Properties

Label 8281.2.a.co.1.6
Level $8281$
Weight $2$
Character 8281.1
Self dual yes
Analytic conductor $66.124$
Analytic rank $1$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 8281 = 7^{2} \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8281.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(66.1241179138\)
Analytic rank: \(1\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - 16 x^{10} + 88 x^{8} - 197 x^{6} + 172 x^{4} - 36 x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(-0.180824\) of defining polynomial
Character \(\chi\) \(=\) 8281.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.180824 q^{2} +1.82601 q^{3} -1.96730 q^{4} +2.68664 q^{5} -0.330186 q^{6} +0.717383 q^{8} +0.334323 q^{9} +O(q^{10})\) \(q-0.180824 q^{2} +1.82601 q^{3} -1.96730 q^{4} +2.68664 q^{5} -0.330186 q^{6} +0.717383 q^{8} +0.334323 q^{9} -0.485809 q^{10} -2.69424 q^{11} -3.59232 q^{12} +4.90584 q^{15} +3.80489 q^{16} -4.76493 q^{17} -0.0604535 q^{18} +0.188424 q^{19} -5.28544 q^{20} +0.487183 q^{22} +4.39929 q^{23} +1.30995 q^{24} +2.21804 q^{25} -4.86756 q^{27} +7.08560 q^{29} -0.887093 q^{30} -3.69931 q^{31} -2.12278 q^{32} -4.91972 q^{33} +0.861613 q^{34} -0.657715 q^{36} -7.95413 q^{37} -0.0340716 q^{38} +1.92735 q^{40} +5.42958 q^{41} -8.01065 q^{43} +5.30039 q^{44} +0.898206 q^{45} -0.795496 q^{46} -1.84889 q^{47} +6.94777 q^{48} -0.401075 q^{50} -8.70083 q^{51} -7.07244 q^{53} +0.880171 q^{54} -7.23846 q^{55} +0.344066 q^{57} -1.28125 q^{58} +7.58888 q^{59} -9.65128 q^{60} +0.411564 q^{61} +0.668922 q^{62} -7.22592 q^{64} +0.889602 q^{66} -11.4010 q^{67} +9.37407 q^{68} +8.03315 q^{69} +3.34488 q^{71} +0.239838 q^{72} -14.2158 q^{73} +1.43830 q^{74} +4.05018 q^{75} -0.370688 q^{76} +9.11059 q^{79} +10.2224 q^{80} -9.89120 q^{81} -0.981797 q^{82} +16.5866 q^{83} -12.8017 q^{85} +1.44852 q^{86} +12.9384 q^{87} -1.93280 q^{88} -5.89165 q^{89} -0.162417 q^{90} -8.65473 q^{92} -6.75498 q^{93} +0.334323 q^{94} +0.506229 q^{95} -3.87622 q^{96} -0.451094 q^{97} -0.900747 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 6q^{3} + 8q^{4} + 2q^{9} + O(q^{10}) \) \( 12q - 6q^{3} + 8q^{4} + 2q^{9} - 24q^{10} + 2q^{12} + 16q^{16} - 34q^{17} + 30q^{22} + 6q^{23} - 10q^{25} - 12q^{27} + 2q^{29} + 22q^{30} - 26q^{36} - 38q^{38} - 2q^{40} + 22q^{43} + 38q^{48} + 8q^{51} + 16q^{53} - 30q^{55} + 10q^{61} - 82q^{62} - 2q^{64} - 68q^{66} - 22q^{68} - 14q^{69} + 66q^{74} - 2q^{75} + 70q^{79} - 28q^{81} - 10q^{82} + 20q^{87} - 28q^{88} - 66q^{92} + 2q^{94} + 4q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.180824 −0.127862 −0.0639308 0.997954i \(-0.520364\pi\)
−0.0639308 + 0.997954i \(0.520364\pi\)
\(3\) 1.82601 1.05425 0.527125 0.849788i \(-0.323270\pi\)
0.527125 + 0.849788i \(0.323270\pi\)
\(4\) −1.96730 −0.983651
\(5\) 2.68664 1.20150 0.600751 0.799436i \(-0.294868\pi\)
0.600751 + 0.799436i \(0.294868\pi\)
\(6\) −0.330186 −0.134798
\(7\) 0 0
\(8\) 0.717383 0.253633
\(9\) 0.334323 0.111441
\(10\) −0.485809 −0.153626
\(11\) −2.69424 −0.812345 −0.406172 0.913796i \(-0.633137\pi\)
−0.406172 + 0.913796i \(0.633137\pi\)
\(12\) −3.59232 −1.03701
\(13\) 0 0
\(14\) 0 0
\(15\) 4.90584 1.26668
\(16\) 3.80489 0.951221
\(17\) −4.76493 −1.15567 −0.577833 0.816155i \(-0.696102\pi\)
−0.577833 + 0.816155i \(0.696102\pi\)
\(18\) −0.0604535 −0.0142490
\(19\) 0.188424 0.0432275 0.0216138 0.999766i \(-0.493120\pi\)
0.0216138 + 0.999766i \(0.493120\pi\)
\(20\) −5.28544 −1.18186
\(21\) 0 0
\(22\) 0.487183 0.103868
\(23\) 4.39929 0.917315 0.458657 0.888613i \(-0.348331\pi\)
0.458657 + 0.888613i \(0.348331\pi\)
\(24\) 1.30995 0.267392
\(25\) 2.21804 0.443609
\(26\) 0 0
\(27\) −4.86756 −0.936762
\(28\) 0 0
\(29\) 7.08560 1.31576 0.657882 0.753121i \(-0.271453\pi\)
0.657882 + 0.753121i \(0.271453\pi\)
\(30\) −0.887093 −0.161960
\(31\) −3.69931 −0.664415 −0.332207 0.943206i \(-0.607793\pi\)
−0.332207 + 0.943206i \(0.607793\pi\)
\(32\) −2.12278 −0.375258
\(33\) −4.91972 −0.856414
\(34\) 0.861613 0.147765
\(35\) 0 0
\(36\) −0.657715 −0.109619
\(37\) −7.95413 −1.30765 −0.653826 0.756645i \(-0.726837\pi\)
−0.653826 + 0.756645i \(0.726837\pi\)
\(38\) −0.0340716 −0.00552715
\(39\) 0 0
\(40\) 1.92735 0.304741
\(41\) 5.42958 0.847958 0.423979 0.905672i \(-0.360633\pi\)
0.423979 + 0.905672i \(0.360633\pi\)
\(42\) 0 0
\(43\) −8.01065 −1.22161 −0.610807 0.791780i \(-0.709155\pi\)
−0.610807 + 0.791780i \(0.709155\pi\)
\(44\) 5.30039 0.799064
\(45\) 0.898206 0.133897
\(46\) −0.795496 −0.117289
\(47\) −1.84889 −0.269688 −0.134844 0.990867i \(-0.543053\pi\)
−0.134844 + 0.990867i \(0.543053\pi\)
\(48\) 6.94777 1.00282
\(49\) 0 0
\(50\) −0.401075 −0.0567206
\(51\) −8.70083 −1.21836
\(52\) 0 0
\(53\) −7.07244 −0.971474 −0.485737 0.874105i \(-0.661449\pi\)
−0.485737 + 0.874105i \(0.661449\pi\)
\(54\) 0.880171 0.119776
\(55\) −7.23846 −0.976034
\(56\) 0 0
\(57\) 0.344066 0.0455726
\(58\) −1.28125 −0.168236
\(59\) 7.58888 0.987988 0.493994 0.869465i \(-0.335536\pi\)
0.493994 + 0.869465i \(0.335536\pi\)
