Properties

Label 6034.2.a.n.1.18
Level 6034
Weight 2
Character 6034.1
Self dual Yes
Analytic conductor 48.182
Analytic rank 0
Dimension 24
CM No

Related objects

Downloads

Learn more about

Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 1.18
Character \(\chi\) = 6034.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.56085 q^{3} +1.00000 q^{4} -1.28710 q^{5} -1.56085 q^{6} -1.00000 q^{7} -1.00000 q^{8} -0.563752 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.56085 q^{3} +1.00000 q^{4} -1.28710 q^{5} -1.56085 q^{6} -1.00000 q^{7} -1.00000 q^{8} -0.563752 q^{9} +1.28710 q^{10} -0.685769 q^{11} +1.56085 q^{12} -1.48318 q^{13} +1.00000 q^{14} -2.00897 q^{15} +1.00000 q^{16} -5.29258 q^{17} +0.563752 q^{18} -3.49670 q^{19} -1.28710 q^{20} -1.56085 q^{21} +0.685769 q^{22} +4.10641 q^{23} -1.56085 q^{24} -3.34338 q^{25} +1.48318 q^{26} -5.56248 q^{27} -1.00000 q^{28} +0.0567258 q^{29} +2.00897 q^{30} -6.65582 q^{31} -1.00000 q^{32} -1.07038 q^{33} +5.29258 q^{34} +1.28710 q^{35} -0.563752 q^{36} +2.52754 q^{37} +3.49670 q^{38} -2.31502 q^{39} +1.28710 q^{40} -1.28831 q^{41} +1.56085 q^{42} +9.13119 q^{43} -0.685769 q^{44} +0.725605 q^{45} -4.10641 q^{46} +3.53299 q^{47} +1.56085 q^{48} +1.00000 q^{49} +3.34338 q^{50} -8.26091 q^{51} -1.48318 q^{52} +6.42176 q^{53} +5.56248 q^{54} +0.882653 q^{55} +1.00000 q^{56} -5.45782 q^{57} -0.0567258 q^{58} +7.80975 q^{59} -2.00897 q^{60} +5.85159 q^{61} +6.65582 q^{62} +0.563752 q^{63} +1.00000 q^{64} +1.90900 q^{65} +1.07038 q^{66} +13.6056 q^{67} -5.29258 q^{68} +6.40949 q^{69} -1.28710 q^{70} -10.2221 q^{71} +0.563752 q^{72} +13.5958 q^{73} -2.52754 q^{74} -5.21850 q^{75} -3.49670 q^{76} +0.685769 q^{77} +2.31502 q^{78} -6.53682 q^{79} -1.28710 q^{80} -6.99093 q^{81} +1.28831 q^{82} +15.6785 q^{83} -1.56085 q^{84} +6.81207 q^{85} -9.13119 q^{86} +0.0885403 q^{87} +0.685769 q^{88} +1.36780 q^{89} -0.725605 q^{90} +1.48318 q^{91} +4.10641 q^{92} -10.3887 q^{93} -3.53299 q^{94} +4.50060 q^{95} -1.56085 q^{96} -6.23052 q^{97} -1.00000 q^{98} +0.386604 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 24q^{2} + 7q^{3} + 24q^{4} + 8q^{5} - 7q^{6} - 24q^{7} - 24q^{8} + 19q^{9} + O(q^{10}) \) \( 24q - 24q^{2} + 7q^{3} + 24q^{4} + 8q^{5} - 7q^{6} - 24q^{7} - 24q^{8} + 19q^{9} - 8q^{10} + 15q^{11} + 7q^{12} - 7q^{13} + 24q^{14} + 13q^{15} + 24q^{16} - 5q^{17} - 19q^{18} + 6q^{19} + 8q^{20} - 7q^{21} - 15q^{22} + 3q^{23} - 7q^{24} + 12q^{25} + 7q^{26} + 22q^{27} - 24q^{28} + 5q^{29} - 13q^{30} + 13q^{31} - 24q^{32} - 8q^{33} + 5q^{34} - 8q^{35} + 19q^{36} + 2q^{37} - 6q^{38} + 7q^{39} - 8q^{40} + 25q^{41} + 7q^{42} - 15q^{43} + 15q^{44} + 41q^{45} - 3q^{46} + 35q^{47} + 7q^{48} + 24q^{49} - 12q^{50} + 31q^{51} - 7q^{52} + 2q^{53} - 22q^{54} + 14q^{55} + 24q^{56} - 13q^{57} - 5q^{58} + 35q^{59} + 13q^{60} - 7q^{61} - 13q^{62} - 19q^{63} + 24q^{64} - 4q^{65} + 8q^{66} + 10q^{67} - 5q^{68} + 6q^{69} + 8q^{70} + 58q^{71} - 19q^{72} + 9q^{73} - 2q^{74} + 7q^{75} + 6q^{76} - 15q^{77} - 7q^{78} + 31q^{79} + 8q^{80} + 16q^{81} - 25q^{82} - q^{83} - 7q^{84} - 4q^{85} + 15q^{86} + 30q^{87} - 15q^{88} + 45q^{89} - 41q^{90} + 7q^{91} + 3q^{92} + 25q^{93} - 35q^{94} - 10q^{95} - 7q^{96} - 9q^{97} - 24q^{98} + 64q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 1.56085 0.901156 0.450578 0.892737i \(-0.351218\pi\)
0.450578 + 0.892737i \(0.351218\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.28710 −0.575608 −0.287804 0.957689i \(-0.592925\pi\)
−0.287804 + 0.957689i \(0.592925\pi\)
\(6\) −1.56085 −0.637214
\(7\) −1.00000 −0.377964
\(8\) −1.00000 −0.353553
\(9\) −0.563752 −0.187917
\(10\) 1.28710 0.407016
\(11\) −0.685769 −0.206767 −0.103384 0.994642i \(-0.532967\pi\)
−0.103384 + 0.994642i \(0.532967\pi\)
\(12\) 1.56085 0.450578
\(13\) −1.48318 −0.411361 −0.205680 0.978619i \(-0.565941\pi\)
−0.205680 + 0.978619i \(0.565941\pi\)
\(14\) 1.00000 0.267261
\(15\) −2.00897 −0.518713
\(16\) 1.00000 0.250000
\(17\) −5.29258 −1.28364 −0.641820 0.766856i \(-0.721820\pi\)
−0.641820 + 0.766856i \(0.721820\pi\)
\(18\) 0.563752 0.132878
\(19\) −3.49670 −0.802199 −0.401099 0.916035i \(-0.631372\pi\)
−0.401099 + 0.916035i \(0.631372\pi\)
\(20\) −1.28710 −0.287804
\(21\) −1.56085 −0.340605
\(22\) 0.685769 0.146207
\(23\) 4.10641 0.856246 0.428123 0.903720i \(-0.359175\pi\)
0.428123 + 0.903720i \(0.359175\pi\)
\(24\) −1.56085 −0.318607
\(25\) −3.34338 −0.668675
\(26\) 1.48318 0.290876
\(27\) −5.56248 −1.07050
\(28\) −1.00000 −0.188982
\(29\) 0.0567258 0.0105337 0.00526686 0.999986i \(-0.498323\pi\)
0.00526686 + 0.999986i \(0.498323\pi\)
\(30\) 2.00897 0.366785
\(31\) −6.65582 −1.19542 −0.597711 0.801712i \(-0.703923\pi\)
−0.597711 + 0.801712i \(0.703923\pi\)
\(32\) −1.00000 −0.176777
\(33\) −1.07038 −0.186330
\(34\) 5.29258 0.907670
\(35\) 1.28710 0.217559
\(36\) −0.563752 −0.0939587
\(37\) 2.52754 0.415525 0.207763 0.978179i \(-0.433382\pi\)
0.207763 + 0.978179i \(0.433382\pi\)
\(38\) 3.49670 0.567240
\(39\) −2.31502 −0.370700
\(40\) 1.28710 0.203508
\(41\) −1.28831 −0.201201 −0.100600 0.994927i \(-0.532076\pi\)
−0.100600 + 0.994927i \(0.532076\pi\)
\(42\) 1.56085 0.240844
\(43\) 9.13119 1.39249 0.696247 0.717803i \(-0.254852\pi\)
0.696247 + 0.717803i \(0.254852\pi\)
\(44\) −0.685769 −0.103384
