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Properties

Label 320.7.h.b.319.1
Level $320$
Weight $7$
Character 320.319
Self dual yes
Analytic conductor $73.617$
Analytic rank $0$
Dimension $1$
CM discriminant -20
Inner twists $2$

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [320,7,Mod(319,320)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(320, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0, 1])) N = Newforms(chi, 7, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("320.319"); S:= CuspForms(chi, 7); N := Newforms(S);
 
Level: \( N \) \(=\) \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 320.h (of order \(2\), degree \(1\), not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,0,44,0,125] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(73.6173067584\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 20)
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label 319.1
Character \(\chi\) \(=\) 320.319

$q$-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+44.0000 q^{3} +125.000 q^{5} +524.000 q^{7} +1207.00 q^{9} +5500.00 q^{15} +23056.0 q^{21} +15356.0 q^{23} +15625.0 q^{25} +21032.0 q^{27} -44858.0 q^{29} +65500.0 q^{35} -74338.0 q^{41} +17404.0 q^{43} +150875. q^{45} +26444.0 q^{47} +156927. q^{49} -452342. q^{61} +632468. q^{63} +1276.00 q^{67} +675664. q^{69} +687500. q^{75} +45505.0 q^{81} -1.13172e6 q^{83} -1.97375e6 q^{87} +511058. q^{89} +O(q^{100})\)

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
\(3\) 44.0000 1.62963 0.814815 − 0.579721i \(-0.196839\pi\)
0.814815 + 0.579721i \(0.196839\pi\)
\(4\) 0 0
\(5\) 125.000 1.00000
\(6\) 0 0
\(7\) 524.000 1.52770 0.763848 − 0.645396i \(-0.223308\pi\)
0.763848 + 0.645396i \(0.223308\pi\)
\(8\) 0 0
\(9\) 1207.00 1.65569
\(10\) 0 0
\(11\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(12\) 0 0
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 0 0
\(15\) 5500.00 1.62963
\(16\) 0 0
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) 0 0
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) 0 0
\(21\) 23056.0 2.48958
\(22\) 0 0
\(23\) 15356.0 1.26210 0.631051 − 0.775741i \(-0.282624\pi\)
0.631051 + 0.775741i \(0.282624\pi\)
\(24\) 0 0
\(25\) 15625.0 1.00000
\(26\) 0 0
\(27\) 21032.0 1.06854
\(28\) 0 0
\(29\) −44858.0 −1.83927 −0.919636 − 0.392772i \(-0.871516\pi\)
−0.919636 + 0.392772i \(0.871516\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 65500.0 1.52770
\(36\) 0 0
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −74338.0 −1.07860 −0.539299 − 0.842115i \(-0.681311\pi\)
−0.539299 + 0.842115i \(0.681311\pi\)
\(42\) 0 0
\(43\) 17404.0 0.218899 0.109449 − 0.993992i \(-0.465091\pi\)
0.109449 + 0.993992i \(0.465091\pi\)
\(44\) 0 0
\(45\) 150875. 1.65569
\(46\) 0 0
\(47\) 26444.0 0.254703 0.127351 − 0.991858i \(-0.459352\pi\)
0.127351 + 0.991858i \(0.459352\pi\)
\(48\) 0 0
\(49\) 156927. 1.33386
\(50\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) 0 0
\(61\) −452342. −1.99286 −0.996431 − 0.0844063i \(-0.973101\pi\)
−0.996431 + 0.0844063i \(0.973101\pi\)
\(62\) 0 0
\(63\) 632468. 2.52940
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 1276.00 0.00424254 0.00212127 − 0.999998i \(-0.499325\pi\)
