Properties

Label 1305.4.a.c.1.1
Level $1305$
Weight $4$
Character 1305.1
Self dual yes
Analytic conductor $76.997$
Analytic rank $1$
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] = [1305,4,Mod(1,1305)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1305, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("1305.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1305 = 3^{2} \cdot 5 \cdot 29 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1305.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: \(76.9974925575\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 435)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1305.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -7.00000 q^{4} -5.00000 q^{5} +4.00000 q^{7} -15.0000 q^{8} +O(q^{10})\) \(q+1.00000 q^{2} -7.00000 q^{4} -5.00000 q^{5} +4.00000 q^{7} -15.0000 q^{8} -5.00000 q^{10} +36.0000 q^{11} -22.0000 q^{13} +4.00000 q^{14} +41.0000 q^{16} +2.00000 q^{17} -56.0000 q^{19} +35.0000 q^{20} +36.0000 q^{22} +40.0000 q^{23} +25.0000 q^{25} -22.0000 q^{26} -28.0000 q^{28} -29.0000 q^{29} +152.000 q^{31} +161.000 q^{32} +2.00000 q^{34} -20.0000 q^{35} +34.0000 q^{37} -56.0000 q^{38} +75.0000 q^{40} +250.000 q^{41} -412.000 q^{43} -252.000 q^{44} +40.0000 q^{46} +120.000 q^{47} -327.000 q^{49} +25.0000 q^{50} +154.000 q^{52} +762.000 q^{53} -180.000 q^{55} -60.0000 q^{56} -29.0000 q^{58} +188.000 q^{59} -54.0000 q^{61} +152.000 q^{62} -167.000 q^{64} +110.000 q^{65} -244.000 q^{67} -14.0000 q^{68} -20.0000 q^{70} -600.000 q^{71} +6.00000 q^{73} +34.0000 q^{74} +392.000 q^{76} +144.000 q^{77} -640.000 q^{79} -205.000 q^{80} +250.000 q^{82} -664.000 q^{83} -10.0000 q^{85} -412.000 q^{86} -540.000 q^{88} -150.000 q^{89} -88.0000 q^{91} -280.000 q^{92} +120.000 q^{94} +280.000 q^{95} -1690.00 q^{97} -327.000 q^{98} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.353553 0.176777 0.984251i \(-0.443433\pi\)
0.176777 + 0.984251i \(0.443433\pi\)
\(3\) 0 0
\(4\) −7.00000 −0.875000
\(5\) −5.00000 −0.447214
\(6\) 0 0
\(7\) 4.00000 0.215980 0.107990 0.994152i \(-0.465559\pi\)
0.107990 + 0.994152i \(0.465559\pi\)
\(8\) −15.0000 −0.662913
\(9\) 0 0
\(10\) −5.00000 −0.158114
\(11\) 36.0000 0.986764 0.493382 0.869813i \(-0.335760\pi\)
0.493382 + 0.869813i \(0.335760\pi\)
\(12\) 0 0
\(13\) −22.0000 −0.469362 −0.234681 0.972072i \(-0.575405\pi\)
−0.234681 + 0.972072i \(0.575405\pi\)
\(14\) 4.00000 0.0763604
\(15\) 0 0
\(16\) 41.0000 0.640625
\(17\) 2.00000 0.0285336 0.0142668 0.999898i \(-0.495459\pi\)
0.0142668 + 0.999898i \(0.495459\pi\)
\(18\) 0 0
\(19\) −56.0000 −0.676173 −0.338086 0.941115i \(-0.609780\pi\)
−0.338086 + 0.941115i \(0.609780\pi\)
\(20\) 35.0000 0.391312
\(21\) 0 0
\(22\) 36.0000 0.348874
\(23\) 40.0000 0.362634 0.181317 0.983425i \(-0.441964\pi\)
0.181317 + 0.983425i \(0.441964\pi\)
\(24\) 0 0
\(25\) 25.0000 0.200000
\(26\) −22.0000 −0.165944
\(27\) 0 0
\(28\) −28.0000 −0.188982
\(29\) −29.0000 −0.185695
\(30\) 0 0
\(31\) 152.000 0.880645 0.440323 0.897840i \(-0.354864\pi\)
0.440323 + 0.897840i \(0.354864\pi\)
\(32\) 161.000 0.889408
\(33\) 0 0
\(34\) 2.00000 0.0100882
\(35\) −20.0000 −0.0965891
\(36\) 0 0
\(37\) 34.0000 0.151069 0.0755347 0.997143i \(-0.475934\pi\)
0.0755347 + 0.997143i \(0.475934\pi\)
\(38\) −56.0000 −0.239063
\(39\) 0 0
\(40\) 75.0000 0.296464
\(41\) 250.000 0.952279 0.476140 0.879370i \(-0.342036\pi\)
0.476140 + 0.879370i \(0.342036\pi\)
\(42\) 0 0
\(43\) −412.000 −1.46115 −0.730575 0.682833i \(-0.760748\pi\)
−0.730575 + 0.682833i \(0.760748\pi\)
\(44\) −252.000 −0.863419
\(45\) 0 0
\(46\) 40.0000 0.128210
\(47\) 120.000 0.372421 0.186211 0.982510i \(-0.440379\pi\)
0.186211 + 0.982510i \(0.440379\pi\)
\(48\) 0 0
\(49\) −327.000 −0.953353
\(50\) 25.0000 0.0707107
\(51\) 0 0
\(52\) 154.000 0.410691
\(53\) 762.000 1.97488 0.987441 0.157988i \(-0.0505007\pi\)
0.987441 + 0.157988i \(0.0505007\pi\)
\(54\) 0 0
\(55\) −180.000 −0.441294
\(56\) −60.0000 −0.143176
\(57\) 0 0
\(58\) −29.0000 −0.0656532
\(59\) 188.000 0.414839 0.207420 0.978252i \(-0.433493\pi\)
0.207420 + 0.978252i \(0.433493\pi\)
\(60\) 0 0
\(61\) −54.0000 −0.113344 −0.0566721 0.998393i \(-0.518049\pi\)
−0.0566721 + 0.998393i \(0.518049\pi\)
\(62\) 152.000 0.311355
\(63\) 0 0
\(64\) −167.000 −0.326172
\(65\) 110.000 0.209905
\(66\) 0 0
\(67\) −244.000 −0.444916 −0.222458 0.974942i \(-0.571408\pi\)
−0.222458 + 0.974942i \(0.571408\pi\)
\(68\) −14.0000 −0.0249669
\(69\) 0 0
\(70\) −20.0000 −0.0341494
