Properties

Label 6017.2.a.c.1.18
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 1.18
Character \(\chi\) = 6017.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.11348 q^{2}\) \(-1.48934 q^{3}\) \(+2.46682 q^{4}\) \(+2.94089 q^{5}\) \(+3.14770 q^{6}\) \(+2.33045 q^{7}\) \(-0.986611 q^{8}\) \(-0.781868 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.11348 q^{2}\) \(-1.48934 q^{3}\) \(+2.46682 q^{4}\) \(+2.94089 q^{5}\) \(+3.14770 q^{6}\) \(+2.33045 q^{7}\) \(-0.986611 q^{8}\) \(-0.781868 q^{9}\) \(-6.21552 q^{10}\) \(+1.00000 q^{11}\) \(-3.67393 q^{12}\) \(-3.42037 q^{13}\) \(-4.92536 q^{14}\) \(-4.37998 q^{15}\) \(-2.84845 q^{16}\) \(-4.87276 q^{17}\) \(+1.65247 q^{18}\) \(+4.26422 q^{19}\) \(+7.25463 q^{20}\) \(-3.47082 q^{21}\) \(-2.11348 q^{22}\) \(-6.61193 q^{23}\) \(+1.46940 q^{24}\) \(+3.64881 q^{25}\) \(+7.22889 q^{26}\) \(+5.63249 q^{27}\) \(+5.74878 q^{28}\) \(+2.76190 q^{29}\) \(+9.25702 q^{30}\) \(-5.42277 q^{31}\) \(+7.99337 q^{32}\) \(-1.48934 q^{33}\) \(+10.2985 q^{34}\) \(+6.85358 q^{35}\) \(-1.92873 q^{36}\) \(+0.408175 q^{37}\) \(-9.01236 q^{38}\) \(+5.09409 q^{39}\) \(-2.90151 q^{40}\) \(+5.31352 q^{41}\) \(+7.33553 q^{42}\) \(+6.37473 q^{43}\) \(+2.46682 q^{44}\) \(-2.29939 q^{45}\) \(+13.9742 q^{46}\) \(+11.1181 q^{47}\) \(+4.24230 q^{48}\) \(-1.56902 q^{49}\) \(-7.71171 q^{50}\) \(+7.25720 q^{51}\) \(-8.43742 q^{52}\) \(-8.54051 q^{53}\) \(-11.9042 q^{54}\) \(+2.94089 q^{55}\) \(-2.29924 q^{56}\) \(-6.35087 q^{57}\) \(-5.83724 q^{58}\) \(+2.44664 q^{59}\) \(-10.8046 q^{60}\) \(+5.22885 q^{61}\) \(+11.4609 q^{62}\) \(-1.82210 q^{63}\) \(-11.1970 q^{64}\) \(-10.0589 q^{65}\) \(+3.14770 q^{66}\) \(-12.5428 q^{67}\) \(-12.0202 q^{68}\) \(+9.84740 q^{69}\) \(-14.4849 q^{70}\) \(-8.26044 q^{71}\) \(+0.771400 q^{72}\) \(-11.7201 q^{73}\) \(-0.862671 q^{74}\) \(-5.43432 q^{75}\) \(+10.5190 q^{76}\) \(+2.33045 q^{77}\) \(-10.7663 q^{78}\) \(+11.2458 q^{79}\) \(-8.37696 q^{80}\) \(-6.04308 q^{81}\) \(-11.2301 q^{82}\) \(-9.51713 q^{83}\) \(-8.56189 q^{84}\) \(-14.3302 q^{85}\) \(-13.4729 q^{86}\) \(-4.11341 q^{87}\) \(-0.986611 q^{88}\) \(+8.88591 q^{89}\) \(+4.85972 q^{90}\) \(-7.97098 q^{91}\) \(-16.3104 q^{92}\) \(+8.07634 q^{93}\) \(-23.4980 q^{94}\) \(+12.5406 q^{95}\) \(-11.9048 q^{96}\) \(+5.32020 q^{97}\) \(+3.31611 q^{98}\) \(-0.781868 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(106q \) \(\mathstrut -\mathstrut 13q^{2} \) \(\mathstrut -\mathstrut 15q^{3} \) \(\mathstrut +\mathstrut 93q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 22q^{6} \) \(\mathstrut -\mathstrut 66q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 97q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(106q \) \(\mathstrut -\mathstrut 13q^{2} \) \(\mathstrut -\mathstrut 15q^{3} \) \(\mathstrut +\mathstrut 93q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 22q^{6} \) \(\mathstrut -\mathstrut 66q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 97q^{9} \) \(\mathstrut -\mathstrut 30q^{10} \) \(\mathstrut +\mathstrut 106q^{11} \) \(\mathstrut -\mathstrut 26q^{12} \) \(\mathstrut -\mathstrut 72q^{13} \) \(\mathstrut +\mathstrut 3q^{14} \) \(\mathstrut -\mathstrut 46q^{15} \) \(\mathstrut +\mathstrut 75q^{16} \) \(\mathstrut -\mathstrut 65q^{17} \) \(\mathstrut -\mathstrut 37q^{18} \) \(\mathstrut -\mathstrut 63q^{19} \) \(\mathstrut -\mathstrut 25q^{20} \) \(\mathstrut -\mathstrut 27q^{21} \) \(\mathstrut -\mathstrut 13q^{22} \) \(\mathstrut -\mathstrut 23q^{23} \) \(\mathstrut -\mathstrut 56q^{24} \) \(\mathstrut +\mathstrut 74q^{25} \) \(\mathstrut +\mathstrut 2q^{26} \) \(\mathstrut -\mathstrut 54q^{27} \) \(\mathstrut -\mathstrut 115q^{28} \) \(\mathstrut -\mathstrut 45q^{29} \) \(\mathstrut -\mathstrut 14q^{30} \) \(\mathstrut -\mathstrut 89q^{31} \) \(\mathstrut -\mathstrut 96q^{32} \) \(\mathstrut -\mathstrut 15q^{33} \) \(\mathstrut -\mathstrut 26q^{34} \) \(\mathstrut -\mathstrut 52q^{35} \) \(\mathstrut +\mathstrut 91q^{36} \) \(\mathstrut -\mathstrut 35q^{37} \) \(\mathstrut +\mathstrut 7q^{38} \) \(\mathstrut -\mathstrut 34q^{39} \) \(\mathstrut -\mathstrut 74q^{40} \) \(\mathstrut -\mathstrut 32q^{41} \) \(\mathstrut -\mathstrut 94q^{43} \) \(\mathstrut +\mathstrut 93q^{44} \) \(\mathstrut -\mathstrut 46q^{45} \) \(\mathstrut -\mathstrut 20q^{46} \) \(\mathstrut -\mathstrut 105q^{47} \) \(\mathstrut -\mathstrut 57q^{48} \) \(\mathstrut +\mathstrut 80q^{49} \) \(\mathstrut -\mathstrut 60q^{50} \) \(\mathstrut -\mathstrut 36q^{51} \) \(\mathstrut -\mathstrut 137q^{52} \) \(\mathstrut -\mathstrut 61q^{54} \) \(\mathstrut -\mathstrut 12q^{55} \) \(\mathstrut +\mathstrut 32q^{56} \) \(\mathstrut -\mathstrut 71q^{57} \) \(\mathstrut -\mathstrut 28q^{58} \) \(\mathstrut -\mathstrut 15q^{59} \) \(\mathstrut -\mathstrut 21q^{60} \) \(\mathstrut -\mathstrut 80q^{61} \) \(\mathstrut -\mathstrut 84q^{62} \) \(\mathstrut -\mathstrut 182q^{63} \) \(\mathstrut +\mathstrut 55q^{64} \) \(\mathstrut -\mathstrut 73q^{65} \) \(\mathstrut -\mathstrut 22q^{66} \) \(\mathstrut -\mathstrut 58q^{67} \) \(\mathstrut -\mathstrut 145q^{68} \) \(\mathstrut -\mathstrut 8q^{69} \) \(\mathstrut -\mathstrut 39q^{70} \) \(\mathstrut -\mathstrut 11q^{71} \) \(\mathstrut -\mathstrut 100q^{72} \) \(\mathstrut -\mathstrut 155q^{73} \) \(\mathstrut -\mathstrut 15q^{74} \) \(\mathstrut -\mathstrut 15q^{75} \) \(\mathstrut -\mathstrut 132q^{76} \) \(\mathstrut -\mathstrut 66q^{77} \) \(\mathstrut -\mathstrut 45q^{78} \) \(\mathstrut -\mathstrut 50q^{79} \) \(\mathstrut -\mathstrut 28q^{80} \) \(\mathstrut +\mathstrut 114q^{81} \) \(\mathstrut -\mathstrut 57q^{82} \) \(\mathstrut -\mathstrut 96q^{83} \) \(\mathstrut -\mathstrut 27q^{84} \) \(\mathstrut -\mathstrut 74q^{85} \) \(\mathstrut +\mathstrut 54q^{86} \) \(\mathstrut -\mathstrut 182q^{87} \) \(\mathstrut -\mathstrut 39q^{88} \) \(\mathstrut +\mathstrut 9q^{89} \) \(\mathstrut -\mathstrut 53q^{90} \) \(\mathstrut +\mathstrut 6q^{91} \) \(\mathstrut -\mathstrut 18q^{92} \) \(\mathstrut -\mathstrut 26q^{93} \) \(\mathstrut -\mathstrut 33q^{94} \) \(\mathstrut -\mathstrut 49q^{95} \) \(\mathstrut -\mathstrut 56q^{96} \) \(\mathstrut -\mathstrut 102q^{97} \) \(\mathstrut -\mathstrut 76q^{98} \) \(\mathstrut +\mathstrut 97q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.11348 −1.49446 −0.747230 0.664566i \(-0.768616\pi\)
