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Properties

Label 1800.4.a.j.1.1
Level $1800$
Weight $4$
Character 1800.1
Self dual yes
Analytic conductor $106.203$
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] = [1800,4,Mod(1,1800)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1800, 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("1800.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1800.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: \(106.203438010\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 120)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1800.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-10.0000 q^{7} +O(q^{10})\) \(q-10.0000 q^{7} +46.0000 q^{11} +34.0000 q^{13} +66.0000 q^{17} +104.000 q^{19} +164.000 q^{23} -224.000 q^{29} -72.0000 q^{31} +22.0000 q^{37} -194.000 q^{41} -108.000 q^{43} -480.000 q^{47} -243.000 q^{49} +286.000 q^{53} -426.000 q^{59} +698.000 q^{61} -328.000 q^{67} -188.000 q^{71} +740.000 q^{73} -460.000 q^{77} +1168.00 q^{79} +412.000 q^{83} -1206.00 q^{89} -340.000 q^{91} +1384.00 q^{97} +O(q^{100})\)

Display 100 coefficients 10 coefficients

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
\(3\) 0 0
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −10.0000 −0.539949 −0.269975 − 0.962867i \(-0.587015\pi\)
−0.269975 + 0.962867i \(0.587015\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 46.0000 1.26087 0.630433 − 0.776244i \(-0.282877\pi\)
0.630433 + 0.776244i \(0.282877\pi\)
\(12\) 0 0
\(13\) 34.0000 0.725377 0.362689 − 0.931910i \(-0.381859\pi\)
0.362689 + 0.931910i \(0.381859\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 66.0000 0.941609 0.470804 − 0.882238i \(-0.343964\pi\)
0.470804 + 0.882238i \(0.343964\pi\)
\(18\) 0 0
\(19\) 104.000 1.25575 0.627875 − 0.778314i \(-0.283925\pi\)
0.627875 + 0.778314i \(0.283925\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 164.000 1.48680 0.743399 − 0.668848i \(-0.233212\pi\)
0.743399 + 0.668848i \(0.233212\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −224.000 −1.43434 −0.717168 − 0.696900i \(-0.754562\pi\)
−0.717168 + 0.696900i \(0.754562\pi\)
\(30\) 0 0
\(31\) −72.0000 −0.417148 −0.208574 − 0.978007i \(-0.566882\pi\)
−0.208574 + 0.978007i \(0.566882\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 22.0000 0.0977507 0.0488754 − 0.998805i \(-0.484436\pi\)
0.0488754 + 0.998805i \(0.484436\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −194.000 −0.738969 −0.369484 − 0.929237i \(-0.620466\pi\)
−0.369484 + 0.929237i \(0.620466\pi\)
\(42\) 0 0
\(43\) −108.000 −0.383020 −0.191510 − 0.981491i \(-0.561338\pi\)
−0.191510 + 0.981491i \(0.561338\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −480.000 −1.48969 −0.744843 − 0.667240i \(-0.767475\pi\)
−0.744843 + 0.667240i \(0.767475\pi\)
\(48\) 0 0
\(49\) −243.000 −0.708455
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 286.000 0.741229 0.370614 − 0.928787i \(-0.379147\pi\)
0.370614 + 0.928787i \(0.379147\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −426.000 −0.940008 −0.470004 − 0.882664i \(-0.655748\pi\)
−0.470004 + 0.882664i \(0.655748\pi\)
\(60\) 0 0
\(61\) 698.000 1.46508 0.732539 − 0.680725i \(-0.238335\pi\)
0.732539 + 0.680725i \(0.238335\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −328.000 −0.598083 −0.299042 − 0.954240i \(-0.596667\pi\)
−0.299042 + 0.954240i \(0.596667\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −188.000 −0.314246 −0.157123 − 0.987579i \(-0.550222\pi\)
−0.157123 + 0.987579i \(0.550222\pi\)
\(72\) 0 0
\(73\) 740.000 1.18644 0.593222 − 0.805039i \(-0.297856\pi\)
0.593222 + 0.805039i \(0.297856\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −460.000 −0.680803
\(78\) 0 0
\(79\) 1168.00 1.66342 0.831711 − 0.555209i \(-0.187362\pi\)
