Properties

Label 619.2.a.b.1.1
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 1.1
Character \(\chi\) = 619.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.61841 q^{2} +0.252107 q^{3} +4.85606 q^{4} +3.30541 q^{5} -0.660120 q^{6} -1.70947 q^{7} -7.47834 q^{8} -2.93644 q^{9} +O(q^{10})\) \(q-2.61841 q^{2} +0.252107 q^{3} +4.85606 q^{4} +3.30541 q^{5} -0.660120 q^{6} -1.70947 q^{7} -7.47834 q^{8} -2.93644 q^{9} -8.65491 q^{10} +5.06820 q^{11} +1.22425 q^{12} +5.40015 q^{13} +4.47610 q^{14} +0.833318 q^{15} +9.86923 q^{16} -0.784551 q^{17} +7.68880 q^{18} +1.17656 q^{19} +16.0513 q^{20} -0.430971 q^{21} -13.2706 q^{22} -1.79832 q^{23} -1.88535 q^{24} +5.92572 q^{25} -14.1398 q^{26} -1.49662 q^{27} -8.30131 q^{28} +7.10342 q^{29} -2.18197 q^{30} -9.66396 q^{31} -10.8850 q^{32} +1.27773 q^{33} +2.05428 q^{34} -5.65050 q^{35} -14.2595 q^{36} -3.34566 q^{37} -3.08072 q^{38} +1.36142 q^{39} -24.7190 q^{40} +8.63584 q^{41} +1.12846 q^{42} +1.57817 q^{43} +24.6115 q^{44} -9.70614 q^{45} +4.70874 q^{46} +4.16147 q^{47} +2.48811 q^{48} -4.07771 q^{49} -15.5160 q^{50} -0.197791 q^{51} +26.2235 q^{52} -1.42628 q^{53} +3.91877 q^{54} +16.7525 q^{55} +12.7840 q^{56} +0.296620 q^{57} -18.5997 q^{58} +9.64463 q^{59} +4.04665 q^{60} +13.8920 q^{61} +25.3042 q^{62} +5.01976 q^{63} +8.76290 q^{64} +17.8497 q^{65} -3.34562 q^{66} -10.7620 q^{67} -3.80983 q^{68} -0.453370 q^{69} +14.7953 q^{70} -0.285596 q^{71} +21.9597 q^{72} -16.4070 q^{73} +8.76030 q^{74} +1.49392 q^{75} +5.71346 q^{76} -8.66394 q^{77} -3.56475 q^{78} +7.56950 q^{79} +32.6218 q^{80} +8.43202 q^{81} -22.6122 q^{82} -2.48547 q^{83} -2.09282 q^{84} -2.59326 q^{85} -4.13228 q^{86} +1.79082 q^{87} -37.9017 q^{88} +10.8686 q^{89} +25.4146 q^{90} -9.23141 q^{91} -8.73276 q^{92} -2.43636 q^{93} -10.8964 q^{94} +3.88901 q^{95} -2.74419 q^{96} -0.0677252 q^{97} +10.6771 q^{98} -14.8825 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30q + 9q^{2} + q^{3} + 33q^{4} + 21q^{5} + 6q^{6} + 2q^{7} + 27q^{8} + 43q^{9} + O(q^{10}) \) \( 30q + 9q^{2} + q^{3} + 33q^{4} + 21q^{5} + 6q^{6} + 2q^{7} + 27q^{8} + 43q^{9} + 5q^{10} + 23q^{11} - 6q^{12} + 9q^{13} + 7q^{14} - 2q^{15} + 35q^{16} + 4q^{17} + 10q^{18} - q^{19} + 29q^{20} + 30q^{21} + 4q^{23} + 4q^{24} + 35q^{25} + q^{26} - 5q^{27} - 13q^{28} + 90q^{29} - 31q^{30} + 2q^{31} + 43q^{32} - 6q^{33} - 9q^{34} + 9q^{35} + 33q^{36} + 19q^{37} + 5q^{38} + 32q^{39} - 12q^{40} + 59q^{41} - 25q^{42} - 4q^{43} + 52q^{44} + 30q^{45} - q^{46} + 4q^{47} - 44q^{48} + 30q^{49} + 31q^{50} - 12q^{52} + 34q^{53} - 28q^{54} - 17q^{55} + 2q^{56} - 8q^{57} + 6q^{58} + 13q^{59} - 64q^{60} + 16q^{61} + 28q^{62} - 40q^{63} + 37q^{64} + 31q^{65} - 59q^{66} - 11q^{67} - 52q^{68} + 6q^{69} - 40q^{70} + 42q^{71} + 6q^{72} - 4q^{73} + 16q^{74} - 52q^{75} - 42q^{76} + 29q^{77} - 56q^{78} + 3q^{79} + 21q^{80} + 30q^{81} - 43q^{82} - 11q^{83} - 36q^{84} + 19q^{85} - 11q^{86} - 20q^{87} - 47q^{88} + 58q^{89} - 33q^{90} - 39q^{91} - 7q^{92} - 15q^{93} - 46q^{94} + 23q^{95} - 70q^{96} - 9q^{97} - 8q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.61841 −1.85149 −0.925747 0.378143i \(-0.876563\pi\)
−0.925747 + 0.378143i \(0.876563\pi\)
\(3\) 0.252107 0.145554 0.0727772 0.997348i \(-0.476814\pi\)
0.0727772 + 0.997348i \(0.476814\pi\)
\(4\) 4.85606 2.42803
\(5\) 3.30541 1.47822 0.739112 0.673583i \(-0.235246\pi\)
0.739112 + 0.673583i \(0.235246\pi\)
\(6\) −0.660120 −0.269493
\(7\) −1.70947 −0.646120 −0.323060 0.946379i \(-0.604712\pi\)
−0.323060 + 0.946379i \(0.604712\pi\)
\(8\) −7.47834 −2.64399
\(9\) −2.93644 −0.978814
\(10\) −8.65491 −2.73692
\(11\) 5.06820 1.52812 0.764059 0.645146i \(-0.223203\pi\)
0.764059 + 0.645146i \(0.223203\pi\)
\(12\) 1.22425 0.353411
\(13\) 5.40015 1.49773 0.748867 0.662721i \(-0.230598\pi\)
0.748867 + 0.662721i \(0.230598\pi\)
\(14\) 4.47610 1.19629
\(15\) 0.833318 0.215162
\(16\) 9.86923 2.46731
\(17\) −0.784551 −0.190282 −0.0951408 0.995464i \(-0.530330\pi\)
−0.0951408 + 0.995464i \(0.530330\pi\)
\(18\) 7.68880 1.81227
\(19\) 1.17656 0.269922 0.134961 0.990851i \(-0.456909\pi\)
0.134961 + 0.990851i \(0.456909\pi\)
\(20\) 16.0513 3.58917
\(21\) −0.430971 −0.0940455
\(22\) −13.2706 −2.82930
\(23\) −1.79832 −0.374976 −0.187488 0.982267i \(-0.560035\pi\)
−0.187488 + 0.982267i \(0.560035\pi\)
\(24\) −1.88535 −0.384845
\(25\) 5.92572 1.18514
\(26\) −14.1398 −2.77305
\(27\) −1.49662 −0.288025
\(28\) −8.30131 −1.56880
\(29\) 7.10342 1.31907 0.659536 0.751673i \(-0.270753\pi\)
0.659536 + 0.751673i \(0.270753\pi\)
\(30\) −2.18197 −0.398371
\(31\) −9.66396 −1.73570 −0.867849 0.496828i \(-0.834498\pi\)
−0.867849 + 0.496828i \(0.834498\pi\)
\(32\) −10.8850 −1.92421
\(33\) 1.27773 0.222424
\(34\) 2.05428 0.352305
\(35\) −5.65050 −0.955109
\(36\) −14.2595 −2.37659
\(37\) −3.34566 −0.550023 −0.275011 0.961441i \(-0.588682\pi\)
−0.275011 + 0.961441i \(0.588682\pi\)
\(38\) −3.08072 −0.499758
\(39\) 1.36142 0.218002
\(40\) −24.7190 −3.90841
\(41\) 8.63584 1.34869 0.674346 0.738416i \(-0.264426\pi\)
0.674346 + 0.738416i \(0.264426\pi\)
\(42\) 1.12846 0.174125
\(43\) 1.57817 0.240668 0.120334 0.992733i \(-0.461603\pi\)
0.120334 + 0.992733i \(0.461603\pi\)
\(44\) 24.6115 3.71032
