Properties

Label 8041.2.a.g.1.7
Level 8041
Weight 2
Character 8041.1
Self dual Yes
Analytic conductor 64.208
Analytic rank 1
Dimension 69
CM No

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Newspace parameters

Level: \( N \) = \( 8041 = 11 \cdot 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8041.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2077082653\)
Analytic rank: \(1\)
Dimension: \(69\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) = 8041.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.47238 q^{2} -0.879695 q^{3} +4.11267 q^{4} -2.32585 q^{5} +2.17494 q^{6} +1.92542 q^{7} -5.22332 q^{8} -2.22614 q^{9} +O(q^{10})\) \(q-2.47238 q^{2} -0.879695 q^{3} +4.11267 q^{4} -2.32585 q^{5} +2.17494 q^{6} +1.92542 q^{7} -5.22332 q^{8} -2.22614 q^{9} +5.75038 q^{10} -1.00000 q^{11} -3.61789 q^{12} -4.82240 q^{13} -4.76038 q^{14} +2.04604 q^{15} +4.68871 q^{16} +1.00000 q^{17} +5.50386 q^{18} -4.21529 q^{19} -9.56544 q^{20} -1.69378 q^{21} +2.47238 q^{22} -6.36962 q^{23} +4.59493 q^{24} +0.409567 q^{25} +11.9228 q^{26} +4.59741 q^{27} +7.91862 q^{28} -3.79631 q^{29} -5.05858 q^{30} +7.93702 q^{31} -1.14563 q^{32} +0.879695 q^{33} -2.47238 q^{34} -4.47824 q^{35} -9.15536 q^{36} +2.21625 q^{37} +10.4218 q^{38} +4.24224 q^{39} +12.1487 q^{40} +3.28743 q^{41} +4.18768 q^{42} +1.00000 q^{43} -4.11267 q^{44} +5.17765 q^{45} +15.7481 q^{46} +2.42265 q^{47} -4.12463 q^{48} -3.29275 q^{49} -1.01261 q^{50} -0.879695 q^{51} -19.8329 q^{52} -2.66086 q^{53} -11.3665 q^{54} +2.32585 q^{55} -10.0571 q^{56} +3.70817 q^{57} +9.38592 q^{58} +15.1369 q^{59} +8.41467 q^{60} +9.46522 q^{61} -19.6233 q^{62} -4.28625 q^{63} -6.54499 q^{64} +11.2162 q^{65} -2.17494 q^{66} +14.5555 q^{67} +4.11267 q^{68} +5.60332 q^{69} +11.0719 q^{70} -5.67883 q^{71} +11.6278 q^{72} +7.91191 q^{73} -5.47941 q^{74} -0.360294 q^{75} -17.3361 q^{76} -1.92542 q^{77} -10.4884 q^{78} +3.11018 q^{79} -10.9052 q^{80} +2.63409 q^{81} -8.12778 q^{82} -0.124396 q^{83} -6.96597 q^{84} -2.32585 q^{85} -2.47238 q^{86} +3.33959 q^{87} +5.22332 q^{88} -3.66791 q^{89} -12.8011 q^{90} -9.28515 q^{91} -26.1961 q^{92} -6.98216 q^{93} -5.98972 q^{94} +9.80412 q^{95} +1.00780 q^{96} -13.6924 q^{97} +8.14093 q^{98} +2.22614 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 69q - 11q^{2} - 3q^{3} + 65q^{4} - 6q^{5} - 10q^{6} - 11q^{7} - 33q^{8} + 56q^{9} + O(q^{10}) \) \( 69q - 11q^{2} - 3q^{3} + 65q^{4} - 6q^{5} - 10q^{6} - 11q^{7} - 33q^{8} + 56q^{9} - q^{10} - 69q^{11} - 3q^{12} - 28q^{13} - 15q^{14} - 45q^{15} + 53q^{16} + 69q^{17} - 17q^{18} - 32q^{19} - 21q^{20} - 38q^{21} + 11q^{22} - 41q^{23} - 11q^{24} + 67q^{25} - 6q^{26} - 3q^{27} - 21q^{28} - 22q^{29} - 22q^{30} - 27q^{31} - 87q^{32} + 3q^{33} - 11q^{34} - 44q^{35} + 59q^{36} + 24q^{37} - 22q^{38} - 59q^{39} + q^{40} - 43q^{41} - 15q^{42} + 69q^{43} - 65q^{44} - 12q^{45} - 21q^{46} - 99q^{47} + 2q^{48} + 64q^{49} - 78q^{50} - 3q^{51} - 57q^{52} - 50q^{53} + 20q^{54} + 6q^{55} - 59q^{56} - 15q^{57} + 22q^{58} - 82q^{59} - 86q^{60} - 24q^{61} + 15q^{62} - 63q^{63} + 63q^{64} - 23q^{65} + 10q^{66} - 54q^{67} + 65q^{68} + 36q^{69} + 9q^{70} - 128q^{71} - 69q^{72} + 2q^{73} - 58q^{74} - 31q^{75} - 76q^{76} + 11q^{77} - 19q^{78} - 43q^{79} - 19q^{80} + 49q^{81} - 2q^{82} - 62q^{83} - 82q^{84} - 6q^{85} - 11q^{86} - 62q^{87} + 33q^{88} - 49q^{89} - 37q^{90} - 2q^{91} - 96q^{92} - 29q^{93} - 75q^{94} - 133q^{95} - 86q^{96} + 5q^{97} - 72q^{98} - 56q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.47238 −1.74824 −0.874119 0.485712i \(-0.838560\pi\)
−0.874119 + 0.485712i \(0.838560\pi\)
\(3\) −0.879695 −0.507892 −0.253946 0.967218i \(-0.581729\pi\)
−0.253946 + 0.967218i \(0.581729\pi\)
\(4\) 4.11267 2.05633
\(5\) −2.32585 −1.04015 −0.520075 0.854120i \(-0.674096\pi\)
−0.520075 + 0.854120i \(0.674096\pi\)
\(6\) 2.17494 0.887916
\(7\) 1.92542 0.727741 0.363871 0.931450i \(-0.381455\pi\)
0.363871 + 0.931450i \(0.381455\pi\)
\(8\) −5.22332 −1.84672
\(9\) −2.22614 −0.742046
\(10\) 5.75038 1.81843
\(11\) −1.00000 −0.301511
\(12\) −3.61789 −1.04440
\(13\) −4.82240 −1.33749 −0.668746 0.743491i \(-0.733169\pi\)
−0.668746 + 0.743491i \(0.733169\pi\)
\(14\) −4.76038 −1.27226
\(15\) 2.04604 0.528284
\(16\) 4.68871 1.17218
\(17\) 1.00000 0.242536
\(18\) 5.50386 1.29727
\(19\) −4.21529 −0.967053 −0.483527 0.875330i \(-0.660644\pi\)
−0.483527 + 0.875330i \(0.660644\pi\)
\(20\) −9.56544 −2.13890
\(21\) −1.69378 −0.369614
\(22\) 2.47238 0.527113
\(23\) −6.36962 −1.32816 −0.664078 0.747663i \(-0.731176\pi\)
−0.664078 + 0.747663i \(0.731176\pi\)
\(24\) 4.59493 0.937937
\(25\) 0.409567 0.0819134
\(26\) 11.9228 2.33825
\(27\) 4.59741 0.884771
\(28\) 7.91862 1.49648
\(29\) −3.79631 −0.704957 −0.352478 0.935820i \(-0.614661\pi\)
−0.352478 + 0.935820i \(0.614661\pi\)
\(30\) −5.05858 −0.923567
\(31\) 7.93702 1.42553 0.712765 0.701402i \(-0.247442\pi\)
0.712765 + 0.701402i \(0.247442\pi\)
\(32\) −1.14563 −0.202521
\(33\) 0.879695 0.153135
\(34\) −2.47238 −0.424010
\(35\) −4.47824 −0.756960
\(36\) −9.15536 −1.52589
\(37\) 2.21625 0.364349 0.182174 0.983266i \(-0.441686\pi\)
0.182174 + 0.983266i \(0.441686\pi\)
\(38\) 10.4218 1.69064
\(39\) 4.24224 0.679302
\(40\) 12.1487 1.92087
