Properties

Label 8034.2.a.z.1.2
Level $8034$
Weight $2$
Character 8034.1
Self dual yes
Analytic conductor $64.152$
Analytic rank $0$
Dimension $14$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8034.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(64.1518129839\)
Analytic rank: \(0\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Defining polynomial: \(x^{14} - 3 x^{13} - 36 x^{12} + 108 x^{11} + 434 x^{10} - 1239 x^{9} - 2404 x^{8} + 6204 x^{7} + 6361 x^{6} - 14618 x^{5} - 7015 x^{4} + 15763 x^{3} + 1118 x^{2} - 6316 x + 1552\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(3.65422\) of defining polynomial
Character \(\chi\) \(=\) 8034.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.65422 q^{5} +1.00000 q^{6} -2.98447 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.65422 q^{5} +1.00000 q^{6} -2.98447 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.65422 q^{10} +3.60891 q^{11} -1.00000 q^{12} +1.00000 q^{13} +2.98447 q^{14} +3.65422 q^{15} +1.00000 q^{16} -3.22106 q^{17} -1.00000 q^{18} +3.44921 q^{19} -3.65422 q^{20} +2.98447 q^{21} -3.60891 q^{22} +3.62176 q^{23} +1.00000 q^{24} +8.35335 q^{25} -1.00000 q^{26} -1.00000 q^{27} -2.98447 q^{28} +10.0281 q^{29} -3.65422 q^{30} +10.2641 q^{31} -1.00000 q^{32} -3.60891 q^{33} +3.22106 q^{34} +10.9059 q^{35} +1.00000 q^{36} +1.67832 q^{37} -3.44921 q^{38} -1.00000 q^{39} +3.65422 q^{40} -8.55999 q^{41} -2.98447 q^{42} +5.42205 q^{43} +3.60891 q^{44} -3.65422 q^{45} -3.62176 q^{46} -11.8155 q^{47} -1.00000 q^{48} +1.90705 q^{49} -8.35335 q^{50} +3.22106 q^{51} +1.00000 q^{52} -1.05673 q^{53} +1.00000 q^{54} -13.1878 q^{55} +2.98447 q^{56} -3.44921 q^{57} -10.0281 q^{58} -5.39663 q^{59} +3.65422 q^{60} -6.09399 q^{61} -10.2641 q^{62} -2.98447 q^{63} +1.00000 q^{64} -3.65422 q^{65} +3.60891 q^{66} +0.180935 q^{67} -3.22106 q^{68} -3.62176 q^{69} -10.9059 q^{70} -2.75179 q^{71} -1.00000 q^{72} -6.96603 q^{73} -1.67832 q^{74} -8.35335 q^{75} +3.44921 q^{76} -10.7707 q^{77} +1.00000 q^{78} -10.7353 q^{79} -3.65422 q^{80} +1.00000 q^{81} +8.55999 q^{82} -10.8822 q^{83} +2.98447 q^{84} +11.7705 q^{85} -5.42205 q^{86} -10.0281 q^{87} -3.60891 q^{88} +14.5772 q^{89} +3.65422 q^{90} -2.98447 q^{91} +3.62176 q^{92} -10.2641 q^{93} +11.8155 q^{94} -12.6042 q^{95} +1.00000 q^{96} +4.83370 q^{97} -1.90705 q^{98} +3.60891 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q - 14q^{2} - 14q^{3} + 14q^{4} - 3q^{5} + 14q^{6} + 4q^{7} - 14q^{8} + 14q^{9} + O(q^{10}) \) \( 14q - 14q^{2} - 14q^{3} + 14q^{4} - 3q^{5} + 14q^{6} + 4q^{7} - 14q^{8} + 14q^{9} + 3q^{10} + 5q^{11} - 14q^{12} + 14q^{13} - 4q^{14} + 3q^{15} + 14q^{16} - 7q^{17} - 14q^{18} + 31q^{19} - 3q^{20} - 4q^{21} - 5q^{22} + 14q^{23} + 14q^{24} + 11q^{25} - 14q^{26} - 14q^{27} + 4q^{28} + 9q^{29} - 3q^{30} + 23q^{31} - 14q^{32} - 5q^{33} + 7q^{34} - 2q^{35} + 14q^{36} + 12q^{37} - 31q^{38} - 14q^{39} + 3q^{40} - 5q^{41} + 4q^{42} - 2q^{43} + 5q^{44} - 3q^{45} - 14q^{46} - 11q^{47} - 14q^{48} + 52q^{49} - 11q^{50} + 7q^{51} + 14q^{52} + 6q^{53} + 14q^{54} + 30q^{55} - 4q^{56} - 31q^{57} - 9q^{58} - 4q^{59} + 3q^{60} + 12q^{61} - 23q^{62} + 4q^{63} + 14q^{64} - 3q^{65} + 5q^{66} + 24q^{67} - 7q^{68} - 14q^{69} + 2q^{70} + 20q^{71} - 14q^{72} + 2q^{73} - 12q^{74} - 11q^{75} + 31q^{76} - 28q^{77} + 14q^{78} + 59q^{79} - 3q^{80} + 14q^{81} + 5q^{82} + q^{83} - 4q^{84} - 29q^{85} + 2q^{86} - 9q^{87} - 5q^{88} + 6q^{89} + 3q^{90} + 4q^{91} + 14q^{92} - 23q^{93} + 11q^{94} - 58q^{95} + 14q^{96} - 6q^{97} - 52q^{98} + 5q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −1.00000 −0.577350
\(4\) 1.00000 0.500000
\(5\) −3.65422 −1.63422 −0.817109 0.576483i \(-0.804425\pi\)
−0.817109 + 0.576483i \(0.804425\pi\)
\(6\) 1.00000 0.408248
\(7\) −2.98447 −1.12802 −0.564012 0.825767i \(-0.690743\pi\)
−0.564012 + 0.825767i \(0.690743\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) 3.65422 1.15557
\(11\) 3.60891 1.08813 0.544064 0.839044i \(-0.316885\pi\)
0.544064 + 0.839044i \(0.316885\pi\)
\(12\) −1.00000 −0.288675
\(13\) 1.00000 0.277350
\(14\) 2.98447 0.797633
\(15\) 3.65422 0.943517
\(16\) 1.00000 0.250000
\(17\) −3.22106 −0.781221 −0.390611 0.920556i \(-0.627736\pi\)
−0.390611 + 0.920556i \(0.627736\pi\)
\(18\) −1.00000 −0.235702
\(19\) 3.44921 0.791304 0.395652 0.918401i \(-0.370519\pi\)
0.395652 + 0.918401i \(0.370519\pi\)
\(20\) −3.65422 −0.817109
\(21\) 2.98447 0.651265
\(22\) −3.60891 −0.769423
\(23\) 3.62176 0.755188 0.377594 0.925971i \(-0.376751\pi\)
0.377594 + 0.925971i \(0.376751\pi\)
\(24\) 1.00000 0.204124
\(25\) 8.35335 1.67067
\(26\) −1.00000 −0.196116
\(27\) −1.00000 −0.192450
\(28\) −2.98447 −0.564012
\(29\) 10.0281 1.86216 0.931082 0.364809i \(-0.118866\pi\)
0.931082 + 0.364809i \(0.118866\pi\)
\(30\) −3.65422 −0.667167
\(31\) 10.2641 1.84349 0.921745 0.387798i \(-0.126764\pi\)
0.921745 + 0.387798i \(0.126764\pi\)
\(32\) −1.00000 −0.176777
\(33\) −3.60891 −0.628231
\(34\) 3.22106 0.552407
\(35\) 10.9059 1.84344
\(36\) 1.00000 0.166667
\(37\) 1.67832 0.275913 0.137957 0.990438i \(-0.455947\pi\)
0.137957 + 0.990438i \(0.455947\pi\)
\(38\) −3.44921 −0.559536
\(39\) −1.00000 −0.160128
\(40\) 3.65422 0.577784
\(41\) −8.55999 −1.33685 −0.668423 0.743781i \(-0.733030\pi\)
