Properties

Label 2520.2.t.k.1009.4
Level $2520$
Weight $2$
Character 2520.1009
Analytic conductor $20.122$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2520 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2520.t (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(20.1223013094\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.350464.1
Defining polynomial: \( x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: no (minimal twist has level 840)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1009.4
Root \(1.45161 - 1.45161i\) of defining polynomial
Character \(\chi\) \(=\) 2520.1009
Dual form 2520.2.t.k.1009.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.311108 + 2.21432i) q^{5} -1.00000i q^{7} +O(q^{10})\) \(q+(0.311108 + 2.21432i) q^{5} -1.00000i q^{7} +5.05086 q^{11} -3.37778i q^{13} -7.18421i q^{17} -8.23506 q^{19} -6.23506i q^{23} +(-4.80642 + 1.37778i) q^{25} -2.00000 q^{29} -4.62222 q^{31} +(2.21432 - 0.311108i) q^{35} -4.85728i q^{37} +3.37778 q^{41} -1.24443i q^{43} -1.00000 q^{49} +4.62222i q^{53} +(1.57136 + 11.1842i) q^{55} -11.6128 q^{59} +0.488863 q^{61} +(7.47949 - 1.05086i) q^{65} +3.61285i q^{67} +10.2953 q^{71} -16.2351i q^{73} -5.05086i q^{77} -1.24443 q^{79} +11.6128i q^{83} +(15.9081 - 2.23506i) q^{85} +6.99063 q^{89} -3.37778 q^{91} +(-2.56199 - 18.2351i) q^{95} -8.23506i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 2 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 2 q^{5} + 4 q^{11} + 4 q^{19} - 2 q^{25} - 12 q^{29} - 28 q^{31} + 20 q^{41} - 6 q^{49} + 36 q^{55} - 16 q^{59} + 4 q^{61} - 8 q^{65} + 36 q^{71} - 8 q^{79} + 16 q^{85} - 12 q^{89} - 20 q^{91} + 12 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2520\mathbb{Z}\right)^\times\).

\(n\) \(281\) \(631\) \(1081\) \(1261\) \(2017\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) 0.311108 + 2.21432i 0.139132 + 0.990274i
\(6\) 0 0
\(7\) 1.00000i 0.377964i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 5.05086 1.52289 0.761445 0.648229i \(-0.224490\pi\)
0.761445 + 0.648229i \(0.224490\pi\)
\(12\) 0 0
\(13\) 3.37778i 0.936829i −0.883509 0.468414i \(-0.844825\pi\)
0.883509 0.468414i \(-0.155175\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 7.18421i 1.74243i −0.490905 0.871213i \(-0.663334\pi\)
0.490905 0.871213i \(-0.336666\pi\)
\(18\) 0 0
\(19\) −8.23506 −1.88925 −0.944627 0.328147i \(-0.893576\pi\)
−0.944627 + 0.328147i \(0.893576\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 6.23506i 1.30010i −0.759891 0.650050i \(-0.774748\pi\)
0.759891 0.650050i \(-0.225252\pi\)
\(24\) 0 0
\(25\) −4.80642 + 1.37778i −0.961285 + 0.275557i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −2.00000 −0.371391 −0.185695 0.982607i \(-0.559454\pi\)
−0.185695 + 0.982607i \(0.559454\pi\)
\(30\) 0 0
\(31\) −4.62222 −0.830174 −0.415087 0.909782i \(-0.636249\pi\)
−0.415087 + 0.909782i \(0.636249\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 2.21432 0.311108i 0.374288 0.0525868i
\(36\) 0 0
\(37\) 4.85728i 0.798532i −0.916835 0.399266i \(-0.869265\pi\)
0.916835 0.399266i \(-0.130735\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 3.37778 0.527521 0.263761 0.964588i \(-0.415037\pi\)
0.263761 + 0.964588i \(0.415037\pi\)
\(42\) 0 0
\(43\) 1.24443i 0.189774i −0.995488 0.0948870i \(-0.969751\pi\)
0.995488 0.0948870i \(-0.0302490\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) 0 0
