Properties

Label 4009.2.a.c.1.20
Level 4009
Weight 2
Character 4009.1
Self dual Yes
Analytic conductor 32.012
Analytic rank 1
Dimension 71
CM No

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Newspace parameters

Level: \( N \) = \( 4009 = 19 \cdot 211 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4009.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0120261703\)
Analytic rank: \(1\)
Dimension: \(71\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.20
Character \(\chi\) = 4009.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.69413 q^{2}\) \(-0.649307 q^{3}\) \(+0.870061 q^{4}\) \(-0.0469641 q^{5}\) \(+1.10001 q^{6}\) \(+3.97959 q^{7}\) \(+1.91426 q^{8}\) \(-2.57840 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.69413 q^{2}\) \(-0.649307 q^{3}\) \(+0.870061 q^{4}\) \(-0.0469641 q^{5}\) \(+1.10001 q^{6}\) \(+3.97959 q^{7}\) \(+1.91426 q^{8}\) \(-2.57840 q^{9}\) \(+0.0795630 q^{10}\) \(-5.59218 q^{11}\) \(-0.564937 q^{12}\) \(+4.37998 q^{13}\) \(-6.74193 q^{14}\) \(+0.0304941 q^{15}\) \(-4.98312 q^{16}\) \(+0.0418001 q^{17}\) \(+4.36813 q^{18}\) \(+1.00000 q^{19}\) \(-0.0408616 q^{20}\) \(-2.58398 q^{21}\) \(+9.47386 q^{22}\) \(+3.81507 q^{23}\) \(-1.24294 q^{24}\) \(-4.99779 q^{25}\) \(-7.42024 q^{26}\) \(+3.62210 q^{27}\) \(+3.46249 q^{28}\) \(+2.20513 q^{29}\) \(-0.0516608 q^{30}\) \(-1.50758 q^{31}\) \(+4.61351 q^{32}\) \(+3.63105 q^{33}\) \(-0.0708146 q^{34}\) \(-0.186898 q^{35}\) \(-2.24336 q^{36}\) \(+2.23622 q^{37}\) \(-1.69413 q^{38}\) \(-2.84395 q^{39}\) \(-0.0899014 q^{40}\) \(+1.18167 q^{41}\) \(+4.37758 q^{42}\) \(-7.41488 q^{43}\) \(-4.86554 q^{44}\) \(+0.121092 q^{45}\) \(-6.46321 q^{46}\) \(-9.98963 q^{47}\) \(+3.23557 q^{48}\) \(+8.83716 q^{49}\) \(+8.46689 q^{50}\) \(-0.0271411 q^{51}\) \(+3.81085 q^{52}\) \(-11.3478 q^{53}\) \(-6.13629 q^{54}\) \(+0.262632 q^{55}\) \(+7.61797 q^{56}\) \(-0.649307 q^{57}\) \(-3.73577 q^{58}\) \(+10.0208 q^{59}\) \(+0.0265317 q^{60}\) \(-5.26917 q^{61}\) \(+2.55403 q^{62}\) \(-10.2610 q^{63}\) \(+2.15037 q^{64}\) \(-0.205702 q^{65}\) \(-6.15145 q^{66}\) \(-0.395036 q^{67}\) \(+0.0363686 q^{68}\) \(-2.47715 q^{69}\) \(+0.316628 q^{70}\) \(+2.82311 q^{71}\) \(-4.93572 q^{72}\) \(+3.30543 q^{73}\) \(-3.78845 q^{74}\) \(+3.24510 q^{75}\) \(+0.870061 q^{76}\) \(-22.2546 q^{77}\) \(+4.81802 q^{78}\) \(-1.69175 q^{79}\) \(+0.234027 q^{80}\) \(+5.38335 q^{81}\) \(-2.00189 q^{82}\) \(-12.4114 q^{83}\) \(-2.24822 q^{84}\) \(-0.00196310 q^{85}\) \(+12.5617 q^{86}\) \(-1.43181 q^{87}\) \(-10.7049 q^{88}\) \(-3.52728 q^{89}\) \(-0.205145 q^{90}\) \(+17.4305 q^{91}\) \(+3.31935 q^{92}\) \(+0.978881 q^{93}\) \(+16.9237 q^{94}\) \(-0.0469641 q^{95}\) \(-2.99558 q^{96}\) \(+12.5900 q^{97}\) \(-14.9713 q^{98}\) \(+14.4189 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(71q \) \(\mathstrut -\mathstrut 15q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 18q^{5} \) \(\mathstrut -\mathstrut 9q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 63q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(71q \) \(\mathstrut -\mathstrut 15q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 18q^{5} \) \(\mathstrut -\mathstrut 9q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 63q^{9} \) \(\mathstrut -\mathstrut 10q^{10} \) \(\mathstrut -\mathstrut 52q^{11} \) \(\mathstrut -\mathstrut 9q^{12} \) \(\mathstrut -\mathstrut 15q^{13} \) \(\mathstrut -\mathstrut 53q^{14} \) \(\mathstrut -\mathstrut 33q^{15} \) \(\mathstrut +\mathstrut 53q^{16} \) \(\mathstrut -\mathstrut 10q^{17} \) \(\mathstrut -\mathstrut 35q^{18} \) \(\mathstrut +\mathstrut 71q^{19} \) \(\mathstrut -\mathstrut 33q^{20} \) \(\mathstrut -\mathstrut 38q^{21} \) \(\mathstrut -\mathstrut 6q^{22} \) \(\mathstrut -\mathstrut 65q^{23} \) \(\mathstrut -\mathstrut 30q^{24} \) \(\mathstrut +\mathstrut 51q^{25} \) \(\mathstrut -\mathstrut 4q^{26} \) \(\mathstrut -\mathstrut 23q^{27} \) \(\mathstrut -\mathstrut 29q^{28} \) \(\mathstrut -\mathstrut 97q^{29} \) \(\mathstrut -\mathstrut 27q^{30} \) \(\mathstrut -\mathstrut 53q^{31} \) \(\mathstrut -\mathstrut 78q^{32} \) \(\mathstrut -\mathstrut 17q^{33} \) \(\mathstrut -\mathstrut 24q^{34} \) \(\mathstrut -\mathstrut 38q^{35} \) \(\mathstrut +\mathstrut 24q^{36} \) \(\mathstrut -\mathstrut 33q^{37} \) \(\mathstrut -\mathstrut 15q^{38} \) \(\mathstrut -\mathstrut 86q^{39} \) \(\mathstrut +\mathstrut 25q^{40} \) \(\mathstrut -\mathstrut 69q^{41} \) \(\mathstrut +\mathstrut 64q^{42} \) \(\mathstrut -\mathstrut 10q^{43} \) \(\mathstrut -\mathstrut 94q^{44} \) \(\mathstrut -\mathstrut 34q^{45} \) \(\mathstrut -\mathstrut 6q^{46} \) \(\mathstrut -\mathstrut 37q^{47} \) \(\mathstrut -\mathstrut q^{48} \) \(\mathstrut +\mathstrut 74q^{49} \) \(\mathstrut -\mathstrut 41q^{50} \) \(\mathstrut -\mathstrut 46q^{51} \) \(\mathstrut -\mathstrut 30q^{52} \) \(\mathstrut -\mathstrut 50q^{53} \) \(\mathstrut -\mathstrut 17q^{54} \) \(\mathstrut -\mathstrut 30q^{55} \) \(\mathstrut -\mathstrut 116q^{56} \) \(\mathstrut -\mathstrut 8q^{57} \) \(\mathstrut +\mathstrut 11q^{58} \) \(\mathstrut -\mathstrut 93q^{59} \) \(\mathstrut -\mathstrut 56q^{60} \) \(\mathstrut -\mathstrut 18q^{61} \) \(\mathstrut -\mathstrut q^{62} \) \(\mathstrut -\mathstrut 84q^{63} \) \(\mathstrut +\mathstrut 93q^{64} \) \(\mathstrut -\mathstrut 78q^{65} \) \(\mathstrut -\mathstrut 53q^{66} \) \(\mathstrut -\mathstrut 5q^{67} \) \(\mathstrut -\mathstrut 9q^{68} \) \(\mathstrut -\mathstrut 69q^{69} \) \(\mathstrut -\mathstrut 10q^{70} \) \(\mathstrut -\mathstrut 221q^{71} \) \(\mathstrut -\mathstrut 73q^{72} \) \(\mathstrut -\mathstrut 34q^{73} \) \(\mathstrut -\mathstrut 58q^{74} \) \(\mathstrut -\mathstrut 70q^{75} \) \(\mathstrut +\mathstrut 