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Properties

Label 2100.4.a.j.1.1
Level $2100$
Weight $4$
Character 2100.1
Self dual yes
Analytic conductor $123.904$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2100,4,Mod(1,2100)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2100, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2100.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2100.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: \(123.904011012\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 2100.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+3.00000 q^{3} -7.00000 q^{7} +9.00000 q^{9} -26.0000 q^{11} +39.0000 q^{13} +101.000 q^{17} -48.0000 q^{19} -21.0000 q^{21} -57.0000 q^{23} +27.0000 q^{27} -291.000 q^{29} -79.0000 q^{31} -78.0000 q^{33} -322.000 q^{37} +117.000 q^{39} +455.000 q^{41} +307.000 q^{43} -508.000 q^{47} +49.0000 q^{49} +303.000 q^{51} +31.0000 q^{53} -144.000 q^{57} +211.000 q^{59} -797.000 q^{61} -63.0000 q^{63} +924.000 q^{67} -171.000 q^{69} +212.000 q^{71} -22.0000 q^{73} +182.000 q^{77} +874.000 q^{79} +81.0000 q^{81} +587.000 q^{83} -873.000 q^{87} -266.000 q^{89} -273.000 q^{91} -237.000 q^{93} -1822.00 q^{97} -234.000 q^{99} +O(q^{100})\)

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
\(3\) 3.00000 0.577350
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −7.00000 −0.377964
\(8\) 0 0
\(9\) 9.00000 0.333333
\(10\) 0 0
\(11\) −26.0000 −0.712663 −0.356332 − 0.934360i \(-0.615973\pi\)
−0.356332 + 0.934360i \(0.615973\pi\)
\(12\) 0 0
\(13\) 39.0000 0.832050 0.416025 − 0.909353i \(-0.363423\pi\)
0.416025 + 0.909353i \(0.363423\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 101.000 1.44095 0.720473 − 0.693482i \(-0.243925\pi\)
0.720473 + 0.693482i \(0.243925\pi\)
\(18\) 0 0
\(19\) −48.0000 −0.579577 −0.289788 − 0.957091i \(-0.593585\pi\)
−0.289788 + 0.957091i \(0.593585\pi\)
\(20\) 0 0
\(21\) −21.0000 −0.218218
\(22\) 0 0
\(23\) −57.0000 −0.516753 −0.258377 − 0.966044i \(-0.583188\pi\)
−0.258377 + 0.966044i \(0.583188\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 27.0000 0.192450
\(28\) 0 0
\(29\) −291.000 −1.86336 −0.931678 − 0.363284i \(-0.881655\pi\)
−0.931678 + 0.363284i \(0.881655\pi\)
\(30\) 0 0
\(31\) −79.0000 −0.457704 −0.228852 − 0.973461i \(-0.573497\pi\)
−0.228852 + 0.973461i \(0.573497\pi\)
\(32\) 0 0
\(33\) −78.0000 −0.411456
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −322.000 −1.43072 −0.715358 − 0.698758i \(-0.753736\pi\)
−0.715358 + 0.698758i \(0.753736\pi\)
\(38\) 0 0
\(39\) 117.000 0.480384
\(40\) 0 0
\(41\) 455.000 1.73315 0.866574 − 0.499049i \(-0.166317\pi\)
0.866574 + 0.499049i \(0.166317\pi\)
\(42\) 0 0
\(43\) 307.000 1.08877 0.544384 − 0.838836i \(-0.316763\pi\)
0.544384 + 0.838836i \(0.316763\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −508.000 −1.57658 −0.788292 − 0.615302i \(-0.789034\pi\)
−0.788292 + 0.615302i \(0.789034\pi\)
\(48\) 0 0
\(49\) 49.0000 0.142857
\(50\) 0 0
\(51\) 303.000 0.831931
\(52\) 0 0
\(53\) 31.0000 0.0803430 0.0401715 − 0.999193i \(-0.487210\pi\)
0.0401715 + 0.999193i \(0.487210\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −144.000 −0.334619
\(58\) 0 0
\(59\) 211.000 0.465591 0.232795 − 0.972526i \(-0.425213\pi\)
0.232795 + 0.972526i \(0.425213\pi\)
\(60\) 0 0
\(61\) −797.000 −1.67288 −0.836438 − 0.548062i \(-0.815366\pi\)
−0.836438 + 0.548062i \(0.815366\pi\)
\(62\) 0 0
\(63\) −63.0000 −0.125988
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 924.000 1.68484 0.842422 − 0.538818i \(-0.181129\pi\)
0.842422 + 0.538818i \(0.181129\pi\)
\(68\) 0 0
\(69\) −171.000 −0.298348
\(70\) 0 0
\(71\) 212.000 0.354363 0.177181 − 0.984178i \(-0.443302\pi\)
0.177181 + 0.984178i \(0.443302\pi\)
\(72\) 0 0
\(73\) −22.0000 −0.0352727 −0.0176363 − 0.999844i \(-0.505614\pi\)
−0.0176363 + 0.999844i \(0.505614\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 182.000 0.269361
\(78\) 0 0
\(79\) 874.000 1.24472 0.622359 − 0.782732i \(-0.286175\pi\)
0.622359 + 0.782732i \(0.286175\pi\)
\(80\) 0 0
\(81\) 81.0000 0.111111
