Properties

Label 2600.1.b.a.1299.1
Level $2600$
Weight $1$
Character 2600.1299
Analytic conductor $1.298$
Analytic rank $0$
Dimension $2$
Projective image $D_{3}$
CM discriminant -104
Inner twists $4$

Related objects

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Newspace parameters

Level: \( N \) \(=\) \( 2600 = 2^{3} \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2600.b (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.29756903285\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
Defining polynomial: \(x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 104)
Projective image \(D_{3}\)
Projective field Galois closure of 3.1.104.1
Artin image $C_2\times C_4\times S_3$
Artin field Galois closure of \(\mathbb{Q}[x]/(x^{24} - \cdots)\)

Embedding invariants

Embedding label 1299.1
Root \(1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 2600.1299
Dual form 2600.1.b.a.1299.2

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} +1.00000i q^{7} +1.00000i q^{8} +O(q^{10})\) \(q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} +1.00000i q^{7} +1.00000i q^{8} +1.00000i q^{12} +1.00000i q^{13} +1.00000 q^{14} +1.00000 q^{16} +1.00000i q^{17} +1.00000 q^{21} +1.00000 q^{24} +1.00000 q^{26} -1.00000i q^{27} -1.00000i q^{28} +2.00000 q^{31} -1.00000i q^{32} +1.00000 q^{34} +1.00000i q^{37} +1.00000 q^{39} -1.00000i q^{42} -1.00000i q^{43} +1.00000i q^{47} -1.00000i q^{48} +1.00000 q^{51} -1.00000i q^{52} -1.00000 q^{54} -1.00000 q^{56} -2.00000i q^{62} -1.00000 q^{64} -1.00000i q^{68} -1.00000 q^{71} +1.00000 q^{74} -1.00000i q^{78} -1.00000 q^{81} -1.00000 q^{84} -1.00000 q^{86} -1.00000 q^{91} -2.00000i q^{93} +1.00000 q^{94} -1.00000 q^{96} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 2q^{4} - 2q^{6} + O(q^{10}) \) \( 2q - 2q^{4} - 2q^{6} + 2q^{14} + 2q^{16} + 2q^{21} + 2q^{24} + 2q^{26} + 4q^{31} + 2q^{34} + 2q^{39} + 2q^{51} - 2q^{54} - 2q^{56} - 2q^{64} - 2q^{71} + 2q^{74} - 2q^{81} - 2q^{84} - 2q^{86} - 2q^{91} + 2q^{94} - 2q^{96} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2600\mathbb{Z}\right)^\times\).

\(n\) \(1301\) \(1601\) \(1951\) \(1977\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) − 1.00000i − 1.00000i
\(3\) − 1.00000i − 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(4\) −1.00000 −1.00000
\(5\) 0 0
\(6\) −1.00000 −1.00000
\(7\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(8\) 1.00000i 1.00000i
\(9\) 0 0
\(10\) 0 0
\(11\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(12\) 1.00000i 1.00000i
\(13\) 1.00000i 1.00000i
\(14\) 1.00000 1.00000
\(15\) 0 0
\(16\) 1.00000 1.00000
\(17\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(18\) 0 0
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) 0 0
\(21\) 1.00000 1.00000
\(22\) 0 0
\(23\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) 1.00000 1.00000
\(25\) 0 0
\(26\) 1.00000 1.00000
\(27\) − 1.00000i − 1.00000i
\(28\) − 1.00000i − 1.00000i
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(32\) − 1.00000i − 1.00000i
\(33\) 0 0
\(34\) 1.00000 1.00000
\(35\) 0 0
\(36\) 0 0
\(37\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(38\) 0 0
\(39\) 1.00000 1.00000
\(40\) 0 0
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) − 1.00000i − 1.00000i
\(43\) − 1.00000i − 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(48\) − 1.00000i − 1.00000i
\(49\) 0 0
\(50\) 0 0
\(51\) 1.00000 1.00000
\(52\) − 1.00000i − 1.00000i
\(53\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(54\) −1.00000 −1.00000
\(55\) 0 0
\(56\) −1.00000 −1.00000
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) 0 0
\(61\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(62\) − 2.00000i − 2.00000i
\(63\) 0 0
\(64\) −1.00000 −1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(68\) − 1.00000i − 1.00000i
\(69\) 0 0
\(70\) 0 0
\(71\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(72\) 0 0
\(73\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(74\) 1.00000 1.00000
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) − 1.00000i − 1.00000i
