Properties

Label 4017.2.a.j.1.3
Level 4017
Weight 2
Character 4017.1
Self dual Yes
Analytic conductor 32.076
Analytic rank 0
Dimension 25
CM No

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Newspace parameters

Level: \( N \) = \( 4017 = 3 \cdot 13 \cdot 103 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4017.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0759064919\)
Analytic rank: \(0\)
Dimension: \(25\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Character \(\chi\) = 4017.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.18299 q^{2} -1.00000 q^{3} +2.76546 q^{4} +2.14752 q^{5} +2.18299 q^{6} +0.603238 q^{7} -1.67100 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.18299 q^{2} -1.00000 q^{3} +2.76546 q^{4} +2.14752 q^{5} +2.18299 q^{6} +0.603238 q^{7} -1.67100 q^{8} +1.00000 q^{9} -4.68803 q^{10} -1.05632 q^{11} -2.76546 q^{12} +1.00000 q^{13} -1.31686 q^{14} -2.14752 q^{15} -1.88315 q^{16} +5.27690 q^{17} -2.18299 q^{18} +6.92975 q^{19} +5.93890 q^{20} -0.603238 q^{21} +2.30593 q^{22} -3.16152 q^{23} +1.67100 q^{24} -0.388137 q^{25} -2.18299 q^{26} -1.00000 q^{27} +1.66823 q^{28} +6.31547 q^{29} +4.68803 q^{30} +1.92623 q^{31} +7.45289 q^{32} +1.05632 q^{33} -11.5194 q^{34} +1.29547 q^{35} +2.76546 q^{36} -7.58967 q^{37} -15.1276 q^{38} -1.00000 q^{39} -3.58851 q^{40} -6.70449 q^{41} +1.31686 q^{42} +3.27034 q^{43} -2.92120 q^{44} +2.14752 q^{45} +6.90157 q^{46} +0.617887 q^{47} +1.88315 q^{48} -6.63610 q^{49} +0.847301 q^{50} -5.27690 q^{51} +2.76546 q^{52} +14.2897 q^{53} +2.18299 q^{54} -2.26847 q^{55} -1.00801 q^{56} -6.92975 q^{57} -13.7866 q^{58} +8.58769 q^{59} -5.93890 q^{60} +2.25155 q^{61} -4.20495 q^{62} +0.603238 q^{63} -12.5033 q^{64} +2.14752 q^{65} -2.30593 q^{66} +6.67280 q^{67} +14.5931 q^{68} +3.16152 q^{69} -2.82800 q^{70} +2.12217 q^{71} -1.67100 q^{72} +11.5346 q^{73} +16.5682 q^{74} +0.388137 q^{75} +19.1640 q^{76} -0.637210 q^{77} +2.18299 q^{78} +3.02621 q^{79} -4.04411 q^{80} +1.00000 q^{81} +14.6359 q^{82} +6.20971 q^{83} -1.66823 q^{84} +11.3323 q^{85} -7.13912 q^{86} -6.31547 q^{87} +1.76510 q^{88} -6.13977 q^{89} -4.68803 q^{90} +0.603238 q^{91} -8.74305 q^{92} -1.92623 q^{93} -1.34884 q^{94} +14.8818 q^{95} -7.45289 q^{96} -5.90264 q^{97} +14.4866 q^{98} -1.05632 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 25q + 6q^{2} - 25q^{3} + 28q^{4} + 7q^{5} - 6q^{6} + 17q^{7} + 21q^{8} + 25q^{9} + O(q^{10}) \) \( 25q + 6q^{2} - 25q^{3} + 28q^{4} + 7q^{5} - 6q^{6} + 17q^{7} + 21q^{8} + 25q^{9} - 6q^{10} + 21q^{11} - 28q^{12} + 25q^{13} + 10q^{14} - 7q^{15} + 30q^{16} + 14q^{17} + 6q^{18} + 12q^{19} + 24q^{20} - 17q^{21} + 3q^{22} + 41q^{23} - 21q^{24} + 30q^{25} + 6q^{26} - 25q^{27} + 14q^{28} + 22q^{29} + 6q^{30} + 14q^{31} + 28q^{32} - 21q^{33} - 11q^{34} + 14q^{35} + 28q^{36} - 6q^{37} + 16q^{38} - 25q^{39} - 34q^{40} + 33q^{41} - 10q^{42} + 35q^{43} + 45q^{44} + 7q^{45} + 3q^{46} + 48q^{47} - 30q^{48} - 4q^{49} + 7q^{50} - 14q^{51} + 28q^{52} + 18q^{53} - 6q^{54} + 10q^{55} + 32q^{56} - 12q^{57} + 33q^{58} + 46q^{59} - 24q^{60} - 19q^{61} + 5q^{62} + 17q^{63} + 29q^{64} + 7q^{65} - 3q^{66} + 16q^{67} + 20q^{68} - 41q^{69} - 43q^{70} + 60q^{71} + 21q^{72} - 14q^{73} - 50q^{74} - 30q^{75} + 59q^{77} - 6q^{78} + 7q^{79} + 32q^{80} + 25q^{81} + 18q^{82} + 23q^{83} - 14q^{84} - 9q^{85} - 9q^{86} - 22q^{87} + 23q^{88} + 10q^{89} - 6q^{90} + 17q^{91} + 69q^{92} - 14q^{93} - 30q^{94} + 81q^{95} - 28q^{96} - 10q^{97} + 55q^{98} + 21q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.18299 −1.54361 −0.771805 0.635860i \(-0.780646\pi\)
−0.771805 + 0.635860i \(0.780646\pi\)
\(3\) −1.00000 −0.577350
\(4\) 2.76546 1.38273
\(5\) 2.14752 0.960402 0.480201 0.877158i \(-0.340564\pi\)
0.480201 + 0.877158i \(0.340564\pi\)
\(6\) 2.18299 0.891203
\(7\) 0.603238 0.228002 0.114001 0.993481i \(-0.463633\pi\)
0.114001 + 0.993481i \(0.463633\pi\)
\(8\) −1.67100 −0.590786
\(9\) 1.00000 0.333333
\(10\) −4.68803 −1.48249
\(11\) −1.05632 −0.318492 −0.159246 0.987239i \(-0.550906\pi\)
−0.159246 + 0.987239i \(0.550906\pi\)
\(12\) −2.76546 −0.798320
\(13\) 1.00000 0.277350
\(14\) −1.31686 −0.351947
\(15\) −2.14752 −0.554489
\(16\) −1.88315 −0.470787
\(17\) 5.27690 1.27984 0.639918 0.768443i \(-0.278968\pi\)
0.639918 + 0.768443i \(0.278968\pi\)
\(18\) −2.18299 −0.514537
\(19\) 6.92975 1.58979 0.794897 0.606744i \(-0.207525\pi\)
0.794897 + 0.606744i \(0.207525\pi\)
\(20\) 5.93890 1.32798
\(21\) −0.603238 −0.131637
\(22\) 2.30593 0.491627
\(23\) −3.16152 −0.659222 −0.329611 0.944117i \(-0.606918\pi\)
−0.329611 + 0.944117i \(0.606918\pi\)
\(24\) 1.67100 0.341091
\(25\) −0.388137 −0.0776275
\(26\) −2.18299 −0.428120
\(27\) −1.00000 −0.192450
\(28\) 1.66823 0.315266
\(29\) 6.31547 1.17275 0.586377 0.810038i \(-0.300554\pi\)
0.586377 + 0.810038i \(0.300554\pi\)
\(30\) 4.68803 0.855914
\(31\) 1.92623 0.345962 0.172981 0.984925i \(-0.444660\pi\)
0.172981 + 0.984925i \(0.444660\pi\)
\(32\) 7.45289 1.31750
\(33\) 1.05632 0.183881
\(34\) −11.5194 −1.97557
\(35\) 1.29547 0.218974
\(36\) 2.76546 0.460910
\(37\) −7.58967 −1.24773 −0.623867 0.781530i \(-0.714439\pi\)
−0.623867 + 0.781530i \(0.714439\pi\)
\(38\) −15.1276 −2.45402
\(39\) −1.00000 −0.160128
\(40\) −3.58851 −0.567392
