Properties

Label 6023.2.a.b.1.20
Level 6023
Weight 2
Character 6023.1
Self dual Yes
Analytic conductor 48.094
Analytic rank 1
Dimension 99
CM No

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Newspace parameters

Level: \( N \) = \( 6023 = 19 \cdot 317 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6023.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0938971374\)
Analytic rank: \(1\)
Dimension: \(99\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.20
Character \(\chi\) = 6023.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.88369 q^{2}\) \(+2.22834 q^{3}\) \(+1.54829 q^{4}\) \(+0.640943 q^{5}\) \(-4.19751 q^{6}\) \(-4.86422 q^{7}\) \(+0.850890 q^{8}\) \(+1.96551 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.88369 q^{2}\) \(+2.22834 q^{3}\) \(+1.54829 q^{4}\) \(+0.640943 q^{5}\) \(-4.19751 q^{6}\) \(-4.86422 q^{7}\) \(+0.850890 q^{8}\) \(+1.96551 q^{9}\) \(-1.20734 q^{10}\) \(+4.50890 q^{11}\) \(+3.45011 q^{12}\) \(-0.00706194 q^{13}\) \(+9.16269 q^{14}\) \(+1.42824 q^{15}\) \(-4.69938 q^{16}\) \(-6.43690 q^{17}\) \(-3.70241 q^{18}\) \(-1.00000 q^{19}\) \(+0.992363 q^{20}\) \(-10.8392 q^{21}\) \(-8.49336 q^{22}\) \(-0.234352 q^{23}\) \(+1.89607 q^{24}\) \(-4.58919 q^{25}\) \(+0.0133025 q^{26}\) \(-2.30520 q^{27}\) \(-7.53121 q^{28}\) \(+8.13953 q^{29}\) \(-2.69036 q^{30}\) \(+10.5789 q^{31}\) \(+7.15040 q^{32}\) \(+10.0474 q^{33}\) \(+12.1251 q^{34}\) \(-3.11769 q^{35}\) \(+3.04317 q^{36}\) \(+1.87236 q^{37}\) \(+1.88369 q^{38}\) \(-0.0157364 q^{39}\) \(+0.545372 q^{40}\) \(+0.709329 q^{41}\) \(+20.4176 q^{42}\) \(+2.98280 q^{43}\) \(+6.98106 q^{44}\) \(+1.25978 q^{45}\) \(+0.441446 q^{46}\) \(-8.81646 q^{47}\) \(-10.4718 q^{48}\) \(+16.6607 q^{49}\) \(+8.64461 q^{50}\) \(-14.3436 q^{51}\) \(-0.0109339 q^{52}\) \(+6.85127 q^{53}\) \(+4.34227 q^{54}\) \(+2.88995 q^{55}\) \(-4.13892 q^{56}\) \(-2.22834 q^{57}\) \(-15.3323 q^{58}\) \(-9.51976 q^{59}\) \(+2.21133 q^{60}\) \(+2.64579 q^{61}\) \(-19.9273 q^{62}\) \(-9.56069 q^{63}\) \(-4.07036 q^{64}\) \(-0.00452630 q^{65}\) \(-18.9261 q^{66}\) \(+5.68863 q^{67}\) \(-9.96615 q^{68}\) \(-0.522217 q^{69}\) \(+5.87276 q^{70}\) \(-12.5229 q^{71}\) \(+1.67243 q^{72}\) \(+3.68045 q^{73}\) \(-3.52695 q^{74}\) \(-10.2263 q^{75}\) \(-1.54829 q^{76}\) \(-21.9323 q^{77}\) \(+0.0296425 q^{78}\) \(-9.08704 q^{79}\) \(-3.01204 q^{80}\) \(-11.0333 q^{81}\) \(-1.33616 q^{82}\) \(+10.1242 q^{83}\) \(-16.7821 q^{84}\) \(-4.12568 q^{85}\) \(-5.61867 q^{86}\) \(+18.1377 q^{87}\) \(+3.83657 q^{88}\) \(-9.09239 q^{89}\) \(-2.37304 q^{90}\) \(+0.0343509 q^{91}\) \(-0.362844 q^{92}\) \(+23.5734 q^{93}\) \(+16.6075 q^{94}\) \(-0.640943 q^{95}\) \(+15.9335 q^{96}\) \(-7.06949 q^{97}\) \(-31.3835 q^{98}\) \(+8.86229 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(99q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 80q^{4} \) \(\mathstrut -\mathstrut 15q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 58q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(99q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 80q^{4} \) \(\mathstrut -\mathstrut 15q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 58q^{9} \) \(\mathstrut -\mathstrut 6q^{10} \) \(\mathstrut -\mathstrut 9q^{11} \) \(\mathstrut -\mathstrut 27q^{12} \) \(\mathstrut -\mathstrut 28q^{13} \) \(\mathstrut -\mathstrut 13q^{14} \) \(\mathstrut -\mathstrut 10q^{15} \) \(\mathstrut +\mathstrut 38q^{16} \) \(\mathstrut -\mathstrut 36q^{17} \) \(\mathstrut -\mathstrut 14q^{18} \) \(\mathstrut -\mathstrut 99q^{19} \) \(\mathstrut -\mathstrut 34q^{20} \) \(\mathstrut -\mathstrut 20q^{21} \) \(\mathstrut -\mathstrut 53q^{22} \) \(\mathstrut -\mathstrut 38q^{23} \) \(\mathstrut -\mathstrut 25q^{24} \) \(\mathstrut -\mathstrut 8q^{25} \) \(\mathstrut -\mathstrut 3q^{26} \) \(\mathstrut -\mathstrut 3q^{27} \) \(\mathstrut -\mathstrut 63q^{28} \) \(\mathstrut -\mathstrut 34q^{29} \) \(\mathstrut -\mathstrut 30q^{30} \) \(\mathstrut -\mathstrut 16q^{31} \) \(\mathstrut -\mathstrut 43q^{32} \) \(\mathstrut -\mathstrut 41q^{33} \) \(\mathstrut -\mathstrut 14q^{34} \) \(\mathstrut -\mathstrut 25q^{35} \) \(\mathstrut -\mathstrut 16q^{36} \) \(\mathstrut -\mathstrut 80q^{37} \) \(\mathstrut +\mathstrut 4q^{38} \) \(\mathstrut -\mathstrut 48q^{39} \) \(\mathstrut -\mathstrut 10q^{40} \) \(\mathstrut -\mathstrut 32q^{41} \) \(\mathstrut -\mathstrut 37q^{42} \) \(\mathstrut -\mathstrut 76q^{43} \) \(\mathstrut -\mathstrut 21q^{44} \) \(\mathstrut -\mathstrut 53q^{45} \) \(\mathstrut -\mathstrut 23q^{46} \) \(\mathstrut -\mathstrut 31q^{47} \) \(\mathstrut -\mathstrut 74q^{48} \) \(\mathstrut -\mathstrut 32q^{49} \) \(\mathstrut -\mathstrut 29q^{50} \) \(\mathstrut -\mathstrut 30q^{51} \) \(\mathstrut -\mathstrut 71q^{52} \) \(\mathstrut -\mathstrut 35q^{53} \) \(\mathstrut -\mathstrut 80q^{54} \) \(\mathstrut -\mathstrut 45q^{55} \) \(\mathstrut -\mathstrut 33q^{56} \) \(\mathstrut +\mathstrut 3q^{57} \) \(\mathstrut -\mathstrut 91q^{58} \) \(\mathstrut +\mathstrut 12q^{59} \) \(\mathstrut -\mathstrut 56q^{60} \) \(\mathstrut -\mathstrut 61q^{61} \) \(\mathstrut -\mathstrut 46q^{62} \) \(\mathstrut -\mathstrut 43q^{63} \) \(\mathstrut -\mathstrut 30q^{64} \) \(\mathstrut -\mathstrut 46q^{65} \) \(\mathstrut -\mathstrut 75q^{66} \) \(\mathstrut -\mathstrut 26q^{67} \) \(\mathstrut -\mathstrut 55q^{68} \) \(\mathstrut -\mathstrut 45q^{69} \) \(\mathstrut -\mathstrut 76q^{70} \) \(\mathstrut -\mathstrut 41q^{71} \) \(\mathstrut -\mathstrut 77q^{72} \) \(\mathstrut -\mathstrut 143q^{73} \) \(\mathstrut -\mathstrut 64q^{74} \) \(\mathstrut -\mathstrut 8q^{75} \) \(\mathstrut -\mathstrut 80q^{76} \) \(\mathstrut -\mathstrut 58q^{77} \) \(\mathstrut -\mathstrut 34q^{78} \) \(\mathstrut -\mathstrut 22q^{79} \) \(\mathstrut -\mathstrut 36q^{80} \) \(\mathstrut -\mathstrut 81q^{81} \) \(\mathstrut -\mathstrut 109q^{82} \) \(\mathstrut -\mathstrut 7q^{83} \) \(\mathstrut -\mathstrut 6q^{84} \) \(\mathstrut -\mathstrut 80q^{85} \) \(\mathstrut +\mathstrut 32q^{86} \) \(\mathstrut -\mathstrut 57q^{87} \) \(\mathstrut -\mathstrut 120q^{88} \) \(\mathstrut -\mathstrut 28q^{89} \) \(\mathstrut -\mathstrut 12q^{90} \) \(\mathstrut -\mathstrut 30q^{91} \) \(\mathstrut -\mathstrut 107q^{92} \) \(\mathstrut -\mathstrut 121q^{93} \) \(\mathstrut +\mathstrut 8q^{94} \) \(\mathstrut +\mathstrut 15q^{95} \) \(\mathstrut +\mathstrut 4q^{96} \) \(\mathstrut -\mathstrut 128q^{97} \) \(\mathstrut +\mathstrut 54q^{98} \) \(\mathstrut -\mathstrut 34q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.88369 −1.33197 −0.665985 0.745965i \(-0.731988\pi\)
−0.665985 + 0.745965i \(0.731988\pi\)
\(3\) 2.22834 1.28653 0.643267 0.765642i \(-0.277578\pi\)
0.643267 + 0.765642i \(0.277578\pi\)
\(4\) 1.54829 0.774143
\(5\) 0.640943 0.286639 0.143319 0.989677i \(-0.454222\pi\)
0.143319 + 0.989677i \(0.454222\pi\)
\(6\) −4.19751 −1.71362
\(7\) −4.86422 −1.83850 −0.919252 0.393670i \(-0.871205\pi\)
−0.919252 + 0.393670i \(0.871205\pi\)
\(8\) 0.850890 0.300835
\(9\) 1.96551 0.655170
\(10\) −1.20734 −0.381794
\(11\) 4.50890 1.35948 0.679742 0.733452i \(-0.262092\pi\)
0.679742 + 0.733452i \(0.262092\pi\)
\(12\) 3.45011 0.995961
\(13\) −0.00706194 −0.00195863 −0.000979315 1.00000i \(-0.500312\pi\)
−0.000979315 1.00000i \(0.500312\pi\)
\(14\) 9.16269 2.44883
\(15\) 1.42824 0.368770
\(16\) −4.69938 −1.17485
\(17\) −6.43690 −1.56118 −0.780588 0.625046i \(-0.785080\pi\)
−0.780588 + 0.625046i \(0.785080\pi\)
\(18\) −3.70241 −0.872667
\(19\) −1.00000 −0.229416
\(20\) 0.992363 0.221899
\(21\) −10.8392 −2.36530
\(22\) −8.49336 −1.81079
\(23\) −0.234352 −0.0488658 −0.0244329 0.999701i \(-0.507778\pi\)
−0.0244329 + 0.999701i \(0.507778\pi\)
\(24\) 1.89607 0.387034
\(25\) −4.58919 −0.917838
\(26\) 0.0133025 0.00260884
\(27\) −2.30520 −0.443635
\(28\) −7.53121 −1.42326
\(29\) 8.13953 1.51147 0.755736 0.654876i \(-0.227279\pi\)
0.755736 + 0.654876i \(0.227279\pi\)
\(30\) −2.69036 −0.491191
\(31\) 10.5789 1.90002 0.950011 0.312217i \(-0.101072\pi\)
0.950011 + 0.312217i \(0.101072\pi\)
\(32\) 7.15040 1.26402
\(33\) 10.0474 1.74902
\(34\) 12.1251 2.07944
\(35\) −3.11769 −0.526986
\(36\) 3.04317 0.507196
\(37\) 1.87236 0.307814 0.153907 0.988085i \(-0.450814\pi\)
0.153907 + 0.988085i \(0.450814\pi\)
\(38\) 1.88369 0.305575
\(39\) −0.0157364 −0.00251984
\(40\) 0.545372 0.0862309
\(41\) 0.709329 0.110779 0.0553893 0.998465i \(-0.482360\pi\)
0.0553893 + 0.998465i \(0.482360\pi\)
\(42\) 20.4176 3.15051
\(43\) 2.98280 0.454873 0.227436 0.973793i \(-0.426966\pi\)
0.227436 + 0.973793i \(0.426966\pi\)
\(44\) 6.98106 1.05243
\(45\) 1.25978 0.187797
\(46\) 0.441446 0.0650877
\(47\) −8.81646 −1.28601 −0.643006 0.765861i \(-0.722313\pi\)
−0.643006 + 0.765861i \(0.722313\pi\)
\(48\) −10.4718 −1.51148
\(49\) 16.6607 2.38010
\(50\) 8.64461 1.22253
\(51\) −14.3436 −2.00851
\(52\) −0.0109339 −0.00151626
\(53\) 6.85127 0.941094 0.470547 0.882375i \(-0.344057\pi\)
0.470547 + 0.882375i \(0.344057\pi\)
\(54\) 4.34227 0.590908
\(55\) 2.88995 0.389680
\(56\) −4.13892 −0.553086
\(57\) −2.22834 −0.295151
\(58\) −15.3323 −2.01323
\(59\) −9.51976 −1.23937 −0.619684 0.784852i \(-0.712739\pi\)
−0.619684 + 0.784852i \(0.712739\pi\)
\(60\) 2.21133 0.285481
\(61\) 2.64579 0.338758 0.169379 0.985551i \(-0.445824\pi\)
0.169379 + 0.985551i \(0.445824\pi\)
\(62\) −19.9273 −2.53077
\(63\) −9.56069 −1.20453
\(64\) −4.07036 −0.508795
\(65\) −0.00452630 −0.000561419 0
\(66\) −18.9261 −2.32964
\(67\) 5.68863 0.694977 0.347489 0.937684i \(-0.387035\pi\)
0.347489 + 0.937684i \(0.387035\pi\)
\(68\) −9.96615 −1.20857
\(69\) −0.522217 −0.0628675
\(70\) 5.87276 0.701929
\(71\) −12.5229 −1.48620 −0.743098 0.669183i \(-0.766644\pi\)
−0.743098 + 0.669183i \(0.766644\pi\)
\(72\) 1.67243 0.197098
\(73\) 3.68045 0.430764 0.215382 0.976530i \(-0.430900\pi\)
0.215382 + 0.976530i \(0.430900\pi\)
\(74\) −3.52695 −0.409999
\(75\) −10.2263 −1.18083
\(76\) −1.54829 −0.177601
\(77\) −21.9323 −2.49941
\(78\) 0.0296425 0.00335636
\(79\) −9.08704 −1.02237 −0.511186 0.859470i \(-0.670794\pi\)
−0.511186 + 0.859470i \(0.670794\pi\)
\(80\) −3.01204 −0.336756
\(81\) −11.0333 −1.22592
\(82\) −1.33616 −0.147554
\(83\) 10.1242 1.11127 0.555637 0.831425i \(-0.312475\pi\)
0.555637 + 0.831425i \(0.312475\pi\)
\(84\) −16.7821 −1.83108
\(85\) −4.12568 −0.447493
\(86\) −5.61867 −0.605876
\(87\) 18.1377 1.94456
\(88\) 3.83657 0.408980
\(89\) −9.09239 −0.963791 −0.481896 0.876229i \(-0.660052\pi\)
−0.481896 + 0.876229i \(0.660052\pi\)
\(90\) −2.37304 −0.250140
\(91\) 0.0343509 0.00360095
\(92\) −0.362844 −0.0378291
\(93\) 23.5734 2.44444
\(94\) 16.6075 1.71293
\(95\) −0.640943 −0.0657594
\(96\) 15.9335 1.62621
\(97\) −7.06949 −0.717798 −0.358899 0.933376i \(-0.616848\pi\)
−0.358899 + 0.933376i \(0.616848\pi\)
\(98\) −31.3835 −3.17022
\(99\) 8.86229 0.890693
\(100\) −7.10538 −0.710538
\(101\) −11.2418 −1.11860 −0.559300 0.828965i \(-0.688930\pi\)
−0.559300 + 0.828965i \(0.688930\pi\)
\(102\) 27.0189 2.67527
\(103\) −15.7547 −1.55236 −0.776179 0.630513i \(-0.782845\pi\)
−0.776179 + 0.630513i \(0.782845\pi\)
\(104\) −0.00600893 −0.000589224 0
\(105\) −6.94729 −0.677986
\(106\) −12.9057 −1.25351
\(107\) 7.79754 0.753817 0.376908 0.926251i \(-0.376987\pi\)
0.376908 + 0.926251i \(0.376987\pi\)
\(108\) −3.56910 −0.343437
\(109\) −13.6411 −1.30658 −0.653289 0.757108i \(-0.726611\pi\)
