Properties

Label 4034.2.a.d.1.16
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 1.16
Character \(\chi\) = 4034.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.04358 q^{3} +1.00000 q^{4} +1.25349 q^{5} -1.04358 q^{6} +0.828851 q^{7} +1.00000 q^{8} -1.91094 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.04358 q^{3} +1.00000 q^{4} +1.25349 q^{5} -1.04358 q^{6} +0.828851 q^{7} +1.00000 q^{8} -1.91094 q^{9} +1.25349 q^{10} +6.21529 q^{11} -1.04358 q^{12} +0.865537 q^{13} +0.828851 q^{14} -1.30811 q^{15} +1.00000 q^{16} -6.80039 q^{17} -1.91094 q^{18} +6.14782 q^{19} +1.25349 q^{20} -0.864972 q^{21} +6.21529 q^{22} +5.96113 q^{23} -1.04358 q^{24} -3.42877 q^{25} +0.865537 q^{26} +5.12496 q^{27} +0.828851 q^{28} -3.08253 q^{29} -1.30811 q^{30} +1.21145 q^{31} +1.00000 q^{32} -6.48615 q^{33} -6.80039 q^{34} +1.03896 q^{35} -1.91094 q^{36} -2.09272 q^{37} +6.14782 q^{38} -0.903257 q^{39} +1.25349 q^{40} +10.4877 q^{41} -0.864972 q^{42} +6.70944 q^{43} +6.21529 q^{44} -2.39534 q^{45} +5.96113 q^{46} -3.80558 q^{47} -1.04358 q^{48} -6.31301 q^{49} -3.42877 q^{50} +7.09675 q^{51} +0.865537 q^{52} -13.0641 q^{53} +5.12496 q^{54} +7.79080 q^{55} +0.828851 q^{56} -6.41574 q^{57} -3.08253 q^{58} -2.61789 q^{59} -1.30811 q^{60} +15.2222 q^{61} +1.21145 q^{62} -1.58389 q^{63} +1.00000 q^{64} +1.08494 q^{65} -6.48615 q^{66} +10.1005 q^{67} -6.80039 q^{68} -6.22091 q^{69} +1.03896 q^{70} +11.9824 q^{71} -1.91094 q^{72} -10.2155 q^{73} -2.09272 q^{74} +3.57819 q^{75} +6.14782 q^{76} +5.15155 q^{77} -0.903257 q^{78} -13.2547 q^{79} +1.25349 q^{80} +0.384529 q^{81} +10.4877 q^{82} -7.59965 q^{83} -0.864972 q^{84} -8.52421 q^{85} +6.70944 q^{86} +3.21687 q^{87} +6.21529 q^{88} +14.7901 q^{89} -2.39534 q^{90} +0.717402 q^{91} +5.96113 q^{92} -1.26424 q^{93} -3.80558 q^{94} +7.70622 q^{95} -1.04358 q^{96} +12.8202 q^{97} -6.31301 q^{98} -11.8771 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 52q + 52q^{2} + 16q^{3} + 52q^{4} + 24q^{5} + 16q^{6} + 12q^{7} + 52q^{8} + 70q^{9} + O(q^{10}) \) \( 52q + 52q^{2} + 16q^{3} + 52q^{4} + 24q^{5} + 16q^{6} + 12q^{7} + 52q^{8} + 70q^{9} + 24q^{10} + 19q^{11} + 16q^{12} + 27q^{13} + 12q^{14} + 5q^{15} + 52q^{16} + 43q^{17} + 70q^{18} + 35q^{19} + 24q^{20} + 29q^{21} + 19q^{22} + 2q^{23} + 16q^{24} + 88q^{25} + 27q^{26} + 49q^{27} + 12q^{28} + 31q^{29} + 5q^{30} + 59q^{31} + 52q^{32} + 45q^{33} + 43q^{34} + 18q^{35} + 70q^{36} + 60q^{37} + 35q^{38} + 6q^{39} + 24q^{40} + 56q^{41} + 29q^{42} + 34q^{43} + 19q^{44} + 61q^{45} + 2q^{46} - 4q^{47} + 16q^{48} + 102q^{49} + 88q^{50} + 23q^{51} + 27q^{52} + 30q^{53} + 49q^{54} + 24q^{55} + 12q^{56} + 32q^{57} + 31q^{58} + 27q^{59} + 5q^{60} + 107q^{61} + 59q^{62} - 4q^{63} + 52q^{64} + 46q^{65} + 45q^{66} + 22q^{67} + 43q^{68} + 36q^{69} + 18q^{70} + 8q^{71} + 70q^{72} + 66q^{73} + 60q^{74} + 53q^{75} + 35q^{76} + 26q^{77} + 6q^{78} + 50q^{79} + 24q^{80} + 108q^{81} + 56q^{82} + 52q^{83} + 29q^{84} + 19q^{85} + 34q^{86} - 32q^{87} + 19q^{88} + 62q^{89} + 61q^{90} + 69q^{91} + 2q^{92} + 21q^{93} - 4q^{94} - 44q^{95} + 16q^{96} + 82q^{97} + 102q^{98} + 16q^{99} + O(q^{100}) \)

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
\(3\) −1.04358 −0.602511 −0.301255 0.953544i \(-0.597406\pi\)
−0.301255 + 0.953544i \(0.597406\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.25349 0.560577 0.280288 0.959916i \(-0.409570\pi\)
0.280288 + 0.959916i \(0.409570\pi\)
\(6\) −1.04358 −0.426039
\(7\) 0.828851 0.313276 0.156638 0.987656i \(-0.449934\pi\)
0.156638 + 0.987656i \(0.449934\pi\)
\(8\) 1.00000 0.353553
\(9\) −1.91094 −0.636981
\(10\) 1.25349 0.396388
\(11\) 6.21529 1.87398 0.936991 0.349354i \(-0.113599\pi\)
0.936991 + 0.349354i \(0.113599\pi\)
\(12\) −1.04358 −0.301255
\(13\) 0.865537 0.240057 0.120028 0.992770i \(-0.461701\pi\)
0.120028 + 0.992770i \(0.461701\pi\)
\(14\) 0.828851 0.221520
\(15\) −1.30811 −0.337754
\(16\) 1.00000 0.250000
\(17\) −6.80039 −1.64934 −0.824669 0.565616i \(-0.808639\pi\)
−0.824669 + 0.565616i \(0.808639\pi\)
\(18\) −1.91094 −0.450413
\(19\) 6.14782 1.41041 0.705203 0.709005i \(-0.250856\pi\)
0.705203 + 0.709005i \(0.250856\pi\)
\(20\) 1.25349 0.280288
\(21\) −0.864972 −0.188752
\(22\) 6.21529 1.32510
\(23\) 5.96113 1.24298 0.621491 0.783421i \(-0.286527\pi\)
0.621491 + 0.783421i \(0.286527\pi\)
\(24\) −1.04358 −0.213020
\(25\) −3.42877 −0.685753
\(26\) 0.865537 0.169746
\(27\) 5.12496 0.986298
\(28\) 0.828851 0.156638
\(29\) −3.08253 −0.572412 −0.286206 0.958168i \(-0.592394\pi\)
−0.286206 + 0.958168i \(0.592394\pi\)
\(30\) −1.30811 −0.238828
\(31\) 1.21145 0.217583 0.108791 0.994065i \(-0.465302\pi\)
0.108791 + 0.994065i \(0.465302\pi\)
\(32\) 1.00000 0.176777
\(33\) −6.48615 −1.12909
\(34\) −6.80039 −1.16626
\(35\) 1.03896 0.175616
\(36\) −1.91094 −0.318490
\(37\) −2.09272 −0.344042 −0.172021 0.985093i \(-0.555030\pi\)
−0.172021 + 0.985093i \(0.555030\pi\)
\(38\) 6.14782 0.997308
\(39\) −0.903257 −0.144637
\(40\) 1.25349 0.198194
\(41\) 10.4877 1.63790 0.818952 0.573862i \(-0.194555\pi\)
0.818952 + 0.573862i \(0.194555\pi\)
\(42\) −0.864972 −0.133468
\(43\) 6.70944 1.02318 0.511590 0.859230i \(-0.329057\pi\)
0.511590 + 0.859230i \(0.329057\pi\)
\(44\) 6.21529 0.936991
\(45\) −2.39534 −0.357077
