Properties

Label 619.2.a.b.1.12
Level 619
Weight 2
Character 619.1
Self dual Yes
Analytic conductor 4.943
Analytic rank 0
Dimension 30
CM No

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Newspace parameters

Level: \( N \) = \( 619 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 619.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(4.94273988512\)
Analytic rank: \(0\)
Dimension: \(30\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Character \(\chi\) = 619.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.386745 q^{2} -1.55323 q^{3} -1.85043 q^{4} -3.75067 q^{5} +0.600704 q^{6} -2.84697 q^{7} +1.48913 q^{8} -0.587469 q^{9} +O(q^{10})\) \(q-0.386745 q^{2} -1.55323 q^{3} -1.85043 q^{4} -3.75067 q^{5} +0.600704 q^{6} -2.84697 q^{7} +1.48913 q^{8} -0.587469 q^{9} +1.45055 q^{10} +0.341105 q^{11} +2.87415 q^{12} -4.58045 q^{13} +1.10105 q^{14} +5.82567 q^{15} +3.12494 q^{16} -4.50331 q^{17} +0.227200 q^{18} -4.60284 q^{19} +6.94035 q^{20} +4.42200 q^{21} -0.131920 q^{22} -6.46872 q^{23} -2.31297 q^{24} +9.06755 q^{25} +1.77147 q^{26} +5.57217 q^{27} +5.26811 q^{28} +9.68231 q^{29} -2.25305 q^{30} +7.65931 q^{31} -4.18682 q^{32} -0.529815 q^{33} +1.74163 q^{34} +10.6780 q^{35} +1.08707 q^{36} -0.361034 q^{37} +1.78012 q^{38} +7.11451 q^{39} -5.58525 q^{40} -7.84535 q^{41} -1.71018 q^{42} -9.06924 q^{43} -0.631190 q^{44} +2.20340 q^{45} +2.50174 q^{46} +2.68206 q^{47} -4.85376 q^{48} +1.10521 q^{49} -3.50683 q^{50} +6.99468 q^{51} +8.47580 q^{52} -1.93004 q^{53} -2.15501 q^{54} -1.27937 q^{55} -4.23951 q^{56} +7.14928 q^{57} -3.74458 q^{58} -0.518734 q^{59} -10.7800 q^{60} -7.90323 q^{61} -2.96219 q^{62} +1.67250 q^{63} -4.63066 q^{64} +17.1798 q^{65} +0.204903 q^{66} +6.35561 q^{67} +8.33305 q^{68} +10.0474 q^{69} -4.12967 q^{70} -6.34036 q^{71} -0.874818 q^{72} -13.6292 q^{73} +0.139628 q^{74} -14.0840 q^{75} +8.51722 q^{76} -0.971114 q^{77} -2.75150 q^{78} -12.1347 q^{79} -11.7206 q^{80} -6.89247 q^{81} +3.03415 q^{82} -5.17657 q^{83} -8.18259 q^{84} +16.8904 q^{85} +3.50748 q^{86} -15.0389 q^{87} +0.507950 q^{88} +0.605819 q^{89} -0.852154 q^{90} +13.0404 q^{91} +11.9699 q^{92} -11.8967 q^{93} -1.03727 q^{94} +17.2637 q^{95} +6.50310 q^{96} -0.592886 q^{97} -0.427434 q^{98} -0.200388 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30q + 9q^{2} + q^{3} + 33q^{4} + 21q^{5} + 6q^{6} + 2q^{7} + 27q^{8} + 43q^{9} + O(q^{10}) \) \( 30q + 9q^{2} + q^{3} + 33q^{4} + 21q^{5} + 6q^{6} + 2q^{7} + 27q^{8} + 43q^{9} + 5q^{10} + 23q^{11} - 6q^{12} + 9q^{13} + 7q^{14} - 2q^{15} + 35q^{16} + 4q^{17} + 10q^{18} - q^{19} + 29q^{20} + 30q^{21} + 4q^{23} + 4q^{24} + 35q^{25} + q^{26} - 5q^{27} - 13q^{28} + 90q^{29} - 31q^{30} + 2q^{31} + 43q^{32} - 6q^{33} - 9q^{34} + 9q^{35} + 33q^{36} + 19q^{37} + 5q^{38} + 32q^{39} - 12q^{40} + 59q^{41} - 25q^{42} - 4q^{43} + 52q^{44} + 30q^{45} - q^{46} + 4q^{47} - 44q^{48} + 30q^{49} + 31q^{50} - 12q^{52} + 34q^{53} - 28q^{54} - 17q^{55} + 2q^{56} - 8q^{57} + 6q^{58} + 13q^{59} - 64q^{60} + 16q^{61} + 28q^{62} - 40q^{63} + 37q^{64} + 31q^{65} - 59q^{66} - 11q^{67} - 52q^{68} + 6q^{69} - 40q^{70} + 42q^{71} + 6q^{72} - 4q^{73} + 16q^{74} - 52q^{75} - 42q^{76} + 29q^{77} - 56q^{78} + 3q^{79} + 21q^{80} + 30q^{81} - 43q^{82} - 11q^{83} - 36q^{84} + 19q^{85} - 11q^{86} - 20q^{87} - 47q^{88} + 58q^{89} - 33q^{90} - 39q^{91} - 7q^{92} - 15q^{93} - 46q^{94} + 23q^{95} - 70q^{96} - 9q^{97} - 8q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.386745 −0.273470 −0.136735 0.990608i \(-0.543661\pi\)
−0.136735 + 0.990608i \(0.543661\pi\)
\(3\) −1.55323 −0.896759 −0.448380 0.893843i \(-0.647999\pi\)
−0.448380 + 0.893843i \(0.647999\pi\)
\(4\) −1.85043 −0.925214
\(5\) −3.75067 −1.67735 −0.838676 0.544630i \(-0.816670\pi\)
−0.838676 + 0.544630i \(0.816670\pi\)
\(6\) 0.600704 0.245236
\(7\) −2.84697 −1.07605 −0.538026 0.842928i \(-0.680830\pi\)
−0.538026 + 0.842928i \(0.680830\pi\)
\(8\) 1.48913 0.526488
\(9\) −0.587469 −0.195823
\(10\) 1.45055 0.458705
\(11\) 0.341105 0.102847 0.0514235 0.998677i \(-0.483624\pi\)
0.0514235 + 0.998677i \(0.483624\pi\)
\(12\) 2.87415 0.829695
\(13\) −4.58045 −1.27039 −0.635195 0.772352i \(-0.719080\pi\)
−0.635195 + 0.772352i \(0.719080\pi\)
\(14\) 1.10105 0.294268
\(15\) 5.82567 1.50418
\(16\) 3.12494 0.781236
\(17\) −4.50331 −1.09221 −0.546106 0.837716i \(-0.683891\pi\)
−0.546106 + 0.837716i \(0.683891\pi\)
\(18\) 0.227200 0.0535516
\(19\) −4.60284 −1.05596 −0.527982 0.849256i \(-0.677051\pi\)
−0.527982 + 0.849256i \(0.677051\pi\)
\(20\) 6.94035 1.55191
\(21\) 4.42200 0.964959
\(22\) −0.131920 −0.0281255
\(23\) −6.46872 −1.34882 −0.674410 0.738357i \(-0.735602\pi\)
−0.674410 + 0.738357i \(0.735602\pi\)
\(24\) −2.31297 −0.472133
\(25\) 9.06755 1.81351
\(26\) 1.77147 0.347413
\(27\) 5.57217 1.07237
\(28\) 5.26811 0.995578
\(29\) 9.68231 1.79796 0.898980 0.437989i \(-0.144309\pi\)
0.898980 + 0.437989i \(0.144309\pi\)
\(30\) −2.25305 −0.411348
\(31\) 7.65931 1.37565 0.687826 0.725876i \(-0.258565\pi\)
0.687826 + 0.725876i \(0.258565\pi\)
\(32\) −4.18682 −0.740132
\(33\) −0.529815 −0.0922290
\(34\) 1.74163 0.298687
\(35\) 10.6780 1.80492
\(36\) 1.08707 0.181178
\(37\) −0.361034 −0.0593537 −0.0296768 0.999560i \(-0.509448\pi\)
−0.0296768 + 0.999560i \(0.509448\pi\)
