Properties

Label 6048.2.c.a.3025.1
Level 6048
Weight 2
Character 6048.3025
Analytic conductor 48.294
Analytic rank 0
Dimension 2
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6048.c (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(48.2935231425\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1512)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 3025.1
Root \(-1.00000i\)
Character \(\chi\) = 6048.3025
Dual form 6048.2.c.a.3025.2

$q$-expansion

\(f(q)\) \(=\) \(q-2.00000i q^{5} +1.00000 q^{7} +O(q^{10})\) \(q-2.00000i q^{5} +1.00000 q^{7} +5.00000i q^{13} -1.00000 q^{17} -4.00000i q^{19} -5.00000 q^{23} +1.00000 q^{25} +9.00000i q^{29} +7.00000 q^{31} -2.00000i q^{35} +2.00000i q^{37} -2.00000 q^{41} -5.00000i q^{43} +1.00000 q^{49} +9.00000i q^{53} +1.00000i q^{59} +6.00000i q^{61} +10.0000 q^{65} +9.00000i q^{67} -15.0000 q^{71} +14.0000 q^{79} +4.00000i q^{83} +2.00000i q^{85} +13.0000 q^{89} +5.00000i q^{91} -8.00000 q^{95} -14.0000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 2q^{7} + O(q^{10}) \) \( 2q + 2q^{7} - 2q^{17} - 10q^{23} + 2q^{25} + 14q^{31} - 4q^{41} + 2q^{49} + 20q^{65} - 30q^{71} + 28q^{79} + 26q^{89} - 16q^{95} - 28q^{97} + O(q^{100}) \)

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
\(5\) − 2.00000i − 0.894427i −0.894427 0.447214i \(-0.852416\pi\)
0.894427 0.447214i \(-0.147584\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(12\) 0 0
\(13\) 5.00000i 1.38675i 0.720577 + 0.693375i \(0.243877\pi\)
−0.720577 + 0.693375i \(0.756123\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1.00000 −0.242536 −0.121268 0.992620i \(-0.538696\pi\)
−0.121268 + 0.992620i \(0.538696\pi\)
\(18\) 0 0
\(19\) − 4.00000i − 0.917663i −0.888523 0.458831i \(-0.848268\pi\)
0.888523 0.458831i \(-0.151732\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −5.00000 −1.04257 −0.521286 0.853382i \(-0.674548\pi\)
−0.521286 + 0.853382i \(0.674548\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 9.00000i 1.67126i 0.549294 + 0.835629i \(0.314897\pi\)
−0.549294 + 0.835629i \(0.685103\pi\)
\(30\) 0 0
\(31\) 7.00000 1.25724 0.628619 0.777714i \(-0.283621\pi\)
0.628619 + 0.777714i \(0.283621\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) − 2.00000i − 0.338062i
\(36\) 0 0
\(37\) 2.00000i 0.328798i 0.986394 + 0.164399i \(0.0525685\pi\)
−0.986394 + 0.164399i \(0.947432\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −2.00000 −0.312348 −0.156174 0.987730i \(-0.549916\pi\)
−0.156174 + 0.987730i \(0.549916\pi\)
\(42\) 0 0
\(43\) − 5.00000i − 0.762493i −0.924473 0.381246i \(-0.875495\pi\)
0.924473 0.381246i \(-0.124505\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 9.00000i 1.23625i 0.786082 + 0.618123i \(0.212106\pi\)
−0.786082 + 0.618123i \(0.787894\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 1.00000i 0.130189i 0.997879 + 0.0650945i \(0.0207349\pi\)
−0.997879 + 0.0650945i \(0.979265\pi\)
\(60\) 0 0
\(61\) 6.00000i 0.768221i 0.923287 + 0.384111i \(0.125492\pi\)
−0.923287 + 0.384111i \(0.874508\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 10.0000 1.24035
\(66\) 0 0
\(67\) 9.00000i 1.09952i 0.835321 + 0.549762i \(0.185282\pi\)
−0.835321 + 0.549762i \(0.814718\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −15.0000 −1.78017 −0.890086 0.455792i \(-0.849356\pi\)
−0.890086 + 0.455792i \(0.849356\pi\)
\(72\) 0 0
\(73\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 14.0000 1.57512 0.787562 0.616236i \(-0.211343\pi\)
0.787562 + 0.616236i \(0.211343\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 4.00000i 0.439057i 0.975606 + 0.219529i \(0.0704519\pi\)
−0.975606 + 0.219529i \(0.929548\pi\)
\(84\) 0 0
\(85\) 2.00000i 0.216930i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 13.0000 1.37800 0.688999 0.724763i \(-0.258051\pi\)