\(60\) −9.65128 −1.24597
\(61\) 0.411564 0.0526954 0.0263477 0.999653i \(-0.491612\pi\)
0.0263477 + 0.999653i \(0.491612\pi\)
\(62\) 0.668922 0.0849532
\(63\) 0 0
\(64\) −7.22592 −0.903240
\(65\) 0 0
\(66\) 0.889602 0.109502
\(67\) −11.4010 −1.39286 −0.696429 0.717626i \(-0.745229\pi\)
−0.696429 + 0.717626i \(0.745229\pi\)
\(68\) 9.37407 1.13677
\(69\) 8.03315 0.967078
\(70\) 0 0
\(71\) 3.34488 0.396965 0.198482 0.980104i \(-0.436399\pi\)
0.198482 + 0.980104i \(0.436399\pi\)
\(72\) 0.239838 0.0282651
\(73\) −14.2158 −1.66383 −0.831917 0.554900i \(-0.812756\pi\)
−0.831917 + 0.554900i \(0.812756\pi\)
\(74\) 1.43830 0.167199
\(75\) 4.05018 0.467674
\(76\) −0.370688 −0.0425208
\(77\) 0 0
\(78\) 0 0
\(79\) 9.11059 1.02502 0.512511 0.858681i \(-0.328715\pi\)
0.512511 + 0.858681i \(0.328715\pi\)
\(80\) 10.2224 1.14290
\(81\) −9.89120 −1.09902
\(82\) −0.981797 −0.108421
\(83\) 16.5866 1.82061 0.910307 0.413934i \(-0.135845\pi\)
0.910307 + 0.413934i \(0.135845\pi\)
\(84\) 0 0
\(85\) −12.8017 −1.38854
\(86\) 1.44852 0.156198
\(87\) 12.9384 1.38714
\(88\) −1.93280 −0.206037
\(89\) −5.89165 −0.624513 −0.312257 0.949998i \(-0.601085\pi\)
−0.312257 + 0.949998i \(0.601085\pi\)
\(90\) −0.162417 −0.0171203
\(91\) 0 0
\(92\) −8.65473 −0.902318
\(93\) −6.75498 −0.700459
\(94\) 0.334323 0.0344828
\(95\) 0.506229 0.0519380
\(96\) −3.87622 −0.395615
\(97\) −0.451094 −0.0458016 −0.0229008 0.999738i \(-0.507290\pi\)
−0.0229008 + 0.999738i \(0.507290\pi\)
\(98\) 0 0
\(99\) −0.900747 −0.0905285
\(100\) −4.36356 −0.436356
\(101\) 7.65680 0.761880 0.380940 0.924600i \(-0.375600\pi\)
0.380940 + 0.924600i \(0.375600\pi\)
\(102\) 1.57332 0.155782
\(103\) −5.15740 −0.508173 −0.254087 0.967181i \(-0.581775\pi\)
−0.254087 + 0.967181i \(0.581775\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 1.27887 0.124214
\(107\) 8.03289 0.776569 0.388284 0.921540i \(-0.373068\pi\)
0.388284 + 0.921540i \(0.373068\pi\)
\(108\) 9.57597 0.921448
\(109\) −1.33356 −0.127732 −0.0638660 0.997958i \(-0.520343\pi\)
−0.0638660 + 0.997958i \(0.520343\pi\)
\(110\) 1.30889 0.124797
\(111\) −14.5243 −1.37859
\(112\) 0 0
\(113\) −19.9383 −1.87564 −0.937821 0.347119i \(-0.887160\pi\)
−0.937821 + 0.347119i \(0.887160\pi\)
\(114\) −0.0622152 −0.00582699
\(115\) 11.8193 1.10216
\(116\) −13.9395 −1.29425
\(117\) 0 0
\(118\) −1.37225 −0.126326
\(119\) 0 0
\(120\) 3.51937 0.321273
\(121\) −3.74106 −0.340096
\(122\) −0.0744205 −0.00673772
\(123\) 9.91448 0.893959
\(124\) 7.27765 0.653553
\(125\) −7.47412 −0.668505
\(126\) 0 0
\(127\) −7.96722 −0.706976 −0.353488 0.935439i \(-0.615005\pi\)
−0.353488 + 0.935439i \(0.615005\pi\)
\(128\) 5.55218 0.490748
\(129\) −14.6276 −1.28788
\(130\) 0 0
\(131\) −10.0179 −0.875271 −0.437636 0.899152i \(-0.644184\pi\)
−0.437636 + 0.899152i \(0.644184\pi\)
\(132\) 9.67858 0.842412
\(133\) 0 0
\(134\) 2.06158 0.178093
\(135\) −13.0774 −1.12552
\(136\) −3.41828 −0.293115
\(137\) 5.06696 0.432899 0.216450 0.976294i \(-0.430552\pi\)
0.216450 + 0.976294i \(0.430552\pi\)
\(138\) −1.45259 −0.123652
\(139\) −7.72578 −0.655292 −0.327646 0.944800i \(-0.606255\pi\)
−0.327646 + 0.944800i \(0.606255\pi\)
\(140\) 0 0
\(141\) −3.37610 −0.284319
\(142\) −0.604834 −0.0507566
\(143\) 0 0
\(144\) 1.27206 0.106005
\(145\) 19.0365 1.58089
\(146\) 2.57055 0.212741
\(147\) 0 0
\(148\) 15.6482 1.28627
\(149\) −14.3185 −1.17301 −0.586507 0.809944i \(-0.699498\pi\)
−0.586507 + 0.809944i \(0.699498\pi\)
\(150\) −0.732368 −0.0597976
\(151\) 6.47249 0.526724 0.263362 0.964697i \(-0.415169\pi\)
0.263362 + 0.964697i \(0.415169\pi\)
\(152\) 0.135172 0.0109639
\(153\) −1.59303 −0.128789
\(154\) 0 0
\(155\) −9.93871 −0.798296
\(156\) 0 0
\(157\) −15.9187 −1.27045 −0.635227 0.772326i \(-0.719093\pi\)
−0.635227 + 0.772326i \(0.719093\pi\)
\(158\) −1.64741 −0.131061
\(159\) −12.9144 −1.02418
\(160\) −5.70315 −0.450873
\(161\) 0 0
\(162\) 1.78856 0.140523
\(163\) −4.78162 −0.374525 −0.187263 0.982310i \(-0.559962\pi\)
−0.187263 + 0.982310i \(0.559962\pi\)
\(164\) −10.6816 −0.834095
\(165\) −13.2175 −1.02898
\(166\) −2.99925 −0.232787
\(167\) 2.71042 0.209739 0.104869 0.994486i \(-0.466558\pi\)
0.104869 + 0.994486i \(0.466558\pi\)
\(168\) 0 0
\(169\) 0 0
\(170\) 2.31485 0.177541
\(171\) 0.0629946 0.00481732
\(172\) 15.7594 1.20164
\(173\) 0.899816 0.0684118 0.0342059 0.999415i \(-0.489110\pi\)
0.0342059 + 0.999415i \(0.489110\pi\)
\(174\) −2.33957 −0.177362
\(175\) 0 0
\(176\) −10.2513 −0.772720
\(177\) 13.8574 1.04159
\(178\) 1.06535 0.0798513
\(179\) −11.0558 −0.826351 −0.413175 0.910651i \(-0.635580\pi\)
−0.413175 + 0.910651i \(0.635580\pi\)
\(180\) −1.76704 −0.131708
\(181\) −3.52898 −0.262307 −0.131153 0.991362i \(-0.541868\pi\)
−0.131153 + 0.991362i \(0.541868\pi\)
\(182\) 0 0
\(183\) 0.751521 0.0555540
\(184\) 3.15597 0.232661
\(185\) −21.3699 −1.57115
\(186\) 1.22146 0.0895619
\(187\) 12.8379 0.938799
\(188\) 3.63732 0.265279
\(189\) 0 0
\(190\) −0.0915382 −0.00664088
\(191\) −20.4004 −1.47612 −0.738059 0.674736i \(-0.764258\pi\)
