Properties

Label 619.2.a.b.1.11
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 1.11
Character \(\chi\) = 619.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.394547 q^{2} +1.27337 q^{3} -1.84433 q^{4} +1.92856 q^{5} -0.502406 q^{6} +3.31459 q^{7} +1.51677 q^{8} -1.37852 q^{9} +O(q^{10})\) \(q-0.394547 q^{2} +1.27337 q^{3} -1.84433 q^{4} +1.92856 q^{5} -0.502406 q^{6} +3.31459 q^{7} +1.51677 q^{8} -1.37852 q^{9} -0.760909 q^{10} +2.52548 q^{11} -2.34852 q^{12} -4.15823 q^{13} -1.30776 q^{14} +2.45578 q^{15} +3.09023 q^{16} +2.64063 q^{17} +0.543891 q^{18} +6.63734 q^{19} -3.55691 q^{20} +4.22072 q^{21} -0.996422 q^{22} -4.34053 q^{23} +1.93142 q^{24} -1.28064 q^{25} +1.64062 q^{26} -5.57549 q^{27} -6.11321 q^{28} +0.725269 q^{29} -0.968922 q^{30} +6.55612 q^{31} -4.25278 q^{32} +3.21588 q^{33} -1.04185 q^{34} +6.39241 q^{35} +2.54245 q^{36} +6.31493 q^{37} -2.61874 q^{38} -5.29499 q^{39} +2.92519 q^{40} -0.0915471 q^{41} -1.66527 q^{42} +0.725844 q^{43} -4.65783 q^{44} -2.65856 q^{45} +1.71254 q^{46} +10.3201 q^{47} +3.93501 q^{48} +3.98653 q^{49} +0.505274 q^{50} +3.36251 q^{51} +7.66917 q^{52} -4.81831 q^{53} +2.19979 q^{54} +4.87055 q^{55} +5.02748 q^{56} +8.45182 q^{57} -0.286153 q^{58} +12.8732 q^{59} -4.52928 q^{60} -3.71827 q^{61} -2.58670 q^{62} -4.56923 q^{63} -4.50253 q^{64} -8.01942 q^{65} -1.26882 q^{66} -7.85813 q^{67} -4.87020 q^{68} -5.52711 q^{69} -2.52211 q^{70} -8.16026 q^{71} -2.09090 q^{72} -12.1531 q^{73} -2.49154 q^{74} -1.63074 q^{75} -12.2415 q^{76} +8.37095 q^{77} +2.08912 q^{78} +14.4595 q^{79} +5.95970 q^{80} -2.96412 q^{81} +0.0361197 q^{82} -2.55883 q^{83} -7.78440 q^{84} +5.09262 q^{85} -0.286380 q^{86} +0.923538 q^{87} +3.83058 q^{88} -9.14859 q^{89} +1.04893 q^{90} -13.7829 q^{91} +8.00538 q^{92} +8.34839 q^{93} -4.07177 q^{94} +12.8005 q^{95} -5.41538 q^{96} +0.730351 q^{97} -1.57288 q^{98} -3.48143 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30q + 9q^{2} + q^{3} + 33q^{4} + 21q^{5} + 6q^{6} + 2q^{7} + 27q^{8} + 43q^{9} + O(q^{10}) \) \( 30q + 9q^{2} + q^{3} + 33q^{4} + 21q^{5} + 6q^{6} + 2q^{7} + 27q^{8} + 43q^{9} + 5q^{10} + 23q^{11} - 6q^{12} + 9q^{13} + 7q^{14} - 2q^{15} + 35q^{16} + 4q^{17} + 10q^{18} - q^{19} + 29q^{20} + 30q^{21} + 4q^{23} + 4q^{24} + 35q^{25} + q^{26} - 5q^{27} - 13q^{28} + 90q^{29} - 31q^{30} + 2q^{31} + 43q^{32} - 6q^{33} - 9q^{34} + 9q^{35} + 33q^{36} + 19q^{37} + 5q^{38} + 32q^{39} - 12q^{40} + 59q^{41} - 25q^{42} - 4q^{43} + 52q^{44} + 30q^{45} - q^{46} + 4q^{47} - 44q^{48} + 30q^{49} + 31q^{50} - 12q^{52} + 34q^{53} - 28q^{54} - 17q^{55} + 2q^{56} - 8q^{57} + 6q^{58} + 13q^{59} - 64q^{60} + 16q^{61} + 28q^{62} - 40q^{63} + 37q^{64} + 31q^{65} - 59q^{66} - 11q^{67} - 52q^{68} + 6q^{69} - 40q^{70} + 42q^{71} + 6q^{72} - 4q^{73} + 16q^{74} - 52q^{75} - 42q^{76} + 29q^{77} - 56q^{78} + 3q^{79} + 21q^{80} + 30q^{81} - 43q^{82} - 11q^{83} - 36q^{84} + 19q^{85} - 11q^{86} - 20q^{87} - 47q^{88} + 58q^{89} - 33q^{90} - 39q^{91} - 7q^{92} - 15q^{93} - 46q^{94} + 23q^{95} - 70q^{96} - 9q^{97} - 8q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.394547 −0.278987 −0.139493 0.990223i \(-0.544547\pi\)
−0.139493 + 0.990223i \(0.544547\pi\)
\(3\) 1.27337 0.735183 0.367591 0.929987i \(-0.380183\pi\)
0.367591 + 0.929987i \(0.380183\pi\)
\(4\) −1.84433 −0.922166
\(5\) 1.92856 0.862480 0.431240 0.902237i \(-0.358076\pi\)
0.431240 + 0.902237i \(0.358076\pi\)
\(6\) −0.502406 −0.205106
\(7\) 3.31459 1.25280 0.626399 0.779502i \(-0.284528\pi\)
0.626399 + 0.779502i \(0.284528\pi\)
\(8\) 1.51677 0.536259
\(9\) −1.37852 −0.459507
\(10\) −0.760909 −0.240621
\(11\) 2.52548 0.761461 0.380731 0.924686i \(-0.375672\pi\)
0.380731 + 0.924686i \(0.375672\pi\)
\(12\) −2.34852 −0.677961
\(13\) −4.15823 −1.15329 −0.576643 0.816996i \(-0.695638\pi\)
−0.576643 + 0.816996i \(0.695638\pi\)
\(14\) −1.30776 −0.349515
\(15\) 2.45578 0.634080
\(16\) 3.09023 0.772557
\(17\) 2.64063 0.640447 0.320223 0.947342i \(-0.396242\pi\)
0.320223 + 0.947342i \(0.396242\pi\)
\(18\) 0.543891 0.128196
\(19\) 6.63734 1.52271 0.761355 0.648335i \(-0.224534\pi\)
0.761355 + 0.648335i \(0.224534\pi\)
\(20\) −3.55691 −0.795350
\(21\) 4.22072 0.921036
\(22\) −0.996422 −0.212438
\(23\) −4.34053 −0.905063 −0.452531 0.891749i \(-0.649479\pi\)
−0.452531 + 0.891749i \(0.649479\pi\)
\(24\) 1.93142 0.394249
\(25\) −1.28064 −0.256128
\(26\) 1.64062 0.321752
\(27\) −5.57549 −1.07300
\(28\) −6.11321 −1.15529
\(29\) 0.725269 0.134679 0.0673395 0.997730i \(-0.478549\pi\)
0.0673395 + 0.997730i \(0.478549\pi\)
\(30\) −0.968922 −0.176900
\(31\) 6.55612 1.17751 0.588757 0.808310i \(-0.299617\pi\)
0.588757 + 0.808310i \(0.299617\pi\)
\(32\) −4.25278 −0.751793
\(33\) 3.21588 0.559813
\(34\) −1.04185 −0.178676
\(35\) 6.39241 1.08051
\(36\) 2.54245 0.423741
\(37\) 6.31493 1.03817 0.519084 0.854723i \(-0.326273\pi\)
0.519084 + 0.854723i \(0.326273\pi\)
\(38\) −2.61874 −0.424816
\(39\) −5.29499 −0.847876
\(40\) 2.92519 0.462513
\(41\) −0.0915471 −0.0142973 −0.00714863 0.999974i \(-0.502275\pi\)
−0.00714863 + 0.999974i \(0.502275\pi\)
\(42\) −1.66527 −0.256957
\(43\) 0.725844 0.110690 0.0553451 0.998467i \(-0.482374\pi\)
0.0553451 + 0.998467i \(0.482374\pi\)
\(44\) −4.65783 −0.702194
