Properties

Label 4034.2.a.d.1.12
Level 4034
Weight 2
Character 4034.1
Self dual yes
Analytic conductor 32.212
Analytic rank 0
Dimension 52
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4034 = 2 \cdot 2017 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4034.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.2116521754\)
Analytic rank: \(0\)
Dimension: \(52\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Character \(\chi\) = 4034.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.53830 q^{3} +1.00000 q^{4} +3.94371 q^{5} -1.53830 q^{6} -3.54174 q^{7} +1.00000 q^{8} -0.633629 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.53830 q^{3} +1.00000 q^{4} +3.94371 q^{5} -1.53830 q^{6} -3.54174 q^{7} +1.00000 q^{8} -0.633629 q^{9} +3.94371 q^{10} +4.54195 q^{11} -1.53830 q^{12} +3.47054 q^{13} -3.54174 q^{14} -6.06662 q^{15} +1.00000 q^{16} +3.19553 q^{17} -0.633629 q^{18} +1.14712 q^{19} +3.94371 q^{20} +5.44826 q^{21} +4.54195 q^{22} -3.21056 q^{23} -1.53830 q^{24} +10.5529 q^{25} +3.47054 q^{26} +5.58962 q^{27} -3.54174 q^{28} +4.23477 q^{29} -6.06662 q^{30} -8.64344 q^{31} +1.00000 q^{32} -6.98689 q^{33} +3.19553 q^{34} -13.9676 q^{35} -0.633629 q^{36} -4.09499 q^{37} +1.14712 q^{38} -5.33874 q^{39} +3.94371 q^{40} -5.96700 q^{41} +5.44826 q^{42} +7.60529 q^{43} +4.54195 q^{44} -2.49885 q^{45} -3.21056 q^{46} +4.18276 q^{47} -1.53830 q^{48} +5.54389 q^{49} +10.5529 q^{50} -4.91569 q^{51} +3.47054 q^{52} -0.668336 q^{53} +5.58962 q^{54} +17.9122 q^{55} -3.54174 q^{56} -1.76462 q^{57} +4.23477 q^{58} -0.928020 q^{59} -6.06662 q^{60} +8.93473 q^{61} -8.64344 q^{62} +2.24415 q^{63} +1.00000 q^{64} +13.6868 q^{65} -6.98689 q^{66} -4.43454 q^{67} +3.19553 q^{68} +4.93881 q^{69} -13.9676 q^{70} -11.0025 q^{71} -0.633629 q^{72} -14.9609 q^{73} -4.09499 q^{74} -16.2335 q^{75} +1.14712 q^{76} -16.0864 q^{77} -5.33874 q^{78} +13.8183 q^{79} +3.94371 q^{80} -6.69763 q^{81} -5.96700 q^{82} +9.97381 q^{83} +5.44826 q^{84} +12.6023 q^{85} +7.60529 q^{86} -6.51436 q^{87} +4.54195 q^{88} +8.67852 q^{89} -2.49885 q^{90} -12.2917 q^{91} -3.21056 q^{92} +13.2962 q^{93} +4.18276 q^{94} +4.52392 q^{95} -1.53830 q^{96} +14.3327 q^{97} +5.54389 q^{98} -2.87791 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 52q + 52q^{2} + 16q^{3} + 52q^{4} + 24q^{5} + 16q^{6} + 12q^{7} + 52q^{8} + 70q^{9} + O(q^{10}) \) \( 52q + 52q^{2} + 16q^{3} + 52q^{4} + 24q^{5} + 16q^{6} + 12q^{7} + 52q^{8} + 70q^{9} + 24q^{10} + 19q^{11} + 16q^{12} + 27q^{13} + 12q^{14} + 5q^{15} + 52q^{16} + 43q^{17} + 70q^{18} + 35q^{19} + 24q^{20} + 29q^{21} + 19q^{22} + 2q^{23} + 16q^{24} + 88q^{25} + 27q^{26} + 49q^{27} + 12q^{28} + 31q^{29} + 5q^{30} + 59q^{31} + 52q^{32} + 45q^{33} + 43q^{34} + 18q^{35} + 70q^{36} + 60q^{37} + 35q^{38} + 6q^{39} + 24q^{40} + 56q^{41} + 29q^{42} + 34q^{43} + 19q^{44} + 61q^{45} + 2q^{46} - 4q^{47} + 16q^{48} + 102q^{49} + 88q^{50} + 23q^{51} + 27q^{52} + 30q^{53} + 49q^{54} + 24q^{55} + 12q^{56} + 32q^{57} + 31q^{58} + 27q^{59} + 5q^{60} + 107q^{61} + 59q^{62} - 4q^{63} + 52q^{64} + 46q^{65} + 45q^{66} + 22q^{67} + 43q^{68} + 36q^{69} + 18q^{70} + 8q^{71} + 70q^{72} + 66q^{73} + 60q^{74} + 53q^{75} + 35q^{76} + 26q^{77} + 6q^{78} + 50q^{79} + 24q^{80} + 108q^{81} + 56q^{82} + 52q^{83} + 29q^{84} + 19q^{85} + 34q^{86} - 32q^{87} + 19q^{88} + 62q^{89} + 61q^{90} + 69q^{91} + 2q^{92} + 21q^{93} - 4q^{94} - 44q^{95} + 16q^{96} + 82q^{97} + 102q^{98} + 16q^{99} + O(q^{100}) \)

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
\(3\) −1.53830 −0.888139 −0.444069 0.895992i \(-0.646466\pi\)
−0.444069 + 0.895992i \(0.646466\pi\)
\(4\) 1.00000 0.500000
\(5\) 3.94371 1.76368 0.881841 0.471546i \(-0.156304\pi\)
0.881841 + 0.471546i \(0.156304\pi\)
\(6\) −1.53830 −0.628009
\(7\) −3.54174 −1.33865 −0.669325 0.742970i \(-0.733417\pi\)
−0.669325 + 0.742970i \(0.733417\pi\)
\(8\) 1.00000 0.353553
\(9\) −0.633629 −0.211210
\(10\) 3.94371 1.24711
\(11\) 4.54195 1.36945 0.684725 0.728802i \(-0.259922\pi\)
0.684725 + 0.728802i \(0.259922\pi\)
\(12\) −1.53830 −0.444069
\(13\) 3.47054 0.962556 0.481278 0.876568i \(-0.340173\pi\)
0.481278 + 0.876568i \(0.340173\pi\)
\(14\) −3.54174 −0.946569
\(15\) −6.06662 −1.56639
\(16\) 1.00000 0.250000
\(17\) 3.19553 0.775030 0.387515 0.921863i \(-0.373334\pi\)
0.387515 + 0.921863i \(0.373334\pi\)
\(18\) −0.633629 −0.149348
\(19\) 1.14712 0.263168 0.131584 0.991305i \(-0.457994\pi\)
0.131584 + 0.991305i \(0.457994\pi\)
\(20\) 3.94371 0.881841
\(21\) 5.44826 1.18891
\(22\) 4.54195 0.968347
\(23\) −3.21056 −0.669448 −0.334724 0.942316i \(-0.608643\pi\)
−0.334724 + 0.942316i \(0.608643\pi\)
\(24\) −1.53830 −0.314004
\(25\) 10.5529 2.11058
\(26\) 3.47054 0.680630
\(27\) 5.58962 1.07572
\(28\) −3.54174 −0.669325
\(29\) 4.23477 0.786378 0.393189 0.919458i \(-0.371372\pi\)
0.393189 + 0.919458i \(0.371372\pi\)
\(30\) −6.06662 −1.10761
\(31\) −8.64344 −1.55241 −0.776204 0.630482i \(-0.782857\pi\)
−0.776204 + 0.630482i \(0.782857\pi\)
\(32\) 1.00000 0.176777
\(33\) −6.98689 −1.21626
\(34\) 3.19553 0.548029
\(35\) −13.9676 −2.36095
\(36\) −0.633629 −0.105605
\(37\) −4.09499 −0.673213 −0.336606 0.941645i \(-0.609279\pi\)
−0.336606 + 0.941645i \(0.609279\pi\)
\(38\) 1.14712 0.186088
\(39\) −5.33874 −0.854883
