Properties

Label 8002.2.a.e.1.6
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 1.6
Character \(\chi\) = 8002.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -2.69277 q^{3} +1.00000 q^{4} +0.930791 q^{5} +2.69277 q^{6} -2.75733 q^{7} -1.00000 q^{8} +4.25101 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -2.69277 q^{3} +1.00000 q^{4} +0.930791 q^{5} +2.69277 q^{6} -2.75733 q^{7} -1.00000 q^{8} +4.25101 q^{9} -0.930791 q^{10} +1.87937 q^{11} -2.69277 q^{12} -1.88739 q^{13} +2.75733 q^{14} -2.50640 q^{15} +1.00000 q^{16} -3.64409 q^{17} -4.25101 q^{18} -3.78639 q^{19} +0.930791 q^{20} +7.42487 q^{21} -1.87937 q^{22} -1.94353 q^{23} +2.69277 q^{24} -4.13363 q^{25} +1.88739 q^{26} -3.36868 q^{27} -2.75733 q^{28} -10.1187 q^{29} +2.50640 q^{30} -9.02661 q^{31} -1.00000 q^{32} -5.06072 q^{33} +3.64409 q^{34} -2.56650 q^{35} +4.25101 q^{36} -0.0607967 q^{37} +3.78639 q^{38} +5.08231 q^{39} -0.930791 q^{40} -6.84750 q^{41} -7.42487 q^{42} +9.48945 q^{43} +1.87937 q^{44} +3.95680 q^{45} +1.94353 q^{46} +8.53876 q^{47} -2.69277 q^{48} +0.602891 q^{49} +4.13363 q^{50} +9.81271 q^{51} -1.88739 q^{52} -1.06001 q^{53} +3.36868 q^{54} +1.74930 q^{55} +2.75733 q^{56} +10.1959 q^{57} +10.1187 q^{58} -5.02007 q^{59} -2.50640 q^{60} -7.43945 q^{61} +9.02661 q^{62} -11.7215 q^{63} +1.00000 q^{64} -1.75677 q^{65} +5.06072 q^{66} +6.67092 q^{67} -3.64409 q^{68} +5.23348 q^{69} +2.56650 q^{70} -11.3277 q^{71} -4.25101 q^{72} +1.49471 q^{73} +0.0607967 q^{74} +11.1309 q^{75} -3.78639 q^{76} -5.18206 q^{77} -5.08231 q^{78} -5.20048 q^{79} +0.930791 q^{80} -3.68195 q^{81} +6.84750 q^{82} -1.01903 q^{83} +7.42487 q^{84} -3.39189 q^{85} -9.48945 q^{86} +27.2473 q^{87} -1.87937 q^{88} -6.26525 q^{89} -3.95680 q^{90} +5.20417 q^{91} -1.94353 q^{92} +24.3066 q^{93} -8.53876 q^{94} -3.52434 q^{95} +2.69277 q^{96} -3.11516 q^{97} -0.602891 q^{98} +7.98923 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 77q - 77q^{2} + 10q^{3} + 77q^{4} + 18q^{5} - 10q^{6} + 21q^{7} - 77q^{8} + 71q^{9} + O(q^{10}) \) \( 77q - 77q^{2} + 10q^{3} + 77q^{4} + 18q^{5} - 10q^{6} + 21q^{7} - 77q^{8} + 71q^{9} - 18q^{10} + 30q^{11} + 10q^{12} - 2q^{13} - 21q^{14} + 21q^{15} + 77q^{16} + 60q^{17} - 71q^{18} - 3q^{19} + 18q^{20} + 10q^{21} - 30q^{22} + 53q^{23} - 10q^{24} + 59q^{25} + 2q^{26} + 43q^{27} + 21q^{28} + 30q^{29} - 21q^{30} + 22q^{31} - 77q^{32} + 31q^{33} - 60q^{34} + 41q^{35} + 71q^{36} - 3q^{37} + 3q^{38} + 44q^{39} - 18q^{40} + 48q^{41} - 10q^{42} + 21q^{43} + 30q^{44} + 33q^{45} - 53q^{46} + 107q^{47} + 10q^{48} + 24q^{49} - 59q^{50} + 18q^{51} - 2q^{52} + 42q^{53} - 43q^{54} + 49q^{55} - 21q^{56} + 32q^{57} - 30q^{58} + 42q^{59} + 21q^{60} - 31q^{61} - 22q^{62} + 109q^{63} + 77q^{64} + 39q^{65} - 31q^{66} - q^{67} + 60q^{68} - 33q^{69} - 41q^{70} + 58q^{71} - 71q^{72} + 35q^{73} + 3q^{74} + 34q^{75} - 3q^{76} + 86q^{77} - 44q^{78} + 25q^{79} + 18q^{80} + 53q^{81} - 48q^{82} + 107q^{83} + 10q^{84} + 21q^{85} - 21q^{86} + 100q^{87} - 30q^{88} + 34q^{89} - 33q^{90} - 51q^{91} + 53q^{92} + 48q^{93} - 107q^{94} + 118q^{95} - 10q^{96} - 13q^{97} - 24q^{98} + 63q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −2.69277 −1.55467 −0.777336 0.629086i \(-0.783429\pi\)
−0.777336 + 0.629086i \(0.783429\pi\)
\(4\) 1.00000 0.500000
\(5\) 0.930791 0.416262 0.208131 0.978101i \(-0.433262\pi\)
0.208131 + 0.978101i \(0.433262\pi\)
\(6\) 2.69277 1.09932
\(7\) −2.75733 −1.04217 −0.521087 0.853503i \(-0.674473\pi\)
−0.521087 + 0.853503i \(0.674473\pi\)
\(8\) −1.00000 −0.353553
\(9\) 4.25101 1.41700
\(10\) −0.930791 −0.294342
\(11\) 1.87937 0.566652 0.283326 0.959024i \(-0.408562\pi\)
0.283326 + 0.959024i \(0.408562\pi\)
\(12\) −2.69277 −0.777336
\(13\) −1.88739 −0.523468 −0.261734 0.965140i \(-0.584294\pi\)
−0.261734 + 0.965140i \(0.584294\pi\)
\(14\) 2.75733 0.736929
\(15\) −2.50640 −0.647151
\(16\) 1.00000 0.250000
\(17\) −3.64409 −0.883823 −0.441911 0.897059i \(-0.645699\pi\)
−0.441911 + 0.897059i \(0.645699\pi\)
\(18\) −4.25101 −1.00197
\(19\) −3.78639 −0.868657 −0.434329 0.900754i \(-0.643014\pi\)
−0.434329 + 0.900754i \(0.643014\pi\)
\(20\) 0.930791 0.208131
\(21\) 7.42487 1.62024
\(22\) −1.87937 −0.400684
\(23\) −1.94353 −0.405254 −0.202627 0.979256i \(-0.564948\pi\)
−0.202627 + 0.979256i \(0.564948\pi\)
\(24\) 2.69277 0.549659
\(25\) −4.13363 −0.826726
\(26\) 1.88739 0.370148
\(27\) −3.36868 −0.648303
\(28\) −2.75733 −0.521087
\(29\) −10.1187 −1.87899 −0.939496 0.342561i \(-0.888706\pi\)
−0.939496 + 0.342561i \(0.888706\pi\)
\(30\) 2.50640 0.457605
\(31\) −9.02661 −1.62123 −0.810614 0.585581i \(-0.800866\pi\)
−0.810614 + 0.585581i \(0.800866\pi\)
\(32\) −1.00000 −0.176777
\(33\) −5.06072 −0.880958
\(34\) 3.64409 0.624957
\(35\) −2.56650 −0.433818
\(36\) 4.25101 0.708502
\(37\) −0.0607967 −0.00999492 −0.00499746 0.999988i \(-0.501591\pi\)
−0.00499746 + 0.999988i \(0.501591\pi\)
\(38\) 3.78639 0.614233
\(39\) 5.08231 0.813821
\(40\) −0.930791 −0.147171
\(41\) −6.84750 −1.06940 −0.534700 0.845042i \(-0.679575\pi\)
−0.534700 + 0.845042i \(0.679575\pi\)
\(42\) −7.42487 −1.14568
\(43\) 9.48945 1.44713 0.723564 0.690257i \(-0.242503\pi\)
0.723564 + 0.690257i \(0.242503\pi\)
\(44\) 1.87937 0.283326
\(45\) 3.95680 0.589845