\(82\) 0 0
\(83\) 587.000 0.776285 0.388142 − 0.921599i \(-0.373117\pi\)
0.388142 + 0.921599i \(0.373117\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −873.000 −1.07581
\(88\) 0 0
\(89\) −266.000 −0.316808 −0.158404 − 0.987374i \(-0.550635\pi\)
−0.158404 + 0.987374i \(0.550635\pi\)
\(90\) 0 0
\(91\) −273.000 −0.314485
\(92\) 0 0
\(93\) −237.000 −0.264255
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −1822.00 −1.90718 −0.953588 − 0.301114i \(-0.902641\pi\)
−0.953588 + 0.301114i \(0.902641\pi\)
\(98\) 0 0
\(99\) −234.000 −0.237554
\(100\) 0 0
\(101\) −1872.00 −1.84427 −0.922133 − 0.386872i \(-0.873556\pi\)
−0.922133 + 0.386872i \(0.873556\pi\)
\(102\) 0 0
\(103\) −1595.00 −1.52583 −0.762913 − 0.646501i \(-0.776231\pi\)
−0.762913 + 0.646501i \(0.776231\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1026.00 −0.926983 −0.463491 − 0.886101i \(-0.653404\pi\)
−0.463491 + 0.886101i \(0.653404\pi\)
\(108\) 0 0
\(109\) −588.000 −0.516699 −0.258349 − 0.966052i \(-0.583179\pi\)
−0.258349 + 0.966052i \(0.583179\pi\)
\(110\) 0 0
\(111\) −966.000 −0.826024
\(112\) 0 0
\(113\) −22.0000 −0.0183149 −0.00915746 − 0.999958i \(-0.502915\pi\)
−0.00915746 + 0.999958i \(0.502915\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 351.000 0.277350
\(118\) 0 0
\(119\) −707.000 −0.544627
\(120\) 0 0
\(121\) −655.000 −0.492111
\(122\) 0 0
\(123\) 1365.00 1.00063
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 1750.00 1.22274 0.611368 − 0.791347i \(-0.290620\pi\)
0.611368 + 0.791347i \(0.290620\pi\)
\(128\) 0 0
\(129\) 921.000 0.628601
\(130\) 0 0
\(131\) 1664.00 1.10980 0.554902 − 0.831916i \(-0.312756\pi\)
0.554902 + 0.831916i \(0.312756\pi\)
\(132\) 0 0
\(133\) 336.000 0.219059
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −1080.00 −0.673508 −0.336754 − 0.941593i \(-0.609329\pi\)
−0.336754 + 0.941593i \(0.609329\pi\)
\(138\) 0 0
\(139\) −896.000 −0.546746 −0.273373 − 0.961908i \(-0.588139\pi\)
−0.273373 + 0.961908i \(0.588139\pi\)
\(140\) 0 0
\(141\) −1524.00 −0.910241
\(142\) 0 0
\(143\) −1014.00 −0.592972
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 147.000 0.0824786
\(148\) 0 0
\(149\) −591.000 −0.324944 −0.162472 − 0.986713i \(-0.551947\pi\)
−0.162472 + 0.986713i \(0.551947\pi\)
\(150\) 0 0
\(151\) −1606.00 −0.865526 −0.432763 − 0.901508i \(-0.642461\pi\)
−0.432763 + 0.901508i \(0.642461\pi\)
\(152\) 0 0
\(153\) 909.000 0.480316
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −3554.00 −1.80662 −0.903312 − 0.428983i \(-0.858872\pi\)
−0.903312 + 0.428983i \(0.858872\pi\)
\(158\) 0 0
\(159\) 93.0000 0.0463860
\(160\) 0 0
\(161\) 399.000 0.195314
\(162\) 0 0
\(163\) 2897.00 1.39209 0.696045 − 0.717999i \(-0.254942\pi\)
0.696045 + 0.717999i \(0.254942\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 66.0000 0.0305822 0.0152911 − 0.999883i \(-0.495132\pi\)
0.0152911 + 0.999883i \(0.495132\pi\)
\(168\) 0 0
\(169\) −676.000 −0.307692
\(170\) 0 0
\(171\) −432.000 −0.193192
\(172\) 0 0
\(173\) −1672.00 −0.734797 −0.367398 − 0.930064i \(-0.619751\pi\)
−0.367398 + 0.930064i \(0.619751\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 633.000 0.268809
\(178\) 0 0
\(179\) 4710.00 1.96671 0.983357 − 0.181682i \(-0.0581541\pi\)
0.983357 + 0.181682i \(0.0581541\pi\)
\(180\) 0 0
\(181\) 2842.00 1.16710 0.583548 − 0.812079i \(-0.301664\pi\)
0.583548 + 0.812079i \(0.301664\pi\)
\(182\) 0 0
\(183\) −2391.00 −0.965835
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −2626.00 −1.02691
\(188\) 0 0
\(189\) −189.000 −0.0727393
\(190\) 0 0
\(191\) −4197.00 −1.58997 −0.794985 − 0.606629i \(-0.792521\pi\)
−0.794985 + 0.606629i \(0.792521\pi\)
\(192\) 0 0
\(193\) −2662.00 −0.992824 −0.496412 − 0.868087i \(-0.665349\pi\)
−0.496412 + 0.868087i \(0.665349\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −3601.00 −1.30234 −0.651169 − 0.758933i \(-0.725721\pi\)
−0.651169 + 0.758933i \(0.725721\pi\)
\(198\) 0 0
\(199\) −1840.00 −0.655448 −0.327724 − 0.944774i \(-0.606282\pi\)
−0.327724 + 0.944774i \(0.606282\pi\)
\(200\) 0 0
\(201\) 2772.00 0.972745