\(41\) 3.28743 0.513411 0.256705 0.966490i \(-0.417363\pi\)
0.256705 + 0.966490i \(0.417363\pi\)
\(42\) 4.18768 0.646173
\(43\) 1.00000 0.152499
\(44\) −4.11267 −0.620008
\(45\) 5.17765 0.771839
\(46\) 15.7481 2.32193
\(47\) 2.42265 0.353380 0.176690 0.984267i \(-0.443461\pi\)
0.176690 + 0.984267i \(0.443461\pi\)
\(48\) −4.12463 −0.595340
\(49\) −3.29275 −0.470393
\(50\) −1.01261 −0.143204
\(51\) −0.879695 −0.123182
\(52\) −19.8329 −2.75033
\(53\) −2.66086 −0.365497 −0.182749 0.983160i \(-0.558499\pi\)
−0.182749 + 0.983160i \(0.558499\pi\)
\(54\) −11.3665 −1.54679
\(55\) 2.32585 0.313617
\(56\) −10.0571 −1.34394
\(57\) 3.70817 0.491159
\(58\) 9.38592 1.23243
\(59\) 15.1369 1.97066 0.985328 0.170673i \(-0.0545942\pi\)
0.985328 + 0.170673i \(0.0545942\pi\)
\(60\) 8.41467 1.08633
\(61\) 9.46522 1.21190 0.605949 0.795504i \(-0.292794\pi\)
0.605949 + 0.795504i \(0.292794\pi\)
\(62\) −19.6233 −2.49217
\(63\) −4.28625 −0.540017
\(64\) −6.54499 −0.818123
\(65\) 11.2162 1.39119
\(66\) −2.17494 −0.267717
\(67\) 14.5555 1.77824 0.889121 0.457672i \(-0.151317\pi\)
0.889121 + 0.457672i \(0.151317\pi\)
\(68\) 4.11267 0.498734
\(69\) 5.60332 0.674560
\(70\) 11.0719 1.32335
\(71\) −5.67883 −0.673954 −0.336977 0.941513i \(-0.609404\pi\)
−0.336977 + 0.941513i \(0.609404\pi\)
\(72\) 11.6278 1.37035
\(73\) 7.91191 0.926019 0.463009 0.886353i \(-0.346770\pi\)
0.463009 + 0.886353i \(0.346770\pi\)
\(74\) −5.47941 −0.636968
\(75\) −0.360294 −0.0416032
\(76\) −17.3361 −1.98859
\(77\) −1.92542 −0.219422
\(78\) −10.4884 −1.18758
\(79\) 3.11018 0.349923 0.174962 0.984575i \(-0.444020\pi\)
0.174962 + 0.984575i \(0.444020\pi\)
\(80\) −10.9052 −1.21924
\(81\) 2.63409 0.292677
\(82\) −8.12778 −0.897564
\(83\) −0.124396 −0.0136543 −0.00682713 0.999977i \(-0.502173\pi\)
−0.00682713 + 0.999977i \(0.502173\pi\)
\(84\) −6.96597 −0.760050
\(85\) −2.32585 −0.252274
\(86\) −2.47238 −0.266604
\(87\) 3.33959 0.358042
\(88\) 5.22332 0.556808
\(89\) −3.66791 −0.388798 −0.194399 0.980923i \(-0.562276\pi\)
−0.194399 + 0.980923i \(0.562276\pi\)
\(90\) −12.8011 −1.34936
\(91\) −9.28515 −0.973348
\(92\) −26.1961 −2.73113
\(93\) −6.98216 −0.724016
\(94\) −5.98972 −0.617792
\(95\) 9.80412 1.00588
\(96\) 1.00780 0.102859
\(97\) −13.6924 −1.39026 −0.695129 0.718885i \(-0.744653\pi\)
−0.695129 + 0.718885i \(0.744653\pi\)
\(98\) 8.14093 0.822359
\(99\) 2.22614 0.223735
\(100\) 1.68441 0.168441
\(101\) −12.0405 −1.19808 −0.599039 0.800720i \(-0.704450\pi\)
−0.599039 + 0.800720i \(0.704450\pi\)
\(102\) 2.17494 0.215351
\(103\) 10.7199 1.05627 0.528134 0.849161i \(-0.322892\pi\)
0.528134 + 0.849161i \(0.322892\pi\)
\(104\) 25.1889 2.46998
\(105\) 3.93948 0.384454
\(106\) 6.57866 0.638976
\(107\) 10.0113 0.967833 0.483917 0.875114i \(-0.339214\pi\)
0.483917 + 0.875114i \(0.339214\pi\)
\(108\) 18.9076 1.81939
\(109\) 16.8931 1.61806 0.809032 0.587764i \(-0.199992\pi\)
0.809032 + 0.587764i \(0.199992\pi\)
\(110\) −5.75038 −0.548277
\(111\) −1.94962 −0.185050
\(112\) 9.02774 0.853042
\(113\) −14.5747 −1.37107 −0.685536 0.728039i \(-0.740432\pi\)
−0.685536 + 0.728039i \(0.740432\pi\)
\(114\) −9.16801 −0.858662
\(115\) 14.8148 1.38148
\(116\) −15.6130 −1.44963
\(117\) 10.7353 0.992480
\(118\) −37.4242 −3.44517
\(119\) 1.92542 0.176503
\(120\) −10.6871 −0.975595
\(121\) 1.00000 0.0909091
\(122\) −23.4016 −2.11868
\(123\) −2.89194 −0.260757
\(124\) 32.6423 2.93137
\(125\) 10.6766 0.954948
\(126\) 10.5972 0.944078
\(127\) −2.79346 −0.247880 −0.123940 0.992290i \(-0.539553\pi\)
−0.123940 + 0.992290i \(0.539553\pi\)
\(128\) 18.4730 1.63279
\(129\) −0.879695 −0.0774528
\(130\) −27.7306 −2.43214
\(131\) −14.6459 −1.27961 −0.639807 0.768535i \(-0.720986\pi\)
−0.639807 + 0.768535i \(0.720986\pi\)
\(132\) 3.61789 0.314897
\(133\) −8.11621 −0.703765
\(134\) −35.9868 −3.10879
\(135\) −10.6929 −0.920295
\(136\) −5.22332 −0.447896
\(137\) 7.29802 0.623512 0.311756 0.950162i \(-0.399083\pi\)
0.311756 + 0.950162i \(0.399083\pi\)
\(138\) −13.8535 −1.17929
\(139\) −8.44780 −0.716533 −0.358266 0.933619i \(-0.616632\pi\)
−0.358266 + 0.933619i \(0.616632\pi\)
\(140\) −18.4175 −1.55656
\(141\) −2.13119 −0.179479
\(142\) 14.0402 1.17823
\(143\) 4.82240 0.403269
\(144\) −10.4377 −0.869809
\(145\) 8.82964 0.733261
\(146\) −19.5613 −1.61890
\(147\) 2.89662 0.238909
\(148\) 9.11469 0.749223
\(149\) −2.58036 −0.211391 −0.105696 0.994399i \(-0.533707\pi\)
−0.105696 + 0.994399i \(0.533707\pi\)
\(150\) 0.890785 0.0727323
\(151\) 17.5091 1.42487 0.712436 0.701737i \(-0.247592\pi\)
0.712436 + 0.701737i \(0.247592\pi\)
\(152\) 22.0178 1.78588
\(153\) −2.22614 −0.179972
\(154\) 4.76038 0.383602
\(155\) −18.4603 −1.48277
\(156\) 17.4469 1.39687
\(157\) 0.587939 0.0469227 0.0234613 0.999725i \(-0.492531\pi\)
0.0234613 + 0.999725i \(0.492531\pi\)
\(158\) −7.68956 −0.611749
\(159\) 2.34075 0.185633
\(160\) 2.66456 0.210652
\(161\) −12.2642 −0.966554
\(162\) −6.51248 −0.511669
\(163\) 15.9060 1.24585 0.622925 0.782281i \(-0.285944\pi\)
0.622925 + 0.782281i \(0.285944\pi\)
\(164\) 13.5201 1.05574
\(165\) −2.04604 −0.159284
\(166\) 0.307555 0.0238709
\(167\) −0.386377 −0.0298988 −0.0149494 0.999888i \(-0.504759\pi\)
−0.0149494 + 0.999888i \(0.504759\pi\)
\(168\) 8.84718 0.682575
\(169\) 10.2555 0.788885
