Properties

Label 6023.2.a.b.1.7
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 1.7
Character \(\chi\) = 6023.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.48734 q^{2}\) \(-0.305991 q^{3}\) \(+4.18686 q^{4}\) \(-0.333485 q^{5}\) \(+0.761103 q^{6}\) \(+2.33440 q^{7}\) \(-5.43948 q^{8}\) \(-2.90637 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.48734 q^{2}\) \(-0.305991 q^{3}\) \(+4.18686 q^{4}\) \(-0.333485 q^{5}\) \(+0.761103 q^{6}\) \(+2.33440 q^{7}\) \(-5.43948 q^{8}\) \(-2.90637 q^{9}\) \(+0.829491 q^{10}\) \(+5.64108 q^{11}\) \(-1.28114 q^{12}\) \(-5.88144 q^{13}\) \(-5.80644 q^{14}\) \(+0.102043 q^{15}\) \(+5.15610 q^{16}\) \(-4.23276 q^{17}\) \(+7.22913 q^{18}\) \(-1.00000 q^{19}\) \(-1.39626 q^{20}\) \(-0.714303 q^{21}\) \(-14.0313 q^{22}\) \(-5.07913 q^{23}\) \(+1.66443 q^{24}\) \(-4.88879 q^{25}\) \(+14.6292 q^{26}\) \(+1.80729 q^{27}\) \(+9.77380 q^{28}\) \(+3.03815 q^{29}\) \(-0.253816 q^{30}\) \(+5.90976 q^{31}\) \(-1.94603 q^{32}\) \(-1.72612 q^{33}\) \(+10.5283 q^{34}\) \(-0.778486 q^{35}\) \(-12.1686 q^{36}\) \(+9.27079 q^{37}\) \(+2.48734 q^{38}\) \(+1.79967 q^{39}\) \(+1.81398 q^{40}\) \(+7.13705 q^{41}\) \(+1.77672 q^{42}\) \(+10.5909 q^{43}\) \(+23.6184 q^{44}\) \(+0.969231 q^{45}\) \(+12.6335 q^{46}\) \(-0.0898896 q^{47}\) \(-1.57772 q^{48}\) \(-1.55060 q^{49}\) \(+12.1601 q^{50}\) \(+1.29519 q^{51}\) \(-24.6248 q^{52}\) \(-8.17447 q^{53}\) \(-4.49536 q^{54}\) \(-1.88122 q^{55}\) \(-12.6979 q^{56}\) \(+0.305991 q^{57}\) \(-7.55692 q^{58}\) \(+0.903345 q^{59}\) \(+0.427241 q^{60}\) \(-1.56508 q^{61}\) \(-14.6996 q^{62}\) \(-6.78462 q^{63}\) \(-5.47176 q^{64}\) \(+1.96137 q^{65}\) \(+4.29344 q^{66}\) \(-7.39866 q^{67}\) \(-17.7220 q^{68}\) \(+1.55417 q^{69}\) \(+1.93636 q^{70}\) \(+9.00344 q^{71}\) \(+15.8091 q^{72}\) \(-10.4696 q^{73}\) \(-23.0596 q^{74}\) \(+1.49592 q^{75}\) \(-4.18686 q^{76}\) \(+13.1685 q^{77}\) \(-4.47638 q^{78}\) \(+5.95569 q^{79}\) \(-1.71948 q^{80}\) \(+8.16609 q^{81}\) \(-17.7523 q^{82}\) \(+2.13433 q^{83}\) \(-2.99069 q^{84}\) \(+1.41156 q^{85}\) \(-26.3431 q^{86}\) \(-0.929646 q^{87}\) \(-30.6845 q^{88}\) \(+9.25404 q^{89}\) \(-2.41081 q^{90}\) \(-13.7296 q^{91}\) \(-21.2656 q^{92}\) \(-1.80833 q^{93}\) \(+0.223586 q^{94}\) \(+0.333485 q^{95}\) \(+0.595468 q^{96}\) \(-15.2436 q^{97}\) \(+3.85686 q^{98}\) \(-16.3951 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(99q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 80q^{4} \) \(\mathstrut -\mathstrut 15q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 58q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(99q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 80q^{4} \) \(\mathstrut -\mathstrut 15q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 58q^{9} \) \(\mathstrut -\mathstrut 6q^{10} \) \(\mathstrut -\mathstrut 9q^{11} \) \(\mathstrut -\mathstrut 27q^{12} \) \(\mathstrut -\mathstrut 28q^{13} \) \(\mathstrut -\mathstrut 13q^{14} \) \(\mathstrut -\mathstrut 10q^{15} \) \(\mathstrut +\mathstrut 38q^{16} \) \(\mathstrut -\mathstrut 36q^{17} \) \(\mathstrut -\mathstrut 14q^{18} \) \(\mathstrut -\mathstrut 99q^{19} \) \(\mathstrut -\mathstrut 34q^{20} \) \(\mathstrut -\mathstrut 20q^{21} \) \(\mathstrut -\mathstrut 53q^{22} \) \(\mathstrut -\mathstrut 38q^{23} \) \(\mathstrut -\mathstrut 25q^{24} \) \(\mathstrut -\mathstrut 8q^{25} \) \(\mathstrut -\mathstrut 3q^{26} \) \(\mathstrut -\mathstrut 3q^{27} \) \(\mathstrut -\mathstrut 63q^{28} \) \(\mathstrut -\mathstrut 34q^{29} \) \(\mathstrut -\mathstrut 30q^{30} \) \(\mathstrut -\mathstrut 16q^{31} \) \(\mathstrut -\mathstrut 43q^{32} \) \(\mathstrut -\mathstrut 41q^{33} \) \(\mathstrut -\mathstrut 14q^{34} \) \(\mathstrut -\mathstrut 25q^{35} \) \(\mathstrut -\mathstrut 16q^{36} \) \(\mathstrut -\mathstrut 80q^{37} \) \(\mathstrut +\mathstrut 4q^{38} \) \(\mathstrut -\mathstrut 48q^{39} \) \(\mathstrut -\mathstrut 10q^{40} \) \(\mathstrut -\mathstrut 32q^{41} \) \(\mathstrut -\mathstrut 37q^{42} \) \(\mathstrut -\mathstrut 76q^{43} \) \(\mathstrut -\mathstrut 21q^{44} \) \(\mathstrut -\mathstrut 53q^{45} \) \(\mathstrut -\mathstrut 23q^{46} \) \(\mathstrut -\mathstrut 31q^{47} \) \(\mathstrut -\mathstrut 74q^{48} \) \(\mathstrut -\mathstrut 32q^{49} \) \(\mathstrut -\mathstrut 29q^{50} \) \(\mathstrut -\mathstrut 30q^{51} \) \(\mathstrut -\mathstrut 71q^{52} \) \(\mathstrut -\mathstrut 35q^{53} \) \(\mathstrut -\mathstrut 80q^{54} \) \(\mathstrut -\mathstrut 45q^{55} \) \(\mathstrut -\mathstrut 33q^{56} \) \(\mathstrut +\mathstrut 3q^{57} \) \(\mathstrut -\mathstrut 91q^{58} \) \(\mathstrut +\mathstrut 12q^{59} \) \(\mathstrut -\mathstrut 56q^{60} \) \(\mathstrut -\mathstrut 61q^{61} \) \(\mathstrut -\mathstrut 46q^{62} \) \(\mathstrut -\mathstrut 43q^{63} \) \(\mathstrut -\mathstrut 30q^{64} \) \(\mathstrut -\mathstrut 46q^{65} \) \(\mathstrut -\mathstrut 75q^{66} \) \(\mathstrut -\mathstrut 26q^{67} \) \(\mathstrut -\mathstrut 55q^{68} \) \(\mathstrut -\mathstrut 45q^{69} \) \(\mathstrut -\mathstrut 76q^{70} \) \(\mathstrut -\mathstrut 41q^{71} \) \(\mathstrut -\mathstrut 77q^{72} \) \(\mathstrut -\mathstrut 143q^{73} \) \(\mathstrut -\mathstrut 64q^{74} \) \(\mathstrut -\mathstrut 8q^{75} \) \(\mathstrut -\mathstrut 80q^{76} \) \(\mathstrut -\mathstrut 58q^{77} \) \(\mathstrut -\mathstrut 34q^{78} \) \(\mathstrut -\mathstrut 22q^{79} \) \(\mathstrut -\mathstrut 36q^{80} \) \(\mathstrut -\mathstrut 81q^{81} \) \(\mathstrut -\mathstrut 109q^{82} \) \(\mathstrut -\mathstrut 7q^{83} \) \(\mathstrut -\mathstrut 6q^{84} \) \(\mathstrut -\mathstrut 80q^{85} \) \(\mathstrut +\mathstrut 32q^{86} \) \(\mathstrut -\mathstrut 57q^{87} \) \(\mathstrut -\mathstrut 120q^{88} \) \(\mathstrut -\mathstrut 28q^{89} \) \(\mathstrut -\mathstrut 12q^{90} \) \(\mathstrut -\mathstrut 30q^{91} \) \(\mathstrut -\mathstrut 107q^{92} \) \(\mathstrut -\mathstrut 121q^{93} \) \(\mathstrut +\mathstrut 8q^{94} \) \(\mathstrut +\mathstrut 15q^{95} \) \(\mathstrut +\mathstrut 4q^{96} \) \(\mathstrut -\mathstrut 128q^{97} \) \(\mathstrut +\mathstrut 54q^{98} \) \(\mathstrut -\mathstrut 34q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.48734 −1.75882 −0.879408 0.476069i \(-0.842061\pi\)
