Properties

Label 5054.2.a.bk.1.9
Level $5054$
Weight $2$
Character 5054.1
Self dual yes
Analytic conductor $40.356$
Analytic rank $0$
Dimension $9$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 5054 = 2 \cdot 7 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5054.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(40.3563931816\)
Analytic rank: \(0\)
Dimension: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
Defining polynomial: \( x^{9} - 3x^{8} - 15x^{7} + 40x^{6} + 81x^{5} - 162x^{4} - 205x^{3} + 204x^{2} + 210x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 266)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Root \(3.30594\) of defining polynomial
Character \(\chi\) \(=\) 5054.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +3.30594 q^{3} +1.00000 q^{4} +1.60566 q^{5} +3.30594 q^{6} -1.00000 q^{7} +1.00000 q^{8} +7.92924 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +3.30594 q^{3} +1.00000 q^{4} +1.60566 q^{5} +3.30594 q^{6} -1.00000 q^{7} +1.00000 q^{8} +7.92924 q^{9} +1.60566 q^{10} -1.00497 q^{11} +3.30594 q^{12} +3.99407 q^{13} -1.00000 q^{14} +5.30820 q^{15} +1.00000 q^{16} +4.17047 q^{17} +7.92924 q^{18} +1.60566 q^{20} -3.30594 q^{21} -1.00497 q^{22} -3.41425 q^{23} +3.30594 q^{24} -2.42187 q^{25} +3.99407 q^{26} +16.2958 q^{27} -1.00000 q^{28} -9.28749 q^{29} +5.30820 q^{30} +3.52169 q^{31} +1.00000 q^{32} -3.32238 q^{33} +4.17047 q^{34} -1.60566 q^{35} +7.92924 q^{36} +6.29853 q^{37} +13.2042 q^{39} +1.60566 q^{40} -11.8943 q^{41} -3.30594 q^{42} -3.45997 q^{43} -1.00497 q^{44} +12.7316 q^{45} -3.41425 q^{46} -6.77599 q^{47} +3.30594 q^{48} +1.00000 q^{49} -2.42187 q^{50} +13.7873 q^{51} +3.99407 q^{52} -0.844502 q^{53} +16.2958 q^{54} -1.61364 q^{55} -1.00000 q^{56} -9.28749 q^{58} -13.3841 q^{59} +5.30820 q^{60} -2.17110 q^{61} +3.52169 q^{62} -7.92924 q^{63} +1.00000 q^{64} +6.41311 q^{65} -3.32238 q^{66} +1.83197 q^{67} +4.17047 q^{68} -11.2873 q^{69} -1.60566 q^{70} +1.00901 q^{71} +7.92924 q^{72} +4.42347 q^{73} +6.29853 q^{74} -8.00656 q^{75} +1.00497 q^{77} +13.2042 q^{78} +3.58891 q^{79} +1.60566 q^{80} +30.0851 q^{81} -11.8943 q^{82} +9.90796 q^{83} -3.30594 q^{84} +6.69634 q^{85} -3.45997 q^{86} -30.7039 q^{87} -1.00497 q^{88} +0.861489 q^{89} +12.7316 q^{90} -3.99407 q^{91} -3.41425 q^{92} +11.6425 q^{93} -6.77599 q^{94} +3.30594 q^{96} -14.3251 q^{97} +1.00000 q^{98} -7.96868 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9 q + 9 q^{2} + 3 q^{3} + 9 q^{4} + 3 q^{5} + 3 q^{6} - 9 q^{7} + 9 q^{8} + 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 9 q + 9 q^{2} + 3 q^{3} + 9 q^{4} + 3 q^{5} + 3 q^{6} - 9 q^{7} + 9 q^{8} + 12 q^{9} + 3 q^{10} - 3 q^{11} + 3 q^{12} + 12 q^{13} - 9 q^{14} - 6 q^{15} + 9 q^{16} + 12 q^{17} + 12 q^{18} + 3 q^{20} - 3 q^{21} - 3 q^{22} + 6 q^{23} + 3 q^{24} + 12 q^{26} + 24 q^{27} - 9 q^{28} - 6 q^{29} - 6 q^{30} + 9 q^{31} + 9 q^{32} - 3 q^{33} + 12 q^{34} - 3 q^{35} + 12 q^{36} + 9 q^{37} + 33 q^{39} + 3 q^{40} + 3 q^{41} - 3 q^{42} + 21 q^{43} - 3 q^{44} + 18 q^{45} + 6 q^{46} + 21 q^{47} + 3 q^{48} + 9 q^{49} + 39 q^{51} + 12 q^{52} + 24 q^{54} + 24 q^{55} - 9 q^{56} - 6 q^{58} - 9 q^{59} - 6 q^{60} + 6 q^{61} + 9 q^{62} - 12 q^{63} + 9 q^{64} - 3 q^{65} - 3 q^{66} + 27 q^{67} + 12 q^{68} + 6 q^{69} - 3 q^{70} + 9 q^{71} + 12 q^{72} + 51 q^{73} + 9 q^{74} - 3 q^{75} + 3 q^{77} + 33 q^{78} + 24 q^{79} + 3 q^{80} - 3 q^{81} + 3 q^{82} + 9 q^{83} - 3 q^{84} + 6 q^{85} + 21 q^{86} - 3 q^{87} - 3 q^{88} + 9 q^{89} + 18 q^{90} - 12 q^{91} + 6 q^{92} + 3 q^{93} + 21 q^{94} + 3 q^{96} - 12 q^{97} + 9 q^{98} - 15 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 3.30594 1.90869 0.954343 0.298714i \(-0.0965576\pi\)
0.954343 + 0.298714i \(0.0965576\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.60566 0.718071 0.359035 0.933324i \(-0.383106\pi\)
0.359035 + 0.933324i \(0.383106\pi\)
\(6\) 3.30594 1.34964
\(7\) −1.00000 −0.377964
\(8\) 1.00000 0.353553
\(9\) 7.92924 2.64308
\(10\) 1.60566 0.507753
\(11\) −1.00497 −0.303011 −0.151506 0.988456i \(-0.548412\pi\)
−0.151506 + 0.988456i \(0.548412\pi\)
\(12\) 3.30594 0.954343
\(13\) 3.99407 1.10776 0.553878 0.832598i \(-0.313147\pi\)
0.553878 + 0.832598i \(0.313147\pi\)
\(14\) −1.00000 −0.267261
\(15\) 5.30820 1.37057
\(16\) 1.00000 0.250000
\(17\) 4.17047 1.01149 0.505744 0.862684i \(-0.331218\pi\)
0.505744 + 0.862684i \(0.331218\pi\)
\(18\) 7.92924 1.86894
\(19\) 0 0
\(20\) 1.60566 0.359035
\(21\) −3.30594 −0.721415
\(22\) −1.00497 −0.214261
\(23\) −3.41425 −0.711920 −0.355960 0.934501i \(-0.615846\pi\)
−0.355960 + 0.934501i \(0.615846\pi\)
\(24\) 3.30594 0.674822
\(25\) −2.42187 −0.484374
\(26\) 3.99407 0.783302
\(27\) 16.2958 3.13612
\(28\) −1.00000 −0.188982
\(29\) −9.28749 −1.72464 −0.862322 0.506360i \(-0.830991\pi\)
−0.862322 + 0.506360i \(0.830991\pi\)
\(30\) 5.30820 0.969140
\(31\) 3.52169 0.632515 0.316257 0.948673i \(-0.397574\pi\)
0.316257 + 0.948673i \(0.397574\pi\)
\(32\) 1.00000 0.176777
\(33\) −3.32238 −0.578353
\(34\) 4.17047 0.715230
\(35\) −1.60566 −0.271405
\(36\) 7.92924 1.32154
\(37\) 6.29853 1.03547 0.517736 0.855540i \(-0.326775\pi\)
0.517736 + 0.855540i \(0.326775\pi\)
\(38\) 0 0
