Properties

Label 4017.2.a.j.1.8
Level 4017
Weight 2
Character 4017.1
Self dual Yes
Analytic conductor 32.076
Analytic rank 0
Dimension 25
CM No

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 1.8
Character \(\chi\) = 4017.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.925244 q^{2} -1.00000 q^{3} -1.14392 q^{4} +3.08995 q^{5} +0.925244 q^{6} -0.0396192 q^{7} +2.90890 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-0.925244 q^{2} -1.00000 q^{3} -1.14392 q^{4} +3.08995 q^{5} +0.925244 q^{6} -0.0396192 q^{7} +2.90890 q^{8} +1.00000 q^{9} -2.85895 q^{10} +3.49434 q^{11} +1.14392 q^{12} +1.00000 q^{13} +0.0366574 q^{14} -3.08995 q^{15} -0.403588 q^{16} +4.97266 q^{17} -0.925244 q^{18} +5.15461 q^{19} -3.53467 q^{20} +0.0396192 q^{21} -3.23311 q^{22} +5.51853 q^{23} -2.90890 q^{24} +4.54778 q^{25} -0.925244 q^{26} -1.00000 q^{27} +0.0453214 q^{28} -6.50685 q^{29} +2.85895 q^{30} +6.23092 q^{31} -5.44437 q^{32} -3.49434 q^{33} -4.60092 q^{34} -0.122421 q^{35} -1.14392 q^{36} +10.4013 q^{37} -4.76927 q^{38} -1.00000 q^{39} +8.98834 q^{40} +8.28965 q^{41} -0.0366574 q^{42} +8.81740 q^{43} -3.99726 q^{44} +3.08995 q^{45} -5.10598 q^{46} -10.5346 q^{47} +0.403588 q^{48} -6.99843 q^{49} -4.20781 q^{50} -4.97266 q^{51} -1.14392 q^{52} -0.138518 q^{53} +0.925244 q^{54} +10.7973 q^{55} -0.115248 q^{56} -5.15461 q^{57} +6.02042 q^{58} +12.9656 q^{59} +3.53467 q^{60} +1.88482 q^{61} -5.76512 q^{62} -0.0396192 q^{63} +5.84455 q^{64} +3.08995 q^{65} +3.23311 q^{66} +5.01033 q^{67} -5.68834 q^{68} -5.51853 q^{69} +0.113269 q^{70} -14.7803 q^{71} +2.90890 q^{72} -7.21359 q^{73} -9.62371 q^{74} -4.54778 q^{75} -5.89649 q^{76} -0.138443 q^{77} +0.925244 q^{78} -16.9142 q^{79} -1.24707 q^{80} +1.00000 q^{81} -7.66995 q^{82} -11.0487 q^{83} -0.0453214 q^{84} +15.3653 q^{85} -8.15824 q^{86} +6.50685 q^{87} +10.1647 q^{88} +2.35669 q^{89} -2.85895 q^{90} -0.0396192 q^{91} -6.31278 q^{92} -6.23092 q^{93} +9.74704 q^{94} +15.9275 q^{95} +5.44437 q^{96} -14.7503 q^{97} +6.47525 q^{98} +3.49434 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 25q + 6q^{2} - 25q^{3} + 28q^{4} + 7q^{5} - 6q^{6} + 17q^{7} + 21q^{8} + 25q^{9} + O(q^{10}) \) \( 25q + 6q^{2} - 25q^{3} + 28q^{4} + 7q^{5} - 6q^{6} + 17q^{7} + 21q^{8} + 25q^{9} - 6q^{10} + 21q^{11} - 28q^{12} + 25q^{13} + 10q^{14} - 7q^{15} + 30q^{16} + 14q^{17} + 6q^{18} + 12q^{19} + 24q^{20} - 17q^{21} + 3q^{22} + 41q^{23} - 21q^{24} + 30q^{25} + 6q^{26} - 25q^{27} + 14q^{28} + 22q^{29} + 6q^{30} + 14q^{31} + 28q^{32} - 21q^{33} - 11q^{34} + 14q^{35} + 28q^{36} - 6q^{37} + 16q^{38} - 25q^{39} - 34q^{40} + 33q^{41} - 10q^{42} + 35q^{43} + 45q^{44} + 7q^{45} + 3q^{46} + 48q^{47} - 30q^{48} - 4q^{49} + 7q^{50} - 14q^{51} + 28q^{52} + 18q^{53} - 6q^{54} + 10q^{55} + 32q^{56} - 12q^{57} + 33q^{58} + 46q^{59} - 24q^{60} - 19q^{61} + 5q^{62} + 17q^{63} + 29q^{64} + 7q^{65} - 3q^{66} + 16q^{67} + 20q^{68} - 41q^{69} - 43q^{70} + 60q^{71} + 21q^{72} - 14q^{73} - 50q^{74} - 30q^{75} + 59q^{77} - 6q^{78} + 7q^{79} + 32q^{80} + 25q^{81} + 18q^{82} + 23q^{83} - 14q^{84} - 9q^{85} - 9q^{86} - 22q^{87} + 23q^{88} + 10q^{89} - 6q^{90} + 17q^{91} + 69q^{92} - 14q^{93} - 30q^{94} + 81q^{95} - 28q^{96} - 10q^{97} + 55q^{98} + 21q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.925244 −0.654246 −0.327123 0.944982i \(-0.606079\pi\)
−0.327123 + 0.944982i \(0.606079\pi\)
\(3\) −1.00000 −0.577350
\(4\) −1.14392 −0.571962
\(5\) 3.08995 1.38187 0.690934 0.722918i \(-0.257200\pi\)
0.690934 + 0.722918i \(0.257200\pi\)
\(6\) 0.925244 0.377729
\(7\) −0.0396192 −0.0149746 −0.00748732 0.999972i \(-0.502383\pi\)
−0.00748732 + 0.999972i \(0.502383\pi\)
\(8\) 2.90890 1.02845
\(9\) 1.00000 0.333333
\(10\) −2.85895 −0.904081
\(11\) 3.49434 1.05358 0.526791 0.849995i \(-0.323395\pi\)
0.526791 + 0.849995i \(0.323395\pi\)
\(12\) 1.14392 0.330223
\(13\) 1.00000 0.277350
\(14\) 0.0366574 0.00979710
\(15\) −3.08995 −0.797821
\(16\) −0.403588 −0.100897
\(17\) 4.97266 1.20605 0.603023 0.797724i \(-0.293963\pi\)
0.603023 + 0.797724i \(0.293963\pi\)
\(18\) −0.925244 −0.218082
\(19\) 5.15461 1.18255 0.591275 0.806470i \(-0.298625\pi\)
0.591275 + 0.806470i \(0.298625\pi\)
\(20\) −3.53467 −0.790376
\(21\) 0.0396192 0.00864562
\(22\) −3.23311 −0.689302
\(23\) 5.51853 1.15069 0.575346 0.817910i \(-0.304867\pi\)
0.575346 + 0.817910i \(0.304867\pi\)
\(24\) −2.90890 −0.593776
\(25\) 4.54778 0.909556
\(26\) −0.925244 −0.181455
\(27\) −1.00000 −0.192450
\(28\) 0.0453214 0.00856493
\(29\) −6.50685 −1.20829 −0.604146 0.796874i \(-0.706486\pi\)
−0.604146 + 0.796874i \(0.706486\pi\)
\(30\) 2.85895 0.521971
\(31\) 6.23092 1.11911 0.559553 0.828794i \(-0.310973\pi\)
0.559553 + 0.828794i \(0.310973\pi\)
\(32\) −5.44437 −0.962438
\(33\) −3.49434 −0.608286
\(34\) −4.60092 −0.789051
\(35\) −0.122421 −0.0206930
\(36\) −1.14392 −0.190654
\(37\) 10.4013 1.70996 0.854980 0.518662i \(-0.173570\pi\)
0.854980 + 0.518662i \(0.173570\pi\)
\(38\) −4.76927 −0.773678
\(39\) −1.00000 −0.160128
\(40\) 8.98834 1.42118
\(41\) 8.28965 1.29463 0.647313 0.762224i \(-0.275893\pi\)
0.647313 + 0.762224i \(0.275893\pi\)
\(42\) −0.0366574 −0.00565636
\(43\) 8.81740 1.34464 0.672321 0.740260i \(-0.265298\pi\)
0.672321 + 0.740260i \(0.265298\pi\)
\(44\) −3.99726 −0.602609