−0.879408 + 0.476069i \(0.842061\pi\)
\(3\) −0.305991 −0.176664 −0.0883319 0.996091i \(-0.528154\pi\)
−0.0883319 + 0.996091i \(0.528154\pi\)
\(4\) 4.18686 2.09343
\(5\) −0.333485 −0.149139 −0.0745695 0.997216i \(-0.523758\pi\)
−0.0745695 + 0.997216i \(0.523758\pi\)
\(6\) 0.761103 0.310719
\(7\) 2.33440 0.882319 0.441159 0.897429i \(-0.354567\pi\)
0.441159 + 0.897429i \(0.354567\pi\)
\(8\) −5.43948 −1.92315
\(9\) −2.90637 −0.968790
\(10\) 0.829491 0.262308
\(11\) 5.64108 1.70085 0.850425 0.526097i \(-0.176345\pi\)
0.850425 + 0.526097i \(0.176345\pi\)
\(12\) −1.28114 −0.369834
\(13\) −5.88144 −1.63122 −0.815610 0.578603i \(-0.803598\pi\)
−0.815610 + 0.578603i \(0.803598\pi\)
\(14\) −5.80644 −1.55184
\(15\) 0.102043 0.0263475
\(16\) 5.15610 1.28903
\(17\) −4.23276 −1.02660 −0.513298 0.858210i \(-0.671576\pi\)
−0.513298 + 0.858210i \(0.671576\pi\)
\(18\) 7.22913 1.70392
\(19\) −1.00000 −0.229416
\(20\) −1.39626 −0.312212
\(21\) −0.714303 −0.155874
\(22\) −14.0313 −2.99148
\(23\) −5.07913 −1.05907 −0.529536 0.848288i \(-0.677634\pi\)
−0.529536 + 0.848288i \(0.677634\pi\)
\(24\) 1.66443 0.339750
\(25\) −4.88879 −0.977758
\(26\) 14.6292 2.86901
\(27\) 1.80729 0.347814
\(28\) 9.77380 1.84707
\(29\) 3.03815 0.564171 0.282085 0.959389i \(-0.408974\pi\)
0.282085 + 0.959389i \(0.408974\pi\)
\(30\) −0.253816 −0.0463403
\(31\) 5.90976 1.06142 0.530712 0.847552i \(-0.321925\pi\)
0.530712 + 0.847552i \(0.321925\pi\)
\(32\) −1.94603 −0.344013
\(33\) −1.72612 −0.300478
\(34\) 10.5283 1.80559
\(35\) −0.778486 −0.131588
\(36\) −12.1686 −2.02810
\(37\) 9.27079 1.52411 0.762054 0.647513i \(-0.224191\pi\)
0.762054 + 0.647513i \(0.224191\pi\)
\(38\) 2.48734 0.403500
\(39\) 1.79967 0.288177
\(40\) 1.81398 0.286816
\(41\) 7.13705 1.11462 0.557310 0.830305i \(-0.311834\pi\)
0.557310 + 0.830305i \(0.311834\pi\)
\(42\) 1.77672 0.274153
\(43\) 10.5909 1.61509 0.807547 0.589803i \(-0.200794\pi\)
0.807547 + 0.589803i \(0.200794\pi\)
\(44\) 23.6184 3.56061
\(45\) 0.969231 0.144484
\(46\) 12.6335 1.86271
\(47\) −0.0898896 −0.0131117 −0.00655587 0.999979i \(-0.502087\pi\)
−0.00655587 + 0.999979i \(0.502087\pi\)
\(48\) −1.57772 −0.227724
\(49\) −1.55060 −0.221514
\(50\) 12.1601 1.71970
\(51\) 1.29519 0.181362
\(52\) −24.6248 −3.41485
\(53\) −8.17447 −1.12285 −0.561425 0.827528i \(-0.689747\pi\)
−0.561425 + 0.827528i \(0.689747\pi\)
\(54\) −4.49536 −0.611740
\(55\) −1.88122 −0.253663
\(56\) −12.6979 −1.69683
\(57\) 0.305991 0.0405294
\(58\) −7.55692 −0.992272
\(59\) 0.903345 0.117605 0.0588027 0.998270i \(-0.481272\pi\)
0.0588027 + 0.998270i \(0.481272\pi\)
\(60\) 0.427241 0.0551566
\(61\) −1.56508 −0.200388 −0.100194 0.994968i \(-0.531946\pi\)
−0.100194 + 0.994968i \(0.531946\pi\)
\(62\) −14.6996 −1.86685
\(63\) −6.78462 −0.854781
\(64\) −5.47176 −0.683970
\(65\) 1.96137 0.243278
\(66\) 4.29344 0.528486
\(67\) −7.39866 −0.903890 −0.451945 0.892046i \(-0.649270\pi\)
−0.451945 + 0.892046i \(0.649270\pi\)
\(68\) −17.7220 −2.14911
\(69\) 1.55417 0.187100
\(70\) 1.93636 0.231439
\(71\) 9.00344 1.06851 0.534256 0.845323i \(-0.320592\pi\)
0.534256 + 0.845323i \(0.320592\pi\)
\(72\) 15.8091 1.86312
\(73\) −10.4696 −1.22537 −0.612684 0.790328i \(-0.709910\pi\)
−0.612684 + 0.790328i \(0.709910\pi\)
\(74\) −23.0596 −2.68063
\(75\) 1.49592 0.172734
\(76\) −4.18686 −0.480266
\(77\) 13.1685 1.50069
\(78\) −4.47638 −0.506851
\(79\) 5.95569 0.670067 0.335034 0.942206i \(-0.391252\pi\)
0.335034 + 0.942206i \(0.391252\pi\)
\(80\) −1.71948 −0.192244
\(81\) 8.16609 0.907344
\(82\) −17.7523 −1.96041
\(83\) 2.13433 0.234273 0.117137 0.993116i \(-0.462628\pi\)
0.117137 + 0.993116i \(0.462628\pi\)
\(84\) −2.99069 −0.326311
\(85\) 1.41156 0.153106
\(86\) −26.3431 −2.84065
\(87\) −0.929646 −0.0996685
\(88\) −30.6845 −3.27098
\(89\) 9.25404 0.980927 0.490463 0.871462i \(-0.336828\pi\)
0.490463 + 0.871462i \(0.336828\pi\)
\(90\) −2.41081 −0.254121
\(91\) −13.7296 −1.43926
\(92\) −21.2656 −2.21709
\(93\) −1.80833 −0.187515
\(94\) 0.223586 0.0230611
\(95\) 0.333485 0.0342148
\(96\) 0.595468 0.0607747
\(97\) −15.2436 −1.54775 −0.773875 0.633338i \(-0.781684\pi\)
−0.773875 + 0.633338i \(0.781684\pi\)
\(98\) 3.85686 0.389602
\(99\) −16.3951 −1.64777
\(100\) −20.4687 −2.04687
\(101\) −0.203196 −0.0202188 −0.0101094 0.999949i \(-0.503218\pi\)
−0.0101094 + 0.999949i \(0.503218\pi\)
\(102\) −3.22157 −0.318983
\(103\) −7.89007 −0.777432 −0.388716 0.921358i \(-0.627081\pi\)
−0.388716 + 0.921358i \(0.627081\pi\)
\(104\) 31.9920 3.13707
\(105\) 0.238209 0.0232469
\(106\) 20.3327 1.97489
\(107\) 15.9432 1.54129 0.770644 0.637266i \(-0.219935\pi\)
0.770644 + 0.637266i \(0.219935\pi\)
\(108\) 7.56689 0.728125
\(109\) −1.06672 −0.102173 −0.0510867 0.998694i \(-0.516268\pi\)
−0.0510867 + 0.998694i \(0.516268\pi\)
\(110\) 4.67922 0.446146
\(111\) −2.83678 −0.269255
\(112\) 12.0364 1.13733
\(113\) 13.1327 1.23542 0.617712 0.786405i \(-0.288060\pi\)
0.617712 + 0.786405i \(0.288060\pi\)
\(114\) −0.761103 −0.0712838