69q^{76} \) \(\mathstrut -\mathstrut 2q^{77} \) \(\mathstrut +\mathstrut 7q^{78} \) \(\mathstrut -\mathstrut 68q^{79} \) \(\mathstrut -\mathstrut 71q^{80} \) \(\mathstrut +\mathstrut 39q^{81} \) \(\mathstrut +\mathstrut 26q^{82} \) \(\mathstrut -\mathstrut 45q^{83} \) \(\mathstrut -\mathstrut 10q^{84} \) \(\mathstrut -\mathstrut 44q^{85} \) \(\mathstrut -\mathstrut 80q^{86} \) \(\mathstrut -\mathstrut 7q^{87} \) \(\mathstrut -\mathstrut 46q^{88} \) \(\mathstrut -\mathstrut 143q^{89} \) \(\mathstrut +\mathstrut 41q^{90} \) \(\mathstrut -\mathstrut 30q^{91} \) \(\mathstrut -\mathstrut 46q^{92} \) \(\mathstrut +\mathstrut 32q^{93} \) \(\mathstrut +\mathstrut 41q^{94} \) \(\mathstrut -\mathstrut 18q^{95} \) \(\mathstrut -\mathstrut 140q^{96} \) \(\mathstrut -\mathstrut 18q^{97} \) \(\mathstrut -\mathstrut 97q^{98} \) \(\mathstrut -\mathstrut 142q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.69413 −1.19793 −0.598964 0.800776i \(-0.704421\pi\)
−0.598964 + 0.800776i \(0.704421\pi\)
\(3\) −0.649307 −0.374878 −0.187439 0.982276i \(-0.560019\pi\)
−0.187439 + 0.982276i \(0.560019\pi\)
\(4\) 0.870061 0.435030
\(5\) −0.0469641 −0.0210030 −0.0105015 0.999945i \(-0.503343\pi\)
−0.0105015 + 0.999945i \(0.503343\pi\)
\(6\) 1.10001 0.449076
\(7\) 3.97959 1.50414 0.752072 0.659081i \(-0.229054\pi\)
0.752072 + 0.659081i \(0.229054\pi\)
\(8\) 1.91426 0.676793
\(9\) −2.57840 −0.859467
\(10\) 0.0795630 0.0251600
\(11\) −5.59218 −1.68611 −0.843053 0.537830i \(-0.819244\pi\)
−0.843053 + 0.537830i \(0.819244\pi\)
\(12\) −0.564937 −0.163083
\(13\) 4.37998 1.21479 0.607394 0.794401i \(-0.292215\pi\)
0.607394 + 0.794401i \(0.292215\pi\)
\(14\) −6.74193 −1.80186
\(15\) 0.0304941 0.00787355
\(16\) −4.98312 −1.24578
\(17\) 0.0418001 0.0101380 0.00506901 0.999987i \(-0.498386\pi\)
0.00506901 + 0.999987i \(0.498386\pi\)
\(18\) 4.36813 1.02958
\(19\) 1.00000 0.229416
\(20\) −0.0408616 −0.00913693
\(21\) −2.58398 −0.563870
\(22\) 9.47386 2.01983
\(23\) 3.81507 0.795498 0.397749 0.917494i \(-0.369792\pi\)
0.397749 + 0.917494i \(0.369792\pi\)
\(24\) −1.24294 −0.253715
\(25\) −4.99779 −0.999559
\(26\) −7.42024 −1.45523
\(27\) 3.62210 0.697073
\(28\) 3.46249 0.654349
\(29\) 2.20513 0.409483 0.204742 0.978816i \(-0.434365\pi\)
0.204742 + 0.978816i \(0.434365\pi\)
\(30\) −0.0516608 −0.00943194
\(31\) −1.50758 −0.270769 −0.135384 0.990793i \(-0.543227\pi\)
−0.135384 + 0.990793i \(0.543227\pi\)
\(32\) 4.61351 0.815560
\(33\) 3.63105 0.632084
\(34\) −0.0708146 −0.0121446
\(35\) −0.186898 −0.0315915
\(36\) −2.24336 −0.373894
\(37\) 2.23622 0.367633 0.183817 0.982961i \(-0.441155\pi\)
0.183817 + 0.982961i \(0.441155\pi\)
\(38\) −1.69413 −0.274823
\(39\) −2.84395 −0.455397
\(40\) −0.0899014 −0.0142147
\(41\) 1.18167 0.184546 0.0922728 0.995734i \(-0.470587\pi\)
0.0922728 + 0.995734i \(0.470587\pi\)
\(42\) 4.37758 0.675476
\(43\) −7.41488 −1.13076 −0.565379 0.824831i \(-0.691270\pi\)
−0.565379 + 0.824831i \(0.691270\pi\)
\(44\) −4.86554 −0.733508
\(45\) 0.121092 0.0180513
\(46\) −6.46321 −0.952948
\(47\) −9.98963 −1.45714 −0.728568 0.684973i \(-0.759814\pi\)
−0.728568 + 0.684973i \(0.759814\pi\)
\(48\) 3.23557 0.467015
\(49\) 8.83716 1.26245
\(50\) 8.46689 1.19740
\(51\) −0.0271411 −0.00380052
\(52\) 3.81085 0.528470
\(53\) −11.3478 −1.55875 −0.779373 0.626560i \(-0.784462\pi\)
−0.779373 + 0.626560i \(0.784462\pi\)
\(54\) −6.13629 −0.835043
\(55\) 0.262632 0.0354132
\(56\) 7.61797 1.01799
\(57\) −0.649307 −0.0860029
\(58\) −3.73577 −0.490531
\(59\) 10.0208 1.30459 0.652296 0.757964i \(-0.273806\pi\)
0.652296 + 0.757964i \(0.273806\pi\)
\(60\) 0.0265317 0.00342523
\(61\) −5.26917 −0.674648 −0.337324 0.941389i \(-0.609522\pi\)
−0.337324 + 0.941389i \(0.609522\pi\)
\(62\) 2.55403 0.324362
\(63\) −10.2610 −1.29276
\(64\) 2.15037 0.268797
\(65\) −0.205702 −0.0255142
\(66\) −6.15145 −0.757191
\(67\) −0.395036 −0.0482613 −0.0241307 0.999709i \(-0.507682\pi\)
−0.0241307 + 0.999709i \(0.507682\pi\)
\(68\) 0.0363686 0.00441035
\(69\) −2.47715 −0.298214
\(70\) 0.316628 0.0378443
\(71\) 2.82311 0.335041 0.167521 0.985869i \(-0.446424\pi\)
0.167521 + 0.985869i \(0.446424\pi\)
\(72\) −4.93572 −0.581681
\(73\) 3.30543 0.386871 0.193436 0.981113i \(-0.438037\pi\)
0.193436 + 0.981113i \(0.438037\pi\)
\(74\) −3.78845 −0.440398
\(75\) 3.24510 0.374712
\(76\) 0.870061 0.0998028
\(77\) −22.2546 −2.53615
\(78\) 4.81802 0.545533
\(79\) −1.69175 −0.190336 −0.0951682 0.995461i \(-0.530339\pi\)
−0.0951682 + 0.995461i \(0.530339\pi\)
\(80\) 0.234027 0.0261651
\(81\) 5.38335 0.598150
\(82\) −2.00189 −0.221072
\(83\) −12.4114 −1.36232 −0.681162 0.732133i \(-0.738525\pi\)
−0.681162 + 0.732133i \(0.738525\pi\)
\(84\) −2.24822 −0.245301
\(85\) −0.00196310 −0.000212928 0
\(86\) 12.5617 1.35457
\(87\) −1.43181 −0.153506
\(88\) −10.7049 −1.14114
\(89\) −3.52728 −0.373891 −0.186946 0.982370i \(-0.559859\pi\)
−0.186946 + 0.982370i \(0.559859\pi\)
\(90\) −0.205145 −0.0216242
\(91\) 17.4305 1.82722
\(92\) 3.31935 0.346066
\(93\) 0.978881 0.101505
\(94\) 16.9237 1.74554
\(95\) −0.0469641 −0.00481841
\(96\) −2.99558 −0.305735
\(97\) 12.5900 1.27832 0.639158 0.769075i \(-0.279283\pi\)
0.639158 + 0.769075i \(0.279283\pi\)
\(98\) −14.9713 −1.51232
\(99\) 14.4189 1.44915
\(100\) −4.34839 −0.434839
\(101\) −13.7879 −1.37195 −0.685974 0.727626i \(-0.740623\pi\)
−0.685974 + 0.727626i \(0.740623\pi\)
\(102\) 0.0459805 0.00455274
\(103\) 9.21485 0.907966 0.453983 0.891010i \(-0.350003\pi\)
0.453983 + 0.891010i \(0.350003\pi\)
\(104\) 8.38442 0.822160
\(105\) 0.121354 0.0118430
\(106\) 19.2247 1.86726
\(107\) −2.88604 −0.279004 −0.139502 0.990222i \(-0.544550\pi\)
−0.139502 + 0.990222i \(0.544550\pi\)
\(108\) 3.15144 0.303248
