Properties

Label 4003.2.a.b.1.17
Level 4003
Weight 2
Character 4003.1
Self dual Yes
Analytic conductor 31.964
Analytic rank 1
Dimension 152
CM No

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Newspace parameters

Level: \( N \) = \( 4003 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4003.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(31.9641159291\)
Analytic rank: \(1\)
Dimension: \(152\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Character \(\chi\) = 4003.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.41802 q^{2} +1.98760 q^{3} +3.84680 q^{4} +1.18517 q^{5} -4.80604 q^{6} -3.98093 q^{7} -4.46560 q^{8} +0.950540 q^{9} +O(q^{10})\) \(q-2.41802 q^{2} +1.98760 q^{3} +3.84680 q^{4} +1.18517 q^{5} -4.80604 q^{6} -3.98093 q^{7} -4.46560 q^{8} +0.950540 q^{9} -2.86577 q^{10} -0.0380846 q^{11} +7.64589 q^{12} -4.40285 q^{13} +9.62596 q^{14} +2.35564 q^{15} +3.10429 q^{16} +7.19381 q^{17} -2.29842 q^{18} +1.70361 q^{19} +4.55912 q^{20} -7.91249 q^{21} +0.0920891 q^{22} +2.13708 q^{23} -8.87581 q^{24} -3.59537 q^{25} +10.6462 q^{26} -4.07350 q^{27} -15.3139 q^{28} -1.31015 q^{29} -5.69599 q^{30} +1.94251 q^{31} +1.42498 q^{32} -0.0756967 q^{33} -17.3948 q^{34} -4.71809 q^{35} +3.65654 q^{36} -3.58057 q^{37} -4.11936 q^{38} -8.75110 q^{39} -5.29250 q^{40} +9.66585 q^{41} +19.1325 q^{42} +6.38812 q^{43} -0.146504 q^{44} +1.12655 q^{45} -5.16748 q^{46} -9.04545 q^{47} +6.17007 q^{48} +8.84782 q^{49} +8.69366 q^{50} +14.2984 q^{51} -16.9369 q^{52} -8.91888 q^{53} +9.84979 q^{54} -0.0451368 q^{55} +17.7772 q^{56} +3.38609 q^{57} +3.16795 q^{58} +14.0599 q^{59} +9.06170 q^{60} +3.91881 q^{61} -4.69703 q^{62} -3.78404 q^{63} -9.65421 q^{64} -5.21814 q^{65} +0.183036 q^{66} +5.52385 q^{67} +27.6732 q^{68} +4.24764 q^{69} +11.4084 q^{70} -9.15115 q^{71} -4.24473 q^{72} -1.82962 q^{73} +8.65788 q^{74} -7.14614 q^{75} +6.55346 q^{76} +0.151612 q^{77} +21.1603 q^{78} -11.8647 q^{79} +3.67911 q^{80} -10.9481 q^{81} -23.3722 q^{82} -7.24574 q^{83} -30.4378 q^{84} +8.52591 q^{85} -15.4466 q^{86} -2.60404 q^{87} +0.170070 q^{88} +2.78275 q^{89} -2.72402 q^{90} +17.5275 q^{91} +8.22091 q^{92} +3.86094 q^{93} +21.8720 q^{94} +2.01907 q^{95} +2.83229 q^{96} -8.45647 q^{97} -21.3942 q^{98} -0.0362009 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 152q - 22q^{2} - 18q^{3} + 138q^{4} - 59q^{5} - 17q^{6} - 19q^{7} - 66q^{8} + 106q^{9} + O(q^{10}) \) \( 152q - 22q^{2} - 18q^{3} + 138q^{4} - 59q^{5} - 17q^{6} - 19q^{7} - 66q^{8} + 106q^{9} - 15q^{10} - 40q^{11} - 53q^{12} - 59q^{13} - 36q^{14} - 40q^{15} + 118q^{16} - 93q^{17} - 59q^{18} - 16q^{19} - 108q^{20} - 62q^{21} - 37q^{22} - 107q^{23} - 31q^{24} + 101q^{25} - 64q^{26} - 63q^{27} - 53q^{28} - 124q^{29} - 68q^{30} - 15q^{31} - 129q^{32} - 49q^{33} - 76q^{35} + 45q^{36} - 98q^{37} - 125q^{38} - 47q^{39} - 7q^{40} - 56q^{41} - 84q^{42} - 62q^{43} - 114q^{44} - 142q^{45} - 3q^{46} - 111q^{47} - 92q^{48} + 117q^{49} - 64q^{50} - 21q^{51} - 85q^{52} - 347q^{53} + 3q^{54} - 16q^{55} - 73q^{56} - 115q^{57} - 29q^{58} - 50q^{59} - 54q^{60} - 62q^{61} - 55q^{62} - 70q^{63} + 64q^{64} - 147q^{65} + 34q^{66} - 86q^{67} - 174q^{68} - 104q^{69} - 7q^{70} - 86q^{71} - 139q^{72} - 27q^{73} - 52q^{74} - 49q^{75} - 11q^{76} - 346q^{77} - 59q^{78} - 17q^{79} - 149q^{80} - 8q^{81} - 31q^{82} - 106q^{83} - 51q^{84} - 69q^{85} - 85q^{86} - 32q^{87} - 113q^{88} - 59q^{89} + 10q^{90} - 9q^{91} - 314q^{92} - 230q^{93} + 7q^{94} - 74q^{95} - 54q^{96} - 60q^{97} - 77q^{98} - 96q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.41802 −1.70980 −0.854898 0.518796i \(-0.826380\pi\)
−0.854898 + 0.518796i \(0.826380\pi\)
\(3\) 1.98760 1.14754 0.573770 0.819017i \(-0.305480\pi\)
0.573770 + 0.819017i \(0.305480\pi\)
\(4\) 3.84680 1.92340
\(5\) 1.18517 0.530025 0.265013 0.964245i \(-0.414624\pi\)
0.265013 + 0.964245i \(0.414624\pi\)
\(6\) −4.80604 −1.96206
\(7\) −3.98093 −1.50465 −0.752326 0.658792i \(-0.771068\pi\)
−0.752326 + 0.658792i \(0.771068\pi\)
\(8\) −4.46560 −1.57883
\(9\) 0.950540 0.316847
\(10\) −2.86577 −0.906235
\(11\) −0.0380846 −0.0114829 −0.00574146 0.999984i \(-0.501828\pi\)
−0.00574146 + 0.999984i \(0.501828\pi\)
\(12\) 7.64589 2.20718
\(13\) −4.40285 −1.22113 −0.610566 0.791965i \(-0.709058\pi\)
−0.610566 + 0.791965i \(0.709058\pi\)
\(14\) 9.62596 2.57265
\(15\) 2.35564 0.608225
\(16\) 3.10429 0.776072
\(17\) 7.19381 1.74476 0.872378 0.488832i \(-0.162577\pi\)
0.872378 + 0.488832i \(0.162577\pi\)
\(18\) −2.29842 −0.541743
\(19\) 1.70361 0.390835 0.195418 0.980720i \(-0.437394\pi\)
0.195418 + 0.980720i \(0.437394\pi\)
\(20\) 4.55912 1.01945
\(21\) −7.91249 −1.72665
\(22\) 0.0920891 0.0196335
\(23\) 2.13708 0.445611 0.222805 0.974863i \(-0.428479\pi\)
0.222805 + 0.974863i \(0.428479\pi\)
\(24\) −8.87581 −1.81177
\(25\) −3.59537 −0.719073
\(26\) 10.6462 2.08789
\(27\) −4.07350 −0.783945
\(28\) −15.3139 −2.89405
\(29\) −1.31015 −0.243288 −0.121644 0.992574i \(-0.538817\pi\)
−0.121644 + 0.992574i \(0.538817\pi\)
\(30\) −5.69599 −1.03994
\(31\) 1.94251 0.348886 0.174443 0.984667i \(-0.444188\pi\)
0.174443 + 0.984667i \(0.444188\pi\)
\(32\) 1.42498 0.251904
\(33\) −0.0756967 −0.0131771
\(34\) −17.3948 −2.98318
\(35\) −4.71809 −0.797503
\(36\) 3.65654 0.609423
