Properties

Label 395.3.c.b.394.4
Level $395$
Weight $3$
Character 395.394
Self dual yes
Analytic conductor $10.763$
Analytic rank $0$
Dimension $4$
CM discriminant -395
Inner twists $4$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [395,3,Mod(394,395)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(395, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("395.394");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 395 = 5 \cdot 79 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 395.c (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(10.7629704422\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: 4.4.31600.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - 19x^{2} + 79 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label 394.4
Root \(3.58526\) of defining polynomial
Character \(\chi\) \(=\) 395.394

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+5.80108 q^{3} +4.00000 q^{4} +5.00000 q^{5} -10.2327 q^{7} +24.6525 q^{9} +O(q^{10})\) \(q+5.80108 q^{3} +4.00000 q^{4} +5.00000 q^{5} -10.2327 q^{7} +24.6525 q^{9} -20.1246 q^{11} +23.2043 q^{12} +29.0054 q^{15} +16.0000 q^{16} -1.04617 q^{17} +13.4164 q^{19} +20.0000 q^{20} -59.3607 q^{21} +25.0000 q^{25} +90.8012 q^{27} -40.9308 q^{28} -17.0000 q^{31} -116.744 q^{33} -51.1635 q^{35} +98.6099 q^{36} -67.5969 q^{37} -25.5436 q^{43} -80.4984 q^{44} +123.262 q^{45} -58.4104 q^{47} +92.8172 q^{48} +55.7082 q^{49} -6.06888 q^{51} +27.7122 q^{53} -100.623 q^{55} +77.8296 q^{57} +116.022 q^{60} -252.261 q^{63} +64.0000 q^{64} -4.18466 q^{68} +145.027 q^{75} +53.6656 q^{76} +205.929 q^{77} -79.0000 q^{79} +80.0000 q^{80} +304.872 q^{81} -237.443 q^{84} -5.23083 q^{85} +174.413 q^{89} -98.6183 q^{93} +67.0820 q^{95} -496.122 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 16 q^{4} + 20 q^{5} + 36 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 16 q^{4} + 20 q^{5} + 36 q^{9} + 64 q^{16} + 80 q^{20} - 148 q^{21} + 100 q^{25} - 68 q^{31} + 144 q^{36} + 180 q^{45} + 196 q^{49} + 92 q^{51} + 256 q^{64} - 316 q^{79} + 320 q^{80} + 656 q^{81} - 592 q^{84} - 1260 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/395\mathbb{Z}\right)^\times\).

\(n\) \(161\) \(317\)
\(\chi(n)\) \(-1\) \(-1\)

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 1.00000 \(0\)
−1.00000 \(\pi\)
\(3\) 5.80108 1.93369 0.966846 0.255361i \(-0.0821942\pi\)
0.966846 + 0.255361i \(0.0821942\pi\)
\(4\) 4.00000 1.00000
\(5\) 5.00000 1.00000
\(6\) 0 0
\(7\) −10.2327 −1.46181 −0.730907 0.682477i \(-0.760903\pi\)
−0.730907 + 0.682477i \(0.760903\pi\)
\(8\) 0 0
\(9\) 24.6525 2.73916
\(10\) 0 0
\(11\) −20.1246 −1.82951 −0.914755 0.404009i \(-0.867616\pi\)
−0.914755 + 0.404009i \(0.867616\pi\)
\(12\) 23.2043 1.93369
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 0 0
\(15\) 29.0054 1.93369
\(16\) 16.0000 1.00000
\(17\) −1.04617 −0.0615391 −0.0307696 0.999527i \(-0.509796\pi\)
−0.0307696 + 0.999527i \(0.509796\pi\)
\(18\) 0 0
\(19\) 13.4164 0.706127 0.353063 0.935599i \(-0.385140\pi\)
0.353063 + 0.935599i \(0.385140\pi\)
\(20\) 20.0000 1.00000
\(21\) −59.3607 −2.82670
\(22\) 0 0
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) 0 0
\(25\) 25.0000 1.00000
\(26\) 0 0
\(27\) 90.8012 3.36301
\(28\) −40.9308 −1.46181
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) −17.0000 −0.548387 −0.274194 0.961675i \(-0.588411\pi\)