0.00212127 + 0.999998i \(0.499325\pi\)
\(68\) 0 0
\(69\) 675664. 2.05676
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 0 0
\(73\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(74\) 0 0
\(75\) 687500. 1.62963
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(80\) 0 0
\(81\) 45505.0 0.0856257
\(82\) 0 0
\(83\) −1.13172e6 −1.97926 −0.989631 − 0.143635i \(-0.954121\pi\)
−0.989631 + 0.143635i \(0.954121\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −1.97375e6 −2.99733
\(88\) 0 0
\(89\) 511058. 0.724937 0.362468 − 0.931996i \(-0.381934\pi\)
0.362468 + 0.931996i \(0.381934\pi\)
\(90\) 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
\(101\) 1.91772e6 1.86132 0.930659 − 0.365887i \(-0.119234\pi\)
0.930659 + 0.365887i \(0.119234\pi\)
\(102\) 0 0
\(103\) −1.31520e6 −1.20360 −0.601799 − 0.798648i \(-0.705549\pi\)
−0.601799 + 0.798648i \(0.705549\pi\)
\(104\) 0 0
\(105\) 2.88200e6 2.48958
\(106\) 0 0
\(107\) −2.35240e6 −1.92026 −0.960131 − 0.279550i \(-0.909815\pi\)
−0.960131 + 0.279550i \(0.909815\pi\)
\(108\) 0 0
\(109\) 1.29956e6 1.00350 0.501750 − 0.865013i \(-0.332690\pi\)
0.501750 + 0.865013i \(0.332690\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) 1.91950e6 1.26210
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 1.77156e6 1.00000
\(122\) 0 0
\(123\) −3.27087e6 −1.75771
\(124\) 0 0
\(125\) 1.95312e6 1.00000
\(126\) 0 0
\(127\) 1.72492e6 0.842091 0.421045 − 0.907040i \(-0.361663\pi\)
0.421045 + 0.907040i \(0.361663\pi\)
\(128\) 0 0
\(129\) 765776. 0.356724
\(130\) 0 0
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 2.62900e6 1.06854
\(136\) 0 0
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) 0 0
\(141\) 1.16354e6 0.415071
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) −5.60725e6 −1.83927
\(146\) 0 0
\(147\) 6.90479e6 2.17369
\(148\) 0 0
\(149\) −2.96932e6 −0.897631 −0.448816 − 0.893624i \(-0.648154\pi\)
−0.448816 + 0.893624i \(0.648154\pi\)
\(150\) 0 0
\(151\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(152\) 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
\(161\) 8.04654e6 1.92811
\(162\) 0 0
\(163\) 8.66100e6 1.99989 0.999943 − 0.0106368i \(-0.00338586\pi\)
0.999943 + 0.0106368i \(0.00338586\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 5.88796e6 1.26420 0.632100 − 0.774887i \(-0.282193\pi\)
0.632100 + 0.774887i \(0.282193\pi\)
\(168\) 0 0
\(169\) 4.82681e6 1.00000
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(174\) 0 0
\(175\) 8.18750e6 1.52770
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) 0 0
\(181\) 1.06974e7 1.80402 0.902012 − 0.431710i \(-0.142090\pi\)
0.902012 + 0.431710i \(0.142090\pi\)
\(182\) 0 0
\(183\) −1.99030e7 −3.24763
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 1.10208e7 1.63240
\(190\) 0 0
\(191\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(192\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) 0 0
\(201\) 56144.0 0.00691377
\(202\) 0 0
\(203\) −2.35056e7 −2.80985
\(204\) 0 0
\(205\) −9.29225e6 −1.07860
\(206\) 0 0
\(207\) 1.85347e7 2.08965
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 2.17550e6 0.218899
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −1.78363e7 −1.60839 −0.804194 − 0.594367i \(-0.797403\pi\)
