Properties

Label 6017.2.a.c.1.2
Level 6017
Weight 2
Character 6017.1
Self dual Yes
Analytic conductor 48.046
Analytic rank 1
Dimension 106
CM No

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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 1.2
Character \(\chi\) = 6017.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.76753 q^{2}\) \(-2.67959 q^{3}\) \(+5.65924 q^{4}\) \(+2.34491 q^{5}\) \(+7.41585 q^{6}\) \(-2.59530 q^{7}\) \(-10.1271 q^{8}\) \(+4.18020 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.76753 q^{2}\) \(-2.67959 q^{3}\) \(+5.65924 q^{4}\) \(+2.34491 q^{5}\) \(+7.41585 q^{6}\) \(-2.59530 q^{7}\) \(-10.1271 q^{8}\) \(+4.18020 q^{9}\) \(-6.48960 q^{10}\) \(+1.00000 q^{11}\) \(-15.1644 q^{12}\) \(+4.83498 q^{13}\) \(+7.18257 q^{14}\) \(-6.28338 q^{15}\) \(+16.7085 q^{16}\) \(-1.57013 q^{17}\) \(-11.5688 q^{18}\) \(-3.15115 q^{19}\) \(+13.2704 q^{20}\) \(+6.95433 q^{21}\) \(-2.76753 q^{22}\) \(+1.05830 q^{23}\) \(+27.1364 q^{24}\) \(+0.498582 q^{25}\) \(-13.3810 q^{26}\) \(-3.16246 q^{27}\) \(-14.6874 q^{28}\) \(-2.77317 q^{29}\) \(+17.3895 q^{30}\) \(+3.26591 q^{31}\) \(-25.9872 q^{32}\) \(-2.67959 q^{33}\) \(+4.34540 q^{34}\) \(-6.08573 q^{35}\) \(+23.6568 q^{36}\) \(-4.96234 q^{37}\) \(+8.72090 q^{38}\) \(-12.9558 q^{39}\) \(-23.7470 q^{40}\) \(+7.87936 q^{41}\) \(-19.2463 q^{42}\) \(-1.52434 q^{43}\) \(+5.65924 q^{44}\) \(+9.80218 q^{45}\) \(-2.92888 q^{46}\) \(+2.09019 q^{47}\) \(-44.7720 q^{48}\) \(-0.264435 q^{49}\) \(-1.37984 q^{50}\) \(+4.20731 q^{51}\) \(+27.3623 q^{52}\) \(+0.760993 q^{53}\) \(+8.75220 q^{54}\) \(+2.34491 q^{55}\) \(+26.2827 q^{56}\) \(+8.44378 q^{57}\) \(+7.67484 q^{58}\) \(+8.30600 q^{59}\) \(-35.5592 q^{60}\) \(+3.19891 q^{61}\) \(-9.03852 q^{62}\) \(-10.8489 q^{63}\) \(+38.5035 q^{64}\) \(+11.3376 q^{65}\) \(+7.41585 q^{66}\) \(-7.44214 q^{67}\) \(-8.88576 q^{68}\) \(-2.83581 q^{69}\) \(+16.8424 q^{70}\) \(+0.478170 q^{71}\) \(-42.3332 q^{72}\) \(-4.36898 q^{73}\) \(+13.7334 q^{74}\) \(-1.33599 q^{75}\) \(-17.8331 q^{76}\) \(-2.59530 q^{77}\) \(+35.8555 q^{78}\) \(-13.5573 q^{79}\) \(+39.1799 q^{80}\) \(-4.06652 q^{81}\) \(-21.8064 q^{82}\) \(-3.93301 q^{83}\) \(+39.3562 q^{84}\) \(-3.68181 q^{85}\) \(+4.21867 q^{86}\) \(+7.43096 q^{87}\) \(-10.1271 q^{88}\) \(+14.5055 q^{89}\) \(-27.1279 q^{90}\) \(-12.5482 q^{91}\) \(+5.98918 q^{92}\) \(-8.75130 q^{93}\) \(-5.78467 q^{94}\) \(-7.38914 q^{95}\) \(+69.6351 q^{96}\) \(-0.483083 q^{97}\) \(+0.731833 q^{98}\) \(+4.18020 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(106q \) \(\mathstrut -\mathstrut 13q^{2} \) \(\mathstrut -\mathstrut 15q^{3} \) \(\mathstrut +\mathstrut 93q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 22q^{6} \) \(\mathstrut -\mathstrut 66q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 97q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(106q \) \(\mathstrut -\mathstrut 13q^{2} \) \(\mathstrut -\mathstrut 15q^{3} \) \(\mathstrut +\mathstrut 93q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 22q^{6} \) \(\mathstrut -\mathstrut 66q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 97q^{9} \) \(\mathstrut -\mathstrut 30q^{10} \) \(\mathstrut +\mathstrut 106q^{11} \) \(\mathstrut -\mathstrut 26q^{12} \) \(\mathstrut -\mathstrut 72q^{13} \) \(\mathstrut +\mathstrut 3q^{14} \) \(\mathstrut -\mathstrut 46q^{15} \) \(\mathstrut +\mathstrut 75q^{16} \) \(\mathstrut -\mathstrut 65q^{17} \) \(\mathstrut -\mathstrut 37q^{18} \) \(\mathstrut -\mathstrut 63q^{19} \) \(\mathstrut -\mathstrut 25q^{20} \) \(\mathstrut -\mathstrut 27q^{21} \) \(\mathstrut -\mathstrut 13q^{22} \) \(\mathstrut -\mathstrut 23q^{23} \) \(\mathstrut -\mathstrut 56q^{24} \) \(\mathstrut +\mathstrut 74q^{25} \) \(\mathstrut +\mathstrut 2q^{26} \) \(\mathstrut -\mathstrut 54q^{27} \) \(\mathstrut -\mathstrut 115q^{28} \) \(\mathstrut -\mathstrut 45q^{29} \) \(\mathstrut -\mathstrut 14q^{30} \) \(\mathstrut -\mathstrut 89q^{31} \) \(\mathstrut -\mathstrut 96q^{32} \) \(\mathstrut -\mathstrut 15q^{33} \) \(\mathstrut -\mathstrut 26q^{34} \) \(\mathstrut -\mathstrut 52q^{35} \) \(\mathstrut +\mathstrut 91q^{36} \) \(\mathstrut -\mathstrut 35q^{37} \) \(\mathstrut +\mathstrut 7q^{38} \) \(\mathstrut -\mathstrut 34q^{39} \) \(\mathstrut -\mathstrut 74q^{40} \) \(\mathstrut -\mathstrut 32q^{41} \) \(\mathstrut -\mathstrut 94q^{43} \) \(\mathstrut +\mathstrut 93q^{44} \) \(\mathstrut -\mathstrut 46q^{45} \) \(\mathstrut -\mathstrut 20q^{46} \) \(\mathstrut -\mathstrut 105q^{47} \) \(\mathstrut -\mathstrut 57q^{48} \) \(\mathstrut +\mathstrut 80q^{49} \) \(\mathstrut -\mathstrut 60q^{50} \) \(\mathstrut -\mathstrut 36q^{51} \) \(\mathstrut -\mathstrut 137q^{52} \) \(\mathstrut -\mathstrut 61q^{54} \) \(\mathstrut -\mathstrut 12q^{55} \) \(\mathstrut +\mathstrut 32q^{56} \) \(\mathstrut -\mathstrut 71q^{57} \) \(\mathstrut -\mathstrut 28q^{58} \) \(\mathstrut -\mathstrut 15q^{59} \) \(\mathstrut -\mathstrut 21q^{60} \) \(\mathstrut -\mathstrut 80q^{61} \) \(\mathstrut -\mathstrut 84q^{62} \) \(\mathstrut -\mathstrut 182q^{63} \) \(\mathstrut +\mathstrut 55q^{64} \) \(\mathstrut -\mathstrut 73q^{65} \) \(\mathstrut -\mathstrut 22q^{66} \) \(\mathstrut -\mathstrut 58q^{67} \) \(\mathstrut -\mathstrut 145q^{68} \) \(\mathstrut -\mathstrut 8q^{69} \) \(\mathstrut -\mathstrut 39q^{70} \) \(\mathstrut -\mathstrut 11q^{71} \) \(\mathstrut -\mathstrut 100q^{72} \) \(\mathstrut -\mathstrut 155q^{73} \) \(\mathstrut -\mathstrut 15q^{74} \) \(\mathstrut -\mathstrut 15q^{75} \) \(\mathstrut -\mathstrut 132q^{76} \) \(\mathstrut -\mathstrut 66q^{77} \) \(\mathstrut -\mathstrut 45q^{78} \) \(\mathstrut -\mathstrut 50q^{79} \) \(\mathstrut -\mathstrut 28q^{80} \) \(\mathstrut +\mathstrut 114q^{81} \) \(\mathstrut -\mathstrut 57q^{82} \) \(\mathstrut -\mathstrut 96q^{83} \) \(\mathstrut -\mathstrut 27q^{84} \) \(\mathstrut -\mathstrut 74q^{85} \) \(\mathstrut +\mathstrut 54q^{86} \) \(\mathstrut -\mathstrut 182q^{87} \) \(\mathstrut -\mathstrut 39q^{88} \) \(\mathstrut +\mathstrut 9q^{89} \) \(\mathstrut -\mathstrut 53q^{90} \) \(\mathstrut +\mathstrut 6q^{91} \) \(\mathstrut -\mathstrut 18q^{92} \) \(\mathstrut -\mathstrut 26q^{93} \) \(\mathstrut -\mathstrut 33q^{94} \) \(\mathstrut -\mathstrut 49q^{95} \) \(\mathstrut -\mathstrut 56q^{96} \) \(\mathstrut -\mathstrut 102q^{97} \) \(\mathstrut -\mathstrut 76q^{98} \) \(\mathstrut +\mathstrut 97q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.76753 −1.95694 −0.978471 0.206386i \(-0.933830\pi\)
−0.978471 + 0.206386i \(0.933830\pi\)
\(3\) −2.67959 −1.54706 −0.773531 0.633759i \(-0.781511\pi\)
−0.773531 + 0.633759i \(0.781511\pi\)
\(4\) 5.65924 2.82962
\(5\) 2.34491 1.04867 0.524337 0.851511i \(-0.324313\pi\)
0.524337 + 0.851511i \(0.324313\pi\)
\(6\) 7.41585 3.02751
\(7\) −2.59530 −0.980930 −0.490465 0.871461i \(-0.663173\pi\)
−0.490465 + 0.871461i \(0.663173\pi\)
\(8\) −10.1271 −3.58046
\(9\) 4.18020 1.39340
\(10\) −6.48960 −2.05219
\(11\) 1.00000 0.301511
\(12\) −15.1644 −4.37760
\(13\) 4.83498 1.34098 0.670491 0.741918i \(-0.266084\pi\)
0.670491 + 0.741918i \(0.266084\pi\)
\(14\) 7.18257 1.91962
\(15\) −6.28338 −1.62236
\(16\) 16.7085 4.17713
\(17\) −1.57013 −0.380813 −0.190407 0.981705i \(-0.560981\pi\)
−0.190407 + 0.981705i \(0.560981\pi\)
\(18\) −11.5688 −2.72680
\(19\) −3.15115 −0.722923 −0.361461 0.932387i \(-0.617722\pi\)
−0.361461 + 0.932387i \(0.617722\pi\)
\(20\) 13.2704 2.96735
\(21\) 6.95433 1.51756
\(22\) −2.76753 −0.590040
\(23\) 1.05830 0.220671 0.110335 0.993894i \(-0.464807\pi\)
0.110335 + 0.993894i \(0.464807\pi\)
\(24\) 27.1364 5.53919
\(25\) 0.498582 0.0997164
\(26\) −13.3810 −2.62422
\(27\) −3.16246 −0.608615
\(28\) −14.6874 −2.77566
\(29\) −2.77317 −0.514965 −0.257482 0.966283i \(-0.582893\pi\)
−0.257482 + 0.966283i \(0.582893\pi\)
\(30\) 17.3895 3.17487
\(31\) 3.26591 0.586575 0.293288 0.956024i \(-0.405251\pi\)
0.293288 + 0.956024i \(0.405251\pi\)
\(32\) −25.9872 −4.59394
\(33\) −2.67959 −0.466457
\(34\) 4.34540 0.745229
\(35\) −6.08573 −1.02868
\(36\) 23.6568 3.94279
\(37\) −4.96234 −0.815804 −0.407902 0.913026i \(-0.633739\pi\)
−0.407902 + 0.913026i \(0.633739\pi\)
\(38\) 8.72090 1.41472
\(39\) −12.9558 −2.07458
\(40\) −23.7470 −3.75473
\(41\) 7.87936 1.23055 0.615275 0.788313i \(-0.289045\pi\)
0.615275 + 0.788313i \(0.289045\pi\)
\(42\) −19.2463 −2.96977
\(43\) −1.52434 −0.232460 −0.116230 0.993222i \(-0.537081\pi\)
−0.116230 + 0.993222i \(0.537081\pi\)
\(44\) 5.65924 0.853162
\(45\) 9.80218 1.46122
\(46\) −2.92888 −0.431840
\(47\) 2.09019 0.304885 0.152443 0.988312i \(-0.451286\pi\)
0.152443 + 0.988312i \(0.451286\pi\)
\(48\) −44.7720 −6.46228
\(49\) −0.264435 −0.0377765
\(50\) −1.37984 −0.195139
\(51\) 4.20731 0.589142
\(52\) 27.3623 3.79447
\(53\) 0.760993 0.104530 0.0522652 0.998633i \(-0.483356\pi\)
0.0522652 + 0.998633i \(0.483356\pi\)
\(54\) 8.75220 1.19102
\(55\) 2.34491 0.316187
\(56\) 26.2827 3.51218
\(57\) 8.44378 1.11841
\(58\) 7.67484 1.00776
\(59\) 8.30600 1.08135 0.540675 0.841232i \(-0.318169\pi\)
0.540675 + 0.841232i \(0.318169\pi\)
\(60\) −35.5592 −4.59067
\(61\) 3.19891 0.409579 0.204789 0.978806i \(-0.434349\pi\)
0.204789 + 0.978806i \(0.434349\pi\)
\(62\) −9.03852 −1.14789
\(63\) −10.8489 −1.36683
\(64\) 38.5035 4.81294
\(65\) 11.3376 1.40625
\(66\) 7.41585 0.912828
\(67\) −7.44214 −0.909202 −0.454601 0.890695i \(-0.650218\pi\)
−0.454601 + 0.890695i \(0.650218\pi\)
\(68\) −8.88576 −1.07756
\(69\) −2.83581 −0.341392
\(70\) 16.8424 2.01306
\(71\) 0.478170 0.0567483 0.0283741 0.999597i \(-0.490967\pi\)
0.0283741 + 0.999597i \(0.490967\pi\)
\(72\) −42.3332 −4.98901
\(73\) −4.36898 −0.511351 −0.255675 0.966763i \(-0.582298\pi\)
−0.255675 + 0.966763i \(0.582298\pi\)
\(74\) 13.7334 1.59648
\(75\) −1.33599 −0.154267
\(76\) −17.8331 −2.04560
\(77\) −2.59530 −0.295762
\(78\) 35.8555 4.05984
\(79\) −13.5573 −1.52531 −0.762656 0.646804i \(-0.776105\pi\)
−0.762656 + 0.646804i \(0.776105\pi\)
\(80\) 39.1799 4.38044
\(81\) −4.06652 −0.451835
\(82\) −21.8064 −2.40811
\(83\) −3.93301 −0.431704 −0.215852 0.976426i \(-0.569253\pi\)
−0.215852 + 0.976426i \(0.569253\pi\)
\(84\) 39.3562 4.29412
\(85\) −3.68181 −0.399349
\(86\) 4.21867 0.454911
\(87\) 7.43096 0.796683
\(88\) −10.1271 −1.07955
\(89\) 14.5055 1.53758 0.768791 0.639501i \(-0.220859\pi\)
0.768791 + 0.639501i \(0.220859\pi\)
\(90\) −27.1279 −2.85953
\(91\) −12.5482 −1.31541
\(92\) 5.98918 0.624415
\(93\) −8.75130 −0.907468
\(94\) −5.78467 −0.596643
\(95\) −7.38914 −0.758110
\(96\) 69.6351 7.10710
\(97\) −0.483083 −0.0490496 −0.0245248 0.999699i \(-0.507807\pi\)
−0.0245248 + 0.999699i \(0.507807\pi\)
\(98\) 0.731833 0.0739263
\(99\) 4.18020 0.420126
\(100\) 2.82159 0.282159
\(101\) 7.61480 0.757701 0.378851 0.925458i \(-0.376319\pi\)
0.378851 + 0.925458i \(0.376319\pi\)
\(102\) −11.6439 −1.15292
\(103\) 5.27641 0.519900 0.259950 0.965622i \(-0.416294\pi\)
0.259950 + 0.965622i \(0.416294\pi\)
\(104\) −48.9642 −4.80133
\(105\) 16.3072 1.59142
\(106\) −2.10607 −0.204560
\(107\) −13.3985 −1.29528 −0.647642 0.761945i \(-0.724245\pi\)
−0.647642 + 0.761945i \(0.724245\pi\)
\(108\) −17.8971 −1.72215