\(37\) −3.58057 −0.588642 −0.294321 0.955707i \(-0.595093\pi\)
−0.294321 + 0.955707i \(0.595093\pi\)
\(38\) −4.11936 −0.668249
\(39\) −8.75110 −1.40130
\(40\) −5.29250 −0.836818
\(41\) 9.66585 1.50955 0.754776 0.655983i \(-0.227746\pi\)
0.754776 + 0.655983i \(0.227746\pi\)
\(42\) 19.1325 2.95221
\(43\) 6.38812 0.974178 0.487089 0.873352i \(-0.338059\pi\)
0.487089 + 0.873352i \(0.338059\pi\)
\(44\) −0.146504 −0.0220863
\(45\) 1.12655 0.167937
\(46\) −5.16748 −0.761904
\(47\) −9.04545 −1.31941 −0.659707 0.751523i \(-0.729320\pi\)
−0.659707 + 0.751523i \(0.729320\pi\)
\(48\) 6.17007 0.890573
\(49\) 8.84782 1.26397
\(50\) 8.69366 1.22947
\(51\) 14.2984 2.00218
\(52\) −16.9369 −2.34873
\(53\) −8.91888 −1.22510 −0.612552 0.790431i \(-0.709857\pi\)
−0.612552 + 0.790431i \(0.709857\pi\)
\(54\) 9.84979 1.34039
\(55\) −0.0451368 −0.00608624
\(56\) 17.7772 2.37558
\(57\) 3.38609 0.448499
\(58\) 3.16795 0.415973
\(59\) 14.0599 1.83045 0.915223 0.402948i \(-0.132014\pi\)
0.915223 + 0.402948i \(0.132014\pi\)
\(60\) 9.06170 1.16986
\(61\) 3.91881 0.501753 0.250876 0.968019i \(-0.419281\pi\)
0.250876 + 0.968019i \(0.419281\pi\)
\(62\) −4.69703 −0.596524
\(63\) −3.78404 −0.476744
\(64\) −9.65421 −1.20678
\(65\) −5.21814 −0.647230
\(66\) 0.183036 0.0225302
\(67\) 5.52385 0.674846 0.337423 0.941353i \(-0.390445\pi\)
0.337423 + 0.941353i \(0.390445\pi\)
\(68\) 27.6732 3.35587
\(69\) 4.24764 0.511356
\(70\) 11.4084 1.36357
\(71\) −9.15115 −1.08604 −0.543021 0.839719i \(-0.682720\pi\)
−0.543021 + 0.839719i \(0.682720\pi\)
\(72\) −4.24473 −0.500246
\(73\) −1.82962 −0.214140 −0.107070 0.994251i \(-0.534147\pi\)
−0.107070 + 0.994251i \(0.534147\pi\)
\(74\) 8.65788 1.00646
\(75\) −7.14614 −0.825165
\(76\) 6.55346 0.751733
\(77\) 0.151612 0.0172778
\(78\) 21.1603 2.39593
\(79\) −11.8647 −1.33488 −0.667441 0.744663i \(-0.732610\pi\)
−0.667441 + 0.744663i \(0.732610\pi\)
\(80\) 3.67911 0.411337
\(81\) −10.9481 −1.21645
\(82\) −23.3722 −2.58103
\(83\) −7.24574 −0.795324 −0.397662 0.917532i \(-0.630178\pi\)
−0.397662 + 0.917532i \(0.630178\pi\)
\(84\) −30.4378 −3.32103
\(85\) 8.52591 0.924765
\(86\) −15.4466 −1.66565
\(87\) −2.60404 −0.279183
\(88\) 0.170070 0.0181296
\(89\) 2.78275 0.294971 0.147486 0.989064i \(-0.452882\pi\)
0.147486 + 0.989064i \(0.452882\pi\)
\(90\) −2.72402 −0.287137
\(91\) 17.5275 1.83738
\(92\) 8.22091 0.857089
\(93\) 3.86094 0.400360
\(94\) 21.8720 2.25593
\(95\) 2.01907 0.207152
\(96\) 2.83229 0.289070
\(97\) −8.45647 −0.858624 −0.429312 0.903156i \(-0.641244\pi\)
−0.429312 + 0.903156i \(0.641244\pi\)
\(98\) −21.3942 −2.16114
\(99\) −0.0362009 −0.00363833
\(100\) −13.8307 −1.38307
\(101\) 1.57357 0.156576 0.0782879 0.996931i \(-0.475055\pi\)
0.0782879 + 0.996931i \(0.475055\pi\)
\(102\) −34.5738 −3.42331
\(103\) −5.21843 −0.514187 −0.257093 0.966387i \(-0.582765\pi\)
−0.257093 + 0.966387i \(0.582765\pi\)
\(104\) 19.6614 1.92796
\(105\) −9.37766 −0.915166
\(106\) 21.5660 2.09468
\(107\) −2.01408 −0.194709 −0.0973544 0.995250i \(-0.531038\pi\)
−0.0973544 + 0.995250i \(0.531038\pi\)
\(108\) −15.6699 −1.50784
\(109\) −9.79023 −0.937734 −0.468867 0.883269i \(-0.655338\pi\)
−0.468867 + 0.883269i \(0.655338\pi\)
\(110\) 0.109141 0.0104062
\(111\) −7.11673 −0.675490
\(112\) −12.3580 −1.16772
\(113\) −8.42747 −0.792789 −0.396395 0.918080i \(-0.629739\pi\)
−0.396395 + 0.918080i \(0.629739\pi\)
\(114\) −8.18763 −0.766841
\(115\) 2.53280 0.236185
\(116\) −5.03987 −0.467940
\(117\) −4.18509 −0.386912
\(118\) −33.9971 −3.12969
\(119\) −28.6381 −2.62525
\(120\) −10.5194 −0.960282
\(121\) −10.9985 −0.999868
\(122\) −9.47576 −0.857895
\(123\) 19.2118 1.73227
\(124\) 7.47247 0.671048
\(125\) −10.1870 −0.911152
\(126\) 9.14986 0.815134
\(127\) −19.4601 −1.72681 −0.863403 0.504515i \(-0.831671\pi\)
−0.863403 + 0.504515i \(0.831671\pi\)
\(128\) 20.4941 1.81144
\(129\) 12.6970 1.11791
\(130\) 12.6175 1.10663
\(131\) −2.40274 −0.209928 −0.104964 0.994476i \(-0.533473\pi\)
−0.104964 + 0.994476i \(0.533473\pi\)
\(132\) −0.291190 −0.0253449
\(133\) −6.78196 −0.588071
\(134\) −13.3568 −1.15385
\(135\) −4.82780 −0.415511
\(136\) −32.1247 −2.75467
\(137\) −2.09096 −0.178642 −0.0893212 0.996003i \(-0.528470\pi\)
−0.0893212 + 0.996003i \(0.528470\pi\)
\(138\) −10.2709 −0.874315
\(139\) 3.51975 0.298541 0.149271 0.988796i \(-0.452307\pi\)
0.149271 + 0.988796i \(0.452307\pi\)
\(140\) −18.1496 −1.53392
\(141\) −17.9787 −1.51408
\(142\) 22.1276 1.85691
\(143\) 0.167681 0.0140222
\(144\) 2.95075 0.245896
\(145\) −1.55275 −0.128949
\(146\) 4.42404 0.366136
\(147\) 17.5859 1.45046
\(148\) −13.7737 −1.13219
\(149\) −12.9329 −1.05950 −0.529752 0.848153i \(-0.677715\pi\)
−0.529752 + 0.848153i \(0.677715\pi\)
\(150\) 17.2795 1.41086
\(151\) 5.82111 0.473715 0.236858 0.971544i \(-0.423882\pi\)
0.236858 + 0.971544i \(0.423882\pi\)
\(152\) −7.60765 −0.617062
\(153\) 6.83801 0.552820
\(154\) −0.366600 −0.0295415
\(155\) 2.30221 0.184918
\(156\) −33.6637 −2.69526
\(157\) −18.3839 −1.46720 −0.733599 0.679582i \(-0.762161\pi\)
−0.733599 + 0.679582i \(0.762161\pi\)
\(158\) 28.6890 2.28238
\(159\) −17.7271 −1.40585
\(160\) 1.68885 0.133515
\(161\) −8.50755 −0.670489
\(162\) 26.4727 2.07989
\(163\) 4.44173 0.347903 0.173952 0.984754i \(-0.444346\pi\)
0.173952 + 0.984754i \(0.444346\pi\)