−0.653289 + 0.757108i \(0.726611\pi\)
\(110\) −5.44376 −0.519042
\(111\) 4.17226 0.396014
\(112\) 22.8589 2.15996
\(113\) 0.00537413 0.000505555 0 0.000252778 1.00000i \(-0.499920\pi\)
0.000252778 1.00000i \(0.499920\pi\)
\(114\) 4.19751 0.393132
\(115\) −0.150206 −0.0140068
\(116\) 12.6023 1.17010
\(117\) −0.0138803 −0.00128324
\(118\) 17.9323 1.65080
\(119\) 31.3105 2.87023
\(120\) 1.21528 0.110939
\(121\) 9.33014 0.848194
\(122\) −4.98384 −0.451216
\(123\) 1.58063 0.142521
\(124\) 16.3791 1.47089
\(125\) −6.14613 −0.549726
\(126\) 18.0094 1.60440
\(127\) −17.3073 −1.53577 −0.767886 0.640587i \(-0.778691\pi\)
−0.767886 + 0.640587i \(0.778691\pi\)
\(128\) −6.63350 −0.586324
\(129\) 6.64670 0.585209
\(130\) 0.00852615 0.000747793 0
\(131\) 12.8052 1.11880 0.559399 0.828898i \(-0.311032\pi\)
0.559399 + 0.828898i \(0.311032\pi\)
\(132\) 15.5562 1.35399
\(133\) 4.86422 0.421782
\(134\) −10.7156 −0.925688
\(135\) −1.47750 −0.127163
\(136\) −5.47709 −0.469656
\(137\) −12.9295 −1.10464 −0.552321 0.833632i \(-0.686258\pi\)
−0.552321 + 0.833632i \(0.686258\pi\)
\(138\) 0.983694 0.0837376
\(139\) 16.2582 1.37900 0.689499 0.724286i \(-0.257831\pi\)
0.689499 + 0.724286i \(0.257831\pi\)
\(140\) −4.82708 −0.407963
\(141\) −19.6461 −1.65450
\(142\) 23.5893 1.97957
\(143\) −0.0318415 −0.00266272
\(144\) −9.23669 −0.769724
\(145\) 5.21698 0.433246
\(146\) −6.93282 −0.573764
\(147\) 37.1257 3.06208
\(148\) 2.89895 0.238292
\(149\) −9.79216 −0.802205 −0.401103 0.916033i \(-0.631373\pi\)
−0.401103 + 0.916033i \(0.631373\pi\)
\(150\) 19.2632 1.57283
\(151\) 20.4959 1.66793 0.833966 0.551816i \(-0.186065\pi\)
0.833966 + 0.551816i \(0.186065\pi\)
\(152\) −0.850890 −0.0690163
\(153\) −12.6518 −1.02284
\(154\) 41.3136 3.32914
\(155\) 6.78046 0.544620
\(156\) −0.0243645 −0.00195072
\(157\) 6.60026 0.526758 0.263379 0.964692i \(-0.415163\pi\)
0.263379 + 0.964692i \(0.415163\pi\)
\(158\) 17.1172 1.36177
\(159\) 15.2670 1.21075
\(160\) 4.58300 0.362318
\(161\) 1.13994 0.0898399
\(162\) 20.7833 1.63289
\(163\) −19.7074 −1.54360 −0.771802 0.635863i \(-0.780644\pi\)
−0.771802 + 0.635863i \(0.780644\pi\)
\(164\) 1.09824 0.0857585
\(165\) 6.43979 0.501337
\(166\) −19.0708 −1.48018
\(167\) −17.9528 −1.38923 −0.694616 0.719381i \(-0.744426\pi\)
−0.694616 + 0.719381i \(0.744426\pi\)
\(168\) −9.22293 −0.711564
\(169\) −13.0000 −0.999996
\(170\) 7.77151 0.596048
\(171\) −1.96551 −0.150306
\(172\) 4.61823 0.352136
\(173\) −17.6545 −1.34225 −0.671125 0.741345i \(-0.734188\pi\)
−0.671125 + 0.741345i \(0.734188\pi\)
\(174\) −34.1657 −2.59010
\(175\) 22.3229 1.68745
\(176\) −21.1890 −1.59718
\(177\) −21.2133 −1.59449
\(178\) 17.1272 1.28374
\(179\) 9.02938 0.674888 0.337444 0.941346i \(-0.390438\pi\)
0.337444 + 0.941346i \(0.390438\pi\)
\(180\) 1.95050 0.145382
\(181\) 1.96760 0.146251 0.0731255 0.997323i \(-0.476703\pi\)
0.0731255 + 0.997323i \(0.476703\pi\)
\(182\) −0.0647063 −0.00479635
\(183\) 5.89572 0.435824
\(184\) −0.199408 −0.0147005
\(185\) 1.20008 0.0882314
\(186\) −44.4049 −3.25592
\(187\) −29.0233 −2.12239
\(188\) −13.6504 −0.995558
\(189\) 11.2130 0.815625
\(190\) 1.20734 0.0875895
\(191\) −21.6261 −1.56481 −0.782403 0.622772i \(-0.786006\pi\)
−0.782403 + 0.622772i \(0.786006\pi\)
\(192\) −9.07017 −0.654583
\(193\) −7.77340 −0.559541 −0.279771 0.960067i \(-0.590258\pi\)
−0.279771 + 0.960067i \(0.590258\pi\)
\(194\) 13.3167 0.956086
\(195\) −0.0100862 −0.000722285 0
\(196\) 25.7955 1.84253
\(197\) 16.2108 1.15497 0.577485 0.816401i \(-0.304034\pi\)
0.577485 + 0.816401i \(0.304034\pi\)
\(198\) −16.6938 −1.18638
\(199\) 9.46490 0.670949 0.335474 0.942049i \(-0.391103\pi\)
0.335474 + 0.942049i \(0.391103\pi\)
\(200\) −3.90490 −0.276118
\(201\) 12.6762 0.894112
\(202\) 21.1761 1.48994
\(203\) −39.5925 −2.77885
\(204\) −22.2080 −1.55487
\(205\) 0.454640 0.0317534
\(206\) 29.6770 2.06769
\(207\) −0.460622 −0.0320154
\(208\) 0.0331868 0.00230109
\(209\) −4.50890 −0.311887
\(210\) 13.0865 0.903056
\(211\) 9.01433 0.620572 0.310286 0.950643i \(-0.399575\pi\)
0.310286 + 0.950643i \(0.399575\pi\)
\(212\) 10.6077 0.728541
\(213\) −27.9053 −1.91204
\(214\) −14.6881 −1.00406
\(215\) 1.91181 0.130384
\(216\) −1.96147 −0.133461
\(217\) −51.4580 −3.49320
\(218\) 25.6956 1.74032
\(219\) 8.20130 0.554193
\(220\) 4.47446 0.301668
\(221\) 0.0454570 0.00305777
\(222\) −7.85924 −0.527478
\(223\) −20.3344 −1.36169 −0.680847 0.732426i \(-0.738388\pi\)
−0.680847 + 0.732426i \(0.738388\pi\)
\(224\) −34.7811 −2.32391
\(225\) −9.02011 −0.601341
\(226\) −0.0101232 −0.000673384 0
\(227\) −26.4399 −1.75488 −0.877438 0.479689i \(-0.840749\pi\)
−0.877438 + 0.479689i \(0.840749\pi\)
\(228\) −3.45011 −0.228489
\(229\) −4.30401 −0.284417 −0.142208 0.989837i \(-0.545420\pi\)
−0.142208 + 0.989837i \(0.545420\pi\)
\(230\) 0.282942 0.0186567
\(231\) −48.8726 −3.21558
\(232\) 6.92584 0.454704
\(233\) −15.6891 −1.02783 −0.513914 0.857842i \(-0.671805\pi\)
−0.513914 + 0.857842i \(0.671805\pi\)
\(234\) 0.0261462 0.00170923
\(235\) −5.65085 −0.368621
\(236\) −14.7393 −0.959447
\(237\) −20.2490 −1.31532
\(238\) −58.9793 −3.82306
\(239\) 15.5769 1.00759 0.503793 0.863824i \(-0.331937\pi\)
0.503793 + 0.863824i \(0.331937\pi\)
\(240\) −6.71185 −0.433248
\(241\) 7.98140 0.514127 0.257064 0.966395i \(-0.417245\pi\)
0.257064 + 0.966395i \(0.417245\pi\)
\(242\) −17.5751 −1.12977
\(243\) −17.6704 −1.13356
\(244\) 4.09643 0.262247
\(245\) 10.6785 0.682227
\(246\) −2.97741 −0.189833
\(247\) 0.00706194 0.000449340 0
\(248\) 9.00145 0.571593
\(249\) 22.5601 1.42969
\(250\) 11.5774 0.732219
\(251\) −20.9390 −1.32166 −0.660828 0.750537i \(-0.729795\pi\)
−0.660828 + 0.750537i \(0.729795\pi\)