\(71\) −600.000 −1.00291 −0.501457 0.865183i \(-0.667202\pi\)
−0.501457 + 0.865183i \(0.667202\pi\)
\(72\) 0 0
\(73\) 6.00000 0.00961982 0.00480991 0.999988i \(-0.498469\pi\)
0.00480991 + 0.999988i \(0.498469\pi\)
\(74\) 34.0000 0.0534111
\(75\) 0 0
\(76\) 392.000 0.591651
\(77\) 144.000 0.213121
\(78\) 0 0
\(79\) −640.000 −0.911464 −0.455732 0.890117i \(-0.650622\pi\)
−0.455732 + 0.890117i \(0.650622\pi\)
\(80\) −205.000 −0.286496
\(81\) 0 0
\(82\) 250.000 0.336681
\(83\) −664.000 −0.878114 −0.439057 0.898459i \(-0.644687\pi\)
−0.439057 + 0.898459i \(0.644687\pi\)
\(84\) 0 0
\(85\) −10.0000 −0.0127606
\(86\) −412.000 −0.516594
\(87\) 0 0
\(88\) −540.000 −0.654139
\(89\) −150.000 −0.178651 −0.0893257 0.996002i \(-0.528471\pi\)
−0.0893257 + 0.996002i \(0.528471\pi\)
\(90\) 0 0
\(91\) −88.0000 −0.101373
\(92\) −280.000 −0.317305
\(93\) 0 0
\(94\) 120.000 0.131671
\(95\) 280.000 0.302394
\(96\) 0 0
\(97\) −1690.00 −1.76901 −0.884503 0.466535i \(-0.845502\pi\)
−0.884503 + 0.466535i \(0.845502\pi\)
\(98\) −327.000 −0.337061
\(99\) 0 0
\(100\) −175.000 −0.175000
\(101\) −502.000 −0.494563 −0.247282 0.968944i \(-0.579537\pi\)
−0.247282 + 0.968944i \(0.579537\pi\)
\(102\) 0 0
\(103\) −828.000 −0.792090 −0.396045 0.918231i \(-0.629618\pi\)
−0.396045 + 0.918231i \(0.629618\pi\)
\(104\) 330.000 0.311146
\(105\) 0 0
\(106\) 762.000 0.698226
\(107\) 1176.00 1.06251 0.531253 0.847213i \(-0.321721\pi\)
0.531253 + 0.847213i \(0.321721\pi\)
\(108\) 0 0
\(109\) −1922.00 −1.68894 −0.844469 0.535605i \(-0.820084\pi\)
−0.844469 + 0.535605i \(0.820084\pi\)
\(110\) −180.000 −0.156021
\(111\) 0 0
\(112\) 164.000 0.138362
\(113\) 322.000 0.268064 0.134032 0.990977i \(-0.457208\pi\)
0.134032 + 0.990977i \(0.457208\pi\)
\(114\) 0 0
\(115\) −200.000 −0.162175
\(116\) 203.000 0.162483
\(117\) 0 0
\(118\) 188.000 0.146668
\(119\) 8.00000 0.00616268
\(120\) 0 0
\(121\) −35.0000 −0.0262960
\(122\) −54.0000 −0.0400732
\(123\) 0 0
\(124\) −1064.00 −0.770565
\(125\) −125.000 −0.0894427
\(126\) 0 0
\(127\) 1568.00 1.09557 0.547785 0.836619i \(-0.315471\pi\)
0.547785 + 0.836619i \(0.315471\pi\)
\(128\) −1455.00 −1.00473
\(129\) 0 0
\(130\) 110.000 0.0742126
\(131\) −1124.00 −0.749651 −0.374826 0.927095i \(-0.622297\pi\)
−0.374826 + 0.927095i \(0.622297\pi\)
\(132\) 0 0
\(133\) −224.000 −0.146040
\(134\) −244.000 −0.157301
\(135\) 0 0
\(136\) −30.0000 −0.0189153
\(137\) −2646.00 −1.65010 −0.825048 0.565063i \(-0.808852\pi\)
−0.825048 + 0.565063i \(0.808852\pi\)
\(138\) 0 0
\(139\) −1956.00 −1.19357 −0.596783 0.802402i \(-0.703555\pi\)
−0.596783 + 0.802402i \(0.703555\pi\)
\(140\) 140.000 0.0845154
\(141\) 0 0
\(142\) −600.000 −0.354584
\(143\) −792.000 −0.463149
\(144\) 0 0
\(145\) 145.000 0.0830455
\(146\) 6.00000 0.00340112
\(147\) 0 0
\(148\) −238.000 −0.132186
\(149\) −2126.00 −1.16892 −0.584459 0.811423i \(-0.698693\pi\)
−0.584459 + 0.811423i \(0.698693\pi\)
\(150\) 0 0
\(151\) 1208.00 0.651031 0.325515 0.945537i \(-0.394462\pi\)
0.325515 + 0.945537i \(0.394462\pi\)
\(152\) 840.000 0.448243
\(153\) 0 0
\(154\) 144.000 0.0753497
\(155\) −760.000 −0.393837
\(156\) 0 0
\(157\) 490.000 0.249084 0.124542 0.992214i \(-0.460254\pi\)
0.124542 + 0.992214i \(0.460254\pi\)
\(158\) −640.000 −0.322251
\(159\) 0 0
\(160\) −805.000 −0.397755
\(161\) 160.000 0.0783215
\(162\) 0 0
\(163\) 1780.00 0.855340 0.427670 0.903935i \(-0.359335\pi\)
0.427670 + 0.903935i \(0.359335\pi\)
\(164\) −1750.00 −0.833244
\(165\) 0 0
\(166\) −664.000 −0.310460
\(167\) −2520.00 −1.16769 −0.583843 0.811867i \(-0.698452\pi\)
−0.583843 + 0.811867i \(0.698452\pi\)
\(168\) 0 0
\(169\) −1713.00 −0.779700
\(170\) −10.0000 −0.00451156
\(171\) 0 0
\(172\) 2884.00 1.27851
\(173\) −382.000 −0.167878 −0.0839391 0.996471i \(-0.526750\pi\)
−0.0839391 + 0.996471i \(0.526750\pi\)
\(174\) 0 0
\(175\) 100.000 0.0431959
\(176\) 1476.00 0.632146
\(177\) 0 0
\(178\) −150.000 −0.0631628
\(179\) 1908.00 0.796707 0.398354 0.917232i \(-0.369582\pi\)
0.398354 + 0.917232i \(0.369582\pi\)
\(180\) 0 0
\(181\) −450.000 −0.184797 −0.0923984 0.995722i \(-0.529453\pi\)
−0.0923984 + 0.995722i \(0.529453\pi\)
\(182\) −88.0000 −0.0358406
\(183\) 0 0
\(184\) −600.000 −0.240394
\(185\) −170.000 −0.0675603
\(186\) 0 0
\(187\) 72.0000 0.0281559
\(188\) −840.000 −0.325869
\(189\) 0 0
\(190\) 280.000 0.106912
\(191\) −1412.00 −0.534915 −0.267457 0.963570i \(-0.586183\pi\)
−0.267457 + 0.963570i \(0.586183\pi\)
\(192\) 0 0
\(193\) −418.000 −0.155898 −0.0779490 0.996957i \(-0.524837\pi\)
