Properties

Label 6041.2.a.f.1.6
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 1.6
Character \(\chi\) = 6041.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.65744 q^{2}\) \(+2.58260 q^{3}\) \(+5.06196 q^{4}\) \(+1.09780 q^{5}\) \(-6.86308 q^{6}\) \(+1.00000 q^{7}\) \(-8.13696 q^{8}\) \(+3.66980 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.65744 q^{2}\) \(+2.58260 q^{3}\) \(+5.06196 q^{4}\) \(+1.09780 q^{5}\) \(-6.86308 q^{6}\) \(+1.00000 q^{7}\) \(-8.13696 q^{8}\) \(+3.66980 q^{9}\) \(-2.91732 q^{10}\) \(-0.201709 q^{11}\) \(+13.0730 q^{12}\) \(+6.89294 q^{13}\) \(-2.65744 q^{14}\) \(+2.83516 q^{15}\) \(+11.4995 q^{16}\) \(-3.73459 q^{17}\) \(-9.75226 q^{18}\) \(-0.944972 q^{19}\) \(+5.55700 q^{20}\) \(+2.58260 q^{21}\) \(+0.536029 q^{22}\) \(+9.13542 q^{23}\) \(-21.0145 q^{24}\) \(-3.79484 q^{25}\) \(-18.3175 q^{26}\) \(+1.72982 q^{27}\) \(+5.06196 q^{28}\) \(+1.11926 q^{29}\) \(-7.53426 q^{30}\) \(-3.58061 q^{31}\) \(-14.2853 q^{32}\) \(-0.520934 q^{33}\) \(+9.92444 q^{34}\) \(+1.09780 q^{35}\) \(+18.5764 q^{36}\) \(-0.763262 q^{37}\) \(+2.51120 q^{38}\) \(+17.8017 q^{39}\) \(-8.93273 q^{40}\) \(+2.89507 q^{41}\) \(-6.86308 q^{42}\) \(+2.11050 q^{43}\) \(-1.02104 q^{44}\) \(+4.02869 q^{45}\) \(-24.2768 q^{46}\) \(+1.83346 q^{47}\) \(+29.6986 q^{48}\) \(+1.00000 q^{49}\) \(+10.0845 q^{50}\) \(-9.64495 q^{51}\) \(+34.8918 q^{52}\) \(-4.73158 q^{53}\) \(-4.59689 q^{54}\) \(-0.221436 q^{55}\) \(-8.13696 q^{56}\) \(-2.44048 q^{57}\) \(-2.97437 q^{58}\) \(+12.8856 q^{59}\) \(+14.3515 q^{60}\) \(+5.93740 q^{61}\) \(+9.51523 q^{62}\) \(+3.66980 q^{63}\) \(+14.9633 q^{64}\) \(+7.56704 q^{65}\) \(+1.38435 q^{66}\) \(+12.7010 q^{67}\) \(-18.9044 q^{68}\) \(+23.5931 q^{69}\) \(-2.91732 q^{70}\) \(-10.9366 q^{71}\) \(-29.8610 q^{72}\) \(+7.90022 q^{73}\) \(+2.02832 q^{74}\) \(-9.80055 q^{75}\) \(-4.78341 q^{76}\) \(-0.201709 q^{77}\) \(-47.3068 q^{78}\) \(+1.83529 q^{79}\) \(+12.6241 q^{80}\) \(-6.54197 q^{81}\) \(-7.69347 q^{82}\) \(-15.4099 q^{83}\) \(+13.0730 q^{84}\) \(-4.09982 q^{85}\) \(-5.60851 q^{86}\) \(+2.89061 q^{87}\) \(+1.64130 q^{88}\) \(-4.53745 q^{89}\) \(-10.7060 q^{90}\) \(+6.89294 q^{91}\) \(+46.2431 q^{92}\) \(-9.24726 q^{93}\) \(-4.87231 q^{94}\) \(-1.03739 q^{95}\) \(-36.8932 q^{96}\) \(+3.12512 q^{97}\) \(-2.65744 q^{98}\) \(-0.740233 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(132q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 174q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 16q^{6} \) \(\mathstrut +\mathstrut 132q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 178q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(132q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 174q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 16q^{6} \) \(\mathstrut +\mathstrut 132q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 178q^{9} \) \(\mathstrut +\mathstrut 22q^{10} \) \(\mathstrut +\mathstrut 32q^{11} \) \(\mathstrut +\mathstrut 30q^{12} \) \(\mathstrut +\mathstrut 16q^{13} \) \(\mathstrut +\mathstrut 8q^{14} \) \(\mathstrut +\mathstrut 59q^{15} \) \(\mathstrut +\mathstrut 254q^{16} \) \(\mathstrut +\mathstrut 11q^{17} \) \(\mathstrut +\mathstrut 33q^{18} \) \(\mathstrut +\mathstrut 40q^{19} \) \(\mathstrut +\mathstrut 4q^{20} \) \(\mathstrut +\mathstrut 10q^{21} \) \(\mathstrut +\mathstrut 66q^{22} \) \(\mathstrut +\mathstrut 62q^{23} \) \(\mathstrut +\mathstrut 36q^{24} \) \(\mathstrut +\mathstrut 235q^{25} \) \(\mathstrut +\mathstrut 25q^{26} \) \(\mathstrut +\mathstrut 37q^{27} \) \(\mathstrut +\mathstrut 174q^{28} \) \(\mathstrut +\mathstrut 28q^{29} \) \(\mathstrut +\mathstrut 45q^{30} \) \(\mathstrut +\mathstrut 121q^{31} \) \(\mathstrut +\mathstrut 53q^{32} \) \(\mathstrut -\mathstrut 13q^{33} \) \(\mathstrut +\mathstrut 44q^{34} \) \(\mathstrut +\mathstrut 11q^{35} \) \(\mathstrut +\mathstrut 274q^{36} \) \(\mathstrut +\mathstrut 61q^{37} \) \(\mathstrut -\mathstrut 28q^{38} \) \(\mathstrut +\mathstrut 114q^{39} \) \(\mathstrut +\mathstrut 32q^{40} \) \(\mathstrut -\mathstrut q^{41} \) \(\mathstrut +\mathstrut 16q^{42} \) \(\mathstrut +\mathstrut 105q^{43} \) \(\mathstrut +\mathstrut 54q^{44} \) \(\mathstrut +\mathstrut 29q^{45} \) \(\mathstrut +\mathstrut 104q^{46} \) \(\mathstrut +\mathstrut 33q^{47} \) \(\mathstrut +\mathstrut 16q^{48} \) \(\mathstrut +\mathstrut 132q^{49} \) \(\mathstrut -\mathstrut 14q^{50} \) \(\mathstrut +\mathstrut 53q^{51} \) \(\mathstrut -\mathstrut 11q^{52} \) \(\mathstrut +\mathstrut 48q^{53} \) \(\mathstrut +\mathstrut 11q^{54} \) \(\mathstrut +\mathstrut 118q^{55} \) \(\mathstrut +\mathstrut 30q^{56} \) \(\mathstrut +\mathstrut 93q^{57} \) \(\mathstrut +\mathstrut 87q^{58} \) \(\mathstrut +\mathstrut 12q^{59} \) \(\mathstrut +\mathstrut 41q^{60} \) \(\mathstrut +\mathstrut 54q^{61} \) \(\mathstrut -\mathstrut 28q^{62} \) \(\mathstrut +\mathstrut 178q^{63} \) \(\mathstrut +\mathstrut 376q^{64} \) \(\mathstrut +\mathstrut 22q^{65} \) \(\mathstrut +\mathstrut 6q^{66} \) \(\mathstrut +\mathstrut 123q^{67} \) \(\mathstrut -\mathstrut 47q^{68} \) \(\mathstrut +\mathstrut 58q^{69} \) \(\mathstrut +\mathstrut 22q^{70} \) \(\mathstrut +\mathstrut 108q^{71} \) \(\mathstrut +\mathstrut 97q^{72} \) \(\mathstrut +\mathstrut q^{73} \) \(\mathstrut -\mathstrut 10q^{74} \) \(\mathstrut +\mathstrut 23q^{75} \) \(\mathstrut +\mathstrut 71q^{76} \) \(\mathstrut +\mathstrut 32q^{77} \) \(\mathstrut +\mathstrut 5q^{78} \) \(\mathstrut +\mathstrut 204q^{79} \) \(\mathstrut -\mathstrut 10q^{80} \) \(\mathstrut +\mathstrut 296q^{81} \) \(\mathstrut +\mathstrut 80q^{82} \) \(\mathstrut -\mathstrut 10q^{83} \) \(\mathstrut +\mathstrut 30q^{84} \) \(\mathstrut +\mathstrut 94q^{85} \) \(\mathstrut +\mathstrut 48q^{86} \) \(\mathstrut +\mathstrut 4q^{87} \) \(\mathstrut +\mathstrut 155q^{88} \) \(\mathstrut +\mathstrut q^{89} \) \(\mathstrut -\mathstrut 66q^{90} \) \(\mathstrut +\mathstrut 16q^{91} \) \(\mathstrut +\mathstrut 49q^{92} \) \(\mathstrut +\mathstrut 90q^{93} \) \(\mathstrut +\mathstrut 79q^{94} \) \(\mathstrut +\mathstrut 100q^{95} \) \(\mathstrut +\mathstrut q^{96} \) \(\mathstrut +\mathstrut 18q^{97} \) \(\mathstrut +\mathstrut 8q^{98} \) \(\mathstrut +\mathstrut 96q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.65744 −1.87909 −0.939545 0.342425i \(-0.888752\pi\)
