Properties

Label 6017.2.a.c.1.14
Level 6017
Weight 2
Character 6017.1
Self dual Yes
Analytic conductor 48.046
Analytic rank 1
Dimension 106
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 6017 = 11 \cdot 547 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6017.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0459868962\)
Analytic rank: \(1\)
Dimension: \(106\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Character \(\chi\) = 6017.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.32740 q^{2} -3.07559 q^{3} +3.41677 q^{4} -1.26158 q^{5} +7.15812 q^{6} +0.599145 q^{7} -3.29739 q^{8} +6.45928 q^{9} +O(q^{10})\) \(q-2.32740 q^{2} -3.07559 q^{3} +3.41677 q^{4} -1.26158 q^{5} +7.15812 q^{6} +0.599145 q^{7} -3.29739 q^{8} +6.45928 q^{9} +2.93620 q^{10} +1.00000 q^{11} -10.5086 q^{12} +1.48585 q^{13} -1.39445 q^{14} +3.88011 q^{15} +0.840783 q^{16} +3.03080 q^{17} -15.0333 q^{18} +5.86101 q^{19} -4.31053 q^{20} -1.84273 q^{21} -2.32740 q^{22} -1.31387 q^{23} +10.1414 q^{24} -3.40842 q^{25} -3.45817 q^{26} -10.6393 q^{27} +2.04714 q^{28} +6.74213 q^{29} -9.03054 q^{30} +2.93038 q^{31} +4.63794 q^{32} -3.07559 q^{33} -7.05387 q^{34} -0.755869 q^{35} +22.0699 q^{36} +0.755218 q^{37} -13.6409 q^{38} -4.56988 q^{39} +4.15992 q^{40} +5.51301 q^{41} +4.28876 q^{42} -9.33971 q^{43} +3.41677 q^{44} -8.14889 q^{45} +3.05790 q^{46} +8.42855 q^{47} -2.58591 q^{48} -6.64103 q^{49} +7.93273 q^{50} -9.32151 q^{51} +5.07682 q^{52} -11.8926 q^{53} +24.7619 q^{54} -1.26158 q^{55} -1.97561 q^{56} -18.0261 q^{57} -15.6916 q^{58} -2.97044 q^{59} +13.2574 q^{60} -1.92843 q^{61} -6.82016 q^{62} +3.87005 q^{63} -12.4759 q^{64} -1.87452 q^{65} +7.15812 q^{66} -6.53515 q^{67} +10.3556 q^{68} +4.04094 q^{69} +1.75921 q^{70} -8.59133 q^{71} -21.2987 q^{72} -5.44367 q^{73} -1.75769 q^{74} +10.4829 q^{75} +20.0257 q^{76} +0.599145 q^{77} +10.6359 q^{78} -2.92252 q^{79} -1.06072 q^{80} +13.3444 q^{81} -12.8310 q^{82} +6.65119 q^{83} -6.29618 q^{84} -3.82360 q^{85} +21.7372 q^{86} -20.7361 q^{87} -3.29739 q^{88} -6.64813 q^{89} +18.9657 q^{90} +0.890242 q^{91} -4.48920 q^{92} -9.01267 q^{93} -19.6166 q^{94} -7.39413 q^{95} -14.2644 q^{96} -12.4665 q^{97} +15.4563 q^{98} +6.45928 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 106q - 13q^{2} - 15q^{3} + 93q^{4} - 12q^{5} - 22q^{6} - 66q^{7} - 39q^{8} + 97q^{9} + O(q^{10}) \) \( 106q - 13q^{2} - 15q^{3} + 93q^{4} - 12q^{5} - 22q^{6} - 66q^{7} - 39q^{8} + 97q^{9} - 30q^{10} + 106q^{11} - 26q^{12} - 72q^{13} + 3q^{14} - 46q^{15} + 75q^{16} - 65q^{17} - 37q^{18} - 63q^{19} - 25q^{20} - 27q^{21} - 13q^{22} - 23q^{23} - 56q^{24} + 74q^{25} + 2q^{26} - 54q^{27} - 115q^{28} - 45q^{29} - 14q^{30} - 89q^{31} - 96q^{32} - 15q^{33} - 26q^{34} - 52q^{35} + 91q^{36} - 35q^{37} + 7q^{38} - 34q^{39} - 74q^{40} - 32q^{41} - 94q^{43} + 93q^{44} - 46q^{45} - 20q^{46} - 105q^{47} - 57q^{48} + 80q^{49} - 60q^{50} - 36q^{51} - 137q^{52} - 61q^{54} - 12q^{55} + 32q^{56} - 71q^{57} - 28q^{58} - 15q^{59} - 21q^{60} - 80q^{61} - 84q^{62} - 182q^{63} + 55q^{64} - 73q^{65} - 22q^{66} - 58q^{67} - 145q^{68} - 8q^{69} - 39q^{70} - 11q^{71} - 100q^{72} - 155q^{73} - 15q^{74} - 15q^{75} - 132q^{76} - 66q^{77} - 45q^{78} - 50q^{79} - 28q^{80} + 114q^{81} - 57q^{82} - 96q^{83} - 27q^{84} - 74q^{85} + 54q^{86} - 182q^{87} - 39q^{88} + 9q^{89} - 53q^{90} + 6q^{91} - 18q^{92} - 26q^{93} - 33q^{94} - 49q^{95} - 56q^{96} - 102q^{97} - 76q^{98} + 97q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.32740 −1.64572 −0.822859 0.568246i \(-0.807622\pi\)
−0.822859 + 0.568246i \(0.807622\pi\)
\(3\) −3.07559 −1.77569 −0.887847 0.460138i \(-0.847800\pi\)
−0.887847 + 0.460138i \(0.847800\pi\)
\(4\) 3.41677 1.70839
\(5\) −1.26158 −0.564196 −0.282098 0.959386i \(-0.591030\pi\)
−0.282098 + 0.959386i \(0.591030\pi\)
\(6\) 7.15812 2.92229
\(7\) 0.599145 0.226456 0.113228 0.993569i \(-0.463881\pi\)
0.113228 + 0.993569i \(0.463881\pi\)
\(8\) −3.29739 −1.16580
\(9\) 6.45928 2.15309
\(10\) 2.93620 0.928506
\(11\) 1.00000 0.301511
\(12\) −10.5086 −3.03357
\(13\) 1.48585 0.412101 0.206051 0.978541i \(-0.433939\pi\)
0.206051 + 0.978541i \(0.433939\pi\)
\(14\) −1.39445 −0.372682
\(15\) 3.88011 1.00184
\(16\) 0.840783 0.210196
\(17\) 3.03080 0.735077 0.367539 0.930008i \(-0.380201\pi\)
0.367539 + 0.930008i \(0.380201\pi\)
\(18\) −15.0333 −3.54338
\(19\) 5.86101 1.34461 0.672303 0.740276i \(-0.265305\pi\)
0.672303 + 0.740276i \(0.265305\pi\)
\(20\) −4.31053 −0.963864
\(21\) −1.84273 −0.402116
\(22\) −2.32740 −0.496202
\(23\) −1.31387 −0.273961 −0.136981 0.990574i \(-0.543740\pi\)
−0.136981 + 0.990574i \(0.543740\pi\)
\(24\) 10.1414 2.07011
\(25\) −3.40842 −0.681683
\(26\) −3.45817 −0.678202
\(27\) −10.6393 −2.04754
\(28\) 2.04714 0.386873
\(29\) 6.74213 1.25198 0.625991 0.779830i \(-0.284695\pi\)
0.625991 + 0.779830i \(0.284695\pi\)
\(30\) −9.03054 −1.64874
\(31\) 2.93038 0.526312 0.263156 0.964753i \(-0.415237\pi\)
0.263156 + 0.964753i \(0.415237\pi\)
\(32\) 4.63794 0.819880
\(33\) −3.07559 −0.535392
\(34\) −7.05387 −1.20973
\(35\) −0.755869 −0.127765
\(36\) 22.0699 3.67831
\(37\) 0.755218 0.124157 0.0620786 0.998071i \(-0.480227\pi\)
0.0620786 + 0.998071i \(0.480227\pi\)
\(38\) −13.6409 −2.21284