−0.274194 + 0.961675i \(0.588411\pi\)
\(32\) 0 0
\(33\) −116.744 −3.53771
\(34\) 0 0
\(35\) −51.1635 −1.46181
\(36\) 98.6099 2.73916
\(37\) −67.5969 −1.82694 −0.913472 0.406903i \(-0.866609\pi\)
−0.913472 + 0.406903i \(0.866609\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) −25.5436 −0.594037 −0.297019 0.954872i \(-0.595992\pi\)
−0.297019 + 0.954872i \(0.595992\pi\)
\(44\) −80.4984 −1.82951
\(45\) 123.262 2.73916
\(46\) 0 0
\(47\) −58.4104 −1.24277 −0.621387 0.783504i \(-0.713430\pi\)
−0.621387 + 0.783504i \(0.713430\pi\)
\(48\) 92.8172 1.93369
\(49\) 55.7082 1.13690
\(50\) 0 0
\(51\) −6.06888 −0.118998
\(52\) 0 0
\(53\) 27.7122 0.522873 0.261436 0.965221i \(-0.415804\pi\)
0.261436 + 0.965221i \(0.415804\pi\)
\(54\) 0 0
\(55\) −100.623 −1.82951
\(56\) 0 0
\(57\) 77.8296 1.36543
\(58\) 0 0
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) 116.022 1.93369
\(61\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(62\) 0 0
\(63\) −252.261 −4.00415
\(64\) 64.0000 1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) −4.18466 −0.0615391
\(69\) 0 0
\(70\) 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
\(75\) 145.027 1.93369
\(76\) 53.6656 0.706127
\(77\) 205.929 2.67440
\(78\) 0 0
\(79\) −79.0000 −1.00000
\(80\) 80.0000 1.00000
\(81\) 304.872 3.76386
\(82\) 0 0
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) −237.443 −2.82670
\(85\) −5.23083 −0.0615391
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 174.413 1.95970 0.979850 0.199735i \(-0.0640080\pi\)
0.979850 + 0.199735i \(0.0640080\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −98.6183 −1.06041
\(94\) 0 0
\(95\) 67.0820 0.706127
\(96\) 0 0
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) 0 0
\(99\) −496.122 −5.01133
\(100\) 100.000 1.00000
\(101\) −193.000 −1.91089 −0.955446 0.295167i \(-0.904625\pi\)
−0.955446 + 0.295167i \(0.904625\pi\)
\(102\) 0 0
\(103\) 120.929 1.17407 0.587034 0.809562i \(-0.300295\pi\)
0.587034 + 0.809562i \(0.300295\pi\)
\(104\) 0 0
\(105\) −296.803 −2.82670
\(106\) 0 0
\(107\) −213.993 −1.99994 −0.999968 0.00795763i \(-0.997467\pi\)
−0.999968 + 0.00795763i \(0.997467\pi\)
\(108\) 363.205 3.36301
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 0 0
\(111\) −392.135 −3.53274
\(112\) −163.723 −1.46181
\(113\) 38.7622 0.343028 0.171514 0.985182i \(-0.445134\pi\)
0.171514 + 0.985182i \(0.445134\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 10.7051 0.0899588
\(120\) 0 0
\(121\) 284.000 2.34711
\(122\) 0 0
\(123\) 0 0
\(124\) −68.0000 −0.548387
\(125\) 125.000 1.00000
\(126\) 0 0
\(127\) 191.359 1.50677 0.753383 0.657582i \(-0.228421\pi\)
0.753383 + 0.657582i \(0.228421\pi\)
\(128\) 0 0
\(129\) −148.180 −1.14868
\(130\) 0 0
\(131\) −46.9574 −0.358454 −0.179227 0.983808i \(-0.557360\pi\)
−0.179227 + 0.983808i \(0.557360\pi\)
\(132\) −466.978 −3.53771
\(133\) −137.286 −1.03223
\(134\) 0 0
\(135\) 454.006 3.36301
\(136\) 0 0
\(137\) −271.357 −1.98071 −0.990356 0.138549i \(-0.955756\pi\)
−0.990356 + 0.138549i \(0.955756\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) −204.654 −1.46181
\(141\) −338.843 −2.40314
\(142\) 0 0
\(143\) 0 0
\(144\) 394.440 2.73916
\(145\) 0 0
\(146\) 0 0
\(147\) 323.167 2.19842
\(148\) −270.388 −1.82694
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) 0 0
\(151\) 301.869 1.99913 0.999567 0.0294311i \(-0.00936957\pi\)
0.999567 + 0.0294311i \(0.00936957\pi\)