\(46\) 5.96113 0.878921
\(47\) −3.80558 −0.555101 −0.277551 0.960711i \(-0.589523\pi\)
−0.277551 + 0.960711i \(0.589523\pi\)
\(48\) −1.04358 −0.150628
\(49\) −6.31301 −0.901858
\(50\) −3.42877 −0.484901
\(51\) 7.09675 0.993744
\(52\) 0.865537 0.120028
\(53\) −13.0641 −1.79449 −0.897244 0.441535i \(-0.854434\pi\)
−0.897244 + 0.441535i \(0.854434\pi\)
\(54\) 5.12496 0.697418
\(55\) 7.79080 1.05051
\(56\) 0.828851 0.110760
\(57\) −6.41574 −0.849785
\(58\) −3.08253 −0.404756
\(59\) −2.61789 −0.340820 −0.170410 0.985373i \(-0.554509\pi\)
−0.170410 + 0.985373i \(0.554509\pi\)
\(60\) −1.30811 −0.168877
\(61\) 15.2222 1.94900 0.974499 0.224394i \(-0.0720402\pi\)
0.974499 + 0.224394i \(0.0720402\pi\)
\(62\) 1.21145 0.153854
\(63\) −1.58389 −0.199551
\(64\) 1.00000 0.125000
\(65\) 1.08494 0.134570
\(66\) −6.48615 −0.798390
\(67\) 10.1005 1.23398 0.616988 0.786973i \(-0.288353\pi\)
0.616988 + 0.786973i \(0.288353\pi\)
\(68\) −6.80039 −0.824669
\(69\) −6.22091 −0.748910
\(70\) 1.03896 0.124179
\(71\) 11.9824 1.42205 0.711024 0.703167i \(-0.248231\pi\)
0.711024 + 0.703167i \(0.248231\pi\)
\(72\) −1.91094 −0.225207
\(73\) −10.2155 −1.19564 −0.597818 0.801632i \(-0.703965\pi\)
−0.597818 + 0.801632i \(0.703965\pi\)
\(74\) −2.09272 −0.243274
\(75\) 3.57819 0.413174
\(76\) 6.14782 0.705203
\(77\) 5.15155 0.587074
\(78\) −0.903257 −0.102274
\(79\) −13.2547 −1.49127 −0.745633 0.666357i \(-0.767853\pi\)
−0.745633 + 0.666357i \(0.767853\pi\)
\(80\) 1.25349 0.140144
\(81\) 0.384529 0.0427254
\(82\) 10.4877 1.15817
\(83\) −7.59965 −0.834170 −0.417085 0.908867i \(-0.636948\pi\)
−0.417085 + 0.908867i \(0.636948\pi\)
\(84\) −0.864972 −0.0943762
\(85\) −8.52421 −0.924581
\(86\) 6.70944 0.723497
\(87\) 3.21687 0.344884
\(88\) 6.21529 0.662552
\(89\) 14.7901 1.56774 0.783872 0.620922i \(-0.213242\pi\)
0.783872 + 0.620922i \(0.213242\pi\)
\(90\) −2.39534 −0.252491
\(91\) 0.717402 0.0752041
\(92\) 5.96113 0.621491
\(93\) −1.26424 −0.131096
\(94\) −3.80558 −0.392516
\(95\) 7.70622 0.790642
\(96\) −1.04358 −0.106510
\(97\) 12.8202 1.30169 0.650846 0.759210i \(-0.274414\pi\)
0.650846 + 0.759210i \(0.274414\pi\)
\(98\) −6.31301 −0.637710
\(99\) −11.8771 −1.19369
\(100\) −3.42877 −0.342877
\(101\) −11.4101 −1.13535 −0.567675 0.823253i \(-0.692157\pi\)
−0.567675 + 0.823253i \(0.692157\pi\)
\(102\) 7.09675 0.702683
\(103\) 7.64058 0.752849 0.376425 0.926447i \(-0.377153\pi\)
0.376425 + 0.926447i \(0.377153\pi\)
\(104\) 0.865537 0.0848729
\(105\) −1.08423 −0.105810
\(106\) −13.0641 −1.26889
\(107\) 4.91583 0.475231 0.237615 0.971359i \(-0.423634\pi\)
0.237615 + 0.971359i \(0.423634\pi\)
\(108\) 5.12496 0.493149
\(109\) −11.3104 −1.08334 −0.541668 0.840592i \(-0.682207\pi\)
−0.541668 + 0.840592i \(0.682207\pi\)
\(110\) 7.79080 0.742823
\(111\) 2.18392 0.207289
\(112\) 0.828851 0.0783191
\(113\) 5.23842 0.492789 0.246395 0.969170i \(-0.420754\pi\)
0.246395 + 0.969170i \(0.420754\pi\)
\(114\) −6.41574 −0.600889
\(115\) 7.47221 0.696787
\(116\) −3.08253 −0.286206
\(117\) −1.65399 −0.152912
\(118\) −2.61789 −0.240996
\(119\) −5.63652 −0.516699
\(120\) −1.30811 −0.119414
\(121\) 27.6299 2.51181
\(122\) 15.2222 1.37815
\(123\) −10.9448 −0.986855
\(124\) 1.21145 0.108791
\(125\) −10.5654 −0.944995
\(126\) −1.58389 −0.141104
\(127\) 3.45432 0.306521 0.153261 0.988186i \(-0.451023\pi\)
0.153261 + 0.988186i \(0.451023\pi\)
\(128\) 1.00000 0.0883883
\(129\) −7.00183 −0.616477
\(130\) 1.08494 0.0951556
\(131\) 1.25780 0.109894 0.0549471 0.998489i \(-0.482501\pi\)
0.0549471 + 0.998489i \(0.482501\pi\)
\(132\) −6.48615 −0.564547
\(133\) 5.09563 0.441847
\(134\) 10.1005 0.872552
\(135\) 6.42407 0.552896
\(136\) −6.80039 −0.583129
\(137\) 16.0337 1.36985 0.684926 0.728612i \(-0.259834\pi\)
0.684926 + 0.728612i \(0.259834\pi\)
\(138\) −6.22091 −0.529559
\(139\) 1.20032 0.101810 0.0509048 0.998704i \(-0.483789\pi\)
0.0509048 + 0.998704i \(0.483789\pi\)
\(140\) 1.03896 0.0878078
\(141\) 3.97143 0.334454
\(142\) 11.9824 1.00554
\(143\) 5.37957 0.449862
\(144\) −1.91094 −0.159245
\(145\) −3.86392 −0.320881
\(146\) −10.2155 −0.845442
\(147\) 6.58812 0.543379
\(148\) −2.09272 −0.172021
\(149\) 9.79280 0.802257 0.401129 0.916022i \(-0.368618\pi\)
0.401129 + 0.916022i \(0.368618\pi\)
\(150\) 3.57819 0.292158
\(151\) −10.8680 −0.884426 −0.442213 0.896910i \(-0.645807\pi\)
−0.442213 + 0.896910i \(0.645807\pi\)
\(152\) 6.14782 0.498654
\(153\) 12.9952 1.05060
\(154\) 5.15155 0.415124
\(155\) 1.51854 0.121972
\(156\) −0.903257 −0.0723184
\(157\) −13.6618 −1.09033 −0.545167 0.838327i \(-0.683534\pi\)
−0.545167 + 0.838327i \(0.683534\pi\)
\(158\) −13.2547 −1.05448
\(159\) 13.6334 1.08120
\(160\) 1.25349 0.0990969
\(161\) 4.94089 0.389397
\(162\) 0.384529 0.0302115
\(163\) 3.22517 0.252614 0.126307 0.991991i \(-0.459687\pi\)
0.126307 + 0.991991i \(0.459687\pi\)
\(164\) 10.4877 0.818952
\(165\) −8.13031 −0.632944
\(166\) −7.59965 −0.589847
\(167\) −9.12706 −0.706273 −0.353136 0.935572i \(-0.614885\pi\)
−0.353136 + 0.935572i \(0.614885\pi\)
\(168\) −0.864972 −0.0667340
\(169\) −12.2508 −0.942373
\(170\) −8.52421 −0.653777
\(171\) −11.7481 −0.898402
\(172\) 6.70944 0.511590
\(173\) −4.78033 −0.363441 −0.181721 0.983350i \(-0.558167\pi\)
−0.181721 + 0.983350i \(0.558167\pi\)
