Properties

Label 5292.2.x.a.881.5
Level $5292$
Weight $2$
Character 5292.881
Analytic conductor $42.257$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 5292 = 2^{2} \cdot 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5292.x (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(42.2568327497\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} - 156 x^{7} + 558 x^{6} - 837 x^{5} + 1782 x^{4} - 4131 x^{3} + 3645 x^{2} - 4374 x + 6561\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 3^{6} \)
Twist minimal: no (minimal twist has level 252)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 881.5
Root \(1.08696 - 1.34852i\) of defining polynomial
Character \(\chi\) \(=\) 5292.881
Dual form 5292.2.x.a.4409.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.0382122 + 0.0661855i) q^{5} +O(q^{10})\) \(q+(-0.0382122 + 0.0661855i) q^{5} +(4.66300 - 2.69219i) q^{11} +(4.60313 + 2.65762i) q^{13} +3.78183 q^{17} +5.01070i q^{19} +(-2.02463 - 1.16892i) q^{23} +(2.49708 + 4.32507i) q^{25} +(-8.84430 + 5.10626i) q^{29} +(4.97636 + 2.87310i) q^{31} -0.708972 q^{37} +(3.29910 - 5.71422i) q^{41} +(0.716520 + 1.24105i) q^{43} +(-1.46192 - 2.53213i) q^{47} +12.1053i q^{53} +0.411498i q^{55} +(-0.289951 + 0.502210i) q^{59} +(-2.40641 + 1.38934i) q^{61} +(-0.351792 + 0.203107i) q^{65} +(-2.63593 + 4.56556i) q^{67} -3.32103i q^{71} -7.12826i q^{73} +(-0.469123 - 0.812544i) q^{79} +(-6.49790 - 11.2547i) q^{83} +(-0.144512 + 0.250303i) q^{85} +3.03588 q^{89} +(-0.331636 - 0.191470i) q^{95} +(-6.18183 + 3.56908i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + O(q^{10}) \) \( 16 q - 6 q^{11} - 3 q^{13} + 18 q^{17} + 21 q^{23} - 8 q^{25} - 6 q^{29} + 6 q^{31} - 2 q^{37} + 6 q^{41} - 2 q^{43} - 18 q^{47} - 15 q^{59} + 3 q^{61} - 39 q^{65} - 7 q^{67} - q^{79} + 6 q^{85} + 42 q^{89} + 6 q^{95} - 3 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/5292\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\) \(2647\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(1\)

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
\(5\) −0.0382122 + 0.0661855i −0.0170890 + 0.0295991i −0.874443 0.485127i \(-0.838773\pi\)
0.857354 + 0.514727i \(0.172107\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 4.66300 2.69219i 1.40595 0.811725i 0.410954 0.911656i \(-0.365196\pi\)
0.994994 + 0.0999316i \(0.0318624\pi\)
\(12\) 0 0
\(13\) 4.60313 + 2.65762i 1.27668 + 0.737091i 0.976236 0.216709i \(-0.0695324\pi\)
0.300442 + 0.953800i \(0.402866\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 3.78183 0.917229 0.458615 0.888635i \(-0.348346\pi\)
0.458615 + 0.888635i \(0.348346\pi\)
\(18\) 0 0
\(19\) 5.01070i 1.14953i 0.818317 + 0.574767i \(0.194907\pi\)
−0.818317 + 0.574767i \(0.805093\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −2.02463 1.16892i −0.422164 0.243737i 0.273839 0.961776i \(-0.411707\pi\)
−0.696003 + 0.718039i \(0.745040\pi\)
\(24\) 0 0
\(25\) 2.49708 + 4.32507i 0.499416 + 0.865014i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −8.84430 + 5.10626i −1.64235 + 0.948209i −0.662349 + 0.749196i \(0.730440\pi\)
−0.979997 + 0.199013i \(0.936226\pi\)
\(30\) 0 0
\(31\) 4.97636 + 2.87310i 0.893780 + 0.516024i 0.875177 0.483803i \(-0.160745\pi\)
0.0186031 + 0.999827i \(0.494078\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −0.708972 −0.116554 −0.0582771 0.998300i \(-0.518561\pi\)
−0.0582771 + 0.998300i \(0.518561\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 3.29910 5.71422i 0.515234 0.892411i −0.484610 0.874730i \(-0.661039\pi\)
0.999844 0.0176805i \(-0.00562816\pi\)
