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Properties

Label 195.3.e.b.194.1
Level $195$
Weight $3$
Character 195.194
Self dual yes
Analytic conductor $5.313$
Analytic rank $0$
Dimension $1$
CM discriminant -195
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] = [195,3,Mod(194,195)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("195.194"); S:= CuspForms(chi, 3); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(195, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1])) N = Newforms(chi, 3, names="a")
 
Level: \( N \) \(=\) \( 195 = 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 195.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,0,-3,4,5] 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: \(5.31336515503\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label 194.1
Character \(\chi\) \(=\) 195.194

$q$-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)
 
\(f(q)\) \(=\) \(q-3.00000 q^{3} +4.00000 q^{4} +5.00000 q^{5} -1.00000 q^{7} +9.00000 q^{9} -17.0000 q^{11} -12.0000 q^{12} +13.0000 q^{13} -15.0000 q^{15} +16.0000 q^{16} +31.0000 q^{17} +20.0000 q^{20} +3.00000 q^{21} +19.0000 q^{23} +25.0000 q^{25} -27.0000 q^{27} -4.00000 q^{28} +51.0000 q^{33} -5.00000 q^{35} +36.0000 q^{36} -61.0000 q^{37} -39.0000 q^{39} +43.0000 q^{41} -68.0000 q^{44} +45.0000 q^{45} -48.0000 q^{48} -48.0000 q^{49} -93.0000 q^{51} +52.0000 q^{52} -41.0000 q^{53} -85.0000 q^{55} -38.0000 q^{59} -60.0000 q^{60} -73.0000 q^{61} -9.00000 q^{63} +64.0000 q^{64} +65.0000 q^{65} +74.0000 q^{67} +124.000 q^{68} -57.0000 q^{69} +103.000 q^{71} -94.0000 q^{73} -75.0000 q^{75} +17.0000 q^{77} -37.0000 q^{79} +80.0000 q^{80} +81.0000 q^{81} +12.0000 q^{84} +155.000 q^{85} -173.000 q^{89} -13.0000 q^{91} +76.0000 q^{92} -181.000 q^{97} -153.000 q^{99} +O(q^{100})\)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/195\mathbb{Z}\right)^\times\).

\(n\) \(106\) \(131\) \(157\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

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 1.00000 \(0\)
−1.00000 \(\pi\)
\(3\) −3.00000 −1.00000
\(4\) 4.00000 1.00000
\(5\) 5.00000 1.00000
\(6\) 0 0
\(7\) −1.00000 −0.142857 −0.0714286 − 0.997446i \(-0.522756\pi\)
−0.0714286 + 0.997446i \(0.522756\pi\)
\(8\) 0 0
\(9\) 9.00000 1.00000
\(10\) 0 0
\(11\) −17.0000 −1.54545 −0.772727 − 0.634738i \(-0.781108\pi\)
−0.772727 + 0.634738i \(0.781108\pi\)
\(12\) −12.0000 −1.00000
\(13\) 13.0000 1.00000
\(14\) 0 0
\(15\) −15.0000 −1.00000
\(16\) 16.0000 1.00000
\(17\) 31.0000 1.82353 0.911765 − 0.410713i \(-0.134720\pi\)
0.911765 + 0.410713i \(0.134720\pi\)
\(18\) 0 0
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) 20.0000 1.00000
\(21\) 3.00000 0.142857
\(22\) 0 0
\(23\) 19.0000 0.826087 0.413043 − 0.910711i \(-0.364466\pi\)
0.413043 + 0.910711i \(0.364466\pi\)
\(24\) 0 0
\(25\) 25.0000 1.00000
\(26\) 0 0
\(27\) −27.0000 −1.00000
\(28\) −4.00000 −0.142857
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) 0 0
\(33\) 51.0000 1.54545
\(34\) 0 0
\(35\) −5.00000 −0.142857
\(36\) 36.0000 1.00000
\(37\) −61.0000 −1.64865 −0.824324 − 0.566118i \(-0.808445\pi\)
−0.824324 + 0.566118i \(0.808445\pi\)
\(38\) 0 0
\(39\) −39.0000 −1.00000
\(40\) 0 0
\(41\) 43.0000 1.04878 0.524390 − 0.851478i \(-0.324293\pi\)
0.524390 + 0.851478i \(0.324293\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) −68.0000 −1.54545
\(45\) 45.0000 1.00000
\(46\) 0 0
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) −48.0000 −1.00000
\(49\) −48.0000 −0.979592
\(50\) 0 0