\(79\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(80\) 0 0
\(81\) −1.00000 −1.00000
\(82\) 0 0
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) −1.00000 −1.00000
\(85\) 0 0
\(86\) −1.00000 −1.00000
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) 0 0
\(91\) −1.00000 −1.00000
\(92\) 0 0
\(93\) − 2.00000i − 2.00000i
\(94\) 1.00000 1.00000
\(95\) 0 0
\(96\) −1.00000 −1.00000
\(97\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) − 1.00000i − 1.00000i
\(103\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(104\) −1.00000 −1.00000
\(105\) 0 0
\(106\) 0 0
\(107\) − 2.00000i − 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(108\) 1.00000i 1.00000i
\(109\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(110\) 0 0
\(111\) 1.00000 1.00000
\(112\) 1.00000i 1.00000i
\(113\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −1.00000 −1.00000
\(120\) 0 0
\(121\) 1.00000 1.00000
\(122\) 0 0
\(123\) 0 0
\(124\) −2.00000 −2.00000
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) 1.00000i 1.00000i
\(129\) −1.00000 −1.00000
\(130\) 0 0
\(131\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) −1.00000 −1.00000
\(137\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(138\) 0 0
\(139\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(140\) 0 0
\(141\) 1.00000 1.00000
\(142\) 1.00000i 1.00000i
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) − 1.00000i − 1.00000i
\(149\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(150\) 0 0
\(151\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) −1.00000 −1.00000
\(157\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 1.00000i 1.00000i
\(163\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) − 2.00000i − 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(168\) 1.00000i 1.00000i
\(169\) −1.00000 −1.00000
\(170\) 0 0
\(171\) 0 0
\(172\) 1.00000i 1.00000i
\(173\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) 1.00000i 1.00000i
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) −2.00000 −2.00000
\(187\) 0 0
\(188\) − 1.00000i − 1.00000i
\(189\) 1.00000 1.00000
\(190\) 0 0
\(191\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(192\) 1.00000i 1.00000i
\(193\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) −1.00000 −1.00000
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 1.00000i 1.00000i
\(209\) 0 0
\(210\) 0 0
\(211\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(212\) 0 0
\(213\) 1.00000i 1.00000i
\(214\) −2.00000 −2.00000
\(215\) 0 0
\(216\) 1.00000 1.00000
\(217\) 2.00000i 2.00000i
\(218\) − 1.00000i − 1.00000i
\(219\) 0 0
\(220\) 0 0
\(221\) −1.00000 −1.00000
\(222\) − 1.00000i − 1.00000i
\(223\) − 1.00000i − 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(224\) 1.00000 1.00000
\(225\) 0 0
\(226\) 2.00000 2.00000
\(227\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(228\) 0 0
\(229\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) − 1.00000i − 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 1.00000i 1.00000i
\(239\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(240\) 0 0
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) − 1.00000i − 1.00000i
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 2.00000i 2.00000i
\(249\) 0 0
\(250\) 0 0
\(251\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 1.00000 1.00000
\(257\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(258\) 1.00000i 1.00000i
\(259\) −1.00000 −1.00000
\(260\) 0 0
\(261\) 0 0
\(262\) 1.00000i 1.00000i
\(263\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(272\) 1.00000i 1.00000i
\(273\) 1.00000i 1.00000i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(278\) − 1.00000i − 1.00000i
\(279\) 0 0
\(280\) 0 0
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) − 1.00000i − 1.00000i
\(283\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(284\) 1.00000 1.00000
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 0 0
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) − 1.00000i − 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −1.00000 −1.00000
