Properties

Label 6034.2.a.n.1.5
Level 6034
Weight 2
Character 6034.1
Self dual Yes
Analytic conductor 48.182
Analytic rank 0
Dimension 24
CM No

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Newspace parameters

Level: \( N \) = \( 6034 = 2 \cdot 7 \cdot 431 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6034.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1817325796\)
Analytic rank: \(0\)
Dimension: \(24\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Character \(\chi\) = 6034.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-1.91791 q^{3}\) \(+1.00000 q^{4}\) \(+0.374562 q^{5}\) \(+1.91791 q^{6}\) \(-1.00000 q^{7}\) \(-1.00000 q^{8}\) \(+0.678384 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-1.91791 q^{3}\) \(+1.00000 q^{4}\) \(+0.374562 q^{5}\) \(+1.91791 q^{6}\) \(-1.00000 q^{7}\) \(-1.00000 q^{8}\) \(+0.678384 q^{9}\) \(-0.374562 q^{10}\) \(-1.13103 q^{11}\) \(-1.91791 q^{12}\) \(+0.0849041 q^{13}\) \(+1.00000 q^{14}\) \(-0.718376 q^{15}\) \(+1.00000 q^{16}\) \(-4.64310 q^{17}\) \(-0.678384 q^{18}\) \(+4.04521 q^{19}\) \(+0.374562 q^{20}\) \(+1.91791 q^{21}\) \(+1.13103 q^{22}\) \(+0.619341 q^{23}\) \(+1.91791 q^{24}\) \(-4.85970 q^{25}\) \(-0.0849041 q^{26}\) \(+4.45265 q^{27}\) \(-1.00000 q^{28}\) \(+8.48928 q^{29}\) \(+0.718376 q^{30}\) \(-2.63740 q^{31}\) \(-1.00000 q^{32}\) \(+2.16922 q^{33}\) \(+4.64310 q^{34}\) \(-0.374562 q^{35}\) \(+0.678384 q^{36}\) \(-5.53403 q^{37}\) \(-4.04521 q^{38}\) \(-0.162839 q^{39}\) \(-0.374562 q^{40}\) \(+0.897076 q^{41}\) \(-1.91791 q^{42}\) \(-3.73812 q^{43}\) \(-1.13103 q^{44}\) \(+0.254097 q^{45}\) \(-0.619341 q^{46}\) \(-12.8473 q^{47}\) \(-1.91791 q^{48}\) \(+1.00000 q^{49}\) \(+4.85970 q^{50}\) \(+8.90506 q^{51}\) \(+0.0849041 q^{52}\) \(-9.09566 q^{53}\) \(-4.45265 q^{54}\) \(-0.423641 q^{55}\) \(+1.00000 q^{56}\) \(-7.75835 q^{57}\) \(-8.48928 q^{58}\) \(+1.43086 q^{59}\) \(-0.718376 q^{60}\) \(+7.69562 q^{61}\) \(+2.63740 q^{62}\) \(-0.678384 q^{63}\) \(+1.00000 q^{64}\) \(+0.0318018 q^{65}\) \(-2.16922 q^{66}\) \(-4.04819 q^{67}\) \(-4.64310 q^{68}\) \(-1.18784 q^{69}\) \(+0.374562 q^{70}\) \(+10.9888 q^{71}\) \(-0.678384 q^{72}\) \(+0.0269734 q^{73}\) \(+5.53403 q^{74}\) \(+9.32048 q^{75}\) \(+4.04521 q^{76}\) \(+1.13103 q^{77}\) \(+0.162839 q^{78}\) \(-3.39249 q^{79}\) \(+0.374562 q^{80}\) \(-10.5749 q^{81}\) \(-0.897076 q^{82}\) \(+0.337072 q^{83}\) \(+1.91791 q^{84}\) \(-1.73913 q^{85}\) \(+3.73812 q^{86}\) \(-16.2817 q^{87}\) \(+1.13103 q^{88}\) \(-3.97680 q^{89}\) \(-0.254097 q^{90}\) \(-0.0849041 q^{91}\) \(+0.619341 q^{92}\) \(+5.05829 q^{93}\) \(+12.8473 q^{94}\) \(+1.51518 q^{95}\) \(+1.91791 q^{96}\) \(-5.17035 q^{97}\) \(-1.00000 q^{98}\) \(-0.767274 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(24q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 24q^{4} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 7q^{6} \) \(\mathstrut -\mathstrut 24q^{7} \) \(\mathstrut -\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(24q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 24q^{4} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 7q^{6} \) \(\mathstrut -\mathstrut 24q^{7} \) \(\mathstrut -\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut -\mathstrut 8q^{10} \) \(\mathstrut +\mathstrut 15q^{11} \) \(\mathstrut +\mathstrut 7q^{12} \) \(\mathstrut -\mathstrut 7q^{13} \) \(\mathstrut +\mathstrut 24q^{14} \) \(\mathstrut +\mathstrut 13q^{15} \) \(\mathstrut +\mathstrut 24q^{16} \) \(\mathstrut -\mathstrut 5q^{17} \) \(\mathstrut -\mathstrut 19q^{18} \) \(\mathstrut +\mathstrut 6q^{19} \) \(\mathstrut +\mathstrut 8q^{20} \) \(\mathstrut -\mathstrut 7q^{21} \) \(\mathstrut -\mathstrut 15q^{22} \) \(\mathstrut +\mathstrut 3q^{23} \) \(\mathstrut -\mathstrut 7q^{24} \) \(\mathstrut +\mathstrut 12q^{25} \) \(\mathstrut +\mathstrut 7q^{26} \) \(\mathstrut +\mathstrut 22q^{27} \) \(\mathstrut -\mathstrut 24q^{28} \) \(\mathstrut +\mathstrut 5q^{29} \) \(\mathstrut -\mathstrut 13q^{30} \) \(\mathstrut +\mathstrut 13q^{31} \) \(\mathstrut -\mathstrut 24q^{32} \) \(\mathstrut -\mathstrut 8q^{33} \) \(\mathstrut +\mathstrut 5q^{34} \) \(\mathstrut -\mathstrut 8q^{35} \) \(\mathstrut +\mathstrut 19q^{36} \) \(\mathstrut +\mathstrut 2q^{37} \) \(\mathstrut -\mathstrut 6q^{38} \) \(\mathstrut +\mathstrut 7q^{39} \) \(\mathstrut -\mathstrut 8q^{40} \) \(\mathstrut +\mathstrut 25q^{41} \) \(\mathstrut +\mathstrut 7q^{42} \) \(\mathstrut -\mathstrut 15q^{43} \) \(\mathstrut +\mathstrut 15q^{44} \) \(\mathstrut +\mathstrut 41q^{45} \) \(\mathstrut -\mathstrut 3q^{46} \) \(\mathstrut +\mathstrut 35q^{47} \) \(\mathstrut +\mathstrut 7q^{48} \) \(\mathstrut +\mathstrut 24q^{49} \) \(\mathstrut -\mathstrut 12q^{50} \) \(\mathstrut +\mathstrut 31q^{51} \) \(\mathstrut -\mathstrut 7q^{52} \) \(\mathstrut +\mathstrut 2q^{53} \) \(\mathstrut -\mathstrut 22q^{54} \) \(\mathstrut +\mathstrut 14q^{55} \) \(\mathstrut +\mathstrut 24q^{56} \) \(\mathstrut -\mathstrut 13q^{57} \) \(\mathstrut -\mathstrut 5q^{58} \) \(\mathstrut +\mathstrut 35q^{59} \) \(\mathstrut +\mathstrut 13q^{60} \) \(\mathstrut -\mathstrut 7q^{61} \) \(\mathstrut -\mathstrut 13q^{62} \) \(\mathstrut -\mathstrut 19q^{63} \) \(\mathstrut +\mathstrut 24q^{64} \) \(\mathstrut -\mathstrut 4q^{65} \) \(\mathstrut +\mathstrut 8q^{66} \) \(\mathstrut +\mathstrut 10q^{67} \) \(\mathstrut -\mathstrut 5q^{68} \) \(\mathstrut +\mathstrut 6q^{69} \) \(\mathstrut +\mathstrut 8q^{70} \) \(\mathstrut +\mathstrut 58q^{71} \) \(\mathstrut -\mathstrut 19q^{72} \) \(\mathstrut +\mathstrut 9q^{73} \) \(\mathstrut -\mathstrut 2q^{74} \) \(\mathstrut +\mathstrut 7q^{75} \) \(\mathstrut +\mathstrut 