Properties

Label 196.6.a.b.1.1
Level $196$
Weight $6$
Character 196.1
Self dual yes
Analytic conductor $31.435$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [196,6,Mod(1,196)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(196, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("196.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 196 = 2^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 196.a (trivial)

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: \(31.4352286833\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 28)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 196.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-19.0000 q^{3} +19.0000 q^{5} +118.000 q^{9} +O(q^{10})\) \(q-19.0000 q^{3} +19.0000 q^{5} +118.000 q^{9} -559.000 q^{11} +282.000 q^{13} -361.000 q^{15} +1259.00 q^{17} -1957.00 q^{19} -2977.00 q^{23} -2764.00 q^{25} +2375.00 q^{27} -62.0000 q^{29} +2037.00 q^{31} +10621.0 q^{33} +6023.00 q^{37} -5358.00 q^{39} -2178.00 q^{41} +23180.0 q^{43} +2242.00 q^{45} +26235.0 q^{47} -23921.0 q^{51} +30267.0 q^{53} -10621.0 q^{55} +37183.0 q^{57} +44965.0 q^{59} +27639.0 q^{61} +5358.00 q^{65} -58667.0 q^{67} +56563.0 q^{69} -9520.00 q^{71} -6785.00 q^{73} +52516.0 q^{75} -16929.0 q^{79} -73799.0 q^{81} -59572.0 q^{83} +23921.0 q^{85} +1178.00 q^{87} -51873.0 q^{89} -38703.0 q^{93} -37183.0 q^{95} +134110. q^{97} -65962.0 q^{99} +O(q^{100})\)

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
\(3\) −19.0000 −1.21885 −0.609425 0.792844i \(-0.708600\pi\)
−0.609425 + 0.792844i \(0.708600\pi\)
\(4\) 0 0
\(5\) 19.0000 0.339882 0.169941 0.985454i \(-0.445642\pi\)
0.169941 + 0.985454i \(0.445642\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 118.000 0.485597
\(10\) 0 0
\(11\) −559.000 −1.39293 −0.696466 0.717590i \(-0.745245\pi\)
−0.696466 + 0.717590i \(0.745245\pi\)
\(12\) 0 0
\(13\) 282.000 0.462797 0.231399 0.972859i \(-0.425670\pi\)
0.231399 + 0.972859i \(0.425670\pi\)
\(14\) 0 0
\(15\) −361.000 −0.414266
\(16\) 0 0
\(17\) 1259.00 1.05658 0.528291 0.849063i \(-0.322833\pi\)
0.528291 + 0.849063i \(0.322833\pi\)
\(18\) 0 0
\(19\) −1957.00 −1.24367 −0.621837 0.783146i \(-0.713614\pi\)
−0.621837 + 0.783146i \(0.713614\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −2977.00 −1.17344 −0.586718 0.809791i \(-0.699580\pi\)
−0.586718 + 0.809791i \(0.699580\pi\)
\(24\) 0 0
\(25\) −2764.00 −0.884480
\(26\) 0 0
\(27\) 2375.00 0.626981
\(28\) 0 0
\(29\) −62.0000 −0.0136898 −0.00684489 0.999977i \(-0.502179\pi\)
−0.00684489 + 0.999977i \(0.502179\pi\)
\(30\) 0 0
\(31\) 2037.00 0.380703 0.190352 0.981716i \(-0.439037\pi\)
0.190352 + 0.981716i \(0.439037\pi\)
\(32\) 0 0
\(33\) 10621.0 1.69778
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 6023.00 0.723283 0.361642 0.932317i \(-0.382216\pi\)
0.361642 + 0.932317i \(0.382216\pi\)
\(38\) 0 0
\(39\) −5358.00 −0.564081
\(40\) 0 0
\(41\) −2178.00 −0.202348 −0.101174 0.994869i \(-0.532260\pi\)
−0.101174 + 0.994869i \(0.532260\pi\)
\(42\) 0 0
\(43\) 23180.0 1.91180 0.955900 0.293694i \(-0.0948845\pi\)
0.955900 + 0.293694i \(0.0948845\pi\)
\(44\) 0 0
\(45\) 2242.00 0.165046
\(46\) 0 0
\(47\) 26235.0 1.73235 0.866177 0.499738i \(-0.166570\pi\)
0.866177 + 0.499738i \(0.166570\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −23921.0 −1.28782
\(52\) 0 0
\(53\) 30267.0 1.48006 0.740031 0.672573i \(-0.234811\pi\)
0.740031 + 0.672573i \(0.234811\pi\)
\(54\) 0 0
\(55\) −10621.0 −0.473433
\(56\) 0 0
\(57\) 37183.0 1.51585
\(58\) 0 0
\(59\) 44965.0 1.68168 0.840842 0.541280i \(-0.182060\pi\)
0.840842 + 0.541280i \(0.182060\pi\)
\(60\) 0 0
\(61\) 27639.0 0.951038 0.475519 0.879706i \(-0.342260\pi\)
0.475519 + 0.879706i \(0.342260\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 5358.00 0.157297
\(66\) 0 0
\(67\) −58667.0 −1.59664 −0.798320 0.602234i \(-0.794277\pi\)
−0.798320 + 0.602234i \(0.794277\pi\)
\(68\) 0 0
\(69\) 56563.0 1.43024
\(70\) 0 0
\(71\) −9520.00 −0.224125 −0.112063 0.993701i \(-0.535746\pi\)
−0.112063 + 0.993701i \(0.535746\pi\)
\(72\) 0 0
\(73\) −6785.00 −0.149019 −0.0745097 0.997220i \(-0.523739\pi\)
−0.0745097 + 0.997220i \(0.523739\pi\)
\(74\) 0 0
\(75\) 52516.0 1.07805
