Properties

Label 8002.2.a.e.1.15
Level 8002
Weight 2
Character 8002.1
Self dual Yes
Analytic conductor 63.896
Analytic rank 0
Dimension 77
CM No

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Newspace parameters

Level: \( N \) = \( 8002 = 2 \cdot 4001 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8002.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.8962916974\)
Analytic rank: \(0\)
Dimension: \(77\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) = 8002.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -2.13252 q^{3} +1.00000 q^{4} +2.05525 q^{5} +2.13252 q^{6} -1.57763 q^{7} -1.00000 q^{8} +1.54765 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -2.13252 q^{3} +1.00000 q^{4} +2.05525 q^{5} +2.13252 q^{6} -1.57763 q^{7} -1.00000 q^{8} +1.54765 q^{9} -2.05525 q^{10} -0.539258 q^{11} -2.13252 q^{12} -4.22122 q^{13} +1.57763 q^{14} -4.38287 q^{15} +1.00000 q^{16} +1.51411 q^{17} -1.54765 q^{18} -1.49923 q^{19} +2.05525 q^{20} +3.36432 q^{21} +0.539258 q^{22} -2.07190 q^{23} +2.13252 q^{24} -0.775936 q^{25} +4.22122 q^{26} +3.09718 q^{27} -1.57763 q^{28} +1.24065 q^{29} +4.38287 q^{30} -2.21396 q^{31} -1.00000 q^{32} +1.14998 q^{33} -1.51411 q^{34} -3.24242 q^{35} +1.54765 q^{36} +3.58632 q^{37} +1.49923 q^{38} +9.00185 q^{39} -2.05525 q^{40} -6.73794 q^{41} -3.36432 q^{42} +6.54335 q^{43} -0.539258 q^{44} +3.18080 q^{45} +2.07190 q^{46} -10.5798 q^{47} -2.13252 q^{48} -4.51109 q^{49} +0.775936 q^{50} -3.22886 q^{51} -4.22122 q^{52} -4.06456 q^{53} -3.09718 q^{54} -1.10831 q^{55} +1.57763 q^{56} +3.19714 q^{57} -1.24065 q^{58} +3.66265 q^{59} -4.38287 q^{60} -7.62494 q^{61} +2.21396 q^{62} -2.44161 q^{63} +1.00000 q^{64} -8.67568 q^{65} -1.14998 q^{66} +5.18167 q^{67} +1.51411 q^{68} +4.41838 q^{69} +3.24242 q^{70} +3.98532 q^{71} -1.54765 q^{72} -6.83686 q^{73} -3.58632 q^{74} +1.65470 q^{75} -1.49923 q^{76} +0.850749 q^{77} -9.00185 q^{78} -8.38457 q^{79} +2.05525 q^{80} -11.2477 q^{81} +6.73794 q^{82} +2.62510 q^{83} +3.36432 q^{84} +3.11187 q^{85} -6.54335 q^{86} -2.64570 q^{87} +0.539258 q^{88} -5.11640 q^{89} -3.18080 q^{90} +6.65952 q^{91} -2.07190 q^{92} +4.72131 q^{93} +10.5798 q^{94} -3.08130 q^{95} +2.13252 q^{96} +5.66283 q^{97} +4.51109 q^{98} -0.834581 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 77q - 77q^{2} + 10q^{3} + 77q^{4} + 18q^{5} - 10q^{6} + 21q^{7} - 77q^{8} + 71q^{9} + O(q^{10}) \) \( 77q - 77q^{2} + 10q^{3} + 77q^{4} + 18q^{5} - 10q^{6} + 21q^{7} - 77q^{8} + 71q^{9} - 18q^{10} + 30q^{11} + 10q^{12} - 2q^{13} - 21q^{14} + 21q^{15} + 77q^{16} + 60q^{17} - 71q^{18} - 3q^{19} + 18q^{20} + 10q^{21} - 30q^{22} + 53q^{23} - 10q^{24} + 59q^{25} + 2q^{26} + 43q^{27} + 21q^{28} + 30q^{29} - 21q^{30} + 22q^{31} - 77q^{32} + 31q^{33} - 60q^{34} + 41q^{35} + 71q^{36} - 3q^{37} + 3q^{38} + 44q^{39} - 18q^{40} + 48q^{41} - 10q^{42} + 21q^{43} + 30q^{44} + 33q^{45} - 53q^{46} + 107q^{47} + 10q^{48} + 24q^{49} - 59q^{50} + 18q^{51} - 2q^{52} + 42q^{53} - 43q^{54} + 49q^{55} - 21q^{56} + 32q^{57} - 30q^{58} + 42q^{59} + 21q^{60} - 31q^{61} - 22q^{62} + 109q^{63} + 77q^{64} + 39q^{65} - 31q^{66} - q^{67} + 60q^{68} - 33q^{69} - 41q^{70} + 58q^{71} - 71q^{72} + 35q^{73} + 3q^{74} + 34q^{75} - 3q^{76} + 86q^{77} - 44q^{78} + 25q^{79} + 18q^{80} + 53q^{81} - 48q^{82} + 107q^{83} + 10q^{84} + 21q^{85} - 21q^{86} + 100q^{87} - 30q^{88} + 34q^{89} - 33q^{90} - 51q^{91} + 53q^{92} + 48q^{93} - 107q^{94} + 118q^{95} - 10q^{96} - 13q^{97} - 24q^{98} + 63q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −2.13252 −1.23121 −0.615606 0.788054i \(-0.711089\pi\)
−0.615606 + 0.788054i \(0.711089\pi\)
\(4\) 1.00000 0.500000
\(5\) 2.05525 0.919137 0.459569 0.888142i \(-0.348004\pi\)
0.459569 + 0.888142i \(0.348004\pi\)
\(6\) 2.13252 0.870598
\(7\) −1.57763 −0.596287 −0.298144 0.954521i \(-0.596367\pi\)
−0.298144 + 0.954521i \(0.596367\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.54765 0.515882
\(10\) −2.05525 −0.649928
\(11\) −0.539258 −0.162592 −0.0812962 0.996690i \(-0.525906\pi\)
−0.0812962 + 0.996690i \(0.525906\pi\)
\(12\) −2.13252 −0.615606
\(13\) −4.22122 −1.17076 −0.585378 0.810760i \(-0.699054\pi\)
−0.585378 + 0.810760i \(0.699054\pi\)
\(14\) 1.57763 0.421639
\(15\) −4.38287 −1.13165
\(16\) 1.00000 0.250000
\(17\) 1.51411 0.367224 0.183612 0.982999i \(-0.441221\pi\)
0.183612 + 0.982999i \(0.441221\pi\)
\(18\) −1.54765 −0.364784
\(19\) −1.49923 −0.343947 −0.171974 0.985102i \(-0.555014\pi\)
−0.171974 + 0.985102i \(0.555014\pi\)
\(20\) 2.05525 0.459569
\(21\) 3.36432 0.734156
\(22\) 0.539258 0.114970
\(23\) −2.07190 −0.432022 −0.216011 0.976391i \(-0.569305\pi\)
−0.216011 + 0.976391i \(0.569305\pi\)
\(24\) 2.13252 0.435299
\(25\) −0.775936 −0.155187
\(26\) 4.22122 0.827850
\(27\) 3.09718 0.596052
\(28\) −1.57763 −0.298144
\(29\) 1.24065 0.230382 0.115191 0.993343i \(-0.463252\pi\)
0.115191 + 0.993343i \(0.463252\pi\)
\(30\) 4.38287 0.800199
\(31\) −2.21396 −0.397638 −0.198819 0.980036i \(-0.563711\pi\)
−0.198819 + 0.980036i \(0.563711\pi\)
\(32\) −1.00000 −0.176777
\(33\) 1.14998 0.200186
\(34\) −1.51411 −0.259667
\(35\) −3.24242 −0.548070
\(36\) 1.54765 0.257941
\(37\) 3.58632 0.589588 0.294794 0.955561i \(-0.404749\pi\)
0.294794 + 0.955561i \(0.404749\pi\)
\(38\) 1.49923 0.243208
