Properties

Label 8041.2.a.g.1.2
Level 8041
Weight 2
Character 8041.1
Self dual Yes
Analytic conductor 64.208
Analytic rank 1
Dimension 69
CM No

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Newspace parameters

Level: \( N \) = \( 8041 = 11 \cdot 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8041.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2077082653\)
Analytic rank: \(1\)
Dimension: \(69\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Character \(\chi\) = 8041.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.75821 q^{2} +0.843025 q^{3} +5.60771 q^{4} +3.43649 q^{5} -2.32524 q^{6} -0.344850 q^{7} -9.95082 q^{8} -2.28931 q^{9} +O(q^{10})\) \(q-2.75821 q^{2} +0.843025 q^{3} +5.60771 q^{4} +3.43649 q^{5} -2.32524 q^{6} -0.344850 q^{7} -9.95082 q^{8} -2.28931 q^{9} -9.47854 q^{10} -1.00000 q^{11} +4.72744 q^{12} -4.61873 q^{13} +0.951168 q^{14} +2.89704 q^{15} +16.2310 q^{16} +1.00000 q^{17} +6.31439 q^{18} +7.54894 q^{19} +19.2708 q^{20} -0.290717 q^{21} +2.75821 q^{22} +1.39026 q^{23} -8.38879 q^{24} +6.80944 q^{25} +12.7394 q^{26} -4.45902 q^{27} -1.93382 q^{28} -4.70625 q^{29} -7.99065 q^{30} +2.92736 q^{31} -24.8669 q^{32} -0.843025 q^{33} -2.75821 q^{34} -1.18507 q^{35} -12.8378 q^{36} +5.72242 q^{37} -20.8216 q^{38} -3.89370 q^{39} -34.1959 q^{40} -10.2164 q^{41} +0.801858 q^{42} +1.00000 q^{43} -5.60771 q^{44} -7.86718 q^{45} -3.83462 q^{46} +10.5798 q^{47} +13.6832 q^{48} -6.88108 q^{49} -18.7818 q^{50} +0.843025 q^{51} -25.9005 q^{52} -14.0191 q^{53} +12.2989 q^{54} -3.43649 q^{55} +3.43154 q^{56} +6.36395 q^{57} +12.9808 q^{58} +3.89484 q^{59} +16.2458 q^{60} -11.6936 q^{61} -8.07428 q^{62} +0.789469 q^{63} +36.1260 q^{64} -15.8722 q^{65} +2.32524 q^{66} -6.76294 q^{67} +5.60771 q^{68} +1.17202 q^{69} +3.26868 q^{70} -14.7033 q^{71} +22.7805 q^{72} -2.55243 q^{73} -15.7836 q^{74} +5.74052 q^{75} +42.3323 q^{76} +0.344850 q^{77} +10.7396 q^{78} -12.7313 q^{79} +55.7777 q^{80} +3.10887 q^{81} +28.1790 q^{82} +17.1811 q^{83} -1.63026 q^{84} +3.43649 q^{85} -2.75821 q^{86} -3.96748 q^{87} +9.95082 q^{88} +2.44192 q^{89} +21.6993 q^{90} +1.59277 q^{91} +7.79616 q^{92} +2.46784 q^{93} -29.1814 q^{94} +25.9418 q^{95} -20.9634 q^{96} +6.64432 q^{97} +18.9794 q^{98} +2.28931 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 69q - 11q^{2} - 3q^{3} + 65q^{4} - 6q^{5} - 10q^{6} - 11q^{7} - 33q^{8} + 56q^{9} + O(q^{10}) \) \( 69q - 11q^{2} - 3q^{3} + 65q^{4} - 6q^{5} - 10q^{6} - 11q^{7} - 33q^{8} + 56q^{9} - q^{10} - 69q^{11} - 3q^{12} - 28q^{13} - 15q^{14} - 45q^{15} + 53q^{16} + 69q^{17} - 17q^{18} - 32q^{19} - 21q^{20} - 38q^{21} + 11q^{22} - 41q^{23} - 11q^{24} + 67q^{25} - 6q^{26} - 3q^{27} - 21q^{28} - 22q^{29} - 22q^{30} - 27q^{31} - 87q^{32} + 3q^{33} - 11q^{34} - 44q^{35} + 59q^{36} + 24q^{37} - 22q^{38} - 59q^{39} + q^{40} - 43q^{41} - 15q^{42} + 69q^{43} - 65q^{44} - 12q^{45} - 21q^{46} - 99q^{47} + 2q^{48} + 64q^{49} - 78q^{50} - 3q^{51} - 57q^{52} - 50q^{53} + 20q^{54} + 6q^{55} - 59q^{56} - 15q^{57} + 22q^{58} - 82q^{59} - 86q^{60} - 24q^{61} + 15q^{62} - 63q^{63} + 63q^{64} - 23q^{65} + 10q^{66} - 54q^{67} + 65q^{68} + 36q^{69} + 9q^{70} - 128q^{71} - 69q^{72} + 2q^{73} - 58q^{74} - 31q^{75} - 76q^{76} + 11q^{77} - 19q^{78} - 43q^{79} - 19q^{80} + 49q^{81} - 2q^{82} - 62q^{83} - 82q^{84} - 6q^{85} - 11q^{86} - 62q^{87} + 33q^{88} - 49q^{89} - 37q^{90} - 2q^{91} - 96q^{92} - 29q^{93} - 75q^{94} - 133q^{95} - 86q^{96} + 5q^{97} - 72q^{98} - 56q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.75821 −1.95035 −0.975174 0.221440i \(-0.928924\pi\)
−0.975174 + 0.221440i \(0.928924\pi\)
\(3\) 0.843025 0.486721 0.243360 0.969936i \(-0.421750\pi\)
0.243360 + 0.969936i \(0.421750\pi\)
\(4\) 5.60771 2.80386
\(5\) 3.43649 1.53684 0.768422 0.639944i \(-0.221042\pi\)
0.768422 + 0.639944i \(0.221042\pi\)
\(6\) −2.32524 −0.949274
\(7\) −0.344850 −0.130341 −0.0651705 0.997874i \(-0.520759\pi\)
−0.0651705 + 0.997874i \(0.520759\pi\)
\(8\) −9.95082 −3.51815
\(9\) −2.28931 −0.763103
\(10\) −9.47854 −2.99738
\(11\) −1.00000 −0.301511
\(12\) 4.72744 1.36469
\(13\) −4.61873 −1.28101 −0.640503 0.767956i \(-0.721274\pi\)
−0.640503 + 0.767956i \(0.721274\pi\)
\(14\) 0.951168 0.254210
\(15\) 2.89704 0.748013
\(16\) 16.2310 4.05776
\(17\) 1.00000 0.242536
\(18\) 6.31439 1.48832
\(19\) 7.54894 1.73185 0.865923 0.500177i \(-0.166732\pi\)
0.865923 + 0.500177i \(0.166732\pi\)
\(20\) 19.2708 4.30909
\(21\) −0.290717 −0.0634397
\(22\) 2.75821 0.588052
\(23\) 1.39026 0.289889 0.144944 0.989440i \(-0.453700\pi\)
0.144944 + 0.989440i \(0.453700\pi\)
\(24\) −8.38879 −1.71235
\(25\) 6.80944 1.36189
\(26\) 12.7394 2.49841
\(27\) −4.45902 −0.858138
\(28\) −1.93382 −0.365458
\(29\) −4.70625 −0.873929 −0.436964 0.899479i \(-0.643946\pi\)
−0.436964 + 0.899479i \(0.643946\pi\)
\(30\) −7.99065 −1.45889
\(31\) 2.92736 0.525770 0.262885 0.964827i \(-0.415326\pi\)
0.262885 + 0.964827i \(0.415326\pi\)
\(32\) −24.8669 −4.39589
\(33\) −0.843025 −0.146752
\(34\) −2.75821 −0.473029
\(35\) −1.18507 −0.200314
\(36\) −12.8378 −2.13963
\(37\) 5.72242 0.940760 0.470380 0.882464i \(-0.344117\pi\)
0.470380 + 0.882464i \(0.344117\pi\)
\(38\) −20.8216 −3.37770
\(39\) −3.89370 −0.623492
