Properties

Label 4032.2.v.e.1583.7
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 1583.7
Character \(\chi\) = 4032.1583
Dual form 4032.2.v.e.3599.7

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.925496 - 0.925496i) q^{5} -1.00000 q^{7} +O(q^{10})\) \(q+(-0.925496 - 0.925496i) q^{5} -1.00000 q^{7} +(-1.72403 + 1.72403i) q^{11} +(0.328273 + 0.328273i) q^{13} -2.34181i q^{17} +(1.77976 - 1.77976i) q^{19} +6.17143i q^{23} -3.28691i q^{25} +(0.122671 - 0.122671i) q^{29} -1.74700i q^{31} +(0.925496 + 0.925496i) q^{35} +(-1.68105 + 1.68105i) q^{37} -2.88812 q^{41} +(-2.77330 - 2.77330i) q^{43} +5.92184 q^{47} +1.00000 q^{49} +(0.973689 + 0.973689i) q^{53} +3.19117 q^{55} +(-8.33124 + 8.33124i) q^{59} +(4.28808 + 4.28808i) q^{61} -0.607630i q^{65} +(-1.78259 + 1.78259i) q^{67} +8.57053i q^{71} +6.41750i q^{73} +(1.72403 - 1.72403i) q^{77} -5.38299i q^{79} +(-3.46360 - 3.46360i) q^{83} +(-2.16734 + 2.16734i) q^{85} +1.51391 q^{89} +(-0.328273 - 0.328273i) q^{91} -3.29433 q^{95} +15.7177 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q - 40q^{7} + O(q^{10}) \) \( 40q - 40q^{7} - 24q^{13} + 32q^{19} - 8q^{37} - 32q^{43} + 40q^{49} - 48q^{55} - 24q^{61} + 64q^{85} + 24q^{91} + 64q^{97} + O(q^{100}) \)

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
\(5\) −0.925496 0.925496i −0.413894 0.413894i 0.469198 0.883093i \(-0.344543\pi\)
−0.883093 + 0.469198i \(0.844543\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −1.72403 + 1.72403i −0.519815 + 0.519815i −0.917515 0.397701i \(-0.869808\pi\)
0.397701 + 0.917515i \(0.369808\pi\)
\(12\) 0 0
\(13\) 0.328273 + 0.328273i 0.0910464 + 0.0910464i 0.751163 0.660117i \(-0.229493\pi\)
−0.660117 + 0.751163i \(0.729493\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.34181i 0.567973i −0.958828 0.283986i \(-0.908343\pi\)
0.958828 0.283986i \(-0.0916570\pi\)
\(18\) 0 0
\(19\) 1.77976 1.77976i 0.408306 0.408306i −0.472842 0.881147i \(-0.656772\pi\)
0.881147 + 0.472842i \(0.156772\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 6.17143i 1.28683i 0.765517 + 0.643416i \(0.222483\pi\)
−0.765517 + 0.643416i \(0.777517\pi\)
\(24\) 0 0
\(25\) 3.28691i 0.657383i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 0.122671 0.122671i 0.0227794 0.0227794i −0.695625 0.718405i \(-0.744873\pi\)
0.718405 + 0.695625i \(0.244873\pi\)
\(30\) 0 0
\(31\) 1.74700i 0.313770i −0.987617 0.156885i \(-0.949855\pi\)
0.987617 0.156885i \(-0.0501452\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0.925496 + 0.925496i 0.156437 + 0.156437i
\(36\) 0 0
\(37\) −1.68105 + 1.68105i −0.276363 + 0.276363i −0.831655 0.555292i \(-0.812606\pi\)
0.555292 + 0.831655i \(0.312606\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −2.88812 −0.451048 −0.225524 0.974238i \(-0.572409\pi\)
−0.225524 + 0.974238i \(0.572409\pi\)
\(42\) 0 0
\(43\) −2.77330 2.77330i −0.422924 0.422924i 0.463285 0.886209i \(-0.346670\pi\)
−0.886209 + 0.463285i \(0.846670\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 5.92184 0.863789 0.431894 0.901924i \(-0.357845\pi\)
0.431894 + 0.901924i \(0.357845\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 0.973689 + 0.973689i 0.133746 + 0.133746i 0.770811 0.637064i \(-0.219851\pi\)
−0.637064 + 0.770811i \(0.719851\pi\)
\(54\) 0 0
\(55\) 3.19117 0.430297
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −8.33124 + 8.33124i −1.08464 + 1.08464i −0.0885647 + 0.996070i \(0.528228\pi\)
−0.996070 + 0.0885647i \(0.971772\pi\)
\(60\) 0 0
\(61\) 4.28808 + 4.28808i 0.549033 + 0.549033i 0.926161 0.377128i \(-0.123088\pi\)