\(170\) 5.75038 0.441034
\(171\) 9.38381 0.717598
\(172\) 4.11267 0.313588
\(173\) −22.5833 −1.71697 −0.858486 0.512836i \(-0.828595\pi\)
−0.858486 + 0.512836i \(0.828595\pi\)
\(174\) −8.25675 −0.625943
\(175\) 0.788590 0.0596118
\(176\) −4.68871 −0.353425
\(177\) −13.3158 −1.00088
\(178\) 9.06847 0.679711
\(179\) −8.95790 −0.669545 −0.334772 0.942299i \(-0.608659\pi\)
−0.334772 + 0.942299i \(0.608659\pi\)
\(180\) 21.2940 1.58716
\(181\) −4.85208 −0.360652 −0.180326 0.983607i \(-0.557715\pi\)
−0.180326 + 0.983607i \(0.557715\pi\)
\(182\) 22.9564 1.70164
\(183\) −8.32651 −0.615513
\(184\) 33.2706 2.45274
\(185\) −5.15465 −0.378978
\(186\) 17.2626 1.26575
\(187\) −1.00000 −0.0731272
\(188\) 9.96356 0.726668
\(189\) 8.85195 0.643884
\(190\) −24.2395 −1.75852
\(191\) −21.2646 −1.53865 −0.769325 0.638858i \(-0.779407\pi\)
−0.769325 + 0.638858i \(0.779407\pi\)
\(192\) 5.75759 0.415518
\(193\) 0.104969 0.00755585 0.00377793 0.999993i \(-0.498797\pi\)
0.00377793 + 0.999993i \(0.498797\pi\)
\(194\) 33.8529 2.43050
\(195\) −9.86680 −0.706576
\(196\) −13.5420 −0.967285
\(197\) 21.2183 1.51174 0.755870 0.654722i \(-0.227214\pi\)
0.755870 + 0.654722i \(0.227214\pi\)
\(198\) −5.50386 −0.391142
\(199\) −1.00995 −0.0715932 −0.0357966 0.999359i \(-0.511397\pi\)
−0.0357966 + 0.999359i \(0.511397\pi\)
\(200\) −2.13930 −0.151271
\(201\) −12.8044 −0.903155
\(202\) 29.7688 2.09452
\(203\) −7.30950 −0.513026
\(204\) −3.61789 −0.253303
\(205\) −7.64607 −0.534024
\(206\) −26.5038 −1.84661
\(207\) 14.1796 0.985553
\(208\) −22.6108 −1.56778
\(209\) 4.21529 0.291578
\(210\) −9.73991 −0.672117
\(211\) 8.38416 0.577189 0.288595 0.957451i \(-0.406812\pi\)
0.288595 + 0.957451i \(0.406812\pi\)
\(212\) −10.9432 −0.751585
\(213\) 4.99564 0.342296
\(214\) −24.7519 −1.69200
\(215\) −2.32585 −0.158621
\(216\) −24.0137 −1.63393
\(217\) 15.2821 1.03742
\(218\) −41.7662 −2.82876
\(219\) −6.96007 −0.470318
\(220\) 9.56544 0.644902
\(221\) −4.82240 −0.324389
\(222\) 4.82021 0.323511
\(223\) 12.0564 0.807354 0.403677 0.914902i \(-0.367732\pi\)
0.403677 + 0.914902i \(0.367732\pi\)
\(224\) −2.20582 −0.147382
\(225\) −0.911752 −0.0607835
\(226\) 36.0342 2.39696
\(227\) 2.76081 0.183241 0.0916206 0.995794i \(-0.470795\pi\)
0.0916206 + 0.995794i \(0.470795\pi\)
\(228\) 15.2505 1.00999
\(229\) 3.87880 0.256318 0.128159 0.991754i \(-0.459093\pi\)
0.128159 + 0.991754i \(0.459093\pi\)
\(230\) −36.6277 −2.41516
\(231\) 1.69378 0.111443
\(232\) 19.8294 1.30186
\(233\) −18.3748 −1.20377 −0.601886 0.798582i \(-0.705584\pi\)
−0.601886 + 0.798582i \(0.705584\pi\)
\(234\) −26.5418 −1.73509
\(235\) −5.63472 −0.367568
\(236\) 62.2530 4.05233
\(237\) −2.73601 −0.177723
\(238\) −4.76038 −0.308569
\(239\) −18.5901 −1.20249 −0.601245 0.799064i \(-0.705329\pi\)
−0.601245 + 0.799064i \(0.705329\pi\)
\(240\) 9.59327 0.619243
\(241\) −26.5930 −1.71300 −0.856501 0.516145i \(-0.827367\pi\)
−0.856501 + 0.516145i \(0.827367\pi\)
\(242\) −2.47238 −0.158931
\(243\) −16.1094 −1.03342
\(244\) 38.9273 2.49207
\(245\) 7.65844 0.489279
\(246\) 7.14997 0.455866
\(247\) 20.3278 1.29343
\(248\) −41.4576 −2.63256
\(249\) 0.109431 0.00693489
\(250\) −26.3967 −1.66948
\(251\) −1.52484 −0.0962469 −0.0481234 0.998841i \(-0.515324\pi\)
−0.0481234 + 0.998841i \(0.515324\pi\)
\(252\) −17.6279 −1.11046
\(253\) 6.36962 0.400454
\(254\) 6.90650 0.433352
\(255\) 2.04604 0.128128
\(256\) −32.5822 −2.03639
\(257\) −4.63335 −0.289020 −0.144510 0.989503i \(-0.546161\pi\)
−0.144510 + 0.989503i \(0.546161\pi\)
\(258\) 2.17494 0.135406
\(259\) 4.26721 0.265152
\(260\) 46.1283 2.86076
\(261\) 8.45110 0.523110
\(262\) 36.2101 2.23707
\(263\) 15.6670 0.966066 0.483033 0.875602i \(-0.339535\pi\)
0.483033 + 0.875602i \(0.339535\pi\)
\(264\) −4.59493 −0.282799
\(265\) 6.18876 0.380172
\(266\) 20.0664 1.23035
\(267\) 3.22664 0.197467
\(268\) 59.8621 3.65666
\(269\) −2.11295 −0.128829 −0.0644145 0.997923i \(-0.520518\pi\)
−0.0644145 + 0.997923i \(0.520518\pi\)
\(270\) 26.4368 1.60890
\(271\) 20.2685 1.23122 0.615611 0.788050i \(-0.288909\pi\)
0.615611 + 0.788050i \(0.288909\pi\)
\(272\) 4.68871 0.284295
\(273\) 8.16810 0.494356
\(274\) −18.0435 −1.09005
\(275\) −0.409567 −0.0246978
\(276\) 23.0446 1.38712
\(277\) 19.6328 1.17962 0.589810 0.807542i \(-0.299203\pi\)
0.589810 + 0.807542i \(0.299203\pi\)
\(278\) 20.8862 1.25267
\(279\) −17.6689 −1.05781
\(280\) 23.3913 1.39790
\(281\) 30.9921 1.84884 0.924418 0.381380i \(-0.124551\pi\)
0.924418 + 0.381380i \(0.124551\pi\)
\(282\) 5.26913 0.313772
\(283\) −10.2422 −0.608834 −0.304417 0.952539i \(-0.598462\pi\)
−0.304417 + 0.952539i \(0.598462\pi\)
\(284\) −23.3552 −1.38587
\(285\) −8.62463 −0.510879
\(286\) −11.9228 −0.705010
\(287\) 6.32969 0.373630
\(288\) 2.55033 0.150279
\(289\) 1.00000 0.0588235
\(290\) −21.8302 −1.28192
\(291\) 12.0452 0.706101
\(292\) 32.5391 1.90420
\(293\) −8.75262 −0.511333 −0.255667 0.966765i \(-0.582295\pi\)
−0.255667 + 0.966765i \(0.582295\pi\)
\(294\) −7.16154 −0.417669
\(295\) −35.2061 −2.04978
\(296\) −11.5762 −0.672852
\(297\) −4.59741 −0.266769
\(298\) 6.37963 0.369562
\(299\) 30.7168 1.77640
\(300\) −1.48177 −0.0855501
\(301\) 1.92542 0.110979
\(302\) −43.2892 −2.49101
\(303\) 10.5920 0.608494