\(152\) 0 0
\(153\) −25.7906 −0.168566
\(154\) 0 0
\(155\) −85.0000 −0.548387
\(156\) 0 0
\(157\) 310.272 1.97626 0.988128 0.153633i \(-0.0490972\pi\)
0.988128 + 0.153633i \(0.0490972\pi\)
\(158\) 0 0
\(159\) 160.761 1.01107
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(164\) 0 0
\(165\) −583.722 −3.53771
\(166\) 0 0
\(167\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(168\) 0 0
\(169\) 169.000 1.00000
\(170\) 0 0
\(171\) 330.748 1.93420
\(172\) −102.174 −0.594037
\(173\) 276.588 1.59878 0.799388 0.600815i \(-0.205157\pi\)
0.799388 + 0.600815i \(0.205157\pi\)
\(174\) 0 0
\(175\) −255.818 −1.46181
\(176\) −321.994 −1.82951
\(177\) 0 0
\(178\) 0 0
\(179\) −353.000 −1.97207 −0.986034 0.166547i \(-0.946738\pi\)
−0.986034 + 0.166547i \(0.946738\pi\)
\(180\) 493.050 2.73916
\(181\) −234.787 −1.29717 −0.648583 0.761144i \(-0.724638\pi\)
−0.648583 + 0.761144i \(0.724638\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −337.984 −1.82694
\(186\) 0 0
\(187\) 21.0537 0.112586
\(188\) −233.641 −1.24277
\(189\) −929.142 −4.91609
\(190\) 0 0
\(191\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(192\) 371.269 1.93369
\(193\) 339.031 1.75664 0.878318 0.478077i \(-0.158666\pi\)
0.878318 + 0.478077i \(0.158666\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 222.833 1.13690
\(197\) −33.5313 −0.170210 −0.0851049 0.996372i \(-0.527123\pi\)
−0.0851049 + 0.996372i \(0.527123\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) −24.2755 −0.118998
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −270.000 −1.29187
\(210\) 0 0
\(211\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(212\) 110.849 0.522873
\(213\) 0 0
\(214\) 0 0
\(215\) −127.718 −0.594037
\(216\) 0 0
\(217\) 173.956 0.801640
\(218\) 0 0
\(219\) 0 0
\(220\) −402.492 −1.82951
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(224\) 0 0
\(225\) 616.312 2.73916
\(226\) 0 0
\(227\) 374.578 1.65012 0.825062 0.565043i \(-0.191140\pi\)
0.825062 + 0.565043i \(0.191140\pi\)
\(228\) 311.318 1.36543
\(229\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(230\) 0 0
\(231\) 1194.61 5.17147
\(232\) 0 0
\(233\) 240.354 1.03156 0.515781 0.856720i \(-0.327502\pi\)
0.515781 + 0.856720i \(0.327502\pi\)
\(234\) 0 0
\(235\) −292.052 −1.24277
\(236\) 0 0
\(237\) −458.285 −1.93369
\(238\) 0 0
\(239\) −233.000 −0.974895 −0.487448 0.873152i \(-0.662072\pi\)
−0.487448 + 0.873152i \(0.662072\pi\)
\(240\) 464.086 1.93369
\(241\) 281.745 1.16906 0.584532 0.811370i \(-0.301278\pi\)
0.584532 + 0.811370i \(0.301278\pi\)
\(242\) 0 0
\(243\) 951.376 3.91513
\(244\) 0 0
\(245\) 278.541 1.13690
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) −1009.05 −4.00415
\(253\) 0 0
\(254\) 0 0
\(255\) −30.3444 −0.118998
\(256\) 256.000 1.00000
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) 0 0
\(259\) 691.699 2.67065
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(264\) 0 0
\(265\) 138.561 0.522873
\(266\) 0 0
\(267\) 1011.78 3.78946
\(268\) 0 0
\(269\) −395.784 −1.47132 −0.735658 0.677353i \(-0.763127\pi\)
−0.735658 + 0.677353i \(0.763127\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) −16.7386 −0.0615391
\(273\) 0 0
\(274\) 0 0
\(275\) −503.115 −1.82951
\(276\) 0 0
\(277\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(278\) 0 0
\(279\) −419.092 −1.50212
\(280\) 0 0
\(281\) 167.000 0.594306 0.297153 0.954830i \(-0.403963\pi\)
