 x^{11} + 88 x^{10} - 128 x^{9} - 496 x^{8} - 512 x^{7} + 1408 x^{6} + 3584 x^{5} + 2560 x^{4} - 4096 x^{3} - 24576 x^{2} + 65536\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{12} \)
Twist minimal: no (minimal twist has level 48)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 19.8
Root \(1.84258 + 0.777752i\) of defining polynomial
Character \(\chi\) \(=\) 144.19
Dual form 144.3.m.c.91.8

$q$-expansion

\(f(q)\) \(=\) \(q+(1.84258 - 0.777752i) q^{2} +(2.79020 - 2.86614i) q^{4} +(4.78830 - 4.78830i) q^{5} -10.3302 q^{7} +(2.91202 - 7.45118i) q^{8} +O(q^{10})\) \(q+(1.84258 - 0.777752i) q^{2} +(2.79020 - 2.86614i) q^{4} +(4.78830 - 4.78830i) q^{5} -10.3302 q^{7} +(2.91202 - 7.45118i) q^{8} +(5.09872 - 12.5469i) q^{10} +(0.526169 + 0.526169i) q^{11} +(17.2840 + 17.2840i) q^{13} +(-19.0343 + 8.03437i) q^{14} +(-0.429536 - 15.9942i) q^{16} -4.71650 q^{17} +(-2.53604 + 2.53604i) q^{19} +(-0.363618 - 27.0843i) q^{20} +(1.37874 + 0.560279i) q^{22} +12.5864 q^{23} -20.8557i q^{25} +(45.2897 + 18.4044i) q^{26} +(-28.8235 + 29.6080i) q^{28} +(2.19683 + 2.19683i) q^{29} +28.0521i q^{31} +(-13.2310 - 29.1366i) q^{32} +(-8.69052 + 3.66827i) q^{34} +(-49.4644 + 49.4644i) q^{35} +(-32.1128 + 32.1128i) q^{37} +(-2.70044 + 6.64526i) q^{38} +(-21.7349 - 49.6222i) q^{40} +23.1145i q^{41} +(4.79441 + 4.79441i) q^{43} +(2.97619 - 0.0399566i) q^{44} +(23.1915 - 9.78913i) q^{46} +39.0095i q^{47} +57.7141 q^{49} +(-16.2206 - 38.4283i) q^{50} +(97.7640 - 1.31252i) q^{52} +(27.9768 - 27.9768i) q^{53} +5.03891 q^{55} +(-30.0819 + 76.9726i) q^{56} +(5.75642 + 2.33924i) q^{58} +(-79.8538 - 79.8538i) q^{59} +(-36.7762 - 36.7762i) q^{61} +(21.8176 + 51.6883i) q^{62} +(-47.0402 - 43.3960i) q^{64} +165.522 q^{65} +(-10.9869 + 10.9869i) q^{67} +(-13.1600 + 13.5181i) q^{68} +(-52.6711 + 129.613i) q^{70} -52.6605 q^{71} -67.8061i q^{73} +(-34.1946 + 84.1462i) q^{74} +(0.192584 + 14.3447i) q^{76} +(-5.43545 - 5.43545i) q^{77} +56.4602i q^{79} +(-78.6420 - 74.5285i) q^{80} +(17.9773 + 42.5903i) q^{82} +(58.3697 - 58.3697i) q^{83} +(-22.5840 + 22.5840i) q^{85} +(12.5629 + 5.10522i) q^{86} +(5.45279 - 2.38836i) q^{88} -131.566i q^{89} +(-178.548 - 178.548i) q^{91} +(35.1187 - 36.0745i) q^{92} +(30.3397 + 71.8781i) q^{94} +24.2866i q^{95} +60.9413 q^{97} +(106.343 - 44.8872i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 12q^{4} + 12q^{8} + O(q^{10}) \) \( 16q + 12q^{4} + 12q^{8} - 56q^{10} - 32q^{11} + 44q^{14} + 32q^{16} - 32q^{19} - 80q^{20} + 32q^{22} + 128q^{23} + 100q^{26} - 120q^{28} - 32q^{29} - 160q^{32} + 96q^{34} - 96q^{35} - 96q^{37} - 168q^{38} + 48q^{40} + 160q^{43} - 88q^{44} + 136q^{46} + 112q^{49} + 236q^{50} - 48q^{52} + 160q^{53} - 256q^{55} + 224q^{56} + 144q^{58} + 128q^{59} - 32q^{61} + 276q^{62} - 408q^{64} + 32q^{65} + 320q^{67} + 448q^{68} - 384q^{70} - 512q^{71} - 348q^{74} + 72q^{76} - 224q^{77} - 552q^{80} - 40q^{82} + 160q^{83} + 160q^{85} - 528q^{86} + 480q^{88} - 480q^{91} - 496q^{92} + 312q^{94} + 440q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.84258 0.777752i 0.921290 0.388876i
\(3\) 0 0
\(4\) 2.79020 2.86614i 0.697551 0.716535i
\(5\) 4.78830 4.78830i 0.957661 0.957661i −0.0414785 0.999139i \(-0.513207\pi\)
0.999139 + 0.0414785i \(0.0132068\pi\)
\(6\) 0 0
\(7\) −10.3302 −1.47575 −0.737875 0.674937i \(-0.764171\pi\)
−0.737875 + 0.674937i \(0.764171\pi\)
\(8\) 2.91202 7.45118i 0.364003 0.931398i
\(9\) 0 0
\(10\) 5.09872 12.5469i 0.509872 1.25469i
\(11\) 0.526169 + 0.526169i 0.0478335 + 0.0478335i 0.730619 0.682785i \(-0.239232\pi\)
−0.682785 + 0.730619i \(0.739232\pi\)
\(12\) 0 0
\(13\) 17.2840 + 17.2840i 1.32953 + 1.32953i 0.905774 + 0.423761i \(0.139290\pi\)
0.423761 + 0.905774i \(0.360710\pi\)
\(14\) −19.0343 + 8.03437i −1.35959 + 0.573884i
\(15\) 0 0
\(16\) −0.429536 15.9942i −0.0268460 0.999640i
\(17\) −4.71650 −0.277441 −0.138721 0.990332i \(-0.544299\pi\)
−0.138721 + 0.990332i \(0.544299\pi\)
\(18\) 0 0
\(19\) −2.53604 + 2.53604i −0.133476 + 0.133476i −0.770688 0.637213i \(-0.780087\pi\)
0.637213 + 0.770688i \(0.280087\pi\)
\(20\) −0.363618 27.0843i −0.0181809 1.35422i
\(21\) 0 0
\(22\) 1.37874 + 0.560279i 0.0626698 + 0.0254672i
\(23\) 12.5864 0.547236 0.273618 0.961838i \(-0.411780\pi\)
0.273618 + 0.961838i \(0.411780\pi\)
\(24\) 0 0
\(25\) 20.8557i 0.834229i
\(26\) 45.2897 + 18.4044i 1.74191 + 0.707863i
\(27\) 0 0
\(28\) −28.8235 + 29.6080i −1.02941 + 1.05743i
\(29\) 2.19683 + 2.19683i 0.0757526 + 0.0757526i 0.743968 0.668215i \(-0.232942\pi\)
−0.668215 + 0.743968i \(0.732942\pi\)
\(30\) 0 0
\(31\) 28.0521i 0.904908i 0.891788 + 0.452454i \(0.149451\pi\)
−0.891788 + 0.452454i \(0.850549\pi\)
\(32\) −13.2310 29.1366i −0.413469 0.910518i
\(33\) 0 0
\(34\) −8.69052 + 3.66827i −0.255604 + 0.107890i
\(35\) −49.4644 + 49.4644i −1.41327 + 1.41327i
