Properties

Label 8027.2.a.e.1.18
Level $8027$
Weight $2$
Character 8027.1
Self dual yes
Analytic conductor $64.096$
Analytic rank $0$
Dimension $169$
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] = [8027,2,Mod(1,8027)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8027, 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("8027.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8027 = 23 \cdot 349 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8027.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: \(64.0959177025\)
Analytic rank: \(0\)
Dimension: \(169\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) \(=\) 8027.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.35439 q^{2} -0.664496 q^{3} +3.54317 q^{4} -2.57609 q^{5} +1.56449 q^{6} +5.27951 q^{7} -3.63324 q^{8} -2.55844 q^{9} +O(q^{10})\) \(q-2.35439 q^{2} -0.664496 q^{3} +3.54317 q^{4} -2.57609 q^{5} +1.56449 q^{6} +5.27951 q^{7} -3.63324 q^{8} -2.55844 q^{9} +6.06514 q^{10} +2.79332 q^{11} -2.35442 q^{12} +5.32795 q^{13} -12.4300 q^{14} +1.71180 q^{15} +1.46772 q^{16} -1.92061 q^{17} +6.02359 q^{18} +5.13540 q^{19} -9.12754 q^{20} -3.50821 q^{21} -6.57659 q^{22} -1.00000 q^{23} +2.41427 q^{24} +1.63625 q^{25} -12.5441 q^{26} +3.69357 q^{27} +18.7062 q^{28} +1.16397 q^{29} -4.03026 q^{30} +2.64100 q^{31} +3.81087 q^{32} -1.85615 q^{33} +4.52188 q^{34} -13.6005 q^{35} -9.06501 q^{36} +4.37306 q^{37} -12.0908 q^{38} -3.54040 q^{39} +9.35955 q^{40} +3.73840 q^{41} +8.25972 q^{42} -0.476886 q^{43} +9.89723 q^{44} +6.59079 q^{45} +2.35439 q^{46} +4.70831 q^{47} -0.975297 q^{48} +20.8732 q^{49} -3.85238 q^{50} +1.27624 q^{51} +18.8779 q^{52} -13.4409 q^{53} -8.69611 q^{54} -7.19586 q^{55} -19.1817 q^{56} -3.41246 q^{57} -2.74044 q^{58} -10.9624 q^{59} +6.06521 q^{60} +4.95692 q^{61} -6.21796 q^{62} -13.5073 q^{63} -11.9077 q^{64} -13.7253 q^{65} +4.37012 q^{66} +13.2442 q^{67} -6.80507 q^{68} +0.664496 q^{69} +32.0210 q^{70} +9.98798 q^{71} +9.29543 q^{72} +8.89751 q^{73} -10.2959 q^{74} -1.08728 q^{75} +18.1956 q^{76} +14.7474 q^{77} +8.33551 q^{78} -9.04039 q^{79} -3.78099 q^{80} +5.22098 q^{81} -8.80167 q^{82} +9.12073 q^{83} -12.4302 q^{84} +4.94768 q^{85} +1.12278 q^{86} -0.773452 q^{87} -10.1488 q^{88} +15.0901 q^{89} -15.5173 q^{90} +28.1290 q^{91} -3.54317 q^{92} -1.75494 q^{93} -11.0852 q^{94} -13.2293 q^{95} -2.53231 q^{96} -8.07812 q^{97} -49.1438 q^{98} -7.14657 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 169 q + 6 q^{2} + 2 q^{3} + 186 q^{4} + 28 q^{5} + 5 q^{6} + 38 q^{7} + 18 q^{8} + 185 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 169 q + 6 q^{2} + 2 q^{3} + 186 q^{4} + 28 q^{5} + 5 q^{6} + 38 q^{7} + 18 q^{8} + 185 q^{9} + 28 q^{10} + 17 q^{11} + 10 q^{12} + 91 q^{13} + 20 q^{14} + 29 q^{15} + 200 q^{16} + 16 q^{17} + 31 q^{18} + 30 q^{19} + 45 q^{20} + 49 q^{21} + 76 q^{22} - 169 q^{23} + 3 q^{24} + 241 q^{25} - 15 q^{26} + 14 q^{27} + 118 q^{28} + 23 q^{29} + 52 q^{30} + 45 q^{31} + 42 q^{32} + 62 q^{33} + 65 q^{34} - 16 q^{35} + 199 q^{36} + 226 q^{37} + 49 q^{38} + 17 q^{39} + 95 q^{40} + 19 q^{41} + 32 q^{42} + 71 q^{43} + 46 q^{44} + 127 q^{45} - 6 q^{46} + 27 q^{47} + 5 q^{48} + 239 q^{49} + 24 q^{50} + 39 q^{51} + 154 q^{52} + 111 q^{53} + 22 q^{54} + 47 q^{55} + 39 q^{56} + 122 q^{57} + 146 q^{58} - 73 q^{59} + 109 q^{60} + 125 q^{61} + 14 q^{62} + 109 q^{63} + 260 q^{64} + 73 q^{65} + 26 q^{66} + 152 q^{67} + 40 q^{68} - 2 q^{69} + 76 q^{70} - 79 q^{71} + 126 q^{72} + 106 q^{73} + 23 q^{74} + 12 q^{75} + 122 q^{76} + 63 q^{77} + 101 q^{78} + 82 q^{79} + 134 q^{80} + 225 q^{81} + 125 q^{82} + 28 q^{83} + 73 q^{84} + 197 q^{85} + 97 q^{86} + 18 q^{87} + 183 q^{88} + 54 q^{89} + 52 q^{90} + 106 q^{91} - 186 q^{92} + 194 q^{93} + q^{94} + 18 q^{95} - 39 q^{96} + 239 q^{97} + 5 q^{98} + 85 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.35439 −1.66481 −0.832404 0.554169i \(-0.813036\pi\)
−0.832404 + 0.554169i \(0.813036\pi\)
\(3\) −0.664496 −0.383647 −0.191824 0.981429i \(-0.561440\pi\)
−0.191824 + 0.981429i \(0.561440\pi\)
\(4\) 3.54317 1.77159
\(5\) −2.57609 −1.15206 −0.576032 0.817427i \(-0.695400\pi\)
−0.576032 + 0.817427i \(0.695400\pi\)
\(6\) 1.56449 0.638699
\(7\) 5.27951 1.99547 0.997734 0.0672890i \(-0.0214350\pi\)
0.997734 + 0.0672890i \(0.0214350\pi\)
\(8\) −3.63324 −1.28454
\(9\) −2.55844 −0.852815
\(10\) 6.06514 1.91796
\(11\) 2.79332 0.842219 0.421109 0.907010i \(-0.361641\pi\)
0.421109 + 0.907010i \(0.361641\pi\)
\(12\) −2.35442 −0.679664
\(13\) 5.32795 1.47771 0.738854 0.673865i \(-0.235367\pi\)
0.738854 + 0.673865i \(0.235367\pi\)
\(14\) −12.4300 −3.32207
\(15\) 1.71180 0.441986
\(16\) 1.46772 0.366931
\(17\) −1.92061 −0.465817 −0.232909 0.972499i \(-0.574824\pi\)
−0.232909 + 0.972499i \(0.574824\pi\)
\(18\) 6.02359 1.41977
\(19\) 5.13540 1.17814 0.589071 0.808081i \(-0.299494\pi\)
0.589071 + 0.808081i \(0.299494\pi\)
\(20\) −9.12754 −2.04098
\(21\) −3.50821 −0.765555
\(22\) −6.57659 −1.40213
\(23\) −1.00000 −0.208514
\(24\) 2.41427 0.492811
\(25\) 1.63625 0.327251
\(26\) −12.5441 −2.46010
\(27\) 3.69357 0.710827
\(28\) 18.7062 3.53514
\(29\) 1.16397 0.216143 0.108072 0.994143i \(-0.465532\pi\)
0.108072 + 0.994143i \(0.465532\pi\)
\(30\) −4.03026 −0.735821
