Properties

Label 4019.2.a.b.1.15
Level 4019
Weight 2
Character 4019.1
Self dual Yes
Analytic conductor 32.092
Analytic rank 0
Dimension 186
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 4019 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4019.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0918765724\)
Analytic rank: \(0\)
Dimension: \(186\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) = 4019.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.52937 q^{2}\) \(+0.978887 q^{3}\) \(+4.39770 q^{4}\) \(-0.161932 q^{5}\) \(-2.47596 q^{6}\) \(-2.77531 q^{7}\) \(-6.06468 q^{8}\) \(-2.04178 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.52937 q^{2}\) \(+0.978887 q^{3}\) \(+4.39770 q^{4}\) \(-0.161932 q^{5}\) \(-2.47596 q^{6}\) \(-2.77531 q^{7}\) \(-6.06468 q^{8}\) \(-2.04178 q^{9}\) \(+0.409586 q^{10}\) \(-5.90921 q^{11}\) \(+4.30485 q^{12}\) \(-4.84469 q^{13}\) \(+7.01979 q^{14}\) \(-0.158513 q^{15}\) \(+6.54440 q^{16}\) \(-7.33022 q^{17}\) \(+5.16442 q^{18}\) \(+4.31064 q^{19}\) \(-0.712130 q^{20}\) \(-2.71672 q^{21}\) \(+14.9466 q^{22}\) \(+0.421572 q^{23}\) \(-5.93663 q^{24}\) \(-4.97378 q^{25}\) \(+12.2540 q^{26}\) \(-4.93533 q^{27}\) \(-12.2050 q^{28}\) \(-4.33717 q^{29}\) \(+0.400939 q^{30}\) \(+6.27802 q^{31}\) \(-4.42384 q^{32}\) \(-5.78444 q^{33}\) \(+18.5408 q^{34}\) \(+0.449413 q^{35}\) \(-8.97915 q^{36}\) \(-2.79770 q^{37}\) \(-10.9032 q^{38}\) \(-4.74240 q^{39}\) \(+0.982067 q^{40}\) \(+0.785168 q^{41}\) \(+6.87158 q^{42}\) \(-2.17649 q^{43}\) \(-25.9870 q^{44}\) \(+0.330630 q^{45}\) \(-1.06631 q^{46}\) \(-7.48652 q^{47}\) \(+6.40622 q^{48}\) \(+0.702360 q^{49}\) \(+12.5805 q^{50}\) \(-7.17546 q^{51}\) \(-21.3055 q^{52}\) \(-5.34627 q^{53}\) \(+12.4833 q^{54}\) \(+0.956891 q^{55}\) \(+16.8314 q^{56}\) \(+4.21962 q^{57}\) \(+10.9703 q^{58}\) \(-0.387777 q^{59}\) \(-0.697095 q^{60}\) \(+8.26994 q^{61}\) \(-15.8794 q^{62}\) \(+5.66658 q^{63}\) \(-1.89929 q^{64}\) \(+0.784511 q^{65}\) \(+14.6310 q^{66}\) \(-4.85640 q^{67}\) \(-32.2362 q^{68}\) \(+0.412671 q^{69}\) \(-1.13673 q^{70}\) \(-12.5617 q^{71}\) \(+12.3827 q^{72}\) \(-6.31076 q^{73}\) \(+7.07642 q^{74}\) \(-4.86876 q^{75}\) \(+18.9569 q^{76}\) \(+16.3999 q^{77}\) \(+11.9953 q^{78}\) \(+11.4447 q^{79}\) \(-1.05975 q^{80}\) \(+1.29421 q^{81}\) \(-1.98598 q^{82}\) \(+2.64018 q^{83}\) \(-11.9473 q^{84}\) \(+1.18700 q^{85}\) \(+5.50513 q^{86}\) \(-4.24560 q^{87}\) \(+35.8374 q^{88}\) \(-3.89044 q^{89}\) \(-0.836286 q^{90}\) \(+13.4455 q^{91}\) \(+1.85395 q^{92}\) \(+6.14547 q^{93}\) \(+18.9362 q^{94}\) \(-0.698031 q^{95}\) \(-4.33043 q^{96}\) \(-6.96996 q^{97}\) \(-1.77653 q^{98}\) \(+12.0653 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(186q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 212q^{4} \) \(\mathstrut +\mathstrut 38q^{5} \) \(\mathstrut +\mathstrut 47q^{6} \) \(\mathstrut +\mathstrut 32q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 216q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(186q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 212q^{4} \) \(\mathstrut +\mathstrut 38q^{5} \) \(\mathstrut +\mathstrut 47q^{6} \) \(\mathstrut +\mathstrut 32q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 216q^{9} \) \(\mathstrut +\mathstrut 50q^{10} \) \(\mathstrut +\mathstrut 25q^{11} \) \(\mathstrut +\mathstrut 17q^{12} \) \(\mathstrut +\mathstrut 113q^{13} \) \(\mathstrut +\mathstrut 12q^{14} \) \(\mathstrut +\mathstrut 12q^{15} \) \(\mathstrut +\mathstrut 252q^{16} \) \(\mathstrut +\mathstrut 35q^{17} \) \(\mathstrut +\mathstrut 13q^{18} \) \(\mathstrut +\mathstrut 97q^{19} \) \(\mathstrut +\mathstrut 55q^{20} \) \(\mathstrut +\mathstrut 115q^{21} \) \(\mathstrut +\mathstrut 14q^{22} \) \(\mathstrut +\mathstrut 27q^{23} \) \(\mathstrut +\mathstrut 122q^{24} \) \(\mathstrut +\mathstrut 244q^{25} \) \(\mathstrut +\mathstrut 39q^{26} \) \(\mathstrut +\mathstrut 34q^{27} \) \(\mathstrut +\mathstrut 66q^{28} \) \(\mathstrut +\mathstrut 91q^{29} \) \(\mathstrut +\mathstrut 4q^{30} \) \(\mathstrut +\mathstrut 135q^{31} \) \(\mathstrut +\mathstrut 21q^{32} \) \(\mathstrut +\mathstrut 32q^{33} \) \(\mathstrut +\mathstrut 58q^{34} \) \(\mathstrut +\mathstrut 17q^{35} \) \(\mathstrut +\mathstrut 273q^{36} \) \(\mathstrut +\mathstrut 133q^{37} \) \(\mathstrut -\mathstrut 3q^{38} \) \(\mathstrut +\mathstrut 55q^{39} \) \(\mathstrut +\mathstrut 142q^{40} \) \(\mathstrut +\mathstrut 97q^{41} \) \(\mathstrut -\mathstrut 8q^{42} \) \(\mathstrut +\mathstrut 67q^{43} \) \(\mathstrut +\mathstrut 44q^{44} \) \(\mathstrut +\mathstrut 154q^{45} \) \(\mathstrut +\mathstrut 101q^{46} \) \(\mathstrut +\mathstrut 20q^{47} \) \(\mathstrut -\mathstrut 7q^{48} \) \(\mathstrut +\mathstrut 312q^{49} \) \(\mathstrut +\mathstrut 21q^{50} \) \(\mathstrut +\mathstrut 23q^{51} \) \(\mathstrut +\mathstrut 193q^{52} \) \(\mathstrut +\mathstrut 22q^{53} \) \(\mathstrut +\mathstrut 141q^{54} \) \(\mathstrut +\mathstrut 88q^{55} \) \(\mathstrut +\mathstrut 28q^{56} \) \(\mathstrut +\mathstrut 65q^{57} \) \(\mathstrut +\mathstrut 62q^{58} \) \(\mathstrut +\mathstrut 41q^{59} \) \(\mathstrut +\mathstrut q^{60} \) \(\mathstrut +\mathstrut 377q^{61} \) \(\mathstrut +\mathstrut 29q^{62} \) \(\mathstrut +\mathstrut 39q^{63} \) \(\mathstrut +\mathstrut 311q^{64} \) \(\mathstrut +\mathstrut 21q^{65} \) \(\mathstrut +\mathstrut 35q^{66} \) \(\mathstrut +\mathstrut 42q^{67} \) \(\mathstrut +\mathstrut 24q^{68} \) \(\mathstrut +\mathstrut 137q^{69} \) \(\mathstrut +\mathstrut 35q^{70} \) \(\mathstrut +\mathstrut 17q^{71} \) \(\mathstrut -\mathstrut 8q^{72} \) \(\mathstrut +\mathstrut 213q^{73} \) \(\mathstrut -\mathstrut 