Properties

Label 6017.2.a.c.1.12
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 1.12
Character \(\chi\) = 6017.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.39408 q^{2}\) \(-0.179689 q^{3}\) \(+3.73161 q^{4}\) \(-1.83517 q^{5}\) \(+0.430189 q^{6}\) \(+0.373924 q^{7}\) \(-4.14560 q^{8}\) \(-2.96771 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.39408 q^{2}\) \(-0.179689 q^{3}\) \(+3.73161 q^{4}\) \(-1.83517 q^{5}\) \(+0.430189 q^{6}\) \(+0.373924 q^{7}\) \(-4.14560 q^{8}\) \(-2.96771 q^{9}\) \(+4.39353 q^{10}\) \(+1.00000 q^{11}\) \(-0.670529 q^{12}\) \(+6.01413 q^{13}\) \(-0.895203 q^{14}\) \(+0.329759 q^{15}\) \(+2.46168 q^{16}\) \(+5.84884 q^{17}\) \(+7.10493 q^{18}\) \(-3.17074 q^{19}\) \(-6.84812 q^{20}\) \(-0.0671900 q^{21}\) \(-2.39408 q^{22}\) \(+0.679989 q^{23}\) \(+0.744919 q^{24}\) \(-1.63217 q^{25}\) \(-14.3983 q^{26}\) \(+1.07233 q^{27}\) \(+1.39534 q^{28}\) \(+5.00335 q^{29}\) \(-0.789469 q^{30}\) \(-9.34384 q^{31}\) \(+2.39776 q^{32}\) \(-0.179689 q^{33}\) \(-14.0026 q^{34}\) \(-0.686213 q^{35}\) \(-11.0743 q^{36}\) \(-3.30410 q^{37}\) \(+7.59100 q^{38}\) \(-1.08067 q^{39}\) \(+7.60787 q^{40}\) \(+0.161876 q^{41}\) \(+0.160858 q^{42}\) \(+3.21975 q^{43}\) \(+3.73161 q^{44}\) \(+5.44624 q^{45}\) \(-1.62795 q^{46}\) \(-5.62611 q^{47}\) \(-0.442336 q^{48}\) \(-6.86018 q^{49}\) \(+3.90753 q^{50}\) \(-1.05097 q^{51}\) \(+22.4424 q^{52}\) \(-3.08764 q^{53}\) \(-2.56725 q^{54}\) \(-1.83517 q^{55}\) \(-1.55014 q^{56}\) \(+0.569747 q^{57}\) \(-11.9784 q^{58}\) \(-8.99236 q^{59}\) \(+1.23053 q^{60}\) \(-2.58651 q^{61}\) \(+22.3699 q^{62}\) \(-1.10970 q^{63}\) \(-10.6638 q^{64}\) \(-11.0369 q^{65}\) \(+0.430189 q^{66}\) \(+7.79770 q^{67}\) \(+21.8256 q^{68}\) \(-0.122187 q^{69}\) \(+1.64285 q^{70}\) \(-11.9224 q^{71}\) \(+12.3029 q^{72}\) \(-5.11901 q^{73}\) \(+7.91026 q^{74}\) \(+0.293282 q^{75}\) \(-11.8320 q^{76}\) \(+0.373924 q^{77}\) \(+2.58721 q^{78}\) \(-1.78467 q^{79}\) \(-4.51758 q^{80}\) \(+8.71045 q^{81}\) \(-0.387545 q^{82}\) \(+13.2223 q^{83}\) \(-0.250727 q^{84}\) \(-10.7336 q^{85}\) \(-7.70833 q^{86}\) \(-0.899047 q^{87}\) \(-4.14560 q^{88}\) \(+17.1332 q^{89}\) \(-13.0387 q^{90}\) \(+2.24883 q^{91}\) \(+2.53745 q^{92}\) \(+1.67898 q^{93}\) \(+13.4693 q^{94}\) \(+5.81883 q^{95}\) \(-0.430851 q^{96}\) \(+15.6825 q^{97}\) \(+16.4238 q^{98}\) \(-2.96771 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(106q \) \(\mathstrut -\mathstrut 13q^{2} \) \(\mathstrut -\mathstrut 15q^{3} \) \(\mathstrut +\mathstrut 93q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 22q^{6} \) \(\mathstrut -\mathstrut 66q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 97q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(106q \) \(\mathstrut -\mathstrut 13q^{2} \) \(\mathstrut -\mathstrut 15q^{3} \) \(\mathstrut +\mathstrut 93q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 22q^{6} \) \(\mathstrut -\mathstrut 66q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 97q^{9} \) \(\mathstrut -\mathstrut 30q^{10} \) \(\mathstrut +\mathstrut 106q^{11} \) \(\mathstrut -\mathstrut 26q^{12} \) \(\mathstrut -\mathstrut 72q^{13} \) \(\mathstrut +\mathstrut 3q^{14} \) \(\mathstrut -\mathstrut 46q^{15} \) \(\mathstrut +\mathstrut 75q^{16} \) \(\mathstrut -\mathstrut 65q^{17} \) \(\mathstrut -\mathstrut 37q^{18} \) \(\mathstrut -\mathstrut 63q^{19} \) \(\mathstrut -\mathstrut 25q^{20} \) \(\mathstrut -\mathstrut 27q^{21} \) \(\mathstrut -\mathstrut 13q^{22} \) \(\mathstrut -\mathstrut 23q^{23} \) \(\mathstrut -\mathstrut 56q^{24} \) \(\mathstrut +\mathstrut 74q^{25} \) \(\mathstrut +\mathstrut 2q^{26} \) \(\mathstrut -\mathstrut 54q^{27} \) \(\mathstrut -\mathstrut 115q^{28} \) \(\mathstrut -\mathstrut 45q^{29} \) \(\mathstrut -\mathstrut 14q^{30} \) \(\mathstrut -\mathstrut 89q^{31} \) \(\mathstrut -\mathstrut 96q^{32} \) \(\mathstrut -\mathstrut 15q^{33} \) \(\mathstrut -\mathstrut 26q^{34} \) \(\mathstrut -\mathstrut 52q^{35} \) \(\mathstrut +\mathstrut 91q^{36} \) \(\mathstrut -\mathstrut 35q^{37} \) \(\mathstrut +\mathstrut 7q^{38} \) \(\mathstrut -\mathstrut 34q^{39} \) \(\mathstrut -\mathstrut 74q^{40} \) \(\mathstrut -\mathstrut 32q^{41} \) \(\mathstrut -\mathstrut 94q^{43} \) \(\mathstrut +\mathstrut 93q^{44} \) \(\mathstrut -\mathstrut 46q^{45} \) \(\mathstrut -\mathstrut 20q^{46} \) \(\mathstrut -\mathstrut 105q^{47} \) \(\mathstrut -\mathstrut 57q^{48} \) \(\mathstrut +\mathstrut 80q^{49} \) \(\mathstrut -\mathstrut 60q^{50} \) \(\mathstrut -\mathstrut 36q^{51} \) \(\mathstrut -\mathstrut 137q^{52} \) \(\mathstrut -\mathstrut 61q^{54} \) \(\mathstrut -\mathstrut 12q^{55} \) \(\mathstrut +\mathstrut 32q^{56} \) \(\mathstrut -\mathstrut 71q^{57} \) \(\mathstrut -\mathstrut 28q^{58} \) \(\mathstrut -\mathstrut 15q^{59} \) \(\mathstrut -\mathstrut 21q^{60} \) \(\mathstrut -\mathstrut 80q^{61} \) \(\mathstrut -\mathstrut 84q^{62} \) \(\mathstrut -\mathstrut 182q^{63} \) \(\mathstrut +\mathstrut 55q^{64} \) \(\mathstrut -\mathstrut 73q^{65} \) \(\mathstrut -\mathstrut 22q^{66} \) \(\mathstrut -\mathstrut 58q^{67} \) \(\mathstrut -\mathstrut 145q^{68} \) \(\mathstrut -\mathstrut 8q^{69} \) \(\mathstrut -\mathstrut 39q^{70} \) \(\mathstrut -\mathstrut 11q^{71} \) \(\mathstrut -\mathstrut 100q^{72} \) \(\mathstrut -\mathstrut 155q^{73} \) \(\mathstrut -\mathstrut 15q^{74} \) \(\mathstrut -\mathstrut 15q^{75} \) \(\mathstrut -\mathstrut 132q^{76} \) \(\mathstrut -\mathstrut 66q^{77} \) \(\mathstrut -\mathstrut 45q^{78} \) \(\mathstrut -\mathstrut 50q^{79} \) \(\mathstrut -\mathstrut 28q^{80} \) \(\mathstrut +\mathstrut 114q^{81} \) \(\mathstrut -\mathstrut 57q^{82} \) \(\mathstrut -\mathstrut 96q^{83} \) \(\mathstrut -\mathstrut 27q^{84} \) \(\mathstrut -\mathstrut 74q^{85} \) \(\mathstrut +\mathstrut 54q^{86} \) \(\mathstrut -\mathstrut 182q^{87} \) \(\mathstrut -\mathstrut 39q^{88} \) \(\mathstrut +\mathstrut 9q^{89} \) \(\mathstrut -\mathstrut 53q^{90} \) \(\mathstrut +\mathstrut 6q^{91} \) \(\mathstrut -\mathstrut 18q^{92} \) \(\mathstrut -\mathstrut 26q^{93} \) \(\mathstrut -\mathstrut 33q^{94} \) \(\mathstrut -\mathstrut 49q^{95} \) \(\mathstrut -\mathstrut 56q^{96} \) \(\mathstrut -\mathstrut 102q^{97} \) \(\mathstrut -\mathstrut 76q^{98} \) \(\mathstrut +\mathstrut 97q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.39408 −1.69287 −0.846434 0.532493i \(-0.821255\pi\)