−0.939545 + 0.342425i \(0.888752\pi\)
\(3\) 2.58260 1.49106 0.745531 0.666471i \(-0.232196\pi\)
0.745531 + 0.666471i \(0.232196\pi\)
\(4\) 5.06196 2.53098
\(5\) 1.09780 0.490949 0.245475 0.969403i \(-0.421056\pi\)
0.245475 + 0.969403i \(0.421056\pi\)
\(6\) −6.86308 −2.80184
\(7\) 1.00000 0.377964
\(8\) −8.13696 −2.87685
\(9\) 3.66980 1.22327
\(10\) −2.91732 −0.922538
\(11\) −0.201709 −0.0608176 −0.0304088 0.999538i \(-0.509681\pi\)
−0.0304088 + 0.999538i \(0.509681\pi\)
\(12\) 13.0730 3.77385
\(13\) 6.89294 1.91176 0.955879 0.293761i \(-0.0949070\pi\)
0.955879 + 0.293761i \(0.0949070\pi\)
\(14\) −2.65744 −0.710229
\(15\) 2.83516 0.732036
\(16\) 11.4995 2.87488
\(17\) −3.73459 −0.905772 −0.452886 0.891568i \(-0.649606\pi\)
−0.452886 + 0.891568i \(0.649606\pi\)
\(18\) −9.75226 −2.29863
\(19\) −0.944972 −0.216792 −0.108396 0.994108i \(-0.534571\pi\)
−0.108396 + 0.994108i \(0.534571\pi\)
\(20\) 5.55700 1.24258
\(21\) 2.58260 0.563569
\(22\) 0.536029 0.114282
\(23\) 9.13542 1.90487 0.952433 0.304747i \(-0.0985718\pi\)
0.952433 + 0.304747i \(0.0985718\pi\)
\(24\) −21.0145 −4.28956
\(25\) −3.79484 −0.758969
\(26\) −18.3175 −3.59237
\(27\) 1.72982 0.332905
\(28\) 5.06196 0.956621
\(29\) 1.11926 0.207842 0.103921 0.994586i \(-0.466861\pi\)
0.103921 + 0.994586i \(0.466861\pi\)
\(30\) −7.53426 −1.37556
\(31\) −3.58061 −0.643096 −0.321548 0.946893i \(-0.604203\pi\)
−0.321548 + 0.946893i \(0.604203\pi\)
\(32\) −14.2853 −2.52531
\(33\) −0.520934 −0.0906829
\(34\) 9.92444 1.70203
\(35\) 1.09780 0.185561
\(36\) 18.5764 3.09606
\(37\) −0.763262 −0.125479 −0.0627397 0.998030i \(-0.519984\pi\)
−0.0627397 + 0.998030i \(0.519984\pi\)
\(38\) 2.51120 0.407371
\(39\) 17.8017 2.85055
\(40\) −8.93273 −1.41239
\(41\) 2.89507 0.452134 0.226067 0.974112i \(-0.427413\pi\)
0.226067 + 0.974112i \(0.427413\pi\)
\(42\) −6.86308 −1.05900
\(43\) 2.11050 0.321848 0.160924 0.986967i \(-0.448553\pi\)
0.160924 + 0.986967i \(0.448553\pi\)
\(44\) −1.02104 −0.153928
\(45\) 4.02869 0.600562
\(46\) −24.2768 −3.57942
\(47\) 1.83346 0.267438 0.133719 0.991019i \(-0.457308\pi\)
0.133719 + 0.991019i \(0.457308\pi\)
\(48\) 29.6986 4.28663
\(49\) 1.00000 0.142857
\(50\) 10.0845 1.42617
\(51\) −9.64495 −1.35056
\(52\) 34.8918 4.83862
\(53\) −4.73158 −0.649933 −0.324966 0.945726i \(-0.605353\pi\)
−0.324966 + 0.945726i \(0.605353\pi\)
\(54\) −4.59689 −0.625558
\(55\) −0.221436 −0.0298584
\(56\) −8.13696 −1.08735
\(57\) −2.44048 −0.323250
\(58\) −2.97437 −0.390554
\(59\) 12.8856 1.67756 0.838781 0.544468i \(-0.183269\pi\)
0.838781 + 0.544468i \(0.183269\pi\)
\(60\) 14.3515 1.85277
\(61\) 5.93740 0.760206 0.380103 0.924944i \(-0.375889\pi\)
0.380103 + 0.924944i \(0.375889\pi\)
\(62\) 9.51523 1.20844
\(63\) 3.66980 0.462351
\(64\) 14.9633 1.87041
\(65\) 7.56704 0.938576
\(66\) 1.38435 0.170401
\(67\) 12.7010 1.55167 0.775834 0.630937i \(-0.217329\pi\)
0.775834 + 0.630937i \(0.217329\pi\)
\(68\) −18.9044 −2.29249
\(69\) 23.5931 2.84028
\(70\) −2.91732 −0.348687
\(71\) −10.9366 −1.29794 −0.648969 0.760815i \(-0.724800\pi\)
−0.648969 + 0.760815i \(0.724800\pi\)
\(72\) −29.8610 −3.51916
\(73\) 7.90022 0.924651 0.462326 0.886710i \(-0.347015\pi\)
0.462326 + 0.886710i \(0.347015\pi\)
\(74\) 2.02832 0.235787
\(75\) −9.80055 −1.13167
\(76\) −4.78341 −0.548695
\(77\) −0.201709 −0.0229869
\(78\) −47.3068 −5.35644
\(79\) 1.83529 0.206486 0.103243 0.994656i \(-0.467078\pi\)
0.103243 + 0.994656i \(0.467078\pi\)
\(80\) 12.6241 1.41142
\(81\) −6.54197 −0.726885
\(82\) −7.69347 −0.849601
\(83\) −15.4099 −1.69145 −0.845727 0.533615i \(-0.820833\pi\)
−0.845727 + 0.533615i \(0.820833\pi\)
\(84\) 13.0730 1.42638
\(85\) −4.09982 −0.444688
\(86\) −5.60851 −0.604781
\(87\) 2.89061 0.309906
\(88\) 1.64130 0.174963
\(89\) −4.53745 −0.480969 −0.240485 0.970653i \(-0.577306\pi\)
−0.240485 + 0.970653i \(0.577306\pi\)
\(90\) −10.7060 −1.12851
\(91\) 6.89294 0.722576
\(92\) 46.2431 4.82118
\(93\) −9.24726 −0.958896
\(94\) −4.87231 −0.502540
\(95\) −1.03739 −0.106434
\(96\) −36.8932 −3.76540
\(97\) 3.12512 0.317308 0.158654 0.987334i \(-0.449285\pi\)
0.158654 + 0.987334i \(0.449285\pi\)
\(98\) −2.65744 −0.268441
\(99\) −0.740233 −0.0743962
\(100\) −19.2093 −1.92093
\(101\) 6.23661 0.620566 0.310283 0.950644i \(-0.399576\pi\)
0.310283 + 0.950644i \(0.399576\pi\)
\(102\) 25.6308 2.53783
\(103\) 19.7729 1.94829 0.974143 0.225933i \(-0.0725429\pi\)
0.974143 + 0.225933i \(0.0725429\pi\)
\(104\) −56.0876 −5.49984
\(105\) 2.83516 0.276684
\(106\) 12.5739 1.22128
\(107\) −15.1879 −1.46827 −0.734137 0.679002i \(-0.762413\pi\)
−0.734137 + 0.679002i \(0.762413\pi\)
\(108\) 8.75630 0.842575
\(109\) 2.73020 0.261506 0.130753 0.991415i \(-0.458261\pi\)
0.130753 + 0.991415i \(0.458261\pi\)
\(110\) 0.588451 0.0561066
\(111\) −1.97120 −0.187098
\(112\) 11.4995 1.08660
