Properties

Label 576.4.k.a.145.2
Level $576$
Weight $4$
Character 576.145
Analytic conductor $33.985$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 576.k (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(33.9851001633\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Defining polynomial: \(x^{10} - 2 x^{9} - x^{8} + 6 x^{7} + 14 x^{6} - 80 x^{5} + 56 x^{4} + 96 x^{3} - 64 x^{2} - 512 x + 1024\)
Coefficient ring: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 2^{20} \)
Twist minimal: no (minimal twist has level 16)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 145.2
Root \(-1.62580 + 1.16481i\) of defining polynomial
Character \(\chi\) \(=\) 576.145
Dual form 576.4.k.a.433.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-8.22587 + 8.22587i) q^{5} +2.67171i q^{7} +O(q^{10})\) \(q+(-8.22587 + 8.22587i) q^{5} +2.67171i q^{7} +(-45.2213 + 45.2213i) q^{11} +(35.3968 + 35.3968i) q^{13} +72.4991 q^{17} +(-19.4427 - 19.4427i) q^{19} -139.462i q^{23} -10.3299i q^{25} +(-66.0434 - 66.0434i) q^{29} -188.682 q^{31} +(-21.9771 - 21.9771i) q^{35} +(-84.0653 + 84.0653i) q^{37} -104.629i q^{41} +(31.4857 - 31.4857i) q^{43} -488.151 q^{47} +335.862 q^{49} +(-149.560 + 149.560i) q^{53} -743.968i q^{55} +(284.698 - 284.698i) q^{59} +(-228.069 - 228.069i) q^{61} -582.338 q^{65} +(-139.151 - 139.151i) q^{67} -453.655i q^{71} -259.747i q^{73} +(-120.818 - 120.818i) q^{77} -323.190 q^{79} +(-563.897 - 563.897i) q^{83} +(-596.368 + 596.368i) q^{85} -866.853i q^{89} +(-94.5697 + 94.5697i) q^{91} +319.866 q^{95} -936.077 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q + 2q^{5} + O(q^{10}) \) \( 10q + 2q^{5} + 18q^{11} - 2q^{13} + 4q^{17} + 26q^{19} + 202q^{29} - 368q^{31} + 476q^{35} - 10q^{37} + 838q^{43} - 944q^{47} + 94q^{49} + 378q^{53} + 1706q^{59} + 910q^{61} + 492q^{65} - 1942q^{67} + 268q^{77} + 4416q^{79} - 2562q^{83} - 12q^{85} - 3332q^{91} + 6900q^{95} - 4q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).

\(n\) \(65\) \(127\) \(325\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{3}{4}\right)\)

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
\(5\) −8.22587 + 8.22587i −0.735744 + 0.735744i −0.971751 0.236007i \(-0.924161\pi\)
0.236007 + 0.971751i \(0.424161\pi\)
\(6\) 0 0
\(7\) 2.67171i 0.144259i 0.997395 + 0.0721293i \(0.0229794\pi\)
−0.997395 + 0.0721293i \(0.977021\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −45.2213 + 45.2213i −1.23952 + 1.23952i −0.279323 + 0.960197i \(0.590110\pi\)
−0.960197 + 0.279323i \(0.909890\pi\)
\(12\) 0 0
\(13\) 35.3968 + 35.3968i 0.755176 + 0.755176i 0.975440 0.220264i \(-0.0706918\pi\)
−0.220264 + 0.975440i \(0.570692\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 72.4991 1.03433 0.517165 0.855886i \(-0.326987\pi\)
0.517165 + 0.855886i \(0.326987\pi\)
\(18\) 0 0
\(19\) −19.4427 19.4427i −0.234761 0.234761i 0.579916 0.814676i \(-0.303085\pi\)
−0.814676 + 0.579916i \(0.803085\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 139.462i 1.26434i −0.774830 0.632170i \(-0.782165\pi\)
0.774830 0.632170i \(-0.217835\pi\)
\(24\) 0 0
\(25\) 10.3299i 0.0826390i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −66.0434 66.0434i −0.422895 0.422895i 0.463304 0.886199i \(-0.346664\pi\)
−0.886199 + 0.463304i \(0.846664\pi\)
\(30\) 0 0
\(31\) −188.682 −1.09317 −0.546584 0.837404i \(-0.684072\pi\)
−0.546584 + 0.837404i \(0.684072\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −21.9771 21.9771i −0.106137 0.106137i
\(36\) 0 0
\(37\) −84.0653 + 84.0653i −0.373520 + 0.373520i −0.868758 0.495237i \(-0.835081\pi\)
0.495237 + 0.868758i \(0.335081\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 104.629i 0.398545i −0.979944 0.199272i \(-0.936142\pi\)