9q^{74} \) \(\mathstrut +\mathstrut 2q^{75} \) \(\mathstrut +\mathstrut 242q^{76} \) \(\mathstrut +\mathstrut 60q^{77} \) \(\mathstrut +\mathstrut 103q^{79} \) \(\mathstrut +\mathstrut 80q^{80} \) \(\mathstrut +\mathstrut 270q^{81} \) \(\mathstrut +\mathstrut 84q^{82} \) \(\mathstrut +\mathstrut 42q^{83} \) \(\mathstrut +\mathstrut 137q^{84} \) \(\mathstrut +\mathstrut 294q^{85} \) \(\mathstrut -\mathstrut 9q^{86} \) \(\mathstrut +\mathstrut 22q^{87} \) \(\mathstrut -\mathstrut 13q^{88} \) \(\mathstrut +\mathstrut 78q^{89} \) \(\mathstrut +\mathstrut 69q^{90} \) \(\mathstrut +\mathstrut 118q^{91} \) \(\mathstrut +\mathstrut 49q^{92} \) \(\mathstrut +\mathstrut 51q^{93} \) \(\mathstrut +\mathstrut 93q^{94} \) \(\mathstrut +\mathstrut 10q^{95} \) \(\mathstrut +\mathstrut 260q^{96} \) \(\mathstrut +\mathstrut 142q^{97} \) \(\mathstrut -\mathstrut 31q^{98} \) \(\mathstrut +\mathstrut 78q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.52937 −1.78853 −0.894267 0.447534i \(-0.852302\pi\)
−0.894267 + 0.447534i \(0.852302\pi\)
\(3\) 0.978887 0.565160 0.282580 0.959244i \(-0.408810\pi\)
0.282580 + 0.959244i \(0.408810\pi\)
\(4\) 4.39770 2.19885
\(5\) −0.161932 −0.0724183 −0.0362092 0.999344i \(-0.511528\pi\)
−0.0362092 + 0.999344i \(0.511528\pi\)
\(6\) −2.47596 −1.01081
\(7\) −2.77531 −1.04897 −0.524485 0.851420i \(-0.675742\pi\)
−0.524485 + 0.851420i \(0.675742\pi\)
\(8\) −6.06468 −2.14419
\(9\) −2.04178 −0.680594
\(10\) 0.409586 0.129523
\(11\) −5.90921 −1.78169 −0.890847 0.454304i \(-0.849888\pi\)
−0.890847 + 0.454304i \(0.849888\pi\)
\(12\) 4.30485 1.24270
\(13\) −4.84469 −1.34367 −0.671837 0.740699i \(-0.734494\pi\)
−0.671837 + 0.740699i \(0.734494\pi\)
\(14\) 7.01979 1.87612
\(15\) −0.158513 −0.0409280
\(16\) 6.54440 1.63610
\(17\) −7.33022 −1.77784 −0.888920 0.458062i \(-0.848544\pi\)
−0.888920 + 0.458062i \(0.848544\pi\)
\(18\) 5.16442 1.21726
\(19\) 4.31064 0.988928 0.494464 0.869198i \(-0.335364\pi\)
0.494464 + 0.869198i \(0.335364\pi\)
\(20\) −0.712130 −0.159237
\(21\) −2.71672 −0.592836
\(22\) 14.9466 3.18662
\(23\) 0.421572 0.0879038 0.0439519 0.999034i \(-0.486005\pi\)
0.0439519 + 0.999034i \(0.486005\pi\)
\(24\) −5.93663 −1.21181
\(25\) −4.97378 −0.994756
\(26\) 12.2540 2.40321
\(27\) −4.93533 −0.949805
\(28\) −12.2050 −2.30653
\(29\) −4.33717 −0.805392 −0.402696 0.915334i \(-0.631927\pi\)
−0.402696 + 0.915334i \(0.631927\pi\)
\(30\) 0.400939 0.0732010
\(31\) 6.27802 1.12757 0.563783 0.825923i \(-0.309346\pi\)
0.563783 + 0.825923i \(0.309346\pi\)
\(32\) −4.42384 −0.782031
\(33\) −5.78444 −1.00694
\(34\) 18.5408 3.17973
\(35\) 0.449413 0.0759646
\(36\) −8.97915 −1.49653
\(37\) −2.79770 −0.459939 −0.229970 0.973198i \(-0.573863\pi\)
−0.229970 + 0.973198i \(0.573863\pi\)
\(38\) −10.9032 −1.76873
\(39\) −4.74240 −0.759391
\(40\) 0.982067 0.155278
\(41\) 0.785168 0.122623 0.0613113 0.998119i \(-0.480472\pi\)
0.0613113 + 0.998119i \(0.480472\pi\)
\(42\) 6.87158 1.06031
\(43\) −2.17649 −0.331911 −0.165955 0.986133i \(-0.553071\pi\)
−0.165955 + 0.986133i \(0.553071\pi\)
\(44\) −25.9870 −3.91768
\(45\) 0.330630 0.0492874
\(46\) −1.06631 −0.157219
\(47\) −7.48652 −1.09202 −0.546010 0.837778i \(-0.683854\pi\)
−0.546010 + 0.837778i \(0.683854\pi\)
\(48\) 6.40622 0.924659
\(49\) 0.702360 0.100337
\(50\) 12.5805 1.77915
\(51\) −7.17546 −1.00477
\(52\) −21.3055 −2.95454
\(53\) −5.34627 −0.734367 −0.367183 0.930149i \(-0.619678\pi\)
−0.367183 + 0.930149i \(0.619678\pi\)
\(54\) 12.4833 1.69876
\(55\) 0.956891 0.129027
\(56\) 16.8314 2.24919
\(57\) 4.21962 0.558903
\(58\) 10.9703 1.44047
\(59\) −0.387777 −0.0504843 −0.0252421 0.999681i \(-0.508036\pi\)
−0.0252421 + 0.999681i \(0.508036\pi\)
\(60\) −0.697095 −0.0899945
\(61\) 8.26994 1.05886 0.529429 0.848354i \(-0.322406\pi\)
0.529429 + 0.848354i \(0.322406\pi\)
\(62\) −15.8794 −2.01669
\(63\) 5.66658 0.713922
\(64\) −1.89929 −0.237411
\(65\) 0.784511 0.0973066
\(66\) 14.6310 1.80095
\(67\) −4.85640 −0.593304 −0.296652 0.954986i \(-0.595870\pi\)
−0.296652 + 0.954986i \(0.595870\pi\)
\(68\) −32.2362 −3.90921
\(69\) 0.412671 0.0496797
\(70\) −1.13673 −0.135865
\(71\) −12.5617 −1.49080 −0.745399 0.666618i \(-0.767741\pi\)
−0.745399 + 0.666618i \(0.767741\pi\)
\(72\) 12.3827 1.45932
\(73\) −6.31076 −0.738618 −0.369309 0.929307i \(-0.620406\pi\)
−0.369309 + 0.929307i \(0.620406\pi\)
\(74\) 7.07642 0.822617
\(75\) −4.86876 −0.562196
\(76\) 18.9569 2.17451
\(77\) 16.3999 1.86894
\(78\) 11.9953 1.35820
\(79\) 11.4447 1.28763 0.643816 0.765180i \(-0.277350\pi\)
0.643816 + 0.765180i \(0.277350\pi\)
\(80\) −1.05975 −0.118484
\(81\) 1.29421 0.143802
\(82\) −1.98598 −0.219315
\(83\) 2.64018 0.289797 0.144898 0.989447i \(-0.453714\pi\)
0.144898 + 0.989447i \(0.453714\pi\)
\(84\) −11.9473 −1.30356
\(85\) 1.18700 0.128748
\(86\) 5.50513 0.593634
\(87\) −4.24560 −0.455176
\(88\) 35.8374 3.82028
\(89\) −3.89044 −0.412385 −0.206193 0.978511i \(-0.566107\pi\)
−0.206193 + 0.978511i \(0.566107\pi\)
\(90\) −0.836286 −0.0881522
\(91\) 13.4455 1.40947
\(92\) 1.85395 0.193287
\(93\) 6.14547 0.637255
\(94\) 18.9362 1.95312
\(95\) −0.698031 −0.0716165
\(96\) −4.33043 −0.441973
\(97\) −6.96996 −0.707692 −0.353846 0.935304i \(-0.615126\pi\)
−0.353846 + 0.935304i \(0.615126\pi\)
\(98\) −1.77653 −0.179456
\(99\) 12.0653 1.21261
\(100\) −21.8732 −2.18732
\(101\) 10.6031 1.05505 0.527523 0.849541i \(-0.323121\pi\)
0.527523 + 0.849541i \(0.323121\pi\)
\(102\) 18.1494 1.79706
\(103\) −8.56052 −0.843493 −0.421746 0.906714i \(-0.638583\pi\)
−0.421746 + 0.906714i \(0.638583\pi\)
\(104\) 29.3815 2.88109
\(105\) 0.439924 0.0429322
\(106\) 13.5227 1.31344
\(107\) 11.3294 1.09526 0.547628 0.836722i \(-0.315531\pi\)