0.297153 + 0.954830i \(0.403963\pi\)
\(282\) 0 0
\(283\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(284\) 0 0
\(285\) 389.148 1.36543
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −287.906 −0.996213
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −91.5061 −0.312307 −0.156154 0.987733i \(-0.549910\pi\)
−0.156154 + 0.987733i \(0.549910\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −1827.34 −6.15266
\(298\) 0 0
\(299\) 0 0
\(300\) 580.108 1.93369
\(301\) 261.380 0.868372
\(302\) 0 0
\(303\) −1119.61 −3.69507
\(304\) 214.663 0.706127
\(305\) 0 0
\(306\) 0 0
\(307\) 335.151 1.09170 0.545849 0.837884i \(-0.316207\pi\)
0.545849 + 0.837884i \(0.316207\pi\)
\(308\) 823.717 2.67440
\(309\) 701.519 2.27029
\(310\) 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
\(315\) −1261.31 −4.00415
\(316\) −316.000 −1.00000
\(317\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 320.000 1.00000
\(321\) −1241.39 −3.86726
\(322\) 0 0
\(323\) −14.0358 −0.0434544
\(324\) 1219.49 3.76386
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 597.696 1.81670
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) 0 0
\(333\) −1666.43 −5.00430
\(334\) 0 0
\(335\) 0 0
\(336\) −949.771 −2.82670
\(337\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(338\) 0 0
\(339\) 224.862 0.663310
\(340\) −20.9233 −0.0615391
\(341\) 342.118 1.00328
\(342\) 0 0
\(343\) −68.6431 −0.200126
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 486.015 1.37681 0.688407 0.725325i \(-0.258310\pi\)
0.688407 + 0.725325i \(0.258310\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 697.653 1.95970
\(357\) 62.1011 0.173953
\(358\) 0 0
\(359\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(360\) 0 0
\(361\) −181.000 −0.501385
\(362\) 0 0
\(363\) 1647.51 4.53858
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −283.571 −0.764343
\(372\) −394.473 −1.06041
\(373\) −656.550 −1.76019 −0.880093 0.474801i \(-0.842520\pi\)
−0.880093 + 0.474801i \(0.842520\pi\)
\(374\) 0 0
\(375\) 725.134 1.93369
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) 268.328 0.706127
\(381\) 1110.09 2.91362
\(382\) 0 0
\(383\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(384\) 0 0
\(385\) 1029.65 2.67440
\(386\) 0 0
\(387\) −629.713 −1.62717
\(388\) 0 0
\(389\) 67.0000 0.172237 0.0861183 0.996285i \(-0.472554\pi\)
0.0861183 + 0.996285i \(0.472554\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) −272.404 −0.693139
\(394\) 0 0
\(395\) −395.000 −1.00000
\(396\) −1984.49 −5.01133
\(397\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(398\) 0 0
\(399\) −796.407 −1.99601
\(400\) 400.000 1.00000
\(401\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) −772.000 −1.91089
\(405\) 1524.36 3.76386
\(406\) 0 0
\(407\) 1360.36 3.34241
\(408\) 0 0
\(409\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(410\) 0 0
\(411\) −1574.16 −3.83008
\(412\) 483.716 1.17407
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) −1187.21 −2.82670
\(421\) −288.453 −0.685161 −0.342580 0.939488i \(-0.611301\pi\)
−0.342580 + 0.939488i \(0.611301\pi\)
\(422\) 0 0
\(423\) −1439.96 −3.40416
\(424\) 0 0
\(425\) −26.1541 −0.0615391
\(426\) 0 0
\(427\) 0 0
\(428\) −855.973 −1.99994
\(429\) 0 0
\(430\) 0 0
\(431\) −718.000 −1.66589 −0.832947 0.553353i \(-0.813348\pi\)
−0.832947 + 0.553353i \(0.813348\pi\)
\(432\) 1452.82 3.36301