6q^{76} \) \(\mathstrut -\mathstrut 15q^{77} \) \(\mathstrut -\mathstrut 7q^{78} \) \(\mathstrut +\mathstrut 31q^{79} \) \(\mathstrut +\mathstrut 8q^{80} \) \(\mathstrut +\mathstrut 16q^{81} \) \(\mathstrut -\mathstrut 25q^{82} \) \(\mathstrut -\mathstrut q^{83} \) \(\mathstrut -\mathstrut 7q^{84} \) \(\mathstrut -\mathstrut 4q^{85} \) \(\mathstrut +\mathstrut 15q^{86} \) \(\mathstrut +\mathstrut 30q^{87} \) \(\mathstrut -\mathstrut 15q^{88} \) \(\mathstrut +\mathstrut 45q^{89} \) \(\mathstrut -\mathstrut 41q^{90} \) \(\mathstrut +\mathstrut 7q^{91} \) \(\mathstrut +\mathstrut 3q^{92} \) \(\mathstrut +\mathstrut 25q^{93} \) \(\mathstrut -\mathstrut 35q^{94} \) \(\mathstrut -\mathstrut 10q^{95} \) \(\mathstrut -\mathstrut 7q^{96} \) \(\mathstrut -\mathstrut 9q^{97} \) \(\mathstrut -\mathstrut 24q^{98} \) \(\mathstrut +\mathstrut 64q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −1.91791 −1.10731 −0.553653 0.832747i \(-0.686767\pi\)
−0.553653 + 0.832747i \(0.686767\pi\)
\(4\) 1.00000 0.500000
\(5\) 0.374562 0.167509 0.0837545 0.996486i \(-0.473309\pi\)
0.0837545 + 0.996486i \(0.473309\pi\)
\(6\) 1.91791 0.782984
\(7\) −1.00000 −0.377964
\(8\) −1.00000 −0.353553
\(9\) 0.678384 0.226128
\(10\) −0.374562 −0.118447
\(11\) −1.13103 −0.341019 −0.170509 0.985356i \(-0.554541\pi\)
−0.170509 + 0.985356i \(0.554541\pi\)
\(12\) −1.91791 −0.553653
\(13\) 0.0849041 0.0235482 0.0117741 0.999931i \(-0.496252\pi\)
0.0117741 + 0.999931i \(0.496252\pi\)
\(14\) 1.00000 0.267261
\(15\) −0.718376 −0.185484
\(16\) 1.00000 0.250000
\(17\) −4.64310 −1.12612 −0.563059 0.826417i \(-0.690376\pi\)
−0.563059 + 0.826417i \(0.690376\pi\)
\(18\) −0.678384 −0.159897
\(19\) 4.04521 0.928034 0.464017 0.885826i \(-0.346408\pi\)
0.464017 + 0.885826i \(0.346408\pi\)
\(20\) 0.374562 0.0837545
\(21\) 1.91791 0.418523
\(22\) 1.13103 0.241137
\(23\) 0.619341 0.129141 0.0645707 0.997913i \(-0.479432\pi\)
0.0645707 + 0.997913i \(0.479432\pi\)
\(24\) 1.91791 0.391492
\(25\) −4.85970 −0.971941
\(26\) −0.0849041 −0.0166511
\(27\) 4.45265 0.856914
\(28\) −1.00000 −0.188982
\(29\) 8.48928 1.57642 0.788210 0.615406i \(-0.211008\pi\)
0.788210 + 0.615406i \(0.211008\pi\)
\(30\) 0.718376 0.131157
\(31\) −2.63740 −0.473690 −0.236845 0.971547i \(-0.576113\pi\)
−0.236845 + 0.971547i \(0.576113\pi\)
\(32\) −1.00000 −0.176777
\(33\) 2.16922 0.377612
\(34\) 4.64310 0.796286
\(35\) −0.374562 −0.0633125
\(36\) 0.678384 0.113064
\(37\) −5.53403 −0.909790 −0.454895 0.890545i \(-0.650323\pi\)
−0.454895 + 0.890545i \(0.650323\pi\)
\(38\) −4.04521 −0.656219
\(39\) −0.162839 −0.0260750
\(40\) −0.374562 −0.0592234
\(41\) 0.897076 0.140100 0.0700499 0.997543i \(-0.477684\pi\)
0.0700499 + 0.997543i \(0.477684\pi\)
\(42\) −1.91791 −0.295940
\(43\) −3.73812 −0.570058 −0.285029 0.958519i \(-0.592003\pi\)
−0.285029 + 0.958519i \(0.592003\pi\)
\(44\) −1.13103 −0.170509
\(45\) 0.254097 0.0378785
\(46\) −0.619341 −0.0913168
\(47\) −12.8473 −1.87396 −0.936982 0.349377i \(-0.886393\pi\)
−0.936982 + 0.349377i \(0.886393\pi\)
\(48\) −1.91791 −0.276827
\(49\) 1.00000 0.142857
\(50\) 4.85970 0.687266
\(51\) 8.90506 1.24696
\(52\) 0.0849041 0.0117741
\(53\) −9.09566 −1.24939 −0.624693 0.780871i \(-0.714776\pi\)
−0.624693 + 0.780871i \(0.714776\pi\)
\(54\) −4.45265 −0.605929
\(55\) −0.423641 −0.0571237
\(56\) 1.00000 0.133631
\(57\) −7.75835 −1.02762
\(58\) −8.48928 −1.11470
\(59\) 1.43086 0.186282 0.0931409 0.995653i \(-0.470309\pi\)
0.0931409 + 0.995653i \(0.470309\pi\)
\(60\) −0.718376 −0.0927419
\(61\) 7.69562 0.985323 0.492662 0.870221i \(-0.336024\pi\)
0.492662 + 0.870221i \(0.336024\pi\)
\(62\) 2.63740 0.334950
\(63\) −0.678384 −0.0854684
\(64\) 1.00000 0.125000
\(65\) 0.0318018 0.00394453
\(66\) −2.16922 −0.267012
\(67\) −4.04819 −0.494565 −0.247282 0.968943i \(-0.579538\pi\)
−0.247282 + 0.968943i \(0.579538\pi\)
\(68\) −4.64310 −0.563059
\(69\) −1.18784 −0.142999
\(70\) 0.374562 0.0447687
\(71\) 10.9888 1.30413 0.652064 0.758164i \(-0.273903\pi\)
0.652064 + 0.758164i \(0.273903\pi\)
\(72\) −0.678384 −0.0799484
\(73\) 0.0269734 0.00315700 0.00157850 0.999999i \(-0.499498\pi\)
0.00157850 + 0.999999i \(0.499498\pi\)
\(74\) 5.53403 0.643318
\(75\) 9.32048 1.07624
\(76\) 4.04521 0.464017
\(77\) 1.13103 0.128893
\(78\) 0.162839 0.0184378
\(79\) −3.39249 −0.381685 −0.190842 0.981621i \(-0.561122\pi\)
−0.190842 + 0.981621i \(0.561122\pi\)
\(80\) 0.374562 0.0418773
\(81\) −10.5749 −1.17499
\(82\) −0.897076 −0.0990655
\(83\) 0.337072 0.0369985 0.0184992 0.999829i \(-0.494111\pi\)
0.0184992 + 0.999829i \(0.494111\pi\)
\(84\) 1.91791 0.209261
\(85\) −1.73913 −0.188635
\(86\) 3.73812 0.403092
\(87\) −16.2817 −1.74558
\(88\) 1.13103 0.120568
\(89\) −3.97680 −0.421540 −0.210770 0.977536i \(-0.567597\pi\)
−0.210770 + 0.977536i \(0.567597\pi\)
\(90\) −0.254097 −0.0267841
\(91\) −0.0849041 −0.00890037
\(92\) 0.619341 0.0645707
\(93\) 5.05829 0.524520
\(94\) 12.8473 1.32509
\(95\) 1.51518 0.155454
\(96\) 1.91791 0.195746
\(97\) −5.17035 −0.524970 −0.262485 0.964936i \(-0.584542\pi\)
−0.262485 + 0.964936i \(0.584542\pi\)
\(98\) −1.00000 −0.101015
\(99\) −0.767274 −0.0771139
\(100\) −4.85970 −0.485970
\(101\) 8.50211 0.845992 0.422996 0.906132i \(-0.360978\pi\)
0.422996 + 0.906132i \(0.360978\pi\)
\(102\) −8.90506 −0.881733
\(103\) −12.1665 −1.19880 −0.599399 0.800450i \(-0.704594\pi\)
−0.599399 + 0.800450i \(0.704594\pi\)
\(104\) −0.0849041 −0.00832553
\(105\) 0.718376 0.0701063
\(106\) 9.09566 0.883449
\(107\) 18.5559 1.79386 0.896932 0.442168i \(-0.145791\pi\)
0.896932 + 0.442168i \(0.145791\pi\)
\(108\) 4.45265 0.428457
\(109\) 12.8769 1.23338 0.616692 0.787205i \(-0.288473\pi\)
0.616692 + 0.787205i \(0.288473\pi\)
\(110\) 0.423641 0.0403926
