Properties

Label 6047.2.a.a.1.4
Level 6047
Weight 2
Character 6047.1
Self dual Yes
Analytic conductor 48.286
Analytic rank 1
Dimension 217
CM No

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Newspace parameters

Level: \( N \) = \( 6047 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6047.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.2855381023\)
Analytic rank: \(1\)
Dimension: \(217\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Character \(\chi\) = 6047.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.74777 q^{2} +2.83106 q^{3} +5.55022 q^{4} -0.268060 q^{5} -7.77911 q^{6} +0.663291 q^{7} -9.75518 q^{8} +5.01493 q^{9} +O(q^{10})\) \(q-2.74777 q^{2} +2.83106 q^{3} +5.55022 q^{4} -0.268060 q^{5} -7.77911 q^{6} +0.663291 q^{7} -9.75518 q^{8} +5.01493 q^{9} +0.736566 q^{10} -0.384723 q^{11} +15.7130 q^{12} -5.76370 q^{13} -1.82257 q^{14} -0.758895 q^{15} +15.7045 q^{16} +4.35813 q^{17} -13.7799 q^{18} -0.449082 q^{19} -1.48779 q^{20} +1.87782 q^{21} +1.05713 q^{22} -6.98624 q^{23} -27.6175 q^{24} -4.92814 q^{25} +15.8373 q^{26} +5.70439 q^{27} +3.68141 q^{28} +8.69575 q^{29} +2.08527 q^{30} +3.46104 q^{31} -23.6420 q^{32} -1.08918 q^{33} -11.9751 q^{34} -0.177802 q^{35} +27.8340 q^{36} -7.57075 q^{37} +1.23397 q^{38} -16.3174 q^{39} +2.61497 q^{40} -2.18675 q^{41} -5.15981 q^{42} +2.89706 q^{43} -2.13530 q^{44} -1.34430 q^{45} +19.1966 q^{46} -11.2441 q^{47} +44.4605 q^{48} -6.56005 q^{49} +13.5414 q^{50} +12.3382 q^{51} -31.9898 q^{52} +8.78614 q^{53} -15.6743 q^{54} +0.103129 q^{55} -6.47052 q^{56} -1.27138 q^{57} -23.8939 q^{58} -2.66440 q^{59} -4.21203 q^{60} -7.78497 q^{61} -9.51014 q^{62} +3.32636 q^{63} +33.5536 q^{64} +1.54502 q^{65} +2.99280 q^{66} -14.3711 q^{67} +24.1886 q^{68} -19.7785 q^{69} +0.488558 q^{70} +10.8117 q^{71} -48.9215 q^{72} -9.56377 q^{73} +20.8027 q^{74} -13.9519 q^{75} -2.49250 q^{76} -0.255184 q^{77} +44.8364 q^{78} +2.68890 q^{79} -4.20975 q^{80} +1.10472 q^{81} +6.00869 q^{82} -10.9813 q^{83} +10.4223 q^{84} -1.16824 q^{85} -7.96046 q^{86} +24.6182 q^{87} +3.75305 q^{88} +12.7262 q^{89} +3.69383 q^{90} -3.82301 q^{91} -38.7752 q^{92} +9.79844 q^{93} +30.8962 q^{94} +0.120381 q^{95} -66.9320 q^{96} -11.9138 q^{97} +18.0255 q^{98} -1.92936 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 217q - 20q^{2} - 27q^{3} + 184q^{4} - 19q^{5} - 17q^{6} - 48q^{7} - 57q^{8} + 152q^{9} + O(q^{10}) \) \( 217q - 20q^{2} - 27q^{3} + 184q^{4} - 19q^{5} - 17q^{6} - 48q^{7} - 57q^{8} + 152q^{9} - 46q^{10} - 32q^{11} - 72q^{12} - 80q^{13} - 22q^{14} - 43q^{15} + 122q^{16} - 61q^{17} - 88q^{18} - 43q^{19} - 41q^{20} - 61q^{21} - 93q^{22} - 60q^{23} - 41q^{24} + 26q^{25} - 9q^{26} - 93q^{27} - 126q^{28} - 47q^{29} - 36q^{30} - 100q^{31} - 114q^{32} - 133q^{33} - 75q^{34} - 37q^{35} + 75q^{36} - 264q^{37} - 35q^{38} - 47q^{39} - 118q^{40} - 72q^{41} - 64q^{42} - 107q^{43} - 59q^{44} - 69q^{45} - 111q^{46} - 54q^{47} - 135q^{48} + 33q^{49} - 42q^{50} - 26q^{51} - 173q^{52} - 103q^{53} - 28q^{54} - 78q^{55} - 44q^{56} - 205q^{57} - 189q^{58} - 38q^{59} - 105q^{60} - 108q^{61} - 14q^{62} - 116q^{63} + 39q^{64} - 146q^{65} + 5q^{66} - 206q^{67} - 62q^{68} - 55q^{69} - 125q^{70} - 78q^{71} - 225q^{72} - 326q^{73} + 3q^{74} - 95q^{75} - 84q^{76} - 79q^{77} - 86q^{78} - 117q^{79} - 39q^{80} + q^{81} - 96q^{82} - 23q^{83} - 57q^{84} - 224q^{85} - 7q^{86} - 45q^{87} - 250q^{88} - 104q^{89} - 36q^{90} - 96q^{91} - 137q^{92} - 155q^{93} - 48q^{94} - 38q^{95} - 33q^{96} - 447q^{97} - 46q^{98} - 94q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.74777 −1.94296 −0.971482 0.237112i \(-0.923799\pi\)
−0.971482 + 0.237112i \(0.923799\pi\)
\(3\) 2.83106 1.63452 0.817258 0.576272i \(-0.195493\pi\)
0.817258 + 0.576272i \(0.195493\pi\)
\(4\) 5.55022 2.77511
\(5\) −0.268060 −0.119880 −0.0599400 0.998202i \(-0.519091\pi\)
−0.0599400 + 0.998202i \(0.519091\pi\)
\(6\) −7.77911 −3.17581
\(7\) 0.663291 0.250700 0.125350 0.992113i \(-0.459995\pi\)
0.125350 + 0.992113i \(0.459995\pi\)
\(8\) −9.75518 −3.44898
\(9\) 5.01493 1.67164
\(10\) 0.736566 0.232923
\(11\) −0.384723 −0.115998 −0.0579992 0.998317i \(-0.518472\pi\)
−0.0579992 + 0.998317i \(0.518472\pi\)
\(12\) 15.7130 4.53596
\(13\) −5.76370 −1.59856 −0.799281 0.600957i \(-0.794786\pi\)
−0.799281 + 0.600957i \(0.794786\pi\)
\(14\) −1.82257 −0.487102
\(15\) −0.758895 −0.195946
\(16\) 15.7045 3.92613
\(17\) 4.35813 1.05700 0.528501 0.848933i \(-0.322754\pi\)
0.528501 + 0.848933i \(0.322754\pi\)
\(18\) −13.7799 −3.24794
\(19\) −0.449082 −0.103026 −0.0515132 0.998672i \(-0.516404\pi\)
−0.0515132 + 0.998672i \(0.516404\pi\)
\(20\) −1.48779 −0.332680
\(21\) 1.87782 0.409774
\(22\) 1.05713 0.225381
\(23\) −6.98624 −1.45673 −0.728366 0.685188i \(-0.759720\pi\)
−0.728366 + 0.685188i \(0.759720\pi\)
\(24\) −27.6175 −5.63741
\(25\) −4.92814 −0.985629
\(26\) 15.8373 3.10595
\(27\) 5.70439 1.09781
\(28\) 3.68141 0.695721
\(29\) 8.69575 1.61476 0.807380 0.590032i \(-0.200885\pi\)
0.807380 + 0.590032i \(0.200885\pi\)
\(30\) 2.08527 0.380716
\(31\) 3.46104 0.621622 0.310811 0.950472i \(-0.399399\pi\)
0.310811 + 0.950472i \(0.399399\pi\)
\(32\) −23.6420 −4.17935
\(33\) −1.08918 −0.189601
\(34\) −11.9751 −2.05372
\(35\) −0.177802 −0.0300540
\(36\) 27.8340 4.63899
