Properties

Label 6041.2.a.f.1.19
Level 6041
Weight 2
Character 6041.1
Self dual Yes
Analytic conductor 48.238
Analytic rank 0
Dimension 132
CM No

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Newspace parameters

Level: \( N \) = \( 6041 = 7 \cdot 863 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6041.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.2376278611\)
Analytic rank: \(0\)
Dimension: \(132\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
Character \(\chi\) = 6041.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.23793 q^{2}\) \(+1.90424 q^{3}\) \(+3.00834 q^{4}\) \(+4.23440 q^{5}\) \(-4.26157 q^{6}\) \(+1.00000 q^{7}\) \(-2.25659 q^{8}\) \(+0.626144 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.23793 q^{2}\) \(+1.90424 q^{3}\) \(+3.00834 q^{4}\) \(+4.23440 q^{5}\) \(-4.26157 q^{6}\) \(+1.00000 q^{7}\) \(-2.25659 q^{8}\) \(+0.626144 q^{9}\) \(-9.47631 q^{10}\) \(-0.780283 q^{11}\) \(+5.72861 q^{12}\) \(-5.45043 q^{13}\) \(-2.23793 q^{14}\) \(+8.06334 q^{15}\) \(-0.966582 q^{16}\) \(+1.79938 q^{17}\) \(-1.40127 q^{18}\) \(-4.44901 q^{19}\) \(+12.7385 q^{20}\) \(+1.90424 q^{21}\) \(+1.74622 q^{22}\) \(+7.54904 q^{23}\) \(-4.29710 q^{24}\) \(+12.9302 q^{25}\) \(+12.1977 q^{26}\) \(-4.52040 q^{27}\) \(+3.00834 q^{28}\) \(+4.65814 q^{29}\) \(-18.0452 q^{30}\) \(+9.66318 q^{31}\) \(+6.67632 q^{32}\) \(-1.48585 q^{33}\) \(-4.02690 q^{34}\) \(+4.23440 q^{35}\) \(+1.88365 q^{36}\) \(-2.02034 q^{37}\) \(+9.95657 q^{38}\) \(-10.3790 q^{39}\) \(-9.55531 q^{40}\) \(+9.44210 q^{41}\) \(-4.26157 q^{42}\) \(-8.07255 q^{43}\) \(-2.34736 q^{44}\) \(+2.65135 q^{45}\) \(-16.8942 q^{46}\) \(+8.51500 q^{47}\) \(-1.84061 q^{48}\) \(+1.00000 q^{49}\) \(-28.9369 q^{50}\) \(+3.42646 q^{51}\) \(-16.3967 q^{52}\) \(-11.9054 q^{53}\) \(+10.1163 q^{54}\) \(-3.30404 q^{55}\) \(-2.25659 q^{56}\) \(-8.47199 q^{57}\) \(-10.4246 q^{58}\) \(+8.64103 q^{59}\) \(+24.2572 q^{60}\) \(-4.55315 q^{61}\) \(-21.6255 q^{62}\) \(+0.626144 q^{63}\) \(-13.0080 q^{64}\) \(-23.0793 q^{65}\) \(+3.32523 q^{66}\) \(-4.69394 q^{67}\) \(+5.41315 q^{68}\) \(+14.3752 q^{69}\) \(-9.47631 q^{70}\) \(+14.4213 q^{71}\) \(-1.41295 q^{72}\) \(+8.77726 q^{73}\) \(+4.52139 q^{74}\) \(+24.6222 q^{75}\) \(-13.3841 q^{76}\) \(-0.780283 q^{77}\) \(+23.2274 q^{78}\) \(-6.49617 q^{79}\) \(-4.09290 q^{80}\) \(-10.4864 q^{81}\) \(-21.1308 q^{82}\) \(-0.00279464 q^{83}\) \(+5.72861 q^{84}\) \(+7.61932 q^{85}\) \(+18.0658 q^{86}\) \(+8.87023 q^{87}\) \(+1.76078 q^{88}\) \(+8.85786 q^{89}\) \(-5.93353 q^{90}\) \(-5.45043 q^{91}\) \(+22.7101 q^{92}\) \(+18.4011 q^{93}\) \(-19.0560 q^{94}\) \(-18.8389 q^{95}\) \(+12.7133 q^{96}\) \(+5.10013 q^{97}\) \(-2.23793 q^{98}\) \(-0.488570 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(132q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 174q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 16q^{6} \) \(\mathstrut +\mathstrut 132q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 178q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(132q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 174q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 16q^{6} \) \(\mathstrut +\mathstrut 132q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 178q^{9} \) \(\mathstrut +\mathstrut 22q^{10} \) \(\mathstrut +\mathstrut 32q^{11} \) \(\mathstrut +\mathstrut 30q^{12} \) \(\mathstrut +\mathstrut 16q^{13} \) \(\mathstrut +\mathstrut 8q^{14} \) \(\mathstrut +\mathstrut 59q^{15} \) \(\mathstrut +\mathstrut 254q^{16} \) \(\mathstrut +\mathstrut 11q^{17} \) \(\mathstrut +\mathstrut 33q^{18} \) \(\mathstrut +\mathstrut 40q^{19} \) \(\mathstrut +\mathstrut 4q^{20} \) \(\mathstrut +\mathstrut 10q^{21} \) \(\mathstrut +\mathstrut 66q^{22} \) \(\mathstrut +\mathstrut 62q^{23} \) \(\mathstrut +\mathstrut 36q^{24} \) \(\mathstrut +\mathstrut 235q^{25} \) \(\mathstrut +\mathstrut 25q^{26} \) \(\mathstrut +\mathstrut 37q^{27} \) \(\mathstrut +\mathstrut 174q^{28} \) \(\mathstrut +\mathstrut 28q^{29} \) \(\mathstrut +\mathstrut 45q^{30} \) \(\mathstrut +\mathstrut 121q^{31} \) \(\mathstrut +\mathstrut 53q^{32} \) \(\mathstrut -\mathstrut 13q^{33} \) \(\mathstrut +\mathstrut 44q^{34} \) \(\mathstrut +\mathstrut 11q^{35} \) \(\mathstrut +\mathstrut 274q^{36} \) \(\mathstrut +\mathstrut 61q^{37} \) \(\mathstrut -\mathstrut 28q^{38} \) \(\mathstrut +\mathstrut 114q^{39} \) \(\mathstrut +\mathstrut 32q^{40} \) \(\mathstrut -\mathstrut q^{41} \) \(\mathstrut +\mathstrut 16q^{42} \) \(\mathstrut +\mathstrut 105q^{43} \) \(\mathstrut +\mathstrut 54q^{44} \) \(\mathstrut +\mathstrut 29q^{45} \) \(\mathstrut +\mathstrut 104q^{46} \) \(\mathstrut +\mathstrut 33q^{47} \) \(\mathstrut +\mathstrut 16q^{48} \) \(\mathstrut +\mathstrut 132q^{49} \) \(\mathstrut -\mathstrut 14q^{50} \) \(\mathstrut +\mathstrut 53q^{51} \) \(\mathstrut -\mathstrut 11q^{52} \) \(\mathstrut +\mathstrut 48q^{53} \) \(\mathstrut +\mathstrut 11q^{54} \) \(\mathstrut +\mathstrut 118q^{55} \) \(\mathstrut +\mathstrut 30q^{56} \) \(\mathstrut +\mathstrut 93q^{57} \) \(\mathstrut +\mathstrut 87q^{58} \) \(\mathstrut +\mathstrut 12q^{59} \) \(\mathstrut +\mathstrut 41q^{60} \) \(\mathstrut +\mathstrut 54q^{61} \) \(\mathstrut -\mathstrut 28q^{62} \) \(\mathstrut +\mathstrut 178q^{63} \) \(\mathstrut +\mathstrut 376q^{64} \) \(\mathstrut +\mathstrut 22q^{65} \) \(\mathstrut +\mathstrut 6q^{66} \) \(\mathstrut +\mathstrut 123q^{67} \) \(\mathstrut -\mathstrut 47q^{68} \) \(\mathstrut +\mathstrut 58q^{69} \) \(\mathstrut +\mathstrut 22q^{70} \) \(\mathstrut +\mathstrut 108q^{71} \) \(\mathstrut +\mathstrut 