\(51\) −93.0000 −1.82353
\(52\) 52.0000 1.00000
\(53\) −41.0000 −0.773585 −0.386792 − 0.922167i \(-0.626417\pi\)
−0.386792 + 0.922167i \(0.626417\pi\)
\(54\) 0 0
\(55\) −85.0000 −1.54545
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −38.0000 −0.644068 −0.322034 − 0.946728i \(-0.604367\pi\)
−0.322034 + 0.946728i \(0.604367\pi\)
\(60\) −60.0000 −1.00000
\(61\) −73.0000 −1.19672 −0.598361 − 0.801227i \(-0.704181\pi\)
−0.598361 + 0.801227i \(0.704181\pi\)
\(62\) 0 0
\(63\) −9.00000 −0.142857
\(64\) 64.0000 1.00000
\(65\) 65.0000 1.00000
\(66\) 0 0
\(67\) 74.0000 1.10448 0.552239 − 0.833686i \(-0.313774\pi\)
0.552239 + 0.833686i \(0.313774\pi\)
\(68\) 124.000 1.82353
\(69\) −57.0000 −0.826087
\(70\) 0 0
\(71\) 103.000 1.45070 0.725352 − 0.688378i \(-0.241677\pi\)
0.725352 + 0.688378i \(0.241677\pi\)
\(72\) 0 0
\(73\) −94.0000 −1.28767 −0.643836 − 0.765164i \(-0.722658\pi\)
−0.643836 + 0.765164i \(0.722658\pi\)
\(74\) 0 0
\(75\) −75.0000 −1.00000
\(76\) 0 0
\(77\) 17.0000 0.220779
\(78\) 0 0
\(79\) −37.0000 −0.468354 −0.234177 − 0.972194i \(-0.575240\pi\)
−0.234177 + 0.972194i \(0.575240\pi\)
\(80\) 80.0000 1.00000
\(81\) 81.0000 1.00000
\(82\) 0 0
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) 12.0000 0.142857
\(85\) 155.000 1.82353
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −173.000 −1.94382 −0.971910 − 0.235352i \(-0.924376\pi\)
−0.971910 + 0.235352i \(0.924376\pi\)
\(90\) 0 0
\(91\) −13.0000 −0.142857
\(92\) 76.0000 0.826087
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −181.000 −1.86598 −0.932990 − 0.359903i \(-0.882810\pi\)
−0.932990 + 0.359903i \(0.882810\pi\)
\(98\) 0 0
\(99\) −153.000 −1.54545
\(100\) 100.000 1.00000
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) 0 0
\(105\) 15.0000 0.142857
\(106\) 0 0
\(107\) −149.000 −1.39252 −0.696262 − 0.717788i \(-0.745155\pi\)
−0.696262 + 0.717788i \(0.745155\pi\)
\(108\) −108.000 −1.00000
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 0 0
\(111\) 183.000 1.64865
\(112\) −16.0000 −0.142857
\(113\) 34.0000 0.300885 0.150442 − 0.988619i \(-0.451930\pi\)
0.150442 + 0.988619i \(0.451930\pi\)
\(114\) 0 0
\(115\) 95.0000 0.826087
\(116\) 0 0
\(117\) 117.000 1.00000
\(118\) 0 0
\(119\) −31.0000 −0.260504
\(120\) 0 0
\(121\) 168.000 1.38843
\(122\) 0 0
\(123\) −129.000 −1.04878
\(124\) 0 0
\(125\) 125.000 1.00000
\(126\) 0 0
\(127\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 204.000 1.54545
\(133\) 0 0
\(134\) 0 0
\(135\) −135.000 −1.00000
\(136\) 0 0
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) 0 0
\(139\) 83.0000 0.597122 0.298561 − 0.954391i \(-0.403493\pi\)
0.298561 + 0.954391i \(0.403493\pi\)
\(140\) −20.0000 −0.142857
\(141\) 0 0
\(142\) 0 0
\(143\) −221.000 −1.54545
\(144\) 144.000 1.00000
\(145\) 0 0
\(146\) 0 0
\(147\) 144.000 0.979592
\(148\) −244.000 −1.64865
\(149\) −53.0000 −0.355705 −0.177852 − 0.984057i \(-0.556915\pi\)
−0.177852 + 0.984057i \(0.556915\pi\)
\(150\) 0 0
\(151\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(152\) 0 0
\(153\) 279.000 1.82353
\(154\) 0 0
\(155\) 0 0
\(156\) −156.000 −1.00000
\(157\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(158\) 0 0
\(159\) 123.000 0.773585
\(160\) 0 0
\(161\) −19.0000 −0.118012
\(162\) 0 0
\(163\) 311.000 1.90798 0.953988 − 0.299846i \(-0.0969352\pi\)
0.953988 + 0.299846i \(0.0969352\pi\)
\(164\) 172.000 1.04878
\(165\) 255.000 1.54545
\(166\) 0 0
\(167\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(168\) 0 0
\(169\) 169.000 1.00000
