Properties

Label 4032.2.v.e.1583.9
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 1583.9
Character \(\chi\) = 4032.1583
Dual form 4032.2.v.e.3599.9

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.111394 - 0.111394i) q^{5} -1.00000 q^{7} +O(q^{10})\) \(q+(-0.111394 - 0.111394i) q^{5} -1.00000 q^{7} +(-3.61173 + 3.61173i) q^{11} +(-1.94473 - 1.94473i) q^{13} +4.79732i q^{17} +(-3.03275 + 3.03275i) q^{19} -6.58652i q^{23} -4.97518i q^{25} +(1.53154 - 1.53154i) q^{29} -3.26529i q^{31} +(0.111394 + 0.111394i) q^{35} +(1.05597 - 1.05597i) q^{37} -1.26613 q^{41} +(-0.484499 - 0.484499i) q^{43} +11.2247 q^{47} +1.00000 q^{49} +(4.00870 + 4.00870i) q^{53} +0.804648 q^{55} +(7.61474 - 7.61474i) q^{59} +(5.44215 + 5.44215i) q^{61} +0.433262i q^{65} +(0.897143 - 0.897143i) q^{67} -2.83052i q^{71} -15.7394i q^{73} +(3.61173 - 3.61173i) q^{77} +15.4151i q^{79} +(7.57988 + 7.57988i) q^{83} +(0.534392 - 0.534392i) q^{85} +13.1420 q^{89} +(1.94473 + 1.94473i) q^{91} +0.675660 q^{95} -10.4839 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q - 40q^{7} + O(q^{10}) \) \( 40q - 40q^{7} - 24q^{13} + 32q^{19} - 8q^{37} - 32q^{43} + 40q^{49} - 48q^{55} - 24q^{61} + 64q^{85} + 24q^{91} + 64q^{97} + O(q^{100}) \)

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
\(5\) −0.111394 0.111394i −0.0498168 0.0498168i 0.681760 0.731576i \(-0.261215\pi\)
−0.731576 + 0.681760i \(0.761215\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −3.61173 + 3.61173i −1.08898 + 1.08898i −0.0933436 + 0.995634i \(0.529755\pi\)
−0.995634 + 0.0933436i \(0.970245\pi\)
\(12\) 0 0
\(13\) −1.94473 1.94473i −0.539372 0.539372i 0.383973 0.923344i \(-0.374556\pi\)
−0.923344 + 0.383973i \(0.874556\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 4.79732i 1.16352i 0.813360 + 0.581761i \(0.197636\pi\)
−0.813360 + 0.581761i \(0.802364\pi\)
\(18\) 0 0
\(19\) −3.03275 + 3.03275i −0.695761 + 0.695761i −0.963493 0.267732i \(-0.913726\pi\)
0.267732 + 0.963493i \(0.413726\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 6.58652i 1.37339i −0.726948 0.686693i \(-0.759062\pi\)
0.726948 0.686693i \(-0.240938\pi\)
\(24\) 0 0
\(25\) 4.97518i 0.995037i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 1.53154 1.53154i 0.284399 0.284399i −0.550462 0.834861i \(-0.685548\pi\)
0.834861 + 0.550462i \(0.185548\pi\)
\(30\) 0 0
\(31\) 3.26529i 0.586464i −0.956041 0.293232i \(-0.905269\pi\)
0.956041 0.293232i \(-0.0947308\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0.111394 + 0.111394i 0.0188290 + 0.0188290i
\(36\) 0 0
\(37\) 1.05597 1.05597i 0.173601 0.173601i −0.614959 0.788559i \(-0.710827\pi\)
0.788559 + 0.614959i \(0.210827\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −1.26613 −0.197737 −0.0988684 0.995101i \(-0.531522\pi\)
−0.0988684 + 0.995101i \(0.531522\pi\)
\(42\) 0 0
\(43\) −0.484499 0.484499i −0.0738855 0.0738855i 0.669198 0.743084i \(-0.266638\pi\)
−0.743084 + 0.669198i \(0.766638\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 11.2247 1.63729 0.818644 0.574301i \(-0.194726\pi\)
0.818644 + 0.574301i \(0.194726\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 4.00870 + 4.00870i 0.550637 + 0.550637i 0.926625 0.375988i \(-0.122697\pi\)
−0.375988 + 0.926625i \(0.622697\pi\)
\(54\) 0 0
\(55\) 0.804648 0.108499
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 7.61474 7.61474i 0.991354 0.991354i −0.00860874 0.999963i \(-0.502740\pi\)
0.999963 + 0.00860874i \(0.00274028\pi\)
\(60\) 0 0
\(61\) 5.44215 + 5.44215i 0.696796 + 0.696796i 0.963718 0.266922i \(-0.0860066\pi\)