\(113\) 7.22884 0.680032 0.340016 0.940420i \(-0.389568\pi\)
0.340016 + 0.940420i \(0.389568\pi\)
\(114\) 6.48542 0.607415
\(115\) 10.0288 0.935193
\(116\) 5.66567 0.526044
\(117\) 25.2957 2.33859
\(118\) −34.2427 −3.15229
\(119\) −3.73459 −0.342350
\(120\) −23.0696 −2.10596
\(121\) −10.9593 −0.996301
\(122\) −15.7782 −1.42850
\(123\) 7.47680 0.674160
\(124\) −18.1249 −1.62766
\(125\) −9.65495 −0.863565
\(126\) −9.75226 −0.868800
\(127\) 9.33001 0.827904 0.413952 0.910299i \(-0.364148\pi\)
0.413952 + 0.910299i \(0.364148\pi\)
\(128\) −11.1932 −0.989352
\(129\) 5.45056 0.479895
\(130\) −20.1089 −1.76367
\(131\) −12.8113 −1.11933 −0.559663 0.828720i \(-0.689070\pi\)
−0.559663 + 0.828720i \(0.689070\pi\)
\(132\) −2.63695 −0.229517
\(133\) −0.944972 −0.0819395
\(134\) −33.7520 −2.91573
\(135\) 1.89899 0.163439
\(136\) 30.3882 2.60577
\(137\) 9.59042 0.819365 0.409682 0.912228i \(-0.365640\pi\)
0.409682 + 0.912228i \(0.365640\pi\)
\(138\) −62.6971 −5.33713
\(139\) 7.32695 0.621464 0.310732 0.950498i \(-0.399426\pi\)
0.310732 + 0.950498i \(0.399426\pi\)
\(140\) 5.55700 0.469652
\(141\) 4.73509 0.398767
\(142\) 29.0634 2.43894
\(143\) −1.39037 −0.116269
\(144\) 42.2010 3.51675
\(145\) 1.22872 0.102040
\(146\) −20.9943 −1.73750
\(147\) 2.58260 0.213009
\(148\) −3.86360 −0.317586
\(149\) −16.1427 −1.32246 −0.661232 0.750181i \(-0.729966\pi\)
−0.661232 + 0.750181i \(0.729966\pi\)
\(150\) 26.0443 2.12651
\(151\) −8.66249 −0.704943 −0.352472 0.935823i \(-0.614659\pi\)
−0.352472 + 0.935823i \(0.614659\pi\)
\(152\) 7.68920 0.623677
\(153\) −13.7052 −1.10800
\(154\) 0.536029 0.0431945
\(155\) −3.93078 −0.315728
\(156\) 90.1114 7.21469
\(157\) −13.9430 −1.11278 −0.556388 0.830923i \(-0.687813\pi\)
−0.556388 + 0.830923i \(0.687813\pi\)
\(158\) −4.87717 −0.388007
\(159\) −12.2198 −0.969090
\(160\) −15.6824 −1.23980
\(161\) 9.13542 0.719972
\(162\) 17.3848 1.36588
\(163\) 19.8922 1.55808 0.779038 0.626977i \(-0.215708\pi\)
0.779038 + 0.626977i \(0.215708\pi\)
\(164\) 14.6547 1.14434
\(165\) −0.571879 −0.0445207
\(166\) 40.9508 3.17840
\(167\) −19.3471 −1.49713 −0.748563 0.663063i \(-0.769256\pi\)
−0.748563 + 0.663063i \(0.769256\pi\)
\(168\) −21.0145 −1.62130
\(169\) 34.5126 2.65482
\(170\) 10.8950 0.835610
\(171\) −3.46786 −0.265194
\(172\) 10.6833 0.814591
\(173\) 11.9286 0.906917 0.453459 0.891277i \(-0.350190\pi\)
0.453459 + 0.891277i \(0.350190\pi\)
\(174\) −7.68160 −0.582340
\(175\) −3.79484 −0.286863
\(176\) −2.31956 −0.174844
\(177\) 33.2783 2.50135
\(178\) 12.0580 0.903785
\(179\) 24.0119 1.79473 0.897366 0.441287i \(-0.145478\pi\)
0.897366 + 0.441287i \(0.145478\pi\)
\(180\) 20.3931 1.52001
\(181\) 19.0889 1.41887 0.709433 0.704773i \(-0.248951\pi\)
0.709433 + 0.704773i \(0.248951\pi\)
\(182\) −18.3175 −1.35779
\(183\) 15.3339 1.13351
\(184\) −74.3346 −5.48002
\(185\) −0.837906 −0.0616041
\(186\) 24.5740 1.80185
\(187\) 0.753302 0.0550869
\(188\) 9.28092 0.676881
\(189\) 1.72982 0.125826
\(190\) 2.75679 0.199998
\(191\) −4.94147 −0.357552 −0.178776 0.983890i \(-0.557214\pi\)
−0.178776 + 0.983890i \(0.557214\pi\)
\(192\) 38.6440 2.78889
\(193\) 16.7400 1.20497 0.602487 0.798129i \(-0.294176\pi\)
0.602487 + 0.798129i \(0.294176\pi\)
\(194\) −8.30480 −0.596250
\(195\) 19.5426 1.39948
\(196\) 5.06196 0.361569
\(197\) −15.2947 −1.08970 −0.544851 0.838533i \(-0.683414\pi\)
−0.544851 + 0.838533i \(0.683414\pi\)
\(198\) 1.96712 0.139797
\(199\) 3.44503 0.244212 0.122106 0.992517i \(-0.461035\pi\)
0.122106 + 0.992517i \(0.461035\pi\)
\(200\) 30.8785 2.18344
\(201\) 32.8014 2.31364
\(202\) −16.5734 −1.16610
\(203\) 1.11926 0.0785569
\(204\) −48.8223 −3.41825
\(205\) 3.17820 0.221975
\(206\) −52.5453 −3.66101
\(207\) 33.5252 2.33016
\(208\) 79.2655 5.49608
\(209\) 0.190610 0.0131847
\(210\) −7.53426 −0.519914
\(211\) 3.02911 0.208532 0.104266 0.994549i \(-0.466751\pi\)
0.104266 + 0.994549i \(0.466751\pi\)
\(212\) −23.9511 −1.64497
\(213\) −28.2449 −1.93531
\(214\) 40.3610 2.75902
\(215\) 2.31690 0.158011
\(216\) −14.0755 −0.957717
\(217\) −3.58061 −0.243067
\(218\) −7.25533 −0.491393
\(219\) 20.4031 1.37871
\(220\) −1.12090 −0.0755710
\(221\) −25.7423 −1.73162
\(222\) 5.23833 0.351573
\(223\) −23.7583 −1.59097 −0.795487 0.605971i \(-0.792785\pi\)
−0.795487 + 0.605971i \(0.792785\pi\)
\(224\) −14.2853 −0.954478
\(225\) −13.9263 −0.928421
\(226\) −19.2102 −1.27784
\(227\) 3.07064 0.203805 0.101903 0.994794i \(-0.467507\pi\)
0.101903 + 0.994794i \(0.467507\pi\)
\(228\) −12.3536 −0.818139
\(229\) 10.3733 0.685484 0.342742 0.939430i \(-0.388644\pi\)
0.342742 + 0.939430i \(0.388644\pi\)
\(230\) −26.6510 −1.75731
\(231\) −0.520934 −0.0342749
\(232\) −9.10741 −0.597931
\(233\) 26.6664 1.74697 0.873486 0.486849i \(-0.161854\pi\)
0.873486 + 0.486849i \(0.161854\pi\)
\(234\) −67.2217 −4.39442
\(235\) 2.01277 0.131299
\(236\) 65.2264 4.24588
\(237\) 4.73981 0.307884
\(238\) 9.92444 0.643306
\(239\) 2.85091 0.184410 0.0922049 0.995740i \(-0.470609\pi\)
0.0922049 + 0.995740i \(0.470609\pi\)
\(240\) 32.6030 2.10452
\(241\) 16.6970 1.07555 0.537775 0.843088i \(-0.319265\pi\)
0.537775 + 0.843088i \(0.319265\pi\)
\(242\) 29.1237 1.87214
\(243\) −22.0847 −1.41674
\(244\) 30.0549 1.92407
\(245\) 1.09780 0.0701356
\(246\) −19.8691 −1.26681
\(247\) −6.51364 −0.414453
\(248\) 29.1353 1.85009
\(249\) −39.7975 −2.52206
\(250\) 25.6574 1.62272
\(251\) −12.2581 −0.773723 −0.386861 0.922138i \(-0.626441\pi\)
−0.386861 + 0.922138i \(0.626441\pi\)
\(252\) 18.5764 1.17020
\(253\) −1.84270 −0.115850
\(254\) −24.7939 −1.55571
\(255\) −10.5882 −0.663058