\(49\) −1.00000 −0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 4.62222i 0.634910i 0.948273 + 0.317455i \(0.102828\pi\)
−0.948273 + 0.317455i \(0.897172\pi\)
\(54\) 0 0
\(55\) 1.57136 + 11.1842i 0.211882 + 1.50808i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −11.6128 −1.51186 −0.755932 0.654650i \(-0.772816\pi\)
−0.755932 + 0.654650i \(0.772816\pi\)
\(60\) 0 0
\(61\) 0.488863 0.0625924 0.0312962 0.999510i \(-0.490036\pi\)
0.0312962 + 0.999510i \(0.490036\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 7.47949 1.05086i 0.927717 0.130343i
\(66\) 0 0
\(67\) 3.61285i 0.441380i 0.975344 + 0.220690i \(0.0708308\pi\)
−0.975344 + 0.220690i \(0.929169\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 10.2953 1.22183 0.610913 0.791698i \(-0.290803\pi\)
0.610913 + 0.791698i \(0.290803\pi\)
\(72\) 0 0
\(73\) 16.2351i 1.90017i −0.311991 0.950085i \(-0.600996\pi\)
0.311991 0.950085i \(-0.399004\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 5.05086i 0.575598i
\(78\) 0 0
\(79\) −1.24443 −0.140009 −0.0700047 0.997547i \(-0.522301\pi\)
−0.0700047 + 0.997547i \(0.522301\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 11.6128i 1.27468i 0.770585 + 0.637338i \(0.219964\pi\)
−0.770585 + 0.637338i \(0.780036\pi\)
\(84\) 0 0
\(85\) 15.9081 2.23506i 1.72548 0.242427i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 6.99063 0.741006 0.370503 0.928831i \(-0.379185\pi\)
0.370503 + 0.928831i \(0.379185\pi\)
\(90\) 0 0
\(91\) −3.37778 −0.354088
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −2.56199 18.2351i −0.262855 1.87088i
\(96\) 0 0
\(97\) 8.23506i 0.836144i −0.908414 0.418072i \(-0.862706\pi\)
0.908414 0.418072i \(-0.137294\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 9.47949 0.943245 0.471622 0.881801i \(-0.343669\pi\)
0.471622 + 0.881801i \(0.343669\pi\)
\(102\) 0 0
\(103\) 16.8573i 1.66100i −0.557021 0.830499i \(-0.688056\pi\)
0.557021 0.830499i \(-0.311944\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 15.4795i 1.49646i −0.663440 0.748230i \(-0.730904\pi\)
0.663440 0.748230i \(-0.269096\pi\)
\(108\) 0 0
\(109\) 1.61285 0.154483 0.0772414 0.997012i \(-0.475389\pi\)
0.0772414 + 0.997012i \(0.475389\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 1.86665i 0.175599i 0.996138 + 0.0877997i \(0.0279835\pi\)
−0.996138 + 0.0877997i \(0.972016\pi\)
\(114\) 0 0
\(115\) 13.8064 1.93978i 1.28746 0.180885i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −7.18421 −0.658575
\(120\) 0 0
\(121\) 14.5111 1.31919
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −4.54617 10.2143i −0.406622 0.913597i
\(126\) 0 0
\(127\) 12.8573i 1.14090i 0.821333 + 0.570450i \(0.193231\pi\)
−0.821333 + 0.570450i \(0.806769\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −21.7146 −1.89721 −0.948605 0.316463i \(-0.897505\pi\)
−0.948605 + 0.316463i \(0.897505\pi\)
\(132\) 0 0
\(133\) 8.23506i 0.714071i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 9.47949i 0.809888i −0.914342 0.404944i \(-0.867291\pi\)
0.914342 0.404944i \(-0.132709\pi\)
\(138\) 0 0
\(139\) −10.1334 −0.859500 −0.429750 0.902948i \(-0.641398\pi\)
−0.429750 + 0.902948i \(0.641398\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 17.0607i 1.42669i
\(144\) 0 0
\(145\) −0.622216 4.42864i −0.0516722 0.367778i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 7.24443 0.593487 0.296743 0.954957i \(-0.404099\pi\)
