Properties

Label 8002.2.a.e.1.16
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 1.16
Character \(\chi\) = 8002.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.85869 q^{3} +1.00000 q^{4} -0.435894 q^{5} +1.85869 q^{6} +1.03466 q^{7} -1.00000 q^{8} +0.454718 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.85869 q^{3} +1.00000 q^{4} -0.435894 q^{5} +1.85869 q^{6} +1.03466 q^{7} -1.00000 q^{8} +0.454718 q^{9} +0.435894 q^{10} +0.520763 q^{11} -1.85869 q^{12} +4.30262 q^{13} -1.03466 q^{14} +0.810191 q^{15} +1.00000 q^{16} -6.53111 q^{17} -0.454718 q^{18} -4.45215 q^{19} -0.435894 q^{20} -1.92311 q^{21} -0.520763 q^{22} -3.22721 q^{23} +1.85869 q^{24} -4.81000 q^{25} -4.30262 q^{26} +4.73088 q^{27} +1.03466 q^{28} +3.89653 q^{29} -0.810191 q^{30} -7.29886 q^{31} -1.00000 q^{32} -0.967935 q^{33} +6.53111 q^{34} -0.451002 q^{35} +0.454718 q^{36} -4.64766 q^{37} +4.45215 q^{38} -7.99722 q^{39} +0.435894 q^{40} -1.79580 q^{41} +1.92311 q^{42} -5.48331 q^{43} +0.520763 q^{44} -0.198209 q^{45} +3.22721 q^{46} +7.14256 q^{47} -1.85869 q^{48} -5.92948 q^{49} +4.81000 q^{50} +12.1393 q^{51} +4.30262 q^{52} +5.49063 q^{53} -4.73088 q^{54} -0.226997 q^{55} -1.03466 q^{56} +8.27516 q^{57} -3.89653 q^{58} -2.34835 q^{59} +0.810191 q^{60} +12.0427 q^{61} +7.29886 q^{62} +0.470478 q^{63} +1.00000 q^{64} -1.87549 q^{65} +0.967935 q^{66} +7.04743 q^{67} -6.53111 q^{68} +5.99836 q^{69} +0.451002 q^{70} -1.51568 q^{71} -0.454718 q^{72} +1.54224 q^{73} +4.64766 q^{74} +8.94028 q^{75} -4.45215 q^{76} +0.538813 q^{77} +7.99722 q^{78} +8.77247 q^{79} -0.435894 q^{80} -10.1574 q^{81} +1.79580 q^{82} +0.586340 q^{83} -1.92311 q^{84} +2.84687 q^{85} +5.48331 q^{86} -7.24243 q^{87} -0.520763 q^{88} -3.03939 q^{89} +0.198209 q^{90} +4.45175 q^{91} -3.22721 q^{92} +13.5663 q^{93} -7.14256 q^{94} +1.94067 q^{95} +1.85869 q^{96} -17.0736 q^{97} +5.92948 q^{98} +0.236800 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 77q - 77q^{2} + 10q^{3} + 77q^{4} + 18q^{5} - 10q^{6} + 21q^{7} - 77q^{8} + 71q^{9} + O(q^{10}) \) \( 77q - 77q^{2} + 10q^{3} + 77q^{4} + 18q^{5} - 10q^{6} + 21q^{7} - 77q^{8} + 71q^{9} - 18q^{10} + 30q^{11} + 10q^{12} - 2q^{13} - 21q^{14} + 21q^{15} + 77q^{16} + 60q^{17} - 71q^{18} - 3q^{19} + 18q^{20} + 10q^{21} - 30q^{22} + 53q^{23} - 10q^{24} + 59q^{25} + 2q^{26} + 43q^{27} + 21q^{28} + 30q^{29} - 21q^{30} + 22q^{31} - 77q^{32} + 31q^{33} - 60q^{34} + 41q^{35} + 71q^{36} - 3q^{37} + 3q^{38} + 44q^{39} - 18q^{40} + 48q^{41} - 10q^{42} + 21q^{43} + 30q^{44} + 33q^{45} - 53q^{46} + 107q^{47} + 10q^{48} + 24q^{49} - 59q^{50} + 18q^{51} - 2q^{52} + 42q^{53} - 43q^{54} + 49q^{55} - 21q^{56} + 32q^{57} - 30q^{58} + 42q^{59} + 21q^{60} - 31q^{61} - 22q^{62} + 109q^{63} + 77q^{64} + 39q^{65} - 31q^{66} - q^{67} + 60q^{68} - 33q^{69} - 41q^{70} + 58q^{71} - 71q^{72} + 35q^{73} + 3q^{74} + 34q^{75} - 3q^{76} + 86q^{77} - 44q^{78} + 25q^{79} + 18q^{80} + 53q^{81} - 48q^{82} + 107q^{83} + 10q^{84} + 21q^{85} - 21q^{86} + 100q^{87} - 30q^{88} + 34q^{89} - 33q^{90} - 51q^{91} + 53q^{92} + 48q^{93} - 107q^{94} + 118q^{95} - 10q^{96} - 13q^{97} - 24q^{98} + 63q^{99} + O(q^{100}) \)

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
\(3\) −1.85869 −1.07311 −0.536557 0.843864i \(-0.680275\pi\)
−0.536557 + 0.843864i \(0.680275\pi\)
\(4\) 1.00000 0.500000
\(5\) −0.435894 −0.194938 −0.0974689 0.995239i \(-0.531075\pi\)
−0.0974689 + 0.995239i \(0.531075\pi\)
\(6\) 1.85869 0.758806
\(7\) 1.03466 0.391065 0.195532 0.980697i \(-0.437357\pi\)
0.195532 + 0.980697i \(0.437357\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0.454718 0.151573
\(10\) 0.435894 0.137842
\(11\) 0.520763 0.157016 0.0785080 0.996913i \(-0.474984\pi\)
0.0785080 + 0.996913i \(0.474984\pi\)
\(12\) −1.85869 −0.536557
\(13\) 4.30262 1.19333 0.596666 0.802490i \(-0.296492\pi\)
0.596666 + 0.802490i \(0.296492\pi\)
\(14\) −1.03466 −0.276525
\(15\) 0.810191 0.209190
\(16\) 1.00000 0.250000
\(17\) −6.53111 −1.58403 −0.792013 0.610504i \(-0.790967\pi\)
−0.792013 + 0.610504i \(0.790967\pi\)
\(18\) −0.454718 −0.107178
\(19\) −4.45215 −1.02139 −0.510697 0.859761i \(-0.670613\pi\)
−0.510697 + 0.859761i \(0.670613\pi\)
\(20\) −0.435894 −0.0974689
\(21\) −1.92311 −0.419657
\(22\) −0.520763 −0.111027
\(23\) −3.22721 −0.672919 −0.336459 0.941698i \(-0.609229\pi\)
−0.336459 + 0.941698i \(0.609229\pi\)
\(24\) 1.85869 0.379403
\(25\) −4.81000 −0.961999
\(26\) −4.30262 −0.843813
\(27\) 4.73088 0.910459
\(28\) 1.03466 0.195532
\(29\) 3.89653 0.723568 0.361784 0.932262i \(-0.382168\pi\)
0.361784 + 0.932262i \(0.382168\pi\)
\(30\) −0.810191 −0.147920
\(31\) −7.29886 −1.31091 −0.655457 0.755232i \(-0.727524\pi\)
−0.655457 + 0.755232i \(0.727524\pi\)
\(32\) −1.00000 −0.176777
\(33\) −0.967935 −0.168496
\(34\) 6.53111 1.12008
\(35\) −0.451002 −0.0762333
\(36\) 0.454718 0.0757863
\(37\) −4.64766 −0.764070 −0.382035 0.924148i \(-0.624777\pi\)
−0.382035 + 0.924148i \(0.624777\pi\)
\(38\) 4.45215 0.722235
\(39\) −7.99722 −1.28058
\(40\) 0.435894 0.0689209
\(41\) −1.79580 −0.280457 −0.140228 0.990119i \(-0.544784\pi\)
−0.140228 + 0.990119i \(0.544784\pi\)
\(42\) 1.92311 0.296742
\(43\) −5.48331 −0.836198 −0.418099 0.908402i \(-0.637303\pi\)
−0.418099 + 0.908402i \(0.637303\pi\)