−0.738059 + 0.674736i \(0.764258\pi\)
\(192\) −13.1946 −0.952240
\(193\) 17.2646 1.24273 0.621365 0.783521i \(-0.286578\pi\)
0.621365 + 0.783521i \(0.286578\pi\)
\(194\) 0.0815684 0.00585627
\(195\) 0 0
\(196\) 0 0
\(197\) 4.95672 0.353152 0.176576 0.984287i \(-0.443498\pi\)
0.176576 + 0.984287i \(0.443498\pi\)
\(198\) 0.162877 0.0115751
\(199\) −7.18195 −0.509115 −0.254557 0.967058i \(-0.581930\pi\)
−0.254557 + 0.967058i \(0.581930\pi\)
\(200\) 1.59119 0.112514
\(201\) −20.8184 −1.46842
\(202\) −1.38453 −0.0974153
\(203\) 0 0
\(204\) 17.1172 1.19844
\(205\) 14.5873 1.01882
\(206\) 0.932580 0.0649759
\(207\) 1.47078 0.102226
\(208\) 0 0
\(209\) −0.507661 −0.0351157
\(210\) 0 0
\(211\) −17.5927 −1.21113 −0.605566 0.795795i \(-0.707053\pi\)
−0.605566 + 0.795795i \(0.707053\pi\)
\(212\) 13.9136 0.955592
\(213\) 6.10780 0.418499
\(214\) −1.45254 −0.0992934
\(215\) −21.5218 −1.46777
\(216\) −3.49190 −0.237594
\(217\) 0 0
\(218\) 0.241140 0.0163320
\(219\) −25.9582 −1.75410
\(220\) 14.2403 0.960078
\(221\) 0 0
\(222\) 2.62635 0.176269
\(223\) 14.1054 0.944569 0.472284 0.881446i \(-0.343430\pi\)
0.472284 + 0.881446i \(0.343430\pi\)
\(224\) 0 0
\(225\) 0.741543 0.0494362
\(226\) 3.60533 0.239823
\(227\) 2.86877 0.190407 0.0952035 0.995458i \(-0.469650\pi\)
0.0952035 + 0.995458i \(0.469650\pi\)
\(228\) −0.676881 −0.0448275
\(229\) 8.77411 0.579810 0.289905 0.957055i \(-0.406376\pi\)
0.289905 + 0.957055i \(0.406376\pi\)
\(230\) −2.13721 −0.140924
\(231\) 0 0
\(232\) 5.08309 0.333721
\(233\) 5.10743 0.334599 0.167299 0.985906i \(-0.446495\pi\)
0.167299 + 0.985906i \(0.446495\pi\)
\(234\) 0 0
\(235\) −4.96730 −0.324031
\(236\) −14.9296 −0.971836
\(237\) 16.6361 1.08063
\(238\) 0 0
\(239\) −2.49797 −0.161580 −0.0807901 0.996731i \(-0.525744\pi\)
−0.0807901 + 0.996731i \(0.525744\pi\)
\(240\) 18.6662 1.20490
\(241\) −7.98512 −0.514367 −0.257183 0.966363i \(-0.582794\pi\)
−0.257183 + 0.966363i \(0.582794\pi\)
\(242\) 0.676472 0.0434853
\(243\) −3.45877 −0.221880
\(244\) −0.809671 −0.0518339
\(245\) 0 0
\(246\) −1.79277 −0.114303
\(247\) 0 0
\(248\) −2.65382 −0.168518
\(249\) 30.2873 1.91938
\(250\) 1.35150 0.0854762
\(251\) −25.2570 −1.59421 −0.797105 0.603841i \(-0.793636\pi\)
−0.797105 + 0.603841i \(0.793636\pi\)
\(252\) 0 0
\(253\) −11.8527 −0.745176
\(254\) 1.44066 0.0903952
\(255\) −23.3760 −1.46386
\(256\) 13.4479 0.840493
\(257\) 3.37363 0.210442 0.105221 0.994449i \(-0.466445\pi\)
0.105221 + 0.994449i \(0.466445\pi\)
\(258\) 2.64501 0.164671
\(259\) 0 0
\(260\) 0 0
\(261\) 2.36888 0.146630
\(262\) 1.81148 0.111914
\(263\) −0.158935 −0.00980037 −0.00490019 0.999988i \(-0.501560\pi\)
−0.00490019 + 0.999988i \(0.501560\pi\)
\(264\) −3.52932 −0.217215
\(265\) −19.0011 −1.16723
\(266\) 0 0
\(267\) −10.7582 −0.658392
\(268\) 22.4293 1.37009
\(269\) 23.3266 1.42225 0.711124 0.703066i \(-0.248186\pi\)
0.711124 + 0.703066i \(0.248186\pi\)
\(270\) 2.36470 0.143911
\(271\) 11.8210 0.718074 0.359037 0.933323i \(-0.383105\pi\)
0.359037 + 0.933323i \(0.383105\pi\)
\(272\) −18.1300 −1.09929
\(273\) 0 0
\(274\) −0.916226 −0.0553513
\(275\) −5.97595 −0.360363
\(276\) −15.8036 −0.951268
\(277\) −27.3653 −1.64422 −0.822111 0.569327i \(-0.807204\pi\)
−0.822111 + 0.569327i \(0.807204\pi\)
\(278\) 1.39701 0.0837868
\(279\) −1.23676 −0.0740431
\(280\) 0 0
\(281\) −28.5383 −1.70245 −0.851225 0.524801i \(-0.824140\pi\)
−0.851225 + 0.524801i \(0.824140\pi\)
\(282\) 0.610478 0.0363534
\(283\) −17.9721 −1.06833 −0.534165 0.845380i \(-0.679374\pi\)
−0.534165 + 0.845380i \(0.679374\pi\)
\(284\) −6.58040 −0.390475
\(285\) 0.924381 0.0547556
\(286\) 0 0
\(287\) 0 0
\(288\) −0.709694 −0.0418191
\(289\) 5.70459 0.335564
\(290\) −3.44225 −0.202136
\(291\) −0.823703 −0.0482863
\(292\) 27.9668 1.63663
\(293\) 14.8891 0.869828 0.434914 0.900472i \(-0.356779\pi\)
0.434914 + 0.900472i \(0.356779\pi\)
\(294\) 0 0
\(295\) 20.3886 1.18707
\(296\) −5.70616 −0.331664
\(297\) 13.1144 0.760974
\(298\) 2.58912 0.149984
\(299\) 0 0
\(300\) −7.96793 −0.460028
\(301\) 0 0
\(302\) −1.17038 −0.0673478
\(303\) 13.9814 0.803211
\(304\) 0.716934 0.0411190
\(305\) 1.10572 0.0633136
\(306\) 0.288057 0.0164671
\(307\) −23.5161 −1.34214 −0.671068 0.741396i \(-0.734164\pi\)
−0.671068 + 0.741396i \(0.734164\pi\)
\(308\) 0 0
\(309\) −9.41747 −0.535741
\(310\) 1.79715 0.102072
\(311\) −1.63090 −0.0924799 −0.0462399 0.998930i \(-0.514724\pi\)
−0.0462399 + 0.998930i \(0.514724\pi\)
\(312\) 0 0
\(313\) 0.696734 0.0393817 0.0196909 0.999806i \(-0.493732\pi\)
0.0196909 + 0.999806i \(0.493732\pi\)
\(314\) 2.87849 0.162442
\(315\) 0 0
\(316\) −17.9233 −1.00826
\(317\) 21.4288 1.20356 0.601780 0.798662i \(-0.294458\pi\)
0.601780 + 0.798662i \(0.294458\pi\)
\(318\) 2.33522 0.130953
\(319\) −19.0903 −1.06885
\(320\) −19.4135 −1.08525
\(321\) 14.6682 0.818697
\(322\) 0 0
\(323\) −0.897830 −0.0499566
\(324\) 19.4590 1.08105
\(325\) 0 0
\(326\) 0.864630 0.0478874
\(327\) −2.43510 −0.134661
\(328\) 3.89509 0.215070
\(329\) 0 0
\(330\) 2.39004 0.131568