\(39\) 13.2042 2.11436
\(40\) 1.60566 0.253876
\(41\) −11.8943 −1.85759 −0.928793 0.370600i \(-0.879152\pi\)
−0.928793 + 0.370600i \(0.879152\pi\)
\(42\) −3.30594 −0.510118
\(43\) −3.45997 −0.527640 −0.263820 0.964572i \(-0.584982\pi\)
−0.263820 + 0.964572i \(0.584982\pi\)
\(44\) −1.00497 −0.151506
\(45\) 12.7316 1.89792
\(46\) −3.41425 −0.503404
\(47\) −6.77599 −0.988380 −0.494190 0.869354i \(-0.664535\pi\)
−0.494190 + 0.869354i \(0.664535\pi\)
\(48\) 3.30594 0.477171
\(49\) 1.00000 0.142857
\(50\) −2.42187 −0.342504
\(51\) 13.7873 1.93061
\(52\) 3.99407 0.553878
\(53\) −0.844502 −0.116001 −0.0580006 0.998317i \(-0.518473\pi\)
−0.0580006 + 0.998317i \(0.518473\pi\)
\(54\) 16.2958 2.21757
\(55\) −1.61364 −0.217583
\(56\) −1.00000 −0.133631
\(57\) 0 0
\(58\) −9.28749 −1.21951
\(59\) −13.3841 −1.74247 −0.871234 0.490868i \(-0.836680\pi\)
−0.871234 + 0.490868i \(0.836680\pi\)
\(60\) 5.30820 0.685286
\(61\) −2.17110 −0.277981 −0.138991 0.990294i \(-0.544386\pi\)
−0.138991 + 0.990294i \(0.544386\pi\)
\(62\) 3.52169 0.447255
\(63\) −7.92924 −0.998990
\(64\) 1.00000 0.125000
\(65\) 6.41311 0.795448
\(66\) −3.32238 −0.408957
\(67\) 1.83197 0.223811 0.111905 0.993719i \(-0.464305\pi\)
0.111905 + 0.993719i \(0.464305\pi\)
\(68\) 4.17047 0.505744
\(69\) −11.2873 −1.35883
\(70\) −1.60566 −0.191913
\(71\) 1.00901 0.119748 0.0598738 0.998206i \(-0.480930\pi\)
0.0598738 + 0.998206i \(0.480930\pi\)
\(72\) 7.92924 0.934470
\(73\) 4.42347 0.517728 0.258864 0.965914i \(-0.416652\pi\)
0.258864 + 0.965914i \(0.416652\pi\)
\(74\) 6.29853 0.732189
\(75\) −8.00656 −0.924518
\(76\) 0 0
\(77\) 1.00497 0.114527
\(78\) 13.2042 1.49508
\(79\) 3.58891 0.403783 0.201892 0.979408i \(-0.435291\pi\)
0.201892 + 0.979408i \(0.435291\pi\)
\(80\) 1.60566 0.179518
\(81\) 30.0851 3.34279
\(82\) −11.8943 −1.31351
\(83\) 9.90796 1.08754 0.543770 0.839234i \(-0.316996\pi\)
0.543770 + 0.839234i \(0.316996\pi\)
\(84\) −3.30594 −0.360708
\(85\) 6.69634 0.726320
\(86\) −3.45997 −0.373098
\(87\) −30.7039 −3.29180
\(88\) −1.00497 −0.107131
\(89\) 0.861489 0.0913176 0.0456588 0.998957i \(-0.485461\pi\)
0.0456588 + 0.998957i \(0.485461\pi\)
\(90\) 12.7316 1.34203
\(91\) −3.99407 −0.418693
\(92\) −3.41425 −0.355960
\(93\) 11.6425 1.20727
\(94\) −6.77599 −0.698890
\(95\) 0 0
\(96\) 3.30594 0.337411
\(97\) −14.3251 −1.45450 −0.727248 0.686374i \(-0.759201\pi\)
−0.727248 + 0.686374i \(0.759201\pi\)
\(98\) 1.00000 0.101015
\(99\) −7.96868 −0.800883
\(100\) −2.42187 −0.242187
\(101\) −7.44763 −0.741067 −0.370533 0.928819i \(-0.620825\pi\)
−0.370533 + 0.928819i \(0.620825\pi\)
\(102\) 13.7873 1.36515
\(103\) −0.208292 −0.0205236 −0.0102618 0.999947i \(-0.503266\pi\)
−0.0102618 + 0.999947i \(0.503266\pi\)
\(104\) 3.99407 0.391651
\(105\) −5.30820 −0.518027
\(106\) −0.844502 −0.0820252
\(107\) −1.35041 −0.130549 −0.0652747 0.997867i \(-0.520792\pi\)
−0.0652747 + 0.997867i \(0.520792\pi\)
\(108\) 16.2958 1.56806
\(109\) 17.4667 1.67301 0.836505 0.547960i \(-0.184595\pi\)
0.836505 + 0.547960i \(0.184595\pi\)
\(110\) −1.61364 −0.153855
\(111\) 20.8226 1.97639
\(112\) −1.00000 −0.0944911
\(113\) 5.83241 0.548667 0.274334 0.961635i \(-0.411543\pi\)
0.274334 + 0.961635i \(0.411543\pi\)
\(114\) 0 0
\(115\) −5.48211 −0.511209
\(116\) −9.28749 −0.862322
\(117\) 31.6700 2.92789
\(118\) −13.3841 −1.23211
\(119\) −4.17047 −0.382306
\(120\) 5.30820 0.484570
\(121\) −9.99003 −0.908184
\(122\) −2.17110 −0.196562
\(123\) −39.3220 −3.54555
\(124\) 3.52169 0.316257
\(125\) −11.9170 −1.06589
\(126\) −7.92924 −0.706393
\(127\) −1.15749 −0.102710 −0.0513552 0.998680i \(-0.516354\pi\)
−0.0513552 + 0.998680i \(0.516354\pi\)
\(128\) 1.00000 0.0883883
\(129\) −11.4384 −1.00710
\(130\) 6.41311 0.562467
\(131\) −17.2178 −1.50432 −0.752161 0.658979i \(-0.770988\pi\)
−0.752161 + 0.658979i \(0.770988\pi\)
\(132\) −3.32238 −0.289176
\(133\) 0 0
\(134\) 1.83197 0.158258
\(135\) 26.1654 2.25196
\(136\) 4.17047 0.357615
\(137\) −6.98319 −0.596614 −0.298307 0.954470i \(-0.596422\pi\)
−0.298307 + 0.954470i \(0.596422\pi\)
\(138\) −11.2873 −0.960839
\(139\) 21.5790 1.83031 0.915154 0.403104i \(-0.132069\pi\)
0.915154 + 0.403104i \(0.132069\pi\)
\(140\) −1.60566 −0.135703
\(141\) −22.4010 −1.88651
\(142\) 1.00901 0.0846743
\(143\) −4.01394 −0.335663
\(144\) 7.92924 0.660770
\(145\) −14.9125 −1.23842
\(146\) 4.42347 0.366089
\(147\) 3.30594 0.272669
\(148\) 6.29853 0.517736
\(149\) −17.3627 −1.42241 −0.711205 0.702984i \(-0.751850\pi\)
−0.711205 + 0.702984i \(0.751850\pi\)
\(150\) −8.00656 −0.653733
\(151\) 19.3294 1.57300 0.786500 0.617590i \(-0.211891\pi\)
0.786500 + 0.617590i \(0.211891\pi\)
\(152\) 0 0
\(153\) 33.0687 2.67344
\(154\) 1.00497 0.0809831
\(155\) 5.65462 0.454190
\(156\) 13.2042 1.05718
\(157\) 12.3453 0.985262 0.492631 0.870238i \(-0.336035\pi\)
0.492631 + 0.870238i \(0.336035\pi\)
\(158\) 3.58891 0.285518
\(159\) −2.79187 −0.221410
\(160\) 1.60566 0.126938
\(161\) 3.41425 0.269081
\(162\) 30.0851 2.36371
\(163\) 10.6114 0.831146 0.415573 0.909560i \(-0.363581\pi\)
0.415573 + 0.909560i \(0.363581\pi\)
\(164\) −11.8943 −0.928793
\(165\) −5.33460 −0.415298
\(166\) 9.90796 0.769007
\(167\) 12.3986 0.959435 0.479717 0.877423i \(-0.340739\pi\)