\(37\) −7.57075 −1.24462 −0.622312 0.782769i \(-0.713806\pi\)
−0.622312 + 0.782769i \(0.713806\pi\)
\(38\) 1.23397 0.200177
\(39\) −16.3174 −2.61288
\(40\) 2.61497 0.413463
\(41\) −2.18675 −0.341514 −0.170757 0.985313i \(-0.554621\pi\)
−0.170757 + 0.985313i \(0.554621\pi\)
\(42\) −5.15981 −0.796176
\(43\) 2.89706 0.441798 0.220899 0.975297i \(-0.429101\pi\)
0.220899 + 0.975297i \(0.429101\pi\)
\(44\) −2.13530 −0.321909
\(45\) −1.34430 −0.200397
\(46\) 19.1966 2.83038
\(47\) −11.2441 −1.64012 −0.820061 0.572276i \(-0.806061\pi\)
−0.820061 + 0.572276i \(0.806061\pi\)
\(48\) 44.4605 6.41732
\(49\) −6.56005 −0.937149
\(50\) 13.5414 1.91504
\(51\) 12.3382 1.72769
\(52\) −31.9898 −4.43619
\(53\) 8.78614 1.20687 0.603435 0.797412i \(-0.293798\pi\)
0.603435 + 0.797412i \(0.293798\pi\)
\(54\) −15.6743 −2.13301
\(55\) 0.103129 0.0139059
\(56\) −6.47052 −0.864660
\(57\) −1.27138 −0.168398
\(58\) −23.8939 −3.13742
\(59\) −2.66440 −0.346875 −0.173437 0.984845i \(-0.555487\pi\)
−0.173437 + 0.984845i \(0.555487\pi\)
\(60\) −4.21203 −0.543771
\(61\) −7.78497 −0.996764 −0.498382 0.866958i \(-0.666072\pi\)
−0.498382 + 0.866958i \(0.666072\pi\)
\(62\) −9.51014 −1.20779
\(63\) 3.32636 0.419082
\(64\) 33.5536 4.19420
\(65\) 1.54502 0.191636
\(66\) 2.99280 0.368389
\(67\) −14.3711 −1.75571 −0.877855 0.478927i \(-0.841026\pi\)
−0.877855 + 0.478927i \(0.841026\pi\)
\(68\) 24.1886 2.93330
\(69\) −19.7785 −2.38105
\(70\) 0.488558 0.0583938
\(71\) 10.8117 1.28312 0.641558 0.767074i \(-0.278288\pi\)
0.641558 + 0.767074i \(0.278288\pi\)
\(72\) −48.9215 −5.76546
\(73\) −9.56377 −1.11935 −0.559677 0.828711i \(-0.689075\pi\)
−0.559677 + 0.828711i \(0.689075\pi\)
\(74\) 20.8027 2.41826
\(75\) −13.9519 −1.61103
\(76\) −2.49250 −0.285910
\(77\) −0.255184 −0.0290809
\(78\) 44.8364 5.07673
\(79\) 2.68890 0.302525 0.151263 0.988494i \(-0.451666\pi\)
0.151263 + 0.988494i \(0.451666\pi\)
\(80\) −4.20975 −0.470664
\(81\) 1.10472 0.122747
\(82\) 6.00869 0.663549
\(83\) −10.9813 −1.20536 −0.602680 0.797983i \(-0.705900\pi\)
−0.602680 + 0.797983i \(0.705900\pi\)
\(84\) 10.4223 1.13717
\(85\) −1.16824 −0.126713
\(86\) −7.96046 −0.858398
\(87\) 24.6182 2.63935
\(88\) 3.75305 0.400076
\(89\) 12.7262 1.34897 0.674486 0.738288i \(-0.264365\pi\)
0.674486 + 0.738288i \(0.264365\pi\)
\(90\) 3.69383 0.389363
\(91\) −3.82301 −0.400760
\(92\) −38.7752 −4.04259
\(93\) 9.79844 1.01605
\(94\) 30.8962 3.18670
\(95\) 0.120381 0.0123508
\(96\) −66.9320 −6.83122
\(97\) −11.9138 −1.20966 −0.604831 0.796354i \(-0.706759\pi\)
−0.604831 + 0.796354i \(0.706759\pi\)
\(98\) 18.0255 1.82085
\(99\) −1.92936 −0.193908
\(100\) −27.3523 −2.73523
\(101\) 10.3128 1.02616 0.513081 0.858340i \(-0.328504\pi\)
0.513081 + 0.858340i \(0.328504\pi\)
\(102\) −33.9024 −3.35683
\(103\) −4.82667 −0.475586 −0.237793 0.971316i \(-0.576424\pi\)
−0.237793 + 0.971316i \(0.576424\pi\)
\(104\) 56.2259 5.51341
\(105\) −0.503368 −0.0491237
\(106\) −24.1423 −2.34491
\(107\) 17.4002 1.68214 0.841070 0.540927i \(-0.181926\pi\)
0.841070 + 0.540927i \(0.181926\pi\)
\(108\) 31.6606 3.04655
\(109\) 13.1502 1.25956 0.629781 0.776773i \(-0.283145\pi\)
0.629781 + 0.776773i \(0.283145\pi\)
\(110\) −0.283374 −0.0270187
\(111\) −21.4333 −2.03436
\(112\) 10.4167 0.984282
\(113\) 1.50871 0.141928 0.0709639 0.997479i \(-0.477392\pi\)
0.0709639 + 0.997479i \(0.477392\pi\)
\(114\) 3.49345 0.327192
\(115\) 1.87273 0.174633
\(116\) 48.2633 4.48114
\(117\) −28.9045 −2.67223
\(118\) 7.32114 0.673965
\(119\) 2.89071 0.264991
\(120\) 7.40316 0.675813
\(121\) −10.8520 −0.986544
\(122\) 21.3913 1.93668
\(123\) −6.19084 −0.558210
\(124\) 19.2096 1.72507
\(125\) 2.66134 0.238037
\(126\) −9.14005 −0.814261
\(127\) −3.14345 −0.278936 −0.139468 0.990227i \(-0.544539\pi\)
−0.139468 + 0.990227i \(0.544539\pi\)
\(128\) −44.9136 −3.96984
\(129\) 8.20178 0.722126
\(130\) −4.24534 −0.372341
\(131\) −6.34072 −0.553991 −0.276996 0.960871i \(-0.589339\pi\)
−0.276996 + 0.960871i \(0.589339\pi\)
\(132\) −6.04517 −0.526165
\(133\) −0.297872 −0.0258288
\(134\) 39.4884 3.41128
\(135\) −1.52912 −0.131606
\(136\) −42.5144 −3.64558
\(137\) −13.1477 −1.12328 −0.561641 0.827381i \(-0.689830\pi\)
−0.561641 + 0.827381i \(0.689830\pi\)
\(138\) 54.3467 4.62630
\(139\) −9.10485 −0.772263 −0.386132 0.922444i \(-0.626189\pi\)
−0.386132 + 0.922444i \(0.626189\pi\)
\(140\) −0.986839 −0.0834031
\(141\) −31.8328 −2.68081
\(142\) −29.7081 −2.49305
\(143\) 2.21743 0.185431
\(144\) 78.7570 6.56309
\(145\) −2.33098 −0.193577
\(146\) 26.2790 2.17487
\(147\) −18.5719 −1.53179
\(148\) −42.0193 −3.45397
\(149\) −18.3745 −1.50530 −0.752648 0.658423i \(-0.771224\pi\)
−0.752648 + 0.658423i \(0.771224\pi\)
\(150\) 38.3366 3.13017
\(151\) 14.5444 1.18361 0.591803 0.806082i \(-0.298416\pi\)
0.591803 + 0.806082i \(0.298416\pi\)
\(152\) 4.38087 0.355336
\(153\) 21.8557 1.76693
\(154\) 0.701185 0.0565031
\(155\) −0.927767 −0.0745200
\(156\) −90.5652 −7.25102
\(157\) 22.9546 1.83198 0.915990 0.401201i \(-0.131407\pi\)
0.915990 + 0.401201i \(0.131407\pi\)
\(158\) −7.38848 −0.587796
\(159\) 24.8741 1.97265
\(160\) 6.33747 0.501021
\(161\) −4.63391 −0.365203
\(162\) −3.03551 −0.238493
\(163\) 0.356555 0.0279275 0.0139638 0.999903i \(-0.495555\pi\)
0.0139638 + 0.999903i \(0.495555\pi\)
