Properties

Label 1225.4.a.f.1.1
Level $1225$
Weight $4$
Character 1225.1
Self dual yes
Analytic conductor $72.277$
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] = [1225,4,Mod(1,1225)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1225, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("1225.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1225 = 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1225.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: \(72.2773397570\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 245)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1225.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -6.00000 q^{3} -7.00000 q^{4} +6.00000 q^{6} +15.0000 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -6.00000 q^{3} -7.00000 q^{4} +6.00000 q^{6} +15.0000 q^{8} +9.00000 q^{9} -44.0000 q^{11} +42.0000 q^{12} -6.00000 q^{13} +41.0000 q^{16} +24.0000 q^{17} -9.00000 q^{18} -114.000 q^{19} +44.0000 q^{22} +52.0000 q^{23} -90.0000 q^{24} +6.00000 q^{26} +108.000 q^{27} +146.000 q^{29} -276.000 q^{31} -161.000 q^{32} +264.000 q^{33} -24.0000 q^{34} -63.0000 q^{36} +210.000 q^{37} +114.000 q^{38} +36.0000 q^{39} +444.000 q^{41} -492.000 q^{43} +308.000 q^{44} -52.0000 q^{46} +612.000 q^{47} -246.000 q^{48} -144.000 q^{51} +42.0000 q^{52} -50.0000 q^{53} -108.000 q^{54} +684.000 q^{57} -146.000 q^{58} +294.000 q^{59} +450.000 q^{61} +276.000 q^{62} -167.000 q^{64} -264.000 q^{66} +668.000 q^{67} -168.000 q^{68} -312.000 q^{69} -308.000 q^{71} +135.000 q^{72} -12.0000 q^{73} -210.000 q^{74} +798.000 q^{76} -36.0000 q^{78} +596.000 q^{79} -891.000 q^{81} -444.000 q^{82} +966.000 q^{83} +492.000 q^{86} -876.000 q^{87} -660.000 q^{88} -408.000 q^{89} -364.000 q^{92} +1656.00 q^{93} -612.000 q^{94} +966.000 q^{96} +1200.00 q^{97} -396.000 q^{99} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.353553 −0.176777 0.984251i \(-0.556567\pi\)
−0.176777 + 0.984251i \(0.556567\pi\)
\(3\) −6.00000 −1.15470 −0.577350 0.816497i \(-0.695913\pi\)
−0.577350 + 0.816497i \(0.695913\pi\)
\(4\) −7.00000 −0.875000
\(5\) 0 0
\(6\) 6.00000 0.408248
\(7\) 0 0
\(8\) 15.0000 0.662913
\(9\) 9.00000 0.333333
\(10\) 0 0
\(11\) −44.0000 −1.20605 −0.603023 0.797724i \(-0.706037\pi\)
−0.603023 + 0.797724i \(0.706037\pi\)
\(12\) 42.0000 1.01036
\(13\) −6.00000 −0.128008 −0.0640039 0.997950i \(-0.520387\pi\)
−0.0640039 + 0.997950i \(0.520387\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 41.0000 0.640625
\(17\) 24.0000 0.342403 0.171202 0.985236i \(-0.445235\pi\)
0.171202 + 0.985236i \(0.445235\pi\)
\(18\) −9.00000 −0.117851
\(19\) −114.000 −1.37649 −0.688247 0.725476i \(-0.741620\pi\)
−0.688247 + 0.725476i \(0.741620\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 44.0000 0.426401
\(23\) 52.0000 0.471424 0.235712 0.971823i \(-0.424258\pi\)
0.235712 + 0.971823i \(0.424258\pi\)
\(24\) −90.0000 −0.765466
\(25\) 0 0
\(26\) 6.00000 0.0452576
\(27\) 108.000 0.769800
\(28\) 0 0
\(29\) 146.000 0.934880 0.467440 0.884025i \(-0.345176\pi\)
0.467440 + 0.884025i \(0.345176\pi\)
\(30\) 0 0
\(31\) −276.000 −1.59907 −0.799533 0.600622i \(-0.794920\pi\)
−0.799533 + 0.600622i \(0.794920\pi\)
\(32\) −161.000 −0.889408
\(33\) 264.000 1.39262
\(34\) −24.0000 −0.121058
\(35\) 0 0
\(36\) −63.0000 −0.291667
\(37\) 210.000 0.933075 0.466538 0.884501i \(-0.345501\pi\)
0.466538 + 0.884501i \(0.345501\pi\)
\(38\) 114.000 0.486664
\(39\) 36.0000 0.147811
\(40\) 0 0
\(41\) 444.000 1.69125 0.845624 0.533779i \(-0.179229\pi\)
0.845624 + 0.533779i \(0.179229\pi\)
\(42\) 0 0
\(43\) −492.000 −1.74487 −0.872434 0.488733i \(-0.837459\pi\)
−0.872434 + 0.488733i \(0.837459\pi\)
\(44\) 308.000 1.05529
\(45\) 0 0
\(46\) −52.0000 −0.166674
\(47\) 612.000 1.89935 0.949674 0.313239i \(-0.101414\pi\)
0.949674 + 0.313239i \(0.101414\pi\)
\(48\) −246.000 −0.739730
\(49\) 0 0
\(50\) 0 0
\(51\) −144.000 −0.395373
\(52\) 42.0000 0.112007
\(53\) −50.0000 −0.129585 −0.0647927 0.997899i \(-0.520639\pi\)
−0.0647927 + 0.997899i \(0.520639\pi\)
\(54\) −108.000 −0.272166
\(55\) 0 0
\(56\) 0 0
\(57\) 684.000 1.58944
\(58\) −146.000 −0.330530
\(59\) 294.000 0.648738 0.324369 0.945931i \(-0.394848\pi\)
0.324369 + 0.945931i \(0.394848\pi\)
\(60\) 0 0
\(61\) 450.000 0.944534 0.472267 0.881455i \(-0.343436\pi\)
0.472267 + 0.881455i \(0.343436\pi\)
\(62\) 276.000 0.565355
\(63\) 0 0
\(64\) −167.000 −0.326172
\(65\) 0 0
\(66\) −264.000 −0.492366
\(67\) 668.000 1.21805 0.609024 0.793152i \(-0.291561\pi\)
0.609024 + 0.793152i \(0.291561\pi\)
\(68\) −168.000 −0.299603
\(69\) −312.000 −0.544353
\(70\) 0 0
