Properties

Label 6019.2.a.c.1.5
Level 6019
Weight 2
Character 6019.1
Self dual Yes
Analytic conductor 48.062
Analytic rank 1
Dimension 108
CM No

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Newspace parameters

Level: \( N \) = \( 6019 = 13 \cdot 463 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6019.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0619569766\)
Analytic rank: \(1\)
Dimension: \(108\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Character \(\chi\) = 6019.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.62196 q^{2}\) \(-0.813055 q^{3}\) \(+4.87469 q^{4}\) \(+0.562087 q^{5}\) \(+2.13180 q^{6}\) \(-5.01388 q^{7}\) \(-7.53732 q^{8}\) \(-2.33894 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.62196 q^{2}\) \(-0.813055 q^{3}\) \(+4.87469 q^{4}\) \(+0.562087 q^{5}\) \(+2.13180 q^{6}\) \(-5.01388 q^{7}\) \(-7.53732 q^{8}\) \(-2.33894 q^{9}\) \(-1.47377 q^{10}\) \(-2.09845 q^{11}\) \(-3.96339 q^{12}\) \(-1.00000 q^{13}\) \(+13.1462 q^{14}\) \(-0.457007 q^{15}\) \(+10.0132 q^{16}\) \(+3.74319 q^{17}\) \(+6.13262 q^{18}\) \(-0.888994 q^{19}\) \(+2.74000 q^{20}\) \(+4.07656 q^{21}\) \(+5.50205 q^{22}\) \(+3.39137 q^{23}\) \(+6.12826 q^{24}\) \(-4.68406 q^{25}\) \(+2.62196 q^{26}\) \(+4.34085 q^{27}\) \(-24.4411 q^{28}\) \(+3.62001 q^{29}\) \(+1.19826 q^{30}\) \(-8.47651 q^{31}\) \(-11.1796 q^{32}\) \(+1.70615 q^{33}\) \(-9.81451 q^{34}\) \(-2.81823 q^{35}\) \(-11.4016 q^{36}\) \(+2.48870 q^{37}\) \(+2.33091 q^{38}\) \(+0.813055 q^{39}\) \(-4.23663 q^{40}\) \(-7.93225 q^{41}\) \(-10.6886 q^{42}\) \(+6.00589 q^{43}\) \(-10.2293 q^{44}\) \(-1.31469 q^{45}\) \(-8.89206 q^{46}\) \(+1.50624 q^{47}\) \(-8.14128 q^{48}\) \(+18.1390 q^{49}\) \(+12.2814 q^{50}\) \(-3.04342 q^{51}\) \(-4.87469 q^{52}\) \(-2.70934 q^{53}\) \(-11.3816 q^{54}\) \(-1.17951 q^{55}\) \(+37.7912 q^{56}\) \(+0.722801 q^{57}\) \(-9.49153 q^{58}\) \(+11.4174 q^{59}\) \(-2.22777 q^{60}\) \(-0.919060 q^{61}\) \(+22.2251 q^{62}\) \(+11.7272 q^{63}\) \(+9.28607 q^{64}\) \(-0.562087 q^{65}\) \(-4.47347 q^{66}\) \(-2.20779 q^{67}\) \(+18.2469 q^{68}\) \(-2.75737 q^{69}\) \(+7.38930 q^{70}\) \(+1.75234 q^{71}\) \(+17.6294 q^{72}\) \(+9.37638 q^{73}\) \(-6.52527 q^{74}\) \(+3.80840 q^{75}\) \(-4.33357 q^{76}\) \(+10.5214 q^{77}\) \(-2.13180 q^{78}\) \(+6.77830 q^{79}\) \(+5.62829 q^{80}\) \(+3.48747 q^{81}\) \(+20.7981 q^{82}\) \(+8.69805 q^{83}\) \(+19.8719 q^{84}\) \(+2.10400 q^{85}\) \(-15.7472 q^{86}\) \(-2.94327 q^{87}\) \(+15.8167 q^{88}\) \(-11.1990 q^{89}\) \(+3.44706 q^{90}\) \(+5.01388 q^{91}\) \(+16.5319 q^{92}\) \(+6.89187 q^{93}\) \(-3.94930 q^{94}\) \(-0.499691 q^{95}\) \(+9.08962 q^{96}\) \(-6.56447 q^{97}\) \(-47.5597 q^{98}\) \(+4.90815 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(108q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut +\mathstrut q^{3} \) \(\mathstrut +\mathstrut 95q^{4} \) \(\mathstrut -\mathstrut 40q^{5} \) \(\mathstrut -\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut 33q^{8} \) \(\mathstrut +\mathstrut 79q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(108q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut +\mathstrut q^{3} \) \(\mathstrut +\mathstrut 95q^{4} \) \(\mathstrut -\mathstrut 40q^{5} \) \(\mathstrut -\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut 33q^{8} \) \(\mathstrut +\mathstrut 79q^{9} \) \(\mathstrut -\mathstrut q^{10} \) \(\mathstrut -\mathstrut 45q^{11} \) \(\mathstrut -\mathstrut 6q^{12} \) \(\mathstrut -\mathstrut 108q^{13} \) \(\mathstrut -\mathstrut 31q^{14} \) \(\mathstrut -\mathstrut 39q^{15} \) \(\mathstrut +\mathstrut 73q^{16} \) \(\mathstrut +\mathstrut 21q^{17} \) \(\mathstrut -\mathstrut 35q^{18} \) \(\mathstrut -\mathstrut 19q^{19} \) \(\mathstrut -\mathstrut 79q^{20} \) \(\mathstrut -\mathstrut 72q^{21} \) \(\mathstrut -\mathstrut 26q^{23} \) \(\mathstrut -\mathstrut 23q^{24} \) \(\mathstrut +\mathstrut 92q^{25} \) \(\mathstrut +\mathstrut 11q^{26} \) \(\mathstrut +\mathstrut 7q^{27} \) \(\mathstrut -\mathstrut 21q^{28} \) \(\mathstrut -\mathstrut 94q^{29} \) \(\mathstrut -\mathstrut 24q^{30} \) \(\mathstrut -\mathstrut 36q^{31} \) \(\mathstrut -\mathstrut 77q^{32} \) \(\mathstrut -\mathstrut 32q^{33} \) \(\mathstrut -\mathstrut 58q^{34} \) \(\mathstrut -\mathstrut 10q^{35} \) \(\mathstrut +\mathstrut 17q^{36} \) \(\mathstrut -\mathstrut 54q^{37} \) \(\mathstrut -\mathstrut 12q^{38} \) \(\mathstrut -\mathstrut q^{39} \) \(\mathstrut -\mathstrut 4q^{40} \) \(\mathstrut -\mathstrut 68q^{41} \) \(\mathstrut -\mathstrut 11q^{42} \) \(\mathstrut -\mathstrut 32q^{43} \) \(\mathstrut -\mathstrut 151q^{44} \) \(\mathstrut -\mathstrut 121q^{45} \) \(\mathstrut -\mathstrut 33q^{46} \) \(\mathstrut -\mathstrut 51q^{47} \) \(\mathstrut -\mathstrut 27q^{48} \) \(\mathstrut +\mathstrut 72q^{49} \) \(\mathstrut -\mathstrut 45q^{50} \) \(\mathstrut -\mathstrut 24q^{51} \) \(\mathstrut -\mathstrut 95q^{52} \) \(\mathstrut -\mathstrut 81q^{53} \) \(\mathstrut -\mathstrut 29q^{54} \) \(\mathstrut +\mathstrut 4q^{55} \) \(\mathstrut -\mathstrut 68q^{56} \) \(\mathstrut -\mathstrut 45q^{57} \) \(\mathstrut -\mathstrut 30q^{58} \) \(\mathstrut -\mathstrut 94q^{59} \) \(\mathstrut -\mathstrut 108q^{60} \) \(\mathstrut -\mathstrut 39q^{61} \) \(\mathstrut -\mathstrut 9q^{62} \) \(\mathstrut -\mathstrut 52q^{63} \) \(\mathstrut +\mathstrut 31q^{64} \) \(\mathstrut +\mathstrut 40q^{65} \) \(\mathstrut -\mathstrut 40q^{66} \) \(\mathstrut -\mathstrut 47q^{67} \) \(\mathstrut +\mathstrut 24q^{68} \) \(\mathstrut -\mathstrut 60q^{69} \) \(\mathstrut -\mathstrut 66q^{70} \) \(\mathstrut -\mathstrut 