\(36\) 0 0
\(37\) −32.1128 + 32.1128i −0.867914 + 0.867914i −0.992241 0.124327i \(-0.960323\pi\)
0.124327 + 0.992241i \(0.460323\pi\)
\(38\) −2.70044 + 6.64526i −0.0710643 + 0.174875i
\(39\) 0 0
\(40\) −21.7349 49.6222i −0.543372 1.24055i
\(41\) 23.1145i 0.563768i 0.959449 + 0.281884i \(0.0909593\pi\)
−0.959449 + 0.281884i \(0.909041\pi\)
\(42\) 0 0
\(43\) 4.79441 + 4.79441i 0.111498 + 0.111498i 0.760655 0.649157i \(-0.224878\pi\)
−0.649157 + 0.760655i \(0.724878\pi\)
\(44\) 2.97619 0.0399566i 0.0676407 0.000908104i
\(45\) 0 0
\(46\) 23.1915 9.78913i 0.504163 0.212807i
\(47\) 39.0095i 0.829989i 0.909824 + 0.414994i \(0.136216\pi\)
−0.909824 + 0.414994i \(0.863784\pi\)
\(48\) 0 0
\(49\) 57.7141 1.17784
\(50\) −16.2206 38.4283i −0.324412 0.768567i
\(51\) 0 0
\(52\) 97.7640 1.31252i 1.88008 0.0252408i
\(53\) 27.9768 27.9768i 0.527864 0.527864i −0.392071 0.919935i \(-0.628241\pi\)
0.919935 + 0.392071i \(0.128241\pi\)
\(54\) 0 0
\(55\) 5.03891 0.0916166
\(56\) −30.0819 + 76.9726i −0.537177 + 1.37451i
\(57\) 0 0
\(58\) 5.75642 + 2.33924i 0.0992485 + 0.0403318i
\(59\) −79.8538 79.8538i −1.35345 1.35345i −0.881764 0.471691i \(-0.843644\pi\)
−0.471691 0.881764i \(-0.656356\pi\)
\(60\) 0 0
\(61\) −36.7762 36.7762i −0.602888 0.602888i 0.338190 0.941078i \(-0.390185\pi\)
−0.941078 + 0.338190i \(0.890185\pi\)
\(62\) 21.8176 + 51.6883i 0.351897 + 0.833682i
\(63\) 0 0
\(64\) −47.0402 43.3960i −0.735004 0.678063i
\(65\) 165.522 2.54649
\(66\) 0 0
\(67\) −10.9869 + 10.9869i −0.163984 + 0.163984i −0.784329 0.620345i \(-0.786992\pi\)
0.620345 + 0.784329i \(0.286992\pi\)
\(68\) −13.1600 + 13.5181i −0.193529 + 0.198796i
\(69\) 0 0
\(70\) −52.6711 + 129.613i −0.752444 + 1.85162i
\(71\) −52.6605 −0.741697 −0.370849 0.928693i \(-0.620933\pi\)
−0.370849 + 0.928693i \(0.620933\pi\)
\(72\) 0 0
\(73\) 67.8061i 0.928850i −0.885612 0.464425i \(-0.846261\pi\)
0.885612 0.464425i \(-0.153739\pi\)
\(74\) −34.1946 + 84.1462i −0.462089 + 1.13711i
\(75\) 0 0
\(76\) 0.192584 + 14.3447i 0.00253399 + 0.188746i
\(77\) −5.43545 5.43545i −0.0705903 0.0705903i
\(78\) 0 0
\(79\) 56.4602i 0.714686i 0.933973 + 0.357343i \(0.116317\pi\)
−0.933973 + 0.357343i \(0.883683\pi\)
\(80\) −78.6420 74.5285i −0.983025 0.931606i
\(81\) 0 0
\(82\) 17.9773 + 42.5903i 0.219236 + 0.519394i
\(83\) 58.3697 58.3697i 0.703249 0.703249i −0.261857 0.965107i \(-0.584335\pi\)
0.965107 + 0.261857i \(0.0843349\pi\)
\(84\) 0 0
\(85\) −22.5840 + 22.5840i −0.265694 + 0.265694i
\(86\) 12.5629 + 5.10522i 0.146081 + 0.0593630i
\(87\) 0 0
\(88\) 5.45279 2.38836i 0.0619636 0.0271405i
\(89\) 131.566i 1.47827i −0.673558 0.739135i \(-0.735235\pi\)
0.673558 0.739135i \(-0.264765\pi\)
\(90\) 0 0
\(91\) −178.548 178.548i −1.96206 1.96206i
\(92\) 35.1187 36.0745i 0.381725 0.392114i
\(93\) 0 0
\(94\) 30.3397 + 71.8781i 0.322763 + 0.764661i
\(95\) 24.2866i 0.255649i
\(96\) 0 0
\(97\) 60.9413 0.628261 0.314131 0.949380i \(-0.398287\pi\)
0.314131 + 0.949380i \(0.398287\pi\)
\(98\) 106.343 44.8872i 1.08513 0.458033i
\(99\) 0 0
\(100\) −59.7755 58.1917i −0.597755 0.581917i
\(101\) −109.986 + 109.986i −1.08897 + 1.08897i −0.0933326 + 0.995635i \(0.529752\pi\)
−0.995635 + 0.0933326i \(0.970248\pi\)
\(102\) 0 0
\(103\) 173.295 1.68248 0.841239 0.540663i \(-0.181826\pi\)
0.841239 + 0.540663i \(0.181826\pi\)
\(104\) 179.117 78.4546i 1.72228 0.754371i
\(105\) 0 0
\(106\) 29.7905 73.3085i 0.281042 0.691589i
\(107\) 25.4747 + 25.4747i 0.238081 + 0.238081i 0.816055 0.577974i \(-0.196156\pi\)
−0.577974 + 0.816055i \(0.696156\pi\)
\(108\) 0 0
\(109\) 33.0605 + 33.0605i 0.303307 + 0.303307i 0.842306 0.538999i \(-0.181197\pi\)
−0.538999 + 0.842306i \(0.681197\pi\)
\(110\) 9.28460 3.91902i 0.0844054 0.0356275i
\(111\) 0 0
\(112\) 4.43721 + 165.224i 0.0396180 + 1.47522i
\(113\) −140.159 −1.24034 −0.620171 0.784466i \(-0.712937\pi\)
−0.620171 + 0.784466i \(0.712937\pi\)
\(114\) 0 0
\(115\) 60.2677 60.2677i 0.524067 0.524067i
\(116\) 12.4260 0.166824i 0.107121 0.00143814i
\(117\) 0 0
\(118\) −209.244 85.0306i −1.77325 0.720598i
\(119\) 48.7226 0.409434
\(120\) 0 0
\(121\) 120.446i 0.995424i
\(122\) −96.3658 39.1603i −0.789883 0.320986i
\(123\) 0 0
\(124\) 80.4014 + 78.2712i 0.648398 + 0.631219i
\(125\) 19.8441 + 19.8441i 0.158752 + 0.158752i
\(126\) 0 0
\(127\) 40.8458i 0.321620i −0.986985 0.160810i \(-0.948589\pi\)
0.986985 0.160810i \(-0.0514107\pi\)
\(128\) −120.427 43.3750i −0.940834 0.338868i
\(129\) 0 0
\(130\) 304.987 128.735i 2.34605 0.990268i
\(131\) 75.0168 75.0168i 0.572647 0.572647i −0.360220 0.932867i \(-0.617298\pi\)
0.932867 + 0.360220i \(0.117298\pi\)
\(132\) 0 0
\(133\) 26.1979 26.1979i 0.196977 0.196977i
\(134\) −11.6992 + 28.7893i −0.0873071 + 0.214846i
\(135\) 0 0
\(136\) −13.7346 + 35.1435i −0.100989 + 0.258408i