\(42\) 0 0
\(43\) 0.716520 + 1.24105i 0.109268 + 0.189258i 0.915474 0.402377i \(-0.131816\pi\)
−0.806206 + 0.591635i \(0.798483\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −1.46192 2.53213i −0.213244 0.369349i 0.739484 0.673174i \(-0.235069\pi\)
−0.952728 + 0.303825i \(0.901736\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 12.1053i 1.66279i 0.555683 + 0.831394i \(0.312457\pi\)
−0.555683 + 0.831394i \(0.687543\pi\)
\(54\) 0 0
\(55\) 0.411498i 0.0554863i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −0.289951 + 0.502210i −0.0377484 + 0.0653822i −0.884282 0.466953i \(-0.845352\pi\)
0.846534 + 0.532335i \(0.178685\pi\)
\(60\) 0 0
\(61\) −2.40641 + 1.38934i −0.308109 + 0.177887i −0.646080 0.763270i \(-0.723593\pi\)
0.337971 + 0.941156i \(0.390259\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −0.351792 + 0.203107i −0.0436344 + 0.0251923i
\(66\) 0 0
\(67\) −2.63593 + 4.56556i −0.322030 + 0.557771i −0.980907 0.194479i \(-0.937698\pi\)
0.658877 + 0.752251i \(0.271032\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 3.32103i 0.394134i −0.980390 0.197067i \(-0.936858\pi\)
0.980390 0.197067i \(-0.0631416\pi\)
\(72\) 0 0
\(73\) 7.12826i 0.834300i −0.908838 0.417150i \(-0.863029\pi\)
0.908838 0.417150i \(-0.136971\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −0.469123 0.812544i −0.0527804 0.0914184i 0.838428 0.545012i \(-0.183475\pi\)
−0.891208 + 0.453594i \(0.850142\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −6.49790 11.2547i −0.713238 1.23536i −0.963635 0.267221i \(-0.913895\pi\)
0.250398 0.968143i \(-0.419439\pi\)
\(84\) 0 0
\(85\) −0.144512 + 0.250303i −0.0156746 + 0.0271491i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 3.03588 0.321802 0.160901 0.986971i \(-0.448560\pi\)
0.160901 + 0.986971i \(0.448560\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −0.331636 0.191470i −0.0340251 0.0196444i
\(96\) 0 0
\(97\) −6.18183 + 3.56908i −0.627670 + 0.362385i −0.779849 0.625967i \(-0.784704\pi\)
0.152179 + 0.988353i \(0.451371\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −4.08628 7.07765i −0.406600 0.704252i 0.587906 0.808929i \(-0.299952\pi\)
−0.994506 + 0.104677i \(0.966619\pi\)
\(102\) 0 0
\(103\) 6.46599 + 3.73314i 0.637113 + 0.367837i 0.783502 0.621390i \(-0.213432\pi\)
−0.146389 + 0.989227i \(0.546765\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 4.61870i 0.446507i −0.974760 0.223253i \(-0.928332\pi\)
0.974760 0.223253i \(-0.0716677\pi\)
\(108\) 0 0
\(109\) −10.4558 −1.00149 −0.500744 0.865595i \(-0.666940\pi\)
−0.500744 + 0.865595i \(0.666940\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 16.6379 + 9.60591i 1.56516 + 0.903648i 0.996720 + 0.0809270i \(0.0257881\pi\)
0.568445 + 0.822721i \(0.307545\pi\)
\(114\) 0 0
\(115\) 0.154731 0.0893340i 0.0144287 0.00833044i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 8.99573 15.5811i 0.817793 1.41646i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −0.763798 −0.0683162
\(126\) 0 0
\(127\) 1.26488 0.112240 0.0561198 0.998424i \(-0.482127\pi\)
0.0561198 + 0.998424i \(0.482127\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 7.24394 12.5469i 0.632906 1.09623i −0.354049 0.935227i \(-0.615195\pi\)
0.986955 0.160998i \(-0.0514714\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −13.3414 + 7.70264i −1.13983 + 0.658081i −0.946389 0.323030i \(-0.895298\pi\)
−0.193442 + 0.981112i \(0.561965\pi\)
\(138\) 0 0
\(139\) 0.374701 + 0.216333i 0.0317817 + 0.0183492i 0.515807 0.856705i \(-0.327492\pi\)
