Properties

Label 4033.2.a.d.1.8
Level 4033
Weight 2
Character 4033.1
Self dual Yes
Analytic conductor 32.204
Analytic rank 1
Dimension 79
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 4033 = 37 \cdot 109 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4033.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.2036671352\)
Analytic rank: \(1\)
Dimension: \(79\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Character \(\chi\) = 4033.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.50943 q^{2}\) \(+1.55716 q^{3}\) \(+4.29722 q^{4}\) \(-3.66304 q^{5}\) \(-3.90758 q^{6}\) \(+4.73862 q^{7}\) \(-5.76470 q^{8}\) \(-0.575254 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.50943 q^{2}\) \(+1.55716 q^{3}\) \(+4.29722 q^{4}\) \(-3.66304 q^{5}\) \(-3.90758 q^{6}\) \(+4.73862 q^{7}\) \(-5.76470 q^{8}\) \(-0.575254 q^{9}\) \(+9.19213 q^{10}\) \(+5.22371 q^{11}\) \(+6.69145 q^{12}\) \(-3.90099 q^{13}\) \(-11.8912 q^{14}\) \(-5.70394 q^{15}\) \(+5.87164 q^{16}\) \(-3.68586 q^{17}\) \(+1.44356 q^{18}\) \(-5.02658 q^{19}\) \(-15.7409 q^{20}\) \(+7.37878 q^{21}\) \(-13.1085 q^{22}\) \(-0.531824 q^{23}\) \(-8.97655 q^{24}\) \(+8.41787 q^{25}\) \(+9.78925 q^{26}\) \(-5.56724 q^{27}\) \(+20.3629 q^{28}\) \(+7.93297 q^{29}\) \(+14.3136 q^{30}\) \(+9.09986 q^{31}\) \(-3.20506 q^{32}\) \(+8.13415 q^{33}\) \(+9.24940 q^{34}\) \(-17.3577 q^{35}\) \(-2.47199 q^{36}\) \(-1.00000 q^{37}\) \(+12.6138 q^{38}\) \(-6.07447 q^{39}\) \(+21.1163 q^{40}\) \(-9.30734 q^{41}\) \(-18.5165 q^{42}\) \(-1.44956 q^{43}\) \(+22.4474 q^{44}\) \(+2.10718 q^{45}\) \(+1.33457 q^{46}\) \(-4.67692 q^{47}\) \(+9.14309 q^{48}\) \(+15.4545 q^{49}\) \(-21.1240 q^{50}\) \(-5.73948 q^{51}\) \(-16.7634 q^{52}\) \(-9.23111 q^{53}\) \(+13.9706 q^{54}\) \(-19.1347 q^{55}\) \(-27.3167 q^{56}\) \(-7.82719 q^{57}\) \(-19.9072 q^{58}\) \(-13.6370 q^{59}\) \(-24.5111 q^{60}\) \(+7.43229 q^{61}\) \(-22.8354 q^{62}\) \(-2.72591 q^{63}\) \(-3.70043 q^{64}\) \(+14.2895 q^{65}\) \(-20.4120 q^{66}\) \(+6.71252 q^{67}\) \(-15.8390 q^{68}\) \(-0.828134 q^{69}\) \(+43.5580 q^{70}\) \(-3.82404 q^{71}\) \(+3.31617 q^{72}\) \(-14.4234 q^{73}\) \(+2.50943 q^{74}\) \(+13.1080 q^{75}\) \(-21.6003 q^{76}\) \(+24.7532 q^{77}\) \(+15.2434 q^{78}\) \(+3.11017 q^{79}\) \(-21.5081 q^{80}\) \(-6.94332 q^{81}\) \(+23.3561 q^{82}\) \(-6.20380 q^{83}\) \(+31.7082 q^{84}\) \(+13.5015 q^{85}\) \(+3.63757 q^{86}\) \(+12.3529 q^{87}\) \(-30.1131 q^{88}\) \(-2.99085 q^{89}\) \(-5.28781 q^{90}\) \(-18.4853 q^{91}\) \(-2.28536 q^{92}\) \(+14.1699 q^{93}\) \(+11.7364 q^{94}\) \(+18.4126 q^{95}\) \(-4.99079 q^{96}\) \(+16.5707 q^{97}\) \(-38.7819 q^{98}\) \(-3.00496 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(79q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 79q^{4} \) \(\mathstrut -\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 14q^{6} \) \(\mathstrut -\mathstrut 15q^{7} \) \(\mathstrut -\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 76q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(79q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 79q^{4} \) \(\mathstrut -\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 14q^{6} \) \(\mathstrut -\mathstrut 15q^{7} \) \(\mathstrut -\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 76q^{9} \) \(\mathstrut -\mathstrut 13q^{10} \) \(\mathstrut -\mathstrut 5q^{11} \) \(\mathstrut -\mathstrut 40q^{12} \) \(\mathstrut -\mathstrut 18q^{13} \) \(\mathstrut -\mathstrut 42q^{14} \) \(\mathstrut -\mathstrut 49q^{15} \) \(\mathstrut +\mathstrut 83q^{16} \) \(\mathstrut -\mathstrut 62q^{17} \) \(\mathstrut -\mathstrut 33q^{18} \) \(\mathstrut -\mathstrut 25q^{19} \) \(\mathstrut -\mathstrut 39q^{20} \) \(\mathstrut -\mathstrut 15q^{21} \) \(\mathstrut -\mathstrut 31q^{22} \) \(\mathstrut -\mathstrut 94q^{23} \) \(\mathstrut -\mathstrut 39q^{24} \) \(\mathstrut +\mathstrut 71q^{25} \) \(\mathstrut -\mathstrut 35q^{26} \) \(\mathstrut -\mathstrut 47q^{27} \) \(\mathstrut -\mathstrut 13q^{28} \) \(\mathstrut -\mathstrut 17q^{29} \) \(\mathstrut +\mathstrut 15q^{30} \) \(\mathstrut -\mathstrut 37q^{31} \) \(\mathstrut -\mathstrut 105q^{32} \) \(\mathstrut -\mathstrut 60q^{33} \) \(\mathstrut +\mathstrut 9q^{34} \) \(\mathstrut -\mathstrut 60q^{35} \) \(\mathstrut +\mathstrut 43q^{36} \) \(\mathstrut -\mathstrut 79q^{37} \) \(\mathstrut -\mathstrut 80q^{38} \) \(\mathstrut -\mathstrut 41q^{39} \) \(\mathstrut -\mathstrut 64q^{40} \) \(\mathstrut -\mathstrut 37q^{41} \) \(\mathstrut -\mathstrut 30q^{42} \) \(\mathstrut -\mathstrut 20q^{43} \) \(\mathstrut -\mathstrut 14q^{44} \) \(\mathstrut -\mathstrut 8q^{45} \) \(\mathstrut +\mathstrut 61q^{46} \) \(\mathstrut -\mathstrut 148q^{47} \) \(\mathstrut -\mathstrut 39q^{48} \) \(\mathstrut +\mathstrut 82q^{49} \) \(\mathstrut -\mathstrut 90q^{50} \) \(\mathstrut -\mathstrut 45q^{51} \) \(\mathstrut -\mathstrut 27q^{52} \) \(\mathstrut -\mathstrut 70q^{53} \) \(\mathstrut -\mathstrut 41q^{54} \) \(\mathstrut -\mathstrut 105q^{55} \) \(\mathstrut -\mathstrut 68q^{56} \) \(\mathstrut -\mathstrut 31q^{57} \) \(\mathstrut -\mathstrut 14q^{58} \) \(\mathstrut -\mathstrut 96q^{59} \) \(\mathstrut -\mathstrut 74q^{60} \) \(\mathstrut -\mathstrut 21q^{61} \) \(\mathstrut +\mathstrut 4q^{62} \) \(\mathstrut -\mathstrut 60q^{63} \) \(\mathstrut +\mathstrut 132q^{64} \) \(\mathstrut -\mathstrut 15q^{65} \) \(\mathstrut +\mathstrut 71q^{66} \) \(\mathstrut -\mathstrut 44q^{67} \) \(\mathstrut -\mathstrut 166q^{68} \) \(\mathstrut -\mathstrut 72q^{69} \) \(\mathstrut -\mathstrut 9q^{70} \) \(\mathstrut -\mathstrut 55q^{71} \) \(\mathstrut -\mathstrut 