\(304\) −19.7643 −1.13356
\(305\) −22.0147 −1.26056
\(306\) 5.50386 0.314635
\(307\) 11.7814 0.672399 0.336200 0.941791i \(-0.390858\pi\)
0.336200 + 0.941791i \(0.390858\pi\)
\(308\) −7.91862 −0.451205
\(309\) −9.43028 −0.536470
\(310\) 45.6409 2.59223
\(311\) 21.0055 1.19111 0.595556 0.803314i \(-0.296932\pi\)
0.595556 + 0.803314i \(0.296932\pi\)
\(312\) −22.1586 −1.25448
\(313\) −15.0488 −0.850611 −0.425305 0.905050i \(-0.639833\pi\)
−0.425305 + 0.905050i \(0.639833\pi\)
\(314\) −1.45361 −0.0820319
\(315\) 9.96917 0.561699
\(316\) 12.7912 0.719559
\(317\) 12.5377 0.704189 0.352095 0.935964i \(-0.385470\pi\)
0.352095 + 0.935964i \(0.385470\pi\)
\(318\) −5.78722 −0.324531
\(319\) 3.79631 0.212553
\(320\) 15.2226 0.850971
\(321\) −8.80693 −0.491555
\(322\) 30.3218 1.68977
\(323\) −4.21529 −0.234545
\(324\) 10.8332 0.601842
\(325\) −1.97509 −0.109559
\(326\) −39.3256 −2.17804
\(327\) −14.8608 −0.821802
\(328\) −17.1713 −0.948127
\(329\) 4.66463 0.257169
\(330\) 5.05858 0.278466
\(331\) 6.38221 0.350798 0.175399 0.984497i \(-0.443878\pi\)
0.175399 + 0.984497i \(0.443878\pi\)
\(332\) −0.511601 −0.0280777
\(333\) −4.93367 −0.270363
\(334\) 0.955271 0.0522701
\(335\) −33.8540 −1.84964
\(336\) −7.94166 −0.433253
\(337\) −18.6515 −1.01601 −0.508006 0.861353i \(-0.669617\pi\)
−0.508006 + 0.861353i \(0.669617\pi\)
\(338\) −25.3555 −1.37916
\(339\) 12.8213 0.696357
\(340\) −9.56544 −0.518759
\(341\) −7.93702 −0.429814
\(342\) −23.2003 −1.25453
\(343\) −19.8179 −1.07007
\(344\) −5.22332 −0.281623
\(345\) −13.0325 −0.701645
\(346\) 55.8344 3.00168
\(347\) 23.4081 1.25661 0.628306 0.777966i \(-0.283748\pi\)
0.628306 + 0.777966i \(0.283748\pi\)
\(348\) 13.7346 0.736254
\(349\) −13.5389 −0.724722 −0.362361 0.932038i \(-0.618029\pi\)
−0.362361 + 0.932038i \(0.618029\pi\)
\(350\) −1.94969 −0.104216
\(351\) −22.1705 −1.18337
\(352\) 1.14563 0.0610622
\(353\) −15.2733 −0.812916 −0.406458 0.913669i \(-0.633236\pi\)
−0.406458 + 0.913669i \(0.633236\pi\)
\(354\) 32.9219 1.74978
\(355\) 13.2081 0.701013
\(356\) −15.0849 −0.799498
\(357\) −1.69378 −0.0896446
\(358\) 22.1473 1.17052
\(359\) −22.7515 −1.20078 −0.600390 0.799708i \(-0.704988\pi\)
−0.600390 + 0.799708i \(0.704988\pi\)
\(360\) −27.0446 −1.42537
\(361\) −1.23135 −0.0648077
\(362\) 11.9962 0.630505
\(363\) −0.879695 −0.0461720
\(364\) −38.1867 −2.00153
\(365\) −18.4019 −0.963199
\(366\) 20.5863 1.07606
\(367\) −0.881547 −0.0460164 −0.0230082 0.999735i \(-0.507324\pi\)
−0.0230082 + 0.999735i \(0.507324\pi\)
\(368\) −29.8653 −1.55684
\(369\) −7.31827 −0.380974
\(370\) 12.7443 0.662543
\(371\) −5.12328 −0.265987
\(372\) −28.7153 −1.48882
\(373\) −1.33566 −0.0691579 −0.0345789 0.999402i \(-0.511009\pi\)
−0.0345789 + 0.999402i \(0.511009\pi\)
\(374\) 2.47238 0.127844
\(375\) −9.39219 −0.485011
\(376\) −12.6543 −0.652595
\(377\) 18.3073 0.942874
\(378\) −21.8854 −1.12566
\(379\) −7.51912 −0.386231 −0.193116 0.981176i \(-0.561859\pi\)
−0.193116 + 0.981176i \(0.561859\pi\)
\(380\) 40.3211 2.06843
\(381\) 2.45739 0.125896
\(382\) 52.5741 2.68993
\(383\) 26.2712 1.34240 0.671198 0.741278i \(-0.265780\pi\)
0.671198 + 0.741278i \(0.265780\pi\)
\(384\) −16.2506 −0.829284
\(385\) 4.47824 0.228232
\(386\) −0.259524 −0.0132094
\(387\) −2.22614 −0.113161
\(388\) −56.3125 −2.85883
\(389\) −9.85098 −0.499465 −0.249732 0.968315i \(-0.580343\pi\)
−0.249732 + 0.968315i \(0.580343\pi\)
\(390\) 24.3945 1.23526
\(391\) −6.36962 −0.322125
\(392\) 17.1991 0.868686
\(393\) 12.8839 0.649906
\(394\) −52.4597 −2.64288
\(395\) −7.23381 −0.363973
\(396\) 9.15536 0.460074
\(397\) −27.3557 −1.37294 −0.686471 0.727157i \(-0.740841\pi\)
−0.686471 + 0.727157i \(0.740841\pi\)
\(398\) 2.49697 0.125162
\(399\) 7.13979 0.357437
\(400\) 1.92034 0.0960171
\(401\) −24.1483 −1.20591 −0.602954 0.797776i \(-0.706010\pi\)
−0.602954 + 0.797776i \(0.706010\pi\)
\(402\) 31.6574 1.57893
\(403\) −38.2754 −1.90664
\(404\) −49.5187 −2.46365
\(405\) −6.12650 −0.304428
\(406\) 18.0719 0.896892
\(407\) −2.21625 −0.109855
\(408\) 4.59493 0.227483
\(409\) 33.6102 1.66192 0.830959 0.556334i \(-0.187793\pi\)
0.830959 + 0.556334i \(0.187793\pi\)
\(410\) 18.9040 0.933601
\(411\) −6.42003 −0.316677
\(412\) 44.0876 2.17204
\(413\) 29.1449 1.43413
\(414\) −35.0575 −1.72298
\(415\) 0.289327 0.0142025
\(416\) 5.52468 0.270870
\(417\) 7.43149 0.363921
\(418\) −10.4218 −0.509747
\(419\) 33.5302 1.63806 0.819028 0.573754i \(-0.194514\pi\)
0.819028 + 0.573754i \(0.194514\pi\)
\(420\) 16.2018 0.790567
\(421\) 38.5745 1.88001 0.940003 0.341166i \(-0.110822\pi\)
0.940003 + 0.341166i \(0.110822\pi\)
\(422\) −20.7288 −1.00906
\(423\) −5.39315 −0.262224
\(424\) 13.8985 0.674972
\(425\) 0.409567 0.0198669
\(426\) −12.3511 −0.598414
\(427\) 18.2245 0.881948
\(428\) 41.1734 1.99019
\(429\) −4.24224 −0.204817
\(430\) 5.75038 0.277308
\(431\) −3.38003 −0.162811 −0.0814053 0.996681i \(-0.525941\pi\)
−0.0814053 + 0.996681i \(0.525941\pi\)
\(432\) 21.5559 1.03711
\(433\) 8.55798 0.411270 0.205635 0.978629i \(-0.434074\pi\)
0.205635 + 0.978629i \(0.434074\pi\)
\(434\) −37.7832 −1.81365
\(435\) −7.76739 −0.372418
\(436\) 69.4757 3.32728
\(437\) 26.8498 1.28440
\(438\) 17.2079 0.822227
\(439\) −26.9160 −1.28463 −0.642316 0.766440i \(-0.722026\pi\)