\(45\) 0.725605 0.108167
\(46\) −4.10641 −0.605458
\(47\) 3.53299 0.515340 0.257670 0.966233i \(-0.417045\pi\)
0.257670 + 0.966233i \(0.417045\pi\)
\(48\) 1.56085 0.225289
\(49\) 1.00000 0.142857
\(50\) 3.34338 0.472825
\(51\) −8.26091 −1.15676
\(52\) −1.48318 −0.205680
\(53\) 6.42176 0.882097 0.441049 0.897483i \(-0.354607\pi\)
0.441049 + 0.897483i \(0.354607\pi\)
\(54\) 5.56248 0.756957
\(55\) 0.882653 0.119017
\(56\) 1.00000 0.133631
\(57\) −5.45782 −0.722906
\(58\) −0.0567258 −0.00744846
\(59\) 7.80975 1.01674 0.508371 0.861138i \(-0.330248\pi\)
0.508371 + 0.861138i \(0.330248\pi\)
\(60\) −2.00897 −0.259356
\(61\) 5.85159 0.749220 0.374610 0.927183i \(-0.377777\pi\)
0.374610 + 0.927183i \(0.377777\pi\)
\(62\) 6.65582 0.845291
\(63\) 0.563752 0.0710261
\(64\) 1.00000 0.125000
\(65\) 1.90900 0.236783
\(66\) 1.07038 0.131755
\(67\) 13.6056 1.66219 0.831095 0.556130i \(-0.187714\pi\)
0.831095 + 0.556130i \(0.187714\pi\)
\(68\) −5.29258 −0.641820
\(69\) 6.40949 0.771612
\(70\) −1.28710 −0.153838
\(71\) −10.2221 −1.21313 −0.606567 0.795032i \(-0.707454\pi\)
−0.606567 + 0.795032i \(0.707454\pi\)
\(72\) 0.563752 0.0664389
\(73\) 13.5958 1.59127 0.795635 0.605776i \(-0.207137\pi\)
0.795635 + 0.605776i \(0.207137\pi\)
\(74\) −2.52754 −0.293821
\(75\) −5.21850 −0.602581
\(76\) −3.49670 −0.401099
\(77\) 0.685769 0.0781507
\(78\) 2.31502 0.262125
\(79\) −6.53682 −0.735450 −0.367725 0.929935i \(-0.619863\pi\)
−0.367725 + 0.929935i \(0.619863\pi\)
\(80\) −1.28710 −0.143902
\(81\) −6.99093 −0.776770
\(82\) 1.28831 0.142270
\(83\) 15.6785 1.72094 0.860470 0.509502i \(-0.170170\pi\)
0.860470 + 0.509502i \(0.170170\pi\)
\(84\) −1.56085 −0.170303
\(85\) 6.81207 0.738873
\(86\) −9.13119 −0.984642
\(87\) 0.0885403 0.00949252
\(88\) 0.685769 0.0731033
\(89\) 1.36780 0.144987 0.0724934 0.997369i \(-0.476904\pi\)
0.0724934 + 0.997369i \(0.476904\pi\)
\(90\) −0.725605 −0.0764855
\(91\) 1.48318 0.155480
\(92\) 4.10641 0.428123
\(93\) −10.3887 −1.07726
\(94\) −3.53299 −0.364400
\(95\) 4.50060 0.461752
\(96\) −1.56085 −0.159303
\(97\) −6.23052 −0.632613 −0.316307 0.948657i \(-0.602443\pi\)
−0.316307 + 0.948657i \(0.602443\pi\)
\(98\) −1.00000 −0.101015
\(99\) 0.386604 0.0388552
\(100\) −3.34338 −0.334338
\(101\) 13.3302 1.32640 0.663200 0.748442i \(-0.269198\pi\)
0.663200 + 0.748442i \(0.269198\pi\)
\(102\) 8.26091 0.817952
\(103\) 0.500539 0.0493195 0.0246598 0.999696i \(-0.492150\pi\)
0.0246598 + 0.999696i \(0.492150\pi\)
\(104\) 1.48318 0.145438
\(105\) 2.00897 0.196055
\(106\) −6.42176 −0.623737
\(107\) −7.34326 −0.709900 −0.354950 0.934885i \(-0.615502\pi\)
−0.354950 + 0.934885i \(0.615502\pi\)
\(108\) −5.56248 −0.535250
\(109\) 8.93552 0.855868 0.427934 0.903810i \(-0.359242\pi\)
0.427934 + 0.903810i \(0.359242\pi\)
\(110\) −0.882653 −0.0841577
\(111\) 3.94511 0.374453
\(112\) −1.00000 −0.0944911
\(113\) 1.16529 0.109622 0.0548108 0.998497i \(-0.482544\pi\)
0.0548108 + 0.998497i \(0.482544\pi\)
\(114\) 5.45782 0.511172
\(115\) −5.28536 −0.492862
\(116\) 0.0567258 0.00526686
\(117\) 0.836147 0.0773018
\(118\) −7.80975 −0.718946
\(119\) 5.29258 0.485170
\(120\) 2.00897 0.183393
\(121\) −10.5297 −0.957247
\(122\) −5.85159 −0.529778
\(123\) −2.01086 −0.181313
\(124\) −6.65582 −0.597711
\(125\) 10.7388 0.960503
\(126\) −0.563752 −0.0502231
\(127\) −10.7080 −0.950178 −0.475089 0.879938i \(-0.657584\pi\)
−0.475089 + 0.879938i \(0.657584\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 14.2524 1.25485
\(130\) −1.90900 −0.167431
\(131\) 15.5805 1.36127 0.680635 0.732623i \(-0.261704\pi\)
0.680635 + 0.732623i \(0.261704\pi\)
\(132\) −1.07038 −0.0931648
\(133\) 3.49670 0.303203
\(134\) −13.6056 −1.17535
\(135\) 7.15946 0.616188
\(136\) 5.29258 0.453835
\(137\) −4.25947 −0.363911 −0.181956 0.983307i \(-0.558243\pi\)
−0.181956 + 0.983307i \(0.558243\pi\)
\(138\) −6.40949 −0.545612
\(139\) 17.4365 1.47894 0.739471 0.673188i \(-0.235076\pi\)
0.739471 + 0.673188i \(0.235076\pi\)
\(140\) 1.28710 0.108780
\(141\) 5.51447 0.464402
\(142\) 10.2221 0.857816
\(143\) 1.01712 0.0850559
\(144\) −0.563752 −0.0469794
\(145\) −0.0730117 −0.00606329
\(146\) −13.5958 −1.12520
\(147\) 1.56085 0.128737
\(148\) 2.52754 0.207763
\(149\) −4.88372 −0.400090 −0.200045 0.979787i \(-0.564109\pi\)
−0.200045 + 0.979787i \(0.564109\pi\)
\(150\) 5.21850 0.426089
\(151\) −14.8201 −1.20605 −0.603023 0.797724i \(-0.706037\pi\)
−0.603023 + 0.797724i \(0.706037\pi\)
\(152\) 3.49670 0.283620
\(153\) 2.98370 0.241218
\(154\) −0.685769 −0.0552609
\(155\) 8.56671 0.688094
\(156\) −2.31502 −0.185350
\(157\) −0.00574047 −0.000458140 0 −0.000229070 1.00000i \(-0.500073\pi\)
−0.000229070 1.00000i \(0.500073\pi\)
\(158\) 6.53682 0.520041
\(159\) 10.0234 0.794907
\(160\) 1.28710 0.101754
\(161\) −4.10641 −0.323631
\(162\) 6.99093 0.549259
\(163\) 5.85030 0.458231 0.229115 0.973399i \(-0.426417\pi\)
0.229115 + 0.973399i \(0.426417\pi\)
\(164\) −1.28831 −0.100600
\(165\) 1.37769 0.107253
\(166\) −15.6785 −1.21689
\(167\) −13.1245 −1.01561 −0.507803 0.861473i \(-0.669542\pi\)
−0.507803 + 0.861473i \(0.669542\pi\)
\(168\) 1.56085 0.120422
\(169\) −10.8002 −0.830782
\(170\) −6.81207 −0.522462
\(171\) 1.97128 0.150747
\(172\) 9.13119 0.696247
\(173\) 16.0789 1.22245 0.611227 0.791455i \(-0.290676\pi\)