\(174\) 3.21687 0.243870
\(175\) −2.84194 −0.214830
\(176\) 6.21529 0.468495
\(177\) 2.73198 0.205348
\(178\) 14.7901 1.10856
\(179\) −8.25300 −0.616858 −0.308429 0.951247i \(-0.599803\pi\)
−0.308429 + 0.951247i \(0.599803\pi\)
\(180\) −2.39534 −0.178538
\(181\) 22.4047 1.66533 0.832663 0.553780i \(-0.186815\pi\)
0.832663 + 0.553780i \(0.186815\pi\)
\(182\) 0.717402 0.0531773
\(183\) −15.8855 −1.17429
\(184\) 5.96113 0.439460
\(185\) −2.62320 −0.192862
\(186\) −1.26424 −0.0926989
\(187\) −42.2664 −3.09083
\(188\) −3.80558 −0.277551
\(189\) 4.24783 0.308984
\(190\) 7.70622 0.559068
\(191\) 20.7592 1.50209 0.751043 0.660253i \(-0.229551\pi\)
0.751043 + 0.660253i \(0.229551\pi\)
\(192\) −1.04358 −0.0753138
\(193\) 11.7359 0.844771 0.422385 0.906416i \(-0.361193\pi\)
0.422385 + 0.906416i \(0.361193\pi\)
\(194\) 12.8202 0.920435
\(195\) −1.13222 −0.0810801
\(196\) −6.31301 −0.450929
\(197\) −10.7241 −0.764058 −0.382029 0.924150i \(-0.624775\pi\)
−0.382029 + 0.924150i \(0.624775\pi\)
\(198\) −11.8771 −0.844066
\(199\) 8.16835 0.579039 0.289520 0.957172i \(-0.406504\pi\)
0.289520 + 0.957172i \(0.406504\pi\)
\(200\) −3.42877 −0.242450
\(201\) −10.5407 −0.743483
\(202\) −11.4101 −0.802813
\(203\) −2.55496 −0.179323
\(204\) 7.09675 0.496872
\(205\) 13.1462 0.918172
\(206\) 7.64058 0.532345
\(207\) −11.3914 −0.791755
\(208\) 0.865537 0.0600142
\(209\) 38.2105 2.64308
\(210\) −1.08423 −0.0748191
\(211\) 26.6914 1.83751 0.918757 0.394823i \(-0.129194\pi\)
0.918757 + 0.394823i \(0.129194\pi\)
\(212\) −13.0641 −0.897244
\(213\) −12.5046 −0.856800
\(214\) 4.91583 0.336039
\(215\) 8.41020 0.573571
\(216\) 5.12496 0.348709
\(217\) 1.00411 0.0681636
\(218\) −11.3104 −0.766034
\(219\) 10.6607 0.720383
\(220\) 7.79080 0.525255
\(221\) −5.88599 −0.395935
\(222\) 2.18392 0.146575
\(223\) 15.0713 1.00925 0.504625 0.863338i \(-0.331631\pi\)
0.504625 + 0.863338i \(0.331631\pi\)
\(224\) 0.828851 0.0553800
\(225\) 6.55218 0.436812
\(226\) 5.23842 0.348455
\(227\) −25.6143 −1.70008 −0.850039 0.526720i \(-0.823422\pi\)
−0.850039 + 0.526720i \(0.823422\pi\)
\(228\) −6.41574 −0.424893
\(229\) −3.02832 −0.200117 −0.100059 0.994982i \(-0.531903\pi\)
−0.100059 + 0.994982i \(0.531903\pi\)
\(230\) 7.47221 0.492703
\(231\) −5.37605 −0.353718
\(232\) −3.08253 −0.202378
\(233\) −16.3038 −1.06810 −0.534049 0.845453i \(-0.679330\pi\)
−0.534049 + 0.845453i \(0.679330\pi\)
\(234\) −1.65399 −0.108125
\(235\) −4.77025 −0.311177
\(236\) −2.61789 −0.170410
\(237\) 13.8323 0.898504
\(238\) −5.63652 −0.365361
\(239\) 28.0855 1.81670 0.908350 0.418211i \(-0.137343\pi\)
0.908350 + 0.418211i \(0.137343\pi\)
\(240\) −1.30811 −0.0844384
\(241\) −19.7801 −1.27415 −0.637073 0.770804i \(-0.719855\pi\)
−0.637073 + 0.770804i \(0.719855\pi\)
\(242\) 27.6299 1.77612
\(243\) −15.7762 −1.01204
\(244\) 15.2222 0.974499
\(245\) −7.91328 −0.505561
\(246\) −10.9448 −0.697812
\(247\) 5.32117 0.338578
\(248\) 1.21145 0.0769272
\(249\) 7.93084 0.502596
\(250\) −10.5654 −0.668212
\(251\) 28.5753 1.80365 0.901827 0.432096i \(-0.142226\pi\)
0.901827 + 0.432096i \(0.142226\pi\)
\(252\) −1.58389 −0.0997755
\(253\) 37.0502 2.32932
\(254\) 3.45432 0.216743
\(255\) 8.89569 0.557070
\(256\) 1.00000 0.0625000
\(257\) 7.77246 0.484833 0.242417 0.970172i \(-0.422060\pi\)
0.242417 + 0.970172i \(0.422060\pi\)
\(258\) −7.00183 −0.435915
\(259\) −1.73456 −0.107780
\(260\) 1.08494 0.0672852
\(261\) 5.89054 0.364615
\(262\) 1.25780 0.0777070
\(263\) 0.0139729 0.000861606 0 0.000430803 1.00000i \(-0.499863\pi\)
0.000430803 1.00000i \(0.499863\pi\)
\(264\) −6.48615 −0.399195
\(265\) −16.3757 −1.00595
\(266\) 5.09563 0.312433
\(267\) −15.4346 −0.944583
\(268\) 10.1005 0.616988
\(269\) 29.5427 1.80125 0.900625 0.434597i \(-0.143109\pi\)
0.900625 + 0.434597i \(0.143109\pi\)
\(270\) 6.42407 0.390957
\(271\) −4.31315 −0.262005 −0.131003 0.991382i \(-0.541820\pi\)
−0.131003 + 0.991382i \(0.541820\pi\)
\(272\) −6.80039 −0.412334
\(273\) −0.748665 −0.0453113
\(274\) 16.0337 0.968632
\(275\) −21.3108 −1.28509
\(276\) −6.22091 −0.374455
\(277\) −3.14142 −0.188749 −0.0943747 0.995537i \(-0.530085\pi\)
−0.0943747 + 0.995537i \(0.530085\pi\)
\(278\) 1.20032 0.0719903
\(279\) −2.31501 −0.138596
\(280\) 1.03896 0.0620895
\(281\) −14.3643 −0.856901 −0.428451 0.903565i \(-0.640940\pi\)
−0.428451 + 0.903565i \(0.640940\pi\)
\(282\) 3.97143 0.236495
\(283\) −13.0024 −0.772913 −0.386456 0.922308i \(-0.626301\pi\)
−0.386456 + 0.922308i \(0.626301\pi\)
\(284\) 11.9824 0.711024
\(285\) −8.04205 −0.476370
\(286\) 5.37957 0.318100
\(287\) 8.69275 0.513117
\(288\) −1.91094 −0.112603
\(289\) 29.2454 1.72032
\(290\) −3.86392 −0.226897
\(291\) −13.3789 −0.784283
\(292\) −10.2155 −0.597818
\(293\) 0.623583 0.0364301 0.0182150 0.999834i \(-0.494202\pi\)
0.0182150 + 0.999834i \(0.494202\pi\)
\(294\) 6.58812 0.384227
\(295\) −3.28150 −0.191056
\(296\) −2.09272 −0.121637
\(297\) 31.8531 1.84831
\(298\) 9.79280 0.567281
\(299\) 5.15958 0.298386
\(300\) 3.57819 0.206587
\(301\) 5.56112 0.320538
\(302\) −10.8680 −0.625384
\(303\) 11.9074 0.684060
\(304\) 6.14782 0.352602
\(305\) 19.0808 1.09256
\(306\) 12.9952 0.742884
\(307\) 10.1719 0.580542 0.290271 0.956944i \(-0.406255\pi\)
0.290271 + 0.956944i \(0.406255\pi\)
\(308\) 5.15155 0.293537