\(38\) 1.78012 0.288774
\(39\) 7.11451 1.13923
\(40\) −5.58525 −0.883105
\(41\) −7.84535 −1.22524 −0.612619 0.790378i \(-0.709884\pi\)
−0.612619 + 0.790378i \(0.709884\pi\)
\(42\) −1.71018 −0.263887
\(43\) −9.06924 −1.38305 −0.691523 0.722354i \(-0.743060\pi\)
−0.691523 + 0.722354i \(0.743060\pi\)
\(44\) −0.631190 −0.0951555
\(45\) 2.20340 0.328464
\(46\) 2.50174 0.368861
\(47\) 2.68206 0.391218 0.195609 0.980682i \(-0.437332\pi\)
0.195609 + 0.980682i \(0.437332\pi\)
\(48\) −4.85376 −0.700581
\(49\) 1.10521 0.157887
\(50\) −3.50683 −0.495940
\(51\) 6.99468 0.979452
\(52\) 8.47580 1.17538
\(53\) −1.93004 −0.265112 −0.132556 0.991176i \(-0.542318\pi\)
−0.132556 + 0.991176i \(0.542318\pi\)
\(54\) −2.15501 −0.293259
\(55\) −1.27937 −0.172511
\(56\) −4.23951 −0.566528
\(57\) 7.14928 0.946945
\(58\) −3.74458 −0.491688
\(59\) −0.518734 −0.0675335 −0.0337667 0.999430i \(-0.510750\pi\)
−0.0337667 + 0.999430i \(0.510750\pi\)
\(60\) −10.7800 −1.39169
\(61\) −7.90323 −1.01190 −0.505952 0.862561i \(-0.668859\pi\)
−0.505952 + 0.862561i \(0.668859\pi\)
\(62\) −2.96219 −0.376199
\(63\) 1.67250 0.210716
\(64\) −4.63066 −0.578832
\(65\) 17.1798 2.13089
\(66\) 0.204903 0.0252218
\(67\) 6.35561 0.776461 0.388231 0.921562i \(-0.373086\pi\)
0.388231 + 0.921562i \(0.373086\pi\)
\(68\) 8.33305 1.01053
\(69\) 10.0474 1.20957
\(70\) −4.12967 −0.493590
\(71\) −6.34036 −0.752462 −0.376231 0.926526i \(-0.622780\pi\)
−0.376231 + 0.926526i \(0.622780\pi\)
\(72\) −0.874818 −0.103098
\(73\) −13.6292 −1.59518 −0.797588 0.603202i \(-0.793891\pi\)
−0.797588 + 0.603202i \(0.793891\pi\)
\(74\) 0.139628 0.0162314
\(75\) −14.0840 −1.62628
\(76\) 8.51722 0.976992
\(77\) −0.971114 −0.110669
\(78\) −2.75150 −0.311546
\(79\) −12.1347 −1.36526 −0.682631 0.730763i \(-0.739165\pi\)
−0.682631 + 0.730763i \(0.739165\pi\)
\(80\) −11.7206 −1.31041
\(81\) −6.89247 −0.765831
\(82\) 3.03415 0.335065
\(83\) −5.17657 −0.568203 −0.284101 0.958794i \(-0.591695\pi\)
−0.284101 + 0.958794i \(0.591695\pi\)
\(84\) −8.18259 −0.892794
\(85\) 16.8904 1.83203
\(86\) 3.50748 0.378221
\(87\) −15.0389 −1.61234
\(88\) 0.507950 0.0541477
\(89\) 0.605819 0.0642167 0.0321084 0.999484i \(-0.489778\pi\)
0.0321084 + 0.999484i \(0.489778\pi\)
\(90\) −0.852154 −0.0898249
\(91\) 13.0404 1.36700
\(92\) 11.9699 1.24795
\(93\) −11.8967 −1.23363
\(94\) −1.03727 −0.106986
\(95\) 17.2637 1.77122
\(96\) 6.50310 0.663720
\(97\) −0.592886 −0.0601985 −0.0300992 0.999547i \(-0.509582\pi\)
−0.0300992 + 0.999547i \(0.509582\pi\)
\(98\) −0.427434 −0.0431774
\(99\) −0.200388 −0.0201398
\(100\) −16.7789 −1.67789
\(101\) 18.3855 1.82943 0.914713 0.404104i \(-0.132417\pi\)
0.914713 + 0.404104i \(0.132417\pi\)
\(102\) −2.70516 −0.267850
\(103\) −16.4296 −1.61886 −0.809431 0.587216i \(-0.800224\pi\)
−0.809431 + 0.587216i \(0.800224\pi\)
\(104\) −6.82090 −0.668844
\(105\) −16.5855 −1.61858
\(106\) 0.746434 0.0725000
\(107\) 6.16752 0.596237 0.298118 0.954529i \(-0.403641\pi\)
0.298118 + 0.954529i \(0.403641\pi\)
\(108\) −10.3109 −0.992168
\(109\) −8.53548 −0.817551 −0.408775 0.912635i \(-0.634044\pi\)
−0.408775 + 0.912635i \(0.634044\pi\)
\(110\) 0.494791 0.0471764
\(111\) 0.560770 0.0532260
\(112\) −8.89661 −0.840650
\(113\) 13.0938 1.23177 0.615883 0.787838i \(-0.288800\pi\)
0.615883 + 0.787838i \(0.288800\pi\)
\(114\) −2.76494 −0.258961
\(115\) 24.2620 2.26245
\(116\) −17.9164 −1.66350
\(117\) 2.69087 0.248771
\(118\) 0.200618 0.0184684
\(119\) 12.8208 1.17528
\(120\) 8.67519 0.791933
\(121\) −10.8836 −0.989422
\(122\) 3.05653 0.276725
\(123\) 12.1857 1.09874
\(124\) −14.1730 −1.27277
\(125\) −15.2561 −1.36454
\(126\) −0.646831 −0.0576243
\(127\) 15.5483 1.37969 0.689845 0.723957i \(-0.257678\pi\)
0.689845 + 0.723957i \(0.257678\pi\)
\(128\) 10.1645 0.898425
\(129\) 14.0866 1.24026
\(130\) −6.64419 −0.582734
\(131\) −2.54669 −0.222505 −0.111253 0.993792i \(-0.535486\pi\)
−0.111253 + 0.993792i \(0.535486\pi\)
\(132\) 0.980386 0.0853316
\(133\) 13.1041 1.13627
\(134\) −2.45800 −0.212339
\(135\) −20.8994 −1.79873
\(136\) −6.70602 −0.575036
\(137\) 6.24822 0.533822 0.266911 0.963721i \(-0.413997\pi\)
0.266911 + 0.963721i \(0.413997\pi\)
\(138\) −3.88578 −0.330780
\(139\) −5.69101 −0.482705 −0.241353 0.970437i \(-0.577591\pi\)
−0.241353 + 0.970437i \(0.577591\pi\)
\(140\) −19.7589 −1.66994
\(141\) −4.16586 −0.350829
\(142\) 2.45210 0.205776
\(143\) −1.56242 −0.130656
\(144\) −1.83581 −0.152984
\(145\) −36.3152 −3.01581
\(146\) 5.27102 0.436232
\(147\) −1.71665 −0.141587
\(148\) 0.668068 0.0549149
\(149\) 22.5542 1.84771 0.923855 0.382743i \(-0.125020\pi\)
0.923855 + 0.382743i \(0.125020\pi\)
\(150\) 5.44692 0.444739
\(151\) 12.1464 0.988459 0.494229 0.869332i \(-0.335450\pi\)
0.494229 + 0.869332i \(0.335450\pi\)
\(152\) −6.85423 −0.555952
\(153\) 2.64555 0.213880
\(154\) 0.375573 0.0302645
\(155\) −28.7276 −2.30745
\(156\) −13.1649 −1.05403
\(157\) −12.6078 −1.00621 −0.503106 0.864225i \(-0.667809\pi\)
−0.503106 + 0.864225i \(0.667809\pi\)
\(158\) 4.69304 0.373358
\(159\) 2.99781 0.237741
\(160\) 15.7034 1.24146
\(161\) 18.4162 1.45140
\(162\) 2.66563 0.209431
\(163\) −11.7366 −0.919281 −0.459640 0.888105i \(-0.652022\pi\)
−0.459640 + 0.888105i \(0.652022\pi\)
\(164\) 14.5173 1.13361
\(165\) 1.98716 0.154701