−0.747230 + 0.664566i \(0.768616\pi\)
\(3\) −1.48934 −0.859871 −0.429935 0.902860i \(-0.641464\pi\)
−0.429935 + 0.902860i \(0.641464\pi\)
\(4\) 2.46682 1.23341
\(5\) 2.94089 1.31520 0.657602 0.753365i \(-0.271571\pi\)
0.657602 + 0.753365i \(0.271571\pi\)
\(6\) 3.14770 1.28504
\(7\) 2.33045 0.880826 0.440413 0.897795i \(-0.354832\pi\)
0.440413 + 0.897795i \(0.354832\pi\)
\(8\) −0.986611 −0.348820
\(9\) −0.781868 −0.260623
\(10\) −6.21552 −1.96552
\(11\) 1.00000 0.301511
\(12\) −3.67393 −1.06057
\(13\) −3.42037 −0.948639 −0.474320 0.880353i \(-0.657306\pi\)
−0.474320 + 0.880353i \(0.657306\pi\)
\(14\) −4.92536 −1.31636
\(15\) −4.37998 −1.13091
\(16\) −2.84845 −0.712112
\(17\) −4.87276 −1.18182 −0.590909 0.806738i \(-0.701231\pi\)
−0.590909 + 0.806738i \(0.701231\pi\)
\(18\) 1.65247 0.389490
\(19\) 4.26422 0.978279 0.489139 0.872206i \(-0.337311\pi\)
0.489139 + 0.872206i \(0.337311\pi\)
\(20\) 7.25463 1.62218
\(21\) −3.47082 −0.757396
\(22\) −2.11348 −0.450596
\(23\) −6.61193 −1.37868 −0.689341 0.724437i \(-0.742100\pi\)
−0.689341 + 0.724437i \(0.742100\pi\)
\(24\) 1.46940 0.299940
\(25\) 3.64881 0.729763
\(26\) 7.22889 1.41770
\(27\) 5.63249 1.08397
\(28\) 5.74878 1.08642
\(29\) 2.76190 0.512872 0.256436 0.966561i \(-0.417452\pi\)
0.256436 + 0.966561i \(0.417452\pi\)
\(30\) 9.25702 1.69009
\(31\) −5.42277 −0.973957 −0.486979 0.873414i \(-0.661901\pi\)
−0.486979 + 0.873414i \(0.661901\pi\)
\(32\) 7.99337 1.41304
\(33\) −1.48934 −0.259261
\(34\) 10.2985 1.76618
\(35\) 6.85358 1.15847
\(36\) −1.92873 −0.321454
\(37\) 0.408175 0.0671035 0.0335517 0.999437i \(-0.489318\pi\)
0.0335517 + 0.999437i \(0.489318\pi\)
\(38\) −9.01236 −1.46200
\(39\) 5.09409 0.815707
\(40\) −2.90151 −0.458769
\(41\) 5.31352 0.829833 0.414917 0.909859i \(-0.363811\pi\)
0.414917 + 0.909859i \(0.363811\pi\)
\(42\) 7.33553 1.13190
\(43\) 6.37473 0.972137 0.486068 0.873921i \(-0.338431\pi\)
0.486068 + 0.873921i \(0.338431\pi\)
\(44\) 2.46682 0.371887
\(45\) −2.29939 −0.342772
\(46\) 13.9742 2.06038
\(47\) 11.1181 1.62174 0.810872 0.585223i \(-0.198993\pi\)
0.810872 + 0.585223i \(0.198993\pi\)
\(48\) 4.24230 0.612324
\(49\) −1.56902 −0.224146
\(50\) −7.71171 −1.09060
\(51\) 7.25720 1.01621
\(52\) −8.43742 −1.17006
\(53\) −8.54051 −1.17313 −0.586565 0.809902i \(-0.699520\pi\)
−0.586565 + 0.809902i \(0.699520\pi\)
\(54\) −11.9042 −1.61995
\(55\) 2.94089 0.396549
\(56\) −2.29924 −0.307249
\(57\) −6.35087 −0.841193
\(58\) −5.83724 −0.766467
\(59\) 2.44664 0.318526 0.159263 0.987236i \(-0.449088\pi\)
0.159263 + 0.987236i \(0.449088\pi\)
\(60\) −10.8046 −1.39487
\(61\) 5.22885 0.669486 0.334743 0.942309i \(-0.391350\pi\)
0.334743 + 0.942309i \(0.391350\pi\)
\(62\) 11.4609 1.45554
\(63\) −1.82210 −0.229563
\(64\) −11.1970 −1.39962
\(65\) −10.0589 −1.24765
\(66\) 3.14770 0.387455
\(67\) −12.5428 −1.53234 −0.766172 0.642636i \(-0.777841\pi\)
−0.766172 + 0.642636i \(0.777841\pi\)
\(68\) −12.0202 −1.45766
\(69\) 9.84740 1.18549
\(70\) −14.4849 −1.73128
\(71\) −8.26044 −0.980334 −0.490167 0.871629i \(-0.663064\pi\)
−0.490167 + 0.871629i \(0.663064\pi\)
\(72\) 0.771400 0.0909103
\(73\) −11.7201 −1.37173 −0.685866 0.727728i \(-0.740576\pi\)
−0.685866 + 0.727728i \(0.740576\pi\)
\(74\) −0.862671 −0.100283
\(75\) −5.43432 −0.627502
\(76\) 10.5190 1.20662
\(77\) 2.33045 0.265579
\(78\) −10.7663 −1.21904
\(79\) 11.2458 1.26525 0.632625 0.774458i \(-0.281977\pi\)
0.632625 + 0.774458i \(0.281977\pi\)
\(80\) −8.37696 −0.936573
\(81\) −6.04308 −0.671453
\(82\) −11.2301 −1.24015
\(83\) −9.51713 −1.04464 −0.522320 0.852749i \(-0.674933\pi\)
−0.522320 + 0.852749i \(0.674933\pi\)
\(84\) −8.56189 −0.934179
\(85\) −14.3302 −1.55433
\(86\) −13.4729 −1.45282
\(87\) −4.11341 −0.441004
\(88\) −0.986611 −0.105173
\(89\) 8.88591 0.941905 0.470952 0.882159i \(-0.343910\pi\)
0.470952 + 0.882159i \(0.343910\pi\)
\(90\) 4.85972 0.512259
\(91\) −7.97098 −0.835586
\(92\) −16.3104 −1.70048
\(93\) 8.07634 0.837477
\(94\) −23.4980 −2.42363
\(95\) 12.5406 1.28664
\(96\) −11.9048 −1.21503
\(97\) 5.32020 0.540184 0.270092 0.962834i \(-0.412946\pi\)
0.270092 + 0.962834i \(0.412946\pi\)
\(98\) 3.31611 0.334977
\(99\) −0.781868 −0.0785807
\(100\) 9.00096 0.900096
\(101\) −5.05945 −0.503434 −0.251717 0.967801i \(-0.580995\pi\)
−0.251717 + 0.967801i \(0.580995\pi\)
\(102\) −15.3380 −1.51869
\(103\) 18.7064 1.84319 0.921596 0.388149i \(-0.126886\pi\)
0.921596 + 0.388149i \(0.126886\pi\)
\(104\) 3.37457 0.330904
\(105\) −10.2073 −0.996131
\(106\) 18.0502 1.75319
\(107\) −2.12300 −0.205238 −0.102619 0.994721i \(-0.532722\pi\)
−0.102619 + 0.994721i \(0.532722\pi\)
\(108\) 13.8943 1.33698
\(109\) −8.02847 −0.768988 −0.384494 0.923128i \(-0.625624\pi\)
−0.384494 + 0.923128i \(0.625624\pi\)
\(110\) −6.21552 −0.592626
\(111\) −0.607910 −0.0577003