\(40\) −34.1959 −5.40684
\(41\) −10.2164 −1.59554 −0.797768 0.602965i \(-0.793986\pi\)
−0.797768 + 0.602965i \(0.793986\pi\)
\(42\) 0.801858 0.123729
\(43\) 1.00000 0.152499
\(44\) −5.60771 −0.845395
\(45\) −7.86718 −1.17277
\(46\) −3.83462 −0.565384
\(47\) 10.5798 1.54323 0.771614 0.636091i \(-0.219450\pi\)
0.771614 + 0.636091i \(0.219450\pi\)
\(48\) 13.6832 1.97499
\(49\) −6.88108 −0.983011
\(50\) −18.7818 −2.65615
\(51\) 0.843025 0.118047
\(52\) −25.9005 −3.59176
\(53\) −14.0191 −1.92567 −0.962836 0.270087i \(-0.912948\pi\)
−0.962836 + 0.270087i \(0.912948\pi\)
\(54\) 12.2989 1.67367
\(55\) −3.43649 −0.463376
\(56\) 3.43154 0.458559
\(57\) 6.36395 0.842925
\(58\) 12.9808 1.70446
\(59\) 3.89484 0.507065 0.253533 0.967327i \(-0.418407\pi\)
0.253533 + 0.967327i \(0.418407\pi\)
\(60\) 16.2458 2.09732
\(61\) −11.6936 −1.49721 −0.748603 0.663018i \(-0.769275\pi\)
−0.748603 + 0.663018i \(0.769275\pi\)
\(62\) −8.07428 −1.02543
\(63\) 0.789469 0.0994637
\(64\) 36.1260 4.51575
\(65\) −15.8722 −1.96870
\(66\) 2.32524 0.286217
\(67\) −6.76294 −0.826225 −0.413113 0.910680i \(-0.635558\pi\)
−0.413113 + 0.910680i \(0.635558\pi\)
\(68\) 5.60771 0.680035
\(69\) 1.17202 0.141095
\(70\) 3.26868 0.390682
\(71\) −14.7033 −1.74496 −0.872481 0.488647i \(-0.837490\pi\)
−0.872481 + 0.488647i \(0.837490\pi\)
\(72\) 22.7805 2.68471
\(73\) −2.55243 −0.298739 −0.149370 0.988781i \(-0.547724\pi\)
−0.149370 + 0.988781i \(0.547724\pi\)
\(74\) −15.7836 −1.83481
\(75\) 5.74052 0.662859
\(76\) 42.3323 4.85585
\(77\) 0.344850 0.0392993
\(78\) 10.7396 1.21603
\(79\) −12.7313 −1.43238 −0.716191 0.697904i \(-0.754116\pi\)
−0.716191 + 0.697904i \(0.754116\pi\)
\(80\) 55.7777 6.23613
\(81\) 3.10887 0.345430
\(82\) 28.1790 3.11185
\(83\) 17.1811 1.88587 0.942934 0.332980i \(-0.108054\pi\)
0.942934 + 0.332980i \(0.108054\pi\)
\(84\) −1.63026 −0.177876
\(85\) 3.43649 0.372739
\(86\) −2.75821 −0.297425
\(87\) −3.96748 −0.425359
\(88\) 9.95082 1.06076
\(89\) 2.44192 0.258843 0.129421 0.991590i \(-0.458688\pi\)
0.129421 + 0.991590i \(0.458688\pi\)
\(90\) 21.6993 2.28731
\(91\) 1.59277 0.166968
\(92\) 7.79616 0.812806
\(93\) 2.46784 0.255903
\(94\) −29.1814 −3.00983
\(95\) 25.9418 2.66158
\(96\) −20.9634 −2.13957
\(97\) 6.64432 0.674629 0.337314 0.941392i \(-0.390481\pi\)
0.337314 + 0.941392i \(0.390481\pi\)
\(98\) 18.9794 1.91721
\(99\) 2.28931 0.230084
\(100\) 38.1854 3.81854
\(101\) −4.18900 −0.416822 −0.208411 0.978041i \(-0.566829\pi\)
−0.208411 + 0.978041i \(0.566829\pi\)
\(102\) −2.32524 −0.230233
\(103\) 0.197597 0.0194698 0.00973491 0.999953i \(-0.496901\pi\)
0.00973491 + 0.999953i \(0.496901\pi\)
\(104\) 45.9602 4.50677
\(105\) −0.999046 −0.0974969
\(106\) 38.6676 3.75573
\(107\) −15.6538 −1.51331 −0.756654 0.653815i \(-0.773167\pi\)
−0.756654 + 0.653815i \(0.773167\pi\)
\(108\) −25.0049 −2.40610
\(109\) −10.6755 −1.02253 −0.511266 0.859423i \(-0.670823\pi\)
−0.511266 + 0.859423i \(0.670823\pi\)
\(110\) 9.47854 0.903744
\(111\) 4.82414 0.457887
\(112\) −5.59727 −0.528892
\(113\) −12.5996 −1.18527 −0.592633 0.805473i \(-0.701912\pi\)
−0.592633 + 0.805473i \(0.701912\pi\)
\(114\) −17.5531 −1.64400
\(115\) 4.77760 0.445513
\(116\) −26.3913 −2.45037
\(117\) 10.5737 0.977539
\(118\) −10.7428 −0.988954
\(119\) −0.344850 −0.0316124
\(120\) −28.8280 −2.63162
\(121\) 1.00000 0.0909091
\(122\) 32.2533 2.92007
\(123\) −8.61269 −0.776580
\(124\) 16.4158 1.47418
\(125\) 6.21811 0.556164
\(126\) −2.17752 −0.193989
\(127\) 6.62272 0.587672 0.293836 0.955856i \(-0.405068\pi\)
0.293836 + 0.955856i \(0.405068\pi\)
\(128\) −49.9093 −4.41140
\(129\) 0.843025 0.0742242
\(130\) 43.7788 3.83966
\(131\) 15.7179 1.37328 0.686638 0.726999i \(-0.259086\pi\)
0.686638 + 0.726999i \(0.259086\pi\)
\(132\) −4.72744 −0.411471
\(133\) −2.60325 −0.225731
\(134\) 18.6536 1.61143
\(135\) −15.3234 −1.31882
\(136\) −9.95082 −0.853276
\(137\) 12.3664 1.05653 0.528267 0.849078i \(-0.322842\pi\)
0.528267 + 0.849078i \(0.322842\pi\)
\(138\) −3.23268 −0.275184
\(139\) 9.72315 0.824706 0.412353 0.911024i \(-0.364707\pi\)
0.412353 + 0.911024i \(0.364707\pi\)
\(140\) −6.64555 −0.561651
\(141\) 8.91906 0.751121
\(142\) 40.5548 3.40328
\(143\) 4.61873 0.386238
\(144\) −37.1578 −3.09649
\(145\) −16.1730 −1.34309
\(146\) 7.04013 0.582645
\(147\) −5.80092 −0.478452
\(148\) 32.0897 2.63775
\(149\) −10.9685 −0.898572 −0.449286 0.893388i \(-0.648322\pi\)
−0.449286 + 0.893388i \(0.648322\pi\)
\(150\) −15.8336 −1.29280
\(151\) −13.2818 −1.08086 −0.540429 0.841390i \(-0.681738\pi\)
−0.540429 + 0.841390i \(0.681738\pi\)
\(152\) −75.1182 −6.09289
\(153\) −2.28931 −0.185080
\(154\) −0.951168 −0.0766473
\(155\) 10.0598 0.808026
\(156\) −21.8348 −1.74818
\(157\) −5.78336 −0.461562 −0.230781 0.973006i \(-0.574128\pi\)
−0.230781 + 0.973006i \(0.574128\pi\)
\(158\) 35.1156 2.79364
\(159\) −11.8185 −0.937264
\(160\) −85.4547 −6.75579
\(161\) −0.479430 −0.0377844
\(162\) −8.57490 −0.673708
\(163\) 5.96634 0.467320 0.233660 0.972318i \(-0.424930\pi\)
0.233660 + 0.972318i \(0.424930\pi\)
\(164\) −57.2907 −4.47365
\(165\) −2.89704 −0.225534
\(166\) −47.3890 −3.67810
\(167\) 20.7034 1.60208 0.801040 0.598611i \(-0.204280\pi\)
0.801040 + 0.598611i \(0.204280\pi\)
\(168\) 2.89288 0.223190