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −16929.0 −0.305185 −0.152593 0.988289i \(-0.548762\pi\)
−0.152593 + 0.988289i \(0.548762\pi\)
\(80\) 0 0
\(81\) −73799.0 −1.24979
\(82\) 0 0
\(83\) −59572.0 −0.949176 −0.474588 0.880208i \(-0.657403\pi\)
−0.474588 + 0.880208i \(0.657403\pi\)
\(84\) 0 0
\(85\) 23921.0 0.359114
\(86\) 0 0
\(87\) 1178.00 0.0166858
\(88\) 0 0
\(89\) −51873.0 −0.694171 −0.347085 0.937834i \(-0.612829\pi\)
−0.347085 + 0.937834i \(0.612829\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −38703.0 −0.464021
\(94\) 0 0
\(95\) −37183.0 −0.422703
\(96\) 0 0
\(97\) 134110. 1.44721 0.723605 0.690214i \(-0.242484\pi\)
0.723605 + 0.690214i \(0.242484\pi\)
\(98\) 0 0
\(99\) −65962.0 −0.676403
\(100\) 0 0
\(101\) 122047. 1.19048 0.595242 0.803546i \(-0.297056\pi\)
0.595242 + 0.803546i \(0.297056\pi\)
\(102\) 0 0
\(103\) −80617.0 −0.748744 −0.374372 0.927279i \(-0.622142\pi\)
−0.374372 + 0.927279i \(0.622142\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1467.00 0.0123871 0.00619356 0.999981i \(-0.498029\pi\)
0.00619356 + 0.999981i \(0.498029\pi\)
\(108\) 0 0
\(109\) 200527. 1.61662 0.808308 0.588761i \(-0.200384\pi\)
0.808308 + 0.588761i \(0.200384\pi\)
\(110\) 0 0
\(111\) −114437. −0.881574
\(112\) 0 0
\(113\) −722.000 −0.00531914 −0.00265957 0.999996i \(-0.500847\pi\)
−0.00265957 + 0.999996i \(0.500847\pi\)
\(114\) 0 0
\(115\) −56563.0 −0.398830
\(116\) 0 0
\(117\) 33276.0 0.224733
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 151430. 0.940261
\(122\) 0 0
\(123\) 41382.0 0.246632
\(124\) 0 0
\(125\) −111891. −0.640501
\(126\) 0 0
\(127\) 147288. 0.810323 0.405161 0.914245i \(-0.367215\pi\)
0.405161 + 0.914245i \(0.367215\pi\)
\(128\) 0 0
\(129\) −440420. −2.33020
\(130\) 0 0
\(131\) −53993.0 −0.274890 −0.137445 0.990509i \(-0.543889\pi\)
−0.137445 + 0.990509i \(0.543889\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 45125.0 0.213100
\(136\) 0 0
\(137\) 122563. 0.557902 0.278951 0.960305i \(-0.410013\pi\)
0.278951 + 0.960305i \(0.410013\pi\)
\(138\) 0 0
\(139\) −128108. −0.562392 −0.281196 0.959650i \(-0.590731\pi\)
−0.281196 + 0.959650i \(0.590731\pi\)
\(140\) 0 0
\(141\) −498465. −2.11148
\(142\) 0 0
\(143\) −157638. −0.644645
\(144\) 0 0
\(145\) −1178.00 −0.00465292
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 131955. 0.486923 0.243461 0.969911i \(-0.421717\pi\)
0.243461 + 0.969911i \(0.421717\pi\)
\(150\) 0 0
\(151\) 140125. 0.500119 0.250059 0.968230i \(-0.419550\pi\)
0.250059 + 0.968230i \(0.419550\pi\)
\(152\) 0 0
\(153\) 148562. 0.513073
\(154\) 0 0
\(155\) 38703.0 0.129394
\(156\) 0 0
\(157\) 323339. 1.04691 0.523455 0.852054i \(-0.324643\pi\)
0.523455 + 0.852054i \(0.324643\pi\)
\(158\) 0 0
\(159\) −575073. −1.80397
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 122159. 0.360128 0.180064 0.983655i \(-0.442370\pi\)
0.180064 + 0.983655i \(0.442370\pi\)
\(164\) 0 0
\(165\) 201799. 0.577044
\(166\) 0 0
\(167\) 185404. 0.514432 0.257216 0.966354i \(-0.417195\pi\)
0.257216 + 0.966354i \(0.417195\pi\)
\(168\) 0 0
\(169\) −291769. −0.785819
\(170\) 0 0
\(171\) −230926. −0.603924
\(172\) 0 0
\(173\) −358625. −0.911015 −0.455507 0.890232i \(-0.650542\pi\)
−0.455507 + 0.890232i \(0.650542\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −854335. −2.04972
\(178\) 0 0
\(179\) −460551. −1.07435 −0.537174 0.843471i \(-0.680508\pi\)
−0.537174 + 0.843471i \(0.680508\pi\)
\(180\) 0 0
\(181\) −332538. −0.754475 −0.377237 0.926117i \(-0.623126\pi\)
−0.377237 + 0.926117i \(0.623126\pi\)
\(182\) 0 0
\(183\) −525141. −1.15917
\(184\) 0 0
\(185\) 114437. 0.245831
\(186\) 0 0
\(187\) −703781. −1.47175
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 987867. 1.95936 0.979682 0.200558i \(-0.0642755\pi\)
0.979682 + 0.200558i \(0.0642755\pi\)
\(192\) 0 0
\(193\) −344413. −0.665559 −0.332779 0.943005i \(-0.607986\pi\)
−0.332779 + 0.943005i \(0.607986\pi\)
\(194\) 0 0
\(195\) −101802. −0.191721
\(196\) 0 0
\(197\) 582362. 1.06912 0.534561 0.845130i \(-0.320477\pi\)
0.534561 + 0.845130i \(0.320477\pi\)
\(198\) 0 0
\(199\) −150955. −0.270218 −0.135109 0.990831i \(-0.543139\pi\)
−0.135109 + 0.990831i \(0.543139\pi\)
\(200\) 0 0
\(201\) 1.11467e6 1.94606
