Properties

Label 320.6.c.h.129.1
Level 320
Weight 6
Character 320.129
Analytic conductor 51.323
Analytic rank 0
Dimension 4
CM discriminant -20
Inner twists 4

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 320.c (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(51.3228223402\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(i, \sqrt{5})\)
Defining polynomial: \(x^{4} + 3 x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{4}\cdot 5^{2} \)
Twist minimal: no (minimal twist has level 160)
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label 129.1
Root \(-1.61803i\) of defining polynomial
Character \(\chi\) \(=\) 320.129
Dual form 320.6.c.h.129.4

$q$-expansion

\(f(q)\) \(=\) \(q-30.1803i q^{3} +55.9017 q^{5} +194.180i q^{7} -667.853 q^{9} +O(q^{10})\) \(q-30.1803i q^{3} +55.9017 q^{5} +194.180i q^{7} -667.853 q^{9} -1687.13i q^{15} +5860.43 q^{21} +5068.74i q^{23} +3125.00 q^{25} +12822.2i q^{27} -1686.00 q^{29} +10855.0i q^{35} +21041.4 q^{41} +10157.5i q^{43} -37334.1 q^{45} +3217.05i q^{47} -20899.0 q^{49} +52256.9 q^{61} -129684. i q^{63} +63577.5i q^{67} +152976. q^{69} -94313.6i q^{75} +224690. q^{81} -116480. i q^{83} +50884.1i q^{87} -149286. q^{89} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 972q^{9} + O(q^{10}) \) \( 4q - 972q^{9} + 14408q^{21} + 12500q^{25} - 6744q^{29} - 95000q^{45} - 67228q^{49} + 302344q^{69} + 485804q^{81} - 597144q^{89} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/320\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(257\) \(261\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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
\(3\) − 30.1803i − 1.93607i −0.250816 0.968035i \(-0.580699\pi\)
0.250816 0.968035i \(-0.419301\pi\)
\(4\) 0 0
\(5\) 55.9017 1.00000
\(6\) 0 0
\(7\) 194.180i 1.49782i 0.662671 + 0.748911i \(0.269423\pi\)
−0.662671 + 0.748911i \(0.730577\pi\)
\(8\) 0 0
\(9\) −667.853 −2.74837
\(10\) 0 0
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) 0 0
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 0 0
\(15\) − 1687.13i − 1.93607i
\(16\) 0 0
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) 0 0
\(19\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(20\) 0 0
\(21\) 5860.43 2.89989
\(22\) 0 0
\(23\) 5068.74i 1.99793i 0.0454752 + 0.998965i \(0.485520\pi\)
−0.0454752 + 0.998965i \(0.514480\pi\)
\(24\) 0 0
\(25\) 3125.00 1.00000
\(26\) 0 0
\(27\) 12822.2i 3.38496i
\(28\) 0 0
\(29\) −1686.00 −0.372274 −0.186137 0.982524i \(-0.559597\pi\)
−0.186137 + 0.982524i \(0.559597\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 10855.0i 1.49782i
\(36\) 0 0
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 21041.4 1.95486 0.977428 0.211267i \(-0.0677588\pi\)
0.977428 + 0.211267i \(0.0677588\pi\)
\(42\) 0 0
\(43\) 10157.5i 0.837753i 0.908043 + 0.418877i \(0.137576\pi\)
−0.908043 + 0.418877i \(0.862424\pi\)
\(44\) 0 0
\(45\) −37334.1 −2.74837
\(46\) 0 0
\(47\) 3217.05i 0.212429i 0.994343 + 0.106214i \(0.0338730\pi\)
−0.994343 + 0.106214i \(0.966127\pi\)
\(48\) 0 0
\(49\) −20899.0 −1.24347
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) 0 0
\(61\) 52256.9 1.79812 0.899061 0.437824i \(-0.144251\pi\)
0.899061 + 0.437824i \(0.144251\pi\)
\(62\) 0 0
\(63\) − 129684.i − 4.11656i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 63577.5i 1.73028i 0.501530 + 0.865140i \(0.332771\pi\)
−0.501530 + 0.865140i \(0.667229\pi\)
\(68\) 0 0
\(69\) 152976. 3.86813
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(74\) 0 0
\(75\) − 94313.6i − 1.93607i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) 0 0
\(81\) 224690. 3.80515
\(82\) 0 0
\(83\) − 116480.i − 1.85591i −0.372694 0.927954i \(-0.621566\pi\)