\(109\) 7.00535 0.670991 0.335495 0.942042i \(-0.391096\pi\)
0.335495 + 0.942042i \(0.391096\pi\)
\(110\) −6.48960 −0.618759
\(111\) 13.2970 1.26210
\(112\) −43.3635 −4.09747
\(113\) −18.2537 −1.71716 −0.858581 0.512678i \(-0.828654\pi\)
−0.858581 + 0.512678i \(0.828654\pi\)
\(114\) −23.3684 −2.18866
\(115\) 2.48162 0.231412
\(116\) −15.6940 −1.45715
\(117\) 20.2112 1.86852
\(118\) −22.9871 −2.11614
\(119\) 4.07496 0.373551
\(120\) 63.6323 5.80880
\(121\) 1.00000 0.0909091
\(122\) −8.85310 −0.801522
\(123\) −21.1135 −1.90374
\(124\) 18.4826 1.65978
\(125\) −10.5554 −0.944104
\(126\) 30.0246 2.67480
\(127\) −10.4582 −0.928015 −0.464008 0.885831i \(-0.653589\pi\)
−0.464008 + 0.885831i \(0.653589\pi\)
\(128\) −54.5852 −4.82470
\(129\) 4.08461 0.359630
\(130\) −31.3771 −2.75195
\(131\) −10.1453 −0.886403 −0.443202 0.896422i \(-0.646157\pi\)
−0.443202 + 0.896422i \(0.646157\pi\)
\(132\) −15.1644 −1.31990
\(133\) 8.17816 0.709136
\(134\) 20.5964 1.77925
\(135\) −7.41566 −0.638239
\(136\) 15.9008 1.36349
\(137\) −10.9591 −0.936298 −0.468149 0.883650i \(-0.655079\pi\)
−0.468149 + 0.883650i \(0.655079\pi\)
\(138\) 7.84820 0.668083
\(139\) −18.8862 −1.60191 −0.800955 0.598724i \(-0.795675\pi\)
−0.800955 + 0.598724i \(0.795675\pi\)
\(140\) −34.4406 −2.91076
\(141\) −5.60085 −0.471677
\(142\) −1.32335 −0.111053
\(143\) 4.83498 0.404321
\(144\) 69.8449 5.82041
\(145\) −6.50282 −0.540030
\(146\) 12.0913 1.00068
\(147\) 0.708578 0.0584425
\(148\) −28.0831 −2.30842
\(149\) −4.87364 −0.399264 −0.199632 0.979871i \(-0.563975\pi\)
−0.199632 + 0.979871i \(0.563975\pi\)
\(150\) 3.69741 0.301892
\(151\) −19.8255 −1.61337 −0.806687 0.590979i \(-0.798741\pi\)
−0.806687 + 0.590979i \(0.798741\pi\)
\(152\) 31.9119 2.58839
\(153\) −6.56347 −0.530625
\(154\) 7.18257 0.578788
\(155\) 7.65826 0.615126
\(156\) −73.3198 −5.87028
\(157\) −0.374807 −0.0299128 −0.0149564 0.999888i \(-0.504761\pi\)
−0.0149564 + 0.999888i \(0.504761\pi\)
\(158\) 37.5202 2.98495
\(159\) −2.03915 −0.161715
\(160\) −60.9376 −4.81754
\(161\) −2.74660 −0.216463
\(162\) 11.2542 0.884215
\(163\) 20.5773 1.61174 0.805871 0.592091i \(-0.201697\pi\)
0.805871 + 0.592091i \(0.201697\pi\)
\(164\) 44.5912 3.48199
\(165\) −6.28338 −0.489161
\(166\) 10.8847 0.844819
\(167\) 4.54815 0.351946 0.175973 0.984395i \(-0.443693\pi\)
0.175973 + 0.984395i \(0.443693\pi\)
\(168\) −70.4270 −5.43356
\(169\) 10.3770 0.798232
\(170\) 10.1895 0.781502
\(171\) −13.1724 −1.00732
\(172\) −8.62662 −0.657774
\(173\) 23.3608 1.77609 0.888045 0.459756i \(-0.152063\pi\)
0.888045 + 0.459756i \(0.152063\pi\)
\(174\) −20.5654 −1.55906
\(175\) −1.29397 −0.0978148
\(176\) 16.7085 1.25945
\(177\) −22.2567 −1.67291
\(178\) −40.1445 −3.00896
\(179\) 10.7005 0.799789 0.399895 0.916561i \(-0.369047\pi\)
0.399895 + 0.916561i \(0.369047\pi\)
\(180\) 55.4729 4.13470
\(181\) 19.7792 1.47018 0.735089 0.677971i \(-0.237141\pi\)
0.735089 + 0.677971i \(0.237141\pi\)
\(182\) 34.7276 2.57418
\(183\) −8.57177 −0.633644
\(184\) −10.7175 −0.790103
\(185\) −11.6362 −0.855512
\(186\) 24.2195 1.77586
\(187\) −1.57013 −0.114820
\(188\) 11.8289 0.862710
\(189\) 8.20751 0.597009
\(190\) 20.4497 1.48358
\(191\) −5.76313 −0.417006 −0.208503 0.978022i \(-0.566859\pi\)
−0.208503 + 0.978022i \(0.566859\pi\)
\(192\) −103.174 −7.44591
\(193\) 12.5873 0.906057 0.453029 0.891496i \(-0.350344\pi\)
0.453029 + 0.891496i \(0.350344\pi\)
\(194\) 1.33695 0.0959873
\(195\) −30.3800 −2.17556
\(196\) −1.49650 −0.106893
\(197\) 8.12958 0.579209 0.289604 0.957146i \(-0.406476\pi\)
0.289604 + 0.957146i \(0.406476\pi\)
\(198\) −11.5688 −0.822162
\(199\) −9.40327 −0.666580 −0.333290 0.942824i \(-0.608159\pi\)
−0.333290 + 0.942824i \(0.608159\pi\)
\(200\) −5.04917 −0.357030
\(201\) 19.9419 1.40659
\(202\) −21.0742 −1.48278
\(203\) 7.19720 0.505144
\(204\) 23.8102 1.66705
\(205\) 18.4764 1.29044
\(206\) −14.6026 −1.01741
\(207\) 4.42391 0.307483
\(208\) 80.7853 5.60145
\(209\) −3.15115 −0.217969
\(210\) −45.1308 −3.11432
\(211\) −15.1946 −1.04604 −0.523019 0.852321i \(-0.675194\pi\)
−0.523019 + 0.852321i \(0.675194\pi\)
\(212\) 4.30664 0.295781
\(213\) −1.28130 −0.0877931
\(214\) 37.0809 2.53480
\(215\) −3.57444 −0.243775
\(216\) 32.0264 2.17912
\(217\) −8.47601 −0.575389
\(218\) −19.3875 −1.31309
\(219\) 11.7071 0.791091
\(220\) 13.2704 0.894689
\(221\) −7.59156 −0.510664
\(222\) −36.8000 −2.46985
\(223\) 2.83111 0.189585 0.0947926 0.995497i \(-0.469781\pi\)
0.0947926 + 0.995497i \(0.469781\pi\)
\(224\) 67.4446 4.50633
\(225\) 2.08417 0.138945
\(226\) 50.5177 3.36039
\(227\) 16.4286 1.09040 0.545202 0.838305i \(-0.316453\pi\)
0.545202 + 0.838305i \(0.316453\pi\)
\(228\) 47.7854 3.16466
\(229\) 8.15162 0.538674 0.269337 0.963046i \(-0.413195\pi\)
0.269337 + 0.963046i \(0.413195\pi\)
\(230\) −6.86795 −0.452859
\(231\) 6.95433 0.457561
\(232\) 28.0841 1.84381
\(233\) −20.2574 −1.32711 −0.663554 0.748128i \(-0.730953\pi\)
−0.663554 + 0.748128i \(0.730953\pi\)
\(234\) −55.9351 −3.65659
\(235\) 4.90130 0.319725
\(236\) 47.0057 3.05981
\(237\) 36.3279 2.35975
\(238\) −11.2776 −0.731018
\(239\) 14.5530 0.941357 0.470679 0.882305i \(-0.344009\pi\)
0.470679 + 0.882305i \(0.344009\pi\)
\(240\) −104.986 −6.77682
\(241\) 28.4585 1.83317 0.916586 0.399838i \(-0.130933\pi\)
0.916586 + 0.399838i \(0.130933\pi\)
\(242\) −2.76753 −0.177904
\(243\) 20.3840 1.30763
\(244\) 18.1034 1.15895
\(245\) −0.620076 −0.0396152
\(246\) 58.4322 3.72550
\(247\) −15.2357 −0.969426
\(248\) −33.0741 −2.10021
\(249\) 10.5389 0.667873
\(250\) 29.2124 1.84756
\(251\) −0.352474 −0.0222480 −0.0111240 0.999938i \(-0.503541\pi\)