\(109\) −4.00971 −0.384061 −0.192030 0.981389i \(-0.561507\pi\)
−0.192030 + 0.981389i \(0.561507\pi\)
\(110\) −0.444931 −0.0424225
\(111\) −1.45200 −0.137817
\(112\) −19.8308 −1.87383
\(113\) −9.39425 −0.883737 −0.441869 0.897080i \(-0.645684\pi\)
−0.441869 + 0.897080i \(0.645684\pi\)
\(114\) 1.10001 0.103025
\(115\) −0.179171 −0.0167078
\(116\) 1.91860 0.178138
\(117\) −11.2933 −1.04407
\(118\) −16.9764 −1.56281
\(119\) 0.166347 0.0152490
\(120\) 0.0583736 0.00532876
\(121\) 20.2725 1.84296
\(122\) 8.92664 0.808180
\(123\) −0.767266 −0.0691820
\(124\) −1.31168 −0.117793
\(125\) 0.469537 0.0419967
\(126\) 17.3834 1.54864
\(127\) −1.34897 −0.119702 −0.0598508 0.998207i \(-0.519063\pi\)
−0.0598508 + 0.998207i \(0.519063\pi\)
\(128\) −12.8700 −1.13756
\(129\) 4.81454 0.423896
\(130\) 0.348485 0.0305641
\(131\) 11.3864 0.994831 0.497416 0.867512i \(-0.334282\pi\)
0.497416 + 0.867512i \(0.334282\pi\)
\(132\) 3.15923 0.274976
\(133\) 3.97959 0.345074
\(134\) 0.669241 0.0578136
\(135\) −0.170108 −0.0146406
\(136\) 0.0800162 0.00686133
\(137\) −2.44545 −0.208929 −0.104465 0.994529i \(-0.533313\pi\)
−0.104465 + 0.994529i \(0.533313\pi\)
\(138\) 4.19661 0.357239
\(139\) 6.69864 0.568171 0.284086 0.958799i \(-0.408310\pi\)
0.284086 + 0.958799i \(0.408310\pi\)
\(140\) −0.162612 −0.0137433
\(141\) 6.48634 0.546248
\(142\) −4.78270 −0.401355
\(143\) −24.4937 −2.04826
\(144\) 12.8485 1.07071
\(145\) −0.103562 −0.00860036
\(146\) −5.59981 −0.463443
\(147\) −5.73803 −0.473265
\(148\) 1.94565 0.159932
\(149\) 5.75888 0.471786 0.235893 0.971779i \(-0.424199\pi\)
0.235893 + 0.971779i \(0.424199\pi\)
\(150\) −5.49761 −0.448878
\(151\) 3.03478 0.246967 0.123484 0.992347i \(-0.460593\pi\)
0.123484 + 0.992347i \(0.460593\pi\)
\(152\) 1.91426 0.155267
\(153\) −0.107777 −0.00871329
\(154\) 37.7021 3.03812
\(155\) 0.0708020 0.00568695
\(156\) −2.47441 −0.198112
\(157\) 19.1663 1.52964 0.764819 0.644245i \(-0.222828\pi\)
0.764819 + 0.644245i \(0.222828\pi\)
\(158\) 2.86603 0.228009
\(159\) 7.36824 0.584339
\(160\) −0.216669 −0.0171292
\(161\) 15.1824 1.19654
\(162\) −9.12006 −0.716540
\(163\) 10.7188 0.839559 0.419780 0.907626i \(-0.362107\pi\)
0.419780 + 0.907626i \(0.362107\pi\)
\(164\) 1.02812 0.0802829
\(165\) −0.170529 −0.0132756
\(166\) 21.0264 1.63197
\(167\) 0.0602231 0.00466020 0.00233010 0.999997i \(-0.499258\pi\)
0.00233010 + 0.999997i \(0.499258\pi\)
\(168\) −4.94640 −0.381623
\(169\) 6.18425 0.475711
\(170\) 0.00332574 0.000255073 0
\(171\) −2.57840 −0.197175
\(172\) −6.45140 −0.491915
\(173\) 6.97111 0.530004 0.265002 0.964248i \(-0.414627\pi\)
0.265002 + 0.964248i \(0.414627\pi\)
\(174\) 2.42567 0.183889
\(175\) −19.8892 −1.50348
\(176\) 27.8665 2.10052
\(177\) −6.50656 −0.489063
\(178\) 5.97566 0.447895
\(179\) −15.8642 −1.18575 −0.592875 0.805295i \(-0.702007\pi\)
−0.592875 + 0.805295i \(0.702007\pi\)
\(180\) 0.105358 0.00785289
\(181\) 6.35385 0.472278 0.236139 0.971719i \(-0.424118\pi\)
0.236139 + 0.971719i \(0.424118\pi\)
\(182\) −29.5295 −2.18887
\(183\) 3.42131 0.252911
\(184\) 7.30303 0.538387
\(185\) −0.105022 −0.00772139
\(186\) −1.65835 −0.121596
\(187\) −0.233754 −0.0170938
\(188\) −8.69158 −0.633899
\(189\) 14.4145 1.04850
\(190\) 0.0795630 0.00577211
\(191\) −26.6079 −1.92528 −0.962638 0.270791i \(-0.912715\pi\)
−0.962638 + 0.270791i \(0.912715\pi\)
\(192\) −1.39625 −0.100766
\(193\) −5.31613 −0.382664 −0.191332 0.981525i \(-0.561281\pi\)
−0.191332 + 0.981525i \(0.561281\pi\)
\(194\) −21.3290 −1.53133
\(195\) 0.133564 0.00956469
\(196\) 7.68886 0.549205
\(197\) 25.0274 1.78313 0.891565 0.452893i \(-0.149608\pi\)
0.891565 + 0.452893i \(0.149608\pi\)
\(198\) −24.4274 −1.73598
\(199\) −14.6298 −1.03708 −0.518538 0.855054i \(-0.673524\pi\)
−0.518538 + 0.855054i \(0.673524\pi\)
\(200\) −9.56707 −0.676494
\(201\) 0.256500 0.0180921
\(202\) 23.3584 1.64349
\(203\) 8.77553 0.615922
\(204\) −0.0236144 −0.00165334
\(205\) −0.0554959 −0.00387600
\(206\) −15.6111 −1.08768
\(207\) −9.83678 −0.683704
\(208\) −21.8260 −1.51336
\(209\) −5.59218 −0.386819
\(210\) −0.205589 −0.0141870
\(211\) 1.00000 0.0688428
\(212\) −9.87331 −0.678102
\(213\) −1.83306 −0.125599
\(214\) 4.88932 0.334227
\(215\) 0.348233 0.0237493
\(216\) 6.93363 0.471774
\(217\) −5.99955 −0.407276
\(218\) 6.79295 0.460077
\(219\) −2.14624 −0.145029
\(220\) 0.228506 0.0154058
\(221\) 0.183084 0.0123155
\(222\) 2.45987 0.165095
\(223\) −18.2330 −1.22098 −0.610488 0.792026i \(-0.709026\pi\)
−0.610488 + 0.792026i \(0.709026\pi\)
\(224\) 18.3599 1.22672
\(225\) 12.8863 0.859088
\(226\) 15.9150 1.05865
\(227\) −6.13636 −0.407285 −0.203642 0.979045i \(-0.565278\pi\)
−0.203642 + 0.979045i \(0.565278\pi\)
\(228\) −0.564937 −0.0374139
\(229\) 0.785484 0.0519062 0.0259531 0.999663i \(-0.491738\pi\)
0.0259531 + 0.999663i \(0.491738\pi\)
\(230\) 0.303539 0.0200147
\(231\) 14.4501 0.950746
\(232\) 4.22120 0.277135
\(233\) −9.74435 −0.638374 −0.319187 0.947692i \(-0.603410\pi\)
−0.319187 + 0.947692i \(0.603410\pi\)
\(234\) 19.1323 1.25072
\(235\) 0.469153 0.0306042
\(236\) 8.71867 0.567537
\(237\) 1.09846 0.0713529
\(238\) −0.281813 −0.0182672
\(239\) −24.5938 −1.59084 −0.795422 0.606056i \(-0.792751\pi\)
−0.795422 + 0.606056i \(0.792751\pi\)
\(240\) −0.151956 −0.00980870
\(241\) −24.7850 −1.59654 −0.798272 0.602297i \(-0.794252\pi\)
−0.798272 + 0.602297i \(0.794252\pi\)
\(242\) −34.3442 −2.20773
\(243\) −14.3617 −0.921306
\(244\) −4.58450 −0.293493
\(245\) −0.415029 −0.0265152
\(246\) 1.29984 0.0828751
\(247\) 4.37998 0.278692
\(248\) −2.88589 −0.183254
\(249\) 8.05879 0.510705
\(250\) −0.795455 −0.0503090
\(251\) −5.49044 −0.346553 −0.173277 0.984873i \(-0.555435\pi\)
−0.173277 + 0.984873i \(0.555435\pi\)
\(252\) −8.92768 −0.562391
\(253\) −21.3346 −1.34129