\(297\) 0 0
\(298\) 2.00000i 2.00000i
\(299\) 0 0
\(300\) 0 0
\(301\) 1.00000 1.00000
\(302\) 1.00000i 1.00000i
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) 1.00000i 1.00000i
\(313\) − 1.00000i − 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) − 2.00000i − 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) −2.00000 −2.00000
\(322\) 0 0
\(323\) 0 0
\(324\) 1.00000 1.00000
\(325\) 0 0
\(326\) 0 0
\(327\) − 1.00000i − 1.00000i
\(328\) 0 0
\(329\) −1.00000 −1.00000
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) −2.00000 −2.00000
\(335\) 0 0
\(336\) 1.00000 1.00000
\(337\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(338\) 1.00000i 1.00000i
\(339\) 2.00000 2.00000
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 1.00000i 1.00000i
\(344\) 1.00000 1.00000
\(345\) 0 0
\(346\) 0 0
\(347\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(348\) 0 0
\(349\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(350\) 0 0
\(351\) 1.00000 1.00000
\(352\) 0 0
\(353\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 1.00000i 1.00000i
\(358\) − 1.00000i − 1.00000i
\(359\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(360\) 0 0
\(361\) 1.00000 1.00000
\(362\) 0 0
\(363\) − 1.00000i − 1.00000i
\(364\) 1.00000 1.00000
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 2.00000i 2.00000i
\(373\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −1.00000 −1.00000
\(377\) 0 0
\(378\) − 1.00000i − 1.00000i
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) − 1.00000i − 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(384\) 1.00000 1.00000
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 1.00000i 1.00000i
\(394\) 1.00000 1.00000
\(395\) 0 0
\(396\) 0 0
\(397\) − 2.00000i − 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(402\) 0 0
\(403\) 2.00000i 2.00000i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 1.00000i 1.00000i
\(409\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 1.00000 1.00000
\(417\) − 1.00000i − 1.00000i
\(418\) 0 0
\(419\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(420\) 0 0
\(421\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(422\) 1.00000i 1.00000i
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 1.00000 1.00000
\(427\) 0 0
\(428\) 2.00000i 2.00000i
\(429\) 0 0
\(430\) 0 0
\(431\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(432\) − 1.00000i − 1.00000i
\(433\) − 1.00000i − 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(434\) 2.00000 2.00000
\(435\) 0 0
\(436\) −1.00000 −1.00000
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 1.00000i 1.00000i
\(443\) − 1.00000i − 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(444\) −1.00000 −1.00000
\(445\) 0 0
\(446\) −1.00000 −1.00000
\(447\) 2.00000i 2.00000i
\(448\) − 1.00000i − 1.00000i
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) − 2.00000i − 2.00000i
\(453\) 1.00000i 1.00000i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(458\) − 1.00000i − 1.00000i
\(459\) 1.00000 1.00000
\(460\) 0 0
\(461\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(462\) 0 0
\(463\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −1.00000 −1.00000
\(467\) − 2.00000i − 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 1.00000 1.00000
\(477\) 0 0
\(478\) − 1.00000i − 1.00000i
\(479\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(480\) 0 0
\(481\) −1.00000 −1.00000
\(482\) 0 0
\(483\) 0 0
\(484\) −1.00000 −1.00000
\(485\) 0 0
\(486\) 0 0
\(487\) − 2.00000i − 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 2.00000 2.00000
\(497\) − 1.00000i − 1.00000i
\(498\) 0 0
\(499\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(500\) 0 0
\(501\) −2.00000 −2.00000
\(502\) − 2.00000i − 2.00000i
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 1.00000i 1.00000i
\(508\) 0 0
\(509\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) − 1.00000i − 1.00000i
\(513\) 0 0
\(514\) 1.00000 1.00000
\(515\) 0 0
\(516\) 1.00000 1.00000
\(517\) 0 0
\(518\) 1.00000i 1.00000i
\(519\) 0 0
\(520\) 0 0