\(166\) 2.00201 0.155386
\(167\) −17.2393 −1.33402 −0.667010 0.745049i \(-0.732426\pi\)
−0.667010 + 0.745049i \(0.732426\pi\)
\(168\) 6.58494 0.508039
\(169\) 7.98055 0.613889
\(170\) −6.53228 −0.501003
\(171\) 2.70402 0.206782
\(172\) 16.7820 1.27961
\(173\) 18.6950 1.42135 0.710676 0.703520i \(-0.248389\pi\)
0.710676 + 0.703520i \(0.248389\pi\)
\(174\) 5.81621 0.440925
\(175\) −25.8150 −1.95143
\(176\) 1.06593 0.0803478
\(177\) 0.805715 0.0605613
\(178\) −0.234297 −0.0175613
\(179\) −4.75236 −0.355208 −0.177604 0.984102i \(-0.556835\pi\)
−0.177604 + 0.984102i \(0.556835\pi\)
\(180\) −4.07724 −0.303900
\(181\) −0.480494 −0.0357149 −0.0178574 0.999841i \(-0.505684\pi\)
−0.0178574 + 0.999841i \(0.505684\pi\)
\(182\) −5.04330 −0.373834
\(183\) 12.2755 0.907435
\(184\) −9.63277 −0.710137
\(185\) 1.35412 0.0995570
\(186\) 4.60098 0.337360
\(187\) −1.53610 −0.112331
\(188\) −4.96296 −0.361961
\(189\) −15.8638 −1.15392
\(190\) −6.67666 −0.484376
\(191\) −18.7352 −1.35563 −0.677815 0.735232i \(-0.737073\pi\)
−0.677815 + 0.735232i \(0.737073\pi\)
\(192\) 7.19249 0.519073
\(193\) 23.6723 1.70397 0.851983 0.523569i \(-0.175400\pi\)
0.851983 + 0.523569i \(0.175400\pi\)
\(194\) 0.229296 0.0164625
\(195\) −26.6842 −1.91090
\(196\) −2.04511 −0.146080
\(197\) 13.6004 0.968986 0.484493 0.874795i \(-0.339004\pi\)
0.484493 + 0.874795i \(0.339004\pi\)
\(198\) 0.0774991 0.00550762
\(199\) −1.24337 −0.0881403 −0.0440702 0.999028i \(-0.514033\pi\)
−0.0440702 + 0.999028i \(0.514033\pi\)
\(200\) 13.5028 0.954791
\(201\) −9.87174 −0.696299
\(202\) −7.11049 −0.500293
\(203\) −27.5652 −1.93470
\(204\) −12.9432 −0.906203
\(205\) 29.4254 2.05516
\(206\) 6.35408 0.442709
\(207\) 3.80017 0.264130
\(208\) −14.3137 −0.992474
\(209\) −1.57005 −0.108603
\(210\) 6.41434 0.442632
\(211\) 5.32658 0.366697 0.183348 0.983048i \(-0.441306\pi\)
0.183348 + 0.983048i \(0.441306\pi\)
\(212\) 3.57141 0.245285
\(213\) 9.84805 0.674778
\(214\) −2.38526 −0.163053
\(215\) 34.0158 2.31986
\(216\) 8.29770 0.564587
\(217\) −21.8058 −1.48027
\(218\) 3.30105 0.223575
\(219\) 21.1693 1.43049
\(220\) 2.36739 0.159609
\(221\) 20.6272 1.38753
\(222\) −0.216875 −0.0145557
\(223\) −28.9946 −1.94162 −0.970811 0.239845i \(-0.922904\pi\)
−0.970811 + 0.239845i \(0.922904\pi\)
\(224\) 11.9197 0.796420
\(225\) −5.32690 −0.355127
\(226\) −5.06397 −0.336850
\(227\) −20.9969 −1.39361 −0.696807 0.717258i \(-0.745397\pi\)
−0.696807 + 0.717258i \(0.745397\pi\)
\(228\) −13.2292 −0.876127
\(229\) 11.7145 0.774119 0.387059 0.922055i \(-0.373491\pi\)
0.387059 + 0.922055i \(0.373491\pi\)
\(230\) −9.38321 −0.618711
\(231\) 1.50837 0.0992432
\(232\) 14.4182 0.946604
\(233\) −10.2552 −0.671841 −0.335920 0.941890i \(-0.609047\pi\)
−0.335920 + 0.941890i \(0.609047\pi\)
\(234\) −1.04068 −0.0680314
\(235\) −10.0595 −0.656211
\(236\) 0.959881 0.0624829
\(237\) 18.8480 1.22431
\(238\) −4.95836 −0.321403
\(239\) −15.7389 −1.01806 −0.509032 0.860748i \(-0.669996\pi\)
−0.509032 + 0.860748i \(0.669996\pi\)
\(240\) 18.2049 1.17512
\(241\) 20.2633 1.30527 0.652636 0.757672i \(-0.273663\pi\)
0.652636 + 0.757672i \(0.273663\pi\)
\(242\) 4.20919 0.270577
\(243\) −6.01090 −0.385600
\(244\) 14.6244 0.936229
\(245\) −4.14529 −0.264833
\(246\) −4.71274 −0.300473
\(247\) 21.0831 1.34148
\(248\) 11.4057 0.724264
\(249\) 8.04042 0.509541
\(250\) 5.90020 0.373161
\(251\) 13.0249 0.822127 0.411064 0.911607i \(-0.365157\pi\)
0.411064 + 0.911607i \(0.365157\pi\)
\(252\) −3.09485 −0.194957
\(253\) −2.20651 −0.138722
\(254\) −6.01323 −0.377304
\(255\) −26.2348 −1.64289
\(256\) 5.33024 0.333140
\(257\) −11.3779 −0.709735 −0.354868 0.934917i \(-0.615474\pi\)
−0.354868 + 0.934917i \(0.615474\pi\)
\(258\) −5.44793 −0.339173
\(259\) 1.02785 0.0638676
\(260\) −31.7900 −1.97153
\(261\) −5.68806 −0.352082
\(262\) 0.984919 0.0608485
\(263\) 0.114792 0.00707838 0.00353919 0.999994i \(-0.498873\pi\)
0.00353919 + 0.999994i \(0.498873\pi\)
\(264\) −0.788965 −0.0485574
\(265\) 7.23896 0.444686
\(266\) −5.06795 −0.310736
\(267\) −0.940979 −0.0575870
\(268\) −11.7606 −0.718393
\(269\) 3.61966 0.220694 0.110347 0.993893i \(-0.464804\pi\)
0.110347 + 0.993893i \(0.464804\pi\)
\(270\) 8.08273 0.491899
\(271\) 11.4084 0.693012 0.346506 0.938048i \(-0.387368\pi\)
0.346506 + 0.938048i \(0.387368\pi\)
\(272\) −14.0726 −0.853276
\(273\) −20.2548 −1.22587
\(274\) −2.41647 −0.145984
\(275\) 3.09299 0.186514
\(276\) −18.5920 −1.11911
\(277\) −11.1126 −0.667690 −0.333845 0.942628i \(-0.608346\pi\)
−0.333845 + 0.942628i \(0.608346\pi\)
\(278\) 2.20097 0.132005
\(279\) −4.49960 −0.269384
\(280\) 15.9010 0.950267
\(281\) 19.8098 1.18175 0.590876 0.806762i \(-0.298782\pi\)
0.590876 + 0.806762i \(0.298782\pi\)
\(282\) 1.61112 0.0959410
\(283\) 6.81139 0.404895 0.202448 0.979293i \(-0.435110\pi\)
0.202448 + 0.979293i \(0.435110\pi\)
\(284\) 11.7324 0.696189
\(285\) −26.8146 −1.58836
\(286\) 0.604256 0.0357304
\(287\) 22.3354 1.31842
\(288\) 2.45962 0.144935
\(289\) 3.27978 0.192928
\(290\) 14.0447 0.824733
\(291\) 0.920890 0.0539835
\(292\) 25.2199 1.47588
\(293\) 18.8865 1.10336 0.551680 0.834056i \(-0.313987\pi\)
0.551680 + 0.834056i \(0.313987\pi\)
\(294\) 0.663905 0.0387197
\(295\) 1.94560 0.113277
\(296\) −0.537628 −0.0312490
\(297\) 1.90070 0.110290
\(298\) −8.72270 −0.505293
