Properties

Label 4032.2.v.e.1583.10
Level 4032
Weight 2
Character 4032.1583
Analytic conductor 32.196
Analytic rank 0
Dimension 40
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4032.v (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(32.1956820950\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(i)\)
Coefficient ring index: multiple of None
Twist minimal: no (minimal twist has level 1008)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 1583.10
Character \(\chi\) = 4032.1583
Dual form 4032.2.v.e.3599.10

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.0893433 - 0.0893433i) q^{5} -1.00000 q^{7} +O(q^{10})\) \(q+(-0.0893433 - 0.0893433i) q^{5} -1.00000 q^{7} +(-2.42480 + 2.42480i) q^{11} +(-3.86569 - 3.86569i) q^{13} +0.794810i q^{17} +(2.65233 - 2.65233i) q^{19} +3.92175i q^{23} -4.98404i q^{25} +(7.47818 - 7.47818i) q^{29} +5.55554i q^{31} +(0.0893433 + 0.0893433i) q^{35} +(-6.35455 + 6.35455i) q^{37} +6.96091 q^{41} +(1.25316 + 1.25316i) q^{43} -6.48295 q^{47} +1.00000 q^{49} +(-0.620687 - 0.620687i) q^{53} +0.433280 q^{55} +(3.39065 - 3.39065i) q^{59} +(7.51460 + 7.51460i) q^{61} +0.690747i q^{65} +(-2.22915 + 2.22915i) q^{67} +7.95182i q^{71} +12.9376i q^{73} +(2.42480 - 2.42480i) q^{77} +10.1941i q^{79} +(11.2820 + 11.2820i) q^{83} +(0.0710109 - 0.0710109i) q^{85} +5.52785 q^{89} +(3.86569 + 3.86569i) q^{91} -0.473935 q^{95} -4.33616 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q - 40q^{7} + O(q^{10}) \) \( 40q - 40q^{7} - 24q^{13} + 32q^{19} - 8q^{37} - 32q^{43} + 40q^{49} - 48q^{55} - 24q^{61} + 64q^{85} + 24q^{91} + 64q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4032\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(1793\) \(3781\)
\(\chi(n)\) \(-1\) \(1\) \(-1\) \(e\left(\frac{3}{4}\right)\)

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 0
\(3\) 0 0
\(4\) 0 0
\(5\) −0.0893433 0.0893433i −0.0399555 0.0399555i 0.686847 0.726802i \(-0.258994\pi\)
−0.726802 + 0.686847i \(0.758994\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −2.42480 + 2.42480i −0.731106 + 0.731106i −0.970839 0.239733i \(-0.922940\pi\)
0.239733 + 0.970839i \(0.422940\pi\)
\(12\) 0 0
\(13\) −3.86569 3.86569i −1.07215 1.07215i −0.997186 0.0749629i \(-0.976116\pi\)
−0.0749629 0.997186i \(-0.523884\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 0.794810i 0.192770i 0.995344 + 0.0963848i \(0.0307280\pi\)
−0.995344 + 0.0963848i \(0.969272\pi\)
\(18\) 0 0
\(19\) 2.65233 2.65233i 0.608485 0.608485i −0.334065 0.942550i \(-0.608420\pi\)
0.942550 + 0.334065i \(0.108420\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 3.92175i 0.817741i 0.912592 + 0.408871i \(0.134077\pi\)
−0.912592 + 0.408871i \(0.865923\pi\)
\(24\) 0 0
\(25\) 4.98404i 0.996807i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 7.47818 7.47818i 1.38866 1.38866i 0.560525 0.828138i \(-0.310599\pi\)
0.828138 0.560525i \(-0.189401\pi\)
\(30\) 0 0
\(31\) 5.55554i 0.997804i 0.866658 + 0.498902i \(0.166263\pi\)
−0.866658 + 0.498902i \(0.833737\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0.0893433 + 0.0893433i 0.0151018 + 0.0151018i
\(36\) 0 0
\(37\) −6.35455 + 6.35455i −1.04468 + 1.04468i −0.0457270 + 0.998954i \(0.514560\pi\)
−0.998954 + 0.0457270i \(0.985440\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 6.96091 1.08711 0.543556 0.839373i \(-0.317078\pi\)
0.543556 + 0.839373i \(0.317078\pi\)
\(42\) 0 0
\(43\) 1.25316 + 1.25316i 0.191105 + 0.191105i 0.796173 0.605069i \(-0.206854\pi\)
−0.605069 + 0.796173i \(0.706854\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −6.48295 −0.945635 −0.472818 0.881160i \(-0.656763\pi\)