0.688999 + 0.724763i \(0.258051\pi\)
\(90\) 0 0
\(91\) 5.00000i 0.524142i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −8.00000 −0.820783
\(96\) 0 0
\(97\) −14.0000 −1.42148 −0.710742 0.703452i \(-0.751641\pi\)
−0.710742 + 0.703452i \(0.751641\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) − 8.00000i − 0.796030i −0.917379 0.398015i \(-0.869699\pi\)
0.917379 0.398015i \(-0.130301\pi\)
\(102\) 0 0
\(103\) 3.00000 0.295599 0.147799 0.989017i \(-0.452781\pi\)
0.147799 + 0.989017i \(0.452781\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) 0 0
\(109\) 16.0000i 1.53252i 0.642529 + 0.766261i \(0.277885\pi\)
−0.642529 + 0.766261i \(0.722115\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −6.00000 −0.564433 −0.282216 0.959351i \(-0.591070\pi\)
−0.282216 + 0.959351i \(0.591070\pi\)
\(114\) 0 0
\(115\) 10.0000i 0.932505i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −1.00000 −0.0916698
\(120\) 0 0
\(121\) 11.0000 1.00000
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) − 12.0000i − 1.07331i
\(126\) 0 0
\(127\) 8.00000 0.709885 0.354943 0.934888i \(-0.384500\pi\)
0.354943 + 0.934888i \(0.384500\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 13.0000i 1.13582i 0.823092 + 0.567908i \(0.192247\pi\)
−0.823092 + 0.567908i \(0.807753\pi\)
\(132\) 0 0
\(133\) − 4.00000i − 0.346844i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 12.0000 1.02523 0.512615 0.858619i \(-0.328677\pi\)
0.512615 + 0.858619i \(0.328677\pi\)
\(138\) 0 0
\(139\) 20.0000i 1.69638i 0.529694 + 0.848189i \(0.322307\pi\)
−0.529694 + 0.848189i \(0.677693\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 18.0000 1.49482
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) − 9.00000i − 0.737309i −0.929567 0.368654i \(-0.879819\pi\)
0.929567 0.368654i \(-0.120181\pi\)
\(150\) 0 0
\(151\) −12.0000 −0.976546 −0.488273 0.872691i \(-0.662373\pi\)
−0.488273 + 0.872691i \(0.662373\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) − 14.0000i − 1.12451i
\(156\) 0 0
\(157\) − 13.0000i − 1.03751i −0.854922 0.518756i \(-0.826395\pi\)
0.854922 0.518756i \(-0.173605\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −5.00000 −0.394055
\(162\) 0 0
\(163\) − 11.0000i − 0.861586i −0.902451 0.430793i \(-0.858234\pi\)
0.902451 0.430793i \(-0.141766\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −4.00000 −0.309529 −0.154765 0.987951i \(-0.549462\pi\)
−0.154765 + 0.987951i \(0.549462\pi\)
\(168\) 0 0
\(169\) −12.0000 −0.923077
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) − 6.00000i − 0.456172i −0.973641 0.228086i \(-0.926753\pi\)
0.973641 0.228086i \(-0.0732467\pi\)
\(174\) 0 0
\(175\) 1.00000 0.0755929
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 10.0000i 0.747435i 0.927543 + 0.373718i \(0.121917\pi\)
−0.927543 + 0.373718i \(0.878083\pi\)
\(180\) 0 0
\(181\) 19.0000i 1.41226i 0.708083 + 0.706129i \(0.249560\pi\)
−0.708083 + 0.706129i \(0.750440\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 4.00000 0.294086
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 4.00000 0.289430 0.144715 0.989473i \(-0.453773\pi\)
0.144715 + 0.989473i \(0.453773\pi\)
\(192\) 0 0
\(193\) 9.00000 0.647834 0.323917 0.946085i \(-0.395000\pi\)
0.323917 + 0.946085i \(0.395000\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 14.0000i 0.997459i 0.866758 + 0.498729i \(0.166200\pi\)
−0.866758 + 0.498729i \(0.833800\pi\)
\(198\) 0 0
\(199\) −13.0000 −0.921546 −0.460773 0.887518i \(-0.652428\pi\)
−0.460773 + 0.887518i \(0.652428\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 9.00000i 0.631676i
\(204\) 0 0
\(205\) 4.00000i 0.279372i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 1.00000i 0.0688428i 0.999407 + 0.0344214i \(0.0109588\pi\)