\(45\) −2.65856 −0.396315
\(46\) 1.71254 0.252501
\(47\) 10.3201 1.50534 0.752671 0.658397i \(-0.228765\pi\)
0.752671 + 0.658397i \(0.228765\pi\)
\(48\) 3.93501 0.567970
\(49\) 3.98653 0.569505
\(50\) 0.505274 0.0714565
\(51\) 3.36251 0.470845
\(52\) 7.66917 1.06352
\(53\) −4.81831 −0.661845 −0.330923 0.943658i \(-0.607360\pi\)
−0.330923 + 0.943658i \(0.607360\pi\)
\(54\) 2.19979 0.299354
\(55\) 4.87055 0.656745
\(56\) 5.02748 0.671825
\(57\) 8.45182 1.11947
\(58\) −0.286153 −0.0375737
\(59\) 12.8732 1.67595 0.837974 0.545710i \(-0.183740\pi\)
0.837974 + 0.545710i \(0.183740\pi\)
\(60\) −4.52928 −0.584727
\(61\) −3.71827 −0.476076 −0.238038 0.971256i \(-0.576504\pi\)
−0.238038 + 0.971256i \(0.576504\pi\)
\(62\) −2.58670 −0.328511
\(63\) −4.56923 −0.575669
\(64\) −4.50253 −0.562817
\(65\) −8.01942 −0.994687
\(66\) −1.26882 −0.156181
\(67\) −7.85813 −0.960023 −0.480012 0.877262i \(-0.659368\pi\)
−0.480012 + 0.877262i \(0.659368\pi\)
\(68\) −4.87020 −0.590598
\(69\) −5.52711 −0.665386
\(70\) −2.52211 −0.301449
\(71\) −8.16026 −0.968445 −0.484223 0.874945i \(-0.660898\pi\)
−0.484223 + 0.874945i \(0.660898\pi\)
\(72\) −2.09090 −0.246415
\(73\) −12.1531 −1.42241 −0.711205 0.702984i \(-0.751850\pi\)
−0.711205 + 0.702984i \(0.751850\pi\)
\(74\) −2.49154 −0.289635
\(75\) −1.63074 −0.188301
\(76\) −12.2415 −1.40419
\(77\) 8.37095 0.953958
\(78\) 2.08912 0.236546
\(79\) 14.4595 1.62683 0.813413 0.581686i \(-0.197607\pi\)
0.813413 + 0.581686i \(0.197607\pi\)
\(80\) 5.95970 0.666315
\(81\) −2.96412 −0.329347
\(82\) 0.0361197 0.00398875
\(83\) −2.55883 −0.280868 −0.140434 0.990090i \(-0.544850\pi\)
−0.140434 + 0.990090i \(0.544850\pi\)
\(84\) −7.78440 −0.849348
\(85\) 5.09262 0.552372
\(86\) −0.286380 −0.0308811
\(87\) 0.923538 0.0990137
\(88\) 3.83058 0.408341
\(89\) −9.14859 −0.969748 −0.484874 0.874584i \(-0.661135\pi\)
−0.484874 + 0.874584i \(0.661135\pi\)
\(90\) 1.04893 0.110567
\(91\) −13.7829 −1.44484
\(92\) 8.00538 0.834618
\(93\) 8.34839 0.865688
\(94\) −4.07177 −0.419971
\(95\) 12.8005 1.31331
\(96\) −5.41538 −0.552705
\(97\) 0.730351 0.0741559 0.0370780 0.999312i \(-0.488195\pi\)
0.0370780 + 0.999312i \(0.488195\pi\)
\(98\) −1.57288 −0.158884
\(99\) −3.48143 −0.349897
\(100\) 2.36193 0.236193
\(101\) −3.22161 −0.320563 −0.160281 0.987071i \(-0.551240\pi\)
−0.160281 + 0.987071i \(0.551240\pi\)
\(102\) −1.32667 −0.131360
\(103\) 3.68117 0.362716 0.181358 0.983417i \(-0.441951\pi\)
0.181358 + 0.983417i \(0.441951\pi\)
\(104\) −6.30709 −0.618461
\(105\) 8.13992 0.794375
\(106\) 1.90105 0.184646
\(107\) −9.76971 −0.944474 −0.472237 0.881472i \(-0.656553\pi\)
−0.472237 + 0.881472i \(0.656553\pi\)
\(108\) 10.2831 0.989488
\(109\) −18.7013 −1.79126 −0.895631 0.444798i \(-0.853275\pi\)
−0.895631 + 0.444798i \(0.853275\pi\)
\(110\) −1.92166 −0.183223
\(111\) 8.04126 0.763243
\(112\) 10.2429 0.967858
\(113\) 7.61333 0.716202 0.358101 0.933683i \(-0.383424\pi\)
0.358101 + 0.933683i \(0.383424\pi\)
\(114\) −3.33464 −0.312318
\(115\) −8.37098 −0.780598
\(116\) −1.33764 −0.124196
\(117\) 5.73221 0.529943
\(118\) −5.07908 −0.467568
\(119\) 8.75261 0.802351
\(120\) 3.72486 0.340031
\(121\) −4.62194 −0.420176
\(122\) 1.46703 0.132819
\(123\) −0.116574 −0.0105111
\(124\) −12.0917 −1.08586
\(125\) −12.1126 −1.08339
\(126\) 1.80278 0.160604
\(127\) −15.5583 −1.38057 −0.690287 0.723535i \(-0.742516\pi\)
−0.690287 + 0.723535i \(0.742516\pi\)
\(128\) 10.2820 0.908811
\(129\) 0.924270 0.0813774
\(130\) 3.16404 0.277505
\(131\) −1.28101 −0.111923 −0.0559614 0.998433i \(-0.517822\pi\)
−0.0559614 + 0.998433i \(0.517822\pi\)
\(132\) −5.93116 −0.516241
\(133\) 22.0001 1.90765
\(134\) 3.10040 0.267834
\(135\) −10.7527 −0.925444
\(136\) 4.00523 0.343446
\(137\) 0.214753 0.0183476 0.00917378 0.999958i \(-0.497080\pi\)
0.00917378 + 0.999958i \(0.497080\pi\)
\(138\) 2.18071 0.185634
\(139\) −4.63534 −0.393165 −0.196582 0.980487i \(-0.562984\pi\)
−0.196582 + 0.980487i \(0.562984\pi\)
\(140\) −11.7897 −0.996413
\(141\) 13.1414 1.10670
\(142\) 3.21961 0.270184
\(143\) −10.5015 −0.878183
\(144\) −4.25994 −0.354995
\(145\) 1.39873 0.116158
\(146\) 4.79496 0.396834
\(147\) 5.07635 0.418690
\(148\) −11.6468 −0.957363
\(149\) 2.25407 0.184660 0.0923302 0.995728i \(-0.470568\pi\)
0.0923302 + 0.995728i \(0.470568\pi\)
\(150\) 0.643402 0.0525336
\(151\) −22.3859 −1.82174 −0.910870 0.412694i \(-0.864588\pi\)
−0.910870 + 0.412694i \(0.864588\pi\)
\(152\) 10.0673 0.816568
\(153\) −3.64016 −0.294289
\(154\) −3.30273 −0.266142
\(155\) 12.6439 1.01558
\(156\) 9.76571 0.781883
\(157\) −7.69459 −0.614095 −0.307047 0.951694i \(-0.599341\pi\)
−0.307047 + 0.951694i \(0.599341\pi\)
\(158\) −5.70497 −0.453863
\(159\) −6.13550 −0.486577
\(160\) −8.20176 −0.648406
\(161\) −14.3871 −1.13386
\(162\) 1.16949 0.0918836
\(163\) −20.7421 −1.62465 −0.812325 0.583205i \(-0.801798\pi\)
−0.812325 + 0.583205i \(0.801798\pi\)
\(164\) 0.168843 0.0131844
\(165\) 6.20203 0.482828
\(166\) 1.00958 0.0783584
\(167\) 9.68268 0.749268 0.374634 0.927173i \(-0.377768\pi\)
0.374634 + 0.927173i \(0.377768\pi\)
\(168\) 6.40186 0.493914
\(169\) 4.29091 0.330070
\(170\) −2.00928 −0.154105
\(171\) −9.14971 −0.699696
\(172\) −1.33870 −0.102075
\(173\) −13.6349 −1.03664 −0.518322 0.855186i \(-0.673443\pi\)