\(45\) 3.08995 0.460622
\(46\) −5.10598 −0.752836
\(47\) −10.5346 −1.53662 −0.768312 0.640076i \(-0.778903\pi\)
−0.768312 + 0.640076i \(0.778903\pi\)
\(48\) 0.403588 0.0582529
\(49\) −6.99843 −0.999776
\(50\) −4.20781 −0.595074
\(51\) −4.97266 −0.696311
\(52\) −1.14392 −0.158634
\(53\) −0.138518 −0.0190269 −0.00951344 0.999955i \(-0.503028\pi\)
−0.00951344 + 0.999955i \(0.503028\pi\)
\(54\) 0.925244 0.125910
\(55\) 10.7973 1.45591
\(56\) −0.115248 −0.0154007
\(57\) −5.15461 −0.682745
\(58\) 6.02042 0.790520
\(59\) 12.9656 1.68798 0.843991 0.536358i \(-0.180200\pi\)
0.843991 + 0.536358i \(0.180200\pi\)
\(60\) 3.53467 0.456324
\(61\) 1.88482 0.241327 0.120663 0.992693i \(-0.461498\pi\)
0.120663 + 0.992693i \(0.461498\pi\)
\(62\) −5.76512 −0.732171
\(63\) −0.0396192 −0.00499155
\(64\) 5.84455 0.730569
\(65\) 3.08995 0.383261
\(66\) 3.23311 0.397968
\(67\) 5.01033 0.612110 0.306055 0.952014i \(-0.400991\pi\)
0.306055 + 0.952014i \(0.400991\pi\)
\(68\) −5.68834 −0.689813
\(69\) −5.51853 −0.664353
\(70\) 0.113269 0.0135383
\(71\) −14.7803 −1.75410 −0.877050 0.480399i \(-0.840492\pi\)
−0.877050 + 0.480399i \(0.840492\pi\)
\(72\) 2.90890 0.342817
\(73\) −7.21359 −0.844287 −0.422143 0.906529i \(-0.638722\pi\)
−0.422143 + 0.906529i \(0.638722\pi\)
\(74\) −9.62371 −1.11873
\(75\) −4.54778 −0.525133
\(76\) −5.89649 −0.676374
\(77\) −0.138443 −0.0157770
\(78\) 0.925244 0.104763
\(79\) −16.9142 −1.90299 −0.951497 0.307658i \(-0.900455\pi\)
−0.951497 + 0.307658i \(0.900455\pi\)
\(80\) −1.24707 −0.139426
\(81\) 1.00000 0.111111
\(82\) −7.66995 −0.847004
\(83\) −11.0487 −1.21276 −0.606379 0.795176i \(-0.707378\pi\)
−0.606379 + 0.795176i \(0.707378\pi\)
\(84\) −0.0453214 −0.00494497
\(85\) 15.3653 1.66660
\(86\) −8.15824 −0.879726
\(87\) 6.50685 0.697608
\(88\) 10.1647 1.08356
\(89\) 2.35669 0.249809 0.124905 0.992169i \(-0.460138\pi\)
0.124905 + 0.992169i \(0.460138\pi\)
\(90\) −2.85895 −0.301360
\(91\) −0.0396192 −0.00415322
\(92\) −6.31278 −0.658153
\(93\) −6.23092 −0.646116
\(94\) 9.74704 1.00533
\(95\) 15.9275 1.63413
\(96\) 5.44437 0.555664
\(97\) −14.7503 −1.49767 −0.748835 0.662756i \(-0.769387\pi\)
−0.748835 + 0.662756i \(0.769387\pi\)
\(98\) 6.47525 0.654099
\(99\) 3.49434 0.351194
\(100\) −5.20232 −0.520232
\(101\) 0.117677 0.0117093 0.00585465 0.999983i \(-0.498136\pi\)
0.00585465 + 0.999983i \(0.498136\pi\)
\(102\) 4.60092 0.455559
\(103\) −1.00000 −0.0985329
\(104\) 2.90890 0.285241
\(105\) 0.122421 0.0119471
\(106\) 0.128163 0.0124483
\(107\) 7.92558 0.766195 0.383097 0.923708i \(-0.374857\pi\)
0.383097 + 0.923708i \(0.374857\pi\)
\(108\) 1.14392 0.110074
\(109\) 14.0736 1.34801 0.674004 0.738728i \(-0.264573\pi\)
0.674004 + 0.738728i \(0.264573\pi\)
\(110\) −9.99015 −0.952523
\(111\) −10.4013 −0.987245
\(112\) 0.0159898 0.00151090
\(113\) −12.0428 −1.13289 −0.566444 0.824100i \(-0.691681\pi\)
−0.566444 + 0.824100i \(0.691681\pi\)
\(114\) 4.76927 0.446683
\(115\) 17.0520 1.59010
\(116\) 7.44335 0.691097
\(117\) 1.00000 0.0924500
\(118\) −11.9964 −1.10436
\(119\) −0.197013 −0.0180601
\(120\) −8.98834 −0.820519
\(121\) 1.21038 0.110035
\(122\) −1.74392 −0.157887
\(123\) −8.28965 −0.747453
\(124\) −7.12770 −0.640086
\(125\) −1.39733 −0.124981
\(126\) 0.0366574 0.00326570
\(127\) 3.37378 0.299375 0.149687 0.988733i \(-0.452173\pi\)
0.149687 + 0.988733i \(0.452173\pi\)
\(128\) 5.48112 0.484467
\(129\) −8.81740 −0.776329
\(130\) −2.85895 −0.250747
\(131\) 6.99071 0.610781 0.305391 0.952227i \(-0.401213\pi\)
0.305391 + 0.952227i \(0.401213\pi\)
\(132\) 3.99726 0.347916
\(133\) −0.204222 −0.0177083
\(134\) −4.63578 −0.400470
\(135\) −3.08995 −0.265940
\(136\) 14.4649 1.24036
\(137\) −0.643737 −0.0549981 −0.0274991 0.999622i \(-0.508754\pi\)
−0.0274991 + 0.999622i \(0.508754\pi\)
\(138\) 5.10598 0.434650
\(139\) −3.97850 −0.337452 −0.168726 0.985663i \(-0.553965\pi\)
−0.168726 + 0.985663i \(0.553965\pi\)
\(140\) 0.140041 0.0118356
\(141\) 10.5346 0.887170
\(142\) 13.6754 1.14761
\(143\) 3.49434 0.292211
\(144\) −0.403588 −0.0336323
\(145\) −20.1058 −1.66970
\(146\) 6.67433 0.552371
\(147\) 6.99843 0.577221
\(148\) −11.8983 −0.978032
\(149\) −13.2124 −1.08240 −0.541202 0.840893i \(-0.682031\pi\)
−0.541202 + 0.840893i \(0.682031\pi\)
\(150\) 4.20781 0.343566
\(151\) −5.11702 −0.416417 −0.208209 0.978084i \(-0.566763\pi\)
−0.208209 + 0.978084i \(0.566763\pi\)
\(152\) 14.9942 1.21619
\(153\) 4.97266 0.402016
\(154\) 0.128093 0.0103220
\(155\) 19.2532 1.54646
\(156\) 1.14392 0.0915873
\(157\) −13.0212 −1.03921 −0.519604 0.854407i \(-0.673920\pi\)
−0.519604 + 0.854407i \(0.673920\pi\)
\(158\) 15.6497 1.24503
\(159\) 0.138518 0.0109852
\(160\) −16.8228 −1.32996
\(161\) −0.218640 −0.0172312
\(162\) −0.925244 −0.0726940
\(163\) −22.2970 −1.74644 −0.873218 0.487330i \(-0.837971\pi\)
−0.873218 + 0.487330i \(0.837971\pi\)
\(164\) −9.48274 −0.740477
\(165\) −10.7973 −0.840570
\(166\) 10.2228 0.793441
\(167\) 12.9274 1.00036 0.500178 0.865923i \(-0.333268\pi\)
0.500178 + 0.865923i \(0.333268\pi\)
\(168\) 0.115248 0.00889158
\(169\) 1.00000 0.0769231
\(170\) −14.2166 −1.09036
\(171\) 5.15461 0.394183
\(172\) −10.0864 −0.769084
\(173\) −24.2997 −1.84747 −0.923737 0.383028i \(-0.874881\pi\)
−0.923737 + 0.383028i \(0.874881\pi\)
\(174\) −6.02042 −0.456407