\(41\) −6.70449 −1.04707 −0.523533 0.852006i \(-0.675386\pi\)
−0.523533 + 0.852006i \(0.675386\pi\)
\(42\) 1.31686 0.203197
\(43\) 3.27034 0.498721 0.249361 0.968411i \(-0.419780\pi\)
0.249361 + 0.968411i \(0.419780\pi\)
\(44\) −2.92120 −0.440388
\(45\) 2.14752 0.320134
\(46\) 6.90157 1.01758
\(47\) 0.617887 0.0901281 0.0450641 0.998984i \(-0.485651\pi\)
0.0450641 + 0.998984i \(0.485651\pi\)
\(48\) 1.88315 0.271809
\(49\) −6.63610 −0.948015
\(50\) 0.847301 0.119827
\(51\) −5.27690 −0.738913
\(52\) 2.76546 0.383500
\(53\) 14.2897 1.96284 0.981421 0.191867i \(-0.0614542\pi\)
0.981421 + 0.191867i \(0.0614542\pi\)
\(54\) 2.18299 0.297068
\(55\) −2.26847 −0.305880
\(56\) −1.00801 −0.134701
\(57\) −6.92975 −0.917868
\(58\) −13.7866 −1.81027
\(59\) 8.58769 1.11802 0.559011 0.829160i \(-0.311181\pi\)
0.559011 + 0.829160i \(0.311181\pi\)
\(60\) −5.93890 −0.766708
\(61\) 2.25155 0.288282 0.144141 0.989557i \(-0.453958\pi\)
0.144141 + 0.989557i \(0.453958\pi\)
\(62\) −4.20495 −0.534030
\(63\) 0.603238 0.0760008
\(64\) −12.5033 −1.56291
\(65\) 2.14752 0.266368
\(66\) −2.30593 −0.283841
\(67\) 6.67280 0.815213 0.407606 0.913158i \(-0.366364\pi\)
0.407606 + 0.913158i \(0.366364\pi\)
\(68\) 14.5931 1.76967
\(69\) 3.16152 0.380602
\(70\) −2.82800 −0.338011
\(71\) 2.12217 0.251855 0.125927 0.992039i \(-0.459809\pi\)
0.125927 + 0.992039i \(0.459809\pi\)
\(72\) −1.67100 −0.196929
\(73\) 11.5346 1.35002 0.675010 0.737808i \(-0.264139\pi\)
0.675010 + 0.737808i \(0.264139\pi\)
\(74\) 16.5682 1.92601
\(75\) 0.388137 0.0448182
\(76\) 19.1640 2.19826
\(77\) −0.637210 −0.0726169
\(78\) 2.18299 0.247175
\(79\) 3.02621 0.340475 0.170237 0.985403i \(-0.445547\pi\)
0.170237 + 0.985403i \(0.445547\pi\)
\(80\) −4.04411 −0.452145
\(81\) 1.00000 0.111111
\(82\) 14.6359 1.61626
\(83\) 6.20971 0.681604 0.340802 0.940135i \(-0.389301\pi\)
0.340802 + 0.940135i \(0.389301\pi\)
\(84\) −1.66823 −0.182019
\(85\) 11.3323 1.22916
\(86\) −7.13912 −0.769831
\(87\) −6.31547 −0.677090
\(88\) 1.76510 0.188160
\(89\) −6.13977 −0.650815 −0.325407 0.945574i \(-0.605501\pi\)
−0.325407 + 0.945574i \(0.605501\pi\)
\(90\) −4.68803 −0.494162
\(91\) 0.603238 0.0632365
\(92\) −8.74305 −0.911526
\(93\) −1.92623 −0.199741
\(94\) −1.34884 −0.139123
\(95\) 14.8818 1.52684
\(96\) −7.45289 −0.760658
\(97\) −5.90264 −0.599323 −0.299661 0.954046i \(-0.596874\pi\)
−0.299661 + 0.954046i \(0.596874\pi\)
\(98\) 14.4866 1.46336
\(99\) −1.05632 −0.106164
\(100\) −1.07338 −0.107338
\(101\) 7.67214 0.763407 0.381703 0.924285i \(-0.375338\pi\)
0.381703 + 0.924285i \(0.375338\pi\)
\(102\) 11.5194 1.14059
\(103\) −1.00000 −0.0985329
\(104\) −1.67100 −0.163855
\(105\) −1.29547 −0.126425
\(106\) −31.1943 −3.02986
\(107\) 14.0593 1.35916 0.679582 0.733599i \(-0.262161\pi\)
0.679582 + 0.733599i \(0.262161\pi\)
\(108\) −2.76546 −0.266107
\(109\) −14.1233 −1.35276 −0.676381 0.736552i \(-0.736453\pi\)
−0.676381 + 0.736552i \(0.736453\pi\)
\(110\) 4.95205 0.472159
\(111\) 7.58967 0.720380
\(112\) −1.13599 −0.107341
\(113\) −19.9292 −1.87478 −0.937392 0.348276i \(-0.886767\pi\)
−0.937392 + 0.348276i \(0.886767\pi\)
\(114\) 15.1276 1.41683
\(115\) −6.78943 −0.633118
\(116\) 17.4652 1.62160
\(117\) 1.00000 0.0924500
\(118\) −18.7469 −1.72579
\(119\) 3.18322 0.291806
\(120\) 3.58851 0.327584
\(121\) −9.88419 −0.898563
\(122\) −4.91512 −0.444994
\(123\) 6.70449 0.604523
\(124\) 5.32692 0.478372
\(125\) −11.5712 −1.03496
\(126\) −1.31686 −0.117316
\(127\) −7.73839 −0.686671 −0.343336 0.939213i \(-0.611557\pi\)
−0.343336 + 0.939213i \(0.611557\pi\)
\(128\) 12.3889 1.09503
\(129\) −3.27034 −0.287937
\(130\) −4.68803 −0.411168
\(131\) 5.61500 0.490585 0.245293 0.969449i \(-0.421116\pi\)
0.245293 + 0.969449i \(0.421116\pi\)
\(132\) 2.92120 0.254258
\(133\) 4.18029 0.362477
\(134\) −14.5667 −1.25837
\(135\) −2.14752 −0.184830
\(136\) −8.81767 −0.756109
\(137\) −11.3859 −0.972766 −0.486383 0.873746i \(-0.661684\pi\)
−0.486383 + 0.873746i \(0.661684\pi\)
\(138\) −6.90157 −0.587501
\(139\) 12.3445 1.04704 0.523522 0.852012i \(-0.324618\pi\)
0.523522 + 0.852012i \(0.324618\pi\)
\(140\) 3.58257 0.302782
\(141\) −0.617887 −0.0520355
\(142\) −4.63267 −0.388765
\(143\) −1.05632 −0.0883337
\(144\) −1.88315 −0.156929
\(145\) 13.5626 1.12632
\(146\) −25.1799 −2.08391
\(147\) 6.63610 0.547337
\(148\) −20.9889 −1.72528
\(149\) 5.16781 0.423364 0.211682 0.977339i \(-0.432106\pi\)
0.211682 + 0.977339i \(0.432106\pi\)
\(150\) −0.847301 −0.0691819
\(151\) −9.03652 −0.735382 −0.367691 0.929948i \(-0.619852\pi\)
−0.367691 + 0.929948i \(0.619852\pi\)
\(152\) −11.5796 −0.939228
\(153\) 5.27690 0.426612
\(154\) 1.39103 0.112092
\(155\) 4.13663 0.332262
\(156\) −2.76546 −0.221414
\(157\) −7.10949 −0.567399 −0.283700 0.958913i \(-0.591562\pi\)
−0.283700 + 0.958913i \(0.591562\pi\)
\(158\) −6.60619 −0.525560
\(159\) −14.2897 −1.13325
\(160\) 16.0053 1.26533
\(161\) −1.90715 −0.150304
\(162\) −2.18299 −0.171512
\(163\) −2.59103 −0.202945 −0.101472 0.994838i \(-0.532355\pi\)
−0.101472 + 0.994838i \(0.532355\pi\)
\(164\) −18.5410 −1.44781
\(165\) 2.26847 0.176600
\(166\) −13.5558 −1.05213
\(167\) 14.1263 1.09312 0.546562 0.837418i \(-0.315936\pi\)
0.546562 + 0.837418i \(0.315936\pi\)
\(168\) 1.00801 0.0777695
