Properties

Label 6023.2.a.b.1.13
Level 6023
Weight 2
Character 6023.1
Self dual Yes
Analytic conductor 48.094
Analytic rank 1
Dimension 99
CM No

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Newspace parameters

Level: \( N \) = \( 6023 = 19 \cdot 317 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6023.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0938971374\)
Analytic rank: \(1\)
Dimension: \(99\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Character \(\chi\) = 6023.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.20989 q^{2} -1.74865 q^{3} +2.88361 q^{4} +1.63174 q^{5} +3.86432 q^{6} +4.01021 q^{7} -1.95267 q^{8} +0.0577689 q^{9} +O(q^{10})\) \(q-2.20989 q^{2} -1.74865 q^{3} +2.88361 q^{4} +1.63174 q^{5} +3.86432 q^{6} +4.01021 q^{7} -1.95267 q^{8} +0.0577689 q^{9} -3.60597 q^{10} -3.13294 q^{11} -5.04241 q^{12} -2.02366 q^{13} -8.86212 q^{14} -2.85334 q^{15} -1.45202 q^{16} -1.32438 q^{17} -0.127663 q^{18} -1.00000 q^{19} +4.70530 q^{20} -7.01245 q^{21} +6.92344 q^{22} -0.160657 q^{23} +3.41454 q^{24} -2.33742 q^{25} +4.47206 q^{26} +5.14493 q^{27} +11.5639 q^{28} -3.17316 q^{29} +6.30557 q^{30} +2.56696 q^{31} +7.11416 q^{32} +5.47840 q^{33} +2.92672 q^{34} +6.54363 q^{35} +0.166583 q^{36} +2.99162 q^{37} +2.20989 q^{38} +3.53867 q^{39} -3.18626 q^{40} +9.36527 q^{41} +15.4967 q^{42} -3.77478 q^{43} -9.03416 q^{44} +0.0942640 q^{45} +0.355034 q^{46} -2.24021 q^{47} +2.53908 q^{48} +9.08181 q^{49} +5.16543 q^{50} +2.31587 q^{51} -5.83544 q^{52} +8.94639 q^{53} -11.3697 q^{54} -5.11215 q^{55} -7.83063 q^{56} +1.74865 q^{57} +7.01233 q^{58} +9.63212 q^{59} -8.22792 q^{60} -11.0070 q^{61} -5.67269 q^{62} +0.231666 q^{63} -12.8174 q^{64} -3.30209 q^{65} -12.1067 q^{66} +0.661575 q^{67} -3.81898 q^{68} +0.280933 q^{69} -14.4607 q^{70} -8.70148 q^{71} -0.112804 q^{72} +0.404097 q^{73} -6.61115 q^{74} +4.08732 q^{75} -2.88361 q^{76} -12.5637 q^{77} -7.82006 q^{78} -13.1806 q^{79} -2.36933 q^{80} -9.16997 q^{81} -20.6962 q^{82} +4.71291 q^{83} -20.2211 q^{84} -2.16104 q^{85} +8.34185 q^{86} +5.54874 q^{87} +6.11760 q^{88} -5.22329 q^{89} -0.208313 q^{90} -8.11531 q^{91} -0.463272 q^{92} -4.48871 q^{93} +4.95061 q^{94} -1.63174 q^{95} -12.4402 q^{96} +3.17382 q^{97} -20.0698 q^{98} -0.180987 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 99q - 4q^{2} - 3q^{3} + 80q^{4} - 15q^{5} - 12q^{6} - 19q^{7} - 12q^{8} + 58q^{9} + O(q^{10}) \) \( 99q - 4q^{2} - 3q^{3} + 80q^{4} - 15q^{5} - 12q^{6} - 19q^{7} - 12q^{8} + 58q^{9} - 6q^{10} - 9q^{11} - 27q^{12} - 28q^{13} - 13q^{14} - 10q^{15} + 38q^{16} - 36q^{17} - 14q^{18} - 99q^{19} - 34q^{20} - 20q^{21} - 53q^{22} - 38q^{23} - 25q^{24} - 8q^{25} - 3q^{26} - 3q^{27} - 63q^{28} - 34q^{29} - 30q^{30} - 16q^{31} - 43q^{32} - 41q^{33} - 14q^{34} - 25q^{35} - 16q^{36} - 80q^{37} + 4q^{38} - 48q^{39} - 10q^{40} - 32q^{41} - 37q^{42} - 76q^{43} - 21q^{44} - 53q^{45} - 23q^{46} - 31q^{47} - 74q^{48} - 32q^{49} - 29q^{50} - 30q^{51} - 71q^{52} - 35q^{53} - 80q^{54} - 45q^{55} - 33q^{56} + 3q^{57} - 91q^{58} + 12q^{59} - 56q^{60} - 61q^{61} - 46q^{62} - 43q^{63} - 30q^{64} - 46q^{65} - 75q^{66} - 26q^{67} - 55q^{68} - 45q^{69} - 76q^{70} - 41q^{71} - 77q^{72} - 143q^{73} - 64q^{74} - 8q^{75} - 80q^{76} - 58q^{77} - 34q^{78} - 22q^{79} - 36q^{80} - 81q^{81} - 109q^{82} - 7q^{83} - 6q^{84} - 80q^{85} + 32q^{86} - 57q^{87} - 120q^{88} - 28q^{89} - 12q^{90} - 30q^{91} - 107q^{92} - 121q^{93} + 8q^{94} + 15q^{95} + 4q^{96} - 128q^{97} + 54q^{98} - 34q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.20989 −1.56263 −0.781314 0.624139i \(-0.785450\pi\)
−0.781314 + 0.624139i \(0.785450\pi\)
\(3\) −1.74865 −1.00958 −0.504791 0.863242i \(-0.668430\pi\)
−0.504791 + 0.863242i \(0.668430\pi\)
\(4\) 2.88361 1.44180
\(5\) 1.63174 0.729737 0.364869 0.931059i \(-0.381114\pi\)
0.364869 + 0.931059i \(0.381114\pi\)
\(6\) 3.86432 1.57760
\(7\) 4.01021 1.51572 0.757859 0.652418i \(-0.226245\pi\)
0.757859 + 0.652418i \(0.226245\pi\)
\(8\) −1.95267 −0.690374
\(9\) 0.0577689 0.0192563
\(10\) −3.60597 −1.14031
\(11\) −3.13294 −0.944616 −0.472308 0.881433i \(-0.656579\pi\)
−0.472308 + 0.881433i \(0.656579\pi\)
\(12\) −5.04241 −1.45562
\(13\) −2.02366 −0.561262 −0.280631 0.959816i \(-0.590544\pi\)
−0.280631 + 0.959816i \(0.590544\pi\)
\(14\) −8.86212 −2.36850
\(15\) −2.85334 −0.736730
\(16\) −1.45202 −0.363006
\(17\) −1.32438 −0.321209 −0.160604 0.987019i \(-0.551344\pi\)
−0.160604 + 0.987019i \(0.551344\pi\)
\(18\) −0.127663 −0.0300904
\(19\) −1.00000 −0.229416
\(20\) 4.70530 1.05214
\(21\) −7.01245 −1.53024
\(22\) 6.92344 1.47608
\(23\) −0.160657 −0.0334993 −0.0167497 0.999860i \(-0.505332\pi\)
−0.0167497 + 0.999860i \(0.505332\pi\)
\(24\) 3.41454 0.696989
\(25\) −2.33742 −0.467483
\(26\) 4.47206 0.877044
\(27\) 5.14493 0.990141
\(28\) 11.5639 2.18537
\(29\) −3.17316 −0.589241 −0.294621 0.955614i \(-0.595193\pi\)
−0.294621 + 0.955614i \(0.595193\pi\)
\(30\) 6.30557 1.15123
\(31\) 2.56696 0.461039 0.230520 0.973068i \(-0.425957\pi\)
0.230520 + 0.973068i \(0.425957\pi\)
\(32\) 7.11416 1.25762
\(33\) 5.47840 0.953668
\(34\) 2.92672 0.501929
\(35\) 6.54363 1.10608
\(36\) 0.166583 0.0277638
\(37\) 2.99162 0.491819 0.245910 0.969293i \(-0.420913\pi\)
0.245910 + 0.969293i \(0.420913\pi\)