\(164\) 37.1826 2.90347
\(165\) −0.0897137 −0.00698420
\(166\) 17.5203 1.35984
\(167\) −18.7029 −1.44728 −0.723639 0.690179i \(-0.757532\pi\)
−0.723639 + 0.690179i \(0.757532\pi\)
\(168\) 35.3340 2.72608
\(169\) 6.38512 0.491163
\(170\) −20.6158 −1.58116
\(171\) 1.61935 0.123835
\(172\) 24.5738 1.87374
\(173\) 1.92716 0.146519 0.0732596 0.997313i \(-0.476660\pi\)
0.0732596 + 0.997313i \(0.476660\pi\)
\(174\) 6.29661 0.477345
\(175\) 14.3129 1.08195
\(176\) −0.118225 −0.00891157
\(177\) 27.9454 2.10051
\(178\) −6.72875 −0.504341
\(179\) −23.8105 −1.77968 −0.889841 0.456271i \(-0.849185\pi\)
−0.889841 + 0.456271i \(0.849185\pi\)
\(180\) 4.33363 0.323010
\(181\) −13.1009 −0.973780 −0.486890 0.873463i \(-0.661869\pi\)
−0.486890 + 0.873463i \(0.661869\pi\)
\(182\) −42.3817 −3.14154
\(183\) 7.78902 0.575781
\(184\) −9.54332 −0.703543
\(185\) −4.24359 −0.311995
\(186\) −9.33580 −0.684534
\(187\) −0.273973 −0.0200349
\(188\) −34.7961 −2.53776
\(189\) 16.2163 1.17956
\(190\) −4.88215 −0.354188
\(191\) 2.97286 0.215108 0.107554 0.994199i \(-0.465698\pi\)
0.107554 + 0.994199i \(0.465698\pi\)
\(192\) −19.1887 −1.38482
\(193\) 17.6884 1.27324 0.636619 0.771178i \(-0.280332\pi\)
0.636619 + 0.771178i \(0.280332\pi\)
\(194\) 20.4479 1.46807
\(195\) −10.3716 −0.742722
\(196\) 34.0358 2.43113
\(197\) 3.95275 0.281622 0.140811 0.990037i \(-0.455029\pi\)
0.140811 + 0.990037i \(0.455029\pi\)
\(198\) 0.0875344 0.00622080
\(199\) −25.4381 −1.80326 −0.901629 0.432511i \(-0.857628\pi\)
−0.901629 + 0.432511i \(0.857628\pi\)
\(200\) 16.0555 1.13529
\(201\) 10.9792 0.774413
\(202\) −3.80491 −0.267713
\(203\) 5.21560 0.366064
\(204\) 55.0031 3.85099
\(205\) 11.4557 0.800100
\(206\) 12.6182 0.879155
\(207\) 2.03138 0.141190
\(208\) −13.6677 −0.947686
\(209\) −0.0648813 −0.00448793
\(210\) 22.6753 1.56475
\(211\) 1.61604 0.111253 0.0556265 0.998452i \(-0.482284\pi\)
0.0556265 + 0.998452i \(0.482284\pi\)
\(212\) −34.3092 −2.35636
\(213\) −18.1888 −1.24628
\(214\) 4.87008 0.332912
\(215\) 7.57102 0.516339
\(216\) 18.1906 1.23771
\(217\) −7.73302 −0.524952
\(218\) 23.6729 1.60333
\(219\) −3.63654 −0.245734
\(220\) −0.173632 −0.0117063
\(221\) −31.6733 −2.13058
\(222\) 17.2084 1.15495
\(223\) 16.3278 1.09339 0.546696 0.837331i \(-0.315885\pi\)
0.546696 + 0.837331i \(0.315885\pi\)
\(224\) −5.67276 −0.379028
\(225\) −3.41754 −0.227836
\(226\) 20.3778 1.35551
\(227\) 15.8393 1.05129 0.525645 0.850704i \(-0.323824\pi\)
0.525645 + 0.850704i \(0.323824\pi\)
\(228\) 13.0256 0.862643
\(229\) 23.6857 1.56520 0.782598 0.622527i \(-0.213894\pi\)
0.782598 + 0.622527i \(0.213894\pi\)
\(230\) −6.12436 −0.403828
\(231\) 0.301344 0.0198270
\(232\) 5.85059 0.384110
\(233\) −2.04580 −0.134025 −0.0670125 0.997752i \(-0.521347\pi\)
−0.0670125 + 0.997752i \(0.521347\pi\)
\(234\) 10.1196 0.661540
\(235\) −10.7204 −0.699323
\(236\) 54.0857 3.52068
\(237\) −23.5822 −1.53183
\(238\) 69.2474 4.48864
\(239\) −8.98564 −0.581232 −0.290616 0.956840i \(-0.593860\pi\)
−0.290616 + 0.956840i \(0.593860\pi\)
\(240\) 7.31259 0.472026
\(241\) −2.76429 −0.178063 −0.0890317 0.996029i \(-0.528377\pi\)
−0.0890317 + 0.996029i \(0.528377\pi\)
\(242\) 26.5947 1.70957
\(243\) −9.53990 −0.611985
\(244\) 15.0749 0.965072
\(245\) 10.4862 0.669938
\(246\) −46.4545 −2.96183
\(247\) −7.50075 −0.477261
\(248\) −8.67449 −0.550831
\(249\) −14.4016 −0.912665
\(250\) 24.6323 1.55788
\(251\) −20.1402 −1.27124 −0.635619 0.772003i \(-0.719255\pi\)
−0.635619 + 0.772003i \(0.719255\pi\)
\(252\) −14.5564 −0.916970
\(253\) −0.0813896 −0.00511692
\(254\) 47.0549 2.95249
\(255\) 16.9461 1.06120
\(256\) −30.2466 −1.89041
\(257\) −20.4148 −1.27344 −0.636721 0.771094i \(-0.719710\pi\)
−0.636721 + 0.771094i \(0.719710\pi\)
\(258\) −30.7015 −1.91139
\(259\) 14.2540 0.885701
\(260\) −20.0731 −1.24488
\(261\) −1.24535 −0.0770850
\(262\) 5.80986 0.358935
\(263\) −28.8916 −1.78153 −0.890766 0.454462i \(-0.849832\pi\)
−0.890766 + 0.454462i \(0.849832\pi\)
\(264\) 0.338031 0.0208044
\(265\) −10.5704 −0.649335
\(266\) 16.3989 1.00548
\(267\) 5.53099 0.338491
\(268\) 21.2492 1.29800
\(269\) 26.7773 1.63264 0.816321 0.577599i \(-0.196010\pi\)
0.816321 + 0.577599i \(0.196010\pi\)
\(270\) 11.6737 0.710438
\(271\) 23.0889 1.40255 0.701275 0.712891i \(-0.252615\pi\)
0.701275 + 0.712891i \(0.252615\pi\)
\(272\) 22.3317 1.35406
\(273\) 34.8375 2.10846
\(274\) 5.05596 0.305442
\(275\) 0.136928 0.00825707
\(276\) 16.3398 0.983543
\(277\) 9.19091 0.552229 0.276114 0.961125i \(-0.410953\pi\)
0.276114 + 0.961125i \(0.410953\pi\)
\(278\) −8.51081 −0.510444
\(279\) 1.84644 0.110543
\(280\) 21.0691 1.25912
\(281\) −15.4595 −0.922237 −0.461119 0.887338i \(-0.652552\pi\)
−0.461119 + 0.887338i \(0.652552\pi\)
\(282\) 43.4728 2.58877
\(283\) 13.9620 0.829952 0.414976 0.909832i \(-0.363790\pi\)
0.414976 + 0.909832i \(0.363790\pi\)
\(284\) −35.2027 −2.08889
\(285\) 4.01310 0.237716
\(286\) −0.405455 −0.0239750
\(287\) −38.4791 −2.27135
\(288\) 1.35450 0.0798149
\(289\) 34.7510 2.04417
\(290\) 3.75457 0.220476
\(291\) −16.8080 −0.985305
\(292\) −7.03817 −0.411878
\(293\) −10.1841 −0.594963 −0.297482 0.954728i \(-0.596147\pi\)
−0.297482 + 0.954728i \(0.596147\pi\)
\(294\) −42.5230 −2.47999
\(295\) 16.6634 0.970182
\(296\) 15.9894 0.929364