\(256\) −0.181202 −0.0113251
\(257\) 18.7470 1.16940 0.584702 0.811248i \(-0.301211\pi\)
0.584702 + 0.811248i \(0.301211\pi\)
\(258\) −14.4845 −0.901766
\(259\) −0.763262 −0.0474268
\(260\) 38.3041 2.37552
\(261\) 4.10748 0.254246
\(262\) 34.0451 2.10332
\(263\) −4.93348 −0.304212 −0.152106 0.988364i \(-0.548605\pi\)
−0.152106 + 0.988364i \(0.548605\pi\)
\(264\) 4.23882 0.260881
\(265\) −5.19431 −0.319084
\(266\) 2.51120 0.153972
\(267\) −11.7184 −0.717155
\(268\) 64.2918 3.92724
\(269\) −1.78068 −0.108570 −0.0542851 0.998525i \(-0.517288\pi\)
−0.0542851 + 0.998525i \(0.517288\pi\)
\(270\) −5.04645 −0.307117
\(271\) −12.0063 −0.729329 −0.364665 0.931139i \(-0.618816\pi\)
−0.364665 + 0.931139i \(0.618816\pi\)
\(272\) −42.9461 −2.60399
\(273\) 17.8017 1.07741
\(274\) −25.4859 −1.53966
\(275\) 0.765455 0.0461587
\(276\) 119.427 7.18868
\(277\) −7.22540 −0.434132 −0.217066 0.976157i \(-0.569649\pi\)
−0.217066 + 0.976157i \(0.569649\pi\)
\(278\) −19.4709 −1.16779
\(279\) −13.1401 −0.786678
\(280\) −8.93273 −0.533833
\(281\) −9.73464 −0.580720 −0.290360 0.956918i \(-0.593775\pi\)
−0.290360 + 0.956918i \(0.593775\pi\)
\(282\) −12.5832 −0.749319
\(283\) −2.40515 −0.142971 −0.0714856 0.997442i \(-0.522774\pi\)
−0.0714856 + 0.997442i \(0.522774\pi\)
\(284\) −55.3608 −3.28506
\(285\) −2.67915 −0.158699
\(286\) 3.69482 0.218479
\(287\) 2.89507 0.170891
\(288\) −52.4243 −3.08913
\(289\) −3.05281 −0.179577
\(290\) −3.26525 −0.191742
\(291\) 8.07092 0.473126
\(292\) 39.9906 2.34027
\(293\) −6.60931 −0.386120 −0.193060 0.981187i \(-0.561841\pi\)
−0.193060 + 0.981187i \(0.561841\pi\)
\(294\) −6.86308 −0.400263
\(295\) 14.1458 0.823598
\(296\) 6.21063 0.360986
\(297\) −0.348922 −0.0202465
\(298\) 42.8983 2.48503
\(299\) 62.9699 3.64164
\(300\) −49.6100 −2.86423
\(301\) 2.11050 0.121647
\(302\) 23.0200 1.32465
\(303\) 16.1066 0.925302
\(304\) −10.8667 −0.623250
\(305\) 6.51805 0.373223
\(306\) 36.4207 2.08203
\(307\) −30.6581 −1.74975 −0.874875 0.484349i \(-0.839057\pi\)
−0.874875 + 0.484349i \(0.839057\pi\)
\(308\) −1.02104 −0.0581794
\(309\) 51.0655 2.90502
\(310\) 10.4458 0.593281
\(311\) −3.30973 −0.187678 −0.0938388 0.995587i \(-0.529914\pi\)
−0.0938388 + 0.995587i \(0.529914\pi\)
\(312\) −144.852 −8.20061
\(313\) 7.35994 0.416009 0.208004 0.978128i \(-0.433303\pi\)
0.208004 + 0.978128i \(0.433303\pi\)
\(314\) 37.0527 2.09101
\(315\) 4.02869 0.226991
\(316\) 9.29017 0.522613
\(317\) −11.7650 −0.660787 −0.330393 0.943843i \(-0.607181\pi\)
−0.330393 + 0.943843i \(0.607181\pi\)
\(318\) 32.4732 1.82101
\(319\) −0.225766 −0.0126405
\(320\) 16.4266 0.918275
\(321\) −39.2243 −2.18929
\(322\) −24.2768 −1.35289
\(323\) 3.52909 0.196364
\(324\) −33.1152 −1.83973
\(325\) −26.1576 −1.45096
\(326\) −52.8622 −2.92777
\(327\) 7.05100 0.389921
\(328\) −23.5571 −1.30072
\(329\) 1.83346 0.101082
\(330\) 1.51973 0.0836584
\(331\) 18.1959 1.00014 0.500068 0.865986i \(-0.333308\pi\)
0.500068 + 0.865986i \(0.333308\pi\)
\(332\) −78.0042 −4.28104
\(333\) −2.80102 −0.153495
\(334\) 51.4138 2.81324
\(335\) 13.9431 0.761791
\(336\) 29.6986 1.62019
\(337\) 16.9310 0.922290 0.461145 0.887325i \(-0.347439\pi\)
0.461145 + 0.887325i \(0.347439\pi\)
\(338\) −91.7151 −4.98864
\(339\) 18.6692 1.01397
\(340\) −20.7531 −1.12550
\(341\) 0.722242 0.0391116
\(342\) 9.21561 0.498323
\(343\) 1.00000 0.0539949
\(344\) −17.1730 −0.925908
\(345\) 25.9004 1.39443
\(346\) −31.6996 −1.70418
\(347\) −2.89197 −0.155249 −0.0776246 0.996983i \(-0.524734\pi\)
−0.0776246 + 0.996983i \(0.524734\pi\)
\(348\) 14.6321 0.784365
\(349\) −6.48634 −0.347206 −0.173603 0.984816i \(-0.555541\pi\)
−0.173603 + 0.984816i \(0.555541\pi\)
\(350\) 10.0845 0.539042
\(351\) 11.9236 0.636433
\(352\) 2.88148 0.153583
\(353\) 2.63388 0.140187 0.0700936 0.997540i \(-0.477670\pi\)
0.0700936 + 0.997540i \(0.477670\pi\)
\(354\) −88.4349 −4.70026
\(355\) −12.0062 −0.637222
\(356\) −22.9684 −1.21732
\(357\) −9.64495 −0.510465
\(358\) −63.8100 −3.37246
\(359\) −12.7545 −0.673156 −0.336578 0.941656i \(-0.609270\pi\)
−0.336578 + 0.941656i \(0.609270\pi\)
\(360\) −32.7813 −1.72773
\(361\) −18.1070 −0.953001
\(362\) −50.7275 −2.66618
\(363\) −28.3035 −1.48555
\(364\) 34.8918 1.82883
\(365\) 8.67284 0.453957
\(366\) −40.7488 −2.12998
\(367\) −10.0193 −0.523001 −0.261501 0.965203i \(-0.584217\pi\)
−0.261501 + 0.965203i \(0.584217\pi\)
\(368\) 105.053 5.47627
\(369\) 10.6243 0.553081
\(370\) 2.22668 0.115760
\(371\) −4.73158 −0.245652
\(372\) −46.8093 −2.42695
\(373\) −5.03488 −0.260696 −0.130348 0.991468i \(-0.541610\pi\)
−0.130348 + 0.991468i \(0.541610\pi\)
\(374\) −2.00185 −0.103513
\(375\) −24.9348 −1.28763
\(376\) −14.9188 −0.769379
\(377\) 7.71502 0.397344
\(378\) −4.59689 −0.236439
\(379\) −14.4989 −0.744758 −0.372379 0.928081i \(-0.621458\pi\)
−0.372379 + 0.928081i \(0.621458\pi\)
\(380\) −5.25121 −0.269382
\(381\) 24.0956 1.23446
\(382\) 13.1316 0.671873
\(383\) 17.0756 0.872522 0.436261 0.899820i \(-0.356302\pi\)
0.436261 + 0.899820i \(0.356302\pi\)
\(384\) −28.9076 −1.47519
\(385\) −0.221436 −0.0112854
\(386\) −44.4856 −2.26426
\(387\) 7.74510 0.393706
\(388\) 15.8192 0.803100
\(389\) −15.1910 −0.770215 −0.385107 0.922872i \(-0.625836\pi\)
−0.385107 + 0.922872i \(0.625836\pi\)
\(390\) −51.9332 −2.62974
\(391\) −34.1171 −1.72538
\(392\) −8.13696 −0.410979
\(393\) −33.0864 −1.66899
\(394\) 40.6447 2.04765
\(395\) 2.01478 0.101374
\(396\) −3.74703 −0.188295
\(397\) 28.4481 1.42777 0.713885 0.700263i \(-0.246934\pi\)
0.713885 + 0.700263i \(0.246934\pi\)
\(398\) −9.15495 −0.458896
\(399\) −2.44048 −0.122177
