Properties

Label 6048.2.h.f.2591.7
Level 6048
Weight 2
Character 6048.2591
Analytic conductor 48.294
Analytic rank 0
Dimension 8
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6048.h (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(48.2935231425\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\Q(\zeta_{24})\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 2591.7
Root \(-0.258819 + 0.965926i\)
Character \(\chi\) = 6048.2591
Dual form 6048.2.h.f.2591.2

$q$-expansion

\(f(q)\) \(=\) \(q+3.34607i q^{5} -1.00000i q^{7} +O(q^{10})\) \(q+3.34607i q^{5} -1.00000i q^{7} +0.896575 q^{11} +4.00000 q^{13} -6.31319i q^{17} +1.00000i q^{19} -7.20977 q^{23} -6.19615 q^{25} -7.72741i q^{29} +3.73205i q^{31} +3.34607 q^{35} -11.7321 q^{37} -7.86611i q^{41} +7.46410i q^{43} -8.76268 q^{47} -1.00000 q^{49} -2.82843i q^{53} +3.00000i q^{55} +3.86370 q^{59} -12.3923 q^{61} +13.3843i q^{65} +10.9282i q^{67} -5.79555 q^{71} -14.3923 q^{73} -0.896575i q^{77} -7.46410i q^{79} +6.96953 q^{83} +21.1244 q^{85} -13.2456i q^{89} -4.00000i q^{91} -3.34607 q^{95} +2.92820 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + O(q^{10}) \) \( 8q + 32q^{13} - 8q^{25} - 80q^{37} - 8q^{49} - 16q^{61} - 32q^{73} + 72q^{85} - 32q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/6048\mathbb{Z}\right)^\times\).

\(n\) \(2593\) \(3781\) \(3809\) \(4159\)
\(\chi(n)\) \(1\) \(1\) \(-1\) \(-1\)

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
\(5\) 3.34607i 1.49641i 0.663470 + 0.748203i \(0.269083\pi\)
−0.663470 + 0.748203i \(0.730917\pi\)
\(6\) 0 0
\(7\) − 1.00000i − 0.377964i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 0.896575 0.270328 0.135164 0.990823i \(-0.456844\pi\)
0.135164 + 0.990823i \(0.456844\pi\)
\(12\) 0 0
\(13\) 4.00000 1.10940 0.554700 0.832050i \(-0.312833\pi\)
0.554700 + 0.832050i \(0.312833\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) − 6.31319i − 1.53117i −0.643332 0.765587i \(-0.722449\pi\)
0.643332 0.765587i \(-0.277551\pi\)
\(18\) 0 0
\(19\) 1.00000i 0.229416i 0.993399 + 0.114708i \(0.0365932\pi\)
−0.993399 + 0.114708i \(0.963407\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −7.20977 −1.50334 −0.751670 0.659539i \(-0.770752\pi\)
−0.751670 + 0.659539i \(0.770752\pi\)
\(24\) 0 0
\(25\) −6.19615 −1.23923
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) − 7.72741i − 1.43494i −0.696588 0.717472i \(-0.745299\pi\)
0.696588 0.717472i \(-0.254701\pi\)
\(30\) 0 0
\(31\) 3.73205i 0.670296i 0.942165 + 0.335148i \(0.108786\pi\)
−0.942165 + 0.335148i \(0.891214\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 3.34607 0.565588
\(36\) 0 0
\(37\) −11.7321 −1.92874 −0.964369 0.264562i \(-0.914773\pi\)
−0.964369 + 0.264562i \(0.914773\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) − 7.86611i − 1.22848i −0.789119 0.614240i \(-0.789463\pi\)
0.789119 0.614240i \(-0.210537\pi\)
\(42\) 0 0
\(43\) 7.46410i 1.13826i 0.822246 + 0.569132i \(0.192721\pi\)
−0.822246 + 0.569132i \(0.807279\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −8.76268 −1.27817 −0.639084 0.769137i \(-0.720687\pi\)
−0.639084 + 0.769137i \(0.720687\pi\)
\(48\) 0 0
\(49\) −1.00000 −0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) − 2.82843i − 0.388514i −0.980951 0.194257i \(-0.937770\pi\)
0.980951 0.194257i \(-0.0622296\pi\)
\(54\) 0 0
\(55\) 3.00000i 0.404520i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 3.86370 0.503011 0.251506 0.967856i \(-0.419074\pi\)
0.251506 + 0.967856i \(0.419074\pi\)
\(60\) 0 0
\(61\) −12.3923 −1.58667 −0.793336 0.608784i \(-0.791658\pi\)
−0.793336 + 0.608784i \(0.791658\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 13.3843i 1.66011i
\(66\) 0 0
\(67\) 10.9282i 1.33509i 0.744568 + 0.667546i \(0.232655\pi\)
−0.744568 + 0.667546i \(0.767345\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −5.79555 −0.687806 −0.343903 0.939005i \(-0.611749\pi\)
−0.343903 + 0.939005i \(0.611749\pi\)
\(72\) 0 0
\(73\) −14.3923 −1.68449 −0.842246 0.539093i \(-0.818767\pi\)