−0.668423 + 0.743781i \(0.733030\pi\)
\(42\) −2.98447 −0.460514
\(43\) 5.42205 0.826855 0.413428 0.910537i \(-0.364331\pi\)
0.413428 + 0.910537i \(0.364331\pi\)
\(44\) 3.60891 0.544064
\(45\) −3.65422 −0.544740
\(46\) −3.62176 −0.533999
\(47\) −11.8155 −1.72347 −0.861737 0.507355i \(-0.830623\pi\)
−0.861737 + 0.507355i \(0.830623\pi\)
\(48\) −1.00000 −0.144338
\(49\) 1.90705 0.272436
\(50\) −8.35335 −1.18134
\(51\) 3.22106 0.451038
\(52\) 1.00000 0.138675
\(53\) −1.05673 −0.145153 −0.0725767 0.997363i \(-0.523122\pi\)
−0.0725767 + 0.997363i \(0.523122\pi\)
\(54\) 1.00000 0.136083
\(55\) −13.1878 −1.77824
\(56\) 2.98447 0.398816
\(57\) −3.44921 −0.456859
\(58\) −10.0281 −1.31675
\(59\) −5.39663 −0.702582 −0.351291 0.936266i \(-0.614257\pi\)
−0.351291 + 0.936266i \(0.614257\pi\)
\(60\) 3.65422 0.471758
\(61\) −6.09399 −0.780255 −0.390128 0.920761i \(-0.627569\pi\)
−0.390128 + 0.920761i \(0.627569\pi\)
\(62\) −10.2641 −1.30354
\(63\) −2.98447 −0.376008
\(64\) 1.00000 0.125000
\(65\) −3.65422 −0.453251
\(66\) 3.60891 0.444227
\(67\) 0.180935 0.0221047 0.0110524 0.999939i \(-0.496482\pi\)
0.0110524 + 0.999939i \(0.496482\pi\)
\(68\) −3.22106 −0.390611
\(69\) −3.62176 −0.436008
\(70\) −10.9059 −1.30351
\(71\) −2.75179 −0.326577 −0.163288 0.986578i \(-0.552210\pi\)
−0.163288 + 0.986578i \(0.552210\pi\)
\(72\) −1.00000 −0.117851
\(73\) −6.96603 −0.815313 −0.407656 0.913135i \(-0.633654\pi\)
−0.407656 + 0.913135i \(0.633654\pi\)
\(74\) −1.67832 −0.195100
\(75\) −8.35335 −0.964562
\(76\) 3.44921 0.395652
\(77\) −10.7707 −1.22743
\(78\) 1.00000 0.113228
\(79\) −10.7353 −1.20782 −0.603908 0.797054i \(-0.706391\pi\)
−0.603908 + 0.797054i \(0.706391\pi\)
\(80\) −3.65422 −0.408555
\(81\) 1.00000 0.111111
\(82\) 8.55999 0.945293
\(83\) −10.8822 −1.19447 −0.597236 0.802065i \(-0.703734\pi\)
−0.597236 + 0.802065i \(0.703734\pi\)
\(84\) 2.98447 0.325632
\(85\) 11.7705 1.27669
\(86\) −5.42205 −0.584675
\(87\) −10.0281 −1.07512
\(88\) −3.60891 −0.384711
\(89\) 14.5772 1.54518 0.772591 0.634904i \(-0.218960\pi\)
0.772591 + 0.634904i \(0.218960\pi\)
\(90\) 3.65422 0.385189
\(91\) −2.98447 −0.312857
\(92\) 3.62176 0.377594
\(93\) −10.2641 −1.06434
\(94\) 11.8155 1.21868
\(95\) −12.6042 −1.29316
\(96\) 1.00000 0.102062
\(97\) 4.83370 0.490788 0.245394 0.969423i \(-0.421083\pi\)
0.245394 + 0.969423i \(0.421083\pi\)
\(98\) −1.90705 −0.192642
\(99\) 3.60891 0.362709
\(100\) 8.35335 0.835335
\(101\) 19.3390 1.92431 0.962153 0.272510i \(-0.0878538\pi\)
0.962153 + 0.272510i \(0.0878538\pi\)
\(102\) −3.22106 −0.318932
\(103\) −1.00000 −0.0985329
\(104\) −1.00000 −0.0980581
\(105\) −10.9059 −1.06431
\(106\) 1.05673 0.102639
\(107\) −3.71319 −0.358968 −0.179484 0.983761i \(-0.557443\pi\)
−0.179484 + 0.983761i \(0.557443\pi\)
\(108\) −1.00000 −0.0962250
\(109\) 3.22996 0.309374 0.154687 0.987964i \(-0.450563\pi\)
0.154687 + 0.987964i \(0.450563\pi\)
\(110\) 13.1878 1.25741
\(111\) −1.67832 −0.159299
\(112\) −2.98447 −0.282006
\(113\) 10.2893 0.967933 0.483966 0.875087i \(-0.339196\pi\)
0.483966 + 0.875087i \(0.339196\pi\)
\(114\) 3.44921 0.323048
\(115\) −13.2347 −1.23414
\(116\) 10.0281 0.931082
\(117\) 1.00000 0.0924500
\(118\) 5.39663 0.496800
\(119\) 9.61314 0.881236
\(120\) −3.65422 −0.333583
\(121\) 2.02426 0.184023
\(122\) 6.09399 0.551724
\(123\) 8.55999 0.771828
\(124\) 10.2641 0.921745
\(125\) −12.2539 −1.09602
\(126\) 2.98447 0.265878
\(127\) −2.88893 −0.256351 −0.128175 0.991752i \(-0.540912\pi\)
−0.128175 + 0.991752i \(0.540912\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −5.42205 −0.477385
\(130\) 3.65422 0.320497
\(131\) −12.7736 −1.11604 −0.558018 0.829829i \(-0.688438\pi\)
−0.558018 + 0.829829i \(0.688438\pi\)
\(132\) −3.60891 −0.314116
\(133\) −10.2941 −0.892609
\(134\) −0.180935 −0.0156304
\(135\) 3.65422 0.314506
\(136\) 3.22106 0.276203
\(137\) 6.17778 0.527804 0.263902 0.964550i \(-0.414990\pi\)
0.263902 + 0.964550i \(0.414990\pi\)
\(138\) 3.62176 0.308304
\(139\) 21.1507 1.79398 0.896988 0.442056i \(-0.145751\pi\)
0.896988 + 0.442056i \(0.145751\pi\)
\(140\) 10.9059 0.921718
\(141\) 11.8155 0.995048
\(142\) 2.75179 0.230925
\(143\) 3.60891 0.301793
\(144\) 1.00000 0.0833333
\(145\) −36.6448 −3.04318
\(146\) 6.96603 0.576513
\(147\) −1.90705 −0.157291
\(148\) 1.67832 0.137957
\(149\) −18.7861 −1.53901 −0.769507 0.638639i \(-0.779498\pi\)
−0.769507 + 0.638639i \(0.779498\pi\)
\(150\) 8.35335 0.682048
\(151\) −3.44672 −0.280490 −0.140245 0.990117i \(-0.544789\pi\)
−0.140245 + 0.990117i \(0.544789\pi\)
\(152\) −3.44921 −0.279768
\(153\) −3.22106 −0.260407
\(154\) 10.7707 0.867927
\(155\) −37.5074 −3.01266
\(156\) −1.00000 −0.0800641
\(157\) 10.8821 0.868485 0.434243 0.900796i \(-0.357016\pi\)
0.434243 + 0.900796i \(0.357016\pi\)
\(158\) 10.7353 0.854055
\(159\) 1.05673 0.0838044
\(160\) 3.65422 0.288892
\(161\) −10.8090 −0.851870
\(162\) −1.00000 −0.0785674
\(163\) −12.0749 −0.945783 −0.472891 0.881121i \(-0.656790\pi\)
−0.472891 + 0.881121i \(0.656790\pi\)
\(164\) −8.55999 −0.668423
\(165\) 13.1878 1.02667
\(166\) 10.8822 0.844619
\(167\) −8.34086 −0.645435 −0.322718 0.946495i \(-0.604596\pi\)
−0.322718 + 0.946495i \(0.604596\pi\)
\(168\) −2.98447 −0.230257
\(169\) 1.00000 0.0769231
\(170\) −11.7705 −0.902753
\(171\) 3.44921 0.263768
