Properties

Label 4014.2.a.v.1.7
Level $4014$
Weight $2$
Character 4014.1
Self dual yes
Analytic conductor $32.052$
Analytic rank $0$
Dimension $7$
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] = [4014,2,Mod(1,4014)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4014, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("4014.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4014 = 2 \cdot 3^{2} \cdot 223 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4014.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: \(32.0519513713\)
Analytic rank: \(0\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{7} - 18x^{5} - 8x^{4} + 51x^{3} + 47x^{2} - 2x - 8 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1338)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(-0.788998\) of defining polynomial
Character \(\chi\) \(=\) 4014.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{4} +3.73564 q^{5} +2.27800 q^{7} -1.00000 q^{8} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{4} +3.73564 q^{5} +2.27800 q^{7} -1.00000 q^{8} -3.73564 q^{10} +6.01441 q^{11} +0.852078 q^{13} -2.27800 q^{14} +1.00000 q^{16} -4.60921 q^{17} +1.48612 q^{19} +3.73564 q^{20} -6.01441 q^{22} -4.21204 q^{23} +8.95498 q^{25} -0.852078 q^{26} +2.27800 q^{28} -1.52437 q^{29} +6.58406 q^{31} -1.00000 q^{32} +4.60921 q^{34} +8.50979 q^{35} +4.42642 q^{37} -1.48612 q^{38} -3.73564 q^{40} -10.1716 q^{41} +0.917382 q^{43} +6.01441 q^{44} +4.21204 q^{46} +8.32897 q^{47} -1.81071 q^{49} -8.95498 q^{50} +0.852078 q^{52} +6.28830 q^{53} +22.4676 q^{55} -2.27800 q^{56} +1.52437 q^{58} -4.62427 q^{59} +2.47563 q^{61} -6.58406 q^{62} +1.00000 q^{64} +3.18305 q^{65} +3.43979 q^{67} -4.60921 q^{68} -8.50979 q^{70} -0.919349 q^{71} -1.20422 q^{73} -4.42642 q^{74} +1.48612 q^{76} +13.7008 q^{77} +12.3064 q^{79} +3.73564 q^{80} +10.1716 q^{82} -12.1582 q^{83} -17.2183 q^{85} -0.917382 q^{86} -6.01441 q^{88} +1.06503 q^{89} +1.94104 q^{91} -4.21204 q^{92} -8.32897 q^{94} +5.55162 q^{95} -2.53493 q^{97} +1.81071 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7 q - 7 q^{2} + 7 q^{4} - 6 q^{5} + 3 q^{7} - 7 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 7 q - 7 q^{2} + 7 q^{4} - 6 q^{5} + 3 q^{7} - 7 q^{8} + 6 q^{10} + q^{11} + 8 q^{13} - 3 q^{14} + 7 q^{16} - 16 q^{17} + 2 q^{19} - 6 q^{20} - q^{22} - 8 q^{23} + 19 q^{25} - 8 q^{26} + 3 q^{28} - 4 q^{29} + 11 q^{31} - 7 q^{32} + 16 q^{34} + 17 q^{37} - 2 q^{38} + 6 q^{40} - 18 q^{41} - q^{43} + q^{44} + 8 q^{46} - 5 q^{47} + 24 q^{49} - 19 q^{50} + 8 q^{52} - 6 q^{53} + 21 q^{55} - 3 q^{56} + 4 q^{58} + 7 q^{59} + 24 q^{61} - 11 q^{62} + 7 q^{64} - 11 q^{65} - 4 q^{67} - 16 q^{68} + 7 q^{71} + 28 q^{73} - 17 q^{74} + 2 q^{76} + 2 q^{77} - 6 q^{80} + 18 q^{82} + 2 q^{83} + 4 q^{85} + q^{86} - q^{88} - 5 q^{89} + 2 q^{91} - 8 q^{92} + 5 q^{94} + 14 q^{95} + 23 q^{97} - 24 q^{98}+O(q^{100}) \) Copy content Toggle raw display

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 −0.707107
\(3\) 0 0
\(4\) 1.00000 0.500000
\(5\) 3.73564 1.67063 0.835314 0.549774i \(-0.185286\pi\)
0.835314 + 0.549774i \(0.185286\pi\)
\(6\) 0 0
\(7\) 2.27800 0.861004 0.430502 0.902590i \(-0.358337\pi\)
0.430502 + 0.902590i \(0.358337\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) −3.73564 −1.18131
\(11\) 6.01441 1.81341 0.906706 0.421763i \(-0.138589\pi\)
0.906706 + 0.421763i \(0.138589\pi\)
\(12\) 0 0
\(13\) 0.852078 0.236324 0.118162 0.992994i \(-0.462300\pi\)
0.118162 + 0.992994i \(0.462300\pi\)
\(14\) −2.27800 −0.608822
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −4.60921 −1.11790 −0.558949 0.829202i \(-0.688795\pi\)
−0.558949 + 0.829202i \(0.688795\pi\)
\(18\) 0 0
\(19\) 1.48612 0.340940 0.170470 0.985363i \(-0.445471\pi\)
0.170470 + 0.985363i \(0.445471\pi\)
\(20\) 3.73564 0.835314
\(21\) 0 0
\(22\) −6.01441 −1.28228
\(23\) −4.21204 −0.878271 −0.439136 0.898421i \(-0.644715\pi\)
−0.439136 + 0.898421i \(0.644715\pi\)
\(24\) 0 0
\(25\) 8.95498 1.79100
\(26\) −0.852078 −0.167106
\(27\) 0 0
\(28\) 2.27800 0.430502
\(29\) −1.52437 −0.283068 −0.141534 0.989933i \(-0.545203\pi\)
−0.141534 + 0.989933i \(0.545203\pi\)
\(30\) 0 0
\(31\) 6.58406 1.18253 0.591266 0.806476i \(-0.298628\pi\)
0.591266 + 0.806476i \(0.298628\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) 4.60921 0.790473
\(35\) 8.50979 1.43842
\(36\) 0 0
\(37\) 4.42642 0.727699 0.363850 0.931458i \(-0.381462\pi\)
0.363850 + 0.931458i \(0.381462\pi\)
\(38\) −1.48612 −0.241081
\(39\) 0 0
\(40\) −3.73564 −0.590656
\(41\) −10.1716 −1.58853 −0.794267 0.607568i \(-0.792145\pi\)
−0.794267 + 0.607568i \(0.792145\pi\)