0.979944 0.199272i \(-0.0638578\pi\)
\(42\) 0 0
\(43\) 31.4857 31.4857i 0.111663 0.111663i −0.649067 0.760731i \(-0.724841\pi\)
0.760731 + 0.649067i \(0.224841\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −488.151 −1.51498 −0.757491 0.652846i \(-0.773575\pi\)
−0.757491 + 0.652846i \(0.773575\pi\)
\(48\) 0 0
\(49\) 335.862 0.979189
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −149.560 + 149.560i −0.387617 + 0.387617i −0.873837 0.486220i \(-0.838376\pi\)
0.486220 + 0.873837i \(0.338376\pi\)
\(54\) 0 0
\(55\) 743.968i 1.82394i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 284.698 284.698i 0.628212 0.628212i −0.319406 0.947618i \(-0.603483\pi\)
0.947618 + 0.319406i \(0.103483\pi\)
\(60\) 0 0
\(61\) −228.069 228.069i −0.478709 0.478709i 0.426010 0.904719i \(-0.359919\pi\)
−0.904719 + 0.426010i \(0.859919\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −582.338 −1.11123
\(66\) 0 0
\(67\) −139.151 139.151i −0.253730 0.253730i 0.568768 0.822498i \(-0.307420\pi\)
−0.822498 + 0.568768i \(0.807420\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 453.655i 0.758294i −0.925336 0.379147i \(-0.876217\pi\)
0.925336 0.379147i \(-0.123783\pi\)
\(72\) 0 0
\(73\) 259.747i 0.416454i −0.978081 0.208227i \(-0.933231\pi\)
0.978081 0.208227i \(-0.0667692\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −120.818 120.818i −0.178811 0.178811i
\(78\) 0 0
\(79\) −323.190 −0.460275 −0.230138 0.973158i \(-0.573918\pi\)
−0.230138 + 0.973158i \(0.573918\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −563.897 563.897i −0.745732 0.745732i 0.227943 0.973674i \(-0.426800\pi\)
−0.973674 + 0.227943i \(0.926800\pi\)
\(84\) 0 0
\(85\) −596.368 + 596.368i −0.761002 + 0.761002i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 866.853i 1.03243i −0.856459 0.516215i \(-0.827341\pi\)
0.856459 0.516215i \(-0.172659\pi\)
\(90\) 0 0
\(91\) −94.5697 + 94.5697i −0.108941 + 0.108941i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 319.866 0.345448
\(96\) 0 0
\(97\) −936.077 −0.979837 −0.489919 0.871768i \(-0.662974\pi\)
−0.489919 + 0.871768i \(0.662974\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 1.58844 1.58844i 0.00156491 0.00156491i −0.706324 0.707889i \(-0.749648\pi\)
0.707889 + 0.706324i \(0.249648\pi\)
\(102\) 0 0
\(103\) 1388.28i 1.32807i 0.747700 + 0.664036i \(0.231158\pi\)
−0.747700 + 0.664036i \(0.768842\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −821.526 + 821.526i −0.742243 + 0.742243i −0.973009 0.230767i \(-0.925877\pi\)
0.230767 + 0.973009i \(0.425877\pi\)
\(108\) 0 0
\(109\) 532.797 + 532.797i 0.468190 + 0.468190i 0.901328 0.433138i \(-0.142594\pi\)
−0.433138 + 0.901328i \(0.642594\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 67.2680 0.0560003 0.0280002 0.999608i \(-0.491086\pi\)
0.0280002 + 0.999608i \(0.491086\pi\)
\(114\) 0 0
\(115\) 1147.19 + 1147.19i 0.930230 + 0.930230i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 193.696i 0.149211i
\(120\) 0 0
\(121\) 2758.92i 2.07282i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −943.262 943.262i −0.674943 0.674943i
\(126\) 0 0
\(127\) −1903.59 −1.33005 −0.665026 0.746820i \(-0.731579\pi\)
−0.665026 + 0.746820i \(0.731579\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 918.430 + 918.430i 0.612546 + 0.612546i 0.943609 0.331062i \(-0.107407\pi\)
−0.331062 + 0.943609i \(0.607407\pi\)
\(132\) 0 0
\(133\) 51.9451 51.9451i 0.0338662 0.0338662i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 477.234i 0.297612i −0.988866 0.148806i \(-0.952457\pi\)
0.988866 0.148806i \(-0.0475430\pi\)
\(138\) 0 0
\(139\) 1513.89 1513.89i 0.923788 0.923788i −0.0735064 0.997295i \(-0.523419\pi\)