−0.266922 + 0.963718i \(0.586007\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0.433262i 0.0537395i
\(66\) 0 0
\(67\) 0.897143 0.897143i 0.109603 0.109603i −0.650178 0.759782i \(-0.725306\pi\)
0.759782 + 0.650178i \(0.225306\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 2.83052i 0.335921i −0.985794 0.167960i \(-0.946282\pi\)
0.985794 0.167960i \(-0.0537181\pi\)
\(72\) 0 0
\(73\) 15.7394i 1.84216i −0.389372 0.921080i \(-0.627308\pi\)
0.389372 0.921080i \(-0.372692\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 3.61173 3.61173i 0.411595 0.411595i
\(78\) 0 0
\(79\) 15.4151i 1.73433i 0.498020 + 0.867165i \(0.334061\pi\)
−0.498020 + 0.867165i \(0.665939\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 7.57988 + 7.57988i 0.832000 + 0.832000i 0.987790 0.155790i \(-0.0497924\pi\)
−0.155790 + 0.987790i \(0.549792\pi\)
\(84\) 0 0
\(85\) 0.534392 0.534392i 0.0579629 0.0579629i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 13.1420 1.39305 0.696525 0.717532i \(-0.254728\pi\)
0.696525 + 0.717532i \(0.254728\pi\)
\(90\) 0 0
\(91\) 1.94473 + 1.94473i 0.203863 + 0.203863i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0.675660 0.0693212
\(96\) 0 0
\(97\) −10.4839 −1.06447 −0.532237 0.846595i \(-0.678648\pi\)
−0.532237 + 0.846595i \(0.678648\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 0.472060 + 0.472060i 0.0469717 + 0.0469717i 0.730202 0.683231i \(-0.239426\pi\)
−0.683231 + 0.730202i \(0.739426\pi\)
\(102\) 0 0
\(103\) 16.5554 1.63125 0.815624 0.578583i \(-0.196394\pi\)
0.815624 + 0.578583i \(0.196394\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 7.98789 7.98789i 0.772218 0.772218i −0.206276 0.978494i \(-0.566134\pi\)
0.978494 + 0.206276i \(0.0661343\pi\)
\(108\) 0 0
\(109\) −6.01886 6.01886i −0.576502 0.576502i 0.357436 0.933938i \(-0.383651\pi\)
−0.933938 + 0.357436i \(0.883651\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 7.81071i 0.734770i −0.930069 0.367385i \(-0.880253\pi\)
0.930069 0.367385i \(-0.119747\pi\)
\(114\) 0 0
\(115\) −0.733698 + 0.733698i −0.0684177 + 0.0684177i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 4.79732i 0.439770i
\(120\) 0 0
\(121\) 15.0892i 1.37174i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −1.11117 + 1.11117i −0.0993863 + 0.0993863i
\(126\) 0 0
\(127\) 6.59439i 0.585157i −0.956241 0.292579i \(-0.905487\pi\)
0.956241 0.292579i \(-0.0945133\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −6.27211 6.27211i −0.547997 0.547997i 0.377864 0.925861i \(-0.376659\pi\)
−0.925861 + 0.377864i \(0.876659\pi\)
\(132\) 0 0
\(133\) 3.03275 3.03275i 0.262973 0.262973i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −22.4152 −1.91506 −0.957530 0.288333i \(-0.906899\pi\)
−0.957530 + 0.288333i \(0.906899\pi\)
\(138\) 0 0
\(139\) −9.44120 9.44120i −0.800792 0.800792i 0.182427 0.983219i \(-0.441605\pi\)
−0.983219 + 0.182427i \(0.941605\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 14.0477 1.17473
\(144\) 0 0
\(145\) −0.341207 −0.0283357
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 10.6024 + 10.6024i 0.868581 + 0.868581i 0.992315 0.123735i \(-0.0394872\pi\)
−0.123735 + 0.992315i \(0.539487\pi\)
\(150\) 0 0
\(151\) 0.651929 0.0530532 0.0265266 0.999648i \(-0.491555\pi\)
0.0265266 + 0.999648i \(0.491555\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −0.363733 + 0.363733i −0.0292157 + 0.0292157i
\(156\) 0 0
\(157\) −15.6768 15.6768i −1.25114 1.25114i −0.955209 0.295934i \(-0.904369\pi\)
−0.295934 0.955209i \(-0.595631\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 6.58652i 0.519091i