\(115\) 1.69381 0.157949
\(116\) 12.7203 1.18105
\(117\) 17.0937 1.58031
\(118\) −2.24693 −0.206846
\(119\) −9.88094 −0.905785
\(120\) −0.555062 −0.0506700
\(121\) 20.8218 1.89289
\(122\) 3.89289 0.352446
\(123\) −2.18387 −0.196913
\(124\) 24.7434 2.22202
\(125\) 3.29776 0.294961
\(126\) 16.8757 1.50340
\(127\) −4.66947 −0.414348 −0.207174 0.978304i \(-0.566427\pi\)
−0.207174 + 0.978304i \(0.566427\pi\)
\(128\) 17.5022 1.54699
\(129\) −3.24071 −0.285329
\(130\) −4.87860 −0.427882
\(131\) −12.8980 −1.12691 −0.563454 0.826148i \(-0.690528\pi\)
−0.563454 + 0.826148i \(0.690528\pi\)
\(132\) −7.22702 −0.629031
\(133\) −2.33440 −0.202418
\(134\) 18.4030 1.58978
\(135\) −0.602705 −0.0518726
\(136\) 23.0240 1.97429
\(137\) 0.164002 0.0140116 0.00700581 0.999975i \(-0.497770\pi\)
0.00700581 + 0.999975i \(0.497770\pi\)
\(138\) −3.86574 −0.329074
\(139\) −19.3645 −1.64247 −0.821237 0.570587i \(-0.806716\pi\)
−0.821237 + 0.570587i \(0.806716\pi\)
\(140\) −3.25942 −0.275471
\(141\) 0.0275054 0.00231637
\(142\) −22.3946 −1.87932
\(143\) −33.1777 −2.77446
\(144\) −14.9855 −1.24880
\(145\) −1.01318 −0.0841399
\(146\) 26.0413 2.15520
\(147\) 0.474468 0.0391334
\(148\) 38.8156 3.19062
\(149\) −10.2177 −0.837064 −0.418532 0.908202i \(-0.637455\pi\)
−0.418532 + 0.908202i \(0.637455\pi\)
\(150\) −3.72087 −0.303808
\(151\) −21.2493 −1.72924 −0.864620 0.502426i \(-0.832441\pi\)
−0.864620 + 0.502426i \(0.832441\pi\)
\(152\) 5.43948 0.441200
\(153\) 12.3020 0.994556
\(154\) −32.7546 −2.63944
\(155\) −1.97082 −0.158300
\(156\) 7.53496 0.603280
\(157\) 5.44540 0.434590 0.217295 0.976106i \(-0.430277\pi\)
0.217295 + 0.976106i \(0.430277\pi\)
\(158\) −14.8138 −1.17852
\(159\) 2.50131 0.198367
\(160\) 0.648973 0.0513058
\(161\) −11.8567 −0.934439
\(162\) −20.3119 −1.59585
\(163\) −21.4071 −1.67674 −0.838368 0.545105i \(-0.816490\pi\)
−0.838368 + 0.545105i \(0.816490\pi\)
\(164\) 29.8819 2.33338
\(165\) 0.575634 0.0448131
\(166\) −5.30881 −0.412044
\(167\) −6.71767 −0.519829 −0.259914 0.965632i \(-0.583694\pi\)
−0.259914 + 0.965632i \(0.583694\pi\)
\(168\) 3.88544 0.299768
\(169\) 21.5914 1.66088
\(170\) −3.51104 −0.269284
\(171\) 2.90637 0.222256
\(172\) 44.3426 3.38109
\(173\) −3.74493 −0.284722 −0.142361 0.989815i \(-0.545469\pi\)
−0.142361 + 0.989815i \(0.545469\pi\)
\(174\) 2.31235 0.175299
\(175\) −11.4124 −0.862694
\(176\) 29.0860 2.19244
\(177\) −0.276415 −0.0207766
\(178\) −23.0180 −1.72527
\(179\) −11.7883 −0.881097 −0.440549 0.897729i \(-0.645216\pi\)
−0.440549 + 0.897729i \(0.645216\pi\)
\(180\) 4.05804 0.302468
\(181\) 23.5490 1.75038 0.875192 0.483775i \(-0.160735\pi\)
0.875192 + 0.483775i \(0.160735\pi\)
\(182\) 34.1502 2.53138
\(183\) 0.478900 0.0354013
\(184\) 27.6278 2.03675
\(185\) −3.09167 −0.227304
\(186\) 4.49794 0.329805
\(187\) −23.8774 −1.74609
\(188\) −0.376356 −0.0274485
\(189\) 4.21894 0.306883
\(190\) −0.829491 −0.0601776
\(191\) −19.8495 −1.43626 −0.718128 0.695911i \(-0.755001\pi\)
−0.718128 + 0.695911i \(0.755001\pi\)
\(192\) 1.67431 0.120833
\(193\) −16.5428 −1.19077 −0.595387 0.803439i \(-0.703001\pi\)
−0.595387 + 0.803439i \(0.703001\pi\)
\(194\) 37.9160 2.72221
\(195\) −0.600162 −0.0429785
\(196\) −6.49214 −0.463724
\(197\) −4.34082 −0.309271 −0.154635 0.987972i \(-0.549420\pi\)
−0.154635 + 0.987972i \(0.549420\pi\)
\(198\) 40.7801 2.89812
\(199\) 27.4020 1.94247 0.971237 0.238114i \(-0.0765292\pi\)
0.971237 + 0.238114i \(0.0765292\pi\)
\(200\) 26.5924 1.88037
\(201\) 2.26392 0.159685
\(202\) 0.505419 0.0355611
\(203\) 7.09225 0.497778
\(204\) 5.42277 0.379670
\(205\) −2.38010 −0.166233
\(206\) 19.6253 1.36736
\(207\) 14.7618 1.02602
\(208\) −30.3253 −2.10268
\(209\) −5.64108 −0.390202
\(210\) −0.592508 −0.0408869
\(211\) −17.7844 −1.22433 −0.612163 0.790731i \(-0.709701\pi\)
−0.612163 + 0.790731i \(0.709701\pi\)
\(212\) −34.2254 −2.35061
\(213\) −2.75497 −0.188767
\(214\) −39.6562 −2.71084
\(215\) −3.53190 −0.240874
\(216\) −9.83073 −0.668897
\(217\) 13.7957 0.936515
\(218\) 2.65330 0.179704
\(219\) 3.20358 0.216478
\(220\) −7.87639 −0.531026
\(221\) 24.8948 1.67460
\(222\) 7.05603 0.473570
\(223\) 4.06392 0.272140 0.136070 0.990699i \(-0.456553\pi\)
0.136070 + 0.990699i \(0.456553\pi\)
\(224\) −4.54281 −0.303529
\(225\) 14.2086 0.947242
\(226\) −32.6656 −2.17288
\(227\) 11.3929 0.756171 0.378085 0.925771i \(-0.376583\pi\)
0.378085 + 0.925771i \(0.376583\pi\)
\(228\) 1.28114 0.0848456
\(229\) −23.0907 −1.52587 −0.762937 0.646473i \(-0.776243\pi\)
−0.762937 + 0.646473i \(0.776243\pi\)
\(230\) −4.21309 −0.277803
\(231\) −4.02944 −0.265118
\(232\) −16.5260 −1.08498
\(233\) 9.67528 0.633849 0.316924 0.948451i \(-0.397350\pi\)
0.316924 + 0.948451i \(0.397350\pi\)
\(234\) −42.5177 −2.77947
\(235\) 0.0299768 0.00195547
\(236\) 3.78218 0.246199
\(237\) −1.82238 −0.118377
\(238\) 24.5773 1.59311
\(239\) −20.1259 −1.30184 −0.650919 0.759147i \(-0.725616\pi\)
−0.650919 + 0.759147i \(0.725616\pi\)
\(240\) 0.526146 0.0339626
\(241\) 24.4920 1.57767 0.788834 0.614606i \(-0.210685\pi\)
0.788834 + 0.614606i \(0.210685\pi\)
\(242\) −51.7909 −3.32924
\(243\) −7.92063 −0.508109
\(244\) −6.55279 −0.419499
\(245\) 0.517101 0.0330363
\(246\) 5.43203 0.346334
\(247\) 5.88144 0.374227
\(248\) −32.1460 −2.04127
\(249\) −0.653086 −0.0413876
\(250\) −8.20266 −0.518782
\(251\) 11.1112 0.701336 0.350668 0.936500i \(-0.385955\pi\)
0.350668 + 0.936500i \(0.385955\pi\)
\(252\) −28.4063 −1.78943
\(253\) −28.6518 −1.80132
\(254\) 11.6146 0.728762
\(255\) −0.431925 −0.0270482
\(256\) −32.5904 −2.03690
\(257\) −10.5583 −0.658608 −0.329304 0.944224i \(-0.606814\pi\)