\(309\) −7.97355 −0.453600
\(310\) 1.51854 0.0862472
\(311\) −26.4309 −1.49876 −0.749378 0.662142i \(-0.769648\pi\)
−0.749378 + 0.662142i \(0.769648\pi\)
\(312\) −0.903257 −0.0511368
\(313\) 33.5439 1.89601 0.948005 0.318254i \(-0.103097\pi\)
0.948005 + 0.318254i \(0.103097\pi\)
\(314\) −13.6618 −0.770983
\(315\) −1.98538 −0.111864
\(316\) −13.2547 −0.745633
\(317\) −19.8086 −1.11256 −0.556282 0.830993i \(-0.687773\pi\)
−0.556282 + 0.830993i \(0.687773\pi\)
\(318\) 13.6334 0.764523
\(319\) −19.1588 −1.07269
\(320\) 1.25349 0.0700721
\(321\) −5.13005 −0.286332
\(322\) 4.94089 0.275345
\(323\) −41.8076 −2.32624
\(324\) 0.384529 0.0213627
\(325\) −2.96773 −0.164620
\(326\) 3.22517 0.178625
\(327\) 11.8033 0.652722
\(328\) 10.4877 0.579087
\(329\) −3.15426 −0.173900
\(330\) −8.13031 −0.447559
\(331\) −26.7987 −1.47299 −0.736494 0.676444i \(-0.763520\pi\)
−0.736494 + 0.676444i \(0.763520\pi\)
\(332\) −7.59965 −0.417085
\(333\) 3.99907 0.219148
\(334\) −9.12706 −0.499410
\(335\) 12.6609 0.691738
\(336\) −0.864972 −0.0471881
\(337\) −24.9822 −1.36086 −0.680432 0.732811i \(-0.738208\pi\)
−0.680432 + 0.732811i \(0.738208\pi\)
\(338\) −12.2508 −0.666358
\(339\) −5.46671 −0.296911
\(340\) −8.52421 −0.462290
\(341\) 7.52952 0.407746
\(342\) −11.7481 −0.635266
\(343\) −11.0345 −0.595807
\(344\) 6.70944 0.361749
\(345\) −7.79784 −0.419822
\(346\) −4.78033 −0.256992
\(347\) 8.83481 0.474277 0.237139 0.971476i \(-0.423790\pi\)
0.237139 + 0.971476i \(0.423790\pi\)
\(348\) 3.21687 0.172442
\(349\) 6.49505 0.347672 0.173836 0.984775i \(-0.444384\pi\)
0.173836 + 0.984775i \(0.444384\pi\)
\(350\) −2.84194 −0.151908
\(351\) 4.43584 0.236768
\(352\) 6.21529 0.331276
\(353\) 4.24613 0.225999 0.112999 0.993595i \(-0.463954\pi\)
0.112999 + 0.993595i \(0.463954\pi\)
\(354\) 2.73198 0.145203
\(355\) 15.0198 0.797168
\(356\) 14.7901 0.783872
\(357\) 5.88215 0.311316
\(358\) −8.25300 −0.436184
\(359\) −5.56784 −0.293860 −0.146930 0.989147i \(-0.546939\pi\)
−0.146930 + 0.989147i \(0.546939\pi\)
\(360\) −2.39534 −0.126246
\(361\) 18.7957 0.989248
\(362\) 22.4047 1.17756
\(363\) −28.8340 −1.51339
\(364\) 0.717402 0.0376021
\(365\) −12.8050 −0.670245
\(366\) −15.8855 −0.830350
\(367\) 10.3769 0.541671 0.270836 0.962626i \(-0.412700\pi\)
0.270836 + 0.962626i \(0.412700\pi\)
\(368\) 5.96113 0.310745
\(369\) −20.0414 −1.04331
\(370\) −2.62320 −0.136374
\(371\) −10.8282 −0.562171
\(372\) −1.26424 −0.0655480
\(373\) −15.1138 −0.782562 −0.391281 0.920271i \(-0.627968\pi\)
−0.391281 + 0.920271i \(0.627968\pi\)
\(374\) −42.2664 −2.18555
\(375\) 11.0258 0.569369
\(376\) −3.80558 −0.196258
\(377\) −2.66805 −0.137411
\(378\) 4.24783 0.218485
\(379\) −20.1927 −1.03723 −0.518615 0.855008i \(-0.673552\pi\)
−0.518615 + 0.855008i \(0.673552\pi\)
\(380\) 7.70622 0.395321
\(381\) −3.60486 −0.184682
\(382\) 20.7592 1.06214
\(383\) −2.49821 −0.127653 −0.0638263 0.997961i \(-0.520330\pi\)
−0.0638263 + 0.997961i \(0.520330\pi\)
\(384\) −1.04358 −0.0532549
\(385\) 6.45741 0.329100
\(386\) 11.7359 0.597343
\(387\) −12.8213 −0.651746
\(388\) 12.8202 0.650846
\(389\) −35.4660 −1.79820 −0.899099 0.437746i \(-0.855777\pi\)
−0.899099 + 0.437746i \(0.855777\pi\)
\(390\) −1.13222 −0.0573323
\(391\) −40.5380 −2.05010
\(392\) −6.31301 −0.318855
\(393\) −1.31261 −0.0662125
\(394\) −10.7241 −0.540270
\(395\) −16.6146 −0.835969
\(396\) −11.8771 −0.596845
\(397\) −21.4444 −1.07626 −0.538131 0.842861i \(-0.680870\pi\)
−0.538131 + 0.842861i \(0.680870\pi\)
\(398\) 8.16835 0.409443
\(399\) −5.31769 −0.266218
\(400\) −3.42877 −0.171438
\(401\) −0.576737 −0.0288009 −0.0144004 0.999896i \(-0.504584\pi\)
−0.0144004 + 0.999896i \(0.504584\pi\)
\(402\) −10.5407 −0.525722
\(403\) 1.04856 0.0522323
\(404\) −11.4101 −0.567675
\(405\) 0.482003 0.0239509
\(406\) −2.55496 −0.126801
\(407\) −13.0069 −0.644728
\(408\) 7.09675 0.351341
\(409\) −15.9873 −0.790522 −0.395261 0.918569i \(-0.629346\pi\)
−0.395261 + 0.918569i \(0.629346\pi\)
\(410\) 13.1462 0.649245
\(411\) −16.7325 −0.825351
\(412\) 7.64058 0.376425
\(413\) −2.16984 −0.106771
\(414\) −11.3914 −0.559856
\(415\) −9.52607 −0.467617
\(416\) 0.865537 0.0424365
\(417\) −1.25263 −0.0613414
\(418\) 38.2105 1.86894
\(419\) 8.90380 0.434979 0.217490 0.976063i \(-0.430213\pi\)
0.217490 + 0.976063i \(0.430213\pi\)
\(420\) −1.08423 −0.0529051
\(421\) −28.5443 −1.39116 −0.695581 0.718448i \(-0.744853\pi\)
−0.695581 + 0.718448i \(0.744853\pi\)
\(422\) 26.6914 1.29932
\(423\) 7.27225 0.353589
\(424\) −13.0641 −0.634447
\(425\) 23.3170 1.13104
\(426\) −12.5046 −0.605849
\(427\) 12.6169 0.610575
\(428\) 4.91583 0.237615
\(429\) −5.61400 −0.271047
\(430\) 8.41020 0.405576
\(431\) 9.60792 0.462797 0.231399 0.972859i \(-0.425670\pi\)
0.231399 + 0.972859i \(0.425670\pi\)
\(432\) 5.12496 0.246575
\(433\) −5.66799 −0.272386 −0.136193 0.990682i \(-0.543487\pi\)
−0.136193 + 0.990682i \(0.543487\pi\)
\(434\) 1.00411 0.0481989
\(435\) 4.03230 0.193334
\(436\) −11.3104 −0.541668
\(437\) 36.6480 1.75311
\(438\) 10.6607 0.509388
\(439\) −2.24501 −0.107148 −0.0535742 0.998564i \(-0.517061\pi\)
−0.0535742 + 0.998564i \(0.517061\pi\)
\(440\) 7.79080 0.371412
\(441\) 12.0638 0.574466
\(442\) −5.88599 −0.279968
\(443\) −6.40432 −0.304279 −0.152139 0.988359i \(-0.548616\pi\)