−0.846434 + 0.532493i \(0.821255\pi\)
\(3\) −0.179689 −0.103743 −0.0518717 0.998654i \(-0.516519\pi\)
−0.0518717 + 0.998654i \(0.516519\pi\)
\(4\) 3.73161 1.86580
\(5\) −1.83517 −0.820711 −0.410356 0.911926i \(-0.634595\pi\)
−0.410356 + 0.911926i \(0.634595\pi\)
\(6\) 0.430189 0.175624
\(7\) 0.373924 0.141330 0.0706650 0.997500i \(-0.477488\pi\)
0.0706650 + 0.997500i \(0.477488\pi\)
\(8\) −4.14560 −1.46569
\(9\) −2.96771 −0.989237
\(10\) 4.39353 1.38936
\(11\) 1.00000 0.301511
\(12\) −0.670529 −0.193565
\(13\) 6.01413 1.66802 0.834009 0.551750i \(-0.186040\pi\)
0.834009 + 0.551750i \(0.186040\pi\)
\(14\) −0.895203 −0.239253
\(15\) 0.329759 0.0851434
\(16\) 2.46168 0.615419
\(17\) 5.84884 1.41855 0.709276 0.704931i \(-0.249022\pi\)
0.709276 + 0.704931i \(0.249022\pi\)
\(18\) 7.10493 1.67465
\(19\) −3.17074 −0.727418 −0.363709 0.931513i \(-0.618490\pi\)
−0.363709 + 0.931513i \(0.618490\pi\)
\(20\) −6.84812 −1.53129
\(21\) −0.0671900 −0.0146621
\(22\) −2.39408 −0.510419
\(23\) 0.679989 0.141788 0.0708938 0.997484i \(-0.477415\pi\)
0.0708938 + 0.997484i \(0.477415\pi\)
\(24\) 0.744919 0.152056
\(25\) −1.63217 −0.326433
\(26\) −14.3983 −2.82374
\(27\) 1.07233 0.206370
\(28\) 1.39534 0.263694
\(29\) 5.00335 0.929099 0.464549 0.885547i \(-0.346216\pi\)
0.464549 + 0.885547i \(0.346216\pi\)
\(30\) −0.789469 −0.144137
\(31\) −9.34384 −1.67820 −0.839101 0.543975i \(-0.816919\pi\)
−0.839101 + 0.543975i \(0.816919\pi\)
\(32\) 2.39776 0.423868
\(33\) −0.179689 −0.0312798
\(34\) −14.0026 −2.40142
\(35\) −0.686213 −0.115991
\(36\) −11.0743 −1.84572
\(37\) −3.30410 −0.543190 −0.271595 0.962412i \(-0.587551\pi\)
−0.271595 + 0.962412i \(0.587551\pi\)
\(38\) 7.59100 1.23142
\(39\) −1.08067 −0.173046
\(40\) 7.60787 1.20291
\(41\) 0.161876 0.0252809 0.0126404 0.999920i \(-0.495976\pi\)
0.0126404 + 0.999920i \(0.495976\pi\)
\(42\) 0.160858 0.0248209
\(43\) 3.21975 0.491007 0.245504 0.969396i \(-0.421047\pi\)
0.245504 + 0.969396i \(0.421047\pi\)
\(44\) 3.73161 0.562561
\(45\) 5.44624 0.811878
\(46\) −1.62795 −0.240028
\(47\) −5.62611 −0.820652 −0.410326 0.911939i \(-0.634585\pi\)
−0.410326 + 0.911939i \(0.634585\pi\)
\(48\) −0.442336 −0.0638457
\(49\) −6.86018 −0.980026
\(50\) 3.90753 0.552608
\(51\) −1.05097 −0.147165
\(52\) 22.4424 3.11220
\(53\) −3.08764 −0.424120 −0.212060 0.977257i \(-0.568017\pi\)
−0.212060 + 0.977257i \(0.568017\pi\)
\(54\) −2.56725 −0.349358
\(55\) −1.83517 −0.247454
\(56\) −1.55014 −0.207146
\(57\) 0.569747 0.0754648
\(58\) −11.9784 −1.57284
\(59\) −8.99236 −1.17071 −0.585353 0.810778i \(-0.699044\pi\)
−0.585353 + 0.810778i \(0.699044\pi\)
\(60\) 1.23053 0.158861
\(61\) −2.58651 −0.331168 −0.165584 0.986196i \(-0.552951\pi\)
−0.165584 + 0.986196i \(0.552951\pi\)
\(62\) 22.3699 2.84098
\(63\) −1.10970 −0.139809
\(64\) −10.6638 −1.33297
\(65\) −11.0369 −1.36896
\(66\) 0.430189 0.0529526
\(67\) 7.79770 0.952641 0.476320 0.879272i \(-0.341970\pi\)
0.476320 + 0.879272i \(0.341970\pi\)
\(68\) 21.8256 2.64674
\(69\) −0.122187 −0.0147095
\(70\) 1.64285 0.196358
\(71\) −11.9224 −1.41493 −0.707466 0.706748i \(-0.750162\pi\)
−0.707466 + 0.706748i \(0.750162\pi\)
\(72\) 12.3029 1.44992
\(73\) −5.11901 −0.599135 −0.299567 0.954075i \(-0.596842\pi\)
−0.299567 + 0.954075i \(0.596842\pi\)
\(74\) 7.91026 0.919550
\(75\) 0.293282 0.0338653
\(76\) −11.8320 −1.35722
\(77\) 0.373924 0.0426126
\(78\) 2.58721 0.292944
\(79\) −1.78467 −0.200791 −0.100396 0.994948i \(-0.532011\pi\)
−0.100396 + 0.994948i \(0.532011\pi\)
\(80\) −4.51758 −0.505081
\(81\) 8.71045 0.967828
\(82\) −0.387545 −0.0427972
\(83\) 13.2223 1.45133 0.725666 0.688047i \(-0.241532\pi\)
0.725666 + 0.688047i \(0.241532\pi\)
\(84\) −0.250727 −0.0273565
\(85\) −10.7336 −1.16422
\(86\) −7.70833 −0.831211
\(87\) −0.899047 −0.0963879
\(88\) −4.14560 −0.441923
\(89\) 17.1332 1.81612 0.908058 0.418844i \(-0.137565\pi\)
0.908058 + 0.418844i \(0.137565\pi\)
\(90\) −13.0387 −1.37440
\(91\) 2.24883 0.235741
\(92\) 2.53745 0.264548
\(93\) 1.67898 0.174103
\(94\) 13.4693 1.38926
\(95\) 5.81883 0.597000
\(96\) −0.430851 −0.0439735
\(97\) 15.6825 1.59231 0.796157 0.605090i \(-0.206863\pi\)
0.796157 + 0.605090i \(0.206863\pi\)
\(98\) 16.4238 1.65905
\(99\) −2.96771 −0.298266
\(100\) −6.09060 −0.609060
\(101\) 15.1463 1.50711 0.753555 0.657385i \(-0.228337\pi\)
0.753555 + 0.657385i \(0.228337\pi\)
\(102\) 2.51611 0.249132
\(103\) −0.217065 −0.0213881 −0.0106940 0.999943i \(-0.503404\pi\)
−0.0106940 + 0.999943i \(0.503404\pi\)
\(104\) −24.9322 −2.44480
\(105\) 0.123305 0.0120333
\(106\) 7.39205 0.717979
\(107\) −1.51562 −0.146521 −0.0732604 0.997313i \(-0.523340\pi\)
−0.0732604 + 0.997313i \(0.523340\pi\)
\(108\) 4.00152 0.385047
\(109\) 2.48417 0.237941 0.118970 0.992898i \(-0.462041\pi\)
0.118970 + 0.992898i \(0.462041\pi\)
\(110\) 4.39353 0.418907
\(111\) 0.593710 0.0563524
\(112\) 0.920479 0.0869771