\(297\) 0.155137 0.00900199
\(298\) 31.2719 1.81153
\(299\) −9.40923 −0.544150
\(300\) −27.4898 −1.58712
\(301\) −25.4307 −1.46580
\(302\) −14.0755 −0.809957
\(303\) 3.12762 0.179677
\(304\) 5.28850 0.303316
\(305\) 4.64447 0.265941
\(306\) −16.5344 −0.945210
\(307\) −0.715150 −0.0408158 −0.0204079 0.999792i \(-0.506496\pi\)
−0.0204079 + 0.999792i \(0.506496\pi\)
\(308\) 0.583222 0.0332321
\(309\) −10.3721 −0.590050
\(310\) −5.56679 −0.316172
\(311\) −19.8097 −1.12330 −0.561652 0.827373i \(-0.689834\pi\)
−0.561652 + 0.827373i \(0.689834\pi\)
\(312\) 39.0789 2.21241
\(313\) −24.6558 −1.39363 −0.696815 0.717251i \(-0.745400\pi\)
−0.696815 + 0.717251i \(0.745400\pi\)
\(314\) 44.4527 2.50861
\(315\) −4.48473 −0.252686
\(316\) −45.6411 −2.56751
\(317\) 15.7692 0.885689 0.442845 0.896598i \(-0.353969\pi\)
0.442845 + 0.896598i \(0.353969\pi\)
\(318\) 42.8645 2.40372
\(319\) 0.0498963 0.00279366
\(320\) −11.4419 −0.639621
\(321\) −4.00318 −0.223436
\(322\) 20.5714 1.14640
\(323\) 12.2555 0.681912
\(324\) −42.1152 −2.33973
\(325\) 15.8299 0.878083
\(326\) −10.7402 −0.594843
\(327\) −19.4590 −1.07609
\(328\) −43.1638 −2.38332
\(329\) 36.0093 1.98526
\(330\) 0.216929 0.0119416
\(331\) 21.9236 1.20503 0.602515 0.798108i \(-0.294165\pi\)
0.602515 + 0.798108i \(0.294165\pi\)
\(332\) −27.8729 −1.52973
\(333\) −3.40348 −0.186509
\(334\) 45.2240 2.47455
\(335\) 6.54672 0.357685
\(336\) −24.5626 −1.34000
\(337\) 12.2221 0.665779 0.332889 0.942966i \(-0.391976\pi\)
0.332889 + 0.942966i \(0.391976\pi\)
\(338\) −15.4393 −0.839788
\(339\) −16.7504 −0.909757
\(340\) 32.7975 1.77869
\(341\) −0.0739798 −0.00400623
\(342\) −3.91562 −0.211732
\(343\) −7.35606 −0.397190
\(344\) −28.5268 −1.53806
\(345\) 5.03419 0.271032
\(346\) −4.65990 −0.250518
\(347\) 16.0200 0.860000 0.430000 0.902829i \(-0.358514\pi\)
0.430000 + 0.902829i \(0.358514\pi\)
\(348\) −10.0172 −0.536980
\(349\) 21.0489 1.12672 0.563362 0.826210i \(-0.309508\pi\)
0.563362 + 0.826210i \(0.309508\pi\)
\(350\) −34.6089 −1.84992
\(351\) 17.9350 0.957301
\(352\) −0.0542699 −0.00289259
\(353\) −20.1480 −1.07237 −0.536185 0.844101i \(-0.680135\pi\)
−0.536185 + 0.844101i \(0.680135\pi\)
\(354\) −67.5726 −3.59144
\(355\) −10.8457 −0.575629
\(356\) 10.7047 0.567348
\(357\) −56.9210 −3.01258
\(358\) 57.5742 3.04289
\(359\) 29.8810 1.57706 0.788529 0.614998i \(-0.210843\pi\)
0.788529 + 0.614998i \(0.210843\pi\)
\(360\) −5.03074 −0.265143
\(361\) −16.0977 −0.847248
\(362\) 31.6781 1.66496
\(363\) −21.8607 −1.14739
\(364\) 67.4247 3.53401
\(365\) −2.16841 −0.113500
\(366\) −18.8340 −0.984468
\(367\) 4.29453 0.224173 0.112086 0.993698i \(-0.464247\pi\)
0.112086 + 0.993698i \(0.464247\pi\)
\(368\) 6.63409 0.345826
\(369\) 9.18778 0.478297
\(370\) 10.2611 0.533448
\(371\) 35.5055 1.84335
\(372\) 14.8523 0.770054
\(373\) 28.1049 1.45522 0.727608 0.685993i \(-0.240632\pi\)
0.727608 + 0.685993i \(0.240632\pi\)
\(374\) 0.662472 0.0342556
\(375\) −20.2476 −1.04558
\(376\) 40.3933 2.08313
\(377\) 5.76838 0.297087
\(378\) −39.2113 −2.01681
\(379\) 23.1014 1.18664 0.593321 0.804966i \(-0.297817\pi\)
0.593321 + 0.804966i \(0.297817\pi\)
\(380\) 7.76697 0.398437
\(381\) −38.6789 −1.98158
\(382\) −7.18842 −0.367791
\(383\) 18.2406 0.932053 0.466027 0.884771i \(-0.345685\pi\)
0.466027 + 0.884771i \(0.345685\pi\)
\(384\) 40.7339 2.07869
\(385\) 0.179686 0.00915767
\(386\) −42.7708 −2.17698
\(387\) 6.07216 0.308665
\(388\) −32.5304 −1.65148
\(389\) 21.7415 1.10234 0.551168 0.834394i \(-0.314182\pi\)
0.551168 + 0.834394i \(0.314182\pi\)
\(390\) 25.0786 1.26990
\(391\) 15.3737 0.777483
\(392\) −39.5108 −1.99560
\(393\) −4.77568 −0.240901
\(394\) −9.55781 −0.481516
\(395\) −14.0617 −0.707521
\(396\) −0.139258 −0.00699796
\(397\) −34.1794 −1.71541 −0.857707 0.514139i \(-0.828112\pi\)
−0.857707 + 0.514139i \(0.828112\pi\)
\(398\) 61.5097 3.08320
\(399\) −13.4798 −0.674834
\(400\) −11.1610 −0.558052
\(401\) −10.9417 −0.546404 −0.273202 0.961957i \(-0.588083\pi\)
−0.273202 + 0.961957i \(0.588083\pi\)
\(402\) −26.5479 −1.32409
\(403\) −8.55261 −0.426036
\(404\) 6.05321 0.301158
\(405\) −12.9754 −0.644752
\(406\) −12.6114 −0.625894
\(407\) 0.136364 0.00675933
\(408\) −63.8509 −3.16109
\(409\) −16.6049 −0.821059 −0.410530 0.911847i \(-0.634656\pi\)
−0.410530 + 0.911847i \(0.634656\pi\)
\(410\) −27.7001 −1.36801
\(411\) −4.15598 −0.204999
\(412\) −20.0743 −0.988988
\(413\) −55.9716 −2.75418
\(414\) −4.91190 −0.241407
\(415\) −8.58745 −0.421542
\(416\) −6.27400 −0.307608
\(417\) 6.99584 0.342588
\(418\) 0.156884 0.00767345
\(419\) −16.5458 −0.808314 −0.404157 0.914690i \(-0.632435\pi\)
−0.404157 + 0.914690i \(0.632435\pi\)
\(420\) −36.0740 −1.76023
\(421\) −23.8031 −1.16009 −0.580047 0.814583i \(-0.696966\pi\)
−0.580047 + 0.814583i \(0.696966\pi\)
\(422\) −3.90762 −0.190220
\(423\) −8.59806 −0.418052
\(424\) 39.8282 1.93423
\(425\) −25.8644 −1.25461
\(426\) 43.9808 2.13088
\(427\) −15.6005 −0.754963
\(428\) −7.74778 −0.374503
\(429\) 0.333282 0.0160910
\(430\) −18.3068 −0.882834
\(431\) −30.7888 −1.48304 −0.741521 0.670929i \(-0.765895\pi\)
−0.741521 + 0.670929i \(0.765895\pi\)
\(432\) −12.6453 −0.608398
\(433\) −13.4275 −0.645285 −0.322642 0.946521i \(-0.604571\pi\)
−0.322642 + 0.946521i \(0.604571\pi\)
\(434\) 18.6986 0.897560