0.547628 + 0.836722i \(0.315531\pi\)
\(108\) −21.7041 −2.08848
\(109\) −13.8526 −1.32684 −0.663421 0.748247i \(-0.730896\pi\)
−0.663421 + 0.748247i \(0.730896\pi\)
\(110\) −2.42033 −0.230769
\(111\) −2.73863 −0.259939
\(112\) −18.1627 −1.71622
\(113\) 5.60689 0.527452 0.263726 0.964598i \(-0.415048\pi\)
0.263726 + 0.964598i \(0.415048\pi\)
\(114\) −10.6730 −0.999616
\(115\) −0.0682660 −0.00636584
\(116\) −19.0736 −1.77094
\(117\) 9.89179 0.914496
\(118\) 0.980831 0.0902928
\(119\) 20.3437 1.86490
\(120\) 0.961332 0.0877572
\(121\) 23.9187 2.17443
\(122\) −20.9177 −1.89380
\(123\) 0.768590 0.0693015
\(124\) 27.6089 2.47935
\(125\) 1.61508 0.144457
\(126\) −14.3329 −1.27687
\(127\) 12.1835 1.08111 0.540555 0.841309i \(-0.318214\pi\)
0.540555 + 0.841309i \(0.318214\pi\)
\(128\) 13.6517 1.20665
\(129\) −2.13053 −0.187583
\(130\) −1.98432 −0.174036
\(131\) −3.49359 −0.305237 −0.152618 0.988285i \(-0.548771\pi\)
−0.152618 + 0.988285i \(0.548771\pi\)
\(132\) −25.4383 −2.21412
\(133\) −11.9634 −1.03735
\(134\) 12.2836 1.06114
\(135\) 0.799189 0.0687833
\(136\) 44.4555 3.81202
\(137\) 2.76726 0.236423 0.118212 0.992988i \(-0.462284\pi\)
0.118212 + 0.992988i \(0.462284\pi\)
\(138\) −1.04380 −0.0888539
\(139\) 6.93485 0.588206 0.294103 0.955774i \(-0.404979\pi\)
0.294103 + 0.955774i \(0.404979\pi\)
\(140\) 1.97638 0.167035
\(141\) −7.32845 −0.617167
\(142\) 31.7732 2.66634
\(143\) 28.6283 2.39401
\(144\) −13.3622 −1.11352
\(145\) 0.702327 0.0583251
\(146\) 15.9622 1.32104
\(147\) 0.687531 0.0567066
\(148\) −12.3035 −1.01134
\(149\) −8.29142 −0.679259 −0.339630 0.940559i \(-0.610302\pi\)
−0.339630 + 0.940559i \(0.610302\pi\)
\(150\) 12.3149 1.00551
\(151\) 1.74227 0.141784 0.0708919 0.997484i \(-0.477415\pi\)
0.0708919 + 0.997484i \(0.477415\pi\)
\(152\) −26.1426 −2.12045
\(153\) 14.9667 1.20999
\(154\) −41.4814 −3.34267
\(155\) −1.01661 −0.0816564
\(156\) −20.8557 −1.66979
\(157\) −19.0365 −1.51928 −0.759639 0.650345i \(-0.774624\pi\)
−0.759639 + 0.650345i \(0.774624\pi\)
\(158\) −28.9479 −2.30297
\(159\) −5.23339 −0.415035
\(160\) 0.716362 0.0566334
\(161\) −1.16999 −0.0922084
\(162\) −3.27354 −0.257194
\(163\) 6.52152 0.510805 0.255402 0.966835i \(-0.417792\pi\)
0.255402 + 0.966835i \(0.417792\pi\)
\(164\) 3.45294 0.269629
\(165\) 0.936688 0.0729211
\(166\) −6.67798 −0.518311
\(167\) 1.85396 0.143464 0.0717320 0.997424i \(-0.477147\pi\)
0.0717320 + 0.997424i \(0.477147\pi\)
\(168\) 16.4760 1.27115
\(169\) 10.4710 0.805460
\(170\) −3.00236 −0.230270
\(171\) −8.80137 −0.673058
\(172\) −9.57154 −0.729823
\(173\) 3.33392 0.253473 0.126737 0.991936i \(-0.459550\pi\)
0.126737 + 0.991936i \(0.459550\pi\)
\(174\) 10.7387 0.814097
\(175\) 13.8038 1.04347
\(176\) −38.6722 −2.91503
\(177\) −0.379590 −0.0285317
\(178\) 9.84035 0.737565
\(179\) −17.8353 −1.33307 −0.666535 0.745473i \(-0.732223\pi\)
−0.666535 + 0.745473i \(0.732223\pi\)
\(180\) 1.45401 0.108376
\(181\) −4.80281 −0.356990 −0.178495 0.983941i \(-0.557123\pi\)
−0.178495 + 0.983941i \(0.557123\pi\)
\(182\) −34.0087 −2.52089
\(183\) 8.09533 0.598424
\(184\) −2.55670 −0.188482
\(185\) 0.453038 0.0333080
\(186\) −15.5441 −1.13975
\(187\) 43.3158 3.16757
\(188\) −32.9235 −2.40119
\(189\) 13.6971 0.996317
\(190\) 1.76558 0.128088
\(191\) −5.30196 −0.383637 −0.191818 0.981430i \(-0.561438\pi\)
−0.191818 + 0.981430i \(0.561438\pi\)
\(192\) −1.85918 −0.134175
\(193\) −7.62107 −0.548577 −0.274288 0.961647i \(-0.588442\pi\)
−0.274288 + 0.961647i \(0.588442\pi\)
\(194\) 17.6296 1.26573
\(195\) 0.767947 0.0549938
\(196\) 3.08877 0.220627
\(197\) −9.54886 −0.680328 −0.340164 0.940366i \(-0.610483\pi\)
−0.340164 + 0.940366i \(0.610483\pi\)
\(198\) −30.5176 −2.16879
\(199\) −2.40958 −0.170810 −0.0854052 0.996346i \(-0.527218\pi\)
−0.0854052 + 0.996346i \(0.527218\pi\)
\(200\) 30.1644 2.13294
\(201\) −4.75386 −0.335312
\(202\) −26.8191 −1.88698
\(203\) 12.0370 0.844832
\(204\) −31.5555 −2.20933
\(205\) −0.127144 −0.00888012
\(206\) 21.6527 1.50862
\(207\) −0.860757 −0.0598267
\(208\) −31.7055 −2.19838
\(209\) −25.4724 −1.76197
\(210\) −1.11273 −0.0767856
\(211\) 19.4546 1.33931 0.669656 0.742671i \(-0.266441\pi\)
0.669656 + 0.742671i \(0.266441\pi\)
\(212\) −23.5113 −1.61476
\(213\) −12.2965 −0.842541
\(214\) −28.6563 −1.95890
\(215\) 0.352443 0.0240364
\(216\) 29.9312 2.03656
\(217\) −17.4235 −1.18278
\(218\) 35.0384 2.37310
\(219\) −6.17752 −0.417438
\(220\) 4.20813 0.283712
\(221\) 35.5126 2.38884
\(222\) 6.92701 0.464910
\(223\) 22.5652 1.51108 0.755540 0.655102i \(-0.227374\pi\)
0.755540 + 0.655102i \(0.227374\pi\)
\(224\) 12.2775 0.820327
\(225\) 10.1554 0.677024
\(226\) −14.1819 −0.943366
\(227\) 26.5079 1.75939 0.879697 0.475535i \(-0.157746\pi\)
0.879697 + 0.475535i \(0.157746\pi\)
\(228\) 18.5567 1.22894
\(229\) −18.6626 −1.23326 −0.616630 0.787253i \(-0.711503\pi\)
−0.616630 + 0.787253i \(0.711503\pi\)
\(230\) 0.172670 0.0113855
\(231\) 16.0536 1.05625
\(232\) 26.3035 1.72691
\(233\) −0.0871996 −0.00571263 −0.00285632 0.999996i \(-0.500909\pi\)
−0.00285632 + 0.999996i \(0.500909\pi\)
\(234\) −25.0200 −1.63561
\(235\) 1.21231 0.0790823
\(236\) −1.70533 −0.111007
\(237\) 11.2031 0.727719
\(238\) −51.4566 −3.33544
\(239\) −19.4038 −1.25513 −0.627563 0.778566i \(-0.715947\pi\)
−0.627563 + 0.778566i \(0.715947\pi\)
\(240\) −1.03737 −0.0669622
\(241\) 24.5488 1.58133 0.790665 0.612250i \(-0.209735\pi\)
0.790665 + 0.612250i \(0.209735\pi\)
\(242\) −60.4993 −3.88904
\(243\) 16.0729 1.03108
\(244\) 36.3688 2.32827
\(245\) −0.113735 −0.00726625
\(246\) −1.94405 −0.123948
\(247\) −20.8837 −1.32880
\(248\) −38.0742 −2.41771
\(249\) 2.58443 0.163782