−0.842246 + 0.539093i \(0.818767\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) − 0.896575i − 0.102174i
\(78\) 0 0
\(79\) − 7.46410i − 0.839777i −0.907576 0.419889i \(-0.862069\pi\)
0.907576 0.419889i \(-0.137931\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 6.96953 0.765006 0.382503 0.923954i \(-0.375062\pi\)
0.382503 + 0.923954i \(0.375062\pi\)
\(84\) 0 0
\(85\) 21.1244 2.29126
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) − 13.2456i − 1.40403i −0.712164 0.702013i \(-0.752285\pi\)
0.712164 0.702013i \(-0.247715\pi\)
\(90\) 0 0
\(91\) − 4.00000i − 0.419314i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −3.34607 −0.343299
\(96\) 0 0
\(97\) 2.92820 0.297314 0.148657 0.988889i \(-0.452505\pi\)
0.148657 + 0.988889i \(0.452505\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) − 0.656339i − 0.0653082i −0.999467 0.0326541i \(-0.989604\pi\)
0.999467 0.0326541i \(-0.0103960\pi\)
\(102\) 0 0
\(103\) 18.1244i 1.78585i 0.450210 + 0.892923i \(0.351349\pi\)
−0.450210 + 0.892923i \(0.648651\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −4.52004 −0.436969 −0.218484 0.975840i \(-0.570111\pi\)
−0.218484 + 0.975840i \(0.570111\pi\)
\(108\) 0 0
\(109\) −3.53590 −0.338678 −0.169339 0.985558i \(-0.554163\pi\)
−0.169339 + 0.985558i \(0.554163\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 9.52056i 0.895619i 0.894129 + 0.447809i \(0.147796\pi\)
−0.894129 + 0.447809i \(0.852204\pi\)
\(114\) 0 0
\(115\) − 24.1244i − 2.24961i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −6.31319 −0.578729
\(120\) 0 0
\(121\) −10.1962 −0.926923
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) − 4.00240i − 0.357986i
\(126\) 0 0
\(127\) 16.3923i 1.45458i 0.686329 + 0.727291i \(0.259221\pi\)
−0.686329 + 0.727291i \(0.740779\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 5.37945 0.470005 0.235002 0.971995i \(-0.424490\pi\)
0.235002 + 0.971995i \(0.424490\pi\)
\(132\) 0 0
\(133\) 1.00000 0.0867110
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) − 1.31268i − 0.112150i −0.998427 0.0560748i \(-0.982141\pi\)
0.998427 0.0560748i \(-0.0178585\pi\)
\(138\) 0 0
\(139\) 0.535898i 0.0454543i 0.999742 + 0.0227272i \(0.00723490\pi\)
−0.999742 + 0.0227272i \(0.992765\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 3.58630 0.299902
\(144\) 0 0
\(145\) 25.8564 2.14726
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) − 6.69213i − 0.548241i −0.961695 0.274120i \(-0.911613\pi\)
0.961695 0.274120i \(-0.0883867\pi\)
\(150\) 0 0
\(151\) 17.3205i 1.40952i 0.709444 + 0.704761i \(0.248946\pi\)
−0.709444 + 0.704761i \(0.751054\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −12.4877 −1.00304
\(156\) 0 0
\(157\) −1.46410 −0.116848 −0.0584240 0.998292i \(-0.518608\pi\)
−0.0584240 + 0.998292i \(0.518608\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 7.20977i 0.568209i
\(162\) 0 0
\(163\) − 19.3205i − 1.51330i −0.653821 0.756649i \(-0.726835\pi\)
0.653821 0.756649i \(-0.273165\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −10.8332 −0.838301 −0.419150 0.907917i \(-0.637672\pi\)
−0.419150 + 0.907917i \(0.637672\pi\)
\(168\) 0 0
\(169\) 3.00000 0.230769
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) − 1.17398i − 0.0892558i −0.999004 0.0446279i \(-0.985790\pi\)
0.999004 0.0446279i \(-0.0142102\pi\)
\(174\) 0 0
\(175\) 6.19615i 0.468385i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −8.10634 −0.605897 −0.302948 0.953007i \(-0.597971\pi\)
−0.302948 + 0.953007i \(0.597971\pi\)
\(180\) 0 0
\(181\) 3.46410 0.257485 0.128742 0.991678i \(-0.458906\pi\)
0.128742 + 0.991678i \(0.458906\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) − 39.2562i − 2.88617i
\(186\) 0 0
\(187\) − 5.66025i − 0.413919i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −25.7704 −1.86468 −0.932341 0.361581i \(-0.882237\pi\)
−0.932341 + 0.361581i \(0.882237\pi\)
\(192\) 0 0
\(193\) 14.9282 1.07456 0.537278 0.843405i \(-0.319453\pi\)
0.537278 + 0.843405i \(0.319453\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) − 8.76268i − 0.624315i −0.950030 0.312158i \(-0.898948\pi\)
0.950030 0.312158i \(-0.101052\pi\)
