Properties

Label 8047.2.a.b.1.17
Level 8047
Weight 2
Character 8047.1
Self dual Yes
Analytic conductor 64.256
Analytic rank 1
Dimension 142
CM No

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Newspace parameters

Level: \( N \) = \( 8047 = 13 \cdot 619 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8047.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2556185065\)
Analytic rank: \(1\)
Dimension: \(142\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Character \(\chi\) = 8047.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.27884 q^{2} -1.20174 q^{3} +3.19313 q^{4} -1.58295 q^{5} +2.73859 q^{6} +1.25281 q^{7} -2.71895 q^{8} -1.55581 q^{9} +O(q^{10})\) \(q-2.27884 q^{2} -1.20174 q^{3} +3.19313 q^{4} -1.58295 q^{5} +2.73859 q^{6} +1.25281 q^{7} -2.71895 q^{8} -1.55581 q^{9} +3.60730 q^{10} -5.51479 q^{11} -3.83732 q^{12} +1.00000 q^{13} -2.85495 q^{14} +1.90230 q^{15} -0.190201 q^{16} -0.404259 q^{17} +3.54545 q^{18} -2.11797 q^{19} -5.05456 q^{20} -1.50555 q^{21} +12.5673 q^{22} +1.39164 q^{23} +3.26748 q^{24} -2.49426 q^{25} -2.27884 q^{26} +5.47492 q^{27} +4.00036 q^{28} -6.67488 q^{29} -4.33505 q^{30} +1.02871 q^{31} +5.87133 q^{32} +6.62737 q^{33} +0.921243 q^{34} -1.98313 q^{35} -4.96789 q^{36} -2.15141 q^{37} +4.82652 q^{38} -1.20174 q^{39} +4.30396 q^{40} -0.133329 q^{41} +3.43092 q^{42} +4.96077 q^{43} -17.6094 q^{44} +2.46277 q^{45} -3.17133 q^{46} +10.2848 q^{47} +0.228573 q^{48} -5.43048 q^{49} +5.68404 q^{50} +0.485817 q^{51} +3.19313 q^{52} +12.7026 q^{53} -12.4765 q^{54} +8.72965 q^{55} -3.40631 q^{56} +2.54526 q^{57} +15.2110 q^{58} -7.36247 q^{59} +6.07429 q^{60} +4.42081 q^{61} -2.34426 q^{62} -1.94913 q^{63} -12.9994 q^{64} -1.58295 q^{65} -15.1027 q^{66} +6.49853 q^{67} -1.29085 q^{68} -1.67240 q^{69} +4.51924 q^{70} -9.06311 q^{71} +4.23016 q^{72} +6.63616 q^{73} +4.90273 q^{74} +2.99747 q^{75} -6.76294 q^{76} -6.90896 q^{77} +2.73859 q^{78} +0.656280 q^{79} +0.301079 q^{80} -1.91203 q^{81} +0.303836 q^{82} +3.15024 q^{83} -4.80742 q^{84} +0.639923 q^{85} -11.3048 q^{86} +8.02150 q^{87} +14.9944 q^{88} +9.20804 q^{89} -5.61227 q^{90} +1.25281 q^{91} +4.44368 q^{92} -1.23624 q^{93} -23.4374 q^{94} +3.35264 q^{95} -7.05584 q^{96} +5.02123 q^{97} +12.3752 q^{98} +8.57996 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 142q - 13q^{2} - 26q^{3} + 129q^{4} - 37q^{5} - 15q^{6} - 14q^{7} - 39q^{8} + 98q^{9} + O(q^{10}) \) \( 142q - 13q^{2} - 26q^{3} + 129q^{4} - 37q^{5} - 15q^{6} - 14q^{7} - 39q^{8} + 98q^{9} - 25q^{10} - 25q^{11} - 62q^{12} + 142q^{13} - 57q^{14} - 14q^{15} + 111q^{16} - 141q^{17} - 29q^{18} - 3q^{19} - 87q^{20} - 19q^{21} - 24q^{22} - 69q^{23} - 40q^{24} + 87q^{25} - 13q^{26} - 95q^{27} - 34q^{28} - 147q^{29} - 2q^{30} - 21q^{31} - 66q^{32} - 62q^{33} - 6q^{34} - 59q^{35} + 74q^{36} - 37q^{37} - 76q^{38} - 26q^{39} - 61q^{40} - 97q^{41} - 29q^{42} - 33q^{43} - 57q^{44} - 86q^{45} - q^{46} - 102q^{47} - 141q^{48} + 70q^{49} - 28q^{50} - 13q^{51} + 129q^{52} - 137q^{53} - 29q^{54} - 24q^{55} - 130q^{56} - 65q^{57} - 15q^{58} - 56q^{59} + 11q^{60} - 77q^{61} - 150q^{62} - 32q^{63} + 73q^{64} - 37q^{65} - 32q^{66} - 9q^{67} - 226q^{68} - 113q^{69} + 6q^{70} - 18q^{71} - 82q^{72} - 117q^{73} - 70q^{74} - 83q^{75} + 40q^{76} - 214q^{77} - 15q^{78} - 52q^{79} - 161q^{80} - 10q^{81} - 36q^{82} - 74q^{83} + 53q^{84} + 2q^{85} + 17q^{86} - 49q^{87} - 29q^{88} - 171q^{89} - 57q^{90} - 14q^{91} - 187q^{92} - 39q^{93} + 13q^{94} - 150q^{95} - 47q^{96} - 126q^{97} - 85q^{98} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.27884 −1.61139 −0.805693 0.592334i \(-0.798207\pi\)
−0.805693 + 0.592334i \(0.798207\pi\)
\(3\) −1.20174 −0.693828 −0.346914 0.937897i \(-0.612770\pi\)
−0.346914 + 0.937897i \(0.612770\pi\)
\(4\) 3.19313 1.59656
\(5\) −1.58295 −0.707917 −0.353959 0.935261i \(-0.615165\pi\)
−0.353959 + 0.935261i \(0.615165\pi\)
\(6\) 2.73859 1.11802
\(7\) 1.25281 0.473516 0.236758 0.971569i \(-0.423915\pi\)
0.236758 + 0.971569i \(0.423915\pi\)
\(8\) −2.71895 −0.961292
\(9\) −1.55581 −0.518603
\(10\) 3.60730 1.14073
\(11\) −5.51479 −1.66277 −0.831386 0.555695i \(-0.812452\pi\)
−0.831386 + 0.555695i \(0.812452\pi\)
\(12\) −3.83732 −1.10774
\(13\) 1.00000 0.277350
\(14\) −2.85495 −0.763017
\(15\) 1.90230 0.491173
\(16\) −0.190201 −0.0475503
\(17\) −0.404259 −0.0980473 −0.0490236 0.998798i \(-0.515611\pi\)
−0.0490236 + 0.998798i \(0.515611\pi\)
\(18\) 3.54545 0.835669
\(19\) −2.11797 −0.485895 −0.242948 0.970039i \(-0.578114\pi\)
−0.242948 + 0.970039i \(0.578114\pi\)
\(20\) −5.05456 −1.13023
\(21\) −1.50555 −0.328538
\(22\) 12.5673 2.67937
\(23\) 1.39164 0.290177 0.145089 0.989419i \(-0.453653\pi\)
0.145089 + 0.989419i \(0.453653\pi\)
\(24\) 3.26748 0.666971
\(25\) −2.49426 −0.498853
\(26\) −2.27884 −0.446918
\(27\) 5.47492 1.05365
\(28\) 4.00036 0.755998
\(29\) −6.67488 −1.23949 −0.619747 0.784802i \(-0.712765\pi\)
−0.619747 + 0.784802i \(0.712765\pi\)
\(30\) −4.33505 −0.791469
\(31\) 1.02871 0.184761 0.0923807 0.995724i \(-0.470552\pi\)
0.0923807 + 0.995724i \(0.470552\pi\)
\(32\) 5.87133 1.03791
\(33\) 6.62737 1.15368
\(34\) 0.921243 0.157992
\(35\) −1.98313 −0.335210
\(36\) −4.96789 −0.827982
\(37\) −2.15141 −0.353690 −0.176845 0.984239i \(-0.556589\pi\)
