Properties

Label 1143.2.a.h.1.4
Level $1143$
Weight $2$
Character 1143.1
Self dual yes
Analytic conductor $9.127$
Analytic rank $0$
Dimension $5$
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] = [1143,2,Mod(1,1143)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1143, 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("1143.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1143 = 3^{2} \cdot 127 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1143.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: \(9.12690095103\)
Analytic rank: \(0\)
Dimension: \(5\)
Coefficient field: 5.5.81509.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{5} - x^{4} - 5x^{3} + 3x^{2} + 5x - 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 381)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(1.21568\) of defining polynomial
Character \(\chi\) \(=\) 1143.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.21568 q^{2} -0.522133 q^{4} -1.83044 q^{5} -2.18527 q^{7} -3.06610 q^{8} +O(q^{10})\) \(q+1.21568 q^{2} -0.522133 q^{4} -1.83044 q^{5} -2.18527 q^{7} -3.06610 q^{8} -2.22522 q^{10} +4.11261 q^{11} +2.89879 q^{13} -2.65657 q^{14} -2.68311 q^{16} +2.75779 q^{17} +4.55536 q^{19} +0.955734 q^{20} +4.99960 q^{22} +8.48701 q^{23} -1.64948 q^{25} +3.52398 q^{26} +1.14100 q^{28} +6.07653 q^{29} -9.34154 q^{31} +2.87040 q^{32} +3.35257 q^{34} +4.00000 q^{35} +4.54827 q^{37} +5.53784 q^{38} +5.61231 q^{40} +8.30158 q^{41} -1.38708 q^{43} -2.14733 q^{44} +10.3175 q^{46} +1.75070 q^{47} -2.22462 q^{49} -2.00524 q^{50} -1.51355 q^{52} -9.57494 q^{53} -7.52789 q^{55} +6.70023 q^{56} +7.38708 q^{58} +4.21813 q^{59} +2.40296 q^{61} -11.3563 q^{62} +8.85570 q^{64} -5.30606 q^{65} +5.62093 q^{67} -1.43993 q^{68} +4.86270 q^{70} -8.49454 q^{71} -5.92994 q^{73} +5.52922 q^{74} -2.37850 q^{76} -8.98715 q^{77} +3.59193 q^{79} +4.91128 q^{80} +10.0920 q^{82} +15.1872 q^{83} -5.04797 q^{85} -1.68625 q^{86} -12.6097 q^{88} -1.27835 q^{89} -6.33462 q^{91} -4.43135 q^{92} +2.12828 q^{94} -8.33832 q^{95} +17.8730 q^{97} -2.70441 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5 q + q^{2} + q^{4} + 5 q^{5} + 3 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 5 q + q^{2} + q^{4} + 5 q^{5} + 3 q^{8} - 2 q^{10} + 16 q^{11} + 3 q^{13} + 6 q^{14} - 7 q^{16} + 6 q^{17} - 8 q^{19} + 12 q^{20} - 8 q^{22} + 9 q^{23} + 4 q^{25} + 2 q^{26} + 2 q^{28} + 17 q^{29} - 9 q^{31} + 2 q^{32} - q^{34} + 20 q^{35} - q^{37} - q^{38} + 16 q^{40} + 2 q^{41} - 4 q^{43} - 3 q^{44} + 4 q^{46} + 8 q^{47} + 13 q^{49} - 15 q^{50} + 13 q^{52} + 15 q^{53} + 20 q^{55} - 8 q^{56} + 34 q^{58} + 19 q^{59} + q^{61} - 15 q^{62} + q^{64} + 5 q^{65} - 2 q^{67} - 14 q^{68} + 4 q^{70} + 13 q^{73} + 17 q^{74} + 8 q^{76} - 2 q^{77} - 28 q^{79} - 12 q^{80} + 30 q^{82} + q^{83} + 6 q^{85} - 32 q^{86} + 3 q^{88} - q^{89} - 18 q^{91} - 12 q^{92} + 16 q^{94} - 4 q^{95} + 28 q^{97} - 15 q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.21568 0.859612 0.429806 0.902921i \(-0.358582\pi\)
0.429806 + 0.902921i \(0.358582\pi\)
\(3\) 0 0
\(4\) −0.522133 −0.261067
\(5\) −1.83044 −0.818598 −0.409299 0.912400i \(-0.634227\pi\)
−0.409299 + 0.912400i \(0.634227\pi\)
\(6\) 0 0
\(7\) −2.18527 −0.825953 −0.412976 0.910742i \(-0.635511\pi\)
−0.412976 + 0.910742i \(0.635511\pi\)
\(8\) −3.06610 −1.08403
\(9\) 0 0
\(10\) −2.22522 −0.703677
\(11\) 4.11261 1.24000 0.619999 0.784602i \(-0.287133\pi\)
0.619999 + 0.784602i \(0.287133\pi\)
\(12\) 0 0
\(13\) 2.89879 0.803979 0.401989 0.915644i \(-0.368319\pi\)
0.401989 + 0.915644i \(0.368319\pi\)
\(14\) −2.65657 −0.709999
\(15\) 0 0
\(16\) −2.68311 −0.670778
\(17\) 2.75779 0.668862 0.334431 0.942420i \(-0.391456\pi\)
0.334431 + 0.942420i \(0.391456\pi\)
\(18\) 0 0
\(19\) 4.55536 1.04507 0.522536 0.852617i \(-0.324986\pi\)
0.522536 + 0.852617i \(0.324986\pi\)
\(20\) 0.955734 0.213709
\(21\) 0 0
\(22\) 4.99960 1.06592
\(23\) 8.48701 1.76966 0.884832 0.465909i \(-0.154273\pi\)
0.884832 + 0.465909i \(0.154273\pi\)
\(24\) 0 0
\(25\) −1.64948 −0.329897
\(26\) 3.52398 0.691110
\(27\) 0 0
\(28\) 1.14100 0.215629
\(29\) 6.07653 1.12838 0.564191 0.825644i \(-0.309188\pi\)
0.564191 + 0.825644i \(0.309188\pi\)
\(30\) 0 0
\(31\) −9.34154 −1.67779 −0.838895 0.544294i \(-0.816798\pi\)
−0.838895 + 0.544294i \(0.816798\pi\)
\(32\) 2.87040 0.507420
\(33\) 0 0
\(34\) 3.35257 0.574962
\(35\) 4.00000 0.676123
\(36\) 0 0
\(37\) 4.54827 0.747731 0.373866 0.927483i \(-0.378032\pi\)
0.373866 + 0.927483i \(0.378032\pi\)
\(38\) 5.53784 0.898356
\(39\) 0 0
\(40\) 5.61231 0.887384
\(41\) 8.30158 1.29649 0.648244 0.761432i \(-0.275504\pi\)