0.831711 + 0.555209i \(0.187362\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 412.000 0.544854 0.272427 − 0.962176i \(-0.412174\pi\)
0.272427 + 0.962176i \(0.412174\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −1206.00 −1.43636 −0.718178 − 0.695859i \(-0.755024\pi\)
−0.718178 + 0.695859i \(0.755024\pi\)
\(90\) 0 0
\(91\) −340.000 −0.391667
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 1384.00 1.44870 0.724350 − 0.689432i \(-0.242140\pi\)
0.724350 + 0.689432i \(0.242140\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 1128.00 1.11129 0.555645 − 0.831420i \(-0.312472\pi\)
0.555645 + 0.831420i \(0.312472\pi\)
\(102\) 0 0
\(103\) 758.000 0.725126 0.362563 − 0.931959i \(-0.381902\pi\)
0.362563 + 0.931959i \(0.381902\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1324.00 1.19622 0.598112 − 0.801413i \(-0.295918\pi\)
0.598112 + 0.801413i \(0.295918\pi\)
\(108\) 0 0
\(109\) 1602.00 1.40774 0.703871 − 0.710328i \(-0.251454\pi\)
0.703871 + 0.710328i \(0.251454\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −2074.00 −1.72660 −0.863299 − 0.504693i \(-0.831606\pi\)
−0.863299 + 0.504693i \(0.831606\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −660.000 −0.508421
\(120\) 0 0
\(121\) 785.000 0.589782
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 534.000 0.373109 0.186554 − 0.982445i \(-0.440268\pi\)
0.186554 + 0.982445i \(0.440268\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −1806.00 −1.20451 −0.602256 − 0.798303i \(-0.705731\pi\)
−0.602256 + 0.798303i \(0.705731\pi\)
\(132\) 0 0
\(133\) −1040.00 −0.678041
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 1822.00 1.13623 0.568117 − 0.822948i \(-0.307672\pi\)
0.568117 + 0.822948i \(0.307672\pi\)
\(138\) 0 0
\(139\) 532.000 0.324631 0.162315 − 0.986739i \(-0.448104\pi\)
0.162315 + 0.986739i \(0.448104\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 1564.00 0.914603
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 1284.00 0.705969 0.352984 − 0.935629i \(-0.385167\pi\)
0.352984 + 0.935629i \(0.385167\pi\)
\(150\) 0 0
\(151\) 184.000 0.0991636 0.0495818 − 0.998770i \(-0.484211\pi\)
0.0495818 + 0.998770i \(0.484211\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 3746.00 1.90423 0.952113 − 0.305748i \(-0.0989064\pi\)
0.952113 + 0.305748i \(0.0989064\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −1640.00 −0.802796
\(162\) 0 0
\(163\) −1504.00 −0.722714 −0.361357 − 0.932428i \(-0.617686\pi\)
−0.361357 + 0.932428i \(0.617686\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 3012.00 1.39566 0.697831 − 0.716262i \(-0.254149\pi\)
0.697831 + 0.716262i \(0.254149\pi\)
\(168\) 0 0
\(169\) −1041.00 −0.473828
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −438.000 −0.192489 −0.0962443 − 0.995358i \(-0.530683\pi\)
−0.0962443 + 0.995358i \(0.530683\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 1462.00 0.610475 0.305237 − 0.952276i \(-0.401264\pi\)
0.305237 + 0.952276i \(0.401264\pi\)
\(180\) 0 0
\(181\) 586.000 0.240647 0.120323 − 0.992735i \(-0.461607\pi\)
0.120323 + 0.992735i \(0.461607\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 3036.00 1.18724
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −60.0000 −0.0227301 −0.0113650 − 0.999935i \(-0.503618\pi\)
−0.0113650 + 0.999935i \(0.503618\pi\)
\(192\) 0 0
\(193\) 4676.00 1.74397 0.871984 − 0.489534i \(-0.162833\pi\)
0.871984 + 0.489534i \(0.162833\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 2286.00 0.826755 0.413378 − 0.910560i \(-0.364349\pi\)
0.413378 + 0.910560i \(0.364349\pi\)
\(198\) 0 0
\(199\) −3536.00 −1.25960 −0.629800 − 0.776757i \(-0.716863\pi\)
−0.629800 + 0.776757i \(0.716863\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 2240.00 0.774469
