Properties

Label 6025.2.a.h.1.10
Level 6025
Weight 2
Character 6025.1
Self dual Yes
Analytic conductor 48.110
Analytic rank 0
Dimension 12
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6025 = 5^{2} \cdot 241 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6025.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1098672178\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Root \(-1.32986\)
Character \(\chi\) = 6025.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.32986 q^{2}\) \(+2.18147 q^{3}\) \(-0.231473 q^{4}\) \(+2.90104 q^{6}\) \(+3.83334 q^{7}\) \(-2.96755 q^{8}\) \(+1.75880 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.32986 q^{2}\) \(+2.18147 q^{3}\) \(-0.231473 q^{4}\) \(+2.90104 q^{6}\) \(+3.83334 q^{7}\) \(-2.96755 q^{8}\) \(+1.75880 q^{9}\) \(+4.78120 q^{11}\) \(-0.504950 q^{12}\) \(-1.75719 q^{13}\) \(+5.09781 q^{14}\) \(-3.48347 q^{16}\) \(+6.01977 q^{17}\) \(+2.33895 q^{18}\) \(-4.20086 q^{19}\) \(+8.36231 q^{21}\) \(+6.35832 q^{22}\) \(-4.28435 q^{23}\) \(-6.47360 q^{24}\) \(-2.33681 q^{26}\) \(-2.70764 q^{27}\) \(-0.887315 q^{28}\) \(+4.96202 q^{29}\) \(+4.59803 q^{31}\) \(+1.30256 q^{32}\) \(+10.4300 q^{33}\) \(+8.00545 q^{34}\) \(-0.407113 q^{36}\) \(+10.0806 q^{37}\) \(-5.58655 q^{38}\) \(-3.83325 q^{39}\) \(+1.12501 q^{41}\) \(+11.1207 q^{42}\) \(+9.09669 q^{43}\) \(-1.10672 q^{44}\) \(-5.69758 q^{46}\) \(-7.19156 q^{47}\) \(-7.59908 q^{48}\) \(+7.69453 q^{49}\) \(+13.1319 q^{51}\) \(+0.406741 q^{52}\) \(-6.07855 q^{53}\) \(-3.60079 q^{54}\) \(-11.3756 q^{56}\) \(-9.16403 q^{57}\) \(+6.59879 q^{58}\) \(+1.36242 q^{59}\) \(-10.9181 q^{61}\) \(+6.11473 q^{62}\) \(+6.74207 q^{63}\) \(+8.69917 q^{64}\) \(+13.8705 q^{66}\) \(-9.85684 q^{67}\) \(-1.39341 q^{68}\) \(-9.34616 q^{69}\) \(+11.9533 q^{71}\) \(-5.21931 q^{72}\) \(+0.162452 q^{73}\) \(+13.4057 q^{74}\) \(+0.972384 q^{76}\) \(+18.3280 q^{77}\) \(-5.09768 q^{78}\) \(+14.5772 q^{79}\) \(-11.1830 q^{81}\) \(+1.49611 q^{82}\) \(+5.77030 q^{83}\) \(-1.93565 q^{84}\) \(+12.0973 q^{86}\) \(+10.8245 q^{87}\) \(-14.1884 q^{88}\) \(+4.73628 q^{89}\) \(-6.73591 q^{91}\) \(+0.991709 q^{92}\) \(+10.0304 q^{93}\) \(-9.56377 q^{94}\) \(+2.84149 q^{96}\) \(-0.439068 q^{97}\) \(+10.2326 q^{98}\) \(+8.40915 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(12q \) \(\mathstrut -\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 13q^{4} \) \(\mathstrut -\mathstrut q^{6} \) \(\mathstrut -\mathstrut 3q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 15q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(12q \) \(\mathstrut -\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 13q^{4} \) \(\mathstrut -\mathstrut q^{6} \) \(\mathstrut -\mathstrut 3q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 15q^{9} \) \(\mathstrut +\mathstrut 22q^{11} \) \(\mathstrut +\mathstrut 7q^{12} \) \(\mathstrut +\mathstrut 5q^{13} \) \(\mathstrut +\mathstrut 6q^{14} \) \(\mathstrut +\mathstrut 15q^{16} \) \(\mathstrut +\mathstrut 4q^{17} \) \(\mathstrut +\mathstrut q^{18} \) \(\mathstrut -\mathstrut 6q^{19} \) \(\mathstrut -\mathstrut 14q^{21} \) \(\mathstrut +\mathstrut 12q^{22} \) \(\mathstrut -\mathstrut 32q^{23} \) \(\mathstrut -\mathstrut 15q^{24} \) \(\mathstrut +\mathstrut 8q^{26} \) \(\mathstrut +\mathstrut 5q^{27} \) \(\mathstrut +\mathstrut 11q^{28} \) \(\mathstrut +\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 8q^{31} \) \(\mathstrut -\mathstrut q^{32} \) \(\mathstrut +\mathstrut 24q^{33} \) \(\mathstrut -\mathstrut 19q^{34} \) \(\mathstrut -\mathstrut 8q^{36} \) \(\mathstrut +\mathstrut 8q^{37} \) \(\mathstrut +\mathstrut 10q^{38} \) \(\mathstrut +\mathstrut 31q^{39} \) \(\mathstrut -\mathstrut q^{41} \) \(\mathstrut +\mathstrut 49q^{42} \) \(\mathstrut +\mathstrut 2q^{43} \) \(\mathstrut +\mathstrut 42q^{44} \) \(\mathstrut -\mathstrut 25q^{46} \) \(\mathstrut -\mathstrut 34q^{47} \) \(\mathstrut +\mathstrut 49q^{48} \) \(\mathstrut -\mathstrut 9q^{49} \) \(\mathstrut -\mathstrut 3q^{51} \) \(\mathstrut +\mathstrut 41q^{52} \) \(\mathstrut -\mathstrut 5q^{53} \) \(\mathstrut -\mathstrut 40q^{54} \) \(\mathstrut +\mathstrut q^{56} \) \(\mathstrut +\mathstrut 22q^{57} \) \(\mathstrut +\mathstrut 33q^{58} \) \(\mathstrut +\mathstrut 26q^{59} \) \(\mathstrut -\mathstrut 26q^{61} \) \(\mathstrut +\mathstrut 17q^{62} \) \(\mathstrut +\mathstrut 4q^{63} \) \(\mathstrut +\mathstrut 13q^{64} \) \(\mathstrut -\mathstrut 2q^{66} \) \(\mathstrut -\mathstrut 6q^{67} \) \(\mathstrut +\mathstrut 35q^{68} \) \(\mathstrut -\mathstrut 2q^{69} \) \(\mathstrut +\mathstrut 94q^{71} \) \(\mathstrut -\mathstrut 17q^{72} \) \(\mathstrut +\mathstrut 22q^{73} \) \(\mathstrut +\mathstrut 26q^{74} \) \(\mathstrut -\mathstrut 20q^{76} \) \(\mathstrut +\mathstrut 7q^{77} \) \(\mathstrut -\mathstrut 54q^{78} \) \(\mathstrut +\mathstrut 9q^{79} \) \(\mathstrut +\mathstrut 4q^{81} \) \(\mathstrut -\mathstrut 15q^{82} \) \(\mathstrut +\mathstrut 8q^{83} \) \(\mathstrut +\mathstrut 2q^{84} \) \(\mathstrut +\mathstrut 9q^{86} \) \(\mathstrut -\mathstrut 4q^{87} \) \(\mathstrut -\mathstrut 6q^{88} \) \(\mathstrut -\mathstrut 3q^{89} \) \(\mathstrut -\mathstrut 20q^{91} \) \(\mathstrut -\mathstrut 36q^{92} \) \(\mathstrut -\mathstrut 12q^{93} \) \(\mathstrut +\mathstrut 48q^{94} \) \(\mathstrut -\mathstrut 23q^{96} \) \(\mathstrut +\mathstrut 29q^{97} \) \(\mathstrut -\mathstrut 28q^{98} \) \(\mathstrut +\mathstrut 36q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.32986 0.940353 0.470176 0.882572i \(-0.344190\pi\)