−0.484025 + 0.875054i \(0.660826\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 28.6192 2.39326
\(144\) 0 0
\(145\) 0.780486i 0.0648159i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −4.04535 2.33558i −0.331408 0.191338i 0.325058 0.945694i \(-0.394616\pi\)
−0.656466 + 0.754356i \(0.727949\pi\)
\(150\) 0 0
\(151\) 4.12276 + 7.14083i 0.335506 + 0.581113i 0.983582 0.180463i \(-0.0577595\pi\)
−0.648076 + 0.761575i \(0.724426\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −0.380316 + 0.219575i −0.0305477 + 0.0176367i
\(156\) 0 0
\(157\) 15.2334 + 8.79500i 1.21576 + 0.701917i 0.964007 0.265875i \(-0.0856609\pi\)
0.251749 + 0.967793i \(0.418994\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 10.5419 0.825709 0.412854 0.910797i \(-0.364532\pi\)
0.412854 + 0.910797i \(0.364532\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −4.59146 + 7.95265i −0.355298 + 0.615395i −0.987169 0.159679i \(-0.948954\pi\)
0.631871 + 0.775074i \(0.282287\pi\)
\(168\) 0 0
\(169\) 7.62587 + 13.2084i 0.586605 + 1.01603i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −1.22358 2.11931i −0.0930274 0.161128i 0.815756 0.578396i \(-0.196321\pi\)
−0.908784 + 0.417268i \(0.862988\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 5.83712i 0.436287i 0.975917 + 0.218143i \(0.0700001\pi\)
−0.975917 + 0.218143i \(0.930000\pi\)
\(180\) 0 0
\(181\) 16.0704i 1.19451i 0.802053 + 0.597253i \(0.203741\pi\)
−0.802053 + 0.597253i \(0.796259\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0.0270914 0.0469237i 0.00199180 0.00344990i
\(186\) 0 0
\(187\) 17.6347 10.1814i 1.28958 0.744537i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −6.90415 + 3.98611i −0.499567 + 0.288425i −0.728535 0.685009i \(-0.759798\pi\)
0.228968 + 0.973434i \(0.426465\pi\)
\(192\) 0 0
\(193\) −0.359027 + 0.621853i −0.0258433 + 0.0447620i −0.878658 0.477452i \(-0.841560\pi\)
0.852814 + 0.522214i \(0.174894\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 13.5035i 0.962083i 0.876698 + 0.481042i \(0.159741\pi\)
−0.876698 + 0.481042i \(0.840259\pi\)
\(198\) 0 0
\(199\) 24.5452i 1.73997i 0.493082 + 0.869983i \(0.335870\pi\)
−0.493082 + 0.869983i \(0.664130\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0.252132 + 0.436706i 0.0176097 + 0.0305009i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 13.4897 + 23.3649i 0.933105 + 1.61618i
\(210\) 0 0
\(211\) −11.7838 + 20.4101i −0.811227 + 1.40509i 0.100778 + 0.994909i \(0.467867\pi\)
−0.912005 + 0.410178i \(0.865467\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −0.109519 −0.00746916
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 17.4083 + 10.0507i 1.17101 + 0.676081i
\(222\) 0 0
\(223\) 6.47489 3.73828i 0.433590 0.250334i −0.267285 0.963618i \(-0.586126\pi\)
0.700875 + 0.713284i \(0.252793\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −0.318701 0.552006i −0.0211529 0.0366379i 0.855255 0.518207i \(-0.173400\pi\)
−0.876408 + 0.481569i \(0.840067\pi\)
\(228\) 0 0
\(229\) 1.58351 + 0.914239i 0.104641 + 0.0604146i 0.551407 0.834236i \(-0.314091\pi\)
−0.446766 + 0.894651i \(0.647424\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 20.1186i 1.31801i −0.752136 0.659007i \(-0.770977\pi\)
0.752136 0.659007i \(-0.229023\pi\)
\(234\) 0 0
\(235\) 0.223454 0.0145765
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 2.41455 + 1.39404i 0.156184 + 0.0901730i 0.576055 0.817411i \(-0.304591\pi\)
−0.419871 + 0.907584i \(0.637925\pi\)
\(240\) 0 0
\(241\) 20.0304 11.5645i 1.29027 0.744938i 0.311568 0.950224i \(-0.399146\pi\)