−0.329304 + 0.944224i \(0.606814\pi\)
\(258\) 8.06075 0.501841
\(259\) 21.6417 1.34475
\(260\) 8.21200 0.509287
\(261\) −8.83000 −0.546563
\(262\) 32.0818 1.98202
\(263\) 8.47745 0.522742 0.261371 0.965238i \(-0.415825\pi\)
0.261371 + 0.965238i \(0.415825\pi\)
\(264\) 9.38917 0.577864
\(265\) 2.72606 0.167461
\(266\) 5.80644 0.356016
\(267\) −2.83165 −0.173294
\(268\) −30.9772 −1.89223
\(269\) 1.08324 0.0660466 0.0330233 0.999455i \(-0.489486\pi\)
0.0330233 + 0.999455i \(0.489486\pi\)
\(270\) 1.49913 0.0912344
\(271\) 8.68000 0.527273 0.263636 0.964622i \(-0.415078\pi\)
0.263636 + 0.964622i \(0.415078\pi\)
\(272\) −21.8246 −1.32331
\(273\) 4.20113 0.254264
\(274\) −0.407928 −0.0246438
\(275\) −27.5780 −1.66302
\(276\) 6.50708 0.391680
\(277\) −21.8149 −1.31073 −0.655365 0.755312i \(-0.727485\pi\)
−0.655365 + 0.755312i \(0.727485\pi\)
\(278\) 48.1661 2.88881
\(279\) −17.1759 −1.02830
\(280\) 4.23456 0.253063
\(281\) 25.5444 1.52385 0.761926 0.647664i \(-0.224254\pi\)
0.761926 + 0.647664i \(0.224254\pi\)
\(282\) −0.0684152 −0.00407407
\(283\) −25.3017 −1.50403 −0.752016 0.659144i \(-0.770919\pi\)
−0.752016 + 0.659144i \(0.770919\pi\)
\(284\) 37.6962 2.23686
\(285\) −0.102043 −0.00604452
\(286\) 82.5242 4.87976
\(287\) 16.6607 0.983450
\(288\) 5.65589 0.333277
\(289\) 0.916284 0.0538991
\(290\) 2.52012 0.147987
\(291\) 4.66439 0.273431
\(292\) −43.8346 −2.56523
\(293\) −16.1594 −0.944041 −0.472021 0.881587i \(-0.656475\pi\)
−0.472021 + 0.881587i \(0.656475\pi\)
\(294\) −1.18016 −0.0688285
\(295\) −0.301252 −0.0175396
\(296\) −50.4283 −2.93108
\(297\) 10.1951 0.591579
\(298\) 25.4148 1.47224
\(299\) 29.8726 1.72758
\(300\) 6.26323 0.361608
\(301\) 24.7233 1.42503
\(302\) 52.8542 3.04142
\(303\) 0.0621762 0.00357193
\(304\) −5.15610 −0.295723
\(305\) 0.521932 0.0298857
\(306\) −30.5992 −1.74924
\(307\) −2.65740 −0.151666 −0.0758330 0.997121i \(-0.524162\pi\)
−0.0758330 + 0.997121i \(0.524162\pi\)
\(308\) 55.1348 3.14160
\(309\) 2.41429 0.137344
\(310\) 4.90209 0.278420
\(311\) 22.4582 1.27349 0.636744 0.771075i \(-0.280281\pi\)
0.636744 + 0.771075i \(0.280281\pi\)
\(312\) −9.78924 −0.554207
\(313\) −8.10086 −0.457888 −0.228944 0.973440i \(-0.573527\pi\)
−0.228944 + 0.973440i \(0.573527\pi\)
\(314\) −13.5446 −0.764363
\(315\) 2.26257 0.127481
\(316\) 24.9357 1.40274
\(317\) −1.00000 −0.0561656
\(318\) −6.22161 −0.348891
\(319\) 17.1385 0.959570
\(320\) 1.82475 0.102007
\(321\) −4.87847 −0.272290
\(322\) 29.4916 1.64351
\(323\) 4.23276 0.235517
\(324\) 34.1903 1.89946
\(325\) 28.7531 1.59494
\(326\) 53.2468 2.94907
\(327\) 0.326407 0.0180503
\(328\) −38.8218 −2.14358
\(329\) −0.209838 −0.0115687
\(330\) −1.43180 −0.0788179
\(331\) 19.1862 1.05457 0.527283 0.849690i \(-0.323211\pi\)
0.527283 + 0.849690i \(0.323211\pi\)
\(332\) 8.93616 0.490436
\(333\) −26.9444 −1.47654
\(334\) 16.7091 0.914283
\(335\) 2.46734 0.134805
\(336\) −3.68302 −0.200925
\(337\) −15.3887 −0.838276 −0.419138 0.907922i \(-0.637668\pi\)
−0.419138 + 0.907922i \(0.637668\pi\)
\(338\) −53.7052 −2.92118
\(339\) −4.01849 −0.218255
\(340\) 5.91002 0.320516
\(341\) 33.3374 1.80532
\(342\) −7.22913 −0.390907
\(343\) −19.9605 −1.07776
\(344\) −57.6089 −3.10606
\(345\) −0.518291 −0.0279038
\(346\) 9.31492 0.500773
\(347\) 8.27371 0.444156 0.222078 0.975029i \(-0.428716\pi\)
0.222078 + 0.975029i \(0.428716\pi\)
\(348\) −3.89230 −0.208649
\(349\) 9.93165 0.531629 0.265814 0.964024i \(-0.414359\pi\)
0.265814 + 0.964024i \(0.414359\pi\)
\(350\) 28.3864 1.51732
\(351\) −10.6295 −0.567361
\(352\) −10.9777 −0.585115
\(353\) 11.2119 0.596749 0.298375 0.954449i \(-0.403556\pi\)
0.298375 + 0.954449i \(0.403556\pi\)
\(354\) 0.687538 0.0365423
\(355\) −3.00251 −0.159357
\(356\) 38.7454 2.05350
\(357\) 3.02348 0.160019
\(358\) 29.3215 1.54969
\(359\) −3.23673 −0.170828 −0.0854140 0.996346i \(-0.527221\pi\)
−0.0854140 + 0.996346i \(0.527221\pi\)
\(360\) −5.27211 −0.277864
\(361\) 1.00000 0.0526316
\(362\) −58.5744 −3.07860
\(363\) −6.37127 −0.334405
\(364\) −57.4841 −3.01298
\(365\) 3.49144 0.182750
\(366\) −1.19119 −0.0622644
\(367\) 3.04889 0.159151 0.0795754 0.996829i \(-0.474644\pi\)
0.0795754 + 0.996829i \(0.474644\pi\)
\(368\) −26.1885 −1.36517
\(369\) −20.7429 −1.07983
\(370\) 7.69004 0.399786
\(371\) −19.0824 −0.990711
\(372\) −7.57124 −0.392550
\(373\) −14.4516 −0.748277 −0.374139 0.927373i \(-0.622062\pi\)
−0.374139 + 0.927373i \(0.622062\pi\)
\(374\) 59.3911 3.07104
\(375\) −1.00908 −0.0521089
\(376\) 0.488952 0.0252158
\(377\) −17.8687 −0.920286
\(378\) −10.4939 −0.539750
\(379\) −0.281718 −0.0144709 −0.00723545 0.999974i \(-0.502303\pi\)
−0.00723545 + 0.999974i \(0.502303\pi\)
\(380\) 1.39626 0.0716264
\(381\) 1.42881 0.0732003
\(382\) 49.3724 2.52611
\(383\) 25.5536 1.30573 0.652863 0.757476i \(-0.273568\pi\)
0.652863 + 0.757476i \(0.273568\pi\)
\(384\) −5.35551 −0.273297
\(385\) −4.39150 −0.223812
\(386\) 41.1475 2.09435
\(387\) −30.7810 −1.56469
\(388\) −63.8228 −3.24011
\(389\) −27.5950 −1.39912 −0.699560 0.714574i \(-0.746621\pi\)
−0.699560 + 0.714574i \(0.746621\pi\)
\(390\) 1.49281 0.0755912
\(391\) 21.4988 1.08724
\(392\) 8.43443 0.426003
\(393\) 3.94668 0.199084
\(394\) 10.7971 0.543950
\(395\) −1.98613 −0.0999332
\(396\) −68.6439 −3.44949
\(397\) 9.83774 0.493742 0.246871 0.969048i \(-0.420598\pi\)
0.246871 + 0.969048i \(0.420598\pi\)
\(398\) −68.1580 −3.41645
\(399\) 0.714303 0.0357599
\(400\) −25.2071 −1.26035
\(401\) −30.7020 −1.53318 −0.766592 0.642135i \(-0.778049\pi\)
−0.766592 + 0.642135i \(0.778049\pi\)
\(402\) −5.63114 −0.280856
\(403\) −34.7579 −1.73142