\(299\) 29.6296 1.71353
\(300\) 26.0615 1.50466
\(301\) 25.8198 1.48823
\(302\) −4.69755 −0.270313
\(303\) −28.5570 −1.64055
\(304\) −14.3836 −0.824957
\(305\) 29.6424 1.69732
\(306\) −1.02315 −0.0584897
\(307\) −11.3470 −0.647609 −0.323805 0.946124i \(-0.604962\pi\)
−0.323805 + 0.946124i \(0.604962\pi\)
\(308\) 1.79698 0.102392
\(309\) 25.5191 1.45173
\(310\) 11.1102 0.631018
\(311\) 15.0458 0.853167 0.426583 0.904448i \(-0.359717\pi\)
0.426583 + 0.904448i \(0.359717\pi\)
\(312\) 10.5944 0.599792
\(313\) −3.58250 −0.202495 −0.101247 0.994861i \(-0.532283\pi\)
−0.101247 + 0.994861i \(0.532283\pi\)
\(314\) 4.87600 0.275168
\(315\) −6.27301 −0.353444
\(316\) 22.4544 1.26316
\(317\) 25.9494 1.45746 0.728731 0.684800i \(-0.240111\pi\)
0.728731 + 0.684800i \(0.240111\pi\)
\(318\) −1.15938 −0.0650151
\(319\) 3.30269 0.184915
\(320\) 17.3681 0.970906
\(321\) −9.57960 −0.534681
\(322\) −7.12237 −0.396914
\(323\) 20.7280 1.15334
\(324\) 12.7540 0.708557
\(325\) −41.5335 −2.30386
\(326\) 4.53906 0.251395
\(327\) 13.2576 0.733146
\(328\) −11.6828 −0.645073
\(329\) −7.63573 −0.420971
\(330\) −0.768525 −0.0423059
\(331\) −19.6181 −1.07831 −0.539153 0.842208i \(-0.681256\pi\)
−0.539153 + 0.842208i \(0.681256\pi\)
\(332\) 9.57888 0.525709
\(333\) 0.212096 0.0116228
\(334\) 6.66722 0.364814
\(335\) −23.8378 −1.30240
\(336\) 13.8185 0.753861
\(337\) −25.4533 −1.38653 −0.693265 0.720683i \(-0.743828\pi\)
−0.693265 + 0.720683i \(0.743828\pi\)
\(338\) −3.08643 −0.167880
\(339\) −20.3378 −1.10460
\(340\) −31.2545 −1.69502
\(341\) 2.61263 0.141482
\(342\) −1.04577 −0.0565485
\(343\) 16.7823 0.906157
\(344\) −13.5053 −0.728157
\(345\) −37.6846 −2.02887
\(346\) −7.23017 −0.388696
\(347\) 14.9640 0.803310 0.401655 0.915791i \(-0.368435\pi\)
0.401655 + 0.915791i \(0.368435\pi\)
\(348\) 27.8284 1.49176
\(349\) 18.5127 0.990963 0.495481 0.868619i \(-0.334992\pi\)
0.495481 + 0.868619i \(0.334992\pi\)
\(350\) 9.98381 0.533657
\(351\) −25.5231 −1.36232
\(352\) −1.42814 −0.0761204
\(353\) −23.0672 −1.22774 −0.613872 0.789406i \(-0.710389\pi\)
−0.613872 + 0.789406i \(0.710389\pi\)
\(354\) −0.311606 −0.0165617
\(355\) 23.7806 1.26214
\(356\) −1.12103 −0.0594142
\(357\) −19.9136 −1.05394
\(358\) 1.83795 0.0971387
\(359\) −24.0589 −1.26978 −0.634889 0.772603i \(-0.718954\pi\)
−0.634889 + 0.772603i \(0.718954\pi\)
\(360\) 3.28116 0.172932
\(361\) 2.18612 0.115059
\(362\) 0.185829 0.00976693
\(363\) 16.9048 0.887274
\(364\) −24.1303 −1.26477
\(365\) 51.1187 2.67567
\(366\) −4.74750 −0.248156
\(367\) −10.8139 −0.564482 −0.282241 0.959343i \(-0.591078\pi\)
−0.282241 + 0.959343i \(0.591078\pi\)
\(368\) −20.2144 −1.05375
\(369\) 4.60890 0.239930
\(370\) −0.523699 −0.0272258
\(371\) 5.49477 0.285274
\(372\) 22.0140 1.14137
\(373\) −2.09981 −0.108724 −0.0543620 0.998521i \(-0.517312\pi\)
−0.0543620 + 0.998521i \(0.517312\pi\)
\(374\) 0.594078 0.0307191
\(375\) 23.6962 1.22367
\(376\) 3.99394 0.205972
\(377\) −44.3494 −2.28411
\(378\) 6.13523 0.315562
\(379\) −21.1009 −1.08388 −0.541939 0.840418i \(-0.682310\pi\)
−0.541939 + 0.840418i \(0.682310\pi\)
\(380\) −31.9453 −1.63876
\(381\) −24.1502 −1.23725
\(382\) 7.24573 0.370724
\(383\) 7.65222 0.391010 0.195505 0.980703i \(-0.437365\pi\)
0.195505 + 0.980703i \(0.437365\pi\)
\(384\) −15.7879 −0.805671
\(385\) 3.64233 0.185630
\(386\) −9.15512 −0.465983
\(387\) 5.32790 0.270832
\(388\) 1.09709 0.0556965
\(389\) −0.495935 −0.0251449 −0.0125725 0.999921i \(-0.504002\pi\)
−0.0125725 + 0.999921i \(0.504002\pi\)
\(390\) 10.3200 0.522572
\(391\) 29.1306 1.47320
\(392\) 1.64581 0.0831257
\(393\) 3.95560 0.199534
\(394\) −5.25987 −0.264988
\(395\) 45.5134 2.29003
\(396\) 0.370805 0.0186336
\(397\) 5.91573 0.296902 0.148451 0.988920i \(-0.452571\pi\)
0.148451 + 0.988920i \(0.452571\pi\)
\(398\) 0.480867 0.0241037
\(399\) −20.3537 −1.01896
\(400\) 28.3356 1.41678
\(401\) −12.2436 −0.611414 −0.305707 0.952126i \(-0.598893\pi\)
−0.305707 + 0.952126i \(0.598893\pi\)
\(402\) 3.81784 0.190417
\(403\) −35.0831 −1.74761
\(404\) −34.0211 −1.69261
\(405\) 25.8514 1.28457
\(406\) 10.6607 0.529081
\(407\) −0.123151 −0.00610435
\(408\) 10.4160 0.515669
\(409\) 0.425047 0.0210172 0.0105086 0.999945i \(-0.496655\pi\)
0.0105086 + 0.999945i \(0.496655\pi\)
\(410\) −11.3801 −0.562023
\(411\) −9.70494 −0.478709
\(412\) 30.4019 1.49779
\(413\) 1.47682 0.0726695
\(414\) −1.46969 −0.0722315
\(415\) 19.4156 0.953076
\(416\) 19.1775 0.940256
\(417\) 8.83947 0.432871
\(418\) 0.607209 0.0296995
\(419\) −6.01181 −0.293696 −0.146848 0.989159i \(-0.546913\pi\)
−0.146848 + 0.989159i \(0.546913\pi\)
\(420\) 30.6902 1.49753
\(421\) 13.1235 0.639598 0.319799 0.947485i \(-0.396385\pi\)
0.319799 + 0.947485i \(0.396385\pi\)
\(422\) −2.06003 −0.100280
\(423\) −1.57563 −0.0766095
\(424\) −2.87409 −0.139578
\(425\) −40.8340 −1.98074
\(426\) −3.80868 −0.184531
\(427\) 22.5002 1.08886
\(428\) −11.4126 −0.551647
\(429\) 2.42679 0.117167
\(430\) −13.1554 −0.634410
\(431\) −2.19415 −0.105688 −0.0528441 0.998603i \(-0.516829\pi\)
−0.0528441 + 0.998603i \(0.516829\pi\)
\(432\) 17.4127 0.837770
\(433\) −25.9473 −1.24695 −0.623473 0.781845i \(-0.714279\pi\)
−0.623473 + 0.781845i \(0.714279\pi\)
\(434\) 8.43326 0.404810
\(435\) 56.4060 2.70446
\(436\) 15.7943 0.756410
