Properties

Label 8035.2.a.e.1.9
Level 8035
Weight 2
Character 8035.1
Self dual Yes
Analytic conductor 64.160
Analytic rank 0
Dimension 153
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8035 = 5 \cdot 1607 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8035.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.1597980241\)
Analytic rank: \(0\)
Dimension: \(153\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) = 8035.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.55001 q^{2}\) \(+2.17323 q^{3}\) \(+4.50255 q^{4}\) \(+1.00000 q^{5}\) \(-5.54177 q^{6}\) \(+4.37483 q^{7}\) \(-6.38153 q^{8}\) \(+1.72295 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.55001 q^{2}\) \(+2.17323 q^{3}\) \(+4.50255 q^{4}\) \(+1.00000 q^{5}\) \(-5.54177 q^{6}\) \(+4.37483 q^{7}\) \(-6.38153 q^{8}\) \(+1.72295 q^{9}\) \(-2.55001 q^{10}\) \(+0.414044 q^{11}\) \(+9.78509 q^{12}\) \(-0.0505392 q^{13}\) \(-11.1559 q^{14}\) \(+2.17323 q^{15}\) \(+7.26785 q^{16}\) \(+4.30754 q^{17}\) \(-4.39353 q^{18}\) \(+2.90038 q^{19}\) \(+4.50255 q^{20}\) \(+9.50752 q^{21}\) \(-1.05582 q^{22}\) \(+1.21348 q^{23}\) \(-13.8685 q^{24}\) \(+1.00000 q^{25}\) \(+0.128875 q^{26}\) \(-2.77534 q^{27}\) \(+19.6979 q^{28}\) \(-0.288416 q^{29}\) \(-5.54177 q^{30}\) \(-9.27330 q^{31}\) \(-5.77005 q^{32}\) \(+0.899814 q^{33}\) \(-10.9843 q^{34}\) \(+4.37483 q^{35}\) \(+7.75765 q^{36}\) \(-8.86161 q^{37}\) \(-7.39599 q^{38}\) \(-0.109833 q^{39}\) \(-6.38153 q^{40}\) \(+0.791597 q^{41}\) \(-24.2443 q^{42}\) \(+8.18713 q^{43}\) \(+1.86425 q^{44}\) \(+1.72295 q^{45}\) \(-3.09438 q^{46}\) \(+12.8197 q^{47}\) \(+15.7947 q^{48}\) \(+12.1391 q^{49}\) \(-2.55001 q^{50}\) \(+9.36129 q^{51}\) \(-0.227555 q^{52}\) \(+5.43213 q^{53}\) \(+7.07714 q^{54}\) \(+0.414044 q^{55}\) \(-27.9181 q^{56}\) \(+6.30320 q^{57}\) \(+0.735463 q^{58}\) \(+3.33042 q^{59}\) \(+9.78509 q^{60}\) \(-9.22386 q^{61}\) \(+23.6470 q^{62}\) \(+7.53759 q^{63}\) \(+0.177967 q^{64}\) \(-0.0505392 q^{65}\) \(-2.29453 q^{66}\) \(+8.47720 q^{67}\) \(+19.3949 q^{68}\) \(+2.63717 q^{69}\) \(-11.1559 q^{70}\) \(+13.4144 q^{71}\) \(-10.9950 q^{72}\) \(-15.2007 q^{73}\) \(+22.5972 q^{74}\) \(+2.17323 q^{75}\) \(+13.0591 q^{76}\) \(+1.81137 q^{77}\) \(+0.280076 q^{78}\) \(+0.578251 q^{79}\) \(+7.26785 q^{80}\) \(-11.2003 q^{81}\) \(-2.01858 q^{82}\) \(-13.9339 q^{83}\) \(+42.8081 q^{84}\) \(+4.30754 q^{85}\) \(-20.8773 q^{86}\) \(-0.626794 q^{87}\) \(-2.64223 q^{88}\) \(+16.2546 q^{89}\) \(-4.39353 q^{90}\) \(-0.221100 q^{91}\) \(+5.46374 q^{92}\) \(-20.1530 q^{93}\) \(-32.6904 q^{94}\) \(+2.90038 q^{95}\) \(-12.5397 q^{96}\) \(-0.156259 q^{97}\) \(-30.9549 q^{98}\) \(+0.713374 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(153q \) \(\mathstrut +\mathstrut 18q^{2} \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 176q^{4} \) \(\mathstrut +\mathstrut 153q^{5} \) \(\mathstrut +\mathstrut 19q^{6} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 57q^{8} \) \(\mathstrut +\mathstrut 206q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(153q \) \(\mathstrut +\mathstrut 18q^{2} \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 176q^{4} \) \(\mathstrut +\mathstrut 153q^{5} \) \(\mathstrut +\mathstrut 19q^{6} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 57q^{8} \) \(\mathstrut +\mathstrut 206q^{9} \) \(\mathstrut +\mathstrut 18q^{10} \) \(\mathstrut +\mathstrut 38q^{11} \) \(\mathstrut +\mathstrut 14q^{12} \) \(\mathstrut +\mathstrut 28q^{13} \) \(\mathstrut +\mathstrut 53q^{14} \) \(\mathstrut +\mathstrut 7q^{15} \) \(\mathstrut +\mathstrut 214q^{16} \) \(\mathstrut +\mathstrut 50q^{17} \) \(\mathstrut +\mathstrut 47q^{18} \) \(\mathstrut +\mathstrut 65q^{19} \) \(\mathstrut +\mathstrut 176q^{20} \) \(\mathstrut +\mathstrut 109q^{21} \) \(\mathstrut +\mathstrut 13q^{22} \) \(\mathstrut +\mathstrut 52q^{23} \) \(\mathstrut +\mathstrut 66q^{24} \) \(\mathstrut +\mathstrut 153q^{25} \) \(\mathstrut +\mathstrut 36q^{26} \) \(\mathstrut +\mathstrut 19q^{27} \) \(\mathstrut +\mathstrut 26q^{28} \) \(\mathstrut +\mathstrut 172q^{29} \) \(\mathstrut +\mathstrut 19q^{30} \) \(\mathstrut +\mathstrut 60q^{31} \) \(\mathstrut +\mathstrut 107q^{32} \) \(\mathstrut +\mathstrut 4q^{33} \) \(\mathstrut +\mathstrut 40q^{34} \) \(\mathstrut +\mathstrut 5q^{35} \) \(\mathstrut +\mathstrut 241q^{36} \) \(\mathstrut +\mathstrut 65q^{37} \) \(\mathstrut +\mathstrut 29q^{38} \) \(\mathstrut +\mathstrut 56q^{39} \) \(\mathstrut +\mathstrut 57q^{40} \) \(\mathstrut +\mathstrut 152q^{41} \) \(\mathstrut -\mathstrut 19q^{42} \) \(\mathstrut +\mathstrut 22q^{43} \) \(\mathstrut +\mathstrut 97q^{44} \) \(\mathstrut +\mathstrut 206q^{45} \) \(\mathstrut +\mathstrut 86q^{46} \) \(\mathstrut +\mathstrut 37q^{47} \) \(\mathstrut -\mathstrut 4q^{48} \) \(\mathstrut +\mathstrut 260q^{49} \) \(\mathstrut +\mathstrut 18q^{50} \) \(\mathstrut +\mathstrut 102q^{51} \) \(\mathstrut -\mathstrut 6q^{52} \) \(\mathstrut +\mathstrut 169q^{53} \) \(\mathstrut +\mathstrut 64q^{54} \) \(\mathstrut +\mathstrut 38q^{55} \) \(\mathstrut +\mathstrut 146q^{56} \) \(\mathstrut +\mathstrut 40q^{57} \) \(\mathstrut -\mathstrut 9q^{58} \) \(\mathstrut +\mathstrut 64q^{59} \) \(\mathstrut +\mathstrut 14q^{60} \) \(\mathstrut +\mathstrut 164q^{61} \) \(\mathstrut +\mathstrut 12q^{62} \) \(\mathstrut +\mathstrut 19q^{63} \) \(\mathstrut +\mathstrut 259q^{64} \) \(\mathstrut +\mathstrut 28q^{65} \) \(\mathstrut +\mathstrut 6q^{66} \) \(\mathstrut +\mathstrut 5q^{67} \) \(\mathstrut +\mathstrut 112q^{68} \) \(\mathstrut +\mathstrut 119q^{69} \) \(\mathstrut +\mathstrut 53q^{70} \) \(\mathstrut +\mathstrut 100q^{71} \) \(\mathstrut +\mathstrut 77q^{72} \) \(\mathstrut +\mathstrut 10q^{73} \) \(\mathstrut +\mathstrut 98q^{74} \) \(\mathstrut +\mathstrut 7q^{75} \) \(\mathstrut +\mathstrut 126q^{76} \) \(\mathstrut +\mathstrut 80q^{77} \) \(\mathstrut -\mathstrut 4q^{78} \) \(\mathstrut +\mathstrut 110q^{79} \) \(\mathstrut +\mathstrut 214q^{80} \) \(\mathstrut +\mathstrut 305q^{81} \) \(\mathstrut -\mathstrut 27q^{82} \) \(\mathstrut +\mathstrut 36q^{83} \) \(\mathstrut +\mathstrut 172q^{84} \) \(\mathstrut +\mathstrut 50q^{85} \) \(\mathstrut +\mathstrut 44q^{86} \) \(\mathstrut +\mathstrut 23q^{87} \) \(\mathstrut +\mathstrut 47q^{88} \) \(\mathstrut +\mathstrut 143q^{89} \) \(\mathstrut +\mathstrut 47q^{90} \) \(\mathstrut +\mathstrut 82q^{91} \) \(\mathstrut +\mathstrut 130q^{92} \) \(\mathstrut +\mathstrut 31q^{93} \) \(\mathstrut +\mathstrut 77q^{94} \) \(\mathstrut +\mathstrut 65q^{95} \) \(\mathstrut +\mathstrut 57q^{96} \) \(\mathstrut +\mathstrut 11q^{97} \) \(\mathstrut +\mathstrut 29q^{98} \) \(\mathstrut +\mathstrut 99q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.55001 −1.80313 −0.901565 0.432645i \(-0.857581\pi\)
−0.901565 + 0.432645i \(0.857581\pi\)
\(3\) 2.17323 1.25472 0.627359 0.778731i \(-0.284136\pi\)
0.627359 + 0.778731i \(0.284136\pi\)
\(4\) 4.50255 2.25127
\(5\) 1.00000 0.447214
\(6\) −5.54177 −2.26242
\(7\) 4.37483 1.65353 0.826765 0.562548i \(-0.190179\pi\)
0.826765 + 0.562548i \(0.190179\pi\)
\(8\) −6.38153 −2.25621
\(9\) 1.72295 0.574315
\(10\) −2.55001 −0.806384
\(11\) 0.414044 0.124839 0.0624194 0.998050i \(-0.480118\pi\)
0.0624194 + 0.998050i \(0.480118\pi\)
\(12\) 9.78509 2.82471
\(13\) −0.0505392 −0.0140170 −0.00700852 0.999975i \(-0.502231\pi\)
−0.00700852 + 0.999975i \(0.502231\pi\)
\(14\) −11.1559 −2.98153
\(15\) 2.17323 0.561127
\(16\) 7.26785 1.81696
\(17\) 4.30754 1.04473 0.522366 0.852722i \(-0.325050\pi\)
0.522366 + 0.852722i \(0.325050\pi\)
\(18\) −4.39353 −1.03556
\(19\) 2.90038 0.665392 0.332696 0.943034i \(-0.392042\pi\)
0.332696 + 0.943034i \(0.392042\pi\)
\(20\) 4.50255 1.00680
\(21\) 9.50752 2.07471
\(22\) −1.05582 −0.225101
\(23\) 1.21348 0.253028 0.126514 0.991965i \(-0.459621\pi\)
0.126514 + 0.991965i \(0.459621\pi\)
\(24\) −13.8685 −2.83091
\(25\) 1.00000 0.200000
\(26\) 0.128875 0.0252745
\(27\) −2.77534 −0.534114
\(28\) 19.6979 3.72255
\(29\) −0.288416 −0.0535574 −0.0267787 0.999641i \(-0.508525\pi\)
−0.0267787 + 0.999641i \(0.508525\pi\)
\(30\) −5.54177 −1.01178
\(31\) −9.27330 −1.66553 −0.832767 0.553624i \(-0.813244\pi\)
−0.832767 + 0.553624i \(0.813244\pi\)
\(32\) −5.77005 −1.02001
\(33\) 0.899814 0.156637
\(34\) −10.9843 −1.88379
\(35\) 4.37483 0.739481
\(36\) 7.75765 1.29294
\(37\) −8.86161 −1.45684 −0.728420 0.685131i \(-0.759745\pi\)
−0.728420 + 0.685131i \(0.759745\pi\)
\(38\) −7.39599 −1.19979
\(39\) −0.109833 −0.0175874
\(40\) −6.38153 −1.00901
\(41\) 0.791597 0.123627 0.0618133 0.998088i \(-0.480312\pi\)
0.0618133 + 0.998088i \(0.480312\pi\)
\(42\) −24.2443 −3.74097
\(43\) 8.18713 1.24853 0.624263 0.781214i \(-0.285399\pi\)
0.624263 + 0.781214i \(0.285399\pi\)
\(44\) 1.86425 0.281047
\(45\) 1.72295 0.256842
\(46\) −3.09438 −0.456241
\(47\) 12.8197 1.86995 0.934974 0.354716i \(-0.115422\pi\)
0.934974 + 0.354716i \(0.115422\pi\)
\(48\) 15.7947 2.27978
\(49\) 12.1391 1.73416
\(50\) −2.55001 −0.360626
\(51\) 9.36129 1.31084
\(52\) −0.227555 −0.0315562
\(53\) 5.43213 0.746160 0.373080 0.927799i \(-0.378302\pi\)
0.373080 + 0.927799i \(0.378302\pi\)
\(54\) 7.07714 0.963077
\(55\) 0.414044 0.0558296
\(56\) −27.9181 −3.73071
\(57\) 6.30320 0.834879
\(58\) 0.735463 0.0965710
\(59\) 3.33042 0.433583 0.216792 0.976218i \(-0.430441\pi\)
0.216792 + 0.976218i \(0.430441\pi\)
\(60\) 9.78509 1.26325
\(61\) −9.22386 −1.18099 −0.590497 0.807040i \(-0.701068\pi\)
−0.590497 + 0.807040i \(0.701068\pi\)
\(62\) 23.6470 3.00317
\(63\) 7.53759 0.949647
\(64\) 0.177967 0.0222459
\(65\) −0.0505392 −0.00626861
\(66\) −2.29453 −0.282438
\(67\) 8.47720 1.03565 0.517827 0.855485i \(-0.326741\pi\)
0.517827 + 0.855485i \(0.326741\pi\)
\(68\) 19.3949 2.35198
\(69\) 2.63717 0.317478
\(70\) −11.1559 −1.33338
\(71\) 13.4144 1.59199 0.795996 0.605302i \(-0.206948\pi\)
0.795996 + 0.605302i \(0.206948\pi\)
\(72\) −10.9950 −1.29578
\(73\) −15.2007 −1.77911 −0.889555 0.456828i \(-0.848985\pi\)
−0.889555 + 0.456828i \(0.848985\pi\)
\(74\) 22.5972 2.62687
\(75\) 2.17323 0.250943
\(76\) 13.0591 1.49798
\(77\) 1.81137 0.206425
\(78\) 0.280076 0.0317124
\(79\) 0.578251 0.0650583 0.0325292 0.999471i \(-0.489644\pi\)
0.0325292 + 0.999471i \(0.489644\pi\)
\(80\) 7.26785 0.812571
\(81\) −11.2003 −1.24448
\(82\) −2.01858 −0.222915
\(83\) −13.9339 −1.52944 −0.764720 0.644362i \(-0.777123\pi\)
−0.764720 + 0.644362i \(0.777123\pi\)
\(84\) 42.8081 4.67075
\(85\) 4.30754 0.467218
\(86\) −20.8773 −2.25125
\(87\) −0.626794 −0.0671994
\(88\) −2.64223 −0.281663
\(89\) 16.2546 1.72298 0.861491 0.507772i \(-0.169531\pi\)
0.861491 + 0.507772i \(0.169531\pi\)
\(90\) −4.39353 −0.463118
\(91\) −0.221100 −0.0231776
\(92\) 5.46374 0.569634
\(93\) −20.1530 −2.08977
\(94\) −32.6904 −3.37176
\(95\) 2.90038 0.297572
\(96\) −12.5397 −1.27982
\(97\) −0.156259 −0.0158657 −0.00793287 0.999969i \(-0.502525\pi\)
−0.00793287 + 0.999969i \(0.502525\pi\)
\(98\) −30.9549 −3.12691
\(99\) 0.713374 0.0716968
\(100\) 4.50255 0.450255
\(101\) −14.6880 −1.46151 −0.730757 0.682638i \(-0.760833\pi\)
−0.730757 + 0.682638i \(0.760833\pi\)
\(102\) −23.8714 −2.36362
\(103\) 13.0272 1.28361 0.641806 0.766867i \(-0.278185\pi\)
0.641806 + 0.766867i \(0.278185\pi\)
\(104\) 0.322517 0.0316254
\(105\) 9.50752 0.927839
\(106\) −13.8520 −1.34542