0.611227 + 0.791455i \(0.290676\pi\)
\(174\) −0.0885403 −0.00671223
\(175\) 3.34338 0.252735
\(176\) −0.685769 −0.0516918
\(177\) 12.1898 0.916244
\(178\) −1.36780 −0.102521
\(179\) −15.5798 −1.16449 −0.582245 0.813013i \(-0.697826\pi\)
−0.582245 + 0.813013i \(0.697826\pi\)
\(180\) 0.725605 0.0540834
\(181\) −5.82553 −0.433008 −0.216504 0.976282i \(-0.569465\pi\)
−0.216504 + 0.976282i \(0.569465\pi\)
\(182\) −1.48318 −0.109941
\(183\) 9.13345 0.675164
\(184\) −4.10641 −0.302729
\(185\) −3.25320 −0.239180
\(186\) 10.3887 0.761739
\(187\) 3.62949 0.265415
\(188\) 3.53299 0.257670
\(189\) 5.56248 0.404611
\(190\) −4.50060 −0.326508
\(191\) −4.73249 −0.342431 −0.171216 0.985234i \(-0.554769\pi\)
−0.171216 + 0.985234i \(0.554769\pi\)
\(192\) 1.56085 0.112645
\(193\) 7.62722 0.549019 0.274510 0.961584i \(-0.411484\pi\)
0.274510 + 0.961584i \(0.411484\pi\)
\(194\) 6.23052 0.447325
\(195\) 2.97966 0.213378
\(196\) 1.00000 0.0714286
\(197\) 5.31752 0.378858 0.189429 0.981894i \(-0.439336\pi\)
0.189429 + 0.981894i \(0.439336\pi\)
\(198\) −0.386604 −0.0274748
\(199\) 6.13870 0.435161 0.217580 0.976042i \(-0.430184\pi\)
0.217580 + 0.976042i \(0.430184\pi\)
\(200\) 3.34338 0.236412
\(201\) 21.2363 1.49789
\(202\) −13.3302 −0.937906
\(203\) −0.0567258 −0.00398137
\(204\) −8.26091 −0.578380
\(205\) 1.65819 0.115813
\(206\) −0.500539 −0.0348742
\(207\) −2.31500 −0.160904
\(208\) −1.48318 −0.102840
\(209\) 2.39793 0.165868
\(210\) −2.00897 −0.138632
\(211\) −8.79347 −0.605368 −0.302684 0.953091i \(-0.597883\pi\)
−0.302684 + 0.953091i \(0.597883\pi\)
\(212\) 6.42176 0.441049
\(213\) −15.9551 −1.09322
\(214\) 7.34326 0.501975
\(215\) −11.7527 −0.801531
\(216\) 5.56248 0.378479
\(217\) 6.65582 0.451827
\(218\) −8.93552 −0.605190
\(219\) 21.2210 1.43398
\(220\) 0.882653 0.0595085
\(221\) 7.84986 0.528039
\(222\) −3.94511 −0.264778
\(223\) −4.69820 −0.314615 −0.157307 0.987550i \(-0.550281\pi\)
−0.157307 + 0.987550i \(0.550281\pi\)
\(224\) 1.00000 0.0668153
\(225\) 1.88484 0.125656
\(226\) −1.16529 −0.0775142
\(227\) 12.1876 0.808923 0.404461 0.914555i \(-0.367459\pi\)
0.404461 + 0.914555i \(0.367459\pi\)
\(228\) −5.45782 −0.361453
\(229\) 10.4784 0.692430 0.346215 0.938155i \(-0.387467\pi\)
0.346215 + 0.938155i \(0.387467\pi\)
\(230\) 5.28536 0.348506
\(231\) 1.07038 0.0704260
\(232\) −0.0567258 −0.00372423
\(233\) 12.8979 0.844967 0.422483 0.906371i \(-0.361159\pi\)
0.422483 + 0.906371i \(0.361159\pi\)
\(234\) −0.836147 −0.0546607
\(235\) −4.54731 −0.296634
\(236\) 7.80975 0.508371
\(237\) −10.2030 −0.662755
\(238\) −5.29258 −0.343067
\(239\) −10.2758 −0.664684 −0.332342 0.943159i \(-0.607839\pi\)
−0.332342 + 0.943159i \(0.607839\pi\)
\(240\) −2.00897 −0.129678
\(241\) −16.2211 −1.04489 −0.522446 0.852672i \(-0.674980\pi\)
−0.522446 + 0.852672i \(0.674980\pi\)
\(242\) 10.5297 0.676876
\(243\) 5.77566 0.370509
\(244\) 5.85159 0.374610
\(245\) −1.28710 −0.0822297
\(246\) 2.01086 0.128208
\(247\) 5.18625 0.329993
\(248\) 6.65582 0.422645
\(249\) 24.4718 1.55084
\(250\) −10.7388 −0.679178
\(251\) −16.5451 −1.04432 −0.522160 0.852847i \(-0.674874\pi\)
−0.522160 + 0.852847i \(0.674874\pi\)
\(252\) 0.563752 0.0355131
\(253\) −2.81605 −0.177044
\(254\) 10.7080 0.671877
\(255\) 10.6326 0.665840
\(256\) 1.00000 0.0625000
\(257\) 25.4276 1.58613 0.793066 0.609136i \(-0.208483\pi\)
0.793066 + 0.609136i \(0.208483\pi\)
\(258\) −14.2524 −0.887316
\(259\) −2.52754 −0.157054
\(260\) 1.90900 0.118391
\(261\) −0.0319793 −0.00197947
\(262\) −15.5805 −0.962563
\(263\) −1.20088 −0.0740495 −0.0370247 0.999314i \(-0.511788\pi\)
−0.0370247 + 0.999314i \(0.511788\pi\)
\(264\) 1.07038 0.0658775
\(265\) −8.26545 −0.507742
\(266\) −3.49670 −0.214397
\(267\) 2.13493 0.130656
\(268\) 13.6056 0.831095
\(269\) 7.18336 0.437977 0.218988 0.975727i \(-0.429724\pi\)
0.218988 + 0.975727i \(0.429724\pi\)
\(270\) −7.15946 −0.435711
\(271\) 22.3543 1.35793 0.678963 0.734172i \(-0.262430\pi\)
0.678963 + 0.734172i \(0.262430\pi\)
\(272\) −5.29258 −0.320910
\(273\) 2.31502 0.140111
\(274\) 4.25947 0.257324
\(275\) 2.29278 0.138260
\(276\) 6.40949 0.385806
\(277\) −3.45053 −0.207322 −0.103661 0.994613i \(-0.533056\pi\)
−0.103661 + 0.994613i \(0.533056\pi\)
\(278\) −17.4365 −1.04577
\(279\) 3.75224 0.224641
\(280\) −1.28710 −0.0769189
\(281\) 3.76411 0.224548 0.112274 0.993677i \(-0.464187\pi\)
0.112274 + 0.993677i \(0.464187\pi\)
\(282\) −5.51447 −0.328382
\(283\) 6.87260 0.408534 0.204267 0.978915i \(-0.434519\pi\)
0.204267 + 0.978915i \(0.434519\pi\)
\(284\) −10.2221 −0.606567
\(285\) 7.02476 0.416111
\(286\) −1.01712 −0.0601436
\(287\) 1.28831 0.0760467
\(288\) 0.563752 0.0332194
\(289\) 11.0114 0.647729
\(290\) 0.0730117 0.00428739
\(291\) −9.72490 −0.570084
\(292\) 13.5958 0.795635
\(293\) −1.81374 −0.105960 −0.0529799 0.998596i \(-0.516872\pi\)
−0.0529799 + 0.998596i \(0.516872\pi\)
\(294\) −1.56085 −0.0910305
\(295\) −10.0519 −0.585246
\(296\) −2.52754 −0.146910
\(297\) 3.81458 0.221344
\(298\) 4.88372 0.282906
\(299\) −6.09056 −0.352226
\(300\) −5.21850 −0.301290
\(301\) −9.13119 −0.526313
\(302\) 14.8201 0.852803
\(303\) 20.8063 1.19529
\(304\) −3.49670 −0.200550
\(305\) −7.53158 −0.431257
\(306\) −2.98370 −0.170567
\(307\) −7.36628 −0.420416 −0.210208 0.977657i \(-0.567414\pi\)