\(433\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) −610.447 −1.39054 −0.695269 0.718749i \(-0.744715\pi\)
−0.695269 + 0.718749i \(0.744715\pi\)
\(440\) 0 0
\(441\) 1373.35 3.11416
\(442\) 0 0
\(443\) −592.244 −1.33689 −0.668447 0.743760i \(-0.733041\pi\)
−0.668447 + 0.743760i \(0.733041\pi\)
\(444\) −1568.54 −3.53274
\(445\) 872.067 1.95970
\(446\) 0 0
\(447\) 0 0
\(448\) −654.893 −1.46181
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 155.049 0.343028
\(453\) 1751.17 3.86571
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(458\) 0 0
\(459\) −94.9931 −0.206957
\(460\) 0 0
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) −869.497 −1.87796 −0.938981 0.343968i \(-0.888229\pi\)
−0.938981 + 0.343968i \(0.888229\pi\)
\(464\) 0 0
\(465\) −493.091 −1.06041
\(466\) 0 0
\(467\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 1799.91 3.82147
\(472\) 0 0
\(473\) 514.055 1.08680
\(474\) 0 0
\(475\) 335.410 0.706127
\(476\) 42.8204 0.0899588
\(477\) 683.175 1.43223
\(478\) 0 0
\(479\) 563.000 1.17537 0.587683 0.809092i \(-0.300040\pi\)
0.587683 + 0.809092i \(0.300040\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 1136.00 2.34711
\(485\) 0 0
\(486\) 0 0
\(487\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) −2480.61 −5.01133
\(496\) −272.000 −0.548387
\(497\) 0 0
\(498\) 0 0
\(499\) 436.033 0.873814 0.436907 0.899507i \(-0.356074\pi\)
0.436907 + 0.899507i \(0.356074\pi\)
\(500\) 500.000 1.00000
\(501\) 0 0
\(502\) 0 0
\(503\) −467.337 −0.929099 −0.464550 0.885547i \(-0.653784\pi\)
−0.464550 + 0.885547i \(0.653784\pi\)
\(504\) 0 0
\(505\) −965.000 −1.91089
\(506\) 0 0
\(507\) 980.382 1.93369
\(508\) 765.437 1.50677
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 1218.23 2.37471
\(514\) 0 0
\(515\) 604.645 1.17407
\(516\) −592.721 −1.14868
\(517\) 1175.49 2.27367
\(518\) 0 0
\(519\) 1604.51 3.09154
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 0 0
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) −187.830 −0.358454
\(525\) −1484.02 −2.82670
\(526\) 0 0
\(527\) 17.7848 0.0337473
\(528\) −1867.91 −3.53771
\(529\) 529.000 1.00000
\(530\) 0 0
\(531\) 0 0
\(532\) −549.144 −1.03223
\(533\) 0 0
\(534\) 0 0
\(535\) −1069.97 −1.99994
\(536\) 0 0
\(537\) −2047.78 −3.81337
\(538\) 0 0
\(539\) −1121.11 −2.07997
\(540\) 1816.02 3.36301
\(541\) −845.234 −1.56235 −0.781177 0.624309i \(-0.785380\pi\)
−0.781177 + 0.624309i \(0.785380\pi\)
\(542\) 0 0
\(543\) −1362.02 −2.50832
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(548\) −1085.43 −1.98071
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 808.384 1.46181
\(554\) 0 0
\(555\) −1960.67 −3.53274
\(556\) 0 0
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) −818.616 −1.46181
\(561\) 122.134 0.217708
\(562\) 0 0
\(563\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(564\) −1355.37 −2.40314
\(565\) 193.811 0.343028
\(566\) 0 0
\(567\) −3119.67 −5.50206
\(568\) 0 0
\(569\) 597.030 1.04926 0.524631 0.851330i \(-0.324203\pi\)
0.524631 + 0.851330i \(0.324203\pi\)
\(570\) 0 0
\(571\) 1063.00 1.86165 0.930823 0.365470i \(-0.119092\pi\)
0.930823 + 0.365470i \(0.119092\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 1577.76 2.73916
\(577\) 1152.87 1.99805 0.999024 0.0441665i \(-0.0140632\pi\)
0.999024 + 0.0441665i \(0.0140632\pi\)
\(578\) 0 0
\(579\) 1966.74 3.39679