\(198\) 0 0
\(199\) − 26.4641i − 1.87599i −0.346648 0.937995i \(-0.612680\pi\)
0.346648 0.937995i \(-0.387320\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −7.72741 −0.542358
\(204\) 0 0
\(205\) 26.3205 1.83830
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0.896575i 0.0620174i
\(210\) 0 0
\(211\) − 13.3205i − 0.917022i −0.888689 0.458511i \(-0.848383\pi\)
0.888689 0.458511i \(-0.151617\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −24.9754 −1.70331
\(216\) 0 0
\(217\) 3.73205 0.253348
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) − 25.2528i − 1.69869i
\(222\) 0 0
\(223\) − 7.53590i − 0.504641i −0.967644 0.252321i \(-0.918806\pi\)
0.967644 0.252321i \(-0.0811937\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −20.0764 −1.33252 −0.666258 0.745721i \(-0.732105\pi\)
−0.666258 + 0.745721i \(0.732105\pi\)
\(228\) 0 0
\(229\) −11.3205 −0.748080 −0.374040 0.927413i \(-0.622028\pi\)
−0.374040 + 0.927413i \(0.622028\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) − 9.52056i − 0.623712i −0.950129 0.311856i \(-0.899049\pi\)
0.950129 0.311856i \(-0.100951\pi\)
\(234\) 0 0
\(235\) − 29.3205i − 1.91266i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 22.2485 1.43913 0.719567 0.694423i \(-0.244340\pi\)
0.719567 + 0.694423i \(0.244340\pi\)
\(240\) 0 0
\(241\) −12.9282 −0.832779 −0.416389 0.909186i \(-0.636705\pi\)
−0.416389 + 0.909186i \(0.636705\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) − 3.34607i − 0.213772i
\(246\) 0 0
\(247\) 4.00000i 0.254514i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −9.04008 −0.570605 −0.285303 0.958438i \(-0.592094\pi\)
−0.285303 + 0.958438i \(0.592094\pi\)
\(252\) 0 0
\(253\) −6.46410 −0.406395
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 12.8666i 0.802598i 0.915947 + 0.401299i \(0.131441\pi\)
−0.915947 + 0.401299i \(0.868559\pi\)
\(258\) 0 0
\(259\) 11.7321i 0.728994i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 24.7351 1.52523 0.762617 0.646850i \(-0.223914\pi\)
0.762617 + 0.646850i \(0.223914\pi\)
\(264\) 0 0
\(265\) 9.46410 0.581375
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 27.3877i 1.66986i 0.550358 + 0.834929i \(0.314491\pi\)
−0.550358 + 0.834929i \(0.685509\pi\)
\(270\) 0 0
\(271\) − 7.46410i − 0.453412i −0.973963 0.226706i \(-0.927204\pi\)
0.973963 0.226706i \(-0.0727956\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −5.55532 −0.334998
\(276\) 0 0
\(277\) −0.803848 −0.0482985 −0.0241493 0.999708i \(-0.507688\pi\)
−0.0241493 + 0.999708i \(0.507688\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) − 5.17638i − 0.308797i −0.988009 0.154398i \(-0.950656\pi\)
0.988009 0.154398i \(-0.0493440\pi\)
\(282\) 0 0
\(283\) − 17.8564i − 1.06145i −0.847543 0.530727i \(-0.821919\pi\)
0.847543 0.530727i \(-0.178081\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −7.86611 −0.464322
\(288\) 0 0
\(289\) −22.8564 −1.34449
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) − 2.17209i − 0.126895i −0.997985 0.0634474i \(-0.979790\pi\)
0.997985 0.0634474i \(-0.0202095\pi\)
\(294\) 0 0
\(295\) 12.9282i 0.752709i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −28.8391 −1.66781
\(300\) 0 0
\(301\) 7.46410 0.430224
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) − 41.4655i − 2.37431i
\(306\) 0 0
\(307\) 5.00000i 0.285365i 0.989769 + 0.142683i \(0.0455728\pi\)
−0.989769 + 0.142683i \(0.954427\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −15.4548 −0.876362 −0.438181 0.898887i \(-0.644377\pi\)
−0.438181 + 0.898887i \(0.644377\pi\)
\(312\) 0 0
\(313\) 12.3923 0.700454 0.350227 0.936665i \(-0.386104\pi\)
0.350227 + 0.936665i \(0.386104\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) − 23.4596i − 1.31762i −0.752308 0.658812i \(-0.771059\pi\)
0.752308 0.658812i \(-0.228941\pi\)
\(318\) 0 0
\(319\) − 6.92820i − 0.387905i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 6.31319 0.351275
\(324\) 0 0
\(325\) −24.7846 −1.37480
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 8.76268i 0.483102i
\(330\) 0 0