−0.518322 + 0.855186i \(0.673443\pi\)
\(174\) −0.364379 −0.0276235
\(175\) −4.24481 −0.320877
\(176\) 7.80431 0.588272
\(177\) 16.3924 1.23213
\(178\) 3.60955 0.270547
\(179\) 21.4754 1.60515 0.802575 0.596551i \(-0.203463\pi\)
0.802575 + 0.596551i \(0.203463\pi\)
\(180\) 4.90327 0.365469
\(181\) 11.5422 0.857922 0.428961 0.903323i \(-0.358880\pi\)
0.428961 + 0.903323i \(0.358880\pi\)
\(182\) 5.43799 0.403090
\(183\) −4.73475 −0.350003
\(184\) −6.58358 −0.485348
\(185\) 12.1787 0.895399
\(186\) −3.29384 −0.241516
\(187\) 6.66886 0.487676
\(188\) −19.0337 −1.38818
\(189\) −18.4805 −1.34426
\(190\) −5.05042 −0.366396
\(191\) −13.8904 −1.00507 −0.502536 0.864556i \(-0.667599\pi\)
−0.502536 + 0.864556i \(0.667599\pi\)
\(192\) −5.73341 −0.413773
\(193\) 16.8713 1.21442 0.607210 0.794541i \(-0.292289\pi\)
0.607210 + 0.794541i \(0.292289\pi\)
\(194\) −0.288158 −0.0206885
\(195\) −10.2117 −0.731276
\(196\) −7.35249 −0.525178
\(197\) 26.7475 1.90568 0.952840 0.303473i \(-0.0981461\pi\)
0.952840 + 0.303473i \(0.0981461\pi\)
\(198\) 1.37359 0.0976166
\(199\) −16.1990 −1.14832 −0.574159 0.818744i \(-0.694671\pi\)
−0.574159 + 0.818744i \(0.694671\pi\)
\(200\) −1.94244 −0.137351
\(201\) −10.0063 −0.705792
\(202\) 1.27108 0.0894328
\(203\) 2.40397 0.168726
\(204\) −6.20158 −0.434198
\(205\) −0.176554 −0.0123311
\(206\) −1.45239 −0.101193
\(207\) 5.98350 0.415882
\(208\) −12.8499 −0.890980
\(209\) 16.7625 1.15949
\(210\) −3.21158 −0.221620
\(211\) −17.5817 −1.21038 −0.605188 0.796082i \(-0.706902\pi\)
−0.605188 + 0.796082i \(0.706902\pi\)
\(212\) 8.88656 0.610331
\(213\) −10.3911 −0.711984
\(214\) 3.85461 0.263496
\(215\) 1.39984 0.0954680
\(216\) −8.45674 −0.575408
\(217\) 21.7309 1.47519
\(218\) 7.37855 0.499739
\(219\) −15.4754 −1.04573
\(220\) −8.98292 −0.605628
\(221\) −10.9804 −0.738619
\(222\) −3.17266 −0.212935
\(223\) 2.98314 0.199766 0.0998830 0.994999i \(-0.468153\pi\)
0.0998830 + 0.994999i \(0.468153\pi\)
\(224\) −14.0962 −0.941845
\(225\) 1.76539 0.117693
\(226\) −3.00382 −0.199811
\(227\) −0.00326963 −0.000217013 0 −0.000108507 1.00000i \(-0.500035\pi\)
−0.000108507 1.00000i \(0.500035\pi\)
\(228\) −15.5880 −1.03234
\(229\) −6.94976 −0.459253 −0.229627 0.973279i \(-0.573750\pi\)
−0.229627 + 0.973279i \(0.573750\pi\)
\(230\) 3.30275 0.217777
\(231\) 10.6593 0.701333
\(232\) 1.10007 0.0722229
\(233\) 1.93016 0.126449 0.0632246 0.997999i \(-0.479862\pi\)
0.0632246 + 0.997999i \(0.479862\pi\)
\(234\) −2.26163 −0.147847
\(235\) 19.9030 1.29833
\(236\) −23.7425 −1.54550
\(237\) 18.4124 1.19601
\(238\) −3.45332 −0.223845
\(239\) −8.21315 −0.531265 −0.265632 0.964074i \(-0.585581\pi\)
−0.265632 + 0.964074i \(0.585581\pi\)
\(240\) 7.58893 0.489863
\(241\) 13.0765 0.842328 0.421164 0.906984i \(-0.361622\pi\)
0.421164 + 0.906984i \(0.361622\pi\)
\(242\) 1.82357 0.117224
\(243\) 12.9520 0.830874
\(244\) 6.85773 0.439021
\(245\) 7.68828 0.491186
\(246\) 0.0459938 0.00293246
\(247\) −27.5996 −1.75612
\(248\) 9.94413 0.631453
\(249\) −3.25834 −0.206489
\(250\) 4.77900 0.302250
\(251\) 5.46727 0.345091 0.172545 0.985002i \(-0.444801\pi\)
0.172545 + 0.985002i \(0.444801\pi\)
\(252\) 8.42719 0.530863
\(253\) −10.9619 −0.689170
\(254\) 6.13848 0.385162
\(255\) 6.48481 0.406095
\(256\) 4.94832 0.309270
\(257\) −12.6379 −0.788330 −0.394165 0.919040i \(-0.628966\pi\)
−0.394165 + 0.919040i \(0.628966\pi\)
\(258\) −0.364668 −0.0227032
\(259\) 20.9314 1.30061
\(260\) 14.7905 0.917266
\(261\) −0.999798 −0.0618859
\(262\) 0.505421 0.0312250
\(263\) −15.9455 −0.983244 −0.491622 0.870809i \(-0.663596\pi\)
−0.491622 + 0.870809i \(0.663596\pi\)
\(264\) 4.87775 0.300205
\(265\) −9.29241 −0.570828
\(266\) −8.68008 −0.532210
\(267\) −11.6496 −0.712942
\(268\) 14.4930 0.885301
\(269\) 27.9611 1.70482 0.852409 0.522876i \(-0.175141\pi\)
0.852409 + 0.522876i \(0.175141\pi\)
\(270\) 4.24244 0.258187
\(271\) 9.71775 0.590311 0.295156 0.955449i \(-0.404629\pi\)
0.295156 + 0.955449i \(0.404629\pi\)
\(272\) 8.16015 0.494782
\(273\) −17.5507 −1.06222
\(274\) −0.0847301 −0.00511873
\(275\) −3.23424 −0.195032
\(276\) 10.1938 0.613597
\(277\) 4.10155 0.246438 0.123219 0.992379i \(-0.460678\pi\)
0.123219 + 0.992379i \(0.460678\pi\)
\(278\) 1.82886 0.109688
\(279\) −9.03775 −0.541076
\(280\) 9.69581 0.579436
\(281\) 14.7833 0.881899 0.440950 0.897532i \(-0.354642\pi\)
0.440950 + 0.897532i \(0.354642\pi\)
\(282\) −5.18488 −0.308755
\(283\) −2.82855 −0.168140 −0.0840699 0.996460i \(-0.526792\pi\)
−0.0840699 + 0.996460i \(0.526792\pi\)
\(284\) 15.0502 0.893067
\(285\) 16.2999 0.965521
\(286\) 4.14335 0.245002
\(287\) −0.303442 −0.0179116
\(288\) 5.86254 0.345454
\(289\) −10.0271 −0.589828
\(290\) −0.551864 −0.0324066
\(291\) 0.930010 0.0545182
\(292\) 22.4143 1.31170
\(293\) −3.10899 −0.181629 −0.0908147 0.995868i \(-0.528947\pi\)
−0.0908147 + 0.995868i \(0.528947\pi\)
\(294\) −2.00286 −0.116809
\(295\) 24.8268 1.44547
\(296\) 9.57829 0.556727
\(297\) −14.0808 −0.817051
\(298\) −0.889336 −0.0515179
\(299\) 18.0489 1.04380
\(300\) 3.00762 0.173645
\(301\) 2.40588 0.138672
\(302\) 8.83230 0.508242
\(303\) −4.10232 −0.235672
\(304\) 20.5109 1.17638
\(305\) −7.17092 −0.410606
\(306\) 1.43621 0.0821029