−0.0111240 + 0.999938i \(0.503541\pi\)
\(252\) −61.3963 −3.86760
\(253\) 1.05830 0.0665348
\(254\) 28.9434 1.81607
\(255\) 9.86575 0.617817
\(256\) 74.0594 4.62871
\(257\) 12.0977 0.754637 0.377318 0.926084i \(-0.376846\pi\)
0.377318 + 0.926084i \(0.376846\pi\)
\(258\) −11.3043 −0.703775
\(259\) 12.8787 0.800247
\(260\) 64.1620 3.97916
\(261\) −11.5924 −0.717552
\(262\) 28.0776 1.73464
\(263\) 7.88835 0.486417 0.243208 0.969974i \(-0.421800\pi\)
0.243208 + 0.969974i \(0.421800\pi\)
\(264\) 27.1364 1.67013
\(265\) 1.78446 0.109618
\(266\) −22.6333 −1.38774
\(267\) −38.8688 −2.37873
\(268\) −42.1168 −2.57270
\(269\) 13.9394 0.849901 0.424951 0.905217i \(-0.360291\pi\)
0.424951 + 0.905217i \(0.360291\pi\)
\(270\) 20.5231 1.24900
\(271\) −13.6281 −0.827849 −0.413925 0.910311i \(-0.635842\pi\)
−0.413925 + 0.910311i \(0.635842\pi\)
\(272\) −26.2346 −1.59071
\(273\) 33.6240 2.03502
\(274\) 30.3296 1.83228
\(275\) 0.498582 0.0300656
\(276\) −16.0485 −0.966008
\(277\) −1.10973 −0.0666775 −0.0333387 0.999444i \(-0.510614\pi\)
−0.0333387 + 0.999444i \(0.510614\pi\)
\(278\) 52.2683 3.13485
\(279\) 13.6522 0.817334
\(280\) 61.6305 3.68313
\(281\) 4.75075 0.283406 0.141703 0.989909i \(-0.454742\pi\)
0.141703 + 0.989909i \(0.454742\pi\)
\(282\) 15.5005 0.923043
\(283\) −17.0013 −1.01063 −0.505313 0.862936i \(-0.668623\pi\)
−0.505313 + 0.862936i \(0.668623\pi\)
\(284\) 2.70608 0.160576
\(285\) 19.7999 1.17284
\(286\) −13.3810 −0.791233
\(287\) −20.4493 −1.20708
\(288\) −108.632 −6.40119
\(289\) −14.5347 −0.854981
\(290\) 17.9968 1.05681
\(291\) 1.29446 0.0758828
\(292\) −24.7251 −1.44693
\(293\) −27.3560 −1.59815 −0.799077 0.601228i \(-0.794678\pi\)
−0.799077 + 0.601228i \(0.794678\pi\)
\(294\) −1.96101 −0.114369
\(295\) 19.4768 1.13398
\(296\) 50.2540 2.92095
\(297\) −3.16246 −0.183504
\(298\) 13.4880 0.781337
\(299\) 5.11686 0.295916
\(300\) −7.56071 −0.436518
\(301\) 3.95612 0.228027
\(302\) 54.8676 3.15728
\(303\) −20.4046 −1.17221
\(304\) −52.6510 −3.01974
\(305\) 7.50115 0.429514
\(306\) 18.1646 1.03840
\(307\) −11.0899 −0.632934 −0.316467 0.948604i \(-0.602497\pi\)
−0.316467 + 0.948604i \(0.602497\pi\)
\(308\) −14.6874 −0.836893
\(309\) −14.1386 −0.804317
\(310\) −21.1945 −1.20377
\(311\) 12.7481 0.722878 0.361439 0.932396i \(-0.382286\pi\)
0.361439 + 0.932396i \(0.382286\pi\)
\(312\) 131.204 7.42795
\(313\) 23.1882 1.31068 0.655338 0.755335i \(-0.272526\pi\)
0.655338 + 0.755335i \(0.272526\pi\)
\(314\) 1.03729 0.0585377
\(315\) −25.4396 −1.43336
\(316\) −76.7238 −4.31605
\(317\) −20.0562 −1.12647 −0.563234 0.826298i \(-0.690443\pi\)
−0.563234 + 0.826298i \(0.690443\pi\)
\(318\) 5.64341 0.316467
\(319\) −2.77317 −0.155268
\(320\) 90.2870 5.04720
\(321\) 35.9026 2.00389
\(322\) 7.60132 0.423605
\(323\) 4.94772 0.275299
\(324\) −23.0134 −1.27852
\(325\) 2.41063 0.133718
\(326\) −56.9485 −3.15409
\(327\) −18.7715 −1.03806
\(328\) −79.7948 −4.40593
\(329\) −5.42466 −0.299071
\(330\) 17.3895 0.957259
\(331\) −34.8398 −1.91497 −0.957484 0.288486i \(-0.906848\pi\)
−0.957484 + 0.288486i \(0.906848\pi\)
\(332\) −22.2578 −1.22156
\(333\) −20.7436 −1.13674
\(334\) −12.5872 −0.688739
\(335\) −17.4511 −0.953456
\(336\) 116.197 6.33904
\(337\) −12.7390 −0.693937 −0.346969 0.937877i \(-0.612789\pi\)
−0.346969 + 0.937877i \(0.612789\pi\)
\(338\) −28.7188 −1.56209
\(339\) 48.9124 2.65656
\(340\) −20.8363 −1.13001
\(341\) 3.26591 0.176859
\(342\) 36.4551 1.97127
\(343\) 18.8534 1.01799
\(344\) 15.4371 0.832314
\(345\) −6.64971 −0.358008
\(346\) −64.6519 −3.47571
\(347\) −26.3773 −1.41601 −0.708004 0.706209i \(-0.750404\pi\)
−0.708004 + 0.706209i \(0.750404\pi\)
\(348\) 42.0536 2.25431
\(349\) −12.0583 −0.645466 −0.322733 0.946490i \(-0.604602\pi\)
−0.322733 + 0.946490i \(0.604602\pi\)
\(350\) 3.58110 0.191418
\(351\) −15.2904 −0.816142
\(352\) −25.9872 −1.38512
\(353\) 28.9669 1.54175 0.770877 0.636984i \(-0.219818\pi\)
0.770877 + 0.636984i \(0.219818\pi\)
\(354\) 61.5961 3.27380
\(355\) 1.12126 0.0595104
\(356\) 82.0902 4.35077
\(357\) −10.9192 −0.577907
\(358\) −29.6139 −1.56514
\(359\) 30.9236 1.63209 0.816043 0.577992i \(-0.196163\pi\)
0.816043 + 0.577992i \(0.196163\pi\)
\(360\) −99.2673 −5.23185
\(361\) −9.07028 −0.477383
\(362\) −54.7396 −2.87705
\(363\) −2.67959 −0.140642
\(364\) −71.0133 −3.72211
\(365\) −10.2448 −0.536240
\(366\) 23.7227 1.24000
\(367\) 0.117527 0.00613488 0.00306744 0.999995i \(-0.499024\pi\)
0.00306744 + 0.999995i \(0.499024\pi\)
\(368\) 17.6826 0.921771
\(369\) 32.9373 1.71465
\(370\) 32.2036 1.67419
\(371\) −1.97500 −0.102537
\(372\) −49.5257 −2.56779
\(373\) 26.2717 1.36030 0.680148 0.733075i \(-0.261915\pi\)
0.680148 + 0.733075i \(0.261915\pi\)
\(374\) 4.34540 0.224695
\(375\) 28.2841 1.46059
\(376\) −21.1675 −1.09163
\(377\) −13.4082 −0.690559
\(378\) −22.7146 −1.16831
\(379\) −10.9948 −0.564764 −0.282382 0.959302i \(-0.591125\pi\)
−0.282382 + 0.959302i \(0.591125\pi\)
\(380\) −41.8169 −2.14516
\(381\) 28.0237 1.43570
\(382\) 15.9497 0.816056
\(383\) 6.21619 0.317632 0.158816 0.987308i \(-0.449232\pi\)
0.158816 + 0.987308i \(0.449232\pi\)
\(384\) 146.266 7.46411
\(385\) −6.08573 −0.310157
\(386\) −34.8359 −1.77310
\(387\) −6.37206 −0.323910
\(388\) −2.73388 −0.138792
\(389\) −0.423588 −0.0214768 −0.0107384 0.999942i \(-0.503418\pi\)
−0.0107384 + 0.999942i \(0.503418\pi\)
\(390\) 84.0778 4.25744
\(391\) −1.66167 −0.0840344
\(392\) 2.67795 0.135257
\(393\) 27.1854 1.37132
\(394\) −22.4989 −1.13348
\(395\) −31.7905 −1.59955
\(396\) 23.6568 1.18880
\(397\) −12.9970 −0.652301 −0.326150 0.945318i \(-0.605752\pi\)
