Properties

Label 4009.2.a.c.1.7
Level 4009
Weight 2
Character 4009.1
Self dual Yes
Analytic conductor 32.012
Analytic rank 1
Dimension 71
CM No

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Newspace parameters

Level: \( N \) = \( 4009 = 19 \cdot 211 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4009.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0120261703\)
Analytic rank: \(1\)
Dimension: \(71\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) = 4009.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.51184 q^{2}\) \(-2.51408 q^{3}\) \(+4.30932 q^{4}\) \(+3.86977 q^{5}\) \(+6.31496 q^{6}\) \(+2.24136 q^{7}\) \(-5.80064 q^{8}\) \(+3.32060 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.51184 q^{2}\) \(-2.51408 q^{3}\) \(+4.30932 q^{4}\) \(+3.86977 q^{5}\) \(+6.31496 q^{6}\) \(+2.24136 q^{7}\) \(-5.80064 q^{8}\) \(+3.32060 q^{9}\) \(-9.72023 q^{10}\) \(-3.66849 q^{11}\) \(-10.8340 q^{12}\) \(-4.71240 q^{13}\) \(-5.62993 q^{14}\) \(-9.72891 q^{15}\) \(+5.95162 q^{16}\) \(+5.95455 q^{17}\) \(-8.34081 q^{18}\) \(+1.00000 q^{19}\) \(+16.6761 q^{20}\) \(-5.63496 q^{21}\) \(+9.21464 q^{22}\) \(-5.33707 q^{23}\) \(+14.5833 q^{24}\) \(+9.97511 q^{25}\) \(+11.8368 q^{26}\) \(-0.806021 q^{27}\) \(+9.65875 q^{28}\) \(-4.89281 q^{29}\) \(+24.4374 q^{30}\) \(+1.00382 q^{31}\) \(-3.34822 q^{32}\) \(+9.22288 q^{33}\) \(-14.9569 q^{34}\) \(+8.67355 q^{35}\) \(+14.3096 q^{36}\) \(+5.73851 q^{37}\) \(-2.51184 q^{38}\) \(+11.8474 q^{39}\) \(-22.4472 q^{40}\) \(-8.57893 q^{41}\) \(+14.1541 q^{42}\) \(-1.69839 q^{43}\) \(-15.8087 q^{44}\) \(+12.8500 q^{45}\) \(+13.4058 q^{46}\) \(+0.701681 q^{47}\) \(-14.9629 q^{48}\) \(-1.97630 q^{49}\) \(-25.0559 q^{50}\) \(-14.9702 q^{51}\) \(-20.3073 q^{52}\) \(+0.437181 q^{53}\) \(+2.02459 q^{54}\) \(-14.1962 q^{55}\) \(-13.0013 q^{56}\) \(-2.51408 q^{57}\) \(+12.2899 q^{58}\) \(+13.5962 q^{59}\) \(-41.9250 q^{60}\) \(-0.0150536 q^{61}\) \(-2.52144 q^{62}\) \(+7.44267 q^{63}\) \(-3.49307 q^{64}\) \(-18.2359 q^{65}\) \(-23.1664 q^{66}\) \(+1.84947 q^{67}\) \(+25.6601 q^{68}\) \(+13.4178 q^{69}\) \(-21.7865 q^{70}\) \(-13.3069 q^{71}\) \(-19.2616 q^{72}\) \(-8.08633 q^{73}\) \(-14.4142 q^{74}\) \(-25.0782 q^{75}\) \(+4.30932 q^{76}\) \(-8.22241 q^{77}\) \(-29.7586 q^{78}\) \(-4.80577 q^{79}\) \(+23.0314 q^{80}\) \(-7.93541 q^{81}\) \(+21.5489 q^{82}\) \(-15.3828 q^{83}\) \(-24.2829 q^{84}\) \(+23.0427 q^{85}\) \(+4.26607 q^{86}\) \(+12.3009 q^{87}\) \(+21.2796 q^{88}\) \(+8.34046 q^{89}\) \(-32.2770 q^{90}\) \(-10.5622 q^{91}\) \(-22.9992 q^{92}\) \(-2.52369 q^{93}\) \(-1.76251 q^{94}\) \(+3.86977 q^{95}\) \(+8.41769 q^{96}\) \(+0.165235 q^{97}\) \(+4.96414 q^{98}\) \(-12.1816 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(71q \) \(\mathstrut -\mathstrut 15q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 18q^{5} \) \(\mathstrut -\mathstrut 9q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 63q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(71q \) \(\mathstrut -\mathstrut 15q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 18q^{5} \) \(\mathstrut -\mathstrut 9q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 63q^{9} \) \(\mathstrut -\mathstrut 10q^{10} \) \(\mathstrut -\mathstrut 52q^{11} \) \(\mathstrut -\mathstrut 9q^{12} \) \(\mathstrut -\mathstrut 15q^{13} \) \(\mathstrut -\mathstrut 53q^{14} \) \(\mathstrut -\mathstrut 33q^{15} \) \(\mathstrut +\mathstrut 53q^{16} \) \(\mathstrut -\mathstrut 10q^{17} \) \(\mathstrut -\mathstrut 35q^{18} \) \(\mathstrut +\mathstrut 71q^{19} \) \(\mathstrut -\mathstrut 33q^{20} \) \(\mathstrut -\mathstrut 38q^{21} \) \(\mathstrut -\mathstrut 6q^{22} \) \(\mathstrut -\mathstrut 65q^{23} \) \(\mathstrut -\mathstrut 30q^{24} \) \(\mathstrut +\mathstrut 51q^{25} \) \(\mathstrut -\mathstrut 4q^{26} \) \(\mathstrut -\mathstrut 23q^{27} \) \(\mathstrut -\mathstrut 29q^{28} \) \(\mathstrut -\mathstrut 97q^{29} \) \(\mathstrut -\mathstrut 27q^{30} \) \(\mathstrut -\mathstrut 53q^{31} \) \(\mathstrut -\mathstrut 78q^{32} \) \(\mathstrut -\mathstrut 17q^{33} \) \(\mathstrut -\mathstrut 24q^{34} \) \(\mathstrut -\mathstrut 38q^{35} \) \(\mathstrut +\mathstrut 24q^{36} \) \(\mathstrut -\mathstrut 33q^{37} \) \(\mathstrut -\mathstrut 15q^{38} \) \(\mathstrut -\mathstrut 86q^{39} \) \(\mathstrut +\mathstrut 25q^{40} \) \(\mathstrut -\mathstrut 69q^{41} \) \(\mathstrut +\mathstrut 64q^{42} \) \(\mathstrut -\mathstrut 10q^{43} \) \(\mathstrut -\mathstrut 94q^{44} \) \(\mathstrut -\mathstrut 34q^{45} \) \(\mathstrut -\mathstrut 6q^{46} \) \(\mathstrut -\mathstrut 37q^{47} \) \(\mathstrut -\mathstrut q^{48} \) \(\mathstrut +\mathstrut 74q^{49} \) \(\mathstrut -\mathstrut 41q^{50} \) \(\mathstrut -\mathstrut 46q^{51} \) \(\mathstrut -\mathstrut 30q^{52} \) \(\mathstrut -\mathstrut 50q^{53} \) \(\mathstrut -\mathstrut 17q^{54} \) \(\mathstrut -\mathstrut 30q^{55} \) \(\mathstrut -\mathstrut 116q^{56} \) \(\mathstrut -\mathstrut 8q^{57} \) \(\mathstrut +\mathstrut 11q^{58} \) \(\mathstrut -\mathstrut 93q^{59} \) \(\mathstrut -\mathstrut 56q^{60} \) \(\mathstrut -\mathstrut 18q^{61} \) \(\mathstrut -\mathstrut q^{62} \) \(\mathstrut -\mathstrut 84q^{63} \) \(\mathstrut +\mathstrut 93q^{64} \) \(\mathstrut -\mathstrut 78q^{65} \) \(\mathstrut -\mathstrut 53q^{66} \) \(\mathstrut -\mathstrut 5q^{67} \) \(\mathstrut -\mathstrut 9q^{68} \) \(\mathstrut -\mathstrut 69q^{69} \) \(\mathstrut -\mathstrut 10q^{70} \) \(\mathstrut -\mathstrut 221q^{71} \) \(\mathstrut -\mathstrut 73q^{72} \) \(\mathstrut -\mathstrut 34q^{73} \) \(\mathstrut -\mathstrut 