\(435\) −3.08624 −0.147974
\(436\) −37.6611 −1.80364
\(437\) 3.64075 0.174161
\(438\) 8.79321 0.420156
\(439\) 9.28285 0.443046 0.221523 0.975155i \(-0.428897\pi\)
0.221523 + 0.975155i \(0.428897\pi\)
\(440\) 0.201563 0.00960912
\(441\) 8.41021 0.400486
\(442\) 76.5866 3.64285
\(443\) −24.9339 −1.18465 −0.592323 0.805700i \(-0.701789\pi\)
−0.592323 + 0.805700i \(0.701789\pi\)
\(444\) −27.3766 −1.29924
\(445\) 3.29804 0.156342
\(446\) −39.4810 −1.86948
\(447\) −25.7054 −1.21582
\(448\) 38.4327 1.81578
\(449\) 7.49398 0.353663 0.176831 0.984241i \(-0.443415\pi\)
0.176831 + 0.984241i \(0.443415\pi\)
\(450\) 8.26367 0.389553
\(451\) −0.368120 −0.0173341
\(452\) −32.4188 −1.52485
\(453\) 11.5700 0.543607
\(454\) −38.2996 −1.79749
\(455\) 20.7731 0.973856
\(456\) −15.1209 −0.708103
\(457\) −17.7743 −0.831448 −0.415724 0.909491i \(-0.636472\pi\)
−0.415724 + 0.909491i \(0.636472\pi\)
\(458\) −57.2725 −2.67617
\(459\) −29.3040 −1.36779
\(460\) 9.74319 0.454279
\(461\) 0.0813028 0.00378665 0.00189332 0.999998i \(-0.499397\pi\)
0.00189332 + 0.999998i \(0.499397\pi\)
\(462\) −0.728654 −0.0339000
\(463\) 16.8166 0.781533 0.390766 0.920490i \(-0.372210\pi\)
0.390766 + 0.920490i \(0.372210\pi\)
\(464\) −4.06707 −0.188809
\(465\) 4.57587 0.212201
\(466\) 4.94678 0.229155
\(467\) −11.1678 −0.516783 −0.258392 0.966040i \(-0.583192\pi\)
−0.258392 + 0.966040i \(0.583192\pi\)
\(468\) −16.0992 −0.744186
\(469\) −21.9901 −1.01541
\(470\) 25.9221 1.19570
\(471\) −36.5399 −1.68367
\(472\) −62.7860 −2.88996
\(473\) −0.243289 −0.0111864
\(474\) 57.0222 2.61912
\(475\) −6.12511 −0.281039
\(476\) −110.165 −5.04941
\(477\) −8.47776 −0.388170
\(478\) 21.7274 0.993789
\(479\) 13.9707 0.638339 0.319170 0.947698i \(-0.396596\pi\)
0.319170 + 0.947698i \(0.396596\pi\)
\(480\) 3.35675 0.153214
\(481\) 15.7647 0.718809
\(482\) 6.68409 0.304452
\(483\) −16.9096 −0.769413
\(484\) −42.3093 −1.92315
\(485\) −10.0224 −0.455092
\(486\) 23.0676 1.04637
\(487\) 3.31761 0.150335 0.0751677 0.997171i \(-0.476051\pi\)
0.0751677 + 0.997171i \(0.476051\pi\)
\(488\) −17.4999 −0.792181
\(489\) 8.82837 0.399233
\(490\) −25.3558 −1.14546
\(491\) 16.1274 0.727817 0.363909 0.931435i \(-0.381442\pi\)
0.363909 + 0.931435i \(0.381442\pi\)
\(492\) 73.9040 3.33185
\(493\) −9.42495 −0.424478
\(494\) 18.1369 0.816019
\(495\) −0.0429043 −0.00192840
\(496\) 6.03012 0.270760
\(497\) 36.4301 1.63411
\(498\) 34.8233 1.56047
\(499\) 8.39383 0.375759 0.187880 0.982192i \(-0.439839\pi\)
0.187880 + 0.982192i \(0.439839\pi\)
\(500\) −39.1873 −1.75251
\(501\) −37.1739 −1.66081
\(502\) 48.6993 2.17356
\(503\) 32.2495 1.43793 0.718967 0.695044i \(-0.244615\pi\)
0.718967 + 0.695044i \(0.244615\pi\)
\(504\) 16.8980 0.752696
\(505\) 1.86495 0.0829891
\(506\) 0.196801 0.00874889
\(507\) 12.6910 0.563629
\(508\) −74.8592 −3.32134
\(509\) 14.5939 0.646863 0.323432 0.946252i \(-0.395163\pi\)
0.323432 + 0.946252i \(0.395163\pi\)
\(510\) −40.9759 −1.81444
\(511\) 7.28358 0.322206
\(512\) 32.1486 1.42078
\(513\) −6.93966 −0.306394
\(514\) 49.3634 2.17733
\(515\) −6.18473 −0.272532
\(516\) 48.8428 2.15019
\(517\) 0.344492 0.0151507
\(518\) −34.4664 −1.51437
\(519\) 3.83042 0.168137
\(520\) 23.3021 1.02187
\(521\) 3.80211 0.166574 0.0832868 0.996526i \(-0.473458\pi\)
0.0832868 + 0.996526i \(0.473458\pi\)
\(522\) 3.01127 0.131800
\(523\) 15.5976 0.682036 0.341018 0.940057i \(-0.389228\pi\)
0.341018 + 0.940057i \(0.389228\pi\)
\(524\) −9.24287 −0.403777
\(525\) 28.4483 1.24159
\(526\) 69.8604 3.04606
\(527\) 13.9741 0.608721
\(528\) −0.234984 −0.0102264
\(529\) −18.4329 −0.801431
\(530\) 25.5594 1.11023
\(531\) 13.3645 0.579971
\(532\) −26.0889 −1.13110
\(533\) −42.5573 −1.84336
\(534\) −13.3740 −0.578751
\(535\) −2.38703 −0.103200
\(536\) −24.6673 −1.06547
\(537\) −47.3257 −2.04225
\(538\) −64.7480 −2.79148
\(539\) −0.336965 −0.0145141
\(540\) −18.5716 −0.799194
\(541\) −27.9575 −1.20199 −0.600994 0.799253i \(-0.705229\pi\)
−0.600994 + 0.799253i \(0.705229\pi\)
\(542\) −55.8293 −2.39807
\(543\) −26.0392 −1.11745
\(544\) 10.2511 0.439511
\(545\) −11.6031 −0.497023
\(546\) −84.2377 −3.60504
\(547\) −39.1298 −1.67307 −0.836534 0.547915i \(-0.815422\pi\)
−0.836534 + 0.547915i \(0.815422\pi\)
\(548\) −8.04349 −0.343601
\(549\) 3.72499 0.158979
\(550\) −0.331094 −0.0141179
\(551\) −2.23198 −0.0950855
\(552\) −18.9683 −0.807343
\(553\) 47.2325 2.00853
\(554\) −22.2238 −0.944198
\(555\) −8.43455 −0.358027
\(556\) 13.5398 0.574215
\(557\) 15.8261 0.670573 0.335286 0.942116i \(-0.391167\pi\)
0.335286 + 0.942116i \(0.391167\pi\)
\(558\) −4.46472 −0.189007
\(559\) −28.1259 −1.18960
\(560\) −14.6463 −0.618919
\(561\) −0.544548 −0.0229908
\(562\) 37.3814 1.57684
\(563\) −18.1927 −0.766731 −0.383366 0.923597i \(-0.625235\pi\)
−0.383366 + 0.923597i \(0.625235\pi\)
\(564\) −69.1605 −2.91218
\(565\) −9.98800 −0.420198
\(566\) −33.7602 −1.41905
\(567\) 43.5836 1.83034
\(568\) 40.8654 1.71467
\(569\) 13.7968 0.578394 0.289197 0.957270i \(-0.406612\pi\)
0.289197 + 0.957270i \(0.406612\pi\)
\(570\) −9.70375 −0.406445
\(571\) −16.6615 −0.697261 −0.348630 0.937260i \(-0.613353\pi\)
−0.348630 + 0.937260i \(0.613353\pi\)
\(572\) 0.645035 0.0269703
\(573\) 5.90884 0.246845
\(574\) 93.0431 3.88354
\(575\) −7.68357 −0.320427
\(576\) −9.17671 −0.382363