\(331\) − 22.2487i − 1.22290i −0.791283 0.611450i \(-0.790587\pi\)
0.791283 0.611450i \(-0.209413\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −36.5665 −1.99784
\(336\) 0 0
\(337\) 22.7128 1.23725 0.618623 0.785688i \(-0.287691\pi\)
0.618623 + 0.785688i \(0.287691\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 3.34607i 0.181200i
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 16.1755 0.868348 0.434174 0.900829i \(-0.357040\pi\)
0.434174 + 0.900829i \(0.357040\pi\)
\(348\) 0 0
\(349\) 13.3205 0.713030 0.356515 0.934290i \(-0.383965\pi\)
0.356515 + 0.934290i \(0.383965\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 11.1750i 0.594786i 0.954755 + 0.297393i \(0.0961171\pi\)
−0.954755 + 0.297393i \(0.903883\pi\)
\(354\) 0 0
\(355\) − 19.3923i − 1.02924i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 18.6622 0.984952 0.492476 0.870326i \(-0.336092\pi\)
0.492476 + 0.870326i \(0.336092\pi\)
\(360\) 0 0
\(361\) 18.0000 0.947368
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) − 48.1576i − 2.52068i
\(366\) 0 0
\(367\) 18.4641i 0.963818i 0.876221 + 0.481909i \(0.160056\pi\)
−0.876221 + 0.481909i \(0.839944\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −2.82843 −0.146845
\(372\) 0 0
\(373\) 15.3923 0.796983 0.398492 0.917172i \(-0.369534\pi\)
0.398492 + 0.917172i \(0.369534\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) − 30.9096i − 1.59193i
\(378\) 0 0
\(379\) 17.3205i 0.889695i 0.895606 + 0.444847i \(0.146742\pi\)
−0.895606 + 0.444847i \(0.853258\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 15.1774 0.775530 0.387765 0.921758i \(-0.373247\pi\)
0.387765 + 0.921758i \(0.373247\pi\)
\(384\) 0 0
\(385\) 3.00000 0.152894
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 35.2538i 1.78744i 0.448626 + 0.893719i \(0.351913\pi\)
−0.448626 + 0.893719i \(0.648087\pi\)
\(390\) 0 0
\(391\) 45.5167i 2.30188i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 24.9754 1.25665
\(396\) 0 0
\(397\) 2.00000 0.100377 0.0501886 0.998740i \(-0.484018\pi\)
0.0501886 + 0.998740i \(0.484018\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) − 2.27362i − 0.113539i −0.998387 0.0567697i \(-0.981920\pi\)
0.998387 0.0567697i \(-0.0180801\pi\)
\(402\) 0 0
\(403\) 14.9282i 0.743627i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −10.5187 −0.521391
\(408\) 0 0
\(409\) −26.3923 −1.30502 −0.652508 0.757782i \(-0.726283\pi\)
−0.652508 + 0.757782i \(0.726283\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) − 3.86370i − 0.190120i
\(414\) 0 0
\(415\) 23.3205i 1.14476i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 7.45001 0.363957 0.181978 0.983303i \(-0.441750\pi\)
0.181978 + 0.983303i \(0.441750\pi\)
\(420\) 0 0
\(421\) −17.5885 −0.857209 −0.428604 0.903492i \(-0.640995\pi\)
−0.428604 + 0.903492i \(0.640995\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 39.1175i 1.89748i
\(426\) 0 0
\(427\) 12.3923i 0.599706i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −36.5293 −1.75956 −0.879778 0.475385i \(-0.842309\pi\)
−0.879778 + 0.475385i \(0.842309\pi\)
\(432\) 0 0
\(433\) 4.00000 0.192228 0.0961139 0.995370i \(-0.469359\pi\)
0.0961139 + 0.995370i \(0.469359\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) − 7.20977i − 0.344890i
\(438\) 0 0
\(439\) − 26.9282i − 1.28521i −0.766196 0.642607i \(-0.777853\pi\)
0.766196 0.642607i \(-0.222147\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −4.76028 −0.226168 −0.113084 0.993585i \(-0.536073\pi\)
−0.113084 + 0.993585i \(0.536073\pi\)
\(444\) 0 0
\(445\) 44.3205 2.10099
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) − 5.93426i − 0.280055i −0.990148 0.140027i \(-0.955281\pi\)
0.990148 0.140027i \(-0.0447191\pi\)
\(450\) 0 0
\(451\) − 7.05256i − 0.332092i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 13.3843 0.627464
\(456\) 0 0
\(457\) −3.78461 −0.177037 −0.0885183 0.996075i \(-0.528213\pi\)
−0.0885183 + 0.996075i \(0.528213\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 37.7405i 1.75775i 0.477054 + 0.878874i \(0.341705\pi\)
−0.477054 + 0.878874i \(0.658295\pi\)
