Properties

Label 619.2.a.b.1.19
Level 619
Weight 2
Character 619.1
Self dual Yes
Analytic conductor 4.943
Analytic rank 0
Dimension 30
CM No

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Newspace parameters

Level: \( N \) = \( 619 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 619.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(4.94273988512\)
Analytic rank: \(0\)
Dimension: \(30\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
Character \(\chi\) = 619.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.39793 q^{2} +2.10519 q^{3} -0.0457880 q^{4} +3.90881 q^{5} +2.94291 q^{6} -1.82243 q^{7} -2.85987 q^{8} +1.43181 q^{9} +O(q^{10})\) \(q+1.39793 q^{2} +2.10519 q^{3} -0.0457880 q^{4} +3.90881 q^{5} +2.94291 q^{6} -1.82243 q^{7} -2.85987 q^{8} +1.43181 q^{9} +5.46425 q^{10} +4.06764 q^{11} -0.0963923 q^{12} -2.56773 q^{13} -2.54763 q^{14} +8.22879 q^{15} -3.90633 q^{16} +2.96017 q^{17} +2.00158 q^{18} -3.33421 q^{19} -0.178977 q^{20} -3.83656 q^{21} +5.68628 q^{22} -9.09190 q^{23} -6.02057 q^{24} +10.2788 q^{25} -3.58952 q^{26} -3.30132 q^{27} +0.0834454 q^{28} +7.13218 q^{29} +11.5033 q^{30} +3.95596 q^{31} +0.258965 q^{32} +8.56314 q^{33} +4.13812 q^{34} -7.12354 q^{35} -0.0655599 q^{36} -2.67606 q^{37} -4.66099 q^{38} -5.40556 q^{39} -11.1787 q^{40} -9.73483 q^{41} -5.36325 q^{42} +3.74301 q^{43} -0.186249 q^{44} +5.59670 q^{45} -12.7098 q^{46} -6.42485 q^{47} -8.22355 q^{48} -3.67874 q^{49} +14.3691 q^{50} +6.23171 q^{51} +0.117571 q^{52} +1.59008 q^{53} -4.61502 q^{54} +15.8996 q^{55} +5.21192 q^{56} -7.01913 q^{57} +9.97029 q^{58} -11.4488 q^{59} -0.376779 q^{60} +11.9419 q^{61} +5.53016 q^{62} -2.60938 q^{63} +8.17467 q^{64} -10.0368 q^{65} +11.9707 q^{66} -1.47790 q^{67} -0.135540 q^{68} -19.1402 q^{69} -9.95823 q^{70} +15.1260 q^{71} -4.09481 q^{72} -7.51431 q^{73} -3.74095 q^{74} +21.6388 q^{75} +0.152667 q^{76} -7.41299 q^{77} -7.55660 q^{78} +1.32751 q^{79} -15.2691 q^{80} -11.2454 q^{81} -13.6086 q^{82} +9.23897 q^{83} +0.175668 q^{84} +11.5708 q^{85} +5.23248 q^{86} +15.0146 q^{87} -11.6329 q^{88} +6.11475 q^{89} +7.82380 q^{90} +4.67952 q^{91} +0.416300 q^{92} +8.32804 q^{93} -8.98150 q^{94} -13.0328 q^{95} +0.545169 q^{96} +14.0971 q^{97} -5.14263 q^{98} +5.82411 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30q + 9q^{2} + q^{3} + 33q^{4} + 21q^{5} + 6q^{6} + 2q^{7} + 27q^{8} + 43q^{9} + O(q^{10}) \) \( 30q + 9q^{2} + q^{3} + 33q^{4} + 21q^{5} + 6q^{6} + 2q^{7} + 27q^{8} + 43q^{9} + 5q^{10} + 23q^{11} - 6q^{12} + 9q^{13} + 7q^{14} - 2q^{15} + 35q^{16} + 4q^{17} + 10q^{18} - q^{19} + 29q^{20} + 30q^{21} + 4q^{23} + 4q^{24} + 35q^{25} + q^{26} - 5q^{27} - 13q^{28} + 90q^{29} - 31q^{30} + 2q^{31} + 43q^{32} - 6q^{33} - 9q^{34} + 9q^{35} + 33q^{36} + 19q^{37} + 5q^{38} + 32q^{39} - 12q^{40} + 59q^{41} - 25q^{42} - 4q^{43} + 52q^{44} + 30q^{45} - q^{46} + 4q^{47} - 44q^{48} + 30q^{49} + 31q^{50} - 12q^{52} + 34q^{53} - 28q^{54} - 17q^{55} + 2q^{56} - 8q^{57} + 6q^{58} + 13q^{59} - 64q^{60} + 16q^{61} + 28q^{62} - 40q^{63} + 37q^{64} + 31q^{65} - 59q^{66} - 11q^{67} - 52q^{68} + 6q^{69} - 40q^{70} + 42q^{71} + 6q^{72} - 4q^{73} + 16q^{74} - 52q^{75} - 42q^{76} + 29q^{77} - 56q^{78} + 3q^{79} + 21q^{80} + 30q^{81} - 43q^{82} - 11q^{83} - 36q^{84} + 19q^{85} - 11q^{86} - 20q^{87} - 47q^{88} + 58q^{89} - 33q^{90} - 39q^{91} - 7q^{92} - 15q^{93} - 46q^{94} + 23q^{95} - 70q^{96} - 9q^{97} - 8q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.39793 0.988487 0.494243 0.869324i \(-0.335445\pi\)
0.494243 + 0.869324i \(0.335445\pi\)
\(3\) 2.10519 1.21543 0.607715 0.794155i \(-0.292086\pi\)
0.607715 + 0.794155i \(0.292086\pi\)
\(4\) −0.0457880 −0.0228940
\(5\) 3.90881 1.74807 0.874037 0.485859i \(-0.161493\pi\)
0.874037 + 0.485859i \(0.161493\pi\)
\(6\) 2.94291 1.20144
\(7\) −1.82243 −0.688814 −0.344407 0.938820i \(-0.611920\pi\)
−0.344407 + 0.938820i \(0.611920\pi\)
\(8\) −2.85987 −1.01112
\(9\) 1.43181 0.477272
\(10\) 5.46425 1.72795
\(11\) 4.06764 1.22644 0.613220 0.789913i \(-0.289874\pi\)
0.613220 + 0.789913i \(0.289874\pi\)
\(12\) −0.0963923 −0.0278260
\(13\) −2.56773 −0.712161 −0.356081 0.934455i \(-0.615887\pi\)
−0.356081 + 0.934455i \(0.615887\pi\)
\(14\) −2.54763 −0.680884
\(15\) 8.22879 2.12466
\(16\) −3.90633 −0.976582
\(17\) 2.96017 0.717947 0.358973 0.933348i \(-0.383127\pi\)
0.358973 + 0.933348i \(0.383127\pi\)
\(18\) 2.00158 0.471777
\(19\) −3.33421 −0.764919 −0.382460 0.923972i \(-0.624923\pi\)
−0.382460 + 0.923972i \(0.624923\pi\)
\(20\) −0.178977 −0.0400204
\(21\) −3.83656 −0.837206
\(22\) 5.68628 1.21232
\(23\) −9.09190 −1.89579 −0.947896 0.318580i \(-0.896794\pi\)
−0.947896 + 0.318580i \(0.896794\pi\)
\(24\) −6.02057 −1.22894
\(25\) 10.2788 2.05576
\(26\) −3.58952 −0.703962
\(27\) −3.30132 −0.635340
\(28\) 0.0834454 0.0157697
\(29\) 7.13218 1.32441 0.662206 0.749322i \(-0.269620\pi\)
0.662206 + 0.749322i \(0.269620\pi\)
\(30\) 11.5033 2.10020
\(31\) 3.95596 0.710512 0.355256 0.934769i \(-0.384394\pi\)
0.355256 + 0.934769i \(0.384394\pi\)
\(32\) 0.258965 0.0457789
\(33\) 8.56314 1.49065
\(34\) 4.13812 0.709681
\(35\) −7.12354 −1.20410
\(36\) −0.0655599 −0.0109266
\(37\) −2.67606 −0.439942 −0.219971 0.975506i \(-0.570596\pi\)
−0.219971 + 0.975506i \(0.570596\pi\)