−0.472818 + 0.881160i \(0.656763\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −0.620687 0.620687i −0.0852579 0.0852579i 0.663192 0.748450i \(-0.269201\pi\)
−0.748450 + 0.663192i \(0.769201\pi\)
\(54\) 0 0
\(55\) 0.433280 0.0584234
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 3.39065 3.39065i 0.441425 0.441425i −0.451066 0.892491i \(-0.648956\pi\)
0.892491 + 0.451066i \(0.148956\pi\)
\(60\) 0 0
\(61\) 7.51460 + 7.51460i 0.962146 + 0.962146i 0.999309 0.0371630i \(-0.0118321\pi\)
−0.0371630 + 0.999309i \(0.511832\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0.690747i 0.0856766i
\(66\) 0 0
\(67\) −2.22915 + 2.22915i −0.272334 + 0.272334i −0.830039 0.557705i \(-0.811682\pi\)
0.557705 + 0.830039i \(0.311682\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 7.95182i 0.943707i 0.881677 + 0.471853i \(0.156415\pi\)
−0.881677 + 0.471853i \(0.843585\pi\)
\(72\) 0 0
\(73\) 12.9376i 1.51423i 0.653283 + 0.757114i \(0.273391\pi\)
−0.653283 + 0.757114i \(0.726609\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 2.42480 2.42480i 0.276332 0.276332i
\(78\) 0 0
\(79\) 10.1941i 1.14693i 0.819230 + 0.573465i \(0.194401\pi\)
−0.819230 + 0.573465i \(0.805599\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 11.2820 + 11.2820i 1.23836 + 1.23836i 0.960670 + 0.277694i \(0.0895700\pi\)
0.277694 + 0.960670i \(0.410430\pi\)
\(84\) 0 0
\(85\) 0.0710109 0.0710109i 0.00770221 0.00770221i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 5.52785 0.585951 0.292976 0.956120i \(-0.405355\pi\)
0.292976 + 0.956120i \(0.405355\pi\)
\(90\) 0 0
\(91\) 3.86569 + 3.86569i 0.405234 + 0.405234i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −0.473935 −0.0486247
\(96\) 0 0
\(97\) −4.33616 −0.440270 −0.220135 0.975469i \(-0.570650\pi\)
−0.220135 + 0.975469i \(0.570650\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 9.66216 + 9.66216i 0.961421 + 0.961421i 0.999283 0.0378620i \(-0.0120547\pi\)
−0.0378620 + 0.999283i \(0.512055\pi\)
\(102\) 0 0
\(103\) −16.4000 −1.61594 −0.807969 0.589225i \(-0.799433\pi\)
−0.807969 + 0.589225i \(0.799433\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −5.48912 + 5.48912i −0.530653 + 0.530653i −0.920767 0.390114i \(-0.872436\pi\)
0.390114 + 0.920767i \(0.372436\pi\)
\(108\) 0 0
\(109\) −14.6355 14.6355i −1.40183 1.40183i −0.794301 0.607524i \(-0.792163\pi\)
−0.607524 0.794301i \(-0.707837\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 8.28264i 0.779165i 0.920992 + 0.389582i \(0.127381\pi\)
−0.920992 + 0.389582i \(0.872619\pi\)
\(114\) 0 0
\(115\) 0.350382 0.350382i 0.0326733 0.0326733i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0.794810i 0.0728601i
\(120\) 0 0
\(121\) 0.759336i 0.0690305i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −0.892006 + 0.892006i −0.0797835 + 0.0797835i
\(126\) 0 0
\(127\) 3.39522i 0.301277i 0.988589 + 0.150638i \(0.0481329\pi\)
−0.988589 + 0.150638i \(0.951867\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 8.73455 + 8.73455i 0.763141 + 0.763141i 0.976889 0.213748i \(-0.0685671\pi\)
−0.213748 + 0.976889i \(0.568567\pi\)
\(132\) 0 0
\(133\) −2.65233 + 2.65233i −0.229986 + 0.229986i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −4.84889 −0.414269 −0.207134 0.978313i \(-0.566414\pi\)
−0.207134 + 0.978313i \(0.566414\pi\)
\(138\) 0 0
\(139\) 2.19464 + 2.19464i 0.186147 + 0.186147i 0.794028 0.607881i \(-0.207980\pi\)
−0.607881 + 0.794028i \(0.707980\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 18.7471 1.56771
\(144\) 0 0
\(145\) −1.33625 −0.110969