\(307\) −6.67202 −0.380792 −0.190396 0.981707i \(-0.560977\pi\)
−0.190396 + 0.981707i \(0.560977\pi\)
\(308\) −15.4388 −0.879708
\(309\) 4.68750 0.266663
\(310\) −4.98862 −0.283334
\(311\) 34.7399 1.96992 0.984960 0.172782i \(-0.0552755\pi\)
0.984960 + 0.172782i \(0.0552755\pi\)
\(312\) −8.03128 −0.454682
\(313\) 14.6252 0.826667 0.413334 0.910580i \(-0.364364\pi\)
0.413334 + 0.910580i \(0.364364\pi\)
\(314\) 3.03588 0.171324
\(315\) −8.81206 −0.496503
\(316\) −26.6682 −1.50020
\(317\) −22.0932 −1.24088 −0.620438 0.784255i \(-0.713045\pi\)
−0.620438 + 0.784255i \(0.713045\pi\)
\(318\) 2.42075 0.135749
\(319\) 1.83165 0.102553
\(320\) −8.68342 −0.485418
\(321\) −12.4405 −0.694361
\(322\) 5.67638 0.316333
\(323\) 17.5268 0.975215
\(324\) 5.46683 0.303713
\(325\) 5.32521 0.295389
\(326\) 8.18375 0.453256
\(327\) −23.8138 −1.31690
\(328\) −0.138856 −0.00766704
\(329\) 34.2070 1.88589
\(330\) −2.44699 −0.134703
\(331\) −22.8034 −1.25339 −0.626694 0.779266i \(-0.715592\pi\)
−0.626694 + 0.779266i \(0.715592\pi\)
\(332\) 4.71933 0.259007
\(333\) −8.70525 −0.477045
\(334\) −3.82027 −0.209036
\(335\) −15.1549 −0.828001
\(336\) 13.0430 0.711553
\(337\) −14.0107 −0.763214 −0.381607 0.924325i \(-0.624629\pi\)
−0.381607 + 0.924325i \(0.624629\pi\)
\(338\) −1.69297 −0.0920853
\(339\) 9.69461 0.526539
\(340\) −9.39249 −0.509379
\(341\) 16.5574 0.896632
\(342\) 3.60999 0.195206
\(343\) −9.98842 −0.539324
\(344\) 1.10094 0.0593586
\(345\) −10.6594 −0.573882
\(346\) 5.37962 0.289210
\(347\) 17.8681 0.959208 0.479604 0.877485i \(-0.340780\pi\)
0.479604 + 0.877485i \(0.340780\pi\)
\(348\) −1.70331 −0.0913071
\(349\) 30.5664 1.63618 0.818090 0.575090i \(-0.195033\pi\)
0.818090 + 0.575090i \(0.195033\pi\)
\(350\) 1.67478 0.0895206
\(351\) 23.1842 1.23748
\(352\) −10.7403 −0.572461
\(353\) 15.6993 0.835591 0.417796 0.908541i \(-0.362803\pi\)
0.417796 + 0.908541i \(0.362803\pi\)
\(354\) −6.46757 −0.343748
\(355\) −15.7376 −0.835265
\(356\) 16.8730 0.894269
\(357\) 11.1453 0.589874
\(358\) −8.47307 −0.447816
\(359\) 10.8785 0.574147 0.287073 0.957909i \(-0.407318\pi\)
0.287073 + 0.957909i \(0.407318\pi\)
\(360\) −4.03243 −0.212528
\(361\) 25.0543 1.31865
\(362\) −4.55393 −0.239349
\(363\) −5.88546 −0.308906
\(364\) 25.4202 1.33238
\(365\) −23.4380 −1.22680
\(366\) 1.86808 0.0976462
\(367\) 34.1890 1.78465 0.892324 0.451395i \(-0.149073\pi\)
0.892324 + 0.451395i \(0.149073\pi\)
\(368\) −13.4132 −0.699212
\(369\) 0.126200 0.00656968
\(370\) −4.80509 −0.249805
\(371\) −15.9707 −0.829159
\(372\) −15.3972 −0.798308
\(373\) −11.4843 −0.594635 −0.297317 0.954779i \(-0.596092\pi\)
−0.297317 + 0.954779i \(0.596092\pi\)
\(374\) −2.63118 −0.136055
\(375\) −15.4239 −0.796486
\(376\) 15.6532 0.807254
\(377\) −3.01584 −0.155324
\(378\) 7.29142 0.375030
\(379\) −29.6409 −1.52255 −0.761276 0.648428i \(-0.775427\pi\)
−0.761276 + 0.648428i \(0.775427\pi\)
\(380\) −23.6085 −1.21109
\(381\) −19.8115 −1.01497
\(382\) 5.48040 0.280402
\(383\) 1.97866 0.101105 0.0505525 0.998721i \(-0.483902\pi\)
0.0505525 + 0.998721i \(0.483902\pi\)
\(384\) 13.0929 0.668142
\(385\) 16.1439 0.822770
\(386\) −6.65651 −0.338807
\(387\) −1.00059 −0.0508628
\(388\) −1.34701 −0.0683841
\(389\) 30.4944 1.54613 0.773065 0.634327i \(-0.218723\pi\)
0.773065 + 0.634327i \(0.218723\pi\)
\(390\) 4.02900 0.204017
\(391\) −11.4617 −0.579644
\(392\) 6.04666 0.305402
\(393\) −1.63121 −0.0822837
\(394\) −10.5531 −0.531660
\(395\) 27.8862 1.40311
\(396\) 6.42091 0.322663
\(397\) −3.31961 −0.166607 −0.0833033 0.996524i \(-0.526547\pi\)
−0.0833033 + 0.996524i \(0.526547\pi\)
\(398\) 6.39128 0.320366
\(399\) 28.0143 1.40247
\(400\) −3.95747 −0.197874
\(401\) 0.0340859 0.00170217 0.000851085 1.00000i \(-0.499729\pi\)
0.000851085 1.00000i \(0.499729\pi\)
\(402\) 3.94797 0.196907
\(403\) −27.2619 −1.35801
\(404\) 5.94173 0.295612
\(405\) −5.71650 −0.284055
\(406\) −0.948480 −0.0470723
\(407\) 15.9482 0.790525
\(408\) 5.10015 0.252495
\(409\) −24.4981 −1.21135 −0.605677 0.795711i \(-0.707098\pi\)
−0.605677 + 0.795711i \(0.707098\pi\)
\(410\) 0.0696591 0.00344022
\(411\) 0.273460 0.0134888
\(412\) −6.78930 −0.334485
\(413\) 42.6694 2.09963
\(414\) −2.36077 −0.116026
\(415\) −4.93486 −0.242243
\(416\) 17.6841 0.867032
\(417\) −5.90252 −0.289048
\(418\) −6.61359 −0.323481
\(419\) 27.6511 1.35085 0.675423 0.737431i \(-0.263961\pi\)
0.675423 + 0.737431i \(0.263961\pi\)
\(420\) −15.0127 −0.732546
\(421\) 10.5638 0.514846 0.257423 0.966299i \(-0.417127\pi\)
0.257423 + 0.966299i \(0.417127\pi\)
\(422\) 6.93683 0.337679
\(423\) −14.2265 −0.691715
\(424\) −7.30826 −0.354921
\(425\) −3.38170 −0.164037
\(426\) 4.09976 0.198634
\(427\) −12.3246 −0.596427
\(428\) 18.0186 0.870962
\(429\) −13.3724 −0.645625
\(430\) −0.552301 −0.0266343
\(431\) 29.3274 1.41265 0.706327 0.707886i \(-0.250351\pi\)
0.706327 + 0.707886i \(0.250351\pi\)
\(432\) −17.2295 −0.828957
\(433\) −8.94627 −0.429930 −0.214965 0.976622i \(-0.568964\pi\)
−0.214965 + 0.976622i \(0.568964\pi\)
\(434\) −8.57386 −0.411558
\(435\) 1.78110 0.0853973
\(436\) 34.4915 1.65184
\(437\) −28.8096 −1.37815
\(438\) 6.10578 0.291745
\(439\) 18.8444 0.899395 0.449698 0.893181i \(-0.351532\pi\)
0.449698 + 0.893181i \(0.351532\pi\)
\(440\) 7.38751 0.352186