\(202\) 0 0
\(203\) 2037.00 0.704283
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −513.000 −0.172251
\(208\) 0 0
\(209\) 1248.00 0.413043
\(210\) 0 0
\(211\) −1733.00 −0.565425 −0.282712 − 0.959205i \(-0.591234\pi\)
−0.282712 + 0.959205i \(0.591234\pi\)
\(212\) 0 0
\(213\) 636.000 0.204592
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 553.000 0.172996
\(218\) 0 0
\(219\) −66.0000 −0.0203647
\(220\) 0 0
\(221\) 3939.00 1.19894
\(222\) 0 0
\(223\) −4727.00 −1.41948 −0.709738 − 0.704465i \(-0.751187\pi\)
−0.709738 + 0.704465i \(0.751187\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −2863.00 −0.837110 −0.418555 − 0.908191i \(-0.637463\pi\)
−0.418555 + 0.908191i \(0.637463\pi\)
\(228\) 0 0
\(229\) 5578.00 1.60963 0.804814 − 0.593528i \(-0.202265\pi\)
0.804814 + 0.593528i \(0.202265\pi\)
\(230\) 0 0
\(231\) 546.000 0.155516
\(232\) 0 0
\(233\) −5016.00 −1.41034 −0.705170 − 0.709039i \(-0.749129\pi\)
−0.705170 + 0.709039i \(0.749129\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 2622.00 0.718638
\(238\) 0 0
\(239\) 2992.00 0.809776 0.404888 − 0.914366i \(-0.367311\pi\)
0.404888 + 0.914366i \(0.367311\pi\)
\(240\) 0 0
\(241\) −1574.00 −0.420706 −0.210353 − 0.977625i \(-0.567461\pi\)
−0.210353 + 0.977625i \(0.567461\pi\)
\(242\) 0 0
\(243\) 243.000 0.0641500
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −1872.00 −0.482237
\(248\) 0 0
\(249\) 1761.00 0.448188
\(250\) 0 0
\(251\) −5697.00 −1.43264 −0.716318 − 0.697774i \(-0.754174\pi\)
−0.716318 + 0.697774i \(0.754174\pi\)
\(252\) 0 0
\(253\) 1482.00 0.368271
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −2599.00 −0.630822 −0.315411 − 0.948955i \(-0.602142\pi\)
−0.315411 + 0.948955i \(0.602142\pi\)
\(258\) 0 0
\(259\) 2254.00 0.540760
\(260\) 0 0
\(261\) −2619.00 −0.621119
\(262\) 0 0
\(263\) 1115.00 0.261421 0.130711 − 0.991421i \(-0.458274\pi\)
0.130711 + 0.991421i \(0.458274\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −798.000 −0.182909
\(268\) 0 0
\(269\) 4194.00 0.950605 0.475302 − 0.879822i \(-0.342339\pi\)
0.475302 + 0.879822i \(0.342339\pi\)
\(270\) 0 0
\(271\) −3972.00 −0.890339 −0.445169 − 0.895446i \(-0.646857\pi\)
−0.445169 + 0.895446i \(0.646857\pi\)
\(272\) 0 0
\(273\) −819.000 −0.181568
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 1842.00 0.399549 0.199774 − 0.979842i \(-0.435979\pi\)
0.199774 + 0.979842i \(0.435979\pi\)
\(278\) 0 0
\(279\) −711.000 −0.152568
\(280\) 0 0
\(281\) −2680.00 −0.568952 −0.284476 − 0.958683i \(-0.591820\pi\)
−0.284476 + 0.958683i \(0.591820\pi\)
\(282\) 0 0
\(283\) −2680.00 −0.562931 −0.281465 − 0.959571i \(-0.590820\pi\)
−0.281465 + 0.959571i \(0.590820\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −3185.00 −0.655068
\(288\) 0 0
\(289\) 5288.00 1.07633
\(290\) 0 0
\(291\) −5466.00 −1.10111
\(292\) 0 0
\(293\) 5656.00 1.12774 0.563869 − 0.825864i \(-0.309312\pi\)
0.563869 + 0.825864i \(0.309312\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −702.000 −0.137152
\(298\) 0 0
\(299\) −2223.00 −0.429965
\(300\) 0 0
\(301\) −2149.00 −0.411516
\(302\) 0 0
\(303\) −5616.00 −1.06479
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −6998.00 −1.30097 −0.650484 − 0.759520i \(-0.725434\pi\)
−0.650484 + 0.759520i \(0.725434\pi\)
\(308\) 0 0
\(309\) −4785.00 −0.880936
\(310\) 0 0
\(311\) 5610.00 1.02287 0.511437 − 0.859321i \(-0.329113\pi\)
0.511437 + 0.859321i \(0.329113\pi\)
\(312\) 0 0
\(313\) −166.000 −0.0299772 −0.0149886 − 0.999888i \(-0.504771\pi\)
−0.0149886 + 0.999888i \(0.504771\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −5333.00 −0.944893 −0.472447 − 0.881359i \(-0.656629\pi\)
−0.472447 + 0.881359i \(0.656629\pi\)
\(318\) 0 0
\(319\) 7566.00 1.32795
\(320\) 0 0
\(321\) −3078.00 −0.535194
\(322\) 0 0
\(323\) −4848.00 −0.835139
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −1764.00 −0.298316
\(328\) 0 0
\(329\) 3556.00 0.595892
\(330\) 0 0
\(331\) 6481.00 1.07622 0.538109 − 0.842875i \(-0.319139\pi\)
0.538109 + 0.842875i \(0.319139\pi\)
\(332\) 0 0
\(333\) −2898.00 −0.476905