\(38\) −4.66099 −0.756113
\(39\) −5.40556 −0.865582
\(40\) −11.1787 −1.76751
\(41\) −9.73483 −1.52032 −0.760162 0.649733i \(-0.774881\pi\)
−0.760162 + 0.649733i \(0.774881\pi\)
\(42\) −5.36325 −0.827567
\(43\) 3.74301 0.570804 0.285402 0.958408i \(-0.407873\pi\)
0.285402 + 0.958408i \(0.407873\pi\)
\(44\) −0.186249 −0.0280781
\(45\) 5.59670 0.834306
\(46\) −12.7098 −1.87397
\(47\) −6.42485 −0.937161 −0.468580 0.883421i \(-0.655234\pi\)
−0.468580 + 0.883421i \(0.655234\pi\)
\(48\) −8.22355 −1.18697
\(49\) −3.67874 −0.525535
\(50\) 14.3691 2.03210
\(51\) 6.23171 0.872615
\(52\) 0.117571 0.0163042
\(53\) 1.59008 0.218414 0.109207 0.994019i \(-0.465169\pi\)
0.109207 + 0.994019i \(0.465169\pi\)
\(54\) −4.61502 −0.628025
\(55\) 15.8996 2.14391
\(56\) 5.21192 0.696472
\(57\) −7.01913 −0.929707
\(58\) 9.97029 1.30916
\(59\) −11.4488 −1.49051 −0.745256 0.666779i \(-0.767673\pi\)
−0.745256 + 0.666779i \(0.767673\pi\)
\(60\) −0.376779 −0.0486420
\(61\) 11.9419 1.52901 0.764504 0.644619i \(-0.222984\pi\)
0.764504 + 0.644619i \(0.222984\pi\)
\(62\) 5.53016 0.702331
\(63\) −2.60938 −0.328752
\(64\) 8.17467 1.02183
\(65\) −10.0368 −1.24491
\(66\) 11.9707 1.47349
\(67\) −1.47790 −0.180554 −0.0902772 0.995917i \(-0.528775\pi\)
−0.0902772 + 0.995917i \(0.528775\pi\)
\(68\) −0.135540 −0.0164367
\(69\) −19.1402 −2.30420
\(70\) −9.95823 −1.19024
\(71\) 15.1260 1.79512 0.897561 0.440890i \(-0.145337\pi\)
0.897561 + 0.440890i \(0.145337\pi\)
\(72\) −4.09481 −0.482578
\(73\) −7.51431 −0.879483 −0.439741 0.898124i \(-0.644930\pi\)
−0.439741 + 0.898124i \(0.644930\pi\)
\(74\) −3.74095 −0.434877
\(75\) 21.6388 2.49864
\(76\) 0.152667 0.0175121
\(77\) −7.41299 −0.844789
\(78\) −7.55660 −0.855617
\(79\) 1.32751 0.149356 0.0746782 0.997208i \(-0.476207\pi\)
0.0746782 + 0.997208i \(0.476207\pi\)
\(80\) −15.2691 −1.70714
\(81\) −11.2454 −1.24948
\(82\) −13.6086 −1.50282
\(83\) 9.23897 1.01411 0.507055 0.861914i \(-0.330734\pi\)
0.507055 + 0.861914i \(0.330734\pi\)
\(84\) 0.175668 0.0191670
\(85\) 11.5708 1.25502
\(86\) 5.23248 0.564232
\(87\) 15.0146 1.60973
\(88\) −11.6329 −1.24007
\(89\) 6.11475 0.648162 0.324081 0.946029i \(-0.394945\pi\)
0.324081 + 0.946029i \(0.394945\pi\)
\(90\) 7.82380 0.824701
\(91\) 4.67952 0.490547
\(92\) 0.416300 0.0434022
\(93\) 8.32804 0.863578
\(94\) −8.98150 −0.926371
\(95\) −13.0328 −1.33714
\(96\) 0.545169 0.0556411
\(97\) 14.0971 1.43134 0.715671 0.698438i \(-0.246121\pi\)
0.715671 + 0.698438i \(0.246121\pi\)
\(98\) −5.14263 −0.519484
\(99\) 5.82411 0.585345
\(100\) −0.470646 −0.0470646
\(101\) 1.48940 0.148201 0.0741004 0.997251i \(-0.476391\pi\)
0.0741004 + 0.997251i \(0.476391\pi\)
\(102\) 8.71151 0.862568
\(103\) −16.7916 −1.65452 −0.827260 0.561819i \(-0.810102\pi\)
−0.827260 + 0.561819i \(0.810102\pi\)
\(104\) 7.34339 0.720078
\(105\) −14.9964 −1.46350
\(106\) 2.22282 0.215899
\(107\) −2.61690 −0.252985 −0.126492 0.991968i \(-0.540372\pi\)
−0.126492 + 0.991968i \(0.540372\pi\)
\(108\) 0.151161 0.0145455
\(109\) 17.2308 1.65041 0.825206 0.564832i \(-0.191059\pi\)
0.825206 + 0.564832i \(0.191059\pi\)
\(110\) 22.2266 2.11922
\(111\) −5.63361 −0.534719
\(112\) 7.11902 0.672684
\(113\) −18.5328 −1.74342 −0.871710 0.490023i \(-0.836989\pi\)
−0.871710 + 0.490023i \(0.836989\pi\)
\(114\) −9.81226 −0.919003
\(115\) −35.5385 −3.31399
\(116\) −0.326568 −0.0303211
\(117\) −3.67652 −0.339894
\(118\) −16.0047 −1.47335
\(119\) −5.39471 −0.494532
\(120\) −23.5333 −2.14828
\(121\) 5.54568 0.504153
\(122\) 16.6940 1.51140
\(123\) −20.4936 −1.84785
\(124\) −0.181135 −0.0162664
\(125\) 20.6339 1.84555
\(126\) −3.64774 −0.324967
\(127\) −0.429692 −0.0381290 −0.0190645 0.999818i \(-0.506069\pi\)
−0.0190645 + 0.999818i \(0.506069\pi\)
\(128\) 10.9097 0.964290
\(129\) 7.87974 0.693773
\(130\) −14.0307 −1.23058
\(131\) −5.27070 −0.460504 −0.230252 0.973131i \(-0.573955\pi\)
−0.230252 + 0.973131i \(0.573955\pi\)
\(132\) −0.392089 −0.0341270
\(133\) 6.07636 0.526888
\(134\) −2.06600 −0.178476
\(135\) −12.9043 −1.11062
\(136\) −8.46571 −0.725928
\(137\) −3.67358 −0.313855 −0.156928 0.987610i \(-0.550159\pi\)
−0.156928 + 0.987610i \(0.550159\pi\)
\(138\) −26.7566 −2.27767
\(139\) 14.1968 1.20415 0.602077 0.798438i \(-0.294340\pi\)
0.602077 + 0.798438i \(0.294340\pi\)
\(140\) 0.326173 0.0275666
\(141\) −13.5255 −1.13905
\(142\) 21.1451 1.77445
\(143\) −10.4446 −0.873422
\(144\) −5.59314 −0.466095
\(145\) 27.8784 2.31517
\(146\) −10.5045 −0.869357
\(147\) −7.74444 −0.638751
\(148\) 0.122531 0.0100720
\(149\) −6.70971 −0.549681 −0.274840 0.961490i \(-0.588625\pi\)
−0.274840 + 0.961490i \(0.588625\pi\)
\(150\) 30.2496 2.46987
\(151\) 3.13432 0.255068 0.127534 0.991834i \(-0.459294\pi\)
0.127534 + 0.991834i \(0.459294\pi\)
\(152\) 9.53540 0.773423
\(153\) 4.23842 0.342656
\(154\) −10.3629 −0.835063
\(155\) 15.4631 1.24203
\(156\) 0.247510 0.0198166
\(157\) 1.34412 0.107273 0.0536364 0.998561i \(-0.482919\pi\)
0.0536364 + 0.998561i \(0.482919\pi\)
\(158\) 1.85577 0.147637
\(159\) 3.34741 0.265467
\(160\) 1.01224 0.0800249
\(161\) 16.5694 1.30585
\(162\) −15.7202 −1.23510
\(163\) −23.3324 −1.82753 −0.913767 0.406238i \(-0.866840\pi\)
−0.913767 + 0.406238i \(0.866840\pi\)
\(164\) 0.445738 0.0348063
\(165\) 33.4717 2.60577
