Properties

Label 4003.2.a.b.1.15
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 1.15
Character \(\chi\) = 4003.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.43441 q^{2} +1.77953 q^{3} +3.92633 q^{4} -0.360928 q^{5} -4.33209 q^{6} -1.53438 q^{7} -4.68946 q^{8} +0.166714 q^{9} +O(q^{10})\) \(q-2.43441 q^{2} +1.77953 q^{3} +3.92633 q^{4} -0.360928 q^{5} -4.33209 q^{6} -1.53438 q^{7} -4.68946 q^{8} +0.166714 q^{9} +0.878646 q^{10} -2.71903 q^{11} +6.98700 q^{12} +5.42134 q^{13} +3.73530 q^{14} -0.642281 q^{15} +3.56340 q^{16} +1.82952 q^{17} -0.405849 q^{18} -1.34221 q^{19} -1.41712 q^{20} -2.73047 q^{21} +6.61922 q^{22} +6.95468 q^{23} -8.34502 q^{24} -4.86973 q^{25} -13.1977 q^{26} -5.04191 q^{27} -6.02447 q^{28} -6.05028 q^{29} +1.56357 q^{30} +3.54754 q^{31} +0.704175 q^{32} -4.83859 q^{33} -4.45379 q^{34} +0.553801 q^{35} +0.654572 q^{36} -1.69847 q^{37} +3.26748 q^{38} +9.64741 q^{39} +1.69256 q^{40} -5.25484 q^{41} +6.64706 q^{42} -3.53428 q^{43} -10.6758 q^{44} -0.0601717 q^{45} -16.9305 q^{46} +0.427352 q^{47} +6.34116 q^{48} -4.64568 q^{49} +11.8549 q^{50} +3.25568 q^{51} +21.2860 q^{52} +2.88425 q^{53} +12.2740 q^{54} +0.981375 q^{55} +7.19541 q^{56} -2.38850 q^{57} +14.7288 q^{58} -13.7321 q^{59} -2.52181 q^{60} +8.87911 q^{61} -8.63616 q^{62} -0.255802 q^{63} -8.84104 q^{64} -1.95671 q^{65} +11.7791 q^{66} +9.16717 q^{67} +7.18330 q^{68} +12.3760 q^{69} -1.34817 q^{70} +5.39556 q^{71} -0.781797 q^{72} +11.6556 q^{73} +4.13476 q^{74} -8.66581 q^{75} -5.26995 q^{76} +4.17202 q^{77} -23.4857 q^{78} -2.01441 q^{79} -1.28613 q^{80} -9.47235 q^{81} +12.7924 q^{82} -6.98293 q^{83} -10.7207 q^{84} -0.660326 q^{85} +8.60386 q^{86} -10.7666 q^{87} +12.7508 q^{88} +1.05385 q^{89} +0.146482 q^{90} -8.31838 q^{91} +27.3064 q^{92} +6.31295 q^{93} -1.04035 q^{94} +0.484441 q^{95} +1.25310 q^{96} -0.00171825 q^{97} +11.3095 q^{98} -0.453299 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 152q - 22q^{2} - 18q^{3} + 138q^{4} - 59q^{5} - 17q^{6} - 19q^{7} - 66q^{8} + 106q^{9} + O(q^{10}) \) \( 152q - 22q^{2} - 18q^{3} + 138q^{4} - 59q^{5} - 17q^{6} - 19q^{7} - 66q^{8} + 106q^{9} - 15q^{10} - 40q^{11} - 53q^{12} - 59q^{13} - 36q^{14} - 40q^{15} + 118q^{16} - 93q^{17} - 59q^{18} - 16q^{19} - 108q^{20} - 62q^{21} - 37q^{22} - 107q^{23} - 31q^{24} + 101q^{25} - 64q^{26} - 63q^{27} - 53q^{28} - 124q^{29} - 68q^{30} - 15q^{31} - 129q^{32} - 49q^{33} - 76q^{35} + 45q^{36} - 98q^{37} - 125q^{38} - 47q^{39} - 7q^{40} - 56q^{41} - 84q^{42} - 62q^{43} - 114q^{44} - 142q^{45} - 3q^{46} - 111q^{47} - 92q^{48} + 117q^{49} - 64q^{50} - 21q^{51} - 85q^{52} - 347q^{53} + 3q^{54} - 16q^{55} - 73q^{56} - 115q^{57} - 29q^{58} - 50q^{59} - 54q^{60} - 62q^{61} - 55q^{62} - 70q^{63} + 64q^{64} - 147q^{65} + 34q^{66} - 86q^{67} - 174q^{68} - 104q^{69} - 7q^{70} - 86q^{71} - 139q^{72} - 27q^{73} - 52q^{74} - 49q^{75} - 11q^{76} - 346q^{77} - 59q^{78} - 17q^{79} - 149q^{80} - 8q^{81} - 31q^{82} - 106q^{83} - 51q^{84} - 69q^{85} - 85q^{86} - 32q^{87} - 113q^{88} - 59q^{89} + 10q^{90} - 9q^{91} - 314q^{92} - 230q^{93} + 7q^{94} - 74q^{95} - 54q^{96} - 60q^{97} - 77q^{98} - 96q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.43441 −1.72138 −0.860692 0.509126i \(-0.829969\pi\)
−0.860692 + 0.509126i \(0.829969\pi\)
\(3\) 1.77953 1.02741 0.513705 0.857967i \(-0.328273\pi\)
0.513705 + 0.857967i \(0.328273\pi\)
\(4\) 3.92633 1.96316
\(5\) −0.360928 −0.161412 −0.0807060 0.996738i \(-0.525717\pi\)
−0.0807060 + 0.996738i \(0.525717\pi\)
\(6\) −4.33209 −1.76857
\(7\) −1.53438 −0.579940 −0.289970 0.957036i \(-0.593645\pi\)
−0.289970 + 0.957036i \(0.593645\pi\)
\(8\) −4.68946 −1.65798
\(9\) 0.166714 0.0555712
\(10\) 0.878646 0.277852
\(11\) −2.71903 −0.819818 −0.409909 0.912126i \(-0.634440\pi\)
−0.409909 + 0.912126i \(0.634440\pi\)
\(12\) 6.98700 2.01697
\(13\) 5.42134 1.50361 0.751804 0.659386i \(-0.229184\pi\)
0.751804 + 0.659386i \(0.229184\pi\)
\(14\) 3.73530 0.998300
\(15\) −0.642281 −0.165836
\(16\) 3.56340 0.890849
\(17\) 1.82952 0.443724 0.221862 0.975078i \(-0.428787\pi\)
0.221862 + 0.975078i \(0.428787\pi\)
\(18\) −0.405849 −0.0956594
\(19\) −1.34221 −0.307924 −0.153962 0.988077i \(-0.549203\pi\)
−0.153962 + 0.988077i \(0.549203\pi\)
\(20\) −1.41712 −0.316878
\(21\) −2.73047 −0.595837
\(22\) 6.61922 1.41122
\(23\) 6.95468 1.45015 0.725076 0.688669i \(-0.241805\pi\)
0.725076 + 0.688669i \(0.241805\pi\)
\(24\) −8.34502 −1.70342
\(25\) −4.86973 −0.973946
\(26\) −13.1977 −2.58829
\(27\) −5.04191 −0.970316
\(28\) −6.02447 −1.13852
\(29\) −6.05028 −1.12351 −0.561755 0.827304i \(-0.689874\pi\)
−0.561755 + 0.827304i \(0.689874\pi\)
\(30\) 1.56357 0.285468
\(31\) 3.54754 0.637157 0.318579 0.947896i \(-0.396794\pi\)
0.318579 + 0.947896i \(0.396794\pi\)
\(32\) 0.704175 0.124482
\(33\) −4.83859 −0.842290
\(34\) −4.45379 −0.763819
\(35\) 0.553801 0.0936094
\(36\) 0.654572 0.109095
\(37\) −1.69847 −0.279227 −0.139613 0.990206i \(-0.544586\pi\)
−0.139613 + 0.990206i \(0.544586\pi\)
\(38\) 3.26748 0.530055
\(39\) 9.64741 1.54482
\(40\) 1.69256 0.267617
\(41\) −5.25484 −0.820668 −0.410334 0.911935i \(-0.634588\pi\)
−0.410334 + 0.911935i \(0.634588\pi\)
\(42\) 6.64706 1.02566
\(43\) −3.53428 −0.538972 −0.269486 0.963004i \(-0.586854\pi\)