58q^{74} \) \(\mathstrut -\mathstrut 70q^{75} \) \(\mathstrut +\mathstrut 69q^{76} \) \(\mathstrut -\mathstrut 2q^{77} \) \(\mathstrut +\mathstrut 7q^{78} \) \(\mathstrut -\mathstrut 68q^{79} \) \(\mathstrut -\mathstrut 71q^{80} \) \(\mathstrut +\mathstrut 39q^{81} \) \(\mathstrut +\mathstrut 26q^{82} \) \(\mathstrut -\mathstrut 45q^{83} \) \(\mathstrut -\mathstrut 10q^{84} \) \(\mathstrut -\mathstrut 44q^{85} \) \(\mathstrut -\mathstrut 80q^{86} \) \(\mathstrut -\mathstrut 7q^{87} \) \(\mathstrut -\mathstrut 46q^{88} \) \(\mathstrut -\mathstrut 143q^{89} \) \(\mathstrut +\mathstrut 41q^{90} \) \(\mathstrut -\mathstrut 30q^{91} \) \(\mathstrut -\mathstrut 46q^{92} \) \(\mathstrut +\mathstrut 32q^{93} \) \(\mathstrut +\mathstrut 41q^{94} \) \(\mathstrut -\mathstrut 18q^{95} \) \(\mathstrut -\mathstrut 140q^{96} \) \(\mathstrut -\mathstrut 18q^{97} \) \(\mathstrut -\mathstrut 97q^{98} \) \(\mathstrut -\mathstrut 142q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.51184 −1.77614 −0.888068 0.459711i \(-0.847953\pi\)
−0.888068 + 0.459711i \(0.847953\pi\)
\(3\) −2.51408 −1.45151 −0.725753 0.687956i \(-0.758508\pi\)
−0.725753 + 0.687956i \(0.758508\pi\)
\(4\) 4.30932 2.15466
\(5\) 3.86977 1.73061 0.865307 0.501243i \(-0.167124\pi\)
0.865307 + 0.501243i \(0.167124\pi\)
\(6\) 6.31496 2.57807
\(7\) 2.24136 0.847155 0.423578 0.905860i \(-0.360774\pi\)
0.423578 + 0.905860i \(0.360774\pi\)
\(8\) −5.80064 −2.05084
\(9\) 3.32060 1.10687
\(10\) −9.72023 −3.07381
\(11\) −3.66849 −1.10609 −0.553045 0.833151i \(-0.686534\pi\)
−0.553045 + 0.833151i \(0.686534\pi\)
\(12\) −10.8340 −3.12750
\(13\) −4.71240 −1.30699 −0.653493 0.756933i \(-0.726697\pi\)
−0.653493 + 0.756933i \(0.726697\pi\)
\(14\) −5.62993 −1.50466
\(15\) −9.72891 −2.51199
\(16\) 5.95162 1.48791
\(17\) 5.95455 1.44419 0.722095 0.691794i \(-0.243179\pi\)
0.722095 + 0.691794i \(0.243179\pi\)
\(18\) −8.34081 −1.96595
\(19\) 1.00000 0.229416
\(20\) 16.6761 3.72889
\(21\) −5.63496 −1.22965
\(22\) 9.21464 1.96457
\(23\) −5.33707 −1.11286 −0.556428 0.830896i \(-0.687828\pi\)
−0.556428 + 0.830896i \(0.687828\pi\)
\(24\) 14.5833 2.97680
\(25\) 9.97511 1.99502
\(26\) 11.8368 2.32138
\(27\) −0.806021 −0.155119
\(28\) 9.65875 1.82533
\(29\) −4.89281 −0.908572 −0.454286 0.890856i \(-0.650106\pi\)
−0.454286 + 0.890856i \(0.650106\pi\)
\(30\) 24.4374 4.46165
\(31\) 1.00382 0.180292 0.0901460 0.995929i \(-0.471267\pi\)
0.0901460 + 0.995929i \(0.471267\pi\)
\(32\) −3.34822 −0.591887
\(33\) 9.22288 1.60550
\(34\) −14.9569 −2.56508
\(35\) 8.67355 1.46610
\(36\) 14.3096 2.38493
\(37\) 5.73851 0.943405 0.471703 0.881758i \(-0.343640\pi\)
0.471703 + 0.881758i \(0.343640\pi\)
\(38\) −2.51184 −0.407474
\(39\) 11.8474 1.89710
\(40\) −22.4472 −3.54921
\(41\) −8.57893 −1.33980 −0.669902 0.742449i \(-0.733664\pi\)
−0.669902 + 0.742449i \(0.733664\pi\)
\(42\) 14.1541 2.18403
\(43\) −1.69839 −0.259002 −0.129501 0.991579i \(-0.541337\pi\)
−0.129501 + 0.991579i \(0.541337\pi\)
\(44\) −15.8087 −2.38325
\(45\) 12.8500 1.91556
\(46\) 13.4058 1.97658
\(47\) 0.701681 0.102351 0.0511753 0.998690i \(-0.483703\pi\)
0.0511753 + 0.998690i \(0.483703\pi\)
\(48\) −14.9629 −2.15970
\(49\) −1.97630 −0.282328
\(50\) −25.0559 −3.54343
\(51\) −14.9702 −2.09625
\(52\) −20.3073 −2.81611
\(53\) 0.437181 0.0600514 0.0300257 0.999549i \(-0.490441\pi\)
0.0300257 + 0.999549i \(0.490441\pi\)
\(54\) 2.02459 0.275512
\(55\) −14.1962 −1.91422
\(56\) −13.0013 −1.73738
\(57\) −2.51408 −0.332998
\(58\) 12.2899 1.61375
\(59\) 13.5962 1.77008 0.885040 0.465515i \(-0.154131\pi\)
0.885040 + 0.465515i \(0.154131\pi\)
\(60\) −41.9250 −5.41250
\(61\) −0.0150536 −0.00192742 −0.000963711 1.00000i \(-0.500307\pi\)
−0.000963711 1.00000i \(0.500307\pi\)
\(62\) −2.52144 −0.320223
\(63\) 7.44267 0.937688
\(64\) −3.49307 −0.436634
\(65\) −18.2359 −2.26189
\(66\) −23.1664 −2.85158
\(67\) 1.84947 0.225948 0.112974 0.993598i \(-0.463962\pi\)
0.112974 + 0.993598i \(0.463962\pi\)
\(68\) 25.6601 3.11174
\(69\) 13.4178 1.61532
\(70\) −21.7865 −2.60399
\(71\) −13.3069 −1.57924 −0.789621 0.613595i \(-0.789723\pi\)
−0.789621 + 0.613595i \(0.789723\pi\)
\(72\) −19.2616 −2.27001
\(73\) −8.08633 −0.946434 −0.473217 0.880946i \(-0.656907\pi\)
−0.473217 + 0.880946i \(0.656907\pi\)
\(74\) −14.4142 −1.67562
\(75\) −25.0782 −2.89579
\(76\) 4.30932 0.494313
\(77\) −8.22241 −0.937030
\(78\) −29.7586 −3.36950
\(79\) −4.80577 −0.540691 −0.270346 0.962763i \(-0.587138\pi\)
−0.270346 + 0.962763i \(0.587138\pi\)
\(80\) 23.0314 2.57499
\(81\) −7.93541 −0.881712
\(82\) 21.5489 2.37968
\(83\) −15.3828 −1.68848 −0.844241 0.535964i \(-0.819948\pi\)
−0.844241 + 0.535964i \(0.819948\pi\)
\(84\) −24.2829 −2.64948
\(85\) 23.0427 2.49933
\(86\) 4.26607 0.460022
\(87\) 12.3009 1.31880
\(88\) 21.2796 2.26841
\(89\) 8.34046 0.884087 0.442044 0.896994i \(-0.354254\pi\)
0.442044 + 0.896994i \(0.354254\pi\)
\(90\) −32.2770 −3.40230
\(91\) −10.5622 −1.10722
\(92\) −22.9992 −2.39783
\(93\) −2.52369 −0.261695
\(94\) −1.76251 −0.181789
\(95\) 3.86977 0.397030
\(96\) 8.41769 0.859127
\(97\) 0.165235 0.0167770 0.00838852 0.999965i \(-0.497330\pi\)
0.00838852 + 0.999965i \(0.497330\pi\)
\(98\) 4.96414 0.501454
\(99\) −12.1816 −1.22430
\(100\) 42.9860 4.29860
\(101\) 9.50154 0.945438 0.472719 0.881213i \(-0.343273\pi\)
0.472719 + 0.881213i \(0.343273\pi\)
\(102\) 37.6027 3.72323
\(103\) 3.86988 0.381311 0.190656 0.981657i \(-0.438939\pi\)
0.190656 + 0.981657i \(0.438939\pi\)
\(104\) 27.3350 2.68041
\(105\) −21.8060 −2.12805
\(106\) −1.09813 −0.106659
\(107\) −5.54097 −0.535665 −0.267833 0.963465i \(-0.586307\pi\)