\(166\) 12.9154 1.00243
\(167\) 1.80311 0.139529 0.0697643 0.997564i \(-0.477775\pi\)
0.0697643 + 0.997564i \(0.477775\pi\)
\(168\) 10.9721 0.846514
\(169\) −6.40674 −0.492827
\(170\) 16.1751 1.24057
\(171\) −4.77397 −0.365074
\(172\) −0.171385 −0.0130680
\(173\) −13.8430 −1.05247 −0.526233 0.850340i \(-0.676396\pi\)
−0.526233 + 0.850340i \(0.676396\pi\)
\(174\) 20.9893 1.59120
\(175\) −18.7324 −1.41604
\(176\) −15.8895 −1.19772
\(177\) −24.1019 −1.81161
\(178\) 8.54800 0.640700
\(179\) −16.9237 −1.26494 −0.632469 0.774585i \(-0.717959\pi\)
−0.632469 + 0.774585i \(0.717959\pi\)
\(180\) −0.256261 −0.0191006
\(181\) 6.28833 0.467408 0.233704 0.972308i \(-0.424915\pi\)
0.233704 + 0.972308i \(0.424915\pi\)
\(182\) 6.54165 0.484899
\(183\) 25.1400 1.85840
\(184\) 26.0017 1.91687
\(185\) −10.4602 −0.769051
\(186\) 11.6420 0.853635
\(187\) 12.0409 0.880518
\(188\) 0.294181 0.0214553
\(189\) 6.01644 0.437631
\(190\) −18.2189 −1.32174
\(191\) 23.0612 1.66865 0.834323 0.551275i \(-0.185859\pi\)
0.834323 + 0.551275i \(0.185859\pi\)
\(192\) 17.2092 1.24197
\(193\) 22.3229 1.60684 0.803418 0.595415i \(-0.203012\pi\)
0.803418 + 0.595415i \(0.203012\pi\)
\(194\) 19.7067 1.41486
\(195\) −21.1293 −1.51310
\(196\) 0.168442 0.0120316
\(197\) 7.74217 0.551607 0.275804 0.961214i \(-0.411056\pi\)
0.275804 + 0.961214i \(0.411056\pi\)
\(198\) 8.14170 0.578605
\(199\) 19.1916 1.36045 0.680227 0.733002i \(-0.261881\pi\)
0.680227 + 0.733002i \(0.261881\pi\)
\(200\) −29.3961 −2.07862
\(201\) −3.11126 −0.219451
\(202\) 2.08208 0.146495
\(203\) −12.9979 −0.912274
\(204\) −0.285338 −0.0199776
\(205\) −38.0516 −2.65764
\(206\) −23.4734 −1.63547
\(207\) −13.0179 −0.904808
\(208\) 10.0304 0.695484
\(209\) −13.5623 −0.938127
\(210\) −20.9639 −1.44665
\(211\) 6.89545 0.474702 0.237351 0.971424i \(-0.423721\pi\)
0.237351 + 0.971424i \(0.423721\pi\)
\(212\) −0.0728064 −0.00500037
\(213\) 31.8430 2.18185
\(214\) −3.65824 −0.250072
\(215\) 14.6307 0.997808
\(216\) 9.44136 0.642403
\(217\) −7.20947 −0.489411
\(218\) 24.0875 1.63141
\(219\) −15.8190 −1.06895
\(220\) −0.728012 −0.0490826
\(221\) −7.60093 −0.511294
\(222\) −7.87540 −0.528562
\(223\) −6.29320 −0.421424 −0.210712 0.977548i \(-0.567578\pi\)
−0.210712 + 0.977548i \(0.567578\pi\)
\(224\) −0.471945 −0.0315332
\(225\) 14.7174 0.981158
\(226\) −25.9076 −1.72335
\(227\) 9.01887 0.598603 0.299302 0.954159i \(-0.403246\pi\)
0.299302 + 0.954159i \(0.403246\pi\)
\(228\) 0.321392 0.0212847
\(229\) 16.0739 1.06219 0.531097 0.847311i \(-0.321780\pi\)
0.531097 + 0.847311i \(0.321780\pi\)
\(230\) −49.6804 −3.27583
\(231\) −15.6057 −1.02678
\(232\) −20.3971 −1.33914
\(233\) 9.93384 0.650788 0.325394 0.945579i \(-0.394503\pi\)
0.325394 + 0.945579i \(0.394503\pi\)
\(234\) −5.13952 −0.335981
\(235\) −25.1135 −1.63823
\(236\) 0.524219 0.0341237
\(237\) 2.79465 0.181532
\(238\) −7.54143 −0.488838
\(239\) −5.63614 −0.364571 −0.182286 0.983246i \(-0.558350\pi\)
−0.182286 + 0.983246i \(0.558350\pi\)
\(240\) −32.1443 −2.07491
\(241\) −6.89445 −0.444110 −0.222055 0.975034i \(-0.571277\pi\)
−0.222055 + 0.975034i \(0.571277\pi\)
\(242\) 7.75248 0.498348
\(243\) −13.7696 −0.883320
\(244\) −0.546797 −0.0350051
\(245\) −14.3795 −0.918674
\(246\) −28.6487 −1.82657
\(247\) 8.56135 0.544746
\(248\) −11.3135 −0.718411
\(249\) 19.4498 1.23258
\(250\) 28.8448 1.82431
\(251\) 6.50916 0.410854 0.205427 0.978672i \(-0.434142\pi\)
0.205427 + 0.978672i \(0.434142\pi\)
\(252\) 0.119478 0.00752643
\(253\) −36.9826 −2.32507
\(254\) −0.600680 −0.0376900
\(255\) 24.3586 1.52540
\(256\) −1.09833 −0.0686457
\(257\) 6.61342 0.412534 0.206267 0.978496i \(-0.433869\pi\)
0.206267 + 0.978496i \(0.433869\pi\)
\(258\) 11.0153 0.685785
\(259\) 4.87694 0.303038
\(260\) 0.459564 0.0285010
\(261\) 10.2120 0.632104
\(262\) −7.36808 −0.455202
\(263\) −1.67328 −0.103179 −0.0515894 0.998668i \(-0.516429\pi\)
−0.0515894 + 0.998668i \(0.516429\pi\)
\(264\) −24.4895 −1.50722
\(265\) 6.21532 0.381804
\(266\) 8.49434 0.520821
\(267\) 12.8727 0.787796
\(268\) 0.0676701 0.00413361
\(269\) 14.8051 0.902684 0.451342 0.892351i \(-0.350945\pi\)
0.451342 + 0.892351i \(0.350945\pi\)
\(270\) −18.0393 −1.09783
\(271\) 3.80387 0.231068 0.115534 0.993304i \(-0.463142\pi\)
0.115534 + 0.993304i \(0.463142\pi\)
\(272\) −11.5634 −0.701134
\(273\) 9.85127 0.596226
\(274\) −5.13542 −0.310242
\(275\) 41.8105 2.52127
\(276\) 0.876389 0.0527524
\(277\) 4.51184 0.271090 0.135545 0.990771i \(-0.456721\pi\)
0.135545 + 0.990771i \(0.456721\pi\)
\(278\) 19.8461 1.19029
\(279\) 5.66421 0.339107
\(280\) 20.3724 1.21748
\(281\) 23.8229 1.42115 0.710577 0.703620i \(-0.248434\pi\)
0.710577 + 0.703620i \(0.248434\pi\)
\(282\) −18.9077 −1.12594
\(283\) −25.2254 −1.49949 −0.749747 0.661725i \(-0.769825\pi\)
−0.749747 + 0.661725i \(0.769825\pi\)
\(284\) −0.692587 −0.0410975
\(285\) −27.4365 −1.62520
\(286\) −14.6008 −0.863366
\(287\) 17.7411 1.04722
\(288\) 0.370789 0.0218490
\(289\) −8.23739 −0.484552
\(290\) 38.9720 2.28852
\(291\) 29.6770 1.73970
\(292\) 0.344065 0.0201349
\(293\) 27.0327 1.57926 0.789632 0.613580i \(-0.210271\pi\)
0.789632 + 0.613580i \(0.210271\pi\)
\(294\) −10.8262 −0.631397
\(295\) −44.7514 −2.60552
\(296\) 7.65319 0.444833
\(297\) −13.4286 −0.779206
\(298\) −9.37971 −0.543352
