Properties

Label 8021.2.a.a.1.8
Level 8021
Weight 2
Character 8021.1
Self dual Yes
Analytic conductor 64.048
Analytic rank 1
Dimension 134
CM No

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Newspace parameters

Level: \( N \) = \( 8021 = 13 \cdot 617 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8021.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0480074613\)
Analytic rank: \(1\)
Dimension: \(134\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Character \(\chi\) = 8021.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.48492 q^{2}\) \(-2.97194 q^{3}\) \(+4.17482 q^{4}\) \(+3.21951 q^{5}\) \(+7.38503 q^{6}\) \(+2.90175 q^{7}\) \(-5.40425 q^{8}\) \(+5.83242 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.48492 q^{2}\) \(-2.97194 q^{3}\) \(+4.17482 q^{4}\) \(+3.21951 q^{5}\) \(+7.38503 q^{6}\) \(+2.90175 q^{7}\) \(-5.40425 q^{8}\) \(+5.83242 q^{9}\) \(-8.00022 q^{10}\) \(-2.09665 q^{11}\) \(-12.4073 q^{12}\) \(+1.00000 q^{13}\) \(-7.21062 q^{14}\) \(-9.56819 q^{15}\) \(+5.07949 q^{16}\) \(+0.183348 q^{17}\) \(-14.4931 q^{18}\) \(-8.32967 q^{19}\) \(+13.4409 q^{20}\) \(-8.62384 q^{21}\) \(+5.21000 q^{22}\) \(-5.93575 q^{23}\) \(+16.0611 q^{24}\) \(+5.36524 q^{25}\) \(-2.48492 q^{26}\) \(-8.41779 q^{27}\) \(+12.1143 q^{28}\) \(-2.88281 q^{29}\) \(+23.7762 q^{30}\) \(+1.57653 q^{31}\) \(-1.81360 q^{32}\) \(+6.23111 q^{33}\) \(-0.455605 q^{34}\) \(+9.34222 q^{35}\) \(+24.3493 q^{36}\) \(-7.21849 q^{37}\) \(+20.6986 q^{38}\) \(-2.97194 q^{39}\) \(-17.3990 q^{40}\) \(+5.76504 q^{41}\) \(+21.4295 q^{42}\) \(-2.35176 q^{43}\) \(-8.75313 q^{44}\) \(+18.7775 q^{45}\) \(+14.7498 q^{46}\) \(-4.35501 q^{47}\) \(-15.0959 q^{48}\) \(+1.42017 q^{49}\) \(-13.3322 q^{50}\) \(-0.544899 q^{51}\) \(+4.17482 q^{52}\) \(+13.5183 q^{53}\) \(+20.9175 q^{54}\) \(-6.75018 q^{55}\) \(-15.6818 q^{56}\) \(+24.7553 q^{57}\) \(+7.16355 q^{58}\) \(+4.68363 q^{59}\) \(-39.9455 q^{60}\) \(+9.39936 q^{61}\) \(-3.91754 q^{62}\) \(+16.9243 q^{63}\) \(-5.65231 q^{64}\) \(+3.21951 q^{65}\) \(-15.4838 q^{66}\) \(+1.23974 q^{67}\) \(+0.765445 q^{68}\) \(+17.6407 q^{69}\) \(-23.2147 q^{70}\) \(+4.77974 q^{71}\) \(-31.5199 q^{72}\) \(+5.14672 q^{73}\) \(+17.9373 q^{74}\) \(-15.9452 q^{75}\) \(-34.7749 q^{76}\) \(-6.08395 q^{77}\) \(+7.38503 q^{78}\) \(-0.243317 q^{79}\) \(+16.3534 q^{80}\) \(+7.51990 q^{81}\) \(-14.3257 q^{82}\) \(-1.78723 q^{83}\) \(-36.0030 q^{84}\) \(+0.590291 q^{85}\) \(+5.84394 q^{86}\) \(+8.56754 q^{87}\) \(+11.3308 q^{88}\) \(+1.59612 q^{89}\) \(-46.6607 q^{90}\) \(+2.90175 q^{91}\) \(-24.7807 q^{92}\) \(-4.68535 q^{93}\) \(+10.8219 q^{94}\) \(-26.8174 q^{95}\) \(+5.38992 q^{96}\) \(+9.98920 q^{97}\) \(-3.52901 q^{98}\) \(-12.2285 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(134q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 33q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut -\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 16q^{6} \) \(\mathstrut -\mathstrut 32q^{7} \) \(\mathstrut -\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 101q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(134q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 33q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut -\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 16q^{6} \) \(\mathstrut -\mathstrut 32q^{7} \) \(\mathstrut -\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 101q^{9} \) \(\mathstrut -\mathstrut 33q^{10} \) \(\mathstrut -\mathstrut 47q^{11} \) \(\mathstrut -\mathstrut 53q^{12} \) \(\mathstrut +\mathstrut 134q^{13} \) \(\mathstrut -\mathstrut 28q^{14} \) \(\mathstrut -\mathstrut 30q^{15} \) \(\mathstrut +\mathstrut 30q^{16} \) \(\mathstrut -\mathstrut 17q^{17} \) \(\mathstrut -\mathstrut 14q^{18} \) \(\mathstrut -\mathstrut 87q^{19} \) \(\mathstrut -\mathstrut 12q^{20} \) \(\mathstrut -\mathstrut 24q^{21} \) \(\mathstrut -\mathstrut 52q^{22} \) \(\mathstrut -\mathstrut 44q^{23} \) \(\mathstrut -\mathstrut 36q^{24} \) \(\mathstrut +\mathstrut 58q^{25} \) \(\mathstrut -\mathstrut 6q^{26} \) \(\mathstrut -\mathstrut 117q^{27} \) \(\mathstrut -\mathstrut 71q^{28} \) \(\mathstrut -\mathstrut 42q^{29} \) \(\mathstrut -\mathstrut 21q^{30} \) \(\mathstrut -\mathstrut 82q^{31} \) \(\mathstrut -\mathstrut 31q^{32} \) \(\mathstrut +\mathstrut 12q^{33} \) \(\mathstrut -\mathstrut 30q^{34} \) \(\mathstrut -\mathstrut 54q^{35} \) \(\mathstrut +\mathstrut 32q^{36} \) \(\mathstrut -\mathstrut 55q^{37} \) \(\mathstrut -\mathstrut 12q^{38} \) \(\mathstrut -\mathstrut 33q^{39} \) \(\mathstrut -\mathstrut 86q^{40} \) \(\mathstrut -\mathstrut 16q^{41} \) \(\mathstrut +\mathstrut 6q^{42} \) \(\mathstrut -\mathstrut 148q^{43} \) \(\mathstrut -\mathstrut 54q^{44} \) \(\mathstrut -\mathstrut 24q^{45} \) \(\mathstrut -\mathstrut 57q^{46} \) \(\mathstrut -\mathstrut 21q^{47} \) \(\mathstrut -\mathstrut 82q^{48} \) \(\mathstrut +\mathstrut 12q^{49} \) \(\mathstrut -\mathstrut 17q^{50} \) \(\mathstrut -\mathstrut 123q^{51} \) \(\mathstrut +\mathstrut 98q^{52} \) \(\mathstrut -\mathstrut 17q^{53} \) \(\mathstrut -\mathstrut 10q^{54} \) \(\mathstrut -\mathstrut 148q^{55} \) \(\mathstrut -\mathstrut 47q^{56} \) \(\mathstrut -\mathstrut q^{57} \) \(\mathstrut -\mathstrut 58q^{58} \) \(\mathstrut -\mathstrut 64q^{59} \) \(\mathstrut -\mathstrut 16q^{60} \) \(\mathstrut -\mathstrut 112q^{61} \) \(\mathstrut -\mathstrut 15q^{62} \) \(\mathstrut -\mathstrut 58q^{63} \) \(\mathstrut -\mathstrut 65q^{64} \) \(\mathstrut -\mathstrut 8q^{65} \) \(\mathstrut -\mathstrut 20q^{66} \) \(\mathstrut -\mathstrut 110q^{67} \) \(\mathstrut -\mathstrut 