−0.267833 + 0.963465i \(0.586307\pi\)
\(108\) −3.47341 −0.334229
\(109\) 1.31470 0.125926 0.0629628 0.998016i \(-0.479945\pi\)
0.0629628 + 0.998016i \(0.479945\pi\)
\(110\) 35.6585 3.39991
\(111\) −14.4271 −1.36936
\(112\) 13.3397 1.26049
\(113\) 5.08727 0.478570 0.239285 0.970949i \(-0.423087\pi\)
0.239285 + 0.970949i \(0.423087\pi\)
\(114\) 6.31496 0.591450
\(115\) −20.6532 −1.92592
\(116\) −21.0847 −1.95766
\(117\) −15.6480 −1.44666
\(118\) −34.1515 −3.14390
\(119\) 13.3463 1.22345
\(120\) 56.4340 5.15169
\(121\) 2.45780 0.223437
\(122\) 0.0378123 0.00342336
\(123\) 21.5681 1.94473
\(124\) 4.32580 0.388468
\(125\) 19.2525 1.72200
\(126\) −18.6948 −1.66546
\(127\) −8.44650 −0.749506 −0.374753 0.927125i \(-0.622272\pi\)
−0.374753 + 0.927125i \(0.622272\pi\)
\(128\) 15.4705 1.36741
\(129\) 4.26988 0.375942
\(130\) 45.8056 4.01742
\(131\) −19.3216 −1.68814 −0.844068 0.536235i \(-0.819846\pi\)
−0.844068 + 0.536235i \(0.819846\pi\)
\(132\) 39.7444 3.45930
\(133\) 2.24136 0.194351
\(134\) −4.64556 −0.401315
\(135\) −3.11912 −0.268451
\(136\) −34.5402 −2.96180
\(137\) −11.2507 −0.961210 −0.480605 0.876937i \(-0.659583\pi\)
−0.480605 + 0.876937i \(0.659583\pi\)
\(138\) −33.7034 −2.86902
\(139\) −17.6209 −1.49459 −0.747294 0.664494i \(-0.768647\pi\)
−0.747294 + 0.664494i \(0.768647\pi\)
\(140\) 37.3771 3.15895
\(141\) −1.76408 −0.148563
\(142\) 33.4248 2.80495
\(143\) 17.2874 1.44564
\(144\) 19.7630 1.64691
\(145\) −18.9340 −1.57239
\(146\) 20.3115 1.68100
\(147\) 4.96857 0.409801
\(148\) 24.7291 2.03272
\(149\) −2.69684 −0.220934 −0.110467 0.993880i \(-0.535235\pi\)
−0.110467 + 0.993880i \(0.535235\pi\)
\(150\) 62.9924 5.14331
\(151\) 6.78790 0.552391 0.276196 0.961101i \(-0.410926\pi\)
0.276196 + 0.961101i \(0.410926\pi\)
\(152\) −5.80064 −0.470494
\(153\) 19.7727 1.59853
\(154\) 20.6533 1.66429
\(155\) 3.88456 0.312016
\(156\) 51.0541 4.08760
\(157\) 21.5192 1.71742 0.858710 0.512461i \(-0.171266\pi\)
0.858710 + 0.512461i \(0.171266\pi\)
\(158\) 12.0713 0.960342
\(159\) −1.09911 −0.0871649
\(160\) −12.9568 −1.02433
\(161\) −11.9623 −0.942761
\(162\) 19.9324 1.56604
\(163\) 10.4381 0.817571 0.408786 0.912630i \(-0.365952\pi\)
0.408786 + 0.912630i \(0.365952\pi\)
\(164\) −36.9694 −2.88683
\(165\) 35.6904 2.77849
\(166\) 38.6391 2.99897
\(167\) −7.03352 −0.544270 −0.272135 0.962259i \(-0.587730\pi\)
−0.272135 + 0.962259i \(0.587730\pi\)
\(168\) 32.6864 2.52181
\(169\) 9.20673 0.708210
\(170\) −57.8796 −4.43916
\(171\) 3.32060 0.253933
\(172\) −7.31890 −0.558061
\(173\) 16.2628 1.23644 0.618218 0.786007i \(-0.287855\pi\)
0.618218 + 0.786007i \(0.287855\pi\)
\(174\) −30.8979 −2.34236
\(175\) 22.3578 1.69009
\(176\) −21.8335 −1.64576
\(177\) −34.1821 −2.56928
\(178\) −20.9499 −1.57026
\(179\) −16.3585 −1.22269 −0.611344 0.791365i \(-0.709371\pi\)
−0.611344 + 0.791365i \(0.709371\pi\)
\(180\) 55.3747 4.12738
\(181\) −20.9874 −1.55998 −0.779990 0.625792i \(-0.784776\pi\)
−0.779990 + 0.625792i \(0.784776\pi\)
\(182\) 26.5305 1.96657
\(183\) 0.0378461 0.00279766
\(184\) 30.9584 2.28229
\(185\) 22.2067 1.63267
\(186\) 6.33910 0.464806
\(187\) −21.8442 −1.59741
\(188\) 3.02377 0.220531
\(189\) −1.80659 −0.131410
\(190\) −9.72023 −0.705179
\(191\) −9.80803 −0.709684 −0.354842 0.934926i \(-0.615465\pi\)
−0.354842 + 0.934926i \(0.615465\pi\)
\(192\) 8.78186 0.633776
\(193\) 15.2445 1.09732 0.548660 0.836046i \(-0.315138\pi\)
0.548660 + 0.836046i \(0.315138\pi\)
\(194\) −0.415043 −0.0297983
\(195\) 45.8465 3.28314
\(196\) −8.51651 −0.608322
\(197\) 20.1164 1.43323 0.716616 0.697468i \(-0.245690\pi\)
0.716616 + 0.697468i \(0.245690\pi\)
\(198\) 30.5982 2.17452
\(199\) 17.9659 1.27357 0.636785 0.771042i \(-0.280264\pi\)
0.636785 + 0.771042i \(0.280264\pi\)
\(200\) −57.8621 −4.09147
\(201\) −4.64971 −0.327965
\(202\) −23.8663 −1.67923
\(203\) −10.9666 −0.769701
\(204\) −64.5115 −4.51671
\(205\) −33.1985 −2.31868
\(206\) −9.72052 −0.677261
\(207\) −17.7223 −1.23178
\(208\) −28.0464 −1.94467
\(209\) −3.66849 −0.253755
\(210\) 54.7731 3.77971
\(211\) 1.00000 0.0688428
\(212\) 1.88395 0.129390
\(213\) 33.4547 2.29228
\(214\) 13.9180 0.951415
\(215\) −6.57236 −0.448231
\(216\) 4.67544 0.318124
\(217\) 2.24993 0.152735
\(218\) −3.30232 −0.223661
\(219\) 20.3297 1.37375
\(220\) −61.1760 −4.12449
\(221\) −28.0602 −1.88753
\(222\) 36.2385 2.43217
\(223\) 7.87139 0.527107 0.263554 0.964645i \(-0.415105\pi\)
0.263554 + 0.964645i \(0.415105\pi\)
\(224\) −7.50457 −0.501420
\(225\) 33.1234 2.20823
\(226\) −12.7784 −0.850006
\(227\) −23.4109 −1.55384 −0.776918 0.629602i \(-0.783218\pi\)
−0.776918 + 0.629602i \(0.783218\pi\)
\(228\) −10.8340 −0.717498
\(229\) 3.65273 0.241379 0.120690 0.992690i \(-0.461489\pi\)
0.120690 + 0.992690i \(0.461489\pi\)
\(230\) 51.8775 3.42070
\(231\) 20.6718 1.36010
\(232\) 28.3814 1.86333
\(233\) 24.4712 1.60316 0.801581 0.597887i \(-0.203993\pi\)
0.801581 + 0.597887i \(0.203993\pi\)
\(234\) 39.3053 2.56947
\(235\) 2.71534 0.177129
\(236\) 58.5906 3.81392
\(237\) 12.0821 0.784816
\(238\) −33.5237 −2.17302
\(239\) −19.1928 −1.24148 −0.620740 0.784016i \(-0.713168\pi\)
−0.620740 + 0.784016i \(0.713168\pi\)
\(240\) −57.9028 −3.73761
\(241\) −15.0736 −0.970977 −0.485489 0.874243i \(-0.661358\pi\)
−0.485489 + 0.874243i \(0.661358\pi\)
\(242\) −6.17360 −0.396854
\(243\) 22.3683 1.43493
\(244\) −0.0648710 −0.00415294
\(245\) −7.64782 −0.488601
\(246\) −54.1756 −3.45411
\(247\) −4.71240 −0.299843
\(248\) −5.82282 −0.369749
\(249\) 38.6736 2.45084
\(250\) −48.3592 −3.05851
\(251\) −26.0152 −1.64207 −0.821034 0.570879i \(-0.806602\pi\)