0.296743 + 0.954957i \(0.404099\pi\)
\(150\) 0 0
\(151\) −8.85728 −0.720795 −0.360398 0.932799i \(-0.617359\pi\)
−0.360398 + 0.932799i \(0.617359\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −1.43801 10.2351i −0.115504 0.822100i
\(156\) 0 0
\(157\) 13.4795i 1.07578i 0.843015 + 0.537890i \(0.180779\pi\)
−0.843015 + 0.537890i \(0.819221\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −6.23506 −0.491392
\(162\) 0 0
\(163\) 4.00000i 0.313304i −0.987654 0.156652i \(-0.949930\pi\)
0.987654 0.156652i \(-0.0500701\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 2.10171i 0.162635i −0.996688 0.0813176i \(-0.974087\pi\)
0.996688 0.0813176i \(-0.0259128\pi\)
\(168\) 0 0
\(169\) 1.59057 0.122352
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 11.1842i 0.850320i 0.905118 + 0.425160i \(0.139782\pi\)
−0.905118 + 0.425160i \(0.860218\pi\)
\(174\) 0 0
\(175\) 1.37778 + 4.80642i 0.104151 + 0.363331i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 20.6637 1.54448 0.772239 0.635332i \(-0.219137\pi\)
0.772239 + 0.635332i \(0.219137\pi\)
\(180\) 0 0
\(181\) 24.9590 1.85519 0.927594 0.373591i \(-0.121874\pi\)
0.927594 + 0.373591i \(0.121874\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 10.7556 1.51114i 0.790765 0.111101i
\(186\) 0 0
\(187\) 36.2864i 2.65352i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −9.52098 −0.688914 −0.344457 0.938802i \(-0.611937\pi\)
−0.344457 + 0.938802i \(0.611937\pi\)
\(192\) 0 0
\(193\) 22.9590i 1.65262i 0.563212 + 0.826312i \(0.309565\pi\)
−0.563212 + 0.826312i \(0.690435\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 19.8479i 1.41411i 0.707161 + 0.707053i \(0.249976\pi\)
−0.707161 + 0.707053i \(0.750024\pi\)
\(198\) 0 0
\(199\) 8.23506 0.583768 0.291884 0.956454i \(-0.405718\pi\)
0.291884 + 0.956454i \(0.405718\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 2.00000i 0.140372i
\(204\) 0 0
\(205\) 1.05086 + 7.47949i 0.0733949 + 0.522391i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −41.5941 −2.87712
\(210\) 0 0
\(211\) −11.6128 −0.799461 −0.399731 0.916633i \(-0.630896\pi\)
−0.399731 + 0.916633i \(0.630896\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 2.75557 0.387152i 0.187928 0.0264036i
\(216\) 0 0
\(217\) 4.62222i 0.313776i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −24.2667 −1.63236
\(222\) 0 0
\(223\) 2.48886i 0.166667i −0.996522 0.0833333i \(-0.973443\pi\)
0.996522 0.0833333i \(-0.0265566\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 0.857279i 0.0568996i 0.999595 + 0.0284498i \(0.00905708\pi\)
−0.999595 + 0.0284498i \(0.990943\pi\)
\(228\) 0 0
\(229\) 14.4701 0.956213 0.478106 0.878302i \(-0.341323\pi\)
0.478106 + 0.878302i \(0.341323\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 3.96836i 0.259976i −0.991516 0.129988i \(-0.958506\pi\)
0.991516 0.129988i \(-0.0414938\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 1.90813 0.123427 0.0617135 0.998094i \(-0.480344\pi\)
0.0617135 + 0.998094i \(0.480344\pi\)
\(240\) 0 0
\(241\) 0.755569 0.0486705 0.0243352 0.999704i \(-0.492253\pi\)
0.0243352 + 0.999704i \(0.492253\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −0.311108 2.21432i −0.0198759 0.141468i
\(246\) 0 0
\(247\) 27.8163i 1.76991i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 9.12399 0.575901 0.287950 0.957645i \(-0.407026\pi\)
0.287950 + 0.957645i \(0.407026\pi\)
\(252\) 0 0
