Properties

Label 8280.2.p.a.1241.18
Level $8280$
Weight $2$
Character 8280.1241
Analytic conductor $66.116$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 8280 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8280.p (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(66.1161328736\)
Analytic rank: \(0\)
Dimension: \(48\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1241.18
Character \(\chi\) \(=\) 8280.1241
Dual form 8280.2.p.a.1241.31

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{5} -1.44649i q^{7} +O(q^{10})\) \(q-1.00000 q^{5} -1.44649i q^{7} -1.36137 q^{11} -1.07559 q^{13} -0.324623 q^{17} -0.711387i q^{19} +(-0.999812 + 4.69046i) q^{23} +1.00000 q^{25} -2.07643i q^{29} +5.82838 q^{31} +1.44649i q^{35} +6.84151i q^{37} -1.86885i q^{41} -5.81876i q^{43} +12.1813i q^{47} +4.90766 q^{49} +7.33172 q^{53} +1.36137 q^{55} -9.74251i q^{59} -9.45083i q^{61} +1.07559 q^{65} -9.90647i q^{67} -13.5958i q^{71} -4.12968 q^{73} +1.96921i q^{77} +11.4503i q^{79} +0.800104 q^{83} +0.324623 q^{85} -8.45302 q^{89} +1.55583i q^{91} +0.711387i q^{95} -8.16643i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q - 48 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 48 q - 48 q^{5} - 8 q^{11} + 4 q^{23} + 48 q^{25} + 8 q^{31} - 32 q^{49} + 8 q^{55} - 16 q^{73} - 32 q^{83} - 8 q^{89}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/8280\mathbb{Z}\right)^\times\).

\(n\) \(1657\) \(2071\) \(3961\) \(4141\) \(4601\)
\(\chi(n)\) \(1\) \(1\) \(-1\) \(1\) \(-1\)

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
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) 1.44649i 0.546723i −0.961911 0.273361i \(-0.911865\pi\)
0.961911 0.273361i \(-0.0881355\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −1.36137 −0.410468 −0.205234 0.978713i \(-0.565795\pi\)
−0.205234 + 0.978713i \(0.565795\pi\)
\(12\) 0 0
\(13\) −1.07559 −0.298314 −0.149157 0.988814i \(-0.547656\pi\)
−0.149157 + 0.988814i \(0.547656\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −0.324623 −0.0787326 −0.0393663 0.999225i \(-0.512534\pi\)
−0.0393663 + 0.999225i \(0.512534\pi\)
\(18\) 0 0
\(19\) 0.711387i 0.163203i −0.996665 0.0816016i \(-0.973996\pi\)
0.996665 0.0816016i \(-0.0260035\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −0.999812 + 4.69046i −0.208475 + 0.978028i
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 2.07643i 0.385583i −0.981240 0.192792i \(-0.938246\pi\)
0.981240 0.192792i \(-0.0617541\pi\)
\(30\) 0 0
\(31\) 5.82838 1.04681 0.523404 0.852084i \(-0.324662\pi\)
0.523404 + 0.852084i \(0.324662\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 1.44649i 0.244502i
\(36\) 0 0
\(37\) 6.84151i 1.12474i 0.826886 + 0.562369i \(0.190110\pi\)
−0.826886 + 0.562369i \(0.809890\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 1.86885i 0.291865i −0.989295 0.145933i \(-0.953382\pi\)
0.989295 0.145933i \(-0.0466183\pi\)
\(42\) 0 0
\(43\) 5.81876i 0.887353i −0.896187 0.443677i \(-0.853674\pi\)
0.896187 0.443677i \(-0.146326\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 12.1813i 1.77682i 0.459047 + 0.888412i \(0.348191\pi\)
−0.459047 + 0.888412i \(0.651809\pi\)
\(48\) 0 0
\(49\) 4.90766 0.701094
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 7.33172 1.00709 0.503544 0.863969i \(-0.332029\pi\)