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 4784.00 1.58333
\(210\) 0 0
\(211\) −3500.00 −1.14194 −0.570971 − 0.820970i \(-0.693433\pi\)
−0.570971 + 0.820970i \(0.693433\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 720.000 0.225239
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 2244.00 0.683022
\(222\) 0 0
\(223\) −5874.00 −1.76391 −0.881955 − 0.471333i \(-0.843773\pi\)
−0.881955 + 0.471333i \(0.843773\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −124.000 −0.0362563 −0.0181281 − 0.999836i \(-0.505771\pi\)
−0.0181281 + 0.999836i \(0.505771\pi\)
\(228\) 0 0
\(229\) −1362.00 −0.393028 −0.196514 − 0.980501i \(-0.562962\pi\)
−0.196514 + 0.980501i \(0.562962\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −3870.00 −1.08812 −0.544060 − 0.839046i \(-0.683114\pi\)
−0.544060 + 0.839046i \(0.683114\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −6116.00 −1.65528 −0.827638 − 0.561262i \(-0.810316\pi\)
−0.827638 + 0.561262i \(0.810316\pi\)
\(240\) 0 0
\(241\) −5962.00 −1.59355 −0.796776 − 0.604274i \(-0.793463\pi\)
−0.796776 + 0.604274i \(0.793463\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 3536.00 0.910892
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 1490.00 0.374693 0.187347 − 0.982294i \(-0.440011\pi\)
0.187347 + 0.982294i \(0.440011\pi\)
\(252\) 0 0
\(253\) 7544.00 1.87465
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −5394.00 −1.30922 −0.654608 − 0.755969i \(-0.727166\pi\)
−0.654608 + 0.755969i \(0.727166\pi\)
\(258\) 0 0
\(259\) −220.000 −0.0527804
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −636.000 −0.149116 −0.0745579 − 0.997217i \(-0.523755\pi\)
−0.0745579 + 0.997217i \(0.523755\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 3360.00 0.761572 0.380786 − 0.924663i \(-0.375653\pi\)
0.380786 + 0.924663i \(0.375653\pi\)
\(270\) 0 0
\(271\) 5768.00 1.29292 0.646459 − 0.762948i \(-0.276249\pi\)
0.646459 + 0.762948i \(0.276249\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 1398.00 0.303241 0.151620 − 0.988439i \(-0.451551\pi\)
0.151620 + 0.988439i \(0.451551\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 4194.00 0.890367 0.445183 − 0.895439i \(-0.353138\pi\)
0.445183 + 0.895439i \(0.353138\pi\)
\(282\) 0 0
\(283\) 8256.00 1.73416 0.867082 − 0.498166i \(-0.165993\pi\)
0.867082 + 0.498166i \(0.165993\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 1940.00 0.399006
\(288\) 0 0
\(289\) −557.000 −0.113373
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 5534.00 1.10341 0.551706 − 0.834039i \(-0.313977\pi\)
0.551706 + 0.834039i \(0.313977\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 5576.00 1.07849
\(300\) 0 0
\(301\) 1080.00 0.206811
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 484.000 0.0899783 0.0449892 − 0.998987i \(-0.485675\pi\)
0.0449892 + 0.998987i \(0.485675\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 2724.00 0.496668 0.248334 − 0.968674i \(-0.420117\pi\)
0.248334 + 0.968674i \(0.420117\pi\)
\(312\) 0 0
\(313\) −5308.00 −0.958549 −0.479275 − 0.877665i \(-0.659100\pi\)
−0.479275 + 0.877665i \(0.659100\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 4218.00 0.747339 0.373670 − 0.927562i \(-0.378099\pi\)
0.373670 + 0.927562i \(0.378099\pi\)
\(318\) 0 0
\(319\) −10304.0 −1.80851
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 6864.00 1.18242
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 4800.00 0.804354
\(330\) 0 0
\(331\) −4640.00 −0.770506 −0.385253 − 0.922811i \(-0.625886\pi\)
−0.385253 + 0.922811i \(0.625886\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 8156.00 1.31835 0.659177 − 0.751987i \(-0.270905\pi\)
0.659177 + 0.751987i \(0.270905\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −3312.00 −0.525967
\(342\) 0 0