\(39\) 9.00185 1.44145
\(40\) −2.05525 −0.324964
\(41\) −6.73794 −1.05229 −0.526145 0.850395i \(-0.676363\pi\)
−0.526145 + 0.850395i \(0.676363\pi\)
\(42\) −3.36432 −0.519127
\(43\) 6.54335 0.997852 0.498926 0.866645i \(-0.333728\pi\)
0.498926 + 0.866645i \(0.333728\pi\)
\(44\) −0.539258 −0.0812962
\(45\) 3.18080 0.474166
\(46\) 2.07190 0.305486
\(47\) −10.5798 −1.54322 −0.771609 0.636097i \(-0.780548\pi\)
−0.771609 + 0.636097i \(0.780548\pi\)
\(48\) −2.13252 −0.307803
\(49\) −4.51109 −0.644442
\(50\) 0.775936 0.109734
\(51\) −3.22886 −0.452131
\(52\) −4.22122 −0.585378
\(53\) −4.06456 −0.558310 −0.279155 0.960246i \(-0.590054\pi\)
−0.279155 + 0.960246i \(0.590054\pi\)
\(54\) −3.09718 −0.421472
\(55\) −1.10831 −0.149445
\(56\) 1.57763 0.210819
\(57\) 3.19714 0.423472
\(58\) −1.24065 −0.162905
\(59\) 3.66265 0.476836 0.238418 0.971163i \(-0.423371\pi\)
0.238418 + 0.971163i \(0.423371\pi\)
\(60\) −4.38287 −0.565826
\(61\) −7.62494 −0.976274 −0.488137 0.872767i \(-0.662323\pi\)
−0.488137 + 0.872767i \(0.662323\pi\)
\(62\) 2.21396 0.281173
\(63\) −2.44161 −0.307614
\(64\) 1.00000 0.125000
\(65\) −8.67568 −1.07609
\(66\) −1.14998 −0.141553
\(67\) 5.18167 0.633042 0.316521 0.948585i \(-0.397485\pi\)
0.316521 + 0.948585i \(0.397485\pi\)
\(68\) 1.51411 0.183612
\(69\) 4.41838 0.531911
\(70\) 3.24242 0.387544
\(71\) 3.98532 0.472970 0.236485 0.971635i \(-0.424005\pi\)
0.236485 + 0.971635i \(0.424005\pi\)
\(72\) −1.54765 −0.182392
\(73\) −6.83686 −0.800194 −0.400097 0.916473i \(-0.631023\pi\)
−0.400097 + 0.916473i \(0.631023\pi\)
\(74\) −3.58632 −0.416901
\(75\) 1.65470 0.191068
\(76\) −1.49923 −0.171974
\(77\) 0.850749 0.0969518
\(78\) −9.00185 −1.01926
\(79\) −8.38457 −0.943338 −0.471669 0.881776i \(-0.656348\pi\)
−0.471669 + 0.881776i \(0.656348\pi\)
\(80\) 2.05525 0.229784
\(81\) −11.2477 −1.24975
\(82\) 6.73794 0.744081
\(83\) 2.62510 0.288142 0.144071 0.989567i \(-0.453981\pi\)
0.144071 + 0.989567i \(0.453981\pi\)
\(84\) 3.36432 0.367078
\(85\) 3.11187 0.337530
\(86\) −6.54335 −0.705588
\(87\) −2.64570 −0.283649
\(88\) 0.539258 0.0574851
\(89\) −5.11640 −0.542337 −0.271168 0.962532i \(-0.587410\pi\)
−0.271168 + 0.962532i \(0.587410\pi\)
\(90\) −3.18080 −0.335286
\(91\) 6.65952 0.698107
\(92\) −2.07190 −0.216011
\(93\) 4.72131 0.489577
\(94\) 10.5798 1.09122
\(95\) −3.08130 −0.316135
\(96\) 2.13252 0.217650
\(97\) 5.66283 0.574974 0.287487 0.957785i \(-0.407180\pi\)
0.287487 + 0.957785i \(0.407180\pi\)
\(98\) 4.51109 0.455689
\(99\) −0.834581 −0.0838785
\(100\) −0.775936 −0.0775936
\(101\) 12.7730 1.27096 0.635480 0.772117i \(-0.280802\pi\)
0.635480 + 0.772117i \(0.280802\pi\)
\(102\) 3.22886 0.319705
\(103\) 19.3648 1.90807 0.954036 0.299691i \(-0.0968836\pi\)
0.954036 + 0.299691i \(0.0968836\pi\)
\(104\) 4.22122 0.413925
\(105\) 6.91454 0.674790
\(106\) 4.06456 0.394785
\(107\) 12.8255 1.23989 0.619944 0.784646i \(-0.287155\pi\)
0.619944 + 0.784646i \(0.287155\pi\)
\(108\) 3.09718 0.298026
\(109\) −7.21852 −0.691409 −0.345704 0.938343i \(-0.612360\pi\)
−0.345704 + 0.938343i \(0.612360\pi\)
\(110\) 1.10831 0.105673
\(111\) −7.64791 −0.725907
\(112\) −1.57763 −0.149072
\(113\) −7.45013 −0.700850 −0.350425 0.936591i \(-0.613963\pi\)
−0.350425 + 0.936591i \(0.613963\pi\)
\(114\) −3.19714 −0.299440
\(115\) −4.25829 −0.397087
\(116\) 1.24065 0.115191
\(117\) −6.53296 −0.603972
\(118\) −3.66265 −0.337174
\(119\) −2.38869 −0.218971
\(120\) 4.38287 0.400099
\(121\) −10.7092 −0.973564
\(122\) 7.62494 0.690330
\(123\) 14.3688 1.29559
\(124\) −2.21396 −0.198819
\(125\) −11.8710 −1.06178
\(126\) 2.44161 0.217516
\(127\) 17.0872 1.51625 0.758123 0.652112i \(-0.226117\pi\)
0.758123 + 0.652112i \(0.226117\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −13.9538 −1.22857
\(130\) 8.67568 0.760908
\(131\) 8.83066 0.771539 0.385769 0.922595i \(-0.373936\pi\)
0.385769 + 0.922595i \(0.373936\pi\)
\(132\) 1.14998 0.100093
\(133\) 2.36523 0.205091
\(134\) −5.18167 −0.447628
\(135\) 6.36548 0.547853
\(136\) −1.51411 −0.129833
\(137\) −15.3920 −1.31503 −0.657513 0.753444i \(-0.728391\pi\)
−0.657513 + 0.753444i \(0.728391\pi\)
\(138\) −4.41838 −0.376118
\(139\) 13.3769 1.13461 0.567307 0.823506i \(-0.307985\pi\)
0.567307 + 0.823506i \(0.307985\pi\)
\(140\) −3.24242 −0.274035
\(141\) 22.5616 1.90003
\(142\) −3.98532 −0.334440
\(143\) 2.27633 0.190356
\(144\) 1.54765 0.128970
\(145\) 2.54984 0.211753
\(146\) 6.83686 0.565822
\(147\) 9.62000 0.793444
\(148\) 3.58632 0.294794
\(149\) −5.91612 −0.484667 −0.242334 0.970193i \(-0.577913\pi\)
−0.242334 + 0.970193i \(0.577913\pi\)
\(150\) −1.65470 −0.135106
\(151\) 1.81956 0.148074 0.0740368 0.997256i \(-0.476412\pi\)
0.0740368 + 0.997256i \(0.476412\pi\)
\(152\) 1.49923 0.121604
\(153\) 2.34330 0.189444
\(154\) −0.850749 −0.0685553
\(155\) −4.55024 −0.365484
\(156\) 9.00185 0.720725
\(157\) −0.625142 −0.0498918 −0.0249459 0.999689i \(-0.507941\pi\)
−0.0249459 + 0.999689i \(0.507941\pi\)
\(158\) 8.38457 0.667040
\(159\) 8.66776 0.687398
\(160\) −2.05525 −0.162482
\(161\) 3.26869 0.257609
\(162\) 11.2477 0.883705
\(163\) 15.9699 1.25086 0.625431 0.780280i \(-0.284923\pi\)
0.625431 + 0.780280i \(0.284923\pi\)
\(164\) −6.73794 −0.526145
\(165\) 2.36350 0.183998
\(166\) −2.62510 −0.203747