\(40\) 3.94371 0.623556
\(41\) −5.96700 −0.931889 −0.465944 0.884814i \(-0.654285\pi\)
−0.465944 + 0.884814i \(0.654285\pi\)
\(42\) 5.44826 0.840684
\(43\) 7.60529 1.15980 0.579898 0.814689i \(-0.303092\pi\)
0.579898 + 0.814689i \(0.303092\pi\)
\(44\) 4.54195 0.684725
\(45\) −2.49885 −0.372507
\(46\) −3.21056 −0.473372
\(47\) 4.18276 0.610118 0.305059 0.952333i \(-0.401324\pi\)
0.305059 + 0.952333i \(0.401324\pi\)
\(48\) −1.53830 −0.222035
\(49\) 5.54389 0.791985
\(50\) 10.5529 1.49240
\(51\) −4.91569 −0.688334
\(52\) 3.47054 0.481278
\(53\) −0.668336 −0.0918031 −0.0459015 0.998946i \(-0.514616\pi\)
−0.0459015 + 0.998946i \(0.514616\pi\)
\(54\) 5.58962 0.760650
\(55\) 17.9122 2.41527
\(56\) −3.54174 −0.473284
\(57\) −1.76462 −0.233729
\(58\) 4.23477 0.556053
\(59\) −0.928020 −0.120818 −0.0604090 0.998174i \(-0.519240\pi\)
−0.0604090 + 0.998174i \(0.519240\pi\)
\(60\) −6.06662 −0.783197
\(61\) 8.93473 1.14397 0.571987 0.820262i \(-0.306173\pi\)
0.571987 + 0.820262i \(0.306173\pi\)
\(62\) −8.64344 −1.09772
\(63\) 2.24415 0.282736
\(64\) 1.00000 0.125000
\(65\) 13.6868 1.69764
\(66\) −6.98689 −0.860027
\(67\) −4.43454 −0.541765 −0.270883 0.962612i \(-0.587316\pi\)
−0.270883 + 0.962612i \(0.587316\pi\)
\(68\) 3.19553 0.387515
\(69\) 4.93881 0.594563
\(70\) −13.9676 −1.66945
\(71\) −11.0025 −1.30575 −0.652877 0.757464i \(-0.726438\pi\)
−0.652877 + 0.757464i \(0.726438\pi\)
\(72\) −0.633629 −0.0746739
\(73\) −14.9609 −1.75104 −0.875521 0.483180i \(-0.839482\pi\)
−0.875521 + 0.483180i \(0.839482\pi\)
\(74\) −4.09499 −0.476033
\(75\) −16.2335 −1.87448
\(76\) 1.14712 0.131584
\(77\) −16.0864 −1.83321
\(78\) −5.33874 −0.604493
\(79\) 13.8183 1.55467 0.777337 0.629084i \(-0.216570\pi\)
0.777337 + 0.629084i \(0.216570\pi\)
\(80\) 3.94371 0.440921
\(81\) −6.69763 −0.744181
\(82\) −5.96700 −0.658945
\(83\) 9.97381 1.09477 0.547384 0.836882i \(-0.315624\pi\)
0.547384 + 0.836882i \(0.315624\pi\)
\(84\) 5.44826 0.594454
\(85\) 12.6023 1.36691
\(86\) 7.60529 0.820100
\(87\) −6.51436 −0.698412
\(88\) 4.54195 0.484174
\(89\) 8.67852 0.919921 0.459961 0.887939i \(-0.347863\pi\)
0.459961 + 0.887939i \(0.347863\pi\)
\(90\) −2.49885 −0.263402
\(91\) −12.2917 −1.28853
\(92\) −3.21056 −0.334724
\(93\) 13.2962 1.37875
\(94\) 4.18276 0.431419
\(95\) 4.52392 0.464144
\(96\) −1.53830 −0.157002
\(97\) 14.3327 1.45526 0.727632 0.685968i \(-0.240621\pi\)
0.727632 + 0.685968i \(0.240621\pi\)
\(98\) 5.54389 0.560018
\(99\) −2.87791 −0.289241
\(100\) 10.5529 1.05529
\(101\) 16.2470 1.61664 0.808320 0.588744i \(-0.200377\pi\)
0.808320 + 0.588744i \(0.200377\pi\)
\(102\) −4.91569 −0.486726
\(103\) −2.47083 −0.243458 −0.121729 0.992563i \(-0.538844\pi\)
−0.121729 + 0.992563i \(0.538844\pi\)
\(104\) 3.47054 0.340315
\(105\) 21.4864 2.09685
\(106\) −0.668336 −0.0649146
\(107\) −3.62630 −0.350567 −0.175284 0.984518i \(-0.556084\pi\)
−0.175284 + 0.984518i \(0.556084\pi\)
\(108\) 5.58962 0.537861
\(109\) 11.4090 1.09278 0.546391 0.837530i \(-0.316001\pi\)
0.546391 + 0.837530i \(0.316001\pi\)
\(110\) 17.9122 1.70786
\(111\) 6.29933 0.597906
\(112\) −3.54174 −0.334663
\(113\) 5.67163 0.533542 0.266771 0.963760i \(-0.414043\pi\)
0.266771 + 0.963760i \(0.414043\pi\)
\(114\) −1.76462 −0.165272
\(115\) −12.6615 −1.18069
\(116\) 4.23477 0.393189
\(117\) −2.19904 −0.203301
\(118\) −0.928020 −0.0854312
\(119\) −11.3177 −1.03749
\(120\) −6.06662 −0.553804
\(121\) 9.62932 0.875393
\(122\) 8.93473 0.808912
\(123\) 9.17904 0.827646
\(124\) −8.64344 −0.776204
\(125\) 21.8990 1.95870
\(126\) 2.24415 0.199924
\(127\) 0.710995 0.0630906 0.0315453 0.999502i \(-0.489957\pi\)
0.0315453 + 0.999502i \(0.489957\pi\)
\(128\) 1.00000 0.0883883
\(129\) −11.6992 −1.03006
\(130\) 13.6868 1.20041
\(131\) 15.7031 1.37199 0.685995 0.727606i \(-0.259367\pi\)
0.685995 + 0.727606i \(0.259367\pi\)
\(132\) −6.98689 −0.608131
\(133\) −4.06280 −0.352290
\(134\) −4.43454 −0.383086
\(135\) 22.0438 1.89723
\(136\) 3.19553 0.274014
\(137\) 7.06102 0.603264 0.301632 0.953424i \(-0.402469\pi\)
0.301632 + 0.953424i \(0.402469\pi\)
\(138\) 4.93881 0.420420
\(139\) −13.0236 −1.10465 −0.552325 0.833629i \(-0.686259\pi\)
−0.552325 + 0.833629i \(0.686259\pi\)
\(140\) −13.9676 −1.18048
\(141\) −6.43434 −0.541869
\(142\) −11.0025 −0.923308
\(143\) 15.7630 1.31817
\(144\) −0.633629 −0.0528024
\(145\) 16.7007 1.38692
\(146\) −14.9609 −1.23817
\(147\) −8.52818 −0.703392
\(148\) −4.09499 −0.336606
\(149\) 11.5078 0.942757 0.471379 0.881931i \(-0.343756\pi\)
0.471379 + 0.881931i \(0.343756\pi\)
\(150\) −16.2335 −1.32546
\(151\) −4.74768 −0.386361 −0.193180 0.981163i \(-0.561880\pi\)
−0.193180 + 0.981163i \(0.561880\pi\)
\(152\) 1.14712 0.0930438
\(153\) −2.02478 −0.163694
\(154\) −16.0864 −1.29628
\(155\) −34.0872 −2.73795
\(156\) −5.33874 −0.427441
\(157\) −18.4666 −1.47380 −0.736898 0.676004i \(-0.763710\pi\)
−0.736898 + 0.676004i \(0.763710\pi\)
\(158\) 13.8183 1.09932
\(159\) 1.02810 0.0815339
\(160\) 3.94371 0.311778
\(161\) 11.3710 0.896157
\(162\) −6.69763 −0.526215
\(163\) −22.9352 −1.79642 −0.898211 0.439564i \(-0.855133\pi\)
−0.898211 + 0.439564i \(0.855133\pi\)
\(164\) −5.96700 −0.465944
\(165\) −27.5543 −2.14510
\(166\) 9.97381 0.774118
\(167\) −9.37258 −0.725272 −0.362636 0.931931i \(-0.618123\pi\)