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −41382.0 −0.0687744
\(206\) 0 0
\(207\) −351286. −0.569816
\(208\) 0 0
\(209\) 1.09396e6 1.73236
\(210\) 0 0
\(211\) 272156. 0.420835 0.210417 0.977612i \(-0.432518\pi\)
0.210417 + 0.977612i \(0.432518\pi\)
\(212\) 0 0
\(213\) 180880. 0.273175
\(214\) 0 0
\(215\) 440420. 0.649787
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 128915. 0.181632
\(220\) 0 0
\(221\) 355038. 0.488983
\(222\) 0 0
\(223\) −939112. −1.26461 −0.632303 0.774721i \(-0.717890\pi\)
−0.632303 + 0.774721i \(0.717890\pi\)
\(224\) 0 0
\(225\) −326152. −0.429501
\(226\) 0 0
\(227\) 481713. 0.620474 0.310237 0.950659i \(-0.399592\pi\)
0.310237 + 0.950659i \(0.399592\pi\)
\(228\) 0 0
\(229\) 523147. 0.659227 0.329614 0.944116i \(-0.393082\pi\)
0.329614 + 0.944116i \(0.393082\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −1.22603e6 −1.47949 −0.739743 0.672889i \(-0.765053\pi\)
−0.739743 + 0.672889i \(0.765053\pi\)
\(234\) 0 0
\(235\) 498465. 0.588796
\(236\) 0 0
\(237\) 321651. 0.371975
\(238\) 0 0
\(239\) 1.32568e6 1.50121 0.750607 0.660749i \(-0.229761\pi\)
0.750607 + 0.660749i \(0.229761\pi\)
\(240\) 0 0
\(241\) 271871. 0.301523 0.150761 0.988570i \(-0.451827\pi\)
0.150761 + 0.988570i \(0.451827\pi\)
\(242\) 0 0
\(243\) 825056. 0.896330
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −551874. −0.575569
\(248\) 0 0
\(249\) 1.13187e6 1.15690
\(250\) 0 0
\(251\) −781368. −0.782837 −0.391418 0.920213i \(-0.628015\pi\)
−0.391418 + 0.920213i \(0.628015\pi\)
\(252\) 0 0
\(253\) 1.66414e6 1.63452
\(254\) 0 0
\(255\) −454499. −0.437706
\(256\) 0 0
\(257\) 1.00337e6 0.947608 0.473804 0.880630i \(-0.342881\pi\)
0.473804 + 0.880630i \(0.342881\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −7316.00 −0.00664772
\(262\) 0 0
\(263\) −1.10958e6 −0.989169 −0.494584 0.869130i \(-0.664680\pi\)
−0.494584 + 0.869130i \(0.664680\pi\)
\(264\) 0 0
\(265\) 575073. 0.503047
\(266\) 0 0
\(267\) 985587. 0.846090
\(268\) 0 0
\(269\) 1.72416e6 1.45277 0.726383 0.687290i \(-0.241200\pi\)
0.726383 + 0.687290i \(0.241200\pi\)
\(270\) 0 0
\(271\) 831399. 0.687680 0.343840 0.939028i \(-0.388272\pi\)
0.343840 + 0.939028i \(0.388272\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 1.54508e6 1.23202
\(276\) 0 0
\(277\) −696757. −0.545609 −0.272805 0.962069i \(-0.587951\pi\)
−0.272805 + 0.962069i \(0.587951\pi\)
\(278\) 0 0
\(279\) 240366. 0.184868
\(280\) 0 0
\(281\) −2.26355e6 −1.71011 −0.855054 0.518539i \(-0.826476\pi\)
−0.855054 + 0.518539i \(0.826476\pi\)
\(282\) 0 0
\(283\) 423985. 0.314691 0.157346 0.987544i \(-0.449706\pi\)
0.157346 + 0.987544i \(0.449706\pi\)
\(284\) 0 0
\(285\) 706477. 0.515212
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 165224. 0.116367
\(290\) 0 0
\(291\) −2.54809e6 −1.76393
\(292\) 0 0
\(293\) 1.03724e6 0.705845 0.352923 0.935653i \(-0.385188\pi\)
0.352923 + 0.935653i \(0.385188\pi\)
\(294\) 0 0
\(295\) 854335. 0.571575
\(296\) 0 0
\(297\) −1.32762e6 −0.873342
\(298\) 0 0
\(299\) −839514. −0.543063
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −2.31889e6 −1.45102
\(304\) 0 0
\(305\) 525141. 0.323241
\(306\) 0 0
\(307\) −152684. −0.0924587 −0.0462293 0.998931i \(-0.514720\pi\)
−0.0462293 + 0.998931i \(0.514720\pi\)
\(308\) 0 0
\(309\) 1.53172e6 0.912608
\(310\) 0 0
\(311\) 1.66634e6 0.976931 0.488466 0.872583i \(-0.337557\pi\)
0.488466 + 0.872583i \(0.337557\pi\)
\(312\) 0 0
\(313\) 64471.0 0.0371966 0.0185983 0.999827i \(-0.494080\pi\)
0.0185983 + 0.999827i \(0.494080\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 1.28934e6 0.720643 0.360322 0.932828i \(-0.382667\pi\)
0.360322 + 0.932828i \(0.382667\pi\)
\(318\) 0 0
\(319\) 34658.0 0.0190690
\(320\) 0 0
\(321\) −27873.0 −0.0150981
\(322\) 0 0
\(323\) −2.46386e6 −1.31405
\(324\) 0 0
\(325\) −779448. −0.409335
\(326\) 0 0
\(327\) −3.81001e6 −1.97041
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −2.64238e6 −1.32564 −0.662819 0.748780i \(-0.730640\pi\)
−0.662819 + 0.748780i \(0.730640\pi\)
\(332\) 0 0
\(333\) 710714. 0.351224
\(334\) 0 0
\(335\) −1.11467e6 −0.542670
\(336\) 0 0
\(337\) −3.00561e6 −1.44164 −0.720822 0.693120i \(-0.756235\pi\)
−0.720822 + 0.693120i \(0.756235\pi\)
\(338\) 0 0
\(339\) 13718.0 0.00648323