0.470176 + 0.882572i \(0.344190\pi\)
\(3\) 2.18147 1.25947 0.629735 0.776810i \(-0.283163\pi\)
0.629735 + 0.776810i \(0.283163\pi\)
\(4\) −0.231473 −0.115736
\(5\) 0 0
\(6\) 2.90104 1.18435
\(7\) 3.83334 1.44887 0.724434 0.689344i \(-0.242101\pi\)
0.724434 + 0.689344i \(0.242101\pi\)
\(8\) −2.96755 −1.04919
\(9\) 1.75880 0.586266
\(10\) 0 0
\(11\) 4.78120 1.44159 0.720793 0.693151i \(-0.243778\pi\)
0.720793 + 0.693151i \(0.243778\pi\)
\(12\) −0.504950 −0.145767
\(13\) −1.75719 −0.487356 −0.243678 0.969856i \(-0.578354\pi\)
−0.243678 + 0.969856i \(0.578354\pi\)
\(14\) 5.09781 1.36245
\(15\) 0 0
\(16\) −3.48347 −0.870869
\(17\) 6.01977 1.46001 0.730004 0.683443i \(-0.239518\pi\)
0.730004 + 0.683443i \(0.239518\pi\)
\(18\) 2.33895 0.551296
\(19\) −4.20086 −0.963743 −0.481871 0.876242i \(-0.660043\pi\)
−0.481871 + 0.876242i \(0.660043\pi\)
\(20\) 0 0
\(21\) 8.36231 1.82481
\(22\) 6.35832 1.35560
\(23\) −4.28435 −0.893348 −0.446674 0.894697i \(-0.647392\pi\)
−0.446674 + 0.894697i \(0.647392\pi\)
\(24\) −6.47360 −1.32142
\(25\) 0 0
\(26\) −2.33681 −0.458287
\(27\) −2.70764 −0.521086
\(28\) −0.887315 −0.167687
\(29\) 4.96202 0.921423 0.460712 0.887550i \(-0.347594\pi\)
0.460712 + 0.887550i \(0.347594\pi\)
\(30\) 0 0
\(31\) 4.59803 0.825830 0.412915 0.910770i \(-0.364511\pi\)
0.412915 + 0.910770i \(0.364511\pi\)
\(32\) 1.30256 0.230262
\(33\) 10.4300 1.81563
\(34\) 8.00545 1.37292
\(35\) 0 0
\(36\) −0.407113 −0.0678522
\(37\) 10.0806 1.65723 0.828617 0.559816i \(-0.189128\pi\)
0.828617 + 0.559816i \(0.189128\pi\)
\(38\) −5.58655 −0.906258
\(39\) −3.83325 −0.613811
\(40\) 0 0
\(41\) 1.12501 0.175698 0.0878488 0.996134i \(-0.472001\pi\)
0.0878488 + 0.996134i \(0.472001\pi\)
\(42\) 11.1207 1.71596
\(43\) 9.09669 1.38723 0.693616 0.720345i \(-0.256016\pi\)
0.693616 + 0.720345i \(0.256016\pi\)
\(44\) −1.10672 −0.166844
\(45\) 0 0
\(46\) −5.69758 −0.840062
\(47\) −7.19156 −1.04900 −0.524499 0.851411i \(-0.675747\pi\)
−0.524499 + 0.851411i \(0.675747\pi\)
\(48\) −7.59908 −1.09683
\(49\) 7.69453 1.09922
\(50\) 0 0
\(51\) 13.1319 1.83884
\(52\) 0.406741 0.0564049
\(53\) −6.07855 −0.834953 −0.417477 0.908688i \(-0.637085\pi\)
−0.417477 + 0.908688i \(0.637085\pi\)
\(54\) −3.60079 −0.490005
\(55\) 0 0
\(56\) −11.3756 −1.52013
\(57\) −9.16403 −1.21381
\(58\) 6.59879 0.866463
\(59\) 1.36242 0.177372 0.0886862 0.996060i \(-0.471733\pi\)
0.0886862 + 0.996060i \(0.471733\pi\)
\(60\) 0 0
\(61\) −10.9181 −1.39791 −0.698957 0.715164i \(-0.746352\pi\)
−0.698957 + 0.715164i \(0.746352\pi\)
\(62\) 6.11473 0.776571
\(63\) 6.74207 0.849421
\(64\) 8.69917 1.08740
\(65\) 0 0
\(66\) 13.8705 1.70734
\(67\) −9.85684 −1.20421 −0.602103 0.798419i \(-0.705670\pi\)
−0.602103 + 0.798419i \(0.705670\pi\)
\(68\) −1.39341 −0.168976
\(69\) −9.34616 −1.12514
\(70\) 0 0
\(71\) 11.9533 1.41859 0.709296 0.704911i \(-0.249013\pi\)
0.709296 + 0.704911i \(0.249013\pi\)
\(72\) −5.21931 −0.615102
\(73\) 0.162452 0.0190135 0.00950676 0.999955i \(-0.496974\pi\)
0.00950676 + 0.999955i \(0.496974\pi\)
\(74\) 13.4057 1.55838
\(75\) 0 0
\(76\) 0.972384 0.111540
\(77\) 18.3280 2.08867
\(78\) −5.09768 −0.577199
\(79\) 14.5772 1.64006 0.820031 0.572319i \(-0.193956\pi\)
0.820031 + 0.572319i \(0.193956\pi\)
\(80\) 0 0
\(81\) −11.1830 −1.24256
\(82\) 1.49611 0.165218
\(83\) 5.77030 0.633372 0.316686 0.948530i \(-0.397430\pi\)
0.316686 + 0.948530i \(0.397430\pi\)
\(84\) −1.93565 −0.211196
\(85\) 0 0
\(86\) 12.0973 1.30449
\(87\) 10.8245 1.16051
\(88\) −14.1884 −1.51249
\(89\) 4.73628 0.502044 0.251022 0.967981i \(-0.419233\pi\)
0.251022 + 0.967981i \(0.419233\pi\)
\(90\) 0 0
\(91\) −6.73591 −0.706115
\(92\) 0.991709 0.103393
\(93\) 10.0304 1.04011
\(94\) −9.56377 −0.986428
\(95\) 0 0
\(96\) 2.84149 0.290008
\(97\) −0.439068 −0.0445806 −0.0222903 0.999752i \(-0.507096\pi\)
−0.0222903 + 0.999752i \(0.507096\pi\)
\(98\) 10.2326 1.03365
\(99\) 8.40915 0.845152
\(100\) 0 0
\(101\) −4.54961 −0.452703 −0.226352 0.974046i \(-0.572680\pi\)
−0.226352 + 0.974046i \(0.572680\pi\)
\(102\) 17.4636 1.72916
\(103\) −10.9977 −1.08364 −0.541819 0.840495i \(-0.682264\pi\)
−0.541819 + 0.840495i \(0.682264\pi\)
\(104\) 5.21454 0.511327
\(105\) 0 0
\(106\) −8.08362 −0.785151
\(107\) −0.634979 −0.0613858 −0.0306929 0.999529i \(-0.509771\pi\)
−0.0306929 + 0.999529i \(0.509771\pi\)
\(108\) 0.626746 0.0603086
\(109\) 5.56974 0.533484 0.266742 0.963768i \(-0.414053\pi\)
0.266742 + 0.963768i \(0.414053\pi\)
\(110\) 0 0
\(111\) 21.9904 2.08724
\(112\) −13.3534 −1.26177
\(113\) −4.78347 −0.449991 −0.224995 0.974360i \(-0.572237\pi\)
−0.224995 + 0.974360i \(0.572237\pi\)
\(114\) −12.1869 −1.14141
\(115\) 0 0
\(116\) −1.14857 −0.106642
\(117\) −3.09054 −0.285720
\(118\) 1.81183 0.166793
\(119\) 23.0758 2.11536