\(107\) 9.74404 0.941992 0.470996 0.882135i \(-0.343895\pi\)
0.470996 + 0.882135i \(0.343895\pi\)
\(108\) −12.4961 −1.20244
\(109\) −4.54438 −0.435272 −0.217636 0.976030i \(-0.569835\pi\)
−0.217636 + 0.976030i \(0.569835\pi\)
\(110\) −1.05582 −0.100668
\(111\) −19.2584 −1.82792
\(112\) 31.7956 3.00440
\(113\) −3.43480 −0.323119 −0.161559 0.986863i \(-0.551652\pi\)
−0.161559 + 0.986863i \(0.551652\pi\)
\(114\) −16.0732 −1.50539
\(115\) 1.21348 0.113157
\(116\) −1.29861 −0.120572
\(117\) −0.0870762 −0.00805020
\(118\) −8.49260 −0.781807
\(119\) 18.8447 1.72749
\(120\) −13.8685 −1.26602
\(121\) −10.8286 −0.984415
\(122\) 23.5209 2.12948
\(123\) 1.72033 0.155117
\(124\) −41.7535 −3.74957
\(125\) 1.00000 0.0894427
\(126\) −19.2209 −1.71234
\(127\) 11.6011 1.02943 0.514716 0.857361i \(-0.327897\pi\)
0.514716 + 0.857361i \(0.327897\pi\)
\(128\) 11.0863 0.979898
\(129\) 17.7925 1.56655
\(130\) 0.128875 0.0113031
\(131\) 4.33058 0.378364 0.189182 0.981942i \(-0.439416\pi\)
0.189182 + 0.981942i \(0.439416\pi\)
\(132\) 4.05146 0.352634
\(133\) 12.6886 1.10025
\(134\) −21.6169 −1.86742
\(135\) −2.77534 −0.238863
\(136\) −27.4887 −2.35713
\(137\) −1.35067 −0.115396 −0.0576980 0.998334i \(-0.518376\pi\)
−0.0576980 + 0.998334i \(0.518376\pi\)
\(138\) −6.72481 −0.572454
\(139\) −1.27217 −0.107904 −0.0539522 0.998544i \(-0.517182\pi\)
−0.0539522 + 0.998544i \(0.517182\pi\)
\(140\) 19.6979 1.66477
\(141\) 27.8603 2.34626
\(142\) −34.2068 −2.87057
\(143\) −0.0209254 −0.00174987
\(144\) 12.5221 1.04351
\(145\) −0.288416 −0.0239516
\(146\) 38.7620 3.20797
\(147\) 26.3811 2.17588
\(148\) −39.8998 −3.27975
\(149\) 16.7025 1.36832 0.684160 0.729332i \(-0.260169\pi\)
0.684160 + 0.729332i \(0.260169\pi\)
\(150\) −5.54177 −0.452483
\(151\) −4.82225 −0.392429 −0.196215 0.980561i \(-0.562865\pi\)
−0.196215 + 0.980561i \(0.562865\pi\)
\(152\) −18.5088 −1.50126
\(153\) 7.42165 0.600005
\(154\) −4.61901 −0.372210
\(155\) −9.27330 −0.744849
\(156\) −0.494530 −0.0395941
\(157\) −8.16529 −0.651661 −0.325831 0.945428i \(-0.605644\pi\)
−0.325831 + 0.945428i \(0.605644\pi\)
\(158\) −1.47455 −0.117309
\(159\) 11.8053 0.936220
\(160\) −5.77005 −0.456162
\(161\) 5.30875 0.418388
\(162\) 28.5609 2.24395
\(163\) 12.4823 0.977688 0.488844 0.872371i \(-0.337419\pi\)
0.488844 + 0.872371i \(0.337419\pi\)
\(164\) 3.56421 0.278318
\(165\) 0.899814 0.0700504
\(166\) 35.5315 2.75778
\(167\) 13.5204 1.04624 0.523119 0.852259i \(-0.324768\pi\)
0.523119 + 0.852259i \(0.324768\pi\)
\(168\) −60.6725 −4.68099
\(169\) −12.9974 −0.999804
\(170\) −10.9843 −0.842454
\(171\) 4.99719 0.382145
\(172\) 36.8630 2.81077
\(173\) 8.73296 0.663955 0.331977 0.943287i \(-0.392284\pi\)
0.331977 + 0.943287i \(0.392284\pi\)
\(174\) 1.59833 0.121169
\(175\) 4.37483 0.330706
\(176\) 3.00921 0.226828
\(177\) 7.23778 0.544025
\(178\) −41.4494 −3.10676
\(179\) 15.5193 1.15997 0.579984 0.814628i \(-0.303059\pi\)
0.579984 + 0.814628i \(0.303059\pi\)
\(180\) 7.75765 0.578221
\(181\) 21.3470 1.58671 0.793355 0.608760i \(-0.208333\pi\)
0.793355 + 0.608760i \(0.208333\pi\)
\(182\) 0.563807 0.0417922
\(183\) −20.0456 −1.48181
\(184\) −7.74384 −0.570883
\(185\) −8.86161 −0.651519
\(186\) 51.3904 3.76813
\(187\) 1.78351 0.130423
\(188\) 57.7214 4.20977
\(189\) −12.1416 −0.883173
\(190\) −7.39599 −0.536561
\(191\) 6.65046 0.481210 0.240605 0.970623i \(-0.422654\pi\)
0.240605 + 0.970623i \(0.422654\pi\)
\(192\) 0.386764 0.0279123
\(193\) 21.5266 1.54952 0.774758 0.632258i \(-0.217872\pi\)
0.774758 + 0.632258i \(0.217872\pi\)
\(194\) 0.398463 0.0286080
\(195\) −0.109833 −0.00786533
\(196\) 54.6570 3.90407
\(197\) −25.4393 −1.81247 −0.906237 0.422769i \(-0.861058\pi\)
−0.906237 + 0.422769i \(0.861058\pi\)
\(198\) −1.81911 −0.129279
\(199\) −8.51895 −0.603892 −0.301946 0.953325i \(-0.597636\pi\)
−0.301946 + 0.953325i \(0.597636\pi\)
\(200\) −6.38153 −0.451242
\(201\) 18.4229 1.29945
\(202\) 37.4546 2.63530
\(203\) −1.26177 −0.0885588
\(204\) 42.1497 2.95107
\(205\) 0.791597 0.0552875
\(206\) −33.2196 −2.31452
\(207\) 2.09075 0.145318
\(208\) −0.367311 −0.0254684
\(209\) 1.20088 0.0830668
\(210\) −24.2443 −1.67301
\(211\) −15.1613 −1.04375 −0.521875 0.853022i \(-0.674767\pi\)
−0.521875 + 0.853022i \(0.674767\pi\)
\(212\) 24.4584 1.67981
\(213\) 29.1525 1.99750
\(214\) −24.8474 −1.69853
\(215\) 8.18713 0.558358
\(216\) 17.7109 1.20507
\(217\) −40.5691 −2.75401
\(218\) 11.5882 0.784852
\(219\) −33.0347 −2.23228
\(220\) 1.86425 0.125688
\(221\) −0.217699 −0.0146440
\(222\) 49.1090 3.29598
\(223\) −22.6066 −1.51385 −0.756923 0.653504i \(-0.773298\pi\)
−0.756923 + 0.653504i \(0.773298\pi\)
\(224\) −25.2430 −1.68662
\(225\) 1.72295 0.114863
\(226\) 8.75877 0.582625
\(227\) −26.8604 −1.78278 −0.891392 0.453233i \(-0.850271\pi\)
−0.891392 + 0.453233i \(0.850271\pi\)
\(228\) 28.3805 1.87954
\(229\) −0.108712 −0.00718390 −0.00359195 0.999994i \(-0.501143\pi\)
−0.00359195 + 0.999994i \(0.501143\pi\)
\(230\) −3.09438 −0.204037
\(231\) 3.93653 0.259005
\(232\) 1.84053 0.120837
\(233\) 15.9636 1.04581 0.522904 0.852392i \(-0.324849\pi\)
0.522904 + 0.852392i \(0.324849\pi\)
\(234\) 0.222045 0.0145155
\(235\) 12.8197 0.836266
\(236\) 14.9954 0.976115
\(237\) 1.25667 0.0816298
\(238\) −48.0543 −3.11489
\(239\) −2.92586 −0.189258 −0.0946291 0.995513i \(-0.530167\pi\)
−0.0946291 + 0.995513i \(0.530167\pi\)
\(240\) 15.7947 1.01955
\(241\) 16.5688 1.06729 0.533646 0.845708i \(-0.320821\pi\)
0.533646 + 0.845708i \(0.320821\pi\)
\(242\) 27.6130 1.77503
\(243\) −16.0148 −1.02735
\(244\) −41.5309 −2.65874
\(245\) 12.1391 0.775540
\(246\) −4.38685 −0.279695
\(247\) −0.146583 −0.00932682
\(248\) 59.1778 3.75779
\(249\) −30.2816 −1.91902