\(252\) −14.8027 −0.932481
\(253\) −1.05667 −0.0664322
\(254\) 32.6015 2.04560
\(255\) −9.19344 −0.575716
\(256\) 20.6362 1.28976
\(257\) 21.3983 1.33479 0.667394 0.744705i \(-0.267410\pi\)
0.667394 + 0.744705i \(0.267410\pi\)
\(258\) −12.5203 −0.779481
\(259\) −9.10758 −0.565918
\(260\) −0.00700801 −0.000434618 0
\(261\) 15.9983 0.990272
\(262\) −24.1211 −1.49021
\(263\) 11.4105 0.703600 0.351800 0.936075i \(-0.385570\pi\)
0.351800 + 0.936075i \(0.385570\pi\)
\(264\) 8.54920 0.526167
\(265\) 4.39127 0.269754
\(266\) −9.16269 −0.561800
\(267\) −20.2610 −1.23995
\(268\) 8.80763 0.538012
\(269\) −10.6531 −0.649528 −0.324764 0.945795i \(-0.605285\pi\)
−0.324764 + 0.945795i \(0.605285\pi\)
\(270\) 2.78315 0.169377
\(271\) 2.39657 0.145581 0.0727905 0.997347i \(-0.476810\pi\)
0.0727905 + 0.997347i \(0.476810\pi\)
\(272\) 30.2494 1.83414
\(273\) 0.0765455 0.00463274
\(274\) 24.3552 1.47135
\(275\) −20.6922 −1.24779
\(276\) −0.808541 −0.0486684
\(277\) 5.35349 0.321660 0.160830 0.986982i \(-0.448583\pi\)
0.160830 + 0.986982i \(0.448583\pi\)
\(278\) −30.6253 −1.83678
\(279\) 20.7929 1.24484
\(280\) −2.65281 −0.158536
\(281\) −12.3671 −0.737761 −0.368880 0.929477i \(-0.620259\pi\)
−0.368880 + 0.929477i \(0.620259\pi\)
\(282\) 37.0071 2.20374
\(283\) −16.7113 −0.993385 −0.496692 0.867927i \(-0.665452\pi\)
−0.496692 + 0.867927i \(0.665452\pi\)
\(284\) −19.3890 −1.15053
\(285\) −1.42824 −0.0846017
\(286\) 0.0599796 0.00354667
\(287\) −3.45034 −0.203667
\(288\) 14.0542 0.828151
\(289\) 24.4336 1.43727
\(290\) −9.82716 −0.577071
\(291\) −15.7533 −0.923472
\(292\) 5.69839 0.333473
\(293\) 31.7293 1.85365 0.926823 0.375498i \(-0.122528\pi\)
0.926823 + 0.375498i \(0.122528\pi\)
\(294\) −69.9333 −4.07859
\(295\) −6.10163 −0.355250
\(296\) 1.59317 0.0926012
\(297\) −10.3939 −0.603114
\(298\) 18.4454 1.06851
\(299\) 0.00165498 9.57100e−5 0
\(300\) −15.8332 −0.914131
\(301\) −14.5090 −0.836285
\(302\) −38.6079 −2.22163
\(303\) −25.0506 −1.43912
\(304\) 4.69938 0.269528
\(305\) 1.69580 0.0971012
\(306\) 23.8320 1.36239
\(307\) 5.83357 0.332940 0.166470 0.986047i \(-0.446763\pi\)
0.166470 + 0.986047i \(0.446763\pi\)
\(308\) −33.9574 −1.93490
\(309\) −35.1069 −1.99716
\(310\) −12.7723 −0.725417
\(311\) 1.90870 0.108232 0.0541162 0.998535i \(-0.482766\pi\)
0.0541162 + 0.998535i \(0.482766\pi\)
\(312\) −0.0133900 −0.000758057 0
\(313\) −27.4581 −1.55202 −0.776011 0.630719i \(-0.782760\pi\)
−0.776011 + 0.630719i \(0.782760\pi\)
\(314\) −12.4328 −0.701626
\(315\) −6.12786 −0.345266
\(316\) −14.0693 −0.791461
\(317\) −1.00000 −0.0561656
\(318\) −28.7582 −1.61268
\(319\) 36.7003 2.05482
\(320\) −2.60887 −0.145840
\(321\) 17.3756 0.969811
\(322\) −2.14729 −0.119664
\(323\) 6.43690 0.358158
\(324\) −17.0827 −0.949039
\(325\) 0.0324086 0.00179771
\(326\) 37.1226 2.05603
\(327\) −30.3970 −1.68096
\(328\) 0.603561 0.0333261
\(329\) 42.8852 2.36434
\(330\) −12.1306 −0.667766
\(331\) −20.7970 −1.14311 −0.571553 0.820565i \(-0.693659\pi\)
−0.571553 + 0.820565i \(0.693659\pi\)
\(332\) 15.6751 0.860284
\(333\) 3.68015 0.201671
\(334\) 33.8175 1.85041
\(335\) 3.64609 0.199207
\(336\) 50.9374 2.77886
\(337\) −0.0755458 −0.00411524 −0.00205762 0.999998i \(-0.500655\pi\)
−0.00205762 + 0.999998i \(0.500655\pi\)
\(338\) 24.4879 1.33196
\(339\) 0.0119754 0.000650414 0
\(340\) −6.38774 −0.346424
\(341\) 47.6990 2.58305
\(342\) 3.70241 0.200204
\(343\) −46.9917 −2.53731
\(344\) 2.53803 0.136842
\(345\) −0.334711 −0.0180203
\(346\) 33.2557 1.78784
\(347\) 2.55204 0.137001 0.0685004 0.997651i \(-0.478179\pi\)
0.0685004 + 0.997651i \(0.478179\pi\)
\(348\) 28.0823 1.50537
\(349\) 30.9630 1.65741 0.828704 0.559686i \(-0.189078\pi\)
0.828704 + 0.559686i \(0.189078\pi\)
\(350\) −42.0493 −2.24763
\(351\) 0.0162791 0.000868917 0
\(352\) 32.2404 1.71842
\(353\) −28.2608 −1.50417 −0.752085 0.659067i \(-0.770952\pi\)
−0.752085 + 0.659067i \(0.770952\pi\)
\(354\) 39.9592 2.12381
\(355\) −8.02647 −0.426001
\(356\) −14.0776 −0.746112
\(357\) 69.7705 3.69265
\(358\) −17.0085 −0.898930
\(359\) −7.32781 −0.386747 −0.193373 0.981125i \(-0.561943\pi\)
−0.193373 + 0.981125i \(0.561943\pi\)
\(360\) 1.07193 0.0564959
\(361\) 1.00000 0.0526316
\(362\) −3.70636 −0.194802
\(363\) 20.7907 1.09123
\(364\) 0.0531849 0.00278765
\(365\) 2.35896 0.123474
\(366\) −11.1057 −0.580504
\(367\) 12.6177 0.658637 0.329319 0.944219i \(-0.393181\pi\)
0.329319 + 0.944219i \(0.393181\pi\)
\(368\) 1.10131 0.0574098
\(369\) 1.39420 0.0725789
\(370\) −2.26057 −0.117522
\(371\) −33.3261 −1.73020
\(372\) 36.4983 1.89235
\(373\) 15.0084 0.777108 0.388554 0.921426i \(-0.372975\pi\)
0.388554 + 0.921426i \(0.372975\pi\)
\(374\) 54.6709 2.82696
\(375\) −13.6957 −0.707242
\(376\) −7.50183 −0.386877
\(377\) −0.0574808 −0.00296041
\(378\) −21.1218 −1.08639
\(379\) −6.21863 −0.319430 −0.159715 0.987163i \(-0.551057\pi\)
−0.159715 + 0.987163i \(0.551057\pi\)
\(380\) −0.992363 −0.0509072
\(381\) −38.5665 −1.97582
\(382\) 40.7368 2.08428
\(383\) 31.8025 1.62503 0.812517 0.582938i \(-0.198097\pi\)
0.812517 + 0.582938i \(0.198097\pi\)
\(384\) −14.7817 −0.754326
\(385\) −14.0573 −0.716429
\(386\) 14.6427 0.745292
\(387\) 5.86273 0.298019
\(388\) −10.9456 −0.555678
\(389\) −6.94914 −0.352335 −0.176168 0.984360i \(-0.556370\pi\)
−0.176168 + 0.984360i \(0.556370\pi\)
\(390\) 0.0189992 0.000962061 0
\(391\) 1.50850 0.0762881
\(392\) 14.1764 0.716016
\(393\) 28.5345 1.43937
\(394\) −30.5361 −1.53839
\(395\) −5.82427 −0.293051
\(396\) 13.7213 0.689524
\(397\) −6.61385 −0.331940 −0.165970 0.986131i \(-0.553075\pi\)
−0.165970 + 0.986131i \(0.553075\pi\)
\(398\) −17.8289 −0.893683
\(399\) 10.8392 0.542637
\(400\) 21.5664 1.07832