\(343\) 5860.00 0.922479
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 4124.00 0.638006 0.319003 − 0.947754i \(-0.396652\pi\)
0.319003 + 0.947754i \(0.396652\pi\)
\(348\) 0 0
\(349\) 3650.00 0.559828 0.279914 − 0.960025i \(-0.409694\pi\)
0.279914 + 0.960025i \(0.409694\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 6834.00 1.03042 0.515208 − 0.857065i \(-0.327715\pi\)
0.515208 + 0.857065i \(0.327715\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −3904.00 −0.573942 −0.286971 − 0.957939i \(-0.592648\pi\)
−0.286971 + 0.957939i \(0.592648\pi\)
\(360\) 0 0
\(361\) 3957.00 0.576906
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 13174.0 1.87378 0.936890 − 0.349624i \(-0.113691\pi\)
0.936890 + 0.349624i \(0.113691\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −2860.00 −0.400226
\(372\) 0 0
\(373\) 1090.00 0.151308 0.0756542 − 0.997134i \(-0.475895\pi\)
0.0756542 + 0.997134i \(0.475895\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −7616.00 −1.04043
\(378\) 0 0
\(379\) −9220.00 −1.24960 −0.624802 − 0.780784i \(-0.714820\pi\)
−0.624802 + 0.780784i \(0.714820\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −3960.00 −0.528320 −0.264160 − 0.964479i \(-0.585095\pi\)
−0.264160 + 0.964479i \(0.585095\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 1788.00 0.233047 0.116523 − 0.993188i \(-0.462825\pi\)
0.116523 + 0.993188i \(0.462825\pi\)
\(390\) 0 0
\(391\) 10824.0 1.39998
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −9642.00 −1.21894 −0.609469 − 0.792810i \(-0.708617\pi\)
−0.609469 + 0.792810i \(0.708617\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 410.000 0.0510584 0.0255292 − 0.999674i \(-0.491873\pi\)
0.0255292 + 0.999674i \(0.491873\pi\)
\(402\) 0 0
\(403\) −2448.00 −0.302589
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 1012.00 0.123251
\(408\) 0 0
\(409\) 13766.0 1.66427 0.832133 − 0.554576i \(-0.187120\pi\)
0.832133 + 0.554576i \(0.187120\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 4260.00 0.507557
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −16998.0 −1.98188 −0.990939 − 0.134315i \(-0.957117\pi\)
−0.990939 + 0.134315i \(0.957117\pi\)
\(420\) 0 0
\(421\) −2450.00 −0.283624 −0.141812 − 0.989894i \(-0.545293\pi\)
−0.141812 + 0.989894i \(0.545293\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −6980.00 −0.791068
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 9248.00 1.03355 0.516776 − 0.856121i \(-0.327132\pi\)
0.516776 + 0.856121i \(0.327132\pi\)
\(432\) 0 0
\(433\) 5028.00 0.558038 0.279019 − 0.960286i \(-0.409991\pi\)
0.279019 + 0.960286i \(0.409991\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 17056.0 1.86705
\(438\) 0 0
\(439\) 3120.00 0.339202 0.169601 − 0.985513i \(-0.445752\pi\)
0.169601 + 0.985513i \(0.445752\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −8220.00 −0.881589 −0.440795 − 0.897608i \(-0.645303\pi\)
−0.440795 + 0.897608i \(0.645303\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 5826.00 0.612352 0.306176 − 0.951975i \(-0.400950\pi\)
0.306176 + 0.951975i \(0.400950\pi\)
\(450\) 0 0
\(451\) −8924.00 −0.931740
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 16896.0 1.72946 0.864728 − 0.502240i \(-0.167491\pi\)
0.864728 + 0.502240i \(0.167491\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 996.000 0.100625 0.0503127 − 0.998734i \(-0.483978\pi\)
0.0503127 + 0.998734i \(0.483978\pi\)
\(462\) 0 0
\(463\) −10046.0 −1.00837 −0.504187 − 0.863594i \(-0.668208\pi\)
−0.504187 + 0.863594i \(0.668208\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −8388.00 −0.831157 −0.415579 − 0.909557i \(-0.636421\pi\)
−0.415579 + 0.909557i \(0.636421\pi\)
\(468\) 0 0
\(469\) 3280.00 0.322935
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −4968.00 −0.482936