\(441\) −5.49551 −0.261691
\(442\) 4.33227 0.206065
\(443\) −23.5362 −1.11824 −0.559119 0.829087i \(-0.688861\pi\)
−0.559119 + 0.829087i \(0.688861\pi\)
\(444\) −14.8308 −0.703837
\(445\) −17.6436 −0.836389
\(446\) −1.17699 −0.0557321
\(447\) 2.87027 0.135759
\(448\) −14.9241 −0.705096
\(449\) 10.1071 0.476982 0.238491 0.971145i \(-0.423347\pi\)
0.238491 + 0.971145i \(0.423347\pi\)
\(450\) −0.696530 −0.0328347
\(451\) −0.231201 −0.0108868
\(452\) −14.0415 −0.660457
\(453\) −28.5056 −1.33931
\(454\) 0.00129002 6.05438e−5 0
\(455\) −26.5811 −1.24614
\(456\) 12.8195 0.600326
\(457\) −4.98983 −0.233415 −0.116707 0.993166i \(-0.537234\pi\)
−0.116707 + 0.993166i \(0.537234\pi\)
\(458\) 2.74201 0.128126
\(459\) −14.7228 −0.687202
\(460\) 15.4389 0.719841
\(461\) −15.0962 −0.703099 −0.351549 0.936169i \(-0.614345\pi\)
−0.351549 + 0.936169i \(0.614345\pi\)
\(462\) −4.20561 −0.195663
\(463\) −1.29951 −0.0603933 −0.0301967 0.999544i \(-0.509613\pi\)
−0.0301967 + 0.999544i \(0.509613\pi\)
\(464\) 2.24125 0.104047
\(465\) 16.1004 0.746639
\(466\) −0.761541 −0.0352777
\(467\) 24.1905 1.11940 0.559702 0.828694i \(-0.310916\pi\)
0.559702 + 0.828694i \(0.310916\pi\)
\(468\) −10.5721 −0.488695
\(469\) −26.0465 −1.20272
\(470\) −7.85267 −0.362216
\(471\) −9.79809 −0.451472
\(472\) 19.5257 0.898743
\(473\) 1.83311 0.0842863
\(474\) −7.26456 −0.333672
\(475\) −8.50006 −0.390009
\(476\) −16.1427 −0.739901
\(477\) 6.64213 0.304122
\(478\) 3.24048 0.148216
\(479\) 1.78150 0.0813990 0.0406995 0.999171i \(-0.487041\pi\)
0.0406995 + 0.999171i \(0.487041\pi\)
\(480\) −10.4439 −0.476697
\(481\) −26.2589 −1.19730
\(482\) −5.15928 −0.234999
\(483\) −18.3201 −0.833595
\(484\) 8.52440 0.387473
\(485\) 1.40853 0.0639580
\(486\) −5.11019 −0.231803
\(487\) −36.1287 −1.63715 −0.818574 0.574401i \(-0.805235\pi\)
−0.818574 + 0.574401i \(0.805235\pi\)
\(488\) −5.63976 −0.255300
\(489\) −26.4125 −1.19441
\(490\) −3.03339 −0.137035
\(491\) −20.4601 −0.923352 −0.461676 0.887049i \(-0.652752\pi\)
−0.461676 + 0.887049i \(0.652752\pi\)
\(492\) 0.215001 0.00969298
\(493\) 1.91517 0.0862548
\(494\) 10.8894 0.489935
\(495\) −6.71415 −0.301779
\(496\) 20.2599 0.909697
\(497\) −27.0480 −1.21327
\(498\) 1.28557 0.0576078
\(499\) −26.8942 −1.20395 −0.601974 0.798516i \(-0.705619\pi\)
−0.601974 + 0.798516i \(0.705619\pi\)
\(500\) 22.3397 0.999062
\(501\) 12.3297 0.550849
\(502\) −2.15709 −0.0962759
\(503\) −39.3954 −1.75655 −0.878276 0.478154i \(-0.841306\pi\)
−0.878276 + 0.478154i \(0.841306\pi\)
\(504\) −6.93048 −0.308708
\(505\) −6.21309 −0.276479
\(506\) 4.32500 0.192270
\(507\) 5.46393 0.242662
\(508\) 28.6947 1.27312
\(509\) −13.0536 −0.578591 −0.289296 0.957240i \(-0.593421\pi\)
−0.289296 + 0.957240i \(0.593421\pi\)
\(510\) −2.55856 −0.113295
\(511\) −40.2825 −1.78199
\(512\) −22.5164 −0.995093
\(513\) −37.0064 −1.63387
\(514\) 4.98624 0.219934
\(515\) 7.09937 0.312835
\(516\) −1.70466 −0.0750435
\(517\) 26.0632 1.14626
\(518\) −8.25843 −0.362855
\(519\) −17.3623 −0.762122
\(520\) −12.1636 −0.533410
\(521\) −11.3612 −0.497744 −0.248872 0.968536i \(-0.580060\pi\)
−0.248872 + 0.968536i \(0.580060\pi\)
\(522\) 0.394467 0.0172654
\(523\) −12.1481 −0.531201 −0.265600 0.964083i \(-0.585570\pi\)
−0.265600 + 0.964083i \(0.585570\pi\)
\(524\) 2.36262 0.103211
\(525\) −5.40523 −0.235903
\(526\) 6.29126 0.274312
\(527\) 17.3123 0.754135
\(528\) 9.93781 0.432488
\(529\) −4.15982 −0.180862
\(530\) 3.66629 0.159254
\(531\) −17.7460 −0.770109
\(532\) −40.5755 −1.75917
\(533\) 0.380674 0.0164888
\(534\) 4.59630 0.198902
\(535\) −18.8415 −0.814590
\(536\) −11.9190 −0.514821
\(537\) 27.3463 1.18008
\(538\) −11.0320 −0.475622
\(539\) 10.0679 0.433656
\(540\) 19.8315 0.853413
\(541\) 39.5763 1.70152 0.850760 0.525554i \(-0.176142\pi\)
0.850760 + 0.525554i \(0.176142\pi\)
\(542\) −3.83411 −0.164689
\(543\) 14.6975 0.630729
\(544\) −11.2300 −0.481483
\(545\) −36.0667 −1.54493
\(546\) 6.92459 0.296345
\(547\) 27.1079 1.15905 0.579524 0.814955i \(-0.303238\pi\)
0.579524 + 0.814955i \(0.303238\pi\)
\(548\) −0.396075 −0.0169195
\(549\) 5.12571 0.218760
\(550\) 1.27606 0.0544114
\(551\) 4.81386 0.205077
\(552\) −8.38336 −0.356820
\(553\) 47.9275 2.03809
\(554\) −1.61826 −0.0687531
\(555\) 15.5081 0.658281
\(556\) 8.54911 0.362563
\(557\) 20.0432 0.849256 0.424628 0.905368i \(-0.360405\pi\)
0.424628 + 0.905368i \(0.360405\pi\)
\(558\) 3.56582 0.150953
\(559\) −3.01823 −0.127657
\(560\) 19.7540 0.834758
\(561\) 8.49195 0.358531
\(562\) −5.83272 −0.246038
\(563\) 30.9096 1.30269 0.651343 0.758784i \(-0.274206\pi\)
0.651343 + 0.758784i \(0.274206\pi\)
\(564\) −24.2370 −1.02056
\(565\) 14.6828 0.617710
\(566\) 1.11600 0.0469088
\(567\) −9.82487 −0.412606
\(568\) −12.3772 −0.519338
\(569\) 5.05123 0.211759 0.105879 0.994379i \(-0.466234\pi\)
0.105879 + 0.994379i \(0.466234\pi\)
\(570\) −6.43107 −0.269368
\(571\) −13.6965 −0.573182 −0.286591 0.958053i \(-0.592522\pi\)
−0.286591 + 0.958053i \(0.592522\pi\)
\(572\) 19.3683 0.809831
\(573\) −17.6876 −0.738911
\(574\) 0.119722 0.00499710
\(575\) 5.55866 0.231812
\(576\) 6.20683 0.258618
\(577\) −8.28905 −0.345078 −0.172539 0.985003i \(-0.555197\pi\)
−0.172539 + 0.985003i \(0.555197\pi\)
\(578\) 3.95615 0.164554