\(340\) 0 0
\(341\) −1.13868e6 −0.530294
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 1.07470e6 0.486114
\(346\) 0 0
\(347\) −185307. −0.0826168 −0.0413084 0.999146i \(-0.513153\pi\)
−0.0413084 + 0.999146i \(0.513153\pi\)
\(348\) 0 0
\(349\) 2.82147e6 1.23997 0.619987 0.784612i \(-0.287138\pi\)
0.619987 + 0.784612i \(0.287138\pi\)
\(350\) 0 0
\(351\) 669750. 0.290165
\(352\) 0 0
\(353\) 1.30752e6 0.558486 0.279243 0.960220i \(-0.409916\pi\)
0.279243 + 0.960220i \(0.409916\pi\)
\(354\) 0 0
\(355\) −180880. −0.0761763
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 2.89605e6 1.18596 0.592980 0.805217i \(-0.297951\pi\)
0.592980 + 0.805217i \(0.297951\pi\)
\(360\) 0 0
\(361\) 1.35375e6 0.546727
\(362\) 0 0
\(363\) −2.87717e6 −1.14604
\(364\) 0 0
\(365\) −128915. −0.0506490
\(366\) 0 0
\(367\) −4.71893e6 −1.82885 −0.914427 0.404752i \(-0.867358\pi\)
−0.914427 + 0.404752i \(0.867358\pi\)
\(368\) 0 0
\(369\) −257004. −0.0982594
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 438079. 0.163035 0.0815174 0.996672i \(-0.474023\pi\)
0.0815174 + 0.996672i \(0.474023\pi\)
\(374\) 0 0
\(375\) 2.12593e6 0.780676
\(376\) 0 0
\(377\) −17484.0 −0.00633560
\(378\) 0 0
\(379\) −549632. −0.196550 −0.0982752 0.995159i \(-0.531333\pi\)
−0.0982752 + 0.995159i \(0.531333\pi\)
\(380\) 0 0
\(381\) −2.79847e6 −0.987662
\(382\) 0 0
\(383\) 3.53000e6 1.22964 0.614820 0.788667i \(-0.289229\pi\)
0.614820 + 0.788667i \(0.289229\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 2.73524e6 0.928363
\(388\) 0 0
\(389\) 3.13395e6 1.05007 0.525035 0.851081i \(-0.324052\pi\)
0.525035 + 0.851081i \(0.324052\pi\)
\(390\) 0 0
\(391\) −3.74804e6 −1.23983
\(392\) 0 0
\(393\) 1.02587e6 0.335050
\(394\) 0 0
\(395\) −321651. −0.103727
\(396\) 0 0
\(397\) −2.55391e6 −0.813260 −0.406630 0.913593i \(-0.633296\pi\)
−0.406630 + 0.913593i \(0.633296\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −702837. −0.218270 −0.109135 0.994027i \(-0.534808\pi\)
−0.109135 + 0.994027i \(0.534808\pi\)
\(402\) 0 0
\(403\) 574434. 0.176188
\(404\) 0 0
\(405\) −1.40218e6 −0.424782
\(406\) 0 0
\(407\) −3.36686e6 −1.00749
\(408\) 0 0
\(409\) −5.47715e6 −1.61900 −0.809499 0.587121i \(-0.800261\pi\)
−0.809499 + 0.587121i \(0.800261\pi\)
\(410\) 0 0
\(411\) −2.32870e6 −0.679999
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −1.13187e6 −0.322608
\(416\) 0 0
\(417\) 2.43405e6 0.685472
\(418\) 0 0
\(419\) 5.80976e6 1.61668 0.808339 0.588718i \(-0.200367\pi\)
0.808339 + 0.588718i \(0.200367\pi\)
\(420\) 0 0
\(421\) 1.69370e6 0.465726 0.232863 0.972510i \(-0.425191\pi\)
0.232863 + 0.972510i \(0.425191\pi\)
\(422\) 0 0
\(423\) 3.09573e6 0.841225
\(424\) 0 0
\(425\) −3.47988e6 −0.934526
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 2.99512e6 0.785726
\(430\) 0 0
\(431\) −1.46468e6 −0.379794 −0.189897 0.981804i \(-0.560815\pi\)
−0.189897 + 0.981804i \(0.560815\pi\)
\(432\) 0 0
\(433\) −3.23418e6 −0.828980 −0.414490 0.910054i \(-0.636040\pi\)
−0.414490 + 0.910054i \(0.636040\pi\)
\(434\) 0 0
\(435\) 22382.0 0.00567121
\(436\) 0 0
\(437\) 5.82599e6 1.45937
\(438\) 0 0
\(439\) −2.54217e6 −0.629570 −0.314785 0.949163i \(-0.601932\pi\)
−0.314785 + 0.949163i \(0.601932\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 65939.0 0.0159637 0.00798184 0.999968i \(-0.497459\pi\)
0.00798184 + 0.999968i \(0.497459\pi\)
\(444\) 0 0
\(445\) −985587. −0.235936
\(446\) 0 0
\(447\) −2.50714e6 −0.593486
\(448\) 0 0
\(449\) −5.32399e6 −1.24630 −0.623149 0.782103i \(-0.714147\pi\)
−0.623149 + 0.782103i \(0.714147\pi\)
\(450\) 0 0
\(451\) 1.21750e6 0.281857
\(452\) 0 0
\(453\) −2.66238e6 −0.609570
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −4.05825e6 −0.908967 −0.454484 0.890755i \(-0.650176\pi\)
−0.454484 + 0.890755i \(0.650176\pi\)
\(458\) 0 0
\(459\) 2.99012e6 0.662457
\(460\) 0 0
\(461\) 3.73021e6 0.817487 0.408744 0.912649i \(-0.365967\pi\)
0.408744 + 0.912649i \(0.365967\pi\)
\(462\) 0 0
\(463\) −3.45186e6 −0.748342 −0.374171 0.927360i \(-0.622073\pi\)
−0.374171 + 0.927360i \(0.622073\pi\)
\(464\) 0 0
\(465\) −735357. −0.157712
\(466\) 0 0
\(467\) 3.92062e6 0.831884 0.415942 0.909391i \(-0.363452\pi\)