0.997295 + 0.0735064i \(0.0234189\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −3201.37 −1.87211
\(144\) 0 0
\(145\) 1086.53 0.622285
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −375.353 + 375.353i −0.206377 + 0.206377i −0.802725 0.596349i \(-0.796618\pi\)
0.596349 + 0.802725i \(0.296618\pi\)
\(150\) 0 0
\(151\) 2997.52i 1.61546i −0.589553 0.807730i \(-0.700696\pi\)
0.589553 0.807730i \(-0.299304\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 1552.07 1552.07i 0.804293 0.804293i
\(156\) 0 0
\(157\) −1509.01 1509.01i −0.767082 0.767082i 0.210510 0.977592i \(-0.432488\pi\)
−0.977592 + 0.210510i \(0.932488\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 372.601 0.182392
\(162\) 0 0
\(163\) 1425.19 + 1425.19i 0.684844 + 0.684844i 0.961088 0.276244i \(-0.0890898\pi\)
−0.276244 + 0.961088i \(0.589090\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 792.415i 0.367179i −0.983003 0.183590i \(-0.941228\pi\)
0.983003 0.183590i \(-0.0587717\pi\)
\(168\) 0 0
\(169\) 308.861i 0.140583i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 773.594 + 773.594i 0.339972 + 0.339972i 0.856357 0.516384i \(-0.172722\pi\)
−0.516384 + 0.856357i \(0.672722\pi\)
\(174\) 0 0
\(175\) 27.5984 0.0119214
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 426.050 + 426.050i 0.177902 + 0.177902i 0.790441 0.612539i \(-0.209852\pi\)
−0.612539 + 0.790441i \(0.709852\pi\)
\(180\) 0 0
\(181\) −2618.06 + 2618.06i −1.07513 + 1.07513i −0.0781951 + 0.996938i \(0.524916\pi\)
−0.996938 + 0.0781951i \(0.975084\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 1383.02i 0.549631i
\(186\) 0 0
\(187\) −3278.50 + 3278.50i −1.28207 + 1.28207i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 3216.39 1.21848 0.609240 0.792986i \(-0.291475\pi\)
0.609240 + 0.792986i \(0.291475\pi\)
\(192\) 0 0
\(193\) 2852.57 1.06390 0.531950 0.846776i \(-0.321459\pi\)
0.531950 + 0.846776i \(0.321459\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −1609.02 + 1609.02i −0.581918 + 0.581918i −0.935430 0.353512i \(-0.884987\pi\)
0.353512 + 0.935430i \(0.384987\pi\)
\(198\) 0 0
\(199\) 747.136i 0.266146i −0.991106 0.133073i \(-0.957516\pi\)
0.991106 0.133073i \(-0.0424845\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 176.449 176.449i 0.0610062 0.0610062i
\(204\) 0 0
\(205\) 860.666 + 860.666i 0.293227 + 0.293227i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 1758.44 0.581981
\(210\) 0 0
\(211\) 2227.13 + 2227.13i 0.726645 + 0.726645i 0.969950 0.243305i \(-0.0782315\pi\)
−0.243305 + 0.969950i \(0.578231\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 517.995i 0.164311i
\(216\) 0 0
\(217\) 504.102i 0.157699i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 2566.23 + 2566.23i 0.781102 + 0.781102i
\(222\) 0 0
\(223\) 358.053 0.107520 0.0537601 0.998554i \(-0.482879\pi\)
0.0537601 + 0.998554i \(0.482879\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 3455.40 + 3455.40i 1.01032 + 1.01032i 0.999946 + 0.0103741i \(0.00330223\pi\)
0.0103741 + 0.999946i \(0.496698\pi\)
\(228\) 0 0
\(229\) −1430.03 + 1430.03i −0.412659 + 0.412659i −0.882664 0.470005i \(-0.844252\pi\)
0.470005 + 0.882664i \(0.344252\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 926.479i 0.260496i 0.991481 + 0.130248i \(0.0415774\pi\)
−0.991481 + 0.130248i \(0.958423\pi\)
\(234\) 0 0
\(235\) 4015.47 4015.47i 1.11464 1.11464i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −792.472 −0.214480 −0.107240 0.994233i \(-0.534201\pi\)
−0.107240 + 0.994233i \(0.534201\pi\)
\(240\) 0 0
\(241\) 1449.01 0.387299 0.193650 0.981071i \(-0.437967\pi\)
0.193650 + 0.981071i \(0.437967\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −2762.76 + 2762.76i −0.720433 + 0.720433i