−0.804194 + 0.594367i \(0.797403\pi\)
\(224\) 0 0
\(225\) 1.88594e7 1.65569
\(226\) 0 0
\(227\) 9.91496e6 0.847643 0.423822 − 0.905746i \(-0.360688\pi\)
0.423822 + 0.905746i \(0.360688\pi\)
\(228\) 0 0
\(229\) −2.32339e7 −1.93471 −0.967354 − 0.253427i \(-0.918442\pi\)
−0.967354 + 0.253427i \(0.918442\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(234\) 0 0
\(235\) 3.30550e6 0.254703
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) −2.50778e7 −1.79159 −0.895794 − 0.444470i \(-0.853392\pi\)
−0.895794 + 0.444470i \(0.853392\pi\)
\(242\) 0 0
\(243\) −1.33301e7 −0.928998
\(244\) 0 0
\(245\) 1.96159e7 1.33386
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) −4.97955e7 −3.22546
\(250\) 0 0
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) 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
\(261\) −5.41436e7 −3.04527
\(262\) 0 0
\(263\) −3.60257e7 −1.98036 −0.990182 − 0.139785i \(-0.955359\pi\)
−0.990182 + 0.139785i \(0.955359\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 2.24866e7 1.18138
\(268\) 0 0
\(269\) 8.19428e6 0.420973 0.210486 − 0.977597i \(-0.432495\pi\)
0.210486 + 0.977597i \(0.432495\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) 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
\(281\) 2.59825e7 1.17101 0.585506 − 0.810668i \(-0.300896\pi\)
0.585506 + 0.810668i \(0.300896\pi\)
\(282\) 0 0
\(283\) −4.43699e7 −1.95762 −0.978811 − 0.204765i \(-0.934357\pi\)
−0.978811 + 0.204765i \(0.934357\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −3.89531e7 −1.64777
\(288\) 0 0
\(289\) 2.41376e7 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
\(301\) 9.11970e6 0.334411
\(302\) 0 0
\(303\) 8.43796e7 3.03326
\(304\) 0 0
\(305\) −5.65428e7 −1.99286
\(306\) 0 0
\(307\) −4.31915e7 −1.49274 −0.746369 − 0.665533i \(-0.768204\pi\)
−0.746369 + 0.665533i \(0.768204\pi\)
\(308\) 0 0
\(309\) −5.78690e7 −1.96142
\(310\) 0 0
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) 0 0
\(313\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(314\) 0 0
\(315\) 7.90585e7 2.52940
\(316\) 0 0
\(317\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) −1.03506e8 −3.12932
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 5.71807e7 1.63533
\(328\) 0 0
\(329\) 1.38567e7 0.389109
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 159500. 0.00424254
\(336\) 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
\(343\) 2.05817e7 0.510033
\(344\) 0 0
\(345\) 8.44580e7 2.05676
\(346\) 0 0
\(347\) 4.03414e7 0.965524 0.482762 − 0.875752i \(-0.339634\pi\)
0.482762 + 0.875752i \(0.339634\pi\)
\(348\) 0 0
\(349\) −8.02822e6 −0.188861 −0.0944306 − 0.995531i \(-0.530103\pi\)
−0.0944306 + 0.995531i \(0.530103\pi\)
\(350\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(360\) 0 0
\(361\) 4.70459e7 1.00000
\(362\) 0 0
\(363\) 7.79487e7 1.62963
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −8.69589e7 −1.75920 −0.879601 − 0.475711i \(-0.842191\pi\)
−0.879601 + 0.475711i \(0.842191\pi\)
\(368\) 0 0
\(369\) −8.97260e7 −1.78583
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) 8.59375e7 1.62963
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) 0 0
\(381\) 7.58967e7 1.37230
\(382\) 0 0