\(162\) 0 0
\(163\) 4.07211 4.07211i 0.318952 0.318952i −0.529412 0.848365i \(-0.677588\pi\)
0.848365 + 0.529412i \(0.177588\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 8.04509i 0.622548i 0.950320 + 0.311274i \(0.100756\pi\)
−0.950320 + 0.311274i \(0.899244\pi\)
\(168\) 0 0
\(169\) 5.43603i 0.418156i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −0.546907 + 0.546907i −0.0415806 + 0.0415806i −0.727591 0.686011i \(-0.759360\pi\)
0.686011 + 0.727591i \(0.259360\pi\)
\(174\) 0 0
\(175\) 4.97518i 0.376088i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 15.4071 + 15.4071i 1.15158 + 1.15158i 0.986236 + 0.165345i \(0.0528739\pi\)
0.165345 + 0.986236i \(0.447126\pi\)
\(180\) 0 0
\(181\) −4.10925 + 4.10925i −0.305438 + 0.305438i −0.843137 0.537699i \(-0.819294\pi\)
0.537699 + 0.843137i \(0.319294\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −0.235257 −0.0172965
\(186\) 0 0
\(187\) −17.3266 17.3266i −1.26705 1.26705i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 7.56461 0.547356 0.273678 0.961821i \(-0.411760\pi\)
0.273678 + 0.961821i \(0.411760\pi\)
\(192\) 0 0
\(193\) 14.0355 1.01030 0.505149 0.863032i \(-0.331438\pi\)
0.505149 + 0.863032i \(0.331438\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 9.59894 + 9.59894i 0.683896 + 0.683896i 0.960876 0.276980i \(-0.0893335\pi\)
−0.276980 + 0.960876i \(0.589334\pi\)
\(198\) 0 0
\(199\) 12.5176 0.887349 0.443675 0.896188i \(-0.353675\pi\)
0.443675 + 0.896188i \(0.353675\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −1.53154 + 1.53154i −0.107493 + 0.107493i
\(204\) 0 0
\(205\) 0.141039 + 0.141039i 0.00985062 + 0.00985062i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 21.9070i 1.51534i
\(210\) 0 0
\(211\) −6.19384 + 6.19384i −0.426401 + 0.426401i −0.887401 0.460999i \(-0.847491\pi\)
0.460999 + 0.887401i \(0.347491\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0.107940i 0.00736148i
\(216\) 0 0
\(217\) 3.26529i 0.221662i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 9.32951 9.32951i 0.627571 0.627571i
\(222\) 0 0
\(223\) 23.4809i 1.57240i −0.617972 0.786200i \(-0.712045\pi\)
0.617972 0.786200i \(-0.287955\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 13.8869 + 13.8869i 0.921707 + 0.921707i 0.997150 0.0754430i \(-0.0240371\pi\)
−0.0754430 + 0.997150i \(0.524037\pi\)
\(228\) 0 0
\(229\) −2.96200 + 2.96200i −0.195735 + 0.195735i −0.798169 0.602434i \(-0.794198\pi\)
0.602434 + 0.798169i \(0.294198\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 1.94090 0.127153 0.0635763 0.997977i \(-0.479749\pi\)
0.0635763 + 0.997977i \(0.479749\pi\)
\(234\) 0 0
\(235\) −1.25036 1.25036i −0.0815645 0.0815645i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −3.73260 −0.241442 −0.120721 0.992686i \(-0.538521\pi\)
−0.120721 + 0.992686i \(0.538521\pi\)
\(240\) 0 0
\(241\) −6.72519 −0.433208 −0.216604 0.976260i \(-0.569498\pi\)
−0.216604 + 0.976260i \(0.569498\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −0.111394 0.111394i −0.00711669 0.00711669i
\(246\) 0 0
\(247\) 11.7958 0.750548
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −7.29389 + 7.29389i −0.460387 + 0.460387i −0.898782 0.438396i \(-0.855547\pi\)
0.438396 + 0.898782i \(0.355547\pi\)
\(252\) 0 0
\(253\) 23.7887 + 23.7887i 1.49559 + 1.49559i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 3.33778i 0.208205i −0.994567 0.104103i \(-0.966803\pi\)
0.994567 0.104103i \(-0.0331970\pi\)
\(258\) 0 0