\(400\) −43.6389 −2.18194
\(401\) −33.4919 −1.67251 −0.836254 0.548343i \(-0.815259\pi\)
−0.836254 + 0.548343i \(0.815259\pi\)
\(402\) −87.1677 −4.34753
\(403\) −24.6809 −1.22944
\(404\) 31.5695 1.57064
\(405\) −7.18175 −0.356864
\(406\) −2.97437 −0.147616
\(407\) 0.153957 0.00763136
\(408\) 78.4806 3.88537
\(409\) −35.5569 −1.75818 −0.879088 0.476659i \(-0.841848\pi\)
−0.879088 + 0.476659i \(0.841848\pi\)
\(410\) −8.44586 −0.417111
\(411\) 24.7682 1.22172
\(412\) 100.090 4.93107
\(413\) 12.8856 0.634059
\(414\) −89.0910 −4.37858
\(415\) −16.9169 −0.830419
\(416\) −98.4679 −4.82778
\(417\) 18.9225 0.926641
\(418\) −0.506533 −0.0247753
\(419\) 22.1475 1.08198 0.540989 0.841030i \(-0.318050\pi\)
0.540989 + 0.841030i \(0.318050\pi\)
\(420\) 14.3515 0.700281
\(421\) 14.6863 0.715764 0.357882 0.933767i \(-0.383499\pi\)
0.357882 + 0.933767i \(0.383499\pi\)
\(422\) −8.04965 −0.391851
\(423\) 6.72844 0.327148
\(424\) 38.5007 1.86976
\(425\) 14.1722 0.687453
\(426\) 75.0589 3.63662
\(427\) 5.93740 0.287331
\(428\) −76.8808 −3.71617
\(429\) −3.59076 −0.173364
\(430\) −6.15700 −0.296917
\(431\) 12.5056 0.602372 0.301186 0.953565i \(-0.402618\pi\)
0.301186 + 0.953565i \(0.402618\pi\)
\(432\) 19.8922 0.957062
\(433\) −22.4937 −1.08098 −0.540489 0.841351i \(-0.681761\pi\)
−0.540489 + 0.841351i \(0.681761\pi\)
\(434\) 9.51523 0.456746
\(435\) 3.17330 0.152148
\(436\) 13.8202 0.661866
\(437\) −8.63272 −0.412959
\(438\) −54.2199 −2.59073
\(439\) −28.8453 −1.37671 −0.688355 0.725374i \(-0.741667\pi\)
−0.688355 + 0.725374i \(0.741667\pi\)
\(440\) 1.80181 0.0858981
\(441\) 3.66980 0.174752
\(442\) 68.4086 3.25386
\(443\) 14.5488 0.691236 0.345618 0.938375i \(-0.387669\pi\)
0.345618 + 0.938375i \(0.387669\pi\)
\(444\) −9.97812 −0.473540
\(445\) −4.98120 −0.236132
\(446\) 63.1361 2.98958
\(447\) −41.6902 −1.97188
\(448\) 14.9633 0.706947
\(449\) −37.5508 −1.77213 −0.886066 0.463558i \(-0.846573\pi\)
−0.886066 + 0.463558i \(0.846573\pi\)
\(450\) 37.0083 1.74459
\(451\) −0.583963 −0.0274977
\(452\) 36.5921 1.72115
\(453\) −22.3717 −1.05111
\(454\) −8.16002 −0.382969
\(455\) 7.56704 0.354749
\(456\) 19.8581 0.929941
\(457\) −9.27077 −0.433668 −0.216834 0.976208i \(-0.569573\pi\)
−0.216834 + 0.976208i \(0.569573\pi\)
\(458\) −27.5663 −1.28809
\(459\) −6.46019 −0.301536
\(460\) 50.7655 2.36696
\(461\) 6.04166 0.281388 0.140694 0.990053i \(-0.455067\pi\)
0.140694 + 0.990053i \(0.455067\pi\)
\(462\) 1.38435 0.0644057
\(463\) 29.4709 1.36963 0.684814 0.728718i \(-0.259884\pi\)
0.684814 + 0.728718i \(0.259884\pi\)
\(464\) 12.8710 0.597521
\(465\) −10.1516 −0.470770
\(466\) −70.8642 −3.28272
\(467\) 5.00460 0.231585 0.115793 0.993273i \(-0.463059\pi\)
0.115793 + 0.993273i \(0.463059\pi\)
\(468\) 128.046 5.91893
\(469\) 12.7010 0.586476
\(470\) −5.34880 −0.246722
\(471\) −36.0092 −1.65922
\(472\) −104.850 −4.82610
\(473\) −0.425707 −0.0195740
\(474\) −12.5957 −0.578542
\(475\) 3.58602 0.164538
\(476\) −18.9044 −0.866480
\(477\) −17.3640 −0.795041
\(478\) −7.57610 −0.346523
\(479\) 14.1068 0.644554 0.322277 0.946645i \(-0.395552\pi\)
0.322277 + 0.946645i \(0.395552\pi\)
\(480\) −40.5012 −1.84862
\(481\) −5.26112 −0.239886
\(482\) −44.3713 −2.02106
\(483\) 23.5931 1.07352
\(484\) −55.4756 −2.52162
\(485\) 3.43074 0.155782
\(486\) 58.6887 2.66217
\(487\) −3.48237 −0.157801 −0.0789005 0.996882i \(-0.525141\pi\)
−0.0789005 + 0.996882i \(0.525141\pi\)
\(488\) −48.3124 −2.18700
\(489\) 51.3735 2.32319
\(490\) −2.91732 −0.131791
\(491\) −25.2607 −1.14000 −0.570001 0.821644i \(-0.693057\pi\)
−0.570001 + 0.821644i \(0.693057\pi\)
\(492\) 37.8473 1.70629
\(493\) −4.18000 −0.188258
\(494\) 17.3096 0.778794
\(495\) −0.812625 −0.0365248
\(496\) −41.1753 −1.84883
\(497\) −10.9366 −0.490575
\(498\) 105.759 4.73919
\(499\) 23.5572 1.05457 0.527283 0.849690i \(-0.323211\pi\)
0.527283 + 0.849690i \(0.323211\pi\)
\(500\) −48.8730 −2.18567
\(501\) −49.9658 −2.23231
\(502\) 32.5750 1.45390
\(503\) −11.5947 −0.516984 −0.258492 0.966013i \(-0.583226\pi\)
−0.258492 + 0.966013i \(0.583226\pi\)
\(504\) −29.8610 −1.33012
\(505\) 6.84653 0.304666
\(506\) 4.89685 0.217692
\(507\) 89.1322 3.95850
\(508\) 47.2281 2.09541
\(509\) −23.2492 −1.03050 −0.515251 0.857039i \(-0.672301\pi\)
−0.515251 + 0.857039i \(0.672301\pi\)
\(510\) 28.1374 1.24595
\(511\) 7.90022 0.349485
\(512\) 22.8680 1.01063
\(513\) −1.63464 −0.0721709
\(514\) −49.8189 −2.19742
\(515\) 21.7067 0.956510
\(516\) 27.5905 1.21461
\(517\) −0.369827 −0.0162650
\(518\) 2.02832 0.0891192
\(519\) 30.8068 1.35227
\(520\) −61.5728 −2.70014
\(521\) 28.3399 1.24159 0.620797 0.783972i \(-0.286809\pi\)
0.620797 + 0.783972i \(0.286809\pi\)
\(522\) −10.9153 −0.477752
\(523\) 26.8051 1.17210 0.586052 0.810273i \(-0.300681\pi\)
0.586052 + 0.810273i \(0.300681\pi\)
\(524\) −64.8502 −2.83299
\(525\) −9.80055 −0.427731
\(526\) 13.1104 0.571641
\(527\) 13.3721 0.582498
\(528\) −5.99049 −0.260703
\(529\) 60.4559 2.62852
\(530\) 13.8036 0.599588
\(531\) 47.2876 2.05211
\(532\) −4.78341 −0.207387
\(533\) 19.9556 0.864371
\(534\) 31.1409 1.34760
\(535\) −16.6733 −0.720848
\(536\) −103.347 −4.46392
\(537\) 62.0130 2.67606
\(538\) 4.73205 0.204013
\(539\) −0.201709 −0.00868823
\(540\) 9.61264 0.413662
\(541\) −35.3368 −1.51925 −0.759624 0.650362i \(-0.774617\pi\)
−0.759624 + 0.650362i \(0.774617\pi\)
\(542\) 31.9059 1.37048
\(543\) 49.2989 2.11562
\(544\) 53.3499 2.28736
\(545\) 2.99720 0.128386
\(546\) −47.3068 −2.02454
\(547\) −18.4131 −0.787288 −0.393644 0.919263i \(-0.628786\pi\)
−0.393644 + 0.919263i \(0.628786\pi\)
\(548\) 48.5463 2.07380