0.372694 0.927954i \(-0.378434\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 50884.1i 0.720748i
\(88\) 0 0
\(89\) −149286. −1.99776 −0.998882 0.0472789i \(-0.984945\pi\)
−0.998882 + 0.0472789i \(0.984945\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −137502. −1.34124 −0.670619 0.741802i \(-0.733971\pi\)
−0.670619 + 0.741802i \(0.733971\pi\)
\(102\) 0 0
\(103\) 110367.i 1.02506i 0.858670 + 0.512528i \(0.171291\pi\)
−0.858670 + 0.512528i \(0.828709\pi\)
\(104\) 0 0
\(105\) 327608. 2.89989
\(106\) 0 0
\(107\) 6085.43i 0.0513845i 0.999670 + 0.0256922i \(0.00817900\pi\)
−0.999670 + 0.0256922i \(0.991821\pi\)
\(108\) 0 0
\(109\) 84456.3 0.680872 0.340436 0.940268i \(-0.389425\pi\)
0.340436 + 0.940268i \(0.389425\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) 283351.i 1.99793i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −161051. −1.00000
\(122\) 0 0
\(123\) − 635037.i − 3.78474i
\(124\) 0 0
\(125\) 174693. 1.00000
\(126\) 0 0
\(127\) − 58431.5i − 0.321468i −0.986998 0.160734i \(-0.948614\pi\)
0.986998 0.160734i \(-0.0513861\pi\)
\(128\) 0 0
\(129\) 306557. 1.62195
\(130\) 0 0
\(131\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 716783.i 3.38496i
\(136\) 0 0
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(140\) 0 0
\(141\) 97091.7 0.411277
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) −94250.3 −0.372274
\(146\) 0 0
\(147\) 630739.i 2.40745i
\(148\) 0 0
\(149\) 431583. 1.59257 0.796286 0.604920i \(-0.206795\pi\)
0.796286 + 0.604920i \(0.206795\pi\)
\(150\) 0 0
\(151\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −984250. −2.99254
\(162\) 0 0
\(163\) 169773.i 0.500494i 0.968182 + 0.250247i \(0.0805118\pi\)
−0.968182 + 0.250247i \(0.919488\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 330923.i 0.918198i 0.888385 + 0.459099i \(0.151828\pi\)
−0.888385 + 0.459099i \(0.848172\pi\)
\(168\) 0 0
\(169\) 371293. 1.00000
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(174\) 0 0
\(175\) 606814.i 1.49782i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(180\) 0 0
\(181\) 320402. 0.726940 0.363470 0.931606i \(-0.381592\pi\)
0.363470 + 0.931606i \(0.381592\pi\)
\(182\) 0 0
\(183\) − 1.57713e6i − 3.48129i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) −2.48982e6 −5.07006
\(190\) 0 0
\(191\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) 0 0
\(193\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(200\) 0 0
\(201\) 1.91879e6 3.34994
\(202\) 0 0
\(203\) − 327388.i − 0.557600i
\(204\) 0 0
\(205\) 1.17625e6 1.95486
\(206\) 0 0
\(207\) − 3.38517e6i − 5.49105i
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 567822.i 0.837753i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 374640.i 0.504490i 0.967663 + 0.252245i \(0.0811689\pi\)
−0.967663 + 0.252245i \(0.918831\pi\)
\(224\) 0 0
\(225\) −2.08704e6 −2.74837
\(226\) 0 0
\(227\) 979335.i 1.26144i 0.776011 + 0.630720i \(0.217240\pi\)
−0.776011 + 0.630720i \(0.782760\pi\)
\(228\) 0 0
\(229\) −1.06681e6 −1.34431 −0.672156 0.740410i \(-0.734632\pi\)
−0.672156 + 0.740410i \(0.734632\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(234\) 0 0
\(235\) 179839.i 0.212429i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 0 0
\(241\) −1.42086e6 −1.57583 −0.787916 0.615782i \(-0.788840\pi\)
−0.787916 + 0.615782i \(0.788840\pi\)
\(242\) 0 0
\(243\) − 3.66543e6i − 3.98208i
\(244\) 0 0
\(245\) −1.16829e6 −1.24347
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) −3.51541e6 −3.59317
\(250\) 0 0
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 1.12600e6 1.02314
\(262\) 0 0
\(263\) 324007.i 0.288845i 0.989516 + 0.144423i \(0.0461325\pi\)