\(259\) −1.05597 + 1.05597i −0.0656149 + 0.0656149i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 16.2784i 1.00377i −0.864934 0.501886i \(-0.832640\pi\)
0.864934 0.501886i \(-0.167360\pi\)
\(264\) 0 0
\(265\) 0.893087i 0.0548619i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 16.6895 16.6895i 1.01758 1.01758i 0.0177322 0.999843i \(-0.494355\pi\)
0.999843 0.0177322i \(-0.00564465\pi\)
\(270\) 0 0
\(271\) 19.4291i 1.18023i −0.807318 0.590116i \(-0.799082\pi\)
0.807318 0.590116i \(-0.200918\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 17.9690 + 17.9690i 1.08357 + 1.08357i
\(276\) 0 0
\(277\) −20.2943 + 20.2943i −1.21937 + 1.21937i −0.251511 + 0.967854i \(0.580927\pi\)
−0.967854 + 0.251511i \(0.919073\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 8.67930 0.517763 0.258882 0.965909i \(-0.416646\pi\)
0.258882 + 0.965909i \(0.416646\pi\)
\(282\) 0 0
\(283\) 5.11240 + 5.11240i 0.303901 + 0.303901i 0.842538 0.538637i \(-0.181061\pi\)
−0.538637 + 0.842538i \(0.681061\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 1.26613 0.0747375
\(288\) 0 0
\(289\) −6.01430 −0.353782
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −4.21225 4.21225i −0.246082 0.246082i 0.573279 0.819361i \(-0.305671\pi\)
−0.819361 + 0.573279i \(0.805671\pi\)
\(294\) 0 0
\(295\) −1.69647 −0.0987722
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −12.8090 + 12.8090i −0.740765 + 0.740765i
\(300\) 0 0
\(301\) 0.484499 + 0.484499i 0.0279261 + 0.0279261i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 1.21244i 0.0694243i
\(306\) 0 0
\(307\) −5.47769 + 5.47769i −0.312628 + 0.312628i −0.845927 0.533299i \(-0.820952\pi\)
0.533299 + 0.845927i \(0.320952\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 10.8058i 0.612740i −0.951913 0.306370i \(-0.900886\pi\)
0.951913 0.306370i \(-0.0991144\pi\)
\(312\) 0 0
\(313\) 26.1747i 1.47948i −0.672893 0.739740i \(-0.734949\pi\)
0.672893 0.739740i \(-0.265051\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 14.7908 14.7908i 0.830735 0.830735i −0.156883 0.987617i \(-0.550144\pi\)
0.987617 + 0.156883i \(0.0501444\pi\)
\(318\) 0 0
\(319\) 11.0630i 0.619408i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −14.5491 14.5491i −0.809533 0.809533i
\(324\) 0 0
\(325\) −9.67540 + 9.67540i −0.536695 + 0.536695i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −11.2247 −0.618837
\(330\) 0 0
\(331\) −12.8239 12.8239i −0.704868 0.704868i 0.260583 0.965451i \(-0.416085\pi\)
−0.965451 + 0.260583i \(0.916085\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −0.199872 −0.0109202
\(336\) 0 0
\(337\) 11.5576 0.629582 0.314791 0.949161i \(-0.398066\pi\)
0.314791 + 0.949161i \(0.398066\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 11.7934 + 11.7934i 0.638646 + 0.638646i
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 2.89704 2.89704i 0.155521 0.155521i −0.625058 0.780579i \(-0.714924\pi\)
0.780579 + 0.625058i \(0.214924\pi\)
\(348\) 0 0
\(349\) 8.35296 + 8.35296i 0.447124 + 0.447124i 0.894397 0.447273i \(-0.147605\pi\)
−0.447273 + 0.894397i \(0.647605\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 11.6486i 0.619993i −0.950738 0.309996i \(-0.899672\pi\)
0.950738 0.309996i \(-0.100328\pi\)
\(354\) 0 0
\(355\) −0.315302 + 0.315302i −0.0167345 + 0.0167345i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 24.0137i 1.26739i −0.773582 0.633696i \(-0.781537\pi\)
0.773582 0.633696i \(-0.218463\pi\)
\(360\) 0 0
\(361\) 0.604810i 0.0318321i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −1.75327 + 1.75327i −0.0917706 + 0.0917706i
\(366\) 0 0
