Properties

Label 6028.2.a.f.1.2
Level $6028$
Weight $2$
Character 6028.1
Self dual yes
Analytic conductor $48.134$
Analytic rank $0$
Dimension $29$
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] = [6028,2,Mod(1,6028)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6028, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("6028.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6028 = 2^{2} \cdot 11 \cdot 137 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6028.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: \(48.1338223384\)
Analytic rank: \(0\)
Dimension: \(29\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Character \(\chi\) \(=\) 6028.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.90851 q^{3} +0.776599 q^{5} -2.27589 q^{7} +5.45943 q^{9} +O(q^{10})\) \(q-2.90851 q^{3} +0.776599 q^{5} -2.27589 q^{7} +5.45943 q^{9} +1.00000 q^{11} -2.17535 q^{13} -2.25874 q^{15} +5.46266 q^{17} +8.46623 q^{19} +6.61945 q^{21} +8.47742 q^{23} -4.39689 q^{25} -7.15327 q^{27} -7.09951 q^{29} +1.35214 q^{31} -2.90851 q^{33} -1.76745 q^{35} -1.08994 q^{37} +6.32701 q^{39} +3.64877 q^{41} +4.94036 q^{43} +4.23978 q^{45} +0.962432 q^{47} -1.82032 q^{49} -15.8882 q^{51} +1.67850 q^{53} +0.776599 q^{55} -24.6241 q^{57} -3.04816 q^{59} -3.49641 q^{61} -12.4251 q^{63} -1.68937 q^{65} +6.77072 q^{67} -24.6567 q^{69} -7.61897 q^{71} -10.9447 q^{73} +12.7884 q^{75} -2.27589 q^{77} +8.86549 q^{79} +4.42707 q^{81} +2.91904 q^{83} +4.24229 q^{85} +20.6490 q^{87} -0.376105 q^{89} +4.95085 q^{91} -3.93271 q^{93} +6.57486 q^{95} +2.23944 q^{97} +5.45943 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 29 q + 14 q^{3} + 9 q^{5} + 14 q^{7} + 43 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 29 q + 14 q^{3} + 9 q^{5} + 14 q^{7} + 43 q^{9} + 29 q^{11} + 10 q^{15} + 29 q^{17} + 7 q^{19} + 2 q^{21} + 36 q^{23} + 36 q^{25} + 50 q^{27} + 9 q^{29} + 28 q^{31} + 14 q^{33} + 15 q^{35} + 25 q^{37} + 9 q^{39} + 19 q^{41} + 23 q^{43} + 5 q^{45} + 27 q^{47} + 27 q^{49} + 13 q^{51} + 4 q^{53} + 9 q^{55} + 14 q^{57} + 40 q^{59} + 20 q^{61} - 17 q^{63} + 9 q^{65} + 59 q^{67} + 30 q^{69} + 29 q^{71} - 5 q^{73} + 46 q^{75} + 14 q^{77} + 29 q^{79} + 61 q^{81} + 35 q^{83} - 57 q^{85} + 45 q^{87} + 39 q^{89} + 45 q^{91} - 8 q^{93} + q^{95} + 55 q^{97} + 43 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −2.90851 −1.67923 −0.839614 0.543183i \(-0.817219\pi\)
−0.839614 + 0.543183i \(0.817219\pi\)
\(4\) 0 0
\(5\) 0.776599 0.347305 0.173653 0.984807i \(-0.444443\pi\)
0.173653 + 0.984807i \(0.444443\pi\)
\(6\) 0 0
\(7\) −2.27589 −0.860206 −0.430103 0.902780i \(-0.641523\pi\)
−0.430103 + 0.902780i \(0.641523\pi\)
\(8\) 0 0
\(9\) 5.45943 1.81981
\(10\) 0 0
\(11\) 1.00000 0.301511
\(12\) 0 0
\(13\) −2.17535 −0.603332 −0.301666 0.953414i \(-0.597543\pi\)
−0.301666 + 0.953414i \(0.597543\pi\)
\(14\) 0 0
\(15\) −2.25874 −0.583205
\(16\) 0 0
\(17\) 5.46266 1.32489 0.662445 0.749111i \(-0.269519\pi\)
0.662445 + 0.749111i \(0.269519\pi\)
\(18\) 0 0
\(19\) 8.46623 1.94229 0.971143 0.238499i \(-0.0766555\pi\)
0.971143 + 0.238499i \(0.0766555\pi\)
\(20\) 0 0
\(21\) 6.61945 1.44448
\(22\) 0 0
\(23\) 8.47742 1.76766 0.883832 0.467804i \(-0.154955\pi\)
0.883832 + 0.467804i \(0.154955\pi\)
\(24\) 0 0
\(25\) −4.39689 −0.879379
\(26\) 0 0
\(27\) −7.15327 −1.37665
\(28\) 0 0
\(29\) −7.09951 −1.31835 −0.659173 0.751991i \(-0.729094\pi\)
−0.659173 + 0.751991i \(0.729094\pi\)
\(30\) 0 0
\(31\) 1.35214 0.242851 0.121426 0.992601i \(-0.461253\pi\)
0.121426 + 0.992601i \(0.461253\pi\)
\(32\) 0 0
\(33\) −2.90851 −0.506307
\(34\) 0 0
\(35\) −1.76745 −0.298754
\(36\) 0 0
\(37\) −1.08994 −0.179185 −0.0895927 0.995978i \(-0.528557\pi\)
−0.0895927 + 0.995978i \(0.528557\pi\)
\(38\) 0 0
\(39\) 6.32701 1.01313
\(40\) 0 0
\(41\) 3.64877 0.569842 0.284921 0.958551i \(-0.408033\pi\)
0.284921 + 0.958551i \(0.408033\pi\)
\(42\) 0 0
\(43\) 4.94036 0.753398 0.376699 0.926336i \(-0.377059\pi\)
0.376699 + 0.926336i \(0.377059\pi\)
\(44\) 0 0
\(45\) 4.23978 0.632030
\(46\) 0 0
\(47\) 0.962432 0.140385 0.0701926 0.997533i \(-0.477639\pi\)
0.0701926 + 0.997533i \(0.477639\pi\)
\(48\) 0 0
\(49\) −1.82032 −0.260046
\(50\) 0 0
\(51\) −15.8882 −2.22479
\(52\) 0 0