\(31\) 2.64100 0.474338 0.237169 0.971468i \(-0.423780\pi\)
0.237169 + 0.971468i \(0.423780\pi\)
\(32\) 3.81087 0.673673
\(33\) −1.85615 −0.323115
\(34\) 4.52188 0.775496
\(35\) −13.6005 −2.29890
\(36\) −9.06501 −1.51084
\(37\) 4.37306 0.718927 0.359463 0.933159i \(-0.382960\pi\)
0.359463 + 0.933159i \(0.382960\pi\)
\(38\) −12.0908 −1.96138
\(39\) −3.54040 −0.566918
\(40\) 9.35955 1.47987
\(41\) 3.73840 0.583840 0.291920 0.956443i \(-0.405706\pi\)
0.291920 + 0.956443i \(0.405706\pi\)
\(42\) 8.25972 1.27450
\(43\) −0.476886 −0.0727245 −0.0363622 0.999339i \(-0.511577\pi\)
−0.0363622 + 0.999339i \(0.511577\pi\)
\(44\) 9.89723 1.49206
\(45\) 6.59079 0.982497
\(46\) 2.35439 0.347136
\(47\) 4.70831 0.686778 0.343389 0.939193i \(-0.388425\pi\)
0.343389 + 0.939193i \(0.388425\pi\)
\(48\) −0.975297 −0.140772
\(49\) 20.8732 2.98189
\(50\) −3.85238 −0.544809
\(51\) 1.27624 0.178709
\(52\) 18.8779 2.61789
\(53\) −13.4409 −1.84625 −0.923127 0.384496i \(-0.874375\pi\)
−0.923127 + 0.384496i \(0.874375\pi\)
\(54\) −8.69611 −1.18339
\(55\) −7.19586 −0.970290
\(56\) −19.1817 −2.56326
\(57\) −3.41246 −0.451991
\(58\) −2.74044 −0.359837
\(59\) −10.9624 −1.42718 −0.713591 0.700562i \(-0.752933\pi\)
−0.713591 + 0.700562i \(0.752933\pi\)
\(60\) 6.06521 0.783016
\(61\) 4.95692 0.634668 0.317334 0.948314i \(-0.397212\pi\)
0.317334 + 0.948314i \(0.397212\pi\)
\(62\) −6.21796 −0.789682
\(63\) −13.5073 −1.70176
\(64\) −11.9077 −1.48847
\(65\) −13.7253 −1.70241
\(66\) 4.37012 0.537924
\(67\) 13.2442 1.61804 0.809020 0.587781i \(-0.199998\pi\)
0.809020 + 0.587781i \(0.199998\pi\)
\(68\) −6.80507 −0.825235
\(69\) 0.664496 0.0799959
\(70\) 32.0210 3.82724
\(71\) 9.98798 1.18536 0.592678 0.805440i \(-0.298071\pi\)
0.592678 + 0.805440i \(0.298071\pi\)
\(72\) 9.29543 1.09548
\(73\) 8.89751 1.04137 0.520687 0.853748i \(-0.325676\pi\)
0.520687 + 0.853748i \(0.325676\pi\)
\(74\) −10.2959 −1.19688
\(75\) −1.08728 −0.125549
\(76\) 18.1956 2.08718
\(77\) 14.7474 1.68062
\(78\) 8.33551 0.943810
\(79\) −9.04039 −1.01712 −0.508561 0.861026i \(-0.669823\pi\)
−0.508561 + 0.861026i \(0.669823\pi\)
\(80\) −3.78099 −0.422728
\(81\) 5.22098 0.580108
\(82\) −8.80167 −0.971982
\(83\) 9.12073 1.00113 0.500565 0.865699i \(-0.333126\pi\)
0.500565 + 0.865699i \(0.333126\pi\)
\(84\) −12.4302 −1.35625
\(85\) 4.94768 0.536651
\(86\) 1.12278 0.121072
\(87\) −0.773452 −0.0829227
\(88\) −10.1488 −1.08187
\(89\) 15.0901 1.59954 0.799771 0.600305i \(-0.204954\pi\)
0.799771 + 0.600305i \(0.204954\pi\)
\(90\) −15.5173 −1.63567
\(91\) 28.1290 2.94872
\(92\) −3.54317 −0.369401
\(93\) −1.75494 −0.181978
\(94\) −11.0852 −1.14335
\(95\) −13.2293 −1.35729
\(96\) −2.53231 −0.258453
\(97\) −8.07812 −0.820209 −0.410104 0.912039i \(-0.634508\pi\)
−0.410104 + 0.912039i \(0.634508\pi\)
\(98\) −49.1438 −4.96427
\(99\) −7.14657 −0.718257
\(100\) 5.79753 0.579753
\(101\) 10.9538 1.08995 0.544973 0.838453i \(-0.316540\pi\)
0.544973 + 0.838453i \(0.316540\pi\)
\(102\) −3.00477 −0.297517
\(103\) 6.12042 0.603063 0.301531 0.953456i \(-0.402502\pi\)
0.301531 + 0.953456i \(0.402502\pi\)
\(104\) −19.3577 −1.89818
\(105\) 9.03748 0.881968
\(106\) 31.6452 3.07366
\(107\) −10.8595 −1.04983 −0.524913 0.851156i \(-0.675902\pi\)
−0.524913 + 0.851156i \(0.675902\pi\)
\(108\) 13.0869 1.25929
\(109\) −3.34788 −0.320669 −0.160334 0.987063i \(-0.551257\pi\)
−0.160334 + 0.987063i \(0.551257\pi\)
\(110\) 16.9419 1.61535
\(111\) −2.90588 −0.275814
\(112\) 7.74886 0.732199
\(113\) 4.18428 0.393624 0.196812 0.980441i \(-0.436941\pi\)
0.196812 + 0.980441i \(0.436941\pi\)
\(114\) 8.03427 0.752478
\(115\) 2.57609 0.240222
\(116\) 4.12414 0.382916
\(117\) −13.6313 −1.26021
\(118\) 25.8098 2.37598
\(119\) −10.1399 −0.929523
\(120\) −6.21939 −0.567750
\(121\) −3.19734 −0.290667
\(122\) −11.6705 −1.05660
\(123\) −2.48415 −0.223989
\(124\) 9.35753 0.840331
\(125\) 8.66532 0.775050
\(126\) 31.8016 2.83311
\(127\) 14.4500 1.28223 0.641113 0.767446i \(-0.278473\pi\)
0.641113 + 0.767446i \(0.278473\pi\)
\(128\) 20.4138 1.80434
\(129\) 0.316889 0.0279005
\(130\) 32.3148 2.83419
\(131\) 21.7044 1.89633 0.948163 0.317786i \(-0.102939\pi\)
0.948163 + 0.317786i \(0.102939\pi\)
\(132\) −6.57667 −0.572426
\(133\) 27.1124 2.35094
\(134\) −31.1821 −2.69373
\(135\) −9.51497 −0.818918
\(136\) 6.97804 0.598362
\(137\) −15.7186 −1.34293 −0.671466 0.741035i \(-0.734335\pi\)
−0.671466 + 0.741035i \(0.734335\pi\)
\(138\) −1.56449 −0.133178
\(139\) −22.8942 −1.94186 −0.970930 0.239363i \(-0.923061\pi\)
−0.970930 + 0.239363i \(0.923061\pi\)
\(140\) −48.1889 −4.07271
\(141\) −3.12865 −0.263480
\(142\) −23.5157 −1.97339
\(143\) 14.8827 1.24455
\(144\) −3.75509 −0.312924
\(145\) −2.99849 −0.249011
\(146\) −20.9482 −1.73369
\(147\) −13.8702 −1.14399
\(148\) 15.4945 1.27364
\(149\) 4.23477 0.346926 0.173463 0.984840i \(-0.444504\pi\)
0.173463 + 0.984840i \(0.444504\pi\)
\(150\) 2.55989 0.209014
\(151\) −15.6609 −1.27446 −0.637232 0.770672i \(-0.719921\pi\)
−0.637232 + 0.770672i \(0.719921\pi\)
\(152\) −18.6581 −1.51337
\(153\) 4.91379 0.397256
\(154\) −34.7211 −2.79791
\(155\) −6.80347 −0.546468
\(156\) −12.5443 −1.00434
\(157\) −0.565708 −0.0451484 −0.0225742 0.999745i \(-0.507186\pi\)
−0.0225742 + 0.999745i \(0.507186\pi\)
\(158\) 21.2846 1.69331
\(159\) 8.93144 0.708309