\(111\) 10.6138 1.00742
\(112\) −1.00000 −0.0944911
\(113\) 5.48435 0.515924 0.257962 0.966155i \(-0.416949\pi\)
0.257962 + 0.966155i \(0.416949\pi\)
\(114\) 7.75835 0.726636
\(115\) 0.231981 0.0216324
\(116\) 8.48928 0.788210
\(117\) 0.0575976 0.00532490
\(118\) −1.43086 −0.131721
\(119\) 4.64310 0.425633
\(120\) 0.718376 0.0655784
\(121\) −9.72077 −0.883706
\(122\) −7.69562 −0.696729
\(123\) −1.72051 −0.155133
\(124\) −2.63740 −0.236845
\(125\) −3.69307 −0.330318
\(126\) 0.678384 0.0604353
\(127\) −1.16750 −0.103599 −0.0517993 0.998658i \(-0.516496\pi\)
−0.0517993 + 0.998658i \(0.516496\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 7.16938 0.631229
\(130\) −0.0318018 −0.00278920
\(131\) −17.0004 −1.48533 −0.742664 0.669664i \(-0.766438\pi\)
−0.742664 + 0.669664i \(0.766438\pi\)
\(132\) 2.16922 0.188806
\(133\) −4.04521 −0.350764
\(134\) 4.04819 0.349710
\(135\) 1.66779 0.143541
\(136\) 4.64310 0.398143
\(137\) −0.338549 −0.0289242 −0.0144621 0.999895i \(-0.504604\pi\)
−0.0144621 + 0.999895i \(0.504604\pi\)
\(138\) 1.18784 0.101116
\(139\) 8.76034 0.743043 0.371521 0.928424i \(-0.378836\pi\)
0.371521 + 0.928424i \(0.378836\pi\)
\(140\) −0.374562 −0.0316562
\(141\) 24.6399 2.07505
\(142\) −10.9888 −0.922158
\(143\) −0.0960292 −0.00803036
\(144\) 0.678384 0.0565320
\(145\) 3.17976 0.264065
\(146\) −0.0269734 −0.00223234
\(147\) −1.91791 −0.158187
\(148\) −5.53403 −0.454895
\(149\) −1.29509 −0.106098 −0.0530489 0.998592i \(-0.516894\pi\)
−0.0530489 + 0.998592i \(0.516894\pi\)
\(150\) −9.32048 −0.761014
\(151\) −20.9656 −1.70616 −0.853078 0.521783i \(-0.825267\pi\)
−0.853078 + 0.521783i \(0.825267\pi\)
\(152\) −4.04521 −0.328110
\(153\) −3.14981 −0.254647
\(154\) −1.13103 −0.0911411
\(155\) −0.987867 −0.0793474
\(156\) −0.162839 −0.0130375
\(157\) 2.38855 0.190627 0.0953135 0.995447i \(-0.469615\pi\)
0.0953135 + 0.995447i \(0.469615\pi\)
\(158\) 3.39249 0.269892
\(159\) 17.4447 1.38345
\(160\) −0.374562 −0.0296117
\(161\) −0.619341 −0.0488109
\(162\) 10.5749 0.830846
\(163\) 10.2810 0.805274 0.402637 0.915360i \(-0.368094\pi\)
0.402637 + 0.915360i \(0.368094\pi\)
\(164\) 0.897076 0.0700499
\(165\) 0.812505 0.0632535
\(166\) −0.337072 −0.0261619
\(167\) 21.2172 1.64183 0.820917 0.571048i \(-0.193463\pi\)
0.820917 + 0.571048i \(0.193463\pi\)
\(168\) −1.91791 −0.147970
\(169\) −12.9928 −0.999445
\(170\) 1.73913 0.133385
\(171\) 2.74421 0.209855
\(172\) −3.73812 −0.285029
\(173\) −3.47327 −0.264068 −0.132034 0.991245i \(-0.542151\pi\)
−0.132034 + 0.991245i \(0.542151\pi\)
\(174\) 16.2817 1.23431
\(175\) 4.85970 0.367359
\(176\) −1.13103 −0.0852547
\(177\) −2.74426 −0.206271
\(178\) 3.97680 0.298074
\(179\) −8.61150 −0.643654 −0.321827 0.946799i \(-0.604297\pi\)
−0.321827 + 0.946799i \(0.604297\pi\)
\(180\) 0.254097 0.0189392
\(181\) −18.3747 −1.36578 −0.682891 0.730521i \(-0.739277\pi\)
−0.682891 + 0.730521i \(0.739277\pi\)
\(182\) 0.0849041 0.00629351
\(183\) −14.7595 −1.09106
\(184\) −0.619341 −0.0456584
\(185\) −2.07284 −0.152398
\(186\) −5.05829 −0.370892
\(187\) 5.25149 0.384027
\(188\) −12.8473 −0.936982
\(189\) −4.45265 −0.323883
\(190\) −1.51518 −0.109923
\(191\) −5.44412 −0.393922 −0.196961 0.980411i \(-0.563107\pi\)
−0.196961 + 0.980411i \(0.563107\pi\)
\(192\) −1.91791 −0.138413
\(193\) −9.57267 −0.689056 −0.344528 0.938776i \(-0.611961\pi\)
−0.344528 + 0.938776i \(0.611961\pi\)
\(194\) 5.17035 0.371210
\(195\) −0.0609930 −0.00436780
\(196\) 1.00000 0.0714286
\(197\) −18.7361 −1.33489 −0.667445 0.744659i \(-0.732612\pi\)
−0.667445 + 0.744659i \(0.732612\pi\)
\(198\) 0.767274 0.0545278
\(199\) 11.0058 0.780178 0.390089 0.920777i \(-0.372444\pi\)
0.390089 + 0.920777i \(0.372444\pi\)
\(200\) 4.85970 0.343633
\(201\) 7.76407 0.547635
\(202\) −8.50211 −0.598207
\(203\) −8.48928 −0.595831
\(204\) 8.90506 0.623479
\(205\) 0.336010 0.0234680
\(206\) 12.1665 0.847679
\(207\) 0.420151 0.0292025
\(208\) 0.0849041 0.00588704
\(209\) −4.57526 −0.316477
\(210\) −0.718376 −0.0495726
\(211\) 6.31098 0.434466 0.217233 0.976120i \(-0.430297\pi\)
0.217233 + 0.976120i \(0.430297\pi\)
\(212\) −9.09566 −0.624693
\(213\) −21.0755 −1.44407
\(214\) −18.5559 −1.26845
\(215\) −1.40016 −0.0954898
\(216\) −4.45265 −0.302965
\(217\) 2.63740 0.179038
\(218\) −12.8769 −0.872133
\(219\) −0.0517326 −0.00349577
\(220\) −0.423641 −0.0285619
\(221\) −0.394218 −0.0265180
\(222\) −10.6138 −0.712351
\(223\) 5.62649 0.376778 0.188389 0.982094i \(-0.439673\pi\)
0.188389 + 0.982094i \(0.439673\pi\)
\(224\) 1.00000 0.0668153
\(225\) −3.29675 −0.219783
\(226\) −5.48435 −0.364814
\(227\) 18.9786 1.25966 0.629828 0.776735i \(-0.283126\pi\)
0.629828 + 0.776735i \(0.283126\pi\)
\(228\) −7.75835 −0.513809
\(229\) 11.8209 0.781147 0.390574 0.920572i \(-0.372277\pi\)
0.390574 + 0.920572i \(0.372277\pi\)
\(230\) −0.231981 −0.0152964
\(231\) −2.16922 −0.142724
\(232\) −8.48928 −0.557349
\(233\) 27.5762 1.80657 0.903287 0.429037i \(-0.141147\pi\)
0.903287 + 0.429037i \(0.141147\pi\)
\(234\) −0.0575976 −0.00376527
\(235\) −4.81209 −0.313906
\(236\) 1.43086 0.0931409
\(237\) 6.50649 0.422642
\(238\) −4.64310 −0.300968
\(239\) −6.76335 −0.437485 −0.218742 0.975783i \(-0.570195\pi\)
−0.218742 + 0.975783i \(0.570195\pi\)
\(240\) −0.718376 −0.0463710
\(241\) −19.1051 −1.23067 −0.615334 0.788266i \(-0.710979\pi\)
−0.615334 + 0.788266i \(0.710979\pi\)
\(242\) 9.72077 0.624875
\(243\) 6.92385 0.444165
\(244\) 7.69562 0.492662
\(245\) 0.374562 0.0239299
\(246\) 1.72051 0.109696
\(247\) 0.343455 0.0218535
\(248\) 2.63740 0.167475
\(249\) −0.646474 −0.0409686
\(250\) 3.69307 0.233570
\(251\) 14.2456 0.899177 0.449589 0.893236i \(-0.351571\pi\)
0.449589 + 0.893236i \(0.351571\pi\)