−0.176845 + 0.984239i \(0.556589\pi\)
\(38\) 4.82652 0.782965
\(39\) −1.20174 −0.192433
\(40\) 4.30396 0.680516
\(41\) −0.133329 −0.0208225 −0.0104112 0.999946i \(-0.503314\pi\)
−0.0104112 + 0.999946i \(0.503314\pi\)
\(42\) 3.43092 0.529402
\(43\) 4.96077 0.756510 0.378255 0.925701i \(-0.376524\pi\)
0.378255 + 0.925701i \(0.376524\pi\)
\(44\) −17.6094 −2.65472
\(45\) 2.46277 0.367128
\(46\) −3.17133 −0.467587
\(47\) 10.2848 1.50019 0.750096 0.661329i \(-0.230007\pi\)
0.750096 + 0.661329i \(0.230007\pi\)
\(48\) 0.228573 0.0329917
\(49\) −5.43048 −0.775783
\(50\) 5.68404 0.803844
\(51\) 0.485817 0.0680279
\(52\) 3.19313 0.442807
\(53\) 12.7026 1.74484 0.872418 0.488760i \(-0.162551\pi\)
0.872418 + 0.488760i \(0.162551\pi\)
\(54\) −12.4765 −1.69783
\(55\) 8.72965 1.17711
\(56\) −3.40631 −0.455187
\(57\) 2.54526 0.337128
\(58\) 15.2110 1.99730
\(59\) −7.36247 −0.958512 −0.479256 0.877675i \(-0.659093\pi\)
−0.479256 + 0.877675i \(0.659093\pi\)
\(60\) 6.07429 0.784188
\(61\) 4.42081 0.566027 0.283014 0.959116i \(-0.408666\pi\)
0.283014 + 0.959116i \(0.408666\pi\)
\(62\) −2.34426 −0.297722
\(63\) −1.94913 −0.245567
\(64\) −12.9994 −1.62493
\(65\) −1.58295 −0.196341
\(66\) −15.1027 −1.85902
\(67\) 6.49853 0.793922 0.396961 0.917836i \(-0.370065\pi\)
0.396961 + 0.917836i \(0.370065\pi\)
\(68\) −1.29085 −0.156539
\(69\) −1.67240 −0.201333
\(70\) 4.51924 0.540153
\(71\) −9.06311 −1.07559 −0.537797 0.843075i \(-0.680743\pi\)
−0.537797 + 0.843075i \(0.680743\pi\)
\(72\) 4.23016 0.498529
\(73\) 6.63616 0.776704 0.388352 0.921511i \(-0.373045\pi\)
0.388352 + 0.921511i \(0.373045\pi\)
\(74\) 4.90273 0.569930
\(75\) 2.99747 0.346118
\(76\) −6.76294 −0.775762
\(77\) −6.90896 −0.787349
\(78\) 2.73859 0.310084
\(79\) 0.656280 0.0738373 0.0369187 0.999318i \(-0.488246\pi\)
0.0369187 + 0.999318i \(0.488246\pi\)
\(80\) 0.301079 0.0336617
\(81\) −1.91203 −0.212448
\(82\) 0.303836 0.0335531
\(83\) 3.15024 0.345783 0.172892 0.984941i \(-0.444689\pi\)
0.172892 + 0.984941i \(0.444689\pi\)
\(84\) −4.80742 −0.524532
\(85\) 0.639923 0.0694094
\(86\) −11.3048 −1.21903
\(87\) 8.02150 0.859996
\(88\) 14.9944 1.59841
\(89\) 9.20804 0.976050 0.488025 0.872830i \(-0.337717\pi\)
0.488025 + 0.872830i \(0.337717\pi\)
\(90\) −5.61227 −0.591585
\(91\) 1.25281 0.131330
\(92\) 4.44368 0.463286
\(93\) −1.23624 −0.128193
\(94\) −23.4374 −2.41739
\(95\) 3.35264 0.343974
\(96\) −7.05584 −0.720134
\(97\) 5.02123 0.509828 0.254914 0.966964i \(-0.417953\pi\)
0.254914 + 0.966964i \(0.417953\pi\)
\(98\) 12.3752 1.25008
\(99\) 8.57996 0.862319
\(100\) −7.96450 −0.796450
\(101\) 5.63421 0.560625 0.280313 0.959909i \(-0.409562\pi\)
0.280313 + 0.959909i \(0.409562\pi\)
\(102\) −1.10710 −0.109619
\(103\) 13.2046 1.30108 0.650542 0.759470i \(-0.274542\pi\)
0.650542 + 0.759470i \(0.274542\pi\)
\(104\) −2.71895 −0.266615
\(105\) 2.38322 0.232578
\(106\) −28.9472 −2.81160
\(107\) −9.98320 −0.965112 −0.482556 0.875865i \(-0.660292\pi\)
−0.482556 + 0.875865i \(0.660292\pi\)
\(108\) 17.4821 1.68222
\(109\) 6.28771 0.602254 0.301127 0.953584i \(-0.402637\pi\)
0.301127 + 0.953584i \(0.402637\pi\)
\(110\) −19.8935 −1.89677
\(111\) 2.58545 0.245400
\(112\) −0.238285 −0.0225158
\(113\) −18.2093 −1.71299 −0.856493 0.516159i \(-0.827361\pi\)
−0.856493 + 0.516159i \(0.827361\pi\)
\(114\) −5.80024 −0.543243
\(115\) −2.20290 −0.205421
\(116\) −21.3137 −1.97893
\(117\) −1.55581 −0.143835
\(118\) 16.7779 1.54453
\(119\) −0.506458 −0.0464269
\(120\) −5.17226 −0.472161
\(121\) 19.4129 1.76481
\(122\) −10.0743 −0.912088
\(123\) 0.160227 0.0144472
\(124\) 3.28479 0.294983
\(125\) 11.8631 1.06106
\(126\) 4.44175 0.395703
\(127\) 1.71002 0.151740 0.0758698 0.997118i \(-0.475827\pi\)
0.0758698 + 0.997118i \(0.475827\pi\)
\(128\) 17.8810 1.58047
\(129\) −5.96158 −0.524888
\(130\) 3.60730 0.316381
\(131\) −21.6601 −1.89245 −0.946224 0.323512i \(-0.895136\pi\)
−0.946224 + 0.323512i \(0.895136\pi\)
\(132\) 21.1620 1.84192
\(133\) −2.65340 −0.230079
\(134\) −14.8091 −1.27931
\(135\) −8.66653 −0.745896
\(136\) 1.09916 0.0942521
\(137\) −2.59661 −0.221844 −0.110922 0.993829i \(-0.535380\pi\)
−0.110922 + 0.993829i \(0.535380\pi\)
\(138\) 3.81113 0.324425
\(139\) 4.16822 0.353544 0.176772 0.984252i \(-0.443434\pi\)
0.176772 + 0.984252i \(0.443434\pi\)
\(140\) −6.33238 −0.535184
\(141\) −12.3597 −1.04087
\(142\) 20.6534 1.73320
\(143\) −5.51479 −0.461170
\(144\) 0.295917 0.0246597
\(145\) 10.5660 0.877460
\(146\) −15.1228 −1.25157
\(147\) 6.52605 0.538260
\(148\) −6.86972 −0.564688
\(149\) 1.07574 0.0881284 0.0440642 0.999029i \(-0.485969\pi\)
0.0440642 + 0.999029i \(0.485969\pi\)
\(150\) −6.83076 −0.557729
\(151\) −3.68162 −0.299606 −0.149803 0.988716i \(-0.547864\pi\)
−0.149803 + 0.988716i \(0.547864\pi\)
\(152\) 5.75864 0.467088
\(153\) 0.628950 0.0508476
\(154\) 15.7444 1.26872
\(155\) −1.62839 −0.130796
\(156\) −3.83732 −0.307232
\(157\) −4.02538 −0.321261 −0.160630 0.987015i \(-0.551353\pi\)
−0.160630 + 0.987015i \(0.551353\pi\)
\(158\) −1.49556 −0.118980
\(159\) −15.2653 −1.21062
\(160\) −9.29403 −0.734758
\(161\) 1.74346 0.137404
\(162\) 4.35721 0.342335
\(163\) 7.44504 0.583141 0.291570 0.956549i \(-0.405822\pi\)
0.291570 + 0.956549i \(0.405822\pi\)
\(164\) −0.425736 −0.0332444
\(165\) −10.4908 −0.816708
\(166\) −7.17889 −0.557190