\(53\) 1.67850 0.230559 0.115280 0.993333i \(-0.463224\pi\)
0.115280 + 0.993333i \(0.463224\pi\)
\(54\) 0 0
\(55\) 0.776599 0.104717
\(56\) 0 0
\(57\) −24.6241 −3.26154
\(58\) 0 0
\(59\) −3.04816 −0.396837 −0.198418 0.980117i \(-0.563580\pi\)
−0.198418 + 0.980117i \(0.563580\pi\)
\(60\) 0 0
\(61\) −3.49641 −0.447669 −0.223835 0.974627i \(-0.571858\pi\)
−0.223835 + 0.974627i \(0.571858\pi\)
\(62\) 0 0
\(63\) −12.4251 −1.56541
\(64\) 0 0
\(65\) −1.68937 −0.209541
\(66\) 0 0
\(67\) 6.77072 0.827175 0.413588 0.910464i \(-0.364276\pi\)
0.413588 + 0.910464i \(0.364276\pi\)
\(68\) 0 0
\(69\) −24.6567 −2.96831
\(70\) 0 0
\(71\) −7.61897 −0.904206 −0.452103 0.891966i \(-0.649326\pi\)
−0.452103 + 0.891966i \(0.649326\pi\)
\(72\) 0 0
\(73\) −10.9447 −1.28098 −0.640491 0.767965i \(-0.721269\pi\)
−0.640491 + 0.767965i \(0.721269\pi\)
\(74\) 0 0
\(75\) 12.7884 1.47668
\(76\) 0 0
\(77\) −2.27589 −0.259362
\(78\) 0 0
\(79\) 8.86549 0.997446 0.498723 0.866761i \(-0.333803\pi\)
0.498723 + 0.866761i \(0.333803\pi\)
\(80\) 0 0
\(81\) 4.42707 0.491897
\(82\) 0 0
\(83\) 2.91904 0.320407 0.160203 0.987084i \(-0.448785\pi\)
0.160203 + 0.987084i \(0.448785\pi\)
\(84\) 0 0
\(85\) 4.24229 0.460141
\(86\) 0 0
\(87\) 20.6490 2.21381
\(88\) 0 0
\(89\) −0.376105 −0.0398670 −0.0199335 0.999801i \(-0.506345\pi\)
−0.0199335 + 0.999801i \(0.506345\pi\)
\(90\) 0 0
\(91\) 4.95085 0.518990
\(92\) 0 0
\(93\) −3.93271 −0.407803
\(94\) 0 0
\(95\) 6.57486 0.674566
\(96\) 0 0
\(97\) 2.23944 0.227381 0.113690 0.993516i \(-0.463733\pi\)
0.113690 + 0.993516i \(0.463733\pi\)
\(98\) 0 0
\(99\) 5.45943 0.548693
\(100\) 0 0
\(101\) −11.3690 −1.13126 −0.565630 0.824659i \(-0.691367\pi\)
−0.565630 + 0.824659i \(0.691367\pi\)
\(102\) 0 0
\(103\) 6.95094 0.684896 0.342448 0.939537i \(-0.388744\pi\)
0.342448 + 0.939537i \(0.388744\pi\)
\(104\) 0 0
\(105\) 5.14066 0.501677
\(106\) 0 0
\(107\) −2.23638 −0.216199 −0.108099 0.994140i \(-0.534476\pi\)
−0.108099 + 0.994140i \(0.534476\pi\)
\(108\) 0 0
\(109\) 6.25227 0.598859 0.299430 0.954118i \(-0.403204\pi\)
0.299430 + 0.954118i \(0.403204\pi\)
\(110\) 0 0
\(111\) 3.17011 0.300893
\(112\) 0 0
\(113\) 9.29764 0.874648 0.437324 0.899304i \(-0.355926\pi\)
0.437324 + 0.899304i \(0.355926\pi\)
\(114\) 0 0
\(115\) 6.58355 0.613920
\(116\) 0 0
\(117\) −11.8761 −1.09795
\(118\) 0 0
\(119\) −12.4324 −1.13968
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) −10.6125 −0.956896
\(124\) 0 0
\(125\) −7.29761 −0.652718
\(126\) 0 0
\(127\) 9.88726 0.877352 0.438676 0.898645i \(-0.355448\pi\)
0.438676 + 0.898645i \(0.355448\pi\)
\(128\) 0 0
\(129\) −14.3691 −1.26513
\(130\) 0 0
\(131\) −19.3171 −1.68774 −0.843870 0.536548i \(-0.819728\pi\)
−0.843870 + 0.536548i \(0.819728\pi\)
\(132\) 0 0
\(133\) −19.2682 −1.67077
\(134\) 0 0
\(135\) −5.55522 −0.478117
\(136\) 0 0
\(137\) 1.00000 0.0854358
\(138\) 0 0
\(139\) −5.13447 −0.435500 −0.217750 0.976005i \(-0.569872\pi\)
−0.217750 + 0.976005i \(0.569872\pi\)
\(140\) 0 0
\(141\) −2.79924 −0.235739
\(142\) 0 0
\(143\) −2.17535 −0.181912
\(144\) 0 0
\(145\) −5.51347 −0.457869
\(146\) 0 0
\(147\) 5.29442 0.436676
\(148\) 0 0
\(149\) −12.0520 −0.987339 −0.493669 0.869650i \(-0.664345\pi\)
−0.493669 + 0.869650i \(0.664345\pi\)
\(150\) 0 0
\(151\) 20.4687 1.66572 0.832861 0.553482i \(-0.186701\pi\)
0.832861 + 0.553482i \(0.186701\pi\)
\(152\) 0 0
\(153\) 29.8230 2.41105
\(154\) 0 0
\(155\) 1.05007 0.0843436
\(156\) 0 0
\(157\) 18.0882 1.44360 0.721799 0.692103i \(-0.243316\pi\)
0.721799 + 0.692103i \(0.243316\pi\)
\(158\) 0 0
\(159\) −4.88192 −0.387162
\(160\) 0 0
\(161\) −19.2937 −1.52056
\(162\) 0 0
\(163\) −11.7760 −0.922366 −0.461183 0.887305i \(-0.652575\pi\)
−0.461183 + 0.887305i \(0.652575\pi\)
\(164\) 0 0
\(165\) −2.25874 −0.175843
\(166\) 0 0
\(167\) −11.0879 −0.858004 −0.429002 0.903304i \(-0.641135\pi\)
−0.429002 + 0.903304i \(0.641135\pi\)
\(168\) 0 0
\(169\) −8.26787 −0.635990
\(170\) 0 0
\(171\) 46.2208 3.53459
\(172\) 0 0
\(173\) 25.2206 1.91748 0.958742 0.284278i \(-0.0917539\pi\)
0.958742 + 0.284278i \(0.0917539\pi\)
\(174\) 0 0
\(175\) 10.0069 0.756447
\(176\) 0 0
\(177\) 8.86560 0.666379
\(178\) 0 0
\(179\) −15.7112 −1.17431 −0.587154 0.809475i \(-0.699752\pi\)