8q^{68} \) \(\mathstrut -\mathstrut 57q^{69} \) \(\mathstrut -\mathstrut 40q^{70} \) \(\mathstrut -\mathstrut 78q^{71} \) \(\mathstrut -\mathstrut 28q^{72} \) \(\mathstrut -\mathstrut 43q^{73} \) \(\mathstrut -\mathstrut 52q^{74} \) \(\mathstrut -\mathstrut 150q^{75} \) \(\mathstrut -\mathstrut 96q^{76} \) \(\mathstrut -\mathstrut 24q^{77} \) \(\mathstrut -\mathstrut 16q^{78} \) \(\mathstrut -\mathstrut 228q^{79} \) \(\mathstrut +\mathstrut 20q^{80} \) \(\mathstrut +\mathstrut 54q^{81} \) \(\mathstrut -\mathstrut 89q^{82} \) \(\mathstrut -\mathstrut 12q^{83} \) \(\mathstrut +\mathstrut 6q^{84} \) \(\mathstrut -\mathstrut 77q^{85} \) \(\mathstrut +\mathstrut 29q^{86} \) \(\mathstrut -\mathstrut 77q^{87} \) \(\mathstrut -\mathstrut 95q^{88} \) \(\mathstrut -\mathstrut 32q^{89} \) \(\mathstrut -\mathstrut 46q^{90} \) \(\mathstrut -\mathstrut 32q^{91} \) \(\mathstrut -\mathstrut 62q^{92} \) \(\mathstrut -\mathstrut 9q^{93} \) \(\mathstrut -\mathstrut 87q^{94} \) \(\mathstrut -\mathstrut 61q^{95} \) \(\mathstrut -\mathstrut 54q^{96} \) \(\mathstrut -\mathstrut 38q^{97} \) \(\mathstrut +\mathstrut 6q^{98} \) \(\mathstrut -\mathstrut 193q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.48492 −1.75710 −0.878551 0.477648i \(-0.841490\pi\)
−0.878551 + 0.477648i \(0.841490\pi\)
\(3\) −2.97194 −1.71585 −0.857925 0.513775i \(-0.828247\pi\)
−0.857925 + 0.513775i \(0.828247\pi\)
\(4\) 4.17482 2.08741
\(5\) 3.21951 1.43981 0.719904 0.694074i \(-0.244186\pi\)
0.719904 + 0.694074i \(0.244186\pi\)
\(6\) 7.38503 3.01492
\(7\) 2.90175 1.09676 0.548380 0.836229i \(-0.315245\pi\)
0.548380 + 0.836229i \(0.315245\pi\)
\(8\) −5.40425 −1.91069
\(9\) 5.83242 1.94414
\(10\) −8.00022 −2.52989
\(11\) −2.09665 −0.632163 −0.316082 0.948732i \(-0.602367\pi\)
−0.316082 + 0.948732i \(0.602367\pi\)
\(12\) −12.4073 −3.58168
\(13\) 1.00000 0.277350
\(14\) −7.21062 −1.92712
\(15\) −9.56819 −2.47049
\(16\) 5.07949 1.26987
\(17\) 0.183348 0.0444684 0.0222342 0.999753i \(-0.492922\pi\)
0.0222342 + 0.999753i \(0.492922\pi\)
\(18\) −14.4931 −3.41606
\(19\) −8.32967 −1.91096 −0.955479 0.295060i \(-0.904660\pi\)
−0.955479 + 0.295060i \(0.904660\pi\)
\(20\) 13.4409 3.00547
\(21\) −8.62384 −1.88188
\(22\) 5.21000 1.11078
\(23\) −5.93575 −1.23769 −0.618844 0.785514i \(-0.712399\pi\)
−0.618844 + 0.785514i \(0.712399\pi\)
\(24\) 16.0611 3.27846
\(25\) 5.36524 1.07305
\(26\) −2.48492 −0.487333
\(27\) −8.41779 −1.62000
\(28\) 12.1143 2.28939
\(29\) −2.88281 −0.535325 −0.267662 0.963513i \(-0.586251\pi\)
−0.267662 + 0.963513i \(0.586251\pi\)
\(30\) 23.7762 4.34091
\(31\) 1.57653 0.283153 0.141576 0.989927i \(-0.454783\pi\)
0.141576 + 0.989927i \(0.454783\pi\)
\(32\) −1.81360 −0.320603
\(33\) 6.23111 1.08470
\(34\) −0.455605 −0.0781356
\(35\) 9.34222 1.57912
\(36\) 24.3493 4.05822
\(37\) −7.21849 −1.18671 −0.593356 0.804940i \(-0.702197\pi\)
−0.593356 + 0.804940i \(0.702197\pi\)
\(38\) 20.6986 3.35775
\(39\) −2.97194 −0.475891
\(40\) −17.3990 −2.75103
\(41\) 5.76504 0.900348 0.450174 0.892941i \(-0.351362\pi\)
0.450174 + 0.892941i \(0.351362\pi\)
\(42\) 21.4295 3.30665
\(43\) −2.35176 −0.358641 −0.179320 0.983791i \(-0.557390\pi\)
−0.179320 + 0.983791i \(0.557390\pi\)
\(44\) −8.75313 −1.31958
\(45\) 18.7775 2.79919
\(46\) 14.7498 2.17475
\(47\) −4.35501 −0.635244 −0.317622 0.948217i \(-0.602884\pi\)
−0.317622 + 0.948217i \(0.602884\pi\)
\(48\) −15.0959 −2.17891
\(49\) 1.42017 0.202882
\(50\) −13.3322 −1.88545
\(51\) −0.544899 −0.0763011
\(52\) 4.17482 0.578943
\(53\) 13.5183 1.85688 0.928442 0.371478i \(-0.121149\pi\)
0.928442 + 0.371478i \(0.121149\pi\)
\(54\) 20.9175 2.84652
\(55\) −6.75018 −0.910193
\(56\) −15.6818 −2.09557
\(57\) 24.7553 3.27892
\(58\) 7.16355 0.940621
\(59\) 4.68363 0.609757 0.304879 0.952391i \(-0.401384\pi\)
0.304879 + 0.952391i \(0.401384\pi\)
\(60\) −39.9455 −5.15694
\(61\) 9.39936 1.20347 0.601733 0.798698i \(-0.294477\pi\)
0.601733 + 0.798698i \(0.294477\pi\)
\(62\) −3.91754 −0.497528
\(63\) 16.9243 2.13226
\(64\) −5.65231 −0.706539
\(65\) 3.21951 0.399331
\(66\) −15.4838 −1.90592
\(67\) 1.23974 0.151458 0.0757289 0.997128i \(-0.475872\pi\)
0.0757289 + 0.997128i \(0.475872\pi\)
\(68\) 0.765445 0.0928238
\(69\) 17.6407 2.12369
\(70\) −23.2147 −2.77468
\(71\) 4.77974 0.567251 0.283625 0.958935i \(-0.408463\pi\)
0.283625 + 0.958935i \(0.408463\pi\)
\(72\) −31.5199 −3.71465
\(73\) 5.14672 0.602378 0.301189 0.953565i \(-0.402617\pi\)
0.301189 + 0.953565i \(0.402617\pi\)
\(74\) 17.9373 2.08517
\(75\) −15.9452 −1.84119
\(76\) −34.7749 −3.98895
\(77\) −6.08395 −0.693331
\(78\) 7.38503 0.836190
\(79\) −0.243317 −0.0273753 −0.0136877 0.999906i \(-0.504357\pi\)
−0.0136877 + 0.999906i \(0.504357\pi\)
\(80\) 16.3534 1.82837
\(81\) 7.51990 0.835544
\(82\) −14.3257 −1.58200
\(83\) −1.78723 −0.196174 −0.0980869 0.995178i \(-0.531272\pi\)
−0.0980869 + 0.995178i \(0.531272\pi\)
\(84\) −36.0030 −3.92825
\(85\) 0.590291 0.0640260
\(86\) 5.84394 0.630168
\(87\) 8.56754 0.918537
\(88\) 11.3308 1.20787
\(89\) 1.59612 0.169189 0.0845943 0.996415i \(-0.473041\pi\)
0.0845943 + 0.996415i \(0.473041\pi\)
\(90\) −46.6607 −4.91847
\(91\) 2.90175 0.304186
\(92\) −24.7807 −2.58356
\(93\) −4.68535 −0.485848
\(94\) 10.8219 1.11619
\(95\) −26.8174 −2.75141
\(96\) 5.38992 0.550107
\(97\) 9.98920 1.01425 0.507125 0.861873i \(-0.330708\pi\)
0.507125 + 0.861873i \(0.330708\pi\)
\(98\) −3.52901 −0.356484
\(99\) −12.2285 −1.22901
\(100\) 22.3989 2.23989
\(101\) −12.2968 −1.22358 −0.611790 0.791020i \(-0.709550\pi\)
−0.611790 + 0.791020i \(0.709550\pi\)
\(102\) 1.35403 0.134069
\(103\) 7.46049 0.735104 0.367552 0.930003i \(-0.380196\pi\)