\(45\) −9.70614 −1.44691
\(46\) 4.70874 0.694266
\(47\) 4.16147 0.607013 0.303506 0.952829i \(-0.401843\pi\)
0.303506 + 0.952829i \(0.401843\pi\)
\(48\) 2.48811 0.359127
\(49\) −4.07771 −0.582529
\(50\) −15.5160 −2.19429
\(51\) −0.197791 −0.0276963
\(52\) 26.2235 3.63655
\(53\) −1.42628 −0.195914 −0.0979572 0.995191i \(-0.531231\pi\)
−0.0979572 + 0.995191i \(0.531231\pi\)
\(54\) 3.91877 0.533277
\(55\) 16.7525 2.25890
\(56\) 12.7840 1.70834
\(57\) 0.296620 0.0392883
\(58\) −18.5997 −2.44225
\(59\) 9.64463 1.25562 0.627812 0.778365i \(-0.283951\pi\)
0.627812 + 0.778365i \(0.283951\pi\)
\(60\) 4.04665 0.522420
\(61\) 13.8920 1.77869 0.889345 0.457237i \(-0.151161\pi\)
0.889345 + 0.457237i \(0.151161\pi\)
\(62\) 25.3042 3.21364
\(63\) 5.01976 0.632431
\(64\) 8.76290 1.09536
\(65\) 17.8497 2.21398
\(66\) −3.34562 −0.411817
\(67\) −10.7620 −1.31479 −0.657394 0.753547i \(-0.728341\pi\)
−0.657394 + 0.753547i \(0.728341\pi\)
\(68\) −3.80983 −0.462010
\(69\) −0.453370 −0.0545794
\(70\) 14.7953 1.76838
\(71\) −0.285596 −0.0338940 −0.0169470 0.999856i \(-0.505395\pi\)
−0.0169470 + 0.999856i \(0.505395\pi\)
\(72\) 21.9597 2.58798
\(73\) −16.4070 −1.92030 −0.960149 0.279487i \(-0.909836\pi\)
−0.960149 + 0.279487i \(0.909836\pi\)
\(74\) 8.76030 1.01836
\(75\) 1.49392 0.172503
\(76\) 5.71346 0.655378
\(77\) −8.66394 −0.987348
\(78\) −3.56475 −0.403629
\(79\) 7.56950 0.851635 0.425818 0.904809i \(-0.359986\pi\)
0.425818 + 0.904809i \(0.359986\pi\)
\(80\) 32.6218 3.64723
\(81\) 8.43202 0.936891
\(82\) −22.6122 −2.49710
\(83\) −2.48547 −0.272816 −0.136408 0.990653i \(-0.543556\pi\)
−0.136408 + 0.990653i \(0.543556\pi\)
\(84\) −2.09282 −0.228346
\(85\) −2.59326 −0.281279
\(86\) −4.13228 −0.445596
\(87\) 1.79082 0.191997
\(88\) −37.9017 −4.04034
\(89\) 10.8686 1.15207 0.576033 0.817426i \(-0.304600\pi\)
0.576033 + 0.817426i \(0.304600\pi\)
\(90\) 25.4146 2.67894
\(91\) −9.23141 −0.967715
\(92\) −8.73276 −0.910453
\(93\) −2.43636 −0.252638
\(94\) −10.8964 −1.12388
\(95\) 3.88901 0.399004
\(96\) −2.74419 −0.280078
\(97\) −0.0677252 −0.00687645 −0.00343823 0.999994i \(-0.501094\pi\)
−0.00343823 + 0.999994i \(0.501094\pi\)
\(98\) 10.6771 1.07855
\(99\) −14.8825 −1.49574
\(100\) 28.7757 2.87757
\(101\) −10.5228 −1.04706 −0.523529 0.852008i \(-0.675385\pi\)
−0.523529 + 0.852008i \(0.675385\pi\)
\(102\) 0.517898 0.0512796
\(103\) 18.0538 1.77889 0.889445 0.457042i \(-0.151091\pi\)
0.889445 + 0.457042i \(0.151091\pi\)
\(104\) −40.3842 −3.96000
\(105\) −1.42453 −0.139020
\(106\) 3.73458 0.362734
\(107\) 5.71828 0.552807 0.276403 0.961042i \(-0.410857\pi\)
0.276403 + 0.961042i \(0.410857\pi\)
\(108\) −7.26769 −0.699334
\(109\) 9.50553 0.910465 0.455233 0.890373i \(-0.349556\pi\)
0.455233 + 0.890373i \(0.349556\pi\)
\(110\) −43.8648 −4.18234
\(111\) −0.843465 −0.0800582
\(112\) −16.8712 −1.59418
\(113\) 14.3872 1.35343 0.676715 0.736245i \(-0.263403\pi\)
0.676715 + 0.736245i \(0.263403\pi\)
\(114\) −0.776672 −0.0727420
\(115\) −5.94419 −0.554298
\(116\) 34.4947 3.20275
\(117\) −15.8572 −1.46600
\(118\) −25.2536 −2.32478
\(119\) 1.34117 0.122945
\(120\) −6.23184 −0.568886
\(121\) 14.6866 1.33515
\(122\) −36.3750 −3.29323
\(123\) 2.17716 0.196308
\(124\) −46.9288 −4.21433
\(125\) 3.05989 0.273685
\(126\) −13.1438 −1.17094
\(127\) −9.34245 −0.829008 −0.414504 0.910047i \(-0.636045\pi\)
−0.414504 + 0.910047i \(0.636045\pi\)
\(128\) −1.17487 −0.103844
\(129\) 0.397867 0.0350303
\(130\) −46.7379 −4.09918
\(131\) −0.740956 −0.0647377 −0.0323688 0.999476i \(-0.510305\pi\)
−0.0323688 + 0.999476i \(0.510305\pi\)
\(132\) 6.20474 0.540053
\(133\) −2.01130 −0.174402
\(134\) 28.1793 2.43432
\(135\) −4.94694 −0.425765
\(136\) 5.86714 0.503103
\(137\) −2.52142 −0.215419 −0.107710 0.994182i \(-0.534352\pi\)
−0.107710 + 0.994182i \(0.534352\pi\)
\(138\) 1.18711 0.101053
\(139\) −0.597484 −0.0506780 −0.0253390 0.999679i \(-0.508067\pi\)
−0.0253390 + 0.999679i \(0.508067\pi\)
\(140\) −27.4392 −2.31904
\(141\) 1.04914 0.0883533
\(142\) 0.747807 0.0627546
\(143\) 27.3690 2.28871
\(144\) −28.9804 −2.41504
\(145\) 23.4797 1.94988
\(146\) 42.9603 3.55542
\(147\) −1.02802 −0.0847897
\(148\) −16.2467 −1.33547
\(149\) 17.6301 1.44432 0.722159 0.691727i \(-0.243150\pi\)
0.722159 + 0.691727i \(0.243150\pi\)
\(150\) −3.91169 −0.319388
\(151\) −6.88670 −0.560432 −0.280216 0.959937i \(-0.590406\pi\)
−0.280216 + 0.959937i \(0.590406\pi\)
\(152\) −8.79873 −0.713671
\(153\) 2.30379 0.186250
\(154\) 22.6857 1.82807
\(155\) −31.9433 −2.56575
\(156\) 6.61114 0.529315
\(157\) 5.22375 0.416900 0.208450 0.978033i \(-0.433158\pi\)
0.208450 + 0.978033i \(0.433158\pi\)
\(158\) −19.8200 −1.57680
\(159\) −0.359575 −0.0285162
\(160\) −35.9793 −2.84442
\(161\) 3.07418 0.242279
\(162\) −22.0785 −1.73465
\(163\) 2.57402 0.201613 0.100806 0.994906i \(-0.467858\pi\)
0.100806 + 0.994906i \(0.467858\pi\)
\(164\) 41.9362 3.27467
\(165\) 4.22342 0.328793
\(166\) 6.50798 0.505117
\(167\) −22.4337 −1.73597 −0.867985 0.496591i \(-0.834585\pi\)
−0.867985 + 0.496591i \(0.834585\pi\)
\(168\) 3.22295 0.248656
\(169\) 16.1617 1.24321
\(170\) 6.79022 0.520786
\(171\) −3.45490 −0.264203
\(172\) 7.66368 0.584350
\(173\) −5.91288 −0.449548 −0.224774 0.974411i \(-0.572164\pi\)