\(38\) 2.20989 0.358491
\(39\) 3.53867 0.566640
\(40\) −3.18626 −0.503792
\(41\) 9.36527 1.46261 0.731304 0.682051i \(-0.238912\pi\)
0.731304 + 0.682051i \(0.238912\pi\)
\(42\) 15.4967 2.39120
\(43\) −3.77478 −0.575649 −0.287825 0.957683i \(-0.592932\pi\)
−0.287825 + 0.957683i \(0.592932\pi\)
\(44\) −9.03416 −1.36195
\(45\) 0.0942640 0.0140521
\(46\) 0.355034 0.0523470
\(47\) −2.24021 −0.326768 −0.163384 0.986563i \(-0.552241\pi\)
−0.163384 + 0.986563i \(0.552241\pi\)
\(48\) 2.53908 0.366485
\(49\) 9.08181 1.29740
\(50\) 5.16543 0.730502
\(51\) 2.31587 0.324286
\(52\) −5.83544 −0.809230
\(53\) 8.94639 1.22888 0.614441 0.788963i \(-0.289382\pi\)
0.614441 + 0.788963i \(0.289382\pi\)
\(54\) −11.3697 −1.54722
\(55\) −5.11215 −0.689322
\(56\) −7.83063 −1.04641
\(57\) 1.74865 0.231614
\(58\) 7.01233 0.920764
\(59\) 9.63212 1.25400 0.626998 0.779021i \(-0.284284\pi\)
0.626998 + 0.779021i \(0.284284\pi\)
\(60\) −8.22792 −1.06222
\(61\) −11.0070 −1.40930 −0.704652 0.709553i \(-0.748897\pi\)
−0.704652 + 0.709553i \(0.748897\pi\)
\(62\) −5.67269 −0.720433
\(63\) 0.231666 0.0291871
\(64\) −12.8174 −1.60218
\(65\) −3.30209 −0.409574
\(66\) −12.1067 −1.49023
\(67\) 0.661575 0.0808242 0.0404121 0.999183i \(-0.487133\pi\)
0.0404121 + 0.999183i \(0.487133\pi\)
\(68\) −3.81898 −0.463120
\(69\) 0.280933 0.0338203
\(70\) −14.4607 −1.72838
\(71\) −8.70148 −1.03268 −0.516338 0.856385i \(-0.672705\pi\)
−0.516338 + 0.856385i \(0.672705\pi\)
\(72\) −0.112804 −0.0132941
\(73\) 0.404097 0.0472959 0.0236480 0.999720i \(-0.492472\pi\)
0.0236480 + 0.999720i \(0.492472\pi\)
\(74\) −6.61115 −0.768530
\(75\) 4.08732 0.471963
\(76\) −2.88361 −0.330772
\(77\) −12.5637 −1.43177
\(78\) −7.82006 −0.885448
\(79\) −13.1806 −1.48293 −0.741465 0.670992i \(-0.765869\pi\)
−0.741465 + 0.670992i \(0.765869\pi\)
\(80\) −2.36933 −0.264899
\(81\) −9.16997 −1.01889
\(82\) −20.6962 −2.28551
\(83\) 4.71291 0.517309 0.258655 0.965970i \(-0.416721\pi\)
0.258655 + 0.965970i \(0.416721\pi\)
\(84\) −20.2211 −2.20631
\(85\) −2.16104 −0.234398
\(86\) 8.34185 0.899525
\(87\) 5.54874 0.594887
\(88\) 6.11760 0.652139
\(89\) −5.22329 −0.553668 −0.276834 0.960918i \(-0.589285\pi\)
−0.276834 + 0.960918i \(0.589285\pi\)
\(90\) −0.208313 −0.0219581
\(91\) −8.11531 −0.850715
\(92\) −0.463272 −0.0482995
\(93\) −4.48871 −0.465457
\(94\) 4.95061 0.510616
\(95\) −1.63174 −0.167413
\(96\) −12.4402 −1.26967
\(97\) 3.17382 0.322252 0.161126 0.986934i \(-0.448487\pi\)
0.161126 + 0.986934i \(0.448487\pi\)
\(98\) −20.0698 −2.02735
\(99\) −0.180987 −0.0181898
\(100\) −6.74019 −0.674019
\(101\) 13.6980 1.36300 0.681501 0.731817i \(-0.261327\pi\)
0.681501 + 0.731817i \(0.261327\pi\)
\(102\) −5.11781 −0.506739
\(103\) −2.16215 −0.213043 −0.106521 0.994310i \(-0.533971\pi\)
−0.106521 + 0.994310i \(0.533971\pi\)
\(104\) 3.95155 0.387481
\(105\) −11.4425 −1.11667
\(106\) −19.7705 −1.92028
\(107\) 15.0798 1.45782 0.728909 0.684610i \(-0.240028\pi\)
0.728909 + 0.684610i \(0.240028\pi\)
\(108\) 14.8359 1.42759
\(109\) 8.16718 0.782274 0.391137 0.920332i \(-0.372082\pi\)
0.391137 + 0.920332i \(0.372082\pi\)
\(110\) 11.2973 1.07715
\(111\) −5.23129 −0.496532
\(112\) −5.82293 −0.550215
\(113\) 7.37268 0.693564 0.346782 0.937946i \(-0.387274\pi\)
0.346782 + 0.937946i \(0.387274\pi\)
\(114\) −3.86432 −0.361926
\(115\) −0.262151 −0.0244457
\(116\) −9.15015 −0.849570
\(117\) −0.116905 −0.0108078
\(118\) −21.2859 −1.95953
\(119\) −5.31103 −0.486862
\(120\) 5.57165 0.508619
\(121\) −1.18470 −0.107700
\(122\) 24.3243 2.20222
\(123\) −16.3766 −1.47662
\(124\) 7.40210 0.664728
\(125\) −11.9728 −1.07088
\(126\) −0.511955 −0.0456086
\(127\) −20.8981 −1.85441 −0.927203 0.374560i \(-0.877794\pi\)
−0.927203 + 0.374560i \(0.877794\pi\)
\(128\) 14.0968 1.24599
\(129\) 6.60077 0.581165
\(130\) 7.29726 0.640012
\(131\) 1.96426 0.171619 0.0858093 0.996312i \(-0.472652\pi\)
0.0858093 + 0.996312i \(0.472652\pi\)
\(132\) 15.7976 1.37500
\(133\) −4.01021 −0.347730
\(134\) −1.46201 −0.126298
\(135\) 8.39519 0.722543
\(136\) 2.58607 0.221754
\(137\) −8.23158 −0.703272 −0.351636 0.936137i \(-0.614374\pi\)
−0.351636 + 0.936137i \(0.614374\pi\)
\(138\) −0.620830 −0.0528486
\(139\) −9.26251 −0.785636 −0.392818 0.919616i \(-0.628500\pi\)
−0.392818 + 0.919616i \(0.628500\pi\)
\(140\) 18.8693 1.59474
\(141\) 3.91733 0.329899
\(142\) 19.2293 1.61369
\(143\) 6.34000 0.530178
\(144\) −0.0838819 −0.00699016
\(145\) −5.17778 −0.429991
\(146\) −0.893009 −0.0739059
\(147\) −15.8809 −1.30983
\(148\) 8.62666 0.709107
\(149\) −3.04992 −0.249859 −0.124930 0.992166i \(-0.539871\pi\)
−0.124930 + 0.992166i \(0.539871\pi\)
\(150\) −9.03252 −0.737502
\(151\) 9.66999 0.786933 0.393466 0.919339i \(-0.371276\pi\)
0.393466 + 0.919339i \(0.371276\pi\)
\(152\) 1.95267 0.158383
\(153\) −0.0765078 −0.00618529
\(154\) 27.7645 2.23733
\(155\) 4.18862 0.336438
\(156\) 10.2041 0.816984
\(157\) 0.628130 0.0501302 0.0250651 0.999686i \(-0.492021\pi\)
0.0250651 + 0.999686i \(0.492021\pi\)
\(158\) 29.1276 2.31727
\(159\) −15.6441 −1.24066
\(160\) 11.6085 0.917730
\(161\) −0.644269 −0.0507755
\(162\) 20.2646 1.59214
\(163\) −13.4268 −1.05167 −0.525834 0.850587i \(-0.676247\pi\)
−0.525834 + 0.850587i \(0.676247\pi\)
\(164\) 27.0057 2.10879
\(165\) 8.93935 0.695927
\(166\) −10.4150 −0.808362