−0.587154 + 0.809475i \(0.699752\pi\)
\(180\) 0 0
\(181\) −10.4428 −0.776207 −0.388104 0.921616i \(-0.626870\pi\)
−0.388104 + 0.921616i \(0.626870\pi\)
\(182\) 0 0
\(183\) 10.1693 0.751739
\(184\) 0 0
\(185\) −0.846447 −0.0622320
\(186\) 0 0
\(187\) 5.46266 0.399469
\(188\) 0 0
\(189\) 16.2801 1.18420
\(190\) 0 0
\(191\) 7.16004 0.518082 0.259041 0.965866i \(-0.416593\pi\)
0.259041 + 0.965866i \(0.416593\pi\)
\(192\) 0 0
\(193\) 8.34321 0.600558 0.300279 0.953851i \(-0.402920\pi\)
0.300279 + 0.953851i \(0.402920\pi\)
\(194\) 0 0
\(195\) 4.91355 0.351867
\(196\) 0 0
\(197\) 13.7561 0.980079 0.490040 0.871700i \(-0.336982\pi\)
0.490040 + 0.871700i \(0.336982\pi\)
\(198\) 0 0
\(199\) 9.56292 0.677897 0.338949 0.940805i \(-0.389929\pi\)
0.338949 + 0.940805i \(0.389929\pi\)
\(200\) 0 0
\(201\) −19.6927 −1.38902
\(202\) 0 0
\(203\) 16.1577 1.13405
\(204\) 0 0
\(205\) 2.83363 0.197909
\(206\) 0 0
\(207\) 46.2819 3.21681
\(208\) 0 0
\(209\) 8.46623 0.585621
\(210\) 0 0
\(211\) 5.71044 0.393123 0.196561 0.980492i \(-0.437023\pi\)
0.196561 + 0.980492i \(0.437023\pi\)
\(212\) 0 0
\(213\) 22.1599 1.51837
\(214\) 0 0
\(215\) 3.83668 0.261659
\(216\) 0 0
\(217\) −3.07732 −0.208902
\(218\) 0 0
\(219\) 31.8328 2.15106
\(220\) 0 0
\(221\) −11.8832 −0.799349
\(222\) 0 0
\(223\) −24.5661 −1.64507 −0.822535 0.568714i \(-0.807441\pi\)
−0.822535 + 0.568714i \(0.807441\pi\)
\(224\) 0 0
\(225\) −24.0045 −1.60030
\(226\) 0 0
\(227\) 24.6377 1.63526 0.817631 0.575743i \(-0.195287\pi\)
0.817631 + 0.575743i \(0.195287\pi\)
\(228\) 0 0
\(229\) −11.8100 −0.780429 −0.390214 0.920724i \(-0.627599\pi\)
−0.390214 + 0.920724i \(0.627599\pi\)
\(230\) 0 0
\(231\) 6.61945 0.435528
\(232\) 0 0
\(233\) 23.5551 1.54314 0.771572 0.636142i \(-0.219471\pi\)
0.771572 + 0.636142i \(0.219471\pi\)
\(234\) 0 0
\(235\) 0.747423 0.0487565
\(236\) 0 0
\(237\) −25.7854 −1.67494
\(238\) 0 0
\(239\) −13.1792 −0.852493 −0.426246 0.904607i \(-0.640164\pi\)
−0.426246 + 0.904607i \(0.640164\pi\)
\(240\) 0 0
\(241\) −12.4210 −0.800109 −0.400055 0.916491i \(-0.631009\pi\)
−0.400055 + 0.916491i \(0.631009\pi\)
\(242\) 0 0
\(243\) 8.58363 0.550640
\(244\) 0 0
\(245\) −1.41366 −0.0903153
\(246\) 0 0
\(247\) −18.4170 −1.17184
\(248\) 0 0
\(249\) −8.49007 −0.538036
\(250\) 0 0
\(251\) 11.5751 0.730611 0.365305 0.930888i \(-0.380965\pi\)
0.365305 + 0.930888i \(0.380965\pi\)
\(252\) 0 0
\(253\) 8.47742 0.532971
\(254\) 0 0
\(255\) −12.3388 −0.772683
\(256\) 0 0
\(257\) 0.616266 0.0384416 0.0192208 0.999815i \(-0.493881\pi\)
0.0192208 + 0.999815i \(0.493881\pi\)
\(258\) 0 0
\(259\) 2.48059 0.154136
\(260\) 0 0
\(261\) −38.7593 −2.39914
\(262\) 0 0
\(263\) 15.0318 0.926901 0.463450 0.886123i \(-0.346611\pi\)
0.463450 + 0.886123i \(0.346611\pi\)
\(264\) 0 0
\(265\) 1.30352 0.0800745
\(266\) 0 0
\(267\) 1.09390 0.0669459
\(268\) 0 0
\(269\) 23.0401 1.40478 0.702390 0.711792i \(-0.252116\pi\)
0.702390 + 0.711792i \(0.252116\pi\)
\(270\) 0 0
\(271\) 6.48764 0.394096 0.197048 0.980394i \(-0.436864\pi\)
0.197048 + 0.980394i \(0.436864\pi\)
\(272\) 0 0
\(273\) −14.3996 −0.871503
\(274\) 0 0
\(275\) −4.39689 −0.265143
\(276\) 0 0
\(277\) −10.5551 −0.634193 −0.317096 0.948393i \(-0.602708\pi\)
−0.317096 + 0.948393i \(0.602708\pi\)
\(278\) 0 0
\(279\) 7.38191 0.441943
\(280\) 0 0
\(281\) −30.2747 −1.80604 −0.903019 0.429600i \(-0.858655\pi\)
−0.903019 + 0.429600i \(0.858655\pi\)
\(282\) 0 0
\(283\) 19.0442 1.13206 0.566029 0.824385i \(-0.308479\pi\)
0.566029 + 0.824385i \(0.308479\pi\)
\(284\) 0 0
\(285\) −19.1230 −1.13275
\(286\) 0 0
\(287\) −8.30421 −0.490182
\(288\) 0 0
\(289\) 12.8407 0.755334
\(290\) 0 0
\(291\) −6.51343 −0.381824
\(292\) 0 0
\(293\) 4.85669 0.283731 0.141865 0.989886i \(-0.454690\pi\)
0.141865 + 0.989886i \(0.454690\pi\)
\(294\) 0 0
\(295\) −2.36720 −0.137823
\(296\) 0 0
\(297\) −7.15327 −0.415075
\(298\) 0 0
\(299\) −18.4413 −1.06649
\(300\) 0 0
\(301\) −11.2437 −0.648077
\(302\) 0 0
\(303\) 33.0669 1.89964
\(304\) 0 0
\(305\) −2.71530 −0.155478
\(306\) 0 0
\(307\) −24.4403 −1.39488 −0.697440 0.716643i \(-0.745678\pi\)
−0.697440 + 0.716643i \(0.745678\pi\)
\(308\) 0 0
\(309\) −20.2169 −1.15010
\(310\) 0 0
\(311\) 7.30450 0.414200 0.207100 0.978320i \(-0.433597\pi\)