0.648244 + 0.761432i \(0.275504\pi\)
\(42\) 0 0
\(43\) −1.38708 −0.211528 −0.105764 0.994391i \(-0.533729\pi\)
−0.105764 + 0.994391i \(0.533729\pi\)
\(44\) −2.14733 −0.323722
\(45\) 0 0
\(46\) 10.3175 1.52123
\(47\) 1.75070 0.255366 0.127683 0.991815i \(-0.459246\pi\)
0.127683 + 0.991815i \(0.459246\pi\)
\(48\) 0 0
\(49\) −2.22462 −0.317802
\(50\) −2.00524 −0.283584
\(51\) 0 0
\(52\) −1.51355 −0.209892
\(53\) −9.57494 −1.31522 −0.657610 0.753359i \(-0.728432\pi\)
−0.657610 + 0.753359i \(0.728432\pi\)
\(54\) 0 0
\(55\) −7.52789 −1.01506
\(56\) 6.70023 0.895356
\(57\) 0 0
\(58\) 7.38708 0.969972
\(59\) 4.21813 0.549154 0.274577 0.961565i \(-0.411462\pi\)
0.274577 + 0.961565i \(0.411462\pi\)
\(60\) 0 0
\(61\) 2.40296 0.307668 0.153834 0.988097i \(-0.450838\pi\)
0.153834 + 0.988097i \(0.450838\pi\)
\(62\) −11.3563 −1.44225
\(63\) 0 0
\(64\) 8.85570 1.10696
\(65\) −5.30606 −0.658136
\(66\) 0 0
\(67\) 5.62093 0.686705 0.343353 0.939207i \(-0.388437\pi\)
0.343353 + 0.939207i \(0.388437\pi\)
\(68\) −1.43993 −0.174617
\(69\) 0 0
\(70\) 4.86270 0.581204
\(71\) −8.49454 −1.00812 −0.504058 0.863670i \(-0.668160\pi\)
−0.504058 + 0.863670i \(0.668160\pi\)
\(72\) 0 0
\(73\) −5.92994 −0.694046 −0.347023 0.937857i \(-0.612807\pi\)
−0.347023 + 0.937857i \(0.612807\pi\)
\(74\) 5.52922 0.642759
\(75\) 0 0
\(76\) −2.37850 −0.272833
\(77\) −8.98715 −1.02418
\(78\) 0 0
\(79\) 3.59193 0.404124 0.202062 0.979373i \(-0.435236\pi\)
0.202062 + 0.979373i \(0.435236\pi\)
\(80\) 4.91128 0.549097
\(81\) 0 0
\(82\) 10.0920 1.11448
\(83\) 15.1872 1.66702 0.833508 0.552507i \(-0.186329\pi\)
0.833508 + 0.552507i \(0.186329\pi\)
\(84\) 0 0
\(85\) −5.04797 −0.547529
\(86\) −1.68625 −0.181832
\(87\) 0 0
\(88\) −12.6097 −1.34419
\(89\) −1.27835 −0.135504 −0.0677522 0.997702i \(-0.521583\pi\)
−0.0677522 + 0.997702i \(0.521583\pi\)
\(90\) 0 0
\(91\) −6.33462 −0.664048
\(92\) −4.43135 −0.462000
\(93\) 0 0
\(94\) 2.12828 0.219515
\(95\) −8.33832 −0.855493
\(96\) 0 0
\(97\) 17.8730 1.81473 0.907363 0.420347i \(-0.138092\pi\)
0.907363 + 0.420347i \(0.138092\pi\)
\(98\) −2.70441 −0.273187
\(99\) 0 0
\(100\) 0.861251 0.0861251
\(101\) 6.16506 0.613446 0.306723 0.951799i \(-0.400767\pi\)
0.306723 + 0.951799i \(0.400767\pi\)
\(102\) 0 0
\(103\) −5.09114 −0.501645 −0.250823 0.968033i \(-0.580701\pi\)
−0.250823 + 0.968033i \(0.580701\pi\)
\(104\) −8.88796 −0.871536
\(105\) 0 0
\(106\) −11.6400 −1.13058
\(107\) −14.0265 −1.35599 −0.677995 0.735066i \(-0.737151\pi\)
−0.677995 + 0.735066i \(0.737151\pi\)
\(108\) 0 0
\(109\) −14.5027 −1.38911 −0.694554 0.719440i \(-0.744398\pi\)
−0.694554 + 0.719440i \(0.744398\pi\)
\(110\) −9.15148 −0.872559
\(111\) 0 0
\(112\) 5.86331 0.554031
\(113\) −11.1075 −1.04491 −0.522453 0.852668i \(-0.674983\pi\)
−0.522453 + 0.852668i \(0.674983\pi\)
\(114\) 0 0
\(115\) −15.5350 −1.44864
\(116\) −3.17276 −0.294583
\(117\) 0 0
\(118\) 5.12788 0.472060
\(119\) −6.02650 −0.552448
\(120\) 0 0
\(121\) 5.91357 0.537597
\(122\) 2.92122 0.264475
\(123\) 0 0
\(124\) 4.87752 0.438015
\(125\) 12.1715 1.08865
\(126\) 0 0
\(127\) −1.00000 −0.0887357
\(128\) 5.02485 0.444139
\(129\) 0 0
\(130\) −6.45045 −0.565741
\(131\) 11.5951 1.01307 0.506536 0.862219i \(-0.330926\pi\)
0.506536 + 0.862219i \(0.330926\pi\)
\(132\) 0 0
\(133\) −9.95467 −0.863179
\(134\) 6.83322 0.590300
\(135\) 0 0
\(136\) −8.45564 −0.725065
\(137\) 8.85755 0.756751 0.378376 0.925652i \(-0.376483\pi\)
0.378376 + 0.925652i \(0.376483\pi\)
\(138\) 0 0
\(139\) 16.2036 1.37437 0.687184 0.726483i \(-0.258847\pi\)
0.687184 + 0.726483i \(0.258847\pi\)
\(140\) −2.08853 −0.176513
\(141\) 0 0
\(142\) −10.3266 −0.866589
\(143\) 11.9216 0.996933
\(144\) 0 0
\(145\) −11.1227 −0.923692
\(146\) −7.20888 −0.596611
\(147\) 0 0
\(148\) −2.37480 −0.195208
\(149\) 21.9339 1.79690 0.898448 0.439081i \(-0.144696\pi\)
0.898448 + 0.439081i \(0.144696\pi\)
\(150\) 0 0
\(151\) 16.8638 1.37236 0.686180 0.727432i \(-0.259286\pi\)
0.686180 + 0.727432i \(0.259286\pi\)
\(152\) −13.9672 −1.13289
\(153\) 0 0
\(154\) −10.9255 −0.880398
\(155\) 17.0991 1.37344
\(156\) 0 0
\(157\) 17.5711 1.40232 0.701162 0.713002i \(-0.252665\pi\)
0.701162 + 0.713002i \(0.252665\pi\)
\(158\) 4.36662 0.347390
\(159\) 0 0
\(160\) −5.25410 −0.415373
\(161\) −18.5464 −1.46166
\(162\) 0 0
\(163\) 3.46184 0.271152 0.135576 0.990767i \(-0.456711\pi\)
0.135576 + 0.990767i \(0.456711\pi\)
\(164\) −4.33453 −0.338470
\(165\) 0 0
\(166\) 18.4628 1.43299
\(167\) −5.79387 −0.448343 −0.224172 0.974550i \(-0.571968\pi\)
−0.224172 + 0.974550i \(0.571968\pi\)
\(168\) 0 0
\(169\) −4.59704 −0.353618
\(170\) −6.13669 −0.470663
\(171\) 0 0