\(246\) 0 0
\(247\) 1376.42i 0.354572i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −3580.04 + 3580.04i −0.900280 + 0.900280i −0.995460 0.0951802i \(-0.969657\pi\)
0.0951802 + 0.995460i \(0.469657\pi\)
\(252\) 0 0
\(253\) 6306.64 + 6306.64i 1.56717 + 1.56717i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 4708.87 1.14292 0.571461 0.820629i \(-0.306377\pi\)
0.571461 + 0.820629i \(0.306377\pi\)
\(258\) 0 0
\(259\) −224.598 224.598i −0.0538835 0.0538835i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 2967.82i 0.695830i −0.937526 0.347915i \(-0.886890\pi\)
0.937526 0.347915i \(-0.113110\pi\)
\(264\) 0 0
\(265\) 2460.53i 0.570374i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 663.633 + 663.633i 0.150418 + 0.150418i 0.778305 0.627887i \(-0.216080\pi\)
−0.627887 + 0.778305i \(0.716080\pi\)
\(270\) 0 0
\(271\) −8058.74 −1.80640 −0.903199 0.429223i \(-0.858788\pi\)
−0.903199 + 0.429223i \(0.858788\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 467.130 + 467.130i 0.102433 + 0.102433i
\(276\) 0 0
\(277\) 482.477 482.477i 0.104654 0.104654i −0.652841 0.757495i \(-0.726423\pi\)
0.757495 + 0.652841i \(0.226423\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 5899.10i 1.25235i 0.779682 + 0.626175i \(0.215381\pi\)
−0.779682 + 0.626175i \(0.784619\pi\)
\(282\) 0 0
\(283\) 679.897 679.897i 0.142812 0.142812i −0.632086 0.774898i \(-0.717801\pi\)
0.774898 + 0.632086i \(0.217801\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 279.538 0.0574935
\(288\) 0 0
\(289\) 343.118 0.0698388
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 3552.87 3552.87i 0.708398 0.708398i −0.257800 0.966198i \(-0.582998\pi\)
0.966198 + 0.257800i \(0.0829976\pi\)
\(294\) 0 0
\(295\) 4683.78i 0.924407i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 4936.50 4936.50i 0.954799 0.954799i
\(300\) 0 0
\(301\) 84.1205 + 84.1205i 0.0161084 + 0.0161084i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 3752.13 0.704415
\(306\) 0 0
\(307\) −2735.56 2735.56i −0.508556 0.508556i 0.405527 0.914083i \(-0.367088\pi\)
−0.914083 + 0.405527i \(0.867088\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 5796.70i 1.05692i 0.848960 + 0.528458i \(0.177229\pi\)
−0.848960 + 0.528458i \(0.822771\pi\)
\(312\) 0 0
\(313\) 8362.62i 1.51017i 0.655627 + 0.755085i \(0.272404\pi\)
−0.655627 + 0.755085i \(0.727596\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 344.406 + 344.406i 0.0610214 + 0.0610214i 0.736959 0.675938i \(-0.236261\pi\)
−0.675938 + 0.736959i \(0.736261\pi\)
\(318\) 0 0
\(319\) 5973.13 1.04837
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −1409.58 1409.58i −0.242820 0.242820i
\(324\) 0 0
\(325\) 365.644 365.644i 0.0624071 0.0624071i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 1304.20i 0.218549i
\(330\) 0 0
\(331\) −2687.86 + 2687.86i −0.446339 + 0.446339i −0.894135 0.447797i \(-0.852209\pi\)
0.447797 + 0.894135i \(0.352209\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 2289.27 0.373361
\(336\) 0 0
\(337\) −1795.31 −0.290199 −0.145099 0.989417i \(-0.546350\pi\)
−0.145099 + 0.989417i \(0.546350\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 8532.42 8532.42i 1.35500 1.35500i
\(342\) 0 0
\(343\) 1813.72i 0.285515i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −1967.33 + 1967.33i −0.304357 + 0.304357i −0.842716 0.538359i \(-0.819045\pi\)
0.538359 + 0.842716i \(0.319045\pi\)
\(348\) 0 0
\(349\) −7363.37 7363.37i −1.12938 1.12938i −0.990279 0.139097i \(-0.955580\pi\)
−0.139097 0.990279i \(-0.544420\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −10644.3 −1.60493 −0.802466 0.596698i \(-0.796479\pi\)
−0.802466 + 0.596698i \(0.796479\pi\)
\(354\) 0 0