\(462\) 0 0
\(463\) − 12.1436i − 0.564361i −0.959361 0.282180i \(-0.908942\pi\)
0.959361 0.282180i \(-0.0910576\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 2.55103 0.118047 0.0590237 0.998257i \(-0.481201\pi\)
0.0590237 + 0.998257i \(0.481201\pi\)
\(468\) 0 0
\(469\) 10.9282 0.504618
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 6.69213i 0.307704i
\(474\) 0 0
\(475\) − 6.19615i − 0.284299i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 2.62536 0.119956 0.0599778 0.998200i \(-0.480897\pi\)
0.0599778 + 0.998200i \(0.480897\pi\)
\(480\) 0 0
\(481\) −46.9282 −2.13974
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 9.79796i 0.444902i
\(486\) 0 0
\(487\) 29.7128i 1.34642i 0.739453 + 0.673208i \(0.235084\pi\)
−0.739453 + 0.673208i \(0.764916\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 8.52245 0.384613 0.192306 0.981335i \(-0.438403\pi\)
0.192306 + 0.981335i \(0.438403\pi\)
\(492\) 0 0
\(493\) −48.7846 −2.19715
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 5.79555i 0.259966i
\(498\) 0 0
\(499\) − 18.0000i − 0.805791i −0.915246 0.402895i \(-0.868004\pi\)
0.915246 0.402895i \(-0.131996\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 38.8401 1.73179 0.865897 0.500222i \(-0.166748\pi\)
0.865897 + 0.500222i \(0.166748\pi\)
\(504\) 0 0
\(505\) 2.19615 0.0977275
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) − 41.0122i − 1.81783i −0.416978 0.908917i \(-0.636911\pi\)
0.416978 0.908917i \(-0.363089\pi\)
\(510\) 0 0
\(511\) 14.3923i 0.636678i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −60.6453 −2.67235
\(516\) 0 0
\(517\) −7.85641 −0.345524
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) − 25.7704i − 1.12902i −0.825425 0.564511i \(-0.809065\pi\)
0.825425 0.564511i \(-0.190935\pi\)
\(522\) 0 0
\(523\) − 28.6603i − 1.25323i −0.779331 0.626613i \(-0.784441\pi\)
0.779331 0.626613i \(-0.215559\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 23.5612 1.02634
\(528\) 0 0
\(529\) 28.9808 1.26003
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) − 31.4644i − 1.36288i
\(534\) 0 0
\(535\) − 15.1244i − 0.653883i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −0.896575 −0.0386182
\(540\) 0 0
\(541\) −17.3397 −0.745494 −0.372747 0.927933i \(-0.621584\pi\)
−0.372747 + 0.927933i \(0.621584\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) − 11.8313i − 0.506799i
\(546\) 0 0
\(547\) − 29.8564i − 1.27657i −0.769801 0.638284i \(-0.779645\pi\)
0.769801 0.638284i \(-0.220355\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 7.72741 0.329199
\(552\) 0 0
\(553\) −7.46410 −0.317406
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) − 11.7942i − 0.499736i −0.968280 0.249868i \(-0.919613\pi\)
0.968280 0.249868i \(-0.0803872\pi\)
\(558\) 0 0
\(559\) 29.8564i 1.26279i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −27.5264 −1.16010 −0.580050 0.814581i \(-0.696967\pi\)
−0.580050 + 0.814581i \(0.696967\pi\)
\(564\) 0 0
\(565\) −31.8564 −1.34021
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 15.9353i 0.668042i 0.942566 + 0.334021i \(0.108406\pi\)
−0.942566 + 0.334021i \(0.891594\pi\)
\(570\) 0 0
\(571\) 5.60770i 0.234675i 0.993092 + 0.117337i \(0.0374359\pi\)
−0.993092 + 0.117337i \(0.962564\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 44.6728 1.86299
\(576\) 0 0
\(577\) 37.3205 1.55367 0.776837 0.629702i \(-0.216823\pi\)
0.776837 + 0.629702i \(0.216823\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) − 6.96953i − 0.289145i
\(582\) 0 0
\(583\) − 2.53590i − 0.105026i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −35.5312 −1.46653 −0.733265 0.679943i \(-0.762004\pi\)
−0.733265 + 0.679943i \(0.762004\pi\)
\(588\) 0 0
\(589\) −3.73205 −0.153776
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 10.3156i 0.423611i 0.977312 + 0.211805i \(0.0679343\pi\)
−0.977312 + 0.211805i \(0.932066\pi\)
\(594\) 0 0
\(595\) − 21.1244i − 0.866014i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 7.69024 0.314215 0.157107 0.987582i \(-0.449783\pi\)
0.157107 + 0.987582i \(0.449783\pi\)
\(600\) 0 0