97q^{72} \) \(\mathstrut +\mathstrut q^{73} \) \(\mathstrut -\mathstrut 10q^{74} \) \(\mathstrut +\mathstrut 23q^{75} \) \(\mathstrut +\mathstrut 71q^{76} \) \(\mathstrut +\mathstrut 32q^{77} \) \(\mathstrut +\mathstrut 5q^{78} \) \(\mathstrut +\mathstrut 204q^{79} \) \(\mathstrut -\mathstrut 10q^{80} \) \(\mathstrut +\mathstrut 296q^{81} \) \(\mathstrut +\mathstrut 80q^{82} \) \(\mathstrut -\mathstrut 10q^{83} \) \(\mathstrut +\mathstrut 30q^{84} \) \(\mathstrut +\mathstrut 94q^{85} \) \(\mathstrut +\mathstrut 48q^{86} \) \(\mathstrut +\mathstrut 4q^{87} \) \(\mathstrut +\mathstrut 155q^{88} \) \(\mathstrut +\mathstrut q^{89} \) \(\mathstrut -\mathstrut 66q^{90} \) \(\mathstrut +\mathstrut 16q^{91} \) \(\mathstrut +\mathstrut 49q^{92} \) \(\mathstrut +\mathstrut 90q^{93} \) \(\mathstrut +\mathstrut 79q^{94} \) \(\mathstrut +\mathstrut 100q^{95} \) \(\mathstrut +\mathstrut q^{96} \) \(\mathstrut +\mathstrut 18q^{97} \) \(\mathstrut +\mathstrut 8q^{98} \) \(\mathstrut +\mathstrut 96q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.23793 −1.58246 −0.791228 0.611521i \(-0.790558\pi\)
−0.791228 + 0.611521i \(0.790558\pi\)
\(3\) 1.90424 1.09942 0.549708 0.835357i \(-0.314739\pi\)
0.549708 + 0.835357i \(0.314739\pi\)
\(4\) 3.00834 1.50417
\(5\) 4.23440 1.89368 0.946842 0.321700i \(-0.104254\pi\)
0.946842 + 0.321700i \(0.104254\pi\)
\(6\) −4.26157 −1.73978
\(7\) 1.00000 0.377964
\(8\) −2.25659 −0.797825
\(9\) 0.626144 0.208715
\(10\) −9.47631 −2.99667
\(11\) −0.780283 −0.235264 −0.117632 0.993057i \(-0.537530\pi\)
−0.117632 + 0.993057i \(0.537530\pi\)
\(12\) 5.72861 1.65371
\(13\) −5.45043 −1.51168 −0.755839 0.654757i \(-0.772771\pi\)
−0.755839 + 0.654757i \(0.772771\pi\)
\(14\) −2.23793 −0.598112
\(15\) 8.06334 2.08195
\(16\) −0.966582 −0.241645
\(17\) 1.79938 0.436414 0.218207 0.975902i \(-0.429979\pi\)
0.218207 + 0.975902i \(0.429979\pi\)
\(18\) −1.40127 −0.330282
\(19\) −4.44901 −1.02067 −0.510336 0.859975i \(-0.670479\pi\)
−0.510336 + 0.859975i \(0.670479\pi\)
\(20\) 12.7385 2.84842
\(21\) 1.90424 0.415540
\(22\) 1.74622 0.372296
\(23\) 7.54904 1.57408 0.787042 0.616900i \(-0.211612\pi\)
0.787042 + 0.616900i \(0.211612\pi\)
\(24\) −4.29710 −0.877141
\(25\) 12.9302 2.58604
\(26\) 12.1977 2.39216
\(27\) −4.52040 −0.869951
\(28\) 3.00834 0.568522
\(29\) 4.65814 0.864994 0.432497 0.901635i \(-0.357633\pi\)
0.432497 + 0.901635i \(0.357633\pi\)
\(30\) −18.0452 −3.29459
\(31\) 9.66318 1.73556 0.867780 0.496949i \(-0.165546\pi\)
0.867780 + 0.496949i \(0.165546\pi\)
\(32\) 6.67632 1.18022
\(33\) −1.48585 −0.258653
\(34\) −4.02690 −0.690607
\(35\) 4.23440 0.715745
\(36\) 1.88365 0.313942
\(37\) −2.02034 −0.332143 −0.166071 0.986114i \(-0.553108\pi\)
−0.166071 + 0.986114i \(0.553108\pi\)
\(38\) 9.95657 1.61517
\(39\) −10.3790 −1.66196
\(40\) −9.55531 −1.51083
\(41\) 9.44210 1.47461 0.737304 0.675561i \(-0.236099\pi\)
0.737304 + 0.675561i \(0.236099\pi\)
\(42\) −4.26157 −0.657574
\(43\) −8.07255 −1.23105 −0.615526 0.788117i \(-0.711056\pi\)
−0.615526 + 0.788117i \(0.711056\pi\)
\(44\) −2.34736 −0.353877
\(45\) 2.65135 0.395240
\(46\) −16.8942 −2.49092
\(47\) 8.51500 1.24204 0.621020 0.783794i \(-0.286718\pi\)
0.621020 + 0.783794i \(0.286718\pi\)
\(48\) −1.84061 −0.265669
\(49\) 1.00000 0.142857
\(50\) −28.9369 −4.09229
\(51\) 3.42646 0.479801
\(52\) −16.3967 −2.27382
\(53\) −11.9054 −1.63534 −0.817668 0.575691i \(-0.804733\pi\)
−0.817668 + 0.575691i \(0.804733\pi\)
\(54\) 10.1163 1.37666
\(55\) −3.30404 −0.445516
\(56\) −2.25659 −0.301549
\(57\) −8.47199 −1.12214
\(58\) −10.4246 −1.36882
\(59\) 8.64103 1.12497 0.562483 0.826809i \(-0.309846\pi\)
0.562483 + 0.826809i \(0.309846\pi\)
\(60\) 24.2572 3.13160
\(61\) −4.55315 −0.582971 −0.291485 0.956575i \(-0.594149\pi\)
−0.291485 + 0.956575i \(0.594149\pi\)
\(62\) −21.6255 −2.74645
\(63\) 0.626144 0.0788867
\(64\) −13.0080 −1.62600
\(65\) −23.0793 −2.86264
\(66\) 3.32523 0.409308
\(67\) −4.69394 −0.573455 −0.286728 0.958012i \(-0.592568\pi\)
−0.286728 + 0.958012i \(0.592568\pi\)
\(68\) 5.41315 0.656441
\(69\) 14.3752 1.73057
\(70\) −9.47631 −1.13264
\(71\) 14.4213 1.71150 0.855748 0.517393i \(-0.173097\pi\)
0.855748 + 0.517393i \(0.173097\pi\)
\(72\) −1.41295 −0.166518
\(73\) 8.77726 1.02730 0.513650 0.858000i \(-0.328293\pi\)
0.513650 + 0.858000i \(0.328293\pi\)
\(74\) 4.52139 0.525601
\(75\) 24.6222 2.84313
\(76\) −13.3841 −1.53526
\(77\) −0.780283 −0.0889215
\(78\) 23.2274 2.62998
\(79\) −6.49617 −0.730876 −0.365438 0.930836i \(-0.619081\pi\)
−0.365438 + 0.930836i \(0.619081\pi\)
\(80\) −4.09290 −0.457600
\(81\) −10.4864 −1.16515
\(82\) −21.1308 −2.33350
\(83\) −0.00279464 −0.000306752 0 −0.000153376 1.00000i \(-0.500049\pi\)
−0.000153376 1.00000i \(0.500049\pi\)
\(84\) 5.72861 0.625042
\(85\) 7.61932 0.826431
\(86\) 18.0658 1.94809
\(87\) 8.87023 0.950988
\(88\) 1.76078 0.187700
\(89\) 8.85786 0.938931 0.469466 0.882951i \(-0.344447\pi\)
0.469466 + 0.882951i \(0.344447\pi\)
\(90\) −5.93353 −0.625449
\(91\) −5.45043 −0.571361
\(92\) 22.7101 2.36769
\(93\) 18.4011 1.90810
\(94\) −19.0560 −1.96548
\(95\) −18.8389 −1.93283
\(96\) 12.7133 1.29755
\(97\) 5.10013 0.517840 0.258920 0.965899i \(-0.416633\pi\)
0.258920 + 0.965899i \(0.416633\pi\)
\(98\) −2.23793 −0.226065
\(99\) −0.488570 −0.0491031
\(100\) 38.8984 3.88984
\(101\) 7.80750 0.776875 0.388438 0.921475i \(-0.373015\pi\)
0.388438 + 0.921475i \(0.373015\pi\)
\(102\) −7.66819 −0.759264
\(103\) −6.10831 −0.601870 −0.300935 0.953645i \(-0.597299\pi\)
−0.300935 + 0.953645i \(0.597299\pi\)
\(104\) 12.2994 1.20605
\(105\) 8.06334 0.786901
\(106\) 26.6435 2.58785