\(71\) −308.000 −0.514829 −0.257415 0.966301i \(-0.582871\pi\)
−0.257415 + 0.966301i \(0.582871\pi\)
\(72\) 135.000 0.220971
\(73\) −12.0000 −0.0192396 −0.00961982 0.999954i \(-0.503062\pi\)
−0.00961982 + 0.999954i \(0.503062\pi\)
\(74\) −210.000 −0.329892
\(75\) 0 0
\(76\) 798.000 1.20443
\(77\) 0 0
\(78\) −36.0000 −0.0522589
\(79\) 596.000 0.848800 0.424400 0.905475i \(-0.360485\pi\)
0.424400 + 0.905475i \(0.360485\pi\)
\(80\) 0 0
\(81\) −891.000 −1.22222
\(82\) −444.000 −0.597946
\(83\) 966.000 1.27750 0.638749 0.769415i \(-0.279452\pi\)
0.638749 + 0.769415i \(0.279452\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 492.000 0.616904
\(87\) −876.000 −1.07951
\(88\) −660.000 −0.799503
\(89\) −408.000 −0.485932 −0.242966 0.970035i \(-0.578120\pi\)
−0.242966 + 0.970035i \(0.578120\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −364.000 −0.412496
\(93\) 1656.00 1.84644
\(94\) −612.000 −0.671521
\(95\) 0 0
\(96\) 966.000 1.02700
\(97\) 1200.00 1.25610 0.628049 0.778174i \(-0.283854\pi\)
0.628049 + 0.778174i \(0.283854\pi\)
\(98\) 0 0
\(99\) −396.000 −0.402015
\(100\) 0 0
\(101\) 1098.00 1.08173 0.540867 0.841108i \(-0.318096\pi\)
0.540867 + 0.841108i \(0.318096\pi\)
\(102\) 144.000 0.139786
\(103\) −972.000 −0.929845 −0.464922 0.885351i \(-0.653918\pi\)
−0.464922 + 0.885351i \(0.653918\pi\)
\(104\) −90.0000 −0.0848579
\(105\) 0 0
\(106\) 50.0000 0.0458154
\(107\) −1516.00 −1.36969 −0.684847 0.728687i \(-0.740131\pi\)
−0.684847 + 0.728687i \(0.740131\pi\)
\(108\) −756.000 −0.673575
\(109\) 930.000 0.817228 0.408614 0.912707i \(-0.366012\pi\)
0.408614 + 0.912707i \(0.366012\pi\)
\(110\) 0 0
\(111\) −1260.00 −1.07742
\(112\) 0 0
\(113\) −1694.00 −1.41025 −0.705124 0.709084i \(-0.749109\pi\)
−0.705124 + 0.709084i \(0.749109\pi\)
\(114\) −684.000 −0.561951
\(115\) 0 0
\(116\) −1022.00 −0.818020
\(117\) −54.0000 −0.0426692
\(118\) −294.000 −0.229364
\(119\) 0 0
\(120\) 0 0
\(121\) 605.000 0.454545
\(122\) −450.000 −0.333943
\(123\) −2664.00 −1.95288
\(124\) 1932.00 1.39918
\(125\) 0 0
\(126\) 0 0
\(127\) −916.000 −0.640015 −0.320007 0.947415i \(-0.603685\pi\)
−0.320007 + 0.947415i \(0.603685\pi\)
\(128\) 1455.00 1.00473
\(129\) 2952.00 2.01480
\(130\) 0 0
\(131\) −1002.00 −0.668284 −0.334142 0.942523i \(-0.608446\pi\)
−0.334142 + 0.942523i \(0.608446\pi\)
\(132\) −1848.00 −1.21854
\(133\) 0 0
\(134\) −668.000 −0.430645
\(135\) 0 0
\(136\) 360.000 0.226983
\(137\) 274.000 0.170872 0.0854358 0.996344i \(-0.472772\pi\)
0.0854358 + 0.996344i \(0.472772\pi\)
\(138\) 312.000 0.192458
\(139\) −270.000 −0.164756 −0.0823781 0.996601i \(-0.526251\pi\)
−0.0823781 + 0.996601i \(0.526251\pi\)
\(140\) 0 0
\(141\) −3672.00 −2.19318
\(142\) 308.000 0.182020
\(143\) 264.000 0.154383
\(144\) 369.000 0.213542
\(145\) 0 0
\(146\) 12.0000 0.00680224
\(147\) 0 0
\(148\) −1470.00 −0.816441
\(149\) −530.000 −0.291405 −0.145702 0.989328i \(-0.546544\pi\)
−0.145702 + 0.989328i \(0.546544\pi\)
\(150\) 0 0
\(151\) −3120.00 −1.68147 −0.840735 0.541447i \(-0.817877\pi\)
−0.840735 + 0.541447i \(0.817877\pi\)
\(152\) −1710.00 −0.912495
\(153\) 216.000 0.114134
\(154\) 0 0
\(155\) 0 0
\(156\) −252.000 −0.129334
\(157\) 2106.00 1.07055 0.535277 0.844676i \(-0.320207\pi\)
0.535277 + 0.844676i \(0.320207\pi\)
\(158\) −596.000 −0.300096
\(159\) 300.000 0.149632
\(160\) 0 0
\(161\) 0 0
\(162\) 891.000 0.432121
\(163\) −628.000 −0.301772 −0.150886 0.988551i \(-0.548213\pi\)
−0.150886 + 0.988551i \(0.548213\pi\)
\(164\) −3108.00 −1.47984
\(165\) 0 0
\(166\) −966.000 −0.451663
\(167\) −1284.00 −0.594963 −0.297482 0.954728i \(-0.596147\pi\)
−0.297482 + 0.954728i \(0.596147\pi\)
\(168\) 0 0
\(169\) −2161.00 −0.983614
\(170\) 0 0
\(171\) −1026.00 −0.458831
\(172\) 3444.00 1.52676
\(173\) 906.000 0.398161 0.199081 0.979983i \(-0.436204\pi\)
0.199081 + 0.979983i \(0.436204\pi\)
\(174\) 876.000 0.381663
\(175\) 0 0
\(176\) −1804.00 −0.772623
\(177\) −1764.00 −0.749098
\(178\) 408.000 0.171803
\(179\) −2084.00 −0.870198 −0.435099 0.900383i \(-0.643287\pi\)
−0.435099 + 0.900383i \(0.643287\pi\)
\(180\) 0 0
\(181\) −4674.00 −1.91942 −0.959712 0.280986i \(-0.909339\pi\)
−0.959712 + 0.280986i \(0.909339\pi\)
\(182\) 0 0
\(183\) −2700.00 −1.09065
\(184\) 780.000 0.312513
\(185\) 0 0
\(186\) −1656.00 −0.652816
\(187\) −1056.00 −0.412954
\(188\) −4284.00 −1.66193
\(189\) 0 0
\(190\) 0 0
\(191\) 2012.00 0.762216 0.381108 0.924531i \(-0.375543\pi\)
0.381108 + 0.924531i \(0.375543\pi\)
\(192\) 1002.00 0.376631
\(193\) −4206.00 −1.56868 −0.784338 0.620334i \(-0.786997\pi\)
−0.784338 + 0.620334i \(0.786997\pi\)
\(194\) −1200.00 −0.444098
\(195\) 0 0