0.367552 + 0.930003i \(0.380196\pi\)
\(104\) −5.40425 −0.529931
\(105\) −27.7645 −2.70954
\(106\) −33.5919 −3.26274
\(107\) −4.70758 −0.455099 −0.227550 0.973766i \(-0.573071\pi\)
−0.227550 + 0.973766i \(0.573071\pi\)
\(108\) −35.1428 −3.38162
\(109\) 5.95064 0.569968 0.284984 0.958532i \(-0.408012\pi\)
0.284984 + 0.958532i \(0.408012\pi\)
\(110\) 16.7736 1.59930
\(111\) 21.4529 2.03622
\(112\) 14.7394 1.39274
\(113\) 6.79701 0.639409 0.319705 0.947517i \(-0.396416\pi\)
0.319705 + 0.947517i \(0.396416\pi\)
\(114\) −61.5148 −5.76139
\(115\) −19.1102 −1.78203
\(116\) −12.0352 −1.11744
\(117\) 5.83242 0.539208
\(118\) −11.6385 −1.07141
\(119\) 0.532031 0.0487712
\(120\) 51.7089 4.72035
\(121\) −6.60407 −0.600370
\(122\) −23.3567 −2.11461
\(123\) −17.1333 −1.54486
\(124\) 6.58172 0.591056
\(125\) 1.17589 0.105174
\(126\) −42.0554 −3.74659
\(127\) 4.67102 0.414486 0.207243 0.978289i \(-0.433551\pi\)
0.207243 + 0.978289i \(0.433551\pi\)
\(128\) 17.6727 1.56206
\(129\) 6.98930 0.615373
\(130\) −8.00022 −0.701666
\(131\) 8.28139 0.723548 0.361774 0.932266i \(-0.382171\pi\)
0.361774 + 0.932266i \(0.382171\pi\)
\(132\) 26.0138 2.26421
\(133\) −24.1706 −2.09586
\(134\) −3.08064 −0.266127
\(135\) −27.1012 −2.33250
\(136\) −0.990859 −0.0849654
\(137\) −0.0830003 −0.00709119 −0.00354560 0.999994i \(-0.501129\pi\)
−0.00354560 + 0.999994i \(0.501129\pi\)
\(138\) −43.8356 −3.73154
\(139\) −6.32545 −0.536517 −0.268259 0.963347i \(-0.586448\pi\)
−0.268259 + 0.963347i \(0.586448\pi\)
\(140\) 39.0021 3.29628
\(141\) 12.9428 1.08998
\(142\) −11.8773 −0.996718
\(143\) −2.09665 −0.175330
\(144\) 29.6257 2.46881
\(145\) −9.28124 −0.770765
\(146\) −12.7892 −1.05844
\(147\) −4.22067 −0.348115
\(148\) −30.1359 −2.47715
\(149\) 4.21733 0.345497 0.172749 0.984966i \(-0.444735\pi\)
0.172749 + 0.984966i \(0.444735\pi\)
\(150\) 39.6224 3.23516
\(151\) −19.0672 −1.55167 −0.775835 0.630935i \(-0.782671\pi\)
−0.775835 + 0.630935i \(0.782671\pi\)
\(152\) 45.0156 3.65125
\(153\) 1.06936 0.0864529
\(154\) 15.1181 1.21825
\(155\) 5.07565 0.407686
\(156\) −12.4073 −0.993380
\(157\) −22.1506 −1.76781 −0.883904 0.467669i \(-0.845094\pi\)
−0.883904 + 0.467669i \(0.845094\pi\)
\(158\) 0.604624 0.0481013
\(159\) −40.1756 −3.18613
\(160\) −5.83892 −0.461607
\(161\) −17.2241 −1.35745
\(162\) −18.6863 −1.46814
\(163\) −3.69841 −0.289682 −0.144841 0.989455i \(-0.546267\pi\)
−0.144841 + 0.989455i \(0.546267\pi\)
\(164\) 24.0680 1.87940
\(165\) 20.0611 1.56176
\(166\) 4.44112 0.344698
\(167\) 1.11275 0.0861075 0.0430538 0.999073i \(-0.486291\pi\)
0.0430538 + 0.999073i \(0.486291\pi\)
\(168\) 46.6054 3.59568
\(169\) 1.00000 0.0769231
\(170\) −1.46682 −0.112500
\(171\) −48.5822 −3.71517
\(172\) −9.81819 −0.748630
\(173\) 11.4521 0.870688 0.435344 0.900264i \(-0.356627\pi\)
0.435344 + 0.900264i \(0.356627\pi\)
\(174\) −21.2896 −1.61396
\(175\) 15.5686 1.17688
\(176\) −10.6499 −0.802766
\(177\) −13.9195 −1.04625
\(178\) −3.96624 −0.297282
\(179\) 22.9916 1.71847 0.859237 0.511578i \(-0.170939\pi\)
0.859237 + 0.511578i \(0.170939\pi\)
\(180\) 78.3929 5.84306
\(181\) −12.6962 −0.943704 −0.471852 0.881678i \(-0.656414\pi\)
−0.471852 + 0.881678i \(0.656414\pi\)
\(182\) −7.21062 −0.534487
\(183\) −27.9343 −2.06497
\(184\) 32.0783 2.36484
\(185\) −23.2400 −1.70864
\(186\) 11.6427 0.853684
\(187\) −0.384416 −0.0281113
\(188\) −18.1814 −1.32602
\(189\) −24.4264 −1.77676
\(190\) 66.6392 4.83451
\(191\) −16.0887 −1.16414 −0.582070 0.813139i \(-0.697757\pi\)
−0.582070 + 0.813139i \(0.697757\pi\)
\(192\) 16.7983 1.21231
\(193\) −3.64340 −0.262258 −0.131129 0.991365i \(-0.541860\pi\)
−0.131129 + 0.991365i \(0.541860\pi\)
\(194\) −24.8223 −1.78214
\(195\) −9.56819 −0.685192
\(196\) 5.92897 0.423498
\(197\) 22.6044 1.61050 0.805248 0.592939i \(-0.202032\pi\)
0.805248 + 0.592939i \(0.202032\pi\)
\(198\) 30.3869 2.15950
\(199\) 7.00495 0.496568 0.248284 0.968687i \(-0.420133\pi\)
0.248284 + 0.968687i \(0.420133\pi\)
\(200\) −28.9951 −2.05026
\(201\) −3.68442 −0.259879
\(202\) 30.5566 2.14996
\(203\) −8.36521 −0.587123
\(204\) −2.27486 −0.159272
\(205\) 18.5606 1.29633
\(206\) −18.5387 −1.29165
\(207\) −34.6198 −2.40624
\(208\) 5.07949 0.352199
\(209\) 17.4644 1.20804
\(210\) 68.9926 4.76094
\(211\) −9.47921 −0.652576 −0.326288 0.945270i \(-0.605798\pi\)
−0.326288 + 0.945270i \(0.605798\pi\)
\(212\) 56.4365 3.87608
\(213\) −14.2051 −0.973317
\(214\) 11.6980 0.799656
\(215\) −7.57152 −0.516374
\(216\) 45.4919 3.09533
\(217\) 4.57469 0.310551
\(218\) −14.7869 −1.00149
\(219\) −15.2957 −1.03359
\(220\) −28.1808 −1.89995
\(221\) 0.183348 0.0123333
\(222\) −53.3087 −3.57785
\(223\) 17.5511 1.17531 0.587654 0.809112i \(-0.300052\pi\)
0.587654 + 0.809112i \(0.300052\pi\)
\(224\) −5.26263 −0.351624
\(225\) 31.2923 2.08616
\(226\) −16.8900 −1.12351
\(227\) 12.2735 0.814618 0.407309 0.913290i \(-0.366467\pi\)
0.407309 + 0.913290i \(0.366467\pi\)
\(228\) 103.349 6.84444
\(229\) −13.0076 −0.859565 −0.429782 0.902933i \(-0.641410\pi\)
−0.429782 + 0.902933i \(0.641410\pi\)
\(230\) 47.4873 3.13122
\(231\) 18.0811 1.18965
\(232\) 15.5794 1.02284
\(233\) 14.0818 0.922529 0.461264 0.887263i \(-0.347396\pi\)
0.461264 + 0.887263i \(0.347396\pi\)
\(234\) −14.4931 −0.947444
\(235\) −14.0210 −0.914630
\(236\) 19.5533 1.27281
\(237\) 0.723124 0.0469720
\(238\) −1.32205 −0.0856960
\(239\) −6.81839 −0.441045 −0.220522 0.975382i \(-0.570776\pi\)
−0.220522 + 0.975382i \(0.570776\pi\)
\(240\) −48.6015 −3.13721
\(241\) −12.9302 −0.832905 −0.416452 0.909157i \(-0.636727\pi\)
−0.416452 + 0.909157i \(0.636727\pi\)
\(242\) 16.4106 1.05491
\(243\) 2.90470 0.186336
\(244\) 39.2407 2.51213