\(42\) 0 0
\(43\) 0.917382 0.139899 0.0699497 0.997551i \(-0.477716\pi\)
0.0699497 + 0.997551i \(0.477716\pi\)
\(44\) 6.01441 0.906706
\(45\) 0 0
\(46\) 4.21204 0.621032
\(47\) 8.32897 1.21490 0.607452 0.794356i \(-0.292192\pi\)
0.607452 + 0.794356i \(0.292192\pi\)
\(48\) 0 0
\(49\) −1.81071 −0.258673
\(50\) −8.95498 −1.26643
\(51\) 0 0
\(52\) 0.852078 0.118162
\(53\) 6.28830 0.863764 0.431882 0.901930i \(-0.357850\pi\)
0.431882 + 0.901930i \(0.357850\pi\)
\(54\) 0 0
\(55\) 22.4676 3.02954
\(56\) −2.27800 −0.304411
\(57\) 0 0
\(58\) 1.52437 0.200159
\(59\) −4.62427 −0.602029 −0.301014 0.953620i \(-0.597325\pi\)
−0.301014 + 0.953620i \(0.597325\pi\)
\(60\) 0 0
\(61\) 2.47563 0.316973 0.158486 0.987361i \(-0.449339\pi\)
0.158486 + 0.987361i \(0.449339\pi\)
\(62\) −6.58406 −0.836177
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 3.18305 0.394809
\(66\) 0 0
\(67\) 3.43979 0.420238 0.210119 0.977676i \(-0.432615\pi\)
0.210119 + 0.977676i \(0.432615\pi\)
\(68\) −4.60921 −0.558949
\(69\) 0 0
\(70\) −8.50979 −1.01711
\(71\) −0.919349 −0.109107 −0.0545533 0.998511i \(-0.517373\pi\)
−0.0545533 + 0.998511i \(0.517373\pi\)
\(72\) 0 0
\(73\) −1.20422 −0.140944 −0.0704718 0.997514i \(-0.522450\pi\)
−0.0704718 + 0.997514i \(0.522450\pi\)
\(74\) −4.42642 −0.514561
\(75\) 0 0
\(76\) 1.48612 0.170470
\(77\) 13.7008 1.56135
\(78\) 0 0
\(79\) 12.3064 1.38457 0.692287 0.721623i \(-0.256603\pi\)
0.692287 + 0.721623i \(0.256603\pi\)
\(80\) 3.73564 0.417657
\(81\) 0 0
\(82\) 10.1716 1.12326
\(83\) −12.1582 −1.33453 −0.667266 0.744820i \(-0.732535\pi\)
−0.667266 + 0.744820i \(0.732535\pi\)
\(84\) 0 0
\(85\) −17.2183 −1.86759
\(86\) −0.917382 −0.0989239
\(87\) 0 0
\(88\) −6.01441 −0.641138
\(89\) 1.06503 0.112893 0.0564466 0.998406i \(-0.482023\pi\)
0.0564466 + 0.998406i \(0.482023\pi\)
\(90\) 0 0
\(91\) 1.94104 0.203476
\(92\) −4.21204 −0.439136
\(93\) 0 0
\(94\) −8.32897 −0.859067
\(95\) 5.55162 0.569584
\(96\) 0 0
\(97\) −2.53493 −0.257383 −0.128692 0.991685i \(-0.541078\pi\)
−0.128692 + 0.991685i \(0.541078\pi\)
\(98\) 1.81071 0.182909
\(99\) 0 0
\(100\) 8.95498 0.895498
\(101\) −4.75076 −0.472718 −0.236359 0.971666i \(-0.575954\pi\)
−0.236359 + 0.971666i \(0.575954\pi\)
\(102\) 0 0
\(103\) 8.46155 0.833742 0.416871 0.908966i \(-0.363127\pi\)
0.416871 + 0.908966i \(0.363127\pi\)
\(104\) −0.852078 −0.0835531
\(105\) 0 0
\(106\) −6.28830 −0.610773
\(107\) −1.43645 −0.138867 −0.0694333 0.997587i \(-0.522119\pi\)
−0.0694333 + 0.997587i \(0.522119\pi\)
\(108\) 0 0
\(109\) 12.5744 1.20441 0.602205 0.798342i \(-0.294289\pi\)
0.602205 + 0.798342i \(0.294289\pi\)
\(110\) −22.4676 −2.14221
\(111\) 0 0
\(112\) 2.27800 0.215251
\(113\) −1.42716 −0.134256 −0.0671279 0.997744i \(-0.521384\pi\)
−0.0671279 + 0.997744i \(0.521384\pi\)
\(114\) 0 0
\(115\) −15.7347 −1.46726
\(116\) −1.52437 −0.141534
\(117\) 0 0
\(118\) 4.62427 0.425699
\(119\) −10.4998 −0.962514
\(120\) 0 0
\(121\) 25.1731 2.28846
\(122\) −2.47563 −0.224133
\(123\) 0 0
\(124\) 6.58406 0.591266
\(125\) 14.7744 1.32146
\(126\) 0 0
\(127\) −21.3436 −1.89394 −0.946971 0.321319i \(-0.895874\pi\)
−0.946971 + 0.321319i \(0.895874\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 0 0
\(130\) −3.18305 −0.279172
\(131\) −17.7225 −1.54842 −0.774209 0.632930i \(-0.781852\pi\)
−0.774209 + 0.632930i \(0.781852\pi\)
\(132\) 0 0
\(133\) 3.38539 0.293551
\(134\) −3.43979 −0.297153
\(135\) 0 0
\(136\) 4.60921 0.395236
\(137\) −8.40769 −0.718318 −0.359159 0.933276i \(-0.616936\pi\)
−0.359159 + 0.933276i \(0.616936\pi\)
\(138\) 0 0
\(139\) −16.6796 −1.41474 −0.707371 0.706842i \(-0.750119\pi\)
−0.707371 + 0.706842i \(0.750119\pi\)
\(140\) 8.50979 0.719208
\(141\) 0 0
\(142\) 0.919349 0.0771500
\(143\) 5.12474 0.428553
\(144\) 0 0
\(145\) −5.69448 −0.472900
\(146\) 1.20422 0.0996622
\(147\) 0 0
\(148\) 4.42642 0.363850
\(149\) 20.0642 1.64372 0.821861 0.569688i \(-0.192936\pi\)
0.821861 + 0.569688i \(0.192936\pi\)
\(150\) 0 0
\(151\) −17.7405 −1.44370 −0.721852 0.692048i \(-0.756709\pi\)
−0.721852 + 0.692048i \(0.756709\pi\)
\(152\) −1.48612 −0.120541
\(153\) 0 0
\(154\) −13.7008 −1.10404
\(155\) 24.5957 1.97557
\(156\) 0 0
\(157\) −2.78869 −0.222562 −0.111281 0.993789i \(-0.535495\pi\)
−0.111281 + 0.993789i \(0.535495\pi\)
\(158\) −12.3064 −0.979041
\(159\) 0 0
\(160\) −3.73564 −0.295328
\(161\) −9.59504 −0.756195
\(162\) 0 0
\(163\) −14.9595 −1.17172 −0.585859 0.810413i \(-0.699243\pi\)
−0.585859 + 0.810413i \(0.699243\pi\)
\(164\) −10.1716 −0.794267
\(165\) 0 0
\(166\) 12.1582 0.943656
\(167\) −8.34896 −0.646062 −0.323031 0.946388i \(-0.604702\pi\)