\(383\) −1.92778e7 −0.343131 −0.171566 − 0.985173i \(-0.554883\pi\)
−0.171566 + 0.985173i \(0.554883\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 2.10066e7 0.362429
\(388\) 0 0
\(389\) −8.34581e7 −1.41782 −0.708908 − 0.705301i \(-0.750812\pi\)
−0.708908 + 0.705301i \(0.750812\pi\)
\(390\) 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
\(401\) 1.21373e8 1.88230 0.941152 − 0.337982i \(-0.109744\pi\)
0.941152 + 0.337982i \(0.109744\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 5.68812e6 0.0856257
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −1.13372e8 −1.65704 −0.828522 − 0.559956i \(-0.810818\pi\)
−0.828522 + 0.559956i \(0.810818\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −1.41464e8 −1.97926
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) 5.72305e7 0.766975 0.383487 − 0.923546i \(-0.374723\pi\)
0.383487 + 0.923546i \(0.374723\pi\)
\(422\) 0 0
\(423\) 3.19179e7 0.421709
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −2.37027e8 −3.04449
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) 0 0
\(433\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(434\) 0 0
\(435\) −2.46719e8 −2.99733
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(440\) 0 0
\(441\) 1.89411e8 2.20846
\(442\) 0 0
\(443\) 3.57157e7 0.410817 0.205408 − 0.978676i \(-0.434148\pi\)
0.205408 + 0.978676i \(0.434148\pi\)
\(444\) 0 0
\(445\) 6.38822e7 0.724937
\(446\) 0 0
\(447\) −1.30650e8 −1.46281
\(448\) 0 0
\(449\) −1.77667e8 −1.96276 −0.981380 − 0.192076i \(-0.938478\pi\)
−0.981380 + 0.192076i \(0.938478\pi\)
\(450\) 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
\(461\) −6.01196e7 −0.613640 −0.306820 − 0.951768i \(-0.599265\pi\)
−0.306820 + 0.951768i \(0.599265\pi\)
\(462\) 0 0
\(463\) −4.53900e7 −0.457317 −0.228658 − 0.973507i \(-0.573434\pi\)
−0.228658 + 0.973507i \(0.573434\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −7.92225e7 −0.777854 −0.388927 − 0.921269i \(-0.627154\pi\)
−0.388927 + 0.921269i \(0.627154\pi\)
\(468\) 0 0
\(469\) 668624. 0.00648132
\(470\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 3.54048e8 3.14210
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 2.30989e8 1.99989 0.999943 − 0.0106586i \(-0.00339280\pi\)
0.999943 + 0.0106586i \(0.00339280\pi\)
\(488\) 0 0
\(489\) 3.81084e8 3.25907
\(490\) 0 0
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(500\) 0 0
\(501\) 2.59070e8 2.06018
\(502\) 0 0
\(503\) −7.33066e7 −0.576022 −0.288011 − 0.957627i \(-0.592994\pi\)
−0.288011 + 0.957627i \(0.592994\pi\)
\(504\) 0 0
\(505\) 2.39715e8 1.86132
\(506\) 0 0
\(507\) 2.12380e8 1.62963
\(508\) 0 0
\(509\) 1.83714e8 1.39312 0.696559 − 0.717500i \(-0.254714\pi\)
0.696559 + 0.717500i \(0.254714\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −1.64400e8 −1.20360
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −2.11574e8 −1.49606 −0.748031 − 0.663664i \(-0.769000\pi\)
−0.748031 + 0.663664i \(0.769000\pi\)
\(522\) 0 0
\(523\) 1.30165e8 0.909893 0.454946 − 0.890519i \(-0.349658\pi\)
0.454946 + 0.890519i \(0.349658\pi\)
\(524\) 0 0
\(525\) 3.60250e8 2.48958
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 8.77708e7 0.592902
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) −2.94050e8 −1.92026