\(245\) 4.57226 0.292111
\(246\) 42.5750 2.71448
\(247\) −8.32967 −0.530004
\(248\) −8.51995 −0.541018
\(249\) 5.31154 0.336605
\(250\) −2.92198 −0.184802
\(251\) −10.8124 −0.682472 −0.341236 0.939978i \(-0.610846\pi\)
−0.341236 + 0.939978i \(0.610846\pi\)
\(252\) 70.6557 4.45089
\(253\) 12.4452 0.782421
\(254\) −11.6071 −0.728295
\(255\) −1.75431 −0.109859
\(256\) −32.6107 −2.03817
\(257\) 22.8276 1.42395 0.711974 0.702206i \(-0.247801\pi\)
0.711974 + 0.702206i \(0.247801\pi\)
\(258\) −17.3678 −1.08127
\(259\) −20.9463 −1.30154
\(260\) 13.4409 0.833568
\(261\) −16.8138 −1.04075
\(262\) −20.5786 −1.27135
\(263\) 21.5441 1.32847 0.664235 0.747524i \(-0.268758\pi\)
0.664235 + 0.747524i \(0.268758\pi\)
\(264\) −33.6745 −2.07252
\(265\) 43.5223 2.67356
\(266\) 60.0621 3.68264
\(267\) −4.74358 −0.290302
\(268\) 5.17568 0.316155
\(269\) −13.1105 −0.799363 −0.399682 0.916654i \(-0.630879\pi\)
−0.399682 + 0.916654i \(0.630879\pi\)
\(270\) 67.3442 4.09844
\(271\) 4.56445 0.277270 0.138635 0.990344i \(-0.455728\pi\)
0.138635 + 0.990344i \(0.455728\pi\)
\(272\) 0.931314 0.0564692
\(273\) −8.62384 −0.521938
\(274\) 0.206249 0.0124600
\(275\) −11.2490 −0.678341
\(276\) 73.6467 4.43301
\(277\) −14.6492 −0.880186 −0.440093 0.897952i \(-0.645055\pi\)
−0.440093 + 0.897952i \(0.645055\pi\)
\(278\) 15.7182 0.942716
\(279\) 9.19498 0.550489
\(280\) −50.4877 −3.01722
\(281\) −16.8473 −1.00503 −0.502513 0.864570i \(-0.667591\pi\)
−0.502513 + 0.864570i \(0.667591\pi\)
\(282\) −32.1619 −1.91521
\(283\) −12.5817 −0.747906 −0.373953 0.927448i \(-0.621998\pi\)
−0.373953 + 0.927448i \(0.621998\pi\)
\(284\) 19.9546 1.18409
\(285\) 79.6998 4.72101
\(286\) 5.21000 0.308074
\(287\) 16.7287 0.987465
\(288\) −10.5777 −0.623298
\(289\) −16.9664 −0.998023
\(290\) 23.0631 1.35431
\(291\) −29.6873 −1.74030
\(292\) 21.4866 1.25741
\(293\) −13.8851 −0.811176 −0.405588 0.914056i \(-0.632933\pi\)
−0.405588 + 0.914056i \(0.632933\pi\)
\(294\) 10.4880 0.611673
\(295\) 15.0790 0.877933
\(296\) 39.0105 2.26744
\(297\) 17.6491 1.02411
\(298\) −10.4797 −0.607074
\(299\) −5.93575 −0.343273
\(300\) −66.5682 −3.84332
\(301\) −6.82424 −0.393342
\(302\) 47.3806 2.72644
\(303\) 36.5454 2.09948
\(304\) −42.3104 −2.42667
\(305\) 30.2613 1.73276
\(306\) −2.65728 −0.151907
\(307\) −22.8210 −1.30246 −0.651231 0.758880i \(-0.725747\pi\)
−0.651231 + 0.758880i \(0.725747\pi\)
\(308\) −25.3994 −1.44727
\(309\) −22.1721 −1.26133
\(310\) −12.6126 −0.716346
\(311\) −30.3364 −1.72022 −0.860109 0.510110i \(-0.829605\pi\)
−0.860109 + 0.510110i \(0.829605\pi\)
\(312\) 16.0611 0.909281
\(313\) 33.2689 1.88047 0.940235 0.340528i \(-0.110606\pi\)
0.940235 + 0.340528i \(0.110606\pi\)
\(314\) 55.0424 3.10622
\(315\) 54.4878 3.07004
\(316\) −1.01581 −0.0571436
\(317\) −3.63936 −0.204407 −0.102203 0.994764i \(-0.532589\pi\)
−0.102203 + 0.994764i \(0.532589\pi\)
\(318\) 99.8331 5.59836
\(319\) 6.04424 0.338412
\(320\) −18.1977 −1.01728
\(321\) 13.9907 0.780882
\(322\) 42.8004 2.38517
\(323\) −1.52723 −0.0849773
\(324\) 31.3942 1.74412
\(325\) 5.36524 0.297610
\(326\) 9.19025 0.509001
\(327\) −17.6849 −0.977979
\(328\) −31.1557 −1.72029
\(329\) −12.6372 −0.696710
\(330\) −49.8502 −2.74416
\(331\) −1.20071 −0.0659969 −0.0329985 0.999455i \(-0.510506\pi\)
−0.0329985 + 0.999455i \(0.510506\pi\)
\(332\) −7.46136 −0.409495
\(333\) −42.1013 −2.30714
\(334\) −2.76510 −0.151300
\(335\) 3.99134 0.218070
\(336\) −43.8046 −2.38974
\(337\) 33.3699 1.81777 0.908887 0.417042i \(-0.136933\pi\)
0.908887 + 0.417042i \(0.136933\pi\)
\(338\) −2.48492 −0.135162
\(339\) −20.2003 −1.09713
\(340\) 2.46436 0.133649
\(341\) −3.30542 −0.178999
\(342\) 120.723 6.52794
\(343\) −16.1913 −0.874247
\(344\) 12.7095 0.685251
\(345\) 56.7943 3.05770
\(346\) −28.4576 −1.52989
\(347\) −5.77220 −0.309868 −0.154934 0.987925i \(-0.549517\pi\)
−0.154934 + 0.987925i \(0.549517\pi\)
\(348\) 35.7679 1.91736
\(349\) −31.7550 −1.69980 −0.849902 0.526940i \(-0.823339\pi\)
−0.849902 + 0.526940i \(0.823339\pi\)
\(350\) −38.6867 −2.06789
\(351\) −8.41779 −0.449309
\(352\) 3.80249 0.202673
\(353\) −23.6652 −1.25957 −0.629785 0.776770i \(-0.716857\pi\)
−0.629785 + 0.776770i \(0.716857\pi\)
\(354\) 34.5888 1.83837
\(355\) 15.3884 0.816732
\(356\) 6.66353 0.353166
\(357\) −1.58116 −0.0836840
\(358\) −57.1323 −3.01953
\(359\) −3.84041 −0.202689 −0.101345 0.994851i \(-0.532314\pi\)
−0.101345 + 0.994851i \(0.532314\pi\)
\(360\) −101.479 −5.34839
\(361\) 50.3834 2.65176
\(362\) 31.5491 1.65818
\(363\) 19.6269 1.03014
\(364\) 12.1143 0.634962
\(365\) 16.5699 0.867308
\(366\) 69.4146 3.62836
\(367\) −25.3415 −1.32281 −0.661407 0.750027i \(-0.730040\pi\)
−0.661407 + 0.750027i \(0.730040\pi\)
\(368\) −30.1505 −1.57171
\(369\) 33.6241 1.75040
\(370\) 57.7495 3.00225
\(371\) 39.2268 2.03656
\(372\) −19.5605 −1.01416
\(373\) −25.6899 −1.33017 −0.665087 0.746766i \(-0.731606\pi\)
−0.665087 + 0.746766i \(0.731606\pi\)
\(374\) 0.955243 0.0493944
\(375\) −3.49466 −0.180464
\(376\) 23.5356 1.21376
\(377\) −2.88281 −0.148472
\(378\) 60.6975 3.12194
\(379\) −17.4252 −0.895073 −0.447537 0.894266i \(-0.647699\pi\)
−0.447537 + 0.894266i \(0.647699\pi\)
\(380\) −111.958 −5.74333
\(381\) −13.8820 −0.711196
\(382\) 39.9792 2.04551
\(383\) −36.0833 −1.84377 −0.921885 0.387464i \(-0.873351\pi\)
−0.921885 + 0.387464i \(0.873351\pi\)
\(384\) −52.5223 −2.68027
\(385\) −19.5873 −0.998263
\(386\) 9.05355 0.460814
\(387\) −13.7165 −0.697248
\(388\) 41.7031 2.11715
\(389\) −3.90269 −0.197874 −0.0989370 0.995094i \(-0.531544\pi\)
−0.0989370 + 0.995094i \(0.531544\pi\)
\(390\) 23.7762 1.20395
\(391\) −1.08831 −0.0550381