\(253\) 31.4924i 1.97991i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 1.28592i 0.0802134i 0.999195 + 0.0401067i \(0.0127698\pi\)
−0.999195 + 0.0401067i \(0.987230\pi\)
\(258\) 0 0
\(259\) −4.85728 −0.301817
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 7.00937i 0.432216i 0.976369 + 0.216108i \(0.0693364\pi\)
−0.976369 + 0.216108i \(0.930664\pi\)
\(264\) 0 0
\(265\) −10.2351 + 1.43801i −0.628735 + 0.0883361i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 23.1941 1.41417 0.707083 0.707130i \(-0.250011\pi\)
0.707083 + 0.707130i \(0.250011\pi\)
\(270\) 0 0
\(271\) 7.11108 0.431967 0.215984 0.976397i \(-0.430704\pi\)
0.215984 + 0.976397i \(0.430704\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −24.2766 + 6.95899i −1.46393 + 0.419643i
\(276\) 0 0
\(277\) 7.34614i 0.441387i 0.975343 + 0.220693i \(0.0708320\pi\)
−0.975343 + 0.220693i \(0.929168\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 19.9813 1.19198 0.595991 0.802991i \(-0.296759\pi\)
0.595991 + 0.802991i \(0.296759\pi\)
\(282\) 0 0
\(283\) 4.85728i 0.288735i −0.989524 0.144368i \(-0.953885\pi\)
0.989524 0.144368i \(-0.0461148\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 3.37778i 0.199384i
\(288\) 0 0
\(289\) −34.6128 −2.03605
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 11.1842i 0.653388i −0.945130 0.326694i \(-0.894065\pi\)
0.945130 0.326694i \(-0.105935\pi\)
\(294\) 0 0
\(295\) −3.61285 25.7146i −0.210348 1.49716i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −21.0607 −1.21797
\(300\) 0 0
\(301\) −1.24443 −0.0717278
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0.152089 + 1.08250i 0.00870859 + 0.0619837i
\(306\) 0 0
\(307\) 23.3461i 1.33243i −0.745758 0.666217i \(-0.767912\pi\)
0.745758 0.666217i \(-0.232088\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 32.8573 1.86317 0.931583 0.363530i \(-0.118428\pi\)
0.931583 + 0.363530i \(0.118428\pi\)
\(312\) 0 0
\(313\) 28.8256i 1.62932i −0.579938 0.814661i \(-0.696923\pi\)
0.579938 0.814661i \(-0.303077\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 25.3590i 1.42431i −0.702024 0.712153i \(-0.747720\pi\)
0.702024 0.712153i \(-0.252280\pi\)
\(318\) 0 0
\(319\) −10.1017 −0.565587
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 59.1624i 3.29188i
\(324\) 0 0
\(325\) 4.65386 + 16.2351i 0.258150 + 0.900559i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 1.89829 0.104339 0.0521697 0.998638i \(-0.483386\pi\)
0.0521697 + 0.998638i \(0.483386\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −8.00000 + 1.12399i −0.437087 + 0.0614099i
\(336\) 0 0
\(337\) 23.2257i 1.26518i 0.774485 + 0.632592i \(0.218009\pi\)
−0.774485 + 0.632592i \(0.781991\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −23.3461 −1.26426
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 7.47949i 0.401520i −0.979640 0.200760i \(-0.935659\pi\)
0.979640 0.200760i \(-0.0643412\pi\)
\(348\) 0 0
\(349\) −29.2257 −1.56442 −0.782208 0.623018i \(-0.785906\pi\)
−0.782208 + 0.623018i \(0.785906\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 30.4099i 1.61856i −0.587426 0.809278i \(-0.699859\pi\)
0.587426 0.809278i \(-0.300141\pi\)
\(354\) 0 0
\(355\) 3.20294 + 22.7971i 0.169995 + 1.20994i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −16.1936 −0.854664 −0.427332 0.904095i \(-0.640546\pi\)
−0.427332 + 0.904095i \(0.640546\pi\)
\(360\) 0 0
\(361\) 48.8163 2.56928