\(437\) 29.7744 1.42430
\(438\) −8.18711 −0.391195
\(439\) 23.0473 1.09999 0.549994 0.835169i \(-0.314630\pi\)
0.549994 + 0.835169i \(0.314630\pi\)
\(440\) −1.90516 −0.0908248
\(441\) −0.649277 −0.0309179
\(442\) −7.97745 −0.379449
\(443\) −8.60542 −0.408856 −0.204428 0.978882i \(-0.565533\pi\)
−0.204428 + 0.978882i \(0.565533\pi\)
\(444\) −1.03767 −0.0492454
\(445\) −2.27223 −0.107714
\(446\) 11.2135 0.530975
\(447\) −35.0319 −1.65695
\(448\) 13.1833 0.622853
\(449\) −11.5453 −0.544858 −0.272429 0.962176i \(-0.587827\pi\)
−0.272429 + 0.962176i \(0.587827\pi\)
\(450\) 2.06015 0.0971164
\(451\) −2.67609 −0.126012
\(452\) −24.2292 −1.13965
\(453\) −18.8662 −0.886409
\(454\) 8.12045 0.381111
\(455\) −48.9103 −2.29295
\(456\) 10.6462 0.498555
\(457\) −20.4197 −0.955193 −0.477597 0.878579i \(-0.658492\pi\)
−0.477597 + 0.878579i \(0.658492\pi\)
\(458\) −4.53054 −0.211698
\(459\) −25.0932 −1.17125
\(460\) −44.8952 −2.09325
\(461\) 11.4092 0.531377 0.265689 0.964059i \(-0.414401\pi\)
0.265689 + 0.964059i \(0.414401\pi\)
\(462\) −0.583352 −0.0271400
\(463\) 14.9737 0.695887 0.347944 0.937515i \(-0.386880\pi\)
0.347944 + 0.937515i \(0.386880\pi\)
\(464\) 30.2567 1.40463
\(465\) 44.6206 2.06923
\(466\) 3.96614 0.183728
\(467\) −5.56500 −0.257518 −0.128759 0.991676i \(-0.541099\pi\)
−0.128759 + 0.991676i \(0.541099\pi\)
\(468\) −4.97927 −0.230167
\(469\) −18.0942 −0.835513
\(470\) 3.89047 0.179454
\(471\) 19.5828 0.902330
\(472\) −0.772464 −0.0355555
\(473\) −3.09356 −0.142242
\(474\) −7.28938 −0.334812
\(475\) −41.7365 −1.91500
\(476\) −23.7239 −1.08738
\(477\) 1.13384 0.0519150
\(478\) 6.08692 0.278409
\(479\) 1.52115 0.0695033 0.0347517 0.999396i \(-0.488936\pi\)
0.0347517 + 0.999396i \(0.488936\pi\)
\(480\) −24.3910 −1.11329
\(481\) 1.65370 0.0754023
\(482\) −7.83671 −0.356952
\(483\) −28.6047 −1.30156
\(484\) 20.1394 0.915428
\(485\) 2.22372 0.100974
\(486\) 2.32468 0.105450
\(487\) −5.20782 −0.235989 −0.117995 0.993014i \(-0.537647\pi\)
−0.117995 + 0.993014i \(0.537647\pi\)
\(488\) −11.7689 −0.532755
\(489\) 18.2297 0.824373
\(490\) 1.60317 0.0724237
\(491\) 37.7702 1.70455 0.852273 0.523097i \(-0.175224\pi\)
0.852273 + 0.523097i \(0.175224\pi\)
\(492\) −22.5487 −1.01657
\(493\) −43.6024 −1.96376
\(494\) −8.15377 −0.366855
\(495\) 0.751592 0.0337815
\(496\) 23.9349 1.07471
\(497\) 18.0508 0.809688
\(498\) −3.10959 −0.139344
\(499\) −26.8162 −1.20046 −0.600228 0.799829i \(-0.704924\pi\)
−0.600228 + 0.799829i \(0.704924\pi\)
\(500\) 28.2303 1.26250
\(501\) 26.7767 1.19629
\(502\) −5.03733 −0.224827
\(503\) 15.9323 0.710386 0.355193 0.934793i \(-0.384415\pi\)
0.355193 + 0.934793i \(0.384415\pi\)
\(504\) 2.49058 0.110939
\(505\) −68.9580 −3.06859
\(506\) 0.853356 0.0379363
\(507\) −12.3957 −0.550510
\(508\) −28.7711 −1.27651
\(509\) −37.8221 −1.67644 −0.838218 0.545335i \(-0.816403\pi\)
−0.838218 + 0.545335i \(0.816403\pi\)
\(510\) 10.1462 0.449279
\(511\) 38.8018 1.71649
\(512\) −22.3905 −0.989529
\(513\) −25.6478 −1.13238
\(514\) 4.40035 0.194091
\(515\) 61.6222 2.71540
\(516\) −26.0663 −1.14751
\(517\) 0.914864 0.0402357
\(518\) −0.397516 −0.0174659
\(519\) −29.0376 −1.27461
\(520\) 25.5830 1.12189
\(521\) 42.4318 1.85897 0.929486 0.368856i \(-0.120251\pi\)
0.929486 + 0.368856i \(0.120251\pi\)
\(522\) 2.19982 0.0962837
\(523\) −33.0283 −1.44423 −0.722114 0.691774i \(-0.756829\pi\)
−0.722114 + 0.691774i \(0.756829\pi\)
\(524\) 4.71247 0.205865
\(525\) 40.0967 1.74996
\(526\) −0.0443952 −0.00193572
\(527\) −34.4922 −1.50250
\(528\) −1.65564 −0.0720526
\(529\) 18.8443 0.819316
\(530\) −2.79963 −0.121608
\(531\) 0.304740 0.0132246
\(532\) −24.2482 −1.05129
\(533\) 35.9353 1.55653
\(534\) 0.363918 0.0157483
\(535\) −23.1324 −1.00010
\(536\) 9.46434 0.408797
\(537\) 7.38152 0.318536
\(538\) −1.39988 −0.0603532
\(539\) 0.376993 0.0162382
\(540\) 38.6729 1.66421
\(541\) 9.85861 0.423855 0.211927 0.977285i \(-0.432026\pi\)
0.211927 + 0.977285i \(0.432026\pi\)
\(542\) −4.41214 −0.189518
\(543\) 0.746320 0.0320276
\(544\) 18.8545 0.808381
\(545\) 32.0138 1.37132
\(546\) 7.83342 0.335239
\(547\) 14.4283 0.616911 0.308455 0.951239i \(-0.400188\pi\)
0.308455 + 0.951239i \(0.400188\pi\)
\(548\) −11.5619 −0.493899
\(549\) 4.64290 0.198154
\(550\) −1.19620 −0.0510060
\(551\) −44.5661 −1.89858
\(552\) 14.9619 0.636822
\(553\) 34.5471 1.46909
\(554\) 4.29772 0.182593
\(555\) −2.10327 −0.0892787
\(556\) 10.5308 0.446606
\(557\) −17.0881 −0.724048 −0.362024 0.932169i \(-0.617914\pi\)
−0.362024 + 0.932169i \(0.617914\pi\)
\(558\) 1.74020 0.0736684
\(559\) 41.5412 1.75701
\(560\) 33.3683 1.41007
\(561\) 2.38592 0.100734
\(562\) −7.66132 −0.323173
\(563\) −17.1848 −0.724252 −0.362126 0.932129i \(-0.617949\pi\)
−0.362126 + 0.932129i \(0.617949\pi\)
\(564\) 7.70863 0.324592
\(565\) −49.1107 −2.06610
\(566\) −2.63427 −0.110727
\(567\) 19.6226 0.824073
\(568\) −9.44163 −0.396162
\(569\) −10.2475 −0.429599 −0.214800 0.976658i \(-0.568910\pi\)
−0.214800 + 0.976658i \(0.568910\pi\)
\(570\) 10.3704 0.434368
\(571\) −35.0635 −1.46736 −0.733681 0.679494i \(-0.762199\pi\)
−0.733681 + 0.679494i \(0.762199\pi\)
\(572\) 2.89114 0.120885
\(573\) 29.1001 1.21567
\(574\) −8.63811 −0.360548
\(575\) −58.6554 −2.44610
\(576\) 2.72037 0.113349