−0.269486 + 0.963004i \(0.586854\pi\)
\(44\) −10.6758 −1.60944
\(45\) −0.0601717 −0.00896986
\(46\) −16.9305 −2.49627
\(47\) 0.427352 0.0623357 0.0311679 0.999514i \(-0.490077\pi\)
0.0311679 + 0.999514i \(0.490077\pi\)
\(48\) 6.34116 0.915267
\(49\) −4.64568 −0.663669
\(50\) 11.8549 1.67654
\(51\) 3.25568 0.455886
\(52\) 21.2860 2.95183
\(53\) 2.88425 0.396182 0.198091 0.980184i \(-0.436526\pi\)
0.198091 + 0.980184i \(0.436526\pi\)
\(54\) 12.2740 1.67029
\(55\) 0.981375 0.132329
\(56\) 7.19541 0.961527
\(57\) −2.38850 −0.316364
\(58\) 14.7288 1.93399
\(59\) −13.7321 −1.78777 −0.893886 0.448295i \(-0.852032\pi\)
−0.893886 + 0.448295i \(0.852032\pi\)
\(60\) −2.52181 −0.325564
\(61\) 8.87911 1.13685 0.568427 0.822734i \(-0.307552\pi\)
0.568427 + 0.822734i \(0.307552\pi\)
\(62\) −8.63616 −1.09679
\(63\) −0.255802 −0.0322280
\(64\) −8.84104 −1.10513
\(65\) −1.95671 −0.242701
\(66\) 11.7791 1.44990
\(67\) 9.16717 1.11995 0.559974 0.828510i \(-0.310811\pi\)
0.559974 + 0.828510i \(0.310811\pi\)
\(68\) 7.18330 0.871103
\(69\) 12.3760 1.48990
\(70\) −1.34817 −0.161138
\(71\) 5.39556 0.640335 0.320168 0.947361i \(-0.396261\pi\)
0.320168 + 0.947361i \(0.396261\pi\)
\(72\) −0.781797 −0.0921357
\(73\) 11.6556 1.36419 0.682093 0.731266i \(-0.261070\pi\)
0.682093 + 0.731266i \(0.261070\pi\)
\(74\) 4.13476 0.480656
\(75\) −8.66581 −1.00064
\(76\) −5.26995 −0.604505
\(77\) 4.17202 0.475446
\(78\) −23.4857 −2.65923
\(79\) −2.01441 −0.226639 −0.113320 0.993559i \(-0.536148\pi\)
−0.113320 + 0.993559i \(0.536148\pi\)
\(80\) −1.28613 −0.143794
\(81\) −9.47235 −1.05248
\(82\) 12.7924 1.41268
\(83\) −6.98293 −0.766477 −0.383238 0.923650i \(-0.625191\pi\)
−0.383238 + 0.923650i \(0.625191\pi\)
\(84\) −10.7207 −1.16972
\(85\) −0.660326 −0.0716224
\(86\) 8.60386 0.927778
\(87\) −10.7666 −1.15430
\(88\) 12.7508 1.35924
\(89\) 1.05385 0.111708 0.0558540 0.998439i \(-0.482212\pi\)
0.0558540 + 0.998439i \(0.482212\pi\)
\(90\) 0.146482 0.0154406
\(91\) −8.31838 −0.872003
\(92\) 27.3064 2.84689
\(93\) 6.31295 0.654622
\(94\) −1.04035 −0.107304
\(95\) 0.484441 0.0497026
\(96\) 1.25310 0.127894
\(97\) −0.00171825 −0.000174462 0 −8.72309e−5 1.00000i \(-0.500028\pi\)
−8.72309e−5 1.00000i \(0.500028\pi\)
\(98\) 11.3095 1.14243
\(99\) −0.453299 −0.0455583
\(100\) −19.1202 −1.91202
\(101\) −10.8815 −1.08275 −0.541373 0.840783i \(-0.682095\pi\)
−0.541373 + 0.840783i \(0.682095\pi\)
\(102\) −7.92564 −0.784756
\(103\) 9.23290 0.909745 0.454872 0.890557i \(-0.349685\pi\)
0.454872 + 0.890557i \(0.349685\pi\)
\(104\) −25.4232 −2.49295
\(105\) 0.985503 0.0961752
\(106\) −7.02144 −0.681982
\(107\) −18.9603 −1.83296 −0.916481 0.400078i \(-0.868983\pi\)
−0.916481 + 0.400078i \(0.868983\pi\)
\(108\) −19.7962 −1.90489
\(109\) 2.88088 0.275938 0.137969 0.990437i \(-0.455943\pi\)
0.137969 + 0.990437i \(0.455943\pi\)
\(110\) −2.38906 −0.227788
\(111\) −3.02247 −0.286880
\(112\) −5.46760 −0.516639
\(113\) −10.4326 −0.981417 −0.490709 0.871324i \(-0.663262\pi\)
−0.490709 + 0.871324i \(0.663262\pi\)
\(114\) 5.81457 0.544584
\(115\) −2.51014 −0.234072
\(116\) −23.7554 −2.20563
\(117\) 0.903811 0.0835574
\(118\) 33.4296 3.07744
\(119\) −2.80718 −0.257333
\(120\) 3.01196 0.274953
\(121\) −3.60688 −0.327898
\(122\) −21.6153 −1.95696
\(123\) −9.35112 −0.843162
\(124\) 13.9288 1.25084
\(125\) 3.56227 0.318619
\(126\) 0.622725 0.0554768
\(127\) 1.76375 0.156507 0.0782537 0.996933i \(-0.475066\pi\)
0.0782537 + 0.996933i \(0.475066\pi\)
\(128\) 20.1143 1.77787
\(129\) −6.28934 −0.553745
\(130\) 4.76344 0.417781
\(131\) −11.3760 −0.993928 −0.496964 0.867771i \(-0.665552\pi\)
−0.496964 + 0.867771i \(0.665552\pi\)
\(132\) −18.9979 −1.65355
\(133\) 2.05946 0.178578
\(134\) −22.3166 −1.92786
\(135\) 1.81977 0.156621
\(136\) −8.57947 −0.735683
\(137\) −7.11757 −0.608095 −0.304047 0.952657i \(-0.598338\pi\)
−0.304047 + 0.952657i \(0.598338\pi\)
\(138\) −30.1283 −2.56469
\(139\) 0.279750 0.0237281 0.0118640 0.999930i \(-0.496223\pi\)
0.0118640 + 0.999930i \(0.496223\pi\)
\(140\) 2.17440 0.183771
\(141\) 0.760485 0.0640444
\(142\) −13.1350 −1.10226
\(143\) −14.7408 −1.23269
\(144\) 0.594067 0.0495056
\(145\) 2.18372 0.181348
\(146\) −28.3745 −2.34829
\(147\) −8.26712 −0.681860
\(148\) −6.66875 −0.548168
\(149\) 0.431693 0.0353656 0.0176828 0.999844i \(-0.494371\pi\)
0.0176828 + 0.999844i \(0.494371\pi\)
\(150\) 21.0961 1.72249
\(151\) −0.974531 −0.0793062 −0.0396531 0.999214i \(-0.512625\pi\)
−0.0396531 + 0.999214i \(0.512625\pi\)
\(152\) 6.29424 0.510530
\(153\) 0.305006 0.0246583
\(154\) −10.1564 −0.818425
\(155\) −1.28041 −0.102845
\(156\) 37.8789 3.03274
\(157\) 2.38774 0.190563 0.0952813 0.995450i \(-0.469625\pi\)
0.0952813 + 0.995450i \(0.469625\pi\)
\(158\) 4.90390 0.390133
\(159\) 5.13260 0.407042
\(160\) −0.254157 −0.0200929
\(161\) −10.6711 −0.841001
\(162\) 23.0595 1.81173
\(163\) −1.77098 −0.138714 −0.0693571 0.997592i \(-0.522095\pi\)
−0.0693571 + 0.997592i \(0.522095\pi\)
\(164\) −20.6322 −1.61111
\(165\) 1.74638 0.135956
\(166\) 16.9993 1.31940
\(167\) 16.4248 1.27099 0.635496 0.772104i \(-0.280795\pi\)
0.635496 + 0.772104i \(0.280795\pi\)
\(168\) 12.8044 0.987882
\(169\) 16.3909 1.26084
\(170\) 1.60750 0.123290
\(171\) −0.223765 −0.0171117