\(252\) −0.678384 −0.0427342
\(253\) −0.700493 −0.0440396
\(254\) 1.16750 0.0732553
\(255\) 3.33549 0.208877
\(256\) 1.00000 0.0625000
\(257\) −29.8277 −1.86060 −0.930300 0.366799i \(-0.880454\pi\)
−0.930300 + 0.366799i \(0.880454\pi\)
\(258\) −7.16938 −0.446346
\(259\) 5.53403 0.343868
\(260\) 0.0318018 0.00197226
\(261\) 5.75900 0.356473
\(262\) 17.0004 1.05029
\(263\) 1.39805 0.0862072 0.0431036 0.999071i \(-0.486275\pi\)
0.0431036 + 0.999071i \(0.486275\pi\)
\(264\) −2.16922 −0.133506
\(265\) −3.40689 −0.209283
\(266\) 4.04521 0.248028
\(267\) 7.62716 0.466775
\(268\) −4.04819 −0.247282
\(269\) 3.95250 0.240988 0.120494 0.992714i \(-0.461552\pi\)
0.120494 + 0.992714i \(0.461552\pi\)
\(270\) −1.66779 −0.101499
\(271\) 13.4976 0.819923 0.409961 0.912103i \(-0.365542\pi\)
0.409961 + 0.912103i \(0.365542\pi\)
\(272\) −4.64310 −0.281530
\(273\) 0.162839 0.00985544
\(274\) 0.338549 0.0204525
\(275\) 5.49648 0.331450
\(276\) −1.18784 −0.0714996
\(277\) 9.78792 0.588099 0.294050 0.955790i \(-0.404997\pi\)
0.294050 + 0.955790i \(0.404997\pi\)
\(278\) −8.76034 −0.525410
\(279\) −1.78917 −0.107115
\(280\) 0.374562 0.0223843
\(281\) 27.7828 1.65738 0.828691 0.559707i \(-0.189086\pi\)
0.828691 + 0.559707i \(0.189086\pi\)
\(282\) −24.6399 −1.46728
\(283\) 29.3970 1.74747 0.873736 0.486401i \(-0.161691\pi\)
0.873736 + 0.486401i \(0.161691\pi\)
\(284\) 10.9888 0.652064
\(285\) −2.90598 −0.172135
\(286\) 0.0960292 0.00567832
\(287\) −0.897076 −0.0529527
\(288\) −0.678384 −0.0399742
\(289\) 4.55841 0.268142
\(290\) −3.17976 −0.186722
\(291\) 9.91628 0.581303
\(292\) 0.0269734 0.00157850
\(293\) 13.0696 0.763532 0.381766 0.924259i \(-0.375316\pi\)
0.381766 + 0.924259i \(0.375316\pi\)
\(294\) 1.91791 0.111855
\(295\) 0.535944 0.0312039
\(296\) 5.53403 0.321659
\(297\) −5.03609 −0.292224
\(298\) 1.29509 0.0750224
\(299\) 0.0525845 0.00304104
\(300\) 9.32048 0.538118
\(301\) 3.73812 0.215462
\(302\) 20.9656 1.20643
\(303\) −16.3063 −0.936773
\(304\) 4.04521 0.232009
\(305\) 2.88248 0.165051
\(306\) 3.14981 0.180063
\(307\) −9.13612 −0.521426 −0.260713 0.965416i \(-0.583958\pi\)
−0.260713 + 0.965416i \(0.583958\pi\)
\(308\) 1.13103 0.0644465
\(309\) 23.3342 1.32744
\(310\) 0.987867 0.0561071
\(311\) 11.1115 0.630077 0.315038 0.949079i \(-0.397983\pi\)
0.315038 + 0.949079i \(0.397983\pi\)
\(312\) 0.162839 0.00921892
\(313\) 5.66679 0.320306 0.160153 0.987092i \(-0.448801\pi\)
0.160153 + 0.987092i \(0.448801\pi\)
\(314\) −2.38855 −0.134794
\(315\) −0.254097 −0.0143167
\(316\) −3.39249 −0.190842
\(317\) 0.787739 0.0442438 0.0221219 0.999755i \(-0.492958\pi\)
0.0221219 + 0.999755i \(0.492958\pi\)
\(318\) −17.4447 −0.978249
\(319\) −9.60164 −0.537589
\(320\) 0.374562 0.0209386
\(321\) −35.5885 −1.98636
\(322\) 0.619341 0.0345145
\(323\) −18.7823 −1.04508
\(324\) −10.5749 −0.587497
\(325\) −0.412609 −0.0228874
\(326\) −10.2810 −0.569415
\(327\) −24.6967 −1.36573
\(328\) −0.897076 −0.0495327
\(329\) 12.8473 0.708292
\(330\) −0.812505 −0.0447270
\(331\) 15.6030 0.857616 0.428808 0.903396i \(-0.358934\pi\)
0.428808 + 0.903396i \(0.358934\pi\)
\(332\) 0.337072 0.0184992
\(333\) −3.75420 −0.205729
\(334\) −21.2172 −1.16095
\(335\) −1.51630 −0.0828441
\(336\) 1.91791 0.104631
\(337\) −24.5838 −1.33917 −0.669583 0.742737i \(-0.733527\pi\)
−0.669583 + 0.742737i \(0.733527\pi\)
\(338\) 12.9928 0.706715
\(339\) −10.5185 −0.571286
\(340\) −1.73913 −0.0943175
\(341\) 2.98298 0.161537
\(342\) −2.74421 −0.148390
\(343\) −1.00000 −0.0539949
\(344\) 3.73812 0.201546
\(345\) −0.444919 −0.0239537
\(346\) 3.47327 0.186724
\(347\) −1.09594 −0.0588331 −0.0294165 0.999567i \(-0.509365\pi\)
−0.0294165 + 0.999567i \(0.509365\pi\)
\(348\) −16.2817 −0.872790
\(349\) 18.6415 0.997855 0.498928 0.866644i \(-0.333727\pi\)
0.498928 + 0.866644i \(0.333727\pi\)
\(350\) −4.85970 −0.259762
\(351\) 0.378048 0.0201787
\(352\) 1.13103 0.0602842
\(353\) 17.6943 0.941771 0.470886 0.882194i \(-0.343934\pi\)
0.470886 + 0.882194i \(0.343934\pi\)
\(354\) 2.74426 0.145856
\(355\) 4.11598 0.218453
\(356\) −3.97680 −0.210770
\(357\) −8.90506 −0.471306
\(358\) 8.61150 0.455132
\(359\) 27.5567 1.45439 0.727194 0.686432i \(-0.240824\pi\)
0.727194 + 0.686432i \(0.240824\pi\)
\(360\) −0.254097 −0.0133921
\(361\) −2.63629 −0.138752
\(362\) 18.3747 0.965753
\(363\) 18.6436 0.978534
\(364\) −0.0849041 −0.00445018
\(365\) 0.0101032 0.000528826 0
\(366\) 14.7595 0.771492
\(367\) 24.6436 1.28638 0.643192 0.765705i \(-0.277610\pi\)
0.643192 + 0.765705i \(0.277610\pi\)
\(368\) 0.619341 0.0322854
\(369\) 0.608562 0.0316805
\(370\) 2.07284 0.107762
\(371\) 9.09566 0.472223
\(372\) 5.05829 0.262260
\(373\) 2.78023 0.143955 0.0719774 0.997406i \(-0.477069\pi\)
0.0719774 + 0.997406i \(0.477069\pi\)
\(374\) −5.25149 −0.271548
\(375\) 7.08297 0.365763
\(376\) 12.8473 0.662547
\(377\) 0.720775 0.0371218
\(378\) 4.45265 0.229020
\(379\) −18.3802 −0.944128 −0.472064 0.881564i \(-0.656491\pi\)
−0.472064 + 0.881564i \(0.656491\pi\)
\(380\) 1.51518 0.0777271
\(381\) 2.23916 0.114715
\(382\) 5.44412 0.278545
\(383\) 12.9687 0.662671 0.331336 0.943513i \(-0.392501\pi\)
0.331336 + 0.943513i \(0.392501\pi\)
\(384\) 1.91791 0.0978730
\(385\) 0.423641 0.0215907
\(386\) 9.57267 0.487236
\(387\) −2.53588 −0.128906
\(388\) −5.17035 −0.262485
\(389\) −9.22742 −0.467849 −0.233924 0.972255i \(-0.575157\pi\)
−0.233924 + 0.972255i \(0.575157\pi\)
\(390\) 0.0609930 0.00308850
\(391\) −2.87566 −0.145429
\(392\) −1.00000 −0.0505076
\(393\) 32.6052 1.64471
\(394\) 18.7361 0.943910
\(395\) −1.27070 −0.0639356
\(396\) −0.767274 −0.0385570
\(397\) −5.31928 −0.266967 −0.133484 0.991051i \(-0.542616\pi\)
−0.133484 + 0.991051i \(0.542616\pi\)
\(398\) −11.0058 −0.551669