\(39\) −4.56988 −0.731766
\(40\) 4.15992 0.657741
\(41\) 5.51301 0.860988 0.430494 0.902593i \(-0.358339\pi\)
0.430494 + 0.902593i \(0.358339\pi\)
\(42\) 4.28876 0.661769
\(43\) −9.33971 −1.42429 −0.712146 0.702031i \(-0.752277\pi\)
−0.712146 + 0.702031i \(0.752277\pi\)
\(44\) 3.41677 0.515098
\(45\) −8.14889 −1.21477
\(46\) 3.05790 0.450863
\(47\) 8.42855 1.22943 0.614715 0.788749i \(-0.289271\pi\)
0.614715 + 0.788749i \(0.289271\pi\)
\(48\) −2.58591 −0.373244
\(49\) −6.64103 −0.948718
\(50\) 7.93273 1.12186
\(51\) −9.32151 −1.30527
\(52\) 5.07682 0.704028
\(53\) −11.8926 −1.63358 −0.816788 0.576938i \(-0.804247\pi\)
−0.816788 + 0.576938i \(0.804247\pi\)
\(54\) 24.7619 3.36967
\(55\) −1.26158 −0.170111
\(56\) −1.97561 −0.264003
\(57\) −18.0261 −2.38761
\(58\) −15.6916 −2.06041
\(59\) −2.97044 −0.386719 −0.193359 0.981128i \(-0.561938\pi\)
−0.193359 + 0.981128i \(0.561938\pi\)
\(60\) 13.2574 1.71153
\(61\) −1.92843 −0.246910 −0.123455 0.992350i \(-0.539397\pi\)
−0.123455 + 0.992350i \(0.539397\pi\)
\(62\) −6.82016 −0.866162
\(63\) 3.87005 0.487580
\(64\) −12.4759 −1.55949
\(65\) −1.87452 −0.232506
\(66\) 7.15812 0.881104
\(67\) −6.53515 −0.798396 −0.399198 0.916865i \(-0.630711\pi\)
−0.399198 + 0.916865i \(0.630711\pi\)
\(68\) 10.3556 1.25580
\(69\) 4.04094 0.486472
\(70\) 1.75921 0.210265
\(71\) −8.59133 −1.01960 −0.509802 0.860292i \(-0.670281\pi\)
−0.509802 + 0.860292i \(0.670281\pi\)
\(72\) −21.2987 −2.51008
\(73\) −5.44367 −0.637134 −0.318567 0.947900i \(-0.603202\pi\)
−0.318567 + 0.947900i \(0.603202\pi\)
\(74\) −1.75769 −0.204328
\(75\) 10.4829 1.21046
\(76\) 20.0257 2.29711
\(77\) 0.599145 0.0682789
\(78\) 10.6359 1.20428
\(79\) −2.92252 −0.328809 −0.164404 0.986393i \(-0.552570\pi\)
−0.164404 + 0.986393i \(0.552570\pi\)
\(80\) −1.06072 −0.118592
\(81\) 13.3444 1.48272
\(82\) −12.8310 −1.41694
\(83\) 6.65119 0.730063 0.365031 0.930995i \(-0.381058\pi\)
0.365031 + 0.930995i \(0.381058\pi\)
\(84\) −6.29618 −0.686969
\(85\) −3.82360 −0.414727
\(86\) 21.7372 2.34398
\(87\) −20.7361 −2.22314
\(88\) −3.29739 −0.351503
\(89\) −6.64813 −0.704700 −0.352350 0.935868i \(-0.614617\pi\)
−0.352350 + 0.935868i \(0.614617\pi\)
\(90\) 18.9657 1.99916
\(91\) 0.890242 0.0933227
\(92\) −4.48920 −0.468032
\(93\) −9.01267 −0.934570
\(94\) −19.6166 −2.02330
\(95\) −7.39413 −0.758621
\(96\) −14.2644 −1.45586
\(97\) −12.4665 −1.26578 −0.632891 0.774241i \(-0.718132\pi\)
−0.632891 + 0.774241i \(0.718132\pi\)
\(98\) 15.4563 1.56132
\(99\) 6.45928 0.649182
\(100\) −11.6458 −1.16458
\(101\) 4.01472 0.399479 0.199740 0.979849i \(-0.435990\pi\)
0.199740 + 0.979849i \(0.435990\pi\)
\(102\) 21.6948 2.14811
\(103\) −9.06336 −0.893040 −0.446520 0.894774i \(-0.647337\pi\)
−0.446520 + 0.894774i \(0.647337\pi\)
\(104\) −4.89943 −0.480429
\(105\) 2.32475 0.226872
\(106\) 27.6788 2.68840
\(107\) 4.43708 0.428949 0.214474 0.976730i \(-0.431196\pi\)
0.214474 + 0.976730i \(0.431196\pi\)
\(108\) −36.3522 −3.49799
\(109\) 13.3755 1.28114 0.640570 0.767900i \(-0.278698\pi\)
0.640570 + 0.767900i \(0.278698\pi\)
\(110\) 2.93620 0.279955
\(111\) −2.32274 −0.220465
\(112\) 0.503751 0.0476000
\(113\) −7.11965 −0.669760 −0.334880 0.942261i \(-0.608696\pi\)
−0.334880 + 0.942261i \(0.608696\pi\)
\(114\) 41.9538 3.92933
\(115\) 1.65756 0.154568
\(116\) 23.0363 2.13887
\(117\) 9.59754 0.887293
\(118\) 6.91339 0.636430
\(119\) 1.81589 0.166462
\(120\) −12.7942 −1.16795
\(121\) 1.00000 0.0909091
\(122\) 4.48821 0.406343
\(123\) −16.9558 −1.52885
\(124\) 10.0125 0.899145
\(125\) 10.6079 0.948798
\(126\) −9.00713 −0.802419
\(127\) −1.34382 −0.119245 −0.0596223 0.998221i \(-0.518990\pi\)
−0.0596223 + 0.998221i \(0.518990\pi\)
\(128\) 19.7604 1.74659
\(129\) 28.7252 2.52911
\(130\) 4.36275 0.382639
\(131\) −2.41096 −0.210646 −0.105323 0.994438i \(-0.533588\pi\)
−0.105323 + 0.994438i \(0.533588\pi\)
\(132\) −10.5086 −0.914656
\(133\) 3.51159 0.304494
\(134\) 15.2099 1.31393
\(135\) 13.4224 1.15521
\(136\) −9.99372 −0.856955
\(137\) −4.70465 −0.401945 −0.200973 0.979597i \(-0.564410\pi\)
−0.200973 + 0.979597i \(0.564410\pi\)
\(138\) −9.40486 −0.800595
\(139\) −8.67075 −0.735443 −0.367722 0.929936i \(-0.619862\pi\)
−0.367722 + 0.929936i \(0.619862\pi\)
\(140\) −2.58263 −0.218272
\(141\) −25.9228 −2.18309
\(142\) 19.9954 1.67798
\(143\) 1.48585 0.124253
\(144\) 5.43085 0.452571
\(145\) −8.50573 −0.706363
\(146\) 12.6696 1.04854
\(147\) 20.4251 1.68463
\(148\) 2.58041 0.212108
\(149\) 15.8353 1.29728 0.648641 0.761094i \(-0.275338\pi\)
0.648641 + 0.761094i \(0.275338\pi\)
\(150\) −24.3979 −1.99208
\(151\) −7.08609 −0.576658 −0.288329 0.957531i \(-0.593100\pi\)
−0.288329 + 0.957531i \(0.593100\pi\)
\(152\) −19.3260 −1.56755
\(153\) 19.5768 1.58269
\(154\) −1.39445 −0.112368
\(155\) −3.69691 −0.296943
\(156\) −15.6142 −1.25014
\(157\) 9.84115 0.785409 0.392704 0.919665i \(-0.371540\pi\)
0.392704 + 0.919665i \(0.371540\pi\)
\(158\) 6.80186 0.541127
\(159\) 36.5768 2.90073
\(160\) −5.85113 −0.462572
\(161\) −0.787201 −0.0620401
\(162\) −31.0578 −2.44013
\(163\) −19.5654 −1.53248 −0.766240 0.642554i \(-0.777875\pi\)
−0.766240 + 0.642554i \(0.777875\pi\)
\(164\) 18.8367 1.47090
\(165\) 3.88011 0.302066
\(166\) −15.4800 −1.20148