\(331\) 1.52046 0.0835722 0.0417861 0.999127i \(-0.486695\pi\)
0.0417861 + 0.999127i \(0.486695\pi\)
\(332\) −32.6308 −1.79085
\(333\) −2.65925 −0.145726
\(334\) −0.490108 −0.0268175
\(335\) −30.6305 −1.67352
\(336\) 0 0
\(337\) 32.2304 1.75570 0.877850 0.478936i \(-0.158977\pi\)
0.877850 + 0.478936i \(0.158977\pi\)
\(338\) 0 0
\(339\) −36.4077 −1.97739
\(340\) 25.1848 1.36584
\(341\) 9.96683 0.539734
\(342\) −0.0113909 −0.000615951 0
\(343\) 0 0
\(344\) −5.74670 −0.309841
\(345\) 21.5822 1.16195
\(346\) −0.162708 −0.00874724
\(347\) 8.18431 0.439357 0.219678 0.975572i \(-0.429499\pi\)
0.219678 + 0.975572i \(0.429499\pi\)
\(348\) −25.4538 −1.36446
\(349\) 21.8493 1.16956 0.584782 0.811190i \(-0.301180\pi\)
0.584782 + 0.811190i \(0.301180\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 5.71928 0.304839
\(353\) 0.567179 0.0301879 0.0150940 0.999886i \(-0.495195\pi\)
0.0150940 + 0.999886i \(0.495195\pi\)
\(354\) −2.50575 −0.133179
\(355\) 8.98650 0.476954
\(356\) 11.5907 0.614303
\(357\) 0 0
\(358\) 1.99915 0.105659
\(359\) 32.4043 1.71024 0.855118 0.518434i \(-0.173485\pi\)
0.855118 + 0.518434i \(0.173485\pi\)
\(360\) 0.644358 0.0339606
\(361\) −18.9645 −0.998131
\(362\) 0.638123 0.0335390
\(363\) −6.83122 −0.358546
\(364\) 0 0
\(365\) −38.1928 −1.99910
\(366\) −0.135893 −0.00710323
\(367\) 7.86888 0.410752 0.205376 0.978683i \(-0.434158\pi\)
0.205376 + 0.978683i \(0.434158\pi\)
\(368\) 16.7388 0.872569
\(369\) 1.81523 0.0944973
\(370\) 3.86419 0.200889
\(371\) 0 0
\(372\) 13.2891 0.689007
\(373\) −2.09163 −0.108300 −0.0541502 0.998533i \(-0.517245\pi\)
−0.0541502 + 0.998533i \(0.517245\pi\)
\(374\) −2.32139 −0.120036
\(375\) −13.6478 −0.704771
\(376\) −1.32636 −0.0684018
\(377\) 0 0
\(378\) 0 0
\(379\) −14.3163 −0.735381 −0.367691 0.929948i \(-0.619851\pi\)
−0.367691 + 0.929948i \(0.619851\pi\)
\(380\) −0.995906 −0.0510889
\(381\) −14.5482 −0.745329
\(382\) 3.68887 0.188739
\(383\) 25.1873 1.28701 0.643507 0.765441i \(-0.277479\pi\)
0.643507 + 0.765441i \(0.277479\pi\)
\(384\) 10.1383 0.517370
\(385\) 0 0
\(386\) −3.12184 −0.158898
\(387\) −2.67815 −0.136138
\(388\) 0.887438 0.0450528
\(389\) 28.1023 1.42484 0.712422 0.701752i \(-0.247598\pi\)
0.712422 + 0.701752i \(0.247598\pi\)
\(390\) 0 0
\(391\) −20.9623 −1.06011
\(392\) 0 0
\(393\) −18.2929 −0.922754
\(394\) −0.896292 −0.0451546
\(395\) 24.4769 1.23157
\(396\) 1.77204 0.0890485
\(397\) 21.7765 1.09293 0.546465 0.837482i \(-0.315973\pi\)
0.546465 + 0.837482i \(0.315973\pi\)
\(398\) 1.29867 0.0650963
\(399\) 0 0
\(400\) 8.43941 0.421970
\(401\) 20.5290 1.02517 0.512584 0.858637i \(-0.328688\pi\)
0.512584 + 0.858637i \(0.328688\pi\)
\(402\) 3.76447 0.187754
\(403\) 0 0
\(404\) −15.0632 −0.749424
\(405\) −26.5741 −1.32048
\(406\) 0 0
\(407\) 21.4304 1.06226
\(408\) −6.24182 −0.309016
\(409\) 6.26862 0.309963 0.154982 0.987917i \(-0.450468\pi\)
0.154982 + 0.987917i \(0.450468\pi\)
\(410\) −2.63774 −0.130269
\(411\) 9.25233 0.456384
\(412\) 10.1462 0.499865
\(413\) 0 0
\(414\) −0.265953 −0.0130709
\(415\) 44.5622 2.18747
\(416\) 0 0
\(417\) −14.1074 −0.690841
\(418\) 0.0917972 0.00448995
\(419\) −34.1635 −1.66899 −0.834497 0.551013i \(-0.814242\pi\)
−0.834497 + 0.551013i \(0.814242\pi\)
\(420\) 0 0
\(421\) −11.5233 −0.561613 −0.280806 0.959764i \(-0.590602\pi\)
−0.280806 + 0.959764i \(0.590602\pi\)
\(422\) 3.18118 0.154858
\(423\) −0.618126 −0.0300543
\(424\) −5.07364 −0.246398
\(425\) −10.5688 −0.512664
\(426\) −1.10444 −0.0535101
\(427\) 0 0
\(428\) −15.8031 −0.763873
\(429\) 0 0
\(430\) 3.89164 0.187672
\(431\) −8.77001 −0.422436 −0.211218 0.977439i \(-0.567743\pi\)
−0.211218 + 0.977439i \(0.567743\pi\)
\(432\) −18.5205 −0.891069
\(433\) −22.1069 −1.06239 −0.531196 0.847249i \(-0.678257\pi\)
−0.531196 + 0.847249i \(0.678257\pi\)
\(434\) 0 0
\(435\) 34.7609 1.66666
\(436\) 2.62352 0.125644
\(437\) 0.828933 0.0396533
\(438\) 4.69387 0.224282
\(439\) 10.3709 0.494978 0.247489 0.968891i \(-0.420395\pi\)
0.247489 + 0.968891i \(0.420395\pi\)
\(440\) −5.19275 −0.247555
\(441\) 0 0
\(442\) 0 0
\(443\) 35.8137 1.70156 0.850780 0.525522i \(-0.176130\pi\)
0.850780 + 0.525522i \(0.176130\pi\)
\(444\) 28.5738 1.35605
\(445\) −15.8287 −0.750354
\(446\) −2.55059 −0.120774
\(447\) −26.1457 −1.23665
\(448\) 0 0
\(449\) 22.7502 1.07365 0.536825 0.843693i \(-0.319623\pi\)
0.536825 + 0.843693i \(0.319623\pi\)
\(450\) −0.134089 −0.00632100
\(451\) −14.6286 −0.688834
\(452\) 39.2248 1.84498
\(453\) 11.8188 0.555298
\(454\) −0.518742 −0.0243458
\(455\) 0 0
\(456\) 0.246827 0.0115587
\(457\) −31.3172 −1.46496 −0.732478 0.680791i \(-0.761636\pi\)
−0.732478 + 0.680791i \(0.761636\pi\)
\(458\) −1.58657 −0.0741354
\(459\) 23.1936 1.08258
\(460\) −23.2522 −1.08414
\(461\) 8.40753 0.391578 0.195789 0.980646i \(-0.437273\pi\)
0.195789 + 0.980646i \(0.437273\pi\)
\(462\) 0 0
\(463\) −10.0392 −0.466563 −0.233281 0.972409i \(-0.574946\pi\)
−0.233281 + 0.972409i \(0.574946\pi\)
\(464\) 26.9599 1.25158
\(465\) −18.1482 −0.841603
\(466\) −0.923545 −0.0427824