\(112\) −6.63815 −0.627246
\(113\) −5.94679 −0.559427 −0.279714 0.960084i \(-0.590239\pi\)
−0.279714 + 0.960084i \(0.590239\pi\)
\(114\) 13.4225 1.25713
\(115\) −19.4449 −1.81325
\(116\) 6.81311 0.632581
\(117\) 2.67428 0.247237
\(118\) −5.17094 −0.476024
\(119\) −11.3557 −1.04098
\(120\) 4.32134 0.394482
\(121\) 1.00000 0.0909091
\(122\) −11.0511 −1.00052
\(123\) −7.91364 −0.713549
\(124\) −13.3770 −1.20129
\(125\) −3.97368 −0.355417
\(126\) 3.85098 0.343073
\(127\) −13.5929 −1.20618 −0.603088 0.797674i \(-0.706063\pi\)
−0.603088 + 0.797674i \(0.706063\pi\)
\(128\) 7.67789 0.678636
\(129\) −9.49413 −0.835912
\(130\) 21.2594 1.86457
\(131\) 4.25643 0.371886 0.185943 0.982561i \(-0.440466\pi\)
0.185943 + 0.982561i \(0.440466\pi\)
\(132\) −3.67393 −0.319774
\(133\) 9.93753 0.861693
\(134\) 26.5090 2.29002
\(135\) 16.5645 1.42565
\(136\) 4.80752 0.412242
\(137\) 2.67943 0.228919 0.114460 0.993428i \(-0.463486\pi\)
0.114460 + 0.993428i \(0.463486\pi\)
\(138\) −20.8123 −1.77166
\(139\) −1.75258 −0.148652 −0.0743258 0.997234i \(-0.523680\pi\)
−0.0743258 + 0.997234i \(0.523680\pi\)
\(140\) 16.9065 1.42886
\(141\) −16.5587 −1.39449
\(142\) 17.4583 1.46507
\(143\) −3.42037 −0.286025
\(144\) 2.22711 0.185592
\(145\) 8.12244 0.674532
\(146\) 24.7702 2.05000
\(147\) 2.33681 0.192737
\(148\) 1.00689 0.0827660
\(149\) −12.6328 −1.03492 −0.517458 0.855708i \(-0.673122\pi\)
−0.517458 + 0.855708i \(0.673122\pi\)
\(150\) 11.4854 0.937776
\(151\) −9.01307 −0.733473 −0.366736 0.930325i \(-0.619525\pi\)
−0.366736 + 0.930325i \(0.619525\pi\)
\(152\) −4.20713 −0.341243
\(153\) 3.80986 0.308009
\(154\) −4.92536 −0.396897
\(155\) −15.9477 −1.28095
\(156\) 12.5662 1.00610
\(157\) 19.3187 1.54180 0.770900 0.636956i \(-0.219807\pi\)
0.770900 + 0.636956i \(0.219807\pi\)
\(158\) −23.7678 −1.89086
\(159\) 12.7197 1.00874
\(160\) 23.5076 1.85844
\(161\) −15.4087 −1.21438
\(162\) 12.7720 1.00346
\(163\) −9.98298 −0.781927 −0.390964 0.920406i \(-0.627858\pi\)
−0.390964 + 0.920406i \(0.627858\pi\)
\(164\) 13.1075 1.02352
\(165\) −4.37998 −0.340981
\(166\) 20.1143 1.56117
\(167\) 1.04128 0.0805768 0.0402884 0.999188i \(-0.487172\pi\)
0.0402884 + 0.999188i \(0.487172\pi\)
\(168\) 3.42435 0.264195
\(169\) −1.30109 −0.100084
\(170\) 30.2867 2.32289
\(171\) −3.33406 −0.254962
\(172\) 15.7253 1.19904
\(173\) −16.3068 −1.23978 −0.619892 0.784687i \(-0.712824\pi\)
−0.619892 + 0.784687i \(0.712824\pi\)
\(174\) 8.69363 0.659062
\(175\) 8.50336 0.642794
\(176\) −2.84845 −0.214710
\(177\) −3.64388 −0.273891
\(178\) −18.7802 −1.40764
\(179\) 1.29711 0.0969509 0.0484754 0.998824i \(-0.484564\pi\)
0.0484754 + 0.998824i \(0.484564\pi\)
\(180\) −5.67216 −0.422778
\(181\) 9.24697 0.687322 0.343661 0.939094i \(-0.388333\pi\)
0.343661 + 0.939094i \(0.388333\pi\)
\(182\) 16.8465 1.24875
\(183\) −7.78754 −0.575671
\(184\) 6.52340 0.480912
\(185\) 1.20040 0.0882548
\(186\) −17.0692 −1.25158
\(187\) −4.87276 −0.356332
\(188\) 27.4264 2.00027
\(189\) 13.1262 0.954791
\(190\) −26.5043 −1.92283
\(191\) 17.7346 1.28323 0.641614 0.767028i \(-0.278265\pi\)
0.641614 + 0.767028i \(0.278265\pi\)
\(192\) 16.6761 1.20349
\(193\) −23.5776 −1.69715 −0.848576 0.529074i \(-0.822539\pi\)
−0.848576 + 0.529074i \(0.822539\pi\)
\(194\) −11.2442 −0.807284
\(195\) 14.9811 1.07282
\(196\) −3.87049 −0.276464
\(197\) 4.20495 0.299591 0.149795 0.988717i \(-0.452139\pi\)
0.149795 + 0.988717i \(0.452139\pi\)
\(198\) 1.65247 0.117436
\(199\) −18.6988 −1.32552 −0.662761 0.748831i \(-0.730615\pi\)
−0.662761 + 0.748831i \(0.730615\pi\)
\(200\) −3.59996 −0.254556
\(201\) 18.6804 1.31762
\(202\) 10.6931 0.752362
\(203\) 6.43646 0.451751
\(204\) 17.9022 1.25340
\(205\) 15.6265 1.09140
\(206\) −39.5356 −2.75458
\(207\) 5.16965 0.359316
\(208\) 9.74273 0.675537
\(209\) 4.26422 0.294962
\(210\) 21.5730 1.48868
\(211\) −21.8305 −1.50287 −0.751435 0.659807i \(-0.770638\pi\)
−0.751435 + 0.659807i \(0.770638\pi\)
\(212\) −21.0679 −1.44695
\(213\) 12.3026 0.842960
\(214\) 4.48693 0.306720
\(215\) 18.7473 1.27856
\(216\) −5.55707 −0.378111
\(217\) −12.6375 −0.857887
\(218\) 16.9680 1.14922
\(219\) 17.4552 1.17951
\(220\) 7.25463 0.489107
\(221\) 16.6666 1.12112
\(222\) 1.28481 0.0862308
\(223\) −7.62030 −0.510293 −0.255146 0.966902i \(-0.582124\pi\)
−0.255146 + 0.966902i \(0.582124\pi\)
\(224\) 18.6281 1.24464
\(225\) −2.85289 −0.190193
\(226\) 12.5685 0.836041
\(227\) 16.4618 1.09261 0.546304 0.837587i \(-0.316034\pi\)
0.546304 + 0.837587i \(0.316034\pi\)
\(228\) −15.6664 −1.03753
\(229\) −16.7032 −1.10378 −0.551889 0.833917i \(-0.686093\pi\)
−0.551889 + 0.833917i \(0.686093\pi\)
\(230\) 41.0966 2.70983
\(231\) −3.47082 −0.228363
\(232\) −2.72492 −0.178900
\(233\) −23.7521 −1.55606 −0.778028 0.628230i \(-0.783780\pi\)
−0.778028 + 0.628230i \(0.783780\pi\)
\(234\) −5.65204 −0.369485
\(235\) 32.6971 2.13293
\(236\) 6.03542 0.392872
\(237\) −16.7488 −1.08795
\(238\) 24.0001 1.55570
\(239\) 4.56806 0.295483 0.147741 0.989026i \(-0.452800\pi\)
0.147741 + 0.989026i \(0.452800\pi\)
\(240\) 12.4761 0.805331
\(241\) 7.58643 0.488685 0.244342 0.969689i \(-0.421428\pi\)
0.244342 + 0.969689i \(0.421428\pi\)
\(242\) −2.11348 −0.135860
\(243\) −7.89726 −0.506610
\(244\) 12.8986 0.825750
\(245\) −4.61432 −0.294798
\(246\) 16.7254 1.06637
\(247\) −14.5852 −0.928033
\(248\) 5.35016 0.339736
\(249\) 14.1742 0.898256
\(250\) 8.39832 0.531156
\(251\) 16.4138 1.03603 0.518014 0.855372i \(-0.326672\pi\)
0.518014 + 0.855372i \(0.326672\pi\)
\(252\) −4.49479 −0.283145
\(253\) −6.61193 −0.415688
\(254\) 28.7284 1.80258
\(255\) 21.3426 1.33652
\(256\) 6.16685 0.385428