−0.821034 + 0.570879i \(0.806602\pi\)
\(252\) 32.0729 2.02040
\(253\) 19.5790 1.23092
\(254\) 21.2162 1.33122
\(255\) −57.9313 −3.62780
\(256\) −31.8731 −1.99207
\(257\) −29.6834 −1.85160 −0.925799 0.378017i \(-0.876606\pi\)
−0.925799 + 0.378017i \(0.876606\pi\)
\(258\) −10.7252 −0.667725
\(259\) 12.8621 0.799211
\(260\) −78.5844 −4.87360
\(261\) −16.2471 −1.00567
\(262\) 48.5327 2.99836
\(263\) −23.3222 −1.43811 −0.719053 0.694955i \(-0.755424\pi\)
−0.719053 + 0.694955i \(0.755424\pi\)
\(264\) −53.4986 −3.29261
\(265\) 1.69179 0.103926
\(266\) −5.62993 −0.345193
\(267\) −20.9686 −1.28326
\(268\) 7.96996 0.486842
\(269\) −19.1515 −1.16769 −0.583843 0.811866i \(-0.698452\pi\)
−0.583843 + 0.811866i \(0.698452\pi\)
\(270\) 7.83471 0.476805
\(271\) −5.71778 −0.347331 −0.173665 0.984805i \(-0.555561\pi\)
−0.173665 + 0.984805i \(0.555561\pi\)
\(272\) 35.4392 2.14882
\(273\) 26.5542 1.60713
\(274\) 28.2599 1.70724
\(275\) −36.5936 −2.20668
\(276\) 57.8217 3.48046
\(277\) 16.8896 1.01480 0.507399 0.861711i \(-0.330607\pi\)
0.507399 + 0.861711i \(0.330607\pi\)
\(278\) 44.2609 2.65459
\(279\) 3.33330 0.199559
\(280\) −50.3122 −3.00673
\(281\) −15.4220 −0.920002 −0.460001 0.887918i \(-0.652151\pi\)
−0.460001 + 0.887918i \(0.652151\pi\)
\(282\) 4.43109 0.263867
\(283\) −10.9939 −0.653517 −0.326758 0.945108i \(-0.605956\pi\)
−0.326758 + 0.945108i \(0.605956\pi\)
\(284\) −57.3438 −3.40273
\(285\) −9.72891 −0.576291
\(286\) −43.4231 −2.56766
\(287\) −19.2285 −1.13502
\(288\) −11.1181 −0.655141
\(289\) 18.4566 1.08568
\(290\) 47.5592 2.79277
\(291\) −0.415413 −0.0243520
\(292\) −34.8466 −2.03924
\(293\) −1.44814 −0.0846012 −0.0423006 0.999105i \(-0.513469\pi\)
−0.0423006 + 0.999105i \(0.513469\pi\)
\(294\) −12.4802 −0.727863
\(295\) 52.6143 3.06332
\(296\) −33.2871 −1.93477
\(297\) 2.95688 0.171576
\(298\) 6.77403 0.392409
\(299\) 25.1504 1.45449
\(300\) −108.070 −6.23944
\(301\) −3.80670 −0.219414
\(302\) −17.0501 −0.981123
\(303\) −23.8876 −1.37231
\(304\) 5.95162 0.341349
\(305\) −0.0582541 −0.00333562
\(306\) −49.6658 −2.83920
\(307\) 3.45110 0.196965 0.0984823 0.995139i \(-0.468601\pi\)
0.0984823 + 0.995139i \(0.468601\pi\)
\(308\) −35.4330 −2.01898
\(309\) −9.72920 −0.553475
\(310\) −9.75739 −0.554182
\(311\) −3.20625 −0.181810 −0.0909049 0.995860i \(-0.528976\pi\)
−0.0909049 + 0.995860i \(0.528976\pi\)
\(312\) −68.7223 −3.89064
\(313\) −4.24418 −0.239895 −0.119948 0.992780i \(-0.538273\pi\)
−0.119948 + 0.992780i \(0.538273\pi\)
\(314\) −54.0528 −3.05037
\(315\) 28.8014 1.62278
\(316\) −20.7096 −1.16501
\(317\) 26.1975 1.47140 0.735699 0.677309i \(-0.236854\pi\)
0.735699 + 0.677309i \(0.236854\pi\)
\(318\) 2.76078 0.154817
\(319\) 17.9492 1.00496
\(320\) −13.5174 −0.755644
\(321\) 13.9304 0.777521
\(322\) 30.0473 1.67447
\(323\) 5.95455 0.331320
\(324\) −34.1962 −1.89979
\(325\) −47.0067 −2.60746
\(326\) −26.2187 −1.45212
\(327\) −3.30527 −0.182782
\(328\) 49.7633 2.74772
\(329\) 1.57272 0.0867069
\(330\) −89.6485 −4.93499
\(331\) 17.7740 0.976945 0.488472 0.872579i \(-0.337554\pi\)
0.488472 + 0.872579i \(0.337554\pi\)
\(332\) −66.2894 −3.63811
\(333\) 19.0553 1.04422
\(334\) 17.6670 0.966698
\(335\) 7.15701 0.391029
\(336\) −33.5372 −1.82960
\(337\) 18.5094 1.00827 0.504135 0.863625i \(-0.331811\pi\)
0.504135 + 0.863625i \(0.331811\pi\)
\(338\) −23.1258 −1.25788
\(339\) −12.7898 −0.694647
\(340\) 99.2986 5.38522
\(341\) −3.68251 −0.199419
\(342\) −8.34081 −0.451019
\(343\) −20.1191 −1.08633
\(344\) 9.85174 0.531170
\(345\) 51.9239 2.79549
\(346\) −40.8495 −2.19608
\(347\) 4.93695 0.265030 0.132515 0.991181i \(-0.457695\pi\)
0.132515 + 0.991181i \(0.457695\pi\)
\(348\) 53.0086 2.84156
\(349\) 21.4593 1.14869 0.574346 0.818613i \(-0.305257\pi\)
0.574346 + 0.818613i \(0.305257\pi\)
\(350\) −56.1592 −3.00184
\(351\) 3.79830 0.202738
\(352\) 12.2829 0.654681
\(353\) −19.8723 −1.05770 −0.528848 0.848717i \(-0.677376\pi\)
−0.528848 + 0.848717i \(0.677376\pi\)
\(354\) 85.8597 4.56339
\(355\) −51.4947 −2.73306
\(356\) 35.9418 1.90491
\(357\) −33.5537 −1.77585
\(358\) 41.0898 2.17166
\(359\) −23.3055 −1.23002 −0.615009 0.788520i \(-0.710848\pi\)
−0.615009 + 0.788520i \(0.710848\pi\)
\(360\) −74.5381 −3.92850
\(361\) 1.00000 0.0526316
\(362\) 52.7169 2.77074
\(363\) −6.17912 −0.324320
\(364\) −45.5159 −2.38568
\(365\) −31.2922 −1.63791
\(366\) −0.0950631 −0.00496903
\(367\) −5.44203 −0.284071 −0.142036 0.989862i \(-0.545365\pi\)
−0.142036 + 0.989862i \(0.545365\pi\)
\(368\) −31.7642 −1.65582
\(369\) −28.4872 −1.48299
\(370\) −55.7796 −2.89985
\(371\) 0.979880 0.0508728
\(372\) −10.8754 −0.563864
\(373\) 10.1229 0.524144 0.262072 0.965048i \(-0.415594\pi\)
0.262072 + 0.965048i \(0.415594\pi\)
\(374\) 54.8690 2.83721
\(375\) −48.4024 −2.49949
\(376\) −4.07020 −0.209905
\(377\) 23.0569 1.18749
\(378\) 4.53785 0.233402
\(379\) 25.3608 1.30270 0.651348 0.758779i \(-0.274204\pi\)
0.651348 + 0.758779i \(0.274204\pi\)
\(380\) 16.6761 0.855465
\(381\) 21.2352 1.08791
\(382\) 24.6362 1.26050
\(383\) −6.28404 −0.321100 −0.160550 0.987028i \(-0.551327\pi\)
−0.160550 + 0.987028i \(0.551327\pi\)
\(384\) −38.8940 −1.98480
\(385\) −31.8188 −1.62164
\(386\) −38.2916 −1.94899
\(387\) −5.63967 −0.286680
\(388\) 0.712050 0.0361489
\(389\) 4.92909 0.249915 0.124958 0.992162i \(-0.460121\pi\)
0.124958 + 0.992162i \(0.460121\pi\)
\(390\) −115.159 −5.83130
\(391\) −31.7798 −1.60717
\(392\) 11.4638 0.579009
\(393\) 48.5761 2.45034
\(394\) −50.5290 −2.54562
\(395\) −18.5972 −0.935728
\(396\) −52.4944 −2.63794
\(397\) 30.2060 1.51599 0.757997 0.652258i \(-0.226178\pi\)