86q^{71} \) \(\mathstrut -\mathstrut 91q^{72} \) \(\mathstrut -\mathstrut 51q^{73} \) \(\mathstrut -\mathstrut 110q^{74} \) \(\mathstrut -\mathstrut 7q^{75} \) \(\mathstrut -\mathstrut 51q^{76} \) \(\mathstrut -\mathstrut 96q^{77} \) \(\mathstrut +\mathstrut 10q^{78} \) \(\mathstrut -\mathstrut 18q^{79} \) \(\mathstrut -\mathstrut 136q^{80} \) \(\mathstrut -\mathstrut 24q^{81} \) \(\mathstrut -\mathstrut 33q^{82} \) \(\mathstrut -\mathstrut 77q^{83} \) \(\mathstrut -\mathstrut 113q^{84} \) \(\mathstrut -\mathstrut 95q^{85} \) \(\mathstrut -\mathstrut 137q^{86} \) \(\mathstrut +\mathstrut 23q^{87} \) \(\mathstrut +\mathstrut 19q^{88} \) \(\mathstrut -\mathstrut 112q^{89} \) \(\mathstrut -\mathstrut 19q^{90} \) \(\mathstrut +\mathstrut 8q^{91} \) \(\mathstrut -\mathstrut 111q^{92} \) \(\mathstrut -\mathstrut 124q^{93} \) \(\mathstrut -\mathstrut 20q^{94} \) \(\mathstrut -\mathstrut 73q^{95} \) \(\mathstrut -\mathstrut 77q^{96} \) \(\mathstrut -\mathstrut 41q^{97} \) \(\mathstrut -\mathstrut 80q^{98} \) \(\mathstrut -\mathstrut 154q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.62196 −1.85401 −0.927004 0.375052i \(-0.877625\pi\)
−0.927004 + 0.375052i \(0.877625\pi\)
\(3\) −0.813055 −0.469417 −0.234709 0.972066i \(-0.575414\pi\)
−0.234709 + 0.972066i \(0.575414\pi\)
\(4\) 4.87469 2.43734
\(5\) 0.562087 0.251373 0.125686 0.992070i \(-0.459887\pi\)
0.125686 + 0.992070i \(0.459887\pi\)
\(6\) 2.13180 0.870303
\(7\) −5.01388 −1.89507 −0.947534 0.319656i \(-0.896433\pi\)
−0.947534 + 0.319656i \(0.896433\pi\)
\(8\) −7.53732 −2.66485
\(9\) −2.33894 −0.779647
\(10\) −1.47377 −0.466047
\(11\) −2.09845 −0.632706 −0.316353 0.948642i \(-0.602458\pi\)
−0.316353 + 0.948642i \(0.602458\pi\)
\(12\) −3.96339 −1.14413
\(13\) −1.00000 −0.277350
\(14\) 13.1462 3.51347
\(15\) −0.457007 −0.117999
\(16\) 10.0132 2.50330
\(17\) 3.74319 0.907858 0.453929 0.891038i \(-0.350022\pi\)
0.453929 + 0.891038i \(0.350022\pi\)
\(18\) 6.13262 1.44547
\(19\) −0.888994 −0.203949 −0.101975 0.994787i \(-0.532516\pi\)
−0.101975 + 0.994787i \(0.532516\pi\)
\(20\) 2.74000 0.612682
\(21\) 4.07656 0.889578
\(22\) 5.50205 1.17304
\(23\) 3.39137 0.707151 0.353575 0.935406i \(-0.384966\pi\)
0.353575 + 0.935406i \(0.384966\pi\)
\(24\) 6.12826 1.25093
\(25\) −4.68406 −0.936812
\(26\) 2.62196 0.514209
\(27\) 4.34085 0.835397
\(28\) −24.4411 −4.61893
\(29\) 3.62001 0.672219 0.336110 0.941823i \(-0.390889\pi\)
0.336110 + 0.941823i \(0.390889\pi\)
\(30\) 1.19826 0.218771
\(31\) −8.47651 −1.52243 −0.761213 0.648502i \(-0.775396\pi\)
−0.761213 + 0.648502i \(0.775396\pi\)
\(32\) −11.1796 −1.97629
\(33\) 1.70615 0.297003
\(34\) −9.81451 −1.68317
\(35\) −2.81823 −0.476368
\(36\) −11.4016 −1.90027
\(37\) 2.48870 0.409139 0.204570 0.978852i \(-0.434421\pi\)
0.204570 + 0.978852i \(0.434421\pi\)
\(38\) 2.33091 0.378123
\(39\) 0.813055 0.130193
\(40\) −4.23663 −0.669870
\(41\) −7.93225 −1.23881 −0.619405 0.785072i \(-0.712626\pi\)
−0.619405 + 0.785072i \(0.712626\pi\)
\(42\) −10.6886 −1.64928
\(43\) 6.00589 0.915890 0.457945 0.888981i \(-0.348586\pi\)
0.457945 + 0.888981i \(0.348586\pi\)
\(44\) −10.2293 −1.54212
\(45\) −1.31469 −0.195982
\(46\) −8.89206 −1.31106
\(47\) 1.50624 0.219708 0.109854 0.993948i \(-0.464962\pi\)
0.109854 + 0.993948i \(0.464962\pi\)
\(48\) −8.14128 −1.17509
\(49\) 18.1390 2.59128
\(50\) 12.2814 1.73686
\(51\) −3.04342 −0.426164
\(52\) −4.87469 −0.675997
\(53\) −2.70934 −0.372156 −0.186078 0.982535i \(-0.559578\pi\)
−0.186078 + 0.982535i \(0.559578\pi\)
\(54\) −11.3816 −1.54883
\(55\) −1.17951 −0.159045
\(56\) 37.7912 5.05006
\(57\) 0.722801 0.0957373
\(58\) −9.49153 −1.24630
\(59\) 11.4174 1.48642 0.743212 0.669056i \(-0.233301\pi\)
0.743212 + 0.669056i \(0.233301\pi\)
\(60\) −2.22777 −0.287604
\(61\) −0.919060 −0.117674 −0.0588368 0.998268i \(-0.518739\pi\)
−0.0588368 + 0.998268i \(0.518739\pi\)
\(62\) 22.2251 2.82259
\(63\) 11.7272 1.47748
\(64\) 9.28607 1.16076
\(65\) −0.562087 −0.0697183
\(66\) −4.47347 −0.550646
\(67\) −2.20779 −0.269724 −0.134862 0.990864i \(-0.543059\pi\)
−0.134862 + 0.990864i \(0.543059\pi\)
\(68\) 18.2469 2.21276
\(69\) −2.75737 −0.331949
\(70\) 7.38930 0.883191
\(71\) 1.75234 0.207964 0.103982 0.994579i \(-0.466842\pi\)
0.103982 + 0.994579i \(0.466842\pi\)
\(72\) 17.6294 2.07764
\(73\) 9.37638 1.09742 0.548711 0.836012i \(-0.315119\pi\)
0.548711 + 0.836012i \(0.315119\pi\)
\(74\) −6.52527 −0.758547
\(75\) 3.80840 0.439756
\(76\) −4.33357 −0.497094
\(77\) 10.5214 1.19902
\(78\) −2.13180 −0.241379
\(79\) 6.77830 0.762618 0.381309 0.924448i \(-0.375473\pi\)
0.381309 + 0.924448i \(0.375473\pi\)
\(80\) 5.62829 0.629262
\(81\) 3.48747 0.387497
\(82\) 20.7981 2.29676
\(83\) 8.69805 0.954735 0.477367 0.878704i \(-0.341591\pi\)
0.477367 + 0.878704i \(0.341591\pi\)
\(84\) 19.8719 2.16821
\(85\) 2.10400 0.228211
\(86\) −15.7472 −1.69807
\(87\) −2.94327 −0.315551
\(88\) 15.8167 1.68606
\(89\) −11.1990 −1.18710 −0.593548 0.804799i \(-0.702273\pi\)
−0.593548 + 0.804799i \(0.702273\pi\)
\(90\) 3.44706 0.363352
\(91\) 5.01388 0.525597
\(92\) 16.5319 1.72357
\(93\) 6.89187 0.714653
\(94\) −3.94930 −0.407340
\(95\) −0.499691 −0.0512673
\(96\) 9.08962 0.927706
\(97\) −6.56447 −0.666521 −0.333261 0.942835i \(-0.608149\pi\)
−0.333261 + 0.942835i \(0.608149\pi\)
\(98\) −47.5597 −4.80425
\(99\) 4.90815 0.493288
\(100\) −22.8333 −2.28333
\(101\) −2.20644 −0.219549 −0.109774 0.993957i \(-0.535013\pi\)
−0.109774 + 0.993957i \(0.535013\pi\)
\(102\) 7.97974 0.790112
\(103\) 8.75090 0.862252 0.431126 0.902292i \(-0.358116\pi\)
0.431126 + 0.902292i \(0.358116\pi\)
\(104\) 7.53732 0.739095
\(105\) 2.29138 0.223616