\(399\) 7.75835 0.388403
\(400\) −4.85970 −0.242985
\(401\) −20.4634 −1.02189 −0.510947 0.859612i \(-0.670705\pi\)
−0.510947 + 0.859612i \(0.670705\pi\)
\(402\) −7.76407 −0.387236
\(403\) −0.223926 −0.0111545
\(404\) 8.50211 0.422996
\(405\) −3.96097 −0.196822
\(406\) 8.48928 0.421316
\(407\) 6.25916 0.310255
\(408\) −8.90506 −0.440866
\(409\) 0.0314586 0.00155553 0.000777764 1.00000i \(-0.499752\pi\)
0.000777764 1.00000i \(0.499752\pi\)
\(410\) −0.336010 −0.0165944
\(411\) 0.649306 0.0320279
\(412\) −12.1665 −0.599399
\(413\) −1.43086 −0.0704079
\(414\) −0.420151 −0.0206493
\(415\) 0.126254 0.00619757
\(416\) −0.0849041 −0.00416277
\(417\) −16.8016 −0.822776
\(418\) 4.57526 0.223783
\(419\) 13.8327 0.675770 0.337885 0.941187i \(-0.390289\pi\)
0.337885 + 0.941187i \(0.390289\pi\)
\(420\) 0.718376 0.0350532
\(421\) −11.1791 −0.544838 −0.272419 0.962179i \(-0.587824\pi\)
−0.272419 + 0.962179i \(0.587824\pi\)
\(422\) −6.31098 −0.307214
\(423\) −8.71538 −0.423756
\(424\) 9.09566 0.441724
\(425\) 22.5641 1.09452
\(426\) 21.0755 1.02111
\(427\) −7.69562 −0.372417
\(428\) 18.5559 0.896932
\(429\) 0.184175 0.00889207
\(430\) 1.40016 0.0675215
\(431\) 1.00000 0.0481683
\(432\) 4.45265 0.214228
\(433\) 12.5297 0.602137 0.301068 0.953603i \(-0.402657\pi\)
0.301068 + 0.953603i \(0.402657\pi\)
\(434\) −2.63740 −0.126599
\(435\) −6.09850 −0.292401
\(436\) 12.8769 0.616692
\(437\) 2.50536 0.119848
\(438\) 0.0517326 0.00247188
\(439\) 16.1550 0.771034 0.385517 0.922701i \(-0.374023\pi\)
0.385517 + 0.922701i \(0.374023\pi\)
\(440\) 0.423641 0.0201963
\(441\) 0.678384 0.0323040
\(442\) 0.394218 0.0187511
\(443\) 20.8897 0.992499 0.496250 0.868180i \(-0.334710\pi\)
0.496250 + 0.868180i \(0.334710\pi\)
\(444\) 10.6138 0.503708
\(445\) −1.48956 −0.0706118
\(446\) −5.62649 −0.266422
\(447\) 2.48386 0.117483
\(448\) −1.00000 −0.0472456
\(449\) −11.4910 −0.542292 −0.271146 0.962538i \(-0.587403\pi\)
−0.271146 + 0.962538i \(0.587403\pi\)
\(450\) 3.29675 0.155410
\(451\) −1.01462 −0.0477766
\(452\) 5.48435 0.257962
\(453\) 40.2102 1.88924
\(454\) −18.9786 −0.890711
\(455\) −0.0318018 −0.00149089
\(456\) 7.75835 0.363318
\(457\) −3.51310 −0.164336 −0.0821678 0.996619i \(-0.526184\pi\)
−0.0821678 + 0.996619i \(0.526184\pi\)
\(458\) −11.8209 −0.552355
\(459\) −20.6741 −0.964986
\(460\) 0.231981 0.0108162
\(461\) 14.4346 0.672286 0.336143 0.941811i \(-0.390877\pi\)
0.336143 + 0.941811i \(0.390877\pi\)
\(462\) 2.16922 0.100921
\(463\) 23.4921 1.09177 0.545884 0.837860i \(-0.316194\pi\)
0.545884 + 0.837860i \(0.316194\pi\)
\(464\) 8.48928 0.394105
\(465\) 1.89464 0.0878619
\(466\) −27.5762 −1.27744
\(467\) 23.6821 1.09588 0.547940 0.836518i \(-0.315412\pi\)
0.547940 + 0.836518i \(0.315412\pi\)
\(468\) 0.0575976 0.00266245
\(469\) 4.04819 0.186928
\(470\) 4.81209 0.221965
\(471\) −4.58102 −0.211082
\(472\) −1.43086 −0.0658606
\(473\) 4.22793 0.194400
\(474\) −6.50649 −0.298853
\(475\) −19.6585 −0.901994
\(476\) 4.64310 0.212816
\(477\) −6.17036 −0.282521
\(478\) 6.76335 0.309348
\(479\) 14.7311 0.673081 0.336540 0.941669i \(-0.390743\pi\)
0.336540 + 0.941669i \(0.390743\pi\)
\(480\) 0.718376 0.0327892
\(481\) −0.469862 −0.0214239
\(482\) 19.1051 0.870214
\(483\) 1.18784 0.0540486
\(484\) −9.72077 −0.441853
\(485\) −1.93662 −0.0879372
\(486\) −6.92385 −0.314072
\(487\) −26.0270 −1.17940 −0.589698 0.807624i \(-0.700753\pi\)
−0.589698 + 0.807624i \(0.700753\pi\)
\(488\) −7.69562 −0.348364
\(489\) −19.7181 −0.891685
\(490\) −0.374562 −0.0169210
\(491\) −12.4349 −0.561180 −0.280590 0.959828i \(-0.590530\pi\)
−0.280590 + 0.959828i \(0.590530\pi\)
\(492\) −1.72051 −0.0775667
\(493\) −39.4166 −1.77524
\(494\) −0.343455 −0.0154528
\(495\) −0.287391 −0.0129173
\(496\) −2.63740 −0.118423
\(497\) −10.9888 −0.492914
\(498\) 0.646474 0.0289692
\(499\) 35.7961 1.60245 0.801227 0.598360i \(-0.204181\pi\)
0.801227 + 0.598360i \(0.204181\pi\)
\(500\) −3.69307 −0.165159
\(501\) −40.6926 −1.81801
\(502\) −14.2456 −0.635814
\(503\) 39.5513 1.76350 0.881752 0.471713i \(-0.156364\pi\)
0.881752 + 0.471713i \(0.156364\pi\)
\(504\) 0.678384 0.0302176
\(505\) 3.18457 0.141711
\(506\) 0.700493 0.0311407
\(507\) 24.9190 1.10669
\(508\) −1.16750 −0.0517993
\(509\) −7.82845 −0.346990 −0.173495 0.984835i \(-0.555506\pi\)
−0.173495 + 0.984835i \(0.555506\pi\)
\(510\) −3.33549 −0.147698
\(511\) −0.0269734 −0.00119323
\(512\) −1.00000 −0.0441942
\(513\) 18.0119 0.795245
\(514\) 29.8277 1.31564
\(515\) −4.55709 −0.200810
\(516\) 7.16938 0.315614
\(517\) 14.5306 0.639057
\(518\) −5.53403 −0.243152
\(519\) 6.66142 0.292404
\(520\) −0.0318018 −0.00139460
\(521\) 3.29042 0.144156 0.0720781 0.997399i \(-0.477037\pi\)
0.0720781 + 0.997399i \(0.477037\pi\)
\(522\) −5.75900 −0.252064
\(523\) 22.9420 1.00318 0.501591 0.865105i \(-0.332748\pi\)
0.501591 + 0.865105i \(0.332748\pi\)
\(524\) −17.0004 −0.742664
\(525\) −9.32048 −0.406779
\(526\) −1.39805 −0.0609577
\(527\) 12.2457 0.533431
\(528\) 2.16922 0.0944031
\(529\) −22.6164 −0.983322
\(530\) 3.40689 0.147986
\(531\) 0.970672 0.0421236
\(532\) −4.04521 −0.175382
\(533\) 0.0761654 0.00329909
\(534\) −7.62716 −0.330059
\(535\) 6.95032 0.300488
\(536\) 4.04819 0.174855
\(537\) 16.5161 0.712722
\(538\) −3.95250 −0.170405
\(539\) −1.13103 −0.0487170
\(540\) 1.66779 0.0717704
\(541\) 19.9708 0.858610 0.429305 0.903160i \(-0.358759\pi\)
0.429305 + 0.903160i \(0.358759\pi\)
\(542\) −13.4976 −0.579773
\(543\) 35.2411 1.51234
\(544\) 4.64310 0.199071
\(545\) 4.82319 0.206603
\(546\) −0.162839 −0.00696885
\(547\) 18.2878 0.781931 0.390966 0.920405i \(-0.372141\pi\)
0.390966 + 0.920405i \(0.372141\pi\)
\(548\) −0.338549 −0.0144621
\(549\) 5.22059 0.222809
\(550\) −5.49648 −0.234371
