Properties

Label 8007.2.a.e.1.17
Level 8007
Weight 2
Character 8007.1
Self dual Yes
Analytic conductor 63.936
Analytic rank 1
Dimension 46
CM No

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Newspace parameters

Level: \( N \) = \( 8007 = 3 \cdot 17 \cdot 157 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8007.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9362168984\)
Analytic rank: \(1\)
Dimension: \(46\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.943890 q^{2} +1.00000 q^{3} -1.10907 q^{4} +3.50883 q^{5} -0.943890 q^{6} -2.32814 q^{7} +2.93462 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-0.943890 q^{2} +1.00000 q^{3} -1.10907 q^{4} +3.50883 q^{5} -0.943890 q^{6} -2.32814 q^{7} +2.93462 q^{8} +1.00000 q^{9} -3.31195 q^{10} -5.01861 q^{11} -1.10907 q^{12} +1.00539 q^{13} +2.19751 q^{14} +3.50883 q^{15} -0.551813 q^{16} -1.00000 q^{17} -0.943890 q^{18} +3.26521 q^{19} -3.89155 q^{20} -2.32814 q^{21} +4.73701 q^{22} -3.55015 q^{23} +2.93462 q^{24} +7.31191 q^{25} -0.948979 q^{26} +1.00000 q^{27} +2.58208 q^{28} -4.86661 q^{29} -3.31195 q^{30} +2.30575 q^{31} -5.34839 q^{32} -5.01861 q^{33} +0.943890 q^{34} -8.16906 q^{35} -1.10907 q^{36} -1.16260 q^{37} -3.08200 q^{38} +1.00539 q^{39} +10.2971 q^{40} -10.1573 q^{41} +2.19751 q^{42} +10.0192 q^{43} +5.56600 q^{44} +3.50883 q^{45} +3.35095 q^{46} +9.68937 q^{47} -0.551813 q^{48} -1.57975 q^{49} -6.90163 q^{50} -1.00000 q^{51} -1.11505 q^{52} +10.3774 q^{53} -0.943890 q^{54} -17.6094 q^{55} -6.83222 q^{56} +3.26521 q^{57} +4.59354 q^{58} -5.16679 q^{59} -3.89155 q^{60} -1.49433 q^{61} -2.17637 q^{62} -2.32814 q^{63} +6.15192 q^{64} +3.52775 q^{65} +4.73701 q^{66} -3.48575 q^{67} +1.10907 q^{68} -3.55015 q^{69} +7.71069 q^{70} -6.84335 q^{71} +2.93462 q^{72} -1.60666 q^{73} +1.09736 q^{74} +7.31191 q^{75} -3.62136 q^{76} +11.6840 q^{77} -0.948979 q^{78} -11.4385 q^{79} -1.93622 q^{80} +1.00000 q^{81} +9.58739 q^{82} +8.66231 q^{83} +2.58208 q^{84} -3.50883 q^{85} -9.45697 q^{86} -4.86661 q^{87} -14.7277 q^{88} -16.3560 q^{89} -3.31195 q^{90} -2.34070 q^{91} +3.93738 q^{92} +2.30575 q^{93} -9.14569 q^{94} +11.4571 q^{95} -5.34839 q^{96} -6.59296 q^{97} +1.49111 q^{98} -5.01861 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 46q - 5q^{2} + 46q^{3} + 43q^{4} - 19q^{5} - 5q^{6} + q^{7} - 18q^{8} + 46q^{9} + O(q^{10}) \) \( 46q - 5q^{2} + 46q^{3} + 43q^{4} - 19q^{5} - 5q^{6} + q^{7} - 18q^{8} + 46q^{9} - 10q^{10} - 25q^{11} + 43q^{12} - 8q^{13} - 28q^{14} - 19q^{15} + 33q^{16} - 46q^{17} - 5q^{18} - 2q^{19} - 56q^{20} + q^{21} - 19q^{22} - 64q^{23} - 18q^{24} + 11q^{25} - 13q^{26} + 46q^{27} - 38q^{28} - 51q^{29} - 10q^{30} - 19q^{31} - 61q^{32} - 25q^{33} + 5q^{34} - 39q^{35} + 43q^{36} - 46q^{37} - 48q^{38} - 8q^{39} - 10q^{40} - 53q^{41} - 28q^{42} - 33q^{43} - 62q^{44} - 19q^{45} + 2q^{46} - 45q^{47} + 33q^{48} + 21q^{49} - 60q^{50} - 46q^{51} - 63q^{52} - 47q^{53} - 5q^{54} + 5q^{55} - 82q^{56} - 2q^{57} - 21q^{58} - 65q^{59} - 56q^{60} - 37q^{61} - 46q^{62} + q^{63} + 74q^{64} - 85q^{65} - 19q^{66} - 52q^{67} - 43q^{68} - 64q^{69} - 20q^{70} - 48q^{71} - 18q^{72} - 39q^{73} - 16q^{74} + 11q^{75} + 42q^{76} - 78q^{77} - 13q^{78} - 26q^{79} - 78q^{80} + 46q^{81} + 3q^{82} - 47q^{83} - 38q^{84} + 19q^{85} - 6q^{86} - 51q^{87} - 58q^{88} - 58q^{89} - 10q^{90} - 43q^{91} - 68q^{92} - 19q^{93} - 78q^{95} - 61q^{96} - 44q^{97} - 4q^{98} - 25q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.943890 −0.667431 −0.333715 0.942674i \(-0.608302\pi\)
−0.333715 + 0.942674i \(0.608302\pi\)
\(3\) 1.00000 0.577350
\(4\) −1.10907 −0.554536
\(5\) 3.50883 1.56920 0.784599 0.620004i \(-0.212869\pi\)
0.784599 + 0.620004i \(0.212869\pi\)
\(6\) −0.943890 −0.385341
\(7\) −2.32814 −0.879955 −0.439978 0.898009i \(-0.645014\pi\)
−0.439978 + 0.898009i \(0.645014\pi\)
\(8\) 2.93462 1.03755
\(9\) 1.00000 0.333333
\(10\) −3.31195 −1.04733
\(11\) −5.01861 −1.51317 −0.756583 0.653897i \(-0.773133\pi\)
−0.756583 + 0.653897i \(0.773133\pi\)
\(12\) −1.10907 −0.320162
\(13\) 1.00539 0.278846 0.139423 0.990233i \(-0.455475\pi\)
0.139423 + 0.990233i \(0.455475\pi\)
\(14\) 2.19751 0.587309
\(15\) 3.50883 0.905977
\(16\) −0.551813 −0.137953
\(17\) −1.00000 −0.242536
\(18\) −0.943890 −0.222477
\(19\) 3.26521 0.749091 0.374546 0.927209i \(-0.377799\pi\)
0.374546 + 0.927209i \(0.377799\pi\)
\(20\) −3.89155 −0.870177
\(21\) −2.32814 −0.508042
\(22\) 4.73701 1.00993
\(23\) −3.55015 −0.740258 −0.370129 0.928980i \(-0.620686\pi\)
−0.370129 + 0.928980i \(0.620686\pi\)
\(24\) 2.93462 0.599027
\(25\) 7.31191 1.46238
\(26\) −0.948979 −0.186110
\(27\) 1.00000 0.192450
\(28\) 2.58208 0.487967
\(29\) −4.86661 −0.903706 −0.451853 0.892092i \(-0.649237\pi\)
−0.451853 + 0.892092i \(0.649237\pi\)
\(30\) −3.31195 −0.604677
\(31\) 2.30575 0.414124 0.207062 0.978328i \(-0.433610\pi\)
0.207062 + 0.978328i \(0.433610\pi\)
\(32\) −5.34839 −0.945471
\(33\) −5.01861 −0.873627
\(34\) 0.943890 0.161876
\(35\) −8.16906 −1.38082
\(36\) −1.10907 −0.184845
\(37\) −1.16260 −0.191129 −0.0955647 0.995423i \(-0.530466\pi\)
−0.0955647 + 0.995423i \(0.530466\pi\)
\(38\) −3.08200 −0.499966
\(39\) 1.00539 0.160992
\(40\) 10.2971 1.62811
\(41\) −10.1573 −1.58631 −0.793153 0.609022i \(-0.791562\pi\)