\(549\) 21.7891 0.929935
\(550\) −2.03415 −0.0867363
\(551\) −1.05767 −0.0450584
\(552\) −191.976 −8.17105
\(553\) 1.83529 0.0780445
\(554\) 19.2010 0.815773
\(555\) −2.16397 −0.0918555
\(556\) 37.0887 1.57291
\(557\) −5.77220 −0.244576 −0.122288 0.992495i \(-0.539023\pi\)
−0.122288 + 0.992495i \(0.539023\pi\)
\(558\) 34.9190 1.47824
\(559\) 14.5475 0.615295
\(560\) 12.6241 0.533467
\(561\) 1.94548 0.0821380
\(562\) 25.8692 1.09123
\(563\) −34.1916 −1.44100 −0.720502 0.693453i \(-0.756089\pi\)
−0.720502 + 0.693453i \(0.756089\pi\)
\(564\) 23.9689 1.00927
\(565\) 7.93579 0.333861
\(566\) 6.39153 0.268656
\(567\) −6.54197 −0.274737
\(568\) 88.9909 3.73398
\(569\) 31.9694 1.34023 0.670114 0.742258i \(-0.266245\pi\)
0.670114 + 0.742258i \(0.266245\pi\)
\(570\) 7.11967 0.298210
\(571\) −15.5859 −0.652251 −0.326125 0.945326i \(-0.605743\pi\)
−0.326125 + 0.945326i \(0.605743\pi\)
\(572\) −7.03800 −0.294274
\(573\) −12.7618 −0.533132
\(574\) −7.69347 −0.321119
\(575\) −34.6675 −1.44573
\(576\) 54.9122 2.28801
\(577\) −24.3062 −1.01188 −0.505939 0.862569i \(-0.668854\pi\)
−0.505939 + 0.862569i \(0.668854\pi\)
\(578\) 8.11264 0.337441
\(579\) 43.2328 1.79669
\(580\) 6.21975 0.258261
\(581\) −15.4099 −0.639310
\(582\) −21.4479 −0.889046
\(583\) 0.954404 0.0395274
\(584\) −64.2838 −2.66008
\(585\) 27.7695 1.14813
\(586\) 17.5638 0.725554
\(587\) −9.05280 −0.373649 −0.186824 0.982393i \(-0.559820\pi\)
−0.186824 + 0.982393i \(0.559820\pi\)
\(588\) 13.0730 0.539121
\(589\) 3.38358 0.139418
\(590\) −37.5915 −1.54762
\(591\) −39.5000 −1.62481
\(592\) −8.77715 −0.360738
\(593\) 6.99060 0.287069 0.143535 0.989645i \(-0.454153\pi\)
0.143535 + 0.989645i \(0.454153\pi\)
\(594\) 0.927236 0.0380450
\(595\) −4.09982 −0.168076
\(596\) −81.7139 −3.34713
\(597\) 8.89712 0.364135
\(598\) −167.338 −6.84298
\(599\) 39.1328 1.59892 0.799461 0.600718i \(-0.205118\pi\)
0.799461 + 0.600718i \(0.205118\pi\)
\(600\) 79.7467 3.25564
\(601\) 15.3010 0.624140 0.312070 0.950059i \(-0.398978\pi\)
0.312070 + 0.950059i \(0.398978\pi\)
\(602\) −5.60851 −0.228586
\(603\) 46.6100 1.89811
\(604\) −43.8492 −1.78420
\(605\) −12.0311 −0.489134
\(606\) −42.8024 −1.73873
\(607\) −24.1083 −0.978524 −0.489262 0.872137i \(-0.662734\pi\)
−0.489262 + 0.872137i \(0.662734\pi\)
\(608\) 13.4992 0.547466
\(609\) 2.89061 0.117133
\(610\) −17.3213 −0.701319
\(611\) 12.6380 0.511277
\(612\) −69.3753 −2.80433
\(613\) −2.78503 −0.112486 −0.0562431 0.998417i \(-0.517912\pi\)
−0.0562431 + 0.998417i \(0.517912\pi\)
\(614\) 81.4719 3.28794
\(615\) 8.20800 0.330979
\(616\) 1.64130 0.0661299
\(617\) −3.63539 −0.146355 −0.0731777 0.997319i \(-0.523314\pi\)
−0.0731777 + 0.997319i \(0.523314\pi\)
\(618\) −135.703 −5.45879
\(619\) 26.9666 1.08388 0.541939 0.840418i \(-0.317690\pi\)
0.541939 + 0.840418i \(0.317690\pi\)
\(620\) −19.8974 −0.799101
\(621\) 15.8027 0.634139
\(622\) 8.79539 0.352663
\(623\) −4.53745 −0.181789
\(624\) 204.711 8.19499
\(625\) 8.37505 0.335002
\(626\) −19.5586 −0.781718
\(627\) 0.492268 0.0196593
\(628\) −70.5791 −2.81641
\(629\) 2.85047 0.113656
\(630\) −10.7060 −0.426537
\(631\) 12.3049 0.489850 0.244925 0.969542i \(-0.421237\pi\)
0.244925 + 0.969542i \(0.421237\pi\)
\(632\) −14.9337 −0.594030
\(633\) 7.82295 0.310935
\(634\) 31.2647 1.24168
\(635\) 10.2425 0.406459
\(636\) −61.8560 −2.45275
\(637\) 6.89294 0.273108
\(638\) 0.599958 0.0237526
\(639\) −40.1352 −1.58773
\(640\) −12.2879 −0.485722
\(641\) 14.2533 0.562973 0.281487 0.959565i \(-0.409173\pi\)
0.281487 + 0.959565i \(0.409173\pi\)
\(642\) 104.236 4.11387
\(643\) −3.20817 −0.126518 −0.0632590 0.997997i \(-0.520149\pi\)
−0.0632590 + 0.997997i \(0.520149\pi\)
\(644\) 46.2431 1.82223
\(645\) 5.98361 0.235604
\(646\) −9.37832 −0.368985
\(647\) 21.8809 0.860228 0.430114 0.902775i \(-0.358473\pi\)
0.430114 + 0.902775i \(0.358473\pi\)
\(648\) 53.2317 2.09114
\(649\) −2.59915 −0.102025
\(650\) 69.5122 2.72649
\(651\) −9.24726 −0.362429
\(652\) 100.693 3.94346
\(653\) −39.1116 −1.53056 −0.765278 0.643699i \(-0.777399\pi\)
−0.765278 + 0.643699i \(0.777399\pi\)
\(654\) −18.7376 −0.732697
\(655\) −14.0642 −0.549533
\(656\) 33.2920 1.29983
\(657\) 28.9922 1.13110
\(658\) −4.87231 −0.189942
\(659\) 28.9293 1.12693 0.563463 0.826142i \(-0.309469\pi\)
0.563463 + 0.826142i \(0.309469\pi\)
\(660\) −2.89483 −0.112681
\(661\) 20.3113 0.790017 0.395009 0.918677i \(-0.370742\pi\)
0.395009 + 0.918677i \(0.370742\pi\)
\(662\) −48.3543 −1.87934
\(663\) −66.4820 −2.58195
\(664\) 125.390 4.86606
\(665\) −1.03739 −0.0402282
\(666\) 7.44352 0.288431
\(667\) 10.2249 0.395912
\(668\) −97.9345 −3.78920
\(669\) −61.3581 −2.37224
\(670\) −37.0528 −1.43147
\(671\) −1.19763 −0.0462339
\(672\) −36.8932 −1.42319
\(673\) −26.7623 −1.03161 −0.515805 0.856706i \(-0.672507\pi\)
−0.515805 + 0.856706i \(0.672507\pi\)
\(674\) −44.9930 −1.73307
\(675\) −6.56441 −0.252664
\(676\) 174.702 6.71929
\(677\) 36.4205 1.39975 0.699876 0.714264i \(-0.253239\pi\)
0.699876 + 0.714264i \(0.253239\pi\)
\(678\) −49.6121 −1.90534
\(679\) 3.12512 0.119931
\(680\) 33.3601 1.27930
\(681\) 7.93022 0.303887
\(682\) −1.91931 −0.0734942
\(683\) −37.7085 −1.44288 −0.721438 0.692479i \(-0.756519\pi\)
−0.721438 + 0.692479i \(0.756519\pi\)
\(684\) −17.5542 −0.671201
\(685\) 10.5283 0.402267
\(686\) −2.65744 −0.101461
\(687\) 26.7899 1.02210
\(688\) 24.2697 0.925274
\(689\) −32.6145 −1.24251
\(690\) −68.8287 −2.62026
\(691\) −19.1993 −0.730377 −0.365188 0.930934i \(-0.618995\pi\)
−0.365188 + 0.930934i \(0.618995\pi\)
\(692\) 60.3823 2.29539
\(693\) −0.740233 −0.0281191