\(160\) −9.81715 −0.776114
\(161\) −5.27951 −0.416084
\(162\) −12.2922 −0.965769
\(163\) −14.6626 −1.14847 −0.574234 0.818692i \(-0.694700\pi\)
−0.574234 + 0.818692i \(0.694700\pi\)
\(164\) 13.2458 1.03432
\(165\) 4.78162 0.372249
\(166\) −21.4738 −1.66669
\(167\) 16.0896 1.24505 0.622526 0.782599i \(-0.286107\pi\)
0.622526 + 0.782599i \(0.286107\pi\)
\(168\) 12.7462 0.983388
\(169\) 15.3871 1.18362
\(170\) −11.6488 −0.893421
\(171\) −13.1386 −1.00474
\(172\) −1.68969 −0.128838
\(173\) −3.44496 −0.261916 −0.130958 0.991388i \(-0.541805\pi\)
−0.130958 + 0.991388i \(0.541805\pi\)
\(174\) 1.82101 0.138050
\(175\) 8.63861 0.653018
\(176\) 4.09983 0.309036
\(177\) 7.28447 0.547534
\(178\) −35.5279 −2.66293
\(179\) 12.7332 0.951721 0.475860 0.879521i \(-0.342137\pi\)
0.475860 + 0.879521i \(0.342137\pi\)
\(180\) 23.3523 1.74058
\(181\) −0.976934 −0.0726149 −0.0363075 0.999341i \(-0.511560\pi\)
−0.0363075 + 0.999341i \(0.511560\pi\)
\(182\) −66.2267 −4.90905
\(183\) −3.29385 −0.243488
\(184\) 3.63324 0.267846
\(185\) −11.2654 −0.828249
\(186\) 4.13181 0.302959
\(187\) −5.36490 −0.392320
\(188\) 16.6824 1.21669
\(189\) 19.5002 1.41843
\(190\) 31.1469 2.25964
\(191\) 22.0741 1.59723 0.798613 0.601845i \(-0.205567\pi\)
0.798613 + 0.601845i \(0.205567\pi\)
\(192\) 7.91264 0.571046
\(193\) −21.4358 −1.54298 −0.771491 0.636240i \(-0.780489\pi\)
−0.771491 + 0.636240i \(0.780489\pi\)
\(194\) 19.0191 1.36549
\(195\) 9.12041 0.653126
\(196\) 73.9574 5.28267
\(197\) −19.4469 −1.38553 −0.692766 0.721163i \(-0.743608\pi\)
−0.692766 + 0.721163i \(0.743608\pi\)
\(198\) 16.8258 1.19576
\(199\) −4.56548 −0.323638 −0.161819 0.986820i \(-0.551736\pi\)
−0.161819 + 0.986820i \(0.551736\pi\)
\(200\) −5.94489 −0.420367
\(201\) −8.80074 −0.620756
\(202\) −25.7896 −1.81455
\(203\) 6.14518 0.431307
\(204\) 4.52194 0.316599
\(205\) −9.63047 −0.672621
\(206\) −14.4099 −1.00398
\(207\) 2.55844 0.177824
\(208\) 7.81997 0.542217
\(209\) 14.3448 0.992254
\(210\) −21.2778 −1.46831
\(211\) 17.9262 1.23409 0.617046 0.786927i \(-0.288329\pi\)
0.617046 + 0.786927i \(0.288329\pi\)
\(212\) −47.6235 −3.27080
\(213\) −6.63698 −0.454758
\(214\) 25.5675 1.74776
\(215\) 1.22850 0.0837832
\(216\) −13.4196 −0.913088
\(217\) 13.9432 0.946526
\(218\) 7.88224 0.533852
\(219\) −5.91236 −0.399520
\(220\) −25.4962 −1.71895
\(221\) −10.2329 −0.688342
\(222\) 6.84159 0.459178
\(223\) −4.49245 −0.300837 −0.150418 0.988622i \(-0.548062\pi\)
−0.150418 + 0.988622i \(0.548062\pi\)
\(224\) 20.1195 1.34429
\(225\) −4.18626 −0.279084
\(226\) −9.85145 −0.655309
\(227\) 12.2062 0.810155 0.405078 0.914282i \(-0.367244\pi\)
0.405078 + 0.914282i \(0.367244\pi\)
\(228\) −12.0909 −0.800741
\(229\) −26.1308 −1.72677 −0.863386 0.504543i \(-0.831661\pi\)
−0.863386 + 0.504543i \(0.831661\pi\)
\(230\) −6.06514 −0.399923
\(231\) −9.79958 −0.644765
\(232\) −4.22897 −0.277645
\(233\) −19.8797 −1.30236 −0.651180 0.758923i \(-0.725726\pi\)
−0.651180 + 0.758923i \(0.725726\pi\)
\(234\) 32.0934 2.09801
\(235\) −12.1290 −0.791211
\(236\) −38.8416 −2.52838
\(237\) 6.00730 0.390216
\(238\) 23.8733 1.54748
\(239\) 5.22114 0.337727 0.168864 0.985639i \(-0.445990\pi\)
0.168864 + 0.985639i \(0.445990\pi\)
\(240\) 2.51246 0.162178
\(241\) −1.65231 −0.106435 −0.0532173 0.998583i \(-0.516948\pi\)
−0.0532173 + 0.998583i \(0.516948\pi\)
\(242\) 7.52780 0.483905
\(243\) −14.5500 −0.933384
\(244\) 17.5632 1.12437
\(245\) −53.7713 −3.43533
\(246\) 5.84868 0.372898
\(247\) 27.3612 1.74095
\(248\) −9.59539 −0.609308
\(249\) −6.06069 −0.384081
\(250\) −20.4016 −1.29031
\(251\) 25.3961 1.60299 0.801495 0.598002i \(-0.204038\pi\)
0.801495 + 0.598002i \(0.204038\pi\)
\(252\) −47.8588 −3.01482
\(253\) −2.79332 −0.175615
\(254\) −34.0209 −2.13466
\(255\) −3.28771 −0.205885
\(256\) −24.2466 −1.51541
\(257\) −11.7728 −0.734365 −0.367182 0.930149i \(-0.619678\pi\)
−0.367182 + 0.930149i \(0.619678\pi\)
\(258\) −0.746082 −0.0464490
\(259\) 23.0876 1.43459
\(260\) −48.6311 −3.01597
\(261\) −2.97795 −0.184330
\(262\) −51.1008 −3.15702
\(263\) −5.95698 −0.367323 −0.183662 0.982990i \(-0.558795\pi\)
−0.183662 + 0.982990i \(0.558795\pi\)
\(264\) 6.74384 0.415055
\(265\) 34.6251 2.12700
\(266\) −63.8333 −3.91387
\(267\) −10.0273 −0.613660
\(268\) 46.9266 2.86650
\(269\) −5.79447 −0.353295 −0.176648 0.984274i \(-0.556525\pi\)
−0.176648 + 0.984274i \(0.556525\pi\)
\(270\) 22.4020 1.36334
\(271\) −18.0197 −1.09462 −0.547311 0.836930i \(-0.684348\pi\)
−0.547311 + 0.836930i \(0.684348\pi\)
\(272\) −2.81893 −0.170923
\(273\) −18.6916 −1.13127
\(274\) 37.0078 2.23572
\(275\) 4.57058 0.275617
\(276\) 2.35442 0.141720
\(277\) −5.91958 −0.355673 −0.177836 0.984060i \(-0.556910\pi\)
−0.177836 + 0.984060i \(0.556910\pi\)
\(278\) 53.9020 3.23282
\(279\) −6.75686 −0.404523
\(280\) 49.4138 2.95304
\(281\) −23.6554 −1.41116 −0.705582 0.708629i \(-0.749314\pi\)
−0.705582 + 0.708629i \(0.749314\pi\)
\(282\) 7.36608 0.438644
\(283\) 27.6601 1.64422 0.822111 0.569327i \(-0.192796\pi\)
0.822111 + 0.569327i \(0.192796\pi\)
\(284\) 35.3891 2.09996
\(285\) 8.79080 0.520722
\(286\) −35.0397 −2.07194
\(287\) 19.7369 1.16503
\(288\) −9.74990 −0.574518
\(289\) −13.3112 −0.783014
\(290\) 7.05962 0.414555
\(291\) 5.36788 0.314671
\(292\) 31.5254 1.84488