\(106\) 7.10378 0.689980
\(107\) 10.2031 0.986374 0.493187 0.869923i \(-0.335832\pi\)
0.493187 + 0.869923i \(0.335832\pi\)
\(108\) 21.1603 2.03615
\(109\) 15.6191 1.49604 0.748018 0.663678i \(-0.231005\pi\)
0.748018 + 0.663678i \(0.231005\pi\)
\(110\) 3.09263 0.294871
\(111\) −2.02345 −0.192057
\(112\) −50.2050 −4.74392
\(113\) −11.8151 −1.11147 −0.555734 0.831360i \(-0.687563\pi\)
−0.555734 + 0.831360i \(0.687563\pi\)
\(114\) −1.89516 −0.177498
\(115\) 1.90625 0.177758
\(116\) 17.6464 1.63843
\(117\) 2.33894 0.216235
\(118\) −29.9361 −2.75584
\(119\) −18.7679 −1.72045
\(120\) 3.44461 0.314449
\(121\) −6.59651 −0.599683
\(122\) 2.40974 0.218168
\(123\) 6.44936 0.581519
\(124\) −41.3203 −3.71067
\(125\) −5.44328 −0.486862
\(126\) −30.7482 −2.73927
\(127\) 14.2707 1.26632 0.633158 0.774023i \(-0.281758\pi\)
0.633158 + 0.774023i \(0.281758\pi\)
\(128\) −1.98855 −0.175765
\(129\) −4.88312 −0.429935
\(130\) 1.47377 0.129258
\(131\) −1.93359 −0.168938 −0.0844692 0.996426i \(-0.526919\pi\)
−0.0844692 + 0.996426i \(0.526919\pi\)
\(132\) 8.31697 0.723899
\(133\) 4.45731 0.386497
\(134\) 5.78873 0.500070
\(135\) 2.43994 0.209996
\(136\) −28.2137 −2.41930
\(137\) −9.68430 −0.827386 −0.413693 0.910417i \(-0.635761\pi\)
−0.413693 + 0.910417i \(0.635761\pi\)
\(138\) 7.22973 0.615436
\(139\) 2.19805 0.186436 0.0932181 0.995646i \(-0.470285\pi\)
0.0932181 + 0.995646i \(0.470285\pi\)
\(140\) −13.7380 −1.16107
\(141\) −1.22466 −0.103135
\(142\) −4.59456 −0.385567
\(143\) 2.09845 0.175481
\(144\) −23.4203 −1.95169
\(145\) 2.03476 0.168978
\(146\) −24.5845 −2.03463
\(147\) −14.7480 −1.21639
\(148\) 12.1316 0.997213
\(149\) −10.2179 −0.837079 −0.418540 0.908199i \(-0.637458\pi\)
−0.418540 + 0.908199i \(0.637458\pi\)
\(150\) −9.98547 −0.815310
\(151\) −8.30980 −0.676242 −0.338121 0.941103i \(-0.609791\pi\)
−0.338121 + 0.941103i \(0.609791\pi\)
\(152\) 6.70063 0.543493
\(153\) −8.75511 −0.707809
\(154\) −27.5866 −2.22299
\(155\) −4.76453 −0.382696
\(156\) 3.96339 0.317325
\(157\) 13.7126 1.09438 0.547191 0.837008i \(-0.315697\pi\)
0.547191 + 0.837008i \(0.315697\pi\)
\(158\) −17.7725 −1.41390
\(159\) 2.20284 0.174697
\(160\) −6.28390 −0.496786
\(161\) −17.0039 −1.34010
\(162\) −9.14403 −0.718423
\(163\) 19.7219 1.54474 0.772368 0.635175i \(-0.219072\pi\)
0.772368 + 0.635175i \(0.219072\pi\)
\(164\) −38.6673 −3.01941
\(165\) 0.959006 0.0746585
\(166\) −22.8060 −1.77009
\(167\) 6.83061 0.528568 0.264284 0.964445i \(-0.414864\pi\)
0.264284 + 0.964445i \(0.414864\pi\)
\(168\) −30.7263 −2.37059
\(169\) 1.00000 0.0769231
\(170\) −5.51661 −0.423104
\(171\) 2.07930 0.159008
\(172\) 29.2768 2.23234
\(173\) −21.7859 −1.65635 −0.828176 0.560468i \(-0.810621\pi\)
−0.828176 + 0.560468i \(0.810621\pi\)
\(174\) 7.71714 0.585035
\(175\) 23.4853 1.77532
\(176\) −21.0122 −1.58385
\(177\) −9.28301 −0.697753
\(178\) 29.3635 2.20089
\(179\) 2.06612 0.154429 0.0772146 0.997014i \(-0.475397\pi\)
0.0772146 + 0.997014i \(0.475397\pi\)
\(180\) −6.40869 −0.477676
\(181\) −1.16015 −0.0862336 −0.0431168 0.999070i \(-0.513729\pi\)
−0.0431168 + 0.999070i \(0.513729\pi\)
\(182\) −13.1462 −0.974461
\(183\) 0.747246 0.0552380
\(184\) −25.5619 −1.88445
\(185\) 1.39886 0.102846
\(186\) −18.0702 −1.32497
\(187\) −7.85490 −0.574407
\(188\) 7.34245 0.535503
\(189\) −21.7645 −1.58313
\(190\) 1.31017 0.0950499
\(191\) 2.49479 0.180517 0.0902584 0.995918i \(-0.471231\pi\)
0.0902584 + 0.995918i \(0.471231\pi\)
\(192\) −7.55009 −0.544881
\(193\) 14.0195 1.00915 0.504574 0.863369i \(-0.331650\pi\)
0.504574 + 0.863369i \(0.331650\pi\)
\(194\) 17.2118 1.23573
\(195\) 0.457007 0.0327270
\(196\) 88.4218 6.31584
\(197\) −21.9338 −1.56272 −0.781359 0.624082i \(-0.785473\pi\)
−0.781359 + 0.624082i \(0.785473\pi\)
\(198\) −12.8690 −0.914559
\(199\) −15.6165 −1.10702 −0.553512 0.832841i \(-0.686713\pi\)
−0.553512 + 0.832841i \(0.686713\pi\)
\(200\) 35.3053 2.49646
\(201\) 1.79505 0.126613
\(202\) 5.78519 0.407045
\(203\) −18.1503 −1.27390
\(204\) −14.8357 −1.03871
\(205\) −4.45861 −0.311403
\(206\) −22.9445 −1.59862
\(207\) −7.93223 −0.551328
\(208\) −10.0132 −0.694291
\(209\) 1.86551 0.129040
\(210\) −6.00791 −0.414585
\(211\) 10.7220 0.738135 0.369067 0.929403i \(-0.379677\pi\)
0.369067 + 0.929403i \(0.379677\pi\)
\(212\) −13.2072 −0.907073
\(213\) −1.42474 −0.0976219
\(214\) −26.7522 −1.82875
\(215\) 3.37583 0.230230
\(216\) −32.7184 −2.22621
\(217\) 42.5002 2.88510
\(218\) −40.9526 −2.77366
\(219\) −7.62351 −0.515149
\(220\) −5.74974 −0.387648
\(221\) −3.74319 −0.251794
\(222\) 5.30540 0.356075
\(223\) 16.4526 1.10175 0.550873 0.834589i \(-0.314295\pi\)
0.550873 + 0.834589i \(0.314295\pi\)
\(224\) 56.0531 3.74521
\(225\) 10.9557 0.730383
\(226\) 30.9787 2.06067
\(227\) 24.7655 1.64374 0.821872 0.569672i \(-0.192930\pi\)
0.821872 + 0.569672i \(0.192930\pi\)
\(228\) 3.52343 0.233345
\(229\) 18.5878 1.22832 0.614158 0.789183i \(-0.289496\pi\)
0.614158 + 0.789183i \(0.289496\pi\)
\(230\) −4.99811 −0.329565
\(231\) −8.55445 −0.562841
\(232\) −27.2852 −1.79136
\(233\) −23.9474 −1.56885 −0.784424 0.620224i \(-0.787042\pi\)
−0.784424 + 0.620224i \(0.787042\pi\)
\(234\) −6.13262 −0.400902
\(235\) 0.846637 0.0552285
\(236\) 55.6565 3.62293
\(237\) −5.51113 −0.357986
\(238\) 49.2088 3.18973
\(239\) −9.32840 −0.603404 −0.301702 0.953402i \(-0.597555\pi\)
−0.301702 + 0.953402i \(0.597555\pi\)
\(240\) −4.57611 −0.295386
\(241\) −26.5400 −1.70959 −0.854797 0.518962i \(-0.826319\pi\)
−0.854797 + 0.518962i \(0.826319\pi\)
\(242\) 17.2958 1.11182
\(243\) −15.8581 −1.01730
\(244\) −4.48013 −0.286811
\(245\) 10.1957 0.651377
\(246\) −16.9100 −1.07814
\(247\) 0.888994 0.0565653