−0.326150 + 0.945318i \(0.605752\pi\)
\(398\) 26.0239 1.30446
\(399\) −21.9141 −1.09708
\(400\) 8.33056 0.416528
\(401\) 20.8329 1.04034 0.520172 0.854061i \(-0.325868\pi\)
0.520172 + 0.854061i \(0.325868\pi\)
\(402\) −55.1898 −2.75262
\(403\) 15.7906 0.786587
\(404\) 43.0940 2.14401
\(405\) −9.53560 −0.473828
\(406\) −19.9185 −0.988538
\(407\) −4.96234 −0.245974
\(408\) −42.6077 −2.10940
\(409\) −0.965610 −0.0477464 −0.0238732 0.999715i \(-0.507600\pi\)
−0.0238732 + 0.999715i \(0.507600\pi\)
\(410\) −51.1339 −2.52533
\(411\) 29.3658 1.44851
\(412\) 29.8605 1.47112
\(413\) −21.5565 −1.06073
\(414\) −12.2433 −0.601726
\(415\) −9.22254 −0.452717
\(416\) −125.648 −6.16039
\(417\) 50.6074 2.47826
\(418\) 8.72090 0.426553
\(419\) 12.4059 0.606066 0.303033 0.952980i \(-0.402001\pi\)
0.303033 + 0.952980i \(0.402001\pi\)
\(420\) 92.2866 4.50313
\(421\) −12.6096 −0.614555 −0.307278 0.951620i \(-0.599418\pi\)
−0.307278 + 0.951620i \(0.599418\pi\)
\(422\) 42.0515 2.04704
\(423\) 8.73741 0.424827
\(424\) −7.70662 −0.374267
\(425\) −0.782840 −0.0379733
\(426\) 3.54604 0.171806
\(427\) −8.30213 −0.401768
\(428\) −75.8255 −3.66516
\(429\) −12.9558 −0.625510
\(430\) 9.89238 0.477053
\(431\) 31.8829 1.53575 0.767874 0.640601i \(-0.221315\pi\)
0.767874 + 0.640601i \(0.221315\pi\)
\(432\) −52.8399 −2.54226
\(433\) 26.2392 1.26098 0.630488 0.776199i \(-0.282855\pi\)
0.630488 + 0.776199i \(0.282855\pi\)
\(434\) 23.4576 1.12600
\(435\) 17.4249 0.835460
\(436\) 39.6449 1.89865
\(437\) −3.33486 −0.159528
\(438\) −32.3997 −1.54812
\(439\) −7.62837 −0.364082 −0.182041 0.983291i \(-0.558270\pi\)
−0.182041 + 0.983291i \(0.558270\pi\)
\(440\) −23.7470 −1.13209
\(441\) −1.10539 −0.0526377
\(442\) 21.0099 0.999339
\(443\) 31.2874 1.48651 0.743256 0.669007i \(-0.233281\pi\)
0.743256 + 0.669007i \(0.233281\pi\)
\(444\) 75.2511 3.57126
\(445\) 34.0141 1.61242
\(446\) −7.83519 −0.371007
\(447\) 13.0594 0.617687
\(448\) −99.9280 −4.72115
\(449\) 7.79128 0.367693 0.183847 0.982955i \(-0.441145\pi\)
0.183847 + 0.982955i \(0.441145\pi\)
\(450\) −5.76802 −0.271907
\(451\) 7.87936 0.371025
\(452\) −103.302 −4.85892
\(453\) 53.1241 2.49599
\(454\) −45.4666 −2.13386
\(455\) −29.4244 −1.37944
\(456\) −85.5107 −4.00441
\(457\) 2.59913 0.121582 0.0607910 0.998151i \(-0.480638\pi\)
0.0607910 + 0.998151i \(0.480638\pi\)
\(458\) −22.5599 −1.05415
\(459\) 4.96548 0.231769
\(460\) 14.0441 0.654807
\(461\) 12.3598 0.575652 0.287826 0.957683i \(-0.407068\pi\)
0.287826 + 0.957683i \(0.407068\pi\)
\(462\) −19.2463 −0.895421
\(463\) −35.0196 −1.62750 −0.813750 0.581215i \(-0.802578\pi\)
−0.813750 + 0.581215i \(0.802578\pi\)
\(464\) −46.3356 −2.15107
\(465\) −20.5210 −0.951638
\(466\) 56.0631 2.59707
\(467\) 1.75566 0.0812423 0.0406211 0.999175i \(-0.487066\pi\)
0.0406211 + 0.999175i \(0.487066\pi\)
\(468\) 114.380 5.28721
\(469\) 19.3146 0.891863
\(470\) −13.5645 −0.625684
\(471\) 1.00433 0.0462770
\(472\) −84.1155 −3.87173
\(473\) −1.52434 −0.0700894
\(474\) −100.539 −4.61790
\(475\) −1.57110 −0.0720872
\(476\) 23.0612 1.05701
\(477\) 3.18110 0.145653
\(478\) −40.2760 −1.84218
\(479\) −34.9581 −1.59728 −0.798639 0.601810i \(-0.794446\pi\)
−0.798639 + 0.601810i \(0.794446\pi\)
\(480\) 163.288 7.45303
\(481\) −23.9928 −1.09398
\(482\) −78.7598 −3.58741
\(483\) 7.35977 0.334881
\(484\) 5.65924 0.257238
\(485\) −1.13278 −0.0514371
\(486\) −56.4133 −2.55896
\(487\) 14.7032 0.666264 0.333132 0.942880i \(-0.391894\pi\)
0.333132 + 0.942880i \(0.391894\pi\)
\(488\) −32.3956 −1.46648
\(489\) −55.1389 −2.49347
\(490\) 1.71608 0.0775246
\(491\) −35.6718 −1.60984 −0.804922 0.593380i \(-0.797793\pi\)
−0.804922 + 0.593380i \(0.797793\pi\)
\(492\) −119.486 −5.38685
\(493\) 4.35425 0.196105
\(494\) 42.1654 1.89711
\(495\) 9.80218 0.440575
\(496\) 54.5685 2.45020
\(497\) −1.24099 −0.0556661
\(498\) −29.1666 −1.30699
\(499\) −30.7157 −1.37502 −0.687512 0.726173i \(-0.741297\pi\)
−0.687512 + 0.726173i \(0.741297\pi\)
\(500\) −59.7355 −2.67145
\(501\) −12.1872 −0.544483
\(502\) 0.975484 0.0435380
\(503\) −21.4954 −0.958431 −0.479215 0.877697i \(-0.659079\pi\)
−0.479215 + 0.877697i \(0.659079\pi\)
\(504\) 109.867 4.89387
\(505\) 17.8560 0.794581
\(506\) −2.92888 −0.130205
\(507\) −27.8062 −1.23492
\(508\) −59.1855 −2.62593
\(509\) 7.38957 0.327537 0.163768 0.986499i \(-0.447635\pi\)
0.163768 + 0.986499i \(0.447635\pi\)
\(510\) −27.3038 −1.20903
\(511\) 11.3388 0.501599
\(512\) −95.7915 −4.23343
\(513\) 9.96536 0.439982
\(514\) −33.4809 −1.47678
\(515\) 12.3727 0.545205
\(516\) 23.1158 1.01762
\(517\) 2.09019 0.0919264
\(518\) −35.6424 −1.56604
\(519\) −62.5974 −2.74772
\(520\) −114.816 −5.03503
\(521\) 32.2438 1.41263 0.706314 0.707899i \(-0.250357\pi\)
0.706314 + 0.707899i \(0.250357\pi\)
\(522\) 32.0824 1.40421
\(523\) 35.1882 1.53867 0.769336 0.638845i \(-0.220587\pi\)
0.769336 + 0.638845i \(0.220587\pi\)
\(524\) −57.4150 −2.50818
\(525\) 3.46730 0.151326
\(526\) −21.8313 −0.951889
\(527\) −5.12792 −0.223376
\(528\) −44.7720 −1.94845
\(529\) −21.8800 −0.951304
\(530\) −4.93854 −0.214516
\(531\) 34.7208 1.50675
\(532\) 46.2822 2.00659
\(533\) 38.0965 1.65014
\(534\) 107.571 4.65504
\(535\) −31.4183 −1.35833
\(536\) 75.3670 3.25536
\(537\) −28.6728 −1.23732
\(538\) −38.5778 −1.66321
\(539\) −0.264435 −0.0113900
\(540\) −41.9670 −1.80597
\(541\) −1.59121 −0.0684113 −0.0342056 0.999415i \(-0.510890\pi\)
−0.0342056 + 0.999415i \(0.510890\pi\)
\(542\) 37.7163 1.62005
\(543\) −53.0002 −2.27446
\(544\) 40.8034 1.74943
\(545\) 16.4269 0.703650
\(546\) −93.0556 −3.98241
\(547\) 1.00000 0.0427569
\(548\) −62.0201 −2.64937