−0.323031 + 0.946388i \(0.604702\pi\)
\(168\) 0 0
\(169\) −12.2740 −0.944151
\(170\) 17.2183 1.32059
\(171\) 0 0
\(172\) 0.917382 0.0699497
\(173\) 1.30257 0.0990327 0.0495163 0.998773i \(-0.484232\pi\)
0.0495163 + 0.998773i \(0.484232\pi\)
\(174\) 0 0
\(175\) 20.3995 1.54205
\(176\) 6.01441 0.453353
\(177\) 0 0
\(178\) −1.06503 −0.0798276
\(179\) 24.7249 1.84803 0.924014 0.382359i \(-0.124888\pi\)
0.924014 + 0.382359i \(0.124888\pi\)
\(180\) 0 0
\(181\) 24.6587 1.83287 0.916435 0.400184i \(-0.131054\pi\)
0.916435 + 0.400184i \(0.131054\pi\)
\(182\) −1.94104 −0.143879
\(183\) 0 0
\(184\) 4.21204 0.310516
\(185\) 16.5355 1.21571
\(186\) 0 0
\(187\) −27.7217 −2.02721
\(188\) 8.32897 0.607452
\(189\) 0 0
\(190\) −5.55162 −0.402757
\(191\) 18.6689 1.35084 0.675418 0.737435i \(-0.263963\pi\)
0.675418 + 0.737435i \(0.263963\pi\)
\(192\) 0 0
\(193\) −21.4822 −1.54633 −0.773163 0.634207i \(-0.781327\pi\)
−0.773163 + 0.634207i \(0.781327\pi\)
\(194\) 2.53493 0.181997
\(195\) 0 0
\(196\) −1.81071 −0.129336
\(197\) −1.74494 −0.124322 −0.0621610 0.998066i \(-0.519799\pi\)
−0.0621610 + 0.998066i \(0.519799\pi\)
\(198\) 0 0
\(199\) −21.8960 −1.55217 −0.776084 0.630630i \(-0.782797\pi\)
−0.776084 + 0.630630i \(0.782797\pi\)
\(200\) −8.95498 −0.633213
\(201\) 0 0
\(202\) 4.75076 0.334262
\(203\) −3.47251 −0.243722
\(204\) 0 0
\(205\) −37.9973 −2.65385
\(206\) −8.46155 −0.589544
\(207\) 0 0
\(208\) 0.852078 0.0590810
\(209\) 8.93815 0.618265
\(210\) 0 0
\(211\) 22.6920 1.56218 0.781091 0.624417i \(-0.214663\pi\)
0.781091 + 0.624417i \(0.214663\pi\)
\(212\) 6.28830 0.431882
\(213\) 0 0
\(214\) 1.43645 0.0981935
\(215\) 3.42701 0.233720
\(216\) 0 0
\(217\) 14.9985 1.01817
\(218\) −12.5744 −0.851646
\(219\) 0 0
\(220\) 22.4676 1.51477
\(221\) −3.92740 −0.264186
\(222\) 0 0
\(223\) −1.00000 −0.0669650
\(224\) −2.27800 −0.152205
\(225\) 0 0
\(226\) 1.42716 0.0949332
\(227\) 22.2803 1.47880 0.739399 0.673268i \(-0.235110\pi\)
0.739399 + 0.673268i \(0.235110\pi\)
\(228\) 0 0
\(229\) 14.5880 0.964000 0.482000 0.876171i \(-0.339910\pi\)
0.482000 + 0.876171i \(0.339910\pi\)
\(230\) 15.7347 1.03751
\(231\) 0 0
\(232\) 1.52437 0.100080
\(233\) −4.82251 −0.315933 −0.157967 0.987444i \(-0.550494\pi\)
−0.157967 + 0.987444i \(0.550494\pi\)
\(234\) 0 0
\(235\) 31.1140 2.02965
\(236\) −4.62427 −0.301014
\(237\) 0 0
\(238\) 10.4998 0.680600
\(239\) −13.8013 −0.892730 −0.446365 0.894851i \(-0.647282\pi\)
−0.446365 + 0.894851i \(0.647282\pi\)
\(240\) 0 0
\(241\) 10.5058 0.676738 0.338369 0.941014i \(-0.390125\pi\)
0.338369 + 0.941014i \(0.390125\pi\)
\(242\) −25.1731 −1.61819
\(243\) 0 0
\(244\) 2.47563 0.158486
\(245\) −6.76415 −0.432145
\(246\) 0 0
\(247\) 1.26629 0.0805723
\(248\) −6.58406 −0.418088
\(249\) 0 0
\(250\) −14.7744 −0.934413
\(251\) −10.4874 −0.661958 −0.330979 0.943638i \(-0.607379\pi\)
−0.330979 + 0.943638i \(0.607379\pi\)
\(252\) 0 0
\(253\) −25.3329 −1.59267
\(254\) 21.3436 1.33922
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −12.5438 −0.782460 −0.391230 0.920293i \(-0.627950\pi\)
−0.391230 + 0.920293i \(0.627950\pi\)
\(258\) 0 0
\(259\) 10.0834 0.626552
\(260\) 3.18305 0.197405
\(261\) 0 0
\(262\) 17.7225 1.09490
\(263\) −25.8499 −1.59397 −0.796986 0.603997i \(-0.793574\pi\)
−0.796986 + 0.603997i \(0.793574\pi\)
\(264\) 0 0
\(265\) 23.4908 1.44303
\(266\) −3.38539 −0.207572
\(267\) 0 0
\(268\) 3.43979 0.210119
\(269\) −19.2755 −1.17525 −0.587623 0.809135i \(-0.699936\pi\)
−0.587623 + 0.809135i \(0.699936\pi\)
\(270\) 0 0
\(271\) −21.8099 −1.32486 −0.662428 0.749125i \(-0.730474\pi\)
−0.662428 + 0.749125i \(0.730474\pi\)
\(272\) −4.60921 −0.279474
\(273\) 0 0
\(274\) 8.40769 0.507927
\(275\) 53.8589 3.24781
\(276\) 0 0
\(277\) 19.4696 1.16981 0.584907 0.811100i \(-0.301131\pi\)
0.584907 + 0.811100i \(0.301131\pi\)
\(278\) 16.6796 1.00037
\(279\) 0 0
\(280\) −8.50979 −0.508557
\(281\) −16.7963 −1.00198 −0.500992 0.865452i \(-0.667031\pi\)
−0.500992 + 0.865452i \(0.667031\pi\)
\(282\) 0 0
\(283\) −24.1812 −1.43743 −0.718713 0.695307i \(-0.755268\pi\)
−0.718713 + 0.695307i \(0.755268\pi\)
\(284\) −0.919349 −0.0545533
\(285\) 0 0
\(286\) −5.12474 −0.303033
\(287\) −23.1709 −1.36773
\(288\) 0 0
\(289\) 4.24479 0.249694
\(290\) 5.69448 0.334391
\(291\) 0 0
\(292\) −1.20422 −0.0704718
\(293\) −26.0052 −1.51924 −0.759619 0.650368i \(-0.774615\pi\)
−0.759619 + 0.650368i \(0.774615\pi\)
\(294\) 0 0
\(295\) −17.2746 −1.00577
\(296\) −4.42642 −0.257281
\(297\) 0 0
\(298\) −20.0642 −1.16229
\(299\) −3.58899 −0.207556
\(300\) 0 0
\(301\) 2.08980 0.120454
\(302\) 17.7405 1.02085
\(303\) 0 0
\(304\) 1.48612 0.0852350