\(196\) 0 0
\(197\) 1574.00 0.569253 0.284627 0.958638i \(-0.408130\pi\)
0.284627 + 0.958638i \(0.408130\pi\)
\(198\) 396.000 0.142134
\(199\) −2724.00 −0.970348 −0.485174 0.874418i \(-0.661244\pi\)
−0.485174 + 0.874418i \(0.661244\pi\)
\(200\) 0 0
\(201\) −4008.00 −1.40648
\(202\) −1098.00 −0.382451
\(203\) 0 0
\(204\) 1008.00 0.345952
\(205\) 0 0
\(206\) 972.000 0.328750
\(207\) 468.000 0.157141
\(208\) −246.000 −0.0820050
\(209\) 5016.00 1.66011
\(210\) 0 0
\(211\) −180.000 −0.0587285 −0.0293642 0.999569i \(-0.509348\pi\)
−0.0293642 + 0.999569i \(0.509348\pi\)
\(212\) 350.000 0.113387
\(213\) 1848.00 0.594474
\(214\) 1516.00 0.484260
\(215\) 0 0
\(216\) 1620.00 0.510310
\(217\) 0 0
\(218\) −930.000 −0.288934
\(219\) 72.0000 0.0222160
\(220\) 0 0
\(221\) −144.000 −0.0438303
\(222\) 1260.00 0.380926
\(223\) 4584.00 1.37654 0.688268 0.725457i \(-0.258372\pi\)
0.688268 + 0.725457i \(0.258372\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 1694.00 0.498598
\(227\) 1686.00 0.492968 0.246484 0.969147i \(-0.420725\pi\)
0.246484 + 0.969147i \(0.420725\pi\)
\(228\) −4788.00 −1.39076
\(229\) −4026.00 −1.16177 −0.580886 0.813985i \(-0.697294\pi\)
−0.580886 + 0.813985i \(0.697294\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 2190.00 0.619744
\(233\) 6074.00 1.70782 0.853908 0.520425i \(-0.174226\pi\)
0.853908 + 0.520425i \(0.174226\pi\)
\(234\) 54.0000 0.0150859
\(235\) 0 0
\(236\) −2058.00 −0.567646
\(237\) −3576.00 −0.980110
\(238\) 0 0
\(239\) 3928.00 1.06310 0.531551 0.847027i \(-0.321610\pi\)
0.531551 + 0.847027i \(0.321610\pi\)
\(240\) 0 0
\(241\) −1236.00 −0.330364 −0.165182 0.986263i \(-0.552821\pi\)
−0.165182 + 0.986263i \(0.552821\pi\)
\(242\) −605.000 −0.160706
\(243\) 2430.00 0.641500
\(244\) −3150.00 −0.826468
\(245\) 0 0
\(246\) 2664.00 0.690449
\(247\) 684.000 0.176202
\(248\) −4140.00 −1.06004
\(249\) −5796.00 −1.47513
\(250\) 0 0
\(251\) −78.0000 −0.0196148 −0.00980740 0.999952i \(-0.503122\pi\)
−0.00980740 + 0.999952i \(0.503122\pi\)
\(252\) 0 0
\(253\) −2288.00 −0.568559
\(254\) 916.000 0.226279
\(255\) 0 0
\(256\) −119.000 −0.0290527
\(257\) 3276.00 0.795141 0.397571 0.917572i \(-0.369853\pi\)
0.397571 + 0.917572i \(0.369853\pi\)
\(258\) −2952.00 −0.712339
\(259\) 0 0
\(260\) 0 0
\(261\) 1314.00 0.311627
\(262\) 1002.00 0.236274
\(263\) −2240.00 −0.525188 −0.262594 0.964906i \(-0.584578\pi\)
−0.262594 + 0.964906i \(0.584578\pi\)
\(264\) 3960.00 0.923186
\(265\) 0 0
\(266\) 0 0
\(267\) 2448.00 0.561105
\(268\) −4676.00 −1.06579
\(269\) 4494.00 1.01860 0.509301 0.860588i \(-0.329904\pi\)
0.509301 + 0.860588i \(0.329904\pi\)
\(270\) 0 0
\(271\) 3216.00 0.720879 0.360439 0.932783i \(-0.382627\pi\)
0.360439 + 0.932783i \(0.382627\pi\)
\(272\) 984.000 0.219352
\(273\) 0 0
\(274\) −274.000 −0.0604122
\(275\) 0 0
\(276\) 2184.00 0.476309
\(277\) −1514.00 −0.328402 −0.164201 0.986427i \(-0.552505\pi\)
−0.164201 + 0.986427i \(0.552505\pi\)
\(278\) 270.000 0.0582501
\(279\) −2484.00 −0.533022
\(280\) 0 0
\(281\) −5690.00 −1.20796 −0.603980 0.796999i \(-0.706419\pi\)
−0.603980 + 0.796999i \(0.706419\pi\)
\(282\) 3672.00 0.775406
\(283\) 7518.00 1.57915 0.789574 0.613656i \(-0.210302\pi\)
0.789574 + 0.613656i \(0.210302\pi\)
\(284\) 2156.00 0.450476
\(285\) 0 0
\(286\) −264.000 −0.0545827
\(287\) 0 0
\(288\) −1449.00 −0.296469
\(289\) −4337.00 −0.882760
\(290\) 0 0
\(291\) −7200.00 −1.45042
\(292\) 84.0000 0.0168347
\(293\) 702.000 0.139970 0.0699851 0.997548i \(-0.477705\pi\)
0.0699851 + 0.997548i \(0.477705\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 3150.00 0.618547
\(297\) −4752.00 −0.928414
\(298\) 530.000 0.103027
\(299\) −312.000 −0.0603459
\(300\) 0 0
\(301\) 0 0
\(302\) 3120.00 0.594489
\(303\) −6588.00 −1.24908
\(304\) −4674.00 −0.881817
\(305\) 0 0
\(306\) −216.000 −0.0403526
\(307\) 10374.0 1.92858 0.964292 0.264840i \(-0.0853193\pi\)
0.964292 + 0.264840i \(0.0853193\pi\)
\(308\) 0 0
\(309\) 5832.00 1.07369
\(310\) 0 0
\(311\) −2784.00 −0.507608 −0.253804 0.967256i \(-0.581682\pi\)
−0.253804 + 0.967256i \(0.581682\pi\)
\(312\) 540.000 0.0979855
\(313\) −6216.00 −1.12252 −0.561261 0.827639i \(-0.689683\pi\)
−0.561261 + 0.827639i \(0.689683\pi\)
\(314\) −2106.00 −0.378498
\(315\) 0 0
\(316\) −4172.00 −0.742700
\(317\) −5066.00 −0.897586 −0.448793 0.893636i \(-0.648146\pi\)
−0.448793 + 0.893636i \(0.648146\pi\)
\(318\) −300.000 −0.0529030
\(319\) −6424.00 −1.12751
\(320\) 0 0
\(321\) 9096.00 1.58159
\(322\) 0 0
\(323\) −2736.00 −0.471316
\(324\) 6237.00 1.06944
\(325\) 0 0
\(326\) 628.000 0.106692
\(327\) −5580.00 −0.943654
\(328\) 6660.00 1.12115