\(367\) 12.1938i 0.636510i −0.948005 0.318255i \(-0.896903\pi\)
0.948005 0.318255i \(-0.103097\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −4.00870 4.00870i −0.208121 0.208121i
\(372\) 0 0
\(373\) 17.3599 17.3599i 0.898859 0.898859i −0.0964762 0.995335i \(-0.530757\pi\)
0.995335 + 0.0964762i \(0.0307572\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −5.95685 −0.306794
\(378\) 0 0
\(379\) −16.2388 16.2388i −0.834130 0.834130i 0.153949 0.988079i \(-0.450801\pi\)
−0.988079 + 0.153949i \(0.950801\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −12.0190 −0.614141 −0.307070 0.951687i \(-0.599349\pi\)
−0.307070 + 0.951687i \(0.599349\pi\)
\(384\) 0 0
\(385\) −0.804648 −0.0410087
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −13.2292 13.2292i −0.670749 0.670749i 0.287140 0.957889i \(-0.407296\pi\)
−0.957889 + 0.287140i \(0.907296\pi\)
\(390\) 0 0
\(391\) 31.5977 1.59796
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 1.71714 1.71714i 0.0863988 0.0863988i
\(396\) 0 0
\(397\) 21.8846 + 21.8846i 1.09836 + 1.09836i 0.994603 + 0.103756i \(0.0330860\pi\)
0.103756 + 0.994603i \(0.466914\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 27.8646i 1.39149i 0.718288 + 0.695746i \(0.244926\pi\)
−0.718288 + 0.695746i \(0.755074\pi\)
\(402\) 0 0
\(403\) −6.35012 + 6.35012i −0.316322 + 0.316322i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 7.62778i 0.378095i
\(408\) 0 0
\(409\) 9.57933i 0.473667i −0.971550 0.236834i \(-0.923890\pi\)
0.971550 0.236834i \(-0.0761097\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −7.61474 + 7.61474i −0.374697 + 0.374697i
\(414\) 0 0
\(415\) 1.68870i 0.0828952i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 6.53866 + 6.53866i 0.319435 + 0.319435i 0.848550 0.529115i \(-0.177476\pi\)
−0.529115 + 0.848550i \(0.677476\pi\)
\(420\) 0 0
\(421\) −17.8801 + 17.8801i −0.871424 + 0.871424i −0.992628 0.121204i \(-0.961325\pi\)
0.121204 + 0.992628i \(0.461325\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 23.8676 1.15775
\(426\) 0 0
\(427\) −5.44215 5.44215i −0.263364 0.263364i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −3.02619 −0.145766 −0.0728832 0.997340i \(-0.523220\pi\)
−0.0728832 + 0.997340i \(0.523220\pi\)
\(432\) 0 0
\(433\) 33.3339 1.60192 0.800962 0.598715i \(-0.204322\pi\)
0.800962 + 0.598715i \(0.204322\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 19.9753 + 19.9753i 0.955549 + 0.955549i
\(438\) 0 0
\(439\) −25.0388 −1.19504 −0.597519 0.801855i \(-0.703847\pi\)
−0.597519 + 0.801855i \(0.703847\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −11.5230 + 11.5230i −0.547473 + 0.547473i −0.925709 0.378236i \(-0.876531\pi\)
0.378236 + 0.925709i \(0.376531\pi\)
\(444\) 0 0
\(445\) −1.46394 1.46394i −0.0693973 0.0693973i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 24.9666i 1.17825i 0.808042 + 0.589124i \(0.200527\pi\)
−0.808042 + 0.589124i \(0.799473\pi\)
\(450\) 0 0
\(451\) 4.57293 4.57293i 0.215331 0.215331i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0.433262i 0.0203116i
\(456\) 0 0
\(457\) 15.0783i 0.705333i −0.935749 0.352666i \(-0.885275\pi\)
0.935749 0.352666i \(-0.114725\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −1.98842 + 1.98842i −0.0926101 + 0.0926101i −0.751894 0.659284i \(-0.770860\pi\)
0.659284 + 0.751894i \(0.270860\pi\)
\(462\) 0 0
\(463\) 13.8131i 0.641949i 0.947088 + 0.320975i \(0.104010\pi\)
−0.947088 + 0.320975i \(0.895990\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −27.8035 27.8035i −1.28659 1.28659i −0.936842 0.349753i \(-0.886266\pi\)