−0.210208 + 0.977657i \(0.567414\pi\)
\(308\) 0.685769 0.0390753
\(309\) 0.781265 0.0444446
\(310\) −8.56671 −0.486556
\(311\) 21.8406 1.23847 0.619234 0.785206i \(-0.287443\pi\)
0.619234 + 0.785206i \(0.287443\pi\)
\(312\) 2.31502 0.131062
\(313\) −9.30745 −0.526088 −0.263044 0.964784i \(-0.584727\pi\)
−0.263044 + 0.964784i \(0.584727\pi\)
\(314\) 0.00574047 0.000323954 0
\(315\) −0.725605 −0.0408832
\(316\) −6.53682 −0.367725
\(317\) 16.6614 0.935798 0.467899 0.883782i \(-0.345011\pi\)
0.467899 + 0.883782i \(0.345011\pi\)
\(318\) −10.0234 −0.562084
\(319\) −0.0389008 −0.00217803
\(320\) −1.28710 −0.0719510
\(321\) −11.4617 −0.639731
\(322\) 4.10641 0.228841
\(323\) 18.5066 1.02973
\(324\) −6.99093 −0.388385
\(325\) 4.95883 0.275067
\(326\) −5.85030 −0.324018
\(327\) 13.9470 0.771270
\(328\) 1.28831 0.0711352
\(329\) −3.53299 −0.194780
\(330\) −1.37769 −0.0758392
\(331\) 23.4187 1.28721 0.643603 0.765359i \(-0.277439\pi\)
0.643603 + 0.765359i \(0.277439\pi\)
\(332\) 15.6785 0.860470
\(333\) −1.42491 −0.0780845
\(334\) 13.1245 0.718141
\(335\) −17.5118 −0.956771
\(336\) −1.56085 −0.0851513
\(337\) −23.8984 −1.30183 −0.650913 0.759152i \(-0.725614\pi\)
−0.650913 + 0.759152i \(0.725614\pi\)
\(338\) 10.8002 0.587452
\(339\) 1.81885 0.0987863
\(340\) 6.81207 0.369437
\(341\) 4.56436 0.247174
\(342\) −1.97128 −0.106594
\(343\) −1.00000 −0.0539949
\(344\) −9.13119 −0.492321
\(345\) −8.24965 −0.444146
\(346\) −16.0789 −0.864406
\(347\) −0.705676 −0.0378827 −0.0189413 0.999821i \(-0.506030\pi\)
−0.0189413 + 0.999821i \(0.506030\pi\)
\(348\) 0.0885403 0.00474626
\(349\) −4.29707 −0.230017 −0.115008 0.993365i \(-0.536689\pi\)
−0.115008 + 0.993365i \(0.536689\pi\)
\(350\) −3.34338 −0.178711
\(351\) 8.25016 0.440361
\(352\) 0.685769 0.0365516
\(353\) −2.41750 −0.128671 −0.0643353 0.997928i \(-0.520493\pi\)
−0.0643353 + 0.997928i \(0.520493\pi\)
\(354\) −12.1898 −0.647883
\(355\) 13.1568 0.698290
\(356\) 1.36780 0.0724934
\(357\) 8.26091 0.437214
\(358\) 15.5798 0.823419
\(359\) −0.342126 −0.0180567 −0.00902837 0.999959i \(-0.502874\pi\)
−0.00902837 + 0.999959i \(0.502874\pi\)
\(360\) −0.725605 −0.0382428
\(361\) −6.77307 −0.356477
\(362\) 5.82553 0.306183
\(363\) −16.4353 −0.862629
\(364\) 1.48318 0.0777398
\(365\) −17.4992 −0.915948
\(366\) −9.13345 −0.477413
\(367\) −33.0569 −1.72555 −0.862777 0.505584i \(-0.831277\pi\)
−0.862777 + 0.505584i \(0.831277\pi\)
\(368\) 4.10641 0.214062
\(369\) 0.726290 0.0378091
\(370\) 3.25320 0.169126
\(371\) −6.42176 −0.333401
\(372\) −10.3887 −0.538631
\(373\) −25.9194 −1.34206 −0.671028 0.741432i \(-0.734147\pi\)
−0.671028 + 0.741432i \(0.734147\pi\)
\(374\) −3.62949 −0.187676
\(375\) 16.7616 0.865563
\(376\) −3.53299 −0.182200
\(377\) −0.0841346 −0.00433315
\(378\) −5.56248 −0.286103
\(379\) −8.35700 −0.429270 −0.214635 0.976694i \(-0.568856\pi\)
−0.214635 + 0.976694i \(0.568856\pi\)
\(380\) 4.50060 0.230876
\(381\) −16.7135 −0.856259
\(382\) 4.73249 0.242135
\(383\) 0.552066 0.0282092 0.0141046 0.999901i \(-0.495510\pi\)
0.0141046 + 0.999901i \(0.495510\pi\)
\(384\) −1.56085 −0.0796517
\(385\) −0.882653 −0.0449842
\(386\) −7.62722 −0.388215
\(387\) −5.14773 −0.261674
\(388\) −6.23052 −0.316307
\(389\) 33.6159 1.70439 0.852196 0.523222i \(-0.175270\pi\)
0.852196 + 0.523222i \(0.175270\pi\)
\(390\) −2.97966 −0.150881
\(391\) −21.7335 −1.09911
\(392\) −1.00000 −0.0505076
\(393\) 24.3187 1.22672
\(394\) −5.31752 −0.267893
\(395\) 8.41353 0.423331
\(396\) 0.386604 0.0194276
\(397\) −5.98087 −0.300171 −0.150086 0.988673i \(-0.547955\pi\)
−0.150086 + 0.988673i \(0.547955\pi\)
\(398\) −6.13870 −0.307705
\(399\) 5.45782 0.273233
\(400\) −3.34338 −0.167169
\(401\) 36.1533 1.80541 0.902705 0.430259i \(-0.141578\pi\)
0.902705 + 0.430259i \(0.141578\pi\)
\(402\) −21.2363 −1.05917
\(403\) 9.87180 0.491749
\(404\) 13.3302 0.663200
\(405\) 8.99801 0.447115
\(406\) 0.0567258 0.00281525
\(407\) −1.73331 −0.0859170
\(408\) 8.26091 0.408976
\(409\) −25.2278 −1.24744 −0.623718 0.781650i \(-0.714379\pi\)
−0.623718 + 0.781650i \(0.714379\pi\)
\(410\) −1.65819 −0.0818920
\(411\) −6.64839 −0.327941
\(412\) 0.500539 0.0246598
\(413\) −7.80975 −0.384293
\(414\) 2.31500 0.113776
\(415\) −20.1798 −0.990587
\(416\) 1.48318 0.0727190
\(417\) 27.2157 1.33276
\(418\) −2.39793 −0.117287
\(419\) −19.0144 −0.928914 −0.464457 0.885596i \(-0.653751\pi\)
−0.464457 + 0.885596i \(0.653751\pi\)
\(420\) 2.00897 0.0980275
\(421\) 35.9865 1.75387 0.876936 0.480606i \(-0.159583\pi\)
0.876936 + 0.480606i \(0.159583\pi\)
\(422\) 8.79347 0.428060
\(423\) −1.99173 −0.0968414
\(424\) −6.42176 −0.311868
\(425\) 17.6951 0.858338
\(426\) 15.9551 0.773026
\(427\) −5.85159 −0.283178
\(428\) −7.34326 −0.354950
\(429\) 1.58757 0.0766486
\(430\) 11.7527 0.566768
\(431\) 1.00000 0.0481683
\(432\) −5.56248 −0.267625
\(433\) −21.2836 −1.02282 −0.511412 0.859335i \(-0.670878\pi\)
−0.511412 + 0.859335i \(0.670878\pi\)
\(434\) −6.65582 −0.319490
\(435\) −0.113960 −0.00546397
\(436\) 8.93552 0.427934
\(437\) −14.3589 −0.686880
\(438\) −21.2210 −1.01398
\(439\) 32.4068 1.54669 0.773346 0.633984i \(-0.218582\pi\)
0.773346 + 0.633984i \(0.218582\pi\)
\(440\) −0.882653 −0.0420788
\(441\) −0.563752 −0.0268454
\(442\) −7.84986 −0.373380