126q^{72} \) \(\mathstrut -\mathstrut 27q^{73} \) \(\mathstrut +\mathstrut 11q^{74} \) \(\mathstrut -\mathstrut 39q^{75} \) \(\mathstrut -\mathstrut 4q^{76} \) \(\mathstrut -\mathstrut 104q^{77} \) \(\mathstrut -\mathstrut 47q^{78} \) \(\mathstrut -\mathstrut 49q^{79} \) \(\mathstrut -\mathstrut 82q^{80} \) \(\mathstrut +\mathstrut 55q^{81} \) \(\mathstrut +\mathstrut 20q^{82} \) \(\mathstrut -\mathstrut 52q^{83} \) \(\mathstrut -\mathstrut 29q^{84} \) \(\mathstrut +\mathstrut 3q^{85} \) \(\mathstrut -\mathstrut 32q^{86} \) \(\mathstrut -\mathstrut 113q^{87} \) \(\mathstrut +\mathstrut 14q^{88} \) \(\mathstrut -\mathstrut 68q^{89} \) \(\mathstrut -\mathstrut 39q^{90} \) \(\mathstrut -\mathstrut 30q^{91} \) \(\mathstrut -\mathstrut 179q^{92} \) \(\mathstrut -\mathstrut 53q^{93} \) \(\mathstrut -\mathstrut 33q^{94} \) \(\mathstrut -\mathstrut 86q^{95} \) \(\mathstrut +\mathstrut 33q^{96} \) \(\mathstrut -\mathstrut 57q^{97} \) \(\mathstrut -\mathstrut 116q^{98} \) \(\mathstrut +\mathstrut q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.50943 −1.77443 −0.887216 0.461354i \(-0.847364\pi\)
−0.887216 + 0.461354i \(0.847364\pi\)
\(3\) 1.55716 0.899026 0.449513 0.893274i \(-0.351597\pi\)
0.449513 + 0.893274i \(0.351597\pi\)
\(4\) 4.29722 2.14861
\(5\) −3.66304 −1.63816 −0.819081 0.573678i \(-0.805516\pi\)
−0.819081 + 0.573678i \(0.805516\pi\)
\(6\) −3.90758 −1.59526
\(7\) 4.73862 1.79103 0.895514 0.445033i \(-0.146808\pi\)
0.895514 + 0.445033i \(0.146808\pi\)
\(8\) −5.76470 −2.03813
\(9\) −0.575254 −0.191751
\(10\) 9.19213 2.90681
\(11\) 5.22371 1.57501 0.787504 0.616310i \(-0.211373\pi\)
0.787504 + 0.616310i \(0.211373\pi\)
\(12\) 6.69145 1.93166
\(13\) −3.90099 −1.08194 −0.540970 0.841042i \(-0.681943\pi\)
−0.540970 + 0.841042i \(0.681943\pi\)
\(14\) −11.8912 −3.17806
\(15\) −5.70394 −1.47275
\(16\) 5.87164 1.46791
\(17\) −3.68586 −0.893953 −0.446976 0.894546i \(-0.647499\pi\)
−0.446976 + 0.894546i \(0.647499\pi\)
\(18\) 1.44356 0.340250
\(19\) −5.02658 −1.15318 −0.576589 0.817034i \(-0.695617\pi\)
−0.576589 + 0.817034i \(0.695617\pi\)
\(20\) −15.7409 −3.51977
\(21\) 7.37878 1.61018
\(22\) −13.1085 −2.79474
\(23\) −0.531824 −0.110893 −0.0554464 0.998462i \(-0.517658\pi\)
−0.0554464 + 0.998462i \(0.517658\pi\)
\(24\) −8.97655 −1.83233
\(25\) 8.41787 1.68357
\(26\) 9.78925 1.91983
\(27\) −5.56724 −1.07142
\(28\) 20.3629 3.84822
\(29\) 7.93297 1.47312 0.736558 0.676374i \(-0.236450\pi\)
0.736558 + 0.676374i \(0.236450\pi\)
\(30\) 14.3136 2.61330
\(31\) 9.09986 1.63438 0.817192 0.576366i \(-0.195530\pi\)
0.817192 + 0.576366i \(0.195530\pi\)
\(32\) −3.20506 −0.566580
\(33\) 8.13415 1.41597
\(34\) 9.24940 1.58626
\(35\) −17.3577 −2.93399
\(36\) −2.47199 −0.411999
\(37\) −1.00000 −0.164399
\(38\) 12.6138 2.04624
\(39\) −6.07447 −0.972693