−0.793153 + 0.609022i \(0.791562\pi\)
\(42\) 2.19751 0.339083
\(43\) 10.0192 1.52791 0.763953 0.645272i \(-0.223256\pi\)
0.763953 + 0.645272i \(0.223256\pi\)
\(44\) 5.56600 0.839106
\(45\) 3.50883 0.523066
\(46\) 3.35095 0.494071
\(47\) 9.68937 1.41334 0.706670 0.707544i \(-0.250197\pi\)
0.706670 + 0.707544i \(0.250197\pi\)
\(48\) −0.551813 −0.0796474
\(49\) −1.57975 −0.225679
\(50\) −6.90163 −0.976039
\(51\) −1.00000 −0.140028
\(52\) −1.11505 −0.154630
\(53\) 10.3774 1.42544 0.712719 0.701449i \(-0.247463\pi\)
0.712719 + 0.701449i \(0.247463\pi\)
\(54\) −0.943890 −0.128447
\(55\) −17.6094 −2.37446
\(56\) −6.83222 −0.912993
\(57\) 3.26521 0.432488
\(58\) 4.59354 0.603161
\(59\) −5.16679 −0.672659 −0.336329 0.941744i \(-0.609186\pi\)
−0.336329 + 0.941744i \(0.609186\pi\)
\(60\) −3.89155 −0.502397
\(61\) −1.49433 −0.191329 −0.0956646 0.995414i \(-0.530498\pi\)
−0.0956646 + 0.995414i \(0.530498\pi\)
\(62\) −2.17637 −0.276399
\(63\) −2.32814 −0.293318
\(64\) 6.15192 0.768990
\(65\) 3.52775 0.437564
\(66\) 4.73701 0.583086
\(67\) −3.48575 −0.425853 −0.212926 0.977068i \(-0.568299\pi\)
−0.212926 + 0.977068i \(0.568299\pi\)
\(68\) 1.10907 0.134495
\(69\) −3.55015 −0.427388
\(70\) 7.71069 0.921604
\(71\) −6.84335 −0.812156 −0.406078 0.913838i \(-0.633104\pi\)
−0.406078 + 0.913838i \(0.633104\pi\)
\(72\) 2.93462 0.345848
\(73\) −1.60666 −0.188045 −0.0940226 0.995570i \(-0.529973\pi\)
−0.0940226 + 0.995570i \(0.529973\pi\)
\(74\) 1.09736 0.127566
\(75\) 7.31191 0.844307
\(76\) −3.62136 −0.415398
\(77\) 11.6840 1.33152
\(78\) −0.948979 −0.107451
\(79\) −11.4385 −1.28693 −0.643467 0.765474i \(-0.722505\pi\)
−0.643467 + 0.765474i \(0.722505\pi\)
\(80\) −1.93622 −0.216476
\(81\) 1.00000 0.111111
\(82\) 9.58739 1.05875
\(83\) 8.66231 0.950812 0.475406 0.879767i \(-0.342301\pi\)
0.475406 + 0.879767i \(0.342301\pi\)
\(84\) 2.58208 0.281728
\(85\) −3.50883 −0.380586
\(86\) −9.45697 −1.01977
\(87\) −4.86661 −0.521755
\(88\) −14.7277 −1.56998
\(89\) −16.3560 −1.73373 −0.866865 0.498543i \(-0.833869\pi\)
−0.866865 + 0.498543i \(0.833869\pi\)
\(90\) −3.31195 −0.349110
\(91\) −2.34070 −0.245372
\(92\) 3.93738 0.410500
\(93\) 2.30575 0.239095
\(94\) −9.14569 −0.943306
\(95\) 11.4571 1.17547
\(96\) −5.34839 −0.545868
\(97\) −6.59296 −0.669414 −0.334707 0.942322i \(-0.608637\pi\)
−0.334707 + 0.942322i \(0.608637\pi\)
\(98\) 1.49111 0.150625
\(99\) −5.01861 −0.504389
\(100\) −8.10944 −0.810944
\(101\) 3.16781 0.315208 0.157604 0.987502i \(-0.449623\pi\)
0.157604 + 0.987502i \(0.449623\pi\)
\(102\) 0.943890 0.0934590
\(103\) 3.10167 0.305617 0.152808 0.988256i \(-0.451168\pi\)
0.152808 + 0.988256i \(0.451168\pi\)
\(104\) 2.95045 0.289315
\(105\) −8.16906 −0.797219
\(106\) −9.79507 −0.951382
\(107\) 8.91967 0.862297 0.431148 0.902281i \(-0.358109\pi\)
0.431148 + 0.902281i \(0.358109\pi\)
\(108\) −1.10907 −0.106721
\(109\) −7.30757 −0.699938 −0.349969 0.936761i \(-0.613808\pi\)
−0.349969 + 0.936761i \(0.613808\pi\)
\(110\) 16.6214 1.58479
\(111\) −1.16260 −0.110349
\(112\) 1.28470 0.121393
\(113\) −13.3017 −1.25131 −0.625657 0.780098i \(-0.715169\pi\)
−0.625657 + 0.780098i \(0.715169\pi\)
\(114\) −3.08200 −0.288656
\(115\) −12.4569 −1.16161
\(116\) 5.39742 0.501138
\(117\) 1.00539 0.0929485
\(118\) 4.87688 0.448953
\(119\) 2.32814 0.213420
\(120\) 10.2971 0.939992
\(121\) 14.1864 1.28967
\(122\) 1.41048 0.127699
\(123\) −10.1573 −0.915854
\(124\) −2.55724 −0.229647
\(125\) 8.11210 0.725569
\(126\) 2.19751 0.195770
\(127\) 10.8779 0.965258 0.482629 0.875825i \(-0.339682\pi\)
0.482629 + 0.875825i \(0.339682\pi\)
\(128\) 4.89005 0.432224
\(129\) 10.0192 0.882137
\(130\) −3.32981 −0.292044
\(131\) 8.73616 0.763282 0.381641 0.924311i \(-0.375359\pi\)
0.381641 + 0.924311i \(0.375359\pi\)
\(132\) 5.56600 0.484458
\(133\) −7.60188 −0.659166
\(134\) 3.29017 0.284227
\(135\) 3.50883 0.301992
\(136\) −2.93462 −0.251642
\(137\) −5.67042 −0.484457 −0.242229 0.970219i \(-0.577878\pi\)
−0.242229 + 0.970219i \(0.577878\pi\)
\(138\) 3.35095 0.285252
\(139\) −6.45656 −0.547638 −0.273819 0.961781i \(-0.588287\pi\)
−0.273819 + 0.961781i \(0.588287\pi\)
\(140\) 9.06008 0.765717
\(141\) 9.68937 0.815992
\(142\) 6.45936 0.542058
\(143\) −5.04567 −0.421940
\(144\) −0.551813 −0.0459844
\(145\) −17.0761 −1.41809
\(146\) 1.51651 0.125507
\(147\) −1.57975 −0.130296
\(148\) 1.28940 0.105988
\(149\) −21.6118 −1.77051 −0.885255 0.465106i \(-0.846016\pi\)
−0.885255 + 0.465106i \(0.846016\pi\)
\(150\) −6.90163 −0.563516
\(151\) 2.51616 0.204762 0.102381 0.994745i \(-0.467354\pi\)
0.102381 + 0.994745i \(0.467354\pi\)
\(152\) 9.58216 0.777216
\(153\) −1.00000 −0.0808452
\(154\) −11.0284 −0.888696
\(155\) 8.09048 0.649843
\(156\) −1.11505 −0.0892757
\(157\) 1.00000 0.0798087
\(158\) 10.7967 0.858939
\(159\) 10.3774 0.822977
\(160\) −18.7666 −1.48363
\(161\) 8.26526 0.651394
\(162\) −0.943890 −0.0741590
\(163\) 17.4822 1.36931 0.684657 0.728865i \(-0.259952\pi\)
0.684657 + 0.728865i \(0.259952\pi\)
\(164\) 11.2652 0.879664
\(165\) −17.6094 −1.37089
\(166\) −8.17626 −0.634601
\(167\) −16.1605 −1.25054 −0.625268 0.780410i \(-0.715010\pi\)
−0.625268 + 0.780410i \(0.715010\pi\)
\(168\) −6.83222 −0.527117
\(169\) −11.9892 −0.922245
\(170\) 3.31195 0.254015