\(443\) −8.62872 −0.409963 −0.204982 0.978766i \(-0.565713\pi\)
−0.204982 + 0.978766i \(0.565713\pi\)
\(444\) 3.94511 0.187227
\(445\) −1.76050 −0.0834556
\(446\) 4.69820 0.222466
\(447\) −7.62274 −0.360543
\(448\) −1.00000 −0.0472456
\(449\) 20.2400 0.955186 0.477593 0.878581i \(-0.341509\pi\)
0.477593 + 0.878581i \(0.341509\pi\)
\(450\) −1.88484 −0.0888520
\(451\) 0.883486 0.0416017
\(452\) 1.16529 0.0548108
\(453\) −23.1320 −1.08684
\(454\) −12.1876 −0.571995
\(455\) −1.90900 −0.0894954
\(456\) 5.45782 0.255586
\(457\) −25.7216 −1.20321 −0.601604 0.798795i \(-0.705471\pi\)
−0.601604 + 0.798795i \(0.705471\pi\)
\(458\) −10.4784 −0.489622
\(459\) 29.4399 1.37413
\(460\) −5.28536 −0.246431
\(461\) 18.8955 0.880052 0.440026 0.897985i \(-0.354969\pi\)
0.440026 + 0.897985i \(0.354969\pi\)
\(462\) −1.07038 −0.0497987
\(463\) 30.6007 1.42214 0.711068 0.703123i \(-0.248212\pi\)
0.711068 + 0.703123i \(0.248212\pi\)
\(464\) 0.0567258 0.00263343
\(465\) 13.3713 0.620081
\(466\) −12.8979 −0.597482
\(467\) 22.4074 1.03689 0.518446 0.855110i \(-0.326511\pi\)
0.518446 + 0.855110i \(0.326511\pi\)
\(468\) 0.836147 0.0386509
\(469\) −13.6056 −0.628249
\(470\) 4.54731 0.209752
\(471\) −0.00896001 −0.000412855 0
\(472\) −7.80975 −0.359473
\(473\) −6.26189 −0.287922
\(474\) 10.2030 0.468639
\(475\) 11.6908 0.536410
\(476\) 5.29258 0.242585
\(477\) −3.62029 −0.165761
\(478\) 10.2758 0.470003
\(479\) 13.2769 0.606638 0.303319 0.952889i \(-0.401905\pi\)
0.303319 + 0.952889i \(0.401905\pi\)
\(480\) 2.00897 0.0916963
\(481\) −3.74880 −0.170931
\(482\) 16.2211 0.738851
\(483\) −6.40949 −0.291642
\(484\) −10.5297 −0.478624
\(485\) 8.01930 0.364137
\(486\) −5.77566 −0.261989
\(487\) 9.18887 0.416388 0.208194 0.978088i \(-0.433242\pi\)
0.208194 + 0.978088i \(0.433242\pi\)
\(488\) −5.85159 −0.264889
\(489\) 9.13143 0.412937
\(490\) 1.28710 0.0581452
\(491\) −21.9214 −0.989298 −0.494649 0.869093i \(-0.664703\pi\)
−0.494649 + 0.869093i \(0.664703\pi\)
\(492\) −2.01086 −0.0906566
\(493\) −0.300226 −0.0135215
\(494\) −5.18625 −0.233340
\(495\) −0.497598 −0.0223654
\(496\) −6.65582 −0.298855
\(497\) 10.2221 0.458522
\(498\) −24.4718 −1.09661
\(499\) −34.9671 −1.56534 −0.782671 0.622436i \(-0.786143\pi\)
−0.782671 + 0.622436i \(0.786143\pi\)
\(500\) 10.7388 0.480252
\(501\) −20.4854 −0.915219
\(502\) 16.5451 0.738446
\(503\) −35.2365 −1.57112 −0.785558 0.618788i \(-0.787624\pi\)
−0.785558 + 0.618788i \(0.787624\pi\)
\(504\) −0.563752 −0.0251115
\(505\) −17.1572 −0.763487
\(506\) 2.81605 0.125189
\(507\) −16.8574 −0.748665
\(508\) −10.7080 −0.475089
\(509\) 35.2264 1.56138 0.780690 0.624918i \(-0.214868\pi\)
0.780690 + 0.624918i \(0.214868\pi\)
\(510\) −10.6326 −0.470820
\(511\) −13.5958 −0.601444
\(512\) −1.00000 −0.0441942
\(513\) 19.4503 0.858753
\(514\) −25.4276 −1.12156
\(515\) −0.644243 −0.0283887
\(516\) 14.2524 0.627427
\(517\) −2.42282 −0.106555
\(518\) 2.52754 0.111054
\(519\) 25.0967 1.10162
\(520\) −1.90900 −0.0837153
\(521\) 23.8281 1.04393 0.521963 0.852968i \(-0.325200\pi\)
0.521963 + 0.852968i \(0.325200\pi\)
\(522\) 0.0319793 0.00139970
\(523\) −25.8259 −1.12929 −0.564645 0.825334i \(-0.690987\pi\)
−0.564645 + 0.825334i \(0.690987\pi\)
\(524\) 15.5805 0.680635
\(525\) 5.21850 0.227754
\(526\) 1.20088 0.0523609
\(527\) 35.2265 1.53449
\(528\) −1.07038 −0.0465824
\(529\) −6.13737 −0.266842
\(530\) 8.26545 0.359028
\(531\) −4.40277 −0.191064
\(532\) 3.49670 0.151601
\(533\) 1.91080 0.0827661
\(534\) −2.13493 −0.0923876
\(535\) 9.45150 0.408624
\(536\) −13.6056 −0.587673
\(537\) −24.3177 −1.04939
\(538\) −7.18336 −0.309696
\(539\) −0.685769 −0.0295382
\(540\) 7.15946 0.308094
\(541\) −22.6498 −0.973790 −0.486895 0.873461i \(-0.661871\pi\)
−0.486895 + 0.873461i \(0.661871\pi\)
\(542\) −22.3543 −0.960199
\(543\) −9.09277 −0.390208
\(544\) 5.29258 0.226917
\(545\) −11.5009 −0.492644
\(546\) −2.31502 −0.0990738
\(547\) −32.8054 −1.40266 −0.701329 0.712838i \(-0.747410\pi\)
−0.701329 + 0.712838i \(0.747410\pi\)
\(548\) −4.25947 −0.181956
\(549\) −3.29885 −0.140791
\(550\) −2.29278 −0.0977647
\(551\) −0.198353 −0.00845013
\(552\) −6.40949 −0.272806
\(553\) 6.53682 0.277974
\(554\) 3.45053 0.146599
\(555\) −5.07775 −0.215538
\(556\) 17.4365 0.739471
\(557\) −29.0838 −1.23232 −0.616160 0.787621i \(-0.711313\pi\)
−0.616160 + 0.787621i \(0.711313\pi\)
\(558\) −3.75224 −0.158845
\(559\) −13.5432 −0.572817
\(560\) 1.28710 0.0543899
\(561\) 5.66508 0.239180
\(562\) −3.76411 −0.158779
\(563\) −2.59111 −0.109202 −0.0546012 0.998508i \(-0.517389\pi\)
−0.0546012 + 0.998508i \(0.517389\pi\)
\(564\) 5.51447 0.232201
\(565\) −1.49985 −0.0630991
\(566\) −6.87260 −0.288877
\(567\) 6.99093 0.293591
\(568\) 10.2221 0.428908
\(569\) −1.42121 −0.0595802 −0.0297901 0.999556i \(-0.509484\pi\)
−0.0297901 + 0.999556i \(0.509484\pi\)
\(570\) −7.02476 −0.294235
\(571\) 6.13588 0.256779 0.128389 0.991724i \(-0.459019\pi\)
0.128389 + 0.991724i \(0.459019\pi\)
\(572\) 1.01712 0.0425279
\(573\) −7.38671 −0.308584
\(574\) −1.28831 −0.0537732
\(575\) −13.7293 −0.572551
\(576\) −0.563752 −0.0234897
\(577\) 19.0189 0.791768 0.395884 0.918300i \(-0.370438\pi\)
0.395884 + 0.918300i \(0.370438\pi\)
\(578\) −11.0114 −0.458014
\(579\) 11.9049 0.494752
\(580\) −0.0730117 −0.00303165