\(40\) 21.1163 3.33878
\(41\) −9.30734 −1.45356 −0.726781 0.686869i \(-0.758985\pi\)
−0.726781 + 0.686869i \(0.758985\pi\)
\(42\) −18.5165 −2.85716
\(43\) −1.44956 −0.221056 −0.110528 0.993873i \(-0.535254\pi\)
−0.110528 + 0.993873i \(0.535254\pi\)
\(44\) 22.4474 3.38408
\(45\) 2.10718 0.314120
\(46\) 1.33457 0.196772
\(47\) −4.67692 −0.682199 −0.341100 0.940027i \(-0.610799\pi\)
−0.341100 + 0.940027i \(0.610799\pi\)
\(48\) 9.14309 1.31969
\(49\) 15.4545 2.20778
\(50\) −21.1240 −2.98739
\(51\) −5.73948 −0.803687
\(52\) −16.7634 −2.32467
\(53\) −9.23111 −1.26799 −0.633995 0.773337i \(-0.718586\pi\)
−0.633995 + 0.773337i \(0.718586\pi\)
\(54\) 13.9706 1.90115
\(55\) −19.1347 −2.58012
\(56\) −27.3167 −3.65035
\(57\) −7.82719 −1.03674
\(58\) −19.9072 −2.61394
\(59\) −13.6370 −1.77538 −0.887692 0.460438i \(-0.847693\pi\)
−0.887692 + 0.460438i \(0.847693\pi\)
\(60\) −24.5111 −3.16437
\(61\) 7.43229 0.951607 0.475804 0.879552i \(-0.342157\pi\)
0.475804 + 0.879552i \(0.342157\pi\)
\(62\) −22.8354 −2.90010
\(63\) −2.72591 −0.343432
\(64\) −3.70043 −0.462554
\(65\) 14.2895 1.77239
\(66\) −20.4120 −2.51255
\(67\) 6.71252 0.820065 0.410032 0.912071i \(-0.365517\pi\)
0.410032 + 0.912071i \(0.365517\pi\)
\(68\) −15.8390 −1.92076
\(69\) −0.828134 −0.0996956
\(70\) 43.5580 5.20617
\(71\) −3.82404 −0.453831 −0.226915 0.973914i \(-0.572864\pi\)
−0.226915 + 0.973914i \(0.572864\pi\)
\(72\) 3.31617 0.390814
\(73\) −14.4234 −1.68813 −0.844066 0.536240i \(-0.819844\pi\)
−0.844066 + 0.536240i \(0.819844\pi\)
\(74\) 2.50943 0.291715
\(75\) 13.1080 1.51358
\(76\) −21.6003 −2.47773
\(77\) 24.7532 2.82088
\(78\) 15.2434 1.72598
\(79\) 3.11017 0.349922 0.174961 0.984575i \(-0.444020\pi\)
0.174961 + 0.984575i \(0.444020\pi\)
\(80\) −21.5081 −2.40468
\(81\) −6.94332 −0.771480
\(82\) 23.3561 2.57925
\(83\) −6.20380 −0.680956 −0.340478 0.940253i \(-0.610589\pi\)
−0.340478 + 0.940253i \(0.610589\pi\)
\(84\) 31.7082 3.45965
\(85\) 13.5015 1.46444
\(86\) 3.63757 0.392249
\(87\) 12.3529 1.32437
\(88\) −30.1131 −3.21007
\(89\) −2.99085 −0.317029 −0.158515 0.987357i \(-0.550671\pi\)
−0.158515 + 0.987357i \(0.550671\pi\)
\(90\) −5.28781 −0.557384
\(91\) −18.4853 −1.93779
\(92\) −2.28536 −0.238265
\(93\) 14.1699 1.46935
\(94\) 11.7364 1.21052
\(95\) 18.4126 1.88909
\(96\) −4.99079 −0.509370
\(97\) 16.5707 1.68250 0.841252 0.540644i \(-0.181819\pi\)
0.841252 + 0.540644i \(0.181819\pi\)
\(98\) −38.7819 −3.91756
\(99\) −3.00496 −0.302010
\(100\) 36.1734 3.61734
\(101\) −4.02565 −0.400567 −0.200283 0.979738i \(-0.564186\pi\)
−0.200283 + 0.979738i \(0.564186\pi\)
\(102\) 14.4028 1.42609
\(103\) −5.99485 −0.590690 −0.295345 0.955391i \(-0.595435\pi\)
−0.295345 + 0.955391i \(0.595435\pi\)
\(104\) 22.4880 2.20513
\(105\) −27.0288 −2.63774
\(106\) 23.1648 2.24996