\(175\) −0.180179 −0.0136203
\(176\) −1.41027 −0.106303
\(177\) −12.9656 −0.974557
\(178\) −2.18052 −0.163437
\(179\) −14.0277 −1.04848 −0.524240 0.851570i \(-0.675651\pi\)
−0.524240 + 0.851570i \(0.675651\pi\)
\(180\) −3.53467 −0.263459
\(181\) 24.2888 1.80537 0.902686 0.430300i \(-0.141592\pi\)
0.902686 + 0.430300i \(0.141592\pi\)
\(182\) 0.0366574 0.00271723
\(183\) −1.88482 −0.139330
\(184\) 16.0528 1.18343
\(185\) 32.1394 2.36294
\(186\) 5.76512 0.422719
\(187\) 17.3761 1.27067
\(188\) 12.0507 0.878891
\(189\) 0.0396192 0.00288187
\(190\) −14.7368 −1.06912
\(191\) 18.9728 1.37283 0.686413 0.727212i \(-0.259184\pi\)
0.686413 + 0.727212i \(0.259184\pi\)
\(192\) −5.84455 −0.421794
\(193\) −2.82839 −0.203592 −0.101796 0.994805i \(-0.532459\pi\)
−0.101796 + 0.994805i \(0.532459\pi\)
\(194\) 13.6477 0.979845
\(195\) −3.08995 −0.221276
\(196\) 8.00568 0.571834
\(197\) 4.88664 0.348159 0.174079 0.984732i \(-0.444305\pi\)
0.174079 + 0.984732i \(0.444305\pi\)
\(198\) −3.23311 −0.229767
\(199\) −18.9501 −1.34334 −0.671669 0.740851i \(-0.734422\pi\)
−0.671669 + 0.740851i \(0.734422\pi\)
\(200\) 13.2290 0.935433
\(201\) −5.01033 −0.353402
\(202\) −0.108880 −0.00766077
\(203\) 0.257796 0.0180937
\(204\) 5.68834 0.398264
\(205\) 25.6146 1.78900
\(206\) 0.925244 0.0644648
\(207\) 5.51853 0.383564
\(208\) −0.403588 −0.0279838
\(209\) 18.0119 1.24591
\(210\) −0.113269 −0.00781634
\(211\) 4.22079 0.290571 0.145286 0.989390i \(-0.453590\pi\)
0.145286 + 0.989390i \(0.453590\pi\)
\(212\) 0.158454 0.0108827
\(213\) 14.7803 1.01273
\(214\) −7.33309 −0.501280
\(215\) 27.2453 1.85812
\(216\) −2.90890 −0.197925
\(217\) −0.246864 −0.0167582
\(218\) −13.0215 −0.881929
\(219\) 7.21359 0.487449
\(220\) −12.3513 −0.832725
\(221\) 4.97266 0.334497
\(222\) 9.62371 0.645901
\(223\) −6.30900 −0.422482 −0.211241 0.977434i \(-0.567750\pi\)
−0.211241 + 0.977434i \(0.567750\pi\)
\(224\) 0.215702 0.0144122
\(225\) 4.54778 0.303185
\(226\) 11.1425 0.741188
\(227\) 7.02933 0.466553 0.233277 0.972410i \(-0.425055\pi\)
0.233277 + 0.972410i \(0.425055\pi\)
\(228\) 5.89649 0.390504
\(229\) −2.10554 −0.139138 −0.0695691 0.997577i \(-0.522162\pi\)
−0.0695691 + 0.997577i \(0.522162\pi\)
\(230\) −15.7772 −1.04032
\(231\) 0.138443 0.00910886
\(232\) −18.9278 −1.24267
\(233\) −2.25624 −0.147811 −0.0739054 0.997265i \(-0.523546\pi\)
−0.0739054 + 0.997265i \(0.523546\pi\)
\(234\) −0.925244 −0.0604851
\(235\) −32.5513 −2.12341
\(236\) −14.8317 −0.965462
\(237\) 16.9142 1.09869
\(238\) 0.182285 0.0118158
\(239\) −9.86302 −0.637986 −0.318993 0.947757i \(-0.603345\pi\)
−0.318993 + 0.947757i \(0.603345\pi\)
\(240\) 1.24707 0.0804978
\(241\) −27.9348 −1.79944 −0.899720 0.436467i \(-0.856230\pi\)
−0.899720 + 0.436467i \(0.856230\pi\)
\(242\) −1.11990 −0.0719897
\(243\) −1.00000 −0.0641500
\(244\) −2.15609 −0.138030
\(245\) −21.6248 −1.38156
\(246\) 7.66995 0.489018
\(247\) 5.15461 0.327980
\(248\) 18.1251 1.15094
\(249\) 11.0487 0.700186
\(250\) 1.29287 0.0817683
\(251\) −8.79781 −0.555313 −0.277656 0.960680i \(-0.589558\pi\)
−0.277656 + 0.960680i \(0.589558\pi\)
\(252\) 0.0453214 0.00285498
\(253\) 19.2836 1.21235
\(254\) −3.12157 −0.195865
\(255\) −15.3653 −0.962210
\(256\) −16.7605 −1.04753
\(257\) 8.62454 0.537984 0.268992 0.963142i \(-0.413309\pi\)
0.268992 + 0.963142i \(0.413309\pi\)
\(258\) 8.15824 0.507910
\(259\) −0.412090 −0.0256060
\(260\) −3.53467 −0.219211
\(261\) −6.50685 −0.402764
\(262\) −6.46811 −0.399601
\(263\) 22.6581 1.39716 0.698581 0.715531i \(-0.253815\pi\)
0.698581 + 0.715531i \(0.253815\pi\)
\(264\) −10.1647 −0.625591
\(265\) −0.428013 −0.0262926
\(266\) 0.188955 0.0115856
\(267\) −2.35669 −0.144227
\(268\) −5.73144 −0.350104
\(269\) −2.34779 −0.143147 −0.0715737 0.997435i \(-0.522802\pi\)
−0.0715737 + 0.997435i \(0.522802\pi\)
\(270\) 2.85895 0.173990
\(271\) 4.60693 0.279851 0.139926 0.990162i \(-0.455314\pi\)
0.139926 + 0.990162i \(0.455314\pi\)
\(272\) −2.00691 −0.121687
\(273\) 0.0396192 0.00239786
\(274\) 0.595613 0.0359823
\(275\) 15.8915 0.958292
\(276\) 6.31278 0.379985
\(277\) 7.68137 0.461529 0.230764 0.973010i \(-0.425877\pi\)
0.230764 + 0.973010i \(0.425877\pi\)
\(278\) 3.68109 0.220777
\(279\) 6.23092 0.373035
\(280\) −0.356111 −0.0212817
\(281\) 3.05880 0.182473 0.0912365 0.995829i \(-0.470918\pi\)
0.0912365 + 0.995829i \(0.470918\pi\)
\(282\) −9.74704 −0.580428
\(283\) 20.9541 1.24559 0.622797 0.782383i \(-0.285996\pi\)
0.622797 + 0.782383i \(0.285996\pi\)
\(284\) 16.9076 1.00328
\(285\) −15.9275 −0.943463
\(286\) −3.23311 −0.191178
\(287\) −0.328429 −0.0193866
\(288\) −5.44437 −0.320813
\(289\) 7.72733 0.454549
\(290\) 18.6028 1.09239
\(291\) 14.7503 0.864681
\(292\) 8.25180 0.482900
\(293\) 15.9826 0.933714 0.466857 0.884333i \(-0.345386\pi\)
0.466857 + 0.884333i \(0.345386\pi\)
\(294\) −6.47525 −0.377644
\(295\) 40.0631 2.33257
\(296\) 30.2562 1.75861
\(297\) −3.49434 −0.202762
\(298\) 12.2247 0.708158
\(299\) 5.51853 0.319145
\(300\) 5.20232 0.300356
\(301\) −0.349338 −0.0201355
\(302\) 4.73449 0.272439
\(303\) −0.117677 −0.00676037
\(304\) −2.08034 −0.119316
\(305\) 5.82400 0.333481
\(306\) −4.60092 −0.263017
\(307\) −0.519759 −0.0296642 −0.0148321 0.999890i \(-0.504721\pi\)
−0.0148321 + 0.999890i \(0.504721\pi\)
\(308\) 0.158368 0.00902386