\(107\) −15.0486 −1.45481 −0.727404 0.686210i \(-0.759273\pi\)
−0.727404 + 0.686210i \(0.759273\pi\)
\(108\) −13.5989 −1.30855
\(109\) 8.87387 0.849963 0.424981 0.905202i \(-0.360281\pi\)
0.424981 + 0.905202i \(0.360281\pi\)
\(110\) 7.39421 0.705010
\(111\) −3.84723 −0.365163
\(112\) −0.966582 −0.0913334
\(113\) −8.23910 −0.775069 −0.387534 0.921855i \(-0.626673\pi\)
−0.387534 + 0.921855i \(0.626673\pi\)
\(114\) 18.9597 1.77574
\(115\) 31.9657 2.98082
\(116\) 14.0132 1.30110
\(117\) −3.41276 −0.315509
\(118\) −19.3380 −1.78021
\(119\) 1.79938 0.164949
\(120\) −18.1956 −1.66103
\(121\) −10.3912 −0.944651
\(122\) 10.1896 0.922526
\(123\) 17.9801 1.62121
\(124\) 29.0701 2.61057
\(125\) 33.5796 3.00345
\(126\) −1.40127 −0.124835
\(127\) −0.0938159 −0.00832482 −0.00416241 0.999991i \(-0.501325\pi\)
−0.00416241 + 0.999991i \(0.501325\pi\)
\(128\) 15.7583 1.39285
\(129\) −15.3721 −1.35344
\(130\) 51.6500 4.53000
\(131\) 9.13967 0.798537 0.399268 0.916834i \(-0.369264\pi\)
0.399268 + 0.916834i \(0.369264\pi\)
\(132\) −4.46994 −0.389058
\(133\) −4.44901 −0.385778
\(134\) 10.5047 0.907468
\(135\) −19.1412 −1.64741
\(136\) −4.06047 −0.348182
\(137\) 6.41396 0.547981 0.273991 0.961732i \(-0.411656\pi\)
0.273991 + 0.961732i \(0.411656\pi\)
\(138\) −32.1707 −2.73855
\(139\) −17.9791 −1.52497 −0.762483 0.647008i \(-0.776020\pi\)
−0.762483 + 0.647008i \(0.776020\pi\)
\(140\) 12.7385 1.07660
\(141\) 16.2146 1.36552
\(142\) −32.2739 −2.70837
\(143\) 4.25288 0.355644
\(144\) −0.605219 −0.0504350
\(145\) 19.7244 1.63803
\(146\) −19.6429 −1.62566
\(147\) 1.90424 0.157059
\(148\) −6.07788 −0.499599
\(149\) −17.0364 −1.39568 −0.697838 0.716256i \(-0.745854\pi\)
−0.697838 + 0.716256i \(0.745854\pi\)
\(150\) −55.1028 −4.49913
\(151\) 19.4012 1.57884 0.789422 0.613850i \(-0.210380\pi\)
0.789422 + 0.613850i \(0.210380\pi\)
\(152\) 10.0396 0.814318
\(153\) 1.12667 0.0910861
\(154\) 1.74622 0.140714
\(155\) 40.9178 3.28660
\(156\) −31.2234 −2.49987
\(157\) 16.4556 1.31330 0.656649 0.754196i \(-0.271973\pi\)
0.656649 + 0.754196i \(0.271973\pi\)
\(158\) 14.5380 1.15658
\(159\) −22.6708 −1.79791
\(160\) 28.2703 2.23496
\(161\) 7.54904 0.594948
\(162\) 23.4678 1.84380
\(163\) 16.3744 1.28254 0.641269 0.767316i \(-0.278408\pi\)
0.641269 + 0.767316i \(0.278408\pi\)
\(164\) 28.4050 2.21806
\(165\) −6.29169 −0.489807
\(166\) 0.00625422 0.000485421 0
\(167\) −8.56460 −0.662748 −0.331374 0.943499i \(-0.607512\pi\)
−0.331374 + 0.943499i \(0.607512\pi\)
\(168\) −4.29710 −0.331528
\(169\) 16.7072 1.28517
\(170\) −17.0515 −1.30779
\(171\) −2.78572 −0.213029
\(172\) −24.2849 −1.85171
\(173\) 7.37599 0.560786 0.280393 0.959885i \(-0.409535\pi\)
0.280393 + 0.959885i \(0.409535\pi\)
\(174\) −19.8510 −1.50490
\(175\) 12.9302 0.977430
\(176\) 0.754208 0.0568505
\(177\) 16.4546 1.23681
\(178\) −19.8233 −1.48582
\(179\) 16.4120 1.22669 0.613346 0.789815i \(-0.289823\pi\)
0.613346 + 0.789815i \(0.289823\pi\)
\(180\) 7.97615 0.594507
\(181\) −17.4423 −1.29648 −0.648240 0.761436i \(-0.724495\pi\)
−0.648240 + 0.761436i \(0.724495\pi\)
\(182\) 12.1977 0.904153
\(183\) −8.67030 −0.640927
\(184\) −17.0351 −1.25584
\(185\) −8.55496 −0.628973
\(186\) −41.1803 −3.01949
\(187\) −1.40403 −0.102673
\(188\) 25.6160 1.86824
\(189\) −4.52040 −0.328811
\(190\) 42.1602 3.05862
\(191\) −15.0200 −1.08681 −0.543406 0.839470i \(-0.682866\pi\)
−0.543406 + 0.839470i \(0.682866\pi\)
\(192\) −24.7704 −1.78765
\(193\) 10.6285 0.765055 0.382527 0.923944i \(-0.375054\pi\)
0.382527 + 0.923944i \(0.375054\pi\)
\(194\) −11.4137 −0.819459
\(195\) −43.9487 −3.14723
\(196\) 3.00834 0.214881
\(197\) −6.49218 −0.462549 −0.231274 0.972889i \(-0.574289\pi\)
−0.231274 + 0.972889i \(0.574289\pi\)
\(198\) 1.09339 0.0777035
\(199\) −23.2383 −1.64732 −0.823661 0.567083i \(-0.808072\pi\)
−0.823661 + 0.567083i \(0.808072\pi\)
\(200\) −29.1781 −2.06320
\(201\) −8.93840 −0.630466
\(202\) −17.4726 −1.22937
\(203\) 4.65814 0.326937
\(204\) 10.3080 0.721701
\(205\) 39.9817 2.79244
\(206\) 13.6700 0.952433
\(207\) 4.72679 0.328534
\(208\) 5.26829 0.365290
\(209\) 3.47149 0.240128
\(210\) −18.0452 −1.24524
\(211\) −11.2526 −0.774660 −0.387330 0.921941i \(-0.626603\pi\)
−0.387330 + 0.921941i \(0.626603\pi\)
\(212\) −35.8155 −2.45982
\(213\) 27.4617 1.88165
\(214\) 33.6778 2.30217
\(215\) −34.1824 −2.33122
\(216\) 10.2007 0.694069
\(217\) 9.66318 0.655980
\(218\) −19.8591 −1.34503
\(219\) 16.7140 1.12943
\(220\) −9.93965 −0.670131
\(221\) −9.80742 −0.659718
\(222\) 8.60984 0.577854
\(223\) 3.09800 0.207458 0.103729 0.994606i \(-0.466923\pi\)
0.103729 + 0.994606i \(0.466923\pi\)
\(224\) 6.67632 0.446081
\(225\) 8.09616 0.539744
\(226\) 18.4385 1.22651
\(227\) 7.62786 0.506279 0.253139 0.967430i \(-0.418537\pi\)
0.253139 + 0.967430i \(0.418537\pi\)
\(228\) −25.4866 −1.68789
\(229\) 9.39304 0.620709 0.310355 0.950621i \(-0.399552\pi\)
0.310355 + 0.950621i \(0.399552\pi\)
\(230\) −71.5370 −4.71701
\(231\) −1.48585 −0.0977617
\(232\) −10.5115 −0.690114
\(233\) 13.7944 0.903699 0.451849 0.892094i \(-0.350764\pi\)
0.451849 + 0.892094i \(0.350764\pi\)
\(234\) 7.63752 0.499280
\(235\) 36.0560 2.35203
\(236\) 25.9951 1.69214
\(237\) −12.3703 −0.803536
\(238\) −4.02690 −0.261025
\(239\) 16.4955 1.06700 0.533501 0.845799i \(-0.320876\pi\)
0.533501 + 0.845799i \(0.320876\pi\)
\(240\) −7.79388 −0.503093
\(241\) −2.85396 −0.183840 −0.0919198 0.995766i \(-0.529300\pi\)
−0.0919198 + 0.995766i \(0.529300\pi\)
\(242\) 23.2547 1.49487
\(243\) −6.40741 −0.411036
\(244\) −13.6974 −0.876886
\(245\) 4.23440 0.270526
\(246\) −40.2381 −2.56549
\(247\) 24.2490 1.54293
\(248\) −21.8058 −1.38467
\(249\) −0.00532168 −0.000337248 0