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 2.70414e8 1.70780 0.853900 − 0.520438i \(-0.174231\pi\)
0.853900 + 0.520438i \(0.174231\pi\)
\(542\) 0 0
\(543\) 4.70686e8 2.93989
\(544\) 0 0
\(545\) 1.62445e8 1.00350
\(546\) 0 0
\(547\) 3.00733e8 1.83747 0.918733 − 0.394880i \(-0.129214\pi\)
0.918733 + 0.394880i \(0.129214\pi\)
\(548\) 0 0
\(549\) −5.45977e8 −3.29957
\(550\) 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
\(563\) −3.51215e8 −1.96810 −0.984052 − 0.177881i \(-0.943076\pi\)
−0.984052 + 0.177881i \(0.943076\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 2.38446e7 0.130810
\(568\) 0 0
\(569\) −1.49518e8 −0.811630 −0.405815 − 0.913955i \(-0.633012\pi\)
−0.405815 + 0.913955i \(0.633012\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 2.39938e8 1.26210
\(576\) 0 0
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −5.93019e8 −3.02371
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −1.33498e8 −0.660026 −0.330013 − 0.943976i \(-0.607053\pi\)
−0.330013 + 0.943976i \(0.607053\pi\)
\(588\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(600\) 0 0
\(601\) 3.79911e8 1.75008 0.875042 − 0.484047i \(-0.160834\pi\)
0.875042 + 0.484047i \(0.160834\pi\)
\(602\) 0 0
\(603\) 1.54013e6 0.00702435
\(604\) 0 0
\(605\) 2.21445e8 1.00000
\(606\) 0 0
\(607\) 1.69713e8 0.758839 0.379419 − 0.925225i \(-0.376124\pi\)
0.379419 + 0.925225i \(0.376124\pi\)
\(608\) 0 0
\(609\) −1.03425e9 −4.57901
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(614\) 0 0
\(615\) −4.08859e8 −1.75771
\(616\) 0 0
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) 0 0
\(619\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(620\) 0 0
\(621\) 3.22967e8 1.34860
\(622\) 0 0
\(623\) 2.67794e8 1.10748
\(624\) 0 0
\(625\) 2.44141e8 1.00000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 2.15616e8 0.842091
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −7.10123e7 −0.269625 −0.134812 − 0.990871i \(-0.543043\pi\)
−0.134812 + 0.990871i \(0.543043\pi\)
\(642\) 0 0
\(643\) 4.35161e8 1.63688 0.818440 − 0.574592i \(-0.194839\pi\)
0.818440 + 0.574592i \(0.194839\pi\)
\(644\) 0 0
\(645\) 9.57220e7 0.356724
\(646\) 0 0
\(647\) −3.26848e8 −1.20679 −0.603396 − 0.797441i \(-0.706186\pi\)
−0.603396 + 0.797441i \(0.706186\pi\)
\(648\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) −3.64144e8 −1.26086 −0.630432 − 0.776244i \(-0.717122\pi\)
−0.630432 + 0.776244i \(0.717122\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −6.88839e8 −2.32135
\(668\) 0 0
\(669\) −7.84798e8 −2.62108
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) 0 0
\(675\) 3.28625e8 1.06854
\(676\) 0 0
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 4.36258e8 1.38134
\(682\) 0 0
\(683\) −6.06224e8 −1.90270 −0.951352 − 0.308107i \(-0.900304\pi\)
−0.951352 + 0.308107i \(0.900304\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −1.02229e9 −3.15286
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(692\) 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
\(701\) 5.95860e8 1.72978 0.864889 − 0.501963i \(-0.167389\pi\)
0.864889 + 0.501963i \(0.167389\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 1.45442e8 0.415071
\(706\) 0 0