\(172\) 0.724243 0.0552230
\(173\) −14.0982 −1.07187 −0.535934 0.844260i \(-0.680040\pi\)
−0.535934 + 0.844260i \(0.680040\pi\)
\(174\) 0 0
\(175\) 3.60456 0.272479
\(176\) −11.0346 −0.831764
\(177\) 0 0
\(178\) −1.55405 −0.116481
\(179\) 3.46373 0.258892 0.129446 0.991586i \(-0.458680\pi\)
0.129446 + 0.991586i \(0.458680\pi\)
\(180\) 0 0
\(181\) −17.8558 −1.32721 −0.663607 0.748082i \(-0.730975\pi\)
−0.663607 + 0.748082i \(0.730975\pi\)
\(182\) −7.70084 −0.570824
\(183\) 0 0
\(184\) −26.0220 −1.91837
\(185\) −8.32534 −0.612091
\(186\) 0 0
\(187\) 11.3417 0.829388
\(188\) −0.914097 −0.0666674
\(189\) 0 0
\(190\) −10.1367 −0.735393
\(191\) −1.22583 −0.0886980 −0.0443490 0.999016i \(-0.514121\pi\)
−0.0443490 + 0.999016i \(0.514121\pi\)
\(192\) 0 0
\(193\) 9.74900 0.701748 0.350874 0.936423i \(-0.385885\pi\)
0.350874 + 0.936423i \(0.385885\pi\)
\(194\) 21.7278 1.55996
\(195\) 0 0
\(196\) 1.16155 0.0829675
\(197\) 20.1537 1.43589 0.717946 0.696099i \(-0.245082\pi\)
0.717946 + 0.696099i \(0.245082\pi\)
\(198\) 0 0
\(199\) −20.9093 −1.48222 −0.741112 0.671382i \(-0.765701\pi\)
−0.741112 + 0.671382i \(0.765701\pi\)
\(200\) 5.05748 0.357618
\(201\) 0 0
\(202\) 7.49471 0.527326
\(203\) −13.2788 −0.931991
\(204\) 0 0
\(205\) −15.1956 −1.06130
\(206\) −6.18918 −0.431220
\(207\) 0 0
\(208\) −7.77777 −0.539291
\(209\) 18.7344 1.29589
\(210\) 0 0
\(211\) −14.3050 −0.984794 −0.492397 0.870371i \(-0.663879\pi\)
−0.492397 + 0.870371i \(0.663879\pi\)
\(212\) 4.99939 0.343360
\(213\) 0 0
\(214\) −17.0516 −1.16563
\(215\) 2.53898 0.173157
\(216\) 0 0
\(217\) 20.4137 1.38577
\(218\) −17.6306 −1.19410
\(219\) 0 0
\(220\) 3.93056 0.264998
\(221\) 7.99424 0.537751
\(222\) 0 0
\(223\) −19.7522 −1.32271 −0.661354 0.750074i \(-0.730018\pi\)
−0.661354 + 0.750074i \(0.730018\pi\)
\(224\) −6.27258 −0.419105
\(225\) 0 0
\(226\) −13.5031 −0.898214
\(227\) −11.0311 −0.732163 −0.366082 0.930583i \(-0.619301\pi\)
−0.366082 + 0.930583i \(0.619301\pi\)
\(228\) 0 0
\(229\) 9.27769 0.613087 0.306543 0.951857i \(-0.400828\pi\)
0.306543 + 0.951857i \(0.400828\pi\)
\(230\) −18.8855 −1.24527
\(231\) 0 0
\(232\) −18.6312 −1.22320
\(233\) 14.1129 0.924564 0.462282 0.886733i \(-0.347031\pi\)
0.462282 + 0.886733i \(0.347031\pi\)
\(234\) 0 0
\(235\) −3.20455 −0.209042
\(236\) −2.20243 −0.143366
\(237\) 0 0
\(238\) −7.32626 −0.474891
\(239\) −8.82209 −0.570653 −0.285327 0.958430i \(-0.592102\pi\)
−0.285327 + 0.958430i \(0.592102\pi\)
\(240\) 0 0
\(241\) 3.80699 0.245230 0.122615 0.992454i \(-0.460872\pi\)
0.122615 + 0.992454i \(0.460872\pi\)
\(242\) 7.18898 0.462125
\(243\) 0 0
\(244\) −1.25467 −0.0803218
\(245\) 4.07203 0.260152
\(246\) 0 0
\(247\) 13.2050 0.840215
\(248\) 28.6420 1.81877
\(249\) 0 0
\(250\) 14.7966 0.935818
\(251\) −20.6019 −1.30038 −0.650189 0.759772i \(-0.725310\pi\)
−0.650189 + 0.759772i \(0.725310\pi\)
\(252\) 0 0
\(253\) 34.9038 2.19438
\(254\) −1.21568 −0.0762783
\(255\) 0 0
\(256\) −11.6028 −0.725175
\(257\) 0.849271 0.0529761 0.0264880 0.999649i \(-0.491568\pi\)
0.0264880 + 0.999649i \(0.491568\pi\)
\(258\) 0 0
\(259\) −9.93918 −0.617591
\(260\) 2.77047 0.171817
\(261\) 0 0
\(262\) 14.0959 0.870850
\(263\) −6.26932 −0.386583 −0.193291 0.981141i \(-0.561916\pi\)
−0.193291 + 0.981141i \(0.561916\pi\)
\(264\) 0 0
\(265\) 17.5264 1.07664
\(266\) −12.1016 −0.742000
\(267\) 0 0
\(268\) −2.93487 −0.179276
\(269\) −1.25858 −0.0767367 −0.0383684 0.999264i \(-0.512216\pi\)
−0.0383684 + 0.999264i \(0.512216\pi\)
\(270\) 0 0
\(271\) −3.95401 −0.240189 −0.120095 0.992762i \(-0.538320\pi\)
−0.120095 + 0.992762i \(0.538320\pi\)
\(272\) −7.39945 −0.448657
\(273\) 0 0
\(274\) 10.7679 0.650513
\(275\) −6.78369 −0.409072
\(276\) 0 0
\(277\) 29.3123 1.76121 0.880604 0.473853i \(-0.157137\pi\)
0.880604 + 0.473853i \(0.157137\pi\)
\(278\) 19.6983 1.18142
\(279\) 0 0
\(280\) −12.2644 −0.732937
\(281\) −17.6591 −1.05345 −0.526727 0.850034i \(-0.676581\pi\)
−0.526727 + 0.850034i \(0.676581\pi\)
\(282\) 0 0
\(283\) −3.33208 −0.198071 −0.0990357 0.995084i \(-0.531576\pi\)
−0.0990357 + 0.995084i \(0.531576\pi\)
\(284\) 4.43528 0.263185
\(285\) 0 0
\(286\) 14.4928 0.856976
\(287\) −18.1412 −1.07084
\(288\) 0 0
\(289\) −9.39461 −0.552624
\(290\) −13.5216 −0.794017
\(291\) 0 0
\(292\) 3.09622 0.181192
\(293\) −32.5210 −1.89990 −0.949949 0.312405i \(-0.898865\pi\)
−0.949949 + 0.312405i \(0.898865\pi\)
\(294\) 0 0
\(295\) −7.72105 −0.449537
\(296\) −13.9454 −0.810562
\(297\) 0 0
\(298\) 26.6645 1.54463
\(299\) 24.6020 1.42277
\(300\) 0 0
\(301\) 3.03115 0.174713
\(302\) 20.5010 1.17970
\(303\) 0 0
\(304\) −12.2225 −0.701011
\(305\) −4.39848 −0.251856