\(549\) 13.3721 0.570707
\(550\) −1.37984 −0.0588367
\(551\) 8.73867 0.372280
\(552\) 28.7185 1.22234
\(553\) 35.1851 1.49622
\(554\) 3.07123 0.130484
\(555\) 31.1803 1.32353
\(556\) −106.882 −4.53280
\(557\) −14.7719 −0.625907 −0.312954 0.949768i \(-0.601318\pi\)
−0.312954 + 0.949768i \(0.601318\pi\)
\(558\) −37.7828 −1.59947
\(559\) −7.37017 −0.311725
\(560\) −101.683 −4.29691
\(561\) 4.20731 0.177633
\(562\) −13.1478 −0.554608
\(563\) −17.0871 −0.720135 −0.360067 0.932926i \(-0.617246\pi\)
−0.360067 + 0.932926i \(0.617246\pi\)
\(564\) −31.6965 −1.33467
\(565\) −42.8032 −1.80074
\(566\) 47.0518 1.97773
\(567\) 10.5538 0.443219
\(568\) −4.84245 −0.203185
\(569\) −30.6916 −1.28666 −0.643329 0.765590i \(-0.722447\pi\)
−0.643329 + 0.765590i \(0.722447\pi\)
\(570\) −54.7968 −2.29518
\(571\) 10.5882 0.443104 0.221552 0.975149i \(-0.428888\pi\)
0.221552 + 0.975149i \(0.428888\pi\)
\(572\) 27.3623 1.14408
\(573\) 15.4428 0.645134
\(574\) 56.5941 2.36219
\(575\) 0.527650 0.0220045
\(576\) 160.952 6.70635
\(577\) −23.0617 −0.960070 −0.480035 0.877249i \(-0.659376\pi\)
−0.480035 + 0.877249i \(0.659376\pi\)
\(578\) 40.2252 1.67315
\(579\) −33.7289 −1.40173
\(580\) −36.8010 −1.52808
\(581\) 10.2073 0.423471
\(582\) −3.58247 −0.148498
\(583\) 0.760993 0.0315171
\(584\) 44.2450 1.83087
\(585\) 47.3933 1.95947
\(586\) 75.7086 3.12749
\(587\) −3.57697 −0.147637 −0.0738186 0.997272i \(-0.523519\pi\)
−0.0738186 + 0.997272i \(0.523519\pi\)
\(588\) 4.01001 0.165370
\(589\) −10.2914 −0.424048
\(590\) −53.9027 −2.21914
\(591\) −21.7840 −0.896072
\(592\) −82.9133 −3.40772
\(593\) 3.19176 0.131070 0.0655349 0.997850i \(-0.479125\pi\)
0.0655349 + 0.997850i \(0.479125\pi\)
\(594\) 8.75220 0.359107
\(595\) 9.55540 0.391733
\(596\) −27.5811 −1.12977
\(597\) 25.1969 1.03124
\(598\) −14.1611 −0.579090
\(599\) −42.1356 −1.72161 −0.860807 0.508932i \(-0.830041\pi\)
−0.860807 + 0.508932i \(0.830041\pi\)
\(600\) 13.5297 0.552348
\(601\) −29.4312 −1.20052 −0.600261 0.799804i \(-0.704937\pi\)
−0.600261 + 0.799804i \(0.704937\pi\)
\(602\) −10.9487 −0.446236
\(603\) −31.1096 −1.26688
\(604\) −112.197 −4.56523
\(605\) 2.34491 0.0953340
\(606\) 56.4703 2.29395
\(607\) 13.4651 0.546533 0.273267 0.961938i \(-0.411896\pi\)
0.273267 + 0.961938i \(0.411896\pi\)
\(608\) 81.8896 3.32106
\(609\) −19.2855 −0.781490
\(610\) −20.7597 −0.840535
\(611\) 10.1060 0.408846
\(612\) −37.1443 −1.50147
\(613\) −39.9387 −1.61311 −0.806555 0.591159i \(-0.798670\pi\)
−0.806555 + 0.591159i \(0.798670\pi\)
\(614\) 30.6917 1.23861
\(615\) −49.5091 −1.99640
\(616\) 26.2827 1.05896
\(617\) 31.5094 1.26852 0.634261 0.773119i \(-0.281305\pi\)
0.634261 + 0.773119i \(0.281305\pi\)
\(618\) 39.1291 1.57400
\(619\) −41.3778 −1.66311 −0.831557 0.555440i \(-0.812550\pi\)
−0.831557 + 0.555440i \(0.812550\pi\)
\(620\) 43.3399 1.74057
\(621\) −3.34683 −0.134304
\(622\) −35.2808 −1.41463
\(623\) −37.6461 −1.50826
\(624\) −216.471 −8.66579
\(625\) −27.2443 −1.08977
\(626\) −64.1742 −2.56492
\(627\) 8.44378 0.337212
\(628\) −2.12112 −0.0846419
\(629\) 7.79154 0.310669
\(630\) 70.4048 2.80500
\(631\) 12.3307 0.490879 0.245439 0.969412i \(-0.421068\pi\)
0.245439 + 0.969412i \(0.421068\pi\)
\(632\) 137.295 5.46132
\(633\) 40.7153 1.61829
\(634\) 55.5062 2.20443
\(635\) −24.5235 −0.973185
\(636\) −11.5400 −0.457592
\(637\) −1.27854 −0.0506576
\(638\) 7.67484 0.303850
\(639\) 1.99885 0.0790731
\(640\) −127.997 −5.05953
\(641\) −44.2626 −1.74827 −0.874133 0.485687i \(-0.838570\pi\)
−0.874133 + 0.485687i \(0.838570\pi\)
\(642\) −99.3615 −3.92149
\(643\) −29.3680 −1.15816 −0.579081 0.815270i \(-0.696588\pi\)
−0.579081 + 0.815270i \(0.696588\pi\)
\(644\) −15.5437 −0.612507
\(645\) 9.57803 0.377135
\(646\) −13.6930 −0.538743
\(647\) 28.2325 1.10994 0.554968 0.831872i \(-0.312731\pi\)
0.554968 + 0.831872i \(0.312731\pi\)
\(648\) 41.1819 1.61778
\(649\) 8.30600 0.326039
\(650\) −6.67151 −0.261678
\(651\) 22.7122 0.890163
\(652\) 116.452 4.56062
\(653\) 32.5393 1.27336 0.636680 0.771128i \(-0.280307\pi\)
0.636680 + 0.771128i \(0.280307\pi\)
\(654\) 51.9506 2.03143
\(655\) −23.7899 −0.929548
\(656\) 131.652 5.14016
\(657\) −18.2632 −0.712516
\(658\) 15.0129 0.585265
\(659\) 30.2874 1.17983 0.589915 0.807466i \(-0.299161\pi\)
0.589915 + 0.807466i \(0.299161\pi\)
\(660\) −35.5592 −1.38414
\(661\) −40.5808 −1.57841 −0.789206 0.614129i \(-0.789507\pi\)
−0.789206 + 0.614129i \(0.789507\pi\)
\(662\) 96.4203 3.74748
\(663\) 20.3423 0.790028
\(664\) 39.8299 1.54570
\(665\) 19.1770 0.743653
\(666\) 57.4086 2.22454
\(667\) −2.93485 −0.113638
\(668\) 25.7391 0.995875
\(669\) −7.58622 −0.293300
\(670\) 48.2965 1.86586
\(671\) 3.19891 0.123493
\(672\) −180.724 −6.97157
\(673\) −3.02994 −0.116796 −0.0583978 0.998293i \(-0.518599\pi\)
−0.0583978 + 0.998293i \(0.518599\pi\)
\(674\) 35.2556 1.35799
\(675\) −1.57674 −0.0606889
\(676\) 58.7261 2.25869
\(677\) −27.6777 −1.06374 −0.531869 0.846826i \(-0.678510\pi\)
−0.531869 + 0.846826i \(0.678510\pi\)
\(678\) −135.367 −5.19873
\(679\) 1.25374 0.0481143
\(680\) 37.2860 1.42985
\(681\) −44.0219 −1.68692
\(682\) −9.03852 −0.346103
\(683\) 10.4081 0.398256 0.199128 0.979974i \(-0.436189\pi\)
0.199128 + 0.979974i \(0.436189\pi\)
\(684\) −74.5459 −2.85033
\(685\) −25.6980 −0.981871
\(686\) −52.1773 −1.99214
\(687\) −21.8430 −0.833363
\(688\) −25.4695 −0.971016
\(689\) 3.67938 0.140173
\(690\) 18.4033 0.700601
\(691\) −34.1734 −1.30002 −0.650009 0.759927i \(-0.725235\pi\)
−0.650009 + 0.759927i \(0.725235\pi\)
\(692\) 132.205 5.02566
\(693\) −10.8489 −0.412114
\(694\) 73.0001 2.77104