\(299\) 23.3456 1.35011
\(300\) −0.990799 −0.0572038
\(301\) −6.82139 −0.393178
\(302\) 4.38157 0.252131
\(303\) 3.13547 0.180128
\(304\) 13.0245 0.747006
\(305\) 46.6788 2.67282
\(306\) 5.92502 0.338711
\(307\) 0.337749 0.0192764 0.00963819 0.999954i \(-0.496932\pi\)
0.00963819 + 0.999954i \(0.496932\pi\)
\(308\) 0.339426 0.0193406
\(309\) −35.3494 −2.01096
\(310\) 21.6164 1.22773
\(311\) 4.79950 0.272154 0.136077 0.990698i \(-0.456550\pi\)
0.136077 + 0.990698i \(0.456550\pi\)
\(312\) 15.4592 0.875205
\(313\) 6.45585 0.364906 0.182453 0.983215i \(-0.441596\pi\)
0.182453 + 0.983215i \(0.441596\pi\)
\(314\) 1.87899 0.106038
\(315\) −10.1996 −0.574682
\(316\) −0.0607839 −0.00341936
\(317\) 14.8403 0.833513 0.416756 0.909018i \(-0.363167\pi\)
0.416756 + 0.909018i \(0.363167\pi\)
\(318\) 4.67945 0.262411
\(319\) 29.0111 1.62431
\(320\) 31.9533 1.78624
\(321\) −5.50906 −0.307486
\(322\) 23.1628 1.29081
\(323\) −9.86982 −0.549171
\(324\) 0.514902 0.0286057
\(325\) −26.3933 −1.46404
\(326\) −32.6171 −1.80649
\(327\) 36.2741 2.00596
\(328\) 27.8403 1.53723
\(329\) 11.7088 0.645530
\(330\) 46.7912 2.57577
\(331\) −7.46778 −0.410466 −0.205233 0.978713i \(-0.565795\pi\)
−0.205233 + 0.978713i \(0.565795\pi\)
\(332\) −0.423034 −0.0232170
\(333\) −3.83162 −0.209972
\(334\) 2.52062 0.137922
\(335\) −5.77684 −0.315622
\(336\) 14.9869 0.817600
\(337\) 31.2200 1.70066 0.850330 0.526250i \(-0.176402\pi\)
0.850330 + 0.526250i \(0.176402\pi\)
\(338\) −8.95619 −0.487152
\(339\) −39.0150 −2.11901
\(340\) −0.529801 −0.0287325
\(341\) 16.0914 0.871399
\(342\) −6.67368 −0.360871
\(343\) 19.4613 1.05081
\(344\) −10.7045 −0.577150
\(345\) −74.8153 −4.02792
\(346\) −19.3516 −1.04035
\(347\) 12.6664 0.679967 0.339983 0.940431i \(-0.389579\pi\)
0.339983 + 0.940431i \(0.389579\pi\)
\(348\) −0.687487 −0.0368532
\(349\) −16.6138 −0.889315 −0.444657 0.895701i \(-0.646675\pi\)
−0.444657 + 0.895701i \(0.646675\pi\)
\(350\) −26.1867 −1.39974
\(351\) 8.47692 0.452464
\(352\) 1.05337 0.0561450
\(353\) 9.37962 0.499227 0.249613 0.968346i \(-0.419696\pi\)
0.249613 + 0.968346i \(0.419696\pi\)
\(354\) −33.6929 −1.79076
\(355\) 59.1246 3.13801
\(356\) −0.279982 −0.0148390
\(357\) −11.3569 −0.601069
\(358\) −23.6582 −1.25038
\(359\) −21.0027 −1.10848 −0.554241 0.832356i \(-0.686991\pi\)
−0.554241 + 0.832356i \(0.686991\pi\)
\(360\) −16.0058 −0.843581
\(361\) −7.88307 −0.414898
\(362\) 8.79065 0.462027
\(363\) 11.6747 0.612763
\(364\) −0.214266 −0.0112306
\(365\) −29.3720 −1.53740
\(366\) 35.1440 1.83701
\(367\) 12.0236 0.627627 0.313813 0.949485i \(-0.398393\pi\)
0.313813 + 0.949485i \(0.398393\pi\)
\(368\) 35.5159 1.85140
\(369\) −13.9385 −0.725608
\(370\) −14.6227 −0.760197
\(371\) −2.89781 −0.150447
\(372\) −0.381324 −0.0197707
\(373\) −8.30339 −0.429933 −0.214967 0.976621i \(-0.568964\pi\)
−0.214967 + 0.976621i \(0.568964\pi\)
\(374\) 16.8324 0.870380
\(375\) 43.4383 2.24314
\(376\) 18.3742 0.947579
\(377\) −18.3135 −0.943195
\(378\) 8.41057 0.432593
\(379\) −11.8196 −0.607133 −0.303566 0.952810i \(-0.598177\pi\)
−0.303566 + 0.952810i \(0.598177\pi\)
\(380\) 0.596745 0.0306124
\(381\) −0.904582 −0.0463432
\(382\) 32.2379 1.64943
\(383\) 5.44234 0.278091 0.139045 0.990286i \(-0.455597\pi\)
0.139045 + 0.990286i \(0.455597\pi\)
\(384\) 22.9670 1.17203
\(385\) −28.9760 −1.47675
\(386\) 31.2059 1.58834
\(387\) 5.35930 0.272429
\(388\) −0.645477 −0.0327691
\(389\) 1.80435 0.0914841 0.0457421 0.998953i \(-0.485435\pi\)
0.0457421 + 0.998953i \(0.485435\pi\)
\(390\) −29.5373 −1.49568
\(391\) −26.9136 −1.36108
\(392\) 10.5207 0.531377
\(393\) −11.0958 −0.559710
\(394\) 10.8230 0.545256
\(395\) 5.18898 0.261086
\(396\) −0.266674 −0.0134009
\(397\) −24.4295 −1.22608 −0.613040 0.790052i \(-0.710054\pi\)
−0.613040 + 0.790052i \(0.710054\pi\)
\(398\) 26.8285 1.34479
\(399\) 12.7919 0.640395
\(400\) −40.1524 −2.00762
\(401\) 11.1686 0.557735 0.278868 0.960330i \(-0.410041\pi\)
0.278868 + 0.960330i \(0.410041\pi\)
\(402\) −4.34933 −0.216925
\(403\) −10.1579 −0.505999
\(404\) −0.0681966 −0.00339291
\(405\) −43.9560 −2.18419
\(406\) −18.1702 −0.901771
\(407\) −10.8852 −0.539562
\(408\) −17.8219 −0.882316
\(409\) 3.26343 0.161366 0.0806832 0.996740i \(-0.474290\pi\)
0.0806832 + 0.996740i \(0.474290\pi\)
\(410\) −53.1935 −2.62704
\(411\) −7.73358 −0.381470
\(412\) 0.768851 0.0378786
\(413\) 20.8647 1.02669
\(414\) −18.1982 −0.894390
\(415\) 36.1134 1.77274
\(416\) −0.664952 −0.0326020
\(417\) 29.8869 1.46357
\(418\) −18.9592 −0.927326
\(419\) 11.2453 0.549368 0.274684 0.961535i \(-0.411427\pi\)
0.274684 + 0.961535i \(0.411427\pi\)
\(420\) 0.686655 0.0335053
\(421\) −8.53714 −0.416075 −0.208037 0.978121i \(-0.566708\pi\)
−0.208037 + 0.978121i \(0.566708\pi\)
\(422\) 9.63936 0.469237
\(423\) −9.19920 −0.447280
\(424\) −4.54742 −0.220842
\(425\) 30.4271 1.47593
\(426\) 44.5143 2.15673
\(427\) −21.7634 −1.05320
\(428\) 0.119822 0.00579183
\(429\) −21.9879 −1.06158
\(430\) 20.4528 0.986320
\(431\) 23.9686 1.15453 0.577263 0.816558i \(-0.304121\pi\)
0.577263 + 0.816558i \(0.304121\pi\)
\(432\) 12.8961 0.620462
\(433\) 27.2069 1.30748 0.653740 0.756719i \(-0.273199\pi\)
0.653740 + 0.756719i \(0.273199\pi\)
\(434\) −10.0783 −0.483776
\(435\) 58.6892 2.81393
\(436\) −0.788963 −0.0377845