\(257\) −4.83405 −0.301540 −0.150770 0.988569i \(-0.548175\pi\)
−0.150770 + 0.988569i \(0.548175\pi\)
\(258\) 20.0657 1.24924
\(259\) 0.951229 0.0591065
\(260\) −24.8135 −1.53887
\(261\) −2.15944 −0.133666
\(262\) −8.99590 −0.555769
\(263\) 5.26733 0.324798 0.162399 0.986725i \(-0.448077\pi\)
0.162399 + 0.986725i \(0.448077\pi\)
\(264\) 1.46940 0.0904353
\(265\) −25.1167 −1.54290
\(266\) −21.0028 −1.28777
\(267\) −13.2341 −0.809916
\(268\) −30.9407 −1.89001
\(269\) 30.1641 1.83914 0.919570 0.392927i \(-0.128538\pi\)
0.919570 + 0.392927i \(0.128538\pi\)
\(270\) −35.0088 −2.13057
\(271\) 2.67872 0.162721 0.0813604 0.996685i \(-0.474074\pi\)
0.0813604 + 0.996685i \(0.474074\pi\)
\(272\) 13.8798 0.841587
\(273\) 11.8715 0.718495
\(274\) −5.66294 −0.342111
\(275\) 3.64881 0.220032
\(276\) 24.2917 1.46219
\(277\) 3.83685 0.230534 0.115267 0.993335i \(-0.463228\pi\)
0.115267 + 0.993335i \(0.463228\pi\)
\(278\) 3.70404 0.222154
\(279\) 4.23989 0.253835
\(280\) −6.76182 −0.404096
\(281\) −21.7601 −1.29810 −0.649049 0.760747i \(-0.724833\pi\)
−0.649049 + 0.760747i \(0.724833\pi\)
\(282\) 34.9965 2.08401
\(283\) −2.40905 −0.143203 −0.0716016 0.997433i \(-0.522811\pi\)
−0.0716016 + 0.997433i \(0.522811\pi\)
\(284\) −20.3770 −1.20915
\(285\) −18.6772 −1.10634
\(286\) 7.22889 0.427453
\(287\) 12.3829 0.730938
\(288\) −6.24976 −0.368271
\(289\) 6.74381 0.396694
\(290\) −17.1667 −1.00806
\(291\) −7.92358 −0.464489
\(292\) −28.9113 −1.69191
\(293\) 21.3915 1.24970 0.624852 0.780743i \(-0.285159\pi\)
0.624852 + 0.780743i \(0.285159\pi\)
\(294\) −4.93881 −0.288037
\(295\) 7.19530 0.418926
\(296\) −0.402710 −0.0234070
\(297\) 5.63249 0.326830
\(298\) 26.6992 1.54664
\(299\) 22.6152 1.30787
\(300\) −13.4055 −0.773966
\(301\) 14.8560 0.856283
\(302\) 19.0490 1.09615
\(303\) 7.53524 0.432888
\(304\) −12.1464 −0.696644
\(305\) 15.3775 0.880511
\(306\) −8.05207 −0.460306
\(307\) −25.0124 −1.42753 −0.713766 0.700384i \(-0.753012\pi\)
−0.713766 + 0.700384i \(0.753012\pi\)
\(308\) 5.74878 0.327567
\(309\) −27.8601 −1.58491
\(310\) 33.7053 1.91433
\(311\) −0.223132 −0.0126527 −0.00632634 0.999980i \(-0.502014\pi\)
−0.00632634 + 0.999980i \(0.502014\pi\)
\(312\) −5.02588 −0.284535
\(313\) 23.5044 1.32855 0.664273 0.747490i \(-0.268741\pi\)
0.664273 + 0.747490i \(0.268741\pi\)
\(314\) −40.8298 −2.30416
\(315\) −5.35859 −0.301922
\(316\) 27.7413 1.56057
\(317\) 0.223585 0.0125578 0.00627889 0.999980i \(-0.498001\pi\)
0.00627889 + 0.999980i \(0.498001\pi\)
\(318\) −26.8829 −1.50752
\(319\) 2.76190 0.154637
\(320\) −32.9290 −1.84079
\(321\) 3.16187 0.176478
\(322\) 32.5661 1.81484
\(323\) −20.7785 −1.15615
\(324\) −14.9072 −0.828176
\(325\) −12.4803 −0.692282
\(326\) 21.0989 1.16856
\(327\) 11.9571 0.661230
\(328\) −5.24238 −0.289462
\(329\) 25.9102 1.42847
\(330\) 9.25702 0.509582
\(331\) 3.82195 0.210073 0.105037 0.994468i \(-0.466504\pi\)
0.105037 + 0.994468i \(0.466504\pi\)
\(332\) −23.4770 −1.28847
\(333\) −0.319139 −0.0174887
\(334\) −2.20073 −0.120419
\(335\) −36.8869 −2.01534
\(336\) 9.88646 0.539351
\(337\) 23.7006 1.29105 0.645527 0.763738i \(-0.276638\pi\)
0.645527 + 0.763738i \(0.276638\pi\)
\(338\) 2.74983 0.149571
\(339\) 8.85679 0.481035
\(340\) −35.3501 −1.91713
\(341\) −5.42277 −0.293659
\(342\) 7.04648 0.381030
\(343\) −19.9696 −1.07826
\(344\) −6.28938 −0.339100
\(345\) 28.9601 1.55916
\(346\) 34.4642 1.85281
\(347\) −25.7266 −1.38108 −0.690538 0.723296i \(-0.742626\pi\)
−0.690538 + 0.723296i \(0.742626\pi\)
\(348\) −10.1470 −0.543938
\(349\) 4.43754 0.237536 0.118768 0.992922i \(-0.462106\pi\)
0.118768 + 0.992922i \(0.462106\pi\)
\(350\) −17.9717 −0.960629
\(351\) −19.2652 −1.02830
\(352\) 7.99337 0.426048
\(353\) −5.91155 −0.314640 −0.157320 0.987548i \(-0.550285\pi\)
−0.157320 + 0.987548i \(0.550285\pi\)
\(354\) 7.70128 0.409319
\(355\) −24.2930 −1.28934
\(356\) 21.9199 1.16175
\(357\) 16.9125 0.895105
\(358\) −2.74143 −0.144889
\(359\) −17.6887 −0.933575 −0.466787 0.884370i \(-0.654589\pi\)
−0.466787 + 0.884370i \(0.654589\pi\)
\(360\) 2.26860 0.119566
\(361\) −0.816445 −0.0429708
\(362\) −19.5433 −1.02717
\(363\) −1.48934 −0.0781700
\(364\) −19.6629 −1.03062
\(365\) −34.4674 −1.80411
\(366\) 16.4588 0.860318
\(367\) −21.2944 −1.11156 −0.555780 0.831329i \(-0.687580\pi\)
−0.555780 + 0.831329i \(0.687580\pi\)
\(368\) 18.8337 0.981776
\(369\) −4.15447 −0.216273
\(370\) −2.53702 −0.131893
\(371\) −19.9032 −1.03332
\(372\) 19.9229 1.03295
\(373\) −12.5623 −0.650451 −0.325225 0.945637i \(-0.605440\pi\)
−0.325225 + 0.945637i \(0.605440\pi\)
\(374\) 10.2985 0.532523
\(375\) 5.91816 0.305613
\(376\) −10.9693 −0.565697
\(377\) −9.44672 −0.486531
\(378\) −27.7420 −1.42690
\(379\) −17.2743 −0.887320 −0.443660 0.896195i \(-0.646320\pi\)
−0.443660 + 0.896195i \(0.646320\pi\)
\(380\) 30.9353 1.58695
\(381\) 20.2445 1.03716
\(382\) −37.4817 −1.91773
\(383\) −31.0724 −1.58773 −0.793864 0.608096i \(-0.791934\pi\)
−0.793864 + 0.608096i \(0.791934\pi\)
\(384\) −11.4350 −0.583539
\(385\) 6.85358 0.349291
\(386\) 49.8308 2.53632
\(387\) −4.98419 −0.253361
\(388\) 13.1240 0.666268
\(389\) 9.47721 0.480513 0.240257 0.970709i \(-0.422768\pi\)
0.240257 + 0.970709i \(0.422768\pi\)
\(390\) −31.6624 −1.60329
\(391\) 32.2183 1.62935
\(392\) 1.54802 0.0781866
\(393\) −6.33927 −0.319774
\(394\) −8.88711 −0.447726
\(395\) 33.0726 1.66406
\(396\) −1.92873 −0.0969221
\(397\) −13.8117 −0.693189 −0.346595 0.938015i \(-0.612662\pi\)
−0.346595 + 0.938015i \(0.612662\pi\)
\(398\) 39.5196 1.98094
\(399\) −14.8004 −0.740944
\(400\) −10.3935 −0.519673