\(329\) 0 0
\(330\) 0 0
\(331\) −6468.00 −1.07406 −0.537029 0.843564i \(-0.680454\pi\)
−0.537029 + 0.843564i \(0.680454\pi\)
\(332\) −6762.00 −1.11781
\(333\) 1890.00 0.311025
\(334\) 1284.00 0.210351
\(335\) 0 0
\(336\) 0 0
\(337\) 3438.00 0.555726 0.277863 0.960621i \(-0.410374\pi\)
0.277863 + 0.960621i \(0.410374\pi\)
\(338\) 2161.00 0.347760
\(339\) 10164.0 1.62842
\(340\) 0 0
\(341\) 12144.0 1.92855
\(342\) 1026.00 0.162221
\(343\) 0 0
\(344\) −7380.00 −1.15669
\(345\) 0 0
\(346\) −906.000 −0.140771
\(347\) −2212.00 −0.342209 −0.171104 0.985253i \(-0.554734\pi\)
−0.171104 + 0.985253i \(0.554734\pi\)
\(348\) 6132.00 0.944568
\(349\) 2910.00 0.446329 0.223164 0.974781i \(-0.428361\pi\)
0.223164 + 0.974781i \(0.428361\pi\)
\(350\) 0 0
\(351\) −648.000 −0.0985404
\(352\) 7084.00 1.07267
\(353\) −8364.00 −1.26111 −0.630554 0.776146i \(-0.717172\pi\)
−0.630554 + 0.776146i \(0.717172\pi\)
\(354\) 1764.00 0.264846
\(355\) 0 0
\(356\) 2856.00 0.425190
\(357\) 0 0
\(358\) 2084.00 0.307662
\(359\) −6712.00 −0.986757 −0.493379 0.869815i \(-0.664238\pi\)
−0.493379 + 0.869815i \(0.664238\pi\)
\(360\) 0 0
\(361\) 6137.00 0.894737
\(362\) 4674.00 0.678619
\(363\) −3630.00 −0.524864
\(364\) 0 0
\(365\) 0 0
\(366\) 2700.00 0.385605
\(367\) −456.000 −0.0648583 −0.0324292 0.999474i \(-0.510324\pi\)
−0.0324292 + 0.999474i \(0.510324\pi\)
\(368\) 2132.00 0.302006
\(369\) 3996.00 0.563749
\(370\) 0 0
\(371\) 0 0
\(372\) −11592.0 −1.61564
\(373\) 2558.00 0.355089 0.177545 0.984113i \(-0.443185\pi\)
0.177545 + 0.984113i \(0.443185\pi\)
\(374\) 1056.00 0.146001
\(375\) 0 0
\(376\) 9180.00 1.25910
\(377\) −876.000 −0.119672
\(378\) 0 0
\(379\) 2004.00 0.271606 0.135803 0.990736i \(-0.456639\pi\)
0.135803 + 0.990736i \(0.456639\pi\)
\(380\) 0 0
\(381\) 5496.00 0.739025
\(382\) −2012.00 −0.269484
\(383\) −11340.0 −1.51292 −0.756458 0.654042i \(-0.773072\pi\)
−0.756458 + 0.654042i \(0.773072\pi\)
\(384\) −8730.00 −1.16016
\(385\) 0 0
\(386\) 4206.00 0.554611
\(387\) −4428.00 −0.581622
\(388\) −8400.00 −1.09909
\(389\) 10522.0 1.37143 0.685715 0.727870i \(-0.259489\pi\)
0.685715 + 0.727870i \(0.259489\pi\)
\(390\) 0 0
\(391\) 1248.00 0.161417
\(392\) 0 0
\(393\) 6012.00 0.771667
\(394\) −1574.00 −0.201261
\(395\) 0 0
\(396\) 2772.00 0.351763
\(397\) 2898.00 0.366364 0.183182 0.983079i \(-0.441360\pi\)
0.183182 + 0.983079i \(0.441360\pi\)
\(398\) 2724.00 0.343070
\(399\) 0 0
\(400\) 0 0
\(401\) 3026.00 0.376836 0.188418 0.982089i \(-0.439664\pi\)
0.188418 + 0.982089i \(0.439664\pi\)
\(402\) 4008.00 0.497266
\(403\) 1656.00 0.204693
\(404\) −7686.00 −0.946517
\(405\) 0 0
\(406\) 0 0
\(407\) −9240.00 −1.12533
\(408\) −2160.00 −0.262098
\(409\) −8940.00 −1.08082 −0.540409 0.841402i \(-0.681730\pi\)
−0.540409 + 0.841402i \(0.681730\pi\)
\(410\) 0 0
\(411\) −1644.00 −0.197305
\(412\) 6804.00 0.813614
\(413\) 0 0
\(414\) −468.000 −0.0555578
\(415\) 0 0
\(416\) 966.000 0.113851
\(417\) 1620.00 0.190244
\(418\) −5016.00 −0.586939
\(419\) 2994.00 0.349085 0.174542 0.984650i \(-0.444155\pi\)
0.174542 + 0.984650i \(0.444155\pi\)
\(420\) 0 0
\(421\) 15766.0 1.82515 0.912575 0.408910i \(-0.134091\pi\)
0.912575 + 0.408910i \(0.134091\pi\)
\(422\) 180.000 0.0207637
\(423\) 5508.00 0.633116
\(424\) −750.000 −0.0859038
\(425\) 0 0
\(426\) −1848.00 −0.210178
\(427\) 0 0
\(428\) 10612.0 1.19848
\(429\) −1584.00 −0.178266
\(430\) 0 0
\(431\) 14720.0 1.64510 0.822549 0.568694i \(-0.192551\pi\)
0.822549 + 0.568694i \(0.192551\pi\)
\(432\) 4428.00 0.493153
\(433\) −4440.00 −0.492778 −0.246389 0.969171i \(-0.579244\pi\)
−0.246389 + 0.969171i \(0.579244\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −6510.00 −0.715074
\(437\) −5928.00 −0.648912
\(438\) −72.0000 −0.00785455
\(439\) −1488.00 −0.161773 −0.0808865 0.996723i \(-0.525775\pi\)
−0.0808865 + 0.996723i \(0.525775\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 144.000 0.0154963
\(443\) 5828.00 0.625049 0.312524 0.949910i \(-0.398825\pi\)
0.312524 + 0.949910i \(0.398825\pi\)
\(444\) 8820.00 0.942745
\(445\) 0 0
\(446\) −4584.00 −0.486679
\(447\) 3180.00 0.336485
\(448\) 0 0
\(449\) −6958.00 −0.731333 −0.365666 0.930746i \(-0.619159\pi\)
−0.365666 + 0.930746i \(0.619159\pi\)
\(450\) 0 0
\(451\) −19536.0 −2.03972
\(452\) 11858.0 1.23397
\(453\) 18720.0 1.94159
\(454\) −1686.00 −0.174291
\(455\) 0 0
\(456\) 10260.0 1.05366
\(457\) −18102.0 −1.85290 −0.926451 0.376416i \(-0.877156\pi\)
−0.926451 + 0.376416i \(0.877156\pi\)
\(458\) 4026.00 0.410748
\(459\) 2592.00 0.263582
\(460\) 0 0
\(461\) 2574.00 0.260050 0.130025 0.991511i \(-0.458494\pi\)
0.130025 + 0.991511i \(0.458494\pi\)