\(254\) 2.28532 0.143394
\(255\) 0.00127466 7.98221e−5 0
\(256\) 17.5027 1.09392
\(257\) −24.1694 −1.50764 −0.753822 0.657079i \(-0.771792\pi\)
−0.753822 + 0.657079i \(0.771792\pi\)
\(258\) −8.15643 −0.507797
\(259\) 8.89926 0.552973
\(260\) −0.178973 −0.0110994
\(261\) −5.68572 −0.351937
\(262\) −19.2899 −1.19174
\(263\) −12.7144 −0.784001 −0.392001 0.919965i \(-0.628217\pi\)
−0.392001 + 0.919965i \(0.628217\pi\)
\(264\) 6.95076 0.427790
\(265\) 0.532941 0.0327383
\(266\) −6.74193 −0.413374
\(267\) 2.29029 0.140164
\(268\) −0.343705 −0.0209952
\(269\) −8.39307 −0.511735 −0.255867 0.966712i \(-0.582361\pi\)
−0.255867 + 0.966712i \(0.582361\pi\)
\(270\) 0.288185 0.0175384
\(271\) 23.8246 1.44724 0.723620 0.690199i \(-0.242477\pi\)
0.723620 + 0.690199i \(0.242477\pi\)
\(272\) −0.208295 −0.0126297
\(273\) −11.3178 −0.684983
\(274\) 4.14290 0.250282
\(275\) 27.9486 1.68536
\(276\) −2.15528 −0.129732
\(277\) 0.490616 0.0294783 0.0147391 0.999891i \(-0.495308\pi\)
0.0147391 + 0.999891i \(0.495308\pi\)
\(278\) −11.3483 −0.680628
\(279\) 3.88714 0.232717
\(280\) −0.357771 −0.0213809
\(281\) −1.91950 −0.114508 −0.0572539 0.998360i \(-0.518234\pi\)
−0.0572539 + 0.998360i \(0.518234\pi\)
\(282\) −10.9887 −0.654366
\(283\) 3.13947 0.186622 0.0933110 0.995637i \(-0.470255\pi\)
0.0933110 + 0.995637i \(0.470255\pi\)
\(284\) 2.45628 0.145753
\(285\) 0.0304941 0.00180632
\(286\) 41.4953 2.45367
\(287\) 4.70256 0.277583
\(288\) −11.8955 −0.700947
\(289\) −16.9983 −0.999897
\(290\) 0.175447 0.0103026
\(291\) −8.17475 −0.479212
\(292\) 2.87592 0.168301
\(293\) 22.5970 1.32013 0.660067 0.751207i \(-0.270528\pi\)
0.660067 + 0.751207i \(0.270528\pi\)
\(294\) 9.72094 0.566937
\(295\) −0.470616 −0.0274003
\(296\) 4.28071 0.248811
\(297\) −20.2554 −1.17534
\(298\) −9.75627 −0.565165
\(299\) 16.7100 0.966361
\(300\) 2.82344 0.163011
\(301\) −29.5082 −1.70082
\(302\) −5.14130 −0.295849
\(303\) 8.95258 0.514313
\(304\) −4.98312 −0.285801
\(305\) 0.247462 0.0141696
\(306\) 0.182588 0.0104379
\(307\) −31.2785 −1.78516 −0.892580 0.450888i \(-0.851107\pi\)
−0.892580 + 0.450888i \(0.851107\pi\)
\(308\) −19.3629 −1.10330
\(309\) −5.98327 −0.340376
\(310\) −0.119947 −0.00681256
\(311\) −8.01458 −0.454465 −0.227232 0.973841i \(-0.572968\pi\)
−0.227232 + 0.973841i \(0.572968\pi\)
\(312\) −5.44407 −0.308209
\(313\) −30.1947 −1.70670 −0.853352 0.521335i \(-0.825434\pi\)
−0.853352 + 0.521335i \(0.825434\pi\)
\(314\) −32.4701 −1.83240
\(315\) 0.481897 0.0271518
\(316\) −1.47192 −0.0828021
\(317\) −18.6900 −1.04973 −0.524866 0.851185i \(-0.675885\pi\)
−0.524866 + 0.851185i \(0.675885\pi\)
\(318\) −12.4827 −0.699996
\(319\) −12.3315 −0.690432
\(320\) −0.100990 −0.00564553
\(321\) 1.87393 0.104593
\(322\) −25.7209 −1.43337
\(323\) 0.0418001 0.00232582
\(324\) 4.68384 0.260213
\(325\) −21.8903 −1.21425
\(326\) −18.1590 −1.00573
\(327\) 2.60353 0.143976
\(328\) 2.26202 0.124899
\(329\) −39.7546 −2.19174
\(330\) 0.288897 0.0159033
\(331\) 25.0126 1.37482 0.687409 0.726270i \(-0.258748\pi\)
0.687409 + 0.726270i \(0.258748\pi\)
\(332\) −10.7986 −0.592653
\(333\) −5.76588 −0.315968
\(334\) −0.102025 −0.00558258
\(335\) 0.0185525 0.00101363
\(336\) 12.8763 0.702458
\(337\) −4.69437 −0.255719 −0.127859 0.991792i \(-0.540811\pi\)
−0.127859 + 0.991792i \(0.540811\pi\)
\(338\) −10.4769 −0.569868
\(339\) 6.09976 0.331293
\(340\) −0.00170802 −9.26303e−5 0
\(341\) 8.43065 0.456545
\(342\) 4.36813 0.236202
\(343\) 7.31114 0.394764
\(344\) −14.1940 −0.765289
\(345\) 0.116337 0.00626339
\(346\) −11.8099 −0.634906
\(347\) −1.44912 −0.0777927 −0.0388963 0.999243i \(-0.512384\pi\)
−0.0388963 + 0.999243i \(0.512384\pi\)
\(348\) −1.24576 −0.0667798
\(349\) 14.1974 0.759968 0.379984 0.924993i \(-0.375929\pi\)
0.379984 + 0.924993i \(0.375929\pi\)
\(350\) 33.6948 1.80106
\(351\) 15.8647 0.846796
\(352\) −25.7996 −1.37512
\(353\) −3.09965 −0.164978 −0.0824889 0.996592i \(-0.526287\pi\)
−0.0824889 + 0.996592i \(0.526287\pi\)
\(354\) 11.0229 0.585862
\(355\) −0.132585 −0.00703686
\(356\) −3.06895 −0.162654
\(357\) −0.108011 −0.00571653
\(358\) 26.8760 1.42044
\(359\) 12.0498 0.635963 0.317982 0.948097i \(-0.396995\pi\)
0.317982 + 0.948097i \(0.396995\pi\)
\(360\) 0.231802 0.0122170
\(361\) 1.00000 0.0526316
\(362\) −10.7642 −0.565755
\(363\) −13.1631 −0.690883
\(364\) 15.1656 0.794895
\(365\) −0.155236 −0.00812544
\(366\) −5.79613 −0.302969
\(367\) −2.02994 −0.105962 −0.0529810 0.998596i \(-0.516872\pi\)
−0.0529810 + 0.998596i \(0.516872\pi\)
\(368\) −19.0109 −0.991014
\(369\) −3.04681 −0.158611
\(370\) 0.177921 0.00924966
\(371\) −45.1598 −2.34458
\(372\) 0.851686 0.0441579
\(373\) −25.2477 −1.30728 −0.653639 0.756807i \(-0.726758\pi\)
−0.653639 + 0.756807i \(0.726758\pi\)
\(374\) 0.396008 0.0204771
\(375\) −0.304874 −0.0157436
\(376\) −19.1227 −0.986180
\(377\) 9.65845 0.497435
\(378\) −24.4199 −1.25602
\(379\) 14.8010 0.760278 0.380139 0.924929i \(-0.375876\pi\)
0.380139 + 0.924929i \(0.375876\pi\)
\(380\) −0.0408616 −0.00209616
\(381\) 0.875896 0.0448735
\(382\) 45.0770 2.30634
\(383\) −22.9268 −1.17150 −0.585752 0.810491i \(-0.699201\pi\)
−0.585752 + 0.810491i \(0.699201\pi\)
\(384\) 8.35660 0.426446
\(385\) 1.04517 0.0532666
\(386\) 9.00620 0.458403
\(387\) 19.1185 0.971850
\(388\) 10.9540 0.556106
\(389\) 14.0991 0.714852 0.357426 0.933941i \(-0.383654\pi\)
0.357426 + 0.933941i \(0.383654\pi\)
\(390\) −0.226274 −0.0114578
\(391\) 0.159470 0.00806477
\(392\) 16.9166 0.854417
\(393\) −7.39325 −0.372940
\(394\) −42.3996 −2.13606
\(395\) 0.0794513 0.00399763
\(396\) 12.5453 0.630425
\(397\) −26.1372 −1.31179 −0.655894 0.754853i \(-0.727708\pi\)
−0.655894 + 0.754853i \(0.727708\pi\)
\(398\) 24.7847 1.24234
\(399\) −2.58398 −0.129361