0.415942 + 0.909391i \(0.363452\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −6.14344e6 −1.27603
\(472\) 0 0
\(473\) −1.29576e7 −2.66301
\(474\) 0 0
\(475\) 5.40915e6 1.10001
\(476\) 0 0
\(477\) 3.57151e6 0.718713
\(478\) 0 0
\(479\) −5.98674e6 −1.19221 −0.596103 0.802908i \(-0.703285\pi\)
−0.596103 + 0.802908i \(0.703285\pi\)
\(480\) 0 0
\(481\) 1.69849e6 0.334734
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 2.54809e6 0.491881
\(486\) 0 0
\(487\) 71873.0 0.0137323 0.00686615 0.999976i \(-0.497814\pi\)
0.00686615 + 0.999976i \(0.497814\pi\)
\(488\) 0 0
\(489\) −2.32102e6 −0.438942
\(490\) 0 0
\(491\) 1.01122e6 0.189295 0.0946477 0.995511i \(-0.469828\pi\)
0.0946477 + 0.995511i \(0.469828\pi\)
\(492\) 0 0
\(493\) −78058.0 −0.0144644
\(494\) 0 0
\(495\) −1.25328e6 −0.229898
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 7.80469e6 1.40315 0.701575 0.712596i \(-0.252481\pi\)
0.701575 + 0.712596i \(0.252481\pi\)
\(500\) 0 0
\(501\) −3.52268e6 −0.627016
\(502\) 0 0
\(503\) 7.89298e6 1.39098 0.695490 0.718536i \(-0.255187\pi\)
0.695490 + 0.718536i \(0.255187\pi\)
\(504\) 0 0
\(505\) 2.31889e6 0.404625
\(506\) 0 0
\(507\) 5.54361e6 0.957796
\(508\) 0 0
\(509\) 6.62650e6 1.13368 0.566839 0.823829i \(-0.308166\pi\)
0.566839 + 0.823829i \(0.308166\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −4.64788e6 −0.779760
\(514\) 0 0
\(515\) −1.53172e6 −0.254485
\(516\) 0 0
\(517\) −1.46654e7 −2.41305
\(518\) 0 0
\(519\) 6.81387e6 1.11039
\(520\) 0 0
\(521\) 7.27862e6 1.17477 0.587387 0.809306i \(-0.300157\pi\)
0.587387 + 0.809306i \(0.300157\pi\)
\(522\) 0 0
\(523\) 4.75278e6 0.759790 0.379895 0.925030i \(-0.375960\pi\)
0.379895 + 0.925030i \(0.375960\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 2.56458e6 0.402245
\(528\) 0 0
\(529\) 2.42619e6 0.376951
\(530\) 0 0
\(531\) 5.30587e6 0.816621
\(532\) 0 0
\(533\) −614196. −0.0936459
\(534\) 0 0
\(535\) 27873.0 0.00421017
\(536\) 0 0
\(537\) 8.75047e6 1.30947
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −9.25161e6 −1.35902 −0.679508 0.733668i \(-0.737807\pi\)
−0.679508 + 0.733668i \(0.737807\pi\)
\(542\) 0 0
\(543\) 6.31822e6 0.919592
\(544\) 0 0
\(545\) 3.81001e6 0.549459
\(546\) 0 0
\(547\) 4.66834e6 0.667104 0.333552 0.942732i \(-0.391753\pi\)
0.333552 + 0.942732i \(0.391753\pi\)
\(548\) 0 0
\(549\) 3.26140e6 0.461821
\(550\) 0 0
\(551\) 121334. 0.0170256
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −2.17430e6 −0.299632
\(556\) 0 0
\(557\) −6.50094e6 −0.887848 −0.443924 0.896065i \(-0.646414\pi\)
−0.443924 + 0.896065i \(0.646414\pi\)
\(558\) 0 0
\(559\) 6.53676e6 0.884775
\(560\) 0 0
\(561\) 1.33718e7 1.79384
\(562\) 0 0
\(563\) 1.06422e7 1.41501 0.707505 0.706708i \(-0.249821\pi\)
0.707505 + 0.706708i \(0.249821\pi\)
\(564\) 0 0
\(565\) −13718.0 −0.00180788
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 9.71001e6 1.25730 0.628650 0.777688i \(-0.283608\pi\)
0.628650 + 0.777688i \(0.283608\pi\)
\(570\) 0 0
\(571\) 1.15693e7 1.48497 0.742485 0.669862i \(-0.233647\pi\)
0.742485 + 0.669862i \(0.233647\pi\)
\(572\) 0 0
\(573\) −1.87695e7 −2.38817
\(574\) 0 0
\(575\) 8.22843e6 1.03788
\(576\) 0 0
\(577\) −5.72550e6 −0.715936 −0.357968 0.933734i \(-0.616530\pi\)
−0.357968 + 0.933734i \(0.616530\pi\)
\(578\) 0 0
\(579\) 6.54385e6 0.811216
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −1.69193e7 −2.06163
\(584\) 0 0
\(585\) 632244. 0.0763827
\(586\) 0 0
\(587\) 2.35929e6 0.282609 0.141305 0.989966i \(-0.454870\pi\)
0.141305 + 0.989966i \(0.454870\pi\)
\(588\) 0 0
\(589\) −3.98641e6 −0.473471
\(590\) 0 0
\(591\) −1.10649e7 −1.30310
\(592\) 0 0
\(593\) 2.91024e6 0.339854 0.169927 0.985457i \(-0.445647\pi\)
0.169927 + 0.985457i \(0.445647\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 2.86814e6 0.329356
\(598\) 0 0
\(599\) 9.99466e6 1.13815 0.569077 0.822284i \(-0.307301\pi\)
0.569077 + 0.822284i \(0.307301\pi\)
\(600\) 0 0
\(601\) 6.12412e6 0.691604 0.345802 0.938308i \(-0.387607\pi\)
0.345802 + 0.938308i \(0.387607\pi\)
\(602\) 0 0
\(603\) −6.92271e6 −0.775323
\(604\) 0 0
\(605\) 2.87717e6 0.319578
\(606\) 0 0
\(607\) 1.77047e7 1.95037 0.975185 0.221391i \(-0.0710599\pi\)
0.975185 + 0.221391i \(0.0710599\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 7.39827e6 0.801728