\(401\) −30.7993 −1.53805 −0.769023 0.639222i \(-0.779257\pi\)
−0.769023 + 0.639222i \(0.779257\pi\)
\(402\) −23.8781 −1.19093
\(403\) −0.0747074 −0.00372144
\(404\) −17.4055 −0.865957
\(405\) −7.07172 −0.351397
\(406\) 74.5799 3.70134
\(407\) 8.44228 0.418468
\(408\) −12.2048 −0.604229
\(409\) −24.6120 −1.21699 −0.608493 0.793560i \(-0.708226\pi\)
−0.608493 + 0.793560i \(0.708226\pi\)
\(410\) −0.856400 −0.0422946
\(411\) −28.8113 −1.42116
\(412\) −24.3928 −1.20175
\(413\) 46.3062 2.27858
\(414\) 0.867668 0.0426436
\(415\) 6.48903 0.318534
\(416\) −0.0504957 −0.00247575
\(417\) 36.2287 1.77413
\(418\) 8.49336 0.415424
\(419\) 21.7303 1.06160 0.530798 0.847498i \(-0.321892\pi\)
0.530798 + 0.847498i \(0.321892\pi\)
\(420\) −10.7564 −0.524858
\(421\) 8.37727 0.408283 0.204142 0.978941i \(-0.434560\pi\)
0.204142 + 0.978941i \(0.434560\pi\)
\(422\) −16.9802 −0.826583
\(423\) −17.3289 −0.842558
\(424\) 5.82967 0.283114
\(425\) 29.5401 1.43291
\(426\) 52.5650 2.54678
\(427\) −12.8697 −0.622808
\(428\) 12.0728 0.583562
\(429\) −0.0709539 −0.00342569
\(430\) −3.60125 −0.173668
\(431\) −30.4200 −1.46528 −0.732640 0.680616i \(-0.761712\pi\)
−0.732640 + 0.680616i \(0.761712\pi\)
\(432\) 10.8330 0.521203
\(433\) −34.3801 −1.65220 −0.826102 0.563521i \(-0.809446\pi\)
−0.826102 + 0.563521i \(0.809446\pi\)
\(434\) 96.9309 4.65283
\(435\) 11.6252 0.557386
\(436\) −21.1203 −1.01148
\(437\) 0.234352 0.0112106
\(438\) −15.4487 −0.738168
\(439\) −1.91118 −0.0912154 −0.0456077 0.998959i \(-0.514522\pi\)
−0.0456077 + 0.998959i \(0.514522\pi\)
\(440\) 2.45903 0.117229
\(441\) 32.7467 1.55937
\(442\) −0.0856268 −0.00407285
\(443\) −19.4956 −0.926266 −0.463133 0.886289i \(-0.653275\pi\)
−0.463133 + 0.886289i \(0.653275\pi\)
\(444\) 6.45985 0.306571
\(445\) −5.82771 −0.276260
\(446\) 38.3037 1.81373
\(447\) −21.8203 −1.03206
\(448\) 19.7992 0.935422
\(449\) 29.3232 1.38385 0.691925 0.721970i \(-0.256763\pi\)
0.691925 + 0.721970i \(0.256763\pi\)
\(450\) 16.9911 0.800967
\(451\) 3.19829 0.150602
\(452\) 0.00832069 0.000391372 0
\(453\) 45.6719 2.14585
\(454\) 49.8045 2.33744
\(455\) 0.0220170 0.00103217
\(456\) −1.89607 −0.0887918
\(457\) −0.0902563 −0.00422201 −0.00211101 0.999998i \(-0.500672\pi\)
−0.00211101 + 0.999998i \(0.500672\pi\)
\(458\) 8.10741 0.378834
\(459\) 14.8383 0.692592
\(460\) −0.232562 −0.0108433
\(461\) 29.3079 1.36500 0.682502 0.730883i \(-0.260892\pi\)
0.682502 + 0.730883i \(0.260892\pi\)
\(462\) 92.0609 4.28306
\(463\) −33.5933 −1.56121 −0.780606 0.625023i \(-0.785090\pi\)
−0.780606 + 0.625023i \(0.785090\pi\)
\(464\) −38.2508 −1.77575
\(465\) 15.1092 0.700672
\(466\) 29.5534 1.36904
\(467\) 5.37396 0.248677 0.124339 0.992240i \(-0.460319\pi\)
0.124339 + 0.992240i \(0.460319\pi\)
\(468\) −0.0214907 −0.000993408 0
\(469\) −27.6708 −1.27772
\(470\) 10.6444 0.490992
\(471\) 14.7076 0.677692
\(472\) −8.10027 −0.372845
\(473\) 13.4491 0.618392
\(474\) 38.1429 1.75196
\(475\) 4.58919 0.210567
\(476\) 48.4776 2.22197
\(477\) 13.4662 0.616577
\(478\) −29.3421 −1.34207
\(479\) 36.8426 1.68338 0.841690 0.539961i \(-0.181561\pi\)
0.841690 + 0.539961i \(0.181561\pi\)
\(480\) 10.2125 0.466134
\(481\) −0.0132225 −0.000602894 0
\(482\) −15.0345 −0.684802
\(483\) 2.54018 0.115582
\(484\) 14.4457 0.656624
\(485\) −4.53115 −0.205749
\(486\) 33.2855 1.50986
\(487\) −32.1548 −1.45708 −0.728538 0.685006i \(-0.759800\pi\)
−0.728538 + 0.685006i \(0.759800\pi\)
\(488\) 2.25127 0.101910
\(489\) −43.9149 −1.98590
\(490\) −20.1151 −0.908706
\(491\) −14.1248 −0.637443 −0.318722 0.947848i \(-0.603254\pi\)
−0.318722 + 0.947848i \(0.603254\pi\)
\(492\) 2.44727 0.110331
\(493\) −52.3933 −2.35967
\(494\) −0.0133025 −0.000598508 0
\(495\) 5.68022 0.255307
\(496\) −49.7142 −2.23223
\(497\) 60.9142 2.73238
\(498\) −42.4963 −1.90431
\(499\) 7.34031 0.328597 0.164299 0.986411i \(-0.447464\pi\)
0.164299 + 0.986411i \(0.447464\pi\)
\(500\) −9.51596 −0.425567
\(501\) −40.0050 −1.78729
\(502\) 39.4425 1.76041
\(503\) 14.4031 0.642202 0.321101 0.947045i \(-0.395947\pi\)
0.321101 + 0.947045i \(0.395947\pi\)
\(504\) −8.13509 −0.362366
\(505\) −7.20535 −0.320634
\(506\) 1.99044 0.0884857
\(507\) −28.9683 −1.28653
\(508\) −26.7966 −1.18891
\(509\) 35.6530 1.58029 0.790146 0.612919i \(-0.210005\pi\)
0.790146 + 0.612919i \(0.210005\pi\)
\(510\) 17.3176 0.766836
\(511\) −17.9025 −0.791961
\(512\) −25.6051 −1.13160
\(513\) 2.30520 0.101777
\(514\) −40.3077 −1.77790
\(515\) −10.0979 −0.444966
\(516\) 10.2910 0.453036
\(517\) −39.7525 −1.74831
\(518\) 17.1559 0.753785
\(519\) −39.3404 −1.72685
\(520\) −0.00385138 −0.000168894 0
\(521\) −6.85409 −0.300283 −0.150142 0.988665i \(-0.547973\pi\)
−0.150142 + 0.988665i \(0.547973\pi\)
\(522\) −30.1359 −1.31901
\(523\) 23.2697 1.01751 0.508757 0.860910i \(-0.330105\pi\)
0.508757 + 0.860910i \(0.330105\pi\)
\(524\) 19.8262 0.866110
\(525\) 49.7430 2.17096
\(526\) −21.4938 −0.937174
\(527\) −68.0951 −2.96627
\(528\) −47.2164 −2.05483
\(529\) −22.9451 −0.997612
\(530\) −8.27179 −0.359304
\(531\) −18.7112 −0.811997
\(532\) 7.53121 0.326519
\(533\) −0.00500924 −0.000216974 0
\(534\) 38.1653 1.65158
\(535\) 4.99778 0.216073
\(536\) 4.84040 0.209073
\(537\) 20.1206 0.868266
\(538\) 20.0670 0.865152
\(539\) 75.1212 3.23570
\(540\) −2.28759 −0.0984422
\(541\) −20.1655 −0.866982 −0.433491 0.901158i \(-0.642718\pi\)
−0.433491 + 0.901158i \(0.642718\pi\)
\(542\) −4.51438 −0.193909
\(543\) 4.38450 0.188157
\(544\) −46.0264 −1.97336
\(545\) −8.74316 −0.374516
\(546\) −0.144188 −0.00617067
\(547\) 12.6986 0.542952 0.271476 0.962445i \(-0.412488\pi\)
0.271476 + 0.962445i \(0.412488\pi\)
\(548\) −20.0186 −0.855150
\(549\) 5.20032 0.221944