−0.362636 + 0.931931i \(0.618123\pi\)
\(168\) 5.44826 0.420342
\(169\) −0.955327 −0.0734867
\(170\) 12.6023 0.966549
\(171\) −0.726849 −0.0555836
\(172\) 7.60529 0.579898
\(173\) 6.83501 0.519656 0.259828 0.965655i \(-0.416334\pi\)
0.259828 + 0.965655i \(0.416334\pi\)
\(174\) −6.51436 −0.493852
\(175\) −37.3755 −2.82532
\(176\) 4.54195 0.342362
\(177\) 1.42757 0.107303
\(178\) 8.67852 0.650483
\(179\) 2.24249 0.167611 0.0838056 0.996482i \(-0.473293\pi\)
0.0838056 + 0.996482i \(0.473293\pi\)
\(180\) −2.49885 −0.186253
\(181\) 3.30251 0.245474 0.122737 0.992439i \(-0.460833\pi\)
0.122737 + 0.992439i \(0.460833\pi\)
\(182\) −12.2917 −0.911125
\(183\) −13.7443 −1.01601
\(184\) −3.21056 −0.236686
\(185\) −16.1495 −1.18733
\(186\) 13.2962 0.974925
\(187\) 14.5139 1.06136
\(188\) 4.18276 0.305059
\(189\) −19.7969 −1.44002
\(190\) 4.52392 0.328200
\(191\) −2.01137 −0.145537 −0.0727687 0.997349i \(-0.523183\pi\)
−0.0727687 + 0.997349i \(0.523183\pi\)
\(192\) −1.53830 −0.111017
\(193\) 13.1695 0.947962 0.473981 0.880535i \(-0.342817\pi\)
0.473981 + 0.880535i \(0.342817\pi\)
\(194\) 14.3327 1.02903
\(195\) −21.0545 −1.50774
\(196\) 5.54389 0.395992
\(197\) 15.5252 1.10612 0.553062 0.833140i \(-0.313459\pi\)
0.553062 + 0.833140i \(0.313459\pi\)
\(198\) −2.87791 −0.204524
\(199\) −5.96083 −0.422552 −0.211276 0.977426i \(-0.567762\pi\)
−0.211276 + 0.977426i \(0.567762\pi\)
\(200\) 10.5529 0.746201
\(201\) 6.82166 0.481163
\(202\) 16.2470 1.14314
\(203\) −14.9984 −1.05268
\(204\) −4.91569 −0.344167
\(205\) −23.5321 −1.64356
\(206\) −2.47083 −0.172151
\(207\) 2.03431 0.141394
\(208\) 3.47054 0.240639
\(209\) 5.21017 0.360395
\(210\) 21.4864 1.48270
\(211\) 2.41890 0.166524 0.0832619 0.996528i \(-0.473466\pi\)
0.0832619 + 0.996528i \(0.473466\pi\)
\(212\) −0.668336 −0.0459015
\(213\) 16.9251 1.15969
\(214\) −3.62630 −0.247889
\(215\) 29.9931 2.04551
\(216\) 5.58962 0.380325
\(217\) 30.6128 2.07813
\(218\) 11.4090 0.772713
\(219\) 23.0144 1.55517
\(220\) 17.9122 1.20764
\(221\) 11.0902 0.746009
\(222\) 6.29933 0.422784
\(223\) −12.9507 −0.867240 −0.433620 0.901096i \(-0.642764\pi\)
−0.433620 + 0.901096i \(0.642764\pi\)
\(224\) −3.54174 −0.236642
\(225\) −6.68661 −0.445774
\(226\) 5.67163 0.377271
\(227\) 7.68669 0.510183 0.255092 0.966917i \(-0.417894\pi\)
0.255092 + 0.966917i \(0.417894\pi\)
\(228\) −1.76462 −0.116865
\(229\) −30.1383 −1.99160 −0.995798 0.0915756i \(-0.970810\pi\)
−0.995798 + 0.0915756i \(0.970810\pi\)
\(230\) −12.6615 −0.834877
\(231\) 24.7457 1.62815
\(232\) 4.23477 0.278026
\(233\) 16.6289 1.08939 0.544697 0.838633i \(-0.316645\pi\)
0.544697 + 0.838633i \(0.316645\pi\)
\(234\) −2.19904 −0.143756
\(235\) 16.4956 1.07605
\(236\) −0.928020 −0.0604090
\(237\) −21.2566 −1.38077
\(238\) −11.3177 −0.733619
\(239\) 2.46990 0.159765 0.0798824 0.996804i \(-0.474546\pi\)
0.0798824 + 0.996804i \(0.474546\pi\)
\(240\) −6.06662 −0.391599
\(241\) 29.0581 1.87179 0.935897 0.352273i \(-0.114591\pi\)
0.935897 + 0.352273i \(0.114591\pi\)
\(242\) 9.62932 0.618996
\(243\) −6.46588 −0.414786
\(244\) 8.93473 0.571987
\(245\) 21.8635 1.39681
\(246\) 9.17904 0.585234
\(247\) 3.98113 0.253314
\(248\) −8.64344 −0.548859
\(249\) −15.3427 −0.972306
\(250\) 21.8990 1.38501
\(251\) 12.6754 0.800065 0.400032 0.916501i \(-0.368999\pi\)
0.400032 + 0.916501i \(0.368999\pi\)
\(252\) 2.24415 0.141368
\(253\) −14.5822 −0.916776
\(254\) 0.710995 0.0446118
\(255\) −19.3861 −1.21400
\(256\) 1.00000 0.0625000
\(257\) −10.8375 −0.676024 −0.338012 0.941142i \(-0.609754\pi\)
−0.338012 + 0.941142i \(0.609754\pi\)
\(258\) −11.6992 −0.728362
\(259\) 14.5034 0.901196
\(260\) 13.6868 0.848821
\(261\) −2.68328 −0.166091
\(262\) 15.7031 0.970143
\(263\) −6.89673 −0.425271 −0.212635 0.977132i \(-0.568205\pi\)
−0.212635 + 0.977132i \(0.568205\pi\)
\(264\) −6.98689 −0.430013
\(265\) −2.63573 −0.161911
\(266\) −4.06280 −0.249106
\(267\) −13.3502 −0.817018
\(268\) −4.43454 −0.270883
\(269\) −18.2225 −1.11104 −0.555521 0.831502i \(-0.687481\pi\)
−0.555521 + 0.831502i \(0.687481\pi\)
\(270\) 22.0438 1.34155
\(271\) −11.8484 −0.719738 −0.359869 0.933003i \(-0.617179\pi\)
−0.359869 + 0.933003i \(0.617179\pi\)
\(272\) 3.19553 0.193757
\(273\) 18.9084 1.14439
\(274\) 7.06102 0.426572
\(275\) 47.9307 2.89033
\(276\) 4.93881 0.297282
\(277\) −15.4431 −0.927886 −0.463943 0.885865i \(-0.653566\pi\)
−0.463943 + 0.885865i \(0.653566\pi\)
\(278\) −13.0236 −0.781106
\(279\) 5.47673 0.327883
\(280\) −13.9676 −0.834723
\(281\) 17.7149 1.05678 0.528390 0.849002i \(-0.322796\pi\)
0.528390 + 0.849002i \(0.322796\pi\)
\(282\) −6.43434 −0.383160
\(283\) −14.4636 −0.859770 −0.429885 0.902884i \(-0.641446\pi\)
−0.429885 + 0.902884i \(0.641446\pi\)
\(284\) −11.0025 −0.652877
\(285\) −6.95915 −0.412224
\(286\) 15.7630 0.932088
\(287\) 21.1335 1.24747
\(288\) −0.633629 −0.0373369
\(289\) −6.78859 −0.399329
\(290\) 16.7007 0.980701
\(291\) −22.0480 −1.29248
\(292\) −14.9609 −0.875521
\(293\) −31.4451 −1.83704 −0.918520 0.395374i \(-0.870615\pi\)
−0.918520 + 0.395374i \(0.870615\pi\)
\(294\) −8.52818 −0.497374
\(295\) −3.65985 −0.213084
\(296\) −4.09499 −0.238017
\(297\) 25.3878 1.47315
\(298\) 11.5078 0.666630
\(299\) −11.1424 −0.644381
\(300\) −16.2335 −0.937242
\(301\) −26.9359 −1.55256
\(302\) −4.74768 −0.273198