\(171\) 3.26521 0.249697
\(172\) −11.1120 −0.847279
\(173\) 6.75760 0.513771 0.256885 0.966442i \(-0.417304\pi\)
0.256885 + 0.966442i \(0.417304\pi\)
\(174\) 4.59354 0.348235
\(175\) −17.0232 −1.28683
\(176\) 2.76933 0.208746
\(177\) −5.16679 −0.388360
\(178\) 15.4382 1.15714
\(179\) −18.5229 −1.38447 −0.692235 0.721672i \(-0.743374\pi\)
−0.692235 + 0.721672i \(0.743374\pi\)
\(180\) −3.89155 −0.290059
\(181\) −20.7954 −1.54571 −0.772854 0.634584i \(-0.781172\pi\)
−0.772854 + 0.634584i \(0.781172\pi\)
\(182\) 2.20936 0.163769
\(183\) −1.49433 −0.110464
\(184\) −10.4183 −0.768051
\(185\) −4.07935 −0.299920
\(186\) −2.17637 −0.159579
\(187\) 5.01861 0.366997
\(188\) −10.7462 −0.783748
\(189\) −2.32814 −0.169347
\(190\) −10.8142 −0.784546
\(191\) 13.5891 0.983271 0.491636 0.870801i \(-0.336399\pi\)
0.491636 + 0.870801i \(0.336399\pi\)
\(192\) 6.15192 0.443976
\(193\) −13.8923 −0.999991 −0.499996 0.866028i \(-0.666665\pi\)
−0.499996 + 0.866028i \(0.666665\pi\)
\(194\) 6.22303 0.446787
\(195\) 3.52775 0.252628
\(196\) 1.75206 0.125147
\(197\) 5.71584 0.407237 0.203618 0.979050i \(-0.434730\pi\)
0.203618 + 0.979050i \(0.434730\pi\)
\(198\) 4.73701 0.336645
\(199\) −24.5328 −1.73908 −0.869541 0.493861i \(-0.835585\pi\)
−0.869541 + 0.493861i \(0.835585\pi\)
\(200\) 21.4577 1.51729
\(201\) −3.48575 −0.245866
\(202\) −2.99006 −0.210380
\(203\) 11.3302 0.795221
\(204\) 1.10907 0.0776506
\(205\) −35.6403 −2.48923
\(206\) −2.92764 −0.203978
\(207\) −3.55015 −0.246753
\(208\) −0.554789 −0.0384677
\(209\) −16.3868 −1.13350
\(210\) 7.71069 0.532088
\(211\) −2.65539 −0.182805 −0.0914023 0.995814i \(-0.529135\pi\)
−0.0914023 + 0.995814i \(0.529135\pi\)
\(212\) −11.5092 −0.790457
\(213\) −6.84335 −0.468898
\(214\) −8.41918 −0.575523
\(215\) 35.1555 2.39759
\(216\) 2.93462 0.199676
\(217\) −5.36811 −0.364411
\(218\) 6.89754 0.467160
\(219\) −1.60666 −0.108568
\(220\) 19.5302 1.31672
\(221\) −1.00539 −0.0676300
\(222\) 1.09736 0.0736501
\(223\) 8.14373 0.545345 0.272672 0.962107i \(-0.412093\pi\)
0.272672 + 0.962107i \(0.412093\pi\)
\(224\) 12.4518 0.831972
\(225\) 7.31191 0.487461
\(226\) 12.5553 0.835166
\(227\) −25.2961 −1.67896 −0.839479 0.543392i \(-0.817140\pi\)
−0.839479 + 0.543392i \(0.817140\pi\)
\(228\) −3.62136 −0.239830
\(229\) −17.9428 −1.18569 −0.592847 0.805315i \(-0.701996\pi\)
−0.592847 + 0.805315i \(0.701996\pi\)
\(230\) 11.7579 0.775295
\(231\) 11.6840 0.768753
\(232\) −14.2816 −0.937636
\(233\) 3.92422 0.257084 0.128542 0.991704i \(-0.458970\pi\)
0.128542 + 0.991704i \(0.458970\pi\)
\(234\) −0.948979 −0.0620367
\(235\) 33.9984 2.21781
\(236\) 5.73034 0.373014
\(237\) −11.4385 −0.743012
\(238\) −2.19751 −0.142443
\(239\) −3.38682 −0.219075 −0.109537 0.993983i \(-0.534937\pi\)
−0.109537 + 0.993983i \(0.534937\pi\)
\(240\) −1.93622 −0.124983
\(241\) 26.9066 1.73321 0.866604 0.498996i \(-0.166298\pi\)
0.866604 + 0.498996i \(0.166298\pi\)
\(242\) −13.3904 −0.860767
\(243\) 1.00000 0.0641500
\(244\) 1.65732 0.106099
\(245\) −5.54309 −0.354135
\(246\) 9.58739 0.611269
\(247\) 3.28282 0.208881
\(248\) 6.76649 0.429673
\(249\) 8.66231 0.548952
\(250\) −7.65693 −0.484267
\(251\) −18.0513 −1.13939 −0.569693 0.821858i \(-0.692938\pi\)
−0.569693 + 0.821858i \(0.692938\pi\)
\(252\) 2.58208 0.162656
\(253\) 17.8168 1.12013
\(254\) −10.2675 −0.644243
\(255\) −3.50883 −0.219732
\(256\) −16.9195 −1.05747
\(257\) 9.84097 0.613863 0.306931 0.951732i \(-0.400698\pi\)
0.306931 + 0.951732i \(0.400698\pi\)
\(258\) −9.45697 −0.588765
\(259\) 2.70669 0.168185
\(260\) −3.91253 −0.242645
\(261\) −4.86661 −0.301235
\(262\) −8.24597 −0.509438
\(263\) −26.3248 −1.62326 −0.811628 0.584175i \(-0.801418\pi\)
−0.811628 + 0.584175i \(0.801418\pi\)
\(264\) −14.7277 −0.906428
\(265\) 36.4124 2.23680
\(266\) 7.17533 0.439948
\(267\) −16.3560 −1.00097
\(268\) 3.86595 0.236151
\(269\) −26.8069 −1.63444 −0.817222 0.576323i \(-0.804487\pi\)
−0.817222 + 0.576323i \(0.804487\pi\)
\(270\) −3.31195 −0.201559
\(271\) −14.8379 −0.901339 −0.450670 0.892691i \(-0.648815\pi\)
−0.450670 + 0.892691i \(0.648815\pi\)
\(272\) 0.551813 0.0334586
\(273\) −2.34070 −0.141665
\(274\) 5.35225 0.323342
\(275\) −36.6956 −2.21283
\(276\) 3.93738 0.237002
\(277\) −18.8597 −1.13317 −0.566584 0.824004i \(-0.691735\pi\)
−0.566584 + 0.824004i \(0.691735\pi\)
\(278\) 6.09428 0.365511
\(279\) 2.30575 0.138041
\(280\) −23.9731 −1.43267
\(281\) 24.0689 1.43583 0.717916 0.696129i \(-0.245096\pi\)
0.717916 + 0.696129i \(0.245096\pi\)
\(282\) −9.14569 −0.544618
\(283\) 15.7161 0.934228 0.467114 0.884197i \(-0.345294\pi\)
0.467114 + 0.884197i \(0.345294\pi\)
\(284\) 7.58977 0.450370
\(285\) 11.4571 0.678659
\(286\) 4.76255 0.281616
\(287\) 23.6477 1.39588
\(288\) −5.34839 −0.315157
\(289\) 1.00000 0.0588235
\(290\) 16.1180 0.946479
\(291\) −6.59296 −0.386486
\(292\) 1.78190 0.104278
\(293\) −2.79213 −0.163118 −0.0815590 0.996669i \(-0.525990\pi\)
−0.0815590 + 0.996669i \(0.525990\pi\)
\(294\) 1.49111 0.0869635
\(295\) −18.1294 −1.05553
\(296\) −3.41178 −0.198305
\(297\) −5.01861 −0.291209
\(298\) 20.3992 1.18169
\(299\) −3.56929 −0.206418
\(300\) −8.10944 −0.468199
\(301\) −23.3260 −1.34449
\(302\) −2.37498 −0.136665
\(303\) 3.16781 0.181986
\(304\) −1.80179 −0.103340