\(437\) 30.3143 1.45013
\(438\) −22.1139 −1.05664
\(439\) −29.8150 −1.42299 −0.711496 0.702690i \(-0.751982\pi\)
−0.711496 + 0.702690i \(0.751982\pi\)
\(440\) −45.4709 −2.16774
\(441\) −5.26728 −0.250823
\(442\) −10.6256 −0.505407
\(443\) −39.7850 −1.89024 −0.945122 0.326718i \(-0.894057\pi\)
−0.945122 + 0.326718i \(0.894057\pi\)
\(444\) 0.257952 0.0122418
\(445\) 23.9014 1.13304
\(446\) −8.79746 −0.416572
\(447\) −14.1252 −0.668099
\(448\) −14.8978 −0.703854
\(449\) −23.0458 −1.08760 −0.543799 0.839216i \(-0.683015\pi\)
−0.543799 + 0.839216i \(0.683015\pi\)
\(450\) 20.5739 0.969862
\(451\) −39.5977 −1.86459
\(452\) 0.848579 0.0399138
\(453\) 6.59834 0.310017
\(454\) 12.6078 0.591711
\(455\) 18.2914 0.857512
\(456\) 20.0738 0.940042
\(457\) 11.6277 0.543920 0.271960 0.962309i \(-0.412328\pi\)
0.271960 + 0.962309i \(0.412328\pi\)
\(458\) 22.4702 1.04997
\(459\) −9.77248 −0.456140
\(460\) 1.62724 0.0758703
\(461\) −29.5994 −1.37858 −0.689292 0.724484i \(-0.742078\pi\)
−0.689292 + 0.724484i \(0.742078\pi\)
\(462\) −21.8158 −1.01496
\(463\) 37.2162 1.72959 0.864793 0.502129i \(-0.167450\pi\)
0.864793 + 0.502129i \(0.167450\pi\)
\(464\) −27.8606 −1.29340
\(465\) 32.5528 1.50960
\(466\) 13.8868 0.643295
\(467\) 11.6426 0.538757 0.269379 0.963034i \(-0.413182\pi\)
0.269379 + 0.963034i \(0.413182\pi\)
\(468\) 0.168340 0.00778153
\(469\) 2.69337 0.124368
\(470\) −35.1070 −1.61937
\(471\) 2.82963 0.130383
\(472\) 32.7422 1.50708
\(473\) 15.2252 0.700056
\(474\) 3.90673 0.179442
\(475\) −34.2717 −1.57249
\(476\) 0.247013 0.0113218
\(477\) 2.27670 0.104243
\(478\) −7.87893 −0.360374
\(479\) −21.0171 −0.960294 −0.480147 0.877188i \(-0.659417\pi\)
−0.480147 + 0.877188i \(0.659417\pi\)
\(480\) 2.13096 0.0972647
\(481\) 6.87141 0.313309
\(482\) −9.63796 −0.438997
\(483\) 34.8816 1.58717
\(484\) −0.253925 −0.0115421
\(485\) 55.1028 2.50209
\(486\) −19.2490 −0.873150
\(487\) −23.6622 −1.07224 −0.536118 0.844143i \(-0.680110\pi\)
−0.536118 + 0.844143i \(0.680110\pi\)
\(488\) −34.1524 −1.54601
\(489\) −49.1191 −2.22124
\(490\) −20.1016 −0.908097
\(491\) −3.74577 −0.169044 −0.0845222 0.996422i \(-0.526936\pi\)
−0.0845222 + 0.996422i \(0.526936\pi\)
\(492\) 0.938362 0.0423046
\(493\) 21.1125 0.950857
\(494\) 11.9682 0.538474
\(495\) 22.7653 1.02323
\(496\) −15.4533 −0.693873
\(497\) −27.5660 −1.23651
\(498\) 27.1894 1.21839
\(499\) −37.1028 −1.66095 −0.830474 0.557058i \(-0.811930\pi\)
−0.830474 + 0.557058i \(0.811930\pi\)
\(500\) −0.944785 −0.0422521
\(501\) 3.79588 0.169587
\(502\) 9.09935 0.406124
\(503\) −0.661745 −0.0295058 −0.0147529 0.999891i \(-0.504696\pi\)
−0.0147529 + 0.999891i \(0.504696\pi\)
\(504\) 7.46250 0.332406
\(505\) 5.82179 0.259066
\(506\) −51.6991 −2.29830
\(507\) −13.4874 −0.598996
\(508\) 0.0196747 0.000872925 0
\(509\) −18.2795 −0.810227 −0.405113 0.914266i \(-0.632768\pi\)
−0.405113 + 0.914266i \(0.632768\pi\)
\(510\) 34.0517 1.50783
\(511\) 13.6943 0.605801
\(512\) −23.3548 −1.03215
\(513\) 11.0073 0.485984
\(514\) 9.24510 0.407784
\(515\) −65.6350 −2.89223
\(516\) −0.360797 −0.0158832
\(517\) −26.1340 −1.14937
\(518\) 6.81763 0.299549
\(519\) −29.1422 −1.27920
\(520\) 28.7039 1.25875
\(521\) −12.4144 −0.543883 −0.271941 0.962314i \(-0.587666\pi\)
−0.271941 + 0.962314i \(0.587666\pi\)
\(522\) 14.2756 0.624827
\(523\) 3.75347 0.164128 0.0820640 0.996627i \(-0.473849\pi\)
0.0820640 + 0.996627i \(0.473849\pi\)
\(524\) 0.241335 0.0105428
\(525\) −39.4353 −1.72110
\(526\) −2.33913 −0.101991
\(527\) 11.7103 0.510110
\(528\) −33.4504 −1.45574
\(529\) 59.6626 2.59403
\(530\) 8.68859 0.377408
\(531\) −16.3926 −0.711379
\(532\) −0.278224 −0.0120626
\(533\) 24.9964 1.08272
\(534\) 17.9952 0.778726
\(535\) −10.2290 −0.442236
\(536\) 4.22661 0.182562
\(537\) −35.6276 −1.53745
\(538\) 20.6966 0.892292
\(539\) −14.9638 −0.644536
\(540\) 0.590860 0.0254266
\(541\) −36.1009 −1.55210 −0.776050 0.630671i \(-0.782780\pi\)
−0.776050 + 0.630671i \(0.782780\pi\)
\(542\) 5.31754 0.228408
\(543\) 13.2381 0.568102
\(544\) 0.766579 0.0328668
\(545\) 67.3520 2.88504
\(546\) 13.7714 0.589361
\(547\) 16.2537 0.694958 0.347479 0.937688i \(-0.387038\pi\)
0.347479 + 0.937688i \(0.387038\pi\)
\(548\) 0.168206 0.00718540
\(549\) 17.0986 0.729752
\(550\) 58.4482 2.49224
\(551\) −23.7802 −1.01307
\(552\) 54.7384 2.32982
\(553\) −2.41929 −0.102879
\(554\) 6.30724 0.267969
\(555\) −22.0207 −0.934728
\(556\) −0.650041 −0.0275679
\(557\) −11.9802 −0.507619 −0.253809 0.967254i \(-0.581684\pi\)
−0.253809 + 0.967254i \(0.581684\pi\)
\(558\) 7.91817 0.335203
\(559\) −9.61106 −0.406505
\(560\) 27.8269 1.17590
\(561\) 25.3484 1.07021
\(562\) 33.3027 1.40479
\(563\) −38.3464 −1.61611 −0.808055 0.589107i \(-0.799480\pi\)
−0.808055 + 0.589107i \(0.799480\pi\)
\(564\) 0.619306 0.0260775
\(565\) −72.4413 −3.04763
\(566\) −35.2634 −1.48223
\(567\) 20.4939 0.860662
\(568\) −43.2583 −1.81508
\(569\) 31.4489 1.31841 0.659203 0.751965i \(-0.270894\pi\)
0.659203 + 0.751965i \(0.270894\pi\)
\(570\) −38.3543 −1.60648
\(571\) 9.85904 0.412588 0.206294 0.978490i \(-0.433860\pi\)
0.206294 + 0.978490i \(0.433860\pi\)
\(572\) 0.478237 0.0199961
\(573\) 48.5481 2.02812
\(574\) 24.8008 1.03516
\(575\) −93.4540 −3.89730
\(576\) 11.7046 0.487692