\(137\) 134.028i 0.978308i −0.872197 0.489154i \(-0.837306\pi\)
0.872197 0.489154i \(-0.162694\pi\)
\(138\) 0 0
\(139\) 22.8798 + 22.8798i 0.164603 + 0.164603i 0.784602 0.619999i \(-0.212867\pi\)
−0.619999 + 0.784602i \(0.712867\pi\)
\(140\) 3.75626 + 279.788i 0.0268305 + 1.99848i
\(141\) 0 0
\(142\) −97.0312 + 40.9568i −0.683318 + 0.288428i
\(143\) 18.1885i 0.127193i
\(144\) 0 0
\(145\) 21.0381 0.145091
\(146\) −52.7363 124.938i −0.361208 0.855740i
\(147\) 0 0
\(148\) 2.43861 + 181.641i 0.0164771 + 1.22730i
\(149\) 9.32124 9.32124i 0.0625587 0.0625587i −0.675135 0.737694i \(-0.735915\pi\)
0.737694 + 0.675135i \(0.235915\pi\)
\(150\) 0 0
\(151\) −50.5403 −0.334704 −0.167352 0.985897i \(-0.553522\pi\)
−0.167352 + 0.985897i \(0.553522\pi\)
\(152\) 11.5115 + 26.2815i 0.0757334 + 0.172904i
\(153\) 0 0
\(154\) −14.2427 5.78782i −0.0924850 0.0375833i
\(155\) 134.322 + 134.322i 0.866595 + 0.866595i
\(156\) 0 0
\(157\) −95.8844 95.8844i −0.610729 0.610729i 0.332407 0.943136i \(-0.392139\pi\)
−0.943136 + 0.332407i \(0.892139\pi\)
\(158\) 43.9120 + 104.032i 0.277924 + 0.658433i
\(159\) 0 0
\(160\) −202.869 76.1608i −1.26793 0.476005i
\(161\) −130.021 −0.807584
\(162\) 0 0
\(163\) −140.885 + 140.885i −0.864324 + 0.864324i −0.991837 0.127513i \(-0.959301\pi\)
0.127513 + 0.991837i \(0.459301\pi\)
\(164\) 66.2494 + 64.4941i 0.403959 + 0.393257i
\(165\) 0 0
\(166\) 62.1537 152.948i 0.374420 0.921374i
\(167\) 107.849 0.645800 0.322900 0.946433i \(-0.395342\pi\)
0.322900 + 0.946433i \(0.395342\pi\)
\(168\) 0 0
\(169\) 428.470i 2.53533i
\(170\) −24.0481 + 59.1777i −0.141459 + 0.348104i
\(171\) 0 0
\(172\) 27.1188 0.364082i 0.157668 0.00211675i
\(173\) 53.8845 + 53.8845i 0.311471 + 0.311471i 0.845479 0.534008i \(-0.179315\pi\)
−0.534008 + 0.845479i \(0.679315\pi\)
\(174\) 0 0
\(175\) 215.445i 1.23111i
\(176\) 8.18965 8.64167i 0.0465321 0.0491004i
\(177\) 0 0
\(178\) −102.326 242.421i −0.574864 1.36191i
\(179\) −104.178 + 104.178i −0.582002 + 0.582002i −0.935453 0.353451i \(-0.885008\pi\)
0.353451 + 0.935453i \(0.385008\pi\)
\(180\) 0 0
\(181\) −205.498 + 205.498i −1.13535 + 1.13535i −0.146073 + 0.989274i \(0.546664\pi\)
−0.989274 + 0.146073i \(0.953336\pi\)
\(182\) −467.854 190.122i −2.57063 1.04463i
\(183\) 0 0
\(184\) 36.6520 93.7838i 0.199196 0.509695i
\(185\) 307.532i 1.66233i
\(186\) 0 0
\(187\) −2.48167 2.48167i −0.0132710 0.0132710i
\(188\) 111.807 + 108.844i 0.594716 + 0.578959i
\(189\) 0 0
\(190\) 18.8890 + 44.7501i 0.0994157 + 0.235527i
\(191\) 248.255i 1.29977i −0.760034 0.649883i \(-0.774818\pi\)
0.760034 0.649883i \(-0.225182\pi\)
\(192\) 0 0
\(193\) −129.921 −0.673166 −0.336583 0.941654i \(-0.609271\pi\)
−0.336583 + 0.941654i \(0.609271\pi\)
\(194\) 112.289 47.3973i 0.578811 0.244316i
\(195\) 0 0
\(196\) 161.034 165.417i 0.821602 0.843963i
\(197\) −237.001 + 237.001i −1.20305 + 1.20305i −0.229816 + 0.973234i \(0.573812\pi\)
−0.973234 + 0.229816i \(0.926188\pi\)
\(198\) 0 0
\(199\) 246.508 1.23873 0.619366 0.785102i \(-0.287390\pi\)
0.619366 + 0.785102i \(0.287390\pi\)
\(200\) −155.400 60.7324i −0.776999 0.303662i
\(201\) 0 0
\(202\) −117.116 + 288.199i −0.579781 + 1.42673i
\(203\) −22.6938 22.6938i −0.111792 0.111792i
\(204\) 0 0
\(205\) 110.679 + 110.679i 0.539898 + 0.539898i
\(206\) 319.311 134.781i 1.55005 0.654276i
\(207\) 0 0
\(208\) 269.020 283.868i 1.29336 1.36475i
\(209\) −2.66877 −0.0127692
\(210\) 0 0
\(211\) −13.4139 + 13.4139i −0.0635728 + 0.0635728i −0.738178 0.674606i \(-0.764314\pi\)
0.674606 + 0.738178i \(0.264314\pi\)
\(212\) −2.12452 158.246i −0.0100213 0.746445i
\(213\) 0 0
\(214\) 66.7522 + 27.1262i 0.311926 + 0.126758i
\(215\) 45.9142 0.213554
\(216\) 0 0
\(217\) 289.786i 1.33542i
\(218\) 86.6295 + 35.2037i 0.397383 + 0.161485i
\(219\) 0 0
\(220\) 14.0596 14.4422i 0.0639072 0.0656465i
\(221\) −81.5197 81.5197i −0.368867 0.368867i
\(222\) 0 0
\(223\) 295.580i 1.32547i −0.748854 0.662735i \(-0.769396\pi\)
0.748854 0.662735i \(-0.230604\pi\)
\(224\) 136.680 + 300.988i 0.610177 + 1.34370i
\(225\) 0 0
\(226\) −258.254 + 109.009i −1.14272 + 0.482340i
\(227\) 97.0742 97.0742i 0.427640 0.427640i −0.460184 0.887824i \(-0.652217\pi\)
0.887824 + 0.460184i \(0.152217\pi\)
\(228\) 0 0
\(229\) 34.2565 34.2565i 0.149592 0.149592i −0.628344 0.777936i \(-0.716267\pi\)
0.777936 + 0.628344i \(0.216267\pi\)
\(230\) 64.1747 157.921i 0.279021 0.686615i
\(231\) 0 0
\(232\) 22.7662 9.97174i 0.0981300 0.0429816i
\(233\) 62.8176i 0.269604i 0.990873 + 0.134802i \(0.0430398\pi\)
−0.990873 + 0.134802i \(0.956960\pi\)
\(234\) 0 0
\(235\) 186.789 + 186.789i 0.794848 + 0.794848i
\(236\) −451.681 + 6.06400i −1.91390 + 0.0256949i
\(237\) 0 0
\(238\) 89.7753 37.8941i 0.377207 0.159219i
\(239\) 355.910i 1.48916i 0.667532 + 0.744581i \(0.267351\pi\)
−0.667532 + 0.744581i \(0.732649\pi\)
\(240\) 0 0