−0.349753 0.936842i \(1.38627\pi\)
\(468\) 0 0
\(469\) −0.897143 + 0.897143i −0.0414262 + 0.0414262i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 3.49976 0.160919
\(474\) 0 0
\(475\) 15.0885 + 15.0885i 0.692308 + 0.692308i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 21.4026 0.977909 0.488954 0.872309i \(-0.337378\pi\)
0.488954 + 0.872309i \(0.337378\pi\)
\(480\) 0 0
\(481\) −4.10717 −0.187271
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 1.16784 + 1.16784i 0.0530287 + 0.0530287i
\(486\) 0 0
\(487\) 27.9883 1.26827 0.634136 0.773222i \(-0.281356\pi\)
0.634136 + 0.773222i \(0.281356\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −22.0491 + 22.0491i −0.995063 + 0.995063i −0.999988 0.00492464i \(-0.998432\pi\)
0.00492464 + 0.999988i \(0.498432\pi\)
\(492\) 0 0
\(493\) 7.34727 + 7.34727i 0.330904 + 0.330904i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 2.83052i 0.126966i
\(498\) 0 0
\(499\) −5.60480 + 5.60480i −0.250905 + 0.250905i −0.821342 0.570436i \(-0.806774\pi\)
0.570436 + 0.821342i \(0.306774\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 5.02371i 0.223996i −0.993708 0.111998i \(-0.964275\pi\)
0.993708 0.111998i \(-0.0357250\pi\)
\(504\) 0 0
\(505\) 0.105169i 0.00467996i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 26.3372 26.3372i 1.16738 1.16738i 0.184555 0.982822i \(-0.440915\pi\)
0.982822 0.184555i \(-0.0590845\pi\)
\(510\) 0 0
\(511\) 15.7394i 0.696271i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −1.84416 1.84416i −0.0812635 0.0812635i
\(516\) 0 0
\(517\) −40.5405 + 40.5405i −1.78297 + 1.78297i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0.453686 0.0198763 0.00993817 0.999951i \(-0.496837\pi\)
0.00993817 + 0.999951i \(0.496837\pi\)
\(522\) 0 0
\(523\) −26.5974 26.5974i −1.16302 1.16302i −0.983810 0.179214i \(-0.942645\pi\)
−0.179214 0.983810i \(-0.557355\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 15.6647 0.682363
\(528\) 0 0
\(529\) −20.3823 −0.886187
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 2.46229 + 2.46229i 0.106654 + 0.106654i
\(534\) 0 0
\(535\) −1.77960 −0.0769389
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −3.61173 + 3.61173i −0.155568 + 0.155568i
\(540\) 0 0
\(541\) −17.5559 17.5559i −0.754785 0.754785i 0.220583 0.975368i \(-0.429204\pi\)
−0.975368 + 0.220583i \(0.929204\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 1.34093i 0.0574390i
\(546\) 0 0
\(547\) −6.76713 + 6.76713i −0.289342 + 0.289342i −0.836820 0.547478i \(-0.815588\pi\)
0.547478 + 0.836820i \(0.315588\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 9.28954i 0.395748i
\(552\) 0 0
\(553\) 15.4151i 0.655515i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −29.6889 + 29.6889i −1.25796 + 1.25796i −0.305893 + 0.952066i \(0.598955\pi\)
−0.952066 + 0.305893i \(0.901045\pi\)
\(558\) 0 0
\(559\) 1.88444i 0.0797035i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 25.1503 + 25.1503i 1.05996 + 1.05996i 0.998084 + 0.0618753i \(0.0197081\pi\)
0.0618753 + 0.998084i \(0.480292\pi\)
\(564\) 0 0
\(565\) −0.870065 + 0.870065i −0.0366039 + 0.0366039i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −17.4528 −0.731660 −0.365830 0.930682i \(-0.619215\pi\)
−0.365830 + 0.930682i \(0.619215\pi\)
\(570\) 0 0
\(571\) 22.4569 + 22.4569i 0.939793 + 0.939793i 0.998288 0.0584947i \(-0.0186301\pi\)
−0.0584947 + 0.998288i \(0.518630\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −32.7692 −1.36657
\(576\) 0 0
\(577\) 40.6265 1.69130 0.845652 0.533734i \(-0.179212\pi\)