\(113\) −7.35374 −0.691781 −0.345891 0.938275i \(-0.612423\pi\)
−0.345891 + 0.938275i \(0.612423\pi\)
\(114\) −1.36402 −0.127752
\(115\) −1.24789 −0.116367
\(116\) 18.6705 1.73352
\(117\) −17.8482 −1.65007
\(118\) 21.5284 1.98185
\(119\) 2.18702 0.200484
\(120\) −1.36705 −0.124794
\(121\) 1.00000 0.0909091
\(122\) 6.19230 0.560624
\(123\) −0.0290874 −0.00262272
\(124\) −34.8675 −3.13120
\(125\) 12.1711 1.08862
\(126\) 2.65670 0.236678
\(127\) 10.4142 0.924114 0.462057 0.886850i \(-0.347112\pi\)
0.462057 + 0.886850i \(0.347112\pi\)
\(128\) 20.7344 1.83268
\(129\) −0.578554 −0.0509388
\(130\) 26.4232 2.31747
\(131\) −2.04204 −0.178413 −0.0892067 0.996013i \(-0.528433\pi\)
−0.0892067 + 0.996013i \(0.528433\pi\)
\(132\) −0.670529 −0.0583620
\(133\) −1.18562 −0.102806
\(134\) −18.6683 −1.61270
\(135\) −1.96791 −0.169371
\(136\) −24.2469 −2.07916
\(137\) 14.0680 1.20191 0.600954 0.799283i \(-0.294787\pi\)
0.600954 + 0.799283i \(0.294787\pi\)
\(138\) 0.292524 0.0249013
\(139\) −10.3244 −0.875706 −0.437853 0.899047i \(-0.644261\pi\)
−0.437853 + 0.899047i \(0.644261\pi\)
\(140\) −2.56068 −0.216417
\(141\) 1.01095 0.0851373
\(142\) 28.5432 2.39529
\(143\) 6.01413 0.502927
\(144\) −7.30554 −0.608795
\(145\) −9.18198 −0.762522
\(146\) 12.2553 1.01426
\(147\) 1.23270 0.101671
\(148\) −12.3296 −1.01349
\(149\) −19.0969 −1.56448 −0.782238 0.622980i \(-0.785922\pi\)
−0.782238 + 0.622980i \(0.785922\pi\)
\(150\) −0.702140 −0.0573295
\(151\) −17.1066 −1.39212 −0.696059 0.717984i \(-0.745065\pi\)
−0.696059 + 0.717984i \(0.745065\pi\)
\(152\) 13.1446 1.06617
\(153\) −17.3577 −1.40328
\(154\) −0.895203 −0.0721375
\(155\) 17.1475 1.37732
\(156\) −4.03264 −0.322870
\(157\) −20.7553 −1.65646 −0.828228 0.560391i \(-0.810651\pi\)
−0.828228 + 0.560391i \(0.810651\pi\)
\(158\) 4.27264 0.339913
\(159\) 0.554815 0.0439997
\(160\) −4.40029 −0.347873
\(161\) 0.254264 0.0200388
\(162\) −20.8535 −1.63840
\(163\) −16.2746 −1.27473 −0.637363 0.770564i \(-0.719975\pi\)
−0.637363 + 0.770564i \(0.719975\pi\)
\(164\) 0.604059 0.0471691
\(165\) 0.329759 0.0256717
\(166\) −31.6551 −2.45692
\(167\) −1.72474 −0.133464 −0.0667320 0.997771i \(-0.521257\pi\)
−0.0667320 + 0.997771i \(0.521257\pi\)
\(168\) 0.278543 0.0214901
\(169\) 23.1697 1.78229
\(170\) 25.6970 1.97087
\(171\) 9.40984 0.719589
\(172\) 12.0148 0.916123
\(173\) 9.09979 0.691844 0.345922 0.938263i \(-0.387566\pi\)
0.345922 + 0.938263i \(0.387566\pi\)
\(174\) 2.15239 0.163172
\(175\) −0.610306 −0.0461348
\(176\) 2.46168 0.185556
\(177\) 1.61583 0.121453
\(178\) −41.0182 −3.07445
\(179\) −20.0313 −1.49721 −0.748605 0.663017i \(-0.769276\pi\)
−0.748605 + 0.663017i \(0.769276\pi\)
\(180\) 20.3232 1.51481
\(181\) 9.25128 0.687642 0.343821 0.939035i \(-0.388279\pi\)
0.343821 + 0.939035i \(0.388279\pi\)
\(182\) −5.38386 −0.399079
\(183\) 0.464767 0.0343565
\(184\) −2.81896 −0.207817
\(185\) 6.06357 0.445802
\(186\) −4.01962 −0.294733
\(187\) 5.84884 0.427709
\(188\) −20.9944 −1.53117
\(189\) 0.400971 0.0291663
\(190\) −13.9307 −1.01064
\(191\) 11.0791 0.801657 0.400828 0.916153i \(-0.368722\pi\)
0.400828 + 0.916153i \(0.368722\pi\)
\(192\) 1.91616 0.138287
\(193\) 15.1622 1.09140 0.545699 0.837982i \(-0.316264\pi\)
0.545699 + 0.837982i \(0.316264\pi\)
\(194\) −37.5451 −2.69558
\(195\) 1.98321 0.142021
\(196\) −25.5995 −1.82854
\(197\) −16.6652 −1.18735 −0.593673 0.804707i \(-0.702323\pi\)
−0.593673 + 0.804707i \(0.702323\pi\)
\(198\) 7.10493 0.504926
\(199\) −22.9383 −1.62605 −0.813027 0.582226i \(-0.802182\pi\)
−0.813027 + 0.582226i \(0.802182\pi\)
\(200\) 6.76630 0.478450
\(201\) −1.40116 −0.0988303
\(202\) −36.2613 −2.55134
\(203\) 1.87087 0.131309
\(204\) −3.92181 −0.274582
\(205\) −0.297070 −0.0207483
\(206\) 0.519670 0.0362072
\(207\) −2.01801 −0.140262
\(208\) 14.8048 1.02653
\(209\) −3.17074 −0.219325
\(210\) −0.295201 −0.0203708
\(211\) 2.81573 0.193843 0.0969213 0.995292i \(-0.469100\pi\)
0.0969213 + 0.995292i \(0.469100\pi\)
\(212\) −11.5219 −0.791324
\(213\) 2.14233 0.146790
\(214\) 3.62852 0.248041
\(215\) −5.90878 −0.402975
\(216\) −4.44546 −0.302475
\(217\) −3.49388 −0.237180
\(218\) −5.94731 −0.402802
\(219\) 0.919830 0.0621563
\(220\) −6.84812 −0.461700
\(221\) 35.1756 2.36617
\(222\) −1.42139 −0.0953973
\(223\) −23.4098 −1.56763 −0.783817 0.620992i \(-0.786730\pi\)
−0.783817 + 0.620992i \(0.786730\pi\)
\(224\) 0.896580 0.0599053
\(225\) 4.84380 0.322920
\(226\) 17.6054 1.17109
\(227\) −9.86918 −0.655041 −0.327520 0.944844i \(-0.606213\pi\)
−0.327520 + 0.944844i \(0.606213\pi\)
\(228\) 2.12607 0.140803
\(229\) −2.01835 −0.133376 −0.0666880 0.997774i \(-0.521243\pi\)
−0.0666880 + 0.997774i \(0.521243\pi\)
\(230\) 2.98755 0.196993
\(231\) −0.0671900 −0.00442078
\(232\) −20.7419 −1.36177
\(233\) 16.8723 1.10534 0.552670 0.833400i \(-0.313609\pi\)
0.552670 + 0.833400i \(0.313609\pi\)
\(234\) 42.7300 2.79335
\(235\) 10.3248 0.673518
\(236\) −33.5560 −2.18431
\(237\) 0.320686 0.0208308
\(238\) −5.23589 −0.339393
\(239\) 28.1658 1.82190 0.910948 0.412522i \(-0.135352\pi\)
0.910948 + 0.412522i \(0.135352\pi\)
\(240\) 0.811760 0.0523989
\(241\) 11.9948 0.772656 0.386328 0.922361i \(-0.373743\pi\)
0.386328 + 0.922361i \(0.373743\pi\)
\(242\) −2.39408 −0.153897
\(243\) −4.78217 −0.306776
\(244\) −9.65182 −0.617895
\(245\) 12.5896 0.804318
\(246\) 0.0696375 0.00443993
\(247\) −19.0692 −1.21335
\(248\) 38.7358 2.45973
\(249\) −2.37590 −0.150566
\(250\) −29.1386 −1.84289
\(251\) −9.30790 −0.587509 −0.293755 0.955881i \(-0.594905\pi\)
−0.293755 + 0.955881i \(0.594905\pi\)
\(252\) −4.14096 −0.260856
\(253\) 0.679989 0.0427506
\(254\) −24.9325 −1.56440
\(255\) 1.92871 0.120780