\(305\) −5.24335 −0.300233
\(306\) 0.943890 0.0539586
\(307\) 27.0903 1.54612 0.773062 0.634330i \(-0.218724\pi\)
0.773062 + 0.634330i \(0.218724\pi\)
\(308\) −12.9584 −0.738375
\(309\) 3.10167 0.176448
\(310\) −7.63652 −0.433725
\(311\) 24.4301 1.38530 0.692652 0.721272i \(-0.256442\pi\)
0.692652 + 0.721272i \(0.256442\pi\)
\(312\) 2.95045 0.167036
\(313\) 28.9536 1.63655 0.818276 0.574825i \(-0.194930\pi\)
0.818276 + 0.574825i \(0.194930\pi\)
\(314\) −0.943890 −0.0532668
\(315\) −8.16906 −0.460275
\(316\) 12.6861 0.713652
\(317\) −5.24581 −0.294634 −0.147317 0.989089i \(-0.547064\pi\)
−0.147317 + 0.989089i \(0.547064\pi\)
\(318\) −9.79507 −0.549280
\(319\) 24.4236 1.36746
\(320\) 21.5861 1.20670
\(321\) 8.91967 0.497847
\(322\) −7.80149 −0.434760
\(323\) −3.26521 −0.181681
\(324\) −1.10907 −0.0616151
\(325\) 7.35134 0.407779
\(326\) −16.5013 −0.913923
\(327\) −7.30757 −0.404109
\(328\) −29.8079 −1.64586
\(329\) −22.5582 −1.24367
\(330\) 16.6214 0.914977
\(331\) −17.9999 −0.989364 −0.494682 0.869074i \(-0.664715\pi\)
−0.494682 + 0.869074i \(0.664715\pi\)
\(332\) −9.60713 −0.527260
\(333\) −1.16260 −0.0637098
\(334\) 15.2537 0.834647
\(335\) −12.2309 −0.668247
\(336\) 1.28470 0.0700861
\(337\) −33.1093 −1.80358 −0.901789 0.432177i \(-0.857746\pi\)
−0.901789 + 0.432177i \(0.857746\pi\)
\(338\) 11.3165 0.615535
\(339\) −13.3017 −0.722447
\(340\) 3.89155 0.211049
\(341\) −11.5716 −0.626639
\(342\) −3.08200 −0.166655
\(343\) 19.9749 1.07854
\(344\) 29.4024 1.58527
\(345\) −12.4569 −0.670656
\(346\) −6.37843 −0.342906
\(347\) −4.18747 −0.224795 −0.112398 0.993663i \(-0.535853\pi\)
−0.112398 + 0.993663i \(0.535853\pi\)
\(348\) 5.39742 0.289332
\(349\) 23.6159 1.26413 0.632066 0.774915i \(-0.282207\pi\)
0.632066 + 0.774915i \(0.282207\pi\)
\(350\) 16.0680 0.858870
\(351\) 1.00539 0.0536639
\(352\) 26.8415 1.43066
\(353\) −4.53137 −0.241181 −0.120590 0.992702i \(-0.538479\pi\)
−0.120590 + 0.992702i \(0.538479\pi\)
\(354\) 4.87688 0.259203
\(355\) −24.0122 −1.27443
\(356\) 18.1400 0.961416
\(357\) 2.32814 0.123218
\(358\) 17.4836 0.924037
\(359\) −3.37665 −0.178213 −0.0891065 0.996022i \(-0.528401\pi\)
−0.0891065 + 0.996022i \(0.528401\pi\)
\(360\) 10.2971 0.542705
\(361\) −8.33839 −0.438863
\(362\) 19.6285 1.03165
\(363\) 14.1864 0.744593
\(364\) 2.59600 0.136067
\(365\) −5.63750 −0.295080
\(366\) 1.41048 0.0737270
\(367\) −30.0202 −1.56704 −0.783521 0.621365i \(-0.786578\pi\)
−0.783521 + 0.621365i \(0.786578\pi\)
\(368\) 1.95902 0.102121
\(369\) −10.1573 −0.528769
\(370\) 3.85046 0.200176
\(371\) −24.1599 −1.25432
\(372\) −2.55724 −0.132587
\(373\) −4.41263 −0.228477 −0.114239 0.993453i \(-0.536443\pi\)
−0.114239 + 0.993453i \(0.536443\pi\)
\(374\) −4.73701 −0.244945
\(375\) 8.11210 0.418907
\(376\) 28.4346 1.46640
\(377\) −4.89285 −0.251995
\(378\) 2.19751 0.113028
\(379\) −20.0683 −1.03084 −0.515419 0.856938i \(-0.672364\pi\)
−0.515419 + 0.856938i \(0.672364\pi\)
\(380\) −12.7067 −0.651842
\(381\) 10.8779 0.557292
\(382\) −12.8266 −0.656265
\(383\) 22.4140 1.14530 0.572651 0.819799i \(-0.305915\pi\)
0.572651 + 0.819799i \(0.305915\pi\)
\(384\) 4.89005 0.249544
\(385\) 40.9973 2.08942
\(386\) 13.1128 0.667425
\(387\) 10.0192 0.509302
\(388\) 7.31207 0.371214
\(389\) 3.95429 0.200490 0.100245 0.994963i \(-0.468037\pi\)
0.100245 + 0.994963i \(0.468037\pi\)
\(390\) −3.32981 −0.168611
\(391\) 3.55015 0.179539
\(392\) −4.63598 −0.234152
\(393\) 8.73616 0.440681
\(394\) −5.39513 −0.271802
\(395\) −40.1359 −2.01945
\(396\) 5.56600 0.279702
\(397\) 21.5545 1.08179 0.540894 0.841091i \(-0.318086\pi\)
0.540894 + 0.841091i \(0.318086\pi\)
\(398\) 23.1562 1.16072
\(399\) −7.60188 −0.380570
\(400\) −4.03481 −0.201740
\(401\) 16.5882 0.828375 0.414187 0.910192i \(-0.364066\pi\)
0.414187 + 0.910192i \(0.364066\pi\)
\(402\) 3.29017 0.164099
\(403\) 2.31818 0.115477
\(404\) −3.51333 −0.174795
\(405\) 3.50883 0.174355
\(406\) −10.6944 −0.530755
\(407\) 5.83461 0.289211
\(408\) −2.93462 −0.145285
\(409\) 37.6527 1.86181 0.930903 0.365267i \(-0.119022\pi\)
0.930903 + 0.365267i \(0.119022\pi\)
\(410\) 33.6405 1.66139
\(411\) −5.67042 −0.279701
\(412\) −3.43998 −0.169476
\(413\) 12.0290 0.591909
\(414\) 3.35095 0.164690
\(415\) 30.3946 1.49201
\(416\) −5.37723 −0.263640
\(417\) −6.45656 −0.316179
\(418\) 15.4673 0.756532
\(419\) −17.8056 −0.869859 −0.434930 0.900464i \(-0.643227\pi\)
−0.434930 + 0.900464i \(0.643227\pi\)
\(420\) 9.06008 0.442087
\(421\) 19.0402 0.927961 0.463981 0.885845i \(-0.346421\pi\)
0.463981 + 0.885845i \(0.346421\pi\)
\(422\) 2.50640 0.122009
\(423\) 9.68937 0.471113
\(424\) 30.4536 1.47896
\(425\) −7.31191 −0.354680
\(426\) 6.45936 0.312957
\(427\) 3.47901 0.168361
\(428\) −9.89256 −0.478175
\(429\) −5.04567 −0.243607
\(430\) −33.1829 −1.60022
\(431\) 30.5449 1.47130 0.735648 0.677364i \(-0.236878\pi\)
0.735648 + 0.677364i \(0.236878\pi\)
\(432\) −0.551813 −0.0265491
\(433\) 4.19960 0.201820 0.100910 0.994896i \(-0.467825\pi\)
0.100910 + 0.994896i \(0.467825\pi\)
\(434\) 5.06690 0.243219
\(435\) −17.0761 −0.818737
\(436\) 8.10462 0.388141
\(437\) −11.5920 −0.554520
\(438\) 1.51651 0.0724616
\(439\) 29.3668 1.40160 0.700801 0.713357i \(-0.252826\pi\)
0.700801 + 0.713357i \(0.252826\pi\)
\(440\) −51.6771 −2.46361