\(309\) 1.00000 0.0568880
\(310\) −17.8139 −1.01176
\(311\) 8.79637 0.498796 0.249398 0.968401i \(-0.419767\pi\)
0.249398 + 0.968401i \(0.419767\pi\)
\(312\) −2.90890 −0.164684
\(313\) 19.0398 1.07619 0.538097 0.842883i \(-0.319143\pi\)
0.538097 + 0.842883i \(0.319143\pi\)
\(314\) 12.0478 0.679897
\(315\) −0.122421 −0.00689766
\(316\) 19.3485 1.08844
\(317\) −22.5286 −1.26533 −0.632666 0.774425i \(-0.718039\pi\)
−0.632666 + 0.774425i \(0.718039\pi\)
\(318\) −0.128163 −0.00718701
\(319\) −22.7371 −1.27303
\(320\) 18.0594 1.00955
\(321\) −7.92558 −0.442363
\(322\) 0.202295 0.0112735
\(323\) 25.6321 1.42621
\(324\) −1.14392 −0.0635514
\(325\) 4.54778 0.252266
\(326\) 20.6302 1.14260
\(327\) −14.0736 −0.778273
\(328\) 24.1137 1.33146
\(329\) 0.417371 0.0230104
\(330\) 9.99015 0.549940
\(331\) 12.3109 0.676670 0.338335 0.941026i \(-0.390136\pi\)
0.338335 + 0.941026i \(0.390136\pi\)
\(332\) 12.6389 0.693651
\(333\) 10.4013 0.569986
\(334\) −11.9610 −0.654479
\(335\) 15.4817 0.845854
\(336\) −0.0159898 −0.000872317 0
\(337\) −25.2345 −1.37461 −0.687305 0.726369i \(-0.741206\pi\)
−0.687305 + 0.726369i \(0.741206\pi\)
\(338\) −0.925244 −0.0503266
\(339\) 12.0428 0.654073
\(340\) −17.5767 −0.953230
\(341\) 21.7729 1.17907
\(342\) −4.76927 −0.257893
\(343\) 0.554606 0.0299459
\(344\) 25.6489 1.38290
\(345\) −17.0520 −0.918047
\(346\) 22.4832 1.20870
\(347\) 20.5346 1.10235 0.551176 0.834389i \(-0.314179\pi\)
0.551176 + 0.834389i \(0.314179\pi\)
\(348\) −7.44335 −0.399005
\(349\) 3.83016 0.205024 0.102512 0.994732i \(-0.467312\pi\)
0.102512 + 0.994732i \(0.467312\pi\)
\(350\) 0.166710 0.00891102
\(351\) −1.00000 −0.0533761
\(352\) −19.0245 −1.01401
\(353\) 3.43213 0.182674 0.0913369 0.995820i \(-0.470886\pi\)
0.0913369 + 0.995820i \(0.470886\pi\)
\(354\) 11.9964 0.637600
\(355\) −45.6704 −2.42393
\(356\) −2.69588 −0.142881
\(357\) 0.197013 0.0104270
\(358\) 12.9790 0.685964
\(359\) −28.7278 −1.51619 −0.758097 0.652142i \(-0.773871\pi\)
−0.758097 + 0.652142i \(0.773871\pi\)
\(360\) 8.98834 0.473727
\(361\) 7.57003 0.398423
\(362\) −22.4730 −1.18116
\(363\) −1.21038 −0.0635285
\(364\) 0.0453214 0.00237548
\(365\) −22.2896 −1.16669
\(366\) 1.74392 0.0911561
\(367\) 33.4088 1.74392 0.871962 0.489574i \(-0.162848\pi\)
0.871962 + 0.489574i \(0.162848\pi\)
\(368\) −2.22721 −0.116101
\(369\) 8.28965 0.431542
\(370\) −29.7368 −1.54594
\(371\) 0.00548796 0.000284921 0
\(372\) 7.12770 0.369554
\(373\) 22.8382 1.18252 0.591260 0.806481i \(-0.298631\pi\)
0.591260 + 0.806481i \(0.298631\pi\)
\(374\) −16.0772 −0.831330
\(375\) 1.39733 0.0721578
\(376\) −30.6439 −1.58034
\(377\) −6.50685 −0.335120
\(378\) −0.0366574 −0.00188545
\(379\) 24.4997 1.25847 0.629233 0.777216i \(-0.283369\pi\)
0.629233 + 0.777216i \(0.283369\pi\)
\(380\) −18.2198 −0.934658
\(381\) −3.37378 −0.172844
\(382\) −17.5545 −0.898165
\(383\) 9.37695 0.479140 0.239570 0.970879i \(-0.422994\pi\)
0.239570 + 0.970879i \(0.422994\pi\)
\(384\) −5.48112 −0.279707
\(385\) −0.427781 −0.0218017
\(386\) 2.61695 0.133199
\(387\) 8.81740 0.448214
\(388\) 16.8733 0.856611
\(389\) −1.69589 −0.0859848 −0.0429924 0.999075i \(-0.513689\pi\)
−0.0429924 + 0.999075i \(0.513689\pi\)
\(390\) 2.85895 0.144769
\(391\) 27.4417 1.38779
\(392\) −20.3577 −1.02822
\(393\) −6.99071 −0.352635
\(394\) −4.52134 −0.227782
\(395\) −52.2640 −2.62968
\(396\) −3.99726 −0.200870
\(397\) 3.85526 0.193490 0.0967449 0.995309i \(-0.469157\pi\)
0.0967449 + 0.995309i \(0.469157\pi\)
\(398\) 17.5335 0.878874
\(399\) 0.204222 0.0102239
\(400\) −1.83543 −0.0917716
\(401\) 6.36716 0.317961 0.158980 0.987282i \(-0.449179\pi\)
0.158980 + 0.987282i \(0.449179\pi\)
\(402\) 4.63578 0.231212
\(403\) 6.23092 0.310384
\(404\) −0.134614 −0.00669728
\(405\) 3.08995 0.153541
\(406\) −0.238524 −0.0118378
\(407\) 36.3455 1.80158
\(408\) −14.4649 −0.716121
\(409\) −39.8948 −1.97267 −0.986335 0.164751i \(-0.947318\pi\)
−0.986335 + 0.164751i \(0.947318\pi\)
\(410\) −23.6997 −1.17045
\(411\) 0.643737 0.0317532
\(412\) 1.14392 0.0563571
\(413\) −0.513688 −0.0252769
\(414\) −5.10598 −0.250945
\(415\) −34.1400 −1.67587
\(416\) −5.44437 −0.266932
\(417\) 3.97850 0.194828
\(418\) −16.6654 −0.815133
\(419\) −3.00337 −0.146724 −0.0733621 0.997305i \(-0.523373\pi\)
−0.0733621 + 0.997305i \(0.523373\pi\)
\(420\) −0.140041 −0.00683328
\(421\) −3.79669 −0.185039 −0.0925197 0.995711i \(-0.529492\pi\)
−0.0925197 + 0.995711i \(0.529492\pi\)
\(422\) −3.90526 −0.190105
\(423\) −10.5346 −0.512208
\(424\) −0.402934 −0.0195682
\(425\) 22.6146 1.09697
\(426\) −13.6754 −0.662575
\(427\) −0.0746751 −0.00361378
\(428\) −9.06626 −0.438234
\(429\) −3.49434 −0.168708
\(430\) −25.2086 −1.21566
\(431\) −11.6764 −0.562431 −0.281215 0.959645i \(-0.590738\pi\)
−0.281215 + 0.959645i \(0.590738\pi\)
\(432\) 0.403588 0.0194176
\(433\) −24.5667 −1.18060 −0.590300 0.807184i \(-0.700990\pi\)
−0.590300 + 0.807184i \(0.700990\pi\)
\(434\) 0.228409 0.0109640
\(435\) 20.1058 0.964001
\(436\) −16.0992 −0.771010
\(437\) 28.4459 1.36075
\(438\) −6.67433 −0.318912
\(439\) 28.0249 1.33755 0.668777 0.743463i \(-0.266818\pi\)
0.668777 + 0.743463i \(0.266818\pi\)
\(440\) 31.4083 1.49733
\(441\) −6.99843 −0.333259
\(442\) −4.60092 −0.218843
\(443\) 25.5952 1.21606 0.608032 0.793913i \(-0.291959\pi\)