\(256\) −28.3122 −1.76951
\(257\) 12.7303 0.794092 0.397046 0.917799i \(-0.370035\pi\)
0.397046 + 0.917799i \(0.370035\pi\)
\(258\) 1.38510 0.0862327
\(259\) −1.23548 −0.0767691
\(260\) −41.1855 −2.55421
\(261\) −14.8485 −0.919099
\(262\) 4.88879 0.302031
\(263\) 14.7742 0.911016 0.455508 0.890232i \(-0.349458\pi\)
0.455508 + 0.890232i \(0.349458\pi\)
\(264\) 0.744919 0.0458466
\(265\) 5.66633 0.348080
\(266\) 2.83846 0.174037
\(267\) −3.07865 −0.188410
\(268\) 29.0980 1.77744
\(269\) 25.5398 1.55719 0.778594 0.627528i \(-0.215933\pi\)
0.778594 + 0.627528i \(0.215933\pi\)
\(270\) 4.71132 0.286722
\(271\) 1.65583 0.100584 0.0502922 0.998735i \(-0.483985\pi\)
0.0502922 + 0.998735i \(0.483985\pi\)
\(272\) 14.3979 0.873003
\(273\) −0.404089 −0.0244566
\(274\) −33.6798 −2.03467
\(275\) −1.63217 −0.0984233
\(276\) −0.455952 −0.0274451
\(277\) −17.5359 −1.05363 −0.526815 0.849980i \(-0.676614\pi\)
−0.526815 + 0.849980i \(0.676614\pi\)
\(278\) 24.7175 1.48245
\(279\) 27.7298 1.66014
\(280\) 2.84476 0.170007
\(281\) −19.5215 −1.16456 −0.582278 0.812990i \(-0.697839\pi\)
−0.582278 + 0.812990i \(0.697839\pi\)
\(282\) −2.42029 −0.144126
\(283\) −0.449425 −0.0267155 −0.0133578 0.999911i \(-0.504252\pi\)
−0.0133578 + 0.999911i \(0.504252\pi\)
\(284\) −44.4898 −2.63998
\(285\) −1.04558 −0.0619348
\(286\) −14.3983 −0.851389
\(287\) 0.0605295 0.00357294
\(288\) −7.11586 −0.419306
\(289\) 17.2089 1.01229
\(290\) 21.9824 1.29085
\(291\) −2.81797 −0.165192
\(292\) −19.1021 −1.11787
\(293\) 2.21724 0.129533 0.0647663 0.997900i \(-0.479370\pi\)
0.0647663 + 0.997900i \(0.479370\pi\)
\(294\) −2.95118 −0.172116
\(295\) 16.5025 0.960812
\(296\) 13.6975 0.796149
\(297\) 1.07233 0.0622230
\(298\) 45.7194 2.64845
\(299\) 4.08954 0.236504
\(300\) 1.09441 0.0631860
\(301\) 1.20394 0.0693940
\(302\) 40.9546 2.35667
\(303\) −2.72162 −0.156353
\(304\) −7.80533 −0.447666
\(305\) 4.74667 0.271793
\(306\) 41.5556 2.37557
\(307\) −16.4096 −0.936544 −0.468272 0.883584i \(-0.655123\pi\)
−0.468272 + 0.883584i \(0.655123\pi\)
\(308\) 1.39534 0.0795067
\(309\) 0.0390042 0.00221887
\(310\) −41.0524 −2.33162
\(311\) 29.3948 1.66683 0.833414 0.552648i \(-0.186383\pi\)
0.833414 + 0.552648i \(0.186383\pi\)
\(312\) 4.48004 0.253632
\(313\) 17.9042 1.01201 0.506003 0.862532i \(-0.331122\pi\)
0.506003 + 0.862532i \(0.331122\pi\)
\(314\) 49.6899 2.80416
\(315\) 2.03648 0.114743
\(316\) −6.65969 −0.374637
\(317\) −26.2139 −1.47232 −0.736159 0.676808i \(-0.763363\pi\)
−0.736159 + 0.676808i \(0.763363\pi\)
\(318\) −1.32827 −0.0744857
\(319\) 5.00335 0.280134
\(320\) 19.5698 1.09398
\(321\) 0.272341 0.0152006
\(322\) −0.608728 −0.0339231
\(323\) −18.5451 −1.03188
\(324\) 32.5040 1.80578
\(325\) −9.81605 −0.544496
\(326\) 38.9627 2.15794
\(327\) −0.446379 −0.0246848
\(328\) −0.671075 −0.0370539
\(329\) −2.10374 −0.115983
\(330\) −0.789469 −0.0434588
\(331\) −6.00895 −0.330282 −0.165141 0.986270i \(-0.552808\pi\)
−0.165141 + 0.986270i \(0.552808\pi\)
\(332\) 49.3403 2.70790
\(333\) 9.80561 0.537344
\(334\) 4.12915 0.225937
\(335\) −14.3101 −0.781843
\(336\) −0.165400 −0.00902331
\(337\) 0.779994 0.0424890 0.0212445 0.999774i \(-0.493237\pi\)
0.0212445 + 0.999774i \(0.493237\pi\)
\(338\) −55.4701 −3.01718
\(339\) 1.32139 0.0717678
\(340\) −40.0535 −2.17221
\(341\) −9.34384 −0.505997
\(342\) −22.5279 −1.21817
\(343\) −5.18265 −0.279837
\(344\) −13.3478 −0.719665
\(345\) 0.224233 0.0120723
\(346\) −21.7856 −1.17120
\(347\) 14.2370 0.764280 0.382140 0.924104i \(-0.375187\pi\)
0.382140 + 0.924104i \(0.375187\pi\)
\(348\) −3.35489 −0.179841
\(349\) −32.3854 −1.73355 −0.866775 0.498700i \(-0.833811\pi\)
−0.866775 + 0.498700i \(0.833811\pi\)
\(350\) 1.46112 0.0781001
\(351\) 6.44914 0.344230
\(352\) 2.39776 0.127801
\(353\) −9.89812 −0.526824 −0.263412 0.964683i \(-0.584848\pi\)
−0.263412 + 0.964683i \(0.584848\pi\)
\(354\) −3.86842 −0.205604
\(355\) 21.8796 1.16125
\(356\) 63.9344 3.38852
\(357\) −0.392983 −0.0207989
\(358\) 47.9565 2.53458
\(359\) −21.5311 −1.13637 −0.568184 0.822902i \(-0.692354\pi\)
−0.568184 + 0.822902i \(0.692354\pi\)
\(360\) −22.5780 −1.18996
\(361\) −8.94641 −0.470864
\(362\) −22.1483 −1.16409
\(363\) −0.179689 −0.00943123
\(364\) 8.39174 0.439846
\(365\) 9.39424 0.491717
\(366\) −1.11269 −0.0581611
\(367\) −8.90435 −0.464803 −0.232402 0.972620i \(-0.574658\pi\)
−0.232402 + 0.972620i \(0.574658\pi\)
\(368\) 1.67391 0.0872587
\(369\) −0.480403 −0.0250088
\(370\) −14.5167 −0.754685
\(371\) −1.15454 −0.0599409
\(372\) 6.26531 0.324841
\(373\) −13.5296 −0.700534 −0.350267 0.936650i \(-0.613909\pi\)
−0.350267 + 0.936650i \(0.613909\pi\)
\(374\) −14.0026 −0.724055
\(375\) −2.18702 −0.112937
\(376\) 23.3236 1.20282
\(377\) 30.0908 1.54975
\(378\) −0.959955 −0.0493747
\(379\) −7.85566 −0.403518 −0.201759 0.979435i \(-0.564666\pi\)
−0.201759 + 0.979435i \(0.564666\pi\)
\(380\) 21.7136 1.11388
\(381\) −1.87132 −0.0958708
\(382\) −26.5243 −1.35710
\(383\) 4.79601 0.245065 0.122532 0.992465i \(-0.460898\pi\)
0.122532 + 0.992465i \(0.460898\pi\)
\(384\) −3.72574 −0.190128
\(385\) −0.686213 −0.0349726
\(386\) −36.2994 −1.84759
\(387\) −9.55529 −0.485723
\(388\) 58.5208 2.97095
\(389\) 5.34323 0.270913 0.135456 0.990783i \(-0.456750\pi\)
0.135456 + 0.990783i \(0.456750\pi\)
\(390\) −4.74797 −0.240423
\(391\) 3.97715 0.201133
\(392\) 28.4396 1.43642
\(393\) 0.366931 0.0185092
\(394\) 39.8977 2.01002
\(395\) 3.27517 0.164792
\(396\) −11.0743 −0.556506
\(397\) −13.1684 −0.660901 −0.330451 0.943823i \(-0.607201\pi\)
−0.330451 + 0.943823i \(0.607201\pi\)
\(398\) 54.9161 2.75270
\(399\) 0.213042 0.0106654
\(400\) −4.01786 −0.200893