\(167\) 6.46145 0.500002 0.250001 0.968246i \(-0.419569\pi\)
0.250001 + 0.968246i \(0.419569\pi\)
\(168\) 6.07619 0.468788
\(169\) −10.7922 −0.830172
\(170\) 8.89902 0.682524
\(171\) 37.8579 2.89506
\(172\) −31.9117 −2.43324
\(173\) −7.20310 −0.547642 −0.273821 0.961781i \(-0.588288\pi\)
−0.273821 + 0.961781i \(0.588288\pi\)
\(174\) 48.2610 3.65866
\(175\) −2.04214 −0.154371
\(176\) 0.840783 0.0633764
\(177\) 9.13587 0.686694
\(178\) 15.4728 1.15974
\(179\) −8.81980 −0.659223 −0.329612 0.944117i \(-0.606918\pi\)
−0.329612 + 0.944117i \(0.606918\pi\)
\(180\) −27.8429 −2.07529
\(181\) −9.19110 −0.683169 −0.341585 0.939851i \(-0.610964\pi\)
−0.341585 + 0.939851i \(0.610964\pi\)
\(182\) −2.07194 −0.153583
\(183\) 5.93105 0.438436
\(184\) 4.33235 0.319385
\(185\) −0.952768 −0.0700489
\(186\) 20.9761 1.53804
\(187\) 3.03080 0.221634
\(188\) 28.7984 2.10034
\(189\) −6.37451 −0.463677
\(190\) 17.2091 1.24848
\(191\) 5.68987 0.411704 0.205852 0.978583i \(-0.434003\pi\)
0.205852 + 0.978583i \(0.434003\pi\)
\(192\) 38.3708 2.76917
\(193\) 12.9483 0.932037 0.466019 0.884775i \(-0.345688\pi\)
0.466019 + 0.884775i \(0.345688\pi\)
\(194\) 29.0145 2.08312
\(195\) 5.76527 0.412859
\(196\) −22.6909 −1.62078
\(197\) 22.2473 1.58505 0.792527 0.609837i \(-0.208765\pi\)
0.792527 + 0.609837i \(0.208765\pi\)
\(198\) −15.0333 −1.06837
\(199\) 14.0715 0.997500 0.498750 0.866746i \(-0.333793\pi\)
0.498750 + 0.866746i \(0.333793\pi\)
\(200\) 11.2389 0.794708
\(201\) 20.0995 1.41771
\(202\) −9.34383 −0.657430
\(203\) 4.03951 0.283518
\(204\) −31.8495 −2.22991
\(205\) −6.95511 −0.485766
\(206\) 21.0940 1.46969
\(207\) −8.48667 −0.589864
\(208\) 1.24928 0.0866220
\(209\) 5.86101 0.405414
\(210\) −5.41061 −0.373367
\(211\) −11.8254 −0.814093 −0.407046 0.913408i \(-0.633441\pi\)
−0.407046 + 0.913408i \(0.633441\pi\)
\(212\) −40.6343 −2.79078
\(213\) 26.4234 1.81050
\(214\) −10.3268 −0.705928
\(215\) 11.7828 0.803580
\(216\) 35.0820 2.38703
\(217\) 1.75573 0.119186
\(218\) −31.1301 −2.10839
\(219\) 16.7425 1.13135
\(220\) −4.31053 −0.290616
\(221\) 4.50332 0.302926
\(222\) 5.40595 0.362823
\(223\) −12.8055 −0.857519 −0.428759 0.903419i \(-0.641049\pi\)
−0.428759 + 0.903419i \(0.641049\pi\)
\(224\) 2.77880 0.185666
\(225\) −22.0159 −1.46773
\(226\) 16.5702 1.10224
\(227\) −14.5984 −0.968930 −0.484465 0.874811i \(-0.660986\pi\)
−0.484465 + 0.874811i \(0.660986\pi\)
\(228\) −61.5910 −4.07896
\(229\) 21.5271 1.42255 0.711276 0.702913i \(-0.248118\pi\)
0.711276 + 0.702913i \(0.248118\pi\)
\(230\) −3.85779 −0.254375
\(231\) −1.84273 −0.121243
\(232\) −22.2314 −1.45956
\(233\) −15.4722 −1.01362 −0.506808 0.862059i \(-0.669175\pi\)
−0.506808 + 0.862059i \(0.669175\pi\)
\(234\) −22.3373 −1.46023
\(235\) −10.6333 −0.693639
\(236\) −10.1493 −0.660665
\(237\) 8.98848 0.583864
\(238\) −4.22629 −0.273950
\(239\) −25.8610 −1.67281 −0.836406 0.548111i \(-0.815347\pi\)
−0.836406 + 0.548111i \(0.815347\pi\)
\(240\) 3.26233 0.210582
\(241\) 20.7697 1.33790 0.668948 0.743309i \(-0.266745\pi\)
0.668948 + 0.743309i \(0.266745\pi\)
\(242\) −2.32740 −0.149611
\(243\) −9.12407 −0.585309
\(244\) −6.58899 −0.421817
\(245\) 8.37818 0.535262
\(246\) 39.4628 2.51606
\(247\) 8.70859 0.554114
\(248\) −9.66261 −0.613576
\(249\) −20.4564 −1.29637
\(250\) −24.6888 −1.56145
\(251\) −1.62608 −0.102637 −0.0513185 0.998682i \(-0.516342\pi\)
−0.0513185 + 0.998682i \(0.516342\pi\)
\(252\) 13.2231 0.832974
\(253\) −1.31387 −0.0826025
\(254\) 3.12760 0.196243
\(255\) 11.7598 0.736429
\(256\) −21.0386 −1.31491
\(257\) 26.8034 1.67195 0.835975 0.548768i \(-0.184903\pi\)
0.835975 + 0.548768i \(0.184903\pi\)
\(258\) −66.8548 −4.16220
\(259\) 0.452485 0.0281161
\(260\) −6.40481 −0.397210
\(261\) 43.5493 2.69563
\(262\) 5.61125 0.346664
\(263\) 4.93641 0.304392 0.152196 0.988350i \(-0.451366\pi\)
0.152196 + 0.988350i \(0.451366\pi\)
\(264\) 10.1414 0.624162
\(265\) 15.0035 0.921656
\(266\) −8.17287 −0.501111
\(267\) 20.4469 1.25133
\(268\) −22.3291 −1.36397
\(269\) −4.98870 −0.304167 −0.152083 0.988368i \(-0.548598\pi\)
−0.152083 + 0.988368i \(0.548598\pi\)
\(270\) −31.2392 −1.90115
\(271\) 25.3831 1.54191 0.770957 0.636888i \(-0.219778\pi\)
0.770957 + 0.636888i \(0.219778\pi\)
\(272\) 2.54825 0.154510
\(273\) −2.73802 −0.165713
\(274\) 10.9496 0.661488
\(275\) −3.40842 −0.205535
\(276\) 13.8070 0.831082
\(277\) −21.5445 −1.29448 −0.647242 0.762284i \(-0.724078\pi\)
−0.647242 + 0.762284i \(0.724078\pi\)
\(278\) 20.1803 1.21033
\(279\) 18.9282 1.13320
\(280\) 2.49239 0.148949
\(281\) 25.9749 1.54953 0.774767 0.632247i \(-0.217867\pi\)
0.774767 + 0.632247i \(0.217867\pi\)
\(282\) 60.3326 3.59276
\(283\) −18.8315 −1.11942 −0.559709 0.828689i \(-0.689087\pi\)
−0.559709 + 0.828689i \(0.689087\pi\)
\(284\) −29.3546 −1.74188
\(285\) 22.7413 1.34708
\(286\) −3.45817 −0.204486
\(287\) 3.30310 0.194976
\(288\) 29.9577 1.76528
\(289\) −7.81425 −0.459662
\(290\) 19.7962 1.16247
\(291\) 38.3419 2.24764
\(292\) −18.5998 −1.08847
\(293\) −17.7174 −1.03506 −0.517532 0.855664i \(-0.673149\pi\)
−0.517532 + 0.855664i \(0.673149\pi\)
\(294\) −47.5373 −2.77243
\(295\) 3.74745 0.218185
\(296\) −2.49025 −0.144743
\(297\) −10.6393 −0.617357
\(298\) −36.8551 −2.13496
\(299\) −1.95222 −0.112900