\(577\) −15.2362 −0.634292 −0.317146 0.948377i \(-0.602725\pi\)
−0.317146 + 0.948377i \(0.602725\pi\)
\(578\) −11.5153 −0.478974
\(579\) 46.9939 1.95300
\(580\) −1.27649 −0.0530035
\(581\) −16.8374 −0.698533
\(582\) 41.4864 1.71967
\(583\) 6.46786 0.267871
\(584\) 21.4899 0.889260
\(585\) −14.3708 −0.594161
\(586\) 37.7898 1.56108
\(587\) −9.30734 −0.384155 −0.192077 0.981380i \(-0.561522\pi\)
−0.192077 + 0.981380i \(0.561522\pi\)
\(588\) 0.354602 0.0146236
\(589\) −13.1900 −0.543484
\(590\) −62.5593 −2.57553
\(591\) 16.2987 0.670440
\(592\) 10.4536 0.429639
\(593\) 24.8888 1.02206 0.511031 0.859562i \(-0.329264\pi\)
0.511031 + 0.859562i \(0.329264\pi\)
\(594\) −18.7722 −0.770235
\(595\) −21.0869 −0.864479
\(596\) 0.307224 0.0125844
\(597\) 40.4018 1.65354
\(598\) 32.6355 1.33457
\(599\) −28.8020 −1.17682 −0.588409 0.808564i \(-0.700245\pi\)
−0.588409 + 0.808564i \(0.700245\pi\)
\(600\) −61.8843 −2.52642
\(601\) −4.36509 −0.178056 −0.0890279 0.996029i \(-0.528376\pi\)
−0.0890279 + 0.996029i \(0.528376\pi\)
\(602\) −9.53583 −0.388651
\(603\) −2.11608 −0.0861735
\(604\) −0.143514 −0.00583951
\(605\) 21.6770 0.881296
\(606\) 4.38317 0.178054
\(607\) −41.6146 −1.68909 −0.844543 0.535488i \(-0.820128\pi\)
−0.844543 + 0.535488i \(0.820128\pi\)
\(608\) −0.863441 −0.0350172
\(609\) −27.3630 −1.10881
\(610\) 65.2538 2.64205
\(611\) 16.4973 0.667409
\(612\) −0.194068 −0.00784475
\(613\) −33.4091 −1.34938 −0.674691 0.738101i \(-0.735723\pi\)
−0.674691 + 0.738101i \(0.735723\pi\)
\(614\) 0.472150 0.0190544
\(615\) −80.1058 −3.23018
\(616\) 21.2002 0.854181
\(617\) −39.6814 −1.59751 −0.798756 0.601655i \(-0.794508\pi\)
−0.798756 + 0.601655i \(0.794508\pi\)
\(618\) −49.4160 −1.98780
\(619\) 1.00000 0.0401934
\(620\) −0.708025 −0.0284350
\(621\) 30.0153 1.20447
\(622\) 6.70937 0.269021
\(623\) −11.1437 −0.446464
\(624\) 21.1159 0.845312
\(625\) 29.2600 1.17040
\(626\) 9.02483 0.360705
\(627\) −28.5513 −1.14023
\(628\) −0.0615447 −0.00245590
\(629\) −7.92160 −0.315855
\(630\) −14.2583 −0.568066
\(631\) 36.3762 1.44811 0.724056 0.689741i \(-0.242276\pi\)
0.724056 + 0.689741i \(0.242276\pi\)
\(632\) −3.79650 −0.151017
\(633\) 14.5162 0.576968
\(634\) 20.7457 0.823916
\(635\) −1.67959 −0.0666523
\(636\) −0.153271 −0.00607760
\(637\) 9.44603 0.374265
\(638\) 40.5556 1.60561
\(639\) 21.6576 0.856761
\(640\) 42.6440 1.68565
\(641\) −2.56023 −0.101123 −0.0505615 0.998721i \(-0.516101\pi\)
−0.0505615 + 0.998721i \(0.516101\pi\)
\(642\) −7.70128 −0.303945
\(643\) −15.3718 −0.606205 −0.303102 0.952958i \(-0.598022\pi\)
−0.303102 + 0.952958i \(0.598022\pi\)
\(644\) −0.758677 −0.0298961
\(645\) 30.8004 1.21277
\(646\) −13.7973 −0.542849
\(647\) 34.7874 1.36763 0.683817 0.729653i \(-0.260319\pi\)
0.683817 + 0.729653i \(0.260319\pi\)
\(648\) 32.1603 1.26337
\(649\) −46.5697 −1.82802
\(650\) −36.8960 −1.44718
\(651\) −15.1773 −0.594845
\(652\) 1.06834 0.0418396
\(653\) −33.8299 −1.32386 −0.661932 0.749564i \(-0.730263\pi\)
−0.661932 + 0.749564i \(0.730263\pi\)
\(654\) 50.7087 1.98287
\(655\) −20.6022 −0.804994
\(656\) 38.0274 1.48472
\(657\) −10.7591 −0.419752
\(658\) 16.3682 0.638098
\(659\) 0.903033 0.0351772 0.0175886 0.999845i \(-0.494401\pi\)
0.0175886 + 0.999845i \(0.494401\pi\)
\(660\) −1.53260 −0.0596565
\(661\) −18.8171 −0.731901 −0.365950 0.930634i \(-0.619256\pi\)
−0.365950 + 0.930634i \(0.619256\pi\)
\(662\) −10.4394 −0.405740
\(663\) −16.0014 −0.621442
\(664\) −26.4223 −1.02538
\(665\) 23.7514 0.921039
\(666\) −5.35635 −0.207554
\(667\) −64.8450 −2.51081
\(668\) −0.0825605 −0.00319436
\(669\) −13.2484 −0.512212
\(670\) −8.07562 −0.311989
\(671\) 48.5755 1.87524
\(672\) −0.993533 −0.0383264
\(673\) −3.47042 −0.133775 −0.0668874 0.997761i \(-0.521307\pi\)
−0.0668874 + 0.997761i \(0.521307\pi\)
\(674\) 43.6434 1.68108
\(675\) −33.9337 −1.30611
\(676\) 0.293352 0.0112828
\(677\) 19.4420 0.747215 0.373608 0.927587i \(-0.378121\pi\)
0.373608 + 0.927587i \(0.378121\pi\)
\(678\) −54.5403 −2.09461
\(679\) −25.6910 −0.985929
\(680\) −33.0909 −1.26898
\(681\) 18.9864 0.727561
\(682\) 22.4947 0.861367
\(683\) −17.1368 −0.655723 −0.327861 0.944726i \(-0.606328\pi\)
−0.327861 + 0.944726i \(0.606328\pi\)
\(684\) 0.218590 0.00835801
\(685\) −14.3594 −0.548643
\(686\) 27.2055 1.03871
\(687\) 33.8386 1.29102
\(688\) −14.6214 −0.557437
\(689\) −4.08290 −0.155546
\(690\) −104.587 −3.98154
\(691\) −34.0837 −1.29661 −0.648303 0.761383i \(-0.724521\pi\)
−0.648303 + 0.761383i \(0.724521\pi\)
\(692\) 0.633844 0.0240951
\(693\) −10.6140 −0.403194
\(694\) 17.7067 0.672138
\(695\) 55.4925 2.10495
\(696\) −42.9397 −1.62763
\(697\) −28.8167 −1.09151
\(698\) −23.2249 −0.879076
\(699\) 20.9126 0.790987
\(700\) 0.857721 0.0324188
\(701\) 29.8339 1.12681 0.563405 0.826181i \(-0.309491\pi\)
0.563405 + 0.826181i \(0.309491\pi\)
\(702\) 11.8502 0.447255
\(703\) 8.92254 0.336520
\(704\) 33.2516 1.25322
\(705\) −52.8687 −1.99115
\(706\) 13.1121 0.493479
\(707\) −2.71433 −0.102083
\(708\) 1.10358 0.0414750
\(709\) 24.2367 0.910227 0.455114 0.890433i \(-0.349599\pi\)
0.455114 + 0.890433i \(0.349599\pi\)
\(710\) 82.6521 3.10188
\(711\) 1.90075 0.0712835
\(712\) −17.4874 −0.655368
\(713\) −35.9672 −1.34698
\(714\) −15.8761 −0.594149
\(715\) −40.8260 −1.52681
\(716\) 0.774903 0.0289595
\(717\) −11.8651 −0.443111