\(120\) 0 0
\(121\) 11.8598 1.07817
\(122\) −14.5195 −1.31453
\(123\) 2.45418 0.221286
\(124\) −1.06432 −0.0955785
\(125\) 0 0
\(126\) 8.96601 0.798756
\(127\) 6.09612 0.540944 0.270472 0.962728i \(-0.412820\pi\)
0.270472 + 0.962728i \(0.412820\pi\)
\(128\) 8.96356 0.792274
\(129\) 19.8441 1.74718
\(130\) 0 0
\(131\) −6.72698 −0.587739 −0.293869 0.955846i \(-0.594943\pi\)
−0.293869 + 0.955846i \(0.594943\pi\)
\(132\) −2.41427 −0.210135
\(133\) −16.1033 −1.39634
\(134\) −13.1082 −1.13238
\(135\) 0 0
\(136\) −17.8639 −1.53182
\(137\) 9.94109 0.849325 0.424663 0.905352i \(-0.360393\pi\)
0.424663 + 0.905352i \(0.360393\pi\)
\(138\) −12.4291 −1.05803
\(139\) 3.28633 0.278743 0.139372 0.990240i \(-0.455492\pi\)
0.139372 + 0.990240i \(0.455492\pi\)
\(140\) 0 0
\(141\) −15.6882 −1.32118
\(142\) 15.8962 1.33398
\(143\) −8.40146 −0.702566
\(144\) −6.12672 −0.510560
\(145\) 0 0
\(146\) 0.216038 0.0178794
\(147\) 16.7854 1.38443
\(148\) −2.33337 −0.191802
\(149\) 9.42710 0.772298 0.386149 0.922436i \(-0.373805\pi\)
0.386149 + 0.922436i \(0.373805\pi\)
\(150\) 0 0
\(151\) −2.34993 −0.191234 −0.0956171 0.995418i \(-0.530482\pi\)
−0.0956171 + 0.995418i \(0.530482\pi\)
\(152\) 12.4662 1.01115
\(153\) 10.5875 0.855952
\(154\) 24.3736 1.96408
\(155\) 0 0
\(156\) 0.887292 0.0710402
\(157\) −19.8666 −1.58552 −0.792762 0.609531i \(-0.791358\pi\)
−0.792762 + 0.609531i \(0.791358\pi\)
\(158\) 19.3856 1.54224
\(159\) −13.2602 −1.05160
\(160\) 0 0
\(161\) −16.4234 −1.29434
\(162\) −14.8719 −1.16844
\(163\) 2.10105 0.164567 0.0822836 0.996609i \(-0.473779\pi\)
0.0822836 + 0.996609i \(0.473779\pi\)
\(164\) −0.260410 −0.0203346
\(165\) 0 0
\(166\) 7.67368 0.595593
\(167\) −21.9087 −1.69535 −0.847673 0.530518i \(-0.821997\pi\)
−0.847673 + 0.530518i \(0.821997\pi\)
\(168\) −24.8156 −1.91456
\(169\) −9.91229 −0.762484
\(170\) 0 0
\(171\) −7.38845 −0.565009
\(172\) −2.10564 −0.160553
\(173\) 5.60734 0.426318 0.213159 0.977018i \(-0.431625\pi\)
0.213159 + 0.977018i \(0.431625\pi\)
\(174\) 14.3950 1.09128
\(175\) 0 0
\(176\) −16.6552 −1.25543
\(177\) 2.97208 0.223395
\(178\) 6.29859 0.472099
\(179\) −23.8279 −1.78098 −0.890492 0.454999i \(-0.849640\pi\)
−0.890492 + 0.454999i \(0.849640\pi\)
\(180\) 0 0
\(181\) 6.57832 0.488963 0.244481 0.969654i \(-0.421382\pi\)
0.244481 + 0.969654i \(0.421382\pi\)
\(182\) −8.95781 −0.663997
\(183\) −23.8174 −1.76063
\(184\) 12.7140 0.937288
\(185\) 0 0
\(186\) 13.3391 0.978069
\(187\) 28.7817 2.10473
\(188\) 1.66465 0.121407
\(189\) −10.3793 −0.754985
\(190\) 0 0
\(191\) 19.1620 1.38652 0.693258 0.720689i \(-0.256174\pi\)
0.693258 + 0.720689i \(0.256174\pi\)
\(192\) 18.9769 1.36954
\(193\) −6.37070 −0.458573 −0.229286 0.973359i \(-0.573639\pi\)
−0.229286 + 0.973359i \(0.573639\pi\)
\(194\) −0.583899 −0.0419215
\(195\) 0 0
\(196\) −1.78107 −0.127220
\(197\) 12.1752 0.867450 0.433725 0.901045i \(-0.357199\pi\)
0.433725 + 0.901045i \(0.357199\pi\)
\(198\) 11.1830 0.794741
\(199\) −1.12984 −0.0800919 −0.0400459 0.999198i \(-0.512750\pi\)
−0.0400459 + 0.999198i \(0.512750\pi\)
\(200\) 0 0
\(201\) −21.5024 −1.51666
\(202\) −6.05035 −0.425701
\(203\) 19.0211 1.33502
\(204\) −3.03968 −0.212820
\(205\) 0 0
\(206\) −14.6254 −1.01900
\(207\) −7.53529 −0.523739
\(208\) 6.12112 0.424423
\(209\) −20.0851 −1.38932
\(210\) 0 0
\(211\) 27.7361 1.90943 0.954716 0.297520i \(-0.0961596\pi\)
0.954716 + 0.297520i \(0.0961596\pi\)
\(212\) 1.40702 0.0966345
\(213\) 26.0757 1.78668
\(214\) −0.844433 −0.0577243
\(215\) 0 0
\(216\) 8.03506 0.546716
\(217\) 17.6258 1.19652
\(218\) 7.40697 0.501664
\(219\) 0.354383 0.0239470
\(220\) 0 0
\(221\) −10.5779 −0.711544
\(222\) 29.2442 1.96274
\(223\) 9.10518 0.609728 0.304864 0.952396i \(-0.401389\pi\)
0.304864 + 0.952396i \(0.401389\pi\)
\(224\) 4.99316 0.333619
\(225\) 0 0
\(226\) −6.36134 −0.423150
\(227\) −24.1258 −1.60129 −0.800644 0.599141i \(-0.795509\pi\)
−0.800644 + 0.599141i \(0.795509\pi\)
\(228\) 2.12122 0.140481
\(229\) −29.6552 −1.95967 −0.979835 0.199809i \(-0.935968\pi\)
−0.979835 + 0.199809i \(0.935968\pi\)
\(230\) 0 0
\(231\) 39.9819 2.63061
\(232\) −14.7250 −0.966744
\(233\) 5.36189 0.351269 0.175635 0.984455i \(-0.443802\pi\)
0.175635 + 0.984455i \(0.443802\pi\)
\(234\) −4.10998 −0.268678
\(235\) 0 0
\(236\) −0.315364 −0.0205284
\(237\) 31.7996 2.06561
\(238\) 30.6876 1.98918
\(239\) 2.14131 0.138510 0.0692549 0.997599i \(-0.477938\pi\)
0.0692549 + 0.997599i \(0.477938\pi\)
\(240\) 0 0
\(241\) 1.00000 0.0644157
\(242\) 15.7719 1.01386
\(243\) −16.2725 −1.04388
\(244\) 2.52723 0.161789
\(245\) 0 0
\(246\) 3.26371 0.208087
\(247\) 7.38170 0.469686
\(248\) −13.6449 −0.866449
\(249\) 12.5877 0.797713
\(250\) 0 0
\(251\) −28.1462 −1.77657 −0.888285 0.459293i \(-0.848103\pi\)
−0.888285 + 0.459293i \(0.848103\pi\)
\(252\) −1.56061 −0.0983090
\(253\) −20.4843 −1.28784
\(254\) 8.10699 0.508678
\(255\) 0 0
\(256\) −5.47806 −0.342379
\(257\) −1.23067 −0.0767674 −0.0383837 0.999263i \(-0.512221\pi\)
−0.0383837 + 0.999263i \(0.512221\pi\)
\(258\) 26.3899 1.64296
\(259\) 38.6423 2.40111
\(260\) 0 0
\(261\) 8.72718 0.540199
\(262\) −8.94594 −0.552682
\(263\) 15.0159 0.925919 0.462960 0.886379i \(-0.346787\pi\)