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −11396.0 −1.08705 −0.543525 − 0.839393i \(-0.682911\pi\)
−0.543525 + 0.839393i \(0.682911\pi\)
\(480\) 0 0
\(481\) 748.000 0.0709062
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −6454.00 −0.600531 −0.300266 − 0.953856i \(-0.597075\pi\)
−0.300266 + 0.953856i \(0.597075\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −18638.0 −1.71308 −0.856539 − 0.516083i \(-0.827390\pi\)
−0.856539 + 0.516083i \(0.827390\pi\)
\(492\) 0 0
\(493\) −14784.0 −1.35058
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 1880.00 0.169677
\(498\) 0 0
\(499\) 17768.0 1.59400 0.796999 − 0.603981i \(-0.206420\pi\)
0.796999 + 0.603981i \(0.206420\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −7952.00 −0.704895 −0.352447 − 0.935832i \(-0.614650\pi\)
−0.352447 + 0.935832i \(0.614650\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 12896.0 1.12300 0.561498 − 0.827478i \(-0.310225\pi\)
0.561498 + 0.827478i \(0.310225\pi\)
\(510\) 0 0
\(511\) −7400.00 −0.640620
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −22080.0 −1.87829
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 2714.00 0.228220 0.114110 − 0.993468i \(-0.463598\pi\)
0.114110 + 0.993468i \(0.463598\pi\)
\(522\) 0 0
\(523\) 13792.0 1.15312 0.576560 − 0.817055i \(-0.304395\pi\)
0.576560 + 0.817055i \(0.304395\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −4752.00 −0.392790
\(528\) 0 0
\(529\) 14729.0 1.21057
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −6596.00 −0.536031
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −11178.0 −0.893266
\(540\) 0 0
\(541\) 6802.00 0.540556 0.270278 − 0.962782i \(-0.412884\pi\)
0.270278 + 0.962782i \(0.412884\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 18188.0 1.42169 0.710843 − 0.703350i \(-0.248313\pi\)
0.710843 + 0.703350i \(0.248313\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −23296.0 −1.80117
\(552\) 0 0
\(553\) −11680.0 −0.898163
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 21462.0 1.63263 0.816314 − 0.577608i \(-0.196014\pi\)
0.816314 + 0.577608i \(0.196014\pi\)
\(558\) 0 0
\(559\) −3672.00 −0.277834
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −17244.0 −1.29085 −0.645424 − 0.763824i \(-0.723319\pi\)
−0.645424 + 0.763824i \(0.723319\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −8790.00 −0.647620 −0.323810 − 0.946122i \(-0.604964\pi\)
−0.323810 + 0.946122i \(0.604964\pi\)
\(570\) 0 0
\(571\) −5984.00 −0.438568 −0.219284 − 0.975661i \(-0.570372\pi\)
−0.219284 + 0.975661i \(0.570372\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 9344.00 0.674170 0.337085 − 0.941474i \(-0.390559\pi\)
0.337085 + 0.941474i \(0.390559\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −4120.00 −0.294193
\(582\) 0 0
\(583\) 13156.0 0.934590
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −6932.00 −0.487418 −0.243709 − 0.969848i \(-0.578364\pi\)
−0.243709 + 0.969848i \(0.578364\pi\)
\(588\) 0 0
\(589\) −7488.00 −0.523833
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 9382.00 0.649701 0.324850 − 0.945765i \(-0.394686\pi\)
0.324850 + 0.945765i \(0.394686\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −4096.00 −0.279396 −0.139698 − 0.990194i \(-0.544613\pi\)
−0.139698 + 0.990194i \(0.544613\pi\)
\(600\) 0 0
\(601\) 22962.0 1.55847 0.779234 − 0.626733i \(-0.215608\pi\)
0.779234 + 0.626733i \(0.215608\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 3490.00 0.233369 0.116684 − 0.993169i \(-0.462773\pi\)
0.116684 + 0.993169i \(0.462773\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −16320.0 −1.08058
\(612\) 0 0
\(613\) −6386.00 −0.420764 −0.210382 − 0.977619i \(-0.567471\pi\)
−0.210382 + 0.977619i \(0.567471\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −19534.0 −1.27457 −0.637285 − 0.770629i \(-0.719942\pi\)