\(241\) 66.2545 0.274915 0.137458 0.990508i \(-0.456107\pi\)
0.137458 + 0.990508i \(0.456107\pi\)
\(242\) −93.6774 221.932i −0.387097 0.917074i
\(243\) 0 0
\(244\) −208.019 + 2.79274i −0.852535 + 0.0114456i
\(245\) 276.352 276.352i 1.12797 1.12797i
\(246\) 0 0
\(247\) −87.6655 −0.354921
\(248\) 209.022 + 81.6885i 0.842829 + 0.329389i
\(249\) 0 0
\(250\) 51.9980 + 21.1305i 0.207992 + 0.0845220i
\(251\) −325.395 325.395i −1.29640 1.29640i −0.930757 0.365638i \(-0.880851\pi\)
−0.365638 0.930757i \(-0.619149\pi\)
\(252\) 0 0
\(253\) 6.62259 + 6.62259i 0.0261762 + 0.0261762i
\(254\) −31.7679 75.2616i −0.125070 0.296306i
\(255\) 0 0
\(256\) −255.631 + 13.7402i −0.998559 + 0.0536726i
\(257\) 312.011 1.21405 0.607026 0.794682i \(-0.292362\pi\)
0.607026 + 0.794682i \(0.292362\pi\)
\(258\) 0 0
\(259\) 331.733 331.733i 1.28082 1.28082i
\(260\) 461.839 474.409i 1.77630 1.82465i
\(261\) 0 0
\(262\) 79.8800 196.569i 0.304885 0.750263i
\(263\) 168.163 0.639403 0.319702 0.947518i \(-0.396417\pi\)
0.319702 + 0.947518i \(0.396417\pi\)
\(264\) 0 0
\(265\) 267.923i 1.01103i
\(266\) 27.8962 68.6472i 0.104873 0.258072i
\(267\) 0 0
\(268\) 0.834331 + 62.1457i 0.00311318 + 0.231887i
\(269\) −212.116 212.116i −0.788535 0.788535i 0.192719 0.981254i \(-0.438269\pi\)
−0.981254 + 0.192719i \(0.938269\pi\)
\(270\) 0 0
\(271\) 173.450i 0.640037i 0.947411 + 0.320019i \(0.103689\pi\)
−0.947411 + 0.320019i \(0.896311\pi\)
\(272\) 2.02590 + 75.4368i 0.00744818 + 0.277341i
\(273\) 0 0
\(274\) −104.241 246.958i −0.380441 0.901305i
\(275\) 10.9736 10.9736i 0.0399041 0.0399041i
\(276\) 0 0
\(277\) −38.4049 + 38.4049i −0.138646 + 0.138646i −0.773023 0.634377i \(-0.781257\pi\)
0.634377 + 0.773023i \(0.281257\pi\)
\(278\) 59.9526 + 24.3630i 0.215657 + 0.0876368i
\(279\) 0 0
\(280\) 224.527 + 512.610i 0.801881 + 1.83075i
\(281\) 223.573i 0.795632i 0.917465 + 0.397816i \(0.130232\pi\)
−0.917465 + 0.397816i \(0.869768\pi\)
\(282\) 0 0
\(283\) 247.755 + 247.755i 0.875459 + 0.875459i 0.993061 0.117602i \(-0.0375206\pi\)
−0.117602 + 0.993061i \(0.537521\pi\)
\(284\) −146.933 + 150.932i −0.517371 + 0.531452i
\(285\) 0 0
\(286\) 14.1462 + 33.5139i 0.0494622 + 0.117181i
\(287\) 238.778i 0.831980i
\(288\) 0 0
\(289\) −266.755 −0.923026
\(290\) 38.7645 16.3625i 0.133671 0.0564223i
\(291\) 0 0
\(292\) −194.342 189.193i −0.665554 0.647920i
\(293\) 102.262 102.262i 0.349016 0.349016i −0.510727 0.859743i \(-0.670624\pi\)
0.859743 + 0.510727i \(0.170624\pi\)
\(294\) 0 0
\(295\) −764.729 −2.59230
\(296\) 145.765 + 332.792i 0.492450 + 1.12430i
\(297\) 0 0
\(298\) 9.92552 24.4247i 0.0333071 0.0819622i
\(299\) 217.543 + 217.543i 0.727570 + 0.727570i
\(300\) 0 0
\(301\) −49.5275 49.5275i −0.164543 0.164543i
\(302\) −93.1246 + 39.3079i −0.308360 + 0.130158i
\(303\) 0 0
\(304\) 41.6513 + 39.4726i 0.137011 + 0.129844i
\(305\) −352.191 −1.15472
\(306\) 0 0
\(307\) 138.292 138.292i 0.450463 0.450463i −0.445045 0.895508i \(-0.646812\pi\)
0.895508 + 0.445045i \(0.146812\pi\)
\(308\) −30.7448 + 0.412762i −0.0998208 + 0.00134014i
\(309\) 0 0
\(310\) 351.969 + 143.030i 1.13538 + 0.461387i
\(311\) −205.789 −0.661702 −0.330851 0.943683i \(-0.607336\pi\)
−0.330851 + 0.943683i \(0.607336\pi\)
\(312\) 0 0
\(313\) 223.861i 0.715209i 0.933873 + 0.357605i \(0.116406\pi\)
−0.933873 + 0.357605i \(0.883594\pi\)
\(314\) −251.249 102.100i −0.800156 0.325161i
\(315\) 0 0
\(316\) 161.823 + 157.535i 0.512098 + 0.498530i
\(317\) 176.488 + 176.488i 0.556744 + 0.556744i 0.928379 0.371635i \(-0.121203\pi\)
−0.371635 + 0.928379i \(0.621203\pi\)
\(318\) 0 0
\(319\) 2.31180i 0.00724703i
\(320\) −433.036 + 17.4495i −1.35324 + 0.0545296i
\(321\) 0 0
\(322\) −239.574 + 101.124i −0.744019 + 0.314050i
\(323\) 11.9612 11.9612i 0.0370316 0.0370316i
\(324\) 0 0
\(325\) 360.469 360.469i 1.10914 1.10914i
\(326\) −150.018 + 369.165i −0.460178 + 1.13241i
\(327\) 0 0
\(328\) 172.230 + 67.3099i 0.525092 + 0.205213i
\(329\) 402.978i 1.22486i
\(330\) 0 0
\(331\) −183.939 183.939i −0.555706 0.555706i 0.372376 0.928082i \(-0.378543\pi\)
−0.928082 + 0.372376i \(0.878543\pi\)
\(332\) −4.43252 330.159i −0.0133510 0.994455i
\(333\) 0 0
\(334\) 198.720 83.8795i 0.594969 0.251136i
\(335\) 105.217i 0.314081i
\(336\) 0 0
\(337\) 12.7162 0.0377336 0.0188668 0.999822i \(-0.493994\pi\)
0.0188668 + 0.999822i \(0.493994\pi\)
\(338\) 333.244 + 789.490i 0.985928 + 2.33577i
\(339\) 0 0
\(340\) 1.71500 + 127.743i 0.00504413 + 0.375715i
\(341\) −14.7602 + 14.7602i −0.0432849 + 0.0432849i
\(342\) 0 0
\(343\) −90.0184 −0.262444
\(344\) 49.6855 21.7626i 0.144435 0.0632633i
\(345\) 0 0
\(346\) 141.195 + 57.3777i 0.408079 + 0.165831i
\(347\) 113.546 + 113.546i 0.327221 + 0.327221i 0.851529 0.524308i \(-0.175676\pi\)
−0.524308 + 0.851529i \(0.675676\pi\)
\(348\) 0 0