0.503544 + 0.863969i \(0.332029\pi\)
\(54\) 0 0
\(55\) 1.36137 0.183567
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 9.74251i 1.26837i −0.773183 0.634183i \(-0.781337\pi\)
0.773183 0.634183i \(-0.218663\pi\)
\(60\) 0 0
\(61\) 9.45083i 1.21005i −0.796205 0.605027i \(-0.793162\pi\)
0.796205 0.605027i \(-0.206838\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 1.07559 0.133410
\(66\) 0 0
\(67\) 9.90647i 1.21027i −0.796124 0.605134i \(-0.793120\pi\)
0.796124 0.605134i \(-0.206880\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 13.5958i 1.61353i −0.590874 0.806764i \(-0.701217\pi\)
0.590874 0.806764i \(-0.298783\pi\)
\(72\) 0 0
\(73\) −4.12968 −0.483342 −0.241671 0.970358i \(-0.577696\pi\)
−0.241671 + 0.970358i \(0.577696\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 1.96921i 0.224412i
\(78\) 0 0
\(79\) 11.4503i 1.28826i 0.764918 + 0.644128i \(0.222779\pi\)
−0.764918 + 0.644128i \(0.777221\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 0.800104 0.0878228 0.0439114 0.999035i \(-0.486018\pi\)
0.0439114 + 0.999035i \(0.486018\pi\)
\(84\) 0 0
\(85\) 0.324623 0.0352103
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −8.45302 −0.896018 −0.448009 0.894029i \(-0.647867\pi\)
−0.448009 + 0.894029i \(0.647867\pi\)
\(90\) 0 0
\(91\) 1.55583i 0.163095i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0.711387i 0.0729867i
\(96\) 0 0
\(97\) 8.16643i 0.829176i −0.910009 0.414588i \(-0.863926\pi\)
0.910009 0.414588i \(-0.136074\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 10.6670i 1.06140i 0.847559 + 0.530701i \(0.178071\pi\)
−0.847559 + 0.530701i \(0.821929\pi\)
\(102\) 0 0
\(103\) 5.07517i 0.500071i 0.968237 + 0.250035i \(0.0804423\pi\)
−0.968237 + 0.250035i \(0.919558\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −13.4723 −1.30242 −0.651209 0.758899i \(-0.725738\pi\)
−0.651209 + 0.758899i \(0.725738\pi\)
\(108\) 0 0
\(109\) 18.9560i 1.81565i −0.419345 0.907827i \(-0.637740\pi\)
0.419345 0.907827i \(-0.362260\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −17.3332 −1.63057 −0.815285 0.579060i \(-0.803420\pi\)
−0.815285 + 0.579060i \(0.803420\pi\)
\(114\) 0 0
\(115\) 0.999812 4.69046i 0.0932329 0.437387i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0.469565i 0.0430449i
\(120\) 0 0
\(121\) −9.14668 −0.831516
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 11.4374 1.01490 0.507452 0.861680i \(-0.330588\pi\)
0.507452 + 0.861680i \(0.330588\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 20.4026i 1.78258i 0.453432 + 0.891291i \(0.350199\pi\)
−0.453432 + 0.891291i \(0.649801\pi\)
\(132\) 0 0
\(133\) −1.02902 −0.0892269
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 13.2191 1.12938 0.564692 0.825302i \(-0.308995\pi\)
0.564692 + 0.825302i \(0.308995\pi\)
\(138\) 0 0
\(139\) −6.49107 −0.550566 −0.275283 0.961363i \(-0.588771\pi\)
−0.275283 + 0.961363i \(0.588771\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 1.46427 0.122448
\(144\) 0 0
\(145\) 2.07643i 0.172438i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −2.16983 −0.177760 −0.0888799 0.996042i \(-0.528329\pi\)
−0.0888799 + 0.996042i \(0.528329\pi\)
\(150\) 0 0
\(151\) −16.6384 −1.35401 −0.677007 0.735977i \(-0.736723\pi\)
−0.677007 + 0.735977i \(0.736723\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −5.82838 −0.468147