\(248\) 63.8902 4.05703
\(249\) −7.07199 −0.448169
\(250\) 14.2721 0.902645
\(251\) −6.99970 −0.441817 −0.220909 0.975295i \(-0.570902\pi\)
−0.220909 + 0.975295i \(0.570902\pi\)
\(252\) 57.1663 3.60114
\(253\) −7.11663 −0.447418
\(254\) −37.4171 −2.34776
\(255\) −1.71067 −0.107126
\(256\) −13.3582 −0.834890
\(257\) 28.6673 1.78821 0.894107 0.447853i \(-0.147811\pi\)
0.894107 + 0.447853i \(0.147811\pi\)
\(258\) 12.8034 0.797102
\(259\) −12.4780 −0.775346
\(260\) −2.74000 −0.169927
\(261\) −8.46700 −0.524094
\(262\) 5.06980 0.313213
\(263\) −4.80013 −0.295989 −0.147994 0.988988i \(-0.547282\pi\)
−0.147994 + 0.988988i \(0.547282\pi\)
\(264\) −12.8598 −0.791468
\(265\) −1.52288 −0.0935499
\(266\) −11.6869 −0.716569
\(267\) 9.10544 0.557244
\(268\) −10.7623 −0.657410
\(269\) 0.988540 0.0602724 0.0301362 0.999546i \(-0.490406\pi\)
0.0301362 + 0.999546i \(0.490406\pi\)
\(270\) −6.39742 −0.389334
\(271\) 14.4614 0.878467 0.439233 0.898373i \(-0.355250\pi\)
0.439233 + 0.898373i \(0.355250\pi\)
\(272\) 37.4813 2.27264
\(273\) −4.07656 −0.246724
\(274\) 25.3919 1.53398
\(275\) 9.82926 0.592727
\(276\) −13.4413 −0.809073
\(277\) −4.12998 −0.248147 −0.124073 0.992273i \(-0.539596\pi\)
−0.124073 + 0.992273i \(0.539596\pi\)
\(278\) −5.76320 −0.345654
\(279\) 19.8261 1.18696
\(280\) 21.2419 1.26945
\(281\) −18.1710 −1.08399 −0.541994 0.840382i \(-0.682330\pi\)
−0.541994 + 0.840382i \(0.682330\pi\)
\(282\) 3.21100 0.191212
\(283\) 11.0345 0.655931 0.327966 0.944690i \(-0.393637\pi\)
0.327966 + 0.944690i \(0.393637\pi\)
\(284\) 8.54209 0.506880
\(285\) 0.406277 0.0240657
\(286\) −5.50205 −0.325343
\(287\) 39.7713 2.34763
\(288\) 26.1484 1.54081
\(289\) −2.98850 −0.175794
\(290\) −5.33506 −0.313286
\(291\) 5.33727 0.312877
\(292\) 45.7069 2.67480
\(293\) 1.02235 0.0597265 0.0298633 0.999554i \(-0.490493\pi\)
0.0298633 + 0.999554i \(0.490493\pi\)
\(294\) 38.6686 2.25520
\(295\) 6.41759 0.373647
\(296\) −18.7581 −1.09029
\(297\) −9.10906 −0.528561
\(298\) 26.7908 1.55195
\(299\) −3.39137 −0.196128
\(300\) 18.5647 1.07184
\(301\) −30.1128 −1.73567
\(302\) 21.7880 1.25376
\(303\) 1.79395 0.103060
\(304\) −8.90167 −0.510546
\(305\) −0.516591 −0.0295799
\(306\) 22.9556 1.31228
\(307\) −33.2990 −1.90047 −0.950236 0.311530i \(-0.899159\pi\)
−0.950236 + 0.311530i \(0.899159\pi\)
\(308\) 51.2884 2.92243
\(309\) −7.11496 −0.404756
\(310\) 12.4924 0.709522
\(311\) 1.63927 0.0929547 0.0464773 0.998919i \(-0.485200\pi\)
0.0464773 + 0.998919i \(0.485200\pi\)
\(312\) −6.12826 −0.346944
\(313\) −27.2970 −1.54292 −0.771460 0.636278i \(-0.780473\pi\)
−0.771460 + 0.636278i \(0.780473\pi\)
\(314\) −35.9538 −2.02899
\(315\) 6.59168 0.371399
\(316\) 33.0421 1.85876
\(317\) 23.6522 1.32844 0.664221 0.747536i \(-0.268763\pi\)
0.664221 + 0.747536i \(0.268763\pi\)
\(318\) −5.77577 −0.323889
\(319\) −7.59641 −0.425317
\(320\) 5.21958 0.291783
\(321\) −8.29571 −0.463021
\(322\) 44.5837 2.48455
\(323\) −3.32768 −0.185157
\(324\) 17.0003 0.944464
\(325\) 4.68406 0.259825
\(326\) −51.7100 −2.86395
\(327\) −12.6992 −0.702266
\(328\) 59.7880 3.30124
\(329\) −7.55210 −0.416361
\(330\) −2.51448 −0.138418
\(331\) −1.34847 −0.0741188 −0.0370594 0.999313i \(-0.511799\pi\)
−0.0370594 + 0.999313i \(0.511799\pi\)
\(332\) 42.4003 2.32702
\(333\) −5.82092 −0.318984
\(334\) −17.9096 −0.979969
\(335\) −1.24097 −0.0678013
\(336\) 40.8194 2.22688
\(337\) −11.3712 −0.619431 −0.309715 0.950829i \(-0.600234\pi\)
−0.309715 + 0.950829i \(0.600234\pi\)
\(338\) −2.62196 −0.142616
\(339\) 9.60630 0.521743
\(340\) 10.2563 0.556228
\(341\) 17.7875 0.963248
\(342\) −5.45186 −0.294803
\(343\) −55.8494 −3.01558
\(344\) −45.2683 −2.44070
\(345\) −1.54988 −0.0834429
\(346\) 57.1219 3.07089
\(347\) 22.9134 1.23006 0.615029 0.788504i \(-0.289144\pi\)
0.615029 + 0.788504i \(0.289144\pi\)
\(348\) −14.3475 −0.769107
\(349\) 31.5274 1.68763 0.843813 0.536638i \(-0.180306\pi\)
0.843813 + 0.536638i \(0.180306\pi\)
\(350\) −61.5776 −3.29146
\(351\) −4.34085 −0.231698
\(352\) 23.4598 1.25041
\(353\) 20.9025 1.11253 0.556263 0.831007i \(-0.312235\pi\)
0.556263 + 0.831007i \(0.312235\pi\)
\(354\) 24.3397 1.29364
\(355\) 0.984964 0.0522765
\(356\) −54.5918 −2.89336
\(357\) 15.2593 0.807610
\(358\) −5.41729 −0.286313
\(359\) −10.0267 −0.529187 −0.264593 0.964360i \(-0.585238\pi\)
−0.264593 + 0.964360i \(0.585238\pi\)
\(360\) 9.90923 0.522262
\(361\) −18.2097 −0.958405
\(362\) 3.04188 0.159878
\(363\) 5.36333 0.281502
\(364\) 24.4411 1.28106
\(365\) 5.27034 0.275862
\(366\) −1.95925 −0.102412
\(367\) −37.6234 −1.96392 −0.981962 0.189079i \(-0.939450\pi\)
−0.981962 + 0.189079i \(0.939450\pi\)
\(368\) 33.9585 1.77021
\(369\) 18.5531 0.965835
\(370\) −3.66777 −0.190678
\(371\) 13.5843 0.705261
\(372\) 33.5957 1.74186
\(373\) 4.63586 0.240036 0.120018 0.992772i \(-0.461705\pi\)
0.120018 + 0.992772i \(0.461705\pi\)
\(374\) 20.5953 1.06496
\(375\) 4.42569 0.228541
\(376\) −11.3530 −0.585487
\(377\) −3.62001 −0.186440
\(378\) 57.0657 2.93514
\(379\) 14.7956 0.760000 0.380000 0.924987i \(-0.375924\pi\)
0.380000 + 0.924987i \(0.375924\pi\)
\(380\) −2.43584 −0.124956
\(381\) −11.6028 −0.594431
\(382\) −6.54125 −0.334680
\(383\) 0.137910 0.00704685 0.00352343 0.999994i \(-0.498878\pi\)
0.00352343 + 0.999994i \(0.498878\pi\)
\(384\) 1.61680 0.0825070
\(385\) 5.91392 0.301401
\(386\) −36.7587 −1.87097
\(387\) −14.0474 −0.714071
\(388\) −31.9997 −1.62454
\(389\) 9.66166 0.489866 0.244933 0.969540i \(-0.421234\pi\)
0.244933 + 0.969540i \(0.421234\pi\)
\(390\) −1.19826 −0.0606760
\(391\) 12.6946 0.641992
\(392\) −136.719 −6.90536
\(393\) 1.57211 0.0793027
\(394\) 57.5095 2.89729
\(395\) 3.80999 0.191702