\(172\) −13.8767 −1.05809
\(173\) −17.3309 −1.31765 −0.658823 0.752298i \(-0.728945\pi\)
−0.658823 + 0.752298i \(0.728945\pi\)
\(174\) 26.2104 1.98700
\(175\) 7.47201 0.564831
\(176\) −9.68898 −0.730335
\(177\) −24.4367 −1.83677
\(178\) −2.56550 −0.192292
\(179\) −13.4213 −1.00315 −0.501577 0.865113i \(-0.667247\pi\)
−0.501577 + 0.865113i \(0.667247\pi\)
\(180\) −0.236254 −0.0176093
\(181\) −11.0756 −0.823241 −0.411620 0.911355i \(-0.635037\pi\)
−0.411620 + 0.911355i \(0.635037\pi\)
\(182\) 20.2503 1.50105
\(183\) 15.8006 1.16801
\(184\) −32.6137 −2.40432
\(185\) 0.613026 0.0450705
\(186\) −15.3683 −1.12686
\(187\) −4.97452 −0.363773
\(188\) 1.67793 0.122375
\(189\) 7.73619 0.562725
\(190\) −1.17933 −0.0855574
\(191\) −25.9102 −1.87480 −0.937398 0.348259i \(-0.886773\pi\)
−0.937398 + 0.348259i \(0.886773\pi\)
\(192\) −15.7329 −1.13542
\(193\) −7.76187 −0.558711 −0.279356 0.960188i \(-0.590121\pi\)
−0.279356 + 0.960188i \(0.590121\pi\)
\(194\) 0.00418291 0.000300316 0
\(195\) −3.48203 −0.249353
\(196\) −18.2405 −1.30289
\(197\) −7.21440 −0.514005 −0.257002 0.966411i \(-0.582735\pi\)
−0.257002 + 0.966411i \(0.582735\pi\)
\(198\) 1.10351 0.0784234
\(199\) −8.30703 −0.588870 −0.294435 0.955672i \(-0.595131\pi\)
−0.294435 + 0.955672i \(0.595131\pi\)
\(200\) 22.8364 1.61478
\(201\) 16.3132 1.15065
\(202\) 26.4899 1.86382
\(203\) 9.28342 0.651569
\(204\) 12.7829 0.894980
\(205\) 1.89662 0.132466
\(206\) −22.4766 −1.56602
\(207\) 1.15944 0.0805867
\(208\) 19.3184 1.33949
\(209\) 3.64951 0.252442
\(210\) −2.39911 −0.165554
\(211\) 2.41851 0.166497 0.0832485 0.996529i \(-0.473470\pi\)
0.0832485 + 0.996529i \(0.473470\pi\)
\(212\) 11.3245 0.777771
\(213\) 9.60154 0.657887
\(214\) 46.1571 3.15523
\(215\) 1.27562 0.0869966
\(216\) 23.6438 1.60876
\(217\) −5.44327 −0.369513
\(218\) −7.01322 −0.474995
\(219\) 20.7415 1.40158
\(220\) 3.85320 0.259783
\(221\) 9.91845 0.667187
\(222\) 7.35792 0.493831
\(223\) 1.47657 0.0988787 0.0494394 0.998777i \(-0.484257\pi\)
0.0494394 + 0.998777i \(0.484257\pi\)
\(224\) −1.08047 −0.0721920
\(225\) −0.811851 −0.0541234
\(226\) 25.3972 1.68940
\(227\) −6.29268 −0.417660 −0.208830 0.977952i \(-0.566965\pi\)
−0.208830 + 0.977952i \(0.566965\pi\)
\(228\) −9.37802 −0.621075
\(229\) 10.3797 0.685908 0.342954 0.939352i \(-0.388572\pi\)
0.342954 + 0.939352i \(0.388572\pi\)
\(230\) 6.11070 0.402928
\(231\) 7.42422 0.488478
\(232\) 28.3726 1.86275
\(233\) 6.96882 0.456543 0.228271 0.973598i \(-0.426693\pi\)
0.228271 + 0.973598i \(0.426693\pi\)
\(234\) −2.20024 −0.143834
\(235\) −0.154244 −0.0100617
\(236\) −53.9169 −3.50969
\(237\) −3.58470 −0.232851
\(238\) 6.83380 0.442970
\(239\) 3.81790 0.246959 0.123480 0.992347i \(-0.460595\pi\)
0.123480 + 0.992347i \(0.460595\pi\)
\(240\) −2.28870 −0.147735
\(241\) 3.58227 0.230754 0.115377 0.993322i \(-0.463192\pi\)
0.115377 + 0.993322i \(0.463192\pi\)
\(242\) 8.78060 0.564438
\(243\) −1.73057 −0.111016
\(244\) 34.8623 2.23183
\(245\) 1.67676 0.107124
\(246\) 22.7644 1.45141
\(247\) −7.27657 −0.462997
\(248\) −16.6361 −1.05639
\(249\) −12.4263 −0.787486
\(250\) −8.67200 −0.548465
\(251\) −8.55140 −0.539759 −0.269880 0.962894i \(-0.586984\pi\)
−0.269880 + 0.962894i \(0.586984\pi\)
\(252\) −1.00436 −0.0632688
\(253\) −18.9100 −1.18886
\(254\) −4.29368 −0.269409
\(255\) −1.17507 −0.0735856
\(256\) −31.2843 −1.95527
\(257\) 6.56368 0.409431 0.204716 0.978821i \(-0.434373\pi\)
0.204716 + 0.978821i \(0.434373\pi\)
\(258\) 15.3108 0.953208
\(259\) 2.60609 0.161935
\(260\) −7.68270 −0.476461
\(261\) −1.00866 −0.0624348
\(262\) 27.6938 1.71093
\(263\) 29.7712 1.83577 0.917884 0.396849i \(-0.129896\pi\)
0.917884 + 0.396849i \(0.129896\pi\)
\(264\) 22.6904 1.39650
\(265\) −1.04101 −0.0639486
\(266\) −5.01355 −0.307401
\(267\) 1.87536 0.114770
\(268\) 35.9933 2.19864
\(269\) −8.69549 −0.530173 −0.265087 0.964225i \(-0.585401\pi\)
−0.265087 + 0.964225i \(0.585401\pi\)
\(270\) −4.43005 −0.269604
\(271\) −2.99039 −0.181653 −0.0908266 0.995867i \(-0.528951\pi\)
−0.0908266 + 0.995867i \(0.528951\pi\)
\(272\) 6.51931 0.395291
\(273\) −14.8028 −0.895905
\(274\) 17.3270 1.04676
\(275\) 13.2409 0.798459
\(276\) 48.5924 2.92492
\(277\) −9.40388 −0.565025 −0.282512 0.959264i \(-0.591168\pi\)
−0.282512 + 0.959264i \(0.591168\pi\)
\(278\) −0.681025 −0.0408451
\(279\) 0.591424 0.0354076
\(280\) −2.59703 −0.155202
\(281\) 23.4111 1.39659 0.698294 0.715811i \(-0.253943\pi\)
0.698294 + 0.715811i \(0.253943\pi\)
\(282\) −1.85133 −0.110245
\(283\) −26.0157 −1.54647 −0.773235 0.634119i \(-0.781363\pi\)
−0.773235 + 0.634119i \(0.781363\pi\)
\(284\) 21.1847 1.25708
\(285\) 0.862076 0.0510650
\(286\) 35.8850 2.12193
\(287\) 8.06291 0.475938
\(288\) 0.117396 0.00691760
\(289\) −13.6529 −0.803109
\(290\) −5.31606 −0.312170
\(291\) −0.00305767 −0.000179244 0
\(292\) 45.7637 2.67812
\(293\) 0.0159037 0.000929102 0 0.000464551 1.00000i \(-0.499852\pi\)
0.000464551 1.00000i \(0.499852\pi\)
\(294\) 20.1255 1.17374
\(295\) 4.95632 0.288568
\(296\) 7.96491 0.462951
\(297\) 13.7091 0.795483
\(298\) −1.05091 −0.0608779
\(299\) 37.7037 2.18046
\(300\) −34.0248 −1.96442
\(301\) 5.42292 0.312572
\(302\) 2.37240 0.136517
\(303\) −19.3638 −1.11242
\(304\) −4.78282 −0.274314
\(305\) −3.20472 −0.183502