\(44\) 0.520763 0.0785080
\(45\) −0.198209 −0.0295472
\(46\) 3.22721 0.475825
\(47\) 7.14256 1.04185 0.520925 0.853603i \(-0.325587\pi\)
0.520925 + 0.853603i \(0.325587\pi\)
\(48\) −1.85869 −0.268278
\(49\) −5.92948 −0.847068
\(50\) 4.81000 0.680236
\(51\) 12.1393 1.69984
\(52\) 4.30262 0.596666
\(53\) 5.49063 0.754196 0.377098 0.926173i \(-0.376922\pi\)
0.377098 + 0.926173i \(0.376922\pi\)
\(54\) −4.73088 −0.643792
\(55\) −0.226997 −0.0306083
\(56\) −1.03466 −0.138262
\(57\) 8.27516 1.09607
\(58\) −3.89653 −0.511640
\(59\) −2.34835 −0.305729 −0.152865 0.988247i \(-0.548850\pi\)
−0.152865 + 0.988247i \(0.548850\pi\)
\(60\) 0.810191 0.104595
\(61\) 12.0427 1.54190 0.770952 0.636893i \(-0.219781\pi\)
0.770952 + 0.636893i \(0.219781\pi\)
\(62\) 7.29886 0.926957
\(63\) 0.470478 0.0592747
\(64\) 1.00000 0.125000
\(65\) −1.87549 −0.232625
\(66\) 0.967935 0.119145
\(67\) 7.04743 0.860980 0.430490 0.902595i \(-0.358341\pi\)
0.430490 + 0.902595i \(0.358341\pi\)
\(68\) −6.53111 −0.792013
\(69\) 5.99836 0.722118
\(70\) 0.451002 0.0539051
\(71\) −1.51568 −0.179879 −0.0899393 0.995947i \(-0.528667\pi\)
−0.0899393 + 0.995947i \(0.528667\pi\)
\(72\) −0.454718 −0.0535890
\(73\) 1.54224 0.180506 0.0902528 0.995919i \(-0.471233\pi\)
0.0902528 + 0.995919i \(0.471233\pi\)
\(74\) 4.64766 0.540279
\(75\) 8.94028 1.03233
\(76\) −4.45215 −0.510697
\(77\) 0.538813 0.0614034
\(78\) 7.99722 0.905507
\(79\) 8.77247 0.986980 0.493490 0.869751i \(-0.335721\pi\)
0.493490 + 0.869751i \(0.335721\pi\)
\(80\) −0.435894 −0.0487344
\(81\) −10.1574 −1.12860
\(82\) 1.79580 0.198313
\(83\) 0.586340 0.0643592 0.0321796 0.999482i \(-0.489755\pi\)
0.0321796 + 0.999482i \(0.489755\pi\)
\(84\) −1.92311 −0.209828
\(85\) 2.84687 0.308786
\(86\) 5.48331 0.591281
\(87\) −7.24243 −0.776470
\(88\) −0.520763 −0.0555135
\(89\) −3.03939 −0.322175 −0.161087 0.986940i \(-0.551500\pi\)
−0.161087 + 0.986940i \(0.551500\pi\)
\(90\) 0.198209 0.0208930
\(91\) 4.45175 0.466670
\(92\) −3.22721 −0.336459
\(93\) 13.5663 1.40676
\(94\) −7.14256 −0.736699
\(95\) 1.94067 0.199108
\(96\) 1.85869 0.189701
\(97\) −17.0736 −1.73356 −0.866782 0.498687i \(-0.833816\pi\)
−0.866782 + 0.498687i \(0.833816\pi\)
\(98\) 5.92948 0.598968
\(99\) 0.236800 0.0237993
\(100\) −4.81000 −0.481000
\(101\) 14.0107 1.39412 0.697058 0.717015i \(-0.254492\pi\)
0.697058 + 0.717015i \(0.254492\pi\)
\(102\) −12.1393 −1.20197
\(103\) −10.7851 −1.06269 −0.531346 0.847155i \(-0.678314\pi\)
−0.531346 + 0.847155i \(0.678314\pi\)
\(104\) −4.30262 −0.421906
\(105\) 0.838272 0.0818070
\(106\) −5.49063 −0.533297
\(107\) −0.570891 −0.0551901 −0.0275951 0.999619i \(-0.508785\pi\)
−0.0275951 + 0.999619i \(0.508785\pi\)
\(108\) 4.73088 0.455229
\(109\) −6.25788 −0.599396 −0.299698 0.954034i \(-0.596886\pi\)
−0.299698 + 0.954034i \(0.596886\pi\)
\(110\) 0.226997 0.0216434
\(111\) 8.63854 0.819934
\(112\) 1.03466 0.0977662
\(113\) −6.51293 −0.612685 −0.306342 0.951921i \(-0.599105\pi\)
−0.306342 + 0.951921i \(0.599105\pi\)
\(114\) −8.27516 −0.775040
\(115\) 1.40672 0.131177
\(116\) 3.89653 0.361784
\(117\) 1.95648 0.180876
\(118\) 2.34835 0.216183
\(119\) −6.75747 −0.619457
\(120\) −0.810191 −0.0739600
\(121\) −10.7288 −0.975346
\(122\) −12.0427 −1.09029
\(123\) 3.33783 0.300962
\(124\) −7.29886 −0.655457
\(125\) 4.27612 0.382468
\(126\) −0.470478 −0.0419135
\(127\) 4.57387 0.405866 0.202933 0.979193i \(-0.434953\pi\)
0.202933 + 0.979193i \(0.434953\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 10.1918 0.897335
\(130\) 1.87549 0.164491
\(131\) 19.1978 1.67732 0.838661 0.544653i \(-0.183339\pi\)
0.838661 + 0.544653i \(0.183339\pi\)
\(132\) −0.967935 −0.0842480
\(133\) −4.60647 −0.399431
\(134\) −7.04743 −0.608805
\(135\) −2.06216 −0.177483
\(136\) 6.53111 0.560038
\(137\) −2.72558 −0.232862 −0.116431 0.993199i \(-0.537145\pi\)
−0.116431 + 0.993199i \(0.537145\pi\)
\(138\) −5.99836 −0.510615
\(139\) 1.00198 0.0849866 0.0424933 0.999097i \(-0.486470\pi\)
0.0424933 + 0.999097i \(0.486470\pi\)
\(140\) −0.451002 −0.0381166
\(141\) −13.2758 −1.11802
\(142\) 1.51568 0.127193
\(143\) 2.24064 0.187372
\(144\) 0.454718 0.0378931
\(145\) −1.69848 −0.141051
\(146\) −1.54224 −0.127637
\(147\) 11.0210 0.909000
\(148\) −4.64766 −0.382035
\(149\) −7.18757 −0.588829 −0.294414 0.955678i \(-0.595125\pi\)
−0.294414 + 0.955678i \(0.595125\pi\)
\(150\) −8.94028 −0.729971
\(151\) −2.78209 −0.226403 −0.113202 0.993572i \(-0.536111\pi\)
−0.113202 + 0.993572i \(0.536111\pi\)
\(152\) 4.45215 0.361117
\(153\) −2.96981 −0.240095
\(154\) −0.538813 −0.0434188
\(155\) 3.18153 0.255547
\(156\) −7.99722 −0.640290
\(157\) 0.0507138 0.00404740 0.00202370 0.999998i \(-0.499356\pi\)
0.00202370 + 0.999998i \(0.499356\pi\)
\(158\) −8.77247 −0.697900
\(159\) −10.2054 −0.809338
\(160\) 0.435894 0.0344605
\(161\) −3.33906 −0.263155
\(162\) 10.1574 0.798040
\(163\) 4.43377 0.347279 0.173640 0.984809i \(-0.444447\pi\)
0.173640 + 0.984809i \(0.444447\pi\)
\(164\) −1.79580 −0.140228
\(165\) 0.421917 0.0328462
\(166\) −0.586340 −0.0455088
\(167\) −6.52642 −0.505030 −0.252515 0.967593i \(-0.581258\pi\)
−0.252515 + 0.967593i \(0.581258\pi\)
\(168\) 1.92311 0.148371
\(169\) 5.51251 0.424039
\(170\) −2.84687 −0.218345
\(171\) −2.02447 −0.154815
\(172\) −5.48331 −0.418099