\(601\) −16.7846 −0.684659 −0.342329 0.939580i \(-0.611216\pi\)
−0.342329 + 0.939580i \(0.611216\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) − 34.1170i − 1.38705i
\(606\) 0 0
\(607\) 20.7846i 0.843621i 0.906684 + 0.421811i \(0.138605\pi\)
−0.906684 + 0.421811i \(0.861395\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −35.0507 −1.41800
\(612\) 0 0
\(613\) 25.5359 1.03139 0.515693 0.856774i \(-0.327535\pi\)
0.515693 + 0.856774i \(0.327535\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) − 17.0449i − 0.686202i −0.939299 0.343101i \(-0.888523\pi\)
0.939299 0.343101i \(-0.111477\pi\)
\(618\) 0 0
\(619\) 12.1244i 0.487319i 0.969861 + 0.243659i \(0.0783479\pi\)
−0.969861 + 0.243659i \(0.921652\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −13.2456 −0.530672
\(624\) 0 0
\(625\) −17.5885 −0.703538
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 74.0667i 2.95323i
\(630\) 0 0
\(631\) 38.7846i 1.54399i 0.635628 + 0.771995i \(0.280741\pi\)
−0.635628 + 0.771995i \(0.719259\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −54.8497 −2.17664
\(636\) 0 0
\(637\) −4.00000 −0.158486
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 10.2784i 0.405974i 0.979181 + 0.202987i \(0.0650649\pi\)
−0.979181 + 0.202987i \(0.934935\pi\)
\(642\) 0 0
\(643\) − 23.9282i − 0.943636i −0.881696 0.471818i \(-0.843598\pi\)
0.881696 0.471818i \(-0.156402\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 16.6932 0.656276 0.328138 0.944630i \(-0.393579\pi\)
0.328138 + 0.944630i \(0.393579\pi\)
\(648\) 0 0
\(649\) 3.46410 0.135978
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 2.55103i 0.0998294i 0.998753 + 0.0499147i \(0.0158949\pi\)
−0.998753 + 0.0499147i \(0.984105\pi\)
\(654\) 0 0
\(655\) 18.0000i 0.703318i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 30.5679 1.19075 0.595377 0.803446i \(-0.297003\pi\)
0.595377 + 0.803446i \(0.297003\pi\)
\(660\) 0 0
\(661\) −16.7846 −0.652846 −0.326423 0.945224i \(-0.605843\pi\)
−0.326423 + 0.945224i \(0.605843\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 3.34607i 0.129755i
\(666\) 0 0
\(667\) 55.7128i 2.15721i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −11.1106 −0.428921
\(672\) 0 0
\(673\) 20.0000 0.770943 0.385472 0.922720i \(-0.374039\pi\)
0.385472 + 0.922720i \(0.374039\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 15.6950i 0.603210i 0.953433 + 0.301605i \(0.0975223\pi\)
−0.953433 + 0.301605i \(0.902478\pi\)
\(678\) 0 0
\(679\) − 2.92820i − 0.112374i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 8.62398 0.329988 0.164994 0.986295i \(-0.447240\pi\)
0.164994 + 0.986295i \(0.447240\pi\)
\(684\) 0 0
\(685\) 4.39230 0.167821
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) − 11.3137i − 0.431018i
\(690\) 0 0
\(691\) 24.5359i 0.933390i 0.884418 + 0.466695i \(0.154555\pi\)
−0.884418 + 0.466695i \(0.845445\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −1.79315 −0.0680181
\(696\) 0 0
\(697\) −49.6603 −1.88102
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) − 44.0908i − 1.66529i −0.553809 0.832644i \(-0.686826\pi\)
0.553809 0.832644i \(-0.313174\pi\)
\(702\) 0 0
\(703\) − 11.7321i − 0.442483i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −0.656339 −0.0246842
\(708\) 0 0
\(709\) 0.607695 0.0228225 0.0114112 0.999935i \(-0.496368\pi\)
0.0114112 + 0.999935i \(0.496368\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) − 26.9072i − 1.00768i
\(714\) 0 0
\(715\) 12.0000i 0.448775i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 3.30890 0.123401 0.0617006 0.998095i \(-0.480348\pi\)
0.0617006 + 0.998095i \(0.480348\pi\)
\(720\) 0 0
\(721\) 18.1244 0.674986
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 47.8802i 1.77823i
\(726\) 0 0
\(727\) − 14.6795i − 0.544432i −0.962236 0.272216i \(-0.912243\pi\)
0.962236 0.272216i \(-0.0877566\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 47.1223 1.74288
\(732\) 0 0
\(733\) −14.0000 −0.517102 −0.258551 0.965998i \(-0.583245\pi\)
−0.258551 + 0.965998i \(0.583245\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 9.79796i 0.360912i