\(441\) −1.57975 −0.0752264
\(442\) 0.948979 0.0451383
\(443\) 24.7954 1.17807 0.589033 0.808109i \(-0.299509\pi\)
0.589033 + 0.808109i \(0.299509\pi\)
\(444\) 1.28940 0.0611923
\(445\) −57.3904 −2.72057
\(446\) −7.68678 −0.363980
\(447\) −21.6118 −1.02220
\(448\) −14.3225 −0.676676
\(449\) −4.65991 −0.219915 −0.109957 0.993936i \(-0.535071\pi\)
−0.109957 + 0.993936i \(0.535071\pi\)
\(450\) −6.90163 −0.325346
\(451\) 50.9756 2.40035
\(452\) 14.7525 0.693899
\(453\) 2.51616 0.118220
\(454\) 23.8767 1.12059
\(455\) −8.21311 −0.385037
\(456\) 9.58216 0.448726
\(457\) −4.81819 −0.225385 −0.112693 0.993630i \(-0.535948\pi\)
−0.112693 + 0.993630i \(0.535948\pi\)
\(458\) 16.9360 0.791368
\(459\) −1.00000 −0.0466760
\(460\) 13.8156 0.644155
\(461\) −7.87020 −0.366552 −0.183276 0.983062i \(-0.558670\pi\)
−0.183276 + 0.983062i \(0.558670\pi\)
\(462\) −11.0284 −0.513089
\(463\) 4.08451 0.189823 0.0949116 0.995486i \(-0.469743\pi\)
0.0949116 + 0.995486i \(0.469743\pi\)
\(464\) 2.68546 0.124669
\(465\) 8.09048 0.375187
\(466\) −3.70403 −0.171586
\(467\) −16.2716 −0.752961 −0.376481 0.926424i \(-0.622866\pi\)
−0.376481 + 0.926424i \(0.622866\pi\)
\(468\) −1.11505 −0.0515433
\(469\) 8.11533 0.374731
\(470\) −32.0907 −1.48023
\(471\) 1.00000 0.0460776
\(472\) −15.1626 −0.697914
\(473\) −50.2822 −2.31198
\(474\) 10.7967 0.495909
\(475\) 23.8749 1.09546
\(476\) −2.58208 −0.118349
\(477\) 10.3774 0.475146
\(478\) 3.19678 0.146217
\(479\) −31.3862 −1.43407 −0.717037 0.697035i \(-0.754502\pi\)
−0.717037 + 0.697035i \(0.754502\pi\)
\(480\) −18.7666 −0.856575
\(481\) −1.16886 −0.0532956
\(482\) −25.3969 −1.15680
\(483\) 8.26526 0.376082
\(484\) −15.7337 −0.715170
\(485\) −23.1336 −1.05044
\(486\) −0.943890 −0.0428157
\(487\) −14.7583 −0.668762 −0.334381 0.942438i \(-0.608527\pi\)
−0.334381 + 0.942438i \(0.608527\pi\)
\(488\) −4.38529 −0.198513
\(489\) 17.4822 0.790574
\(490\) 5.23207 0.236361
\(491\) −17.0491 −0.769417 −0.384708 0.923038i \(-0.625698\pi\)
−0.384708 + 0.923038i \(0.625698\pi\)
\(492\) 11.2652 0.507874
\(493\) 4.86661 0.219181
\(494\) −3.09862 −0.139413
\(495\) −17.6094 −0.791486
\(496\) −1.27234 −0.0571298
\(497\) 15.9323 0.714660
\(498\) −8.17626 −0.366387
\(499\) −6.81219 −0.304955 −0.152478 0.988307i \(-0.548725\pi\)
−0.152478 + 0.988307i \(0.548725\pi\)
\(500\) −8.99691 −0.402354
\(501\) −16.1605 −0.721998
\(502\) 17.0384 0.760461
\(503\) −25.1211 −1.12009 −0.560047 0.828461i \(-0.689217\pi\)
−0.560047 + 0.828461i \(0.689217\pi\)
\(504\) −6.83222 −0.304331
\(505\) 11.1153 0.494624
\(506\) −16.8171 −0.747611
\(507\) −11.9892 −0.532458
\(508\) −12.0644 −0.535271
\(509\) −14.8097 −0.656427 −0.328214 0.944604i \(-0.606447\pi\)
−0.328214 + 0.944604i \(0.606447\pi\)
\(510\) 3.31195 0.146656
\(511\) 3.74053 0.165471
\(512\) 6.19004 0.273564
\(513\) 3.26521 0.144163
\(514\) −9.28879 −0.409711
\(515\) 10.8832 0.479573
\(516\) −11.1120 −0.489177
\(517\) −48.6271 −2.13862
\(518\) −2.55481 −0.112252
\(519\) 6.75760 0.296626
\(520\) 10.3526 0.453992
\(521\) −18.6113 −0.815374 −0.407687 0.913122i \(-0.633665\pi\)
−0.407687 + 0.913122i \(0.633665\pi\)
\(522\) 4.59354 0.201054
\(523\) 12.2074 0.533790 0.266895 0.963726i \(-0.414002\pi\)
0.266895 + 0.963726i \(0.414002\pi\)
\(524\) −9.68903 −0.423267
\(525\) −17.0232 −0.742952
\(526\) 24.8477 1.08341
\(527\) −2.30575 −0.100440
\(528\) 2.76933 0.120520
\(529\) −10.3964 −0.452018
\(530\) −34.3693 −1.49291
\(531\) −5.16679 −0.224220
\(532\) 8.43103 0.365532
\(533\) −10.2121 −0.442335
\(534\) 15.4382 0.668078
\(535\) 31.2976 1.35311
\(536\) −10.2294 −0.441841
\(537\) −18.5229 −0.799324
\(538\) 25.3027 1.09088
\(539\) 7.92816 0.341490
\(540\) −3.89155 −0.167466
\(541\) 2.27708 0.0978993 0.0489497 0.998801i \(-0.484413\pi\)
0.0489497 + 0.998801i \(0.484413\pi\)
\(542\) 14.0054 0.601582
\(543\) −20.7954 −0.892415
\(544\) 5.34839 0.229310
\(545\) −25.6410 −1.09834
\(546\) 2.20936 0.0945518
\(547\) −19.5696 −0.836736 −0.418368 0.908278i \(-0.637398\pi\)
−0.418368 + 0.908278i \(0.637398\pi\)
\(548\) 6.28891 0.268649
\(549\) −1.49433 −0.0637764
\(550\) 34.6366 1.47691
\(551\) −15.8905 −0.676958
\(552\) −10.4183 −0.443434
\(553\) 26.6305 1.13244
\(554\) 17.8014 0.756310
\(555\) −4.07935 −0.173159
\(556\) 7.16079 0.303685
\(557\) 4.77606 0.202368 0.101184 0.994868i \(-0.467737\pi\)
0.101184 + 0.994868i \(0.467737\pi\)
\(558\) −2.17637 −0.0921331
\(559\) 10.0732 0.426050
\(560\) 4.50780 0.190489
\(561\) 5.01861 0.211886
\(562\) −22.7184 −0.958319
\(563\) 12.6274 0.532181 0.266091 0.963948i \(-0.414268\pi\)
0.266091 + 0.963948i \(0.414268\pi\)
\(564\) −10.7462 −0.452497
\(565\) −46.6733 −1.96356
\(566\) −14.8343 −0.623532
\(567\) −2.32814 −0.0977728
\(568\) −20.0826 −0.842648
\(569\) −15.3620 −0.644007 −0.322003 0.946739i \(-0.604356\pi\)
−0.322003 + 0.946739i \(0.604356\pi\)
\(570\) −10.8142 −0.452958
\(571\) −11.6263 −0.486544 −0.243272 0.969958i \(-0.578221\pi\)
−0.243272 + 0.969958i \(0.578221\pi\)
\(572\) 5.59601 0.233981
\(573\) 13.5891 0.567692
\(574\) −22.3208 −0.931652
\(575\) −25.9584 −1.08254
\(576\) 6.15192 0.256330
\(577\) 0.662416 0.0275768 0.0137884 0.999905i \(-0.495611\pi\)
0.0137884 + 0.999905i \(0.495611\pi\)
\(578\) −0.943890 −0.0392606
\(579\) −13.8923 −0.577345