\(164\) −12.1370 −0.947738
\(165\) 0.291965 0.0227294
\(166\) 30.1742 2.34197
\(167\) −6.51146 −0.503872 −0.251936 0.967744i \(-0.581067\pi\)
−0.251936 + 0.967744i \(0.581067\pi\)
\(168\) −18.3185 −1.41330
\(169\) 20.2202 1.55540
\(170\) 3.21005 0.246200
\(171\) −2.25211 −0.172223
\(172\) 16.0794 1.22604
\(173\) −22.2534 −1.69190 −0.845948 0.533266i \(-0.820964\pi\)
−0.845948 + 0.533266i \(0.820964\pi\)
\(174\) −67.6452 −5.12817
\(175\) −3.26879 −0.247098
\(176\) −6.04190 −0.455425
\(177\) −7.54308 −0.566972
\(178\) −34.9686 −2.62100
\(179\) 9.48252 0.708757 0.354379 0.935102i \(-0.384692\pi\)
0.354379 + 0.935102i \(0.384692\pi\)
\(180\) −7.46117 −0.556123
\(181\) −12.1978 −0.906658 −0.453329 0.891343i \(-0.649764\pi\)
−0.453329 + 0.891343i \(0.649764\pi\)
\(182\) 10.5047 0.778663
\(183\) −22.0398 −1.62923
\(184\) 68.1521 5.02424
\(185\) 2.02941 0.149206
\(186\) −26.9238 −1.97415
\(187\) −1.67668 −0.122611
\(188\) −62.4073 −4.55152
\(189\) 3.78367 0.275222
\(190\) −0.330778 −0.0239972
\(191\) −16.5971 −1.20093 −0.600463 0.799653i \(-0.705017\pi\)
−0.600463 + 0.799653i \(0.705017\pi\)
\(192\) 94.9925 6.85549
\(193\) 0.940517 0.0676999 0.0338499 0.999427i \(-0.489223\pi\)
0.0338499 + 0.999427i \(0.489223\pi\)
\(194\) 32.7363 2.35033
\(195\) 4.37404 0.313232
\(196\) −36.4097 −2.60069
\(197\) 18.2047 1.29703 0.648515 0.761202i \(-0.275390\pi\)
0.648515 + 0.761202i \(0.275390\pi\)
\(198\) 5.30143 0.376756
\(199\) −26.0927 −1.84966 −0.924830 0.380382i \(-0.875793\pi\)
−0.924830 + 0.380382i \(0.875793\pi\)
\(200\) 48.0749 3.39941
\(201\) −40.6855 −2.86973
\(202\) −28.3372 −1.99380
\(203\) 5.76781 0.404821
\(204\) 68.4795 4.79452
\(205\) 0.586181 0.0409407
\(206\) 13.2626 0.924046
\(207\) −35.0355 −2.43514
\(208\) −90.5161 −6.27616
\(209\) 0.172772 0.0119509
\(210\) 1.38314 0.0954456
\(211\) 7.01319 0.482808 0.241404 0.970425i \(-0.422392\pi\)
0.241404 + 0.970425i \(0.422392\pi\)
\(212\) 48.7650 3.34920
\(213\) 30.6087 2.09727
\(214\) −47.8116 −3.26834
\(215\) −0.776587 −0.0529628
\(216\) −55.6474 −3.78632
\(217\) 2.29568 0.155841
\(218\) −36.1337 −2.44728
\(219\) −27.0756 −1.82960
\(220\) 0.572388 0.0385904
\(221\) −25.1190 −1.68968
\(222\) 58.8937 3.95268
\(223\) −7.35233 −0.492349 −0.246174 0.969226i \(-0.579174\pi\)
−0.246174 + 0.969226i \(0.579174\pi\)
\(224\) −15.6815 −1.04777
\(225\) −24.7143 −1.64762
\(226\) −4.14559 −0.275761
\(227\) −6.32180 −0.419592 −0.209796 0.977745i \(-0.567280\pi\)
−0.209796 + 0.977745i \(0.567280\pi\)
\(228\) −7.05644 −0.467324
\(229\) −8.49816 −0.561574 −0.280787 0.959770i \(-0.590596\pi\)
−0.280787 + 0.959770i \(0.590596\pi\)
\(230\) −5.14583 −0.339306
\(231\) −0.722441 −0.0475332
\(232\) −84.8286 −5.56927
\(233\) 4.34378 0.284570 0.142285 0.989826i \(-0.454555\pi\)
0.142285 + 0.989826i \(0.454555\pi\)
\(234\) 79.4229 5.19204
\(235\) 3.01409 0.196618
\(236\) −14.7880 −0.962616
\(237\) 7.61246 0.494482
\(238\) −7.94299 −0.514868
\(239\) 11.0112 0.712253 0.356127 0.934438i \(-0.384097\pi\)
0.356127 + 0.934438i \(0.384097\pi\)
\(240\) −11.9181 −0.769309
\(241\) −28.1245 −1.81166 −0.905830 0.423642i \(-0.860751\pi\)
−0.905830 + 0.423642i \(0.860751\pi\)
\(242\) 29.8187 1.91682
\(243\) −13.9856 −0.897179
\(244\) −43.2083 −2.76613
\(245\) 1.75848 0.112345
\(246\) 17.0110 1.08458
\(247\) 2.58837 0.164694
\(248\) −33.7631 −2.14396
\(249\) −31.0889 −1.97018
\(250\) −7.31273 −0.462498
\(251\) −19.8691 −1.25413 −0.627063 0.778969i \(-0.715743\pi\)
−0.627063 + 0.778969i \(0.715743\pi\)
\(252\) 18.4620 1.16300
\(253\) 2.68777 0.168979
\(254\) 8.63748 0.541964
\(255\) −3.30736 −0.207115
\(256\) 56.3048 3.51905
\(257\) −23.1575 −1.44453 −0.722263 0.691619i \(-0.756898\pi\)
−0.722263 + 0.691619i \(0.756898\pi\)
\(258\) −22.5366 −1.40307
\(259\) −5.02161 −0.312028
\(260\) 8.57518 0.531810
\(261\) 43.6086 2.69930
\(262\) 17.4228 1.07639
\(263\) 8.06607 0.497375 0.248687 0.968584i \(-0.420001\pi\)
0.248687 + 0.968584i \(0.420001\pi\)
\(264\) 10.6251 0.653931
\(265\) −2.35521 −0.144680
\(266\) 0.818483 0.0501844
\(267\) 36.0286 2.20492
\(268\) −79.7628 −4.87229
\(269\) 5.08067 0.309774 0.154887 0.987932i \(-0.450499\pi\)
0.154887 + 0.987932i \(0.450499\pi\)
\(270\) 4.20166 0.255705
\(271\) 23.0088 1.39769 0.698843 0.715275i \(-0.253699\pi\)
0.698843 + 0.715275i \(0.253699\pi\)
\(272\) 68.4423 4.14993
\(273\) −10.8232 −0.655049
\(274\) 36.1267 2.18250
\(275\) 1.89597 0.114331
\(276\) −109.775 −6.60769
\(277\) −4.15471 −0.249632 −0.124816 0.992180i \(-0.539834\pi\)
−0.124816 + 0.992180i \(0.539834\pi\)
\(278\) 25.0180 1.50048
\(279\) 17.3569 1.03913
\(280\) 1.73449 0.103655
\(281\) −1.15765 −0.0690598 −0.0345299 0.999404i \(-0.510993\pi\)
−0.0345299 + 0.999404i \(0.510993\pi\)
\(282\) 87.4691 5.20871
\(283\) 6.61994 0.393515 0.196757 0.980452i \(-0.436959\pi\)
0.196757 + 0.980452i \(0.436959\pi\)
\(284\) 60.0075 3.56079
\(285\) 0.340806 0.0201876
\(286\) −6.09298 −0.360286
\(287\) −1.45045 −0.0856176
\(288\) −118.563 −6.98638
\(289\) 1.99331 0.117253
\(290\) 6.40499 0.376114
\(291\) −33.7287 −1.97721
\(292\) −53.0810 −3.10633
\(293\) −21.8019 −1.27368 −0.636839 0.770997i \(-0.719758\pi\)
−0.636839 + 0.770997i \(0.719758\pi\)
\(294\) 51.0313 2.97620
\(295\) 0.714218 0.0415834
\(296\) 73.8540 4.29268