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −86.0000 −0.497110 −0.248555 − 0.968618i \(-0.579956\pi\)
−0.248555 + 0.968618i \(0.579956\pi\)
\(174\) 0 0
\(175\) −25.0000 −0.142857
\(176\) −272.000 −1.54545
\(177\) 114.000 0.644068
\(178\) 0 0
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) 180.000 1.00000
\(181\) 167.000 0.922652 0.461326 − 0.887231i \(-0.347374\pi\)
0.461326 + 0.887231i \(0.347374\pi\)
\(182\) 0 0
\(183\) 219.000 1.19672
\(184\) 0 0
\(185\) −305.000 −1.64865
\(186\) 0 0
\(187\) −527.000 −2.81818
\(188\) 0 0
\(189\) 27.0000 0.142857
\(190\) 0 0
\(191\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(192\) −192.000 −1.00000
\(193\) 251.000 1.30052 0.650259 − 0.759713i \(-0.274660\pi\)
0.650259 + 0.759713i \(0.274660\pi\)
\(194\) 0 0
\(195\) −195.000 −1.00000
\(196\) −192.000 −0.979592
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 0 0
\(199\) −382.000 −1.91960 −0.959799 − 0.280688i \(-0.909437\pi\)
−0.959799 + 0.280688i \(0.909437\pi\)
\(200\) 0 0
\(201\) −222.000 −1.10448
\(202\) 0 0
\(203\) 0 0
\(204\) −372.000 −1.82353
\(205\) 215.000 1.04878
\(206\) 0 0
\(207\) 171.000 0.826087
\(208\) 208.000 1.00000
\(209\) 0 0
\(210\) 0 0
\(211\) −358.000 −1.69668 −0.848341 − 0.529450i \(-0.822398\pi\)
−0.848341 + 0.529450i \(0.822398\pi\)
\(212\) −164.000 −0.773585
\(213\) −309.000 −1.45070
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 282.000 1.28767
\(220\) −340.000 −1.54545
\(221\) 403.000 1.82353
\(222\) 0 0
\(223\) 386.000 1.73094 0.865471 − 0.500959i \(-0.167019\pi\)
0.865471 + 0.500959i \(0.167019\pi\)
\(224\) 0 0
\(225\) 225.000 1.00000
\(226\) 0 0
\(227\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(228\) 0 0
\(229\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(230\) 0 0
\(231\) −51.0000 −0.220779
\(232\) 0 0
\(233\) −401.000 −1.72103 −0.860515 − 0.509425i \(-0.829858\pi\)
−0.860515 + 0.509425i \(0.829858\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −152.000 −0.644068
\(237\) 111.000 0.468354
\(238\) 0 0
\(239\) 127.000 0.531381 0.265690 − 0.964058i \(-0.414400\pi\)
0.265690 + 0.964058i \(0.414400\pi\)
\(240\) −240.000 −1.00000
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) 0 0
\(243\) −243.000 −1.00000
\(244\) −292.000 −1.19672
\(245\) −240.000 −0.979592
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) −36.0000 −0.142857
\(253\) −323.000 −1.27668
\(254\) 0 0
\(255\) −465.000 −1.82353
\(256\) 256.000 1.00000
\(257\) −254.000 −0.988327 −0.494163 − 0.869369i \(-0.664526\pi\)
−0.494163 + 0.869369i \(0.664526\pi\)
\(258\) 0 0
\(259\) 61.0000 0.235521
\(260\) 260.000 1.00000
\(261\) 0 0
\(262\) 0 0
\(263\) 514.000 1.95437 0.977186 − 0.212384i \(-0.0681227\pi\)
0.977186 + 0.212384i \(0.0681227\pi\)
\(264\) 0 0
\(265\) −205.000 −0.773585
\(266\) 0 0
\(267\) 519.000 1.94382
\(268\) 296.000 1.10448
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) 496.000 1.82353
\(273\) 39.0000 0.142857
\(274\) 0 0
\(275\) −425.000 −1.54545
\(276\) −228.000 −0.826087
\(277\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −62.0000 −0.220641 −0.110320 − 0.993896i \(-0.535188\pi\)
−0.110320 + 0.993896i \(0.535188\pi\)
\(282\) 0 0
\(283\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(284\) 412.000 1.45070
\(285\) 0 0
\(286\) 0 0
\(287\) −43.0000 −0.149826
\(288\) 0 0
\(289\) 672.000 2.32526
\(290\) 0 0
\(291\) 543.000 1.86598
\(292\) −376.000 −1.28767
\(293\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(294\) 0 0
\(295\) −190.000 −0.644068
\(296\) 0 0
\(297\) 459.000 1.54545
\(298\) 0 0
\(299\) 247.000 0.826087