\(172\) 5.42205 0.413428
\(173\) 0.521491 0.0396482 0.0198241 0.999803i \(-0.493689\pi\)
0.0198241 + 0.999803i \(0.493689\pi\)
\(174\) 10.0281 0.760226
\(175\) −24.9303 −1.88455
\(176\) 3.60891 0.272032
\(177\) 5.39663 0.405636
\(178\) −14.5772 −1.09261
\(179\) 0.618878 0.0462571 0.0231286 0.999732i \(-0.492637\pi\)
0.0231286 + 0.999732i \(0.492637\pi\)
\(180\) −3.65422 −0.272370
\(181\) −2.04131 −0.151730 −0.0758648 0.997118i \(-0.524172\pi\)
−0.0758648 + 0.997118i \(0.524172\pi\)
\(182\) 2.98447 0.221224
\(183\) 6.09399 0.450481
\(184\) −3.62176 −0.266999
\(185\) −6.13294 −0.450903
\(186\) 10.2641 0.752601
\(187\) −11.6245 −0.850069
\(188\) −11.8155 −0.861737
\(189\) 2.98447 0.217088
\(190\) 12.6042 0.914404
\(191\) 6.52988 0.472486 0.236243 0.971694i \(-0.424084\pi\)
0.236243 + 0.971694i \(0.424084\pi\)
\(192\) −1.00000 −0.0721688
\(193\) 24.4949 1.76318 0.881590 0.472017i \(-0.156474\pi\)
0.881590 + 0.472017i \(0.156474\pi\)
\(194\) −4.83370 −0.347040
\(195\) 3.65422 0.261684
\(196\) 1.90705 0.136218
\(197\) 9.11126 0.649151 0.324575 0.945860i \(-0.394779\pi\)
0.324575 + 0.945860i \(0.394779\pi\)
\(198\) −3.60891 −0.256474
\(199\) 12.5933 0.892713 0.446356 0.894855i \(-0.352721\pi\)
0.446356 + 0.894855i \(0.352721\pi\)
\(200\) −8.35335 −0.590671
\(201\) −0.180935 −0.0127622
\(202\) −19.3390 −1.36069
\(203\) −29.9284 −2.10056
\(204\) 3.22106 0.225519
\(205\) 31.2801 2.18470
\(206\) 1.00000 0.0696733
\(207\) 3.62176 0.251729
\(208\) 1.00000 0.0693375
\(209\) 12.4479 0.861040
\(210\) 10.9059 0.752580
\(211\) 17.7445 1.22158 0.610791 0.791792i \(-0.290851\pi\)
0.610791 + 0.791792i \(0.290851\pi\)
\(212\) −1.05673 −0.0725767
\(213\) 2.75179 0.188549
\(214\) 3.71319 0.253828
\(215\) −19.8134 −1.35126
\(216\) 1.00000 0.0680414
\(217\) −30.6329 −2.07950
\(218\) −3.22996 −0.218760
\(219\) 6.96603 0.470721
\(220\) −13.1878 −0.889120
\(221\) −3.22106 −0.216672
\(222\) 1.67832 0.112641
\(223\) −3.57710 −0.239540 −0.119770 0.992802i \(-0.538216\pi\)
−0.119770 + 0.992802i \(0.538216\pi\)
\(224\) 2.98447 0.199408
\(225\) 8.35335 0.556890
\(226\) −10.2893 −0.684432
\(227\) −9.58324 −0.636062 −0.318031 0.948080i \(-0.603022\pi\)
−0.318031 + 0.948080i \(0.603022\pi\)
\(228\) −3.44921 −0.228430
\(229\) 1.79903 0.118883 0.0594415 0.998232i \(-0.481068\pi\)
0.0594415 + 0.998232i \(0.481068\pi\)
\(230\) 13.2347 0.872671
\(231\) 10.7707 0.708659
\(232\) −10.0281 −0.658375
\(233\) −11.6052 −0.760281 −0.380140 0.924929i \(-0.624124\pi\)
−0.380140 + 0.924929i \(0.624124\pi\)
\(234\) −1.00000 −0.0653720
\(235\) 43.1766 2.81653
\(236\) −5.39663 −0.351291
\(237\) 10.7353 0.697333
\(238\) −9.61314 −0.623128
\(239\) 13.3711 0.864904 0.432452 0.901657i \(-0.357648\pi\)
0.432452 + 0.901657i \(0.357648\pi\)
\(240\) 3.65422 0.235879
\(241\) −24.8787 −1.60258 −0.801290 0.598276i \(-0.795853\pi\)
−0.801290 + 0.598276i \(0.795853\pi\)
\(242\) −2.02426 −0.130124
\(243\) −1.00000 −0.0641500
\(244\) −6.09399 −0.390128
\(245\) −6.96880 −0.445221
\(246\) −8.55999 −0.545765
\(247\) 3.44921 0.219468
\(248\) −10.2641 −0.651772
\(249\) 10.8822 0.689629
\(250\) 12.2539 0.775004
\(251\) −11.1588 −0.704338 −0.352169 0.935936i \(-0.614556\pi\)
−0.352169 + 0.935936i \(0.614556\pi\)
\(252\) −2.98447 −0.188004
\(253\) 13.0706 0.821742
\(254\) 2.88893 0.181267
\(255\) −11.7705 −0.737095
\(256\) 1.00000 0.0625000
\(257\) 3.46229 0.215972 0.107986 0.994152i \(-0.465560\pi\)
0.107986 + 0.994152i \(0.465560\pi\)
\(258\) 5.42205 0.337562
\(259\) −5.00888 −0.311237
\(260\) −3.65422 −0.226625
\(261\) 10.0281 0.620722
\(262\) 12.7736 0.789156
\(263\) 13.6573 0.842145 0.421073 0.907027i \(-0.361654\pi\)
0.421073 + 0.907027i \(0.361654\pi\)
\(264\) 3.60891 0.222113
\(265\) 3.86154 0.237212
\(266\) 10.2941 0.631170
\(267\) −14.5772 −0.892112
\(268\) 0.180935 0.0110524
\(269\) −5.74928 −0.350540 −0.175270 0.984520i \(-0.556080\pi\)
−0.175270 + 0.984520i \(0.556080\pi\)
\(270\) −3.65422 −0.222389
\(271\) 27.8621 1.69250 0.846251 0.532784i \(-0.178854\pi\)
0.846251 + 0.532784i \(0.178854\pi\)
\(272\) −3.22106 −0.195305
\(273\) 2.98447 0.180628
\(274\) −6.17778 −0.373214
\(275\) 30.1465 1.81790
\(276\) −3.62176 −0.218004
\(277\) −15.1301 −0.909080 −0.454540 0.890726i \(-0.650196\pi\)
−0.454540 + 0.890726i \(0.650196\pi\)
\(278\) −21.1507 −1.26853
\(279\) 10.2641 0.614496
\(280\) −10.9059 −0.651753
\(281\) −12.8516 −0.766660 −0.383330 0.923611i \(-0.625223\pi\)
−0.383330 + 0.923611i \(0.625223\pi\)
\(282\) −11.8155 −0.703605
\(283\) 15.6158 0.928265 0.464133 0.885766i \(-0.346366\pi\)
0.464133 + 0.885766i \(0.346366\pi\)
\(284\) −2.75179 −0.163288
\(285\) 12.6042 0.746608
\(286\) −3.60891 −0.213400
\(287\) 25.5470 1.50799
\(288\) −1.00000 −0.0589256
\(289\) −6.62479 −0.389694
\(290\) 36.6448 2.15186
\(291\) −4.83370 −0.283357
\(292\) −6.96603 −0.407656
\(293\) −0.430891 −0.0251729 −0.0125865 0.999921i \(-0.504006\pi\)
−0.0125865 + 0.999921i \(0.504006\pi\)
\(294\) 1.90705 0.111222
\(295\) 19.7205 1.14817
\(296\) −1.67832 −0.0975501
\(297\) −3.60891 −0.209410
\(298\) 18.7861 1.08825
\(299\) 3.62176 0.209452
\(300\) −8.35335 −0.482281
\(301\) −16.1819 −0.932712
\(302\) 3.44672 0.198336
\(303\) −19.3390 −1.11100
\(304\) 3.44921 0.197826
\(305\) 22.2688 1.27511