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 2.83836 + 2.83836i 0.232528 + 0.232528i 0.813747 0.581219i \(-0.197424\pi\)
−0.581219 + 0.813747i \(0.697424\pi\)
\(150\) 0 0
\(151\) 18.9821 1.54474 0.772370 0.635172i \(-0.219071\pi\)
0.772370 + 0.635172i \(0.219071\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0.496350 0.496350i 0.0398678 0.0398678i
\(156\) 0 0
\(157\) −12.3221 12.3221i −0.983412 0.983412i 0.0164522 0.999865i \(-0.494763\pi\)
−0.999865 + 0.0164522i \(0.994763\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 3.92175i 0.309077i
\(162\) 0 0
\(163\) 3.50400 3.50400i 0.274454 0.274454i −0.556436 0.830890i \(-0.687832\pi\)
0.830890 + 0.556436i \(0.187832\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 17.4719i 1.35202i −0.736893 0.676009i \(-0.763708\pi\)
0.736893 0.676009i \(-0.236292\pi\)
\(168\) 0 0
\(169\) 16.8871i 1.29901i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −1.45528 + 1.45528i −0.110643 + 0.110643i −0.760261 0.649618i \(-0.774929\pi\)
0.649618 + 0.760261i \(0.274929\pi\)
\(174\) 0 0
\(175\) 4.98404i 0.376758i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −2.22288 2.22288i −0.166146 0.166146i 0.619137 0.785283i \(-0.287482\pi\)
−0.785283 + 0.619137i \(0.787482\pi\)
\(180\) 0 0
\(181\) 3.13227 3.13227i 0.232820 0.232820i −0.581049 0.813869i \(-0.697358\pi\)
0.813869 + 0.581049i \(0.197358\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 1.13547 0.0834816
\(186\) 0 0
\(187\) −1.92726 1.92726i −0.140935 0.140935i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 3.61134 0.261308 0.130654 0.991428i \(-0.458292\pi\)
0.130654 + 0.991428i \(0.458292\pi\)
\(192\) 0 0
\(193\) −3.01689 −0.217160 −0.108580 0.994088i \(-0.534630\pi\)
−0.108580 + 0.994088i \(0.534630\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −0.282108 0.282108i −0.0200994 0.0200994i 0.696986 0.717085i \(-0.254524\pi\)
−0.717085 + 0.696986i \(0.754524\pi\)
\(198\) 0 0
\(199\) −3.40015 −0.241030 −0.120515 0.992712i \(-0.538455\pi\)
−0.120515 + 0.992712i \(0.538455\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −7.47818 + 7.47818i −0.524865 + 0.524865i
\(204\) 0 0
\(205\) −0.621911 0.621911i −0.0434361 0.0434361i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 12.8627i 0.889734i
\(210\) 0 0
\(211\) −6.04290 + 6.04290i −0.416010 + 0.416010i −0.883826 0.467816i \(-0.845041\pi\)
0.467816 + 0.883826i \(0.345041\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0.223922i 0.0152714i
\(216\) 0 0
\(217\) 5.55554i 0.377135i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 3.07249 3.07249i 0.206678 0.206678i
\(222\) 0 0
\(223\) 22.2108i 1.48734i 0.668545 + 0.743672i \(0.266918\pi\)
−0.668545 + 0.743672i \(0.733082\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 16.1859 + 16.1859i 1.07430 + 1.07430i 0.997009 + 0.0772896i \(0.0246266\pi\)
0.0772896 + 0.997009i \(0.475373\pi\)
\(228\) 0 0
\(229\) −7.75579 + 7.75579i −0.512517 + 0.512517i −0.915297 0.402780i \(-0.868044\pi\)
0.402780 + 0.915297i \(0.368044\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 18.7060 1.22547 0.612734 0.790289i \(-0.290070\pi\)
0.612734 + 0.790289i \(0.290070\pi\)
\(234\) 0 0
\(235\) 0.579208 + 0.579208i 0.0377834 + 0.0377834i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −20.3964 −1.31933 −0.659667 0.751558i \(-0.729303\pi\)
−0.659667 + 0.751558i \(0.729303\pi\)
\(240\) 0 0
\(241\) 10.4808 0.675129 0.337565 0.941302i \(-0.390397\pi\)
0.337565 + 0.941302i \(0.390397\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −0.0893433 0.0893433i −0.00570793 0.00570793i
\(246\) 0 0
\(247\) −20.5061 −1.30477