−0.642316 + 0.766440i \(0.722026\pi\)
\(440\) −12.1487 −0.579164
\(441\) 7.33011 0.349053
\(442\) 11.9228 0.567110
\(443\) 2.84538 0.135188 0.0675941 0.997713i \(-0.478468\pi\)
0.0675941 + 0.997713i \(0.478468\pi\)
\(444\) −8.01815 −0.380525
\(445\) 8.53100 0.404408
\(446\) −29.8079 −1.41145
\(447\) 2.26993 0.107364
\(448\) −12.6019 −0.595382
\(449\) 4.83131 0.228004 0.114002 0.993481i \(-0.463633\pi\)
0.114002 + 0.993481i \(0.463633\pi\)
\(450\) 2.25420 0.106264
\(451\) −3.28743 −0.154799
\(452\) −59.9409 −2.81938
\(453\) −15.4027 −0.723681
\(454\) −6.82577 −0.320349
\(455\) 21.5958 1.01243
\(456\) −19.3690 −0.907035
\(457\) 7.41184 0.346711 0.173356 0.984859i \(-0.444539\pi\)
0.173356 + 0.984859i \(0.444539\pi\)
\(458\) −9.58987 −0.448105
\(459\) 4.59741 0.214589
\(460\) 60.9282 2.84079
\(461\) −34.8948 −1.62521 −0.812607 0.582812i \(-0.801952\pi\)
−0.812607 + 0.582812i \(0.801952\pi\)
\(462\) −4.18768 −0.194829
\(463\) 1.63086 0.0757924 0.0378962 0.999282i \(-0.487934\pi\)
0.0378962 + 0.999282i \(0.487934\pi\)
\(464\) −17.7998 −0.826334
\(465\) 16.2394 0.753086
\(466\) 45.4295 2.10448
\(467\) 40.5057 1.87438 0.937191 0.348818i \(-0.113417\pi\)
0.937191 + 0.348818i \(0.113417\pi\)
\(468\) 44.1508 2.04087
\(469\) 28.0256 1.29410
\(470\) 13.9312 0.642597
\(471\) −0.517207 −0.0238317
\(472\) −79.0649 −3.63926
\(473\) −1.00000 −0.0459800
\(474\) 6.76447 0.310702
\(475\) −1.72644 −0.0792147
\(476\) 7.91862 0.362950
\(477\) 5.92344 0.271216
\(478\) 45.9617 2.10224
\(479\) −23.1740 −1.05885 −0.529424 0.848358i \(-0.677592\pi\)
−0.529424 + 0.848358i \(0.677592\pi\)
\(480\) −2.34400 −0.106988
\(481\) −10.6876 −0.487314
\(482\) 65.7479 2.99474
\(483\) 10.7888 0.490905
\(484\) 4.11267 0.186940
\(485\) 31.8465 1.44608
\(486\) 39.8286 1.80666
\(487\) −13.4942 −0.611483 −0.305741 0.952115i \(-0.598904\pi\)
−0.305741 + 0.952115i \(0.598904\pi\)
\(488\) −49.4399 −2.23804
\(489\) −13.9924 −0.632758
\(490\) −18.9346 −0.855377
\(491\) 28.9031 1.30438 0.652190 0.758056i \(-0.273851\pi\)
0.652190 + 0.758056i \(0.273851\pi\)
\(492\) −11.8936 −0.536204
\(493\) −3.79631 −0.170977
\(494\) −50.2580 −2.26122
\(495\) −5.17765 −0.232718
\(496\) 37.2144 1.67097
\(497\) −10.9342 −0.490464
\(498\) −0.270555 −0.0121238
\(499\) 25.5567 1.14407 0.572037 0.820228i \(-0.306153\pi\)
0.572037 + 0.820228i \(0.306153\pi\)
\(500\) 43.9095 1.96369
\(501\) 0.339894 0.0151853
\(502\) 3.76998 0.168262
\(503\) 19.6078 0.874268 0.437134 0.899396i \(-0.355994\pi\)
0.437134 + 0.899396i \(0.355994\pi\)
\(504\) 22.3885 0.997262
\(505\) 28.0044 1.24618
\(506\) −15.7481 −0.700089
\(507\) −9.02171 −0.400668
\(508\) −11.4886 −0.509723
\(509\) −16.5529 −0.733694 −0.366847 0.930281i \(-0.619563\pi\)
−0.366847 + 0.930281i \(0.619563\pi\)
\(510\) −5.05858 −0.223998
\(511\) 15.2338 0.673902
\(512\) 43.6098 1.92730
\(513\) −19.3794 −0.855621
\(514\) 11.4554 0.505276
\(515\) −24.9330 −1.09868
\(516\) −3.61789 −0.159269
\(517\) −2.42265 −0.106548
\(518\) −10.5502 −0.463548
\(519\) 19.8664 0.872037
\(520\) −58.5856 −2.56915
\(521\) −18.9400 −0.829775 −0.414888 0.909873i \(-0.636179\pi\)
−0.414888 + 0.909873i \(0.636179\pi\)
\(522\) −20.8943 −0.914521
\(523\) −19.6565 −0.859517 −0.429759 0.902944i \(-0.641401\pi\)
−0.429759 + 0.902944i \(0.641401\pi\)
\(524\) −60.2336 −2.63132
\(525\) −0.693718 −0.0302764
\(526\) −38.7347 −1.68891
\(527\) 7.93702 0.345742
\(528\) 4.12463 0.179502
\(529\) 17.5720 0.764000
\(530\) −15.3010 −0.664631
\(531\) −33.6968 −1.46232
\(532\) −33.3793 −1.44718
\(533\) −15.8533 −0.686682
\(534\) −7.97749 −0.345220
\(535\) −23.2849 −1.00669
\(536\) −76.0283 −3.28392
\(537\) 7.88022 0.340057
\(538\) 5.22402 0.225224
\(539\) 3.29275 0.141829
\(540\) −43.9762 −1.89244
\(541\) 16.4944 0.709149 0.354575 0.935028i \(-0.384626\pi\)
0.354575 + 0.935028i \(0.384626\pi\)
\(542\) −50.1114 −2.15247
\(543\) 4.26835 0.183172
\(544\) −1.14563 −0.0491184
\(545\) −39.2908 −1.68303
\(546\) −20.1947 −0.864251
\(547\) −5.64959 −0.241559 −0.120780 0.992679i \(-0.538539\pi\)
−0.120780 + 0.992679i \(0.538539\pi\)
\(548\) 30.0143 1.28215
\(549\) −21.0709 −0.899283
\(550\) 1.01261 0.0431777
\(551\) 16.0025 0.681731
\(552\) −29.2680 −1.24573
\(553\) 5.98842 0.254653
\(554\) −48.5397 −2.06225
\(555\) 4.53452 0.192480
\(556\) −34.7430 −1.47343
\(557\) −14.8480 −0.629129 −0.314564 0.949236i \(-0.601858\pi\)
−0.314564 + 0.949236i \(0.601858\pi\)
\(558\) 43.6842 1.84930
\(559\) −4.82240 −0.203966
\(560\) −20.9972 −0.887292
\(561\) 0.879695 0.0371408
\(562\) −76.6244 −3.23221
\(563\) 45.5967 1.92167 0.960836 0.277118i \(-0.0893795\pi\)
0.960836 + 0.277118i \(0.0893795\pi\)
\(564\) −8.76490 −0.369069
\(565\) 33.8985 1.42612
\(566\) 25.3226 1.06439
\(567\) 5.07174 0.212993
\(568\) 29.6624 1.24461
\(569\) −2.81528 −0.118023 −0.0590113 0.998257i \(-0.518795\pi\)
−0.0590113 + 0.998257i \(0.518795\pi\)
\(570\) 21.3234 0.893138
\(571\) −27.2558 −1.14062 −0.570310 0.821430i \(-0.693177\pi\)
−0.570310 + 0.821430i \(0.693177\pi\)
\(572\) 19.8329 0.829256
\(573\) 18.7063 0.781468
\(574\) −15.6494 −0.653194
\(575\) −2.60879 −0.108794
\(576\) 14.5700 0.607085
\(577\) −9.83680 −0.409511 −0.204756 0.978813i \(-0.565640\pi\)
−0.204756 + 0.978813i \(0.565640\pi\)