−0.224774 + 0.974411i \(0.572164\pi\)
\(174\) −4.68911 −0.355481
\(175\) −10.1299 −0.765745
\(176\) 50.0192 3.77034
\(177\) 2.43148 0.182761
\(178\) −28.4584 −2.13305
\(179\) −10.2097 −0.763111 −0.381556 0.924346i \(-0.624612\pi\)
−0.381556 + 0.924346i \(0.624612\pi\)
\(180\) −47.1336 −3.51313
\(181\) −23.9368 −1.77921 −0.889603 0.456735i \(-0.849019\pi\)
−0.889603 + 0.456735i \(0.849019\pi\)
\(182\) 24.1716 1.79172
\(183\) 3.50228 0.258896
\(184\) 13.4485 0.991434
\(185\) −11.0588 −0.813057
\(186\) 6.37938 0.467759
\(187\) −3.97626 −0.290773
\(188\) 20.2084 1.47385
\(189\) 2.55843 0.186099
\(190\) −10.1830 −0.738755
\(191\) −20.4041 −1.47639 −0.738195 0.674587i \(-0.764322\pi\)
−0.738195 + 0.674587i \(0.764322\pi\)
\(192\) 2.20919 0.159435
\(193\) −6.29806 −0.453345 −0.226672 0.973971i \(-0.572785\pi\)
−0.226672 + 0.973971i \(0.572785\pi\)
\(194\) 0.177332 0.0127317
\(195\) 4.50005 0.322255
\(196\) −19.8016 −1.41440
\(197\) 3.45995 0.246511 0.123256 0.992375i \(-0.460666\pi\)
0.123256 + 0.992375i \(0.460666\pi\)
\(198\) 38.9684 2.76936
\(199\) −5.57896 −0.395482 −0.197741 0.980254i \(-0.563361\pi\)
−0.197741 + 0.980254i \(0.563361\pi\)
\(200\) −44.3146 −3.13351
\(201\) −2.71318 −0.191373
\(202\) 27.5530 1.93862
\(203\) −12.1431 −0.852278
\(204\) −0.960487 −0.0672475
\(205\) 28.5450 1.99367
\(206\) −47.2721 −3.29361
\(207\) 5.28067 0.367032
\(208\) 53.2954 3.69537
\(209\) 5.96304 0.412472
\(210\) 3.73001 0.257395
\(211\) −19.2958 −1.32838 −0.664190 0.747564i \(-0.731224\pi\)
−0.664190 + 0.747564i \(0.731224\pi\)
\(212\) −6.92610 −0.475686
\(213\) −0.0720009 −0.00493342
\(214\) −14.9728 −1.02352
\(215\) 5.21648 0.355761
\(216\) 11.1922 0.761536
\(217\) 16.5203 1.12147
\(218\) −24.8894 −1.68572
\(219\) −4.13634 −0.279508
\(220\) 81.3510 5.48468
\(221\) −4.23670 −0.284991
\(222\) 2.20854 0.148227
\(223\) −19.5492 −1.30911 −0.654555 0.756014i \(-0.727144\pi\)
−0.654555 + 0.756014i \(0.727144\pi\)
\(224\) 18.6076 1.24327
\(225\) −17.4005 −1.16004
\(226\) −37.6715 −2.50587
\(227\) −10.8304 −0.718840 −0.359420 0.933176i \(-0.617025\pi\)
−0.359420 + 0.933176i \(0.617025\pi\)
\(228\) 1.44040 0.0953931
\(229\) −9.28215 −0.613382 −0.306691 0.951809i \(-0.599222\pi\)
−0.306691 + 0.951809i \(0.599222\pi\)
\(230\) 15.5643 1.02628
\(231\) −2.18424 −0.143713
\(232\) −53.1218 −3.48762
\(233\) 8.22304 0.538709 0.269355 0.963041i \(-0.413190\pi\)
0.269355 + 0.963041i \(0.413190\pi\)
\(234\) 41.5207 2.71430
\(235\) 13.7554 0.897300
\(236\) 46.8349 3.04869
\(237\) 1.90833 0.123959
\(238\) −3.51173 −0.227631
\(239\) −6.85298 −0.443282 −0.221641 0.975128i \(-0.571141\pi\)
−0.221641 + 0.975128i \(0.571141\pi\)
\(240\) 8.22421 0.530870
\(241\) 17.0291 1.09694 0.548472 0.836169i \(-0.315210\pi\)
0.548472 + 0.836169i \(0.315210\pi\)
\(242\) −38.4556 −2.47202
\(243\) 6.61564 0.424393
\(244\) 67.4605 4.31872
\(245\) −13.4785 −0.861109
\(246\) −5.70069 −0.363463
\(247\) 6.35361 0.404271
\(248\) 72.2704 4.58918
\(249\) −0.626606 −0.0397095
\(250\) −8.01205 −0.506727
\(251\) −22.9201 −1.44670 −0.723351 0.690480i \(-0.757399\pi\)
−0.723351 + 0.690480i \(0.757399\pi\)
\(252\) 24.3763 1.53556
\(253\) −9.11425 −0.573008
\(254\) 24.4624 1.53490
\(255\) −0.653781 −0.0409413
\(256\) −14.4495 −0.903095
\(257\) 5.29694 0.330414 0.165207 0.986259i \(-0.447171\pi\)
0.165207 + 0.986259i \(0.447171\pi\)
\(258\) −1.04178 −0.0648584
\(259\) 5.71931 0.355381
\(260\) 86.6794 5.37563
\(261\) −20.8588 −1.29113
\(262\) 1.94013 0.119861
\(263\) −17.9004 −1.10379 −0.551893 0.833915i \(-0.686094\pi\)
−0.551893 + 0.833915i \(0.686094\pi\)
\(264\) −9.55531 −0.588088
\(265\) −4.71443 −0.289605
\(266\) 5.26640 0.322904
\(267\) 2.74005 0.167688
\(268\) −52.2609 −3.19235
\(269\) −8.53581 −0.520437 −0.260219 0.965550i \(-0.583795\pi\)
−0.260219 + 0.965550i \(0.583795\pi\)
\(270\) 12.9531 0.788302
\(271\) 23.7832 1.44473 0.722365 0.691512i \(-0.243055\pi\)
0.722365 + 0.691512i \(0.243055\pi\)
\(272\) −7.74292 −0.469483
\(273\) −2.32731 −0.140855
\(274\) 6.60210 0.398848
\(275\) 30.0327 1.81104
\(276\) −2.20159 −0.132520
\(277\) −27.8210 −1.67160 −0.835801 0.549032i \(-0.814996\pi\)
−0.835801 + 0.549032i \(0.814996\pi\)
\(278\) 1.56446 0.0938300
\(279\) 28.3777 1.69893
\(280\) 42.2564 2.52530
\(281\) −0.382276 −0.0228047 −0.0114023 0.999935i \(-0.503630\pi\)
−0.0114023 + 0.999935i \(0.503630\pi\)
\(282\) −2.74707 −0.163586
\(283\) 22.2189 1.32078 0.660389 0.750924i \(-0.270391\pi\)
0.660389 + 0.750924i \(0.270391\pi\)
\(284\) −1.38687 −0.0822957
\(285\) 0.980450 0.0580768
\(286\) −71.6634 −4.23754
\(287\) −14.7627 −0.871416
\(288\) 31.9631 1.88345
\(289\) −16.3845 −0.963793
\(290\) −61.4794 −3.61020
\(291\) −0.0170740 −0.00100090
\(292\) −79.6736 −4.66255
\(293\) 32.2860 1.88617 0.943084 0.332553i \(-0.107910\pi\)
0.943084 + 0.332553i \(0.107910\pi\)
\(294\) 2.69178 0.156988
\(295\) 31.8794 1.85609
\(296\) 25.0200 1.45426
\(297\) −7.58517 −0.440136
\(298\) −46.1629 −2.67415
\(299\) −9.71121 −0.561614
\(300\) 7.25457 0.418843
\(301\) −2.69783 −0.155500
\(302\) 18.0322 1.03764
\(303\) −2.65288 −0.152404
\(304\) 11.6118 0.665980
\(305\) 45.9188 2.62930
\(306\) −6.03226 −0.344841