\(169\) 1.00000 0.0769231
\(170\) −24.7383 −1.89734
\(171\) 6.92975 0.529931
\(172\) 9.04398 0.689597
\(173\) 20.8676 1.58654 0.793269 0.608872i \(-0.208378\pi\)
0.793269 + 0.608872i \(0.208378\pi\)
\(174\) 13.7866 1.04516
\(175\) −0.234139 −0.0176993
\(176\) 1.98920 0.149942
\(177\) −8.58769 −0.645490
\(178\) 13.4031 1.00460
\(179\) 3.05765 0.228540 0.114270 0.993450i \(-0.463547\pi\)
0.114270 + 0.993450i \(0.463547\pi\)
\(180\) 5.93890 0.442659
\(181\) −18.0793 −1.34382 −0.671912 0.740631i \(-0.734527\pi\)
−0.671912 + 0.740631i \(0.734527\pi\)
\(182\) −1.31686 −0.0976125
\(183\) −2.25155 −0.166440
\(184\) 5.28288 0.389459
\(185\) −16.2990 −1.19833
\(186\) 4.20495 0.308322
\(187\) −5.57408 −0.407617
\(188\) 1.70874 0.124623
\(189\) −0.603238 −0.0438791
\(190\) −32.4869 −2.35685
\(191\) −11.8236 −0.855525 −0.427763 0.903891i \(-0.640698\pi\)
−0.427763 + 0.903891i \(0.640698\pi\)
\(192\) 12.5033 0.902349
\(193\) 7.57274 0.545098 0.272549 0.962142i \(-0.412133\pi\)
0.272549 + 0.962142i \(0.412133\pi\)
\(194\) 12.8854 0.925120
\(195\) −2.14752 −0.153787
\(196\) −18.3519 −1.31085
\(197\) −20.4137 −1.45442 −0.727208 0.686418i \(-0.759182\pi\)
−0.727208 + 0.686418i \(0.759182\pi\)
\(198\) 2.30593 0.163876
\(199\) −20.4533 −1.44990 −0.724948 0.688803i \(-0.758136\pi\)
−0.724948 + 0.688803i \(0.758136\pi\)
\(200\) 0.648576 0.0458612
\(201\) −6.67280 −0.470663
\(202\) −16.7482 −1.17840
\(203\) 3.80973 0.267391
\(204\) −14.5931 −1.02172
\(205\) −14.3981 −1.00560
\(206\) 2.18299 0.152096
\(207\) −3.16152 −0.219741
\(208\) −1.88315 −0.130573
\(209\) −7.32001 −0.506336
\(210\) 2.82800 0.195150
\(211\) −10.0266 −0.690263 −0.345132 0.938554i \(-0.612166\pi\)
−0.345132 + 0.938554i \(0.612166\pi\)
\(212\) 39.5176 2.71408
\(213\) −2.12217 −0.145408
\(214\) −30.6914 −2.09802
\(215\) 7.02313 0.478973
\(216\) 1.67100 0.113697
\(217\) 1.16198 0.0788801
\(218\) 30.8310 2.08814
\(219\) −11.5346 −0.779435
\(220\) −6.27336 −0.422950
\(221\) 5.27690 0.354963
\(222\) −16.5682 −1.11199
\(223\) −7.81693 −0.523460 −0.261730 0.965141i \(-0.584293\pi\)
−0.261730 + 0.965141i \(0.584293\pi\)
\(224\) 4.49587 0.300393
\(225\) −0.388137 −0.0258758
\(226\) 43.5054 2.89393
\(227\) 17.4432 1.15774 0.578872 0.815418i \(-0.303493\pi\)
0.578872 + 0.815418i \(0.303493\pi\)
\(228\) −19.1640 −1.26916
\(229\) 8.39787 0.554947 0.277473 0.960733i \(-0.410503\pi\)
0.277473 + 0.960733i \(0.410503\pi\)
\(230\) 14.8213 0.977287
\(231\) 0.637210 0.0419254
\(232\) −10.5531 −0.692847
\(233\) 27.1373 1.77782 0.888911 0.458080i \(-0.151463\pi\)
0.888911 + 0.458080i \(0.151463\pi\)
\(234\) −2.18299 −0.142707
\(235\) 1.32693 0.0865593
\(236\) 23.7489 1.54592
\(237\) −3.02621 −0.196573
\(238\) −6.94896 −0.450434
\(239\) 17.3407 1.12168 0.560839 0.827925i \(-0.310479\pi\)
0.560839 + 0.827925i \(0.310479\pi\)
\(240\) 4.04411 0.261046
\(241\) −11.9353 −0.768822 −0.384411 0.923162i \(-0.625595\pi\)
−0.384411 + 0.923162i \(0.625595\pi\)
\(242\) 21.5771 1.38703
\(243\) −1.00000 −0.0641500
\(244\) 6.22658 0.398616
\(245\) −14.2512 −0.910476
\(246\) −14.6359 −0.933148
\(247\) 6.92975 0.440929
\(248\) −3.21873 −0.204389
\(249\) −6.20971 −0.393524
\(250\) 25.2598 1.59757
\(251\) 14.6678 0.925823 0.462911 0.886405i \(-0.346805\pi\)
0.462911 + 0.886405i \(0.346805\pi\)
\(252\) 1.66823 0.105089
\(253\) 3.33956 0.209957
\(254\) 16.8929 1.05995
\(255\) −11.3323 −0.709654
\(256\) −2.03821 −0.127388
\(257\) −12.1143 −0.755669 −0.377835 0.925873i \(-0.623331\pi\)
−0.377835 + 0.925873i \(0.623331\pi\)
\(258\) 7.13912 0.444462
\(259\) −4.57838 −0.284487
\(260\) 5.93890 0.368315
\(261\) 6.31547 0.390918
\(262\) −12.2575 −0.757272
\(263\) 14.7217 0.907779 0.453889 0.891058i \(-0.350036\pi\)
0.453889 + 0.891058i \(0.350036\pi\)
\(264\) −1.76510 −0.108634
\(265\) 30.6875 1.88512
\(266\) −9.12554 −0.559523
\(267\) 6.13977 0.375748
\(268\) 18.4534 1.12722
\(269\) 26.8565 1.63747 0.818733 0.574174i \(-0.194677\pi\)
0.818733 + 0.574174i \(0.194677\pi\)
\(270\) 4.68803 0.285305
\(271\) 18.3421 1.11420 0.557101 0.830445i \(-0.311914\pi\)
0.557101 + 0.830445i \(0.311914\pi\)
\(272\) −9.93718 −0.602530
\(273\) −0.603238 −0.0365096
\(274\) 24.8554 1.50157
\(275\) 0.409996 0.0247237
\(276\) 8.74305 0.526270
\(277\) −21.2918 −1.27930 −0.639651 0.768666i \(-0.720921\pi\)
−0.639651 + 0.768666i \(0.720921\pi\)
\(278\) −26.9479 −1.61623
\(279\) 1.92623 0.115321
\(280\) −2.16472 −0.129367
\(281\) −32.8578 −1.96013 −0.980067 0.198668i \(-0.936339\pi\)
−0.980067 + 0.198668i \(0.936339\pi\)
\(282\) 1.34884 0.0803225
\(283\) −14.5898 −0.867276 −0.433638 0.901087i \(-0.642770\pi\)
−0.433638 + 0.901087i \(0.642770\pi\)
\(284\) 5.86876 0.348247
\(285\) −14.8818 −0.881522
\(286\) 2.30593 0.136353
\(287\) −4.04440 −0.238733
\(288\) 7.45289 0.439166
\(289\) 10.8456 0.637979
\(290\) −29.6071 −1.73859
\(291\) 5.90264 0.346019
\(292\) 31.8984 1.86671
\(293\) 22.6706 1.32443 0.662215 0.749314i \(-0.269617\pi\)
0.662215 + 0.749314i \(0.269617\pi\)
\(294\) −14.4866 −0.844874
\(295\) 18.4423 1.07375
\(296\) 12.6823 0.737144
\(297\) 1.05632 0.0612937
\(298\) −11.2813 −0.653508
\(299\) −3.16152 −0.182835
\(300\) 1.07338 0.0619716
\(301\) 1.97279 0.113710
\(302\) 19.7267 1.13514
\(303\) −7.67214 −0.440753
\(304\) −13.0497 −0.748454