\(305\) 9.24807 0.529543
\(306\) 0 0
\(307\) 26.1554 1.49277 0.746383 0.665516i \(-0.231789\pi\)
0.746383 + 0.665516i \(0.231789\pi\)
\(308\) 13.7008 0.780677
\(309\) 0 0
\(310\) −24.5957 −1.39694
\(311\) −2.36626 −0.134178 −0.0670892 0.997747i \(-0.521371\pi\)
−0.0670892 + 0.997747i \(0.521371\pi\)
\(312\) 0 0
\(313\) −11.2794 −0.637548 −0.318774 0.947831i \(-0.603271\pi\)
−0.318774 + 0.947831i \(0.603271\pi\)
\(314\) 2.78869 0.157375
\(315\) 0 0
\(316\) 12.3064 0.692287
\(317\) 28.7306 1.61367 0.806835 0.590777i \(-0.201179\pi\)
0.806835 + 0.590777i \(0.201179\pi\)
\(318\) 0 0
\(319\) −9.16816 −0.513318
\(320\) 3.73564 0.208828
\(321\) 0 0
\(322\) 9.59504 0.534711
\(323\) −6.84985 −0.381136
\(324\) 0 0
\(325\) 7.63034 0.423255
\(326\) 14.9595 0.828530
\(327\) 0 0
\(328\) 10.1716 0.561632
\(329\) 18.9734 1.04604
\(330\) 0 0
\(331\) 7.33457 0.403145 0.201572 0.979474i \(-0.435395\pi\)
0.201572 + 0.979474i \(0.435395\pi\)
\(332\) −12.1582 −0.667266
\(333\) 0 0
\(334\) 8.34896 0.456835
\(335\) 12.8498 0.702060
\(336\) 0 0
\(337\) 6.40802 0.349067 0.174534 0.984651i \(-0.444158\pi\)
0.174534 + 0.984651i \(0.444158\pi\)
\(338\) 12.2740 0.667616
\(339\) 0 0
\(340\) −17.2183 −0.933795
\(341\) 39.5992 2.14442
\(342\) 0 0
\(343\) −20.0708 −1.08372
\(344\) −0.917382 −0.0494619
\(345\) 0 0
\(346\) −1.30257 −0.0700267
\(347\) −7.39309 −0.396882 −0.198441 0.980113i \(-0.563588\pi\)
−0.198441 + 0.980113i \(0.563588\pi\)
\(348\) 0 0
\(349\) 20.8521 1.11619 0.558093 0.829778i \(-0.311533\pi\)
0.558093 + 0.829778i \(0.311533\pi\)
\(350\) −20.3995 −1.09040
\(351\) 0 0
\(352\) −6.01441 −0.320569
\(353\) −3.49981 −0.186276 −0.0931381 0.995653i \(-0.529690\pi\)
−0.0931381 + 0.995653i \(0.529690\pi\)
\(354\) 0 0
\(355\) −3.43435 −0.182277
\(356\) 1.06503 0.0564466
\(357\) 0 0
\(358\) −24.7249 −1.30675
\(359\) 30.5897 1.61446 0.807232 0.590234i \(-0.200965\pi\)
0.807232 + 0.590234i \(0.200965\pi\)
\(360\) 0 0
\(361\) −16.7914 −0.883760
\(362\) −24.6587 −1.29603
\(363\) 0 0
\(364\) 1.94104 0.101738
\(365\) −4.49854 −0.235464
\(366\) 0 0
\(367\) 10.9138 0.569697 0.284848 0.958573i \(-0.408057\pi\)
0.284848 + 0.958573i \(0.408057\pi\)
\(368\) −4.21204 −0.219568
\(369\) 0 0
\(370\) −16.5355 −0.859640
\(371\) 14.3247 0.743704
\(372\) 0 0
\(373\) 23.2262 1.20261 0.601304 0.799020i \(-0.294648\pi\)
0.601304 + 0.799020i \(0.294648\pi\)
\(374\) 27.7217 1.43345
\(375\) 0 0
\(376\) −8.32897 −0.429534
\(377\) −1.29888 −0.0668956
\(378\) 0 0
\(379\) 7.46237 0.383316 0.191658 0.981462i \(-0.438613\pi\)
0.191658 + 0.981462i \(0.438613\pi\)
\(380\) 5.55162 0.284792
\(381\) 0 0
\(382\) −18.6689 −0.955186
\(383\) −9.04126 −0.461987 −0.230993 0.972955i \(-0.574198\pi\)
−0.230993 + 0.972955i \(0.574198\pi\)
\(384\) 0 0
\(385\) 51.1813 2.60844
\(386\) 21.4822 1.09342
\(387\) 0 0
\(388\) −2.53493 −0.128692
\(389\) 23.3946 1.18615 0.593076 0.805147i \(-0.297914\pi\)
0.593076 + 0.805147i \(0.297914\pi\)
\(390\) 0 0
\(391\) 19.4142 0.981817
\(392\) 1.81071 0.0914546
\(393\) 0 0
\(394\) 1.74494 0.0879090
\(395\) 45.9721 2.31311
\(396\) 0 0
\(397\) 37.9849 1.90641 0.953203 0.302331i \(-0.0977649\pi\)
0.953203 + 0.302331i \(0.0977649\pi\)
\(398\) 21.8960 1.09755
\(399\) 0 0
\(400\) 8.95498 0.447749
\(401\) 11.8561 0.592064 0.296032 0.955178i \(-0.404337\pi\)
0.296032 + 0.955178i \(0.404337\pi\)
\(402\) 0 0
\(403\) 5.61014 0.279461
\(404\) −4.75076 −0.236359
\(405\) 0 0
\(406\) 3.47251 0.172338
\(407\) 26.6223 1.31962
\(408\) 0 0
\(409\) 25.8663 1.27900 0.639502 0.768789i \(-0.279140\pi\)
0.639502 + 0.768789i \(0.279140\pi\)
\(410\) 37.9973 1.87655
\(411\) 0 0
\(412\) 8.46155 0.416871
\(413\) −10.5341 −0.518349
\(414\) 0 0
\(415\) −45.4185 −2.22950
\(416\) −0.852078 −0.0417766
\(417\) 0 0
\(418\) −8.93815 −0.437179
\(419\) −19.7538 −0.965036 −0.482518 0.875886i \(-0.660278\pi\)
−0.482518 + 0.875886i \(0.660278\pi\)
\(420\) 0 0
\(421\) −4.44190 −0.216485 −0.108243 0.994125i \(-0.534522\pi\)
−0.108243 + 0.994125i \(0.534522\pi\)
\(422\) −22.6920 −1.10463
\(423\) 0 0
\(424\) −6.28830 −0.305387
\(425\) −41.2754 −2.00215
\(426\) 0 0
\(427\) 5.63950 0.272915
\(428\) −1.43645 −0.0694333
\(429\) 0 0
\(430\) −3.42701 −0.165265
\(431\) −10.1940 −0.491026 −0.245513 0.969393i \(-0.578956\pi\)
−0.245513 + 0.969393i \(0.578956\pi\)
\(432\) 0 0
\(433\) 18.5071 0.889396 0.444698 0.895681i \(-0.353311\pi\)
0.444698 + 0.895681i \(0.353311\pi\)
\(434\) −14.9985 −0.719951
\(435\) 0 0
\(436\) 12.5744 0.602205
\(437\) −6.25961 −0.299438
\(438\) 0 0
\(439\) 10.4648 0.499456 0.249728 0.968316i \(-0.419659\pi\)
0.249728 + 0.968316i \(0.419659\pi\)
\(440\) −22.4676 −1.07110