0.207100 + 0.978320i \(0.433597\pi\)
\(312\) 0 0
\(313\) 33.3926 1.88746 0.943729 0.330719i \(-0.107291\pi\)
0.943729 + 0.330719i \(0.107291\pi\)
\(314\) 0 0
\(315\) −9.64929 −0.543676
\(316\) 0 0
\(317\) −26.9814 −1.51543 −0.757713 0.652587i \(-0.773684\pi\)
−0.757713 + 0.652587i \(0.773684\pi\)
\(318\) 0 0
\(319\) −7.09951 −0.397496
\(320\) 0 0
\(321\) 6.50452 0.363047
\(322\) 0 0
\(323\) 46.2481 2.57331
\(324\) 0 0
\(325\) 9.56477 0.530558
\(326\) 0 0
\(327\) −18.1848 −1.00562
\(328\) 0 0
\(329\) −2.19039 −0.120760
\(330\) 0 0
\(331\) 29.2312 1.60669 0.803346 0.595513i \(-0.203051\pi\)
0.803346 + 0.595513i \(0.203051\pi\)
\(332\) 0 0
\(333\) −5.95046 −0.326083
\(334\) 0 0
\(335\) 5.25813 0.287282
\(336\) 0 0
\(337\) 8.23610 0.448649 0.224324 0.974515i \(-0.427982\pi\)
0.224324 + 0.974515i \(0.427982\pi\)
\(338\) 0 0
\(339\) −27.0423 −1.46873
\(340\) 0 0
\(341\) 1.35214 0.0732225
\(342\) 0 0
\(343\) 20.0741 1.08390
\(344\) 0 0
\(345\) −19.1483 −1.03091
\(346\) 0 0
\(347\) −18.6655 −1.00202 −0.501008 0.865443i \(-0.667037\pi\)
−0.501008 + 0.865443i \(0.667037\pi\)
\(348\) 0 0
\(349\) 2.14780 0.114969 0.0574844 0.998346i \(-0.481692\pi\)
0.0574844 + 0.998346i \(0.481692\pi\)
\(350\) 0 0
\(351\) 15.5608 0.830576
\(352\) 0 0
\(353\) −24.4143 −1.29944 −0.649722 0.760172i \(-0.725115\pi\)
−0.649722 + 0.760172i \(0.725115\pi\)
\(354\) 0 0
\(355\) −5.91688 −0.314036
\(356\) 0 0
\(357\) 36.1598 1.91378
\(358\) 0 0
\(359\) −28.1105 −1.48362 −0.741808 0.670613i \(-0.766031\pi\)
−0.741808 + 0.670613i \(0.766031\pi\)
\(360\) 0 0
\(361\) 52.6770 2.77247
\(362\) 0 0
\(363\) −2.90851 −0.152657
\(364\) 0 0
\(365\) −8.49965 −0.444892
\(366\) 0 0
\(367\) 11.1869 0.583952 0.291976 0.956426i \(-0.405687\pi\)
0.291976 + 0.956426i \(0.405687\pi\)
\(368\) 0 0
\(369\) 19.9202 1.03700
\(370\) 0 0
\(371\) −3.82008 −0.198328
\(372\) 0 0
\(373\) −14.6708 −0.759623 −0.379812 0.925064i \(-0.624011\pi\)
−0.379812 + 0.925064i \(0.624011\pi\)
\(374\) 0 0
\(375\) 21.2252 1.09606
\(376\) 0 0
\(377\) 15.4439 0.795401
\(378\) 0 0
\(379\) 8.21465 0.421958 0.210979 0.977491i \(-0.432335\pi\)
0.210979 + 0.977491i \(0.432335\pi\)
\(380\) 0 0
\(381\) −28.7572 −1.47328
\(382\) 0 0
\(383\) 16.5081 0.843526 0.421763 0.906706i \(-0.361412\pi\)
0.421763 + 0.906706i \(0.361412\pi\)
\(384\) 0 0
\(385\) −1.76745 −0.0900778
\(386\) 0 0
\(387\) 26.9715 1.37104
\(388\) 0 0
\(389\) 4.68802 0.237692 0.118846 0.992913i \(-0.462081\pi\)
0.118846 + 0.992913i \(0.462081\pi\)
\(390\) 0 0
\(391\) 46.3093 2.34196
\(392\) 0 0
\(393\) 56.1839 2.83410
\(394\) 0 0
\(395\) 6.88493 0.346418
\(396\) 0 0
\(397\) −9.83885 −0.493798 −0.246899 0.969041i \(-0.579412\pi\)
−0.246899 + 0.969041i \(0.579412\pi\)
\(398\) 0 0
\(399\) 56.0418 2.80560
\(400\) 0 0
\(401\) 26.0445 1.30060 0.650301 0.759677i \(-0.274643\pi\)
0.650301 + 0.759677i \(0.274643\pi\)
\(402\) 0 0
\(403\) −2.94137 −0.146520
\(404\) 0 0
\(405\) 3.43806 0.170838
\(406\) 0 0
\(407\) −1.08994 −0.0540264
\(408\) 0 0
\(409\) 34.7729 1.71941 0.859704 0.510793i \(-0.170648\pi\)
0.859704 + 0.510793i \(0.170648\pi\)
\(410\) 0 0
\(411\) −2.90851 −0.143466
\(412\) 0 0
\(413\) 6.93728 0.341361
\(414\) 0 0
\(415\) 2.26693 0.111279
\(416\) 0 0
\(417\) 14.9337 0.731305
\(418\) 0 0
\(419\) 10.1538 0.496045 0.248023 0.968754i \(-0.420219\pi\)
0.248023 + 0.968754i \(0.420219\pi\)
\(420\) 0 0
\(421\) 14.4245 0.703009 0.351504 0.936186i \(-0.385670\pi\)
0.351504 + 0.936186i \(0.385670\pi\)
\(422\) 0 0
\(423\) 5.25433 0.255474
\(424\) 0 0
\(425\) −24.0187 −1.16508
\(426\) 0 0
\(427\) 7.95744 0.385088
\(428\) 0 0
\(429\) 6.32701 0.305471
\(430\) 0 0
\(431\) 18.1177 0.872700 0.436350 0.899777i \(-0.356271\pi\)
0.436350 + 0.899777i \(0.356271\pi\)
\(432\) 0 0
\(433\) 23.0489 1.10766 0.553830 0.832630i \(-0.313166\pi\)
0.553830 + 0.832630i \(0.313166\pi\)
\(434\) 0 0
\(435\) 16.0360 0.768867
\(436\) 0 0
\(437\) 71.7718 3.43331
\(438\) 0 0
\(439\) −39.0897 −1.86565 −0.932826 0.360328i \(-0.882665\pi\)
−0.932826 + 0.360328i \(0.882665\pi\)
\(440\) 0 0
\(441\) −9.93791 −0.473234
\(442\) 0 0
\(443\) −16.1318 −0.766446 −0.383223 0.923656i \(-0.625186\pi\)
−0.383223 + 0.923656i \(0.625186\pi\)
\(444\) 0 0
\(445\) −0.292083 −0.0138460