\(462\) 0 0
\(463\) 12832.0 1.28802 0.644010 0.765017i \(-0.277269\pi\)
0.644010 + 0.765017i \(0.277269\pi\)
\(464\) 5986.00 0.598907
\(465\) 0 0
\(466\) −6074.00 −0.603804
\(467\) −7170.00 −0.710467 −0.355233 0.934778i \(-0.615599\pi\)
−0.355233 + 0.934778i \(0.615599\pi\)
\(468\) 378.000 0.0373356
\(469\) 0 0
\(470\) 0 0
\(471\) −12636.0 −1.23617
\(472\) 4410.00 0.430057
\(473\) 21648.0 2.10439
\(474\) 3576.00 0.346521
\(475\) 0 0
\(476\) 0 0
\(477\) −450.000 −0.0431951
\(478\) −3928.00 −0.375863
\(479\) −10164.0 −0.969530 −0.484765 0.874644i \(-0.661095\pi\)
−0.484765 + 0.874644i \(0.661095\pi\)
\(480\) 0 0
\(481\) −1260.00 −0.119441
\(482\) 1236.00 0.116801
\(483\) 0 0
\(484\) −4235.00 −0.397727
\(485\) 0 0
\(486\) −2430.00 −0.226805
\(487\) −10212.0 −0.950205 −0.475103 0.879930i \(-0.657589\pi\)
−0.475103 + 0.879930i \(0.657589\pi\)
\(488\) 6750.00 0.626144
\(489\) 3768.00 0.348456
\(490\) 0 0
\(491\) −7972.00 −0.732732 −0.366366 0.930471i \(-0.619398\pi\)
−0.366366 + 0.930471i \(0.619398\pi\)
\(492\) 18648.0 1.70877
\(493\) 3504.00 0.320106
\(494\) −684.000 −0.0622968
\(495\) 0 0
\(496\) −11316.0 −1.02440
\(497\) 0 0
\(498\) 5796.00 0.521536
\(499\) −1548.00 −0.138874 −0.0694369 0.997586i \(-0.522120\pi\)
−0.0694369 + 0.997586i \(0.522120\pi\)
\(500\) 0 0
\(501\) 7704.00 0.687005
\(502\) 78.0000 0.00693488
\(503\) −1368.00 −0.121265 −0.0606323 0.998160i \(-0.519312\pi\)
−0.0606323 + 0.998160i \(0.519312\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 2288.00 0.201016
\(507\) 12966.0 1.13578
\(508\) 6412.00 0.560013
\(509\) −8274.00 −0.720508 −0.360254 0.932854i \(-0.617310\pi\)
−0.360254 + 0.932854i \(0.617310\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −11521.0 −0.994455
\(513\) −12312.0 −1.05963
\(514\) −3276.00 −0.281125
\(515\) 0 0
\(516\) −20664.0 −1.76295
\(517\) −26928.0 −2.29070
\(518\) 0 0
\(519\) −5436.00 −0.459757
\(520\) 0 0
\(521\) 20268.0 1.70433 0.852166 0.523271i \(-0.175289\pi\)
0.852166 + 0.523271i \(0.175289\pi\)
\(522\) −1314.00 −0.110177
\(523\) 1302.00 0.108858 0.0544288 0.998518i \(-0.482666\pi\)
0.0544288 + 0.998518i \(0.482666\pi\)
\(524\) 7014.00 0.584748
\(525\) 0 0
\(526\) 2240.00 0.185682
\(527\) −6624.00 −0.547526
\(528\) 10824.0 0.892148
\(529\) −9463.00 −0.777760
\(530\) 0 0
\(531\) 2646.00 0.216246
\(532\) 0 0
\(533\) −2664.00 −0.216493
\(534\) −2448.00 −0.198381
\(535\) 0 0
\(536\) 10020.0 0.807459
\(537\) 12504.0 1.00482
\(538\) −4494.00 −0.360130
\(539\) 0 0
\(540\) 0 0
\(541\) −8314.00 −0.660715 −0.330357 0.943856i \(-0.607169\pi\)
−0.330357 + 0.943856i \(0.607169\pi\)
\(542\) −3216.00 −0.254869
\(543\) 28044.0 2.21636
\(544\) −3864.00 −0.304536
\(545\) 0 0
\(546\) 0 0
\(547\) 9484.00 0.741328 0.370664 0.928767i \(-0.379130\pi\)
0.370664 + 0.928767i \(0.379130\pi\)
\(548\) −1918.00 −0.149513
\(549\) 4050.00 0.314845
\(550\) 0 0
\(551\) −16644.0 −1.28686
\(552\) −4680.00 −0.360859
\(553\) 0 0
\(554\) 1514.00 0.116108
\(555\) 0 0
\(556\) 1890.00 0.144162
\(557\) −23218.0 −1.76621 −0.883104 0.469177i \(-0.844551\pi\)
−0.883104 + 0.469177i \(0.844551\pi\)
\(558\) 2484.00 0.188452
\(559\) 2952.00 0.223357
\(560\) 0 0
\(561\) 6336.00 0.476838
\(562\) 5690.00 0.427079
\(563\) −5334.00 −0.399292 −0.199646 0.979868i \(-0.563979\pi\)
−0.199646 + 0.979868i \(0.563979\pi\)
\(564\) 25704.0 1.91903
\(565\) 0 0
\(566\) −7518.00 −0.558313
\(567\) 0 0
\(568\) −4620.00 −0.341287
\(569\) −182.000 −0.0134092 −0.00670460 0.999978i \(-0.502134\pi\)
−0.00670460 + 0.999978i \(0.502134\pi\)
\(570\) 0 0
\(571\) 14164.0 1.03808 0.519041 0.854749i \(-0.326289\pi\)
0.519041 + 0.854749i \(0.326289\pi\)
\(572\) −1848.00 −0.135085
\(573\) −12072.0 −0.880131
\(574\) 0 0
\(575\) 0 0
\(576\) −1503.00 −0.108724
\(577\) 13740.0 0.991341 0.495670 0.868511i \(-0.334922\pi\)
0.495670 + 0.868511i \(0.334922\pi\)
\(578\) 4337.00 0.312103
\(579\) 25236.0 1.81135
\(580\) 0 0
\(581\) 0 0
\(582\) 7200.00 0.512800
\(583\) 2200.00 0.156286
\(584\) −180.000 −0.0127542
\(585\) 0 0
\(586\) −702.000 −0.0494870
\(587\) −9174.00 −0.645062 −0.322531 0.946559i \(-0.604534\pi\)
−0.322531 + 0.946559i \(0.604534\pi\)
\(588\) 0 0
\(589\) 31464.0 2.20111
\(590\) 0 0
\(591\) −9444.00 −0.657317
\(592\) 8610.00 0.597751
\(593\) −14580.0 −1.00966 −0.504830 0.863219i \(-0.668445\pi\)
−0.504830 + 0.863219i \(0.668445\pi\)
\(594\) 4752.00 0.328244
\(595\) 0 0
\(596\) 3710.00 0.254979
\(597\) 16344.0 1.12046
\(598\) 312.000 0.0213355
\(599\) 1988.00 0.135605 0.0678026 0.997699i \(-0.478401\pi\)
0.0678026 + 0.997699i \(0.478401\pi\)
\(600\) 0 0
\(601\) −7800.00 −0.529399 −0.264699 0.964331i \(-0.585273\pi\)