\(349\) 90.9653 + 90.9653i 0.260645 + 0.260645i 0.825316 0.564671i \(-0.190997\pi\)
−0.564671 + 0.825316i \(0.690997\pi\)
\(350\) 167.563 + 396.974i 0.478751 + 1.13421i
\(351\) 0 0
\(352\) 8.36902 22.2925i 0.0237756 0.0633309i
\(353\) −36.2208 −0.102609 −0.0513043 0.998683i \(-0.516338\pi\)
−0.0513043 + 0.998683i \(0.516338\pi\)
\(354\) 0 0
\(355\) −252.155 + 252.155i −0.710294 + 0.710294i
\(356\) −377.087 367.096i −1.05923 1.03117i
\(357\) 0 0
\(358\) −110.932 + 272.982i −0.309866 + 0.762520i
\(359\) −142.121 −0.395880 −0.197940 0.980214i \(-0.563425\pi\)
−0.197940 + 0.980214i \(0.563425\pi\)
\(360\) 0 0
\(361\) 348.137i 0.964369i
\(362\) −218.820 + 538.473i −0.604475 + 1.48749i
\(363\) 0 0
\(364\) −1009.93 + 13.5587i −2.77452 + 0.0372491i
\(365\) −324.676 324.676i −0.889523 0.889523i
\(366\) 0 0
\(367\) 654.218i 1.78261i −0.453404 0.891305i \(-0.649791\pi\)
0.453404 0.891305i \(-0.350209\pi\)
\(368\) −5.40633 201.310i −0.0146911 0.547039i
\(369\) 0 0
\(370\) 239.184 + 566.652i 0.646442 + 1.53149i
\(371\) −289.007 + 289.007i −0.778995 + 0.778995i
\(372\) 0 0
\(373\) 335.277 335.277i 0.898867 0.898867i −0.0964690 0.995336i \(-0.530755\pi\)
0.995336 + 0.0964690i \(0.0307549\pi\)
\(374\) −6.50281 2.64255i −0.0173872 0.00706565i
\(375\) 0 0
\(376\) 290.667 + 113.597i 0.773050 + 0.302118i
\(377\) 75.9397i 0.201432i
\(378\) 0 0
\(379\) −98.7497 98.7497i −0.260553 0.260553i 0.564725 0.825279i \(-0.308982\pi\)
−0.825279 + 0.564725i \(0.808982\pi\)
\(380\) 69.6089 + 67.7646i 0.183181 + 0.178328i
\(381\) 0 0
\(382\) −193.081 457.430i −0.505448 1.19746i
\(383\) 156.144i 0.407687i −0.979003 0.203844i \(-0.934657\pi\)
0.979003 0.203844i \(-0.0653434\pi\)
\(384\) 0 0
\(385\) −52.0532 −0.135203
\(386\) −239.390 + 101.046i −0.620181 + 0.261778i
\(387\) 0 0
\(388\) 170.039 174.667i 0.438244 0.450171i
\(389\) 391.047 391.047i 1.00526 1.00526i 0.00527486 0.999986i \(-0.498321\pi\)
0.999986 0.00527486i \(-0.00167905\pi\)
\(390\) 0 0
\(391\) −59.3639 −0.151826
\(392\) 168.065 430.038i 0.428737 1.09704i
\(393\) 0 0
\(394\) −252.365 + 621.021i −0.640520 + 1.57620i
\(395\) 270.349 + 270.349i 0.684427 + 0.684427i
\(396\) 0 0
\(397\) 243.862 + 243.862i 0.614262 + 0.614262i 0.944054 0.329791i \(-0.106978\pi\)
−0.329791 + 0.944054i \(0.606978\pi\)
\(398\) 454.210 191.722i 1.14123 0.481713i
\(399\) 0 0
\(400\) −333.571 + 8.95828i −0.833928 + 0.0223957i
\(401\) 175.261 0.437059 0.218529 0.975830i \(-0.429874\pi\)
0.218529 + 0.975830i \(0.429874\pi\)
\(402\) 0 0
\(403\) −484.852 + 484.852i −1.20311 + 1.20311i
\(404\) 8.35218 + 622.117i 0.0206737 + 1.53989i
\(405\) 0 0
\(406\) −59.4652 24.1650i −0.146466 0.0595196i
\(407\) −33.7935 −0.0830307
\(408\) 0 0
\(409\) 44.4504i 0.108681i −0.998522 0.0543404i \(-0.982694\pi\)
0.998522 0.0543404i \(-0.0173056\pi\)
\(410\) 290.016 + 117.854i 0.707356 + 0.287449i
\(411\) 0 0
\(412\) 483.529 496.689i 1.17361 1.20556i
\(413\) 824.910 + 824.910i 1.99736 + 1.99736i
\(414\) 0 0
\(415\) 558.984i 1.34695i
\(416\) 274.911 732.279i 0.660844 1.76029i
\(417\) 0 0
\(418\) −4.91741 + 2.07564i −0.0117641 + 0.00496564i
\(419\) −14.9985 + 14.9985i −0.0357959 + 0.0357959i −0.724778 0.688982i \(-0.758058\pi\)
0.688982 + 0.724778i \(0.258058\pi\)
\(420\) 0 0
\(421\) 312.907 312.907i 0.743247 0.743247i −0.229954 0.973201i \(-0.573858\pi\)
0.973201 + 0.229954i \(0.0738576\pi\)
\(422\) −14.2834 + 35.1488i −0.0338470 + 0.0832909i
\(423\) 0 0
\(424\) −126.991 289.929i −0.299507 0.683795i
\(425\) 98.3660i 0.231449i
\(426\) 0 0
\(427\) 379.907 + 379.907i 0.889712 + 0.889712i
\(428\) 144.094 1.93452i 0.336667 0.00451990i
\(429\) 0 0
\(430\) 84.6006 35.7099i 0.196746 0.0830462i
\(431\) 532.400i 1.23527i −0.786466 0.617633i \(-0.788092\pi\)
0.786466 0.617633i \(-0.211908\pi\)
\(432\) 0 0
\(433\) 553.451 1.27818 0.639089 0.769133i \(-0.279312\pi\)
0.639089 + 0.769133i \(0.279312\pi\)
\(434\) −225.381 533.953i −0.519312 1.23031i
\(435\) 0 0
\(436\) 187.001 2.51057i 0.428903 0.00575819i
\(437\) −31.9197 + 31.9197i −0.0730427 + 0.0730427i
\(438\) 0 0
\(439\) 645.291 1.46991 0.734956 0.678115i \(-0.237203\pi\)
0.734956 + 0.678115i \(0.237203\pi\)
\(440\) 14.6734 37.5458i 0.0333487 0.0853315i
\(441\) 0 0
\(442\) −213.609 86.8045i −0.483278 0.196390i
\(443\) −315.833 315.833i −0.712941 0.712941i 0.254208 0.967149i \(-0.418185\pi\)
−0.967149 + 0.254208i \(0.918185\pi\)
\(444\) 0 0
\(445\) −629.978 629.978i −1.41568 1.41568i
\(446\) −229.888 544.630i −0.515444 1.22114i
\(447\) 0 0
\(448\) 485.937 + 448.292i 1.08468 + 1.00065i
\(449\) −218.589 −0.486835 −0.243417 0.969922i \(-0.578268\pi\)
−0.243417 + 0.969922i \(0.578268\pi\)
\(450\) 0 0
\(451\) −12.1621 + 12.1621i −0.0269670 + 0.0269670i
\(452\) −391.071 + 401.715i −0.865202 + 0.888749i
\(453\) 0 0
\(454\) 103.367 254.367i 0.227681 0.560279i
\(455\) −1709.88 −3.75798