\(392\) −7.67497 −0.387645
\(393\) −24.6118 −1.24150
\(394\) −56.1700 −2.82981
\(395\) −0.783362 −0.0394152
\(396\) −51.0519 −2.56546
\(397\) 24.8256 1.24596 0.622981 0.782237i \(-0.285921\pi\)
0.622981 + 0.782237i \(0.285921\pi\)
\(398\) −17.4067 −0.872521
\(399\) 71.8337 3.59618
\(400\) 27.2526 1.36263
\(401\) −24.5023 −1.22359 −0.611793 0.791018i \(-0.709552\pi\)
−0.611793 + 0.791018i \(0.709552\pi\)
\(402\) 9.15549 0.456634
\(403\) 1.57653 0.0785324
\(404\) −51.3371 −2.55411
\(405\) 24.2104 1.20302
\(406\) 20.7869 1.03163
\(407\) 15.1346 0.750195
\(408\) 2.94477 0.145788
\(409\) −3.83502 −0.189630 −0.0948148 0.995495i \(-0.530226\pi\)
−0.0948148 + 0.995495i \(0.530226\pi\)
\(410\) −46.1216 −2.27778
\(411\) 0.246672 0.0121674
\(412\) 31.1462 1.53446
\(413\) 13.5908 0.668757
\(414\) 86.0274 4.22801
\(415\) −5.75400 −0.282453
\(416\) −1.81360 −0.0889193
\(417\) 18.7988 0.920583
\(418\) −43.3976 −2.12264
\(419\) −10.5334 −0.514592 −0.257296 0.966333i \(-0.582831\pi\)
−0.257296 + 0.966333i \(0.582831\pi\)
\(420\) −115.912 −5.65592
\(421\) −17.4816 −0.852000 −0.426000 0.904723i \(-0.640078\pi\)
−0.426000 + 0.904723i \(0.640078\pi\)
\(422\) 23.5551 1.14664
\(423\) −25.4003 −1.23500
\(424\) −73.0564 −3.54793
\(425\) 0.983706 0.0477167
\(426\) 35.2985 1.71022
\(427\) 27.2746 1.31991
\(428\) −19.6533 −0.949979
\(429\) 6.23111 0.300841
\(430\) 18.8146 0.907321
\(431\) 20.5691 0.990779 0.495390 0.868671i \(-0.335025\pi\)
0.495390 + 0.868671i \(0.335025\pi\)
\(432\) −42.7581 −2.05720
\(433\) −31.5371 −1.51558 −0.757788 0.652501i \(-0.773720\pi\)
−0.757788 + 0.652501i \(0.773720\pi\)
\(434\) −11.3677 −0.545669
\(435\) 27.5833 1.32252
\(436\) 24.8428 1.18976
\(437\) 49.4428 2.36517
\(438\) 38.0086 1.81612
\(439\) 3.48597 0.166376 0.0831880 0.996534i \(-0.473490\pi\)
0.0831880 + 0.996534i \(0.473490\pi\)
\(440\) 36.4797 1.73910
\(441\) 8.28305 0.394431
\(442\) −0.455605 −0.0216709
\(443\) 2.79285 0.132692 0.0663461 0.997797i \(-0.478866\pi\)
0.0663461 + 0.997797i \(0.478866\pi\)
\(444\) 89.5620 4.25043
\(445\) 5.13873 0.243599
\(446\) −43.6130 −2.06514
\(447\) −12.5336 −0.592821
\(448\) −16.4016 −0.774903
\(449\) −32.2595 −1.52242 −0.761209 0.648506i \(-0.775394\pi\)
−0.761209 + 0.648506i \(0.775394\pi\)
\(450\) −77.7589 −3.66559
\(451\) −12.0873 −0.569167
\(452\) 28.3763 1.33471
\(453\) 56.6667 2.66243
\(454\) −30.4985 −1.43137
\(455\) 9.34222 0.437970
\(456\) −133.784 −6.26500
\(457\) −36.3839 −1.70197 −0.850983 0.525193i \(-0.823993\pi\)
−0.850983 + 0.525193i \(0.823993\pi\)
\(458\) 32.3228 1.51034
\(459\) −1.54339 −0.0720391
\(460\) −79.7816 −3.71984
\(461\) 10.2042 0.475255 0.237627 0.971356i \(-0.423630\pi\)
0.237627 + 0.971356i \(0.423630\pi\)
\(462\) −44.9302 −2.09034
\(463\) −2.94791 −0.137001 −0.0685004 0.997651i \(-0.521821\pi\)
−0.0685004 + 0.997651i \(0.521821\pi\)
\(464\) −14.6432 −0.679794
\(465\) −15.0845 −0.699527
\(466\) −34.9921 −1.62098
\(467\) −28.3766 −1.31311 −0.656556 0.754277i \(-0.727987\pi\)
−0.656556 + 0.754277i \(0.727987\pi\)
\(468\) 24.3493 1.12555
\(469\) 3.59741 0.166113
\(470\) 34.8411 1.60710
\(471\) 65.8301 3.03329
\(472\) −25.3115 −1.16506
\(473\) 4.93082 0.226719
\(474\) −1.79691 −0.0825346
\(475\) −44.6907 −2.05055
\(476\) 2.22113 0.101805
\(477\) 78.8446 3.61004
\(478\) 16.9431 0.774961
\(479\) −15.1302 −0.691315 −0.345658 0.938361i \(-0.612344\pi\)
−0.345658 + 0.938361i \(0.612344\pi\)
\(480\) 17.3529 0.792048
\(481\) −7.21849 −0.329135
\(482\) 32.1304 1.46350
\(483\) 51.1889 2.32918
\(484\) −27.5708 −1.25322
\(485\) 32.1603 1.46032
\(486\) −7.21793 −0.327412
\(487\) 22.6418 1.02600 0.513000 0.858389i \(-0.328534\pi\)
0.513000 + 0.858389i \(0.328534\pi\)
\(488\) −50.7965 −2.29945
\(489\) 10.9914 0.497050
\(490\) −11.3617 −0.513269
\(491\) 39.8025 1.79626 0.898131 0.439729i \(-0.144925\pi\)
0.898131 + 0.439729i \(0.144925\pi\)
\(492\) −71.5286 −3.22476
\(493\) −0.528558 −0.0238050
\(494\) 20.6986 0.931272
\(495\) −39.3699 −1.76954
\(496\) 8.00795 0.359568
\(497\) 13.8696 0.622138
\(498\) −13.1987 −0.591450
\(499\) 5.11428 0.228946 0.114473 0.993426i \(-0.463482\pi\)
0.114473 + 0.993426i \(0.463482\pi\)
\(500\) 4.90911 0.219542
\(501\) −3.30704 −0.147748
\(502\) 26.8679 1.19917
\(503\) 5.84452 0.260594 0.130297 0.991475i \(-0.458407\pi\)
0.130297 + 0.991475i \(0.458407\pi\)
\(504\) −91.4629 −4.07408
\(505\) −39.5898 −1.76172
\(506\) −30.9252 −1.37479
\(507\) −2.97194 −0.131988
\(508\) 19.5007 0.865203
\(509\) 12.9254 0.572909 0.286455 0.958094i \(-0.407523\pi\)
0.286455 + 0.958094i \(0.407523\pi\)
\(510\) 4.35931 0.193034
\(511\) 14.9345 0.660663
\(512\) 45.6895 2.01921
\(513\) 70.1174 3.09576
\(514\) −56.7248 −2.50202
\(515\) 24.0191 1.05841
\(516\) 29.1791 1.28454
\(517\) 9.13093 0.401578
\(518\) 52.0498 2.28694
\(519\) −34.0350 −1.49397
\(520\) −17.3990 −0.762998
\(521\) −43.6812 −1.91371 −0.956854 0.290570i \(-0.906155\pi\)
−0.956854 + 0.290570i \(0.906155\pi\)
\(522\) 41.7809 1.82870
\(523\) −29.5266 −1.29111 −0.645555 0.763714i \(-0.723374\pi\)
−0.645555 + 0.763714i \(0.723374\pi\)
\(524\) 34.5733 1.51034
\(525\) −46.2689 −2.01934
\(526\) −53.5355 −2.33426
\(527\) 0.289053 0.0125914
\(528\) 31.6508 1.37743
\(529\) 12.2331 0.531873
\(530\) −108.149 −4.69771
\(531\) 27.3169 1.18545
\(532\) −100.908 −4.37492
\(533\) 5.76504 0.249712
\(534\) 11.7874 0.510091
\(535\) −15.1561 −0.655256
\(536\) −6.69985 −0.289389
\(537\) −68.3297 −2.94864
\(538\) 32.5786 1.40456
\(539\) −2.97760 −0.128254
\(540\) −113.142 −4.86888
\(541\) −3.99342 −0.171690 −0.0858452 0.996308i \(-0.527359\pi\)
−0.0858452 + 0.996308i \(0.527359\pi\)
\(542\) −11.3423 −0.487193