\(107\) −6.82101 −0.659412 −0.329706 0.944084i \(-0.606950\pi\)
−0.329706 + 0.944084i \(0.606950\pi\)
\(108\) −23.9236 −2.30205
\(109\) −1.00000 −0.0957826
\(110\) 48.0170 4.57824
\(111\) −1.55716 −0.147799
\(112\) 27.8235 2.62907
\(113\) −18.3601 −1.72717 −0.863586 0.504202i \(-0.831787\pi\)
−0.863586 + 0.504202i \(0.831787\pi\)
\(114\) 19.6418 1.83962
\(115\) 1.94809 0.181660
\(116\) 34.0897 3.16515
\(117\) 2.24406 0.207464
\(118\) 34.2210 3.15030
\(119\) −17.4659 −1.60110
\(120\) 32.8815 3.00165
\(121\) 16.2871 1.48065
\(122\) −18.6508 −1.68856
\(123\) −14.4930 −1.30679
\(124\) 39.1041 3.51165
\(125\) −12.5198 −1.11980
\(126\) 6.84046 0.609397
\(127\) −9.74732 −0.864934 −0.432467 0.901650i \(-0.642357\pi\)
−0.432467 + 0.901650i \(0.642357\pi\)
\(128\) 15.6961 1.38735
\(129\) −2.25720 −0.198735
\(130\) −35.8584 −3.14499
\(131\) 15.9375 1.39246 0.696232 0.717817i \(-0.254858\pi\)
0.696232 + 0.717817i \(0.254858\pi\)
\(132\) 34.9542 3.04237
\(133\) −23.8191 −2.06537
\(134\) −16.8446 −1.45515
\(135\) 20.3930 1.75515
\(136\) 21.2479 1.82199
\(137\) 11.4835 0.981098 0.490549 0.871414i \(-0.336796\pi\)
0.490549 + 0.871414i \(0.336796\pi\)
\(138\) 2.07814 0.176903
\(139\) 11.6112 0.984845 0.492423 0.870356i \(-0.336111\pi\)
0.492423 + 0.870356i \(0.336111\pi\)
\(140\) −74.5900 −6.30401
\(141\) −7.28272 −0.613315
\(142\) 9.59616 0.805291
\(143\) −20.3776 −1.70406
\(144\) −3.37769 −0.281474
\(145\) −29.0588 −2.41320
\(146\) 36.1944 2.99547
\(147\) 24.0651 1.98485
\(148\) −4.29722 −0.353229
\(149\) 9.55511 0.782785 0.391392 0.920224i \(-0.371994\pi\)
0.391392 + 0.920224i \(0.371994\pi\)
\(150\) −32.8935 −2.68574
\(151\) −15.5153 −1.26262 −0.631308 0.775533i \(-0.717481\pi\)
−0.631308 + 0.775533i \(0.717481\pi\)
\(152\) 28.9767 2.35032
\(153\) 2.12031 0.171417
\(154\) −62.1162 −5.00547
\(155\) −33.3332 −2.67738
\(156\) −26.1033 −2.08994
\(157\) −10.5711 −0.843668 −0.421834 0.906673i \(-0.638614\pi\)
−0.421834 + 0.906673i \(0.638614\pi\)
\(158\) −7.80475 −0.620912
\(159\) −14.3743 −1.13996
\(160\) 11.7403 0.928149
\(161\) −2.52011 −0.198612
\(162\) 17.4237 1.36894
\(163\) 3.97477 0.311328 0.155664 0.987810i \(-0.450248\pi\)
0.155664 + 0.987810i \(0.450248\pi\)
\(164\) −39.9957 −3.12314
\(165\) −29.7957 −2.31959
\(166\) 15.5680 1.20831
\(167\) 1.19905 0.0927855 0.0463927 0.998923i \(-0.485227\pi\)
0.0463927 + 0.998923i \(0.485227\pi\)
\(168\) −42.5364 −3.28176
\(169\) 2.21774 0.170595
\(170\) −33.8809 −2.59855
\(171\) 2.89156 0.221123
\(172\) −6.22908 −0.474963
\(173\) 10.8966 0.828457 0.414228 0.910173i \(-0.364052\pi\)
0.414228 + 0.910173i \(0.364052\pi\)
\(174\) −30.9987 −2.35001
\(175\) 39.8891 3.01533
\(176\) 30.6718 2.31197
\(177\) −21.2350 −1.59612
\(178\) 7.50531 0.562547
\(179\) 9.55455 0.714141 0.357070 0.934077i \(-0.383776\pi\)
0.357070 + 0.934077i \(0.383776\pi\)