\(156\) 0 0
\(157\) 17.7007i 1.41267i −0.707879 0.706333i \(-0.750348\pi\)
0.707879 0.706333i \(-0.249652\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 6.78471 + 1.44622i 0.534710 + 0.113978i
\(162\) 0 0
\(163\) 1.24897 0.0978269 0.0489135 0.998803i \(-0.484424\pi\)
0.0489135 + 0.998803i \(0.484424\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 9.14250i 0.707468i −0.935346 0.353734i \(-0.884912\pi\)
0.935346 0.353734i \(-0.115088\pi\)
\(168\) 0 0
\(169\) −11.8431 −0.911009
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 6.91436i 0.525689i −0.964838 0.262844i \(-0.915339\pi\)
0.964838 0.262844i \(-0.0846606\pi\)
\(174\) 0 0
\(175\) 1.44649i 0.109345i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 8.36565i 0.625278i 0.949872 + 0.312639i \(0.101213\pi\)
−0.949872 + 0.312639i \(0.898787\pi\)
\(180\) 0 0
\(181\) 3.04417i 0.226272i −0.993580 0.113136i \(-0.963910\pi\)
0.993580 0.113136i \(-0.0360895\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 6.84151i 0.502998i
\(186\) 0 0
\(187\) 0.441931 0.0323172
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −24.9282 −1.80374 −0.901872 0.432004i \(-0.857807\pi\)
−0.901872 + 0.432004i \(0.857807\pi\)
\(192\) 0 0
\(193\) −2.12064 −0.152647 −0.0763237 0.997083i \(-0.524318\pi\)
−0.0763237 + 0.997083i \(0.524318\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 12.6353i 0.900227i −0.892971 0.450114i \(-0.851384\pi\)
0.892971 0.450114i \(-0.148616\pi\)
\(198\) 0 0
\(199\) 21.0395i 1.49145i −0.666255 0.745724i \(-0.732104\pi\)
0.666255 0.745724i \(-0.267896\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −3.00354 −0.210807
\(204\) 0 0
\(205\) 1.86885i 0.130526i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0.968458i 0.0669897i
\(210\) 0 0
\(211\) 23.2656 1.60167 0.800836 0.598884i \(-0.204389\pi\)
0.800836 + 0.598884i \(0.204389\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 5.81876i 0.396836i
\(216\) 0 0
\(217\) 8.43071i 0.572314i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0.349160 0.0234870
\(222\) 0 0
\(223\) 0.706022 0.0472787 0.0236393 0.999721i \(-0.492475\pi\)
0.0236393 + 0.999721i \(0.492475\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 3.68475 0.244565 0.122283 0.992495i \(-0.460979\pi\)
0.122283 + 0.992495i \(0.460979\pi\)
\(228\) 0 0
\(229\) 4.10883i 0.271519i 0.990742 + 0.135760i \(0.0433475\pi\)
−0.990742 + 0.135760i \(0.956653\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 6.42318i 0.420796i 0.977616 + 0.210398i \(0.0674760\pi\)
−0.977616 + 0.210398i \(0.932524\pi\)
\(234\) 0 0
\(235\) 12.1813i 0.794620i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 7.99705i 0.517286i −0.965973 0.258643i \(-0.916725\pi\)
0.965973 0.258643i \(-0.0832753\pi\)
\(240\) 0 0
\(241\) 15.1920i 0.978605i 0.872114 + 0.489302i \(0.162749\pi\)
−0.872114 + 0.489302i \(0.837251\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −4.90766 −0.313539
\(246\) 0 0
\(247\) 0.765157i 0.0486858i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −10.2901 −0.649504 −0.324752 0.945799i \(-0.605281\pi\)
−0.324752 + 0.945799i \(0.605281\pi\)
\(252\) 0 0
\(253\) 1.36111 6.38543i 0.0855723 0.401449i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 18.4588i 1.15143i 0.817650 + 0.575715i \(0.195276\pi\)