\(300\) 35.8177 2.06794
\(301\) −5.59584 −0.322539
\(302\) 16.4921 0.949016
\(303\) −12.3476 −0.709353
\(304\) 4.92784 0.282631
\(305\) 2.43286 0.139305
\(306\) −45.5629 −2.60466
\(307\) 9.95065 0.567914 0.283957 0.958837i \(-0.408353\pi\)
0.283957 + 0.958837i \(0.408353\pi\)
\(308\) 2.04714 0.116647
\(309\) 27.8752 1.58577
\(310\) 8.60418 0.488685
\(311\) −6.58665 −0.373495 −0.186747 0.982408i \(-0.559795\pi\)
−0.186747 + 0.982408i \(0.559795\pi\)
\(312\) 15.0687 0.853095
\(313\) −34.8239 −1.96837 −0.984183 0.177156i \(-0.943310\pi\)
−0.984183 + 0.177156i \(0.943310\pi\)
\(314\) −22.9042 −1.29256
\(315\) −4.88237 −0.275090
\(316\) −9.98557 −0.561732
\(317\) 13.2304 0.743093 0.371546 0.928414i \(-0.378828\pi\)
0.371546 + 0.928414i \(0.378828\pi\)
\(318\) −85.1288 −4.77379
\(319\) 6.74213 0.377487
\(320\) 15.7393 0.879855
\(321\) −13.6467 −0.761682
\(322\) 1.83213 0.102100
\(323\) 17.7635 0.988390
\(324\) 45.5949 2.53305
\(325\) −5.06441 −0.280923
\(326\) 45.5364 2.52203
\(327\) −41.1376 −2.27491
\(328\) −18.1785 −1.00374
\(329\) 5.04993 0.278411
\(330\) −9.03054 −0.497115
\(331\) 10.5750 0.581254 0.290627 0.956836i \(-0.406136\pi\)
0.290627 + 0.956836i \(0.406136\pi\)
\(332\) 22.7256 1.24723
\(333\) 4.87817 0.267322
\(334\) −15.0383 −0.822862
\(335\) 8.24462 0.450452
\(336\) −1.54933 −0.0845231
\(337\) 14.6928 0.800365 0.400183 0.916435i \(-0.368947\pi\)
0.400183 + 0.916435i \(0.368947\pi\)
\(338\) 25.1178 1.36623
\(339\) 21.8972 1.18929
\(340\) −13.0644 −0.708514
\(341\) 2.93038 0.158689
\(342\) −88.1102 −4.76446
\(343\) −8.17295 −0.441298
\(344\) 30.7966 1.66044
\(345\) −5.09797 −0.274465
\(346\) 16.7645 0.901263
\(347\) 11.0607 0.593768 0.296884 0.954914i \(-0.404052\pi\)
0.296884 + 0.954914i \(0.404052\pi\)
\(348\) −70.8503 −3.79798
\(349\) −19.6971 −1.05436 −0.527180 0.849754i \(-0.676751\pi\)
−0.527180 + 0.849754i \(0.676751\pi\)
\(350\) 4.75286 0.254051
\(351\) −15.8085 −0.843794
\(352\) 4.63794 0.247203
\(353\) 6.06512 0.322814 0.161407 0.986888i \(-0.448397\pi\)
0.161407 + 0.986888i \(0.448397\pi\)
\(354\) −21.2628 −1.13010
\(355\) 10.8387 0.575256
\(356\) −22.7151 −1.20390
\(357\) −5.58494 −0.295586
\(358\) 20.5272 1.08489
\(359\) 18.9962 1.00258 0.501290 0.865279i \(-0.332859\pi\)
0.501290 + 0.865279i \(0.332859\pi\)
\(360\) 26.8701 1.41618
\(361\) 15.3514 0.807968
\(362\) 21.3913 1.12430
\(363\) −3.07559 −0.161427
\(364\) 3.04175 0.159431
\(365\) 6.86763 0.359468
\(366\) −13.8039 −0.721542
\(367\) −18.4004 −0.960494 −0.480247 0.877133i \(-0.659453\pi\)
−0.480247 + 0.877133i \(0.659453\pi\)
\(368\) −1.10468 −0.0575855
\(369\) 35.6101 1.85379
\(370\) 2.21747 0.115281
\(371\) −7.12540 −0.369932
\(372\) −30.7942 −1.59661
\(373\) 30.0371 1.55526 0.777632 0.628720i \(-0.216421\pi\)
0.777632 + 0.628720i \(0.216421\pi\)
\(374\) −7.05387 −0.364747
\(375\) −32.6256 −1.68478
\(376\) −27.7922 −1.43327
\(377\) 10.0178 0.515944
\(378\) 14.8360 0.763081
\(379\) 8.65654 0.444656 0.222328 0.974972i \(-0.428634\pi\)
0.222328 + 0.974972i \(0.428634\pi\)
\(380\) −25.2640 −1.29602
\(381\) 4.13304 0.211742
\(382\) −13.2426 −0.677549
\(383\) −18.6866 −0.954843 −0.477421 0.878674i \(-0.658428\pi\)
−0.477421 + 0.878674i \(0.658428\pi\)
\(384\) −60.7751 −3.10142
\(385\) −0.755869 −0.0385227
\(386\) −30.1358 −1.53387
\(387\) −60.3278 −3.06663
\(388\) −42.5952 −2.16245
\(389\) 31.3284 1.58841 0.794206 0.607648i \(-0.207887\pi\)
0.794206 + 0.607648i \(0.207887\pi\)
\(390\) −13.4181 −0.679450
\(391\) −3.98209 −0.201383
\(392\) 21.8980 1.10602
\(393\) 7.41512 0.374044
\(394\) −51.7782 −2.60855
\(395\) 3.68699 0.185513
\(396\) 22.0699 1.10905
\(397\) −4.38014 −0.219833 −0.109916 0.993941i \(-0.535058\pi\)
−0.109916 + 0.993941i \(0.535058\pi\)
\(398\) −32.7499 −1.64160
\(399\) −10.8002 −0.540688
\(400\) −2.86574 −0.143287
\(401\) −0.895888 −0.0447385 −0.0223693 0.999750i \(-0.507121\pi\)
−0.0223693 + 0.999750i \(0.507121\pi\)
\(402\) −46.7794 −2.33315
\(403\) 4.35412 0.216894
\(404\) 13.7174 0.682464
\(405\) −16.8351 −0.836541
\(406\) −9.40155 −0.466591
\(407\) 0.755218 0.0374348
\(408\) 30.7366 1.52169
\(409\) 8.26149 0.408504 0.204252 0.978918i \(-0.434524\pi\)
0.204252 + 0.978918i \(0.434524\pi\)
\(410\) 16.1873 0.799433
\(411\) 14.4696 0.713732
\(412\) −30.9674 −1.52566
\(413\) −1.77973 −0.0875746
\(414\) 19.7518 0.970750
\(415\) −8.39101 −0.411898
\(416\) 6.89130 0.337874
\(417\) 26.6677 1.30592
\(418\) −13.6409 −0.667197
\(419\) −32.8640 −1.60551 −0.802756 0.596307i \(-0.796634\pi\)
−0.802756 + 0.596307i \(0.796634\pi\)
\(420\) 7.94313 0.387585
\(421\) 1.08937 0.0530928 0.0265464 0.999648i \(-0.491549\pi\)
0.0265464 + 0.999648i \(0.491549\pi\)
\(422\) 27.5223 1.33977
\(423\) 54.4424 2.64708
\(424\) 39.2145 1.90443
\(425\) −10.3302 −0.501090
\(426\) −61.4978 −2.97958
\(427\) −1.15541 −0.0559141
\(428\) 15.1605 0.732810
\(429\) −4.56988 −0.220636
\(430\) −27.4232 −1.32247
\(431\) −24.5816 −1.18406 −0.592028 0.805917i \(-0.701672\pi\)
−0.592028 + 0.805917i \(0.701672\pi\)
\(432\) −8.94537 −0.430385
\(433\) −25.5381 −1.22728 −0.613641 0.789585i \(-0.710296\pi\)
−0.613641 + 0.789585i \(0.710296\pi\)
\(434\) −4.08627 −0.196147
\(435\) 26.1602 1.25428
\(436\) 45.7010 2.18868
\(437\) −7.70062 −0.368370