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 22.2508 22.2508i 1.40446 1.40446i 0.619320 0.785139i \(-0.287408\pi\)
0.785139 0.619320i \(-0.212592\pi\)
\(252\) 0 0
\(253\) −9.50947 9.50947i −0.597855 0.597855i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 29.3780i 1.83255i 0.400547 + 0.916276i \(0.368820\pi\)
−0.400547 + 0.916276i \(0.631180\pi\)
\(258\) 0 0
\(259\) 6.35455 6.35455i 0.394852 0.394852i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 8.75090i 0.539603i 0.962916 + 0.269802i \(0.0869582\pi\)
−0.962916 + 0.269802i \(0.913042\pi\)
\(264\) 0 0
\(265\) 0.110908i 0.00681305i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 8.92219 8.92219i 0.543996 0.543996i −0.380702 0.924698i \(-0.624318\pi\)
0.924698 + 0.380702i \(0.124318\pi\)
\(270\) 0 0
\(271\) 3.36141i 0.204191i −0.994775 0.102096i \(-0.967445\pi\)
0.994775 0.102096i \(-0.0325548\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 12.0853 + 12.0853i 0.728771 + 0.728771i
\(276\) 0 0
\(277\) 0.516082 0.516082i 0.0310083 0.0310083i −0.691433 0.722441i \(-0.743020\pi\)
0.722441 + 0.691433i \(0.243020\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −13.0206 −0.776747 −0.388373 0.921502i \(-0.626963\pi\)
−0.388373 + 0.921502i \(0.626963\pi\)
\(282\) 0 0
\(283\) −7.04669 7.04669i −0.418882 0.418882i 0.465936 0.884818i \(-0.345718\pi\)
−0.884818 + 0.465936i \(0.845718\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −6.96091 −0.410890
\(288\) 0 0
\(289\) 16.3683 0.962840
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 3.61446 + 3.61446i 0.211159 + 0.211159i 0.804760 0.593601i \(-0.202294\pi\)
−0.593601 + 0.804760i \(0.702294\pi\)
\(294\) 0 0
\(295\) −0.605864 −0.0352747
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 15.1603 15.1603i 0.876741 0.876741i
\(300\) 0 0
\(301\) −1.25316 1.25316i −0.0722308 0.0722308i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 1.34276i 0.0768861i
\(306\) 0 0
\(307\) 15.5015 15.5015i 0.884715 0.884715i −0.109295 0.994009i \(-0.534859\pi\)
0.994009 + 0.109295i \(0.0348592\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 17.6216i 0.999227i 0.866248 + 0.499613i \(0.166525\pi\)
−0.866248 + 0.499613i \(0.833475\pi\)
\(312\) 0 0
\(313\) 18.5910i 1.05083i 0.850847 + 0.525414i \(0.176089\pi\)
−0.850847 + 0.525414i \(0.823911\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 13.0237 13.0237i 0.731486 0.731486i −0.239428 0.970914i \(-0.576960\pi\)
0.970914 + 0.239428i \(0.0769600\pi\)
\(318\) 0 0
\(319\) 36.2662i 2.03052i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 2.10810 + 2.10810i 0.117298 + 0.117298i
\(324\) 0 0
\(325\) −19.2667 + 19.2667i −1.06873 + 1.06873i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 6.48295 0.357417
\(330\) 0 0
\(331\) 0.844531 + 0.844531i 0.0464196 + 0.0464196i 0.729936 0.683516i \(-0.239550\pi\)
−0.683516 + 0.729936i \(0.739550\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0.398319 0.0217625
\(336\) 0 0
\(337\) 24.2226 1.31949 0.659746 0.751489i \(-0.270664\pi\)
0.659746 + 0.751489i \(0.270664\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −13.4711 13.4711i −0.729500 0.729500i
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 8.75310 8.75310i 0.469891 0.469891i −0.431988 0.901879i \(-0.642188\pi\)
0.901879 + 0.431988i \(0.142188\pi\)
\(348\) 0 0
\(349\) −6.87743 6.87743i −0.368140 0.368140i 0.498658 0.866799i \(-0.333826\pi\)
−0.866799 + 0.498658i \(0.833826\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 22.8780i 1.21767i 0.793295 + 0.608837i \(0.208364\pi\)
−0.793295 + 0.608837i \(0.791636\pi\)
\(354\) 0 0