\(250\) −4.08512 −0.258366
\(251\) −26.3471 −1.66301 −0.831507 0.555515i \(-0.812521\pi\)
−0.831507 + 0.555515i \(0.812521\pi\)
\(252\) 24.9200 1.56981
\(253\) −2.49115 −0.156618
\(254\) −30.8165 −1.93360
\(255\) 1.16194 0.0727634
\(256\) −30.7315 −1.92072
\(257\) −26.5632 −1.65697 −0.828484 0.560013i \(-0.810796\pi\)
−0.828484 + 0.560013i \(0.810796\pi\)
\(258\) 5.38890 0.335498
\(259\) 7.76449 0.482462
\(260\) 3.45005 0.213963
\(261\) 8.85555 0.548145
\(262\) 8.83658 0.545926
\(263\) −29.8178 −1.83864 −0.919321 0.393508i \(-0.871261\pi\)
−0.919321 + 0.393508i \(0.871261\pi\)
\(264\) 35.0808 2.15907
\(265\) 0.865734 0.0531816
\(266\) 30.2597 1.85534
\(267\) −3.80830 −0.233064
\(268\) −21.3570 −1.30459
\(269\) −21.3456 −1.30147 −0.650733 0.759307i \(-0.725538\pi\)
−0.650733 + 0.759307i \(0.725538\pi\)
\(270\) −2.02144 −0.123021
\(271\) −1.41354 −0.0858666 −0.0429333 0.999078i \(-0.513670\pi\)
−0.0429333 + 0.999078i \(0.513670\pi\)
\(272\) −47.9719 −2.90872
\(273\) 13.1616 0.796578
\(274\) −6.99943 −0.422851
\(275\) 29.3911 1.77235
\(276\) 1.81480 0.109238
\(277\) −31.9542 −1.91994 −0.959972 0.280097i \(-0.909633\pi\)
−0.959972 + 0.280097i \(0.909633\pi\)
\(278\) −17.5408 −1.05203
\(279\) −12.8183 −0.767414
\(280\) −2.72554 −0.162882
\(281\) 8.01829 0.478331 0.239165 0.970979i \(-0.423126\pi\)
0.239165 + 0.970979i \(0.423126\pi\)
\(282\) 18.5364 1.10382
\(283\) 11.5504 0.686598 0.343299 0.939226i \(-0.388456\pi\)
0.343299 + 0.939226i \(0.388456\pi\)
\(284\) −55.2426 −3.27805
\(285\) −0.683293 −0.0404748
\(286\) −72.4114 −4.28178
\(287\) −2.17909 −0.128627
\(288\) 9.03250 0.532245
\(289\) 36.7322 2.16072
\(290\) −1.77644 −0.104316
\(291\) −6.82280 −0.399960
\(292\) −27.7529 −1.62411
\(293\) −16.5509 −0.966916 −0.483458 0.875368i \(-0.660619\pi\)
−0.483458 + 0.875368i \(0.660619\pi\)
\(294\) −1.73902 −0.101422
\(295\) 0.0627936 0.00365598
\(296\) 16.9672 0.986196
\(297\) 29.1639 1.69226
\(298\) 20.9721 1.21488
\(299\) −2.04238 −0.118114
\(300\) −21.4114 −1.23619
\(301\) 6.04043 0.348164
\(302\) −4.40684 −0.253585
\(303\) 10.3792 0.596270
\(304\) 28.2105 1.61798
\(305\) −1.33917 −0.0766807
\(306\) −37.8563 −2.16410
\(307\) 7.92647 0.452388 0.226194 0.974082i \(-0.427372\pi\)
0.226194 + 0.974082i \(0.427372\pi\)
\(308\) 72.1219 4.10953
\(309\) −8.37977 −0.476709
\(310\) 2.57139 0.146045
\(311\) −14.3157 −0.811769 −0.405884 0.913924i \(-0.633036\pi\)
−0.405884 + 0.913924i \(0.633036\pi\)
\(312\) 28.7611 1.62828
\(313\) 8.01698 0.453147 0.226573 0.973994i \(-0.427248\pi\)
0.226573 + 0.973994i \(0.427248\pi\)
\(314\) 48.1503 2.71728
\(315\) −0.917602 −0.0517010
\(316\) 50.3305 2.83131
\(317\) −9.23607 −0.518749 −0.259375 0.965777i \(-0.583516\pi\)
−0.259375 + 0.965777i \(0.583516\pi\)
\(318\) 13.2372 0.742304
\(319\) 25.6292 1.43496
\(320\) 0.307556 0.0171929
\(321\) 11.0902 0.618996
\(322\) 2.95934 0.164918
\(323\) −31.5979 −1.75816
\(324\) 5.69157 0.316198
\(325\) 24.0964 1.33663
\(326\) −16.4953 −0.913591
\(327\) −13.5602 −0.749878
\(328\) −4.76179 −0.262926
\(329\) 20.7774 1.14550
\(330\) −2.36923 −0.130422
\(331\) −10.3689 −0.569924 −0.284962 0.958539i \(-0.591981\pi\)
−0.284962 + 0.958539i \(0.591981\pi\)
\(332\) 11.6107 0.637221
\(333\) 5.71229 0.313032
\(334\) −4.68935 −0.256590
\(335\) 0.786408 0.0429660
\(336\) −17.7793 −0.969939
\(337\) −19.9650 −1.08756 −0.543781 0.839227i \(-0.683008\pi\)
−0.543781 + 0.839227i \(0.683008\pi\)
\(338\) −26.4850 −1.44059
\(339\) 5.48851 0.298095
\(340\) 5.22007 0.283098
\(341\) −37.0981 −2.00898
\(342\) 22.2619 1.20379
\(343\) 17.4779 0.943719
\(344\) 13.1997 0.711679
\(345\) −0.0668247 −0.00359772
\(346\) −8.43271 −0.453345
\(347\) −17.6524 −0.947630 −0.473815 0.880624i \(-0.657123\pi\)
−0.473815 + 0.880624i \(0.657123\pi\)
\(348\) −18.6709 −1.00086
\(349\) 26.8928 1.43954 0.719770 0.694213i \(-0.244247\pi\)
0.719770 + 0.694213i \(0.244247\pi\)
\(350\) −34.9149 −1.86628
\(351\) 23.9101 1.27623
\(352\) 26.1414 1.39334
\(353\) 29.0029 1.54367 0.771834 0.635824i \(-0.219339\pi\)
0.771834 + 0.635824i \(0.219339\pi\)
\(354\) 0.960122 0.0510299
\(355\) 2.03414 0.107961
\(356\) −17.1090 −0.906775
\(357\) 19.9141 1.05397
\(358\) 45.1120 2.38424
\(359\) 5.16606 0.272654 0.136327 0.990664i \(-0.456470\pi\)
0.136327 + 0.990664i \(0.456470\pi\)
\(360\) −2.00517 −0.105682
\(361\) −0.418423 −0.0220223
\(362\) 12.1481 0.638489
\(363\) 23.4137 1.22890
\(364\) 59.1294 3.09922
\(365\) 1.02192 0.0534895
\(366\) −20.4761 −1.07030
\(367\) −13.2289 −0.690543 −0.345271 0.938503i \(-0.612213\pi\)
−0.345271 + 0.938503i \(0.612213\pi\)
\(368\) 2.75893 0.143819
\(369\) −1.60314 −0.0834562
\(370\) −1.14590 −0.0595725
\(371\) 14.8376 0.770329
\(372\) 27.0259 1.40123
\(373\) 6.43713 0.333302 0.166651 0.986016i \(-0.446705\pi\)
0.166651 + 0.986016i \(0.446705\pi\)
\(374\) −109.562 −5.66530
\(375\) 1.58098 0.0816413
\(376\) 45.4033 2.34150
\(377\) 21.0122 1.08218
\(378\) −34.6450 −1.78195
\(379\) 17.0804 0.877359 0.438679 0.898644i \(-0.355446\pi\)
0.438679 + 0.898644i \(0.355446\pi\)
\(380\) −3.06973 −0.157474
\(381\) 11.9262 0.611000
\(382\) 13.4106 0.686147
\(383\) −3.91876 −0.200239 −0.100120 0.994975i \(-0.531923\pi\)
−0.100120 + 0.994975i \(0.531923\pi\)
\(384\) 13.3634 0.681950
\(385\) −2.65567 −0.135346
\(386\) 19.2765 0.981148
\(387\) 4.44391 0.225896
\(388\) −30.6518 −1.55611
\(389\) 8.48580 0.430247 0.215124 0.976587i \(-0.430985\pi\)
0.215124 + 0.976587i \(0.430985\pi\)
\(390\) −1.94242 −0.0983583
\(391\) −3.09021 −0.156279
\(392\) −4.25959 −0.215142
\(393\) −3.41983 −0.172508
\(394\) 24.1526 1.21679
\(395\) −1.85327 −0.0932482
\(396\) 53.0597 2.66635