\(695\) −44.2865 −1.67988
\(696\) −75.2538 −2.85249
\(697\) −12.3717 −0.468610
\(698\) 33.3717 1.26314
\(699\) 54.2816 2.05312
\(700\) −7.32287 −0.276779
\(701\) 38.5653 1.45659 0.728296 0.685263i \(-0.240313\pi\)
0.728296 + 0.685263i \(0.240313\pi\)
\(702\) 42.3167 1.59714
\(703\) 15.6371 0.589763
\(704\) 38.5035 1.45115
\(705\) −13.1335 −0.494635
\(706\) −80.1670 −3.01712
\(707\) −19.7627 −0.743252
\(708\) −125.956 −4.73371
\(709\) 9.70096 0.364327 0.182164 0.983268i \(-0.441690\pi\)
0.182164 + 0.983268i \(0.441690\pi\)
\(710\) −3.10313 −0.116458
\(711\) −56.6721 −2.12537
\(712\) −146.898 −5.50525
\(713\) 3.45632 0.129440
\(714\) 30.2193 1.13093
\(715\) 11.3376 0.424001
\(716\) 60.5564 2.26310
\(717\) −38.9961 −1.45634
\(718\) −85.5821 −3.19389
\(719\) −19.3648 −0.722186 −0.361093 0.932530i \(-0.617596\pi\)
−0.361093 + 0.932530i \(0.617596\pi\)
\(720\) 163.780 6.10371
\(721\) −13.6938 −0.509985
\(722\) 25.1023 0.934210
\(723\) −76.2571 −2.83603
\(724\) 111.935 4.16004
\(725\) −1.38265 −0.0513504
\(726\) 7.41585 0.275228
\(727\) −5.55638 −0.206075 −0.103037 0.994677i \(-0.532856\pi\)
−0.103037 + 0.994677i \(0.532856\pi\)
\(728\) 127.077 4.70977
\(729\) −42.4211 −1.57115
\(730\) 28.3530 1.04939
\(731\) 2.39342 0.0885239
\(732\) −48.5097 −1.79297
\(733\) −29.5290 −1.09068 −0.545339 0.838216i \(-0.683599\pi\)
−0.545339 + 0.838216i \(0.683599\pi\)
\(734\) −0.325261 −0.0120056
\(735\) 1.66155 0.0612871
\(736\) −27.5023 −1.01375
\(737\) −7.44214 −0.274135
\(738\) −91.1551 −3.35547
\(739\) −34.6556 −1.27483 −0.637414 0.770522i \(-0.719996\pi\)
−0.637414 + 0.770522i \(0.719996\pi\)
\(740\) −65.8522 −2.42077
\(741\) 40.8255 1.49976
\(742\) 5.46588 0.200659
\(743\) −45.6529 −1.67484 −0.837421 0.546559i \(-0.815938\pi\)
−0.837421 + 0.546559i \(0.815938\pi\)
\(744\) 88.6250 3.24915
\(745\) −11.4282 −0.418698
\(746\) −72.7077 −2.66202
\(747\) −16.4408 −0.601537
\(748\) −8.88576 −0.324896
\(749\) 34.7732 1.27058
\(750\) −78.2773 −2.85828
\(751\) −7.15516 −0.261095 −0.130548 0.991442i \(-0.541674\pi\)
−0.130548 + 0.991442i \(0.541674\pi\)
\(752\) 34.9239 1.27355
\(753\) 0.944487 0.0344190
\(754\) 37.1077 1.35138
\(755\) −46.4888 −1.69190
\(756\) 46.4483 1.68931
\(757\) 20.4453 0.743098 0.371549 0.928413i \(-0.378827\pi\)
0.371549 + 0.928413i \(0.378827\pi\)
\(758\) 30.4284 1.10521
\(759\) −2.83581 −0.102933
\(760\) 74.8303 2.71438
\(761\) 12.8012 0.464043 0.232021 0.972711i \(-0.425466\pi\)
0.232021 + 0.972711i \(0.425466\pi\)
\(762\) −77.5565 −2.80958
\(763\) −18.1810 −0.658195
\(764\) −32.6150 −1.17997
\(765\) −15.3907 −0.556453
\(766\) −17.2035 −0.621588
\(767\) 40.1594 1.45007
\(768\) −198.449 −7.16091
\(769\) 12.6425 0.455902 0.227951 0.973673i \(-0.426797\pi\)
0.227951 + 0.973673i \(0.426797\pi\)
\(770\) 16.8424 0.606960
\(771\) −32.4170 −1.16747
\(772\) 71.2348 2.56380
\(773\) −16.0415 −0.576974 −0.288487 0.957484i \(-0.593152\pi\)
−0.288487 + 0.957484i \(0.593152\pi\)
\(774\) 17.6349 0.633873
\(775\) 1.62832 0.0584911
\(776\) 4.89221 0.175620
\(777\) −34.5098 −1.23803
\(778\) 1.17229 0.0420288
\(779\) −24.8290 −0.889592
\(780\) −171.928 −6.15601
\(781\) 0.478170 0.0171103
\(782\) 4.59874 0.164450
\(783\) 8.77003 0.313415
\(784\) −4.41832 −0.157797
\(785\) −0.878886 −0.0313688
\(786\) −75.2364 −2.68359
\(787\) −22.8750 −0.815405 −0.407703 0.913115i \(-0.633670\pi\)
−0.407703 + 0.913115i \(0.633670\pi\)
\(788\) 46.0073 1.63894
\(789\) −21.1375 −0.752517
\(790\) 87.9813 3.13023
\(791\) 47.3737 1.68442
\(792\) −42.3332 −1.50424
\(793\) 15.4667 0.549238
\(794\) 35.9696 1.27651
\(795\) −4.78161 −0.169586
\(796\) −53.2154 −1.88617
\(797\) −5.01257 −0.177554 −0.0887771 0.996052i \(-0.528296\pi\)
−0.0887771 + 0.996052i \(0.528296\pi\)
\(798\) 60.6480 2.14692
\(799\) −3.28188 −0.116104
\(800\) −12.9568 −0.458091
\(801\) 60.6360 2.14247
\(802\) −57.6557 −2.03589
\(803\) −4.36898 −0.154178
\(804\) 112.856 3.98012
\(805\) −6.44053 −0.226999
\(806\) −43.7011 −1.53930
\(807\) −37.3519 −1.31485
\(808\) −77.1156 −2.71292
\(809\) −12.6219 −0.443764 −0.221882 0.975074i \(-0.571220\pi\)
−0.221882 + 0.975074i \(0.571220\pi\)
\(810\) 26.3901 0.927253
\(811\) 30.9353 1.08629 0.543143 0.839641i \(-0.317234\pi\)
0.543143 + 0.839641i \(0.317234\pi\)
\(812\) 40.7307 1.42937
\(813\) 36.5178 1.28073
\(814\) 13.7334 0.481357
\(815\) 48.2519 1.69019
\(816\) 70.2980 2.46092
\(817\) 4.80343 0.168051
\(818\) 2.67236 0.0934368
\(819\) −52.4540 −1.83289
\(820\) 104.562 3.65147
\(821\) −41.0581 −1.43294 −0.716468 0.697620i \(-0.754242\pi\)
−0.716468 + 0.697620i \(0.754242\pi\)
\(822\) −81.2710 −2.83465
\(823\) 36.9226 1.28704 0.643520 0.765429i \(-0.277473\pi\)
0.643520 + 0.765429i \(0.277473\pi\)
\(824\) −53.4345 −1.86148
\(825\) −1.33599 −0.0465134
\(826\) 59.6584 2.07578
\(827\) 50.3993 1.75256 0.876278 0.481805i \(-0.160019\pi\)
0.876278 + 0.481805i \(0.160019\pi\)
\(828\) 25.0360 0.870060
\(829\) −35.6741 −1.23901 −0.619507 0.784991i \(-0.712667\pi\)
−0.619507 + 0.784991i \(0.712667\pi\)
\(830\) 25.5237 0.885940
\(831\) 2.97363 0.103154
\(832\) 186.164 6.45406
\(833\) 0.415199 0.0143858
\(834\) −140.058 −4.84980
\(835\) 10.6650 0.369077
\(836\) −17.8331 −0.616770
\(837\) −10.3283 −0.356998
\(838\) −34.3336 −1.18604
\(839\) 12.1663 0.420028 0.210014 0.977698i \(-0.432649\pi\)
0.210014 + 0.977698i \(0.432649\pi\)
\(840\) −165.145 −5.69803
\(841\) −21.3095 −0.734811
\(842\) 34.8975 1.20265
\(843\) −12.7301 −0.438446
\(844\) −85.9898 −2.95989
\(845\) 24.3331 0.837085
\(846\) −24.1811 −0.831362
\(847\) −2.59530 −0.0891754
\(848\) 12.7151 0.436637
\(849\) 45.5566 1.56350