\(401\) 20.0745 1.00247 0.501237 0.865310i \(-0.332878\pi\)
0.501237 + 0.865310i \(0.332878\pi\)
\(402\) −39.4808 −1.96912
\(403\) 18.5478 0.923934
\(404\) −12.4807 −0.620940
\(405\) −17.7720 −0.883098
\(406\) −13.6034 −0.675124
\(407\) 0.408175 0.0202325
\(408\) −7.16003 −0.354474
\(409\) −20.6139 −1.01929 −0.509647 0.860384i \(-0.670224\pi\)
−0.509647 + 0.860384i \(0.670224\pi\)
\(410\) −33.0263 −1.63105
\(411\) −3.99058 −0.196841
\(412\) 46.1452 2.27341
\(413\) 5.70177 0.280566
\(414\) −10.9260 −0.536983
\(415\) −27.9888 −1.37392
\(416\) −27.3403 −1.34047
\(417\) 2.61018 0.127821
\(418\) −9.01236 −0.440809
\(419\) −25.9638 −1.26842 −0.634208 0.773163i \(-0.718674\pi\)
−0.634208 + 0.773163i \(0.718674\pi\)
\(420\) −25.1795 −1.22864
\(421\) −26.5292 −1.29295 −0.646477 0.762934i \(-0.723758\pi\)
−0.646477 + 0.762934i \(0.723758\pi\)
\(422\) 46.1383 2.24598
\(423\) −8.69290 −0.422663
\(424\) 8.42616 0.409211
\(425\) −17.7798 −0.862447
\(426\) −26.0014 −1.25977
\(427\) 12.1856 0.589701
\(428\) −5.23705 −0.253142
\(429\) 5.09409 0.245945
\(430\) −39.6222 −1.91075
\(431\) −29.7171 −1.43142 −0.715710 0.698397i \(-0.753897\pi\)
−0.715710 + 0.698397i \(0.753897\pi\)
\(432\) −16.0438 −0.771909
\(433\) 22.6111 1.08662 0.543310 0.839532i \(-0.317171\pi\)
0.543310 + 0.839532i \(0.317171\pi\)
\(434\) 26.7091 1.28208
\(435\) −12.0971 −0.580010
\(436\) −19.8048 −0.948476
\(437\) −28.1947 −1.34874
\(438\) −36.8912 −1.76273
\(439\) 10.4001 0.496370 0.248185 0.968713i \(-0.420166\pi\)
0.248185 + 0.968713i \(0.420166\pi\)
\(440\) −2.90151 −0.138324
\(441\) 1.22677 0.0584176
\(442\) −35.2247 −1.67547
\(443\) −26.1554 −1.24268 −0.621340 0.783541i \(-0.713411\pi\)
−0.621340 + 0.783541i \(0.713411\pi\)
\(444\) −1.49960 −0.0711681
\(445\) 26.1325 1.23880
\(446\) 16.1054 0.762612
\(447\) 18.8145 0.889894
\(448\) −26.0939 −1.23282
\(449\) 1.53347 0.0723689 0.0361845 0.999345i \(-0.488480\pi\)
0.0361845 + 0.999345i \(0.488480\pi\)
\(450\) 6.02954 0.284235
\(451\) 5.31352 0.250204
\(452\) −14.6696 −0.690002
\(453\) 13.4235 0.630692
\(454\) −34.7918 −1.63286
\(455\) −23.4417 −1.09897
\(456\) 6.26584 0.293425
\(457\) 27.1049 1.26791 0.633957 0.773368i \(-0.281429\pi\)
0.633957 + 0.773368i \(0.281429\pi\)
\(458\) 35.3020 1.64955
\(459\) −27.4458 −1.28106
\(460\) −47.9671 −2.23648
\(461\) 12.4309 0.578966 0.289483 0.957183i \(-0.406517\pi\)
0.289483 + 0.957183i \(0.406517\pi\)
\(462\) 7.33553 0.341280
\(463\) −4.09505 −0.190313 −0.0951566 0.995462i \(-0.530335\pi\)
−0.0951566 + 0.995462i \(0.530335\pi\)
\(464\) −7.86713 −0.365222
\(465\) 23.7516 1.10145
\(466\) 50.1998 2.32546
\(467\) 16.2473 0.751837 0.375918 0.926653i \(-0.377327\pi\)
0.375918 + 0.926653i \(0.377327\pi\)
\(468\) 6.59695 0.304944
\(469\) −29.2302 −1.34973
\(470\) −69.1049 −3.18757
\(471\) −28.7721 −1.32575
\(472\) −2.41388 −0.111108
\(473\) 6.37473 0.293110
\(474\) 35.3983 1.62590
\(475\) 15.5593 0.713911
\(476\) −28.0125 −1.28395
\(477\) 6.67755 0.305744
\(478\) −9.65451 −0.441587
\(479\) 19.1366 0.874373 0.437187 0.899371i \(-0.355975\pi\)
0.437187 + 0.899371i \(0.355975\pi\)
\(480\) −35.0108 −1.59802
\(481\) −1.39611 −0.0636570
\(482\) −16.0338 −0.730319
\(483\) 22.9488 1.04421
\(484\) 2.46682 0.112128
\(485\) 15.6461 0.710453
\(486\) 16.6907 0.757107
\(487\) 0.836928 0.0379248 0.0189624 0.999820i \(-0.493964\pi\)
0.0189624 + 0.999820i \(0.493964\pi\)
\(488\) −5.15885 −0.233530
\(489\) 14.8680 0.672356
\(490\) 9.75229 0.440564
\(491\) −0.00676237 −0.000305181 0 −0.000152591 1.00000i \(-0.500049\pi\)
−0.000152591 1.00000i \(0.500049\pi\)
\(492\) −19.5215 −0.880097
\(493\) −13.4581 −0.606122
\(494\) 30.8256 1.38691
\(495\) −2.29939 −0.103350
\(496\) 15.4465 0.693567
\(497\) −19.2505 −0.863503
\(498\) −29.9570 −1.34241
\(499\) 8.81698 0.394702 0.197351 0.980333i \(-0.436766\pi\)
0.197351 + 0.980333i \(0.436766\pi\)
\(500\) −9.80235 −0.438375
\(501\) −1.55082 −0.0692856
\(502\) −34.6902 −1.54830
\(503\) −12.4263 −0.554063 −0.277031 0.960861i \(-0.589351\pi\)
−0.277031 + 0.960861i \(0.589351\pi\)
\(504\) 1.79771 0.0800762
\(505\) −14.8793 −0.662119
\(506\) 13.9742 0.621229
\(507\) 1.93777 0.0860592
\(508\) −33.5313 −1.48771
\(509\) 1.56987 0.0695831 0.0347915 0.999395i \(-0.488923\pi\)
0.0347915 + 0.999395i \(0.488923\pi\)
\(510\) −45.1072 −1.99738
\(511\) −27.3130 −1.20826
\(512\) −28.3893 −1.25464
\(513\) 24.0181 1.06043
\(514\) 10.2167 0.450639
\(515\) 55.0133 2.42418
\(516\) −23.4203 −1.03102
\(517\) 11.1181 0.488974
\(518\) −2.01041 −0.0883322
\(519\) 24.2864 1.06605
\(520\) 9.92423 0.435206
\(521\) 37.0568 1.62349 0.811745 0.584012i \(-0.198518\pi\)
0.811745 + 0.584012i \(0.198518\pi\)
\(522\) 4.56395 0.199759
\(523\) −2.03465 −0.0889690 −0.0444845 0.999010i \(-0.514165\pi\)
−0.0444845 + 0.999010i \(0.514165\pi\)
\(524\) 10.4998 0.458688
\(525\) −12.6644 −0.552720
\(526\) −11.1324 −0.485397
\(527\) 26.4238 1.15104
\(528\) 4.24230 0.184623
\(529\) 20.7176 0.900764
\(530\) 53.0837 2.30581
\(531\) −1.91295 −0.0830150
\(532\) 24.5141 1.06282
\(533\) −18.1742 −0.787212
\(534\) 27.9701 1.21039
\(535\) −6.24350 −0.269930
\(536\) 12.3748 0.534512
\(537\) −1.93184 −0.0833652
\(538\) −63.7514 −2.74852
\(539\) −1.56902 −0.0675826
\(540\) 40.8616 1.75840
\(541\) −1.98888 −0.0855086 −0.0427543 0.999086i \(-0.513613\pi\)
−0.0427543 + 0.999086i \(0.513613\pi\)
\(542\) −5.66144 −0.243180
\(543\) −13.7719 −0.591008
\(544\) −38.9498 −1.66996
\(545\) −23.6108 −1.01138
\(546\) −25.0902 −1.07376
\(547\) 1.00000 0.0427569
\(548\) 6.60967 0.282351
\(549\) −4.08827 −0.174483
\(550\) −7.71171 −0.328829
\(551\) 11.7774 0.501732