\(456\) 0 0
\(457\) 296.561i 0.648930i 0.945898 + 0.324465i \(0.105184\pi\)
−0.945898 + 0.324465i \(0.894816\pi\)
\(458\) 36.4773 89.7634i 0.0796447 0.195990i
\(459\) 0 0
\(460\) −4.57665 340.895i −0.00994925 0.741076i
\(461\) −118.061 118.061i −0.256097 0.256097i 0.567368 0.823465i \(-0.307962\pi\)
−0.823465 + 0.567368i \(0.807962\pi\)
\(462\) 0 0
\(463\) 409.453i 0.884348i 0.896929 + 0.442174i \(0.145793\pi\)
−0.896929 + 0.442174i \(0.854207\pi\)
\(464\) 34.1929 36.0802i 0.0736917 0.0777590i
\(465\) 0 0
\(466\) 48.8565 + 115.747i 0.104842 + 0.248383i
\(467\) −494.764 + 494.764i −1.05945 + 1.05945i −0.0613343 + 0.998117i \(0.519536\pi\)
−0.998117 + 0.0613343i \(0.980464\pi\)
\(468\) 0 0
\(469\) 113.497 113.497i 0.241999 0.241999i
\(470\) 489.450 + 198.898i 1.04138 + 0.423188i
\(471\) 0 0
\(472\) −827.542 + 362.469i −1.75327 + 0.767943i
\(473\) 5.04534i 0.0106667i
\(474\) 0 0
\(475\) 52.8909 + 52.8909i 0.111349 + 0.111349i
\(476\) 135.946 139.646i 0.285601 0.293374i
\(477\) 0 0
\(478\) 276.810 + 655.792i 0.579100 + 1.37195i
\(479\) 558.806i 1.16661i 0.812254 + 0.583305i \(0.198241\pi\)
−0.812254 + 0.583305i \(0.801759\pi\)
\(480\) 0 0
\(481\) −1110.07 −2.30784
\(482\) 122.079 51.5296i 0.253277 0.106908i
\(483\) 0 0
\(484\) −345.216 336.070i −0.713256 0.694359i
\(485\) 291.806 291.806i 0.601661 0.601661i
\(486\) 0 0
\(487\) −361.328 −0.741946 −0.370973 0.928644i \(-0.620976\pi\)
−0.370973 + 0.928644i \(0.620976\pi\)
\(488\) −381.119 + 166.933i −0.780981 + 0.342075i
\(489\) 0 0
\(490\) 294.268 724.135i 0.600547 1.47783i
\(491\) 488.975 + 488.975i 0.995876 + 0.995876i 0.999992 0.00411514i \(-0.00130989\pi\)
−0.00411514 + 0.999992i \(0.501310\pi\)
\(492\) 0 0
\(493\) −10.3613 10.3613i −0.0210169 0.0210169i
\(494\) −161.531 + 68.1820i −0.326985 + 0.138020i
\(495\) 0 0
\(496\) 448.672 12.0494i 0.904582 0.0242931i
\(497\) 543.996 1.09456
\(498\) 0 0
\(499\) −102.895 + 102.895i −0.206203 + 0.206203i −0.802652 0.596448i \(-0.796578\pi\)
0.596448 + 0.802652i \(0.296578\pi\)
\(500\) 112.245 1.50693i 0.224490 0.00301387i
\(501\) 0 0
\(502\) −852.643 346.490i −1.69849 0.690219i
\(503\) 881.975 1.75343 0.876715 0.481011i \(-0.159730\pi\)
0.876715 + 0.481011i \(0.159730\pi\)
\(504\) 0 0
\(505\) 1053.29i 2.08572i
\(506\) 17.3534 + 7.05192i 0.0342952 + 0.0139366i
\(507\) 0 0
\(508\) −117.070 113.968i −0.230452 0.224346i
\(509\) −161.639 161.639i −0.317563 0.317563i 0.530268 0.847830i \(-0.322091\pi\)
−0.847830 + 0.530268i \(0.822091\pi\)
\(510\) 0 0
\(511\) 700.454i 1.37075i
\(512\) −460.334 + 224.135i −0.899090 + 0.437764i
\(513\) 0 0
\(514\) 574.906 242.668i 1.11849 0.472116i
\(515\) 829.791 829.791i 1.61124 1.61124i
\(516\) 0 0
\(517\) −20.5256 + 20.5256i −0.0397013 + 0.0397013i
\(518\) 353.239 869.252i 0.681928 1.67809i
\(519\) 0 0
\(520\) 482.003 1233.33i 0.926929 2.37179i
\(521\) 763.931i 1.46628i −0.680078 0.733140i \(-0.738054\pi\)
0.680078 0.733140i \(-0.261946\pi\)
\(522\) 0 0
\(523\) 295.573 + 295.573i 0.565150 + 0.565150i 0.930766 0.365616i \(-0.119142\pi\)
−0.365616 + 0.930766i \(0.619142\pi\)
\(524\) −5.69668 424.321i −0.0108715 0.809773i
\(525\) 0 0
\(526\) 309.854 130.789i 0.589076 0.248649i
\(527\) 132.308i 0.251059i
\(528\) 0 0
\(529\) −370.582 −0.700532
\(530\) −208.377 493.669i −0.393165 0.931451i
\(531\) 0 0
\(532\) −1.98944 148.184i −0.00373954 0.278542i
\(533\) −399.509 + 399.509i −0.749549 + 0.749549i
\(534\) 0 0
\(535\) 243.961 0.456002
\(536\) 49.8713 + 113.859i 0.0930434 + 0.212424i
\(537\) 0 0
\(538\) −555.814 225.867i −1.03311 0.419827i
\(539\) 30.3673 + 30.3673i 0.0563401 + 0.0563401i
\(540\) 0 0
\(541\) 243.037 + 243.037i 0.449236 + 0.449236i 0.895100 0.445865i \(-0.147104\pi\)
−0.445865 + 0.895100i \(0.647104\pi\)
\(542\) 134.901 + 319.596i 0.248895 + 0.589660i
\(543\) 0 0
\(544\) 62.4040 + 137.423i 0.114713 + 0.252615i
\(545\) 316.607 0.580931
\(546\) 0 0
\(547\) 424.574 424.574i 0.776187 0.776187i −0.202993 0.979180i \(-0.565067\pi\)
0.979180 + 0.202993i \(0.0650669\pi\)
\(548\) −384.144 373.966i −0.700992 0.682419i
\(549\) 0 0
\(550\) 11.6850 28.7545i 0.0212455 0.0522810i
\(551\) −11.1425 −0.0202223
\(552\) 0 0
\(553\) 583.248i 1.05470i
\(554\) −40.8946 + 100.634i −0.0738171 + 0.181649i
\(555\) 0 0
\(556\) 129.416 1.73746i 0.232763 0.00312493i
\(557\) 445.773 + 445.773i 0.800311 + 0.800311i 0.983144 0.182833i \(-0.0585268\pi\)
−0.182833 + 0.983144i \(0.558527\pi\)
\(558\) 0 0
\(559\) 165.733i 0.296481i
\(560\) 812.392 + 769.898i 1.45070 + 1.37482i
\(561\) 0 0
\(562\) 173.884 + 411.951i 0.309402 + 0.733008i
\(563\) 529.295 529.295i 0.940133 0.940133i −0.0581732 0.998307i \(-0.518528\pi\)
0.998307 + 0.0581732i \(0.0185276\pi\)
\(564\) 0 0
\(565\) −671.123 + 671.123i −1.18783 + 1.18783i
\(566\) 649.200 + 263.816i 1.14700 + 0.466107i
\(567\) 0 0