\(355\) 3731.70 + 3731.70i 0.557911 + 0.557911i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 7459.42i 1.09664i 0.836269 + 0.548319i \(0.184732\pi\)
−0.836269 + 0.548319i \(0.815268\pi\)
\(360\) 0 0
\(361\) 6102.96i 0.889775i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 2136.65 + 2136.65i 0.306403 + 0.306403i
\(366\) 0 0
\(367\) 6251.35 0.889149 0.444574 0.895742i \(-0.353355\pi\)
0.444574 + 0.895742i \(0.353355\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −399.582 399.582i −0.0559171 0.0559171i
\(372\) 0 0
\(373\) 8911.86 8911.86i 1.23710 1.23710i 0.275921 0.961180i \(-0.411017\pi\)
0.961180 0.275921i \(-0.0889827\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 4675.45i 0.638721i
\(378\) 0 0
\(379\) −1184.03 + 1184.03i −0.160473 + 0.160473i −0.782776 0.622303i \(-0.786197\pi\)
0.622303 + 0.782776i \(0.286197\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −2880.38 −0.384283 −0.192142 0.981367i \(-0.561543\pi\)
−0.192142 + 0.981367i \(0.561543\pi\)
\(384\) 0 0
\(385\) 1987.66 0.263119
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −9244.24 + 9244.24i −1.20489 + 1.20489i −0.232226 + 0.972662i \(0.574601\pi\)
−0.972662 + 0.232226i \(0.925399\pi\)
\(390\) 0 0
\(391\) 10110.9i 1.30774i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 2658.52 2658.52i 0.338645 0.338645i
\(396\) 0 0
\(397\) −4257.80 4257.80i −0.538270 0.538270i 0.384751 0.923020i \(-0.374287\pi\)
−0.923020 + 0.384751i \(0.874287\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −12722.6 −1.58437 −0.792187 0.610278i \(-0.791058\pi\)
−0.792187 + 0.610278i \(0.791058\pi\)
\(402\) 0 0
\(403\) −6678.72 6678.72i −0.825535 0.825535i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 7603.08i 0.925972i
\(408\) 0 0
\(409\) 232.991i 0.0281678i 0.999901 + 0.0140839i \(0.00448320\pi\)
−0.999901 + 0.0140839i \(0.995517\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 760.629 + 760.629i 0.0906250 + 0.0906250i
\(414\) 0 0
\(415\) 9277.08 1.09734
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −6125.69 6125.69i −0.714223 0.714223i 0.253193 0.967416i \(-0.418519\pi\)
−0.967416 + 0.253193i \(0.918519\pi\)
\(420\) 0 0
\(421\) −8308.44 + 8308.44i −0.961825 + 0.961825i −0.999298 0.0374725i \(-0.988069\pi\)
0.0374725 + 0.999298i \(0.488069\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 748.907i 0.0854760i
\(426\) 0 0
\(427\) 609.333 609.333i 0.0690579 0.0690579i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 8737.57 0.976506 0.488253 0.872702i \(-0.337634\pi\)
0.488253 + 0.872702i \(0.337634\pi\)
\(432\) 0 0
\(433\) −11627.5 −1.29049 −0.645247 0.763974i \(-0.723245\pi\)
−0.645247 + 0.763974i \(0.723245\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −2711.51 + 2711.51i −0.296817 + 0.296817i
\(438\) 0 0
\(439\) 17631.8i 1.91690i 0.285261 + 0.958450i \(0.407920\pi\)
−0.285261 + 0.958450i \(0.592080\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −4549.81 + 4549.81i −0.487964 + 0.487964i −0.907663 0.419699i \(-0.862136\pi\)
0.419699 + 0.907663i \(0.362136\pi\)
\(444\) 0 0
\(445\) 7130.62 + 7130.62i 0.759604 + 0.759604i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 12926.5 1.35867 0.679334 0.733830i \(-0.262269\pi\)
0.679334 + 0.733830i \(0.262269\pi\)
\(450\) 0 0
\(451\) 4731.46 + 4731.46i 0.494004 + 0.494004i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 1555.84i 0.160305i
\(456\) 0 0
\(457\) 9320.32i 0.954018i 0.878898 + 0.477009i \(0.158279\pi\)
−0.878898 + 0.477009i \(0.841721\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −12885.0 12885.0i −1.30177 1.30177i −0.927200 0.374566i \(-0.877792\pi\)
−0.374566 0.927200i \(-0.622208\pi\)
\(462\) 0 0