\(580\) 18.9386 0.786384
\(581\) −20.1671 −0.836672
\(582\) 6.22303 0.257953
\(583\) −52.0798 −2.15693
\(584\) −4.71494 −0.195106
\(585\) 3.52775 0.145855
\(586\) 2.63546 0.108870
\(587\) 19.5779 0.808067 0.404034 0.914744i \(-0.367608\pi\)
0.404034 + 0.914744i \(0.367608\pi\)
\(588\) 1.75206 0.0722538
\(589\) 7.52875 0.310217
\(590\) 17.1121 0.704496
\(591\) 5.71584 0.235118
\(592\) 0.641535 0.0263669
\(593\) −5.06598 −0.208035 −0.104018 0.994575i \(-0.533170\pi\)
−0.104018 + 0.994575i \(0.533170\pi\)
\(594\) 4.73701 0.194362
\(595\) 8.16906 0.334899
\(596\) 23.9691 0.981812
\(597\) −24.5328 −1.00406
\(598\) 3.36902 0.137769
\(599\) −3.15884 −0.129067 −0.0645333 0.997916i \(-0.520556\pi\)
−0.0645333 + 0.997916i \(0.520556\pi\)
\(600\) 21.4577 0.876006
\(601\) −28.8749 −1.17783 −0.588916 0.808194i \(-0.700445\pi\)
−0.588916 + 0.808194i \(0.700445\pi\)
\(602\) 22.0172 0.897353
\(603\) −3.48575 −0.141951
\(604\) −2.79060 −0.113548
\(605\) 49.7777 2.02375
\(606\) −2.99006 −0.121463
\(607\) −17.2862 −0.701626 −0.350813 0.936446i \(-0.614095\pi\)
−0.350813 + 0.936446i \(0.614095\pi\)
\(608\) −17.4636 −0.708244
\(609\) 11.3302 0.459121
\(610\) 4.94914 0.200385
\(611\) 9.74161 0.394103
\(612\) 1.10907 0.0448316
\(613\) −8.17573 −0.330214 −0.165107 0.986276i \(-0.552797\pi\)
−0.165107 + 0.986276i \(0.552797\pi\)
\(614\) −25.5702 −1.03193
\(615\) −35.6403 −1.43716
\(616\) 34.2882 1.38151
\(617\) −7.63160 −0.307237 −0.153618 0.988130i \(-0.549093\pi\)
−0.153618 + 0.988130i \(0.549093\pi\)
\(618\) −2.92764 −0.117767
\(619\) 19.6432 0.789525 0.394763 0.918783i \(-0.370827\pi\)
0.394763 + 0.918783i \(0.370827\pi\)
\(620\) −8.97293 −0.360362
\(621\) −3.55015 −0.142463
\(622\) −23.0593 −0.924594
\(623\) 38.0790 1.52560
\(624\) −0.554789 −0.0222093
\(625\) −8.09553 −0.323821
\(626\) −27.3290 −1.09229
\(627\) −16.3868 −0.654426
\(628\) −1.10907 −0.0442568
\(629\) 1.16260 0.0463557
\(630\) 7.71069 0.307201
\(631\) 43.5189 1.73246 0.866229 0.499647i \(-0.166537\pi\)
0.866229 + 0.499647i \(0.166537\pi\)
\(632\) −33.5677 −1.33525
\(633\) −2.65539 −0.105542
\(634\) 4.95147 0.196648
\(635\) 38.1688 1.51468
\(636\) −11.5092 −0.456371
\(637\) −1.58827 −0.0629296
\(638\) −23.0532 −0.912683
\(639\) −6.84335 −0.270719
\(640\) 17.1584 0.678244
\(641\) −35.6057 −1.40634 −0.703170 0.711022i \(-0.748233\pi\)
−0.703170 + 0.711022i \(0.748233\pi\)
\(642\) −8.41918 −0.332279
\(643\) −38.1629 −1.50500 −0.752500 0.658593i \(-0.771152\pi\)
−0.752500 + 0.658593i \(0.771152\pi\)
\(644\) −9.16677 −0.361221
\(645\) 35.1555 1.38425
\(646\) 3.08200 0.121260
\(647\) 29.6505 1.16568 0.582840 0.812587i \(-0.301942\pi\)
0.582840 + 0.812587i \(0.301942\pi\)
\(648\) 2.93462 0.115283
\(649\) 25.9301 1.01784
\(650\) −6.93885 −0.272164
\(651\) −5.36811 −0.210393
\(652\) −19.3891 −0.759334
\(653\) −20.4813 −0.801496 −0.400748 0.916188i \(-0.631250\pi\)
−0.400748 + 0.916188i \(0.631250\pi\)
\(654\) 6.89754 0.269715
\(655\) 30.6537 1.19774
\(656\) 5.60494 0.218836
\(657\) −1.60666 −0.0626818
\(658\) 21.2925 0.830067
\(659\) 11.2831 0.439528 0.219764 0.975553i \(-0.429471\pi\)
0.219764 + 0.975553i \(0.429471\pi\)
\(660\) 19.5302 0.760210
\(661\) −30.2059 −1.17487 −0.587436 0.809271i \(-0.699863\pi\)
−0.587436 + 0.809271i \(0.699863\pi\)
\(662\) 16.9899 0.660332
\(663\) −1.00539 −0.0390462
\(664\) 25.4206 0.986510
\(665\) −26.6737 −1.03436
\(666\) 1.09736 0.0425219
\(667\) 17.2772 0.668975
\(668\) 17.9232 0.693468
\(669\) 8.14373 0.314855
\(670\) 11.5446 0.446009
\(671\) 7.49945 0.289513
\(672\) 12.4518 0.480339
\(673\) 21.1764 0.816291 0.408145 0.912917i \(-0.366176\pi\)
0.408145 + 0.912917i \(0.366176\pi\)
\(674\) 31.2515 1.20376
\(675\) 7.31191 0.281436
\(676\) 13.2969 0.511418
\(677\) −2.85289 −0.109645 −0.0548227 0.998496i \(-0.517459\pi\)
−0.0548227 + 0.998496i \(0.517459\pi\)
\(678\) 12.5553 0.482183
\(679\) 15.3494 0.589054
\(680\) −10.2971 −0.394876
\(681\) −25.2961 −0.969347
\(682\) 10.9223 0.418238
\(683\) 25.1103 0.960821 0.480410 0.877044i \(-0.340488\pi\)
0.480410 + 0.877044i \(0.340488\pi\)
\(684\) −3.62136 −0.138466
\(685\) −19.8966 −0.760209
\(686\) −18.8541 −0.719852
\(687\) −17.9428 −0.684560
\(688\) −5.52870 −0.210780
\(689\) 10.4333 0.397477
\(690\) 11.7579 0.447617
\(691\) 32.2779 1.22791 0.613955 0.789341i \(-0.289578\pi\)
0.613955 + 0.789341i \(0.289578\pi\)
\(692\) −7.49467 −0.284905
\(693\) 11.6840 0.443840
\(694\) 3.95251 0.150035
\(695\) −22.6550 −0.859353
\(696\) −14.2816 −0.541344
\(697\) 10.1573 0.384736
\(698\) −22.2908 −0.843720
\(699\) 3.92422 0.148427
\(700\) 18.8799 0.713594
\(701\) −4.68951 −0.177120 −0.0885601 0.996071i \(-0.528227\pi\)
−0.0885601 + 0.996071i \(0.528227\pi\)
\(702\) −0.948979 −0.0358169
\(703\) −3.79612 −0.143173
\(704\) −30.8740 −1.16361
\(705\) 33.9984 1.28045
\(706\) 4.27711 0.160971
\(707\) −7.37510 −0.277369
\(708\) 5.73034 0.215359
\(709\) −25.6853 −0.964631 −0.482315 0.875998i \(-0.660204\pi\)
−0.482315 + 0.875998i \(0.660204\pi\)
\(710\) 22.6648 0.850596
\(711\) −11.4385 −0.428978
\(712\) −47.9986 −1.79882
\(713\) −8.18575 −0.306559
\(714\) −2.19751 −0.0822397
\(715\) −17.7044 −0.662107
\(716\) 20.5433 0.767738
\(717\) −3.38682 −0.126483
\(718\) 3.18719 0.118945