\(303\) −24.9928 −1.43580
\(304\) 1.14712 0.0657919
\(305\) 35.2360 2.01761
\(306\) −2.02478 −0.115749
\(307\) 25.5046 1.45562 0.727812 0.685776i \(-0.240537\pi\)
0.727812 + 0.685776i \(0.240537\pi\)
\(308\) −16.0864 −0.916607
\(309\) 3.80088 0.216224
\(310\) −34.0872 −1.93603
\(311\) 12.6107 0.715086 0.357543 0.933897i \(-0.383615\pi\)
0.357543 + 0.933897i \(0.383615\pi\)
\(312\) −5.33874 −0.302247
\(313\) 25.7813 1.45724 0.728621 0.684917i \(-0.240161\pi\)
0.728621 + 0.684917i \(0.240161\pi\)
\(314\) −18.4666 −1.04213
\(315\) 8.85027 0.498656
\(316\) 13.8183 0.777337
\(317\) 34.2888 1.92585 0.962924 0.269772i \(-0.0869482\pi\)
0.962924 + 0.269772i \(0.0869482\pi\)
\(318\) 1.02810 0.0576531
\(319\) 19.2341 1.07690
\(320\) 3.94371 0.220460
\(321\) 5.57834 0.311352
\(322\) 11.3710 0.633679
\(323\) 3.66566 0.203963
\(324\) −6.69763 −0.372090
\(325\) 36.6242 2.03155
\(326\) −22.9352 −1.27026
\(327\) −17.5504 −0.970541
\(328\) −5.96700 −0.329472
\(329\) −14.8142 −0.816735
\(330\) −27.5543 −1.51681
\(331\) 0.306690 0.0168572 0.00842860 0.999964i \(-0.497317\pi\)
0.00842860 + 0.999964i \(0.497317\pi\)
\(332\) 9.97381 0.547384
\(333\) 2.59471 0.142189
\(334\) −9.37258 −0.512845
\(335\) −17.4886 −0.955502
\(336\) 5.44826 0.297227
\(337\) −9.17661 −0.499882 −0.249941 0.968261i \(-0.580411\pi\)
−0.249941 + 0.968261i \(0.580411\pi\)
\(338\) −0.955327 −0.0519629
\(339\) −8.72468 −0.473860
\(340\) 12.6023 0.683453
\(341\) −39.2581 −2.12594
\(342\) −0.726849 −0.0393035
\(343\) 5.15714 0.278460
\(344\) 7.60529 0.410050
\(345\) 19.4773 1.04862
\(346\) 6.83501 0.367453
\(347\) 9.75999 0.523944 0.261972 0.965075i \(-0.415627\pi\)
0.261972 + 0.965075i \(0.415627\pi\)
\(348\) −6.51436 −0.349206
\(349\) 21.7395 1.16369 0.581845 0.813300i \(-0.302331\pi\)
0.581845 + 0.813300i \(0.302331\pi\)
\(350\) −37.3755 −1.99781
\(351\) 19.3990 1.03544
\(352\) 4.54195 0.242087
\(353\) −16.7254 −0.890201 −0.445100 0.895481i \(-0.646832\pi\)
−0.445100 + 0.895481i \(0.646832\pi\)
\(354\) 1.42757 0.0758747
\(355\) −43.3906 −2.30294
\(356\) 8.67852 0.459961
\(357\) 17.4101 0.921439
\(358\) 2.24249 0.118519
\(359\) −8.80493 −0.464707 −0.232353 0.972631i \(-0.574643\pi\)
−0.232353 + 0.972631i \(0.574643\pi\)
\(360\) −2.49885 −0.131701
\(361\) −17.6841 −0.930743
\(362\) 3.30251 0.173576
\(363\) −14.8128 −0.777470
\(364\) −12.2917 −0.644263
\(365\) −59.0016 −3.08828
\(366\) −13.7443 −0.718426
\(367\) 8.30729 0.433637 0.216819 0.976212i \(-0.430432\pi\)
0.216819 + 0.976212i \(0.430432\pi\)
\(368\) −3.21056 −0.167362
\(369\) 3.78086 0.196824
\(370\) −16.1495 −0.839571
\(371\) 2.36707 0.122892
\(372\) 13.2962 0.689376
\(373\) −21.1733 −1.09631 −0.548155 0.836377i \(-0.684670\pi\)
−0.548155 + 0.836377i \(0.684670\pi\)
\(374\) 14.5139 0.750498
\(375\) −33.6872 −1.73960
\(376\) 4.18276 0.215709
\(377\) 14.6970 0.756932
\(378\) −19.7969 −1.01825
\(379\) 11.4427 0.587772 0.293886 0.955840i \(-0.405051\pi\)
0.293886 + 0.955840i \(0.405051\pi\)
\(380\) 4.52392 0.232072
\(381\) −1.09373 −0.0560332
\(382\) −2.01137 −0.102910
\(383\) 24.9349 1.27411 0.637056 0.770818i \(-0.280152\pi\)
0.637056 + 0.770818i \(0.280152\pi\)
\(384\) −1.53830 −0.0785011
\(385\) −63.4401 −3.23321
\(386\) 13.1695 0.670310
\(387\) −4.81893 −0.244960
\(388\) 14.3327 0.727632
\(389\) −7.95651 −0.403411 −0.201706 0.979446i \(-0.564648\pi\)
−0.201706 + 0.979446i \(0.564648\pi\)
\(390\) −21.0545 −1.06613
\(391\) −10.2594 −0.518842
\(392\) 5.54389 0.280009
\(393\) −24.1562 −1.21852
\(394\) 15.5252 0.782148
\(395\) 54.4952 2.74195
\(396\) −2.87791 −0.144621
\(397\) −3.17224 −0.159210 −0.0796052 0.996826i \(-0.525366\pi\)
−0.0796052 + 0.996826i \(0.525366\pi\)
\(398\) −5.96083 −0.298790
\(399\) 6.24981 0.312882
\(400\) 10.5529 0.527644
\(401\) 23.2436 1.16073 0.580364 0.814357i \(-0.302910\pi\)
0.580364 + 0.814357i \(0.302910\pi\)
\(402\) 6.82166 0.340233
\(403\) −29.9974 −1.49428
\(404\) 16.2470 0.808320
\(405\) −26.4135 −1.31250
\(406\) −14.9984 −0.744361
\(407\) −18.5993 −0.921931
\(408\) −4.91569 −0.243363
\(409\) −3.26133 −0.161263 −0.0806313 0.996744i \(-0.525694\pi\)
−0.0806313 + 0.996744i \(0.525694\pi\)
\(410\) −23.5321 −1.16217
\(411\) −10.8620 −0.535782
\(412\) −2.47083 −0.121729
\(413\) 3.28680 0.161733
\(414\) 2.03431 0.0999806
\(415\) 39.3339 1.93082
\(416\) 3.47054 0.170157
\(417\) 20.0343 0.981083
\(418\) 5.21017 0.254838
\(419\) 19.1123 0.933698 0.466849 0.884337i \(-0.345389\pi\)
0.466849 + 0.884337i \(0.345389\pi\)
\(420\) 21.4864 1.04843
\(421\) −32.5597 −1.58686 −0.793432 0.608658i \(-0.791708\pi\)
−0.793432 + 0.608658i \(0.791708\pi\)
\(422\) 2.41890 0.117750
\(423\) −2.65032 −0.128863
\(424\) −0.668336 −0.0324573
\(425\) 33.7220 1.63576
\(426\) 16.9251 0.820025
\(427\) −31.6444 −1.53138
\(428\) −3.62630 −0.175284
\(429\) −24.2483 −1.17072
\(430\) 29.9931 1.44640
\(431\) 18.4181 0.887171 0.443585 0.896232i \(-0.353706\pi\)
0.443585 + 0.896232i \(0.353706\pi\)
\(432\) 5.58962 0.268931
\(433\) −5.93243 −0.285094 −0.142547 0.989788i \(-0.545529\pi\)
−0.142547 + 0.989788i \(0.545529\pi\)
\(434\) 30.6128 1.46946
\(435\) −25.6908 −1.23178
\(436\) 11.4090 0.546391
\(437\) −3.68290 −0.176177
\(438\) 23.0144 1.09967
\(439\) 11.5859 0.552967 0.276483 0.961019i \(-0.410831\pi\)