0.845652 + 0.533734i \(0.179212\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −7.57988 7.57988i −0.314466 0.314466i
\(582\) 0 0
\(583\) −28.9567 −1.19926
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 1.79577 1.79577i 0.0741194 0.0741194i −0.669075 0.743195i \(-0.733310\pi\)
0.743195 + 0.669075i \(0.233310\pi\)
\(588\) 0 0
\(589\) 9.90283 + 9.90283i 0.408039 + 0.408039i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 11.4046i 0.468331i −0.972197 0.234165i \(-0.924764\pi\)
0.972197 0.234165i \(-0.0752357\pi\)
\(594\) 0 0
\(595\) −0.534392 + 0.534392i −0.0219079 + 0.0219079i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 7.81649i 0.319373i 0.987168 + 0.159687i \(0.0510484\pi\)
−0.987168 + 0.159687i \(0.948952\pi\)
\(600\) 0 0
\(601\) 22.2752i 0.908625i 0.890842 + 0.454313i \(0.150115\pi\)
−0.890842 + 0.454313i \(0.849885\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −1.68084 + 1.68084i −0.0683359 + 0.0683359i
\(606\) 0 0
\(607\) 11.5129i 0.467293i −0.972322 0.233646i \(-0.924934\pi\)
0.972322 0.233646i \(-0.0750658\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −21.8290 21.8290i −0.883107 0.883107i
\(612\) 0 0
\(613\) 24.6256 24.6256i 0.994618 0.994618i −0.00536742 0.999986i \(-0.501709\pi\)
0.999986 + 0.00536742i \(0.00170851\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −29.3630 −1.18211 −0.591054 0.806632i \(-0.701288\pi\)
−0.591054 + 0.806632i \(0.701288\pi\)
\(618\) 0 0
\(619\) −32.5316 32.5316i −1.30756 1.30756i −0.923173 0.384384i \(-0.874414\pi\)
−0.384384 0.923173i \(-0.625586\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −13.1420 −0.526524
\(624\) 0 0
\(625\) −24.6284 −0.985134
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 5.06584 + 5.06584i 0.201988 + 0.201988i
\(630\) 0 0
\(631\) 10.4307 0.415240 0.207620 0.978210i \(-0.433428\pi\)
0.207620 + 0.978210i \(0.433428\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −0.734574 + 0.734574i −0.0291507 + 0.0291507i
\(636\) 0 0
\(637\) −1.94473 1.94473i −0.0770531 0.0770531i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 26.3287i 1.03992i −0.854191 0.519960i \(-0.825947\pi\)
0.854191 0.519960i \(-0.174053\pi\)
\(642\) 0 0
\(643\) −10.1662 + 10.1662i −0.400917 + 0.400917i −0.878556 0.477639i \(-0.841493\pi\)
0.477639 + 0.878556i \(0.341493\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 30.4560i 1.19735i −0.800992 0.598675i \(-0.795694\pi\)
0.800992 0.598675i \(-0.204306\pi\)
\(648\) 0 0
\(649\) 55.0047i 2.15912i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 0.424352 0.424352i 0.0166062 0.0166062i −0.698755 0.715361i \(-0.746262\pi\)
0.715361 + 0.698755i \(0.246262\pi\)
\(654\) 0 0
\(655\) 1.39735i 0.0545989i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −21.4421 21.4421i −0.835268 0.835268i 0.152964 0.988232i \(-0.451118\pi\)
−0.988232 + 0.152964i \(0.951118\pi\)
\(660\) 0 0
\(661\) 29.6529 29.6529i 1.15337 1.15337i 0.167492 0.985873i \(-0.446433\pi\)
0.985873 0.167492i \(-0.0535668\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −0.675660 −0.0262010
\(666\) 0 0
\(667\) −10.0875 10.0875i −0.390589 0.390589i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −39.3112 −1.51759
\(672\) 0 0
\(673\) −33.5720 −1.29410 −0.647052 0.762446i \(-0.723998\pi\)
−0.647052 + 0.762446i \(0.723998\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 23.4845 + 23.4845i 0.902584 + 0.902584i 0.995659 0.0930751i \(-0.0296697\pi\)
−0.0930751 + 0.995659i \(0.529670\pi\)
\(678\) 0 0
\(679\) 10.4839 0.402333