\(707\) 1.00488e9 2.84353
\(708\) 0 0
\(709\) 7.12546e8 1.99928 0.999641 − 0.0268005i \(-0.00853187\pi\)
0.999641 + 0.0268005i \(0.00853187\pi\)
\(710\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(720\) 0 0
\(721\) −6.89167e8 −1.83873
\(722\) 0 0
\(723\) −1.10342e9 −2.91962
\(724\) 0 0
\(725\) −7.00906e8 −1.83927
\(726\) 0 0
\(727\) 6.84267e8 1.78083 0.890415 − 0.455150i \(-0.150414\pi\)
0.890415 + 0.455150i \(0.150414\pi\)
\(728\) 0 0
\(729\) −6.19698e8 −1.59955
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(734\) 0 0
\(735\) 8.63098e8 2.17369
\(736\) 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
\(743\) −8.19353e8 −1.99758 −0.998790 − 0.0491695i \(-0.984343\pi\)
−0.998790 + 0.0491695i \(0.984343\pi\)
\(744\) 0 0
\(745\) −3.71165e8 −0.897631
\(746\) 0 0
\(747\) −1.36598e9 −3.27705
\(748\) 0 0
\(749\) −1.23266e9 −2.93358
\(750\) 0 0
\(751\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(752\) 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
\(761\) −4.06269e8 −0.921850 −0.460925 − 0.887439i \(-0.652482\pi\)
−0.460925 + 0.887439i \(0.652482\pi\)
\(762\) 0 0
\(763\) 6.80970e8 1.53304
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) −3.60743e7 −0.0793266 −0.0396633 − 0.999213i \(-0.512629\pi\)
−0.0396633 + 0.999213i \(0.512629\pi\)
\(770\) 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
\(783\) −9.43453e8 −1.96533
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 2.13980e8 0.438983 0.219492 − 0.975614i \(-0.429560\pi\)
0.219492 + 0.975614i \(0.429560\pi\)
\(788\) 0 0
\(789\) −1.58513e9 −3.22726
\(790\) 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
\(801\) 6.16847e8 1.20027
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 1.00582e9 1.92811
\(806\) 0 0
\(807\) 3.60548e8 0.686030
\(808\) 0 0
\(809\) −3.61673e8 −0.683079 −0.341540 − 0.939867i \(-0.610948\pi\)
−0.341540 + 0.939867i \(0.610948\pi\)
\(810\) 0 0
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 1.08263e9 1.99989
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 1.04853e9 1.89474 0.947372 − 0.320135i \(-0.103728\pi\)
0.947372 + 0.320135i \(0.103728\pi\)
\(822\) 0 0
\(823\) 1.16107e8 0.208285 0.104142 − 0.994562i \(-0.466790\pi\)
0.104142 + 0.994562i \(0.466790\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 1.01116e9 1.78773 0.893865 − 0.448337i \(-0.147983\pi\)
0.893865 + 0.448337i \(0.147983\pi\)
\(828\) 0 0
\(829\) −1.81441e8 −0.318472 −0.159236 − 0.987241i \(-0.550903\pi\)
−0.159236 + 0.987241i \(0.550903\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 7.35996e8 1.26420
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(840\) 0 0
\(841\) 1.41742e9 2.38292
\(842\) 0 0
\(843\) 1.14323e9 1.90832
\(844\) 0 0
\(845\) 6.03351e8 1.00000
\(846\) 0 0
\(847\) 9.28298e8 1.52770
\(848\) 0 0
\(849\) −1.95227e9 −3.19020
\(850\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(860\) 0 0
\(861\) −1.71394e9 −2.68525
\(862\) 0 0
\(863\) −7.23421e8 −1.12553 −0.562767 − 0.826615i \(-0.690263\pi\)
−0.562767 + 0.826615i \(0.690263\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 1.06205e9 1.62963
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 1.02344e9 1.52770
\(876\) 0 0