\(463\) −7038.37 −0.706482 −0.353241 0.935532i \(-0.614920\pi\)
−0.353241 + 0.935532i \(0.614920\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 6001.76 + 6001.76i 0.594707 + 0.594707i 0.938899 0.344192i \(-0.111847\pi\)
−0.344192 + 0.938899i \(0.611847\pi\)
\(468\) 0 0
\(469\) 371.769 371.769i 0.0366028 0.0366028i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 2847.65i 0.276818i
\(474\) 0 0
\(475\) −200.840 + 200.840i −0.0194004 + 0.0194004i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −587.317 −0.0560234 −0.0280117 0.999608i \(-0.508918\pi\)
−0.0280117 + 0.999608i \(0.508918\pi\)
\(480\) 0 0
\(481\) −5951.28 −0.564148
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 7700.05 7700.05i 0.720910 0.720910i
\(486\) 0 0
\(487\) 8366.45i 0.778481i 0.921136 + 0.389240i \(0.127262\pi\)
−0.921136 + 0.389240i \(0.872738\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 1529.30 1529.30i 0.140563 0.140563i −0.633324 0.773887i \(-0.718310\pi\)
0.773887 + 0.633324i \(0.218310\pi\)
\(492\) 0 0
\(493\) −4788.09 4788.09i −0.437413 0.437413i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 1212.03 0.109390
\(498\) 0 0
\(499\) −11364.5 11364.5i −1.01952 1.01952i −0.999806 0.0197191i \(-0.993723\pi\)
−0.0197191 0.999806i \(-0.506277\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 12570.2i 1.11427i −0.830421 0.557137i \(-0.811900\pi\)
0.830421 0.557137i \(-0.188100\pi\)
\(504\) 0 0
\(505\) 26.1326i 0.00230274i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −11880.4 11880.4i −1.03456 1.03456i −0.999381 0.0351750i \(-0.988801\pi\)
−0.0351750 0.999381i \(-0.511199\pi\)
\(510\) 0 0
\(511\) 693.968 0.0600770
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −11419.8 11419.8i −0.977122 0.977122i
\(516\) 0 0
\(517\) 22074.8 22074.8i 1.87785 1.87785i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 6612.98i 0.556085i 0.960569 + 0.278042i \(0.0896856\pi\)
−0.960569 + 0.278042i \(0.910314\pi\)
\(522\) 0 0
\(523\) −5129.30 + 5129.30i −0.428850 + 0.428850i −0.888236 0.459387i \(-0.848069\pi\)
0.459387 + 0.888236i \(0.348069\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −13679.3 −1.13070
\(528\) 0 0
\(529\) −7282.60 −0.598553
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 3703.53 3703.53i 0.300972 0.300972i
\(534\) 0 0
\(535\) 13515.5i 1.09220i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −15188.1 + 15188.1i −1.21372 + 1.21372i
\(540\) 0 0
\(541\) −10968.5 10968.5i −0.871672 0.871672i 0.120983 0.992655i \(-0.461395\pi\)
−0.992655 + 0.120983i \(0.961395\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −8765.44 −0.688936
\(546\) 0 0
\(547\) −13088.8 13088.8i −1.02311 1.02311i −0.999727 0.0233784i \(-0.992558\pi\)
−0.0233784 0.999727i \(-0.507442\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 2568.12i 0.198558i
\(552\) 0 0
\(553\) 863.469i 0.0663986i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −5049.87 5049.87i −0.384147 0.384147i 0.488447 0.872594i \(-0.337564\pi\)
−0.872594 + 0.488447i \(0.837564\pi\)
\(558\) 0 0
\(559\) 2228.98 0.168651
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −3249.06 3249.06i −0.243217 0.243217i 0.574962 0.818180i \(-0.305017\pi\)
−0.818180 + 0.574962i \(0.805017\pi\)
\(564\) 0 0
\(565\) −553.338 + 553.338i −0.0412019 + 0.0412019i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 2806.05i 0.206741i −0.994643 0.103371i \(-0.967037\pi\)
0.994643 0.103371i \(-0.0329628\pi\)
\(570\) 0 0
\(571\) 12038.8 12038.8i 0.882324 0.882324i −0.111446 0.993770i \(-0.535548\pi\)
0.993770 + 0.111446i \(0.0355483\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −1440.62 −0.104484
\(576\) 0 0
\(577\) 7206.84 0.519973 0.259987 0.965612i \(-0.416282\pi\)