\(297\) −2.19461 −0.127344
\(298\) 50.4888 2.92474
\(299\) 40.2666 2.32868
\(300\) −77.4361 −4.47078
\(301\) 1.92160 0.110759
\(302\) −39.9646 −2.29971
\(303\) 29.1962 1.67728
\(304\) −7.05261 −0.404495
\(305\) 2.08684 0.119492
\(306\) −60.0544 −3.43308
\(307\) 8.58297 0.489856 0.244928 0.969541i \(-0.421236\pi\)
0.244928 + 0.969541i \(0.421236\pi\)
\(308\) −1.41633 −0.0807026
\(309\) −13.6646 −0.777352
\(310\) 2.54929 0.144790
\(311\) 19.9813 1.13304 0.566518 0.824049i \(-0.308290\pi\)
0.566518 + 0.824049i \(0.308290\pi\)
\(312\) 159.179 9.01175
\(313\) 31.5208 1.78166 0.890831 0.454335i \(-0.150123\pi\)
0.890831 + 0.454335i \(0.150123\pi\)
\(314\) −63.0740 −3.55947
\(315\) −0.891663 −0.0502395
\(316\) 14.9240 0.839541
\(317\) −19.4533 −1.09260 −0.546302 0.837588i \(-0.683965\pi\)
−0.546302 + 0.837588i \(0.683965\pi\)
\(318\) −68.3483 −3.83278
\(319\) −3.34546 −0.187310
\(320\) −8.99438 −0.502801
\(321\) 49.2610 2.74948
\(322\) 12.7329 0.709577
\(323\) −1.95716 −0.108899
\(324\) 6.13144 0.340636
\(325\) 28.4043 1.57559
\(326\) −0.979730 −0.0542622
\(327\) 37.2291 2.05877
\(328\) 21.3322 1.17787
\(329\) −7.45812 −0.411179
\(330\) −0.802251 −0.0441625
\(331\) −19.6916 −1.08235 −0.541174 0.840911i \(-0.682020\pi\)
−0.541174 + 0.840911i \(0.682020\pi\)
\(332\) −60.9489 −3.34501
\(333\) −37.9668 −2.08057
\(334\) 17.8920 0.979005
\(335\) 3.85232 0.210474
\(336\) 29.4903 1.60883
\(337\) −22.2381 −1.21139 −0.605694 0.795697i \(-0.707105\pi\)
−0.605694 + 0.795697i \(0.707105\pi\)
\(338\) −55.5605 −3.02209
\(339\) 4.27127 0.231983
\(340\) −6.48399 −0.351644
\(341\) −1.33155 −0.0721072
\(342\) 6.18828 0.334624
\(343\) −8.99426 −0.485644
\(344\) −28.2614 −1.52375
\(345\) 5.30182 0.285441
\(346\) 61.1472 3.28729
\(347\) 6.06202 0.325426 0.162713 0.986673i \(-0.447976\pi\)
0.162713 + 0.986673i \(0.447976\pi\)
\(348\) 136.637 7.32449
\(349\) −3.33798 −0.178678 −0.0893391 0.996001i \(-0.528475\pi\)
−0.0893391 + 0.996001i \(0.528475\pi\)
\(350\) 8.98188 0.480102
\(351\) −32.8784 −1.75492
\(352\) 9.09563 0.484799
\(353\) −14.4259 −0.767814 −0.383907 0.923372i \(-0.625422\pi\)
−0.383907 + 0.923372i \(0.625422\pi\)
\(354\) 20.7266 1.10161
\(355\) −2.89819 −0.153820
\(356\) 70.6331 3.74355
\(357\) 8.18378 0.433132
\(358\) −26.0558 −1.37709
\(359\) −0.923414 −0.0487359 −0.0243680 0.999703i \(-0.507757\pi\)
−0.0243680 + 0.999703i \(0.507757\pi\)
\(360\) 13.1139 0.691163
\(361\) −18.7983 −0.989386
\(362\) 33.5168 1.76160
\(363\) −30.7227 −1.61252
\(364\) −21.2186 −1.11215
\(365\) 2.56366 0.134188
\(366\) 60.5601 3.16553
\(367\) 23.1871 1.21036 0.605178 0.796090i \(-0.293102\pi\)
0.605178 + 0.796090i \(0.293102\pi\)
\(368\) −109.716 −5.71932
\(369\) −10.9664 −0.570889
\(370\) −5.57636 −0.289901
\(371\) 5.82777 0.302563
\(372\) 54.3835 2.81965
\(373\) 8.19879 0.424517 0.212259 0.977214i \(-0.431918\pi\)
0.212259 + 0.977214i \(0.431918\pi\)
\(374\) 4.60711 0.238228
\(375\) 7.53442 0.389076
\(376\) 109.688 5.65674
\(377\) −50.1197 −2.58130
\(378\) −10.3966 −0.534746
\(379\) −7.74294 −0.397728 −0.198864 0.980027i \(-0.563725\pi\)
−0.198864 + 0.980027i \(0.563725\pi\)
\(380\) 0.668140 0.0342749
\(381\) −8.89932 −0.455926
\(382\) 45.6050 2.33336
\(383\) 13.0305 0.665825 0.332913 0.942958i \(-0.391969\pi\)
0.332913 + 0.942958i \(0.391969\pi\)
\(384\) −127.153 −6.48876
\(385\) 0.0684045 0.00348622
\(386\) −2.58432 −0.131538
\(387\) 14.5286 0.738529
\(388\) −66.1242 −3.35695
\(389\) −1.85451 −0.0940274 −0.0470137 0.998894i \(-0.514970\pi\)
−0.0470137 + 0.998894i \(0.514970\pi\)
\(390\) −12.0188 −0.608598
\(391\) −30.4470 −1.53977
\(392\) 63.9944 3.23221
\(393\) −17.9510 −0.905508
\(394\) −50.0222 −2.52008
\(395\) −0.720787 −0.0362667
\(396\) −10.7084 −0.538116
\(397\) 34.9991 1.75655 0.878276 0.478154i \(-0.158694\pi\)
0.878276 + 0.478154i \(0.158694\pi\)
\(398\) 71.6965 3.59382
\(399\) −0.843295 −0.0422175
\(400\) −77.3941 −3.86971
\(401\) 22.6706 1.13212 0.566059 0.824365i \(-0.308467\pi\)
0.566059 + 0.824365i \(0.308467\pi\)
\(402\) 111.794 5.57579
\(403\) −19.9484 −0.993702
\(404\) 57.2384 2.84772
\(405\) −0.296131 −0.0147149
\(406\) −15.8486 −0.786553
\(407\) 2.91265 0.144374
\(408\) −120.361 −5.95875
\(409\) 8.79769 0.435018 0.217509 0.976058i \(-0.430207\pi\)
0.217509 + 0.976058i \(0.430207\pi\)
\(410\) −1.61069 −0.0795463
\(411\) −37.2219 −1.83602
\(412\) −26.7891 −1.31980
\(413\) −1.76727 −0.0869617
\(414\) 96.2694 4.73138
\(415\) 2.94366 0.144499
\(416\) 136.265 6.68096
\(417\) −25.7764 −1.26228
\(418\) −0.474738 −0.0232202
\(419\) −1.83358 −0.0895762 −0.0447881 0.998997i \(-0.514261\pi\)
−0.0447881 + 0.998997i \(0.514261\pi\)
\(420\) −2.79380 −0.136324
\(421\) −11.2603 −0.548796 −0.274398 0.961616i \(-0.588479\pi\)
−0.274398 + 0.961616i \(0.588479\pi\)
\(422\) −19.2706 −0.938078
\(423\) −56.3884 −2.74170
\(424\) −85.7104 −4.16247
\(425\) −21.4775 −1.04181
\(426\) −84.1056 −4.07493
\(427\) −5.16370 −0.249889
\(428\) 96.5749 4.66812
\(429\) 6.27769 0.303090
\(430\) 2.13388 0.102905
\(431\) 29.3399 1.41326 0.706628 0.707586i \(-0.250216\pi\)
0.706628 + 0.707586i \(0.250216\pi\)
\(432\) 89.5847 4.31015
\(433\) 35.6164 1.71161 0.855807 0.517295i \(-0.173061\pi\)
0.855807 + 0.517295i \(0.173061\pi\)
\(434\) −6.30799 −0.302793