\(396\) 23.9257 1.20231
\(397\) −20.2037 −1.01400 −0.506998 0.861947i \(-0.669245\pi\)
−0.506998 + 0.861947i \(0.669245\pi\)
\(398\) 40.9459 2.05243
\(399\) −3.62403 −0.181429
\(400\) −46.9024 −2.34512
\(401\) 6.18166 0.308697 0.154349 0.988016i \(-0.450672\pi\)
0.154349 + 0.988016i \(0.450672\pi\)
\(402\) −4.70656 −0.234742
\(403\) 8.47651 0.422245
\(404\) −10.7557 −0.535115
\(405\) 1.96026 0.0974062
\(406\) 47.5894 2.36182
\(407\) −5.22240 −0.258865
\(408\) 22.9392 1.13566
\(409\) 7.26938 0.359448 0.179724 0.983717i \(-0.442480\pi\)
0.179724 + 0.983717i \(0.442480\pi\)
\(410\) 11.6903 0.577344
\(411\) 7.87387 0.388389
\(412\) 42.6579 2.10160
\(413\) −57.2456 −2.81687
\(414\) 20.7980 1.02217
\(415\) 4.88906 0.239994
\(416\) 11.1796 0.548125
\(417\) −1.78714 −0.0875164
\(418\) −4.89129 −0.239241
\(419\) 24.0786 1.17632 0.588159 0.808745i \(-0.299853\pi\)
0.588159 + 0.808745i \(0.299853\pi\)
\(420\) 11.1698 0.545028
\(421\) −3.07000 −0.149623 −0.0748114 0.997198i \(-0.523835\pi\)
−0.0748114 + 0.997198i \(0.523835\pi\)
\(422\) −28.1128 −1.36851
\(423\) −3.52301 −0.171294
\(424\) 20.4212 0.991739
\(425\) −17.5333 −0.850492
\(426\) 3.73563 0.180992
\(427\) 4.60805 0.222999
\(428\) 49.7371 2.40413
\(429\) −1.70615 −0.0823739
\(430\) −8.85130 −0.426848
\(431\) −33.3033 −1.60416 −0.802081 0.597215i \(-0.796274\pi\)
−0.802081 + 0.597215i \(0.796274\pi\)
\(432\) 43.4658 2.09125
\(433\) 18.3355 0.881148 0.440574 0.897716i \(-0.354775\pi\)
0.440574 + 0.897716i \(0.354775\pi\)
\(434\) −111.434 −5.34900
\(435\) −1.65437 −0.0793210
\(436\) 76.1381 3.64636
\(437\) −3.01491 −0.144223
\(438\) 19.9886 0.955090
\(439\) −9.67746 −0.461880 −0.230940 0.972968i \(-0.574180\pi\)
−0.230940 + 0.972968i \(0.574180\pi\)
\(440\) 8.89035 0.423831
\(441\) −42.4260 −2.02028
\(442\) 9.81451 0.466829
\(443\) −17.5548 −0.834055 −0.417027 0.908894i \(-0.636928\pi\)
−0.417027 + 0.908894i \(0.636928\pi\)
\(444\) −9.86367 −0.468109
\(445\) −6.29483 −0.298404
\(446\) −43.1381 −2.04265
\(447\) 8.30768 0.392940
\(448\) −46.5592 −2.19972
\(449\) −34.1608 −1.61215 −0.806075 0.591814i \(-0.798412\pi\)
−0.806075 + 0.591814i \(0.798412\pi\)
\(450\) −28.7255 −1.35413
\(451\) 16.6454 0.783803
\(452\) −57.5948 −2.70903
\(453\) 6.75632 0.317440
\(454\) −64.9342 −3.04751
\(455\) 2.81823 0.132121
\(456\) −5.44798 −0.255125
\(457\) 0.967106 0.0452393 0.0226196 0.999744i \(-0.492799\pi\)
0.0226196 + 0.999744i \(0.492799\pi\)
\(458\) −48.7365 −2.27731
\(459\) 16.2487 0.758422
\(460\) 9.29236 0.433258
\(461\) −31.5041 −1.46729 −0.733647 0.679531i \(-0.762183\pi\)
−0.733647 + 0.679531i \(0.762183\pi\)
\(462\) 22.4294 1.04351
\(463\) −1.00000 −0.0464739
\(464\) 36.2479 1.68277
\(465\) 3.87383 0.179644
\(466\) 62.7893 2.90866
\(467\) −9.75935 −0.451609 −0.225804 0.974173i \(-0.572501\pi\)
−0.225804 + 0.974173i \(0.572501\pi\)
\(468\) 11.4016 0.527040
\(469\) 11.0696 0.511145
\(470\) −2.21985 −0.102394
\(471\) −11.1491 −0.513722
\(472\) −86.0569 −3.96109
\(473\) −12.6031 −0.579489
\(474\) 14.4500 0.663709
\(475\) 4.16410 0.191062
\(476\) −91.4877 −4.19333
\(477\) 6.33698 0.290151
\(478\) 24.4587 1.11872
\(479\) 9.44267 0.431447 0.215723 0.976455i \(-0.430789\pi\)
0.215723 + 0.976455i \(0.430789\pi\)
\(480\) 5.10916 0.233200
\(481\) −2.48870 −0.113475
\(482\) 69.5870 3.16960
\(483\) 13.8251 0.629065
\(484\) −32.1559 −1.46163
\(485\) −3.68980 −0.167545
\(486\) 41.5793 1.88607
\(487\) −4.62842 −0.209734 −0.104867 0.994486i \(-0.533442\pi\)
−0.104867 + 0.994486i \(0.533442\pi\)
\(488\) 6.92725 0.313582
\(489\) −16.0350 −0.725126
\(490\) −26.7327 −1.20766
\(491\) −0.442718 −0.0199796 −0.00998978 0.999950i \(-0.503180\pi\)
−0.00998978 + 0.999950i \(0.503180\pi\)
\(492\) 31.4386 1.41736
\(493\) 13.5504 0.610279
\(494\) −2.33091 −0.104873
\(495\) 2.75881 0.123999
\(496\) −84.8770 −3.81109
\(497\) −8.78599 −0.394106
\(498\) 18.5425 0.830909
\(499\) 23.1224 1.03510 0.517551 0.855653i \(-0.326844\pi\)
0.517551 + 0.855653i \(0.326844\pi\)
\(500\) −26.5343 −1.18665
\(501\) −5.55366 −0.248119
\(502\) 18.3530 0.819133
\(503\) 23.9471 1.06775 0.533873 0.845564i \(-0.320736\pi\)
0.533873 + 0.845564i \(0.320736\pi\)
\(504\) −88.3914 −3.93727
\(505\) −1.24021 −0.0551885
\(506\) 18.6595 0.829517
\(507\) −0.813055 −0.0361090
\(508\) 69.5650 3.08645
\(509\) −15.7555 −0.698351 −0.349175 0.937057i \(-0.613538\pi\)
−0.349175 + 0.937057i \(0.613538\pi\)
\(510\) 4.48530 0.198613
\(511\) −47.0120 −2.07969
\(512\) 39.0019 1.72366
\(513\) −3.85899 −0.170379
\(514\) −75.1645 −3.31536
\(515\) 4.91876 0.216747
\(516\) −23.8037 −1.04790
\(517\) −3.16077 −0.139010
\(518\) 32.7169 1.43750
\(519\) 17.7131 0.777521
\(520\) 4.23663 0.185788
\(521\) −5.89432 −0.258235 −0.129117 0.991629i \(-0.541214\pi\)
−0.129117 + 0.991629i \(0.541214\pi\)
\(522\) 22.2001 0.971674
\(523\) 21.5755 0.943432 0.471716 0.881751i \(-0.343635\pi\)
0.471716 + 0.881751i \(0.343635\pi\)
\(524\) −9.42564 −0.411761
\(525\) −19.0948 −0.833367
\(526\) 12.5858 0.548765
\(527\) −31.7292 −1.38215
\(528\) 17.0841 0.743488
\(529\) −11.4986 −0.499938
\(530\) 3.99294 0.173442
\(531\) −26.7047 −1.15889
\(532\) 21.7280 0.942027
\(533\) 7.93225 0.343584
\(534\) −23.8741 −1.03313
\(535\) 5.73505 0.247948
\(536\) 16.6408 0.718773
\(537\) −1.67987 −0.0724918
\(538\) −2.59192 −0.111745
\(539\) −38.0637 −1.63952
\(540\) 11.8939 0.511833
\(541\) 11.6991 0.502982 0.251491 0.967860i \(-0.419079\pi\)
0.251491 + 0.967860i \(0.419079\pi\)
\(542\) −37.9172 −1.62868
\(543\) 0.943270 0.0404796
\(544\) −41.8474 −1.79419
\(545\) 8.77928 0.376063
\(546\) 10.6886 0.457429
\(547\) −17.9749 −0.768552 −0.384276 0.923218i \(-0.625549\pi\)