\(397\) −3.63753 −0.182562 −0.0912812 0.995825i \(-0.529096\pi\)
−0.0912812 + 0.995825i \(0.529096\pi\)
\(398\) 6.09471 0.305500
\(399\) −11.7108 −0.586272
\(400\) −32.5504 −1.62752
\(401\) −27.3949 −1.36803 −0.684017 0.729466i \(-0.739769\pi\)
−0.684017 + 0.729466i \(0.739769\pi\)
\(402\) 12.0243 0.599716
\(403\) −30.4150 −1.51508
\(404\) 46.6292 2.31989
\(405\) −0.209575 −0.0104139
\(406\) −30.4460 −1.51101
\(407\) 16.5322 0.819470
\(408\) 43.5168 2.15440
\(409\) 14.7397 0.728833 0.364417 0.931236i \(-0.381268\pi\)
0.364417 + 0.931236i \(0.381268\pi\)
\(410\) 0.321594 0.0158824
\(411\) 2.70884 0.133617
\(412\) −37.6466 −1.85472
\(413\) 1.07620 0.0529565
\(414\) 2.17717 0.107002
\(415\) −0.427529 −0.0209866
\(416\) 21.4321 1.05079
\(417\) 6.78843 0.332431
\(418\) 64.4292 3.15133
\(419\) −23.6021 −1.15304 −0.576520 0.817083i \(-0.695590\pi\)
−0.576520 + 0.817083i \(0.695590\pi\)
\(420\) 1.93466 0.0944015
\(421\) 29.6978 1.44738 0.723691 0.690124i \(-0.242444\pi\)
0.723691 + 0.690124i \(0.242444\pi\)
\(422\) −49.2080 −2.39541
\(423\) 15.2858 0.743222
\(424\) 32.4234 1.57462
\(425\) 36.4589 1.76852
\(426\) 31.1023 1.50691
\(427\) −22.9517 −1.11071
\(428\) 49.8234 2.40831
\(429\) 28.0238 1.35300
\(430\) −0.891458 −0.0429899
\(431\) 39.8240 1.91825 0.959127 0.282976i \(-0.0913215\pi\)
0.959127 + 0.282976i \(0.0913215\pi\)
\(432\) −32.2988 −1.55398
\(433\) −12.4323 −0.597457 −0.298728 0.954338i \(-0.596562\pi\)
−0.298728 + 0.954338i \(0.596562\pi\)
\(434\) 44.0704 2.11544
\(435\) 0.687499 0.0329630
\(436\) −60.9198 −2.91753
\(437\) 1.81724 0.0869304
\(438\) 15.6252 0.746602
\(439\) −30.3138 −1.44680 −0.723399 0.690430i \(-0.757421\pi\)
−0.723399 + 0.690430i \(0.757421\pi\)
\(440\) −5.80324 −0.276659
\(441\) −1.43407 −0.0682888
\(442\) −89.8245 −4.27252
\(443\) 19.5072 0.926816 0.463408 0.886145i \(-0.346627\pi\)
0.463408 + 0.886145i \(0.346627\pi\)
\(444\) −12.0437 −0.571568
\(445\) 0.629987 0.0298643
\(446\) −57.0758 −2.70262
\(447\) −8.11636 −0.383891
\(448\) 5.27111 0.249037
\(449\) −26.0914 −1.23133 −0.615666 0.788007i \(-0.711113\pi\)
−0.615666 + 0.788007i \(0.711113\pi\)
\(450\) −25.6867 −1.21088
\(451\) −4.63972 −0.218476
\(452\) 24.6575 1.15979
\(453\) 1.70548 0.0801306
\(454\) −67.0483 −3.14673
\(455\) −2.17726 −0.102072
\(456\) −25.5907 −1.19839
\(457\) −21.3783 −1.00003 −0.500017 0.866015i \(-0.666673\pi\)
−0.500017 + 0.866015i \(0.666673\pi\)
\(458\) 47.2046 2.20573
\(459\) 36.1771 1.68860
\(460\) −0.300214 −0.0139975
\(461\) −3.68909 −0.171818 −0.0859090 0.996303i \(-0.527379\pi\)
−0.0859090 + 0.996303i \(0.527379\pi\)
\(462\) −40.6056 −1.88914
\(463\) 14.7447 0.685245 0.342623 0.939473i \(-0.388685\pi\)
0.342623 + 0.939473i \(0.388685\pi\)
\(464\) −28.3842 −1.31770
\(465\) −0.995149 −0.0461489
\(466\) 0.220560 0.0102172
\(467\) −23.1439 −1.07097 −0.535487 0.844544i \(-0.679872\pi\)
−0.535487 + 0.844544i \(0.679872\pi\)
\(468\) 43.5012 2.01084
\(469\) 13.4780 0.622357
\(470\) −3.06637 −0.141441
\(471\) −18.6346 −0.858636
\(472\) 2.35174 0.108248
\(473\) 12.8613 0.591363
\(474\) −28.3367 −1.30155
\(475\) −21.4401 −0.983741
\(476\) 89.4654 4.10064
\(477\) 10.9159 0.499806
\(478\) 49.0793 2.24483
\(479\) −16.5718 −0.757186 −0.378593 0.925563i \(-0.623592\pi\)
−0.378593 + 0.925563i \(0.623592\pi\)
\(480\) 0.701237 0.0320069
\(481\) 13.5540 0.618008
\(482\) −62.0930 −2.82826
\(483\) −1.14529 −0.0521125
\(484\) 105.188 4.78125
\(485\) 1.12866 0.0512499
\(486\) −40.6542 −1.84411
\(487\) 35.5317 1.61010 0.805048 0.593210i \(-0.202140\pi\)
0.805048 + 0.593210i \(0.202140\pi\)
\(488\) −50.1545 −2.27039
\(489\) 6.38383 0.288687
\(490\) 0.287677 0.0129959
\(491\) 4.57004 0.206243 0.103121 0.994669i \(-0.467117\pi\)
0.103121 + 0.994669i \(0.467117\pi\)
\(492\) 3.38003 0.152384
\(493\) 31.7924 1.43186
\(494\) 52.8225 2.37660
\(495\) −1.95376 −0.0878151
\(496\) 41.0858 1.84481
\(497\) 34.8626 1.56380
\(498\) −6.53698 −0.292929
\(499\) 7.29942 0.326767 0.163383 0.986563i \(-0.447759\pi\)
0.163383 + 0.986563i \(0.447759\pi\)
\(500\) 7.10263 0.317639
\(501\) 1.81482 0.0810801
\(502\) 66.6415 2.97436
\(503\) −16.8588 −0.751699 −0.375849 0.926681i \(-0.622649\pi\)
−0.375849 + 0.926681i \(0.622649\pi\)
\(504\) −34.3660 −1.53078
\(505\) −1.71698 −0.0764046
\(506\) 6.30105 0.280116
\(507\) 10.2499 0.455214
\(508\) 53.5794 2.37720
\(509\) 28.5617 1.26598 0.632989 0.774161i \(-0.281828\pi\)
0.632989 + 0.774161i \(0.281828\pi\)
\(510\) −2.93897 −0.130140
\(511\) 17.5143 0.774788
\(512\) 50.4280 2.22862
\(513\) −21.2744 −0.939288
\(514\) 67.1882 2.96354
\(515\) 1.38622 0.0610843
\(516\) −9.36945 −0.412467
\(517\) 44.2394 1.94565
\(518\) −19.6393 −0.862900
\(519\) 3.26353 0.143253
\(520\) −4.75781 −0.208644
\(521\) 3.80707 0.166791 0.0833954 0.996517i \(-0.473424\pi\)
0.0833954 + 0.996517i \(0.473424\pi\)
\(522\) −22.3989 −0.980375
\(523\) −6.09467 −0.266501 −0.133251 0.991082i \(-0.542542\pi\)
−0.133251 + 0.991082i \(0.542542\pi\)
\(524\) −15.3638 −0.671170
\(525\) 13.5123 0.589727
\(526\) 75.4201 3.28847
\(527\) −46.0193 −2.00463
\(528\) −37.8557 −1.64746
\(529\) −22.8223 −0.992273
\(530\) −2.18976 −0.0951171
\(531\) 0.791756 0.0343593
\(532\) −52.6113 −2.28099
\(533\) −3.80389 −0.164765
\(534\) 9.63258 0.416843
\(535\) −1.83460 −0.0793166
\(536\) 29.4525 1.27215
\(537\) −17.4587 −0.753399
\(538\) 53.9909 2.32772
\(539\) −4.15039 −0.178770
\(540\) 3.51460 0.151244
\(541\) −11.8661 −0.510163 −0.255081 0.966920i \(-0.582102\pi\)
−0.255081 + 0.966920i \(0.582102\pi\)
\(542\) 3.57537 0.153575
\(543\) −4.70141 −0.201757
\(544\) 32.4277 1.39033
\(545\) 2.24319 0.0960876
\(546\) −33.2906 −1.42471
\(547\) −30.5823 −1.30760 −0.653801 0.756666i \(-0.726827\pi\)