\(167\) −13.5839 −1.05115 −0.525577 0.850746i \(-0.676151\pi\)
−0.525577 + 0.850746i \(0.676151\pi\)
\(168\) 13.6930 1.05644
\(169\) −8.90480 −0.684985
\(170\) 4.77566 0.366276
\(171\) −0.0577689 −0.00441770
\(172\) −10.8850 −0.829973
\(173\) 1.06143 0.0806988 0.0403494 0.999186i \(-0.487153\pi\)
0.0403494 + 0.999186i \(0.487153\pi\)
\(174\) −12.2621 −0.929587
\(175\) −9.37354 −0.708573
\(176\) 4.54910 0.342902
\(177\) −16.8432 −1.26601
\(178\) 11.5429 0.865177
\(179\) −22.9892 −1.71829 −0.859147 0.511730i \(-0.829005\pi\)
−0.859147 + 0.511730i \(0.829005\pi\)
\(180\) 0.271820 0.0202603
\(181\) −19.1628 −1.42436 −0.712179 0.701998i \(-0.752291\pi\)
−0.712179 + 0.701998i \(0.752291\pi\)
\(182\) 17.9339 1.32935
\(183\) 19.2474 1.42281
\(184\) 0.313711 0.0231271
\(185\) 4.88156 0.358899
\(186\) 9.91954 0.727336
\(187\) 4.14919 0.303419
\(188\) −6.45988 −0.471135
\(189\) 20.6322 1.50078
\(190\) 3.60597 0.261604
\(191\) 22.2910 1.61292 0.806462 0.591286i \(-0.201380\pi\)
0.806462 + 0.591286i \(0.201380\pi\)
\(192\) 22.4132 1.61753
\(193\) 12.7461 0.917481 0.458741 0.888570i \(-0.348301\pi\)
0.458741 + 0.888570i \(0.348301\pi\)
\(194\) −7.01378 −0.503560
\(195\) 5.77420 0.413499
\(196\) 26.1884 1.87060
\(197\) 11.6970 0.833375 0.416687 0.909050i \(-0.363191\pi\)
0.416687 + 0.909050i \(0.363191\pi\)
\(198\) 0.399960 0.0284239
\(199\) 8.35501 0.592271 0.296135 0.955146i \(-0.404302\pi\)
0.296135 + 0.955146i \(0.404302\pi\)
\(200\) 4.56421 0.322738
\(201\) −1.15686 −0.0815987
\(202\) −30.2711 −2.12987
\(203\) −12.7251 −0.893123
\(204\) 6.67805 0.467557
\(205\) 15.2817 1.06732
\(206\) 4.77811 0.332906
\(207\) −0.00928100 −0.000645074 0
\(208\) 2.93840 0.203742
\(209\) 3.13294 0.216710
\(210\) 25.2867 1.74495
\(211\) 19.4530 1.33920 0.669598 0.742724i \(-0.266466\pi\)
0.669598 + 0.742724i \(0.266466\pi\)
\(212\) 25.7979 1.77181
\(213\) 15.2158 1.04257
\(214\) −33.3247 −2.27803
\(215\) −6.15948 −0.420073
\(216\) −10.0464 −0.683568
\(217\) 10.2941 0.698806
\(218\) −18.0486 −1.22240
\(219\) −0.706623 −0.0477491
\(220\) −14.7414 −0.993867
\(221\) 2.68009 0.180282
\(222\) 11.5606 0.775895
\(223\) 16.5342 1.10721 0.553606 0.832779i \(-0.313251\pi\)
0.553606 + 0.832779i \(0.313251\pi\)
\(224\) 28.5293 1.90619
\(225\) −0.135030 −0.00900201
\(226\) −16.2928 −1.08378
\(227\) −14.3082 −0.949669 −0.474835 0.880075i \(-0.657492\pi\)
−0.474835 + 0.880075i \(0.657492\pi\)
\(228\) 5.04241 0.333942
\(229\) 6.81214 0.450159 0.225079 0.974340i \(-0.427736\pi\)
0.225079 + 0.974340i \(0.427736\pi\)
\(230\) 0.579325 0.0381995
\(231\) 21.9696 1.44549
\(232\) 6.19615 0.406797
\(233\) −17.0827 −1.11913 −0.559563 0.828788i \(-0.689031\pi\)
−0.559563 + 0.828788i \(0.689031\pi\)
\(234\) 0.258346 0.0168886
\(235\) −3.65544 −0.238455
\(236\) 27.7753 1.80802
\(237\) 23.0482 1.49714
\(238\) 11.7368 0.760783
\(239\) −5.96041 −0.385547 −0.192773 0.981243i \(-0.561748\pi\)
−0.192773 + 0.981243i \(0.561748\pi\)
\(240\) 4.14312 0.267437
\(241\) −26.1699 −1.68575 −0.842875 0.538110i \(-0.819139\pi\)
−0.842875 + 0.538110i \(0.819139\pi\)
\(242\) 2.61806 0.168295
\(243\) 0.600270 0.0385073
\(244\) −31.7399 −2.03194
\(245\) 14.8192 0.946762
\(246\) 36.1903 2.30741
\(247\) 2.02366 0.128762
\(248\) −5.01243 −0.318290
\(249\) −8.24123 −0.522266
\(250\) 26.4585 1.67338
\(251\) −25.6496 −1.61899 −0.809495 0.587127i \(-0.800259\pi\)
−0.809495 + 0.587127i \(0.800259\pi\)
\(252\) 0.668033 0.0420821
\(253\) 0.503329 0.0316440
\(254\) 46.1824 2.89774
\(255\) 3.77890 0.236644
\(256\) −5.51749 −0.344843
\(257\) 19.2705 1.20206 0.601030 0.799226i \(-0.294757\pi\)
0.601030 + 0.799226i \(0.294757\pi\)
\(258\) −14.5870 −0.908145
\(259\) 11.9970 0.745460
\(260\) −9.52194 −0.590525
\(261\) −0.183310 −0.0113466
\(262\) −4.34081 −0.268176
\(263\) 22.1794 1.36764 0.683821 0.729650i \(-0.260317\pi\)
0.683821 + 0.729650i \(0.260317\pi\)
\(264\) −10.6975 −0.658388
\(265\) 14.5982 0.896761
\(266\) 8.86212 0.543372
\(267\) 9.13370 0.558973
\(268\) 1.90772 0.116533
\(269\) −6.52524 −0.397851 −0.198926 0.980015i \(-0.563745\pi\)
−0.198926 + 0.980015i \(0.563745\pi\)
\(270\) −18.5524 −1.12907
\(271\) 24.7218 1.50174 0.750870 0.660450i \(-0.229635\pi\)
0.750870 + 0.660450i \(0.229635\pi\)
\(272\) 1.92303 0.116601
\(273\) 14.1908 0.858867
\(274\) 18.1909 1.09895
\(275\) 7.32298 0.441592
\(276\) 0.810100 0.0487623
\(277\) −25.1464 −1.51090 −0.755450 0.655206i \(-0.772582\pi\)
−0.755450 + 0.655206i \(0.772582\pi\)
\(278\) 20.4691 1.22766
\(279\) 0.148290 0.00887792
\(280\) −12.7776 −0.763606
\(281\) 10.2901 0.613853 0.306927 0.951733i \(-0.400699\pi\)
0.306927 + 0.951733i \(0.400699\pi\)
\(282\) −8.65687 −0.515509
\(283\) −2.84166 −0.168919 −0.0844597 0.996427i \(-0.526916\pi\)
−0.0844597 + 0.996427i \(0.526916\pi\)
\(284\) −25.0916 −1.48892
\(285\) 2.85334 0.169017
\(286\) −14.0107 −0.828470
\(287\) 37.5567 2.21690
\(288\) 0.410977 0.0242171
\(289\) −15.2460 −0.896825
\(290\) 11.4423 0.671916
\(291\) −5.54989 −0.325340
\(292\) 1.16526 0.0681914
\(293\) −12.1632 −0.710580 −0.355290 0.934756i \(-0.615618\pi\)
−0.355290 + 0.934756i \(0.615618\pi\)
\(294\) 35.0950 2.04678
\(295\) 15.7171 0.915087
\(296\) −5.84166 −0.339539
\(297\) −16.1187 −0.935304
\(298\) 6.73999 0.390437
\(299\) 0.325116 0.0188019