\(169\) 8.33267 0.640975
\(170\) −9.47854 −0.726971
\(171\) −17.2819 −1.32158
\(172\) 5.60771 0.427584
\(173\) −15.2087 −1.15630 −0.578149 0.815931i \(-0.696225\pi\)
−0.578149 + 0.815931i \(0.696225\pi\)
\(174\) 10.9431 0.829598
\(175\) −2.34824 −0.177510
\(176\) −16.2310 −1.22346
\(177\) 3.28345 0.246799
\(178\) −6.73531 −0.504833
\(179\) −13.7044 −1.02431 −0.512157 0.858892i \(-0.671153\pi\)
−0.512157 + 0.858892i \(0.671153\pi\)
\(180\) −44.1169 −3.28828
\(181\) −3.65444 −0.271633 −0.135816 0.990734i \(-0.543366\pi\)
−0.135816 + 0.990734i \(0.543366\pi\)
\(182\) −4.39319 −0.325645
\(183\) −9.85796 −0.728721
\(184\) −13.8342 −1.01987
\(185\) 19.6650 1.44580
\(186\) −6.80681 −0.499100
\(187\) −1.00000 −0.0731272
\(188\) 59.3287 4.32699
\(189\) 1.53769 0.111851
\(190\) −71.5530 −5.19100
\(191\) −26.2661 −1.90055 −0.950275 0.311413i \(-0.899198\pi\)
−0.950275 + 0.311413i \(0.899198\pi\)
\(192\) 30.4551 2.19791
\(193\) 17.4791 1.25817 0.629085 0.777336i \(-0.283430\pi\)
0.629085 + 0.777336i \(0.283430\pi\)
\(194\) −18.3264 −1.31576
\(195\) −13.3807 −0.958209
\(196\) −38.5871 −2.75622
\(197\) −4.26943 −0.304184 −0.152092 0.988366i \(-0.548601\pi\)
−0.152092 + 0.988366i \(0.548601\pi\)
\(198\) −6.31439 −0.448744
\(199\) 13.3638 0.947337 0.473668 0.880703i \(-0.342930\pi\)
0.473668 + 0.880703i \(0.342930\pi\)
\(200\) −67.7595 −4.79132
\(201\) −5.70133 −0.402141
\(202\) 11.5541 0.812947
\(203\) 1.62295 0.113909
\(204\) 4.72744 0.330987
\(205\) −35.1086 −2.45209
\(206\) −0.545014 −0.0379729
\(207\) −3.18273 −0.221215
\(208\) −74.9667 −5.19801
\(209\) −7.54894 −0.522171
\(210\) 2.75558 0.190153
\(211\) 17.3128 1.19187 0.595933 0.803034i \(-0.296782\pi\)
0.595933 + 0.803034i \(0.296782\pi\)
\(212\) −78.6151 −5.39931
\(213\) −12.3953 −0.849309
\(214\) 43.1764 2.95148
\(215\) 3.43649 0.234366
\(216\) 44.3709 3.01906
\(217\) −1.00950 −0.0685294
\(218\) 29.4454 1.99429
\(219\) −2.15176 −0.145402
\(220\) −19.2708 −1.29924
\(221\) −4.61873 −0.310689
\(222\) −13.3060 −0.893039
\(223\) −13.9343 −0.933109 −0.466554 0.884493i \(-0.654505\pi\)
−0.466554 + 0.884493i \(0.654505\pi\)
\(224\) 8.57535 0.572965
\(225\) −15.5889 −1.03926
\(226\) 34.7522 2.31168
\(227\) 8.46055 0.561546 0.280773 0.959774i \(-0.409409\pi\)
0.280773 + 0.959774i \(0.409409\pi\)
\(228\) 35.6872 2.36344
\(229\) 19.4964 1.28836 0.644178 0.764876i \(-0.277200\pi\)
0.644178 + 0.764876i \(0.277200\pi\)
\(230\) −13.1776 −0.868906
\(231\) 0.290717 0.0191278
\(232\) 46.8311 3.07461
\(233\) −4.09287 −0.268133 −0.134067 0.990972i \(-0.542804\pi\)
−0.134067 + 0.990972i \(0.542804\pi\)
\(234\) −29.1645 −1.90654
\(235\) 36.3575 2.37170
\(236\) 21.8412 1.42174
\(237\) −10.7328 −0.697170
\(238\) 0.951168 0.0616551
\(239\) −5.58585 −0.361319 −0.180659 0.983546i \(-0.557823\pi\)
−0.180659 + 0.983546i \(0.557823\pi\)
\(240\) 47.0220 3.03525
\(241\) −28.7151 −1.84971 −0.924853 0.380326i \(-0.875812\pi\)
−0.924853 + 0.380326i \(0.875812\pi\)
\(242\) −2.75821 −0.177304
\(243\) 15.9979 1.02627
\(244\) −65.5741 −4.19795
\(245\) −23.6467 −1.51073
\(246\) 23.7556 1.51460
\(247\) −34.8665 −2.21850
\(248\) −29.1297 −1.84974
\(249\) 14.4841 0.917890
\(250\) −17.1508 −1.08471
\(251\) −17.5154 −1.10556 −0.552782 0.833326i \(-0.686434\pi\)
−0.552782 + 0.833326i \(0.686434\pi\)
\(252\) 4.42711 0.278882
\(253\) −1.39026 −0.0874047
\(254\) −18.2669 −1.14616
\(255\) 2.89704 0.181420
\(256\) 65.4082 4.08801
\(257\) 11.5112 0.718051 0.359026 0.933328i \(-0.383109\pi\)
0.359026 + 0.933328i \(0.383109\pi\)
\(258\) −2.32524 −0.144763
\(259\) −1.97338 −0.122620
\(260\) −89.0068 −5.51997
\(261\) 10.7741 0.666898
\(262\) −43.3531 −2.67837
\(263\) 17.4672 1.07707 0.538537 0.842602i \(-0.318977\pi\)
0.538537 + 0.842602i \(0.318977\pi\)
\(264\) 8.38879 0.516294
\(265\) −48.1765 −2.95946
\(266\) 7.18032 0.440253
\(267\) 2.05860 0.125984
\(268\) −37.9246 −2.31662
\(269\) −5.97011 −0.364004 −0.182002 0.983298i \(-0.558258\pi\)
−0.182002 + 0.983298i \(0.558258\pi\)
\(270\) 42.2650 2.57217
\(271\) 6.15163 0.373685 0.186842 0.982390i \(-0.440175\pi\)
0.186842 + 0.982390i \(0.440175\pi\)
\(272\) 16.2310 0.984150
\(273\) 1.34274 0.0812666
\(274\) −34.1091 −2.06061
\(275\) −6.80944 −0.410625
\(276\) 6.57236 0.395609
\(277\) −0.170065 −0.0102182 −0.00510911 0.999987i \(-0.501626\pi\)
−0.00510911 + 0.999987i \(0.501626\pi\)
\(278\) −26.8185 −1.60846
\(279\) −6.70164 −0.401217
\(280\) 11.7925 0.704734
\(281\) 2.98153 0.177863 0.0889317 0.996038i \(-0.471655\pi\)
0.0889317 + 0.996038i \(0.471655\pi\)
\(282\) −24.6006 −1.46495
\(283\) −11.8819 −0.706304 −0.353152 0.935566i \(-0.614890\pi\)
−0.353152 + 0.935566i \(0.614890\pi\)
\(284\) −82.4520 −4.89263
\(285\) 21.8696 1.29544
\(286\) −12.7394 −0.753298
\(287\) 3.52313 0.207964
\(288\) 56.9280 3.35451
\(289\) 1.00000 0.0588235
\(290\) 44.6084 2.61950
\(291\) 5.60133 0.328356
\(292\) −14.3133 −0.837621
\(293\) 3.53127 0.206299 0.103149 0.994666i \(-0.467108\pi\)
0.103149 + 0.994666i \(0.467108\pi\)
\(294\) 16.0001 0.933147
\(295\) 13.3846 0.779280
\(296\) −56.9428 −3.30973
\(297\) 4.45902 0.258738
\(298\) 30.2533 1.75253
\(299\) −6.42122 −0.371349
\(300\) 32.1912 1.85856
\(301\) −0.344850 −0.0198768
\(302\) 36.6340 2.10805
\(303\) −3.53143 −0.202876