\(306\) −0.742508 −0.0424464
\(307\) 3.89875 0.222514 0.111257 0.993792i \(-0.464512\pi\)
0.111257 + 0.993792i \(0.464512\pi\)
\(308\) 16.3807 0.933378
\(309\) 16.4302 0.934681
\(310\) 3.11703 0.177036
\(311\) −6.30304 −0.357413 −0.178706 0.983902i \(-0.557191\pi\)
−0.178706 + 0.983902i \(0.557191\pi\)
\(312\) −45.2412 −2.56128
\(313\) −9.76144 −0.551749 −0.275874 0.961194i \(-0.588967\pi\)
−0.275874 + 0.961194i \(0.588967\pi\)
\(314\) −5.81273 −0.328031
\(315\) 0.0923261 0.00520199
\(316\) −7.90925 −0.444930
\(317\) −9.23281 −0.518566 −0.259283 0.965801i \(-0.583486\pi\)
−0.259283 + 0.965801i \(0.583486\pi\)
\(318\) −12.4948 −0.700675
\(319\) 16.4509 0.921074
\(320\) 3.19098 0.178381
\(321\) −33.7404 −1.88320
\(322\) 25.9778 1.44769
\(323\) −2.45560 −0.136633
\(324\) −37.1915 −2.06620
\(325\) −26.4005 −1.46443
\(326\) 4.31129 0.238780
\(327\) 5.12660 0.283501
\(328\) 24.6424 1.36065
\(329\) −0.655720 −0.0361510
\(330\) −4.25140 −0.234032
\(331\) −9.86665 −0.542320 −0.271160 0.962534i \(-0.587407\pi\)
−0.271160 + 0.962534i \(0.587407\pi\)
\(332\) −27.4173 −1.50472
\(333\) −0.283158 −0.0155170
\(334\) −39.9847 −2.18787
\(335\) −3.30869 −0.180773
\(336\) −9.72973 −0.530801
\(337\) −29.9516 −1.63157 −0.815785 0.578356i \(-0.803695\pi\)
−0.815785 + 0.578356i \(0.803695\pi\)
\(338\) −39.9021 −2.17039
\(339\) −18.5651 −1.00832
\(340\) −2.59266 −0.140607
\(341\) −9.64588 −0.522353
\(342\) 0.544734 0.0294558
\(343\) 17.8689 0.964829
\(344\) 16.5739 0.893603
\(345\) −4.46686 −0.240488
\(346\) 42.1905 2.26818
\(347\) −17.2299 −0.924951 −0.462475 0.886632i \(-0.653039\pi\)
−0.462475 + 0.886632i \(0.653039\pi\)
\(348\) −42.2734 −2.26609
\(349\) −21.5405 −1.15304 −0.576519 0.817084i \(-0.695589\pi\)
−0.576519 + 0.817084i \(0.695589\pi\)
\(350\) −18.1899 −0.972291
\(351\) −27.3339 −1.45898
\(352\) −1.91467 −0.102052
\(353\) −28.0720 −1.49412 −0.747060 0.664757i \(-0.768535\pi\)
−0.747060 + 0.664757i \(0.768535\pi\)
\(354\) 59.4888 3.16179
\(355\) −1.94741 −0.103358
\(356\) 4.13777 0.219301
\(357\) −4.99544 −0.264387
\(358\) 32.6729 1.72681
\(359\) 14.6434 0.772851 0.386426 0.922321i \(-0.373710\pi\)
0.386426 + 0.922321i \(0.373710\pi\)
\(360\) 0.282173 0.0148718
\(361\) −17.1985 −0.905183
\(362\) 26.9624 1.41711
\(363\) −6.41853 −0.336885
\(364\) −32.6607 −1.71189
\(365\) −4.20684 −0.220196
\(366\) −38.4651 −2.01060
\(367\) 19.7503 1.03096 0.515479 0.856902i \(-0.327614\pi\)
0.515479 + 0.856902i \(0.327614\pi\)
\(368\) 24.7823 1.29187
\(369\) −0.876053 −0.0456055
\(370\) −1.49235 −0.0775837
\(371\) −4.42553 −0.229762
\(372\) 24.7867 1.28513
\(373\) 26.4196 1.36796 0.683978 0.729503i \(-0.260248\pi\)
0.683978 + 0.729503i \(0.260248\pi\)
\(374\) 12.1100 0.626193
\(375\) 6.33915 0.327352
\(376\) −2.00405 −0.103351
\(377\) −32.8006 −1.68932
\(378\) −18.8330 −0.968666
\(379\) −5.76350 −0.296051 −0.148026 0.988984i \(-0.547292\pi\)
−0.148026 + 0.988984i \(0.547292\pi\)
\(380\) 1.90208 0.0975744
\(381\) 3.13864 0.160797
\(382\) 63.0759 3.22725
\(383\) −8.45821 −0.432194 −0.216097 0.976372i \(-0.569333\pi\)
−0.216097 + 0.976372i \(0.569333\pi\)
\(384\) 35.7940 1.82660
\(385\) −1.50580 −0.0767427
\(386\) 18.8955 0.961757
\(387\) −0.589212 −0.0299513
\(388\) −0.00674641 −0.000342497 0
\(389\) −33.0117 −1.67376 −0.836880 0.547387i \(-0.815623\pi\)
−0.836880 + 0.547387i \(0.815623\pi\)
\(390\) 8.47666 0.429232
\(391\) 12.7237 0.643467
\(392\) 21.7858 1.10035
\(393\) −20.2439 −1.02117
\(394\) 17.5628 0.884800
\(395\) 0.727059 0.0365823
\(396\) −1.77980 −0.0894384
\(397\) 13.4482 0.674944 0.337472 0.941336i \(-0.390428\pi\)
0.337472 + 0.941336i \(0.390428\pi\)
\(398\) 20.2227 1.01367
\(399\) 3.66486 0.183472
\(400\) −17.3528 −0.867639
\(401\) −7.22760 −0.360929 −0.180465 0.983581i \(-0.557760\pi\)
−0.180465 + 0.983581i \(0.557760\pi\)
\(402\) −39.7130 −1.98070
\(403\) 19.2324 0.958036
\(404\) −42.7242 −2.12561
\(405\) 3.41884 0.169883
\(406\) −22.5996 −1.12160
\(407\) 4.61819 0.228915
\(408\) −15.2674 −0.755848
\(409\) 17.1033 0.845704 0.422852 0.906199i \(-0.361029\pi\)
0.422852 + 0.906199i \(0.361029\pi\)
\(410\) −4.61714 −0.228024
\(411\) −12.6659 −0.624763
\(412\) 36.2514 1.78598
\(413\) 21.0703 1.03680
\(414\) −2.82255 −0.138721
\(415\) 2.52034 0.123719
\(416\) 3.81757 0.187172
\(417\) 0.497822 0.0243785
\(418\) −8.88438 −0.434549
\(419\) 15.8437 0.774015 0.387008 0.922077i \(-0.373509\pi\)
0.387008 + 0.922077i \(0.373509\pi\)
\(420\) 3.86941 0.188808
\(421\) −12.9353 −0.630430 −0.315215 0.949020i \(-0.602077\pi\)
−0.315215 + 0.949020i \(0.602077\pi\)
\(422\) −5.88763 −0.286605
\(423\) 0.0712455 0.00346407
\(424\) −13.5256 −0.656861
\(425\) −8.90927 −0.432163
\(426\) −23.3740 −1.13248
\(427\) −13.6239 −0.659307
\(428\) −74.4444 −3.59841
\(429\) −26.2316 −1.26647
\(430\) −3.10538 −0.149755
\(431\) 7.16212 0.344987 0.172494 0.985011i \(-0.444818\pi\)
0.172494 + 0.985011i \(0.444818\pi\)
\(432\) −17.9663 −0.864405
\(433\) −18.9370 −0.910052 −0.455026 0.890478i \(-0.650370\pi\)
−0.455026 + 0.890478i \(0.650370\pi\)
\(434\) 13.2511 0.636075
\(435\) 3.88599 0.186319
\(436\) 11.3113 0.541712
\(437\) −9.33464 −0.446536
\(438\) −50.4931 −2.41265
\(439\) 35.9615 1.71635 0.858173 0.513360i \(-0.171599\pi\)
0.858173 + 0.513360i \(0.171599\pi\)