\(300\) 11.7862 0.680478
\(301\) −15.1377 −0.872522
\(302\) −21.3696 −1.22968
\(303\) −23.9530 −1.37606
\(304\) 1.45202 0.0832793
\(305\) −17.9606 −1.02842
\(306\) 0.169074 0.00966530
\(307\) −24.4231 −1.39390 −0.696949 0.717121i \(-0.745460\pi\)
−0.696949 + 0.717121i \(0.745460\pi\)
\(308\) −36.2289 −2.06433
\(309\) 3.78084 0.215084
\(310\) −9.25637 −0.525727
\(311\) −25.5384 −1.44815 −0.724076 0.689721i \(-0.757733\pi\)
−0.724076 + 0.689721i \(0.757733\pi\)
\(312\) −6.90986 −0.391194
\(313\) −1.03364 −0.0584245 −0.0292123 0.999573i \(-0.509300\pi\)
−0.0292123 + 0.999573i \(0.509300\pi\)
\(314\) −1.38810 −0.0783349
\(315\) 0.378019 0.0212989
\(316\) −38.0076 −2.13809
\(317\) −1.00000 −0.0561656
\(318\) 34.5717 1.93868
\(319\) 9.94132 0.556607
\(320\) −20.9148 −1.16917
\(321\) −26.3692 −1.47179
\(322\) 1.42376 0.0793432
\(323\) 1.32438 0.0736903
\(324\) −26.4426 −1.46903
\(325\) 4.73014 0.262381
\(326\) 29.6717 1.64337
\(327\) −14.2815 −0.789770
\(328\) −18.2873 −1.00975
\(329\) −8.98371 −0.495288
\(330\) −19.7550 −1.08747
\(331\) 36.0662 1.98238 0.991188 0.132464i \(-0.0422888\pi\)
0.991188 + 0.132464i \(0.0422888\pi\)
\(332\) 13.5902 0.745859
\(333\) 0.172823 0.00947063
\(334\) 30.0189 1.64256
\(335\) 1.07952 0.0589805
\(336\) 10.1822 0.555487
\(337\) −12.3972 −0.675318 −0.337659 0.941269i \(-0.609635\pi\)
−0.337659 + 0.941269i \(0.609635\pi\)
\(338\) 19.6786 1.07038
\(339\) −12.8922 −0.700210
\(340\) −6.23159 −0.337956
\(341\) −8.04212 −0.435505
\(342\) 0.127663 0.00690322
\(343\) 8.34849 0.450776
\(344\) 7.37092 0.397413
\(345\) 0.458410 0.0246800
\(346\) −2.34563 −0.126102
\(347\) −26.5853 −1.42717 −0.713587 0.700566i \(-0.752931\pi\)
−0.713587 + 0.700566i \(0.752931\pi\)
\(348\) 16.0004 0.857711
\(349\) −17.2399 −0.922830 −0.461415 0.887184i \(-0.652658\pi\)
−0.461415 + 0.887184i \(0.652658\pi\)
\(350\) 20.7145 1.10724
\(351\) −10.4116 −0.555729
\(352\) −22.2882 −1.18797
\(353\) −22.9712 −1.22264 −0.611318 0.791385i \(-0.709360\pi\)
−0.611318 + 0.791385i \(0.709360\pi\)
\(354\) 37.2216 1.97830
\(355\) −14.1986 −0.753582
\(356\) −15.0619 −0.798281
\(357\) 9.28712 0.491527
\(358\) 50.8036 2.68505
\(359\) 24.5048 1.29331 0.646656 0.762782i \(-0.276167\pi\)
0.646656 + 0.762782i \(0.276167\pi\)
\(360\) −0.184067 −0.00970117
\(361\) 1.00000 0.0526316
\(362\) 42.3476 2.22574
\(363\) 2.07162 0.108732
\(364\) −23.4014 −1.22656
\(365\) 0.659382 0.0345136
\(366\) −42.5346 −2.22332
\(367\) −5.28926 −0.276097 −0.138049 0.990425i \(-0.544083\pi\)
−0.138049 + 0.990425i \(0.544083\pi\)
\(368\) 0.233278 0.0121605
\(369\) 0.541021 0.0281645
\(370\) −10.7877 −0.560825
\(371\) 35.8769 1.86264
\(372\) −12.9437 −0.671098
\(373\) 14.1943 0.734954 0.367477 0.930033i \(-0.380222\pi\)
0.367477 + 0.930033i \(0.380222\pi\)
\(374\) −9.16925 −0.474130
\(375\) 20.9362 1.08114
\(376\) 4.37439 0.225592
\(377\) 6.42140 0.330719
\(378\) −45.5950 −2.34515
\(379\) −34.5044 −1.77237 −0.886187 0.463327i \(-0.846655\pi\)
−0.886187 + 0.463327i \(0.846655\pi\)
\(380\) −4.70530 −0.241377
\(381\) 36.5434 1.87217
\(382\) −49.2607 −2.52040
\(383\) −5.90902 −0.301937 −0.150968 0.988539i \(-0.548239\pi\)
−0.150968 + 0.988539i \(0.548239\pi\)
\(384\) −24.6504 −1.25793
\(385\) −20.5008 −1.04482
\(386\) −28.1674 −1.43368
\(387\) −0.218065 −0.0110849
\(388\) 9.15204 0.464625
\(389\) 9.88350 0.501113 0.250557 0.968102i \(-0.419386\pi\)
0.250557 + 0.968102i \(0.419386\pi\)
\(390\) −12.7603 −0.646144
\(391\) 0.212771 0.0107603
\(392\) −17.7338 −0.895692
\(393\) −3.43481 −0.173263
\(394\) −25.8490 −1.30225
\(395\) −21.5073 −1.08215
\(396\) −0.521894 −0.0262262
\(397\) −23.2295 −1.16585 −0.582927 0.812525i \(-0.698093\pi\)
−0.582927 + 0.812525i \(0.698093\pi\)
\(398\) −18.4636 −0.925499
\(399\) 7.01245 0.351062
\(400\) 3.39399 0.169699
\(401\) −14.2443 −0.711326 −0.355663 0.934614i \(-0.615745\pi\)
−0.355663 + 0.934614i \(0.615745\pi\)
\(402\) 2.55653 0.127508
\(403\) −5.19465 −0.258764
\(404\) 39.4997 1.96518
\(405\) −14.9630 −0.743519
\(406\) 28.1209 1.39562
\(407\) −9.37256 −0.464581
\(408\) −4.52213 −0.223879
\(409\) 3.51946 0.174026 0.0870131 0.996207i \(-0.472268\pi\)
0.0870131 + 0.996207i \(0.472268\pi\)
\(410\) −33.7709 −1.66782
\(411\) 14.3941 0.710011
\(412\) −6.23479 −0.307166
\(413\) 38.6269 1.90070
\(414\) 0.0205100 0.00100801
\(415\) 7.69026 0.377500
\(416\) −14.3966 −0.705853
\(417\) 16.1969 0.793164
\(418\) −6.92344 −0.338637
\(419\) −26.3045 −1.28506 −0.642528 0.766262i \(-0.722115\pi\)
−0.642528 + 0.766262i \(0.722115\pi\)
\(420\) −32.9957 −1.61003
\(421\) 35.8626 1.74783 0.873917 0.486075i \(-0.161572\pi\)
0.873917 + 0.486075i \(0.161572\pi\)
\(422\) −42.9889 −2.09266
\(423\) −0.129414 −0.00629234
\(424\) −17.4694 −0.848388
\(425\) 3.09562 0.150160
\(426\) −33.6253 −1.62915
\(427\) −44.1405 −2.13611
\(428\) 43.4842 2.10189
\(429\) −11.0864 −0.535258
\(430\) 13.6118 0.656417
\(431\) 19.2547 0.927467 0.463734 0.885975i \(-0.346510\pi\)
0.463734 + 0.885975i \(0.346510\pi\)
\(432\) −7.47056 −0.359427
\(433\) −32.9122 −1.58166 −0.790831 0.612035i \(-0.790351\pi\)
−0.790831 + 0.612035i \(0.790351\pi\)
\(434\) −22.7487 −1.09197
\(435\) 9.05412 0.434112
\(436\) 23.5509 1.12789
\(437\) 0.160657 0.00768528
\(438\) 1.56156 0.0746141
\(439\) 8.95260 0.427284 0.213642 0.976912i \(-0.431467\pi\)