\(578\) −2.47238 −0.102838
\(579\) −0.0923410 −0.00383756
\(580\) 36.3134 1.50783
\(581\) −0.239515 −0.00993677
\(582\) −29.7803 −1.23443
\(583\) 2.66086 0.110202
\(584\) −41.3264 −1.71010
\(585\) −24.9687 −1.03233
\(586\) 21.6398 0.893932
\(587\) 14.7163 0.607406 0.303703 0.952767i \(-0.401777\pi\)
0.303703 + 0.952767i \(0.401777\pi\)
\(588\) 11.9128 0.491277
\(589\) −33.4568 −1.37856
\(590\) 87.0429 3.58350
\(591\) −18.6656 −0.767801
\(592\) 10.3913 0.427081
\(593\) −37.3870 −1.53530 −0.767650 0.640870i \(-0.778574\pi\)
−0.767650 + 0.640870i \(0.778574\pi\)
\(594\) 11.3665 0.466375
\(595\) −4.47824 −0.183590
\(596\) −10.6122 −0.434691
\(597\) 0.888445 0.0363616
\(598\) −75.9437 −3.10557
\(599\) −1.18108 −0.0482575 −0.0241287 0.999709i \(-0.507681\pi\)
−0.0241287 + 0.999709i \(0.507681\pi\)
\(600\) 1.88193 0.0768296
\(601\) 15.5749 0.635311 0.317656 0.948206i \(-0.397104\pi\)
0.317656 + 0.948206i \(0.397104\pi\)
\(602\) −4.76038 −0.194018
\(603\) −32.4026 −1.31954
\(604\) 72.0092 2.93001
\(605\) −2.32585 −0.0945592
\(606\) −26.1874 −1.06379
\(607\) 24.6929 1.00225 0.501127 0.865374i \(-0.332919\pi\)
0.501127 + 0.865374i \(0.332919\pi\)
\(608\) 4.82916 0.195848
\(609\) 6.43013 0.260562
\(610\) 54.4287 2.20375
\(611\) −11.6830 −0.472643
\(612\) −9.15536 −0.370084
\(613\) −47.9599 −1.93708 −0.968541 0.248855i \(-0.919946\pi\)
−0.968541 + 0.248855i \(0.919946\pi\)
\(614\) −29.1281 −1.17551
\(615\) 6.72621 0.271227
\(616\) 10.0571 0.405212
\(617\) −13.2916 −0.535099 −0.267549 0.963544i \(-0.586214\pi\)
−0.267549 + 0.963544i \(0.586214\pi\)
\(618\) 23.3153 0.937877
\(619\) 17.3840 0.698722 0.349361 0.936988i \(-0.386399\pi\)
0.349361 + 0.936988i \(0.386399\pi\)
\(620\) −75.9211 −3.04906
\(621\) −29.2837 −1.17511
\(622\) −51.9336 −2.08235
\(623\) −7.06228 −0.282944
\(624\) 19.8906 0.796262
\(625\) −26.8801 −1.07520
\(626\) 37.2065 1.48707
\(627\) −3.70817 −0.148090
\(628\) 2.41800 0.0964887
\(629\) 2.21625 0.0883676
\(630\) −24.6476 −0.981983
\(631\) −17.1739 −0.683683 −0.341841 0.939758i \(-0.611051\pi\)
−0.341841 + 0.939758i \(0.611051\pi\)
\(632\) −16.2455 −0.646211
\(633\) −7.37550 −0.293150
\(634\) −30.9981 −1.23109
\(635\) 6.49716 0.257832
\(636\) 9.62671 0.381724
\(637\) 15.8789 0.629147
\(638\) −9.38592 −0.371592
\(639\) 12.6419 0.500104
\(640\) −42.9653 −1.69835
\(641\) 20.4290 0.806898 0.403449 0.915002i \(-0.367811\pi\)
0.403449 + 0.915002i \(0.367811\pi\)
\(642\) 21.7741 0.859355
\(643\) 41.3083 1.62904 0.814520 0.580135i \(-0.197000\pi\)
0.814520 + 0.580135i \(0.197000\pi\)
\(644\) −50.4386 −1.98756
\(645\) 2.04604 0.0805626
\(646\) 10.4218 0.410040
\(647\) 30.7706 1.20972 0.604859 0.796333i \(-0.293230\pi\)
0.604859 + 0.796333i \(0.293230\pi\)
\(648\) −13.7587 −0.540494
\(649\) −15.1369 −0.594175
\(650\) 4.88319 0.191534
\(651\) −13.4436 −0.526896
\(652\) 65.4159 2.56189
\(653\) −29.6311 −1.15955 −0.579777 0.814775i \(-0.696860\pi\)
−0.579777 + 0.814775i \(0.696860\pi\)
\(654\) 36.7415 1.43671
\(655\) 34.0640 1.33099
\(656\) 15.4138 0.601808
\(657\) −17.6130 −0.687148
\(658\) −11.5327 −0.449593
\(659\) −9.52150 −0.370905 −0.185452 0.982653i \(-0.559375\pi\)
−0.185452 + 0.982653i \(0.559375\pi\)
\(660\) −8.41467 −0.327541
\(661\) −32.8213 −1.27660 −0.638300 0.769787i \(-0.720362\pi\)
−0.638300 + 0.769787i \(0.720362\pi\)
\(662\) −15.7793 −0.613278
\(663\) 4.24224 0.164755
\(664\) 0.649762 0.0252156
\(665\) 18.8771 0.732021
\(666\) 12.1979 0.472659
\(667\) 24.1810 0.936293
\(668\) −1.58904 −0.0614818
\(669\) −10.6059 −0.410049
\(670\) 83.6999 3.23361
\(671\) −9.46522 −0.365401
\(672\) 1.94045 0.0748544
\(673\) 34.9681 1.34792 0.673960 0.738768i \(-0.264592\pi\)
0.673960 + 0.738768i \(0.264592\pi\)
\(674\) 46.1137 1.77623
\(675\) 1.88295 0.0724747
\(676\) 42.1775 1.62221
\(677\) 16.3441 0.628153 0.314077 0.949398i \(-0.398305\pi\)
0.314077 + 0.949398i \(0.398305\pi\)
\(678\) −31.6991 −1.21740
\(679\) −26.3637 −1.01175
\(680\) 12.1487 0.465880
\(681\) −2.42867 −0.0930668
\(682\) 19.6233 0.751416
\(683\) −5.48141 −0.209740 −0.104870 0.994486i \(-0.533443\pi\)
−0.104870 + 0.994486i \(0.533443\pi\)
\(684\) 38.5925 1.47562
\(685\) −16.9741 −0.648546
\(686\) 48.9974 1.87073
\(687\) −3.41216 −0.130182
\(688\) 4.68871 0.178755
\(689\) 12.8317 0.488850
\(690\) 32.2212 1.22664
\(691\) 18.5963 0.707436 0.353718 0.935352i \(-0.384917\pi\)
0.353718 + 0.935352i \(0.384917\pi\)
\(692\) −92.8774 −3.53067
\(693\) 4.28625 0.162821
\(694\) −57.8738 −2.19686
\(695\) 19.6483 0.745302
\(696\) −17.4438 −0.661205
\(697\) 3.28743 0.124520
\(698\) 33.4734 1.26699
\(699\) 16.1642 0.611386
\(700\) 3.24321 0.122582
\(701\) −20.1014 −0.759218 −0.379609 0.925147i \(-0.623941\pi\)
−0.379609 + 0.925147i \(0.623941\pi\)
\(702\) 54.8140 2.06882
\(703\) −9.34212 −0.352345
\(704\) 6.54499 0.246673
\(705\) 4.95683 0.186685
\(706\) 37.7614 1.42117
\(707\) −23.1831 −0.871890
\(708\) −54.7637 −2.05815
\(709\) −45.3423 −1.70287 −0.851433 0.524464i \(-0.824266\pi\)
−0.851433 + 0.524464i \(0.824266\pi\)
\(710\) −32.6555 −1.22554
\(711\) −6.92369 −0.259659
\(712\) 19.1587 0.718002
\(713\) −50.5558 −1.89333
\(714\) 4.18768 0.156720
\(715\) −11.2162 −0.419461
\(716\) −36.8409 −1.37681
\(717\) 16.3536 0.610736
\(718\) 56.2504 2.09925