0.978702 + 0.205286i \(0.0658126\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −13.3165 + 23.0649i −0.847310 + 1.46758i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 18.6541 1.17743 0.588717 0.808339i \(-0.299633\pi\)
0.588717 + 0.808339i \(0.299633\pi\)
\(252\) 0 0
\(253\) −12.5878 −0.791388
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −5.43687 + 9.41694i −0.339143 + 0.587413i −0.984272 0.176661i \(-0.943470\pi\)
0.645129 + 0.764074i \(0.276804\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 16.4519 9.49852i 1.01447 0.585704i 0.101972 0.994787i \(-0.467485\pi\)
0.912497 + 0.409083i \(0.134151\pi\)
\(264\) 0 0
\(265\) −0.801194 0.462570i −0.0492170 0.0284154i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 8.59576 0.524093 0.262046 0.965055i \(-0.415603\pi\)
0.262046 + 0.965055i \(0.415603\pi\)
\(270\) 0 0
\(271\) 1.83258i 0.111322i −0.998450 0.0556608i \(-0.982273\pi\)
0.998450 0.0556608i \(-0.0177265\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 23.2878 + 13.4452i 1.40431 + 0.810776i
\(276\) 0 0
\(277\) −7.90931 13.6993i −0.475224 0.823113i 0.524373 0.851489i \(-0.324300\pi\)
−0.999597 + 0.0283760i \(0.990966\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 9.95916 5.74992i 0.594114 0.343012i −0.172609 0.984990i \(-0.555220\pi\)
0.766722 + 0.641979i \(0.221886\pi\)
\(282\) 0 0
\(283\) −8.59806 4.96409i −0.511101 0.295085i 0.222185 0.975005i \(-0.428681\pi\)
−0.733286 + 0.679920i \(0.762014\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −2.69774 −0.158691
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 8.63598 14.9580i 0.504520 0.873854i −0.495467 0.868627i \(-0.665003\pi\)
0.999986 0.00522664i \(-0.00166370\pi\)
\(294\) 0 0
\(295\) −0.0221594 0.0383812i −0.00129017 0.00223464i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −6.21308 10.7614i −0.359312 0.622346i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0.212359i 0.0121596i
\(306\) 0 0
\(307\) 21.6425i 1.23520i −0.786490 0.617602i \(-0.788104\pi\)
0.786490 0.617602i \(-0.211896\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 10.1016 17.4964i 0.572808 0.992133i −0.423468 0.905911i \(-0.639187\pi\)
0.996276 0.0862215i \(-0.0274793\pi\)
\(312\) 0 0
\(313\) −18.9146 + 10.9203i −1.06911 + 0.617254i −0.927939 0.372731i \(-0.878421\pi\)
−0.141175 + 0.989985i \(0.545088\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −21.5288 + 12.4297i −1.20918 + 0.698120i −0.962580 0.270997i \(-0.912647\pi\)
−0.246599 + 0.969117i \(0.579313\pi\)
\(318\) 0 0
\(319\) −27.4940 + 47.6210i −1.53937 + 2.66626i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 18.9496i 1.05439i
\(324\) 0 0
\(325\) 26.5451i 1.47246i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −8.07219 13.9814i −0.443688 0.768490i 0.554272 0.832336i \(-0.312997\pi\)
−0.997960 + 0.0638459i \(0.979663\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −0.201449 0.348920i −0.0110063 0.0190635i
\(336\) 0 0
\(337\) −7.81522 + 13.5364i −0.425722 + 0.737372i −0.996488 0.0837408i \(-0.973313\pi\)
0.570765 + 0.821113i \(0.306647\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 30.9397 1.67548
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 28.0445 + 16.1915i 1.50551 + 0.869206i 0.999980 + 0.00639573i \(0.00203584\pi\)
0.505529 + 0.862810i \(0.331297\pi\)
\(348\) 0 0
\(349\) 26.0421 15.0354i 1.39400 0.804827i 0.400246 0.916408i \(-0.368925\pi\)
0.993755 + 0.111581i \(0.0355915\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −8.50607 14.7329i −0.452733 0.784156i 0.545822 0.837901i \(-0.316217\pi\)
−0.998555 + 0.0537453i \(0.982884\pi\)
\(354\) 0 0