\(300\) −300.000 −1.00000
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −365.000 −1.19672
\(306\) 0 0
\(307\) −601.000 −1.95765 −0.978827 − 0.204688i \(-0.934382\pi\)
−0.978827 + 0.204688i \(0.934382\pi\)
\(308\) 68.0000 0.220779
\(309\) 0 0
\(310\) 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
\(315\) −45.0000 −0.142857
\(316\) −148.000 −0.468354
\(317\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 320.000 1.00000
\(321\) 447.000 1.39252
\(322\) 0 0
\(323\) 0 0
\(324\) 324.000 1.00000
\(325\) 325.000 1.00000
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) 0 0
\(333\) −549.000 −1.64865
\(334\) 0 0
\(335\) 370.000 1.10448
\(336\) 48.0000 0.142857
\(337\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(338\) 0 0
\(339\) −102.000 −0.300885
\(340\) 620.000 1.82353
\(341\) 0 0
\(342\) 0 0
\(343\) 97.0000 0.282799
\(344\) 0 0
\(345\) −285.000 −0.826087
\(346\) 0 0
\(347\) −629.000 −1.81268 −0.906340 − 0.422549i \(-0.861135\pi\)
−0.906340 + 0.422549i \(0.861135\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) 0 0
\(351\) −351.000 −1.00000
\(352\) 0 0
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 0 0
\(355\) 515.000 1.45070
\(356\) −692.000 −1.94382
\(357\) 93.0000 0.260504
\(358\) 0 0
\(359\) 562.000 1.56546 0.782730 − 0.622362i \(-0.213827\pi\)
0.782730 + 0.622362i \(0.213827\pi\)
\(360\) 0 0
\(361\) 361.000 1.00000
\(362\) 0 0
\(363\) −504.000 −1.38843
\(364\) −52.0000 −0.142857
\(365\) −470.000 −1.28767
\(366\) 0 0
\(367\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(368\) 304.000 0.826087
\(369\) 387.000 1.04878
\(370\) 0 0
\(371\) 41.0000 0.110512
\(372\) 0 0
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) −375.000 −1.00000
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(384\) 0 0
\(385\) 85.0000 0.220779
\(386\) 0 0
\(387\) 0 0
\(388\) −724.000 −1.86598
\(389\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(390\) 0 0
\(391\) 589.000 1.50639
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −185.000 −0.468354
\(396\) −612.000 −1.54545
\(397\) 779.000 1.96222 0.981108 − 0.193459i \(-0.0619707\pi\)
0.981108 + 0.193459i \(0.0619707\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 400.000 1.00000
\(401\) 178.000 0.443890 0.221945 − 0.975059i \(-0.428759\pi\)
0.221945 + 0.975059i \(0.428759\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 405.000 1.00000
\(406\) 0 0
\(407\) 1037.00 2.54791
\(408\) 0 0
\(409\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 38.0000 0.0920097
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −249.000 −0.597122
\(418\) 0 0
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 60.0000 0.142857
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 775.000 1.82353
\(426\) 0 0
\(427\) 73.0000 0.170960
\(428\) −596.000 −1.39252
\(429\) 663.000 1.54545
\(430\) 0 0
\(431\) −542.000 −1.25754 −0.628770 − 0.777591i \(-0.716441\pi\)
−0.628770 + 0.777591i \(0.716441\pi\)
\(432\) −432.000 −1.00000
\(433\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) −877.000 −1.99772 −0.998861 − 0.0477138i \(-0.984806\pi\)
−0.998861 + 0.0477138i \(0.984806\pi\)
\(440\) 0 0
\(441\) −432.000 −0.979592
\(442\) 0 0
\(443\) 739.000 1.66817 0.834086 − 0.551635i \(-0.185996\pi\)
0.834086 + 0.551635i \(0.185996\pi\)
\(444\) 732.000 1.64865
\(445\) −865.000 −1.94382
\(446\) 0 0
\(447\) 159.000 0.355705
\(448\) −64.0000 −0.142857
\(449\) 547.000 1.21826 0.609131 − 0.793069i \(-0.291518\pi\)
0.609131 + 0.793069i \(0.291518\pi\)
\(450\) 0 0
\(451\) −731.000 −1.62084