\(250\) −2.55001 −0.161277
\(251\) 16.6331 1.04987 0.524935 0.851142i \(-0.324090\pi\)
0.524935 + 0.851142i \(0.324090\pi\)
\(252\) 33.9384 2.13792
\(253\) 0.502432 0.0315877
\(254\) −29.5829 −1.85620
\(255\) 9.36129 0.586226
\(256\) −28.6260 −1.78913
\(257\) −26.6199 −1.66051 −0.830253 0.557386i \(-0.811804\pi\)
−0.830253 + 0.557386i \(0.811804\pi\)
\(258\) −45.3712 −2.82469
\(259\) −38.7680 −2.40893
\(260\) −0.227555 −0.0141124
\(261\) −0.496924 −0.0307588
\(262\) −11.0430 −0.682240
\(263\) 3.32677 0.205137 0.102569 0.994726i \(-0.467294\pi\)
0.102569 + 0.994726i \(0.467294\pi\)
\(264\) −5.74218 −0.353407
\(265\) 5.43213 0.333693
\(266\) −32.3562 −1.98388
\(267\) 35.3250 2.16186
\(268\) 38.1690 2.33154
\(269\) 23.0366 1.40456 0.702282 0.711899i \(-0.252165\pi\)
0.702282 + 0.711899i \(0.252165\pi\)
\(270\) 7.07714 0.430701
\(271\) 7.42421 0.450988 0.225494 0.974245i \(-0.427600\pi\)
0.225494 + 0.974245i \(0.427600\pi\)
\(272\) 31.3066 1.89824
\(273\) −0.480502 −0.0290813
\(274\) 3.44423 0.208074
\(275\) 0.414044 0.0249678
\(276\) 11.8740 0.714730
\(277\) −7.32500 −0.440117 −0.220058 0.975487i \(-0.570625\pi\)
−0.220058 + 0.975487i \(0.570625\pi\)
\(278\) 3.24406 0.194566
\(279\) −15.9774 −0.956541
\(280\) −27.9181 −1.66842
\(281\) 29.4827 1.75879 0.879394 0.476094i \(-0.157948\pi\)
0.879394 + 0.476094i \(0.157948\pi\)
\(282\) −71.0439 −4.23060
\(283\) 26.3516 1.56644 0.783220 0.621744i \(-0.213576\pi\)
0.783220 + 0.621744i \(0.213576\pi\)
\(284\) 60.3988 3.58401
\(285\) 6.30320 0.373369
\(286\) 0.0533600 0.00315524
\(287\) 3.46310 0.204420
\(288\) −9.94147 −0.585807
\(289\) 1.55488 0.0914635
\(290\) 0.735463 0.0431878
\(291\) −0.339588 −0.0199070
\(292\) −68.4420 −4.00527
\(293\) −5.57505 −0.325698 −0.162849 0.986651i \(-0.552068\pi\)
−0.162849 + 0.986651i \(0.552068\pi\)
\(294\) −67.2722 −3.92339
\(295\) 3.33042 0.193904
\(296\) 56.5506 3.28694
\(297\) −1.14911 −0.0666782
\(298\) −42.5915 −2.46726
\(299\) −0.0613281 −0.00354670
\(300\) 9.78509 0.564943
\(301\) 35.8173 2.06447
\(302\) 12.2968 0.707600
\(303\) −31.9205 −1.83379
\(304\) 21.0795 1.20899
\(305\) −9.22386 −0.528156
\(306\) −18.9253 −1.08189
\(307\) 19.4164 1.10815 0.554076 0.832466i \(-0.313072\pi\)
0.554076 + 0.832466i \(0.313072\pi\)
\(308\) 8.15578 0.464719
\(309\) 28.3112 1.61057
\(310\) 23.6470 1.34306
\(311\) 15.8965 0.901406 0.450703 0.892674i \(-0.351173\pi\)
0.450703 + 0.892674i \(0.351173\pi\)
\(312\) 0.700905 0.0396809
\(313\) −6.95205 −0.392953 −0.196476 0.980509i \(-0.562950\pi\)
−0.196476 + 0.980509i \(0.562950\pi\)
\(314\) 20.8216 1.17503
\(315\) 7.53759 0.424695
\(316\) 2.60360 0.146464
\(317\) 14.2043 0.797792 0.398896 0.916996i \(-0.369393\pi\)
0.398896 + 0.916996i \(0.369393\pi\)
\(318\) −30.1036 −1.68813
\(319\) −0.119417 −0.00668605
\(320\) 0.177967 0.00994866
\(321\) 21.1761 1.18193
\(322\) −13.5374 −0.754408
\(323\) 12.4935 0.695156
\(324\) −50.4299 −2.80166
\(325\) −0.0505392 −0.00280341
\(326\) −31.8299 −1.76290
\(327\) −9.87599 −0.546144
\(328\) −5.05160 −0.278928
\(329\) 56.0841 3.09201
\(330\) −2.29453 −0.126310
\(331\) −5.28025 −0.290229 −0.145114 0.989415i \(-0.546355\pi\)
−0.145114 + 0.989415i \(0.546355\pi\)
\(332\) −62.7379 −3.44319
\(333\) −15.2681 −0.836685
\(334\) −34.4771 −1.88650
\(335\) 8.47720 0.463159
\(336\) 69.0993 3.76968
\(337\) −9.17471 −0.499778 −0.249889 0.968274i \(-0.580394\pi\)
−0.249889 + 0.968274i \(0.580394\pi\)
\(338\) 33.1436 1.80277
\(339\) −7.46462 −0.405423
\(340\) 19.3949 1.05184
\(341\) −3.83955 −0.207923
\(342\) −12.7429 −0.689056
\(343\) 22.4828 1.21395
\(344\) −52.2464 −2.81694
\(345\) 2.63717 0.141980
\(346\) −22.2691 −1.19720
\(347\) −9.71647 −0.521607 −0.260804 0.965392i \(-0.583988\pi\)
−0.260804 + 0.965392i \(0.583988\pi\)
\(348\) −2.82217 −0.151284
\(349\) 12.4856 0.668338 0.334169 0.942513i \(-0.391544\pi\)
0.334169 + 0.942513i \(0.391544\pi\)
\(350\) −11.1559 −0.596305
\(351\) 0.140263 0.00748670
\(352\) −2.38905 −0.127337
\(353\) −32.3163 −1.72002 −0.860012 0.510274i \(-0.829544\pi\)
−0.860012 + 0.510274i \(0.829544\pi\)
\(354\) −18.4564 −0.980946
\(355\) 13.4144 0.711960
\(356\) 73.1871 3.87891
\(357\) 40.9540 2.16752
\(358\) −39.5744 −2.09157
\(359\) −6.29624 −0.332303 −0.166151 0.986100i \(-0.553134\pi\)
−0.166151 + 0.986100i \(0.553134\pi\)
\(360\) −10.9950 −0.579488
\(361\) −10.5878 −0.557254
\(362\) −54.4350 −2.86104
\(363\) −23.5330 −1.23516
\(364\) −0.995514 −0.0521791
\(365\) −15.2007 −0.795642
\(366\) 51.1165 2.67190
\(367\) 0.738646 0.0385570 0.0192785 0.999814i \(-0.493863\pi\)
0.0192785 + 0.999814i \(0.493863\pi\)
\(368\) 8.81938 0.459742
\(369\) 1.36388 0.0710007
\(370\) 22.5972 1.17477
\(371\) 23.7646 1.23380
\(372\) −90.7401 −4.70465
\(373\) 8.66408 0.448609 0.224305 0.974519i \(-0.427989\pi\)
0.224305 + 0.974519i \(0.427989\pi\)
\(374\) −4.54796 −0.235170
\(375\) 2.17323 0.112225
\(376\) −81.8094 −4.21900
\(377\) 0.0145763 0.000750717 0
\(378\) 30.9613 1.59248
\(379\) −11.4394 −0.587601 −0.293800 0.955867i \(-0.594920\pi\)
−0.293800 + 0.955867i \(0.594920\pi\)
\(380\) 13.0591 0.669917
\(381\) 25.2119 1.29165
\(382\) −16.9587 −0.867684
\(383\) −34.4900 −1.76236 −0.881179 0.472783i \(-0.843249\pi\)
−0.881179 + 0.472783i \(0.843249\pi\)
\(384\) 24.0931 1.22949
\(385\) 1.81137 0.0923159
\(386\) −54.8929 −2.79398
\(387\) 14.1060 0.717047
\(388\) −0.703566 −0.0357181
\(389\) −14.8790 −0.754395 −0.377197 0.926133i \(-0.623112\pi\)
−0.377197 + 0.926133i \(0.623112\pi\)
\(390\) 0.280076 0.0141822
\(391\) 5.22710 0.264346
\(392\) −77.4661 −3.91263
\(393\) 9.41136 0.474740
\(394\) 64.8705 3.26813
\(395\) 0.578251 0.0290950
\(396\) 3.21200 0.161409