\(306\) 3.22106 0.184136
\(307\) 14.2854 0.815310 0.407655 0.913136i \(-0.366347\pi\)
0.407655 + 0.913136i \(0.366347\pi\)
\(308\) −10.7707 −0.613717
\(309\) 1.00000 0.0568880
\(310\) 37.5074 2.13028
\(311\) −24.1330 −1.36846 −0.684229 0.729267i \(-0.739861\pi\)
−0.684229 + 0.729267i \(0.739861\pi\)
\(312\) 1.00000 0.0566139
\(313\) −9.19697 −0.519844 −0.259922 0.965630i \(-0.583697\pi\)
−0.259922 + 0.965630i \(0.583697\pi\)
\(314\) −10.8821 −0.614112
\(315\) 10.9059 0.614479
\(316\) −10.7353 −0.603908
\(317\) −2.36054 −0.132581 −0.0662906 0.997800i \(-0.521116\pi\)
−0.0662906 + 0.997800i \(0.521116\pi\)
\(318\) −1.05673 −0.0592586
\(319\) 36.1904 2.02627
\(320\) −3.65422 −0.204277
\(321\) 3.71319 0.207250
\(322\) 10.8090 0.602363
\(323\) −11.1101 −0.618183
\(324\) 1.00000 0.0555556
\(325\) 8.35335 0.463361
\(326\) 12.0749 0.668770
\(327\) −3.22996 −0.178617
\(328\) 8.55999 0.472646
\(329\) 35.2631 1.94412
\(330\) −13.1878 −0.725963
\(331\) 6.21190 0.341437 0.170718 0.985320i \(-0.445391\pi\)
0.170718 + 0.985320i \(0.445391\pi\)
\(332\) −10.8822 −0.597236
\(333\) 1.67832 0.0919711
\(334\) 8.34086 0.456392
\(335\) −0.661178 −0.0361240
\(336\) 2.98447 0.162816
\(337\) −4.22189 −0.229981 −0.114991 0.993367i \(-0.536684\pi\)
−0.114991 + 0.993367i \(0.536684\pi\)
\(338\) −1.00000 −0.0543928
\(339\) −10.2893 −0.558836
\(340\) 11.7705 0.638343
\(341\) 37.0423 2.00595
\(342\) −3.44921 −0.186512
\(343\) 15.1997 0.820709
\(344\) −5.42205 −0.292338
\(345\) 13.2347 0.712533
\(346\) −0.521491 −0.0280355
\(347\) 8.70941 0.467546 0.233773 0.972291i \(-0.424893\pi\)
0.233773 + 0.972291i \(0.424893\pi\)
\(348\) −10.0281 −0.537561
\(349\) 28.7741 1.54024 0.770122 0.637897i \(-0.220195\pi\)
0.770122 + 0.637897i \(0.220195\pi\)
\(350\) 24.9303 1.33258
\(351\) −1.00000 −0.0533761
\(352\) −3.60891 −0.192356
\(353\) −36.8607 −1.96190 −0.980949 0.194266i \(-0.937767\pi\)
−0.980949 + 0.194266i \(0.937767\pi\)
\(354\) −5.39663 −0.286828
\(355\) 10.0556 0.533698
\(356\) 14.5772 0.772591
\(357\) −9.61314 −0.508782
\(358\) −0.618878 −0.0327087
\(359\) −14.3225 −0.755914 −0.377957 0.925823i \(-0.623373\pi\)
−0.377957 + 0.925823i \(0.623373\pi\)
\(360\) 3.65422 0.192595
\(361\) −7.10293 −0.373839
\(362\) 2.04131 0.107289
\(363\) −2.02426 −0.106246
\(364\) −2.98447 −0.156429
\(365\) 25.4554 1.33240
\(366\) −6.09399 −0.318538
\(367\) −34.5226 −1.80207 −0.901033 0.433751i \(-0.857190\pi\)
−0.901033 + 0.433751i \(0.857190\pi\)
\(368\) 3.62176 0.188797
\(369\) −8.55999 −0.445615
\(370\) 6.13294 0.318836
\(371\) 3.15379 0.163736
\(372\) −10.2641 −0.532169
\(373\) 8.12912 0.420910 0.210455 0.977604i \(-0.432505\pi\)
0.210455 + 0.977604i \(0.432505\pi\)
\(374\) 11.6245 0.601089
\(375\) 12.2539 0.632788
\(376\) 11.8155 0.609340
\(377\) 10.0281 0.516472
\(378\) −2.98447 −0.153505
\(379\) 2.40752 0.123666 0.0618330 0.998087i \(-0.480305\pi\)
0.0618330 + 0.998087i \(0.480305\pi\)
\(380\) −12.6042 −0.646581
\(381\) 2.88893 0.148004
\(382\) −6.52988 −0.334098
\(383\) 1.19419 0.0610202 0.0305101 0.999534i \(-0.490287\pi\)
0.0305101 + 0.999534i \(0.490287\pi\)
\(384\) 1.00000 0.0510310
\(385\) 39.3585 2.00590
\(386\) −24.4949 −1.24676
\(387\) 5.42205 0.275618
\(388\) 4.83370 0.245394
\(389\) 8.39661 0.425725 0.212863 0.977082i \(-0.431721\pi\)
0.212863 + 0.977082i \(0.431721\pi\)
\(390\) −3.65422 −0.185039
\(391\) −11.6659 −0.589969
\(392\) −1.90705 −0.0963208
\(393\) 12.7736 0.644343
\(394\) −9.11126 −0.459019
\(395\) 39.2292 1.97383
\(396\) 3.60891 0.181355
\(397\) 27.5942 1.38491 0.692457 0.721459i \(-0.256528\pi\)
0.692457 + 0.721459i \(0.256528\pi\)
\(398\) −12.5933 −0.631243
\(399\) 10.2941 0.515348
\(400\) 8.35335 0.417668
\(401\) −23.5959 −1.17832 −0.589160 0.808016i \(-0.700541\pi\)
−0.589160 + 0.808016i \(0.700541\pi\)
\(402\) 0.180935 0.00902423
\(403\) 10.2641 0.511292
\(404\) 19.3390 0.962153
\(405\) −3.65422 −0.181580
\(406\) 29.9284 1.48532
\(407\) 6.05690 0.300229
\(408\) −3.22106 −0.159466
\(409\) 29.0562 1.43674 0.718369 0.695662i \(-0.244889\pi\)
0.718369 + 0.695662i \(0.244889\pi\)
\(410\) −31.2801 −1.54482
\(411\) −6.17778 −0.304728
\(412\) −1.00000 −0.0492665
\(413\) 16.1061 0.792529
\(414\) −3.62176 −0.178000
\(415\) 39.7658 1.95203
\(416\) −1.00000 −0.0490290
\(417\) −21.1507 −1.03575
\(418\) −12.4479 −0.608847
\(419\) −1.78495 −0.0872007 −0.0436003 0.999049i \(-0.513883\pi\)
−0.0436003 + 0.999049i \(0.513883\pi\)
\(420\) −10.9059 −0.532154
\(421\) 27.8302 1.35636 0.678180 0.734896i \(-0.262769\pi\)
0.678180 + 0.734896i \(0.262769\pi\)
\(422\) −17.7445 −0.863790
\(423\) −11.8155 −0.574491
\(424\) 1.05673 0.0513195
\(425\) −26.9066 −1.30516
\(426\) −2.75179 −0.133324
\(427\) 18.1873 0.880146
\(428\) −3.71319 −0.179484
\(429\) −3.60891 −0.174240
\(430\) 19.8134 0.955487
\(431\) 19.4588 0.937296 0.468648 0.883385i \(-0.344741\pi\)
0.468648 + 0.883385i \(0.344741\pi\)
\(432\) −1.00000 −0.0481125
\(433\) 13.0229 0.625839 0.312919 0.949780i \(-0.398693\pi\)
0.312919 + 0.949780i \(0.398693\pi\)
\(434\) 30.6329 1.47043
\(435\) 36.6448 1.75698
\(436\) 3.22996 0.154687
\(437\) 12.4922 0.597583
\(438\) −6.96603 −0.332850
\(439\) 34.1765 1.63115 0.815577 0.578649i \(-0.196420\pi\)
0.815577 + 0.578649i \(0.196420\pi\)
\(440\) 13.1878 0.628703