\(694\) 7.68522 0.291727
\(695\) 8.04350 0.305107
\(696\) −23.5208 −0.891552
\(697\) −10.8119 −0.409531
\(698\) 17.2370 0.652431
\(699\) 68.8685 2.60485
\(700\) −19.2093 −0.726045
\(701\) 18.1163 0.684241 0.342121 0.939656i \(-0.388855\pi\)
0.342121 + 0.939656i \(0.388855\pi\)
\(702\) −31.6861 −1.19592
\(703\) 0.721261 0.0272029
\(704\) −3.01823 −0.113754
\(705\) 5.19817 0.195774
\(706\) −6.99936 −0.263424
\(707\) 6.23661 0.234552
\(708\) 168.453 6.33087
\(709\) −6.09378 −0.228857 −0.114428 0.993432i \(-0.536504\pi\)
−0.114428 + 0.993432i \(0.536504\pi\)
\(710\) 31.9057 1.19740
\(711\) 6.73515 0.252588
\(712\) 36.9211 1.38368
\(713\) −32.7104 −1.22501
\(714\) 25.6308 0.959209
\(715\) −1.52634 −0.0570820
\(716\) 121.547 4.54243
\(717\) 7.36274 0.274967
\(718\) 33.8942 1.26492
\(719\) 20.5232 0.765387 0.382693 0.923875i \(-0.374997\pi\)
0.382693 + 0.923875i \(0.374997\pi\)
\(720\) 46.3281 1.72655
\(721\) 19.7729 0.736383
\(722\) 48.1182 1.79078
\(723\) 43.1217 1.60371
\(724\) 96.6272 3.59112
\(725\) −4.24743 −0.157746
\(726\) 75.2146 2.79148
\(727\) −45.4401 −1.68528 −0.842639 0.538479i \(-0.818999\pi\)
−0.842639 + 0.538479i \(0.818999\pi\)
\(728\) −56.0876 −2.07874
\(729\) −37.4100 −1.38556
\(730\) −23.0475 −0.853026
\(731\) −7.88185 −0.291521
\(732\) 77.6196 2.86890
\(733\) −16.7882 −0.620088 −0.310044 0.950722i \(-0.600344\pi\)
−0.310044 + 0.950722i \(0.600344\pi\)
\(734\) 26.6255 0.982767
\(735\) 2.83516 0.104577
\(736\) −130.502 −4.81038
\(737\) −2.56190 −0.0943688
\(738\) −28.2335 −1.03929
\(739\) 38.1328 1.40274 0.701369 0.712799i \(-0.252573\pi\)
0.701369 + 0.712799i \(0.252573\pi\)
\(740\) −4.24145 −0.155919
\(741\) −16.8221 −0.617975
\(742\) 12.5739 0.461601
\(743\) −36.3387 −1.33314 −0.666569 0.745443i \(-0.732238\pi\)
−0.666569 + 0.745443i \(0.732238\pi\)
\(744\) 75.2446 2.75860
\(745\) −17.7214 −0.649263
\(746\) 13.3799 0.489872
\(747\) −56.5512 −2.06910
\(748\) 3.81319 0.139424
\(749\) −15.1879 −0.554955
\(750\) 66.2627 2.41957
\(751\) 21.3400 0.778709 0.389354 0.921088i \(-0.372698\pi\)
0.389354 + 0.921088i \(0.372698\pi\)
\(752\) 21.0840 0.768853
\(753\) −31.6577 −1.15367
\(754\) −20.5022 −0.746645
\(755\) −9.50965 −0.346091
\(756\) 8.75630 0.318464
\(757\) −21.3199 −0.774884 −0.387442 0.921894i \(-0.626641\pi\)
−0.387442 + 0.921894i \(0.626641\pi\)
\(758\) 38.5299 1.39947
\(759\) −4.75895 −0.172739
\(760\) 8.44118 0.306194
\(761\) −28.4371 −1.03084 −0.515422 0.856937i \(-0.672365\pi\)
−0.515422 + 0.856937i \(0.672365\pi\)
\(762\) −64.0326 −2.31966
\(763\) 2.73020 0.0988399
\(764\) −25.0135 −0.904957
\(765\) −15.0455 −0.543972
\(766\) −45.3773 −1.63955
\(767\) 88.8197 3.20709
\(768\) −0.467972 −0.0168865
\(769\) −38.5724 −1.39096 −0.695478 0.718548i \(-0.744807\pi\)
−0.695478 + 0.718548i \(0.744807\pi\)
\(770\) 0.588451 0.0212063
\(771\) 48.4159 1.74366
\(772\) 84.7374 3.04977
\(773\) 26.8384 0.965311 0.482655 0.875810i \(-0.339672\pi\)
0.482655 + 0.875810i \(0.339672\pi\)
\(774\) −20.5821 −0.739809
\(775\) 13.5878 0.488090
\(776\) −25.4290 −0.912847
\(777\) −1.97120 −0.0707163
\(778\) 40.3691 1.44730
\(779\) −2.73576 −0.0980189
\(780\) 98.9240 3.54205
\(781\) 2.20602 0.0789376
\(782\) 90.6639 3.24214
\(783\) 1.93613 0.0691916
\(784\) 11.4995 0.410697
\(785\) −15.3066 −0.546316
\(786\) 87.9249 3.13618
\(787\) 45.1165 1.60823 0.804114 0.594475i \(-0.202640\pi\)
0.804114 + 0.594475i \(0.202640\pi\)
\(788\) −77.4212 −2.75801
\(789\) −12.7412 −0.453598
\(790\) −5.35414 −0.190492
\(791\) 7.22884 0.257028
\(792\) 6.02325 0.214027
\(793\) 40.9261 1.45333
\(794\) −75.5990 −2.68291
\(795\) −13.4148 −0.475774
\(796\) 17.4386 0.618095
\(797\) −16.4931 −0.584215 −0.292108 0.956385i \(-0.594357\pi\)
−0.292108 + 0.956385i \(0.594357\pi\)
\(798\) 6.48542 0.229581
\(799\) −6.84724 −0.242238
\(800\) 54.2105 1.91663
\(801\) −16.6516 −0.588354
\(802\) 89.0026 3.14279
\(803\) −1.59355 −0.0562351
\(804\) 166.040 5.85577
\(805\) 10.0288 0.353470
\(806\) 65.5879 2.31024
\(807\) −4.59878 −0.161885
\(808\) −50.7471 −1.78528
\(809\) 40.5318 1.42502 0.712511 0.701661i \(-0.247558\pi\)
0.712511 + 0.701661i \(0.247558\pi\)
\(810\) 19.0850 0.670579
\(811\) −47.1625 −1.65610 −0.828050 0.560654i \(-0.810550\pi\)
−0.828050 + 0.560654i \(0.810550\pi\)
\(812\) 5.66567 0.198826
\(813\) −31.0074 −1.08748
\(814\) −0.409131 −0.0143400
\(815\) 21.8376 0.764936
\(816\) −110.912 −3.88271
\(817\) −1.99436 −0.0697739
\(818\) 94.4902 3.30377
\(819\) 25.2957 0.883904
\(820\) 16.0879 0.561815
\(821\) 16.1751 0.564516 0.282258 0.959338i \(-0.408917\pi\)
0.282258 + 0.959338i \(0.408917\pi\)
\(822\) −65.8198 −2.29573
\(823\) −8.17106 −0.284825 −0.142413 0.989807i \(-0.545486\pi\)
−0.142413 + 0.989807i \(0.545486\pi\)
\(824\) −160.892 −5.60493
\(825\) 1.97686 0.0688255
\(826\) −34.2427 −1.19145
\(827\) −38.1759 −1.32751 −0.663753 0.747952i \(-0.731037\pi\)
−0.663753 + 0.747952i \(0.731037\pi\)
\(828\) 169.703 5.89759
\(829\) −21.2420 −0.737765 −0.368883 0.929476i \(-0.620260\pi\)
−0.368883 + 0.929476i \(0.620260\pi\)
\(830\) 44.9556 1.56043
\(831\) −18.6603 −0.647318
\(832\) 103.141 3.57576
\(833\) −3.73459 −0.129396
\(834\) −50.2854 −1.74124
\(835\) −21.2392 −0.735014
\(836\) 0.964859 0.0333703
\(837\) −6.19382 −0.214090
\(838\) −58.8556 −2.03313
\(839\) 43.1075 1.48824 0.744118 0.668048i \(-0.232870\pi\)
0.744118 + 0.668048i \(0.232870\pi\)
\(840\) −23.0696 −0.795978
\(841\) −27.7472 −0.956802
\(842\) −39.0278 −1.34499
\(843\) −25.1406 −0.865889
\(844\) 15.3332 0.527791
\(845\) 37.8878 1.30338
\(846\) −17.8804 −0.614741
\(847\) −10.9593 −0.376566