0.479717 + 0.877423i \(0.340739\pi\)
\(168\) −3.30594 −0.255059
\(169\) 2.95263 0.227125
\(170\) 6.69634 0.513586
\(171\) 0 0
\(172\) −3.45997 −0.263820
\(173\) 11.8515 0.901053 0.450527 0.892763i \(-0.351236\pi\)
0.450527 + 0.892763i \(0.351236\pi\)
\(174\) −30.7039 −2.32766
\(175\) 2.42187 0.183076
\(176\) −1.00497 −0.0757528
\(177\) −44.2472 −3.32582
\(178\) 0.861489 0.0645713
\(179\) −5.57373 −0.416600 −0.208300 0.978065i \(-0.566793\pi\)
−0.208300 + 0.978065i \(0.566793\pi\)
\(180\) 12.7316 0.948959
\(181\) −0.503474 −0.0374230 −0.0187115 0.999825i \(-0.505956\pi\)
−0.0187115 + 0.999825i \(0.505956\pi\)
\(182\) −3.99407 −0.296060
\(183\) −7.17754 −0.530579
\(184\) −3.41425 −0.251702
\(185\) 10.1133 0.743542
\(186\) 11.6425 0.853670
\(187\) −4.19121 −0.306492
\(188\) −6.77599 −0.494190
\(189\) −16.2958 −1.18534
\(190\) 0 0
\(191\) 20.5992 1.49051 0.745255 0.666780i \(-0.232328\pi\)
0.745255 + 0.666780i \(0.232328\pi\)
\(192\) 3.30594 0.238586
\(193\) −9.42217 −0.678223 −0.339111 0.940746i \(-0.610126\pi\)
−0.339111 + 0.940746i \(0.610126\pi\)
\(194\) −14.3251 −1.02848
\(195\) 21.2013 1.51826
\(196\) 1.00000 0.0714286
\(197\) −6.10840 −0.435205 −0.217603 0.976037i \(-0.569824\pi\)
−0.217603 + 0.976037i \(0.569824\pi\)
\(198\) −7.96868 −0.566310
\(199\) 20.0890 1.42407 0.712036 0.702143i \(-0.247773\pi\)
0.712036 + 0.702143i \(0.247773\pi\)
\(200\) −2.42187 −0.171252
\(201\) 6.05639 0.427185
\(202\) −7.44763 −0.524013
\(203\) 9.28749 0.651854
\(204\) 13.7873 0.965306
\(205\) −19.0982 −1.33388
\(206\) −0.208292 −0.0145124
\(207\) −27.0724 −1.88166
\(208\) 3.99407 0.276939
\(209\) 0 0
\(210\) −5.30820 −0.366301
\(211\) 16.5622 1.14019 0.570095 0.821579i \(-0.306906\pi\)
0.570095 + 0.821579i \(0.306906\pi\)
\(212\) −0.844502 −0.0580006
\(213\) 3.33573 0.228560
\(214\) −1.35041 −0.0923124
\(215\) −5.55551 −0.378883
\(216\) 16.2958 1.10879
\(217\) −3.52169 −0.239068
\(218\) 17.4667 1.18300
\(219\) 14.6237 0.988180
\(220\) −1.61364 −0.108792
\(221\) 16.6572 1.12048
\(222\) 20.8226 1.39752
\(223\) −9.06669 −0.607150 −0.303575 0.952807i \(-0.598180\pi\)
−0.303575 + 0.952807i \(0.598180\pi\)
\(224\) −1.00000 −0.0668153
\(225\) −19.2036 −1.28024
\(226\) 5.83241 0.387966
\(227\) 14.1539 0.939426 0.469713 0.882819i \(-0.344357\pi\)
0.469713 + 0.882819i \(0.344357\pi\)
\(228\) 0 0
\(229\) −28.9957 −1.91609 −0.958044 0.286622i \(-0.907468\pi\)
−0.958044 + 0.286622i \(0.907468\pi\)
\(230\) −5.48211 −0.361480
\(231\) 3.32238 0.218597
\(232\) −9.28749 −0.609754
\(233\) 22.3353 1.46323 0.731617 0.681716i \(-0.238766\pi\)
0.731617 + 0.681716i \(0.238766\pi\)
\(234\) 31.6700 2.07033
\(235\) −10.8799 −0.709727
\(236\) −13.3841 −0.871234
\(237\) 11.8647 0.770696
\(238\) −4.17047 −0.270331
\(239\) 0.263228 0.0170268 0.00851340 0.999964i \(-0.497290\pi\)
0.00851340 + 0.999964i \(0.497290\pi\)
\(240\) 5.30820 0.342643
\(241\) −13.7704 −0.887033 −0.443516 0.896266i \(-0.646269\pi\)
−0.443516 + 0.896266i \(0.646269\pi\)
\(242\) −9.99003 −0.642183
\(243\) 50.5723 3.24422
\(244\) −2.17110 −0.138991
\(245\) 1.60566 0.102582
\(246\) −39.3220 −2.50708
\(247\) 0 0
\(248\) 3.52169 0.223628
\(249\) 32.7551 2.07577
\(250\) −11.9170 −0.753695
\(251\) 5.64849 0.356530 0.178265 0.983983i \(-0.442952\pi\)
0.178265 + 0.983983i \(0.442952\pi\)
\(252\) −7.92924 −0.499495
\(253\) 3.43123 0.215720
\(254\) −1.15749 −0.0726272
\(255\) 22.1377 1.38632
\(256\) 1.00000 0.0625000
\(257\) −5.93091 −0.369960 −0.184980 0.982742i \(-0.559222\pi\)
−0.184980 + 0.982742i \(0.559222\pi\)
\(258\) −11.4384 −0.712126
\(259\) −6.29853 −0.391372
\(260\) 6.41311 0.397724
\(261\) −73.6428 −4.55837
\(262\) −17.2178 −1.06372
\(263\) 25.1607 1.55148 0.775738 0.631056i \(-0.217378\pi\)
0.775738 + 0.631056i \(0.217378\pi\)
\(264\) −3.32238 −0.204479
\(265\) −1.35598 −0.0832971
\(266\) 0 0
\(267\) 2.84803 0.174297
\(268\) 1.83197 0.111905
\(269\) −20.2771 −1.23632 −0.618160 0.786053i \(-0.712121\pi\)
−0.618160 + 0.786053i \(0.712121\pi\)
\(270\) 26.1654 1.59238
\(271\) 14.3611 0.872373 0.436187 0.899856i \(-0.356329\pi\)
0.436187 + 0.899856i \(0.356329\pi\)
\(272\) 4.17047 0.252872
\(273\) −13.2042 −0.799153
\(274\) −6.98319 −0.421870
\(275\) 2.43392 0.146771
\(276\) −11.2873 −0.679416
\(277\) −4.45484 −0.267665 −0.133833 0.991004i \(-0.542728\pi\)
−0.133833 + 0.991004i \(0.542728\pi\)
\(278\) 21.5790 1.29422
\(279\) 27.9243 1.67179
\(280\) −1.60566 −0.0959563
\(281\) −22.9154 −1.36702 −0.683508 0.729943i \(-0.739546\pi\)
−0.683508 + 0.729943i \(0.739546\pi\)
\(282\) −22.4010 −1.33396
\(283\) −3.90540 −0.232152 −0.116076 0.993240i \(-0.537032\pi\)
−0.116076 + 0.993240i \(0.537032\pi\)
\(284\) 1.00901 0.0598738
\(285\) 0 0
\(286\) −4.01394 −0.237349
\(287\) 11.8943 0.702101
\(288\) 7.92924 0.467235
\(289\) 0.392821 0.0231071
\(290\) −14.9125 −0.875693
\(291\) −47.3580 −2.77618
\(292\) 4.42347 0.258864
\(293\) 9.18435 0.536555 0.268278 0.963342i \(-0.413546\pi\)
0.268278 + 0.963342i \(0.413546\pi\)
\(294\) 3.30594 0.192806
\(295\) −21.4903 −1.25122
\(296\) 6.29853 0.366095
\(297\) −16.3768 −0.950280
\(298\) −17.3627 −1.00580
\(299\) −13.6368 −0.788635
\(300\) −8.00656 −0.462259
\(301\) 3.45997 0.199429
\(302\) 19.3294 1.11228