\(355\) 0.219804 + 0.126904i 0.0116660 + 0.00673537i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 29.1783i 1.53997i −0.638060 0.769987i \(-0.720263\pi\)
0.638060 0.769987i \(-0.279737\pi\)
\(360\) 0 0
\(361\) −6.10712 −0.321427
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0.471788 + 0.272387i 0.0246945 + 0.0142574i
\(366\) 0 0
\(367\) 15.6981 9.06329i 0.819433 0.473100i −0.0307880 0.999526i \(-0.509802\pi\)
0.850221 + 0.526426i \(0.176468\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 10.1823 17.6362i 0.527219 0.913170i −0.472278 0.881450i \(-0.656568\pi\)
0.999497 0.0317200i \(-0.0100985\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −54.2820 −2.79566
\(378\) 0 0
\(379\) −21.9961 −1.12986 −0.564931 0.825138i \(-0.691097\pi\)
−0.564931 + 0.825138i \(0.691097\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −16.3127 + 28.2544i −0.833538 + 1.44373i 0.0616774 + 0.998096i \(0.480355\pi\)
−0.895215 + 0.445634i \(0.852978\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −13.6400 + 7.87504i −0.691574 + 0.399280i −0.804201 0.594357i \(-0.797407\pi\)
0.112628 + 0.993637i \(0.464073\pi\)
\(390\) 0 0
\(391\) −7.65680 4.42066i −0.387221 0.223562i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0.0717049 0.00360786
\(396\) 0 0
\(397\) 3.41635i 0.171462i 0.996318 + 0.0857308i \(0.0273225\pi\)
−0.996318 + 0.0857308i \(0.972678\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −0.851348 0.491526i −0.0425143 0.0245456i 0.478592 0.878037i \(-0.341147\pi\)
−0.521106 + 0.853492i \(0.674481\pi\)
\(402\) 0 0
\(403\) 15.2712 + 26.4505i 0.760713 + 1.31759i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −3.30594 + 1.90868i −0.163869 + 0.0946099i
\(408\) 0 0
\(409\) 25.0195 + 14.4450i 1.23714 + 0.714260i 0.968508 0.248984i \(-0.0800966\pi\)
0.268627 + 0.963244i \(0.413430\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0.993198 0.0487542
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 6.28926 10.8933i 0.307251 0.532174i −0.670509 0.741901i \(-0.733924\pi\)
0.977760 + 0.209727i \(0.0672577\pi\)
\(420\) 0 0
\(421\) −13.0232 22.5568i −0.634710 1.09935i −0.986576 0.163300i \(-0.947786\pi\)
0.351866 0.936050i \(-0.385547\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 9.44354 + 16.3567i 0.458079 + 0.793416i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 7.25676i 0.349546i 0.984609 + 0.174773i \(0.0559192\pi\)
−0.984609 + 0.174773i \(0.944081\pi\)
\(432\) 0 0
\(433\) 8.29113i 0.398446i −0.979954 0.199223i \(-0.936158\pi\)
0.979954 0.199223i \(-0.0638419\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 5.85710 10.1448i 0.280183 0.485292i
\(438\) 0 0
\(439\) −2.83357 + 1.63596i −0.135239 + 0.0780802i −0.566093 0.824341i \(-0.691546\pi\)
0.430854 + 0.902422i \(0.358212\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 2.46737 1.42454i 0.117228 0.0676817i −0.440239 0.897880i \(-0.645106\pi\)
0.557468 + 0.830199i \(0.311773\pi\)
\(444\) 0 0
\(445\) −0.116008 + 0.200931i −0.00549929 + 0.00952505i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 19.9802i 0.942925i −0.881886 0.471463i \(-0.843726\pi\)
0.881886 0.471463i \(-0.156274\pi\)
\(450\) 0 0
\(451\) 35.5272i 1.67291i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −9.15008 15.8484i −0.428023 0.741357i 0.568675 0.822563i \(-0.307456\pi\)
−0.996697 + 0.0812053i \(0.974123\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 4.52954 + 7.84539i 0.210962 + 0.365396i 0.952016 0.306049i \(-0.0990071\pi\)
−0.741054 + 0.671445i \(0.765674\pi\)
\(462\) 0 0