\(543\) 37.7324 1.61925
\(544\) −0.332521 −0.0142567
\(545\) 19.1581 0.820644
\(546\) 21.4295 0.917099
\(547\) −8.54036 −0.365160 −0.182580 0.983191i \(-0.558445\pi\)
−0.182580 + 0.983191i \(0.558445\pi\)
\(548\) −0.346511 −0.0148022
\(549\) 54.8211 2.33971
\(550\) 27.9529 1.19191
\(551\) 24.0129 1.02298
\(552\) −95.3347 −4.05771
\(553\) −0.706047 −0.0300242
\(554\) 36.4021 1.54658
\(555\) 69.0678 2.93177
\(556\) −26.4076 −1.11993
\(557\) −13.6219 −0.577176 −0.288588 0.957453i \(-0.593186\pi\)
−0.288588 + 0.957453i \(0.593186\pi\)
\(558\) −22.8488 −0.967266
\(559\) −2.35176 −0.0994690
\(560\) 47.4537 2.00528
\(561\) 1.14246 0.0482348
\(562\) 41.8642 1.76593
\(563\) −38.0085 −1.60187 −0.800934 0.598752i \(-0.795663\pi\)
−0.800934 + 0.598752i \(0.795663\pi\)
\(564\) 54.0340 2.27524
\(565\) 21.8830 0.920626
\(566\) 31.2646 1.31415
\(567\) 21.8209 0.916391
\(568\) −25.8309 −1.08384
\(569\) −8.74108 −0.366445 −0.183223 0.983071i \(-0.558653\pi\)
−0.183223 + 0.983071i \(0.558653\pi\)
\(570\) −198.048 −8.29530
\(571\) 32.3302 1.35298 0.676488 0.736454i \(-0.263501\pi\)
0.676488 + 0.736454i \(0.263501\pi\)
\(572\) −8.75313 −0.365987
\(573\) 47.8147 1.99749
\(574\) −41.5695 −1.73508
\(575\) −31.8467 −1.32810
\(576\) −32.9667 −1.37361
\(577\) 27.6053 1.14922 0.574612 0.818426i \(-0.305153\pi\)
0.574612 + 0.818426i \(0.305153\pi\)
\(578\) 42.1601 1.75363
\(579\) 10.8280 0.449995
\(580\) −38.7475 −1.60890
\(581\) −5.18610 −0.215156
\(582\) 73.7705 3.05789
\(583\) −28.3431 −1.17385
\(584\) −27.8142 −1.15096
\(585\) 18.7775 0.776356
\(586\) 34.5033 1.42532
\(587\) −13.3971 −0.552957 −0.276479 0.961020i \(-0.589167\pi\)
−0.276479 + 0.961020i \(0.589167\pi\)
\(588\) −17.6205 −0.726658
\(589\) −13.1320 −0.541093
\(590\) −37.4701 −1.54262
\(591\) −67.1788 −2.76337
\(592\) −36.6662 −1.50697
\(593\) 16.9036 0.694149 0.347074 0.937838i \(-0.387175\pi\)
0.347074 + 0.937838i \(0.387175\pi\)
\(594\) −43.8567 −1.79946
\(595\) 1.71288 0.0702211
\(596\) 17.6066 0.721194
\(597\) −20.8183 −0.852036
\(598\) 14.7498 0.603166
\(599\) 45.8957 1.87525 0.937625 0.347649i \(-0.113020\pi\)
0.937625 + 0.347649i \(0.113020\pi\)
\(600\) 86.1717 3.51794
\(601\) −20.8397 −0.850069 −0.425034 0.905177i \(-0.639738\pi\)
−0.425034 + 0.905177i \(0.639738\pi\)
\(602\) 16.9577 0.691143
\(603\) 7.23067 0.294456
\(604\) −79.6023 −3.23897
\(605\) −21.2619 −0.864418
\(606\) −90.8124 −3.68900
\(607\) −0.990550 −0.0402052 −0.0201026 0.999798i \(-0.506399\pi\)
−0.0201026 + 0.999798i \(0.506399\pi\)
\(608\) 15.1067 0.612659
\(609\) 24.8609 1.00741
\(610\) −75.1970 −3.04464
\(611\) −4.35501 −0.176185
\(612\) 4.46440 0.180463
\(613\) −26.2120 −1.05869 −0.529347 0.848406i \(-0.677563\pi\)
−0.529347 + 0.848406i \(0.677563\pi\)
\(614\) 56.7083 2.28856
\(615\) −55.1610 −2.22430
\(616\) 32.8792 1.32474
\(617\) 1.00000 0.0402585
\(618\) 55.0959 2.21628
\(619\) 4.04060 0.162406 0.0812028 0.996698i \(-0.474124\pi\)
0.0812028 + 0.996698i \(0.474124\pi\)
\(620\) 21.1899 0.851007
\(621\) 49.9659 2.00506
\(622\) 75.3834 3.02260
\(623\) 4.63155 0.185559
\(624\) −15.0959 −0.604321
\(625\) −23.0404 −0.921616
\(626\) −82.6705 −3.30418
\(627\) −51.9031 −2.07281
\(628\) −92.4746 −3.69014
\(629\) −1.32349 −0.0527712
\(630\) −135.398 −5.39437
\(631\) −34.5964 −1.37726 −0.688630 0.725112i \(-0.741788\pi\)
−0.688630 + 0.725112i \(0.741788\pi\)
\(632\) 1.31495 0.0523058
\(633\) 28.1716 1.11972
\(634\) 9.04350 0.359163
\(635\) 15.0384 0.596781
\(636\) −167.726 −6.65077
\(637\) 1.42017 0.0562693
\(638\) −15.0194 −0.594625
\(639\) 27.8775 1.10282
\(640\) 56.8976 2.24907
\(641\) 7.12855 0.281561 0.140780 0.990041i \(-0.455039\pi\)
0.140780 + 0.990041i \(0.455039\pi\)
\(642\) −34.7656 −1.37209
\(643\) 21.7734 0.858660 0.429330 0.903148i \(-0.358750\pi\)
0.429330 + 0.903148i \(0.358750\pi\)
\(644\) −71.9074 −2.83355
\(645\) 22.5021 0.886020
\(646\) 3.79504 0.149314
\(647\) 3.00795 0.118255 0.0591273 0.998250i \(-0.481168\pi\)
0.0591273 + 0.998250i \(0.481168\pi\)
\(648\) −40.6394 −1.59647
\(649\) −9.81993 −0.385466
\(650\) −13.3322 −0.522931
\(651\) −13.5957 −0.532858
\(652\) −15.4402 −0.604685
\(653\) −27.3771 −1.07135 −0.535675 0.844424i \(-0.679943\pi\)
−0.535675 + 0.844424i \(0.679943\pi\)
\(654\) 43.9456 1.71841
\(655\) 26.6620 1.04177
\(656\) 29.2834 1.14333
\(657\) 30.0178 1.17111
\(658\) 31.4024 1.22419
\(659\) 19.1916 0.747599 0.373800 0.927510i \(-0.378055\pi\)
0.373800 + 0.927510i \(0.378055\pi\)
\(660\) 83.7515 3.26002
\(661\) −14.8002 −0.575659 −0.287830 0.957682i \(-0.592934\pi\)
−0.287830 + 0.957682i \(0.592934\pi\)
\(662\) 2.98366 0.115963
\(663\) −0.544899 −0.0211621
\(664\) 9.65864 0.374828
\(665\) −77.8176 −3.01764
\(666\) 104.618 4.05387
\(667\) 17.1116 0.662565
\(668\) 4.64555 0.179742
\(669\) −52.1608 −2.01665
\(670\) −9.91816 −0.383172
\(671\) −19.7072 −0.760786
\(672\) 15.6402 0.603335
\(673\) −14.3569 −0.553418 −0.276709 0.960954i \(-0.589244\pi\)
−0.276709 + 0.960954i \(0.589244\pi\)
\(674\) −82.9215 −3.19402
\(675\) −45.1635 −1.73834
\(676\) 4.17482 0.160570
\(677\) −1.98720 −0.0763745 −0.0381872 0.999271i \(-0.512158\pi\)
−0.0381872 + 0.999271i \(0.512158\pi\)
\(678\) 50.1961 1.92777
\(679\) 28.9862 1.11239
\(680\) −3.19008 −0.122334
\(681\) −36.4760 −1.39776
\(682\) 8.21371 0.314519
\(683\) −16.9832 −0.649845 −0.324922 0.945741i \(-0.605338\pi\)
−0.324922 + 0.945741i \(0.605338\pi\)
\(684\) −202.822 −7.75509
\(685\) −0.267220 −0.0102100
\(686\) 40.2340 1.53614
\(687\) 38.6577 1.47488
\(688\) −11.9457 −0.455427
\(689\) 13.5183 0.515007
\(690\) −141.129 −5.37270
\(691\) −48.6796 −1.85186 −0.925930 0.377695i \(-0.876717\pi\)