−0.0779490 + 0.996957i \(0.524837\pi\)
\(194\) −1690.00 −0.625438
\(195\) 0 0
\(196\) 2289.00 0.834184
\(197\) −3182.00 −1.15080 −0.575401 0.817871i \(-0.695154\pi\)
−0.575401 + 0.817871i \(0.695154\pi\)
\(198\) 0 0
\(199\) 4976.00 1.77256 0.886280 0.463151i \(-0.153281\pi\)
0.886280 + 0.463151i \(0.153281\pi\)
\(200\) −375.000 −0.132583
\(201\) 0 0
\(202\) −502.000 −0.174854
\(203\) −116.000 −0.0401064
\(204\) 0 0
\(205\) −1250.00 −0.425872
\(206\) −828.000 −0.280046
\(207\) 0 0
\(208\) −902.000 −0.300685
\(209\) −2016.00 −0.667223
\(210\) 0 0
\(211\) −640.000 −0.208812 −0.104406 0.994535i \(-0.533294\pi\)
−0.104406 + 0.994535i \(0.533294\pi\)
\(212\) −5334.00 −1.72802
\(213\) 0 0
\(214\) 1176.00 0.375653
\(215\) 2060.00 0.653446
\(216\) 0 0
\(217\) 608.000 0.190202
\(218\) −1922.00 −0.597130
\(219\) 0 0
\(220\) 1260.00 0.386133
\(221\) −44.0000 −0.0133926
\(222\) 0 0
\(223\) −1724.00 −0.517702 −0.258851 0.965917i \(-0.583344\pi\)
−0.258851 + 0.965917i \(0.583344\pi\)
\(224\) 644.000 0.192094
\(225\) 0 0
\(226\) 322.000 0.0947749
\(227\) −1216.00 −0.355545 −0.177773 0.984072i \(-0.556889\pi\)
−0.177773 + 0.984072i \(0.556889\pi\)
\(228\) 0 0
\(229\) −1806.00 −0.521152 −0.260576 0.965453i \(-0.583912\pi\)
−0.260576 + 0.965453i \(0.583912\pi\)
\(230\) −200.000 −0.0573374
\(231\) 0 0
\(232\) 435.000 0.123100
\(233\) −3654.00 −1.02739 −0.513694 0.857973i \(-0.671723\pi\)
−0.513694 + 0.857973i \(0.671723\pi\)
\(234\) 0 0
\(235\) −600.000 −0.166552
\(236\) −1316.00 −0.362984
\(237\) 0 0
\(238\) 8.00000 0.00217884
\(239\) 5304.00 1.43551 0.717756 0.696295i \(-0.245169\pi\)
0.717756 + 0.696295i \(0.245169\pi\)
\(240\) 0 0
\(241\) 4402.00 1.17659 0.588294 0.808647i \(-0.299800\pi\)
0.588294 + 0.808647i \(0.299800\pi\)
\(242\) −35.0000 −0.00929705
\(243\) 0 0
\(244\) 378.000 0.0991761
\(245\) 1635.00 0.426352
\(246\) 0 0
\(247\) 1232.00 0.317370
\(248\) −2280.00 −0.583791
\(249\) 0 0
\(250\) −125.000 −0.0316228
\(251\) −2268.00 −0.570338 −0.285169 0.958477i \(-0.592050\pi\)
−0.285169 + 0.958477i \(0.592050\pi\)
\(252\) 0 0
\(253\) 1440.00 0.357834
\(254\) 1568.00 0.387343
\(255\) 0 0
\(256\) −119.000 −0.0290527
\(257\) −534.000 −0.129611 −0.0648055 0.997898i \(-0.520643\pi\)
−0.0648055 + 0.997898i \(0.520643\pi\)
\(258\) 0 0
\(259\) 136.000 0.0326279
\(260\) −770.000 −0.183667
\(261\) 0 0
\(262\) −1124.00 −0.265042
\(263\) −5592.00 −1.31109 −0.655547 0.755155i \(-0.727562\pi\)
−0.655547 + 0.755155i \(0.727562\pi\)
\(264\) 0 0
\(265\) −3810.00 −0.883194
\(266\) −224.000 −0.0516328
\(267\) 0 0
\(268\) 1708.00 0.389301
\(269\) 6562.00 1.48733 0.743666 0.668552i \(-0.233085\pi\)
0.743666 + 0.668552i \(0.233085\pi\)
\(270\) 0 0
\(271\) 1192.00 0.267191 0.133596 0.991036i \(-0.457348\pi\)
0.133596 + 0.991036i \(0.457348\pi\)
\(272\) 82.0000 0.0182793
\(273\) 0 0
\(274\) −2646.00 −0.583397
\(275\) 900.000 0.197353
\(276\) 0 0
\(277\) 6474.00 1.40428 0.702139 0.712040i \(-0.252229\pi\)
0.702139 + 0.712040i \(0.252229\pi\)
\(278\) −1956.00 −0.421990
\(279\) 0 0
\(280\) 300.000 0.0640301
\(281\) 3758.00 0.797806 0.398903 0.916993i \(-0.369391\pi\)
0.398903 + 0.916993i \(0.369391\pi\)
\(282\) 0 0
\(283\) 292.000 0.0613343 0.0306671 0.999530i \(-0.490237\pi\)
0.0306671 + 0.999530i \(0.490237\pi\)
\(284\) 4200.00 0.877550
\(285\) 0 0
\(286\) −792.000 −0.163748
\(287\) 1000.00 0.205673
\(288\) 0 0
\(289\) −4909.00 −0.999186
\(290\) 145.000 0.0293610
\(291\) 0 0
\(292\) −42.0000 −0.00841734
\(293\) 1382.00 0.275554 0.137777 0.990463i \(-0.456004\pi\)
0.137777 + 0.990463i \(0.456004\pi\)
\(294\) 0 0
\(295\) −940.000 −0.185522
\(296\) −510.000 −0.100146
\(297\) 0 0
\(298\) −2126.00 −0.413275
\(299\) −880.000 −0.170206
\(300\) 0 0
\(301\) −1648.00 −0.315579
\(302\) 1208.00 0.230174
\(303\) 0 0
\(304\) −2296.00 −0.433173
\(305\) 270.000 0.0506890
\(306\) 0 0
\(307\) −3948.00 −0.733955 −0.366978 0.930230i \(-0.619607\pi\)
−0.366978 + 0.930230i \(0.619607\pi\)
\(308\) −1008.00 −0.186481
\(309\) 0 0
\(310\) −760.000 −0.139242
\(311\) 7396.00 1.34852 0.674258 0.738496i \(-0.264463\pi\)
0.674258 + 0.738496i \(0.264463\pi\)
\(312\) 0 0
\(313\) 3290.00 0.594127 0.297064 0.954858i \(-0.403993\pi\)
0.297064 + 0.954858i \(0.403993\pi\)
\(314\) 490.000 0.0880646
\(315\) 0 0
\(316\) 4480.00 0.797531
\(317\) 1670.00 0.295888 0.147944 0.988996i \(-0.452734\pi\)
0.147944 + 0.988996i \(0.452734\pi\)
\(318\) 0 0
\(319\) −1044.00 −0.183238
\(320\) 835.000 0.145868
\(321\) 0 0
\(322\) 160.000 0.0276908
\(323\) −112.000 −0.0192936