\(397\) 24.3266 1.22092 0.610460 0.792047i \(-0.290985\pi\)
0.610460 + 0.792047i \(0.290985\pi\)
\(398\) 21.7234 1.08890
\(399\) 27.5754 1.38050
\(400\) 7.26785 0.363393
\(401\) −21.3460 −1.06597 −0.532985 0.846125i \(-0.678930\pi\)
−0.532985 + 0.846125i \(0.678930\pi\)
\(402\) −46.9787 −2.34308
\(403\) 0.468665 0.0233458
\(404\) −66.1336 −3.29027
\(405\) −11.2003 −0.556547
\(406\) 3.21752 0.159683
\(407\) −3.66909 −0.181870
\(408\) −59.7393 −2.95754
\(409\) −37.1465 −1.83678 −0.918389 0.395679i \(-0.870509\pi\)
−0.918389 + 0.395679i \(0.870509\pi\)
\(410\) −2.01858 −0.0996906
\(411\) −2.93533 −0.144789
\(412\) 58.6558 2.88976
\(413\) 14.5700 0.716943
\(414\) −5.33145 −0.262026
\(415\) −13.9339 −0.683987
\(416\) 0.291613 0.0142975
\(417\) −2.76473 −0.135390
\(418\) −3.06226 −0.149780
\(419\) −28.3950 −1.38718 −0.693592 0.720368i \(-0.743973\pi\)
−0.693592 + 0.720368i \(0.743973\pi\)
\(420\) 42.8081 2.08882
\(421\) 24.4208 1.19020 0.595098 0.803653i \(-0.297113\pi\)
0.595098 + 0.803653i \(0.297113\pi\)
\(422\) 38.6615 1.88201
\(423\) 22.0877 1.07394
\(424\) −34.6653 −1.68349
\(425\) 4.30754 0.208946
\(426\) −74.3393 −3.60175
\(427\) −40.3528 −1.95281
\(428\) 43.8730 2.12068
\(429\) −0.0454758 −0.00219559
\(430\) −20.8773 −1.00679
\(431\) 16.4191 0.790879 0.395439 0.918492i \(-0.370592\pi\)
0.395439 + 0.918492i \(0.370592\pi\)
\(432\) −20.1708 −0.970466
\(433\) −12.6521 −0.608021 −0.304010 0.952669i \(-0.598326\pi\)
−0.304010 + 0.952669i \(0.598326\pi\)
\(434\) 103.452 4.96583
\(435\) −0.626794 −0.0300525
\(436\) −20.4613 −0.979918
\(437\) 3.51954 0.168362
\(438\) 84.2389 4.02509
\(439\) 3.27648 0.156378 0.0781889 0.996939i \(-0.475086\pi\)
0.0781889 + 0.996939i \(0.475086\pi\)
\(440\) −2.64223 −0.125963
\(441\) 20.9150 0.995954
\(442\) 0.555135 0.0264051
\(443\) 29.4985 1.40152 0.700758 0.713399i \(-0.252845\pi\)
0.700758 + 0.713399i \(0.252845\pi\)
\(444\) −86.7117 −4.11515
\(445\) 16.2546 0.770541
\(446\) 57.6469 2.72966
\(447\) 36.2984 1.71685
\(448\) 0.778575 0.0367842
\(449\) −35.2532 −1.66370 −0.831851 0.555000i \(-0.812718\pi\)
−0.831851 + 0.555000i \(0.812718\pi\)
\(450\) −4.39353 −0.207113
\(451\) 0.327756 0.0154334
\(452\) −15.4654 −0.727429
\(453\) −10.4799 −0.492387
\(454\) 68.4942 3.21459
\(455\) −0.221100 −0.0103653
\(456\) −40.2240 −1.88366
\(457\) −33.4765 −1.56597 −0.782983 0.622043i \(-0.786303\pi\)
−0.782983 + 0.622043i \(0.786303\pi\)
\(458\) 0.277217 0.0129535
\(459\) −11.9549 −0.558006
\(460\) 5.46374 0.254748
\(461\) −9.29039 −0.432697 −0.216348 0.976316i \(-0.569415\pi\)
−0.216348 + 0.976316i \(0.569415\pi\)
\(462\) −10.0382 −0.467019
\(463\) 6.87329 0.319429 0.159714 0.987163i \(-0.448943\pi\)
0.159714 + 0.987163i \(0.448943\pi\)
\(464\) −2.09616 −0.0973119
\(465\) −20.1530 −0.934575
\(466\) −40.7073 −1.88573
\(467\) −40.9205 −1.89358 −0.946788 0.321857i \(-0.895693\pi\)
−0.946788 + 0.321857i \(0.895693\pi\)
\(468\) −0.392065 −0.0181232
\(469\) 37.0863 1.71249
\(470\) −32.6904 −1.50790
\(471\) −17.7451 −0.817651
\(472\) −21.2531 −0.978255
\(473\) 3.38983 0.155864
\(474\) −3.20453 −0.147189
\(475\) 2.90038 0.133078
\(476\) 84.8494 3.88906
\(477\) 9.35926 0.428531
\(478\) 7.46097 0.341257
\(479\) −7.23032 −0.330362 −0.165181 0.986263i \(-0.552821\pi\)
−0.165181 + 0.986263i \(0.552821\pi\)
\(480\) −12.5397 −0.572355
\(481\) 0.447858 0.0204206
\(482\) −42.2507 −1.92447
\(483\) 11.5372 0.524959
\(484\) −48.7562 −2.21619
\(485\) −0.156259 −0.00709537
\(486\) 40.8380 1.85245
\(487\) −3.55416 −0.161054 −0.0805272 0.996752i \(-0.525660\pi\)
−0.0805272 + 0.996752i \(0.525660\pi\)
\(488\) 58.8623 2.66457
\(489\) 27.1269 1.22672
\(490\) −30.9549 −1.39840
\(491\) 33.9028 1.53001 0.765005 0.644024i \(-0.222736\pi\)
0.765005 + 0.644024i \(0.222736\pi\)
\(492\) 7.74585 0.349210
\(493\) −1.24236 −0.0559531
\(494\) 0.373787 0.0168175
\(495\) 0.713374 0.0320638
\(496\) −67.3970 −3.02621
\(497\) 58.6855 2.63241
\(498\) 77.2183 3.46023
\(499\) −39.5980 −1.77265 −0.886325 0.463063i \(-0.846750\pi\)
−0.886325 + 0.463063i \(0.846750\pi\)
\(500\) 4.50255 0.201360
\(501\) 29.3830 1.31273
\(502\) −42.4145 −1.89305
\(503\) −7.77178 −0.346527 −0.173263 0.984876i \(-0.555431\pi\)
−0.173263 + 0.984876i \(0.555431\pi\)
\(504\) −48.1013 −2.14260
\(505\) −14.6880 −0.653609
\(506\) −1.28121 −0.0569566
\(507\) −28.2465 −1.25447
\(508\) 52.2346 2.31753
\(509\) −8.80931 −0.390466 −0.195233 0.980757i \(-0.562546\pi\)
−0.195233 + 0.980757i \(0.562546\pi\)
\(510\) −23.8714 −1.05704
\(511\) −66.5005 −2.94181
\(512\) 50.8241 2.24613
\(513\) −8.04953 −0.355395
\(514\) 67.8811 2.99411
\(515\) 13.0272 0.574049
\(516\) 80.1118 3.52673
\(517\) 5.30792 0.233442
\(518\) 98.8588 4.34361
\(519\) 18.9788 0.833076
\(520\) 0.322517 0.0141433
\(521\) −42.7272 −1.87191 −0.935957 0.352114i \(-0.885463\pi\)
−0.935957 + 0.352114i \(0.885463\pi\)
\(522\) 1.26716 0.0554622
\(523\) 15.8307 0.692228 0.346114 0.938193i \(-0.387501\pi\)
0.346114 + 0.938193i \(0.387501\pi\)
\(524\) 19.4986 0.851802
\(525\) 9.50752 0.414942
\(526\) −8.48329 −0.369889
\(527\) −39.9451 −1.74003
\(528\) 6.53971 0.284604
\(529\) −21.5275 −0.935977
\(530\) −13.8520 −0.601692
\(531\) 5.73813 0.249013
\(532\) 57.1313 2.47695
\(533\) −0.0400066 −0.00173288
\(534\) −90.0791 −3.89811
\(535\) 9.74404 0.421271
\(536\) −54.0975 −2.33665
\(537\) 33.7271 1.45543
\(538\) −58.7434 −2.53261
\(539\) 5.02612 0.216490
\(540\) −12.4961 −0.537747
\(541\) −5.53313 −0.237888 −0.118944 0.992901i \(-0.537951\pi\)
−0.118944 + 0.992901i \(0.537951\pi\)
\(542\) −18.9318 −0.813190
\(543\) 46.3920 1.99087
\(544\) −24.8547 −1.06564
\(545\) −4.54438 −0.194660
\(546\) 1.22529 0.0524374