\(305\) 4.83526 0.276866
\(306\) −11.5194 −0.658522
\(307\) 18.6881 1.06659 0.533293 0.845930i \(-0.320954\pi\)
0.533293 + 0.845930i \(0.320954\pi\)
\(308\) −1.76218 −0.100410
\(309\) 1.00000 0.0568880
\(310\) −9.03024 −0.512883
\(311\) −10.0778 −0.571460 −0.285730 0.958310i \(-0.592236\pi\)
−0.285730 + 0.958310i \(0.592236\pi\)
\(312\) 1.67100 0.0946015
\(313\) 3.34692 0.189179 0.0945895 0.995516i \(-0.469846\pi\)
0.0945895 + 0.995516i \(0.469846\pi\)
\(314\) 15.5200 0.875843
\(315\) 1.29547 0.0729914
\(316\) 8.36886 0.470785
\(317\) −1.89021 −0.106165 −0.0530824 0.998590i \(-0.516905\pi\)
−0.0530824 + 0.998590i \(0.516905\pi\)
\(318\) 31.1943 1.74929
\(319\) −6.67114 −0.373512
\(320\) −26.8512 −1.50103
\(321\) −14.0593 −0.784714
\(322\) 4.16329 0.232011
\(323\) 36.5676 2.03467
\(324\) 2.76546 0.153637
\(325\) −0.388137 −0.0215300
\(326\) 5.65620 0.313268
\(327\) 14.1233 0.781018
\(328\) 11.2032 0.618592
\(329\) 0.372733 0.0205494
\(330\) −4.95205 −0.272601
\(331\) −22.6947 −1.24741 −0.623706 0.781659i \(-0.714374\pi\)
−0.623706 + 0.781659i \(0.714374\pi\)
\(332\) 17.1727 0.942475
\(333\) −7.58967 −0.415911
\(334\) −30.8376 −1.68736
\(335\) 14.3300 0.782932
\(336\) 1.13599 0.0619731
\(337\) 34.4444 1.87631 0.938153 0.346220i \(-0.112535\pi\)
0.938153 + 0.346220i \(0.112535\pi\)
\(338\) −2.18299 −0.118739
\(339\) 19.9292 1.08241
\(340\) 31.3389 1.69959
\(341\) −2.03471 −0.110186
\(342\) −15.1276 −0.818007
\(343\) −8.22581 −0.444152
\(344\) −5.46472 −0.294638
\(345\) 6.78943 0.365531
\(346\) −45.5539 −2.44899
\(347\) −19.0816 −1.02435 −0.512176 0.858881i \(-0.671160\pi\)
−0.512176 + 0.858881i \(0.671160\pi\)
\(348\) −17.4652 −0.936232
\(349\) 21.9421 1.17453 0.587267 0.809393i \(-0.300204\pi\)
0.587267 + 0.809393i \(0.300204\pi\)
\(350\) 0.511124 0.0273207
\(351\) −1.00000 −0.0533761
\(352\) −7.87262 −0.419612
\(353\) −5.60304 −0.298220 −0.149110 0.988821i \(-0.547641\pi\)
−0.149110 + 0.988821i \(0.547641\pi\)
\(354\) 18.7469 0.996384
\(355\) 4.55740 0.241882
\(356\) −16.9793 −0.899901
\(357\) −3.18322 −0.168474
\(358\) −6.67484 −0.352776
\(359\) 13.9845 0.738075 0.369038 0.929414i \(-0.379687\pi\)
0.369038 + 0.929414i \(0.379687\pi\)
\(360\) −3.58851 −0.189131
\(361\) 29.0214 1.52744
\(362\) 39.4670 2.07434
\(363\) 9.88419 0.518786
\(364\) 1.66823 0.0874390
\(365\) 24.7708 1.29656
\(366\) 4.91512 0.256918
\(367\) −7.73232 −0.403624 −0.201812 0.979424i \(-0.564683\pi\)
−0.201812 + 0.979424i \(0.564683\pi\)
\(368\) 5.95360 0.310353
\(369\) −6.70449 −0.349022
\(370\) 35.5806 1.84975
\(371\) 8.62009 0.447533
\(372\) −5.32692 −0.276188
\(373\) −24.1629 −1.25111 −0.625555 0.780180i \(-0.715127\pi\)
−0.625555 + 0.780180i \(0.715127\pi\)
\(374\) 12.1682 0.629201
\(375\) 11.5712 0.597532
\(376\) −1.03249 −0.0532465
\(377\) 6.31547 0.325263
\(378\) 1.31686 0.0677322
\(379\) 8.27854 0.425240 0.212620 0.977135i \(-0.431800\pi\)
0.212620 + 0.977135i \(0.431800\pi\)
\(380\) 41.1551 2.11121
\(381\) 7.73839 0.396450
\(382\) 25.8108 1.32060
\(383\) 14.0812 0.719516 0.359758 0.933046i \(-0.382859\pi\)
0.359758 + 0.933046i \(0.382859\pi\)
\(384\) −12.3889 −0.632217
\(385\) −1.36843 −0.0697414
\(386\) −16.5313 −0.841418
\(387\) 3.27034 0.166240
\(388\) −16.3235 −0.828702
\(389\) −1.09755 −0.0556480 −0.0278240 0.999613i \(-0.508858\pi\)
−0.0278240 + 0.999613i \(0.508858\pi\)
\(390\) 4.68803 0.237388
\(391\) −16.6830 −0.843695
\(392\) 11.0889 0.560074
\(393\) −5.61500 −0.283240
\(394\) 44.5629 2.24505
\(395\) 6.49885 0.326993
\(396\) −2.92120 −0.146796
\(397\) 30.4637 1.52893 0.764464 0.644667i \(-0.223004\pi\)
0.764464 + 0.644667i \(0.223004\pi\)
\(398\) 44.6494 2.23807
\(399\) −4.18029 −0.209276
\(400\) 0.730920 0.0365460
\(401\) 6.94279 0.346706 0.173353 0.984860i \(-0.444540\pi\)
0.173353 + 0.984860i \(0.444540\pi\)
\(402\) 14.5667 0.726520
\(403\) 1.92623 0.0959525
\(404\) 21.2170 1.05559
\(405\) 2.14752 0.106711
\(406\) −8.31662 −0.412747
\(407\) 8.01710 0.397393
\(408\) 8.81767 0.436540
\(409\) −0.773582 −0.0382512 −0.0191256 0.999817i \(-0.506088\pi\)
−0.0191256 + 0.999817i \(0.506088\pi\)
\(410\) 31.4309 1.55226
\(411\) 11.3859 0.561627
\(412\) −2.76546 −0.136244
\(413\) 5.18042 0.254912
\(414\) 6.90157 0.339194
\(415\) 13.3355 0.654614
\(416\) 7.45289 0.365408
\(417\) −12.3445 −0.604511
\(418\) 15.9795 0.781585
\(419\) 27.6118 1.34892 0.674462 0.738310i \(-0.264376\pi\)
0.674462 + 0.738310i \(0.264376\pi\)
\(420\) −3.58257 −0.174811
\(421\) 26.8931 1.31069 0.655344 0.755330i \(-0.272524\pi\)
0.655344 + 0.755330i \(0.272524\pi\)
\(422\) 21.8881 1.06550
\(423\) 0.617887 0.0300427
\(424\) −23.8780 −1.15962
\(425\) −2.04816 −0.0993504
\(426\) 4.63267 0.224454
\(427\) 1.35822 0.0657289
\(428\) 38.8805 1.87936
\(429\) 1.05632 0.0509995
\(430\) −15.3314 −0.739348
\(431\) 20.8097 1.00237 0.501185 0.865340i \(-0.332898\pi\)
0.501185 + 0.865340i \(0.332898\pi\)
\(432\) 1.88315 0.0906030
\(433\) 4.03399 0.193861 0.0969305 0.995291i \(-0.469098\pi\)
0.0969305 + 0.995291i \(0.469098\pi\)
\(434\) −2.53659 −0.121760
\(435\) −13.5626 −0.650278
\(436\) −39.0573 −1.87051
\(437\) −21.9085 −1.04803
\(438\) 25.1799 1.20314
\(439\) −8.85604 −0.422676 −0.211338 0.977413i \(-0.567782\pi\)
−0.211338 + 0.977413i \(0.567782\pi\)