−0.989516 + 0.144423i \(0.953868\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 4.50550e6i 3.86781i
\(268\) 0 0
\(269\) −1.35718e6 −1.14356 −0.571778 0.820409i \(-0.693746\pi\)
−0.571778 + 0.820409i \(0.693746\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 679161. 0.513106 0.256553 0.966530i \(-0.417413\pi\)
0.256553 + 0.966530i \(0.417413\pi\)
\(282\) 0 0
\(283\) 2.68372e6i 1.99192i 0.0898251 + 0.995958i \(0.471369\pi\)
−0.0898251 + 0.995958i \(0.528631\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 4.08583e6i 2.92803i
\(288\) 0 0
\(289\) 1.41986e6 1.00000
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) −1.97239e6 −1.25480
\(302\) 0 0
\(303\) 4.14986e6i 2.59673i
\(304\) 0 0
\(305\) 2.92125e6 1.79812
\(306\) 0 0
\(307\) − 586606.i − 0.355223i −0.984101 0.177611i \(-0.943163\pi\)
0.984101 0.177611i \(-0.0568370\pi\)
\(308\) 0 0
\(309\) 3.33093e6 1.98458
\(310\) 0 0
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0 0
\(313\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(314\) 0 0
\(315\) − 7.24955e6i − 4.11656i
\(316\) 0 0
\(317\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 183660. 0.0994840
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) − 2.54892e6i − 1.31822i
\(328\) 0 0
\(329\) −624688. −0.318180
\(330\) 0 0
\(331\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 3.55409e6i 1.73028i
\(336\) 0 0
\(337\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) − 794587.i − 0.364675i
\(344\) 0 0
\(345\) 8.55164e6 3.86813
\(346\) 0 0
\(347\) − 1.82853e6i − 0.815225i −0.913155 0.407613i \(-0.866361\pi\)
0.913155 0.407613i \(-0.133639\pi\)
\(348\) 0 0
\(349\) −2.95461e6 −1.29849 −0.649243 0.760581i \(-0.724914\pi\)
−0.649243 + 0.760581i \(0.724914\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) 0 0
\(361\) −2.47610e6 −1.00000
\(362\) 0 0
\(363\) 4.86057e6i 1.93607i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) − 4.80709e6i − 1.86302i −0.363716 0.931510i \(-0.618492\pi\)
0.363716 0.931510i \(-0.381508\pi\)
\(368\) 0 0
\(369\) −1.40526e7 −5.37266
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) − 5.27229e6i − 1.93607i
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(380\) 0 0
\(381\) −1.76348e6 −0.622384
\(382\) 0 0
\(383\) 5.68236e6i 1.97939i 0.143188 + 0.989695i \(0.454265\pi\)
−0.143188 + 0.989695i \(0.545735\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) − 6.78372e6i − 2.30245i
\(388\) 0 0
\(389\) 5.91961e6 1.98344 0.991720 0.128419i \(-0.0409902\pi\)
0.991720 + 0.128419i \(0.0409902\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 4.66850e6 1.44983 0.724914 0.688840i \(-0.241880\pi\)
0.724914 + 0.688840i \(0.241880\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 1.25606e7 3.80515
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 5.95306e6 1.75967 0.879837 0.475276i \(-0.157652\pi\)
0.879837 + 0.475276i \(0.157652\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) − 6.51144e6i − 1.85591i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(420\) 0 0
\(421\) 4.04525e6 1.11235 0.556173 0.831067i \(-0.312269\pi\)
0.556173 + 0.831067i \(0.312269\pi\)
\(422\) 0 0
\(423\) − 2.14852e6i − 0.583832i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 1.01473e7i 2.69327i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) 0 0
\(433\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(434\) 0 0
\(435\) 2.84451e6i 0.720748i
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(440\) 0 0
\(441\) 1.39575e7 3.41751
\(442\) 0 0
\(443\) − 7.75688e6i − 1.87792i −0.344023 0.938961i \(-0.611790\pi\)
0.344023 0.938961i \(-0.388210\pi\)
\(444\) 0 0
\(445\) −8.34534e6 −1.99776
\(446\) 0 0
\(447\) − 1.30253e7i − 3.08333i