0.276483 + 0.961019i \(0.410831\pi\)
\(440\) 17.9122 0.853929
\(441\) −3.51277 −0.167275
\(442\) 11.0902 0.527508
\(443\) −9.60530 −0.456361 −0.228181 0.973619i \(-0.573278\pi\)
−0.228181 + 0.973619i \(0.573278\pi\)
\(444\) 6.29933 0.298953
\(445\) 34.2256 1.62245
\(446\) −12.9507 −0.613231
\(447\) −17.7025 −0.837299
\(448\) −3.54174 −0.167331
\(449\) −35.5928 −1.67973 −0.839864 0.542796i \(-0.817366\pi\)
−0.839864 + 0.542796i \(0.817366\pi\)
\(450\) −6.68661 −0.315210
\(451\) −27.1018 −1.27617
\(452\) 5.67163 0.266771
\(453\) 7.30336 0.343142
\(454\) 7.68669 0.360754
\(455\) −48.4751 −2.27255
\(456\) −1.76462 −0.0826358
\(457\) −39.0420 −1.82631 −0.913154 0.407616i \(-0.866360\pi\)
−0.913154 + 0.407616i \(0.866360\pi\)
\(458\) −30.1383 −1.40827
\(459\) 17.8618 0.833717
\(460\) −12.6615 −0.590347
\(461\) 15.9153 0.741249 0.370624 0.928783i \(-0.379144\pi\)
0.370624 + 0.928783i \(0.379144\pi\)
\(462\) 24.7457 1.15127
\(463\) −5.96915 −0.277410 −0.138705 0.990334i \(-0.544294\pi\)
−0.138705 + 0.990334i \(0.544294\pi\)
\(464\) 4.23477 0.196594
\(465\) 52.4365 2.43168
\(466\) 16.6289 0.770318
\(467\) −39.0600 −1.80748 −0.903741 0.428080i \(-0.859190\pi\)
−0.903741 + 0.428080i \(0.859190\pi\)
\(468\) −2.19904 −0.101651
\(469\) 15.7060 0.725234
\(470\) 16.4956 0.760885
\(471\) 28.4072 1.30893
\(472\) −0.928020 −0.0427156
\(473\) 34.5429 1.58828
\(474\) −21.2566 −0.976349
\(475\) 12.1054 0.555435
\(476\) −11.3177 −0.518747
\(477\) 0.423477 0.0193897
\(478\) 2.46990 0.112971
\(479\) −38.1035 −1.74099 −0.870497 0.492174i \(-0.836202\pi\)
−0.870497 + 0.492174i \(0.836202\pi\)
\(480\) −6.06662 −0.276902
\(481\) −14.2118 −0.648005
\(482\) 29.0581 1.32356
\(483\) −17.4920 −0.795912
\(484\) 9.62932 0.437696
\(485\) 56.5240 2.56662
\(486\) −6.46588 −0.293298
\(487\) −17.7659 −0.805049 −0.402524 0.915409i \(-0.631867\pi\)
−0.402524 + 0.915409i \(0.631867\pi\)
\(488\) 8.93473 0.404456
\(489\) 35.2812 1.59547
\(490\) 21.8635 0.987694
\(491\) 11.8118 0.533058 0.266529 0.963827i \(-0.414123\pi\)
0.266529 + 0.963827i \(0.414123\pi\)
\(492\) 9.17904 0.413823
\(493\) 13.5323 0.609466
\(494\) 3.98113 0.179120
\(495\) −11.3497 −0.510129
\(496\) −8.64344 −0.388102
\(497\) 38.9679 1.74795
\(498\) −15.3427 −0.687524
\(499\) −34.9022 −1.56244 −0.781218 0.624259i \(-0.785401\pi\)
−0.781218 + 0.624259i \(0.785401\pi\)
\(500\) 21.8990 0.979352
\(501\) 14.4179 0.644142
\(502\) 12.6754 0.565731
\(503\) 13.7370 0.612501 0.306250 0.951951i \(-0.400926\pi\)
0.306250 + 0.951951i \(0.400926\pi\)
\(504\) 2.24415 0.0999622
\(505\) 64.0736 2.85124
\(506\) −14.5822 −0.648259
\(507\) 1.46958 0.0652664
\(508\) 0.710995 0.0315453
\(509\) −37.3000 −1.65329 −0.826647 0.562720i \(-0.809755\pi\)
−0.826647 + 0.562720i \(0.809755\pi\)
\(510\) −19.3861 −0.858429
\(511\) 52.9876 2.34403
\(512\) 1.00000 0.0441942
\(513\) 6.41197 0.283095
\(514\) −10.8375 −0.478021
\(515\) −9.74424 −0.429382
\(516\) −11.6992 −0.515030
\(517\) 18.9979 0.835526
\(518\) 14.5034 0.637242
\(519\) −10.5143 −0.461527
\(520\) 13.6868 0.600207
\(521\) 7.62525 0.334068 0.167034 0.985951i \(-0.446581\pi\)
0.167034 + 0.985951i \(0.446581\pi\)
\(522\) −2.68328 −0.117444
\(523\) −24.4204 −1.06783 −0.533915 0.845538i \(-0.679280\pi\)
−0.533915 + 0.845538i \(0.679280\pi\)
\(524\) 15.7031 0.685995
\(525\) 57.4948 2.50928
\(526\) −6.89673 −0.300712
\(527\) −27.6204 −1.20316
\(528\) −6.98689 −0.304065
\(529\) −12.6923 −0.551839
\(530\) −2.63573 −0.114489
\(531\) 0.588020 0.0255179
\(532\) −4.06280 −0.176145
\(533\) −20.7087 −0.896995
\(534\) −13.3502 −0.577719
\(535\) −14.3011 −0.618289
\(536\) −4.43454 −0.191543
\(537\) −3.44962 −0.148862
\(538\) −18.2225 −0.785626
\(539\) 25.1801 1.08458
\(540\) 22.0438 0.948616
\(541\) −3.86417 −0.166134 −0.0830668 0.996544i \(-0.526471\pi\)
−0.0830668 + 0.996544i \(0.526471\pi\)
\(542\) −11.8484 −0.508932
\(543\) −5.08026 −0.218015
\(544\) 3.19553 0.137007
\(545\) 44.9937 1.92732
\(546\) 18.9084 0.809205
\(547\) −0.334902 −0.0143194 −0.00715968 0.999974i \(-0.502279\pi\)
−0.00715968 + 0.999974i \(0.502279\pi\)
\(548\) 7.06102 0.301632
\(549\) −5.66130 −0.241619
\(550\) 47.9307 2.04377
\(551\) 4.85780 0.206949
\(552\) 4.93881 0.210210
\(553\) −48.9406 −2.08117
\(554\) −15.4431 −0.656114
\(555\) 24.8428 1.05452
\(556\) −13.0236 −0.552325
\(557\) −14.8858 −0.630731 −0.315365 0.948970i \(-0.602127\pi\)
−0.315365 + 0.948970i \(0.602127\pi\)
\(558\) 5.47673 0.231849
\(559\) 26.3945 1.11637
\(560\) −13.9676 −0.590239
\(561\) −22.3268 −0.942639
\(562\) 17.7149 0.747257
\(563\) −28.9218 −1.21891 −0.609454 0.792821i \(-0.708611\pi\)
−0.609454 + 0.792821i \(0.708611\pi\)
\(564\) −6.43434 −0.270935
\(565\) 22.3673 0.940999
\(566\) −14.4636 −0.607949
\(567\) 23.7212 0.996198
\(568\) −11.0025 −0.461654
\(569\) 38.7476 1.62438 0.812191 0.583391i \(-0.198275\pi\)
0.812191 + 0.583391i \(0.198275\pi\)
\(570\) −6.95915 −0.291487
\(571\) 14.9236 0.624532 0.312266 0.949995i \(-0.398912\pi\)
0.312266 + 0.949995i \(0.398912\pi\)
\(572\) 15.7630 0.659086
\(573\) 3.09409 0.129257
\(574\) 21.1335 0.882097
\(575\) −33.8807 −1.41292
\(576\) −0.633629 −0.0264012
\(577\) −25.6331 −1.06712 −0.533560 0.845762i \(-0.679146\pi\)
−0.533560 + 0.845762i \(0.679146\pi\)
\(578\) −6.78859 −0.282368
\(579\) −20.2587 −0.841921