0.213642 + 0.976912i \(0.431467\pi\)
\(440\) 9.98235 0.475890
\(441\) 0.524646 0.0249832
\(442\) −5.92270 −0.281714
\(443\) 33.3248 1.58331 0.791653 0.610970i \(-0.209221\pi\)
0.791653 + 0.610970i \(0.209221\pi\)
\(444\) −15.0850 −0.715902
\(445\) −8.52307 −0.404032
\(446\) −36.5387 −1.73016
\(447\) 5.33324 0.252254
\(448\) −51.4007 −2.42845
\(449\) 17.5102 0.826359 0.413179 0.910650i \(-0.364418\pi\)
0.413179 + 0.910650i \(0.364418\pi\)
\(450\) 0.298401 0.0140668
\(451\) −29.3408 −1.38160
\(452\) 21.2599 0.999983
\(453\) −16.9094 −0.794473
\(454\) 31.6196 1.48398
\(455\) −13.2421 −0.620799
\(456\) −3.41454 −0.159900
\(457\) −15.9210 −0.744752 −0.372376 0.928082i \(-0.621457\pi\)
−0.372376 + 0.928082i \(0.621457\pi\)
\(458\) −15.0541 −0.703430
\(459\) −6.81382 −0.318042
\(460\) −0.755941 −0.0352459
\(461\) 1.38812 0.0646513 0.0323256 0.999477i \(-0.489709\pi\)
0.0323256 + 0.999477i \(0.489709\pi\)
\(462\) −48.5503 −2.25876
\(463\) −28.5381 −1.32628 −0.663140 0.748496i \(-0.730777\pi\)
−0.663140 + 0.748496i \(0.730777\pi\)
\(464\) 4.60751 0.213898
\(465\) −7.32441 −0.339662
\(466\) 37.7509 1.74878
\(467\) 24.8163 1.14836 0.574181 0.818729i \(-0.305321\pi\)
0.574181 + 0.818729i \(0.305321\pi\)
\(468\) −0.337107 −0.0155828
\(469\) 2.65306 0.122507
\(470\) 8.07812 0.372616
\(471\) −1.09838 −0.0506106
\(472\) −18.8084 −0.865726
\(473\) 11.8262 0.543768
\(474\) −50.9339 −2.33947
\(475\) 2.33742 0.107248
\(476\) −15.3149 −0.701959
\(477\) 0.516824 0.0236637
\(478\) 13.1718 0.602466
\(479\) −23.4699 −1.07237 −0.536185 0.844101i \(-0.680135\pi\)
−0.536185 + 0.844101i \(0.680135\pi\)
\(480\) −20.2991 −0.926524
\(481\) −6.05402 −0.276040
\(482\) 57.8325 2.63420
\(483\) 1.12660 0.0512621
\(484\) −3.41621 −0.155282
\(485\) 5.17885 0.235160
\(486\) −1.32653 −0.0601726
\(487\) −40.0281 −1.81385 −0.906924 0.421294i \(-0.861576\pi\)
−0.906924 + 0.421294i \(0.861576\pi\)
\(488\) 21.4931 0.972947
\(489\) 23.4787 1.06175
\(490\) −32.7487 −1.47944
\(491\) −4.72827 −0.213384 −0.106692 0.994292i \(-0.534026\pi\)
−0.106692 + 0.994292i \(0.534026\pi\)
\(492\) −47.2235 −2.12900
\(493\) 4.20246 0.189269
\(494\) −4.47206 −0.201208
\(495\) −0.295323 −0.0132738
\(496\) −3.72729 −0.167360
\(497\) −34.8948 −1.56524
\(498\) 18.2122 0.816108
\(499\) 21.8266 0.977091 0.488546 0.872538i \(-0.337528\pi\)
0.488546 + 0.872538i \(0.337528\pi\)
\(500\) −34.5248 −1.54399
\(501\) 23.7535 1.06123
\(502\) 56.6828 2.52988
\(503\) 0.957436 0.0426899 0.0213450 0.999772i \(-0.493205\pi\)
0.0213450 + 0.999772i \(0.493205\pi\)
\(504\) −0.452367 −0.0201500
\(505\) 22.3516 0.994634
\(506\) −1.11230 −0.0494478
\(507\) 15.5714 0.691548
\(508\) −60.2619 −2.67369
\(509\) 4.68920 0.207845 0.103923 0.994585i \(-0.466861\pi\)
0.103923 + 0.994585i \(0.466861\pi\)
\(510\) −8.35095 −0.369786
\(511\) 1.62051 0.0716873
\(512\) −16.0006 −0.707133
\(513\) −5.14493 −0.227154
\(514\) −42.5857 −1.87837
\(515\) −3.52807 −0.155465
\(516\) 19.0340 0.837926
\(517\) 7.01843 0.308670
\(518\) −26.5121 −1.16488
\(519\) −1.85606 −0.0814721
\(520\) 6.44791 0.282759
\(521\) 13.3235 0.583711 0.291856 0.956462i \(-0.405727\pi\)
0.291856 + 0.956462i \(0.405727\pi\)
\(522\) 0.405095 0.0177305
\(523\) 6.10968 0.267158 0.133579 0.991038i \(-0.457353\pi\)
0.133579 + 0.991038i \(0.457353\pi\)
\(524\) 5.66417 0.247440
\(525\) 16.3910 0.715363
\(526\) −49.0141 −2.13711
\(527\) −3.39962 −0.148090
\(528\) −7.95478 −0.346187
\(529\) −22.9742 −0.998878
\(530\) −32.2604 −1.40130
\(531\) 0.556437 0.0241473
\(532\) −11.5639 −0.501358
\(533\) −18.9521 −0.820907
\(534\) −20.1845 −0.873467
\(535\) 24.6063 1.06382
\(536\) −1.29184 −0.0557990
\(537\) 40.2000 1.73476
\(538\) 14.4201 0.621693
\(539\) −28.4527 −1.22555
\(540\) 24.2084 1.04177
\(541\) −13.4724 −0.579224 −0.289612 0.957144i \(-0.593526\pi\)
−0.289612 + 0.957144i \(0.593526\pi\)
\(542\) −54.6323 −2.34666
\(543\) 33.5089 1.43801
\(544\) −9.42182 −0.403957
\(545\) 13.3267 0.570855
\(546\) −31.3601 −1.34209
\(547\) −1.54302 −0.0659748 −0.0329874 0.999456i \(-0.510502\pi\)
−0.0329874 + 0.999456i \(0.510502\pi\)
\(548\) −23.7367 −1.01398
\(549\) −0.635864 −0.0271380
\(550\) −16.1830 −0.690044
\(551\) 3.17316 0.135181
\(552\) −0.548570 −0.0233487
\(553\) −52.8569 −2.24770
\(554\) 55.5707 2.36097
\(555\) −8.53612 −0.362338
\(556\) −26.7094 −1.13273
\(557\) −31.9495 −1.35374 −0.676871 0.736101i \(-0.736665\pi\)
−0.676871 + 0.736101i \(0.736665\pi\)
\(558\) −0.327705 −0.0138729
\(559\) 7.63888 0.323090
\(560\) −9.50152 −0.401512
\(561\) −7.25547 −0.306326
\(562\) −22.7399 −0.959224
\(563\) 19.0429 0.802562 0.401281 0.915955i \(-0.368565\pi\)
0.401281 + 0.915955i \(0.368565\pi\)
\(564\) 11.2960 0.475649
\(565\) 12.0303 0.506119
\(566\) 6.27976 0.263958
\(567\) −36.7735 −1.54434
\(568\) 16.9911 0.712932
\(569\) 14.7018 0.616332 0.308166 0.951333i \(-0.400285\pi\)
0.308166 + 0.951333i \(0.400285\pi\)
\(570\) −6.30557 −0.264111
\(571\) 28.4859 1.19210 0.596049 0.802948i \(-0.296736\pi\)
0.596049 + 0.802948i \(0.296736\pi\)
\(572\) 18.2821 0.764412
\(573\) −38.9792 −1.62838
\(574\) −82.9961 −3.46419
\(575\) 0.375523 0.0156604
\(576\) −0.740450 −0.0308521
\(577\) −4.14897 −0.172724 −0.0863620 0.996264i \(-0.527524\pi\)
−0.0863620 + 0.996264i \(0.527524\pi\)