0.462960 + 0.886379i \(0.346787\pi\)
\(264\) −30.9516 −1.90494
\(265\) 0 0
\(266\) −21.4152 −1.31305
\(267\) 10.3320 0.632310
\(268\) 2.28159 0.139370
\(269\) −0.940463 −0.0573410 −0.0286705 0.999589i \(-0.509127\pi\)
−0.0286705 + 0.999589i \(0.509127\pi\)
\(270\) 0 0
\(271\) 5.11230 0.310550 0.155275 0.987871i \(-0.450374\pi\)
0.155275 + 0.987871i \(0.450374\pi\)
\(272\) −20.9697 −1.27148
\(273\) −14.6942 −0.889331
\(274\) 13.2203 0.798665
\(275\) 0 0
\(276\) 2.16338 0.130220
\(277\) −2.39186 −0.143713 −0.0718565 0.997415i \(-0.522892\pi\)
−0.0718565 + 0.997415i \(0.522892\pi\)
\(278\) 4.37036 0.262117
\(279\) 8.08699 0.484155
\(280\) 0 0
\(281\) 7.49067 0.446856 0.223428 0.974720i \(-0.428275\pi\)
0.223428 + 0.974720i \(0.428275\pi\)
\(282\) −20.8630 −1.24238
\(283\) 17.9408 1.06647 0.533235 0.845967i \(-0.320976\pi\)
0.533235 + 0.845967i \(0.320976\pi\)
\(284\) −2.76686 −0.164183
\(285\) 0 0
\(286\) −11.1728 −0.660660
\(287\) 4.31256 0.254563
\(288\) 2.29094 0.134995
\(289\) 19.2376 1.13162
\(290\) 0 0
\(291\) −0.957812 −0.0561479
\(292\) −0.0376031 −0.00220056
\(293\) −12.6436 −0.738644 −0.369322 0.929301i \(-0.620410\pi\)
−0.369322 + 0.929301i \(0.620410\pi\)
\(294\) 22.3222 1.30186
\(295\) 0 0
\(296\) −29.9145 −1.73875
\(297\) −12.9458 −0.751190
\(298\) 12.5367 0.726233
\(299\) 7.52840 0.435379
\(300\) 0 0
\(301\) 34.8708 2.00992
\(302\) −3.12507 −0.179828
\(303\) −9.92483 −0.570167
\(304\) 14.6336 0.839293
\(305\) 0 0
\(306\) 14.0800 0.804897
\(307\) −4.93084 −0.281418 −0.140709 0.990051i \(-0.544938\pi\)
−0.140709 + 0.990051i \(0.544938\pi\)
\(308\) −4.24243 −0.241735
\(309\) −23.9912 −1.36481
\(310\) 0 0
\(311\) 33.2247 1.88400 0.942001 0.335609i \(-0.108942\pi\)
0.942001 + 0.335609i \(0.108942\pi\)
\(312\) 11.3753 0.644002
\(313\) −18.2269 −1.03024 −0.515122 0.857117i \(-0.672253\pi\)
−0.515122 + 0.857117i \(0.672253\pi\)
\(314\) −26.4197 −1.49095
\(315\) 0 0
\(316\) −3.37422 −0.189815
\(317\) −15.7434 −0.884235 −0.442117 0.896957i \(-0.645773\pi\)
−0.442117 + 0.896957i \(0.645773\pi\)
\(318\) −17.6342 −0.988874
\(319\) 23.7244 1.32831
\(320\) 0 0
\(321\) −1.38519 −0.0773135
\(322\) −21.8408 −1.21714
\(323\) −25.2882 −1.40707
\(324\) 2.58857 0.143809
\(325\) 0 0
\(326\) 2.79411 0.154751
\(327\) 12.1502 0.671908
\(328\) −3.33853 −0.184339
\(329\) −27.5677 −1.51986
\(330\) 0 0
\(331\) −7.35834 −0.404451 −0.202225 0.979339i \(-0.564817\pi\)
−0.202225 + 0.979339i \(0.564817\pi\)
\(332\) −1.33567 −0.0733042
\(333\) 17.7297 0.971579
\(334\) −29.1355 −1.59422
\(335\) 0 0
\(336\) −29.1299 −1.58917
\(337\) 21.0122 1.14461 0.572303 0.820042i \(-0.306050\pi\)
0.572303 + 0.820042i \(0.306050\pi\)
\(338\) −13.1820 −0.717004
\(339\) −10.4350 −0.566750
\(340\) 0 0
\(341\) 21.9841 1.19050
\(342\) −9.82561 −0.531308
\(343\) 2.66238 0.143755
\(344\) −26.9949 −1.45547
\(345\) 0 0
\(346\) 7.45697 0.400889
\(347\) 0.799138 0.0429000 0.0214500 0.999770i \(-0.493172\pi\)
0.0214500 + 0.999770i \(0.493172\pi\)
\(348\) −2.50557 −0.134313
\(349\) −1.25641 −0.0672542 −0.0336271 0.999434i \(-0.510706\pi\)
−0.0336271 + 0.999434i \(0.510706\pi\)
\(350\) 0 0
\(351\) 4.75784 0.253955
\(352\) 6.22779 0.331942
\(353\) −30.7996 −1.63930 −0.819649 0.572865i \(-0.805832\pi\)
−0.819649 + 0.572865i \(0.805832\pi\)
\(354\) 3.95245 0.210070
\(355\) 0 0
\(356\) −1.09632 −0.0581048
\(357\) 50.3392 2.66423
\(358\) −31.6878 −1.67475
\(359\) −14.3153 −0.755535 −0.377768 0.925900i \(-0.623308\pi\)
−0.377768 + 0.925900i \(0.623308\pi\)
\(360\) 0 0
\(361\) −1.35280 −0.0712002
\(362\) 8.74825 0.459798
\(363\) 25.8718 1.35792
\(364\) 1.55918 0.0817232
\(365\) 0 0
\(366\) −31.6738 −1.65561
\(367\) −3.37048 −0.175938 −0.0879688 0.996123i \(-0.528038\pi\)
−0.0879688 + 0.996123i \(0.528038\pi\)
\(368\) 14.9244 0.777989
\(369\) 1.97867 0.103005
\(370\) 0 0
\(371\) −23.3012 −1.20974
\(372\) −2.32177 −0.120378
\(373\) −5.72387 −0.296371 −0.148185 0.988960i \(-0.547343\pi\)
−0.148185 + 0.988960i \(0.547343\pi\)
\(374\) 38.2756 1.97919
\(375\) 0 0
\(376\) 21.3413 1.10059
\(377\) −8.71920 −0.449061
\(378\) −13.8031 −0.709953
\(379\) 0.963739 0.0495040 0.0247520 0.999694i \(-0.492120\pi\)
0.0247520 + 0.999694i \(0.492120\pi\)
\(380\) 0 0
\(381\) 13.2985 0.681302
\(382\) 25.4828 1.30382
\(383\) −17.5403 −0.896267 −0.448134 0.893967i \(-0.647911\pi\)
−0.448134 + 0.893967i \(0.647911\pi\)
\(384\) 19.5537 0.997846
\(385\) 0 0
\(386\) −8.47213 −0.431220
\(387\) 15.9992 0.813287
\(388\) 0.101632 0.00515960
\(389\) −16.8395 −0.853796 −0.426898 0.904300i \(-0.640394\pi\)
−0.426898 + 0.904300i \(0.640394\pi\)
\(390\) 0 0
\(391\) −25.7908 −1.30429
\(392\) −22.8339 −1.15328
\(393\) −14.6747 −0.740240
\(394\) 16.1914 0.815709
\(395\) 0 0
\(396\) −1.94649 −0.0978148
\(397\) 2.82968 0.142017 0.0710087 0.997476i \(-0.477378\pi\)
0.0710087 + 0.997476i \(0.477378\pi\)
\(398\) −1.50252 −0.0753146
\(399\) −35.1289 −1.75864
\(400\) 0 0
\(401\) −13.6028 −0.679290 −0.339645 0.940554i \(-0.610307\pi\)
−0.339645 + 0.940554i \(0.610307\pi\)
\(402\) −28.5951 −1.42620
\(403\) −8.07960 −0.402473
\(404\) 1.05311 0.0523943
\(405\) 0 0
\(406\) 25.2954 1.25539