\(448\) 0 0
\(449\) 3.02998e6 0.709291 0.354646 0.935001i \(-0.384602\pi\)
0.354646 + 0.935001i \(0.384602\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 4.54780e6 0.996665 0.498333 0.866986i \(-0.333946\pi\)
0.498333 + 0.866986i \(0.333946\pi\)
\(462\) 0 0
\(463\) 6.05420e6i 1.31252i 0.754537 + 0.656258i \(0.227862\pi\)
−0.754537 + 0.656258i \(0.772138\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) − 8.90843e6i − 1.89020i −0.326774 0.945102i \(-0.605962\pi\)
0.326774 0.945102i \(-0.394038\pi\)
\(468\) 0 0
\(469\) −1.23455e7 −2.59165
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 2.97050e7i 5.79377i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 1.00866e7i 1.92718i 0.267388 + 0.963589i \(0.413839\pi\)
−0.267388 + 0.963589i \(0.586161\pi\)
\(488\) 0 0
\(489\) 5.12380e6 0.968991
\(490\) 0 0
\(491\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(500\) 0 0
\(501\) 9.98738e6 1.77770
\(502\) 0 0
\(503\) 3.13785e6i 0.552983i 0.961016 + 0.276491i \(0.0891717\pi\)
−0.961016 + 0.276491i \(0.910828\pi\)
\(504\) 0 0
\(505\) −7.68660e6 −1.34124
\(506\) 0 0
\(507\) − 1.12057e7i − 1.93607i
\(508\) 0 0
\(509\) −7.23049e6 −1.23701 −0.618505 0.785781i \(-0.712261\pi\)
−0.618505 + 0.785781i \(0.712261\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 6.16972e6i 1.02506i
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −5.30540e6 −0.856295 −0.428148 0.903709i \(-0.640834\pi\)
−0.428148 + 0.903709i \(0.640834\pi\)
\(522\) 0 0
\(523\) 1.15542e7i 1.84707i 0.383509 + 0.923537i \(0.374715\pi\)
−0.383509 + 0.923537i \(0.625285\pi\)
\(524\) 0 0
\(525\) 1.83138e7 2.89989
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −1.92558e7 −2.99173
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 340186.i 0.0513845i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 1.35842e7 1.99545 0.997725 0.0674113i \(-0.0214740\pi\)
0.997725 + 0.0674113i \(0.0214740\pi\)
\(542\) 0 0
\(543\) − 9.66984e6i − 1.40741i
\(544\) 0 0
\(545\) 4.72125e6 0.680872
\(546\) 0 0
\(547\) − 6.05134e6i − 0.864736i −0.901697 0.432368i \(-0.857678\pi\)
0.901697 0.432368i \(-0.142322\pi\)
\(548\) 0 0
\(549\) −3.48999e7 −4.94190
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) − 1.20975e7i − 1.60852i −0.594281 0.804258i \(-0.702563\pi\)
0.594281 0.804258i \(-0.297437\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 4.36304e7i 5.69944i
\(568\) 0 0
\(569\) 6.53945e6 0.846760 0.423380 0.905952i \(-0.360843\pi\)
0.423380 + 0.905952i \(0.360843\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 1.58398e7i 1.99793i
\(576\) 0 0
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 2.26181e7 2.77982
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 4.02285e6i 0.481880i 0.970540 + 0.240940i \(0.0774557\pi\)
−0.970540 + 0.240940i \(0.922544\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) 0 0
\(601\) −1.76169e7 −1.98950 −0.994748 0.102358i \(-0.967361\pi\)
−0.994748 + 0.102358i \(0.967361\pi\)
\(602\) 0 0
\(603\) − 4.24604e7i − 4.75544i
\(604\) 0 0
\(605\) −9.00302e6 −1.00000
\(606\) 0 0
\(607\) − 1.36145e7i − 1.49979i −0.661555 0.749897i \(-0.730103\pi\)
0.661555 0.749897i \(-0.269897\pi\)
\(608\) 0 0
\(609\) −9.88068e6 −1.07955
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(614\) 0 0
\(615\) − 3.54996e7i − 3.78474i
\(616\) 0 0
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) 0 0
\(619\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(620\) 0 0
\(621\) −6.49924e7 −6.76291
\(622\) 0 0
\(623\) − 2.89884e7i − 2.99229i
\(624\) 0 0
\(625\) 9.76562e6 1.00000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) − 3.26642e6i − 0.321468i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −7.61048e6 −0.731589 −0.365794 0.930696i \(-0.619203\pi\)