\(440\) −4.60212 −0.219398
\(441\) −0.774499 −0.0368809
\(442\) −24.1455 −1.14849
\(443\) −6.42771 −0.305390 −0.152695 0.988273i \(-0.548795\pi\)
−0.152695 + 0.988273i \(0.548795\pi\)
\(444\) −11.8672 −0.563193
\(445\) −0.380365 −0.0180310
\(446\) −3.59458 −0.170208
\(447\) 0.768209 0.0363350
\(448\) 13.5655 0.640910
\(449\) −13.8258 −0.652482 −0.326241 0.945287i \(-0.605782\pi\)
−0.326241 + 0.945287i \(0.605782\pi\)
\(450\) 1.97637 0.0931671
\(451\) 14.2881 0.672799
\(452\) −40.9618 −1.92668
\(453\) −1.73420 −0.0814800
\(454\) 15.3189 0.718953
\(455\) 3.00234 0.140752
\(456\) 11.2008 0.524524
\(457\) 29.4748 1.37878 0.689388 0.724393i \(-0.257880\pi\)
0.689388 + 0.724393i \(0.257880\pi\)
\(458\) −25.2683 −1.18071
\(459\) −9.22427 −0.430552
\(460\) −9.85564 −0.459522
\(461\) −24.8082 −1.15543 −0.577716 0.816238i \(-0.696056\pi\)
−0.577716 + 0.816238i \(0.696056\pi\)
\(462\) −18.0736 −0.840858
\(463\) 5.79512 0.269322 0.134661 0.990892i \(-0.457005\pi\)
0.134661 + 0.990892i \(0.457005\pi\)
\(464\) −21.5596 −1.00088
\(465\) −2.27852 −0.105664
\(466\) −16.9649 −0.785885
\(467\) −4.45534 −0.206169 −0.103084 0.994673i \(-0.532871\pi\)
−0.103084 + 0.994673i \(0.532871\pi\)
\(468\) 3.54866 0.164037
\(469\) −14.0659 −0.649503
\(470\) 0.375491 0.0173201
\(471\) 4.24905 0.195786
\(472\) 64.3963 2.96408
\(473\) 9.60980 0.441859
\(474\) 8.72661 0.400827
\(475\) 6.53620 0.299901
\(476\) −11.0219 −0.505188
\(477\) 0.480844 0.0220163
\(478\) −9.29431 −0.425112
\(479\) 27.5003 1.25652 0.628260 0.778003i \(-0.283767\pi\)
0.628260 + 0.778003i \(0.283767\pi\)
\(480\) −0.452279 −0.0206436
\(481\) −9.20798 −0.419848
\(482\) −8.72069 −0.397217
\(483\) −18.9895 −0.864053
\(484\) −14.1618 −0.643717
\(485\) 0.000620165 0 2.81602e−5 0
\(486\) 4.21291 0.191101
\(487\) −43.9550 −1.99179 −0.995895 0.0905110i \(-0.971150\pi\)
−0.995895 + 0.0905110i \(0.971150\pi\)
\(488\) −41.6382 −1.88487
\(489\) −3.15151 −0.142516
\(490\) −4.08191 −0.184402
\(491\) 18.6143 0.840051 0.420026 0.907512i \(-0.362021\pi\)
0.420026 + 0.907512i \(0.362021\pi\)
\(492\) −36.7156 −1.65527
\(493\) −11.0691 −0.498528
\(494\) 17.7141 0.796996
\(495\) 0.163609 0.00735366
\(496\) 12.6413 0.567611
\(497\) −8.27883 −0.371356
\(498\) 30.2507 1.35557
\(499\) 14.9742 0.670339 0.335170 0.942158i \(-0.391206\pi\)
0.335170 + 0.942158i \(0.391206\pi\)
\(500\) 13.9866 0.625501
\(501\) 29.2284 1.30583
\(502\) 20.8176 0.929133
\(503\) −35.6500 −1.58955 −0.794777 0.606902i \(-0.792412\pi\)
−0.794777 + 0.606902i \(0.792412\pi\)
\(504\) 1.19957 0.0534332
\(505\) 3.92743 0.174768
\(506\) 46.0346 2.04649
\(507\) 29.1681 1.29540
\(508\) 6.92505 0.307250
\(509\) 14.4290 0.639554 0.319777 0.947493i \(-0.396392\pi\)
0.319777 + 0.947493i \(0.396392\pi\)
\(510\) 2.86059 0.126669
\(511\) −17.8841 −0.791146
\(512\) 35.9301 1.58790
\(513\) 6.76730 0.298783
\(514\) −15.9787 −0.704789
\(515\) −3.33242 −0.146844
\(516\) −24.6940 −1.08709
\(517\) −1.16198 −0.0511040
\(518\) −6.34429 −0.278752
\(519\) −30.8408 −1.35376
\(520\) 9.17594 0.402392
\(521\) −38.7147 −1.69612 −0.848062 0.529898i \(-0.822230\pi\)
−0.848062 + 0.529898i \(0.822230\pi\)
\(522\) 2.45550 0.107474
\(523\) 9.85415 0.430892 0.215446 0.976516i \(-0.430879\pi\)
0.215446 + 0.976516i \(0.430879\pi\)
\(524\) −44.6660 −1.95124
\(525\) 13.2966 0.580313
\(526\) −72.4750 −3.16006
\(527\) 6.49030 0.282722
\(528\) −17.2418 −0.750353
\(529\) 25.3676 1.10294
\(530\) 2.53424 0.110080
\(531\) −2.28933 −0.0993486
\(532\) 8.08610 0.350577
\(533\) −28.4883 −1.23396
\(534\) −4.56538 −0.197563
\(535\) 6.84331 0.295862
\(536\) −42.9891 −1.85685
\(537\) −23.8835 −1.03065
\(538\) 21.1683 0.912632
\(539\) 12.6318 0.544088
\(540\) 7.14500 0.307472
\(541\) −19.9504 −0.857737 −0.428868 0.903367i \(-0.641088\pi\)
−0.428868 + 0.903367i \(0.641088\pi\)
\(542\) 7.27982 0.312695
\(543\) −19.7093 −0.845806
\(544\) 1.28830 0.0552355
\(545\) −1.03979 −0.0445397
\(546\) 36.0360 1.54220
\(547\) −29.7185 −1.27067 −0.635337 0.772235i \(-0.719139\pi\)
−0.635337 + 0.772235i \(0.719139\pi\)
\(548\) −27.9459 −1.19379
\(549\) 1.48027 0.0631763
\(550\) −32.2338 −1.37445
\(551\) 8.12075 0.345955
\(552\) −58.0370 −2.47022
\(553\) 3.09087 0.131437
\(554\) 22.8929 0.972624
\(555\) 1.09090 0.0463059
\(556\) 1.09839 0.0465821
\(557\) −34.6065 −1.46632 −0.733161 0.680055i \(-0.761956\pi\)
−0.733161 + 0.680055i \(0.761956\pi\)
\(558\) −1.43977 −0.0609501
\(559\) −19.1605 −0.810403
\(560\) 1.97341 0.0833918
\(561\) −8.85229 −0.373744
\(562\) −56.9920 −2.40406
\(563\) −8.96186 −0.377697 −0.188849 0.982006i \(-0.560476\pi\)
−0.188849 + 0.982006i \(0.560476\pi\)
\(564\) 2.98591 0.125730
\(565\) 3.76542 0.158413
\(566\) 63.3326 2.66207
\(567\) 14.5342 0.610377
\(568\) −25.3023 −1.06166
\(569\) 23.1417 0.970151 0.485075 0.874472i \(-0.338792\pi\)
0.485075 + 0.874472i \(0.338792\pi\)
\(570\) −2.09864 −0.0879025
\(571\) −37.6945 −1.57746 −0.788732 0.614737i \(-0.789262\pi\)
−0.788732 + 0.614737i \(0.789262\pi\)
\(572\) −57.8772 −2.41997
\(573\) −46.1079 −1.92618
\(574\) −19.6284 −0.819273
\(575\) −33.8674 −1.41237
\(576\) −1.47392 −0.0614134
\(577\) −9.43782 −0.392902 −0.196451 0.980514i \(-0.562942\pi\)
−0.196451 + 0.980514i \(0.562942\pi\)
\(578\) 33.2366 1.38246