\(404\) −0.850756 −0.0423267
\(405\) −2.72327 −0.135320
\(406\) −17.6408 −0.875500
\(407\) 52.2973 2.59228
\(408\) −7.04513 −0.348786
\(409\) 1.06693 0.0527565 0.0263782 0.999652i \(-0.491603\pi\)
0.0263782 + 0.999652i \(0.491603\pi\)
\(410\) 5.92012 0.292374
\(411\) −0.0501830 −0.00247534
\(412\) −33.0347 −1.62750
\(413\) 2.10876 0.103766
\(414\) −36.7177 −1.80458
\(415\) −0.711768 −0.0349393
\(416\) 11.4455 0.561161
\(417\) 5.92535 0.290166
\(418\) 14.0313 0.686293
\(419\) −34.2091 −1.67122 −0.835611 0.549321i \(-0.814886\pi\)
−0.835611 + 0.549321i \(0.814886\pi\)
\(420\) 0.997350 0.0486657
\(421\) −32.1152 −1.56520 −0.782600 0.622524i \(-0.786107\pi\)
−0.782600 + 0.622524i \(0.786107\pi\)
\(422\) 44.2358 2.15337
\(423\) 0.261252 0.0127025
\(424\) 44.4648 2.15940
\(425\) 20.6931 1.00376
\(426\) 6.85255 0.332007
\(427\) −3.65352 −0.176806
\(428\) 66.7520 3.22658
\(429\) 10.1521 0.490146
\(430\) 8.78504 0.423652
\(431\) −27.5683 −1.32792 −0.663960 0.747768i \(-0.731125\pi\)
−0.663960 + 0.747768i \(0.731125\pi\)
\(432\) 9.31859 0.448341
\(433\) 19.2270 0.923991 0.461996 0.886882i \(-0.347134\pi\)
0.461996 + 0.886882i \(0.347134\pi\)
\(434\) −34.3147 −1.64716
\(435\) 0.310023 0.0148645
\(436\) −4.46622 −0.213893
\(437\) 5.07913 0.242968
\(438\) −7.96841 −0.380745
\(439\) −7.91050 −0.377547 −0.188774 0.982021i \(-0.560451\pi\)
−0.188774 + 0.982021i \(0.560451\pi\)
\(440\) 10.2328 0.487831
\(441\) 4.50661 0.214600
\(442\) −61.9218 −2.94532
\(443\) −40.5112 −1.92474 −0.962372 0.271734i \(-0.912403\pi\)
−0.962372 + 0.271734i \(0.912403\pi\)
\(444\) −11.8772 −0.563667
\(445\) −3.08609 −0.146294
\(446\) −10.1084 −0.478644
\(447\) 3.12651 0.147879
\(448\) −12.7733 −0.603479
\(449\) −15.9096 −0.750820 −0.375410 0.926859i \(-0.622498\pi\)
−0.375410 + 0.926859i \(0.622498\pi\)
\(450\) −35.3417 −1.66602
\(451\) 40.2607 1.89580
\(452\) 54.9850 2.58628
\(453\) 6.50208 0.305494
\(454\) −28.3379 −1.32996
\(455\) 4.57862 0.214649
\(456\) −1.66443 −0.0779440
\(457\) −3.99061 −0.186673 −0.0933364 0.995635i \(-0.529753\pi\)
−0.0933364 + 0.995635i \(0.529753\pi\)
\(458\) 57.4343 2.68373
\(459\) −7.64985 −0.357064
\(460\) 7.09177 0.330655
\(461\) −3.34960 −0.156006 −0.0780031 0.996953i \(-0.524854\pi\)
−0.0780031 + 0.996953i \(0.524854\pi\)
\(462\) 10.0226 0.466293
\(463\) −18.4875 −0.859189 −0.429594 0.903022i \(-0.641343\pi\)
−0.429594 + 0.903022i \(0.641343\pi\)
\(464\) 15.6650 0.727231
\(465\) 0.603051 0.0279658
\(466\) −24.0657 −1.11482
\(467\) 10.4444 0.483310 0.241655 0.970362i \(-0.422310\pi\)
0.241655 + 0.970362i \(0.422310\pi\)
\(468\) 71.5688 3.30827
\(469\) −17.2714 −0.797519
\(470\) −0.0745626 −0.00343932
\(471\) −1.66624 −0.0767763
\(472\) −4.91372 −0.226172
\(473\) 59.7440 2.74703
\(474\) 4.53289 0.208203
\(475\) 4.88879 0.224313
\(476\) −41.3702 −1.89620
\(477\) 23.7580 1.08781
\(478\) 50.0601 2.28969
\(479\) −34.8390 −1.59183 −0.795917 0.605406i \(-0.793011\pi\)
−0.795917 + 0.605406i \(0.793011\pi\)
\(480\) −0.198580 −0.00906388
\(481\) −54.5257 −2.48616
\(482\) −60.9200 −2.77483
\(483\) 3.62804 0.165081
\(484\) 87.1780 3.96263
\(485\) 5.08350 0.230830
\(486\) 19.7013 0.893669
\(487\) −18.8956 −0.856241 −0.428121 0.903722i \(-0.640824\pi\)
−0.428121 + 0.903722i \(0.640824\pi\)
\(488\) 8.51323 0.385376
\(489\) 6.55038 0.296219
\(490\) −1.28621 −0.0581048
\(491\) 38.5124 1.73804 0.869021 0.494776i \(-0.164750\pi\)
0.869021 + 0.494776i \(0.164750\pi\)
\(492\) −9.14357 −0.412224
\(493\) −12.8598 −0.579175
\(494\) −14.6292 −0.658197
\(495\) 5.46751 0.245746
\(496\) 30.4713 1.36820
\(497\) 21.0176 0.942768
\(498\) 1.62445 0.0727932
\(499\) −43.0291 −1.92625 −0.963123 0.269063i \(-0.913286\pi\)
−0.963123 + 0.269063i \(0.913286\pi\)
\(500\) 13.8073 0.617480
\(501\) 2.05554 0.0918349
\(502\) −27.6375 −1.23352
\(503\) 19.1013 0.851687 0.425843 0.904797i \(-0.359977\pi\)
0.425843 + 0.904797i \(0.359977\pi\)
\(504\) 36.9048 1.64387
\(505\) 0.0677629 0.00301541
\(506\) 71.2667 3.16819
\(507\) −6.60676 −0.293417
\(508\) −19.5504 −0.867410
\(509\) −4.95437 −0.219598 −0.109799 0.993954i \(-0.535021\pi\)
−0.109799 + 0.993954i \(0.535021\pi\)
\(510\) 1.07434 0.0475728
\(511\) −24.4401 −1.08117
\(512\) 46.0591 2.03554
\(513\) −1.80729 −0.0797940
\(514\) 26.2621 1.15837
\(515\) 2.63122 0.115945
\(516\) −13.5684 −0.597316
\(517\) −0.507074 −0.0223011
\(518\) −53.8303 −2.36517
\(519\) 1.14591 0.0503000
\(520\) −10.6688 −0.467860
\(521\) 9.66090 0.423252 0.211626 0.977351i \(-0.432124\pi\)
0.211626 + 0.977351i \(0.432124\pi\)
\(522\) 21.9632 0.961304
\(523\) 20.5205 0.897297 0.448649 0.893708i \(-0.351906\pi\)
0.448649 + 0.893708i \(0.351906\pi\)
\(524\) −54.0024 −2.35910
\(525\) 3.49208 0.152407
\(526\) −21.0863 −0.919406
\(527\) −25.0146 −1.08965
\(528\) −8.90004 −0.387324
\(529\) 2.79756 0.121633
\(530\) −6.78065 −0.294533
\(531\) −2.62545 −0.113935
\(532\) −9.77380 −0.423748
\(533\) −41.9762 −1.81819
\(534\) 7.04328 0.304793
\(535\) −5.31682 −0.229866
\(536\) 40.2448 1.73831
\(537\) 3.60710 0.155658
\(538\) −2.69440 −0.116164
\(539\) −8.74704 −0.376762
\(540\) −2.52345 −0.108592
\(541\) −10.6340 −0.457193 −0.228597 0.973521i \(-0.573414\pi\)
−0.228597 + 0.973521i \(0.573414\pi\)
\(542\) −21.5901 −0.927375
\(543\) −7.20578 −0.309230
\(544\) 8.23710 0.353163
\(545\) 0.355735 0.0152380
\(546\) −10.4497 −0.447204
\(547\) 1.19449 0.0510726 0.0255363 0.999674i \(-0.491871\pi\)
0.0255363 + 0.999674i \(0.491871\pi\)
\(548\) 0.686653 0.0293324
\(549\) 4.54871 0.194134
\(550\) 68.5960 2.92494
\(551\) −3.03815 −0.129430
\(552\) −8.45385 −0.359820
\(553\) 13.9029 0.591213