\(446\) 0 0
\(447\) 35.0534 1.65797
\(448\) 0 0
\(449\) 13.2046 0.623165 0.311583 0.950219i \(-0.399141\pi\)
0.311583 + 0.950219i \(0.399141\pi\)
\(450\) 0 0
\(451\) 3.64877 0.171814
\(452\) 0 0
\(453\) −59.5335 −2.79713
\(454\) 0 0
\(455\) 3.84482 0.180248
\(456\) 0 0
\(457\) 33.9227 1.58684 0.793418 0.608677i \(-0.208299\pi\)
0.793418 + 0.608677i \(0.208299\pi\)
\(458\) 0 0
\(459\) −39.0759 −1.82391
\(460\) 0 0
\(461\) 16.2397 0.756359 0.378180 0.925732i \(-0.376550\pi\)
0.378180 + 0.925732i \(0.376550\pi\)
\(462\) 0 0
\(463\) −27.8427 −1.29396 −0.646981 0.762506i \(-0.723969\pi\)
−0.646981 + 0.762506i \(0.723969\pi\)
\(464\) 0 0
\(465\) −3.05414 −0.141632
\(466\) 0 0
\(467\) 37.8361 1.75084 0.875422 0.483359i \(-0.160583\pi\)
0.875422 + 0.483359i \(0.160583\pi\)
\(468\) 0 0
\(469\) −15.4094 −0.711541
\(470\) 0 0
\(471\) −52.6098 −2.42413
\(472\) 0 0
\(473\) 4.94036 0.227158
\(474\) 0 0
\(475\) −37.2251 −1.70800
\(476\) 0 0
\(477\) 9.16363 0.419574
\(478\) 0 0
\(479\) 26.3140 1.20232 0.601158 0.799130i \(-0.294706\pi\)
0.601158 + 0.799130i \(0.294706\pi\)
\(480\) 0 0
\(481\) 2.37100 0.108108
\(482\) 0 0
\(483\) 56.1159 2.55336
\(484\) 0 0
\(485\) 1.73915 0.0789706
\(486\) 0 0
\(487\) 2.33102 0.105629 0.0528144 0.998604i \(-0.483181\pi\)
0.0528144 + 0.998604i \(0.483181\pi\)
\(488\) 0 0
\(489\) 34.2506 1.54886
\(490\) 0 0
\(491\) 8.33436 0.376125 0.188062 0.982157i \(-0.439779\pi\)
0.188062 + 0.982157i \(0.439779\pi\)
\(492\) 0 0
\(493\) −38.7822 −1.74666
\(494\) 0 0
\(495\) 4.23978 0.190564
\(496\) 0 0
\(497\) 17.3400 0.777803
\(498\) 0 0
\(499\) 0.356854 0.0159750 0.00798749 0.999968i \(-0.497457\pi\)
0.00798749 + 0.999968i \(0.497457\pi\)
\(500\) 0 0
\(501\) 32.2491 1.44078
\(502\) 0 0
\(503\) 10.2880 0.458718 0.229359 0.973342i \(-0.426337\pi\)
0.229359 + 0.973342i \(0.426337\pi\)
\(504\) 0 0
\(505\) −8.82917 −0.392893
\(506\) 0 0
\(507\) 24.0472 1.06797
\(508\) 0 0
\(509\) 7.63489 0.338410 0.169205 0.985581i \(-0.445880\pi\)
0.169205 + 0.985581i \(0.445880\pi\)
\(510\) 0 0
\(511\) 24.9090 1.10191
\(512\) 0 0
\(513\) −60.5612 −2.67384
\(514\) 0 0
\(515\) 5.39809 0.237868
\(516\) 0 0
\(517\) 0.962432 0.0423277
\(518\) 0 0
\(519\) −73.3542 −3.21989
\(520\) 0 0
\(521\) 28.6936 1.25709 0.628544 0.777774i \(-0.283651\pi\)
0.628544 + 0.777774i \(0.283651\pi\)
\(522\) 0 0
\(523\) −5.69936 −0.249215 −0.124608 0.992206i \(-0.539767\pi\)
−0.124608 + 0.992206i \(0.539767\pi\)
\(524\) 0 0
\(525\) −29.1050 −1.27025
\(526\) 0 0
\(527\) 7.38628 0.321752
\(528\) 0 0
\(529\) 48.8667 2.12464
\(530\) 0 0
\(531\) −16.6412 −0.722167
\(532\) 0 0
\(533\) −7.93734 −0.343804
\(534\) 0 0
\(535\) −1.73677 −0.0750870
\(536\) 0 0
\(537\) 45.6961 1.97193
\(538\) 0 0
\(539\) −1.82032 −0.0784067
\(540\) 0 0
\(541\) 5.97793 0.257011 0.128506 0.991709i \(-0.458982\pi\)
0.128506 + 0.991709i \(0.458982\pi\)
\(542\) 0 0
\(543\) 30.3730 1.30343
\(544\) 0 0
\(545\) 4.85551 0.207987
\(546\) 0 0
\(547\) 35.4291 1.51484 0.757419 0.652929i \(-0.226460\pi\)
0.757419 + 0.652929i \(0.226460\pi\)
\(548\) 0 0
\(549\) −19.0884 −0.814672
\(550\) 0 0
\(551\) −60.1061 −2.56060
\(552\) 0 0
\(553\) −20.1769 −0.858009
\(554\) 0 0
\(555\) 2.46190 0.104502
\(556\) 0 0
\(557\) −13.6464 −0.578218 −0.289109 0.957296i \(-0.593359\pi\)
−0.289109 + 0.957296i \(0.593359\pi\)
\(558\) 0 0
\(559\) −10.7470 −0.454549
\(560\) 0 0
\(561\) −15.8882 −0.670800
\(562\) 0 0
\(563\) 18.2209 0.767918 0.383959 0.923350i \(-0.374560\pi\)
0.383959 + 0.923350i \(0.374560\pi\)
\(564\) 0 0
\(565\) 7.22053 0.303770
\(566\) 0 0
\(567\) −10.0755 −0.423133
\(568\) 0 0
\(569\) −1.96094 −0.0822071 −0.0411035 0.999155i \(-0.513087\pi\)
−0.0411035 + 0.999155i \(0.513087\pi\)
\(570\) 0 0
\(571\) 26.7693 1.12026 0.560130 0.828405i \(-0.310751\pi\)
0.560130 + 0.828405i \(0.310751\pi\)
\(572\) 0 0
\(573\) −20.8250 −0.869979
\(574\) 0 0
\(575\) −37.2743 −1.55445
\(576\) 0 0
\(577\) 0.224688 0.00935390 0.00467695 0.999989i \(-0.498511\pi\)
0.00467695 + 0.999989i \(0.498511\pi\)
\(578\) 0 0
\(579\) −24.2663 −1.00847
\(580\) 0 0
\(581\) −6.64343 −0.275616
\(582\) 0 0
\(583\) 1.67850 0.0695162
\(584\) 0 0
\(585\) −9.22300 −0.381324
\(586\) 0 0
\(587\) −31.7122 −1.30890 −0.654451 0.756104i \(-0.727100\pi\)