\(452\) 136.000 0.300885
\(453\) 0 0
\(454\) 0 0
\(455\) −65.0000 −0.142857
\(456\) 0 0
\(457\) −901.000 −1.97155 −0.985777 − 0.168060i \(-0.946250\pi\)
−0.985777 + 0.168060i \(0.946250\pi\)
\(458\) 0 0
\(459\) −837.000 −1.82353
\(460\) 380.000 0.826087
\(461\) 883.000 1.91540 0.957701 − 0.287766i \(-0.0929126\pi\)
0.957701 + 0.287766i \(0.0929126\pi\)
\(462\) 0 0
\(463\) −289.000 −0.624190 −0.312095 − 0.950051i \(-0.601031\pi\)
−0.312095 + 0.950051i \(0.601031\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 691.000 1.47966 0.739829 − 0.672795i \(-0.234907\pi\)
0.739829 + 0.672795i \(0.234907\pi\)
\(468\) 468.000 1.00000
\(469\) −74.0000 −0.157783
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) −124.000 −0.260504
\(477\) −369.000 −0.773585
\(478\) 0 0
\(479\) −953.000 −1.98956 −0.994781 − 0.102035i \(-0.967465\pi\)
−0.994781 + 0.102035i \(0.967465\pi\)
\(480\) 0 0
\(481\) −793.000 −1.64865
\(482\) 0 0
\(483\) 57.0000 0.118012
\(484\) 672.000 1.38843
\(485\) −905.000 −1.86598
\(486\) 0 0
\(487\) 599.000 1.22998 0.614990 − 0.788535i \(-0.289160\pi\)
0.614990 + 0.788535i \(0.289160\pi\)
\(488\) 0 0
\(489\) −933.000 −1.90798
\(490\) 0 0
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) −516.000 −1.04878
\(493\) 0 0
\(494\) 0 0
\(495\) −765.000 −1.54545
\(496\) 0 0
\(497\) −103.000 −0.207243
\(498\) 0 0
\(499\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(500\) 500.000 1.00000
\(501\) 0 0
\(502\) 0 0
\(503\) 34.0000 0.0675944 0.0337972 − 0.999429i \(-0.489240\pi\)
0.0337972 + 0.999429i \(0.489240\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −507.000 −1.00000
\(508\) 0 0
\(509\) −893.000 −1.75442 −0.877210 − 0.480106i \(-0.840598\pi\)
−0.877210 + 0.480106i \(0.840598\pi\)
\(510\) 0 0
\(511\) 94.0000 0.183953
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 258.000 0.497110
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 0 0
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) 0 0
\(525\) 75.0000 0.142857
\(526\) 0 0
\(527\) 0 0
\(528\) 816.000 1.54545
\(529\) −168.000 −0.317580
\(530\) 0 0
\(531\) −342.000 −0.644068
\(532\) 0 0
\(533\) 559.000 1.04878
\(534\) 0 0
\(535\) −745.000 −1.39252
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 816.000 1.51391
\(540\) −540.000 −1.00000
\(541\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(542\) 0 0
\(543\) −501.000 −0.922652
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(548\) 0 0
\(549\) −657.000 −1.19672
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 37.0000 0.0669078
\(554\) 0 0
\(555\) 915.000 1.64865
\(556\) 332.000 0.597122
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) −80.0000 −0.142857
\(561\) 1581.00 2.81818
\(562\) 0 0
\(563\) −1061.00 −1.88455 −0.942274 − 0.334844i \(-0.891316\pi\)
−0.942274 + 0.334844i \(0.891316\pi\)
\(564\) 0 0
\(565\) 170.000 0.300885
\(566\) 0 0
\(567\) −81.0000 −0.142857
\(568\) 0 0
\(569\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(570\) 0 0
\(571\) −613.000 −1.07356 −0.536778 − 0.843724i \(-0.680359\pi\)
−0.536778 + 0.843724i \(0.680359\pi\)
\(572\) −884.000 −1.54545
\(573\) 0 0
\(574\) 0 0
\(575\) 475.000 0.826087
\(576\) 576.000 1.00000
\(577\) 419.000 0.726170 0.363085 − 0.931756i \(-0.381723\pi\)
0.363085 + 0.931756i \(0.381723\pi\)
\(578\) 0 0
\(579\) −753.000 −1.30052
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 697.000 1.19554
\(584\) 0 0
\(585\) 585.000 1.00000
\(586\) 0 0
\(587\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(588\) 576.000 0.979592