\(324\) 0 0
\(325\) −550.000 −0.0938723
\(326\) 1780.00 0.302408
\(327\) 0 0
\(328\) −3750.00 −0.631278
\(329\) 480.000 0.0804354
\(330\) 0 0
\(331\) 912.000 0.151444 0.0757221 0.997129i \(-0.475874\pi\)
0.0757221 + 0.997129i \(0.475874\pi\)
\(332\) 4648.00 0.768350
\(333\) 0 0
\(334\) −2520.00 −0.412839
\(335\) 1220.00 0.198972
\(336\) 0 0
\(337\) −3082.00 −0.498182 −0.249091 0.968480i \(-0.580132\pi\)
−0.249091 + 0.968480i \(0.580132\pi\)
\(338\) −1713.00 −0.275665
\(339\) 0 0
\(340\) 70.0000 0.0111655
\(341\) 5472.00 0.868989
\(342\) 0 0
\(343\) −2680.00 −0.421885
\(344\) 6180.00 0.968614
\(345\) 0 0
\(346\) −382.000 −0.0593539
\(347\) 4536.00 0.701744 0.350872 0.936423i \(-0.385885\pi\)
0.350872 + 0.936423i \(0.385885\pi\)
\(348\) 0 0
\(349\) −7130.00 −1.09358 −0.546791 0.837269i \(-0.684151\pi\)
−0.546791 + 0.837269i \(0.684151\pi\)
\(350\) 100.000 0.0152721
\(351\) 0 0
\(352\) 5796.00 0.877636
\(353\) −6814.00 −1.02740 −0.513701 0.857970i \(-0.671726\pi\)
−0.513701 + 0.857970i \(0.671726\pi\)
\(354\) 0 0
\(355\) 3000.00 0.448517
\(356\) 1050.00 0.156320
\(357\) 0 0
\(358\) 1908.00 0.281679
\(359\) −8188.00 −1.20375 −0.601875 0.798590i \(-0.705579\pi\)
−0.601875 + 0.798590i \(0.705579\pi\)
\(360\) 0 0
\(361\) −3723.00 −0.542790
\(362\) −450.000 −0.0653356
\(363\) 0 0
\(364\) 616.000 0.0887010
\(365\) −30.0000 −0.00430211
\(366\) 0 0
\(367\) 624.000 0.0887535 0.0443768 0.999015i \(-0.485870\pi\)
0.0443768 + 0.999015i \(0.485870\pi\)
\(368\) 1640.00 0.232312
\(369\) 0 0
\(370\) −170.000 −0.0238862
\(371\) 3048.00 0.426534
\(372\) 0 0
\(373\) −1206.00 −0.167411 −0.0837055 0.996491i \(-0.526676\pi\)
−0.0837055 + 0.996491i \(0.526676\pi\)
\(374\) 72.0000 0.00995463
\(375\) 0 0
\(376\) −1800.00 −0.246883
\(377\) 638.000 0.0871583
\(378\) 0 0
\(379\) −1728.00 −0.234199 −0.117099 0.993120i \(-0.537360\pi\)
−0.117099 + 0.993120i \(0.537360\pi\)
\(380\) −1960.00 −0.264594
\(381\) 0 0
\(382\) −1412.00 −0.189121
\(383\) −3752.00 −0.500570 −0.250285 0.968172i \(-0.580524\pi\)
−0.250285 + 0.968172i \(0.580524\pi\)
\(384\) 0 0
\(385\) −720.000 −0.0953106
\(386\) −418.000 −0.0551182
\(387\) 0 0
\(388\) 11830.0 1.54788
\(389\) 1250.00 0.162924 0.0814621 0.996676i \(-0.474041\pi\)
0.0814621 + 0.996676i \(0.474041\pi\)
\(390\) 0 0
\(391\) 80.0000 0.0103472
\(392\) 4905.00 0.631990
\(393\) 0 0
\(394\) −3182.00 −0.406870
\(395\) 3200.00 0.407619
\(396\) 0 0
\(397\) 3210.00 0.405807 0.202903 0.979199i \(-0.434962\pi\)
0.202903 + 0.979199i \(0.434962\pi\)
\(398\) 4976.00 0.626694
\(399\) 0 0
\(400\) 1025.00 0.128125
\(401\) −11314.0 −1.40896 −0.704482 0.709722i \(-0.748820\pi\)
−0.704482 + 0.709722i \(0.748820\pi\)
\(402\) 0 0
\(403\) −3344.00 −0.413341
\(404\) 3514.00 0.432743
\(405\) 0 0
\(406\) −116.000 −0.0141798
\(407\) 1224.00 0.149070
\(408\) 0 0
\(409\) −2518.00 −0.304418 −0.152209 0.988348i \(-0.548639\pi\)
−0.152209 + 0.988348i \(0.548639\pi\)
\(410\) −1250.00 −0.150569
\(411\) 0 0
\(412\) 5796.00 0.693079
\(413\) 752.000 0.0895969
\(414\) 0 0
\(415\) 3320.00 0.392705
\(416\) −3542.00 −0.417454
\(417\) 0 0
\(418\) −2016.00 −0.235899
\(419\) 4172.00 0.486433 0.243217 0.969972i \(-0.421797\pi\)
0.243217 + 0.969972i \(0.421797\pi\)
\(420\) 0 0
\(421\) −15838.0 −1.83348 −0.916742 0.399479i \(-0.869191\pi\)
−0.916742 + 0.399479i \(0.869191\pi\)
\(422\) −640.000 −0.0738263
\(423\) 0 0
\(424\) −11430.0 −1.30917
\(425\) 50.0000 0.00570672
\(426\) 0 0
\(427\) −216.000 −0.0244800
\(428\) −8232.00 −0.929693
\(429\) 0 0
\(430\) 2060.00 0.231028
\(431\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) 0 0
\(433\) 7718.00 0.856590 0.428295 0.903639i \(-0.359114\pi\)
0.428295 + 0.903639i \(0.359114\pi\)
\(434\) 608.000 0.0672464
\(435\) 0 0
\(436\) 13454.0 1.47782
\(437\) −2240.00 −0.245203
\(438\) 0 0
\(439\) 6720.00 0.730588 0.365294 0.930892i \(-0.380968\pi\)
0.365294 + 0.930892i \(0.380968\pi\)
\(440\) 2700.00 0.292540
\(441\) 0 0
\(442\) −44.0000 −0.00473499
\(443\) 8652.00 0.927921 0.463960 0.885856i \(-0.346428\pi\)
0.463960 + 0.885856i \(0.346428\pi\)
\(444\) 0 0
\(445\) 750.000 0.0798953
\(446\) −1724.00 −0.183035
\(447\) 0 0
\(448\) −668.000 −0.0704465
\(449\) −4606.00 −0.484122 −0.242061 0.970261i \(-0.577823\pi\)
−0.242061 + 0.970261i \(0.577823\pi\)
\(450\) 0 0
\(451\) 9000.00 0.939675
\(452\) −2254.00 −0.234556
\(453\) 0 0
\(454\) −1216.00 −0.125704
\(455\) 440.000 0.0453352
\(456\) 0 0
\(457\) 1642.00 0.168073 0.0840367 0.996463i \(-0.473219\pi\)
0.0840367 + 0.996463i \(0.473219\pi\)