−0.817650 + 0.575715i \(0.804724\pi\)
\(258\) 0 0
\(259\) 9.89620 0.614920
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −27.4703 −1.69389 −0.846945 0.531681i \(-0.821560\pi\)
−0.846945 + 0.531681i \(0.821560\pi\)
\(264\) 0 0
\(265\) −7.33172 −0.450384
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 15.9569i 0.972911i −0.873705 0.486456i \(-0.838290\pi\)
0.873705 0.486456i \(-0.161710\pi\)
\(270\) 0 0
\(271\) −30.3919 −1.84618 −0.923089 0.384586i \(-0.874344\pi\)
−0.923089 + 0.384586i \(0.874344\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1.36137 −0.0820935
\(276\) 0 0
\(277\) −0.902914 −0.0542508 −0.0271254 0.999632i \(-0.508635\pi\)
−0.0271254 + 0.999632i \(0.508635\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −24.2787 −1.44834 −0.724172 0.689619i \(-0.757778\pi\)
−0.724172 + 0.689619i \(0.757778\pi\)
\(282\) 0 0
\(283\) 12.5371i 0.745255i 0.927981 + 0.372628i \(0.121543\pi\)
−0.927981 + 0.372628i \(0.878457\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −2.70328 −0.159569
\(288\) 0 0
\(289\) −16.8946 −0.993801
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 26.0905 1.52422 0.762112 0.647445i \(-0.224162\pi\)
0.762112 + 0.647445i \(0.224162\pi\)
\(294\) 0 0
\(295\) 9.74251i 0.567231i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 1.07538 5.04499i 0.0621910 0.291759i
\(300\) 0 0
\(301\) −8.41680 −0.485136
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 9.45083i 0.541153i
\(306\) 0 0
\(307\) −18.3379 −1.04660 −0.523299 0.852149i \(-0.675299\pi\)
−0.523299 + 0.852149i \(0.675299\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 2.54818i 0.144494i 0.997387 + 0.0722469i \(0.0230170\pi\)
−0.997387 + 0.0722469i \(0.976983\pi\)
\(312\) 0 0
\(313\) 32.7098i 1.84887i −0.381340 0.924435i \(-0.624537\pi\)
0.381340 0.924435i \(-0.375463\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 26.6634i 1.49757i 0.662815 + 0.748783i \(0.269361\pi\)
−0.662815 + 0.748783i \(0.730639\pi\)
\(318\) 0 0
\(319\) 2.82678i 0.158269i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0.230932i 0.0128494i
\(324\) 0 0
\(325\) −1.07559 −0.0596628
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 17.6201 0.971430
\(330\) 0 0
\(331\) 19.0179 1.04532 0.522660 0.852541i \(-0.324940\pi\)
0.522660 + 0.852541i \(0.324940\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 9.90647i 0.541248i
\(336\) 0 0
\(337\) 13.0972i 0.713448i −0.934210 0.356724i \(-0.883894\pi\)
0.934210 0.356724i \(-0.116106\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −7.93457 −0.429681
\(342\) 0 0
\(343\) 17.2243i 0.930027i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 6.34544i 0.340641i 0.985389 + 0.170320i \(0.0544803\pi\)
−0.985389 + 0.170320i \(0.945520\pi\)
\(348\) 0 0
\(349\) −18.4327 −0.986680 −0.493340 0.869837i \(-0.664224\pi\)
−0.493340 + 0.869837i \(0.664224\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 25.5359i 1.35914i −0.733612 0.679568i \(-0.762167\pi\)
0.733612 0.679568i \(-0.237833\pi\)
\(354\) 0 0
\(355\) 13.5958i 0.721591i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 1.06791 0.0563622 0.0281811 0.999603i \(-0.491028\pi\)
0.0281811 + 0.999603i \(0.491028\pi\)
\(360\) 0 0
\(361\) 18.4939 0.973365
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 4.12968 0.216157