−0.637285 + 0.770629i \(0.719942\pi\)
\(618\) 0 0
\(619\) 8764.00 0.569071 0.284535 − 0.958666i \(-0.408161\pi\)
0.284535 + 0.958666i \(0.408161\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 12060.0 0.775560
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 1452.00 0.0920430
\(630\) 0 0
\(631\) 7856.00 0.495630 0.247815 − 0.968807i \(-0.420288\pi\)
0.247815 + 0.968807i \(0.420288\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −8262.00 −0.513897
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 22974.0 1.41563 0.707815 − 0.706398i \(-0.249681\pi\)
0.707815 + 0.706398i \(0.249681\pi\)
\(642\) 0 0
\(643\) 6216.00 0.381237 0.190618 − 0.981664i \(-0.438951\pi\)
0.190618 + 0.981664i \(0.438951\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 13384.0 0.813260 0.406630 − 0.913593i \(-0.366704\pi\)
0.406630 + 0.913593i \(0.366704\pi\)
\(648\) 0 0
\(649\) −19596.0 −1.18522
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 12882.0 0.771993 0.385997 − 0.922500i \(-0.373858\pi\)
0.385997 + 0.922500i \(0.373858\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 2082.00 0.123070 0.0615351 − 0.998105i \(-0.480400\pi\)
0.0615351 + 0.998105i \(0.480400\pi\)
\(660\) 0 0
\(661\) −9430.00 −0.554893 −0.277447 − 0.960741i \(-0.589488\pi\)
−0.277447 + 0.960741i \(0.589488\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −36736.0 −2.13257
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 32108.0 1.84727
\(672\) 0 0
\(673\) −3268.00 −0.187180 −0.0935900 − 0.995611i \(-0.529834\pi\)
−0.0935900 + 0.995611i \(0.529834\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −15606.0 −0.885949 −0.442974 − 0.896534i \(-0.646077\pi\)
−0.442974 + 0.896534i \(0.646077\pi\)
\(678\) 0 0
\(679\) −13840.0 −0.782225
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 428.000 0.0239780 0.0119890 − 0.999928i \(-0.496184\pi\)
0.0119890 + 0.999928i \(0.496184\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 9724.00 0.537670
\(690\) 0 0
\(691\) −6384.00 −0.351460 −0.175730 − 0.984438i \(-0.556229\pi\)
−0.175730 + 0.984438i \(0.556229\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −12804.0 −0.695819
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 12224.0 0.658622 0.329311 − 0.944221i \(-0.393184\pi\)
0.329311 + 0.944221i \(0.393184\pi\)
\(702\) 0 0
\(703\) 2288.00 0.122750
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −11280.0 −0.600040
\(708\) 0 0
\(709\) 19510.0 1.03345 0.516723 − 0.856153i \(-0.327152\pi\)
0.516723 + 0.856153i \(0.327152\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −11808.0 −0.620215
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 3368.00 0.174694 0.0873472 − 0.996178i \(-0.472161\pi\)
0.0873472 + 0.996178i \(0.472161\pi\)
\(720\) 0 0
\(721\) −7580.00 −0.391531
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −22134.0 −1.12917 −0.564584 − 0.825376i \(-0.690963\pi\)
−0.564584 + 0.825376i \(0.690963\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −7128.00 −0.360655
\(732\) 0 0
\(733\) −32298.0 −1.62750 −0.813748 − 0.581219i \(-0.802576\pi\)
−0.813748 + 0.581219i \(0.802576\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −15088.0 −0.754103
\(738\) 0 0
\(739\) 25104.0 1.24962 0.624808 − 0.780779i \(-0.285177\pi\)
0.624808 + 0.780779i \(0.285177\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −27696.0 −1.36752 −0.683760 − 0.729707i \(-0.739657\pi\)
−0.683760 + 0.729707i \(0.739657\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −13240.0 −0.645900
\(750\) 0 0
\(751\) −2176.00 −0.105730 −0.0528651 − 0.998602i \(-0.516835\pi\)
−0.0528651 + 0.998602i \(0.516835\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −25514.0 −1.22500 −0.612498 − 0.790472i \(-0.709835\pi\)