−0.264699 + 0.964331i \(0.585273\pi\)
\(602\) 0 0
\(603\) 6012.00 0.406016
\(604\) 21840.0 1.47129
\(605\) 0 0
\(606\) 6588.00 0.441616
\(607\) −24288.0 −1.62408 −0.812042 0.583598i \(-0.801644\pi\)
−0.812042 + 0.583598i \(0.801644\pi\)
\(608\) 18354.0 1.22426
\(609\) 0 0
\(610\) 0 0
\(611\) −3672.00 −0.243131
\(612\) −1512.00 −0.0998676
\(613\) 9866.00 0.650055 0.325028 0.945704i \(-0.394626\pi\)
0.325028 + 0.945704i \(0.394626\pi\)
\(614\) −10374.0 −0.681858
\(615\) 0 0
\(616\) 0 0
\(617\) −22858.0 −1.49146 −0.745728 0.666250i \(-0.767898\pi\)
−0.745728 + 0.666250i \(0.767898\pi\)
\(618\) −5832.00 −0.379608
\(619\) −19074.0 −1.23853 −0.619264 0.785183i \(-0.712569\pi\)
−0.619264 + 0.785183i \(0.712569\pi\)
\(620\) 0 0
\(621\) 5616.00 0.362902
\(622\) 2784.00 0.179467
\(623\) 0 0
\(624\) 1476.00 0.0946912
\(625\) 0 0
\(626\) 6216.00 0.396871
\(627\) −30096.0 −1.91694
\(628\) −14742.0 −0.936735
\(629\) 5040.00 0.319488
\(630\) 0 0
\(631\) 22084.0 1.39326 0.696632 0.717428i \(-0.254681\pi\)
0.696632 + 0.717428i \(0.254681\pi\)
\(632\) 8940.00 0.562681
\(633\) 1080.00 0.0678138
\(634\) 5066.00 0.317345
\(635\) 0 0
\(636\) −2100.00 −0.130928
\(637\) 0 0
\(638\) 6424.00 0.398634
\(639\) −2772.00 −0.171610
\(640\) 0 0
\(641\) −16622.0 −1.02423 −0.512114 0.858918i \(-0.671137\pi\)
−0.512114 + 0.858918i \(0.671137\pi\)
\(642\) −9096.00 −0.559175
\(643\) 12906.0 0.791544 0.395772 0.918349i \(-0.370477\pi\)
0.395772 + 0.918349i \(0.370477\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 2736.00 0.166635
\(647\) −3156.00 −0.191770 −0.0958850 0.995392i \(-0.530568\pi\)
−0.0958850 + 0.995392i \(0.530568\pi\)
\(648\) −13365.0 −0.810227
\(649\) −12936.0 −0.782407
\(650\) 0 0
\(651\) 0 0
\(652\) 4396.00 0.264050
\(653\) 3658.00 0.219217 0.109608 0.993975i \(-0.465040\pi\)
0.109608 + 0.993975i \(0.465040\pi\)
\(654\) 5580.00 0.333632
\(655\) 0 0
\(656\) 18204.0 1.08346
\(657\) −108.000 −0.00641321
\(658\) 0 0
\(659\) −12316.0 −0.728017 −0.364009 0.931396i \(-0.618592\pi\)
−0.364009 + 0.931396i \(0.618592\pi\)
\(660\) 0 0
\(661\) 32298.0 1.90052 0.950262 0.311451i \(-0.100815\pi\)
0.950262 + 0.311451i \(0.100815\pi\)
\(662\) 6468.00 0.379737
\(663\) 864.000 0.0506108
\(664\) 14490.0 0.846869
\(665\) 0 0
\(666\) −1890.00 −0.109964
\(667\) 7592.00 0.440725
\(668\) 8988.00 0.520593
\(669\) −27504.0 −1.58949
\(670\) 0 0
\(671\) −19800.0 −1.13915
\(672\) 0 0
\(673\) 23274.0 1.33306 0.666528 0.745480i \(-0.267780\pi\)
0.666528 + 0.745480i \(0.267780\pi\)
\(674\) −3438.00 −0.196479
\(675\) 0 0
\(676\) 15127.0 0.860662
\(677\) −4518.00 −0.256486 −0.128243 0.991743i \(-0.540934\pi\)
−0.128243 + 0.991743i \(0.540934\pi\)
\(678\) −10164.0 −0.575732
\(679\) 0 0
\(680\) 0 0
\(681\) −10116.0 −0.569230
\(682\) −12144.0 −0.681844
\(683\) 19636.0 1.10007 0.550037 0.835140i \(-0.314614\pi\)
0.550037 + 0.835140i \(0.314614\pi\)
\(684\) 7182.00 0.401478
\(685\) 0 0
\(686\) 0 0
\(687\) 24156.0 1.34150
\(688\) −20172.0 −1.11781
\(689\) 300.000 0.0165879
\(690\) 0 0
\(691\) −17226.0 −0.948347 −0.474174 0.880431i \(-0.657253\pi\)
−0.474174 + 0.880431i \(0.657253\pi\)
\(692\) −6342.00 −0.348391
\(693\) 0 0
\(694\) 2212.00 0.120989
\(695\) 0 0
\(696\) −13140.0 −0.715618
\(697\) 10656.0 0.579089
\(698\) −2910.00 −0.157801
\(699\) −36444.0 −1.97202
\(700\) 0 0
\(701\) 21362.0 1.15097 0.575486 0.817812i \(-0.304813\pi\)
0.575486 + 0.817812i \(0.304813\pi\)
\(702\) 648.000 0.0348393
\(703\) −23940.0 −1.28437
\(704\) 7348.00 0.393378
\(705\) 0 0
\(706\) 8364.00 0.445869
\(707\) 0 0
\(708\) 12348.0 0.655461
\(709\) 8658.00 0.458615 0.229307 0.973354i \(-0.426354\pi\)
0.229307 + 0.973354i \(0.426354\pi\)
\(710\) 0 0
\(711\) 5364.00 0.282933
\(712\) −6120.00 −0.322130
\(713\) −14352.0 −0.753838
\(714\) 0 0
\(715\) 0 0
\(716\) 14588.0 0.761423
\(717\) −23568.0 −1.22756
\(718\) 6712.00 0.348871
\(719\) 29484.0 1.52930 0.764651 0.644445i \(-0.222912\pi\)
0.764651 + 0.644445i \(0.222912\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −6137.00 −0.316337
\(723\) 7416.00 0.381472
\(724\) 32718.0 1.67950
\(725\) 0 0
\(726\) 3630.00 0.185567
\(727\) 28260.0 1.44169 0.720843 0.693099i \(-0.243755\pi\)
0.720843 + 0.693099i \(0.243755\pi\)
\(728\) 0 0
\(729\) 9477.00 0.481481
\(730\) 0 0
\(731\) −11808.0 −0.597448
\(732\) 18900.0 0.954323
\(733\) 10950.0 0.551770 0.275885 0.961191i \(-0.411029\pi\)
0.275885 + 0.961191i \(0.411029\pi\)
\(734\) 456.000 0.0229309
\(735\) 0 0
\(736\) −8372.00 −0.419288
\(737\) −29392.0 −1.46902
\(738\) −3996.00 −0.199315
\(739\) −9772.00 −0.486426 −0.243213 0.969973i \(-0.578201\pi\)