\(850\) 2.16654 0.0743116
\(851\) −5.25165 −0.180024
\(852\) −7.25117 −0.248421
\(853\) −10.6006 −0.362958 −0.181479 0.983395i \(-0.558088\pi\)
−0.181479 + 0.983395i \(0.558088\pi\)
\(854\) 22.9764 0.786237
\(855\) −30.8881 −1.05635
\(856\) 135.688 4.63771
\(857\) 6.47711 0.221254 0.110627 0.993862i \(-0.464714\pi\)
0.110627 + 0.993862i \(0.464714\pi\)
\(858\) 35.8555 1.22409
\(859\) 38.5183 1.31423 0.657113 0.753792i \(-0.271777\pi\)
0.657113 + 0.753792i \(0.271777\pi\)
\(860\) −20.2286 −0.689790
\(861\) 54.7957 1.86743
\(862\) −88.2371 −3.00537
\(863\) −42.1746 −1.43564 −0.717820 0.696229i \(-0.754860\pi\)
−0.717820 + 0.696229i \(0.754860\pi\)
\(864\) 82.1835 2.79594
\(865\) 54.7789 1.86254
\(866\) −72.6179 −2.46766
\(867\) 38.9470 1.32271
\(868\) −47.9678 −1.62813
\(869\) −13.5573 −0.459899
\(870\) −48.2240 −1.63495
\(871\) −35.9826 −1.21922
\(872\) −70.9436 −2.40245
\(873\) −2.01938 −0.0683458
\(874\) 9.22934 0.312187
\(875\) 27.3944 0.926100
\(876\) 66.2532 2.23849
\(877\) −1.90536 −0.0643393 −0.0321697 0.999482i \(-0.510242\pi\)
−0.0321697 + 0.999482i \(0.510242\pi\)
\(878\) 21.1118 0.712488
\(879\) 73.3029 2.47244
\(880\) 39.1799 1.32075
\(881\) −43.1569 −1.45399 −0.726996 0.686641i \(-0.759084\pi\)
−0.726996 + 0.686641i \(0.759084\pi\)
\(882\) 3.05921 0.103009
\(883\) −15.1326 −0.509252 −0.254626 0.967040i \(-0.581952\pi\)
−0.254626 + 0.967040i \(0.581952\pi\)
\(884\) −42.9625 −1.44498
\(885\) −52.1898 −1.75434
\(886\) −86.5890 −2.90902
\(887\) −18.5314 −0.622222 −0.311111 0.950374i \(-0.600701\pi\)
−0.311111 + 0.950374i \(0.600701\pi\)
\(888\) −134.660 −4.51889
\(889\) 27.1421 0.910318
\(890\) −94.1350 −3.15541
\(891\) −4.06652 −0.136234
\(892\) 16.0219 0.536454
\(893\) −6.58649 −0.220409
\(894\) −36.1422 −1.20878
\(895\) 25.0915 0.838718
\(896\) 141.665 4.73269
\(897\) −13.7111 −0.457800
\(898\) −21.5626 −0.719554
\(899\) −9.05693 −0.302066
\(900\) 11.7948 0.393161
\(901\) −1.19486 −0.0398066
\(902\) −21.8064 −0.726074
\(903\) −10.6008 −0.352772
\(904\) 184.856 6.14823
\(905\) 46.3804 1.54174
\(906\) −147.023 −4.88450
\(907\) −53.2697 −1.76879 −0.884396 0.466738i \(-0.845429\pi\)
−0.884396 + 0.466738i \(0.845429\pi\)
\(908\) 92.9733 3.08543
\(909\) 31.8314 1.05578
\(910\) 81.4329 2.69947
\(911\) 7.76012 0.257104 0.128552 0.991703i \(-0.458967\pi\)
0.128552 + 0.991703i \(0.458967\pi\)
\(912\) 141.083 4.67172
\(913\) −3.93301 −0.130164
\(914\) −7.19317 −0.237929
\(915\) −20.1000 −0.664485
\(916\) 46.1320 1.52424
\(917\) 26.3302 0.869499
\(918\) −13.7421 −0.453558
\(919\) 49.7322 1.64051 0.820256 0.571996i \(-0.193831\pi\)
0.820256 + 0.571996i \(0.193831\pi\)
\(920\) −25.1315 −0.828560
\(921\) 29.7164 0.979188
\(922\) −34.2061 −1.12652
\(923\) 2.31194 0.0760984
\(924\) 39.3562 1.29472
\(925\) −2.47413 −0.0813490
\(926\) 96.9180 3.18492
\(927\) 22.0564 0.724429
\(928\) 72.0670 2.36572
\(929\) 9.54202 0.313063 0.156532 0.987673i \(-0.449969\pi\)
0.156532 + 0.987673i \(0.449969\pi\)
\(930\) 56.7925 1.86230
\(931\) 0.833274 0.0273095
\(932\) −114.642 −3.75521
\(933\) −34.1596 −1.11834
\(934\) −4.85885 −0.158986
\(935\) −3.68181 −0.120408
\(936\) −204.680 −6.69018
\(937\) −59.6580 −1.94894 −0.974470 0.224516i \(-0.927920\pi\)
−0.974470 + 0.224516i \(0.927920\pi\)
\(938\) −53.4537 −1.74532
\(939\) −62.1350 −2.02770
\(940\) 27.7376 0.904701
\(941\) 46.4903 1.51554 0.757771 0.652521i \(-0.226289\pi\)
0.757771 + 0.652521i \(0.226289\pi\)
\(942\) −2.77951 −0.0905614
\(943\) 8.33873 0.271547
\(944\) 138.781 4.51694
\(945\) 19.2458 0.626067
\(946\) 4.21867 0.137161
\(947\) −54.2903 −1.76420 −0.882100 0.471063i \(-0.843870\pi\)
−0.882100 + 0.471063i \(0.843870\pi\)
\(948\) 205.588 6.67720
\(949\) −21.1239 −0.685712
\(950\) 4.34808 0.141070
\(951\) 53.7424 1.74272
\(952\) −41.2674 −1.33748
\(953\) 26.3785 0.854482 0.427241 0.904138i \(-0.359486\pi\)
0.427241 + 0.904138i \(0.359486\pi\)
\(954\) −8.80381 −0.285034
\(955\) −13.5140 −0.437303
\(956\) 82.3591 2.66368
\(957\) 7.43096 0.240209
\(958\) 96.7478 3.12578
\(959\) 28.4421 0.918442
\(960\) −241.932 −7.80833
\(961\) −20.3338 −0.655930
\(962\) 66.4009 2.14085
\(963\) −56.0085 −1.80485
\(964\) 161.053 5.18718
\(965\) 29.5161 0.950158
\(966\) −20.3684 −0.655343
\(967\) −22.8620 −0.735192 −0.367596 0.929986i \(-0.619819\pi\)
−0.367596 + 0.929986i \(0.619819\pi\)
\(968\) −10.1271 −0.325496
\(969\) −13.2579 −0.425904
\(970\) 3.13502 0.100659
\(971\) 26.3239 0.844773 0.422387 0.906416i \(-0.361192\pi\)
0.422387 + 0.906416i \(0.361192\pi\)
\(972\) 115.358 3.70010
\(973\) 49.0154 1.57136
\(974\) −40.6915 −1.30384
\(975\) −6.45951 −0.206870
\(976\) 53.4491 1.71086
\(977\) −5.94244 −0.190116 −0.0950578 0.995472i \(-0.530304\pi\)
−0.0950578 + 0.995472i \(0.530304\pi\)
\(978\) 152.599 4.87957
\(979\) 14.5055 0.463598
\(980\) −3.50916 −0.112096
\(981\) 29.2838 0.934959
\(982\) 98.7228 3.15037
\(983\) 7.00473 0.223416 0.111708 0.993741i \(-0.464368\pi\)
0.111708 + 0.993741i \(0.464368\pi\)
\(984\) 213.817 6.81625
\(985\) 19.0631 0.607401
\(986\) −12.0505 −0.383767
\(987\) 14.5359 0.462682
\(988\) −86.2226 −2.74311
\(989\) −1.61321 −0.0512972
\(990\) −27.1279 −0.862180
\(991\) 42.8626 1.36158 0.680788 0.732480i \(-0.261637\pi\)
0.680788 + 0.732480i \(0.261637\pi\)
\(992\) −84.8720 −2.69469
\(993\) 93.3563 2.96257
\(994\) 3.43449 0.108935
\(995\) −22.0498 −0.699025
\(996\) 59.6419 1.88983
\(997\) 7.31448 0.231652 0.115826 0.993270i \(-0.463049\pi\)
0.115826 + 0.993270i \(0.463049\pi\)
\(998\) 85.0068 2.69084
\(999\) 15.6932 0.496511
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 \(a_p\))