−0.612498 + 0.790472i \(0.709835\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −18238.0 −0.868761 −0.434380 − 0.900730i \(-0.643033\pi\)
−0.434380 + 0.900730i \(0.643033\pi\)
\(762\) 0 0
\(763\) −16020.0 −0.760109
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −14484.0 −0.681860
\(768\) 0 0
\(769\) −14462.0 −0.678170 −0.339085 − 0.940756i \(-0.610118\pi\)
−0.339085 + 0.940756i \(0.610118\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 34034.0 1.58359 0.791797 − 0.610785i \(-0.209146\pi\)
0.791797 + 0.610785i \(0.209146\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −20176.0 −0.927959
\(780\) 0 0
\(781\) −8648.00 −0.396222
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −22064.0 −0.999360 −0.499680 − 0.866210i \(-0.666549\pi\)
−0.499680 + 0.866210i \(0.666549\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 20740.0 0.932275
\(792\) 0 0
\(793\) 23732.0 1.06273
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −23334.0 −1.03705 −0.518527 − 0.855061i \(-0.673520\pi\)
−0.518527 + 0.855061i \(0.673520\pi\)
\(798\) 0 0
\(799\) −31680.0 −1.40270
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 34040.0 1.49595
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 7566.00 0.328809 0.164404 − 0.986393i \(-0.447430\pi\)
0.164404 + 0.986393i \(0.447430\pi\)
\(810\) 0 0
\(811\) 5964.00 0.258230 0.129115 − 0.991630i \(-0.458786\pi\)
0.129115 + 0.991630i \(0.458786\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −11232.0 −0.480977
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 11880.0 0.505012 0.252506 − 0.967595i \(-0.418745\pi\)
0.252506 + 0.967595i \(0.418745\pi\)
\(822\) 0 0
\(823\) 1762.00 0.0746287 0.0373144 − 0.999304i \(-0.488120\pi\)
0.0373144 + 0.999304i \(0.488120\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −14124.0 −0.593881 −0.296941 − 0.954896i \(-0.595966\pi\)
−0.296941 + 0.954896i \(0.595966\pi\)
\(828\) 0 0
\(829\) −21350.0 −0.894471 −0.447235 − 0.894416i \(-0.647591\pi\)
−0.447235 + 0.894416i \(0.647591\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −16038.0 −0.667087
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 26136.0 1.07546 0.537732 − 0.843116i \(-0.319281\pi\)
0.537732 + 0.843116i \(0.319281\pi\)
\(840\) 0 0
\(841\) 25787.0 1.05732
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −7850.00 −0.318452
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 3608.00 0.145336
\(852\) 0 0
\(853\) 7030.00 0.282184 0.141092 − 0.989997i \(-0.454939\pi\)
0.141092 + 0.989997i \(0.454939\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −9574.00 −0.381612 −0.190806 − 0.981628i \(-0.561110\pi\)
−0.190806 + 0.981628i \(0.561110\pi\)
\(858\) 0 0
\(859\) −43748.0 −1.73767 −0.868837 − 0.495098i \(-0.835132\pi\)
−0.868837 + 0.495098i \(0.835132\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 41436.0 1.63441 0.817206 − 0.576345i \(-0.195522\pi\)
0.817206 + 0.576345i \(0.195522\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 53728.0 2.09735
\(870\) 0 0
\(871\) −11152.0 −0.433836
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −4606.00 −0.177347 −0.0886736 − 0.996061i \(-0.528263\pi\)
−0.0886736 + 0.996061i \(0.528263\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 4610.00 0.176294 0.0881469 − 0.996107i \(-0.471906\pi\)
0.0881469 + 0.996107i \(0.471906\pi\)
\(882\) 0 0
\(883\) −23512.0 −0.896084 −0.448042 − 0.894013i \(-0.647878\pi\)
−0.448042 + 0.894013i \(0.647878\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −30396.0 −1.15062 −0.575309 − 0.817936i \(-0.695118\pi\)
−0.575309 + 0.817936i \(0.695118\pi\)
\(888\) 0 0
\(889\) −5340.00 −0.201460
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −49920.0 −1.87067
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 16128.0 0.598330