\(366\) 0 0
\(367\) 24.3859i 1.27293i −0.771304 0.636467i \(-0.780395\pi\)
0.771304 0.636467i \(-0.219605\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 10.6053i 0.550598i
\(372\) 0 0
\(373\) 17.0185i 0.881185i −0.897707 0.440592i \(-0.854768\pi\)
0.897707 0.440592i \(-0.145232\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 2.23338i 0.115025i
\(378\) 0 0
\(379\) 7.92469i 0.407064i −0.979068 0.203532i \(-0.934758\pi\)
0.979068 0.203532i \(-0.0652421\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 11.3980 0.582409 0.291204 0.956661i \(-0.405944\pi\)
0.291204 + 0.956661i \(0.405944\pi\)
\(384\) 0 0
\(385\) 1.96921i 0.100360i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 14.5063 0.735496 0.367748 0.929925i \(-0.380129\pi\)
0.367748 + 0.929925i \(0.380129\pi\)
\(390\) 0 0
\(391\) 0.324562 1.52263i 0.0164138 0.0770027i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 11.4503i 0.576125i
\(396\) 0 0
\(397\) 8.05311 0.404174 0.202087 0.979368i \(-0.435228\pi\)
0.202087 + 0.979368i \(0.435228\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 4.09759 0.204624 0.102312 0.994752i \(-0.467376\pi\)
0.102312 + 0.994752i \(0.467376\pi\)
\(402\) 0 0
\(403\) −6.26893 −0.312278
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 9.31381i 0.461669i
\(408\) 0 0
\(409\) 8.81983 0.436112 0.218056 0.975936i \(-0.430028\pi\)
0.218056 + 0.975936i \(0.430028\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −14.0925 −0.693445
\(414\) 0 0
\(415\) −0.800104 −0.0392756
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −24.8862 −1.21577 −0.607886 0.794025i \(-0.707982\pi\)
−0.607886 + 0.794025i \(0.707982\pi\)
\(420\) 0 0
\(421\) 39.0434i 1.90286i −0.307867 0.951429i \(-0.599615\pi\)
0.307867 0.951429i \(-0.400385\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −0.324623 −0.0157465
\(426\) 0 0
\(427\) −13.6706 −0.661565
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −15.3323 −0.738529 −0.369264 0.929324i \(-0.620390\pi\)
−0.369264 + 0.929324i \(0.620390\pi\)
\(432\) 0 0
\(433\) 11.4681i 0.551121i −0.961284 0.275560i \(-0.911137\pi\)
0.961284 0.275560i \(-0.0888634\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 3.33673 + 0.711253i 0.159617 + 0.0340238i
\(438\) 0 0
\(439\) 1.49682 0.0714394 0.0357197 0.999362i \(-0.488628\pi\)
0.0357197 + 0.999362i \(0.488628\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 10.3427i 0.491396i 0.969346 + 0.245698i \(0.0790172\pi\)
−0.969346 + 0.245698i \(0.920983\pi\)
\(444\) 0 0
\(445\) 8.45302 0.400712
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 26.6792i 1.25907i 0.776973 + 0.629533i \(0.216754\pi\)
−0.776973 + 0.629533i \(0.783246\pi\)
\(450\) 0 0
\(451\) 2.54419i 0.119801i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 1.55583i 0.0729383i
\(456\) 0 0
\(457\) 17.7567i 0.830623i 0.909679 + 0.415311i \(0.136327\pi\)
−0.909679 + 0.415311i \(0.863673\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 35.8874i 1.67144i −0.549152 0.835722i \(-0.685049\pi\)
0.549152 0.835722i \(-0.314951\pi\)
\(462\) 0 0
\(463\) −14.2698 −0.663172 −0.331586 0.943425i \(-0.607584\pi\)
−0.331586 + 0.943425i \(0.607584\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −36.5261 −1.69023 −0.845113 0.534587i \(-0.820467\pi\)
−0.845113 + 0.534587i \(0.820467\pi\)