\(547\) 17.0406 0.728604 0.364302 0.931281i \(-0.381308\pi\)
0.364302 + 0.931281i \(0.381308\pi\)
\(548\) −6.08148 −0.259788
\(549\) −15.8922 −0.678262
\(550\) −1.05582 −0.0450201
\(551\) −0.836514 −0.0356367
\(552\) −16.8292 −0.716297
\(553\) 2.52975 0.107576
\(554\) 18.6788 0.793587
\(555\) −19.2584 −0.817471
\(556\) −5.72803 −0.242922
\(557\) −23.9518 −1.01487 −0.507435 0.861690i \(-0.669406\pi\)
−0.507435 + 0.861690i \(0.669406\pi\)
\(558\) 40.7425 1.72477
\(559\) −0.413771 −0.0175006
\(560\) 31.7956 1.34361
\(561\) 3.87598 0.163644
\(562\) −75.1811 −3.17132
\(563\) −18.9168 −0.797247 −0.398623 0.917115i \(-0.630512\pi\)
−0.398623 + 0.917115i \(0.630512\pi\)
\(564\) 125.442 5.28207
\(565\) −3.43480 −0.144503
\(566\) −67.1969 −2.82449
\(567\) −48.9994 −2.05778
\(568\) −85.6041 −3.59187
\(569\) 22.4139 0.939641 0.469821 0.882762i \(-0.344319\pi\)
0.469821 + 0.882762i \(0.344319\pi\)
\(570\) −16.0732 −0.673233
\(571\) 41.4043 1.73272 0.866359 0.499422i \(-0.166454\pi\)
0.866359 + 0.499422i \(0.166454\pi\)
\(572\) −0.0942177 −0.00393944
\(573\) 14.4530 0.603783
\(574\) −8.83094 −0.368596
\(575\) 1.21348 0.0506055
\(576\) 0.306627 0.0127761
\(577\) 7.12121 0.296460 0.148230 0.988953i \(-0.452642\pi\)
0.148230 + 0.988953i \(0.452642\pi\)
\(578\) −3.96496 −0.164921
\(579\) 46.7822 1.94420
\(580\) −1.29861 −0.0539217
\(581\) −60.9583 −2.52898
\(582\) 0.865953 0.0358949
\(583\) 2.24914 0.0931498
\(584\) 97.0038 4.01405
\(585\) −0.0870762 −0.00360016
\(586\) 14.2164 0.587276
\(587\) −30.5229 −1.25982 −0.629908 0.776669i \(-0.716908\pi\)
−0.629908 + 0.776669i \(0.716908\pi\)
\(588\) 118.782 4.89850
\(589\) −26.8960 −1.10823
\(590\) −8.49260 −0.349635
\(591\) −55.2855 −2.27414
\(592\) −64.4049 −2.64702
\(593\) 21.4282 0.879950 0.439975 0.898010i \(-0.354987\pi\)
0.439975 + 0.898010i \(0.354987\pi\)
\(594\) 2.93024 0.120229
\(595\) 18.8447 0.772559
\(596\) 75.2037 3.08046
\(597\) −18.5137 −0.757714
\(598\) 0.156387 0.00639515
\(599\) 29.2315 1.19437 0.597184 0.802104i \(-0.296286\pi\)
0.597184 + 0.802104i \(0.296286\pi\)
\(600\) −13.8685 −0.566181
\(601\) −4.25710 −0.173651 −0.0868253 0.996224i \(-0.527672\pi\)
−0.0868253 + 0.996224i \(0.527672\pi\)
\(602\) −91.3344 −3.72251
\(603\) 14.6057 0.594792
\(604\) −21.7124 −0.883466
\(605\) −10.8286 −0.440244
\(606\) 81.3976 3.30655
\(607\) −17.2926 −0.701886 −0.350943 0.936397i \(-0.614139\pi\)
−0.350943 + 0.936397i \(0.614139\pi\)
\(608\) −16.7353 −0.678706
\(609\) −2.74212 −0.111116
\(610\) 23.5209 0.952334
\(611\) −0.647898 −0.0262111
\(612\) 33.4164 1.35078
\(613\) −43.6486 −1.76295 −0.881475 0.472231i \(-0.843449\pi\)
−0.881475 + 0.472231i \(0.843449\pi\)
\(614\) −49.5120 −1.99814
\(615\) 1.72033 0.0693702
\(616\) −11.5593 −0.465737
\(617\) 4.57134 0.184035 0.0920176 0.995757i \(-0.470668\pi\)
0.0920176 + 0.995757i \(0.470668\pi\)
\(618\) −72.1940 −2.90407
\(619\) 34.2670 1.37731 0.688653 0.725091i \(-0.258202\pi\)
0.688653 + 0.725091i \(0.258202\pi\)
\(620\) −41.7535 −1.67686
\(621\) −3.36781 −0.135146
\(622\) −40.5361 −1.62535
\(623\) 71.1110 2.84900
\(624\) −0.798253 −0.0319557
\(625\) 1.00000 0.0400000
\(626\) 17.7278 0.708545
\(627\) 2.60980 0.104225
\(628\) −36.7646 −1.46707
\(629\) −38.1717 −1.52201
\(630\) −19.2209 −0.765780
\(631\) 19.9184 0.792938 0.396469 0.918048i \(-0.370235\pi\)
0.396469 + 0.918048i \(0.370235\pi\)
\(632\) −3.69012 −0.146785
\(633\) −32.9491 −1.30961
\(634\) −36.2211 −1.43852
\(635\) 11.6011 0.460376
\(636\) 53.1539 2.10769
\(637\) −0.613501 −0.0243078
\(638\) 0.304514 0.0120558
\(639\) 23.1122 0.914305
\(640\) 11.0863 0.438224
\(641\) 9.02357 0.356409 0.178205 0.983993i \(-0.442971\pi\)
0.178205 + 0.983993i \(0.442971\pi\)
\(642\) −53.9992 −2.13118
\(643\) −46.4429 −1.83153 −0.915764 0.401716i \(-0.868414\pi\)
−0.915764 + 0.401716i \(0.868414\pi\)
\(644\) 23.9029 0.941907
\(645\) 17.7925 0.700581
\(646\) −31.8585 −1.25346
\(647\) −48.0151 −1.88767 −0.943833 0.330422i \(-0.892809\pi\)
−0.943833 + 0.330422i \(0.892809\pi\)
\(648\) 71.4750 2.80780
\(649\) 1.37894 0.0541280
\(650\) 0.128875 0.00505491
\(651\) −88.1661 −3.45550
\(652\) 56.2021 2.20104
\(653\) −27.4828 −1.07549 −0.537743 0.843109i \(-0.680723\pi\)
−0.537743 + 0.843109i \(0.680723\pi\)
\(654\) 25.1839 0.984768
\(655\) 4.33058 0.169210
\(656\) 5.75321 0.224625
\(657\) −26.1900 −1.02177
\(658\) −143.015 −5.57530
\(659\) 27.5644 1.07376 0.536878 0.843660i \(-0.319604\pi\)
0.536878 + 0.843660i \(0.319604\pi\)
\(660\) 4.05146 0.157703
\(661\) 22.5049 0.875340 0.437670 0.899136i \(-0.355804\pi\)
0.437670 + 0.899136i \(0.355804\pi\)
\(662\) 13.4647 0.523320
\(663\) −0.473112 −0.0183741
\(664\) 88.9194 3.45074
\(665\) 12.6886 0.492045
\(666\) 38.9337 1.50865
\(667\) −0.349986 −0.0135515
\(668\) 60.8762 2.35537
\(669\) −49.1293 −1.89945
\(670\) −21.6169 −0.835135
\(671\) −3.81908 −0.147434
\(672\) −54.8589 −2.11623
\(673\) −37.2790 −1.43700 −0.718501 0.695526i \(-0.755171\pi\)
−0.718501 + 0.695526i \(0.755171\pi\)
\(674\) 23.3956 0.901165
\(675\) −2.77534 −0.106823
\(676\) −58.5216 −2.25083
\(677\) −23.5654 −0.905691 −0.452845 0.891589i \(-0.649591\pi\)
−0.452845 + 0.891589i \(0.649591\pi\)
\(678\) 19.0349 0.731030
\(679\) −0.683608 −0.0262345
\(680\) −27.4887 −1.05414
\(681\) −58.3738 −2.23689
\(682\) 9.79089 0.374912
\(683\) −15.4091 −0.589612 −0.294806 0.955557i \(-0.595255\pi\)
−0.294806 + 0.955557i \(0.595255\pi\)
\(684\) 22.5001 0.860313
\(685\) −1.35067 −0.0516066
\(686\) −57.3312 −2.18892
\(687\) −0.236257 −0.00901377
\(688\) 59.5029 2.26853
\(689\) −0.274535 −0.0104590
\(690\) −6.72481 −0.256009
\(691\) 15.8108 0.601471 0.300735 0.953708i \(-0.402768\pi\)
0.300735 + 0.953708i \(0.402768\pi\)