\(458\) −1806.00 −0.184255
\(459\) 0 0
\(460\) 1400.00 0.141903
\(461\) 3930.00 0.397046 0.198523 0.980096i \(-0.436385\pi\)
0.198523 + 0.980096i \(0.436385\pi\)
\(462\) 0 0
\(463\) −10076.0 −1.01139 −0.505693 0.862714i \(-0.668763\pi\)
−0.505693 + 0.862714i \(0.668763\pi\)
\(464\) −1189.00 −0.118961
\(465\) 0 0
\(466\) −3654.00 −0.363237
\(467\) 3348.00 0.331749 0.165875 0.986147i \(-0.446955\pi\)
0.165875 + 0.986147i \(0.446955\pi\)
\(468\) 0 0
\(469\) −976.000 −0.0960927
\(470\) −600.000 −0.0588850
\(471\) 0 0
\(472\) −2820.00 −0.275002
\(473\) −14832.0 −1.44181
\(474\) 0 0
\(475\) −1400.00 −0.135235
\(476\) −56.0000 −0.00539234
\(477\) 0 0
\(478\) 5304.00 0.507530
\(479\) −3412.00 −0.325466 −0.162733 0.986670i \(-0.552031\pi\)
−0.162733 + 0.986670i \(0.552031\pi\)
\(480\) 0 0
\(481\) −748.000 −0.0709062
\(482\) 4402.00 0.415987
\(483\) 0 0
\(484\) 245.000 0.0230090
\(485\) 8450.00 0.791123
\(486\) 0 0
\(487\) −13084.0 −1.21744 −0.608719 0.793386i \(-0.708316\pi\)
−0.608719 + 0.793386i \(0.708316\pi\)
\(488\) 810.000 0.0751372
\(489\) 0 0
\(490\) 1635.00 0.150738
\(491\) −11788.0 −1.08347 −0.541736 0.840549i \(-0.682233\pi\)
−0.541736 + 0.840549i \(0.682233\pi\)
\(492\) 0 0
\(493\) −58.0000 −0.00529856
\(494\) 1232.00 0.112207
\(495\) 0 0
\(496\) 6232.00 0.564163
\(497\) −2400.00 −0.216609
\(498\) 0 0
\(499\) −17484.0 −1.56852 −0.784260 0.620432i \(-0.786957\pi\)
−0.784260 + 0.620432i \(0.786957\pi\)
\(500\) 875.000 0.0782624
\(501\) 0 0
\(502\) −2268.00 −0.201645
\(503\) −8992.00 −0.797084 −0.398542 0.917150i \(-0.630484\pi\)
−0.398542 + 0.917150i \(0.630484\pi\)
\(504\) 0 0
\(505\) 2510.00 0.221175
\(506\) 1440.00 0.126513
\(507\) 0 0
\(508\) −10976.0 −0.958625
\(509\) −1510.00 −0.131492 −0.0657461 0.997836i \(-0.520943\pi\)
−0.0657461 + 0.997836i \(0.520943\pi\)
\(510\) 0 0
\(511\) 24.0000 0.00207769
\(512\) 11521.0 0.994455
\(513\) 0 0
\(514\) −534.000 −0.0458244
\(515\) 4140.00 0.354233
\(516\) 0 0
\(517\) 4320.00 0.367492
\(518\) 136.000 0.0115357
\(519\) 0 0
\(520\) −1650.00 −0.139149
\(521\) −1482.00 −0.124621 −0.0623106 0.998057i \(-0.519847\pi\)
−0.0623106 + 0.998057i \(0.519847\pi\)
\(522\) 0 0
\(523\) −7524.00 −0.629066 −0.314533 0.949247i \(-0.601848\pi\)
−0.314533 + 0.949247i \(0.601848\pi\)
\(524\) 7868.00 0.655945
\(525\) 0 0
\(526\) −5592.00 −0.463541
\(527\) 304.000 0.0251280
\(528\) 0 0
\(529\) −10567.0 −0.868497
\(530\) −3810.00 −0.312256
\(531\) 0 0
\(532\) 1568.00 0.127785
\(533\) −5500.00 −0.446963
\(534\) 0 0
\(535\) −5880.00 −0.475167
\(536\) 3660.00 0.294940
\(537\) 0 0
\(538\) 6562.00 0.525851
\(539\) −11772.0 −0.940735
\(540\) 0 0
\(541\) 7426.00 0.590145 0.295073 0.955475i \(-0.404656\pi\)
0.295073 + 0.955475i \(0.404656\pi\)
\(542\) 1192.00 0.0944664
\(543\) 0 0
\(544\) 322.000 0.0253780
\(545\) 9610.00 0.755316
\(546\) 0 0
\(547\) 25156.0 1.96635 0.983174 0.182669i \(-0.0584736\pi\)
0.983174 + 0.182669i \(0.0584736\pi\)
\(548\) 18522.0 1.44383
\(549\) 0 0
\(550\) 900.000 0.0697748
\(551\) 1624.00 0.125562
\(552\) 0 0
\(553\) −2560.00 −0.196858
\(554\) 6474.00 0.496487
\(555\) 0 0
\(556\) 13692.0 1.04437
\(557\) 8890.00 0.676268 0.338134 0.941098i \(-0.390204\pi\)
0.338134 + 0.941098i \(0.390204\pi\)
\(558\) 0 0
\(559\) 9064.00 0.685807
\(560\) −820.000 −0.0618774
\(561\) 0 0
\(562\) 3758.00 0.282067
\(563\) 18028.0 1.34954 0.674769 0.738029i \(-0.264243\pi\)
0.674769 + 0.738029i \(0.264243\pi\)
\(564\) 0 0
\(565\) −1610.00 −0.119882
\(566\) 292.000 0.0216849
\(567\) 0 0
\(568\) 9000.00 0.664844
\(569\) 6706.00 0.494078 0.247039 0.969006i \(-0.420542\pi\)
0.247039 + 0.969006i \(0.420542\pi\)
\(570\) 0 0
\(571\) 10060.0 0.737299 0.368650 0.929568i \(-0.379820\pi\)
0.368650 + 0.929568i \(0.379820\pi\)
\(572\) 5544.00 0.405256
\(573\) 0 0
\(574\) 1000.00 0.0727164
\(575\) 1000.00 0.0725268
\(576\) 0 0
\(577\) 2974.00 0.214574 0.107287 0.994228i \(-0.465784\pi\)
0.107287 + 0.994228i \(0.465784\pi\)
\(578\) −4909.00 −0.353266
\(579\) 0 0
\(580\) −1015.00 −0.0726648
\(581\) −2656.00 −0.189655
\(582\) 0 0
\(583\) 27432.0 1.94874
\(584\) −90.0000 −0.00637710
\(585\) 0 0
\(586\) 1382.00 0.0974230
\(587\) −2424.00 −0.170442 −0.0852208 0.996362i \(-0.527160\pi\)
−0.0852208 + 0.996362i \(0.527160\pi\)
\(588\) 0 0
\(589\) −8512.00 −0.595468
\(590\) −940.000 −0.0655918
\(591\) 0 0
\(592\) 1394.00 0.0967788
\(593\) 15002.0 1.03888 0.519442 0.854506i \(-0.326140\pi\)
0.519442 + 0.854506i \(0.326140\pi\)
\(594\) 0 0
\(595\) −40.0000 −0.00275603