\(578\) 33.6920 1.40140
\(579\) −22.2884 −0.926273
\(580\) −14.9307 −0.619963
\(581\) 18.8998 0.784095
\(582\) 12.2646 0.508386
\(583\) −28.0285 −1.16082
\(584\) −0.789069 −0.0326519
\(585\) −0.190758 −0.00788689
\(586\) 26.8793 1.11037
\(587\) −0.823707 −0.0339980 −0.0169990 0.999856i \(-0.505411\pi\)
−0.0169990 + 0.999856i \(0.505411\pi\)
\(588\) −45.7942 −1.88852
\(589\) −2.56696 −0.105770
\(590\) −34.7331 −1.42994
\(591\) −20.4539 −0.841360
\(592\) −4.34391 −0.178533
\(593\) −44.4248 −1.82431 −0.912153 0.409850i \(-0.865581\pi\)
−0.912153 + 0.409850i \(0.865581\pi\)
\(594\) 35.6206 1.46153
\(595\) −8.66624 −0.355281
\(596\) −8.79478 −0.360248
\(597\) −14.6100 −0.597946
\(598\) −0.718469 −0.0293804
\(599\) 5.42162 0.221521 0.110761 0.993847i \(-0.464671\pi\)
0.110761 + 0.993847i \(0.464671\pi\)
\(600\) −7.98120 −0.325831
\(601\) −7.53777 −0.307472 −0.153736 0.988112i \(-0.549131\pi\)
−0.153736 + 0.988112i \(0.549131\pi\)
\(602\) 33.4526 1.36343
\(603\) 0.0382185 0.00155638
\(604\) 27.8845 1.13460
\(605\) −1.93313 −0.0785927
\(606\) 52.9334 2.15027
\(607\) −42.9160 −1.74191 −0.870954 0.491365i \(-0.836498\pi\)
−0.870954 + 0.491365i \(0.836498\pi\)
\(608\) −7.11416 −0.288517
\(609\) 22.2516 0.901682
\(610\) 39.6910 1.60704
\(611\) 4.53342 0.183402
\(612\) −0.220619 −0.00891798
\(613\) 15.8079 0.638474 0.319237 0.947675i \(-0.396573\pi\)
0.319237 + 0.947675i \(0.396573\pi\)
\(614\) 53.9722 2.17814
\(615\) −26.7223 −1.07755
\(616\) 24.5329 0.988458
\(617\) 18.3443 0.738515 0.369258 0.929327i \(-0.379612\pi\)
0.369258 + 0.929327i \(0.379612\pi\)
\(618\) −8.35523 −0.336096
\(619\) −0.840999 −0.0338026 −0.0169013 0.999857i \(-0.505380\pi\)
−0.0169013 + 0.999857i \(0.505380\pi\)
\(620\) 12.0783 0.485077
\(621\) −0.826569 −0.0331691
\(622\) 56.4371 2.26292
\(623\) −20.9465 −0.839205
\(624\) −5.13823 −0.205694
\(625\) −7.84940 −0.313976
\(626\) 2.28422 0.0912957
\(627\) −5.47840 −0.218786
\(628\) 1.81128 0.0722780
\(629\) −3.96203 −0.157977
\(630\) −0.835379 −0.0332823
\(631\) 20.1842 0.803522 0.401761 0.915745i \(-0.368398\pi\)
0.401761 + 0.915745i \(0.368398\pi\)
\(632\) 25.7373 1.02378
\(633\) −34.0164 −1.35203
\(634\) 2.20989 0.0877659
\(635\) −34.1003 −1.35323
\(636\) −45.1114 −1.78878
\(637\) −18.3785 −0.728182
\(638\) −21.9692 −0.869769
\(639\) −0.502675 −0.0198855
\(640\) 23.0024 0.909248
\(641\) −35.2797 −1.39346 −0.696732 0.717331i \(-0.745363\pi\)
−0.696732 + 0.717331i \(0.745363\pi\)
\(642\) 58.2731 2.29986
\(643\) 22.6099 0.891649 0.445825 0.895120i \(-0.352910\pi\)
0.445825 + 0.895120i \(0.352910\pi\)
\(644\) −1.85782 −0.0732084
\(645\) 10.7708 0.424098
\(646\) −2.92672 −0.115150
\(647\) −6.06503 −0.238441 −0.119220 0.992868i \(-0.538040\pi\)
−0.119220 + 0.992868i \(0.538040\pi\)
\(648\) 17.9060 0.703412
\(649\) −30.1768 −1.18454
\(650\) −10.4531 −0.410003
\(651\) −18.0007 −0.705502
\(652\) −38.7176 −1.51630
\(653\) 16.2842 0.637251 0.318626 0.947881i \(-0.396779\pi\)
0.318626 + 0.947881i \(0.396779\pi\)
\(654\) 31.5606 1.23412
\(655\) 3.20517 0.125237
\(656\) −13.5986 −0.530936
\(657\) 0.0233442 0.000910745 0
\(658\) 19.8530 0.773950
\(659\) 43.7962 1.70606 0.853029 0.521863i \(-0.174763\pi\)
0.853029 + 0.521863i \(0.174763\pi\)
\(660\) 25.7776 1.00339
\(661\) −6.23568 −0.242540 −0.121270 0.992620i \(-0.538697\pi\)
−0.121270 + 0.992620i \(0.538697\pi\)
\(662\) −79.7022 −3.09771
\(663\) −4.68653 −0.182010
\(664\) −9.20278 −0.357137
\(665\) −6.54363 −0.253751
\(666\) −0.381919 −0.0147991
\(667\) 0.509791 0.0197392
\(668\) −39.1707 −1.51556
\(669\) −28.9125 −1.11782
\(670\) −2.38562 −0.0921645
\(671\) 34.4843 1.33125
\(672\) −49.8877 −1.92446
\(673\) −19.8516 −0.765224 −0.382612 0.923909i \(-0.624975\pi\)
−0.382612 + 0.923909i \(0.624975\pi\)
\(674\) 27.3964 1.05527
\(675\) −12.0258 −0.462875
\(676\) −25.6779 −0.987613
\(677\) −5.76841 −0.221698 −0.110849 0.993837i \(-0.535357\pi\)
−0.110849 + 0.993837i \(0.535357\pi\)
\(678\) 28.4904 1.09417
\(679\) 12.7277 0.488444
\(680\) 4.21981 0.161822
\(681\) 25.0200 0.958769
\(682\) 17.7722 0.680532
\(683\) −30.6810 −1.17398 −0.586988 0.809595i \(-0.699687\pi\)
−0.586988 + 0.809595i \(0.699687\pi\)
\(684\) −0.166583 −0.00636946
\(685\) −13.4318 −0.513204
\(686\) −18.4492 −0.704395
\(687\) −11.9120 −0.454472
\(688\) 5.48108 0.208964
\(689\) −18.1045 −0.689725
\(690\) −1.01303 −0.0385656
\(691\) 41.6473 1.58434 0.792168 0.610303i \(-0.208952\pi\)
0.792168 + 0.610303i \(0.208952\pi\)
\(692\) 3.06074 0.116352
\(693\) −0.725794 −0.0275706
\(694\) 58.7506 2.23014
\(695\) −15.1140 −0.573308
\(696\) −10.8349 −0.410695
\(697\) −12.4031 −0.469802
\(698\) 38.0982 1.44204
\(699\) 29.8717 1.12985
\(700\) −27.0296 −1.02162
\(701\) −49.0166 −1.85133 −0.925666 0.378341i \(-0.876495\pi\)
−0.925666 + 0.378341i \(0.876495\pi\)
\(702\) 23.0084 0.868397
\(703\) −2.99162 −0.112831
\(704\) 40.1563 1.51345
\(705\) 6.39208 0.240740
\(706\) 50.7639 1.91052
\(707\) 54.9319 2.06593
\(708\) −48.5691 −1.82534
\(709\) −45.2826 −1.70062 −0.850312 0.526280i \(-0.823587\pi\)
−0.850312 + 0.526280i \(0.823587\pi\)
\(710\) 31.3773 1.17757
\(711\) −0.761427 −0.0285558
\(712\) 10.1994 0.382238
\(713\) −0.412400 −0.0154445
\(714\) −20.5235 −0.768073
\(715\) 10.3452 0.386890
\(716\) −66.2918 −2.47744
\(717\) 10.4226 0.389241