\(46\) 1.94353 0.286558
\(47\) 8.53876 1.24551 0.622753 0.782419i \(-0.286014\pi\)
0.622753 + 0.782419i \(0.286014\pi\)
\(48\) −2.69277 −0.388668
\(49\) 0.602891 0.0861272
\(50\) 4.13363 0.584583
\(51\) 9.81271 1.37405
\(52\) −1.88739 −0.261734
\(53\) −1.06001 −0.145603 −0.0728015 0.997346i \(-0.523194\pi\)
−0.0728015 + 0.997346i \(0.523194\pi\)
\(54\) 3.36868 0.458419
\(55\) 1.74930 0.235876
\(56\) 2.75733 0.368464
\(57\) 10.1959 1.35048
\(58\) 10.1187 1.32865
\(59\) −5.02007 −0.653557 −0.326779 0.945101i \(-0.605963\pi\)
−0.326779 + 0.945101i \(0.605963\pi\)
\(60\) −2.50640 −0.323575
\(61\) −7.43945 −0.952524 −0.476262 0.879303i \(-0.658009\pi\)
−0.476262 + 0.879303i \(0.658009\pi\)
\(62\) 9.02661 1.14638
\(63\) −11.7215 −1.47676
\(64\) 1.00000 0.125000
\(65\) −1.75677 −0.217900
\(66\) 5.06072 0.622931
\(67\) 6.67092 0.814983 0.407492 0.913209i \(-0.366404\pi\)
0.407492 + 0.913209i \(0.366404\pi\)
\(68\) −3.64409 −0.441911
\(69\) 5.23348 0.630037
\(70\) 2.56650 0.306755
\(71\) −11.3277 −1.34435 −0.672175 0.740393i \(-0.734640\pi\)
−0.672175 + 0.740393i \(0.734640\pi\)
\(72\) −4.25101 −0.500986
\(73\) 1.49471 0.174943 0.0874714 0.996167i \(-0.472121\pi\)
0.0874714 + 0.996167i \(0.472121\pi\)
\(74\) 0.0607967 0.00706747
\(75\) 11.1309 1.28529
\(76\) −3.78639 −0.434329
\(77\) −5.18206 −0.590550
\(78\) −5.08231 −0.575459
\(79\) −5.20048 −0.585100 −0.292550 0.956250i \(-0.594504\pi\)
−0.292550 + 0.956250i \(0.594504\pi\)
\(80\) 0.930791 0.104066
\(81\) −3.68195 −0.409105
\(82\) 6.84750 0.756179
\(83\) −1.01903 −0.111853 −0.0559265 0.998435i \(-0.517811\pi\)
−0.0559265 + 0.998435i \(0.517811\pi\)
\(84\) 7.42487 0.810119
\(85\) −3.39189 −0.367902
\(86\) −9.48945 −1.02327
\(87\) 27.2473 2.92121
\(88\) −1.87937 −0.200342
\(89\) −6.26525 −0.664115 −0.332057 0.943259i \(-0.607743\pi\)
−0.332057 + 0.943259i \(0.607743\pi\)
\(90\) −3.95680 −0.417083
\(91\) 5.20417 0.545545
\(92\) −1.94353 −0.202627
\(93\) 24.3066 2.52048
\(94\) −8.53876 −0.880705
\(95\) −3.52434 −0.361589
\(96\) 2.69277 0.274830
\(97\) −3.11516 −0.316297 −0.158148 0.987415i \(-0.550552\pi\)
−0.158148 + 0.987415i \(0.550552\pi\)
\(98\) −0.602891 −0.0609012
\(99\) 7.98923 0.802948
\(100\) −4.13363 −0.413363
\(101\) 9.71379 0.966558 0.483279 0.875466i \(-0.339446\pi\)
0.483279 + 0.875466i \(0.339446\pi\)
\(102\) −9.81271 −0.971603
\(103\) −7.53370 −0.742318 −0.371159 0.928569i \(-0.621039\pi\)
−0.371159 + 0.928569i \(0.621039\pi\)
\(104\) 1.88739 0.185074
\(105\) 6.91099 0.674444
\(106\) 1.06001 0.102957
\(107\) 1.13067 0.109306 0.0546529 0.998505i \(-0.482595\pi\)
0.0546529 + 0.998505i \(0.482595\pi\)
\(108\) −3.36868 −0.324151
\(109\) 18.5114 1.77307 0.886537 0.462659i \(-0.153104\pi\)
0.886537 + 0.462659i \(0.153104\pi\)
\(110\) −1.74930 −0.166789
\(111\) 0.163712 0.0155388
\(112\) −2.75733 −0.260544
\(113\) 8.73109 0.821352 0.410676 0.911781i \(-0.365293\pi\)
0.410676 + 0.911781i \(0.365293\pi\)
\(114\) −10.1959 −0.954931
\(115\) −1.80902 −0.168692
\(116\) −10.1187 −0.939496
\(117\) −8.02332 −0.741756
\(118\) 5.02007 0.462135
\(119\) 10.0480 0.921097
\(120\) 2.50640 0.228802
\(121\) −7.46796 −0.678905
\(122\) 7.43945 0.673536
\(123\) 18.4387 1.66256
\(124\) −9.02661 −0.810614
\(125\) −8.50150 −0.760397
\(126\) 11.7215 1.04423
\(127\) −17.2044 −1.52664 −0.763321 0.646020i \(-0.776432\pi\)
−0.763321 + 0.646020i \(0.776432\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −25.5529 −2.24981
\(130\) 1.75677 0.154079
\(131\) −1.57465 −0.137578 −0.0687890 0.997631i \(-0.521914\pi\)
−0.0687890 + 0.997631i \(0.521914\pi\)
\(132\) −5.06072 −0.440479
\(133\) 10.4403 0.905292
\(134\) −6.67092 −0.576280
\(135\) −3.13554 −0.269864
\(136\) 3.64409 0.312478
\(137\) 3.48450 0.297701 0.148851 0.988860i \(-0.452443\pi\)
0.148851 + 0.988860i \(0.452443\pi\)
\(138\) −5.23348 −0.445504
\(139\) 7.78296 0.660142 0.330071 0.943956i \(-0.392927\pi\)
0.330071 + 0.943956i \(0.392927\pi\)
\(140\) −2.56650 −0.216909
\(141\) −22.9929 −1.93635
\(142\) 11.3277 0.950599
\(143\) −3.54711 −0.296625
\(144\) 4.25101 0.354251
\(145\) −9.41837 −0.782153
\(146\) −1.49471 −0.123703
\(147\) −1.62345 −0.133900
\(148\) −0.0607967 −0.00499746
\(149\) −4.30914 −0.353019 −0.176509 0.984299i \(-0.556481\pi\)
−0.176509 + 0.984299i \(0.556481\pi\)
\(150\) −11.1309 −0.908835
\(151\) −8.76686 −0.713437 −0.356718 0.934212i \(-0.616104\pi\)
−0.356718 + 0.934212i \(0.616104\pi\)
\(152\) 3.78639 0.307117
\(153\) −15.4911 −1.25238
\(154\) 5.18206 0.417582
\(155\) −8.40189 −0.674856
\(156\) 5.08231 0.406911
\(157\) −19.0598 −1.52114 −0.760568 0.649258i \(-0.775080\pi\)
−0.760568 + 0.649258i \(0.775080\pi\)
\(158\) 5.20048 0.413728
\(159\) 2.85435 0.226365
\(160\) −0.930791 −0.0735855
\(161\) 5.35897 0.422346
\(162\) 3.68195 0.289281
\(163\) −18.1259 −1.41973 −0.709864 0.704339i \(-0.751244\pi\)
−0.709864 + 0.704339i \(0.751244\pi\)
\(164\) −6.84750 −0.534700
\(165\) −4.71047 −0.366710
\(166\) 1.01903 0.0790920
\(167\) 16.7561 1.29663 0.648313 0.761374i \(-0.275475\pi\)
0.648313 + 0.761374i \(0.275475\pi\)
\(168\) −7.42487 −0.572841
\(169\) −9.43775 −0.725981
\(170\) 3.39189 0.260146
\(171\) −16.0960 −1.23089
\(172\) 9.48945 0.723564
\(173\) −0.220686 −0.0167784 −0.00838921 0.999965i \(-0.502670\pi\)