\(579\) 21.4834 0.892821
\(580\) −2.57972 −0.107117
\(581\) −8.48147 −0.351871
\(582\) −0.366933 −0.0152099
\(583\) −12.1685 −0.503970
\(584\) −18.4334 −0.762781
\(585\) 11.0549 0.457065
\(586\) 1.22664 0.0506722
\(587\) 35.6447 1.47122 0.735608 0.677408i \(-0.236897\pi\)
0.735608 + 0.677408i \(0.236897\pi\)
\(588\) −9.36247 −0.386102
\(589\) 43.5152 1.79301
\(590\) −9.79534 −0.403268
\(591\) 34.0596 1.40102
\(592\) 19.5146 0.802044
\(593\) 3.95476 0.162403 0.0812013 0.996698i \(-0.474124\pi\)
0.0812013 + 0.996698i \(0.474124\pi\)
\(594\) 5.55554 0.227947
\(595\) 16.8800 0.692012
\(596\) −4.15725 −0.170288
\(597\) −20.6274 −0.844224
\(598\) −7.12115 −0.291206
\(599\) −24.0090 −0.980983 −0.490492 0.871446i \(-0.663183\pi\)
−0.490492 + 0.871446i \(0.663183\pi\)
\(600\) −2.47345 −0.100978
\(601\) 37.6063 1.53399 0.766996 0.641652i \(-0.221750\pi\)
0.766996 + 0.641652i \(0.221750\pi\)
\(602\) −0.949232 −0.0386878
\(603\) 10.8326 0.441137
\(604\) 41.2871 1.67995
\(605\) −8.91371 −0.362394
\(606\) 1.61856 0.0657494
\(607\) 28.3565 1.15095 0.575476 0.817818i \(-0.304817\pi\)
0.575476 + 0.817818i \(0.304817\pi\)
\(608\) −28.2272 −1.14476
\(609\) 3.06115 0.124044
\(610\) 2.82927 0.114554
\(611\) −42.9134 −1.73609
\(612\) 6.71367 0.271384
\(613\) −14.7062 −0.593977 −0.296988 0.954881i \(-0.595982\pi\)
−0.296988 + 0.954881i \(0.595982\pi\)
\(614\) 2.63243 0.106236
\(615\) −0.224820 −0.00906561
\(616\) 12.6968 0.511569
\(617\) −43.4416 −1.74889 −0.874447 0.485121i \(-0.838776\pi\)
−0.874447 + 0.485121i \(0.838776\pi\)
\(618\) −1.84944 −0.0743954
\(619\) 1.00000 0.0401934
\(620\) −23.3196 −0.936536
\(621\) 24.2006 0.971136
\(622\) −13.7065 −0.549582
\(623\) −30.3239 −1.21490
\(624\) −16.3627 −0.655033
\(625\) −16.9567 −0.678270
\(626\) −5.77035 −0.230629
\(627\) 21.3449 0.852434
\(628\) 14.1914 0.566298
\(629\) 16.6754 0.664891
\(630\) 3.47677 0.138518
\(631\) 5.19347 0.206749 0.103374 0.994643i \(-0.467036\pi\)
0.103374 + 0.994643i \(0.467036\pi\)
\(632\) 21.9318 0.872401
\(633\) −22.3881 −0.889848
\(634\) 8.71680 0.346188
\(635\) −30.0051 −1.19072
\(636\) 11.3159 0.448705
\(637\) −16.5769 −0.656802
\(638\) −0.722674 −0.0286109
\(639\) 11.2491 0.445007
\(640\) 19.8295 0.783831
\(641\) −4.63923 −0.183239 −0.0916193 0.995794i \(-0.529204\pi\)
−0.0916193 + 0.995794i \(0.529204\pi\)
\(642\) 4.90836 0.193718
\(643\) 19.9911 0.788372 0.394186 0.919031i \(-0.371027\pi\)
0.394186 + 0.919031i \(0.371027\pi\)
\(644\) 26.5346 1.04561
\(645\) 1.78251 0.0701864
\(646\) −6.91513 −0.272072
\(647\) −41.1854 −1.61916 −0.809582 0.587007i \(-0.800306\pi\)
−0.809582 + 0.587007i \(0.800306\pi\)
\(648\) −4.49590 −0.176615
\(649\) 32.5110 1.27617
\(650\) −2.10105 −0.0824098
\(651\) 27.6715 1.08453
\(652\) 38.2554 1.49820
\(653\) −29.6784 −1.16141 −0.580703 0.814115i \(-0.697222\pi\)
−0.580703 + 0.814115i \(0.697222\pi\)
\(654\) 9.39565 0.367399
\(655\) −2.47052 −0.0965311
\(656\) −0.282901 −0.0110454
\(657\) 16.7533 0.653607
\(658\) −13.4963 −0.526139
\(659\) −22.7688 −0.886947 −0.443473 0.896288i \(-0.646254\pi\)
−0.443473 + 0.896288i \(0.646254\pi\)
\(660\) −11.4386 −0.445247
\(661\) 11.6073 0.451473 0.225736 0.974188i \(-0.427521\pi\)
0.225736 + 0.974188i \(0.427521\pi\)
\(662\) 8.99701 0.349679
\(663\) −13.9821 −0.543020
\(664\) −3.88115 −0.150618
\(665\) 42.4286 1.64531
\(666\) 3.43463 0.133089
\(667\) −3.14805 −0.121893
\(668\) −17.8581 −0.690950
\(669\) 3.79865 0.146864
\(670\) 5.97932 0.231001
\(671\) −9.39043 −0.362513
\(672\) −17.9498 −0.692428
\(673\) 8.17196 0.315006 0.157503 0.987519i \(-0.449656\pi\)
0.157503 + 0.987519i \(0.449656\pi\)
\(674\) 5.52790 0.212927
\(675\) 7.14021 0.274827
\(676\) −7.91387 −0.304380
\(677\) 8.58307 0.329874 0.164937 0.986304i \(-0.447258\pi\)
0.164937 + 0.986304i \(0.447258\pi\)
\(678\) −3.82498 −0.146898
\(679\) 2.42082 0.0929025
\(680\) 7.72434 0.296215
\(681\) −0.00416346 −0.000159544 0
\(682\) −6.53266 −0.250149
\(683\) −24.2687 −0.928614 −0.464307 0.885674i \(-0.653697\pi\)
−0.464307 + 0.885674i \(0.653697\pi\)
\(684\) 16.8751 0.645236
\(685\) 0.414164 0.0158244
\(686\) 3.94090 0.150464
\(687\) −8.84964 −0.337635
\(688\) 2.24302 0.0855144
\(689\) 20.0356 0.763297
\(690\) 4.20563 0.160106
\(691\) −3.30802 −0.125843 −0.0629216 0.998018i \(-0.520042\pi\)
−0.0629216 + 0.998018i \(0.520042\pi\)
\(692\) 25.1473 0.955957
\(693\) −11.5395 −0.438350
\(694\) −7.04979 −0.267607
\(695\) −8.93956 −0.339097
\(696\) 1.40080 0.0530970
\(697\) −0.241742 −0.00915663
\(698\) −12.0599 −0.456473
\(699\) 2.45782 0.0929633
\(700\) 7.82884 0.295902
\(701\) 25.8447 0.976142 0.488071 0.872804i \(-0.337701\pi\)
0.488071 + 0.872804i \(0.337701\pi\)
\(702\) −9.14726 −0.345241
\(703\) 41.9143 1.58083
\(704\) −11.3711 −0.428563
\(705\) 25.3439 0.954508
\(706\) −6.19413 −0.233119
\(707\) −10.6783 −0.401600
\(708\) −30.2330 −1.13623
\(709\) −35.5194 −1.33396 −0.666980 0.745076i \(-0.732413\pi\)
−0.666980 + 0.745076i \(0.732413\pi\)
\(710\) 6.20922 0.233028
\(711\) −19.9328 −0.747537
\(712\) −13.8763 −0.520037
\(713\) −28.4570 −1.06572
\(714\) −4.39737 −0.164567
\(715\) −20.2529 −0.757415
\(716\) −39.6079 −1.48022
\(717\) −10.4584 −0.390577
\(718\) −4.29209 −0.160180
\(719\) −39.7181 −1.48123 −0.740617 0.671927i \(-0.765467\pi\)