\(293\) 19.8953 1.16230 0.581148 0.813798i \(-0.302604\pi\)
0.581148 + 0.813798i \(0.302604\pi\)
\(294\) 32.6559 1.90453
\(295\) 28.2401 1.64420
\(296\) −15.8884 −0.923492
\(297\) 10.3173 0.598672
\(298\) −9.97033 −0.577566
\(299\) −5.32795 −0.308123
\(300\) −3.85243 −0.222420
\(301\) −2.51773 −0.145119
\(302\) 36.8719 2.12174
\(303\) −7.27877 −0.418155
\(304\) 7.53736 0.432297
\(305\) −12.7695 −0.731178
\(306\) −11.5690 −0.661355
\(307\) −21.1808 −1.20885 −0.604427 0.796661i \(-0.706598\pi\)
−0.604427 + 0.796661i \(0.706598\pi\)
\(308\) 52.2525 2.97736
\(309\) −4.06699 −0.231363
\(310\) 16.0180 0.909764
\(311\) 17.7846 1.00847 0.504237 0.863565i \(-0.331774\pi\)
0.504237 + 0.863565i \(0.331774\pi\)
\(312\) 12.8631 0.728231
\(313\) −30.7473 −1.73794 −0.868971 0.494863i \(-0.835218\pi\)
−0.868971 + 0.494863i \(0.835218\pi\)
\(314\) 1.33190 0.0751634
\(315\) 34.7961 1.96054
\(316\) −32.0316 −1.80192
\(317\) 17.1704 0.964386 0.482193 0.876065i \(-0.339840\pi\)
0.482193 + 0.876065i \(0.339840\pi\)
\(318\) −21.0281 −1.17920
\(319\) 3.25134 0.182040
\(320\) 30.6754 1.71481
\(321\) 7.21609 0.402763
\(322\) 12.4300 0.692699
\(323\) −9.86313 −0.548799
\(324\) 18.4988 1.02771
\(325\) 8.71788 0.483581
\(326\) 34.5217 1.91198
\(327\) 2.22465 0.123024
\(328\) −13.5825 −0.749968
\(329\) 24.8576 1.37044
\(330\) −11.2578 −0.619723
\(331\) −26.5576 −1.45974 −0.729869 0.683587i \(-0.760419\pi\)
−0.729869 + 0.683587i \(0.760419\pi\)
\(332\) 32.3163 1.77359
\(333\) −11.1882 −0.613112
\(334\) −37.8813 −2.07277
\(335\) −34.1184 −1.86409
\(336\) −5.14909 −0.280906
\(337\) −2.70884 −0.147560 −0.0737800 0.997275i \(-0.523506\pi\)
−0.0737800 + 0.997275i \(0.523506\pi\)
\(338\) −36.2273 −1.97050
\(339\) −2.78044 −0.151013
\(340\) 17.5305 0.950724
\(341\) 7.37718 0.399497
\(342\) 30.9336 1.67270
\(343\) 73.2438 3.95479
\(344\) 1.73264 0.0934177
\(345\) −1.71180 −0.0921604
\(346\) 8.11080 0.436039
\(347\) −27.5750 −1.48030 −0.740152 0.672440i \(-0.765246\pi\)
−0.740152 + 0.672440i \(0.765246\pi\)
\(348\) −2.74047 −0.146905
\(349\) 1.00000 0.0535288
\(350\) −20.3387 −1.08715
\(351\) 19.6791 1.05039
\(352\) 10.6450 0.567380
\(353\) −7.86169 −0.418435 −0.209218 0.977869i \(-0.567092\pi\)
−0.209218 + 0.977869i \(0.567092\pi\)
\(354\) −17.1505 −0.911539
\(355\) −25.7300 −1.36561
\(356\) 53.4667 2.83373
\(357\) 6.73792 0.356609
\(358\) −29.9789 −1.58443
\(359\) 12.5854 0.664233 0.332117 0.943238i \(-0.392237\pi\)
0.332117 + 0.943238i \(0.392237\pi\)
\(360\) −23.9459 −1.26206
\(361\) 7.37237 0.388019
\(362\) 2.30009 0.120890
\(363\) 2.12462 0.111514
\(364\) 99.6658 5.22391
\(365\) −22.9208 −1.19973
\(366\) 7.75502 0.405362
\(367\) 8.89587 0.464361 0.232180 0.972673i \(-0.425414\pi\)
0.232180 + 0.972673i \(0.425414\pi\)
\(368\) −1.46772 −0.0765104
\(369\) −9.56449 −0.497908
\(370\) 26.5232 1.37888
\(371\) −70.9615 −3.68414
\(372\) −6.21804 −0.322390
\(373\) −4.96659 −0.257160 −0.128580 0.991699i \(-0.541042\pi\)
−0.128580 + 0.991699i \(0.541042\pi\)
\(374\) 12.6311 0.653138
\(375\) −5.75807 −0.297346
\(376\) −17.1064 −0.882195
\(377\) 6.20156 0.319397
\(378\) −45.9112 −2.36142
\(379\) 24.8108 1.27445 0.637223 0.770680i \(-0.280083\pi\)
0.637223 + 0.770680i \(0.280083\pi\)
\(380\) −46.8736 −2.40456
\(381\) −9.60194 −0.491922
\(382\) −51.9711 −2.65907
\(383\) −31.7458 −1.62213 −0.811067 0.584954i \(-0.801113\pi\)
−0.811067 + 0.584954i \(0.801113\pi\)
\(384\) −13.5649 −0.692229
\(385\) −37.9906 −1.93618
\(386\) 50.4683 2.56877
\(387\) 1.22009 0.0620205
\(388\) −28.6222 −1.45307
\(389\) −29.5882 −1.50018 −0.750092 0.661334i \(-0.769991\pi\)
−0.750092 + 0.661334i \(0.769991\pi\)
\(390\) −21.4730 −1.08733
\(391\) 1.92061 0.0971296
\(392\) −75.8373 −3.83036
\(393\) −14.4225 −0.727519
\(394\) 45.7856 2.30664
\(395\) 23.2889 1.17179
\(396\) −25.3215 −1.27245
\(397\) −18.7251 −0.939786 −0.469893 0.882723i \(-0.655708\pi\)
−0.469893 + 0.882723i \(0.655708\pi\)
\(398\) 10.7489 0.538796
\(399\) −18.0161 −0.901933
\(400\) 2.40157 0.120078
\(401\) −16.4592 −0.821932 −0.410966 0.911651i \(-0.634809\pi\)
−0.410966 + 0.911651i \(0.634809\pi\)
\(402\) 20.7204 1.03344
\(403\) 14.0711 0.700934
\(404\) 38.8113 1.93093
\(405\) −13.4497 −0.668322
\(406\) −14.4682 −0.718043
\(407\) 12.2154 0.605494
\(408\) −4.63688 −0.229560
\(409\) 28.6441 1.41636 0.708180 0.706032i \(-0.249517\pi\)
0.708180 + 0.706032i \(0.249517\pi\)
\(410\) 22.6739 1.11978
\(411\) 10.4450 0.515212
\(412\) 21.6857 1.06838
\(413\) −57.8761 −2.84790
\(414\) −6.02359 −0.296043
\(415\) −23.4959 −1.15337
\(416\) 20.3041 0.995492
\(417\) 15.2131 0.744989
\(418\) −33.7734 −1.65191
\(419\) −24.2444 −1.18442 −0.592209 0.805784i \(-0.701744\pi\)
−0.592209 + 0.805784i \(0.701744\pi\)
\(420\) 32.0214 1.56248
\(421\) −24.1595 −1.17746 −0.588731 0.808329i \(-0.700372\pi\)
−0.588731 + 0.808329i \(0.700372\pi\)
\(422\) −42.2054 −2.05453
\(423\) −12.0460 −0.585694
\(424\) 48.8340 2.37159
\(425\) −3.14261 −0.152439
\(426\) 15.6261 0.757085
\(427\) 26.1701 1.26646
\(428\) −38.4770 −1.85986
\(429\) −9.88950 −0.477469
\(430\) −2.89238 −0.139483
\(431\) −20.5292 −0.988856 −0.494428 0.869219i \(-0.664622\pi\)
−0.494428 + 0.869219i \(0.664622\pi\)
\(432\) 5.42114 0.260824
\(433\) 30.8535 1.48272 0.741361 0.671106i \(-0.234181\pi\)
0.741361 + 0.671106i \(0.234181\pi\)