\(303\) −24.6214 −1.41446
\(304\) 0 0
\(305\) −3.48604 −0.199610
\(306\) 33.0687 1.89041
\(307\) −18.8767 −1.07735 −0.538675 0.842514i \(-0.681075\pi\)
−0.538675 + 0.842514i \(0.681075\pi\)
\(308\) 1.00497 0.0572637
\(309\) −0.688601 −0.0391731
\(310\) 5.65462 0.321161
\(311\) −14.2998 −0.810867 −0.405433 0.914125i \(-0.632879\pi\)
−0.405433 + 0.914125i \(0.632879\pi\)
\(312\) 13.2042 0.747539
\(313\) −9.27385 −0.524189 −0.262095 0.965042i \(-0.584413\pi\)
−0.262095 + 0.965042i \(0.584413\pi\)
\(314\) 12.3453 0.696686
\(315\) −12.7316 −0.717346
\(316\) 3.58891 0.201892
\(317\) −15.0866 −0.847350 −0.423675 0.905814i \(-0.639260\pi\)
−0.423675 + 0.905814i \(0.639260\pi\)
\(318\) −2.79187 −0.156560
\(319\) 9.33369 0.522586
\(320\) 1.60566 0.0897589
\(321\) −4.46439 −0.249178
\(322\) 3.41425 0.190269
\(323\) 0 0
\(324\) 30.0851 1.67140
\(325\) −9.67313 −0.536569
\(326\) 10.6114 0.587709
\(327\) 57.7440 3.19325
\(328\) −11.8943 −0.656755
\(329\) 6.77599 0.373572
\(330\) −5.33460 −0.293660
\(331\) −32.9502 −1.81110 −0.905552 0.424235i \(-0.860543\pi\)
−0.905552 + 0.424235i \(0.860543\pi\)
\(332\) 9.90796 0.543770
\(333\) 49.9426 2.73684
\(334\) 12.3986 0.678423
\(335\) 2.94151 0.160712
\(336\) −3.30594 −0.180354
\(337\) −5.29047 −0.288190 −0.144095 0.989564i \(-0.546027\pi\)
−0.144095 + 0.989564i \(0.546027\pi\)
\(338\) 2.95263 0.160602
\(339\) 19.2816 1.04723
\(340\) 6.69634 0.363160
\(341\) −3.53921 −0.191659
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) −3.45997 −0.186549
\(345\) −18.1235 −0.975738
\(346\) 11.8515 0.637141
\(347\) 26.6940 1.43301 0.716505 0.697582i \(-0.245741\pi\)
0.716505 + 0.697582i \(0.245741\pi\)
\(348\) −30.7039 −1.64590
\(349\) 18.5294 0.991859 0.495929 0.868363i \(-0.334828\pi\)
0.495929 + 0.868363i \(0.334828\pi\)
\(350\) 2.42187 0.129454
\(351\) 65.0865 3.47406
\(352\) −1.00497 −0.0535653
\(353\) 15.1656 0.807184 0.403592 0.914939i \(-0.367762\pi\)
0.403592 + 0.914939i \(0.367762\pi\)
\(354\) −44.2472 −2.35171
\(355\) 1.62012 0.0859872
\(356\) 0.861489 0.0456588
\(357\) −13.7873 −0.729703
\(358\) −5.57373 −0.294581
\(359\) 4.86384 0.256704 0.128352 0.991729i \(-0.459031\pi\)
0.128352 + 0.991729i \(0.459031\pi\)
\(360\) 12.7316 0.671016
\(361\) 0 0
\(362\) −0.503474 −0.0264620
\(363\) −33.0264 −1.73344
\(364\) −3.99407 −0.209346
\(365\) 7.10257 0.371765
\(366\) −7.17754 −0.375176
\(367\) −15.1487 −0.790753 −0.395377 0.918519i \(-0.629386\pi\)
−0.395377 + 0.918519i \(0.629386\pi\)
\(368\) −3.41425 −0.177980
\(369\) −94.3131 −4.90975
\(370\) 10.1133 0.525764
\(371\) 0.844502 0.0438443
\(372\) 11.6425 0.603636
\(373\) 12.0889 0.625940 0.312970 0.949763i \(-0.398676\pi\)
0.312970 + 0.949763i \(0.398676\pi\)
\(374\) −4.19121 −0.216723
\(375\) −39.3968 −2.03444
\(376\) −6.77599 −0.349445
\(377\) −37.0949 −1.91049
\(378\) −16.2958 −0.838164
\(379\) −2.53167 −0.130043 −0.0650215 0.997884i \(-0.520712\pi\)
−0.0650215 + 0.997884i \(0.520712\pi\)
\(380\) 0 0
\(381\) −3.82658 −0.196042
\(382\) 20.5992 1.05395
\(383\) −17.7672 −0.907861 −0.453931 0.891037i \(-0.649979\pi\)
−0.453931 + 0.891037i \(0.649979\pi\)
\(384\) 3.30594 0.168706
\(385\) 1.61364 0.0822388
\(386\) −9.42217 −0.479576
\(387\) −27.4349 −1.39459
\(388\) −14.3251 −0.727248
\(389\) −7.41576 −0.375994 −0.187997 0.982170i \(-0.560200\pi\)
−0.187997 + 0.982170i \(0.560200\pi\)
\(390\) 21.2013 1.07357
\(391\) −14.2390 −0.720099
\(392\) 1.00000 0.0505076
\(393\) −56.9209 −2.87128
\(394\) −6.10840 −0.307737
\(395\) 5.76255 0.289945
\(396\) −7.96868 −0.400441
\(397\) 23.0391 1.15630 0.578149 0.815931i \(-0.303775\pi\)
0.578149 + 0.815931i \(0.303775\pi\)
\(398\) 20.0890 1.00697
\(399\) 0 0
\(400\) −2.42187 −0.121094
\(401\) −21.7693 −1.08711 −0.543554 0.839374i \(-0.682922\pi\)
−0.543554 + 0.839374i \(0.682922\pi\)
\(402\) 6.05639 0.302065
\(403\) 14.0659 0.700672
\(404\) −7.44763 −0.370533
\(405\) 48.3064 2.40036
\(406\) 9.28749 0.460930
\(407\) −6.32986 −0.313760
\(408\) 13.7873 0.682574
\(409\) −10.8461 −0.536303 −0.268152 0.963377i \(-0.586413\pi\)
−0.268152 + 0.963377i \(0.586413\pi\)
\(410\) −19.0982 −0.943194
\(411\) −23.0860 −1.13875
\(412\) −0.208292 −0.0102618
\(413\) 13.3841 0.658591
\(414\) −27.0724 −1.33054
\(415\) 15.9088 0.780931
\(416\) 3.99407 0.195826
\(417\) 71.3389 3.49348
\(418\) 0 0
\(419\) −10.3984 −0.507994 −0.253997 0.967205i \(-0.581745\pi\)
−0.253997 + 0.967205i \(0.581745\pi\)
\(420\) −5.30820 −0.259014
\(421\) 7.23504 0.352614 0.176307 0.984335i \(-0.443585\pi\)
0.176307 + 0.984335i \(0.443585\pi\)
\(422\) 16.5622 0.806236
\(423\) −53.7285 −2.61237
\(424\) −0.844502 −0.0410126
\(425\) −10.1003 −0.489938
\(426\) 3.33573 0.161617
\(427\) 2.17110 0.105067
\(428\) −1.35041 −0.0652747
\(429\) −13.2699 −0.640674
\(430\) −5.55551 −0.267911
\(431\) 11.2858 0.543616 0.271808 0.962352i \(-0.412378\pi\)
0.271808 + 0.962352i \(0.412378\pi\)
\(432\) 16.2958 0.784031
\(433\) −27.7278 −1.33251 −0.666257 0.745722i \(-0.732105\pi\)
−0.666257 + 0.745722i \(0.732105\pi\)
\(434\) −3.52169 −0.169047
\(435\) −49.2999 −2.36375
\(436\) 17.4667 0.836505
\(437\) 0 0
\(438\) 14.6237 0.698749
\(439\) −16.1949 −0.772942 −0.386471 0.922301i \(-0.626306\pi\)