\(596\) 14882.0 1.02280
\(597\) 0 0
\(598\) −880.000 −0.0601771
\(599\) −3636.00 −0.248018 −0.124009 0.992281i \(-0.539575\pi\)
−0.124009 + 0.992281i \(0.539575\pi\)
\(600\) 0 0
\(601\) −13534.0 −0.918575 −0.459287 0.888288i \(-0.651895\pi\)
−0.459287 + 0.888288i \(0.651895\pi\)
\(602\) −1648.00 −0.111574
\(603\) 0 0
\(604\) −8456.00 −0.569652
\(605\) 175.000 0.0117599
\(606\) 0 0
\(607\) 6760.00 0.452026 0.226013 0.974124i \(-0.427431\pi\)
0.226013 + 0.974124i \(0.427431\pi\)
\(608\) −9016.00 −0.601393
\(609\) 0 0
\(610\) 270.000 0.0179213
\(611\) −2640.00 −0.174800
\(612\) 0 0
\(613\) 15762.0 1.03853 0.519267 0.854612i \(-0.326205\pi\)
0.519267 + 0.854612i \(0.326205\pi\)
\(614\) −3948.00 −0.259492
\(615\) 0 0
\(616\) −2160.00 −0.141281
\(617\) 27786.0 1.81300 0.906501 0.422204i \(-0.138743\pi\)
0.906501 + 0.422204i \(0.138743\pi\)
\(618\) 0 0
\(619\) 17648.0 1.14593 0.572967 0.819579i \(-0.305792\pi\)
0.572967 + 0.819579i \(0.305792\pi\)
\(620\) 5320.00 0.344607
\(621\) 0 0
\(622\) 7396.00 0.476773
\(623\) −600.000 −0.0385851
\(624\) 0 0
\(625\) 625.000 0.0400000
\(626\) 3290.00 0.210056
\(627\) 0 0
\(628\) −3430.00 −0.217949
\(629\) 68.0000 0.00431055
\(630\) 0 0
\(631\) −13136.0 −0.828742 −0.414371 0.910108i \(-0.635998\pi\)
−0.414371 + 0.910108i \(0.635998\pi\)
\(632\) 9600.00 0.604221
\(633\) 0 0
\(634\) 1670.00 0.104612
\(635\) −7840.00 −0.489954
\(636\) 0 0
\(637\) 7194.00 0.447467
\(638\) −1044.00 −0.0647843
\(639\) 0 0
\(640\) 7275.00 0.449328
\(641\) −21974.0 −1.35401 −0.677005 0.735978i \(-0.736723\pi\)
−0.677005 + 0.735978i \(0.736723\pi\)
\(642\) 0 0
\(643\) 21748.0 1.33384 0.666919 0.745131i \(-0.267613\pi\)
0.666919 + 0.745131i \(0.267613\pi\)
\(644\) −1120.00 −0.0685313
\(645\) 0 0
\(646\) −112.000 −0.00682133
\(647\) −31128.0 −1.89145 −0.945725 0.324968i \(-0.894646\pi\)
−0.945725 + 0.324968i \(0.894646\pi\)
\(648\) 0 0
\(649\) 6768.00 0.409349
\(650\) −550.000 −0.0331889
\(651\) 0 0
\(652\) −12460.0 −0.748422
\(653\) 22.0000 0.00131842 0.000659209 1.00000i \(-0.499790\pi\)
0.000659209 1.00000i \(0.499790\pi\)
\(654\) 0 0
\(655\) 5620.00 0.335254
\(656\) 10250.0 0.610054
\(657\) 0 0
\(658\) 480.000 0.0284382
\(659\) −25396.0 −1.50120 −0.750598 0.660760i \(-0.770234\pi\)
−0.750598 + 0.660760i \(0.770234\pi\)
\(660\) 0 0
\(661\) 23534.0 1.38482 0.692410 0.721504i \(-0.256549\pi\)
0.692410 + 0.721504i \(0.256549\pi\)
\(662\) 912.000 0.0535436
\(663\) 0 0
\(664\) 9960.00 0.582113
\(665\) 1120.00 0.0653109
\(666\) 0 0
\(667\) −1160.00 −0.0673394
\(668\) 17640.0 1.02172
\(669\) 0 0
\(670\) 1220.00 0.0703473
\(671\) −1944.00 −0.111844
\(672\) 0 0
\(673\) −28670.0 −1.64212 −0.821060 0.570841i \(-0.806617\pi\)
−0.821060 + 0.570841i \(0.806617\pi\)
\(674\) −3082.00 −0.176134
\(675\) 0 0
\(676\) 11991.0 0.682237
\(677\) 1686.00 0.0957138 0.0478569 0.998854i \(-0.484761\pi\)
0.0478569 + 0.998854i \(0.484761\pi\)
\(678\) 0 0
\(679\) −6760.00 −0.382069
\(680\) 150.000 0.00845917
\(681\) 0 0
\(682\) 5472.00 0.307234
\(683\) 13128.0 0.735474 0.367737 0.929930i \(-0.380133\pi\)
0.367737 + 0.929930i \(0.380133\pi\)
\(684\) 0 0
\(685\) 13230.0 0.737945
\(686\) −2680.00 −0.149159
\(687\) 0 0
\(688\) −16892.0 −0.936049
\(689\) −16764.0 −0.926934
\(690\) 0 0
\(691\) 3052.00 0.168023 0.0840113 0.996465i \(-0.473227\pi\)
0.0840113 + 0.996465i \(0.473227\pi\)
\(692\) 2674.00 0.146893
\(693\) 0 0
\(694\) 4536.00 0.248104
\(695\) 9780.00 0.533779
\(696\) 0 0
\(697\) 500.000 0.0271720
\(698\) −7130.00 −0.386640
\(699\) 0 0
\(700\) −700.000 −0.0377964
\(701\) 11130.0 0.599678 0.299839 0.953990i \(-0.403067\pi\)
0.299839 + 0.953990i \(0.403067\pi\)
\(702\) 0 0
\(703\) −1904.00 −0.102149
\(704\) −6012.00 −0.321855
\(705\) 0 0
\(706\) −6814.00 −0.363241
\(707\) −2008.00 −0.106816
\(708\) 0 0
\(709\) −17082.0 −0.904835 −0.452417 0.891806i \(-0.649438\pi\)
−0.452417 + 0.891806i \(0.649438\pi\)
\(710\) 3000.00 0.158575
\(711\) 0 0
\(712\) 2250.00 0.118430
\(713\) 6080.00 0.319352
\(714\) 0 0
\(715\) 3960.00 0.207127
\(716\) −13356.0 −0.697119
\(717\) 0 0
\(718\) −8188.00 −0.425590
\(719\) −5064.00 −0.262664 −0.131332 0.991338i \(-0.541925\pi\)
−0.131332 + 0.991338i \(0.541925\pi\)
\(720\) 0 0
\(721\) −3312.00 −0.171075
\(722\) −3723.00 −0.191905
\(723\) 0 0
\(724\) 3150.00 0.161697
\(725\) −725.000 −0.0371391
\(726\) 0 0
\(727\) 16240.0 0.828485 0.414242 0.910167i \(-0.364047\pi\)
0.414242 + 0.910167i \(0.364047\pi\)
\(728\) 1320.00 0.0672012
\(729\) 0 0
\(730\) −30.0000 −0.00152103