\(401\) −34.0103 −1.69839 −0.849197 0.528076i \(-0.822914\pi\)
−0.849197 + 0.528076i \(0.822914\pi\)
\(402\) 3.35449 0.167307
\(403\) −56.1950 −2.79927
\(404\) 56.5199 2.81197
\(405\) −15.9851 −0.794307
\(406\) −4.47901 −0.222290
\(407\) −3.30410 −0.163778
\(408\) 4.35691 0.215699
\(409\) 9.68204 0.478746 0.239373 0.970928i \(-0.423058\pi\)
0.239373 + 0.970928i \(0.423058\pi\)
\(410\) 0.711209 0.0351241
\(411\) −2.52786 −0.124690
\(412\) −0.810001 −0.0399059
\(413\) −3.36246 −0.165456
\(414\) 4.83128 0.237444
\(415\) −24.2651 −1.19113
\(416\) 14.4204 0.707020
\(417\) 1.85518 0.0908488
\(418\) 7.59100 0.371288
\(419\) −13.2652 −0.648048 −0.324024 0.946049i \(-0.605036\pi\)
−0.324024 + 0.946049i \(0.605036\pi\)
\(420\) 0.460125 0.0224518
\(421\) 10.2365 0.498898 0.249449 0.968388i \(-0.419751\pi\)
0.249449 + 0.968388i \(0.419751\pi\)
\(422\) −6.74107 −0.328150
\(423\) 16.6967 0.811819
\(424\) 12.8001 0.621629
\(425\) −9.54627 −0.463062
\(426\) −5.12890 −0.248496
\(427\) −0.967157 −0.0468040
\(428\) −5.65571 −0.273379
\(429\) −1.08067 −0.0521754
\(430\) 14.1461 0.682184
\(431\) 19.1015 0.920085 0.460042 0.887897i \(-0.347834\pi\)
0.460042 + 0.887897i \(0.347834\pi\)
\(432\) 2.63973 0.127004
\(433\) −27.6484 −1.32870 −0.664348 0.747423i \(-0.731291\pi\)
−0.664348 + 0.747423i \(0.731291\pi\)
\(434\) 8.36463 0.401515
\(435\) 1.64990 0.0791067
\(436\) 9.26996 0.443951
\(437\) −2.15607 −0.103139
\(438\) −2.20214 −0.105223
\(439\) 17.3620 0.828642 0.414321 0.910131i \(-0.364019\pi\)
0.414321 + 0.910131i \(0.364019\pi\)
\(440\) 7.60787 0.362691
\(441\) 20.3590 0.969478
\(442\) −84.2132 −4.00561
\(443\) −18.2415 −0.866680 −0.433340 0.901230i \(-0.642665\pi\)
−0.433340 + 0.901230i \(0.642665\pi\)
\(444\) 2.21549 0.105143
\(445\) −31.4423 −1.49051
\(446\) 56.0448 2.65380
\(447\) 3.43150 0.162304
\(448\) −3.98744 −0.188389
\(449\) −20.2317 −0.954793 −0.477397 0.878688i \(-0.658419\pi\)
−0.477397 + 0.878688i \(0.658419\pi\)
\(450\) −11.5964 −0.546661
\(451\) 0.161876 0.00762246
\(452\) −27.4413 −1.29073
\(453\) 3.07388 0.144423
\(454\) 23.6276 1.10890
\(455\) −4.12697 −0.193475
\(456\) −2.36194 −0.110608
\(457\) 19.0925 0.893107 0.446554 0.894757i \(-0.352651\pi\)
0.446554 + 0.894757i \(0.352651\pi\)
\(458\) 4.83208 0.225788
\(459\) 6.27189 0.292747
\(460\) −4.65665 −0.217117
\(461\) −20.8789 −0.972429 −0.486214 0.873840i \(-0.661623\pi\)
−0.486214 + 0.873840i \(0.661623\pi\)
\(462\) 0.160858 0.00748380
\(463\) 15.7557 0.732227 0.366114 0.930570i \(-0.380688\pi\)
0.366114 + 0.930570i \(0.380688\pi\)
\(464\) 12.3166 0.571785
\(465\) −3.08122 −0.142888
\(466\) −40.3936 −1.87120
\(467\) −13.7584 −0.636662 −0.318331 0.947980i \(-0.603122\pi\)
−0.318331 + 0.947980i \(0.603122\pi\)
\(468\) −66.6025 −3.07870
\(469\) 2.91575 0.134637
\(470\) −24.7185 −1.14018
\(471\) 3.72951 0.171847
\(472\) 37.2788 1.71589
\(473\) 3.21975 0.148044
\(474\) −0.767746 −0.0352638
\(475\) 5.17517 0.237453
\(476\) 8.16110 0.374063
\(477\) 9.16322 0.419555
\(478\) −67.4312 −3.08423
\(479\) −4.62159 −0.211166 −0.105583 0.994411i \(-0.533671\pi\)
−0.105583 + 0.994411i \(0.533671\pi\)
\(480\) 0.790683 0.0360896
\(481\) −19.8713 −0.906052
\(482\) −28.7166 −1.30800
\(483\) −0.0456885 −0.00207890
\(484\) 3.73161 0.169618
\(485\) −28.7800 −1.30683
\(486\) 11.4489 0.519332
\(487\) −11.0234 −0.499519 −0.249759 0.968308i \(-0.580352\pi\)
−0.249759 + 0.968308i \(0.580352\pi\)
\(488\) 10.7226 0.485390
\(489\) 2.92437 0.132244
\(490\) −30.1404 −1.36160
\(491\) 25.9101 1.16931 0.584653 0.811284i \(-0.301231\pi\)
0.584653 + 0.811284i \(0.301231\pi\)
\(492\) −0.108543 −0.00489349
\(493\) 29.2638 1.31797
\(494\) 45.6532 2.05404
\(495\) 5.44624 0.244790
\(496\) −23.0015 −1.03280
\(497\) −4.45808 −0.199972
\(498\) 5.68808 0.254889
\(499\) −0.375967 −0.0168306 −0.00841530 0.999965i \(-0.502679\pi\)
−0.00841530 + 0.999965i \(0.502679\pi\)
\(500\) 45.4179 2.03115
\(501\) 0.309916 0.0138460
\(502\) 22.2838 0.994576
\(503\) 7.27713 0.324471 0.162236 0.986752i \(-0.448130\pi\)
0.162236 + 0.986752i \(0.448130\pi\)
\(504\) 4.60037 0.204917
\(505\) −27.7959 −1.23690
\(506\) −1.62795 −0.0723711
\(507\) −4.16335 −0.184901
\(508\) 38.8618 1.72421
\(509\) −11.5444 −0.511696 −0.255848 0.966717i \(-0.582355\pi\)
−0.255848 + 0.966717i \(0.582355\pi\)
\(510\) −4.61747 −0.204465
\(511\) −1.91412 −0.0846757
\(512\) 26.3128 1.16287
\(513\) −3.40009 −0.150117
\(514\) −30.4772 −1.34429
\(515\) 0.398350 0.0175534
\(516\) −2.15893 −0.0950418
\(517\) −5.62611 −0.247436
\(518\) 2.95784 0.129960
\(519\) −1.63513 −0.0717743
\(520\) 45.7547 2.00648
\(521\) 30.7442 1.34693 0.673465 0.739219i \(-0.264805\pi\)
0.673465 + 0.739219i \(0.264805\pi\)
\(522\) 35.5485 1.55591
\(523\) 17.6245 0.770666 0.385333 0.922778i \(-0.374087\pi\)
0.385333 + 0.922778i \(0.374087\pi\)
\(524\) −7.62007 −0.332884
\(525\) 0.109665 0.00478618
\(526\) −35.3706 −1.54223
\(527\) −54.6506 −2.38062
\(528\) −0.442336 −0.0192502
\(529\) −22.5376 −0.979896
\(530\) −13.5656 −0.589254
\(531\) 26.6867 1.15811
\(532\) −4.42425 −0.191816
\(533\) 0.973546 0.0421689
\(534\) 7.37052 0.318954
\(535\) 2.78142 0.120251
\(536\) −32.3262 −1.39628
\(537\) 3.59940 0.155326
\(538\) −61.1442 −2.63611
\(539\) −6.86018 −0.295489
\(540\) −7.34346 −0.316012
\(541\) 20.1138 0.864759 0.432380 0.901692i \(-0.357674\pi\)
0.432380 + 0.901692i \(0.357674\pi\)
\(542\) −3.96418 −0.170276
\(543\) −1.66235 −0.0713384
\(544\) 14.0241 0.601278
\(545\) −4.55887 −0.195281
\(546\) 0.967421 0.0414018
\(547\) 1.00000 0.0427569
\(548\) 52.4962 2.24252
\(549\) 7.67600 0.327604
\(550\) 3.90753 0.166618
\(551\) −15.8643 −0.675843
\(552\) 0.506537 0.0215596