\(307\) 15.0228 0.857395 0.428698 0.903448i \(-0.358973\pi\)
0.428698 + 0.903448i \(0.358973\pi\)
\(308\) −42.0726 −2.39731
\(309\) 4.55149 0.258925
\(310\) 83.6407 4.75047
\(311\) −27.8289 −1.57803 −0.789016 0.614372i \(-0.789409\pi\)
−0.789016 + 0.614372i \(0.789409\pi\)
\(312\) −10.1812 −0.576395
\(313\) 7.98394 0.451279 0.225639 0.974211i \(-0.427553\pi\)
0.225639 + 0.974211i \(0.427553\pi\)
\(314\) −13.6779 −0.771889
\(315\) 16.5924 0.934874
\(316\) 36.7580 2.06780
\(317\) −8.67321 −0.487136 −0.243568 0.969884i \(-0.578318\pi\)
−0.243568 + 0.969884i \(0.578318\pi\)
\(318\) 0.941515 0.0527976
\(319\) 36.0015 2.01570
\(320\) 28.9650 1.61919
\(321\) 1.44162 0.0804634
\(322\) −8.04946 −0.448579
\(323\) −0.923072 −0.0513611
\(324\) 40.9464 2.27480
\(325\) 31.9998 1.77503
\(326\) −6.73984 −0.373285
\(327\) 2.39642 0.132522
\(328\) −64.5818 −3.56593
\(329\) −7.11392 −0.392203
\(330\) −11.0586 −0.608758
\(331\) 0.549307 0.0301926 0.0150963 0.999886i \(-0.495195\pi\)
0.0150963 + 0.999886i \(0.495195\pi\)
\(332\) −12.0696 −0.662405
\(333\) 9.82433 0.538370
\(334\) 58.7405 3.21414
\(335\) −35.5728 −1.94355
\(336\) −4.25335 −0.232039
\(337\) 23.2445 1.26621 0.633103 0.774067i \(-0.281781\pi\)
0.633103 + 0.774067i \(0.281781\pi\)
\(338\) −42.3179 −2.30179
\(339\) 3.62711 0.196998
\(340\) −12.5930 −0.682954
\(341\) −48.9789 −2.65235
\(342\) 9.04635 0.489170
\(343\) 18.9370 1.02250
\(344\) −11.8021 −0.636325
\(345\) −1.49857 −0.0806805
\(346\) 15.4823 0.832336
\(347\) −33.9095 −1.82036 −0.910179 0.414216i \(-0.864056\pi\)
−0.910179 + 0.414216i \(0.864056\pi\)
\(348\) 8.69636 0.466174
\(349\) −9.16422 −0.490549 −0.245275 0.969454i \(-0.578878\pi\)
−0.245275 + 0.969454i \(0.578878\pi\)
\(350\) 26.5241 1.41777
\(351\) −8.08199 −0.431385
\(352\) −55.1673 −2.94043
\(353\) −24.5982 −1.30923 −0.654615 0.755962i \(-0.727169\pi\)
−0.654615 + 0.755962i \(0.727169\pi\)
\(354\) −6.36662 −0.338382
\(355\) −0.944011 −0.0501029
\(356\) 52.7785 2.79725
\(357\) 0.338119 0.0178951
\(358\) 26.7333 1.41290
\(359\) 0.901238 0.0475655 0.0237828 0.999717i \(-0.492429\pi\)
0.0237828 + 0.999717i \(0.492429\pi\)
\(360\) 72.5858 3.82561
\(361\) −17.6157 −0.927142
\(362\) 62.6762 3.29419
\(363\) 3.70261 0.194336
\(364\) −44.8283 −2.34964
\(365\) −54.2320 −2.83863
\(366\) −9.17040 −0.479345
\(367\) −19.2141 −1.00297 −0.501483 0.865167i \(-0.667212\pi\)
−0.501483 + 0.865167i \(0.667212\pi\)
\(368\) −17.7480 −0.925181
\(369\) −25.3586 −1.32012
\(370\) 28.9564 1.50537
\(371\) 2.43818 0.126584
\(372\) −11.8311 −0.613414
\(373\) −26.7886 −1.38706 −0.693530 0.720428i \(-0.743946\pi\)
−0.693530 + 0.720428i \(0.743946\pi\)
\(374\) 10.4115 0.538365
\(375\) 0.771422 0.0398361
\(376\) −31.1209 −1.60494
\(377\) 38.3596 1.97562
\(378\) −6.69902 −0.344560
\(379\) 18.8658 0.969071 0.484535 0.874772i \(-0.338989\pi\)
0.484535 + 0.874772i \(0.338989\pi\)
\(380\) 18.8853 0.968796
\(381\) −2.35530 −0.120666
\(382\) 53.4263 2.73353
\(383\) 23.4746 1.19949 0.599747 0.800190i \(-0.295268\pi\)
0.599747 + 0.800190i \(0.295268\pi\)
\(384\) −0.296192 −0.0151150
\(385\) −28.6379 −1.45952
\(386\) 16.4909 0.839365
\(387\) −4.63419 −0.235569
\(388\) −0.328878 −0.0166962
\(389\) 20.9012 1.05974 0.529868 0.848080i \(-0.322242\pi\)
0.529868 + 0.848080i \(0.322242\pi\)
\(390\) −11.7830 −0.596653
\(391\) 1.41088 0.0713510
\(392\) 30.4945 1.54020
\(393\) −0.186801 −0.00942285
\(394\) −9.05956 −0.456414
\(395\) 25.0203 1.25891
\(396\) −72.2702 −3.63171
\(397\) 15.7384 0.789888 0.394944 0.918705i \(-0.370764\pi\)
0.394944 + 0.918705i \(0.370764\pi\)
\(398\) 14.6080 0.732233
\(399\) −0.507063 −0.0253849
\(400\) 58.4823 2.92412
\(401\) −18.6777 −0.932719 −0.466359 0.884595i \(-0.654435\pi\)
−0.466359 + 0.884595i \(0.654435\pi\)
\(402\) 7.10421 0.354326
\(403\) −52.1869 −2.59961
\(404\) −51.0994 −2.54229
\(405\) 27.8713 1.38493
\(406\) 31.7956 1.57799
\(407\) −16.9565 −0.840500
\(408\) 1.47915 0.0732289
\(409\) −8.27923 −0.409382 −0.204691 0.978827i \(-0.565619\pi\)
−0.204691 + 0.978827i \(0.565619\pi\)
\(410\) −74.7424 −3.69127
\(411\) −0.635668 −0.0313552
\(412\) 87.6703 4.31920
\(413\) −16.4872 −0.811283
\(414\) −13.8269 −0.679557
\(415\) −8.21549 −0.403283
\(416\) −58.7806 −2.88196
\(417\) −0.150630 −0.00737640
\(418\) −15.6137 −0.763690
\(419\) −27.2743 −1.33244 −0.666218 0.745757i \(-0.732088\pi\)
−0.666218 + 0.745757i \(0.732088\pi\)
\(420\) −6.91763 −0.337546
\(421\) 20.6546 1.00664 0.503321 0.864100i \(-0.332111\pi\)
0.503321 + 0.864100i \(0.332111\pi\)
\(422\) 50.5244 2.45949
\(423\) −12.2199 −0.594153
\(424\) 10.6662 0.517996
\(425\) −4.64903 −0.225511
\(426\) 0.188528 0.00913420
\(427\) −23.7480 −1.14925
\(428\) 27.7683 1.34223
\(429\) 6.89994 0.333132
\(430\) −13.6589 −0.658690
\(431\) 5.21636 0.251263 0.125632 0.992077i \(-0.459904\pi\)
0.125632 + 0.992077i \(0.459904\pi\)
\(432\) −14.7705 −0.710646
\(433\) −8.58335 −0.412490 −0.206245 0.978500i \(-0.566124\pi\)
−0.206245 + 0.978500i \(0.566124\pi\)
\(434\) −43.2568 −2.07639
\(435\) 5.91941 0.283814
\(436\) 46.1595 2.21064
\(437\) −2.11583 −0.101214
\(438\) 10.8306 0.517507
\(439\) 16.4167 0.783529 0.391764 0.920066i \(-0.371865\pi\)
0.391764 + 0.920066i \(0.371865\pi\)