−0.152139 + 0.988359i \(0.548616\pi\)
\(444\) 2.18392 0.103644
\(445\) 18.5392 0.878842
\(446\) 15.0713 0.713648
\(447\) −10.2196 −0.483368
\(448\) 0.828851 0.0391595
\(449\) −12.0705 −0.569642 −0.284821 0.958581i \(-0.591934\pi\)
−0.284821 + 0.958581i \(0.591934\pi\)
\(450\) 6.55218 0.308873
\(451\) 65.1842 3.06940
\(452\) 5.23842 0.246395
\(453\) 11.3416 0.532876
\(454\) −25.6143 −1.20214
\(455\) 0.899254 0.0421577
\(456\) −6.41574 −0.300444
\(457\) 14.1848 0.663535 0.331768 0.943361i \(-0.392355\pi\)
0.331768 + 0.943361i \(0.392355\pi\)
\(458\) −3.02832 −0.141504
\(459\) −34.8517 −1.62674
\(460\) 7.47221 0.348393
\(461\) −1.76534 −0.0822199 −0.0411099 0.999155i \(-0.513089\pi\)
−0.0411099 + 0.999155i \(0.513089\pi\)
\(462\) −5.37605 −0.250117
\(463\) −24.0956 −1.11982 −0.559908 0.828555i \(-0.689164\pi\)
−0.559908 + 0.828555i \(0.689164\pi\)
\(464\) −3.08253 −0.143103
\(465\) −1.58472 −0.0734894
\(466\) −16.3038 −0.755260
\(467\) −5.03203 −0.232855 −0.116427 0.993199i \(-0.537144\pi\)
−0.116427 + 0.993199i \(0.537144\pi\)
\(468\) −1.65399 −0.0764558
\(469\) 8.37183 0.386575
\(470\) −4.77025 −0.220035
\(471\) 14.2572 0.656938
\(472\) −2.61789 −0.120498
\(473\) 41.7011 1.91742
\(474\) 13.8323 0.635338
\(475\) −21.0794 −0.967191
\(476\) −5.63652 −0.258349
\(477\) 24.9647 1.14305
\(478\) 28.0855 1.28460
\(479\) 14.5764 0.666011 0.333005 0.942925i \(-0.391937\pi\)
0.333005 + 0.942925i \(0.391937\pi\)
\(480\) −1.30811 −0.0597070
\(481\) −1.81133 −0.0825895
\(482\) −19.7801 −0.900957
\(483\) −5.15621 −0.234616
\(484\) 27.6299 1.25590
\(485\) 16.0699 0.729698
\(486\) −15.7762 −0.715621
\(487\) −13.1104 −0.594089 −0.297045 0.954864i \(-0.596001\pi\)
−0.297045 + 0.954864i \(0.596001\pi\)
\(488\) 15.2222 0.689075
\(489\) −3.36572 −0.152203
\(490\) −7.91328 −0.357485
\(491\) 15.5892 0.703530 0.351765 0.936088i \(-0.385582\pi\)
0.351765 + 0.936088i \(0.385582\pi\)
\(492\) −10.9448 −0.493428
\(493\) 20.9624 0.944100
\(494\) 5.32117 0.239411
\(495\) −14.8878 −0.669155
\(496\) 1.21145 0.0543957
\(497\) 9.93163 0.445494
\(498\) 7.93084 0.355389
\(499\) 22.8412 1.02251 0.511255 0.859429i \(-0.329181\pi\)
0.511255 + 0.859429i \(0.329181\pi\)
\(500\) −10.5654 −0.472497
\(501\) 9.52481 0.425537
\(502\) 28.5753 1.27538
\(503\) −38.0256 −1.69548 −0.847739 0.530414i \(-0.822037\pi\)
−0.847739 + 0.530414i \(0.822037\pi\)
\(504\) −1.58389 −0.0705519
\(505\) −14.3025 −0.636451
\(506\) 37.0502 1.64708
\(507\) 12.7847 0.567790
\(508\) 3.45432 0.153261
\(509\) 36.4654 1.61630 0.808149 0.588978i \(-0.200469\pi\)
0.808149 + 0.588978i \(0.200469\pi\)
\(510\) 8.89569 0.393908
\(511\) −8.46714 −0.374564
\(512\) 1.00000 0.0441942
\(513\) 31.5073 1.39108
\(514\) 7.77246 0.342829
\(515\) 9.57738 0.422030
\(516\) −7.00183 −0.308238
\(517\) −23.6528 −1.04025
\(518\) −1.73456 −0.0762120
\(519\) 4.98865 0.218977
\(520\) 1.08494 0.0475778
\(521\) 1.40002 0.0613361 0.0306681 0.999530i \(-0.490237\pi\)
0.0306681 + 0.999530i \(0.490237\pi\)
\(522\) 5.89054 0.257822
\(523\) 3.98865 0.174412 0.0872058 0.996190i \(-0.472206\pi\)
0.0872058 + 0.996190i \(0.472206\pi\)
\(524\) 1.25780 0.0549471
\(525\) 2.96579 0.129438
\(526\) 0.0139729 0.000609247 0
\(527\) −8.23834 −0.358868
\(528\) −6.48615 −0.282273
\(529\) 12.5351 0.545003
\(530\) −16.3757 −0.711313
\(531\) 5.00264 0.217096
\(532\) 5.09563 0.220924
\(533\) 9.07750 0.393190
\(534\) −15.4346 −0.667921
\(535\) 6.16193 0.266404
\(536\) 10.1005 0.436276
\(537\) 8.61266 0.371664
\(538\) 29.5427 1.27368
\(539\) −39.2372 −1.69006
\(540\) 6.42407 0.276448
\(541\) −21.2376 −0.913077 −0.456539 0.889704i \(-0.650911\pi\)
−0.456539 + 0.889704i \(0.650911\pi\)
\(542\) −4.31315 −0.185266
\(543\) −23.3810 −1.00338
\(544\) −6.80039 −0.291565
\(545\) −14.1774 −0.607293
\(546\) −0.748665 −0.0320399
\(547\) −23.0288 −0.984641 −0.492320 0.870414i \(-0.663851\pi\)
−0.492320 + 0.870414i \(0.663851\pi\)
\(548\) 16.0337 0.684926
\(549\) −29.0887 −1.24147
\(550\) −21.3108 −0.908695
\(551\) −18.9508 −0.807333
\(552\) −6.22091 −0.264780
\(553\) −10.9861 −0.467178
\(554\) −3.14142 −0.133466
\(555\) 2.73752 0.116201
\(556\) 1.20032 0.0509048
\(557\) 5.12218 0.217034 0.108517 0.994095i \(-0.465390\pi\)
0.108517 + 0.994095i \(0.465390\pi\)
\(558\) −2.31501 −0.0980023
\(559\) 5.80727 0.245621
\(560\) 1.03896 0.0439039
\(561\) 44.1084 1.86226
\(562\) −14.3643 −0.605921
\(563\) 33.9207 1.42959 0.714794 0.699335i \(-0.246521\pi\)
0.714794 + 0.699335i \(0.246521\pi\)
\(564\) 3.97143 0.167227
\(565\) 6.56630 0.276246
\(566\) −13.0024 −0.546532
\(567\) 0.318717 0.0133849
\(568\) 11.9824 0.502770
\(569\) −41.5207 −1.74064 −0.870318 0.492490i \(-0.836087\pi\)
−0.870318 + 0.492490i \(0.836087\pi\)
\(570\) −8.04205 −0.336845
\(571\) −35.1012 −1.46894 −0.734469 0.678642i \(-0.762569\pi\)
−0.734469 + 0.678642i \(0.762569\pi\)
\(572\) 5.37957 0.224931
\(573\) −21.6639 −0.905023
\(574\) 8.69275 0.362828
\(575\) −20.4393 −0.852379
\(576\) −1.91094 −0.0796226
\(577\) −5.38586 −0.224216 −0.112108 0.993696i \(-0.535760\pi\)
−0.112108 + 0.993696i \(0.535760\pi\)
\(578\) 29.2454 1.21645
\(579\) −12.2474 −0.508983
\(580\) −3.86392 −0.160440
\(581\) −6.29898 −0.261326
\(582\) −13.3789 −0.554572
\(583\) −81.1970 −3.36284
\(584\) −10.2155 −0.422721