\(848\) −54.4110 −1.86848
\(849\) −6.21153 −0.213179
\(850\) −37.6617 −1.29179
\(851\) −6.97271 −0.239022
\(852\) −142.974 −4.89822
\(853\) −38.3179 −1.31198 −0.655990 0.754769i \(-0.727749\pi\)
−0.655990 + 0.754769i \(0.727749\pi\)
\(854\) −15.7782 −0.539920
\(855\) −3.80700 −0.130197
\(856\) 123.584 4.22400
\(857\) 6.33448 0.216382 0.108191 0.994130i \(-0.465494\pi\)
0.108191 + 0.994130i \(0.465494\pi\)
\(858\) 9.54222 0.325766
\(859\) −1.61931 −0.0552501 −0.0276250 0.999618i \(-0.508794\pi\)
−0.0276250 + 0.999618i \(0.508794\pi\)
\(860\) 11.7280 0.399923
\(861\) 7.47680 0.254809
\(862\) −33.2327 −1.13191
\(863\) −1.00000 −0.0340404
\(864\) −24.7111 −0.840688
\(865\) 13.0952 0.445251
\(866\) 59.7755 2.03125
\(867\) −7.88417 −0.267760
\(868\) −18.1249 −0.615199
\(869\) −0.370195 −0.0125580
\(870\) −8.43283 −0.285900
\(871\) 87.5469 2.96642
\(872\) −22.2155 −0.752313
\(873\) 11.4686 0.388152
\(874\) 22.9409 0.775987
\(875\) −9.65495 −0.326397
\(876\) 103.280 3.48950
\(877\) 3.21481 0.108556 0.0542782 0.998526i \(-0.482714\pi\)
0.0542782 + 0.998526i \(0.482714\pi\)
\(878\) 76.6545 2.58696
\(879\) −17.0692 −0.575729
\(880\) −2.54641 −0.0858393
\(881\) −12.7458 −0.429415 −0.214708 0.976678i \(-0.568880\pi\)
−0.214708 + 0.976678i \(0.568880\pi\)
\(882\) −9.75226 −0.328376
\(883\) 52.0451 1.75146 0.875729 0.482803i \(-0.160381\pi\)
0.875729 + 0.482803i \(0.160381\pi\)
\(884\) −130.307 −4.38269
\(885\) 36.5328 1.22804
\(886\) −38.6626 −1.29889
\(887\) 27.0434 0.908027 0.454014 0.890995i \(-0.349992\pi\)
0.454014 + 0.890995i \(0.349992\pi\)
\(888\) 16.0395 0.538252
\(889\) 9.33001 0.312918
\(890\) 13.2372 0.443713
\(891\) 1.31958 0.0442074
\(892\) −120.264 −4.02672
\(893\) −1.73257 −0.0579783
\(894\) 110.789 3.70534
\(895\) 26.3602 0.881123
\(896\) −11.1932 −0.373940
\(897\) 162.626 5.42992
\(898\) 99.7889 3.33000
\(899\) −4.00764 −0.133662
\(900\) −70.4945 −2.34982
\(901\) 17.6705 0.588691
\(902\) 1.55184 0.0516707
\(903\) 5.45056 0.181383
\(904\) −58.8208 −1.95635
\(905\) 20.9557 0.696591
\(906\) 59.4513 1.97514
\(907\) −36.7548 −1.22042 −0.610212 0.792238i \(-0.708916\pi\)
−0.610212 + 0.792238i \(0.708916\pi\)
\(908\) 15.5435 0.515828
\(909\) 22.8871 0.759118
\(910\) −20.1089 −0.666605
\(911\) 46.5940 1.54373 0.771864 0.635787i \(-0.219324\pi\)
0.771864 + 0.635787i \(0.219324\pi\)
\(912\) −28.0644 −0.929305
\(913\) 3.10832 0.102870
\(914\) 24.6365 0.814902
\(915\) 16.8335 0.556498
\(916\) 52.5090 1.73495
\(917\) −12.8113 −0.423066
\(918\) 17.1675 0.566613
\(919\) 16.6303 0.548582 0.274291 0.961647i \(-0.411557\pi\)
0.274291 + 0.961647i \(0.411557\pi\)
\(920\) −81.6042 −2.69041
\(921\) −79.1775 −2.60899
\(922\) −16.0553 −0.528754
\(923\) −75.3855 −2.48134
\(924\) −2.63695 −0.0867491
\(925\) 2.89646 0.0952349
\(926\) −78.3169 −2.57365
\(927\) 72.5628 2.38327
\(928\) −15.9890 −0.524866
\(929\) −3.18717 −0.104568 −0.0522838 0.998632i \(-0.516650\pi\)
−0.0522838 + 0.998632i \(0.516650\pi\)
\(930\) 26.9772 0.884619
\(931\) −0.944972 −0.0309702
\(932\) 134.984 4.42155
\(933\) −8.54770 −0.279839
\(934\) −13.2994 −0.435170
\(935\) 0.826973 0.0270449
\(936\) −205.830 −6.72777
\(937\) 24.2766 0.793082 0.396541 0.918017i \(-0.370210\pi\)
0.396541 + 0.918017i \(0.370210\pi\)
\(938\) −33.7520 −1.10204
\(939\) 19.0078 0.620295
\(940\) 10.1886 0.332314
\(941\) 43.0560 1.40358 0.701792 0.712382i \(-0.252383\pi\)
0.701792 + 0.712382i \(0.252383\pi\)
\(942\) 95.6922 3.11782
\(943\) 26.4477 0.861256
\(944\) 148.178 4.82279
\(945\) 1.89899 0.0617743
\(946\) 1.13129 0.0367814
\(947\) −15.6826 −0.509615 −0.254807 0.966992i \(-0.582012\pi\)
−0.254807 + 0.966992i \(0.582012\pi\)
\(948\) 23.9928 0.779248
\(949\) 54.4558 1.76771
\(950\) −9.52962 −0.309182
\(951\) −30.3842 −0.985274
\(952\) 30.3882 0.984889
\(953\) −33.6534 −1.09014 −0.545071 0.838390i \(-0.683497\pi\)
−0.545071 + 0.838390i \(0.683497\pi\)
\(954\) 46.1436 1.49395
\(955\) −5.42473 −0.175540
\(956\) 14.4312 0.466738
\(957\) −0.583062 −0.0188477
\(958\) −37.4878 −1.21118
\(959\) 9.59042 0.309691
\(960\) 42.4233 1.36921
\(961\) −18.1793 −0.586427
\(962\) 13.9811 0.450768
\(963\) −55.7367 −1.79609
\(964\) 84.5198 2.72220
\(965\) 18.3772 0.591581
\(966\) −62.6971 −2.01725
\(967\) 15.6080 0.501919 0.250959 0.967998i \(-0.419254\pi\)
0.250959 + 0.967998i \(0.419254\pi\)
\(968\) 89.1755 2.86621
\(969\) 9.11421 0.292791
\(970\) −9.11698 −0.292729
\(971\) 29.5832 0.949370 0.474685 0.880156i \(-0.342562\pi\)
0.474685 + 0.880156i \(0.342562\pi\)
\(972\) −111.792 −3.58573
\(973\) 7.32695 0.234891
\(974\) 9.25416 0.296522
\(975\) −67.5546 −2.16348
\(976\) 68.2773 2.18550
\(977\) 50.5527 1.61733 0.808663 0.588273i \(-0.200192\pi\)
0.808663 + 0.588273i \(0.200192\pi\)
\(978\) −136.522 −4.36548
\(979\) 0.915247 0.0292514
\(980\) 5.55700 0.177512
\(981\) 10.0193 0.319891
\(982\) 67.1288 2.14217
\(983\) 29.7400 0.948558 0.474279 0.880375i \(-0.342709\pi\)
0.474279 + 0.880375i \(0.342709\pi\)
\(984\) −60.8384 −1.93946
\(985\) −16.7905 −0.534989
\(986\) 11.1081 0.353753
\(987\) 4.73509 0.150720
\(988\) −32.9718 −1.04897
\(989\) 19.2803 0.613077
\(990\) 2.15950 0.0686334
\(991\) −33.5539 −1.06588 −0.532938 0.846154i \(-0.678912\pi\)
−0.532938 + 0.846154i \(0.678912\pi\)
\(992\) 51.1501 1.62402
\(993\) 46.9926 1.49126
\(994\) 29.0634 0.921834
\(995\) 3.78194 0.119896
\(996\) −201.453 −6.38330
\(997\) −3.59942 −0.113995 −0.0569974 0.998374i \(-0.518153\pi\)
−0.0569974 + 0.998374i \(0.518153\pi\)
\(998\) −62.6017 −1.98162
\(999\) −1.32031 −0.0417727
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 \(a_p\))