\(579\) −13.8124 −0.574026
\(580\) 8.57400 0.356016
\(581\) 10.7145 0.444511
\(582\) 0.00744360 0.000308547 0
\(583\) −7.84237 −0.324798
\(584\) −54.6585 −2.26179
\(585\) −0.326211 −0.0134872
\(586\) −0.0387159 −0.00159934
\(587\) 4.20125 0.173404 0.0867020 0.996234i \(-0.472367\pi\)
0.0867020 + 0.996234i \(0.472367\pi\)
\(588\) −32.4594 −1.33860
\(589\) −4.76155 −0.196196
\(590\) −12.0657 −0.496736
\(591\) −12.8382 −0.528094
\(592\) −6.05232 −0.248749
\(593\) −14.2869 −0.586694 −0.293347 0.956006i \(-0.594769\pi\)
−0.293347 + 0.956006i \(0.594769\pi\)
\(594\) −33.3735 −1.36933
\(595\) 1.01319 0.0415367
\(596\) 1.69497 0.0694286
\(597\) −14.7826 −0.605010
\(598\) −91.7860 −3.75341
\(599\) −8.45517 −0.345469 −0.172734 0.984968i \(-0.555260\pi\)
−0.172734 + 0.984968i \(0.555260\pi\)
\(600\) 40.6380 1.65904
\(601\) −10.3852 −0.423623 −0.211811 0.977311i \(-0.567936\pi\)
−0.211811 + 0.977311i \(0.567936\pi\)
\(602\) −13.2016 −0.538056
\(603\) 1.52829 0.0622369
\(604\) −3.82633 −0.155691
\(605\) 1.30182 0.0529267
\(606\) 47.1394 1.91491
\(607\) 9.68019 0.392907 0.196453 0.980513i \(-0.437058\pi\)
0.196453 + 0.980513i \(0.437058\pi\)
\(608\) −0.945150 −0.0383309
\(609\) 16.5201 0.669428
\(610\) 7.80159 0.315877
\(611\) 2.31682 0.0937286
\(612\) 1.19755 0.0484082
\(613\) −9.12829 −0.368688 −0.184344 0.982862i \(-0.559016\pi\)
−0.184344 + 0.982862i \(0.559016\pi\)
\(614\) −9.49114 −0.383031
\(615\) 3.37509 0.136097
\(616\) −19.5645 −0.788278
\(617\) 38.2907 1.54153 0.770763 0.637122i \(-0.219875\pi\)
0.770763 + 0.637122i \(0.219875\pi\)
\(618\) −39.9977 −1.60894
\(619\) 16.1469 0.648997 0.324499 0.945886i \(-0.394804\pi\)
0.324499 + 0.945886i \(0.394804\pi\)
\(620\) −5.02731 −0.201901
\(621\) −35.0649 −1.40710
\(622\) 15.3442 0.615245
\(623\) −1.61701 −0.0647840
\(624\) 34.3776 1.37620
\(625\) 23.0629 0.922517
\(626\) 23.7633 0.949772
\(627\) 6.49439 0.259361
\(628\) 9.37506 0.374106
\(629\) −3.10738 −0.123900
\(630\) −0.224759 −0.00895462
\(631\) −9.21589 −0.366879 −0.183439 0.983031i \(-0.558723\pi\)
−0.183439 + 0.983031i \(0.558723\pi\)
\(632\) 9.44652 0.375762
\(633\) 4.30380 0.171061
\(634\) 22.4764 0.892652
\(635\) −0.636587 −0.0252622
\(636\) 20.1523 0.799090
\(637\) −25.1858 −0.997899
\(638\) −40.0482 −1.58552
\(639\) 0.899514 0.0355842
\(640\) −7.25983 −0.286970
\(641\) 9.68779 0.382645 0.191322 0.981527i \(-0.438722\pi\)
0.191322 + 0.981527i \(0.438722\pi\)
\(642\) 82.1377 3.24172
\(643\) 24.8826 0.981272 0.490636 0.871365i \(-0.336764\pi\)
0.490636 + 0.871365i \(0.336764\pi\)
\(644\) −41.8983 −1.65102
\(645\) 2.27000 0.0893812
\(646\) 5.97792 0.235198
\(647\) 21.0575 0.827855 0.413928 0.910310i \(-0.364157\pi\)
0.413928 + 0.910310i \(0.364157\pi\)
\(648\) 44.4202 1.74499
\(649\) 37.3381 1.46565
\(650\) 64.2694 2.52085
\(651\) −9.68644 −0.379642
\(652\) −6.95346 −0.272319
\(653\) 25.7195 1.00648 0.503240 0.864146i \(-0.332141\pi\)
0.503240 + 0.864146i \(0.332141\pi\)
\(654\) −12.4802 −0.488015
\(655\) 4.10593 0.160432
\(656\) −18.7251 −0.731091
\(657\) 1.94315 0.0758094
\(658\) 1.59629 0.0622298
\(659\) 23.2097 0.904122 0.452061 0.891987i \(-0.350689\pi\)
0.452061 + 0.891987i \(0.350689\pi\)
\(660\) 6.85687 0.266903
\(661\) −23.1703 −0.901222 −0.450611 0.892720i \(-0.648794\pi\)
−0.450611 + 0.892720i \(0.648794\pi\)
\(662\) 24.0194 0.933542
\(663\) 17.6501 0.685475
\(664\) 32.7462 1.27080
\(665\) −0.743316 −0.0288246
\(666\) 0.689321 0.0267107
\(667\) −42.0778 −1.62926
\(668\) 64.4893 2.49517
\(669\) 2.62760 0.101589
\(670\) 8.05470 0.311180
\(671\) −24.1426 −0.932013
\(672\) −1.92273 −0.0741708
\(673\) 29.2139 1.12611 0.563056 0.826419i \(-0.309626\pi\)
0.563056 + 0.826419i \(0.309626\pi\)
\(674\) 72.9144 2.80856
\(675\) 24.5527 0.945035
\(676\) 64.3561 2.47523
\(677\) −20.5320 −0.789108 −0.394554 0.918873i \(-0.629101\pi\)
−0.394554 + 0.918873i \(0.629101\pi\)
\(678\) 45.1950 1.73570
\(679\) 0.00263644 0.000101177 0
\(680\) 3.09657 0.118748
\(681\) −11.1980 −0.429108
\(682\) 23.4820 0.899171
\(683\) −1.82937 −0.0699990 −0.0349995 0.999387i \(-0.511143\pi\)
−0.0349995 + 0.999387i \(0.511143\pi\)
\(684\) −0.878573 −0.0335931
\(685\) 2.56893 0.0981538
\(686\) −43.5001 −1.66084
\(687\) 18.4709 0.704709
\(688\) −12.5940 −0.480143
\(689\) 15.6365 0.595703
\(690\) 10.8742 0.413972
\(691\) −37.7553 −1.43628 −0.718139 0.695900i \(-0.755006\pi\)
−0.718139 + 0.695900i \(0.755006\pi\)
\(692\) −68.0469 −2.58676
\(693\) 0.695533 0.0264211
\(694\) 41.9446 1.59220
\(695\) −0.100970 −0.00383000
\(696\) 50.4898 1.91381
\(697\) −9.61383 −0.364150
\(698\) 52.4383 1.98482
\(699\) 12.4012 0.469056
\(700\) 29.3376 1.10886
\(701\) 22.9884 0.868260 0.434130 0.900850i \(-0.357056\pi\)
0.434130 + 0.900850i \(0.357056\pi\)
\(702\) 66.5418 2.51146
\(703\) 2.27970 0.0859806
\(704\) 24.0391 0.906006
\(705\) −0.274480 −0.0103375
\(706\) 68.3385 2.57195
\(707\) 16.6963 0.627928
\(708\) −95.9465 −3.60589
\(709\) 23.9602 0.899844 0.449922 0.893068i \(-0.351452\pi\)
0.449922 + 0.893068i \(0.351452\pi\)
\(710\) 4.74079 0.177919
\(711\) −0.335830 −0.0125946
\(712\) −4.94200 −0.185209
\(713\) 24.6720 0.923975
\(714\) 12.1609 0.455111
\(715\) 5.32037 0.198970
\(716\) −52.6964 −1.96936
\(717\) 6.79405 0.253728
\(718\) −35.6481 −1.33037