\(463\) 10.8227 18.7455i 0.502974 0.871176i −0.497021 0.867739i \(-0.665573\pi\)
0.999994 0.00343694i \(-0.00109401\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 27.5523 1.27497 0.637484 0.770464i \(-0.279975\pi\)
0.637484 + 0.770464i \(0.279975\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 6.68227 + 3.85801i 0.307251 + 0.177392i
\(474\) 0 0
\(475\) −21.6716 + 12.5121i −0.994362 + 0.574095i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −2.47325 4.28380i −0.113006 0.195732i 0.803975 0.594663i \(-0.202715\pi\)
−0.916981 + 0.398931i \(0.869381\pi\)
\(480\) 0 0
\(481\) −3.26349 1.88418i −0.148802 0.0859110i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0.545530i 0.0247713i
\(486\) 0 0
\(487\) 9.57146 0.433724 0.216862 0.976202i \(-0.430418\pi\)
0.216862 + 0.976202i \(0.430418\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 33.0010 + 19.0531i 1.48931 + 0.859855i 0.999925 0.0122119i \(-0.00388725\pi\)
0.489387 + 0.872067i \(0.337221\pi\)
\(492\) 0 0
\(493\) −33.4477 + 19.3110i −1.50641 + 0.869725i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 12.4192 21.5107i 0.555960 0.962951i −0.441868 0.897080i \(-0.645684\pi\)
0.997828 0.0658709i \(-0.0209825\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 27.2820 1.21645 0.608223 0.793766i \(-0.291883\pi\)
0.608223 + 0.793766i \(0.291883\pi\)
\(504\) 0 0
\(505\) 0.624584 0.0277936
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −20.8860 + 36.1757i −0.925758 + 1.60346i −0.135420 + 0.990788i \(0.543238\pi\)
−0.790338 + 0.612671i \(0.790095\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −0.494160 + 0.285303i −0.0217753 + 0.0125720i
\(516\) 0 0
\(517\) −13.6339 7.87154i −0.599619 0.346190i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 4.05257 0.177546 0.0887732 0.996052i \(-0.471705\pi\)
0.0887732 + 0.996052i \(0.471705\pi\)
\(522\) 0 0
\(523\) 30.3027i 1.32505i −0.749042 0.662523i \(-0.769486\pi\)
0.749042 0.662523i \(-0.230514\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 18.8198 + 10.8656i 0.819801 + 0.473312i
\(528\) 0 0
\(529\) −8.76726 15.1853i −0.381185 0.660232i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 30.3724 17.5355i 1.31558 0.759548i
\(534\) 0 0
\(535\) 0.305691 + 0.176491i 0.0132162 + 0.00763037i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −17.6536 −0.758988 −0.379494 0.925194i \(-0.623902\pi\)
−0.379494 + 0.925194i \(0.623902\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0.399541 0.692026i 0.0171145 0.0296431i
\(546\) 0 0
\(547\) −2.18319 3.78140i −0.0933466 0.161681i 0.815571 0.578657i \(-0.196423\pi\)
−0.908917 + 0.416976i \(0.863090\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −25.5859 44.3161i −1.09000 1.88793i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 17.0350i 0.721796i −0.932605 0.360898i \(-0.882470\pi\)
0.932605 0.360898i \(-0.117530\pi\)
\(558\) 0 0
\(559\) 7.61695i 0.322163i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −6.45992 + 11.1889i −0.272253 + 0.471556i −0.969438 0.245335i \(-0.921102\pi\)
0.697185 + 0.716891i \(0.254436\pi\)
\(564\) 0 0
\(565\) −1.27155 + 0.734127i −0.0534943 + 0.0308850i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −18.8280 + 10.8704i −0.789313 + 0.455710i −0.839720 0.543019i \(-0.817281\pi\)
0.0504079 + 0.998729i \(0.483948\pi\)
\(570\) 0 0
\(571\) 16.8254 29.1425i 0.704122 1.21958i −0.262885 0.964827i \(-0.584674\pi\)
0.967007 0.254748i \(-0.0819925\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 11.6755i 0.486904i
\(576\) 0 0
\(577\) 14.5028i 0.603760i 0.953346 + 0.301880i \(0.0976142\pi\)