−0.00838921 + 0.999965i \(0.502670\pi\)
\(174\) −27.2473 −2.06561
\(175\) 11.3978 0.861592
\(176\) 1.87937 0.141663
\(177\) 13.5179 1.01607
\(178\) 6.26525 0.469600
\(179\) −16.7066 −1.24871 −0.624356 0.781140i \(-0.714639\pi\)
−0.624356 + 0.781140i \(0.714639\pi\)
\(180\) 3.95680 0.294922
\(181\) 5.62445 0.418062 0.209031 0.977909i \(-0.432969\pi\)
0.209031 + 0.977909i \(0.432969\pi\)
\(182\) −5.20417 −0.385759
\(183\) 20.0327 1.48086
\(184\) 1.94353 0.143279
\(185\) −0.0565890 −0.00416051
\(186\) −24.3066 −1.78225
\(187\) −6.84861 −0.500820
\(188\) 8.53876 0.622753
\(189\) 9.28858 0.675645
\(190\) 3.52434 0.255682
\(191\) −11.8780 −0.859464 −0.429732 0.902956i \(-0.641392\pi\)
−0.429732 + 0.902956i \(0.641392\pi\)
\(192\) −2.69277 −0.194334
\(193\) −11.5145 −0.828835 −0.414418 0.910087i \(-0.636015\pi\)
−0.414418 + 0.910087i \(0.636015\pi\)
\(194\) 3.11516 0.223656
\(195\) 4.73057 0.338763
\(196\) 0.602891 0.0430636
\(197\) −20.8984 −1.48895 −0.744473 0.667653i \(-0.767299\pi\)
−0.744473 + 0.667653i \(0.767299\pi\)
\(198\) −7.98923 −0.567770
\(199\) 17.6607 1.25193 0.625966 0.779851i \(-0.284705\pi\)
0.625966 + 0.779851i \(0.284705\pi\)
\(200\) 4.13363 0.292292
\(201\) −17.9633 −1.26703
\(202\) −9.71379 −0.683460
\(203\) 27.9006 1.95824
\(204\) 9.81271 0.687027
\(205\) −6.37358 −0.445150
\(206\) 7.53370 0.524898
\(207\) −8.26197 −0.574247
\(208\) −1.88739 −0.130867
\(209\) −7.11604 −0.492227
\(210\) −6.91099 −0.476904
\(211\) 22.4666 1.54666 0.773331 0.634003i \(-0.218589\pi\)
0.773331 + 0.634003i \(0.218589\pi\)
\(212\) −1.06001 −0.0728015
\(213\) 30.5029 2.09002
\(214\) −1.13067 −0.0772909
\(215\) 8.83269 0.602385
\(216\) 3.36868 0.229210
\(217\) 24.8894 1.68960
\(218\) −18.5114 −1.25375
\(219\) −4.02492 −0.271979
\(220\) 1.74930 0.117938
\(221\) 6.87783 0.462653
\(222\) −0.163712 −0.0109876
\(223\) 21.9951 1.47290 0.736450 0.676492i \(-0.236501\pi\)
0.736450 + 0.676492i \(0.236501\pi\)
\(224\) 2.75733 0.184232
\(225\) −17.5721 −1.17147
\(226\) −8.73109 −0.580783
\(227\) −26.4944 −1.75849 −0.879246 0.476368i \(-0.841953\pi\)
−0.879246 + 0.476368i \(0.841953\pi\)
\(228\) 10.1959 0.675238
\(229\) 0.892211 0.0589589 0.0294795 0.999565i \(-0.490615\pi\)
0.0294795 + 0.999565i \(0.490615\pi\)
\(230\) 1.80902 0.119283
\(231\) 13.9541 0.918112
\(232\) 10.1187 0.664324
\(233\) −10.8204 −0.708869 −0.354435 0.935081i \(-0.615327\pi\)
−0.354435 + 0.935081i \(0.615327\pi\)
\(234\) 8.02332 0.524501
\(235\) 7.94779 0.518457
\(236\) −5.02007 −0.326779
\(237\) 14.0037 0.909638
\(238\) −10.0480 −0.651314
\(239\) −16.1783 −1.04649 −0.523243 0.852183i \(-0.675278\pi\)
−0.523243 + 0.852183i \(0.675278\pi\)
\(240\) −2.50640 −0.161788
\(241\) 9.39784 0.605368 0.302684 0.953091i \(-0.402117\pi\)
0.302684 + 0.953091i \(0.402117\pi\)
\(242\) 7.46796 0.480058
\(243\) 20.0207 1.28433
\(244\) −7.43945 −0.476262
\(245\) 0.561165 0.0358515
\(246\) −18.4387 −1.17561
\(247\) 7.14640 0.454715
\(248\) 9.02661 0.573191
\(249\) 2.74401 0.173895
\(250\) 8.50150 0.537682
\(251\) −7.38830 −0.466345 −0.233173 0.972435i \(-0.574911\pi\)
−0.233173 + 0.972435i \(0.574911\pi\)
\(252\) −11.7215 −0.738382
\(253\) −3.65262 −0.229638
\(254\) 17.2044 1.07950
\(255\) 9.13357 0.571967
\(256\) 1.00000 0.0625000
\(257\) 19.5737 1.22097 0.610487 0.792026i \(-0.290974\pi\)
0.610487 + 0.792026i \(0.290974\pi\)
\(258\) 25.5529 1.59085
\(259\) 0.167637 0.0104164
\(260\) −1.75677 −0.108950
\(261\) −43.0146 −2.66254
\(262\) 1.57465 0.0972824
\(263\) 3.04083 0.187505 0.0937527 0.995596i \(-0.470114\pi\)
0.0937527 + 0.995596i \(0.470114\pi\)
\(264\) 5.06072 0.311466
\(265\) −0.986643 −0.0606090
\(266\) −10.4403 −0.640138
\(267\) 16.8709 1.03248
\(268\) 6.67092 0.407492
\(269\) −17.8887 −1.09069 −0.545347 0.838210i \(-0.683602\pi\)
−0.545347 + 0.838210i \(0.683602\pi\)
\(270\) 3.13554 0.190823
\(271\) 19.1775 1.16495 0.582476 0.812848i \(-0.302084\pi\)
0.582476 + 0.812848i \(0.302084\pi\)
\(272\) −3.64409 −0.220956
\(273\) −14.0136 −0.848144
\(274\) −3.48450 −0.210507
\(275\) −7.76863 −0.468466
\(276\) 5.23348 0.315019
\(277\) 4.39611 0.264137 0.132068 0.991241i \(-0.457838\pi\)
0.132068 + 0.991241i \(0.457838\pi\)
\(278\) −7.78296 −0.466791
\(279\) −38.3722 −2.29728
\(280\) 2.56650 0.153378
\(281\) −17.0653 −1.01803 −0.509015 0.860757i \(-0.669990\pi\)
−0.509015 + 0.860757i \(0.669990\pi\)
\(282\) 22.9929 1.36921
\(283\) 8.83680 0.525293 0.262647 0.964892i \(-0.415405\pi\)
0.262647 + 0.964892i \(0.415405\pi\)
\(284\) −11.3277 −0.672175
\(285\) 9.49022 0.562152
\(286\) 3.54711 0.209745
\(287\) 18.8808 1.11450
\(288\) −4.25101 −0.250493
\(289\) −3.72058 −0.218858
\(290\) 9.41837 0.553066
\(291\) 8.38841 0.491738
\(292\) 1.49471 0.0874714
\(293\) 16.1859 0.945592 0.472796 0.881172i \(-0.343245\pi\)
0.472796 + 0.881172i \(0.343245\pi\)
\(294\) 1.62345 0.0946813
\(295\) −4.67263 −0.272051
\(296\) 0.0607967 0.00353374
\(297\) −6.33101 −0.367362
\(298\) 4.30914 0.249622
\(299\) 3.66821 0.212138
\(300\) 11.1309 0.642643
\(301\) −26.1656 −1.50816
\(302\) 8.76686 0.504476
\(303\) −26.1570 −1.50268
\(304\) −3.78639 −0.217164
\(305\) −6.92457 −0.396500
\(306\) 15.4911 0.885566
\(307\) 28.5524 1.62957 0.814785 0.579763i \(-0.196855\pi\)