\(441\) 0 0
\(442\) 3.92740 0.186808
\(443\) −19.2885 −0.916427 −0.458213 0.888842i \(-0.651510\pi\)
−0.458213 + 0.888842i \(0.651510\pi\)
\(444\) 0 0
\(445\) 3.97858 0.188603
\(446\) 1.00000 0.0473514
\(447\) 0 0
\(448\) 2.27800 0.107625
\(449\) 2.34935 0.110873 0.0554364 0.998462i \(-0.482345\pi\)
0.0554364 + 0.998462i \(0.482345\pi\)
\(450\) 0 0
\(451\) −61.1761 −2.88067
\(452\) −1.42716 −0.0671279
\(453\) 0 0
\(454\) −22.2803 −1.04567
\(455\) 7.25100 0.339932
\(456\) 0 0
\(457\) 1.65175 0.0772657 0.0386329 0.999253i \(-0.487700\pi\)
0.0386329 + 0.999253i \(0.487700\pi\)
\(458\) −14.5880 −0.681651
\(459\) 0 0
\(460\) −15.7347 −0.733632
\(461\) 24.2317 1.12858 0.564291 0.825576i \(-0.309149\pi\)
0.564291 + 0.825576i \(0.309149\pi\)
\(462\) 0 0
\(463\) 13.6909 0.636272 0.318136 0.948045i \(-0.396943\pi\)
0.318136 + 0.948045i \(0.396943\pi\)
\(464\) −1.52437 −0.0707669
\(465\) 0 0
\(466\) 4.82251 0.223399
\(467\) 26.6189 1.23177 0.615887 0.787835i \(-0.288798\pi\)
0.615887 + 0.787835i \(0.288798\pi\)
\(468\) 0 0
\(469\) 7.83585 0.361826
\(470\) −31.1140 −1.43518
\(471\) 0 0
\(472\) 4.62427 0.212849
\(473\) 5.51751 0.253695
\(474\) 0 0
\(475\) 13.3082 0.610622
\(476\) −10.4998 −0.481257
\(477\) 0 0
\(478\) 13.8013 0.631255
\(479\) 31.6473 1.44600 0.723000 0.690848i \(-0.242763\pi\)
0.723000 + 0.690848i \(0.242763\pi\)
\(480\) 0 0
\(481\) 3.77166 0.171973
\(482\) −10.5058 −0.478526
\(483\) 0 0
\(484\) 25.1731 1.14423
\(485\) −9.46958 −0.429991
\(486\) 0 0
\(487\) −9.72175 −0.440535 −0.220267 0.975440i \(-0.570693\pi\)
−0.220267 + 0.975440i \(0.570693\pi\)
\(488\) −2.47563 −0.112067
\(489\) 0 0
\(490\) 6.76415 0.305573
\(491\) 26.5785 1.19947 0.599736 0.800198i \(-0.295272\pi\)
0.599736 + 0.800198i \(0.295272\pi\)
\(492\) 0 0
\(493\) 7.02612 0.316440
\(494\) −1.26629 −0.0569732
\(495\) 0 0
\(496\) 6.58406 0.295633
\(497\) −2.09428 −0.0939412
\(498\) 0 0
\(499\) −0.377594 −0.0169034 −0.00845172 0.999964i \(-0.502690\pi\)
−0.00845172 + 0.999964i \(0.502690\pi\)
\(500\) 14.7744 0.660730
\(501\) 0 0
\(502\) 10.4874 0.468075
\(503\) −6.34075 −0.282720 −0.141360 0.989958i \(-0.545148\pi\)
−0.141360 + 0.989958i \(0.545148\pi\)
\(504\) 0 0
\(505\) −17.7471 −0.789735
\(506\) 25.3329 1.12619
\(507\) 0 0
\(508\) −21.3436 −0.946971
\(509\) −17.3369 −0.768445 −0.384223 0.923240i \(-0.625530\pi\)
−0.384223 + 0.923240i \(0.625530\pi\)
\(510\) 0 0
\(511\) −2.74322 −0.121353
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 12.5438 0.553283
\(515\) 31.6093 1.39287
\(516\) 0 0
\(517\) 50.0938 2.20312
\(518\) −10.0834 −0.443039
\(519\) 0 0
\(520\) −3.18305 −0.139586
\(521\) −24.0104 −1.05191 −0.525957 0.850511i \(-0.676293\pi\)
−0.525957 + 0.850511i \(0.676293\pi\)
\(522\) 0 0
\(523\) −36.1593 −1.58114 −0.790569 0.612373i \(-0.790215\pi\)
−0.790569 + 0.612373i \(0.790215\pi\)
\(524\) −17.7225 −0.774209
\(525\) 0 0
\(526\) 25.8499 1.12711
\(527\) −30.3473 −1.32195
\(528\) 0 0
\(529\) −5.25871 −0.228640
\(530\) −23.4908 −1.02037
\(531\) 0 0
\(532\) 3.38539 0.146775
\(533\) −8.66698 −0.375409
\(534\) 0 0
\(535\) −5.36605 −0.231994
\(536\) −3.43979 −0.148576
\(537\) 0 0
\(538\) 19.2755 0.831025
\(539\) −10.8903 −0.469080
\(540\) 0 0
\(541\) 13.5548 0.582764 0.291382 0.956607i \(-0.405885\pi\)
0.291382 + 0.956607i \(0.405885\pi\)
\(542\) 21.8099 0.936815
\(543\) 0 0
\(544\) 4.60921 0.197618
\(545\) 46.9734 2.01212
\(546\) 0 0
\(547\) −3.67323 −0.157056 −0.0785279 0.996912i \(-0.525022\pi\)
−0.0785279 + 0.996912i \(0.525022\pi\)
\(548\) −8.40769 −0.359159
\(549\) 0 0
\(550\) −53.8589 −2.29655
\(551\) −2.26540 −0.0965091
\(552\) 0 0
\(553\) 28.0339 1.19212
\(554\) −19.4696 −0.827183
\(555\) 0 0
\(556\) −16.6796 −0.707371
\(557\) −14.4915 −0.614023 −0.307011 0.951706i \(-0.599329\pi\)
−0.307011 + 0.951706i \(0.599329\pi\)
\(558\) 0 0
\(559\) 0.781681 0.0330616
\(560\) 8.50979 0.359604
\(561\) 0 0
\(562\) 16.7963 0.708510
\(563\) 18.2302 0.768312 0.384156 0.923268i \(-0.374493\pi\)
0.384156 + 0.923268i \(0.374493\pi\)
\(564\) 0 0
\(565\) −5.33135 −0.224291
\(566\) 24.1812 1.01641
\(567\) 0 0
\(568\) 0.919349 0.0385750
\(569\) 1.40032 0.0587045 0.0293523 0.999569i \(-0.490656\pi\)
0.0293523 + 0.999569i \(0.490656\pi\)
\(570\) 0 0
\(571\) 38.5377 1.61275 0.806376 0.591403i \(-0.201426\pi\)
0.806376 + 0.591403i \(0.201426\pi\)
\(572\) 5.12474 0.214276
\(573\) 0 0
\(574\) 23.1709 0.967134
\(575\) −37.7187 −1.57298
\(576\) 0 0
\(577\) −39.6408 −1.65027 −0.825135 0.564936i \(-0.808901\pi\)
−0.825135 + 0.564936i \(0.808901\pi\)
\(578\) −4.24479 −0.176560
\(579\) 0 0
\(580\) −5.69448 −0.236450
\(581\) −27.6963 −1.14904