\(440\) 3.79060 0.180710
\(441\) −6.63610 −0.316005
\(442\) −11.5194 −0.547923
\(443\) 35.3295 1.67855 0.839277 0.543704i \(-0.182979\pi\)
0.839277 + 0.543704i \(0.182979\pi\)
\(444\) 20.9889 0.996091
\(445\) −13.1853 −0.625044
\(446\) 17.0643 0.808018
\(447\) −5.16781 −0.244429
\(448\) −7.54248 −0.356348
\(449\) −13.7652 −0.649619 −0.324810 0.945779i \(-0.605300\pi\)
−0.324810 + 0.945779i \(0.605300\pi\)
\(450\) 0.847301 0.0399422
\(451\) 7.08207 0.333481
\(452\) −55.1135 −2.59232
\(453\) 9.03652 0.424573
\(454\) −38.0783 −1.78710
\(455\) 1.29547 0.0607325
\(456\) 11.5796 0.542264
\(457\) −5.99230 −0.280308 −0.140154 0.990130i \(-0.544760\pi\)
−0.140154 + 0.990130i \(0.544760\pi\)
\(458\) −18.3325 −0.856621
\(459\) −5.27690 −0.246304
\(460\) −18.7759 −0.875431
\(461\) −30.2105 −1.40704 −0.703521 0.710675i \(-0.748390\pi\)
−0.703521 + 0.710675i \(0.748390\pi\)
\(462\) −1.39103 −0.0647164
\(463\) −3.79915 −0.176561 −0.0882807 0.996096i \(-0.528137\pi\)
−0.0882807 + 0.996096i \(0.528137\pi\)
\(464\) −11.8930 −0.552117
\(465\) −4.13663 −0.191832
\(466\) −59.2405 −2.74426
\(467\) 0.327390 0.0151498 0.00757489 0.999971i \(-0.497589\pi\)
0.00757489 + 0.999971i \(0.497589\pi\)
\(468\) 2.76546 0.127833
\(469\) 4.02529 0.185871
\(470\) −2.89668 −0.133614
\(471\) 7.10949 0.327588
\(472\) −14.3500 −0.660512
\(473\) −3.45451 −0.158839
\(474\) 6.60619 0.303432
\(475\) −2.68970 −0.123412
\(476\) 8.80308 0.403489
\(477\) 14.2897 0.654281
\(478\) −37.8547 −1.73143
\(479\) 28.1466 1.28605 0.643024 0.765846i \(-0.277679\pi\)
0.643024 + 0.765846i \(0.277679\pi\)
\(480\) −16.0053 −0.730537
\(481\) −7.58967 −0.346059
\(482\) 26.0548 1.18676
\(483\) 1.90715 0.0867782
\(484\) −27.3344 −1.24247
\(485\) −12.6761 −0.575591
\(486\) 2.18299 0.0990226
\(487\) 34.7053 1.57265 0.786323 0.617815i \(-0.211982\pi\)
0.786323 + 0.617815i \(0.211982\pi\)
\(488\) −3.76233 −0.170313
\(489\) 2.59103 0.117170
\(490\) 31.1103 1.40542
\(491\) −30.6696 −1.38410 −0.692049 0.721851i \(-0.743292\pi\)
−0.692049 + 0.721851i \(0.743292\pi\)
\(492\) 18.5410 0.835893
\(493\) 33.3261 1.50093
\(494\) −15.1276 −0.680623
\(495\) −2.26847 −0.101960
\(496\) −3.62738 −0.162874
\(497\) 1.28017 0.0574235
\(498\) 13.5558 0.607448
\(499\) −11.0663 −0.495394 −0.247697 0.968838i \(-0.579674\pi\)
−0.247697 + 0.968838i \(0.579674\pi\)
\(500\) −31.9996 −1.43106
\(501\) −14.1263 −0.631116
\(502\) −32.0197 −1.42911
\(503\) 5.48152 0.244409 0.122204 0.992505i \(-0.461004\pi\)
0.122204 + 0.992505i \(0.461004\pi\)
\(504\) −1.00801 −0.0449002
\(505\) 16.4761 0.733177
\(506\) −7.29024 −0.324091
\(507\) −1.00000 −0.0444116
\(508\) −21.4002 −0.949481
\(509\) −7.49438 −0.332183 −0.166091 0.986110i \(-0.553115\pi\)
−0.166091 + 0.986110i \(0.553115\pi\)
\(510\) 24.7383 1.09543
\(511\) 6.95810 0.307808
\(512\) −20.3284 −0.898395
\(513\) −6.92975 −0.305956
\(514\) 26.4454 1.16646
\(515\) −2.14752 −0.0946312
\(516\) −9.04398 −0.398139
\(517\) −0.652685 −0.0287050
\(518\) 9.99457 0.439136
\(519\) −20.8676 −0.915988
\(520\) −3.58851 −0.157366
\(521\) −28.3150 −1.24050 −0.620251 0.784403i \(-0.712969\pi\)
−0.620251 + 0.784403i \(0.712969\pi\)
\(522\) −13.7866 −0.603425
\(523\) 33.1848 1.45107 0.725535 0.688186i \(-0.241593\pi\)
0.725535 + 0.688186i \(0.241593\pi\)
\(524\) 15.5281 0.678347
\(525\) 0.234139 0.0102187
\(526\) −32.1374 −1.40126
\(527\) 10.1645 0.442774
\(528\) −1.98920 −0.0865689
\(529\) −13.0048 −0.565427
\(530\) −66.9906 −2.90989
\(531\) 8.58769 0.372674
\(532\) 11.5604 0.501208
\(533\) −6.70449 −0.290404
\(534\) −13.4031 −0.580008
\(535\) 30.1927 1.30534
\(536\) −11.1502 −0.481616
\(537\) −3.05765 −0.131948
\(538\) −58.6275 −2.52761
\(539\) 7.00983 0.301935
\(540\) −5.93890 −0.255569
\(541\) 5.17839 0.222636 0.111318 0.993785i \(-0.464493\pi\)
0.111318 + 0.993785i \(0.464493\pi\)
\(542\) −40.0406 −1.71989
\(543\) 18.0793 0.775858
\(544\) 39.3281 1.68618
\(545\) −30.3300 −1.29920
\(546\) 1.31686 0.0563566
\(547\) 19.9967 0.854997 0.427498 0.904016i \(-0.359395\pi\)
0.427498 + 0.904016i \(0.359395\pi\)
\(548\) −31.4874 −1.34507
\(549\) 2.25155 0.0960939
\(550\) −0.895019 −0.0381637
\(551\) 43.7646 1.86444
\(552\) −5.28288 −0.224854
\(553\) 1.82552 0.0776291
\(554\) 46.4799 1.97474
\(555\) 16.2990 0.691854
\(556\) 34.1381 1.44778
\(557\) −28.0503 −1.18853 −0.594265 0.804269i \(-0.702557\pi\)
−0.594265 + 0.804269i \(0.702557\pi\)
\(558\) −4.20495 −0.178010
\(559\) 3.27034 0.138320
\(560\) −2.43956 −0.103090
\(561\) 5.57408 0.235338
\(562\) 71.7284 3.02568
\(563\) −35.5708 −1.49913 −0.749565 0.661930i \(-0.769737\pi\)
−0.749565 + 0.661930i \(0.769737\pi\)
\(564\) −1.70874 −0.0719511
\(565\) −42.7985 −1.80055
\(566\) 31.8495 1.33873
\(567\) 0.603238 0.0253336
\(568\) −3.54613 −0.148792
\(569\) −12.8128 −0.537142 −0.268571 0.963260i \(-0.586551\pi\)
−0.268571 + 0.963260i \(0.586551\pi\)
\(570\) 32.4869 1.36073
\(571\) −2.65151 −0.110962 −0.0554811 0.998460i \(-0.517669\pi\)
−0.0554811 + 0.998460i \(0.517669\pi\)
\(572\) −2.92120 −0.122142
\(573\) 11.8236 0.493938
\(574\) 8.82890 0.368511
\(575\) 1.22710 0.0511737
\(576\) −12.5033 −0.520972
\(577\) 33.7490 1.40499 0.702495 0.711689i \(-0.252069\pi\)
0.702495 + 0.711689i \(0.252069\pi\)
\(578\) −23.6760 −0.984790
\(579\) −7.57274 −0.314712