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −557.698 −0.956601
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 957.788 1.63167 0.815833 0.578288i \(-0.196279\pi\)
0.815833 + 0.578288i \(0.196279\pi\)
\(588\) 1292.67 2.19842
\(589\) −228.079 −0.387231
\(590\) 0 0
\(591\) −194.518 −0.329133
\(592\) −1081.55 −1.82694
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 0 0
\(595\) 53.5255 0.0899588
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −469.574 −0.783930 −0.391965 0.919980i \(-0.628205\pi\)
−0.391965 + 0.919980i \(0.628205\pi\)
\(600\) 0 0
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 1207.48 1.99913
\(605\) 1420.00 2.34711
\(606\) 0 0
\(607\) 1186.86 1.95529 0.977647 0.210254i \(-0.0674292\pi\)
0.977647 + 0.210254i \(0.0674292\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) −103.162 −0.168566
\(613\) 933.291 1.52250 0.761248 0.648460i \(-0.224587\pi\)
0.761248 + 0.648460i \(0.224587\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) 0 0
\(619\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(620\) −340.000 −0.548387
\(621\) 0 0
\(622\) 0 0
\(623\) −1784.72 −2.86472
\(624\) 0 0
\(625\) 625.000 1.00000
\(626\) 0 0
\(627\) −1566.29 −2.49807
\(628\) 1241.09 1.97626
\(629\) 70.7175 0.112428
\(630\) 0 0
\(631\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 956.796 1.50677
\(636\) 643.043 1.01107
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −1220.89 −1.90467 −0.952335 0.305055i \(-0.901325\pi\)
−0.952335 + 0.305055i \(0.901325\pi\)
\(642\) 0 0
\(643\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(644\) 0 0
\(645\) −740.902 −1.14868
\(646\) 0 0
\(647\) −528.580 −0.816971 −0.408486 0.912765i \(-0.633943\pi\)
−0.408486 + 0.912765i \(0.633943\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 1009.13 1.55013
\(652\) 0 0
\(653\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(654\) 0 0
\(655\) −234.787 −0.358454
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) −2334.89 −3.53771
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −686.431 −1.03223
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −289.600 −0.430312 −0.215156 0.976580i \(-0.569026\pi\)
−0.215156 + 0.976580i \(0.569026\pi\)
\(674\) 0 0
\(675\) 2270.03 3.36301
\(676\) 676.000 1.00000
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 2172.96 3.19083
\(682\) 0 0
\(683\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(684\) 1322.99 1.93420
\(685\) −1356.79 −1.98071
\(686\) 0 0
\(687\) 0 0
\(688\) −408.698 −0.594037
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(692\) 1106.35 1.59878
\(693\) 5076.66 7.32563
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 1394.31 1.99472
\(700\) −1023.27 −1.46181
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) −906.907 −1.29005
\(704\) −1287.98 −1.82951
\(705\) −1694.21 −2.40314
\(706\) 0 0
\(707\) 1974.91 2.79337
\(708\) 0 0
\(709\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(710\) 0 0
\(711\) −1947.55 −2.73916
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) −1412.00 −1.97207
\(717\) −1351.65 −1.88515
\(718\) 0 0
\(719\) −142.000 −0.197497 −0.0987483 0.995112i \(-0.531484\pi\)
−0.0987483 + 0.995112i \(0.531484\pi\)
\(720\) 1972.20 2.73916
\(721\) −1237.43 −1.71627
\(722\) 0 0
\(723\) 1634.42 2.26061
\(724\) −939.149 −1.29717
\(725\) 0 0
\(726\) 0 0
\(727\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(728\) 0 0