\(577\) −0.258446 −0.0107592 −0.00537961 0.999986i \(-0.501712\pi\)
−0.00537961 + 0.999986i \(0.501712\pi\)
\(578\) −84.0284 −3.49512
\(579\) 35.1574 1.46109
\(580\) −5.97312 −0.248020
\(581\) 28.8448 1.19668
\(582\) 40.6421 1.68467
\(583\) 0.339672 0.0140678
\(584\) 8.17033 0.338091
\(585\) −4.96005 −0.205073
\(586\) 24.6254 1.01727
\(587\) −28.0773 −1.15887 −0.579437 0.815017i \(-0.696728\pi\)
−0.579437 + 0.815017i \(0.696728\pi\)
\(588\) 67.6495 2.78982
\(589\) 3.30929 0.136357
\(590\) −40.2924 −1.65881
\(591\) 7.85647 0.323172
\(592\) −11.1151 −0.456828
\(593\) −16.4295 −0.674677 −0.337339 0.941383i \(-0.609527\pi\)
−0.337339 + 0.941383i \(0.609527\pi\)
\(594\) −0.375125 −0.0153916
\(595\) −33.9411 −1.39145
\(596\) −49.7503 −2.03785
\(597\) −50.5606 −2.06931
\(598\) 22.7517 0.930385
\(599\) 36.6459 1.49731 0.748656 0.662958i \(-0.230699\pi\)
0.748656 + 0.662958i \(0.230699\pi\)
\(600\) 31.9118 1.30279
\(601\) −8.53950 −0.348334 −0.174167 0.984716i \(-0.555723\pi\)
−0.174167 + 0.984716i \(0.555723\pi\)
\(602\) 61.4917 2.50622
\(603\) 5.25065 0.213823
\(604\) 22.3927 0.911145
\(605\) −13.0352 −0.529955
\(606\) −7.56263 −0.307211
\(607\) 6.19355 0.251388 0.125694 0.992069i \(-0.459884\pi\)
0.125694 + 0.992069i \(0.459884\pi\)
\(608\) 2.42762 0.0984530
\(609\) 10.3665 0.420072
\(610\) −11.2304 −0.454706
\(611\) 39.8258 1.61118
\(612\) 26.3045 1.06330
\(613\) −16.3029 −0.658467 −0.329234 0.944248i \(-0.606790\pi\)
−0.329234 + 0.944248i \(0.606790\pi\)
\(614\) 1.72924 0.0697866
\(615\) 22.7693 0.918147
\(616\) −0.677039 −0.0272787
\(617\) −25.9262 −1.04375 −0.521874 0.853023i \(-0.674767\pi\)
−0.521874 + 0.853023i \(0.674767\pi\)
\(618\) 25.0800 1.00886
\(619\) 36.7414 1.47676 0.738381 0.674384i \(-0.235591\pi\)
0.738381 + 0.674384i \(0.235591\pi\)
\(620\) 8.85616 0.355672
\(621\) −8.70537 −0.349335
\(622\) 47.9002 1.92062
\(623\) −11.0780 −0.443829
\(624\) −27.1659 −1.08751
\(625\) 5.90350 0.236140
\(626\) 59.6182 2.38282
\(627\) −0.128958 −0.00515008
\(628\) −70.7194 −2.82201
\(629\) −25.7580 −1.02704
\(630\) 10.8442 0.432042
\(631\) 46.8575 1.86537 0.932684 0.360695i \(-0.117460\pi\)
0.932684 + 0.360695i \(0.117460\pi\)
\(632\) 52.9829 2.10755
\(633\) 3.21204 0.127667
\(634\) −38.1303 −1.51435
\(635\) −23.0636 −0.915251
\(636\) −68.1928 −2.70402
\(637\) −38.9557 −1.54348
\(638\) −0.120650 −0.00477658
\(639\) −8.69853 −0.344109
\(640\) 24.2890 0.960107
\(641\) 20.8636 0.824062 0.412031 0.911170i \(-0.364819\pi\)
0.412031 + 0.911170i \(0.364819\pi\)
\(642\) 9.67976 0.382030
\(643\) −8.77176 −0.345925 −0.172962 0.984928i \(-0.555334\pi\)
−0.172962 + 0.984928i \(0.555334\pi\)
\(644\) −32.7269 −1.28962
\(645\) 15.0481 0.592519
\(646\) −29.6339 −1.16593
\(647\) 27.5253 1.08213 0.541066 0.840980i \(-0.318021\pi\)
0.541066 + 0.840980i \(0.318021\pi\)
\(648\) 48.8898 1.92057
\(649\) −0.535466 −0.0210189
\(650\) −38.2769 −1.50134
\(651\) −15.3701 −0.602403
\(652\) 17.0865 0.669157
\(653\) −40.0024 −1.56541 −0.782707 0.622390i \(-0.786162\pi\)
−0.782707 + 0.622390i \(0.786162\pi\)
\(654\) 47.0523 1.83989
\(655\) −2.84766 −0.111267
\(656\) 30.0056 1.17152
\(657\) −1.73912 −0.0678496
\(658\) −87.0711 −3.39439
\(659\) 7.53803 0.293640 0.146820 0.989163i \(-0.453096\pi\)
0.146820 + 0.989163i \(0.453096\pi\)
\(660\) −0.345111 −0.0134334
\(661\) −11.3506 −0.441487 −0.220744 0.975332i \(-0.570848\pi\)
−0.220744 + 0.975332i \(0.570848\pi\)
\(662\) −53.0116 −2.06035
\(663\) −62.9538 −2.44492
\(664\) 32.3566 1.25568
\(665\) −8.03779 −0.311692
\(666\) 8.22966 0.318893
\(667\) −2.79988 −0.108412
\(668\) −71.9465 −2.78370
\(669\) 32.4531 1.25471
\(670\) −15.8301 −0.611569
\(671\) −0.149246 −0.00576159
\(672\) −11.2752 −0.434949
\(673\) 2.26081 0.0871479 0.0435740 0.999050i \(-0.486126\pi\)
0.0435740 + 0.999050i \(0.486126\pi\)
\(674\) −29.5532 −1.13835
\(675\) 14.6457 0.563714
\(676\) 24.5623 0.944703
\(677\) 14.0653 0.540572 0.270286 0.962780i \(-0.412882\pi\)
0.270286 + 0.962780i \(0.412882\pi\)
\(678\) 40.5028 1.55550
\(679\) 33.6646 1.29193
\(680\) −38.0733 −1.46004
\(681\) 31.4821 1.20640
\(682\) 0.178884 0.00684984
\(683\) −23.4525 −0.897384 −0.448692 0.893686i \(-0.648110\pi\)
−0.448692 + 0.893686i \(0.648110\pi\)
\(684\) 6.22932 0.238184
\(685\) −2.47814 −0.0946849
\(686\) 17.7871 0.679113
\(687\) 47.0777 1.79612
\(688\) 19.8305 0.756032
\(689\) 39.2685 1.49601
\(690\) −12.1727 −0.463409
\(691\) 18.8679 0.717770 0.358885 0.933382i \(-0.383157\pi\)
0.358885 + 0.933382i \(0.383157\pi\)
\(692\) 7.41340 0.281815
\(693\) 0.144113 0.00547441
\(694\) −38.7367 −1.47042
\(695\) 4.17151 0.158234
\(696\) 11.6286 0.440781
\(697\) 69.5343 2.63380
\(698\) −50.8967 −1.92647
\(699\) −4.06623 −0.153799
\(700\) 55.0590 2.08103
\(701\) 11.0737 0.418248 0.209124 0.977889i \(-0.432939\pi\)
0.209124 + 0.977889i \(0.432939\pi\)
\(702\) −43.3672 −1.63679
\(703\) −6.09990 −0.230062
\(704\) 0.367676 0.0138573
\(705\) −21.3079 −0.802500
\(706\) 48.7182 1.83353
\(707\) −6.26427 −0.235592
\(708\) 107.501 4.04012
\(709\) 13.4467 0.505003 0.252501 0.967597i \(-0.418747\pi\)
0.252501 + 0.967597i \(0.418747\pi\)
\(710\) 26.2250 0.984208
\(711\) −11.2779 −0.422953
\(712\) −12.4267 −0.465709
\(713\) 4.15130 0.155467
\(714\) 137.636 5.15089
\(715\) 0.198731 0.00743210