−0.999407 + 0.0344214i \(0.989041\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −10.0000 −0.681994
\(216\) 0 0
\(217\) 7.00000 0.475191
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) − 5.00000i − 0.336336i
\(222\) 0 0
\(223\) 16.0000 1.07144 0.535720 0.844396i \(-0.320040\pi\)
0.535720 + 0.844396i \(0.320040\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) − 25.0000i − 1.65931i −0.558278 0.829654i \(-0.688538\pi\)
0.558278 0.829654i \(-0.311462\pi\)
\(228\) 0 0
\(229\) 10.0000i 0.660819i 0.943838 + 0.330409i \(0.107187\pi\)
−0.943838 + 0.330409i \(0.892813\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 10.0000 0.655122 0.327561 0.944830i \(-0.393773\pi\)
0.327561 + 0.944830i \(0.393773\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 24.0000 1.55243 0.776215 0.630468i \(-0.217137\pi\)
0.776215 + 0.630468i \(0.217137\pi\)
\(240\) 0 0
\(241\) 26.0000 1.67481 0.837404 0.546585i \(-0.184072\pi\)
0.837404 + 0.546585i \(0.184072\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) − 2.00000i − 0.127775i
\(246\) 0 0
\(247\) 20.0000 1.27257
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 12.0000i 0.757433i 0.925513 + 0.378717i \(0.123635\pi\)
−0.925513 + 0.378717i \(0.876365\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 6.00000 0.374270 0.187135 0.982334i \(-0.440080\pi\)
0.187135 + 0.982334i \(0.440080\pi\)
\(258\) 0 0
\(259\) 2.00000i 0.124274i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −31.0000 −1.91154 −0.955771 0.294112i \(-0.904976\pi\)
−0.955771 + 0.294112i \(0.904976\pi\)
\(264\) 0 0
\(265\) 18.0000 1.10573
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) 15.0000 0.911185 0.455593 0.890188i \(-0.349427\pi\)
0.455593 + 0.890188i \(0.349427\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) − 26.0000i − 1.56219i −0.624413 0.781094i \(-0.714662\pi\)
0.624413 0.781094i \(-0.285338\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 12.0000 0.715860 0.357930 0.933748i \(-0.383483\pi\)
0.357930 + 0.933748i \(0.383483\pi\)
\(282\) 0 0
\(283\) 16.0000i 0.951101i 0.879688 + 0.475551i \(0.157751\pi\)
−0.879688 + 0.475551i \(0.842249\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −2.00000 −0.118056
\(288\) 0 0
\(289\) −16.0000 −0.941176
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 12.0000i 0.701047i 0.936554 + 0.350524i \(0.113996\pi\)
−0.936554 + 0.350524i \(0.886004\pi\)
\(294\) 0 0
\(295\) 2.00000 0.116445
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) − 25.0000i − 1.44579i
\(300\) 0 0
\(301\) − 5.00000i − 0.288195i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 12.0000 0.687118
\(306\) 0 0
\(307\) − 6.00000i − 0.342438i −0.985233 0.171219i \(-0.945229\pi\)
0.985233 0.171219i \(-0.0547706\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 34.0000 1.92796 0.963982 0.265969i \(-0.0856919\pi\)
0.963982 + 0.265969i \(0.0856919\pi\)
\(312\) 0 0
\(313\) 32.0000 1.80875 0.904373 0.426742i \(-0.140339\pi\)
0.904373 + 0.426742i \(0.140339\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) − 14.0000i − 0.786318i −0.919470 0.393159i \(-0.871382\pi\)
0.919470 0.393159i \(-0.128618\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 4.00000i 0.222566i
\(324\) 0 0
\(325\) 5.00000i 0.277350i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 13.0000i 0.714545i 0.934000 + 0.357272i \(0.116293\pi\)
−0.934000 + 0.357272i \(0.883707\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 18.0000 0.983445
\(336\) 0 0
\(337\) 19.0000 1.03500 0.517498 0.855684i \(-0.326864\pi\)
0.517498 + 0.855684i \(0.326864\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) − 16.0000i − 0.858925i −0.903085 0.429463i \(-0.858703\pi\)
0.903085 0.429463i \(-0.141297\pi\)