0.608032 + 0.793913i \(0.291959\pi\)
\(444\) 11.8983 0.564667
\(445\) 7.28206 0.345203
\(446\) 5.83736 0.276407
\(447\) 13.2124 0.624926
\(448\) −0.231556 −0.0109400
\(449\) −10.5815 −0.499372 −0.249686 0.968327i \(-0.580327\pi\)
−0.249686 + 0.968327i \(0.580327\pi\)
\(450\) −4.20781 −0.198358
\(451\) 28.9668 1.36399
\(452\) 13.7760 0.647969
\(453\) 5.11702 0.240419
\(454\) −6.50384 −0.305241
\(455\) −0.122421 −0.00573920
\(456\) −14.9942 −0.702169
\(457\) −36.0492 −1.68631 −0.843154 0.537671i \(-0.819304\pi\)
−0.843154 + 0.537671i \(0.819304\pi\)
\(458\) 1.94814 0.0910306
\(459\) −4.97266 −0.232104
\(460\) −19.5062 −0.909479
\(461\) 1.19909 0.0558473 0.0279236 0.999610i \(-0.491110\pi\)
0.0279236 + 0.999610i \(0.491110\pi\)
\(462\) −0.128093 −0.00595944
\(463\) −0.451840 −0.0209988 −0.0104994 0.999945i \(-0.503342\pi\)
−0.0104994 + 0.999945i \(0.503342\pi\)
\(464\) 2.62609 0.121913
\(465\) −19.2532 −0.892847
\(466\) 2.08757 0.0967047
\(467\) 32.9385 1.52421 0.762107 0.647451i \(-0.224165\pi\)
0.762107 + 0.647451i \(0.224165\pi\)
\(468\) −1.14392 −0.0528779
\(469\) −0.198505 −0.00916612
\(470\) 30.1178 1.38923
\(471\) 13.0212 0.599987
\(472\) 37.7157 1.73600
\(473\) 30.8110 1.41669
\(474\) −15.6497 −0.718816
\(475\) 23.4421 1.07560
\(476\) 0.225368 0.0103297
\(477\) −0.138518 −0.00634230
\(478\) 9.12569 0.417400
\(479\) 5.49293 0.250978 0.125489 0.992095i \(-0.459950\pi\)
0.125489 + 0.992095i \(0.459950\pi\)
\(480\) 16.8228 0.767854
\(481\) 10.4013 0.474257
\(482\) 25.8465 1.17728
\(483\) 0.218640 0.00994844
\(484\) −1.38458 −0.0629356
\(485\) −45.5778 −2.06958
\(486\) 0.925244 0.0419699
\(487\) −3.07810 −0.139482 −0.0697411 0.997565i \(-0.522217\pi\)
−0.0697411 + 0.997565i \(0.522217\pi\)
\(488\) 5.48275 0.248192
\(489\) 22.2970 1.00831
\(490\) 20.0082 0.903878
\(491\) 2.37188 0.107041 0.0535207 0.998567i \(-0.482956\pi\)
0.0535207 + 0.998567i \(0.482956\pi\)
\(492\) 9.48274 0.427515
\(493\) −32.3563 −1.45726
\(494\) −4.76927 −0.214580
\(495\) 10.7973 0.485303
\(496\) −2.51473 −0.112915
\(497\) 0.585584 0.0262670
\(498\) −10.2228 −0.458094
\(499\) 0.0437236 0.00195733 0.000978667 1.00000i \(-0.499688\pi\)
0.000978667 1.00000i \(0.499688\pi\)
\(500\) 1.59844 0.0714844
\(501\) −12.9274 −0.577556
\(502\) 8.14012 0.363311
\(503\) 44.0778 1.96533 0.982666 0.185384i \(-0.0593529\pi\)
0.982666 + 0.185384i \(0.0593529\pi\)
\(504\) −0.115248 −0.00513356
\(505\) 0.363616 0.0161807
\(506\) −17.8420 −0.793174
\(507\) −1.00000 −0.0444116
\(508\) −3.85935 −0.171231
\(509\) 7.51536 0.333113 0.166556 0.986032i \(-0.446735\pi\)
0.166556 + 0.986032i \(0.446735\pi\)
\(510\) 14.2166 0.629522
\(511\) 0.285797 0.0126429
\(512\) 4.54528 0.200875
\(513\) −5.15461 −0.227582
\(514\) −7.97980 −0.351974
\(515\) −3.08995 −0.136159
\(516\) 10.0864 0.444031
\(517\) −36.8113 −1.61896
\(518\) 0.381284 0.0167526
\(519\) 24.2997 1.06664
\(520\) 8.98834 0.394165
\(521\) −20.0023 −0.876317 −0.438158 0.898898i \(-0.644369\pi\)
−0.438158 + 0.898898i \(0.644369\pi\)
\(522\) 6.02042 0.263507
\(523\) −24.5126 −1.07186 −0.535930 0.844262i \(-0.680039\pi\)
−0.535930 + 0.844262i \(0.680039\pi\)
\(524\) −7.99684 −0.349344
\(525\) 0.180179 0.00786368
\(526\) −20.9643 −0.914087
\(527\) 30.9842 1.34969
\(528\) 1.41027 0.0613742
\(529\) 7.45414 0.324093
\(530\) 0.396016 0.0172018
\(531\) 12.9656 0.562661
\(532\) 0.233614 0.0101285
\(533\) 8.28965 0.359065
\(534\) 2.18052 0.0943602
\(535\) 24.4896 1.05878
\(536\) 14.5745 0.629524
\(537\) 14.0277 0.605340
\(538\) 2.17228 0.0936537
\(539\) −24.4549 −1.05335
\(540\) 3.53467 0.152108
\(541\) −19.7988 −0.851215 −0.425607 0.904908i \(-0.639940\pi\)
−0.425607 + 0.904908i \(0.639940\pi\)
\(542\) −4.26253 −0.183091
\(543\) −24.2888 −1.04233
\(544\) −27.0730 −1.16075
\(545\) 43.4868 1.86277
\(546\) −0.0366574 −0.00156879
\(547\) 0.233397 0.00997933 0.00498966 0.999988i \(-0.498412\pi\)
0.00498966 + 0.999988i \(0.498412\pi\)
\(548\) 0.736386 0.0314568
\(549\) 1.88482 0.0804422
\(550\) −14.7035 −0.626959
\(551\) −33.5403 −1.42886
\(552\) −16.0528 −0.683253
\(553\) 0.670126 0.0284967
\(554\) −7.10714 −0.301953
\(555\) −32.1394 −1.36424
\(556\) 4.55111 0.193010
\(557\) 4.92999 0.208890 0.104445 0.994531i \(-0.466693\pi\)
0.104445 + 0.994531i \(0.466693\pi\)
\(558\) −5.76512 −0.244057
\(559\) 8.81740 0.372936
\(560\) 0.0494078 0.00208786
\(561\) −17.3761 −0.733621
\(562\) −2.83014 −0.119382
\(563\) −7.79291 −0.328432 −0.164216 0.986424i \(-0.552509\pi\)
−0.164216 + 0.986424i \(0.552509\pi\)
\(564\) −12.0507 −0.507428
\(565\) −37.2115 −1.56550
\(566\) −19.3877 −0.814925
\(567\) −0.0396192 −0.00166385
\(568\) −42.9944 −1.80400
\(569\) −24.2543 −1.01679 −0.508397 0.861123i \(-0.669762\pi\)
−0.508397 + 0.861123i \(0.669762\pi\)
\(570\) 14.7368 0.617257
\(571\) −23.3775 −0.978317 −0.489159 0.872195i \(-0.662696\pi\)
−0.489159 + 0.872195i \(0.662696\pi\)
\(572\) −3.99726 −0.167134
\(573\) −18.9728 −0.792601
\(574\) 0.303877 0.0126836
\(575\) 25.0971 1.04662
\(576\) 5.84455 0.243523
\(577\) −6.43457 −0.267875 −0.133937 0.990990i \(-0.542762\pi\)
−0.133937 + 0.990990i \(0.542762\pi\)
\(578\) −7.14966 −0.297387
\(579\) 2.82839 0.117544
\(580\) 22.9996 0.955005
\(581\) 0.437742 0.0181606
\(582\) −13.6477 −0.565714
\(583\) −0.484028 −0.0200464