\(250\) −75.1489 −4.75283
\(251\) 11.3670 0.717479 0.358739 0.933438i \(-0.383207\pi\)
0.358739 + 0.933438i \(0.383207\pi\)
\(252\) 1.88365 0.118659
\(253\) −5.89039 −0.370326
\(254\) 0.209954 0.0131737
\(255\) 14.5090 0.908591
\(256\) −9.25011 −0.578132
\(257\) 25.7357 1.60535 0.802676 0.596415i \(-0.203409\pi\)
0.802676 + 0.596415i \(0.203409\pi\)
\(258\) 34.4017 2.14176
\(259\) −2.02034 −0.125538
\(260\) −69.4304 −4.30589
\(261\) 2.91667 0.180537
\(262\) −20.4540 −1.26365
\(263\) 12.2326 0.754297 0.377148 0.926153i \(-0.376905\pi\)
0.377148 + 0.926153i \(0.376905\pi\)
\(264\) 3.35295 0.206360
\(265\) −50.4124 −3.09681
\(266\) 9.95657 0.610477
\(267\) 16.8675 1.03228
\(268\) −14.1209 −0.862574
\(269\) 2.04516 0.124696 0.0623478 0.998054i \(-0.480141\pi\)
0.0623478 + 0.998054i \(0.480141\pi\)
\(270\) 42.8367 2.60696
\(271\) 12.5732 0.763770 0.381885 0.924210i \(-0.375275\pi\)
0.381885 + 0.924210i \(0.375275\pi\)
\(272\) −1.73925 −0.105458
\(273\) −10.3790 −0.628163
\(274\) −14.3540 −0.867157
\(275\) −10.0892 −0.608402
\(276\) 43.2455 2.60307
\(277\) −17.7884 −1.06880 −0.534401 0.845231i \(-0.679463\pi\)
−0.534401 + 0.845231i \(0.679463\pi\)
\(278\) 40.2360 2.41319
\(279\) 6.05055 0.362237
\(280\) −9.55531 −0.571039
\(281\) −14.7088 −0.877455 −0.438727 0.898620i \(-0.644571\pi\)
−0.438727 + 0.898620i \(0.644571\pi\)
\(282\) −36.2873 −2.16087
\(283\) 14.1547 0.841409 0.420704 0.907198i \(-0.361783\pi\)
0.420704 + 0.907198i \(0.361783\pi\)
\(284\) 43.3842 2.57438
\(285\) −35.8738 −2.12498
\(286\) −9.51766 −0.562791
\(287\) 9.44210 0.557349
\(288\) 4.18034 0.246329
\(289\) −13.7622 −0.809542
\(290\) −44.1419 −2.59210
\(291\) 9.71189 0.569321
\(292\) 26.4050 1.54523
\(293\) 4.05424 0.236851 0.118426 0.992963i \(-0.462215\pi\)
0.118426 + 0.992963i \(0.462215\pi\)
\(294\) −4.26157 −0.248540
\(295\) 36.5896 2.13033
\(296\) 4.55909 0.264992
\(297\) 3.52719 0.204669
\(298\) 38.1263 2.20860
\(299\) −41.1455 −2.37951
\(300\) 74.0719 4.27655
\(301\) −8.07255 −0.465294
\(302\) −43.4185 −2.49845
\(303\) 14.8674 0.854109
\(304\) 4.30033 0.246641
\(305\) −19.2799 −1.10396
\(306\) −2.52142 −0.144140
\(307\) 5.72061 0.326492 0.163246 0.986585i \(-0.447804\pi\)
0.163246 + 0.986585i \(0.447804\pi\)
\(308\) −2.34736 −0.133753
\(309\) −11.6317 −0.661705
\(310\) −91.5713 −5.20090
\(311\) 2.26376 0.128366 0.0641830 0.997938i \(-0.479556\pi\)
0.0641830 + 0.997938i \(0.479556\pi\)
\(312\) 23.4210 1.32596
\(313\) −8.47529 −0.479052 −0.239526 0.970890i \(-0.576992\pi\)
−0.239526 + 0.970890i \(0.576992\pi\)
\(314\) −36.8265 −2.07824
\(315\) 2.65135 0.149387
\(316\) −19.5427 −1.09936
\(317\) 21.5313 1.20932 0.604658 0.796485i \(-0.293310\pi\)
0.604658 + 0.796485i \(0.293310\pi\)
\(318\) 50.7357 2.84512
\(319\) −3.63467 −0.203502
\(320\) −55.0811 −3.07913
\(321\) −28.6563 −1.59944
\(322\) −16.8942 −0.941479
\(323\) −8.00547 −0.445436
\(324\) −31.5466 −1.75259
\(325\) −70.4751 −3.90926
\(326\) −36.6447 −2.02956
\(327\) 16.8980 0.934462
\(328\) −21.3069 −1.17648
\(329\) 8.51500 0.469447
\(330\) 14.0804 0.775099
\(331\) −17.8763 −0.982568 −0.491284 0.870999i \(-0.663472\pi\)
−0.491284 + 0.870999i \(0.663472\pi\)
\(332\) −0.00840723 −0.000461407 0
\(333\) −1.26503 −0.0693231
\(334\) 19.1670 1.04877
\(335\) −19.8760 −1.08594
\(336\) −1.84061 −0.100413
\(337\) −9.61868 −0.523963 −0.261982 0.965073i \(-0.584376\pi\)
−0.261982 + 0.965073i \(0.584376\pi\)
\(338\) −37.3896 −2.03373
\(339\) −15.6892 −0.852123
\(340\) 22.9215 1.24309
\(341\) −7.54002 −0.408315
\(342\) 6.23425 0.337110
\(343\) 1.00000 0.0539949
\(344\) 18.2164 0.982164
\(345\) 60.8705 3.27716
\(346\) −16.5070 −0.887420
\(347\) −13.9224 −0.747394 −0.373697 0.927551i \(-0.621910\pi\)
−0.373697 + 0.927551i \(0.621910\pi\)
\(348\) 26.6846 1.43045
\(349\) 2.49357 0.133478 0.0667388 0.997770i \(-0.478741\pi\)
0.0667388 + 0.997770i \(0.478741\pi\)
\(350\) −28.9369 −1.54674
\(351\) 24.6381 1.31509
\(352\) −5.20942 −0.277663
\(353\) −16.2742 −0.866188 −0.433094 0.901349i \(-0.642578\pi\)
−0.433094 + 0.901349i \(0.642578\pi\)
\(354\) −36.8243 −1.95719
\(355\) 61.0657 3.24103
\(356\) 26.6474 1.41231
\(357\) 3.42646 0.181348
\(358\) −36.7290 −1.94119
\(359\) −8.64553 −0.456294 −0.228147 0.973627i \(-0.573267\pi\)
−0.228147 + 0.973627i \(0.573267\pi\)
\(360\) −5.98300 −0.315332
\(361\) 0.793661 0.0417717
\(362\) 39.0348 2.05162
\(363\) −19.7873 −1.03856
\(364\) −16.3967 −0.859423
\(365\) 37.1665 1.94538
\(366\) 19.4035 1.01424
\(367\) 17.5346 0.915300 0.457650 0.889132i \(-0.348691\pi\)
0.457650 + 0.889132i \(0.348691\pi\)
\(368\) −7.29676 −0.380370
\(369\) 5.91211 0.307772
\(370\) 19.1454 0.995323
\(371\) −11.9054 −0.618099
\(372\) 55.3566 2.87011
\(373\) 5.93136 0.307114 0.153557 0.988140i \(-0.450927\pi\)
0.153557 + 0.988140i \(0.450927\pi\)
\(374\) 3.14212 0.162475
\(375\) 63.9438 3.30204
\(376\) −19.2149 −0.990931
\(377\) −25.3889 −1.30759
\(378\) 10.1163 0.520329
\(379\) 6.61805 0.339946 0.169973 0.985449i \(-0.445632\pi\)
0.169973 + 0.985449i \(0.445632\pi\)
\(380\) −56.6737 −2.90730
\(381\) −0.178648 −0.00915244
\(382\) 33.6138 1.71983
\(383\) −7.88970 −0.403145 −0.201573 0.979474i \(-0.564605\pi\)
−0.201573 + 0.979474i \(0.564605\pi\)
\(384\) 30.0077 1.53133
\(385\) −3.30404 −0.168389
\(386\) −23.7858 −1.21067
\(387\) −5.05458 −0.256939
\(388\) 15.3429 0.778918
\(389\) −3.94552 −0.200046 −0.100023 0.994985i \(-0.531892\pi\)
−0.100023 + 0.994985i \(0.531892\pi\)
\(390\) 98.3542 4.98036
\(391\) 13.5836 0.686953
\(392\) −2.25659 −0.113975
\(393\) 17.4042 0.877924
\(394\) 14.5291 0.731963
\(395\) −27.5074 −1.38405
\(396\) −1.46978 −0.0738594