\(582\) 0 0
\(583\) 37.8204 1.56636
\(584\) 1.20422 0.0498311
\(585\) 0 0
\(586\) 26.0052 1.07426
\(587\) −9.32442 −0.384860 −0.192430 0.981311i \(-0.561637\pi\)
−0.192430 + 0.981311i \(0.561637\pi\)
\(588\) 0 0
\(589\) 9.78473 0.403173
\(590\) 17.2746 0.711184
\(591\) 0 0
\(592\) 4.42642 0.181925
\(593\) 19.6791 0.808123 0.404062 0.914732i \(-0.367598\pi\)
0.404062 + 0.914732i \(0.367598\pi\)
\(594\) 0 0
\(595\) −39.2234 −1.60800
\(596\) 20.0642 0.821861
\(597\) 0 0
\(598\) 3.58899 0.146765
\(599\) −12.7036 −0.519057 −0.259528 0.965735i \(-0.583567\pi\)
−0.259528 + 0.965735i \(0.583567\pi\)
\(600\) 0 0
\(601\) −15.7787 −0.643627 −0.321813 0.946803i \(-0.604292\pi\)
−0.321813 + 0.946803i \(0.604292\pi\)
\(602\) −2.08980 −0.0851738
\(603\) 0 0
\(604\) −17.7405 −0.721852
\(605\) 94.0376 3.82317
\(606\) 0 0
\(607\) −3.28948 −0.133516 −0.0667579 0.997769i \(-0.521266\pi\)
−0.0667579 + 0.997769i \(0.521266\pi\)
\(608\) −1.48612 −0.0602703
\(609\) 0 0
\(610\) −9.24807 −0.374443
\(611\) 7.09693 0.287111
\(612\) 0 0
\(613\) 5.83172 0.235541 0.117771 0.993041i \(-0.462425\pi\)
0.117771 + 0.993041i \(0.462425\pi\)
\(614\) −26.1554 −1.05555
\(615\) 0 0
\(616\) −13.7008 −0.552022
\(617\) −8.27184 −0.333012 −0.166506 0.986040i \(-0.553248\pi\)
−0.166506 + 0.986040i \(0.553248\pi\)
\(618\) 0 0
\(619\) −36.3235 −1.45997 −0.729983 0.683466i \(-0.760472\pi\)
−0.729983 + 0.683466i \(0.760472\pi\)
\(620\) 24.5957 0.987786
\(621\) 0 0
\(622\) 2.36626 0.0948784
\(623\) 2.42615 0.0972015
\(624\) 0 0
\(625\) 10.4168 0.416670
\(626\) 11.2794 0.450814
\(627\) 0 0
\(628\) −2.78869 −0.111281
\(629\) −20.4023 −0.813493
\(630\) 0 0
\(631\) −31.2758 −1.24507 −0.622536 0.782592i \(-0.713897\pi\)
−0.622536 + 0.782592i \(0.713897\pi\)
\(632\) −12.3064 −0.489520
\(633\) 0 0
\(634\) −28.7306 −1.14104
\(635\) −79.7321 −3.16407
\(636\) 0 0
\(637\) −1.54286 −0.0611305
\(638\) 9.16816 0.362971
\(639\) 0 0
\(640\) −3.73564 −0.147664
\(641\) −7.82219 −0.308958 −0.154479 0.987996i \(-0.549370\pi\)
−0.154479 + 0.987996i \(0.549370\pi\)
\(642\) 0 0
\(643\) 16.2715 0.641686 0.320843 0.947132i \(-0.396034\pi\)
0.320843 + 0.947132i \(0.396034\pi\)
\(644\) −9.59504 −0.378097
\(645\) 0 0
\(646\) 6.84985 0.269504
\(647\) −12.1262 −0.476731 −0.238366 0.971175i \(-0.576612\pi\)
−0.238366 + 0.971175i \(0.576612\pi\)
\(648\) 0 0
\(649\) −27.8123 −1.09173
\(650\) −7.63034 −0.299287
\(651\) 0 0
\(652\) −14.9595 −0.585859
\(653\) −14.2664 −0.558287 −0.279144 0.960249i \(-0.590051\pi\)
−0.279144 + 0.960249i \(0.590051\pi\)
\(654\) 0 0
\(655\) −66.2047 −2.58683
\(656\) −10.1716 −0.397134
\(657\) 0 0
\(658\) −18.9734 −0.739660
\(659\) 17.3036 0.674054 0.337027 0.941495i \(-0.390579\pi\)
0.337027 + 0.941495i \(0.390579\pi\)
\(660\) 0 0
\(661\) 13.7700 0.535591 0.267795 0.963476i \(-0.413705\pi\)
0.267795 + 0.963476i \(0.413705\pi\)
\(662\) −7.33457 −0.285066
\(663\) 0 0
\(664\) 12.1582 0.471828
\(665\) 12.6466 0.490414
\(666\) 0 0
\(667\) 6.42069 0.248610
\(668\) −8.34896 −0.323031
\(669\) 0 0
\(670\) −12.8498 −0.496432
\(671\) 14.8895 0.574802
\(672\) 0 0
\(673\) −24.4926 −0.944121 −0.472061 0.881566i \(-0.656490\pi\)
−0.472061 + 0.881566i \(0.656490\pi\)
\(674\) −6.40802 −0.246828
\(675\) 0 0
\(676\) −12.2740 −0.472076
\(677\) −27.4584 −1.05531 −0.527656 0.849458i \(-0.676929\pi\)
−0.527656 + 0.849458i \(0.676929\pi\)
\(678\) 0 0
\(679\) −5.77458 −0.221608
\(680\) 17.2183 0.660293
\(681\) 0 0
\(682\) −39.5992 −1.51633
\(683\) 42.0591 1.60935 0.804673 0.593718i \(-0.202340\pi\)
0.804673 + 0.593718i \(0.202340\pi\)
\(684\) 0 0
\(685\) −31.4081 −1.20004
\(686\) 20.0708 0.766307
\(687\) 0 0
\(688\) 0.917382 0.0349749
\(689\) 5.35812 0.204128
\(690\) 0 0
\(691\) −29.3603 −1.11692 −0.558459 0.829532i \(-0.688607\pi\)
−0.558459 + 0.829532i \(0.688607\pi\)
\(692\) 1.30257 0.0495163
\(693\) 0 0
\(694\) 7.39309 0.280638
\(695\) −62.3088 −2.36351
\(696\) 0 0
\(697\) 46.8829 1.77582
\(698\) −20.8521 −0.789263
\(699\) 0 0
\(700\) 20.3995 0.771027
\(701\) 24.2185 0.914720 0.457360 0.889282i \(-0.348795\pi\)
0.457360 + 0.889282i \(0.348795\pi\)
\(702\) 0 0
\(703\) 6.57821 0.248102
\(704\) 6.01441 0.226677
\(705\) 0 0
\(706\) 3.49981 0.131717
\(707\) −10.8222 −0.407012
\(708\) 0 0
\(709\) 25.4904 0.957312 0.478656 0.878002i \(-0.341124\pi\)
0.478656 + 0.878002i \(0.341124\pi\)
\(710\) 3.43435 0.128889
\(711\) 0 0
\(712\) −1.06503 −0.0399138
\(713\) −27.7323 −1.03858
\(714\) 0 0
\(715\) 19.1442 0.715952
\(716\) 24.7249 0.924014
\(717\) 0 0
\(718\) −30.5897 −1.14160
\(719\) −33.6674 −1.25558 −0.627792 0.778381i \(-0.716041\pi\)
−0.627792 + 0.778381i \(0.716041\pi\)