\(355\) 0.710441 0.710441i 0.0377063 0.0377063i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 8.82162i 0.465587i −0.972526 0.232794i \(-0.925213\pi\)
0.972526 0.232794i \(-0.0747867\pi\)
\(360\) 0 0
\(361\) 4.93033i 0.259491i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 1.15588 1.15588i 0.0605017 0.0605017i
\(366\) 0 0
\(367\) 21.0160i 1.09703i 0.836142 + 0.548513i \(0.184806\pi\)
−0.836142 + 0.548513i \(0.815194\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0.620687 + 0.620687i 0.0322245 + 0.0322245i
\(372\) 0 0
\(373\) −10.3425 + 10.3425i −0.535516 + 0.535516i −0.922209 0.386693i \(-0.873617\pi\)
0.386693 + 0.922209i \(0.373617\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −57.8166 −2.97771
\(378\) 0 0
\(379\) −16.1353 16.1353i −0.828813 0.828813i 0.158539 0.987353i \(-0.449322\pi\)
−0.987353 + 0.158539i \(0.949322\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 12.1083 0.618704 0.309352 0.950948i \(-0.399888\pi\)
0.309352 + 0.950948i \(0.399888\pi\)
\(384\) 0 0
\(385\) −0.433280 −0.0220820
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 12.7493 + 12.7493i 0.646414 + 0.646414i 0.952124 0.305711i \(-0.0988941\pi\)
−0.305711 + 0.952124i \(0.598894\pi\)
\(390\) 0 0
\(391\) −3.11704 −0.157636
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0.910778 0.910778i 0.0458262 0.0458262i
\(396\) 0 0
\(397\) 16.1299 + 16.1299i 0.809534 + 0.809534i 0.984563 0.175029i \(-0.0560019\pi\)
−0.175029 + 0.984563i \(0.556002\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 1.54744i 0.0772755i −0.999253 0.0386378i \(-0.987698\pi\)
0.999253 0.0386378i \(-0.0123018\pi\)
\(402\) 0 0
\(403\) 21.4760 21.4760i 1.06980 1.06980i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 30.8170i 1.52754i
\(408\) 0 0
\(409\) 4.58498i 0.226712i 0.993554 + 0.113356i \(0.0361601\pi\)
−0.993554 + 0.113356i \(0.963840\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −3.39065 + 3.39065i −0.166843 + 0.166843i
\(414\) 0 0
\(415\) 2.01595i 0.0989589i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −24.8750 24.8750i −1.21523 1.21523i −0.969285 0.245940i \(-0.920903\pi\)
−0.245940 0.969285i \(1.42090\pi\)
\(420\) 0 0
\(421\) 9.42104 9.42104i 0.459153 0.459153i −0.439224 0.898378i \(-0.644747\pi\)
0.898378 + 0.439224i \(0.144747\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 3.96136 0.192154
\(426\) 0 0
\(427\) −7.51460 7.51460i −0.363657 0.363657i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −8.96634 −0.431893 −0.215947 0.976405i \(-0.569284\pi\)
−0.215947 + 0.976405i \(0.569284\pi\)
\(432\) 0 0
\(433\) 0.679368 0.0326483 0.0163242 0.999867i \(-0.494804\pi\)
0.0163242 + 0.999867i \(0.494804\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 10.4018 + 10.4018i 0.497584 + 0.497584i
\(438\) 0 0
\(439\) −35.4959 −1.69413 −0.847065 0.531490i \(-0.821632\pi\)
−0.847065 + 0.531490i \(0.821632\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −23.4369 + 23.4369i −1.11352 + 1.11352i −0.120853 + 0.992670i \(0.538563\pi\)
−0.992670 + 0.120853i \(0.961437\pi\)
\(444\) 0 0
\(445\) −0.493876 0.493876i −0.0234120 0.0234120i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 4.45807i 0.210389i −0.994452 0.105195i \(-0.966453\pi\)
0.994452 0.105195i \(-0.0335465\pi\)
\(450\) 0 0
\(451\) −16.8788 + 16.8788i −0.794793 + 0.794793i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0.690747i 0.0323827i
\(456\) 0 0
\(457\) 14.9134i 0.697620i 0.937193 + 0.348810i \(0.113414\pi\)
−0.937193 + 0.348810i \(0.886586\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −7.52217 + 7.52217i −0.350342 + 0.350342i −0.860237 0.509895i \(-0.829684\pi\)
0.509895 + 0.860237i \(0.329684\pi\)