\(580\) 16.7007 0.693460
\(581\) −35.3246 −1.46551
\(582\) −22.0480 −0.913918
\(583\) −3.03555 −0.125720
\(584\) −14.9609 −0.619087
\(585\) −8.67237 −0.358559
\(586\) −31.4451 −1.29898
\(587\) −12.2524 −0.505713 −0.252856 0.967504i \(-0.581370\pi\)
−0.252856 + 0.967504i \(0.581370\pi\)
\(588\) −8.52818 −0.351696
\(589\) −9.91507 −0.408543
\(590\) −3.65985 −0.150673
\(591\) −23.8824 −0.982392
\(592\) −4.09499 −0.168303
\(593\) −8.85636 −0.363687 −0.181844 0.983327i \(-0.558206\pi\)
−0.181844 + 0.983327i \(0.558206\pi\)
\(594\) 25.3878 1.04167
\(595\) −44.6339 −1.82981
\(596\) 11.5078 0.471379
\(597\) 9.16956 0.375285
\(598\) −11.1424 −0.455646
\(599\) 36.9916 1.51144 0.755718 0.654897i \(-0.227288\pi\)
0.755718 + 0.654897i \(0.227288\pi\)
\(600\) −16.2335 −0.662730
\(601\) 10.3581 0.422516 0.211258 0.977430i \(-0.432244\pi\)
0.211258 + 0.977430i \(0.432244\pi\)
\(602\) −26.9359 −1.09783
\(603\) 2.80985 0.114426
\(604\) −4.74768 −0.193180
\(605\) 37.9753 1.54391
\(606\) −24.9928 −1.01526
\(607\) −9.37971 −0.380711 −0.190355 0.981715i \(-0.560964\pi\)
−0.190355 + 0.981715i \(0.560964\pi\)
\(608\) 1.14712 0.0465219
\(609\) 23.0721 0.934930
\(610\) 35.2360 1.42666
\(611\) 14.5164 0.587273
\(612\) −2.02478 −0.0818469
\(613\) −40.5790 −1.63897 −0.819486 0.573100i \(-0.805741\pi\)
−0.819486 + 0.573100i \(0.805741\pi\)
\(614\) 25.5046 1.02928
\(615\) 36.1995 1.45971
\(616\) −16.0864 −0.648139
\(617\) −32.2426 −1.29804 −0.649020 0.760771i \(-0.724821\pi\)
−0.649020 + 0.760771i \(0.724821\pi\)
\(618\) 3.80088 0.152894
\(619\) −22.7199 −0.913190 −0.456595 0.889675i \(-0.650931\pi\)
−0.456595 + 0.889675i \(0.650931\pi\)
\(620\) −34.0872 −1.36898
\(621\) −17.9458 −0.720141
\(622\) 12.6107 0.505642
\(623\) −30.7370 −1.23145
\(624\) −5.33874 −0.213721
\(625\) 33.5989 1.34396
\(626\) 25.7813 1.03043
\(627\) −8.01481 −0.320081
\(628\) −18.4666 −0.736898
\(629\) −13.0857 −0.521760
\(630\) 8.85027 0.352603
\(631\) −6.41711 −0.255461 −0.127731 0.991809i \(-0.540769\pi\)
−0.127731 + 0.991809i \(0.540769\pi\)
\(632\) 13.8183 0.549660
\(633\) −3.72100 −0.147896
\(634\) 34.2888 1.36178
\(635\) 2.80396 0.111272
\(636\) 1.02810 0.0407669
\(637\) 19.2403 0.762329
\(638\) 19.2341 0.761487
\(639\) 6.97149 0.275788
\(640\) 3.94371 0.155889
\(641\) 20.6424 0.815326 0.407663 0.913133i \(-0.366344\pi\)
0.407663 + 0.913133i \(0.366344\pi\)
\(642\) 5.57834 0.220159
\(643\) −1.92636 −0.0759684 −0.0379842 0.999278i \(-0.512094\pi\)
−0.0379842 + 0.999278i \(0.512094\pi\)
\(644\) 11.3710 0.448079
\(645\) −46.1384 −1.81670
\(646\) 3.66566 0.144223
\(647\) −6.10757 −0.240113 −0.120057 0.992767i \(-0.538308\pi\)
−0.120057 + 0.992767i \(0.538308\pi\)
\(648\) −6.69763 −0.263108
\(649\) −4.21502 −0.165454
\(650\) 36.6242 1.43652
\(651\) −47.0917 −1.84567
\(652\) −22.9352 −0.898211
\(653\) −4.57799 −0.179151 −0.0895753 0.995980i \(-0.528551\pi\)
−0.0895753 + 0.995980i \(0.528551\pi\)
\(654\) −17.5504 −0.686276
\(655\) 61.9287 2.41975
\(656\) −5.96700 −0.232972
\(657\) 9.47967 0.369837
\(658\) −14.8142 −0.577519
\(659\) 17.9011 0.697328 0.348664 0.937248i \(-0.386635\pi\)
0.348664 + 0.937248i \(0.386635\pi\)
\(660\) −27.5543 −1.07255
\(661\) −17.3864 −0.676251 −0.338125 0.941101i \(-0.609793\pi\)
−0.338125 + 0.941101i \(0.609793\pi\)
\(662\) 0.306690 0.0119198
\(663\) −17.0601 −0.662560
\(664\) 9.97381 0.387059
\(665\) −16.0225 −0.621327
\(666\) 2.59471 0.100543
\(667\) −13.5960 −0.526439
\(668\) −9.37258 −0.362636
\(669\) 19.9220 0.770230
\(670\) −17.4886 −0.675642
\(671\) 40.5811 1.56662
\(672\) 5.44826 0.210171
\(673\) 34.7247 1.33854 0.669269 0.743021i \(-0.266608\pi\)
0.669269 + 0.743021i \(0.266608\pi\)
\(674\) −9.17661 −0.353470
\(675\) 58.9866 2.27039
\(676\) −0.955327 −0.0367433
\(677\) −10.7236 −0.412142 −0.206071 0.978537i \(-0.566068\pi\)
−0.206071 + 0.978537i \(0.566068\pi\)
\(678\) −8.72468 −0.335069
\(679\) −50.7626 −1.94809
\(680\) 12.6023 0.483274
\(681\) −11.8244 −0.453114
\(682\) −39.2581 −1.50327
\(683\) 9.72173 0.371992 0.185996 0.982551i \(-0.440449\pi\)
0.185996 + 0.982551i \(0.440449\pi\)
\(684\) −0.726849 −0.0277918
\(685\) 27.8467 1.06397
\(686\) 5.15714 0.196901
\(687\) 46.3618 1.76881
\(688\) 7.60529 0.289949
\(689\) −2.31949 −0.0883656
\(690\) 19.4773 0.741487
\(691\) 20.8484 0.793109 0.396554 0.918011i \(-0.370206\pi\)
0.396554 + 0.918011i \(0.370206\pi\)
\(692\) 6.83501 0.259828
\(693\) 10.1928 0.387193
\(694\) 9.75999 0.370484
\(695\) −51.3615 −1.94825
\(696\) −6.51436 −0.246926
\(697\) −19.0677 −0.722242
\(698\) 21.7395 0.822852
\(699\) −25.5802 −0.967533
\(700\) −37.3755 −1.41266
\(701\) 14.7538 0.557245 0.278623 0.960401i \(-0.410122\pi\)
0.278623 + 0.960401i \(0.410122\pi\)
\(702\) 19.3990 0.732168
\(703\) −4.69745 −0.177168
\(704\) 4.54195 0.171181
\(705\) −25.3752 −0.955686
\(706\) −16.7254 −0.629467
\(707\) −57.5427 −2.16411
\(708\) 1.42757 0.0536515
\(709\) −26.0324 −0.977666 −0.488833 0.872377i \(-0.662577\pi\)
−0.488833 + 0.872377i \(0.662577\pi\)
\(710\) −43.3906 −1.62842
\(711\) −8.75564 −0.328362
\(712\) 8.67852 0.325241
\(713\) 27.7503 1.03926
\(714\) 17.4101 0.651555
\(715\) 62.1649 2.32484
\(716\) 2.24249 0.0838056
\(717\) −3.79946 −0.141893
\(718\) −8.80493 −0.328597
\(719\) 5.33942 0.199127 0.0995634 0.995031i \(-0.468255\pi\)