\(719\) −51.1045 −1.90588 −0.952938 0.303165i \(-0.901957\pi\)
−0.952938 + 0.303165i \(0.901957\pi\)
\(720\) 24.2765 0.904732
\(721\) 20.6404 0.768689
\(722\) 3.04436 0.113299
\(723\) 23.3937 0.870021
\(724\) −19.9550 −0.741621
\(725\) −1.55484 −0.0577454
\(726\) 2.17494 0.0807197
\(727\) 35.7737 1.32677 0.663386 0.748277i \(-0.269119\pi\)
0.663386 + 0.748277i \(0.269119\pi\)
\(728\) 48.4993 1.79750
\(729\) 6.26910 0.232189
\(730\) 45.4965 1.68390
\(731\) 1.00000 0.0369863
\(732\) −34.2442 −1.26570
\(733\) −22.4995 −0.831040 −0.415520 0.909584i \(-0.636400\pi\)
−0.415520 + 0.909584i \(0.636400\pi\)
\(734\) 2.17952 0.0804476
\(735\) −6.73709 −0.248501
\(736\) 7.29722 0.268979
\(737\) −14.5555 −0.536160
\(738\) 18.0936 0.666033
\(739\) −3.80382 −0.139926 −0.0699628 0.997550i \(-0.522288\pi\)
−0.0699628 + 0.997550i \(0.522288\pi\)
\(740\) −21.1994 −0.779305
\(741\) −17.8823 −0.656921
\(742\) 12.6667 0.465009
\(743\) −19.4553 −0.713746 −0.356873 0.934153i \(-0.616157\pi\)
−0.356873 + 0.934153i \(0.616157\pi\)
\(744\) 36.4701 1.33706
\(745\) 6.00152 0.219879
\(746\) 3.30226 0.120904
\(747\) 0.276923 0.0101321
\(748\) −4.11267 −0.150374
\(749\) 19.2761 0.704332
\(750\) 23.2211 0.847914
\(751\) 14.6071 0.533021 0.266511 0.963832i \(-0.414129\pi\)
0.266511 + 0.963832i \(0.414129\pi\)
\(752\) 11.3591 0.414224
\(753\) 1.34139 0.0488830
\(754\) −45.2626 −1.64837
\(755\) −40.7235 −1.48208
\(756\) 36.4051 1.32404
\(757\) 15.1460 0.550492 0.275246 0.961374i \(-0.411241\pi\)
0.275246 + 0.961374i \(0.411241\pi\)
\(758\) 18.5901 0.675224
\(759\) −5.60332 −0.203388
\(760\) −51.2101 −1.85758
\(761\) −46.6292 −1.69031 −0.845154 0.534523i \(-0.820491\pi\)
−0.845154 + 0.534523i \(0.820491\pi\)
\(762\) −6.07561 −0.220096
\(763\) 32.5263 1.17753
\(764\) −87.4541 −3.16398
\(765\) 5.17765 0.187198
\(766\) −64.9525 −2.34683
\(767\) −72.9961 −2.63574
\(768\) 28.6624 1.03427
\(769\) 29.0299 1.04685 0.523423 0.852073i \(-0.324655\pi\)
0.523423 + 0.852073i \(0.324655\pi\)
\(770\) −11.0719 −0.399004
\(771\) 4.07593 0.146791
\(772\) 0.431704 0.0155374
\(773\) −16.8310 −0.605369 −0.302685 0.953091i \(-0.597883\pi\)
−0.302685 + 0.953091i \(0.597883\pi\)
\(774\) 5.50386 0.197832
\(775\) 3.25074 0.116770
\(776\) 71.5201 2.56742
\(777\) −3.75385 −0.134668
\(778\) 24.3554 0.873183
\(779\) −13.8575 −0.496495
\(780\) −40.5789 −1.45296
\(781\) 5.67883 0.203205
\(782\) 15.7481 0.563152
\(783\) −17.4532 −0.623726
\(784\) −15.4387 −0.551384
\(785\) −1.36746 −0.0488066
\(786\) −31.8539 −1.13619
\(787\) −19.2321 −0.685551 −0.342775 0.939417i \(-0.611367\pi\)
−0.342775 + 0.939417i \(0.611367\pi\)
\(788\) 87.2637 3.10864
\(789\) −13.7821 −0.490657
\(790\) 17.8847 0.636311
\(791\) −28.0624 −0.997786
\(792\) −11.6278 −0.413177
\(793\) −45.6451 −1.62090
\(794\) 67.6337 2.40023
\(795\) −5.44422 −0.193087
\(796\) −4.15357 −0.147220
\(797\) 6.19905 0.219582 0.109791 0.993955i \(-0.464982\pi\)
0.109791 + 0.993955i \(0.464982\pi\)
\(798\) −17.6523 −0.624884
\(799\) 2.42265 0.0857072
\(800\) −0.469212 −0.0165891
\(801\) 8.16527 0.288506
\(802\) 59.7038 2.10822
\(803\) −7.91191 −0.279205
\(804\) −52.6604 −1.85719
\(805\) 28.5247 1.00536
\(806\) 94.6315 3.33325
\(807\) 1.85875 0.0654312
\(808\) 62.8916 2.21252
\(809\) −33.9485 −1.19357 −0.596783 0.802403i \(-0.703555\pi\)
−0.596783 + 0.802403i \(0.703555\pi\)
\(810\) 15.1470 0.532213
\(811\) −45.7766 −1.60743 −0.803717 0.595012i \(-0.797147\pi\)
−0.803717 + 0.595012i \(0.797147\pi\)
\(812\) −30.0615 −1.05495
\(813\) −17.8301 −0.625328
\(814\) 5.47941 0.192053
\(815\) −36.9948 −1.29587
\(816\) −4.12463 −0.144391
\(817\) −4.21529 −0.147474
\(818\) −83.0972 −2.90543
\(819\) 20.6700 0.722268
\(820\) −31.4457 −1.09813
\(821\) 9.55209 0.333370 0.166685 0.986010i \(-0.446694\pi\)
0.166685 + 0.986010i \(0.446694\pi\)
\(822\) 15.8728 0.553626
\(823\) −42.3357 −1.47573 −0.737865 0.674949i \(-0.764166\pi\)
−0.737865 + 0.674949i \(0.764166\pi\)
\(824\) −55.9937 −1.95063
\(825\) 0.360294 0.0125438
\(826\) −72.0573 −2.50719
\(827\) −30.6193 −1.06474 −0.532369 0.846513i \(-0.678698\pi\)
−0.532369 + 0.846513i \(0.678698\pi\)
\(828\) 58.3161 2.02663
\(829\) −22.9937 −0.798605 −0.399303 0.916819i \(-0.630748\pi\)
−0.399303 + 0.916819i \(0.630748\pi\)
\(830\) −0.715326 −0.0248293
\(831\) −17.2709 −0.599119
\(832\) 31.5625 1.09423
\(833\) −3.29275 −0.114087
\(834\) −18.3735 −0.636221
\(835\) 0.898654 0.0310992
\(836\) 17.3361 0.599581
\(837\) 36.4897 1.26127
\(838\) −82.8993 −2.86371
\(839\) 32.3553 1.11703 0.558515 0.829495i \(-0.311371\pi\)
0.558515 + 0.829495i \(0.311371\pi\)
\(840\) −20.5772 −0.709981
\(841\) −14.5880 −0.503036
\(842\) −95.3709 −3.28670
\(843\) −27.2636 −0.939010
\(844\) 34.4813 1.18689
\(845\) −23.8527 −0.820559
\(846\) 13.3339 0.458430
\(847\) 1.92542 0.0661583
\(848\) −12.4760 −0.428428
\(849\) 9.00999 0.309222
\(850\) −1.01261 −0.0347321
\(851\) −14.1166 −0.483912
\(852\) 20.5454 0.703875
\(853\) −19.6699 −0.673485 −0.336743 0.941597i \(-0.609325\pi\)
−0.336743 + 0.941597i \(0.609325\pi\)
\(854\) −45.0580 −1.54185
\(855\) −21.8253 −0.746410
\(856\) −52.2925 −1.78732
\(857\) 8.60350 0.293890 0.146945 0.989145i \(-0.453056\pi\)
0.146945 + 0.989145i \(0.453056\pi\)
\(858\) 10.4884 0.358069