\(397\) −30.8311 −1.54737 −0.773685 0.633570i \(-0.781589\pi\)
−0.773685 + 0.633570i \(0.781589\pi\)
\(398\) 52.0058 2.60681
\(399\) −8.47199 −0.424130
\(400\) −12.4981 −0.624904
\(401\) −19.0739 −0.952508 −0.476254 0.879308i \(-0.658006\pi\)
−0.476254 + 0.879308i \(0.658006\pi\)
\(402\) 20.0035 0.997685
\(403\) −52.6685 −2.62361
\(404\) 23.4876 1.16855
\(405\) −44.4036 −2.20643
\(406\) −10.4246 −0.517364
\(407\) 1.57644 0.0781413
\(408\) −7.73212 −0.382797
\(409\) 9.11863 0.450887 0.225444 0.974256i \(-0.427617\pi\)
0.225444 + 0.974256i \(0.427617\pi\)
\(410\) −89.4762 −4.41892
\(411\) 12.2137 0.602459
\(412\) −18.3759 −0.905314
\(413\) 8.64103 0.425197
\(414\) −10.5782 −0.519891
\(415\) −0.0118336 −0.000580891 0
\(416\) −36.3889 −1.78411
\(417\) −34.2366 −1.67657
\(418\) −7.76895 −0.379992
\(419\) −13.7693 −0.672674 −0.336337 0.941742i \(-0.609188\pi\)
−0.336337 + 0.941742i \(0.609188\pi\)
\(420\) 24.2572 1.18363
\(421\) −15.8348 −0.771743 −0.385872 0.922553i \(-0.626099\pi\)
−0.385872 + 0.922553i \(0.626099\pi\)
\(422\) 25.1825 1.22587
\(423\) 5.33162 0.259232
\(424\) 26.8656 1.30471
\(425\) 23.2664 1.12858
\(426\) −61.4574 −2.97762
\(427\) −4.55315 −0.220342
\(428\) −45.2714 −2.18828
\(429\) 8.09852 0.391000
\(430\) 76.4980 3.68906
\(431\) −25.7789 −1.24173 −0.620864 0.783918i \(-0.713218\pi\)
−0.620864 + 0.783918i \(0.713218\pi\)
\(432\) 4.36934 0.210220
\(433\) 39.9652 1.92060 0.960302 0.278964i \(-0.0899909\pi\)
0.960302 + 0.278964i \(0.0899909\pi\)
\(434\) −21.6255 −1.03806
\(435\) 37.5601 1.80087
\(436\) 26.6956 1.27849
\(437\) −33.5857 −1.60662
\(438\) −37.4049 −1.78727
\(439\) 33.6744 1.60719 0.803597 0.595174i \(-0.202917\pi\)
0.803597 + 0.595174i \(0.202917\pi\)
\(440\) 7.45585 0.355444
\(441\) 0.626144 0.0298164
\(442\) 21.9483 1.04398
\(443\) −16.4230 −0.780282 −0.390141 0.920755i \(-0.627574\pi\)
−0.390141 + 0.920755i \(0.627574\pi\)
\(444\) −11.5738 −0.549266
\(445\) 37.5078 1.77804
\(446\) −6.93312 −0.328293
\(447\) −32.4414 −1.53443
\(448\) −13.0080 −0.614570
\(449\) 15.5613 0.734385 0.367193 0.930145i \(-0.380319\pi\)
0.367193 + 0.930145i \(0.380319\pi\)
\(450\) −18.1186 −0.854121
\(451\) −7.36751 −0.346923
\(452\) −24.7860 −1.16583
\(453\) 36.9446 1.73581
\(454\) −17.0706 −0.801164
\(455\) −23.0793 −1.08198
\(456\) 19.1178 0.895274
\(457\) 16.7543 0.783735 0.391868 0.920022i \(-0.371829\pi\)
0.391868 + 0.920022i \(0.371829\pi\)
\(458\) −21.0210 −0.982246
\(459\) −8.13393 −0.379659
\(460\) 96.1636 4.48365
\(461\) 27.6748 1.28894 0.644472 0.764628i \(-0.277077\pi\)
0.644472 + 0.764628i \(0.277077\pi\)
\(462\) 3.32523 0.154704
\(463\) −34.3806 −1.59780 −0.798902 0.601461i \(-0.794585\pi\)
−0.798902 + 0.601461i \(0.794585\pi\)
\(464\) −4.50247 −0.209022
\(465\) 77.9175 3.61334
\(466\) −30.8708 −1.43006
\(467\) 35.6963 1.65183 0.825915 0.563795i \(-0.190659\pi\)
0.825915 + 0.563795i \(0.190659\pi\)
\(468\) −10.2667 −0.474579
\(469\) −4.69394 −0.216746
\(470\) −80.6908 −3.72199
\(471\) 31.3355 1.44386
\(472\) −19.4993 −0.897526
\(473\) 6.29888 0.289623
\(474\) 27.6838 1.27156
\(475\) −57.5265 −2.63950
\(476\) 5.41315 0.248111
\(477\) −7.45451 −0.341318
\(478\) −36.9157 −1.68849
\(479\) 19.0655 0.871124 0.435562 0.900159i \(-0.356550\pi\)
0.435562 + 0.900159i \(0.356550\pi\)
\(480\) 53.8335 2.45715
\(481\) 11.0118 0.502093
\(482\) 6.38696 0.290918
\(483\) 14.3752 0.654095
\(484\) −31.2601 −1.42091
\(485\) 21.5960 0.980625
\(486\) 14.3394 0.650446
\(487\) −28.0193 −1.26968 −0.634838 0.772645i \(-0.718933\pi\)
−0.634838 + 0.772645i \(0.718933\pi\)
\(488\) 10.2746 0.465108
\(489\) 31.1808 1.41004
\(490\) −9.47631 −0.428096
\(491\) 26.7259 1.20612 0.603062 0.797695i \(-0.293947\pi\)
0.603062 + 0.797695i \(0.293947\pi\)
\(492\) 54.0901 2.43857
\(493\) 8.38177 0.377496
\(494\) −54.2676 −2.44162
\(495\) −2.06880 −0.0929858
\(496\) −9.34026 −0.419390
\(497\) 14.4213 0.646885
\(498\) 0.0119096 0.000533680 0
\(499\) 15.9997 0.716246 0.358123 0.933674i \(-0.383417\pi\)
0.358123 + 0.933674i \(0.383417\pi\)
\(500\) 101.019 4.51770
\(501\) −16.3091 −0.728636
\(502\) −25.4386 −1.13538
\(503\) −6.61831 −0.295096 −0.147548 0.989055i \(-0.547138\pi\)
−0.147548 + 0.989055i \(0.547138\pi\)
\(504\) −1.41295 −0.0629378
\(505\) 33.0601 1.47116
\(506\) 13.1823 0.586024
\(507\) 31.8146 1.41294
\(508\) −0.282230 −0.0125219
\(509\) −24.7080 −1.09516 −0.547582 0.836752i \(-0.684452\pi\)
−0.547582 + 0.836752i \(0.684452\pi\)
\(510\) −32.4702 −1.43781
\(511\) 8.77726 0.388283
\(512\) −10.8156 −0.477985
\(513\) 20.1113 0.887935
\(514\) −57.5948 −2.54040
\(515\) −25.8651 −1.13975
\(516\) −46.2445 −2.03580
\(517\) −6.64412 −0.292208
\(518\) 4.52139 0.198659
\(519\) 14.0457 0.616537
\(520\) 52.0806 2.28389
\(521\) 40.3144 1.76621 0.883103 0.469180i \(-0.155450\pi\)
0.883103 + 0.469180i \(0.155450\pi\)
\(522\) −6.52730 −0.285692
\(523\) −10.3379 −0.452046 −0.226023 0.974122i \(-0.572572\pi\)
−0.226023 + 0.974122i \(0.572572\pi\)
\(524\) 27.4952 1.20113
\(525\) 24.6222 1.07460
\(526\) −27.3758 −1.19364
\(527\) 17.3878 0.757423
\(528\) 1.43620 0.0625024
\(529\) 33.9880 1.47774
\(530\) 112.819 4.90056
\(531\) 5.41053 0.234797
\(532\) −13.3841 −0.580275
\(533\) −51.4635 −2.22913
\(534\) −37.7484 −1.63353
\(535\) −63.7221 −2.75494
\(536\) 10.5923 0.457517
\(537\) 31.2525 1.34864
\(538\) −4.57693 −0.197325
\(539\) −0.780283 −0.0336092
\(540\) −57.5832 −2.47799
\(541\) 9.41479 0.404773 0.202387 0.979306i \(-0.435130\pi\)
0.202387 + 0.979306i \(0.435130\pi\)
\(542\) −28.1380 −1.20863
\(543\) −33.2145 −1.42537
\(544\) 12.0133 0.515064
\(545\) 37.5756 1.60956
\(546\) 23.2274 0.994040