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 35.9496 5.05086i 1.88169 0.264374i
\(366\) 0 0
\(367\) 5.51114i 0.287679i −0.989601 0.143840i \(-0.954055\pi\)
0.989601 0.143840i \(-0.0459449\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 4.62222 0.239973
\(372\) 0 0
\(373\) 1.63158i 0.0844802i −0.999107 0.0422401i \(-0.986551\pi\)
0.999107 0.0422401i \(-0.0134494\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 6.75557i 0.347929i
\(378\) 0 0
\(379\) −20.8573 −1.07137 −0.535683 0.844419i \(-0.679946\pi\)
−0.535683 + 0.844419i \(0.679946\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 20.0830i 1.02619i 0.858331 + 0.513096i \(0.171502\pi\)
−0.858331 + 0.513096i \(0.828498\pi\)
\(384\) 0 0
\(385\) 11.1842 1.57136i 0.570000 0.0800839i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 33.2257 1.68461 0.842305 0.539001i \(-0.181198\pi\)
0.842305 + 0.539001i \(0.181198\pi\)
\(390\) 0 0
\(391\) −44.7940 −2.26533
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −0.387152 2.75557i −0.0194797 0.138648i
\(396\) 0 0
\(397\) 22.7239i 1.14048i 0.821478 + 0.570241i \(0.193150\pi\)
−0.821478 + 0.570241i \(0.806850\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −12.7556 −0.636983 −0.318491 0.947926i \(-0.603176\pi\)
−0.318491 + 0.947926i \(0.603176\pi\)
\(402\) 0 0
\(403\) 15.6128i 0.777731i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 24.5334i 1.21608i
\(408\) 0 0
\(409\) −27.4479 −1.35721 −0.678604 0.734504i \(-0.737415\pi\)
−0.678604 + 0.734504i \(0.737415\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 11.6128i 0.571431i
\(414\) 0 0
\(415\) −25.7146 + 3.61285i −1.26228 + 0.177348i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 2.36842 0.115705 0.0578524 0.998325i \(-0.481575\pi\)
0.0578524 + 0.998325i \(0.481575\pi\)
\(420\) 0 0
\(421\) 39.3274 1.91670 0.958350 0.285596i \(-0.0921914\pi\)
0.958350 + 0.285596i \(0.0921914\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 9.89829 + 34.5303i 0.480138 + 1.67497i
\(426\) 0 0
\(427\) 0.488863i 0.0236577i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −8.19358 −0.394671 −0.197335 0.980336i \(-0.563229\pi\)
−0.197335 + 0.980336i \(0.563229\pi\)
\(432\) 0 0
\(433\) 14.6035i 0.701798i 0.936413 + 0.350899i \(0.114124\pi\)
−0.936413 + 0.350899i \(0.885876\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 51.3461i 2.45622i
\(438\) 0 0
\(439\) −5.27607 −0.251813 −0.125907 0.992042i \(-0.540184\pi\)
−0.125907 + 0.992042i \(0.540184\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 18.5018i 0.879046i 0.898231 + 0.439523i \(0.144852\pi\)
−0.898231 + 0.439523i \(0.855148\pi\)
\(444\) 0 0
\(445\) 2.17484 + 15.4795i 0.103097 + 0.733798i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 11.7146 0.552844 0.276422 0.961036i \(-0.410851\pi\)
0.276422 + 0.961036i \(0.410851\pi\)
\(450\) 0 0
\(451\) 17.0607 0.803357
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −1.05086 7.47949i −0.0492648 0.350644i
\(456\) 0 0
\(457\) 18.9590i 0.886864i −0.896308 0.443432i \(-0.853761\pi\)
0.896308 0.443432i \(-0.146239\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 15.1111 0.703793 0.351897 0.936039i \(-0.385537\pi\)
0.351897 + 0.936039i \(0.385537\pi\)
\(462\) 0 0
\(463\) 22.5718i 1.04900i 0.851410 + 0.524501i \(0.175748\pi\)
−0.851410 + 0.524501i \(0.824252\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 22.3684i 1.03509i 0.855657 + 0.517543i \(0.173153\pi\)