\(348\) 0 0
\(349\) 23.0000i 1.23116i 0.788074 + 0.615581i \(0.211079\pi\)
−0.788074 + 0.615581i \(0.788921\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 33.0000 1.75641 0.878206 0.478282i \(-0.158740\pi\)
0.878206 + 0.478282i \(0.158740\pi\)
\(354\) 0 0
\(355\) 30.0000i 1.59223i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 1.00000 0.0527780 0.0263890 0.999652i \(-0.491599\pi\)
0.0263890 + 0.999652i \(0.491599\pi\)
\(360\) 0 0
\(361\) 3.00000 0.157895
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −21.0000 −1.09619 −0.548096 0.836416i \(-0.684647\pi\)
−0.548096 + 0.836416i \(0.684647\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 9.00000i 0.467257i
\(372\) 0 0
\(373\) 22.0000i 1.13912i 0.821951 + 0.569558i \(0.192886\pi\)
−0.821951 + 0.569558i \(0.807114\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −45.0000 −2.31762
\(378\) 0 0
\(379\) − 16.0000i − 0.821865i −0.911666 0.410932i \(-0.865203\pi\)
0.911666 0.410932i \(-0.134797\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −24.0000 −1.22634 −0.613171 0.789950i \(-0.710106\pi\)
−0.613171 + 0.789950i \(0.710106\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) − 10.0000i − 0.507020i −0.967333 0.253510i \(-0.918415\pi\)
0.967333 0.253510i \(-0.0815851\pi\)
\(390\) 0 0
\(391\) 5.00000 0.252861
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) − 28.0000i − 1.40883i
\(396\) 0 0
\(397\) 10.0000i 0.501886i 0.968002 + 0.250943i \(0.0807406\pi\)
−0.968002 + 0.250943i \(0.919259\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −24.0000 −1.19850 −0.599251 0.800561i \(-0.704535\pi\)
−0.599251 + 0.800561i \(0.704535\pi\)
\(402\) 0 0
\(403\) 35.0000i 1.74347i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −32.0000 −1.58230 −0.791149 0.611623i \(-0.790517\pi\)
−0.791149 + 0.611623i \(0.790517\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 1.00000i 0.0492068i
\(414\) 0 0
\(415\) 8.00000 0.392705
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 15.0000i 0.732798i 0.930458 + 0.366399i \(0.119409\pi\)
−0.930458 + 0.366399i \(0.880591\pi\)
\(420\) 0 0
\(421\) 4.00000i 0.194948i 0.995238 + 0.0974740i \(0.0310763\pi\)
−0.995238 + 0.0974740i \(0.968924\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −1.00000 −0.0485071
\(426\) 0 0
\(427\) 6.00000i 0.290360i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −12.0000 −0.578020 −0.289010 0.957326i \(-0.593326\pi\)
−0.289010 + 0.957326i \(0.593326\pi\)
\(432\) 0 0
\(433\) 8.00000 0.384455 0.192228 0.981350i \(-0.438429\pi\)
0.192228 + 0.981350i \(0.438429\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 20.0000i 0.956730i
\(438\) 0 0
\(439\) −9.00000 −0.429547 −0.214773 0.976664i \(-0.568901\pi\)
−0.214773 + 0.976664i \(0.568901\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) − 6.00000i − 0.285069i −0.989790 0.142534i \(-0.954475\pi\)
0.989790 0.142534i \(-0.0455251\pi\)
\(444\) 0 0
\(445\) − 26.0000i − 1.23252i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −30.0000 −1.41579 −0.707894 0.706319i \(-0.750354\pi\)
−0.707894 + 0.706319i \(0.750354\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 10.0000 0.468807
\(456\) 0 0
\(457\) 5.00000 0.233890 0.116945 0.993138i \(-0.462690\pi\)
0.116945 + 0.993138i \(0.462690\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 12.0000i 0.558896i 0.960161 + 0.279448i \(0.0901514\pi\)
−0.960161 + 0.279448i \(0.909849\pi\)
\(462\) 0 0
\(463\) −16.0000 −0.743583 −0.371792 0.928316i \(-0.621256\pi\)
−0.371792 + 0.928316i \(0.621256\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 32.0000i 1.48078i 0.672176 + 0.740392i \(0.265360\pi\)
−0.672176 + 0.740392i \(0.734640\pi\)
\(468\) 0 0