−0.386471 + 0.922301i \(0.626306\pi\)
\(440\) −1.61364 −0.0769274
\(441\) 7.92924 0.377583
\(442\) 16.6572 0.792301
\(443\) −1.92143 −0.0912898 −0.0456449 0.998958i \(-0.514534\pi\)
−0.0456449 + 0.998958i \(0.514534\pi\)
\(444\) 20.8226 0.988195
\(445\) 1.38325 0.0655725
\(446\) −9.06669 −0.429320
\(447\) −57.4002 −2.71493
\(448\) −1.00000 −0.0472456
\(449\) 7.10807 0.335450 0.167725 0.985834i \(-0.446358\pi\)
0.167725 + 0.985834i \(0.446358\pi\)
\(450\) −19.2036 −0.905266
\(451\) 11.9535 0.562869
\(452\) 5.83241 0.274334
\(453\) 63.9017 3.00236
\(454\) 14.1539 0.664274
\(455\) −6.41311 −0.300651
\(456\) 0 0
\(457\) 21.4257 1.00225 0.501126 0.865374i \(-0.332919\pi\)
0.501126 + 0.865374i \(0.332919\pi\)
\(458\) −28.9957 −1.35488
\(459\) 67.9610 3.17215
\(460\) −5.48211 −0.255605
\(461\) 1.92191 0.0895122 0.0447561 0.998998i \(-0.485749\pi\)
0.0447561 + 0.998998i \(0.485749\pi\)
\(462\) 3.32238 0.154571
\(463\) 13.3363 0.619792 0.309896 0.950770i \(-0.399706\pi\)
0.309896 + 0.950770i \(0.399706\pi\)
\(464\) −9.28749 −0.431161
\(465\) 18.6938 0.866906
\(466\) 22.3353 1.03466
\(467\) 12.5501 0.580751 0.290375 0.956913i \(-0.406220\pi\)
0.290375 + 0.956913i \(0.406220\pi\)
\(468\) 31.6700 1.46395
\(469\) −1.83197 −0.0845926
\(470\) −10.8799 −0.501853
\(471\) 40.8128 1.88056
\(472\) −13.3841 −0.616055
\(473\) 3.47718 0.159881
\(474\) 11.8647 0.544964
\(475\) 0 0
\(476\) −4.17047 −0.191153
\(477\) −6.69626 −0.306601
\(478\) 0.263228 0.0120398
\(479\) −14.6582 −0.669752 −0.334876 0.942262i \(-0.608694\pi\)
−0.334876 + 0.942262i \(0.608694\pi\)
\(480\) 5.30820 0.242285
\(481\) 25.1568 1.14705
\(482\) −13.7704 −0.627227
\(483\) 11.2873 0.513590
\(484\) −9.99003 −0.454092
\(485\) −23.0012 −1.04443
\(486\) 50.5723 2.29401
\(487\) 27.0128 1.22407 0.612033 0.790832i \(-0.290352\pi\)
0.612033 + 0.790832i \(0.290352\pi\)
\(488\) −2.17110 −0.0982812
\(489\) 35.0805 1.58640
\(490\) 1.60566 0.0725361
\(491\) 13.6444 0.615764 0.307882 0.951424i \(-0.400380\pi\)
0.307882 + 0.951424i \(0.400380\pi\)
\(492\) −39.3220 −1.77277
\(493\) −38.7332 −1.74446
\(494\) 0 0
\(495\) −12.7950 −0.575091
\(496\) 3.52169 0.158129
\(497\) −1.00901 −0.0452603
\(498\) 32.7551 1.46779
\(499\) −17.1149 −0.766168 −0.383084 0.923714i \(-0.625138\pi\)
−0.383084 + 0.923714i \(0.625138\pi\)
\(500\) −11.9170 −0.532943
\(501\) 40.9891 1.83126
\(502\) 5.64849 0.252104
\(503\) 21.6483 0.965251 0.482625 0.875827i \(-0.339683\pi\)
0.482625 + 0.875827i \(0.339683\pi\)
\(504\) −7.92924 −0.353196
\(505\) −11.9583 −0.532139
\(506\) 3.43123 0.152537
\(507\) 9.76122 0.433511
\(508\) −1.15749 −0.0513552
\(509\) −3.87595 −0.171799 −0.0858993 0.996304i \(-0.527376\pi\)
−0.0858993 + 0.996304i \(0.527376\pi\)
\(510\) 22.1377 0.980273
\(511\) −4.42347 −0.195683
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −5.93091 −0.261601
\(515\) −0.334445 −0.0147374
\(516\) −11.4384 −0.503549
\(517\) 6.80970 0.299490
\(518\) −6.29853 −0.276742
\(519\) 39.1804 1.71983
\(520\) 6.41311 0.281233
\(521\) −33.3837 −1.46257 −0.731283 0.682074i \(-0.761078\pi\)
−0.731283 + 0.682074i \(0.761078\pi\)
\(522\) −73.6428 −3.22326
\(523\) 28.0440 1.22628 0.613140 0.789974i \(-0.289906\pi\)
0.613140 + 0.789974i \(0.289906\pi\)
\(524\) −17.2178 −0.752161
\(525\) 8.00656 0.349435
\(526\) 25.1607 1.09706
\(527\) 14.6871 0.639781
\(528\) −3.32238 −0.144588
\(529\) −11.3429 −0.493169
\(530\) −1.35598 −0.0588999
\(531\) −106.126 −4.60548
\(532\) 0 0
\(533\) −47.5069 −2.05775
\(534\) 2.84803 0.123246
\(535\) −2.16830 −0.0937438
\(536\) 1.83197 0.0791291
\(537\) −18.4264 −0.795158
\(538\) −20.2771 −0.874210
\(539\) −1.00497 −0.0432873
\(540\) 26.1654 1.12598
\(541\) 7.34681 0.315864 0.157932 0.987450i \(-0.449517\pi\)
0.157932 + 0.987450i \(0.449517\pi\)
\(542\) 14.3611 0.616861
\(543\) −1.66446 −0.0714287
\(544\) 4.17047 0.178807
\(545\) 28.0455 1.20134
\(546\) −13.2042 −0.565086
\(547\) −28.7382 −1.22876 −0.614378 0.789012i \(-0.710593\pi\)
−0.614378 + 0.789012i \(0.710593\pi\)
\(548\) −6.98319 −0.298307
\(549\) −17.2152 −0.734727
\(550\) 2.43392 0.103783
\(551\) 0 0
\(552\) −11.2873 −0.480420
\(553\) −3.58891 −0.152616
\(554\) −4.45484 −0.189268
\(555\) 33.4339 1.41919
\(556\) 21.5790 0.915154
\(557\) −44.1857 −1.87221 −0.936104 0.351724i \(-0.885596\pi\)
−0.936104 + 0.351724i \(0.885596\pi\)
\(558\) 27.9243 1.18213
\(559\) −13.8194 −0.584497
\(560\) −1.60566 −0.0678513
\(561\) −13.8559 −0.584997
\(562\) −22.9154 −0.966626
\(563\) −19.8387 −0.836103 −0.418051 0.908423i \(-0.637287\pi\)
−0.418051 + 0.908423i \(0.637287\pi\)
\(564\) −22.4010 −0.943253
\(565\) 9.36484 0.393982
\(566\) −3.90540 −0.164156
\(567\) −30.0851 −1.26346
\(568\) 1.00901 0.0423372
\(569\) 10.2122 0.428119 0.214060 0.976821i \(-0.431331\pi\)
0.214060 + 0.976821i \(0.431331\pi\)
\(570\) 0 0
\(571\) −29.1274 −1.21894 −0.609472 0.792808i \(-0.708619\pi\)
−0.609472 + 0.792808i \(0.708619\pi\)
\(572\) −4.01394 −0.167831
\(573\) 68.0999 2.84491
\(574\) 11.8943 0.496460
\(575\) 8.26887 0.344836
\(576\) 7.92924 0.330385
\(577\) 41.9370 1.74586 0.872930 0.487845i \(-0.162217\pi\)
0.872930 + 0.487845i \(0.162217\pi\)
\(578\) 0.392821 0.0163392
\(579\) −31.1491 −1.29451
\(580\) −14.9125 −0.619208