\(173\) −9.43170 −0.717079 −0.358539 0.933515i \(-0.616725\pi\)
−0.358539 + 0.933515i \(0.616725\pi\)
\(174\) 7.24243 0.549048
\(175\) −4.97671 −0.376204
\(176\) 0.520763 0.0392540
\(177\) 4.36485 0.328082
\(178\) 3.03939 0.227812
\(179\) 17.4937 1.30754 0.653771 0.756692i \(-0.273186\pi\)
0.653771 + 0.756692i \(0.273186\pi\)
\(180\) −0.198209 −0.0147736
\(181\) 8.94210 0.664661 0.332331 0.943163i \(-0.392165\pi\)
0.332331 + 0.943163i \(0.392165\pi\)
\(182\) −4.45175 −0.329985
\(183\) −22.3835 −1.65464
\(184\) 3.22721 0.237913
\(185\) 2.02589 0.148946
\(186\) −13.5663 −0.994730
\(187\) −3.40116 −0.248717
\(188\) 7.14256 0.520925
\(189\) 4.89486 0.356048
\(190\) −1.94067 −0.140791
\(191\) 7.85435 0.568321 0.284160 0.958777i \(-0.408285\pi\)
0.284160 + 0.958777i \(0.408285\pi\)
\(192\) −1.85869 −0.134139
\(193\) 14.8251 1.06714 0.533568 0.845757i \(-0.320851\pi\)
0.533568 + 0.845757i \(0.320851\pi\)
\(194\) 17.0736 1.22582
\(195\) 3.48594 0.249633
\(196\) −5.92948 −0.423534
\(197\) 9.35429 0.666466 0.333233 0.942845i \(-0.391860\pi\)
0.333233 + 0.942845i \(0.391860\pi\)
\(198\) −0.236800 −0.0168287
\(199\) −19.9525 −1.41439 −0.707196 0.707018i \(-0.750040\pi\)
−0.707196 + 0.707018i \(0.750040\pi\)
\(200\) 4.81000 0.340118
\(201\) −13.0990 −0.923929
\(202\) −14.0107 −0.985788
\(203\) 4.03159 0.282962
\(204\) 12.1393 0.849920
\(205\) 0.782779 0.0546716
\(206\) 10.7851 0.751437
\(207\) −1.46747 −0.101996
\(208\) 4.30262 0.298333
\(209\) −2.31852 −0.160375
\(210\) −0.838272 −0.0578463
\(211\) −6.18616 −0.425873 −0.212936 0.977066i \(-0.568303\pi\)
−0.212936 + 0.977066i \(0.568303\pi\)
\(212\) 5.49063 0.377098
\(213\) 2.81718 0.193030
\(214\) 0.570891 0.0390253
\(215\) 2.39014 0.163007
\(216\) −4.73088 −0.321896
\(217\) −7.55184 −0.512653
\(218\) 6.25788 0.423837
\(219\) −2.86654 −0.193703
\(220\) −0.226997 −0.0153042
\(221\) −28.1008 −1.89027
\(222\) −8.63854 −0.579781
\(223\) 9.93719 0.665444 0.332722 0.943025i \(-0.392033\pi\)
0.332722 + 0.943025i \(0.392033\pi\)
\(224\) −1.03466 −0.0691311
\(225\) −2.18719 −0.145813
\(226\) 6.51293 0.433234
\(227\) −6.46212 −0.428906 −0.214453 0.976734i \(-0.568797\pi\)
−0.214453 + 0.976734i \(0.568797\pi\)
\(228\) 8.27516 0.548036
\(229\) −17.3861 −1.14891 −0.574454 0.818537i \(-0.694786\pi\)
−0.574454 + 0.818537i \(0.694786\pi\)
\(230\) −1.40672 −0.0927564
\(231\) −1.00148 −0.0658928
\(232\) −3.89653 −0.255820
\(233\) 19.3064 1.26481 0.632404 0.774639i \(-0.282068\pi\)
0.632404 + 0.774639i \(0.282068\pi\)
\(234\) −1.95648 −0.127899
\(235\) −3.11340 −0.203096
\(236\) −2.34835 −0.152865
\(237\) −16.3053 −1.05914
\(238\) 6.75747 0.438022
\(239\) −11.9735 −0.774503 −0.387252 0.921974i \(-0.626576\pi\)
−0.387252 + 0.921974i \(0.626576\pi\)
\(240\) 0.810191 0.0522976
\(241\) −12.1999 −0.785862 −0.392931 0.919568i \(-0.628539\pi\)
−0.392931 + 0.919568i \(0.628539\pi\)
\(242\) 10.7288 0.689674
\(243\) 4.68675 0.300655
\(244\) 12.0427 0.770952
\(245\) 2.58462 0.165126
\(246\) −3.33783 −0.212812
\(247\) −19.1559 −1.21886
\(248\) 7.29886 0.463478
\(249\) −1.08982 −0.0690647
\(250\) −4.27612 −0.270446
\(251\) 13.0091 0.821126 0.410563 0.911832i \(-0.365332\pi\)
0.410563 + 0.911832i \(0.365332\pi\)
\(252\) 0.470478 0.0296373
\(253\) −1.68061 −0.105659
\(254\) −4.57387 −0.286990
\(255\) −5.29144 −0.331363
\(256\) 1.00000 0.0625000
\(257\) 18.4616 1.15160 0.575802 0.817589i \(-0.304690\pi\)
0.575802 + 0.817589i \(0.304690\pi\)
\(258\) −10.1918 −0.634512
\(259\) −4.80875 −0.298801
\(260\) −1.87549 −0.116313
\(261\) 1.77182 0.109673
\(262\) −19.1978 −1.18605
\(263\) −0.0843656 −0.00520220 −0.00260110 0.999997i \(-0.500828\pi\)
−0.00260110 + 0.999997i \(0.500828\pi\)
\(264\) 0.967935 0.0595723
\(265\) −2.39333 −0.147021
\(266\) 4.60647 0.282441
\(267\) 5.64927 0.345730
\(268\) 7.04743 0.430490
\(269\) 8.92589 0.544221 0.272110 0.962266i \(-0.412278\pi\)
0.272110 + 0.962266i \(0.412278\pi\)
\(270\) 2.06216 0.125499
\(271\) −1.85248 −0.112530 −0.0562650 0.998416i \(-0.517919\pi\)
−0.0562650 + 0.998416i \(0.517919\pi\)
\(272\) −6.53111 −0.396006
\(273\) −8.27440 −0.500790
\(274\) 2.72558 0.164659
\(275\) −2.50487 −0.151049
\(276\) 5.99836 0.361059
\(277\) −29.7486 −1.78742 −0.893710 0.448646i \(-0.851906\pi\)
−0.893710 + 0.448646i \(0.851906\pi\)
\(278\) −1.00198 −0.0600946
\(279\) −3.31892 −0.198699
\(280\) 0.451002 0.0269525
\(281\) 0.765756 0.0456812 0.0228406 0.999739i \(-0.492729\pi\)
0.0228406 + 0.999739i \(0.492729\pi\)
\(282\) 13.2758 0.790561
\(283\) −10.6552 −0.633384 −0.316692 0.948528i \(-0.602572\pi\)
−0.316692 + 0.948528i \(0.602572\pi\)
\(284\) −1.51568 −0.0899393
\(285\) −3.60709 −0.213666
\(286\) −2.24064 −0.132492
\(287\) −1.85804 −0.109677
\(288\) −0.454718 −0.0267945
\(289\) 25.6553 1.50914
\(290\) 1.69848 0.0997379
\(291\) 31.7345 1.86031
\(292\) 1.54224 0.0902528
\(293\) 16.9540 0.990462 0.495231 0.868761i \(-0.335083\pi\)
0.495231 + 0.868761i \(0.335083\pi\)
\(294\) −11.0210 −0.642760
\(295\) 1.02363 0.0595981
\(296\) 4.64766 0.270140
\(297\) 2.46367 0.142957
\(298\) 7.18757 0.416365
\(299\) −13.8854 −0.803015
\(300\) 8.94028 0.516167
\(301\) −5.67337 −0.327007
\(302\) 2.78209 0.160091
\(303\) −26.0415 −1.49604
\(304\) −4.45215 −0.255348
\(305\) −5.24932 −0.300575
\(306\) 2.96981 0.169773