\(434\) −32.8278 −1.57578
\(435\) 1.99248 0.0955323
\(436\) −11.8621 −0.568093
\(437\) −5.13540 −0.245660
\(438\) 13.9200 0.665124
\(439\) 27.3357 1.30466 0.652332 0.757933i \(-0.273791\pi\)
0.652332 + 0.757933i \(0.273791\pi\)
\(440\) 26.1443 1.24638
\(441\) −53.4030 −2.54300
\(442\) 24.0924 1.14596
\(443\) 24.8170 1.17909 0.589547 0.807734i \(-0.299306\pi\)
0.589547 + 0.807734i \(0.299306\pi\)
\(444\) −10.2960 −0.488628
\(445\) −38.8734 −1.84278
\(446\) 10.5770 0.500835
\(447\) −2.81399 −0.133097
\(448\) −62.8670 −2.97019
\(449\) −12.6673 −0.597809 −0.298904 0.954283i \(-0.596621\pi\)
−0.298904 + 0.954283i \(0.596621\pi\)
\(450\) 9.85611 0.464622
\(451\) 10.4426 0.491721
\(452\) 14.8256 0.697339
\(453\) 10.4066 0.488944
\(454\) −28.7383 −1.34875
\(455\) −72.4629 −3.39711
\(456\) 12.3983 0.580601
\(457\) 41.3665 1.93504 0.967521 0.252792i \(-0.0813488\pi\)
0.967521 + 0.252792i \(0.0813488\pi\)
\(458\) 61.5222 2.87475
\(459\) −7.09391 −0.331115
\(460\) 9.12754 0.425574
\(461\) −0.440990 −0.0205389 −0.0102695 0.999947i \(-0.503269\pi\)
−0.0102695 + 0.999947i \(0.503269\pi\)
\(462\) 23.0721 1.07341
\(463\) 2.61481 0.121521 0.0607603 0.998152i \(-0.480647\pi\)
0.0607603 + 0.998152i \(0.480647\pi\)
\(464\) 1.70838 0.0793097
\(465\) 4.52088 0.209651
\(466\) 46.8046 2.16818
\(467\) 1.89119 0.0875140 0.0437570 0.999042i \(-0.486067\pi\)
0.0437570 + 0.999042i \(0.486067\pi\)
\(468\) −48.2980 −2.23257
\(469\) 69.9230 3.22875
\(470\) 28.5565 1.31722
\(471\) 0.375910 0.0173210
\(472\) 39.8290 1.83328
\(473\) −1.33210 −0.0612499
\(474\) −14.1436 −0.649635
\(475\) 8.40282 0.385548
\(476\) −35.9274 −1.64673
\(477\) 34.3879 1.57451
\(478\) −12.2926 −0.562251
\(479\) 0.667933 0.0305186 0.0152593 0.999884i \(-0.495143\pi\)
0.0152593 + 0.999884i \(0.495143\pi\)
\(480\) 6.52346 0.297754
\(481\) 23.2995 1.06236
\(482\) 3.89019 0.177193
\(483\) 3.50821 0.159629
\(484\) −11.3287 −0.514942
\(485\) 20.8100 0.944933
\(486\) 34.2565 1.55390
\(487\) 13.2822 0.601875 0.300938 0.953644i \(-0.402700\pi\)
0.300938 + 0.953644i \(0.402700\pi\)
\(488\) −18.0096 −0.815258
\(489\) 9.74327 0.440606
\(490\) 126.599 5.71916
\(491\) 11.1947 0.505210 0.252605 0.967570i \(-0.418713\pi\)
0.252605 + 0.967570i \(0.418713\pi\)
\(492\) −8.80178 −0.396815
\(493\) −2.23553 −0.100683
\(494\) −64.4190 −2.89835
\(495\) 18.4102 0.827478
\(496\) 3.87627 0.174049
\(497\) 52.7317 2.36534
\(498\) 14.2693 0.639421
\(499\) 8.73848 0.391188 0.195594 0.980685i \(-0.437336\pi\)
0.195594 + 0.980685i \(0.437336\pi\)
\(500\) 30.7027 1.37307
\(501\) −10.6915 −0.477660
\(502\) −59.7925 −2.66867
\(503\) 30.5405 1.36173 0.680866 0.732408i \(-0.261604\pi\)
0.680866 + 0.732408i \(0.261604\pi\)
\(504\) 49.0753 2.18599
\(505\) −28.2181 −1.25569
\(506\) 6.57659 0.292365
\(507\) −10.2247 −0.454093
\(508\) 51.1987 2.27157
\(509\) −15.0212 −0.665804 −0.332902 0.942961i \(-0.608028\pi\)
−0.332902 + 0.942961i \(0.608028\pi\)
\(510\) 7.74057 0.342758
\(511\) 46.9745 2.07803
\(512\) 16.2585 0.718530
\(513\) 18.9679 0.837455
\(514\) 27.7177 1.22258
\(515\) −15.7668 −0.694766
\(516\) 1.12279 0.0494282
\(517\) 13.1518 0.578417
\(518\) −54.3574 −2.38833
\(519\) 2.28916 0.100483
\(520\) 49.8672 2.18682
\(521\) 35.3551 1.54893 0.774467 0.632614i \(-0.218018\pi\)
0.774467 + 0.632614i \(0.218018\pi\)
\(522\) 7.01126 0.306874
\(523\) −10.0585 −0.439829 −0.219914 0.975519i \(-0.570578\pi\)
−0.219914 + 0.975519i \(0.570578\pi\)
\(524\) 76.9025 3.35950
\(525\) −5.74032 −0.250528
\(526\) 14.0251 0.611523
\(527\) −5.07235 −0.220955
\(528\) −2.72432 −0.118561
\(529\) 1.00000 0.0434783
\(530\) −81.5211 −3.54105
\(531\) 28.0467 1.21712
\(532\) 96.0639 4.16490
\(533\) 19.9180 0.862745
\(534\) 23.6082 1.02163
\(535\) 27.9750 1.20947
\(536\) −48.1194 −2.07844
\(537\) −8.46113 −0.365125
\(538\) 13.6425 0.588169
\(539\) 58.3057 2.51140
\(540\) −33.7132 −1.45078
\(541\) −17.3320 −0.745162 −0.372581 0.928000i \(-0.621527\pi\)
−0.372581 + 0.928000i \(0.621527\pi\)
\(542\) 42.4256 1.82233
\(543\) 0.649169 0.0278585
\(544\) −7.31921 −0.313808
\(545\) 8.62446 0.369431
\(546\) 44.0074 1.88334
\(547\) −28.1777 −1.20479 −0.602396 0.798197i \(-0.705787\pi\)
−0.602396 + 0.798197i \(0.705787\pi\)
\(548\) −55.6938 −2.37912
\(549\) −12.6820 −0.541254
\(550\) −10.7610 −0.458849
\(551\) 5.97744 0.254648
\(552\) −2.41427 −0.102758
\(553\) −47.7288 −2.02964
\(554\) 13.9370 0.592127
\(555\) 7.48582 0.317755
\(556\) −81.1181 −3.44017
\(557\) −25.6868 −1.08838 −0.544192 0.838960i \(-0.683164\pi\)
−0.544192 + 0.838960i \(0.683164\pi\)
\(558\) 15.9083 0.673453
\(559\) −2.54083 −0.107466
\(560\) −19.9618 −0.843540
\(561\) 3.56495 0.150512
\(562\) 55.6942 2.34932
\(563\) −7.37845 −0.310965 −0.155482 0.987839i \(-0.549693\pi\)
−0.155482 + 0.987839i \(0.549693\pi\)
\(564\) −11.0854 −0.466778
\(565\) −10.7791 −0.453480
\(566\) −65.1228 −2.73732
\(567\) 27.5642 1.15759
\(568\) −36.2887 −1.52264
\(569\) −34.5638 −1.44899 −0.724495 0.689280i \(-0.757927\pi\)
−0.724495 + 0.689280i \(0.757927\pi\)
\(570\) −20.6970 −0.866902
\(571\) 21.4148 0.896179 0.448090 0.893989i \(-0.352105\pi\)
0.448090 + 0.893989i \(0.352105\pi\)
\(572\) 52.7320 2.20483
\(573\) −14.6682 −0.612771
\(574\) −46.4685 −1.93956
\(575\) −1.63625 −0.0682365
\(576\) 30.4653 1.26939