\(180\) 9.05501 0.674920
\(181\) −8.00091 −0.594703 −0.297352 0.954768i \(-0.596103\pi\)
−0.297352 + 0.954768i \(0.596103\pi\)
\(182\) 46.3875 3.43847
\(183\) 11.5733 0.855520
\(184\) 3.06580 0.226014
\(185\) 3.66304 0.269312
\(186\) −35.5584 −2.60727
\(187\) −19.2539 −1.40798
\(188\) −20.0978 −1.46578
\(189\) −26.3810 −1.91894
\(190\) −46.2050 −3.35206
\(191\) −9.95153 −0.720067 −0.360034 0.932939i \(-0.617235\pi\)
−0.360034 + 0.932939i \(0.617235\pi\)
\(192\) −5.76216 −0.415848
\(193\) 7.33322 0.527857 0.263928 0.964542i \(-0.414982\pi\)
0.263928 + 0.964542i \(0.414982\pi\)
\(194\) −41.5830 −2.98549
\(195\) 22.2510 1.59343
\(196\) 66.4113 4.74366
\(197\) 5.47193 0.389859 0.194929 0.980817i \(-0.437552\pi\)
0.194929 + 0.980817i \(0.437552\pi\)
\(198\) 7.54072 0.535896
\(199\) 5.04693 0.357767 0.178884 0.983870i \(-0.442751\pi\)
0.178884 + 0.983870i \(0.442751\pi\)
\(200\) −48.5265 −3.43134
\(201\) 10.4525 0.737260
\(202\) 10.1021 0.710778
\(203\) 37.5913 2.63839
\(204\) −24.6638 −1.72681
\(205\) 34.0932 2.38117
\(206\) 15.0436 1.04814
\(207\) 0.305934 0.0212639
\(208\) −22.9052 −1.58819
\(209\) −26.2574 −1.81626
\(210\) 67.8267 4.68049
\(211\) 9.84430 0.677710 0.338855 0.940839i \(-0.389960\pi\)
0.338855 + 0.940839i \(0.389960\pi\)
\(212\) −39.6681 −2.72442
\(213\) −5.95465 −0.408006
\(214\) 17.1168 1.17008
\(215\) 5.30980 0.362126
\(216\) 32.0935 2.18368
\(217\) 43.1207 2.92723
\(218\) 2.50943 0.169960
\(219\) −22.4595 −1.51767
\(220\) −82.2258 −5.54366
\(221\) 14.3785 0.967204
\(222\) 3.90758 0.262259
\(223\) −24.1510 −1.61727 −0.808634 0.588312i \(-0.799793\pi\)
−0.808634 + 0.588312i \(0.799793\pi\)
\(224\) −15.1875 −1.01476
\(225\) −4.84241 −0.322828
\(226\) 46.0733 3.06475
\(227\) 8.18538 0.543283 0.271641 0.962399i \(-0.412434\pi\)
0.271641 + 0.962399i \(0.412434\pi\)
\(228\) −33.6352 −2.22754
\(229\) −14.2098 −0.939012 −0.469506 0.882929i \(-0.655568\pi\)
−0.469506 + 0.882929i \(0.655568\pi\)
\(230\) −4.88859 −0.322344
\(231\) 38.5446 2.53605
\(232\) −45.7312 −3.00240
\(233\) −8.44981 −0.553565 −0.276783 0.960933i \(-0.589268\pi\)
−0.276783 + 0.960933i \(0.589268\pi\)
\(234\) −5.63131 −0.368130
\(235\) 17.1318 1.11755
\(236\) −58.6011 −3.81461
\(237\) 4.84304 0.314589
\(238\) 43.8293 2.84103
\(239\) −0.337644 −0.0218404 −0.0109202 0.999940i \(-0.503476\pi\)
−0.0109202 + 0.999940i \(0.503476\pi\)
\(240\) −33.4915 −2.16187
\(241\) −1.69229 −0.109010 −0.0545049 0.998514i \(-0.517358\pi\)
−0.0545049 + 0.998514i \(0.517358\pi\)
\(242\) −40.8714 −2.62731
\(243\) 5.88987 0.377835
\(244\) 31.9382 2.04463
\(245\) −56.6104 −3.61670
\(246\) 36.3692 2.31881
\(247\) 19.6087 1.24767
\(248\) −52.4579 −3.33108
\(249\) −9.66031 −0.612197
\(250\) 31.4175 1.98702
\(251\) −13.3167 −0.840540 −0.420270 0.907399i \(-0.638065\pi\)
−0.420270 + 0.907399i \(0.638065\pi\)