\(435\) −6.59916 −0.316406
\(436\) 72.9866 3.49543
\(437\) 3.13740 0.150082
\(438\) 74.3975 3.55485
\(439\) 27.6024 1.31739 0.658695 0.752410i \(-0.271109\pi\)
0.658695 + 0.752410i \(0.271109\pi\)
\(440\) −1.00604 −0.0479611
\(441\) −32.8982 −1.56658
\(442\) 69.0210 3.28300
\(443\) −28.2081 −1.34021 −0.670104 0.742267i \(-0.733751\pi\)
−0.670104 + 0.742267i \(0.733751\pi\)
\(444\) −118.959 −5.64557
\(445\) −3.41138 −0.161715
\(446\) 20.2025 0.956616
\(447\) −52.0193 −2.46043
\(448\) 22.2558 1.05149
\(449\) 19.7510 0.932109 0.466054 0.884756i \(-0.345675\pi\)
0.466054 + 0.884756i \(0.345675\pi\)
\(450\) 67.9091 3.20127
\(451\) 0.841296 0.0396151
\(452\) 8.37370 0.393866
\(453\) 41.1761 1.93462
\(454\) 17.3708 0.815253
\(455\) 1.02480 0.0480432
\(456\) 12.4025 0.580802
\(457\) 22.4530 1.05031 0.525155 0.851007i \(-0.324007\pi\)
0.525155 + 0.851007i \(0.324007\pi\)
\(458\) 23.3510 1.09112
\(459\) 24.8605 1.16039
\(460\) 10.3941 0.484626
\(461\) 31.8776 1.48469 0.742345 0.670018i \(-0.233714\pi\)
0.742345 + 0.670018i \(0.233714\pi\)
\(462\) 1.98510 0.0923552
\(463\) −28.7756 −1.33731 −0.668657 0.743571i \(-0.733130\pi\)
−0.668657 + 0.743571i \(0.733130\pi\)
\(464\) 136.563 6.33976
\(465\) −2.62657 −0.121804
\(466\) −11.9357 −0.552910
\(467\) 10.8971 0.504257 0.252128 0.967694i \(-0.418869\pi\)
0.252128 + 0.967694i \(0.418869\pi\)
\(468\) −160.427 −7.41572
\(469\) −9.53222 −0.440157
\(470\) −8.28203 −0.382022
\(471\) 64.9861 2.99440
\(472\) 25.9917 1.19636
\(473\) −1.11457 −0.0512479
\(474\) −20.9173 −0.960762
\(475\) 2.21314 0.101546
\(476\) 16.0441 0.735379
\(477\) 44.0619 2.01746
\(478\) −30.2561 −1.38388
\(479\) 20.8436 0.952369 0.476185 0.879345i \(-0.342019\pi\)
0.476185 + 0.879345i \(0.342019\pi\)
\(480\) 17.9418 0.818927
\(481\) 43.6355 1.98961
\(482\) 77.2796 3.51999
\(483\) −13.1189 −0.596931
\(484\) −60.2309 −2.73777
\(485\) 3.19361 0.145014
\(486\) 38.4293 1.74319
\(487\) −16.1589 −0.732229 −0.366115 0.930570i \(-0.619312\pi\)
−0.366115 + 0.930570i \(0.619312\pi\)
\(488\) 75.9438 3.43782
\(489\) 1.00943 0.0456480
\(490\) −4.83191 −0.218283
\(491\) −36.7588 −1.65890 −0.829450 0.558581i \(-0.811346\pi\)
−0.829450 + 0.558581i \(0.811346\pi\)
\(492\) −34.3606 −1.54909
\(493\) 37.8972 1.70680
\(494\) −7.11224 −0.319995
\(495\) 0.517184 0.0232457
\(496\) 54.3540 2.44057
\(497\) 7.17132 0.321678
\(498\) 85.4251 3.82799
\(499\) 19.7333 0.883384 0.441692 0.897167i \(-0.354378\pi\)
0.441692 + 0.897167i \(0.354378\pi\)
\(500\) 14.7710 0.660580
\(501\) −18.4344 −0.823587
\(502\) 54.5956 2.43672
\(503\) 35.2246 1.57059 0.785294 0.619123i \(-0.212512\pi\)
0.785294 + 0.619123i \(0.212512\pi\)
\(504\) −32.4492 −1.44540
\(505\) −2.76445 −0.123016
\(506\) −7.38537 −0.328320
\(507\) 57.2448 2.54233
\(508\) −17.4469 −0.774080
\(509\) −0.00929338 −0.000411922 0 −0.000205961 1.00000i \(-0.500066\pi\)
−0.000205961 1.00000i \(0.500066\pi\)
\(510\) 9.08786 0.402417
\(511\) −6.34356 −0.280623
\(512\) −64.8852 −2.86755
\(513\) −2.56174 −0.113104
\(514\) 63.6314 2.80666
\(515\) 1.29384 0.0570132
\(516\) 45.5217 2.00398
\(517\) 4.32587 0.190252
\(518\) 13.7982 0.606259
\(519\) −63.0008 −2.76543
\(520\) −15.0719 −0.660947
\(521\) 2.27695 0.0997549 0.0498774 0.998755i \(-0.484117\pi\)
0.0498774 + 0.998755i \(0.484117\pi\)
\(522\) −119.826 −5.24465
\(523\) −5.79464 −0.253382 −0.126691 0.991942i \(-0.540436\pi\)
−0.126691 + 0.991942i \(0.540436\pi\)
\(524\) −35.1924 −1.53739
\(525\) −9.25417 −0.403885
\(526\) −22.1637 −0.966382
\(527\) 15.0837 0.657056
\(528\) −17.1050 −0.744400
\(529\) 25.8076 1.12207
\(530\) 6.47157 0.281107
\(531\) −13.3618 −0.579851
\(532\) −1.65326 −0.0716777
\(533\) 12.6038 0.545931
\(534\) −98.9982 −4.28407
\(535\) −4.66429 −0.201655
\(536\) 140.193 6.05540
\(537\) 26.8456 1.15847
\(538\) −13.9605 −0.601879
\(539\) 2.52380 0.108708
\(540\) −8.48695 −0.365220
\(541\) −29.4409 −1.26576 −0.632881 0.774249i \(-0.718128\pi\)
−0.632881 + 0.774249i \(0.718128\pi\)
\(542\) −63.2229 −2.71565
\(543\) −34.5329 −1.48195
\(544\) −103.035 −4.41758
\(545\) −3.52505 −0.150996
\(546\) 29.7396 1.27274
\(547\) −22.4891 −0.961563 −0.480781 0.876840i \(-0.659647\pi\)
−0.480781 + 0.876840i \(0.659647\pi\)
\(548\) −72.9725 −3.11723
\(549\) −39.0411 −1.66623
\(550\) −5.20969 −0.222142
\(551\) −3.90510 −0.166363
\(552\) 192.943 8.21220
\(553\) 1.78353 0.0758432
\(554\) 11.4162 0.485026
\(555\) 5.74540 0.243879
\(556\) −50.5339 −2.14312
\(557\) −17.9008 −0.758480 −0.379240 0.925298i \(-0.623815\pi\)
−0.379240 + 0.925298i \(0.623815\pi\)
\(558\) −47.6927 −2.01899
\(559\) −16.6978 −0.706242
\(560\) −2.79229 −0.117996
\(561\) −4.74678 −0.200409
\(562\) 3.18096 0.134181
\(563\) 22.5847 0.951833 0.475917 0.879490i \(-0.342116\pi\)
0.475917 + 0.879490i \(0.342116\pi\)
\(564\) −176.679 −7.43953
\(565\) −0.404426 −0.0170143
\(566\) −18.1901 −0.764585
\(567\) 0.732751 0.0307727
\(568\) −105.470 −4.42544
\(569\) −5.26548 −0.220740 −0.110370 0.993891i \(-0.535204\pi\)
−0.110370 + 0.993891i \(0.535204\pi\)
\(570\) −0.936455 −0.0392238
\(571\) −39.5292 −1.65424 −0.827122 0.562023i \(-0.810023\pi\)
−0.827122 + 0.562023i \(0.810023\pi\)
\(572\) 12.3072 0.514591
\(573\) −46.9875 −1.96293
\(574\) 3.98551 0.166352
\(575\) 34.4292 1.43580
\(576\) 168.269 7.01121