−0.377128 + 0.926161i \(0.623088\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0.607630i 0.0753672i
\(66\) 0 0
\(67\) −1.78259 + 1.78259i −0.217778 + 0.217778i −0.807561 0.589783i \(-0.799213\pi\)
0.589783 + 0.807561i \(0.299213\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 8.57053i 1.01713i 0.861022 + 0.508567i \(0.169825\pi\)
−0.861022 + 0.508567i \(0.830175\pi\)
\(72\) 0 0
\(73\) 6.41750i 0.751112i 0.926800 + 0.375556i \(0.122548\pi\)
−0.926800 + 0.375556i \(0.877452\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 1.72403 1.72403i 0.196471 0.196471i
\(78\) 0 0
\(79\) 5.38299i 0.605633i −0.953049 0.302817i \(-0.902073\pi\)
0.953049 0.302817i \(-0.0979270\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −3.46360 3.46360i −0.380179 0.380179i 0.490987 0.871167i \(-0.336636\pi\)
−0.871167 + 0.490987i \(0.836636\pi\)
\(84\) 0 0
\(85\) −2.16734 + 2.16734i −0.235081 + 0.235081i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 1.51391 0.160474 0.0802368 0.996776i \(-0.474432\pi\)
0.0802368 + 0.996776i \(0.474432\pi\)
\(90\) 0 0
\(91\) −0.328273 0.328273i −0.0344123 0.0344123i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −3.29433 −0.337991
\(96\) 0 0
\(97\) 15.7177 1.59589 0.797943 0.602732i \(-0.205921\pi\)
0.797943 + 0.602732i \(0.205921\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 13.6438 + 13.6438i 1.35760 + 1.35760i 0.876861 + 0.480744i \(0.159633\pi\)
0.480744 + 0.876861i \(0.340367\pi\)
\(102\) 0 0
\(103\) 11.9238 1.17489 0.587445 0.809264i \(-0.300134\pi\)
0.587445 + 0.809264i \(0.300134\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −13.6108 + 13.6108i −1.31580 + 1.31580i −0.398740 + 0.917064i \(0.630553\pi\)
−0.917064 + 0.398740i \(0.869447\pi\)
\(108\) 0 0
\(109\) 4.97865 + 4.97865i 0.476868 + 0.476868i 0.904129 0.427260i \(-0.140521\pi\)
−0.427260 + 0.904129i \(0.640521\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0.0768901i 0.00723322i 0.999993 + 0.00361661i \(0.00115120\pi\)
−0.999993 + 0.00361661i \(0.998849\pi\)
\(114\) 0 0
\(115\) 5.71163 5.71163i 0.532612 0.532612i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 2.34181i 0.214673i
\(120\) 0 0
\(121\) 5.05544i 0.459585i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −7.66951 + 7.66951i −0.685981 + 0.685981i
\(126\) 0 0
\(127\) 15.0611i 1.33646i 0.743956 + 0.668229i \(0.232947\pi\)
−0.743956 + 0.668229i \(0.767053\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 3.87027 + 3.87027i 0.338147 + 0.338147i 0.855670 0.517522i \(-0.173146\pi\)
−0.517522 + 0.855670i \(0.673146\pi\)
\(132\) 0 0
\(133\) −1.77976 + 1.77976i −0.154325 + 0.154325i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 5.47491 0.467753 0.233877 0.972266i \(-0.424859\pi\)
0.233877 + 0.972266i \(0.424859\pi\)
\(138\) 0 0
\(139\) −11.1117 11.1117i −0.942478 0.942478i 0.0559554 0.998433i \(-0.482180\pi\)
−0.998433 + 0.0559554i \(0.982180\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −1.13190 −0.0946545
\(144\) 0 0
\(145\) −0.227063 −0.0188565
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 10.2234 + 10.2234i 0.837535 + 0.837535i 0.988534 0.150999i \(-0.0482490\pi\)
−0.150999 + 0.988534i \(0.548249\pi\)
\(150\) 0 0
\(151\) −5.98993 −0.487454 −0.243727 0.969844i \(-0.578370\pi\)
−0.243727 + 0.969844i \(0.578370\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −1.61684 + 1.61684i −0.129868 + 0.129868i
\(156\) 0 0
\(157\) 9.57922 + 9.57922i 0.764505 + 0.764505i 0.977133 0.212628i \(-0.0682023\pi\)