\(581\) −15.6785 −0.650454
\(582\) 9.72490 0.403110
\(583\) −4.40385 −0.182389
\(584\) −13.5958 −0.562599
\(585\) −1.07620 −0.0444956
\(586\) 1.81374 0.0749249
\(587\) 20.3073 0.838171 0.419085 0.907947i \(-0.362351\pi\)
0.419085 + 0.907947i \(0.362351\pi\)
\(588\) 1.56085 0.0643683
\(589\) 23.2734 0.958966
\(590\) 10.0519 0.413831
\(591\) 8.29984 0.341410
\(592\) 2.52754 0.103881
\(593\) −19.1214 −0.785223 −0.392611 0.919704i \(-0.628428\pi\)
−0.392611 + 0.919704i \(0.628428\pi\)
\(594\) −3.81458 −0.156514
\(595\) −6.81207 −0.279268
\(596\) −4.88372 −0.200045
\(597\) 9.58158 0.392148
\(598\) 6.09056 0.249061
\(599\) 32.4193 1.32462 0.662309 0.749231i \(-0.269577\pi\)
0.662309 + 0.749231i \(0.269577\pi\)
\(600\) 5.21850 0.213044
\(601\) 13.4926 0.550374 0.275187 0.961391i \(-0.411260\pi\)
0.275187 + 0.961391i \(0.411260\pi\)
\(602\) 9.13119 0.372160
\(603\) −7.67020 −0.312355
\(604\) −14.8201 −0.603023
\(605\) 13.5528 0.550999
\(606\) −20.8063 −0.845200
\(607\) 24.5089 0.994785 0.497393 0.867526i \(-0.334291\pi\)
0.497393 + 0.867526i \(0.334291\pi\)
\(608\) 3.49670 0.141810
\(609\) −0.0885403 −0.00358784
\(610\) 7.53158 0.304945
\(611\) −5.24007 −0.211991
\(612\) 2.98370 0.120609
\(613\) −24.6395 −0.995179 −0.497590 0.867413i \(-0.665781\pi\)
−0.497590 + 0.867413i \(0.665781\pi\)
\(614\) 7.36628 0.297279
\(615\) 2.58818 0.104365
\(616\) −0.685769 −0.0276304
\(617\) −3.92612 −0.158060 −0.0790299 0.996872i \(-0.525182\pi\)
−0.0790299 + 0.996872i \(0.525182\pi\)
\(618\) −0.781265 −0.0314271
\(619\) −46.4496 −1.86697 −0.933484 0.358620i \(-0.883247\pi\)
−0.933484 + 0.358620i \(0.883247\pi\)
\(620\) 8.56671 0.344047
\(621\) −22.8418 −0.916611
\(622\) −21.8406 −0.875729
\(623\) −1.36780 −0.0547999
\(624\) −2.31502 −0.0926750
\(625\) 2.89504 0.115802
\(626\) 9.30745 0.372001
\(627\) 3.74281 0.149473
\(628\) −0.00574047 −0.000229070 0
\(629\) −13.3772 −0.533384
\(630\) 0.725605 0.0289088
\(631\) −0.209461 −0.00833853 −0.00416926 0.999991i \(-0.501327\pi\)
−0.00416926 + 0.999991i \(0.501327\pi\)
\(632\) 6.53682 0.260021
\(633\) −13.7253 −0.545531
\(634\) −16.6614 −0.661709
\(635\) 13.7822 0.546930
\(636\) 10.0234 0.397454
\(637\) −1.48318 −0.0587658
\(638\) 0.0389008 0.00154010
\(639\) 5.76271 0.227969
\(640\) 1.28710 0.0508771
\(641\) 4.76827 0.188335 0.0941676 0.995556i \(-0.469981\pi\)
0.0941676 + 0.995556i \(0.469981\pi\)
\(642\) 11.4617 0.452358
\(643\) 21.5238 0.848815 0.424407 0.905471i \(-0.360482\pi\)
0.424407 + 0.905471i \(0.360482\pi\)
\(644\) −4.10641 −0.161815
\(645\) −18.3443 −0.722304
\(646\) −18.5066 −0.728132
\(647\) −9.99795 −0.393060 −0.196530 0.980498i \(-0.562967\pi\)
−0.196530 + 0.980498i \(0.562967\pi\)
\(648\) 6.99093 0.274630
\(649\) −5.35569 −0.210229
\(650\) −4.95883 −0.194501
\(651\) 10.3887 0.407167
\(652\) 5.85030 0.229115
\(653\) −24.0390 −0.940718 −0.470359 0.882475i \(-0.655876\pi\)
−0.470359 + 0.882475i \(0.655876\pi\)
\(654\) −13.9470 −0.545371
\(655\) −20.0536 −0.783558
\(656\) −1.28831 −0.0503002
\(657\) −7.66468 −0.299027
\(658\) 3.53299 0.137730
\(659\) 21.1151 0.822528 0.411264 0.911516i \(-0.365087\pi\)
0.411264 + 0.911516i \(0.365087\pi\)
\(660\) 1.37769 0.0536264
\(661\) 34.2536 1.33231 0.666156 0.745812i \(-0.267938\pi\)
0.666156 + 0.745812i \(0.267938\pi\)
\(662\) −23.4187 −0.910192
\(663\) 12.2524 0.475845
\(664\) −15.6785 −0.608444
\(665\) −4.50060 −0.174526
\(666\) 1.42491 0.0552141
\(667\) 0.232939 0.00901945
\(668\) −13.1245 −0.507803
\(669\) −7.33317 −0.283517
\(670\) 17.5118 0.676539
\(671\) −4.01284 −0.154914
\(672\) 1.56085 0.0602110
\(673\) 17.8513 0.688117 0.344059 0.938948i \(-0.388198\pi\)
0.344059 + 0.938948i \(0.388198\pi\)
\(674\) 23.8984 0.920530
\(675\) 18.5975 0.715816
\(676\) −10.8002 −0.415391
\(677\) 34.6122 1.33025 0.665127 0.746731i \(-0.268378\pi\)
0.665127 + 0.746731i \(0.268378\pi\)
\(678\) −1.81885 −0.0698524
\(679\) 6.23052 0.239105
\(680\) −6.81207 −0.261231
\(681\) 19.0231 0.728966
\(682\) −4.56436 −0.174778
\(683\) 29.2202 1.11808 0.559040 0.829140i \(-0.311170\pi\)
0.559040 + 0.829140i \(0.311170\pi\)
\(684\) 1.97128 0.0753736
\(685\) 5.48237 0.209470
\(686\) 1.00000 0.0381802
\(687\) 16.3551 0.623988
\(688\) 9.13119 0.348123
\(689\) −9.52464 −0.362860
\(690\) 8.24965 0.314059
\(691\) 42.2575 1.60755 0.803776 0.594932i \(-0.202821\pi\)
0.803776 + 0.594932i \(0.202821\pi\)
\(692\) 16.0789 0.611227
\(693\) −0.386604 −0.0146859
\(694\) 0.705676 0.0267871
\(695\) −22.4425 −0.851291
\(696\) −0.0885403 −0.00335611
\(697\) 6.81850 0.258269
\(698\) 4.29707 0.162646
\(699\) 20.1316 0.761447
\(700\) 3.34338 0.126368
\(701\) 6.86917 0.259445 0.129723 0.991550i \(-0.458591\pi\)
0.129723 + 0.991550i \(0.458591\pi\)
\(702\) −8.25016 −0.311382
\(703\) −8.83806 −0.333334
\(704\) −0.685769 −0.0258459
\(705\) −7.09767 −0.267314
\(706\) 2.41750 0.0909839
\(707\) −13.3302 −0.501332
\(708\) 12.1898 0.458122
\(709\) 12.3230 0.462800 0.231400 0.972859i \(-0.425669\pi\)
0.231400 + 0.972859i \(0.425669\pi\)
\(710\) −13.1568 −0.493766
\(711\) 3.68515 0.138204
\(712\) −1.36780 −0.0512606
\(713\) −27.3316 −1.02358
\(714\) −8.26091 −0.309157
\(715\) −1.30913 −0.0489589
\(716\) −15.5798 −0.582245
\(717\) −16.0389 −0.598984
\(718\) 0.342126 0.0127680