\(438\) −38.9665 −1.86189
\(439\) −5.15845 −0.246199 −0.123100 0.992394i \(-0.539283\pi\)
−0.123100 + 0.992394i \(0.539283\pi\)
\(440\) 4.15992 0.198316
\(441\) −42.8962 −2.04268
\(442\) −10.4810 −0.498531
\(443\) −27.1359 −1.28926 −0.644632 0.764493i \(-0.722990\pi\)
−0.644632 + 0.764493i \(0.722990\pi\)
\(444\) −7.93629 −0.376640
\(445\) 8.38714 0.397589
\(446\) 29.8034 1.41123
\(447\) −48.7031 −2.30358
\(448\) −7.47487 −0.353154
\(449\) −24.9526 −1.17758 −0.588792 0.808284i \(-0.700396\pi\)
−0.588792 + 0.808284i \(0.700396\pi\)
\(450\) 51.2397 2.41546
\(451\) 5.51301 0.259598
\(452\) −24.3262 −1.14421
\(453\) 21.7939 1.02397
\(454\) 33.9763 1.59459
\(455\) −1.12311 −0.0526522
\(456\) 59.4389 2.78348
\(457\) −16.2422 −0.759779 −0.379889 0.925032i \(-0.624038\pi\)
−0.379889 + 0.925032i \(0.624038\pi\)
\(458\) −50.1021 −2.34112
\(459\) −32.2457 −1.50510
\(460\) 5.66349 0.264061
\(461\) −3.86531 −0.180025 −0.0900127 0.995941i \(-0.528691\pi\)
−0.0900127 + 0.995941i \(0.528691\pi\)
\(462\) 4.28876 0.199531
\(463\) 9.76584 0.453857 0.226928 0.973911i \(-0.427132\pi\)
0.226928 + 0.973911i \(0.427132\pi\)
\(464\) 5.66867 0.263161
\(465\) 11.3702 0.527281
\(466\) 36.0099 1.66813
\(467\) −5.12102 −0.236973 −0.118486 0.992956i \(-0.537804\pi\)
−0.118486 + 0.992956i \(0.537804\pi\)
\(468\) 32.7926 1.51584
\(469\) −3.91551 −0.180801
\(470\) 24.7479 1.14153
\(471\) −30.2674 −1.39465
\(472\) 9.79470 0.450838
\(473\) −9.33971 −0.429440
\(474\) −20.9197 −0.960876
\(475\) −19.9767 −0.916596
\(476\) 6.20448 0.284382
\(477\) −76.8177 −3.51724
\(478\) 60.1889 2.75297
\(479\) −33.9782 −1.55250 −0.776252 0.630423i \(-0.782882\pi\)
−0.776252 + 0.630423i \(0.782882\pi\)
\(480\) 17.9957 0.821388
\(481\) 1.12214 0.0511653
\(482\) −48.3394 −2.20180
\(483\) 2.42111 0.110164
\(484\) 3.41677 0.155308
\(485\) 15.7275 0.714149
\(486\) 21.2353 0.963254
\(487\) −34.9174 −1.58226 −0.791130 0.611648i \(-0.790507\pi\)
−0.791130 + 0.611648i \(0.790507\pi\)
\(488\) 6.35877 0.287848
\(489\) 60.1752 2.72122
\(490\) −19.4993 −0.880891
\(491\) −0.442418 −0.0199660 −0.00998302 0.999950i \(-0.503178\pi\)
−0.00998302 + 0.999950i \(0.503178\pi\)
\(492\) −57.9341 −2.61187
\(493\) 20.4340 0.920303
\(494\) −20.2683 −0.911916
\(495\) −8.14889 −0.366266
\(496\) 2.46382 0.110629
\(497\) −5.14746 −0.230895
\(498\) 47.6100 2.13346
\(499\) −23.7518 −1.06328 −0.531638 0.846972i \(-0.678423\pi\)
−0.531638 + 0.846972i \(0.678423\pi\)
\(500\) 36.2447 1.62091
\(501\) −19.8728 −0.887851
\(502\) 3.78452 0.168911
\(503\) 29.1178 1.29830 0.649149 0.760662i \(-0.275125\pi\)
0.649149 + 0.760662i \(0.275125\pi\)
\(504\) −12.7610 −0.568422
\(505\) −5.06488 −0.225384
\(506\) 3.05790 0.135940
\(507\) 33.1926 1.47413
\(508\) −4.59152 −0.203716
\(509\) 0.324499 0.0143832 0.00719158 0.999974i \(-0.497711\pi\)
0.00719158 + 0.999974i \(0.497711\pi\)
\(510\) −27.3698 −1.21195
\(511\) −3.26155 −0.144282
\(512\) 9.44428 0.417382
\(513\) −62.3572 −2.75314
\(514\) −62.3821 −2.75156
\(515\) 11.4342 0.503849
\(516\) 98.1473 4.32069
\(517\) 8.42855 0.370687
\(518\) −1.05311 −0.0462711
\(519\) 22.1538 0.972445
\(520\) 6.18102 0.271056
\(521\) −23.3740 −1.02403 −0.512017 0.858975i \(-0.671102\pi\)
−0.512017 + 0.858975i \(0.671102\pi\)
\(522\) −101.356 −4.43625
\(523\) −37.8723 −1.65604 −0.828020 0.560698i \(-0.810533\pi\)
−0.828020 + 0.560698i \(0.810533\pi\)
\(524\) −8.23769 −0.359865
\(525\) 6.28078 0.274116
\(526\) −11.4890 −0.500943
\(527\) 8.88141 0.386880
\(528\) −2.58591 −0.112537
\(529\) −21.2737 −0.924945
\(530\) −34.9190 −1.51679
\(531\) −19.1869 −0.832641
\(532\) 11.9983 0.520193
\(533\) 8.19153 0.354814
\(534\) −47.5881 −2.05934
\(535\) −5.59773 −0.242011
\(536\) 21.5489 0.930772
\(537\) 27.1261 1.17058
\(538\) 11.6107 0.500572
\(539\) −6.64103 −0.286049
\(540\) 45.8612 1.97355
\(541\) −4.25778 −0.183056 −0.0915281 0.995802i \(-0.529175\pi\)
−0.0915281 + 0.995802i \(0.529175\pi\)
\(542\) −59.0765 −2.53755
\(543\) 28.2681 1.21310
\(544\) 14.0567 0.602675
\(545\) −16.8742 −0.722813
\(546\) 6.37246 0.272716
\(547\) 1.00000 0.0427569
\(548\) −16.0747 −0.686677
\(549\) −12.4562 −0.531619
\(550\) 7.93273 0.338253
\(551\) 39.5157 1.68342
\(552\) −13.3245 −0.567130
\(553\) −1.75101 −0.0744606
\(554\) 50.1426 2.13036
\(555\) 2.93033 0.124385
\(556\) −29.6260 −1.25642
\(557\) 11.6817 0.494969 0.247485 0.968892i \(-0.420396\pi\)
0.247485 + 0.968892i \(0.420396\pi\)
\(558\) −44.0533 −1.86493
\(559\) −13.8774 −0.586953
\(560\) −0.635522 −0.0268557
\(561\) −9.32151 −0.393555
\(562\) −60.4539 −2.55010
\(563\) −19.6636 −0.828721 −0.414360 0.910113i \(-0.635995\pi\)
−0.414360 + 0.910113i \(0.635995\pi\)
\(564\) −88.5723 −3.72957
\(565\) 8.98201 0.377876
\(566\) 43.8284 1.84225
\(567\) 7.99526 0.335769
\(568\) 28.3290 1.18866
\(569\) 6.22920 0.261142 0.130571 0.991439i \(-0.458319\pi\)
0.130571 + 0.991439i \(0.458319\pi\)
\(570\) −52.9281 −2.21691
\(571\) 29.0965 1.21765 0.608826 0.793304i \(-0.291641\pi\)
0.608826 + 0.793304i \(0.291641\pi\)
\(572\) 5.07682 0.212272
\(573\) −17.4997 −0.731061
\(574\) −7.68761 −0.320875
\(575\) 4.47823 0.186755
\(576\) −80.5852 −3.35772
\(577\) −2.46159 −0.102477 −0.0512387 0.998686i \(-0.516317\pi\)
−0.0512387 + 0.998686i \(0.516317\pi\)