\(547\) −1.02258 −0.0437222 −0.0218611 0.999761i \(-0.506959\pi\)
−0.0218611 + 0.999761i \(0.506959\pi\)
\(548\) 19.2953 0.824256
\(549\) −2.85093 −0.121675
\(550\) 22.5790 0.962770
\(551\) −20.7241 −0.882876
\(552\) −32.4389 −1.38069
\(553\) −6.49617 −0.276245
\(554\) 39.8093 1.69133
\(555\) −16.2907 −0.691503
\(556\) −54.0872 −2.29381
\(557\) 5.97881 0.253330 0.126665 0.991946i \(-0.459573\pi\)
0.126665 + 0.991946i \(0.459573\pi\)
\(558\) −13.5407 −0.573224
\(559\) 43.9989 1.86095
\(560\) −4.09290 −0.172957
\(561\) −2.67361 −0.112880
\(562\) 32.9173 1.38853
\(563\) −44.6473 −1.88166 −0.940830 0.338879i \(-0.889952\pi\)
−0.940830 + 0.338879i \(0.889952\pi\)
\(564\) 48.7791 2.05397
\(565\) −34.8877 −1.46774
\(566\) −31.6772 −1.33149
\(567\) −10.4864 −0.440386
\(568\) −32.5430 −1.36547
\(569\) −16.7375 −0.701671 −0.350835 0.936437i \(-0.614102\pi\)
−0.350835 + 0.936437i \(0.614102\pi\)
\(570\) 80.2832 3.36269
\(571\) 1.66825 0.0698140 0.0349070 0.999391i \(-0.488886\pi\)
0.0349070 + 0.999391i \(0.488886\pi\)
\(572\) 12.7941 0.534948
\(573\) −28.6018 −1.19486
\(574\) −21.1308 −0.881981
\(575\) 97.6105 4.07064
\(576\) −8.14488 −0.339370
\(577\) 10.2857 0.428198 0.214099 0.976812i \(-0.431318\pi\)
0.214099 + 0.976812i \(0.431318\pi\)
\(578\) 30.7989 1.28107
\(579\) 20.2392 0.841113
\(580\) 59.3378 2.46387
\(581\) −0.00279464 −0.000115941 0
\(582\) −21.7345 −0.900926
\(583\) 9.28960 0.384736
\(584\) −19.8067 −0.819606
\(585\) −14.4510 −0.597475
\(586\) −9.07311 −0.374807
\(587\) 39.6359 1.63595 0.817975 0.575254i \(-0.195097\pi\)
0.817975 + 0.575254i \(0.195097\pi\)
\(588\) 5.72861 0.236244
\(589\) −42.9916 −1.77144
\(590\) −81.8850 −3.37115
\(591\) −12.3627 −0.508533
\(592\) 1.95283 0.0802608
\(593\) −32.1884 −1.32182 −0.660910 0.750465i \(-0.729830\pi\)
−0.660910 + 0.750465i \(0.729830\pi\)
\(594\) −7.89362 −0.323879
\(595\) 7.61932 0.312361
\(596\) −51.2512 −2.09933
\(597\) −44.2514 −1.81109
\(598\) 92.0809 3.76547
\(599\) −34.0952 −1.39309 −0.696547 0.717512i \(-0.745281\pi\)
−0.696547 + 0.717512i \(0.745281\pi\)
\(600\) −55.5622 −2.26832
\(601\) −9.01124 −0.367576 −0.183788 0.982966i \(-0.558836\pi\)
−0.183788 + 0.982966i \(0.558836\pi\)
\(602\) 18.0658 0.736307
\(603\) −2.93908 −0.119689
\(604\) 58.3653 2.37485
\(605\) −44.0004 −1.78887
\(606\) −33.2722 −1.35159
\(607\) 5.59646 0.227153 0.113577 0.993529i \(-0.463769\pi\)
0.113577 + 0.993529i \(0.463769\pi\)
\(608\) −29.7030 −1.20462
\(609\) 8.87023 0.359440
\(610\) 43.1470 1.74697
\(611\) −46.4105 −1.87757
\(612\) 3.38941 0.137009
\(613\) −4.20474 −0.169828 −0.0849139 0.996388i \(-0.527062\pi\)
−0.0849139 + 0.996388i \(0.527062\pi\)
\(614\) −12.8023 −0.516660
\(615\) 76.1348 3.07005
\(616\) 1.76078 0.0709438
\(617\) −27.9644 −1.12580 −0.562902 0.826524i \(-0.690315\pi\)
−0.562902 + 0.826524i \(0.690315\pi\)
\(618\) 26.0310 1.04712
\(619\) 20.5778 0.827090 0.413545 0.910484i \(-0.364290\pi\)
0.413545 + 0.910484i \(0.364290\pi\)
\(620\) 123.095 4.94360
\(621\) −34.1247 −1.36938
\(622\) −5.06614 −0.203134
\(623\) 8.85786 0.354883
\(624\) 10.0321 0.401606
\(625\) 77.5387 3.10155
\(626\) 18.9671 0.758079
\(627\) 6.61056 0.264000
\(628\) 49.5040 1.97542
\(629\) −3.63537 −0.144952
\(630\) −5.93353 −0.236398
\(631\) 29.9688 1.19304 0.596520 0.802598i \(-0.296550\pi\)
0.596520 + 0.802598i \(0.296550\pi\)
\(632\) 14.6592 0.583111
\(633\) −21.4277 −0.851673
\(634\) −48.1855 −1.91369
\(635\) −0.397255 −0.0157646
\(636\) −68.2015 −2.70436
\(637\) −5.45043 −0.215954
\(638\) 8.13414 0.322034
\(639\) 9.02982 0.357214
\(640\) 66.7272 2.63762
\(641\) −20.3207 −0.802618 −0.401309 0.915943i \(-0.631445\pi\)
−0.401309 + 0.915943i \(0.631445\pi\)
\(642\) 64.1308 2.53104
\(643\) −1.16807 −0.0460644 −0.0230322 0.999735i \(-0.507332\pi\)
−0.0230322 + 0.999735i \(0.507332\pi\)
\(644\) 22.7101 0.894901
\(645\) −65.0917 −2.56298
\(646\) 17.9157 0.704883
\(647\) −42.6597 −1.67712 −0.838562 0.544806i \(-0.816603\pi\)
−0.838562 + 0.544806i \(0.816603\pi\)
\(648\) 23.6634 0.929588
\(649\) −6.74245 −0.264664
\(650\) 157.718 6.18623
\(651\) 18.4011 0.721194
\(652\) 49.2596 1.92915
\(653\) 10.4011 0.407025 0.203513 0.979072i \(-0.434764\pi\)
0.203513 + 0.979072i \(0.434764\pi\)
\(654\) −37.8166 −1.47875
\(655\) 38.7011 1.51218
\(656\) −9.12656 −0.356332
\(657\) 5.49583 0.214413
\(658\) −19.0560 −0.742880
\(659\) −3.73389 −0.145452 −0.0727258 0.997352i \(-0.523170\pi\)
−0.0727258 + 0.997352i \(0.523170\pi\)
\(660\) −18.9275 −0.736753
\(661\) −28.1953 −1.09667 −0.548335 0.836259i \(-0.684738\pi\)
−0.548335 + 0.836259i \(0.684738\pi\)
\(662\) 40.0058 1.55487
\(663\) −18.6757 −0.725304
\(664\) 0.00630636 0.000244734 0
\(665\) −18.8389 −0.730541
\(666\) 2.83104 0.109701
\(667\) 35.1645 1.36157
\(668\) −25.7652 −0.996885
\(669\) 5.89935 0.228082
\(670\) 44.4812 1.71846
\(671\) 3.55274 0.137152
\(672\) 12.7133 0.490428
\(673\) −16.0766 −0.619707 −0.309853 0.950784i \(-0.600280\pi\)
−0.309853 + 0.950784i \(0.600280\pi\)
\(674\) 21.5260 0.829149
\(675\) −58.4496 −2.24973
\(676\) 50.2610 1.93311
\(677\) −45.9928 −1.76765 −0.883824 0.467819i \(-0.845040\pi\)
−0.883824 + 0.467819i \(0.845040\pi\)
\(678\) 35.1115 1.34845
\(679\) 5.10013 0.195725
\(680\) −17.1937 −0.659347
\(681\) 14.5253 0.556611
\(682\) 16.8741 0.646141
\(683\) 11.2252 0.429519 0.214759 0.976667i \(-0.431103\pi\)
0.214759 + 0.976667i \(0.431103\pi\)
\(684\) −8.38038 −0.320432
\(685\) 27.1593 1.03770
\(686\) −2.23793 −0.0854446
\(687\) 17.8866 0.682418
\(688\) 7.80278 0.297478
\(689\) 64.8897 2.47210
\(690\) −136.224 −5.18596
\(691\) 19.0803 0.725850 0.362925 0.931818i \(-0.381778\pi\)
0.362925 + 0.931818i \(0.381778\pi\)