\(585\) −2.07326 −0.0857187
\(586\) 0.623583 0.0257600
\(587\) 8.69627 0.358934 0.179467 0.983764i \(-0.442563\pi\)
0.179467 + 0.983764i \(0.442563\pi\)
\(588\) 6.58812 0.271690
\(589\) 7.44778 0.306881
\(590\) −3.28150 −0.135097
\(591\) 11.1914 0.460353
\(592\) −2.09272 −0.0860104
\(593\) −7.42580 −0.304941 −0.152471 0.988308i \(-0.548723\pi\)
−0.152471 + 0.988308i \(0.548723\pi\)
\(594\) 31.8531 1.30695
\(595\) −7.06531 −0.289649
\(596\) 9.79280 0.401129
\(597\) −8.52432 −0.348877
\(598\) 5.15958 0.210991
\(599\) −6.23895 −0.254917 −0.127458 0.991844i \(-0.540682\pi\)
−0.127458 + 0.991844i \(0.540682\pi\)
\(600\) 3.57819 0.146079
\(601\) −0.218630 −0.00891811 −0.00445905 0.999990i \(-0.501419\pi\)
−0.00445905 + 0.999990i \(0.501419\pi\)
\(602\) 5.56112 0.226655
\(603\) −19.3015 −0.786019
\(604\) −10.8680 −0.442213
\(605\) 34.6337 1.40806
\(606\) 11.9074 0.483704
\(607\) 25.9579 1.05360 0.526798 0.849990i \(-0.323392\pi\)
0.526798 + 0.849990i \(0.323392\pi\)
\(608\) 6.14782 0.249327
\(609\) 2.66630 0.108044
\(610\) 19.0808 0.772559
\(611\) −3.29387 −0.133256
\(612\) 12.9952 0.525298
\(613\) −4.72664 −0.190907 −0.0954537 0.995434i \(-0.530430\pi\)
−0.0954537 + 0.995434i \(0.530430\pi\)
\(614\) 10.1719 0.410505
\(615\) −13.7191 −0.553208
\(616\) 5.15155 0.207562
\(617\) −13.1225 −0.528292 −0.264146 0.964483i \(-0.585090\pi\)
−0.264146 + 0.964483i \(0.585090\pi\)
\(618\) −7.97355 −0.320743
\(619\) 35.1344 1.41217 0.706086 0.708126i \(-0.250459\pi\)
0.706086 + 0.708126i \(0.250459\pi\)
\(620\) 1.51854 0.0609860
\(621\) 30.5505 1.22595
\(622\) −26.4309 −1.05978
\(623\) 12.2588 0.491137
\(624\) −0.903257 −0.0361592
\(625\) 3.90028 0.156011
\(626\) 33.5439 1.34068
\(627\) −39.8757 −1.59248
\(628\) −13.6618 −0.545167
\(629\) 14.2313 0.567441
\(630\) −1.98538 −0.0790996
\(631\) −1.26963 −0.0505432 −0.0252716 0.999681i \(-0.508045\pi\)
−0.0252716 + 0.999681i \(0.508045\pi\)
\(632\) −13.2547 −0.527242
\(633\) −27.8546 −1.10712
\(634\) −19.8086 −0.786702
\(635\) 4.32995 0.171829
\(636\) 13.6334 0.540599
\(637\) −5.46414 −0.216497
\(638\) −19.1588 −0.758505
\(639\) −22.8977 −0.905818
\(640\) 1.25349 0.0495485
\(641\) −35.6042 −1.40628 −0.703141 0.711051i \(-0.748220\pi\)
−0.703141 + 0.711051i \(0.748220\pi\)
\(642\) −5.13005 −0.202467
\(643\) 49.6708 1.95882 0.979412 0.201873i \(-0.0647028\pi\)
0.979412 + 0.201873i \(0.0647028\pi\)
\(644\) 4.94089 0.194698
\(645\) −8.77671 −0.345583
\(646\) −41.8076 −1.64490
\(647\) −4.33400 −0.170387 −0.0851936 0.996364i \(-0.527151\pi\)
−0.0851936 + 0.996364i \(0.527151\pi\)
\(648\) 0.384529 0.0151057
\(649\) −16.2710 −0.638691
\(650\) −2.96773 −0.116404
\(651\) −1.04787 −0.0410693
\(652\) 3.22517 0.126307
\(653\) 9.19447 0.359807 0.179904 0.983684i \(-0.442421\pi\)
0.179904 + 0.983684i \(0.442421\pi\)
\(654\) 11.8033 0.461544
\(655\) 1.57663 0.0616042
\(656\) 10.4877 0.409476
\(657\) 19.5213 0.761597
\(658\) −3.15426 −0.122966
\(659\) −38.2912 −1.49161 −0.745806 0.666163i \(-0.767935\pi\)
−0.745806 + 0.666163i \(0.767935\pi\)
\(660\) −8.13031 −0.316472
\(661\) −25.3806 −0.987189 −0.493595 0.869692i \(-0.664317\pi\)
−0.493595 + 0.869692i \(0.664317\pi\)
\(662\) −26.7987 −1.04156
\(663\) 6.14250 0.238555
\(664\) −7.59965 −0.294924
\(665\) 6.38731 0.247689
\(666\) 3.99907 0.154961
\(667\) −18.3754 −0.711497
\(668\) −9.12706 −0.353136
\(669\) −15.7281 −0.608084
\(670\) 12.6609 0.489133
\(671\) 94.6101 3.65238
\(672\) −0.864972 −0.0333670
\(673\) −34.9171 −1.34595 −0.672977 0.739663i \(-0.734985\pi\)
−0.672977 + 0.739663i \(0.734985\pi\)
\(674\) −24.9822 −0.962277
\(675\) −17.5723 −0.676358
\(676\) −12.2508 −0.471186
\(677\) −34.3084 −1.31858 −0.659290 0.751888i \(-0.729143\pi\)
−0.659290 + 0.751888i \(0.729143\pi\)
\(678\) −5.46671 −0.209948
\(679\) 10.6260 0.407789
\(680\) −8.52421 −0.326889
\(681\) 26.7305 1.02432
\(682\) 7.52952 0.288320
\(683\) −43.6101 −1.66869 −0.834347 0.551240i \(-0.814155\pi\)
−0.834347 + 0.551240i \(0.814155\pi\)
\(684\) −11.7481 −0.449201
\(685\) 20.0981 0.767908
\(686\) −11.0345 −0.421299
\(687\) 3.16029 0.120573
\(688\) 6.70944 0.255795
\(689\) −11.3074 −0.430779
\(690\) −7.79784 −0.296859
\(691\) 19.5554 0.743921 0.371961 0.928248i \(-0.378686\pi\)
0.371961 + 0.928248i \(0.378686\pi\)
\(692\) −4.78033 −0.181721
\(693\) −9.84432 −0.373955
\(694\) 8.83481 0.335365
\(695\) 1.50458 0.0570721
\(696\) 3.21687 0.121935
\(697\) −71.3205 −2.70146
\(698\) 6.49505 0.245841
\(699\) 17.0143 0.643541
\(700\) −2.84194 −0.107415
\(701\) 42.8634 1.61893 0.809464 0.587170i \(-0.199758\pi\)
0.809464 + 0.587170i \(0.199758\pi\)
\(702\) 4.43584 0.167420
\(703\) −12.8657 −0.485239
\(704\) 6.21529 0.234248
\(705\) 4.97814 0.187487
\(706\) 4.24613 0.159805
\(707\) −9.45729 −0.355678
\(708\) 2.73198 0.102674
\(709\) −27.6891 −1.03989 −0.519943 0.854201i \(-0.674047\pi\)
−0.519943 + 0.854201i \(0.674047\pi\)
\(710\) 15.0198 0.563683
\(711\) 25.3289 0.949908
\(712\) 14.7901 0.554282
\(713\) 7.22162 0.270452
\(714\) 5.88215 0.220134
\(715\) 6.74322 0.252182
\(716\) −8.25300 −0.308429
\(717\) −29.3094 −1.09458
\(718\) −5.56784 −0.207790
\(719\) −23.4596 −0.874896 −0.437448 0.899244i \(-0.644118\pi\)
−0.437448 + 0.899244i \(0.644118\pi\)
\(720\) −2.39534 −0.0892692