−0.654451 + 0.756104i \(0.727100\pi\)
\(588\) 0 0
\(589\) 11.4475 0.471687
\(590\) 0 0
\(591\) −40.0096 −1.64578
\(592\) 0 0
\(593\) 11.0417 0.453429 0.226715 0.973961i \(-0.427202\pi\)
0.226715 + 0.973961i \(0.427202\pi\)
\(594\) 0 0
\(595\) −9.65500 −0.395816
\(596\) 0 0
\(597\) −27.8138 −1.13834
\(598\) 0 0
\(599\) 22.9202 0.936494 0.468247 0.883598i \(-0.344886\pi\)
0.468247 + 0.883598i \(0.344886\pi\)
\(600\) 0 0
\(601\) −7.97492 −0.325304 −0.162652 0.986684i \(-0.552005\pi\)
−0.162652 + 0.986684i \(0.552005\pi\)
\(602\) 0 0
\(603\) 36.9643 1.50530
\(604\) 0 0
\(605\) 0.776599 0.0315732
\(606\) 0 0
\(607\) 15.7978 0.641215 0.320607 0.947212i \(-0.396113\pi\)
0.320607 + 0.947212i \(0.396113\pi\)
\(608\) 0 0
\(609\) −46.9949 −1.90433
\(610\) 0 0
\(611\) −2.09362 −0.0846989
\(612\) 0 0
\(613\) −35.2948 −1.42554 −0.712772 0.701396i \(-0.752561\pi\)
−0.712772 + 0.701396i \(0.752561\pi\)
\(614\) 0 0
\(615\) −8.24164 −0.332335
\(616\) 0 0
\(617\) 33.2245 1.33757 0.668785 0.743456i \(-0.266815\pi\)
0.668785 + 0.743456i \(0.266815\pi\)
\(618\) 0 0
\(619\) 2.19969 0.0884130 0.0442065 0.999022i \(-0.485924\pi\)
0.0442065 + 0.999022i \(0.485924\pi\)
\(620\) 0 0
\(621\) −60.6413 −2.43345
\(622\) 0 0
\(623\) 0.855974 0.0342939
\(624\) 0 0
\(625\) 16.3172 0.652686
\(626\) 0 0
\(627\) −24.6241 −0.983392
\(628\) 0 0
\(629\) −5.95398 −0.237401
\(630\) 0 0
\(631\) −41.7539 −1.66220 −0.831099 0.556125i \(-0.812288\pi\)
−0.831099 + 0.556125i \(0.812288\pi\)
\(632\) 0 0
\(633\) −16.6089 −0.660143
\(634\) 0 0
\(635\) 7.67843 0.304709
\(636\) 0 0
\(637\) 3.95983 0.156894
\(638\) 0 0
\(639\) −41.5952 −1.64548
\(640\) 0 0
\(641\) −10.2230 −0.403782 −0.201891 0.979408i \(-0.564709\pi\)
−0.201891 + 0.979408i \(0.564709\pi\)
\(642\) 0 0
\(643\) 28.6883 1.13136 0.565678 0.824626i \(-0.308614\pi\)
0.565678 + 0.824626i \(0.308614\pi\)
\(644\) 0 0
\(645\) −11.1590 −0.439386
\(646\) 0 0
\(647\) −11.1728 −0.439248 −0.219624 0.975585i \(-0.570483\pi\)
−0.219624 + 0.975585i \(0.570483\pi\)
\(648\) 0 0
\(649\) −3.04816 −0.119651
\(650\) 0 0
\(651\) 8.95042 0.350795
\(652\) 0 0
\(653\) 17.3511 0.679002 0.339501 0.940606i \(-0.389742\pi\)
0.339501 + 0.940606i \(0.389742\pi\)
\(654\) 0 0
\(655\) −15.0016 −0.586161
\(656\) 0 0
\(657\) −59.7519 −2.33114
\(658\) 0 0
\(659\) −23.3534 −0.909718 −0.454859 0.890563i \(-0.650310\pi\)
−0.454859 + 0.890563i \(0.650310\pi\)
\(660\) 0 0
\(661\) −11.6916 −0.454751 −0.227375 0.973807i \(-0.573014\pi\)
−0.227375 + 0.973807i \(0.573014\pi\)
\(662\) 0 0
\(663\) 34.5623 1.34229
\(664\) 0 0
\(665\) −14.9637 −0.580266
\(666\) 0 0
\(667\) −60.1856 −2.33039
\(668\) 0 0
\(669\) 71.4509 2.76245
\(670\) 0 0
\(671\) −3.49641 −0.134977
\(672\) 0 0
\(673\) −7.04115 −0.271416 −0.135708 0.990749i \(-0.543331\pi\)
−0.135708 + 0.990749i \(0.543331\pi\)
\(674\) 0 0
\(675\) 31.4522 1.21059
\(676\) 0 0
\(677\) −25.4862 −0.979515 −0.489757 0.871859i \(-0.662915\pi\)
−0.489757 + 0.871859i \(0.662915\pi\)
\(678\) 0 0
\(679\) −5.09672 −0.195594
\(680\) 0 0
\(681\) −71.6590 −2.74598
\(682\) 0 0
\(683\) 12.7209 0.486751 0.243375 0.969932i \(-0.421745\pi\)
0.243375 + 0.969932i \(0.421745\pi\)
\(684\) 0 0
\(685\) 0.776599 0.0296723
\(686\) 0 0
\(687\) 34.3496 1.31052
\(688\) 0 0
\(689\) −3.65131 −0.139104
\(690\) 0 0
\(691\) −7.14120 −0.271664 −0.135832 0.990732i \(-0.543371\pi\)
−0.135832 + 0.990732i \(0.543371\pi\)
\(692\) 0 0
\(693\) −12.4251 −0.471989
\(694\) 0 0
\(695\) −3.98743 −0.151252
\(696\) 0 0
\(697\) 19.9320 0.754978
\(698\) 0 0
\(699\) −68.5101 −2.59129
\(700\) 0 0
\(701\) −13.5998 −0.513657 −0.256829 0.966457i \(-0.582678\pi\)
−0.256829 + 0.966457i \(0.582678\pi\)
\(702\) 0 0
\(703\) −9.22769 −0.348029
\(704\) 0 0
\(705\) −2.17389 −0.0818734
\(706\) 0 0
\(707\) 25.8747 0.973117
\(708\) 0 0
\(709\) −5.11325 −0.192032 −0.0960160 0.995380i \(-0.530610\pi\)
−0.0960160 + 0.995380i \(0.530610\pi\)
\(710\) 0 0
\(711\) 48.4005 1.81516
\(712\) 0 0
\(713\) 11.4627 0.429280
\(714\) 0 0
\(715\) −1.68937 −0.0631789
\(716\) 0 0
\(717\) 38.3319 1.43153
\(718\) 0 0
\(719\) −7.61492 −0.283989 −0.141994 0.989867i \(-0.545351\pi\)
−0.141994 + 0.989867i \(0.545351\pi\)
\(720\) 0 0
\(721\) −15.8196 −0.589152
\(722\) 0 0
\(723\) 36.1267 1.34357