0.814785 + 0.579763i \(0.196855\pi\)
\(308\) −5.18206 −0.295275
\(309\) 20.2865 1.15406
\(310\) 8.40189 0.477195
\(311\) 12.8152 0.726685 0.363342 0.931656i \(-0.381636\pi\)
0.363342 + 0.931656i \(0.381636\pi\)
\(312\) −5.08231 −0.287729
\(313\) −18.4176 −1.04103 −0.520513 0.853854i \(-0.674259\pi\)
−0.520513 + 0.853854i \(0.674259\pi\)
\(314\) 19.0598 1.07561
\(315\) −10.9102 −0.614721
\(316\) −5.20048 −0.292550
\(317\) −32.1260 −1.80438 −0.902189 0.431340i \(-0.858041\pi\)
−0.902189 + 0.431340i \(0.858041\pi\)
\(318\) −2.85435 −0.160064
\(319\) −19.0168 −1.06473
\(320\) 0.930791 0.0520328
\(321\) −3.04463 −0.169935
\(322\) −5.35897 −0.298643
\(323\) 13.7980 0.767739
\(324\) −3.68195 −0.204553
\(325\) 7.80178 0.432765
\(326\) 18.1259 1.00390
\(327\) −49.8470 −2.75655
\(328\) 6.84750 0.378090
\(329\) −23.5442 −1.29803
\(330\) 4.71047 0.259303
\(331\) 2.52325 0.138690 0.0693451 0.997593i \(-0.477909\pi\)
0.0693451 + 0.997593i \(0.477909\pi\)
\(332\) −1.01903 −0.0559265
\(333\) −0.258447 −0.0141628
\(334\) −16.7561 −0.916853
\(335\) 6.20923 0.339247
\(336\) 7.42487 0.405060
\(337\) −29.9672 −1.63242 −0.816208 0.577759i \(-0.803927\pi\)
−0.816208 + 0.577759i \(0.803927\pi\)
\(338\) 9.43775 0.513346
\(339\) −23.5108 −1.27693
\(340\) −3.39189 −0.183951
\(341\) −16.9644 −0.918672
\(342\) 16.0960 0.870371
\(343\) 17.6390 0.952415
\(344\) −9.48945 −0.511637
\(345\) 4.87128 0.262261
\(346\) 0.220686 0.0118641
\(347\) −5.24849 −0.281754 −0.140877 0.990027i \(-0.544992\pi\)
−0.140877 + 0.990027i \(0.544992\pi\)
\(348\) 27.2473 1.46061
\(349\) 16.6418 0.890816 0.445408 0.895328i \(-0.353059\pi\)
0.445408 + 0.895328i \(0.353059\pi\)
\(350\) −11.3978 −0.609238
\(351\) 6.35802 0.339366
\(352\) −1.87937 −0.100171
\(353\) −1.92631 −0.102527 −0.0512636 0.998685i \(-0.516325\pi\)
−0.0512636 + 0.998685i \(0.516325\pi\)
\(354\) −13.5179 −0.718468
\(355\) −10.5437 −0.559602
\(356\) −6.26525 −0.332057
\(357\) −27.0569 −1.43200
\(358\) 16.7066 0.882973
\(359\) −7.39255 −0.390164 −0.195082 0.980787i \(-0.562497\pi\)
−0.195082 + 0.980787i \(0.562497\pi\)
\(360\) −3.95680 −0.208542
\(361\) −4.66326 −0.245435
\(362\) −5.62445 −0.295615
\(363\) 20.1095 1.05547
\(364\) 5.20417 0.272773
\(365\) 1.39126 0.0728221
\(366\) −20.0327 −1.04713
\(367\) 35.2814 1.84168 0.920838 0.389945i \(-0.127506\pi\)
0.920838 + 0.389945i \(0.127506\pi\)
\(368\) −1.94353 −0.101314
\(369\) −29.1088 −1.51534
\(370\) 0.0565890 0.00294192
\(371\) 2.92279 0.151744
\(372\) 24.3066 1.26024
\(373\) −11.5375 −0.597387 −0.298694 0.954349i \(-0.596551\pi\)
−0.298694 + 0.954349i \(0.596551\pi\)
\(374\) 6.84861 0.354133
\(375\) 22.8926 1.18217
\(376\) −8.53876 −0.440353
\(377\) 19.0979 0.983593
\(378\) −9.28858 −0.477753
\(379\) −13.2385 −0.680015 −0.340007 0.940423i \(-0.610430\pi\)
−0.340007 + 0.940423i \(0.610430\pi\)
\(380\) −3.52434 −0.180795
\(381\) 46.3274 2.37343
\(382\) 11.8780 0.607733
\(383\) −6.63672 −0.339120 −0.169560 0.985520i \(-0.554235\pi\)
−0.169560 + 0.985520i \(0.554235\pi\)
\(384\) 2.69277 0.137415
\(385\) −4.82341 −0.245824
\(386\) 11.5145 0.586075
\(387\) 40.3398 2.05058
\(388\) −3.11516 −0.158148
\(389\) −9.73799 −0.493736 −0.246868 0.969049i \(-0.579401\pi\)
−0.246868 + 0.969049i \(0.579401\pi\)
\(390\) −4.73057 −0.239542
\(391\) 7.08241 0.358173
\(392\) −0.602891 −0.0304506
\(393\) 4.24018 0.213889
\(394\) 20.8984 1.05284
\(395\) −4.84056 −0.243555
\(396\) 7.98923 0.401474
\(397\) 19.8725 0.997373 0.498687 0.866782i \(-0.333816\pi\)
0.498687 + 0.866782i \(0.333816\pi\)
\(398\) −17.6607 −0.885249
\(399\) −28.1134 −1.40743
\(400\) −4.13363 −0.206681
\(401\) −37.2748 −1.86141 −0.930707 0.365765i \(-0.880807\pi\)
−0.930707 + 0.365765i \(0.880807\pi\)
\(402\) 17.9633 0.895926
\(403\) 17.0368 0.848661
\(404\) 9.71379 0.483279
\(405\) −3.42712 −0.170295
\(406\) −27.9006 −1.38468
\(407\) −0.114260 −0.00566364
\(408\) −9.81271 −0.485801
\(409\) −40.2143 −1.98847 −0.994235 0.107221i \(-0.965805\pi\)
−0.994235 + 0.107221i \(0.965805\pi\)
\(410\) 6.37358 0.314769
\(411\) −9.38297 −0.462828
\(412\) −7.53370 −0.371159
\(413\) 13.8420 0.681121
\(414\) 8.26197 0.406054
\(415\) −0.948503 −0.0465602
\(416\) 1.88739 0.0925370
\(417\) −20.9577 −1.02630
\(418\) 7.11604 0.348057
\(419\) 21.5988 1.05517 0.527586 0.849502i \(-0.323097\pi\)
0.527586 + 0.849502i \(0.323097\pi\)
\(420\) 6.91099 0.337222
\(421\) −23.6867 −1.15442 −0.577209 0.816596i \(-0.695858\pi\)
−0.577209 + 0.816596i \(0.695858\pi\)
\(422\) −22.4666 −1.09365
\(423\) 36.2983 1.76489
\(424\) 1.06001 0.0514784
\(425\) 15.0633 0.730679
\(426\) −30.5029 −1.47787
\(427\) 20.5131 0.992696
\(428\) 1.13067 0.0546529
\(429\) 9.55156 0.461154
\(430\) −8.83269 −0.425950
\(431\) 37.8596 1.82363 0.911815 0.410601i \(-0.134681\pi\)
0.911815 + 0.410601i \(0.134681\pi\)
\(432\) −3.36868 −0.162076
\(433\) −36.1347 −1.73652 −0.868261 0.496107i \(-0.834762\pi\)
−0.868261 + 0.496107i \(0.834762\pi\)
\(434\) −24.8894 −1.19473
\(435\) 25.3615 1.21599
\(436\) 18.5114 0.886537
\(437\) 7.35897 0.352027
\(438\) 4.02492 0.192318
\(439\) 6.00547 0.286625 0.143313 0.989677i \(-0.454225\pi\)
0.143313 + 0.989677i \(0.454225\pi\)
\(440\) −1.74930 −0.0833947
\(441\) 2.56289 0.122043