\(721\) 6.33291 0.235850
\(722\) 18.7957 0.699504
\(723\) 20.6421 0.767686
\(724\) 22.4047 0.832663
\(725\) 10.5693 0.392533
\(726\) −28.8340 −1.07013
\(727\) −17.0209 −0.631271 −0.315635 0.948881i \(-0.602218\pi\)
−0.315635 + 0.948881i \(0.602218\pi\)
\(728\) 0.717402 0.0265887
\(729\) 15.3101 0.567040
\(730\) −12.8050 −0.473935
\(731\) −45.6268 −1.68757
\(732\) −15.8855 −0.587146
\(733\) −31.6475 −1.16893 −0.584463 0.811420i \(-0.698695\pi\)
−0.584463 + 0.811420i \(0.698695\pi\)
\(734\) 10.3769 0.383020
\(735\) 8.25813 0.304606
\(736\) 5.96113 0.219730
\(737\) 62.7777 2.31245
\(738\) −20.0414 −0.737734
\(739\) 22.6632 0.833678 0.416839 0.908980i \(-0.363138\pi\)
0.416839 + 0.908980i \(0.363138\pi\)
\(740\) −2.62320 −0.0964309
\(741\) −5.55306 −0.203997
\(742\) −10.8282 −0.397515
\(743\) −20.2456 −0.742739 −0.371370 0.928485i \(-0.621112\pi\)
−0.371370 + 0.928485i \(0.621112\pi\)
\(744\) −1.26424 −0.0463495
\(745\) 12.2752 0.449727
\(746\) −15.1138 −0.553355
\(747\) 14.5225 0.531350
\(748\) −42.2664 −1.54541
\(749\) 4.07449 0.148879
\(750\) 11.0258 0.402605
\(751\) −26.1416 −0.953922 −0.476961 0.878924i \(-0.658262\pi\)
−0.476961 + 0.878924i \(0.658262\pi\)
\(752\) −3.80558 −0.138775
\(753\) −29.8206 −1.08672
\(754\) −2.66805 −0.0971645
\(755\) −13.6229 −0.495789
\(756\) 4.24783 0.154492
\(757\) 44.4605 1.61594 0.807972 0.589220i \(-0.200565\pi\)
0.807972 + 0.589220i \(0.200565\pi\)
\(758\) −20.1927 −0.733433
\(759\) −38.6648 −1.40344
\(760\) 7.70622 0.279534
\(761\) −21.0301 −0.762339 −0.381170 0.924505i \(-0.624479\pi\)
−0.381170 + 0.924505i \(0.624479\pi\)
\(762\) −3.60486 −0.130590
\(763\) −9.37461 −0.339384
\(764\) 20.7592 0.751043
\(765\) 16.2893 0.588940
\(766\) −2.49821 −0.0902640
\(767\) −2.26588 −0.0818163
\(768\) −1.04358 −0.0376569
\(769\) 8.28771 0.298862 0.149431 0.988772i \(-0.452256\pi\)
0.149431 + 0.988772i \(0.452256\pi\)
\(770\) 6.45741 0.232709
\(771\) −8.11118 −0.292117
\(772\) 11.7359 0.422385
\(773\) −21.4183 −0.770361 −0.385181 0.922841i \(-0.625861\pi\)
−0.385181 + 0.922841i \(0.625861\pi\)
\(774\) −12.8213 −0.460854
\(775\) −4.15378 −0.149208
\(776\) 12.8202 0.460217
\(777\) 1.81015 0.0649387
\(778\) −35.4660 −1.27152
\(779\) 64.4766 2.31011
\(780\) −1.13222 −0.0405400
\(781\) 74.4741 2.66489
\(782\) −40.5380 −1.44964
\(783\) −15.7978 −0.564569
\(784\) −6.31301 −0.225464
\(785\) −17.1250 −0.611216
\(786\) −1.31261 −0.0468193
\(787\) 27.4987 0.980222 0.490111 0.871660i \(-0.336956\pi\)
0.490111 + 0.871660i \(0.336956\pi\)
\(788\) −10.7241 −0.382029
\(789\) −0.0145818 −0.000519127 0
\(790\) −16.6146 −0.591120
\(791\) 4.34187 0.154379
\(792\) −11.8771 −0.422033
\(793\) 13.1753 0.467870
\(794\) −21.4444 −0.761033
\(795\) 17.0893 0.606095
\(796\) 8.16835 0.289520
\(797\) −37.3363 −1.32252 −0.661259 0.750158i \(-0.729978\pi\)
−0.661259 + 0.750158i \(0.729978\pi\)
\(798\) −5.31769 −0.188244
\(799\) 25.8795 0.915549
\(800\) −3.42877 −0.121225
\(801\) −28.2630 −0.998623
\(802\) −0.576737 −0.0203653
\(803\) −63.4924 −2.24060
\(804\) −10.5407 −0.371742
\(805\) 6.19335 0.218287
\(806\) 1.04856 0.0369338
\(807\) −30.8301 −1.08527
\(808\) −11.4101 −0.401407
\(809\) −47.8295 −1.68159 −0.840797 0.541350i \(-0.817913\pi\)
−0.840797 + 0.541350i \(0.817913\pi\)
\(810\) 0.482003 0.0169358
\(811\) 29.1721 1.02437 0.512185 0.858875i \(-0.328836\pi\)
0.512185 + 0.858875i \(0.328836\pi\)
\(812\) −2.55496 −0.0896615
\(813\) 4.50111 0.157861
\(814\) −13.0069 −0.455891
\(815\) 4.04271 0.141610
\(816\) 7.09675 0.248436
\(817\) 41.2484 1.44310
\(818\) −15.9873 −0.558983
\(819\) −1.37091 −0.0479036
\(820\) 13.1462 0.459086
\(821\) −24.0734 −0.840167 −0.420084 0.907485i \(-0.637999\pi\)
−0.420084 + 0.907485i \(0.637999\pi\)
\(822\) −16.7325 −0.583611
\(823\) 3.51481 0.122518 0.0612592 0.998122i \(-0.480488\pi\)
0.0612592 + 0.998122i \(0.480488\pi\)
\(824\) 7.64058 0.266172
\(825\) 22.2395 0.774280
\(826\) −2.16984 −0.0754985
\(827\) −33.4872 −1.16446 −0.582232 0.813022i \(-0.697821\pi\)
−0.582232 + 0.813022i \(0.697821\pi\)
\(828\) −11.3914 −0.395878
\(829\) −33.1847 −1.15255 −0.576276 0.817255i \(-0.695495\pi\)
−0.576276 + 0.817255i \(0.695495\pi\)
\(830\) −9.52607 −0.330655
\(831\) 3.27832 0.113724
\(832\) 0.865537 0.0300071
\(833\) 42.9309 1.48747
\(834\) −1.25263 −0.0433749
\(835\) −11.4407 −0.395920
\(836\) 38.2105 1.32154
\(837\) 6.20863 0.214602
\(838\) 8.90380 0.307577
\(839\) 6.80617 0.234975 0.117488 0.993074i \(-0.462516\pi\)
0.117488 + 0.993074i \(0.462516\pi\)
\(840\) −1.08423 −0.0374096
\(841\) −19.4980 −0.672345
\(842\) −28.5443 −0.983700
\(843\) 14.9903 0.516292
\(844\) 26.6914 0.918757
\(845\) −15.3563 −0.528272
\(846\) 7.27225 0.250025
\(847\) 22.9011 0.786889
\(848\) −13.0641 −0.448622
\(849\) 13.5690 0.465688
\(850\) 23.3170 0.799765
\(851\) −12.4750 −0.427637
\(852\) −12.5046 −0.428400
\(853\) −5.72853 −0.196141 −0.0980705 0.995179i \(-0.531267\pi\)
−0.0980705 + 0.995179i \(0.531267\pi\)
\(854\) 12.6169 0.431742
\(855\) −14.7261 −0.503624
\(856\) 4.91583 0.168019
\(857\) −26.4618 −0.903917 −0.451958 0.892039i \(-0.649274\pi\)
−0.451958 + 0.892039i \(0.649274\pi\)
\(858\) −5.61400 −0.191659
\(859\) −50.4440 −1.72113 −0.860564 0.509343i \(-0.829889\pi\)
−0.860564 + 0.509343i \(0.829889\pi\)