\(553\) −0.667331 −0.0283778
\(554\) 41.9823 1.78366
\(555\) −1.08956 −0.0462491
\(556\) −38.5267 −1.63389
\(557\) 25.4636 1.07893 0.539464 0.842009i \(-0.318627\pi\)
0.539464 + 0.842009i \(0.318627\pi\)
\(558\) −66.3873 −2.81040
\(559\) 19.3640 0.819009
\(560\) −1.68923 −0.0713831
\(561\) −1.05097 −0.0443720
\(562\) 46.7360 1.97144
\(563\) −39.2615 −1.65467 −0.827337 0.561706i \(-0.810145\pi\)
−0.827337 + 0.561706i \(0.810145\pi\)
\(564\) 3.77246 0.158849
\(565\) 13.4953 0.567753
\(566\) 1.07596 0.0452259
\(567\) 3.25705 0.136783
\(568\) 49.4256 2.07385
\(569\) −33.7635 −1.41544 −0.707720 0.706493i \(-0.750276\pi\)
−0.707720 + 0.706493i \(0.750276\pi\)
\(570\) 2.50320 0.104848
\(571\) 29.8914 1.25092 0.625458 0.780257i \(-0.284912\pi\)
0.625458 + 0.780257i \(0.284912\pi\)
\(572\) 22.4424 0.938362
\(573\) −1.99080 −0.0831667
\(574\) −0.144912 −0.00604852
\(575\) −1.10985 −0.0462841
\(576\) 31.6470 1.31863
\(577\) −9.61989 −0.400481 −0.200241 0.979747i \(-0.564172\pi\)
−0.200241 + 0.979747i \(0.564172\pi\)
\(578\) −41.1994 −1.71367
\(579\) −2.72448 −0.113225
\(580\) −34.2635 −1.42272
\(581\) 4.94412 0.205117
\(582\) 6.74644 0.279649
\(583\) −3.08764 −0.127877
\(584\) 21.2214 0.878147
\(585\) 32.7544 1.35423
\(586\) −5.30824 −0.219282
\(587\) −16.7346 −0.690711 −0.345355 0.938472i \(-0.612242\pi\)
−0.345355 + 0.938472i \(0.612242\pi\)
\(588\) 4.59995 0.189699
\(589\) 29.6269 1.22075
\(590\) −39.5082 −1.62653
\(591\) 2.99455 0.123179
\(592\) −8.13361 −0.334290
\(593\) −9.13613 −0.375176 −0.187588 0.982248i \(-0.560067\pi\)
−0.187588 + 0.982248i \(0.560067\pi\)
\(594\) −2.56725 −0.105335
\(595\) −4.01354 −0.164539
\(596\) −71.2620 −2.91900
\(597\) 4.12176 0.168692
\(598\) −9.79068 −0.400371
\(599\) 15.4926 0.633009 0.316505 0.948591i \(-0.397491\pi\)
0.316505 + 0.948591i \(0.397491\pi\)
\(600\) −1.21583 −0.0496361
\(601\) −24.0874 −0.982547 −0.491273 0.871005i \(-0.663468\pi\)
−0.491273 + 0.871005i \(0.663468\pi\)
\(602\) −2.88233 −0.117475
\(603\) −23.1413 −0.942388
\(604\) −63.8353 −2.59742
\(605\) −1.83517 −0.0746101
\(606\) 6.51576 0.264685
\(607\) −19.9915 −0.811432 −0.405716 0.913999i \(-0.632978\pi\)
−0.405716 + 0.913999i \(0.632978\pi\)
\(608\) −7.60267 −0.308329
\(609\) −0.336175 −0.0136225
\(610\) −11.3639 −0.460111
\(611\) −33.8361 −1.36886
\(612\) −64.7720 −2.61825
\(613\) −4.93254 −0.199223 −0.0996117 0.995026i \(-0.531760\pi\)
−0.0996117 + 0.995026i \(0.531760\pi\)
\(614\) 39.2858 1.58545
\(615\) 0.0533802 0.00215250
\(616\) −1.55014 −0.0624569
\(617\) −1.73132 −0.0697004 −0.0348502 0.999393i \(-0.511095\pi\)
−0.0348502 + 0.999393i \(0.511095\pi\)
\(618\) −0.0933791 −0.00375626
\(619\) −7.82980 −0.314706 −0.157353 0.987542i \(-0.550296\pi\)
−0.157353 + 0.987542i \(0.550296\pi\)
\(620\) 63.9877 2.56981
\(621\) 0.729174 0.0292608
\(622\) −70.3735 −2.82172
\(623\) 6.40652 0.256672
\(624\) −2.66026 −0.106496
\(625\) −14.1752 −0.567008
\(626\) −42.8641 −1.71319
\(627\) 0.569747 0.0227535
\(628\) −77.4508 −3.09062
\(629\) −19.3251 −0.770543
\(630\) −4.87549 −0.194244
\(631\) −46.0076 −1.83154 −0.915768 0.401708i \(-0.868417\pi\)
−0.915768 + 0.401708i \(0.868417\pi\)
\(632\) 7.39853 0.294298
\(633\) −0.505955 −0.0201099
\(634\) 62.7581 2.49244
\(635\) −19.1118 −0.758430
\(636\) 2.07035 0.0820947
\(637\) −41.2580 −1.63470
\(638\) −11.9784 −0.474230
\(639\) 35.3823 1.39970
\(640\) −38.0510 −1.50410
\(641\) −12.4823 −0.493022 −0.246511 0.969140i \(-0.579284\pi\)
−0.246511 + 0.969140i \(0.579284\pi\)
\(642\) −0.652005 −0.0257326
\(643\) 18.6708 0.736304 0.368152 0.929766i \(-0.379991\pi\)
0.368152 + 0.929766i \(0.379991\pi\)
\(644\) 0.948814 0.0373885
\(645\) 1.06174 0.0418060
\(646\) 44.3985 1.74684
\(647\) −9.76447 −0.383881 −0.191940 0.981407i \(-0.561478\pi\)
−0.191940 + 0.981407i \(0.561478\pi\)
\(648\) −36.1100 −1.41854
\(649\) −8.99236 −0.352981
\(650\) 23.5004 0.921761
\(651\) 0.627813 0.0246059
\(652\) −60.7304 −2.37839
\(653\) 22.2247 0.869719 0.434859 0.900498i \(-0.356798\pi\)
0.434859 + 0.900498i \(0.356798\pi\)
\(654\) 1.06867 0.0417881
\(655\) 3.74747 0.146426
\(656\) 0.398487 0.0155583
\(657\) 15.1917 0.592687
\(658\) 5.03651 0.196343
\(659\) −4.16800 −0.162362 −0.0811812 0.996699i \(-0.525869\pi\)
−0.0811812 + 0.996699i \(0.525869\pi\)
\(660\) 1.23053 0.0478984
\(661\) −41.1100 −1.59900 −0.799498 0.600669i \(-0.794901\pi\)
−0.799498 + 0.600669i \(0.794901\pi\)
\(662\) 14.3859 0.559123
\(663\) −6.32068 −0.245475
\(664\) −54.8143 −2.12721
\(665\) 2.17580 0.0843740
\(666\) −23.4754 −0.909653
\(667\) 3.40222 0.131735
\(668\) −6.43604 −0.249018
\(669\) 4.20648 0.162632
\(670\) 34.2594 1.32356
\(671\) −2.58651 −0.0998510
\(672\) −0.161106 −0.00621478
\(673\) −42.9971 −1.65742 −0.828709 0.559680i \(-0.810924\pi\)
−0.828709 + 0.559680i \(0.810924\pi\)
\(674\) −1.86737 −0.0719282
\(675\) −1.75022 −0.0673661
\(676\) 86.4603 3.32540
\(677\) −9.36046 −0.359752 −0.179876 0.983689i \(-0.557570\pi\)
−0.179876 + 0.983689i \(0.557570\pi\)
\(678\) −3.16350 −0.121493
\(679\) 5.86405 0.225042
\(680\) 44.4972 1.70639
\(681\) 1.77338 0.0679562
\(682\) 22.3699 0.856587
\(683\) −45.6073 −1.74512 −0.872558 0.488511i \(-0.837540\pi\)
−0.872558 + 0.488511i \(0.837540\pi\)
\(684\) 35.1138 1.34261
\(685\) −25.8171 −0.986420
\(686\) 12.4077 0.473727
\(687\) 0.362675 0.0138369
\(688\) 7.92598 0.302175
\(689\) −18.5695 −0.707440
\(690\) −0.536830 −0.0204368
\(691\) −48.4304 −1.84238 −0.921190 0.389113i \(-0.872782\pi\)
−0.921190 + 0.389113i \(0.872782\pi\)
\(692\) 33.9568 1.29085
\(693\) −1.10970 −0.0421540
\(694\) −34.0844 −1.29383
\(695\) 18.9470 0.718702
\(696\) 3.72709 0.141275