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −9221.00 −1.49050 −0.745252 − 0.666783i \(-0.767671\pi\)
−0.745252 + 0.666783i \(0.767671\pi\)
\(338\) 0 0
\(339\) −66.0000 −0.0105741
\(340\) 0 0
\(341\) 2054.00 0.326189
\(342\) 0 0
\(343\) −343.000 −0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −1910.00 −0.295488 −0.147744 − 0.989026i \(-0.547201\pi\)
−0.147744 + 0.989026i \(0.547201\pi\)
\(348\) 0 0
\(349\) 3409.00 0.522864 0.261432 − 0.965222i \(-0.415805\pi\)
0.261432 + 0.965222i \(0.415805\pi\)
\(350\) 0 0
\(351\) 1053.00 0.160128
\(352\) 0 0
\(353\) −2130.00 −0.321157 −0.160579 − 0.987023i \(-0.551336\pi\)
−0.160579 + 0.987023i \(0.551336\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −2121.00 −0.314440
\(358\) 0 0
\(359\) 647.000 0.0951180 0.0475590 − 0.998868i \(-0.484856\pi\)
0.0475590 + 0.998868i \(0.484856\pi\)
\(360\) 0 0
\(361\) −4555.00 −0.664091
\(362\) 0 0
\(363\) −1965.00 −0.284121
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 11503.0 1.63611 0.818054 − 0.575141i \(-0.195053\pi\)
0.818054 + 0.575141i \(0.195053\pi\)
\(368\) 0 0
\(369\) 4095.00 0.577716
\(370\) 0 0
\(371\) −217.000 −0.0303668
\(372\) 0 0
\(373\) 3692.00 0.512505 0.256253 − 0.966610i \(-0.417512\pi\)
0.256253 + 0.966610i \(0.417512\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −11349.0 −1.55041
\(378\) 0 0
\(379\) 8103.00 1.09821 0.549107 − 0.835752i \(-0.314968\pi\)
0.549107 + 0.835752i \(0.314968\pi\)
\(380\) 0 0
\(381\) 5250.00 0.705947
\(382\) 0 0
\(383\) 2664.00 0.355415 0.177708 − 0.984083i \(-0.443132\pi\)
0.177708 + 0.984083i \(0.443132\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 2763.00 0.362923
\(388\) 0 0
\(389\) −2050.00 −0.267196 −0.133598 − 0.991036i \(-0.542653\pi\)
−0.133598 + 0.991036i \(0.542653\pi\)
\(390\) 0 0
\(391\) −5757.00 −0.744614
\(392\) 0 0
\(393\) 4992.00 0.640746
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 1213.00 0.153347 0.0766735 − 0.997056i \(-0.475570\pi\)
0.0766735 + 0.997056i \(0.475570\pi\)
\(398\) 0 0
\(399\) 1008.00 0.126474
\(400\) 0 0
\(401\) 10876.0 1.35442 0.677209 − 0.735791i \(-0.263189\pi\)
0.677209 + 0.735791i \(0.263189\pi\)
\(402\) 0 0
\(403\) −3081.00 −0.380833
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 8372.00 1.01962
\(408\) 0 0
\(409\) −12534.0 −1.51532 −0.757661 − 0.652649i \(-0.773658\pi\)
−0.757661 + 0.652649i \(0.773658\pi\)
\(410\) 0 0
\(411\) −3240.00 −0.388850
\(412\) 0 0
\(413\) −1477.00 −0.175977
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −2688.00 −0.315664
\(418\) 0 0
\(419\) 4569.00 0.532721 0.266361 − 0.963873i \(-0.414179\pi\)
0.266361 + 0.963873i \(0.414179\pi\)
\(420\) 0 0
\(421\) −9262.00 −1.07221 −0.536107 − 0.844150i \(-0.680106\pi\)
−0.536107 + 0.844150i \(0.680106\pi\)
\(422\) 0 0
\(423\) −4572.00 −0.525528
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 5579.00 0.632287
\(428\) 0 0
\(429\) −3042.00 −0.342352
\(430\) 0 0
\(431\) −9429.00 −1.05378 −0.526890 − 0.849934i \(-0.676642\pi\)
−0.526890 + 0.849934i \(0.676642\pi\)
\(432\) 0 0
\(433\) −418.000 −0.0463921 −0.0231961 − 0.999731i \(-0.507384\pi\)
−0.0231961 + 0.999731i \(0.507384\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 2736.00 0.299498
\(438\) 0 0
\(439\) −419.000 −0.0455530 −0.0227765 − 0.999741i \(-0.507251\pi\)
−0.0227765 + 0.999741i \(0.507251\pi\)
\(440\) 0 0
\(441\) 441.000 0.0476190
\(442\) 0 0
\(443\) 9628.00 1.03260 0.516298 − 0.856409i \(-0.327310\pi\)
0.516298 + 0.856409i \(0.327310\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −1773.00 −0.187606
\(448\) 0 0
\(449\) 14052.0 1.47696 0.738480 − 0.674276i \(-0.235544\pi\)
0.738480 + 0.674276i \(0.235544\pi\)
\(450\) 0 0
\(451\) −11830.0 −1.23515
\(452\) 0 0
\(453\) −4818.00 −0.499712
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −12089.0 −1.23742 −0.618708 − 0.785621i \(-0.712344\pi\)
−0.618708 + 0.785621i \(0.712344\pi\)
\(458\) 0 0
\(459\) 2727.00 0.277310
\(460\) 0 0
\(461\) −2744.00 −0.277225 −0.138613 − 0.990347i \(-0.544264\pi\)
−0.138613 + 0.990347i \(0.544264\pi\)
\(462\) 0 0
\(463\) −592.000 −0.0594224 −0.0297112 − 0.999559i \(-0.509459\pi\)