0.757997 + 0.652258i \(0.226178\pi\)
\(398\) −45.1274 −2.26203
\(399\) −5.63496 −0.282101
\(400\) 59.3681 2.96841
\(401\) −9.21321 −0.460086 −0.230043 0.973181i \(-0.573887\pi\)
−0.230043 + 0.973181i \(0.573887\pi\)
\(402\) 11.6793 0.582511
\(403\) −4.73042 −0.235639
\(404\) 40.9452 2.03710
\(405\) −30.7082 −1.52590
\(406\) 27.5462 1.36709
\(407\) −21.0517 −1.04349
\(408\) 86.8369 4.29907
\(409\) 3.70221 0.183062 0.0915312 0.995802i \(-0.470824\pi\)
0.0915312 + 0.995802i \(0.470824\pi\)
\(410\) 83.3892 4.11830
\(411\) 28.2851 1.39520
\(412\) 16.6766 0.821596
\(413\) 30.4741 1.49953
\(414\) 44.5155 2.18782
\(415\) −59.5279 −2.92211
\(416\) 15.7782 0.773587
\(417\) 44.3004 2.16940
\(418\) 9.21464 0.450703
\(419\) −31.9262 −1.55970 −0.779849 0.625967i \(-0.784704\pi\)
−0.779849 + 0.625967i \(0.784704\pi\)
\(420\) −93.9692 −4.58523
\(421\) 19.1099 0.931360 0.465680 0.884953i \(-0.345810\pi\)
0.465680 + 0.884953i \(0.345810\pi\)
\(422\) −2.51184 −0.122274
\(423\) 2.33000 0.113289
\(424\) −2.53593 −0.123156
\(425\) 59.3973 2.88119
\(426\) −84.0327 −4.07140
\(427\) −0.0337407 −0.00163282
\(428\) −23.8778 −1.15418
\(429\) −43.4619 −2.09836
\(430\) 16.5087 0.796120
\(431\) 33.5101 1.61412 0.807062 0.590467i \(-0.201056\pi\)
0.807062 + 0.590467i \(0.201056\pi\)
\(432\) −4.79714 −0.230802
\(433\) −18.0900 −0.869351 −0.434675 0.900587i \(-0.643137\pi\)
−0.434675 + 0.900587i \(0.643137\pi\)
\(434\) −5.65146 −0.271279
\(435\) 47.6017 2.28233
\(436\) 5.66548 0.271327
\(437\) −5.33707 −0.255307
\(438\) −51.0649 −2.43997
\(439\) 7.49629 0.357778 0.178889 0.983869i \(-0.442750\pi\)
0.178889 + 0.983869i \(0.442750\pi\)
\(440\) 82.3471 3.92574
\(441\) −6.56250 −0.312500
\(442\) 70.4827 3.35252
\(443\) −10.0173 −0.475935 −0.237967 0.971273i \(-0.576481\pi\)
−0.237967 + 0.971273i \(0.576481\pi\)
\(444\) −62.1710 −2.95050
\(445\) 32.2757 1.53001
\(446\) −19.7716 −0.936215
\(447\) 6.78008 0.320687
\(448\) −7.82923 −0.369896
\(449\) −2.44501 −0.115387 −0.0576937 0.998334i \(-0.518375\pi\)
−0.0576937 + 0.998334i \(0.518375\pi\)
\(450\) −83.2005 −3.92211
\(451\) 31.4717 1.48195
\(452\) 21.9227 1.03116
\(453\) −17.0653 −0.801799
\(454\) 58.8044 2.75983
\(455\) −40.8733 −1.91617
\(456\) 14.5833 0.682925
\(457\) −26.7420 −1.25094 −0.625470 0.780248i \(-0.715093\pi\)
−0.625470 + 0.780248i \(0.715093\pi\)
\(458\) −9.17506 −0.428723
\(459\) −4.79949 −0.224021
\(460\) −89.0014 −4.14971
\(461\) 3.88863 0.181112 0.0905558 0.995891i \(-0.471136\pi\)
0.0905558 + 0.995891i \(0.471136\pi\)
\(462\) −51.9242 −2.41573
\(463\) 2.74342 0.127497 0.0637487 0.997966i \(-0.479694\pi\)
0.0637487 + 0.997966i \(0.479694\pi\)
\(464\) −29.1202 −1.35187
\(465\) −9.76611 −0.452892
\(466\) −61.4676 −2.84743
\(467\) 41.1650 1.90489 0.952444 0.304715i \(-0.0985612\pi\)
0.952444 + 0.304715i \(0.0985612\pi\)
\(468\) −67.4324 −3.11706
\(469\) 4.14533 0.191413
\(470\) −6.82050 −0.314606
\(471\) −54.1011 −2.49284
\(472\) −78.8670 −3.63015
\(473\) 6.23051 0.286479
\(474\) −30.3482 −1.39394
\(475\) 9.97511 0.457690
\(476\) 57.5135 2.63613
\(477\) 1.45170 0.0664689
\(478\) 48.2092 2.20504
\(479\) −19.9855 −0.913159 −0.456580 0.889683i \(-0.650926\pi\)
−0.456580 + 0.889683i \(0.650926\pi\)
\(480\) 32.5745 1.48682
\(481\) −27.0422 −1.23302
\(482\) 37.8625 1.72459
\(483\) 30.0742 1.36842
\(484\) 10.5915 0.481431
\(485\) 0.639420 0.0290346
\(486\) −56.1856 −2.54863
\(487\) −22.1530 −1.00385 −0.501923 0.864912i \(-0.667374\pi\)
−0.501923 + 0.864912i \(0.667374\pi\)
\(488\) 0.0873208 0.00395283
\(489\) −26.2421 −1.18671
\(490\) 19.2101 0.867822
\(491\) 28.4675 1.28472 0.642360 0.766403i \(-0.277956\pi\)
0.642360 + 0.766403i \(0.277956\pi\)
\(492\) 92.9441 4.19024
\(493\) −29.1345 −1.31215
\(494\) 11.8368 0.532562
\(495\) −47.1399 −2.11878
\(496\) 5.97438 0.268257
\(497\) −29.8256 −1.33786
\(498\) −97.1417 −4.35303
\(499\) −5.14118 −0.230151 −0.115075 0.993357i \(-0.536711\pi\)
−0.115075 + 0.993357i \(0.536711\pi\)
\(500\) 82.9654 3.71033
\(501\) 17.6828 0.790011
\(502\) 65.3461 2.91654
\(503\) 4.36152 0.194471 0.0972353 0.995261i \(-0.469000\pi\)
0.0972353 + 0.995261i \(0.469000\pi\)
\(504\) −43.1723 −1.92305
\(505\) 36.7688 1.63619
\(506\) −49.1792 −2.18628
\(507\) −23.1465 −1.02797
\(508\) −36.3987 −1.61493
\(509\) 1.86957 0.0828670 0.0414335 0.999141i \(-0.486808\pi\)
0.0414335 + 0.999141i \(0.486808\pi\)
\(510\) 145.514 6.44346
\(511\) −18.1244 −0.801776
\(512\) 49.1192 2.17078
\(513\) −0.806021 −0.0355867
\(514\) 74.5598 3.28869
\(515\) 14.9756 0.659902
\(516\) 18.4003 0.810028
\(517\) −2.57411 −0.113209
\(518\) −32.3074 −1.41951
\(519\) −40.8859 −1.79469
\(520\) 105.780 4.63876
\(521\) −27.0090 −1.18329 −0.591644 0.806200i \(-0.701521\pi\)
−0.591644 + 0.806200i \(0.701521\pi\)
\(522\) 40.8100 1.78620
\(523\) 23.3456 1.02083 0.510416 0.859928i \(-0.329492\pi\)
0.510416 + 0.859928i \(0.329492\pi\)
\(524\) −83.2631 −3.63736
\(525\) −56.2094 −2.45318
\(526\) 58.5815 2.55427
\(527\) 5.97731 0.260376
\(528\) 54.8911 2.38883
\(529\) 5.48429 0.238447
\(530\) −4.24950 −0.184586
\(531\) 45.1477 1.95924
\(532\) 9.65875 0.418760
\(533\) 40.4274 1.75110
\(534\) 52.6697 2.27924
\(535\) −21.4423 −0.927030
\(536\) −10.7281 −0.463384
\(537\) 41.1265 1.77474
\(538\) 48.1054 2.07397
\(539\) 7.25003 0.312281
\(540\) −13.4413 −0.578421
\(541\) −36.8758 −1.58541 −0.792706 0.609604i \(-0.791329\pi\)
−0.792706 + 0.609604i \(0.791329\pi\)
\(542\) 14.3621 0.616907
\(543\) 52.7640 2.26432
\(544\) −19.9371 −0.854797
\(545\) 5.08759 0.217929
\(546\) −66.6999 −2.85449
\(547\) −46.6362 −1.99402 −0.997009 0.0772843i \(-0.975375\pi\)