\(581\) −9.90796 −0.411052
\(582\) −47.3580 −1.96305
\(583\) 0.848702 0.0351497
\(584\) 4.42347 0.183044
\(585\) 50.8511 2.10243
\(586\) 9.18435 0.379402
\(587\) 12.9226 0.533371 0.266686 0.963784i \(-0.414071\pi\)
0.266686 + 0.963784i \(0.414071\pi\)
\(588\) 3.30594 0.136335
\(589\) 0 0
\(590\) −21.4903 −0.884743
\(591\) −20.1940 −0.830670
\(592\) 6.29853 0.258868
\(593\) 1.46902 0.0603254 0.0301627 0.999545i \(-0.490397\pi\)
0.0301627 + 0.999545i \(0.490397\pi\)
\(594\) −16.3768 −0.671950
\(595\) −6.69634 −0.274523
\(596\) −17.3627 −0.711205
\(597\) 66.4131 2.71811
\(598\) −13.6368 −0.557649
\(599\) −28.7788 −1.17587 −0.587935 0.808909i \(-0.700059\pi\)
−0.587935 + 0.808909i \(0.700059\pi\)
\(600\) −8.00656 −0.326866
\(601\) −46.1978 −1.88445 −0.942224 0.334983i \(-0.891269\pi\)
−0.942224 + 0.334983i \(0.891269\pi\)
\(602\) 3.45997 0.141018
\(603\) 14.5261 0.591550
\(604\) 19.3294 0.786500
\(605\) −16.0405 −0.652141
\(606\) −24.6214 −1.00018
\(607\) 24.3713 0.989202 0.494601 0.869120i \(-0.335314\pi\)
0.494601 + 0.869120i \(0.335314\pi\)
\(608\) 0 0
\(609\) 30.7039 1.24418
\(610\) −3.48604 −0.141146
\(611\) −27.0638 −1.09488
\(612\) 33.0687 1.33672
\(613\) −6.03281 −0.243663 −0.121831 0.992551i \(-0.538877\pi\)
−0.121831 + 0.992551i \(0.538877\pi\)
\(614\) −18.8767 −0.761801
\(615\) −63.1376 −2.54595
\(616\) 1.00497 0.0404916
\(617\) 23.8645 0.960749 0.480374 0.877064i \(-0.340501\pi\)
0.480374 + 0.877064i \(0.340501\pi\)
\(618\) −0.688601 −0.0276996
\(619\) −22.9388 −0.921987 −0.460994 0.887403i \(-0.652507\pi\)
−0.460994 + 0.887403i \(0.652507\pi\)
\(620\) 5.65462 0.227095
\(621\) −55.6378 −2.23267
\(622\) −14.2998 −0.573369
\(623\) −0.861489 −0.0345148
\(624\) 13.2042 0.528590
\(625\) −7.02519 −0.281007
\(626\) −9.27385 −0.370658
\(627\) 0 0
\(628\) 12.3453 0.492631
\(629\) 26.2678 1.04737
\(630\) −12.7316 −0.507240
\(631\) −41.7210 −1.66089 −0.830444 0.557102i \(-0.811913\pi\)
−0.830444 + 0.557102i \(0.811913\pi\)
\(632\) 3.58891 0.142759
\(633\) 54.7537 2.17627
\(634\) −15.0866 −0.599167
\(635\) −1.85853 −0.0737534
\(636\) −2.79187 −0.110705
\(637\) 3.99407 0.158251
\(638\) 9.33369 0.369524
\(639\) 8.00069 0.316502
\(640\) 1.60566 0.0634691
\(641\) −19.6493 −0.776101 −0.388051 0.921638i \(-0.626851\pi\)
−0.388051 + 0.921638i \(0.626851\pi\)
\(642\) −4.46439 −0.176195
\(643\) 4.88804 0.192765 0.0963827 0.995344i \(-0.469273\pi\)
0.0963827 + 0.995344i \(0.469273\pi\)
\(644\) 3.41425 0.134540
\(645\) −18.3662 −0.723168
\(646\) 0 0
\(647\) 28.2737 1.11155 0.555777 0.831331i \(-0.312421\pi\)
0.555777 + 0.831331i \(0.312421\pi\)
\(648\) 30.0851 1.18186
\(649\) 13.4507 0.527987
\(650\) −9.67313 −0.379411
\(651\) −11.6425 −0.456306
\(652\) 10.6114 0.415573
\(653\) 0.457000 0.0178838 0.00894190 0.999960i \(-0.497154\pi\)
0.00894190 + 0.999960i \(0.497154\pi\)
\(654\) 57.7440 2.25797
\(655\) −27.6458 −1.08021
\(656\) −11.8943 −0.464396
\(657\) 35.0748 1.36840
\(658\) 6.77599 0.264156
\(659\) 34.6704 1.35057 0.675284 0.737557i \(-0.264021\pi\)
0.675284 + 0.737557i \(0.264021\pi\)
\(660\) −5.33460 −0.207649
\(661\) −49.5022 −1.92541 −0.962706 0.270551i \(-0.912794\pi\)
−0.962706 + 0.270551i \(0.912794\pi\)
\(662\) −32.9502 −1.28064
\(663\) 55.0676 2.13865
\(664\) 9.90796 0.384504
\(665\) 0 0
\(666\) 49.9426 1.93523
\(667\) 31.7098 1.22781
\(668\) 12.3986 0.479717
\(669\) −29.9739 −1.15886
\(670\) 2.94151 0.113641
\(671\) 2.18190 0.0842314
\(672\) −3.30594 −0.127529
\(673\) −34.6829 −1.33693 −0.668463 0.743745i \(-0.733047\pi\)
−0.668463 + 0.743745i \(0.733047\pi\)
\(674\) −5.29047 −0.203781
\(675\) −39.4663 −1.51906
\(676\) 2.95263 0.113563
\(677\) 7.08968 0.272478 0.136239 0.990676i \(-0.456498\pi\)
0.136239 + 0.990676i \(0.456498\pi\)
\(678\) 19.2816 0.740506
\(679\) 14.3251 0.549748
\(680\) 6.69634 0.256793
\(681\) 46.7919 1.79307
\(682\) −3.53921 −0.135523
\(683\) 6.70433 0.256534 0.128267 0.991740i \(-0.459059\pi\)
0.128267 + 0.991740i \(0.459059\pi\)
\(684\) 0 0
\(685\) −11.2126 −0.428411
\(686\) −1.00000 −0.0381802
\(687\) −95.8579 −3.65721
\(688\) −3.45997 −0.131910
\(689\) −3.37300 −0.128501
\(690\) −18.1235 −0.689951
\(691\) 9.62186 0.366033 0.183016 0.983110i \(-0.441414\pi\)
0.183016 + 0.983110i \(0.441414\pi\)
\(692\) 11.8515 0.450527
\(693\) 7.96868 0.302705
\(694\) 26.6940 1.01329
\(695\) 34.6485 1.31429
\(696\) −30.7039 −1.16383
\(697\) −49.6050 −1.87892
\(698\) 18.5294 0.701350
\(699\) 73.8391 2.79285
\(700\) 2.42187 0.0915381
\(701\) −47.0077 −1.77546 −0.887728 0.460369i \(-0.847717\pi\)
−0.887728 + 0.460369i \(0.847717\pi\)
\(702\) 65.0865 2.45653
\(703\) 0 0
\(704\) −1.00497 −0.0378764
\(705\) −35.9683 −1.35465
\(706\) 15.1656 0.570765
\(707\) 7.44763 0.280097
\(708\) −44.2472 −1.66291
\(709\) 30.3987 1.14165 0.570823 0.821073i \(-0.306624\pi\)
0.570823 + 0.821073i \(0.306624\pi\)
\(710\) 1.62012 0.0608022
\(711\) 28.4573 1.06723
\(712\) 0.861489 0.0322857
\(713\) −12.0239 −0.450300
\(714\) −13.7873 −0.515978
\(715\) −6.44501 −0.241030
\(716\) −5.57373 −0.208300
\(717\) 0.870215 0.0324988
\(718\) 4.86384 0.181517
\(719\) 7.66631 0.285905 0.142953 0.989730i \(-0.454340\pi\)
0.142953 + 0.989730i \(0.454340\pi\)
\(720\) 12.7316 0.474480
\(721\) 0.208292 0.00775720