\(692\) 22.1895 0.843517
\(693\) −0.488570 −0.0185592
\(694\) 31.1574 1.18272
\(695\) −76.1308 −2.88780
\(696\) −20.0165 −0.758722
\(697\) 16.9900 0.643540
\(698\) −5.58043 −0.211222
\(699\) 26.2678 0.993540
\(700\) 38.8984 1.47022
\(701\) 12.2294 0.461897 0.230948 0.972966i \(-0.425817\pi\)
0.230948 + 0.972966i \(0.425817\pi\)
\(702\) −55.1385 −2.08107
\(703\) 8.98853 0.339009
\(704\) 10.1499 0.382539
\(705\) 68.6593 2.58586
\(706\) 36.4205 1.37070
\(707\) 7.80750 0.293631
\(708\) 49.5011 1.86036
\(709\) 18.4448 0.692710 0.346355 0.938103i \(-0.387419\pi\)
0.346355 + 0.938103i \(0.387419\pi\)
\(710\) −136.661 −5.12879
\(711\) −4.06754 −0.152544
\(712\) −19.9885 −0.749103
\(713\) 72.9478 2.73191
\(714\) −7.66819 −0.286975
\(715\) 18.0084 0.673477
\(716\) 49.3729 1.84515
\(717\) 31.4114 1.17308
\(718\) 19.3481 0.722065
\(719\) −7.97734 −0.297505 −0.148752 0.988874i \(-0.547526\pi\)
−0.148752 + 0.988874i \(0.547526\pi\)
\(720\) −2.56274 −0.0955078
\(721\) −6.10831 −0.227486
\(722\) −1.77616 −0.0661018
\(723\) −5.43463 −0.202116
\(724\) −52.4725 −1.95012
\(725\) 60.2306 2.23691
\(726\) 44.2826 1.64348
\(727\) −0.553970 −0.0205456 −0.0102728 0.999947i \(-0.503270\pi\)
−0.0102728 + 0.999947i \(0.503270\pi\)
\(728\) 12.2994 0.455846
\(729\) 19.2578 0.713254
\(730\) −83.1760 −3.07848
\(731\) −14.5256 −0.537249
\(732\) −26.0832 −0.964062
\(733\) −42.8652 −1.58326 −0.791632 0.610998i \(-0.790768\pi\)
−0.791632 + 0.610998i \(0.790768\pi\)
\(734\) −39.2413 −1.44842
\(735\) 8.06334 0.297421
\(736\) 50.3998 1.85776
\(737\) 3.66260 0.134914
\(738\) −13.2309 −0.487036
\(739\) −8.92735 −0.328398 −0.164199 0.986427i \(-0.552504\pi\)
−0.164199 + 0.986427i \(0.552504\pi\)
\(740\) −25.7362 −0.946082
\(741\) 46.1760 1.69632
\(742\) 26.6435 0.978114
\(743\) 6.35803 0.233253 0.116627 0.993176i \(-0.462792\pi\)
0.116627 + 0.993176i \(0.462792\pi\)
\(744\) −41.5236 −1.52233
\(745\) −72.1390 −2.64297
\(746\) −13.2740 −0.485995
\(747\) −0.00174985 −6.40236e−5 0
\(748\) −4.22379 −0.154437
\(749\) −15.0486 −0.549866
\(750\) −143.102 −5.22534
\(751\) 12.2653 0.447566 0.223783 0.974639i \(-0.428159\pi\)
0.223783 + 0.974639i \(0.428159\pi\)
\(752\) −8.23045 −0.300133
\(753\) 21.6455 0.788808
\(754\) 56.8185 2.06921
\(755\) 82.1524 2.98983
\(756\) −13.5989 −0.494587
\(757\) −0.000105885 0 −3.84844e−6 0 −1.92422e−6 1.00000i \(-0.500001\pi\)
−1.92422e−6 1.00000i \(0.500001\pi\)
\(758\) −14.8107 −0.537950
\(759\) −11.2167 −0.407142
\(760\) 42.5117 1.54206
\(761\) 41.4132 1.50123 0.750613 0.660742i \(-0.229758\pi\)
0.750613 + 0.660742i \(0.229758\pi\)
\(762\) 0.399803 0.0144833
\(763\) 8.87387 0.321256
\(764\) −45.1853 −1.63475
\(765\) 4.77079 0.172488
\(766\) 17.6566 0.637959
\(767\) −47.0973 −1.70059
\(768\) −17.6145 −0.635607
\(769\) −39.5973 −1.42792 −0.713958 0.700188i \(-0.753099\pi\)
−0.713958 + 0.700188i \(0.753099\pi\)
\(770\) 7.39421 0.266469
\(771\) 49.0071 1.76495
\(772\) 31.9741 1.15077
\(773\) −22.6307 −0.813969 −0.406984 0.913435i \(-0.633420\pi\)
−0.406984 + 0.913435i \(0.633420\pi\)
\(774\) 11.3118 0.406594
\(775\) 124.947 4.48822
\(776\) −11.5089 −0.413145
\(777\) −3.84723 −0.138019
\(778\) 8.82980 0.316563
\(779\) −42.0080 −1.50509
\(780\) −132.212 −4.73397
\(781\) −11.2527 −0.402654
\(782\) −30.3992 −1.08707
\(783\) −21.0566 −0.752503
\(784\) −0.966582 −0.0345208
\(785\) 69.6796 2.48697
\(786\) −38.9493 −1.38928
\(787\) 23.0942 0.823220 0.411610 0.911360i \(-0.364967\pi\)
0.411610 + 0.911360i \(0.364967\pi\)
\(788\) −19.5307 −0.695751
\(789\) 23.2939 0.829286
\(790\) 61.5597 2.19019
\(791\) −8.23910 −0.292949
\(792\) 1.10250 0.0391757
\(793\) 24.8166 0.881264
\(794\) 68.9980 2.44865
\(795\) −95.9974 −3.40468
\(796\) −69.9087 −2.47785
\(797\) −14.3777 −0.509284 −0.254642 0.967035i \(-0.581958\pi\)
−0.254642 + 0.967035i \(0.581958\pi\)
\(798\) 18.9597 0.671168
\(799\) 15.3217 0.542045
\(800\) 86.3261 3.05209
\(801\) 5.54630 0.195969
\(802\) 42.6862 1.50730
\(803\) −6.84875 −0.241687
\(804\) −26.8897 −0.948327
\(805\) 31.9657 1.12664
\(806\) 117.869 4.15174
\(807\) 3.89448 0.137092
\(808\) −17.6183 −0.619810
\(809\) 10.5974 0.372583 0.186292 0.982494i \(-0.440353\pi\)
0.186292 + 0.982494i \(0.440353\pi\)
\(810\) 99.3721 3.49158
\(811\) −35.0589 −1.23108 −0.615542 0.788104i \(-0.711063\pi\)
−0.615542 + 0.788104i \(0.711063\pi\)
\(812\) 14.0132 0.491769
\(813\) 23.9425 0.839700
\(814\) −3.52797 −0.123655
\(815\) 69.3356 2.42872
\(816\) −3.31196 −0.115942
\(817\) 35.9148 1.25650
\(818\) −20.4069 −0.713510
\(819\) −3.41276 −0.119251
\(820\) 120.278 4.20030
\(821\) 16.0098 0.558747 0.279374 0.960182i \(-0.409873\pi\)
0.279374 + 0.960182i \(0.409873\pi\)
\(822\) −27.3335 −0.953365
\(823\) −30.7692 −1.07255 −0.536273 0.844044i \(-0.680168\pi\)
−0.536273 + 0.844044i \(0.680168\pi\)
\(824\) 13.7840 0.480187
\(825\) −19.2123 −0.668887
\(826\) −19.3380 −0.672856
\(827\) −28.7589 −1.00004 −0.500022 0.866013i \(-0.666675\pi\)
−0.500022 + 0.866013i \(0.666675\pi\)
\(828\) 14.2198 0.494171
\(829\) −25.3858 −0.881686 −0.440843 0.897584i \(-0.645320\pi\)
−0.440843 + 0.897584i \(0.645320\pi\)
\(830\) 0.0264829 0.000919235 0
\(831\) −33.8735 −1.17506
\(832\) 70.8992 2.45799
\(833\) 1.79938 0.0623449
\(834\) 76.6191 2.65310
\(835\) −36.2660 −1.25504
\(836\) 10.4434 0.361193
\(837\) −43.6815 −1.50985
\(838\) 30.8148 1.06448
\(839\) −2.51518 −0.0868336 −0.0434168 0.999057i \(-0.513824\pi\)
−0.0434168 + 0.999057i \(0.513824\pi\)
\(840\) −18.1956 −0.627809
\(841\) −7.30175 −0.251785
\(842\) 35.4373 1.22125
\(843\) −28.0092 −0.964688
\(844\) −33.8516 −1.16522
\(845\) 70.7451 2.43371