\(521\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(522\) 0 0
\(523\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(524\) 1.00000 1.00000
\(525\) 0 0
\(526\) 0 0
\(527\) 2.00000i 2.00000i
\(528\) 0 0
\(529\) −1.00000 −1.00000
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) − 1.00000i − 1.00000i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(542\) 1.00000i 1.00000i
\(543\) 0 0
\(544\) 1.00000 1.00000
\(545\) 0 0
\(546\) 1.00000 1.00000
\(547\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) −1.00000 −1.00000
\(557\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(558\) 0 0
\(559\) 1.00000 1.00000
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) − 1.00000i − 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(564\) −1.00000 −1.00000
\(565\) 0 0
\(566\) 2.00000 2.00000
\(567\) − 1.00000i − 1.00000i
\(568\) − 1.00000i − 1.00000i
\(569\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(570\) 0 0
\(571\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) −1.00000 −1.00000
\(587\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 1.00000 1.00000
\(592\) 1.00000i 1.00000i
\(593\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 2.00000 2.00000
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(600\) 0 0
\(601\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(602\) − 1.00000i − 1.00000i
\(603\) 0 0
\(604\) 1.00000 1.00000
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −1.00000 −1.00000
\(612\) 0 0
\(613\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(618\) 0 0
\(619\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 1.00000 1.00000
\(625\) 0 0
\(626\) −1.00000 −1.00000
\(627\) 0 0
\(628\) 0 0
\(629\) −1.00000 −1.00000
\(630\) 0 0
\(631\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(632\) 0 0
\(633\) 1.00000i 1.00000i
\(634\) −2.00000 −2.00000
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(642\) 2.00000i 2.00000i
\(643\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(648\) − 1.00000i − 1.00000i
\(649\) 0 0
\(650\) 0 0
\(651\) 2.00000 2.00000
\(652\) 0 0
\(653\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(654\) −1.00000 −1.00000
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 1.00000i 1.00000i
\(659\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(662\) 0 0
\(663\) 1.00000i 1.00000i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 2.00000i 2.00000i
\(669\) −1.00000 −1.00000
\(670\) 0 0
\(671\) 0 0
\(672\) − 1.00000i − 1.00000i
\(673\) − 1.00000i − 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(674\) 1.00000 1.00000
\(675\) 0 0
\(676\) 1.00000 1.00000
\(677\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(678\) − 2.00000i − 2.00000i
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 1.00000 1.00000
\(687\) − 1.00000i − 1.00000i
\(688\) − 1.00000i − 1.00000i
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 1.00000 1.00000
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) − 1.00000i − 1.00000i
\(699\) −1.00000 −1.00000
\(700\) 0 0
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) − 1.00000i − 1.00000i
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 1.00000 1.00000
\(715\) 0 0
\(716\) −1.00000 −1.00000
\(717\) − 1.00000i − 1.00000i
\(718\) 2.00000i 2.00000i
\(719\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) − 1.00000i − 1.00000i
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) −1.00000 −1.00000
\(727\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(728\) − 1.00000i − 1.00000i
\(729\) −1.00000 −1.00000
\(730\) 0 0
\(731\) 1.00000 1.00000
\(732\) 0 0
\(733\) − 1.00000i − 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) − 1.00000i − 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(744\) 2.00000 2.00000
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 2.00000 2.00000
\(750\) 0 0
\(751\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(752\) 1.00000i 1.00000i
\(753\) − 2.00000i − 2.00000i
\(754\) 0 0
\(755\) 0 0
\(756\) −1.00000 −1.00000
\(757\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) 0 0