\(462\) 0 0
\(463\) 40.0015i 1.85903i −0.368787 0.929514i \(-0.620227\pi\)
0.368787 0.929514i \(-0.379773\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 18.9560 + 18.9560i 0.877177 + 0.877177i 0.993242 0.116064i \(-0.0370279\pi\)
−0.116064 + 0.993242i \(0.537028\pi\)
\(468\) 0 0
\(469\) 2.22915 2.22915i 0.102933 0.102933i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −6.07732 −0.279435
\(474\) 0 0
\(475\) −13.2193 13.2193i −0.606543 0.606543i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −21.3112 −0.973733 −0.486866 0.873476i \(-0.661860\pi\)
−0.486866 + 0.873476i \(0.661860\pi\)
\(480\) 0 0
\(481\) 49.1294 2.24011
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0.387407 + 0.387407i 0.0175912 + 0.0175912i
\(486\) 0 0
\(487\) −13.6167 −0.617031 −0.308515 0.951219i \(-0.599832\pi\)
−0.308515 + 0.951219i \(0.599832\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 5.18965 5.18965i 0.234206 0.234206i −0.580240 0.814446i \(-0.697041\pi\)
0.814446 + 0.580240i \(0.197041\pi\)
\(492\) 0 0
\(493\) 5.94373 + 5.94373i 0.267692 + 0.267692i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 7.95182i 0.356688i
\(498\) 0 0
\(499\) 7.15618 7.15618i 0.320355 0.320355i −0.528548 0.848903i \(-0.677264\pi\)
0.848903 + 0.528548i \(0.177264\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 33.5554i 1.49616i 0.663607 + 0.748081i \(0.269025\pi\)
−0.663607 + 0.748081i \(0.730975\pi\)
\(504\) 0 0
\(505\) 1.72650i 0.0768282i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 0.615168 0.615168i 0.0272669 0.0272669i −0.693342 0.720609i \(-0.743862\pi\)
0.720609 + 0.693342i \(0.243862\pi\)
\(510\) 0 0
\(511\) 12.9376i 0.572324i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 1.46523 + 1.46523i 0.0645656 + 0.0645656i
\(516\) 0 0
\(517\) 15.7199 15.7199i 0.691359 0.691359i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 5.91593 0.259182 0.129591 0.991568i \(-0.458634\pi\)
0.129591 + 0.991568i \(0.458634\pi\)
\(522\) 0 0
\(523\) −17.7110 17.7110i −0.774449 0.774449i 0.204432 0.978881i \(-0.434465\pi\)
−0.978881 + 0.204432i \(0.934465\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −4.41560 −0.192346
\(528\) 0 0
\(529\) 7.61988 0.331299
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −26.9087 26.9087i −1.16555 1.16555i
\(534\) 0 0
\(535\) 0.980831 0.0424050
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −2.42480 + 2.42480i −0.104444 + 0.104444i
\(540\) 0 0
\(541\) −9.13769 9.13769i −0.392860 0.392860i 0.482846 0.875706i \(-0.339603\pi\)
−0.875706 + 0.482846i \(0.839603\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 2.61516i 0.112021i
\(546\) 0 0
\(547\) 30.1099 30.1099i 1.28741 1.28741i 0.351052 0.936356i \(-0.385824\pi\)
0.936356 0.351052i \(-0.114176\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 39.6691i 1.68996i
\(552\) 0 0
\(553\) 10.1941i 0.433499i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 16.3306 16.3306i 0.691950 0.691950i −0.270711 0.962661i \(-0.587259\pi\)
0.962661 + 0.270711i \(0.0872588\pi\)
\(558\) 0 0
\(559\) 9.68863i 0.409785i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0.288759 + 0.288759i 0.0121697 + 0.0121697i 0.713165 0.700996i \(-0.247261\pi\)
−0.700996 + 0.713165i \(0.747261\pi\)
\(564\) 0 0
\(565\) 0.739998 0.739998i 0.0311319 0.0311319i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 23.8386 0.999365 0.499683 0.866209i \(-0.333450\pi\)
0.499683 + 0.866209i \(0.333450\pi\)
\(570\) 0 0
\(571\) −1.86113 1.86113i −0.0778857 0.0778857i 0.667091 0.744976i \(-0.267539\pi\)
−0.744976 + 0.667091i \(0.767539\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 19.5461 0.815130