\(550\) 38.9776 1.66201
\(551\) −8.13953 −0.346755
\(552\) −0.444349 −0.0189127
\(553\) 44.2014 1.87963
\(554\) −10.0843 −0.428441
\(555\) 2.67418 0.113513
\(556\) 25.1723 1.06754
\(557\) 3.42970 0.145321 0.0726605 0.997357i \(-0.476851\pi\)
0.0726605 + 0.997357i \(0.476851\pi\)
\(558\) −39.1674 −1.65809
\(559\) −0.0210643 −0.000890927 0
\(560\) 14.6512 0.619127
\(561\) −64.6738 −2.73053
\(562\) 23.2958 0.982675
\(563\) −9.88580 −0.416637 −0.208318 0.978061i \(-0.566799\pi\)
−0.208318 + 0.978061i \(0.566799\pi\)
\(564\) −30.4178 −1.28082
\(565\) 0.00344451 0.000144912 0
\(566\) 31.4789 1.32316
\(567\) 53.6684 2.25386
\(568\) −10.6556 −0.447099
\(569\) −15.5797 −0.653135 −0.326567 0.945174i \(-0.605892\pi\)
−0.326567 + 0.945174i \(0.605892\pi\)
\(570\) 2.69036 0.112687
\(571\) 2.27303 0.0951233 0.0475616 0.998868i \(-0.484855\pi\)
0.0475616 + 0.998868i \(0.484855\pi\)
\(572\) −0.0492998 −0.00206133
\(573\) −48.1903 −2.01318
\(574\) 6.49936 0.271278
\(575\) 1.07549 0.0448509
\(576\) −8.00035 −0.333348
\(577\) −37.1794 −1.54780 −0.773899 0.633309i \(-0.781696\pi\)
−0.773899 + 0.633309i \(0.781696\pi\)
\(578\) −46.0253 −1.91440
\(579\) −17.3218 −0.719869
\(580\) 8.07737 0.335394
\(581\) −49.2463 −2.04308
\(582\) 29.6742 1.23004
\(583\) 30.8916 1.27940
\(584\) 3.13166 0.129589
\(585\) −0.00889650 −0.000367825 0
\(586\) −59.7682 −2.46900
\(587\) −22.7649 −0.939607 −0.469803 0.882771i \(-0.655675\pi\)
−0.469803 + 0.882771i \(0.655675\pi\)
\(588\) 57.4812 2.37048
\(589\) −10.5789 −0.435895
\(590\) 11.4936 0.473183
\(591\) 36.1232 1.48591
\(592\) −8.79894 −0.361634
\(593\) 37.9661 1.55908 0.779541 0.626352i \(-0.215453\pi\)
0.779541 + 0.626352i \(0.215453\pi\)
\(594\) 19.5788 0.803330
\(595\) 20.0683 0.822718
\(596\) −15.1611 −0.621021
\(597\) 21.0910 0.863199
\(598\) −0.00311747 −0.000127483 0
\(599\) −13.7378 −0.561313 −0.280656 0.959808i \(-0.590552\pi\)
−0.280656 + 0.959808i \(0.590552\pi\)
\(600\) −8.70145 −0.355235
\(601\) −7.88485 −0.321630 −0.160815 0.986985i \(-0.551412\pi\)
−0.160815 + 0.986985i \(0.551412\pi\)
\(602\) 27.3305 1.11391
\(603\) 11.1811 0.455329
\(604\) 31.7335 1.29122
\(605\) 5.98009 0.243125
\(606\) 47.1875 1.91686
\(607\) −36.1725 −1.46820 −0.734098 0.679044i \(-0.762395\pi\)
−0.734098 + 0.679044i \(0.762395\pi\)
\(608\) −7.15040 −0.289987
\(609\) −88.2256 −3.57508
\(610\) −3.19436 −0.129336
\(611\) 0.0622613 0.00251882
\(612\) −19.5886 −0.791822
\(613\) 17.5935 0.710595 0.355298 0.934753i \(-0.384380\pi\)
0.355298 + 0.934753i \(0.384380\pi\)
\(614\) −10.9886 −0.443465
\(615\) 1.01309 0.0408519
\(616\) −18.6619 −0.751911
\(617\) 14.4769 0.582817 0.291408 0.956599i \(-0.405876\pi\)
0.291408 + 0.956599i \(0.405876\pi\)
\(618\) 66.1305 2.66016
\(619\) −4.56796 −0.183602 −0.0918009 0.995777i \(-0.529262\pi\)
−0.0918009 + 0.995777i \(0.529262\pi\)
\(620\) 10.4981 0.421613
\(621\) 0.540227 0.0216786
\(622\) −3.59540 −0.144162
\(623\) 44.2274 1.77193
\(624\) 0.0739515 0.00296043
\(625\) 19.0066 0.760266
\(626\) 51.7225 2.06725
\(627\) −10.0474 −0.401253
\(628\) 10.2191 0.407786
\(629\) −12.0522 −0.480552
\(630\) 11.5430 0.459883
\(631\) 10.7287 0.427103 0.213552 0.976932i \(-0.431497\pi\)
0.213552 + 0.976932i \(0.431497\pi\)
\(632\) −7.73206 −0.307565
\(633\) 20.0870 0.798388
\(634\) 1.88369 0.0748109
\(635\) −11.0930 −0.440211
\(636\) 23.6376 0.937293
\(637\) −0.117657 −0.00466173
\(638\) −69.1319 −2.73696
\(639\) −24.6139 −0.973711
\(640\) −4.25169 −0.168063
\(641\) 4.14690 0.163793 0.0818964 0.996641i \(-0.473902\pi\)
0.0818964 + 0.996641i \(0.473902\pi\)
\(642\) −32.7302 −1.29176
\(643\) 4.59085 0.181046 0.0905228 0.995894i \(-0.471146\pi\)
0.0905228 + 0.995894i \(0.471146\pi\)
\(644\) 1.76495 0.0695489
\(645\) 4.26016 0.167744
\(646\) −12.1251 −0.477056
\(647\) −31.0569 −1.22097 −0.610486 0.792027i \(-0.709026\pi\)
−0.610486 + 0.792027i \(0.709026\pi\)
\(648\) −9.38812 −0.368800
\(649\) −42.9236 −1.68490
\(650\) −0.0610477 −0.00239449
\(651\) −114.666 −4.49412
\(652\) −30.5127 −1.19497
\(653\) −19.9388 −0.780265 −0.390133 0.920759i \(-0.627571\pi\)
−0.390133 + 0.920759i \(0.627571\pi\)
\(654\) 57.2585 2.23899
\(655\) 8.20743 0.320691
\(656\) −3.33341 −0.130148
\(657\) 7.23396 0.282224
\(658\) −80.7825 −3.14923
\(659\) −2.94573 −0.114749 −0.0573746 0.998353i \(-0.518273\pi\)
−0.0573746 + 0.998353i \(0.518273\pi\)
\(660\) 9.97064 0.388106
\(661\) −16.4977 −0.641688 −0.320844 0.947132i \(-0.603966\pi\)
−0.320844 + 0.947132i \(0.603966\pi\)
\(662\) 39.1751 1.52258
\(663\) 0.101294 0.00393392
\(664\) 8.61456 0.334310
\(665\) 3.11769 0.120899
\(666\) −6.93225 −0.268619
\(667\) −1.90751 −0.0738593
\(668\) −27.7961 −1.07546
\(669\) −45.3121 −1.75187
\(670\) −6.86810 −0.265338
\(671\) 11.9296 0.460536
\(672\) −77.5043 −2.98979
\(673\) −48.0738 −1.85311 −0.926555 0.376159i \(-0.877244\pi\)
−0.926555 + 0.376159i \(0.877244\pi\)
\(674\) 0.142305 0.00548138
\(675\) 10.5790 0.407185
\(676\) −20.1276 −0.774140
\(677\) 20.6462 0.793497 0.396749 0.917927i \(-0.370139\pi\)
0.396749 + 0.917927i \(0.370139\pi\)
\(678\) −0.0225579 −0.000866332 0
\(679\) 34.3876 1.31968
\(680\) −3.51050 −0.134622
\(681\) −58.9171 −2.25771
\(682\) −89.8502 −3.44054
\(683\) 31.3990 1.20145 0.600724 0.799457i \(-0.294879\pi\)
0.600724 + 0.799457i \(0.294879\pi\)
\(684\) −3.04317 −0.116359
\(685\) −8.28707 −0.316633
\(686\) 88.5177 3.37962
\(687\) −9.59080 −0.365912
\(688\) −14.0173 −0.534405
\(689\) −0.0483832 −0.00184325
\(690\) 0.630492 0.0240024
\(691\) −13.2618 −0.504502 −0.252251 0.967662i \(-0.581171\pi\)
−0.252251 + 0.967662i \(0.581171\pi\)
\(692\) −27.3343 −1.03909
\(693\) −43.1081 −1.63754
\(694\) −4.80725 −0.182481