\(400\) 24.9046 1.24523
\(401\) −14.1607 −0.707151 −0.353576 0.935406i \(-0.615034\pi\)
−0.353576 + 0.935406i \(0.615034\pi\)
\(402\) −0.434543 −0.0216730
\(403\) −6.60317 −0.328927
\(404\) −11.9963 −0.596839
\(405\) −0.252824 −0.0125629
\(406\) −14.8669 −0.737830
\(407\) −12.5054 −0.619869
\(408\) −0.0519551 −0.00257216
\(409\) −22.3803 −1.10663 −0.553316 0.832971i \(-0.686638\pi\)
−0.553316 + 0.832971i \(0.686638\pi\)
\(410\) 0.0940171 0.00464317
\(411\) 1.58785 0.0783229
\(412\) 8.01748 0.394993
\(413\) 39.8786 1.96230
\(414\) 16.6647 0.819027
\(415\) 0.582888 0.0286129
\(416\) 20.2071 0.990733
\(417\) −4.34948 −0.212995
\(418\) 9.47386 0.463382
\(419\) −21.3786 −1.04441 −0.522206 0.852819i \(-0.674891\pi\)
−0.522206 + 0.852819i \(0.674891\pi\)
\(420\) 0.105585 0.00515204
\(421\) −24.4088 −1.18961 −0.594807 0.803869i \(-0.702771\pi\)
−0.594807 + 0.803869i \(0.702771\pi\)
\(422\) −1.69413 −0.0824687
\(423\) 25.7573 1.25236
\(424\) −21.7227 −1.05495
\(425\) −0.208908 −0.0101335
\(426\) 3.10544 0.150459
\(427\) −20.9692 −1.01477
\(428\) −2.51103 −0.121375
\(429\) 15.9039 0.767848
\(430\) −0.589950 −0.0284499
\(431\) 13.6747 0.658688 0.329344 0.944210i \(-0.393172\pi\)
0.329344 + 0.944210i \(0.393172\pi\)
\(432\) −18.0493 −0.868399
\(433\) 29.6189 1.42339 0.711697 0.702487i \(-0.247927\pi\)
0.711697 + 0.702487i \(0.247927\pi\)
\(434\) 10.1640 0.487887
\(435\) 0.0672436 0.00322408
\(436\) −3.48869 −0.167078
\(437\) 3.81507 0.182500
\(438\) 3.63600 0.173735
\(439\) 0.515975 0.0246261 0.0123131 0.999924i \(-0.496081\pi\)
0.0123131 + 0.999924i \(0.496081\pi\)
\(440\) 0.502745 0.0239674
\(441\) −22.7857 −1.08503
\(442\) −0.310167 −0.0147531
\(443\) 13.8425 0.657677 0.328839 0.944386i \(-0.393343\pi\)
0.328839 + 0.944386i \(0.393343\pi\)
\(444\) −1.26333 −0.0599548
\(445\) 0.165656 0.00785283
\(446\) 30.8891 1.46264
\(447\) −3.73928 −0.176862
\(448\) 8.55761 0.404309
\(449\) 5.47108 0.258196 0.129098 0.991632i \(-0.458792\pi\)
0.129098 + 0.991632i \(0.458792\pi\)
\(450\) −21.8310 −1.02912
\(451\) −6.60810 −0.311163
\(452\) −8.17357 −0.384453
\(453\) −1.97051 −0.0925825
\(454\) 10.3958 0.487897
\(455\) −0.818609 −0.0383770
\(456\) −1.24294 −0.0582061
\(457\) −26.0373 −1.21797 −0.608987 0.793180i \(-0.708424\pi\)
−0.608987 + 0.793180i \(0.708424\pi\)
\(458\) −1.33071 −0.0621799
\(459\) 0.151404 0.00706693
\(460\) −0.155890 −0.00726841
\(461\) 5.99343 0.279142 0.139571 0.990212i \(-0.455428\pi\)
0.139571 + 0.990212i \(0.455428\pi\)
\(462\) −24.4803 −1.13892
\(463\) 0.921382 0.0428202 0.0214101 0.999771i \(-0.493184\pi\)
0.0214101 + 0.999771i \(0.493184\pi\)
\(464\) −10.9884 −0.510125
\(465\) −0.0459722 −0.00213191
\(466\) 16.5082 0.764725
\(467\) −33.1359 −1.53335 −0.766674 0.642037i \(-0.778090\pi\)
−0.766674 + 0.642037i \(0.778090\pi\)
\(468\) −9.82590 −0.454202
\(469\) −1.57208 −0.0725920
\(470\) −0.794805 −0.0366616
\(471\) −12.4448 −0.573427
\(472\) 19.1823 0.882938
\(473\) 41.4654 1.90658
\(474\) −1.86094 −0.0854756
\(475\) −4.99779 −0.229315
\(476\) 0.144732 0.00663380
\(477\) 29.2593 1.33969
\(478\) 41.6651 1.90572
\(479\) 9.55220 0.436451 0.218226 0.975898i \(-0.429973\pi\)
0.218226 + 0.975898i \(0.429973\pi\)
\(480\) 0.140685 0.00642135
\(481\) 9.79463 0.446597
\(482\) 41.9889 1.91254
\(483\) −9.85807 −0.448558
\(484\) 17.6383 0.801742
\(485\) −0.591275 −0.0268484
\(486\) 24.3306 1.10366
\(487\) 27.3831 1.24085 0.620423 0.784267i \(-0.286961\pi\)
0.620423 + 0.784267i \(0.286961\pi\)
\(488\) −10.0866 −0.456597
\(489\) −6.95978 −0.314732
\(490\) 0.703111 0.0317633
\(491\) 7.24260 0.326854 0.163427 0.986555i \(-0.447745\pi\)
0.163427 + 0.986555i \(0.447745\pi\)
\(492\) −0.667568 −0.0300963
\(493\) 0.0921748 0.00415135
\(494\) −7.42024 −0.333852
\(495\) −0.677169 −0.0304365
\(496\) 7.51244 0.337318
\(497\) 11.2348 0.503950
\(498\) −13.6526 −0.611788
\(499\) −9.02606 −0.404062 −0.202031 0.979379i \(-0.564754\pi\)
−0.202031 + 0.979379i \(0.564754\pi\)
\(500\) 0.408526 0.0182698
\(501\) −0.0391033 −0.00174701
\(502\) 9.30149 0.415146
\(503\) 8.98411 0.400582 0.200291 0.979736i \(-0.435811\pi\)
0.200291 + 0.979736i \(0.435811\pi\)
\(504\) −19.6422 −0.874932
\(505\) 0.647536 0.0288150
\(506\) 36.1435 1.60677
\(507\) −4.01548 −0.178334
\(508\) −1.17369 −0.0520739
\(509\) −27.4140 −1.21510 −0.607551 0.794281i \(-0.707848\pi\)
−0.607551 + 0.794281i \(0.707848\pi\)
\(510\) −0.00215943 −9.56211e−5 0
\(511\) 13.1543 0.581910
\(512\) −3.91169 −0.172874
\(513\) 3.62210 0.159919
\(514\) 40.9459 1.80605
\(515\) −0.432767 −0.0190700
\(516\) 4.18894 0.184408
\(517\) 55.8638 2.45689
\(518\) −15.0765 −0.662422
\(519\) −4.52640 −0.198687
\(520\) −0.393766 −0.0172678
\(521\) −23.0462 −1.00967 −0.504836 0.863215i \(-0.668447\pi\)
−0.504836 + 0.863215i \(0.668447\pi\)
\(522\) 9.63232 0.421595
\(523\) 7.81240 0.341612 0.170806 0.985305i \(-0.445363\pi\)
0.170806 + 0.985305i \(0.445363\pi\)
\(524\) 9.90683 0.432782
\(525\) 12.9142 0.563622
\(526\) 21.5397 0.939177
\(527\) −0.0630169 −0.00274506
\(528\) −18.0939 −0.787437
\(529\) −8.44522 −0.367184
\(530\) −0.902868 −0.0392181
\(531\) −25.8375 −1.12125
\(532\) 3.46249 0.150118
\(533\) 5.17569 0.224184
\(534\) −3.88004 −0.167906
\(535\) 0.135540 0.00585992
\(536\) −0.756201 −0.0326629
\(537\) 10.3008 0.444511
\(538\) 14.2189 0.613021
\(539\) −49.4190 −2.12863
\(540\) −0.148005 −0.00636910
\(541\) 5.86306 0.252072 0.126036 0.992026i \(-0.459774\pi\)
0.126036 + 0.992026i \(0.459774\pi\)
\(542\) −40.3618 −1.73369
\(543\) −4.12560 −0.177046
\(544\) 0.192845 0.00826816
\(545\) 0.188312 0.00806641
\(546\) 19.1737 0.820560
\(547\) −32.4104 −1.38577 −0.692885 0.721048i \(-0.743661\pi\)
−0.692885 + 0.721048i \(0.743661\pi\)
\(548\) −2.12769 −0.0908905