−0.212628 + 0.977133i \(0.568202\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 6.17143i 0.486377i
\(162\) 0 0
\(163\) 7.81085 7.81085i 0.611793 0.611793i −0.331620 0.943413i \(-0.607595\pi\)
0.943413 + 0.331620i \(0.107595\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 5.28108i 0.408662i −0.978902 0.204331i \(-0.934498\pi\)
0.978902 0.204331i \(-0.0655019\pi\)
\(168\) 0 0
\(169\) 12.7845i 0.983421i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −11.8893 + 11.8893i −0.903929 + 0.903929i −0.995773 0.0918444i \(-0.970724\pi\)
0.0918444 + 0.995773i \(0.470724\pi\)
\(174\) 0 0
\(175\) 3.28691i 0.248467i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 6.38837 + 6.38837i 0.477489 + 0.477489i 0.904328 0.426839i \(-0.140373\pi\)
−0.426839 + 0.904328i \(0.640373\pi\)
\(180\) 0 0
\(181\) 5.56367 5.56367i 0.413545 0.413545i −0.469427 0.882971i \(-0.655539\pi\)
0.882971 + 0.469427i \(0.155539\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 3.11161 0.228770
\(186\) 0 0
\(187\) 4.03735 + 4.03735i 0.295240 + 0.295240i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 2.43241 0.176003 0.0880014 0.996120i \(-0.471952\pi\)
0.0880014 + 0.996120i \(0.471952\pi\)
\(192\) 0 0
\(193\) 24.8507 1.78879 0.894397 0.447273i \(-0.147605\pi\)
0.894397 + 0.447273i \(0.147605\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −1.77151 1.77151i −0.126215 0.126215i 0.641178 0.767393i \(-0.278446\pi\)
−0.767393 + 0.641178i \(0.778446\pi\)
\(198\) 0 0
\(199\) 13.8970 0.985130 0.492565 0.870276i \(-0.336059\pi\)
0.492565 + 0.870276i \(0.336059\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −0.122671 + 0.122671i −0.00860980 + 0.00860980i
\(204\) 0 0
\(205\) 2.67294 + 2.67294i 0.186686 + 0.186686i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 6.13673i 0.424487i
\(210\) 0 0
\(211\) 0.243974 0.243974i 0.0167959 0.0167959i −0.698659 0.715455i \(-0.746220\pi\)
0.715455 + 0.698659i \(0.246220\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 5.13335i 0.350091i
\(216\) 0 0
\(217\) 1.74700i 0.118594i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0.768752 0.768752i 0.0517119 0.0517119i
\(222\) 0 0
\(223\) 7.07187i 0.473568i 0.971562 + 0.236784i \(0.0760933\pi\)
−0.971562 + 0.236784i \(0.923907\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −2.15348 2.15348i −0.142932 0.142932i 0.632020 0.774952i \(-0.282226\pi\)
−0.774952 + 0.632020i \(0.782226\pi\)
\(228\) 0 0
\(229\) −14.4509 + 14.4509i −0.954943 + 0.954943i −0.999028 0.0440845i \(-0.985963\pi\)
0.0440845 + 0.999028i \(0.485963\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −17.7969 −1.16591 −0.582955 0.812504i \(-0.698104\pi\)
−0.582955 + 0.812504i \(0.698104\pi\)
\(234\) 0 0
\(235\) −5.48063 5.48063i −0.357517 0.357517i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 9.62147 0.622361 0.311180 0.950351i \(-0.399276\pi\)
0.311180 + 0.950351i \(0.399276\pi\)
\(240\) 0 0
\(241\) 27.3786 1.76361 0.881805 0.471614i \(-0.156329\pi\)
0.881805 + 0.471614i \(0.156329\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −0.925496 0.925496i −0.0591278 0.0591278i
\(246\) 0 0
\(247\) 1.16849 0.0743495
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 6.56293 6.56293i 0.414249 0.414249i −0.468967 0.883216i \(-0.655374\pi\)
0.883216 + 0.468967i \(0.155374\pi\)
\(252\) 0 0
\(253\) −10.6397 10.6397i −0.668914 0.668914i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 13.6808i 0.853383i 0.904397 + 0.426691i \(0.140321\pi\)
−0.904397 + 0.426691i \(0.859679\pi\)
\(258\) 0 0