\(440\) −125.281 −5.97252
\(441\) 11.9739 0.570188
\(442\) 11.0934 0.527660
\(443\) −12.8410 −0.610092 −0.305046 0.952338i \(-0.598672\pi\)
−0.305046 + 0.952338i \(0.598672\pi\)
\(444\) −4.09592 −0.194384
\(445\) 35.9251 1.70301
\(446\) 51.1877 2.42381
\(447\) 4.44469 0.210227
\(448\) −14.9799 −0.707735
\(449\) 31.8372 1.50249 0.751246 0.660023i \(-0.229453\pi\)
0.751246 + 0.660023i \(0.229453\pi\)
\(450\) 45.5617 2.14780
\(451\) 43.7681 2.06096
\(452\) 69.8650 3.28617
\(453\) −1.73619 −0.0815733
\(454\) 28.3585 1.33093
\(455\) −30.5136 −1.43050
\(456\) −2.21822 −0.103878
\(457\) −2.29825 −0.107508 −0.0537538 0.998554i \(-0.517119\pi\)
−0.0537538 + 0.998554i \(0.517119\pi\)
\(458\) 24.3045 1.13567
\(459\) 1.17418 0.0548059
\(460\) −28.8653 −1.34585
\(461\) −18.8355 −0.877257 −0.438629 0.898668i \(-0.644536\pi\)
−0.438629 + 0.898668i \(0.644536\pi\)
\(462\) 5.71924 0.266083
\(463\) −24.5974 −1.14314 −0.571569 0.820554i \(-0.693665\pi\)
−0.571569 + 0.820554i \(0.693665\pi\)
\(464\) 70.1053 3.25456
\(465\) −8.05315 −0.373456
\(466\) −21.5313 −0.997417
\(467\) −27.4443 −1.26997 −0.634986 0.772523i \(-0.718994\pi\)
−0.634986 + 0.772523i \(0.718994\pi\)
\(468\) −77.0038 −3.55950
\(469\) 18.3973 0.849510
\(470\) −36.0171 −1.66135
\(471\) 1.31695 0.0606817
\(472\) −72.1258 −3.31986
\(473\) 7.99846 0.367769
\(474\) −4.99678 −0.229510
\(475\) 6.97197 0.319896
\(476\) 6.51280 0.298514
\(477\) 4.18818 0.191764
\(478\) 17.9439 0.820734
\(479\) 8.97630 0.410137 0.205069 0.978748i \(-0.434258\pi\)
0.205069 + 0.978748i \(0.434258\pi\)
\(480\) −9.07066 −0.414017
\(481\) −18.0671 −0.823788
\(482\) −44.5893 −2.03099
\(483\) 0.775024 0.0352648
\(484\) 71.3192 3.24178
\(485\) −0.223859 −0.0101649
\(486\) −17.3224 −0.785762
\(487\) −32.2972 −1.46352 −0.731762 0.681560i \(-0.761302\pi\)
−0.731762 + 0.681560i \(0.761302\pi\)
\(488\) −103.889 −4.70284
\(489\) 0.648930 0.0293456
\(490\) 35.2922 1.59434
\(491\) 8.41411 0.379724 0.189862 0.981811i \(-0.439196\pi\)
0.189862 + 0.981811i \(0.439196\pi\)
\(492\) 10.5724 0.476642
\(493\) −5.57300 −0.250995
\(494\) −16.6364 −0.748505
\(495\) −49.1926 −2.21104
\(496\) −95.3759 −4.28250
\(497\) 0.488218 0.0218996
\(498\) 1.64071 0.0735219
\(499\) −41.0243 −1.83650 −0.918250 0.396001i \(-0.870398\pi\)
−0.918250 + 0.396001i \(0.870398\pi\)
\(500\) 14.8590 0.664516
\(501\) −5.65570 −0.252678
\(502\) 60.0141 2.67856
\(503\) 26.9003 1.19942 0.599712 0.800216i \(-0.295282\pi\)
0.599712 + 0.800216i \(0.295282\pi\)
\(504\) −37.5395 −1.67214
\(505\) −34.7822 −1.54779
\(506\) 23.8648 1.06092
\(507\) 4.07448 0.180954
\(508\) −45.3675 −2.01286
\(509\) 9.93633 0.440420 0.220210 0.975453i \(-0.429326\pi\)
0.220210 + 0.975453i \(0.429326\pi\)
\(510\) 1.71187 0.0758027
\(511\) 28.0474 1.24074
\(512\) 40.1845 1.77592
\(513\) −1.76087 −0.0777441
\(514\) −13.8696 −0.611760
\(515\) 59.6751 2.62960
\(516\) 1.93207 0.0850546
\(517\) 21.0911 0.927588
\(518\) −14.9755 −0.657985
\(519\) −1.49068 −0.0654337
\(520\) −133.486 −5.85376
\(521\) −0.0576909 −0.00252749 −0.00126374 0.999999i \(-0.500402\pi\)
−0.00126374 + 0.999999i \(0.500402\pi\)
\(522\) 54.6168 2.39051
\(523\) −2.63561 −0.115247 −0.0576236 0.998338i \(-0.518352\pi\)
−0.0576236 + 0.998338i \(0.518352\pi\)
\(524\) −3.59813 −0.157185
\(525\) −2.55381 −0.111458
\(526\) 46.8705 2.04365
\(527\) 7.58187 0.330272
\(528\) 12.6102 0.548789
\(529\) −19.7660 −0.859393
\(530\) 12.3443 0.536202
\(531\) −28.3209 −1.22902
\(532\) −9.76699 −0.423453
\(533\) 46.6349 2.01998
\(534\) −7.17457 −0.310474
\(535\) 18.9012 0.817172
\(536\) 80.4819 3.47629
\(537\) −2.57395 −0.111074
\(538\) 22.3502 0.963587
\(539\) −20.6666 −0.890174
\(540\) −24.0227 −1.03377
\(541\) −17.6990 −0.760940 −0.380470 0.924793i \(-0.624238\pi\)
−0.380470 + 0.924793i \(0.624238\pi\)
\(542\) −62.2743 −2.67491
\(543\) −6.03464 −0.258971
\(544\) 8.53984 0.366142
\(545\) 31.4197 1.34587
\(546\) 6.09384 0.260792
\(547\) 8.98778 0.384290 0.192145 0.981367i \(-0.438456\pi\)
0.192145 + 0.981367i \(0.438456\pi\)
\(548\) −12.2442 −0.523045
\(549\) −40.7931 −1.74101
\(550\) −78.6380 −3.35313
\(551\) 8.35760 0.356046
\(552\) 3.39046 0.144307
\(553\) −12.9398 −0.550258
\(554\) 72.8468 3.09496
\(555\) −2.78800 −0.118344
\(556\) −2.90142 −0.123048
\(557\) 2.75405 0.116693 0.0583464 0.998296i \(-0.481417\pi\)
0.0583464 + 0.998296i \(0.481417\pi\)
\(558\) −74.3043 −3.14555
\(559\) 8.52234 0.360457
\(560\) −55.7661 −2.35655
\(561\) −1.00245 −0.0423233
\(562\) 1.00096 0.0422228
\(563\) 28.7946 1.21355 0.606774 0.794874i \(-0.292463\pi\)
0.606774 + 0.794874i \(0.292463\pi\)
\(564\) 5.09468 0.214525
\(565\) 47.5554 2.00067
\(566\) −58.1782 −2.44541
\(567\) −14.4143 −0.605343
\(568\) 2.13578 0.0896155
\(569\) −36.3249 −1.52282 −0.761409 0.648272i \(-0.775492\pi\)
−0.761409 + 0.648272i \(0.775492\pi\)
\(570\) −2.56722 −0.107529
\(571\) −33.9472 −1.42065 −0.710324 0.703875i \(-0.751452\pi\)
−0.710324 + 0.703875i \(0.751452\pi\)
\(572\) 132.906 5.55707
\(573\) −5.14403 −0.214895
\(574\) 38.6549 1.61342
\(575\) −10.6564 −0.444401
\(576\) −25.7317 −1.07216
\(577\) 26.8651 1.11841 0.559205 0.829029i \(-0.311107\pi\)
0.559205 + 0.829029i \(0.311107\pi\)
\(578\) 42.9013 1.78446