\(469\) 9.00000i 0.415581i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) − 4.00000i − 0.183533i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 26.0000 1.18797 0.593985 0.804476i \(-0.297554\pi\)
0.593985 + 0.804476i \(0.297554\pi\)
\(480\) 0 0
\(481\) −10.0000 −0.455961
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 28.0000i 1.27141i
\(486\) 0 0
\(487\) 16.0000 0.725029 0.362515 0.931978i \(-0.381918\pi\)
0.362515 + 0.931978i \(0.381918\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 4.00000i 0.180517i 0.995918 + 0.0902587i \(0.0287694\pi\)
−0.995918 + 0.0902587i \(0.971231\pi\)
\(492\) 0 0
\(493\) − 9.00000i − 0.405340i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −15.0000 −0.672842
\(498\) 0 0
\(499\) 24.0000i 1.07439i 0.843459 + 0.537194i \(0.180516\pi\)
−0.843459 + 0.537194i \(0.819484\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 6.00000 0.267527 0.133763 0.991013i \(-0.457294\pi\)
0.133763 + 0.991013i \(0.457294\pi\)
\(504\) 0 0
\(505\) −16.0000 −0.711991
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) − 18.0000i − 0.797836i −0.916987 0.398918i \(-0.869386\pi\)
0.916987 0.398918i \(-0.130614\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) − 6.00000i − 0.264392i
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −39.0000 −1.70862 −0.854311 0.519763i \(-0.826020\pi\)
−0.854311 + 0.519763i \(0.826020\pi\)
\(522\) 0 0
\(523\) 36.0000i 1.57417i 0.616844 + 0.787085i \(0.288411\pi\)
−0.616844 + 0.787085i \(0.711589\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −7.00000 −0.304925
\(528\) 0 0
\(529\) 2.00000 0.0869565
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) − 10.0000i − 0.433148i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 38.0000i 1.63375i 0.576816 + 0.816874i \(0.304295\pi\)
−0.576816 + 0.816874i \(0.695705\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 32.0000 1.37073
\(546\) 0 0
\(547\) − 28.0000i − 1.19719i −0.801050 0.598597i \(-0.795725\pi\)
0.801050 0.598597i \(-0.204275\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 36.0000 1.53365
\(552\) 0 0
\(553\) 14.0000 0.595341
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 33.0000i 1.39825i 0.714997 + 0.699127i \(0.246428\pi\)
−0.714997 + 0.699127i \(0.753572\pi\)
\(558\) 0 0
\(559\) 25.0000 1.05739
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 15.0000i 0.632175i 0.948730 + 0.316087i \(0.102369\pi\)
−0.948730 + 0.316087i \(0.897631\pi\)
\(564\) 0 0
\(565\) 12.0000i 0.504844i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 24.0000 1.00613 0.503066 0.864248i \(-0.332205\pi\)
0.503066 + 0.864248i \(0.332205\pi\)
\(570\) 0 0
\(571\) − 19.0000i − 0.795125i −0.917575 0.397563i \(-0.869856\pi\)
0.917575 0.397563i \(-0.130144\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −5.00000 −0.208514
\(576\) 0 0
\(577\) 30.0000 1.24892 0.624458 0.781058i \(-0.285320\pi\)
0.624458 + 0.781058i \(0.285320\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 4.00000i 0.165948i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) − 23.0000i − 0.949312i −0.880172 0.474656i \(-0.842573\pi\)
0.880172 0.474656i \(-0.157427\pi\)
\(588\) 0 0
\(589\) − 28.0000i − 1.15372i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −6.00000 −0.246390 −0.123195 0.992382i \(-0.539314\pi\)
−0.123195 + 0.992382i \(0.539314\pi\)
\(594\) 0 0
\(595\) 2.00000i 0.0819920i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −35.0000 −1.43006 −0.715031 0.699093i \(-0.753587\pi\)
−0.715031 + 0.699093i \(0.753587\pi\)
\(600\) 0 0
\(601\) 38.0000 1.55005 0.775026 0.631929i \(-0.217737\pi\)
0.775026 + 0.631929i \(0.217737\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) − 22.0000i − 0.894427i
\(606\) 0 0
\(607\) −1.00000 −0.0405887 −0.0202944 0.999794i \(-0.506460\pi\)