\(259\) 1.68105 1.68105i 0.104455 0.104455i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 26.5064i 1.63445i −0.576317 0.817226i \(-0.695511\pi\)
0.576317 0.817226i \(-0.304489\pi\)
\(264\) 0 0
\(265\) 1.80229i 0.110714i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −11.7053 + 11.7053i −0.713684 + 0.713684i −0.967304 0.253620i \(-0.918379\pi\)
0.253620 + 0.967304i \(0.418379\pi\)
\(270\) 0 0
\(271\) 26.7904i 1.62740i 0.581286 + 0.813700i \(0.302550\pi\)
−0.581286 + 0.813700i \(0.697450\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 5.66674 + 5.66674i 0.341717 + 0.341717i
\(276\) 0 0
\(277\) −0.376534 + 0.376534i −0.0226237 + 0.0226237i −0.718328 0.695704i \(-0.755092\pi\)
0.695704 + 0.718328i \(0.255092\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −10.8174 −0.645314 −0.322657 0.946516i \(-0.604576\pi\)
−0.322657 + 0.946516i \(0.604576\pi\)
\(282\) 0 0
\(283\) −0.954650 0.954650i −0.0567481 0.0567481i 0.678163 0.734911i \(-0.262776\pi\)
−0.734911 + 0.678163i \(0.762776\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 2.88812 0.170480
\(288\) 0 0
\(289\) 11.5159 0.677407
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 14.4106 + 14.4106i 0.841877 + 0.841877i 0.989103 0.147226i \(-0.0470346\pi\)
−0.147226 + 0.989103i \(0.547035\pi\)
\(294\) 0 0
\(295\) 15.4211 0.897849
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −2.02591 + 2.02591i −0.117161 + 0.117161i
\(300\) 0 0
\(301\) 2.77330 + 2.77330i 0.159850 + 0.159850i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 7.93721i 0.454483i
\(306\) 0 0
\(307\) −15.9801 + 15.9801i −0.912034 + 0.912034i −0.996432 0.0843977i \(-0.973103\pi\)
0.0843977 + 0.996432i \(0.473103\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 7.61653i 0.431894i 0.976405 + 0.215947i \(0.0692838\pi\)
−0.976405 + 0.215947i \(0.930716\pi\)
\(312\) 0 0
\(313\) 30.7549i 1.73837i −0.494490 0.869184i \(-0.664645\pi\)
0.494490 0.869184i \(-0.335355\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 4.52751 4.52751i 0.254291 0.254291i −0.568437 0.822727i \(-0.692452\pi\)
0.822727 + 0.568437i \(0.192452\pi\)
\(318\) 0 0
\(319\) 0.422976i 0.0236821i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −4.16787 4.16787i −0.231906 0.231906i
\(324\) 0 0
\(325\) 1.07900 1.07900i 0.0598524 0.0598524i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −5.92184 −0.326481
\(330\) 0 0
\(331\) −11.4312 11.4312i −0.628318 0.628318i 0.319326 0.947645i \(-0.396543\pi\)
−0.947645 + 0.319326i \(0.896543\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 3.29956 0.180274
\(336\) 0 0
\(337\) −10.7569 −0.585964 −0.292982 0.956118i \(-0.594648\pi\)
−0.292982 + 0.956118i \(0.594648\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 3.01187 + 3.01187i 0.163102 + 0.163102i
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −16.3589 + 16.3589i −0.878193 + 0.878193i −0.993348 0.115154i \(-0.963264\pi\)
0.115154 + 0.993348i \(0.463264\pi\)
\(348\) 0 0
\(349\) −25.8389 25.8389i −1.38312 1.38312i −0.839013 0.544112i \(-0.816867\pi\)
−0.544112 0.839013i \(-0.683133\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 24.5770i 1.30810i 0.756451 + 0.654051i \(0.226932\pi\)
−0.756451 + 0.654051i \(0.773068\pi\)
\(354\) 0 0
\(355\) 7.93199 7.93199i 0.420986 0.420986i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 17.5485i 0.926176i 0.886312 + 0.463088i \(0.153259\pi\)
−0.886312 + 0.463088i \(0.846741\pi\)
\(360\) 0 0
\(361\) 12.6649i 0.666573i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 5.93937 5.93937i 0.310881 0.310881i
\(366\) 0 0