\(577\) 3.75037 0.156130 0.0780649 0.996948i \(-0.475126\pi\)
0.0780649 + 0.996948i \(0.475126\pi\)
\(578\) 31.3399 1.30357
\(579\) 14.2440 0.591961
\(580\) −10.6242 −0.441144
\(581\) 48.1530 1.99772
\(582\) −12.6381 −0.523866
\(583\) −37.5449 −1.55495
\(584\) −32.3267 −1.33769
\(585\) 35.1154 1.45184
\(586\) −46.8414 −1.93500
\(587\) 16.5557 0.683328 0.341664 0.939822i \(-0.389009\pi\)
0.341664 + 0.939822i \(0.389009\pi\)
\(588\) −49.1444 −2.02668
\(589\) 13.5626 0.558838
\(590\) −66.4884 −2.73729
\(591\) 12.9224 0.531555
\(592\) 6.41845 0.263797
\(593\) 11.3051 0.464246 0.232123 0.972686i \(-0.425433\pi\)
0.232123 + 0.972686i \(0.425433\pi\)
\(594\) −24.2910 −0.996674
\(595\) 26.1213 1.07087
\(596\) 15.0045 0.614610
\(597\) 3.03375 0.124163
\(598\) 12.5441 0.512966
\(599\) 29.4591 1.20366 0.601832 0.798622i \(-0.294438\pi\)
0.601832 + 0.798622i \(0.294438\pi\)
\(600\) 3.95036 0.161273
\(601\) −39.5561 −1.61353 −0.806763 0.590875i \(-0.798783\pi\)
−0.806763 + 0.590875i \(0.798783\pi\)
\(602\) 5.92772 0.241596
\(603\) −33.8846 −1.37989
\(604\) −55.4892 −2.25782
\(605\) 8.23665 0.334867
\(606\) 17.1371 0.696147
\(607\) −5.25178 −0.213163 −0.106582 0.994304i \(-0.533991\pi\)
−0.106582 + 0.994304i \(0.533991\pi\)
\(608\) 19.5704 0.793683
\(609\) −4.08345 −0.165470
\(610\) 30.0644 1.21727
\(611\) 25.0857 1.01486
\(612\) 17.4104 0.703773
\(613\) 21.1096 0.852610 0.426305 0.904580i \(-0.359815\pi\)
0.426305 + 0.904580i \(0.359815\pi\)
\(614\) 49.8680 2.01251
\(615\) 6.39941 0.258049
\(616\) −53.5807 −2.15883
\(617\) 9.37767 0.377531 0.188765 0.982022i \(-0.439551\pi\)
0.188765 + 0.982022i \(0.439551\pi\)
\(618\) 9.57531 0.385175
\(619\) 19.2082 0.772044 0.386022 0.922489i \(-0.373849\pi\)
0.386022 + 0.922489i \(0.373849\pi\)
\(620\) −24.1059 −0.968115
\(621\) −3.69357 −0.148218
\(622\) −41.8720 −1.67892
\(623\) 79.6681 3.19184
\(624\) −5.19634 −0.208020
\(625\) −30.5039 −1.22016
\(626\) 72.3914 2.89334
\(627\) −9.53209 −0.380675
\(628\) −2.00440 −0.0799842
\(629\) −8.39896 −0.334889
\(630\) −81.9238 −3.26392
\(631\) −18.4714 −0.735335 −0.367668 0.929957i \(-0.619844\pi\)
−0.367668 + 0.929957i \(0.619844\pi\)
\(632\) 32.8459 1.30654
\(633\) −11.9119 −0.473456
\(634\) −40.4259 −1.60552
\(635\) −37.2244 −1.47721
\(636\) 31.6456 1.25483
\(637\) 111.212 4.40636
\(638\) −7.65493 −0.303062
\(639\) −25.5537 −1.01089
\(640\) −52.5878 −2.07871
\(641\) −14.1575 −0.559188 −0.279594 0.960118i \(-0.590200\pi\)
−0.279594 + 0.960118i \(0.590200\pi\)
\(642\) −16.9895 −0.670522
\(643\) −33.8500 −1.33491 −0.667456 0.744649i \(-0.732617\pi\)
−0.667456 + 0.744649i \(0.732617\pi\)
\(644\) −18.7062 −0.737128
\(645\) −0.816335 −0.0321432
\(646\) 23.2217 0.913645
\(647\) −17.8895 −0.703310 −0.351655 0.936130i \(-0.614381\pi\)
−0.351655 + 0.936130i \(0.614381\pi\)
\(648\) −18.9690 −0.745174
\(649\) −30.6215 −1.20200
\(650\) −20.5253 −0.805069
\(651\) −9.26520 −0.363132
\(652\) −51.9523 −2.03461
\(653\) 40.8799 1.59975 0.799877 0.600164i \(-0.204898\pi\)
0.799877 + 0.600164i \(0.204898\pi\)
\(654\) −5.23771 −0.204811
\(655\) −55.9126 −2.18469
\(656\) 5.48694 0.214229
\(657\) −22.7638 −0.888100
\(658\) −58.5245 −2.28152
\(659\) −30.1956 −1.17625 −0.588126 0.808769i \(-0.700134\pi\)
−0.588126 + 0.808769i \(0.700134\pi\)
\(660\) 16.9421 0.659471
\(661\) −0.769647 −0.0299358 −0.0149679 0.999888i \(-0.504765\pi\)
−0.0149679 + 0.999888i \(0.504765\pi\)
\(662\) 62.5271 2.43018
\(663\) 6.79975 0.264080
\(664\) −33.1378 −1.28599
\(665\) −69.8441 −2.70844
\(666\) 26.3415 1.02071
\(667\) −1.16397 −0.0450690
\(668\) 57.0083 2.20572
\(669\) 2.98521 0.115415
\(670\) 80.3281 3.10334
\(671\) 13.8463 0.534529
\(672\) −13.3693 −0.515734
\(673\) 47.5846 1.83425 0.917125 0.398599i \(-0.130503\pi\)
0.917125 + 0.398599i \(0.130503\pi\)
\(674\) 6.37768 0.245659
\(675\) 6.04361 0.232619
\(676\) 54.5191 2.09689
\(677\) −26.1501 −1.00503 −0.502516 0.864568i \(-0.667592\pi\)
−0.502516 + 0.864568i \(0.667592\pi\)
\(678\) 6.54625 0.251407
\(679\) −42.6485 −1.63670
\(680\) −17.9761 −0.689351
\(681\) −8.11099 −0.310814
\(682\) −17.3688 −0.665085
\(683\) −16.6038 −0.635327 −0.317663 0.948204i \(-0.602898\pi\)
−0.317663 + 0.948204i \(0.602898\pi\)
\(684\) −46.5525 −1.77998
\(685\) 40.4926 1.54714
\(686\) −172.445 −6.58397
\(687\) 17.3638 0.662471
\(688\) −0.699938 −0.0266849
\(689\) −71.6126 −2.72822
\(690\) 4.03026 0.153429
\(691\) 12.2928 0.467641 0.233820 0.972280i \(-0.424877\pi\)
0.233820 + 0.972280i \(0.424877\pi\)
\(692\) −12.2061 −0.464006
\(693\) −37.7304 −1.43326
\(694\) 64.9224 2.46442
\(695\) 58.9776 2.23715
\(696\) 2.81013 0.106518
\(697\) −7.18003 −0.271963
\(698\) −2.35439 −0.0891151
\(699\) 13.2100 0.499647
\(700\) 30.6081 1.15688
\(701\) −17.0118 −0.642526 −0.321263 0.946990i \(-0.604107\pi\)
−0.321263 + 0.946990i \(0.604107\pi\)
\(702\) −46.3325 −1.74871
\(703\) 22.4574 0.846998
\(704\) −33.2622 −1.25362
\(705\) 8.05970 0.303546
\(706\) 18.5095 0.696614
\(707\) 57.8308 2.17495
\(708\) 25.8101 0.970004
\(709\) −51.7564 −1.94375 −0.971876 0.235491i \(-0.924330\pi\)
−0.971876 + 0.235491i \(0.924330\pi\)
\(710\) 60.5785 2.27347
\(711\) 23.1293 0.867418
\(712\) −54.8257 −2.05468
\(713\) −2.64100 −0.0989064
\(714\) −15.8637 −0.593685
\(715\) −38.3392 −1.43381
\(716\) 45.1158 1.68606