−0.0202944 + 0.999794i \(0.506460\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 16.0000i 0.646234i 0.946359 + 0.323117i \(0.104731\pi\)
−0.946359 + 0.323117i \(0.895269\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −46.0000 −1.85189 −0.925945 0.377658i \(-0.876729\pi\)
−0.925945 + 0.377658i \(0.876729\pi\)
\(618\) 0 0
\(619\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 13.0000 0.520834
\(624\) 0 0
\(625\) −19.0000 −0.760000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) − 2.00000i − 0.0797452i
\(630\) 0 0
\(631\) −34.0000 −1.35352 −0.676759 0.736204i \(-0.736616\pi\)
−0.676759 + 0.736204i \(0.736616\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) − 16.0000i − 0.634941i
\(636\) 0 0
\(637\) 5.00000i 0.198107i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 26.0000 1.02694 0.513469 0.858108i \(-0.328360\pi\)
0.513469 + 0.858108i \(0.328360\pi\)
\(642\) 0 0
\(643\) − 14.0000i − 0.552106i −0.961142 0.276053i \(-0.910973\pi\)
0.961142 0.276053i \(-0.0890266\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 18.0000 0.707653 0.353827 0.935311i \(-0.384880\pi\)
0.353827 + 0.935311i \(0.384880\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) − 21.0000i − 0.821794i −0.911682 0.410897i \(-0.865216\pi\)
0.911682 0.410897i \(-0.134784\pi\)
\(654\) 0 0
\(655\) 26.0000 1.01590
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 36.0000i 1.40236i 0.712984 + 0.701180i \(0.247343\pi\)
−0.712984 + 0.701180i \(0.752657\pi\)
\(660\) 0 0
\(661\) − 22.0000i − 0.855701i −0.903850 0.427850i \(-0.859271\pi\)
0.903850 0.427850i \(-0.140729\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −8.00000 −0.310227
\(666\) 0 0
\(667\) − 45.0000i − 1.74241i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −37.0000 −1.42625 −0.713123 0.701039i \(-0.752720\pi\)
−0.713123 + 0.701039i \(0.752720\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) − 12.0000i − 0.461197i −0.973049 0.230599i \(-0.925932\pi\)
0.973049 0.230599i \(-0.0740685\pi\)
\(678\) 0 0
\(679\) −14.0000 −0.537271
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 46.0000i 1.76014i 0.474843 + 0.880071i \(0.342505\pi\)
−0.474843 + 0.880071i \(0.657495\pi\)
\(684\) 0 0
\(685\) − 24.0000i − 0.916993i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −45.0000 −1.71436
\(690\) 0 0
\(691\) 8.00000i 0.304334i 0.988355 + 0.152167i \(0.0486252\pi\)
−0.988355 + 0.152167i \(0.951375\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 40.0000 1.51729
\(696\) 0 0
\(697\) 2.00000 0.0757554
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 22.0000i 0.830929i 0.909610 + 0.415464i \(0.136381\pi\)
−0.909610 + 0.415464i \(0.863619\pi\)
\(702\) 0 0
\(703\) 8.00000 0.301726
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) − 8.00000i − 0.300871i
\(708\) 0 0
\(709\) 16.0000i 0.600893i 0.953799 + 0.300446i \(0.0971356\pi\)
−0.953799 + 0.300446i \(0.902864\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −35.0000 −1.31076
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −14.0000 −0.522112 −0.261056 0.965324i \(-0.584071\pi\)
−0.261056 + 0.965324i \(0.584071\pi\)
\(720\) 0 0
\(721\) 3.00000 0.111726
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 9.00000i 0.334252i
\(726\) 0 0
\(727\) 33.0000 1.22390 0.611951 0.790896i \(-0.290385\pi\)
0.611951 + 0.790896i \(0.290385\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 5.00000i 0.184932i
\(732\) 0 0
\(733\) − 49.0000i − 1.80986i −0.425564 0.904928i \(-0.639924\pi\)
0.425564 0.904928i \(-0.360076\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) − 32.0000i − 1.17714i −0.808447 0.588570i \(-0.799691\pi\)
0.808447 0.588570i \(-0.200309\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 23.0000 0.843788 0.421894 0.906645i \(-0.361365\pi\)