−0.0297112 + 0.999559i \(0.509459\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −3361.00 −0.333038 −0.166519 − 0.986038i \(-0.553253\pi\)
−0.166519 + 0.986038i \(0.553253\pi\)
\(468\) 0 0
\(469\) −6468.00 −0.636811
\(470\) 0 0
\(471\) −10662.0 −1.04306
\(472\) 0 0
\(473\) −7982.00 −0.775925
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 279.000 0.0267810
\(478\) 0 0
\(479\) 8604.00 0.820724 0.410362 − 0.911923i \(-0.365402\pi\)
0.410362 + 0.911923i \(0.365402\pi\)
\(480\) 0 0
\(481\) −12558.0 −1.19043
\(482\) 0 0
\(483\) 1197.00 0.112765
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −9826.00 −0.914289 −0.457144 − 0.889393i \(-0.651128\pi\)
−0.457144 + 0.889393i \(0.651128\pi\)
\(488\) 0 0
\(489\) 8691.00 0.803723
\(490\) 0 0
\(491\) 4758.00 0.437323 0.218661 − 0.975801i \(-0.429831\pi\)
0.218661 + 0.975801i \(0.429831\pi\)
\(492\) 0 0
\(493\) −29391.0 −2.68500
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −1484.00 −0.133937
\(498\) 0 0
\(499\) −20631.0 −1.85084 −0.925421 − 0.378940i \(-0.876289\pi\)
−0.925421 + 0.378940i \(0.876289\pi\)
\(500\) 0 0
\(501\) 198.000 0.0176567
\(502\) 0 0
\(503\) 7566.00 0.670678 0.335339 − 0.942097i \(-0.391149\pi\)
0.335339 + 0.942097i \(0.391149\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −2028.00 −0.177646
\(508\) 0 0
\(509\) 12028.0 1.04741 0.523705 − 0.851900i \(-0.324549\pi\)
0.523705 + 0.851900i \(0.324549\pi\)
\(510\) 0 0
\(511\) 154.000 0.0133318
\(512\) 0 0
\(513\) −1296.00 −0.111540
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 13208.0 1.12357
\(518\) 0 0
\(519\) −5016.00 −0.424235
\(520\) 0 0
\(521\) 21317.0 1.79254 0.896271 − 0.443506i \(-0.146266\pi\)
0.896271 + 0.443506i \(0.146266\pi\)
\(522\) 0 0
\(523\) −15416.0 −1.28890 −0.644450 − 0.764647i \(-0.722914\pi\)
−0.644450 + 0.764647i \(0.722914\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −7979.00 −0.659527
\(528\) 0 0
\(529\) −8918.00 −0.732966
\(530\) 0 0
\(531\) 1899.00 0.155197
\(532\) 0 0
\(533\) 17745.0 1.44207
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 14130.0 1.13548
\(538\) 0 0
\(539\) −1274.00 −0.101809
\(540\) 0 0
\(541\) 17520.0 1.39232 0.696159 − 0.717888i \(-0.254891\pi\)
0.696159 + 0.717888i \(0.254891\pi\)
\(542\) 0 0
\(543\) 8526.00 0.673823
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −17379.0 −1.35845 −0.679225 − 0.733930i \(-0.737684\pi\)
−0.679225 + 0.733930i \(0.737684\pi\)
\(548\) 0 0
\(549\) −7173.00 −0.557625
\(550\) 0 0
\(551\) 13968.0 1.07996
\(552\) 0 0
\(553\) −6118.00 −0.470459
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −15830.0 −1.20420 −0.602099 − 0.798421i \(-0.705669\pi\)
−0.602099 + 0.798421i \(0.705669\pi\)
\(558\) 0 0
\(559\) 11973.0 0.905910
\(560\) 0 0
\(561\) −7878.00 −0.592887
\(562\) 0 0
\(563\) 7343.00 0.549681 0.274841 − 0.961490i \(-0.411375\pi\)
0.274841 + 0.961490i \(0.411375\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −567.000 −0.0419961
\(568\) 0 0
\(569\) −10806.0 −0.796153 −0.398077 − 0.917352i \(-0.630322\pi\)
−0.398077 + 0.917352i \(0.630322\pi\)
\(570\) 0 0
\(571\) −1593.00 −0.116751 −0.0583756 − 0.998295i \(-0.518592\pi\)
−0.0583756 + 0.998295i \(0.518592\pi\)
\(572\) 0 0
\(573\) −12591.0 −0.917970
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −9314.00 −0.672005 −0.336003 − 0.941861i \(-0.609075\pi\)
−0.336003 + 0.941861i \(0.609075\pi\)
\(578\) 0 0
\(579\) −7986.00 −0.573207
\(580\) 0 0
\(581\) −4109.00 −0.293408
\(582\) 0 0
\(583\) −806.000 −0.0572575
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 3083.00 0.216779 0.108389 − 0.994109i \(-0.465431\pi\)
0.108389 + 0.994109i \(0.465431\pi\)
\(588\) 0 0
\(589\) 3792.00 0.265274
\(590\) 0 0
\(591\) −10803.0 −0.751905
\(592\) 0 0
\(593\) 18882.0 1.30757 0.653787 − 0.756679i \(-0.273179\pi\)
0.653787 + 0.756679i \(0.273179\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −5520.00 −0.378423
\(598\) 0 0
\(599\) 1707.00 0.116438 0.0582188 − 0.998304i \(-0.481458\pi\)
0.0582188 + 0.998304i \(0.481458\pi\)
\(600\) 0 0