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) −976.000 −1.64865
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 0 0
\(595\) −155.000 −0.260504
\(596\) −212.000 −0.355705
\(597\) 1146.00 1.91960
\(598\) 0 0
\(599\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(600\) 0 0
\(601\) 1007.00 1.67554 0.837770 − 0.546023i \(-0.183859\pi\)
0.837770 + 0.546023i \(0.183859\pi\)
\(602\) 0 0
\(603\) 666.000 1.10448
\(604\) 0 0
\(605\) 840.000 1.38843
\(606\) 0 0
\(607\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 1116.00 1.82353
\(613\) −589.000 −0.960848 −0.480424 − 0.877036i \(-0.659517\pi\)
−0.480424 + 0.877036i \(0.659517\pi\)
\(614\) 0 0
\(615\) −645.000 −1.04878
\(616\) 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
\(621\) −513.000 −0.826087
\(622\) 0 0
\(623\) 173.000 0.277689
\(624\) −624.000 −1.00000
\(625\) 625.000 1.00000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −1891.00 −3.00636
\(630\) 0 0
\(631\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(632\) 0 0
\(633\) 1074.00 1.69668
\(634\) 0 0
\(635\) 0 0
\(636\) 492.000 0.773585
\(637\) −624.000 −0.979592
\(638\) 0 0
\(639\) 927.000 1.45070
\(640\) 0 0
\(641\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(642\) 0 0
\(643\) 911.000 1.41680 0.708398 − 0.705813i \(-0.249418\pi\)
0.708398 + 0.705813i \(0.249418\pi\)
\(644\) −76.0000 −0.118012
\(645\) 0 0
\(646\) 0 0
\(647\) −1229.00 −1.89954 −0.949768 − 0.312954i \(-0.898681\pi\)
−0.949768 + 0.312954i \(0.898681\pi\)
\(648\) 0 0
\(649\) 646.000 0.995378
\(650\) 0 0
\(651\) 0 0
\(652\) 1244.00 1.90798
\(653\) −1046.00 −1.60184 −0.800919 − 0.598773i \(-0.795655\pi\)
−0.800919 + 0.598773i \(0.795655\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 688.000 1.04878
\(657\) −846.000 −1.28767
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 1020.00 1.54545
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) 0 0
\(663\) −1209.00 −1.82353
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) −1158.00 −1.73094
\(670\) 0 0
\(671\) 1241.00 1.84948
\(672\) 0 0
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) 0 0
\(675\) −675.000 −1.00000
\(676\) 676.000 1.00000
\(677\) 271.000 0.400295 0.200148 − 0.979766i \(-0.435858\pi\)
0.200148 + 0.979766i \(0.435858\pi\)
\(678\) 0 0
\(679\) 181.000 0.266568
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −533.000 −0.773585
\(690\) 0 0
\(691\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(692\) −344.000 −0.497110
\(693\) 153.000 0.220779
\(694\) 0 0
\(695\) 415.000 0.597122
\(696\) 0 0
\(697\) 1333.00 1.91248
\(698\) 0 0
\(699\) 1203.00 1.72103
\(700\) −100.000 −0.142857
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −1088.00 −1.54545
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 456.000 0.644068
\(709\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(710\) 0 0
\(711\) −333.000 −0.468354
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) −1105.00 −1.54545
\(716\) 0 0
\(717\) −381.000 −0.531381
\(718\) 0 0
\(719\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(720\) 720.000 1.00000
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 668.000 0.922652
\(725\) 0 0
\(726\) 0 0
\(727\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(728\) 0 0
\(729\) 729.000 1.00000
\(730\) 0 0
\(731\) 0 0
\(732\) 876.000 1.19672
\(733\) 731.000 0.997271 0.498636 − 0.866812i \(-0.333835\pi\)
0.498636 + 0.866812i \(0.333835\pi\)
\(734\) 0 0
\(735\) 720.000 0.979592
\(736\) 0 0
\(737\) −1258.00 −1.70692
\(738\) 0 0
\(739\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(740\) −1220.00 −1.64865