\(719\) 25.8487 0.963992 0.481996 0.876173i \(-0.339912\pi\)
0.481996 + 0.876173i \(0.339912\pi\)
\(720\) 0.725605 0.0270417
\(721\) −0.500539 −0.0186410
\(722\) 6.77307 0.252067
\(723\) −25.3187 −0.941611
\(724\) −5.82553 −0.216504
\(725\) −0.189656 −0.00704363
\(726\) 16.4353 0.609971
\(727\) −25.2539 −0.936615 −0.468308 0.883566i \(-0.655136\pi\)
−0.468308 + 0.883566i \(0.655136\pi\)
\(728\) −1.48318 −0.0549704
\(729\) 29.9877 1.11066
\(730\) 17.4992 0.647673
\(731\) −48.3275 −1.78746
\(732\) 9.13345 0.337582
\(733\) 37.9243 1.40076 0.700382 0.713768i \(-0.253013\pi\)
0.700382 + 0.713768i \(0.253013\pi\)
\(734\) 33.0569 1.22015
\(735\) −2.00897 −0.0741018
\(736\) −4.10641 −0.151364
\(737\) −9.33032 −0.343687
\(738\) −0.726290 −0.0267351
\(739\) 5.99027 0.220356 0.110178 0.993912i \(-0.464858\pi\)
0.110178 + 0.993912i \(0.464858\pi\)
\(740\) −3.25320 −0.119590
\(741\) 8.09494 0.297375
\(742\) 6.42176 0.235750
\(743\) −15.6726 −0.574970 −0.287485 0.957785i \(-0.592819\pi\)
−0.287485 + 0.957785i \(0.592819\pi\)
\(744\) 10.3887 0.380869
\(745\) 6.28583 0.230295
\(746\) 25.9194 0.948977
\(747\) −8.83879 −0.323395
\(748\) 3.62949 0.132707
\(749\) 7.34326 0.268317
\(750\) −16.7616 −0.612046
\(751\) 13.4245 0.489867 0.244933 0.969540i \(-0.421234\pi\)
0.244933 + 0.969540i \(0.421234\pi\)
\(752\) 3.53299 0.128835
\(753\) −25.8245 −0.941096
\(754\) 0.0841346 0.00306400
\(755\) 19.0750 0.694210
\(756\) 5.56248 0.202305
\(757\) 13.2676 0.482220 0.241110 0.970498i \(-0.422488\pi\)
0.241110 + 0.970498i \(0.422488\pi\)
\(758\) 8.35700 0.303540
\(759\) −4.39543 −0.159544
\(760\) −4.50060 −0.163254
\(761\) 44.7893 1.62361 0.811806 0.583927i \(-0.198485\pi\)
0.811806 + 0.583927i \(0.198485\pi\)
\(762\) 16.7135 0.605466
\(763\) −8.93552 −0.323488
\(764\) −4.73249 −0.171216
\(765\) −3.84032 −0.138847
\(766\) −0.552066 −0.0199469
\(767\) −11.5833 −0.418248
\(768\) 1.56085 0.0563223
\(769\) 41.7646 1.50607 0.753034 0.657981i \(-0.228589\pi\)
0.753034 + 0.657981i \(0.228589\pi\)
\(770\) 0.882653 0.0318086
\(771\) 39.6887 1.42935
\(772\) 7.62722 0.274510
\(773\) 26.5530 0.955044 0.477522 0.878620i \(-0.341535\pi\)
0.477522 + 0.878620i \(0.341535\pi\)
\(774\) 5.14773 0.185031
\(775\) 22.2529 0.799349
\(776\) 6.23052 0.223663
\(777\) −3.94511 −0.141530
\(778\) −33.6159 −1.20519
\(779\) 4.50485 0.161403
\(780\) 2.97966 0.106689
\(781\) 7.00997 0.250837
\(782\) 21.7335 0.777189
\(783\) −0.315536 −0.0112763
\(784\) 1.00000 0.0357143
\(785\) 0.00738856 0.000263709 0
\(786\) −24.3187 −0.867420
\(787\) 43.2928 1.54322 0.771611 0.636095i \(-0.219451\pi\)
0.771611 + 0.636095i \(0.219451\pi\)
\(788\) 5.31752 0.189429
\(789\) −1.87439 −0.0667302
\(790\) −8.41353 −0.299340
\(791\) −1.16529 −0.0414331
\(792\) −0.386604 −0.0137374
\(793\) −8.67898 −0.308199
\(794\) 5.98087 0.212253
\(795\) −12.9011 −0.457555
\(796\) 6.13870 0.217580
\(797\) −25.8382 −0.915235 −0.457617 0.889149i \(-0.651297\pi\)
−0.457617 + 0.889149i \(0.651297\pi\)
\(798\) −5.45782 −0.193205
\(799\) −18.6987 −0.661511
\(800\) 3.34338 0.118206
\(801\) −0.771102 −0.0272456
\(802\) −36.1533 −1.27662
\(803\) −9.32360 −0.329023
\(804\) 21.2363 0.748947
\(805\) 5.28536 0.186284
\(806\) −9.87180 −0.347719
\(807\) 11.2121 0.394686
\(808\) −13.3302 −0.468953
\(809\) −40.3844 −1.41984 −0.709920 0.704282i \(-0.751269\pi\)
−0.709920 + 0.704282i \(0.751269\pi\)
\(810\) −8.99801 −0.316158
\(811\) 3.69545 0.129765 0.0648824 0.997893i \(-0.479333\pi\)
0.0648824 + 0.997893i \(0.479333\pi\)
\(812\) −0.0567258 −0.00199068
\(813\) 34.8917 1.22370
\(814\) 1.73331 0.0607525
\(815\) −7.52991 −0.263761
\(816\) −8.26091 −0.289190
\(817\) −31.9291 −1.11706
\(818\) 25.2278 0.882070
\(819\) −0.836147 −0.0292174
\(820\) 1.65819 0.0579064
\(821\) 10.2132 0.356442 0.178221 0.983991i \(-0.442966\pi\)
0.178221 + 0.983991i \(0.442966\pi\)
\(822\) 6.64839 0.231889
\(823\) 54.0824 1.88519 0.942597 0.333932i \(-0.108376\pi\)
0.942597 + 0.333932i \(0.108376\pi\)
\(824\) −0.500539 −0.0174371
\(825\) 3.57869 0.124594
\(826\) 7.80975 0.271736
\(827\) 31.8603 1.10789 0.553945 0.832553i \(-0.313122\pi\)
0.553945 + 0.832553i \(0.313122\pi\)
\(828\) −2.31500 −0.0804518
\(829\) 16.8462 0.585092 0.292546 0.956251i \(-0.405497\pi\)
0.292546 + 0.956251i \(0.405497\pi\)
\(830\) 20.1798 0.700451
\(831\) −5.38576 −0.186830
\(832\) −1.48318 −0.0514201
\(833\) −5.29258 −0.183377
\(834\) −27.2157 −0.942402
\(835\) 16.8925 0.584591
\(836\) 2.39793 0.0829342
\(837\) 37.0229 1.27970
\(838\) 19.0144 0.656842
\(839\) −49.5065 −1.70916 −0.854578 0.519323i \(-0.826184\pi\)
−0.854578 + 0.519323i \(0.826184\pi\)
\(840\) −2.00897 −0.0693159
\(841\) −28.9968 −0.999889
\(842\) −35.9865 −1.24018
\(843\) 5.87521 0.202353
\(844\) −8.79347 −0.302684
\(845\) 13.9009 0.478205
\(846\) 1.99173 0.0684772
\(847\) 10.5297 0.361805
\(848\) 6.42176 0.220524
\(849\) 10.7271 0.368153
\(850\) −17.6951 −0.606936
\(851\) 10.3791 0.355792
\(852\) −15.9551 −0.546612
\(853\) 24.3110 0.832392 0.416196 0.909275i \(-0.363363\pi\)
0.416196 + 0.909275i \(0.363363\pi\)
\(854\) 5.85159 0.200237
\(855\) −2.53723 −0.0867713
\(856\) 7.34326 0.250987
\(857\) 29.4567 1.00622 0.503110 0.864222i \(-0.332189\pi\)
0.503110 + 0.864222i \(0.332189\pi\)
\(858\) −1.58757 −0.0541988
\(859\) −24.1958 −0.825549 −0.412774 0.910833i \(-0.635440\pi\)