\(167\) −19.8718 −1.53773 −0.768864 0.639412i \(-0.779178\pi\)
−0.768864 + 0.639412i \(0.779178\pi\)
\(168\) −3.36432 −0.259563
\(169\) 4.81873 0.370672
\(170\) −3.11187 −0.238669
\(171\) −2.32028 −0.177436
\(172\) 6.54335 0.498926
\(173\) 9.43369 0.717230 0.358615 0.933485i \(-0.383249\pi\)
0.358615 + 0.933485i \(0.383249\pi\)
\(174\) 2.64570 0.200570
\(175\) 1.22414 0.0925361
\(176\) −0.539258 −0.0406481
\(177\) −7.81067 −0.587086
\(178\) 5.11640 0.383490
\(179\) −4.12254 −0.308133 −0.154067 0.988060i \(-0.549237\pi\)
−0.154067 + 0.988060i \(0.549237\pi\)
\(180\) 3.18080 0.237083
\(181\) −10.2695 −0.763326 −0.381663 0.924302i \(-0.624648\pi\)
−0.381663 + 0.924302i \(0.624648\pi\)
\(182\) −6.65952 −0.493637
\(183\) 16.2603 1.20200
\(184\) 2.07190 0.152743
\(185\) 7.37080 0.541912
\(186\) −4.72131 −0.346183
\(187\) −0.816494 −0.0597079
\(188\) −10.5798 −0.771609
\(189\) −4.88619 −0.355418
\(190\) 3.08130 0.223541
\(191\) 0.468267 0.0338826 0.0169413 0.999856i \(-0.494607\pi\)
0.0169413 + 0.999856i \(0.494607\pi\)
\(192\) −2.13252 −0.153901
\(193\) 2.92245 0.210362 0.105181 0.994453i \(-0.466458\pi\)
0.105181 + 0.994453i \(0.466458\pi\)
\(194\) −5.66283 −0.406568
\(195\) 18.5011 1.32489
\(196\) −4.51109 −0.322221
\(197\) −20.1726 −1.43724 −0.718619 0.695404i \(-0.755225\pi\)
−0.718619 + 0.695404i \(0.755225\pi\)
\(198\) 0.834581 0.0593111
\(199\) −9.27373 −0.657397 −0.328699 0.944435i \(-0.606610\pi\)
−0.328699 + 0.944435i \(0.606610\pi\)
\(200\) 0.775936 0.0548669
\(201\) −11.0500 −0.779409
\(202\) −12.7730 −0.898705
\(203\) −1.95728 −0.137374
\(204\) −3.22886 −0.226066
\(205\) −13.8482 −0.967198
\(206\) −19.3648 −1.34921
\(207\) −3.20658 −0.222872
\(208\) −4.22122 −0.292689
\(209\) 0.808473 0.0559233
\(210\) −6.91454 −0.477148
\(211\) −27.0455 −1.86189 −0.930944 0.365162i \(-0.881014\pi\)
−0.930944 + 0.365162i \(0.881014\pi\)
\(212\) −4.06456 −0.279155
\(213\) −8.49877 −0.582326
\(214\) −12.8255 −0.876733
\(215\) 13.4482 0.917163
\(216\) −3.09718 −0.210736
\(217\) 3.49280 0.237107
\(218\) 7.21852 0.488900
\(219\) 14.5797 0.985208
\(220\) −1.10831 −0.0747224
\(221\) −6.39138 −0.429931
\(222\) 7.64791 0.513294
\(223\) 5.51140 0.369071 0.184535 0.982826i \(-0.440922\pi\)
0.184535 + 0.982826i \(0.440922\pi\)
\(224\) 1.57763 0.105410
\(225\) −1.20087 −0.0800583
\(226\) 7.45013 0.495575
\(227\) 15.2652 1.01319 0.506594 0.862185i \(-0.330904\pi\)
0.506594 + 0.862185i \(0.330904\pi\)
\(228\) 3.19714 0.211736
\(229\) 25.1307 1.66069 0.830343 0.557252i \(-0.188144\pi\)
0.830343 + 0.557252i \(0.188144\pi\)
\(230\) 4.25829 0.280783
\(231\) −1.81424 −0.119368
\(232\) −1.24065 −0.0814524
\(233\) 19.9210 1.30507 0.652534 0.757760i \(-0.273706\pi\)
0.652534 + 0.757760i \(0.273706\pi\)
\(234\) 6.53296 0.427073
\(235\) −21.7441 −1.41843
\(236\) 3.66265 0.238418
\(237\) 17.8803 1.16145
\(238\) 2.38869 0.154836
\(239\) −2.38712 −0.154410 −0.0772049 0.997015i \(-0.524600\pi\)
−0.0772049 + 0.997015i \(0.524600\pi\)
\(240\) −4.38287 −0.282913
\(241\) 14.2453 0.917620 0.458810 0.888534i \(-0.348276\pi\)
0.458810 + 0.888534i \(0.348276\pi\)
\(242\) 10.7092 0.688413
\(243\) 14.6945 0.942652
\(244\) −7.62494 −0.488137
\(245\) −9.27143 −0.592330
\(246\) −14.3688 −0.916121
\(247\) 6.32859 0.402679
\(248\) 2.21396 0.140586
\(249\) −5.59808 −0.354764
\(250\) 11.8710 0.750788
\(251\) 6.48712 0.409463 0.204732 0.978818i \(-0.434368\pi\)
0.204732 + 0.978818i \(0.434368\pi\)
\(252\) −2.44161 −0.153807
\(253\) 1.11729 0.0702435
\(254\) −17.0872 −1.07215
\(255\) −6.63613 −0.415570
\(256\) 1.00000 0.0625000
\(257\) −11.7158 −0.730812 −0.365406 0.930848i \(-0.619070\pi\)
−0.365406 + 0.930848i \(0.619070\pi\)
\(258\) 13.9538 0.868728
\(259\) −5.65788 −0.351564
\(260\) −8.67568 −0.538043
\(261\) 1.92008 0.118850
\(262\) −8.83066 −0.545560
\(263\) 11.2370 0.692903 0.346452 0.938068i \(-0.387387\pi\)
0.346452 + 0.938068i \(0.387387\pi\)
\(264\) −1.14998 −0.0707764
\(265\) −8.35370 −0.513163
\(266\) −2.36523 −0.145022
\(267\) 10.9108 0.667732
\(268\) 5.18167 0.316521
\(269\) −7.91805 −0.482772 −0.241386 0.970429i \(-0.577602\pi\)
−0.241386 + 0.970429i \(0.577602\pi\)
\(270\) −6.36548 −0.387391
\(271\) −23.4137 −1.42228 −0.711141 0.703049i \(-0.751821\pi\)
−0.711141 + 0.703049i \(0.751821\pi\)
\(272\) 1.51411 0.0918061
\(273\) −14.2016 −0.859518
\(274\) 15.3920 0.929863
\(275\) 0.418430 0.0252323
\(276\) 4.41838 0.265955
\(277\) 32.8131 1.97155 0.985773 0.168083i \(-0.0537577\pi\)
0.985773 + 0.168083i \(0.0537577\pi\)
\(278\) −13.3769 −0.802294
\(279\) −3.42642 −0.205134
\(280\) 3.24242 0.193772
\(281\) −21.3919 −1.27613 −0.638066 0.769981i \(-0.720265\pi\)
−0.638066 + 0.769981i \(0.720265\pi\)
\(282\) −22.5616 −1.34352
\(283\) −4.50672 −0.267896 −0.133948 0.990988i \(-0.542766\pi\)
−0.133948 + 0.990988i \(0.542766\pi\)
\(284\) 3.98532 0.236485
\(285\) 6.57094 0.389229
\(286\) −2.27633 −0.134602
\(287\) 10.6300 0.627467
\(288\) −1.54765 −0.0911959
\(289\) −14.7075 −0.865146
\(290\) −2.54984 −0.149732
\(291\) −12.0761 −0.707914
\(292\) −6.83686 −0.400097
\(293\) −3.14790 −0.183902 −0.0919511 0.995764i \(-0.529310\pi\)
−0.0919511 + 0.995764i \(0.529310\pi\)
\(294\) −9.62000 −0.561050
\(295\) 7.52766 0.438278
\(296\) −3.58632 −0.208451
\(297\) −1.67018 −0.0969135
\(298\) 5.91612 0.342711