\(549\) 13.5860 0.579838
\(550\) −47.3484 −2.01894
\(551\) 2.20513 0.0939419
\(552\) −4.74191 −0.201829
\(553\) −6.73246 −0.286294
\(554\) −0.831165 −0.0353128
\(555\) 0.0681917 0.00289458
\(556\) 5.82822 0.247172
\(557\) −7.69091 −0.325874 −0.162937 0.986636i \(-0.552097\pi\)
−0.162937 + 0.986636i \(0.552097\pi\)
\(558\) −6.58530 −0.278778
\(559\) −32.4771 −1.37363
\(560\) 0.931334 0.0393560
\(561\) 0.151778 0.00640808
\(562\) 3.25187 0.137172
\(563\) 18.5397 0.781354 0.390677 0.920528i \(-0.372241\pi\)
0.390677 + 0.920528i \(0.372241\pi\)
\(564\) 5.64351 0.237635
\(565\) 0.441192 0.0185611
\(566\) −5.31865 −0.223560
\(567\) 21.4235 0.899703
\(568\) 5.40416 0.226753
\(569\) 22.0856 0.925877 0.462938 0.886390i \(-0.346795\pi\)
0.462938 + 0.886390i \(0.346795\pi\)
\(570\) −0.0516608 −0.00216383
\(571\) −33.7721 −1.41332 −0.706659 0.707554i \(-0.749798\pi\)
−0.706659 + 0.707554i \(0.749798\pi\)
\(572\) −21.3110 −0.891057
\(573\) 17.2767 0.721743
\(574\) −7.96672 −0.332525
\(575\) −19.0669 −0.795147
\(576\) −5.54452 −0.231022
\(577\) −0.378368 −0.0157517 −0.00787584 0.999969i \(-0.502507\pi\)
−0.00787584 + 0.999969i \(0.502507\pi\)
\(578\) 28.7972 1.19780
\(579\) 3.45180 0.143452
\(580\) −0.0901053 −0.00374142
\(581\) −49.3922 −2.04913
\(582\) 13.8490 0.574062
\(583\) 63.4592 2.62821
\(584\) 6.32744 0.261831
\(585\) 0.530381 0.0219286
\(586\) −38.2822 −1.58142
\(587\) −41.4042 −1.70893 −0.854467 0.519505i \(-0.826116\pi\)
−0.854467 + 0.519505i \(0.826116\pi\)
\(588\) −4.99244 −0.205885
\(589\) −1.50758 −0.0621187
\(590\) 0.797282 0.0328236
\(591\) −16.2505 −0.668456
\(592\) −11.1434 −0.457990
\(593\) −19.4339 −0.798054 −0.399027 0.916939i \(-0.630652\pi\)
−0.399027 + 0.916939i \(0.630652\pi\)
\(594\) 34.3152 1.40797
\(595\) −0.00781235 −0.000320275 0
\(596\) 5.01058 0.205241
\(597\) 9.49921 0.388777
\(598\) −28.3088 −1.15763
\(599\) −2.27832 −0.0930898 −0.0465449 0.998916i \(-0.514821\pi\)
−0.0465449 + 0.998916i \(0.514821\pi\)
\(600\) 6.21197 0.253603
\(601\) 23.2388 0.947929 0.473964 0.880544i \(-0.342823\pi\)
0.473964 + 0.880544i \(0.342823\pi\)
\(602\) 49.9906 2.03747
\(603\) 1.01856 0.0414790
\(604\) 2.64045 0.107438
\(605\) −0.952080 −0.0387075
\(606\) −15.1668 −0.616109
\(607\) 18.5306 0.752135 0.376067 0.926592i \(-0.377276\pi\)
0.376067 + 0.926592i \(0.377276\pi\)
\(608\) 4.61351 0.187102
\(609\) −5.69802 −0.230895
\(610\) −0.419231 −0.0169742
\(611\) −43.7544 −1.77011
\(612\) −0.0937729 −0.00379054
\(613\) −10.0127 −0.404409 −0.202204 0.979343i \(-0.564811\pi\)
−0.202204 + 0.979343i \(0.564811\pi\)
\(614\) 52.9898 2.13849
\(615\) 0.0360339 0.00145303
\(616\) −42.6011 −1.71645
\(617\) 4.34970 0.175112 0.0875562 0.996160i \(-0.472094\pi\)
0.0875562 + 0.996160i \(0.472094\pi\)
\(618\) 10.1364 0.407746
\(619\) −37.9140 −1.52389 −0.761946 0.647641i \(-0.775756\pi\)
−0.761946 + 0.647641i \(0.775756\pi\)
\(620\) 0.0616020 0.00247400
\(621\) 13.8186 0.554520
\(622\) 13.5777 0.544416
\(623\) −14.0372 −0.562387
\(624\) 14.1718 0.567324
\(625\) 24.9669 0.998677
\(626\) 51.1536 2.04451
\(627\) 3.63105 0.145010
\(628\) 16.6759 0.665439
\(629\) 0.0934744 0.00372707
\(630\) −0.816395 −0.0325259
\(631\) −32.0592 −1.27626 −0.638128 0.769931i \(-0.720291\pi\)
−0.638128 + 0.769931i \(0.720291\pi\)
\(632\) −3.23844 −0.128818
\(633\) −0.649307 −0.0258077
\(634\) 31.6631 1.25750
\(635\) 0.0633531 0.00251409
\(636\) 6.41082 0.254205
\(637\) 38.7066 1.53361
\(638\) 20.8911 0.827088
\(639\) −7.27910 −0.287957
\(640\) 0.604428 0.0238921
\(641\) −15.2515 −0.602399 −0.301199 0.953561i \(-0.597387\pi\)
−0.301199 + 0.953561i \(0.597387\pi\)
\(642\) −3.17467 −0.125294
\(643\) 22.4121 0.883846 0.441923 0.897053i \(-0.354296\pi\)
0.441923 + 0.897053i \(0.354296\pi\)
\(644\) 13.2096 0.520533
\(645\) −0.226110 −0.00890308
\(646\) −0.0708146 −0.00278616
\(647\) −7.31327 −0.287514 −0.143757 0.989613i \(-0.545918\pi\)
−0.143757 + 0.989613i \(0.545918\pi\)
\(648\) 10.3051 0.404823
\(649\) −56.0379 −2.19968
\(650\) 37.0848 1.45459
\(651\) 3.89555 0.152679
\(652\) 9.32599 0.365234
\(653\) 24.7168 0.967244 0.483622 0.875277i \(-0.339321\pi\)
0.483622 + 0.875277i \(0.339321\pi\)
\(654\) −4.41071 −0.172473
\(655\) −0.534750 −0.0208944
\(656\) −5.88839 −0.229903
\(657\) −8.52271 −0.332503
\(658\) 67.3494 2.62555
\(659\) 36.6580 1.42799 0.713997 0.700149i \(-0.246883\pi\)
0.713997 + 0.700149i \(0.246883\pi\)
\(660\) −0.148370 −0.00577531
\(661\) −28.1898 −1.09645 −0.548227 0.836329i \(-0.684697\pi\)
−0.548227 + 0.836329i \(0.684697\pi\)
\(662\) −42.3745 −1.64693
\(663\) −0.118878 −0.00461682
\(664\) −23.7586 −0.922011
\(665\) −0.186898 −0.00724759
\(666\) 9.76813 0.378507
\(667\) 8.41275 0.325743
\(668\) 0.0523977 0.00202733
\(669\) 11.8389 0.457716
\(670\) −0.0314303 −0.00121426
\(671\) 29.4662 1.13753
\(672\) −11.9212 −0.459870
\(673\) 0.223753 0.00862506 0.00431253 0.999991i \(-0.498627\pi\)
0.00431253 + 0.999991i \(0.498627\pi\)
\(674\) 7.95285 0.306332
\(675\) −18.1025 −0.696765
\(676\) 5.38067 0.206949
\(677\) −51.3445 −1.97333 −0.986665 0.162762i \(-0.947960\pi\)
−0.986665 + 0.162762i \(0.947960\pi\)
\(678\) −10.3338 −0.396865
\(679\) 50.1029 1.92277
\(680\) −0.00375789 −0.000144108 0
\(681\) 3.98438 0.152682
\(682\) −14.2826 −0.546908
\(683\) 4.55170 0.174166 0.0870831 0.996201i \(-0.472245\pi\)
0.0870831 + 0.996201i \(0.472245\pi\)
\(684\) −2.24336 −0.0857772
\(685\) 0.114848 0.00438813
\(686\) −12.3860 −0.472899
\(687\) −0.510020 −0.0194585
\(688\) 36.9492 1.40868
\(689\) −49.7034 −1.89355
\(690\) −0.197090 −0.00750308
\(691\) 1.70657 0.0649210 0.0324605 0.999473i \(-0.489666\pi\)
0.0324605 + 0.999473i \(0.489666\pi\)
\(692\) 6.06529 0.230568
\(693\) 57.3813 2.17973
\(694\) 2.45499 0.0931900