\(578\) 18.1868 0.756473
\(579\) −39.8236 −1.65501
\(580\) −29.0621 −1.20674
\(581\) 3.98503 0.165327
\(582\) −89.2369 −3.69899
\(583\) −11.8926 −0.492542
\(584\) 17.9499 0.742772
\(585\) −12.1081 −0.500607
\(586\) 41.2355 1.70342
\(587\) 15.9484 0.658261 0.329130 0.944285i \(-0.393244\pi\)
0.329130 + 0.944285i \(0.393244\pi\)
\(588\) 69.7879 2.87800
\(589\) 17.1750 0.707683
\(590\) −8.72180 −0.359071
\(591\) −68.4236 −2.81457
\(592\) 0.634975 0.0260973
\(593\) −12.7634 −0.524130 −0.262065 0.965050i \(-0.584403\pi\)
−0.262065 + 0.965050i \(0.584403\pi\)
\(594\) 24.7619 1.01599
\(595\) −2.29089 −0.0939173
\(596\) 54.1058 2.21626
\(597\) −43.2781 −1.77126
\(598\) 4.54359 0.185801
\(599\) 9.87514 0.403487 0.201744 0.979438i \(-0.435339\pi\)
0.201744 + 0.979438i \(0.435339\pi\)
\(600\) −34.5662 −1.41116
\(601\) −6.94106 −0.283132 −0.141566 0.989929i \(-0.545214\pi\)
−0.141566 + 0.989929i \(0.545214\pi\)
\(602\) 13.0237 0.530808
\(603\) −42.2124 −1.71902
\(604\) −24.2115 −0.985154
\(605\) −1.26158 −0.0512905
\(606\) 28.7378 1.16739
\(607\) 29.2989 1.18921 0.594603 0.804019i \(-0.297309\pi\)
0.594603 + 0.804019i \(0.297309\pi\)
\(608\) 27.1830 1.10242
\(609\) −12.4239 −0.503442
\(610\) −5.66223 −0.229257
\(611\) 12.5236 0.506650
\(612\) 66.8894 2.70384
\(613\) 31.3333 1.26554 0.632770 0.774340i \(-0.281918\pi\)
0.632770 + 0.774340i \(0.281918\pi\)
\(614\) −23.1591 −0.934625
\(615\) 21.3911 0.862572
\(616\) −1.97561 −0.0795998
\(617\) 20.2638 0.815792 0.407896 0.913028i \(-0.366263\pi\)
0.407896 + 0.913028i \(0.366263\pi\)
\(618\) −64.8767 −2.60972
\(619\) −14.3073 −0.575058 −0.287529 0.957772i \(-0.592834\pi\)
−0.287529 + 0.957772i \(0.592834\pi\)
\(620\) −12.6315 −0.507293
\(621\) 13.9787 0.560947
\(622\) 15.3297 0.614666
\(623\) −3.98319 −0.159583
\(624\) −3.84228 −0.153814
\(625\) 3.65939 0.146376
\(626\) 81.0491 3.23937
\(627\) −18.0261 −0.719892
\(628\) 33.6249 1.34178
\(629\) 2.28892 0.0912651
\(630\) 11.3632 0.452721
\(631\) −3.15968 −0.125785 −0.0628924 0.998020i \(-0.520033\pi\)
−0.0628924 + 0.998020i \(0.520033\pi\)
\(632\) 9.63667 0.383326
\(633\) 36.3701 1.44558
\(634\) −30.7924 −1.22292
\(635\) 1.69533 0.0672773
\(636\) 124.975 4.95557
\(637\) −9.86759 −0.390968
\(638\) −15.6916 −0.621237
\(639\) −55.4938 −2.19530
\(640\) −24.9294 −0.985420
\(641\) 32.0601 1.26630 0.633150 0.774029i \(-0.281762\pi\)
0.633150 + 0.774029i \(0.281762\pi\)
\(642\) 31.7612 1.25351
\(643\) −16.4784 −0.649844 −0.324922 0.945741i \(-0.605338\pi\)
−0.324922 + 0.945741i \(0.605338\pi\)
\(644\) −2.68968 −0.105988
\(645\) −36.2391 −1.42691
\(646\) −41.3428 −1.62661
\(647\) −10.4922 −0.412491 −0.206245 0.978500i \(-0.566125\pi\)
−0.206245 + 0.978500i \(0.566125\pi\)
\(648\) −44.0018 −1.72855
\(649\) −2.97044 −0.116600
\(650\) 11.7869 0.462319
\(651\) −5.39990 −0.211639
\(652\) −66.8505 −2.61807
\(653\) −34.9327 −1.36702 −0.683511 0.729940i \(-0.739548\pi\)
−0.683511 + 0.729940i \(0.739548\pi\)
\(654\) 95.7434 3.74386
\(655\) 3.04161 0.118846
\(656\) 4.63525 0.180976
\(657\) −35.1622 −1.37181
\(658\) −11.7532 −0.458187
\(659\) −15.5209 −0.604608 −0.302304 0.953212i \(-0.597756\pi\)
−0.302304 + 0.953212i \(0.597756\pi\)
\(660\) 13.2574 0.516045
\(661\) 27.8124 1.08178 0.540888 0.841095i \(-0.318088\pi\)
0.540888 + 0.841095i \(0.318088\pi\)
\(662\) −24.6122 −0.956579
\(663\) −13.8504 −0.537905
\(664\) −21.9316 −0.851109
\(665\) −4.43015 −0.171794
\(666\) −11.3534 −0.439936
\(667\) −8.85830 −0.342995
\(668\) 22.0773 0.854196
\(669\) 39.3845 1.52269
\(670\) −19.1885 −0.741316
\(671\) −1.92843 −0.0744460
\(672\) −8.54646 −0.329687
\(673\) −16.6229 −0.640764 −0.320382 0.947288i \(-0.603811\pi\)
−0.320382 + 0.947288i \(0.603811\pi\)
\(674\) −34.1959 −1.31718
\(675\) 36.2633 1.39577
\(676\) −36.8746 −1.41825
\(677\) 13.3423 0.512785 0.256393 0.966573i \(-0.417466\pi\)
0.256393 + 0.966573i \(0.417466\pi\)
\(678\) −50.9633 −1.95724
\(679\) −7.46925 −0.286644
\(680\) 12.6079 0.483490
\(681\) 44.8988 1.72052
\(682\) −6.82016 −0.261158
\(683\) 26.4190 1.01090 0.505448 0.862857i \(-0.331327\pi\)
0.505448 + 0.862857i \(0.331327\pi\)
\(684\) 129.352 4.94588
\(685\) 5.93529 0.226776
\(686\) 19.0217 0.726252
\(687\) −66.2086 −2.52602
\(688\) −7.85267 −0.299380
\(689\) −17.6707 −0.673199
\(690\) 11.8650 0.451692
\(691\) 10.5924 0.402952 0.201476 0.979493i \(-0.435426\pi\)
0.201476 + 0.979493i \(0.435426\pi\)
\(692\) −24.6114 −0.935583
\(693\) 3.87005 0.147011
\(694\) −25.7426 −0.977175
\(695\) 10.9388 0.414934
\(696\) 68.3748 2.59174
\(697\) 16.7088 0.632893
\(698\) 45.8428 1.73518
\(699\) 47.5861 1.79987
\(700\) −6.97751 −0.263725
\(701\) −45.5990 −1.72225 −0.861125 0.508394i \(-0.830239\pi\)
−0.861125 + 0.508394i \(0.830239\pi\)
\(702\) 36.7926 1.38865
\(703\) 4.42634 0.166943
\(704\) −12.4759 −0.470203
\(705\) 32.7037 1.23169
\(706\) −14.1159 −0.531260
\(707\) 2.40540 0.0904643
\(708\) 31.2152 1.17314
\(709\) 35.5322 1.33444 0.667220 0.744861i \(-0.267484\pi\)
0.667220 + 0.744861i \(0.267484\pi\)
\(710\) −25.2258 −0.946708
\(711\) −18.8774 −0.707956
\(712\) 21.9215 0.821541
\(713\) −3.85015 −0.144189
\(714\) 12.9984 0.486452
\(715\) −1.87452 −0.0701031
\(716\) −30.1353 −1.12621
\(717\) 79.5380 2.97040
\(718\) −44.2116 −1.64996