−0.740617 + 0.671927i \(0.765467\pi\)
\(720\) −8.21557 −0.306176
\(721\) 12.2016 0.454410
\(722\) −9.88511 −0.367886
\(723\) 16.6512 0.619265
\(724\) −21.2876 −0.791147
\(725\) −0.928810 −0.0344951
\(726\) 2.32209 0.0861809
\(727\) −35.0458 −1.29978 −0.649888 0.760030i \(-0.725184\pi\)
−0.649888 + 0.760030i \(0.725184\pi\)
\(728\) −20.9054 −0.774807
\(729\) 25.3852 0.940191
\(730\) 9.24739 0.342261
\(731\) 1.91668 0.0708911
\(732\) 8.73245 0.322761
\(733\) −17.5734 −0.649087 −0.324543 0.945871i \(-0.605211\pi\)
−0.324543 + 0.945871i \(0.605211\pi\)
\(734\) −13.4892 −0.497894
\(735\) 9.79006 0.361112
\(736\) 18.4593 0.680419
\(737\) −19.8456 −0.731021
\(738\) −0.0497917 −0.00183286
\(739\) −16.2100 −0.596294 −0.298147 0.954520i \(-0.596369\pi\)
−0.298147 + 0.954520i \(0.596369\pi\)
\(740\) −22.4616 −0.825706
\(741\) −35.1446 −1.29107
\(742\) 6.30121 0.231325
\(743\) 45.8562 1.68230 0.841151 0.540801i \(-0.181879\pi\)
0.841151 + 0.540801i \(0.181879\pi\)
\(744\) 12.6626 0.464233
\(745\) 4.34712 0.159266
\(746\) 4.53110 0.165895
\(747\) 3.52739 0.129061
\(748\) −12.2996 −0.449718
\(749\) −32.3826 −1.18324
\(750\) 6.08545 0.222209
\(751\) 40.1237 1.46414 0.732068 0.681232i \(-0.238555\pi\)
0.732068 + 0.681232i \(0.238555\pi\)
\(752\) 31.8915 1.16296
\(753\) 6.96187 0.253705
\(754\) 1.18989 0.0433333
\(755\) −43.1727 −1.57121
\(756\) 34.0842 1.23963
\(757\) 26.2866 0.955404 0.477702 0.878522i \(-0.341470\pi\)
0.477702 + 0.878522i \(0.341470\pi\)
\(758\) 11.6947 0.424772
\(759\) −13.9586 −0.506666
\(760\) 19.4155 0.704273
\(761\) 39.3968 1.42813 0.714066 0.700079i \(-0.246852\pi\)
0.714066 + 0.700079i \(0.246852\pi\)
\(762\) 7.81658 0.283165
\(763\) −61.9873 −2.24409
\(764\) 25.6185 0.926843
\(765\) −7.02028 −0.253819
\(766\) −0.780676 −0.0282070
\(767\) −53.5298 −1.93285
\(768\) 6.30106 0.227370
\(769\) 22.1652 0.799297 0.399648 0.916668i \(-0.369132\pi\)
0.399648 + 0.916668i \(0.369132\pi\)
\(770\) −6.36953 −0.229542
\(771\) −16.0928 −0.579566
\(772\) −31.1162 −1.11990
\(773\) 7.91637 0.284732 0.142366 0.989814i \(-0.454529\pi\)
0.142366 + 0.989814i \(0.454529\pi\)
\(774\) 0.394780 0.0141901
\(775\) −8.39605 −0.301595
\(776\) 1.10778 0.0397668
\(777\) 26.6535 0.956189
\(778\) −12.0315 −0.431350
\(779\) −0.607630 −0.0217706
\(780\) 18.8338 0.674358
\(781\) −20.6086 −0.737434
\(782\) 4.52219 0.161713
\(783\) −4.04373 −0.144511
\(784\) 12.3193 0.439975
\(785\) −14.8395 −0.529645
\(786\) 0.643589 0.0229561
\(787\) −17.5604 −0.625961 −0.312980 0.949760i \(-0.601327\pi\)
−0.312980 + 0.949760i \(0.601327\pi\)
\(788\) −49.3313 −1.75735
\(789\) −20.3046 −0.722864
\(790\) −11.0024 −0.391448
\(791\) 25.2351 0.897257
\(792\) −5.28052 −0.187635
\(793\) 15.4614 0.549052
\(794\) 1.30974 0.0464811
\(795\) −11.8327 −0.419663
\(796\) 29.8764 1.05894
\(797\) 49.6381 1.75827 0.879136 0.476571i \(-0.158120\pi\)
0.879136 + 0.476571i \(0.158120\pi\)
\(798\) −11.0530 −0.391271
\(799\) 27.2516 0.964092
\(800\) 5.44629 0.192555
\(801\) 12.6115 0.445606
\(802\) −0.0134485 −0.000474883 0
\(803\) −30.6924 −1.08311
\(804\) 18.4550 0.650858
\(805\) −27.7464 −0.977933
\(806\) 10.7561 0.378868
\(807\) 35.6049 1.25335
\(808\) −4.88645 −0.171905
\(809\) 1.41762 0.0498409 0.0249204 0.999689i \(-0.492067\pi\)
0.0249204 + 0.999689i \(0.492067\pi\)
\(810\) 2.25543 0.0792477
\(811\) 31.2800 1.09839 0.549194 0.835695i \(-0.314935\pi\)
0.549194 + 0.835695i \(0.314935\pi\)
\(812\) −4.43372 −0.155593
\(813\) 12.3743 0.433986
\(814\) −6.29233 −0.220546
\(815\) −40.0025 −1.40123
\(816\) 10.3909 0.363755
\(817\) 4.81767 0.168549
\(818\) 9.66566 0.337952
\(819\) 18.9999 0.663912
\(820\) 0.325625 0.0113713
\(821\) −20.8653 −0.728205 −0.364102 0.931359i \(-0.618624\pi\)
−0.364102 + 0.931359i \(0.618624\pi\)
\(822\) −0.107893 −0.00376320
\(823\) 38.3051 1.33523 0.667617 0.744505i \(-0.267315\pi\)
0.667617 + 0.744505i \(0.267315\pi\)
\(824\) 5.58349 0.194510
\(825\) −4.11839 −0.143384
\(826\) −16.8351 −0.585768
\(827\) −55.7253 −1.93776 −0.968880 0.247533i \(-0.920380\pi\)
−0.968880 + 0.247533i \(0.920380\pi\)
\(828\) −11.0356 −0.383513
\(829\) −7.93394 −0.275557 −0.137778 0.990463i \(-0.543996\pi\)
−0.137778 + 0.990463i \(0.543996\pi\)
\(830\) 1.94704 0.0675826
\(831\) 5.22281 0.181177
\(832\) 18.7226 0.649089
\(833\) 10.5270 0.364737
\(834\) 2.32882 0.0806406
\(835\) 18.6737 0.646229
\(836\) −30.9156 −1.06924
\(837\) −36.5536 −1.26348
\(838\) −10.9097 −0.376868
\(839\) 27.8168 0.960342 0.480171 0.877175i \(-0.340575\pi\)
0.480171 + 0.877175i \(0.340575\pi\)
\(840\) 12.3464 0.425991
\(841\) −28.4740 −0.981862
\(842\) −4.16790 −0.143635
\(843\) 18.8247 0.648357
\(844\) 32.4266 1.11617
\(845\) 8.27530 0.284679
\(846\) 5.61301 0.192979
\(847\) −15.3199 −0.526397
\(848\) −14.8897 −0.511313
\(849\) −3.60180 −0.123613
\(850\) 1.33424 0.0457641
\(851\) −27.4101 −0.939607
\(852\) 19.1646 0.656568
\(853\) −3.26689 −0.111856 −0.0559281 0.998435i \(-0.517812\pi\)
−0.0559281 + 0.998435i \(0.517812\pi\)
\(854\) 4.86262 0.166395
\(855\) −17.6458 −0.603473
\(856\) −14.8184 −0.506483
\(857\) 24.4385 0.834805 0.417402 0.908722i \(-0.362941\pi\)
0.417402 + 0.908722i \(0.362941\pi\)
\(858\) 5.27604 0.180121