\(577\) 40.8544 1.70079 0.850396 0.526143i \(-0.176362\pi\)
0.850396 + 0.526143i \(0.176362\pi\)
\(578\) −1.26844 −0.0527600
\(579\) −36.7685 −1.52805
\(580\) 67.1987 2.79027
\(581\) 14.7375 0.611415
\(582\) −0.356149 −0.0147629
\(583\) −0.658347 −0.0272660
\(584\) −20.2957 −0.839841
\(585\) −10.0926 −0.417277
\(586\) −7.30425 −0.301736
\(587\) −29.2242 −1.20621 −0.603106 0.797661i \(-0.706070\pi\)
−0.603106 + 0.797661i \(0.706070\pi\)
\(588\) 3.17654 0.130998
\(589\) −35.2545 −1.45264
\(590\) −0.752451 −0.0309779
\(591\) −21.1245 −0.868947
\(592\) −1.12821 −0.0463692
\(593\) −18.1141 −0.743855 −0.371928 0.928262i \(-0.621303\pi\)
−0.371928 + 0.928262i \(0.621303\pi\)
\(594\) −0.735084 −0.0301609
\(595\) −48.0865 −1.97135
\(596\) −41.7349 −1.70953
\(597\) 1.93125 0.0790406
\(598\) −11.4591 −0.468598
\(599\) 26.3879 1.07818 0.539089 0.842249i \(-0.318769\pi\)
0.539089 + 0.842249i \(0.318769\pi\)
\(600\) −20.9730 −0.856218
\(601\) −39.0984 −1.59486 −0.797428 0.603414i \(-0.793807\pi\)
−0.797428 + 0.603414i \(0.793807\pi\)
\(602\) −9.98568 −0.406986
\(603\) −3.73372 −0.152049
\(604\) −22.4760 −0.914536
\(605\) 40.8210 1.65961
\(606\) 11.0443 0.448642
\(607\) −10.6168 −0.430922 −0.215461 0.976512i \(-0.569125\pi\)
−0.215461 + 0.976512i \(0.569125\pi\)
\(608\) 19.2712 0.781552
\(609\) 42.8152 1.73496
\(610\) −11.4640 −0.464166
\(611\) −12.2850 −0.497000
\(612\) −4.89540 −0.197885
\(613\) 17.5950 0.710655 0.355328 0.934742i \(-0.384369\pi\)
0.355328 + 0.934742i \(0.384369\pi\)
\(614\) 4.38840 0.177101
\(615\) −45.7044 −1.84298
\(616\) −1.44612 −0.0582657
\(617\) −11.3845 −0.458322 −0.229161 0.973388i \(-0.573598\pi\)
−0.229161 + 0.973388i \(0.573598\pi\)
\(618\) −9.86936 −0.397004
\(619\) 1.00000 0.0401934
\(620\) 53.1583 2.13489
\(621\) −36.0448 −1.44643
\(622\) −5.81887 −0.233315
\(623\) −1.72475 −0.0691005
\(624\) 22.2324 0.890010
\(625\) 11.8828 0.475310
\(626\) 1.38551 0.0553762
\(627\) 2.43865 0.0973905
\(628\) 23.3298 0.930962
\(629\) 1.62585 0.0648268
\(630\) 2.42605 0.0966563
\(631\) −27.4304 −1.09198 −0.545992 0.837790i \(-0.683847\pi\)
−0.545992 + 0.837790i \(0.683847\pi\)
\(632\) −18.0702 −0.718794
\(633\) −8.27342 −0.328839
\(634\) −10.0358 −0.398572
\(635\) −58.3167 −2.31423
\(636\) −5.54723 −0.219962
\(637\) −5.06237 −0.200578
\(638\) −1.27730 −0.0505686
\(639\) 3.72476 0.147349
\(640\) −38.1238 −1.50698
\(641\) −12.0302 −0.475166 −0.237583 0.971367i \(-0.576355\pi\)
−0.237583 + 0.971367i \(0.576355\pi\)
\(642\) 3.70486 0.146219
\(643\) 27.9994 1.10419 0.552094 0.833782i \(-0.313829\pi\)
0.552094 + 0.833782i \(0.313829\pi\)
\(644\) −34.0779 −1.34286
\(645\) −52.8344 −2.08035
\(646\) −8.01644 −0.315403
\(647\) −2.24425 −0.0882307 −0.0441153 0.999026i \(-0.514047\pi\)
−0.0441153 + 0.999026i \(0.514047\pi\)
\(648\) −10.2638 −0.403200
\(649\) −0.176943 −0.00694561
\(650\) 16.0629 0.630037
\(651\) 33.8694 1.32745
\(652\) 21.7177 0.850532
\(653\) 27.0093 1.05696 0.528478 0.848947i \(-0.322763\pi\)
0.528478 + 0.848947i \(0.322763\pi\)
\(654\) −5.12730 −0.200493
\(655\) 9.55181 0.373220
\(656\) −24.5163 −0.957200
\(657\) 8.00672 0.312372
\(658\) 2.95308 0.115123
\(659\) −15.2364 −0.593526 −0.296763 0.954951i \(-0.595907\pi\)
−0.296763 + 0.954951i \(0.595907\pi\)
\(660\) −3.67711 −0.143131
\(661\) −35.0111 −1.36178 −0.680888 0.732388i \(-0.738406\pi\)
−0.680888 + 0.732388i \(0.738406\pi\)
\(662\) 7.58718 0.294884
\(663\) −32.0388 −1.24428
\(664\) −7.70860 −0.299152
\(665\) −49.1493 −1.90593
\(666\) −0.0820271 −0.00317849
\(667\) −62.6321 −2.42513
\(668\) 31.9001 1.23425
\(669\) 45.0354 1.74117
\(670\) 9.21915 0.356167
\(671\) −2.69583 −0.104071
\(672\) −18.5141 −0.714197
\(673\) 9.46682 0.364919 0.182460 0.983213i \(-0.441594\pi\)
0.182460 + 0.983213i \(0.441594\pi\)
\(674\) 9.84393 0.379174
\(675\) 50.5260 1.94475
\(676\) −14.7674 −0.567978
\(677\) 27.3050 1.04941 0.524707 0.851283i \(-0.324175\pi\)
0.524707 + 0.851283i \(0.324175\pi\)
\(678\) 7.86553 0.302074
\(679\) 1.68793 0.0647767
\(680\) 25.1521 0.964539
\(681\) 32.6131 1.24974
\(682\) −1.01042 −0.0386909
\(683\) −19.2637 −0.737105 −0.368552 0.929607i \(-0.620146\pi\)
−0.368552 + 0.929607i \(0.620146\pi\)
\(684\) −5.00360 −0.191317
\(685\) −23.4350 −0.895407
\(686\) −6.49045 −0.247806
\(687\) −18.1954 −0.694198
\(688\) −28.3409 −1.08049
\(689\) 8.84047 0.336795
\(690\) 14.5743 0.554834
\(691\) 36.9687 1.40635 0.703177 0.711014i \(-0.251764\pi\)
0.703177 + 0.711014i \(0.251764\pi\)
\(692\) −34.5937 −1.31505
\(693\) 0.570499 0.0216715
\(694\) −5.78725 −0.219681
\(695\) 21.3451 0.809667
\(696\) −22.3949 −0.848876
\(697\) 35.3300 1.33822
\(698\) −7.15969 −0.270998
\(699\) 15.9287 0.602479
\(700\) 47.7688 1.80549
\(701\) 14.1153 0.533128 0.266564 0.963817i \(-0.414112\pi\)
0.266564 + 0.963817i \(0.414112\pi\)
\(702\) 9.87091 0.372554
\(703\) 1.66178 0.0626753
\(704\) −1.57954 −0.0595312
\(705\) 15.6248 0.588463
\(706\) 8.92112 0.335751
\(707\) −52.3429 −1.96856
\(708\) −1.49092 −0.0560321
\(709\) 37.2243 1.39799 0.698994 0.715127i \(-0.253631\pi\)
0.698994 + 0.715127i \(0.253631\pi\)
\(710\) −9.19703 −0.345158
\(711\) 7.12877 0.267350
\(712\) 0.902145 0.0338093
\(713\) −49.5459 −1.85551
\(714\) 7.70148 0.288221
\(715\) 5.86011 0.219156
\(716\) 8.79391 0.328644
\(717\) 24.4461 0.912958