−0.925930 + 0.377695i \(0.876717\pi\)
\(692\) 47.8105 1.81748
\(693\) −35.4842 −1.34793
\(694\) 14.3435 0.544470
\(695\) −20.3648 −0.772482
\(696\) −46.3012 −1.75504
\(697\) 1.05701 0.0400370
\(698\) 78.9085 2.98673
\(699\) −41.8502 −1.58292
\(700\) 64.9961 2.45662
\(701\) −1.24801 −0.0471367 −0.0235684 0.999722i \(-0.507503\pi\)
−0.0235684 + 0.999722i \(0.507503\pi\)
\(702\) 20.9175 0.789481
\(703\) 60.1276 2.26776
\(704\) 11.8509 0.446648
\(705\) 41.6696 1.56937
\(706\) 58.8060 2.21319
\(707\) −35.6824 −1.34197
\(708\) −58.1113 −2.18396
\(709\) −20.6672 −0.776175 −0.388087 0.921623i \(-0.626864\pi\)
−0.388087 + 0.921623i \(0.626864\pi\)
\(710\) −38.2390 −1.43508
\(711\) −1.41913 −0.0532215
\(712\) −8.62585 −0.323267
\(713\) −9.35787 −0.350455
\(714\) 3.92906 0.147041
\(715\) −6.75018 −0.252442
\(716\) 95.9858 3.58716
\(717\) 20.2638 0.756767
\(718\) 9.54311 0.356146
\(719\) −37.6928 −1.40570 −0.702852 0.711336i \(-0.748090\pi\)
−0.702852 + 0.711336i \(0.748090\pi\)
\(720\) 95.3803 3.55461
\(721\) 21.6485 0.806233
\(722\) −125.199 −4.65941
\(723\) 38.4277 1.42914
\(724\) −53.0045 −1.96990
\(725\) −15.4670 −0.574429
\(726\) −48.7712 −1.81007
\(727\) 1.38852 0.0514975 0.0257488 0.999668i \(-0.491803\pi\)
0.0257488 + 0.999668i \(0.491803\pi\)
\(728\) −15.6818 −0.581206
\(729\) −31.1923 −1.15527
\(730\) −41.1749 −1.52395
\(731\) −0.431191 −0.0159482
\(732\) −116.621 −4.31043
\(733\) −14.5001 −0.535573 −0.267786 0.963478i \(-0.586292\pi\)
−0.267786 + 0.963478i \(0.586292\pi\)
\(734\) 62.9715 2.32432
\(735\) −13.5885 −0.501218
\(736\) 10.7651 0.396807
\(737\) −2.59929 −0.0957461
\(738\) −83.5533 −3.07564
\(739\) −19.3119 −0.710401 −0.355201 0.934790i \(-0.615587\pi\)
−0.355201 + 0.934790i \(0.615587\pi\)
\(740\) −97.0227 −3.56663
\(741\) 24.7553 0.909408
\(742\) −97.4755 −3.57844
\(743\) −15.9681 −0.585814 −0.292907 0.956141i \(-0.594623\pi\)
−0.292907 + 0.956141i \(0.594623\pi\)
\(744\) 25.3208 0.928305
\(745\) 13.5777 0.497449
\(746\) 63.8374 2.33725
\(747\) −10.4239 −0.381390
\(748\) −1.60487 −0.0586798
\(749\) −13.6602 −0.499135
\(750\) 8.68395 0.317093
\(751\) −18.6995 −0.682353 −0.341177 0.939999i \(-0.610825\pi\)
−0.341177 + 0.939999i \(0.610825\pi\)
\(752\) −22.1212 −0.806678
\(753\) 32.1338 1.17102
\(754\) 7.16355 0.260881
\(755\) −61.3872 −2.23411
\(756\) −101.976 −3.70882
\(757\) 5.08915 0.184968 0.0924841 0.995714i \(-0.470519\pi\)
0.0924841 + 0.995714i \(0.470519\pi\)
\(758\) 43.3002 1.57274
\(759\) −36.9863 −1.34252
\(760\) 144.928 5.25710
\(761\) 18.4394 0.668428 0.334214 0.942497i \(-0.391529\pi\)
0.334214 + 0.942497i \(0.391529\pi\)
\(762\) 34.4956 1.24964
\(763\) 17.2673 0.625118
\(764\) −67.1675 −2.43004
\(765\) 3.44282 0.124476
\(766\) 89.6640 3.23969
\(767\) 4.68363 0.169116
\(768\) 96.9170 3.49719
\(769\) 28.5432 1.02929 0.514647 0.857402i \(-0.327923\pi\)
0.514647 + 0.857402i \(0.327923\pi\)
\(770\) 48.6730 1.75405
\(771\) −67.8423 −2.44328
\(772\) −15.2105 −0.547439
\(773\) 34.0584 1.22500 0.612498 0.790472i \(-0.290165\pi\)
0.612498 + 0.790472i \(0.290165\pi\)
\(774\) 34.0843 1.22514
\(775\) 8.45845 0.303836
\(776\) −53.9841 −1.93792
\(777\) 62.2510 2.23324
\(778\) 9.69786 0.347685
\(779\) −48.0209 −1.72053
\(780\) −39.9455 −1.43028
\(781\) −10.0214 −0.358595
\(782\) 2.70435 0.0967075
\(783\) 24.2669 0.867229
\(784\) 7.21375 0.257634
\(785\) −71.3139 −2.54530
\(786\) 61.1583 2.18144
\(787\) 31.6915 1.12968 0.564840 0.825200i \(-0.308938\pi\)
0.564840 + 0.825200i \(0.308938\pi\)
\(788\) 94.3692 3.36176
\(789\) −64.0279 −2.27945
\(790\) 1.94659 0.0692566
\(791\) 19.7233 0.701278
\(792\) 66.0861 2.34827
\(793\) 9.39936 0.333781
\(794\) −61.6897 −2.18928
\(795\) −129.346 −4.58742
\(796\) 29.2444 1.03654
\(797\) −11.4920 −0.407067 −0.203534 0.979068i \(-0.565243\pi\)
−0.203534 + 0.979068i \(0.565243\pi\)
\(798\) −178.501 −6.31886
\(799\) −0.798483 −0.0282483
\(800\) −9.73042 −0.344022
\(801\) 9.30926 0.328927
\(802\) 60.8862 2.14997
\(803\) −10.7909 −0.380801
\(804\) −15.3818 −0.542474
\(805\) −55.4530 −1.95446
\(806\) −3.91754 −0.137990
\(807\) 38.9637 1.37159
\(808\) 66.4552 2.33788
\(809\) −28.5864 −1.00504 −0.502522 0.864565i \(-0.667594\pi\)
−0.502522 + 0.864565i \(0.667594\pi\)
\(810\) −60.1608 −2.11384
\(811\) −25.8151 −0.906490 −0.453245 0.891386i \(-0.649734\pi\)
−0.453245 + 0.891386i \(0.649734\pi\)
\(812\) −34.9232 −1.22557
\(813\) −13.5653 −0.475754
\(814\) −37.6083 −1.31817
\(815\) −11.9071 −0.417086
\(816\) −2.76781 −0.0968926
\(817\) 19.5894 0.685347
\(818\) 9.52972 0.333199
\(819\) 16.9243 0.591381
\(820\) 77.4871 2.70597
\(821\) −33.5283 −1.17014 −0.585072 0.810981i \(-0.698934\pi\)
−0.585072 + 0.810981i \(0.698934\pi\)
\(822\) −0.612959 −0.0213794
\(823\) 33.9782 1.18441 0.592203 0.805789i \(-0.298258\pi\)
0.592203 + 0.805789i \(0.298258\pi\)
\(824\) −40.3184 −1.40456
\(825\) 33.4314 1.16393
\(826\) −33.7719 −1.17508
\(827\) −25.2204 −0.877000 −0.438500 0.898731i \(-0.644490\pi\)
−0.438500 + 0.898731i \(0.644490\pi\)
\(828\) −144.531 −5.02281
\(829\) 44.4689 1.54447 0.772235 0.635337i \(-0.219139\pi\)
0.772235 + 0.635337i \(0.219139\pi\)
\(830\) 14.2982 0.496299
\(831\) 43.5366 1.51027
\(832\) −5.65231 −0.195959
\(833\) 0.260386 0.00902183
\(834\) −46.7136 −1.61756
\(835\) 3.58252 0.123978
\(836\) 72.9107 2.52167
\(837\) −13.2709 −0.458709
\(838\) 26.1747 0.904191
\(839\) −37.5001 −1.29465 −0.647323 0.762215i \(-0.724112\pi\)
−0.647323 + 0.762215i \(0.724112\pi\)
\(840\) 150.046 5.17709
\(841\) −20.6894 −0.713427
\(842\) 43.4403 1.49705
\(843\) 50.0692 1.72447
\(844\) −39.5740 −1.36219
\(845\) 3.21951 0.110754
\(846\) 63.1177 2.17003
\(847\) −19.1634 −0.658462