\(860\) 8.41020 0.286785
\(861\) −9.07157 −0.309158
\(862\) 9.60792 0.327247
\(863\) 21.5663 0.734124 0.367062 0.930196i \(-0.380364\pi\)
0.367062 + 0.930196i \(0.380364\pi\)
\(864\) 5.12496 0.174355
\(865\) −5.99208 −0.203737
\(866\) −5.66799 −0.192606
\(867\) −30.5199 −1.03651
\(868\) 1.00411 0.0340818
\(869\) −82.3816 −2.79460
\(870\) 4.03230 0.136708
\(871\) 8.74238 0.296224
\(872\) −11.3104 −0.383017
\(873\) −24.4986 −0.829153
\(874\) 36.6480 1.23964
\(875\) −8.75711 −0.296044
\(876\) 10.6607 0.360191
\(877\) −0.648721 −0.0219057 −0.0109529 0.999940i \(-0.503486\pi\)
−0.0109529 + 0.999940i \(0.503486\pi\)
\(878\) −2.24501 −0.0757653
\(879\) −0.650758 −0.0219495
\(880\) 7.79080 0.262628
\(881\) −16.6564 −0.561167 −0.280583 0.959830i \(-0.590528\pi\)
−0.280583 + 0.959830i \(0.590528\pi\)
\(882\) 12.0638 0.406209
\(883\) −29.0335 −0.977055 −0.488528 0.872548i \(-0.662466\pi\)
−0.488528 + 0.872548i \(0.662466\pi\)
\(884\) −5.88599 −0.197967
\(885\) 3.42450 0.115113
\(886\) −6.40432 −0.215157
\(887\) −23.6703 −0.794770 −0.397385 0.917652i \(-0.630082\pi\)
−0.397385 + 0.917652i \(0.630082\pi\)
\(888\) 2.18392 0.0732876
\(889\) 2.86312 0.0960259
\(890\) 18.5392 0.621435
\(891\) 2.38996 0.0800667
\(892\) 15.0713 0.504625
\(893\) −23.3960 −0.782918
\(894\) −10.2196 −0.341793
\(895\) −10.3450 −0.345796
\(896\) 0.828851 0.0276900
\(897\) −5.38443 −0.179781
\(898\) −12.0705 −0.402798
\(899\) −3.73433 −0.124547
\(900\) 6.55218 0.218406
\(901\) 88.8408 2.95972
\(902\) 65.1842 2.17040
\(903\) −5.80347 −0.193128
\(904\) 5.23842 0.174227
\(905\) 28.0840 0.933543
\(906\) 11.3416 0.376800
\(907\) −1.13307 −0.0376230 −0.0188115 0.999823i \(-0.505988\pi\)
−0.0188115 + 0.999823i \(0.505988\pi\)
\(908\) −25.6143 −0.850039
\(909\) 21.8041 0.723196
\(910\) 0.899254 0.0298100
\(911\) 16.7688 0.555574 0.277787 0.960643i \(-0.410399\pi\)
0.277787 + 0.960643i \(0.410399\pi\)
\(912\) −6.41574 −0.212446
\(913\) −47.2341 −1.56322
\(914\) 14.1848 0.469190
\(915\) −19.9123 −0.658281
\(916\) −3.02832 −0.100059
\(917\) 1.04253 0.0344273
\(918\) −34.8517 −1.15028
\(919\) 53.0530 1.75006 0.875028 0.484072i \(-0.160843\pi\)
0.875028 + 0.484072i \(0.160843\pi\)
\(920\) 7.47221 0.246351
\(921\) −10.6152 −0.349783
\(922\) −1.76534 −0.0581382
\(923\) 10.3712 0.341373
\(924\) −5.37605 −0.176859
\(925\) 7.17546 0.235928
\(926\) −24.0956 −0.791829
\(927\) −14.6007 −0.479550
\(928\) −3.08253 −0.101189
\(929\) −39.7600 −1.30448 −0.652241 0.758012i \(-0.726171\pi\)
−0.652241 + 0.758012i \(0.726171\pi\)
\(930\) −1.58472 −0.0519649
\(931\) −38.8112 −1.27199
\(932\) −16.3038 −0.534049
\(933\) 27.5827 0.903017
\(934\) −5.03203 −0.164653
\(935\) −52.9805 −1.73265
\(936\) −1.65399 −0.0540624
\(937\) 31.3165 1.02307 0.511533 0.859264i \(-0.329078\pi\)
0.511533 + 0.859264i \(0.329078\pi\)
\(938\) 8.37183 0.273350
\(939\) −35.0057 −1.14237
\(940\) −4.77025 −0.155588
\(941\) −28.4497 −0.927434 −0.463717 0.885983i \(-0.653485\pi\)
−0.463717 + 0.885983i \(0.653485\pi\)
\(942\) 14.2572 0.464525
\(943\) 62.5186 2.03589
\(944\) −2.61789 −0.0852051
\(945\) 5.32460 0.173209
\(946\) 41.7011 1.35582
\(947\) −38.1676 −1.24028 −0.620140 0.784491i \(-0.712924\pi\)
−0.620140 + 0.784491i \(0.712924\pi\)
\(948\) 13.8323 0.449252
\(949\) −8.84190 −0.287020
\(950\) −21.0794 −0.683908
\(951\) 20.6719 0.670332
\(952\) −5.63652 −0.182681
\(953\) 13.3366 0.432013 0.216007 0.976392i \(-0.430697\pi\)
0.216007 + 0.976392i \(0.430697\pi\)
\(954\) 24.9647 0.808262
\(955\) 26.0215 0.842035
\(956\) 28.0855 0.908350
\(957\) 19.9938 0.646306
\(958\) 14.5764 0.470941
\(959\) 13.2896 0.429142
\(960\) −1.30811 −0.0422192
\(961\) −29.5324 −0.952658
\(962\) −1.81133 −0.0583996
\(963\) −9.39386 −0.302713
\(964\) −19.7801 −0.637073
\(965\) 14.7109 0.473559
\(966\) −5.15621 −0.165898
\(967\) 46.1912 1.48541 0.742705 0.669619i \(-0.233543\pi\)
0.742705 + 0.669619i \(0.233543\pi\)
\(968\) 27.6299 0.888058
\(969\) 43.6296 1.40158
\(970\) 16.0699 0.515975
\(971\) −45.7609 −1.46854 −0.734268 0.678860i \(-0.762474\pi\)
−0.734268 + 0.678860i \(0.762474\pi\)
\(972\) −15.7762 −0.506021
\(973\) 0.994885 0.0318946
\(974\) −13.1104 −0.420085
\(975\) 3.09706 0.0991852
\(976\) 15.2222 0.487249
\(977\) 14.7173 0.470848 0.235424 0.971893i \(-0.424352\pi\)
0.235424 + 0.971893i \(0.424352\pi\)
\(978\) −3.36572 −0.107624
\(979\) 91.9247 2.93792
\(980\) −7.91328 −0.252780
\(981\) 21.6135 0.690064
\(982\) 15.5892 0.497471
\(983\) −23.0020 −0.733651 −0.366825 0.930290i \(-0.619555\pi\)
−0.366825 + 0.930290i \(0.619555\pi\)
\(984\) −10.9448 −0.348906
\(985\) −13.4425 −0.428313
\(986\) 20.9624 0.667580
\(987\) 3.29172 0.104777
\(988\) 5.32117 0.169289
\(989\) 39.9958 1.27179
\(990\) −14.8878 −0.473164
\(991\) 54.8488 1.74233 0.871165 0.490991i \(-0.163365\pi\)
0.871165 + 0.490991i \(0.163365\pi\)
\(992\) 1.21145 0.0384636
\(993\) 27.9665 0.887491
\(994\) 9.93163 0.315012
\(995\) 10.2389 0.324596
\(996\) 7.93084 0.251298
\(997\) −22.3014 −0.706293 −0.353147 0.935568i \(-0.614888\pi\)
−0.353147 + 0.935568i \(0.614888\pi\)
\(998\) 22.8412 0.723024
\(999\) −10.7251 −0.339328
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.1.16 52
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4034.2.a.d.1.16 52 1.1 even 1 trivial