\(580\) 37.5069 1.55739
\(581\) 3.74593 0.155407
\(582\) −12.8854 −0.534118
\(583\) −15.0945 −0.625149
\(584\) −19.2742 −0.797574
\(585\) 2.14752 0.0887892
\(586\) −49.4897 −2.04440
\(587\) 3.72873 0.153901 0.0769505 0.997035i \(-0.475482\pi\)
0.0769505 + 0.997035i \(0.475482\pi\)
\(588\) 18.3519 0.756819
\(589\) 13.3483 0.550008
\(590\) −40.2593 −1.65745
\(591\) 20.4137 0.839707
\(592\) 14.2925 0.587417
\(593\) 32.6347 1.34015 0.670074 0.742294i \(-0.266262\pi\)
0.670074 + 0.742294i \(0.266262\pi\)
\(594\) −2.30593 −0.0946136
\(595\) 6.83605 0.280251
\(596\) 14.2914 0.585398
\(597\) 20.4533 0.837098
\(598\) 6.90157 0.282226
\(599\) −37.1180 −1.51660 −0.758300 0.651905i \(-0.773970\pi\)
−0.758300 + 0.651905i \(0.773970\pi\)
\(600\) −0.648576 −0.0264780
\(601\) −1.54003 −0.0628192 −0.0314096 0.999507i \(-0.510000\pi\)
−0.0314096 + 0.999507i \(0.510000\pi\)
\(602\) −4.30659 −0.175523
\(603\) 6.67280 0.271738
\(604\) −24.9901 −1.01683
\(605\) −21.2266 −0.862982
\(606\) 16.7482 0.680351
\(607\) 33.7817 1.37116 0.685578 0.727999i \(-0.259550\pi\)
0.685578 + 0.727999i \(0.259550\pi\)
\(608\) 51.6467 2.09455
\(609\) −3.80973 −0.154378
\(610\) −10.5553 −0.427374
\(611\) 0.617887 0.0249970
\(612\) 14.5931 0.589889
\(613\) 32.0731 1.29542 0.647710 0.761887i \(-0.275727\pi\)
0.647710 + 0.761887i \(0.275727\pi\)
\(614\) −40.7960 −1.64639
\(615\) 14.3981 0.580586
\(616\) 1.06478 0.0429010
\(617\) 42.7972 1.72295 0.861475 0.507799i \(-0.169541\pi\)
0.861475 + 0.507799i \(0.169541\pi\)
\(618\) −2.18299 −0.0878129
\(619\) −38.6834 −1.55482 −0.777409 0.628995i \(-0.783467\pi\)
−0.777409 + 0.628995i \(0.783467\pi\)
\(620\) 11.4397 0.459429
\(621\) 3.16152 0.126867
\(622\) 21.9998 0.882112
\(623\) −3.70374 −0.148387
\(624\) 1.88315 0.0753863
\(625\) −22.9087 −0.916346
\(626\) −7.30630 −0.292018
\(627\) 7.32001 0.292333
\(628\) −19.6610 −0.784560
\(629\) −40.0499 −1.59689
\(630\) −2.82800 −0.112670
\(631\) 32.0582 1.27622 0.638109 0.769946i \(-0.279717\pi\)
0.638109 + 0.769946i \(0.279717\pi\)
\(632\) −5.05678 −0.201148
\(633\) 10.0266 0.398524
\(634\) 4.12632 0.163877
\(635\) −16.6184 −0.659481
\(636\) −39.5176 −1.56698
\(637\) −6.63610 −0.262932
\(638\) 14.5631 0.576557
\(639\) 2.12217 0.0839516
\(640\) 26.6054 1.05167
\(641\) −1.75709 −0.0694010 −0.0347005 0.999398i \(-0.511048\pi\)
−0.0347005 + 0.999398i \(0.511048\pi\)
\(642\) 30.6914 1.21129
\(643\) 13.5640 0.534913 0.267457 0.963570i \(-0.413817\pi\)
0.267457 + 0.963570i \(0.413817\pi\)
\(644\) −5.27414 −0.207830
\(645\) −7.02313 −0.276535
\(646\) −79.8268 −3.14074
\(647\) 10.4286 0.409991 0.204996 0.978763i \(-0.434282\pi\)
0.204996 + 0.978763i \(0.434282\pi\)
\(648\) −1.67100 −0.0656429
\(649\) −9.07132 −0.356080
\(650\) 0.847301 0.0332339
\(651\) −1.16198 −0.0455414
\(652\) −7.16538 −0.280618
\(653\) 16.4692 0.644491 0.322246 0.946656i \(-0.395562\pi\)
0.322246 + 0.946656i \(0.395562\pi\)
\(654\) −30.8310 −1.20559
\(655\) 12.0584 0.471159
\(656\) 12.6255 0.492945
\(657\) 11.5346 0.450007
\(658\) −0.813674 −0.0317203
\(659\) −39.2008 −1.52704 −0.763522 0.645781i \(-0.776532\pi\)
−0.763522 + 0.645781i \(0.776532\pi\)
\(660\) 6.27336 0.244190
\(661\) 9.94678 0.386885 0.193442 0.981112i \(-0.438035\pi\)
0.193442 + 0.981112i \(0.438035\pi\)
\(662\) 49.5423 1.92552
\(663\) −5.27690 −0.204938
\(664\) −10.3764 −0.402682
\(665\) 8.97727 0.348124
\(666\) 16.5682 0.642005
\(667\) −19.9665 −0.773105
\(668\) 39.0657 1.51150
\(669\) 7.81693 0.302220
\(670\) −31.2823 −1.20854
\(671\) −2.37835 −0.0918153
\(672\) −4.49587 −0.173432
\(673\) 23.5980 0.909637 0.454819 0.890584i \(-0.349704\pi\)
0.454819 + 0.890584i \(0.349704\pi\)
\(674\) −75.1919 −2.89628
\(675\) 0.388137 0.0149394
\(676\) 2.76546 0.106364
\(677\) 1.96251 0.0754254 0.0377127 0.999289i \(-0.487993\pi\)
0.0377127 + 0.999289i \(0.487993\pi\)
\(678\) −43.5054 −1.67081
\(679\) −3.56070 −0.136647
\(680\) −18.9362 −0.726169
\(681\) −17.4432 −0.668424
\(682\) 4.44176 0.170084
\(683\) −11.7025 −0.447785 −0.223893 0.974614i \(-0.571877\pi\)
−0.223893 + 0.974614i \(0.571877\pi\)
\(684\) 19.1640 0.732752
\(685\) −24.4516 −0.934247
\(686\) 17.9569 0.685598
\(687\) −8.39787 −0.320399
\(688\) −6.15853 −0.234792
\(689\) 14.2897 0.544394
\(690\) −14.8213 −0.564237
\(691\) 23.7265 0.902598 0.451299 0.892373i \(-0.350961\pi\)
0.451299 + 0.892373i \(0.350961\pi\)
\(692\) 57.7086 2.19375
\(693\) −0.637210 −0.0242056
\(694\) 41.6549 1.58120
\(695\) 26.5100 1.00558
\(696\) 10.5531 0.400015
\(697\) −35.3789 −1.34007
\(698\) −47.8995 −1.81302
\(699\) −27.1373 −1.02643
\(700\) −0.647503 −0.0244733
\(701\) 28.7248 1.08492 0.542460 0.840082i \(-0.317493\pi\)
0.542460 + 0.840082i \(0.317493\pi\)
\(702\) 2.18299 0.0823918
\(703\) −52.5945 −1.98364
\(704\) 13.2075 0.497775
\(705\) −1.32693 −0.0499750
\(706\) 12.2314 0.460335
\(707\) 4.62813 0.174059
\(708\) −23.7489 −0.892539
\(709\) 8.87649 0.333364 0.166682 0.986011i \(-0.446695\pi\)
0.166682 + 0.986011i \(0.446695\pi\)
\(710\) −9.94878 −0.373371
\(711\) 3.02621 0.113492
\(712\) 10.2595 0.384492
\(713\) −6.08981 −0.228065
\(714\) 6.94896 0.260058
\(715\) −2.26847 −0.0848358
\(716\) 8.45582 0.316009
\(717\) −17.3407 −0.647601
\(718\) −30.5281 −1.13930
\(719\) 46.4119 1.73087 0.865437 0.501018i \(-0.167041\pi\)