\(738\) 0 0
\(739\) 35.8564i 1.31900i 0.751705 + 0.659500i \(0.229232\pi\)
−0.751705 + 0.659500i \(0.770768\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 14.0778 0.516463 0.258232 0.966083i \(-0.416860\pi\)
0.258232 + 0.966083i \(0.416860\pi\)
\(744\) 0 0
\(745\) 22.3923 0.820391
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 4.52004i 0.165159i
\(750\) 0 0
\(751\) − 23.0718i − 0.841902i −0.907083 0.420951i \(-0.861696\pi\)
0.907083 0.420951i \(-0.138304\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −57.9555 −2.10922
\(756\) 0 0
\(757\) −18.0000 −0.654221 −0.327111 0.944986i \(-0.606075\pi\)
−0.327111 + 0.944986i \(0.606075\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) − 2.92996i − 0.106211i −0.998589 0.0531055i \(-0.983088\pi\)
0.998589 0.0531055i \(-0.0169120\pi\)
\(762\) 0 0
\(763\) 3.53590i 0.128008i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 15.4548 0.558041
\(768\) 0 0
\(769\) −38.2487 −1.37928 −0.689642 0.724151i \(-0.742232\pi\)
−0.689642 + 0.724151i \(0.742232\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) − 22.3872i − 0.805211i −0.915374 0.402605i \(-0.868105\pi\)
0.915374 0.402605i \(-0.131895\pi\)
\(774\) 0 0
\(775\) − 23.1244i − 0.830651i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 7.86611 0.281833
\(780\) 0 0
\(781\) −5.19615 −0.185933
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) − 4.89898i − 0.174852i
\(786\) 0 0
\(787\) 5.60770i 0.199893i 0.994993 + 0.0999464i \(0.0318671\pi\)
−0.994993 + 0.0999464i \(0.968133\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 9.52056 0.338512
\(792\) 0 0
\(793\) −49.5692 −1.76025
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 47.1595i 1.67047i 0.549890 + 0.835237i \(0.314670\pi\)
−0.549890 + 0.835237i \(0.685330\pi\)
\(798\) 0 0
\(799\) 55.3205i 1.95710i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −12.9038 −0.455365
\(804\) 0 0
\(805\) −24.1244 −0.850272
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) − 3.03150i − 0.106582i −0.998579 0.0532909i \(-0.983029\pi\)
0.998579 0.0532909i \(-0.0169711\pi\)
\(810\) 0 0
\(811\) 1.48334i 0.0520871i 0.999661 + 0.0260435i \(0.00829086\pi\)
−0.999661 + 0.0260435i \(0.991709\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 64.6477 2.26451
\(816\) 0 0
\(817\) −7.46410 −0.261136
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 36.8439i 1.28586i 0.765925 + 0.642930i \(0.222281\pi\)
−0.765925 + 0.642930i \(0.777719\pi\)
\(822\) 0 0
\(823\) 37.7128i 1.31459i 0.753635 + 0.657293i \(0.228299\pi\)
−0.753635 + 0.657293i \(0.771701\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 39.4321 1.37119 0.685594 0.727984i \(-0.259543\pi\)
0.685594 + 0.727984i \(0.259543\pi\)
\(828\) 0 0
\(829\) 47.1769 1.63852 0.819261 0.573421i \(-0.194384\pi\)
0.819261 + 0.573421i \(0.194384\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 6.31319i 0.218739i
\(834\) 0 0
\(835\) − 36.2487i − 1.25444i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −45.8096 −1.58152 −0.790762 0.612124i \(-0.790316\pi\)
−0.790762 + 0.612124i \(0.790316\pi\)
\(840\) 0 0
\(841\) −30.7128 −1.05906
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 10.0382i 0.345324i
\(846\) 0 0
\(847\) 10.1962i 0.350344i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 84.5854 2.89955
\(852\) 0 0
\(853\) 9.85641 0.337477 0.168738 0.985661i \(-0.446031\pi\)
0.168738 + 0.985661i \(0.446031\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 47.7415i 1.63082i 0.578885 + 0.815409i \(0.303488\pi\)
−0.578885 + 0.815409i \(0.696512\pi\)
\(858\) 0 0
\(859\) − 42.7128i − 1.45734i −0.684864 0.728671i \(-0.740138\pi\)
0.684864 0.728671i \(-0.259862\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −1.89469 −0.0644959 −0.0322479 0.999480i \(-0.510267\pi\)
−0.0322479 + 0.999480i \(0.510267\pi\)
\(864\) 0 0
\(865\) 3.92820 0.133563
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) − 6.69213i − 0.227015i
\(870\) 0 0
\(871\) 43.7128i 1.48115i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −4.00240 −0.135306