\(167\) −15.0207 −1.16234 −0.581170 0.813783i \(-0.697405\pi\)
−0.581170 + 0.813783i \(0.697405\pi\)
\(168\) 4.09351 0.315822
\(169\) 1.00000 0.0769231
\(170\) −1.45828 −0.111845
\(171\) 3.29516 0.251987
\(172\) 15.8404 1.20782
\(173\) 17.6121 1.33903 0.669513 0.742800i \(-0.266503\pi\)
0.669513 + 0.742800i \(0.266503\pi\)
\(174\) −18.2797 −1.38578
\(175\) −3.12483 −0.236215
\(176\) 1.04892 0.0790652
\(177\) 8.84781 0.665042
\(178\) −20.9837 −1.57279
\(179\) −5.90517 −0.441373 −0.220687 0.975345i \(-0.570830\pi\)
−0.220687 + 0.975345i \(0.570830\pi\)
\(180\) 7.86394 0.586143
\(181\) 24.5488 1.82470 0.912350 0.409412i \(-0.134266\pi\)
0.912350 + 0.409412i \(0.134266\pi\)
\(182\) −2.85495 −0.211623
\(183\) −5.31269 −0.392725
\(184\) −3.78380 −0.278945
\(185\) 3.40558 0.250383
\(186\) 2.81721 0.206568
\(187\) 2.22941 0.163030
\(188\) 32.8406 2.39515
\(189\) 6.85901 0.498920
\(190\) −7.64015 −0.554274
\(191\) −23.8207 −1.72361 −0.861803 0.507243i \(-0.830665\pi\)
−0.861803 + 0.507243i \(0.830665\pi\)
\(192\) 15.6220 1.12742
\(193\) 12.6553 0.910950 0.455475 0.890249i \(-0.349470\pi\)
0.455475 + 0.890249i \(0.349470\pi\)
\(194\) −11.4426 −0.821530
\(195\) 1.90230 0.136227
\(196\) −17.3402 −1.23859
\(197\) −23.4933 −1.67383 −0.836913 0.547336i \(-0.815642\pi\)
−0.836913 + 0.547336i \(0.815642\pi\)
\(198\) −19.5524 −1.38953
\(199\) −16.1734 −1.14650 −0.573252 0.819379i \(-0.694318\pi\)
−0.573252 + 0.819379i \(0.694318\pi\)
\(200\) 6.78177 0.479544
\(201\) −7.80958 −0.550845
\(202\) −12.8395 −0.903383
\(203\) −8.36233 −0.586920
\(204\) 1.55127 0.108611
\(205\) 0.211053 0.0147406
\(206\) −30.0911 −2.09655
\(207\) −2.16513 −0.150487
\(208\) −0.190201 −0.0131881
\(209\) 11.6802 0.807933
\(210\) −5.43098 −0.374773
\(211\) 14.3619 0.988711 0.494355 0.869260i \(-0.335404\pi\)
0.494355 + 0.869260i \(0.335404\pi\)
\(212\) 40.5610 2.78574
\(213\) 10.8915 0.746277
\(214\) 22.7501 1.55517
\(215\) −7.85266 −0.535547
\(216\) −14.8860 −1.01286
\(217\) 1.28877 0.0874875
\(218\) −14.3287 −0.970463
\(219\) −7.97497 −0.538899
\(220\) 27.8749 1.87932
\(221\) −0.404259 −0.0271934
\(222\) −5.89183 −0.395434
\(223\) −13.7175 −0.918592 −0.459296 0.888283i \(-0.651898\pi\)
−0.459296 + 0.888283i \(0.651898\pi\)
\(224\) 7.35563 0.491469
\(225\) 3.88060 0.258707
\(226\) 41.4961 2.76028
\(227\) 28.2378 1.87421 0.937104 0.349050i \(-0.113496\pi\)
0.937104 + 0.349050i \(0.113496\pi\)
\(228\) 8.12733 0.538246
\(229\) 28.8508 1.90652 0.953259 0.302155i \(-0.0977059\pi\)
0.953259 + 0.302155i \(0.0977059\pi\)
\(230\) 5.02006 0.331013
\(231\) 8.30281 0.546284
\(232\) 18.1486 1.19152
\(233\) −4.88368 −0.319941 −0.159970 0.987122i \(-0.551140\pi\)
−0.159970 + 0.987122i \(0.551140\pi\)
\(234\) 3.54545 0.231773
\(235\) −16.2803 −1.06201
\(236\) −23.5093 −1.53032
\(237\) −0.788682 −0.0512304
\(238\) 1.15414 0.0748117
\(239\) 2.21674 0.143389 0.0716944 0.997427i \(-0.477159\pi\)
0.0716944 + 0.997427i \(0.477159\pi\)
\(240\) −0.361820 −0.0233554
\(241\) −0.279201 −0.0179849 −0.00899245 0.999960i \(-0.502862\pi\)
−0.00899245 + 0.999960i \(0.502862\pi\)
\(242\) −44.2390 −2.84379
\(243\) −14.1270 −0.906247
\(244\) 14.1162 0.903698
\(245\) 8.59618 0.549190
\(246\) −0.365133 −0.0232800
\(247\) −2.11797 −0.134763
\(248\) −2.79700 −0.177610
\(249\) −3.78578 −0.239914
\(250\) −27.0340 −1.70978
\(251\) −20.5887 −1.29954 −0.649772 0.760129i \(-0.725136\pi\)
−0.649772 + 0.760129i \(0.725136\pi\)
\(252\) −6.22380 −0.392063
\(253\) −7.67461 −0.482498
\(254\) −3.89686 −0.244511
\(255\) −0.769024 −0.0481581
\(256\) −14.7492 −0.921822
\(257\) −15.6804 −0.978115 −0.489058 0.872252i \(-0.662659\pi\)
−0.489058 + 0.872252i \(0.662659\pi\)
\(258\) 13.5855 0.845796
\(259\) −2.69530 −0.167478
\(260\) −5.05456 −0.313471
\(261\) 10.3848 0.642806
\(262\) 49.3599 3.04946
\(263\) 12.6084 0.777467 0.388733 0.921350i \(-0.372913\pi\)
0.388733 + 0.921350i \(0.372913\pi\)
\(264\) −18.0195 −1.10902
\(265\) −20.1076 −1.23520
\(266\) 6.04669 0.370746
\(267\) −11.0657 −0.677211
\(268\) 20.7506 1.26755
\(269\) 22.0833 1.34644 0.673222 0.739441i \(-0.264910\pi\)
0.673222 + 0.739441i \(0.264910\pi\)
\(270\) 19.7497 1.20193
\(271\) 12.1474 0.737904 0.368952 0.929448i \(-0.379717\pi\)
0.368952 + 0.929448i \(0.379717\pi\)
\(272\) 0.0768905 0.00466217
\(273\) −1.50555 −0.0911202
\(274\) 5.91728 0.357476
\(275\) 13.7553 0.829479
\(276\) −5.34017 −0.321441
\(277\) −13.1346 −0.789180 −0.394590 0.918857i \(-0.629113\pi\)
−0.394590 + 0.918857i \(0.629113\pi\)
\(278\) −9.49873 −0.569696
\(279\) −1.60047 −0.0958178
\(280\) 5.39202 0.322235
\(281\) −6.30905 −0.376366 −0.188183 0.982134i \(-0.560260\pi\)
−0.188183 + 0.982134i \(0.560260\pi\)
\(282\) 28.1658 1.67725
\(283\) 20.4007 1.21270 0.606348 0.795199i \(-0.292634\pi\)
0.606348 + 0.795199i \(0.292634\pi\)
\(284\) −28.9397 −1.71725
\(285\) −4.02902 −0.238659
\(286\) 12.5673 0.743122
\(287\) −0.167035 −0.00985978
\(288\) −9.13467 −0.538266
\(289\) −16.8366 −0.990387
\(290\) −24.0783 −1.41393
\(291\) −6.03423 −0.353733
\(292\) 21.1901 1.24006
\(293\) −20.1893 −1.17947 −0.589737 0.807595i \(-0.700769\pi\)
−0.589737 + 0.807595i \(0.700769\pi\)
\(294\) −14.8718 −0.867344
\(295\) 11.6544 0.678547
\(296\) 5.84957 0.339999
\(297\) −30.1930 −1.75198
\(298\) −2.45145 −0.142009