\(695\) −0.314595 −0.0119333
\(696\) −2.74085 −0.103892
\(697\) 0.0493939 0.00187093
\(698\) −24.0521 −0.910387
\(699\) 6.32708 0.239312
\(700\) −17.3048 −0.654060
\(701\) 0.850966 0.0321405 0.0160703 0.999871i \(-0.494884\pi\)
0.0160703 + 0.999871i \(0.494884\pi\)
\(702\) −26.8768 −1.01440
\(703\) 2.23622 0.0843408
\(704\) −12.0253 −0.453220
\(705\) −0.304625 −0.0114728
\(706\) 5.25120 0.197632
\(707\) −54.8702 −2.06361
\(708\) −5.66110 −0.212757
\(709\) 34.8616 1.30925 0.654627 0.755952i \(-0.272826\pi\)
0.654627 + 0.755952i \(0.272826\pi\)
\(710\) 0.224615 0.00842965
\(711\) 4.36200 0.163588
\(712\) −6.75213 −0.253047
\(713\) −5.75152 −0.215396
\(714\) 0.182983 0.00684799
\(715\) 1.15032 0.0430196
\(716\) −13.8029 −0.515837
\(717\) 15.9690 0.596372
\(718\) −20.4138 −0.761838
\(719\) 2.86737 0.106935 0.0534675 0.998570i \(-0.482973\pi\)
0.0534675 + 0.998570i \(0.482973\pi\)
\(720\) −0.603416 −0.0224880
\(721\) 36.6713 1.36571
\(722\) −1.69413 −0.0630488
\(723\) 16.0931 0.598509
\(724\) 5.52824 0.205455
\(725\) −11.0208 −0.409302
\(726\) 22.2999 0.827628
\(727\) −6.14997 −0.228090 −0.114045 0.993476i \(-0.536381\pi\)
−0.114045 + 0.993476i \(0.536381\pi\)
\(728\) 33.3666 1.23665
\(729\) −6.82486 −0.252773
\(730\) 0.262990 0.00973369
\(731\) −0.309943 −0.0114637
\(732\) 2.97675 0.110024
\(733\) 43.6844 1.61352 0.806761 0.590879i \(-0.201219\pi\)
0.806761 + 0.590879i \(0.201219\pi\)
\(734\) 3.43897 0.126935
\(735\) 0.269481 0.00993997
\(736\) 17.6009 0.648776
\(737\) 2.20911 0.0813738
\(738\) 5.16168 0.190004
\(739\) −52.8011 −1.94232 −0.971161 0.238425i \(-0.923369\pi\)
−0.971161 + 0.238425i \(0.923369\pi\)
\(740\) −0.0913757 −0.00335904
\(741\) −2.84395 −0.104475
\(742\) 76.5063 2.80864
\(743\) −20.2633 −0.743389 −0.371695 0.928355i \(-0.621223\pi\)
−0.371695 + 0.928355i \(0.621223\pi\)
\(744\) 1.87383 0.0686980
\(745\) −0.270461 −0.00990891
\(746\) 42.7728 1.56602
\(747\) 32.0015 1.17087
\(748\) −0.203380 −0.00743631
\(749\) −11.4853 −0.419663
\(750\) 0.516495 0.0188597
\(751\) 26.9787 0.984469 0.492234 0.870463i \(-0.336180\pi\)
0.492234 + 0.870463i \(0.336180\pi\)
\(752\) 49.7795 1.81527
\(753\) 3.56498 0.129915
\(754\) −16.3626 −0.595892
\(755\) −0.142526 −0.00518704
\(756\) 12.5415 0.456129
\(757\) 10.2291 0.371783 0.185892 0.982570i \(-0.440483\pi\)
0.185892 + 0.982570i \(0.440483\pi\)
\(758\) −25.0748 −0.910758
\(759\) 13.8527 0.502821
\(760\) −0.0899014 −0.00326106
\(761\) 15.6756 0.568239 0.284120 0.958789i \(-0.408299\pi\)
0.284120 + 0.958789i \(0.408299\pi\)
\(762\) −1.48388 −0.0537552
\(763\) −15.9570 −0.577683
\(764\) −23.1505 −0.837554
\(765\) 0.00506166 0.000183005 0
\(766\) 38.8408 1.40338
\(767\) 43.8908 1.58480
\(768\) −11.3646 −0.410085
\(769\) 24.2371 0.874012 0.437006 0.899459i \(-0.356039\pi\)
0.437006 + 0.899459i \(0.356039\pi\)
\(770\) −1.77064 −0.0638096
\(771\) 15.6933 0.565182
\(772\) −4.62536 −0.166470
\(773\) −21.2591 −0.764638 −0.382319 0.924030i \(-0.624874\pi\)
−0.382319 + 0.924030i \(0.624874\pi\)
\(774\) −32.3892 −1.16421
\(775\) 7.53456 0.270650
\(776\) 24.1004 0.865155
\(777\) −5.77836 −0.207297
\(778\) −23.8856 −0.856341
\(779\) 1.18167 0.0423377
\(780\) 0.116209 0.00416093
\(781\) −15.7873 −0.564915
\(782\) −0.270163 −0.00966101
\(783\) 7.98721 0.285439
\(784\) −44.0366 −1.57273
\(785\) −0.900128 −0.0321269
\(786\) 12.5251 0.446755
\(787\) −43.3431 −1.54501 −0.772507 0.635007i \(-0.780997\pi\)
−0.772507 + 0.635007i \(0.780997\pi\)
\(788\) 21.7754 0.775716
\(789\) 8.25553 0.293905
\(790\) −0.134600 −0.00478887
\(791\) −37.3853 −1.32927
\(792\) 27.6015 0.980776
\(793\) −23.0789 −0.819555
\(794\) 44.2797 1.57143
\(795\) −0.346042 −0.0122729
\(796\) −12.7288 −0.451160
\(797\) −18.2133 −0.645147 −0.322574 0.946544i \(-0.604548\pi\)
−0.322574 + 0.946544i \(0.604548\pi\)
\(798\) 4.37758 0.154965
\(799\) −0.417568 −0.0147725
\(800\) −23.0574 −0.815201
\(801\) 9.09475 0.321347
\(802\) 23.9900 0.847116
\(803\) −18.4846 −0.652306
\(804\) 0.223170 0.00787062
\(805\) −0.713029 −0.0251310
\(806\) 11.1866 0.394031
\(807\) 5.44968 0.191838
\(808\) −26.3936 −0.928524
\(809\) 19.1842 0.674480 0.337240 0.941419i \(-0.390507\pi\)
0.337240 + 0.941419i \(0.390507\pi\)
\(810\) 0.428315 0.0150495
\(811\) 11.1031 0.389883 0.194942 0.980815i \(-0.437548\pi\)
0.194942 + 0.980815i \(0.437548\pi\)
\(812\) 7.63525 0.267945
\(813\) −15.4695 −0.542538
\(814\) 21.1857 0.742558
\(815\) −0.503397 −0.0176332
\(816\) 0.135247 0.00473460
\(817\) −7.41488 −0.259414
\(818\) 37.9150 1.32567
\(819\) −44.9429 −1.57043
\(820\) −0.0482848 −0.00168618
\(821\) 48.1530 1.68055 0.840276 0.542159i \(-0.182393\pi\)
0.840276 + 0.542159i \(0.182393\pi\)
\(822\) −2.69002 −0.0938251
\(823\) −41.4378 −1.44443 −0.722216 0.691667i \(-0.756876\pi\)
−0.722216 + 0.691667i \(0.756876\pi\)
\(824\) 17.6396 0.614504
\(825\) −18.1472 −0.631805
\(826\) −67.5593 −2.35069
\(827\) −19.0787 −0.663431 −0.331716 0.943379i \(-0.607627\pi\)
−0.331716 + 0.943379i \(0.607627\pi\)
\(828\) −8.55860 −0.297432
\(829\) 20.5643 0.714228 0.357114 0.934061i \(-0.383761\pi\)
0.357114 + 0.934061i \(0.383761\pi\)
\(830\) −0.987486 −0.0342761
\(831\) −0.318561 −0.0110507
\(832\) 9.41860 0.326531
\(833\) 0.369394 0.0127987
\(834\) 7.36856 0.255152
\(835\) −0.00282832 −9.78780e−5 0
\(836\) −4.86554 −0.168278
\(837\) −5.46059 −0.188746
\(838\) 36.2180 1.25113
\(839\) −0.920456 −0.0317777 −0.0158888 0.999874i \(-0.505058\pi\)
−0.0158888 + 0.999874i \(0.505058\pi\)
\(840\) 0.232303 0.00801522
\(841\) −24.1374 −0.832324
\(842\) 41.3516 1.42507
\(843\) 1.24635 0.0429264
\(844\) 0.870061 0.0299487
\(845\) −0.290437 −0.00999135
\(846\) −43.6360 −1.50024
\(847\) 80.6764 2.77207
\(848\) 56.5476 1.94185
\(849\) −2.03848 −0.0699604