\(306\) 0 0
\(307\) 25.6417 1.46345 0.731725 0.681600i \(-0.238716\pi\)
0.731725 + 0.681600i \(0.238716\pi\)
\(308\) 4.69249 0.267379
\(309\) 0 0
\(310\) 20.7870 1.18062
\(311\) 13.3964 0.759638 0.379819 0.925061i \(-0.375986\pi\)
0.379819 + 0.925061i \(0.375986\pi\)
\(312\) 0 0
\(313\) 2.77451 0.156825 0.0784124 0.996921i \(-0.475015\pi\)
0.0784124 + 0.996921i \(0.475015\pi\)
\(314\) 21.3607 1.20545
\(315\) 0 0
\(316\) −1.87547 −0.105503
\(317\) 15.2283 0.855307 0.427654 0.903943i \(-0.359340\pi\)
0.427654 + 0.903943i \(0.359340\pi\)
\(318\) 0 0
\(319\) 24.9904 1.39919
\(320\) −16.2098 −0.906157
\(321\) 0 0
\(322\) −22.5464 −1.25646
\(323\) 12.5627 0.699008
\(324\) 0 0
\(325\) −4.78150 −0.265230
\(326\) 4.20848 0.233086
\(327\) 0 0
\(328\) −25.4534 −1.40543
\(329\) −3.82574 −0.210920
\(330\) 0 0
\(331\) −17.5670 −0.965568 −0.482784 0.875739i \(-0.660374\pi\)
−0.482784 + 0.875739i \(0.660374\pi\)
\(332\) −7.92976 −0.435202
\(333\) 0 0
\(334\) −7.04347 −0.385401
\(335\) −10.2888 −0.562136
\(336\) 0 0
\(337\) 28.8978 1.57416 0.787082 0.616848i \(-0.211591\pi\)
0.787082 + 0.616848i \(0.211591\pi\)
\(338\) −5.58851 −0.303975
\(339\) 0 0
\(340\) 2.63571 0.142941
\(341\) −38.4181 −2.08046
\(342\) 0 0
\(343\) 20.1582 1.08844
\(344\) 4.25293 0.229303
\(345\) 0 0
\(346\) −17.1388 −0.921390
\(347\) 4.73503 0.254190 0.127095 0.991891i \(-0.459435\pi\)
0.127095 + 0.991891i \(0.459435\pi\)
\(348\) 0 0
\(349\) 4.63423 0.248065 0.124032 0.992278i \(-0.460417\pi\)
0.124032 + 0.992278i \(0.460417\pi\)
\(350\) 4.38198 0.234227
\(351\) 0 0
\(352\) 11.8048 0.629200
\(353\) −4.42642 −0.235594 −0.117797 0.993038i \(-0.537583\pi\)
−0.117797 + 0.993038i \(0.537583\pi\)
\(354\) 0 0
\(355\) 15.5488 0.825242
\(356\) 0.667467 0.0353757
\(357\) 0 0
\(358\) 4.21078 0.222546
\(359\) −27.5629 −1.45472 −0.727358 0.686258i \(-0.759252\pi\)
−0.727358 + 0.686258i \(0.759252\pi\)
\(360\) 0 0
\(361\) 1.75131 0.0921740
\(362\) −21.7069 −1.14089
\(363\) 0 0
\(364\) 3.30751 0.173361
\(365\) 10.8544 0.568145
\(366\) 0 0
\(367\) −17.7031 −0.924093 −0.462046 0.886856i \(-0.652885\pi\)
−0.462046 + 0.886856i \(0.652885\pi\)
\(368\) −22.7716 −1.18705
\(369\) 0 0
\(370\) −10.1209 −0.526161
\(371\) 20.9238 1.08631
\(372\) 0 0
\(373\) −23.0169 −1.19177 −0.595885 0.803070i \(-0.703198\pi\)
−0.595885 + 0.803070i \(0.703198\pi\)
\(374\) 13.7878 0.712952
\(375\) 0 0
\(376\) −5.36781 −0.276824
\(377\) 17.6146 0.907196
\(378\) 0 0
\(379\) −20.0972 −1.03232 −0.516161 0.856492i \(-0.672639\pi\)
−0.516161 + 0.856492i \(0.672639\pi\)
\(380\) 4.35371 0.223341
\(381\) 0 0
\(382\) −1.49021 −0.0762459
\(383\) −6.19468 −0.316533 −0.158267 0.987396i \(-0.550591\pi\)
−0.158267 + 0.987396i \(0.550591\pi\)
\(384\) 0 0
\(385\) 16.4504 0.838392
\(386\) 11.8516 0.603231
\(387\) 0 0
\(388\) −9.33208 −0.473764
\(389\) −27.1948 −1.37883 −0.689416 0.724366i \(-0.742133\pi\)
−0.689416 + 0.724366i \(0.742133\pi\)
\(390\) 0 0
\(391\) 23.4054 1.18366
\(392\) 6.82088 0.344507
\(393\) 0 0
\(394\) 24.5004 1.23431
\(395\) −6.57482 −0.330815
\(396\) 0 0
\(397\) −6.87064 −0.344828 −0.172414 0.985025i \(-0.555157\pi\)
−0.172414 + 0.985025i \(0.555157\pi\)
\(398\) −25.4190 −1.27414
\(399\) 0 0
\(400\) 4.42575 0.221288
\(401\) 6.83838 0.341492 0.170746 0.985315i \(-0.445382\pi\)
0.170746 + 0.985315i \(0.445382\pi\)
\(402\) 0 0
\(403\) −27.0791 −1.34891
\(404\) −3.21898 −0.160150
\(405\) 0 0
\(406\) −16.1427 −0.801151
\(407\) 18.7053 0.927186
\(408\) 0 0
\(409\) −5.31912 −0.263014 −0.131507 0.991315i \(-0.541982\pi\)
−0.131507 + 0.991315i \(0.541982\pi\)
\(410\) −18.4729 −0.912309
\(411\) 0 0
\(412\) 2.65825 0.130963
\(413\) −9.21774 −0.453575
\(414\) 0 0
\(415\) −27.7994 −1.36462
\(416\) 8.32067 0.407955
\(417\) 0 0
\(418\) 22.7750 1.11396
\(419\) −1.00985 −0.0493344 −0.0246672 0.999696i \(-0.507853\pi\)
−0.0246672 + 0.999696i \(0.507853\pi\)
\(420\) 0 0
\(421\) −38.1506 −1.85934 −0.929672 0.368388i \(-0.879910\pi\)
−0.929672 + 0.368388i \(0.879910\pi\)
\(422\) −17.3902 −0.846542
\(423\) 0 0
\(424\) 29.3577 1.42573
\(425\) −4.54893 −0.220655
\(426\) 0 0
\(427\) −5.25111 −0.254119
\(428\) 7.32369 0.354004
\(429\) 0 0
\(430\) 3.08657 0.148848
\(431\) −3.70132 −0.178287 −0.0891433 0.996019i \(-0.528413\pi\)
−0.0891433 + 0.996019i \(0.528413\pi\)
\(432\) 0 0
\(433\) −22.7423 −1.09293 −0.546463 0.837483i \(-0.684026\pi\)
−0.546463 + 0.837483i \(0.684026\pi\)
\(434\) 24.8165 1.19123
\(435\) 0 0
\(436\) 7.57235 0.362650
\(437\) 38.6614 1.84943
\(438\) 0 0
\(439\) 32.9769 1.57390 0.786952 0.617015i \(-0.211658\pi\)
0.786952 + 0.617015i \(0.211658\pi\)
\(440\) 23.0812 1.10035
\(441\) 0 0