\(299\) 1.39164 0.0804807
\(300\) 9.57130 0.552599
\(301\) 6.21488 0.358220
\(302\) 8.38984 0.482781
\(303\) −6.77089 −0.388977
\(304\) 0.402840 0.0231045
\(305\) −6.99793 −0.400701
\(306\) −1.43328 −0.0819351
\(307\) 33.5707 1.91598 0.957990 0.286801i \(-0.0925919\pi\)
0.957990 + 0.286801i \(0.0925919\pi\)
\(308\) −22.0612 −1.25705
\(309\) −15.8685 −0.902729
\(310\) 3.71086 0.210762
\(311\) 32.3521 1.83452 0.917260 0.398290i \(-0.130396\pi\)
0.917260 + 0.398290i \(0.130396\pi\)
\(312\) 3.26748 0.184985
\(313\) 24.4579 1.38244 0.691221 0.722643i \(-0.257073\pi\)
0.691221 + 0.722643i \(0.257073\pi\)
\(314\) 9.17322 0.517675
\(315\) 3.08537 0.173841
\(316\) 2.09559 0.117886
\(317\) 17.5639 0.986484 0.493242 0.869892i \(-0.335812\pi\)
0.493242 + 0.869892i \(0.335812\pi\)
\(318\) 34.7872 1.95077
\(319\) 36.8106 2.06100
\(320\) 20.5775 1.15032
\(321\) 11.9973 0.669622
\(322\) −3.97306 −0.221410
\(323\) 0.856209 0.0476407
\(324\) −6.10535 −0.339186
\(325\) −2.49426 −0.138357
\(326\) −16.9661 −0.939665
\(327\) −7.55623 −0.417860
\(328\) 0.362514 0.0200165
\(329\) 12.8848 0.710364
\(330\) 23.9069 1.31603
\(331\) 9.17431 0.504266 0.252133 0.967693i \(-0.418868\pi\)
0.252133 + 0.967693i \(0.418868\pi\)
\(332\) 10.0591 0.552065
\(333\) 3.34718 0.183425
\(334\) 34.2299 1.87298
\(335\) −10.2869 −0.562031
\(336\) 0.286358 0.0156221
\(337\) 2.86123 0.155861 0.0779307 0.996959i \(-0.475169\pi\)
0.0779307 + 0.996959i \(0.475169\pi\)
\(338\) −2.27884 −0.123953
\(339\) 21.8829 1.18852
\(340\) 2.04335 0.110816
\(341\) −5.67311 −0.307216
\(342\) −7.50914 −0.406048
\(343\) −15.5730 −0.840861
\(344\) −13.4881 −0.727227
\(345\) 2.64732 0.142527
\(346\) −40.1353 −2.15769
\(347\) 3.29251 0.176751 0.0883755 0.996087i \(-0.471832\pi\)
0.0883755 + 0.996087i \(0.471832\pi\)
\(348\) 25.6137 1.37304
\(349\) −12.5920 −0.674035 −0.337018 0.941498i \(-0.609418\pi\)
−0.337018 + 0.941498i \(0.609418\pi\)
\(350\) 7.12099 0.380633
\(351\) 5.47492 0.292230
\(352\) −32.3791 −1.72581
\(353\) 11.4564 0.609765 0.304883 0.952390i \(-0.401383\pi\)
0.304883 + 0.952390i \(0.401383\pi\)
\(354\) −20.1628 −1.07164
\(355\) 14.3465 0.761431
\(356\) 29.4024 1.55833
\(357\) 0.608634 0.0322123
\(358\) 13.4570 0.711223
\(359\) 24.4939 1.29274 0.646370 0.763025i \(-0.276286\pi\)
0.646370 + 0.763025i \(0.276286\pi\)
\(360\) −6.69614 −0.352918
\(361\) −14.5142 −0.763906
\(362\) −55.9429 −2.94029
\(363\) −23.3294 −1.22447
\(364\) 4.00036 0.209676
\(365\) −10.5047 −0.549842
\(366\) 12.1068 0.632832
\(367\) 18.0764 0.943579 0.471790 0.881711i \(-0.343608\pi\)
0.471790 + 0.881711i \(0.343608\pi\)
\(368\) −0.264692 −0.0137980
\(369\) 0.207435 0.0107986
\(370\) −7.76078 −0.403464
\(371\) 15.9139 0.826208
\(372\) −3.94748 −0.204667
\(373\) −20.7881 −1.07637 −0.538183 0.842828i \(-0.680889\pi\)
−0.538183 + 0.842828i \(0.680889\pi\)
\(374\) −5.08046 −0.262705
\(375\) −14.2564 −0.736196
\(376\) −27.9638 −1.44212
\(377\) −6.67488 −0.343774
\(378\) −15.6306 −0.803952
\(379\) 27.8653 1.43134 0.715671 0.698437i \(-0.246121\pi\)
0.715671 + 0.698437i \(0.246121\pi\)
\(380\) 10.7054 0.549176
\(381\) −2.05501 −0.105281
\(382\) 54.2837 2.77739
\(383\) −37.3464 −1.90831 −0.954155 0.299312i \(-0.903243\pi\)
−0.954155 + 0.299312i \(0.903243\pi\)
\(384\) −21.4884 −1.09658
\(385\) 10.9365 0.557378
\(386\) −28.8395 −1.46789
\(387\) −7.71801 −0.392328
\(388\) 16.0334 0.813973
\(389\) −0.000727062 0 −3.68635e−5 0 −1.84317e−5 1.00000i \(-0.500006\pi\)
−1.84317e−5 1.00000i \(0.500006\pi\)
\(390\) −4.33505 −0.219514
\(391\) −0.562584 −0.0284511
\(392\) 14.7652 0.745754
\(393\) 26.0299 1.31303
\(394\) 53.5375 2.69718
\(395\) −1.03886 −0.0522707
\(396\) 27.3969 1.37675
\(397\) 8.66853 0.435061 0.217531 0.976053i \(-0.430200\pi\)
0.217531 + 0.976053i \(0.430200\pi\)
\(398\) 36.8567 1.84746
\(399\) 3.18871 0.159635
\(400\) 0.474412 0.0237206
\(401\) −32.0752 −1.60176 −0.800879 0.598826i \(-0.795634\pi\)
−0.800879 + 0.598826i \(0.795634\pi\)
\(402\) 17.7968 0.887623
\(403\) 1.02871 0.0512436
\(404\) 17.9908 0.895073
\(405\) 3.02665 0.150395
\(406\) 19.0564 0.945755
\(407\) 11.8646 0.588105
\(408\) −1.32091 −0.0653947
\(409\) 31.6512 1.56505 0.782525 0.622619i \(-0.213931\pi\)
0.782525 + 0.622619i \(0.213931\pi\)
\(410\) −0.480958 −0.0237528
\(411\) 3.12047 0.153921
\(412\) 42.1638 2.07726
\(413\) −9.22374 −0.453871
\(414\) 4.93399 0.242492
\(415\) −4.98667 −0.244786
\(416\) 5.87133 0.287866
\(417\) −5.00914 −0.245299
\(418\) −26.6172 −1.30189
\(419\) −30.3678 −1.48357 −0.741783 0.670640i \(-0.766019\pi\)
−0.741783 + 0.670640i \(0.766019\pi\)
\(420\) 7.60991 0.371326
\(421\) −35.9963 −1.75435 −0.877175 0.480170i \(-0.840575\pi\)
−0.877175 + 0.480170i \(0.840575\pi\)
\(422\) −32.7284 −1.59319
\(423\) −16.0012 −0.778004
\(424\) −34.5377 −1.67730
\(425\) 1.00833 0.0489112
\(426\) −24.8201 −1.20254
\(427\) 5.53842 0.268023
\(428\) −31.8776 −1.54086
\(429\) 6.62737 0.319972
\(430\) 17.8950 0.862972
\(431\) 32.9212 1.58576 0.792879 0.609380i \(-0.208581\pi\)
0.792879 + 0.609380i \(0.208581\pi\)
\(432\) −1.04134 −0.0501013
\(433\) 6.85005 0.329192 0.164596 0.986361i \(-0.447368\pi\)
0.164596 + 0.986361i \(0.447368\pi\)
\(434\) −2.93691 −0.140976
\(435\) −12.6977 −0.608806
\(436\) 20.0775 0.961536
\(437\) −2.94745 −0.140996