\(718\) −29.3604 −1.09572
\(719\) 2.19158 0.0817320 0.0408660 0.999165i \(-0.486988\pi\)
0.0408660 + 0.999165i \(0.486988\pi\)
\(720\) −21.8625 −0.814768
\(721\) 30.6015 1.13966
\(722\) −11.0200 −0.410121
\(723\) −14.5141 −0.539785
\(724\) −0.287930 −0.0107008
\(725\) 73.3104 2.72268
\(726\) 16.3204 0.605708
\(727\) 0.694630 0.0257624 0.0128812 0.999917i \(-0.495900\pi\)
0.0128812 + 0.999917i \(0.495900\pi\)
\(728\) −13.3828 −0.496000
\(729\) 4.74846 0.175869
\(730\) −41.0601 −1.51970
\(731\) 11.0800 0.409807
\(732\) −1.15111 −0.0425463
\(733\) 4.53396 0.167465 0.0837327 0.996488i \(-0.473316\pi\)
0.0837327 + 0.996488i \(0.473316\pi\)
\(734\) 16.8082 0.620401
\(735\) −30.2716 −1.11658
\(736\) −2.35448 −0.0867873
\(737\) −6.01157 −0.221439
\(738\) −19.4850 −0.717254
\(739\) −6.53051 −0.240229 −0.120114 0.992760i \(-0.538326\pi\)
−0.120114 + 0.992760i \(0.538326\pi\)
\(740\) 0.478952 0.0176066
\(741\) 18.0233 0.662101
\(742\) −4.05094 −0.148715
\(743\) −18.1924 −0.667413 −0.333706 0.942677i \(-0.608299\pi\)
−0.333706 + 0.942677i \(0.608299\pi\)
\(744\) −23.8171 −0.873178
\(745\) −26.2270 −0.960883
\(746\) −11.6076 −0.424983
\(747\) 13.2285 0.484005
\(748\) −0.551328 −0.0201586
\(749\) 4.76911 0.174260
\(750\) 60.7237 2.21732
\(751\) 2.77215 0.101157 0.0505787 0.998720i \(-0.483893\pi\)
0.0505787 + 0.998720i \(0.483893\pi\)
\(752\) 25.0976 0.915214
\(753\) 13.7030 0.499365
\(754\) −25.6011 −0.932336
\(755\) 12.2515 0.445877
\(756\) −0.275480 −0.0100191
\(757\) 39.5313 1.43679 0.718395 0.695635i \(-0.244877\pi\)
0.718395 + 0.695635i \(0.244877\pi\)
\(758\) −16.5230 −0.600143
\(759\) −77.8552 −2.82597
\(760\) 37.2721 1.35200
\(761\) −19.3164 −0.700220 −0.350110 0.936709i \(-0.613856\pi\)
−0.350110 + 0.936709i \(0.613856\pi\)
\(762\) −1.26454 −0.0458096
\(763\) −31.4020 −1.13683
\(764\) −1.05592 −0.0382020
\(765\) 16.5672 0.598988
\(766\) 7.60802 0.274889
\(767\) 29.3976 1.06148
\(768\) −2.31219 −0.0834341
\(769\) 36.0089 1.29851 0.649257 0.760569i \(-0.275080\pi\)
0.649257 + 0.760569i \(0.275080\pi\)
\(770\) −40.5065 −1.45975
\(771\) 13.9225 0.501406
\(772\) −1.02212 −0.0367869
\(773\) 6.72033 0.241713 0.120857 0.992670i \(-0.461436\pi\)
0.120857 + 0.992670i \(0.461436\pi\)
\(774\) 7.49194 0.269292
\(775\) 40.6626 1.46064
\(776\) −40.3158 −1.44725
\(777\) 10.2669 0.368322
\(778\) 2.52236 0.0904308
\(779\) 32.4579 1.16293
\(780\) 0.967469 0.0346409
\(781\) 61.5270 2.20161
\(782\) −37.6233 −1.34541
\(783\) −23.5456 −0.841452
\(784\) 14.3704 0.513228
\(785\) 5.25393 0.187521
\(786\) −15.5112 −0.553266
\(787\) −48.7796 −1.73880 −0.869402 0.494105i \(-0.835496\pi\)
−0.869402 + 0.494105i \(0.835496\pi\)
\(788\) −0.354498 −0.0126285
\(789\) −3.52257 −0.125407
\(790\) 7.25384 0.258080
\(791\) 33.7748 1.20089
\(792\) −16.6562 −0.591852
\(793\) −30.6637 −1.08890
\(794\) −34.1507 −1.21196
\(795\) 13.0844 0.464056
\(796\) −0.878742 −0.0311462
\(797\) 13.1872 0.467116 0.233558 0.972343i \(-0.424963\pi\)
0.233558 + 0.972343i \(0.424963\pi\)
\(798\) 17.8822 0.633022
\(799\) −19.0186 −0.672831
\(800\) 2.66185 0.0941106
\(801\) 8.75519 0.309350
\(802\) 15.6130 0.551314
\(803\) −30.5655 −1.07863
\(804\) 0.142458 0.00502411
\(805\) 64.7665 2.28272
\(806\) −14.2000 −0.500173
\(807\) 31.1676 1.09715
\(808\) −4.25949 −0.149848
\(809\) −1.81667 −0.0638709 −0.0319354 0.999490i \(-0.510167\pi\)
−0.0319354 + 0.999490i \(0.510167\pi\)
\(810\) −61.4474 −2.15904
\(811\) −28.0102 −0.983573 −0.491786 0.870716i \(-0.663656\pi\)
−0.491786 + 0.870716i \(0.663656\pi\)
\(812\) 0.595148 0.0208856
\(813\) 8.00785 0.280848
\(814\) −15.2168 −0.533350
\(815\) −91.2020 −3.19467
\(816\) −24.3431 −0.852180
\(817\) −12.4800 −0.436619
\(818\) 4.56205 0.159508
\(819\) 6.70021 0.234124
\(820\) 1.74231 0.0608440
\(821\) 42.3402 1.47768 0.738841 0.673880i \(-0.235373\pi\)
0.738841 + 0.673880i \(0.235373\pi\)
\(822\) −10.8110 −0.377078
\(823\) −25.5973 −0.892267 −0.446133 0.894967i \(-0.647199\pi\)
−0.446133 + 0.894967i \(0.647199\pi\)
\(824\) 48.0217 1.67291
\(825\) 88.0190 3.06443
\(826\) 29.1674 1.01487
\(827\) 4.68739 0.162996 0.0814982 0.996673i \(-0.474030\pi\)
0.0814982 + 0.996673i \(0.474030\pi\)
\(828\) 0.596064 0.0207147
\(829\) 13.9510 0.484538 0.242269 0.970209i \(-0.422108\pi\)
0.242269 + 0.970209i \(0.422108\pi\)
\(830\) 50.4841 1.75233
\(831\) 9.49826 0.329491
\(832\) −20.9904 −0.727710
\(833\) −10.8897 −0.377306
\(834\) 41.7798 1.44672
\(835\) 7.04800 0.243906
\(836\) 0.620992 0.0214775
\(837\) −13.0599 −0.451417
\(838\) 15.7201 0.543043
\(839\) −24.3899 −0.842033 −0.421017 0.907053i \(-0.638327\pi\)
−0.421017 + 0.907053i \(0.638327\pi\)
\(840\) 42.8878 1.47977
\(841\) 21.8680 0.754068
\(842\) −11.9343 −0.411284
\(843\) 50.1516 1.72731
\(844\) −0.315729 −0.0108678
\(845\) −25.0428 −0.861497
\(846\) −12.8598 −0.442131
\(847\) −10.1066 −0.347268
\(848\) −6.21137 −0.213299
\(849\) −53.1042 −1.82253
\(850\) 42.5349 1.45894
\(851\) 24.3305 0.834038
\(852\) −1.45803 −0.0499512
\(853\) 37.9997 1.30109 0.650543 0.759469i \(-0.274541\pi\)
0.650543 + 0.759469i \(0.274541\pi\)
\(854\) −30.4237 −1.04108
\(855\) −18.6605 −0.638177
\(856\) 7.48399 0.255797
\(857\) −27.0615 −0.924404 −0.462202 0.886775i \(-0.652940\pi\)
−0.462202 + 0.886775i \(0.652940\pi\)