\(729\) 2775.16 3.80680
\(730\) 0 0
\(731\) 26.7228 0.0365565
\(732\) 0 0
\(733\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(734\) 0 0
\(735\) 1615.84 2.19842
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(740\) −1351.94 −1.82694
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 84.2147 0.112586
\(749\) 2189.73 2.92354
\(750\) 0 0
\(751\) −362.243 −0.482348 −0.241174 0.970482i \(-0.577532\pi\)
−0.241174 + 0.970482i \(0.577532\pi\)
\(752\) −934.566 −1.24277
\(753\) 0 0
\(754\) 0 0
\(755\) 1509.35 1.99913
\(756\) −3716.57 −4.91609
\(757\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −717.778 −0.943203 −0.471602 0.881812i \(-0.656324\pi\)
−0.471602 + 0.881812i \(0.656324\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −128.953 −0.168566
\(766\) 0 0
\(767\) 0 0
\(768\) 1485.08 1.93369
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 1356.12 1.75664
\(773\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(774\) 0 0
\(775\) −425.000 −0.548387
\(776\) 0 0
\(777\) 4012.60 5.16422
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 891.331 1.13690
\(785\) 1551.36 1.97626
\(786\) 0 0
\(787\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(788\) −134.125 −0.170210
\(789\) 0 0
\(790\) 0 0
\(791\) −396.642 −0.501443
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 803.804 1.01107
\(796\) 0 0
\(797\) −1558.15 −1.95502 −0.977509 0.210892i \(-0.932363\pi\)
−0.977509 + 0.210892i \(0.932363\pi\)
\(798\) 0 0
\(799\) 61.1069 0.0764792
\(800\) 0 0
\(801\) 4299.72 5.36794
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −2295.97 −2.84507
\(808\) 0 0
\(809\) −1576.43 −1.94861 −0.974307 0.225226i \(-0.927688\pi\)
−0.974307 + 0.225226i \(0.927688\pi\)
\(810\) 0 0
\(811\) 1214.18 1.49715 0.748573 0.663053i \(-0.230739\pi\)
0.748573 + 0.663053i \(0.230739\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) −97.1021 −0.118998
\(817\) −342.703 −0.419466
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 328.702 0.400368 0.200184 0.979758i \(-0.435846\pi\)
0.200184 + 0.979758i \(0.435846\pi\)
\(822\) 0 0
\(823\) −1582.65 −1.92302 −0.961511 0.274766i \(-0.911400\pi\)
−0.961511 + 0.274766i \(0.911400\pi\)
\(824\) 0 0
\(825\) −2918.61 −3.53771
\(826\) 0 0
\(827\) −1524.16 −1.84300 −0.921500 0.388379i \(-0.873035\pi\)
−0.921500 + 0.388379i \(0.873035\pi\)
\(828\) 0 0
\(829\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −58.2800 −0.0699640
\(834\) 0 0
\(835\) 0 0
\(836\) −1080.00 −1.29187
\(837\) −1543.62 −1.84423
\(838\) 0 0
\(839\) 967.000 1.15256 0.576281 0.817251i \(-0.304503\pi\)
0.576281 + 0.817251i \(0.304503\pi\)
\(840\) 0 0
\(841\) 841.000 1.00000
\(842\) 0 0
\(843\) 968.780 1.14920
\(844\) 0 0
\(845\) 845.000 1.00000
\(846\) 0 0
\(847\) −2906.09 −3.43104
\(848\) 443.396 0.522873
\(849\) 0 0
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) −1372.38 −1.60889 −0.804444 0.594029i \(-0.797536\pi\)
−0.804444 + 0.594029i \(0.797536\pi\)
\(854\) 0 0
\(855\) 1653.74 1.93420
\(856\) 0 0
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 0 0
\(859\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(860\) −510.872 −0.594037
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(864\) 0 0
\(865\) 1382.94 1.59878
\(866\) 0 0
\(867\) −1670.16 −1.92637
\(868\) 695.824 0.801640
\(869\) 1589.84 1.82951
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −1279.09 −1.46181