−0.384276 + 0.923218i \(0.625549\pi\)
\(548\) −47.2079 −2.01662
\(549\) 2.14963 0.0917439
\(550\) −25.7719 −1.09892
\(551\) −3.21817 −0.137099
\(552\) 20.7832 0.884592
\(553\) −33.9856 −1.44521
\(554\) 10.8287 0.460066
\(555\) −1.13735 −0.0482779
\(556\) 10.7148 0.454409
\(557\) 31.7006 1.34320 0.671599 0.740915i \(-0.265608\pi\)
0.671599 + 0.740915i \(0.265608\pi\)
\(558\) −51.9832 −2.20062
\(559\) −6.00589 −0.254022
\(560\) −28.2195 −1.19249
\(561\) 6.38646 0.269637
\(562\) 47.6436 2.00972
\(563\) −24.2265 −1.02102 −0.510512 0.859870i \(-0.670544\pi\)
−0.510512 + 0.859870i \(0.670544\pi\)
\(564\) −5.96981 −0.251374
\(565\) −6.64109 −0.279393
\(566\) −28.9320 −1.21610
\(567\) −17.4858 −0.734333
\(568\) −13.2079 −0.554192
\(569\) 14.8480 0.622462 0.311231 0.950334i \(-0.399259\pi\)
0.311231 + 0.950334i \(0.399259\pi\)
\(570\) −1.06524 −0.0446181
\(571\) 16.6210 0.695568 0.347784 0.937575i \(-0.386934\pi\)
0.347784 + 0.937575i \(0.386934\pi\)
\(572\) 10.2293 0.427708
\(573\) −2.02840 −0.0847378
\(574\) −104.279 −4.35252
\(575\) −15.8854 −0.662467
\(576\) −21.7196 −0.904983
\(577\) −25.3377 −1.05482 −0.527411 0.849610i \(-0.676837\pi\)
−0.527411 + 0.849610i \(0.676837\pi\)
\(578\) 7.83575 0.325924
\(579\) −11.3986 −0.473712
\(580\) 9.91882 0.411857
\(581\) −43.6110 −1.80929
\(582\) −13.9941 −0.580076
\(583\) 5.68541 0.235466
\(584\) −70.6728 −2.92446
\(585\) 1.31469 0.0543557
\(586\) −2.68057 −0.110733
\(587\) 15.6762 0.647027 0.323514 0.946224i \(-0.395136\pi\)
0.323514 + 0.946224i \(0.395136\pi\)
\(588\) −71.8918 −2.96477
\(589\) 7.53556 0.310497
\(590\) −16.8267 −0.692744
\(591\) 17.8334 0.733567
\(592\) 24.9198 1.02420
\(593\) −34.0661 −1.39893 −0.699464 0.714668i \(-0.746578\pi\)
−0.699464 + 0.714668i \(0.746578\pi\)
\(594\) 23.8836 0.979956
\(595\) −10.5492 −0.432475
\(596\) −49.8089 −2.04025
\(597\) 12.6971 0.519657
\(598\) 8.89206 0.363623
\(599\) −25.0885 −1.02509 −0.512543 0.858661i \(-0.671297\pi\)
−0.512543 + 0.858661i \(0.671297\pi\)
\(600\) −28.7051 −1.17188
\(601\) 42.8553 1.74810 0.874052 0.485832i \(-0.161483\pi\)
0.874052 + 0.485832i \(0.161483\pi\)
\(602\) 78.9546 3.21795
\(603\) 5.16388 0.210290
\(604\) −40.5077 −1.64823
\(605\) −3.70781 −0.150744
\(606\) −4.70368 −0.191074
\(607\) 20.5538 0.834253 0.417126 0.908849i \(-0.363037\pi\)
0.417126 + 0.908849i \(0.363037\pi\)
\(608\) 9.93859 0.403063
\(609\) 14.7572 0.597991
\(610\) 1.35448 0.0548414
\(611\) −1.50624 −0.0609359
\(612\) −42.6784 −1.72517
\(613\) 7.10589 0.287004 0.143502 0.989650i \(-0.454164\pi\)
0.143502 + 0.989650i \(0.454164\pi\)
\(614\) 87.3086 3.52349
\(615\) 3.62510 0.146178
\(616\) −79.3029 −3.19521
\(617\) 24.8158 0.999045 0.499522 0.866301i \(-0.333509\pi\)
0.499522 + 0.866301i \(0.333509\pi\)
\(618\) 18.6552 0.750421
\(619\) 13.1195 0.527317 0.263658 0.964616i \(-0.415071\pi\)
0.263658 + 0.964616i \(0.415071\pi\)
\(620\) −23.2256 −0.932763
\(621\) 14.7215 0.590752
\(622\) −4.29811 −0.172339
\(623\) 56.1506 2.24963
\(624\) 8.14128 0.325912
\(625\) 20.3607 0.814428
\(626\) 71.5718 2.86059
\(627\) −1.51676 −0.0605736
\(628\) 66.8445 2.66738
\(629\) 9.31567 0.371440
\(630\) −17.2831 −0.688577
\(631\) −45.4849 −1.81072 −0.905362 0.424640i \(-0.860401\pi\)
−0.905362 + 0.424640i \(0.860401\pi\)
\(632\) −51.0902 −2.03226
\(633\) −8.71760 −0.346493
\(634\) −62.0153 −2.46294
\(635\) 8.02134 0.318317
\(636\) 10.7382 0.425796
\(637\) −18.1390 −0.718692
\(638\) 19.9175 0.788541
\(639\) −4.09861 −0.162139
\(640\) −1.11774 −0.0441824
\(641\) −41.4687 −1.63791 −0.818957 0.573855i \(-0.805447\pi\)
−0.818957 + 0.573855i \(0.805447\pi\)
\(642\) 21.7510 0.858445
\(643\) −11.4282 −0.450683 −0.225342 0.974280i \(-0.572350\pi\)
−0.225342 + 0.974280i \(0.572350\pi\)
\(644\) −82.8889 −3.26628
\(645\) −2.74474 −0.108074
\(646\) 8.72504 0.343282
\(647\) −28.1813 −1.10792 −0.553960 0.832544i \(-0.686884\pi\)
−0.553960 + 0.832544i \(0.686884\pi\)
\(648\) −26.2862 −1.03262
\(649\) −23.9589 −0.940470
\(650\) −12.2814 −0.481717
\(651\) −34.5550 −1.35432
\(652\) 96.1379 3.76505
\(653\) 9.95814 0.389692 0.194846 0.980834i \(-0.437579\pi\)
0.194846 + 0.980834i \(0.437579\pi\)
\(654\) 33.2967 1.30201
\(655\) −1.08684 −0.0424665
\(656\) −79.4273 −3.10111
\(657\) −21.9308 −0.855602
\(658\) 19.8013 0.771936
\(659\) −15.6540 −0.609792 −0.304896 0.952386i \(-0.598622\pi\)
−0.304896 + 0.952386i \(0.598622\pi\)
\(660\) 4.67486 0.181969
\(661\) −6.97540 −0.271312 −0.135656 0.990756i \(-0.543314\pi\)
−0.135656 + 0.990756i \(0.543314\pi\)
\(662\) 3.53565 0.137417
\(663\) 3.04342 0.118197
\(664\) −65.5600 −2.54422
\(665\) 2.50539 0.0971549
\(666\) 15.2622 0.591399
\(667\) 12.2768 0.475360
\(668\) 33.2971 1.28830
\(669\) −13.3769 −0.517179
\(670\) 3.25377 0.125704
\(671\) 1.92860 0.0744528
\(672\) −45.5743 −1.75807
\(673\) 44.0869 1.69943 0.849713 0.527245i \(-0.176775\pi\)
0.849713 + 0.527245i \(0.176775\pi\)
\(674\) 29.8149 1.14843
\(675\) −20.3328 −0.782610
\(676\) 4.87469 0.187488
\(677\) −33.0623 −1.27069 −0.635345 0.772229i \(-0.719142\pi\)
−0.635345 + 0.772229i \(0.719142\pi\)
\(678\) −25.1874 −0.967315
\(679\) 32.9135 1.26310
\(680\) −15.8585 −0.608146
\(681\) −20.1357 −0.771602
\(682\) −46.6382 −1.78587
\(683\) 39.7278 1.52014 0.760072 0.649839i \(-0.225164\pi\)
0.760072 + 0.649839i \(0.225164\pi\)
\(684\) 10.1360 0.387558
\(685\) −5.44342 −0.207982
\(686\) 146.435 5.59092
\(687\) −15.1129 −0.576593
\(688\) 60.1382 2.29275
\(689\) 2.70934 0.103218
\(690\) 4.06373 0.154704
\(691\) −2.89062 −0.109964 −0.0549822 0.998487i \(-0.517510\pi\)
−0.0549822 + 0.998487i \(0.517510\pi\)
\(692\) −106.200 −4.03710
\(693\) −24.6089 −0.934813