−0.412774 + 0.910833i \(0.635440\pi\)
\(860\) −11.7527 −0.400765
\(861\) 2.01086 0.0685300
\(862\) −1.00000 −0.0340601
\(863\) 29.8020 1.01447 0.507236 0.861807i \(-0.330667\pi\)
0.507236 + 0.861807i \(0.330667\pi\)
\(864\) 5.56248 0.189239
\(865\) −20.6951 −0.703655
\(866\) 21.2836 0.723246
\(867\) 17.1871 0.583705
\(868\) 6.65582 0.225913
\(869\) 4.48275 0.152067
\(870\) 0.113960 0.00386361
\(871\) −20.1796 −0.683760
\(872\) −8.93552 −0.302595
\(873\) 3.51247 0.118879
\(874\) 14.3589 0.485697
\(875\) −10.7388 −0.363036
\(876\) 21.2210 0.716992
\(877\) −39.3051 −1.32724 −0.663619 0.748070i \(-0.730981\pi\)
−0.663619 + 0.748070i \(0.730981\pi\)
\(878\) −32.4068 −1.09368
\(879\) −2.83097 −0.0954864
\(880\) 0.882653 0.0297542
\(881\) 12.2636 0.413170 0.206585 0.978429i \(-0.433765\pi\)
0.206585 + 0.978429i \(0.433765\pi\)
\(882\) 0.563752 0.0189825
\(883\) −13.1835 −0.443660 −0.221830 0.975085i \(-0.571203\pi\)
−0.221830 + 0.975085i \(0.571203\pi\)
\(884\) 7.84986 0.264019
\(885\) −15.6895 −0.527398
\(886\) 8.62872 0.289888
\(887\) 4.49898 0.151061 0.0755305 0.997143i \(-0.475935\pi\)
0.0755305 + 0.997143i \(0.475935\pi\)
\(888\) −3.94511 −0.132389
\(889\) 10.7080 0.359134
\(890\) 1.76050 0.0590120
\(891\) 4.79416 0.160610
\(892\) −4.69820 −0.157307
\(893\) −12.3538 −0.413405
\(894\) 7.62274 0.254943
\(895\) 20.0528 0.670290
\(896\) 1.00000 0.0334077
\(897\) −9.50644 −0.317411
\(898\) −20.2400 −0.675419
\(899\) −0.377557 −0.0125922
\(900\) 1.88484 0.0628279
\(901\) −33.9877 −1.13229
\(902\) −0.883486 −0.0294169
\(903\) −14.2524 −0.474290
\(904\) −1.16529 −0.0387571
\(905\) 7.49804 0.249243
\(906\) 23.1320 0.768509
\(907\) 31.4632 1.04472 0.522358 0.852726i \(-0.325052\pi\)
0.522358 + 0.852726i \(0.325052\pi\)
\(908\) 12.1876 0.404461
\(909\) −7.51491 −0.249254
\(910\) 1.90900 0.0632828
\(911\) 15.4262 0.511092 0.255546 0.966797i \(-0.417745\pi\)
0.255546 + 0.966797i \(0.417745\pi\)
\(912\) −5.45782 −0.180727
\(913\) −10.7518 −0.355834
\(914\) 25.7216 0.850796
\(915\) −11.7557 −0.388630
\(916\) 10.4784 0.346215
\(917\) −15.5805 −0.514512
\(918\) −29.4399 −0.971660
\(919\) 40.1503 1.32443 0.662217 0.749312i \(-0.269615\pi\)
0.662217 + 0.749312i \(0.269615\pi\)
\(920\) 5.28536 0.174253
\(921\) −11.4977 −0.378861
\(922\) −18.8955 −0.622291
\(923\) 15.1612 0.499036
\(924\) 1.07038 0.0352130
\(925\) −8.45052 −0.277851
\(926\) −30.6007 −1.00560
\(927\) −0.282180 −0.00926800
\(928\) −0.0567258 −0.00186211
\(929\) 5.88873 0.193203 0.0966015 0.995323i \(-0.469203\pi\)
0.0966015 + 0.995323i \(0.469203\pi\)
\(930\) −13.3713 −0.438463
\(931\) −3.49670 −0.114600
\(932\) 12.8979 0.422483
\(933\) 34.0899 1.11605
\(934\) −22.4074 −0.733194
\(935\) −4.67151 −0.152775
\(936\) −0.836147 −0.0273303
\(937\) −28.1823 −0.920674 −0.460337 0.887744i \(-0.652271\pi\)
−0.460337 + 0.887744i \(0.652271\pi\)
\(938\) 13.6056 0.444239
\(939\) −14.5275 −0.474088
\(940\) −4.54731 −0.148317
\(941\) −22.7827 −0.742694 −0.371347 0.928494i \(-0.621104\pi\)
−0.371347 + 0.928494i \(0.621104\pi\)
\(942\) 0.00896001 0.000291933 0
\(943\) −5.29035 −0.172277
\(944\) 7.80975 0.254186
\(945\) −7.15946 −0.232897
\(946\) 6.26189 0.203592
\(947\) −14.9010 −0.484219 −0.242109 0.970249i \(-0.577839\pi\)
−0.242109 + 0.970249i \(0.577839\pi\)
\(948\) −10.2030 −0.331378
\(949\) −20.1651 −0.654586
\(950\) −11.6908 −0.379299
\(951\) 26.0059 0.843300
\(952\) −5.29258 −0.171533
\(953\) 1.51742 0.0491540 0.0245770 0.999698i \(-0.492176\pi\)
0.0245770 + 0.999698i \(0.492176\pi\)
\(954\) 3.62029 0.117211
\(955\) 6.09119 0.197106
\(956\) −10.2758 −0.332342
\(957\) −0.0607182 −0.00196274
\(958\) −13.2769 −0.428958
\(959\) 4.25947 0.137546
\(960\) −2.00897 −0.0648391
\(961\) 13.3000 0.429032
\(962\) 3.74880 0.120866
\(963\) 4.13978 0.133403
\(964\) −16.2211 −0.522446
\(965\) −9.81699 −0.316020
\(966\) 6.40949 0.206222
\(967\) −55.5106 −1.78510 −0.892550 0.450949i \(-0.851086\pi\)
−0.892550 + 0.450949i \(0.851086\pi\)
\(968\) 10.5297 0.338438
\(969\) 28.8860 0.927951
\(970\) −8.01930 −0.257484
\(971\) 12.4622 0.399932 0.199966 0.979803i \(-0.435917\pi\)
0.199966 + 0.979803i \(0.435917\pi\)
\(972\) 5.77566 0.185254
\(973\) −17.4365 −0.558987
\(974\) −9.18887 −0.294430
\(975\) 7.73999 0.247878
\(976\) 5.85159 0.187305
\(977\) 48.3886 1.54809 0.774044 0.633132i \(-0.218231\pi\)
0.774044 + 0.633132i \(0.218231\pi\)
\(978\) −9.13143 −0.291991
\(979\) −0.937997 −0.0299785
\(980\) −1.28710 −0.0411149
\(981\) −5.03742 −0.160832
\(982\) 21.9214 0.699540
\(983\) 40.5832 1.29440 0.647201 0.762319i \(-0.275939\pi\)
0.647201 + 0.762319i \(0.275939\pi\)
\(984\) 2.01086 0.0641039
\(985\) −6.84418 −0.218074
\(986\) 0.300226 0.00956113
\(987\) −5.51447 −0.175527
\(988\) 5.18625 0.164996
\(989\) 37.4964 1.19232
\(990\) 0.497598 0.0158147
\(991\) 58.5872 1.86108 0.930542 0.366186i \(-0.119337\pi\)
0.930542 + 0.366186i \(0.119337\pi\)
\(992\) 6.65582 0.211323
\(993\) 36.5530 1.15997
\(994\) −10.2221 −0.324224
\(995\) −7.90111 −0.250482
\(996\) 24.4718 0.775418
\(997\) −21.5726 −0.683210 −0.341605 0.939844i \(-0.610971\pi\)
−0.341605 + 0.939844i \(0.610971\pi\)
\(998\) 34.9671 1.10686
\(999\) −14.0594 −0.444819
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 \(a_p\))