\(304\) 122.527 7.02741
\(305\) −40.1847 −2.30097
\(306\) 6.31439 0.360970
\(307\) 21.1103 1.20483 0.602416 0.798183i \(-0.294205\pi\)
0.602416 + 0.798183i \(0.294205\pi\)
\(308\) 1.93382 0.110190
\(309\) 0.166579 0.00947636
\(310\) −27.7471 −1.57593
\(311\) −7.04272 −0.399356 −0.199678 0.979862i \(-0.563990\pi\)
−0.199678 + 0.979862i \(0.563990\pi\)
\(312\) 38.7456 2.19354
\(313\) 32.5421 1.83939 0.919694 0.392636i \(-0.128437\pi\)
0.919694 + 0.392636i \(0.128437\pi\)
\(314\) 15.9517 0.900207
\(315\) 2.71300 0.152860
\(316\) −71.3935 −4.01620
\(317\) 14.2873 0.802452 0.401226 0.915979i \(-0.368584\pi\)
0.401226 + 0.915979i \(0.368584\pi\)
\(318\) 32.5977 1.82799
\(319\) 4.70625 0.263499
\(320\) 124.147 6.94000
\(321\) −13.1965 −0.736558
\(322\) 1.32237 0.0736927
\(323\) 7.54894 0.420034
\(324\) 17.4336 0.968535
\(325\) −31.4510 −1.74459
\(326\) −16.4564 −0.911437
\(327\) −8.99975 −0.497687
\(328\) 101.662 5.61333
\(329\) −3.64846 −0.201146
\(330\) 7.99065 0.439871
\(331\) −2.21655 −0.121833 −0.0609164 0.998143i \(-0.519402\pi\)
−0.0609164 + 0.998143i \(0.519402\pi\)
\(332\) 96.3465 5.28770
\(333\) −13.1004 −0.717897
\(334\) −57.1044 −3.12461
\(335\) −23.2408 −1.26978
\(336\) −4.71864 −0.257423
\(337\) −16.2343 −0.884338 −0.442169 0.896932i \(-0.645791\pi\)
−0.442169 + 0.896932i \(0.645791\pi\)
\(338\) −22.9832 −1.25012
\(339\) −10.6217 −0.576893
\(340\) 19.2708 1.04511
\(341\) −2.92736 −0.158526
\(342\) 47.6670 2.57754
\(343\) 4.78689 0.258468
\(344\) −9.95082 −0.536513
\(345\) 4.02763 0.216840
\(346\) 41.9488 2.25518
\(347\) −2.41004 −0.129378 −0.0646888 0.997905i \(-0.520605\pi\)
−0.0646888 + 0.997905i \(0.520605\pi\)
\(348\) −22.2485 −1.19265
\(349\) −15.2425 −0.815910 −0.407955 0.913002i \(-0.633758\pi\)
−0.407955 + 0.913002i \(0.633758\pi\)
\(350\) 6.47692 0.346206
\(351\) 20.5950 1.09928
\(352\) 24.8669 1.32541
\(353\) −15.2917 −0.813894 −0.406947 0.913452i \(-0.633407\pi\)
−0.406947 + 0.913452i \(0.633407\pi\)
\(354\) −9.05644 −0.481344
\(355\) −50.5277 −2.68173
\(356\) 13.6936 0.725758
\(357\) −0.290717 −0.0153864
\(358\) 37.7995 1.99777
\(359\) 16.2209 0.856107 0.428054 0.903753i \(-0.359199\pi\)
0.428054 + 0.903753i \(0.359199\pi\)
\(360\) 78.2849 4.12598
\(361\) 37.9865 1.99929
\(362\) 10.0797 0.529778
\(363\) 0.843025 0.0442473
\(364\) 8.93180 0.468153
\(365\) −8.77138 −0.459115
\(366\) 27.1903 1.42126
\(367\) 14.2452 0.743595 0.371798 0.928314i \(-0.378742\pi\)
0.371798 + 0.928314i \(0.378742\pi\)
\(368\) 22.5653 1.17630
\(369\) 23.3885 1.21756
\(370\) −54.2402 −2.81981
\(371\) 4.83449 0.250994
\(372\) 13.8389 0.717515
\(373\) −10.2116 −0.528739 −0.264369 0.964421i \(-0.585164\pi\)
−0.264369 + 0.964421i \(0.585164\pi\)
\(374\) 2.75821 0.142624
\(375\) 5.24202 0.270697
\(376\) −105.278 −5.42930
\(377\) 21.7369 1.11951
\(378\) −4.24128 −0.218148
\(379\) −2.92142 −0.150063 −0.0750317 0.997181i \(-0.523906\pi\)
−0.0750317 + 0.997181i \(0.523906\pi\)
\(380\) 145.474 7.46268
\(381\) 5.58312 0.286032
\(382\) 72.4474 3.70673
\(383\) −38.0155 −1.94250 −0.971250 0.238063i \(-0.923487\pi\)
−0.971250 + 0.238063i \(0.923487\pi\)
\(384\) −42.0748 −2.14712
\(385\) 1.18507 0.0603969
\(386\) −48.2109 −2.45387
\(387\) −2.28931 −0.116372
\(388\) 37.2595 1.89156
\(389\) 4.57761 0.232094 0.116047 0.993244i \(-0.462978\pi\)
0.116047 + 0.993244i \(0.462978\pi\)
\(390\) 36.9066 1.86884
\(391\) 1.39026 0.0703083
\(392\) 68.4724 3.45838
\(393\) 13.2505 0.668402
\(394\) 11.7760 0.593265
\(395\) −43.7509 −2.20135
\(396\) 12.8378 0.645123
\(397\) 10.1736 0.510596 0.255298 0.966862i \(-0.417826\pi\)
0.255298 + 0.966862i \(0.417826\pi\)
\(398\) −36.8602 −1.84764
\(399\) −2.19461 −0.109868
\(400\) 110.524 5.52621
\(401\) −3.30558 −0.165073 −0.0825364 0.996588i \(-0.526302\pi\)
−0.0825364 + 0.996588i \(0.526302\pi\)
\(402\) 15.7255 0.784314
\(403\) −13.5207 −0.673514
\(404\) −23.4907 −1.16871
\(405\) 10.6836 0.530871
\(406\) −4.47644 −0.222162
\(407\) −5.72242 −0.283650
\(408\) −8.38879 −0.415307
\(409\) −21.4341 −1.05985 −0.529925 0.848044i \(-0.677780\pi\)
−0.529925 + 0.848044i \(0.677780\pi\)
\(410\) 96.8367 4.78243
\(411\) 10.4252 0.514237
\(412\) 1.10807 0.0545906
\(413\) −1.34314 −0.0660915
\(414\) 8.77863 0.431446
\(415\) 59.0425 2.89828
\(416\) 114.853 5.63115
\(417\) 8.19685 0.401402
\(418\) 20.8216 1.01842
\(419\) −29.9182 −1.46160 −0.730800 0.682592i \(-0.760853\pi\)
−0.730800 + 0.682592i \(0.760853\pi\)
\(420\) −5.60236 −0.273367
\(421\) 28.4782 1.38794 0.693971 0.720003i \(-0.255860\pi\)
0.693971 + 0.720003i \(0.255860\pi\)
\(422\) −47.7524 −2.32455
\(423\) −24.2205 −1.17764
\(424\) 139.502 6.77480
\(425\) 6.80944 0.330306
\(426\) 34.1887 1.65645
\(427\) 4.03252 0.195148
\(428\) −87.7819 −4.24310
\(429\) 3.89370 0.187990
\(430\) −9.47854 −0.457096
\(431\) −13.3820 −0.644587 −0.322293 0.946640i \(-0.604454\pi\)
−0.322293 + 0.946640i \(0.604454\pi\)
\(432\) −72.3744 −3.48212
\(433\) −15.8188 −0.760204 −0.380102 0.924945i \(-0.624111\pi\)
−0.380102 + 0.924945i \(0.624111\pi\)
\(434\) 2.78442 0.133656
\(435\) −13.6342 −0.653710
\(436\) −59.8654 −2.86703
\(437\) 10.4950 0.502043
\(438\) 5.93500 0.283585
\(439\) −6.58325 −0.314202 −0.157101 0.987583i \(-0.550215\pi\)