\(579\) −1.58779 −0.0659863
\(580\) 114.019 4.73438
\(581\) 4.24884 0.176272
\(582\) 0.0447068 0.00185316
\(583\) −7.22866 −0.299380
\(584\) 122.697 5.07726
\(585\) −52.4147 −2.16708
\(586\) −84.5380 −3.49223
\(587\) 6.68080 0.275746 0.137873 0.990450i \(-0.455973\pi\)
0.137873 + 0.990450i \(0.455973\pi\)
\(588\) −4.99213 −0.205872
\(589\) −11.3702 −0.468503
\(590\) −83.4734 −3.43654
\(591\) 0.872279 0.0358808
\(592\) −33.0191 −1.35708
\(593\) −0.897450 −0.0368539 −0.0184269 0.999830i \(-0.505866\pi\)
−0.0184269 + 0.999830i \(0.505866\pi\)
\(594\) 19.8611 0.814910
\(595\) 4.43311 0.181740
\(596\) 85.6131 3.50685
\(597\) −1.40650 −0.0575642
\(598\) 25.4279 1.03983
\(599\) −10.2892 −0.420405 −0.210202 0.977658i \(-0.567412\pi\)
−0.210202 + 0.977658i \(0.567412\pi\)
\(600\) −11.1720 −0.456097
\(601\) −13.8082 −0.563247 −0.281624 0.959525i \(-0.590873\pi\)
−0.281624 + 0.959525i \(0.590873\pi\)
\(602\) 7.06402 0.287908
\(603\) 31.6020 1.28693
\(604\) −33.4423 −1.36075
\(605\) 48.5453 1.97365
\(606\) 6.94632 0.282175
\(607\) 7.56231 0.306945 0.153472 0.988153i \(-0.450954\pi\)
0.153472 + 0.988153i \(0.450954\pi\)
\(608\) −12.8069 −0.519387
\(609\) −3.06136 −0.124053
\(610\) −120.234 −4.86814
\(611\) 22.4726 0.909143
\(612\) 11.1873 0.452222
\(613\) −40.2607 −1.62612 −0.813058 0.582183i \(-0.802199\pi\)
−0.813058 + 0.582183i \(0.802199\pi\)
\(614\) −39.3358 −1.58746
\(615\) 7.19640 0.290187
\(616\) 64.7919 2.61054
\(617\) −40.0364 −1.61181 −0.805903 0.592048i \(-0.798320\pi\)
−0.805903 + 0.592048i \(0.798320\pi\)
\(618\) −11.9177 −0.479399
\(619\) 1.00000 0.0401934
\(620\) −155.119 −6.22972
\(621\) 2.69141 0.108002
\(622\) 72.8675 2.92172
\(623\) −18.5795 −0.744373
\(624\) 13.4362 0.537877
\(625\) −19.5144 −0.780577
\(626\) −20.9052 −0.835541
\(627\) 1.50333 0.0600371
\(628\) 25.3669 1.01225
\(629\) 2.62484 0.104659
\(630\) −43.4456 −1.73091
\(631\) 27.7851 1.10611 0.553053 0.833146i \(-0.313463\pi\)
0.553053 + 0.833146i \(0.313463\pi\)
\(632\) −56.6073 −2.25172
\(633\) −4.86463 −0.193352
\(634\) 22.7100 0.901929
\(635\) −30.8806 −1.22546
\(636\) −1.74612 −0.0692382
\(637\) −22.0202 −0.872474
\(638\) −94.2667 −3.73205
\(639\) 0.838636 0.0331759
\(640\) −3.88341 −0.153505
\(641\) 15.6623 0.618625 0.309312 0.950960i \(-0.399901\pi\)
0.309312 + 0.950960i \(0.399901\pi\)
\(642\) −3.77475 −0.148978
\(643\) 41.9228 1.65328 0.826638 0.562735i \(-0.190251\pi\)
0.826638 + 0.562735i \(0.190251\pi\)
\(644\) 14.9284 0.588262
\(645\) 1.31511 0.0517826
\(646\) 2.41698 0.0950948
\(647\) 14.5442 0.571792 0.285896 0.958261i \(-0.407709\pi\)
0.285896 + 0.958261i \(0.407709\pi\)
\(648\) −63.0575 −2.47713
\(649\) 48.8809 1.91874
\(650\) −83.7886 −3.28646
\(651\) 4.16488 0.163235
\(652\) 12.4996 0.489522
\(653\) 45.4250 1.77762 0.888809 0.458279i \(-0.151534\pi\)
0.888809 + 0.458279i \(0.151534\pi\)
\(654\) −6.27480 −0.245364
\(655\) −2.44916 −0.0956967
\(656\) 85.2291 3.32764
\(657\) 48.1783 1.87962
\(658\) 18.6271 0.726161
\(659\) −3.90677 −0.152186 −0.0760931 0.997101i \(-0.524245\pi\)
−0.0760931 + 0.997101i \(0.524245\pi\)
\(660\) 20.5092 0.798319
\(661\) 14.2711 0.555080 0.277540 0.960714i \(-0.410481\pi\)
0.277540 + 0.960714i \(0.410481\pi\)
\(662\) −1.43831 −0.0559015
\(663\) −1.06810 −0.0414817
\(664\) 18.5872 0.721323
\(665\) −6.64816 −0.257805
\(666\) −25.7241 −0.996789
\(667\) −12.7742 −0.494620
\(668\) −108.939 −4.21499
\(669\) −4.92849 −0.190547
\(670\) 93.1441 3.59847
\(671\) 70.4074 2.71805
\(672\) 4.69111 0.180964
\(673\) 31.6147 1.21866 0.609328 0.792918i \(-0.291439\pi\)
0.609328 + 0.792918i \(0.291439\pi\)
\(674\) −60.8635 −2.34437
\(675\) −8.86856 −0.341351
\(676\) 78.4821 3.01854
\(677\) 18.8231 0.723432 0.361716 0.932288i \(-0.382191\pi\)
0.361716 + 0.932288i \(0.382191\pi\)
\(678\) −9.49726 −0.364740
\(679\) 0.115774 0.00444301
\(680\) 19.3933 0.743699
\(681\) −2.73043 −0.104630
\(682\) 128.247 4.91082
\(683\) 7.18185 0.274806 0.137403 0.990515i \(-0.456125\pi\)
0.137403 + 0.990515i \(0.456125\pi\)
\(684\) −16.7772 −0.641493
\(685\) −8.33432 −0.318438
\(686\) −49.5849 −1.89316
\(687\) −2.34010 −0.0892804
\(688\) 15.5753 0.593802
\(689\) −7.70212 −0.293427
\(690\) 3.92388 0.149379
\(691\) −21.2098 −0.806859 −0.403429 0.915011i \(-0.632182\pi\)
−0.403429 + 0.915011i \(0.632182\pi\)
\(692\) −28.7133 −1.09152
\(693\) 25.4412 0.966430
\(694\) 88.7889 3.37038
\(695\) −1.97493 −0.0749134
\(696\) −13.3924 −0.507638
\(697\) −6.77526 −0.256631
\(698\) 23.9957 0.908249
\(699\) 2.07309 0.0784115
\(700\) −49.1912 −1.85925
\(701\) 17.9212 0.676876 0.338438 0.940989i \(-0.390101\pi\)
0.338438 + 0.940989i \(0.390101\pi\)
\(702\) 21.1619 0.798706
\(703\) −3.93637 −0.148463
\(704\) 44.4121 1.67384
\(705\) 3.46783 0.130606
\(706\) 64.4081 2.42403
\(707\) 17.9884 0.676525
\(708\) 11.8074 0.443751
\(709\) 37.0614 1.39187 0.695934 0.718106i \(-0.254991\pi\)
0.695934 + 0.718106i \(0.254991\pi\)
\(710\) 2.47181 0.0927653
\(711\) −22.2274 −0.833593
\(712\) −81.2789 −3.04606
\(713\) 17.3789 0.650845
\(714\) −0.885333 −0.0331327
\(715\) 90.4659 3.38323
\(716\) −49.5791 −1.85286
\(717\) −1.72769 −0.0645216
\(718\) −2.35981 −0.0880673
\(719\) 15.2676 0.569386 0.284693 0.958619i \(-0.408108\pi\)