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(744\) 0 0
\(745\) −265.000 −0.355705
\(746\) 0 0
\(747\) 0 0
\(748\) −2108.00 −2.81818
\(749\) 149.000 0.198932
\(750\) 0 0
\(751\) 1307.00 1.74035 0.870173 − 0.492746i \(-0.164007\pi\)
0.870173 + 0.492746i \(0.164007\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 108.000 0.142857
\(757\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(758\) 0 0
\(759\) 969.000 1.27668
\(760\) 0 0
\(761\) 898.000 1.18003 0.590013 − 0.807394i \(-0.299123\pi\)
0.590013 + 0.807394i \(0.299123\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 1395.00 1.82353
\(766\) 0 0
\(767\) −494.000 −0.644068
\(768\) −768.000 −1.00000
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 762.000 0.988327
\(772\) 1004.00 1.30052
\(773\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −183.000 −0.235521
\(778\) 0 0
\(779\) 0 0
\(780\) −780.000 −1.00000
\(781\) −1751.00 −2.24200
\(782\) 0 0
\(783\) 0 0
\(784\) −768.000 −0.979592
\(785\) 0 0
\(786\) 0 0
\(787\) −1366.00 −1.73571 −0.867853 − 0.496822i \(-0.834500\pi\)
−0.867853 + 0.496822i \(0.834500\pi\)
\(788\) 0 0
\(789\) −1542.00 −1.95437
\(790\) 0 0
\(791\) −34.0000 −0.0429836
\(792\) 0 0
\(793\) −949.000 −1.19672
\(794\) 0 0
\(795\) 615.000 0.773585
\(796\) −1528.00 −1.91960
\(797\) 1591.00 1.99624 0.998118 − 0.0613235i \(-0.0195321\pi\)
0.998118 + 0.0613235i \(0.0195321\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) −1557.00 −1.94382
\(802\) 0 0
\(803\) 1598.00 1.99004
\(804\) −888.000 −1.10448
\(805\) −95.0000 −0.118012
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(810\) 0 0
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 1555.00 1.90798
\(816\) −1488.00 −1.82353
\(817\) 0 0
\(818\) 0 0
\(819\) −117.000 −0.142857
\(820\) 860.000 1.04878
\(821\) −1517.00 −1.84775 −0.923873 − 0.382698i \(-0.874995\pi\)
−0.923873 + 0.382698i \(0.874995\pi\)
\(822\) 0 0
\(823\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(824\) 0 0
\(825\) 1275.00 1.54545
\(826\) 0 0
\(827\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(828\) 684.000 0.826087
\(829\) −1462.00 −1.76357 −0.881785 − 0.471651i \(-0.843658\pi\)
−0.881785 + 0.471651i \(0.843658\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 832.000 1.00000
\(833\) −1488.00 −1.78631
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −233.000 −0.277712 −0.138856 − 0.990313i \(-0.544342\pi\)
−0.138856 + 0.990313i \(0.544342\pi\)
\(840\) 0 0
\(841\) 841.000 1.00000
\(842\) 0 0
\(843\) 186.000 0.220641
\(844\) −1432.00 −1.69668
\(845\) 845.000 1.00000
\(846\) 0 0
\(847\) −168.000 −0.198347
\(848\) −656.000 −0.773585
\(849\) 0 0
\(850\) 0 0
\(851\) −1159.00 −1.36193
\(852\) −1236.00 −1.45070
\(853\) 491.000 0.575615 0.287808 − 0.957688i \(-0.407074\pi\)
0.287808 + 0.957688i \(0.407074\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 1471.00 1.71645 0.858226 − 0.513271i \(-0.171567\pi\)
0.858226 + 0.513271i \(0.171567\pi\)
\(858\) 0 0
\(859\) −37.0000 −0.0430733 −0.0215367 − 0.999768i \(-0.506856\pi\)
−0.0215367 + 0.999768i \(0.506856\pi\)
\(860\) 0 0
\(861\) 129.000 0.149826
\(862\) 0 0
\(863\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(864\) 0 0
\(865\) −430.000 −0.497110
\(866\) 0 0
\(867\) −2016.00 −2.32526
\(868\) 0 0
\(869\) 629.000 0.723820
\(870\) 0 0
\(871\) 962.000 1.10448
\(872\) 0 0
\(873\) −1629.00 −1.86598
\(874\) 0 0
\(875\) −125.000 −0.142857
\(876\) 1128.00 1.28767
\(877\) 794.000 0.905359 0.452680 − 0.891673i \(-0.350468\pi\)