\(577\) −9.67339 −0.402709 −0.201354 0.979518i \(-0.564534\pi\)
−0.201354 + 0.979518i \(0.564534\pi\)
\(578\) −5.47714 −0.227819
\(579\) 2.66266 0.110657
\(580\) −12.9375 −0.537199
\(581\) −7.28383 −0.302184
\(582\) 92.6787 3.84165
\(583\) −3.38024 −0.139995
\(584\) 93.2963 3.86063
\(585\) 7.74815 0.320346
\(586\) 59.9064 2.47471
\(587\) −23.0707 −0.952231 −0.476115 0.879383i \(-0.657956\pi\)
−0.476115 + 0.879383i \(0.657956\pi\)
\(588\) −103.078 −4.25087
\(589\) −1.55429 −0.0640435
\(590\) −1.96250 −0.0807950
\(591\) 51.5386 2.12002
\(592\) −118.895 −4.88655
\(593\) 36.1559 1.48475 0.742373 0.669987i \(-0.233700\pi\)
0.742373 + 0.669987i \(0.233700\pi\)
\(594\) 6.03029 0.247426
\(595\) −0.774883 −0.0317671
\(596\) −101.982 −4.17736
\(597\) −73.8700 −3.02330
\(598\) −110.643 −4.52454
\(599\) −19.1886 −0.784025 −0.392013 0.919960i \(-0.628221\pi\)
−0.392013 + 0.919960i \(0.628221\pi\)
\(600\) 136.103 5.55639
\(601\) −26.2190 −1.06950 −0.534748 0.845012i \(-0.679594\pi\)
−0.534748 + 0.845012i \(0.679594\pi\)
\(602\) −5.28010 −0.215201
\(603\) −72.0700 −2.93492
\(604\) 80.7246 3.28464
\(605\) 2.90898 0.118267
\(606\) −80.2244 −3.25889
\(607\) 18.2805 0.741983 0.370992 0.928636i \(-0.379018\pi\)
0.370992 + 0.928636i \(0.379018\pi\)
\(608\) 10.6172 0.430584
\(609\) 16.3291 0.661687
\(610\) −5.73415 −0.232169
\(611\) 64.8077 2.62184
\(612\) 121.304 4.90343
\(613\) 23.8259 0.962319 0.481160 0.876633i \(-0.340216\pi\)
0.481160 + 0.876633i \(0.340216\pi\)
\(614\) −23.5840 −0.951773
\(615\) 1.65952 0.0669182
\(616\) 2.48936 0.100299
\(617\) −36.0198 −1.45010 −0.725052 0.688694i \(-0.758184\pi\)
−0.725052 + 0.688694i \(0.758184\pi\)
\(618\) 37.5472 1.51037
\(619\) −24.3879 −0.980232 −0.490116 0.871657i \(-0.663046\pi\)
−0.490116 + 0.871657i \(0.663046\pi\)
\(620\) −5.14931 −0.206801
\(621\) −39.8523 −1.59922
\(622\) −54.9040 −2.20145
\(623\) 8.44116 0.338188
\(624\) −256.257 −10.2585
\(625\) 23.9273 0.957093
\(626\) −86.6118 −3.46170
\(627\) 0.489130 0.0195340
\(628\) 127.403 5.08395
\(629\) −32.9943 −1.31557
\(630\) 2.45008 0.0976136
\(631\) −28.1607 −1.12106 −0.560530 0.828134i \(-0.689403\pi\)
−0.560530 + 0.828134i \(0.689403\pi\)
\(632\) −26.2307 −1.04340
\(633\) 19.8548 0.789157
\(634\) 53.4530 2.12289
\(635\) 0.842634 0.0334389
\(636\) 138.057 5.47432
\(637\) 37.8101 1.49809
\(638\) 9.19254 0.363936
\(639\) 54.2201 2.14491
\(640\) 12.0395 0.475904
\(641\) −13.7269 −0.542182 −0.271091 0.962554i \(-0.587384\pi\)
−0.271091 + 0.962554i \(0.587384\pi\)
\(642\) −135.358 −5.34215
\(643\) 24.3853 0.961661 0.480830 0.876814i \(-0.340335\pi\)
0.480830 + 0.876814i \(0.340335\pi\)
\(644\) −25.7192 −1.01348
\(645\) −2.19857 −0.0865685
\(646\) 5.37781 0.211587
\(647\) −2.39454 −0.0941390 −0.0470695 0.998892i \(-0.514988\pi\)
−0.0470695 + 0.998892i \(0.514988\pi\)
\(648\) −10.7768 −0.423351
\(649\) 1.02506 0.0402370
\(650\) −78.0485 −3.06131
\(651\) 6.49922 0.254724
\(652\) 1.97896 0.0775020
\(653\) 2.52179 0.0986853 0.0493427 0.998782i \(-0.484287\pi\)
0.0493427 + 0.998782i \(0.484287\pi\)
\(654\) −102.297 −4.00013
\(655\) 1.69969 0.0664125
\(656\) −34.3419 −1.34083
\(657\) −47.9616 −1.87116
\(658\) 20.4932 0.798907
\(659\) −13.4172 −0.522660 −0.261330 0.965249i \(-0.584161\pi\)
−0.261330 + 0.965249i \(0.584161\pi\)
\(660\) 1.62047 0.0630767
\(661\) −32.0390 −1.24617 −0.623086 0.782153i \(-0.714122\pi\)
−0.623086 + 0.782153i \(0.714122\pi\)
\(662\) 54.1079 2.10296
\(663\) −71.1134 −2.76182
\(664\) 107.125 4.15726
\(665\) 0.0798475 0.00309635
\(666\) 104.324 4.04247
\(667\) −60.7506 −2.35227
\(668\) −36.1400 −1.39830
\(669\) −20.8149 −0.804752
\(670\) −10.5853 −0.408944
\(671\) 2.99506 0.115623
\(672\) −44.3954 −1.71259
\(673\) −22.0019 −0.848112 −0.424056 0.905636i \(-0.639394\pi\)
−0.424056 + 0.905636i \(0.639394\pi\)
\(674\) 61.1052 2.35369
\(675\) −28.1121 −1.08203
\(676\) 112.227 4.31641
\(677\) −2.82608 −0.108615 −0.0543075 0.998524i \(-0.517295\pi\)
−0.0543075 + 0.998524i \(0.517295\pi\)
\(678\) −11.7364 −0.450736
\(679\) −7.90231 −0.303263
\(680\) 11.3964 0.437032
\(681\) −17.8974 −0.685830
\(682\) 3.65878 0.140102
\(683\) −0.781159 −0.0298902 −0.0149451 0.999888i \(-0.504757\pi\)
−0.0149451 + 0.999888i \(0.504757\pi\)
\(684\) −12.4997 −0.477939
\(685\) 3.52436 0.134659
\(686\) 24.7141 0.943589
\(687\) −24.0589 −0.917902
\(688\) 45.4970 1.73456
\(689\) −50.6407 −1.92926
\(690\) −14.5682 −0.554601
\(691\) −21.9947 −0.836716 −0.418358 0.908282i \(-0.637394\pi\)
−0.418358 + 0.908282i \(0.637394\pi\)
\(692\) −123.511 −4.69520
\(693\) −1.27973 −0.0486128
\(694\) −16.6570 −0.632292
\(695\) 2.44065 0.0925790
\(696\) −240.155 −9.10306
\(697\) −9.53016 −0.360981
\(698\) 9.17200 0.347165
\(699\) 12.2975 0.465135
\(700\) −18.1425 −0.685723
\(701\) −14.7395 −0.556703 −0.278351 0.960479i \(-0.589788\pi\)
−0.278351 + 0.960479i \(0.589788\pi\)
\(702\) 90.3422 3.40975
\(703\) 3.39989 0.128229
\(704\) −12.9089 −0.486521
\(705\) 8.53310 0.321375
\(706\) 39.6391 1.49184
\(707\) 6.84039 0.257259
\(708\) −41.8658 −1.57341
\(709\) 35.1932 1.32171 0.660854 0.750515i \(-0.270194\pi\)
0.660854 + 0.750515i \(0.270194\pi\)
\(710\) 7.96355 0.298867
\(711\) 13.4847 0.505714
\(712\) −124.146 −4.65257
\(713\) −24.1797 −0.905537
\(714\) −22.4871 −0.841560