\(716\) −91.5944 −3.42304
\(717\) −17.8598 −0.666987
\(718\) −72.2527 −2.69645
\(719\) 23.6692 0.882713 0.441356 0.897332i \(-0.354497\pi\)
0.441356 + 0.897332i \(0.354497\pi\)
\(720\) 3.49714 0.130331
\(721\) 20.7742 0.773672
\(722\) 38.9245 1.44862
\(723\) −5.49429 −0.204335
\(724\) −50.3964 −1.87297
\(725\) 4.71046 0.174942
\(726\) 52.8595 1.96180
\(727\) −7.57287 −0.280862 −0.140431 0.990090i \(-0.544849\pi\)
−0.140431 + 0.990090i \(0.544849\pi\)
\(728\) −78.2706 −2.90090
\(729\) 13.8828 0.514178
\(730\) 5.24325 0.194061
\(731\) 45.9549 1.69970
\(732\) 29.9628 1.10746
\(733\) −50.4106 −1.86196 −0.930980 0.365071i \(-0.881045\pi\)
−0.930980 + 0.365071i \(0.881045\pi\)
\(734\) −10.3842 −0.383290
\(735\) 20.8423 0.768780
\(736\) 3.04530 0.112251
\(737\) −0.210374 −0.00774921
\(738\) −22.2162 −0.817790
\(739\) −24.1820 −0.889550 −0.444775 0.895642i \(-0.646716\pi\)
−0.444775 + 0.895642i \(0.646716\pi\)
\(740\) −16.3243 −0.600092
\(741\) −14.9085 −0.547676
\(742\) −85.8528 −3.15176
\(743\) 11.0223 0.404370 0.202185 0.979347i \(-0.435196\pi\)
0.202185 + 0.979347i \(0.435196\pi\)
\(744\) −17.2414 −0.632100
\(745\) −15.3277 −0.561563
\(746\) −67.9581 −2.48812
\(747\) −6.88737 −0.251996
\(748\) −1.05392 −0.0385352
\(749\) 8.01793 0.292969
\(750\) 48.9591 1.78773
\(751\) 23.9784 0.874984 0.437492 0.899222i \(-0.355867\pi\)
0.437492 + 0.899222i \(0.355867\pi\)
\(752\) −28.0797 −1.02396
\(753\) −40.0306 −1.45879
\(754\) −13.9480 −0.507958
\(755\) 6.89902 0.251081
\(756\) 62.3810 2.26878
\(757\) 28.3252 1.02950 0.514749 0.857341i \(-0.327885\pi\)
0.514749 + 0.857341i \(0.327885\pi\)
\(758\) −55.8597 −2.02891
\(759\) −0.161770 −0.00587187
\(760\) −9.01637 −0.327058
\(761\) 47.1208 1.70813 0.854064 0.520168i \(-0.174131\pi\)
0.854064 + 0.520168i \(0.174131\pi\)
\(762\) 93.5261 3.38809
\(763\) 38.9743 1.41096
\(764\) 11.4360 0.413740
\(765\) 8.10422 0.293009
\(766\) −44.1062 −1.59362
\(767\) −61.9038 −2.23522
\(768\) −60.1180 −2.16932
\(769\) −28.4705 −1.02667 −0.513337 0.858187i \(-0.671591\pi\)
−0.513337 + 0.858187i \(0.671591\pi\)
\(770\) −0.434485 −0.0156577
\(771\) −40.5765 −1.46133
\(772\) 68.0438 2.44895
\(773\) 33.5823 1.20787 0.603936 0.797033i \(-0.293598\pi\)
0.603936 + 0.797033i \(0.293598\pi\)
\(774\) −14.6826 −0.527755
\(775\) −6.98405 −0.250875
\(776\) 37.7632 1.35562
\(777\) 28.3312 1.01638
\(778\) −52.5712 −1.88477
\(779\) 16.4669 0.589986
\(780\) −39.8973 −1.42855
\(781\) 0.348517 0.0124709
\(782\) −37.1739 −1.32934
\(783\) 5.33688 0.190724
\(784\) 27.4662 0.980935
\(785\) −21.7881 −0.777652
\(786\) 11.5477 0.411892
\(787\) −10.5391 −0.375677 −0.187838 0.982200i \(-0.560148\pi\)
−0.187838 + 0.982200i \(0.560148\pi\)
\(788\) 15.2054 0.541672
\(789\) −57.4249 −2.04438
\(790\) 34.0014 1.20972
\(791\) 33.5492 1.19287
\(792\) 0.161659 0.00574429
\(793\) −17.2540 −0.612706
\(794\) 82.6463 2.93301
\(795\) −21.0097 −0.745138
\(796\) −97.8553 −3.46839
\(797\) −27.0168 −0.956984 −0.478492 0.878092i \(-0.658816\pi\)
−0.478492 + 0.878092i \(0.658816\pi\)
\(798\) 32.5944 1.15383
\(799\) −65.0713 −2.30206
\(800\) −5.12334 −0.181137
\(801\) 2.64512 0.0934607
\(802\) 26.4573 0.934239
\(803\) 0.0696801 0.00245896
\(804\) 42.2348 1.48951
\(805\) −10.0829 −0.355376
\(806\) 20.6803 0.728434
\(807\) 53.2225 1.87352
\(808\) −7.02692 −0.247206
\(809\) 31.4360 1.10523 0.552615 0.833437i \(-0.313630\pi\)
0.552615 + 0.833437i \(0.313630\pi\)
\(810\) 31.3747 1.10239
\(811\) −49.2678 −1.73003 −0.865013 0.501749i \(-0.832690\pi\)
−0.865013 + 0.501749i \(0.832690\pi\)
\(812\) 20.0634 0.704087
\(813\) 45.8914 1.60948
\(814\) −0.329731 −0.0115571
\(815\) 5.26421 0.184397
\(816\) 44.3863 1.55383
\(817\) 10.8829 0.380743
\(818\) 40.1509 1.40384
\(819\) 16.6606 0.582167
\(820\) 44.0678 1.53891
\(821\) 37.4976 1.30868 0.654338 0.756202i \(-0.272947\pi\)
0.654338 + 0.756202i \(0.272947\pi\)
\(822\) 10.0492 0.350507
\(823\) 8.06303 0.281060 0.140530 0.990076i \(-0.455119\pi\)
0.140530 + 0.990076i \(0.455119\pi\)
\(824\) 23.3034 0.811813
\(825\) 0.272158 0.00947531
\(826\) 135.340 4.70909
\(827\) −11.8482 −0.412002 −0.206001 0.978552i \(-0.566045\pi\)
−0.206001 + 0.978552i \(0.566045\pi\)
\(828\) 7.81430 0.271566
\(829\) 4.63772 0.161075 0.0805374 0.996752i \(-0.474336\pi\)
0.0805374 + 0.996752i \(0.474336\pi\)
\(830\) 20.7646 0.720750
\(831\) 18.2678 0.633704
\(832\) 42.5061 1.47363
\(833\) 63.6496 2.20533
\(834\) −16.9161 −0.585755
\(835\) −22.1662 −0.767093
\(836\) −0.249586 −0.00863210
\(837\) −7.91283 −0.273507
\(838\) 40.0079 1.38205
\(839\) −29.4772 −1.01767 −0.508833 0.860865i \(-0.669923\pi\)
−0.508833 + 0.860865i \(0.669923\pi\)
\(840\) 41.8769 1.44489
\(841\) −27.2835 −0.940811
\(842\) 57.5563 1.98352
\(843\) −30.7273 −1.05830
\(844\) 6.21660 0.213984
\(845\) 7.56746 0.260329
\(846\) 20.7903 0.714784
\(847\) 43.7845 1.50445
\(848\) −27.6868 −0.950768
\(849\) 27.7507 0.952402
\(850\) 62.5406 2.14512
\(851\) −7.65195 −0.262305
\(852\) −69.9687 −2.39709
\(853\) −58.0575 −1.98785 −0.993926 0.110051i \(-0.964898\pi\)
−0.993926 + 0.110051i \(0.964898\pi\)
\(854\) 37.7223 1.29083
\(855\) 1.91921 0.0656356
\(856\) 8.99409 0.307412
\(857\) 38.3131 1.30875 0.654376 0.756169i \(-0.272931\pi\)
0.654376 + 0.756169i \(0.272931\pi\)