0.452680 + 0.891673i \(0.350468\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) −1360.00 −1.54545
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) 0 0
\(883\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(884\) 1612.00 1.82353
\(885\) 570.000 0.644068
\(886\) 0 0
\(887\) 1411.00 1.59076 0.795378 − 0.606114i \(-0.207273\pi\)
0.795378 + 0.606114i \(0.207273\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −1377.00 −1.54545
\(892\) 1544.00 1.73094
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −741.000 −0.826087
\(898\) 0 0
\(899\) 0 0
\(900\) 900.000 1.00000
\(901\) −1271.00 −1.41065
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 835.000 0.922652
\(906\) 0 0
\(907\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(908\) 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
\(915\) 1095.00 1.19672
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 1643.00 1.78781 0.893906 − 0.448254i \(-0.147954\pi\)
0.893906 + 0.448254i \(0.147954\pi\)
\(920\) 0 0
\(921\) 1803.00 1.95765
\(922\) 0 0
\(923\) 1339.00 1.45070
\(924\) −204.000 −0.220779
\(925\) −1525.00 −1.64865
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −53.0000 −0.0570506 −0.0285253 − 0.999593i \(-0.509081\pi\)
−0.0285253 + 0.999593i \(0.509081\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) −1604.00 −1.72103
\(933\) 0 0
\(934\) 0 0
\(935\) −2635.00 −2.81818
\(936\) 0 0
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −1277.00 −1.35707 −0.678533 − 0.734569i \(-0.737384\pi\)
−0.678533 + 0.734569i \(0.737384\pi\)
\(942\) 0 0
\(943\) 817.000 0.866384
\(944\) −608.000 −0.644068
\(945\) 135.000 0.142857
\(946\) 0 0
\(947\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(948\) 444.000 0.468354
\(949\) −1222.00 −1.28767
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −281.000 −0.294858 −0.147429 − 0.989073i \(-0.547100\pi\)
−0.147429 + 0.989073i \(0.547100\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 508.000 0.531381
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) −960.000 −1.00000
\(961\) 961.000 1.00000
\(962\) 0 0
\(963\) −1341.00 −1.39252
\(964\) 0 0
\(965\) 1255.00 1.30052
\(966\) 0 0
\(967\) 1394.00 1.44157 0.720786 − 0.693158i \(-0.243781\pi\)
0.720786 + 0.693158i \(0.243781\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(972\) −972.000 −1.00000
\(973\) −83.0000 −0.0853032
\(974\) 0 0
\(975\) −975.000 −1.00000
\(976\) −1168.00 −1.19672
\(977\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(978\) 0 0
\(979\) 2941.00 3.00409
\(980\) −960.000 −0.979592
\(981\) 0 0
\(982\) 0 0
\(983\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 227.000 0.229062 0.114531 − 0.993420i \(-0.463464\pi\)
0.114531 + 0.993420i \(0.463464\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −1910.00 −1.91960
\(996\) 0 0
\(997\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(998\) 0 0
\(999\) 1647.00 1.64865
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 195.3.e.b.194.1 yes 1
3.2 odd 2 195.3.e.c.194.1 yes 1
5.4 even 2 195.3.e.d.194.1 yes 1
13.12 even 2 195.3.e.a.194.1 ✓ 1
15.14 odd 2 195.3.e.a.194.1 ✓ 1
39.38 odd 2 195.3.e.d.194.1 yes 1
65.64 even 2 195.3.e.c.194.1 yes 1
195.194 odd 2 CM 195.3.e.b.194.1 yes 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
195.3.e.a.194.1 ✓ 1 13.12 even 2
195.3.e.a.194.1 ✓ 1 15.14 odd 2
195.3.e.b.194.1 yes 1 1.1 even 1 trivial
195.3.e.b.194.1 yes 1 195.194 odd 2 CM
195.3.e.c.194.1 yes 1 3.2 odd 2
195.3.e.c.194.1 yes 1 65.64 even 2
195.3.e.d.194.1 yes 1 5.4 even 2
195.3.e.d.194.1 yes 1 39.38 odd 2