−0.855657 + 0.517543i \(0.826847\pi\)
\(468\) 0 0
\(469\) 3.61285 0.166826
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 6.28544i 0.289005i
\(474\) 0 0
\(475\) 39.5812 11.3461i 1.81611 0.520597i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −32.8573 −1.50129 −0.750644 0.660707i \(-0.770256\pi\)
−0.750644 + 0.660707i \(0.770256\pi\)
\(480\) 0 0
\(481\) −16.4068 −0.748088
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 18.2351 2.56199i 0.828012 0.116334i
\(486\) 0 0
\(487\) 3.40943i 0.154496i 0.997012 + 0.0772479i \(0.0246133\pi\)
−0.997012 + 0.0772479i \(0.975387\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 33.7877 1.52482 0.762409 0.647096i \(-0.224017\pi\)
0.762409 + 0.647096i \(0.224017\pi\)
\(492\) 0 0
\(493\) 14.3684i 0.647121i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 10.2953i 0.461807i
\(498\) 0 0
\(499\) −13.6316 −0.610233 −0.305117 0.952315i \(-0.598695\pi\)
−0.305117 + 0.952315i \(0.598695\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 7.34614i 0.327548i 0.986498 + 0.163774i \(0.0523668\pi\)
−0.986498 + 0.163774i \(0.947633\pi\)
\(504\) 0 0
\(505\) 2.94914 + 20.9906i 0.131235 + 0.934071i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −15.9684 −0.707785 −0.353892 0.935286i \(-0.615142\pi\)
−0.353892 + 0.935286i \(0.615142\pi\)
\(510\) 0 0
\(511\) −16.2351 −0.718197
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 37.3274 5.24443i 1.64484 0.231097i
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 1.09234 0.0478564 0.0239282 0.999714i \(-0.492383\pi\)
0.0239282 + 0.999714i \(0.492383\pi\)
\(522\) 0 0
\(523\) 17.5111i 0.765709i −0.923809 0.382854i \(-0.874941\pi\)
0.923809 0.382854i \(-0.125059\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 33.2070i 1.44652i
\(528\) 0 0
\(529\) −15.8760 −0.690262
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 11.4094i 0.494197i
\(534\) 0 0
\(535\) 34.2766 4.81579i 1.48190 0.208205i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −5.05086 −0.217556
\(540\) 0 0
\(541\) −15.3274 −0.658977 −0.329488 0.944160i \(-0.606876\pi\)
−0.329488 + 0.944160i \(0.606876\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0.501770 + 3.57136i 0.0214934 + 0.152980i
\(546\) 0 0
\(547\) 5.32741i 0.227783i −0.993493 0.113892i \(-0.963668\pi\)
0.993493 0.113892i \(-0.0363317\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 16.4701 0.701651
\(552\) 0 0
\(553\) 1.24443i 0.0529186i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0.355509i 0.0150634i 0.999972 + 0.00753171i \(0.00239744\pi\)
−0.999972 + 0.00753171i \(0.997603\pi\)
\(558\) 0 0
\(559\) −4.20342 −0.177786
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 16.4701i 0.694133i 0.937841 + 0.347067i \(0.112822\pi\)
−0.937841 + 0.347067i \(0.887178\pi\)
\(564\) 0 0
\(565\) −4.13335 + 0.580728i −0.173891 + 0.0244314i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −20.9590 −0.878647 −0.439323 0.898329i \(-0.644782\pi\)
−0.439323 + 0.898329i \(0.644782\pi\)
\(570\) 0 0
\(571\) 17.5111 0.732818 0.366409 0.930454i \(-0.380587\pi\)
0.366409 + 0.930454i \(0.380587\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 8.59057 + 29.9684i 0.358252 + 1.24977i
\(576\) 0 0
\(577\) 0.152089i 0.00633155i −0.999995 0.00316577i \(-0.998992\pi\)
0.999995 0.00316577i \(-0.00100770\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 11.6128 0.481782