\(697\) 0.946789 0.0358622
\(698\) 77.5331 2.93467
\(699\) −3.03177 −0.114672
\(700\) −2.27742 −0.0860784
\(701\) −36.7901 −1.38954 −0.694771 0.719231i \(-0.744494\pi\)
−0.694771 + 0.719231i \(0.744494\pi\)
\(702\) −15.4397 −0.582736
\(703\) 10.4764 0.395126
\(704\) −10.6638 −0.401906
\(705\) −1.85526 −0.0698731
\(706\) 23.6969 0.891843
\(707\) 5.66355 0.213000
\(708\) 6.02964 0.226608
\(709\) −40.0097 −1.50260 −0.751299 0.659962i \(-0.770572\pi\)
−0.751299 + 0.659962i \(0.770572\pi\)
\(710\) −52.3815 −1.96584
\(711\) 5.29639 0.198630
\(712\) −71.0274 −2.66187
\(713\) −6.35371 −0.237948
\(714\) 0.940833 0.0352098
\(715\) −11.0369 −0.412758
\(716\) −74.7489 −2.79350
\(717\) −5.06109 −0.189010
\(718\) 51.5471 1.92372
\(719\) −42.4355 −1.58258 −0.791288 0.611444i \(-0.790589\pi\)
−0.791288 + 0.611444i \(0.790589\pi\)
\(720\) 13.4069 0.499645
\(721\) −0.0811658 −0.00302277
\(722\) 21.4184 0.797110
\(723\) −2.15534 −0.0801580
\(724\) 34.5221 1.28300
\(725\) −8.16629 −0.303288
\(726\) 0.430189 0.0159658
\(727\) −35.7945 −1.32754 −0.663772 0.747935i \(-0.731045\pi\)
−0.663772 + 0.747935i \(0.731045\pi\)
\(728\) −9.32274 −0.345524
\(729\) −25.2720 −0.936002
\(730\) −22.4905 −0.832412
\(731\) 18.8318 0.696519
\(732\) 1.73433 0.0641025
\(733\) −28.8373 −1.06513 −0.532565 0.846389i \(-0.678772\pi\)
−0.532565 + 0.846389i \(0.678772\pi\)
\(734\) 21.3177 0.786851
\(735\) −2.26221 −0.0834428
\(736\) 1.63045 0.0600992
\(737\) 7.79770 0.287232
\(738\) 1.15012 0.0423365
\(739\) 36.9636 1.35973 0.679864 0.733338i \(-0.262039\pi\)
0.679864 + 0.733338i \(0.262039\pi\)
\(740\) 22.6269 0.831780
\(741\) 3.42653 0.125877
\(742\) 2.76406 0.101472
\(743\) 11.5690 0.424426 0.212213 0.977223i \(-0.431933\pi\)
0.212213 + 0.977223i \(0.431933\pi\)
\(744\) −6.96040 −0.255181
\(745\) 35.0459 1.28398
\(746\) 32.3908 1.18591
\(747\) −39.2399 −1.43571
\(748\) 21.8256 0.798021
\(749\) −0.566728 −0.0207078
\(750\) 5.23589 0.191188
\(751\) −26.6400 −0.972107 −0.486054 0.873929i \(-0.661564\pi\)
−0.486054 + 0.873929i \(0.661564\pi\)
\(752\) −13.8496 −0.505045
\(753\) 1.67253 0.0609503
\(754\) −72.0397 −2.62353
\(755\) 31.3935 1.14253
\(756\) 1.49626 0.0544186
\(757\) 14.0705 0.511401 0.255701 0.966756i \(-0.417694\pi\)
0.255701 + 0.966756i \(0.417694\pi\)
\(758\) 18.8071 0.683103
\(759\) −0.122187 −0.00443509
\(760\) −24.1226 −0.875017
\(761\) 24.4898 0.887755 0.443878 0.896087i \(-0.353602\pi\)
0.443878 + 0.896087i \(0.353602\pi\)
\(762\) 4.48009 0.162297
\(763\) 0.928892 0.0336282
\(764\) 41.3429 1.49573
\(765\) 31.8542 1.15169
\(766\) −11.4820 −0.414862
\(767\) −54.0812 −1.95276
\(768\) 5.08738 0.183575
\(769\) 24.9108 0.898306 0.449153 0.893455i \(-0.351726\pi\)
0.449153 + 0.893455i \(0.351726\pi\)
\(770\) 1.64285 0.0592041
\(771\) −2.28749 −0.0823819
\(772\) 56.5793 2.03633
\(773\) 7.70709 0.277205 0.138602 0.990348i \(-0.455739\pi\)
0.138602 + 0.990348i \(0.455739\pi\)
\(774\) 22.8761 0.822264
\(775\) 15.2507 0.547821
\(776\) −65.0133 −2.33384
\(777\) 0.222002 0.00796429
\(778\) −12.7921 −0.458619
\(779\) −0.513268 −0.0183897
\(780\) 7.40057 0.264983
\(781\) −11.9224 −0.426618
\(782\) −9.52159 −0.340492
\(783\) 5.36525 0.191738
\(784\) −16.8875 −0.603126
\(785\) 38.0895 1.35947
\(786\) −0.878462 −0.0313337
\(787\) 16.1483 0.575626 0.287813 0.957687i \(-0.407072\pi\)
0.287813 + 0.957687i \(0.407072\pi\)
\(788\) −62.1879 −2.21535
\(789\) −2.65476 −0.0945119
\(790\) −7.84101 −0.278970
\(791\) −2.74974 −0.0977694
\(792\) 12.3029 0.437166
\(793\) −15.5556 −0.552395
\(794\) 31.5261 1.11882
\(795\) −1.01818 −0.0361110
\(796\) −85.5968 −3.03390
\(797\) 26.0244 0.921832 0.460916 0.887444i \(-0.347521\pi\)
0.460916 + 0.887444i \(0.347521\pi\)
\(798\) −0.510039 −0.0180552
\(799\) −32.9062 −1.16414
\(800\) −3.91354 −0.138365
\(801\) −50.8464 −1.79657
\(802\) 81.4233 2.87516
\(803\) −5.11901 −0.180646
\(804\) −5.22858 −0.184398
\(805\) −0.466617 −0.0164461
\(806\) 134.535 4.73880
\(807\) −4.58922 −0.161548
\(808\) −62.7904 −2.20896
\(809\) 24.2338 0.852016 0.426008 0.904720i \(-0.359920\pi\)
0.426008 + 0.904720i \(0.359920\pi\)
\(810\) 38.2696 1.34466
\(811\) 29.1767 1.02453 0.512267 0.858826i \(-0.328806\pi\)
0.512267 + 0.858826i \(0.328806\pi\)
\(812\) 6.98136 0.244998
\(813\) −0.297534 −0.0104350
\(814\) 7.91026 0.277255
\(815\) 29.8666 1.04618
\(816\) −2.58715 −0.0905684
\(817\) −10.2090 −0.357167
\(818\) −23.1795 −0.810454
\(819\) −6.67387 −0.233204
\(820\) −1.10855 −0.0387122
\(821\) 10.4657 0.365255 0.182627 0.983182i \(-0.441540\pi\)
0.182627 + 0.983182i \(0.441540\pi\)
\(822\) 6.05189 0.211084
\(823\) 37.0842 1.29267 0.646337 0.763052i \(-0.276300\pi\)
0.646337 + 0.763052i \(0.276300\pi\)
\(824\) 0.899865 0.0313483
\(825\) 0.293282 0.0102108
\(826\) 8.04999 0.280095
\(827\) −23.1002 −0.803274 −0.401637 0.915799i \(-0.631559\pi\)
−0.401637 + 0.915799i \(0.631559\pi\)
\(828\) −7.53043 −0.261700
\(829\) 26.6561 0.925804 0.462902 0.886410i \(-0.346808\pi\)
0.462902 + 0.886410i \(0.346808\pi\)
\(830\) 58.0924 2.01642
\(831\) 3.15101 0.109307
\(832\) −64.1333 −2.22342
\(833\) −40.1241 −1.39022
\(834\) −4.44145 −0.153795
\(835\) 3.16518 0.109535
\(836\) −11.8320 −0.409217
\(837\) −10.0197 −0.346331
\(838\) 31.7579 1.09706
\(839\) 28.1012 0.970163 0.485081 0.874469i \(-0.338790\pi\)
0.485081 + 0.874469i \(0.338790\pi\)
\(840\) −0.511173 −0.0176371
\(841\) −3.96650 −0.136776
\(842\) −24.5070 −0.844568
\(843\) 3.50780 0.120815
\(844\) 10.5072 0.361672
\(845\) −42.5203 −1.46274
\(846\) −39.9731 −1.37430
\(847\) 0.373924 0.0128482
\(848\) −7.60077 −0.261011
\(849\) 0.0807566 0.00277156
\(850\) 22.8545 0.783903
\(851\) −2.24675 −0.0770176