\(722\) 0 0
\(723\) −45.5243 −1.69307
\(724\) −0.503474 −0.0187115
\(725\) 22.4931 0.835373
\(726\) −33.0264 −1.22573
\(727\) 6.99220 0.259326 0.129663 0.991558i \(-0.458610\pi\)
0.129663 + 0.991558i \(0.458610\pi\)
\(728\) −3.99407 −0.148030
\(729\) 76.9337 2.84940
\(730\) 7.10257 0.262878
\(731\) −14.4297 −0.533701
\(732\) −7.17754 −0.265289
\(733\) 14.7249 0.543878 0.271939 0.962314i \(-0.412335\pi\)
0.271939 + 0.962314i \(0.412335\pi\)
\(734\) −15.1487 −0.559147
\(735\) 5.30820 0.195796
\(736\) −3.41425 −0.125851
\(737\) −1.84108 −0.0678172
\(738\) −94.3131 −3.47171
\(739\) 45.0688 1.65788 0.828941 0.559337i \(-0.188944\pi\)
0.828941 + 0.559337i \(0.188944\pi\)
\(740\) 10.1133 0.371771
\(741\) 0 0
\(742\) 0.844502 0.0310026
\(743\) −37.5977 −1.37932 −0.689662 0.724131i \(-0.742241\pi\)
−0.689662 + 0.724131i \(0.742241\pi\)
\(744\) 11.6425 0.426835
\(745\) −27.8786 −1.02139
\(746\) 12.0889 0.442606
\(747\) 78.5626 2.87446
\(748\) −4.19121 −0.153246
\(749\) 1.35041 0.0493431
\(750\) −39.3968 −1.43857
\(751\) −1.17468 −0.0428647 −0.0214324 0.999770i \(-0.506823\pi\)
−0.0214324 + 0.999770i \(0.506823\pi\)
\(752\) −6.77599 −0.247095
\(753\) 18.6736 0.680503
\(754\) −37.0949 −1.35092
\(755\) 31.0363 1.12953
\(756\) −16.2958 −0.592672
\(757\) 26.3197 0.956605 0.478302 0.878195i \(-0.341252\pi\)
0.478302 + 0.878195i \(0.341252\pi\)
\(758\) −2.53167 −0.0919542
\(759\) 11.3435 0.411741
\(760\) 0 0
\(761\) 18.0097 0.652850 0.326425 0.945223i \(-0.394156\pi\)
0.326425 + 0.945223i \(0.394156\pi\)
\(762\) −3.82658 −0.138623
\(763\) −17.4667 −0.632338
\(764\) 20.5992 0.745255
\(765\) 53.0969 1.91972
\(766\) −17.7672 −0.641955
\(767\) −53.4573 −1.93023
\(768\) 3.30594 0.119293
\(769\) 1.24078 0.0447437 0.0223719 0.999750i \(-0.492878\pi\)
0.0223719 + 0.999750i \(0.492878\pi\)
\(770\) 1.61364 0.0581516
\(771\) −19.6072 −0.706137
\(772\) −9.42217 −0.339111
\(773\) 30.1364 1.08393 0.541966 0.840400i \(-0.317680\pi\)
0.541966 + 0.840400i \(0.317680\pi\)
\(774\) −27.4349 −0.986127
\(775\) −8.52908 −0.306374
\(776\) −14.3251 −0.514242
\(777\) −20.8226 −0.747005
\(778\) −7.41576 −0.265868
\(779\) 0 0
\(780\) 21.2013 0.759130
\(781\) −1.01403 −0.0362848
\(782\) −14.2390 −0.509187
\(783\) −151.347 −5.40870
\(784\) 1.00000 0.0357143
\(785\) 19.8223 0.707488
\(786\) −56.9209 −2.03030
\(787\) 31.8145 1.13407 0.567033 0.823695i \(-0.308091\pi\)
0.567033 + 0.823695i \(0.308091\pi\)
\(788\) −6.10840 −0.217603
\(789\) 83.1798 2.96128
\(790\) 5.76255 0.205022
\(791\) −5.83241 −0.207377
\(792\) −7.96868 −0.283155
\(793\) −8.67155 −0.307936
\(794\) 23.0391 0.817626
\(795\) −4.48278 −0.158988
\(796\) 20.0890 0.712036
\(797\) 2.40659 0.0852458 0.0426229 0.999091i \(-0.486429\pi\)
0.0426229 + 0.999091i \(0.486429\pi\)
\(798\) 0 0
\(799\) −28.2591 −0.999734
\(800\) −2.42187 −0.0856261
\(801\) 6.83095 0.241360
\(802\) −21.7693 −0.768701
\(803\) −4.44547 −0.156877
\(804\) 6.05639 0.213592
\(805\) 5.48211 0.193219
\(806\) 14.0659 0.495450
\(807\) −67.0350 −2.35974
\(808\) −7.44763 −0.262007
\(809\) 50.5604 1.77761 0.888805 0.458286i \(-0.151536\pi\)
0.888805 + 0.458286i \(0.151536\pi\)
\(810\) 48.3064 1.69731
\(811\) −6.03456 −0.211902 −0.105951 0.994371i \(-0.533789\pi\)
−0.105951 + 0.994371i \(0.533789\pi\)
\(812\) 9.28749 0.325927
\(813\) 47.4769 1.66509
\(814\) −6.32986 −0.221861
\(815\) 17.0382 0.596822
\(816\) 13.7873 0.482653
\(817\) 0 0
\(818\) −10.8461 −0.379224
\(819\) −31.6700 −1.10664
\(820\) −19.0982 −0.666939
\(821\) 22.9676 0.801573 0.400787 0.916171i \(-0.368737\pi\)
0.400787 + 0.916171i \(0.368737\pi\)
\(822\) −23.0860 −0.805217
\(823\) 20.7187 0.722209 0.361104 0.932525i \(-0.382400\pi\)
0.361104 + 0.932525i \(0.382400\pi\)
\(824\) −0.208292 −0.00725619
\(825\) 8.04639 0.280139
\(826\) 13.3841 0.465694
\(827\) −14.5464 −0.505827 −0.252913 0.967489i \(-0.581389\pi\)
−0.252913 + 0.967489i \(0.581389\pi\)
\(828\) −27.0724 −0.940831
\(829\) 41.2656 1.43321 0.716607 0.697477i \(-0.245694\pi\)
0.716607 + 0.697477i \(0.245694\pi\)
\(830\) 15.9088 0.552202
\(831\) −14.7274 −0.510889
\(832\) 3.99407 0.138470
\(833\) 4.17047 0.144498
\(834\) 71.3389 2.47026
\(835\) 19.9079 0.688942
\(836\) 0 0
\(837\) 57.3887 1.98364
\(838\) −10.3984 −0.359206
\(839\) 17.9654 0.620233 0.310117 0.950699i \(-0.399632\pi\)
0.310117 + 0.950699i \(0.399632\pi\)
\(840\) −5.30820 −0.183150
\(841\) 57.2575 1.97440
\(842\) 7.23504 0.249336
\(843\) −75.7568 −2.60920
\(844\) 16.5622 0.570095
\(845\) 4.74091 0.163092
\(846\) −53.7285 −1.84722
\(847\) 9.99003 0.343261
\(848\) −0.844502 −0.0290003
\(849\) −12.9110 −0.443105
\(850\) −10.1003 −0.346439
\(851\) −21.5048 −0.737174
\(852\) 3.33573 0.114280
\(853\) 53.2831 1.82438 0.912189 0.409771i \(-0.134391\pi\)
0.912189 + 0.409771i \(0.134391\pi\)
\(854\) 2.17110 0.0742936
\(855\) 0 0
\(856\) −1.35041 −0.0461562
\(857\) 20.3916 0.696564 0.348282 0.937390i \(-0.386765\pi\)
0.348282 + 0.937390i \(0.386765\pi\)
\(858\) −13.2699 −0.453025
\(859\) 12.2523 0.418043 0.209022 0.977911i \(-0.432972\pi\)
0.209022 + 0.977911i \(0.432972\pi\)
\(860\) −5.55551 −0.189441
\(861\) 39.3220 1.34009
\(862\) 11.2858 0.384394
\(863\) 38.4927 1.31031 0.655154 0.755496i \(-0.272604\pi\)