\(694\) −60.0782 −2.28054
\(695\) 1.23549 0.0468650
\(696\) 22.1844 0.840896
\(697\) −29.6920 −1.12466
\(698\) −82.6638 −3.12887
\(699\) 19.4706 0.736445
\(700\) 114.483 4.32707
\(701\) 3.01235 0.113775 0.0568874 0.998381i \(-0.481882\pi\)
0.0568874 + 0.998381i \(0.481882\pi\)
\(702\) 11.3816 0.429569
\(703\) −2.21244 −0.0834436
\(704\) −19.4864 −0.734420
\(705\) −0.688362 −0.0259252
\(706\) −54.8054 −2.06263
\(707\) 11.0628 0.416059
\(708\) −45.2517 −1.70066
\(709\) −28.9013 −1.08541 −0.542705 0.839923i \(-0.682600\pi\)
−0.542705 + 0.839923i \(0.682600\pi\)
\(710\) −2.58254 −0.0969210
\(711\) −15.8541 −0.594573
\(712\) 84.4108 3.16343
\(713\) −28.7470 −1.07658
\(714\) −40.0094 −1.49731
\(715\) 1.17951 0.0441112
\(716\) 10.0717 0.376397
\(717\) 7.58450 0.283248
\(718\) 26.2895 0.981116
\(719\) −42.2809 −1.57681 −0.788405 0.615156i \(-0.789093\pi\)
−0.788405 + 0.615156i \(0.789093\pi\)
\(720\) −13.1642 −0.490602
\(721\) −43.8759 −1.63403
\(722\) 47.7451 1.77689
\(723\) 21.5785 0.802513
\(724\) −5.65539 −0.210181
\(725\) −16.9563 −0.629743
\(726\) −14.0624 −0.521906
\(727\) 27.2812 1.01180 0.505902 0.862591i \(-0.331160\pi\)
0.505902 + 0.862591i \(0.331160\pi\)
\(728\) −37.7912 −1.40064
\(729\) 2.43106 0.0900391
\(730\) −13.8186 −0.511450
\(731\) 22.4812 0.831497
\(732\) 3.64259 0.134634
\(733\) −3.17902 −0.117420 −0.0587099 0.998275i \(-0.518699\pi\)
−0.0587099 + 0.998275i \(0.518699\pi\)
\(734\) 98.6471 3.64113
\(735\) −8.28964 −0.305768
\(736\) −37.9142 −1.39754
\(737\) 4.63293 0.170656
\(738\) −48.6455 −1.79066
\(739\) −39.4584 −1.45150 −0.725750 0.687958i \(-0.758507\pi\)
−0.725750 + 0.687958i \(0.758507\pi\)
\(740\) 6.81902 0.250672
\(741\) −0.722801 −0.0265527
\(742\) −35.6175 −1.30756
\(743\) 10.3307 0.378996 0.189498 0.981881i \(-0.439314\pi\)
0.189498 + 0.981881i \(0.439314\pi\)
\(744\) −51.9462 −1.90444
\(745\) −5.74332 −0.210419
\(746\) −12.1551 −0.445028
\(747\) −20.3442 −0.744357
\(748\) −38.2902 −1.40003
\(749\) −51.1573 −1.86925
\(750\) −11.6040 −0.423717
\(751\) −36.0409 −1.31515 −0.657576 0.753388i \(-0.728418\pi\)
−0.657576 + 0.753388i \(0.728418\pi\)
\(752\) 15.0823 0.549994
\(753\) 5.69114 0.207397
\(754\) 9.49153 0.345661
\(755\) −4.67082 −0.169989
\(756\) −106.095 −3.85864
\(757\) −10.1689 −0.369593 −0.184797 0.982777i \(-0.559163\pi\)
−0.184797 + 0.982777i \(0.559163\pi\)
\(758\) −38.7935 −1.40905
\(759\) 5.78621 0.210026
\(760\) 3.76634 0.136619
\(761\) 7.27332 0.263658 0.131829 0.991272i \(-0.457915\pi\)
0.131829 + 0.991272i \(0.457915\pi\)
\(762\) 30.4222 1.10208
\(763\) −78.3122 −2.83509
\(764\) 12.1613 0.439982
\(765\) −4.92113 −0.177924
\(766\) −0.361594 −0.0130649
\(767\) −11.4174 −0.412260
\(768\) 10.8610 0.391912
\(769\) 46.5104 1.67721 0.838603 0.544743i \(-0.183373\pi\)
0.838603 + 0.544743i \(0.183373\pi\)
\(770\) −15.5061 −0.558800
\(771\) −23.3081 −0.839419
\(772\) 68.3408 2.45964
\(773\) −41.2119 −1.48229 −0.741145 0.671345i \(-0.765717\pi\)
−0.741145 + 0.671345i \(0.765717\pi\)
\(774\) 36.8318 1.32389
\(775\) 39.7045 1.42623
\(776\) 49.4785 1.77618
\(777\) 10.1453 0.363961
\(778\) −25.3325 −0.908215
\(779\) 7.05172 0.252654
\(780\) 2.22777 0.0797669
\(781\) −3.67719 −0.131580
\(782\) −33.2847 −1.19026
\(783\) 15.7139 0.561570
\(784\) 181.629 6.48675
\(785\) 7.70765 0.275098
\(786\) −4.12202 −0.147028
\(787\) −15.7266 −0.560594 −0.280297 0.959913i \(-0.590433\pi\)
−0.280297 + 0.959913i \(0.590433\pi\)
\(788\) −106.920 −3.80888
\(789\) 3.90277 0.138942
\(790\) −9.98966 −0.355416
\(791\) 59.2393 2.10631
\(792\) −36.9943 −1.31454
\(793\) 0.919060 0.0326368
\(794\) 52.9734 1.87996
\(795\) 1.23819 0.0439140
\(796\) −76.1256 −2.69820
\(797\) −42.4618 −1.50407 −0.752037 0.659120i \(-0.770929\pi\)
−0.752037 + 0.659120i \(0.770929\pi\)
\(798\) 9.50208 0.336370
\(799\) 5.63815 0.199463
\(800\) 52.3659 1.85141
\(801\) 26.1939 0.925516
\(802\) −16.2081 −0.572327
\(803\) −19.6759 −0.694346
\(804\) 8.75032 0.308600
\(805\) −9.55769 −0.336864
\(806\) −22.2251 −0.782845
\(807\) −0.803737 −0.0282929
\(808\) 16.6306 0.585063
\(809\) −10.0531 −0.353449 −0.176724 0.984260i \(-0.556550\pi\)
−0.176724 + 0.984260i \(0.556550\pi\)
\(810\) −5.13973 −0.180592
\(811\) −2.61121 −0.0916919 −0.0458460 0.998949i \(-0.514598\pi\)
−0.0458460 + 0.998949i \(0.514598\pi\)
\(812\) −88.4770 −3.10493
\(813\) −11.7579 −0.412368
\(814\) 13.6929 0.479937
\(815\) 11.0854 0.388305
\(816\) −30.4744 −1.06682
\(817\) −5.33920 −0.186795
\(818\) −19.0601 −0.666419
\(819\) −11.7272 −0.409780
\(820\) −21.7343 −0.758996
\(821\) 5.35399 0.186855 0.0934277 0.995626i \(-0.470218\pi\)
0.0934277 + 0.995626i \(0.470218\pi\)
\(822\) −20.6450 −0.720077
\(823\) 1.24345 0.0433439 0.0216719 0.999765i \(-0.493101\pi\)
0.0216719 + 0.999765i \(0.493101\pi\)
\(824\) −65.9584 −2.29777
\(825\) −7.99173 −0.278236
\(826\) 150.096 5.22251
\(827\) 5.43062 0.188841 0.0944206 0.995532i \(-0.469900\pi\)
0.0944206 + 0.995532i \(0.469900\pi\)
\(828\) −38.6671 −1.34378
\(829\) −19.9964 −0.694502 −0.347251 0.937772i \(-0.612885\pi\)
−0.347251 + 0.937772i \(0.612885\pi\)
\(830\) −12.8189 −0.444951
\(831\) 3.35790 0.116484
\(832\) −9.28607 −0.321937
\(833\) 67.8976 2.35251
\(834\) 4.68580 0.162256
\(835\) 3.83939 0.132868
\(836\) 9.09377 0.314515
\(837\) −36.7953 −1.27183
\(838\) −63.1333 −2.18090
\(839\) −9.14555 −0.315740 −0.157870 0.987460i \(-0.550463\pi\)
−0.157870 + 0.987460i \(0.550463\pi\)
\(840\) −17.2709 −0.595901
\(841\) −15.8955 −0.548121
\(842\) 8.04943 0.277402
\(843\) 14.7740 0.508843
\(844\) 52.2665 1.79909
\(845\) 0.562087 0.0193364
\(846\) 9.23719 0.317581
\(847\) 33.0741 1.13644
\(848\) −27.1291 −0.931619