\(442\) −6.87783 −0.327145
\(443\) 0.145671 0.00692106 0.00346053 0.999994i \(-0.498898\pi\)
0.00346053 + 0.999994i \(0.498898\pi\)
\(444\) 0.163712 0.00776941
\(445\) −5.83163 −0.276446
\(446\) −21.9951 −1.04150
\(447\) 11.6035 0.548828
\(448\) −2.75733 −0.130272
\(449\) 38.5888 1.82112 0.910558 0.413380i \(-0.135652\pi\)
0.910558 + 0.413380i \(0.135652\pi\)
\(450\) 17.5721 0.828357
\(451\) −12.8690 −0.605977
\(452\) 8.73109 0.410676
\(453\) 23.6071 1.10916
\(454\) 26.4944 1.24344
\(455\) 4.84399 0.227090
\(456\) −10.1959 −0.477466
\(457\) 0.169863 0.00794587 0.00397293 0.999992i \(-0.498735\pi\)
0.00397293 + 0.999992i \(0.498735\pi\)
\(458\) −0.892211 −0.0416903
\(459\) 12.2758 0.572985
\(460\) −1.80902 −0.0843460
\(461\) 28.2291 1.31476 0.657379 0.753560i \(-0.271665\pi\)
0.657379 + 0.753560i \(0.271665\pi\)
\(462\) −13.9541 −0.649203
\(463\) −27.8692 −1.29519 −0.647595 0.761985i \(-0.724225\pi\)
−0.647595 + 0.761985i \(0.724225\pi\)
\(464\) −10.1187 −0.469748
\(465\) 22.6243 1.04918
\(466\) 10.8204 0.501246
\(467\) 23.9808 1.10970 0.554849 0.831951i \(-0.312776\pi\)
0.554849 + 0.831951i \(0.312776\pi\)
\(468\) −8.02332 −0.370878
\(469\) −18.3940 −0.849354
\(470\) −7.94779 −0.366604
\(471\) 51.3236 2.36487
\(472\) 5.02007 0.231067
\(473\) 17.8342 0.820018
\(474\) −14.0037 −0.643211
\(475\) 15.6515 0.718141
\(476\) 10.0480 0.460549
\(477\) −4.50609 −0.206320
\(478\) 16.1783 0.739977
\(479\) −30.1451 −1.37737 −0.688683 0.725063i \(-0.741811\pi\)
−0.688683 + 0.725063i \(0.741811\pi\)
\(480\) 2.50640 0.114401
\(481\) 0.114747 0.00523202
\(482\) −9.39784 −0.428060
\(483\) −14.4305 −0.656609
\(484\) −7.46796 −0.339453
\(485\) −2.89956 −0.131662
\(486\) −20.0207 −0.908156
\(487\) −12.5242 −0.567524 −0.283762 0.958895i \(-0.591583\pi\)
−0.283762 + 0.958895i \(0.591583\pi\)
\(488\) 7.43945 0.336768
\(489\) 48.8088 2.20721
\(490\) −0.561165 −0.0253508
\(491\) 4.59365 0.207308 0.103654 0.994613i \(-0.466946\pi\)
0.103654 + 0.994613i \(0.466946\pi\)
\(492\) 18.4387 0.831282
\(493\) 36.8734 1.66070
\(494\) −7.14640 −0.321532
\(495\) 7.43630 0.334237
\(496\) −9.02661 −0.405307
\(497\) 31.2342 1.40105
\(498\) −2.74401 −0.122962
\(499\) 13.7560 0.615802 0.307901 0.951418i \(-0.400373\pi\)
0.307901 + 0.951418i \(0.400373\pi\)
\(500\) −8.50150 −0.380198
\(501\) −45.1203 −2.01583
\(502\) 7.38830 0.329756
\(503\) 39.7287 1.77142 0.885708 0.464242i \(-0.153673\pi\)
0.885708 + 0.464242i \(0.153673\pi\)
\(504\) 11.7215 0.522115
\(505\) 9.04151 0.402342
\(506\) 3.65262 0.162379
\(507\) 25.4137 1.12866
\(508\) −17.2044 −0.763321
\(509\) 10.8198 0.479577 0.239789 0.970825i \(-0.422922\pi\)
0.239789 + 0.970825i \(0.422922\pi\)
\(510\) −9.13357 −0.404441
\(511\) −4.12142 −0.182321
\(512\) −1.00000 −0.0441942
\(513\) 12.7551 0.563153
\(514\) −19.5737 −0.863359
\(515\) −7.01230 −0.308999
\(516\) −25.5529 −1.12490
\(517\) 16.0475 0.705769
\(518\) −0.167637 −0.00736554
\(519\) 0.594256 0.0260849
\(520\) 1.75677 0.0770393
\(521\) 6.98607 0.306065 0.153033 0.988221i \(-0.451096\pi\)
0.153033 + 0.988221i \(0.451096\pi\)
\(522\) 43.0146 1.88270
\(523\) −10.7300 −0.469192 −0.234596 0.972093i \(-0.575377\pi\)
−0.234596 + 0.972093i \(0.575377\pi\)
\(524\) −1.57465 −0.0687890
\(525\) −30.6916 −1.33949
\(526\) −3.04083 −0.132586
\(527\) 32.8938 1.43288
\(528\) −5.06072 −0.220240
\(529\) −19.2227 −0.835769
\(530\) 0.986643 0.0428570
\(531\) −21.3404 −0.926093
\(532\) 10.4403 0.452646
\(533\) 12.9239 0.559797
\(534\) −16.8709 −0.730074
\(535\) 1.05242 0.0454999
\(536\) −6.67092 −0.288140
\(537\) 44.9871 1.94134
\(538\) 17.8887 0.771238
\(539\) 1.13306 0.0488042
\(540\) −3.13554 −0.134932
\(541\) 3.40665 0.146463 0.0732316 0.997315i \(-0.476669\pi\)
0.0732316 + 0.997315i \(0.476669\pi\)
\(542\) −19.1775 −0.823745
\(543\) −15.1454 −0.649949
\(544\) 3.64409 0.156239
\(545\) 17.2303 0.738063
\(546\) 14.0136 0.599728
\(547\) −24.2792 −1.03810 −0.519052 0.854743i \(-0.673715\pi\)
−0.519052 + 0.854743i \(0.673715\pi\)
\(548\) 3.48450 0.148851
\(549\) −31.6252 −1.34973
\(550\) 7.76863 0.331256
\(551\) 38.3133 1.63220
\(552\) −5.23348 −0.222752
\(553\) 14.3395 0.609776
\(554\) −4.39611 −0.186773
\(555\) 0.152381 0.00646822
\(556\) 7.78296 0.330071
\(557\) −19.0532 −0.807308 −0.403654 0.914912i \(-0.632260\pi\)
−0.403654 + 0.914912i \(0.632260\pi\)
\(558\) 38.3722 1.62443
\(559\) −17.9103 −0.757526
\(560\) −2.56650 −0.108454
\(561\) 18.4417 0.778611
\(562\) 17.0653 0.719856
\(563\) −37.7994 −1.59306 −0.796528 0.604602i \(-0.793332\pi\)
−0.796528 + 0.604602i \(0.793332\pi\)
\(564\) −22.9929 −0.968176
\(565\) 8.12681 0.341898
\(566\) −8.83680 −0.371438
\(567\) 10.1524 0.426359
\(568\) 11.3277 0.475299
\(569\) 2.29819 0.0963449 0.0481725 0.998839i \(-0.484660\pi\)
0.0481725 + 0.998839i \(0.484660\pi\)
\(570\) −9.49022 −0.397502
\(571\) 3.62670 0.151773 0.0758863 0.997116i \(-0.475821\pi\)
0.0758863 + 0.997116i \(0.475821\pi\)
\(572\) −3.54711 −0.148312
\(573\) 31.9848 1.33618
\(574\) −18.8808 −0.788071
\(575\) 8.03384 0.335034
\(576\) 4.25101 0.177125
\(577\) −15.3947 −0.640892 −0.320446 0.947267i \(-0.603833\pi\)
−0.320446 + 0.947267i \(0.603833\pi\)
\(578\) 3.72058 0.154756
\(579\) 31.0060 1.28857
\(580\) −9.41837 −0.391077
\(581\) 2.80981 0.116570