\(858\) −30.7375 −1.04936
\(859\) −27.4404 −0.936254 −0.468127 0.883661i \(-0.655071\pi\)
−0.468127 + 0.883661i \(0.655071\pi\)
\(860\) −0.669912 −0.0228438
\(861\) 37.3482 1.27282
\(862\) 33.5064 1.14123
\(863\) 9.19224 0.312907 0.156454 0.987685i \(-0.449994\pi\)
0.156454 + 0.987685i \(0.449994\pi\)
\(864\) −0.854926 −0.0290852
\(865\) −54.1098 −1.83979
\(866\) 38.0334 1.29243
\(867\) −17.3413 −0.588940
\(868\) 0.330107 0.0112046
\(869\) 5.39982 0.183176
\(870\) 82.0434 2.78153
\(871\) 3.79486 0.128584
\(872\) −49.2779 −1.66876
\(873\) 20.1844 0.683139
\(874\) 42.3773 1.43343
\(875\) −37.6039 −1.27124
\(876\) 0.724321 0.0244725
\(877\) −34.4625 −1.16372 −0.581858 0.813290i \(-0.697674\pi\)
−0.581858 + 0.813290i \(0.697674\pi\)
\(878\) −41.6793 −1.40661
\(879\) 56.9088 1.91949
\(880\) −62.1092 −2.09370
\(881\) −4.94477 −0.166594 −0.0832968 0.996525i \(-0.526545\pi\)
−0.0832968 + 0.996525i \(0.526545\pi\)
\(882\) −7.36329 −0.247935
\(883\) 48.8962 1.64549 0.822745 0.568411i \(-0.192442\pi\)
0.822745 + 0.568411i \(0.192442\pi\)
\(884\) 0.348031 0.0117056
\(885\) −94.2100 −3.16683
\(886\) −55.6167 −1.86848
\(887\) −53.2472 −1.78787 −0.893933 0.448200i \(-0.852065\pi\)
−0.893933 + 0.448200i \(0.852065\pi\)
\(888\) 16.1114 0.540663
\(889\) 0.783084 0.0262638
\(890\) 33.4125 1.11999
\(891\) −45.7420 −1.53242
\(892\) 0.288153 0.00964807
\(893\) 21.4218 0.716852
\(894\) −19.7461 −0.660407
\(895\) −66.1517 −2.21121
\(896\) −19.8822 −0.664217
\(897\) 49.1468 1.64096
\(898\) −32.2164 −1.07508
\(899\) 28.2146 0.941010
\(900\) −0.673878 −0.0224626
\(901\) 4.70690 0.156810
\(902\) −55.3549 −1.84312
\(903\) −14.3603 −0.477881
\(904\) 53.0014 1.76280
\(905\) 24.5799 0.817064
\(906\) 9.22402 0.306448
\(907\) 47.7279 1.58478 0.792389 0.610016i \(-0.208837\pi\)
0.792389 + 0.610016i \(0.208837\pi\)
\(908\) −0.412956 −0.0137044
\(909\) 2.13255 0.0707321
\(910\) 25.5701 0.847640
\(911\) 51.9321 1.72059 0.860294 0.509798i \(-0.170280\pi\)
0.860294 + 0.509798i \(0.170280\pi\)
\(912\) 27.4190 0.907935
\(913\) 37.5808 1.24374
\(914\) 16.2547 0.537658
\(915\) 98.2676 3.24863
\(916\) −0.735992 −0.0243179
\(917\) 9.60550 0.317201
\(918\) −13.6613 −0.450889
\(919\) −15.7211 −0.518590 −0.259295 0.965798i \(-0.583490\pi\)
−0.259295 + 0.965798i \(0.583490\pi\)
\(920\) 101.636 3.35083
\(921\) 0.711026 0.0234291
\(922\) −41.3780 −1.36271
\(923\) −38.8395 −1.27842
\(924\) 0.714555 0.0235071
\(925\) −27.5068 −0.904416
\(926\) 52.0258 1.70967
\(927\) −24.0424 −0.789656
\(928\) 1.84698 0.0606301
\(929\) −42.3764 −1.39033 −0.695163 0.718852i \(-0.744668\pi\)
−0.695163 + 0.718852i \(0.744668\pi\)
\(930\) 45.5065 1.49222
\(931\) 12.2657 0.401992
\(932\) −0.454850 −0.0148991
\(933\) 10.1038 0.330785
\(934\) 16.2756 0.532555
\(935\) 47.0656 1.53921
\(936\) 10.5144 0.343673
\(937\) 15.5160 0.506885 0.253442 0.967350i \(-0.418437\pi\)
0.253442 + 0.967350i \(0.418437\pi\)
\(938\) 3.76515 0.122937
\(939\) 13.5908 0.443518
\(940\) 1.14990 0.0375055
\(941\) 24.7888 0.808090 0.404045 0.914739i \(-0.367604\pi\)
0.404045 + 0.914739i \(0.367604\pi\)
\(942\) 3.95563 0.128881
\(943\) 88.5080 2.88222
\(944\) 44.7229 1.45561
\(945\) 23.5171 0.765012
\(946\) 21.2838 0.691997
\(947\) −15.0199 −0.488081 −0.244041 0.969765i \(-0.578473\pi\)
−0.244041 + 0.969765i \(0.578473\pi\)
\(948\) −0.127961 −0.00415600
\(949\) 19.2947 0.626334
\(950\) −47.9095 −1.55439
\(951\) 31.2416 1.01308
\(952\) 15.4282 0.500030
\(953\) −44.0306 −1.42629 −0.713145 0.701016i \(-0.752730\pi\)
−0.713145 + 0.701016i \(0.752730\pi\)
\(954\) 3.18267 0.103043
\(955\) 90.1417 2.91692
\(956\) 0.258067 0.00834649
\(957\) 61.0738 1.97424
\(958\) −29.3804 −0.949237
\(959\) 6.69486 0.216188
\(960\) 67.2676 2.17105
\(961\) −15.3504 −0.495173
\(962\) 9.60576 0.309702
\(963\) −3.74691 −0.120743
\(964\) 0.315683 0.0101675
\(965\) 87.2560 2.80887
\(966\) 48.7621 1.56890
\(967\) 39.5267 1.27109 0.635546 0.772063i \(-0.280775\pi\)
0.635546 + 0.772063i \(0.280775\pi\)
\(968\) −15.8599 −0.509757
\(969\) −20.7778 −0.667480
\(970\) 77.0300 2.47328
\(971\) −56.0487 −1.79869 −0.899344 0.437243i \(-0.855955\pi\)
−0.899344 + 0.437243i \(0.855955\pi\)
\(972\) 0.630482 0.0202227
\(973\) −25.8726 −0.829439
\(974\) −33.0781 −1.05989
\(975\) −55.5628 −1.77943
\(976\) −46.6491 −1.49320
\(977\) −41.0962 −1.31478 −0.657392 0.753549i \(-0.728340\pi\)
−0.657392 + 0.753549i \(0.728340\pi\)
\(978\) −68.6651 −2.19567
\(979\) 24.8726 0.794932
\(980\) 0.658409 0.0210321
\(981\) 24.6713 0.787695
\(982\) −5.23634 −0.167098
\(983\) −31.9949 −1.02048 −0.510239 0.860032i \(-0.670443\pi\)
−0.510239 + 0.860032i \(0.670443\pi\)
\(984\) 58.6092 1.86839
\(985\) 30.2627 0.964250
\(986\) 29.5138 0.939910
\(987\) 24.6493 0.784597
\(988\) −0.392007 −0.0124714
\(989\) −34.0311 −1.08213
\(990\) 31.8244 1.01145
\(991\) −6.63765 −0.210852 −0.105426 0.994427i \(-0.533621\pi\)
−0.105426 + 0.994427i \(0.533621\pi\)
\(992\) 1.02445 0.0325264
\(993\) −15.7211 −0.498893
\(994\) −38.5354 −1.22227
\(995\) 75.0162 2.37817
\(996\) −0.890565 −0.0282186
\(997\) −35.3560 −1.11973 −0.559867 0.828582i \(-0.689148\pi\)
−0.559867 + 0.828582i \(0.689148\pi\)
\(998\) −51.8671 −1.64182
\(999\) 8.83454 0.279513
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 \(a_p\))