0.421894 + 0.906645i \(0.361365\pi\)
\(744\) 0 0
\(745\) −18.0000 −0.659469
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 46.0000 1.67856 0.839282 0.543696i \(-0.182976\pi\)
0.839282 + 0.543696i \(0.182976\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 24.0000i 0.873449i
\(756\) 0 0
\(757\) − 24.0000i − 0.872295i −0.899875 0.436147i \(-0.856343\pi\)
0.899875 0.436147i \(-0.143657\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 11.0000 0.398750 0.199375 0.979923i \(-0.436109\pi\)
0.199375 + 0.979923i \(0.436109\pi\)
\(762\) 0 0
\(763\) 16.0000i 0.579239i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −5.00000 −0.180540
\(768\) 0 0
\(769\) −2.00000 −0.0721218 −0.0360609 0.999350i \(-0.511481\pi\)
−0.0360609 + 0.999350i \(0.511481\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) − 32.0000i − 1.15096i −0.817816 0.575480i \(-0.804815\pi\)
0.817816 0.575480i \(-0.195185\pi\)
\(774\) 0 0
\(775\) 7.00000 0.251447
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 8.00000i 0.286630i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −26.0000 −0.927980
\(786\) 0 0
\(787\) − 48.0000i − 1.71102i −0.517790 0.855508i \(-0.673245\pi\)
0.517790 0.855508i \(-0.326755\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −6.00000 −0.213335
\(792\) 0 0
\(793\) −30.0000 −1.06533
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 2.00000i 0.0708436i 0.999372 + 0.0354218i \(0.0112775\pi\)
−0.999372 + 0.0354218i \(0.988723\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 10.0000i 0.352454i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −6.00000 −0.210949 −0.105474 0.994422i \(-0.533636\pi\)
−0.105474 + 0.994422i \(0.533636\pi\)
\(810\) 0 0
\(811\) − 14.0000i − 0.491606i −0.969320 0.245803i \(-0.920948\pi\)
0.969320 0.245803i \(-0.0790517\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −22.0000 −0.770626
\(816\) 0 0
\(817\) −20.0000 −0.699711
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) − 35.0000i − 1.22151i −0.791820 0.610754i \(-0.790866\pi\)
0.791820 0.610754i \(-0.209134\pi\)
\(822\) 0 0
\(823\) −44.0000 −1.53374 −0.766872 0.641800i \(-0.778188\pi\)
−0.766872 + 0.641800i \(0.778188\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) − 12.0000i − 0.417281i −0.977992 0.208640i \(-0.933096\pi\)
0.977992 0.208640i \(-0.0669038\pi\)
\(828\) 0 0
\(829\) 34.0000i 1.18087i 0.807086 + 0.590434i \(0.201044\pi\)
−0.807086 + 0.590434i \(0.798956\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −1.00000 −0.0346479
\(834\) 0 0
\(835\) 8.00000i 0.276851i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 44.0000 1.51905 0.759524 0.650479i \(-0.225432\pi\)
0.759524 + 0.650479i \(0.225432\pi\)
\(840\) 0 0
\(841\) −52.0000 −1.79310
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 24.0000i 0.825625i
\(846\) 0 0
\(847\) 11.0000 0.377964
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) − 10.0000i − 0.342796i
\(852\) 0 0
\(853\) 9.00000i 0.308154i 0.988059 + 0.154077i \(0.0492404\pi\)
−0.988059 + 0.154077i \(0.950760\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −9.00000 −0.307434 −0.153717 0.988115i \(-0.549124\pi\)
−0.153717 + 0.988115i \(0.549124\pi\)
\(858\) 0 0
\(859\) − 2.00000i − 0.0682391i −0.999418 0.0341196i \(-0.989137\pi\)
0.999418 0.0341196i \(-0.0108627\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −45.0000 −1.53182 −0.765909 0.642949i \(-0.777711\pi\)
−0.765909 + 0.642949i \(0.777711\pi\)
\(864\) 0 0
\(865\) −12.0000 −0.408012
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) −45.0000 −1.52477
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) − 12.0000i − 0.405674i
\(876\) 0 0
\(877\) 34.0000i 1.14810i 0.818821 + 0.574049i \(0.194628\pi\)