\(719\) −18.5736 −0.692680 −0.346340 0.938109i \(-0.612576\pi\)
−0.346340 + 0.938109i \(0.612576\pi\)
\(720\) −6.85145 −0.255339
\(721\) −5.43027 −0.202234
\(722\) −35.7288 −1.32969
\(723\) −63.8793 −2.37570
\(724\) −31.4039 −1.16712
\(725\) −22.9800 −0.853455
\(726\) 7.15812 0.265663
\(727\) −17.0223 −0.631321 −0.315660 0.948872i \(-0.602226\pi\)
−0.315660 + 0.948872i \(0.602226\pi\)
\(728\) −2.93547 −0.108796
\(729\) −11.9714 −0.443384
\(730\) −15.9837 −0.591583
\(731\) −28.3068 −1.04697
\(732\) 20.2651 0.749018
\(733\) 31.7063 1.17110 0.585550 0.810636i \(-0.300879\pi\)
0.585550 + 0.810636i \(0.300879\pi\)
\(734\) 42.8250 1.58070
\(735\) −25.7679 −0.950463
\(736\) −6.09366 −0.224615
\(737\) −6.53515 −0.240725
\(738\) −82.8788 −3.05081
\(739\) 10.5885 0.389503 0.194751 0.980853i \(-0.437610\pi\)
0.194751 + 0.980853i \(0.437610\pi\)
\(740\) −3.25539 −0.119671
\(741\) −26.7841 −0.983938
\(742\) 16.5836 0.608804
\(743\) −0.934902 −0.0342982 −0.0171491 0.999853i \(-0.505459\pi\)
−0.0171491 + 0.999853i \(0.505459\pi\)
\(744\) 29.7183 1.08952
\(745\) −19.9776 −0.731921
\(746\) −69.9083 −2.55952
\(747\) 42.9619 1.57189
\(748\) 10.3556 0.378636
\(749\) 2.65845 0.0971378
\(750\) 75.9326 2.77267
\(751\) 20.9014 0.762702 0.381351 0.924430i \(-0.375459\pi\)
0.381351 + 0.924430i \(0.375459\pi\)
\(752\) 7.08659 0.258421
\(753\) 5.00115 0.182252
\(754\) −23.3154 −0.849097
\(755\) 8.93967 0.325348
\(756\) −21.7802 −0.792139
\(757\) −47.3148 −1.71969 −0.859844 0.510558i \(-0.829439\pi\)
−0.859844 + 0.510558i \(0.829439\pi\)
\(758\) −20.1472 −0.731779
\(759\) 4.04094 0.146677
\(760\) 24.3813 0.884403
\(761\) −6.35314 −0.230301 −0.115151 0.993348i \(-0.536735\pi\)
−0.115151 + 0.993348i \(0.536735\pi\)
\(762\) −9.61922 −0.348468
\(763\) 8.01386 0.290121
\(764\) 19.4410 0.703350
\(765\) −24.6977 −0.892946
\(766\) 43.4912 1.57140
\(767\) −4.41364 −0.159367
\(768\) 64.7062 2.33488
\(769\) −36.6873 −1.32298 −0.661490 0.749954i \(-0.730075\pi\)
−0.661490 + 0.749954i \(0.730075\pi\)
\(770\) 1.75921 0.0633974
\(771\) −82.4364 −2.96887
\(772\) 44.2413 1.59228
\(773\) 1.47629 0.0530984 0.0265492 0.999648i \(-0.491548\pi\)
0.0265492 + 0.999648i \(0.491548\pi\)
\(774\) 140.407 5.04681
\(775\) −9.98797 −0.358778
\(776\) 41.1069 1.47565
\(777\) −1.39166 −0.0499256
\(778\) −72.9136 −2.61408
\(779\) 32.3118 1.15769
\(780\) 19.6986 0.705323
\(781\) −8.59133 −0.307422
\(782\) 9.26789 0.331419
\(783\) −71.7318 −2.56348
\(784\) −5.58366 −0.199417
\(785\) −12.4154 −0.443124
\(786\) −17.2579 −0.615570
\(787\) 20.5342 0.731965 0.365982 0.930622i \(-0.380733\pi\)
0.365982 + 0.930622i \(0.380733\pi\)
\(788\) 76.0139 2.70788
\(789\) −15.1824 −0.540507
\(790\) −8.58108 −0.305301
\(791\) −4.26570 −0.151671
\(792\) −21.2987 −0.756818
\(793\) −2.86536 −0.101752
\(794\) 10.1943 0.361782
\(795\) −46.1446 −1.63658
\(796\) 48.0790 1.70411
\(797\) −12.5303 −0.443845 −0.221922 0.975064i \(-0.571233\pi\)
−0.221922 + 0.975064i \(0.571233\pi\)
\(798\) 25.1364 0.889820
\(799\) 25.5453 0.903726
\(800\) −15.8080 −0.558898
\(801\) −42.9421 −1.51728
\(802\) 2.08509 0.0736270
\(803\) −5.44367 −0.192103
\(804\) 68.6753 2.42199
\(805\) 0.993116 0.0350027
\(806\) −10.1338 −0.356946
\(807\) 15.3432 0.540107
\(808\) −13.2381 −0.465714
\(809\) −25.2177 −0.886608 −0.443304 0.896371i \(-0.646194\pi\)
−0.443304 + 0.896371i \(0.646194\pi\)
\(810\) 39.1819 1.37671
\(811\) 35.4366 1.24435 0.622175 0.782879i \(-0.286249\pi\)
0.622175 + 0.782879i \(0.286249\pi\)
\(812\) 13.8021 0.484359
\(813\) −78.0681 −2.73797
\(814\) −1.75769 −0.0616071
\(815\) 24.6833 0.864619
\(816\) −7.83737 −0.274363
\(817\) −54.7401 −1.91511
\(818\) −19.2277 −0.672282
\(819\) 5.75032 0.200932
\(820\) −23.7640 −0.829875
\(821\) 41.1793 1.43717 0.718584 0.695441i \(-0.244791\pi\)
0.718584 + 0.695441i \(0.244791\pi\)
\(822\) −33.6764 −1.17460
\(823\) −29.0771 −1.01356 −0.506782 0.862074i \(-0.669165\pi\)
−0.506782 + 0.862074i \(0.669165\pi\)
\(824\) 29.8854 1.04111
\(825\) 10.4829 0.364968
\(826\) 4.14213 0.144123
\(827\) 43.2599 1.50429 0.752147 0.658996i \(-0.229019\pi\)
0.752147 + 0.658996i \(0.229019\pi\)
\(828\) −28.9970 −1.00772
\(829\) 33.4857 1.16301 0.581503 0.813544i \(-0.302465\pi\)
0.581503 + 0.813544i \(0.302465\pi\)
\(830\) 19.5292 0.677868
\(831\) 66.2622 2.29861
\(832\) −18.5373 −0.642666
\(833\) −20.1276 −0.697381
\(834\) −62.0663 −2.14918
\(835\) −8.15163 −0.282099
\(836\) 20.0257 0.692604
\(837\) −31.1773 −1.07765
\(838\) 76.4876 2.64222
\(839\) 8.70338 0.300474 0.150237 0.988650i \(-0.451996\pi\)
0.150237 + 0.988650i \(0.451996\pi\)
\(840\) −7.66559 −0.264488
\(841\) 16.4563 0.567459
\(842\) −2.53540 −0.0873758
\(843\) −79.8883 −2.75150
\(844\) −40.4046 −1.39078
\(845\) 13.6153 0.468380
\(846\) −126.709 −4.35634
\(847\) 0.599145 0.0205869
\(848\) −9.99911 −0.343371
\(849\) 57.9182 1.98775
\(850\) 24.0425 0.824652
\(851\) −0.992261 −0.0340143
\(852\) 90.2829 3.09304
\(853\) 15.0584 0.515590 0.257795 0.966200i \(-0.417004\pi\)
0.257795 + 0.966200i \(0.417004\pi\)
\(854\) 2.68909 0.0920187
\(855\) −47.7607 −1.63338
\(856\) −14.6308 −0.500069
\(857\) −16.9262 −0.578189 −0.289094 0.957301i \(-0.593354\pi\)
−0.289094 + 0.957301i \(0.593354\pi\)
\(858\) 10.6359 0.363104