\(719\) 23.9735 0.894062 0.447031 0.894518i \(-0.352481\pi\)
0.447031 + 0.894518i \(0.352481\pi\)
\(720\) −1.93622 −0.0721587
\(721\) −7.22113 −0.268929
\(722\) 7.87052 0.292910
\(723\) 26.9066 1.00067
\(724\) 23.0636 0.857151
\(725\) −35.5842 −1.32156
\(726\) −13.3904 −0.496964
\(727\) 11.4994 0.426489 0.213245 0.976999i \(-0.431597\pi\)
0.213245 + 0.976999i \(0.431597\pi\)
\(728\) −6.86906 −0.254584
\(729\) 1.00000 0.0370370
\(730\) 5.32118 0.196946
\(731\) −10.0192 −0.370572
\(732\) 1.65732 0.0612563
\(733\) 2.16985 0.0801453 0.0400726 0.999197i \(-0.487241\pi\)
0.0400726 + 0.999197i \(0.487241\pi\)
\(734\) 28.3358 1.04589
\(735\) −5.54309 −0.204460
\(736\) 18.9876 0.699892
\(737\) 17.4936 0.644386
\(738\) 9.58739 0.352917
\(739\) 30.3377 1.11599 0.557995 0.829844i \(-0.311571\pi\)
0.557995 + 0.829844i \(0.311571\pi\)
\(740\) 4.52430 0.166316
\(741\) 3.28282 0.120597
\(742\) 22.8043 0.837173
\(743\) 12.0601 0.442444 0.221222 0.975224i \(-0.428996\pi\)
0.221222 + 0.975224i \(0.428996\pi\)
\(744\) 6.76649 0.248072
\(745\) −75.8323 −2.77828
\(746\) 4.16503 0.152493
\(747\) 8.66231 0.316937
\(748\) −5.56600 −0.203513
\(749\) −20.7663 −0.758782
\(750\) −7.65693 −0.279592
\(751\) −43.1501 −1.57457 −0.787285 0.616589i \(-0.788514\pi\)
−0.787285 + 0.616589i \(0.788514\pi\)
\(752\) −5.34672 −0.194975
\(753\) −18.0513 −0.657825
\(754\) 4.61831 0.168189
\(755\) 8.82878 0.321312
\(756\) 2.58208 0.0939093
\(757\) −12.5373 −0.455675 −0.227838 0.973699i \(-0.573166\pi\)
−0.227838 + 0.973699i \(0.573166\pi\)
\(758\) 18.9422 0.688013
\(759\) 17.8168 0.646709
\(760\) 33.6222 1.21961
\(761\) 16.7430 0.606935 0.303467 0.952842i \(-0.401856\pi\)
0.303467 + 0.952842i \(0.401856\pi\)
\(762\) −10.2675 −0.371954
\(763\) 17.0131 0.615914
\(764\) −15.0713 −0.545259
\(765\) −3.50883 −0.126862
\(766\) −21.1563 −0.764409
\(767\) −5.19465 −0.187568
\(768\) −16.9195 −0.610530
\(769\) −41.8387 −1.50874 −0.754372 0.656447i \(-0.772058\pi\)
−0.754372 + 0.656447i \(0.772058\pi\)
\(770\) −38.6969 −1.39454
\(771\) 9.84097 0.354414
\(772\) 15.4076 0.554531
\(773\) −42.0271 −1.51161 −0.755804 0.654798i \(-0.772754\pi\)
−0.755804 + 0.654798i \(0.772754\pi\)
\(774\) −9.45697 −0.339924
\(775\) 16.8594 0.605608
\(776\) −19.3478 −0.694547
\(777\) 2.70669 0.0971019
\(778\) −3.73241 −0.133813
\(779\) −33.1658 −1.18829
\(780\) −3.91253 −0.140091
\(781\) 34.3441 1.22893
\(782\) −3.35095 −0.119830
\(783\) −4.86661 −0.173918
\(784\) 0.871729 0.0311332
\(785\) 3.50883 0.125236
\(786\) −8.24597 −0.294124
\(787\) 2.07376 0.0739214 0.0369607 0.999317i \(-0.488232\pi\)
0.0369607 + 0.999317i \(0.488232\pi\)
\(788\) −6.33928 −0.225828
\(789\) −26.3248 −0.937187
\(790\) 37.8838 1.34785
\(791\) 30.9681 1.10110
\(792\) −14.7277 −0.523326
\(793\) −1.50239 −0.0533513
\(794\) −20.3450 −0.722018
\(795\) 36.4124 1.29141
\(796\) 27.2086 0.964384
\(797\) 27.2290 0.964501 0.482250 0.876033i \(-0.339820\pi\)
0.482250 + 0.876033i \(0.339820\pi\)
\(798\) 7.17533 0.254004
\(799\) −9.68937 −0.342785
\(800\) −39.1070 −1.38264
\(801\) −16.3560 −0.577910
\(802\) −15.6574 −0.552883
\(803\) 8.06319 0.284544
\(804\) 3.86595 0.136342
\(805\) 29.0014 1.02217
\(806\) −2.18811 −0.0770728
\(807\) −26.8069 −0.943647
\(808\) 9.29631 0.327043
\(809\) −41.9532 −1.47500 −0.737498 0.675350i \(-0.763993\pi\)
−0.737498 + 0.675350i \(0.763993\pi\)
\(810\) −3.31195 −0.116370
\(811\) −6.55463 −0.230164 −0.115082 0.993356i \(-0.536713\pi\)
−0.115082 + 0.993356i \(0.536713\pi\)
\(812\) −12.5660 −0.440979
\(813\) −14.8379 −0.520389
\(814\) −5.50722 −0.193028
\(815\) 61.3422 2.14873
\(816\) 0.551813 0.0193173
\(817\) 32.7147 1.14454
\(818\) −35.5400 −1.24263
\(819\) −2.34070 −0.0817905
\(820\) 39.5277 1.38037
\(821\) 23.4737 0.819237 0.409618 0.912257i \(-0.365662\pi\)
0.409618 + 0.912257i \(0.365662\pi\)
\(822\) 5.35225 0.186681
\(823\) −16.1427 −0.562700 −0.281350 0.959605i \(-0.590782\pi\)
−0.281350 + 0.959605i \(0.590782\pi\)
\(824\) 9.10223 0.317091
\(825\) −36.6956 −1.27758
\(826\) −11.3541 −0.395058
\(827\) 6.01408 0.209130 0.104565 0.994518i \(-0.466655\pi\)
0.104565 + 0.994518i \(0.466655\pi\)
\(828\) 3.93738 0.136833
\(829\) 23.0125 0.799258 0.399629 0.916677i \(-0.369139\pi\)
0.399629 + 0.916677i \(0.369139\pi\)
\(830\) −28.6891 −0.995815
\(831\) −18.8597 −0.654234
\(832\) 6.18509 0.214429
\(833\) 1.57975 0.0547352
\(834\) 6.09428 0.211028
\(835\) −56.7045 −1.96234
\(836\) 18.1742 0.628567
\(837\) 2.30575 0.0796983
\(838\) 16.8065 0.580571
\(839\) −23.0000 −0.794048 −0.397024 0.917808i \(-0.629957\pi\)
−0.397024 + 0.917808i \(0.629957\pi\)
\(840\) −23.9731 −0.827151
\(841\) −5.31614 −0.183315
\(842\) −17.9718 −0.619350
\(843\) 24.0689 0.828978
\(844\) 2.94502 0.101372
\(845\) −42.0681 −1.44719
\(846\) −9.14569 −0.314435
\(847\) −33.0280 −1.13485
\(848\) −5.72636 −0.196644
\(849\) 15.7161 0.539377
\(850\) 6.90163 0.236724
\(851\) 4.12739 0.141485
\(852\) 7.58977 0.260021
\(853\) −56.0393 −1.91875 −0.959374 0.282136i \(-0.908957\pi\)
−0.959374 + 0.282136i \(0.908957\pi\)
\(854\) −3.28380 −0.112369
\(855\) 11.4571 0.391824
\(856\) 26.1758 0.894672
\(857\) −24.5248 −0.837750 −0.418875 0.908044i \(-0.637575\pi\)
−0.418875 + 0.908044i \(0.637575\pi\)
\(858\) 4.76255 0.162591