\(438\) 18.1737 0.868373
\(439\) −32.5582 −1.55392 −0.776959 0.629552i \(-0.783239\pi\)
−0.776959 + 0.629552i \(0.783239\pi\)
\(440\) −23.7354 −1.13154
\(441\) 8.44879 0.402323
\(442\) 0.921243 0.0438191
\(443\) 25.8566 1.22849 0.614243 0.789117i \(-0.289462\pi\)
0.614243 + 0.789117i \(0.289462\pi\)
\(444\) 8.25565 0.391796
\(445\) −14.5759 −0.690963
\(446\) 31.2601 1.48021
\(447\) −1.29277 −0.0611459
\(448\) −16.2858 −0.769430
\(449\) −37.5642 −1.77277 −0.886383 0.462953i \(-0.846790\pi\)
−0.886383 + 0.462953i \(0.846790\pi\)
\(450\) −8.84328 −0.416876
\(451\) 0.735282 0.0346231
\(452\) −58.1445 −2.73489
\(453\) 4.42437 0.207875
\(454\) −64.3495 −3.02007
\(455\) −1.98313 −0.0929706
\(456\) −6.92042 −0.324078
\(457\) −17.3206 −0.810222 −0.405111 0.914267i \(-0.632767\pi\)
−0.405111 + 0.914267i \(0.632767\pi\)
\(458\) −65.7466 −3.07213
\(459\) −2.21329 −0.103307
\(460\) −7.03414 −0.327968
\(461\) 15.0484 0.700873 0.350436 0.936587i \(-0.386033\pi\)
0.350436 + 0.936587i \(0.386033\pi\)
\(462\) −18.9208 −0.880275
\(463\) −25.7021 −1.19448 −0.597240 0.802063i \(-0.703736\pi\)
−0.597240 + 0.802063i \(0.703736\pi\)
\(464\) 1.26957 0.0589383
\(465\) 1.95691 0.0907498
\(466\) 11.1291 0.515547
\(467\) 11.4233 0.528607 0.264304 0.964440i \(-0.414858\pi\)
0.264304 + 0.964440i \(0.414858\pi\)
\(468\) −4.96789 −0.229641
\(469\) 8.14139 0.375935
\(470\) 37.1003 1.71131
\(471\) 4.83748 0.222900
\(472\) 20.0182 0.921410
\(473\) −27.3576 −1.25790
\(474\) 1.79728 0.0825519
\(475\) 5.28278 0.242390
\(476\) −1.61718 −0.0741235
\(477\) −19.7628 −0.904877
\(478\) −5.05159 −0.231054
\(479\) −20.6460 −0.943342 −0.471671 0.881775i \(-0.656349\pi\)
−0.471671 + 0.881775i \(0.656349\pi\)
\(480\) 11.1691 0.509795
\(481\) −2.15141 −0.0980959
\(482\) 0.636255 0.0289806
\(483\) −2.09519 −0.0953344
\(484\) 61.9879 2.81763
\(485\) −7.94836 −0.360916
\(486\) 32.1932 1.46031
\(487\) 19.0480 0.863148 0.431574 0.902077i \(-0.357958\pi\)
0.431574 + 0.902077i \(0.357958\pi\)
\(488\) −12.0200 −0.544118
\(489\) −8.94704 −0.404599
\(490\) −19.5894 −0.884957
\(491\) 2.09167 0.0943958 0.0471979 0.998886i \(-0.484971\pi\)
0.0471979 + 0.998886i \(0.484971\pi\)
\(492\) 0.511626 0.0230659
\(493\) 2.69838 0.121529
\(494\) 4.82652 0.217155
\(495\) −13.5817 −0.610450
\(496\) −0.195661 −0.00878545
\(497\) −11.3543 −0.509311
\(498\) 8.62720 0.386594
\(499\) −20.4098 −0.913668 −0.456834 0.889552i \(-0.651017\pi\)
−0.456834 + 0.889552i \(0.651017\pi\)
\(500\) 37.8802 1.69406
\(501\) 18.0511 0.806463
\(502\) 46.9183 2.09407
\(503\) −18.3337 −0.817457 −0.408729 0.912656i \(-0.634028\pi\)
−0.408729 + 0.912656i \(0.634028\pi\)
\(504\) 5.29957 0.236062
\(505\) −8.91869 −0.396876
\(506\) 17.4892 0.777491
\(507\) −1.20174 −0.0533714
\(508\) 5.46030 0.242262
\(509\) 17.2555 0.764836 0.382418 0.923990i \(-0.375092\pi\)
0.382418 + 0.923990i \(0.375092\pi\)
\(510\) 1.75248 0.0776013
\(511\) 8.31382 0.367782
\(512\) −2.15103 −0.0950628
\(513\) −11.5957 −0.511963
\(514\) 35.7331 1.57612
\(515\) −20.9022 −0.921061
\(516\) −19.0361 −0.838016
\(517\) −56.7185 −2.49448
\(518\) 6.14216 0.269871
\(519\) −21.1653 −0.929054
\(520\) 4.30396 0.188741
\(521\) 0.707893 0.0310134 0.0155067 0.999880i \(-0.495064\pi\)
0.0155067 + 0.999880i \(0.495064\pi\)
\(522\) −23.6654 −1.03581
\(523\) 1.61847 0.0707706 0.0353853 0.999374i \(-0.488734\pi\)
0.0353853 + 0.999374i \(0.488734\pi\)
\(524\) −69.1633 −3.02141
\(525\) 3.75525 0.163892
\(526\) −28.7326 −1.25280
\(527\) −0.415865 −0.0181154
\(528\) −1.26053 −0.0548576
\(529\) −21.0633 −0.915797
\(530\) 45.8221 1.99038
\(531\) 11.4546 0.497087
\(532\) −8.47265 −0.367336
\(533\) −0.133329 −0.00577512
\(534\) 25.2170 1.09125
\(535\) 15.8029 0.683220
\(536\) −17.6691 −0.763191
\(537\) 7.09651 0.306237
\(538\) −50.3244 −2.16964
\(539\) 29.9480 1.28995
\(540\) −27.6733 −1.19087
\(541\) −16.6794 −0.717103 −0.358552 0.933510i \(-0.616729\pi\)
−0.358552 + 0.933510i \(0.616729\pi\)
\(542\) −27.6821 −1.18905
\(543\) −29.5014 −1.26603
\(544\) −2.37354 −0.101765
\(545\) −9.95315 −0.426346
\(546\) 3.43092 0.146830
\(547\) 25.9764 1.11067 0.555335 0.831627i \(-0.312590\pi\)
0.555335 + 0.831627i \(0.312590\pi\)
\(548\) −8.29132 −0.354188
\(549\) −6.87794 −0.293543
\(550\) −31.3463 −1.33661
\(551\) 14.1372 0.602265
\(552\) 4.54716 0.193540
\(553\) 0.822192 0.0349631
\(554\) 29.9316 1.27167
\(555\) −4.09264 −0.173723
\(556\) 13.3097 0.564455
\(557\) 37.3125 1.58098 0.790491 0.612474i \(-0.209826\pi\)
0.790491 + 0.612474i \(0.209826\pi\)
\(558\) 3.64723 0.154399
\(559\) 4.96077 0.209818
\(560\) 0.377193 0.0159393
\(561\) −2.67918 −0.113115
\(562\) 14.3773 0.606471
\(563\) −16.3966 −0.691035 −0.345517 0.938412i \(-0.612297\pi\)
−0.345517 + 0.938412i \(0.612297\pi\)
\(564\) −39.4661 −1.66182
\(565\) 28.8244 1.21265
\(566\) −46.4900 −1.95412
\(567\) −2.39540 −0.100597
\(568\) 24.6421 1.03396
\(569\) 21.4142 0.897732 0.448866 0.893599i \(-0.351828\pi\)
0.448866 + 0.893599i \(0.351828\pi\)
\(570\) 9.18150 0.384571
\(571\) −8.83454 −0.369714 −0.184857 0.982765i \(-0.559182\pi\)
−0.184857 + 0.982765i \(0.559182\pi\)
\(572\) −17.6094 −0.736287
\(573\) 28.6264 1.19589
\(574\) 0.380647 0.0158879
\(575\) −3.47112 −0.144756
\(576\) 20.2246 0.842693
\(577\) −5.84845 −0.243474 −0.121737 0.992562i \(-0.538846\pi\)