\(584\) −20.9836 −0.868307
\(585\) 3.08995 0.127754
\(586\) −14.7878 −0.610878
\(587\) −4.46109 −0.184129 −0.0920644 0.995753i \(-0.529347\pi\)
−0.0920644 + 0.995753i \(0.529347\pi\)
\(588\) −8.00568 −0.330148
\(589\) 32.1180 1.32340
\(590\) −37.0682 −1.52607
\(591\) −4.88664 −0.201010
\(592\) −4.19783 −0.172530
\(593\) −31.3446 −1.28717 −0.643584 0.765376i \(-0.722553\pi\)
−0.643584 + 0.765376i \(0.722553\pi\)
\(594\) 3.23311 0.132656
\(595\) −0.608759 −0.0249567
\(596\) 15.1140 0.619094
\(597\) 18.9501 0.775577
\(598\) −5.10598 −0.208799
\(599\) 25.5143 1.04249 0.521244 0.853408i \(-0.325468\pi\)
0.521244 + 0.853408i \(0.325468\pi\)
\(600\) −13.2290 −0.540073
\(601\) 37.8392 1.54350 0.771748 0.635929i \(-0.219383\pi\)
0.771748 + 0.635929i \(0.219383\pi\)
\(602\) 0.323223 0.0131736
\(603\) 5.01033 0.204037
\(604\) 5.85349 0.238175
\(605\) 3.74001 0.152053
\(606\) 0.108880 0.00442295
\(607\) −28.2513 −1.14668 −0.573342 0.819316i \(-0.694353\pi\)
−0.573342 + 0.819316i \(0.694353\pi\)
\(608\) −28.0636 −1.13813
\(609\) −0.257796 −0.0104464
\(610\) −5.38862 −0.218179
\(611\) −10.5346 −0.426183
\(612\) −5.68834 −0.229938
\(613\) 18.9449 0.765176 0.382588 0.923919i \(-0.375033\pi\)
0.382588 + 0.923919i \(0.375033\pi\)
\(614\) 0.480904 0.0194077
\(615\) −25.6146 −1.03288
\(616\) −0.402715 −0.0162259
\(617\) −12.1713 −0.489998 −0.244999 0.969523i \(-0.578788\pi\)
−0.244999 + 0.969523i \(0.578788\pi\)
\(618\) −0.925244 −0.0372188
\(619\) −16.5244 −0.664171 −0.332086 0.943249i \(-0.607752\pi\)
−0.332086 + 0.943249i \(0.607752\pi\)
\(620\) −22.0242 −0.884514
\(621\) −5.51853 −0.221451
\(622\) −8.13878 −0.326335
\(623\) −0.0933703 −0.00374080
\(624\) 0.403588 0.0161565
\(625\) −27.0566 −1.08226
\(626\) −17.6165 −0.704095
\(627\) −18.0119 −0.719328
\(628\) 14.8953 0.594387
\(629\) 51.7220 2.06229
\(630\) 0.113269 0.00451276
\(631\) 35.0905 1.39693 0.698465 0.715645i \(-0.253867\pi\)
0.698465 + 0.715645i \(0.253867\pi\)
\(632\) −49.2016 −1.95713
\(633\) −4.22079 −0.167761
\(634\) 20.8444 0.827838
\(635\) 10.4248 0.413696
\(636\) −0.158454 −0.00628311
\(637\) −6.99843 −0.277288
\(638\) 21.0374 0.832878
\(639\) −14.7803 −0.584700
\(640\) 16.9364 0.669469
\(641\) −3.37099 −0.133146 −0.0665731 0.997782i \(-0.521207\pi\)
−0.0665731 + 0.997782i \(0.521207\pi\)
\(642\) 7.33309 0.289414
\(643\) 0.0969389 0.00382290 0.00191145 0.999998i \(-0.499392\pi\)
0.00191145 + 0.999998i \(0.499392\pi\)
\(644\) 0.250107 0.00985560
\(645\) −27.2453 −1.07278
\(646\) −23.7160 −0.933092
\(647\) −26.9288 −1.05868 −0.529340 0.848410i \(-0.677560\pi\)
−0.529340 + 0.848410i \(0.677560\pi\)
\(648\) 2.90890 0.114272
\(649\) 45.3063 1.77843
\(650\) −4.20781 −0.165044
\(651\) 0.246864 0.00967536
\(652\) 25.5061 0.998895
\(653\) −16.9084 −0.661678 −0.330839 0.943687i \(-0.607332\pi\)
−0.330839 + 0.943687i \(0.607332\pi\)
\(654\) 13.0215 0.509182
\(655\) 21.6009 0.844018
\(656\) −3.34561 −0.130624
\(657\) −7.21359 −0.281429
\(658\) −0.386170 −0.0150545
\(659\) −8.44346 −0.328910 −0.164455 0.986385i \(-0.552587\pi\)
−0.164455 + 0.986385i \(0.552587\pi\)
\(660\) 12.3513 0.480774
\(661\) −39.3098 −1.52897 −0.764487 0.644640i \(-0.777007\pi\)
−0.764487 + 0.644640i \(0.777007\pi\)
\(662\) −11.3906 −0.442709
\(663\) −4.97266 −0.193122
\(664\) −32.1396 −1.24726
\(665\) −0.631034 −0.0244705
\(666\) −9.62371 −0.372911
\(667\) −35.9082 −1.39037
\(668\) −14.7880 −0.572166
\(669\) 6.30900 0.243920
\(670\) −14.3243 −0.553397
\(671\) 6.58620 0.254257
\(672\) −0.215702 −0.00832087
\(673\) −46.0127 −1.77366 −0.886830 0.462097i \(-0.847097\pi\)
−0.886830 + 0.462097i \(0.847097\pi\)
\(674\) 23.3481 0.899333
\(675\) −4.54778 −0.175044
\(676\) −1.14392 −0.0439971
\(677\) 26.4026 1.01473 0.507367 0.861730i \(-0.330619\pi\)
0.507367 + 0.861730i \(0.330619\pi\)
\(678\) −11.1425 −0.427925
\(679\) 0.584397 0.0224271
\(680\) 44.6959 1.71401
\(681\) −7.02933 −0.269365
\(682\) −20.1453 −0.771402
\(683\) −35.7303 −1.36718 −0.683590 0.729866i \(-0.739582\pi\)
−0.683590 + 0.729866i \(0.739582\pi\)
\(684\) −5.89649 −0.225458
\(685\) −1.98911 −0.0760001
\(686\) −0.513146 −0.0195920
\(687\) 2.10554 0.0803315
\(688\) −3.55860 −0.135670
\(689\) −0.138518 −0.00527711
\(690\) 15.7772 0.600628
\(691\) −32.8307 −1.24894 −0.624469 0.781049i \(-0.714685\pi\)
−0.624469 + 0.781049i \(0.714685\pi\)
\(692\) 27.7970 1.05668
\(693\) −0.138443 −0.00525900
\(694\) −18.9995 −0.721210
\(695\) −12.2934 −0.466314
\(696\) 18.9278 0.717455
\(697\) 41.2216 1.56138
\(698\) −3.54383 −0.134136
\(699\) 2.25624 0.0853387
\(700\) 0.206112 0.00779029
\(701\) −8.30140 −0.313540 −0.156770 0.987635i \(-0.550108\pi\)
−0.156770 + 0.987635i \(0.550108\pi\)
\(702\) 0.925244 0.0349211
\(703\) 53.6145 2.02211
\(704\) 20.4228 0.769714
\(705\) 32.5513 1.22595
\(706\) −3.17555 −0.119514
\(707\) −0.00466227 −0.000175343 0
\(708\) 14.8317 0.557410
\(709\) 2.15128 0.0807929 0.0403965 0.999184i \(-0.487138\pi\)
0.0403965 + 0.999184i \(0.487138\pi\)
\(710\) 42.2562 1.58585
\(711\) −16.9142 −0.634331
\(712\) 6.85538 0.256916
\(713\) 34.3855 1.28775
\(714\) −0.182285 −0.00682183
\(715\) 10.7973 0.403797
\(716\) 16.0466 0.599691
\(717\) 9.86302 0.368341
\(718\) 26.5802 0.991964
\(719\) 24.6132 0.917919 0.458960 0.888457i \(-0.348222\pi\)