\(442\) 9.71840 0.462257
\(443\) 13.3826 0.635827 0.317913 0.948120i \(-0.397018\pi\)
0.317913 + 0.948120i \(0.397018\pi\)
\(444\) 0 0
\(445\) 2.33994 0.110924
\(446\) −24.0123 −1.13702
\(447\) 0 0
\(448\) −19.3520 −0.914298
\(449\) 0.0449421 0.00212095 0.00106047 0.999999i \(-0.499662\pi\)
0.00106047 + 0.999999i \(0.499662\pi\)
\(450\) 0 0
\(451\) 34.1412 1.60764
\(452\) 5.79960 0.272790
\(453\) 0 0
\(454\) −13.4103 −0.629376
\(455\) 11.5951 0.543589
\(456\) 0 0
\(457\) −3.83400 −0.179347 −0.0896735 0.995971i \(-0.528582\pi\)
−0.0896735 + 0.995971i \(0.528582\pi\)
\(458\) 11.2787 0.527017
\(459\) 0 0
\(460\) 8.11133 0.378193
\(461\) 34.8667 1.62390 0.811951 0.583725i \(-0.198405\pi\)
0.811951 + 0.583725i \(0.198405\pi\)
\(462\) 0 0
\(463\) −22.9857 −1.06823 −0.534117 0.845410i \(-0.679356\pi\)
−0.534117 + 0.845410i \(0.679356\pi\)
\(464\) −16.3040 −0.756894
\(465\) 0 0
\(466\) 17.1567 0.794767
\(467\) 6.47557 0.299654 0.149827 0.988712i \(-0.452128\pi\)
0.149827 + 0.988712i \(0.452128\pi\)
\(468\) 0 0
\(469\) −12.2832 −0.567186
\(470\) −3.89569 −0.179695
\(471\) 0 0
\(472\) −12.9332 −0.595299
\(473\) −5.70454 −0.262295
\(474\) 0 0
\(475\) −7.51400 −0.344766
\(476\) 3.14663 0.144226
\(477\) 0 0
\(478\) −10.7248 −0.490541
\(479\) −19.2166 −0.878027 −0.439013 0.898480i \(-0.644672\pi\)
−0.439013 + 0.898480i \(0.644672\pi\)
\(480\) 0 0
\(481\) 13.1845 0.601160
\(482\) 4.62806 0.210803
\(483\) 0 0
\(484\) −3.08767 −0.140349
\(485\) −32.7155 −1.48553
\(486\) 0 0
\(487\) −35.9898 −1.63085 −0.815426 0.578861i \(-0.803497\pi\)
−0.815426 + 0.578861i \(0.803497\pi\)
\(488\) −7.36771 −0.333521
\(489\) 0 0
\(490\) 4.95026 0.223630
\(491\) −1.56415 −0.0705891 −0.0352945 0.999377i \(-0.511237\pi\)
−0.0352945 + 0.999377i \(0.511237\pi\)
\(492\) 0 0
\(493\) 16.7578 0.754732
\(494\) 16.0530 0.722259
\(495\) 0 0
\(496\) 25.0644 1.12542
\(497\) 18.5628 0.832656
\(498\) 0 0
\(499\) −19.2919 −0.863626 −0.431813 0.901963i \(-0.642126\pi\)
−0.431813 + 0.901963i \(0.642126\pi\)
\(500\) −6.35514 −0.284210
\(501\) 0 0
\(502\) −25.0452 −1.11782
\(503\) 20.4806 0.913184 0.456592 0.889676i \(-0.349070\pi\)
0.456592 + 0.889676i \(0.349070\pi\)
\(504\) 0 0
\(505\) −11.2848 −0.502166
\(506\) 42.4317 1.88632
\(507\) 0 0
\(508\) 0.522133 0.0231659
\(509\) −29.1499 −1.29205 −0.646023 0.763318i \(-0.723569\pi\)
−0.646023 + 0.763318i \(0.723569\pi\)
\(510\) 0 0
\(511\) 12.9585 0.573250
\(512\) −24.1549 −1.06751
\(513\) 0 0
\(514\) 1.03244 0.0455389
\(515\) 9.31903 0.410646
\(516\) 0 0
\(517\) 7.19994 0.316653
\(518\) −12.0828 −0.530889
\(519\) 0 0
\(520\) 16.2689 0.713438
\(521\) 40.0882 1.75629 0.878147 0.478390i \(-0.158780\pi\)
0.878147 + 0.478390i \(0.158780\pi\)
\(522\) 0 0
\(523\) 0.957838 0.0418833 0.0209417 0.999781i \(-0.493334\pi\)
0.0209417 + 0.999781i \(0.493334\pi\)
\(524\) −6.05421 −0.264479
\(525\) 0 0
\(526\) −7.62146 −0.332311
\(527\) −25.7620 −1.12221
\(528\) 0 0
\(529\) 49.0294 2.13171
\(530\) 21.3064 0.925490
\(531\) 0 0
\(532\) 5.19766 0.225347
\(533\) 24.0645 1.04235
\(534\) 0 0
\(535\) 25.6746 1.11001
\(536\) −17.2343 −0.744408
\(537\) 0 0
\(538\) −1.53002 −0.0659639
\(539\) −9.14898 −0.394074
\(540\) 0 0
\(541\) 4.85408 0.208693 0.104347 0.994541i \(-0.466725\pi\)
0.104347 + 0.994541i \(0.466725\pi\)
\(542\) −4.80680 −0.206470
\(543\) 0 0
\(544\) 7.91595 0.339393
\(545\) 26.5464 1.13712
\(546\) 0 0
\(547\) 4.87405 0.208399 0.104200 0.994556i \(-0.466772\pi\)
0.104200 + 0.994556i \(0.466772\pi\)
\(548\) −4.62482 −0.197562
\(549\) 0 0
\(550\) −8.24677 −0.351643
\(551\) 27.6808 1.17924
\(552\) 0 0
\(553\) −7.84932 −0.333787
\(554\) 35.6343 1.51396
\(555\) 0 0
\(556\) −8.46041 −0.358802
\(557\) −11.1116 −0.470813 −0.235407 0.971897i \(-0.575642\pi\)
−0.235407 + 0.971897i \(0.575642\pi\)
\(558\) 0 0
\(559\) −4.02086 −0.170064
\(560\) −10.7324 −0.453529
\(561\) 0 0
\(562\) −21.4678 −0.905562
\(563\) 41.4791 1.74814 0.874069 0.485802i \(-0.161473\pi\)
0.874069 + 0.485802i \(0.161473\pi\)
\(564\) 0 0
\(565\) 20.3316 0.855358
\(566\) −4.05073 −0.170265
\(567\) 0 0
\(568\) 26.0451 1.09283
\(569\) −1.35775 −0.0569197 −0.0284598 0.999595i \(-0.509060\pi\)
−0.0284598 + 0.999595i \(0.509060\pi\)
\(570\) 0 0
\(571\) 13.6021 0.569230 0.284615 0.958642i \(-0.408134\pi\)
0.284615 + 0.958642i \(0.408134\pi\)
\(572\) −6.22465 −0.260266
\(573\) 0 0
\(574\) −22.0538 −0.920506
\(575\) −13.9992 −0.583807
\(576\) 0 0
\(577\) −8.39435 −0.349461 −0.174731 0.984616i \(-0.555905\pi\)
−0.174731 + 0.984616i \(0.555905\pi\)
\(578\) −11.4208 −0.475043
\(579\) 0 0
\(580\) 5.80754 0.241145
\(581\) −33.1882 −1.37688
\(582\) 0 0
\(583\) −39.3780 −1.63087