\(367\) 15.7849i 0.823964i 0.911192 + 0.411982i \(0.135163\pi\)
−0.911192 + 0.411982i \(0.864837\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −0.973689 0.973689i −0.0505514 0.0505514i
\(372\) 0 0
\(373\) −11.5837 + 11.5837i −0.599781 + 0.599781i −0.940254 0.340473i \(-0.889413\pi\)
0.340473 + 0.940254i \(0.389413\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0.0805389 0.00414796
\(378\) 0 0
\(379\) 1.84371 + 1.84371i 0.0947049 + 0.0947049i 0.752872 0.658167i \(-0.228668\pi\)
−0.658167 + 0.752872i \(0.728668\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 4.04073 0.206472 0.103236 0.994657i \(-0.467080\pi\)
0.103236 + 0.994657i \(0.467080\pi\)
\(384\) 0 0
\(385\) −3.19117 −0.162637
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −2.92444 2.92444i −0.148275 0.148275i 0.629072 0.777347i \(-0.283435\pi\)
−0.777347 + 0.629072i \(0.783435\pi\)
\(390\) 0 0
\(391\) 14.4523 0.730885
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −4.98193 + 4.98193i −0.250668 + 0.250668i
\(396\) 0 0
\(397\) −21.9555 21.9555i −1.10191 1.10191i −0.994180 0.107735i \(-0.965640\pi\)
−0.107735 0.994180i \(-0.534360\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 3.18398i 0.159000i 0.996835 + 0.0795001i \(0.0253324\pi\)
−0.996835 + 0.0795001i \(0.974668\pi\)
\(402\) 0 0
\(403\) 0.573491 0.573491i 0.0285676 0.0285676i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 5.79636i 0.287315i
\(408\) 0 0
\(409\) 15.1001i 0.746650i 0.927701 + 0.373325i \(0.121782\pi\)
−0.927701 + 0.373325i \(0.878218\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 8.33124 8.33124i 0.409954 0.409954i
\(414\) 0 0
\(415\) 6.41109i 0.314708i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −2.19389 2.19389i −0.107178 0.107178i 0.651484 0.758662i \(-0.274147\pi\)
−0.758662 + 0.651484i \(0.774147\pi\)
\(420\) 0 0
\(421\) −16.8539 + 16.8539i −0.821410 + 0.821410i −0.986310 0.164900i \(-0.947270\pi\)
0.164900 + 0.986310i \(0.447270\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −7.69733 −0.373376
\(426\) 0 0
\(427\) −4.28808 4.28808i −0.207515 0.207515i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 19.9661 0.961735 0.480868 0.876793i \(-0.340322\pi\)
0.480868 + 0.876793i \(0.340322\pi\)
\(432\) 0 0
\(433\) −3.83212 −0.184160 −0.0920800 0.995752i \(-0.529352\pi\)
−0.0920800 + 0.995752i \(0.529352\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 10.9837 + 10.9837i 0.525421 + 0.525421i
\(438\) 0 0
\(439\) 23.0120 1.09830 0.549151 0.835723i \(-0.314951\pi\)
0.549151 + 0.835723i \(0.314951\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −13.6982 + 13.6982i −0.650821 + 0.650821i −0.953191 0.302370i \(-0.902222\pi\)
0.302370 + 0.953191i \(0.402222\pi\)
\(444\) 0 0
\(445\) −1.40111 1.40111i −0.0664191 0.0664191i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 27.3194i 1.28928i −0.764486 0.644640i \(-0.777007\pi\)
0.764486 0.644640i \(-0.222993\pi\)
\(450\) 0 0
\(451\) 4.97920 4.97920i 0.234462 0.234462i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0.607630i 0.0284861i
\(456\) 0 0
\(457\) 30.4516i 1.42447i −0.701942 0.712234i \(-0.747684\pi\)
0.701942 0.712234i \(-0.252316\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −17.8016 + 17.8016i −0.829101 + 0.829101i −0.987392 0.158291i \(-0.949402\pi\)
0.158291 + 0.987392i \(0.449402\pi\)
\(462\) 0 0
\(463\) 8.43314i 0.391921i 0.980612 + 0.195961i \(0.0627825\pi\)
−0.980612 + 0.195961i \(0.937218\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −3.17711 3.17711i −0.147019 0.147019i 0.629766 0.776785i \(-0.283151\pi\)