\(731\) −824.000 −0.0416918
\(732\) 0 0
\(733\) −25878.0 −1.30399 −0.651996 0.758223i \(-0.726068\pi\)
−0.651996 + 0.758223i \(0.726068\pi\)
\(734\) 624.000 0.0313791
\(735\) 0 0
\(736\) 6440.00 0.322529
\(737\) −8784.00 −0.439027
\(738\) 0 0
\(739\) 20896.0 1.04015 0.520076 0.854120i \(-0.325904\pi\)
0.520076 + 0.854120i \(0.325904\pi\)
\(740\) 1190.00 0.0591152
\(741\) 0 0
\(742\) 3048.00 0.150803
\(743\) 14376.0 0.709831 0.354915 0.934898i \(-0.384510\pi\)
0.354915 + 0.934898i \(0.384510\pi\)
\(744\) 0 0
\(745\) 10630.0 0.522756
\(746\) −1206.00 −0.0591887
\(747\) 0 0
\(748\) −504.000 −0.0246365
\(749\) 4704.00 0.229480
\(750\) 0 0
\(751\) −18320.0 −0.890155 −0.445077 0.895492i \(-0.646824\pi\)
−0.445077 + 0.895492i \(0.646824\pi\)
\(752\) 4920.00 0.238582
\(753\) 0 0
\(754\) 638.000 0.0308151
\(755\) −6040.00 −0.291150
\(756\) 0 0
\(757\) −2606.00 −0.125121 −0.0625606 0.998041i \(-0.519927\pi\)
−0.0625606 + 0.998041i \(0.519927\pi\)
\(758\) −1728.00 −0.0828018
\(759\) 0 0
\(760\) −4200.00 −0.200461
\(761\) 33070.0 1.57528 0.787639 0.616137i \(-0.211303\pi\)
0.787639 + 0.616137i \(0.211303\pi\)
\(762\) 0 0
\(763\) −7688.00 −0.364776
\(764\) 9884.00 0.468050
\(765\) 0 0
\(766\) −3752.00 −0.176978
\(767\) −4136.00 −0.194710
\(768\) 0 0
\(769\) −3214.00 −0.150715 −0.0753575 0.997157i \(-0.524010\pi\)
−0.0753575 + 0.997157i \(0.524010\pi\)
\(770\) −720.000 −0.0336974
\(771\) 0 0
\(772\) 2926.00 0.136411
\(773\) −19954.0 −0.928455 −0.464227 0.885716i \(-0.653668\pi\)
−0.464227 + 0.885716i \(0.653668\pi\)
\(774\) 0 0
\(775\) 3800.00 0.176129
\(776\) 25350.0 1.17270
\(777\) 0 0
\(778\) 1250.00 0.0576024
\(779\) −14000.0 −0.643905
\(780\) 0 0
\(781\) −21600.0 −0.989640
\(782\) 80.0000 0.00365830
\(783\) 0 0
\(784\) −13407.0 −0.610742
\(785\) −2450.00 −0.111394
\(786\) 0 0
\(787\) 21108.0 0.956060 0.478030 0.878344i \(-0.341351\pi\)
0.478030 + 0.878344i \(0.341351\pi\)
\(788\) 22274.0 1.00695
\(789\) 0 0
\(790\) 3200.00 0.144115
\(791\) 1288.00 0.0578963
\(792\) 0 0
\(793\) 1188.00 0.0531994
\(794\) 3210.00 0.143474
\(795\) 0 0
\(796\) −34832.0 −1.55099
\(797\) −25946.0 −1.15314 −0.576571 0.817047i \(-0.695610\pi\)
−0.576571 + 0.817047i \(0.695610\pi\)
\(798\) 0 0
\(799\) 240.000 0.0106265
\(800\) 4025.00 0.177882
\(801\) 0 0
\(802\) −11314.0 −0.498144
\(803\) 216.000 0.00949250
\(804\) 0 0
\(805\) −800.000 −0.0350265
\(806\) −3344.00 −0.146138
\(807\) 0 0
\(808\) 7530.00 0.327852
\(809\) 1082.00 0.0470224 0.0235112 0.999724i \(-0.492515\pi\)
0.0235112 + 0.999724i \(0.492515\pi\)
\(810\) 0 0
\(811\) −25076.0 −1.08574 −0.542871 0.839816i \(-0.682663\pi\)
−0.542871 + 0.839816i \(0.682663\pi\)
\(812\) 812.000 0.0350931
\(813\) 0 0
\(814\) 1224.00 0.0527041
\(815\) −8900.00 −0.382520
\(816\) 0 0
\(817\) 23072.0 0.987989
\(818\) −2518.00 −0.107628
\(819\) 0 0
\(820\) 8750.00 0.372638
\(821\) 18194.0 0.773417 0.386708 0.922202i \(-0.373612\pi\)
0.386708 + 0.922202i \(0.373612\pi\)
\(822\) 0 0
\(823\) −21008.0 −0.889785 −0.444892 0.895584i \(-0.646758\pi\)
−0.444892 + 0.895584i \(0.646758\pi\)
\(824\) 12420.0 0.525086
\(825\) 0 0
\(826\) 752.000 0.0316773
\(827\) 21708.0 0.912770 0.456385 0.889782i \(-0.349144\pi\)
0.456385 + 0.889782i \(0.349144\pi\)
\(828\) 0 0
\(829\) −6110.00 −0.255982 −0.127991 0.991775i \(-0.540853\pi\)
−0.127991 + 0.991775i \(0.540853\pi\)
\(830\) 3320.00 0.138842
\(831\) 0 0
\(832\) 3674.00 0.153093
\(833\) −654.000 −0.0272026
\(834\) 0 0
\(835\) 12600.0 0.522205
\(836\) 14112.0 0.583820
\(837\) 0 0
\(838\) 4172.00 0.171980
\(839\) −28588.0 −1.17636 −0.588181 0.808729i \(-0.700156\pi\)
−0.588181 + 0.808729i \(0.700156\pi\)
\(840\) 0 0
\(841\) 841.000 0.0344828
\(842\) −15838.0 −0.648235
\(843\) 0 0
\(844\) 4480.00 0.182711
\(845\) 8565.00 0.348692
\(846\) 0 0
\(847\) −140.000 −0.00567941
\(848\) 31242.0 1.26516
\(849\) 0 0
\(850\) 50.0000 0.00201763
\(851\) 1360.00 0.0547828
\(852\) 0 0
\(853\) 242.000 0.00971386 0.00485693 0.999988i \(-0.498454\pi\)
0.00485693 + 0.999988i \(0.498454\pi\)
\(854\) −216.000 −0.00865500
\(855\) 0 0
\(856\) −17640.0 −0.704349
\(857\) 12002.0 0.478390 0.239195 0.970972i \(-0.423116\pi\)
0.239195 + 0.970972i \(0.423116\pi\)
\(858\) 0 0
\(859\) −34896.0 −1.38607 −0.693036 0.720903i \(-0.743727\pi\)
−0.693036 + 0.720903i \(0.743727\pi\)
\(860\) −14420.0 −0.571765
\(861\) 0 0
\(862\) 0 0
\(863\) −4488.00 −0.177026 −0.0885129 0.996075i \(-0.528211\pi\)
−0.0885129 + 0.996075i \(0.528211\pi\)
\(864\) 0 0
\(865\) 1910.00 0.0750774
\(866\) 7718.00 0.302850