\(568\) −153.349 + 392.383i −0.269980 + 0.690815i
\(569\) 346.814i 0.609516i 0.952430 + 0.304758i \(0.0985755\pi\)
−0.952430 + 0.304758i \(0.901424\pi\)
\(570\) 0 0
\(571\) −155.711 155.711i −0.272699 0.272699i 0.557487 0.830186i \(-0.311766\pi\)
−0.830186 + 0.557487i \(0.811766\pi\)
\(572\) 52.1309 + 50.7497i 0.0911380 + 0.0887233i
\(573\) 0 0
\(574\) −185.710 439.968i −0.323537 0.766495i
\(575\) 262.499i 0.456520i
\(576\) 0 0
\(577\) 620.510 1.07541 0.537704 0.843134i \(-0.319292\pi\)
0.537704 + 0.843134i \(0.319292\pi\)
\(578\) −491.517 + 207.469i −0.850375 + 0.358943i
\(579\) 0 0
\(580\) 58.7007 60.2983i 0.101208 0.103963i
\(581\) −602.974 + 602.974i −1.03782 + 1.03782i
\(582\) 0 0
\(583\) 29.4410 0.0504992
\(584\) −505.235 197.453i −0.865129 0.338104i
\(585\) 0 0
\(586\) 108.891 267.960i 0.185821 0.457269i
\(587\) −561.656 561.656i −0.956825 0.956825i 0.0422810 0.999106i \(-0.486538\pi\)
−0.999106 + 0.0422810i \(0.986538\pi\)
\(588\) 0 0
\(589\) −71.1413 71.1413i −0.120783 0.120783i
\(590\) −1409.07 + 594.770i −2.38826 + 1.00808i
\(591\) 0 0
\(592\) 527.413 + 499.826i 0.890901 + 0.844301i
\(593\) −851.739 −1.43632 −0.718161 0.695877i \(-0.755016\pi\)
−0.718161 + 0.695877i \(0.755016\pi\)
\(594\) 0 0
\(595\) 233.299 233.299i 0.392099 0.392099i
\(596\) −0.707843 52.7241i −0.00118766 0.0884633i
\(597\) 0 0
\(598\) 570.036 + 231.646i 0.953237 + 0.387368i
\(599\) 1001.69 1.67228 0.836138 0.548519i \(-0.184808\pi\)
0.836138 + 0.548519i \(0.184808\pi\)
\(600\) 0 0
\(601\) 955.182i 1.58932i −0.607054 0.794661i \(-0.707649\pi\)
0.607054 0.794661i \(-0.292351\pi\)
\(602\) −129.778 52.7382i −0.215579 0.0876050i
\(603\) 0 0
\(604\) −141.018 + 144.856i −0.233473 + 0.239827i
\(605\) −576.734 576.734i −0.953279 0.953279i
\(606\) 0 0
\(607\) 291.885i 0.480865i 0.970666 + 0.240432i \(0.0772892\pi\)
−0.970666 + 0.240432i \(0.922711\pi\)
\(608\) 107.446 + 40.3371i 0.176720 + 0.0663440i
\(609\) 0 0
\(610\) −648.940 + 273.917i −1.06384 + 0.449045i
\(611\) −674.238 + 674.238i −1.10350 + 1.10350i
\(612\) 0 0
\(613\) −332.933 + 332.933i −0.543121 + 0.543121i −0.924442 0.381322i \(-0.875469\pi\)
0.381322 + 0.924442i \(0.375469\pi\)
\(614\) 147.257 362.371i 0.239833 0.590181i
\(615\) 0 0
\(616\) −56.3287 + 24.6724i −0.0914427 + 0.0400526i
\(617\) 970.864i 1.57352i 0.617257 + 0.786762i \(0.288244\pi\)
−0.617257 + 0.786762i \(0.711756\pi\)
\(618\) 0 0
\(619\) −696.761 696.761i −1.12562 1.12562i −0.990881 0.134744i \(-0.956979\pi\)
−0.134744 0.990881i \(-0.543021\pi\)
\(620\) 759.773 10.2003i 1.22544 0.0164520i
\(621\) 0 0
\(622\) −379.183 + 160.053i −0.609619 + 0.257320i
\(623\) 1359.11i 2.18156i
\(624\) 0 0
\(625\) 711.432 1.13829
\(626\) 174.108 + 412.481i 0.278128 + 0.658915i
\(627\) 0 0
\(628\) −542.355 + 7.28135i −0.863623 + 0.0115945i
\(629\) 151.460 151.460i 0.240795 0.240795i
\(630\) 0 0
\(631\) −377.591 −0.598401 −0.299200 0.954190i \(-0.596720\pi\)
−0.299200 + 0.954190i \(0.596720\pi\)
\(632\) 420.695 + 164.413i 0.665657 + 0.260148i
\(633\) 0 0
\(634\) 462.457 + 187.929i 0.729427 + 0.296418i
\(635\) −195.582 195.582i −0.308003 0.308003i
\(636\) 0 0
\(637\) 997.527 + 997.527i 1.56598 + 1.56598i
\(638\) 1.79801 + 4.25968i 0.00281820 + 0.00667661i
\(639\) 0 0
\(640\) −784.333 + 368.947i −1.22552 + 0.576480i
\(641\) −729.200 −1.13760 −0.568799 0.822477i \(-0.692592\pi\)
−0.568799 + 0.822477i \(0.692592\pi\)
\(642\) 0 0
\(643\) 243.958 243.958i 0.379406 0.379406i −0.491482 0.870888i \(-0.663545\pi\)
0.870888 + 0.491482i \(0.163545\pi\)
\(644\) −362.785 + 372.659i −0.563331 + 0.578663i
\(645\) 0 0
\(646\) 12.7366 31.3423i 0.0197161 0.0485176i
\(647\) 281.594 0.435230 0.217615 0.976035i \(-0.430172\pi\)
0.217615 + 0.976035i \(0.430172\pi\)
\(648\) 0 0
\(649\) 84.0331i 0.129481i
\(650\) 383.838 944.549i 0.590520 1.45315i
\(651\) 0 0
\(652\) 10.6986 + 796.893i 0.0164089 + 1.22223i
\(653\) −323.704 323.704i −0.495718 0.495718i 0.414384 0.910102i \(-0.363997\pi\)
−0.910102 + 0.414384i \(0.863997\pi\)
\(654\) 0 0
\(655\) 718.407i 1.09680i
\(656\) 369.698 9.92850i 0.563564 0.0151349i
\(657\) 0 0
\(658\) −313.417 742.519i −0.476317 1.12845i
\(659\) −507.811 + 507.811i −0.770578 + 0.770578i −0.978208 0.207629i \(-0.933425\pi\)
0.207629 + 0.978208i \(0.433425\pi\)
\(660\) 0 0
\(661\) 57.1593 57.1593i 0.0864741 0.0864741i −0.662547 0.749021i \(-0.730524\pi\)
0.749021 + 0.662547i \(0.230524\pi\)
\(662\) −481.981 195.863i −0.728068 0.295866i
\(663\) 0 0
\(664\) −264.949 604.897i −0.399020 0.910990i
\(665\) 250.887i 0.377274i
\(666\) 0 0
\(667\) 27.6502 + 27.6502i 0.0414546 + 0.0414546i
\(668\) 300.919 309.109i 0.450478 0.462739i
\(669\) 0 0
\(670\) 81.8329 + 193.871i 0.122139 + 0.289360i
\(671\) 38.7009i 0.0576765i
\(672\) 0 0
\(673\) 1110.84 1.65059 0.825293 0.564705i \(-0.191010\pi\)