−0.776785 + 0.629766i \(0.783151\pi\)
\(468\) 0 0
\(469\) 1.78259 1.78259i 0.0823124 0.0823124i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 9.56249 0.439684
\(474\) 0 0
\(475\) −5.84993 5.84993i −0.268413 0.268413i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −0.550076 −0.0251336 −0.0125668 0.999921i \(-0.504000\pi\)
−0.0125668 + 0.999921i \(0.504000\pi\)
\(480\) 0 0
\(481\) −1.10368 −0.0503237
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −14.5466 14.5466i −0.660528 0.660528i
\(486\) 0 0
\(487\) −18.1678 −0.823262 −0.411631 0.911351i \(-0.635041\pi\)
−0.411631 + 0.911351i \(0.635041\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 12.4565 12.4565i 0.562156 0.562156i −0.367764 0.929919i \(-0.619876\pi\)
0.929919 + 0.367764i \(0.119876\pi\)
\(492\) 0 0
\(493\) −0.287272 0.287272i −0.0129381 0.0129381i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 8.57053i 0.384441i
\(498\) 0 0
\(499\) 23.1835 23.1835i 1.03784 1.03784i 0.0385798 0.999256i \(-0.487717\pi\)
0.999256 0.0385798i \(-0.0122834\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 39.4375i 1.75843i −0.476426 0.879215i \(-0.658068\pi\)
0.476426 0.879215i \(-0.341932\pi\)
\(504\) 0 0
\(505\) 25.2545i 1.12381i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 1.26193 1.26193i 0.0559340 0.0559340i −0.678587 0.734520i \(-0.737407\pi\)
0.734520 + 0.678587i \(0.237407\pi\)
\(510\) 0 0
\(511\) 6.41750i 0.283894i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −11.0355 11.0355i −0.486280 0.486280i
\(516\) 0 0
\(517\) −10.2094 + 10.2094i −0.449010 + 0.449010i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −27.2672 −1.19460 −0.597300 0.802018i \(-0.703760\pi\)
−0.597300 + 0.802018i \(0.703760\pi\)
\(522\) 0 0
\(523\) 31.1608 + 31.1608i 1.36257 + 1.36257i 0.870633 + 0.491933i \(0.163709\pi\)
0.491933 + 0.870633i \(0.336291\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −4.09113 −0.178213
\(528\) 0 0
\(529\) −15.0865 −0.655936
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −0.948090 0.948090i −0.0410663 0.0410663i
\(534\) 0 0
\(535\) 25.1935 1.08921
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −1.72403 + 1.72403i −0.0742592 + 0.0742592i
\(540\) 0 0
\(541\) 12.9117 + 12.9117i 0.555119 + 0.555119i 0.927914 0.372795i \(-0.121600\pi\)
−0.372795 + 0.927914i \(0.621600\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 9.21544i 0.394746i
\(546\) 0 0
\(547\) 17.6998 17.6998i 0.756790 0.756790i −0.218947 0.975737i \(-0.570262\pi\)
0.975737 + 0.218947i \(0.0702622\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0.436650i 0.0186019i
\(552\) 0 0
\(553\) 5.38299i 0.228908i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −3.90087 + 3.90087i −0.165285 + 0.165285i −0.784903 0.619618i \(-0.787287\pi\)
0.619618 + 0.784903i \(0.287287\pi\)
\(558\) 0 0
\(559\) 1.82079i 0.0770114i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 27.4905 + 27.4905i 1.15859 + 1.15859i 0.984780 + 0.173807i \(0.0556068\pi\)
0.173807 + 0.984780i \(0.444393\pi\)
\(564\) 0 0
\(565\) 0.0711615 0.0711615i 0.00299379 0.00299379i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 19.2030 0.805031 0.402516 0.915413i \(-0.368136\pi\)
0.402516 + 0.915413i \(0.368136\pi\)
\(570\) 0 0
\(571\) −23.2363 23.2363i −0.972408 0.972408i 0.0272217 0.999629i \(-0.491334\pi\)
−0.999629 + 0.0272217i \(0.991334\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 20.2850 0.845941
\(576\) 0 0
\(577\) 25.0676 1.04358 0.521789 0.853074i \(-0.325265\pi\)