−0.653801 + 0.756666i \(0.726827\pi\)
\(548\) 12.1696 0.519860
\(549\) −16.8854 −0.720652
\(550\) −74.3409 −3.16991
\(551\) −18.6959 −0.796474
\(552\) −2.50272 −0.106523
\(553\) −31.7627 −1.35069
\(554\) 80.8240 3.43388
\(555\) 0.443473 0.0188244
\(556\) 30.4974 1.29338
\(557\) 37.2546 1.57853 0.789265 0.614053i \(-0.210462\pi\)
0.789265 + 0.614053i \(0.210462\pi\)
\(558\) 32.4223 1.37255
\(559\) 10.5444 0.445980
\(560\) 2.94113 0.124286
\(561\) 42.4013 1.79018
\(562\) −20.2812 −0.855511
\(563\) 28.2201 1.18933 0.594667 0.803972i \(-0.297284\pi\)
0.594667 + 0.803972i \(0.297284\pi\)
\(564\) −32.2284 −1.35706
\(565\) −0.907937 −0.0381972
\(566\) −29.2151 −1.22800
\(567\) −3.59185 −0.150843
\(568\) 76.1826 3.19655
\(569\) 15.5926 0.653677 0.326838 0.945080i \(-0.394017\pi\)
0.326838 + 0.945080i \(0.394017\pi\)
\(570\) 1.72830 0.0723905
\(571\) 31.4602 1.31657 0.658284 0.752770i \(-0.271283\pi\)
0.658284 + 0.752770i \(0.271283\pi\)
\(572\) 125.899 5.26409
\(573\) −5.19002 −0.216816
\(574\) 5.51171 0.230054
\(575\) −2.09680 −0.0874428
\(576\) 3.87793 0.161580
\(577\) −9.15920 −0.381302 −0.190651 0.981658i \(-0.561060\pi\)
−0.190651 + 0.981658i \(0.561060\pi\)
\(578\) −92.9092 −3.86451
\(579\) −7.46017 −0.310034
\(580\) 3.08863 0.128248
\(581\) −7.32731 −0.303988
\(582\) 17.2574 0.715341
\(583\) 31.5922 1.30842
\(584\) 38.2727 1.58374
\(585\) −1.60180 −0.0662263
\(586\) 41.8634 1.72936
\(587\) −45.2912 −1.86937 −0.934684 0.355479i \(-0.884318\pi\)
−0.934684 + 0.355479i \(0.884318\pi\)
\(588\) 3.02356 0.124689
\(589\) 27.0622 1.11508
\(590\) −0.158828 −0.00653885
\(591\) −9.34725 −0.384495
\(592\) −18.3093 −0.752506
\(593\) 2.25231 0.0924914 0.0462457 0.998930i \(-0.485274\pi\)
0.0462457 + 0.998930i \(0.485274\pi\)
\(594\) −73.7662 −3.02667
\(595\) −3.29430 −0.135053
\(596\) −36.4632 −1.49359
\(597\) −2.35870 −0.0965352
\(598\) 5.16594 0.211251
\(599\) 43.0609 1.75942 0.879710 0.475510i \(-0.157737\pi\)
0.879710 + 0.475510i \(0.157737\pi\)
\(600\) 29.5275 1.20545
\(601\) −5.90362 −0.240814 −0.120407 0.992725i \(-0.538420\pi\)
−0.120407 + 0.992725i \(0.538420\pi\)
\(602\) −15.2785 −0.622704
\(603\) 9.91571 0.403799
\(604\) 7.66198 0.311762
\(605\) −3.87321 −0.157469
\(606\) −26.2528 −1.06645
\(607\) −37.6439 −1.52792 −0.763960 0.645264i \(-0.776747\pi\)
−0.763960 + 0.645264i \(0.776747\pi\)
\(608\) −19.0695 −0.773372
\(609\) 11.7829 0.477465
\(610\) 3.38726 0.137146
\(611\) 36.2698 1.46732
\(612\) 65.8192 2.66058
\(613\) 1.83469 0.0741023 0.0370511 0.999313i \(-0.488204\pi\)
0.0370511 + 0.999313i \(0.488204\pi\)
\(614\) −20.0490 −0.809110
\(615\) −0.124460 −0.00501869
\(616\) −99.4601 −4.00736
\(617\) 6.79004 0.273357 0.136678 0.990615i \(-0.456357\pi\)
0.136678 + 0.990615i \(0.456357\pi\)
\(618\) 21.1955 0.852609
\(619\) −25.0593 −1.00722 −0.503609 0.863932i \(-0.667995\pi\)
−0.503609 + 0.863932i \(0.667995\pi\)
\(620\) −4.47077 −0.179550
\(621\) −2.08060 −0.0834914
\(622\) 36.2097 1.45188
\(623\) 10.7972 0.432580
\(624\) −31.0361 −1.24244
\(625\) 24.6074 0.984294
\(626\) −20.2779 −0.810468
\(627\) −24.9346 −0.995793
\(628\) −83.7169 −3.34067
\(629\) 20.5078 0.817698
\(630\) 2.32095 0.0924690
\(631\) −31.0347 −1.23547 −0.617736 0.786385i \(-0.711950\pi\)
−0.617736 + 0.786385i \(0.711950\pi\)
\(632\) −69.4086 −2.76093
\(633\) 19.0439 0.756927
\(634\) 23.3614 0.927801
\(635\) −1.97290 −0.0782921
\(636\) −23.0149 −0.912601
\(637\) −3.40271 −0.134820
\(638\) −64.8258 −2.56648
\(639\) 25.6482 1.01463
\(640\) −2.21064 −0.0873834
\(641\) 42.8225 1.69139 0.845694 0.533668i \(-0.179187\pi\)
0.845694 + 0.533668i \(0.179187\pi\)
\(642\) −28.0512 −1.10709
\(643\) −48.7876 −1.92399 −0.961997 0.273060i \(-0.911964\pi\)
−0.961997 + 0.273060i \(0.911964\pi\)
\(644\) −5.14528 −0.202753
\(645\) 0.345002 0.0135844
\(646\) 79.9228 3.14452
\(647\) −12.6130 −0.495869 −0.247934 0.968777i \(-0.579752\pi\)
−0.247934 + 0.968777i \(0.579752\pi\)
\(648\) −7.84899 −0.308337
\(649\) 2.29145 0.0899475
\(650\) −60.9486 −2.39060
\(651\) −17.0556 −0.668461
\(652\) 28.6797 1.12318
\(653\) −18.2472 −0.714067 −0.357034 0.934091i \(-0.616212\pi\)
−0.357034 + 0.934091i \(0.616212\pi\)
\(654\) 34.2986 1.34118
\(655\) 0.565725 0.0221047
\(656\) 5.13845 0.200623
\(657\) 12.8852 0.502699
\(658\) −52.5538 −2.04876
\(659\) −18.6429 −0.726226 −0.363113 0.931745i \(-0.618286\pi\)
−0.363113 + 0.931745i \(0.618286\pi\)
\(660\) 4.11928 0.160343
\(661\) 7.55350 0.293797 0.146899 0.989152i \(-0.453071\pi\)
0.146899 + 0.989152i \(0.453071\pi\)
\(662\) 26.2267 1.01933
\(663\) 34.7628 1.35008
\(664\) −16.0118 −0.621379
\(665\) 1.93725 0.0751235
\(666\) −14.4485 −0.559868
\(667\) −1.82843 −0.0707970
\(668\) 8.15318 0.315456
\(669\) 22.0888 0.854003
\(670\) −1.98911 −0.0768462
\(671\) −48.8688 −1.88656
\(672\) 12.0183 0.463616
\(673\) −41.9897 −1.61858 −0.809292 0.587406i \(-0.800149\pi\)
−0.809292 + 0.587406i \(0.800149\pi\)
\(674\) 50.4988 1.94514
\(675\) 24.5472 0.944824
\(676\) 46.0483 1.77109
\(677\) −8.41749 −0.323510 −0.161755 0.986831i \(-0.551716\pi\)
−0.161755 + 0.986831i \(0.551716\pi\)
\(678\) −13.8825 −0.533153
\(679\) 19.3438 0.742347
\(680\) −7.19877 −0.276060
\(681\) 25.9483 0.994339
\(682\) 93.8348 3.59312
\(683\) −15.4750 −0.592133 −0.296066 0.955167i \(-0.595675\pi\)
−0.296066 + 0.955167i \(0.595675\pi\)
\(684\) −38.7058 −1.47995
\(685\) −0.448109 −0.0171214
\(686\) −44.2081 −1.68787
\(687\) −18.2686 −0.696990
\(688\) −14.2438 −0.543039
\(689\) 25.9010 0.986750
\(690\) 0.169024 0.00643465
\(691\) 25.6059 0.974095 0.487048 0.873375i \(-0.338074\pi\)
0.487048 + 0.873375i \(0.338074\pi\)
\(692\) 14.6616 0.557350