\(718\) 9.30463 0.347246
\(719\) 2.46349 0.0918729 0.0459364 0.998944i \(-0.485373\pi\)
0.0459364 + 0.998944i \(0.485373\pi\)
\(720\) 6.88551 0.256608
\(721\) 46.7746 1.74198
\(722\) −0.845468 −0.0314651
\(723\) −31.4736 −1.17051
\(724\) 0.889121 0.0330439
\(725\) 87.7949 3.26062
\(726\) −6.53785 −0.242642
\(727\) −27.8800 −1.03401 −0.517005 0.855982i \(-0.672953\pi\)
−0.517005 + 0.855982i \(0.672953\pi\)
\(728\) 19.4189 0.719711
\(729\) 30.0138 1.11162
\(730\) −19.7699 −0.731715
\(731\) 40.8416 1.51058
\(732\) −22.7150 −0.839572
\(733\) 1.06781 0.0394404 0.0197202 0.999806i \(-0.493722\pi\)
0.0197202 + 0.999806i \(0.493722\pi\)
\(734\) 4.18223 0.154369
\(735\) 6.43859 0.237491
\(736\) 27.0833 0.998305
\(737\) 2.16793 0.0798567
\(738\) −1.78247 −0.0656135
\(739\) −19.5195 −0.718037 −0.359019 0.933330i \(-0.616889\pi\)
−0.359019 + 0.933330i \(0.616889\pi\)
\(740\) −2.50571 −0.0921116
\(741\) −32.7469 −1.20299
\(742\) −2.12507 −0.0780138
\(743\) 12.4563 0.456978 0.228489 0.973547i \(-0.426622\pi\)
0.228489 + 0.973547i \(0.426622\pi\)
\(744\) −17.7157 −0.649490
\(745\) −84.5934 −3.09926
\(746\) 0.812089 0.0297327
\(747\) 3.04107 0.111267
\(748\) 2.84244 0.103930
\(749\) −17.5587 −0.641582
\(750\) −9.16438 −0.334636
\(751\) −25.7804 −0.940741 −0.470371 0.882469i \(-0.655880\pi\)
−0.470371 + 0.882469i \(0.655880\pi\)
\(752\) 8.38128 0.305634
\(753\) −20.2308 −0.737250
\(754\) 17.1519 0.624635
\(755\) −45.5571 −1.65799
\(756\) 29.3548 1.06762
\(757\) 18.2009 0.661521 0.330761 0.943715i \(-0.392695\pi\)
0.330761 + 0.943715i \(0.392695\pi\)
\(758\) 8.16065 0.296408
\(759\) 3.42722 0.124400
\(760\) 25.7080 0.932527
\(761\) −32.0271 −1.16098 −0.580491 0.814266i \(-0.697139\pi\)
−0.580491 + 0.814266i \(0.697139\pi\)
\(762\) 9.33994 0.338350
\(763\) 24.3002 0.879727
\(764\) 34.6681 1.25425
\(765\) −9.92260 −0.358752
\(766\) −2.95946 −0.106929
\(767\) 2.37604 0.0857938
\(768\) −8.27911 −0.298747
\(769\) 40.8355 1.47256 0.736282 0.676675i \(-0.236580\pi\)
0.736282 + 0.676675i \(0.236580\pi\)
\(770\) −1.40865 −0.0507643
\(771\) 17.6726 0.636462
\(772\) −43.8038 −1.57653
\(773\) −21.9644 −0.790003 −0.395002 0.918680i \(-0.629256\pi\)
−0.395002 + 0.918680i \(0.629256\pi\)
\(774\) −2.06053 −0.0740644
\(775\) 69.4512 2.49476
\(776\) −0.882886 −0.0316938
\(777\) −1.59649 −0.0572739
\(778\) 0.191800 0.00687637
\(779\) 36.1109 1.29381
\(780\) 49.3772 1.76799
\(781\) −2.16273 −0.0773885
\(782\) −11.2661 −0.402875
\(783\) 53.9515 1.92807
\(784\) 3.45372 0.123347
\(785\) 47.2877 1.68777
\(786\) −1.52981 −0.0545664
\(787\) 55.4908 1.97803 0.989017 0.147803i \(-0.0472201\pi\)
0.989017 + 0.147803i \(0.0472201\pi\)
\(788\) −25.1665 −0.896520
\(789\) −0.178299 −0.00634760
\(790\) −17.6021 −0.626253
\(791\) −37.2777 −1.32544
\(792\) −0.298405 −0.0106034
\(793\) 36.2004 1.28551
\(794\) −2.28788 −0.0811937
\(795\) −11.2438 −0.398776
\(796\) 2.30077 0.0815487
\(797\) −12.9732 −0.459534 −0.229767 0.973246i \(-0.573796\pi\)
−0.229767 + 0.973246i \(0.573796\pi\)
\(798\) 7.87170 0.278655
\(799\) −12.0781 −0.427294
\(800\) −37.9642 −1.34224
\(801\) −0.355900 −0.0125751
\(802\) 4.73513 0.167203
\(803\) −4.64899 −0.164059
\(804\) 18.2670 0.644226
\(805\) −69.0732 −2.43451
\(806\) 13.5682 0.477919
\(807\) −5.62217 −0.197910
\(808\) 27.3784 0.963170
\(809\) −20.3113 −0.714109 −0.357054 0.934084i \(-0.616219\pi\)
−0.357054 + 0.934084i \(0.616219\pi\)
\(810\) −9.99790 −0.351290
\(811\) 25.2796 0.887688 0.443844 0.896104i \(-0.353614\pi\)
0.443844 + 0.896104i \(0.353614\pi\)
\(812\) 51.0075 1.79001
\(813\) −17.7199 −0.621465
\(814\) 0.0476278 0.00166935
\(815\) 44.0201 1.54196
\(816\) 21.8580 0.765183
\(817\) 41.7443 1.46045
\(818\) −0.164385 −0.00574758
\(819\) −7.66082 −0.267691
\(820\) −54.4495 −1.90146
\(821\) 39.8004 1.38904 0.694522 0.719471i \(-0.255616\pi\)
0.694522 + 0.719471i \(0.255616\pi\)
\(822\) 3.75333 0.130913
\(823\) 12.2526 0.427100 0.213550 0.976932i \(-0.431497\pi\)
0.213550 + 0.976932i \(0.431497\pi\)
\(824\) −24.4659 −0.852311
\(825\) −4.80413 −0.167258
\(826\) −0.571151 −0.0198729
\(827\) 34.7706 1.20909 0.604547 0.796570i \(-0.293354\pi\)
0.604547 + 0.796570i \(0.293354\pi\)
\(828\) −7.03194 −0.244377
\(829\) 0.614738 0.0213507 0.0106754 0.999943i \(-0.496602\pi\)
0.0106754 + 0.999943i \(0.496602\pi\)
\(830\) −7.50889 −0.260637
\(831\) 17.2604 0.598757
\(832\) 21.2105 0.735342
\(833\) −4.97710 −0.172446
\(834\) −3.41862 −0.118377
\(835\) 64.6591 2.23762
\(836\) 2.90527 0.100481
\(837\) 42.6790 1.47520
\(838\) 2.32503 0.0803170
\(839\) 25.7977 0.890637 0.445318 0.895372i \(-0.353091\pi\)
0.445318 + 0.895372i \(0.353091\pi\)
\(840\) −24.6980 −0.852161
\(841\) 64.7472 2.23266
\(842\) −5.07542 −0.174911
\(843\) −30.7692 −1.05975
\(844\) −9.85646 −0.339273
\(845\) −29.9324 −1.02971
\(846\) 0.609364 0.0209504
\(847\) 30.9854 1.06467
\(848\) −6.03128 −0.207115
\(849\) −10.5797 −0.363094
\(850\) 15.7923 0.541672
\(851\) 2.33543 0.0800575
\(852\) −18.2231 −0.624314
\(853\) 1.99666 0.0683643 0.0341822 0.999416i \(-0.489117\pi\)
0.0341822 + 0.999416i \(0.489117\pi\)
\(854\) −8.70183 −0.297771
\(855\) −10.1419 −0.346846
\(856\) 9.18426 0.313911
\(857\) −54.5879 −1.86469 −0.932343 0.361575i \(-0.882239\pi\)
−0.932343 + 0.361575i \(0.882239\pi\)
\(858\) −0.938549 −0.0320415