\(441\) 1.90705 0.0908121
\(442\) 3.22106 0.153210
\(443\) −8.66649 −0.411758 −0.205879 0.978578i \(-0.566005\pi\)
−0.205879 + 0.978578i \(0.566005\pi\)
\(444\) −1.67832 −0.0796493
\(445\) −53.2684 −2.52517
\(446\) 3.57710 0.169381
\(447\) 18.7861 0.888550
\(448\) −2.98447 −0.141003
\(449\) −36.3559 −1.71574 −0.857869 0.513868i \(-0.828212\pi\)
−0.857869 + 0.513868i \(0.828212\pi\)
\(450\) −8.35335 −0.393781
\(451\) −30.8923 −1.45466
\(452\) 10.2893 0.483966
\(453\) 3.44672 0.161941
\(454\) 9.58324 0.449764
\(455\) 10.9059 0.511277
\(456\) 3.44921 0.161524
\(457\) −18.0303 −0.843423 −0.421711 0.906730i \(-0.638570\pi\)
−0.421711 + 0.906730i \(0.638570\pi\)
\(458\) −1.79903 −0.0840630
\(459\) 3.22106 0.150346
\(460\) −13.2347 −0.617071
\(461\) −14.6852 −0.683960 −0.341980 0.939707i \(-0.611097\pi\)
−0.341980 + 0.939707i \(0.611097\pi\)
\(462\) −10.7707 −0.501098
\(463\) 3.25879 0.151449 0.0757243 0.997129i \(-0.475873\pi\)
0.0757243 + 0.997129i \(0.475873\pi\)
\(464\) 10.0281 0.465541
\(465\) 37.5074 1.73936
\(466\) 11.6052 0.537600
\(467\) 6.15730 0.284926 0.142463 0.989800i \(-0.454498\pi\)
0.142463 + 0.989800i \(0.454498\pi\)
\(468\) 1.00000 0.0462250
\(469\) −0.539995 −0.0249347
\(470\) −43.1766 −1.99159
\(471\) −10.8821 −0.501420
\(472\) 5.39663 0.248400
\(473\) 19.5677 0.899725
\(474\) −10.7353 −0.493089
\(475\) 28.8125 1.32201
\(476\) 9.61314 0.440618
\(477\) −1.05673 −0.0483845
\(478\) −13.3711 −0.611580
\(479\) −2.77400 −0.126748 −0.0633738 0.997990i \(-0.520186\pi\)
−0.0633738 + 0.997990i \(0.520186\pi\)
\(480\) −3.65422 −0.166792
\(481\) 1.67832 0.0765246
\(482\) 24.8787 1.13320
\(483\) 10.8090 0.491827
\(484\) 2.02426 0.0920117
\(485\) −17.6634 −0.802055
\(486\) 1.00000 0.0453609
\(487\) −8.81991 −0.399668 −0.199834 0.979830i \(-0.564040\pi\)
−0.199834 + 0.979830i \(0.564040\pi\)
\(488\) 6.09399 0.275862
\(489\) 12.0749 0.546048
\(490\) 6.96880 0.314818
\(491\) −6.48893 −0.292841 −0.146421 0.989222i \(-0.546775\pi\)
−0.146421 + 0.989222i \(0.546775\pi\)
\(492\) 8.55999 0.385914
\(493\) −32.3010 −1.45476
\(494\) −3.44921 −0.155187
\(495\) −13.1878 −0.592747
\(496\) 10.2641 0.460872
\(497\) 8.21262 0.368386
\(498\) −10.8822 −0.487641
\(499\) 22.9419 1.02702 0.513511 0.858083i \(-0.328345\pi\)
0.513511 + 0.858083i \(0.328345\pi\)
\(500\) −12.2539 −0.548011
\(501\) 8.34086 0.372642
\(502\) 11.1588 0.498042
\(503\) −3.11600 −0.138936 −0.0694678 0.997584i \(-0.522130\pi\)
−0.0694678 + 0.997584i \(0.522130\pi\)
\(504\) 2.98447 0.132939
\(505\) −70.6692 −3.14474
\(506\) −13.0706 −0.581059
\(507\) −1.00000 −0.0444116
\(508\) −2.88893 −0.128175
\(509\) −30.7411 −1.36258 −0.681289 0.732015i \(-0.738580\pi\)
−0.681289 + 0.732015i \(0.738580\pi\)
\(510\) 11.7705 0.521205
\(511\) 20.7899 0.919692
\(512\) −1.00000 −0.0441942
\(513\) −3.44921 −0.152286
\(514\) −3.46229 −0.152715
\(515\) 3.65422 0.161024
\(516\) −5.42205 −0.238693
\(517\) −42.6413 −1.87536
\(518\) 5.00888 0.220078
\(519\) −0.521491 −0.0228909
\(520\) 3.65422 0.160248
\(521\) −14.4527 −0.633184 −0.316592 0.948562i \(-0.602539\pi\)
−0.316592 + 0.948562i \(0.602539\pi\)
\(522\) −10.0281 −0.438916
\(523\) 8.53779 0.373331 0.186666 0.982423i \(-0.440232\pi\)
0.186666 + 0.982423i \(0.440232\pi\)
\(524\) −12.7736 −0.558018
\(525\) 24.9303 1.08805
\(526\) −13.6573 −0.595487
\(527\) −33.0613 −1.44017
\(528\) −3.60891 −0.157058
\(529\) −9.88288 −0.429691
\(530\) −3.86154 −0.167734
\(531\) −5.39663 −0.234194
\(532\) −10.2941 −0.446304
\(533\) −8.55999 −0.370774
\(534\) 14.5772 0.630818
\(535\) 13.5688 0.586632
\(536\) −0.180935 −0.00781521
\(537\) −0.618878 −0.0267066
\(538\) 5.74928 0.247869
\(539\) 6.88239 0.296446
\(540\) 3.65422 0.157253
\(541\) 32.3463 1.39068 0.695339 0.718682i \(-0.255254\pi\)
0.695339 + 0.718682i \(0.255254\pi\)
\(542\) −27.8621 −1.19678
\(543\) 2.04131 0.0876012
\(544\) 3.22106 0.138102
\(545\) −11.8030 −0.505585
\(546\) −2.98447 −0.127723
\(547\) 31.2297 1.33528 0.667642 0.744482i \(-0.267304\pi\)
0.667642 + 0.744482i \(0.267304\pi\)
\(548\) 6.17778 0.263902
\(549\) −6.09399 −0.260085
\(550\) −30.1465 −1.28545
\(551\) 34.5889 1.47354
\(552\) 3.62176 0.154152
\(553\) 32.0392 1.36244
\(554\) 15.1301 0.642817
\(555\) 6.13294 0.260329
\(556\) 21.1507 0.896988
\(557\) −4.47599 −0.189654 −0.0948269 0.995494i \(-0.530230\pi\)
−0.0948269 + 0.995494i \(0.530230\pi\)
\(558\) −10.2641 −0.434515
\(559\) 5.42205 0.229328
\(560\) 10.9059 0.460859
\(561\) 11.6245 0.490787
\(562\) 12.8516 0.542111
\(563\) −17.1857 −0.724291 −0.362146 0.932122i \(-0.617956\pi\)
−0.362146 + 0.932122i \(0.617956\pi\)
\(564\) 11.8155 0.497524
\(565\) −37.5993 −1.58181
\(566\) −15.6158 −0.656382
\(567\) −2.98447 −0.125336
\(568\) 2.75179 0.115462
\(569\) 22.7396 0.953295 0.476647 0.879095i \(-0.341852\pi\)
0.476647 + 0.879095i \(0.341852\pi\)
\(570\) −12.6042 −0.527932
\(571\) −27.4741 −1.14976 −0.574878 0.818239i \(-0.694950\pi\)
−0.574878 + 0.818239i \(0.694950\pi\)
\(572\) 3.60891 0.150896
\(573\) −6.52988 −0.272790
\(574\) −25.5470 −1.06631
\(575\) 30.2538 1.26167
\(576\) 1.00000 0.0416667
\(577\) 3.03374 0.126296 0.0631480 0.998004i \(-0.479886\pi\)
0.0631480 + 0.998004i \(0.479886\pi\)
\(578\) 6.62479 0.275555
\(579\) −24.4949 −1.01797
\(580\) −36.6448 −1.52159
\(581\) 32.4775 1.34739