\(724\) 0 0
\(725\) 31.2158 1.15933
\(726\) 0 0
\(727\) 24.7138 0.916582 0.458291 0.888802i \(-0.348462\pi\)
0.458291 + 0.888802i \(0.348462\pi\)
\(728\) 0 0
\(729\) −38.2468 −1.41655
\(730\) 0 0
\(731\) 26.9875 0.998169
\(732\) 0 0
\(733\) −22.0377 −0.813981 −0.406991 0.913432i \(-0.633422\pi\)
−0.406991 + 0.913432i \(0.633422\pi\)
\(734\) 0 0
\(735\) 4.11164 0.151660
\(736\) 0 0
\(737\) 6.77072 0.249403
\(738\) 0 0
\(739\) −2.57064 −0.0945624 −0.0472812 0.998882i \(-0.515056\pi\)
−0.0472812 + 0.998882i \(0.515056\pi\)
\(740\) 0 0
\(741\) 53.5659 1.96779
\(742\) 0 0
\(743\) −8.96476 −0.328885 −0.164443 0.986387i \(-0.552583\pi\)
−0.164443 + 0.986387i \(0.552583\pi\)
\(744\) 0 0
\(745\) −9.35957 −0.342908
\(746\) 0 0
\(747\) 15.9363 0.583079
\(748\) 0 0
\(749\) 5.08975 0.185975
\(750\) 0 0
\(751\) 51.9137 1.89436 0.947179 0.320705i \(-0.103920\pi\)
0.947179 + 0.320705i \(0.103920\pi\)
\(752\) 0 0
\(753\) −33.6662 −1.22686
\(754\) 0 0
\(755\) 15.8960 0.578514
\(756\) 0 0
\(757\) −38.7842 −1.40963 −0.704817 0.709389i \(-0.748971\pi\)
−0.704817 + 0.709389i \(0.748971\pi\)
\(758\) 0 0
\(759\) −24.6567 −0.894980
\(760\) 0 0
\(761\) −10.2193 −0.370450 −0.185225 0.982696i \(-0.559301\pi\)
−0.185225 + 0.982696i \(0.559301\pi\)
\(762\) 0 0
\(763\) −14.2295 −0.515142
\(764\) 0 0
\(765\) 23.1605 0.837370
\(766\) 0 0
\(767\) 6.63080 0.239424
\(768\) 0 0
\(769\) 34.9017 1.25859 0.629294 0.777167i \(-0.283344\pi\)
0.629294 + 0.777167i \(0.283344\pi\)
\(770\) 0 0
\(771\) −1.79242 −0.0645523
\(772\) 0 0
\(773\) −19.3308 −0.695280 −0.347640 0.937628i \(-0.613017\pi\)
−0.347640 + 0.937628i \(0.613017\pi\)
\(774\) 0 0
\(775\) −5.94522 −0.213558
\(776\) 0 0
\(777\) −7.21482 −0.258830
\(778\) 0 0
\(779\) 30.8913 1.10680
\(780\) 0 0
\(781\) −7.61897 −0.272628
\(782\) 0 0
\(783\) 50.7847 1.81490
\(784\) 0 0
\(785\) 14.0473 0.501369
\(786\) 0 0
\(787\) −2.15418 −0.0767884 −0.0383942 0.999263i \(-0.512224\pi\)
−0.0383942 + 0.999263i \(0.512224\pi\)
\(788\) 0 0
\(789\) −43.7201 −1.55648
\(790\) 0 0
\(791\) −21.1604 −0.752378
\(792\) 0 0
\(793\) 7.60589 0.270093
\(794\) 0 0
\(795\) −3.79130 −0.134463
\(796\) 0 0
\(797\) 54.3976 1.92686 0.963431 0.267957i \(-0.0863486\pi\)
0.963431 + 0.267957i \(0.0863486\pi\)
\(798\) 0 0
\(799\) 5.25744 0.185995
\(800\) 0 0
\(801\) −2.05332 −0.0725504
\(802\) 0 0
\(803\) −10.9447 −0.386231
\(804\) 0 0
\(805\) −14.9835 −0.528097
\(806\) 0 0
\(807\) −67.0124 −2.35895
\(808\) 0 0
\(809\) 27.0473 0.950931 0.475466 0.879734i \(-0.342280\pi\)
0.475466 + 0.879734i \(0.342280\pi\)
\(810\) 0 0
\(811\) −40.5444 −1.42371 −0.711853 0.702329i \(-0.752144\pi\)
−0.711853 + 0.702329i \(0.752144\pi\)
\(812\) 0 0
\(813\) −18.8694 −0.661778
\(814\) 0 0
\(815\) −9.14521 −0.320343
\(816\) 0 0
\(817\) 41.8262 1.46331
\(818\) 0 0
\(819\) 27.0288 0.944463
\(820\) 0 0
\(821\) −23.0882 −0.805785 −0.402892 0.915247i \(-0.631995\pi\)
−0.402892 + 0.915247i \(0.631995\pi\)
\(822\) 0 0
\(823\) −22.7946 −0.794571 −0.397286 0.917695i \(-0.630048\pi\)
−0.397286 + 0.917695i \(0.630048\pi\)
\(824\) 0 0
\(825\) 12.7884 0.445235
\(826\) 0 0
\(827\) −36.6264 −1.27362 −0.636812 0.771019i \(-0.719747\pi\)
−0.636812 + 0.771019i \(0.719747\pi\)
\(828\) 0 0
\(829\) 10.0786 0.350043 0.175021 0.984565i \(-0.444001\pi\)
0.175021 + 0.984565i \(0.444001\pi\)
\(830\) 0 0
\(831\) 30.6995 1.06496
\(832\) 0 0
\(833\) −9.94379 −0.344532
\(834\) 0 0
\(835\) −8.61081 −0.297989
\(836\) 0 0
\(837\) −9.67222 −0.334321
\(838\) 0 0
\(839\) 9.33726 0.322358 0.161179 0.986925i \(-0.448470\pi\)
0.161179 + 0.986925i \(0.448470\pi\)
\(840\) 0 0
\(841\) 21.4031 0.738037
\(842\) 0 0
\(843\) 88.0543 3.03275
\(844\) 0 0
\(845\) −6.42082 −0.220883
\(846\) 0 0
\(847\) −2.27589 −0.0782005
\(848\) 0 0
\(849\) −55.3902 −1.90099
\(850\) 0 0
\(851\) −9.23990 −0.316740
\(852\) 0 0
\(853\) −10.1668 −0.348106 −0.174053 0.984736i \(-0.555686\pi\)
−0.174053 + 0.984736i \(0.555686\pi\)
\(854\) 0 0
\(855\) 35.8950 1.22758
\(856\) 0 0
\(857\) −15.6146 −0.533385 −0.266693 0.963782i \(-0.585931\pi\)
−0.266693 + 0.963782i \(0.585931\pi\)
\(858\) 0 0
\(859\) −24.7718 −0.845202 −0.422601 0.906316i \(-0.638883\pi\)
−0.422601 + 0.906316i \(0.638883\pi\)
\(860\) 0 0
\(861\) 24.1529 0.823127