\(612\) 0 0
\(613\) −8.83215e6 −0.949326 −0.474663 0.880168i \(-0.657430\pi\)
−0.474663 + 0.880168i \(0.657430\pi\)
\(614\) 0 0
\(615\) 786258. 0.0838257
\(616\) 0 0
\(617\) 1.07392e6 0.113569 0.0567843 0.998386i \(-0.481915\pi\)
0.0567843 + 0.998386i \(0.481915\pi\)
\(618\) 0 0
\(619\) −352211. −0.0369468 −0.0184734 0.999829i \(-0.505881\pi\)
−0.0184734 + 0.999829i \(0.505881\pi\)
\(620\) 0 0
\(621\) −7.07038e6 −0.735722
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 6.51157e6 0.666785
\(626\) 0 0
\(627\) −2.07853e7 −2.11148
\(628\) 0 0
\(629\) 7.58296e6 0.764209
\(630\) 0 0
\(631\) 775808. 0.0775677 0.0387838 0.999248i \(-0.487652\pi\)
0.0387838 + 0.999248i \(0.487652\pi\)
\(632\) 0 0
\(633\) −5.17096e6 −0.512935
\(634\) 0 0
\(635\) 2.79847e6 0.275414
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −1.12336e6 −0.108835
\(640\) 0 0
\(641\) −1.18421e7 −1.13837 −0.569187 0.822208i \(-0.692742\pi\)
−0.569187 + 0.822208i \(0.692742\pi\)
\(642\) 0 0
\(643\) 307460. 0.0293266 0.0146633 0.999892i \(-0.495332\pi\)
0.0146633 + 0.999892i \(0.495332\pi\)
\(644\) 0 0
\(645\) −8.36798e6 −0.791993
\(646\) 0 0
\(647\) 1.30708e7 1.22756 0.613780 0.789477i \(-0.289648\pi\)
0.613780 + 0.789477i \(0.289648\pi\)
\(648\) 0 0
\(649\) −2.51354e7 −2.34247
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 927663. 0.0851348 0.0425674 0.999094i \(-0.486446\pi\)
0.0425674 + 0.999094i \(0.486446\pi\)
\(654\) 0 0
\(655\) −1.02587e6 −0.0934303
\(656\) 0 0
\(657\) −800630. −0.0723633
\(658\) 0 0
\(659\) −1.90355e7 −1.70746 −0.853731 0.520715i \(-0.825666\pi\)
−0.853731 + 0.520715i \(0.825666\pi\)
\(660\) 0 0
\(661\) −2.17236e6 −0.193388 −0.0966939 0.995314i \(-0.530827\pi\)
−0.0966939 + 0.995314i \(0.530827\pi\)
\(662\) 0 0
\(663\) −6.74572e6 −0.595998
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 184574. 0.0160641
\(668\) 0 0
\(669\) 1.78431e7 1.54137
\(670\) 0 0
\(671\) −1.54502e7 −1.32473
\(672\) 0 0
\(673\) 1.32268e7 1.12569 0.562844 0.826563i \(-0.309707\pi\)
0.562844 + 0.826563i \(0.309707\pi\)
\(674\) 0 0
\(675\) −6.56450e6 −0.554552
\(676\) 0 0
\(677\) −1.59662e7 −1.33884 −0.669422 0.742882i \(-0.733458\pi\)
−0.669422 + 0.742882i \(0.733458\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −9.15255e6 −0.756265
\(682\) 0 0
\(683\) 1.40029e7 1.14859 0.574297 0.818647i \(-0.305276\pi\)
0.574297 + 0.818647i \(0.305276\pi\)
\(684\) 0 0
\(685\) 2.32870e6 0.189621
\(686\) 0 0
\(687\) −9.93979e6 −0.803499
\(688\) 0 0
\(689\) 8.53529e6 0.684968
\(690\) 0 0
\(691\) −1.05246e7 −0.838514 −0.419257 0.907868i \(-0.637709\pi\)
−0.419257 + 0.907868i \(0.637709\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −2.43405e6 −0.191147
\(696\) 0 0
\(697\) −2.74210e6 −0.213797
\(698\) 0 0
\(699\) 2.32946e7 1.80327
\(700\) 0 0
\(701\) −1.30811e7 −1.00542 −0.502710 0.864455i \(-0.667664\pi\)
−0.502710 + 0.864455i \(0.667664\pi\)
\(702\) 0 0
\(703\) −1.17870e7 −0.899529
\(704\) 0 0
\(705\) −9.47084e6 −0.717655
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 488519. 0.0364977 0.0182489 0.999833i \(-0.494191\pi\)
0.0182489 + 0.999833i \(0.494191\pi\)
\(710\) 0 0
\(711\) −1.99762e6 −0.148197
\(712\) 0 0
\(713\) −6.06415e6 −0.446731
\(714\) 0 0
\(715\) −2.99512e6 −0.219104
\(716\) 0 0
\(717\) −2.51878e7 −1.82976
\(718\) 0 0
\(719\) −8.40850e6 −0.606592 −0.303296 0.952896i \(-0.598087\pi\)
−0.303296 + 0.952896i \(0.598087\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −5.16555e6 −0.367511
\(724\) 0 0
\(725\) 171368. 0.0121083
\(726\) 0 0
\(727\) −2.44145e7 −1.71322 −0.856608 0.515968i \(-0.827432\pi\)
−0.856608 + 0.515968i \(0.827432\pi\)
\(728\) 0 0
\(729\) 2.25709e6 0.157301
\(730\) 0 0
\(731\) 2.91836e7 2.01997
\(732\) 0 0
\(733\) 1.13916e7 0.783111 0.391556 0.920154i \(-0.371937\pi\)
0.391556 + 0.920154i \(0.371937\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 3.27949e7 2.22401
\(738\) 0 0
\(739\) −2.18963e6 −0.147489 −0.0737445 0.997277i \(-0.523495\pi\)
−0.0737445 + 0.997277i \(0.523495\pi\)
\(740\) 0 0
\(741\) 1.04856e7 0.701533
\(742\) 0 0
\(743\) −7.06982e6 −0.469825 −0.234913 0.972016i \(-0.575480\pi\)
−0.234913 + 0.972016i \(0.575480\pi\)
\(744\) 0 0