−0.818821 + 0.574049i \(0.805372\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −47.0000 −1.58347 −0.791735 0.610865i \(-0.790822\pi\)
−0.791735 + 0.610865i \(0.790822\pi\)
\(882\) 0 0
\(883\) − 29.0000i − 0.975928i −0.872864 0.487964i \(-0.837740\pi\)
0.872864 0.487964i \(-0.162260\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −12.0000 −0.402921 −0.201460 0.979497i \(-0.564569\pi\)
−0.201460 + 0.979497i \(0.564569\pi\)
\(888\) 0 0
\(889\) 8.00000 0.268311
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 20.0000 0.668526
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 63.0000i 2.10117i
\(900\) 0 0
\(901\) − 9.00000i − 0.299833i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 38.0000 1.26316
\(906\) 0 0
\(907\) − 28.0000i − 0.929725i −0.885383 0.464862i \(-0.846104\pi\)
0.885383 0.464862i \(-0.153896\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 13.0000i 0.429298i
\(918\) 0 0
\(919\) −18.0000 −0.593765 −0.296883 0.954914i \(-0.595947\pi\)
−0.296883 + 0.954914i \(0.595947\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) − 75.0000i − 2.46866i
\(924\) 0 0
\(925\) 2.00000i 0.0657596i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 14.0000 0.459325 0.229663 0.973270i \(-0.426238\pi\)
0.229663 + 0.973270i \(0.426238\pi\)
\(930\) 0 0
\(931\) − 4.00000i − 0.131095i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −22.0000 −0.718709 −0.359354 0.933201i \(-0.617003\pi\)
−0.359354 + 0.933201i \(0.617003\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 24.0000i 0.782378i 0.920310 + 0.391189i \(0.127936\pi\)
−0.920310 + 0.391189i \(0.872064\pi\)
\(942\) 0 0
\(943\) 10.0000 0.325645
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) − 12.0000i − 0.389948i −0.980808 0.194974i \(-0.937538\pi\)
0.980808 0.194974i \(-0.0624622\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 36.0000 1.16615 0.583077 0.812417i \(-0.301849\pi\)
0.583077 + 0.812417i \(0.301849\pi\)
\(954\) 0 0
\(955\) − 8.00000i − 0.258874i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 12.0000 0.387500
\(960\) 0 0
\(961\) 18.0000 0.580645
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) − 18.0000i − 0.579441i
\(966\) 0 0
\(967\) −50.0000 −1.60789 −0.803946 0.594703i \(-0.797270\pi\)
−0.803946 + 0.594703i \(0.797270\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) − 33.0000i − 1.05902i −0.848304 0.529510i \(-0.822376\pi\)
0.848304 0.529510i \(-0.177624\pi\)
\(972\) 0 0
\(973\) 20.0000i 0.641171i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 56.0000 1.79160 0.895799 0.444459i \(-0.146604\pi\)
0.895799 + 0.444459i \(0.146604\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 62.0000 1.97749 0.988746 0.149601i \(-0.0477989\pi\)
0.988746 + 0.149601i \(0.0477989\pi\)
\(984\) 0 0
\(985\) 28.0000 0.892154
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 25.0000i 0.794954i
\(990\) 0 0
\(991\) −20.0000 −0.635321 −0.317660 0.948205i \(-0.602897\pi\)
−0.317660 + 0.948205i \(0.602897\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 26.0000i 0.824255i
\(996\) 0 0
\(997\) − 57.0000i − 1.80521i −0.430472 0.902604i \(-0.641653\pi\)
0.430472 0.902604i \(-0.358347\pi\)
\(998\) 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.c.a.3025.1 2
3.2 odd 2 6048.2.c.b.3025.2 2
4.3 odd 2 1512.2.c.b.757.2 yes 2
8.3 odd 2 1512.2.c.b.757.1 yes 2
8.5 even 2 inner 6048.2.c.a.3025.2 2
12.11 even 2 1512.2.c.a.757.1 2
24.5 odd 2 6048.2.c.b.3025.1 2
24.11 even 2 1512.2.c.a.757.2 yes 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1512.2.c.a.757.1 2 12.11 even 2
1512.2.c.a.757.2 yes 2 24.11 even 2
1512.2.c.b.757.1 yes 2 8.3 odd 2
1512.2.c.b.757.2 yes 2 4.3 odd 2
6048.2.c.a.3025.1 2 1.1 even 1 trivial
6048.2.c.a.3025.2 2 8.5 even 2 inner
6048.2.c.b.3025.1 2 24.5 odd 2
6048.2.c.b.3025.2 2 3.2 odd 2