\(763\) 1.00000i 1.00000i
\(764\) 0 0
\(765\) 0 0
\(766\) −1.00000 −1.00000
\(767\) 0 0
\(768\) − 1.00000i − 1.00000i
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 1.00000 1.00000
\(772\) 0 0
\(773\) − 1.00000i − 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 1.00000i 1.00000i
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 1.00000 1.00000
\(787\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(788\) − 1.00000i − 1.00000i
\(789\) 0 0
\(790\) 0 0
\(791\) −2.00000 −2.00000
\(792\) 0 0
\(793\) 0 0
\(794\) −2.00000 −2.00000
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(798\) 0 0
\(799\) −1.00000 −1.00000
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 2.00000 2.00000
\(807\) 0 0
\(808\) 0 0
\(809\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(810\) 0 0
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) 0 0
\(813\) 1.00000i 1.00000i
\(814\) 0 0
\(815\) 0 0
\(816\) 1.00000 1.00000
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(822\) 0 0
\(823\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(828\) 0 0
\(829\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) − 1.00000i − 1.00000i
\(833\) 0 0
\(834\) −1.00000 −1.00000
\(835\) 0 0
\(836\) 0 0
\(837\) − 2.00000i − 2.00000i
\(838\) − 1.00000i − 1.00000i
\(839\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(840\) 0 0
\(841\) 1.00000 1.00000
\(842\) 1.00000i 1.00000i
\(843\) 0 0
\(844\) 1.00000 1.00000
\(845\) 0 0
\(846\) 0 0
\(847\) 1.00000i 1.00000i
\(848\) 0 0
\(849\) 2.00000 2.00000
\(850\) 0 0
\(851\) 0 0
\(852\) − 1.00000i − 1.00000i
\(853\) − 1.00000i − 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 2.00000 2.00000
\(857\) − 2.00000i − 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(858\) 0 0
\(859\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 1.00000i 1.00000i
\(863\) − 1.00000i − 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(864\) −1.00000 −1.00000
\(865\) 0 0
\(866\) −1.00000 −1.00000
\(867\) 0 0
\(868\) − 2.00000i − 2.00000i
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 1.00000i 1.00000i
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(878\) 0 0
\(879\) −1.00000 −1.00000
\(880\) 0 0
\(881\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(882\) 0 0
\(883\) − 1.00000i − 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(884\) 1.00000 1.00000
\(885\) 0 0
\(886\) −1.00000 −1.00000
\(887\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(888\) 1.00000i 1.00000i
\(889\) 0 0
\(890\) 0 0
\(891\) 0 0
\(892\) 1.00000i 1.00000i
\(893\) 0 0
\(894\) 2.00000 2.00000
\(895\) 0 0
\(896\) −1.00000 −1.00000
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) − 1.00000i − 1.00000i
\(904\) −2.00000 −2.00000
\(905\) 0 0
\(906\) 1.00000 1.00000
\(907\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) −1.00000 −1.00000
\(917\) − 1.00000i − 1.00000i
\(918\) − 1.00000i − 1.00000i
\(919\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 1.00000i 1.00000i
\(923\) − 1.00000i − 1.00000i
\(924\) 0 0
\(925\) 0 0
\(926\) 2.00000 2.00000
\(927\) 0 0
\(928\) 0 0
\(929\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 1.00000i 1.00000i
\(933\) 0 0
\(934\) −2.00000 −2.00000
\(935\) 0 0
\(936\) 0 0
\(937\) − 2.00000i − 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(938\) 0 0
\(939\) −1.00000 −1.00000
\(940\) 0 0
\(941\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) −2.00000 −2.00000
\(952\) − 1.00000i − 1.00000i
\(953\) − 1.00000i − 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) −1.00000 −1.00000
\(957\) 0 0
\(958\) − 1.00000i − 1.00000i
\(959\) 0 0
\(960\) 0 0
\(961\) 3.00000 3.00000
\(962\) 1.00000i 1.00000i
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(968\) 1.00000i 1.00000i
\(969\) 0 0
\(970\) 0 0
\(971\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(972\) 0 0
\(973\) 1.00000i 1.00000i
\(974\) −2.00000 −2.00000
\(975\) 0 0
\(976\) 0 0
\(977\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 0 0
\(982\) 1.00000i 1.00000i
\(983\) − 1.00000i − 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 1.00000i 1.00000i