−0.157101 + 0.987583i \(0.550215\pi\)
\(440\) 34.1959 1.63022
\(441\) 15.7529 0.750139
\(442\) 12.7394 0.605952
\(443\) −22.6236 −1.07488 −0.537440 0.843302i \(-0.680609\pi\)
−0.537440 + 0.843302i \(0.680609\pi\)
\(444\) 27.0524 1.28385
\(445\) 8.39161 0.397801
\(446\) 38.4337 1.81989
\(447\) −9.24669 −0.437353
\(448\) −12.4581 −0.588588
\(449\) 0.977299 0.0461216 0.0230608 0.999734i \(-0.492659\pi\)
0.0230608 + 0.999734i \(0.492659\pi\)
\(450\) 42.9975 2.02692
\(451\) 10.2164 0.481072
\(452\) −70.6547 −3.32332
\(453\) −11.1969 −0.526076
\(454\) −23.3360 −1.09521
\(455\) 5.47353 0.256603
\(456\) −63.3265 −2.96554
\(457\) 14.4355 0.675265 0.337633 0.941278i \(-0.390374\pi\)
0.337633 + 0.941278i \(0.390374\pi\)
\(458\) −53.7750 −2.51274
\(459\) −4.45902 −0.208129
\(460\) 26.7914 1.24916
\(461\) −19.2912 −0.898480 −0.449240 0.893411i \(-0.648305\pi\)
−0.449240 + 0.893411i \(0.648305\pi\)
\(462\) −0.801858 −0.0373058
\(463\) −31.4459 −1.46142 −0.730708 0.682690i \(-0.760810\pi\)
−0.730708 + 0.682690i \(0.760810\pi\)
\(464\) −76.3872 −3.54619
\(465\) 8.48070 0.393283
\(466\) 11.2890 0.522953
\(467\) −19.5569 −0.904985 −0.452492 0.891768i \(-0.649465\pi\)
−0.452492 + 0.891768i \(0.649465\pi\)
\(468\) 59.2943 2.74088
\(469\) 2.33220 0.107691
\(470\) −100.281 −4.62564
\(471\) −4.87551 −0.224652
\(472\) −38.7569 −1.78393
\(473\) −1.00000 −0.0459800
\(474\) 29.6033 1.35972
\(475\) 51.4041 2.35858
\(476\) −1.93382 −0.0886365
\(477\) 32.0941 1.46949
\(478\) 15.4069 0.704697
\(479\) −35.2365 −1.61000 −0.804998 0.593277i \(-0.797834\pi\)
−0.804998 + 0.593277i \(0.797834\pi\)
\(480\) −72.0404 −3.28818
\(481\) −26.4303 −1.20512
\(482\) 79.2023 3.60757
\(483\) −0.404172 −0.0183904
\(484\) 5.60771 0.254896
\(485\) 22.8331 1.03680
\(486\) −44.1256 −2.00158
\(487\) 29.8165 1.35111 0.675557 0.737308i \(-0.263903\pi\)
0.675557 + 0.737308i \(0.263903\pi\)
\(488\) 116.361 5.26739
\(489\) 5.02977 0.227454
\(490\) 65.2226 2.94646
\(491\) 14.2250 0.641965 0.320983 0.947085i \(-0.395987\pi\)
0.320983 + 0.947085i \(0.395987\pi\)
\(492\) −48.2975 −2.17742
\(493\) −4.70625 −0.211959
\(494\) 96.1692 4.32686
\(495\) 7.86718 0.353603
\(496\) 47.5141 2.13345
\(497\) 5.07044 0.227440
\(498\) −39.9501 −1.79021
\(499\) −18.9730 −0.849347 −0.424673 0.905347i \(-0.639611\pi\)
−0.424673 + 0.905347i \(0.639611\pi\)
\(500\) 34.8694 1.55941
\(501\) 17.4535 0.779765
\(502\) 48.3112 2.15623
\(503\) −16.9084 −0.753908 −0.376954 0.926232i \(-0.623028\pi\)
−0.376954 + 0.926232i \(0.623028\pi\)
\(504\) −7.85586 −0.349928
\(505\) −14.3955 −0.640589
\(506\) 3.83462 0.170470
\(507\) 7.02465 0.311976
\(508\) 37.1383 1.64775
\(509\) −42.8237 −1.89813 −0.949063 0.315087i \(-0.897966\pi\)
−0.949063 + 0.315087i \(0.897966\pi\)
\(510\) −7.99065 −0.353832
\(511\) 0.880205 0.0389380
\(512\) −80.5909 −3.56165
\(513\) −33.6609 −1.48616
\(514\) −31.7504 −1.40045
\(515\) 0.679040 0.0299221
\(516\) 4.72744 0.208114
\(517\) −10.5798 −0.465301
\(518\) 5.44298 0.239151
\(519\) −12.8213 −0.562794
\(520\) 157.942 6.92619
\(521\) −11.7046 −0.512790 −0.256395 0.966572i \(-0.582535\pi\)
−0.256395 + 0.966572i \(0.582535\pi\)
\(522\) −29.7171 −1.30068
\(523\) −24.2057 −1.05844 −0.529222 0.848484i \(-0.677516\pi\)
−0.529222 + 0.848484i \(0.677516\pi\)
\(524\) 88.1413 3.85047
\(525\) −1.97962 −0.0863977
\(526\) −48.1782 −2.10067
\(527\) 2.92736 0.127518
\(528\) −13.6832 −0.595483
\(529\) −21.0672 −0.915965
\(530\) 132.881 5.77197
\(531\) −8.91650 −0.386943
\(532\) −14.5983 −0.632917
\(533\) 47.1869 2.04389
\(534\) −5.67804 −0.245713
\(535\) −53.7940 −2.32572
\(536\) 67.2969 2.90678
\(537\) −11.5531 −0.498554
\(538\) 16.4668 0.709935
\(539\) 6.88108 0.296389
\(540\) −85.9290 −3.69779
\(541\) −12.1754 −0.523463 −0.261731 0.965141i \(-0.584293\pi\)
−0.261731 + 0.965141i \(0.584293\pi\)
\(542\) −16.9675 −0.728816
\(543\) −3.08079 −0.132209
\(544\) −24.8669 −1.06616
\(545\) −36.6864 −1.57147
\(546\) −3.70357 −0.158498
\(547\) 25.8507 1.10530 0.552648 0.833414i \(-0.313617\pi\)
0.552648 + 0.833414i \(0.313617\pi\)
\(548\) 69.3473 2.96237
\(549\) 26.7702 1.14252
\(550\) 18.7818 0.800861
\(551\) −35.5272 −1.51351
\(552\) −11.6626 −0.496392
\(553\) 4.39039 0.186698
\(554\) 0.469075 0.0199291
\(555\) 16.5781 0.703701
\(556\) 54.5246 2.31236
\(557\) 15.9037 0.673861 0.336931 0.941529i \(-0.390611\pi\)
0.336931 + 0.941529i \(0.390611\pi\)
\(558\) 18.4845 0.782512
\(559\) −4.61873 −0.195351
\(560\) −19.2349 −0.812825
\(561\) −0.843025 −0.0355925
\(562\) −8.22369 −0.346895
\(563\) 5.10811 0.215281 0.107641 0.994190i \(-0.465670\pi\)
0.107641 + 0.994190i \(0.465670\pi\)
\(564\) 50.0156 2.10603
\(565\) −43.2982 −1.82157
\(566\) 32.7727 1.37754
\(567\) −1.07209 −0.0450237
\(568\) 146.310 6.13904
\(569\) −18.8457 −0.790054 −0.395027 0.918670i \(-0.629265\pi\)
−0.395027 + 0.918670i \(0.629265\pi\)
\(570\) −60.3209 −2.52657
\(571\) −4.38995 −0.183714 −0.0918569 0.995772i \(-0.529280\pi\)
−0.0918569 + 0.995772i \(0.529280\pi\)
\(572\) 25.9005 1.08295
\(573\) −22.1430 −0.925036
\(574\) −9.71753 −0.405602
\(575\) 9.46687 0.394796
\(576\) −82.7036 −3.44598
\(577\) −15.3782 −0.640204 −0.320102 0.947383i \(-0.603717\pi\)
−0.320102 + 0.947383i \(0.603717\pi\)
\(578\) −2.75821 −0.114726