0.865437 + 0.501018i \(0.167041\pi\)
\(720\) −4.04411 −0.150715
\(721\) −0.603238 −0.0224658
\(722\) −63.3536 −2.35778
\(723\) 11.9353 0.443880
\(724\) −49.9976 −1.85815
\(725\) −2.45127 −0.0910379
\(726\) −21.5771 −0.800803
\(727\) −1.13202 −0.0419844 −0.0209922 0.999780i \(-0.506683\pi\)
−0.0209922 + 0.999780i \(0.506683\pi\)
\(728\) −1.00801 −0.0373593
\(729\) 1.00000 0.0370370
\(730\) −54.0745 −2.00139
\(731\) 17.2572 0.638281
\(732\) −6.22658 −0.230141
\(733\) 44.7170 1.65166 0.825829 0.563920i \(-0.190707\pi\)
0.825829 + 0.563920i \(0.190707\pi\)
\(734\) 16.8796 0.623038
\(735\) 14.2512 0.525663
\(736\) −23.5624 −0.868523
\(737\) −7.04860 −0.259638
\(738\) 14.6359 0.538753
\(739\) 35.9114 1.32102 0.660512 0.750816i \(-0.270339\pi\)
0.660512 + 0.750816i \(0.270339\pi\)
\(740\) −45.0743 −1.65696
\(741\) −6.92975 −0.254571
\(742\) −18.8176 −0.690816
\(743\) −5.46113 −0.200349 −0.100175 0.994970i \(-0.531940\pi\)
−0.100175 + 0.994970i \(0.531940\pi\)
\(744\) 3.21873 0.118004
\(745\) 11.0980 0.406600
\(746\) 52.7475 1.93122
\(747\) 6.20971 0.227201
\(748\) −15.4149 −0.563624
\(749\) 8.48111 0.309893
\(750\) −25.2598 −0.922356
\(751\) −6.65506 −0.242847 −0.121423 0.992601i \(-0.538746\pi\)
−0.121423 + 0.992601i \(0.538746\pi\)
\(752\) −1.16357 −0.0424312
\(753\) −14.6678 −0.534524
\(754\) −13.7866 −0.502080
\(755\) −19.4062 −0.706262
\(756\) −1.66823 −0.0606730
\(757\) −37.9946 −1.38094 −0.690468 0.723363i \(-0.742595\pi\)
−0.690468 + 0.723363i \(0.742595\pi\)
\(758\) −18.0720 −0.656404
\(759\) −3.33956 −0.121218
\(760\) −24.8674 −0.902037
\(761\) 47.7901 1.73239 0.866196 0.499705i \(-0.166558\pi\)
0.866196 + 0.499705i \(0.166558\pi\)
\(762\) −16.8929 −0.611964
\(763\) −8.51968 −0.308433
\(764\) −32.6977 −1.18296
\(765\) 11.3323 0.409719
\(766\) −30.7392 −1.11065
\(767\) 8.58769 0.310083
\(768\) 2.03821 0.0735475
\(769\) −33.6790 −1.21449 −0.607247 0.794513i \(-0.707726\pi\)
−0.607247 + 0.794513i \(0.707726\pi\)
\(770\) 2.98726 0.107653
\(771\) 12.1143 0.436286
\(772\) 20.9421 0.753724
\(773\) −4.76372 −0.171339 −0.0856696 0.996324i \(-0.527303\pi\)
−0.0856696 + 0.996324i \(0.527303\pi\)
\(774\) −7.13912 −0.256610
\(775\) −0.747643 −0.0268561
\(776\) 9.86329 0.354072
\(777\) 4.57838 0.164248
\(778\) 2.39595 0.0858988
\(779\) −46.4604 −1.66462
\(780\) −5.93890 −0.212647
\(781\) −2.24168 −0.0802136
\(782\) 36.4189 1.30234
\(783\) −6.31547 −0.225697
\(784\) 12.4968 0.446313
\(785\) −15.2678 −0.544931
\(786\) 12.2575 0.437211
\(787\) −7.39989 −0.263778 −0.131889 0.991265i \(-0.542104\pi\)
−0.131889 + 0.991265i \(0.542104\pi\)
\(788\) −56.4533 −2.01106
\(789\) −14.7217 −0.524106
\(790\) −14.1870 −0.504749
\(791\) −12.0221 −0.427455
\(792\) 1.76510 0.0627201
\(793\) 2.25155 0.0799550
\(794\) −66.5020 −2.36007
\(795\) −30.6875 −1.08837
\(796\) −56.5628 −2.00482
\(797\) 22.3261 0.790832 0.395416 0.918502i \(-0.370600\pi\)
0.395416 + 0.918502i \(0.370600\pi\)
\(798\) 9.12554 0.323041
\(799\) 3.26053 0.115349
\(800\) −2.89275 −0.102274
\(801\) −6.13977 −0.216938
\(802\) −15.1561 −0.535179
\(803\) −12.1842 −0.429970
\(804\) −18.4534 −0.650800
\(805\) −4.09564 −0.144352
\(806\) −4.20495 −0.148113
\(807\) −26.8565 −0.945392
\(808\) −12.8201 −0.451010
\(809\) 40.3047 1.41704 0.708519 0.705691i \(-0.249363\pi\)
0.708519 + 0.705691i \(0.249363\pi\)
\(810\) −4.68803 −0.164721
\(811\) 9.23529 0.324295 0.162147 0.986767i \(-0.448158\pi\)
0.162147 + 0.986767i \(0.448158\pi\)
\(812\) 10.5357 0.369729
\(813\) −18.3421 −0.643284
\(814\) −17.5013 −0.613419
\(815\) −5.56429 −0.194909
\(816\) 9.93718 0.347871
\(817\) 22.6626 0.792864
\(818\) 1.68873 0.0590449
\(819\) 0.603238 0.0210788
\(820\) −39.8173 −1.39048
\(821\) −13.1297 −0.458230 −0.229115 0.973399i \(-0.573583\pi\)
−0.229115 + 0.973399i \(0.573583\pi\)
\(822\) −24.8554 −0.866933
\(823\) 3.44974 0.120250 0.0601251 0.998191i \(-0.480850\pi\)
0.0601251 + 0.998191i \(0.480850\pi\)
\(824\) 1.67100 0.0582119
\(825\) −0.409996 −0.0142742
\(826\) −11.3088 −0.393484
\(827\) 39.2823 1.36598 0.682990 0.730427i \(-0.260679\pi\)
0.682990 + 0.730427i \(0.260679\pi\)
\(828\) −8.74305 −0.303842
\(829\) −9.59393 −0.333211 −0.166605 0.986024i \(-0.553281\pi\)
−0.166605 + 0.986024i \(0.553281\pi\)
\(830\) −29.1113 −1.01047
\(831\) 21.2918 0.738605
\(832\) −12.5033 −0.433475
\(833\) −35.0180 −1.21330
\(834\) 26.9479 0.933129
\(835\) 30.3365 1.04984
\(836\) −20.2432 −0.700126
\(837\) −1.92623 −0.0665803
\(838\) −60.2763 −2.08221
\(839\) −32.9251 −1.13670 −0.568351 0.822786i \(-0.692418\pi\)
−0.568351 + 0.822786i \(0.692418\pi\)
\(840\) 2.16472 0.0746900
\(841\) 10.8852 0.375351
\(842\) −58.7074 −2.02319
\(843\) 32.8578 1.13168
\(844\) −27.7283 −0.954448
\(845\) 2.14752 0.0738771
\(846\) −1.34884 −0.0463742
\(847\) −5.96252 −0.204875
\(848\) −26.9096 −0.924081
\(849\) 14.5898 0.500722
\(850\) 4.47112 0.153358
\(851\) 23.9949 0.822534
\(852\) −5.86876 −0.201061
\(853\) 3.45990 0.118465 0.0592323 0.998244i \(-0.481135\pi\)
0.0592323 + 0.998244i \(0.481135\pi\)
\(854\) −2.96499 −0.101460
\(855\) 14.8818 0.508947
\(856\) −23.4930 −0.802976
\(857\) −33.5096 −1.14467 −0.572333 0.820021i \(-0.693962\pi\)
−0.572333 + 0.820021i \(0.693962\pi\)
\(858\) −2.30593 −0.0787233