\(582\) 4.83370 0.200363
\(583\) −3.81366 −0.157946
\(584\) 6.96603 0.288257
\(585\) −3.65422 −0.151084
\(586\) 0.430891 0.0177999
\(587\) 11.2031 0.462403 0.231202 0.972906i \(-0.425734\pi\)
0.231202 + 0.972906i \(0.425734\pi\)
\(588\) −1.90705 −0.0786456
\(589\) 35.4031 1.45876
\(590\) −19.7205 −0.811880
\(591\) −9.11126 −0.374787
\(592\) 1.67832 0.0689783
\(593\) −32.3805 −1.32971 −0.664854 0.746973i \(-0.731506\pi\)
−0.664854 + 0.746973i \(0.731506\pi\)
\(594\) 3.60891 0.148076
\(595\) −35.1286 −1.44013
\(596\) −18.7861 −0.769507
\(597\) −12.5933 −0.515408
\(598\) −3.62176 −0.148105
\(599\) −6.75671 −0.276072 −0.138036 0.990427i \(-0.544079\pi\)
−0.138036 + 0.990427i \(0.544079\pi\)
\(600\) 8.35335 0.341024
\(601\) −12.4093 −0.506186 −0.253093 0.967442i \(-0.581448\pi\)
−0.253093 + 0.967442i \(0.581448\pi\)
\(602\) 16.1819 0.659527
\(603\) 0.180935 0.00736825
\(604\) −3.44672 −0.140245
\(605\) −7.39709 −0.300735
\(606\) 19.3390 0.785595
\(607\) −25.9148 −1.05185 −0.525925 0.850531i \(-0.676281\pi\)
−0.525925 + 0.850531i \(0.676281\pi\)
\(608\) −3.44921 −0.139884
\(609\) 29.9284 1.21276
\(610\) −22.2688 −0.901637
\(611\) −11.8155 −0.478006
\(612\) −3.22106 −0.130204
\(613\) −23.1794 −0.936209 −0.468104 0.883673i \(-0.655063\pi\)
−0.468104 + 0.883673i \(0.655063\pi\)
\(614\) −14.2854 −0.576511
\(615\) −31.2801 −1.26134
\(616\) 10.7707 0.433963
\(617\) 40.3280 1.62354 0.811771 0.583975i \(-0.198503\pi\)
0.811771 + 0.583975i \(0.198503\pi\)
\(618\) −1.00000 −0.0402259
\(619\) 43.6810 1.75569 0.877844 0.478947i \(-0.158981\pi\)
0.877844 + 0.478947i \(0.158981\pi\)
\(620\) −37.5074 −1.50633
\(621\) −3.62176 −0.145336
\(622\) 24.1330 0.967646
\(623\) −43.5053 −1.74300
\(624\) −1.00000 −0.0400320
\(625\) 3.01172 0.120469
\(626\) 9.19697 0.367585
\(627\) −12.4479 −0.497122
\(628\) 10.8821 0.434243
\(629\) −5.40595 −0.215549
\(630\) −10.9059 −0.434502
\(631\) 14.6223 0.582106 0.291053 0.956707i \(-0.405994\pi\)
0.291053 + 0.956707i \(0.405994\pi\)
\(632\) 10.7353 0.427027
\(633\) −17.7445 −0.705281
\(634\) 2.36054 0.0937491
\(635\) 10.5568 0.418933
\(636\) 1.05673 0.0419022
\(637\) 1.90705 0.0755602
\(638\) −36.1904 −1.43279
\(639\) −2.75179 −0.108859
\(640\) 3.65422 0.144446
\(641\) 28.3955 1.12156 0.560778 0.827966i \(-0.310502\pi\)
0.560778 + 0.827966i \(0.310502\pi\)
\(642\) −3.71319 −0.146548
\(643\) 0.636461 0.0250996 0.0125498 0.999921i \(-0.496005\pi\)
0.0125498 + 0.999921i \(0.496005\pi\)
\(644\) −10.8090 −0.425935
\(645\) 19.8134 0.780152
\(646\) 11.1101 0.437121
\(647\) 17.1375 0.673745 0.336873 0.941550i \(-0.390631\pi\)
0.336873 + 0.941550i \(0.390631\pi\)
\(648\) −1.00000 −0.0392837
\(649\) −19.4760 −0.764499
\(650\) −8.35335 −0.327645
\(651\) 30.6329 1.20060
\(652\) −12.0749 −0.472891
\(653\) 33.3214 1.30397 0.651983 0.758234i \(-0.273937\pi\)
0.651983 + 0.758234i \(0.273937\pi\)
\(654\) 3.22996 0.126301
\(655\) 46.6776 1.82385
\(656\) −8.55999 −0.334211
\(657\) −6.96603 −0.271771
\(658\) −35.2631 −1.37470
\(659\) 27.5855 1.07458 0.537290 0.843398i \(-0.319448\pi\)
0.537290 + 0.843398i \(0.319448\pi\)
\(660\) 13.1878 0.513334
\(661\) −29.5537 −1.14951 −0.574754 0.818327i \(-0.694902\pi\)
−0.574754 + 0.818327i \(0.694902\pi\)
\(662\) −6.21190 −0.241432
\(663\) 3.22106 0.125095
\(664\) 10.8822 0.422310
\(665\) 37.6168 1.45872
\(666\) −1.67832 −0.0650334
\(667\) 36.3192 1.40629
\(668\) −8.34086 −0.322718
\(669\) 3.57710 0.138299
\(670\) 0.661178 0.0255435
\(671\) −21.9927 −0.849018
\(672\) −2.98447 −0.115128
\(673\) 45.7948 1.76526 0.882629 0.470070i \(-0.155771\pi\)
0.882629 + 0.470070i \(0.155771\pi\)
\(674\) 4.22189 0.162621
\(675\) −8.35335 −0.321521
\(676\) 1.00000 0.0384615
\(677\) 47.4498 1.82364 0.911822 0.410586i \(-0.134676\pi\)
0.911822 + 0.410586i \(0.134676\pi\)
\(678\) 10.2893 0.395157
\(679\) −14.4260 −0.553620
\(680\) −11.7705 −0.451377
\(681\) 9.58324 0.367230
\(682\) −37.0423 −1.41842
\(683\) −43.5510 −1.66643 −0.833217 0.552946i \(-0.813504\pi\)
−0.833217 + 0.552946i \(0.813504\pi\)
\(684\) 3.44921 0.131884
\(685\) −22.5750 −0.862547
\(686\) −15.1997 −0.580329
\(687\) −1.79903 −0.0686371
\(688\) 5.42205 0.206714
\(689\) −1.05673 −0.0402583
\(690\) −13.2347 −0.503837
\(691\) −28.3542 −1.07865 −0.539323 0.842099i \(-0.681320\pi\)
−0.539323 + 0.842099i \(0.681320\pi\)
\(692\) 0.521491 0.0198241
\(693\) −10.7707 −0.409145
\(694\) −8.70941 −0.330605
\(695\) −77.2892 −2.93175
\(696\) 10.0281 0.380113
\(697\) 27.5722 1.04437
\(698\) −28.7741 −1.08912
\(699\) 11.6052 0.438948
\(700\) −24.9303 −0.942277
\(701\) 18.4813 0.698029 0.349015 0.937117i \(-0.386516\pi\)
0.349015 + 0.937117i \(0.386516\pi\)
\(702\) 1.00000 0.0377426
\(703\) 5.78887 0.218331
\(704\) 3.60891 0.136016
\(705\) −43.1766 −1.62613
\(706\) 36.8607 1.38727
\(707\) −57.7167 −2.17066
\(708\) 5.39663 0.202818
\(709\) −14.2180 −0.533967 −0.266983 0.963701i \(-0.586027\pi\)
−0.266983 + 0.963701i \(0.586027\pi\)
\(710\) −10.0556 −0.377382
\(711\) −10.7353 −0.402605
\(712\) −14.5772 −0.546305
\(713\) 37.1741 1.39218
\(714\) 9.61314 0.359763
\(715\) −13.1878 −0.493195
\(716\) 0.618878 0.0231286
\(717\) −13.3711 −0.499353
\(718\) 14.3225 0.534512
\(719\) 15.1883 0.566430 0.283215 0.959056i \(-0.408599\pi\)
0.283215 + 0.959056i \(0.408599\pi\)