\(692\) 39.3206 1.49474
\(693\) 3.12089 0.118553
\(694\) 24.7771 0.940525
\(695\) −1.27217 −0.0482563
\(696\) 3.99991 0.151616
\(697\) 3.40983 0.129157
\(698\) −31.8384 −1.20510
\(699\) 34.6926 1.31219
\(700\) 19.6979 0.744510
\(701\) 37.1097 1.40162 0.700808 0.713350i \(-0.252823\pi\)
0.700808 + 0.713350i \(0.252823\pi\)
\(702\) −0.357673 −0.0134995
\(703\) −25.7020 −0.969369
\(704\) 0.0736861 0.00277715
\(705\) 27.8603 1.04928
\(706\) 82.4069 3.10142
\(707\) −64.2576 −2.41665
\(708\) 32.5884 1.22475
\(709\) 32.3882 1.21636 0.608182 0.793798i \(-0.291899\pi\)
0.608182 + 0.793798i \(0.291899\pi\)
\(710\) −34.2068 −1.28376
\(711\) 0.996295 0.0373640
\(712\) −103.729 −3.88741
\(713\) −11.2529 −0.421426
\(714\) −104.433 −3.90831
\(715\) −0.0209254 −0.000782566 0
\(716\) 69.8765 2.61141
\(717\) −6.35858 −0.237465
\(718\) 16.0555 0.599185
\(719\) −10.1842 −0.379808 −0.189904 0.981803i \(-0.560818\pi\)
−0.189904 + 0.981803i \(0.560818\pi\)
\(720\) 12.5221 0.466672
\(721\) 56.9919 2.12249
\(722\) 26.9990 1.00480
\(723\) 36.0079 1.33915
\(724\) 96.1159 3.57212
\(725\) −0.288416 −0.0107115
\(726\) 60.0094 2.22716
\(727\) −5.22717 −0.193865 −0.0969325 0.995291i \(-0.530903\pi\)
−0.0969325 + 0.995291i \(0.530903\pi\)
\(728\) 1.41096 0.0522935
\(729\) −1.20312 −0.0445599
\(730\) 38.7620 1.43465
\(731\) 35.2664 1.30437
\(732\) −90.2563 −3.33597
\(733\) 27.8809 1.02980 0.514902 0.857249i \(-0.327828\pi\)
0.514902 + 0.857249i \(0.327828\pi\)
\(734\) −1.88355 −0.0695232
\(735\) 26.3811 0.973083
\(736\) −7.00182 −0.258091
\(737\) 3.50993 0.129290
\(738\) −3.47790 −0.128023
\(739\) 0.328447 0.0120821 0.00604106 0.999982i \(-0.498077\pi\)
0.00604106 + 0.999982i \(0.498077\pi\)
\(740\) −39.8998 −1.46675
\(741\) −0.318558 −0.0117025
\(742\) −60.6000 −2.22470
\(743\) 43.8201 1.60760 0.803802 0.594897i \(-0.202807\pi\)
0.803802 + 0.594897i \(0.202807\pi\)
\(744\) 128.607 4.71497
\(745\) 16.7025 0.611931
\(746\) −22.0935 −0.808900
\(747\) −24.0073 −0.878381
\(748\) 8.03033 0.293618
\(749\) 42.6285 1.55761
\(750\) −5.54177 −0.202357
\(751\) 18.7334 0.683590 0.341795 0.939775i \(-0.388965\pi\)
0.341795 + 0.939775i \(0.388965\pi\)
\(752\) 93.1719 3.39763
\(753\) 36.1476 1.31729
\(754\) −0.0371697 −0.00135364
\(755\) −4.82225 −0.175500
\(756\) −54.6683 −1.98827
\(757\) 6.86717 0.249592 0.124796 0.992182i \(-0.460172\pi\)
0.124796 + 0.992182i \(0.460172\pi\)
\(758\) 29.1705 1.05952
\(759\) 1.09190 0.0396336
\(760\) −18.5088 −0.671386
\(761\) 22.4599 0.814169 0.407085 0.913390i \(-0.366545\pi\)
0.407085 + 0.913390i \(0.366545\pi\)
\(762\) −64.2906 −2.32900
\(763\) −19.8809 −0.719736
\(764\) 29.9440 1.08334
\(765\) 7.42165 0.268330
\(766\) 87.9499 3.17776
\(767\) −0.168316 −0.00607756
\(768\) −62.2111 −2.24485
\(769\) −10.6842 −0.385282 −0.192641 0.981269i \(-0.561705\pi\)
−0.192641 + 0.981269i \(0.561705\pi\)
\(770\) −4.61901 −0.166458
\(771\) −57.8514 −2.08347
\(772\) 96.9244 3.48838
\(773\) −25.7258 −0.925292 −0.462646 0.886543i \(-0.653100\pi\)
−0.462646 + 0.886543i \(0.653100\pi\)
\(774\) −35.9704 −1.29293
\(775\) −9.27330 −0.333107
\(776\) 0.997174 0.0357964
\(777\) −84.2520 −3.02252
\(778\) 37.9416 1.36027
\(779\) 2.29593 0.0822602
\(780\) −0.494530 −0.0177070
\(781\) 5.55413 0.198742
\(782\) −13.3292 −0.476650
\(783\) 0.800451 0.0286058
\(784\) 88.2253 3.15090
\(785\) −8.16529 −0.291432
\(786\) −23.9991 −0.856018
\(787\) 14.8966 0.531006 0.265503 0.964110i \(-0.414462\pi\)
0.265503 + 0.964110i \(0.414462\pi\)
\(788\) −114.542 −4.08038
\(789\) 7.22985 0.257389
\(790\) −1.47455 −0.0524620
\(791\) −15.0267 −0.534287
\(792\) −4.55242 −0.161763
\(793\) 0.466166 0.0165540
\(794\) −62.0332 −2.20148
\(795\) 11.8053 0.418690
\(796\) −38.3570 −1.35953
\(797\) −43.5697 −1.54332 −0.771658 0.636037i \(-0.780572\pi\)
−0.771658 + 0.636037i \(0.780572\pi\)
\(798\) −70.3175 −2.48921
\(799\) 55.2214 1.95359
\(800\) −5.77005 −0.204002
\(801\) 28.0058 0.989535
\(802\) 54.4326 1.92208
\(803\) −6.29376 −0.222102
\(804\) 82.9502 2.92543
\(805\) 5.30875 0.187109
\(806\) −1.19510 −0.0420956
\(807\) 50.0638 1.76233
\(808\) 93.7320 3.29748
\(809\) −21.0067 −0.738555 −0.369277 0.929319i \(-0.620395\pi\)
−0.369277 + 0.929319i \(0.620395\pi\)
\(810\) 28.5609 1.00353
\(811\) −13.7041 −0.481216 −0.240608 0.970622i \(-0.577347\pi\)
−0.240608 + 0.970622i \(0.577347\pi\)
\(812\) −5.68117 −0.199370
\(813\) 16.1345 0.565863
\(814\) 9.35622 0.327935
\(815\) 12.4823 0.437235
\(816\) 68.0365 2.38175
\(817\) 23.7458 0.830759
\(818\) 94.7240 3.31195
\(819\) −0.380943 −0.0133112
\(820\) 3.56421 0.124467
\(821\) −27.1989 −0.949248 −0.474624 0.880189i \(-0.657416\pi\)
−0.474624 + 0.880189i \(0.657416\pi\)
\(822\) 7.48513 0.261074
\(823\) 24.1011 0.840113 0.420056 0.907498i \(-0.362010\pi\)
0.420056 + 0.907498i \(0.362010\pi\)
\(824\) −83.1337 −2.89610
\(825\) 0.899814 0.0313275
\(826\) −37.1536 −1.29274
\(827\) 24.2855 0.844489 0.422244 0.906482i \(-0.361242\pi\)
0.422244 + 0.906482i \(0.361242\pi\)
\(828\) 9.41373 0.327150
\(829\) 5.94891 0.206614 0.103307 0.994650i \(-0.467058\pi\)
0.103307 + 0.994650i \(0.467058\pi\)
\(830\) 35.5315 1.23332
\(831\) −15.9189 −0.552222
\(832\) −0.00899430 −0.000311821 0
\(833\) 52.2897 1.81173
\(834\) 7.05009 0.244125
\(835\) 13.5204 0.467892
\(836\) 5.40703 0.187006
\(837\) 25.7365 0.889585
\(838\) 72.4074 2.50127
\(839\) 12.5564 0.433496 0.216748 0.976228i \(-0.430455\pi\)
0.216748 + 0.976228i \(0.430455\pi\)
\(840\) −60.6725 −2.09340
\(841\) −28.9168 −0.997132
\(842\) −62.2732 −2.14608
\(843\) 64.0727 2.20678
\(844\) −68.2646 −2.34977
\(845\) −12.9974 −0.447126
\(846\) −56.3238 −1.93645
\(847\) −47.3731 −1.62776
\(848\) 39.4799 1.35575