−0.365794 + 0.930696i \(0.619203\pi\)
\(642\) 0 0
\(643\) − 1.50256e7i − 1.43319i −0.697489 0.716596i \(-0.745699\pi\)
0.697489 0.716596i \(-0.254301\pi\)
\(644\) 0 0
\(645\) 1.71371e7 1.62195
\(646\) 0 0
\(647\) 1.03477e7i 0.971818i 0.874009 + 0.485909i \(0.161511\pi\)
−0.874009 + 0.485909i \(0.838489\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(660\) 0 0
\(661\) −2.19397e7 −1.95311 −0.976554 0.215275i \(-0.930935\pi\)
−0.976554 + 0.215275i \(0.930935\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) − 8.54590e6i − 0.743778i
\(668\) 0 0
\(669\) 1.13068e7 0.976728
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) 0 0
\(675\) 4.00694e7i 3.38496i
\(676\) 0 0
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 2.95566e7 2.44223
\(682\) 0 0
\(683\) − 1.21745e7i − 0.998619i −0.866424 0.499310i \(-0.833587\pi\)
0.866424 0.499310i \(-0.166413\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 3.21968e7i 2.60268i
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 2.13434e7 1.64047 0.820235 0.572027i \(-0.193843\pi\)
0.820235 + 0.572027i \(0.193843\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 5.42759e6 0.411277
\(706\) 0 0
\(707\) − 2.67002e7i − 2.00893i
\(708\) 0 0
\(709\) 2.34765e7 1.75395 0.876977 0.480533i \(-0.159557\pi\)
0.876977 + 0.480533i \(0.159557\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) 0 0
\(721\) −2.14312e7 −1.53535
\(722\) 0 0
\(723\) 4.28822e7i 3.05092i
\(724\) 0 0
\(725\) −5.26875e6 −0.372274
\(726\) 0 0
\(727\) − 2.63437e7i − 1.84859i −0.381681 0.924294i \(-0.624655\pi\)
0.381681 0.924294i \(-0.375345\pi\)
\(728\) 0 0
\(729\) −5.60243e7 −3.90443
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(734\) 0 0
\(735\) 3.52594e7i 2.40745i
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) − 2.93648e7i − 1.95144i −0.219018 0.975721i \(-0.570285\pi\)
0.219018 0.975721i \(-0.429715\pi\)
\(744\) 0 0
\(745\) 2.41262e7 1.59257
\(746\) 0 0
\(747\) 7.77916e7i 5.10072i
\(748\) 0 0
\(749\) −1.18167e6 −0.0769648
\(750\) 0 0
\(751\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −2.95982e7 −1.85269 −0.926347 0.376672i \(-0.877069\pi\)
−0.926347 + 0.376672i \(0.877069\pi\)
\(762\) 0 0
\(763\) 1.63998e7i 1.01983i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) −3.13824e7 −1.91369 −0.956843 0.290607i \(-0.906143\pi\)
−0.956843 + 0.290607i \(0.906143\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) − 2.16182e7i − 1.26013i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) − 3.41617e7i − 1.96609i −0.183368 0.983044i \(-0.558700\pi\)
0.183368 0.983044i \(-0.441300\pi\)
\(788\) 0 0
\(789\) 9.77864e6 0.559224
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 9.97011e7 5.49058
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) −5.50212e7 −2.99254
\(806\) 0 0
\(807\) 4.09602e7i 2.21400i
\(808\) 0 0
\(809\) 1.06699e6 0.0573175 0.0286588 0.999589i \(-0.490876\pi\)
0.0286588 + 0.999589i \(0.490876\pi\)
\(810\) 0 0
\(811\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 9.49058e6i 0.500494i
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −9.63269e6 −0.498758 −0.249379 0.968406i \(-0.580226\pi\)
−0.249379 + 0.968406i \(0.580226\pi\)
\(822\) 0 0
\(823\) − 3.18414e7i − 1.63868i −0.573311 0.819338i \(-0.694341\pi\)
0.573311 0.819338i \(-0.305659\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 3.13336e7i 1.59311i 0.604565 + 0.796556i \(0.293347\pi\)
−0.604565 + 0.796556i \(0.706653\pi\)
\(828\) 0 0
\(829\) −3.65262e7 −1.84594 −0.922972 0.384867i \(-0.874247\pi\)