\(720\) −3.65422 −0.136185
\(721\) 2.98447 0.111147
\(722\) 7.10293 0.264344
\(723\) 24.8787 0.925250
\(724\) −2.04131 −0.0758648
\(725\) 83.7679 3.11106
\(726\) 2.02426 0.0751273
\(727\) −52.9433 −1.96356 −0.981780 0.190023i \(-0.939144\pi\)
−0.981780 + 0.190023i \(0.939144\pi\)
\(728\) 2.98447 0.110612
\(729\) 1.00000 0.0370370
\(730\) −25.4554 −0.942148
\(731\) −17.4647 −0.645957
\(732\) 6.09399 0.225240
\(733\) 6.09050 0.224958 0.112479 0.993654i \(-0.464121\pi\)
0.112479 + 0.993654i \(0.464121\pi\)
\(734\) 34.5226 1.27425
\(735\) 6.96880 0.257048
\(736\) −3.62176 −0.133500
\(737\) 0.652979 0.0240528
\(738\) 8.55999 0.315098
\(739\) 30.0628 1.10588 0.552939 0.833221i \(-0.313506\pi\)
0.552939 + 0.833221i \(0.313506\pi\)
\(740\) −6.13294 −0.225451
\(741\) −3.44921 −0.126710
\(742\) −3.15379 −0.115779
\(743\) 33.9672 1.24614 0.623068 0.782167i \(-0.285886\pi\)
0.623068 + 0.782167i \(0.285886\pi\)
\(744\) 10.2641 0.376301
\(745\) 68.6484 2.51508
\(746\) −8.12912 −0.297628
\(747\) −10.8822 −0.398157
\(748\) −11.6245 −0.425034
\(749\) 11.0819 0.404924
\(750\) −12.2539 −0.447449
\(751\) 19.3629 0.706564 0.353282 0.935517i \(-0.385066\pi\)
0.353282 + 0.935517i \(0.385066\pi\)
\(752\) −11.8155 −0.430868
\(753\) 11.1588 0.406650
\(754\) −10.0281 −0.365201
\(755\) 12.5951 0.458382
\(756\) 2.98447 0.108544
\(757\) 26.6070 0.967047 0.483523 0.875331i \(-0.339357\pi\)
0.483523 + 0.875331i \(0.339357\pi\)
\(758\) −2.40752 −0.0874451
\(759\) −13.0706 −0.474433
\(760\) 12.6042 0.457202
\(761\) −43.0014 −1.55880 −0.779399 0.626527i \(-0.784476\pi\)
−0.779399 + 0.626527i \(0.784476\pi\)
\(762\) −2.88893 −0.104655
\(763\) −9.63972 −0.348981
\(764\) 6.52988 0.236243
\(765\) 11.7705 0.425562
\(766\) −1.19419 −0.0431478
\(767\) −5.39663 −0.194861
\(768\) −1.00000 −0.0360844
\(769\) −22.3786 −0.806992 −0.403496 0.914981i \(-0.632205\pi\)
−0.403496 + 0.914981i \(0.632205\pi\)
\(770\) −39.3585 −1.41838
\(771\) −3.46229 −0.124692
\(772\) 24.4949 0.881590
\(773\) −19.9798 −0.718623 −0.359311 0.933218i \(-0.616988\pi\)
−0.359311 + 0.933218i \(0.616988\pi\)
\(774\) −5.42205 −0.194892
\(775\) 85.7397 3.07986
\(776\) −4.83370 −0.173520
\(777\) 5.00888 0.179693
\(778\) −8.39661 −0.301033
\(779\) −29.5252 −1.05785
\(780\) 3.65422 0.130842
\(781\) −9.93096 −0.355358
\(782\) 11.6659 0.417171
\(783\) −10.0281 −0.358374
\(784\) 1.90705 0.0681091
\(785\) −39.7656 −1.41929
\(786\) −12.7736 −0.455620
\(787\) −8.82544 −0.314593 −0.157297 0.987551i \(-0.550278\pi\)
−0.157297 + 0.987551i \(0.550278\pi\)
\(788\) 9.11126 0.324575
\(789\) −13.6573 −0.486213
\(790\) −39.2292 −1.39571
\(791\) −30.7080 −1.09185
\(792\) −3.60891 −0.128237
\(793\) −6.09399 −0.216404
\(794\) −27.5942 −0.979282
\(795\) −3.86154 −0.136955
\(796\) 12.5933 0.446356
\(797\) 35.3181 1.25103 0.625516 0.780211i \(-0.284888\pi\)
0.625516 + 0.780211i \(0.284888\pi\)
\(798\) −10.2941 −0.364406
\(799\) 38.0585 1.34641
\(800\) −8.35335 −0.295336
\(801\) 14.5772 0.515061
\(802\) 23.5959 0.833199
\(803\) −25.1398 −0.887165
\(804\) −0.180935 −0.00638109
\(805\) 39.4986 1.39214
\(806\) −10.2641 −0.361538
\(807\) 5.74928 0.202384
\(808\) −19.3390 −0.680345
\(809\) −15.2083 −0.534695 −0.267348 0.963600i \(-0.586147\pi\)
−0.267348 + 0.963600i \(0.586147\pi\)
\(810\) 3.65422 0.128396
\(811\) −28.6151 −1.00481 −0.502406 0.864632i \(-0.667552\pi\)
−0.502406 + 0.864632i \(0.667552\pi\)
\(812\) −29.9284 −1.05028
\(813\) −27.8621 −0.977167
\(814\) −6.05690 −0.212294
\(815\) 44.1246 1.54562
\(816\) 3.22106 0.112760
\(817\) 18.7018 0.654294
\(818\) −29.0562 −1.01593
\(819\) −2.98447 −0.104286
\(820\) 31.2801 1.09235
\(821\) 10.5559 0.368402 0.184201 0.982889i \(-0.441030\pi\)
0.184201 + 0.982889i \(0.441030\pi\)
\(822\) 6.17778 0.215475
\(823\) 45.8400 1.59788 0.798942 0.601409i \(-0.205394\pi\)
0.798942 + 0.601409i \(0.205394\pi\)
\(824\) 1.00000 0.0348367
\(825\) −30.1465 −1.04957
\(826\) −16.1061 −0.560402
\(827\) 18.7075 0.650524 0.325262 0.945624i \(-0.394548\pi\)
0.325262 + 0.945624i \(0.394548\pi\)
\(828\) 3.62176 0.125865
\(829\) 25.2491 0.876939 0.438469 0.898746i \(-0.355521\pi\)
0.438469 + 0.898746i \(0.355521\pi\)
\(830\) −39.7658 −1.38029
\(831\) 15.1301 0.524858
\(832\) 1.00000 0.0346688
\(833\) −6.14273 −0.212833
\(834\) 21.1507 0.732387
\(835\) 30.4794 1.05478
\(836\) 12.4479 0.430520
\(837\) −10.2641 −0.354780
\(838\) 1.78495 0.0616602
\(839\) −2.86052 −0.0987561 −0.0493780 0.998780i \(-0.515724\pi\)
−0.0493780 + 0.998780i \(0.515724\pi\)
\(840\) 10.9059 0.376290
\(841\) 71.5621 2.46766
\(842\) −27.8302 −0.959092
\(843\) 12.8516 0.442631
\(844\) 17.7445 0.610791
\(845\) −3.65422 −0.125709
\(846\) 11.8155 0.406227
\(847\) −6.04133 −0.207583
\(848\) −1.05673 −0.0362884
\(849\) −15.6158 −0.535934
\(850\) 26.9066 0.922889
\(851\) 6.07845 0.208367
\(852\) 2.75179 0.0942746
\(853\) 0.732442 0.0250783 0.0125392 0.999921i \(-0.496009\pi\)
0.0125392 + 0.999921i \(0.496009\pi\)
\(854\) −18.1873 −0.622357
\(855\) −12.6042 −0.431054
\(856\) 3.71319 0.126914
\(857\) 7.42670 0.253691 0.126846 0.991922i \(-0.459515\pi\)
0.126846 + 0.991922i \(0.459515\pi\)
\(858\) 3.60891 0.123206
\(859\) −39.9238 −1.36218 −0.681092 0.732198i \(-0.738494\pi\)
−0.681092 + 0.732198i \(0.738494\pi\)