\(468\) 0 0
\(469\) −14.3296 −0.661681
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 7.92148i 0.364230i
\(474\) 0 0
\(475\) 0.711387i 0.0326407i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −24.1531 −1.10359 −0.551793 0.833981i \(-0.686056\pi\)
−0.551793 + 0.833981i \(0.686056\pi\)
\(480\) 0 0
\(481\) 7.35863i 0.335525i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 8.16643i 0.370819i
\(486\) 0 0
\(487\) −9.43775 −0.427665 −0.213833 0.976870i \(-0.568595\pi\)
−0.213833 + 0.976870i \(0.568595\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 6.48302i 0.292575i 0.989242 + 0.146287i \(0.0467324\pi\)
−0.989242 + 0.146287i \(0.953268\pi\)
\(492\) 0 0
\(493\) 0.674056i 0.0303580i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −19.6663 −0.882152
\(498\) 0 0
\(499\) −19.3397 −0.865763 −0.432881 0.901451i \(-0.642503\pi\)
−0.432881 + 0.901451i \(0.642503\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −19.4517 −0.867309 −0.433654 0.901079i \(-0.642776\pi\)
−0.433654 + 0.901079i \(0.642776\pi\)
\(504\) 0 0
\(505\) 10.6670i 0.474674i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 8.54321i 0.378671i −0.981912 0.189336i \(-0.939367\pi\)
0.981912 0.189336i \(-0.0606334\pi\)
\(510\) 0 0
\(511\) 5.97355i 0.264254i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 5.07517i 0.223639i
\(516\) 0 0
\(517\) 16.5832i 0.729329i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 29.2471 1.28134 0.640669 0.767818i \(-0.278657\pi\)
0.640669 + 0.767818i \(0.278657\pi\)
\(522\) 0 0
\(523\) 31.5199i 1.37827i 0.724634 + 0.689134i \(0.242009\pi\)
−0.724634 + 0.689134i \(0.757991\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −1.89203 −0.0824180
\(528\) 0 0
\(529\) −21.0008 9.37915i −0.913076 0.407789i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 2.01011i 0.0870674i
\(534\) 0 0
\(535\) 13.4723 0.582459
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −6.68113 −0.287777
\(540\) 0 0
\(541\) 23.0706 0.991884 0.495942 0.868356i \(-0.334823\pi\)
0.495942 + 0.868356i \(0.334823\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 18.9560i 0.811985i
\(546\) 0 0
\(547\) 41.5324 1.77580 0.887899 0.460038i \(-0.152164\pi\)
0.887899 + 0.460038i \(0.152164\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −1.47714 −0.0629284
\(552\) 0 0
\(553\) 16.5627 0.704318
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 46.2726 1.96063 0.980317 0.197428i \(-0.0632587\pi\)
0.980317 + 0.197428i \(0.0632587\pi\)
\(558\) 0 0
\(559\) 6.25858i 0.264710i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −27.6298 −1.16446 −0.582228 0.813026i \(-0.697819\pi\)
−0.582228 + 0.813026i \(0.697819\pi\)
\(564\) 0 0
\(565\) 17.3332 0.729213
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −47.5737 −1.99439 −0.997196 0.0748375i \(-0.976156\pi\)
−0.997196 + 0.0748375i \(0.976156\pi\)
\(570\) 0 0
\(571\) 28.3329i 1.18570i −0.805315 0.592848i \(-0.798004\pi\)
0.805315 0.592848i \(-0.201996\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −0.999812 + 4.69046i −0.0416950 + 0.195606i
\(576\) 0 0
\(577\) 28.7626 1.19740 0.598702 0.800972i \(-0.295683\pi\)
0.598702 + 0.800972i \(0.295683\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 1.15734i 0.0480147i
\(582\) 0 0
\(583\) −9.98116 −0.413377