0.458960 + 0.888457i \(0.348222\pi\)
\(720\) −1.24707 −0.0464754
\(721\) 0.0396192 0.00147550
\(722\) −7.00413 −0.260667
\(723\) 27.9348 1.03891
\(724\) −27.7845 −1.03260
\(725\) −29.5917 −1.09901
\(726\) 1.11990 0.0415633
\(727\) −3.34696 −0.124132 −0.0620659 0.998072i \(-0.519769\pi\)
−0.0620659 + 0.998072i \(0.519769\pi\)
\(728\) −0.115248 −0.00427138
\(729\) 1.00000 0.0370370
\(730\) 20.6233 0.763304
\(731\) 43.8459 1.62170
\(732\) 2.15609 0.0796915
\(733\) −37.8232 −1.39703 −0.698517 0.715594i \(-0.746156\pi\)
−0.698517 + 0.715594i \(0.746156\pi\)
\(734\) −30.9112 −1.14095
\(735\) 21.6248 0.797642
\(736\) −30.0449 −1.10747
\(737\) 17.5078 0.644907
\(738\) −7.66995 −0.282335
\(739\) −38.8721 −1.42993 −0.714966 0.699159i \(-0.753558\pi\)
−0.714966 + 0.699159i \(0.753558\pi\)
\(740\) −36.7650 −1.35151
\(741\) −5.15461 −0.189359
\(742\) −0.00507770 −0.000186408 0
\(743\) −34.6307 −1.27048 −0.635239 0.772316i \(-0.719098\pi\)
−0.635239 + 0.772316i \(0.719098\pi\)
\(744\) −18.1251 −0.664498
\(745\) −40.8257 −1.49574
\(746\) −21.1309 −0.773659
\(747\) −11.0487 −0.404252
\(748\) −19.8770 −0.726775
\(749\) −0.314005 −0.0114735
\(750\) −1.29287 −0.0472089
\(751\) −3.59727 −0.131266 −0.0656332 0.997844i \(-0.520907\pi\)
−0.0656332 + 0.997844i \(0.520907\pi\)
\(752\) 4.25162 0.155041
\(753\) 8.79781 0.320610
\(754\) 6.02042 0.219251
\(755\) −15.8113 −0.575434
\(756\) −0.0453214 −0.00164832
\(757\) −23.0015 −0.836005 −0.418002 0.908446i \(-0.637270\pi\)
−0.418002 + 0.908446i \(0.637270\pi\)
\(758\) −22.6682 −0.823347
\(759\) −19.2836 −0.699950
\(760\) 46.3314 1.68062
\(761\) −27.6866 −1.00364 −0.501819 0.864973i \(-0.667336\pi\)
−0.501819 + 0.864973i \(0.667336\pi\)
\(762\) 3.12157 0.113083
\(763\) −0.557585 −0.0201859
\(764\) −21.7035 −0.785204
\(765\) 15.3653 0.555532
\(766\) −8.67596 −0.313475
\(767\) 12.9656 0.468162
\(768\) 16.7605 0.604791
\(769\) 28.4884 1.02732 0.513659 0.857994i \(-0.328290\pi\)
0.513659 + 0.857994i \(0.328290\pi\)
\(770\) 0.395802 0.0142637
\(771\) −8.62454 −0.310605
\(772\) 3.23546 0.116447
\(773\) 15.0656 0.541872 0.270936 0.962597i \(-0.412667\pi\)
0.270936 + 0.962597i \(0.412667\pi\)
\(774\) −8.15824 −0.293242
\(775\) 28.3369 1.01789
\(776\) −42.9072 −1.54028
\(777\) 0.412090 0.0147836
\(778\) 1.56911 0.0562552
\(779\) 42.7300 1.53096
\(780\) 3.53467 0.126561
\(781\) −51.6474 −1.84809
\(782\) −25.3903 −0.907955
\(783\) 6.50685 0.232536
\(784\) 2.82448 0.100874
\(785\) −40.2349 −1.43605
\(786\) 6.46811 0.230710
\(787\) 22.1315 0.788902 0.394451 0.918917i \(-0.370935\pi\)
0.394451 + 0.918917i \(0.370935\pi\)
\(788\) −5.58995 −0.199134
\(789\) −22.6581 −0.806651
\(790\) 48.3569 1.72046
\(791\) 0.477125 0.0169646
\(792\) 10.1647 0.361185
\(793\) 1.88482 0.0669320
\(794\) −3.56705 −0.126590
\(795\) 0.428013 0.0151801
\(796\) 21.6775 0.768339
\(797\) 8.43733 0.298866 0.149433 0.988772i \(-0.452255\pi\)
0.149433 + 0.988772i \(0.452255\pi\)
\(798\) −0.188955 −0.00668892
\(799\) −52.3848 −1.85324
\(800\) −24.7598 −0.875392
\(801\) 2.35669 0.0832697
\(802\) −5.89117 −0.208024
\(803\) −25.2067 −0.889525
\(804\) 5.73144 0.202132
\(805\) −0.675585 −0.0238112
\(806\) −5.76512 −0.203068
\(807\) 2.34779 0.0826462
\(808\) 0.342310 0.0120424
\(809\) 6.14722 0.216125 0.108062 0.994144i \(-0.465535\pi\)
0.108062 + 0.994144i \(0.465535\pi\)
\(810\) −2.85895 −0.100453
\(811\) 23.7060 0.832431 0.416215 0.909266i \(-0.363356\pi\)
0.416215 + 0.909266i \(0.363356\pi\)
\(812\) −0.294899 −0.0103489
\(813\) −4.60693 −0.161572
\(814\) −33.6285 −1.17868
\(815\) −68.8966 −2.41334
\(816\) 2.00691 0.0702558
\(817\) 45.4503 1.59010
\(818\) 36.9124 1.29061
\(819\) −0.0396192 −0.00138441
\(820\) −29.3012 −1.02324
\(821\) 19.4745 0.679663 0.339832 0.940486i \(-0.389630\pi\)
0.339832 + 0.940486i \(0.389630\pi\)
\(822\) −0.595613 −0.0207744
\(823\) 39.5484 1.37857 0.689285 0.724490i \(-0.257925\pi\)
0.689285 + 0.724490i \(0.257925\pi\)
\(824\) −2.90890 −0.101336
\(825\) −15.8915 −0.553270
\(826\) 0.475286 0.0165373
\(827\) −18.5588 −0.645352 −0.322676 0.946509i \(-0.604582\pi\)
−0.322676 + 0.946509i \(0.604582\pi\)
\(828\) −6.31278 −0.219384
\(829\) −48.2351 −1.67527 −0.837637 0.546227i \(-0.816064\pi\)
−0.837637 + 0.546227i \(0.816064\pi\)
\(830\) 31.5879 1.09643
\(831\) −7.68137 −0.266464
\(832\) 5.84455 0.202623
\(833\) −34.8008 −1.20578
\(834\) −3.68109 −0.127466
\(835\) 39.9451 1.38236
\(836\) −20.6043 −0.712615
\(837\) −6.23092 −0.215372
\(838\) 2.77885 0.0959937
\(839\) 26.9694 0.931087 0.465544 0.885025i \(-0.345859\pi\)
0.465544 + 0.885025i \(0.345859\pi\)
\(840\) 0.356111 0.0122870
\(841\) 13.3391 0.459969
\(842\) 3.51287 0.121061
\(843\) −3.05880 −0.105351
\(844\) −4.82827 −0.166196
\(845\) 3.08995 0.106297
\(846\) 9.74704 0.335110
\(847\) −0.0479543 −0.00164773
\(848\) 0.0559042 0.00191976
\(849\) −20.9541 −0.719144
\(850\) −20.9240 −0.717687
\(851\) 57.3997 1.96764
\(852\) −16.9076 −0.579243
\(853\) 23.2990 0.797742 0.398871 0.917007i \(-0.369402\pi\)
0.398871 + 0.917007i \(0.369402\pi\)
\(854\) 0.0690926 0.00236430
\(855\) 15.9275 0.544709
\(856\) 23.0547 0.787993
\(857\) −17.0309 −0.581764 −0.290882 0.956759i \(-0.593949\pi\)
−0.290882 + 0.956759i \(0.593949\pi\)
\(858\) 3.23311 0.110377
\(859\) −41.3719 −1.41159 −0.705795 0.708416i \(-0.749410\pi\)