\(601\) 1440.00 0.0977352 0.0488676 − 0.998805i \(-0.484439\pi\)
0.0488676 + 0.998805i \(0.484439\pi\)
\(602\) 0 0
\(603\) 8316.00 0.561615
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 8284.00 0.553933 0.276966 − 0.960880i \(-0.410671\pi\)
0.276966 + 0.960880i \(0.410671\pi\)
\(608\) 0 0
\(609\) 6111.00 0.406618
\(610\) 0 0
\(611\) −19812.0 −1.31180
\(612\) 0 0
\(613\) 24042.0 1.58409 0.792045 − 0.610463i \(-0.209016\pi\)
0.792045 + 0.610463i \(0.209016\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −862.000 −0.0562444 −0.0281222 − 0.999604i \(-0.508953\pi\)
−0.0281222 + 0.999604i \(0.508953\pi\)
\(618\) 0 0
\(619\) 9890.00 0.642185 0.321093 − 0.947048i \(-0.395950\pi\)
0.321093 + 0.947048i \(0.395950\pi\)
\(620\) 0 0
\(621\) −1539.00 −0.0994492
\(622\) 0 0
\(623\) 1862.00 0.119742
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 3744.00 0.238470
\(628\) 0 0
\(629\) −32522.0 −2.06159
\(630\) 0 0
\(631\) −21646.0 −1.36563 −0.682816 − 0.730590i \(-0.739245\pi\)
−0.682816 + 0.730590i \(0.739245\pi\)
\(632\) 0 0
\(633\) −5199.00 −0.326448
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 1911.00 0.118864
\(638\) 0 0
\(639\) 1908.00 0.118121
\(640\) 0 0
\(641\) 19658.0 1.21130 0.605651 − 0.795731i \(-0.292913\pi\)
0.605651 + 0.795731i \(0.292913\pi\)
\(642\) 0 0
\(643\) 23818.0 1.46079 0.730397 − 0.683023i \(-0.239335\pi\)
0.730397 + 0.683023i \(0.239335\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −28490.0 −1.73116 −0.865578 − 0.500775i \(-0.833049\pi\)
−0.865578 + 0.500775i \(0.833049\pi\)
\(648\) 0 0
\(649\) −5486.00 −0.331809
\(650\) 0 0
\(651\) 1659.00 0.0998792
\(652\) 0 0
\(653\) −11002.0 −0.659329 −0.329664 − 0.944098i \(-0.606936\pi\)
−0.329664 + 0.944098i \(0.606936\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −198.000 −0.0117576
\(658\) 0 0
\(659\) 11506.0 0.680137 0.340068 − 0.940401i \(-0.389550\pi\)
0.340068 + 0.940401i \(0.389550\pi\)
\(660\) 0 0
\(661\) 8398.00 0.494167 0.247083 − 0.968994i \(-0.420528\pi\)
0.247083 + 0.968994i \(0.420528\pi\)
\(662\) 0 0
\(663\) 11817.0 0.692209
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 16587.0 0.962895
\(668\) 0 0
\(669\) −14181.0 −0.819535
\(670\) 0 0
\(671\) 20722.0 1.19220
\(672\) 0 0
\(673\) −1901.00 −0.108883 −0.0544414 − 0.998517i \(-0.517338\pi\)
−0.0544414 + 0.998517i \(0.517338\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −19896.0 −1.12949 −0.564745 − 0.825265i \(-0.691026\pi\)
−0.564745 + 0.825265i \(0.691026\pi\)
\(678\) 0 0
\(679\) 12754.0 0.720845
\(680\) 0 0
\(681\) −8589.00 −0.483306
\(682\) 0 0
\(683\) 15662.0 0.877437 0.438719 − 0.898624i \(-0.355432\pi\)
0.438719 + 0.898624i \(0.355432\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 16734.0 0.929319
\(688\) 0 0
\(689\) 1209.00 0.0668494
\(690\) 0 0
\(691\) 1162.00 0.0639719 0.0319859 − 0.999488i \(-0.489817\pi\)
0.0319859 + 0.999488i \(0.489817\pi\)
\(692\) 0 0
\(693\) 1638.00 0.0897871
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 45955.0 2.49737
\(698\) 0 0
\(699\) −15048.0 −0.814260
\(700\) 0 0
\(701\) 13501.0 0.727426 0.363713 − 0.931511i \(-0.381509\pi\)
0.363713 + 0.931511i \(0.381509\pi\)
\(702\) 0 0
\(703\) 15456.0 0.829209
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 13104.0 0.697067
\(708\) 0 0
\(709\) −20672.0 −1.09500 −0.547499 − 0.836806i \(-0.684420\pi\)
−0.547499 + 0.836806i \(0.684420\pi\)
\(710\) 0 0
\(711\) 7866.00 0.414906
\(712\) 0 0
\(713\) 4503.00 0.236520
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 8976.00 0.467524
\(718\) 0 0
\(719\) −7098.00 −0.368165 −0.184083 − 0.982911i \(-0.558931\pi\)
−0.184083 + 0.982911i \(0.558931\pi\)
\(720\) 0 0
\(721\) 11165.0 0.576708
\(722\) 0 0
\(723\) −4722.00 −0.242895
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 4053.00 0.206764 0.103382 − 0.994642i \(-0.467034\pi\)
0.103382 + 0.994642i \(0.467034\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) 0 0
\(731\) 31007.0 1.56886
\(732\) 0 0
\(733\) −10331.0 −0.520579 −0.260289 − 0.965531i \(-0.583818\pi\)
−0.260289 + 0.965531i \(0.583818\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −24024.0 −1.20073