0.259987 + 0.965612i \(0.416282\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 1506.57 1506.57i 0.107578 0.107578i
\(582\) 0 0
\(583\) 13526.6i 0.960918i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 10377.0 10377.0i 0.729647 0.729647i −0.240903 0.970549i \(-0.577443\pi\)
0.970549 + 0.240903i \(0.0774435\pi\)
\(588\) 0 0
\(589\) 3668.48 + 3668.48i 0.256633 + 0.256633i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 4758.60 0.329531 0.164766 0.986333i \(-0.447313\pi\)
0.164766 + 0.986333i \(0.447313\pi\)
\(594\) 0 0
\(595\) −1593.32 1593.32i −0.109781 0.109781i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 14256.4i 0.972455i 0.873832 + 0.486227i \(0.161627\pi\)
−0.873832 + 0.486227i \(0.838373\pi\)
\(600\) 0 0
\(601\) 10385.2i 0.704862i 0.935838 + 0.352431i \(0.114645\pi\)
−0.935838 + 0.352431i \(0.885355\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 22694.5 + 22694.5i 1.52506 + 1.52506i
\(606\) 0 0
\(607\) 16243.6 1.08618 0.543088 0.839676i \(-0.317255\pi\)
0.543088 + 0.839676i \(0.317255\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −17279.0 17279.0i −1.14408 1.14408i
\(612\) 0 0
\(613\) −500.502 + 500.502i −0.0329773 + 0.0329773i −0.723403 0.690426i \(-0.757423\pi\)
0.690426 + 0.723403i \(0.257423\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 11575.9i 0.755316i −0.925945 0.377658i \(-0.876729\pi\)
0.925945 0.377658i \(-0.123271\pi\)
\(618\) 0 0
\(619\) −18356.1 + 18356.1i −1.19191 + 1.19191i −0.215380 + 0.976530i \(0.569099\pi\)
−0.976530 + 0.215380i \(0.930901\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 2315.98 0.148937
\(624\) 0 0
\(625\) 16809.5 1.07581
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −6094.66 + 6094.66i −0.386343 + 0.386343i
\(630\) 0 0
\(631\) 10224.8i 0.645079i 0.946556 + 0.322539i \(0.104537\pi\)
−0.946556 + 0.322539i \(0.895463\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 15658.7 15658.7i 0.978578 0.978578i
\(636\) 0 0
\(637\) 11888.4 + 11888.4i 0.739461 + 0.739461i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −19804.4 −1.22032 −0.610162 0.792277i \(-0.708896\pi\)
−0.610162 + 0.792277i \(0.708896\pi\)
\(642\) 0 0
\(643\) −15680.7 15680.7i −0.961723 0.961723i 0.0375712 0.999294i \(-0.488038\pi\)
−0.999294 + 0.0375712i \(0.988038\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 9232.26i 0.560985i −0.959856 0.280493i \(-0.909502\pi\)
0.959856 0.280493i \(-0.0904978\pi\)
\(648\) 0 0
\(649\) 25748.8i 1.55736i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 19697.9 + 19697.9i 1.18046 + 1.18046i 0.979626 + 0.200833i \(0.0643648\pi\)
0.200833 + 0.979626i \(0.435635\pi\)
\(654\) 0 0
\(655\) −15109.8 −0.901355
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 3888.06 + 3888.06i 0.229829 + 0.229829i 0.812621 0.582792i \(-0.198040\pi\)
−0.582792 + 0.812621i \(0.698040\pi\)
\(660\) 0 0
\(661\) −8110.20 + 8110.20i −0.477232 + 0.477232i −0.904245 0.427013i \(-0.859566\pi\)
0.427013 + 0.904245i \(0.359566\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 854.587i 0.0498338i
\(666\) 0 0
\(667\) −9210.54 + 9210.54i −0.534683 + 0.534683i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 20627.1 1.18674
\(672\) 0 0
\(673\) −28428.2 −1.62827 −0.814135 0.580676i \(-0.802788\pi\)
−0.814135 + 0.580676i \(0.802788\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 16967.4 16967.4i 0.963235 0.963235i −0.0361128 0.999348i \(-0.511498\pi\)
0.999348 + 0.0361128i \(0.0114975\pi\)
\(678\) 0 0
\(679\) 2500.92i 0.141350i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −9550.16 + 9550.16i −0.535032 + 0.535032i −0.922066 0.387034i \(-0.873500\pi\)
0.387034 + 0.922066i \(0.373500\pi\)
\(684\) 0 0