\(860\) −19.8134 −0.675631
\(861\) −25.5470 −0.870640
\(862\) −19.4588 −0.662768
\(863\) 38.5926 1.31371 0.656854 0.754017i \(-0.271887\pi\)
0.656854 + 0.754017i \(0.271887\pi\)
\(864\) 1.00000 0.0340207
\(865\) −1.90564 −0.0647939
\(866\) −13.0229 −0.442535
\(867\) 6.62479 0.224990
\(868\) −30.6329 −1.03975
\(869\) −38.7428 −1.31426
\(870\) −36.6448 −1.24237
\(871\) 0.180935 0.00613075
\(872\) −3.22996 −0.109380
\(873\) 4.83370 0.163596
\(874\) −12.4922 −0.422555
\(875\) 36.5714 1.23634
\(876\) 6.96603 0.235360
\(877\) −39.9231 −1.34811 −0.674053 0.738683i \(-0.735448\pi\)
−0.674053 + 0.738683i \(0.735448\pi\)
\(878\) −34.1765 −1.15340
\(879\) 0.430891 0.0145336
\(880\) −13.1878 −0.444560
\(881\) 38.7918 1.30693 0.653464 0.756958i \(-0.273315\pi\)
0.653464 + 0.756958i \(0.273315\pi\)
\(882\) −1.90705 −0.0642139
\(883\) 32.9394 1.10850 0.554250 0.832350i \(-0.313005\pi\)
0.554250 + 0.832350i \(0.313005\pi\)
\(884\) −3.22106 −0.108336
\(885\) −19.7205 −0.662898
\(886\) 8.66649 0.291157
\(887\) −26.5041 −0.889921 −0.444960 0.895550i \(-0.646782\pi\)
−0.444960 + 0.895550i \(0.646782\pi\)
\(888\) 1.67832 0.0563206
\(889\) 8.62191 0.289170
\(890\) 53.2684 1.78556
\(891\) 3.60891 0.120903
\(892\) −3.57710 −0.119770
\(893\) −40.7543 −1.36379
\(894\) −18.7861 −0.628300
\(895\) −2.26152 −0.0755942
\(896\) 2.98447 0.0997041
\(897\) −3.62176 −0.120927
\(898\) 36.3559 1.21321
\(899\) 102.929 3.43288
\(900\) 8.35335 0.278445
\(901\) 3.40380 0.113397
\(902\) 30.8923 1.02860
\(903\) 16.1819 0.538502
\(904\) −10.2893 −0.342216
\(905\) 7.45942 0.247959
\(906\) −3.44672 −0.114510
\(907\) 10.6403 0.353305 0.176652 0.984273i \(-0.443473\pi\)
0.176652 + 0.984273i \(0.443473\pi\)
\(908\) −9.58324 −0.318031
\(909\) 19.3390 0.641435
\(910\) −10.9059 −0.361528
\(911\) −6.76727 −0.224210 −0.112105 0.993696i \(-0.535759\pi\)
−0.112105 + 0.993696i \(0.535759\pi\)
\(912\) −3.44921 −0.114215
\(913\) −39.2728 −1.29974
\(914\) 18.0303 0.596390
\(915\) −22.2688 −0.736184
\(916\) 1.79903 0.0594415
\(917\) 38.1224 1.25891
\(918\) −3.22106 −0.106311
\(919\) −5.40519 −0.178301 −0.0891504 0.996018i \(-0.528415\pi\)
−0.0891504 + 0.996018i \(0.528415\pi\)
\(920\) 13.2347 0.436335
\(921\) −14.2854 −0.470719
\(922\) 14.6852 0.483632
\(923\) −2.75179 −0.0905761
\(924\) 10.7707 0.354330
\(925\) 14.0196 0.460960
\(926\) −3.25879 −0.107090
\(927\) −1.00000 −0.0328443
\(928\) −10.0281 −0.329187
\(929\) 21.0061 0.689189 0.344595 0.938752i \(-0.388016\pi\)
0.344595 + 0.938752i \(0.388016\pi\)
\(930\) −37.5074 −1.22991
\(931\) 6.57784 0.215580
\(932\) −11.6052 −0.380140
\(933\) 24.1330 0.790079
\(934\) −6.15730 −0.201473
\(935\) 42.4786 1.38920
\(936\) −1.00000 −0.0326860
\(937\) 18.7281 0.611821 0.305910 0.952060i \(-0.401039\pi\)
0.305910 + 0.952060i \(0.401039\pi\)
\(938\) 0.539995 0.0176315
\(939\) 9.19697 0.300132
\(940\) 43.1766 1.40827
\(941\) −2.89919 −0.0945108 −0.0472554 0.998883i \(-0.515047\pi\)
−0.0472554 + 0.998883i \(0.515047\pi\)
\(942\) 10.8821 0.354558
\(943\) −31.0022 −1.00957
\(944\) −5.39663 −0.175645
\(945\) −10.9059 −0.354770
\(946\) −19.5677 −0.636202
\(947\) 24.6654 0.801519 0.400760 0.916183i \(-0.368746\pi\)
0.400760 + 0.916183i \(0.368746\pi\)
\(948\) 10.7353 0.348666
\(949\) −6.96603 −0.226127
\(950\) −28.8125 −0.934800
\(951\) 2.36054 0.0765458
\(952\) −9.61314 −0.311564
\(953\) 30.6857 0.994007 0.497003 0.867749i \(-0.334434\pi\)
0.497003 + 0.867749i \(0.334434\pi\)
\(954\) 1.05673 0.0342130
\(955\) −23.8616 −0.772145
\(956\) 13.3711 0.432452
\(957\) −36.1904 −1.16987
\(958\) 2.77400 0.0896240
\(959\) −18.4374 −0.595375
\(960\) 3.65422 0.117940
\(961\) 74.3520 2.39845
\(962\) −1.67832 −0.0541111
\(963\) −3.71319 −0.119656
\(964\) −24.8787 −0.801290
\(965\) −89.5097 −2.88142
\(966\) −10.8090 −0.347774
\(967\) 11.1796 0.359512 0.179756 0.983711i \(-0.442469\pi\)
0.179756 + 0.983711i \(0.442469\pi\)
\(968\) −2.02426 −0.0650621
\(969\) 11.1101 0.356908
\(970\) 17.6634 0.567139
\(971\) 28.0430 0.899944 0.449972 0.893043i \(-0.351434\pi\)
0.449972 + 0.893043i \(0.351434\pi\)
\(972\) −1.00000 −0.0320750
\(973\) −63.1235 −2.02365
\(974\) 8.81991 0.282608
\(975\) −8.35335 −0.267521
\(976\) −6.09399 −0.195064
\(977\) −6.07447 −0.194339 −0.0971697 0.995268i \(-0.530979\pi\)
−0.0971697 + 0.995268i \(0.530979\pi\)
\(978\) −12.0749 −0.386114
\(979\) 52.6079 1.68136
\(980\) −6.96880 −0.222610
\(981\) 3.22996 0.103125
\(982\) 6.48893 0.207070
\(983\) 45.8073 1.46103 0.730513 0.682899i \(-0.239281\pi\)
0.730513 + 0.682899i \(0.239281\pi\)
\(984\) −8.55999 −0.272883
\(985\) −33.2946 −1.06085
\(986\) 32.3010 1.02867
\(987\) −35.2631 −1.12244
\(988\) 3.44921 0.109734
\(989\) 19.6374 0.624432
\(990\) 13.1878 0.419135
\(991\) 46.5207 1.47778 0.738889 0.673827i \(-0.235351\pi\)
0.738889 + 0.673827i \(0.235351\pi\)
\(992\) −10.2641 −0.325886
\(993\) −6.21190 −0.197129
\(994\) −8.21262 −0.260488
\(995\) −46.0186 −1.45889
\(996\) 10.8822 0.344814
\(997\) −18.0516 −0.571700 −0.285850 0.958274i \(-0.592276\pi\)
−0.285850 + 0.958274i \(0.592276\pi\)
\(998\) −22.9419 −0.726214
\(999\) −1.67832 −0.0530996
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 8034.2.a.z.1.2 14
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8034.2.a.z.1.2 14 1.1 even 1 trivial