\(846\) −11.9318 −0.410224
\(847\) −10.3912 −0.357044
\(848\) 11.5076 0.395171
\(849\) 26.9540 0.925058
\(850\) −52.0685 −1.78593
\(851\) −15.2517 −0.522820
\(852\) 82.6141 2.83031
\(853\) −39.1245 −1.33960 −0.669799 0.742542i \(-0.733620\pi\)
−0.669799 + 0.742542i \(0.733620\pi\)
\(854\) 10.1896 0.348682
\(855\) −11.7959 −0.403410
\(856\) 33.9586 1.16068
\(857\) −17.9728 −0.613938 −0.306969 0.951719i \(-0.599315\pi\)
−0.306969 + 0.951719i \(0.599315\pi\)
\(858\) −18.1239 −0.618741
\(859\) −10.6897 −0.364727 −0.182363 0.983231i \(-0.558375\pi\)
−0.182363 + 0.983231i \(0.558375\pi\)
\(860\) −102.832 −3.50655
\(861\) 17.9801 0.612759
\(862\) 57.6915 1.96498
\(863\) −1.00000 −0.0340404
\(864\) −30.1797 −1.02673
\(865\) 31.2329 1.06195
\(866\) −89.4393 −3.03927
\(867\) −26.2066 −0.890024
\(868\) 29.0701 0.986704
\(869\) 5.06885 0.171949
\(870\) −84.0570 −2.84980
\(871\) 25.5840 0.866880
\(872\) −20.0247 −0.678121
\(873\) 3.19342 0.108081
\(874\) 75.1625 2.54241
\(875\) 33.5796 1.13520
\(876\) 50.2815 1.69885
\(877\) 21.2618 0.717959 0.358979 0.933345i \(-0.383125\pi\)
0.358979 + 0.933345i \(0.383125\pi\)
\(878\) −75.3611 −2.54331
\(879\) 7.72026 0.260398
\(880\) 3.19362 0.107657
\(881\) 43.4081 1.46246 0.731229 0.682133i \(-0.238947\pi\)
0.731229 + 0.682133i \(0.238947\pi\)
\(882\) −1.40127 −0.0471831
\(883\) −39.5040 −1.32942 −0.664708 0.747103i \(-0.731444\pi\)
−0.664708 + 0.747103i \(0.731444\pi\)
\(884\) −29.5040 −0.992327
\(885\) 69.6755 2.34212
\(886\) 36.7537 1.23476
\(887\) 4.54739 0.152686 0.0763432 0.997082i \(-0.475676\pi\)
0.0763432 + 0.997082i \(0.475676\pi\)
\(888\) 8.68162 0.291336
\(889\) −0.0938159 −0.00314649
\(890\) −83.9398 −2.81367
\(891\) 8.18235 0.274119
\(892\) 9.31984 0.312051
\(893\) −37.8833 −1.26772
\(894\) 72.6017 2.42816
\(895\) 69.4951 2.32297
\(896\) 15.7583 0.526449
\(897\) −78.3511 −2.61607
\(898\) −34.8252 −1.16213
\(899\) 45.0124 1.50125
\(900\) 24.3560 0.811866
\(901\) −21.4224 −0.713684
\(902\) 16.4880 0.548990
\(903\) −15.3721 −0.511551
\(904\) 18.5923 0.618369
\(905\) −73.8580 −2.45512
\(906\) −82.6794 −2.74684
\(907\) 36.2902 1.20500 0.602499 0.798120i \(-0.294172\pi\)
0.602499 + 0.798120i \(0.294172\pi\)
\(908\) 22.9472 0.761528
\(909\) 4.88862 0.162145
\(910\) 51.6500 1.71218
\(911\) −15.0322 −0.498038 −0.249019 0.968499i \(-0.580108\pi\)
−0.249019 + 0.968499i \(0.580108\pi\)
\(912\) 8.18887 0.271161
\(913\) 0.00218061 7.21678e−5 0
\(914\) −37.4951 −1.24023
\(915\) −36.7136 −1.21371
\(916\) 28.2574 0.933652
\(917\) 9.13967 0.301818
\(918\) 18.2032 0.600794
\(919\) 4.76330 0.157127 0.0785634 0.996909i \(-0.474967\pi\)
0.0785634 + 0.996909i \(0.474967\pi\)
\(920\) −72.1334 −2.37817
\(921\) 10.8934 0.358951
\(922\) −61.9343 −2.03970
\(923\) −78.6024 −2.58723
\(924\) −4.46994 −0.147050
\(925\) −26.1234 −0.858933
\(926\) 76.9415 2.52845
\(927\) −3.82469 −0.125619
\(928\) 31.0992 1.02088
\(929\) 29.4215 0.965287 0.482643 0.875817i \(-0.339677\pi\)
0.482643 + 0.875817i \(0.339677\pi\)
\(930\) −174.374 −5.71795
\(931\) −4.44901 −0.145810
\(932\) 41.4981 1.35931
\(933\) 4.31075 0.141128
\(934\) −79.8860 −2.61395
\(935\) −5.94523 −0.194430
\(936\) 7.70119 0.251721
\(937\) −46.3376 −1.51378 −0.756892 0.653540i \(-0.773283\pi\)
−0.756892 + 0.653540i \(0.773283\pi\)
\(938\) 10.5047 0.342991
\(939\) −16.1390 −0.526677
\(940\) 108.469 3.53785
\(941\) −25.4229 −0.828762 −0.414381 0.910104i \(-0.636002\pi\)
−0.414381 + 0.910104i \(0.636002\pi\)
\(942\) −70.1266 −2.28485
\(943\) 71.2788 2.32116
\(944\) −8.35226 −0.271843
\(945\) −19.1412 −0.622663
\(946\) −14.0965 −0.458315
\(947\) 19.6320 0.637955 0.318978 0.947762i \(-0.396660\pi\)
0.318978 + 0.947762i \(0.396660\pi\)
\(948\) −37.2140 −1.20865
\(949\) −47.8399 −1.55295
\(950\) 128.740 4.17689
\(951\) 41.0008 1.32954
\(952\) −4.06047 −0.131601
\(953\) −23.8559 −0.772767 −0.386384 0.922338i \(-0.626276\pi\)
−0.386384 + 0.922338i \(0.626276\pi\)
\(954\) 16.6827 0.540122
\(955\) −63.6009 −2.05808
\(956\) 49.6239 1.60495
\(957\) −6.92129 −0.223734
\(958\) −42.6672 −1.37852
\(959\) 6.41396 0.207117
\(960\) −104.888 −3.38524
\(961\) 62.3771 2.01217
\(962\) −24.6436 −0.794540
\(963\) −9.42262 −0.303640
\(964\) −8.58567 −0.276526
\(965\) 45.0053 1.44877
\(966\) −32.1707 −1.03508
\(967\) 7.92873 0.254971 0.127485 0.991840i \(-0.459309\pi\)
0.127485 + 0.991840i \(0.459309\pi\)
\(968\) 23.4486 0.753666
\(969\) −15.2444 −0.489719
\(970\) −48.3304 −1.55180
\(971\) 40.4870 1.29929 0.649644 0.760239i \(-0.274918\pi\)
0.649644 + 0.760239i \(0.274918\pi\)
\(972\) −19.2757 −0.618267
\(973\) −17.9791 −0.576383
\(974\) 62.7053 2.00921
\(975\) −134.202 −4.29790
\(976\) 4.40099 0.140872
\(977\) −59.1027 −1.89086 −0.945432 0.325820i \(-0.894360\pi\)
−0.945432 + 0.325820i \(0.894360\pi\)
\(978\) −69.7804 −2.23133
\(979\) −6.91164 −0.220897
\(980\) 12.7385 0.406917
\(981\) 5.55632 0.177400
\(982\) −59.8108 −1.90864
\(983\) −6.75717 −0.215520 −0.107760 0.994177i \(-0.534368\pi\)
−0.107760 + 0.994177i \(0.534368\pi\)
\(984\) −40.5736 −1.29344
\(985\) −27.4905 −0.875921
\(986\) −18.7578 −0.597371
\(987\) 16.2146 0.516118
\(988\) 72.9492 2.32082
\(989\) −60.9400 −1.93778
\(990\) 4.62984 0.147146
\(991\) −17.6290 −0.560002 −0.280001 0.960000i \(-0.590335\pi\)
−0.280001 + 0.960000i \(0.590335\pi\)
\(992\) 64.5145 2.04834
\(993\) −34.0408 −1.08025
\(994\) −32.2739 −1.02367
\(995\) −98.4005 −3.11950
\(996\) −0.0160094 −0.000507278 0
\(997\) 31.1846 0.987625 0.493813 0.869568i \(-0.335603\pi\)
0.493813 + 0.869568i \(0.335603\pi\)
\(998\) −35.8063 −1.13343
\(999\) 9.13277 0.288948
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 \(a_p\))