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 46.1231i 1.90370i 0.306559 + 0.951852i \(0.400822\pi\)
−0.306559 + 0.951852i \(0.599178\pi\)
\(588\) 0 0
\(589\) 4.14623i 0.170843i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 41.8567i 1.71885i −0.511261 0.859425i \(-0.670822\pi\)
0.511261 0.859425i \(-0.329178\pi\)
\(594\) 0 0
\(595\) 0.469565i 0.0192503i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 39.7755i 1.62518i −0.582834 0.812591i \(-0.698056\pi\)
0.582834 0.812591i \(-0.301944\pi\)
\(600\) 0 0
\(601\) −39.3403 −1.60473 −0.802363 0.596837i \(-0.796424\pi\)
−0.802363 + 0.596837i \(0.796424\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 9.14668 0.371865
\(606\) 0 0
\(607\) 28.7783 1.16807 0.584037 0.811727i \(-0.301472\pi\)
0.584037 + 0.811727i \(0.301472\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 13.1020i 0.530051i
\(612\) 0 0
\(613\) 21.7678i 0.879193i 0.898195 + 0.439597i \(0.144879\pi\)
−0.898195 + 0.439597i \(0.855121\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 19.0398 0.766512 0.383256 0.923642i \(-0.374803\pi\)
0.383256 + 0.923642i \(0.374803\pi\)
\(618\) 0 0
\(619\) 15.2388i 0.612498i 0.951951 + 0.306249i \(0.0990740\pi\)
−0.951951 + 0.306249i \(0.900926\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 12.2272i 0.489874i
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 2.22091i 0.0885536i
\(630\) 0 0
\(631\) 3.29925i 0.131341i −0.997841 0.0656705i \(-0.979081\pi\)
0.997841 0.0656705i \(-0.0209186\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −11.4374 −0.453879
\(636\) 0 0
\(637\) −5.27861 −0.209146
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 5.41099 0.213721 0.106861 0.994274i \(-0.465920\pi\)
0.106861 + 0.994274i \(0.465920\pi\)
\(642\) 0 0
\(643\) 17.9665i 0.708530i −0.935145 0.354265i \(-0.884731\pi\)
0.935145 0.354265i \(-0.115269\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 32.3550i 1.27201i 0.771687 + 0.636003i \(0.219413\pi\)
−0.771687 + 0.636003i \(0.780587\pi\)
\(648\) 0 0
\(649\) 13.2631i 0.520623i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 40.8784i 1.59970i −0.600202 0.799848i \(-0.704913\pi\)
0.600202 0.799848i \(-0.295087\pi\)
\(654\) 0 0
\(655\) 20.4026i 0.797195i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 20.9165 0.814793 0.407396 0.913251i \(-0.366437\pi\)
0.407396 + 0.913251i \(0.366437\pi\)
\(660\) 0 0
\(661\) 24.6643i 0.959331i −0.877451 0.479665i \(-0.840758\pi\)
0.877451 0.479665i \(-0.159242\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 1.02902 0.0399035
\(666\) 0 0
\(667\) 9.73940 + 2.07604i 0.377111 + 0.0803845i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 12.8661i 0.496688i
\(672\) 0 0
\(673\) −2.52712 −0.0974133 −0.0487067 0.998813i \(-0.515510\pi\)
−0.0487067 + 0.998813i \(0.515510\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −32.1664 −1.23626 −0.618128 0.786077i \(-0.712109\pi\)
−0.618128 + 0.786077i \(0.712109\pi\)
\(678\) 0 0
\(679\) −11.8127 −0.453329
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 13.7669i 0.526777i −0.964690 0.263389i \(-0.915160\pi\)
0.964690 0.263389i \(-0.0848401\pi\)
\(684\) 0 0
\(685\) −13.2191 −0.505076
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −7.88589 −0.300428
\(690\) 0 0
\(691\) −31.3329 −1.19196 −0.595980 0.802999i \(-0.703236\pi\)