\(715\) −0.594404 −0.0222295
\(716\) 52.6301 1.96688
\(717\) 31.1733 1.16419
\(718\) 2.53733 0.0946922
\(719\) 1.76054 0.0656570 0.0328285 0.999461i \(-0.489548\pi\)
0.0328285 + 0.999461i \(0.489548\pi\)
\(720\) −21.1116 −0.786783
\(721\) −3.20148 −0.119230
\(722\) 51.6534 1.92234
\(723\) −79.6223 −2.96119
\(724\) −67.7007 −2.51608
\(725\) −42.8539 −1.59155
\(726\) 84.4188 3.13307
\(727\) 34.4891 1.27913 0.639565 0.768737i \(-0.279115\pi\)
0.639565 + 0.768737i \(0.279115\pi\)
\(728\) 37.2942 1.38221
\(729\) −42.9084 −1.58920
\(730\) −7.04434 −0.260723
\(731\) 12.6258 0.466982
\(732\) −122.326 −4.52128
\(733\) −17.9628 −0.663473 −0.331736 0.943372i \(-0.607634\pi\)
−0.331736 + 0.943372i \(0.607634\pi\)
\(734\) −63.7127 −2.35168
\(735\) 4.97838 0.183630
\(736\) 165.169 6.08820
\(737\) 5.52890 0.203660
\(738\) 30.1332 1.10922
\(739\) −41.6129 −1.53075 −0.765377 0.643582i \(-0.777448\pi\)
−0.765377 + 0.643582i \(0.777448\pi\)
\(740\) 11.2637 0.414062
\(741\) 7.32785 0.269195
\(742\) −16.0134 −0.587869
\(743\) 4.82500 0.177012 0.0885061 0.996076i \(-0.471791\pi\)
0.0885061 + 0.996076i \(0.471791\pi\)
\(744\) −95.5856 −3.50434
\(745\) 4.92546 0.180455
\(746\) −22.5283 −0.824821
\(747\) −55.0707 −2.01493
\(748\) −9.30592 −0.340258
\(749\) 11.5414 0.421713
\(750\) −20.7028 −0.755960
\(751\) 21.5459 0.786221 0.393110 0.919491i \(-0.371399\pi\)
0.393110 + 0.919491i \(0.371399\pi\)
\(752\) −176.583 −6.43933
\(753\) −56.2507 −2.04989
\(754\) 137.717 5.01537
\(755\) −3.89877 −0.141891
\(756\) 21.0002 0.763771
\(757\) −53.9524 −1.96093 −0.980467 0.196683i \(-0.936983\pi\)
−0.980467 + 0.196683i \(0.936983\pi\)
\(758\) 21.2758 0.772772
\(759\) 7.60926 0.276199
\(760\) −1.17434 −0.0425977
\(761\) 20.5337 0.744347 0.372174 0.928163i \(-0.378613\pi\)
0.372174 + 0.928163i \(0.378613\pi\)
\(762\) 24.4533 0.885848
\(763\) 8.72242 0.315773
\(764\) −92.1177 −3.33270
\(765\) −5.85864 −0.211820
\(766\) −35.8047 −1.29367
\(767\) 15.3568 0.554501
\(768\) 159.402 5.75194
\(769\) 47.4625 1.71154 0.855770 0.517357i \(-0.173084\pi\)
0.855770 + 0.517357i \(0.173084\pi\)
\(770\) −0.187960 −0.00677359
\(771\) −65.5604 −2.36110
\(772\) 5.22008 0.187875
\(773\) 5.37205 0.193219 0.0966096 0.995322i \(-0.469200\pi\)
0.0966096 + 0.995322i \(0.469200\pi\)
\(774\) −39.9211 −1.43494
\(775\) −17.0565 −0.612688
\(776\) 116.221 4.17210
\(777\) −14.2165 −0.510014
\(778\) 5.09576 0.182692
\(779\) 0.982032 0.0351849
\(780\) 24.2769 0.869253
\(781\) −4.15953 −0.148840
\(782\) 83.6612 2.99172
\(783\) 49.6040 1.77270
\(784\) −103.022 −3.67937
\(785\) −6.15322 −0.219618
\(786\) 49.3251 1.75937
\(787\) 2.09839 0.0747997 0.0373998 0.999300i \(-0.488092\pi\)
0.0373998 + 0.999300i \(0.488092\pi\)
\(788\) 101.040 3.59940
\(789\) 22.8356 0.812967
\(790\) 1.98055 0.0704650
\(791\) 1.00072 0.0355814
\(792\) 18.8213 0.668784
\(793\) 44.8702 1.59339
\(794\) −96.1692 −3.41292
\(795\) −6.66776 −0.236481
\(796\) −144.820 −5.13301
\(797\) 45.8513 1.62414 0.812069 0.583562i \(-0.198341\pi\)
0.812069 + 0.583562i \(0.198341\pi\)
\(798\) 2.31718 0.0820272
\(799\) −49.0033 −1.73361
\(800\) 116.511 4.11929
\(801\) 63.8208 2.25500
\(802\) −62.2936 −2.19966
\(803\) 3.67941 0.129843
\(804\) −225.814 −7.96383
\(805\) 1.24217 0.0437806
\(806\) 54.8136 1.93073
\(807\) 14.3837 0.506330
\(808\) −100.603 −3.53921
\(809\) −9.69767 −0.340952 −0.170476 0.985362i \(-0.554531\pi\)
−0.170476 + 0.985362i \(0.554531\pi\)
\(810\) 0.813700 0.0285905
\(811\) 18.7242 0.657497 0.328748 0.944418i \(-0.393373\pi\)
0.328748 + 0.944418i \(0.393373\pi\)
\(812\) 32.0126 1.12342
\(813\) 65.1395 2.28454
\(814\) −8.00327 −0.280514
\(815\) −0.0955781 −0.00334795
\(816\) 193.765 6.78312
\(817\) −1.30102 −0.0455169
\(818\) −24.1740 −0.845225
\(819\) −19.1721 −0.669928
\(820\) 3.25344 0.113615
\(821\) 36.3840 1.26981 0.634906 0.772589i \(-0.281039\pi\)
0.634906 + 0.772589i \(0.281039\pi\)
\(822\) 102.277 3.56732
\(823\) 12.4426 0.433723 0.216861 0.976202i \(-0.430418\pi\)
0.216861 + 0.976202i \(0.430418\pi\)
\(824\) 47.0850 1.64028
\(825\) 5.36762 0.186877
\(826\) 4.85605 0.168963
\(827\) −11.4381 −0.397741 −0.198871 0.980026i \(-0.563727\pi\)
−0.198871 + 0.980026i \(0.563727\pi\)
\(828\) −194.455 −6.75777
\(829\) −43.7258 −1.51866 −0.759330 0.650705i \(-0.774473\pi\)
−0.759330 + 0.650705i \(0.774473\pi\)
\(830\) −8.08849 −0.280755
\(831\) −11.7622 −0.408028
\(832\) −193.393 −6.70470
\(833\) −28.5895 −0.990569
\(834\) 70.8276 2.45256
\(835\) 1.74546 0.0604042
\(836\) 0.958925 0.0331651
\(837\) 19.7432 0.682423
\(838\) 5.03825 0.174043
\(839\) 25.5731 0.882883 0.441441 0.897290i \(-0.354467\pi\)
0.441441 + 0.897290i \(0.354467\pi\)
\(840\) 4.91045 0.169427
\(841\) 46.6161 1.60745
\(842\) 30.9408 1.06629
\(843\) −3.27739 −0.112879
\(844\) 38.9248 1.33985
\(845\) −5.42023 −0.186462
\(846\) 154.942 5.32702
\(847\) −7.19803 −0.247327
\(848\) 137.982 4.73833
\(849\) 18.7415 0.643206
\(850\) 59.0151 2.02420
\(851\) 52.8911 1.81308
\(852\) 169.885 5.82017
\(853\) −25.0225 −0.856755 −0.428378 0.903600i \(-0.640915\pi\)
−0.428378 + 0.903600i \(0.640915\pi\)
\(854\) 14.1887 0.485526
\(855\) 0.603701 0.0206461
\(856\) −169.742 −5.80166
\(857\) 15.2920 0.522365 0.261182 0.965289i \(-0.415888\pi\)
0.261182 + 0.965289i \(0.415888\pi\)