−0.121737 + 0.992562i \(0.538846\pi\)
\(578\) 38.3679 1.59589
\(579\) −15.2085 −0.632042
\(580\) 33.7386 1.40092
\(581\) 3.94663 0.163734
\(582\) 13.7511 0.570000
\(583\) −70.0522 −2.90126
\(584\) −18.0434 −0.746639
\(585\) 2.46277 0.101823
\(586\) 46.0083 1.90059
\(587\) 36.2760 1.49727 0.748635 0.662983i \(-0.230710\pi\)
0.748635 + 0.662983i \(0.230710\pi\)
\(588\) 20.8385 0.859365
\(589\) −2.17877 −0.0897747
\(590\) −26.5586 −1.09340
\(591\) 28.2329 1.16135
\(592\) 0.409201 0.0168180
\(593\) 46.7426 1.91949 0.959743 0.280878i \(-0.0906258\pi\)
0.959743 + 0.280878i \(0.0906258\pi\)
\(594\) 68.8052 2.82311
\(595\) 0.801699 0.0328664
\(596\) 3.43499 0.140703
\(597\) 19.4363 0.795476
\(598\) −3.17133 −0.129685
\(599\) −14.5359 −0.593921 −0.296960 0.954890i \(-0.595973\pi\)
−0.296960 + 0.954890i \(0.595973\pi\)
\(600\) −8.14996 −0.332721
\(601\) −16.3889 −0.668516 −0.334258 0.942482i \(-0.608486\pi\)
−0.334258 + 0.942482i \(0.608486\pi\)
\(602\) −14.1627 −0.577230
\(603\) −10.1105 −0.411730
\(604\) −11.7559 −0.478340
\(605\) −30.7297 −1.24934
\(606\) 15.4298 0.626792
\(607\) −24.7393 −1.00414 −0.502068 0.864828i \(-0.667427\pi\)
−0.502068 + 0.864828i \(0.667427\pi\)
\(608\) −12.4353 −0.504318
\(609\) 10.0494 0.407222
\(610\) 15.9472 0.645683
\(611\) 10.2848 0.416078
\(612\) 2.00832 0.0811814
\(613\) 15.9430 0.643930 0.321965 0.946752i \(-0.395657\pi\)
0.321965 + 0.946752i \(0.395657\pi\)
\(614\) −76.5023 −3.08738
\(615\) −0.253632 −0.0102274
\(616\) 18.7851 0.756872
\(617\) −7.85966 −0.316418 −0.158209 0.987406i \(-0.550572\pi\)
−0.158209 + 0.987406i \(0.550572\pi\)
\(618\) 36.1619 1.45464
\(619\) 1.00000 0.0401934
\(620\) −5.19967 −0.208824
\(621\) 7.61912 0.305745
\(622\) −73.7254 −2.95612
\(623\) 11.5359 0.462175
\(624\) 0.228573 0.00915025
\(625\) −6.30732 −0.252293
\(626\) −55.7357 −2.22765
\(627\) −14.0366 −0.560566
\(628\) −12.8536 −0.512913
\(629\) 0.869728 0.0346783
\(630\) −7.03108 −0.280125
\(631\) −5.15456 −0.205200 −0.102600 0.994723i \(-0.532716\pi\)
−0.102600 + 0.994723i \(0.532716\pi\)
\(632\) −1.78439 −0.0709792
\(633\) −17.2593 −0.685995
\(634\) −40.0253 −1.58961
\(635\) −2.70688 −0.107419
\(636\) −48.7440 −1.93282
\(637\) −5.43048 −0.215163
\(638\) −83.8855 −3.32106
\(639\) 14.1005 0.557806
\(640\) −28.3048 −1.11884
\(641\) −18.6613 −0.737077 −0.368538 0.929613i \(-0.620142\pi\)
−0.368538 + 0.929613i \(0.620142\pi\)
\(642\) −27.3399 −1.07902
\(643\) −0.874004 −0.0344674 −0.0172337 0.999851i \(-0.505486\pi\)
−0.0172337 + 0.999851i \(0.505486\pi\)
\(644\) 5.56707 0.219373
\(645\) 9.43689 0.371577
\(646\) −1.95117 −0.0767676
\(647\) −15.2046 −0.597755 −0.298878 0.954291i \(-0.596612\pi\)
−0.298878 + 0.954291i \(0.596612\pi\)
\(648\) 5.19870 0.204224
\(649\) 40.6025 1.59379
\(650\) 5.68404 0.222946
\(651\) −1.54877 −0.0607012
\(652\) 23.7730 0.931021
\(653\) 16.2132 0.634472 0.317236 0.948347i \(-0.397245\pi\)
0.317236 + 0.948347i \(0.397245\pi\)
\(654\) 17.2195 0.673334
\(655\) 34.2868 1.33970
\(656\) 0.0253593 0.000990115 0
\(657\) −10.3246 −0.402801
\(658\) −29.3625 −1.14467
\(659\) −24.0335 −0.936213 −0.468106 0.883672i \(-0.655064\pi\)
−0.468106 + 0.883672i \(0.655064\pi\)
\(660\) −33.4985 −1.30393
\(661\) −22.5613 −0.877535 −0.438767 0.898601i \(-0.644585\pi\)
−0.438767 + 0.898601i \(0.644585\pi\)
\(662\) −20.9068 −0.812566
\(663\) 0.485817 0.0188676
\(664\) −8.56532 −0.332399
\(665\) 4.20021 0.162877
\(666\) −7.62771 −0.295568
\(667\) −9.28904 −0.359673
\(668\) −47.9631 −1.85575
\(669\) 16.4849 0.637345
\(670\) 23.4421 0.905649
\(671\) −24.3799 −0.941174
\(672\) −8.83959 −0.340995
\(673\) −42.7731 −1.64878 −0.824390 0.566022i \(-0.808482\pi\)
−0.824390 + 0.566022i \(0.808482\pi\)
\(674\) −6.52030 −0.251153
\(675\) −13.6559 −0.525616
\(676\) 3.19313 0.122813
\(677\) −46.9698 −1.80520 −0.902598 0.430485i \(-0.858343\pi\)
−0.902598 + 0.430485i \(0.858343\pi\)
\(678\) −49.8677 −1.91516
\(679\) 6.29062 0.241412
\(680\) −1.73992 −0.0667227
\(681\) −33.9346 −1.30038
\(682\) 12.9281 0.495043
\(683\) 11.4193 0.436946 0.218473 0.975843i \(-0.429892\pi\)
0.218473 + 0.975843i \(0.429892\pi\)
\(684\) 10.5218 0.402313
\(685\) 4.11032 0.157047
\(686\) 35.4884 1.35495
\(687\) −34.6714 −1.32279
\(688\) −0.943543 −0.0359722
\(689\) 12.7026 0.483930
\(690\) −6.03284 −0.229666
\(691\) 39.8037 1.51420 0.757101 0.653298i \(-0.226615\pi\)
0.757101 + 0.653298i \(0.226615\pi\)
\(692\) 56.2378 2.13784
\(693\) 10.7490 0.408322
\(694\) −7.50310 −0.284814
\(695\) −6.59810 −0.250280
\(696\) −21.8100 −0.826707
\(697\) 0.0538995 0.00204159
\(698\) 28.6952 1.08613
\(699\) 5.86894 0.221984
\(700\) −9.97797 −0.377132
\(701\) 18.3469 0.692953 0.346477 0.938059i \(-0.387378\pi\)
0.346477 + 0.938059i \(0.387378\pi\)
\(702\) −12.4765 −0.470895
\(703\) 4.55662 0.171856
\(704\) 71.6892 2.70189
\(705\) 19.5648 0.736853
\(706\) −26.1074 −0.982566
\(707\) 7.05857 0.265465
\(708\) 28.2522 1.06178
\(709\) −19.3493 −0.726678 −0.363339 0.931657i \(-0.618363\pi\)
−0.363339 + 0.931657i \(0.618363\pi\)
\(710\) −32.6933 −1.22696
\(711\) −1.02105 −0.0382923
\(712\) −25.0362 −0.938269
\(713\) 1.43159 0.0536135
\(714\) −1.38698 −0.0519064
\(715\) 8.72965 0.326470
\(716\) −18.8560 −0.704680
\(717\) −2.66395 −0.0994871
\(718\) −55.8178 −2.08310