\(717\) −3.46943 −0.129568
\(718\) −29.6311 −1.10582
\(719\) −26.0533 −0.971625 −0.485813 0.874063i \(-0.661476\pi\)
−0.485813 + 0.874063i \(0.661476\pi\)
\(720\) 9.67346 0.360509
\(721\) 32.3128 1.20339
\(722\) −17.3575 −0.645978
\(723\) 1.09795 0.0408333
\(724\) −3.46144 −0.128644
\(725\) 1.90454 0.0707330
\(726\) −5.00220 −0.185649
\(727\) 48.0771 1.78308 0.891540 0.452942i \(-0.149626\pi\)
0.891540 + 0.452942i \(0.149626\pi\)
\(728\) −102.199 −3.78775
\(729\) −5.99450 −0.222018
\(730\) 53.9646 1.99732
\(731\) 0.915914 0.0338763
\(732\) −11.6707 −0.431361
\(733\) 29.0280 1.07218 0.536088 0.844162i \(-0.319902\pi\)
0.536088 + 0.844162i \(0.319902\pi\)
\(734\) −20.9444 −0.773071
\(735\) 35.7309 1.31795
\(736\) −3.81087 −0.140471
\(737\) 36.9954 1.36274
\(738\) 22.5186 0.828921
\(739\) 23.6526 0.870077 0.435038 0.900412i \(-0.356735\pi\)
0.435038 + 0.900412i \(0.356735\pi\)
\(740\) −39.9153 −1.46732
\(741\) −18.1814 −0.667911
\(742\) 167.071 6.13338
\(743\) 7.90002 0.289824 0.144912 0.989445i \(-0.453710\pi\)
0.144912 + 0.989445i \(0.453710\pi\)
\(744\) 6.37610 0.233759
\(745\) −10.9092 −0.399681
\(746\) 11.6933 0.428122
\(747\) −23.3349 −0.853779
\(748\) −19.0088 −0.695029
\(749\) −57.3328 −2.09489
\(750\) 13.5568 0.495023
\(751\) −11.9975 −0.437794 −0.218897 0.975748i \(-0.570246\pi\)
−0.218897 + 0.975748i \(0.570246\pi\)
\(752\) 6.91050 0.252000
\(753\) −16.8756 −0.614982
\(754\) −14.6009 −0.531734
\(755\) 40.3439 1.46826
\(756\) 69.0926 2.51287
\(757\) −10.8266 −0.393500 −0.196750 0.980454i \(-0.563039\pi\)
−0.196750 + 0.980454i \(0.563039\pi\)
\(758\) −58.4144 −2.12171
\(759\) 1.85615 0.0673741
\(760\) 48.0651 1.74350
\(761\) −11.9901 −0.434639 −0.217320 0.976101i \(-0.569731\pi\)
−0.217320 + 0.976101i \(0.569731\pi\)
\(762\) 22.6068 0.818956
\(763\) −17.6752 −0.639884
\(764\) 78.2123 2.82962
\(765\) −12.6584 −0.457664
\(766\) 74.7421 2.70054
\(767\) −58.4071 −2.10896
\(768\) 16.1118 0.581383
\(769\) 21.8900 0.789373 0.394686 0.918816i \(-0.370853\pi\)
0.394686 + 0.918816i \(0.370853\pi\)
\(770\) 89.4449 3.22337
\(771\) 7.82296 0.281737
\(772\) −75.9507 −2.73353
\(773\) 15.3916 0.553597 0.276798 0.960928i \(-0.410727\pi\)
0.276798 + 0.960928i \(0.410727\pi\)
\(774\) −2.87257 −0.103252
\(775\) 4.32135 0.155227
\(776\) 29.3497 1.05359
\(777\) −15.3416 −0.550378
\(778\) 69.6624 2.49752
\(779\) 19.1982 0.687847
\(780\) 32.3152 1.15707
\(781\) 27.8997 0.998329
\(782\) −4.52188 −0.161702
\(783\) 4.29919 0.153640
\(784\) 30.6361 1.09415
\(785\) 1.45731 0.0520138
\(786\) 33.9563 1.21118
\(787\) 23.5168 0.838285 0.419143 0.907920i \(-0.362331\pi\)
0.419143 + 0.907920i \(0.362331\pi\)
\(788\) −68.9036 −2.45459
\(789\) 3.95839 0.140922
\(790\) −54.8312 −1.95081
\(791\) 22.0910 0.785464
\(792\) 25.9652 0.922632
\(793\) 26.4102 0.937854
\(794\) 44.0863 1.56456
\(795\) −23.0082 −0.816018
\(796\) −16.1763 −0.573353
\(797\) −36.6206 −1.29717 −0.648584 0.761143i \(-0.724639\pi\)
−0.648584 + 0.761143i \(0.724639\pi\)
\(798\) 42.4170 1.50154
\(799\) −9.04285 −0.319913
\(800\) 6.23555 0.220460
\(801\) −38.6071 −1.36411
\(802\) 38.7514 1.36836
\(803\) 24.8536 0.877065
\(804\) −31.1825 −1.09972
\(805\) 13.6005 0.479355
\(806\) −33.1290 −1.16692
\(807\) 3.85040 0.135541
\(808\) −39.7978 −1.40008
\(809\) 2.63889 0.0927784 0.0463892 0.998923i \(-0.485229\pi\)
0.0463892 + 0.998923i \(0.485229\pi\)
\(810\) 31.6659 1.11263
\(811\) 39.0416 1.37093 0.685467 0.728103i \(-0.259598\pi\)
0.685467 + 0.728103i \(0.259598\pi\)
\(812\) 21.7734 0.764097
\(813\) 11.9740 0.419948
\(814\) −28.7598 −1.00803
\(815\) 37.7723 1.32311
\(816\) 1.87317 0.0655740
\(817\) −2.44900 −0.0856798
\(818\) −67.4395 −2.35797
\(819\) −71.9664 −2.51471
\(820\) −34.1224 −1.19161
\(821\) 54.1788 1.89085 0.945426 0.325836i \(-0.105646\pi\)
0.945426 + 0.325836i \(0.105646\pi\)
\(822\) −24.5915 −0.857729
\(823\) −15.2423 −0.531312 −0.265656 0.964068i \(-0.585589\pi\)
−0.265656 + 0.964068i \(0.585589\pi\)
\(824\) −22.2369 −0.774660
\(825\) −3.03714 −0.105739
\(826\) 136.263 4.74120
\(827\) 36.5122 1.26965 0.634827 0.772654i \(-0.281071\pi\)
0.634827 + 0.772654i \(0.281071\pi\)
\(828\) 9.06501 0.315031
\(829\) 5.61321 0.194955 0.0974775 0.995238i \(-0.468923\pi\)
0.0974775 + 0.995238i \(0.468923\pi\)
\(830\) 55.3185 1.92013
\(831\) 3.93354 0.136453
\(832\) −63.4439 −2.19952
\(833\) −40.0894 −1.38902
\(834\) −35.8176 −1.24026
\(835\) −41.4483 −1.43438
\(836\) 50.8263 1.75786
\(837\) 9.75472 0.337172
\(838\) 57.0810 1.97183
\(839\) 22.5889 0.779856 0.389928 0.920845i \(-0.372500\pi\)
0.389928 + 0.920845i \(0.372500\pi\)
\(840\) −32.8353 −1.13293
\(841\) −27.6452 −0.953282
\(842\) 56.8810 1.96025
\(843\) 15.7189 0.541389
\(844\) 63.5157 2.18630
\(845\) −39.6386 −1.36361
\(846\) 28.3609 0.975068
\(847\) −16.8804 −0.580017
\(848\) −19.7276 −0.677448
\(849\) −18.3800 −0.630801
\(850\) 7.39894 0.253782
\(851\) −4.37306 −0.149907
\(852\) −23.5160 −0.805643
\(853\) 25.3916 0.869390 0.434695 0.900578i \(-0.356856\pi\)
0.434695 + 0.900578i \(0.356856\pi\)
\(854\) −61.6147 −2.10841
\(855\) 33.8464 1.15752
\(856\) 39.4551 1.34855
\(857\) 29.8582 1.01994 0.509969 0.860193i \(-0.329657\pi\)
0.509969 + 0.860193i \(0.329657\pi\)
\(858\) 23.2838 0.794895
\(859\) 6.04647 0.206303 0.103152 0.994666i \(-0.467107\pi\)