\(467\) 26.3513 1.21939 0.609696 0.792635i \(-0.291291\pi\)
0.609696 + 0.792635i \(0.291291\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0.898206 0.0414312
\(471\) −29.0678 −1.33937
\(472\) 5.44413 0.250586
\(473\) 21.5826 0.992371
\(474\) −3.00819 −0.138171
\(475\) 0.417934 0.0191761
\(476\) 0 0
\(477\) −2.36448 −0.108262
\(478\) 0.451692 0.0206599
\(479\) −8.58414 −0.392220 −0.196110 0.980582i \(-0.562831\pi\)
−0.196110 + 0.980582i \(0.562831\pi\)
\(480\) −10.4140 −0.475333
\(481\) 0 0
\(482\) 1.44390 0.0657678
\(483\) 0 0
\(484\) 7.35979 0.334536
\(485\) −1.21193 −0.0550308
\(486\) 0.625428 0.0283700
\(487\) −21.2562 −0.963212 −0.481606 0.876388i \(-0.659946\pi\)
−0.481606 + 0.876388i \(0.659946\pi\)
\(488\) 0.295249 0.0133653
\(489\) −8.73130 −0.394843
\(490\) 0 0
\(491\) −22.4535 −1.01331 −0.506657 0.862148i \(-0.669119\pi\)
−0.506657 + 0.862148i \(0.669119\pi\)
\(492\) −19.5048 −0.879344
\(493\) −33.7624 −1.52058
\(494\) 0 0
\(495\) −2.41999 −0.108770
\(496\) −14.0754 −0.632006
\(497\) 0 0
\(498\) −5.47667 −0.245415
\(499\) −38.8780 −1.74042 −0.870210 0.492681i \(-0.836017\pi\)
−0.870210 + 0.492681i \(0.836017\pi\)
\(500\) 14.7039 0.657576
\(501\) 4.94926 0.221117
\(502\) 4.56707 0.203838
\(503\) −5.45701 −0.243316 −0.121658 0.992572i \(-0.538821\pi\)
−0.121658 + 0.992572i \(0.538821\pi\)
\(504\) 0 0
\(505\) 20.5711 0.915401
\(506\) 2.14326 0.0952794
\(507\) 0 0
\(508\) 15.6739 0.695418
\(509\) −10.8925 −0.482800 −0.241400 0.970426i \(-0.577607\pi\)
−0.241400 + 0.970426i \(0.577607\pi\)
\(510\) 4.22694 0.187172
\(511\) 0 0
\(512\) −13.5360 −0.598214
\(513\) −0.917168 −0.0404939
\(514\) −0.610033 −0.0269074
\(515\) −13.8561 −0.610572
\(516\) 28.7768 1.26683
\(517\) 4.98136 0.219080
\(518\) 0 0
\(519\) 1.64308 0.0721230
\(520\) 0 0
\(521\) −27.8961 −1.22215 −0.611074 0.791573i \(-0.709262\pi\)
−0.611074 + 0.791573i \(0.709262\pi\)
\(522\) −0.428350 −0.0187484
\(523\) −16.7236 −0.731272 −0.365636 0.930758i \(-0.619148\pi\)
−0.365636 + 0.930758i \(0.619148\pi\)
\(524\) 19.7083 0.860962
\(525\) 0 0
\(526\) 0.0287393 0.00125309
\(527\) 17.6269 0.767842
\(528\) −18.7190 −0.814639
\(529\) −3.64627 −0.158534
\(530\) 3.43585 0.149244
\(531\) 2.53714 0.110102
\(532\) 0 0
\(533\) 0 0
\(534\) 1.94534 0.0841832
\(535\) 21.5815 0.933049
\(536\) −8.17890 −0.353275
\(537\) −20.1881 −0.871179
\(538\) −4.21800 −0.181851
\(539\) 0 0
\(540\) 25.7272 1.10712
\(541\) −11.1605 −0.479828 −0.239914 0.970794i \(-0.577119\pi\)
−0.239914 + 0.970794i \(0.577119\pi\)
\(542\) −2.13751 −0.0918141
\(543\) −6.44396 −0.276537
\(544\) 10.1149 0.433673
\(545\) −3.58280 −0.153470
\(546\) 0 0
\(547\) 36.6556 1.56728 0.783640 0.621215i \(-0.213361\pi\)
0.783640 + 0.621215i \(0.213361\pi\)
\(548\) −9.96824 −0.425822
\(549\) 0.137595 0.00587242
\(550\) 1.08059 0.0460767
\(551\) 1.33510 0.0568772
\(552\) 5.76285 0.245283
\(553\) 0 0
\(554\) 4.94830 0.210233
\(555\) −39.0217 −1.65638
\(556\) 15.1990 0.644579
\(557\) 33.0776 1.40154 0.700772 0.713386i \(-0.252839\pi\)
0.700772 + 0.713386i \(0.252839\pi\)
\(558\) 0.223636 0.00946727
\(559\) 0 0
\(560\) 0 0
\(561\) 23.4421 0.989728
\(562\) 5.16039 0.217678
\(563\) −17.7967 −0.750043 −0.375021 0.927016i \(-0.622365\pi\)
−0.375021 + 0.927016i \(0.622365\pi\)
\(564\) 6.64180 0.279670
\(565\) −53.5672 −2.25359
\(566\) 3.24978 0.136598
\(567\) 0 0
\(568\) 2.39956 0.100683
\(569\) −8.22094 −0.344640 −0.172320 0.985041i \(-0.555126\pi\)
−0.172320 + 0.985041i \(0.555126\pi\)
\(570\) −0.167150 −0.00700114
\(571\) −25.7553 −1.07782 −0.538912 0.842362i \(-0.681165\pi\)
−0.538912 + 0.842362i \(0.681165\pi\)
\(572\) 0 0
\(573\) −37.2513 −1.55620
\(574\) 0 0
\(575\) 9.75781 0.406929
\(576\) −2.41579 −0.100658
\(577\) −0.769393 −0.0320302 −0.0160151 0.999872i \(-0.505098\pi\)
−0.0160151 + 0.999872i \(0.505098\pi\)
\(578\) −1.03152 −0.0429058
\(579\) 31.5253 1.31015
\(580\) −37.4505 −1.55505
\(581\) 0 0
\(582\) 0.148945 0.00617397
\(583\) 19.0549 0.789172
\(584\) −10.1982 −0.422003
\(585\) 0 0
\(586\) −2.69229 −0.111218
\(587\) −12.0929 −0.499127 −0.249563 0.968358i \(-0.580287\pi\)
−0.249563 + 0.968358i \(0.580287\pi\)
\(588\) 0 0
\(589\) −0.697040 −0.0287210
\(590\) −3.68674 −0.151781
\(591\) 9.05103 0.372310
\(592\) −30.2646 −1.24387
\(593\) −15.9481 −0.654911 −0.327456 0.944867i \(-0.606191\pi\)
−0.327456 + 0.944867i \(0.606191\pi\)
\(594\) −2.37139 −0.0972994
\(595\) 0 0
\(596\) 28.1688 1.15384
\(597\) −13.1143 −0.536734
\(598\) 0 0
\(599\) −7.11022 −0.290516 −0.145258 0.989394i \(-0.546401\pi\)
−0.145258 + 0.989394i \(0.546401\pi\)
\(600\) 2.90553 0.118618
\(601\) −20.7905 −0.848064 −0.424032 0.905647i \(-0.639386\pi\)
−0.424032 + 0.905647i \(0.639386\pi\)
\(602\) 0 0
\(603\) −3.81163 −0.155221
\(604\) −12.7333 −0.518112
\(605\) −10.0509 −0.408626
\(606\) −2.52817 −0.102700
\(607\) 7.71405 0.313104 0.156552 0.987670i \(-0.449962\pi\)
0.156552 + 0.987670i \(0.449962\pi\)
\(608\) −0.399983 −0.0162215
\(609\) 0 0
\(610\) −0.199941 −0.00809539
\(611\) 0 0
\(612\) 3.13397 0.126683