\(582\) 0 0
\(583\) 23.3461i 0.966898i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 34.1847i 1.41095i 0.708733 + 0.705476i \(0.249267\pi\)
−0.708733 + 0.705476i \(0.750733\pi\)
\(588\) 0 0
\(589\) 38.0642 1.56841
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 19.3047i 0.792747i −0.918089 0.396374i \(-0.870269\pi\)
0.918089 0.396374i \(-0.129731\pi\)
\(594\) 0 0
\(595\) −2.23506 15.9081i −0.0916287 0.652170i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −25.9081 −1.05858 −0.529289 0.848442i \(-0.677541\pi\)
−0.529289 + 0.848442i \(0.677541\pi\)
\(600\) 0 0
\(601\) −22.7368 −0.927455 −0.463727 0.885978i \(-0.653488\pi\)
−0.463727 + 0.885978i \(0.653488\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 4.51453 + 32.1323i 0.183542 + 1.30636i
\(606\) 0 0
\(607\) 32.9403i 1.33700i 0.743711 + 0.668502i \(0.233064\pi\)
−0.743711 + 0.668502i \(0.766936\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 13.1240i 0.530073i −0.964238 0.265036i \(-0.914616\pi\)
0.964238 0.265036i \(-0.0853840\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 18.2538i 0.734870i 0.930049 + 0.367435i \(0.119764\pi\)
−0.930049 + 0.367435i \(0.880236\pi\)
\(618\) 0 0
\(619\) −7.64449 −0.307258 −0.153629 0.988129i \(-0.549096\pi\)
−0.153629 + 0.988129i \(0.549096\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 6.99063i 0.280074i
\(624\) 0 0
\(625\) 21.2034 13.2444i 0.848137 0.529777i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −34.8957 −1.39138
\(630\) 0 0
\(631\) 28.6735 1.14148 0.570738 0.821132i \(-0.306657\pi\)
0.570738 + 0.821132i \(0.306657\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −28.4701 + 4.00000i −1.12980 + 0.158735i
\(636\) 0 0
\(637\) 3.37778i 0.133833i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −15.4479 −0.610153 −0.305077 0.952328i \(-0.598682\pi\)
−0.305077 + 0.952328i \(0.598682\pi\)
\(642\) 0 0
\(643\) 25.8350i 1.01883i 0.860520 + 0.509417i \(0.170139\pi\)
−0.860520 + 0.509417i \(0.829861\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 23.6128i 0.928317i −0.885752 0.464158i \(-0.846357\pi\)
0.885752 0.464158i \(-0.153643\pi\)
\(648\) 0 0
\(649\) −58.6548 −2.30240
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 36.7052i 1.43639i −0.695844 0.718193i \(-0.744970\pi\)
0.695844 0.718193i \(-0.255030\pi\)
\(654\) 0 0
\(655\) −6.75557 48.0830i −0.263962 1.87876i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 37.9911 1.47992 0.739962 0.672649i \(-0.234844\pi\)
0.739962 + 0.672649i \(0.234844\pi\)
\(660\) 0 0
\(661\) −49.2257 −1.91466 −0.957329 0.289001i \(-0.906677\pi\)
−0.957329 + 0.289001i \(0.906677\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −18.2351 + 2.56199i −0.707125 + 0.0993498i
\(666\) 0 0
\(667\) 12.4701i 0.482845i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 2.46917 0.0953214
\(672\) 0 0
\(673\) 11.2257i 0.432719i −0.976314 0.216359i \(-0.930582\pi\)
0.976314 0.216359i \(-0.0694183\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 9.55262i 0.367137i 0.983007 + 0.183569i \(0.0587649\pi\)
−0.983007 + 0.183569i \(0.941235\pi\)
\(678\) 0 0
\(679\) −8.23506 −0.316033
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 17.9684i 0.687540i 0.939054 + 0.343770i \(0.111704\pi\)
−0.939054 + 0.343770i \(0.888296\pi\)
\(684\) 0 0
\(685\) 20.9906 2.94914i 0.802011 0.112681i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 15.6128 0.594802