0.103152 + 0.994666i \(0.467107\pi\)
\(860\) 4.35280 0.148429
\(861\) −13.1151 −0.446962
\(862\) 48.3338 1.64626
\(863\) 46.7367 1.59094 0.795468 0.605996i \(-0.207225\pi\)
0.795468 + 0.605996i \(0.207225\pi\)
\(864\) 14.0757 0.478865
\(865\) 8.87454 0.301743
\(866\) −72.6412 −2.46845
\(867\) 8.84527 0.300401
\(868\) 49.4032 1.67685
\(869\) −25.2527 −0.856640
\(870\) −4.69109 −0.159043
\(871\) 70.5646 2.39099
\(872\) 12.1636 0.411913
\(873\) 20.6674 0.699486
\(874\) 12.0908 0.408976
\(875\) 45.7487 1.54659
\(876\) −20.9485 −0.707784
\(877\) −41.0299 −1.38548 −0.692740 0.721187i \(-0.743597\pi\)
−0.692740 + 0.721187i \(0.743597\pi\)
\(878\) −64.3591 −2.17201
\(879\) −13.2204 −0.445911
\(880\) −10.5615 −0.356029
\(881\) −5.68596 −0.191565 −0.0957824 0.995402i \(-0.530535\pi\)
−0.0957824 + 0.995402i \(0.530535\pi\)
\(882\) 125.732 4.23361
\(883\) 13.1482 0.442471 0.221236 0.975220i \(-0.428991\pi\)
0.221236 + 0.975220i \(0.428991\pi\)
\(884\) −36.2571 −1.21946
\(885\) −18.7655 −0.630794
\(886\) −58.4291 −1.96296
\(887\) 9.89477 0.332234 0.166117 0.986106i \(-0.446877\pi\)
0.166117 + 0.986106i \(0.446877\pi\)
\(888\) 10.5578 0.354295
\(889\) 76.2887 2.55864
\(890\) 91.5233 3.06787
\(891\) 14.5839 0.488578
\(892\) −15.9175 −0.532958
\(893\) 24.1791 0.809122
\(894\) 6.62524 0.221581
\(895\) −32.8018 −1.09644
\(896\) 107.775 3.60050
\(897\) 3.54040 0.118211
\(898\) 29.8239 0.995237
\(899\) 3.07404 0.102525
\(900\) −14.8326 −0.494422
\(901\) 25.8148 0.860017
\(902\) −24.5859 −0.818621
\(903\) 1.67302 0.0556746
\(904\) −15.2025 −0.505627
\(905\) 2.51667 0.0836570
\(906\) −24.5012 −0.813998
\(907\) 13.1332 0.436079 0.218040 0.975940i \(-0.430034\pi\)
0.218040 + 0.975940i \(0.430034\pi\)
\(908\) 43.2487 1.43526
\(909\) −28.0248 −0.929523
\(910\) 170.606 5.65554
\(911\) 11.6950 0.387473 0.193736 0.981054i \(-0.437939\pi\)
0.193736 + 0.981054i \(0.437939\pi\)
\(912\) −5.00854 −0.165849
\(913\) 25.4772 0.843171
\(914\) −97.3930 −3.22147
\(915\) 8.48527 0.280514
\(916\) −92.5860 −3.05913
\(917\) 114.589 3.78405
\(918\) 16.7019 0.551244
\(919\) 2.64499 0.0872502 0.0436251 0.999048i \(-0.486109\pi\)
0.0436251 + 0.999048i \(0.486109\pi\)
\(920\) −9.35955 −0.308575
\(921\) 14.0746 0.463773
\(922\) 1.03826 0.0341934
\(923\) 53.2155 1.75161
\(924\) −34.7216 −1.14226
\(925\) 7.15543 0.235269
\(926\) −6.15630 −0.202309
\(927\) −15.6588 −0.514301
\(928\) 4.43573 0.145610
\(929\) −34.8081 −1.14202 −0.571008 0.820944i \(-0.693447\pi\)
−0.571008 + 0.820944i \(0.693447\pi\)
\(930\) −10.6439 −0.349028
\(931\) 107.192 3.51309
\(932\) −70.4371 −2.30724
\(933\) −11.8178 −0.386898
\(934\) −4.45261 −0.145694
\(935\) 13.8205 0.451978
\(936\) 49.5256 1.61880
\(937\) 34.0629 1.11279 0.556393 0.830919i \(-0.312185\pi\)
0.556393 + 0.830919i \(0.312185\pi\)
\(938\) −164.626 −5.37524
\(939\) 20.4315 0.666756
\(940\) −42.9753 −1.40170
\(941\) −21.3703 −0.696652 −0.348326 0.937373i \(-0.613250\pi\)
−0.348326 + 0.937373i \(0.613250\pi\)
\(942\) −0.885041 −0.0288362
\(943\) −3.73840 −0.121739
\(944\) −16.0898 −0.523678
\(945\) −50.2344 −1.63412
\(946\) 3.13628 0.101969
\(947\) 29.4520 0.957061 0.478531 0.878071i \(-0.341170\pi\)
0.478531 + 0.878071i \(0.341170\pi\)
\(948\) 21.2849 0.691302
\(949\) 47.4055 1.53885
\(950\) −19.7835 −0.641863
\(951\) −11.4097 −0.369984
\(952\) 36.8406 1.19401
\(953\) 19.4500 0.630048 0.315024 0.949084i \(-0.397987\pi\)
0.315024 + 0.949084i \(0.397987\pi\)
\(954\) −80.9626 −2.62126
\(955\) −56.8649 −1.84011
\(956\) 18.4994 0.598313
\(957\) −2.16050 −0.0698391
\(958\) −1.57258 −0.0508077
\(959\) −82.9866 −2.67978
\(960\) −20.3837 −0.657881
\(961\) −24.0251 −0.775003
\(962\) −54.8561 −1.76863
\(963\) 27.7834 0.895307
\(964\) −5.85442 −0.188558
\(965\) 55.2206 1.77761
\(966\) −8.25972 −0.265752
\(967\) −9.95382 −0.320093 −0.160047 0.987109i \(-0.551164\pi\)
−0.160047 + 0.987109i \(0.551164\pi\)
\(968\) 11.6167 0.373375
\(969\) 6.55401 0.210545
\(970\) −48.9949 −1.57313
\(971\) 26.9705 0.865523 0.432762 0.901508i \(-0.357539\pi\)
0.432762 + 0.901508i \(0.357539\pi\)
\(972\) −51.5532 −1.65357
\(973\) −120.870 −3.87492
\(974\) −31.2716 −1.00201
\(975\) −5.79300 −0.185524
\(976\) 7.27539 0.232879
\(977\) −12.4933 −0.399696 −0.199848 0.979827i \(-0.564045\pi\)
−0.199848 + 0.979827i \(0.564045\pi\)
\(978\) −22.9395 −0.733524
\(979\) 42.1514 1.34717
\(980\) −190.521 −6.08597
\(981\) 8.56537 0.273471
\(982\) −26.3567 −0.841077
\(983\) 34.4942 1.10019 0.550097 0.835101i \(-0.314591\pi\)
0.550097 + 0.835101i \(0.314591\pi\)
\(984\) 9.02551 0.287723
\(985\) 50.0969 1.59622
\(986\) 5.26332 0.167618
\(987\) −16.5178 −0.525766
\(988\) 96.9454 3.08424
\(989\) 0.476886 0.0151641
\(990\) −43.3449 −1.37759
\(991\) −39.1610 −1.24399 −0.621995 0.783022i \(-0.713677\pi\)
−0.621995 + 0.783022i \(0.713677\pi\)
\(992\) 10.0645 0.319549
\(993\) 17.6474 0.560024
\(994\) −124.151 −3.93783
\(995\) 11.7611 0.372852
\(996\) −21.4741 −0.680432
\(997\) 60.3891 1.91254 0.956271 0.292482i \(-0.0944813\pi\)
0.956271 + 0.292482i \(0.0944813\pi\)
\(998\) −20.5738 −0.651253
\(999\) 16.1522 0.511033
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 8027.2.a.e.1.18 169
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8027.2.a.e.1.18 169 1.1 even 1 trivial