\(848\) 68.6661 2.35800
\(849\) 37.3921 1.28330
\(850\) −2.44443 −0.0838432
\(851\) 42.8471 1.46878
\(852\) −59.3037 −2.03171
\(853\) −16.6261 −0.569268 −0.284634 0.958636i \(-0.591872\pi\)
−0.284634 + 0.958636i \(0.591872\pi\)
\(854\) −67.7753 −2.31922
\(855\) −156.411 −5.34913
\(856\) 25.4410 0.869555
\(857\) −2.89273 −0.0988138 −0.0494069 0.998779i \(-0.515733\pi\)
−0.0494069 + 0.998779i \(0.515733\pi\)
\(858\) −15.4838 −0.528608
\(859\) −3.45652 −0.117935 −0.0589674 0.998260i \(-0.518781\pi\)
−0.0589674 + 0.998260i \(0.518781\pi\)
\(860\) −31.6097 −1.07788
\(861\) −49.7167 −1.69434
\(862\) −51.1126 −1.74090
\(863\) 23.4381 0.797841 0.398921 0.916985i \(-0.369385\pi\)
0.398921 + 0.916985i \(0.369385\pi\)
\(864\) 15.2665 0.519378
\(865\) 36.8702 1.25362
\(866\) 78.3671 2.66302
\(867\) 50.4231 1.71246
\(868\) 19.0985 0.648246
\(869\) 0.510151 0.0173057
\(870\) −68.5422 −2.32380
\(871\) 1.23974 0.0420069
\(872\) −32.1588 −1.08903
\(873\) 58.2612 1.97184
\(874\) −122.861 −4.15585
\(875\) 3.41213 0.115351
\(876\) −63.8569 −2.15753
\(877\) 14.1777 0.478747 0.239374 0.970928i \(-0.423058\pi\)
0.239374 + 0.970928i \(0.423058\pi\)
\(878\) −8.66234 −0.292340
\(879\) 41.2656 1.39186
\(880\) −34.2874 −1.15583
\(881\) 25.1830 0.848438 0.424219 0.905560i \(-0.360549\pi\)
0.424219 + 0.905560i \(0.360549\pi\)
\(882\) −20.5827 −0.693056
\(883\) 0.972485 0.0327267 0.0163634 0.999866i \(-0.494791\pi\)
0.0163634 + 0.999866i \(0.494791\pi\)
\(884\) 0.765445 0.0257447
\(885\) −44.8139 −1.50640
\(886\) −6.94000 −0.233154
\(887\) −12.0841 −0.405743 −0.202871 0.979205i \(-0.565027\pi\)
−0.202871 + 0.979205i \(0.565027\pi\)
\(888\) −115.937 −3.89059
\(889\) 13.5542 0.454592
\(890\) −12.7693 −0.428029
\(891\) −15.7666 −0.528200
\(892\) 73.2726 2.45335
\(893\) 36.2758 1.21392
\(894\) 31.1451 1.04165
\(895\) 74.0217 2.47427
\(896\) 51.2819 1.71321
\(897\) 17.6407 0.589005
\(898\) 80.1622 2.67505
\(899\) −4.54483 −0.151579
\(900\) 130.640 4.35466
\(901\) 2.47856 0.0825727
\(902\) 30.0358 1.00008
\(903\) 20.2812 0.674917
\(904\) −36.7328 −1.22171
\(905\) −40.8756 −1.35875
\(906\) −140.812 −4.67817
\(907\) −36.0959 −1.19854 −0.599272 0.800545i \(-0.704543\pi\)
−0.599272 + 0.800545i \(0.704543\pi\)
\(908\) 51.2395 1.70044
\(909\) −71.7203 −2.37881
\(910\) −23.2147 −0.769558
\(911\) 36.5614 1.21133 0.605667 0.795718i \(-0.292906\pi\)
0.605667 + 0.795718i \(0.292906\pi\)
\(912\) 125.744 4.16380
\(913\) 3.74719 0.124014
\(914\) 90.4110 2.99053
\(915\) −89.9349 −2.97315
\(916\) −54.3043 −1.79426
\(917\) 24.0305 0.793559
\(918\) 3.83519 0.126580
\(919\) −30.3768 −1.00204 −0.501019 0.865436i \(-0.667041\pi\)
−0.501019 + 0.865436i \(0.667041\pi\)
\(920\) 103.276 3.40492
\(921\) 67.8226 2.23483
\(922\) −25.3565 −0.835072
\(923\) 4.77974 0.157327
\(924\) 75.4855 2.48329
\(925\) −38.7289 −1.27340
\(926\) 7.32531 0.240725
\(927\) 43.5128 1.42915
\(928\) 5.22828 0.171627
\(929\) −43.9017 −1.44037 −0.720183 0.693784i \(-0.755942\pi\)
−0.720183 + 0.693784i \(0.755942\pi\)
\(930\) 37.4838 1.22914
\(931\) −11.8296 −0.387698
\(932\) 58.7890 1.92570
\(933\) 90.1579 2.95164
\(934\) 70.5135 2.30727
\(935\) −1.23763 −0.0404749
\(936\) −31.5199 −1.03026
\(937\) −42.8830 −1.40093 −0.700463 0.713689i \(-0.747023\pi\)
−0.700463 + 0.713689i \(0.747023\pi\)
\(938\) −8.93927 −0.291877
\(939\) −98.8731 −3.22660
\(940\) −58.5352 −1.90921
\(941\) 47.5161 1.54898 0.774490 0.632586i \(-0.218007\pi\)
0.774490 + 0.632586i \(0.218007\pi\)
\(942\) −163.583 −5.32981
\(943\) −34.2198 −1.11435
\(944\) 23.7905 0.774313
\(945\) −78.6409 −2.55819
\(946\) −12.2527 −0.398369
\(947\) 23.1978 0.753826 0.376913 0.926249i \(-0.376986\pi\)
0.376913 + 0.926249i \(0.376986\pi\)
\(948\) 3.01891 0.0980498
\(949\) 5.14672 0.167069
\(950\) 111.053 3.60302
\(951\) 10.8159 0.350731
\(952\) −2.87523 −0.0931867
\(953\) 16.5489 0.536071 0.268035 0.963409i \(-0.413626\pi\)
0.268035 + 0.963409i \(0.413626\pi\)
\(954\) −195.922 −6.34322
\(955\) −51.7978 −1.67614
\(956\) −28.4656 −0.920642
\(957\) −17.9631 −0.580665
\(958\) 37.5972 1.21471
\(959\) −0.240846 −0.00777734
\(960\) 54.0824 1.74550
\(961\) −28.5146 −0.919825
\(962\) 17.9373 0.578323
\(963\) −27.4566 −0.884777
\(964\) −53.9811 −1.73861
\(965\) −11.7300 −0.377601
\(966\) −127.200 −4.09260
\(967\) 45.4284 1.46088 0.730439 0.682978i \(-0.239316\pi\)
0.730439 + 0.682978i \(0.239316\pi\)
\(968\) 35.6901 1.14712
\(969\) 4.53883 0.145808
\(970\) −79.9158 −2.56594
\(971\) −41.2612 −1.32413 −0.662067 0.749445i \(-0.730321\pi\)
−0.662067 + 0.749445i \(0.730321\pi\)
\(972\) 12.1266 0.388960
\(973\) −18.3549 −0.588431
\(974\) −56.2631 −1.80279
\(975\) −15.9452 −0.510654
\(976\) 47.7439 1.52825
\(977\) 11.7960 0.377389 0.188695 0.982036i \(-0.439574\pi\)
0.188695 + 0.982036i \(0.439574\pi\)
\(978\) −27.3129 −0.873369
\(979\) −3.34651 −0.106955
\(980\) 19.0884 0.609755
\(981\) 34.7066 1.10810
\(982\) −98.9060 −3.15622
\(983\) 53.0743 1.69281 0.846404 0.532541i \(-0.178763\pi\)
0.846404 + 0.532541i \(0.178763\pi\)
\(984\) 92.5929 2.95175
\(985\) 72.7750 2.31880
\(986\) 1.31342 0.0418279
\(987\) 37.5569 1.19545
\(988\) −34.7749 −1.10634
\(989\) 13.9595 0.443885
\(990\) 97.8310 3.10927
\(991\) 35.8277 1.13810 0.569052 0.822302i \(-0.307310\pi\)
0.569052 + 0.822302i \(0.307310\pi\)
\(992\) −2.85920 −0.0907796
\(993\) 3.56843 0.113241
\(994\) −34.4649 −1.09316
\(995\) 22.5525 0.714963
\(996\) 22.1747 0.702633
\(997\) −50.4661 −1.59828 −0.799138 0.601147i \(-0.794710\pi\)
−0.799138 + 0.601147i \(0.794710\pi\)
\(998\) −12.7086 −0.402282
\(999\) 60.7637 1.92248
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 \(a_p\))