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(992\) − 2.00000i − 2.00000i
\(993\) 0 0
\(994\) −1.00000 −1.00000
\(995\) 0 0
\(996\) 0 0
\(997\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(998\) 0 0
\(999\) 1.00000 1.00000
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 2600.1.b.a.1299.1 2
5.2 odd 4 104.1.h.b.51.1 yes 1
5.3 odd 4 2600.1.o.b.51.1 1
5.4 even 2 inner 2600.1.b.a.1299.2 2
8.3 odd 2 2600.1.b.b.1299.2 2
13.12 even 2 2600.1.b.b.1299.2 2
15.2 even 4 936.1.o.a.883.1 1
20.7 even 4 416.1.h.a.207.1 1
40.3 even 4 2600.1.o.d.51.1 1
40.19 odd 2 2600.1.b.b.1299.1 2
40.27 even 4 104.1.h.a.51.1 1
40.37 odd 4 416.1.h.b.207.1 1
60.47 odd 4 3744.1.o.b.2287.1 1
65.2 even 12 1352.1.n.a.867.2 4
65.7 even 12 1352.1.n.a.315.2 4
65.12 odd 4 104.1.h.a.51.1 1
65.17 odd 12 1352.1.p.b.699.1 2
65.22 odd 12 1352.1.p.a.699.1 2
65.32 even 12 1352.1.n.a.315.1 4
65.37 even 12 1352.1.n.a.867.1 4
65.38 odd 4 2600.1.o.d.51.1 1
65.42 odd 12 1352.1.p.a.147.1 2
65.47 even 4 1352.1.g.a.339.2 2
65.57 even 4 1352.1.g.a.339.1 2
65.62 odd 12 1352.1.p.b.147.1 2
65.64 even 2 2600.1.b.b.1299.1 2
80.27 even 4 3328.1.c.a.3327.1 2
80.37 odd 4 3328.1.c.e.3327.2 2
80.67 even 4 3328.1.c.a.3327.2 2
80.77 odd 4 3328.1.c.e.3327.1 2
104.51 odd 2 CM 2600.1.b.a.1299.1 2
120.77 even 4 3744.1.o.a.2287.1 1
120.107 odd 4 936.1.o.b.883.1 1
195.77 even 4 936.1.o.b.883.1 1
260.207 even 4 416.1.h.b.207.1 1
520.67 odd 12 1352.1.n.a.867.1 4
520.77 odd 4 416.1.h.a.207.1 1
520.107 even 12 1352.1.p.b.147.1 2
520.147 even 12 1352.1.p.a.699.1 2
520.187 odd 4 1352.1.g.a.339.2 2
520.227 odd 12 1352.1.n.a.315.2 4
520.259 odd 2 inner 2600.1.b.a.1299.2 2
520.267 odd 12 1352.1.n.a.315.1 4
520.307 odd 4 1352.1.g.a.339.1 2
520.347 even 12 1352.1.p.b.699.1 2
520.363 even 4 2600.1.o.b.51.1 1
520.387 even 12 1352.1.p.a.147.1 2
520.427 odd 12 1352.1.n.a.867.2 4
520.467 even 4 104.1.h.b.51.1 yes 1
780.467 odd 4 3744.1.o.a.2287.1 1
1040.77 odd 4 3328.1.c.a.3327.1 2
1040.467 even 4 3328.1.c.e.3327.2 2
1040.597 odd 4 3328.1.c.a.3327.2 2
1040.987 even 4 3328.1.c.e.3327.1 2
1560.77 even 4 3744.1.o.b.2287.1 1
1560.467 odd 4 936.1.o.a.883.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
104.1.h.a.51.1 1 40.27 even 4
104.1.h.a.51.1 1 65.12 odd 4
104.1.h.b.51.1 yes 1 5.2 odd 4
104.1.h.b.51.1 yes 1 520.467 even 4
416.1.h.a.207.1 1 20.7 even 4
416.1.h.a.207.1 1 520.77 odd 4
416.1.h.b.207.1 1 40.37 odd 4
416.1.h.b.207.1 1 260.207 even 4
936.1.o.a.883.1 1 15.2 even 4
936.1.o.a.883.1 1 1560.467 odd 4
936.1.o.b.883.1 1 120.107 odd 4
936.1.o.b.883.1 1 195.77 even 4
1352.1.g.a.339.1 2 65.57 even 4
1352.1.g.a.339.1 2 520.307 odd 4
1352.1.g.a.339.2 2 65.47 even 4
1352.1.g.a.339.2 2 520.187 odd 4
1352.1.n.a.315.1 4 65.32 even 12
1352.1.n.a.315.1 4 520.267 odd 12
1352.1.n.a.315.2 4 65.7 even 12
1352.1.n.a.315.2 4 520.227 odd 12
1352.1.n.a.867.1 4 65.37 even 12
1352.1.n.a.867.1 4 520.67 odd 12
1352.1.n.a.867.2 4 65.2 even 12
1352.1.n.a.867.2 4 520.427 odd 12
1352.1.p.a.147.1 2 65.42 odd 12
1352.1.p.a.147.1 2 520.387 even 12
1352.1.p.a.699.1 2 65.22 odd 12
1352.1.p.a.699.1 2 520.147 even 12
1352.1.p.b.147.1 2 65.62 odd 12
1352.1.p.b.147.1 2 520.107 even 12
1352.1.p.b.699.1 2 65.17 odd 12
1352.1.p.b.699.1 2 520.347 even 12
2600.1.b.a.1299.1 2 1.1 even 1 trivial
2600.1.b.a.1299.1 2 104.51 odd 2 CM
2600.1.b.a.1299.2 2 5.4 even 2 inner
2600.1.b.a.1299.2 2 520.259 odd 2 inner
2600.1.b.b.1299.1 2 40.19 odd 2
2600.1.b.b.1299.1 2 65.64 even 2
2600.1.b.b.1299.2 2 8.3 odd 2
2600.1.b.b.1299.2 2 13.12 even 2
2600.1.o.b.51.1 1 5.3 odd 4
2600.1.o.b.51.1 1 520.363 even 4
2600.1.o.d.51.1 1 40.3 even 4
2600.1.o.d.51.1 1 65.38 odd 4
3328.1.c.a.3327.1 2 80.27 even 4
3328.1.c.a.3327.1 2 1040.77 odd 4
3328.1.c.a.3327.2 2 80.67 even 4
3328.1.c.a.3327.2 2 1040.597 odd 4
3328.1.c.e.3327.1 2 80.77 odd 4
3328.1.c.e.3327.1 2 1040.987 even 4
3328.1.c.e.3327.2 2 80.37 odd 4
3328.1.c.e.3327.2 2 1040.467 even 4
3744.1.o.a.2287.1 1 120.77 even 4
3744.1.o.a.2287.1 1 780.467 odd 4
3744.1.o.b.2287.1 1 60.47 odd 4
3744.1.o.b.2287.1 1 1560.77 even 4