\(849\) −8.97163 −0.307906
\(850\) 45.9718 1.57682
\(851\) 8.44010 0.289323
\(852\) −6.94519 −0.237938
\(853\) 21.2739 0.728404 0.364202 0.931320i \(-0.381342\pi\)
0.364202 + 0.931320i \(0.381342\pi\)
\(854\) −12.0821 −0.413442
\(855\) 1.16875 0.0399704
\(856\) −76.9043 −2.62854
\(857\) 10.3519 0.353613 0.176806 0.984246i \(-0.443423\pi\)
0.176806 + 0.984246i \(0.443423\pi\)
\(858\) 4.47347 0.152722
\(859\) −35.8691 −1.22384 −0.611919 0.790920i \(-0.709602\pi\)
−0.611919 + 0.790920i \(0.709602\pi\)
\(860\) 16.4561 0.561149
\(861\) −32.3363 −1.10202
\(862\) 87.3199 2.97413
\(863\) −25.9306 −0.882689 −0.441344 0.897338i \(-0.645498\pi\)
−0.441344 + 0.897338i \(0.645498\pi\)
\(864\) −48.5290 −1.65099
\(865\) −12.2456 −0.416362
\(866\) −48.0750 −1.63366
\(867\) 2.42982 0.0825209
\(868\) 207.175 7.03198
\(869\) −14.2239 −0.482513
\(870\) 4.33770 0.147062
\(871\) 2.20779 0.0748080
\(872\) −117.726 −3.98671
\(873\) 15.3539 0.519651
\(874\) 7.90498 0.267390
\(875\) 27.2919 0.922636
\(876\) −37.1622 −1.25560
\(877\) 51.0176 1.72274 0.861372 0.507975i \(-0.169606\pi\)
0.861372 + 0.507975i \(0.169606\pi\)
\(878\) 25.3739 0.856329
\(879\) −0.831229 −0.0280367
\(880\) −11.8107 −0.398138
\(881\) 32.8067 1.10528 0.552642 0.833418i \(-0.313620\pi\)
0.552642 + 0.833418i \(0.313620\pi\)
\(882\) 111.239 3.74562
\(883\) 27.7138 0.932644 0.466322 0.884615i \(-0.345579\pi\)
0.466322 + 0.884615i \(0.345579\pi\)
\(884\) −18.2469 −0.613710
\(885\) −5.21785 −0.175396
\(886\) 46.0281 1.54634
\(887\) −1.16562 −0.0391378 −0.0195689 0.999809i \(-0.506229\pi\)
−0.0195689 + 0.999809i \(0.506229\pi\)
\(888\) 15.2514 0.511803
\(889\) −71.5513 −2.39975
\(890\) 16.5048 0.553243
\(891\) −7.31829 −0.245172
\(892\) 80.2012 2.68534
\(893\) −1.33904 −0.0448092
\(894\) −21.7824 −0.728513
\(895\) 1.16134 0.0388193
\(896\) 9.97034 0.333086
\(897\) 2.75737 0.0920660
\(898\) 89.5684 2.98894
\(899\) −30.6851 −1.02340
\(900\) 53.4058 1.78019
\(901\) −10.1416 −0.337865
\(902\) −43.6437 −1.45318
\(903\) 24.4834 0.814755
\(904\) 89.0540 2.96189
\(905\) −0.652108 −0.0216768
\(906\) −17.7148 −0.588535
\(907\) 19.6835 0.653578 0.326789 0.945097i \(-0.394033\pi\)
0.326789 + 0.945097i \(0.394033\pi\)
\(908\) 120.724 4.00637
\(909\) 5.16073 0.171170
\(910\) −7.38930 −0.244953
\(911\) 35.2446 1.16771 0.583853 0.811859i \(-0.301544\pi\)
0.583853 + 0.811859i \(0.301544\pi\)
\(912\) 7.23755 0.239659
\(913\) −18.2524 −0.604067
\(914\) −2.53571 −0.0838740
\(915\) 0.420017 0.0138853
\(916\) 90.6097 2.99383
\(917\) 9.69478 0.320150
\(918\) −42.6034 −1.40612
\(919\) 15.7467 0.519435 0.259718 0.965685i \(-0.416371\pi\)
0.259718 + 0.965685i \(0.416371\pi\)
\(920\) −14.3680 −0.473699
\(921\) 27.0739 0.892115
\(922\) 82.6026 2.72037
\(923\) −1.75234 −0.0576788
\(924\) −41.7003 −1.37184
\(925\) −11.6572 −0.383286
\(926\) 2.62196 0.0861630
\(927\) −20.4678 −0.672252
\(928\) −40.4703 −1.32850
\(929\) −29.4776 −0.967129 −0.483564 0.875309i \(-0.660658\pi\)
−0.483564 + 0.875309i \(0.660658\pi\)
\(930\) −10.1570 −0.333062
\(931\) −16.1254 −0.528489
\(932\) −116.736 −3.82382
\(933\) −1.33282 −0.0436346
\(934\) 25.5887 0.837286
\(935\) −4.41513 −0.144390
\(936\) −17.6294 −0.576234
\(937\) 39.6974 1.29686 0.648428 0.761276i \(-0.275427\pi\)
0.648428 + 0.761276i \(0.275427\pi\)
\(938\) −29.0240 −0.947667
\(939\) 22.1940 0.724274
\(940\) 4.12709 0.134611
\(941\) 27.4728 0.895587 0.447793 0.894137i \(-0.352210\pi\)
0.447793 + 0.894137i \(0.352210\pi\)
\(942\) 29.2324 0.952444
\(943\) −26.9012 −0.876025
\(944\) 114.325 3.72097
\(945\) −12.2335 −0.397957
\(946\) 33.0447 1.07438
\(947\) 18.9899 0.617088 0.308544 0.951210i \(-0.400158\pi\)
0.308544 + 0.951210i \(0.400158\pi\)
\(948\) −26.8650 −0.872536
\(949\) −9.37638 −0.304370
\(950\) −10.9181 −0.354230
\(951\) −19.2306 −0.623594
\(952\) 141.460 4.58474
\(953\) −20.1527 −0.652811 −0.326405 0.945230i \(-0.605837\pi\)
−0.326405 + 0.945230i \(0.605837\pi\)
\(954\) −16.6153 −0.537941
\(955\) 1.40229 0.0453770
\(956\) −45.4730 −1.47070
\(957\) 6.17630 0.199651
\(958\) −24.7583 −0.799905
\(959\) 48.5559 1.56795
\(960\) −4.24380 −0.136968
\(961\) 40.8512 1.31778
\(962\) 6.52527 0.210383
\(963\) −23.8645 −0.769024
\(964\) −129.374 −4.16687
\(965\) 7.88019 0.253672
\(966\) −36.2490 −1.16629
\(967\) −34.2769 −1.10227 −0.551135 0.834416i \(-0.685805\pi\)
−0.551135 + 0.834416i \(0.685805\pi\)
\(968\) 49.7200 1.59806
\(969\) 2.70558 0.0869158
\(970\) 9.67452 0.310630
\(971\) −44.1526 −1.41692 −0.708462 0.705749i \(-0.750611\pi\)
−0.708462 + 0.705749i \(0.750611\pi\)
\(972\) −77.3031 −2.47950
\(973\) −11.0208 −0.353309
\(974\) 12.1355 0.388848
\(975\) −3.80840 −0.121966
\(976\) −9.20273 −0.294572
\(977\) −53.3340 −1.70630 −0.853152 0.521662i \(-0.825312\pi\)
−0.853152 + 0.521662i \(0.825312\pi\)
\(978\) 42.0431 1.34439
\(979\) 23.5006 0.751083
\(980\) 49.7007 1.58763
\(981\) −36.5321 −1.16638
\(982\) 1.16079 0.0370423
\(983\) −34.2230 −1.09155 −0.545773 0.837933i \(-0.683764\pi\)
−0.545773 + 0.837933i \(0.683764\pi\)
\(984\) −48.6109 −1.54966
\(985\) −12.3287 −0.392825
\(986\) −35.5286 −1.13146
\(987\) 6.14027 0.195447
\(988\) 4.33357 0.137869
\(989\) 20.3682 0.647672
\(990\) −7.23348 −0.229895
\(991\) 44.9566 1.42809 0.714047 0.700098i \(-0.246860\pi\)
0.714047 + 0.700098i \(0.246860\pi\)
\(992\) 94.7639 3.00876
\(993\) 1.09638 0.0347926
\(994\) 23.0365 0.730675
\(995\) −8.77783 −0.278276
\(996\) −34.4737 −1.09234
\(997\) 21.1207 0.668899 0.334450 0.942414i \(-0.391450\pi\)
0.334450 + 0.942414i \(0.391450\pi\)
\(998\) −60.6261 −1.91909
\(999\) 10.8031 0.341794
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 \(a_p\))