\(307\) 14.7678 0.842844 0.421422 0.906865i \(-0.361531\pi\)
0.421422 + 0.906865i \(0.361531\pi\)
\(308\) 0.538813 0.0307017
\(309\) 20.0462 1.14039
\(310\) −3.18153 −0.180699
\(311\) −31.5195 −1.78731 −0.893655 0.448756i \(-0.851867\pi\)
−0.893655 + 0.448756i \(0.851867\pi\)
\(312\) 7.99722 0.452753
\(313\) 19.1415 1.08194 0.540972 0.841041i \(-0.318056\pi\)
0.540972 + 0.841041i \(0.318056\pi\)
\(314\) −0.0507138 −0.00286194
\(315\) −0.205079 −0.0115549
\(316\) 8.77247 0.493490
\(317\) 20.3279 1.14173 0.570865 0.821044i \(-0.306608\pi\)
0.570865 + 0.821044i \(0.306608\pi\)
\(318\) 10.2054 0.572289
\(319\) 2.02917 0.113612
\(320\) −0.435894 −0.0243672
\(321\) 1.06111 0.0592253
\(322\) 3.33906 0.186079
\(323\) 29.0775 1.61791
\(324\) −10.1574 −0.564299
\(325\) −20.6956 −1.14798
\(326\) −4.43377 −0.245564
\(327\) 11.6314 0.643220
\(328\) 1.79580 0.0991565
\(329\) 7.39012 0.407431
\(330\) −0.421917 −0.0232258
\(331\) −12.0119 −0.660233 −0.330117 0.943940i \(-0.607088\pi\)
−0.330117 + 0.943940i \(0.607088\pi\)
\(332\) 0.586340 0.0321796
\(333\) −2.11337 −0.115812
\(334\) 6.52642 0.357110
\(335\) −3.07193 −0.167838
\(336\) −1.92311 −0.104914
\(337\) −26.8853 −1.46454 −0.732269 0.681016i \(-0.761538\pi\)
−0.732269 + 0.681016i \(0.761538\pi\)
\(338\) −5.51251 −0.299841
\(339\) 12.1055 0.657480
\(340\) 2.84687 0.154393
\(341\) −3.80098 −0.205834
\(342\) 2.02447 0.109471
\(343\) −13.3776 −0.722323
\(344\) 5.48331 0.295641
\(345\) −2.61465 −0.140768
\(346\) 9.43170 0.507051
\(347\) 6.88088 0.369385 0.184693 0.982796i \(-0.440871\pi\)
0.184693 + 0.982796i \(0.440871\pi\)
\(348\) −7.24243 −0.388235
\(349\) −13.0921 −0.700806 −0.350403 0.936599i \(-0.613955\pi\)
−0.350403 + 0.936599i \(0.613955\pi\)
\(350\) 4.97671 0.266016
\(351\) 20.3552 1.08648
\(352\) −0.520763 −0.0277568
\(353\) 5.86331 0.312072 0.156036 0.987751i \(-0.450128\pi\)
0.156036 + 0.987751i \(0.450128\pi\)
\(354\) −4.36485 −0.231989
\(355\) 0.660678 0.0350651
\(356\) −3.03939 −0.161087
\(357\) 12.5600 0.664747
\(358\) −17.4937 −0.924572
\(359\) 1.49982 0.0791574 0.0395787 0.999216i \(-0.487398\pi\)
0.0395787 + 0.999216i \(0.487398\pi\)
\(360\) 0.198209 0.0104465
\(361\) 0.821668 0.0432457
\(362\) −8.94210 −0.469987
\(363\) 19.9415 1.04666
\(364\) 4.45175 0.233335
\(365\) −0.672253 −0.0351873
\(366\) 22.3835 1.17001
\(367\) 21.9337 1.14493 0.572465 0.819929i \(-0.305987\pi\)
0.572465 + 0.819929i \(0.305987\pi\)
\(368\) −3.22721 −0.168230
\(369\) −0.816582 −0.0425096
\(370\) −2.02589 −0.105321
\(371\) 5.68094 0.294940
\(372\) 13.5663 0.703380
\(373\) −28.3045 −1.46555 −0.732776 0.680470i \(-0.761776\pi\)
−0.732776 + 0.680470i \(0.761776\pi\)
\(374\) 3.40116 0.175870
\(375\) −7.94797 −0.410431
\(376\) −7.14256 −0.368349
\(377\) 16.7653 0.863456
\(378\) −4.89486 −0.251764
\(379\) 30.2959 1.55620 0.778098 0.628143i \(-0.216185\pi\)
0.778098 + 0.628143i \(0.216185\pi\)
\(380\) 1.94067 0.0995541
\(381\) −8.50140 −0.435540
\(382\) −7.85435 −0.401863
\(383\) 19.9051 1.01710 0.508551 0.861032i \(-0.330181\pi\)
0.508551 + 0.861032i \(0.330181\pi\)
\(384\) 1.85869 0.0948507
\(385\) −0.234865 −0.0119698
\(386\) −14.8251 −0.754579
\(387\) −2.49336 −0.126745
\(388\) −17.0736 −0.866782
\(389\) −9.62178 −0.487844 −0.243922 0.969795i \(-0.578434\pi\)
−0.243922 + 0.969795i \(0.578434\pi\)
\(390\) −3.48594 −0.176517
\(391\) 21.0772 1.06592
\(392\) 5.92948 0.299484
\(393\) −35.6828 −1.79996
\(394\) −9.35429 −0.471263
\(395\) −3.82387 −0.192400
\(396\) 0.236800 0.0118997
\(397\) 20.4751 1.02761 0.513807 0.857906i \(-0.328235\pi\)
0.513807 + 0.857906i \(0.328235\pi\)
\(398\) 19.9525 1.00013
\(399\) 8.56198 0.428635
\(400\) −4.81000 −0.240500
\(401\) 35.9833 1.79692 0.898459 0.439057i \(-0.144687\pi\)
0.898459 + 0.439057i \(0.144687\pi\)
\(402\) 13.0990 0.653317
\(403\) −31.4042 −1.56436
\(404\) 14.0107 0.697058
\(405\) 4.42754 0.220006
\(406\) −4.03159 −0.200084
\(407\) −2.42033 −0.119971
\(408\) −12.1393 −0.600984
\(409\) 4.96671 0.245588 0.122794 0.992432i \(-0.460815\pi\)
0.122794 + 0.992432i \(0.460815\pi\)
\(410\) −0.782779 −0.0386587
\(411\) 5.06601 0.249888
\(412\) −10.7851 −0.531346
\(413\) −2.42974 −0.119560
\(414\) 1.46747 0.0721221
\(415\) −0.255582 −0.0125460
\(416\) −4.30262 −0.210953
\(417\) −1.86236 −0.0912003
\(418\) 2.31852 0.113402
\(419\) −18.1640 −0.887368 −0.443684 0.896183i \(-0.646329\pi\)
−0.443684 + 0.896183i \(0.646329\pi\)
\(420\) 0.838272 0.0409035
\(421\) 30.2360 1.47361 0.736805 0.676105i \(-0.236334\pi\)
0.736805 + 0.676105i \(0.236334\pi\)
\(422\) 6.18616 0.301137
\(423\) 3.24785 0.157916
\(424\) −5.49063 −0.266649
\(425\) 31.4146 1.52383
\(426\) −2.81718 −0.136493
\(427\) 12.4601 0.602985
\(428\) −0.570891 −0.0275951
\(429\) −4.16465 −0.201071
\(430\) −2.39014 −0.115263
\(431\) 27.3266 1.31628 0.658139 0.752897i \(-0.271344\pi\)
0.658139 + 0.752897i \(0.271344\pi\)
\(432\) 4.73088 0.227615
\(433\) 11.8044 0.567283 0.283641 0.958930i \(-0.408457\pi\)
0.283641 + 0.958930i \(0.408457\pi\)
\(434\) 7.55184 0.362500
\(435\) 3.15693 0.151363
\(436\) −6.25788 −0.299698
\(437\) 14.3680 0.687315
\(438\) 2.86654 0.136969
\(439\) 2.00990 0.0959274 0.0479637 0.998849i \(-0.484727\pi\)
0.0479637 + 0.998849i \(0.484727\pi\)
\(440\) 0.226997 0.0108217
\(441\) −2.69624 −0.128392