\(900\) 0 0
\(901\) 18876.0 0.697948
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −3452.00 −0.126375 −0.0631873 − 0.998002i \(-0.520127\pi\)
−0.0631873 + 0.998002i \(0.520127\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −14256.0 −0.518466 −0.259233 − 0.965815i \(-0.583470\pi\)
−0.259233 + 0.965815i \(0.583470\pi\)
\(912\) 0 0
\(913\) 18952.0 0.686988
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 18060.0 0.650375
\(918\) 0 0
\(919\) 8064.00 0.289452 0.144726 − 0.989472i \(-0.453770\pi\)
0.144726 + 0.989472i \(0.453770\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −6392.00 −0.227947
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 40930.0 1.44550 0.722750 − 0.691109i \(-0.242878\pi\)
0.722750 + 0.691109i \(0.242878\pi\)
\(930\) 0 0
\(931\) −25272.0 −0.889642
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −9016.00 −0.314344 −0.157172 − 0.987571i \(-0.550238\pi\)
−0.157172 + 0.987571i \(0.550238\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 10444.0 0.361812 0.180906 − 0.983500i \(-0.442097\pi\)
0.180906 + 0.983500i \(0.442097\pi\)
\(942\) 0 0
\(943\) −31816.0 −1.09870
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 21516.0 0.738306 0.369153 − 0.929369i \(-0.379648\pi\)
0.369153 + 0.929369i \(0.379648\pi\)
\(948\) 0 0
\(949\) 25160.0 0.860620
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −28098.0 −0.955072 −0.477536 − 0.878612i \(-0.658470\pi\)
−0.477536 + 0.878612i \(0.658470\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −18220.0 −0.613508
\(960\) 0 0
\(961\) −24607.0 −0.825988
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 14558.0 0.484130 0.242065 − 0.970260i \(-0.422175\pi\)
0.242065 + 0.970260i \(0.422175\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −24846.0 −0.821160 −0.410580 − 0.911825i \(-0.634674\pi\)
−0.410580 + 0.911825i \(0.634674\pi\)
\(972\) 0 0
\(973\) −5320.00 −0.175284
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −12950.0 −0.424061 −0.212030 − 0.977263i \(-0.568008\pi\)
−0.212030 + 0.977263i \(0.568008\pi\)
\(978\) 0 0
\(979\) −55476.0 −1.81105
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −26728.0 −0.867234 −0.433617 − 0.901097i \(-0.642763\pi\)
−0.433617 + 0.901097i \(0.642763\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −17712.0 −0.569473
\(990\) 0 0
\(991\) 3880.00 0.124372 0.0621858 − 0.998065i \(-0.480193\pi\)
0.0621858 + 0.998065i \(0.480193\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −18582.0 −0.590269 −0.295134 − 0.955456i \(-0.595364\pi\)
−0.295134 + 0.955456i \(0.595364\pi\)
\(998\) 0 0
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1800.4.a.j.1.1 1
3.2 odd 2 600.4.a.b.1.1 1
5.2 odd 4 360.4.f.c.289.1 2
5.3 odd 4 360.4.f.c.289.2 2
5.4 even 2 1800.4.a.y.1.1 1
12.11 even 2 1200.4.a.bh.1.1 1
15.2 even 4 120.4.f.a.49.2 yes 2
15.8 even 4 120.4.f.a.49.1 ✓ 2
15.14 odd 2 600.4.a.o.1.1 1
20.3 even 4 720.4.f.g.289.2 2
20.7 even 4 720.4.f.g.289.1 2
60.23 odd 4 240.4.f.b.49.2 2
60.47 odd 4 240.4.f.b.49.1 2
60.59 even 2 1200.4.a.f.1.1 1
120.53 even 4 960.4.f.l.769.2 2
120.77 even 4 960.4.f.l.769.1 2
120.83 odd 4 960.4.f.g.769.1 2
120.107 odd 4 960.4.f.g.769.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
120.4.f.a.49.1 ✓ 2 15.8 even 4
120.4.f.a.49.2 yes 2 15.2 even 4
240.4.f.b.49.1 2 60.47 odd 4
240.4.f.b.49.2 2 60.23 odd 4
360.4.f.c.289.1 2 5.2 odd 4
360.4.f.c.289.2 2 5.3 odd 4
600.4.a.b.1.1 1 3.2 odd 2
600.4.a.o.1.1 1 15.14 odd 2
720.4.f.g.289.1 2 20.7 even 4
720.4.f.g.289.2 2 20.3 even 4
960.4.f.g.769.1 2 120.83 odd 4
960.4.f.g.769.2 2 120.107 odd 4
960.4.f.l.769.1 2 120.77 even 4
960.4.f.l.769.2 2 120.53 even 4
1200.4.a.f.1.1 1 60.59 even 2
1200.4.a.bh.1.1 1 12.11 even 2
1800.4.a.j.1.1 1 1.1 even 1 trivial
1800.4.a.y.1.1 1 5.4 even 2