\(738\) 0 0
\(739\) −8969.00 −0.446455 −0.223227 − 0.974766i \(-0.571659\pi\)
−0.223227 + 0.974766i \(0.571659\pi\)
\(740\) 0 0
\(741\) −5616.00 −0.278420
\(742\) 0 0
\(743\) 11613.0 0.573405 0.286702 − 0.958020i \(-0.407441\pi\)
0.286702 + 0.958020i \(0.407441\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 5283.00 0.258762
\(748\) 0 0
\(749\) 7182.00 0.350367
\(750\) 0 0
\(751\) −32476.0 −1.57798 −0.788992 − 0.614403i \(-0.789397\pi\)
−0.788992 + 0.614403i \(0.789397\pi\)
\(752\) 0 0
\(753\) −17091.0 −0.827132
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 29914.0 1.43625 0.718126 − 0.695913i \(-0.245000\pi\)
0.718126 + 0.695913i \(0.245000\pi\)
\(758\) 0 0
\(759\) 4446.00 0.212621
\(760\) 0 0
\(761\) −3090.00 −0.147191 −0.0735955 − 0.997288i \(-0.523447\pi\)
−0.0735955 + 0.997288i \(0.523447\pi\)
\(762\) 0 0
\(763\) 4116.00 0.195294
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 8229.00 0.387395
\(768\) 0 0
\(769\) −7760.00 −0.363892 −0.181946 − 0.983309i \(-0.558240\pi\)
−0.181946 + 0.983309i \(0.558240\pi\)
\(770\) 0 0
\(771\) −7797.00 −0.364205
\(772\) 0 0
\(773\) −34020.0 −1.58294 −0.791471 − 0.611207i \(-0.790684\pi\)
−0.791471 + 0.611207i \(0.790684\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 6762.00 0.312208
\(778\) 0 0
\(779\) −21840.0 −1.00449
\(780\) 0 0
\(781\) −5512.00 −0.252541
\(782\) 0 0
\(783\) −7857.00 −0.358603
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 15154.0 0.686381 0.343190 − 0.939266i \(-0.388492\pi\)
0.343190 + 0.939266i \(0.388492\pi\)
\(788\) 0 0
\(789\) 3345.00 0.150932
\(790\) 0 0
\(791\) 154.000 0.00692239
\(792\) 0 0
\(793\) −31083.0 −1.39192
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 13386.0 0.594927 0.297463 − 0.954733i \(-0.403859\pi\)
0.297463 + 0.954733i \(0.403859\pi\)
\(798\) 0 0
\(799\) −51308.0 −2.27177
\(800\) 0 0
\(801\) −2394.00 −0.105603
\(802\) 0 0
\(803\) 572.000 0.0251375
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 12582.0 0.548832
\(808\) 0 0
\(809\) 36468.0 1.58485 0.792427 − 0.609967i \(-0.208817\pi\)
0.792427 + 0.609967i \(0.208817\pi\)
\(810\) 0 0
\(811\) −38422.0 −1.66360 −0.831800 − 0.555076i \(-0.812689\pi\)
−0.831800 + 0.555076i \(0.812689\pi\)
\(812\) 0 0
\(813\) −11916.0 −0.514037
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −14736.0 −0.631025
\(818\) 0 0
\(819\) −2457.00 −0.104828
\(820\) 0 0
\(821\) 19194.0 0.815926 0.407963 − 0.912998i \(-0.366239\pi\)
0.407963 + 0.912998i \(0.366239\pi\)
\(822\) 0 0
\(823\) 7426.00 0.314525 0.157263 − 0.987557i \(-0.449733\pi\)
0.157263 + 0.987557i \(0.449733\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 33170.0 1.39472 0.697360 − 0.716721i \(-0.254358\pi\)
0.697360 + 0.716721i \(0.254358\pi\)
\(828\) 0 0
\(829\) 16397.0 0.686962 0.343481 − 0.939160i \(-0.388394\pi\)
0.343481 + 0.939160i \(0.388394\pi\)
\(830\) 0 0
\(831\) 5526.00 0.230680
\(832\) 0 0
\(833\) 4949.00 0.205850
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −2133.00 −0.0880851
\(838\) 0 0
\(839\) 14996.0 0.617067 0.308534 − 0.951213i \(-0.400162\pi\)
0.308534 + 0.951213i \(0.400162\pi\)
\(840\) 0 0
\(841\) 60292.0 2.47210
\(842\) 0 0
\(843\) −8040.00 −0.328484
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 4585.00 0.186001
\(848\) 0 0
\(849\) −8040.00 −0.325008
\(850\) 0 0
\(851\) 18354.0 0.739327
\(852\) 0 0
\(853\) 21053.0 0.845066 0.422533 − 0.906348i \(-0.361141\pi\)
0.422533 + 0.906348i \(0.361141\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 6390.00 0.254700 0.127350 − 0.991858i \(-0.459353\pi\)
0.127350 + 0.991858i \(0.459353\pi\)
\(858\) 0 0
\(859\) 22176.0 0.880833 0.440416 − 0.897794i \(-0.354831\pi\)
0.440416 + 0.897794i \(0.354831\pi\)
\(860\) 0 0
\(861\) −9555.00 −0.378204
\(862\) 0 0
\(863\) 42472.0 1.67528 0.837638 − 0.546225i \(-0.183936\pi\)
0.837638 + 0.546225i \(0.183936\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 15864.0 0.621418
\(868\) 0 0
\(869\) −22724.0 −0.887064
\(870\) 0 0
\(871\) 36036.0 1.40188
\(872\) 0 0
\(873\) −16398.0 −0.635725