\(554\) 54.2611 2.30533
\(555\) 0.946022 0.0401564
\(556\) −81.0765 −3.43841
\(557\) 41.6099 1.76307 0.881535 0.472120i \(-0.156511\pi\)
0.881535 + 0.472120i \(0.156511\pi\)
\(558\) 42.7224 1.80859
\(559\) −62.2897 −2.63457
\(560\) −4.01395 −0.169621
\(561\) 7.30625 0.308470
\(562\) −63.5377 −2.68018
\(563\) 13.7132 0.577941 0.288971 0.957338i \(-0.406687\pi\)
0.288971 + 0.957338i \(0.406687\pi\)
\(564\) 0.115161 0.00484916
\(565\) −4.37957 −0.184250
\(566\) 62.9341 2.64532
\(567\) 19.0629 0.800566
\(568\) −48.9740 −2.05490
\(569\) −42.8511 −1.79641 −0.898206 0.439575i \(-0.855129\pi\)
−0.898206 + 0.439575i \(0.855129\pi\)
\(570\) 0.253816 0.0106312
\(571\) −41.1484 −1.72201 −0.861003 0.508599i \(-0.830164\pi\)
−0.861003 + 0.508599i \(0.830164\pi\)
\(572\) −138.911 −5.80814
\(573\) 6.07375 0.253735
\(574\) −41.4408 −1.72971
\(575\) 24.8308 1.03552
\(576\) 15.9030 0.662623
\(577\) −18.5775 −0.773391 −0.386696 0.922207i \(-0.626384\pi\)
−0.386696 + 0.922207i \(0.626384\pi\)
\(578\) −2.27911 −0.0947985
\(579\) 5.06193 0.210367
\(580\) −4.24204 −0.176141
\(581\) 4.98238 0.206704
\(582\) −11.6019 −0.480916
\(583\) −46.1128 −1.90980
\(584\) 56.9489 2.35656
\(585\) −5.70048 −0.235686
\(586\) 40.1939 1.66039
\(587\) −7.35887 −0.303733 −0.151867 0.988401i \(-0.548528\pi\)
−0.151867 + 0.988401i \(0.548528\pi\)
\(588\) 1.98653 0.0819232
\(589\) −5.90976 −0.243507
\(590\) 0.749316 0.0308489
\(591\) 1.32825 0.0546369
\(592\) 47.8012 1.96462
\(593\) 47.0838 1.93350 0.966750 0.255722i \(-0.0823132\pi\)
0.966750 + 0.255722i \(0.0823132\pi\)
\(594\) −25.3587 −1.04048
\(595\) 3.29515 0.135088
\(596\) −42.7800 −1.75234
\(597\) −8.38475 −0.343165
\(598\) −74.3034 −3.03849
\(599\) 21.0559 0.860322 0.430161 0.902752i \(-0.358457\pi\)
0.430161 + 0.902752i \(0.358457\pi\)
\(600\) −8.13704 −0.332193
\(601\) 7.28573 0.297191 0.148596 0.988898i \(-0.452525\pi\)
0.148596 + 0.988898i \(0.452525\pi\)
\(602\) −61.4953 −2.50636
\(603\) 21.5032 0.875680
\(604\) −88.9678 −3.62005
\(605\) −6.94375 −0.282304
\(606\) −0.154653 −0.00628236
\(607\) −39.2974 −1.59503 −0.797517 0.603296i \(-0.793854\pi\)
−0.797517 + 0.603296i \(0.793854\pi\)
\(608\) 1.94603 0.0789221
\(609\) −2.17016 −0.0879394
\(610\) −1.29822 −0.0525635
\(611\) 0.528681 0.0213881
\(612\) 51.5067 2.08203
\(613\) −10.4053 −0.420266 −0.210133 0.977673i \(-0.567390\pi\)
−0.210133 + 0.977673i \(0.567390\pi\)
\(614\) 6.60987 0.266753
\(615\) 0.728288 0.0293674
\(616\) −71.6298 −2.88605
\(617\) −0.907254 −0.0365247 −0.0182623 0.999833i \(-0.505813\pi\)
−0.0182623 + 0.999833i \(0.505813\pi\)
\(618\) −6.00516 −0.241563
\(619\) 45.4027 1.82489 0.912444 0.409202i \(-0.134193\pi\)
0.912444 + 0.409202i \(0.134193\pi\)
\(620\) −8.25154 −0.331390
\(621\) −9.17948 −0.368360
\(622\) −55.8612 −2.23983
\(623\) 21.6026 0.865490
\(624\) 9.27927 0.371468
\(625\) 23.3442 0.933767
\(626\) 20.1496 0.805340
\(627\) 1.72612 0.0689345
\(628\) 22.7991 0.909784
\(629\) −39.2411 −1.56464
\(630\) −5.62778 −0.224216
\(631\) −29.2003 −1.16245 −0.581224 0.813744i \(-0.697426\pi\)
−0.581224 + 0.813744i \(0.697426\pi\)
\(632\) −32.3958 −1.28864
\(633\) 5.44185 0.216294
\(634\) 2.48734 0.0987849
\(635\) 1.55720 0.0617955
\(636\) 10.4726 0.415268
\(637\) 9.11975 0.361337
\(638\) −42.6292 −1.68771
\(639\) −26.1673 −1.03516
\(640\) −5.83672 −0.230717
\(641\) −12.1126 −0.478419 −0.239210 0.970968i \(-0.576888\pi\)
−0.239210 + 0.970968i \(0.576888\pi\)
\(642\) 12.1344 0.478907
\(643\) 18.1936 0.717485 0.358742 0.933437i \(-0.383206\pi\)
0.358742 + 0.933437i \(0.383206\pi\)
\(644\) −49.6424 −1.95618
\(645\) 1.08073 0.0425536
\(646\) −10.5283 −0.414231
\(647\) 17.1035 0.672406 0.336203 0.941789i \(-0.390857\pi\)
0.336203 + 0.941789i \(0.390857\pi\)
\(648\) −44.4193 −1.74495
\(649\) 5.09584 0.200029
\(650\) −71.5188 −2.80520
\(651\) −4.22136 −0.165448
\(652\) −89.6288 −3.51013
\(653\) −22.2528 −0.870821 −0.435411 0.900232i \(-0.643397\pi\)
−0.435411 + 0.900232i \(0.643397\pi\)
\(654\) −0.811884 −0.0317472
\(655\) 4.30131 0.168066
\(656\) 36.7994 1.43677
\(657\) 30.4284 1.18712
\(658\) 0.521938 0.0203473
\(659\) −30.7589 −1.19820 −0.599098 0.800676i \(-0.704474\pi\)
−0.599098 + 0.800676i \(0.704474\pi\)
\(660\) 2.41010 0.0938131
\(661\) 34.9010 1.35749 0.678746 0.734373i \(-0.262524\pi\)
0.678746 + 0.734373i \(0.262524\pi\)
\(662\) −47.7225 −1.85479
\(663\) −7.61756 −0.295842
\(664\) −11.6097 −0.450542
\(665\) 0.778486 0.0301884
\(666\) 67.0198 2.59696
\(667\) −15.4312 −0.597497
\(668\) −28.1260 −1.08823
\(669\) −1.24352 −0.0480773
\(670\) −6.13712 −0.237098
\(671\) −8.82875 −0.340830
\(672\) 1.39006 0.0536226
\(673\) 23.5766 0.908810 0.454405 0.890795i \(-0.349852\pi\)
0.454405 + 0.890795i \(0.349852\pi\)
\(674\) 38.2770 1.47437
\(675\) −8.83547 −0.340078
\(676\) 90.4002 3.47693
\(677\) 40.5000 1.55654 0.778271 0.627929i \(-0.216097\pi\)
0.778271 + 0.627929i \(0.216097\pi\)
\(678\) 9.99536 0.383869
\(679\) −35.5845 −1.36561
\(680\) −7.67816 −0.294444
\(681\) −3.48611 −0.133588
\(682\) −82.9216 −3.17523
\(683\) −15.6052 −0.597116 −0.298558 0.954392i \(-0.596506\pi\)
−0.298558 + 0.954392i \(0.596506\pi\)
\(684\) 12.1686 0.465277
\(685\) −0.0546921 −0.00208968
\(686\) 49.6485 1.89559
\(687\) 7.06552 0.269567
\(688\) 54.6077 2.08190
\(689\) 48.0777 1.83161
\(690\) 1.28917 0.0490777
\(691\) −3.94273 −0.149988 −0.0749942 0.997184i \(-0.523894\pi\)
−0.0749942 + 0.997184i \(0.523894\pi\)
\(692\) −15.6795 −0.596046
\(693\) −38.2726 −1.45385
\(694\) −20.5795 −0.781189
\(695\) 6.45777 0.244957
\(696\) 5.05679 0.191677
\(697\) −30.2094 −1.14426
\(698\) −24.7034 −0.935037