\(582\) −8.38841 −0.347711
\(583\) −1.99215 −0.0825062
\(584\) −1.49471 −0.0618516
\(585\) −7.46803 −0.308765
\(586\) −16.1859 −0.668634
\(587\) 29.1237 1.20207 0.601033 0.799225i \(-0.294756\pi\)
0.601033 + 0.799225i \(0.294756\pi\)
\(588\) −1.62345 −0.0669498
\(589\) 34.1783 1.40829
\(590\) 4.67263 0.192369
\(591\) 56.2745 2.31482
\(592\) −0.0607967 −0.00249873
\(593\) 34.8150 1.42968 0.714840 0.699288i \(-0.246500\pi\)
0.714840 + 0.699288i \(0.246500\pi\)
\(594\) 6.33101 0.259764
\(595\) 9.35257 0.383418
\(596\) −4.30914 −0.176509
\(597\) −47.5561 −1.94634
\(598\) −3.66821 −0.150004
\(599\) 18.8411 0.769827 0.384913 0.922953i \(-0.374231\pi\)
0.384913 + 0.922953i \(0.374231\pi\)
\(600\) −11.1309 −0.454418
\(601\) 0.147052 0.00599838 0.00299919 0.999996i \(-0.499045\pi\)
0.00299919 + 0.999996i \(0.499045\pi\)
\(602\) 26.1656 1.06643
\(603\) 28.3582 1.15483
\(604\) −8.76686 −0.356718
\(605\) −6.95110 −0.282603
\(606\) 26.1570 1.06256
\(607\) 25.3306 1.02814 0.514070 0.857748i \(-0.328137\pi\)
0.514070 + 0.857748i \(0.328137\pi\)
\(608\) 3.78639 0.153558
\(609\) −75.1298 −3.04441
\(610\) 6.92457 0.280368
\(611\) −16.1160 −0.651983
\(612\) −15.4911 −0.626190
\(613\) 25.4159 1.02654 0.513269 0.858228i \(-0.328434\pi\)
0.513269 + 0.858228i \(0.328434\pi\)
\(614\) −28.5524 −1.15228
\(615\) 17.1626 0.692063
\(616\) 5.18206 0.208791
\(617\) 42.1789 1.69806 0.849029 0.528347i \(-0.177188\pi\)
0.849029 + 0.528347i \(0.177188\pi\)
\(618\) −20.2865 −0.816044
\(619\) 12.3983 0.498329 0.249164 0.968461i \(-0.419844\pi\)
0.249164 + 0.968461i \(0.419844\pi\)
\(620\) −8.40189 −0.337428
\(621\) 6.54714 0.262728
\(622\) −12.8152 −0.513844
\(623\) 17.2754 0.692123
\(624\) 5.08231 0.203455
\(625\) 12.7550 0.510201
\(626\) 18.4176 0.736117
\(627\) 19.1619 0.765251
\(628\) −19.0598 −0.760568
\(629\) 0.221549 0.00883373
\(630\) 10.9102 0.434673
\(631\) 7.26420 0.289183 0.144592 0.989491i \(-0.453813\pi\)
0.144592 + 0.989491i \(0.453813\pi\)
\(632\) 5.20048 0.206864
\(633\) −60.4973 −2.40455
\(634\) 32.1260 1.27589
\(635\) −16.0137 −0.635483
\(636\) 2.85435 0.113182
\(637\) −1.13789 −0.0450849
\(638\) 19.0168 0.752881
\(639\) −48.1541 −1.90495
\(640\) −0.930791 −0.0367927
\(641\) −3.21485 −0.126979 −0.0634894 0.997983i \(-0.520223\pi\)
−0.0634894 + 0.997983i \(0.520223\pi\)
\(642\) 3.04463 0.120162
\(643\) 15.8284 0.624210 0.312105 0.950048i \(-0.398966\pi\)
0.312105 + 0.950048i \(0.398966\pi\)
\(644\) 5.35897 0.211173
\(645\) −23.7844 −0.936510
\(646\) −13.7980 −0.542873
\(647\) 44.6033 1.75354 0.876768 0.480913i \(-0.159695\pi\)
0.876768 + 0.480913i \(0.159695\pi\)
\(648\) 3.68195 0.144641
\(649\) −9.43458 −0.370340
\(650\) −7.80178 −0.306011
\(651\) −67.0214 −2.62678
\(652\) −18.1259 −0.709864
\(653\) 0.0506975 0.00198395 0.000991974 1.00000i \(-0.499684\pi\)
0.000991974 1.00000i \(0.499684\pi\)
\(654\) 49.8470 1.94917
\(655\) −1.46567 −0.0572685
\(656\) −6.84750 −0.267350
\(657\) 6.35404 0.247895
\(658\) 23.5442 0.917849
\(659\) 16.7782 0.653586 0.326793 0.945096i \(-0.394032\pi\)
0.326793 + 0.945096i \(0.394032\pi\)
\(660\) −4.71047 −0.183355
\(661\) −43.9945 −1.71119 −0.855593 0.517649i \(-0.826807\pi\)
−0.855593 + 0.517649i \(0.826807\pi\)
\(662\) −2.52325 −0.0980688
\(663\) −18.5204 −0.719274
\(664\) 1.01903 0.0395460
\(665\) 9.71777 0.376839
\(666\) 0.258447 0.0100146
\(667\) 19.6660 0.761469
\(668\) 16.7561 0.648313
\(669\) −59.2277 −2.28988
\(670\) −6.20923 −0.239884
\(671\) −13.9815 −0.539750
\(672\) −7.42487 −0.286420
\(673\) 15.9081 0.613213 0.306606 0.951836i \(-0.400806\pi\)
0.306606 + 0.951836i \(0.400806\pi\)
\(674\) 29.9672 1.15429
\(675\) 13.9249 0.535969
\(676\) −9.43775 −0.362990
\(677\) 19.1096 0.734442 0.367221 0.930134i \(-0.380309\pi\)
0.367221 + 0.930134i \(0.380309\pi\)
\(678\) 23.5108 0.902927
\(679\) 8.58954 0.329636
\(680\) 3.39189 0.130073
\(681\) 71.3432 2.73388
\(682\) 16.9644 0.649599
\(683\) 24.0946 0.921956 0.460978 0.887412i \(-0.347499\pi\)
0.460978 + 0.887412i \(0.347499\pi\)
\(684\) −16.0960 −0.615445
\(685\) 3.24334 0.123922
\(686\) −17.6390 −0.673459
\(687\) −2.40252 −0.0916618
\(688\) 9.48945 0.361782
\(689\) 2.00065 0.0762185
\(690\) −4.87128 −0.185446
\(691\) 20.8389 0.792749 0.396375 0.918089i \(-0.370268\pi\)
0.396375 + 0.918089i \(0.370268\pi\)
\(692\) −0.220686 −0.00838921
\(693\) −22.0290 −0.836812
\(694\) 5.24849 0.199230
\(695\) 7.24430 0.274792
\(696\) −27.2473 −1.03281
\(697\) 24.9529 0.945159
\(698\) −16.6418 −0.629902
\(699\) 29.1369 1.10206
\(700\) 11.3978 0.430796
\(701\) 16.3691 0.618253 0.309127 0.951021i \(-0.399963\pi\)
0.309127 + 0.951021i \(0.399963\pi\)
\(702\) −6.35802 −0.239968
\(703\) 0.230200 0.00868216
\(704\) 1.87937 0.0708315
\(705\) −21.4016 −0.806030
\(706\) 1.92631 0.0724976
\(707\) −26.7842 −1.00732
\(708\) 13.5179 0.508033
\(709\) −17.2049 −0.646144 −0.323072 0.946374i \(-0.604716\pi\)
−0.323072 + 0.946374i \(0.604716\pi\)
\(710\) 10.5437 0.395698
\(711\) −22.1073 −0.829088
\(712\) 6.26525 0.234800
\(713\) 17.5435 0.657010
\(714\) 27.0569 1.01258
\(715\) −3.30162 −0.123474
\(716\) −16.7066 −0.624356
\(717\) 43.5644 1.62694
\(718\) 7.39255 0.275887
\(719\) −35.4297 −1.32130 −0.660652 0.750692i \(-0.729720\pi\)