\(407\) 48.1971 2.38904
\(408\) −38.9696 −1.92928
\(409\) 24.6420 1.21847 0.609234 0.792990i \(-0.291477\pi\)
0.609234 + 0.792990i \(0.291477\pi\)
\(410\) 0 0
\(411\) 21.6862 1.06970
\(412\) 2.54567 0.125416
\(413\) 5.22264 0.256989
\(414\) −10.0209 −0.492499
\(415\) 0 0
\(416\) −2.28884 −0.112220
\(417\) 7.16902 0.351069
\(418\) −26.7104 −1.30645
\(419\) −7.82622 −0.382336 −0.191168 0.981557i \(-0.561228\pi\)
−0.191168 + 0.981557i \(0.561228\pi\)
\(420\) 0 0
\(421\) 21.3683 1.04143 0.520715 0.853731i \(-0.325666\pi\)
0.520715 + 0.853731i \(0.325666\pi\)
\(422\) 36.8851 1.79554
\(423\) −12.6485 −0.614991
\(424\) 18.0384 0.876021
\(425\) 0 0
\(426\) 34.6770 1.68011
\(427\) −41.8527 −2.02539
\(428\) 0.146980 0.00710457
\(429\) −18.3275 −0.884860
\(430\) 0 0
\(431\) 33.9239 1.63406 0.817028 0.576598i \(-0.195620\pi\)
0.817028 + 0.576598i \(0.195620\pi\)
\(432\) 9.43201 0.453798
\(433\) −34.5154 −1.65871 −0.829353 0.558725i \(-0.811291\pi\)
−0.829353 + 0.558725i \(0.811291\pi\)
\(434\) 23.4399 1.12515
\(435\) 0 0
\(436\) −1.28924 −0.0617435
\(437\) 17.9979 0.860957
\(438\) 0.471279 0.0225186
\(439\) 2.28531 0.109072 0.0545360 0.998512i \(-0.482632\pi\)
0.0545360 + 0.998512i \(0.482632\pi\)
\(440\) 0 0
\(441\) 13.5331 0.644434
\(442\) −14.0671 −0.669103
\(443\) −18.3736 −0.872957 −0.436478 0.899715i \(-0.643774\pi\)
−0.436478 + 0.899715i \(0.643774\pi\)
\(444\) −5.09018 −0.241569
\(445\) 0 0
\(446\) 12.1086 0.573360
\(447\) 20.5649 0.972687
\(448\) 33.3469 1.57549
\(449\) 26.0138 1.22767 0.613833 0.789436i \(-0.289627\pi\)
0.613833 + 0.789436i \(0.289627\pi\)
\(450\) 0 0
\(451\) 5.37891 0.253283
\(452\) 1.10724 0.0520803
\(453\) −5.12628 −0.240854
\(454\) −32.0840 −1.50578
\(455\) 0 0
\(456\) 27.1947 1.27351
\(457\) −9.10237 −0.425791 −0.212895 0.977075i \(-0.568289\pi\)
−0.212895 + 0.977075i \(0.568289\pi\)
\(458\) −39.4372 −1.84278
\(459\) −16.2994 −0.760790
\(460\) 0 0
\(461\) 12.3824 0.576708 0.288354 0.957524i \(-0.406892\pi\)
0.288354 + 0.957524i \(0.406892\pi\)
\(462\) 53.1703 2.47371
\(463\) −25.3698 −1.17904 −0.589518 0.807755i \(-0.700682\pi\)
−0.589518 + 0.807755i \(0.700682\pi\)
\(464\) −17.2851 −0.802439
\(465\) 0 0
\(466\) 7.13057 0.330317
\(467\) 21.2025 0.981137 0.490568 0.871403i \(-0.336789\pi\)
0.490568 + 0.871403i \(0.336789\pi\)
\(468\) 0.715375 0.0330682
\(469\) −37.7847 −1.74473
\(470\) 0 0
\(471\) −43.3382 −1.99692
\(472\) −4.04306 −0.186097
\(473\) 43.4931 1.99981
\(474\) 42.2891 1.94240
\(475\) 0 0
\(476\) −5.34143 −0.244824
\(477\) −10.6909 −0.489504
\(478\) 2.84764 0.130248
\(479\) −26.5866 −1.21477 −0.607385 0.794407i \(-0.707782\pi\)
−0.607385 + 0.794407i \(0.707782\pi\)
\(480\) 0 0
\(481\) −17.7134 −0.807663
\(482\) 1.32986 0.0605735
\(483\) −35.8270 −1.63019
\(484\) −2.74523 −0.124783
\(485\) 0 0
\(486\) −21.6401 −0.981615
\(487\) 17.1209 0.775822 0.387911 0.921697i \(-0.373197\pi\)
0.387911 + 0.921697i \(0.373197\pi\)
\(488\) 32.3998 1.46667
\(489\) 4.58338 0.207267
\(490\) 0 0
\(491\) −5.11790 −0.230968 −0.115484 0.993309i \(-0.536842\pi\)
−0.115484 + 0.993309i \(0.536842\pi\)
\(492\) −0.568076 −0.0256108
\(493\) 29.8702 1.34529
\(494\) 9.81662 0.441671
\(495\) 0 0
\(496\) −16.0171 −0.719189
\(497\) 45.8210 2.05535
\(498\) 16.7399 0.750132
\(499\) 29.2980 1.31156 0.655780 0.754952i \(-0.272340\pi\)
0.655780 + 0.754952i \(0.272340\pi\)
\(500\) 0 0
\(501\) −47.7931 −2.13524
\(502\) −37.4305 −1.67060
\(503\) −12.8905 −0.574761 −0.287380 0.957817i \(-0.592784\pi\)
−0.287380 + 0.957817i \(0.592784\pi\)
\(504\) −20.0074 −0.891201
\(505\) 0 0
\(506\) −27.2412 −1.21102
\(507\) −21.6233 −0.960326
\(508\) −1.41109 −0.0626068
\(509\) −11.2706 −0.499559 −0.249780 0.968303i \(-0.580358\pi\)
−0.249780 + 0.968303i \(0.580358\pi\)
\(510\) 0 0
\(511\) 0.622733 0.0275481
\(512\) −25.2122 −1.11423
\(513\) 11.3744 0.502193
\(514\) −1.63662 −0.0721884
\(515\) 0 0
\(516\) −4.59338 −0.202212
\(517\) −34.3843 −1.51222
\(518\) 51.3888 2.25789
\(519\) 12.2322 0.536935
\(520\) 0 0
\(521\) 41.5318 1.81954 0.909771 0.415110i \(-0.136257\pi\)
0.909771 + 0.415110i \(0.136257\pi\)
\(522\) 11.6059 0.507977
\(523\) 8.02470 0.350896 0.175448 0.984489i \(-0.443863\pi\)
0.175448 + 0.984489i \(0.443863\pi\)
\(524\) 1.55711 0.0680228
\(525\) 0 0
\(526\) 19.9690 0.870691
\(527\) 27.6790 1.20572
\(528\) −36.3327 −1.58118
\(529\) −4.64439 −0.201930
\(530\) 0 0
\(531\) 2.39623 0.103987
\(532\) 3.72748 0.161607
\(533\) −1.97686 −0.0856273
\(534\) 13.7402 0.594595
\(535\) 0 0
\(536\) 29.2506 1.26344
\(537\) −51.9799 −2.24310
\(538\) −1.25068 −0.0539208
\(539\) 36.7891 1.58462
\(540\) 0 0
\(541\) 9.87706 0.424648 0.212324 0.977199i \(-0.431897\pi\)
0.212324 + 0.977199i \(0.431897\pi\)
\(542\) 6.79864 0.292027
\(543\) 14.3504 0.615834
\(544\) 7.84110 0.336184
\(545\) 0 0
\(546\) −19.5412 −0.836285
\(547\) −19.3803 −0.828641 −0.414320 0.910131i \(-0.635981\pi\)
−0.414320 + 0.910131i \(0.635981\pi\)
\(548\) −2.30109 −0.0982978
\(549\) −19.2026 −0.819549
\(550\) 0 0
\(551\) −20.8447 −0.888015
\(552\) 27.7351 1.18049
\(553\) 55.8794 2.37623
\(554\) −3.18084 −0.135141
\(555\) 0 0
\(556\) −0.760696 −0.0322607