\(442\) 28.1008 1.33662
\(443\) 23.5392 1.11838 0.559190 0.829040i \(-0.311112\pi\)
0.559190 + 0.829040i \(0.311112\pi\)
\(444\) 8.63854 0.409967
\(445\) 1.32485 0.0628040
\(446\) −9.93719 −0.470540
\(447\) 13.3594 0.631880
\(448\) 1.03466 0.0488831
\(449\) −11.6494 −0.549767 −0.274883 0.961478i \(-0.588639\pi\)
−0.274883 + 0.961478i \(0.588639\pi\)
\(450\) 2.18719 0.103105
\(451\) −0.935186 −0.0440362
\(452\) −6.51293 −0.306342
\(453\) 5.17103 0.242956
\(454\) 6.46212 0.303282
\(455\) −1.94049 −0.0909716
\(456\) −8.27516 −0.387520
\(457\) 11.7228 0.548370 0.274185 0.961677i \(-0.411592\pi\)
0.274185 + 0.961677i \(0.411592\pi\)
\(458\) 17.3861 0.812401
\(459\) −30.8979 −1.44219
\(460\) 1.40672 0.0655886
\(461\) 0.0193888 0.000903027 0 0.000451513 1.00000i \(-0.499856\pi\)
0.000451513 1.00000i \(0.499856\pi\)
\(462\) 1.00148 0.0465933
\(463\) 32.6526 1.51749 0.758746 0.651386i \(-0.225812\pi\)
0.758746 + 0.651386i \(0.225812\pi\)
\(464\) 3.89653 0.180892
\(465\) −5.91347 −0.274231
\(466\) −19.3064 −0.894354
\(467\) −27.5535 −1.27502 −0.637511 0.770441i \(-0.720036\pi\)
−0.637511 + 0.770441i \(0.720036\pi\)
\(468\) 1.95648 0.0904381
\(469\) 7.29169 0.336699
\(470\) 3.11340 0.143610
\(471\) −0.0942611 −0.00434332
\(472\) 2.34835 0.108092
\(473\) −2.85551 −0.131296
\(474\) 16.3053 0.748926
\(475\) 21.4148 0.982580
\(476\) −6.75747 −0.309728
\(477\) 2.49669 0.114315
\(478\) 11.9735 0.547656
\(479\) −9.91352 −0.452960 −0.226480 0.974016i \(-0.572722\pi\)
−0.226480 + 0.974016i \(0.572722\pi\)
\(480\) −0.810191 −0.0369800
\(481\) −19.9971 −0.911789
\(482\) 12.1999 0.555689
\(483\) 6.20627 0.282395
\(484\) −10.7288 −0.487673
\(485\) 7.44230 0.337937
\(486\) −4.68675 −0.212595
\(487\) 26.6498 1.20762 0.603810 0.797129i \(-0.293649\pi\)
0.603810 + 0.797129i \(0.293649\pi\)
\(488\) −12.0427 −0.545146
\(489\) −8.24099 −0.372670
\(490\) −2.58462 −0.116761
\(491\) −4.95333 −0.223541 −0.111770 0.993734i \(-0.535652\pi\)
−0.111770 + 0.993734i \(0.535652\pi\)
\(492\) 3.33783 0.150481
\(493\) −25.4487 −1.14615
\(494\) 19.1559 0.861865
\(495\) −0.103220 −0.00463938
\(496\) −7.29886 −0.327729
\(497\) −1.56822 −0.0703442
\(498\) 1.08982 0.0488361
\(499\) 27.3781 1.22561 0.612806 0.790233i \(-0.290041\pi\)
0.612806 + 0.790233i \(0.290041\pi\)
\(500\) 4.27612 0.191234
\(501\) 12.1306 0.541954
\(502\) −13.0091 −0.580624
\(503\) 8.13098 0.362542 0.181271 0.983433i \(-0.441979\pi\)
0.181271 + 0.983433i \(0.441979\pi\)
\(504\) −0.470478 −0.0209568
\(505\) −6.10718 −0.271766
\(506\) 1.68061 0.0747122
\(507\) −10.2460 −0.455042
\(508\) 4.57387 0.202933
\(509\) 42.7146 1.89329 0.946645 0.322277i \(-0.104448\pi\)
0.946645 + 0.322277i \(0.104448\pi\)
\(510\) 5.29144 0.234309
\(511\) 1.59569 0.0705893
\(512\) −1.00000 −0.0441942
\(513\) −21.0626 −0.929937
\(514\) −18.4616 −0.814307
\(515\) 4.70118 0.207159
\(516\) 10.1918 0.448668
\(517\) 3.71958 0.163587
\(518\) 4.80875 0.211284
\(519\) 17.5306 0.769507
\(520\) 1.87549 0.0822455
\(521\) −25.7134 −1.12652 −0.563262 0.826278i \(-0.690454\pi\)
−0.563262 + 0.826278i \(0.690454\pi\)
\(522\) −1.77182 −0.0775506
\(523\) −30.1438 −1.31810 −0.659048 0.752101i \(-0.729041\pi\)
−0.659048 + 0.752101i \(0.729041\pi\)
\(524\) 19.1978 0.838661
\(525\) 9.25015 0.403710
\(526\) 0.0843656 0.00367851
\(527\) 47.6697 2.07652
\(528\) −0.967935 −0.0421240
\(529\) −12.5851 −0.547180
\(530\) 2.39333 0.103960
\(531\) −1.06784 −0.0463401
\(532\) −4.60647 −0.199716
\(533\) −7.72664 −0.334678
\(534\) −5.64927 −0.244468
\(535\) 0.248848 0.0107586
\(536\) −7.04743 −0.304402
\(537\) −32.5154 −1.40314
\(538\) −8.92589 −0.384822
\(539\) −3.08785 −0.133003
\(540\) −2.06216 −0.0887414
\(541\) −20.0448 −0.861791 −0.430896 0.902402i \(-0.641802\pi\)
−0.430896 + 0.902402i \(0.641802\pi\)
\(542\) 1.85248 0.0795708
\(543\) −16.6206 −0.713257
\(544\) 6.53111 0.280019
\(545\) 2.72777 0.116845
\(546\) 8.27440 0.354112
\(547\) 3.85550 0.164849 0.0824247 0.996597i \(-0.473734\pi\)
0.0824247 + 0.996597i \(0.473734\pi\)
\(548\) −2.72558 −0.116431
\(549\) 5.47601 0.233710
\(550\) 2.50487 0.106808
\(551\) −17.3480 −0.739048
\(552\) −5.99836 −0.255307
\(553\) 9.07653 0.385973
\(554\) 29.7486 1.26390
\(555\) −3.76549 −0.159836
\(556\) 1.00198 0.0424933
\(557\) −24.7677 −1.04944 −0.524721 0.851274i \(-0.675830\pi\)
−0.524721 + 0.851274i \(0.675830\pi\)
\(558\) 3.31892 0.140501
\(559\) −23.5926 −0.997861
\(560\) −0.451002 −0.0190583
\(561\) 6.32169 0.266902
\(562\) −0.765756 −0.0323015
\(563\) 14.2251 0.599517 0.299758 0.954015i \(-0.403094\pi\)
0.299758 + 0.954015i \(0.403094\pi\)
\(564\) −13.2758 −0.559011
\(565\) 2.83895 0.119435
\(566\) 10.6552 0.447870
\(567\) −10.5094 −0.441355
\(568\) 1.51568 0.0635967
\(569\) −5.37623 −0.225383 −0.112692 0.993630i \(-0.535947\pi\)
−0.112692 + 0.993630i \(0.535947\pi\)
\(570\) 3.60709 0.151085
\(571\) −8.49024 −0.355305 −0.177653 0.984093i \(-0.556850\pi\)
−0.177653 + 0.984093i \(0.556850\pi\)
\(572\) 2.24064 0.0936860
\(573\) −14.5988 −0.609872
\(574\) 1.85804 0.0775532
\(575\) 15.5228 0.647347
\(576\) 0.454718 0.0189466
\(577\) 3.62440 0.150886 0.0754430 0.997150i \(-0.475963\pi\)
0.0754430 + 0.997150i \(0.475963\pi\)
\(578\) −25.6553 −1.06712
\(579\) −27.5553 −1.14516
\(580\) −1.69848 −0.0705254