−0.953346 + 0.301880i \(0.902386\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 32.5897 + 56.4469i 1.34973 + 2.33779i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 15.8417 + 27.4386i 0.653857 + 1.13251i 0.982179 + 0.187948i \(0.0601837\pi\)
−0.328322 + 0.944566i \(0.606483\pi\)
\(588\) 0 0
\(589\) −14.3963 + 24.9350i −0.593187 + 1.02743i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 7.08201 0.290823 0.145412 0.989371i \(-0.453549\pi\)
0.145412 + 0.989371i \(0.453549\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −5.20178 3.00325i −0.212539 0.122709i 0.389952 0.920835i \(-0.372492\pi\)
−0.602491 + 0.798126i \(0.705825\pi\)
\(600\) 0 0
\(601\) 0.530083 0.306043i 0.0216225 0.0124838i −0.489150 0.872200i \(-0.662693\pi\)
0.510772 + 0.859716i \(0.329360\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0.687494 + 1.19077i 0.0279506 + 0.0484119i
\(606\) 0 0
\(607\) −1.77500 1.02480i −0.0720450 0.0415952i 0.463545 0.886073i \(-0.346577\pi\)
−0.535590 + 0.844478i \(0.679911\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 15.5409i 0.628719i
\(612\) 0 0
\(613\) 9.86332 0.398376 0.199188 0.979961i \(-0.436170\pi\)
0.199188 + 0.979961i \(0.436170\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −23.2143 13.4028i −0.934571 0.539575i −0.0463170 0.998927i \(-0.514748\pi\)
−0.888254 + 0.459352i \(0.848082\pi\)
\(618\) 0 0
\(619\) −0.0603011 + 0.0348148i −0.00242370 + 0.00139933i −0.501211 0.865325i \(-0.667112\pi\)
0.498788 + 0.866724i \(0.333779\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −12.4562 + 21.5748i −0.498248 + 0.862992i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −2.68121 −0.106907
\(630\) 0 0
\(631\) 11.8214 0.470603 0.235301 0.971922i \(-0.424392\pi\)
0.235301 + 0.971922i \(0.424392\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −0.0483338 + 0.0837165i −0.00191807 + 0.00332219i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −17.7673 + 10.2580i −0.701766 + 0.405165i −0.808005 0.589176i \(-0.799453\pi\)
0.106239 + 0.994341i \(0.466119\pi\)
\(642\) 0 0
\(643\) 15.6081 + 9.01132i 0.615522 + 0.355372i 0.775123 0.631810i \(-0.217688\pi\)
−0.159602 + 0.987182i \(0.551021\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 18.2365 0.716952 0.358476 0.933539i \(-0.383296\pi\)
0.358476 + 0.933539i \(0.383296\pi\)
\(648\) 0 0
\(649\) 3.12241i 0.122565i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −7.79559 4.50079i −0.305065 0.176129i 0.339651 0.940552i \(-0.389691\pi\)
−0.644716 + 0.764422i \(0.723024\pi\)
\(654\) 0 0
\(655\) 0.553614 + 0.958888i 0.0216315 + 0.0374669i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −30.4806 + 17.5980i −1.18735 + 0.685519i −0.957704 0.287754i \(-0.907091\pi\)
−0.229650 + 0.973273i \(0.573758\pi\)
\(660\) 0 0
\(661\) −10.8797 6.28141i −0.423172 0.244318i 0.273262 0.961940i \(-0.411898\pi\)
−0.696433 + 0.717621i \(0.745231\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 23.8752 0.924452
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −7.48072 + 12.9570i −0.288790 + 0.500199i
\(672\) 0 0
\(673\) 23.8913 + 41.3810i 0.920942 + 1.59512i 0.797960 + 0.602710i \(0.205913\pi\)
0.122982 + 0.992409i \(0.460754\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −18.5235 32.0837i −0.711918 1.23308i −0.964136 0.265407i \(-0.914494\pi\)
0.252219 0.967670i \(-0.418840\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 25.0390i 0.958092i −0.877790 0.479046i \(-0.840983\pi\)
0.877790 0.479046i \(-0.159017\pi\)
\(684\) 0 0