\(867\) 0 0
\(868\) −4256.00 −0.166426
\(869\) −23040.0 −0.899400
\(870\) 0 0
\(871\) 5368.00 0.208826
\(872\) 28830.0 1.11962
\(873\) 0 0
\(874\) −2240.00 −0.0866924
\(875\) −500.000 −0.0193178
\(876\) 0 0
\(877\) 5794.00 0.223089 0.111545 0.993759i \(-0.464420\pi\)
0.111545 + 0.993759i \(0.464420\pi\)
\(878\) 6720.00 0.258302
\(879\) 0 0
\(880\) −7380.00 −0.282704
\(881\) 14034.0 0.536683 0.268341 0.963324i \(-0.413524\pi\)
0.268341 + 0.963324i \(0.413524\pi\)
\(882\) 0 0
\(883\) 29884.0 1.13893 0.569466 0.822015i \(-0.307150\pi\)
0.569466 + 0.822015i \(0.307150\pi\)
\(884\) 308.000 0.0117185
\(885\) 0 0
\(886\) 8652.00 0.328070
\(887\) −11440.0 −0.433053 −0.216526 0.976277i \(-0.569473\pi\)
−0.216526 + 0.976277i \(0.569473\pi\)
\(888\) 0 0
\(889\) 6272.00 0.236621
\(890\) 750.000 0.0282473
\(891\) 0 0
\(892\) 12068.0 0.452989
\(893\) −6720.00 −0.251821
\(894\) 0 0
\(895\) −9540.00 −0.356298
\(896\) −5820.00 −0.217001
\(897\) 0 0
\(898\) −4606.00 −0.171163
\(899\) −4408.00 −0.163532
\(900\) 0 0
\(901\) 1524.00 0.0563505
\(902\) 9000.00 0.332225
\(903\) 0 0
\(904\) −4830.00 −0.177703
\(905\) 2250.00 0.0826437
\(906\) 0 0
\(907\) −2532.00 −0.0926942 −0.0463471 0.998925i \(-0.514758\pi\)
−0.0463471 + 0.998925i \(0.514758\pi\)
\(908\) 8512.00 0.311102
\(909\) 0 0
\(910\) 440.000 0.0160284
\(911\) −18188.0 −0.661466 −0.330733 0.943724i \(-0.607296\pi\)
−0.330733 + 0.943724i \(0.607296\pi\)
\(912\) 0 0
\(913\) −23904.0 −0.866492
\(914\) 1642.00 0.0594229
\(915\) 0 0
\(916\) 12642.0 0.456008
\(917\) −4496.00 −0.161909
\(918\) 0 0
\(919\) −12680.0 −0.455141 −0.227571 0.973762i \(-0.573078\pi\)
−0.227571 + 0.973762i \(0.573078\pi\)
\(920\) 3000.00 0.107508
\(921\) 0 0
\(922\) 3930.00 0.140377
\(923\) 13200.0 0.470729
\(924\) 0 0
\(925\) 850.000 0.0302139
\(926\) −10076.0 −0.357579
\(927\) 0 0
\(928\) −4669.00 −0.165159
\(929\) −32090.0 −1.13330 −0.566652 0.823957i \(-0.691761\pi\)
−0.566652 + 0.823957i \(0.691761\pi\)
\(930\) 0 0
\(931\) 18312.0 0.644631
\(932\) 25578.0 0.898965
\(933\) 0 0
\(934\) 3348.00 0.117291
\(935\) −360.000 −0.0125917
\(936\) 0 0
\(937\) 49914.0 1.74026 0.870128 0.492826i \(-0.164036\pi\)
0.870128 + 0.492826i \(0.164036\pi\)
\(938\) −976.000 −0.0339739
\(939\) 0 0
\(940\) 4200.00 0.145733
\(941\) 36842.0 1.27632 0.638159 0.769905i \(-0.279696\pi\)
0.638159 + 0.769905i \(0.279696\pi\)
\(942\) 0 0
\(943\) 10000.0 0.345329
\(944\) 7708.00 0.265756
\(945\) 0 0
\(946\) −14832.0 −0.509757
\(947\) −31788.0 −1.09078 −0.545391 0.838182i \(-0.683619\pi\)
−0.545391 + 0.838182i \(0.683619\pi\)
\(948\) 0 0
\(949\) −132.000 −0.00451518
\(950\) −1400.00 −0.0478126
\(951\) 0 0
\(952\) −120.000 −0.00408532
\(953\) 34122.0 1.15983 0.579916 0.814676i \(-0.303085\pi\)
0.579916 + 0.814676i \(0.303085\pi\)
\(954\) 0 0
\(955\) 7060.00 0.239221
\(956\) −37128.0 −1.25607
\(957\) 0 0
\(958\) −3412.00 −0.115070
\(959\) −10584.0 −0.356387
\(960\) 0 0
\(961\) −6687.00 −0.224464
\(962\) −748.000 −0.0250691
\(963\) 0 0
\(964\) −30814.0 −1.02951
\(965\) 2090.00 0.0697197
\(966\) 0 0
\(967\) −6200.00 −0.206183 −0.103091 0.994672i \(-0.532873\pi\)
−0.103091 + 0.994672i \(0.532873\pi\)
\(968\) 525.000 0.0174320
\(969\) 0 0
\(970\) 8450.00 0.279704
\(971\) −19788.0 −0.653993 −0.326996 0.945026i \(-0.606037\pi\)
−0.326996 + 0.945026i \(0.606037\pi\)
\(972\) 0 0
\(973\) −7824.00 −0.257786
\(974\) −13084.0 −0.430430
\(975\) 0 0
\(976\) −2214.00 −0.0726111
\(977\) 23226.0 0.760558 0.380279 0.924872i \(-0.375828\pi\)
0.380279 + 0.924872i \(0.375828\pi\)
\(978\) 0 0
\(979\) −5400.00 −0.176287
\(980\) −11445.0 −0.373058
\(981\) 0 0
\(982\) −11788.0 −0.383065
\(983\) −43056.0 −1.39702 −0.698511 0.715599i \(-0.746154\pi\)
−0.698511 + 0.715599i \(0.746154\pi\)
\(984\) 0 0
\(985\) 15910.0 0.514655
\(986\) −58.0000 −0.00187332
\(987\) 0 0
\(988\) −8624.00 −0.277698
\(989\) −16480.0 −0.529862
\(990\) 0 0
\(991\) −24200.0 −0.775720 −0.387860 0.921718i \(-0.626786\pi\)
−0.387860 + 0.921718i \(0.626786\pi\)
\(992\) 24472.0 0.783253
\(993\) 0 0
\(994\) −2400.00 −0.0765829
\(995\) −24880.0 −0.792713
\(996\) 0 0
\(997\) −31582.0 −1.00322 −0.501611 0.865093i \(-0.667259\pi\)
−0.501611 + 0.865093i \(0.667259\pi\)
\(998\) −17484.0 −0.554555
\(999\) 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 1305.4.a.c.1.1 1
3.2 odd 2 435.4.a.b.1.1 1
15.14 odd 2 2175.4.a.b.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
435.4.a.b.1.1 1 3.2 odd 2
1305.4.a.c.1.1 1 1.1 even 1 trivial
2175.4.a.b.1.1 1 15.14 odd 2