0.825293 + 0.564705i \(0.191010\pi\)
\(674\) 23.4307 9.89007i 0.0347636 0.0146737i
\(675\) 0 0
\(676\) 1228.06 + 1195.52i 1.81665 + 1.76852i
\(677\) −397.465 + 397.465i −0.587097 + 0.587097i −0.936844 0.349747i \(-0.886268\pi\)
0.349747 + 0.936844i \(0.386268\pi\)
\(678\) 0 0
\(679\) −629.539 −0.927156
\(680\) 102.512 + 234.043i 0.150754 + 0.344181i
\(681\) 0 0
\(682\) −15.7170 + 38.6765i −0.0230455 + 0.0567104i
\(683\) 238.015 + 238.015i 0.348485 + 0.348485i 0.859545 0.511060i \(-0.170747\pi\)
−0.511060 + 0.859545i \(0.670747\pi\)
\(684\) 0 0
\(685\) −641.768 641.768i −0.936887 0.936887i
\(686\) −165.866 + 70.0120i −0.241787 + 0.102058i
\(687\) 0 0
\(688\) 74.6236 78.7423i 0.108464 0.114451i
\(689\) 967.099 1.40363
\(690\) 0 0
\(691\) −685.172 + 685.172i −0.991565 + 0.991565i −0.999965 0.00839951i \(-0.997326\pi\)
0.00839951 + 0.999965i \(0.497326\pi\)
\(692\) 304.789 4.09192i 0.440447 0.00591318i
\(693\) 0 0
\(694\) 297.528 + 120.907i 0.428714 + 0.174217i
\(695\) 219.111 0.315267
\(696\) 0 0
\(697\) 109.019i 0.156412i
\(698\) 238.359 + 96.8624i 0.341489 + 0.138771i
\(699\) 0 0
\(700\) 617.495 + 601.135i 0.882136 + 0.858764i
\(701\) −543.074 543.074i −0.774713 0.774713i 0.204214 0.978926i \(-0.434536\pi\)
−0.978926 + 0.204214i \(0.934536\pi\)
\(702\) 0 0
\(703\) 162.879i 0.231691i
\(704\) −1.91746 47.5847i −0.00272366 0.0675919i
\(705\) 0 0
\(706\) −66.7398 + 28.1708i −0.0945323 + 0.0399020i
\(707\) 1136.18 1136.18i 1.60704 1.60704i
\(708\) 0 0
\(709\) −488.019 + 488.019i −0.688320 + 0.688320i −0.961860 0.273541i \(-0.911805\pi\)
0.273541 + 0.961860i \(0.411805\pi\)
\(710\) −268.501 + 660.729i −0.378171 + 0.930604i
\(711\) 0 0
\(712\) −980.322 383.123i −1.37686 0.538094i
\(713\) 353.076i 0.495198i
\(714\) 0 0
\(715\) 87.0923 + 87.0923i 0.121807 + 0.121807i
\(716\) 7.91118 + 589.269i 0.0110491 + 0.823002i
\(717\) 0 0
\(718\) −261.869 + 110.535i −0.364721 + 0.153948i
\(719\) 297.369i 0.413587i −0.978385 0.206793i \(-0.933697\pi\)
0.978385 0.206793i \(-0.0663028\pi\)
\(720\) 0 0
\(721\) −1790.18 −2.48292
\(722\) 270.764 + 641.470i 0.375020 + 0.888463i
\(723\) 0 0
\(724\) 15.6053 + 1162.37i 0.0215542 + 1.60548i
\(725\) 45.8164 45.8164i 0.0631950 0.0631950i
\(726\) 0 0
\(727\) 1158.85 1.59402 0.797009 0.603967i \(-0.206414\pi\)
0.797009 + 0.603967i \(0.206414\pi\)
\(728\) −1850.33 + 810.456i −2.54166 + 1.11326i
\(729\) 0 0
\(730\) −850.759 345.724i −1.16542 0.473595i
\(731\) −22.6128 22.6128i −0.0309341 0.0309341i
\(732\) 0 0
\(733\) −348.835 348.835i −0.475901 0.475901i 0.427917 0.903818i \(-0.359248\pi\)
−0.903818 + 0.427917i \(0.859248\pi\)
\(734\) −508.819 1205.45i −0.693215 1.64230i
\(735\) 0 0
\(736\) −166.531 366.726i −0.226265 0.498269i
\(737\) −11.5619 −0.0156878
\(738\) 0 0
\(739\) 825.489 825.489i 1.11703 1.11703i 0.124860 0.992174i \(-0.460152\pi\)
0.992174 0.124860i \(-0.0398482\pi\)
\(740\) 881.430 + 858.076i 1.19112 + 1.15956i
\(741\) 0 0
\(742\) −307.743 + 757.295i −0.414748 + 1.02061i
\(743\) 899.725 1.21094 0.605468 0.795870i \(-0.292986\pi\)
0.605468 + 0.795870i \(0.292986\pi\)
\(744\) 0 0
\(745\) 89.2659i 0.119820i
\(746\) 357.013 878.538i 0.478569 1.17767i
\(747\) 0 0
\(748\) −14.0372 + 0.188455i −0.0187663 + 0.000251945i
\(749\) −263.160 263.160i −0.351348 0.351348i
\(750\) 0 0
\(751\) 80.4386i 0.107109i −0.998565 0.0535543i \(-0.982945\pi\)
0.998565 0.0535543i \(-0.0170550\pi\)
\(752\) 623.927 16.7560i 0.829690 0.0222819i
\(753\) 0 0
\(754\) 59.0623 + 139.925i 0.0783319 + 0.185577i
\(755\) −242.003 + 242.003i −0.320533 + 0.320533i
\(756\) 0 0
\(757\) 233.298 233.298i 0.308187 0.308187i −0.536019 0.844206i \(-0.680072\pi\)
0.844206 + 0.536019i \(0.180072\pi\)
\(758\) −258.757 105.151i −0.341368 0.138722i
\(759\) 0 0
\(760\) 180.964 + 70.7233i 0.238111 + 0.0930569i
\(761\) 56.1906i 0.0738378i 0.999318 + 0.0369189i \(0.0117543\pi\)
−0.999318 + 0.0369189i \(0.988246\pi\)
\(762\) 0 0
\(763\) −341.523 341.523i −0.447606 0.447606i
\(764\) −711.535 692.682i −0.931328 0.906652i
\(765\) 0 0
\(766\) −121.441 287.708i −0.158540 0.375598i
\(767\) 2760.38i 3.59893i
\(768\) 0 0
\(769\) 517.343 0.672748 0.336374 0.941728i \(-0.390799\pi\)
0.336374 + 0.941728i \(0.390799\pi\)
\(770\) −95.9122 + 40.4845i −0.124561 + 0.0525773i
\(771\) 0 0
\(772\) −362.506 + 372.372i −0.469567 + 0.482347i
\(773\) 523.925 523.925i 0.677781 0.677781i −0.281716 0.959498i \(-0.590904\pi\)
0.959498 + 0.281716i \(0.0909037\pi\)
\(774\) 0 0
\(775\) 585.048 0.754900
\(776\) 177.463 454.085i 0.228689 0.585161i
\(777\) 0 0
\(778\) 416.397 1024.67i 0.535215 1.31706i
\(779\) −58.6192 58.6192i −0.0752492 0.0752492i
\(780\) 0 0
\(781\) −27.7083 27.7083i −0.0354780 0.0354780i
\(782\) −109.383 + 46.1704i −0.139876 + 0.0590414i
\(783\) 0 0
\(784\) −24.7903 923.092i −0.0316202 1.17741i
\(785\) −918.248