\(718\) −54.1528 −2.02096
\(719\) 46.7159 1.74221 0.871104 0.491099i \(-0.163405\pi\)
0.871104 + 0.491099i \(0.163405\pi\)
\(720\) −0.136874 −0.00510098
\(721\) −8.67068 −0.322913
\(722\) −2.20989 −0.0822435
\(723\) 45.7619 1.70190
\(724\) −55.2579 −2.05364
\(725\) 7.41700 0.275460
\(726\) −4.57806 −0.169908
\(727\) −32.3260 −1.19891 −0.599453 0.800410i \(-0.704615\pi\)
−0.599453 + 0.800410i \(0.704615\pi\)
\(728\) 15.8465 0.587312
\(729\) 26.4602 0.980009
\(730\) −1.45716 −0.0539319
\(731\) 4.99924 0.184903
\(732\) 55.5019 2.05141
\(733\) 49.4555 1.82668 0.913341 0.407196i \(-0.133493\pi\)
0.913341 + 0.407196i \(0.133493\pi\)
\(734\) 11.6887 0.431437
\(735\) −25.9135 −0.955834
\(736\) −1.14294 −0.0421293
\(737\) −2.07267 −0.0763479
\(738\) −1.19560 −0.0440105
\(739\) −19.9517 −0.733936 −0.366968 0.930234i \(-0.619604\pi\)
−0.366968 + 0.930234i \(0.619604\pi\)
\(740\) 14.0765 0.517462
\(741\) −3.53867 −0.129996
\(742\) −79.2840 −2.91061
\(743\) −26.7031 −0.979641 −0.489821 0.871823i \(-0.662938\pi\)
−0.489821 + 0.871823i \(0.662938\pi\)
\(744\) 8.76498 0.321340
\(745\) −4.97669 −0.182332
\(746\) −31.3679 −1.14846
\(747\) 0.272260 0.00996147
\(748\) 11.9646 0.437470
\(749\) 60.4732 2.20964
\(750\) −46.2666 −1.68942
\(751\) 7.58256 0.276691 0.138346 0.990384i \(-0.455822\pi\)
0.138346 + 0.990384i \(0.455822\pi\)
\(752\) 3.25284 0.118619
\(753\) 44.8521 1.63450
\(754\) −14.1906 −0.516790
\(755\) 15.7789 0.574254
\(756\) 59.4953 2.16382
\(757\) 38.8407 1.41169 0.705845 0.708367i \(-0.250568\pi\)
0.705845 + 0.708367i \(0.250568\pi\)
\(758\) 76.2510 2.76956
\(759\) −0.880145 −0.0319472
\(760\) 3.18626 0.115578
\(761\) −3.41598 −0.123829 −0.0619146 0.998081i \(-0.519721\pi\)
−0.0619146 + 0.998081i \(0.519721\pi\)
\(762\) −80.7568 −2.92551
\(763\) 32.7521 1.18571
\(764\) 64.2786 2.32552
\(765\) −0.124841 −0.00451364
\(766\) 13.0583 0.471815
\(767\) −19.4921 −0.703820
\(768\) 9.64814 0.348147
\(769\) −17.2737 −0.622905 −0.311452 0.950262i \(-0.600815\pi\)
−0.311452 + 0.950262i \(0.600815\pi\)
\(770\) 45.3045 1.63266
\(771\) −33.6973 −1.21358
\(772\) 36.7546 1.32283
\(773\) −49.2610 −1.77180 −0.885898 0.463881i \(-0.846457\pi\)
−0.885898 + 0.463881i \(0.846457\pi\)
\(774\) 0.481900 0.0173215
\(775\) −6.00005 −0.215528
\(776\) −6.19743 −0.222475
\(777\) −20.9786 −0.752603
\(778\) −21.8414 −0.783053
\(779\) −9.36527 −0.335545
\(780\) 16.6505 0.596184
\(781\) 27.2612 0.975482
\(782\) −0.470199 −0.0168143
\(783\) −16.3257 −0.583432
\(784\) −13.1870 −0.470964
\(785\) 1.02495 0.0365819
\(786\) 7.59054 0.270746
\(787\) 38.9695 1.38911 0.694556 0.719438i \(-0.255601\pi\)
0.694556 + 0.719438i \(0.255601\pi\)
\(788\) 33.7295 1.20156
\(789\) −38.7840 −1.38075
\(790\) 47.5287 1.69100
\(791\) 29.5660 1.05125
\(792\) 0.353407 0.0125578
\(793\) 22.2745 0.790989
\(794\) 51.3345 1.82179
\(795\) −25.5271 −0.905354
\(796\) 24.0926 0.853938
\(797\) −29.9676 −1.06151 −0.530753 0.847527i \(-0.678091\pi\)
−0.530753 + 0.847527i \(0.678091\pi\)
\(798\) −15.4967 −0.548578
\(799\) 2.96688 0.104961
\(800\) −16.6288 −0.587915
\(801\) −0.301744 −0.0106616
\(802\) 31.4783 1.11154
\(803\) −1.26601 −0.0446765
\(804\) −3.33593 −0.117649
\(805\) −1.05128 −0.0370528
\(806\) 11.4796 0.404352
\(807\) 11.4104 0.401663
\(808\) −26.7477 −0.940982
\(809\) −16.0591 −0.564607 −0.282303 0.959325i \(-0.591098\pi\)
−0.282303 + 0.959325i \(0.591098\pi\)
\(810\) 33.0666 1.16184
\(811\) 16.6986 0.586366 0.293183 0.956056i \(-0.405285\pi\)
0.293183 + 0.956056i \(0.405285\pi\)
\(812\) −36.6940 −1.28771
\(813\) −43.2296 −1.51613
\(814\) 20.7123 0.725966
\(815\) −21.9091 −0.767442
\(816\) −3.36270 −0.117718
\(817\) 3.77478 0.132063
\(818\) −7.77762 −0.271938
\(819\) −0.468813 −0.0163816
\(820\) 44.0664 1.53887
\(821\) 45.1930 1.57725 0.788623 0.614877i \(-0.210794\pi\)
0.788623 + 0.614877i \(0.210794\pi\)
\(822\) −31.8094 −1.10948
\(823\) −42.8117 −1.49232 −0.746161 0.665765i \(-0.768105\pi\)
−0.746161 + 0.665765i \(0.768105\pi\)
\(824\) 4.22197 0.147079
\(825\) −12.8053 −0.445824
\(826\) −85.3610 −2.97009
\(827\) −15.4640 −0.537735 −0.268868 0.963177i \(-0.586649\pi\)
−0.268868 + 0.963177i \(0.586649\pi\)
\(828\) −0.0267627 −0.000930070 0
\(829\) 13.1407 0.456397 0.228198 0.973615i \(-0.426716\pi\)
0.228198 + 0.973615i \(0.426716\pi\)
\(830\) −16.9946 −0.589892
\(831\) 43.9722 1.52538
\(832\) 25.9382 0.899244
\(833\) −12.0277 −0.416736
\(834\) −35.7933 −1.23942
\(835\) −22.1654 −0.767067
\(836\) 9.03416 0.312453
\(837\) 13.2068 0.456494
\(838\) 58.1299 2.00806
\(839\) −52.3665 −1.80789 −0.903946 0.427647i \(-0.859343\pi\)
−0.903946 + 0.427647i \(0.859343\pi\)
\(840\) 22.3435 0.770923
\(841\) −18.9310 −0.652795
\(842\) −79.2522 −2.73121
\(843\) −17.9937 −0.619735
\(844\) 56.0947 1.93086
\(845\) −14.5303 −0.499859
\(846\) 0.285991 0.00983259
\(847\) −4.75090 −0.163243
\(848\) −12.9904 −0.446091
\(849\) 4.96907 0.170538
\(850\) −6.84097 −0.234643
\(851\) −0.480625 −0.0164756
\(852\) 43.8764 1.50318
\(853\) −15.5622 −0.532841 −0.266421 0.963857i \(-0.585841\pi\)
−0.266421 + 0.963857i \(0.585841\pi\)
\(854\) 97.5455 3.33794
\(855\) −0.0942640 −0.00322376
\(856\) −29.4459 −1.00644
\(857\) −3.51387 −0.120032 −0.0600158 0.998197i \(-0.519115\pi\)
−0.0600158 + 0.998197i \(0.519115\pi\)