\(859\) −35.4021 −1.20791 −0.603953 0.797020i \(-0.706408\pi\)
−0.603953 + 0.797020i \(0.706408\pi\)
\(860\) 40.2591 1.37282
\(861\) −10.1590 −0.346217
\(862\) 57.2112 1.94862
\(863\) −42.8410 −1.45833 −0.729163 0.684340i \(-0.760090\pi\)
−0.729163 + 0.684340i \(0.760090\pi\)
\(864\) −49.3446 −1.67874
\(865\) 9.08729 0.308977
\(866\) 59.4372 2.01976
\(867\) 24.0335 0.816219
\(868\) 5.99891 0.203616
\(869\) −2.92252 −0.0991396
\(870\) −60.8851 −2.06420
\(871\) −9.71028 −0.329020
\(872\) −44.1042 −1.49356
\(873\) −80.5247 −2.72535
\(874\) 17.9224 0.606234
\(875\) 6.35567 0.214861
\(876\) 57.2054 1.93279
\(877\) −26.2919 −0.887816 −0.443908 0.896072i \(-0.646408\pi\)
−0.443908 + 0.896072i \(0.646408\pi\)
\(878\) 12.0057 0.405174
\(879\) 54.4916 1.83796
\(880\) −1.06072 −0.0357567
\(881\) −34.4620 −1.16106 −0.580528 0.814240i \(-0.697154\pi\)
−0.580528 + 0.814240i \(0.697154\pi\)
\(882\) 99.8365 3.36167
\(883\) −4.28090 −0.144064 −0.0720318 0.997402i \(-0.522948\pi\)
−0.0720318 + 0.997402i \(0.522948\pi\)
\(884\) 15.3868 0.517515
\(885\) −11.5256 −0.387430
\(886\) 63.1559 2.12177
\(887\) 16.7400 0.562073 0.281037 0.959697i \(-0.409322\pi\)
0.281037 + 0.959697i \(0.409322\pi\)
\(888\) 7.65899 0.257019
\(889\) −0.805143 −0.0270036
\(890\) −19.5202 −0.654319
\(891\) 13.3444 0.447056
\(892\) −43.7534 −1.46497
\(893\) 49.3998 1.65310
\(894\) 113.351 3.79104
\(895\) 11.1269 0.371931
\(896\) 11.8394 0.395526
\(897\) 6.00424 0.200476
\(898\) 58.0745 1.93797
\(899\) 19.7570 0.658934
\(900\) −75.2233 −2.50744
\(901\) −36.0441 −1.20080
\(902\) −12.8310 −0.427224
\(903\) 17.2105 0.572731
\(904\) 23.4762 0.780808
\(905\) 11.5953 0.385441
\(906\) −50.7231 −1.68516
\(907\) 22.4839 0.746566 0.373283 0.927717i \(-0.378232\pi\)
0.373283 + 0.927717i \(0.378232\pi\)
\(908\) −49.8794 −1.65531
\(909\) 25.9322 0.860116
\(910\) 2.61392 0.0866507
\(911\) −24.5921 −0.814772 −0.407386 0.913256i \(-0.633560\pi\)
−0.407386 + 0.913256i \(0.633560\pi\)
\(912\) −15.1560 −0.501866
\(913\) 6.65119 0.220122
\(914\) 37.8021 1.25038
\(915\) −7.48250 −0.247364
\(916\) 73.5532 2.43027
\(917\) −1.44451 −0.0477020
\(918\) 75.0485 2.47697
\(919\) −4.09733 −0.135158 −0.0675792 0.997714i \(-0.521528\pi\)
−0.0675792 + 0.997714i \(0.521528\pi\)
\(920\) −5.46560 −0.180196
\(921\) −30.6042 −1.00844
\(922\) 8.99611 0.296271
\(923\) −12.7655 −0.420180
\(924\) −6.29618 −0.207129
\(925\) −2.57410 −0.0846358
\(926\) −22.7290 −0.746920
\(927\) −58.5428 −1.92280
\(928\) 31.2696 1.02647
\(929\) −30.4192 −0.998020 −0.499010 0.866596i \(-0.666303\pi\)
−0.499010 + 0.866596i \(0.666303\pi\)
\(930\) −26.4630 −0.867755
\(931\) −38.9231 −1.27565
\(932\) −52.8649 −1.73165
\(933\) 20.2579 0.663212
\(934\) 11.9187 0.389990
\(935\) −3.82360 −0.125045
\(936\) −31.6468 −1.03441
\(937\) −25.3829 −0.829224 −0.414612 0.909998i \(-0.636083\pi\)
−0.414612 + 0.909998i \(0.636083\pi\)
\(938\) 9.11293 0.297548
\(939\) 107.104 3.49522
\(940\) −36.3315 −1.18500
\(941\) 29.7991 0.971422 0.485711 0.874119i \(-0.338561\pi\)
0.485711 + 0.874119i \(0.338561\pi\)
\(942\) 70.4441 2.29519
\(943\) −7.24340 −0.235877
\(944\) −2.49750 −0.0812866
\(945\) 8.04195 0.261605
\(946\) 21.7372 0.706738
\(947\) 32.2793 1.04893 0.524467 0.851430i \(-0.324264\pi\)
0.524467 + 0.851430i \(0.324264\pi\)
\(948\) 30.7116 0.997466
\(949\) −8.08849 −0.262564
\(950\) 46.4938 1.50846
\(951\) −40.6913 −1.31951
\(952\) −5.98769 −0.194062
\(953\) −41.6583 −1.34945 −0.674723 0.738071i \(-0.735737\pi\)
−0.674723 + 0.738071i \(0.735737\pi\)
\(954\) 178.785 5.78838
\(955\) −7.17822 −0.232282
\(956\) −88.3612 −2.85781
\(957\) −20.7361 −0.670301
\(958\) 79.0807 2.55498
\(959\) −2.81877 −0.0910227
\(960\) −48.4078 −1.56235
\(961\) −22.4129 −0.722995
\(962\) −2.61167 −0.0842037
\(963\) 28.6603 0.923566
\(964\) 70.9655 2.28564
\(965\) −16.3353 −0.525851
\(966\) −5.63488 −0.181299
\(967\) 10.2163 0.328534 0.164267 0.986416i \(-0.447474\pi\)
0.164267 + 0.986416i \(0.447474\pi\)
\(968\) −3.29739 −0.105982
\(969\) −54.6334 −1.75508
\(970\) −36.6041 −1.17529
\(971\) 22.4164 0.719375 0.359687 0.933073i \(-0.382883\pi\)
0.359687 + 0.933073i \(0.382883\pi\)
\(972\) −31.1749 −0.999934
\(973\) −5.19504 −0.166545
\(974\) 81.2667 2.60395
\(975\) 15.5761 0.498833
\(976\) −1.62139 −0.0518994
\(977\) 34.1828 1.09360 0.546802 0.837262i \(-0.315845\pi\)
0.546802 + 0.837262i \(0.315845\pi\)
\(978\) −140.052 −4.47836
\(979\) −6.64813 −0.212475
\(980\) 28.6263 0.914435
\(981\) 86.3960 2.75841
\(982\) 1.02968 0.0328585
\(983\) −37.1639 −1.18535 −0.592673 0.805443i \(-0.701927\pi\)
−0.592673 + 0.805443i \(0.701927\pi\)
\(984\) 55.9098 1.78234
\(985\) −28.0667 −0.894280
\(986\) −47.5581 −1.51456
\(987\) −15.5315 −0.494374
\(988\) 29.7553 0.946641
\(989\) 12.2712 0.390201
\(990\) 18.9657 0.602770
\(991\) 15.1619 0.481634 0.240817 0.970571i \(-0.422585\pi\)
0.240817 + 0.970571i \(0.422585\pi\)
\(992\) 13.5909 0.431513
\(993\) −32.5244 −1.03213
\(994\) 11.9802 0.379988
\(995\) −17.7523 −0.562785
\(996\) −69.8947 −2.21470
\(997\) 5.77715 0.182964 0.0914821 0.995807i \(-0.470840\pi\)
0.0914821 + 0.995807i \(0.470840\pi\)
\(998\) 55.2798 1.74985
\(999\) −8.03502 −0.254217
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 \(a_p\))