0.0995634 + 0.995031i \(0.468255\pi\)
\(720\) −2.49885 −0.0931267
\(721\) 8.75102 0.325905
\(722\) −17.6841 −0.658135
\(723\) −44.7001 −1.66241
\(724\) 3.30251 0.122737
\(725\) 44.6891 1.65971
\(726\) −14.8128 −0.549754
\(727\) −34.4170 −1.27646 −0.638228 0.769848i \(-0.720332\pi\)
−0.638228 + 0.769848i \(0.720332\pi\)
\(728\) −12.2917 −0.455563
\(729\) 30.0394 1.11257
\(730\) −59.0016 −2.18375
\(731\) 24.3029 0.898877
\(732\) −13.7443 −0.508004
\(733\) −51.6198 −1.90662 −0.953310 0.301995i \(-0.902348\pi\)
−0.953310 + 0.301995i \(0.902348\pi\)
\(734\) 8.30729 0.306628
\(735\) −33.6327 −1.24056
\(736\) −3.21056 −0.118343
\(737\) −20.1415 −0.741920
\(738\) 3.78086 0.139176
\(739\) −9.38370 −0.345185 −0.172592 0.984993i \(-0.555214\pi\)
−0.172592 + 0.984993i \(0.555214\pi\)
\(740\) −16.1495 −0.593667
\(741\) −6.12419 −0.224978
\(742\) 2.36707 0.0868979
\(743\) −28.7225 −1.05373 −0.526863 0.849950i \(-0.676632\pi\)
−0.526863 + 0.849950i \(0.676632\pi\)
\(744\) 13.2962 0.487463
\(745\) 45.3836 1.66272
\(746\) −21.1733 −0.775208
\(747\) −6.31970 −0.231226
\(748\) 14.5139 0.530682
\(749\) 12.8434 0.469287
\(750\) −33.6872 −1.23008
\(751\) −8.95709 −0.326849 −0.163425 0.986556i \(-0.552254\pi\)
−0.163425 + 0.986556i \(0.552254\pi\)
\(752\) 4.18276 0.152530
\(753\) −19.4986 −0.710569
\(754\) 14.6970 0.535232
\(755\) −18.7235 −0.681417
\(756\) −19.7969 −0.720008
\(757\) 27.2589 0.990740 0.495370 0.868682i \(-0.335032\pi\)
0.495370 + 0.868682i \(0.335032\pi\)
\(758\) 11.4427 0.415618
\(759\) 22.4318 0.814224
\(760\) 4.52392 0.164100
\(761\) 6.03567 0.218793 0.109396 0.993998i \(-0.465108\pi\)
0.109396 + 0.993998i \(0.465108\pi\)
\(762\) −1.09373 −0.0396215
\(763\) −40.4076 −1.46285
\(764\) −2.01137 −0.0727687
\(765\) −7.98515 −0.288704
\(766\) 24.9349 0.900933
\(767\) −3.22073 −0.116294
\(768\) −1.53830 −0.0555087
\(769\) −40.8408 −1.47276 −0.736378 0.676571i \(-0.763465\pi\)
−0.736378 + 0.676571i \(0.763465\pi\)
\(770\) −63.4401 −2.28622
\(771\) 16.6713 0.600403
\(772\) 13.1695 0.473981
\(773\) 36.1085 1.29873 0.649365 0.760477i \(-0.275035\pi\)
0.649365 + 0.760477i \(0.275035\pi\)
\(774\) −4.81893 −0.173213
\(775\) −91.2132 −3.27647
\(776\) 14.3327 0.514513
\(777\) −22.3106 −0.800387
\(778\) −7.95651 −0.285255
\(779\) −6.84487 −0.245243
\(780\) −21.0545 −0.753871
\(781\) −49.9727 −1.78817
\(782\) −10.2594 −0.366877
\(783\) 23.6708 0.845924
\(784\) 5.54389 0.197996
\(785\) −72.8270 −2.59931
\(786\) −24.1562 −0.861622
\(787\) −24.2501 −0.864423 −0.432212 0.901772i \(-0.642267\pi\)
−0.432212 + 0.901772i \(0.642267\pi\)
\(788\) 15.5252 0.553062
\(789\) 10.6093 0.377700
\(790\) 54.4952 1.93885
\(791\) −20.0874 −0.714227
\(792\) −2.87791 −0.102262
\(793\) 31.0084 1.10114
\(794\) −3.17224 −0.112579
\(795\) 4.05454 0.143800
\(796\) −5.96083 −0.211276
\(797\) −55.4003 −1.96238 −0.981189 0.193050i \(-0.938162\pi\)
−0.981189 + 0.193050i \(0.938162\pi\)
\(798\) 6.24981 0.221241
\(799\) 13.3661 0.472860
\(800\) 10.5529 0.373101
\(801\) −5.49896 −0.194296
\(802\) 23.2436 0.820758
\(803\) −67.9517 −2.39796
\(804\) 6.82166 0.240581
\(805\) 44.8438 1.58054
\(806\) −29.9974 −1.05661
\(807\) 28.0316 0.986760
\(808\) 16.2470 0.571568
\(809\) −21.6575 −0.761437 −0.380718 0.924691i \(-0.624323\pi\)
−0.380718 + 0.924691i \(0.624323\pi\)
\(810\) −26.4135 −0.928077
\(811\) 26.1574 0.918512 0.459256 0.888304i \(-0.348116\pi\)
0.459256 + 0.888304i \(0.348116\pi\)
\(812\) −14.9984 −0.526342
\(813\) 18.2264 0.639227
\(814\) −18.5993 −0.651904
\(815\) −90.4498 −3.16832
\(816\) −4.91569 −0.172083
\(817\) 8.72419 0.305221
\(818\) −3.26133 −0.114030
\(819\) 7.78841 0.272149
\(820\) −23.5321 −0.821778
\(821\) −39.0897 −1.36424 −0.682120 0.731240i \(-0.738942\pi\)
−0.682120 + 0.731240i \(0.738942\pi\)
\(822\) −10.8620 −0.378855
\(823\) 23.5206 0.819878 0.409939 0.912113i \(-0.365550\pi\)
0.409939 + 0.912113i \(0.365550\pi\)
\(824\) −2.47083 −0.0860754
\(825\) −73.7318 −2.56701
\(826\) 3.28680 0.114362
\(827\) 37.2711 1.29604 0.648022 0.761622i \(-0.275597\pi\)
0.648022 + 0.761622i \(0.275597\pi\)
\(828\) 2.03431 0.0706970
\(829\) 2.33787 0.0811975 0.0405988 0.999176i \(-0.487073\pi\)
0.0405988 + 0.999176i \(0.487073\pi\)
\(830\) 39.3339 1.36530
\(831\) 23.7561 0.824091
\(832\) 3.47054 0.120319
\(833\) 17.7157 0.613812
\(834\) 20.0343 0.693730
\(835\) −36.9628 −1.27915
\(836\) 5.21017 0.180197
\(837\) −48.3135 −1.66996
\(838\) 19.1123 0.660224
\(839\) 16.1157 0.556377 0.278188 0.960527i \(-0.410266\pi\)
0.278188 + 0.960527i \(0.410266\pi\)
\(840\) 21.4864 0.741350
\(841\) −11.0667 −0.381610
\(842\) −32.5597 −1.12208
\(843\) −27.2508 −0.938568
\(844\) 2.41890 0.0832619
\(845\) −3.76754 −0.129607
\(846\) −2.65032 −0.0911198
\(847\) −34.1045 −1.17184
\(848\) −0.668336 −0.0229508
\(849\) 22.2493 0.763595
\(850\) 33.7220 1.15666
\(851\) 13.1472 0.450681
\(852\) 16.9251 0.579846
\(853\) −22.8859 −0.783599 −0.391800 0.920051i \(-0.628147\pi\)
−0.391800 + 0.920051i \(0.628147\pi\)
\(854\) −31.6444 −1.08285
\(855\) −2.86649 −0.0980318
\(856\) −3.62630 −0.123944
\(857\) −20.7919 −0.710238 −0.355119 0.934821i \(-0.615560\pi\)
−0.355119 + 0.934821i \(0.615560\pi\)
\(858\) −24.2483 −0.827823
\(859\) −12.5793 −0.429201 −0.214600 0.976702i \(-0.568845\pi\)