\(693\) −33.4850 −1.27199
\(694\) 44.6494 1.69487
\(695\) −1.12298 −0.0425969
\(696\) 25.7482 0.975982
\(697\) −5.75546 −0.218003
\(698\) −68.0218 −2.57466
\(699\) −0.0853585 −0.00322855
\(700\) 60.7050 2.29443
\(701\) −3.13580 −0.118438 −0.0592188 0.998245i \(-0.518861\pi\)
−0.0592188 + 0.998245i \(0.518861\pi\)
\(702\) −60.4775 −2.28258
\(703\) −12.0599 −0.454846
\(704\) 11.2233 0.422993
\(705\) 1.18671 0.0446942
\(706\) −73.3590 −2.76090
\(707\) −29.4269 −1.10671
\(708\) −1.66932 −0.0627370
\(709\) 31.3755 1.17833 0.589165 0.808012i \(-0.299457\pi\)
0.589165 + 0.808012i \(0.299457\pi\)
\(710\) −5.14510 −0.193092
\(711\) −23.3676 −0.876355
\(712\) 23.5942 0.884232
\(713\) 2.64663 0.0991172
\(714\) −50.3702 −1.88506
\(715\) −4.63584 −0.173370
\(716\) −78.4343 −2.93123
\(717\) −18.9941 −0.709347
\(718\) −13.0669 −0.487652
\(719\) −33.4250 −1.24654 −0.623271 0.782006i \(-0.714197\pi\)
−0.623271 + 0.782006i \(0.714197\pi\)
\(720\) 2.16378 0.0806392
\(721\) 23.7581 0.884798
\(722\) 1.05835 0.0393876
\(723\) 24.0305 0.893705
\(724\) −21.1214 −0.784969
\(725\) 21.5721 0.801168
\(726\) −59.2219 −2.19793
\(727\) 30.0575 1.11477 0.557385 0.830254i \(-0.311805\pi\)
0.557385 + 0.830254i \(0.311805\pi\)
\(728\) −81.5427 −3.02218
\(729\) 11.8509 0.438922
\(730\) −2.58480 −0.0956678
\(731\) 15.9541 0.590085
\(732\) 35.6009 1.31585
\(733\) 40.3323 1.48971 0.744853 0.667228i \(-0.232519\pi\)
0.744853 + 0.667228i \(0.232519\pi\)
\(734\) 33.4608 1.23506
\(735\) −0.111333 −0.00410659
\(736\) −1.86496 −0.0687435
\(737\) 28.6975 1.05709
\(738\) 4.05493 0.149264
\(739\) −21.2826 −0.782895 −0.391447 0.920201i \(-0.628025\pi\)
−0.391447 + 0.920201i \(0.628025\pi\)
\(740\) 1.99233 0.0732394
\(741\) −20.4427 −0.750983
\(742\) −37.5297 −1.37776
\(743\) 23.3360 0.856114 0.428057 0.903752i \(-0.359198\pi\)
0.428057 + 0.903752i \(0.359198\pi\)
\(744\) −37.2703 −1.36639
\(745\) 1.34265 0.0491908
\(746\) −16.2819 −0.596122
\(747\) −5.39066 −0.197234
\(748\) 190.490 6.96501
\(749\) −31.4427 −1.14889
\(750\) −3.99887 −0.146018
\(751\) −29.3268 −1.07015 −0.535074 0.844805i \(-0.679716\pi\)
−0.535074 + 0.844805i \(0.679716\pi\)
\(752\) −48.9947 −1.78665
\(753\) −25.7908 −0.939869
\(754\) −53.1476 −1.93552
\(755\) −0.282129 −0.0102677
\(756\) 60.2358 2.19075
\(757\) 10.7547 0.390886 0.195443 0.980715i \(-0.437386\pi\)
0.195443 + 0.980715i \(0.437386\pi\)
\(758\) −43.2025 −1.56919
\(759\) −2.43856 −0.0885140
\(760\) 4.23333 0.153559
\(761\) 9.57577 0.347122 0.173561 0.984823i \(-0.444473\pi\)
0.173561 + 0.984823i \(0.444473\pi\)
\(762\) −30.1659 −1.09279
\(763\) 38.4454 1.39182
\(764\) −23.3165 −0.843560
\(765\) −2.42359 −0.0876252
\(766\) 9.91198 0.358134
\(767\) 1.87866 0.0678344
\(768\) −30.0827 −1.08551
\(769\) −53.5550 −1.93124 −0.965621 0.259955i \(-0.916292\pi\)
−0.965621 + 0.259955i \(0.916292\pi\)
\(770\) 6.71717 0.242070
\(771\) −26.0024 −0.936453
\(772\) −33.5152 −1.20624
\(773\) 20.2335 0.727750 0.363875 0.931448i \(-0.381454\pi\)
0.363875 + 0.931448i \(0.381454\pi\)
\(774\) −11.2403 −0.404023
\(775\) −31.2255 −1.12165
\(776\) 42.2706 1.51742
\(777\) 7.60056 0.272669
\(778\) −21.4637 −0.769512
\(779\) 3.38457 0.121265
\(780\) 3.37720 0.120923
\(781\) 74.2297 2.65615
\(782\) 7.81629 0.279510
\(783\) 21.4054 0.764965
\(784\) 4.59652 0.164162
\(785\) 3.08262 0.110024
\(786\) 8.65001 0.308536
\(787\) −7.56890 −0.269802 −0.134901 0.990859i \(-0.543072\pi\)
−0.134901 + 0.990859i \(0.543072\pi\)
\(788\) −41.9931 −1.49594
\(789\) −29.1882 −1.03913
\(790\) 4.68760 0.166777
\(791\) −15.5609 −0.553281
\(792\) −73.1722 −2.60006
\(793\) −40.0653 −1.42276
\(794\) 9.20065 0.326519
\(795\) 0.847455 0.0300561
\(796\) −10.5966 −0.375587
\(797\) −55.9963 −1.98349 −0.991745 0.128229i \(-0.959071\pi\)
−0.991745 + 0.128229i \(0.959071\pi\)
\(798\) 29.6209 1.04857
\(799\) 54.8778 1.94144
\(800\) 22.0032 0.777930
\(801\) 7.94342 0.280667
\(802\) 69.2917 2.44678
\(803\) 37.2916 1.31599
\(804\) −20.9061 −0.737301
\(805\) 0.189460 0.00667757
\(806\) 76.9308 2.70977
\(807\) −20.8949 −0.735537
\(808\) −64.3043 −2.26222
\(809\) −46.9221 −1.64969 −0.824846 0.565357i \(-0.808738\pi\)
−0.824846 + 0.565357i \(0.808738\pi\)
\(810\) 0.530092 0.0186255
\(811\) 26.6826 0.936953 0.468476 0.883476i \(-0.344803\pi\)
0.468476 + 0.883476i \(0.344803\pi\)
\(812\) 52.9352 1.85766
\(813\) −1.38370 −0.0485284
\(814\) −41.8160 −1.46565
\(815\) −1.05604 −0.0369916
\(816\) −46.9590 −1.64390
\(817\) −9.38203 −0.328236
\(818\) −37.2822 −1.30354
\(819\) −27.4528 −0.959279
\(820\) −0.559142 −0.0195261
\(821\) 5.80456 0.202581 0.101290 0.994857i \(-0.467703\pi\)
0.101290 + 0.994857i \(0.467703\pi\)
\(822\) −6.85165 −0.238979
\(823\) −53.0223 −1.84824 −0.924120 0.382102i \(-0.875200\pi\)
−0.924120 + 0.382102i \(0.875200\pi\)
\(824\) 51.9168 1.80861
\(825\) 28.7705 1.00166
\(826\) −2.72211 −0.0947144
\(827\) −52.3758 −1.82129 −0.910643 0.413194i \(-0.864413\pi\)
−0.910643 + 0.413194i \(0.864413\pi\)
\(828\) −3.78536 −0.131550
\(829\) −12.1802 −0.423035 −0.211518 0.977374i \(-0.567841\pi\)
−0.211518 + 0.977374i \(0.567841\pi\)
\(830\) 1.08138 0.0375352
\(831\) −31.2796 −1.08508
\(832\) 9.20144 0.319003
\(833\) −5.14846 −0.178383
\(834\) −17.1704 −0.594564
\(835\) −0.300216 −0.0103894
\(836\) −112.020 −3.87430
\(837\) −30.9841 −1.07097
\(838\) 59.6985 2.06225
\(839\) 29.2163 1.00866 0.504330 0.863511i \(-0.331740\pi\)
0.504330 + 0.863511i \(0.331740\pi\)
\(840\) −2.66800 −0.0920547
\(841\) −10.1890 −0.351344
\(842\) −75.1167 −2.58869
\(843\) 7.84899 0.270334
\(844\) 85.5558 2.94495
\(845\) −1.69559 −0.0583300
\(846\) −38.6635 −1.32928
\(847\) −66.3820 −2.28091
\(848\) −34.9881 −1.20150