\(551\) 34.3409 1.46297
\(552\) 1.18784 0.0505578
\(553\) 3.39249 0.144263
\(554\) −9.78792 −0.415849
\(555\) 3.97552 0.168751
\(556\) 8.76034 0.371521
\(557\) 8.92322 0.378089 0.189045 0.981969i \(-0.439461\pi\)
0.189045 + 0.981969i \(0.439461\pi\)
\(558\) 1.78917 0.0757415
\(559\) −0.317382 −0.0134238
\(560\) −0.374562 −0.0158281
\(561\) −10.0719 −0.425236
\(562\) −27.7828 −1.17195
\(563\) −3.42778 −0.144464 −0.0722318 0.997388i \(-0.523012\pi\)
−0.0722318 + 0.997388i \(0.523012\pi\)
\(564\) 24.6399 1.03753
\(565\) 2.05423 0.0864220
\(566\) −29.3970 −1.23565
\(567\) 10.5749 0.444106
\(568\) −10.9888 −0.461079
\(569\) 35.6879 1.49611 0.748057 0.663635i \(-0.230987\pi\)
0.748057 + 0.663635i \(0.230987\pi\)
\(570\) 2.90598 0.121718
\(571\) 9.37967 0.392527 0.196263 0.980551i \(-0.437119\pi\)
0.196263 + 0.980551i \(0.437119\pi\)
\(572\) −0.0960292 −0.00401518
\(573\) 10.4413 0.436193
\(574\) 0.897076 0.0374432
\(575\) −3.00981 −0.125518
\(576\) 0.678384 0.0282660
\(577\) −5.20382 −0.216638 −0.108319 0.994116i \(-0.534547\pi\)
−0.108319 + 0.994116i \(0.534547\pi\)
\(578\) −4.55841 −0.189605
\(579\) 18.3595 0.762996
\(580\) 3.17976 0.132032
\(581\) −0.337072 −0.0139841
\(582\) −9.91628 −0.411043
\(583\) 10.2875 0.426064
\(584\) −0.0269734 −0.00111617
\(585\) 0.0215738 0.000891969 0
\(586\) −13.0696 −0.539899
\(587\) 39.5427 1.63210 0.816052 0.577979i \(-0.196158\pi\)
0.816052 + 0.577979i \(0.196158\pi\)
\(588\) −1.91791 −0.0790933
\(589\) −10.6688 −0.439601
\(590\) −0.535944 −0.0220645
\(591\) 35.9341 1.47813
\(592\) −5.53403 −0.227447
\(593\) −23.0366 −0.945999 −0.472999 0.881063i \(-0.656829\pi\)
−0.472999 + 0.881063i \(0.656829\pi\)
\(594\) 5.03609 0.206633
\(595\) 1.73913 0.0712973
\(596\) −1.29509 −0.0530489
\(597\) −21.1081 −0.863897
\(598\) −0.0525845 −0.00215034
\(599\) 12.6645 0.517458 0.258729 0.965950i \(-0.416696\pi\)
0.258729 + 0.965950i \(0.416696\pi\)
\(600\) −9.32048 −0.380507
\(601\) 19.3119 0.787748 0.393874 0.919164i \(-0.371135\pi\)
0.393874 + 0.919164i \(0.371135\pi\)
\(602\) −3.73812 −0.152354
\(603\) −2.74623 −0.111835
\(604\) −20.9656 −0.853078
\(605\) −3.64103 −0.148029
\(606\) 16.3063 0.662398
\(607\) −1.42969 −0.0580294 −0.0290147 0.999579i \(-0.509237\pi\)
−0.0290147 + 0.999579i \(0.509237\pi\)
\(608\) −4.04521 −0.164055
\(609\) 16.2817 0.659767
\(610\) −2.88248 −0.116708
\(611\) −1.09078 −0.0441284
\(612\) −3.14981 −0.127323
\(613\) −19.1170 −0.772128 −0.386064 0.922472i \(-0.626166\pi\)
−0.386064 + 0.922472i \(0.626166\pi\)
\(614\) 9.13612 0.368704
\(615\) −0.644438 −0.0259862
\(616\) −1.13103 −0.0455705
\(617\) 30.4341 1.22523 0.612615 0.790381i \(-0.290117\pi\)
0.612615 + 0.790381i \(0.290117\pi\)
\(618\) −23.3342 −0.938640
\(619\) 30.4860 1.22534 0.612668 0.790340i \(-0.290096\pi\)
0.612668 + 0.790340i \(0.290096\pi\)
\(620\) −0.987867 −0.0396737
\(621\) 2.75771 0.110663
\(622\) −11.1115 −0.445532
\(623\) 3.97680 0.159327
\(624\) −0.162839 −0.00651876
\(625\) 22.9152 0.916610
\(626\) −5.66679 −0.226491
\(627\) 8.77494 0.350437
\(628\) 2.38855 0.0953135
\(629\) 25.6951 1.02453
\(630\) 0.254097 0.0101235
\(631\) 2.84517 0.113265 0.0566323 0.998395i \(-0.481964\pi\)
0.0566323 + 0.998395i \(0.481964\pi\)
\(632\) 3.39249 0.134946
\(633\) −12.1039 −0.481087
\(634\) −0.787739 −0.0312851
\(635\) −0.437300 −0.0173537
\(636\) 17.4447 0.691726
\(637\) 0.0849041 0.00336402
\(638\) 9.60164 0.380133
\(639\) 7.45462 0.294900
\(640\) −0.374562 −0.0148058
\(641\) −16.0222 −0.632840 −0.316420 0.948619i \(-0.602481\pi\)
−0.316420 + 0.948619i \(0.602481\pi\)
\(642\) 35.5885 1.40457
\(643\) −14.6429 −0.577460 −0.288730 0.957411i \(-0.593233\pi\)
−0.288730 + 0.957411i \(0.593233\pi\)
\(644\) −0.619341 −0.0244054
\(645\) 2.68537 0.105737
\(646\) 18.7823 0.738981
\(647\) −20.1457 −0.792010 −0.396005 0.918248i \(-0.629604\pi\)
−0.396005 + 0.918248i \(0.629604\pi\)
\(648\) 10.5749 0.415423
\(649\) −1.61834 −0.0635256
\(650\) 0.412609 0.0161838
\(651\) −5.05829 −0.198250
\(652\) 10.2810 0.402637
\(653\) −35.7939 −1.40072 −0.700361 0.713788i \(-0.746978\pi\)
−0.700361 + 0.713788i \(0.746978\pi\)
\(654\) 24.6967 0.965719
\(655\) −6.36768 −0.248806
\(656\) 0.897076 0.0350249
\(657\) 0.0182983 0.000713887 0
\(658\) −12.8473 −0.500838
\(659\) 28.9817 1.12897 0.564483 0.825445i \(-0.309076\pi\)
0.564483 + 0.825445i \(0.309076\pi\)
\(660\) 0.812505 0.0316267
\(661\) −21.7990 −0.847881 −0.423941 0.905690i \(-0.639353\pi\)
−0.423941 + 0.905690i \(0.639353\pi\)
\(662\) −15.6030 −0.606426
\(663\) 0.756076 0.0293636
\(664\) −0.337072 −0.0130809
\(665\) −1.51518 −0.0587561
\(666\) 3.75420 0.145472
\(667\) 5.25776 0.203581
\(668\) 21.2172 0.820917
\(669\) −10.7911 −0.417209
\(670\) 1.51630 0.0585796
\(671\) −8.70399 −0.336014
\(672\) −1.91791 −0.0739850
\(673\) 30.3942 1.17161 0.585806 0.810452i \(-0.300778\pi\)
0.585806 + 0.810452i \(0.300778\pi\)
\(674\) 24.5838 0.946933
\(675\) −21.6386 −0.832869
\(676\) −12.9928 −0.499723
\(677\) −6.78209 −0.260657 −0.130328 0.991471i \(-0.541603\pi\)
−0.130328 + 0.991471i \(0.541603\pi\)
\(678\) 10.5185 0.403961
\(679\) 5.17035 0.198420
\(680\) 1.73913 0.0666925
\(681\) −36.3993 −1.39482
\(682\) −2.98298 −0.114224
\(683\) 5.71109 0.218529 0.109264 0.994013i \(-0.465150\pi\)
0.109264 + 0.994013i \(0.465150\pi\)
\(684\) 2.74421 0.104927
\(685\) −0.126807 −0.00484506
\(686\) 1.00000 0.0381802
\(687\) −22.6714 −0.864970
\(688\) −3.73812 −0.142514
\(689\) −0.772259 −0.0294207
\(690\) 0.444919 0.0169378
\(691\) 17.0937 0.650273 0.325137 0.945667i \(-0.394590\pi\)
0.325137 + 0.945667i \(0.394590\pi\)
\(692\) −3.47327 −0.132034
\(693\) 0.767274 0.0291463
\(694\) 1.09594 0.0416013
\(695\) 3.28129 0.124466
\(696\) 16.2817 0.617156