\(581\) 0.606663 0.0251686
\(582\) −31.7345 −1.31544
\(583\) 2.85932 0.118421
\(584\) −1.54224 −0.0638183
\(585\) −0.852816 −0.0352596
\(586\) −16.9540 −0.700363
\(587\) 28.0307 1.15695 0.578476 0.815699i \(-0.303648\pi\)
0.578476 + 0.815699i \(0.303648\pi\)
\(588\) 11.0210 0.454500
\(589\) 32.4957 1.33896
\(590\) −1.02363 −0.0421422
\(591\) −17.3867 −0.715194
\(592\) −4.64766 −0.191018
\(593\) 22.0893 0.907101 0.453550 0.891231i \(-0.350157\pi\)
0.453550 + 0.891231i \(0.350157\pi\)
\(594\) −2.46367 −0.101086
\(595\) 2.94554 0.120756
\(596\) −7.18757 −0.294414
\(597\) 37.0854 1.51780
\(598\) 13.8854 0.567817
\(599\) 40.1422 1.64016 0.820082 0.572246i \(-0.193928\pi\)
0.820082 + 0.572246i \(0.193928\pi\)
\(600\) −8.94028 −0.364985
\(601\) 25.2196 1.02873 0.514365 0.857571i \(-0.328028\pi\)
0.514365 + 0.857571i \(0.328028\pi\)
\(602\) 5.67337 0.231229
\(603\) 3.20459 0.130501
\(604\) −2.78209 −0.113202
\(605\) 4.67662 0.190132
\(606\) 26.0415 1.05786
\(607\) 37.9757 1.54138 0.770692 0.637208i \(-0.219911\pi\)
0.770692 + 0.637208i \(0.219911\pi\)
\(608\) 4.45215 0.180559
\(609\) −7.49346 −0.303650
\(610\) 5.24932 0.212539
\(611\) 30.7317 1.24327
\(612\) −2.96981 −0.120047
\(613\) −31.3025 −1.26429 −0.632147 0.774848i \(-0.717826\pi\)
−0.632147 + 0.774848i \(0.717826\pi\)
\(614\) −14.7678 −0.595980
\(615\) −1.45494 −0.0586689
\(616\) −0.538813 −0.0217094
\(617\) 4.83656 0.194713 0.0973564 0.995250i \(-0.468961\pi\)
0.0973564 + 0.995250i \(0.468961\pi\)
\(618\) −20.0462 −0.806377
\(619\) −25.3804 −1.02012 −0.510061 0.860138i \(-0.670377\pi\)
−0.510061 + 0.860138i \(0.670377\pi\)
\(620\) 3.18153 0.127773
\(621\) −15.2675 −0.612665
\(622\) 31.5195 1.26382
\(623\) −3.14473 −0.125991
\(624\) −7.99722 −0.320145
\(625\) 22.1860 0.887442
\(626\) −19.1415 −0.765050
\(627\) 4.30940 0.172101
\(628\) 0.0507138 0.00202370
\(629\) 30.3543 1.21031
\(630\) 0.205079 0.00817053
\(631\) −27.4582 −1.09309 −0.546546 0.837429i \(-0.684058\pi\)
−0.546546 + 0.837429i \(0.684058\pi\)
\(632\) −8.77247 −0.348950
\(633\) 11.4981 0.457010
\(634\) −20.3279 −0.807325
\(635\) −1.99372 −0.0791185
\(636\) −10.2054 −0.404669
\(637\) −25.5123 −1.01083
\(638\) −2.02917 −0.0803356
\(639\) −0.689209 −0.0272647
\(640\) 0.435894 0.0172302
\(641\) −40.0826 −1.58317 −0.791583 0.611062i \(-0.790743\pi\)
−0.791583 + 0.611062i \(0.790743\pi\)
\(642\) −1.06111 −0.0418786
\(643\) −3.76213 −0.148364 −0.0741819 0.997245i \(-0.523635\pi\)
−0.0741819 + 0.997245i \(0.523635\pi\)
\(644\) −3.33906 −0.131577
\(645\) −4.44253 −0.174924
\(646\) −29.0775 −1.14404
\(647\) −4.96817 −0.195319 −0.0976595 0.995220i \(-0.531136\pi\)
−0.0976595 + 0.995220i \(0.531136\pi\)
\(648\) 10.1574 0.399020
\(649\) −1.22293 −0.0480043
\(650\) 20.6956 0.811747
\(651\) 14.0365 0.550134
\(652\) 4.43377 0.173640
\(653\) −22.2952 −0.872478 −0.436239 0.899831i \(-0.643690\pi\)
−0.436239 + 0.899831i \(0.643690\pi\)
\(654\) −11.6314 −0.454825
\(655\) −8.36822 −0.326974
\(656\) −1.79580 −0.0701142
\(657\) 0.701284 0.0273597
\(658\) −7.39012 −0.288097
\(659\) −9.12111 −0.355308 −0.177654 0.984093i \(-0.556851\pi\)
−0.177654 + 0.984093i \(0.556851\pi\)
\(660\) 0.421917 0.0164231
\(661\) −3.40820 −0.132564 −0.0662819 0.997801i \(-0.521114\pi\)
−0.0662819 + 0.997801i \(0.521114\pi\)
\(662\) 12.0119 0.466856
\(663\) 52.2307 2.02847
\(664\) −0.586340 −0.0227544
\(665\) 2.00793 0.0778642
\(666\) 2.11337 0.0818915
\(667\) −12.5749 −0.486902
\(668\) −6.52642 −0.252515
\(669\) −18.4701 −0.714097
\(670\) 3.07193 0.118679
\(671\) 6.27137 0.242104
\(672\) 1.92311 0.0741856
\(673\) 22.5940 0.870933 0.435467 0.900205i \(-0.356583\pi\)
0.435467 + 0.900205i \(0.356583\pi\)
\(674\) 26.8853 1.03558
\(675\) −22.7555 −0.875861
\(676\) 5.51251 0.212020
\(677\) 0.214420 0.00824082 0.00412041 0.999992i \(-0.498688\pi\)
0.00412041 + 0.999992i \(0.498688\pi\)
\(678\) −12.1055 −0.464909
\(679\) −17.6654 −0.677936
\(680\) −2.84687 −0.109173
\(681\) 12.0111 0.460265
\(682\) 3.80098 0.145547
\(683\) 18.3807 0.703317 0.351659 0.936128i \(-0.385618\pi\)
0.351659 + 0.936128i \(0.385618\pi\)
\(684\) −2.02447 −0.0774077
\(685\) 1.18807 0.0453937
\(686\) 13.3776 0.510760
\(687\) 32.3154 1.23291
\(688\) −5.48331 −0.209049
\(689\) 23.6241 0.900006
\(690\) 2.61465 0.0995381
\(691\) 40.6511 1.54644 0.773221 0.634136i \(-0.218644\pi\)
0.773221 + 0.634136i \(0.218644\pi\)
\(692\) −9.43170 −0.358539
\(693\) 0.245008 0.00930707
\(694\) −6.88088 −0.261195
\(695\) −0.436756 −0.0165671
\(696\) 7.24243 0.274524
\(697\) 11.7286 0.444251
\(698\) 13.0921 0.495544
\(699\) −35.8846 −1.35728
\(700\) −4.97671 −0.188102
\(701\) −9.53820 −0.360253 −0.180126 0.983643i \(-0.557651\pi\)
−0.180126 + 0.983643i \(0.557651\pi\)
\(702\) −20.3552 −0.768257
\(703\) 20.6921 0.780417
\(704\) 0.520763 0.0196270
\(705\) 5.78684 0.217945
\(706\) −5.86331 −0.220669
\(707\) 14.4963 0.545189
\(708\) 4.36485 0.164041
\(709\) 11.4919 0.431586 0.215793 0.976439i \(-0.430766\pi\)
0.215793 + 0.976439i \(0.430766\pi\)
\(710\) −0.660678 −0.0247948
\(711\) 3.98900 0.149599
\(712\) 3.03939 0.113906
\(713\) 23.5549 0.882139
\(714\) −12.5600 −0.470047
\(715\) −0.976683 −0.0365259
\(716\) 17.4937 0.653771
\(717\) 22.2550 0.831130
\(718\) −1.49982 −0.0559728
\(719\) 12.8652 0.479790 0.239895 0.970799i \(-0.422887\pi\)