\(720\) 0 0
\(721\) 19.2754 0.717855
\(722\) 16.7914 0.624913
\(723\) 0 0
\(724\) 24.6587 0.916435
\(725\) −13.6507 −0.506973
\(726\) 0 0
\(727\) −29.1086 −1.07958 −0.539788 0.841801i \(-0.681496\pi\)
−0.539788 + 0.841801i \(0.681496\pi\)
\(728\) −1.94104 −0.0719395
\(729\) 0 0
\(730\) 4.49854 0.166498
\(731\) −4.22840 −0.156393
\(732\) 0 0
\(733\) 1.05662 0.0390273 0.0195137 0.999810i \(-0.493788\pi\)
0.0195137 + 0.999810i \(0.493788\pi\)
\(734\) −10.9138 −0.402836
\(735\) 0 0
\(736\) 4.21204 0.155258
\(737\) 20.6883 0.762064
\(738\) 0 0
\(739\) −53.2785 −1.95988 −0.979941 0.199289i \(-0.936137\pi\)
−0.979941 + 0.199289i \(0.936137\pi\)
\(740\) 16.5355 0.607857
\(741\) 0 0
\(742\) −14.3247 −0.525878
\(743\) −49.6908 −1.82298 −0.911489 0.411325i \(-0.865066\pi\)
−0.911489 + 0.411325i \(0.865066\pi\)
\(744\) 0 0
\(745\) 74.9525 2.74605
\(746\) −23.2262 −0.850373
\(747\) 0 0
\(748\) −27.7217 −1.01360
\(749\) −3.27223 −0.119565
\(750\) 0 0
\(751\) −13.5295 −0.493697 −0.246849 0.969054i \(-0.579395\pi\)
−0.246849 + 0.969054i \(0.579395\pi\)
\(752\) 8.32897 0.303726
\(753\) 0 0
\(754\) 1.29888 0.0473024
\(755\) −66.2722 −2.41189
\(756\) 0 0
\(757\) 46.9354 1.70589 0.852947 0.521997i \(-0.174813\pi\)
0.852947 + 0.521997i \(0.174813\pi\)
\(758\) −7.46237 −0.271046
\(759\) 0 0
\(760\) −5.55162 −0.201378
\(761\) 27.4191 0.993940 0.496970 0.867768i \(-0.334446\pi\)
0.496970 + 0.867768i \(0.334446\pi\)
\(762\) 0 0
\(763\) 28.6445 1.03700
\(764\) 18.6689 0.675418
\(765\) 0 0
\(766\) 9.04126 0.326674
\(767\) −3.94024 −0.142274
\(768\) 0 0
\(769\) 33.1069 1.19386 0.596932 0.802292i \(-0.296386\pi\)
0.596932 + 0.802292i \(0.296386\pi\)
\(770\) −51.1813 −1.84445
\(771\) 0 0
\(772\) −21.4822 −0.773163
\(773\) −34.4021 −1.23736 −0.618678 0.785645i \(-0.712331\pi\)
−0.618678 + 0.785645i \(0.712331\pi\)
\(774\) 0 0
\(775\) 58.9602 2.11791
\(776\) 2.53493 0.0909987
\(777\) 0 0
\(778\) −23.3946 −0.838736
\(779\) −15.1162 −0.541595
\(780\) 0 0
\(781\) −5.52934 −0.197855
\(782\) −19.4142 −0.694249
\(783\) 0 0
\(784\) −1.81071 −0.0646681
\(785\) −10.4175 −0.371818
\(786\) 0 0
\(787\) −8.78386 −0.313111 −0.156555 0.987669i \(-0.550039\pi\)
−0.156555 + 0.987669i \(0.550039\pi\)
\(788\) −1.74494 −0.0621610
\(789\) 0 0
\(790\) −45.9721 −1.63561
\(791\) −3.25107 −0.115595
\(792\) 0 0
\(793\) 2.10943 0.0749082
\(794\) −37.9849 −1.34803
\(795\) 0 0
\(796\) −21.8960 −0.776084
\(797\) −9.49402 −0.336295 −0.168148 0.985762i \(-0.553779\pi\)
−0.168148 + 0.985762i \(0.553779\pi\)
\(798\) 0 0
\(799\) −38.3899 −1.35814
\(800\) −8.95498 −0.316606
\(801\) 0 0
\(802\) −11.8561 −0.418652
\(803\) −7.24269 −0.255589
\(804\) 0 0
\(805\) −35.8436 −1.26332
\(806\) −5.61014 −0.197609
\(807\) 0 0
\(808\) 4.75076 0.167131
\(809\) 19.8140 0.696624 0.348312 0.937379i \(-0.386755\pi\)
0.348312 + 0.937379i \(0.386755\pi\)
\(810\) 0 0
\(811\) −35.4976 −1.24649 −0.623245 0.782026i \(-0.714186\pi\)
−0.623245 + 0.782026i \(0.714186\pi\)
\(812\) −3.47251 −0.121861
\(813\) 0 0
\(814\) −26.6223 −0.933112
\(815\) −55.8833 −1.95751
\(816\) 0 0
\(817\) 1.36334 0.0476973
\(818\) −25.8663 −0.904393
\(819\) 0 0
\(820\) −37.9973 −1.32692
\(821\) 14.8442 0.518066 0.259033 0.965869i \(-0.416596\pi\)
0.259033 + 0.965869i \(0.416596\pi\)
\(822\) 0 0
\(823\) −5.84581 −0.203772 −0.101886 0.994796i \(-0.532488\pi\)
−0.101886 + 0.994796i \(0.532488\pi\)
\(824\) −8.46155 −0.294772
\(825\) 0 0
\(826\) 10.5341 0.366528
\(827\) −34.7754 −1.20926 −0.604630 0.796507i \(-0.706679\pi\)
−0.604630 + 0.796507i \(0.706679\pi\)
\(828\) 0 0
\(829\) −36.0468 −1.25196 −0.625979 0.779840i \(-0.715300\pi\)
−0.625979 + 0.779840i \(0.715300\pi\)
\(830\) 45.4185 1.57650
\(831\) 0 0
\(832\) 0.852078 0.0295405
\(833\) 8.34593 0.289169
\(834\) 0 0
\(835\) −31.1887 −1.07933
\(836\) 8.93815 0.309133
\(837\) 0 0
\(838\) 19.7538 0.682384
\(839\) 23.3118 0.804812 0.402406 0.915461i \(-0.368174\pi\)
0.402406 + 0.915461i \(0.368174\pi\)
\(840\) 0 0
\(841\) −26.6763 −0.919873
\(842\) 4.44190 0.153078
\(843\) 0 0
\(844\) 22.6920 0.781091
\(845\) −45.8511 −1.57732
\(846\) 0 0
\(847\) 57.3444 1.97038
\(848\) 6.28830 0.215941
\(849\) 0 0
\(850\) 41.2754 1.41573
\(851\) −18.6443 −0.639118
\(852\) 0 0
\(853\) −32.6519 −1.11798 −0.558990 0.829174i \(-0.688811\pi\)
−0.558990 + 0.829174i \(0.688811\pi\)
\(854\) −5.63950 −0.192980
\(855\) 0 0
\(856\) 1.43645 0.0490968
\(857\) −31.0079 −1.05921 −0.529605 0.848245i \(-0.677660\pi\)
−0.529605 + 0.848245i \(0.677660\pi\)
\(858\) 0 0
\(859\) −31.8330 −1.08613 −0.543064 0.839691i \(-0.682736\pi\)
−0.543064 + 0.839691i \(0.682736\pi\)
\(860\) 3.42701 0.116860