\(697\) −4.16522 −0.157769
\(698\) −18.6415 −0.705590
\(699\) −52.8886 −2.00043
\(700\) 4.85970 0.183680
\(701\) 26.0168 0.982642 0.491321 0.870979i \(-0.336514\pi\)
0.491321 + 0.870979i \(0.336514\pi\)
\(702\) −0.378048 −0.0142685
\(703\) −22.3863 −0.844316
\(704\) −1.13103 −0.0426273
\(705\) 9.22916 0.347590
\(706\) −17.6943 −0.665933
\(707\) −8.50211 −0.319755
\(708\) −2.74426 −0.103136
\(709\) −30.7062 −1.15319 −0.576597 0.817028i \(-0.695620\pi\)
−0.576597 + 0.817028i \(0.695620\pi\)
\(710\) −4.11598 −0.154470
\(711\) −2.30141 −0.0863097
\(712\) 3.97680 0.149037
\(713\) −1.63345 −0.0611730
\(714\) 8.90506 0.333264
\(715\) −0.0359688 −0.00134516
\(716\) −8.61150 −0.321827
\(717\) 12.9715 0.484430
\(718\) −27.5567 −1.02841
\(719\) 7.41077 0.276375 0.138188 0.990406i \(-0.455872\pi\)
0.138188 + 0.990406i \(0.455872\pi\)
\(720\) 0.254097 0.00946962
\(721\) 12.1665 0.453103
\(722\) 2.63629 0.0981126
\(723\) 36.6419 1.36273
\(724\) −18.3747 −0.682891
\(725\) −41.2554 −1.53219
\(726\) −18.6436 −0.691928
\(727\) −12.7969 −0.474610 −0.237305 0.971435i \(-0.576264\pi\)
−0.237305 + 0.971435i \(0.576264\pi\)
\(728\) 0.0849041 0.00314675
\(729\) 18.4455 0.683167
\(730\) −0.0101032 −0.000373937 0
\(731\) 17.3565 0.641953
\(732\) −14.7595 −0.545528
\(733\) −3.99740 −0.147647 −0.0738237 0.997271i \(-0.523520\pi\)
−0.0738237 + 0.997271i \(0.523520\pi\)
\(734\) −24.6436 −0.909611
\(735\) −0.718376 −0.0264977
\(736\) −0.619341 −0.0228292
\(737\) 4.57863 0.168656
\(738\) −0.608562 −0.0224015
\(739\) 4.57525 0.168303 0.0841516 0.996453i \(-0.473182\pi\)
0.0841516 + 0.996453i \(0.473182\pi\)
\(740\) −2.07284 −0.0761990
\(741\) −0.658716 −0.0241985
\(742\) −9.09566 −0.333912
\(743\) 31.6605 1.16151 0.580755 0.814078i \(-0.302757\pi\)
0.580755 + 0.814078i \(0.302757\pi\)
\(744\) −5.05829 −0.185446
\(745\) −0.485090 −0.0177723
\(746\) −2.78023 −0.101791
\(747\) 0.228664 0.00836639
\(748\) 5.25149 0.192014
\(749\) −18.5559 −0.678017
\(750\) −7.08297 −0.258634
\(751\) 8.16944 0.298107 0.149054 0.988829i \(-0.452377\pi\)
0.149054 + 0.988829i \(0.452377\pi\)
\(752\) −12.8473 −0.468491
\(753\) −27.3219 −0.995665
\(754\) −0.720775 −0.0262491
\(755\) −7.85291 −0.285797
\(756\) −4.45265 −0.161941
\(757\) −19.2913 −0.701153 −0.350576 0.936534i \(-0.614014\pi\)
−0.350576 + 0.936534i \(0.614014\pi\)
\(758\) 18.3802 0.667599
\(759\) 1.34348 0.0487654
\(760\) −1.51518 −0.0549613
\(761\) 41.6094 1.50834 0.754170 0.656679i \(-0.228039\pi\)
0.754170 + 0.656679i \(0.228039\pi\)
\(762\) −2.23916 −0.0811161
\(763\) −12.8769 −0.466175
\(764\) −5.44412 −0.196961
\(765\) −1.17980 −0.0426557
\(766\) −12.9687 −0.468579
\(767\) 0.121486 0.00438659
\(768\) −1.91791 −0.0692067
\(769\) 14.7376 0.531451 0.265725 0.964049i \(-0.414389\pi\)
0.265725 + 0.964049i \(0.414389\pi\)
\(770\) −0.423641 −0.0152670
\(771\) 57.2069 2.06026
\(772\) −9.57267 −0.344528
\(773\) −24.4036 −0.877735 −0.438868 0.898552i \(-0.644620\pi\)
−0.438868 + 0.898552i \(0.644620\pi\)
\(774\) 2.53588 0.0911504
\(775\) 12.8170 0.460399
\(776\) 5.17035 0.185605
\(777\) −10.6138 −0.380768
\(778\) 9.22742 0.330819
\(779\) 3.62886 0.130017
\(780\) −0.0609930 −0.00218390
\(781\) −12.4287 −0.444732
\(782\) 2.87566 0.102833
\(783\) 37.7998 1.35086
\(784\) 1.00000 0.0357143
\(785\) 0.894658 0.0319317
\(786\) −32.6052 −1.16299
\(787\) 42.7338 1.52330 0.761648 0.647991i \(-0.224391\pi\)
0.761648 + 0.647991i \(0.224391\pi\)
\(788\) −18.7361 −0.667445
\(789\) −2.68133 −0.0954578
\(790\) 1.27070 0.0452093
\(791\) −5.48435 −0.195001
\(792\) 0.767274 0.0272639
\(793\) 0.653390 0.0232025
\(794\) 5.31928 0.188774
\(795\) 6.53411 0.231741
\(796\) 11.0058 0.390089
\(797\) −15.7509 −0.557927 −0.278964 0.960302i \(-0.589991\pi\)
−0.278964 + 0.960302i \(0.589991\pi\)
\(798\) −7.75835 −0.274643
\(799\) 59.6511 2.11031
\(800\) 4.85970 0.171816
\(801\) −2.69780 −0.0953221
\(802\) 20.4634 0.722589
\(803\) −0.0305078 −0.00107660
\(804\) 7.76407 0.273818
\(805\) −0.231981 −0.00817626
\(806\) 0.223926 0.00788745
\(807\) −7.58055 −0.266848
\(808\) −8.50211 −0.299103
\(809\) −22.1383 −0.778342 −0.389171 0.921165i \(-0.627239\pi\)
−0.389171 + 0.921165i \(0.627239\pi\)
\(810\) 3.96097 0.139174
\(811\) −37.8564 −1.32932 −0.664659 0.747147i \(-0.731423\pi\)
−0.664659 + 0.747147i \(0.731423\pi\)
\(812\) −8.48928 −0.297915
\(813\) −25.8873 −0.907906
\(814\) −6.25916 −0.219384
\(815\) 3.85089 0.134891
\(816\) 8.90506 0.311740
\(817\) −15.1215 −0.529033
\(818\) −0.0314586 −0.00109992
\(819\) −0.0575976 −0.00201262
\(820\) 0.336010 0.0117340
\(821\) 30.5930 1.06770 0.533851 0.845578i \(-0.320744\pi\)
0.533851 + 0.845578i \(0.320744\pi\)
\(822\) −0.649306 −0.0226472
\(823\) −19.1524 −0.667610 −0.333805 0.942642i \(-0.608333\pi\)
−0.333805 + 0.942642i \(0.608333\pi\)
\(824\) 12.1665 0.423839
\(825\) −10.5418 −0.367017
\(826\) 1.43086 0.0497859
\(827\) 46.0121 1.60000 0.800000 0.600001i \(-0.204833\pi\)
0.800000 + 0.600001i \(0.204833\pi\)
\(828\) 0.420151 0.0146013
\(829\) 45.6645 1.58599 0.792996 0.609226i \(-0.208520\pi\)
0.792996 + 0.609226i \(0.208520\pi\)
\(830\) −0.126254 −0.00438235
\(831\) −18.7724 −0.651206
\(832\) 0.0849041 0.00294352
\(833\) −4.64310 −0.160874
\(834\) 16.8016 0.581790
\(835\) 7.94713 0.275022
\(836\) −4.57526 −0.158239
\(837\) −11.7434 −0.405912
\(838\) −13.8327 −0.477841
\(839\) −14.7372 −0.508784 −0.254392 0.967101i \(-0.581875\pi\)
−0.254392 + 0.967101i \(0.581875\pi\)
\(840\) −0.718376 −0.0247863
\(841\) 43.0679 1.48510
\(842\) 11.1791 0.385259
\(843\) −53.2849 −1.83523
\(844\) 6.31098 0.217233
\(845\) −4.86660 −0.167416
\(846\) 8.71538 0.299641
\(847\) 9.72077 0.334010
\(848\) −9.09566 −0.312346
\(849\) −56.3809 −1.93499