\(576\) 0 0
\(577\) −32.0148 −1.33279 −0.666396 0.745598i \(-0.732164\pi\)
−0.666396 + 0.745598i \(0.732164\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −11.2820 11.2820i −0.468057 0.468057i
\(582\) 0 0
\(583\) 3.01009 0.124665
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −1.73084 + 1.73084i −0.0714394 + 0.0714394i −0.741924 0.670484i \(-0.766086\pi\)
0.670484 + 0.741924i \(0.266086\pi\)
\(588\) 0 0
\(589\) 14.7351 + 14.7351i 0.607149 + 0.607149i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 22.8985i 0.940328i 0.882579 + 0.470164i \(0.155805\pi\)
−0.882579 + 0.470164i \(0.844195\pi\)
\(594\) 0 0
\(595\) −0.0710109 + 0.0710109i −0.00291116 + 0.00291116i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 26.0002i 1.06234i −0.847266 0.531169i \(-0.821753\pi\)
0.847266 0.531169i \(-0.178247\pi\)
\(600\) 0 0
\(601\) 21.0502i 0.858654i 0.903149 + 0.429327i \(0.141249\pi\)
−0.903149 + 0.429327i \(0.858751\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −0.0678415 + 0.0678415i −0.00275815 + 0.00275815i
\(606\) 0 0
\(607\) 32.7336i 1.32861i −0.747460 0.664307i \(-0.768727\pi\)
0.747460 0.664307i \(-0.231273\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 25.0611 + 25.0611i 1.01386 + 1.01386i
\(612\) 0 0
\(613\) 7.14939 7.14939i 0.288761 0.288761i −0.547829 0.836590i \(-0.684546\pi\)
0.836590 + 0.547829i \(0.184546\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 15.8667 0.638769 0.319384 0.947625i \(-0.396524\pi\)
0.319384 + 0.947625i \(0.396524\pi\)
\(618\) 0 0
\(619\) 20.4351 + 20.4351i 0.821355 + 0.821355i 0.986302 0.164947i \(-0.0527453\pi\)
−0.164947 + 0.986302i \(0.552745\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −5.52785 −0.221469
\(624\) 0 0
\(625\) −24.7608 −0.990432
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −5.05066 5.05066i −0.201383 0.201383i
\(630\) 0 0
\(631\) −39.1876 −1.56003 −0.780017 0.625758i \(-0.784790\pi\)
−0.780017 + 0.625758i \(0.784790\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0.303340 0.303340i 0.0120377 0.0120377i
\(636\) 0 0
\(637\) −3.86569 3.86569i −0.153164 0.153164i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 32.1293i 1.26903i −0.772911 0.634515i \(-0.781200\pi\)
0.772911 0.634515i \(-0.218800\pi\)
\(642\) 0 0
\(643\) −13.7452 + 13.7452i −0.542059 + 0.542059i −0.924132 0.382073i \(-0.875210\pi\)
0.382073 + 0.924132i \(0.375210\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 5.78120i 0.227282i 0.993522 + 0.113641i \(0.0362514\pi\)
−0.993522 + 0.113641i \(0.963749\pi\)
\(648\) 0 0
\(649\) 16.4433i 0.645457i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 13.9854 13.9854i 0.547293 0.547293i −0.378364 0.925657i \(-0.623513\pi\)
0.925657 + 0.378364i \(0.123513\pi\)
\(654\) 0 0
\(655\) 1.56075i 0.0609834i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −19.6810 19.6810i −0.766661 0.766661i 0.210856 0.977517i \(-0.432375\pi\)
−0.977517 + 0.210856i \(0.932375\pi\)
\(660\) 0 0
\(661\) 12.7655 12.7655i 0.496519 0.496519i −0.413833 0.910353i \(-0.635810\pi\)
0.910353 + 0.413833i \(0.135810\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0.473935 0.0183784
\(666\) 0 0
\(667\) 29.3275 + 29.3275i 1.13557 + 1.13557i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −36.4429 −1.40686
\(672\) 0 0
\(673\) 43.7910 1.68802 0.844010 0.536328i \(-0.180189\pi\)
0.844010 + 0.536328i \(0.180189\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 25.0415 + 25.0415i 0.962422 + 0.962422i 0.999319 0.0368968i \(-0.0117473\pi\)
−0.0368968 + 0.999319i \(0.511747\pi\)
\(678\) 0 0