\(685\) 3925.66 + 3925.66i 0.218966 + 0.218966i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −10587.9 −0.585439
\(690\) 0 0
\(691\) 20859.7 + 20859.7i 1.14839 + 1.14839i 0.986868 + 0.161527i \(0.0516418\pi\)
0.161527 + 0.986868i \(0.448358\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 24906.1i 1.35934i
\(696\) 0 0
\(697\) 7585.52i 0.412227i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −23495.4 23495.4i −1.26592 1.26592i −0.948178 0.317740i \(-0.897076\pi\)
−0.317740 0.948178i \(-0.602924\pi\)
\(702\) 0 0
\(703\) 3268.91 0.175376
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 4.24384 + 4.24384i 0.000225751 + 0.000225751i
\(708\) 0 0
\(709\) 4559.45 4559.45i 0.241515 0.241515i −0.575962 0.817477i \(-0.695372\pi\)
0.817477 + 0.575962i \(0.195372\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 26313.9i 1.38214i
\(714\) 0 0
\(715\) 26334.1 26334.1i 1.37740 1.37740i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −6494.67 −0.336871 −0.168436 0.985713i \(-0.553872\pi\)
−0.168436 + 0.985713i \(0.553872\pi\)
\(720\) 0 0
\(721\) −3709.08 −0.191586
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −682.221 + 682.221i −0.0349476 + 0.0349476i
\(726\) 0 0
\(727\) 24866.4i 1.26856i 0.773103 + 0.634280i \(0.218704\pi\)
−0.773103 + 0.634280i \(0.781296\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 2282.68 2282.68i 0.115497 0.115497i
\(732\) 0 0
\(733\) −14914.3 14914.3i −0.751533 0.751533i 0.223232 0.974765i \(-0.428339\pi\)
−0.974765 + 0.223232i \(0.928339\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 12585.1 0.629008
\(738\) 0 0
\(739\) −8451.86 8451.86i −0.420713 0.420713i 0.464737 0.885449i \(-0.346149\pi\)
−0.885449 + 0.464737i \(0.846149\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 5622.43i 0.277614i −0.990319 0.138807i \(-0.955673\pi\)
0.990319 0.138807i \(-0.0443267\pi\)
\(744\) 0 0
\(745\) 6175.21i 0.303681i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −2194.88 2194.88i −0.107075 0.107075i
\(750\) 0 0
\(751\) 32314.9 1.57016 0.785079 0.619396i \(-0.212622\pi\)
0.785079 + 0.619396i \(0.212622\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 24657.2 + 24657.2i 1.18857 + 1.18857i
\(756\) 0 0
\(757\) 12692.8 12692.8i 0.609418 0.609418i −0.333376 0.942794i \(-0.608188\pi\)
0.942794 + 0.333376i \(0.108188\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 13108.2i 0.624404i 0.950016 + 0.312202i \(0.101067\pi\)
−0.950016 + 0.312202i \(0.898933\pi\)
\(762\) 0 0
\(763\) −1423.48 + 1423.48i −0.0675404 + 0.0675404i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 20154.8 0.948822
\(768\) 0 0
\(769\) 23661.2 1.10955 0.554776 0.832000i \(-0.312804\pi\)
0.554776 + 0.832000i \(0.312804\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −21370.5 + 21370.5i −0.994362 + 0.994362i −0.999984 0.00562228i \(-0.998210\pi\)
0.00562228 + 0.999984i \(0.498210\pi\)
\(774\) 0 0
\(775\) 1949.06i 0.0903384i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −2034.27 + 2034.27i −0.0935627 + 0.0935627i
\(780\) 0 0
\(781\) 20514.8 + 20514.8i 0.939921 + 0.939921i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 24825.8 1.12875
\(786\) 0 0
\(787\) 20890.9 + 20890.9i 0.946226 + 0.946226i 0.998626 0.0524002i \(-0.0166872\pi\)
−0.0524002 + 0.998626i \(0.516687\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 179.720i 0.00807853i
\(792\) 0 0
\(793\) 16145.8i 0.723020i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 6834.83 + 6834.83i 0.303767 + 0.303767i 0.842486 0.538719i \(-0.181092\pi\)
−0.538719 + 0.842486i \(0.681092\pi\)
\(798\) 0 0
\(799\) −35390.5 −1.56699
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 11746.1 + 11746.1i 0.516203 + 0.516203i
\(804\) 0