0.521789 + 0.853074i \(0.325265\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 3.46360 + 3.46360i 0.143694 + 0.143694i
\(582\) 0 0
\(583\) −3.35734 −0.139047
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 6.53626 6.53626i 0.269780 0.269780i −0.559231 0.829012i \(-0.688904\pi\)
0.829012 + 0.559231i \(0.188904\pi\)
\(588\) 0 0
\(589\) −3.10924 3.10924i −0.128114 0.128114i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 15.1162i 0.620749i −0.950614 0.310375i \(-0.899545\pi\)
0.950614 0.310375i \(-0.100455\pi\)
\(594\) 0 0
\(595\) 2.16734 2.16734i 0.0888521 0.0888521i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 29.1264i 1.19007i −0.803700 0.595035i \(-0.797138\pi\)
0.803700 0.595035i \(-0.202862\pi\)
\(600\) 0 0
\(601\) 14.2202i 0.580053i 0.957019 + 0.290026i \(0.0936641\pi\)
−0.957019 + 0.290026i \(0.906336\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 4.67879 4.67879i 0.190220 0.190220i
\(606\) 0 0
\(607\) 26.8584i 1.09015i 0.838387 + 0.545075i \(0.183499\pi\)
−0.838387 + 0.545075i \(0.816501\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 1.94398 + 1.94398i 0.0786448 + 0.0786448i
\(612\) 0 0
\(613\) −28.2483 + 28.2483i −1.14094 + 1.14094i −0.152659 + 0.988279i \(0.548784\pi\)
−0.988279 + 0.152659i \(0.951216\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −31.4617 −1.26660 −0.633300 0.773906i \(-0.718300\pi\)
−0.633300 + 0.773906i \(0.718300\pi\)
\(618\) 0 0
\(619\) −13.3846 13.3846i −0.537973 0.537973i 0.384961 0.922933i \(-0.374215\pi\)
−0.922933 + 0.384961i \(0.874215\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −1.51391 −0.0606533
\(624\) 0 0
\(625\) −2.23838 −0.0895353
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 3.93670 + 3.93670i 0.156966 + 0.156966i
\(630\) 0 0
\(631\) −15.5279 −0.618154 −0.309077 0.951037i \(-0.600020\pi\)
−0.309077 + 0.951037i \(0.600020\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 13.9390 13.9390i 0.553152 0.553152i
\(636\) 0 0
\(637\) 0.328273 + 0.328273i 0.0130066 + 0.0130066i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 33.1261i 1.30840i −0.756320 0.654201i \(-0.773005\pi\)
0.756320 0.654201i \(-0.226995\pi\)
\(642\) 0 0
\(643\) −28.5683 + 28.5683i −1.12662 + 1.12662i −0.135902 + 0.990722i \(0.543393\pi\)
−0.990722 + 0.135902i \(0.956607\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 48.7052i 1.91480i 0.288765 + 0.957400i \(0.406755\pi\)
−0.288765 + 0.957400i \(0.593245\pi\)
\(648\) 0 0
\(649\) 28.7266i 1.12762i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −2.67453 + 2.67453i −0.104662 + 0.104662i −0.757499 0.652836i \(-0.773579\pi\)
0.652836 + 0.757499i \(0.273579\pi\)
\(654\) 0 0
\(655\) 7.16384i 0.279915i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −20.0589 20.0589i −0.781384 0.781384i 0.198680 0.980064i \(-0.436334\pi\)
−0.980064 + 0.198680i \(0.936334\pi\)
\(660\) 0 0
\(661\) 3.44403 3.44403i 0.133957 0.133957i −0.636949 0.770906i \(-0.719804\pi\)
0.770906 + 0.636949i \(0.219804\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 3.29433 0.127749
\(666\) 0 0
\(667\) 0.757054 + 0.757054i 0.0293132 + 0.0293132i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −14.7856 −0.570791
\(672\) 0 0
\(673\) −32.1701 −1.24007 −0.620033 0.784576i \(-0.712881\pi\)
−0.620033 + 0.784576i \(0.712881\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −3.59090 3.59090i −0.138009 0.138009i 0.634727 0.772736i \(-0.281113\pi\)
−0.772736 + 0.634727i \(0.781113\pi\)
\(678\) 0 0
\(679\) −15.7177 −0.603188