\(745\) 2.50714e6 0.165496
\(746\) 0 0
\(747\) −7.02950e6 −0.460917
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 6.55880e6 0.424350 0.212175 0.977232i \(-0.431945\pi\)
0.212175 + 0.977232i \(0.431945\pi\)
\(752\) 0 0
\(753\) 1.48460e7 0.954161
\(754\) 0 0
\(755\) 2.66238e6 0.169982
\(756\) 0 0
\(757\) 2.17588e6 0.138005 0.0690026 0.997616i \(-0.478018\pi\)
0.0690026 + 0.997616i \(0.478018\pi\)
\(758\) 0 0
\(759\) −3.16187e7 −1.99223
\(760\) 0 0
\(761\) 1.58632e7 0.992954 0.496477 0.868050i \(-0.334627\pi\)
0.496477 + 0.868050i \(0.334627\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 2.82268e6 0.174384
\(766\) 0 0
\(767\) 1.26801e7 0.778279
\(768\) 0 0
\(769\) −1.86634e7 −1.13809 −0.569044 0.822307i \(-0.692687\pi\)
−0.569044 + 0.822307i \(0.692687\pi\)
\(770\) 0 0
\(771\) −1.90640e7 −1.15499
\(772\) 0 0
\(773\) −2.26397e7 −1.36277 −0.681384 0.731926i \(-0.738622\pi\)
−0.681384 + 0.731926i \(0.738622\pi\)
\(774\) 0 0
\(775\) −5.63027e6 −0.336725
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 4.26235e6 0.251655
\(780\) 0 0
\(781\) 5.32168e6 0.312192
\(782\) 0 0
\(783\) −147250. −0.00858323
\(784\) 0 0
\(785\) 6.14344e6 0.355826
\(786\) 0 0
\(787\) −9.66053e6 −0.555986 −0.277993 0.960583i \(-0.589669\pi\)
−0.277993 + 0.960583i \(0.589669\pi\)
\(788\) 0 0
\(789\) 2.10821e7 1.20565
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 7.79420e6 0.440138
\(794\) 0 0
\(795\) −1.09264e7 −0.613139
\(796\) 0 0
\(797\) 1.15546e7 0.644330 0.322165 0.946684i \(-0.395589\pi\)
0.322165 + 0.946684i \(0.395589\pi\)
\(798\) 0 0
\(799\) 3.30299e7 1.83037
\(800\) 0 0
\(801\) −6.12101e6 −0.337087
\(802\) 0 0
\(803\) 3.79282e6 0.207574
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −3.27589e7 −1.77070
\(808\) 0 0
\(809\) 1.85307e7 0.995453 0.497727 0.867334i \(-0.334168\pi\)
0.497727 + 0.867334i \(0.334168\pi\)
\(810\) 0 0
\(811\) −1.31357e7 −0.701298 −0.350649 0.936507i \(-0.614039\pi\)
−0.350649 + 0.936507i \(0.614039\pi\)
\(812\) 0 0
\(813\) −1.57966e7 −0.838179
\(814\) 0 0
\(815\) 2.32102e6 0.122401
\(816\) 0 0
\(817\) −4.53633e7 −2.37766
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −4.20868e6 −0.217915 −0.108958 0.994046i \(-0.534751\pi\)
−0.108958 + 0.994046i \(0.534751\pi\)
\(822\) 0 0
\(823\) 1.10437e7 0.568350 0.284175 0.958772i \(-0.408280\pi\)
0.284175 + 0.958772i \(0.408280\pi\)
\(824\) 0 0
\(825\) −2.93564e7 −1.50165
\(826\) 0 0
\(827\) 1.74824e7 0.888867 0.444433 0.895812i \(-0.353405\pi\)
0.444433 + 0.895812i \(0.353405\pi\)
\(828\) 0 0
\(829\) 2.35418e7 1.18974 0.594871 0.803821i \(-0.297203\pi\)
0.594871 + 0.803821i \(0.297203\pi\)
\(830\) 0 0
\(831\) 1.32384e7 0.665016
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 3.52268e6 0.174846
\(836\) 0 0
\(837\) 4.83788e6 0.238694
\(838\) 0 0
\(839\) 2.64326e7 1.29639 0.648195 0.761474i \(-0.275524\pi\)
0.648195 + 0.761474i \(0.275524\pi\)
\(840\) 0 0
\(841\) −2.05073e7 −0.999813
\(842\) 0 0
\(843\) 4.30074e7 2.08437
\(844\) 0 0
\(845\) −5.54361e6 −0.267086
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −8.05572e6 −0.383561
\(850\) 0 0
\(851\) −1.79305e7 −0.848727
\(852\) 0 0
\(853\) 3.86472e7 1.81863 0.909317 0.416103i \(-0.136605\pi\)
0.909317 + 0.416103i \(0.136605\pi\)
\(854\) 0 0
\(855\) −4.38759e6 −0.205263
\(856\) 0 0
\(857\) 2.46708e7 1.14744 0.573721 0.819051i \(-0.305499\pi\)
0.573721 + 0.819051i \(0.305499\pi\)
\(858\) 0 0
\(859\) 2.74324e7 1.26847 0.634235 0.773140i \(-0.281315\pi\)
0.634235 + 0.773140i \(0.281315\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −6.10970e6 −0.279250 −0.139625 0.990204i \(-0.544590\pi\)
−0.139625 + 0.990204i \(0.544590\pi\)
\(864\) 0 0
\(865\) −6.81388e6 −0.309638
\(866\) 0 0
\(867\) −3.13926e6 −0.141834
\(868\) 0 0
\(869\) 9.46331e6 0.425103
\(870\) 0 0
\(871\) −1.65441e7 −0.738920
\(872\) 0 0
\(873\) 1.58250e7 0.702761
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −7.62612e6 −0.334815 −0.167408 0.985888i \(-0.553540\pi\)
−0.167408 + 0.985888i \(0.553540\pi\)
\(878\) 0 0
\(879\) −1.97075e7 −0.860320
\(880\) 0 0
\(881\) −3.22357e6 −0.139925 −0.0699627 0.997550i \(-0.522288\pi\)
−0.0699627 + 0.997550i \(0.522288\pi\)
\(882\) 0 0
\(883\) 7.31409e6 0.315688 0.157844 0.987464i \(-0.449546\pi\)