\(690\) 0 0
\(691\) 0.355509 0.0135242 0.00676211 0.999977i \(-0.497848\pi\)
0.00676211 + 0.999977i \(0.497848\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −3.15257 22.4385i −0.119584 0.851140i
\(696\) 0 0
\(697\) 24.2667i 0.919167i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −13.2257 −0.499528 −0.249764 0.968307i \(-0.580353\pi\)
−0.249764 + 0.968307i \(0.580353\pi\)
\(702\) 0 0
\(703\) 40.0000i 1.50863i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 9.47949i 0.356513i
\(708\) 0 0
\(709\) 10.9777 0.412277 0.206139 0.978523i \(-0.433910\pi\)
0.206139 + 0.978523i \(0.433910\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 28.8198i 1.07931i
\(714\) 0 0
\(715\) 37.7778 5.30772i 1.41281 0.198497i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −21.9813 −0.819763 −0.409881 0.912139i \(-0.634430\pi\)
−0.409881 + 0.912139i \(0.634430\pi\)
\(720\) 0 0
\(721\) −16.8573 −0.627798
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 9.61285 2.75557i 0.357012 0.102339i
\(726\) 0 0
\(727\) 13.0607i 0.484395i 0.970227 + 0.242197i \(0.0778681\pi\)
−0.970227 + 0.242197i \(0.922132\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −8.94025 −0.330667
\(732\) 0 0
\(733\) 13.5625i 0.500941i 0.968124 + 0.250471i \(0.0805853\pi\)
−0.968124 + 0.250471i \(0.919415\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 18.2480i 0.672173i
\(738\) 0 0
\(739\) −10.2854 −0.378356 −0.189178 0.981943i \(-0.560582\pi\)
−0.189178 + 0.981943i \(0.560582\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 21.4608i 0.787319i −0.919256 0.393659i \(-0.871209\pi\)
0.919256 0.393659i \(-0.128791\pi\)
\(744\) 0 0
\(745\) 2.25380 + 16.0415i 0.0825728 + 0.587715i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −15.4795 −0.565608
\(750\) 0 0
\(751\) 46.0642 1.68091 0.840454 0.541883i \(-0.182288\pi\)
0.840454 + 0.541883i \(0.182288\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −2.75557 19.6128i −0.100285 0.713785i
\(756\) 0 0
\(757\) 27.1052i 0.985157i −0.870268 0.492579i \(-0.836054\pi\)
0.870268 0.492579i \(-0.163946\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −39.4608 −1.43045 −0.715226 0.698894i \(-0.753676\pi\)
−0.715226 + 0.698894i \(0.753676\pi\)
\(762\) 0 0
\(763\) 1.61285i 0.0583890i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 39.2257i 1.41636i
\(768\) 0 0
\(769\) 7.51114 0.270859 0.135429 0.990787i \(-0.456759\pi\)
0.135429 + 0.990787i \(0.456759\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 1.46965i 0.0528596i −0.999651 0.0264298i \(-0.991586\pi\)
0.999651 0.0264298i \(-0.00841385\pi\)
\(774\) 0 0
\(775\) 22.2163 6.36842i 0.798034 0.228760i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −27.8163 −0.996621
\(780\) 0 0
\(781\) 52.0000 1.86071
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −29.8479 + 4.19358i −1.06532 + 0.149675i
\(786\) 0 0
\(787\) 16.2034i 0.577590i 0.957391 + 0.288795i \(0.0932545\pi\)
−0.957391 + 0.288795i \(0.906745\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 1.86665 0.0663703
\(792\) 0 0
\(793\) 1.65127i 0.0586384i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0.161933i 0.00573597i −0.999996 0.00286799i \(-0.999087\pi\)
0.999996 0.00286799i \(-0.000912909\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 82.0010i 2.89375i
\(804\) 0 0
\(805\) −1.93978 13.8064i −0.0683682 0.486613i
\(806\) 0 0
\(807\) 0