\(877\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −4.68316e8 −0.684874 −0.342437 − 0.939541i \(-0.611252\pi\)
−0.342437 + 0.939541i \(0.611252\pi\)
\(882\) 0 0
\(883\) −9.07097e8 −1.31756 −0.658782 − 0.752334i \(-0.728928\pi\)
−0.658782 + 0.752334i \(0.728928\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 1.37949e9 1.97674 0.988369 − 0.152074i \(-0.0485953\pi\)
0.988369 + 0.152074i \(0.0485953\pi\)
\(888\) 0 0
\(889\) 9.03860e8 1.28646
\(890\) 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
\(903\) 4.01267e8 0.544966
\(904\) 0 0
\(905\) 1.33717e9 1.80402
\(906\) 0 0
\(907\) −1.36077e9 −1.82374 −0.911872 − 0.410474i \(-0.865363\pi\)
−0.911872 + 0.410474i \(0.865363\pi\)
\(908\) 0 0
\(909\) 2.31469e9 3.08177
\(910\) 0 0
\(911\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) −2.48788e9 −3.24763
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(920\) 0 0
\(921\) −1.90043e9 −2.43261
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −1.58745e9 −1.99279
\(928\) 0 0
\(929\) 1.27758e9 1.59346 0.796731 − 0.604334i \(-0.206561\pi\)
0.796731 + 0.604334i \(0.206561\pi\)
\(930\) 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
\(941\) −3.11817e8 −0.374224 −0.187112 − 0.982339i \(-0.559913\pi\)
−0.187112 + 0.982339i \(0.559913\pi\)
\(942\) 0 0
\(943\) −1.14153e9 −1.36130
\(944\) 0 0
\(945\) 1.37760e9 1.63240
\(946\) 0 0
\(947\) 1.01744e9 1.19800 0.599001 − 0.800749i \(-0.295565\pi\)
0.599001 + 0.800749i \(0.295565\pi\)
\(948\) 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
\(961\) 8.87504e8 1.00000
\(962\) 0 0
\(963\) −2.83935e9 −3.17936
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 6.69958e8 0.740915 0.370458 − 0.928849i \(-0.379201\pi\)
0.370458 + 0.928849i \(0.379201\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(972\) 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
\(981\) 1.56857e9 1.66149
\(982\) 0 0
\(983\) −8.00372e8 −0.842619 −0.421310 − 0.906917i \(-0.638429\pi\)
−0.421310 + 0.906917i \(0.638429\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 6.09693e8 0.634103
\(988\) 0 0
\(989\) 2.67256e8 0.276273
\(990\) 0 0
\(991\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(992\) 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 320.7.h.b.319.1 1
4.3 odd 2 320.7.h.a.319.1 1
5.4 even 2 320.7.h.a.319.1 1
8.3 odd 2 20.7.d.b.19.1 yes 1
8.5 even 2 20.7.d.a.19.1 ✓ 1
20.19 odd 2 CM 320.7.h.b.319.1 1
24.5 odd 2 180.7.f.b.19.1 1
24.11 even 2 180.7.f.a.19.1 1
40.3 even 4 100.7.b.d.51.1 2
40.13 odd 4 100.7.b.d.51.2 2
40.19 odd 2 20.7.d.a.19.1 ✓ 1
40.27 even 4 100.7.b.d.51.2 2
40.29 even 2 20.7.d.b.19.1 yes 1
40.37 odd 4 100.7.b.d.51.1 2
120.29 odd 2 180.7.f.a.19.1 1
120.59 even 2 180.7.f.b.19.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
20.7.d.a.19.1 ✓ 1 8.5 even 2
20.7.d.a.19.1 ✓ 1 40.19 odd 2
20.7.d.b.19.1 yes 1 8.3 odd 2
20.7.d.b.19.1 yes 1 40.29 even 2
100.7.b.d.51.1 2 40.3 even 4
100.7.b.d.51.1 2 40.37 odd 4
100.7.b.d.51.2 2 40.13 odd 4
100.7.b.d.51.2 2 40.27 even 4
180.7.f.a.19.1 1 24.11 even 2
180.7.f.a.19.1 1 120.29 odd 2
180.7.f.b.19.1 1 24.5 odd 2
180.7.f.b.19.1 1 120.59 even 2
320.7.h.a.319.1 1 4.3 odd 2
320.7.h.a.319.1 1 5.4 even 2
320.7.h.b.319.1 1 1.1 even 1 trivial
320.7.h.b.319.1 1 20.19 odd 2 CM