\(685\) 1.17734i 0.0449839i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −32.1712 + 55.7222i −1.22563 + 2.12285i
\(690\) 0 0
\(691\) 40.2655 23.2473i 1.53177 0.884370i 0.532493 0.846434i \(-0.321255\pi\)
0.999280 0.0379352i \(-0.0120781\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −0.0286363 + 0.0165332i −0.00108624 + 0.000627139i
\(696\) 0 0
\(697\) 12.4767 21.6102i 0.472587 0.818545i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 36.0041i 1.35986i 0.733279 + 0.679928i \(0.237989\pi\)
−0.733279 + 0.679928i \(0.762011\pi\)
\(702\) 0 0
\(703\) 3.55244i 0.133983i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −15.9158 27.5670i −0.597731 1.03530i −0.993155 0.116802i \(-0.962736\pi\)
0.395424 0.918499i \(-0.370598\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −6.71685 11.6339i −0.251548 0.435694i
\(714\) 0 0
\(715\) −1.09360 + 1.89418i −0.0408985 + 0.0708382i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 40.0541 1.49377 0.746883 0.664955i \(-0.231550\pi\)
0.746883 + 0.664955i \(0.231550\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −44.1699 25.5015i −1.64043 0.947101i
\(726\) 0 0
\(727\) 3.39242 1.95862i 0.125818 0.0726411i −0.435770 0.900058i \(-0.643524\pi\)
0.561588 + 0.827417i \(0.310191\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 2.70976 + 4.69344i 0.100224 + 0.173593i
\(732\) 0 0
\(733\) −20.4239 11.7918i −0.754376 0.435539i 0.0728971 0.997339i \(-0.476776\pi\)
−0.827273 + 0.561800i \(0.810109\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 28.3856i 1.04560i
\(738\) 0 0
\(739\) −33.7282 −1.24071 −0.620355 0.784321i \(-0.713011\pi\)
−0.620355 + 0.784321i \(0.713011\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −29.4003 16.9743i −1.07859 0.622725i −0.148076 0.988976i \(-0.547308\pi\)
−0.930516 + 0.366251i \(0.880641\pi\)
\(744\) 0 0
\(745\) 0.309164 0.178496i 0.0113269 0.00653958i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −1.69831 + 2.94157i −0.0619724 + 0.107339i −0.895347 0.445369i \(-0.853072\pi\)
0.833375 + 0.552709i \(0.186406\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −0.630160 −0.0229339
\(756\) 0 0
\(757\) 29.1344 1.05891 0.529454 0.848339i \(-0.322397\pi\)
0.529454 + 0.848339i \(0.322397\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −8.36288 + 14.4849i −0.303154 + 0.525079i −0.976849 0.213931i \(-0.931373\pi\)
0.673694 + 0.739010i \(0.264706\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −2.66937 + 1.54116i −0.0963852 + 0.0556480i
\(768\) 0 0
\(769\) 24.0816 + 13.9035i 0.868404 + 0.501373i 0.866818 0.498625i \(-0.166162\pi\)
0.00158643 + 0.999999i \(0.499495\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 12.8448 0.461994 0.230997 0.972954i \(-0.425801\pi\)
0.230997 + 0.972954i \(0.425801\pi\)
\(774\) 0 0
\(775\) 28.6975i 1.03084i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 28.6322 + 16.5308i 1.02586 + 0.592278i
\(780\) 0 0
\(781\) −8.94083 15.4860i −0.319928 0.554132i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −1.16420 + 0.672153i −0.0415522 + 0.0239902i
\(786\) 0 0
\(787\) 6.55243 + 3.78305i 0.233569 + 0.134851i 0.612217 0.790689i \(-0.290278\pi\)
−0.378648 + 0.925541i \(0.623611\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −14.7693 −0.524474
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −4.03362 + 6.98643i −0.142878 + 0.247472i −0.928579 0.371134i \(-0.878969\pi\)
0.785701 + 0.618606i \(0.212302\pi\)
\(798\) 0 0
\(799\) −5.52875 9.57608i −0.195593 0.338777i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −19.1906 33.2391i −0.677222 1.17298i
\(804\) 0 0
\(805\) 0 0
\(806\)