\(850\) −22.5641 −0.773943
\(851\) −3.42745 −0.117492
\(852\) −21.0755 −0.722035
\(853\) 34.4596 1.17987 0.589937 0.807449i \(-0.299152\pi\)
0.589937 + 0.807449i \(0.299152\pi\)
\(854\) 7.69562 0.263339
\(855\) 1.02787 0.0351525
\(856\) −18.5559 −0.634227
\(857\) 33.7112 1.15155 0.575776 0.817608i \(-0.304700\pi\)
0.575776 + 0.817608i \(0.304700\pi\)
\(858\) −0.184175 −0.00628764
\(859\) 1.43061 0.0488118 0.0244059 0.999702i \(-0.492231\pi\)
0.0244059 + 0.999702i \(0.492231\pi\)
\(860\) −1.40016 −0.0477449
\(861\) 1.72051 0.0586349
\(862\) −1.00000 −0.0340601
\(863\) −26.1745 −0.890990 −0.445495 0.895284i \(-0.646972\pi\)
−0.445495 + 0.895284i \(0.646972\pi\)
\(864\) −4.45265 −0.151482
\(865\) −1.30095 −0.0442337
\(866\) −12.5297 −0.425775
\(867\) −8.74263 −0.296915
\(868\) 2.63740 0.0895191
\(869\) 3.83701 0.130162
\(870\) 6.09850 0.206758
\(871\) −0.343708 −0.0116461
\(872\) −12.8769 −0.436067
\(873\) −3.50749 −0.118710
\(874\) −2.50536 −0.0847451
\(875\) 3.69307 0.124848
\(876\) −0.0517326 −0.00174788
\(877\) 7.68450 0.259487 0.129744 0.991548i \(-0.458585\pi\)
0.129744 + 0.991548i \(0.458585\pi\)
\(878\) −16.1550 −0.545204
\(879\) −25.0663 −0.845464
\(880\) −0.423641 −0.0142809
\(881\) 33.8698 1.14110 0.570551 0.821262i \(-0.306730\pi\)
0.570551 + 0.821262i \(0.306730\pi\)
\(882\) −0.678384 −0.0228424
\(883\) −31.0495 −1.04490 −0.522450 0.852670i \(-0.674982\pi\)
−0.522450 + 0.852670i \(0.674982\pi\)
\(884\) −0.394218 −0.0132590
\(885\) −1.02789 −0.0345523
\(886\) −20.8897 −0.701803
\(887\) −13.6669 −0.458891 −0.229445 0.973322i \(-0.573691\pi\)
−0.229445 + 0.973322i \(0.573691\pi\)
\(888\) −10.6138 −0.356175
\(889\) 1.16750 0.0391566
\(890\) 1.48956 0.0499301
\(891\) 11.9606 0.400695
\(892\) 5.62649 0.188389
\(893\) −51.9698 −1.73910
\(894\) −2.48386 −0.0830729
\(895\) −3.22554 −0.107818
\(896\) 1.00000 0.0334077
\(897\) −0.100853 −0.00336737
\(898\) 11.4910 0.383459
\(899\) −22.3896 −0.746735
\(900\) −3.29675 −0.109892
\(901\) 42.2321 1.40696
\(902\) 1.01462 0.0337832
\(903\) −7.16938 −0.238582
\(904\) −5.48435 −0.182407
\(905\) −6.88246 −0.228781
\(906\) −40.2102 −1.33589
\(907\) 15.5681 0.516931 0.258466 0.966020i \(-0.416783\pi\)
0.258466 + 0.966020i \(0.416783\pi\)
\(908\) 18.9786 0.629828
\(909\) 5.76770 0.191303
\(910\) 0.0318018 0.00105422
\(911\) 19.8186 0.656618 0.328309 0.944570i \(-0.393521\pi\)
0.328309 + 0.944570i \(0.393521\pi\)
\(912\) −7.75835 −0.256905
\(913\) −0.381239 −0.0126172
\(914\) 3.51310 0.116203
\(915\) −5.52835 −0.182762
\(916\) 11.8209 0.390574
\(917\) 17.0004 0.561402
\(918\) 20.6741 0.682348
\(919\) −41.9862 −1.38500 −0.692498 0.721419i \(-0.743490\pi\)
−0.692498 + 0.721419i \(0.743490\pi\)
\(920\) −0.231981 −0.00764819
\(921\) 17.5223 0.577378
\(922\) −14.4346 −0.475378
\(923\) 0.932993 0.0307098
\(924\) −2.16922 −0.0713620
\(925\) 26.8938 0.884262
\(926\) −23.4921 −0.771997
\(927\) −8.25355 −0.271082
\(928\) −8.48928 −0.278674
\(929\) 24.4665 0.802721 0.401361 0.915920i \(-0.368537\pi\)
0.401361 + 0.915920i \(0.368537\pi\)
\(930\) −1.89464 −0.0621278
\(931\) 4.04521 0.132576
\(932\) 27.5762 0.903287
\(933\) −21.3109 −0.697688
\(934\) −23.6821 −0.774904
\(935\) 1.96701 0.0643280
\(936\) −0.0575976 −0.00188264
\(937\) −24.4087 −0.797396 −0.398698 0.917082i \(-0.630538\pi\)
−0.398698 + 0.917082i \(0.630538\pi\)
\(938\) −4.04819 −0.132178
\(939\) −10.8684 −0.354677
\(940\) −4.81209 −0.156953
\(941\) −45.8036 −1.49315 −0.746577 0.665299i \(-0.768304\pi\)
−0.746577 + 0.665299i \(0.768304\pi\)
\(942\) 4.58102 0.149258
\(943\) 0.555596 0.0180927
\(944\) 1.43086 0.0465705
\(945\) −1.66779 −0.0542533
\(946\) −4.22793 −0.137462
\(947\) 41.6781 1.35436 0.677178 0.735819i \(-0.263203\pi\)
0.677178 + 0.735819i \(0.263203\pi\)
\(948\) 6.50649 0.211321
\(949\) 0.00229015 7.43415e−5 0
\(950\) 19.6585 0.637806
\(951\) −1.51081 −0.0489915
\(952\) −4.64310 −0.150484
\(953\) −57.2421 −1.85425 −0.927127 0.374746i \(-0.877730\pi\)
−0.927127 + 0.374746i \(0.877730\pi\)
\(954\) 6.17036 0.199773
\(955\) −2.03916 −0.0659856
\(956\) −6.76335 −0.218742
\(957\) 18.4151 0.595276
\(958\) −14.7311 −0.475940
\(959\) 0.338549 0.0109323
\(960\) −0.718376 −0.0231855
\(961\) −24.0441 −0.775617
\(962\) 0.469862 0.0151490
\(963\) 12.5880 0.405643
\(964\) −19.1051 −0.615334
\(965\) −3.58555 −0.115423
\(966\) −1.18784 −0.0382181
\(967\) 15.4385 0.496468 0.248234 0.968700i \(-0.420150\pi\)
0.248234 + 0.968700i \(0.420150\pi\)
\(968\) 9.72077 0.312437
\(969\) 36.0228 1.15722
\(970\) 1.93662 0.0621810
\(971\) 35.5013 1.13929 0.569646 0.821890i \(-0.307080\pi\)
0.569646 + 0.821890i \(0.307080\pi\)
\(972\) 6.92385 0.222083
\(973\) −8.76034 −0.280844
\(974\) 26.0270 0.833959
\(975\) 0.791347 0.0253434
\(976\) 7.69562 0.246331
\(977\) −34.5771 −1.10622 −0.553110 0.833108i \(-0.686559\pi\)
−0.553110 + 0.833108i \(0.686559\pi\)
\(978\) 19.7181 0.630517
\(979\) 4.49789 0.143753
\(980\) 0.374562 0.0119649
\(981\) 8.73548 0.278903
\(982\) 12.4349 0.396814
\(983\) 33.1448 1.05716 0.528578 0.848885i \(-0.322726\pi\)
0.528578 + 0.848885i \(0.322726\pi\)
\(984\) 1.72051 0.0548479
\(985\) −7.01781 −0.223606
\(986\) 39.4166 1.25528
\(987\) −24.6399 −0.784297
\(988\) 0.343455 0.0109267
\(989\) −2.31517 −0.0736181
\(990\) 0.287391 0.00913389
\(991\) 15.6202 0.496191 0.248096 0.968736i \(-0.420195\pi\)
0.248096 + 0.968736i \(0.420195\pi\)
\(992\) 2.63740 0.0837374
\(993\) −29.9251 −0.949644
\(994\) 10.9888 0.348543
\(995\) 4.12234 0.130687
\(996\) −0.646474 −0.0204843
\(997\) 17.2903 0.547589 0.273795 0.961788i \(-0.411721\pi\)
0.273795 + 0.961788i \(0.411721\pi\)
\(998\) −35.7961 −1.13311
\(999\) −24.6411 −0.779611
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 \(a_p\))