\(613\) −20.4378 −0.825476 −0.412738 0.910850i \(-0.635428\pi\)
−0.412738 + 0.910850i \(0.635428\pi\)
\(614\) 4.25227 0.171608
\(615\) 26.6367 1.07409
\(616\) 0 0
\(617\) −4.59812 −0.185113 −0.0925567 0.995707i \(-0.529504\pi\)
−0.0925567 + 0.995707i \(0.529504\pi\)
\(618\) 1.70290 0.0685008
\(619\) 10.0528 0.404057 0.202028 0.979380i \(-0.435247\pi\)
0.202028 + 0.979380i \(0.435247\pi\)
\(620\) 19.5525 0.785245
\(621\) −21.4138 −0.859306
\(622\) 0.294906 0.0118246
\(623\) 0 0
\(624\) 0 0
\(625\) −31.1705 −1.24682
\(626\) −0.125986 −0.00503541
\(627\) −0.926996 −0.0370207
\(628\) 31.3170 1.24968
\(629\) 37.9009 1.51121
\(630\) 0 0
\(631\) 7.27372 0.289562 0.144781 0.989464i \(-0.453752\pi\)
0.144781 + 0.989464i \(0.453752\pi\)
\(632\) 6.53578 0.259979
\(633\) −32.1245 −1.27684
\(634\) −3.87483 −0.153889
\(635\) −21.4051 −0.849434
\(636\) 25.4065 1.00743
\(637\) 0 0
\(638\) 3.45199 0.136665
\(639\) 1.11827 0.0442381
\(640\) 14.9167 0.589635
\(641\) 3.85033 0.152079 0.0760394 0.997105i \(-0.475773\pi\)
0.0760394 + 0.997105i \(0.475773\pi\)
\(642\) −2.65235 −0.104680
\(643\) −2.87709 −0.113461 −0.0567307 0.998390i \(-0.518068\pi\)
−0.0567307 + 0.998390i \(0.518068\pi\)
\(644\) 0 0
\(645\) −39.2990 −1.54740
\(646\) 0.162349 0.00638754
\(647\) −37.1001 −1.45856 −0.729278 0.684218i \(-0.760144\pi\)
−0.729278 + 0.684218i \(0.760144\pi\)
\(648\) −7.09577 −0.278748
\(649\) −20.4463 −0.802587
\(650\) 0 0
\(651\) 0 0
\(652\) 9.40689 0.368402
\(653\) 20.0950 0.786377 0.393189 0.919458i \(-0.371372\pi\)
0.393189 + 0.919458i \(0.371372\pi\)
\(654\) 0.440324 0.0172180
\(655\) −26.9146 −1.05164
\(656\) 20.6589 0.806596
\(657\) −4.75267 −0.185419
\(658\) 0 0
\(659\) 9.91058 0.386061 0.193031 0.981193i \(-0.438168\pi\)
0.193031 + 0.981193i \(0.438168\pi\)
\(660\) 26.0029 1.01216
\(661\) 47.2266 1.83690 0.918450 0.395537i \(-0.129442\pi\)
0.918450 + 0.395537i \(0.129442\pi\)
\(662\) −0.274936 −0.0106857
\(663\) 0 0
\(664\) 11.8989 0.461768
\(665\) 0 0
\(666\) 0.480855 0.0186328
\(667\) 31.1716 1.20697
\(668\) −5.33222 −0.206310
\(669\) 25.7567 0.995811
\(670\) 5.53872 0.213979
\(671\) −1.10885 −0.0428068
\(672\) 0 0
\(673\) 6.91689 0.266627 0.133313 0.991074i \(-0.457438\pi\)
0.133313 + 0.991074i \(0.457438\pi\)
\(674\) −5.82801 −0.224487
\(675\) −10.7965 −0.415556
\(676\) 0 0
\(677\) 12.3291 0.473844 0.236922 0.971529i \(-0.423861\pi\)
0.236922 + 0.971529i \(0.423861\pi\)
\(678\) 6.58337 0.252833
\(679\) 0 0
\(680\) −9.18369 −0.352179
\(681\) 5.23841 0.200736
\(682\) −1.80224 −0.0690113
\(683\) 24.5364 0.938859 0.469430 0.882970i \(-0.344460\pi\)
0.469430 + 0.882970i \(0.344460\pi\)
\(684\) −0.123930 −0.00473856
\(685\) 13.6131 0.520130
\(686\) 0 0
\(687\) 16.0216 0.611264
\(688\) −30.4796 −1.16202
\(689\) 0 0
\(690\) −3.90258 −0.148569
\(691\) 9.10716 0.346453 0.173226 0.984882i \(-0.444581\pi\)
0.173226 + 0.984882i \(0.444581\pi\)
\(692\) −1.77021 −0.0672933
\(693\) 0 0
\(694\) −1.47992 −0.0561769
\(695\) −20.7564 −0.787336
\(696\) 9.28179 0.351825
\(697\) −25.8716 −0.979956
\(698\) −3.95087 −0.149542
\(699\) 9.32623 0.352750
\(700\) 0 0
\(701\) −0.286950 −0.0108380 −0.00541898 0.999985i \(-0.501725\pi\)
−0.00541898 + 0.999985i \(0.501725\pi\)
\(702\) 0 0
\(703\) −1.49875 −0.0565265
\(704\) 19.4684 0.733742
\(705\) −9.07036 −0.341609
\(706\) −0.102559 −0.00385988
\(707\) 0 0
\(708\) −27.2617 −1.02456
\(709\) 18.5848 0.697967 0.348984 0.937129i \(-0.386527\pi\)
0.348984 + 0.937129i \(0.386527\pi\)
\(710\) −1.62497 −0.0609841
\(711\) 3.04588 0.114229
\(712\) −4.22656 −0.158397
\(713\) −16.2743 −0.609478
\(714\) 0 0
\(715\) 0 0
\(716\) 21.7501 0.812841
\(717\) −4.56132 −0.170346
\(718\) −5.85947 −0.218674
\(719\) −41.6949 −1.55496 −0.777479 0.628909i \(-0.783502\pi\)
−0.777479 + 0.628909i \(0.783502\pi\)
\(720\) 3.41757 0.127365
\(721\) 0 0
\(722\) 3.42923 0.127623
\(723\) −14.5809 −0.542271
\(724\) 6.94257 0.258019
\(725\) 15.7162 0.583684
\(726\) 1.23525 0.0458443
\(727\) 32.7039 1.21292 0.606461 0.795113i \(-0.292589\pi\)
0.606461 + 0.795113i \(0.292589\pi\)
\(728\) 0 0
\(729\) 23.3578 0.865105
\(730\) 6.90616 0.255608
\(731\) 38.1702 1.41178
\(732\) −1.47847 −0.0546458
\(733\) −9.93531 −0.366969 −0.183484 0.983023i \(-0.558738\pi\)
−0.183484 + 0.983023i \(0.558738\pi\)
\(734\) −1.42288 −0.0525195
\(735\) 0 0
\(736\) −9.33871 −0.344230
\(737\) 30.7171 1.13148
\(738\) −0.328237 −0.0120826
\(739\) 10.4022 0.382649 0.191325 0.981527i \(-0.438722\pi\)
0.191325 + 0.981527i \(0.438722\pi\)
\(740\) 42.0411 1.54546
\(741\) 0 0
\(742\) 0 0
\(743\) 1.70863 0.0626837 0.0313419 0.999509i \(-0.490022\pi\)
0.0313419 + 0.999509i \(0.490022\pi\)
\(744\) −4.84590 −0.177659
\(745\) −38.4686 −1.40938
\(746\) 0.378216 0.0138475
\(747\) 5.54528 0.202891
\(748\) −25.2560 −0.923451
\(749\) 0 0
\(750\) 2.46785 0.0901132
\(751\) 29.9812 1.09403 0.547015 0.837123i \(-0.315764\pi\)
0.547015 + 0.837123i \(0.315764\pi\)
\(752\) −7.03481 −0.256533
\(753\) −46.1197 −1.68069
\(754\) 0 0
\(755\) 17.3893 0.632860