\(552\) −9.71556 −0.413522
\(553\) 26.2077 1.11446
\(554\) −8.10913 −0.344524
\(555\) −1.78780 −0.0758877
\(556\) −4.32328 −0.183348
\(557\) −23.2245 −0.984053 −0.492026 0.870580i \(-0.663744\pi\)
−0.492026 + 0.870580i \(0.663744\pi\)
\(558\) −8.96094 −0.379347
\(559\) −21.8039 −0.922207
\(560\) −19.5220 −0.824957
\(561\) 7.25720 0.306399
\(562\) 45.9896 1.93995
\(563\) 15.1882 0.640104 0.320052 0.947400i \(-0.396300\pi\)
0.320052 + 0.947400i \(0.396300\pi\)
\(564\) −40.8472 −1.71998
\(565\) −17.4888 −0.735761
\(566\) 5.09149 0.214011
\(567\) −14.0831 −0.591433
\(568\) 8.14984 0.341960
\(569\) 11.7207 0.491356 0.245678 0.969351i \(-0.420989\pi\)
0.245678 + 0.969351i \(0.420989\pi\)
\(570\) 39.4739 1.65338
\(571\) −9.80671 −0.410398 −0.205199 0.978720i \(-0.565784\pi\)
−0.205199 + 0.978720i \(0.565784\pi\)
\(572\) −8.43742 −0.352786
\(573\) −26.4128 −1.10341
\(574\) −26.1710 −1.09236
\(575\) −24.1257 −1.00611
\(576\) 8.75456 0.364773
\(577\) −42.4332 −1.76652 −0.883258 0.468887i \(-0.844655\pi\)
−0.883258 + 0.468887i \(0.844655\pi\)
\(578\) −14.2529 −0.592844
\(579\) 35.1150 1.45933
\(580\) 20.0366 0.831974
\(581\) −22.1792 −0.920146
\(582\) 16.7464 0.694159
\(583\) −8.54051 −0.353712
\(584\) 11.5632 0.478487
\(585\) 7.86474 0.325167
\(586\) −45.2106 −1.86763
\(587\) −13.5382 −0.558782 −0.279391 0.960177i \(-0.590133\pi\)
−0.279391 + 0.960177i \(0.590133\pi\)
\(588\) 5.76448 0.237723
\(589\) −23.1239 −0.952802
\(590\) −15.2071 −0.626068
\(591\) −6.26261 −0.257609
\(592\) −1.16266 −0.0477852
\(593\) 41.1233 1.68873 0.844366 0.535767i \(-0.179977\pi\)
0.844366 + 0.535767i \(0.179977\pi\)
\(594\) −11.9042 −0.488434
\(595\) −33.3958 −1.36910
\(596\) −31.1627 −1.27648
\(597\) 27.8488 1.13978
\(598\) −47.7969 −1.95456
\(599\) 14.7183 0.601374 0.300687 0.953723i \(-0.402784\pi\)
0.300687 + 0.953723i \(0.402784\pi\)
\(600\) 5.36156 0.218885
\(601\) −35.4469 −1.44591 −0.722955 0.690896i \(-0.757216\pi\)
−0.722955 + 0.690896i \(0.757216\pi\)
\(602\) −31.3978 −1.27968
\(603\) 9.80679 0.399363
\(604\) −22.2336 −0.904672
\(605\) 2.94089 0.119564
\(606\) −15.9256 −0.646934
\(607\) −16.4130 −0.666184 −0.333092 0.942894i \(-0.608092\pi\)
−0.333092 + 0.942894i \(0.608092\pi\)
\(608\) 34.0855 1.38235
\(609\) −9.58608 −0.388448
\(610\) −32.5000 −1.31589
\(611\) −38.0281 −1.53845
\(612\) 9.39822 0.379901
\(613\) −42.2064 −1.70470 −0.852349 0.522973i \(-0.824823\pi\)
−0.852349 + 0.522973i \(0.824823\pi\)
\(614\) 52.8633 2.13339
\(615\) −23.2731 −0.938463
\(616\) −2.29924 −0.0926392
\(617\) −15.6251 −0.629041 −0.314521 0.949251i \(-0.601844\pi\)
−0.314521 + 0.949251i \(0.601844\pi\)
\(618\) 58.8820 2.36858
\(619\) 12.7887 0.514023 0.257012 0.966408i \(-0.417262\pi\)
0.257012 + 0.966408i \(0.417262\pi\)
\(620\) −39.3402 −1.57994
\(621\) −37.2416 −1.49445
\(622\) 0.471587 0.0189089
\(623\) 20.7081 0.829654
\(624\) −14.5102 −0.580874
\(625\) −29.9302 −1.19721
\(626\) −49.6761 −1.98546
\(627\) −6.35087 −0.253629
\(628\) 47.6557 1.90167
\(629\) −1.98894 −0.0793041
\(630\) 11.3253 0.451211
\(631\) −4.04846 −0.161166 −0.0805832 0.996748i \(-0.525678\pi\)
−0.0805832 + 0.996748i \(0.525678\pi\)
\(632\) −11.0952 −0.441344
\(633\) 32.5130 1.29227
\(634\) −0.472543 −0.0187671
\(635\) −39.9752 −1.58637
\(636\) 31.3772 1.24419
\(637\) 5.36663 0.212634
\(638\) −5.83724 −0.231098
\(639\) 6.45857 0.255497
\(640\) 22.5798 0.892545
\(641\) 5.11439 0.202006 0.101003 0.994886i \(-0.467795\pi\)
0.101003 + 0.994886i \(0.467795\pi\)
\(642\) −6.68256 −0.263739
\(643\) −27.8473 −1.09819 −0.549095 0.835760i \(-0.685027\pi\)
−0.549095 + 0.835760i \(0.685027\pi\)
\(644\) −38.0105 −1.49783
\(645\) −27.9212 −1.09939
\(646\) 43.9151 1.72782
\(647\) 5.28949 0.207951 0.103976 0.994580i \(-0.466844\pi\)
0.103976 + 0.994580i \(0.466844\pi\)
\(648\) 5.96217 0.234216
\(649\) 2.44664 0.0960391
\(650\) 26.3769 1.03459
\(651\) 18.8215 0.737672
\(652\) −24.6262 −0.964436
\(653\) −34.4019 −1.34625 −0.673126 0.739528i \(-0.735049\pi\)
−0.673126 + 0.739528i \(0.735049\pi\)
\(654\) −25.2712 −0.988181
\(655\) 12.5177 0.489106
\(656\) −15.1353 −0.590934
\(657\) 9.16356 0.357504
\(658\) −54.7608 −2.13480
\(659\) −9.58292 −0.373298 −0.186649 0.982427i \(-0.559763\pi\)
−0.186649 + 0.982427i \(0.559763\pi\)
\(660\) −10.8046 −0.420569
\(661\) −13.3803 −0.520434 −0.260217 0.965550i \(-0.583794\pi\)
−0.260217 + 0.965550i \(0.583794\pi\)
\(662\) −8.07763 −0.313946
\(663\) −24.8223 −0.964017
\(664\) 9.38971 0.364391
\(665\) 29.2251 1.13330
\(666\) 0.674495 0.0261361
\(667\) −18.2615 −0.707088
\(668\) 2.56865 0.0993841
\(669\) 11.3492 0.438786
\(670\) 77.9598 3.01185
\(671\) 5.22885 0.201858
\(672\) −27.7436 −1.07023
\(673\) 7.19490 0.277343 0.138671 0.990338i \(-0.455717\pi\)
0.138671 + 0.990338i \(0.455717\pi\)
\(674\) −50.0908 −1.92943
\(675\) 20.5519 0.791043
\(676\) −3.20955 −0.123444
\(677\) 1.55456 0.0597465 0.0298733 0.999554i \(-0.490490\pi\)
0.0298733 + 0.999554i \(0.490490\pi\)
\(678\) −18.7187 −0.718887
\(679\) 12.3984 0.475808
\(680\) 14.1384 0.542182
\(681\) −24.5172 −0.939502
\(682\) 11.4609 0.438862
\(683\) −13.9100 −0.532253 −0.266126 0.963938i \(-0.585744\pi\)
−0.266126 + 0.963938i \(0.585744\pi\)
\(684\) −8.22451 −0.314472
\(685\) 7.87990 0.301076
\(686\) 42.2055 1.61141
\(687\) 24.8767 0.949107
\(688\) −18.1581 −0.692270
\(689\) 29.2117 1.11288
\(690\) −61.2067 −2.33010
\(691\) −41.6406 −1.58408 −0.792041 0.610468i \(-0.790981\pi\)
−0.792041 + 0.610468i \(0.790981\pi\)
\(692\) −40.2259 −1.52916
\(693\) −1.82210 −0.0692159
\(694\) 54.3727 2.06396
\(695\) −5.15413 −0.195507