0.655154 + 0.755496i \(0.272604\pi\)
\(864\) 16.2958 0.554394
\(865\) 19.0294 0.647020
\(866\) −27.7278 −0.942230
\(867\) 1.29864 0.0441042
\(868\) −3.52169 −0.119534
\(869\) −3.60676 −0.122351
\(870\) −49.2999 −1.67142
\(871\) 7.31703 0.247928
\(872\) 17.4667 0.591498
\(873\) −113.587 −3.84435
\(874\) 0 0
\(875\) 11.9170 0.402867
\(876\) 14.6237 0.494090
\(877\) 32.9843 1.11380 0.556901 0.830579i \(-0.311990\pi\)
0.556901 + 0.830579i \(0.311990\pi\)
\(878\) −16.1949 −0.546553
\(879\) 30.3629 1.02412
\(880\) −1.61364 −0.0543959
\(881\) 5.07102 0.170847 0.0854236 0.996345i \(-0.472776\pi\)
0.0854236 + 0.996345i \(0.472776\pi\)
\(882\) 7.92924 0.266991
\(883\) 27.6866 0.931728 0.465864 0.884856i \(-0.345744\pi\)
0.465864 + 0.884856i \(0.345744\pi\)
\(884\) 16.6572 0.560241
\(885\) −71.0457 −2.38818
\(886\) −1.92143 −0.0645516
\(887\) 35.2956 1.18511 0.592556 0.805530i \(-0.298119\pi\)
0.592556 + 0.805530i \(0.298119\pi\)
\(888\) 20.8226 0.698760
\(889\) 1.15749 0.0388209
\(890\) 1.38325 0.0463668
\(891\) −30.2348 −1.01290
\(892\) −9.06669 −0.303575
\(893\) 0 0
\(894\) −57.4002 −1.91975
\(895\) −8.94949 −0.299148
\(896\) −1.00000 −0.0334077
\(897\) −45.0823 −1.50526
\(898\) 7.10807 0.237199
\(899\) −32.7077 −1.09086
\(900\) −19.2036 −0.640120
\(901\) −3.52197 −0.117334
\(902\) 11.9535 0.398008
\(903\) 11.4384 0.380647
\(904\) 5.83241 0.193983
\(905\) −0.808406 −0.0268723
\(906\) 63.9017 2.12299
\(907\) 25.1085 0.833715 0.416857 0.908972i \(-0.363131\pi\)
0.416857 + 0.908972i \(0.363131\pi\)
\(908\) 14.1539 0.469713
\(909\) −59.0540 −1.95870
\(910\) −6.41311 −0.212592
\(911\) 18.6010 0.616278 0.308139 0.951341i \(-0.400294\pi\)
0.308139 + 0.951341i \(0.400294\pi\)
\(912\) 0 0
\(913\) −9.95725 −0.329537
\(914\) 21.4257 0.708700
\(915\) −11.5247 −0.380993
\(916\) −28.9957 −0.958044
\(917\) 17.2178 0.568580
\(918\) 67.9610 2.24305
\(919\) 16.9273 0.558381 0.279191 0.960236i \(-0.409934\pi\)
0.279191 + 0.960236i \(0.409934\pi\)
\(920\) −5.48211 −0.180740
\(921\) −62.4052 −2.05632
\(922\) 1.92191 0.0632947
\(923\) 4.03006 0.132651
\(924\) 3.32238 0.109298
\(925\) −15.2542 −0.501556
\(926\) 13.3363 0.438259
\(927\) −1.65160 −0.0542456
\(928\) −9.28749 −0.304877
\(929\) 4.96916 0.163033 0.0815164 0.996672i \(-0.474024\pi\)
0.0815164 + 0.996672i \(0.474024\pi\)
\(930\) 18.6938 0.612995
\(931\) 0 0
\(932\) 22.3353 0.731617
\(933\) −47.2742 −1.54769
\(934\) 12.5501 0.410653
\(935\) −6.72965 −0.220083
\(936\) 31.6700 1.03517
\(937\) −13.5173 −0.441592 −0.220796 0.975320i \(-0.570865\pi\)
−0.220796 + 0.975320i \(0.570865\pi\)
\(938\) −1.83197 −0.0598160
\(939\) −30.6588 −1.00051
\(940\) −10.8799 −0.354863
\(941\) −20.5294 −0.669239 −0.334619 0.942353i \(-0.608608\pi\)
−0.334619 + 0.942353i \(0.608608\pi\)
\(942\) 40.8128 1.32975
\(943\) 40.6103 1.32245
\(944\) −13.3841 −0.435617
\(945\) −26.1654 −0.851160
\(946\) 3.47718 0.113053
\(947\) 0.960158 0.0312009 0.0156005 0.999878i \(-0.495034\pi\)
0.0156005 + 0.999878i \(0.495034\pi\)
\(948\) 11.8647 0.385348
\(949\) 17.6677 0.573517
\(950\) 0 0
\(951\) −49.8755 −1.61732
\(952\) −4.17047 −0.135166
\(953\) 14.1493 0.458342 0.229171 0.973386i \(-0.426398\pi\)
0.229171 + 0.973386i \(0.426398\pi\)
\(954\) −6.69626 −0.216799
\(955\) 33.0753 1.07029
\(956\) 0.263228 0.00851340
\(957\) 30.8566 0.997453
\(958\) −14.6582 −0.473586
\(959\) 6.98319 0.225499
\(960\) 5.30820 0.171321
\(961\) −18.5977 −0.599925
\(962\) 25.1568 0.811088
\(963\) −10.7078 −0.345053
\(964\) −13.7704 −0.443516
\(965\) −15.1288 −0.487012
\(966\) 11.2873 0.363163
\(967\) 5.94491 0.191175 0.0955877 0.995421i \(-0.469527\pi\)
0.0955877 + 0.995421i \(0.469527\pi\)
\(968\) −9.99003 −0.321092
\(969\) 0 0
\(970\) −23.0012 −0.738525
\(971\) 20.5310 0.658872 0.329436 0.944178i \(-0.393141\pi\)
0.329436 + 0.944178i \(0.393141\pi\)
\(972\) 50.5723 1.62211
\(973\) −21.5790 −0.691791
\(974\) 27.0128 0.865545
\(975\) −31.9788 −1.02414
\(976\) −2.17110 −0.0694953
\(977\) 19.7977 0.633384 0.316692 0.948528i \(-0.397428\pi\)
0.316692 + 0.948528i \(0.397428\pi\)
\(978\) 35.0805 1.12175
\(979\) −0.865774 −0.0276703
\(980\) 1.60566 0.0512908
\(981\) 138.498 4.42190
\(982\) 13.6444 0.435411
\(983\) −58.6875 −1.87184 −0.935920 0.352213i \(-0.885429\pi\)
−0.935920 + 0.352213i \(0.885429\pi\)
\(984\) −39.3220 −1.25354
\(985\) −9.80798 −0.312508
\(986\) −38.7332 −1.23352
\(987\) 22.4010 0.713032
\(988\) 0 0
\(989\) 11.8132 0.375638
\(990\) −12.7950 −0.406650
\(991\) 17.2451 0.547808 0.273904 0.961757i \(-0.411685\pi\)
0.273904 + 0.961757i \(0.411685\pi\)
\(992\) 3.52169 0.111814
\(993\) −108.931 −3.45683
\(994\) −1.00901 −0.0320039
\(995\) 32.2560 1.02258
\(996\) 32.7551 1.03789
\(997\) −11.9959 −0.379915 −0.189957 0.981792i \(-0.560835\pi\)
−0.189957 + 0.981792i \(0.560835\pi\)
\(998\) −17.1149 −0.541763
\(999\) 102.639 3.24737
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 5054.2.a.bk.1.9 9
19.6 even 9 266.2.u.c.169.3 yes 18
19.16 even 9 266.2.u.c.85.3 18
19.18 odd 2 5054.2.a.bj.1.1 9
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
266.2.u.c.85.3 18 19.16 even 9
266.2.u.c.169.3 yes 18 19.6 even 9
5054.2.a.bj.1.1 9 19.18 odd 2
5054.2.a.bk.1.9 9 1.1 even 1 trivial