\(850\) 0.353917 0.0121393
\(851\) 8.53136 0.292451
\(852\) −1.59488 −0.0546396
\(853\) 53.8465 1.84367 0.921834 0.387584i \(-0.126690\pi\)
0.921834 + 0.387584i \(0.126690\pi\)
\(854\) 35.5244 1.21562
\(855\) 0.121092 0.00414126
\(856\) −5.52463 −0.188828
\(857\) −32.4862 −1.10971 −0.554854 0.831948i \(-0.687226\pi\)
−0.554854 + 0.831948i \(0.687226\pi\)
\(858\) −26.9432 −0.919827
\(859\) −45.7593 −1.56129 −0.780643 0.624977i \(-0.785108\pi\)
−0.780643 + 0.624977i \(0.785108\pi\)
\(860\) 0.302984 0.0103317
\(861\) −3.05341 −0.104060
\(862\) −23.1667 −0.789061
\(863\) 23.4558 0.798444 0.399222 0.916854i \(-0.369280\pi\)
0.399222 + 0.916854i \(0.369280\pi\)
\(864\) 16.7106 0.568505
\(865\) −0.327392 −0.0111317
\(866\) −50.1781 −1.70512
\(867\) 11.0371 0.374839
\(868\) −5.21997 −0.177177
\(869\) 9.46056 0.320928
\(870\) −0.113919 −0.00386222
\(871\) −1.73025 −0.0586273
\(872\) −7.67562 −0.259929
\(873\) −32.4619 −1.09867
\(874\) −6.46321 −0.218621
\(875\) 1.86857 0.0631691
\(876\) −1.86736 −0.0630922
\(877\) −16.9046 −0.570829 −0.285414 0.958404i \(-0.592131\pi\)
−0.285414 + 0.958404i \(0.592131\pi\)
\(878\) −0.874127 −0.0295003
\(879\) −14.6724 −0.494889
\(880\) −1.30872 −0.0441171
\(881\) 50.1948 1.69111 0.845554 0.533891i \(-0.179271\pi\)
0.845554 + 0.533891i \(0.179271\pi\)
\(882\) 38.6019 1.29979
\(883\) −9.03340 −0.303998 −0.151999 0.988381i \(-0.548571\pi\)
−0.151999 + 0.988381i \(0.548571\pi\)
\(884\) 0.159294 0.00535764
\(885\) 0.305574 0.0102718
\(886\) −23.4509 −0.787850
\(887\) −30.9520 −1.03927 −0.519634 0.854389i \(-0.673932\pi\)
−0.519634 + 0.854389i \(0.673932\pi\)
\(888\) −2.77950 −0.0932739
\(889\) −5.36835 −0.180049
\(890\) −0.280641 −0.00940712
\(891\) −30.1047 −1.00854
\(892\) −15.8639 −0.531161
\(893\) −9.98963 −0.334290
\(894\) 6.33482 0.211868
\(895\) 0.745049 0.0249042
\(896\) −51.2174 −1.71105
\(897\) −10.8499 −0.362267
\(898\) −9.26869 −0.309300
\(899\) −3.32441 −0.110875
\(900\) 11.2119 0.373729
\(901\) −0.474341 −0.0158026
\(902\) 11.1950 0.372751
\(903\) 19.1599 0.637601
\(904\) −17.9830 −0.598107
\(905\) −0.298403 −0.00991924
\(906\) 3.33828 0.110907
\(907\) 26.4279 0.877524 0.438762 0.898603i \(-0.355417\pi\)
0.438762 + 0.898603i \(0.355417\pi\)
\(908\) −5.33901 −0.177181
\(909\) 35.5507 1.17914
\(910\) 1.38683 0.0459729
\(911\) 18.9340 0.627310 0.313655 0.949537i \(-0.398446\pi\)
0.313655 + 0.949537i \(0.398446\pi\)
\(912\) 3.23557 0.107141
\(913\) 69.4066 2.29702
\(914\) 44.1105 1.45904
\(915\) −0.160679 −0.00531188
\(916\) 0.683419 0.0225808
\(917\) 45.3131 1.49637
\(918\) −0.256497 −0.00846568
\(919\) −23.5153 −0.775697 −0.387848 0.921723i \(-0.626782\pi\)
−0.387848 + 0.921723i \(0.626782\pi\)
\(920\) −0.342980 −0.0113077
\(921\) 20.3094 0.669217
\(922\) −10.1536 −0.334392
\(923\) 12.3652 0.407004
\(924\) 12.5725 0.413603
\(925\) −11.1762 −0.367471
\(926\) −1.56094 −0.0512955
\(927\) −23.7596 −0.780366
\(928\) 10.1734 0.333958
\(929\) 0.813057 0.0266755 0.0133378 0.999911i \(-0.495754\pi\)
0.0133378 + 0.999911i \(0.495754\pi\)
\(930\) 0.0778828 0.00255388
\(931\) 8.83716 0.289626
\(932\) −8.47818 −0.277712
\(933\) 5.20392 0.170369
\(934\) 56.1364 1.83684
\(935\) 0.0109780 0.000359020 0
\(936\) −21.6184 −0.706619
\(937\) −7.29291 −0.238249 −0.119124 0.992879i \(-0.538009\pi\)
−0.119124 + 0.992879i \(0.538009\pi\)
\(938\) 2.66330 0.0869600
\(939\) 19.6056 0.639806
\(940\) 0.408192 0.0133138
\(941\) −8.70623 −0.283815 −0.141908 0.989880i \(-0.545324\pi\)
−0.141908 + 0.989880i \(0.545324\pi\)
\(942\) 21.0831 0.686924
\(943\) 4.50815 0.146806
\(944\) −49.9346 −1.62523
\(945\) −0.676962 −0.0220216
\(946\) −70.2476 −2.28394
\(947\) −28.3874 −0.922465 −0.461233 0.887279i \(-0.652593\pi\)
−0.461233 + 0.887279i \(0.652593\pi\)
\(948\) 0.955730 0.0310407
\(949\) 14.4777 0.469966
\(950\) 8.46689 0.274702
\(951\) 12.1355 0.393521
\(952\) 0.318432 0.0103204
\(953\) −50.4152 −1.63311 −0.816554 0.577270i \(-0.804118\pi\)
−0.816554 + 0.577270i \(0.804118\pi\)
\(954\) −49.5689 −1.60485
\(955\) 1.24961 0.0404365
\(956\) −21.3981 −0.692065
\(957\) 8.00694 0.258828
\(958\) −16.1826 −0.522837
\(959\) −9.73190 −0.314260
\(960\) 0.0655737 0.00211638
\(961\) −28.7272 −0.926684
\(962\) −16.5933 −0.534990
\(963\) 7.44137 0.239795
\(964\) −21.5645 −0.694545
\(965\) 0.249667 0.00803707
\(966\) 16.7008 0.537339
\(967\) 52.8099 1.69825 0.849126 0.528190i \(-0.177129\pi\)
0.849126 + 0.528190i \(0.177129\pi\)
\(968\) 38.8068 1.24730
\(969\) −0.0271411 −0.000871898 0
\(970\) 1.00169 0.0321625
\(971\) −4.55841 −0.146286 −0.0731432 0.997321i \(-0.523303\pi\)
−0.0731432 + 0.997321i \(0.523303\pi\)
\(972\) −12.4956 −0.400796
\(973\) 26.6579 0.854612
\(974\) −46.3904 −1.48644
\(975\) 14.2135 0.455196
\(976\) 26.2569 0.840463
\(977\) 48.8332 1.56231 0.781157 0.624335i \(-0.214630\pi\)
0.781157 + 0.624335i \(0.214630\pi\)
\(978\) 11.7907 0.377026
\(979\) 19.7252 0.630421
\(980\) −0.361100 −0.0115349
\(981\) 10.3386 0.330087
\(982\) −12.2699 −0.391548
\(983\) 48.1842 1.53684 0.768419 0.639947i \(-0.221044\pi\)
0.768419 + 0.639947i \(0.221044\pi\)
\(984\) −1.46875 −0.0468219
\(985\) −1.17539 −0.0374510
\(986\) −0.156156 −0.00497301
\(987\) 25.8130 0.821636
\(988\) 3.81085 0.121239
\(989\) −28.2883 −0.899516
\(990\) 1.14721 0.0364607
\(991\) −42.5023 −1.35013 −0.675065 0.737758i \(-0.735885\pi\)
−0.675065 + 0.737758i \(0.735885\pi\)
\(992\) −6.95522 −0.220828
\(993\) −16.2409 −0.515389
\(994\) −19.0332 −0.603696
\(995\) 0.687073 0.0217817
\(996\) 7.01164 0.222172
\(997\) 12.1169 0.383746 0.191873 0.981420i \(-0.438544\pi\)
0.191873 + 0.981420i \(0.438544\pi\)
\(998\) 15.2913 0.484037
\(999\) 8.09982 0.256267
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 \(a_p\))