\(696\) 4.05834 0.153831
\(697\) −25.8915 −0.980712
\(698\) −9.37867 −0.354988
\(699\) 35.3750 1.33801
\(700\) 20.9762 0.792828
\(701\) 7.81212 0.295060 0.147530 0.989058i \(-0.452868\pi\)
0.147530 + 0.989058i \(0.452868\pi\)
\(702\) 40.7166 1.53675
\(703\) 1.74055 0.0656459
\(704\) −11.1970 −0.422002
\(705\) −48.6971 −1.83404
\(706\) 12.4940 0.470217
\(707\) −11.7908 −0.443438
\(708\) −8.98879 −0.337819
\(709\) 39.4816 1.48276 0.741381 0.671084i \(-0.234171\pi\)
0.741381 + 0.671084i \(0.234171\pi\)
\(710\) 51.3429 1.92687
\(711\) −8.79272 −0.329753
\(712\) −8.76694 −0.328555
\(713\) 35.8549 1.34278
\(714\) −35.7443 −1.33770
\(715\) −10.0589 −0.376182
\(716\) 3.19974 0.119580
\(717\) −6.80338 −0.254077
\(718\) 37.3848 1.39519
\(719\) 21.9108 0.817135 0.408568 0.912728i \(-0.366028\pi\)
0.408568 + 0.912728i \(0.366028\pi\)
\(720\) 6.54968 0.244092
\(721\) 43.5942 1.62353
\(722\) 1.72554 0.0642181
\(723\) −11.2988 −0.420206
\(724\) 22.8106 0.847749
\(725\) 10.0777 0.374275
\(726\) 3.14770 0.116822
\(727\) 17.1636 0.636561 0.318281 0.947997i \(-0.396895\pi\)
0.318281 + 0.947997i \(0.396895\pi\)
\(728\) 7.86426 0.291469
\(729\) 29.8909 1.10707
\(730\) 72.8464 2.69617
\(731\) −31.0625 −1.14889
\(732\) −19.2104 −0.710038
\(733\) 28.9145 1.06798 0.533991 0.845490i \(-0.320692\pi\)
0.533991 + 0.845490i \(0.320692\pi\)
\(734\) 45.0055 1.66118
\(735\) 6.87229 0.253488
\(736\) −52.8516 −1.94814
\(737\) −12.5428 −0.462019
\(738\) 8.78042 0.323212
\(739\) −33.9146 −1.24757 −0.623785 0.781596i \(-0.714406\pi\)
−0.623785 + 0.781596i \(0.714406\pi\)
\(740\) 2.96116 0.108854
\(741\) 21.7223 0.797989
\(742\) 42.0651 1.54426
\(743\) 17.3021 0.634754 0.317377 0.948300i \(-0.397198\pi\)
0.317377 + 0.948300i \(0.397198\pi\)
\(744\) −7.96821 −0.292129
\(745\) −37.1515 −1.36113
\(746\) 26.5502 0.972072
\(747\) 7.44114 0.272257
\(748\) −12.0202 −0.439503
\(749\) −4.94753 −0.180779
\(750\) −12.5079 −0.456726
\(751\) −14.4276 −0.526470 −0.263235 0.964732i \(-0.584789\pi\)
−0.263235 + 0.964732i \(0.584789\pi\)
\(752\) −31.6694 −1.15486
\(753\) −24.4457 −0.890849
\(754\) 19.9655 0.727100
\(755\) −26.5064 −0.964667
\(756\) 32.3799 1.17765
\(757\) 1.25464 0.0456008 0.0228004 0.999740i \(-0.492742\pi\)
0.0228004 + 0.999740i \(0.492742\pi\)
\(758\) 36.5089 1.32606
\(759\) 9.84740 0.357438
\(760\) −12.3727 −0.448804
\(761\) −23.9754 −0.869109 −0.434554 0.900646i \(-0.643094\pi\)
−0.434554 + 0.900646i \(0.643094\pi\)
\(762\) −42.7864 −1.54999
\(763\) −18.7099 −0.677344
\(764\) 43.7479 1.58274
\(765\) 11.2044 0.405094
\(766\) 65.6711 2.37279
\(767\) −8.36841 −0.302166
\(768\) −9.18453 −0.331418
\(769\) 47.5382 1.71427 0.857136 0.515090i \(-0.172241\pi\)
0.857136 + 0.515090i \(0.172241\pi\)
\(770\) −14.4849 −0.522001
\(771\) 7.19955 0.259285
\(772\) −58.1616 −2.09328
\(773\) −7.61291 −0.273817 −0.136909 0.990584i \(-0.543717\pi\)
−0.136909 + 0.990584i \(0.543717\pi\)
\(774\) 10.5340 0.378637
\(775\) −19.7867 −0.710758
\(776\) −5.24897 −0.188427
\(777\) −1.41670 −0.0508239
\(778\) −20.0299 −0.718108
\(779\) 22.6580 0.811808
\(780\) 36.9557 1.32323
\(781\) −8.26044 −0.295582
\(782\) −68.0930 −2.43500
\(783\) 15.5564 0.555939
\(784\) 4.46928 0.159617
\(785\) 56.8141 2.02778
\(786\) 13.3980 0.477889
\(787\) −14.7105 −0.524374 −0.262187 0.965017i \(-0.584444\pi\)
−0.262187 + 0.965017i \(0.584444\pi\)
\(788\) 10.3729 0.369518
\(789\) −7.84485 −0.279284
\(790\) −69.8984 −2.48687
\(791\) −13.8587 −0.492758
\(792\) 0.771400 0.0274105
\(793\) −17.8846 −0.635101
\(794\) 29.1908 1.03594
\(795\) 37.4072 1.32670
\(796\) −46.1265 −1.63491
\(797\) 15.2499 0.540180 0.270090 0.962835i \(-0.412946\pi\)
0.270090 + 0.962835i \(0.412946\pi\)
\(798\) 31.2803 1.10731
\(799\) −54.1760 −1.91661
\(800\) 29.1663 1.03119
\(801\) −6.94761 −0.245482
\(802\) −42.4272 −1.49816
\(803\) −11.7201 −0.413593
\(804\) 46.0812 1.62516
\(805\) −45.3153 −1.59716
\(806\) −39.2006 −1.38078
\(807\) −44.9246 −1.58142
\(808\) 4.99171 0.175608
\(809\) 16.3680 0.575470 0.287735 0.957710i \(-0.407098\pi\)
0.287735 + 0.957710i \(0.407098\pi\)
\(810\) 37.5609 1.31975
\(811\) −19.7654 −0.694056 −0.347028 0.937855i \(-0.612809\pi\)
−0.347028 + 0.937855i \(0.612809\pi\)
\(812\) 15.8776 0.557194
\(813\) −3.98953 −0.139919
\(814\) −0.862671 −0.0302366
\(815\) −29.3588 −1.02839
\(816\) −20.6717 −0.723656
\(817\) 27.1832 0.951020
\(818\) 43.5673 1.52329
\(819\) 6.23225 0.217773
\(820\) 38.5477 1.34614
\(821\) −21.8987 −0.764270 −0.382135 0.924106i \(-0.624811\pi\)
−0.382135 + 0.924106i \(0.624811\pi\)
\(822\) 8.43404 0.294171
\(823\) −20.0877 −0.700213 −0.350106 0.936710i \(-0.613855\pi\)
−0.350106 + 0.936710i \(0.613855\pi\)
\(824\) −18.4559 −0.642942
\(825\) −5.43432 −0.189199
\(826\) −12.0506 −0.419294
\(827\) 4.71736 0.164039 0.0820194 0.996631i \(-0.473863\pi\)
0.0820194 + 0.996631i \(0.473863\pi\)
\(828\) 12.7526 0.443183
\(829\) 11.2029 0.389091 0.194546 0.980893i \(-0.437677\pi\)
0.194546 + 0.980893i \(0.437677\pi\)
\(830\) 59.1539 2.05326
\(831\) −5.71437 −0.198229
\(832\) 38.2978 1.32774
\(833\) 7.64547 0.264900
\(834\) −5.51658 −0.191023
\(835\) 3.06229 0.105975
\(836\) 10.5190 0.363809
\(837\) −30.5436 −1.05574
\(838\) 54.8741 1.89560
\(839\) 48.6292 1.67887 0.839433 0.543463i \(-0.182887\pi\)
0.839433 + 0.543463i \(0.182887\pi\)
\(840\) 10.0706 0.347470
\(841\) −21.3719 −0.736962
\(842\) 56.0690 1.93227
\(843\) 32.4082 1.11620
\(844\) −53.8518 −1.85365
\(845\) −3.82636 −0.131631
\(846\) 18.3723 0.631653
\(847\) 2.33045 0.0800751
\(848\) 24.3272 0.835399
\(849\) 3.58789 0.123136
\(850\) 37.5773 1.28889
\(851\) −2.69882 −0.0925144