\(859\) −9.56397 −0.326318 −0.163159 0.986600i \(-0.552168\pi\)
−0.163159 + 0.986600i \(0.552168\pi\)
\(860\) −9.56544 −0.326179
\(861\) −5.56820 −0.189764
\(862\) 8.35673 0.284632
\(863\) 5.33449 0.181588 0.0907940 0.995870i \(-0.471060\pi\)
0.0907940 + 0.995870i \(0.471060\pi\)
\(864\) −5.26692 −0.179184
\(865\) 52.5252 1.78591
\(866\) −21.1586 −0.718998
\(867\) −0.879695 −0.0298760
\(868\) 62.8503 2.13328
\(869\) −3.11018 −0.105506
\(870\) 19.2039 0.651075
\(871\) −70.1926 −2.37838
\(872\) −88.2381 −2.98812
\(873\) 30.4813 1.03163
\(874\) −66.3829 −2.24543
\(875\) 20.5571 0.694955
\(876\) −28.6244 −0.967130
\(877\) 15.4148 0.520521 0.260260 0.965538i \(-0.416192\pi\)
0.260260 + 0.965538i \(0.416192\pi\)
\(878\) 66.5467 2.24584
\(879\) 7.69964 0.259702
\(880\) 10.9052 0.367615
\(881\) 32.0065 1.07833 0.539164 0.842201i \(-0.318740\pi\)
0.539164 + 0.842201i \(0.318740\pi\)
\(882\) −18.1228 −0.610227
\(883\) 42.0395 1.41474 0.707372 0.706842i \(-0.249881\pi\)
0.707372 + 0.706842i \(0.249881\pi\)
\(884\) −19.8329 −0.667053
\(885\) 30.9706 1.04107
\(886\) −7.03487 −0.236341
\(887\) 13.6350 0.457817 0.228909 0.973448i \(-0.426484\pi\)
0.228909 + 0.973448i \(0.426484\pi\)
\(888\) 10.1835 0.341736
\(889\) −5.37859 −0.180392
\(890\) −21.0919 −0.707002
\(891\) −2.63409 −0.0882455
\(892\) 49.5839 1.66019
\(893\) −10.2122 −0.341737
\(894\) −5.61213 −0.187698
\(895\) 20.8347 0.696428
\(896\) 35.5682 1.18825
\(897\) −27.0214 −0.902219
\(898\) −11.9448 −0.398605
\(899\) −30.1314 −1.00494
\(900\) −3.74974 −0.124991
\(901\) −2.66086 −0.0886461
\(902\) 8.12778 0.270626
\(903\) −1.69378 −0.0563656
\(904\) 76.1284 2.53199
\(905\) 11.2852 0.375132
\(906\) 38.0813 1.26517
\(907\) 11.6591 0.387135 0.193568 0.981087i \(-0.437994\pi\)
0.193568 + 0.981087i \(0.437994\pi\)
\(908\) 11.3543 0.376805
\(909\) 26.8039 0.889028
\(910\) −53.3931 −1.76997
\(911\) 13.4950 0.447109 0.223555 0.974691i \(-0.428234\pi\)
0.223555 + 0.974691i \(0.428234\pi\)
\(912\) 17.3865 0.575725
\(913\) 0.124396 0.00411691
\(914\) −18.3249 −0.606134
\(915\) 19.3662 0.640227
\(916\) 15.9522 0.527076
\(917\) −28.1995 −0.931228
\(918\) −11.3665 −0.375152
\(919\) −56.1596 −1.85253 −0.926267 0.376868i \(-0.877001\pi\)
−0.926267 + 0.376868i \(0.877001\pi\)
\(920\) −77.3823 −2.55122
\(921\) −10.3640 −0.341506
\(922\) 86.2733 2.84126
\(923\) 27.3856 0.901407
\(924\) 6.96597 0.229164
\(925\) 0.907702 0.0298451
\(926\) −4.03210 −0.132503
\(927\) −23.8641 −0.783799
\(928\) 4.34916 0.142768
\(929\) −29.9165 −0.981529 −0.490764 0.871292i \(-0.663282\pi\)
−0.490764 + 0.871292i \(0.663282\pi\)
\(930\) −40.1501 −1.31657
\(931\) 13.8799 0.454895
\(932\) −75.5694 −2.47536
\(933\) −18.4784 −0.604957
\(934\) −100.146 −3.27686
\(935\) 2.32585 0.0760634
\(936\) −56.0740 −1.83284
\(937\) −57.7875 −1.88784 −0.943918 0.330181i \(-0.892890\pi\)
−0.943918 + 0.330181i \(0.892890\pi\)
\(938\) −69.2899 −2.26239
\(939\) 13.2384 0.432019
\(940\) −23.1737 −0.755844
\(941\) −24.5572 −0.800542 −0.400271 0.916397i \(-0.631084\pi\)
−0.400271 + 0.916397i \(0.631084\pi\)
\(942\) 1.27873 0.0416634
\(943\) −20.9397 −0.681890
\(944\) 70.9725 2.30996
\(945\) −20.5883 −0.669737
\(946\) 2.47238 0.0803840
\(947\) 16.2524 0.528132 0.264066 0.964505i \(-0.414936\pi\)
0.264066 + 0.964505i \(0.414936\pi\)
\(948\) −11.2523 −0.365458
\(949\) −38.1543 −1.23854
\(950\) 4.26843 0.138486
\(951\) −11.0294 −0.357652
\(952\) −10.0571 −0.325953
\(953\) 54.5931 1.76844 0.884222 0.467066i \(-0.154689\pi\)
0.884222 + 0.467066i \(0.154689\pi\)
\(954\) −14.6450 −0.474149
\(955\) 49.4581 1.60043
\(956\) −76.4548 −2.47272
\(957\) −3.33959 −0.107954
\(958\) 57.2950 1.85112
\(959\) 14.0518 0.453755
\(960\) −13.3913 −0.432202
\(961\) 31.9963 1.03214
\(962\) 26.4239 0.851940
\(963\) −22.2866 −0.718176
\(964\) −109.368 −3.52251
\(965\) −0.244143 −0.00785923
\(966\) −26.6739 −0.858219
\(967\) −49.1662 −1.58108 −0.790539 0.612412i \(-0.790200\pi\)
−0.790539 + 0.612412i \(0.790200\pi\)
\(968\) −5.22332 −0.167884
\(969\) 3.70817 0.119124
\(970\) −78.7368 −2.52809
\(971\) −22.3824 −0.718286 −0.359143 0.933282i \(-0.616931\pi\)
−0.359143 + 0.933282i \(0.616931\pi\)
\(972\) −66.2527 −2.12506
\(973\) −16.2656 −0.521450
\(974\) 33.3629 1.06902
\(975\) 1.73748 0.0556439
\(976\) 44.3797 1.42056
\(977\) 17.3735 0.555827 0.277914 0.960606i \(-0.410357\pi\)
0.277914 + 0.960606i \(0.410357\pi\)
\(978\) 34.5945 1.10621
\(979\) 3.66791 0.117227
\(980\) 31.4966 1.00612
\(981\) −37.6063 −1.20068
\(982\) −71.4595 −2.28036
\(983\) 44.3865 1.41571 0.707855 0.706357i \(-0.249663\pi\)
0.707855 + 0.706357i \(0.249663\pi\)
\(984\) 15.1055 0.481547
\(985\) −49.3505 −1.57244
\(986\) 9.38592 0.298909
\(987\) −4.10345 −0.130614
\(988\) 83.6015 2.65972
\(989\) −6.36962 −0.202542
\(990\) 12.8011 0.406847
\(991\) 36.0813 1.14616 0.573080 0.819500i \(-0.305749\pi\)
0.573080 + 0.819500i \(0.305749\pi\)
\(992\) −9.09288 −0.288699
\(993\) −5.61440 −0.178168
\(994\) 27.0334 0.857447
\(995\) 2.34898 0.0744677
\(996\) 0.450053 0.0142605
\(997\) 5.97118 0.189109 0.0945546 0.995520i \(-0.469857\pi\)
0.0945546 + 0.995520i \(0.469857\pi\)
\(998\) −63.1858 −2.00011
\(999\) 10.1890 0.322365
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 \(a_p\))