−0.922972 + 0.384867i \(0.874247\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 1.84992e7i 0.918198i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(840\) 0 0
\(841\) −1.76686e7 −0.861412
\(842\) 0 0
\(843\) − 2.04973e7i − 0.993409i
\(844\) 0 0
\(845\) 2.07559e7 1.00000
\(846\) 0 0
\(847\) − 3.12729e7i − 1.49782i
\(848\) 0 0
\(849\) 8.09955e7 3.85649
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 0 0
\(859\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(860\) 0 0
\(861\) 1.23312e8 5.66887
\(862\) 0 0
\(863\) 4.37437e7i 1.99935i 0.0254879 + 0.999675i \(0.491886\pi\)
−0.0254879 + 0.999675i \(0.508114\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) − 4.28518e7i − 1.93607i
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 3.39219e7i 1.49782i
\(876\) 0 0
\(877\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 2.42030e7 1.05058 0.525291 0.850922i \(-0.323956\pi\)
0.525291 + 0.850922i \(0.323956\pi\)
\(882\) 0 0
\(883\) − 4.17673e7i − 1.80275i −0.433043 0.901373i \(-0.642560\pi\)
0.433043 0.901373i \(-0.357440\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) − 4.64402e7i − 1.98192i −0.134171 0.990958i \(-0.542837\pi\)
0.134171 0.990958i \(-0.457163\pi\)
\(888\) 0 0
\(889\) 1.13462e7 0.481502
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) 5.95274e7i 2.42939i
\(904\) 0 0
\(905\) 1.79110e7 0.726940
\(906\) 0 0
\(907\) − 2.07876e7i − 0.839046i −0.907745 0.419523i \(-0.862197\pi\)
0.907745 0.419523i \(-0.137803\pi\)
\(908\) 0 0
\(909\) 9.18311e7 3.68621
\(910\) 0 0
\(911\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) − 8.81643e7i − 3.48129i
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(920\) 0 0
\(921\) −1.77040e7 −0.687736
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) − 7.37092e7i − 2.81723i
\(928\) 0 0
\(929\) 5.26024e7 1.99971 0.999853 0.0171747i \(-0.00546715\pi\)
0.999853 + 0.0171747i \(0.00546715\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −3.19418e7 −1.17594 −0.587970 0.808883i \(-0.700073\pi\)
−0.587970 + 0.808883i \(0.700073\pi\)
\(942\) 0 0
\(943\) 1.06653e8i 3.90567i
\(944\) 0 0
\(945\) −1.39185e8 −5.07006
\(946\) 0 0
\(947\) 640893.i 0.0232226i 0.999933 + 0.0116113i \(0.00369607\pi\)
−0.999933 + 0.0116113i \(0.996304\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −2.86292e7 −1.00000
\(962\) 0 0
\(963\) − 4.06417e6i − 0.141223i
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) − 1.80869e7i − 0.622012i −0.950408 0.311006i \(-0.899334\pi\)
0.950408 0.311006i \(-0.100666\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) −5.64044e7 −1.87129
\(982\) 0 0
\(983\) − 5.66561e7i − 1.87009i −0.354526 0.935046i \(-0.615358\pi\)
0.354526 0.935046i \(-0.384642\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 1.88533e7i 0.616020i
\(988\) 0 0
\(989\) −5.14858e7 −1.67377
\(990\) 0 0
\(991\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(998\) 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 320.6.c.h.129.1 4
4.3 odd 2 inner 320.6.c.h.129.4 4
5.4 even 2 inner 320.6.c.h.129.4 4
8.3 odd 2 160.6.c.b.129.1 4
8.5 even 2 160.6.c.b.129.4 yes 4
20.19 odd 2 CM 320.6.c.h.129.1 4
40.3 even 4 800.6.a.m.1.2 2
40.13 odd 4 800.6.a.f.1.1 2
40.19 odd 2 160.6.c.b.129.4 yes 4
40.27 even 4 800.6.a.f.1.1 2
40.29 even 2 160.6.c.b.129.1 4
40.37 odd 4 800.6.a.m.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
160.6.c.b.129.1 4 8.3 odd 2
160.6.c.b.129.1 4 40.29 even 2
160.6.c.b.129.4 yes 4 8.5 even 2
160.6.c.b.129.4 yes 4 40.19 odd 2
320.6.c.h.129.1 4 1.1 even 1 trivial
320.6.c.h.129.1 4 20.19 odd 2 CM
320.6.c.h.129.4 4 4.3 odd 2 inner
320.6.c.h.129.4 4 5.4 even 2 inner
800.6.a.f.1.1 2 40.13 odd 4
800.6.a.f.1.1 2 40.27 even 4
800.6.a.m.1.2 2 40.3 even 4
800.6.a.m.1.2 2 40.37 odd 4