0.239895 + 0.970799i \(0.422887\pi\)
\(720\) −0.198209 −0.00738680
\(721\) −11.1590 −0.415581
\(722\) −0.821668 −0.0305793
\(723\) 22.6757 0.843319
\(724\) 8.94210 0.332331
\(725\) −18.7423 −0.696072
\(726\) −19.9415 −0.740098
\(727\) 26.1465 0.969721 0.484861 0.874591i \(-0.338870\pi\)
0.484861 + 0.874591i \(0.338870\pi\)
\(728\) −4.45175 −0.164993
\(729\) 21.7610 0.805961
\(730\) 0.672253 0.0248812
\(731\) 35.8121 1.32456
\(732\) −22.3835 −0.827319
\(733\) −32.1623 −1.18794 −0.593971 0.804487i \(-0.702440\pi\)
−0.593971 + 0.804487i \(0.702440\pi\)
\(734\) −21.9337 −0.809588
\(735\) −4.80401 −0.177199
\(736\) 3.22721 0.118956
\(737\) 3.67004 0.135188
\(738\) 0.816582 0.0300588
\(739\) 27.3003 1.00426 0.502130 0.864792i \(-0.332550\pi\)
0.502130 + 0.864792i \(0.332550\pi\)
\(740\) 2.02589 0.0744731
\(741\) 35.6048 1.30798
\(742\) −5.68094 −0.208554
\(743\) 21.3312 0.782565 0.391283 0.920271i \(-0.372032\pi\)
0.391283 + 0.920271i \(0.372032\pi\)
\(744\) −13.5663 −0.497365
\(745\) 3.13302 0.114785
\(746\) 28.3045 1.03630
\(747\) 0.266619 0.00975509
\(748\) −3.40116 −0.124359
\(749\) −0.590678 −0.0215829
\(750\) 7.94797 0.290219
\(751\) −30.4559 −1.11135 −0.555676 0.831399i \(-0.687540\pi\)
−0.555676 + 0.831399i \(0.687540\pi\)
\(752\) 7.14256 0.260462
\(753\) −24.1798 −0.881162
\(754\) −16.7653 −0.610556
\(755\) 1.21270 0.0441345
\(756\) 4.89486 0.178024
\(757\) −19.2823 −0.700827 −0.350413 0.936595i \(-0.613959\pi\)
−0.350413 + 0.936595i \(0.613959\pi\)
\(758\) −30.2959 −1.10040
\(759\) 3.12373 0.113384
\(760\) −1.94067 −0.0703954
\(761\) −11.3371 −0.410971 −0.205485 0.978660i \(-0.565877\pi\)
−0.205485 + 0.978660i \(0.565877\pi\)
\(762\) 8.50140 0.307973
\(763\) −6.47478 −0.234403
\(764\) 7.85435 0.284160
\(765\) 1.29452 0.0468036
\(766\) −19.9051 −0.719199
\(767\) −10.1040 −0.364836
\(768\) −1.85869 −0.0670696
\(769\) 5.01036 0.180678 0.0903391 0.995911i \(-0.471205\pi\)
0.0903391 + 0.995911i \(0.471205\pi\)
\(770\) 0.234865 0.00846396
\(771\) −34.3144 −1.23580
\(772\) 14.8251 0.533568
\(773\) 27.8337 1.00111 0.500555 0.865705i \(-0.333129\pi\)
0.500555 + 0.865705i \(0.333129\pi\)
\(774\) 2.49336 0.0896220
\(775\) 35.1075 1.26110
\(776\) 17.0736 0.612908
\(777\) 8.93795 0.320647
\(778\) 9.62178 0.344958
\(779\) 7.99518 0.286457
\(780\) 3.48594 0.124817
\(781\) −0.789312 −0.0282438
\(782\) −21.0772 −0.753720
\(783\) 18.4340 0.658779
\(784\) −5.92948 −0.211767
\(785\) −0.0221058 −0.000788991 0
\(786\) 35.6828 1.27276
\(787\) 38.9035 1.38676 0.693380 0.720572i \(-0.256121\pi\)
0.693380 + 0.720572i \(0.256121\pi\)
\(788\) 9.35429 0.333233
\(789\) 0.156809 0.00558256
\(790\) 3.82387 0.136047
\(791\) −6.73867 −0.239599
\(792\) −0.236800 −0.00841433
\(793\) 51.8149 1.84000
\(794\) −20.4751 −0.726633
\(795\) 4.44846 0.157771
\(796\) −19.9525 −0.707196
\(797\) 15.8799 0.562494 0.281247 0.959635i \(-0.409252\pi\)
0.281247 + 0.959635i \(0.409252\pi\)
\(798\) −8.56198 −0.303091
\(799\) −46.6488 −1.65032
\(800\) 4.81000 0.170059
\(801\) −1.38206 −0.0488328
\(802\) −35.9833 −1.27061
\(803\) 0.803141 0.0283422
\(804\) −13.0990 −0.461965
\(805\) 1.45548 0.0512988
\(806\) 31.4042 1.10617
\(807\) −16.5904 −0.584011
\(808\) −14.0107 −0.492894
\(809\) 6.03265 0.212097 0.106048 0.994361i \(-0.466180\pi\)
0.106048 + 0.994361i \(0.466180\pi\)
\(810\) −4.42754 −0.155568
\(811\) 43.7916 1.53773 0.768866 0.639410i \(-0.220821\pi\)
0.768866 + 0.639410i \(0.220821\pi\)
\(812\) 4.03159 0.141481
\(813\) 3.44318 0.120758
\(814\) 2.42033 0.0848324
\(815\) −1.93265 −0.0676979
\(816\) 12.1393 0.424960
\(817\) 24.4126 0.854087
\(818\) −4.96671 −0.173657
\(819\) 2.02429 0.0707343
\(820\) 0.782779 0.0273358
\(821\) −7.84406 −0.273760 −0.136880 0.990588i \(-0.543707\pi\)
−0.136880 + 0.990588i \(0.543707\pi\)
\(822\) −5.06601 −0.176697
\(823\) −7.37256 −0.256991 −0.128496 0.991710i \(-0.541015\pi\)
−0.128496 + 0.991710i \(0.541015\pi\)
\(824\) 10.7851 0.375718
\(825\) 4.65577 0.162093
\(826\) 2.42974 0.0845416
\(827\) 29.0652 1.01070 0.505348 0.862916i \(-0.331364\pi\)
0.505348 + 0.862916i \(0.331364\pi\)
\(828\) −1.46747 −0.0509980
\(829\) 10.0430 0.348808 0.174404 0.984674i \(-0.444200\pi\)
0.174404 + 0.984674i \(0.444200\pi\)
\(830\) 0.255582 0.00887139
\(831\) 55.2933 1.91810
\(832\) 4.30262 0.149166
\(833\) 38.7261 1.34178
\(834\) 1.86236 0.0644883
\(835\) 2.84483 0.0984494
\(836\) −2.31852 −0.0801876
\(837\) −34.5301 −1.19353
\(838\) 18.1640 0.627464
\(839\) −23.4626 −0.810018 −0.405009 0.914313i \(-0.632732\pi\)
−0.405009 + 0.914313i \(0.632732\pi\)
\(840\) −0.838272 −0.0289231
\(841\) −13.8170 −0.476450
\(842\) −30.2360 −1.04200
\(843\) −1.42330 −0.0490211
\(844\) −6.18616 −0.212936
\(845\) −2.40287 −0.0826612
\(846\) −3.24785 −0.111663
\(847\) −11.1007 −0.381423
\(848\) 5.49063 0.188549
\(849\) 19.8046 0.679693
\(850\) −31.4146 −1.07751
\(851\) 14.9989 0.514157
\(852\) 2.81718 0.0965151
\(853\) 39.3787 1.34830 0.674150 0.738595i \(-0.264510\pi\)
0.674150 + 0.738595i \(0.264510\pi\)
\(854\) −12.4601 −0.426374
\(855\) 0.882456 0.0301794
\(856\) 0.570891 0.0195127
\(857\) 9.10463 0.311008 0.155504 0.987835i \(-0.450300\pi\)
0.155504 + 0.987835i \(0.450300\pi\)
\(858\) 4.16465 0.142179
\(859\) 43.7039 1.49116 0.745579 0.666417i \(-0.232173\pi\)