\(695\) 10.4206 0.395274
\(696\) 15.4331 0.584992
\(697\) −4.56588 −0.172945
\(698\) −58.3246 −2.20762
\(699\) −34.9607 −1.32234
\(700\) 34.5622 1.30633
\(701\) −13.2660 −0.501050 −0.250525 0.968110i \(-0.580603\pi\)
−0.250525 + 0.968110i \(0.580603\pi\)
\(702\) −0.0306649 −0.00115737
\(703\) −1.87236 −0.0706174
\(704\) −18.3528 −0.691699
\(705\) −12.5920 −0.474243
\(706\) 53.2345 2.00351
\(707\) 54.6826 2.05655
\(708\) −32.8442 −1.23436
\(709\) 22.0145 0.826773 0.413386 0.910556i \(-0.364346\pi\)
0.413386 + 0.910556i \(0.364346\pi\)
\(710\) 15.1194 0.567420
\(711\) −17.8607 −0.669828
\(712\) −7.73662 −0.289942
\(713\) −2.47918 −0.0928460
\(714\) −131.426 −4.91849
\(715\) −0.0204086 −0.000763239 0
\(716\) 13.9801 0.522459
\(717\) 34.7107 1.29629
\(718\) 13.8033 0.515135
\(719\) 4.32667 0.161357 0.0806787 0.996740i \(-0.474291\pi\)
0.0806787 + 0.996740i \(0.474291\pi\)
\(720\) −5.92020 −0.220633
\(721\) 76.6344 2.85402
\(722\) −1.88369 −0.0701037
\(723\) 17.7853 0.661442
\(724\) 3.04641 0.113219
\(725\) −37.3538 −1.38729
\(726\) −39.1633 −1.45349
\(727\) −14.3121 −0.530808 −0.265404 0.964137i \(-0.585505\pi\)
−0.265404 + 0.964137i \(0.585505\pi\)
\(728\) 0.0292288 0.00108329
\(729\) −6.27578 −0.232436
\(730\) −4.44355 −0.164463
\(731\) −19.2000 −0.710136
\(732\) 9.12826 0.337390
\(733\) −19.6707 −0.726553 −0.363277 0.931681i \(-0.618342\pi\)
−0.363277 + 0.931681i \(0.618342\pi\)
\(734\) −23.7678 −0.877285
\(735\) 23.7955 0.877709
\(736\) −1.67571 −0.0617675
\(737\) 25.6495 0.944810
\(738\) −2.62623 −0.0966729
\(739\) −33.1384 −1.21902 −0.609508 0.792780i \(-0.708633\pi\)
−0.609508 + 0.792780i \(0.708633\pi\)
\(740\) 1.85806 0.0683037
\(741\) 0.0157364 0.000578092 0
\(742\) 62.7760 2.30458
\(743\) −1.88309 −0.0690839 −0.0345419 0.999403i \(-0.510997\pi\)
−0.0345419 + 0.999403i \(0.510997\pi\)
\(744\) 20.0583 0.735374
\(745\) −6.27622 −0.229943
\(746\) −28.2712 −1.03508
\(747\) 19.8992 0.728074
\(748\) −44.9363 −1.64304
\(749\) −37.9290 −1.38590
\(750\) 25.7984 0.942025
\(751\) 45.7503 1.66945 0.834726 0.550666i \(-0.185626\pi\)
0.834726 + 0.550666i \(0.185626\pi\)
\(752\) 41.4319 1.51087
\(753\) −46.6592 −1.70036
\(754\) 0.108276 0.00394318
\(755\) 13.1367 0.478094
\(756\) 17.3609 0.631410
\(757\) 44.7764 1.62743 0.813713 0.581267i \(-0.197443\pi\)
0.813713 + 0.581267i \(0.197443\pi\)
\(758\) 11.7140 0.425471
\(759\) −2.35462 −0.0854673
\(760\) −0.545372 −0.0197827
\(761\) −41.8409 −1.51673 −0.758366 0.651829i \(-0.774002\pi\)
−0.758366 + 0.651829i \(0.774002\pi\)
\(762\) 72.6473 2.63174
\(763\) 66.3533 2.40215
\(764\) −33.4833 −1.21138
\(765\) −8.10908 −0.293184
\(766\) −59.9061 −2.16450
\(767\) 0.0672280 0.00242746
\(768\) 45.9845 1.65932
\(769\) 30.6861 1.10657 0.553285 0.832992i \(-0.313374\pi\)
0.553285 + 0.832992i \(0.313374\pi\)
\(770\) 26.4797 0.954261
\(771\) 47.6827 1.71725
\(772\) −12.0354 −0.433165
\(773\) 20.0074 0.719617 0.359809 0.933026i \(-0.382842\pi\)
0.359809 + 0.933026i \(0.382842\pi\)
\(774\) −11.0436 −0.396952
\(775\) −48.5485 −1.74391
\(776\) −6.01536 −0.215939
\(777\) −20.2948 −0.728072
\(778\) 13.0900 0.469300
\(779\) −0.709329 −0.0254144
\(780\) −0.0156162 −0.000559151 0
\(781\) −56.4645 −2.02046
\(782\) −2.84154 −0.101613
\(783\) −18.7632 −0.670542
\(784\) −78.2949 −2.79625
\(785\) 4.23039 0.150989
\(786\) −53.7501 −1.91720
\(787\) −51.1664 −1.82388 −0.911942 0.410320i \(-0.865417\pi\)
−0.911942 + 0.410320i \(0.865417\pi\)
\(788\) 25.0989 0.894112
\(789\) 25.4264 0.905205
\(790\) 10.9711 0.390335
\(791\) −0.0261410 −0.000929466 0
\(792\) 7.54083 0.267952
\(793\) −0.0186844 −0.000663502 0
\(794\) 12.4584 0.442133
\(795\) 9.78526 0.347047
\(796\) 14.6544 0.519410
\(797\) 39.8304 1.41087 0.705433 0.708776i \(-0.250752\pi\)
0.705433 + 0.708776i \(0.250752\pi\)
\(798\) −20.4176 −0.722775
\(799\) 56.7506 2.00769
\(800\) −32.8145 −1.16017
\(801\) −17.8712 −0.631448
\(802\) 58.0164 2.04863
\(803\) 16.5948 0.585616
\(804\) 19.6264 0.692170
\(805\) 0.730637 0.0257516
\(806\) 0.140725 0.00495684
\(807\) −23.7387 −0.835640
\(808\) −9.56553 −0.336514
\(809\) 16.0888 0.565653 0.282826 0.959171i \(-0.408728\pi\)
0.282826 + 0.959171i \(0.408728\pi\)
\(810\) 13.3209 0.468050
\(811\) 48.4330 1.70071 0.850357 0.526206i \(-0.176386\pi\)
0.850357 + 0.526206i \(0.176386\pi\)
\(812\) −61.3005 −2.15122
\(813\) 5.34037 0.187295
\(814\) −15.9026 −0.557387
\(815\) −12.6313 −0.442456
\(816\) 67.4061 2.35969
\(817\) −2.98280 −0.104355
\(818\) 46.3614 1.62099
\(819\) 0.0675170 0.00235923
\(820\) 0.703912 0.0245817
\(821\) 28.1834 0.983609 0.491805 0.870706i \(-0.336337\pi\)
0.491805 + 0.870706i \(0.336337\pi\)
\(822\) 54.2716 1.89294
\(823\) 20.5763 0.717245 0.358622 0.933483i \(-0.383247\pi\)
0.358622 + 0.933483i \(0.383247\pi\)
\(824\) −13.4055 −0.467003
\(825\) −46.1093 −1.60532
\(826\) −87.2266 −3.03500
\(827\) 46.4822 1.61634 0.808172 0.588946i \(-0.200457\pi\)
0.808172 + 0.588946i \(0.200457\pi\)
\(828\) −0.713174 −0.0247845
\(829\) 29.6562 1.03000 0.515002 0.857189i \(-0.327791\pi\)
0.515002 + 0.857189i \(0.327791\pi\)
\(830\) −12.2233 −0.424277
\(831\) 11.9294 0.413827
\(832\) 0.0287447 0.000996542 0
\(833\) −107.243 −3.71575
\(834\) −68.2437 −2.36309
\(835\) −11.5067 −0.398207
\(836\) −6.98106 −0.241445
\(837\) −24.3864 −0.842916
\(838\) −40.9332 −1.41401
\(839\) −5.64087 −0.194745 −0.0973723 0.995248i \(-0.531044\pi\)
−0.0973723 + 0.995248i \(0.531044\pi\)
\(840\) −5.91137 −0.203962
\(841\) 37.2519 1.28455
\(842\) −15.7802 −0.543821
\(843\) −27.5582 −0.949155
\(844\) 13.9568 0.480412
\(845\) −8.33223 −0.286637
\(846\) 32.6422 1.12226
\(847\) −45.3839 −1.55941
\(848\) −32.1967 −1.10564
\(849\) −37.2385 −1.27802