−0.705795 + 0.708416i \(0.749410\pi\)
\(860\) −31.1666 −1.06277
\(861\) 0.328429 0.0111928
\(862\) 10.8035 0.367968
\(863\) 40.2530 1.37023 0.685114 0.728436i \(-0.259752\pi\)
0.685114 + 0.728436i \(0.259752\pi\)
\(864\) 5.44437 0.185221
\(865\) −75.0849 −2.55296
\(866\) 22.7302 0.772403
\(867\) −7.72733 −0.262434
\(868\) 0.282394 0.00958507
\(869\) −59.1038 −2.00496
\(870\) −18.6028 −0.630694
\(871\) 5.01033 0.169769
\(872\) 40.9387 1.38636
\(873\) −14.7503 −0.499224
\(874\) −26.3194 −0.890266
\(875\) 0.0553610 0.00187154
\(876\) −8.25180 −0.278803
\(877\) 14.0124 0.473166 0.236583 0.971611i \(-0.423973\pi\)
0.236583 + 0.971611i \(0.423973\pi\)
\(878\) −25.9298 −0.875089
\(879\) −15.9826 −0.539080
\(880\) −4.35767 −0.146897
\(881\) −13.3109 −0.448456 −0.224228 0.974537i \(-0.571986\pi\)
−0.224228 + 0.974537i \(0.571986\pi\)
\(882\) 6.47525 0.218033
\(883\) 54.7584 1.84277 0.921384 0.388653i \(-0.127060\pi\)
0.921384 + 0.388653i \(0.127060\pi\)
\(884\) −5.68834 −0.191320
\(885\) −40.0631 −1.34671
\(886\) −23.6818 −0.795604
\(887\) −19.7016 −0.661514 −0.330757 0.943716i \(-0.607304\pi\)
−0.330757 + 0.943716i \(0.607304\pi\)
\(888\) −30.2562 −1.01533
\(889\) −0.133667 −0.00448303
\(890\) −6.73768 −0.225848
\(891\) 3.49434 0.117065
\(892\) 7.21702 0.241644
\(893\) −54.3016 −1.81713
\(894\) −12.2247 −0.408855
\(895\) −43.3449 −1.44886
\(896\) −0.217157 −0.00725472
\(897\) −5.51853 −0.184258
\(898\) 9.79046 0.326712
\(899\) −40.5437 −1.35221
\(900\) −5.20232 −0.173411
\(901\) −0.688802 −0.0229473
\(902\) −26.8014 −0.892388
\(903\) 0.349338 0.0116253
\(904\) −35.0312 −1.16512
\(905\) 75.0511 2.49478
\(906\) −4.73449 −0.157293
\(907\) −46.7872 −1.55354 −0.776771 0.629783i \(-0.783144\pi\)
−0.776771 + 0.629783i \(0.783144\pi\)
\(908\) −8.04103 −0.266851
\(909\) 0.117677 0.00390310
\(910\) 0.113269 0.00375485
\(911\) −39.0032 −1.29223 −0.646117 0.763239i \(-0.723608\pi\)
−0.646117 + 0.763239i \(0.723608\pi\)
\(912\) 2.08034 0.0688870
\(913\) −38.6080 −1.27774
\(914\) 33.3543 1.10326
\(915\) −5.82400 −0.192536
\(916\) 2.40858 0.0795818
\(917\) −0.276966 −0.00914623
\(918\) 4.60092 0.151853
\(919\) 3.26717 0.107774 0.0538869 0.998547i \(-0.482839\pi\)
0.0538869 + 0.998547i \(0.482839\pi\)
\(920\) 49.6024 1.63534
\(921\) 0.519759 0.0171266
\(922\) −1.10945 −0.0365379
\(923\) −14.7803 −0.486500
\(924\) −0.158368 −0.00520993
\(925\) 47.3027 1.55530
\(926\) 0.418062 0.0137384
\(927\) −1.00000 −0.0328443
\(928\) 35.4257 1.16291
\(929\) −34.3270 −1.12623 −0.563117 0.826377i \(-0.690398\pi\)
−0.563117 + 0.826377i \(0.690398\pi\)
\(930\) 17.8139 0.584141
\(931\) −36.0742 −1.18228
\(932\) 2.58096 0.0845422
\(933\) −8.79637 −0.287980
\(934\) −30.4762 −0.997211
\(935\) 53.6914 1.75590
\(936\) 2.90890 0.0950802
\(937\) −48.6897 −1.59062 −0.795312 0.606200i \(-0.792693\pi\)
−0.795312 + 0.606200i \(0.792693\pi\)
\(938\) 0.183666 0.00599690
\(939\) −19.0398 −0.621341
\(940\) 37.2362 1.21451
\(941\) 40.9092 1.33360 0.666801 0.745236i \(-0.267663\pi\)
0.666801 + 0.745236i \(0.267663\pi\)
\(942\) −12.0478 −0.392539
\(943\) 45.7467 1.48972
\(944\) −5.23278 −0.170312
\(945\) 0.122421 0.00398236
\(946\) −28.5076 −0.926863
\(947\) 15.7819 0.512842 0.256421 0.966565i \(-0.417457\pi\)
0.256421 + 0.966565i \(0.417457\pi\)
\(948\) −19.3485 −0.628412
\(949\) −7.21359 −0.234163
\(950\) −21.6896 −0.703704
\(951\) 22.5286 0.730539
\(952\) −0.573089 −0.0185739
\(953\) 8.51027 0.275675 0.137837 0.990455i \(-0.455985\pi\)
0.137837 + 0.990455i \(0.455985\pi\)
\(954\) 0.128163 0.00414942
\(955\) 58.6250 1.89706
\(956\) 11.2825 0.364904
\(957\) 22.7371 0.734987
\(958\) −5.08230 −0.164202
\(959\) 0.0255043 0.000823577 0
\(960\) −18.0594 −0.582863
\(961\) 7.82436 0.252399
\(962\) −9.62371 −0.310281
\(963\) 7.92558 0.255398
\(964\) 31.9553 1.02921
\(965\) −8.73957 −0.281337
\(966\) −0.202295 −0.00650873
\(967\) −28.5713 −0.918793 −0.459396 0.888231i \(-0.651934\pi\)
−0.459396 + 0.888231i \(0.651934\pi\)
\(968\) 3.52087 0.113165
\(969\) −25.6321 −0.823423
\(970\) 42.1706 1.35402
\(971\) 51.1769 1.64235 0.821173 0.570679i \(-0.193320\pi\)
0.821173 + 0.570679i \(0.193320\pi\)
\(972\) 1.14392 0.0366914
\(973\) 0.157625 0.00505323
\(974\) 2.84800 0.0912557
\(975\) −4.54778 −0.145646
\(976\) −0.760692 −0.0243491
\(977\) 22.2794 0.712780 0.356390 0.934337i \(-0.384007\pi\)
0.356390 + 0.934337i \(0.384007\pi\)
\(978\) −20.6302 −0.659680
\(979\) 8.23508 0.263194
\(980\) 24.7371 0.790198
\(981\) 14.0736 0.449336
\(982\) −2.19457 −0.0700314
\(983\) 6.64162 0.211835 0.105917 0.994375i \(-0.466222\pi\)
0.105917 + 0.994375i \(0.466222\pi\)
\(984\) −24.1137 −0.768718
\(985\) 15.0995 0.481109
\(986\) 29.9375 0.953404
\(987\) −0.417371 −0.0132851
\(988\) −5.89649 −0.187592
\(989\) 48.6591 1.54727
\(990\) −9.99015 −0.317508
\(991\) 36.9847 1.17486 0.587429 0.809276i \(-0.300140\pi\)
0.587429 + 0.809276i \(0.300140\pi\)
\(992\) −33.9235 −1.07707
\(993\) −12.3109 −0.390676
\(994\) −0.541808 −0.0171851
\(995\) −58.5549 −1.85631
\(996\) −12.6389 −0.400480
\(997\) 48.2436 1.52789 0.763945 0.645281i \(-0.223260\pi\)
0.763945 + 0.645281i \(0.223260\pi\)
\(998\) −0.0404549 −0.00128058
\(999\) −10.4013 −0.329082
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 \(a_p\))