0.745579 + 0.666417i \(0.232173\pi\)
\(860\) 2.39014 0.0815033
\(861\) 3.45352 0.117696
\(862\) −27.3266 −0.930749
\(863\) 53.8352 1.83257 0.916285 0.400527i \(-0.131173\pi\)
0.916285 + 0.400527i \(0.131173\pi\)
\(864\) −4.73088 −0.160948
\(865\) 4.11122 0.139786
\(866\) −11.8044 −0.401130
\(867\) −47.6853 −1.61948
\(868\) −7.55184 −0.256326
\(869\) 4.56838 0.154972
\(870\) −3.15693 −0.107030
\(871\) 30.3224 1.02743
\(872\) 6.25788 0.211919
\(873\) −7.76368 −0.262761
\(874\) −14.3680 −0.486005
\(875\) 4.42433 0.149570
\(876\) −2.86654 −0.0968514
\(877\) 42.5724 1.43757 0.718784 0.695234i \(-0.244699\pi\)
0.718784 + 0.695234i \(0.244699\pi\)
\(878\) −2.00990 −0.0678309
\(879\) −31.5121 −1.06288
\(880\) −0.226997 −0.00765208
\(881\) 31.0494 1.04608 0.523040 0.852308i \(-0.324798\pi\)
0.523040 + 0.852308i \(0.324798\pi\)
\(882\) 2.69624 0.0907871
\(883\) 43.4054 1.46071 0.730354 0.683068i \(-0.239355\pi\)
0.730354 + 0.683068i \(0.239355\pi\)
\(884\) −28.1008 −0.945134
\(885\) −1.90261 −0.0639556
\(886\) −23.5392 −0.790814
\(887\) 51.6225 1.73332 0.866658 0.498903i \(-0.166264\pi\)
0.866658 + 0.498903i \(0.166264\pi\)
\(888\) −8.63854 −0.289890
\(889\) 4.73240 0.158720
\(890\) −1.32485 −0.0444091
\(891\) −5.28959 −0.177208
\(892\) 9.93719 0.332722
\(893\) −31.7998 −1.06414
\(894\) −13.3594 −0.446807
\(895\) −7.62541 −0.254889
\(896\) −1.03466 −0.0345656
\(897\) 25.8087 0.861726
\(898\) 11.6494 0.388744
\(899\) −28.4403 −0.948536
\(900\) −2.18719 −0.0729063
\(901\) −35.8599 −1.19467
\(902\) 0.935186 0.0311383
\(903\) 10.5450 0.350916
\(904\) 6.51293 0.216617
\(905\) −3.89781 −0.129568
\(906\) −5.17103 −0.171796
\(907\) 13.8163 0.458764 0.229382 0.973336i \(-0.426329\pi\)
0.229382 + 0.973336i \(0.426329\pi\)
\(908\) −6.46212 −0.214453
\(909\) 6.37091 0.211310
\(910\) 1.94049 0.0643266
\(911\) −37.9538 −1.25747 −0.628733 0.777621i \(-0.716426\pi\)
−0.628733 + 0.777621i \(0.716426\pi\)
\(912\) 8.27516 0.274018
\(913\) 0.305344 0.0101054
\(914\) −11.7228 −0.387756
\(915\) 9.75685 0.322552
\(916\) −17.3861 −0.574454
\(917\) 19.8632 0.655942
\(918\) 30.8979 1.01978
\(919\) 28.7653 0.948881 0.474440 0.880288i \(-0.342650\pi\)
0.474440 + 0.880288i \(0.342650\pi\)
\(920\) −1.40672 −0.0463782
\(921\) −27.4487 −0.904467
\(922\) −0.0193888 −0.000638536 0
\(923\) −6.52141 −0.214655
\(924\) −1.00148 −0.0329464
\(925\) 22.3552 0.735035
\(926\) −32.6526 −1.07303
\(927\) −4.90420 −0.161075
\(928\) −3.89653 −0.127910
\(929\) −44.0018 −1.44365 −0.721826 0.692075i \(-0.756697\pi\)
−0.721826 + 0.692075i \(0.756697\pi\)
\(930\) 5.91347 0.193910
\(931\) 26.3989 0.865191
\(932\) 19.3064 0.632404
\(933\) 58.5850 1.91799
\(934\) 27.5535 0.901577
\(935\) 1.48254 0.0484844
\(936\) −1.95648 −0.0639494
\(937\) 30.9671 1.01165 0.505826 0.862636i \(-0.331188\pi\)
0.505826 + 0.862636i \(0.331188\pi\)
\(938\) −7.29169 −0.238082
\(939\) −35.5781 −1.16105
\(940\) −3.11340 −0.101548
\(941\) −44.0721 −1.43671 −0.718355 0.695677i \(-0.755104\pi\)
−0.718355 + 0.695677i \(0.755104\pi\)
\(942\) 0.0942611 0.00307119
\(943\) 5.79542 0.188725
\(944\) −2.34835 −0.0764323
\(945\) −2.13364 −0.0694073
\(946\) 2.85551 0.0928405
\(947\) −1.91844 −0.0623408 −0.0311704 0.999514i \(-0.509923\pi\)
−0.0311704 + 0.999514i \(0.509923\pi\)
\(948\) −16.3053 −0.529571
\(949\) 6.63567 0.215403
\(950\) −21.4148 −0.694789
\(951\) −37.7832 −1.22521
\(952\) 6.75747 0.219011
\(953\) −36.0234 −1.16691 −0.583457 0.812144i \(-0.698300\pi\)
−0.583457 + 0.812144i \(0.698300\pi\)
\(954\) −2.49669 −0.0808333
\(955\) −3.42366 −0.110787
\(956\) −11.9735 −0.387252
\(957\) −3.77159 −0.121918
\(958\) 9.91352 0.320291
\(959\) −2.82005 −0.0910643
\(960\) 0.810191 0.0261488
\(961\) 22.2734 0.718497
\(962\) 19.9971 0.644732
\(963\) −0.259594 −0.00836531
\(964\) −12.1999 −0.392931
\(965\) −6.46218 −0.208025
\(966\) −6.20627 −0.199683
\(967\) 11.7727 0.378585 0.189292 0.981921i \(-0.439381\pi\)
0.189292 + 0.981921i \(0.439381\pi\)
\(968\) 10.7288 0.344837
\(969\) −54.0459 −1.73621
\(970\) −7.44230 −0.238958
\(971\) −4.77578 −0.153262 −0.0766311 0.997060i \(-0.524416\pi\)
−0.0766311 + 0.997060i \(0.524416\pi\)
\(972\) 4.68675 0.150328
\(973\) 1.03671 0.0332353
\(974\) −26.6498 −0.853916
\(975\) 38.4666 1.23192
\(976\) 12.0427 0.385476
\(977\) −7.85800 −0.251400 −0.125700 0.992068i \(-0.540118\pi\)
−0.125700 + 0.992068i \(0.540118\pi\)
\(978\) 8.24099 0.263518
\(979\) −1.58280 −0.0505865
\(980\) 2.58462 0.0825628
\(981\) −2.84557 −0.0908520
\(982\) 4.95333 0.158067
\(983\) −21.7065 −0.692331 −0.346166 0.938173i \(-0.612516\pi\)
−0.346166 + 0.938173i \(0.612516\pi\)
\(984\) −3.33783 −0.106406
\(985\) −4.07748 −0.129919
\(986\) 25.4487 0.810451
\(987\) −13.7359 −0.437219
\(988\) −19.1559 −0.609431
\(989\) 17.6958 0.562693
\(990\) 0.103220 0.00328054
\(991\) 39.5243 1.25553 0.627765 0.778403i \(-0.283970\pi\)
0.627765 + 0.778403i \(0.283970\pi\)
\(992\) 7.29886 0.231739
\(993\) 22.3264 0.708505
\(994\) 1.56822 0.0497409
\(995\) 8.69716 0.275718
\(996\) −1.08982 −0.0345324
\(997\) 8.52245 0.269909 0.134954 0.990852i \(-0.456911\pi\)
0.134954 + 0.990852i \(0.456911\pi\)
\(998\) −27.3781 −0.866639
\(999\) −21.9875 −0.695654
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 \(a_p\))