\(849\) 57.2682 1.96544
\(850\) −10.9843 −0.376757
\(851\) −10.7534 −0.368621
\(852\) 131.261 4.49692
\(853\) −40.1927 −1.37617 −0.688086 0.725629i \(-0.741549\pi\)
−0.688086 + 0.725629i \(0.741549\pi\)
\(854\) 102.900 3.52116
\(855\) 4.99719 0.170900
\(856\) −62.1818 −2.12533
\(857\) 16.3040 0.556935 0.278468 0.960446i \(-0.410174\pi\)
0.278468 + 0.960446i \(0.410174\pi\)
\(858\) 0.115964 0.00395894
\(859\) 24.4070 0.832756 0.416378 0.909192i \(-0.363299\pi\)
0.416378 + 0.909192i \(0.363299\pi\)
\(860\) 36.8630 1.25702
\(861\) 7.52613 0.256490
\(862\) −41.8688 −1.42606
\(863\) −45.7326 −1.55676 −0.778379 0.627795i \(-0.783958\pi\)
−0.778379 + 0.627795i \(0.783958\pi\)
\(864\) 16.0138 0.544802
\(865\) 8.73296 0.296930
\(866\) 32.2630 1.09634
\(867\) 3.37912 0.114761
\(868\) −182.664 −6.20003
\(869\) 0.239421 0.00812181
\(870\) 1.59833 0.0541885
\(871\) −0.428430 −0.0145168
\(872\) 29.0001 0.982066
\(873\) −0.269226 −0.00911193
\(874\) −8.97486 −0.303579
\(875\) 4.37483 0.147896
\(876\) −148.740 −5.02548
\(877\) −40.5333 −1.36871 −0.684356 0.729148i \(-0.739917\pi\)
−0.684356 + 0.729148i \(0.739917\pi\)
\(878\) −8.35505 −0.281969
\(879\) −12.1159 −0.408659
\(880\) 3.00921 0.101440
\(881\) −45.2063 −1.52304 −0.761520 0.648142i \(-0.775547\pi\)
−0.761520 + 0.648142i \(0.775547\pi\)
\(882\) −53.3335 −1.79583
\(883\) 51.8961 1.74644 0.873222 0.487322i \(-0.162026\pi\)
0.873222 + 0.487322i \(0.162026\pi\)
\(884\) −0.980202 −0.0329678
\(885\) 7.23778 0.243295
\(886\) −75.2215 −2.52712
\(887\) 43.9301 1.47503 0.737514 0.675332i \(-0.236000\pi\)
0.737514 + 0.675332i \(0.236000\pi\)
\(888\) 122.898 4.12418
\(889\) 50.7528 1.70220
\(890\) −41.4494 −1.38939
\(891\) −4.63741 −0.155359
\(892\) −101.787 −3.40809
\(893\) 37.1820 1.24425
\(894\) −92.5612 −3.09571
\(895\) 15.5193 0.518754
\(896\) 48.5005 1.62029
\(897\) −0.133280 −0.00445010
\(898\) 89.8960 2.99987
\(899\) 2.67456 0.0892017
\(900\) 7.75765 0.258588
\(901\) 23.3991 0.779537
\(902\) −0.835780 −0.0278284
\(903\) 77.8393 2.59033
\(904\) 21.9193 0.729024
\(905\) 21.3470 0.709598
\(906\) 26.7238 0.887838
\(907\) −39.8261 −1.32240 −0.661201 0.750208i \(-0.729953\pi\)
−0.661201 + 0.750208i \(0.729953\pi\)
\(908\) −120.940 −4.01354
\(909\) −25.3067 −0.839369
\(910\) 0.563807 0.0186900
\(911\) 0.284598 0.00942917 0.00471458 0.999989i \(-0.498499\pi\)
0.00471458 + 0.999989i \(0.498499\pi\)
\(912\) 45.8107 1.51694
\(913\) −5.76923 −0.190934
\(914\) 85.3655 2.82364
\(915\) −20.0456 −0.662687
\(916\) −0.489482 −0.0161729
\(917\) 18.9455 0.625637
\(918\) 30.4850 1.00616
\(919\) −0.329286 −0.0108621 −0.00543107 0.999985i \(-0.501729\pi\)
−0.00543107 + 0.999985i \(0.501729\pi\)
\(920\) −7.74384 −0.255307
\(921\) 42.1964 1.39042
\(922\) 23.6906 0.780208
\(923\) −0.677951 −0.0223150
\(924\) 17.7244 0.583091
\(925\) −8.86161 −0.291368
\(926\) −17.5269 −0.575971
\(927\) 22.4452 0.737198
\(928\) 1.66417 0.0546291
\(929\) −28.0272 −0.919541 −0.459771 0.888038i \(-0.652068\pi\)
−0.459771 + 0.888038i \(0.652068\pi\)
\(930\) 51.3904 1.68516
\(931\) 35.2080 1.15390
\(932\) 71.8768 2.35440
\(933\) 34.5467 1.13101
\(934\) 104.348 3.41436
\(935\) 1.78351 0.0583270
\(936\) 0.555679 0.0181629
\(937\) −35.5755 −1.16220 −0.581101 0.813832i \(-0.697378\pi\)
−0.581101 + 0.813832i \(0.697378\pi\)
\(938\) −94.5704 −3.08783
\(939\) −15.1084 −0.493045
\(940\) 57.7214 1.88267
\(941\) 26.3928 0.860380 0.430190 0.902738i \(-0.358446\pi\)
0.430190 + 0.902738i \(0.358446\pi\)
\(942\) 45.2502 1.47433
\(943\) 0.960585 0.0312810
\(944\) 24.2050 0.787805
\(945\) −12.1416 −0.394967
\(946\) −8.64410 −0.281044
\(947\) 10.0450 0.326417 0.163209 0.986592i \(-0.447816\pi\)
0.163209 + 0.986592i \(0.447816\pi\)
\(948\) 5.65824 0.183771
\(949\) 0.768232 0.0249379
\(950\) −7.39599 −0.239958
\(951\) 30.8692 1.00100
\(952\) −120.258 −3.89759
\(953\) −49.3773 −1.59949 −0.799745 0.600340i \(-0.795032\pi\)
−0.799745 + 0.600340i \(0.795032\pi\)
\(954\) −23.8662 −0.772697
\(955\) 6.65046 0.215204
\(956\) −13.1738 −0.426072
\(957\) −0.259520 −0.00838910
\(958\) 18.4374 0.595685
\(959\) −5.90897 −0.190811
\(960\) 0.386764 0.0124828
\(961\) 54.9940 1.77400
\(962\) −1.14204 −0.0368209
\(963\) 16.7884 0.541000
\(964\) 74.6020 2.40277
\(965\) 21.5266 0.692964
\(966\) −29.4199 −0.946569
\(967\) −25.0855 −0.806696 −0.403348 0.915047i \(-0.632154\pi\)
−0.403348 + 0.915047i \(0.632154\pi\)
\(968\) 69.1028 2.22105
\(969\) 27.1513 0.872224
\(970\) 0.398463 0.0127939
\(971\) 19.8577 0.637265 0.318633 0.947878i \(-0.396776\pi\)
0.318633 + 0.947878i \(0.396776\pi\)
\(972\) −72.1076 −2.31285
\(973\) −5.56554 −0.178423
\(974\) 9.06314 0.290402
\(975\) −0.109833 −0.00351748
\(976\) −67.0376 −2.14582
\(977\) 35.7493 1.14372 0.571861 0.820351i \(-0.306222\pi\)
0.571861 + 0.820351i \(0.306222\pi\)
\(978\) −69.1739 −2.21194
\(979\) 6.73011 0.215095
\(980\) 54.6570 1.74595
\(981\) −7.82971 −0.249984
\(982\) −86.4524 −2.75881
\(983\) 34.6952 1.10661 0.553303 0.832980i \(-0.313367\pi\)
0.553303 + 0.832980i \(0.313367\pi\)
\(984\) −10.9783 −0.349975
\(985\) −25.4393 −0.810563
\(986\) 3.16803 0.100891
\(987\) 121.884 3.87960
\(988\) −0.659995 −0.0209972
\(989\) 9.93490 0.315911
\(990\) −1.81911 −0.0578152
\(991\) 24.0117 0.762758 0.381379 0.924419i \(-0.375449\pi\)
0.381379 + 0.924419i \(0.375449\pi\)
\(992\) 53.5073 1.69886
\(993\) −11.4752 −0.364155
\(994\) −149.649 −4.74657
\(995\) −8.51895 −0.270069
\(996\) −136.344 −4.32023
\(997\) −14.7271 −0.466413 −0.233207 0.972427i \(-0.574922\pi\)
−0.233207 + 0.972427i \(0.574922\pi\)
\(998\) 100.975 3.19632
\(999\) 24.5940 0.778119
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 \(a_p\))