\(699\) −2.96055 −0.111978
\(700\) −47.7820 −1.80599
\(701\) 34.6640 1.30924 0.654621 0.755957i \(-0.272828\pi\)
0.654621 + 0.755957i \(0.272828\pi\)
\(702\) 26.4392 0.997883
\(703\) −9.27079 −0.349655
\(704\) −30.8666 −1.16333
\(705\) −0.00917263 −0.000345461 0
\(706\) −27.8878 −1.04957
\(707\) −0.474341 −0.0178394
\(708\) −1.15731 −0.0434945
\(709\) −30.8405 −1.15824 −0.579120 0.815242i \(-0.696604\pi\)
−0.579120 + 0.815242i \(0.696604\pi\)
\(710\) 7.46828 0.280279
\(711\) −17.3094 −0.649154
\(712\) −50.3372 −1.88646
\(713\) −30.0164 −1.12412
\(714\) −7.52042 −0.281444
\(715\) 11.0643 0.413780
\(716\) −49.3559 −1.84452
\(717\) 6.15835 0.229988
\(718\) 8.05084 0.300455
\(719\) 32.0397 1.19488 0.597439 0.801915i \(-0.296185\pi\)
0.597439 + 0.801915i \(0.296185\pi\)
\(720\) 4.99745 0.186244
\(721\) −18.4185 −0.685943
\(722\) −2.48734 −0.0925692
\(723\) −7.49432 −0.278717
\(724\) 98.5965 3.66431
\(725\) −14.8529 −0.551622
\(726\) 15.8475 0.588156
\(727\) −29.7727 −1.10421 −0.552104 0.833775i \(-0.686175\pi\)
−0.552104 + 0.833775i \(0.686175\pi\)
\(728\) 74.6819 2.76790
\(729\) −22.0746 −0.817579
\(730\) −8.68440 −0.321424
\(731\) −44.8287 −1.65805
\(732\) 2.00509 0.0741103
\(733\) −54.0820 −1.99756 −0.998782 0.0493439i \(-0.984287\pi\)
−0.998782 + 0.0493439i \(0.984287\pi\)
\(734\) −7.58363 −0.279917
\(735\) −0.158228 −0.00583632
\(736\) 9.88415 0.364335
\(737\) −41.7364 −1.53738
\(738\) 51.5947 1.89923
\(739\) 52.7803 1.94155 0.970777 0.239983i \(-0.0771418\pi\)
0.970777 + 0.239983i \(0.0771418\pi\)
\(740\) −12.9444 −0.475846
\(741\) −1.79967 −0.0661124
\(742\) 47.4645 1.74248
\(743\) 22.2579 0.816564 0.408282 0.912856i \(-0.366128\pi\)
0.408282 + 0.912856i \(0.366128\pi\)
\(744\) 9.83637 0.360619
\(745\) 3.40744 0.124839
\(746\) 35.9461 1.31608
\(747\) −6.20316 −0.226962
\(748\) −99.9712 −3.65531
\(749\) 37.2177 1.35991
\(750\) 2.50994 0.0916499
\(751\) −46.6337 −1.70169 −0.850844 0.525419i \(-0.823909\pi\)
−0.850844 + 0.525419i \(0.823909\pi\)
\(752\) −0.463480 −0.0169014
\(753\) −3.39994 −0.123901
\(754\) 44.4456 1.61861
\(755\) 7.08631 0.257897
\(756\) 17.6641 0.642438
\(757\) −28.0542 −1.01965 −0.509823 0.860279i \(-0.670289\pi\)
−0.509823 + 0.860279i \(0.670289\pi\)
\(758\) 0.700729 0.0254516
\(759\) 8.76717 0.318228
\(760\) −1.81398 −0.0658001
\(761\) 12.0870 0.438152 0.219076 0.975708i \(-0.429696\pi\)
0.219076 + 0.975708i \(0.429696\pi\)
\(762\) −3.55395 −0.128746
\(763\) −2.49015 −0.0901494
\(764\) −83.1070 −3.00671
\(765\) −4.10252 −0.148327
\(766\) −63.5604 −2.29653
\(767\) −5.31297 −0.191840
\(768\) 9.97236 0.359846
\(769\) 28.5387 1.02913 0.514565 0.857451i \(-0.327953\pi\)
0.514565 + 0.857451i \(0.327953\pi\)
\(770\) 10.9232 0.393643
\(771\) 3.23074 0.116352
\(772\) −69.2623 −2.49281
\(773\) −14.4280 −0.518940 −0.259470 0.965751i \(-0.583548\pi\)
−0.259470 + 0.965751i \(0.583548\pi\)
\(774\) 76.5629 2.75200
\(775\) −28.8916 −1.03782
\(776\) 82.9171 2.97655
\(777\) −6.62216 −0.237569
\(778\) 68.6381 2.46079
\(779\) −7.13705 −0.255711
\(780\) −2.51280 −0.0899725
\(781\) 50.7891 1.81738
\(782\) −53.4747 −1.91225
\(783\) 5.49083 0.196226
\(784\) −7.99503 −0.285537
\(785\) −1.81596 −0.0648143
\(786\) −9.81674 −0.350152
\(787\) 9.95770 0.354954 0.177477 0.984125i \(-0.443207\pi\)
0.177477 + 0.984125i \(0.443207\pi\)
\(788\) −18.1744 −0.647437
\(789\) −2.59402 −0.0923495
\(790\) 4.94019 0.175764
\(791\) 30.6570 1.09004
\(792\) 89.1806 3.16889
\(793\) 9.20495 0.326877
\(794\) −24.4698 −0.868401
\(795\) −0.834150 −0.0295842
\(796\) 114.728 4.06644
\(797\) −10.5310 −0.373028 −0.186514 0.982452i \(-0.559719\pi\)
−0.186514 + 0.982452i \(0.559719\pi\)
\(798\) −1.77672 −0.0628950
\(799\) 0.380481 0.0134605
\(800\) 9.51374 0.336362
\(801\) −26.8957 −0.950312
\(802\) 76.3663 2.69659
\(803\) −59.0596 −2.08417
\(804\) 9.47873 0.334289
\(805\) 3.95403 0.139361
\(806\) 86.4548 3.04524
\(807\) −0.331463 −0.0116680
\(808\) 1.10528 0.0388837
\(809\) −13.9718 −0.491223 −0.245611 0.969368i \(-0.578989\pi\)
−0.245611 + 0.969368i \(0.578989\pi\)
\(810\) 6.77370 0.238004
\(811\) −49.9644 −1.75449 −0.877244 0.480044i \(-0.840621\pi\)
−0.877244 + 0.480044i \(0.840621\pi\)
\(812\) 29.6943 1.04207
\(813\) −2.65600 −0.0931499
\(814\) −130.081 −4.55934
\(815\) 7.13896 0.250067
\(816\) 6.67811 0.233781
\(817\) −10.5909 −0.370528
\(818\) −2.65383 −0.0927889
\(819\) 39.9034 1.39434
\(820\) −9.96515 −0.347998
\(821\) 8.15054 0.284456 0.142228 0.989834i \(-0.454573\pi\)
0.142228 + 0.989834i \(0.454573\pi\)
\(822\) 0.124822 0.00435367
\(823\) 4.77565 0.166469 0.0832344 0.996530i \(-0.473475\pi\)
0.0832344 + 0.996530i \(0.473475\pi\)
\(824\) 42.9179 1.49511
\(825\) 8.43862 0.293795
\(826\) −5.24522 −0.182504
\(827\) −39.0985 −1.35959 −0.679794 0.733403i \(-0.737931\pi\)
−0.679794 + 0.733403i \(0.737931\pi\)
\(828\) 61.8058 2.14790
\(829\) 32.3495 1.12354 0.561771 0.827292i \(-0.310120\pi\)
0.561771 + 0.827292i \(0.310120\pi\)
\(830\) 1.77041 0.0614518
\(831\) 6.67516 0.231559
\(832\) 32.1818 1.11570
\(833\) 6.56331 0.227405
\(834\) −14.7384 −0.510348
\(835\) 2.24024 0.0775268
\(836\) −23.6184 −0.816861
\(837\) 10.6807 0.369178
\(838\) 85.0896 2.93937
\(839\) −18.8784 −0.651753 −0.325877 0.945412i \(-0.605659\pi\)
−0.325877 + 0.945412i \(0.605659\pi\)
\(840\) −1.29573 −0.0447071
\(841\) −19.7696 −0.681711
\(842\) 79.8815 2.75290
\(843\) −7.81635 −0.269209
\(844\) −74.4608 −2.56305
\(845\) −7.20041 −0.247701
\(846\) −0.649824 −0.0223414
\(847\) 48.6063 1.67013
\(848\) −42.1484 −1.44738
\(849\) 7.74210 0.265708
\(850\) −51.4707 −1.76543
\(851\) −47.0876 −1.61414