\(859\) −32.1134 −1.09569 −0.547847 0.836579i \(-0.684552\pi\)
−0.547847 + 0.836579i \(0.684552\pi\)
\(860\) 19.4222 0.662291
\(861\) 4.04440 0.137833
\(862\) −45.4275 −1.54727
\(863\) −55.9802 −1.90559 −0.952793 0.303620i \(-0.901805\pi\)
−0.952793 + 0.303620i \(0.901805\pi\)
\(864\) −7.45289 −0.253553
\(865\) 44.8138 1.52371
\(866\) −8.80617 −0.299246
\(867\) −10.8456 −0.368337
\(868\) 3.21340 0.109070
\(869\) −3.19663 −0.108438
\(870\) 29.6071 1.00378
\(871\) 6.67280 0.226099
\(872\) 23.5999 0.799194
\(873\) −5.90264 −0.199774
\(874\) 47.8262 1.61774
\(875\) −6.98016 −0.235973
\(876\) −31.8984 −1.07775
\(877\) 36.0850 1.21850 0.609252 0.792977i \(-0.291470\pi\)
0.609252 + 0.792977i \(0.291470\pi\)
\(878\) 19.3327 0.652446
\(879\) −22.6706 −0.764660
\(880\) 4.27186 0.144004
\(881\) −35.2781 −1.18855 −0.594274 0.804262i \(-0.702561\pi\)
−0.594274 + 0.804262i \(0.702561\pi\)
\(882\) 14.4866 0.487788
\(883\) 10.7259 0.360954 0.180477 0.983579i \(-0.442236\pi\)
0.180477 + 0.983579i \(0.442236\pi\)
\(884\) 14.5931 0.490817
\(885\) −18.4423 −0.619930
\(886\) −77.1240 −2.59103
\(887\) −21.0020 −0.705179 −0.352590 0.935778i \(-0.614699\pi\)
−0.352590 + 0.935778i \(0.614699\pi\)
\(888\) −12.6823 −0.425591
\(889\) −4.66809 −0.156563
\(890\) 28.7835 0.964824
\(891\) −1.05632 −0.0353879
\(892\) −21.6174 −0.723805
\(893\) 4.28181 0.143285
\(894\) 11.2813 0.377303
\(895\) 6.56639 0.219490
\(896\) 7.47344 0.249670
\(897\) 3.16152 0.105560
\(898\) 30.0493 1.00276
\(899\) 12.1651 0.405728
\(900\) −1.07338 −0.0357793
\(901\) 75.4053 2.51211
\(902\) −15.4601 −0.514765
\(903\) −1.97279 −0.0656503
\(904\) 33.3017 1.10760
\(905\) −38.8258 −1.29061
\(906\) −19.7267 −0.655375
\(907\) −52.4356 −1.74110 −0.870549 0.492082i \(-0.836236\pi\)
−0.870549 + 0.492082i \(0.836236\pi\)
\(908\) 48.2384 1.60085
\(909\) 7.67214 0.254469
\(910\) −2.82800 −0.0937473
\(911\) −9.84115 −0.326052 −0.163026 0.986622i \(-0.552125\pi\)
−0.163026 + 0.986622i \(0.552125\pi\)
\(912\) 13.0497 0.432120
\(913\) −6.55942 −0.217085
\(914\) 13.0812 0.432686
\(915\) −4.83526 −0.159849
\(916\) 23.2240 0.767342
\(917\) 3.38718 0.111855
\(918\) 11.5194 0.380198
\(919\) −27.0275 −0.891556 −0.445778 0.895144i \(-0.647073\pi\)
−0.445778 + 0.895144i \(0.647073\pi\)
\(920\) 11.3451 0.374037
\(921\) −18.6881 −0.615794
\(922\) 65.9492 2.17192
\(923\) 2.12217 0.0698519
\(924\) 1.76218 0.0579715
\(925\) 2.94584 0.0968585
\(926\) 8.29351 0.272542
\(927\) −1.00000 −0.0328443
\(928\) 47.0685 1.54510
\(929\) 3.35293 0.110006 0.0550031 0.998486i \(-0.482483\pi\)
0.0550031 + 0.998486i \(0.482483\pi\)
\(930\) 9.03024 0.296113
\(931\) −45.9865 −1.50715
\(932\) 75.0471 2.45825
\(933\) 10.0778 0.329933
\(934\) −0.714689 −0.0233853
\(935\) −11.9705 −0.391476
\(936\) −1.67100 −0.0546182
\(937\) −1.87747 −0.0613342 −0.0306671 0.999530i \(-0.509763\pi\)
−0.0306671 + 0.999530i \(0.509763\pi\)
\(938\) −8.78718 −0.286912
\(939\) −3.34692 −0.109223
\(940\) 3.66957 0.119688
\(941\) 7.46359 0.243306 0.121653 0.992573i \(-0.461180\pi\)
0.121653 + 0.992573i \(0.461180\pi\)
\(942\) −15.5200 −0.505668
\(943\) 21.1963 0.690248
\(944\) −16.1719 −0.526350
\(945\) −1.29547 −0.0421416
\(946\) 7.54117 0.245185
\(947\) −26.2180 −0.851970 −0.425985 0.904730i \(-0.640072\pi\)
−0.425985 + 0.904730i \(0.640072\pi\)
\(948\) −8.36886 −0.271808
\(949\) 11.5346 0.374428
\(950\) 5.87159 0.190499
\(951\) 1.89021 0.0612943
\(952\) −5.31915 −0.172395
\(953\) −44.6207 −1.44541 −0.722703 0.691159i \(-0.757100\pi\)
−0.722703 + 0.691159i \(0.757100\pi\)
\(954\) −31.1943 −1.00995
\(955\) −25.3915 −0.821648
\(956\) 47.9551 1.55098
\(957\) 6.67114 0.215647
\(958\) −61.4437 −1.98516
\(959\) −6.86843 −0.221793
\(960\) 26.8512 0.866618
\(961\) −27.2896 −0.880311
\(962\) 16.5682 0.534180
\(963\) 14.0593 0.453055
\(964\) −33.0067 −1.06307
\(965\) 16.2627 0.523513
\(966\) −4.16329 −0.133952
\(967\) 53.2215 1.71149 0.855744 0.517400i \(-0.173100\pi\)
0.855744 + 0.517400i \(0.173100\pi\)
\(968\) 16.5164 0.530859
\(969\) −36.5676 −1.17472
\(970\) 27.6718 0.888488
\(971\) 15.3042 0.491135 0.245568 0.969379i \(-0.421026\pi\)
0.245568 + 0.969379i \(0.421026\pi\)
\(972\) −2.76546 −0.0887022
\(973\) 7.44665 0.238729
\(974\) −75.7614 −2.42755
\(975\) 0.388137 0.0124303
\(976\) −4.24001 −0.135719
\(977\) 4.73103 0.151359 0.0756795 0.997132i \(-0.475887\pi\)
0.0756795 + 0.997132i \(0.475887\pi\)
\(978\) −5.65620 −0.180865
\(979\) 6.48555 0.207279
\(980\) −39.4111 −1.25894
\(981\) −14.1233 −0.450921
\(982\) 66.9515 2.13651
\(983\) 2.48434 0.0792382 0.0396191 0.999215i \(-0.487386\pi\)
0.0396191 + 0.999215i \(0.487386\pi\)
\(984\) −11.2032 −0.357144
\(985\) −43.8389 −1.39682
\(986\) −72.7506 −2.31685
\(987\) −0.372733 −0.0118642
\(988\) 19.1640 0.609687
\(989\) −10.3392 −0.328768
\(990\) 4.95205 0.157386
\(991\) 31.9034 1.01344 0.506722 0.862109i \(-0.330857\pi\)
0.506722 + 0.862109i \(0.330857\pi\)
\(992\) 14.3560 0.455804
\(993\) 22.6947 0.720194
\(994\) −2.79460 −0.0886394
\(995\) −43.9240 −1.39248
\(996\) −17.1727 −0.544138
\(997\) −7.36795 −0.233345 −0.116673 0.993170i \(-0.537223\pi\)
−0.116673 + 0.993170i \(0.537223\pi\)
\(998\) 24.1576 0.764695
\(999\) 7.58967 0.240127
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 \(a_p\))