\(859\) −43.5237 −1.48501 −0.742506 0.669840i \(-0.766363\pi\)
−0.742506 + 0.669840i \(0.766363\pi\)
\(860\) −38.9900 −1.32955
\(861\) 23.6477 0.805911
\(862\) −28.8310 −0.981988
\(863\) −26.1440 −0.889952 −0.444976 0.895543i \(-0.646788\pi\)
−0.444976 + 0.895543i \(0.646788\pi\)
\(864\) −5.34839 −0.181956
\(865\) 23.7113 0.806208
\(866\) −3.96396 −0.134701
\(867\) 1.00000 0.0339618
\(868\) 5.95362 0.202079
\(869\) 57.4054 1.94735
\(870\) 16.1180 0.546450
\(871\) −3.50455 −0.118747
\(872\) −21.4449 −0.726217
\(873\) −6.59296 −0.223138
\(874\) 10.9416 0.370104
\(875\) −18.8861 −0.638468
\(876\) 1.78190 0.0602049
\(877\) −13.6800 −0.461941 −0.230970 0.972961i \(-0.574190\pi\)
−0.230970 + 0.972961i \(0.574190\pi\)
\(878\) −27.7190 −0.935472
\(879\) −2.79213 −0.0941762
\(880\) 9.71713 0.327564
\(881\) −19.4123 −0.654018 −0.327009 0.945021i \(-0.606041\pi\)
−0.327009 + 0.945021i \(0.606041\pi\)
\(882\) 1.49111 0.0502084
\(883\) −23.0824 −0.776785 −0.388392 0.921494i \(-0.626969\pi\)
−0.388392 + 0.921494i \(0.626969\pi\)
\(884\) 1.11505 0.0375033
\(885\) −18.1294 −0.609413
\(886\) −23.4042 −0.786278
\(887\) −12.6679 −0.425347 −0.212674 0.977123i \(-0.568217\pi\)
−0.212674 + 0.977123i \(0.568217\pi\)
\(888\) −3.41178 −0.114492
\(889\) −25.3253 −0.849384
\(890\) 54.1702 1.81579
\(891\) −5.01861 −0.168130
\(892\) −9.03199 −0.302413
\(893\) 31.6378 1.05872
\(894\) 20.3992 0.682251
\(895\) −64.9939 −2.17251
\(896\) −11.3847 −0.380337
\(897\) −3.56929 −0.119175
\(898\) 4.39844 0.146778
\(899\) −11.2212 −0.374247
\(900\) −8.10944 −0.270315
\(901\) −10.3774 −0.345720
\(902\) −48.1153 −1.60206
\(903\) −23.3260 −0.776241
\(904\) −39.0353 −1.29830
\(905\) −72.9675 −2.42552
\(906\) −2.37498 −0.0789033
\(907\) 31.7150 1.05308 0.526540 0.850150i \(-0.323489\pi\)
0.526540 + 0.850150i \(0.323489\pi\)
\(908\) 28.0552 0.931043
\(909\) 3.16781 0.105069
\(910\) 7.75227 0.256985
\(911\) 9.15482 0.303313 0.151656 0.988433i \(-0.451539\pi\)
0.151656 + 0.988433i \(0.451539\pi\)
\(912\) −1.80179 −0.0596631
\(913\) −43.4727 −1.43874
\(914\) 4.54784 0.150429
\(915\) −5.24335 −0.173340
\(916\) 19.8999 0.657510
\(917\) −20.3390 −0.671653
\(918\) 0.943890 0.0311530
\(919\) −33.2804 −1.09782 −0.548909 0.835882i \(-0.684957\pi\)
−0.548909 + 0.835882i \(0.684957\pi\)
\(920\) −36.5562 −1.20522
\(921\) 27.0903 0.892655
\(922\) 7.42860 0.244648
\(923\) −6.88025 −0.226466
\(924\) −12.9584 −0.426301
\(925\) −8.50079 −0.279504
\(926\) −3.85533 −0.126694
\(927\) 3.10167 0.101872
\(928\) 26.0285 0.854428
\(929\) −24.3960 −0.800407 −0.400204 0.916426i \(-0.631061\pi\)
−0.400204 + 0.916426i \(0.631061\pi\)
\(930\) −7.63652 −0.250411
\(931\) −5.15823 −0.169054
\(932\) −4.35224 −0.142562
\(933\) 24.4301 0.799805
\(934\) 15.3586 0.502550
\(935\) 17.6094 0.575891
\(936\) 2.95045 0.0964383
\(937\) 46.8690 1.53114 0.765571 0.643351i \(-0.222456\pi\)
0.765571 + 0.643351i \(0.222456\pi\)
\(938\) −7.65998 −0.250107
\(939\) 28.9536 0.944864
\(940\) −37.7067 −1.22986
\(941\) −57.9973 −1.89066 −0.945328 0.326120i \(-0.894259\pi\)
−0.945328 + 0.326120i \(0.894259\pi\)
\(942\) −0.943890 −0.0307536
\(943\) 36.0600 1.17428
\(944\) 2.85110 0.0927955
\(945\) −8.16906 −0.265740
\(946\) 47.4608 1.54308
\(947\) 26.2220 0.852101 0.426050 0.904699i \(-0.359905\pi\)
0.426050 + 0.904699i \(0.359905\pi\)
\(948\) 12.6861 0.412027
\(949\) −1.61532 −0.0524356
\(950\) −22.5353 −0.731142
\(951\) −5.24581 −0.170107
\(952\) 6.83222 0.221433
\(953\) 33.6122 1.08881 0.544404 0.838823i \(-0.316756\pi\)
0.544404 + 0.838823i \(0.316756\pi\)
\(954\) −9.79507 −0.317127
\(955\) 47.6818 1.54295
\(956\) 3.75622 0.121485
\(957\) 24.4236 0.789502
\(958\) 29.6251 0.957145
\(959\) 13.2016 0.426300
\(960\) 21.5861 0.696687
\(961\) −25.6835 −0.828501
\(962\) 1.10328 0.0355711
\(963\) 8.91967 0.287432
\(964\) −29.8414 −0.961127
\(965\) −48.7458 −1.56918
\(966\) −7.80149 −0.251009
\(967\) −41.2020 −1.32497 −0.662484 0.749076i \(-0.730498\pi\)
−0.662484 + 0.749076i \(0.730498\pi\)
\(968\) 41.6317 1.33809
\(969\) −3.26521 −0.104894
\(970\) 21.8356 0.701098
\(971\) −4.14084 −0.132886 −0.0664429 0.997790i \(-0.521165\pi\)
−0.0664429 + 0.997790i \(0.521165\pi\)
\(972\) −1.10907 −0.0355735
\(973\) 15.0318 0.481897
\(974\) 13.9302 0.446353
\(975\) 7.35134 0.235431
\(976\) 0.824590 0.0263945
\(977\) −6.84908 −0.219122 −0.109561 0.993980i \(-0.534944\pi\)
−0.109561 + 0.993980i \(0.534944\pi\)
\(978\) −16.5013 −0.527653
\(979\) 82.0842 2.62342
\(980\) 6.14769 0.196381
\(981\) −7.30757 −0.233313
\(982\) 16.0925 0.513532
\(983\) 13.9052 0.443508 0.221754 0.975103i \(-0.428822\pi\)
0.221754 + 0.975103i \(0.428822\pi\)
\(984\) −29.8079 −0.950240
\(985\) 20.0559 0.639035
\(986\) −4.59354 −0.146288
\(987\) −22.5582 −0.718036
\(988\) −3.64088 −0.115832
\(989\) −35.5695 −1.13104
\(990\) 16.6214 0.528262
\(991\) 56.9848 1.81018 0.905091 0.425218i \(-0.139802\pi\)
0.905091 + 0.425218i \(0.139802\pi\)
\(992\) −12.3320 −0.391543
\(993\) −17.9999 −0.571209
\(994\) −15.0383 −0.476986
\(995\) −86.0814 −2.72896
\(996\) −9.60713 −0.304414
\(997\) 45.0997 1.42832 0.714161 0.699982i \(-0.246808\pi\)
0.714161 + 0.699982i \(0.246808\pi\)
\(998\) 6.42995 0.203537
\(999\) −1.16260 −0.0367829
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 \(a_p\))