\(579\) 14.7353 0.612377
\(580\) −90.6933 −3.76584
\(581\) −5.92490 −0.245806
\(582\) −15.4496 −0.640408
\(583\) 14.0191 0.580612
\(584\) 25.3988 1.05101
\(585\) 36.3364 1.50232
\(586\) −9.73998 −0.402355
\(587\) −2.12660 −0.0877742 −0.0438871 0.999036i \(-0.513974\pi\)
−0.0438871 + 0.999036i \(0.513974\pi\)
\(588\) −32.5299 −1.34151
\(589\) 22.0985 0.910553
\(590\) −36.9174 −1.51987
\(591\) −3.59923 −0.148053
\(592\) 92.8807 3.81737
\(593\) 47.1226 1.93510 0.967548 0.252689i \(-0.0813150\pi\)
0.967548 + 0.252689i \(0.0813150\pi\)
\(594\) −12.2989 −0.504630
\(595\) −1.18507 −0.0485832
\(596\) −61.5080 −2.51947
\(597\) 11.2660 0.461088
\(598\) 17.7111 0.724259
\(599\) −18.0705 −0.738341 −0.369170 0.929362i \(-0.620358\pi\)
−0.369170 + 0.929362i \(0.620358\pi\)
\(600\) −57.1229 −2.33203
\(601\) 16.9968 0.693315 0.346657 0.937992i \(-0.387317\pi\)
0.346657 + 0.937992i \(0.387317\pi\)
\(602\) 0.951168 0.0387667
\(603\) 15.4825 0.630495
\(604\) −74.4806 −3.03057
\(605\) 3.43649 0.139713
\(606\) 9.74043 0.395678
\(607\) −40.0404 −1.62519 −0.812594 0.582830i \(-0.801945\pi\)
−0.812594 + 0.582830i \(0.801945\pi\)
\(608\) −187.719 −7.61300
\(609\) 1.36819 0.0554418
\(610\) 110.838 4.48769
\(611\) −48.8654 −1.97688
\(612\) −12.8378 −0.518937
\(613\) −22.7463 −0.918716 −0.459358 0.888251i \(-0.651921\pi\)
−0.459358 + 0.888251i \(0.651921\pi\)
\(614\) −58.2267 −2.34984
\(615\) −29.5974 −1.19348
\(616\) −3.43154 −0.138261
\(617\) −18.1913 −0.732355 −0.366178 0.930545i \(-0.619334\pi\)
−0.366178 + 0.930545i \(0.619334\pi\)
\(618\) −0.459460 −0.0184822
\(619\) −17.7054 −0.711641 −0.355821 0.934554i \(-0.615799\pi\)
−0.355821 + 0.934554i \(0.615799\pi\)
\(620\) 56.4127 2.26559
\(621\) −6.19918 −0.248765
\(622\) 19.4253 0.778883
\(623\) −0.842095 −0.0337378
\(624\) −63.1988 −2.52998
\(625\) −12.6787 −0.507150
\(626\) −89.7579 −3.58745
\(627\) −6.36395 −0.254151
\(628\) −32.4314 −1.29415
\(629\) 5.72242 0.228168
\(630\) −7.48301 −0.298130
\(631\) 10.7013 0.426012 0.213006 0.977051i \(-0.431675\pi\)
0.213006 + 0.977051i \(0.431675\pi\)
\(632\) 126.687 5.03933
\(633\) 14.5952 0.580105
\(634\) −39.4072 −1.56506
\(635\) 22.7589 0.903159
\(636\) −66.2745 −2.62795
\(637\) 31.7818 1.25924
\(638\) −12.9808 −0.513915
\(639\) 33.6604 1.33159
\(640\) −171.513 −6.77963
\(641\) 0.451181 0.0178206 0.00891029 0.999960i \(-0.497164\pi\)
0.00891029 + 0.999960i \(0.497164\pi\)
\(642\) 36.3988 1.43655
\(643\) 18.5369 0.731023 0.365511 0.930807i \(-0.380894\pi\)
0.365511 + 0.930807i \(0.380894\pi\)
\(644\) −2.68851 −0.105942
\(645\) 2.89704 0.114071
\(646\) −20.8216 −0.819213
\(647\) −13.9157 −0.547081 −0.273541 0.961860i \(-0.588195\pi\)
−0.273541 + 0.961860i \(0.588195\pi\)
\(648\) −30.9358 −1.21527
\(649\) −3.89484 −0.152886
\(650\) 86.7483 3.40255
\(651\) −0.851035 −0.0333547
\(652\) 33.4575 1.31030
\(653\) −32.2093 −1.26045 −0.630224 0.776413i \(-0.717037\pi\)
−0.630224 + 0.776413i \(0.717037\pi\)
\(654\) 24.8232 0.970663
\(655\) 54.0142 2.11051
\(656\) −165.823 −6.47429
\(657\) 5.84330 0.227969
\(658\) 10.0632 0.392305
\(659\) −9.15591 −0.356664 −0.178332 0.983970i \(-0.557070\pi\)
−0.178332 + 0.983970i \(0.557070\pi\)
\(660\) −16.2458 −0.632366
\(661\) 33.8763 1.31764 0.658818 0.752302i \(-0.271057\pi\)
0.658818 + 0.752302i \(0.271057\pi\)
\(662\) 6.11371 0.237616
\(663\) −3.89370 −0.151219
\(664\) −170.966 −6.63476
\(665\) −8.94605 −0.346913
\(666\) 36.1336 1.40015
\(667\) −6.54290 −0.253342
\(668\) 116.099 4.49200
\(669\) −11.7469 −0.454163
\(670\) 64.1029 2.47651
\(671\) 11.6936 0.451425
\(672\) 7.22923 0.278874
\(673\) −1.83556 −0.0707557 −0.0353779 0.999374i \(-0.511263\pi\)
−0.0353779 + 0.999374i \(0.511263\pi\)
\(674\) 44.7776 1.72477
\(675\) −30.3634 −1.16869
\(676\) 46.7272 1.79720
\(677\) −22.6730 −0.871393 −0.435697 0.900094i \(-0.643498\pi\)
−0.435697 + 0.900094i \(0.643498\pi\)
\(678\) 29.2970 1.12514
\(679\) −2.29130 −0.0879319
\(680\) −34.1959 −1.31135
\(681\) 7.13245 0.273316
\(682\) 8.07428 0.309180
\(683\) 20.3405 0.778306 0.389153 0.921173i \(-0.372768\pi\)
0.389153 + 0.921173i \(0.372768\pi\)
\(684\) −96.9118 −3.70551
\(685\) 42.4970 1.62373
\(686\) −13.2032 −0.504102
\(687\) 16.4359 0.627069
\(688\) 16.2310 0.618802
\(689\) 64.7505 2.46680
\(690\) −11.1091 −0.422914
\(691\) 13.6126 0.517847 0.258924 0.965898i \(-0.416632\pi\)
0.258924 + 0.965898i \(0.416632\pi\)
\(692\) −85.2862 −3.24209
\(693\) −0.789469 −0.0299894
\(694\) 6.64738 0.252331
\(695\) 33.4135 1.26744
\(696\) 39.4797 1.49648
\(697\) −10.2164 −0.386974
\(698\) 42.0419 1.59131
\(699\) −3.45039 −0.130506
\(700\) −13.1682 −0.497712
\(701\) 5.85699 0.221216 0.110608 0.993864i \(-0.464720\pi\)
0.110608 + 0.993864i \(0.464720\pi\)
\(702\) −56.8053 −2.14398
\(703\) 43.1982 1.62925
\(704\) −36.1260 −1.36155
\(705\) 30.6502 1.15435
\(706\) 42.1776 1.58738
\(707\) 1.44458 0.0543290
\(708\) 18.4126 0.691989
\(709\) 38.8223 1.45800 0.729001 0.684512i \(-0.239985\pi\)
0.729001 + 0.684512i \(0.239985\pi\)
\(710\) 139.366 5.23031
\(711\) 29.1459 1.09306
\(712\) −24.2991 −0.910647
\(713\) 4.06979 0.152415
\(714\) 0.801858 0.0300088
\(715\) 15.8722 0.593587
\(716\) −76.8502 −2.87203
\(717\) −4.70901 −0.175861
\(718\) −44.7407 −1.66971