\(849\) 11.3065 0.388038
\(850\) −92.2180 −3.16305
\(851\) −1.17943 −0.0404304
\(852\) −54.0763 −1.85262
\(853\) −5.93669 −0.203268 −0.101634 0.994822i \(-0.532407\pi\)
−0.101634 + 0.994822i \(0.532407\pi\)
\(854\) 58.0532 1.98654
\(855\) 1.42523 0.0487417
\(856\) −68.7093 −2.34844
\(857\) 29.0652 0.992847 0.496424 0.868080i \(-0.334646\pi\)
0.496424 + 0.868080i \(0.334646\pi\)
\(858\) −70.8825 −2.41989
\(859\) −35.6817 −1.21745 −0.608723 0.793383i \(-0.708318\pi\)
−0.608723 + 0.793383i \(0.708318\pi\)
\(860\) 1.54994 0.0528525
\(861\) −2.13308 −0.0726951
\(862\) −100.730 −3.43086
\(863\) 22.4626 0.764636 0.382318 0.924031i \(-0.375126\pi\)
0.382318 + 0.924031i \(0.375126\pi\)
\(864\) 21.8331 0.742777
\(865\) −0.539869 −0.0183561
\(866\) 31.4458 1.06857
\(867\) 35.9566 1.22115
\(868\) −76.6232 −2.60076
\(869\) −67.6293 −2.29417
\(870\) −1.73894 −0.0589555
\(871\) 23.5277 0.797207
\(872\) 84.0118 2.84500
\(873\) 14.2311 0.481651
\(874\) −4.59647 −0.155478
\(875\) −4.48234 −0.151531
\(876\) −27.1669 −0.917884
\(877\) −9.38224 −0.316816 −0.158408 0.987374i \(-0.550636\pi\)
−0.158408 + 0.987374i \(0.550636\pi\)
\(878\) 76.6747 2.58765
\(879\) −16.2015 −0.546463
\(880\) 6.26228 0.211101
\(881\) −45.3864 −1.52911 −0.764554 0.644560i \(-0.777041\pi\)
−0.764554 + 0.644560i \(0.777041\pi\)
\(882\) 3.62728 0.122137
\(883\) 39.8325 1.34047 0.670235 0.742149i \(-0.266193\pi\)
0.670235 + 0.742149i \(0.266193\pi\)
\(884\) 156.174 5.25270
\(885\) 0.0614678 0.00206622
\(886\) −49.3409 −1.65764
\(887\) −41.7081 −1.40042 −0.700211 0.713936i \(-0.746911\pi\)
−0.700211 + 0.713936i \(0.746911\pi\)
\(888\) 16.6089 0.557359
\(889\) −33.8130 −1.13405
\(890\) −1.59347 −0.0534132
\(891\) −7.64778 −0.256210
\(892\) 99.2353 3.32264
\(893\) −32.2716 −1.07993
\(894\) 20.5293 0.686601
\(895\) 2.88811 0.0965387
\(896\) −37.8876 −1.26574
\(897\) −1.99926 −0.0667534
\(898\) 65.9949 2.20228
\(899\) −27.2288 −0.908132
\(900\) 44.6603 1.48868
\(901\) 39.1894 1.30559
\(902\) 11.7356 0.390751
\(903\) 5.91289 0.196769
\(904\) −34.0040 −1.13096
\(905\) 0.777730 0.0258526
\(906\) −4.31380 −0.143316
\(907\) −52.0669 −1.72885 −0.864426 0.502760i \(-0.832318\pi\)
−0.864426 + 0.502760i \(0.832318\pi\)
\(908\) 116.574 3.86865
\(909\) −21.6492 −0.718057
\(910\) 5.50710 0.182559
\(911\) 49.2509 1.63176 0.815878 0.578224i \(-0.196254\pi\)
0.815878 + 0.578224i \(0.196254\pi\)
\(912\) 27.6149 0.914420
\(913\) −15.6013 −0.516329
\(914\) 54.0736 1.78860
\(915\) −1.31090 −0.0433369
\(916\) −82.0727 −2.71176
\(917\) 9.69581 0.320184
\(918\) −91.5052 −3.02012
\(919\) −21.4075 −0.706169 −0.353084 0.935591i \(-0.614867\pi\)
−0.353084 + 0.935591i \(0.614867\pi\)
\(920\) 0.414012 0.0136496
\(921\) 7.75912 0.255672
\(922\) 9.33106 0.307302
\(923\) 60.8575 2.00315
\(924\) 70.5992 2.32254
\(925\) 13.9151 0.457527
\(926\) −37.2948 −1.22558
\(927\) 17.4787 0.574076
\(928\) 19.1869 0.629841
\(929\) −3.33104 −0.109288 −0.0546440 0.998506i \(-0.517402\pi\)
−0.0546440 + 0.998506i \(0.517402\pi\)
\(930\) 2.51710 0.0825389
\(931\) 3.02762 0.0992262
\(932\) −0.383478 −0.0125612
\(933\) −14.0134 −0.458780
\(934\) 58.5395 1.91547
\(935\) −7.01423 −0.229390
\(936\) −59.9905 −1.96085
\(937\) 10.5731 0.345407 0.172703 0.984974i \(-0.444750\pi\)
0.172703 + 0.984974i \(0.444750\pi\)
\(938\) −34.0909 −1.11311
\(939\) 7.84772 0.256101
\(940\) 5.33137 0.173890
\(941\) 19.3227 0.629903 0.314952 0.949108i \(-0.398012\pi\)
0.314952 + 0.949108i \(0.398012\pi\)
\(942\) 47.1337 1.53570
\(943\) 0.331005 0.0107790
\(944\) −2.53777 −0.0825973
\(945\) −2.21800 −0.0721516
\(946\) −32.5310 −1.05767
\(947\) 18.9656 0.616300 0.308150 0.951338i \(-0.400290\pi\)
0.308150 + 0.951338i \(0.400290\pi\)
\(948\) 49.2679 1.60015
\(949\) 30.5736 0.992462
\(950\) 54.2300 1.75945
\(951\) −9.04106 −0.293177
\(952\) −123.378 −3.99870
\(953\) 21.5103 0.696789 0.348394 0.937348i \(-0.386727\pi\)
0.348394 + 0.937348i \(0.386727\pi\)
\(954\) −27.6104 −0.893919
\(955\) 0.858559 0.0277823
\(956\) −85.3320 −2.75984
\(957\) 25.0881 0.810983
\(958\) 41.9163 1.35425
\(959\) −7.68002 −0.248001
\(960\) 0.301062 0.00971673
\(961\) 8.41350 0.271403
\(962\) −34.2830 −1.10533
\(963\) −23.1322 −0.745425
\(964\) 107.959 3.47711
\(965\) 1.23410 0.0397270
\(966\) 2.89686 0.0932050
\(967\) 14.8608 0.477891 0.238946 0.971033i \(-0.423198\pi\)
0.238946 + 0.971033i \(0.423198\pi\)
\(968\) −145.059 −4.66239
\(969\) −30.9308 −0.993640
\(970\) −2.85480 −0.0916621
\(971\) −0.00316838 −0.000101678 0 −5.08390e−5 1.00000i \(-0.500016\pi\)
−5.08390e−5 1.00000i \(0.500016\pi\)
\(972\) 70.6838 2.26718
\(973\) −19.2464 −0.617010
\(974\) −89.8728 −2.87971
\(975\) 23.5876 0.755409
\(976\) 54.1218 1.73240
\(977\) 47.5620 1.52164 0.760822 0.648960i \(-0.224796\pi\)
0.760822 + 0.648960i \(0.224796\pi\)
\(978\) −16.1470 −0.516326
\(979\) 22.9894 0.734744
\(980\) −0.500172 −0.0159774
\(981\) 28.2840 0.903040
\(982\) −11.5593 −0.368872
\(983\) 25.1112 0.800922 0.400461 0.916314i \(-0.368850\pi\)
0.400461 + 0.916314i \(0.368850\pi\)
\(984\) −4.66125 −0.148595
\(985\) 1.54627 0.0492682
\(986\) −80.4147 −2.56093
\(987\) 20.3387 0.647389
\(988\) −91.8402 −2.92183
\(989\) −0.917544 −0.0291762
\(990\) 4.94179 0.157060
\(991\) 7.27648 0.231145 0.115572 0.993299i \(-0.463130\pi\)
0.115572 + 0.993299i \(0.463130\pi\)
\(992\) −27.7729 −0.881791
\(993\) −10.1499 −0.322098
\(994\) −88.1804 −2.79691
\(995\) 0.390188 0.0123698
\(996\) 11.3656 0.360132
\(997\) −26.3317 −0.833932 −0.416966 0.908922i \(-0.636907\pi\)
−0.416966 + 0.908922i \(0.636907\pi\)
\(998\) −18.4629 −0.584434
\(999\) 13.8076 0.436853
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 \(a_p\))