\(858\) −17.2496 −0.588893
\(859\) −17.8572 −0.609279 −0.304639 0.952468i \(-0.598536\pi\)
−0.304639 + 0.952468i \(0.598536\pi\)
\(860\) −4.31023 −0.146978
\(861\) −4.10633 −0.139943
\(862\) −80.6193 −2.74591
\(863\) −34.1387 −1.16210 −0.581048 0.813870i \(-0.697357\pi\)
−0.581048 + 0.813870i \(0.697357\pi\)
\(864\) −134.863 −4.58814
\(865\) 5.96524 0.202824
\(866\) −97.8655 −3.32561
\(867\) 5.64318 0.191652
\(868\) 12.7415 0.432476
\(869\) −1.03448 −0.0350925
\(870\) 18.1330 0.614765
\(871\) 82.8307 2.80661
\(872\) −128.283 −4.34420
\(873\) −59.7468 −2.02212
\(874\) −8.62083 −0.291604
\(875\) 1.76524 0.0596760
\(876\) −150.276 −5.07735
\(877\) −40.8185 −1.37834 −0.689171 0.724599i \(-0.742025\pi\)
−0.689171 + 0.724599i \(0.742025\pi\)
\(878\) −75.8449 −2.55964
\(879\) −61.7225 −2.08185
\(880\) 1.61959 0.0545964
\(881\) 30.3932 1.02397 0.511986 0.858994i \(-0.328910\pi\)
0.511986 + 0.858994i \(0.328910\pi\)
\(882\) 90.3965 3.04381
\(883\) 41.1549 1.38497 0.692486 0.721431i \(-0.256515\pi\)
0.692486 + 0.721431i \(0.256515\pi\)
\(884\) −139.416 −4.68906
\(885\) 2.02200 0.0679687
\(886\) 77.5093 2.60398
\(887\) 51.8259 1.74014 0.870072 0.492925i \(-0.164072\pi\)
0.870072 + 0.492925i \(0.164072\pi\)
\(888\) 209.086 7.01645
\(889\) −2.08503 −0.0699295
\(890\) 9.37367 0.314206
\(891\) −0.425012 −0.0142384
\(892\) −40.8071 −1.36632
\(893\) 5.04953 0.168976
\(894\) 142.937 4.78053
\(895\) −2.54188 −0.0849658
\(896\) −29.7908 −0.995240
\(897\) 113.997 3.80626
\(898\) −54.2712 −1.81105
\(899\) 30.0964 1.00377
\(900\) −137.170 −4.57233
\(901\) 38.2912 1.27566
\(902\) −2.31168 −0.0769707
\(903\) 5.44017 0.181037
\(904\) −14.7178 −0.489506
\(905\) 3.26975 0.108690
\(906\) −113.142 −3.75890
\(907\) 18.2405 0.605665 0.302833 0.953044i \(-0.402068\pi\)
0.302833 + 0.953044i \(0.402068\pi\)
\(908\) −35.0874 −1.16442
\(909\) 51.7180 1.71538
\(910\) −2.81590 −0.0933461
\(911\) 32.3369 1.07137 0.535685 0.844418i \(-0.320054\pi\)
0.535685 + 0.844418i \(0.320054\pi\)
\(912\) −19.9664 −0.661154
\(913\) 4.22478 0.139820
\(914\) −61.6957 −2.04071
\(915\) 5.90798 0.195312
\(916\) −47.1667 −1.55843
\(917\) −4.20574 −0.138886
\(918\) −68.3108 −2.25459
\(919\) −10.0951 −0.333006 −0.166503 0.986041i \(-0.553248\pi\)
−0.166503 + 0.986041i \(0.553248\pi\)
\(920\) −18.2688 −0.602306
\(921\) 24.2989 0.800677
\(922\) −87.5923 −2.88470
\(923\) −62.3156 −2.05114
\(924\) −4.00971 −0.131910
\(925\) 37.3097 1.22674
\(926\) 79.0685 2.59835
\(927\) −24.2054 −0.795009
\(928\) −205.585 −6.74865
\(929\) −24.2582 −0.795887 −0.397943 0.917410i \(-0.630276\pi\)
−0.397943 + 0.917410i \(0.630276\pi\)
\(930\) 7.21720 0.236661
\(931\) 2.94600 0.0965511
\(932\) 24.1089 0.789714
\(933\) 56.5684 1.85197
\(934\) −29.9426 −0.979753
\(935\) 0.449449 0.0146986
\(936\) 281.969 9.21645
\(937\) −11.4323 −0.373477 −0.186738 0.982410i \(-0.559792\pi\)
−0.186738 + 0.982410i \(0.559792\pi\)
\(938\) 26.1923 0.855210
\(939\) 89.2375 2.91215
\(940\) 16.7289 0.545636
\(941\) −46.2305 −1.50707 −0.753536 0.657407i \(-0.771653\pi\)
−0.753536 + 0.657407i \(0.771653\pi\)
\(942\) −178.567 −5.81801
\(943\) 15.2772 0.497494
\(944\) −41.8431 −1.36188
\(945\) −1.01425 −0.0329936
\(946\) 3.06258 0.0995729
\(947\) −29.9459 −0.973110 −0.486555 0.873650i \(-0.661747\pi\)
−0.486555 + 0.873650i \(0.661747\pi\)
\(948\) 42.2508 1.37224
\(949\) 55.1227 1.78936
\(950\) −6.08119 −0.197300
\(951\) −55.0734 −1.78588
\(952\) −28.1994 −0.913947
\(953\) 31.5644 1.02247 0.511235 0.859441i \(-0.329188\pi\)
0.511235 + 0.859441i \(0.329188\pi\)
\(954\) −121.072 −3.91984
\(955\) 4.44902 0.143967
\(956\) 61.1144 1.97658
\(957\) −9.47121 −0.306161
\(958\) −57.2734 −1.85042
\(959\) −8.72073 −0.281607
\(960\) −25.4637 −0.821837
\(961\) −19.0212 −0.613586
\(962\) −119.900 −3.86574
\(963\) 87.2607 2.81194
\(964\) −156.097 −5.02756
\(965\) −0.252115 −0.00811586
\(966\) 36.0477 1.15982
\(967\) 16.6516 0.535478 0.267739 0.963491i \(-0.413723\pi\)
0.267739 + 0.963491i \(0.413723\pi\)
\(968\) 105.863 3.40257
\(969\) −5.54084 −0.177997
\(970\) −8.77530 −0.281758
\(971\) −40.4620 −1.29849 −0.649244 0.760580i \(-0.724915\pi\)
−0.649244 + 0.760580i \(0.724915\pi\)
\(972\) −77.6234 −2.48977
\(973\) −6.03917 −0.193607
\(974\) 44.4009 1.42270
\(975\) 80.4145 2.57533
\(976\) −122.259 −3.91342
\(977\) −31.3387 −1.00262 −0.501308 0.865269i \(-0.667148\pi\)
−0.501308 + 0.865269i \(0.667148\pi\)
\(978\) −2.77368 −0.0886925
\(979\) −4.89606 −0.156479
\(980\) 9.75998 0.311771
\(981\) 65.9474 2.10554
\(982\) 101.005 3.22318
\(983\) 15.9832 0.509784 0.254892 0.966970i \(-0.417960\pi\)
0.254892 + 0.966970i \(0.417960\pi\)
\(984\) 60.3928 1.92525
\(985\) −4.87994 −0.155488
\(986\) −104.133 −3.31626
\(987\) −21.1144 −0.672079
\(988\) 14.3660 0.457045
\(989\) −20.2396 −0.643582
\(990\) −1.42110 −0.0451656
\(991\) −47.9200 −1.52223 −0.761114 0.648618i \(-0.775347\pi\)
−0.761114 + 0.648618i \(0.775347\pi\)
\(992\) −81.8260 −2.59798
\(993\) −55.7482 −1.76911
\(994\) −19.7051 −0.625009
\(995\) 6.99439 0.221737
\(996\) −172.550 −5.46747
\(997\) 53.1162 1.68221 0.841103 0.540875i \(-0.181907\pi\)
0.841103 + 0.540875i \(0.181907\pi\)
\(998\) −54.2225 −1.71638
\(999\) −43.1865 −1.36636
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 \(a_p\))