−0.214600 + 0.976702i \(0.568845\pi\)
\(860\) 29.9931 1.02276
\(861\) −32.5097 −1.10793
\(862\) 18.4181 0.627325
\(863\) 38.7324 1.31847 0.659233 0.751939i \(-0.270881\pi\)
0.659233 + 0.751939i \(0.270881\pi\)
\(864\) 5.58962 0.190163
\(865\) 26.9553 0.916509
\(866\) −5.93243 −0.201592
\(867\) 10.4429 0.354659
\(868\) 30.6128 1.03907
\(869\) 62.7618 2.12905
\(870\) −25.6908 −0.870998
\(871\) −15.3903 −0.521479
\(872\) 11.4090 0.386357
\(873\) −9.08160 −0.307366
\(874\) −3.68290 −0.124576
\(875\) −77.5604 −2.62202
\(876\) 23.0144 0.777584
\(877\) 4.33349 0.146331 0.0731657 0.997320i \(-0.476690\pi\)
0.0731657 + 0.997320i \(0.476690\pi\)
\(878\) 11.5859 0.391006
\(879\) 48.3720 1.63155
\(880\) 17.9122 0.603819
\(881\) −6.87192 −0.231521 −0.115760 0.993277i \(-0.536930\pi\)
−0.115760 + 0.993277i \(0.536930\pi\)
\(882\) −3.51277 −0.118281
\(883\) −31.0302 −1.04425 −0.522125 0.852869i \(-0.674861\pi\)
−0.522125 + 0.852869i \(0.674861\pi\)
\(884\) 11.0902 0.373005
\(885\) 5.62995 0.189249
\(886\) −9.60530 −0.322696
\(887\) −13.7576 −0.461936 −0.230968 0.972961i \(-0.574189\pi\)
−0.230968 + 0.972961i \(0.574189\pi\)
\(888\) 6.29933 0.211392
\(889\) −2.51816 −0.0844563
\(890\) 34.2256 1.14724
\(891\) −30.4203 −1.01912
\(892\) −12.9507 −0.433620
\(893\) 4.79813 0.160563
\(894\) −17.7025 −0.592060
\(895\) 8.84372 0.295613
\(896\) −3.54174 −0.118321
\(897\) 17.1404 0.572300
\(898\) −35.5928 −1.18775
\(899\) −36.6030 −1.22078
\(900\) −6.68661 −0.222887
\(901\) −2.13569 −0.0711501
\(902\) −27.1018 −0.902392
\(903\) 41.4356 1.37889
\(904\) 5.67163 0.188636
\(905\) 13.0242 0.432938
\(906\) 7.30336 0.242638
\(907\) −24.3310 −0.807897 −0.403949 0.914782i \(-0.632363\pi\)
−0.403949 + 0.914782i \(0.632363\pi\)
\(908\) 7.68669 0.255092
\(909\) −10.2946 −0.341450
\(910\) −48.4751 −1.60694
\(911\) −51.9475 −1.72110 −0.860548 0.509370i \(-0.829879\pi\)
−0.860548 + 0.509370i \(0.829879\pi\)
\(912\) −1.76462 −0.0584324
\(913\) 45.3006 1.49923
\(914\) −39.0420 −1.29139
\(915\) −54.2036 −1.79192
\(916\) −30.1383 −0.995798
\(917\) −55.6164 −1.83661
\(918\) 17.8618 0.589527
\(919\) −47.1052 −1.55386 −0.776929 0.629588i \(-0.783224\pi\)
−0.776929 + 0.629588i \(0.783224\pi\)
\(920\) −12.6615 −0.417439
\(921\) −39.2338 −1.29280
\(922\) 15.9153 0.524142
\(923\) −38.1846 −1.25686
\(924\) 24.7457 0.814074
\(925\) −43.2140 −1.42087
\(926\) −5.96915 −0.196158
\(927\) 1.56559 0.0514207
\(928\) 4.23477 0.139013
\(929\) 47.8679 1.57050 0.785248 0.619182i \(-0.212536\pi\)
0.785248 + 0.619182i \(0.212536\pi\)
\(930\) 52.4365 1.71946
\(931\) 6.35952 0.208425
\(932\) 16.6289 0.544697
\(933\) −19.3990 −0.635095
\(934\) −39.0600 −1.27808
\(935\) 57.2388 1.87191
\(936\) −2.19904 −0.0718778
\(937\) −29.4302 −0.961442 −0.480721 0.876874i \(-0.659625\pi\)
−0.480721 + 0.876874i \(0.659625\pi\)
\(938\) 15.7060 0.512818
\(939\) −39.6593 −1.29423
\(940\) 16.4956 0.538027
\(941\) 16.6307 0.542146 0.271073 0.962559i \(-0.412621\pi\)
0.271073 + 0.962559i \(0.412621\pi\)
\(942\) 28.4072 0.925557
\(943\) 19.1574 0.623851
\(944\) −0.928020 −0.0302045
\(945\) −78.0735 −2.53973
\(946\) 34.5429 1.12309
\(947\) −6.20208 −0.201541 −0.100770 0.994910i \(-0.532131\pi\)
−0.100770 + 0.994910i \(0.532131\pi\)
\(948\) −21.2566 −0.690383
\(949\) −51.9225 −1.68548
\(950\) 12.1054 0.392752
\(951\) −52.7464 −1.71042
\(952\) −11.3177 −0.366810
\(953\) −8.44933 −0.273701 −0.136850 0.990592i \(-0.543698\pi\)
−0.136850 + 0.990592i \(0.543698\pi\)
\(954\) 0.423477 0.0137106
\(955\) −7.93226 −0.256682
\(956\) 2.46990 0.0798824
\(957\) −29.5879 −0.956441
\(958\) −38.1035 −1.23107
\(959\) −25.0083 −0.807559
\(960\) −6.06662 −0.195799
\(961\) 43.7090 1.40997
\(962\) −14.2118 −0.458208
\(963\) 2.29773 0.0740432
\(964\) 29.0581 0.935897
\(965\) 51.9368 1.67190
\(966\) −17.4920 −0.562795
\(967\) −30.5271 −0.981687 −0.490843 0.871248i \(-0.663311\pi\)
−0.490843 + 0.871248i \(0.663311\pi\)
\(968\) 9.62932 0.309498
\(969\) −5.63889 −0.181147
\(970\) 56.5240 1.81488
\(971\) 41.0564 1.31756 0.658781 0.752335i \(-0.271072\pi\)
0.658781 + 0.752335i \(0.271072\pi\)
\(972\) −6.46588 −0.207393
\(973\) 46.1263 1.47874
\(974\) −17.7659 −0.569256
\(975\) −56.3391 −1.80430
\(976\) 8.93473 0.285994
\(977\) 28.4888 0.911438 0.455719 0.890124i \(-0.349382\pi\)
0.455719 + 0.890124i \(0.349382\pi\)
\(978\) 35.2812 1.12817
\(979\) 39.4174 1.25979
\(980\) 21.8635 0.698405
\(981\) −7.22906 −0.230806
\(982\) 11.8118 0.376929
\(983\) −0.0729452 −0.00232659 −0.00116330 0.999999i \(-0.500370\pi\)
−0.00116330 + 0.999999i \(0.500370\pi\)
\(984\) 9.17904 0.292617
\(985\) 61.2269 1.95085
\(986\) 13.5323 0.430958
\(987\) 22.7887 0.725374
\(988\) 3.98113 0.126657
\(989\) −24.4173 −0.776424
\(990\) −11.3497 −0.360716
\(991\) 23.8192 0.756641 0.378320 0.925675i \(-0.376502\pi\)
0.378320 + 0.925675i \(0.376502\pi\)
\(992\) −8.64344 −0.274429
\(993\) −0.471782 −0.0149715
\(994\) 38.9679 1.23599
\(995\) −23.5078 −0.745248
\(996\) −15.3427 −0.486153
\(997\) 32.6055 1.03263 0.516313 0.856400i \(-0.327304\pi\)
0.516313 + 0.856400i \(0.327304\pi\)
\(998\) −34.9022 −1.10481
\(999\) −22.8894 −0.724190
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 4034.2.a.d.1.12 52
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4034.2.a.d.1.12 52 1.1 even 1 trivial