−0.997009 + 0.0772843i \(0.975375\pi\)
\(548\) −48.4828 −2.07108
\(549\) −0.0499872 −0.00213340
\(550\) 91.9171 3.91936
\(551\) −4.89281 −0.208441
\(552\) −77.8320 −3.31275
\(553\) −10.7715 −0.458049
\(554\) −42.4239 −1.80242
\(555\) −55.8295 −2.36983
\(556\) −75.9343 −3.22033
\(557\) 20.8434 0.883165 0.441582 0.897221i \(-0.354417\pi\)
0.441582 + 0.897221i \(0.354417\pi\)
\(558\) −8.37270 −0.354445
\(559\) 8.00348 0.338511
\(560\) 51.6217 2.18142
\(561\) 54.9181 2.31864
\(562\) 38.7377 1.63405
\(563\) −25.4415 −1.07223 −0.536115 0.844145i \(-0.680109\pi\)
−0.536115 + 0.844145i \(0.680109\pi\)
\(564\) −7.60200 −0.320102
\(565\) 19.6866 0.828219
\(566\) 27.6148 1.16074
\(567\) −17.7861 −0.746947
\(568\) 77.1887 3.23877
\(569\) −28.6096 −1.19938 −0.599689 0.800233i \(-0.704709\pi\)
−0.599689 + 0.800233i \(0.704709\pi\)
\(570\) 24.4374 1.02357
\(571\) 37.2341 1.55820 0.779099 0.626901i \(-0.215677\pi\)
0.779099 + 0.626901i \(0.215677\pi\)
\(572\) 74.4970 3.11487
\(573\) 24.6582 1.03011
\(574\) 48.2988 2.01595
\(575\) −53.2379 −2.22017
\(576\) −11.5991 −0.483296
\(577\) 13.9850 0.582204 0.291102 0.956692i \(-0.405978\pi\)
0.291102 + 0.956692i \(0.405978\pi\)
\(578\) −46.3601 −1.92832
\(579\) −38.3258 −1.59277
\(580\) −81.5929 −3.38796
\(581\) −34.4784 −1.43041
\(582\) 1.04345 0.0432524
\(583\) −1.60379 −0.0664223
\(584\) 46.9059 1.94098
\(585\) −60.5542 −2.50361
\(586\) 3.63749 0.150263
\(587\) 23.5859 0.973494 0.486747 0.873543i \(-0.338183\pi\)
0.486747 + 0.873543i \(0.338183\pi\)
\(588\) 21.4112 0.882983
\(589\) 1.00382 0.0413618
\(590\) −132.159 −5.44088
\(591\) −50.5742 −2.08034
\(592\) 34.1535 1.40370
\(593\) 1.45578 0.0597816 0.0298908 0.999553i \(-0.490484\pi\)
0.0298908 + 0.999553i \(0.490484\pi\)
\(594\) −7.42720 −0.304742
\(595\) 51.6471 2.11732
\(596\) −11.6216 −0.476038
\(597\) −45.1677 −1.84859
\(598\) −63.1737 −2.58337
\(599\) 28.6379 1.17011 0.585057 0.810992i \(-0.301072\pi\)
0.585057 + 0.810992i \(0.301072\pi\)
\(600\) 145.470 5.93879
\(601\) 5.63985 0.230054 0.115027 0.993362i \(-0.463304\pi\)
0.115027 + 0.993362i \(0.463304\pi\)
\(602\) 9.56180 0.389710
\(603\) 6.14135 0.250095
\(604\) 29.2513 1.19022
\(605\) 9.51114 0.386683
\(606\) 60.0018 2.43741
\(607\) −2.85271 −0.115788 −0.0578940 0.998323i \(-0.518439\pi\)
−0.0578940 + 0.998323i \(0.518439\pi\)
\(608\) −3.34822 −0.135788
\(609\) 27.5708 1.11723
\(610\) 0.146325 0.00592452
\(611\) −3.30660 −0.133771
\(612\) 85.2069 3.44429
\(613\) −38.7463 −1.56495 −0.782474 0.622684i \(-0.786042\pi\)
−0.782474 + 0.622684i \(0.786042\pi\)
\(614\) −8.66860 −0.349836
\(615\) 83.4637 3.36558
\(616\) 47.6953 1.92170
\(617\) −3.84843 −0.154932 −0.0774660 0.996995i \(-0.524683\pi\)
−0.0774660 + 0.996995i \(0.524683\pi\)
\(618\) 24.4382 0.983047
\(619\) 15.3763 0.618024 0.309012 0.951058i \(-0.400002\pi\)
0.309012 + 0.951058i \(0.400002\pi\)
\(620\) 16.7398 0.672288
\(621\) 4.30179 0.172625
\(622\) 8.05358 0.322919
\(623\) 18.6940 0.748959
\(624\) 70.5110 2.82270
\(625\) 24.6273 0.985093
\(626\) 10.6607 0.426087
\(627\) 9.22288 0.368326
\(628\) 92.7333 3.70046
\(629\) 34.1702 1.36246
\(630\) −72.3445 −2.88227
\(631\) −21.5442 −0.857662 −0.428831 0.903385i \(-0.641074\pi\)
−0.428831 + 0.903385i \(0.641074\pi\)
\(632\) 27.8766 1.10887
\(633\) −2.51408 −0.0999257
\(634\) −65.8038 −2.61340
\(635\) −32.6860 −1.29710
\(636\) −4.73641 −0.187811
\(637\) 9.31311 0.368999
\(638\) −45.0855 −1.78495
\(639\) −44.1870 −1.74801
\(640\) 59.8671 2.36645
\(641\) −5.09331 −0.201174 −0.100587 0.994928i \(-0.532072\pi\)
−0.100587 + 0.994928i \(0.532072\pi\)
\(642\) −34.9910 −1.38098
\(643\) 43.2382 1.70515 0.852573 0.522607i \(-0.175041\pi\)
0.852573 + 0.522607i \(0.175041\pi\)
\(644\) −51.5494 −2.03133
\(645\) 16.5235 0.650610
\(646\) −14.9569 −0.588469
\(647\) −25.1713 −0.989587 −0.494793 0.869011i \(-0.664756\pi\)
−0.494793 + 0.869011i \(0.664756\pi\)
\(648\) 46.0305 1.80825
\(649\) −49.8777 −1.95787
\(650\) 118.073 4.63121
\(651\) −5.65651 −0.221696
\(652\) 44.9810 1.76159
\(653\) −45.8672 −1.79492 −0.897461 0.441094i \(-0.854591\pi\)
−0.897461 + 0.441094i \(0.854591\pi\)
\(654\) 8.30229 0.324645
\(655\) −74.7702 −2.92151
\(656\) −51.0586 −1.99350
\(657\) −26.8515 −1.04758
\(658\) −3.95042 −0.154003
\(659\) −5.20393 −0.202716 −0.101358 0.994850i \(-0.532319\pi\)
−0.101358 + 0.994850i \(0.532319\pi\)
\(660\) 153.801 5.98671
\(661\) −32.1290 −1.24967 −0.624837 0.780755i \(-0.714835\pi\)
−0.624837 + 0.780755i \(0.714835\pi\)
\(662\) −44.6453 −1.73519
\(663\) 70.5457 2.73977
\(664\) 89.2301 3.46280
\(665\) 8.67355 0.336346
\(666\) −47.8638 −1.85469
\(667\) 26.1132 1.01111
\(668\) −30.3097 −1.17272
\(669\) −19.7893 −0.765099
\(670\) −17.9772 −0.694522
\(671\) 0.0552241 0.00213190
\(672\) 18.8671 0.727814
\(673\) −19.9867 −0.770432 −0.385216 0.922826i \(-0.625873\pi\)
−0.385216 + 0.922826i \(0.625873\pi\)
\(674\) −46.4925 −1.79083
\(675\) −8.04016 −0.309466
\(676\) 39.6748 1.52595
\(677\) −27.9200 −1.07305 −0.536526 0.843884i \(-0.680264\pi\)
−0.536526 + 0.843884i \(0.680264\pi\)
\(678\) 32.1259 1.23379
\(679\) 0.370351 0.0142128
\(680\) −133.663 −5.12573
\(681\) 58.8569 2.25540
\(682\) 9.24987 0.354196
\(683\) −36.0837 −1.38071 −0.690353 0.723473i \(-0.742545\pi\)
−0.690353 + 0.723473i \(0.742545\pi\)
\(684\) 14.3096 0.547139
\(685\) −43.5375 −1.66348
\(686\) 50.5360 1.92947
\(687\) −9.18326 −0.350363
\(688\) −10.1082 −0.385370
\(689\) −2.06017 −0.0784863
\(690\) −130.424 −4.96517
\(691\) −47.9756 −1.82508 −0.912539 0.408990i \(-0.865881\pi\)
−0.912539 + 0.408990i \(0.865881\pi\)
\(692\) 70.0816 2.66410
\(693\) −27.3034 −1.03717