\(299\) 8.74598 0.505793
\(300\) 1.65470 0.0955341
\(301\) −10.3230 −0.595006
\(302\) −1.81956 −0.104704
\(303\) −27.2387 −1.56482
\(304\) −1.49923 −0.0859868
\(305\) −15.6712 −0.897329
\(306\) −2.34330 −0.133957
\(307\) −24.7438 −1.41220 −0.706102 0.708111i \(-0.749548\pi\)
−0.706102 + 0.708111i \(0.749548\pi\)
\(308\) 0.850749 0.0484759
\(309\) −41.2959 −2.34924
\(310\) 4.55024 0.258436
\(311\) 2.56106 0.145224 0.0726122 0.997360i \(-0.476866\pi\)
0.0726122 + 0.997360i \(0.476866\pi\)
\(312\) −9.00185 −0.509629
\(313\) 11.3528 0.641696 0.320848 0.947131i \(-0.396032\pi\)
0.320848 + 0.947131i \(0.396032\pi\)
\(314\) 0.625142 0.0352788
\(315\) −5.01812 −0.282739
\(316\) −8.38457 −0.471669
\(317\) 20.5751 1.15561 0.577806 0.816174i \(-0.303909\pi\)
0.577806 + 0.816174i \(0.303909\pi\)
\(318\) −8.66776 −0.486064
\(319\) −0.669029 −0.0374584
\(320\) 2.05525 0.114892
\(321\) −27.3506 −1.52656
\(322\) −3.26869 −0.182157
\(323\) −2.26999 −0.126306
\(324\) −11.2477 −0.624874
\(325\) 3.27540 0.181686
\(326\) −15.9699 −0.884493
\(327\) 15.3936 0.851270
\(328\) 6.73794 0.372040
\(329\) 16.6909 0.920202
\(330\) −2.36350 −0.130106
\(331\) 5.06505 0.278400 0.139200 0.990264i \(-0.455547\pi\)
0.139200 + 0.990264i \(0.455547\pi\)
\(332\) 2.62510 0.144071
\(333\) 5.55036 0.304158
\(334\) 19.8718 1.08734
\(335\) 10.6496 0.581853
\(336\) 3.36432 0.183539
\(337\) 5.57117 0.303481 0.151740 0.988420i \(-0.451512\pi\)
0.151740 + 0.988420i \(0.451512\pi\)
\(338\) −4.81873 −0.262105
\(339\) 15.8876 0.862894
\(340\) 3.11187 0.168765
\(341\) 1.19389 0.0646530
\(342\) 2.32028 0.125466
\(343\) 18.1602 0.980559
\(344\) −6.54335 −0.352794
\(345\) 9.08089 0.488899
\(346\) −9.43369 −0.507158
\(347\) −4.57946 −0.245838 −0.122919 0.992417i \(-0.539226\pi\)
−0.122919 + 0.992417i \(0.539226\pi\)
\(348\) −2.64570 −0.141825
\(349\) 19.2750 1.03177 0.515884 0.856658i \(-0.327464\pi\)
0.515884 + 0.856658i \(0.327464\pi\)
\(350\) −1.22414 −0.0654329
\(351\) −13.0739 −0.697832
\(352\) 0.539258 0.0287426
\(353\) 32.0319 1.70489 0.852444 0.522819i \(-0.175120\pi\)
0.852444 + 0.522819i \(0.175120\pi\)
\(354\) 7.81067 0.415132
\(355\) 8.19084 0.434724
\(356\) −5.11640 −0.271168
\(357\) 5.09394 0.269600
\(358\) 4.12254 0.217883
\(359\) 20.0777 1.05966 0.529829 0.848104i \(-0.322256\pi\)
0.529829 + 0.848104i \(0.322256\pi\)
\(360\) −3.18080 −0.167643
\(361\) −16.7523 −0.881700
\(362\) 10.2695 0.539753
\(363\) 22.8376 1.19866
\(364\) 6.65952 0.349054
\(365\) −14.0515 −0.735487
\(366\) −16.2603 −0.849942
\(367\) −18.5710 −0.969396 −0.484698 0.874681i \(-0.661071\pi\)
−0.484698 + 0.874681i \(0.661071\pi\)
\(368\) −2.07190 −0.108006
\(369\) −10.4279 −0.542857
\(370\) −7.37080 −0.383190
\(371\) 6.41236 0.332913
\(372\) 4.72131 0.244788
\(373\) −36.6028 −1.89522 −0.947611 0.319426i \(-0.896510\pi\)
−0.947611 + 0.319426i \(0.896510\pi\)
\(374\) 0.816494 0.0422199
\(375\) 25.3152 1.30727
\(376\) 10.5798 0.545610
\(377\) −5.23705 −0.269722
\(378\) 4.88619 0.251319
\(379\) 23.8074 1.22291 0.611453 0.791281i \(-0.290585\pi\)
0.611453 + 0.791281i \(0.290585\pi\)
\(380\) −3.08130 −0.158067
\(381\) −36.4389 −1.86682
\(382\) −0.468267 −0.0239586
\(383\) −5.05536 −0.258317 −0.129158 0.991624i \(-0.541228\pi\)
−0.129158 + 0.991624i \(0.541228\pi\)
\(384\) 2.13252 0.108825
\(385\) 1.74850 0.0891120
\(386\) −2.92245 −0.148749
\(387\) 10.1268 0.514774
\(388\) 5.66283 0.287487
\(389\) −16.5141 −0.837300 −0.418650 0.908148i \(-0.637497\pi\)
−0.418650 + 0.908148i \(0.637497\pi\)
\(390\) −18.5011 −0.936838
\(391\) −3.13708 −0.158649
\(392\) 4.51109 0.227844
\(393\) −18.8316 −0.949927
\(394\) 20.1726 1.01628
\(395\) −17.2324 −0.867057
\(396\) −0.834581 −0.0419393
\(397\) −1.63192 −0.0819039 −0.0409519 0.999161i \(-0.513039\pi\)
−0.0409519 + 0.999161i \(0.513039\pi\)
\(398\) 9.27373 0.464850
\(399\) −5.04390 −0.252511
\(400\) −0.775936 −0.0387968
\(401\) 30.1398 1.50511 0.752556 0.658528i \(-0.228821\pi\)
0.752556 + 0.658528i \(0.228821\pi\)
\(402\) 11.0500 0.551125
\(403\) 9.34560 0.465538
\(404\) 12.7730 0.635480
\(405\) −23.1169 −1.14869
\(406\) 1.95728 0.0971381
\(407\) −1.93395 −0.0958625
\(408\) 3.22886 0.159852
\(409\) −1.10386 −0.0545822 −0.0272911 0.999628i \(-0.508688\pi\)
−0.0272911 + 0.999628i \(0.508688\pi\)
\(410\) 13.8482 0.683912
\(411\) 32.8237 1.61907
\(412\) 19.3648 0.954036
\(413\) −5.77829 −0.284331
\(414\) 3.20658 0.157595
\(415\) 5.39525 0.264842
\(416\) 4.22122 0.206963
\(417\) −28.5265 −1.39695
\(418\) −0.808473 −0.0395437
\(419\) −6.88494 −0.336351 −0.168176 0.985757i \(-0.553788\pi\)
−0.168176 + 0.985757i \(0.553788\pi\)
\(420\) 6.91454 0.337395
\(421\) 28.8068 1.40396 0.701978 0.712199i \(-0.252301\pi\)
0.701978 + 0.712199i \(0.252301\pi\)
\(422\) 27.0455 1.31655
\(423\) −16.3737 −0.796119
\(424\) 4.06456 0.197392
\(425\) −1.17485 −0.0569885
\(426\) 8.49877 0.411767
\(427\) 12.0293 0.582140
\(428\) 12.8255 0.619944
\(429\) −4.85432 −0.234369
\(430\) −13.4482 −0.648532
\(431\) −19.3378 −0.931471 −0.465735 0.884924i \(-0.654210\pi\)
−0.465735 + 0.884924i \(0.654210\pi\)
\(432\) 3.09718 0.149013
\(433\) 29.8366 1.43386 0.716928 0.697147i \(-0.245547\pi\)
0.716928 + 0.697147i \(0.245547\pi\)
\(434\) −3.49280 −0.167660
\(435\) −5.43759 −0.260713
\(436\) −7.21852 −0.345704
\(437\) 3.10627 0.148593