−0.660652 + 0.750692i \(0.729720\pi\)
\(720\) 3.95680 0.147461
\(721\) 20.7729 0.773625
\(722\) 4.66326 0.173548
\(723\) −25.3062 −0.941148
\(724\) 5.62445 0.209031
\(725\) 41.8269 1.55341
\(726\) −20.1095 −0.746333
\(727\) −8.40604 −0.311763 −0.155881 0.987776i \(-0.549822\pi\)
−0.155881 + 0.987776i \(0.549822\pi\)
\(728\) −5.20417 −0.192879
\(729\) −42.8652 −1.58760
\(730\) −1.39126 −0.0514930
\(731\) −34.5805 −1.27900
\(732\) 20.0327 0.740431
\(733\) −15.3711 −0.567745 −0.283873 0.958862i \(-0.591619\pi\)
−0.283873 + 0.958862i \(0.591619\pi\)
\(734\) −35.2814 −1.30226
\(735\) −1.51109 −0.0557373
\(736\) 1.94353 0.0716395
\(737\) 12.5372 0.461812
\(738\) 29.1088 1.07151
\(739\) 8.31178 0.305754 0.152877 0.988245i \(-0.451146\pi\)
0.152877 + 0.988245i \(0.451146\pi\)
\(740\) −0.0565890 −0.00208025
\(741\) −19.2436 −0.706932
\(742\) −2.92279 −0.107299
\(743\) −15.8483 −0.581416 −0.290708 0.956812i \(-0.593891\pi\)
−0.290708 + 0.956812i \(0.593891\pi\)
\(744\) −24.3066 −0.891123
\(745\) −4.01091 −0.146948
\(746\) 11.5375 0.422417
\(747\) −4.33190 −0.158496
\(748\) −6.84861 −0.250410
\(749\) −3.11763 −0.113916
\(750\) −22.8926 −0.835918
\(751\) 29.0199 1.05895 0.529475 0.848325i \(-0.322389\pi\)
0.529475 + 0.848325i \(0.322389\pi\)
\(752\) 8.53876 0.311376
\(753\) 19.8950 0.725013
\(754\) −19.0979 −0.695505
\(755\) −8.16011 −0.296977
\(756\) 9.28858 0.337822
\(757\) 44.4841 1.61680 0.808401 0.588632i \(-0.200333\pi\)
0.808401 + 0.588632i \(0.200333\pi\)
\(758\) 13.2385 0.480843
\(759\) 9.83567 0.357012
\(760\) 3.52434 0.127841
\(761\) 40.4438 1.46609 0.733043 0.680183i \(-0.238100\pi\)
0.733043 + 0.680183i \(0.238100\pi\)
\(762\) −46.3274 −1.67827
\(763\) −51.0422 −1.84785
\(764\) −11.8780 −0.429732
\(765\) −14.4189 −0.521318
\(766\) 6.63672 0.239794
\(767\) 9.47484 0.342117
\(768\) −2.69277 −0.0971670
\(769\) −0.856635 −0.0308910 −0.0154455 0.999881i \(-0.504917\pi\)
−0.0154455 + 0.999881i \(0.504917\pi\)
\(770\) 4.82341 0.173824
\(771\) −52.7075 −1.89821
\(772\) −11.5145 −0.414418
\(773\) 35.7972 1.28754 0.643769 0.765220i \(-0.277370\pi\)
0.643769 + 0.765220i \(0.277370\pi\)
\(774\) −40.3398 −1.44998
\(775\) 37.3127 1.34031
\(776\) 3.11516 0.111828
\(777\) −0.451407 −0.0161942
\(778\) 9.73799 0.349124
\(779\) 25.9273 0.928941
\(780\) 4.73057 0.169382
\(781\) −21.2890 −0.761779
\(782\) −7.08241 −0.253266
\(783\) 34.0866 1.21816
\(784\) 0.602891 0.0215318
\(785\) −17.7407 −0.633192
\(786\) −4.24018 −0.151242
\(787\) −48.6549 −1.73436 −0.867180 0.497995i \(-0.834070\pi\)
−0.867180 + 0.497995i \(0.834070\pi\)
\(788\) −20.8984 −0.744473
\(789\) −8.18825 −0.291509
\(790\) 4.84056 0.172219
\(791\) −24.0745 −0.855992
\(792\) −7.98923 −0.283885
\(793\) 14.0412 0.498616
\(794\) −19.8725 −0.705249
\(795\) 2.65680 0.0942271
\(796\) 17.6607 0.625966
\(797\) −2.97919 −0.105528 −0.0527642 0.998607i \(-0.516803\pi\)
−0.0527642 + 0.998607i \(0.516803\pi\)
\(798\) 28.1134 0.995205
\(799\) −31.1160 −1.10081
\(800\) 4.13363 0.146146
\(801\) −26.6336 −0.941053
\(802\) 37.2748 1.31622
\(803\) 2.80912 0.0991318
\(804\) −17.9633 −0.633515
\(805\) 4.98807 0.175807
\(806\) −17.0368 −0.600094
\(807\) 48.1702 1.69567
\(808\) −9.71379 −0.341730
\(809\) 27.8000 0.977397 0.488699 0.872453i \(-0.337472\pi\)
0.488699 + 0.872453i \(0.337472\pi\)
\(810\) 3.42712 0.120417
\(811\) 18.5492 0.651349 0.325675 0.945482i \(-0.394409\pi\)
0.325675 + 0.945482i \(0.394409\pi\)
\(812\) 27.9006 0.979118
\(813\) −51.6406 −1.81112
\(814\) 0.114260 0.00400480
\(815\) −16.8714 −0.590979
\(816\) 9.81271 0.343513
\(817\) −35.9308 −1.25706
\(818\) 40.2143 1.40606
\(819\) 22.1230 0.773039
\(820\) −6.37358 −0.222575
\(821\) 5.69917 0.198902 0.0994512 0.995042i \(-0.468291\pi\)
0.0994512 + 0.995042i \(0.468291\pi\)
\(822\) 9.38297 0.327269
\(823\) 39.7512 1.38564 0.692819 0.721111i \(-0.256368\pi\)
0.692819 + 0.721111i \(0.256368\pi\)
\(824\) 7.53370 0.262449
\(825\) 20.9191 0.728311
\(826\) −13.8420 −0.481625
\(827\) −17.8431 −0.620466 −0.310233 0.950661i \(-0.600407\pi\)
−0.310233 + 0.950661i \(0.600407\pi\)
\(828\) −8.26197 −0.287123
\(829\) −36.0410 −1.25175 −0.625877 0.779922i \(-0.715259\pi\)
−0.625877 + 0.779922i \(0.715259\pi\)
\(830\) 0.948503 0.0329230
\(831\) −11.8377 −0.410646
\(832\) −1.88739 −0.0654335
\(833\) −2.19699 −0.0761212
\(834\) 20.9577 0.725706
\(835\) 15.5964 0.539736
\(836\) −7.11604 −0.246113
\(837\) 30.4078 1.05105
\(838\) −21.5988 −0.746119
\(839\) −44.7801 −1.54598 −0.772991 0.634417i \(-0.781240\pi\)
−0.772991 + 0.634417i \(0.781240\pi\)
\(840\) −6.91099 −0.238452
\(841\) 73.3877 2.53061
\(842\) 23.6867 0.816297
\(843\) 45.9529 1.58270
\(844\) 22.4666 0.773331
\(845\) −8.78457 −0.302198
\(846\) −36.2983 −1.24796
\(847\) 20.5917 0.707538
\(848\) −1.06001 −0.0364007
\(849\) −23.7955 −0.816658
\(850\) −15.0633 −0.516668
\(851\) 0.118160 0.00405048
\(852\) 30.5029 1.04501
\(853\) −36.0059 −1.23282 −0.616410 0.787426i \(-0.711413\pi\)
−0.616410 + 0.787426i \(0.711413\pi\)
\(854\) −20.5131 −0.701942
\(855\) −14.9820 −0.512373
\(856\) −1.13067 −0.0386455
\(857\) 31.3917 1.07232 0.536160 0.844116i \(-0.319874\pi\)
0.536160 + 0.844116i \(0.319874\pi\)
\(858\) −9.55156 −0.326085
\(859\) −50.0090 −1.70628 −0.853142 0.521679i \(-0.825306\pi\)