\(694\) −12.4008 −0.470729
\(695\) −68.1889 −2.58655
\(696\) −71.3532 −2.70464
\(697\) −51.0837 −1.93493
\(698\) −53.9023 −2.04023
\(699\) −61.5226 −2.32700
\(700\) 96.3472 3.64158
\(701\) 19.7008 0.744090 0.372045 0.928215i \(-0.378657\pi\)
0.372045 + 0.928215i \(0.378657\pi\)
\(702\) −9.54070 −0.360091
\(703\) 5.73851 0.216432
\(704\) 12.8143 0.482956
\(705\) −6.82659 −0.257104
\(706\) 49.9160 1.87861
\(707\) 21.2964 0.800933
\(708\) −147.302 −5.53593
\(709\) −43.7682 −1.64375 −0.821874 0.569669i \(-0.807071\pi\)
−0.821874 + 0.569669i \(0.807071\pi\)
\(710\) 129.346 4.85428
\(711\) −15.9581 −0.598474
\(712\) −48.3801 −1.81312
\(713\) −5.35747 −0.200639
\(714\) 84.2813 3.15415
\(715\) 66.8982 2.50185
\(716\) −70.4939 −2.63448
\(717\) 48.2523 1.80202
\(718\) 58.5397 2.18468
\(719\) −9.88300 −0.368574 −0.184287 0.982872i \(-0.558998\pi\)
−0.184287 + 0.982872i \(0.558998\pi\)
\(720\) 76.4782 2.85017
\(721\) 8.67381 0.323030
\(722\) −2.51184 −0.0934809
\(723\) 37.8963 1.40938
\(724\) −90.4414 −3.36123
\(725\) −48.8063 −1.81262
\(726\) 15.5209 0.576036
\(727\) 45.9201 1.70308 0.851540 0.524289i \(-0.175669\pi\)
0.851540 + 0.524289i \(0.175669\pi\)
\(728\) 61.2675 2.27073
\(729\) −32.4295 −1.20109
\(730\) 78.6010 2.90915
\(731\) −10.1131 −0.374047
\(732\) 0.163091 0.00602802
\(733\) 16.6835 0.616218 0.308109 0.951351i \(-0.400304\pi\)
0.308109 + 0.951351i \(0.400304\pi\)
\(734\) 13.6695 0.504550
\(735\) 19.2272 0.709207
\(736\) 17.8697 0.658685
\(737\) −6.78475 −0.249919
\(738\) 71.5553 2.63399
\(739\) 18.8710 0.694182 0.347091 0.937831i \(-0.387169\pi\)
0.347091 + 0.937831i \(0.387169\pi\)
\(740\) 95.6959 3.51785
\(741\) 11.8474 0.435224
\(742\) −2.46130 −0.0903571
\(743\) 14.3438 0.526221 0.263111 0.964766i \(-0.415252\pi\)
0.263111 + 0.964766i \(0.415252\pi\)
\(744\) 14.6390 0.536693
\(745\) −10.4362 −0.382351
\(746\) −25.4271 −0.930952
\(747\) −51.0802 −1.86892
\(748\) −94.1337 −3.44187
\(749\) −12.4193 −0.453792
\(750\) 121.579 4.43944
\(751\) −29.9408 −1.09255 −0.546277 0.837605i \(-0.683955\pi\)
−0.546277 + 0.837605i \(0.683955\pi\)
\(752\) 4.17614 0.152288
\(753\) 65.4044 2.38347
\(754\) −57.9151 −2.10914
\(755\) 26.2676 0.955976
\(756\) −7.78516 −0.283144
\(757\) −1.44824 −0.0526371 −0.0263185 0.999654i \(-0.508378\pi\)
−0.0263185 + 0.999654i \(0.508378\pi\)
\(758\) −63.7022 −2.31377
\(759\) −49.2231 −1.78669
\(760\) −22.4472 −0.814244
\(761\) −48.5606 −1.76032 −0.880159 0.474678i \(-0.842564\pi\)
−0.880159 + 0.474678i \(0.842564\pi\)
\(762\) −53.3393 −1.93228
\(763\) 2.94672 0.106679
\(764\) −42.2660 −1.52913
\(765\) 76.5157 2.76643
\(766\) 15.7845 0.570317
\(767\) −64.0710 −2.31347
\(768\) 80.1316 2.89150
\(769\) 7.63086 0.275176 0.137588 0.990490i \(-0.456065\pi\)
0.137588 + 0.990490i \(0.456065\pi\)
\(770\) 79.9237 2.88025
\(771\) 74.6264 2.68760
\(772\) 65.6933 2.36435
\(773\) 15.6049 0.561270 0.280635 0.959815i \(-0.409455\pi\)
0.280635 + 0.959815i \(0.409455\pi\)
\(774\) 14.1659 0.509184
\(775\) 10.0132 0.359687
\(776\) −0.958468 −0.0344070
\(777\) −32.3363 −1.16006
\(778\) −12.3811 −0.443883
\(779\) −8.57893 −0.307372
\(780\) 197.568 7.07406
\(781\) 48.8163 1.74678
\(782\) 79.8257 2.85456
\(783\) 3.94371 0.140937
\(784\) −11.7622 −0.420078
\(785\) 83.2744 2.97219
\(786\) −122.015 −4.35214
\(787\) −38.7918 −1.38278 −0.691389 0.722483i \(-0.743001\pi\)
−0.691389 + 0.722483i \(0.743001\pi\)
\(788\) 86.6879 3.08813
\(789\) 58.6338 2.08742
\(790\) 46.7132 1.66198
\(791\) 11.4024 0.405423
\(792\) 70.6611 2.51083
\(793\) 0.0709388 0.00251911
\(794\) −75.8725 −2.69261
\(795\) −4.25329 −0.150849
\(796\) 77.4209 2.74411
\(797\) 28.7351 1.01785 0.508925 0.860811i \(-0.330043\pi\)
0.508925 + 0.860811i \(0.330043\pi\)
\(798\) 14.1541 0.501050
\(799\) 4.17819 0.147814
\(800\) −33.3989 −1.18083
\(801\) 27.6954 0.978568
\(802\) 23.1421 0.817175
\(803\) 29.6646 1.04684
\(804\) −20.0371 −0.706654
\(805\) −46.2913 −1.63156
\(806\) 11.8820 0.418527
\(807\) 48.1484 1.69490
\(808\) −55.1150 −1.93894
\(809\) 13.4142 0.471619 0.235809 0.971799i \(-0.424226\pi\)
0.235809 + 0.971799i \(0.424226\pi\)
\(810\) 77.1340 2.71021
\(811\) 51.1579 1.79640 0.898199 0.439589i \(-0.144876\pi\)
0.898199 + 0.439589i \(0.144876\pi\)
\(812\) −47.2584 −1.65845
\(813\) 14.3750 0.504152
\(814\) 52.8783 1.85338
\(815\) 40.3929 1.41490
\(816\) −89.0971 −3.11902
\(817\) −1.69839 −0.0594190
\(818\) −9.29934 −0.325144
\(819\) −35.0729 −1.22554
\(820\) −143.063 −4.99598
\(821\) 17.7760 0.620386 0.310193 0.950674i \(-0.399606\pi\)
0.310193 + 0.950674i \(0.399606\pi\)
\(822\) −71.0476 −2.47807
\(823\) −24.5914 −0.857201 −0.428600 0.903494i \(-0.640993\pi\)
−0.428600 + 0.903494i \(0.640993\pi\)
\(824\) −22.4478 −0.782007
\(825\) 91.9992 3.20300
\(826\) −76.5460 −2.66337
\(827\) −39.2562 −1.36507 −0.682536 0.730852i \(-0.739123\pi\)
−0.682536 + 0.730852i \(0.739123\pi\)
\(828\) −76.3711 −2.65408
\(829\) −32.1395 −1.11625 −0.558126 0.829756i \(-0.688479\pi\)
−0.558126 + 0.829756i \(0.688479\pi\)
\(830\) 149.524 5.19006
\(831\) −42.4619 −1.47299
\(832\) 16.4607 0.570674
\(833\) −11.7680 −0.407736
\(834\) −111.275 −3.85316
\(835\) −27.2181 −0.941921
\(836\) −15.8087 −0.546755
\(837\) −0.809103 −0.0279667
\(838\) 80.1935 2.77024
\(839\) −34.0142 −1.17430 −0.587150 0.809478i \(-0.699750\pi\)
−0.587150 + 0.809478i \(0.699750\pi\)
\(840\) 126.489 4.36428
\(841\) −5.06043 −0.174497
\(842\) −48.0010 −1.65422
\(843\) 38.7723 1.33539
\(844\) 4.30932 0.148333
\(845\) 35.6279 1.22564
\(846\) −5.85259 −0.201216
\(847\) 5.50883 0.189286
\(848\) 2.60193 0.0893508
\(849\) 27.6394 0.948583