−0.243213 + 0.969973i \(0.578201\pi\)
\(740\) 0 0
\(741\) −4104.00 −0.203460
\(742\) 0 0
\(743\) −7844.00 −0.387306 −0.193653 0.981070i \(-0.562034\pi\)
−0.193653 + 0.981070i \(0.562034\pi\)
\(744\) 24840.0 1.22403
\(745\) 0 0
\(746\) −2558.00 −0.125543
\(747\) 8694.00 0.425832
\(748\) 7392.00 0.361335
\(749\) 0 0
\(750\) 0 0
\(751\) 1800.00 0.0874606 0.0437303 0.999043i \(-0.486076\pi\)
0.0437303 + 0.999043i \(0.486076\pi\)
\(752\) 25092.0 1.21677
\(753\) 468.000 0.0226492
\(754\) 876.000 0.0423104
\(755\) 0 0
\(756\) 0 0
\(757\) 11274.0 0.541295 0.270648 0.962678i \(-0.412762\pi\)
0.270648 + 0.962678i \(0.412762\pi\)
\(758\) −2004.00 −0.0960271
\(759\) 13728.0 0.656515
\(760\) 0 0
\(761\) 22668.0 1.07978 0.539891 0.841735i \(-0.318465\pi\)
0.539891 + 0.841735i \(0.318465\pi\)
\(762\) −5496.00 −0.261285
\(763\) 0 0
\(764\) −14084.0 −0.666939
\(765\) 0 0
\(766\) 11340.0 0.534897
\(767\) −1764.00 −0.0830435
\(768\) 714.000 0.0335472
\(769\) −15468.0 −0.725345 −0.362673 0.931917i \(-0.618136\pi\)
−0.362673 + 0.931917i \(0.618136\pi\)
\(770\) 0 0
\(771\) −19656.0 −0.918150
\(772\) 29442.0 1.37259
\(773\) −28986.0 −1.34871 −0.674356 0.738407i \(-0.735579\pi\)
−0.674356 + 0.738407i \(0.735579\pi\)
\(774\) 4428.00 0.205635
\(775\) 0 0
\(776\) 18000.0 0.832683
\(777\) 0 0
\(778\) −10522.0 −0.484874
\(779\) −50616.0 −2.32799
\(780\) 0 0
\(781\) 13552.0 0.620907
\(782\) −1248.00 −0.0570696
\(783\) 15768.0 0.719671
\(784\) 0 0
\(785\) 0 0
\(786\) −6012.00 −0.272826
\(787\) −20562.0 −0.931329 −0.465665 0.884961i \(-0.654185\pi\)
−0.465665 + 0.884961i \(0.654185\pi\)
\(788\) −11018.0 −0.498096
\(789\) 13440.0 0.606434
\(790\) 0 0
\(791\) 0 0
\(792\) −5940.00 −0.266501
\(793\) −2700.00 −0.120908
\(794\) −2898.00 −0.129529
\(795\) 0 0
\(796\) 19068.0 0.849054
\(797\) 20826.0 0.925589 0.462795 0.886465i \(-0.346847\pi\)
0.462795 + 0.886465i \(0.346847\pi\)
\(798\) 0 0
\(799\) 14688.0 0.650343
\(800\) 0 0
\(801\) −3672.00 −0.161977
\(802\) −3026.00 −0.133232
\(803\) 528.000 0.0232039
\(804\) 28056.0 1.23067
\(805\) 0 0
\(806\) −1656.00 −0.0723699
\(807\) −26964.0 −1.17618
\(808\) 16470.0 0.717095
\(809\) −4250.00 −0.184700 −0.0923498 0.995727i \(-0.529438\pi\)
−0.0923498 + 0.995727i \(0.529438\pi\)
\(810\) 0 0
\(811\) 24342.0 1.05396 0.526981 0.849877i \(-0.323324\pi\)
0.526981 + 0.849877i \(0.323324\pi\)
\(812\) 0 0
\(813\) −19296.0 −0.832399
\(814\) 9240.00 0.397865
\(815\) 0 0
\(816\) −5904.00 −0.253286
\(817\) 56088.0 2.40180
\(818\) 8940.00 0.382127
\(819\) 0 0
\(820\) 0 0
\(821\) −2138.00 −0.0908852 −0.0454426 0.998967i \(-0.514470\pi\)
−0.0454426 + 0.998967i \(0.514470\pi\)
\(822\) 1644.00 0.0697580
\(823\) −9560.00 −0.404910 −0.202455 0.979292i \(-0.564892\pi\)
−0.202455 + 0.979292i \(0.564892\pi\)
\(824\) −14580.0 −0.616406
\(825\) 0 0
\(826\) 0 0
\(827\) −7748.00 −0.325785 −0.162893 0.986644i \(-0.552082\pi\)
−0.162893 + 0.986644i \(0.552082\pi\)
\(828\) −3276.00 −0.137499
\(829\) −5334.00 −0.223471 −0.111736 0.993738i \(-0.535641\pi\)
−0.111736 + 0.993738i \(0.535641\pi\)
\(830\) 0 0
\(831\) 9084.00 0.379206
\(832\) 1002.00 0.0417525
\(833\) 0 0
\(834\) −1620.00 −0.0672614
\(835\) 0 0
\(836\) −35112.0 −1.45260
\(837\) −29808.0 −1.23096
\(838\) −2994.00 −0.123420
\(839\) −36444.0 −1.49963 −0.749813 0.661650i \(-0.769857\pi\)
−0.749813 + 0.661650i \(0.769857\pi\)
\(840\) 0 0
\(841\) −3073.00 −0.125999
\(842\) −15766.0 −0.645288
\(843\) 34140.0 1.39483
\(844\) 1260.00 0.0513874
\(845\) 0 0
\(846\) −5508.00 −0.223840
\(847\) 0 0
\(848\) −2050.00 −0.0830157
\(849\) −45108.0 −1.82344
\(850\) 0 0
\(851\) 10920.0 0.439874
\(852\) −12936.0 −0.520164
\(853\) −21030.0 −0.844142 −0.422071 0.906563i \(-0.638697\pi\)
−0.422071 + 0.906563i \(0.638697\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −22740.0 −0.907987
\(857\) 32328.0 1.28857 0.644284 0.764786i \(-0.277155\pi\)
0.644284 + 0.764786i \(0.277155\pi\)
\(858\) 1584.00 0.0630267
\(859\) −43518.0 −1.72854 −0.864269 0.503029i \(-0.832219\pi\)
−0.864269 + 0.503029i \(0.832219\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) −14720.0 −0.581630
\(863\) 5032.00 0.198484 0.0992418 0.995063i \(-0.468358\pi\)
0.0992418 + 0.995063i \(0.468358\pi\)
\(864\) −17388.0 −0.684666
\(865\) 0 0
\(866\) 4440.00 0.174223
\(867\) 26022.0 1.01932
\(868\) 0 0
\(869\) −26224.0 −1.02369
\(870\) 0 0
\(871\) −4008.00 −0.155920
\(872\) 13950.0 0.541751
\(873\) 10800.0 0.418699
\(874\) 5928.00 0.229425
\(875\) 0 0
\(876\) −504.000 −0.0194390
\(877\) −4286.00 −0.165026 −0.0825131 0.996590i \(-0.526295\pi\)
−0.0825131 + 0.996590i \(0.526295\pi\)
\(878\) 1488.00 0.0571954