\(876\) 0 0
\(877\) 50.7846 1.71487 0.857437 0.514589i \(-0.172055\pi\)
0.857437 + 0.514589i \(0.172055\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 20.0120i 0.674222i 0.941465 + 0.337111i \(0.109450\pi\)
−0.941465 + 0.337111i \(0.890550\pi\)
\(882\) 0 0
\(883\) 0.679492i 0.0228667i 0.999935 + 0.0114334i \(0.00363943\pi\)
−0.999935 + 0.0114334i \(0.996361\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −42.9812 −1.44317 −0.721584 0.692327i \(-0.756586\pi\)
−0.721584 + 0.692327i \(0.756586\pi\)
\(888\) 0 0
\(889\) 16.3923 0.549780
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) − 8.76268i − 0.293232i
\(894\) 0 0
\(895\) − 27.1244i − 0.906667i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 28.8391 0.961837
\(900\) 0 0
\(901\) −17.8564 −0.594883
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 11.5911i 0.385302i
\(906\) 0 0
\(907\) − 38.7846i − 1.28782i −0.765100 0.643911i \(-0.777311\pi\)
0.765100 0.643911i \(-0.222689\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −45.6338 −1.51191 −0.755957 0.654621i \(-0.772828\pi\)
−0.755957 + 0.654621i \(0.772828\pi\)
\(912\) 0 0
\(913\) 6.24871 0.206802
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) − 5.37945i − 0.177645i
\(918\) 0 0
\(919\) 50.9282i 1.67997i 0.542612 + 0.839983i \(0.317435\pi\)
−0.542612 + 0.839983i \(0.682565\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −23.1822 −0.763052
\(924\) 0 0
\(925\) 72.6936 2.39015
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 25.9091i 0.850050i 0.905182 + 0.425025i \(0.139735\pi\)
−0.905182 + 0.425025i \(0.860265\pi\)
\(930\) 0 0
\(931\) − 1.00000i − 0.0327737i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 18.9396 0.619390
\(936\) 0 0
\(937\) −23.3205 −0.761848 −0.380924 0.924606i \(-0.624394\pi\)
−0.380924 + 0.924606i \(0.624394\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) − 13.0697i − 0.426060i −0.977046 0.213030i \(-0.931667\pi\)
0.977046 0.213030i \(-0.0683332\pi\)
\(942\) 0 0
\(943\) 56.7128i 1.84682i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 1.34984 0.0438640 0.0219320 0.999759i \(-0.493018\pi\)
0.0219320 + 0.999759i \(0.493018\pi\)
\(948\) 0 0
\(949\) −57.5692 −1.86878
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) − 35.2538i − 1.14198i −0.820956 0.570991i \(-0.806559\pi\)
0.820956 0.570991i \(-0.193441\pi\)
\(954\) 0 0
\(955\) − 86.2295i − 2.79032i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −1.31268 −0.0423886
\(960\) 0 0
\(961\) 17.0718 0.550703
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 49.9507i 1.60797i
\(966\) 0 0
\(967\) − 12.5359i − 0.403127i −0.979475 0.201564i \(-0.935398\pi\)
0.979475 0.201564i \(-0.0646023\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 33.7381 1.08271 0.541353 0.840796i \(-0.317912\pi\)
0.541353 + 0.840796i \(0.317912\pi\)
\(972\) 0 0
\(973\) 0.535898 0.0171801
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) − 34.4959i − 1.10362i −0.833969 0.551811i \(-0.813937\pi\)
0.833969 0.551811i \(-0.186063\pi\)
\(978\) 0 0
\(979\) − 11.8756i − 0.379547i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −54.5723 −1.74059 −0.870293 0.492534i \(-0.836071\pi\)
−0.870293 + 0.492534i \(0.836071\pi\)
\(984\) 0 0
\(985\) 29.3205 0.934229
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) − 53.8144i − 1.71120i
\(990\) 0 0
\(991\) − 24.3923i − 0.774847i −0.921902 0.387424i \(-0.873365\pi\)
0.921902 0.387424i \(-0.126635\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 88.5506 2.80724
\(996\) 0 0
\(997\) −36.2487 −1.14801 −0.574004 0.818852i \(-0.694611\pi\)
−0.574004 + 0.818852i \(0.694611\pi\)
\(998\) 0 0
\(999\) 0 0
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 6048.2.h.f.2591.7 yes 8
3.2 odd 2 inner 6048.2.h.f.2591.1 8
4.3 odd 2 inner 6048.2.h.f.2591.8 yes 8
12.11 even 2 inner 6048.2.h.f.2591.2 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6048.2.h.f.2591.1 8 3.2 odd 2 inner
6048.2.h.f.2591.2 yes 8 12.11 even 2 inner
6048.2.h.f.2591.7 yes 8 1.1 even 1 trivial
6048.2.h.f.2591.8 yes 8 4.3 odd 2 inner