\(584\) 18.1817 0.752366
\(585\) 0 0
\(586\) −39.5350 −1.63318
\(587\) −2.56937 −0.106049 −0.0530247 0.998593i \(-0.516886\pi\)
−0.0530247 + 0.998593i \(0.516886\pi\)
\(588\) 0 0
\(589\) −42.5541 −1.75341
\(590\) −9.38629 −0.386427
\(591\) 0 0
\(592\) −12.2035 −0.501561
\(593\) 30.4114 1.24885 0.624423 0.781086i \(-0.285334\pi\)
0.624423 + 0.781086i \(0.285334\pi\)
\(594\) 0 0
\(595\) 11.0311 0.452233
\(596\) −11.4524 −0.469109
\(597\) 0 0
\(598\) 29.9081 1.22303
\(599\) −34.9094 −1.42636 −0.713179 0.700982i \(-0.752745\pi\)
−0.713179 + 0.700982i \(0.752745\pi\)
\(600\) 0 0
\(601\) 3.18273 0.129826 0.0649130 0.997891i \(-0.479323\pi\)
0.0649130 + 0.997891i \(0.479323\pi\)
\(602\) 3.68489 0.150185
\(603\) 0 0
\(604\) −8.80517 −0.358277
\(605\) −10.8244 −0.440076
\(606\) 0 0
\(607\) 19.0528 0.773328 0.386664 0.922221i \(-0.373627\pi\)
0.386664 + 0.922221i \(0.373627\pi\)
\(608\) 13.0757 0.530290
\(609\) 0 0
\(610\) −5.34713 −0.216499
\(611\) 5.07490 0.205308
\(612\) 0 0
\(613\) −9.13899 −0.369120 −0.184560 0.982821i \(-0.559086\pi\)
−0.184560 + 0.982821i \(0.559086\pi\)
\(614\) 31.1720 1.25800
\(615\) 0 0
\(616\) 27.5555 1.11024
\(617\) 19.8514 0.799186 0.399593 0.916693i \(-0.369151\pi\)
0.399593 + 0.916693i \(0.369151\pi\)
\(618\) 0 0
\(619\) −26.0742 −1.04801 −0.524005 0.851715i \(-0.675563\pi\)
−0.524005 + 0.851715i \(0.675563\pi\)
\(620\) −8.92802 −0.358558
\(621\) 0 0
\(622\) 16.2856 0.652994
\(623\) 2.79353 0.111920
\(624\) 0 0
\(625\) −14.0318 −0.561271
\(626\) 3.37291 0.134808
\(627\) 0 0
\(628\) −9.17443 −0.366100
\(629\) 12.5432 0.500129
\(630\) 0 0
\(631\) 6.67533 0.265740 0.132870 0.991133i \(-0.457581\pi\)
0.132870 + 0.991133i \(0.457581\pi\)
\(632\) −11.0132 −0.438082
\(633\) 0 0
\(634\) 18.5127 0.735233
\(635\) 1.83044 0.0726388
\(636\) 0 0
\(637\) −6.44868 −0.255506
\(638\) 30.3802 1.20276
\(639\) 0 0
\(640\) −9.19770 −0.363571
\(641\) 28.8713 1.14035 0.570174 0.821524i \(-0.306876\pi\)
0.570174 + 0.821524i \(0.306876\pi\)
\(642\) 0 0
\(643\) −16.5900 −0.654245 −0.327122 0.944982i \(-0.606079\pi\)
−0.327122 + 0.944982i \(0.606079\pi\)
\(644\) 9.68368 0.381590
\(645\) 0 0
\(646\) 15.2722 0.600876
\(647\) −14.2463 −0.560078 −0.280039 0.959989i \(-0.590347\pi\)
−0.280039 + 0.959989i \(0.590347\pi\)
\(648\) 0 0
\(649\) 17.3475 0.680951
\(650\) −5.81276 −0.227995
\(651\) 0 0
\(652\) −1.80754 −0.0707888
\(653\) −18.3296 −0.717291 −0.358645 0.933474i \(-0.616761\pi\)
−0.358645 + 0.933474i \(0.616761\pi\)
\(654\) 0 0
\(655\) −21.2242 −0.829299
\(656\) −22.2741 −0.869656
\(657\) 0 0
\(658\) −4.65086 −0.181309
\(659\) 3.64832 0.142119 0.0710593 0.997472i \(-0.477362\pi\)
0.0710593 + 0.997472i \(0.477362\pi\)
\(660\) 0 0
\(661\) 37.2032 1.44704 0.723518 0.690305i \(-0.242524\pi\)
0.723518 + 0.690305i \(0.242524\pi\)
\(662\) −21.3557 −0.830015
\(663\) 0 0
\(664\) −46.5655 −1.80709
\(665\) 18.2214 0.706597
\(666\) 0 0
\(667\) 51.5716 1.99686
\(668\) 3.02517 0.117047
\(669\) 0 0
\(670\) −12.5078 −0.483219
\(671\) 9.88245 0.381508
\(672\) 0 0
\(673\) 18.1826 0.700887 0.350443 0.936584i \(-0.386031\pi\)
0.350443 + 0.936584i \(0.386031\pi\)
\(674\) 35.1304 1.35317
\(675\) 0 0
\(676\) 2.40026 0.0923179
\(677\) 22.8068 0.876536 0.438268 0.898844i \(-0.355592\pi\)
0.438268 + 0.898844i \(0.355592\pi\)
\(678\) 0 0
\(679\) −39.0572 −1.49888
\(680\) 15.4775 0.593537
\(681\) 0 0
\(682\) −46.7039 −1.78839
\(683\) 15.4171 0.589918 0.294959 0.955510i \(-0.404694\pi\)
0.294959 + 0.955510i \(0.404694\pi\)
\(684\) 0 0
\(685\) −16.2132 −0.619475
\(686\) 24.5059 0.935638
\(687\) 0 0
\(688\) 3.72170 0.141889
\(689\) −27.7557 −1.05741
\(690\) 0 0
\(691\) 11.2213 0.426880 0.213440 0.976956i \(-0.431533\pi\)
0.213440 + 0.976956i \(0.431533\pi\)
\(692\) 7.36114 0.279829
\(693\) 0 0
\(694\) 5.75626 0.218505
\(695\) −29.6597 −1.12506
\(696\) 0 0
\(697\) 22.8940 0.867172
\(698\) 5.63372 0.213240
\(699\) 0 0
\(700\) −1.88206 −0.0711352
\(701\) 21.5132 0.812543 0.406272 0.913752i \(-0.366829\pi\)
0.406272 + 0.913752i \(0.366829\pi\)
\(702\) 0 0
\(703\) 20.7190 0.781432
\(704\) 36.4200 1.37263
\(705\) 0 0
\(706\) −5.38108 −0.202520
\(707\) −13.4723 −0.506678
\(708\) 0 0
\(709\) 18.8987 0.709757 0.354878 0.934912i \(-0.384522\pi\)
0.354878 + 0.934912i \(0.384522\pi\)
\(710\) 18.9022 0.709389
\(711\) 0 0
\(712\) 3.91953 0.146891
\(713\) −79.2817 −2.96912
\(714\) 0 0
\(715\) −21.8218 −0.816087
\(716\) −1.80853 −0.0675879
\(717\) 0 0
\(718\) −33.5076 −1.25049
\(719\) 1.02016 0.0380456 0.0190228 0.999819i \(-0.493944\pi\)
0.0190228 + 0.999819i \(0.493944\pi\)
\(720\) 0 0
\(721\) 11.1255 0.414335
\(722\) 2.12902 0.0792339