−0.595980 + 0.802999i \(0.703236\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 6.49107 0.246220
\(696\) 0 0
\(697\) 0.606671i 0.0229793i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 3.30429 0.124801 0.0624006 0.998051i \(-0.480124\pi\)
0.0624006 + 0.998051i \(0.480124\pi\)
\(702\) 0 0
\(703\) 4.86696 0.183561
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 15.4297 0.580293
\(708\) 0 0
\(709\) 23.0295i 0.864890i −0.901660 0.432445i \(-0.857651\pi\)
0.901660 0.432445i \(-0.142349\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −5.82729 + 27.3378i −0.218234 + 1.02381i
\(714\) 0 0
\(715\) −1.46427 −0.0547605
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 37.0799i 1.38285i −0.722449 0.691424i \(-0.756984\pi\)
0.722449 0.691424i \(-0.243016\pi\)
\(720\) 0 0
\(721\) 7.34119 0.273400
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 2.07643i 0.0771166i
\(726\) 0 0
\(727\) 9.03043i 0.334920i 0.985879 + 0.167460i \(0.0535565\pi\)
−0.985879 + 0.167460i \(0.946443\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 1.88890i 0.0698636i
\(732\) 0 0
\(733\) 46.8214i 1.72939i −0.502298 0.864695i \(-0.667512\pi\)
0.502298 0.864695i \(-0.332488\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 13.4863i 0.496776i
\(738\) 0 0
\(739\) 32.6487 1.20100 0.600501 0.799624i \(-0.294968\pi\)
0.600501 + 0.799624i \(0.294968\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 22.9376 0.841499 0.420750 0.907177i \(-0.361767\pi\)
0.420750 + 0.907177i \(0.361767\pi\)
\(744\) 0 0
\(745\) 2.16983 0.0794966
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 19.4876i 0.712061i
\(750\) 0 0
\(751\) 50.7815i 1.85304i 0.376241 + 0.926522i \(0.377216\pi\)
−0.376241 + 0.926522i \(0.622784\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 16.6384 0.605533
\(756\) 0 0
\(757\) 25.5700i 0.929358i −0.885479 0.464679i \(-0.846170\pi\)
0.885479 0.464679i \(-0.153830\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0.0869257i 0.00315106i 0.999999 + 0.00157553i \(0.000501506\pi\)
−0.999999 + 0.00157553i \(0.999498\pi\)
\(762\) 0 0
\(763\) −27.4197 −0.992659
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 10.4789i 0.378371i
\(768\) 0 0
\(769\) 37.3837i 1.34809i −0.738690 0.674045i \(-0.764555\pi\)
0.738690 0.674045i \(-0.235445\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −7.32009 −0.263285 −0.131643 0.991297i \(-0.542025\pi\)
−0.131643 + 0.991297i \(0.542025\pi\)
\(774\) 0 0
\(775\) 5.82838 0.209362
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −1.32947 −0.0476333
\(780\) 0 0
\(781\) 18.5089i 0.662301i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 17.7007i 0.631764i
\(786\) 0 0
\(787\) 4.62475i 0.164855i 0.996597 + 0.0824273i \(0.0262672\pi\)
−0.996597 + 0.0824273i \(0.973733\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 25.0723i 0.891470i
\(792\) 0 0
\(793\) 10.1652i 0.360976i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 26.4223 0.935925 0.467963 0.883748i \(-0.344988\pi\)
0.467963 + 0.883748i \(0.344988\pi\)
\(798\) 0 0
\(799\) 3.95433i 0.139894i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 5.62201 0.198396
\(804\) 0 0
\(805\) −6.78471 1.44622i −0.239130 0.0509726i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 31.6609i 1.11314i −0.830802