\(679\) 4.33616 0.166407
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −12.6770 + 12.6770i −0.485071 + 0.485071i −0.906747 0.421676i \(-0.861442\pi\)
0.421676 + 0.906747i \(0.361442\pi\)
\(684\) 0 0
\(685\) 0.433216 + 0.433216i 0.0165523 + 0.0165523i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 4.79877i 0.182818i
\(690\) 0 0
\(691\) −11.5147 + 11.5147i −0.438041 + 0.438041i −0.891352 0.453312i \(-0.850243\pi\)
0.453312 + 0.891352i \(0.350243\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0.392153i 0.0148752i
\(696\) 0 0
\(697\) 5.53260i 0.209562i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −24.5725 + 24.5725i −0.928089 + 0.928089i −0.997582 0.0694930i \(-0.977862\pi\)
0.0694930 + 0.997582i \(0.477862\pi\)
\(702\) 0 0
\(703\) 33.7087i 1.27135i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −9.66216 9.66216i −0.363383 0.363383i
\(708\) 0 0
\(709\) −11.9488 + 11.9488i −0.448745 + 0.448745i −0.894937 0.446192i \(-0.852780\pi\)
0.446192 + 0.894937i \(0.352780\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −21.7874 −0.815946
\(714\) 0 0
\(715\) −1.67492 1.67492i −0.0626386 0.0626386i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 20.8496 0.777559 0.388779 0.921331i \(-0.372897\pi\)
0.388779 + 0.921331i \(0.372897\pi\)
\(720\) 0 0
\(721\) 16.4000 0.610767
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −37.2715 37.2715i −1.38423 1.38423i
\(726\) 0 0
\(727\) 49.4099 1.83251 0.916257 0.400592i \(-0.131195\pi\)
0.916257 + 0.400592i \(0.131195\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −0.996021 + 0.996021i −0.0368392 + 0.0368392i
\(732\) 0 0
\(733\) −22.8419 22.8419i −0.843686 0.843686i 0.145650 0.989336i \(-0.453473\pi\)
−0.989336 + 0.145650i \(0.953473\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 10.8105i 0.398210i
\(738\) 0 0
\(739\) 3.95695 3.95695i 0.145559 0.145559i −0.630572 0.776131i \(-0.717180\pi\)
0.776131 + 0.630572i \(0.217180\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 1.72532i 0.0632958i −0.999499 0.0316479i \(-0.989924\pi\)
0.999499 0.0316479i \(-0.0100755\pi\)
\(744\) 0 0
\(745\) 0.507177i 0.0185815i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 5.48912 5.48912i 0.200568 0.200568i
\(750\) 0 0
\(751\) 28.0700i 1.02429i 0.858900 + 0.512144i \(0.171148\pi\)
−0.858900 + 0.512144i \(0.828852\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −1.69592 1.69592i −0.0617209 0.0617209i
\(756\) 0 0
\(757\) −21.3781 + 21.3781i −0.777001 + 0.777001i −0.979320 0.202319i \(-0.935152\pi\)
0.202319 + 0.979320i \(0.435152\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −17.0483 −0.618001 −0.309001 0.951062i \(-0.599995\pi\)
−0.309001 + 0.951062i \(0.599995\pi\)
\(762\) 0 0
\(763\) 14.6355 + 14.6355i 0.529840 + 0.529840i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −26.2144 −0.946547
\(768\) 0 0
\(769\) 17.6693 0.637172 0.318586 0.947894i \(-0.396792\pi\)
0.318586 + 0.947894i \(0.396792\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 3.41723 + 3.41723i 0.122909 + 0.122909i 0.765886 0.642977i \(-0.222301\pi\)
−0.642977 + 0.765886i \(0.722301\pi\)
\(774\) 0 0
\(775\) 27.6890 0.994618
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 18.4626 18.4626i 0.661492 0.661492i
\(780\) 0 0
\(781\) −19.2816 19.2816i −0.689949 0.689949i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 2.20180i 0.0785855i
\(786\) 0 0
\(787\) 16.5567 16.5567i 0.590183 0.590183i −0.347498 0.937681i \(-0.612969\pi\)
0.937681 + 0.347498i \(0.112969\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 8.28264i 0.294497i
\(792\) 0 0
\(793\) 58.0982i 2.06313i
\(794\) 0 0