\(858\) 24.4998 0.836408
\(859\) 21.5578 0.735541 0.367771 0.929917i \(-0.380121\pi\)
0.367771 + 0.929917i \(0.380121\pi\)
\(860\) −17.7615 −0.605662
\(861\) −65.6735 −2.23815
\(862\) −42.5508 −1.44929
\(863\) 25.7255 0.875707 0.437854 0.899046i \(-0.355739\pi\)
0.437854 + 0.899046i \(0.355739\pi\)
\(864\) 36.6018 1.24522
\(865\) 1.73198 0.0588889
\(866\) 72.7324 2.47155
\(867\) 26.6599 0.905419
\(868\) 29.6840 1.00754
\(869\) 41.2939 1.40080
\(870\) −20.0086 −0.678355
\(871\) −1.33880 −0.0453636
\(872\) −15.9478 −0.540062
\(873\) 0.183348 0.00620539
\(874\) −0.355034 −0.0120092
\(875\) −48.0134 −1.62315
\(876\) −2.03762 −0.0688449
\(877\) −40.8738 −1.38021 −0.690106 0.723709i \(-0.742436\pi\)
−0.690106 + 0.723709i \(0.742436\pi\)
\(878\) −19.7842 −0.667686
\(879\) 21.2691 0.717389
\(880\) 7.42296 0.250228
\(881\) 22.1032 0.744675 0.372338 0.928097i \(-0.378556\pi\)
0.372338 + 0.928097i \(0.378556\pi\)
\(882\) −1.15941 −0.0390394
\(883\) 33.6906 1.13378 0.566889 0.823794i \(-0.308147\pi\)
0.566889 + 0.823794i \(0.308147\pi\)
\(884\) 7.72832 0.259932
\(885\) −27.4837 −0.923856
\(886\) −73.6440 −2.47412
\(887\) 28.9842 0.973193 0.486597 0.873627i \(-0.338238\pi\)
0.486597 + 0.873627i \(0.338238\pi\)
\(888\) 10.2150 0.342793
\(889\) −83.8058 −2.81076
\(890\) 18.8350 0.631352
\(891\) 28.7289 0.962456
\(892\) 47.6781 1.59638
\(893\) 2.24021 0.0749657
\(894\) −11.7859 −0.394178
\(895\) −37.5124 −1.25390
\(896\) 56.5312 1.88858
\(897\) −0.568513 −0.0189821
\(898\) −38.6956 −1.29129
\(899\) −8.14537 −0.271663
\(900\) −0.389374 −0.0129791
\(901\) −11.8484 −0.394727
\(902\) 64.8399 2.15893
\(903\) 26.4705 0.880883
\(904\) −14.3964 −0.478819
\(905\) −31.2687 −1.03941
\(906\) 37.3679 1.24147
\(907\) −17.7822 −0.590450 −0.295225 0.955428i \(-0.595395\pi\)
−0.295225 + 0.955428i \(0.595395\pi\)
\(908\) −41.2593 −1.36924
\(909\) 0.791319 0.0262464
\(910\) 29.2635 0.970077
\(911\) −24.7058 −0.818540 −0.409270 0.912413i \(-0.634217\pi\)
−0.409270 + 0.912413i \(0.634217\pi\)
\(912\) −2.53908 −0.0840773
\(913\) −14.7653 −0.488659
\(914\) 35.1836 1.16377
\(915\) 31.4068 1.03828
\(916\) 19.6435 0.649040
\(917\) 7.87712 0.260125
\(918\) 15.0578 0.496981
\(919\) 25.8814 0.853749 0.426875 0.904311i \(-0.359615\pi\)
0.426875 + 0.904311i \(0.359615\pi\)
\(920\) 0.511895 0.0168767
\(921\) 42.7073 1.40725
\(922\) −3.06759 −0.101026
\(923\) 17.6088 0.579602
\(924\) 63.3516 2.08411
\(925\) −6.99266 −0.229917
\(926\) 63.0661 2.07248
\(927\) −0.124905 −0.00410242
\(928\) −22.5744 −0.741040
\(929\) −24.6722 −0.809468 −0.404734 0.914434i \(-0.632636\pi\)
−0.404734 + 0.914434i \(0.632636\pi\)
\(930\) 16.1861 0.530764
\(931\) −9.08181 −0.297644
\(932\) −49.2599 −1.61356
\(933\) 44.6577 1.46203
\(934\) −54.8412 −1.79446
\(935\) 6.77041 0.221416
\(936\) 0.228277 0.00746146
\(937\) −57.7633 −1.88704 −0.943522 0.331311i \(-0.892509\pi\)
−0.943522 + 0.331311i \(0.892509\pi\)
\(938\) −5.86296 −0.191432
\(939\) 1.80746 0.0589843
\(940\) −10.5409 −0.343805
\(941\) 42.0207 1.36984 0.684918 0.728620i \(-0.259838\pi\)
0.684918 + 0.728620i \(0.259838\pi\)
\(942\) 2.42729 0.0790855
\(943\) −1.50460 −0.0489964
\(944\) −13.9861 −0.455208
\(945\) 33.6665 1.09517
\(946\) −26.1345 −0.849706
\(947\) −0.527420 −0.0171389 −0.00856943 0.999963i \(-0.502728\pi\)
−0.00856943 + 0.999963i \(0.502728\pi\)
\(948\) 66.4618 2.15858
\(949\) −0.817754 −0.0265454
\(950\) −5.16543 −0.167589
\(951\) 1.74865 0.0567038
\(952\) 10.3707 0.336117
\(953\) 5.86206 0.189891 0.0949453 0.995482i \(-0.469732\pi\)
0.0949453 + 0.995482i \(0.469732\pi\)
\(954\) −1.14212 −0.0369776
\(955\) 36.3732 1.17701
\(956\) −17.1875 −0.555882
\(957\) −17.3839 −0.561940
\(958\) 51.8660 1.67571
\(959\) −33.0104 −1.06596
\(960\) 36.5726 1.18037
\(961\) −24.4107 −0.787443
\(962\) 13.3787 0.431347
\(963\) 0.871144 0.0280722
\(964\) −75.4636 −2.43052
\(965\) 20.7983 0.669520
\(966\) −2.48966 −0.0801035
\(967\) −27.7812 −0.893384 −0.446692 0.894688i \(-0.647398\pi\)
−0.446692 + 0.894688i \(0.647398\pi\)
\(968\) 2.31333 0.0743533
\(969\) −2.31587 −0.0743964
\(970\) −11.4447 −0.367467
\(971\) 12.3910 0.397647 0.198824 0.980035i \(-0.436288\pi\)
0.198824 + 0.980035i \(0.436288\pi\)
\(972\) 1.73094 0.0555200
\(973\) −37.1446 −1.19080
\(974\) 88.4577 2.83437
\(975\) −8.27134 −0.264895
\(976\) 15.9825 0.511586
\(977\) 1.52197 0.0486921 0.0243461 0.999704i \(-0.492250\pi\)
0.0243461 + 0.999704i \(0.492250\pi\)
\(978\) −51.8854 −1.65911
\(979\) 16.3643 0.523004
\(980\) 42.7327 1.36504
\(981\) 0.471809 0.0150637
\(982\) 10.4490 0.333440
\(983\) −39.6194 −1.26366 −0.631832 0.775105i \(-0.717697\pi\)
−0.631832 + 0.775105i \(0.717697\pi\)
\(984\) 31.9780 1.01942
\(985\) 19.0864 0.608145
\(986\) −9.28697 −0.295757
\(987\) 15.7093 0.500034
\(988\) 5.83544 0.185650
\(989\) 0.606446 0.0192839
\(990\) 0.652632 0.0207420
\(991\) 27.6644 0.878790 0.439395 0.898294i \(-0.355193\pi\)
0.439395 + 0.898294i \(0.355193\pi\)
\(992\) 18.2617 0.579811
\(993\) −63.0670 −2.00137
\(994\) 77.1136 2.44589
\(995\) 13.6332 0.432202
\(996\) −23.7645 −0.753006
\(997\) 8.83091 0.279678 0.139839 0.990174i \(-0.455342\pi\)
0.139839 + 0.990174i \(0.455342\pi\)
\(998\) −48.2343 −1.52683
\(999\) 15.3917 0.486971
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 \(a_p\))