0.284693 + 0.958619i \(0.408108\pi\)
\(720\) −95.7921 −3.56996
\(721\) −30.8624 −1.14938
\(722\) 46.1251 1.71660
\(723\) 4.29317 0.159665
\(724\) −116.238 −4.31997
\(725\) 42.0929 1.56329
\(726\) −9.69494 −0.359813
\(727\) 6.85952 0.254405 0.127203 0.991877i \(-0.459400\pi\)
0.127203 + 0.991877i \(0.459400\pi\)
\(728\) 69.0357 2.55863
\(729\) −23.6282 −0.875118
\(730\) 142.001 5.25571
\(731\) −1.23815 −0.0457947
\(732\) 17.0073 0.628608
\(733\) −3.81613 −0.140952 −0.0704760 0.997513i \(-0.522452\pi\)
−0.0704760 + 0.997513i \(0.522452\pi\)
\(734\) 50.3103 1.85699
\(735\) −3.39803 −0.125338
\(736\) 19.5747 0.721534
\(737\) −54.5439 −2.00915
\(738\) 66.3993 2.44419
\(739\) −5.79329 −0.213109 −0.106555 0.994307i \(-0.533982\pi\)
−0.106555 + 0.994307i \(0.533982\pi\)
\(740\) −53.7021 −1.97413
\(741\) 1.60179 0.0588433
\(742\) −6.38416 −0.234370
\(743\) −33.3268 −1.22264 −0.611320 0.791383i \(-0.709361\pi\)
−0.611320 + 0.791383i \(0.709361\pi\)
\(744\) 18.2199 0.667974
\(745\) 58.2748 2.13502
\(746\) 70.1435 2.56813
\(747\) 7.29844 0.267036
\(748\) −19.3090 −0.706006
\(749\) −9.77524 −0.357179
\(750\) −2.01990 −0.0737563
\(751\) 9.43349 0.344233 0.172117 0.985077i \(-0.444939\pi\)
0.172117 + 0.985077i \(0.444939\pi\)
\(752\) 41.0705 1.49769
\(753\) −5.77832 −0.210574
\(754\) −100.441 −3.65785
\(755\) −22.7634 −0.828443
\(756\) 12.4239 0.451853
\(757\) −39.1745 −1.42382 −0.711910 0.702270i \(-0.752170\pi\)
−0.711910 + 0.702270i \(0.752170\pi\)
\(758\) −49.3984 −1.79423
\(759\) −2.29777 −0.0834037
\(760\) −29.0834 −1.05497
\(761\) −27.9002 −1.01138 −0.505691 0.862714i \(-0.668763\pi\)
−0.505691 + 0.862714i \(0.668763\pi\)
\(762\) 6.16714 0.223412
\(763\) −16.2494 −0.588269
\(764\) −99.0837 −3.58472
\(765\) 7.61496 0.275320
\(766\) −61.4660 −2.22086
\(767\) 52.0825 1.88059
\(768\) −3.64283 −0.131449
\(769\) 11.2033 0.404000 0.202000 0.979385i \(-0.435256\pi\)
0.202000 + 0.979385i \(0.435256\pi\)
\(770\) 74.9856 2.70229
\(771\) 1.33540 0.0480932
\(772\) −30.5838 −1.10074
\(773\) 30.9853 1.11446 0.557232 0.830357i \(-0.311863\pi\)
0.557232 + 0.830357i \(0.311863\pi\)
\(774\) 12.1342 0.436155
\(775\) −57.2660 −2.05705
\(776\) 0.506472 0.0181813
\(777\) 1.44188 0.0517272
\(778\) −54.7280 −1.96209
\(779\) 10.1606 0.364041
\(780\) 21.8525 0.782446
\(781\) −1.44746 −0.0517941
\(782\) −3.69425 −0.132106
\(783\) −10.6311 −0.379925
\(784\) −40.2438 −1.43728
\(785\) 17.2666 0.616272
\(786\) 0.489120 0.0174463
\(787\) 7.77104 0.277008 0.138504 0.990362i \(-0.455771\pi\)
0.138504 + 0.990362i \(0.455771\pi\)
\(788\) 16.8017 0.598537
\(789\) −4.51282 −0.160661
\(790\) −65.5133 −2.33086
\(791\) −24.5944 −0.874478
\(792\) 111.296 3.95474
\(793\) 75.0190 2.66400
\(794\) −41.2096 −1.46247
\(795\) −1.18854 −0.0421533
\(796\) −27.0918 −0.960244
\(797\) 35.2344 1.24807 0.624033 0.781398i \(-0.285493\pi\)
0.624033 + 0.781398i \(0.285493\pi\)
\(798\) 1.32770 0.0470000
\(799\) −3.26489 −0.115503
\(800\) −64.5015 −2.28047
\(801\) −31.9149 −1.12766
\(802\) 48.9058 1.72692
\(803\) −83.1541 −2.93444
\(804\) −13.1754 −0.464660
\(805\) 10.1614 0.358143
\(806\) 136.647 4.81317
\(807\) −2.15194 −0.0757519
\(808\) 78.6932 2.76842
\(809\) −35.0943 −1.23385 −0.616925 0.787022i \(-0.711622\pi\)
−0.616925 + 0.787022i \(0.711622\pi\)
\(810\) −72.9783 −2.56420
\(811\) 1.49321 0.0524337 0.0262168 0.999656i \(-0.491654\pi\)
0.0262168 + 0.999656i \(0.491654\pi\)
\(812\) −58.9676 −2.06936
\(813\) 5.99593 0.210287
\(814\) 44.3989 1.55618
\(815\) 8.50819 0.298029
\(816\) −1.95205 −0.0683353
\(817\) 1.85681 0.0649615
\(818\) 21.6784 0.757968
\(819\) 27.1075 0.947213
\(820\) 138.616 4.84069
\(821\) −7.80078 −0.272249 −0.136125 0.990692i \(-0.543465\pi\)
−0.136125 + 0.990692i \(0.543465\pi\)
\(822\) 1.66444 0.0580540
\(823\) 4.44031 0.154779 0.0773897 0.997001i \(-0.475341\pi\)
0.0773897 + 0.997001i \(0.475341\pi\)
\(824\) −135.012 −4.70338
\(825\) 7.57148 0.263605
\(826\) 43.1703 1.50209
\(827\) 39.0009 1.35619 0.678097 0.734973i \(-0.262805\pi\)
0.678097 + 0.734973i \(0.262805\pi\)
\(828\) 25.6433 0.891165
\(829\) −37.2181 −1.29264 −0.646320 0.763067i \(-0.723693\pi\)
−0.646320 + 0.763067i \(0.723693\pi\)
\(830\) 21.5115 0.746676
\(831\) −7.01388 −0.243309
\(832\) 47.3210 1.64056
\(833\) 3.19917 0.110845
\(834\) 0.394412 0.0136574
\(835\) −74.1524 −2.56615
\(836\) 28.9569 1.00150
\(837\) 14.4633 0.499924
\(838\) 71.4152 2.46700
\(839\) −31.1291 −1.07469 −0.537347 0.843361i \(-0.680574\pi\)
−0.537347 + 0.843361i \(0.680574\pi\)
\(840\) 10.6532 0.367569
\(841\) 21.4585 0.739950
\(842\) −54.0821 −1.86379
\(843\) −0.0963747 −0.00331932
\(844\) −93.7018 −3.22535
\(845\) 53.4209 1.83774
\(846\) 31.9967 1.10007
\(847\) −25.1064 −0.862665
\(848\) −14.0763 −0.483381
\(849\) 5.60156 0.192245
\(850\) 12.1731 0.417533
\(851\) 6.01657 0.206245
\(852\) −0.349641 −0.0119785
\(853\) 11.4891 0.393379 0.196690 0.980466i \(-0.436981\pi\)
0.196690 + 0.980466i \(0.436981\pi\)
\(854\) 62.1820 2.12782
\(855\) −11.4199 −0.390551
\(856\) −42.7632 −1.46162
\(857\) −9.67575 −0.330517 −0.165259 0.986250i \(-0.552846\pi\)
−0.165259 + 0.986250i \(0.552846\pi\)
\(858\) −18.0669 −0.616793
\(859\) 1.37280 0.0468394 0.0234197 0.999726i \(-0.492545\pi\)