\(719\) −1.81047 −0.0675190 −0.0337595 0.999430i \(-0.510748\pi\)
−0.0337595 + 0.999430i \(0.510748\pi\)
\(720\) −0.468422 −0.0174570
\(721\) 16.5428 0.616084
\(722\) 33.0756 1.23095
\(723\) 0.335528 0.0124784
\(724\) 78.3875 2.91325
\(725\) 16.6489 0.618325
\(726\) 53.1640 1.97310
\(727\) 7.14913 0.265146 0.132573 0.991173i \(-0.457676\pi\)
0.132573 + 0.991173i \(0.457676\pi\)
\(728\) −3.40631 −0.126246
\(729\) 22.7131 0.841227
\(730\) 23.9386 0.886008
\(731\) −2.00544 −0.0741738
\(732\) −16.9641 −0.627011
\(733\) −24.6905 −0.911966 −0.455983 0.889989i \(-0.650712\pi\)
−0.455983 + 0.889989i \(0.650712\pi\)
\(734\) −41.1932 −1.52047
\(735\) −10.3304 −0.381043
\(736\) 8.17078 0.301179
\(737\) −35.8380 −1.32011
\(738\) −0.472711 −0.0174007
\(739\) −49.8940 −1.83538 −0.917690 0.397297i \(-0.869948\pi\)
−0.917690 + 0.397297i \(0.869948\pi\)
\(740\) 10.8744 0.399752
\(741\) 2.54526 0.0935024
\(742\) −36.2652 −1.33134
\(743\) −3.11518 −0.114285 −0.0571424 0.998366i \(-0.518199\pi\)
−0.0571424 + 0.998366i \(0.518199\pi\)
\(744\) 3.36128 0.123231
\(745\) −1.70285 −0.0623876
\(746\) 47.3727 1.73444
\(747\) −4.90117 −0.179324
\(748\) 7.11877 0.260288
\(749\) −12.5070 −0.456996
\(750\) 32.4880 1.18629
\(751\) −34.0670 −1.24312 −0.621561 0.783366i \(-0.713501\pi\)
−0.621561 + 0.783366i \(0.713501\pi\)
\(752\) −1.95618 −0.0713345
\(753\) 24.7423 0.901660
\(754\) 15.2110 0.553952
\(755\) 5.82783 0.212096
\(756\) 21.9017 0.796556
\(757\) −47.0231 −1.70908 −0.854541 0.519384i \(-0.826161\pi\)
−0.854541 + 0.519384i \(0.826161\pi\)
\(758\) −63.5006 −2.30644
\(759\) 9.22292 0.334771
\(760\) −9.11565 −0.330659
\(761\) 11.1877 0.405554 0.202777 0.979225i \(-0.435003\pi\)
0.202777 + 0.979225i \(0.435003\pi\)
\(762\) 4.68304 0.169648
\(763\) 7.87728 0.285177
\(764\) −76.0625 −2.75184
\(765\) −0.995598 −0.0359959
\(766\) 85.1065 3.07502
\(767\) −7.36247 −0.265843
\(768\) 17.7247 0.639586
\(769\) −3.91063 −0.141021 −0.0705104 0.997511i \(-0.522463\pi\)
−0.0705104 + 0.997511i \(0.522463\pi\)
\(770\) −24.9227 −0.898151
\(771\) 18.8438 0.678643
\(772\) 40.4100 1.45439
\(773\) 32.6096 1.17289 0.586443 0.809990i \(-0.300528\pi\)
0.586443 + 0.809990i \(0.300528\pi\)
\(774\) 17.5881 0.632192
\(775\) −2.56587 −0.0921688
\(776\) −13.6524 −0.490094
\(777\) 3.23906 0.116201
\(778\) 0.00165686 5.94013e−5 0
\(779\) 0.282387 0.0101176
\(780\) 6.07429 0.217495
\(781\) 49.9812 1.78847
\(782\) 1.28204 0.0458457
\(783\) −36.5444 −1.30599
\(784\) 1.03288 0.0368887
\(785\) 6.37199 0.227426
\(786\) −59.3180 −2.11580
\(787\) 41.1731 1.46766 0.733832 0.679331i \(-0.237730\pi\)
0.733832 + 0.679331i \(0.237730\pi\)
\(788\) −75.0170 −2.67237
\(789\) −15.1521 −0.539428
\(790\) 2.36740 0.0842283
\(791\) −22.8127 −0.811126
\(792\) −23.3284 −0.828940
\(793\) 4.42081 0.156988
\(794\) −19.7542 −0.701051
\(795\) 24.1642 0.857016
\(796\) −51.6438 −1.83046
\(797\) −10.6317 −0.376595 −0.188297 0.982112i \(-0.560297\pi\)
−0.188297 + 0.982112i \(0.560297\pi\)
\(798\) −7.26658 −0.257234
\(799\) −4.15772 −0.147090
\(800\) −14.6446 −0.517767
\(801\) −14.3260 −0.506183
\(802\) 73.0943 2.58105
\(803\) −36.5970 −1.29148
\(804\) −24.9370 −0.879458
\(805\) −2.75980 −0.0972703
\(806\) −2.34426 −0.0825732
\(807\) −26.5385 −0.934200
\(808\) −15.3191 −0.538925
\(809\) −56.6132 −1.99042 −0.995208 0.0977821i \(-0.968825\pi\)
−0.995208 + 0.0977821i \(0.968825\pi\)
\(810\) −6.89726 −0.242345
\(811\) −48.6660 −1.70890 −0.854448 0.519537i \(-0.826104\pi\)
−0.854448 + 0.519537i \(0.826104\pi\)
\(812\) −26.7020 −0.937055
\(813\) −14.5981 −0.511978
\(814\) −27.0375 −0.947664
\(815\) −11.7851 −0.412816
\(816\) −0.0924028 −0.00323475
\(817\) −10.5068 −0.367585
\(818\) −72.1281 −2.52190
\(819\) −1.94913 −0.0681080
\(820\) 0.673920 0.0235343
\(821\) 15.6395 0.545821 0.272911 0.962039i \(-0.412014\pi\)
0.272911 + 0.962039i \(0.412014\pi\)
\(822\) −7.11106 −0.248027
\(823\) −7.91483 −0.275894 −0.137947 0.990440i \(-0.544050\pi\)
−0.137947 + 0.990440i \(0.544050\pi\)
\(824\) −35.9025 −1.25072
\(825\) −16.5304 −0.575515
\(826\) 21.0195 0.731360
\(827\) −22.8187 −0.793484 −0.396742 0.917930i \(-0.629859\pi\)
−0.396742 + 0.917930i \(0.629859\pi\)
\(828\) −6.91353 −0.240262
\(829\) −30.7783 −1.06897 −0.534487 0.845177i \(-0.679495\pi\)
−0.534487 + 0.845177i \(0.679495\pi\)
\(830\) 11.3638 0.394445
\(831\) 15.7844 0.547555
\(832\) −12.9994 −0.450674
\(833\) 2.19532 0.0760634
\(834\) 11.4150 0.395271
\(835\) 23.7771 0.822840
\(836\) 37.2962 1.28992
\(837\) 5.63209 0.194674
\(838\) 69.2035 2.39060
\(839\) −19.6920 −0.679842 −0.339921 0.940454i \(-0.610400\pi\)
−0.339921 + 0.940454i \(0.610400\pi\)
\(840\) −6.47983 −0.223576
\(841\) 15.5540 0.536346
\(842\) 82.0298 2.82694
\(843\) 7.58187 0.261133
\(844\) 45.8592 1.57854
\(845\) −1.58295 −0.0544552
\(846\) 36.4642 1.25366
\(847\) 24.3206 0.835666
\(848\) −2.41605 −0.0829674
\(849\) −24.5164 −0.841402
\(850\) −2.29782 −0.0788147
\(851\) −2.99399 −0.102633
\(852\) 34.7781 1.19148
\(853\) 15.8191 0.541634 0.270817 0.962631i \(-0.412706\pi\)
0.270817 + 0.962631i \(0.412706\pi\)
\(854\) −12.6212 −0.431888
\(855\) −5.21607 −0.178386
\(856\) 27.1438 0.927755
\(857\) −54.2269 −1.85236 −0.926178 0.377087i \(-0.876926\pi\)
−0.926178 + 0.377087i \(0.876926\pi\)
\(858\) −15.1027 −0.515599