\(252\) −11.7138 −0.737901
\(253\) −2.77809 −0.174657
\(254\) 24.4602 1.53477
\(255\) 21.0239 1.31657
\(256\) −31.9873 −1.99920
\(257\) −18.7641 −1.17047 −0.585235 0.810864i \(-0.698998\pi\)
−0.585235 + 0.810864i \(0.698998\pi\)
\(258\) 5.66427 0.352642
\(259\) −4.73862 −0.294443
\(260\) 61.4051 3.80818
\(261\) −4.56348 −0.282472
\(262\) −39.9939 −2.47083
\(263\) −6.87208 −0.423751 −0.211875 0.977297i \(-0.567957\pi\)
−0.211875 + 0.977297i \(0.567957\pi\)
\(264\) −46.8909 −2.88594
\(265\) 33.8139 2.07717
\(266\) 59.7721 3.66487
\(267\) −4.65723 −0.285018
\(268\) 28.8452 1.76200
\(269\) −5.47400 −0.333756 −0.166878 0.985978i \(-0.553369\pi\)
−0.166878 + 0.985978i \(0.553369\pi\)
\(270\) −51.1748 −3.11440
\(271\) −2.04932 −0.124488 −0.0622438 0.998061i \(-0.519826\pi\)
−0.0622438 + 0.998061i \(0.519826\pi\)
\(272\) −21.6421 −1.31224
\(273\) −28.7846 −1.74212
\(274\) −28.8169 −1.74089
\(275\) 43.9725 2.65164
\(276\) −3.55867 −0.214207
\(277\) −9.80283 −0.588995 −0.294498 0.955652i \(-0.595152\pi\)
−0.294498 + 0.955652i \(0.595152\pi\)
\(278\) −29.1373 −1.74754
\(279\) −5.23473 −0.313395
\(280\) 100.062 5.97986
\(281\) −19.7388 −1.17752 −0.588759 0.808308i \(-0.700383\pi\)
−0.588759 + 0.808308i \(0.700383\pi\)
\(282\) 18.2754 1.08829
\(283\) −31.2603 −1.85823 −0.929117 0.369785i \(-0.879431\pi\)
−0.929117 + 0.369785i \(0.879431\pi\)
\(284\) −16.4328 −0.975104
\(285\) 28.6713 1.69834
\(286\) 51.1362 3.02375
\(287\) −44.1039 −2.60337
\(288\) 1.84372 0.108642
\(289\) −3.41442 −0.200848
\(290\) 72.9209 4.28206
\(291\) 25.8033 1.51262
\(292\) −61.9805 −3.62713
\(293\) 8.12219 0.474504 0.237252 0.971448i \(-0.423753\pi\)
0.237252 + 0.971448i \(0.423753\pi\)
\(294\) −60.3896 −3.52199
\(295\) 49.9528 2.90837
\(296\) 5.76470 0.335066
\(297\) −29.0817 −1.68749
\(298\) −23.9778 −1.38900
\(299\) 2.07464 0.119979
\(300\) 56.3278 3.25209
\(301\) −6.86892 −0.395918
\(302\) 38.9344 2.24042
\(303\) −6.26857 −0.360120
\(304\) −29.5143 −1.69276
\(305\) −27.2248 −1.55889
\(306\) −5.32075 −0.304167
\(307\) −2.84533 −0.162392 −0.0811959 0.996698i \(-0.525874\pi\)
−0.0811959 + 0.996698i \(0.525874\pi\)
\(308\) 106.370 6.06097
\(309\) −9.33494 −0.531046
\(310\) 83.6471 4.75084
\(311\) 14.5820 0.826871 0.413435 0.910533i \(-0.364329\pi\)
0.413435 + 0.910533i \(0.364329\pi\)
\(312\) 35.0175 1.98247
\(313\) −2.09216 −0.118256 −0.0591279 0.998250i \(-0.518832\pi\)
−0.0591279 + 0.998250i \(0.518832\pi\)
\(314\) 26.5275 1.49703
\(315\) 9.98511 0.562597
\(316\) 13.3651 0.751845
\(317\) 8.86131 0.497701 0.248850 0.968542i \(-0.419947\pi\)
0.248850 + 0.968542i \(0.419947\pi\)
\(318\) 36.0713 2.02278
\(319\) 41.4395 2.32017
\(320\) 13.5548 0.757738
\(321\) −10.6214 −0.592829
\(322\) 6.32402 0.352424
\(323\) 18.5273 1.03089
\(324\) −29.8370 −1.65761
\(325\) −32.8380 −1.82153