\(719\) 31.4605 1.17328 0.586639 0.809848i \(-0.300451\pi\)
0.586639 + 0.809848i \(0.300451\pi\)
\(720\) −0.214416 −0.00799080
\(721\) −14.1668 −0.527598
\(722\) 41.8681 1.55817
\(723\) 6.37474 0.237079
\(724\) −43.4863 −1.61616
\(725\) 29.4633 1.09424
\(726\) 15.6253 0.579909
\(727\) −1.16498 −0.0432068 −0.0216034 0.999767i \(-0.506877\pi\)
−0.0216034 + 0.999767i \(0.506877\pi\)
\(728\) 39.0088 1.44576
\(729\) 25.3375 0.938424
\(730\) 10.2411 0.379042
\(731\) −6.46603 −0.239155
\(732\) 62.0384 2.29300
\(733\) −22.0307 −0.813721 −0.406860 0.913490i \(-0.633376\pi\)
−0.406860 + 0.913490i \(0.633376\pi\)
\(734\) −48.0803 −1.77468
\(735\) 2.98384 0.110060
\(736\) 4.89731 0.180517
\(737\) −24.9258 −0.918155
\(738\) 2.13267 0.0785046
\(739\) −31.9974 −1.17704 −0.588521 0.808482i \(-0.700290\pi\)
−0.588521 + 0.808482i \(0.700290\pi\)
\(740\) 2.40694 0.0884809
\(741\) −12.9489 −0.475688
\(742\) 10.7735 0.395509
\(743\) −47.2497 −1.73342 −0.866711 0.498810i \(-0.833771\pi\)
−0.866711 + 0.498810i \(0.833771\pi\)
\(744\) −29.6043 −1.08535
\(745\) −0.155810 −0.00570844
\(746\) −64.3160 −2.35478
\(747\) −1.16415 −0.0425940
\(748\) −19.5316 −0.714146
\(749\) 29.0923 1.06301
\(750\) −15.4320 −0.563499
\(751\) 18.0746 0.659551 0.329775 0.944059i \(-0.393027\pi\)
0.329775 + 0.944059i \(0.393027\pi\)
\(752\) 1.52283 0.0555317
\(753\) −15.2174 −0.554554
\(754\) 79.8500 2.90797
\(755\) 0.351736 0.0128010
\(756\) 30.3748 1.10472
\(757\) 42.5737 1.54737 0.773683 0.633573i \(-0.218412\pi\)
0.773683 + 0.633573i \(0.218412\pi\)
\(758\) 14.0307 0.509618
\(759\) −33.6508 −1.22145
\(760\) −2.27177 −0.0824058
\(761\) −3.79319 −0.137503 −0.0687515 0.997634i \(-0.521902\pi\)
−0.0687515 + 0.997634i \(0.521902\pi\)
\(762\) −7.64071 −0.276794
\(763\) −4.42036 −0.160028
\(764\) −101.732 −3.68053
\(765\) −0.110085 −0.00398014
\(766\) 20.5907 0.743973
\(767\) −74.4466 −2.68811
\(768\) −55.6713 −2.00886
\(769\) 25.9928 0.937324 0.468662 0.883378i \(-0.344736\pi\)
0.468662 + 0.883378i \(0.344736\pi\)
\(770\) 3.66573 0.132104
\(771\) 11.6802 0.420654
\(772\) −30.4756 −1.09684
\(773\) −17.9650 −0.646154 −0.323077 0.946373i \(-0.604717\pi\)
−0.323077 + 0.946373i \(0.604717\pi\)
\(774\) 1.43438 0.0515578
\(775\) −17.2756 −0.620557
\(776\) 0.00805766 0.000289253 0
\(777\) 4.63761 0.166373
\(778\) 80.3638 2.88118
\(779\) 7.05309 0.252703
\(780\) −13.6716 −0.489521
\(781\) −14.6707 −0.524959
\(782\) −30.9747 −1.10765
\(783\) 30.5050 1.09016
\(784\) −16.5544 −0.591229
\(785\) −0.861804 −0.0307591
\(786\) 49.2819 1.75783
\(787\) 21.3822 0.762193 0.381096 0.924535i \(-0.375547\pi\)
0.381096 + 0.924535i \(0.375547\pi\)
\(788\) −28.3261 −1.00908
\(789\) 52.9785 1.88609
\(790\) −1.76996 −0.0629722
\(791\) 16.0076 0.569164
\(792\) 2.12573 0.0755346
\(793\) 48.1366 1.70938
\(794\) −32.7383 −1.16184
\(795\) −1.85250 −0.0657014
\(796\) −32.6161 −1.15605
\(797\) −11.1237 −0.394023 −0.197012 0.980401i \(-0.563124\pi\)
−0.197012 + 0.980401i \(0.563124\pi\)
\(798\) −8.92175 −0.315826
\(799\) 0.781850 0.0276599
\(800\) −3.42914 −0.121239
\(801\) 0.175691 0.00620775
\(802\) 17.5949 0.621298
\(803\) −31.6919 −1.11838
\(804\) 64.0511 2.25891
\(805\) 3.85151 0.135748
\(806\) −46.8195 −1.64915
\(807\) −15.4739 −0.544705
\(808\) 51.0282 1.79517
\(809\) −14.7939 −0.520127 −0.260063 0.965592i \(-0.583743\pi\)
−0.260063 + 0.965592i \(0.583743\pi\)
\(810\) −8.32284 −0.292435
\(811\) 17.8191 0.625713 0.312857 0.949800i \(-0.398714\pi\)
0.312857 + 0.949800i \(0.398714\pi\)
\(812\) 36.4498 1.27914
\(813\) −5.32148 −0.186632
\(814\) −11.2425 −0.394051
\(815\) 0.639198 0.0223901
\(816\) 11.6013 0.406126
\(817\) 4.74374 0.165962
\(818\) −41.6364 −1.45578
\(819\) −1.38679 −0.0484583
\(820\) 7.44675 0.260052
\(821\) 3.65192 0.127453 0.0637265 0.997967i \(-0.479701\pi\)
0.0637265 + 0.997967i \(0.479701\pi\)
\(822\) 30.8339 1.07546
\(823\) −41.6032 −1.45020 −0.725098 0.688646i \(-0.758206\pi\)
−0.725098 + 0.688646i \(0.758206\pi\)
\(824\) −43.2973 −1.50833
\(825\) 23.5626 0.820345
\(826\) −51.2936 −1.78473
\(827\) 6.24366 0.217113 0.108557 0.994090i \(-0.465377\pi\)
0.108557 + 0.994090i \(0.465377\pi\)
\(828\) 4.55234 0.158205
\(829\) 28.0990 0.975920 0.487960 0.872866i \(-0.337741\pi\)
0.487960 + 0.872866i \(0.337741\pi\)
\(830\) −6.13553 −0.212967
\(831\) −16.7345 −0.580512
\(832\) −47.9303 −1.66168
\(833\) −8.49937 −0.294486
\(834\) −1.21190 −0.0419647
\(835\) −5.92819 −0.205154
\(836\) 14.3292 0.495585
\(837\) −17.8864 −0.618244
\(838\) −38.5700 −1.33238
\(839\) 33.8225 1.16768 0.583842 0.811868i \(-0.301549\pi\)
0.583842 + 0.811868i \(0.301549\pi\)
\(840\) −4.62148 −0.159456
\(841\) 7.60594 0.262274
\(842\) 31.4899 1.08521
\(843\) 41.6606 1.43487
\(844\) 9.49586 0.326861
\(845\) −5.91595 −0.203515
\(846\) −0.173440 −0.00596300
\(847\) 5.53431 0.190161
\(848\) 10.2777 0.352939
\(849\) −46.2955 −1.58886
\(850\) 21.6888 0.743919
\(851\) −11.8123 −0.404921
\(852\) 37.6988 1.29154
\(853\) 22.7291 0.778229 0.389114 0.921189i \(-0.372781\pi\)
0.389114 + 0.921189i \(0.372781\pi\)
\(854\) 33.1661 1.13492
\(855\) 0.0807630 0.00276204
\(856\) 88.9137 3.03901
\(857\) 33.6001 1.14776 0.573878 0.818941i \(-0.305438\pi\)
0.573878 + 0.818941i \(0.305438\pi\)
\(858\) 63.8584 2.18009