\(859\) −25.9275 −0.884634 −0.442317 0.896859i \(-0.645843\pi\)
−0.442317 + 0.896859i \(0.645843\pi\)
\(860\) −2.58176 −0.0880374
\(861\) −0.386394 −0.0131683
\(862\) −11.5711 −0.394112
\(863\) −23.9799 −0.816286 −0.408143 0.912918i \(-0.633824\pi\)
−0.408143 + 0.912918i \(0.633824\pi\)
\(864\) 23.7113 0.806676
\(865\) −26.2958 −0.894084
\(866\) 3.52972 0.119945
\(867\) −12.7682 −0.433631
\(868\) −40.0790 −1.36037
\(869\) 36.5173 1.23877
\(870\) −0.702729 −0.0238247
\(871\) 32.6759 1.10718
\(872\) −28.3656 −0.960581
\(873\) −1.00680 −0.0340751
\(874\) 11.3667 0.384486
\(875\) −40.1484 −1.35726
\(876\) 28.5418 0.964338
\(877\) −8.83073 −0.298193 −0.149096 0.988823i \(-0.547636\pi\)
−0.149096 + 0.988823i \(0.547636\pi\)
\(878\) −7.43501 −0.250920
\(879\) −3.95891 −0.133531
\(880\) 15.0511 0.507373
\(881\) −38.2539 −1.28881 −0.644403 0.764686i \(-0.722894\pi\)
−0.644403 + 0.764686i \(0.722894\pi\)
\(882\) 2.16824 0.0730084
\(883\) 53.5201 1.80110 0.900548 0.434757i \(-0.143166\pi\)
0.900548 + 0.434757i \(0.143166\pi\)
\(884\) 20.2514 0.681129
\(885\) 31.6138 1.06269
\(886\) 9.28614 0.311974
\(887\) 41.5586 1.39540 0.697701 0.716389i \(-0.254206\pi\)
0.697701 + 0.716389i \(0.254206\pi\)
\(888\) 12.1967 0.409296
\(889\) −51.5694 −1.72958
\(890\) 6.96125 0.233341
\(891\) −7.48584 −0.250785
\(892\) −5.50190 −0.184217
\(893\) 68.4981 2.29220
\(894\) −1.13246 −0.0378750
\(895\) 41.4168 1.38441
\(896\) 34.0807 1.13856
\(897\) 22.9830 0.767381
\(898\) −3.98772 −0.133072
\(899\) 4.75495 0.158587
\(900\) −3.25597 −0.108532
\(901\) −12.7234 −0.423877
\(902\) 0.0912195 0.00303728
\(903\) 3.06358 0.101950
\(904\) 11.5477 0.384070
\(905\) 22.2598 0.739940
\(906\) 11.2468 0.373650
\(907\) 37.3221 1.23926 0.619630 0.784894i \(-0.287283\pi\)
0.619630 + 0.784894i \(0.287283\pi\)
\(908\) 0.00603029 0.000200122 0
\(909\) 4.44106 0.147301
\(910\) 10.4875 0.347657
\(911\) 49.5208 1.64070 0.820349 0.571863i \(-0.193779\pi\)
0.820349 + 0.571863i \(0.193779\pi\)
\(912\) 26.1180 0.864855
\(913\) −6.46227 −0.213870
\(914\) 1.96872 0.0651196
\(915\) −9.13126 −0.301870
\(916\) 12.8177 0.423508
\(917\) −4.24604 −0.140217
\(918\) 5.80884 0.191720
\(919\) 2.37680 0.0784034 0.0392017 0.999231i \(-0.487519\pi\)
0.0392017 + 0.999231i \(0.487519\pi\)
\(920\) −12.6969 −0.418603
\(921\) −8.49597 −0.279952
\(922\) 5.95615 0.196155
\(923\) 33.9323 1.11689
\(924\) −19.6594 −0.646746
\(925\) −8.08716 −0.265904
\(926\) 0.512718 0.0168489
\(927\) −5.07456 −0.166670
\(928\) −3.08441 −0.101251
\(929\) −43.2093 −1.41765 −0.708825 0.705384i \(-0.750774\pi\)
−0.708825 + 0.705384i \(0.750774\pi\)
\(930\) −6.35237 −0.208302
\(931\) 26.4600 0.867191
\(932\) −3.55986 −0.116607
\(933\) 44.2369 1.44825
\(934\) −9.54430 −0.312299
\(935\) 12.8613 0.420610
\(936\) 8.69444 0.284187
\(937\) −2.29674 −0.0750312 −0.0375156 0.999296i \(-0.511944\pi\)
−0.0375156 + 0.999296i \(0.511944\pi\)
\(938\) 10.2766 0.335542
\(939\) 18.6234 0.607752
\(940\) −36.7077 −1.19727
\(941\) 49.7980 1.62337 0.811684 0.584097i \(-0.198551\pi\)
0.811684 + 0.584097i \(0.198551\pi\)
\(942\) 3.86581 0.125955
\(943\) 0.397363 0.0129399
\(944\) 39.7811 1.29477
\(945\) −35.6408 −1.15940
\(946\) −0.723246 −0.0235148
\(947\) −55.2779 −1.79629 −0.898145 0.439699i \(-0.855085\pi\)
−0.898145 + 0.439699i \(0.855085\pi\)
\(948\) −33.9586 −1.10292
\(949\) 50.5354 1.64045
\(950\) 3.35367 0.108808
\(951\) −28.1329 −0.912271
\(952\) 13.2757 0.430268
\(953\) −9.80332 −0.317561 −0.158780 0.987314i \(-0.550756\pi\)
−0.158780 + 0.987314i \(0.550756\pi\)
\(954\) −2.62063 −0.0848461
\(955\) −26.7885 −0.866854
\(956\) 15.1478 0.489914
\(957\) 2.33238 0.0753951
\(958\) −0.702887 −0.0227093
\(959\) 0.711818 0.0229858
\(960\) −11.0572 −0.356871
\(961\) 11.9828 0.386541
\(962\) 10.3604 0.334032
\(963\) 13.4677 0.433992
\(964\) −24.1173 −0.776767
\(965\) 32.5373 1.04741
\(966\) 7.22816 0.232562
\(967\) −6.09145 −0.195888 −0.0979440 0.995192i \(-0.531227\pi\)
−0.0979440 + 0.995192i \(0.531227\pi\)
\(968\) −7.01042 −0.225324
\(969\) 22.3181 0.716961
\(970\) −0.555731 −0.0178434
\(971\) 30.5845 0.981502 0.490751 0.871300i \(-0.336723\pi\)
0.490751 + 0.871300i \(0.336723\pi\)
\(972\) −23.8879 −0.766204
\(973\) −15.3643 −0.492556
\(974\) 14.2545 0.456743
\(975\) 6.78098 0.217165
\(976\) −11.4903 −0.367796
\(977\) 23.2970 0.745337 0.372668 0.927965i \(-0.378443\pi\)
0.372668 + 0.927965i \(0.378443\pi\)
\(978\) 10.4210 0.333226
\(979\) −23.1046 −0.738426
\(980\) −14.1798 −0.452956
\(981\) 25.7801 0.823096
\(982\) 8.07248 0.257603
\(983\) 41.4405 1.32175 0.660873 0.750498i \(-0.270186\pi\)
0.660873 + 0.750498i \(0.270186\pi\)
\(984\) −0.176816 −0.00563667
\(985\) 51.5843 1.64361
\(986\) −0.755624 −0.0240640
\(987\) 43.5582 1.38647
\(988\) 50.9029 1.61944
\(989\) −3.15054 −0.100181
\(990\) 2.64905 0.0841923
\(991\) 44.3684 1.40941 0.704704 0.709502i \(-0.251080\pi\)
0.704704 + 0.709502i \(0.251080\pi\)
\(992\) −27.8818 −0.885247
\(993\) −29.0372 −0.921468
\(994\) 10.6717 0.338486
\(995\) −31.2409 −0.990402
\(996\) 6.00947 0.190417
\(997\) 16.0732 0.509044 0.254522 0.967067i \(-0.418082\pi\)
0.254522 + 0.967067i \(0.418082\pi\)
\(998\) 10.6110 0.335886
\(999\) −35.2088 −1.11396
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 \(a_p\))