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 4.90491 4.90491i 0.187681 0.187681i −0.607012 0.794693i \(-0.707632\pi\)
0.794693 + 0.607012i \(0.207632\pi\)
\(684\) 0 0
\(685\) 2.49691 + 2.49691i 0.0954022 + 0.0954022i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 15.5917i 0.593996i
\(690\) 0 0
\(691\) 19.1177 19.1177i 0.727272 0.727272i −0.242804 0.970075i \(-0.578067\pi\)
0.970075 + 0.242804i \(0.0780671\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 2.10338i 0.0797858i
\(696\) 0 0
\(697\) 6.07405i 0.230071i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 6.01355 6.01355i 0.227129 0.227129i −0.584363 0.811492i \(-0.698656\pi\)
0.811492 + 0.584363i \(0.198656\pi\)
\(702\) 0 0
\(703\) 6.40501i 0.241570i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −0.472060 0.472060i −0.0177536 0.0177536i
\(708\) 0 0
\(709\) −6.33448 + 6.33448i −0.237896 + 0.237896i −0.815979 0.578082i \(-0.803801\pi\)
0.578082 + 0.815979i \(0.303801\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −21.5069 −0.805441
\(714\) 0 0
\(715\) −1.56483 1.56483i −0.0585212 0.0585212i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −19.8643 −0.740814 −0.370407 0.928869i \(-0.620782\pi\)
−0.370407 + 0.928869i \(0.620782\pi\)
\(720\) 0 0
\(721\) −16.5554 −0.616554
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −7.61967 7.61967i −0.282987 0.282987i
\(726\) 0 0
\(727\) 17.0880 0.633759 0.316879 0.948466i \(-0.397365\pi\)
0.316879 + 0.948466i \(0.397365\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 2.32430 2.32430i 0.0859673 0.0859673i
\(732\) 0 0
\(733\) 27.4896 + 27.4896i 1.01535 + 1.01535i 0.999880 + 0.0154724i \(0.00492520\pi\)
0.0154724 + 0.999880i \(0.495075\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 6.48048i 0.238711i
\(738\) 0 0
\(739\) −33.4666 + 33.4666i −1.23109 + 1.23109i −0.267542 + 0.963546i \(0.586212\pi\)
−0.963546 + 0.267542i \(0.913788\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0.720828i 0.0264446i 0.999913 + 0.0132223i \(0.00420892\pi\)
−0.999913 + 0.0132223i \(0.995791\pi\)
\(744\) 0 0
\(745\) 2.36208i 0.0865398i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −7.98789 + 7.98789i −0.291871 + 0.291871i
\(750\) 0 0
\(751\) 8.54158i 0.311687i 0.987782 + 0.155843i \(0.0498095\pi\)
−0.987782 + 0.155843i \(0.950190\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −0.0726208 0.0726208i −0.00264294 0.00264294i
\(756\) 0 0
\(757\) 5.80744 5.80744i 0.211075 0.211075i −0.593649 0.804724i \(-0.702313\pi\)
0.804724 + 0.593649i \(0.202313\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −19.8670 −0.720179 −0.360090 0.932918i \(-0.617254\pi\)
−0.360090 + 0.932918i \(0.617254\pi\)
\(762\) 0 0
\(763\) 6.01886 + 6.01886i 0.217897 + 0.217897i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −29.6172 −1.06942
\(768\) 0 0
\(769\) 51.4781 1.85635 0.928173 0.372148i \(-0.121379\pi\)
0.928173 + 0.372148i \(0.121379\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 17.8748 + 17.8748i 0.642913 + 0.642913i 0.951271 0.308358i \(-0.0997793\pi\)
−0.308358 + 0.951271i \(0.599779\pi\)
\(774\) 0 0
\(775\) −16.2454 −0.583553
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 3.83987 3.83987i 0.137578 0.137578i
\(780\) 0 0
\(781\) 10.2231 + 10.2231i 0.365810 + 0.365810i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 3.49259i 0.124656i
\(786\) 0 0
\(787\) 9.93955 9.93955i 0.354307 0.354307i −0.507403 0.861709i \(-0.669394\pi\)
0.861709 + 0.507403i \(0.169394\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 7.81071i 0.277717i
\(792\) 0 0
\(793\) 21.1671i 0.751664i
\(794\) 0