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 4.35732 4.35732i 0.166728 0.166728i −0.618811 0.785540i \(-0.712385\pi\)
0.785540 + 0.618811i \(0.212385\pi\)
\(684\) 0 0
\(685\) −5.06701 5.06701i −0.193600 0.193600i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0.639271i 0.0243543i
\(690\) 0 0
\(691\) 9.12084 9.12084i 0.346973 0.346973i −0.512008 0.858981i \(-0.671098\pi\)
0.858981 + 0.512008i \(0.171098\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 20.5676i 0.780173i
\(696\) 0 0
\(697\) 6.76343i 0.256183i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 13.1832 13.1832i 0.497923 0.497923i −0.412868 0.910791i \(-0.635473\pi\)
0.910791 + 0.412868i \(0.135473\pi\)
\(702\) 0 0
\(703\) 5.98374i 0.225681i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −13.6438 13.6438i −0.513126 0.513126i
\(708\) 0 0
\(709\) 5.95604 5.95604i 0.223684 0.223684i −0.586364 0.810048i \(-0.699441\pi\)
0.810048 + 0.586364i \(0.199441\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 10.7815 0.403769
\(714\) 0 0
\(715\) 1.04757 + 1.04757i 0.0391770 + 0.0391770i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 38.3917 1.43177 0.715884 0.698220i \(-0.246024\pi\)
0.715884 + 0.698220i \(0.246024\pi\)
\(720\) 0 0
\(721\) −11.9238 −0.444067
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −0.403208 0.403208i −0.0149748 0.0149748i
\(726\) 0 0
\(727\) 5.05200 0.187368 0.0936842 0.995602i \(-0.470136\pi\)
0.0936842 + 0.995602i \(0.470136\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −6.49454 + 6.49454i −0.240209 + 0.240209i
\(732\) 0 0
\(733\) 2.73691 + 2.73691i 0.101090 + 0.101090i 0.755843 0.654753i \(-0.227227\pi\)
−0.654753 + 0.755843i \(0.727227\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 6.14648i 0.226408i
\(738\) 0 0
\(739\) −18.5031 + 18.5031i −0.680648 + 0.680648i −0.960146 0.279498i \(-0.909832\pi\)
0.279498 + 0.960146i \(0.409832\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 41.1110i 1.50822i −0.656751 0.754108i \(-0.728070\pi\)
0.656751 0.754108i \(-0.271930\pi\)
\(744\) 0 0
\(745\) 18.9235i 0.693302i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 13.6108 13.6108i 0.497327 0.497327i
\(750\) 0 0
\(751\) 27.5241i 1.00437i 0.864760 + 0.502185i \(0.167470\pi\)
−0.864760 + 0.502185i \(0.832530\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 5.54366 + 5.54366i 0.201754 + 0.201754i
\(756\) 0 0
\(757\) 6.27349 6.27349i 0.228014 0.228014i −0.583849 0.811863i \(-0.698454\pi\)
0.811863 + 0.583849i \(0.198454\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −23.6884 −0.858704 −0.429352 0.903137i \(-0.641258\pi\)
−0.429352 + 0.903137i \(0.641258\pi\)
\(762\) 0 0
\(763\) −4.97865 4.97865i −0.180239 0.180239i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −5.46983 −0.197504
\(768\) 0 0
\(769\) −4.74756 −0.171201 −0.0856006 0.996330i \(-0.527281\pi\)
−0.0856006 + 0.996330i \(0.527281\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −18.2666 18.2666i −0.657005 0.657005i 0.297666 0.954670i \(-0.403792\pi\)
−0.954670 + 0.297666i \(0.903792\pi\)
\(774\) 0 0
\(775\) −5.74223 −0.206267
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −5.14017 + 5.14017i −0.184166 + 0.184166i
\(780\) 0 0
\(781\) −14.7759 14.7759i −0.528722 0.528722i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 17.7311i 0.632849i
\(786\) 0 0
\(787\) −28.1972 + 28.1972i −1.00512 + 1.00512i −0.00513510 + 0.999987i \(0.501635\pi\)
−0.999987 + 0.00513510i \(0.998365\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0.0768901i 0.00273390i
\(792\) 0 0
\(793\) 2.81532i 0.0999749i
\(794\) 0 0