\(719\) 15.6286 0.582849 0.291424 0.956594i \(-0.405871\pi\)
0.291424 + 0.956594i \(0.405871\pi\)
\(720\) −127.692 −4.75881
\(721\) −0.0681414 −0.00253772
\(722\) −104.775 −3.89931
\(723\) −24.2076 −0.900289
\(724\) −20.4931 −0.761619
\(725\) −32.0469 −1.19019
\(726\) −2.32524 −0.0862977
\(727\) 37.9239 1.40652 0.703259 0.710934i \(-0.251727\pi\)
0.703259 + 0.710934i \(0.251727\pi\)
\(728\) −15.8494 −0.587417
\(729\) 4.16003 0.154075
\(730\) 24.1933 0.895434
\(731\) 1.00000 0.0369863
\(732\) −55.2806 −2.04323
\(733\) 29.4419 1.08746 0.543730 0.839260i \(-0.317011\pi\)
0.543730 + 0.839260i \(0.317011\pi\)
\(734\) −39.2913 −1.45027
\(735\) −19.9348 −0.735305
\(736\) −34.5714 −1.27432
\(737\) 6.76294 0.249116
\(738\) −64.5105 −2.37466
\(739\) 33.7747 1.24242 0.621211 0.783643i \(-0.286641\pi\)
0.621211 + 0.783643i \(0.286641\pi\)
\(740\) 110.276 4.05382
\(741\) −29.3933 −1.07979
\(742\) −13.3345 −0.489526
\(743\) −39.0789 −1.43367 −0.716833 0.697245i \(-0.754409\pi\)
−0.716833 + 0.697245i \(0.754409\pi\)
\(744\) −24.5570 −0.900305
\(745\) −37.6930 −1.38096
\(746\) 28.1658 1.03122
\(747\) −39.3328 −1.43911
\(748\) −5.60771 −0.205038
\(749\) 5.39821 0.197246
\(750\) −14.4586 −0.527953
\(751\) 41.3124 1.50751 0.753756 0.657154i \(-0.228240\pi\)
0.753756 + 0.657154i \(0.228240\pi\)
\(752\) 171.722 6.26204
\(753\) −14.7659 −0.538101
\(754\) −59.9549 −2.18343
\(755\) −45.6427 −1.66111
\(756\) 8.62294 0.313613
\(757\) −46.9320 −1.70577 −0.852886 0.522097i \(-0.825150\pi\)
−0.852886 + 0.522097i \(0.825150\pi\)
\(758\) 8.05790 0.292676
\(759\) −1.17202 −0.0425417
\(760\) −258.143 −9.36382
\(761\) −40.4801 −1.46740 −0.733701 0.679472i \(-0.762209\pi\)
−0.733701 + 0.679472i \(0.762209\pi\)
\(762\) −15.3994 −0.557862
\(763\) 3.68146 0.133278
\(764\) −147.293 −5.32887
\(765\) −7.86718 −0.284439
\(766\) 104.855 3.78855
\(767\) −17.9892 −0.649553
\(768\) 55.1407 1.98972
\(769\) 11.1299 0.401356 0.200678 0.979657i \(-0.435686\pi\)
0.200678 + 0.979657i \(0.435686\pi\)
\(770\) −3.26868 −0.117795
\(771\) 9.70426 0.349490
\(772\) 98.0175 3.52773
\(773\) −41.1186 −1.47893 −0.739466 0.673194i \(-0.764922\pi\)
−0.739466 + 0.673194i \(0.764922\pi\)
\(774\) 6.31439 0.226966
\(775\) 19.9337 0.716040
\(776\) −66.1165 −2.37344
\(777\) −1.66360 −0.0596815
\(778\) −12.6260 −0.452664
\(779\) −77.1231 −2.76322
\(780\) −75.0349 −2.68668
\(781\) 14.7033 0.526126
\(782\) −3.83462 −0.137126
\(783\) 20.9853 0.749952
\(784\) −111.687 −3.98882
\(785\) −19.8744 −0.709349
\(786\) −36.5478 −1.30362
\(787\) 20.1562 0.718491 0.359245 0.933243i \(-0.383034\pi\)
0.359245 + 0.933243i \(0.383034\pi\)
\(788\) −23.9417 −0.852889
\(789\) 14.7253 0.524234
\(790\) 120.674 4.29339
\(791\) 4.34496 0.154489
\(792\) −22.7805 −0.809470
\(793\) 54.0094 1.91793
\(794\) −28.0608 −0.995841
\(795\) −40.6139 −1.44043
\(796\) 74.9405 2.65620
\(797\) −25.3990 −0.899679 −0.449839 0.893110i \(-0.648519\pi\)
−0.449839 + 0.893110i \(0.648519\pi\)
\(798\) 6.05318 0.214280
\(799\) 10.5798 0.374288
\(800\) −169.330 −5.98670
\(801\) −5.59030 −0.197524
\(802\) 9.11748 0.321949
\(803\) 2.55243 0.0900732
\(804\) −31.9714 −1.12754
\(805\) −1.64756 −0.0580687
\(806\) 37.2929 1.31359
\(807\) −5.03295 −0.177168
\(808\) 41.6841 1.46644
\(809\) 8.09152 0.284483 0.142241 0.989832i \(-0.454569\pi\)
0.142241 + 0.989832i \(0.454569\pi\)
\(810\) −29.4675 −1.03538
\(811\) 35.0889 1.23214 0.616069 0.787692i \(-0.288724\pi\)
0.616069 + 0.787692i \(0.288724\pi\)
\(812\) 9.10104 0.319384
\(813\) 5.18598 0.181880
\(814\) 15.7836 0.553215
\(815\) 20.5033 0.718198
\(816\) 13.6832 0.479006
\(817\) 7.54894 0.264104
\(818\) 59.1198 2.06708
\(819\) −3.64634 −0.127414
\(820\) −196.879 −6.87531
\(821\) −26.4519 −0.923179 −0.461589 0.887094i \(-0.652721\pi\)
−0.461589 + 0.887094i \(0.652721\pi\)
\(822\) −28.7548 −1.00294
\(823\) −23.0387 −0.803080 −0.401540 0.915841i \(-0.631525\pi\)
−0.401540 + 0.915841i \(0.631525\pi\)
\(824\) −1.96625 −0.0684977
\(825\) −5.74052 −0.199859
\(826\) 3.70465 0.128901
\(827\) 45.0672 1.56714 0.783570 0.621303i \(-0.213396\pi\)
0.783570 + 0.621303i \(0.213396\pi\)
\(828\) −17.8478 −0.620255
\(829\) 18.9487 0.658116 0.329058 0.944310i \(-0.393269\pi\)
0.329058 + 0.944310i \(0.393269\pi\)
\(830\) −162.852 −5.65266
\(831\) −0.143369 −0.00497342
\(832\) −166.856 −5.78470
\(833\) −6.88108 −0.238415
\(834\) −22.6086 −0.782873
\(835\) 71.1471 2.46215
\(836\) −42.3323 −1.46409
\(837\) −13.0532 −0.451183
\(838\) 82.5206 2.85063
\(839\) −10.6298 −0.366981 −0.183490 0.983022i \(-0.558740\pi\)
−0.183490 + 0.983022i \(0.558740\pi\)
\(840\) 9.94133 0.343008
\(841\) −6.85122 −0.236249
\(842\) −78.5488 −2.70697
\(843\) 2.51351 0.0865697
\(844\) 97.0855 3.34182
\(845\) 28.6351 0.985078
\(846\) 66.8052 2.29681
\(847\) −0.344850 −0.0118492
\(848\) −227.544 −7.81391
\(849\) −10.0167 −0.343773
\(850\) −18.7818 −0.644212
\(851\) 7.95563 0.272715
\(852\) −69.5091 −2.38134
\(853\) −25.4605 −0.871752 −0.435876 0.900007i \(-0.643561\pi\)
−0.435876 + 0.900007i \(0.643561\pi\)
\(854\) −11.1225 −0.380606
\(855\) −59.3889 −2.03106
\(856\) 155.768 5.32404
\(857\) 25.4830 0.870484 0.435242 0.900314i \(-0.356663\pi\)
0.435242 + 0.900314i \(0.356663\pi\)
\(858\) −10.7396 −0.366645