\(861\) 0 0
\(862\) 10.1940 0.347208
\(863\) 44.5320 1.51589 0.757944 0.652319i \(-0.226204\pi\)
0.757944 + 0.652319i \(0.226204\pi\)
\(864\) 0 0
\(865\) 4.86593 0.165447
\(866\) −18.5071 −0.628898
\(867\) 0 0
\(868\) 14.9985 0.509083
\(869\) 74.0154 2.51080
\(870\) 0 0
\(871\) 2.93097 0.0993122
\(872\) −12.5744 −0.425823
\(873\) 0 0
\(874\) 6.25961 0.211735
\(875\) 33.6560 1.13778
\(876\) 0 0
\(877\) 25.9629 0.876703 0.438352 0.898804i \(-0.355562\pi\)
0.438352 + 0.898804i \(0.355562\pi\)
\(878\) −10.4648 −0.353169
\(879\) 0 0
\(880\) 22.4676 0.757384
\(881\) 4.76702 0.160605 0.0803025 0.996771i \(-0.474411\pi\)
0.0803025 + 0.996771i \(0.474411\pi\)
\(882\) 0 0
\(883\) −11.8426 −0.398536 −0.199268 0.979945i \(-0.563856\pi\)
−0.199268 + 0.979945i \(0.563856\pi\)
\(884\) −3.92740 −0.132093
\(885\) 0 0
\(886\) 19.2885 0.648011
\(887\) −43.4389 −1.45853 −0.729267 0.684229i \(-0.760139\pi\)
−0.729267 + 0.684229i \(0.760139\pi\)
\(888\) 0 0
\(889\) −48.6209 −1.63069
\(890\) −3.97858 −0.133362
\(891\) 0 0
\(892\) −1.00000 −0.0334825
\(893\) 12.3779 0.414210
\(894\) 0 0
\(895\) 92.3633 3.08737
\(896\) −2.27800 −0.0761027
\(897\) 0 0
\(898\) −2.34935 −0.0783990
\(899\) −10.0365 −0.334737
\(900\) 0 0
\(901\) −28.9841 −0.965599
\(902\) 61.1761 2.03694
\(903\) 0 0
\(904\) 1.42716 0.0474666
\(905\) 92.1161 3.06204
\(906\) 0 0
\(907\) 3.63494 0.120696 0.0603481 0.998177i \(-0.480779\pi\)
0.0603481 + 0.998177i \(0.480779\pi\)
\(908\) 22.2803 0.739399
\(909\) 0 0
\(910\) −7.25100 −0.240368
\(911\) −9.04333 −0.299619 −0.149810 0.988715i \(-0.547866\pi\)
−0.149810 + 0.988715i \(0.547866\pi\)
\(912\) 0 0
\(913\) −73.1241 −2.42006
\(914\) −1.65175 −0.0546351
\(915\) 0 0
\(916\) 14.5880 0.482000
\(917\) −40.3718 −1.33319
\(918\) 0 0
\(919\) 32.5562 1.07393 0.536965 0.843604i \(-0.319571\pi\)
0.536965 + 0.843604i \(0.319571\pi\)
\(920\) 15.7347 0.518756
\(921\) 0 0
\(922\) −24.2317 −0.798028
\(923\) −0.783357 −0.0257845
\(924\) 0 0
\(925\) 39.6385 1.30331
\(926\) −13.6909 −0.449912
\(927\) 0 0
\(928\) 1.52437 0.0500398
\(929\) 3.06405 0.100528 0.0502642 0.998736i \(-0.483994\pi\)
0.0502642 + 0.998736i \(0.483994\pi\)
\(930\) 0 0
\(931\) −2.69094 −0.0881919
\(932\) −4.82251 −0.157967
\(933\) 0 0
\(934\) −26.6189 −0.870995
\(935\) −103.558 −3.38671
\(936\) 0 0
\(937\) −27.1123 −0.885720 −0.442860 0.896591i \(-0.646036\pi\)
−0.442860 + 0.896591i \(0.646036\pi\)
\(938\) −7.83585 −0.255850
\(939\) 0 0
\(940\) 31.1140 1.01483
\(941\) 34.5485 1.12625 0.563124 0.826372i \(-0.309599\pi\)
0.563124 + 0.826372i \(0.309599\pi\)
\(942\) 0 0
\(943\) 42.8431 1.39516
\(944\) −4.62427 −0.150507
\(945\) 0 0
\(946\) −5.51751 −0.179390
\(947\) 9.62266 0.312694 0.156347 0.987702i \(-0.450028\pi\)
0.156347 + 0.987702i \(0.450028\pi\)
\(948\) 0 0
\(949\) −1.02609 −0.0333084
\(950\) −13.3082 −0.431775
\(951\) 0 0
\(952\) 10.4998 0.340300
\(953\) −42.5824 −1.37938 −0.689689 0.724105i \(-0.742253\pi\)
−0.689689 + 0.724105i \(0.742253\pi\)
\(954\) 0 0
\(955\) 69.7403 2.25674
\(956\) −13.8013 −0.446365
\(957\) 0 0
\(958\) −31.6473 −1.02248
\(959\) −19.1527 −0.618474
\(960\) 0 0
\(961\) 12.3499 0.398384
\(962\) −3.77166 −0.121603
\(963\) 0 0
\(964\) 10.5058 0.338369
\(965\) −80.2499 −2.58333
\(966\) 0 0
\(967\) −24.1986 −0.778175 −0.389088 0.921201i \(-0.627210\pi\)
−0.389088 + 0.921201i \(0.627210\pi\)
\(968\) −25.1731 −0.809094
\(969\) 0 0
\(970\) 9.46958 0.304050
\(971\) 9.35231 0.300130 0.150065 0.988676i \(-0.452052\pi\)
0.150065 + 0.988676i \(0.452052\pi\)
\(972\) 0 0
\(973\) −37.9961 −1.21810
\(974\) 9.72175 0.311505
\(975\) 0 0
\(976\) 2.47563 0.0792431
\(977\) 51.7697 1.65626 0.828129 0.560537i \(-0.189405\pi\)
0.828129 + 0.560537i \(0.189405\pi\)
\(978\) 0 0
\(979\) 6.40554 0.204722
\(980\) −6.76415 −0.216073
\(981\) 0 0
\(982\) −26.5785 −0.848155
\(983\) 61.4372 1.95954 0.979772 0.200119i \(-0.0641327\pi\)
0.979772 + 0.200119i \(0.0641327\pi\)
\(984\) 0 0
\(985\) −6.51847 −0.207696
\(986\) −7.02612 −0.223757
\(987\) 0 0
\(988\) 1.26629 0.0402861
\(989\) −3.86405 −0.122870
\(990\) 0 0
\(991\) 12.3245 0.391501 0.195750 0.980654i \(-0.437286\pi\)
0.195750 + 0.980654i \(0.437286\pi\)
\(992\) −6.58406 −0.209044
\(993\) 0 0
\(994\) 2.09428 0.0664265
\(995\) −81.7956 −2.59309
\(996\) 0 0
\(997\) 38.2719 1.21208 0.606041 0.795433i \(-0.292757\pi\)
0.606041 + 0.795433i \(0.292757\pi\)
\(998\) 0.377594 0.0119525
\(999\) 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 4014.2.a.v.1.7 7
3.2 odd 2 1338.2.a.j.1.1 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1338.2.a.j.1.1 7 3.2 odd 2
4014.2.a.v.1.7 7 1.1 even 1 trivial