\(879\) −4212.00 −0.161624
\(880\) 0 0
\(881\) 19080.0 0.729650 0.364825 0.931076i \(-0.381129\pi\)
0.364825 + 0.931076i \(0.381129\pi\)
\(882\) 0 0
\(883\) −26580.0 −1.01301 −0.506505 0.862237i \(-0.669063\pi\)
−0.506505 + 0.862237i \(0.669063\pi\)
\(884\) 1008.00 0.0383515
\(885\) 0 0
\(886\) −5828.00 −0.220988
\(887\) −12588.0 −0.476509 −0.238255 0.971203i \(-0.576575\pi\)
−0.238255 + 0.971203i \(0.576575\pi\)
\(888\) −18900.0 −0.714237
\(889\) 0 0
\(890\) 0 0
\(891\) 39204.0 1.47406
\(892\) −32088.0 −1.20447
\(893\) −69768.0 −2.61444
\(894\) −3180.00 −0.118965
\(895\) 0 0
\(896\) 0 0
\(897\) 1872.00 0.0696815
\(898\) 6958.00 0.258565
\(899\) −40296.0 −1.49494
\(900\) 0 0
\(901\) −1200.00 −0.0443705
\(902\) 19536.0 0.721150
\(903\) 0 0
\(904\) −25410.0 −0.934872
\(905\) 0 0
\(906\) −18720.0 −0.686457
\(907\) 19332.0 0.707727 0.353864 0.935297i \(-0.384868\pi\)
0.353864 + 0.935297i \(0.384868\pi\)
\(908\) −11802.0 −0.431347
\(909\) 9882.00 0.360578
\(910\) 0 0
\(911\) −43640.0 −1.58711 −0.793555 0.608498i \(-0.791772\pi\)
−0.793555 + 0.608498i \(0.791772\pi\)
\(912\) 28044.0 1.01823
\(913\) −42504.0 −1.54072
\(914\) 18102.0 0.655099
\(915\) 0 0
\(916\) 28182.0 1.01655
\(917\) 0 0
\(918\) −2592.00 −0.0931904
\(919\) 9084.00 0.326065 0.163032 0.986621i \(-0.447872\pi\)
0.163032 + 0.986621i \(0.447872\pi\)
\(920\) 0 0
\(921\) −62244.0 −2.22694
\(922\) −2574.00 −0.0919416
\(923\) 1848.00 0.0659021
\(924\) 0 0
\(925\) 0 0
\(926\) −12832.0 −0.455384
\(927\) −8748.00 −0.309948
\(928\) −23506.0 −0.831489
\(929\) −48228.0 −1.70324 −0.851620 0.524160i \(-0.824379\pi\)
−0.851620 + 0.524160i \(0.824379\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) −42518.0 −1.49434
\(933\) 16704.0 0.586135
\(934\) 7170.00 0.251188
\(935\) 0 0
\(936\) −810.000 −0.0282860
\(937\) −39204.0 −1.36685 −0.683425 0.730021i \(-0.739510\pi\)
−0.683425 + 0.730021i \(0.739510\pi\)
\(938\) 0 0
\(939\) 37296.0 1.29618
\(940\) 0 0
\(941\) 4770.00 0.165247 0.0826236 0.996581i \(-0.473670\pi\)
0.0826236 + 0.996581i \(0.473670\pi\)
\(942\) 12636.0 0.437052
\(943\) 23088.0 0.797295
\(944\) 12054.0 0.415598
\(945\) 0 0
\(946\) −21648.0 −0.744014
\(947\) −56236.0 −1.92970 −0.964849 0.262804i \(-0.915353\pi\)
−0.964849 + 0.262804i \(0.915353\pi\)
\(948\) 25032.0 0.857597
\(949\) 72.0000 0.00246282
\(950\) 0 0
\(951\) 30396.0 1.03644
\(952\) 0 0
\(953\) 52814.0 1.79519 0.897594 0.440824i \(-0.145314\pi\)
0.897594 + 0.440824i \(0.145314\pi\)
\(954\) 450.000 0.0152718
\(955\) 0 0
\(956\) −27496.0 −0.930214
\(957\) 38544.0 1.30193
\(958\) 10164.0 0.342781
\(959\) 0 0
\(960\) 0 0
\(961\) 46385.0 1.55701
\(962\) 1260.00 0.0422287
\(963\) −13644.0 −0.456565
\(964\) 8652.00 0.289069
\(965\) 0 0
\(966\) 0 0
\(967\) 39364.0 1.30906 0.654530 0.756036i \(-0.272867\pi\)
0.654530 + 0.756036i \(0.272867\pi\)
\(968\) 9075.00 0.301324
\(969\) 16416.0 0.544229
\(970\) 0 0
\(971\) −29322.0 −0.969091 −0.484546 0.874766i \(-0.661015\pi\)
−0.484546 + 0.874766i \(0.661015\pi\)
\(972\) −17010.0 −0.561313
\(973\) 0 0
\(974\) 10212.0 0.335948
\(975\) 0 0
\(976\) 18450.0 0.605092
\(977\) 35882.0 1.17499 0.587496 0.809227i \(-0.300114\pi\)
0.587496 + 0.809227i \(0.300114\pi\)
\(978\) −3768.00 −0.123198
\(979\) 17952.0 0.586056
\(980\) 0 0
\(981\) 8370.00 0.272409
\(982\) 7972.00 0.259060
\(983\) 32580.0 1.05711 0.528556 0.848899i \(-0.322734\pi\)
0.528556 + 0.848899i \(0.322734\pi\)
\(984\) −39960.0 −1.29459
\(985\) 0 0
\(986\) −3504.00 −0.113175
\(987\) 0 0
\(988\) −4788.00 −0.154177
\(989\) −25584.0 −0.822572
\(990\) 0 0
\(991\) −30036.0 −0.962790 −0.481395 0.876504i \(-0.659870\pi\)
−0.481395 + 0.876504i \(0.659870\pi\)
\(992\) 44436.0 1.42222
\(993\) 38808.0 1.24022
\(994\) 0 0
\(995\) 0 0
\(996\) 40572.0 1.29074
\(997\) 25134.0 0.798397 0.399198 0.916865i \(-0.369288\pi\)
0.399198 + 0.916865i \(0.369288\pi\)
\(998\) 1548.00 0.0490993
\(999\) 22680.0 0.718282
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 1225.4.a.f.1.1 1
5.4 even 2 245.4.a.c.1.1 yes 1
7.6 odd 2 1225.4.a.g.1.1 1
15.14 odd 2 2205.4.a.n.1.1 1
35.4 even 6 245.4.e.c.226.1 2
35.9 even 6 245.4.e.c.116.1 2
35.19 odd 6 245.4.e.d.116.1 2
35.24 odd 6 245.4.e.d.226.1 2
35.34 odd 2 245.4.a.b.1.1 1
105.104 even 2 2205.4.a.k.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
245.4.a.b.1.1 1 35.34 odd 2
245.4.a.c.1.1 yes 1 5.4 even 2
245.4.e.c.116.1 2 35.9 even 6
245.4.e.c.226.1 2 35.4 even 6
245.4.e.d.116.1 2 35.19 odd 6
245.4.e.d.226.1 2 35.24 odd 6
1225.4.a.f.1.1 1 1.1 even 1 trivial
1225.4.a.g.1.1 1 7.6 odd 2
2205.4.a.k.1.1 1 105.104 even 2
2205.4.a.n.1.1 1 15.14 odd 2