\(859\) −1.97954 −0.0675410 −0.0337705 0.999430i \(-0.510752\pi\)
−0.0337705 + 0.999430i \(0.510752\pi\)
\(860\) 19.2708 0.657130
\(861\) 2.97009 0.101220
\(862\) 36.9103 1.25717
\(863\) −19.0304 −0.647801 −0.323901 0.946091i \(-0.604994\pi\)
−0.323901 + 0.946091i \(0.604994\pi\)
\(864\) 110.882 3.77228
\(865\) −52.2646 −1.77705
\(866\) 43.6316 1.48266
\(867\) 0.843025 0.0286306
\(868\) −5.66100 −0.192147
\(869\) 12.7313 0.431880
\(870\) 37.6060 1.27496
\(871\) 31.2362 1.05840
\(872\) 106.230 3.59742
\(873\) −15.2109 −0.514811
\(874\) −28.9473 −0.979158
\(875\) −2.14432 −0.0724911
\(876\) −12.0664 −0.407688
\(877\) 2.76349 0.0933165 0.0466582 0.998911i \(-0.485143\pi\)
0.0466582 + 0.998911i \(0.485143\pi\)
\(878\) 18.1580 0.612802
\(879\) 2.97695 0.100410
\(880\) −55.7777 −1.88027
\(881\) −3.25101 −0.109529 −0.0547647 0.998499i \(-0.517441\pi\)
−0.0547647 + 0.998499i \(0.517441\pi\)
\(882\) −43.4498 −1.46303
\(883\) −32.5658 −1.09592 −0.547962 0.836503i \(-0.684596\pi\)
−0.547962 + 0.836503i \(0.684596\pi\)
\(884\) −25.9005 −0.871129
\(885\) 11.2835 0.379292
\(886\) 62.4006 2.09639
\(887\) −51.8203 −1.73995 −0.869977 0.493092i \(-0.835867\pi\)
−0.869977 + 0.493092i \(0.835867\pi\)
\(888\) −48.0042 −1.61091
\(889\) −2.28385 −0.0765978
\(890\) −23.1458 −0.775849
\(891\) −3.10887 −0.104151
\(892\) −78.1395 −2.61630
\(893\) 79.8666 2.67263
\(894\) 25.5043 0.852991
\(895\) −47.0949 −1.57421
\(896\) 17.2112 0.574987
\(897\) −5.41325 −0.180743
\(898\) −2.69560 −0.0899532
\(899\) −13.7769 −0.459485
\(900\) −87.4181 −2.91394
\(901\) −14.0191 −0.467044
\(902\) −28.1790 −0.938258
\(903\) −0.290717 −0.00967446
\(904\) 125.376 4.16994
\(905\) −12.5584 −0.417457
\(906\) 30.8834 1.02603
\(907\) −33.5227 −1.11310 −0.556551 0.830813i \(-0.687876\pi\)
−0.556551 + 0.830813i \(0.687876\pi\)
\(908\) 47.4443 1.57450
\(909\) 9.58993 0.318078
\(910\) −15.0971 −0.500465
\(911\) 38.9582 1.29074 0.645371 0.763869i \(-0.276703\pi\)
0.645371 + 0.763869i \(0.276703\pi\)
\(912\) 103.293 3.42038
\(913\) −17.1811 −0.568611
\(914\) −39.8162 −1.31700
\(915\) −33.8767 −1.11993
\(916\) 109.330 3.61236
\(917\) −5.42031 −0.178994
\(918\) 12.2989 0.405924
\(919\) −52.4566 −1.73038 −0.865192 0.501441i \(-0.832803\pi\)
−0.865192 + 0.501441i \(0.832803\pi\)
\(920\) −47.5410 −1.56738
\(921\) 17.7965 0.586416
\(922\) 53.2091 1.75235
\(923\) 67.9107 2.23531
\(924\) 1.63026 0.0536316
\(925\) 38.9664 1.28121
\(926\) 86.7344 2.85027
\(927\) −0.452361 −0.0148575
\(928\) 117.030 3.84169
\(929\) −3.42696 −0.112435 −0.0562174 0.998419i \(-0.517904\pi\)
−0.0562174 + 0.998419i \(0.517904\pi\)
\(930\) −23.3915 −0.767038
\(931\) −51.9449 −1.70242
\(932\) −22.9517 −0.751807
\(933\) −5.93719 −0.194375
\(934\) 53.9420 1.76504
\(935\) −3.43649 −0.112385
\(936\) −105.217 −3.43913
\(937\) −42.3959 −1.38501 −0.692506 0.721412i \(-0.743494\pi\)
−0.692506 + 0.721412i \(0.743494\pi\)
\(938\) −6.43270 −0.210035
\(939\) 27.4338 0.895268
\(940\) 203.882 6.64991
\(941\) −48.3639 −1.57662 −0.788310 0.615279i \(-0.789043\pi\)
−0.788310 + 0.615279i \(0.789043\pi\)
\(942\) 13.4477 0.438149
\(943\) −14.2034 −0.462528
\(944\) 63.2173 2.05755
\(945\) 5.28426 0.171897
\(946\) 2.75821 0.0896771
\(947\) −22.7676 −0.739848 −0.369924 0.929062i \(-0.620616\pi\)
−0.369924 + 0.929062i \(0.620616\pi\)
\(948\) −60.1864 −1.95476
\(949\) 11.7890 0.382686
\(950\) −141.783 −4.60005
\(951\) 12.0445 0.390570
\(952\) 3.43154 0.111217
\(953\) 57.5917 1.86558 0.932789 0.360423i \(-0.117368\pi\)
0.932789 + 0.360423i \(0.117368\pi\)
\(954\) −88.5221 −2.86601
\(955\) −90.2631 −2.92085
\(956\) −31.3239 −1.01309
\(957\) 3.96748 0.128251
\(958\) 97.1896 3.14005
\(959\) −4.26456 −0.137710
\(960\) 104.659 3.37784
\(961\) −22.4305 −0.723566
\(962\) 72.9003 2.35040
\(963\) 35.8364 1.15481
\(964\) −161.026 −5.18631
\(965\) 60.0665 1.93361
\(966\) 1.11479 0.0358678
\(967\) −43.0726 −1.38512 −0.692561 0.721359i \(-0.743518\pi\)
−0.692561 + 0.721359i \(0.743518\pi\)
\(968\) −9.95082 −0.319832
\(969\) 6.36395 0.204439
\(970\) −62.9785 −2.02212
\(971\) 11.3293 0.363575 0.181787 0.983338i \(-0.441812\pi\)
0.181787 + 0.983338i \(0.441812\pi\)
\(972\) 89.7117 2.87750
\(973\) −3.35303 −0.107493
\(974\) −82.2400 −2.63514
\(975\) −26.5139 −0.849125
\(976\) −189.798 −6.07530
\(977\) −21.7646 −0.696310 −0.348155 0.937437i \(-0.613192\pi\)
−0.348155 + 0.937437i \(0.613192\pi\)
\(978\) −13.8732 −0.443615
\(979\) −2.44192 −0.0780440
\(980\) −132.604 −4.23588
\(981\) 24.4396 0.780297
\(982\) −39.2355 −1.25206
\(983\) 18.1781 0.579792 0.289896 0.957058i \(-0.406379\pi\)
0.289896 + 0.957058i \(0.406379\pi\)
\(984\) 85.7034 2.73212
\(985\) −14.6718 −0.467484
\(986\) 12.9808 0.413393
\(987\) −3.07574 −0.0979019
\(988\) −195.522 −6.22037
\(989\) 1.39026 0.0442076
\(990\) −21.6993 −0.689650
\(991\) 44.0954 1.40074 0.700368 0.713782i \(-0.253019\pi\)
0.700368 + 0.713782i \(0.253019\pi\)
\(992\) −72.7944 −2.31122
\(993\) −1.86861 −0.0592985
\(994\) −13.9853 −0.443588
\(995\) 45.9246 1.45591
\(996\) 81.2225 2.57363
\(997\) −48.7887 −1.54515 −0.772577 0.634921i \(-0.781032\pi\)
−0.772577 + 0.634921i \(0.781032\pi\)
\(998\) 52.3314 1.65652
\(999\) −25.5164 −0.807302
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 \(a_p\))