\(876\) 0 0
\(877\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(878\) 0 0
\(879\) −530.834 −0.603906
\(880\) −1609.97 −1.82951
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) 0 0
\(883\) 1751.01 1.98303 0.991514 0.130002i \(-0.0414984\pi\)
0.991514 + 0.130002i \(0.0414984\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(888\) 0 0
\(889\) −1958.12 −2.20261
\(890\) 0 0
\(891\) −6135.44 −6.88601
\(892\) 0 0
\(893\) −783.657 −0.877556
\(894\) 0 0
\(895\) −1765.00 −1.97207
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 2465.25 2.73916
\(901\) −28.9916 −0.0321771
\(902\) 0 0
\(903\) 1516.29 1.67916
\(904\) 0 0
\(905\) −1173.94 −1.29717
\(906\) 0 0
\(907\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(908\) 1498.31 1.65012
\(909\) −4757.93 −5.23424
\(910\) 0 0
\(911\) 1427.00 1.56641 0.783205 0.621763i \(-0.213583\pi\)
0.783205 + 0.621763i \(0.213583\pi\)
\(912\) 1245.27 1.36543
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 480.501 0.523993
\(918\) 0 0
\(919\) −1717.00 −1.86834 −0.934168 0.356835i \(-0.883856\pi\)
−0.934168 + 0.356835i \(0.883856\pi\)
\(920\) 0 0
\(921\) 1944.24 2.11101
\(922\) 0 0
\(923\) 0 0
\(924\) 4778.44 5.17147
\(925\) −1689.92 −1.82694
\(926\) 0 0
\(927\) 2981.20 3.21597
\(928\) 0 0
\(929\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(930\) 0 0
\(931\) 747.404 0.802797
\(932\) 961.416 1.03156
\(933\) 0 0
\(934\) 0 0
\(935\) 105.268 0.112586
\(936\) 0 0
\(937\) −1057.70 −1.12881 −0.564405 0.825498i \(-0.690894\pi\)
−0.564405 + 0.825498i \(0.690894\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) −1168.21 −1.24277
\(941\) 301.869 0.320796 0.160398 0.987052i \(-0.448722\pi\)
0.160398 + 0.987052i \(0.448722\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) −4645.71 −4.91609
\(946\) 0 0
\(947\) −1603.06 −1.69278 −0.846388 0.532567i \(-0.821227\pi\)
−0.846388 + 0.532567i \(0.821227\pi\)
\(948\) −1833.14 −1.93369
\(949\) 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
\(956\) −932.000 −0.974895
\(957\) 0 0
\(958\) 0 0
\(959\) 2776.72 2.89543
\(960\) 1856.34 1.93369
\(961\) −672.000 −0.699272
\(962\) 0 0
\(963\) −5275.46 −5.47815
\(964\) 1126.98 1.16906
\(965\) 1695.15 1.75664
\(966\) 0 0
\(967\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(968\) 0 0
\(969\) −81.4226 −0.0840275
\(970\) 0 0
\(971\) 362.000 0.372812 0.186406 0.982473i \(-0.440316\pi\)
0.186406 + 0.982473i \(0.440316\pi\)
\(972\) 3805.51 3.91513
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −929.596 −0.951480 −0.475740 0.879586i \(-0.657820\pi\)
−0.475740 + 0.879586i \(0.657820\pi\)
\(978\) 0 0
\(979\) −3510.00 −3.58529
\(980\) 1114.16 1.13690
\(981\) 0 0
\(982\) 0 0
\(983\) 364.749 0.371057 0.185529 0.982639i \(-0.440600\pi\)
0.185529 + 0.982639i \(0.440600\pi\)
\(984\) 0 0
\(985\) −167.657 −0.170210
\(986\) 0 0
\(987\) 3467.28 3.51295
\(988\) 0 0
\(989\) 0 0
\(990\) 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
\(999\) −6137.88 −6.14402
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 395.3.c.b.394.4 yes 4
5.4 even 2 inner 395.3.c.b.394.1 4
79.78 odd 2 inner 395.3.c.b.394.1 4
395.394 odd 2 CM 395.3.c.b.394.4 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
395.3.c.b.394.1 4 5.4 even 2 inner
395.3.c.b.394.1 4 79.78 odd 2 inner
395.3.c.b.394.4 yes 4 1.1 even 1 trivial
395.3.c.b.394.4 yes 4 395.394 odd 2 CM