\(557\) 18.9414 0.802571 0.401285 0.915953i \(-0.368564\pi\)
0.401285 + 0.915953i \(0.368564\pi\)
\(558\) 10.7546 0.455277
\(559\) −15.9846 −0.676077
\(560\) 0 0
\(561\) 62.7863 2.65084
\(562\) 9.96154 0.420202
\(563\) −12.0839 −0.509276 −0.254638 0.967036i \(-0.581956\pi\)
−0.254638 + 0.967036i \(0.581956\pi\)
\(564\) 3.63138 0.152909
\(565\) 0 0
\(566\) 23.8588 1.00286
\(567\) −42.8684 −1.80030
\(568\) −35.4719 −1.48837
\(569\) 8.80054 0.368938 0.184469 0.982838i \(-0.440943\pi\)
0.184469 + 0.982838i \(0.440943\pi\)
\(570\) 0 0
\(571\) −35.4541 −1.48371 −0.741854 0.670562i \(-0.766053\pi\)
−0.741854 + 0.670562i \(0.766053\pi\)
\(572\) 1.94471 0.0813124
\(573\) 41.8014 1.74628
\(574\) 5.73511 0.239379
\(575\) 0 0
\(576\) 15.3001 0.637503
\(577\) 22.5404 0.938368 0.469184 0.883100i \(-0.344548\pi\)
0.469184 + 0.883100i \(0.344548\pi\)
\(578\) 25.5833 1.06413
\(579\) −13.8975 −0.577559
\(580\) 0 0
\(581\) 22.1195 0.917673
\(582\) −1.27376 −0.0527989
\(583\) −29.0628 −1.20366
\(584\) −0.482082 −0.0199487
\(585\) 0 0
\(586\) −16.8142 −0.694586
\(587\) −29.8831 −1.23341 −0.616704 0.787195i \(-0.711533\pi\)
−0.616704 + 0.787195i \(0.711533\pi\)
\(588\) −3.88535 −0.160229
\(589\) −19.3156 −0.795887
\(590\) 0 0
\(591\) 26.5599 1.09253
\(592\) −35.1154 −1.44323
\(593\) −30.9659 −1.27162 −0.635808 0.771847i \(-0.719333\pi\)
−0.635808 + 0.771847i \(0.719333\pi\)
\(594\) −17.2161 −0.706384
\(595\) 0 0
\(596\) −2.18212 −0.0893830
\(597\) −2.46470 −0.100873
\(598\) 10.0117 0.409410
\(599\) −22.4899 −0.918912 −0.459456 0.888201i \(-0.651956\pi\)
−0.459456 + 0.888201i \(0.651956\pi\)
\(600\) 0 0
\(601\) −22.2188 −0.906322 −0.453161 0.891429i \(-0.649704\pi\)
−0.453161 + 0.891429i \(0.649704\pi\)
\(602\) 46.3732 1.89003
\(603\) −17.3362 −0.705984
\(604\) 0.543944 0.0221328
\(605\) 0 0
\(606\) −13.1986 −0.536158
\(607\) −17.3047 −0.702378 −0.351189 0.936305i \(-0.614222\pi\)
−0.351189 + 0.936305i \(0.614222\pi\)
\(608\) −5.47186 −0.221913
\(609\) 41.4939 1.68142
\(610\) 0 0
\(611\) 12.6369 0.511235
\(612\) −2.45073 −0.0990648
\(613\) −13.8909 −0.561050 −0.280525 0.959847i \(-0.590509\pi\)
−0.280525 + 0.959847i \(0.590509\pi\)
\(614\) −6.55732 −0.264632
\(615\) 0 0
\(616\) −54.3891 −2.19140
\(617\) −47.6668 −1.91899 −0.959496 0.281722i \(-0.909094\pi\)
−0.959496 + 0.281722i \(0.909094\pi\)
\(618\) −31.9049 −1.28340
\(619\) −36.3518 −1.46110 −0.730551 0.682858i \(-0.760737\pi\)
−0.730551 + 0.682858i \(0.760737\pi\)
\(620\) 0 0
\(621\) 11.6005 0.465511
\(622\) 44.1843 1.77163
\(623\) 18.1558 0.727396
\(624\) 13.3530 0.534549
\(625\) 0 0
\(626\) −24.2392 −0.968792
\(627\) −43.8150 −1.74980
\(628\) 4.59857 0.183503
\(629\) 60.6826 2.41957
\(630\) 0 0
\(631\) −42.0906 −1.67560 −0.837801 0.545976i \(-0.816159\pi\)
−0.837801 + 0.545976i \(0.816159\pi\)
\(632\) −43.2585 −1.72073
\(633\) 60.5053 2.40487
\(634\) −20.9365 −0.831493
\(635\) 0 0
\(636\) 3.06937 0.121708
\(637\) −13.5207 −0.535711
\(638\) 31.5501 1.24908
\(639\) 21.0234 0.831672
\(640\) 0 0
\(641\) 13.6204 0.537972 0.268986 0.963144i \(-0.413311\pi\)
0.268986 + 0.963144i \(0.413311\pi\)
\(642\) −1.84210 −0.0727020
\(643\) 15.5929 0.614925 0.307462 0.951560i \(-0.400520\pi\)
0.307462 + 0.951560i \(0.400520\pi\)
\(644\) 3.80156 0.149803
\(645\) 0 0
\(646\) −33.6297 −1.32314
\(647\) −30.8612 −1.21328 −0.606639 0.794977i \(-0.707483\pi\)
−0.606639 + 0.794977i \(0.707483\pi\)
\(648\) 33.1861 1.30367
\(649\) 6.51402 0.255697
\(650\) 0 0
\(651\) 38.4501 1.50698
\(652\) −0.486336 −0.0190464
\(653\) −41.4375 −1.62157 −0.810787 0.585342i \(-0.800960\pi\)
−0.810787 + 0.585342i \(0.800960\pi\)
\(654\) 16.1581 0.631830
\(655\) 0 0
\(656\) −3.91896 −0.153009
\(657\) 0.285719 0.0111470
\(658\) −36.6612 −1.42920
\(659\) −5.89065 −0.229467 −0.114733 0.993396i \(-0.536601\pi\)
−0.114733 + 0.993396i \(0.536601\pi\)
\(660\) 0 0
\(661\) −12.1895 −0.474118 −0.237059 0.971495i \(-0.576184\pi\)
−0.237059 + 0.971495i \(0.576184\pi\)
\(662\) −9.78556 −0.380327
\(663\) −23.0753 −0.896169
\(664\) −17.1236 −0.664525
\(665\) 0 0
\(666\) 23.5780 0.913627
\(667\) −21.2590 −0.823151
\(668\) 5.07127 0.196213
\(669\) 19.8627 0.767935
\(670\) 0 0
\(671\) −52.2014 −2.01521
\(672\) 10.8924 0.420184
\(673\) 13.4033 0.516658 0.258329 0.966057i \(-0.416828\pi\)
0.258329 + 0.966057i \(0.416828\pi\)
\(674\) 27.9432 1.07633
\(675\) 0 0
\(676\) 2.29443 0.0882471
\(677\) 9.52226 0.365970 0.182985 0.983116i \(-0.441424\pi\)
0.182985 + 0.983116i \(0.441424\pi\)
\(678\) −13.8771 −0.532945
\(679\) −1.68310 −0.0645914
\(680\) 0 0
\(681\) −52.6297 −2.01677
\(682\) 29.2357 1.11949
\(683\) 4.11578 0.157486 0.0787429 0.996895i \(-0.474909\pi\)
0.0787429 + 0.996895i \(0.474909\pi\)
\(684\) 1.71023 0.0653921
\(685\) 0 0
\(686\) 3.54059 0.135180
\(687\) −64.6918 −2.46815
\(688\) −31.6881 −1.20810
\(689\) 10.6812 0.406920
\(690\) 0 0
\(691\) 39.0627 1.48601 0.743007 0.669283i \(-0.233399\pi\)
0.743007 + 0.669283i \(0.233399\pi\)
\(692\) −1.29795 −0.0493405
\(693\) 32.2352 1.22451
\(694\) 1.06274 0.0403411
\(695\) 0 0
\(696\) −32.1221 −1.21759
\(697\) 6.77232 0.256520
\(698\) −1.67085 −0.0632427
\(699\) 11.6968 0.442413
\(700\) 0 0