\(852\) 30.3483 1.03971
\(853\) −34.9585 −1.19696 −0.598478 0.801140i \(-0.704227\pi\)
−0.598478 + 0.801140i \(0.704227\pi\)
\(854\) −25.7540 −0.881284
\(855\) −9.80508 −0.335327
\(856\) 2.09457 0.0715911
\(857\) 24.0338 0.820980 0.410490 0.911865i \(-0.365358\pi\)
0.410490 + 0.911865i \(0.365358\pi\)
\(858\) −10.7663 −0.367555
\(859\) −37.6711 −1.28532 −0.642660 0.766151i \(-0.722169\pi\)
−0.642660 + 0.766151i \(0.722169\pi\)
\(860\) 46.2463 1.57698
\(861\) −18.4423 −0.628512
\(862\) 62.8066 2.13920
\(863\) 37.3379 1.27100 0.635499 0.772102i \(-0.280795\pi\)
0.635499 + 0.772102i \(0.280795\pi\)
\(864\) 45.0225 1.53170
\(865\) −47.9565 −1.63057
\(866\) −47.7882 −1.62391
\(867\) −10.0438 −0.341106
\(868\) −31.1743 −1.05812
\(869\) 11.2458 0.381487
\(870\) 25.5670 0.866802
\(871\) 42.9009 1.45364
\(872\) 7.92098 0.268238
\(873\) −4.15969 −0.140784
\(874\) 59.5891 2.01563
\(875\) −9.26045 −0.313061
\(876\) 43.0587 1.45482
\(877\) −47.3252 −1.59806 −0.799029 0.601292i \(-0.794653\pi\)
−0.799029 + 0.601292i \(0.794653\pi\)
\(878\) −21.9805 −0.741804
\(879\) −31.8592 −1.07458
\(880\) −8.37696 −0.282387
\(881\) 35.2946 1.18911 0.594553 0.804056i \(-0.297329\pi\)
0.594553 + 0.804056i \(0.297329\pi\)
\(882\) −2.59276 −0.0873027
\(883\) 46.8892 1.57795 0.788974 0.614426i \(-0.210612\pi\)
0.788974 + 0.614426i \(0.210612\pi\)
\(884\) 41.1135 1.38280
\(885\) −10.7162 −0.360222
\(886\) 55.2790 1.85713
\(887\) −9.97992 −0.335093 −0.167546 0.985864i \(-0.553584\pi\)
−0.167546 + 0.985864i \(0.553584\pi\)
\(888\) 0.599771 0.0201270
\(889\) −31.6776 −1.06243
\(890\) −55.2305 −1.85133
\(891\) −6.04308 −0.202451
\(892\) −18.7979 −0.629400
\(893\) 47.4101 1.58652
\(894\) −39.7641 −1.32991
\(895\) 3.81467 0.127510
\(896\) 17.8929 0.597760
\(897\) −33.6817 −1.12460
\(898\) −3.24097 −0.108152
\(899\) −14.9771 −0.499516
\(900\) −7.03756 −0.234585
\(901\) 41.6159 1.38643
\(902\) −11.2301 −0.373920
\(903\) −22.1256 −0.736292
\(904\) 5.86717 0.195139
\(905\) 27.1943 0.903969
\(906\) −28.3704 −0.942543
\(907\) 6.43074 0.213529 0.106765 0.994284i \(-0.465951\pi\)
0.106765 + 0.994284i \(0.465951\pi\)
\(908\) 40.6083 1.34763
\(909\) 3.95582 0.131206
\(910\) 49.5438 1.64236
\(911\) 45.9279 1.52166 0.760830 0.648952i \(-0.224792\pi\)
0.760830 + 0.648952i \(0.224792\pi\)
\(912\) 18.0901 0.599023
\(913\) −9.51713 −0.314971
\(914\) −57.2858 −1.89485
\(915\) −22.9023 −0.757126
\(916\) −41.2037 −1.36141
\(917\) 9.91938 0.327567
\(918\) 58.0062 1.91449
\(919\) −28.0926 −0.926689 −0.463344 0.886178i \(-0.653351\pi\)
−0.463344 + 0.886178i \(0.653351\pi\)
\(920\) 19.1846 0.632497
\(921\) 37.2519 1.22749
\(922\) −26.2726 −0.865242
\(923\) 28.2537 0.929983
\(924\) −8.56189 −0.281666
\(925\) 1.48935 0.0489696
\(926\) 8.65483 0.284415
\(927\) −14.6259 −0.480378
\(928\) 22.0769 0.724710
\(929\) 42.4504 1.39275 0.696376 0.717677i \(-0.254795\pi\)
0.696376 + 0.717677i \(0.254795\pi\)
\(930\) −50.1986 −1.64608
\(931\) −6.69066 −0.219277
\(932\) −58.5922 −1.91925
\(933\) 0.332320 0.0108797
\(934\) −34.3385 −1.12359
\(935\) −14.3302 −0.468649
\(936\) −2.63847 −0.0862411
\(937\) −34.7090 −1.13389 −0.566947 0.823754i \(-0.691876\pi\)
−0.566947 + 0.823754i \(0.691876\pi\)
\(938\) 61.7777 2.01711
\(939\) −35.0060 −1.14238
\(940\) 80.6579 2.63077
\(941\) −6.80358 −0.221790 −0.110895 0.993832i \(-0.535372\pi\)
−0.110895 + 0.993832i \(0.535372\pi\)
\(942\) 60.8094 1.98128
\(943\) −35.1326 −1.14408
\(944\) −6.96913 −0.226826
\(945\) 38.6027 1.25574
\(946\) −13.4729 −0.438041
\(947\) −20.4922 −0.665906 −0.332953 0.942943i \(-0.608045\pi\)
−0.332953 + 0.942943i \(0.608045\pi\)
\(948\) −41.3162 −1.34189
\(949\) 40.0870 1.30128
\(950\) −32.8844 −1.06691
\(951\) −0.332994 −0.0107981
\(952\) 11.2037 0.363113
\(953\) −28.2019 −0.913550 −0.456775 0.889582i \(-0.650995\pi\)
−0.456775 + 0.889582i \(0.650995\pi\)
\(954\) −14.1129 −0.456922
\(955\) 52.1553 1.68771
\(956\) 11.2686 0.364451
\(957\) −4.11341 −0.132968
\(958\) −40.4449 −1.30672
\(959\) 6.24427 0.201638
\(960\) 49.0425 1.58284
\(961\) −1.59361 −0.0514069
\(962\) 2.95065 0.0951328
\(963\) 1.65991 0.0534897
\(964\) 18.7143 0.602748
\(965\) −69.3390 −2.23210
\(966\) −48.5020 −1.56053
\(967\) −26.3151 −0.846238 −0.423119 0.906074i \(-0.639065\pi\)
−0.423119 + 0.906074i \(0.639065\pi\)
\(968\) −0.986611 −0.0317109
\(969\) 30.9463 0.994137
\(970\) −33.0678 −1.06174
\(971\) −6.26583 −0.201080 −0.100540 0.994933i \(-0.532057\pi\)
−0.100540 + 0.994933i \(0.532057\pi\)
\(972\) −19.4811 −0.624857
\(973\) −4.08428 −0.130936
\(974\) −1.76884 −0.0566771
\(975\) 18.5874 0.595273
\(976\) −14.8941 −0.476749
\(977\) 38.4043 1.22866 0.614331 0.789049i \(-0.289426\pi\)
0.614331 + 0.789049i \(0.289426\pi\)
\(978\) −31.4234 −1.00481
\(979\) 8.88591 0.283995
\(980\) −11.3827 −0.363606
\(981\) 6.27720 0.200416
\(982\) 0.0142922 0.000456081 0
\(983\) −26.1645 −0.834519 −0.417259 0.908787i \(-0.637009\pi\)
−0.417259 + 0.908787i \(0.637009\pi\)
\(984\) 7.80769 0.248900
\(985\) 12.3663 0.394023
\(986\) 28.4435 0.905825
\(987\) −38.5890 −1.22830
\(988\) −35.9790 −1.14464
\(989\) −42.1492 −1.34027
\(990\) 4.85972 0.154452
\(991\) 42.1196 1.33797 0.668987 0.743275i \(-0.266728\pi\)
0.668987 + 0.743275i \(0.266728\pi\)
\(992\) −43.3462 −1.37624
\(993\) −5.69218 −0.180636
\(994\) 40.6857 1.29047
\(995\) −54.9910 −1.74333
\(996\) 34.9652 1.10792
\(997\) −57.2149 −1.81201 −0.906006 0.423264i \(-0.860884\pi\)
−0.906006 + 0.423264i \(0.860884\pi\)
\(998\) −18.6346 −0.589866
\(999\) 2.29904 0.0727383
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 \(a_p\))