\(862\) 0 0
\(863\) −37.9548 −1.29200 −0.645999 0.763338i \(-0.723559\pi\)
−0.645999 + 0.763338i \(0.723559\pi\)
\(864\) 0 0
\(865\) 19.5863 0.665952
\(866\) 0 0
\(867\) −37.3472 −1.26838
\(868\) 0 0
\(869\) 8.86549 0.300741
\(870\) 0 0
\(871\) −14.7287 −0.499062
\(872\) 0 0
\(873\) 12.2261 0.413790
\(874\) 0 0
\(875\) 16.6086 0.561472
\(876\) 0 0
\(877\) 2.18673 0.0738405 0.0369203 0.999318i \(-0.488245\pi\)
0.0369203 + 0.999318i \(0.488245\pi\)
\(878\) 0 0
\(879\) −14.1257 −0.476449
\(880\) 0 0
\(881\) −15.7981 −0.532253 −0.266126 0.963938i \(-0.585744\pi\)
−0.266126 + 0.963938i \(0.585744\pi\)
\(882\) 0 0
\(883\) −40.9074 −1.37664 −0.688322 0.725405i \(-0.741652\pi\)
−0.688322 + 0.725405i \(0.741652\pi\)
\(884\) 0 0
\(885\) 6.88501 0.231437
\(886\) 0 0
\(887\) −36.5981 −1.22884 −0.614421 0.788978i \(-0.710611\pi\)
−0.614421 + 0.788978i \(0.710611\pi\)
\(888\) 0 0
\(889\) −22.5023 −0.754704
\(890\) 0 0
\(891\) 4.42707 0.148313
\(892\) 0 0
\(893\) 8.14817 0.272668
\(894\) 0 0
\(895\) −12.2013 −0.407844
\(896\) 0 0
\(897\) 53.6368 1.79088
\(898\) 0 0
\(899\) −9.59953 −0.320162
\(900\) 0 0
\(901\) 9.16906 0.305466
\(902\) 0 0
\(903\) 32.7025 1.08827
\(904\) 0 0
\(905\) −8.10986 −0.269581
\(906\) 0 0
\(907\) 20.8110 0.691018 0.345509 0.938415i \(-0.387706\pi\)
0.345509 + 0.938415i \(0.387706\pi\)
\(908\) 0 0
\(909\) −62.0684 −2.05868
\(910\) 0 0
\(911\) 45.5177 1.50807 0.754035 0.656834i \(-0.228105\pi\)
0.754035 + 0.656834i \(0.228105\pi\)
\(912\) 0 0
\(913\) 2.91904 0.0966063
\(914\) 0 0
\(915\) 7.89749 0.261083
\(916\) 0 0
\(917\) 43.9635 1.45180
\(918\) 0 0
\(919\) −27.5488 −0.908750 −0.454375 0.890811i \(-0.650137\pi\)
−0.454375 + 0.890811i \(0.650137\pi\)
\(920\) 0 0
\(921\) 71.0848 2.34232
\(922\) 0 0
\(923\) 16.5739 0.545537
\(924\) 0 0
\(925\) 4.79236 0.157572
\(926\) 0 0
\(927\) 37.9481 1.24638
\(928\) 0 0
\(929\) 13.1293 0.430759 0.215380 0.976530i \(-0.430901\pi\)
0.215380 + 0.976530i \(0.430901\pi\)
\(930\) 0 0
\(931\) −15.4112 −0.505083
\(932\) 0 0
\(933\) −21.2452 −0.695537
\(934\) 0 0
\(935\) 4.24229 0.138738
\(936\) 0 0
\(937\) 0.563467 0.0184077 0.00920383 0.999958i \(-0.497070\pi\)
0.00920383 + 0.999958i \(0.497070\pi\)
\(938\) 0 0
\(939\) −97.1226 −3.16948
\(940\) 0 0
\(941\) −26.6323 −0.868188 −0.434094 0.900868i \(-0.642931\pi\)
−0.434094 + 0.900868i \(0.642931\pi\)
\(942\) 0 0
\(943\) 30.9322 1.00729
\(944\) 0 0
\(945\) 12.6431 0.411279
\(946\) 0 0
\(947\) 43.3481 1.40862 0.704311 0.709891i \(-0.251256\pi\)
0.704311 + 0.709891i \(0.251256\pi\)
\(948\) 0 0
\(949\) 23.8086 0.772858
\(950\) 0 0
\(951\) 78.4757 2.54475
\(952\) 0 0
\(953\) −4.34467 −0.140738 −0.0703689 0.997521i \(-0.522418\pi\)
−0.0703689 + 0.997521i \(0.522418\pi\)
\(954\) 0 0
\(955\) 5.56048 0.179933
\(956\) 0 0
\(957\) 20.6490 0.667487
\(958\) 0 0
\(959\) −2.27589 −0.0734924
\(960\) 0 0
\(961\) −29.1717 −0.941023
\(962\) 0 0
\(963\) −12.2093 −0.393440
\(964\) 0 0
\(965\) 6.47933 0.208577
\(966\) 0 0
\(967\) 52.7645 1.69679 0.848396 0.529362i \(-0.177569\pi\)
0.848396 + 0.529362i \(0.177569\pi\)
\(968\) 0 0
\(969\) −134.513 −4.32118
\(970\) 0 0
\(971\) 21.4278 0.687650 0.343825 0.939034i \(-0.388277\pi\)
0.343825 + 0.939034i \(0.388277\pi\)
\(972\) 0 0
\(973\) 11.6855 0.374620
\(974\) 0 0
\(975\) −27.8192 −0.890928
\(976\) 0 0
\(977\) 45.0915 1.44260 0.721302 0.692621i \(-0.243544\pi\)
0.721302 + 0.692621i \(0.243544\pi\)
\(978\) 0 0
\(979\) −0.376105 −0.0120204
\(980\) 0 0
\(981\) 34.1338 1.08981
\(982\) 0 0
\(983\) −4.68626 −0.149468 −0.0747342 0.997203i \(-0.523811\pi\)
−0.0747342 + 0.997203i \(0.523811\pi\)
\(984\) 0 0
\(985\) 10.6829 0.340387
\(986\) 0 0
\(987\) 6.37077 0.202784
\(988\) 0 0
\(989\) 41.8815 1.33175
\(990\) 0 0
\(991\) −55.3514 −1.75829 −0.879147 0.476551i \(-0.841887\pi\)
−0.879147 + 0.476551i \(0.841887\pi\)
\(992\) 0 0
\(993\) −85.0192 −2.69800
\(994\) 0 0
\(995\) 7.42655 0.235437
\(996\) 0 0
\(997\) −22.0342 −0.697830 −0.348915 0.937154i \(-0.613450\pi\)
−0.348915 + 0.937154i \(0.613450\pi\)
\(998\) 0 0
\(999\) 7.79665 0.246675
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 6028.2.a.f.1.2 29
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6028.2.a.f.1.2 29 1.1 even 1 trivial