\(723\) 0 0
\(724\) 9.32312 0.346491
\(725\) −10.0231 −0.372250
\(726\) 0 0
\(727\) 37.8471 1.40367 0.701836 0.712339i \(-0.252364\pi\)
0.701836 + 0.712339i \(0.252364\pi\)
\(728\) 19.4225 0.719847
\(729\) 0 0
\(730\) 13.1954 0.488385
\(731\) −3.82528 −0.141483
\(732\) 0 0
\(733\) 39.4516 1.45718 0.728590 0.684951i \(-0.240176\pi\)
0.728590 + 0.684951i \(0.240176\pi\)
\(734\) −21.5212 −0.794361
\(735\) 0 0
\(736\) 24.3611 0.897963
\(737\) 23.1167 0.851514
\(738\) 0 0
\(739\) −26.1429 −0.961683 −0.480841 0.876808i \(-0.659669\pi\)
−0.480841 + 0.876808i \(0.659669\pi\)
\(740\) 4.34694 0.159797
\(741\) 0 0
\(742\) 25.4365 0.933804
\(743\) −22.5099 −0.825808 −0.412904 0.910775i \(-0.635485\pi\)
−0.412904 + 0.910775i \(0.635485\pi\)
\(744\) 0 0
\(745\) −40.1487 −1.47094
\(746\) −27.9811 −1.02446
\(747\) 0 0
\(748\) −5.92188 −0.216525
\(749\) 30.6516 1.11998
\(750\) 0 0
\(751\) −48.9403 −1.78586 −0.892929 0.450198i \(-0.851353\pi\)
−0.892929 + 0.450198i \(0.851353\pi\)
\(752\) −4.69732 −0.171294
\(753\) 0 0
\(754\) 21.4136 0.779837
\(755\) −30.8683 −1.12341
\(756\) 0 0
\(757\) 7.02286 0.255250 0.127625 0.991822i \(-0.459265\pi\)
0.127625 + 0.991822i \(0.459265\pi\)
\(758\) −24.4316 −0.887396
\(759\) 0 0
\(760\) 25.5661 0.927379
\(761\) 8.69137 0.315062 0.157531 0.987514i \(-0.449647\pi\)
0.157531 + 0.987514i \(0.449647\pi\)
\(762\) 0 0
\(763\) 31.6923 1.14734
\(764\) 0.640046 0.0231561
\(765\) 0 0
\(766\) −7.53072 −0.272096
\(767\) 12.2275 0.441508
\(768\) 0 0
\(769\) 39.3442 1.41879 0.709394 0.704812i \(-0.248969\pi\)
0.709394 + 0.704812i \(0.248969\pi\)
\(770\) 19.9984 0.720692
\(771\) 0 0
\(772\) −5.09027 −0.183203
\(773\) 20.4406 0.735197 0.367599 0.929985i \(-0.380180\pi\)
0.367599 + 0.929985i \(0.380180\pi\)
\(774\) 0 0
\(775\) 15.4087 0.553498
\(776\) −54.8003 −1.96722
\(777\) 0 0
\(778\) −33.0601 −1.18526
\(779\) 37.8167 1.35492
\(780\) 0 0
\(781\) −34.9347 −1.25006
\(782\) 28.4533 1.01749
\(783\) 0 0
\(784\) 5.96889 0.213175
\(785\) −32.1628 −1.14794
\(786\) 0 0
\(787\) −19.5314 −0.696220 −0.348110 0.937454i \(-0.613176\pi\)
−0.348110 + 0.937454i \(0.613176\pi\)
\(788\) −10.5229 −0.374863
\(789\) 0 0
\(790\) −7.99284 −0.284373
\(791\) 24.2728 0.863043
\(792\) 0 0
\(793\) 6.96568 0.247358
\(794\) −8.35247 −0.296418
\(795\) 0 0
\(796\) 10.9175 0.386959
\(797\) 14.8843 0.527228 0.263614 0.964628i \(-0.415085\pi\)
0.263614 + 0.964628i \(0.415085\pi\)
\(798\) 0 0
\(799\) 4.82805 0.170804
\(800\) −4.73468 −0.167396
\(801\) 0 0
\(802\) 8.31325 0.293551
\(803\) −24.3875 −0.860617
\(804\) 0 0
\(805\) 33.9481 1.19651
\(806\) −32.9194 −1.15954
\(807\) 0 0
\(808\) −18.9027 −0.664993
\(809\) 31.3007 1.10047 0.550237 0.835008i \(-0.314537\pi\)
0.550237 + 0.835008i \(0.314537\pi\)
\(810\) 0 0
\(811\) −42.7322 −1.50053 −0.750266 0.661136i \(-0.770075\pi\)
−0.750266 + 0.661136i \(0.770075\pi\)
\(812\) 6.93331 0.243312
\(813\) 0 0
\(814\) 22.7395 0.797020
\(815\) −6.33670 −0.221965
\(816\) 0 0
\(817\) −6.31867 −0.221062
\(818\) −6.46633 −0.226090
\(819\) 0 0
\(820\) 7.93410 0.277071
\(821\) 0.382081 0.0133347 0.00666735 0.999978i \(-0.497878\pi\)
0.00666735 + 0.999978i \(0.497878\pi\)
\(822\) 0 0
\(823\) −50.0612 −1.74503 −0.872513 0.488591i \(-0.837511\pi\)
−0.872513 + 0.488591i \(0.837511\pi\)
\(824\) 15.6099 0.543797
\(825\) 0 0
\(826\) −11.2058 −0.389899
\(827\) −47.1956 −1.64115 −0.820575 0.571538i \(-0.806347\pi\)
−0.820575 + 0.571538i \(0.806347\pi\)
\(828\) 0 0
\(829\) 7.61126 0.264350 0.132175 0.991226i \(-0.457804\pi\)
0.132175 + 0.991226i \(0.457804\pi\)
\(830\) −33.7950 −1.17304
\(831\) 0 0
\(832\) 25.6708 0.889974
\(833\) −6.13501 −0.212566
\(834\) 0 0
\(835\) 10.6053 0.367013
\(836\) −9.78186 −0.338313
\(837\) 0 0
\(838\) −1.22765 −0.0424084
\(839\) 2.97972 0.102871 0.0514356 0.998676i \(-0.483620\pi\)
0.0514356 + 0.998676i \(0.483620\pi\)
\(840\) 0 0
\(841\) 7.92418 0.273248
\(842\) −46.3787 −1.59832
\(843\) 0 0
\(844\) 7.46910 0.257097
\(845\) 8.41461 0.289471
\(846\) 0 0
\(847\) −12.9227 −0.444030
\(848\) 25.6906 0.882220
\(849\) 0 0
\(850\) −5.53002 −0.189678
\(851\) 38.6012 1.32323
\(852\) 0 0
\(853\) −43.1661 −1.47798 −0.738989 0.673718i \(-0.764696\pi\)
−0.738989 + 0.673718i \(0.764696\pi\)
\(854\) −6.38365 −0.218444
\(855\) 0 0
\(856\) 43.0065 1.46993
\(857\) −33.9924 −1.16116 −0.580579 0.814204i \(-0.697174\pi\)
−0.580579 + 0.814204i \(0.697174\pi\)
\(858\) 0 0
\(859\) 39.1565 1.33600 0.668001 0.744160i \(-0.267150\pi\)
0.668001 + 0.744160i \(0.267150\pi\)
\(860\) −1.32568 −0.0452055
\(861\) 0 0
\(862\) −4.49961 −0.153257
\(863\) −27.7523 −0.944699 −0.472350 0.881411i \(-0.656594\pi\)