\(701\) 4.81641 0.181913 0.0909566 0.995855i \(-0.471008\pi\)
0.0909566 + 0.995855i \(0.471008\pi\)
\(702\) 6.32726 0.238807
\(703\) −42.3470 −1.59715
\(704\) 41.5924 1.56757
\(705\) 0 0
\(706\) −40.9592 −1.54152
\(707\) −17.4402 −0.655908
\(708\) −0.687956 −0.0258550
\(709\) 39.1628 1.47079 0.735394 0.677640i \(-0.236997\pi\)
0.735394 + 0.677640i \(0.236997\pi\)
\(710\) 0 0
\(711\) 25.6383 0.961511
\(712\) −14.0551 −0.526738
\(713\) −19.6995 −0.737753
\(714\) 66.9441 2.50532
\(715\) 0 0
\(716\) 5.51552 0.206125
\(717\) 4.67119 0.174449
\(718\) −19.0374 −0.710470
\(719\) −32.1852 −1.20030 −0.600152 0.799886i \(-0.704893\pi\)
−0.600152 + 0.799886i \(0.704893\pi\)
\(720\) 0 0
\(721\) −42.1581 −1.57005
\(722\) −1.79904 −0.0669533
\(723\) 2.18147 0.0811296
\(724\) −1.52270 −0.0565908
\(725\) 0 0
\(726\) 34.4059 1.27692
\(727\) 1.69429 0.0628377 0.0314188 0.999506i \(-0.489997\pi\)
0.0314188 + 0.999506i \(0.489997\pi\)
\(728\) 19.9891 0.740846
\(729\) −1.94876 −0.0721763
\(730\) 0 0
\(731\) 54.7600 2.02537
\(732\) 5.51307 0.203769
\(733\) −18.2300 −0.673340 −0.336670 0.941623i \(-0.609301\pi\)
−0.336670 + 0.941623i \(0.609301\pi\)
\(734\) −4.48226 −0.165443
\(735\) 0 0
\(736\) −5.58061 −0.205704
\(737\) −47.1275 −1.73596
\(738\) 2.63135 0.0968614
\(739\) −12.4675 −0.458623 −0.229312 0.973353i \(-0.573648\pi\)
−0.229312 + 0.973353i \(0.573648\pi\)
\(740\) 0 0
\(741\) 16.1029 0.591556
\(742\) −30.9873 −1.13758
\(743\) 15.6839 0.575385 0.287693 0.957723i \(-0.407112\pi\)
0.287693 + 0.957723i \(0.407112\pi\)
\(744\) −29.7658 −1.09127
\(745\) 0 0
\(746\) −7.61194 −0.278693
\(747\) 10.1488 0.371324
\(748\) −6.66218 −0.243593
\(749\) −2.43409 −0.0889399
\(750\) 0 0
\(751\) −3.58156 −0.130693 −0.0653465 0.997863i \(-0.520815\pi\)
−0.0653465 + 0.997863i \(0.520815\pi\)
\(752\) 25.0516 0.913539
\(753\) −61.3999 −2.23754
\(754\) −11.5953 −0.422276
\(755\) 0 0
\(756\) 2.40253 0.0873793
\(757\) 15.7026 0.570720 0.285360 0.958420i \(-0.407887\pi\)
0.285360 + 0.958420i \(0.407887\pi\)
\(758\) 1.28164 0.0465512
\(759\) −44.6858 −1.62199
\(760\) 0 0
\(761\) −36.1137 −1.30912 −0.654559 0.756011i \(-0.727146\pi\)
−0.654559 + 0.756011i \(0.727146\pi\)
\(762\) 17.6851 0.640665
\(763\) 21.3507 0.772948
\(764\) −4.43549 −0.160470
\(765\) 0 0
\(766\) −23.3261 −0.842807
\(767\) −2.39403 −0.0864436
\(768\) −11.9502 −0.431216
\(769\) −50.2736 −1.81291 −0.906456 0.422300i \(-0.861223\pi\)
−0.906456 + 0.422300i \(0.861223\pi\)
\(770\) 0 0
\(771\) −2.68467 −0.0966862
\(772\) 1.47464 0.0530736
\(773\) 27.4904 0.988762 0.494381 0.869245i \(-0.335395\pi\)
0.494381 + 0.869245i \(0.335395\pi\)
\(774\) 21.2767 0.764776
\(775\) 0 0
\(776\) 1.30295 0.0467733
\(777\) 84.2968 3.02413
\(778\) −22.3942 −0.802870
\(779\) −4.72602 −0.169327
\(780\) 0 0
\(781\) 57.1509 2.04502
\(782\) −34.2981 −1.22650
\(783\) −13.4354 −0.480141
\(784\) −26.8037 −0.957275
\(785\) 0 0
\(786\) −19.5153 −0.696087
\(787\) −43.4981 −1.55054 −0.775271 0.631629i \(-0.782386\pi\)
−0.775271 + 0.631629i \(0.782386\pi\)
\(788\) −2.81824 −0.100396
\(789\) 32.7567 1.16617
\(790\) 0 0
\(791\) −18.3367 −0.651977
\(792\) −24.9545 −0.886721
\(793\) 19.1851 0.681282
\(794\) 3.76307 0.133547
\(795\) 0 0
\(796\) 0.261526 0.00926955
\(797\) −38.2429 −1.35463 −0.677316 0.735692i \(-0.736857\pi\)
−0.677316 + 0.735692i \(0.736857\pi\)
\(798\) −46.7165 −1.65375
\(799\) −43.2915 −1.53154
\(800\) 0 0
\(801\) 8.33015 0.294331
\(802\) −18.0898 −0.638772
\(803\) 0.776713 0.0274096
\(804\) 4.97721 0.175533
\(805\) 0 0
\(806\) −10.7447 −0.378467
\(807\) −2.05159 −0.0722193
\(808\) 13.5012 0.474970
\(809\) −28.3274 −0.995939 −0.497969 0.867195i \(-0.665921\pi\)
−0.497969 + 0.867195i \(0.665921\pi\)
\(810\) 0 0
\(811\) −39.3902 −1.38318 −0.691589 0.722292i \(-0.743089\pi\)
−0.691589 + 0.722292i \(0.743089\pi\)
\(812\) −4.40287 −0.154510
\(813\) 11.1523 0.391129
\(814\) 64.0954 2.24654
\(815\) 0 0
\(816\) −45.7447 −1.60139
\(817\) −38.2139 −1.33694
\(818\) 32.7704 1.14579
\(819\) −11.8471 −0.413971
\(820\) 0 0
\(821\) 39.6673 1.38440 0.692199 0.721707i \(-0.256642\pi\)
0.692199 + 0.721707i \(0.256642\pi\)
\(822\) 28.8396 1.00590
\(823\) 9.49313 0.330910 0.165455 0.986217i \(-0.447091\pi\)
0.165455 + 0.986217i \(0.447091\pi\)
\(824\) 32.6363 1.13694
\(825\) 0 0
\(826\) 6.94538 0.241661
\(827\) 8.26358 0.287353 0.143676 0.989625i \(-0.454108\pi\)
0.143676 + 0.989625i \(0.454108\pi\)
\(828\) 1.74421 0.0606157
\(829\) −32.7576 −1.13772 −0.568860 0.822435i \(-0.692615\pi\)
−0.568860 + 0.822435i \(0.692615\pi\)
\(830\) 0 0
\(831\) −5.21776 −0.181002
\(832\) −15.2861 −0.529949
\(833\) 46.3193 1.60487
\(834\) 9.53380 0.330128
\(835\) 0 0
\(836\) 4.64916 0.160795
\(837\) −12.4498 −0.430329
\(838\) −10.4078 −0.359531
\(839\) 28.8263 0.995195 0.497597 0.867408i \(-0.334216\pi\)
0.497597 + 0.867408i \(0.334216\pi\)
\(840\) 0 0
\(841\) −4.37839 −0.150979
\(842\) 28.4169 0.979311
\(843\) 16.3406 0.562801
\(844\) −6.42015 −0.220991
\(845\) 0 0
\(846\) −16.8207 −0.578308
\(847\) 45.4629 1.56212
\(848\) 21.1745 0.727135
\(849\) 39.1373 1.34319
\(850\) 0 0
\(851\) −43.1886 −1.48049
\(852\) −6.03581 −0.206783