\(859\) −37.4710 −1.27849 −0.639247 0.769001i \(-0.720754\pi\)
−0.639247 + 0.769001i \(0.720754\pi\)
\(860\) −62.9438 −2.14636
\(861\) −34.6921 −1.18230
\(862\) 0.848574 0.0289025
\(863\) 11.8377 0.402960 0.201480 0.979493i \(-0.435425\pi\)
0.201480 + 0.979493i \(0.435425\pi\)
\(864\) −23.3297 −0.793692
\(865\) −70.1187 −2.38411
\(866\) 10.0350 0.341002
\(867\) −5.09426 −0.173010
\(868\) 40.3500 1.36957
\(869\) −4.13921 −0.140413
\(870\) −21.8147 −0.739587
\(871\) −29.1116 −0.986408
\(872\) −12.7105 −0.430431
\(873\) 0.348302 0.0117882
\(874\) −11.5151 −0.389504
\(875\) 43.4335 1.46832
\(876\) −39.1723 −1.32351
\(877\) 30.5821 1.03268 0.516342 0.856383i \(-0.327293\pi\)
0.516342 + 0.856383i \(0.327293\pi\)
\(878\) −8.91341 −0.300813
\(879\) −29.3351 −0.989449
\(880\) −3.99797 −0.134772
\(881\) −14.1448 −0.476552 −0.238276 0.971198i \(-0.576582\pi\)
−0.238276 + 0.971198i \(0.576582\pi\)
\(882\) 0.251104 0.00845512
\(883\) 35.5810 1.19739 0.598697 0.800975i \(-0.295685\pi\)
0.598697 + 0.800975i \(0.295685\pi\)
\(884\) −38.1691 −1.28377
\(885\) −3.02197 −0.101583
\(886\) 3.32810 0.111810
\(887\) 30.2855 1.01689 0.508443 0.861095i \(-0.330221\pi\)
0.508443 + 0.861095i \(0.330221\pi\)
\(888\) 0.835061 0.0280228
\(889\) −44.2655 −1.48462
\(890\) 0.878773 0.0294565
\(891\) −2.35106 −0.0787634
\(892\) 53.6525 1.79642
\(893\) −12.3451 −0.413112
\(894\) 13.5484 0.453126
\(895\) 17.8246 0.595809
\(896\) −28.9380 −0.966752
\(897\) −46.0217 −1.53662
\(898\) 4.46509 0.149002
\(899\) 74.1598 2.47337
\(900\) 9.85705 0.328568
\(901\) 8.69158 0.289558
\(902\) 1.03496 0.0344605
\(903\) −40.1042 −1.33458
\(904\) 19.4985 0.648509
\(905\) 1.80218 0.0599064
\(906\) 7.29638 0.242406
\(907\) −29.3799 −0.975545 −0.487772 0.872971i \(-0.662190\pi\)
−0.487772 + 0.872971i \(0.662190\pi\)
\(908\) 38.8533 1.28939
\(909\) −10.8009 −0.358243
\(910\) 18.9158 0.627052
\(911\) −26.0571 −0.863310 −0.431655 0.902039i \(-0.642070\pi\)
−0.431655 + 0.902039i \(0.642070\pi\)
\(912\) 22.3411 0.739787
\(913\) −1.76575 −0.0584379
\(914\) 7.89721 0.261216
\(915\) −46.0416 −1.52209
\(916\) −21.6769 −0.716226
\(917\) 7.25034 0.239427
\(918\) 9.70466 0.320302
\(919\) 21.7610 0.717829 0.358914 0.933370i \(-0.383147\pi\)
0.358914 + 0.933370i \(0.383147\pi\)
\(920\) 36.1294 1.19115
\(921\) 17.6246 0.580749
\(922\) −4.41243 −0.145316
\(923\) 29.0417 0.955920
\(924\) −2.79112 −0.0918212
\(925\) −3.27370 −0.107639
\(926\) −5.79100 −0.190304
\(927\) 9.65190 0.317010
\(928\) −40.5381 −1.33073
\(929\) 20.7461 0.680657 0.340329 0.940307i \(-0.389462\pi\)
0.340329 + 0.940307i \(0.389462\pi\)
\(930\) −17.2568 −0.565872
\(931\) −5.08711 −0.166723
\(932\) 18.9765 0.621597
\(933\) −23.3696 −0.765085
\(934\) 2.15223 0.0704233
\(935\) 5.76141 0.188418
\(936\) 4.00706 0.130975
\(937\) −20.0324 −0.654429 −0.327215 0.944950i \(-0.606110\pi\)
−0.327215 + 0.944950i \(0.606110\pi\)
\(938\) 6.99783 0.228487
\(939\) 5.56445 0.181589
\(940\) 18.6144 0.607136
\(941\) 14.9045 0.485874 0.242937 0.970042i \(-0.421889\pi\)
0.242937 + 0.970042i \(0.421889\pi\)
\(942\) −7.57356 −0.246760
\(943\) 50.7493 1.65263
\(944\) −1.62102 −0.0527596
\(945\) 59.4999 1.93553
\(946\) 1.19642 0.0388989
\(947\) 12.9596 0.421131 0.210565 0.977580i \(-0.432469\pi\)
0.210565 + 0.977580i \(0.432469\pi\)
\(948\) −34.8770 −1.13275
\(949\) 62.4279 2.02650
\(950\) 16.1414 0.523695
\(951\) −40.3054 −1.30699
\(952\) 19.0918 0.618769
\(953\) −31.5188 −1.02099 −0.510497 0.859880i \(-0.670539\pi\)
−0.510497 + 0.859880i \(0.670539\pi\)
\(954\) −0.438506 −0.0141972
\(955\) 70.2696 2.27387
\(956\) 29.1237 0.941927
\(957\) −5.12984 −0.165824
\(958\) −0.588298 −0.0190071
\(959\) −17.7885 −0.574420
\(960\) −26.9767 −0.870669
\(961\) 27.6650 0.892418
\(962\) −0.639560 −0.0206202
\(963\) −3.62323 −0.116757
\(964\) −37.4957 −1.20766
\(965\) −88.7869 −2.85815
\(966\) 11.0627 0.355936
\(967\) 2.60046 0.0836253 0.0418126 0.999125i \(-0.486687\pi\)
0.0418126 + 0.999125i \(0.486687\pi\)
\(968\) −16.2072 −0.520919
\(969\) −32.1954 −1.03427
\(970\) −0.860013 −0.0276133
\(971\) −27.1651 −0.871769 −0.435885 0.900003i \(-0.643564\pi\)
−0.435885 + 0.900003i \(0.643564\pi\)
\(972\) 11.1227 0.356762
\(973\) 16.2021 0.519416
\(974\) 2.01410 0.0645359
\(975\) 64.5112 2.06601
\(976\) −24.6971 −0.790536
\(977\) −44.4185 −1.42107 −0.710537 0.703660i \(-0.751548\pi\)
−0.710537 + 0.703660i \(0.751548\pi\)
\(978\) −7.05022 −0.225441
\(979\) 0.206648 0.00660450
\(980\) 7.67056 0.245027
\(981\) 5.01433 0.160095
\(982\) −14.6074 −0.466142
\(983\) −50.1035 −1.59805 −0.799027 0.601295i \(-0.794652\pi\)
−0.799027 + 0.601295i \(0.794652\pi\)
\(984\) 18.1461 0.578475
\(985\) −51.0105 −1.62533
\(986\) 16.8630 0.537027
\(987\) 11.8601 0.377510
\(988\) −39.0127 −1.24116
\(989\) 58.6664 1.86548
\(990\) −0.290674 −0.00923823
\(991\) 2.48996 0.0790961 0.0395480 0.999218i \(-0.487408\pi\)
0.0395480 + 0.999218i \(0.487408\pi\)
\(992\) −32.0681 −1.01816
\(993\) 30.4714 0.966981
\(994\) −6.98104 −0.221425
\(995\) 4.66348 0.147842
\(996\) −14.8782 −0.471435
\(997\) −36.6815 −1.16171 −0.580857 0.814006i \(-0.697282\pi\)
−0.580857 + 0.814006i \(0.697282\pi\)
\(998\) 10.3710 0.328288
\(999\) −2.01175 −0.0636488
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 \(a_p\))