\(438\) −14.5797 −0.696647
\(439\) 13.8301 0.660075 0.330037 0.943968i \(-0.392939\pi\)
0.330037 + 0.943968i \(0.392939\pi\)
\(440\) 1.10831 0.0528367
\(441\) −6.98157 −0.332456
\(442\) 6.39138 0.304007
\(443\) −36.7705 −1.74702 −0.873509 0.486807i \(-0.838161\pi\)
−0.873509 + 0.486807i \(0.838161\pi\)
\(444\) −7.64791 −0.362954
\(445\) −10.5155 −0.498482
\(446\) −5.51140 −0.260973
\(447\) 12.6162 0.596728
\(448\) −1.57763 −0.0745359
\(449\) −22.8089 −1.07642 −0.538209 0.842811i \(-0.680899\pi\)
−0.538209 + 0.842811i \(0.680899\pi\)
\(450\) 1.20087 0.0566097
\(451\) 3.63349 0.171094
\(452\) −7.45013 −0.350425
\(453\) −3.88025 −0.182310
\(454\) −15.2652 −0.716432
\(455\) 13.6870 0.641656
\(456\) −3.19714 −0.149720
\(457\) 5.37626 0.251491 0.125745 0.992063i \(-0.459868\pi\)
0.125745 + 0.992063i \(0.459868\pi\)
\(458\) −25.1307 −1.17428
\(459\) 4.68945 0.218885
\(460\) −4.25829 −0.198544
\(461\) 42.4368 1.97648 0.988240 0.152914i \(-0.0488656\pi\)
0.988240 + 0.152914i \(0.0488656\pi\)
\(462\) 1.81424 0.0844061
\(463\) 30.9487 1.43831 0.719155 0.694850i \(-0.244529\pi\)
0.719155 + 0.694850i \(0.244529\pi\)
\(464\) 1.24065 0.0575956
\(465\) 9.70348 0.449988
\(466\) −19.9210 −0.922822
\(467\) −4.20210 −0.194450 −0.0972249 0.995262i \(-0.530997\pi\)
−0.0972249 + 0.995262i \(0.530997\pi\)
\(468\) −6.53296 −0.301986
\(469\) −8.17475 −0.377475
\(470\) 21.7441 1.00298
\(471\) 1.33313 0.0614274
\(472\) −3.66265 −0.168587
\(473\) −3.52856 −0.162243
\(474\) −17.8803 −0.821268
\(475\) 1.16331 0.0533762
\(476\) −2.38869 −0.109486
\(477\) −6.29050 −0.288022
\(478\) 2.38712 0.109184
\(479\) 22.7379 1.03892 0.519461 0.854494i \(-0.326133\pi\)
0.519461 + 0.854494i \(0.326133\pi\)
\(480\) 4.38287 0.200050
\(481\) −15.1387 −0.690264
\(482\) −14.2453 −0.648855
\(483\) −6.97056 −0.317171
\(484\) −10.7092 −0.486782
\(485\) 11.6386 0.528480
\(486\) −14.6945 −0.666556
\(487\) −0.951488 −0.0431160 −0.0215580 0.999768i \(-0.506863\pi\)
−0.0215580 + 0.999768i \(0.506863\pi\)
\(488\) 7.62494 0.345165
\(489\) −34.0562 −1.54008
\(490\) 9.27143 0.418841
\(491\) −20.4819 −0.924336 −0.462168 0.886792i \(-0.652928\pi\)
−0.462168 + 0.886792i \(0.652928\pi\)
\(492\) 14.3688 0.647795
\(493\) 1.87847 0.0846020
\(494\) −6.32859 −0.284737
\(495\) −1.71527 −0.0770959
\(496\) −2.21396 −0.0994095
\(497\) −6.28735 −0.282026
\(498\) 5.59808 0.250856
\(499\) 6.64782 0.297597 0.148799 0.988868i \(-0.452459\pi\)
0.148799 + 0.988868i \(0.452459\pi\)
\(500\) −11.8710 −0.530888
\(501\) 42.3771 1.89327
\(502\) −6.48712 −0.289534
\(503\) 34.0415 1.51784 0.758918 0.651187i \(-0.225728\pi\)
0.758918 + 0.651187i \(0.225728\pi\)
\(504\) 2.44161 0.108758
\(505\) 26.2517 1.16819
\(506\) −1.11729 −0.0496697
\(507\) −10.2761 −0.456376
\(508\) 17.0872 0.758123
\(509\) 6.91785 0.306628 0.153314 0.988177i \(-0.451005\pi\)
0.153314 + 0.988177i \(0.451005\pi\)
\(510\) 6.63613 0.293853
\(511\) 10.7860 0.477145
\(512\) −1.00000 −0.0441942
\(513\) −4.64338 −0.205010
\(514\) 11.7158 0.516762
\(515\) 39.7996 1.75378
\(516\) −13.9538 −0.614283
\(517\) 5.70523 0.250916
\(518\) 5.65788 0.248593
\(519\) −20.1175 −0.883062
\(520\) 8.67568 0.380454
\(521\) 5.48441 0.240276 0.120138 0.992757i \(-0.461666\pi\)
0.120138 + 0.992757i \(0.461666\pi\)
\(522\) −1.92008 −0.0840397
\(523\) −45.0772 −1.97109 −0.985545 0.169415i \(-0.945812\pi\)
−0.985545 + 0.169415i \(0.945812\pi\)
\(524\) 8.83066 0.385769
\(525\) −2.61050 −0.113932
\(526\) −11.2370 −0.489956
\(527\) −3.35216 −0.146022
\(528\) 1.14998 0.0500464
\(529\) −18.7072 −0.813357
\(530\) 8.35370 0.362861
\(531\) 5.66848 0.245991
\(532\) 2.36523 0.102546
\(533\) 28.4424 1.23197
\(534\) −10.9108 −0.472158
\(535\) 26.3596 1.13963
\(536\) −5.18167 −0.223814
\(537\) 8.79141 0.379377
\(538\) 7.91805 0.341371
\(539\) 2.43264 0.104781
\(540\) 6.36548 0.273927
\(541\) −2.20015 −0.0945920 −0.0472960 0.998881i \(-0.515060\pi\)
−0.0472960 + 0.998881i \(0.515060\pi\)
\(542\) 23.4137 1.00571
\(543\) 21.8999 0.939815
\(544\) −1.51411 −0.0649167
\(545\) −14.8359 −0.635499
\(546\) 14.2016 0.607771
\(547\) 8.13333 0.347756 0.173878 0.984767i \(-0.444370\pi\)
0.173878 + 0.984767i \(0.444370\pi\)
\(548\) −15.3920 −0.657513
\(549\) −11.8007 −0.503642
\(550\) −0.418430 −0.0178419
\(551\) −1.86002 −0.0792394
\(552\) −4.41838 −0.188059
\(553\) 13.2277 0.562500
\(554\) −32.8131 −1.39409
\(555\) −15.7184 −0.667208
\(556\) 13.3769 0.567307
\(557\) −17.1010 −0.724594 −0.362297 0.932063i \(-0.618007\pi\)
−0.362297 + 0.932063i \(0.618007\pi\)
\(558\) 3.42642 0.145052
\(559\) −27.6210 −1.16824
\(560\) −3.24242 −0.137017
\(561\) 1.74119 0.0735131
\(562\) 21.3919 0.902362
\(563\) 28.8336 1.21519 0.607595 0.794247i \(-0.292135\pi\)
0.607595 + 0.794247i \(0.292135\pi\)
\(564\) 22.5616 0.950014
\(565\) −15.3119 −0.644177
\(566\) 4.50672 0.189431
\(567\) 17.7447 0.745209
\(568\) −3.98532 −0.167220
\(569\) 12.8788 0.539906 0.269953 0.962874i \(-0.412992\pi\)
0.269953 + 0.962874i \(0.412992\pi\)
\(570\) −6.57094 −0.275226
\(571\) 14.6165 0.611683 0.305841 0.952082i \(-0.401062\pi\)
0.305841 + 0.952082i \(0.401062\pi\)
\(572\) 2.27633 0.0951781
\(573\) −0.998589 −0.0417166
\(574\) −10.6300 −0.443686
\(575\) 1.60767 0.0670443
\(576\) 1.54765 0.0644852
\(577\) 44.6668 1.85950 0.929752 0.368187i \(-0.120021\pi\)