−0.472350 + 0.881411i \(0.656594\pi\)
\(864\) 0 0
\(865\) 25.8059 0.877428
\(866\) −27.6473 −0.939493
\(867\) 0 0
\(868\) −10.6587 −0.361779
\(869\) 14.7722 0.501113
\(870\) 0 0
\(871\) 16.2939 0.552096
\(872\) 44.4667 1.50583
\(873\) 0 0
\(874\) 46.9997 1.58979
\(875\) −26.5979 −0.899174
\(876\) 0 0
\(877\) 18.6321 0.629160 0.314580 0.949231i \(-0.398136\pi\)
0.314580 + 0.949231i \(0.398136\pi\)
\(878\) 40.0892 1.35295
\(879\) 0 0
\(880\) 20.1982 0.680880
\(881\) 31.1742 1.05029 0.525143 0.851014i \(-0.324012\pi\)
0.525143 + 0.851014i \(0.324012\pi\)
\(882\) 0 0
\(883\) −51.2983 −1.72633 −0.863163 0.504926i \(-0.831520\pi\)
−0.863163 + 0.504926i \(0.831520\pi\)
\(884\) −4.17405 −0.140389
\(885\) 0 0
\(886\) 16.2689 0.546565
\(887\) 16.3317 0.548364 0.274182 0.961678i \(-0.411593\pi\)
0.274182 + 0.961678i \(0.411593\pi\)
\(888\) 0 0
\(889\) 2.18527 0.0732914
\(890\) 2.84461 0.0953514
\(891\) 0 0
\(892\) 10.3133 0.345315
\(893\) 7.97506 0.266875
\(894\) 0 0
\(895\) −6.34016 −0.211928
\(896\) −10.9806 −0.366837
\(897\) 0 0
\(898\) 0.0546350 0.00182319
\(899\) −56.7641 −1.89319
\(900\) 0 0
\(901\) −26.4056 −0.879700
\(902\) 41.5046 1.38195
\(903\) 0 0
\(904\) 34.0567 1.13271
\(905\) 32.6840 1.08645
\(906\) 0 0
\(907\) −38.8600 −1.29032 −0.645162 0.764046i \(-0.723210\pi\)
−0.645162 + 0.764046i \(0.723210\pi\)
\(908\) 5.75973 0.191143
\(909\) 0 0
\(910\) 14.0959 0.467276
\(911\) −24.4819 −0.811120 −0.405560 0.914068i \(-0.632923\pi\)
−0.405560 + 0.914068i \(0.632923\pi\)
\(912\) 0 0
\(913\) 62.4592 2.06710
\(914\) −4.66090 −0.154169
\(915\) 0 0
\(916\) −4.84419 −0.160056
\(917\) −25.3385 −0.836750
\(918\) 0 0
\(919\) 16.7367 0.552092 0.276046 0.961144i \(-0.410976\pi\)
0.276046 + 0.961144i \(0.410976\pi\)
\(920\) 47.6317 1.57037
\(921\) 0 0
\(922\) 42.3866 1.39593
\(923\) −24.6239 −0.810504
\(924\) 0 0
\(925\) −7.50230 −0.246674
\(926\) −27.9431 −0.918268
\(927\) 0 0
\(928\) 17.4421 0.572563
\(929\) 2.51047 0.0823658 0.0411829 0.999152i \(-0.486887\pi\)
0.0411829 + 0.999152i \(0.486887\pi\)
\(930\) 0 0
\(931\) −10.1339 −0.332126
\(932\) −7.36879 −0.241373
\(933\) 0 0
\(934\) 7.87219 0.257586
\(935\) −20.7603 −0.678935
\(936\) 0 0
\(937\) 15.1347 0.494430 0.247215 0.968961i \(-0.420485\pi\)
0.247215 + 0.968961i \(0.420485\pi\)
\(938\) −14.9324 −0.487560
\(939\) 0 0
\(940\) 1.67320 0.0545738
\(941\) −12.6407 −0.412075 −0.206037 0.978544i \(-0.566057\pi\)
−0.206037 + 0.978544i \(0.566057\pi\)
\(942\) 0 0
\(943\) 70.4556 2.29435
\(944\) −11.3177 −0.368360
\(945\) 0 0
\(946\) −6.93487 −0.225472
\(947\) 33.5547 1.09038 0.545190 0.838313i \(-0.316458\pi\)
0.545190 + 0.838313i \(0.316458\pi\)
\(948\) 0 0
\(949\) −17.1896 −0.557999
\(950\) −9.13458 −0.296365
\(951\) 0 0
\(952\) 18.4778 0.598869
\(953\) 33.8876 1.09773 0.548864 0.835912i \(-0.315061\pi\)
0.548864 + 0.835912i \(0.315061\pi\)
\(954\) 0 0
\(955\) 2.24381 0.0726080
\(956\) 4.60630 0.148979
\(957\) 0 0
\(958\) −23.3611 −0.754763
\(959\) −19.3561 −0.625041
\(960\) 0 0
\(961\) 56.2643 1.81498
\(962\) 16.0280 0.516765
\(963\) 0 0
\(964\) −1.98775 −0.0640213
\(965\) −17.8450 −0.574450
\(966\) 0 0
\(967\) 30.6965 0.987131 0.493566 0.869709i \(-0.335693\pi\)
0.493566 + 0.869709i \(0.335693\pi\)
\(968\) −18.1316 −0.582771
\(969\) 0 0
\(970\) −39.7714 −1.27698
\(971\) −58.6273 −1.88144 −0.940719 0.339186i \(-0.889849\pi\)
−0.940719 + 0.339186i \(0.889849\pi\)
\(972\) 0 0
\(973\) −35.4091 −1.13516
\(974\) −43.7519 −1.40190
\(975\) 0 0
\(976\) −6.44742 −0.206377
\(977\) 26.3660 0.843522 0.421761 0.906707i \(-0.361412\pi\)
0.421761 + 0.906707i \(0.361412\pi\)
\(978\) 0 0
\(979\) −5.25734 −0.168025
\(980\) −2.12614 −0.0679171
\(981\) 0 0
\(982\) −1.90150 −0.0606792
\(983\) −56.2112 −1.79286 −0.896429 0.443187i \(-0.853848\pi\)
−0.896429 + 0.443187i \(0.853848\pi\)
\(984\) 0 0
\(985\) −36.8902 −1.17542
\(986\) 20.3720 0.648777
\(987\) 0 0
\(988\) −6.89478 −0.219352
\(989\) −11.7722 −0.374335
\(990\) 0 0
\(991\) −19.1342 −0.607816 −0.303908 0.952701i \(-0.598292\pi\)
−0.303908 + 0.952701i \(0.598292\pi\)
\(992\) −26.8139 −0.851343
\(993\) 0 0
\(994\) 22.5664 0.715762
\(995\) 38.2733 1.21335
\(996\) 0 0
\(997\) −5.83584 −0.184823 −0.0924114 0.995721i \(-0.529457\pi\)
−0.0924114 + 0.995721i \(0.529457\pi\)
\(998\) −23.4527 −0.742384
\(999\) 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 1143.2.a.h.1.4 5
3.2 odd 2 381.2.a.c.1.2 5
12.11 even 2 6096.2.a.be.1.5 5
15.14 odd 2 9525.2.a.k.1.4 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
381.2.a.c.1.2 5 3.2 odd 2
1143.2.a.h.1.4 5 1.1 even 1 trivial
6096.2.a.be.1.5 5 12.11 even 2
9525.2.a.k.1.4 5 15.14 odd 2