\(859\) 5.67293 0.193558 0.0967790 0.995306i \(-0.469146\pi\)
0.0967790 + 0.995306i \(0.469146\pi\)
\(860\) 5.00850 0.170789
\(861\) 14.3482 0.488984
\(862\) −17.4355 −0.593855
\(863\) 25.2822 0.860616 0.430308 0.902682i \(-0.358405\pi\)
0.430308 + 0.902682i \(0.358405\pi\)
\(864\) −3.55039 −0.120787
\(865\) 6.25522 0.212684
\(866\) 46.1002 1.56655
\(867\) −24.2956 −0.825122
\(868\) −21.3721 −0.725415
\(869\) 5.47725 0.185803
\(870\) −9.46006 −0.320726
\(871\) 49.6984 1.68396
\(872\) −13.5098 −0.457499
\(873\) −0.000286456 0 −9.69505e−6 0
\(874\) 22.7243 0.768661
\(875\) −5.46586 −0.184780
\(876\) 81.4378 2.75153
\(877\) −38.7794 −1.30949 −0.654744 0.755851i \(-0.727224\pi\)
−0.654744 + 0.755851i \(0.727224\pi\)
\(878\) −87.5447 −2.95449
\(879\) 0.0283010 0.000954568 0
\(880\) 3.49703 0.117885
\(881\) −25.7886 −0.868838 −0.434419 0.900711i \(-0.643046\pi\)
−0.434419 + 0.900711i \(0.643046\pi\)
\(882\) 1.88544 0.0634862
\(883\) −24.1823 −0.813799 −0.406899 0.913473i \(-0.633390\pi\)
−0.406899 + 0.913473i \(0.633390\pi\)
\(884\) 38.9431 1.30980
\(885\) 8.81990 0.296478
\(886\) 15.6477 0.525693
\(887\) −7.03011 −0.236048 −0.118024 0.993011i \(-0.537656\pi\)
−0.118024 + 0.993011i \(0.537656\pi\)
\(888\) 14.1738 0.475640
\(889\) −2.70626 −0.0907649
\(890\) 0.925962 0.0310383
\(891\) 25.7556 0.862845
\(892\) 5.79752 0.194115
\(893\) −0.573596 −0.0191947
\(894\) −1.87013 −0.0625465
\(895\) 4.84412 0.161921
\(896\) −30.8630 −1.03106
\(897\) 67.0947 2.24023
\(898\) 33.6577 1.12317
\(899\) −21.4636 −0.715852
\(900\) −3.18759 −0.106253
\(901\) 5.27680 0.175796
\(902\) −34.7829 −1.15815
\(903\) 9.65022 0.321139
\(904\) 48.9233 1.62717
\(905\) 3.99749 0.132881
\(906\) 4.22176 0.140258
\(907\) 5.32177 0.176707 0.0883533 0.996089i \(-0.471840\pi\)
0.0883533 + 0.996089i \(0.471840\pi\)
\(908\) −24.7071 −0.819935
\(909\) −1.81409 −0.0601695
\(910\) −7.30891 −0.242288
\(911\) 40.6208 1.34583 0.672913 0.739722i \(-0.265043\pi\)
0.672913 + 0.739722i \(0.265043\pi\)
\(912\) −8.51116 −0.281833
\(913\) 18.9868 0.628372
\(914\) −71.7537 −2.37340
\(915\) −5.70289 −0.188532
\(916\) 40.7540 1.34655
\(917\) 17.4551 0.576419
\(918\) 22.4556 0.741146
\(919\) 39.1305 1.29080 0.645398 0.763847i \(-0.276692\pi\)
0.645398 + 0.763847i \(0.276692\pi\)
\(920\) 11.7712 0.388086
\(921\) 6.93793 0.228613
\(922\) 60.3932 1.98894
\(923\) 29.2512 0.962814
\(924\) 29.1499 0.958962
\(925\) 8.27109 0.271952
\(926\) −14.1077 −0.463607
\(927\) 1.53925 0.0505556
\(928\) −4.26046 −0.139856
\(929\) 41.7517 1.36983 0.684914 0.728623i \(-0.259840\pi\)
0.684914 + 0.728623i \(0.259840\pi\)
\(930\) 5.54684 0.181888
\(931\) 6.23548 0.204360
\(932\) 27.3619 0.896268
\(933\) −11.2164 −0.367209
\(934\) 10.8461 0.354896
\(935\) 1.79545 0.0587174
\(936\) −4.23839 −0.138536
\(937\) −14.1376 −0.461854 −0.230927 0.972971i \(-0.574176\pi\)
−0.230927 + 0.972971i \(0.574176\pi\)
\(938\) 34.2421 1.11805
\(939\) −17.3707 −0.566872
\(940\) −0.605611 −0.0197528
\(941\) 47.9322 1.56254 0.781272 0.624191i \(-0.214571\pi\)
0.781272 + 0.624191i \(0.214571\pi\)
\(942\) −10.3439 −0.337023
\(943\) −36.5457 −1.19009
\(944\) −48.9330 −1.59263
\(945\) −2.79221 −0.0908306
\(946\) −23.3942 −0.760610
\(947\) −10.5619 −0.343215 −0.171607 0.985165i \(-0.554896\pi\)
−0.171607 + 0.985165i \(0.554896\pi\)
\(948\) −14.0747 −0.457125
\(949\) 63.1890 2.05120
\(950\) −15.9118 −0.516245
\(951\) −16.4300 −0.532780
\(952\) 13.1641 0.426653
\(953\) 37.2634 1.20708 0.603540 0.797333i \(-0.293756\pi\)
0.603540 + 0.797333i \(0.293756\pi\)
\(954\) −1.17057 −0.0378986
\(955\) 9.35173 0.302615
\(956\) 14.9903 0.484821
\(957\) 29.2748 0.946320
\(958\) −66.9469 −2.16296
\(959\) 10.9210 0.352659
\(960\) 5.67844 0.183271
\(961\) −18.4149 −0.594030
\(962\) 22.4159 0.722719
\(963\) −3.16094 −0.101860
\(964\) 14.0652 0.453008
\(965\) 2.80148 0.0901828
\(966\) 46.2282 1.48737
\(967\) −24.1777 −0.777501 −0.388751 0.921343i \(-0.627093\pi\)
−0.388751 + 0.921343i \(0.627093\pi\)
\(968\) 16.9143 0.543646
\(969\) −4.36980 −0.140378
\(970\) −0.00150973 −4.84746e−5 0
\(971\) 56.3468 1.80825 0.904127 0.427264i \(-0.140522\pi\)
0.904127 + 0.427264i \(0.140522\pi\)
\(972\) −6.79478 −0.217943
\(973\) −0.429242 −0.0137609
\(974\) 107.004 3.42864
\(975\) −46.9803 −1.50457
\(976\) 31.6398 1.01276
\(977\) −49.4353 −1.58157 −0.790787 0.612091i \(-0.790329\pi\)
−0.790787 + 0.612091i \(0.790329\pi\)
\(978\) 7.67206 0.245325
\(979\) −2.86545 −0.0915803
\(980\) 6.58351 0.210302
\(981\) 0.480282 0.0153342
\(982\) −45.3147 −1.44605
\(983\) −21.5557 −0.687519 −0.343760 0.939058i \(-0.611701\pi\)
−0.343760 + 0.939058i \(0.611701\pi\)
\(984\) 43.8517 1.39794
\(985\) 2.60388 0.0829666
\(986\) 26.9467 0.858158
\(987\) −1.16687 −0.0371419
\(988\) −28.5702 −0.908939
\(989\) −24.5798 −0.781591
\(990\) −0.398290 −0.0126585
\(991\) −10.9082 −0.346509 −0.173255 0.984877i \(-0.555428\pi\)
−0.173255 + 0.984877i \(0.555428\pi\)
\(992\) 2.49809 0.0793145
\(993\) −17.5580 −0.557185
\(994\) 20.1540 0.639247
\(995\) 2.99824 0.0950507
\(996\) −48.7898 −1.54596
\(997\) 55.3657 1.75345 0.876725 0.480993i \(-0.159724\pi\)
0.876725 + 0.480993i \(0.159724\pi\)
\(998\) −36.4534 −1.15391
\(999\) 8.56352 0.270938
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 \(a_p\))