\(852\) 7.99433 0.273881
\(853\) 6.03852 0.206755 0.103377 0.994642i \(-0.467035\pi\)
0.103377 + 0.994642i \(0.467035\pi\)
\(854\) 2.31545 0.0792330
\(855\) −17.2686 −0.590574
\(856\) 6.28317 0.214754
\(857\) −27.8148 −0.950135 −0.475068 0.879949i \(-0.657576\pi\)
−0.475068 + 0.879949i \(0.657576\pi\)
\(858\) 2.58721 0.0883260
\(859\) 33.1787 1.13204 0.566022 0.824390i \(-0.308482\pi\)
0.566022 + 0.824390i \(0.308482\pi\)
\(860\) −22.0492 −0.751872
\(861\) −0.0108765 −0.000370669 0
\(862\) −45.7304 −1.55758
\(863\) 9.26982 0.315548 0.157774 0.987475i \(-0.449568\pi\)
0.157774 + 0.987475i \(0.449568\pi\)
\(864\) 2.57119 0.0874738
\(865\) −16.6996 −0.567804
\(866\) 66.1924 2.24931
\(867\) −3.09225 −0.105018
\(868\) −13.0378 −0.442532
\(869\) −1.78467 −0.0605408
\(870\) −3.94999 −0.133917
\(871\) 46.8964 1.58902
\(872\) −10.2984 −0.348748
\(873\) −46.5411 −1.57518
\(874\) 5.16180 0.174600
\(875\) 4.55108 0.153854
\(876\) 3.43244 0.115972
\(877\) −33.5835 −1.13403 −0.567017 0.823706i \(-0.691903\pi\)
−0.567017 + 0.823706i \(0.691903\pi\)
\(878\) −41.5659 −1.40278
\(879\) −0.398414 −0.0134382
\(880\) −4.51758 −0.152288
\(881\) −27.8492 −0.938264 −0.469132 0.883128i \(-0.655433\pi\)
−0.469132 + 0.883128i \(0.655433\pi\)
\(882\) −48.7411 −1.64120
\(883\) 55.4365 1.86559 0.932794 0.360410i \(-0.117363\pi\)
0.932794 + 0.360410i \(0.117363\pi\)
\(884\) 131.262 4.41481
\(885\) −2.96531 −0.0996780
\(886\) 43.6716 1.46718
\(887\) −22.4463 −0.753673 −0.376837 0.926280i \(-0.622988\pi\)
−0.376837 + 0.926280i \(0.622988\pi\)
\(888\) −2.46128 −0.0825953
\(889\) 3.89413 0.130605
\(890\) 75.2753 2.52323
\(891\) 8.71045 0.291811
\(892\) −87.3560 −2.92490
\(893\) 17.8389 0.596957
\(894\) −8.21527 −0.274760
\(895\) 36.7608 1.22878
\(896\) 7.75308 0.259012
\(897\) −0.734846 −0.0245358
\(898\) 48.4363 1.61634
\(899\) −46.7505 −1.55922
\(900\) 18.0751 0.602505
\(901\) −18.0591 −0.601636
\(902\) −0.387545 −0.0129038
\(903\) −0.216335 −0.00719918
\(904\) 30.4857 1.01394
\(905\) −16.9776 −0.564356
\(906\) −7.35909 −0.244490
\(907\) −54.4198 −1.80698 −0.903490 0.428609i \(-0.859004\pi\)
−0.903490 + 0.428609i \(0.859004\pi\)
\(908\) −36.8279 −1.22218
\(909\) −44.9497 −1.49089
\(910\) 9.88029 0.327528
\(911\) −33.5387 −1.11119 −0.555594 0.831454i \(-0.687509\pi\)
−0.555594 + 0.831454i \(0.687509\pi\)
\(912\) 1.40253 0.0464425
\(913\) 13.2223 0.437593
\(914\) −45.7088 −1.51191
\(915\) −0.852924 −0.0281968
\(916\) −7.53167 −0.248854
\(917\) −0.763566 −0.0252152
\(918\) −15.0154 −0.495582
\(919\) −25.1655 −0.830132 −0.415066 0.909791i \(-0.636241\pi\)
−0.415066 + 0.909791i \(0.636241\pi\)
\(920\) 5.17327 0.170558
\(921\) 2.94862 0.0971603
\(922\) 49.9858 1.64619
\(923\) −71.7030 −2.36013
\(924\) −0.250727 −0.00824830
\(925\) 5.39283 0.177315
\(926\) −37.7203 −1.23956
\(927\) 0.644186 0.0211579
\(928\) 11.9968 0.393815
\(929\) −28.1816 −0.924609 −0.462305 0.886721i \(-0.652977\pi\)
−0.462305 + 0.886721i \(0.652977\pi\)
\(930\) 7.37667 0.241891
\(931\) 21.7518 0.712888
\(932\) 62.9608 2.06235
\(933\) −5.28193 −0.172923
\(934\) 32.9386 1.07779
\(935\) −10.7336 −0.351026
\(936\) 73.9915 2.41849
\(937\) −7.64808 −0.249852 −0.124926 0.992166i \(-0.539869\pi\)
−0.124926 + 0.992166i \(0.539869\pi\)
\(938\) −6.98053 −0.227922
\(939\) −3.21719 −0.104989
\(940\) 38.5282 1.25665
\(941\) −9.55744 −0.311564 −0.155782 0.987791i \(-0.549790\pi\)
−0.155782 + 0.987791i \(0.549790\pi\)
\(942\) −8.92873 −0.290914
\(943\) 0.110074 0.00358451
\(944\) −22.1363 −0.720475
\(945\) −0.735848 −0.0239371
\(946\) −7.70833 −0.250619
\(947\) −0.547314 −0.0177853 −0.00889265 0.999960i \(-0.502831\pi\)
−0.00889265 + 0.999960i \(0.502831\pi\)
\(948\) 1.19667 0.0388661
\(949\) −30.7864 −0.999368
\(950\) −12.3898 −0.401977
\(951\) 4.71035 0.152743
\(952\) −9.06651 −0.293847
\(953\) −37.2177 −1.20560 −0.602800 0.797892i \(-0.705948\pi\)
−0.602800 + 0.797892i \(0.705948\pi\)
\(954\) −21.9375 −0.710252
\(955\) −20.3320 −0.657929
\(956\) 105.104 3.39930
\(957\) −0.899047 −0.0290621
\(958\) 11.0644 0.357476
\(959\) 5.26035 0.169866
\(960\) −3.51648 −0.113494
\(961\) 56.3073 1.81636
\(962\) 47.5733 1.53383
\(963\) 4.49794 0.144944
\(964\) 44.7600 1.44162
\(965\) −27.8251 −0.895722
\(966\) 0.109382 0.00351930
\(967\) 51.6346 1.66046 0.830228 0.557424i \(-0.188210\pi\)
0.830228 + 0.557424i \(0.188210\pi\)
\(968\) −4.14560 −0.133245
\(969\) 3.33236 0.107051
\(970\) 68.9014 2.21229
\(971\) 12.3419 0.396070 0.198035 0.980195i \(-0.436544\pi\)
0.198035 + 0.980195i \(0.436544\pi\)
\(972\) −17.8452 −0.572384
\(973\) −3.86055 −0.123763
\(974\) 26.3909 0.845619
\(975\) 1.76384 0.0564880
\(976\) −6.36714 −0.203807
\(977\) −27.9991 −0.895772 −0.447886 0.894091i \(-0.647823\pi\)
−0.447886 + 0.894091i \(0.647823\pi\)
\(978\) −7.00116 −0.223873
\(979\) 17.1332 0.547580
\(980\) 46.9793 1.50070
\(981\) −7.37231 −0.235380
\(982\) −62.0307 −1.97948
\(983\) 26.0186 0.829864 0.414932 0.909852i \(-0.363805\pi\)
0.414932 + 0.909852i \(0.363805\pi\)
\(984\) 0.120585 0.00384410
\(985\) 30.5834 0.974468
\(986\) −70.0597 −2.23116
\(987\) 0.378018 0.0120324
\(988\) −71.1589 −2.26387
\(989\) 2.18940 0.0696187
\(990\) −13.0387 −0.414398
\(991\) −7.37456 −0.234260 −0.117130 0.993117i \(-0.537369\pi\)
−0.117130 + 0.993117i \(0.537369\pi\)
\(992\) −22.4043 −0.711337
\(993\) 1.07974 0.0342646
\(994\) 10.6730 0.338527
\(995\) 42.0956 1.33452
\(996\) −8.86591 −0.280927
\(997\) 9.38484 0.297221 0.148610 0.988896i \(-0.452520\pi\)
0.148610 + 0.988896i \(0.452520\pi\)
\(998\) 0.900094 0.0284920
\(999\) −3.54309 −0.112098
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 \(a_p\))