\(853\) −1.74141 −0.0596248 −0.0298124 0.999556i \(-0.509491\pi\)
−0.0298124 + 0.999556i \(0.509491\pi\)
\(854\) −55.6582 −1.90458
\(855\) 0 0
\(856\) 1.88433 0.0644051
\(857\) 23.6164 0.806720 0.403360 0.915041i \(-0.367842\pi\)
0.403360 + 0.915041i \(0.367842\pi\)
\(858\) −24.3730 −0.832081
\(859\) 18.0458 0.615714 0.307857 0.951433i \(-0.400388\pi\)
0.307857 + 0.951433i \(0.400388\pi\)
\(860\) 0 0
\(861\) 9.40771 0.320614
\(862\) 45.1140 1.53659
\(863\) −8.06392 −0.274499 −0.137249 0.990537i \(-0.543826\pi\)
−0.137249 + 0.990537i \(0.543826\pi\)
\(864\) −3.52687 −0.119986
\(865\) 0 0
\(866\) −45.9007 −1.55977
\(867\) 41.9662 1.42525
\(868\) −4.07990 −0.138481
\(869\) 69.6964 2.36429
\(870\) 0 0
\(871\) 17.3203 0.586877
\(872\) −16.5285 −0.559724
\(873\) −0.772231 −0.0261361
\(874\) 23.9347 0.809604
\(875\) 0 0
\(876\) −0.0820299 −0.00277153
\(877\) 14.4702 0.488625 0.244312 0.969697i \(-0.421438\pi\)
0.244312 + 0.969697i \(0.421438\pi\)
\(878\) 3.03914 0.102566
\(879\) −27.5815 −0.930301
\(880\) 0 0
\(881\) 10.0284 0.337867 0.168933 0.985627i \(-0.445968\pi\)
0.168933 + 0.985627i \(0.445968\pi\)
\(882\) 17.9971 0.605995
\(883\) −0.730440 −0.0245813 −0.0122906 0.999924i \(-0.503912\pi\)
−0.0122906 + 0.999924i \(0.503912\pi\)
\(884\) 2.44849 0.0823515
\(885\) 0 0
\(886\) −24.4343 −0.820887
\(887\) 29.6147 0.994366 0.497183 0.867646i \(-0.334368\pi\)
0.497183 + 0.867646i \(0.334368\pi\)
\(888\) −65.2575 −2.18990
\(889\) 23.3685 0.783756
\(890\) 0 0
\(891\) −53.4682 −1.79125
\(892\) −2.10760 −0.0705677
\(893\) 30.2107 1.01096
\(894\) 27.3485 0.914669
\(895\) 0 0
\(896\) 34.3604 1.14790
\(897\) 16.4230 0.548346
\(898\) 34.5947 1.15444
\(899\) 22.8155 0.760939
\(900\) 0 0
\(901\) −36.5915 −1.21904
\(902\) 7.15320 0.238175
\(903\) 76.0694 2.53143
\(904\) 14.1952 0.472124
\(905\) 0 0
\(906\) −6.81724 −0.226488
\(907\) 3.96710 0.131725 0.0658627 0.997829i \(-0.479020\pi\)
0.0658627 + 0.997829i \(0.479020\pi\)
\(908\) 5.58447 0.185327
\(909\) −8.00184 −0.265404
\(910\) 0 0
\(911\) 25.8759 0.857307 0.428653 0.903469i \(-0.358988\pi\)
0.428653 + 0.903469i \(0.358988\pi\)
\(912\) 31.9227 1.05706
\(913\) 27.5889 0.913060
\(914\) −12.1049 −0.400394
\(915\) 0 0
\(916\) 6.86437 0.226805
\(917\) −25.7868 −0.851556
\(918\) −21.6759 −0.715411
\(919\) 16.5327 0.545364 0.272682 0.962104i \(-0.412089\pi\)
0.272682 + 0.962104i \(0.412089\pi\)
\(920\) 0 0
\(921\) −10.7565 −0.354437
\(922\) 16.4669 0.542309
\(923\) −21.0041 −0.691360
\(924\) −9.25471 −0.304458
\(925\) 0 0
\(926\) −33.7383 −1.10871
\(927\) −19.3428 −0.635300
\(928\) 6.46332 0.212169
\(929\) −1.50189 −0.0492755 −0.0246378 0.999696i \(-0.507843\pi\)
−0.0246378 + 0.999696i \(0.507843\pi\)
\(930\) 0 0
\(931\) −32.3236 −1.05936
\(932\) −1.24113 −0.0406546
\(933\) 72.4787 2.37285
\(934\) 28.1964 0.922615
\(935\) 0 0
\(936\) 9.17131 0.299774
\(937\) 8.04782 0.262911 0.131455 0.991322i \(-0.458035\pi\)
0.131455 + 0.991322i \(0.458035\pi\)
\(938\) −50.2483 −1.64067
\(939\) −39.7613 −1.29756
\(940\) 0 0
\(941\) −2.66537 −0.0868887 −0.0434443 0.999056i \(-0.513833\pi\)
−0.0434443 + 0.999056i \(0.513833\pi\)
\(942\) −57.6338 −1.87781
\(943\) −4.81995 −0.156959
\(944\) −4.74597 −0.154468
\(945\) 0 0
\(946\) 57.8397 1.88053
\(947\) −39.0257 −1.26816 −0.634082 0.773266i \(-0.718622\pi\)
−0.634082 + 0.773266i \(0.718622\pi\)
\(948\) −7.36075 −0.239066
\(949\) −0.285458 −0.00926636
\(950\) 0 0
\(951\) −34.3436 −1.11367
\(952\) −68.4786 −2.21941
\(953\) 40.4838 1.31140 0.655700 0.755022i \(-0.272374\pi\)
0.655700 + 0.755022i \(0.272374\pi\)
\(954\) −14.2174 −0.460307
\(955\) 0 0
\(956\) −0.495655 −0.0160306
\(957\) 51.7539 1.67297
\(958\) −35.3564 −1.14231
\(959\) 38.1076 1.23056
\(960\) 0 0
\(961\) −9.85816 −0.318005
\(962\) −23.5564 −0.759489
\(963\) −1.11680 −0.0359884
\(964\) −0.231473 −0.00745524
\(965\) 0 0
\(966\) −47.6449 −1.53295
\(967\) −26.3391 −0.847009 −0.423504 0.905894i \(-0.639200\pi\)
−0.423504 + 0.905894i \(0.639200\pi\)
\(968\) −35.1946 −1.13120
\(969\) −55.1653 −1.77217
\(970\) 0 0
\(971\) −9.17879 −0.294561 −0.147281 0.989095i \(-0.547052\pi\)
−0.147281 + 0.989095i \(0.547052\pi\)
\(972\) 3.76663 0.120815
\(973\) 12.5976 0.403862
\(974\) 22.7684 0.729546
\(975\) 0 0
\(976\) 38.0328 1.21740
\(977\) 27.6516 0.884653 0.442326 0.896854i \(-0.354153\pi\)
0.442326 + 0.896854i \(0.354153\pi\)
\(978\) 6.09525 0.194905
\(979\) 22.6451 0.723740
\(980\) 0 0
\(981\) 9.79604 0.312763
\(982\) −6.80610 −0.217191
\(983\) 27.0845 0.863861 0.431930 0.901907i \(-0.357833\pi\)
0.431930 + 0.901907i \(0.357833\pi\)
\(984\) −7.28289 −0.232170
\(985\) 0 0
\(986\) 39.7232 1.26504
\(987\) −60.1381 −1.91422
\(988\) −1.70866 −0.0543598
\(989\) −38.9734 −1.23928
\(990\) 0 0
\(991\) −41.0027 −1.30249 −0.651246 0.758867i \(-0.725753\pi\)
−0.651246 + 0.758867i \(0.725753\pi\)
\(992\) 5.98920 0.190157
\(993\) −16.0520 −0.509394
\(994\) 60.9355 1.93276
\(995\) 0 0
\(996\) −2.91371 −0.0923245
\(997\) 37.9223 1.20101 0.600505 0.799621i \(-0.294966\pi\)
0.600505 + 0.799621i \(0.294966\pi\)
\(998\) 38.9623 1.23333
\(999\) −27.2946 −0.863562
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 \(a_p\))