\(756\) 0 0
\(757\) 8.40458 0.305470 0.152735 0.988267i \(-0.451192\pi\)
0.152735 + 0.988267i \(0.451192\pi\)
\(758\) 2.58874 0.0940271
\(759\) −21.6433 −0.785601
\(760\) 0.363160 0.0131732
\(761\) −51.0590 −1.85089 −0.925444 0.378885i \(-0.876308\pi\)
−0.925444 + 0.378885i \(0.876308\pi\)
\(762\) 2.63067 0.0952990
\(763\) 0 0
\(764\) 40.1337 1.45199
\(765\) −4.27989 −0.154740
\(766\) −4.55447 −0.164560
\(767\) 0 0
\(768\) 24.5560 0.886088
\(769\) −0.704439 −0.0254027 −0.0127014 0.999919i \(-0.504043\pi\)
−0.0127014 + 0.999919i \(0.504043\pi\)
\(770\) 0 0
\(771\) 6.16030 0.221858
\(772\) −33.9646 −1.22241
\(773\) −1.26521 −0.0455066 −0.0227533 0.999741i \(-0.507243\pi\)
−0.0227533 + 0.999741i \(0.507243\pi\)
\(774\) 0.484272 0.0174068
\(775\) −8.20522 −0.294740
\(776\) −0.323607 −0.0116168
\(777\) 0 0
\(778\) −5.08156 −0.182183
\(779\) 1.02307 0.0366551
\(780\) 0 0
\(781\) −9.01193 −0.322472
\(782\) 3.79048 0.135547
\(783\) −34.4896 −1.23256
\(784\) 0 0
\(785\) −42.7679 −1.52645
\(786\) 3.30779 0.117985
\(787\) −43.7969 −1.56119 −0.780595 0.625037i \(-0.785084\pi\)
−0.780595 + 0.625037i \(0.785084\pi\)
\(788\) −9.75137 −0.347378
\(789\) −0.290218 −0.0103320
\(790\) −4.42600 −0.157470
\(791\) 0 0
\(792\) −0.646180 −0.0229610
\(793\) 0 0
\(794\) −3.93770 −0.139744
\(795\) −34.6963 −1.23055
\(796\) 14.1291 0.500792
\(797\) −13.6837 −0.484700 −0.242350 0.970189i \(-0.577918\pi\)
−0.242350 + 0.970189i \(0.577918\pi\)
\(798\) 0 0
\(799\) 8.80983 0.311669
\(800\) −4.70842 −0.166468
\(801\) −1.96971 −0.0695964
\(802\) −3.71212 −0.131080
\(803\) 38.3008 1.35161
\(804\) 40.9561 1.44441
\(805\) 0 0
\(806\) 0 0
\(807\) 42.5947 1.49940
\(808\) 5.49285 0.193238
\(809\) 9.11375 0.320422 0.160211 0.987083i \(-0.448782\pi\)
0.160211 + 0.987083i \(0.448782\pi\)
\(810\) 4.80523 0.168839
\(811\) −2.31899 −0.0814309 −0.0407154 0.999171i \(-0.512964\pi\)
−0.0407154 + 0.999171i \(0.512964\pi\)
\(812\) 0 0
\(813\) 21.5853 0.757028
\(814\) −3.87512 −0.135823
\(815\) −12.8465 −0.449993
\(816\) −33.1057 −1.15893
\(817\) −1.50940 −0.0528073
\(818\) −1.13352 −0.0396325
\(819\) 0 0
\(820\) −28.6977 −1.00217
\(821\) 10.1447 0.354053 0.177026 0.984206i \(-0.443352\pi\)
0.177026 + 0.984206i \(0.443352\pi\)
\(822\) −1.67304 −0.0583540
\(823\) −26.8178 −0.934811 −0.467405 0.884043i \(-0.654811\pi\)
−0.467405 + 0.884043i \(0.654811\pi\)
\(824\) −3.69983 −0.128890
\(825\) −10.9122 −0.379913
\(826\) 0 0
\(827\) 33.6015 1.16844 0.584219 0.811596i \(-0.301401\pi\)
0.584219 + 0.811596i \(0.301401\pi\)
\(828\) −2.89348 −0.100555
\(829\) −11.8666 −0.412142 −0.206071 0.978537i \(-0.566068\pi\)
−0.206071 + 0.978537i \(0.566068\pi\)
\(830\) −8.05791 −0.279694
\(831\) −49.9694 −1.73342
\(832\) 0 0
\(833\) 0 0
\(834\) 2.55095 0.0883322
\(835\) 7.28193 0.252001
\(836\) 0.998723 0.0345416
\(837\) 18.0066 0.622399
\(838\) 6.17756 0.213400
\(839\) −34.6177 −1.19514 −0.597568 0.801818i \(-0.703866\pi\)
−0.597568 + 0.801818i \(0.703866\pi\)
\(840\) 0 0
\(841\) 21.2058 0.731234
\(842\) 2.08369 0.0718088
\(843\) −52.1112 −1.79481
\(844\) 34.6102 1.19133
\(845\) 0 0
\(846\) 0.111772 0.00384280
\(847\) 0 0
\(848\) −26.9098 −0.924087
\(849\) −32.8173 −1.12629
\(850\) 1.91110 0.0655500
\(851\) −34.9925 −1.19953
\(852\) −12.0159 −0.411658
\(853\) 29.1897 0.999436 0.499718 0.866188i \(-0.333437\pi\)
0.499718 + 0.866188i \(0.333437\pi\)
\(854\) 0 0
\(855\) 0.169244 0.00578802
\(856\) 5.76265 0.196963
\(857\) 25.3198 0.864909 0.432455 0.901656i \(-0.357648\pi\)
0.432455 + 0.901656i \(0.357648\pi\)
\(858\) 0 0
\(859\) −26.0849 −0.890004 −0.445002 0.895530i \(-0.646797\pi\)
−0.445002 + 0.895530i \(0.646797\pi\)
\(860\) 42.3398 1.44378
\(861\) 0 0
\(862\) 1.58583 0.0540134
\(863\) 36.0337 1.22660 0.613302 0.789849i \(-0.289841\pi\)
0.613302 + 0.789849i \(0.289841\pi\)
\(864\) 10.3328 0.351527
\(865\) 2.41748 0.0821969
\(866\) 3.99746 0.135839
\(867\) 10.4166 0.353768
\(868\) 0 0
\(869\) −24.5461 −0.832671
\(870\) −6.28559 −0.213101
\(871\) 0 0
\(872\) −0.956674 −0.0323971
\(873\) −0.150811 −0.00510418
\(874\) −0.149891 −0.00507013
\(875\) 0 0
\(876\) 51.0677 1.72542
\(877\) −9.12168 −0.308017 −0.154009 0.988070i \(-0.549218\pi\)
−0.154009 + 0.988070i \(0.549218\pi\)
\(878\) −1.87531 −0.0632887
\(879\) 27.1876 0.917015
\(880\) −27.5415 −0.928425
\(881\) −13.0331 −0.439095 −0.219548 0.975602i \(-0.570458\pi\)
−0.219548 + 0.975602i \(0.570458\pi\)
\(882\) 0 0
\(883\) 2.13222 0.0717548 0.0358774 0.999356i \(-0.488577\pi\)
0.0358774 + 0.999356i \(0.488577\pi\)
\(884\) 0 0
\(885\) 37.2299 1.25147
\(886\) −6.47597 −0.217564
\(887\) 47.1715 1.58386 0.791932 0.610610i \(-0.209076\pi\)
0.791932 + 0.610610i \(0.209076\pi\)
\(888\) −10.4195 −0.349656
\(889\) 0 0
\(890\) 2.86221 0.0959416
\(891\) 26.6493 0.892785
\(892\) −27.7496 −0.929126
\(893\) −0.348376 −0.0116580
\(894\) 4.72777 0.158120
\(895\) −29.7030 −0.992863
\(896\) 0 0
\(897\) 0 0
\(898\) −4.11378 −0.137279
\(899\) −26.2118 −0.874213
\(900\) −1.45884 −0.0486280
\(901\) 33.6997 1.12270