0.929752 + 0.368187i \(0.120021\pi\)
\(578\) 14.7075 0.611751
\(579\) −6.23218 −0.259000
\(580\) 2.54984 0.105876
\(581\) −4.14143 −0.171816
\(582\) 12.0761 0.500571
\(583\) 2.19185 0.0907770
\(584\) 6.83686 0.282911
\(585\) −13.4269 −0.555133
\(586\) 3.14790 0.130039
\(587\) 3.50562 0.144693 0.0723463 0.997380i \(-0.476951\pi\)
0.0723463 + 0.997380i \(0.476951\pi\)
\(588\) 9.62000 0.396722
\(589\) 3.31923 0.136767
\(590\) −7.52766 −0.309909
\(591\) 43.0185 1.76954
\(592\) 3.58632 0.147397
\(593\) −6.50123 −0.266974 −0.133487 0.991051i \(-0.542617\pi\)
−0.133487 + 0.991051i \(0.542617\pi\)
\(594\) 1.67018 0.0685282
\(595\) −4.90937 −0.201265
\(596\) −5.91612 −0.242334
\(597\) 19.7764 0.809395
\(598\) −8.74598 −0.357650
\(599\) 1.55968 0.0637266 0.0318633 0.999492i \(-0.489856\pi\)
0.0318633 + 0.999492i \(0.489856\pi\)
\(600\) −1.65470 −0.0675528
\(601\) 42.7266 1.74285 0.871427 0.490526i \(-0.163195\pi\)
0.871427 + 0.490526i \(0.163195\pi\)
\(602\) 10.3230 0.420733
\(603\) 8.01940 0.326575
\(604\) 1.81956 0.0740368
\(605\) −22.0101 −0.894838
\(606\) 27.2387 1.10650
\(607\) −6.95229 −0.282185 −0.141092 0.989996i \(-0.545061\pi\)
−0.141092 + 0.989996i \(0.545061\pi\)
\(608\) 1.49923 0.0608019
\(609\) 4.17394 0.169136
\(610\) 15.6712 0.634508
\(611\) 44.6596 1.80673
\(612\) 2.34330 0.0947222
\(613\) 29.0612 1.17377 0.586884 0.809671i \(-0.300354\pi\)
0.586884 + 0.809671i \(0.300354\pi\)
\(614\) 24.7438 0.998578
\(615\) 29.5315 1.19083
\(616\) −0.850749 −0.0342776
\(617\) 4.02476 0.162031 0.0810153 0.996713i \(-0.474184\pi\)
0.0810153 + 0.996713i \(0.474184\pi\)
\(618\) 41.2959 1.66116
\(619\) −28.8350 −1.15898 −0.579489 0.814980i \(-0.696748\pi\)
−0.579489 + 0.814980i \(0.696748\pi\)
\(620\) −4.55024 −0.182742
\(621\) −6.41705 −0.257507
\(622\) −2.56106 −0.102689
\(623\) 8.07177 0.323389
\(624\) 9.00185 0.360362
\(625\) −20.5182 −0.820730
\(626\) −11.3528 −0.453747
\(627\) −1.72409 −0.0688534
\(628\) −0.625142 −0.0249459
\(629\) 5.43007 0.216511
\(630\) 5.01812 0.199927
\(631\) −8.09539 −0.322272 −0.161136 0.986932i \(-0.551516\pi\)
−0.161136 + 0.986932i \(0.551516\pi\)
\(632\) 8.38457 0.333520
\(633\) 57.6751 2.29238
\(634\) −20.5751 −0.817140
\(635\) 35.1186 1.39364
\(636\) 8.66776 0.343699
\(637\) 19.0423 0.754484
\(638\) 0.669029 0.0264871
\(639\) 6.16786 0.243997
\(640\) −2.05525 −0.0812410
\(641\) 8.54519 0.337515 0.168757 0.985658i \(-0.446025\pi\)
0.168757 + 0.985658i \(0.446025\pi\)
\(642\) 27.3506 1.07944
\(643\) 17.2679 0.680978 0.340489 0.940249i \(-0.389407\pi\)
0.340489 + 0.940249i \(0.389407\pi\)
\(644\) 3.26869 0.128805
\(645\) −28.6787 −1.12922
\(646\) 2.26999 0.0893117
\(647\) 49.4760 1.94510 0.972552 0.232687i \(-0.0747519\pi\)
0.972552 + 0.232687i \(0.0747519\pi\)
\(648\) 11.2477 0.441853
\(649\) −1.97511 −0.0775299
\(650\) −3.27540 −0.128472
\(651\) −7.44846 −0.291928
\(652\) 15.9699 0.625431
\(653\) 40.0363 1.56674 0.783371 0.621555i \(-0.213499\pi\)
0.783371 + 0.621555i \(0.213499\pi\)
\(654\) −15.3936 −0.601939
\(655\) 18.1492 0.709150
\(656\) −6.73794 −0.263072
\(657\) −10.5810 −0.412805
\(658\) −16.6909 −0.650681
\(659\) −3.82790 −0.149114 −0.0745570 0.997217i \(-0.523754\pi\)
−0.0745570 + 0.997217i \(0.523754\pi\)
\(660\) 2.36350 0.0919991
\(661\) −21.4927 −0.835970 −0.417985 0.908454i \(-0.637264\pi\)
−0.417985 + 0.908454i \(0.637264\pi\)
\(662\) −5.06505 −0.196859
\(663\) 13.6297 0.529336
\(664\) −2.62510 −0.101874
\(665\) 4.86114 0.188507
\(666\) −5.55036 −0.215072
\(667\) −2.57050 −0.0995302
\(668\) −19.8718 −0.768864
\(669\) −11.7532 −0.454404
\(670\) −10.6496 −0.411432
\(671\) 4.11181 0.158735
\(672\) −3.36432 −0.129782
\(673\) 19.3225 0.744827 0.372414 0.928067i \(-0.378530\pi\)
0.372414 + 0.928067i \(0.378530\pi\)
\(674\) −5.57117 −0.214593
\(675\) −2.40321 −0.0924996
\(676\) 4.81873 0.185336
\(677\) −41.2203 −1.58423 −0.792113 0.610375i \(-0.791019\pi\)
−0.792113 + 0.610375i \(0.791019\pi\)
\(678\) −15.8876 −0.610158
\(679\) −8.93384 −0.342849
\(680\) −3.11187 −0.119335
\(681\) −32.5534 −1.24745
\(682\) −1.19389 −0.0457166
\(683\) 17.5984 0.673385 0.336693 0.941615i \(-0.390692\pi\)
0.336693 + 0.941615i \(0.390692\pi\)
\(684\) −2.32028 −0.0887181
\(685\) −31.6344 −1.20869
\(686\) −18.1602 −0.693360
\(687\) −53.5918 −2.04466
\(688\) 6.54335 0.249463
\(689\) 17.1574 0.653645
\(690\) −9.08089 −0.345704
\(691\) −16.9008 −0.642936 −0.321468 0.946920i \(-0.604176\pi\)
−0.321468 + 0.946920i \(0.604176\pi\)
\(692\) 9.43369 0.358615
\(693\) 1.31666 0.0500157
\(694\) 4.57946 0.173834
\(695\) 27.4929 1.04287
\(696\) 2.64570 0.100285
\(697\) −10.2019 −0.386426
\(698\) −19.2750 −0.729570
\(699\) −42.4819 −1.60681
\(700\) 1.22414 0.0462681
\(701\) 20.1076 0.759452 0.379726 0.925099i \(-0.376018\pi\)
0.379726 + 0.925099i \(0.376018\pi\)
\(702\) 13.0739 0.493442
\(703\) −5.37673 −0.202787
\(704\) −0.539258 −0.0203241
\(705\) 46.3698 1.74639
\(706\) −32.0319 −1.20554
\(707\) −20.1510 −0.757858
\(708\) −7.81067 −0.293543
\(709\) −21.5132 −0.807947 −0.403973 0.914771i \(-0.632371\pi\)
−0.403973 + 0.914771i \(0.632371\pi\)
\(710\) −8.19084 −0.307397
\(711\) −12.9763 −0.486651
\(712\) 5.11640 0.191745
\(713\) 4.58711 0.171788
\(714\) −5.09394 −0.190636
\(715\) 4.67843 0.174964
\(716\) −4.12254 −0.154067