−0.853142 + 0.521679i \(0.825306\pi\)
\(860\) 8.83269 0.301192
\(861\) −50.8417 −1.73268
\(862\) −37.8596 −1.28950
\(863\) 36.8503 1.25440 0.627200 0.778858i \(-0.284201\pi\)
0.627200 + 0.778858i \(0.284201\pi\)
\(864\) 3.36868 0.114605
\(865\) −0.205412 −0.00698423
\(866\) 36.1347 1.22791
\(867\) 10.0187 0.340252
\(868\) 24.8894 0.844801
\(869\) −9.77364 −0.331548
\(870\) −25.3615 −0.859835
\(871\) −12.5906 −0.426618
\(872\) −18.5114 −0.626876
\(873\) −13.2426 −0.448194
\(874\) −7.35897 −0.248921
\(875\) 23.4415 0.792466
\(876\) −4.02492 −0.135989
\(877\) 2.94745 0.0995284 0.0497642 0.998761i \(-0.484153\pi\)
0.0497642 + 0.998761i \(0.484153\pi\)
\(878\) −6.00547 −0.202675
\(879\) −43.5850 −1.47008
\(880\) 1.74930 0.0589690
\(881\) 12.1401 0.409009 0.204504 0.978866i \(-0.434442\pi\)
0.204504 + 0.978866i \(0.434442\pi\)
\(882\) −2.56289 −0.0862971
\(883\) 9.43037 0.317357 0.158679 0.987330i \(-0.449277\pi\)
0.158679 + 0.987330i \(0.449277\pi\)
\(884\) 6.87783 0.231327
\(885\) 12.5823 0.422950
\(886\) −0.145671 −0.00489393
\(887\) −8.89817 −0.298771 −0.149386 0.988779i \(-0.547730\pi\)
−0.149386 + 0.988779i \(0.547730\pi\)
\(888\) −0.163712 −0.00549380
\(889\) 47.4382 1.59103
\(890\) 5.83163 0.195477
\(891\) −6.91975 −0.231820
\(892\) 21.9951 0.736450
\(893\) −32.3311 −1.08192
\(894\) −11.6035 −0.388080
\(895\) −15.5504 −0.519792
\(896\) 2.75733 0.0921161
\(897\) −9.87763 −0.329805
\(898\) −38.5888 −1.28772
\(899\) 91.3374 3.04627
\(900\) −17.5721 −0.585737
\(901\) 3.86276 0.128687
\(902\) 12.8690 0.428491
\(903\) 70.4579 2.34469
\(904\) −8.73109 −0.290392
\(905\) 5.23519 0.174024
\(906\) −23.6071 −0.784294
\(907\) 8.66708 0.287786 0.143893 0.989593i \(-0.454038\pi\)
0.143893 + 0.989593i \(0.454038\pi\)
\(908\) −26.4944 −0.879246
\(909\) 41.2934 1.36962
\(910\) −4.84399 −0.160577
\(911\) 13.6303 0.451590 0.225795 0.974175i \(-0.427502\pi\)
0.225795 + 0.974175i \(0.427502\pi\)
\(912\) 10.1959 0.337619
\(913\) −1.91514 −0.0633818
\(914\) −0.169863 −0.00561858
\(915\) 18.6463 0.616427
\(916\) 0.892211 0.0294795
\(917\) 4.34184 0.143380
\(918\) −12.2758 −0.405161
\(919\) 18.4237 0.607741 0.303870 0.952713i \(-0.401721\pi\)
0.303870 + 0.952713i \(0.401721\pi\)
\(920\) 1.80902 0.0596416
\(921\) −76.8850 −2.53345
\(922\) −28.2291 −0.929675
\(923\) 21.3798 0.703724
\(924\) 13.9541 0.459056
\(925\) 0.251311 0.00826306
\(926\) 27.8692 0.915838
\(927\) −32.0258 −1.05187
\(928\) 10.1187 0.332162
\(929\) −14.1475 −0.464165 −0.232083 0.972696i \(-0.574554\pi\)
−0.232083 + 0.972696i \(0.574554\pi\)
\(930\) −22.6243 −0.741882
\(931\) −2.28278 −0.0748151
\(932\) −10.8204 −0.354435
\(933\) −34.5085 −1.12976
\(934\) −23.9808 −0.784675
\(935\) −6.37462 −0.208472
\(936\) 8.02332 0.262250
\(937\) −50.5113 −1.65013 −0.825067 0.565035i \(-0.808863\pi\)
−0.825067 + 0.565035i \(0.808863\pi\)
\(938\) 18.3940 0.600584
\(939\) 49.5944 1.61845
\(940\) 7.94779 0.259228
\(941\) 35.5256 1.15810 0.579052 0.815291i \(-0.303423\pi\)
0.579052 + 0.815291i \(0.303423\pi\)
\(942\) −51.3236 −1.67221
\(943\) 13.3083 0.433379
\(944\) −5.02007 −0.163389
\(945\) 8.64572 0.281245
\(946\) −17.8342 −0.579841
\(947\) −38.6413 −1.25567 −0.627837 0.778345i \(-0.716059\pi\)
−0.627837 + 0.778345i \(0.716059\pi\)
\(948\) 14.0037 0.454819
\(949\) −2.82111 −0.0915771
\(950\) −15.6515 −0.507803
\(951\) 86.5080 2.80522
\(952\) −10.0480 −0.325657
\(953\) 7.13924 0.231263 0.115631 0.993292i \(-0.463111\pi\)
0.115631 + 0.993292i \(0.463111\pi\)
\(954\) 4.50609 0.145890
\(955\) −11.0560 −0.357762
\(956\) −16.1783 −0.523243
\(957\) 51.2078 1.65531
\(958\) 30.1451 0.973944
\(959\) −9.60794 −0.310257
\(960\) −2.50640 −0.0808939
\(961\) 50.4798 1.62838
\(962\) −0.114747 −0.00369960
\(963\) 4.80648 0.154887
\(964\) 9.39784 0.302684
\(965\) −10.7176 −0.345013
\(966\) 14.4305 0.464292
\(967\) −25.9656 −0.834996 −0.417498 0.908678i \(-0.637093\pi\)
−0.417498 + 0.908678i \(0.637093\pi\)
\(968\) 7.46796 0.240029
\(969\) −37.1547 −1.19358
\(970\) 2.89956 0.0930994
\(971\) −10.2381 −0.328556 −0.164278 0.986414i \(-0.552529\pi\)
−0.164278 + 0.986414i \(0.552529\pi\)
\(972\) 20.0207 0.642164
\(973\) −21.4602 −0.687983
\(974\) 12.5242 0.401300
\(975\) −21.0084 −0.672807
\(976\) −7.43945 −0.238131
\(977\) 2.39826 0.0767270 0.0383635 0.999264i \(-0.487786\pi\)
0.0383635 + 0.999264i \(0.487786\pi\)
\(978\) −48.8088 −1.56073
\(979\) −11.7747 −0.376322
\(980\) 0.561165 0.0179258
\(981\) 78.6922 2.51245
\(982\) −4.59365 −0.146589
\(983\) 46.0826 1.46981 0.734903 0.678172i \(-0.237228\pi\)
0.734903 + 0.678172i \(0.237228\pi\)
\(984\) −18.4387 −0.587805
\(985\) −19.4520 −0.619792
\(986\) −36.8734 −1.17429
\(987\) 63.3991 2.01802
\(988\) 7.14640 0.227357
\(989\) −18.4430 −0.586455
\(990\) −7.43630 −0.236341
\(991\) −15.6410 −0.496854 −0.248427 0.968651i \(-0.579914\pi\)
−0.248427 + 0.968651i \(0.579914\pi\)
\(992\) 9.02661 0.286595
\(993\) −6.79453 −0.215618
\(994\) −31.2342 −0.990689
\(995\) 16.4384 0.521132
\(996\) 2.74401 0.0869474
\(997\) 57.5113 1.82140 0.910701 0.413066i \(-0.135542\pi\)
0.910701 + 0.413066i \(0.135542\pi\)
\(998\) −13.7560 −0.435438
\(999\) 0.204805 0.00647973
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 \(a_p\))