\(858\) −0.805880 −0.0275123
\(859\) 18.9783 0.647531 0.323766 0.946137i \(-0.395051\pi\)
0.323766 + 0.946137i \(0.395051\pi\)
\(860\) 29.1242 0.993127
\(861\) −76.4809 −2.60646
\(862\) 74.4477 2.53570
\(863\) −24.9369 −0.848861 −0.424431 0.905460i \(-0.639526\pi\)
−0.424431 + 0.905460i \(0.639526\pi\)
\(864\) −5.80467 −0.197479
\(865\) 2.28402 0.0776589
\(866\) 32.4679 1.10330
\(867\) 69.0709 2.34577
\(868\) −29.7474 −1.00969
\(869\) 0.451861 0.0153284
\(870\) 7.46257 0.253005
\(871\) −24.3207 −0.824076
\(872\) 43.7193 1.48052
\(873\) −8.03821 −0.272052
\(874\) −8.80338 −0.297779
\(875\) 40.5537 1.37097
\(876\) −13.9890 −0.472646
\(877\) 54.2292 1.83119 0.915594 0.402104i \(-0.131721\pi\)
0.915594 + 0.402104i \(0.131721\pi\)
\(878\) −22.4461 −0.757518
\(879\) −20.2419 −0.682744
\(880\) −0.140117 −0.00472336
\(881\) −6.50103 −0.219025 −0.109513 0.993985i \(-0.534929\pi\)
−0.109513 + 0.993985i \(0.534929\pi\)
\(882\) −20.3360 −0.684750
\(883\) 45.5897 1.53422 0.767108 0.641518i \(-0.221695\pi\)
0.767108 + 0.641518i \(0.221695\pi\)
\(884\) −121.841 −4.09796
\(885\) 33.1202 1.11332
\(886\) 60.2907 2.02550
\(887\) −2.49760 −0.0838613 −0.0419306 0.999121i \(-0.513351\pi\)
−0.0419306 + 0.999121i \(0.513351\pi\)
\(888\) 31.7805 1.06648
\(889\) 77.4694 2.59824
\(890\) −7.97472 −0.267313
\(891\) 0.416953 0.0139685
\(892\) 62.8099 2.10303
\(893\) −15.4099 −0.515674
\(894\) 62.1560 2.07881
\(895\) −28.2196 −0.943276
\(896\) −81.5855 −2.72558
\(897\) −18.7018 −0.624433
\(898\) −18.1206 −0.604691
\(899\) −2.54498 −0.0848798
\(900\) −13.1466 −0.438220
\(901\) −64.1608 −2.13751
\(902\) 0.890119 0.0296377
\(903\) −50.5459 −1.68206
\(904\) 37.6337 1.25168
\(905\) −15.5268 −0.516128
\(906\) −27.9765 −0.929457
\(907\) −43.5818 −1.44711 −0.723554 0.690267i \(-0.757493\pi\)
−0.723554 + 0.690267i \(0.757493\pi\)
\(908\) 60.9305 2.02205
\(909\) 1.49574 0.0496106
\(910\) −50.2296 −1.66509
\(911\) 24.3188 0.805719 0.402859 0.915262i \(-0.368016\pi\)
0.402859 + 0.915262i \(0.368016\pi\)
\(912\) 10.5114 0.348067
\(913\) 0.275951 0.00913264
\(914\) 42.9786 1.42161
\(915\) 9.23133 0.305178
\(916\) 91.1143 3.01050
\(917\) 9.56515 0.315869
\(918\) 70.8575 2.33865
\(919\) 34.0017 1.12161 0.560806 0.827947i \(-0.310491\pi\)
0.560806 + 0.827947i \(0.310491\pi\)
\(920\) −11.3105 −0.372895
\(921\) −1.42143 −0.0468377
\(922\) −0.196591 −0.00647439
\(923\) 40.2912 1.32620
\(924\) 1.15921 0.0381352
\(925\) 12.8735 0.423277
\(926\) −40.6628 −1.33626
\(927\) −4.96032 −0.162918
\(928\) −1.86694 −0.0612852
\(929\) 4.80524 0.157655 0.0788274 0.996888i \(-0.474882\pi\)
0.0788274 + 0.996888i \(0.474882\pi\)
\(930\) −11.0645 −0.362820
\(931\) 15.0733 0.494006
\(932\) −7.86979 −0.257784
\(933\) −39.3737 −1.28904
\(934\) 27.0039 0.883593
\(935\) −0.324705 −0.0106190
\(936\) 18.6889 0.610867
\(937\) −40.1814 −1.31267 −0.656335 0.754470i \(-0.727894\pi\)
−0.656335 + 0.754470i \(0.727894\pi\)
\(938\) 53.1724 1.73614
\(939\) −49.0058 −1.59924
\(940\) −41.2393 −1.34508
\(941\) −48.6888 −1.58721 −0.793605 0.608434i \(-0.791798\pi\)
−0.793605 + 0.608434i \(0.791798\pi\)
\(942\) 88.3540 2.87873
\(943\) 20.6566 0.672673
\(944\) 43.6460 1.42056
\(945\) 19.2191 0.625199
\(946\) 0.588276 0.0191265
\(947\) 29.2771 0.951378 0.475689 0.879614i \(-0.342199\pi\)
0.475689 + 0.879614i \(0.342199\pi\)
\(948\) −90.7161 −2.94632
\(949\) 8.05553 0.261494
\(950\) 14.8106 0.480520
\(951\) 31.3429 1.01636
\(952\) 127.886 4.14482
\(953\) 31.2574 1.01253 0.506264 0.862379i \(-0.331026\pi\)
0.506264 + 0.862379i \(0.331026\pi\)
\(954\) 20.4994 0.663691
\(955\) 3.52335 0.114013
\(956\) −34.5660 −1.11794
\(957\) 0.0991738 0.00320583
\(958\) −33.7815 −1.09143
\(959\) 8.32395 0.268794
\(960\) −22.7419 −0.733991
\(961\) −27.2266 −0.878279
\(962\) −38.1194 −1.22902
\(963\) −1.91447 −0.0616928
\(964\) −10.6337 −0.342487
\(965\) 20.9638 0.674848
\(966\) 40.8876 1.31554
\(967\) −2.36055 −0.0759102 −0.0379551 0.999279i \(-0.512084\pi\)
−0.0379551 + 0.999279i \(0.512084\pi\)
\(968\) 49.1151 1.57862
\(969\) 24.3589 0.782521
\(970\) 24.2343 0.778115
\(971\) −23.2067 −0.744739 −0.372369 0.928085i \(-0.621455\pi\)
−0.372369 + 0.928085i \(0.621455\pi\)
\(972\) −36.6981 −1.17709
\(973\) −14.0119 −0.449200
\(974\) −8.02204 −0.257043
\(975\) 31.4634 1.00764
\(976\) 12.1651 0.389396
\(977\) −45.7548 −1.46383 −0.731914 0.681398i \(-0.761373\pi\)
−0.731914 + 0.681398i \(0.761373\pi\)
\(978\) −21.3471 −0.682606
\(979\) −0.105980 −0.00338714
\(980\) 40.3383 1.28856
\(981\) −9.30601 −0.297118
\(982\) −38.9962 −1.24442
\(983\) −40.9871 −1.30729 −0.653643 0.756803i \(-0.726760\pi\)
−0.653643 + 0.756803i \(0.726760\pi\)
\(984\) −85.7922 −2.73496
\(985\) 4.68469 0.149267
\(986\) 22.7897 0.725771
\(987\) 71.5720 2.27816
\(988\) −28.8539 −0.917965
\(989\) 13.6519 0.434105
\(990\) 0.103743 0.00329718
\(991\) 3.65932 0.116242 0.0581211 0.998310i \(-0.481489\pi\)
0.0581211 + 0.998310i \(0.481489\pi\)
\(992\) 2.76805 0.0878857
\(993\) 43.5752 1.38282
\(994\) −88.0886 −2.79400
\(995\) −30.1485 −0.955771
\(996\) −55.4002 −1.75542
\(997\) −33.7286 −1.06819 −0.534097 0.845423i \(-0.679348\pi\)
−0.534097 + 0.845423i \(0.679348\pi\)
\(998\) −20.2964 −0.642472
\(999\) 14.5854 0.461463
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 \(a_p\))