\(850\) −149.196 −5.11739
\(851\) −30.6268 −1.04987
\(852\) 144.167 4.93908
\(853\) −51.8556 −1.77550 −0.887750 0.460325i \(-0.847733\pi\)
−0.887750 + 0.460325i \(0.847733\pi\)
\(854\) 0.0847510 0.00290012
\(855\) 12.8500 0.439460
\(856\) 32.1412 1.09856
\(857\) 19.0989 0.652405 0.326202 0.945300i \(-0.394231\pi\)
0.326202 + 0.945300i \(0.394231\pi\)
\(858\) 109.169 3.72697
\(859\) −16.9110 −0.576996 −0.288498 0.957480i \(-0.593156\pi\)
−0.288498 + 0.957480i \(0.593156\pi\)
\(860\) −28.3224 −0.965787
\(861\) 48.3420 1.64749
\(862\) −84.1719 −2.86690
\(863\) −29.6949 −1.01082 −0.505412 0.862878i \(-0.668660\pi\)
−0.505412 + 0.862878i \(0.668660\pi\)
\(864\) 2.69874 0.0918129
\(865\) 62.9332 2.13979
\(866\) 45.4392 1.54409
\(867\) −46.4015 −1.57588
\(868\) 9.69568 0.329093
\(869\) 17.6299 0.598054
\(870\) −119.568 −4.05373
\(871\) −8.71544 −0.295311
\(872\) −7.62612 −0.258253
\(873\) 0.548679 0.0185700
\(874\) 13.4058 0.453459
\(875\) 43.1519 1.45880
\(876\) 87.6072 2.95997
\(877\) −39.8740 −1.34645 −0.673224 0.739439i \(-0.735091\pi\)
−0.673224 + 0.739439i \(0.735091\pi\)
\(878\) −18.8295 −0.635463
\(879\) 3.64074 0.122799
\(880\) −84.4905 −2.84817
\(881\) −10.3416 −0.348416 −0.174208 0.984709i \(-0.555736\pi\)
−0.174208 + 0.984709i \(0.555736\pi\)
\(882\) 16.4839 0.555043
\(883\) −23.4206 −0.788167 −0.394083 0.919075i \(-0.628938\pi\)
−0.394083 + 0.919075i \(0.628938\pi\)
\(884\) −120.921 −4.06700
\(885\) −132.277 −4.44643
\(886\) 25.1617 0.845326
\(887\) −35.6887 −1.19831 −0.599155 0.800633i \(-0.704497\pi\)
−0.599155 + 0.800633i \(0.704497\pi\)
\(888\) 83.6864 2.80833
\(889\) −18.9317 −0.634947
\(890\) −81.0712 −2.71751
\(891\) 29.1109 0.975253
\(892\) 33.9204 1.13574
\(893\) 0.701681 0.0234809
\(894\) −17.0305 −0.569584
\(895\) −63.3035 −2.11600
\(896\) 34.6749 1.15841
\(897\) −63.2302 −2.11119
\(898\) 6.14148 0.204944
\(899\) −4.91151 −0.163808
\(900\) 142.739 4.75798
\(901\) 2.60321 0.0867256
\(902\) −79.0518 −2.63214
\(903\) 9.57035 0.318481
\(904\) −29.5094 −0.981469
\(905\) −81.2163 −2.69972
\(906\) 42.8653 1.42410
\(907\) 45.9570 1.52598 0.762988 0.646413i \(-0.223731\pi\)
0.762988 + 0.646413i \(0.223731\pi\)
\(908\) −100.885 −3.34799
\(909\) 31.5508 1.04648
\(910\) 102.667 3.40338
\(911\) 37.8284 1.25331 0.626655 0.779297i \(-0.284424\pi\)
0.626655 + 0.779297i \(0.284424\pi\)
\(912\) −14.9629 −0.495470
\(913\) 56.4316 1.86761
\(914\) 67.1717 2.22184
\(915\) 0.146456 0.00484167
\(916\) 15.7408 0.520091
\(917\) −43.3067 −1.43011
\(918\) 12.0555 0.397892
\(919\) 51.1854 1.68845 0.844225 0.535988i \(-0.180061\pi\)
0.844225 + 0.535988i \(0.180061\pi\)
\(920\) 119.802 3.94975
\(921\) −8.67634 −0.285895
\(922\) −9.76761 −0.321679
\(923\) 62.7076 2.06404
\(924\) 89.0815 2.93057
\(925\) 57.2423 1.88212
\(926\) −6.89101 −0.226453
\(927\) 12.8503 0.422061
\(928\) 16.3822 0.537772
\(929\) 0.523188 0.0171652 0.00858262 0.999963i \(-0.497268\pi\)
0.00858262 + 0.999963i \(0.497268\pi\)
\(930\) 24.5309 0.804399
\(931\) −1.97630 −0.0647706
\(932\) 105.454 3.45427
\(933\) 8.06077 0.263898
\(934\) −103.400 −3.38334
\(935\) −84.5320 −2.76449
\(936\) 90.7686 2.96686
\(937\) −12.6585 −0.413536 −0.206768 0.978390i \(-0.566294\pi\)
−0.206768 + 0.978390i \(0.566294\pi\)
\(938\) −10.4124 −0.339976
\(939\) 10.6702 0.348209
\(940\) 11.7013 0.381654
\(941\) −29.5087 −0.961957 −0.480978 0.876732i \(-0.659718\pi\)
−0.480978 + 0.876732i \(0.659718\pi\)
\(942\) 135.893 4.42763
\(943\) 45.7863 1.49101
\(944\) 80.9197 2.63371
\(945\) −6.99107 −0.227419
\(946\) −15.6500 −0.508826
\(947\) −5.55968 −0.180665 −0.0903327 0.995912i \(-0.528793\pi\)
−0.0903327 + 0.995912i \(0.528793\pi\)
\(948\) 52.0656 1.69101
\(949\) 38.1060 1.23697
\(950\) −25.0559 −0.812919
\(951\) −65.8626 −2.13574
\(952\) −77.4171 −2.50910
\(953\) −38.6940 −1.25342 −0.626711 0.779252i \(-0.715599\pi\)
−0.626711 + 0.779252i \(0.715599\pi\)
\(954\) −3.64644 −0.118058
\(955\) −37.9548 −1.22819
\(956\) −82.7081 −2.67497
\(957\) −45.1258 −1.45871
\(958\) 50.2002 1.62190
\(959\) −25.2168 −0.814294
\(960\) 33.9838 1.09682
\(961\) −29.9923 −0.967495
\(962\) 67.9255 2.19001
\(963\) −18.3993 −0.592911
\(964\) −64.9571 −2.09213
\(965\) 58.9925 1.89904
\(966\) −75.5414 −2.43051
\(967\) 45.5036 1.46330 0.731649 0.681682i \(-0.238751\pi\)
0.731649 + 0.681682i \(0.238751\pi\)
\(968\) −14.2569 −0.458233
\(969\) −14.9702 −0.480913
\(970\) −1.60612 −0.0515694
\(971\) 39.9132 1.28087 0.640437 0.768010i \(-0.278753\pi\)
0.640437 + 0.768010i \(0.278753\pi\)
\(972\) 96.3923 3.09178
\(973\) −39.4949 −1.26615
\(974\) 55.6446 1.78297
\(975\) 118.179 3.78475
\(976\) −0.0895936 −0.00286782
\(977\) −21.2315 −0.679255 −0.339628 0.940560i \(-0.610301\pi\)
−0.339628 + 0.940560i \(0.610301\pi\)
\(978\) 65.9159 2.10776
\(979\) −30.5969 −0.977881
\(980\) −32.9569 −1.05277
\(981\) 4.36560 0.139383
\(982\) −71.5056 −2.28184
\(983\) 7.98369 0.254640 0.127320 0.991862i \(-0.459362\pi\)
0.127320 + 0.991862i \(0.459362\pi\)
\(984\) −125.109 −3.98833
\(985\) 77.8457 2.48037
\(986\) 73.1810 2.33056
\(987\) −3.95395 −0.125855
\(988\) −20.3073 −0.646060
\(989\) 9.06440 0.288231
\(990\) 118.408 3.76325
\(991\) 17.0428 0.541381 0.270691 0.962666i \(-0.412748\pi\)
0.270691 + 0.962666i \(0.412748\pi\)
\(992\) −3.36102 −0.106712
\(993\) −44.6851 −1.41804
\(994\) 74.9171 2.37623
\(995\) 69.5239 2.20406
\(996\) 166.657 5.28073
\(997\) 17.1096 0.541866 0.270933 0.962598i \(-0.412668\pi\)
0.270933 + 0.962598i \(0.412668\pi\)
\(998\) 12.9138 0.408779
\(999\) −4.62536 −0.146340
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 \(a_p\))