0.157844 + 0.987464i \(0.449546\pi\)
\(884\) 0 0
\(885\) −1.62324e7 −0.696664
\(886\) 0 0
\(887\) −4.32134e7 −1.84421 −0.922103 0.386944i \(-0.873531\pi\)
−0.922103 + 0.386944i \(0.873531\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 4.12536e7 1.74088
\(892\) 0 0
\(893\) −5.13419e7 −2.15448
\(894\) 0 0
\(895\) −8.75047e6 −0.365152
\(896\) 0 0
\(897\) 1.59508e7 0.661912
\(898\) 0 0
\(899\) −126294. −0.00521175
\(900\) 0 0
\(901\) 3.81062e7 1.56381
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −6.31822e6 −0.256433
\(906\) 0 0
\(907\) −1.48978e7 −0.601317 −0.300659 0.953732i \(-0.597206\pi\)
−0.300659 + 0.953732i \(0.597206\pi\)
\(908\) 0 0
\(909\) 1.44015e7 0.578095
\(910\) 0 0
\(911\) 1.65823e7 0.661987 0.330993 0.943633i \(-0.392616\pi\)
0.330993 + 0.943633i \(0.392616\pi\)
\(912\) 0 0
\(913\) 3.33007e7 1.32214
\(914\) 0 0
\(915\) −9.97768e6 −0.393982
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −1.94331e7 −0.759021 −0.379510 0.925187i \(-0.623908\pi\)
−0.379510 + 0.925187i \(0.623908\pi\)
\(920\) 0 0
\(921\) 2.90100e6 0.112693
\(922\) 0 0
\(923\) −2.68464e6 −0.103725
\(924\) 0 0
\(925\) −1.66476e7 −0.639730
\(926\) 0 0
\(927\) −9.51281e6 −0.363588
\(928\) 0 0
\(929\) 4.61166e7 1.75315 0.876573 0.481269i \(-0.159824\pi\)
0.876573 + 0.481269i \(0.159824\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −3.16606e7 −1.19073
\(934\) 0 0
\(935\) −1.33718e7 −0.500221
\(936\) 0 0
\(937\) 1.59157e7 0.592210 0.296105 0.955155i \(-0.404312\pi\)
0.296105 + 0.955155i \(0.404312\pi\)
\(938\) 0 0
\(939\) −1.22495e6 −0.0453371
\(940\) 0 0
\(941\) −1.07301e7 −0.395031 −0.197516 0.980300i \(-0.563287\pi\)
−0.197516 + 0.980300i \(0.563287\pi\)
\(942\) 0 0
\(943\) 6.48391e6 0.237442
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 2.27632e7 0.824820 0.412410 0.910998i \(-0.364687\pi\)
0.412410 + 0.910998i \(0.364687\pi\)
\(948\) 0 0
\(949\) −1.91337e6 −0.0689657
\(950\) 0 0
\(951\) −2.44975e7 −0.878356
\(952\) 0 0
\(953\) 2.69718e7 0.962005 0.481002 0.876719i \(-0.340273\pi\)
0.481002 + 0.876719i \(0.340273\pi\)
\(954\) 0 0
\(955\) 1.87695e7 0.665953
\(956\) 0 0
\(957\) −658502. −0.0232422
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −2.44798e7 −0.855065
\(962\) 0 0
\(963\) 173106. 0.00601515
\(964\) 0 0
\(965\) −6.54385e6 −0.226212
\(966\) 0 0
\(967\) 1.02880e7 0.353805 0.176902 0.984228i \(-0.443392\pi\)
0.176902 + 0.984228i \(0.443392\pi\)
\(968\) 0 0
\(969\) 4.68134e7 1.60162
\(970\) 0 0
\(971\) 2.85803e7 0.972791 0.486395 0.873739i \(-0.338312\pi\)
0.486395 + 0.873739i \(0.338312\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 1.48095e7 0.498918
\(976\) 0 0
\(977\) −2.84299e6 −0.0952881 −0.0476441 0.998864i \(-0.515171\pi\)
−0.0476441 + 0.998864i \(0.515171\pi\)
\(978\) 0 0
\(979\) 2.89970e7 0.966933
\(980\) 0 0
\(981\) 2.36622e7 0.785023
\(982\) 0 0
\(983\) −5.31666e7 −1.75491 −0.877455 0.479659i \(-0.840760\pi\)
−0.877455 + 0.479659i \(0.840760\pi\)
\(984\) 0 0
\(985\) 1.10649e7 0.363376
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −6.90069e7 −2.24337
\(990\) 0 0
\(991\) 5.41874e7 1.75273 0.876363 0.481652i \(-0.159963\pi\)
0.876363 + 0.481652i \(0.159963\pi\)
\(992\) 0 0
\(993\) 5.02052e7 1.61575
\(994\) 0 0
\(995\) −2.86814e6 −0.0918424
\(996\) 0 0
\(997\) 6.55175e6 0.208747 0.104373 0.994538i \(-0.466716\pi\)
0.104373 + 0.994538i \(0.466716\pi\)
\(998\) 0 0
\(999\) 1.43046e7 0.453485
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 196.6.a.b.1.1 1
4.3 odd 2 784.6.a.k.1.1 1
7.2 even 3 28.6.e.a.25.1 yes 2
7.3 odd 6 196.6.e.b.177.1 2
7.4 even 3 28.6.e.a.9.1 2
7.5 odd 6 196.6.e.b.165.1 2
7.6 odd 2 196.6.a.g.1.1 1
21.2 odd 6 252.6.k.c.109.1 2
21.11 odd 6 252.6.k.c.37.1 2
28.11 odd 6 112.6.i.a.65.1 2
28.23 odd 6 112.6.i.a.81.1 2
28.27 even 2 784.6.a.a.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
28.6.e.a.9.1 2 7.4 even 3
28.6.e.a.25.1 yes 2 7.2 even 3
112.6.i.a.65.1 2 28.11 odd 6
112.6.i.a.81.1 2 28.23 odd 6
196.6.a.b.1.1 1 1.1 even 1 trivial
196.6.a.g.1.1 1 7.6 odd 2
196.6.e.b.165.1 2 7.5 odd 6
196.6.e.b.177.1 2 7.3 odd 6
252.6.k.c.37.1 2 21.11 odd 6
252.6.k.c.109.1 2 21.2 odd 6
784.6.a.a.1.1 1 28.27 even 2
784.6.a.k.1.1 1 4.3 odd 2