\(859\) −22.9581 −0.783322 −0.391661 0.920110i \(-0.628099\pi\)
−0.391661 + 0.920110i \(0.628099\pi\)
\(860\) −25.0745 −0.855034
\(861\) 0.200734 0.00684099
\(862\) −75.0222 −2.55527
\(863\) 46.0740 1.56838 0.784188 0.620523i \(-0.213080\pi\)
0.784188 + 0.620523i \(0.213080\pi\)
\(864\) 32.1451 1.09360
\(865\) −27.8792 −0.947920
\(866\) −15.6102 −0.530456
\(867\) 20.2333 0.687158
\(868\) 4.11521 0.139679
\(869\) −3.61925 −0.122775
\(870\) 28.9360 0.981021
\(871\) 6.49853 0.220194
\(872\) −17.0960 −0.578942
\(873\) −7.81207 −0.264399
\(874\) 6.71678 0.227199
\(875\) 14.8621 0.502431
\(876\) −25.4651 −0.860385
\(877\) −9.66009 −0.326198 −0.163099 0.986610i \(-0.552149\pi\)
−0.163099 + 0.986610i \(0.552149\pi\)
\(878\) 74.1950 2.50396
\(879\) 24.2624 0.818352
\(880\) −1.66039 −0.0559717
\(881\) 46.8334 1.57786 0.788928 0.614485i \(-0.210636\pi\)
0.788928 + 0.614485i \(0.210636\pi\)
\(882\) −19.2535 −0.648298
\(883\) 36.1406 1.21623 0.608114 0.793850i \(-0.291926\pi\)
0.608114 + 0.793850i \(0.291926\pi\)
\(884\) −1.29085 −0.0434160
\(885\) −14.0057 −0.470795
\(886\) −58.9232 −1.97956
\(887\) −22.7884 −0.765158 −0.382579 0.923923i \(-0.624964\pi\)
−0.382579 + 0.923923i \(0.624964\pi\)
\(888\) −7.02969 −0.235901
\(889\) 2.14232 0.0718511
\(890\) 33.2161 1.11341
\(891\) 10.5444 0.353252
\(892\) −43.8017 −1.46659
\(893\) −21.7829 −0.728936
\(894\) 2.94602 0.0985297
\(895\) 9.34760 0.312456
\(896\) 22.4014 0.748379
\(897\) −1.67240 −0.0558397
\(898\) 85.6030 2.85661
\(899\) −6.86650 −0.229011
\(900\) 12.3912 0.413041
\(901\) −5.13514 −0.171076
\(902\) −1.67559 −0.0557911
\(903\) −7.46870 −0.248543
\(904\) 49.5101 1.64668
\(905\) −38.8596 −1.29174
\(906\) −10.0824 −0.334967
\(907\) 22.7419 0.755133 0.377566 0.925983i \(-0.376761\pi\)
0.377566 + 0.925983i \(0.376761\pi\)
\(908\) 90.1668 2.99229
\(909\) −8.76576 −0.290742
\(910\) 4.51924 0.149811
\(911\) 14.4095 0.477409 0.238704 0.971092i \(-0.423277\pi\)
0.238704 + 0.971092i \(0.423277\pi\)
\(912\) −0.484111 −0.0160305
\(913\) −17.3729 −0.574959
\(914\) 39.4709 1.30558
\(915\) 8.40973 0.278017
\(916\) 92.1244 3.04388
\(917\) −27.1358 −0.896104
\(918\) 5.04373 0.166468
\(919\) 17.3943 0.573784 0.286892 0.957963i \(-0.407378\pi\)
0.286892 + 0.957963i \(0.407378\pi\)
\(920\) 5.98957 0.197470
\(921\) −40.3434 −1.32936
\(922\) −34.2929 −1.12938
\(923\) −9.06311 −0.298316
\(924\) 26.5119 0.872177
\(925\) 5.36619 0.176439
\(926\) 58.5711 1.92477
\(927\) −20.5438 −0.674747
\(928\) −39.1904 −1.28649
\(929\) 22.2307 0.729364 0.364682 0.931132i \(-0.381178\pi\)
0.364682 + 0.931132i \(0.381178\pi\)
\(930\) −4.45950 −0.146233
\(931\) 11.5016 0.376949
\(932\) −15.5942 −0.510805
\(933\) −38.8790 −1.27284
\(934\) −26.0319 −0.851790
\(935\) −3.52904 −0.115412
\(936\) 4.23016 0.138267
\(937\) −5.81591 −0.189997 −0.0949987 0.995477i \(-0.530285\pi\)
−0.0949987 + 0.995477i \(0.530285\pi\)
\(938\) −18.5530 −0.605775
\(939\) −29.3922 −0.959177
\(940\) −51.9851 −1.69557
\(941\) −54.4176 −1.77396 −0.886982 0.461805i \(-0.847202\pi\)
−0.886982 + 0.461805i \(0.847202\pi\)
\(942\) −11.0239 −0.359177
\(943\) −0.185546 −0.00604221
\(944\) 1.40035 0.0455775
\(945\) −10.8575 −0.353194
\(946\) 62.3437 2.02697
\(947\) 27.7906 0.903073 0.451536 0.892253i \(-0.350876\pi\)
0.451536 + 0.892253i \(0.350876\pi\)
\(948\) −2.51836 −0.0817925
\(949\) 6.63616 0.215419
\(950\) −12.0386 −0.390584
\(951\) −21.1073 −0.684450
\(952\) 1.37703 0.0446299
\(953\) −36.6055 −1.18577 −0.592884 0.805288i \(-0.702011\pi\)
−0.592884 + 0.805288i \(0.702011\pi\)
\(954\) 45.0364 1.45811
\(955\) 37.7070 1.22017
\(956\) 7.07831 0.228929
\(957\) −44.2369 −1.42998
\(958\) 47.0491 1.52009
\(959\) −3.25305 −0.105047
\(960\) −24.7289 −0.798121
\(961\) −29.9418 −0.965863
\(962\) 4.90273 0.158070
\(963\) 15.5320 0.500510
\(964\) −0.891523 −0.0287140
\(965\) −20.0328 −0.644877
\(966\) 4.77460 0.153620
\(967\) −47.8012 −1.53718 −0.768591 0.639740i \(-0.779042\pi\)
−0.768591 + 0.639740i \(0.779042\pi\)
\(968\) −52.7826 −1.69650
\(969\) −1.02894 −0.0330545
\(970\) 18.1131 0.581575
\(971\) −5.84160 −0.187466 −0.0937330 0.995597i \(-0.529880\pi\)
−0.0937330 + 0.995597i \(0.529880\pi\)
\(972\) −45.1092 −1.44688
\(973\) 5.22197 0.167409
\(974\) −43.4075 −1.39086
\(975\) 2.99747 0.0959959
\(976\) −0.840843 −0.0269147
\(977\) −46.9628 −1.50247 −0.751237 0.660033i \(-0.770542\pi\)
−0.751237 + 0.660033i \(0.770542\pi\)
\(978\) 20.3889 0.651965
\(979\) −50.7804 −1.62295
\(980\) 27.4487 0.876816
\(981\) −9.78248 −0.312331
\(982\) −4.76659 −0.152108
\(983\) 12.1197 0.386557 0.193279 0.981144i \(-0.438088\pi\)
0.193279 + 0.981144i \(0.438088\pi\)
\(984\) −0.435650 −0.0138880
\(985\) 37.1887 1.18493
\(986\) −6.14919 −0.195830
\(987\) −15.4843 −0.492870
\(988\) −6.76294 −0.215158
\(989\) 6.90361 0.219522
\(990\) 30.9505 0.983671
\(991\) −28.7982 −0.914803 −0.457402 0.889260i \(-0.651220\pi\)
−0.457402 + 0.889260i \(0.651220\pi\)
\(992\) 6.03988 0.191766
\(993\) −11.0252 −0.349874
\(994\) 25.8747 0.820696
\(995\) 25.6017 0.811630
\(996\) −12.0885 −0.383038
\(997\) −6.09938 −0.193169 −0.0965846 0.995325i \(-0.530792\pi\)
−0.0965846 + 0.995325i \(0.530792\pi\)
\(998\) 46.5107 1.47227
\(999\) −11.7788 −0.372665
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 \(a_p\))