0.0234197 + 0.999726i \(0.492545\pi\)
\(860\) 25.3316 0.863800
\(861\) −3.72179 −0.126838
\(862\) −13.6586 −0.465212
\(863\) 50.5277 1.71998 0.859992 0.510308i \(-0.170469\pi\)
0.859992 + 0.510308i \(0.170469\pi\)
\(864\) 16.2907 0.554221
\(865\) −19.5445 −0.664532
\(866\) 22.4747 0.763722
\(867\) −4.13065 −0.140284
\(868\) 80.2235 2.72296
\(869\) 38.3637 1.30140
\(870\) −15.4994 −0.525480
\(871\) −58.1165 −1.96920
\(872\) −71.0856 −2.40726
\(873\) 0.198871 0.00673077
\(874\) 5.54012 0.187397
\(875\) −5.23080 −0.176833
\(876\) −20.0863 −0.678654
\(877\) 27.6349 0.933163 0.466581 0.884478i \(-0.345485\pi\)
0.466581 + 0.884478i \(0.345485\pi\)
\(878\) −42.9858 −1.45070
\(879\) 8.13954 0.274540
\(880\) 165.334 5.57340
\(881\) 5.69198 0.191768 0.0958838 0.995393i \(-0.469432\pi\)
0.0958838 + 0.995393i \(0.469432\pi\)
\(882\) −31.3527 −1.05570
\(883\) −45.7074 −1.53818 −0.769089 0.639142i \(-0.779290\pi\)
−0.769089 + 0.639142i \(0.779290\pi\)
\(884\) −20.5737 −0.691968
\(885\) 8.03704 0.270162
\(886\) 33.6229 1.12958
\(887\) 4.92217 0.165270 0.0826352 0.996580i \(-0.473666\pi\)
0.0826352 + 0.996580i \(0.473666\pi\)
\(888\) 6.30772 0.211673
\(889\) 15.9707 0.535639
\(890\) −94.0665 −3.15312
\(891\) 42.7351 1.43168
\(892\) −94.9321 −3.17856
\(893\) 4.89622 0.163846
\(894\) −11.6380 −0.389233
\(895\) −33.7473 −1.12805
\(896\) 2.00840 0.0670959
\(897\) −2.44827 −0.0817453
\(898\) −83.3629 −2.78185
\(899\) −68.6471 −2.28951
\(900\) −84.4981 −2.81660
\(901\) 1.11899 0.0372789
\(902\) −114.603 −3.81586
\(903\) −0.680143 −0.0226337
\(904\) −107.592 −3.57846
\(905\) −79.1208 −2.63006
\(906\) 4.54605 0.151032
\(907\) 2.84636 0.0945118 0.0472559 0.998883i \(-0.484952\pi\)
0.0472559 + 0.998883i \(0.484952\pi\)
\(908\) −52.5932 −1.74537
\(909\) 30.8996 1.02488
\(910\) 79.8970 2.64856
\(911\) 47.0407 1.55853 0.779263 0.626697i \(-0.215593\pi\)
0.779263 + 0.626697i \(0.215593\pi\)
\(912\) 2.92741 0.0969362
\(913\) −12.5969 −0.416895
\(914\) 6.01776 0.199050
\(915\) 11.5765 0.382706
\(916\) −45.0747 −1.48931
\(917\) 1.26664 0.0418283
\(918\) −3.07447 −0.101473
\(919\) −0.826432 −0.0272615 −0.0136307 0.999907i \(-0.504339\pi\)
−0.0136307 + 0.999907i \(0.504339\pi\)
\(920\) 44.4527 1.46556
\(921\) 3.78735 0.124798
\(922\) 49.3191 1.62424
\(923\) −1.54226 −0.0507642
\(924\) −10.6068 −0.348939
\(925\) −19.8254 −0.651857
\(926\) 64.4060 2.11651
\(927\) −53.0138 −1.74120
\(928\) −77.3207 −2.53817
\(929\) 17.9236 0.588056 0.294028 0.955797i \(-0.405004\pi\)
0.294028 + 0.955797i \(0.405004\pi\)
\(930\) 21.0864 0.691452
\(931\) −4.79767 −0.157237
\(932\) 39.9316 1.30800
\(933\) −7.01588 −0.229690
\(934\) 71.8605 2.35135
\(935\) −13.1432 −0.429827
\(936\) 118.586 3.87610
\(937\) −16.6746 −0.544735 −0.272367 0.962193i \(-0.587807\pi\)
−0.272367 + 0.962193i \(0.587807\pi\)
\(938\) −48.1717 −1.57286
\(939\) 2.01281 0.0656856
\(940\) 66.7969 2.17867
\(941\) −49.9379 −1.62793 −0.813964 0.580915i \(-0.802695\pi\)
−0.813964 + 0.580915i \(0.802695\pi\)
\(942\) −3.44830 −0.112352
\(943\) −15.5300 −0.505727
\(944\) 95.1851 3.09801
\(945\) 8.45666 0.275095
\(946\) −20.9432 −0.680923
\(947\) 47.1294 1.53150 0.765750 0.643138i \(-0.222368\pi\)
0.765750 + 0.643138i \(0.222368\pi\)
\(948\) 9.26696 0.300977
\(949\) −88.6006 −2.87610
\(950\) −18.2555 −0.592286
\(951\) −2.18658 −0.0709047
\(952\) −10.0297 −0.325065
\(953\) −51.7129 −1.67514 −0.837572 0.546327i \(-0.816026\pi\)
−0.837572 + 0.546327i \(0.816026\pi\)
\(954\) −10.9664 −0.355049
\(955\) −67.4439 −2.18243
\(956\) −33.2785 −1.07630
\(957\) 9.07625 0.293394
\(958\) −23.5036 −0.759367
\(959\) 4.31029 0.139187
\(960\) 7.30228 0.235680
\(961\) 62.3921 2.01265
\(962\) 47.3070 1.52524
\(963\) −16.7914 −0.541095
\(964\) 82.6946 2.66341
\(965\) −20.8177 −0.670145
\(966\) −2.02933 −0.0652926
\(967\) 0.962194 0.0309421 0.0154710 0.999880i \(-0.495075\pi\)
0.0154710 + 0.999880i \(0.495075\pi\)
\(968\) −109.832 −3.53012
\(969\) −0.232713 −0.00747583
\(970\) 0.586156 0.0188203
\(971\) −15.1556 −0.486367 −0.243183 0.969980i \(-0.578192\pi\)
−0.243183 + 0.969980i \(0.578192\pi\)
\(972\) 32.1260 1.03044
\(973\) 1.02138 0.0327440
\(974\) 84.5672 2.70971
\(975\) 8.06739 0.258363
\(976\) 137.103 4.38858
\(977\) 30.9833 0.991245 0.495623 0.868538i \(-0.334940\pi\)
0.495623 + 0.868538i \(0.334940\pi\)
\(978\) −1.69916 −0.0543333
\(979\) 55.0841 1.76049
\(980\) −65.4524 −2.09080
\(981\) −27.9124 −0.891176
\(982\) −22.0316 −0.703056
\(983\) −4.51938 −0.144146 −0.0720730 0.997399i \(-0.522961\pi\)
−0.0720730 + 0.997399i \(0.522961\pi\)
\(984\) −16.2815 −0.519037
\(985\) 11.4365 0.364399
\(986\) 14.5924 0.464716
\(987\) −1.79347 −0.0570868
\(988\) 30.8535 0.981582
\(989\) −2.83805 −0.0902447
\(990\) 128.806 4.09374
\(991\) 54.6240 1.73519 0.867595 0.497272i \(-0.165665\pi\)
0.867595 + 0.497272i \(0.165665\pi\)
\(992\) 105.192 3.33985
\(993\) 0.138484 0.00439467
\(994\) −1.27836 −0.0405470
\(995\) −18.4408 −0.584611
\(996\) −3.04284 −0.0964160
\(997\) 16.7792 0.531403 0.265701 0.964055i \(-0.414396\pi\)
0.265701 + 0.964055i \(0.414396\pi\)
\(998\) 107.418 3.40027
\(999\) 5.00718 0.158420
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 \(a_p\))