\(850\) −55.6445 −1.90859
\(851\) −0.438792 −0.0150416
\(852\) −43.2054 −1.48019
\(853\) 9.83203 0.336642 0.168321 0.985732i \(-0.446165\pi\)
0.168321 + 0.985732i \(0.446165\pi\)
\(854\) 24.2425 0.829562
\(855\) −1.25978 −0.0430836
\(856\) 6.63485 0.226774
\(857\) 12.8043 0.437388 0.218694 0.975793i \(-0.429820\pi\)
0.218694 + 0.975793i \(0.429820\pi\)
\(858\) 0.133655 0.00456291
\(859\) −19.8645 −0.677768 −0.338884 0.940828i \(-0.610049\pi\)
−0.338884 + 0.940828i \(0.610049\pi\)
\(860\) 2.96002 0.100936
\(861\) −7.68853 −0.262025
\(862\) 57.3018 1.95171
\(863\) −23.5287 −0.800927 −0.400463 0.916313i \(-0.631151\pi\)
−0.400463 + 0.916313i \(0.631151\pi\)
\(864\) −16.4831 −0.560765
\(865\) −11.3156 −0.384740
\(866\) 64.7615 2.20068
\(867\) 54.4465 1.84910
\(868\) −79.6717 −2.70423
\(869\) −40.9725 −1.38990
\(870\) −21.8983 −0.742421
\(871\) −0.0401728 −0.00136120
\(872\) −11.6071 −0.393064
\(873\) −13.8952 −0.470280
\(874\) −0.441446 −0.0149321
\(875\) 29.8961 1.01067
\(876\) 12.6980 0.429024
\(877\) −27.4027 −0.925324 −0.462662 0.886535i \(-0.653106\pi\)
−0.462662 + 0.886535i \(0.653106\pi\)
\(878\) 3.60006 0.121496
\(879\) 70.7038 2.38478
\(880\) −13.5810 −0.457814
\(881\) −29.6207 −0.997945 −0.498973 0.866618i \(-0.666289\pi\)
−0.498973 + 0.866618i \(0.666289\pi\)
\(882\) −61.6847 −2.07703
\(883\) −10.1945 −0.343073 −0.171537 0.985178i \(-0.554873\pi\)
−0.171537 + 0.985178i \(0.554873\pi\)
\(884\) 0.0703804 0.00236715
\(885\) −13.5965 −0.457042
\(886\) 36.7237 1.23376
\(887\) −46.9669 −1.57699 −0.788496 0.615039i \(-0.789140\pi\)
−0.788496 + 0.615039i \(0.789140\pi\)
\(888\) 3.55013 0.119135
\(889\) 84.1864 2.82352
\(890\) 10.9776 0.367970
\(891\) −49.7480 −1.66662
\(892\) −31.4835 −1.05415
\(893\) 8.81646 0.295032
\(894\) 41.1027 1.37468
\(895\) 5.78732 0.193449
\(896\) 32.2668 1.07796
\(897\) 0.00368786 0.000123134 0
\(898\) −55.2359 −1.84325
\(899\) 86.1070 2.87183
\(900\) −13.9657 −0.465523
\(901\) −44.1009 −1.46921
\(902\) −6.02459 −0.200597
\(903\) −32.3310 −1.07591
\(904\) 0.00457279 0.000152089 0
\(905\) 1.26112 0.0419212
\(906\) −86.0316 −2.85821
\(907\) 55.7990 1.85277 0.926387 0.376573i \(-0.122897\pi\)
0.926387 + 0.376573i \(0.122897\pi\)
\(908\) −40.9365 −1.35853
\(909\) −22.0959 −0.732874
\(910\) −0.0414731 −0.00137482
\(911\) −59.0583 −1.95669 −0.978344 0.206987i \(-0.933634\pi\)
−0.978344 + 0.206987i \(0.933634\pi\)
\(912\) 10.4718 0.346757
\(913\) 45.6489 1.51076
\(914\) 0.170015 0.00562359
\(915\) 3.77882 0.124924
\(916\) −6.66383 −0.220179
\(917\) −62.2875 −2.05692
\(918\) −27.9507 −0.922512
\(919\) −46.7807 −1.54315 −0.771577 0.636136i \(-0.780532\pi\)
−0.771577 + 0.636136i \(0.780532\pi\)
\(920\) −0.127809 −0.00421374
\(921\) 12.9992 0.428338
\(922\) −55.2070 −1.81814
\(923\) 0.0884360 0.00291091
\(924\) −75.6688 −2.48932
\(925\) −8.59262 −0.282524
\(926\) 63.2793 2.07949
\(927\) −30.9661 −1.01706
\(928\) 58.2009 1.91054
\(929\) 47.8418 1.56964 0.784820 0.619724i \(-0.212755\pi\)
0.784820 + 0.619724i \(0.212755\pi\)
\(930\) −28.4610 −0.933273
\(931\) −16.6607 −0.546032
\(932\) −24.2912 −0.795686
\(933\) 4.25324 0.139245
\(934\) −10.1229 −0.331230
\(935\) −18.6023 −0.608360
\(936\) −0.0118106 −0.000386042 0
\(937\) −52.4058 −1.71202 −0.856012 0.516957i \(-0.827065\pi\)
−0.856012 + 0.516957i \(0.827065\pi\)
\(938\) 52.1232 1.70188
\(939\) −61.1860 −1.99673
\(940\) −8.74913 −0.285365
\(941\) −35.1544 −1.14600 −0.573000 0.819556i \(-0.694220\pi\)
−0.573000 + 0.819556i \(0.694220\pi\)
\(942\) −27.7046 −0.902666
\(943\) −0.166233 −0.00541328
\(944\) 44.7370 1.45607
\(945\) 7.18689 0.233789
\(946\) −25.3340 −0.823679
\(947\) 9.53111 0.309719 0.154860 0.987936i \(-0.450507\pi\)
0.154860 + 0.987936i \(0.450507\pi\)
\(948\) −31.3513 −1.01824
\(949\) −0.0259911 −0.000843707 0
\(950\) −8.64461 −0.280468
\(951\) −2.22834 −0.0722590
\(952\) 26.6418 0.863465
\(953\) −39.0557 −1.26514 −0.632569 0.774504i \(-0.718000\pi\)
−0.632569 + 0.774504i \(0.718000\pi\)
\(954\) −25.3662 −0.821261
\(955\) −13.8611 −0.448534
\(956\) 24.1175 0.780016
\(957\) 81.7808 2.64360
\(958\) −69.4000 −2.24221
\(959\) 62.8920 2.03089
\(960\) −5.81346 −0.187629
\(961\) 80.9126 2.61008
\(962\) 0.0249071 0.000803036 0
\(963\) 15.3262 0.493878
\(964\) 12.3575 0.398008
\(965\) −4.98231 −0.160386
\(966\) −4.78491 −0.153952
\(967\) 11.6769 0.375502 0.187751 0.982217i \(-0.439880\pi\)
0.187751 + 0.982217i \(0.439880\pi\)
\(968\) 7.93892 0.255166
\(969\) 14.3436 0.460783
\(970\) 8.53527 0.274051
\(971\) 10.5351 0.338088 0.169044 0.985609i \(-0.445932\pi\)
0.169044 + 0.985609i \(0.445932\pi\)
\(972\) −27.3588 −0.877534
\(973\) −79.0833 −2.53529
\(974\) 60.5697 1.94078
\(975\) 0.0722175 0.00231281
\(976\) −12.4336 −0.397989
\(977\) 25.5942 0.818830 0.409415 0.912348i \(-0.365733\pi\)
0.409415 + 0.912348i \(0.365733\pi\)
\(978\) 82.7220 2.64516
\(979\) −40.9966 −1.31026
\(980\) 16.5334 0.528141
\(981\) −26.8117 −0.856032
\(982\) 26.6067 0.849055
\(983\) 22.0953 0.704732 0.352366 0.935862i \(-0.385377\pi\)
0.352366 + 0.935862i \(0.385377\pi\)
\(984\) 1.34494 0.0428751
\(985\) 10.3902 0.331059
\(986\) 98.6927 3.14301
\(987\) 95.5630 3.04180
\(988\) 0.0109339 0.000347854 0
\(989\) −0.699025 −0.0222277
\(990\) −10.6998 −0.340061
\(991\) 6.69407 0.212644 0.106322 0.994332i \(-0.466093\pi\)
0.106322 + 0.994332i \(0.466093\pi\)
\(992\) 75.6432 2.40167
\(993\) −46.3428 −1.47064
\(994\) −114.743 −3.63944
\(995\) 6.06646 0.192320
\(996\) 34.9296 1.10679
\(997\) 36.5166 1.15649 0.578247 0.815862i \(-0.303737\pi\)
0.578247 + 0.815862i \(0.303737\pi\)
\(998\) −13.8269 −0.437682
\(999\) −4.31616 −0.136557
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 \(a_p\))