\(852\) −11.5347 −0.395172
\(853\) −46.9480 −1.60747 −0.803734 0.594989i \(-0.797157\pi\)
−0.803734 + 0.594989i \(0.797157\pi\)
\(854\) 9.08755 0.310970
\(855\) −0.969231 −0.0331470
\(856\) −86.7226 −2.96412
\(857\) −49.2629 −1.68279 −0.841394 0.540423i \(-0.818264\pi\)
−0.841394 + 0.540423i \(0.818264\pi\)
\(858\) −25.2516 −0.862077
\(859\) −53.7341 −1.83338 −0.916692 0.399593i \(-0.869151\pi\)
−0.916692 + 0.399593i \(0.869151\pi\)
\(860\) −14.7876 −0.504253
\(861\) −5.09802 −0.173740
\(862\) 68.5718 2.33556
\(863\) −1.08113 −0.0368022 −0.0184011 0.999831i \(-0.505858\pi\)
−0.0184011 + 0.999831i \(0.505858\pi\)
\(864\) −3.51705 −0.119653
\(865\) 1.24888 0.0424631
\(866\) −47.8241 −1.62513
\(867\) −0.280374 −0.00952201
\(868\) 57.7608 1.96053
\(869\) 33.5965 1.13968
\(870\) −0.771133 −0.0261439
\(871\) 43.5148 1.47444
\(872\) 5.80240 0.196494
\(873\) 44.3035 1.49945
\(874\) −12.6335 −0.427335
\(875\) 7.69828 0.260249
\(876\) 13.4130 0.453182
\(877\) 12.5264 0.422988 0.211494 0.977379i \(-0.432167\pi\)
0.211494 + 0.977379i \(0.432167\pi\)
\(878\) 19.6761 0.664036
\(879\) 4.94462 0.166778
\(880\) −9.69974 −0.326978
\(881\) 29.8243 1.00481 0.502403 0.864634i \(-0.332450\pi\)
0.502403 + 0.864634i \(0.332450\pi\)
\(882\) −11.2095 −0.377442
\(883\) 24.1749 0.813550 0.406775 0.913528i \(-0.366653\pi\)
0.406775 + 0.913528i \(0.366653\pi\)
\(884\) 104.231 3.50567
\(885\) 0.0921803 0.00309861
\(886\) 100.765 3.38527
\(887\) 9.65289 0.324112 0.162056 0.986782i \(-0.448187\pi\)
0.162056 + 0.986782i \(0.448187\pi\)
\(888\) 15.4306 0.517816
\(889\) −10.9004 −0.365587
\(890\) 7.67615 0.257305
\(891\) 46.0656 1.54326
\(892\) 17.0151 0.569707
\(893\) 0.0898896 0.00300804
\(894\) −7.77670 −0.260092
\(895\) 3.93121 0.131406
\(896\) 40.8571 1.36494
\(897\) −9.14074 −0.305200
\(898\) 39.5726 1.32055
\(899\) 17.9548 0.598825
\(900\) 59.4896 1.98299
\(901\) 34.6006 1.15271
\(902\) −100.142 −3.33436
\(903\) −7.56510 −0.251751
\(904\) −71.4352 −2.37590
\(905\) −7.85324 −0.261051
\(906\) −16.1729 −0.537308
\(907\) 14.1432 0.469616 0.234808 0.972042i \(-0.424554\pi\)
0.234808 + 0.972042i \(0.424554\pi\)
\(908\) 47.7004 1.58299
\(909\) 0.590564 0.0195878
\(910\) −11.3886 −0.377528
\(911\) 48.1626 1.59570 0.797848 0.602858i \(-0.205971\pi\)
0.797848 + 0.602858i \(0.205971\pi\)
\(912\) 1.57772 0.0522435
\(913\) 12.0399 0.398464
\(914\) 9.92600 0.328323
\(915\) −0.159706 −0.00527972
\(916\) −96.6774 −3.19431
\(917\) −30.1091 −0.994292
\(918\) 19.0278 0.628010
\(919\) 22.3758 0.738109 0.369054 0.929408i \(-0.379682\pi\)
0.369054 + 0.929408i \(0.379682\pi\)
\(920\) −9.21346 −0.303759
\(921\) 0.813140 0.0267939
\(922\) 8.33159 0.274386
\(923\) −52.9533 −1.74298
\(924\) −16.8707 −0.555006
\(925\) −45.3229 −1.49021
\(926\) 45.9848 1.51115
\(927\) 22.9315 0.753168
\(928\) −5.91235 −0.194082
\(929\) −42.4069 −1.39133 −0.695663 0.718369i \(-0.744889\pi\)
−0.695663 + 0.718369i \(0.744889\pi\)
\(930\) −1.49999 −0.0491867
\(931\) 1.55060 0.0508187
\(932\) 40.5091 1.32692
\(933\) −6.87200 −0.224979
\(934\) −25.9788 −0.850053
\(935\) 7.96274 0.260409
\(936\) −92.9805 −3.03916
\(937\) −51.4560 −1.68099 −0.840497 0.541816i \(-0.817737\pi\)
−0.840497 + 0.541816i \(0.817737\pi\)
\(938\) 42.9599 1.40269
\(939\) 2.47879 0.0808922
\(940\) 0.125509 0.00409365
\(941\) 8.18511 0.266827 0.133414 0.991060i \(-0.457406\pi\)
0.133414 + 0.991060i \(0.457406\pi\)
\(942\) 4.14451 0.135035
\(943\) −36.2500 −1.18046
\(944\) 4.65774 0.151597
\(945\) −1.40695 −0.0457682
\(946\) −148.604 −4.83152
\(947\) 29.3625 0.954152 0.477076 0.878862i \(-0.341697\pi\)
0.477076 + 0.878862i \(0.341697\pi\)
\(948\) −7.63008 −0.247813
\(949\) 61.5761 1.99884
\(950\) −12.1601 −0.394525
\(951\) 0.305991 0.00992242
\(952\) 53.7472 1.74196
\(953\) −32.5726 −1.05513 −0.527565 0.849515i \(-0.676895\pi\)
−0.527565 + 0.849515i \(0.676895\pi\)
\(954\) −59.0943 −1.91325
\(955\) 6.61950 0.214202
\(956\) −84.2645 −2.72531
\(957\) −5.24421 −0.169521
\(958\) 86.6564 2.79974
\(959\) 0.382845 0.0123627
\(960\) −0.558356 −0.0180209
\(961\) 3.92527 0.126622
\(962\) 135.624 4.37269
\(963\) −46.3368 −1.49318
\(964\) 102.545 3.30274
\(965\) 5.51677 0.177591
\(966\) −9.02417 −0.290348
\(967\) 14.7453 0.474177 0.237088 0.971488i \(-0.423807\pi\)
0.237088 + 0.971488i \(0.423807\pi\)
\(968\) −113.260 −3.64030
\(969\) −1.29519 −0.0416074
\(970\) −12.6444 −0.405987
\(971\) −19.3873 −0.622169 −0.311084 0.950382i \(-0.600692\pi\)
−0.311084 + 0.950382i \(0.600692\pi\)
\(972\) −33.1626 −1.06369
\(973\) −45.2044 −1.44919
\(974\) 46.9998 1.50597
\(975\) −8.79819 −0.281768
\(976\) −8.06973 −0.258306
\(977\) −38.6596 −1.23683 −0.618415 0.785851i \(-0.712225\pi\)
−0.618415 + 0.785851i \(0.712225\pi\)
\(978\) −16.2930 −0.520994
\(979\) 52.2028 1.66841
\(980\) 2.16503 0.0691593
\(981\) 3.10029 0.0989845
\(982\) −95.7935 −3.05689
\(983\) 8.31092 0.265077 0.132539 0.991178i \(-0.457687\pi\)
0.132539 + 0.991178i \(0.457687\pi\)
\(984\) 11.8791 0.378692
\(985\) 1.44760 0.0461243
\(986\) 31.9867 1.01866
\(987\) 0.0642084 0.00204378
\(988\) 24.6248 0.783420
\(989\) −53.7925 −1.71050
\(990\) −13.5996 −0.432222
\(991\) −24.5068 −0.778483 −0.389241 0.921136i \(-0.627263\pi\)
−0.389241 + 0.921136i \(0.627263\pi\)
\(992\) −11.5006 −0.365144
\(993\) −5.87078 −0.186304
\(994\) −52.2779 −1.65816
\(995\) −9.13815 −0.289699
\(996\) −2.73438 −0.0866422
\(997\) 17.3337 0.548963 0.274481 0.961592i \(-0.411494\pi\)
0.274481 + 0.961592i \(0.411494\pi\)
\(998\) 107.028 3.38791
\(999\) 16.7550 0.530106
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 \(a_p\))