\(902\) 2.64520 0.0880755
\(903\) 0 0
\(904\) −14.3034 −0.475725
\(905\) −9.48110 −0.315162
\(906\) −2.13713 −0.0710013
\(907\) 16.0431 0.532702 0.266351 0.963876i \(-0.414182\pi\)
0.266351 + 0.963876i \(0.414182\pi\)
\(908\) −5.64374 −0.187294
\(909\) 2.55984 0.0849047
\(910\) 0 0
\(911\) −24.4319 −0.809466 −0.404733 0.914435i \(-0.632636\pi\)
−0.404733 + 0.914435i \(0.632636\pi\)
\(912\) 1.30913 0.0433496
\(913\) −44.6883 −1.47897
\(914\) 5.66289 0.187312
\(915\) 2.01907 0.0667483
\(916\) −17.2613 −0.570331
\(917\) 0 0
\(918\) −4.19395 −0.138421
\(919\) 15.9160 0.525020 0.262510 0.964929i \(-0.415450\pi\)
0.262510 + 0.964929i \(0.415450\pi\)
\(920\) 8.47897 0.279543
\(921\) −42.9407 −1.41494
\(922\) −1.52028 −0.0500678
\(923\) 0 0
\(924\) 0 0
\(925\) −17.6426 −0.580086
\(926\) 1.81533 0.0596555
\(927\) −1.72424 −0.0566314
\(928\) −15.0412 −0.493751
\(929\) −47.3235 −1.55263 −0.776317 0.630342i \(-0.782914\pi\)
−0.776317 + 0.630342i \(0.782914\pi\)
\(930\) 3.28163 0.107609
\(931\) 0 0
\(932\) −10.0479 −0.329129
\(933\) −2.97805 −0.0974968
\(934\) −4.76494 −0.155914
\(935\) 34.4908 1.12797
\(936\) 0 0
\(937\) 29.7044 0.970401 0.485200 0.874403i \(-0.338747\pi\)
0.485200 + 0.874403i \(0.338747\pi\)
\(938\) 0 0
\(939\) 1.27224 0.0415181
\(940\) 9.77219 0.318734
\(941\) 40.4224 1.31773 0.658866 0.752260i \(-0.271036\pi\)
0.658866 + 0.752260i \(0.271036\pi\)
\(942\) 5.25615 0.171255
\(943\) 23.8863 0.777844
\(944\) 28.8748 0.939795
\(945\) 0 0
\(946\) −3.90265 −0.126886
\(947\) −45.9228 −1.49229 −0.746146 0.665783i \(-0.768098\pi\)
−0.746146 + 0.665783i \(0.768098\pi\)
\(948\) −32.7282 −1.06296
\(949\) 0 0
\(950\) −0.0755724 −0.00245189
\(951\) 39.1292 1.26885
\(952\) 0 0
\(953\) 12.3893 0.401329 0.200664 0.979660i \(-0.435690\pi\)
0.200664 + 0.979660i \(0.435690\pi\)
\(954\) 0.427554 0.0138426
\(955\) −54.8085 −1.77356
\(956\) 4.91426 0.158939
\(957\) −34.8592 −1.12684
\(958\) 1.55222 0.0501499
\(959\) 0 0
\(960\) −35.4492 −1.14412
\(961\) −17.3151 −0.558553
\(962\) 0 0
\(963\) 2.68558 0.0865416
\(964\) 15.7091 0.505958
\(965\) 46.3837 1.49314
\(966\) 0 0
\(967\) −9.44932 −0.303870 −0.151935 0.988391i \(-0.548550\pi\)
−0.151935 + 0.988391i \(0.548550\pi\)
\(968\) −2.68377 −0.0862596
\(969\) −1.63945 −0.0526667
\(970\) 0.219145 0.00703633
\(971\) 20.9763 0.673163 0.336581 0.941654i \(-0.390729\pi\)
0.336581 + 0.941654i \(0.390729\pi\)
\(972\) 6.80445 0.218253
\(973\) 0 0
\(974\) 3.84363 0.123158
\(975\) 0 0
\(976\) 1.56595 0.0501249
\(977\) −13.1843 −0.421802 −0.210901 0.977507i \(-0.567640\pi\)
−0.210901 + 0.977507i \(0.567640\pi\)
\(978\) 1.57883 0.0504853
\(979\) 15.8735 0.507320
\(980\) 0 0
\(981\) −0.445840 −0.0142346
\(982\) 4.06013 0.129564
\(983\) 23.3588 0.745032 0.372516 0.928026i \(-0.378495\pi\)
0.372516 + 0.928026i \(0.378495\pi\)
\(984\) 7.11248 0.226738
\(985\) 13.3169 0.424313
\(986\) 6.10505 0.194424
\(987\) 0 0
\(988\) 0 0
\(989\) −35.2412 −1.12060
\(990\) 0.437591 0.0139076
\(991\) 39.4929 1.25453 0.627267 0.778804i \(-0.284173\pi\)
0.627267 + 0.778804i \(0.284173\pi\)
\(992\) 7.85281 0.249327
\(993\) 2.77639 0.0881060
\(994\) 0 0
\(995\) −19.2953 −0.611703
\(996\) −59.5843 −1.88800
\(997\) 51.4791 1.63036 0.815180 0.579208i \(-0.196638\pi\)
0.815180 + 0.579208i \(0.196638\pi\)
\(998\) 7.03007 0.222533
\(999\) 38.7172 1.22496
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 8281.2.a.co.1.6 12
7.3 odd 6 1183.2.e.j.170.7 24
7.5 odd 6 1183.2.e.j.508.7 24
7.6 odd 2 8281.2.a.cp.1.6 12
13.6 odd 12 637.2.q.i.491.4 12
13.11 odd 12 637.2.q.i.589.4 12
13.12 even 2 inner 8281.2.a.co.1.7 12
91.6 even 12 637.2.q.g.491.4 12
91.11 odd 12 637.2.u.g.30.3 12
91.12 odd 6 1183.2.e.j.508.6 24
91.19 even 12 91.2.u.b.88.3 yes 12
91.24 even 12 91.2.u.b.30.3 yes 12
91.32 odd 12 637.2.k.i.569.4 12
91.37 odd 12 637.2.k.i.459.3 12
91.38 odd 6 1183.2.e.j.170.6 24
91.45 even 12 91.2.k.b.23.4 yes 12
91.58 odd 12 637.2.u.g.361.3 12
91.76 even 12 637.2.q.g.589.4 12
91.89 even 12 91.2.k.b.4.3 12
91.90 odd 2 8281.2.a.cp.1.7 12
273.89 odd 12 819.2.bm.f.550.4 12
273.110 odd 12 819.2.do.e.361.4 12
273.206 odd 12 819.2.do.e.667.4 12
273.227 odd 12 819.2.bm.f.478.3 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.2.k.b.4.3 12 91.89 even 12
91.2.k.b.23.4 yes 12 91.45 even 12
91.2.u.b.30.3 yes 12 91.24 even 12
91.2.u.b.88.3 yes 12 91.19 even 12
637.2.k.i.459.3 12 91.37 odd 12
637.2.k.i.569.4 12 91.32 odd 12
637.2.q.g.491.4 12 91.6 even 12
637.2.q.g.589.4 12 91.76 even 12
637.2.q.i.491.4 12 13.6 odd 12
637.2.q.i.589.4 12 13.11 odd 12
637.2.u.g.30.3 12 91.11 odd 12
637.2.u.g.361.3 12 91.58 odd 12
819.2.bm.f.478.3 12 273.227 odd 12
819.2.bm.f.550.4 12 273.89 odd 12
819.2.do.e.361.4 12 273.110 odd 12
819.2.do.e.667.4 12 273.206 odd 12
1183.2.e.j.170.6 24 91.38 odd 6
1183.2.e.j.170.7 24 7.3 odd 6
1183.2.e.j.508.6 24 91.12 odd 6
1183.2.e.j.508.7 24 7.5 odd 6
8281.2.a.co.1.6 12 1.1 even 1 trivial
8281.2.a.co.1.7 12 13.12 even 2 inner
8281.2.a.cp.1.6 12 7.6 odd 2
8281.2.a.cp.1.7 12 91.90 odd 2