\(717\) 5.09058 0.190111
\(718\) −20.0777 −0.749292
\(719\) 12.3192 0.459429 0.229715 0.973258i \(-0.426221\pi\)
0.229715 + 0.973258i \(0.426221\pi\)
\(720\) 3.18080 0.118542
\(721\) −30.5505 −1.13776
\(722\) 16.7523 0.623456
\(723\) −30.3784 −1.12978
\(724\) −10.2695 −0.381663
\(725\) −0.962662 −0.0357524
\(726\) −22.8376 −0.847583
\(727\) −5.21720 −0.193495 −0.0967475 0.995309i \(-0.530844\pi\)
−0.0967475 + 0.995309i \(0.530844\pi\)
\(728\) −6.65952 −0.246818
\(729\) 2.40687 0.0891435
\(730\) 14.0515 0.520068
\(731\) 9.90732 0.366436
\(732\) 16.2603 0.601000
\(733\) 21.1108 0.779745 0.389872 0.920869i \(-0.372519\pi\)
0.389872 + 0.920869i \(0.372519\pi\)
\(734\) 18.5710 0.685467
\(735\) 19.7715 0.729284
\(736\) 2.07190 0.0763714
\(737\) −2.79426 −0.102928
\(738\) 10.4279 0.383858
\(739\) 26.3791 0.970370 0.485185 0.874412i \(-0.338752\pi\)
0.485185 + 0.874412i \(0.338752\pi\)
\(740\) 7.37080 0.270956
\(741\) −13.4959 −0.495783
\(742\) −6.41236 −0.235405
\(743\) 46.8695 1.71948 0.859738 0.510735i \(-0.170627\pi\)
0.859738 + 0.510735i \(0.170627\pi\)
\(744\) −4.72131 −0.173092
\(745\) −12.1591 −0.445475
\(746\) 36.6028 1.34012
\(747\) 4.06273 0.148647
\(748\) −0.816494 −0.0298540
\(749\) −20.2339 −0.739329
\(750\) −25.3152 −0.924379
\(751\) −15.8235 −0.577409 −0.288705 0.957418i \(-0.593225\pi\)
−0.288705 + 0.957418i \(0.593225\pi\)
\(752\) −10.5798 −0.385805
\(753\) −13.8339 −0.504136
\(754\) 5.23705 0.190722
\(755\) 3.73965 0.136100
\(756\) −4.88619 −0.177709
\(757\) 14.6168 0.531257 0.265628 0.964075i \(-0.414421\pi\)
0.265628 + 0.964075i \(0.414421\pi\)
\(758\) −23.8074 −0.864725
\(759\) −2.38265 −0.0864847
\(760\) 3.08130 0.111771
\(761\) 25.5517 0.926250 0.463125 0.886293i \(-0.346728\pi\)
0.463125 + 0.886293i \(0.346728\pi\)
\(762\) 36.4389 1.32004
\(763\) 11.3881 0.412278
\(764\) 0.468267 0.0169413
\(765\) 4.81607 0.174125
\(766\) 5.05536 0.182658
\(767\) −15.4609 −0.558259
\(768\) −2.13252 −0.0769507
\(769\) 37.2920 1.34479 0.672393 0.740195i \(-0.265267\pi\)
0.672393 + 0.740195i \(0.265267\pi\)
\(770\) −1.74850 −0.0630117
\(771\) 24.9842 0.899784
\(772\) 2.92245 0.105181
\(773\) 39.3419 1.41503 0.707514 0.706699i \(-0.249817\pi\)
0.707514 + 0.706699i \(0.249817\pi\)
\(774\) −10.1268 −0.364000
\(775\) 1.71789 0.0617083
\(776\) −5.66283 −0.203284
\(777\) 12.0656 0.432849
\(778\) 16.5141 0.592061
\(779\) 10.1017 0.361932
\(780\) 18.5011 0.662445
\(781\) −2.14912 −0.0769014
\(782\) 3.13708 0.112182
\(783\) 3.84250 0.137320
\(784\) −4.51109 −0.161110
\(785\) −1.28483 −0.0458574
\(786\) 18.8316 0.671700
\(787\) −20.5380 −0.732101 −0.366051 0.930595i \(-0.619290\pi\)
−0.366051 + 0.930595i \(0.619290\pi\)
\(788\) −20.1726 −0.718619
\(789\) −23.9631 −0.853110
\(790\) 17.2324 0.613102
\(791\) 11.7535 0.417908
\(792\) 0.834581 0.0296555
\(793\) 32.1866 1.14298
\(794\) 1.63192 0.0579148
\(795\) 17.8144 0.631813
\(796\) −9.27373 −0.328699
\(797\) 24.4468 0.865949 0.432974 0.901406i \(-0.357464\pi\)
0.432974 + 0.901406i \(0.357464\pi\)
\(798\) 5.04390 0.178552
\(799\) −16.0189 −0.566708
\(800\) 0.775936 0.0274335
\(801\) −7.91837 −0.279782
\(802\) −30.1398 −1.06427
\(803\) 3.68683 0.130105
\(804\) −11.0500 −0.389704
\(805\) 6.71799 0.236778
\(806\) −9.34560 −0.329185
\(807\) 16.8854 0.594394
\(808\) −12.7730 −0.449352
\(809\) −24.5331 −0.862537 −0.431268 0.902224i \(-0.641934\pi\)
−0.431268 + 0.902224i \(0.641934\pi\)
\(810\) 23.1169 0.812246
\(811\) 12.4640 0.437670 0.218835 0.975762i \(-0.429774\pi\)
0.218835 + 0.975762i \(0.429774\pi\)
\(812\) −1.95728 −0.0686870
\(813\) 49.9303 1.75113
\(814\) 1.93395 0.0677850
\(815\) 32.8223 1.14971
\(816\) −3.22886 −0.113033
\(817\) −9.81000 −0.343209
\(818\) 1.10386 0.0385955
\(819\) 10.3066 0.360141
\(820\) −13.8482 −0.483599
\(821\) 28.4681 0.993544 0.496772 0.867881i \(-0.334519\pi\)
0.496772 + 0.867881i \(0.334519\pi\)
\(822\) −32.8237 −1.14486
\(823\) 3.96161 0.138093 0.0690465 0.997613i \(-0.478004\pi\)
0.0690465 + 0.997613i \(0.478004\pi\)
\(824\) −19.3648 −0.674606
\(825\) −0.892310 −0.0310663
\(826\) 5.77829 0.201053
\(827\) 0.711426 0.0247387 0.0123693 0.999923i \(-0.496063\pi\)
0.0123693 + 0.999923i \(0.496063\pi\)
\(828\) −3.20658 −0.111436
\(829\) 21.9546 0.762516 0.381258 0.924469i \(-0.375491\pi\)
0.381258 + 0.924469i \(0.375491\pi\)
\(830\) −5.39525 −0.187272
\(831\) −69.9745 −2.42739
\(832\) −4.22122 −0.146345
\(833\) −6.83027 −0.236655
\(834\) 28.5265 0.987794
\(835\) −40.8416 −1.41338
\(836\) 0.808473 0.0279616
\(837\) −6.85701 −0.237013
\(838\) 6.88494 0.237836
\(839\) 21.7355 0.750392 0.375196 0.926945i \(-0.377575\pi\)
0.375196 + 0.926945i \(0.377575\pi\)
\(840\) −6.91454 −0.238574
\(841\) −27.4608 −0.946924
\(842\) −28.8068 −0.992747
\(843\) 45.6186 1.57119
\(844\) −27.0455 −0.930944
\(845\) 9.90372 0.340698
\(846\) 16.3737 0.562941
\(847\) 16.8951 0.580524
\(848\) −4.06456 −0.139578
\(849\) 9.61067 0.329837
\(850\) 1.17485 0.0402970
\(851\) −7.43052 −0.254715
\(852\) −8.49877 −0.291163
\(853\) −39.1679 −1.34108 −0.670542 0.741871i \(-0.733939\pi\)
−0.670542 + 0.741871i \(0.733939\pi\)
\(854\) −12.0293 −0.411635
\(855\) −4.76876 −0.163088
\(856\) −12.8255 −0.438366
\(857\) 44.0786 1.50570 0.752848 0.658195i \(-0.228680\pi\)
0.752848 + 0.658195i \(0.228680\pi\)