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −3472.00 −0.133684 −0.0668421 − 0.997764i \(-0.521292\pi\)
−0.0668421 + 0.997764i \(0.521292\pi\)
\(878\) 0 0
\(879\) 16968.0 0.651099
\(880\) 0 0
\(881\) 32639.0 1.24817 0.624084 − 0.781357i \(-0.285472\pi\)
0.624084 + 0.781357i \(0.285472\pi\)
\(882\) 0 0
\(883\) 45513.0 1.73458 0.867290 − 0.497803i \(-0.165860\pi\)
0.867290 + 0.497803i \(0.165860\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 27626.0 1.04576 0.522881 − 0.852406i \(-0.324857\pi\)
0.522881 + 0.852406i \(0.324857\pi\)
\(888\) 0 0
\(889\) −12250.0 −0.462151
\(890\) 0 0
\(891\) −2106.00 −0.0791848
\(892\) 0 0
\(893\) 24384.0 0.913751
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −6669.00 −0.248240
\(898\) 0 0
\(899\) 22989.0 0.852865
\(900\) 0 0
\(901\) 3131.00 0.115770
\(902\) 0 0
\(903\) −6447.00 −0.237589
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 11561.0 0.423238 0.211619 − 0.977352i \(-0.432126\pi\)
0.211619 + 0.977352i \(0.432126\pi\)
\(908\) 0 0
\(909\) −16848.0 −0.614756
\(910\) 0 0
\(911\) 25773.0 0.937319 0.468659 − 0.883379i \(-0.344737\pi\)
0.468659 + 0.883379i \(0.344737\pi\)
\(912\) 0 0
\(913\) −15262.0 −0.553229
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −11648.0 −0.419467
\(918\) 0 0
\(919\) −13240.0 −0.475242 −0.237621 − 0.971358i \(-0.576368\pi\)
−0.237621 + 0.971358i \(0.576368\pi\)
\(920\) 0 0
\(921\) −20994.0 −0.751114
\(922\) 0 0
\(923\) 8268.00 0.294848
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −14355.0 −0.508608
\(928\) 0 0
\(929\) −30653.0 −1.08255 −0.541277 − 0.840844i \(-0.682059\pi\)
−0.541277 + 0.840844i \(0.682059\pi\)
\(930\) 0 0
\(931\) −2352.00 −0.0827967
\(932\) 0 0
\(933\) 16830.0 0.590557
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −19030.0 −0.663482 −0.331741 − 0.943370i \(-0.607636\pi\)
−0.331741 + 0.943370i \(0.607636\pi\)
\(938\) 0 0
\(939\) −498.000 −0.0173074
\(940\) 0 0
\(941\) −5320.00 −0.184301 −0.0921504 − 0.995745i \(-0.529374\pi\)
−0.0921504 + 0.995745i \(0.529374\pi\)
\(942\) 0 0
\(943\) −25935.0 −0.895610
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −14524.0 −0.498381 −0.249190 − 0.968455i \(-0.580164\pi\)
−0.249190 + 0.968455i \(0.580164\pi\)
\(948\) 0 0
\(949\) −858.000 −0.0293486
\(950\) 0 0
\(951\) −15999.0 −0.545534
\(952\) 0 0
\(953\) 8688.00 0.295312 0.147656 − 0.989039i \(-0.452827\pi\)
0.147656 + 0.989039i \(0.452827\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 22698.0 0.766690
\(958\) 0 0
\(959\) 7560.00 0.254562
\(960\) 0 0
\(961\) −23550.0 −0.790507
\(962\) 0 0
\(963\) −9234.00 −0.308994
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 19672.0 0.654197 0.327099 − 0.944990i \(-0.393929\pi\)
0.327099 + 0.944990i \(0.393929\pi\)
\(968\) 0 0
\(969\) −14544.0 −0.482168
\(970\) 0 0
\(971\) 45996.0 1.52017 0.760083 − 0.649826i \(-0.225158\pi\)
0.760083 + 0.649826i \(0.225158\pi\)
\(972\) 0 0
\(973\) 6272.00 0.206651
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 32454.0 1.06274 0.531369 − 0.847140i \(-0.321678\pi\)
0.531369 + 0.847140i \(0.321678\pi\)
\(978\) 0 0
\(979\) 6916.00 0.225778
\(980\) 0 0
\(981\) −5292.00 −0.172233
\(982\) 0 0
\(983\) −34048.0 −1.10474 −0.552372 − 0.833598i \(-0.686277\pi\)
−0.552372 + 0.833598i \(0.686277\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 10668.0 0.344039
\(988\) 0 0
\(989\) −17499.0 −0.562625
\(990\) 0 0
\(991\) −14804.0 −0.474535 −0.237268 − 0.971444i \(-0.576252\pi\)
−0.237268 + 0.971444i \(0.576252\pi\)
\(992\) 0 0
\(993\) 19443.0 0.621354
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 35546.0 1.12914 0.564570 − 0.825385i \(-0.309042\pi\)
0.564570 + 0.825385i \(0.309042\pi\)
\(998\) 0 0
\(999\) −8694.00 −0.275341
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 2100.4.a.j.1.1 yes 1
5.2 odd 4 2100.4.k.d.1849.1 2
5.3 odd 4 2100.4.k.d.1849.2 2
5.4 even 2 2100.4.a.e.1.1 ✓ 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2100.4.a.e.1.1 ✓ 1 5.4 even 2
2100.4.a.j.1.1 yes 1 1.1 even 1 trivial
2100.4.k.d.1849.1 2 5.2 odd 4
2100.4.k.d.1849.2 2 5.3 odd 4