\(858\) 4.85432 0.165724
\(859\) −15.2189 −0.519261 −0.259630 0.965708i \(-0.583601\pi\)
−0.259630 + 0.965708i \(0.583601\pi\)
\(860\) 13.4482 0.458581
\(861\) −22.6686 −0.772544
\(862\) 19.3378 0.658649
\(863\) 31.7077 1.07934 0.539672 0.841876i \(-0.318548\pi\)
0.539672 + 0.841876i \(0.318548\pi\)
\(864\) −3.09718 −0.105368
\(865\) 19.3886 0.659233
\(866\) −29.8366 −1.01389
\(867\) 31.3640 1.06518
\(868\) 3.49280 0.118553
\(869\) 4.52145 0.153380
\(870\) 5.43759 0.184352
\(871\) −21.8730 −0.741139
\(872\) 7.21852 0.244450
\(873\) 8.76406 0.296619
\(874\) −3.10627 −0.105071
\(875\) 18.7280 0.633123
\(876\) 14.5797 0.492604
\(877\) −23.6000 −0.796915 −0.398457 0.917187i \(-0.630454\pi\)
−0.398457 + 0.917187i \(0.630454\pi\)
\(878\) −13.8301 −0.466743
\(879\) 6.71296 0.226423
\(880\) −1.10831 −0.0373612
\(881\) −8.06981 −0.271879 −0.135939 0.990717i \(-0.543405\pi\)
−0.135939 + 0.990717i \(0.543405\pi\)
\(882\) 6.98157 0.235082
\(883\) −51.0839 −1.71911 −0.859555 0.511044i \(-0.829259\pi\)
−0.859555 + 0.511044i \(0.829259\pi\)
\(884\) −6.39138 −0.214965
\(885\) −16.0529 −0.539612
\(886\) 36.7705 1.23533
\(887\) 34.5194 1.15905 0.579525 0.814955i \(-0.303238\pi\)
0.579525 + 0.814955i \(0.303238\pi\)
\(888\) 7.64791 0.256647
\(889\) −26.9573 −0.904118
\(890\) 10.5155 0.352480
\(891\) 6.06543 0.203200
\(892\) 5.51140 0.184535
\(893\) 15.8615 0.530786
\(894\) −12.6162 −0.421950
\(895\) −8.47287 −0.283217
\(896\) 1.57763 0.0527048
\(897\) −18.6510 −0.622738
\(898\) 22.8089 0.761143
\(899\) −2.74674 −0.0916088
\(900\) −1.20087 −0.0400291
\(901\) −6.15417 −0.205025
\(902\) −3.63349 −0.120982
\(903\) 22.0140 0.732579
\(904\) 7.45013 0.247788
\(905\) −21.1064 −0.701601
\(906\) 3.88025 0.128913
\(907\) −18.0288 −0.598638 −0.299319 0.954153i \(-0.596759\pi\)
−0.299319 + 0.954153i \(0.596759\pi\)
\(908\) 15.2652 0.506594
\(909\) 19.7681 0.655666
\(910\) −13.6870 −0.453720
\(911\) 23.2001 0.768652 0.384326 0.923197i \(-0.374434\pi\)
0.384326 + 0.923197i \(0.374434\pi\)
\(912\) 3.19714 0.105868
\(913\) −1.41561 −0.0468498
\(914\) −5.37626 −0.177831
\(915\) 33.4191 1.10480
\(916\) 25.1307 0.830343
\(917\) −13.9315 −0.460059
\(918\) −4.68945 −0.154775
\(919\) 28.0082 0.923907 0.461953 0.886904i \(-0.347149\pi\)
0.461953 + 0.886904i \(0.347149\pi\)
\(920\) 4.25829 0.140392
\(921\) 52.7667 1.73872
\(922\) −42.4368 −1.39758
\(923\) −16.8229 −0.553733
\(924\) −1.81424 −0.0596841
\(925\) −2.78276 −0.0914964
\(926\) −30.9487 −1.01704
\(927\) 29.9699 0.984340
\(928\) −1.24065 −0.0407262
\(929\) −49.1574 −1.61280 −0.806401 0.591369i \(-0.798588\pi\)
−0.806401 + 0.591369i \(0.798588\pi\)
\(930\) −9.70348 −0.318190
\(931\) 6.76317 0.221654
\(932\) 19.9210 0.652534
\(933\) −5.46151 −0.178802
\(934\) 4.20210 0.137497
\(935\) −1.67810 −0.0548798
\(936\) 6.53296 0.213536
\(937\) 36.8199 1.20285 0.601427 0.798928i \(-0.294599\pi\)
0.601427 + 0.798928i \(0.294599\pi\)
\(938\) 8.17475 0.266915
\(939\) −24.2100 −0.790063
\(940\) −21.7441 −0.709215
\(941\) 31.3869 1.02318 0.511592 0.859229i \(-0.329056\pi\)
0.511592 + 0.859229i \(0.329056\pi\)
\(942\) −1.33313 −0.0434357
\(943\) 13.9604 0.454612
\(944\) 3.66265 0.119209
\(945\) −10.0424 −0.326678
\(946\) 3.52856 0.114723
\(947\) −15.3089 −0.497473 −0.248737 0.968571i \(-0.580015\pi\)
−0.248737 + 0.968571i \(0.580015\pi\)
\(948\) 17.8803 0.580724
\(949\) 28.8599 0.936832
\(950\) −1.16331 −0.0377427
\(951\) −43.8768 −1.42280
\(952\) 2.38869 0.0774180
\(953\) −34.6606 −1.12277 −0.561384 0.827556i \(-0.689731\pi\)
−0.561384 + 0.827556i \(0.689731\pi\)
\(954\) 6.29050 0.203662
\(955\) 0.962406 0.0311427
\(956\) −2.38712 −0.0772049
\(957\) 1.42672 0.0461193
\(958\) −22.7379 −0.734628
\(959\) 24.2828 0.784133
\(960\) −4.38287 −0.141457
\(961\) −26.0984 −0.841884
\(962\) 15.1387 0.488090
\(963\) 19.8493 0.639636
\(964\) 14.2453 0.458810
\(965\) 6.00637 0.193352
\(966\) 6.97056 0.224274
\(967\) 38.5317 1.23909 0.619547 0.784959i \(-0.287316\pi\)
0.619547 + 0.784959i \(0.287316\pi\)
\(968\) 10.7092 0.344207
\(969\) 4.84081 0.155509
\(970\) −11.6386 −0.373691
\(971\) 30.4723 0.977903 0.488951 0.872311i \(-0.337380\pi\)
0.488951 + 0.872311i \(0.337380\pi\)
\(972\) 14.6945 0.471326
\(973\) −21.1038 −0.676556
\(974\) 0.951488 0.0304876
\(975\) −6.98486 −0.223694
\(976\) −7.62494 −0.244068
\(977\) 45.0465 1.44117 0.720583 0.693369i \(-0.243874\pi\)
0.720583 + 0.693369i \(0.243874\pi\)
\(978\) 34.0562 1.08900
\(979\) 2.75906 0.0881799
\(980\) −9.27143 −0.296165
\(981\) −11.1717 −0.356685
\(982\) 20.4819 0.653604
\(983\) −60.3253 −1.92408 −0.962039 0.272912i \(-0.912013\pi\)
−0.962039 + 0.272912i \(0.912013\pi\)
\(984\) −14.3688 −0.458060
\(985\) −41.4598 −1.32102
\(986\) −1.87847 −0.0598227
\(987\) −35.5938 −1.13296
\(988\) 6.32859 0.201339
\(989\) −13.5572 −0.431094
\(990\) 1.71527 0.0545150
\(991\) 30.2623 0.961312 0.480656 0.876909i \(-0.340399\pi\)
0.480656 + 0.876909i \(0.340399\pi\)
\(992\) 2.21396 0.0702932
\(993\) −10.8013 −0.342769
\(994\) 6.28735 0.199423
\(995\) −19.0599 −0.604238
\(996\) −5.59808 −0.177382
\(997\) −42.6460 −1.35061 −0.675306 0.737538i \(-0.735988\pi\)
−0.675306 + 0.737538i \(0.735988\pi\)
\(998\) −6.64782 −0.210433
\(999\) 11.1075 0.351425
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 \(a_p\))