\(326\) −9.97440 −0.552431
\(327\) −1.55716 −0.0861111
\(328\) 53.6540 2.96255
\(329\) −22.1621 −1.22184
\(330\) 74.7702 4.11596
\(331\) −21.4004 −1.17627 −0.588135 0.808762i \(-0.700138\pi\)
−0.588135 + 0.808762i \(0.700138\pi\)
\(332\) −26.6591 −1.46311
\(333\) 0.575254 0.0315237
\(334\) −3.00893 −0.164641
\(335\) −24.5882 −1.34340
\(336\) 43.3256 2.36360
\(337\) −10.5330 −0.573772 −0.286886 0.957965i \(-0.592620\pi\)
−0.286886 + 0.957965i \(0.592620\pi\)
\(338\) −5.56525 −0.302710
\(339\) −28.5896 −1.55277
\(340\) 58.0187 3.14651
\(341\) 47.5350 2.57417
\(342\) −7.25616 −0.392368
\(343\) 40.0625 2.16317
\(344\) 8.35628 0.450541
\(345\) 3.03349 0.163318
\(346\) −27.3443 −1.47004
\(347\) −15.5095 −0.832595 −0.416298 0.909228i \(-0.636673\pi\)
−0.416298 + 0.909228i \(0.636673\pi\)
\(348\) 53.0831 2.84555
\(349\) −14.5770 −0.780291 −0.390146 0.920753i \(-0.627575\pi\)
−0.390146 + 0.920753i \(0.627575\pi\)
\(350\) −100.099 −5.35050
\(351\) 21.7178 1.15921
\(352\) −16.7423 −0.892368
\(353\) 22.1867 1.18088 0.590439 0.807083i \(-0.298955\pi\)
0.590439 + 0.807083i \(0.298955\pi\)
\(354\) 53.2876 2.83220
\(355\) 14.0076 0.743448
\(356\) −12.8523 −0.681172
\(357\) −27.1972 −1.43943
\(358\) −23.9764 −1.26719
\(359\) −15.3418 −0.809709 −0.404854 0.914381i \(-0.632678\pi\)
−0.404854 + 0.914381i \(0.632678\pi\)
\(360\) −12.1473 −0.640216
\(361\) 6.26655 0.329819
\(362\) 20.0777 1.05526
\(363\) 25.3617 1.33114
\(364\) −79.4354 −4.16354
\(365\) 52.8335 2.76543
\(366\) −29.0422 −1.51806
\(367\) 20.5887 1.07472 0.537361 0.843352i \(-0.319421\pi\)
0.537361 + 0.843352i \(0.319421\pi\)
\(368\) −3.12268 −0.162781
\(369\) 5.35409 0.278723
\(370\) −9.19213 −0.477876
\(371\) −43.7427 −2.27101
\(372\) 60.8913 3.15707
\(373\) −30.3559 −1.57177 −0.785885 0.618373i \(-0.787792\pi\)
−0.785885 + 0.618373i \(0.787792\pi\)
\(374\) 48.3162 2.49837
\(375\) −19.4953 −1.00673
\(376\) 26.9610 1.39041
\(377\) −30.9465 −1.59382
\(378\) 66.2012 3.40502
\(379\) 15.2665 0.784188 0.392094 0.919925i \(-0.371751\pi\)
0.392094 + 0.919925i \(0.371751\pi\)
\(380\) 79.1229 4.05892
\(381\) −15.1781 −0.777599
\(382\) 24.9726 1.27771
\(383\) −8.75892 −0.447560 −0.223780 0.974640i \(-0.571840\pi\)
−0.223780 + 0.974640i \(0.571840\pi\)
\(384\) 24.4413 1.24726
\(385\) −90.6718 −4.62106
\(386\) −18.4022 −0.936646
\(387\) 0.833866 0.0423878
\(388\) 71.2081 3.61504
\(389\) 15.4119 0.781412 0.390706 0.920516i \(-0.372231\pi\)
0.390706 + 0.920516i \(0.372231\pi\)
\(390\) −55.8373 −2.82743
\(391\) 1.96023 0.0991330
\(392\) −89.0904 −4.49974
\(393\) 24.8172 1.25186
\(394\) −13.7314 −0.691778
\(395\) −11.3927 −0.573229
\(396\) −12.9130 −0.648901
\(397\) 26.4379 1.32688 0.663440 0.748229i \(-0.269096\pi\)
0.663440 + 0.748229i \(0.269096\pi\)
\(398\) −12.6649 −0.634833
\(399\) −37.0901 −1.85683
\(400\) 49.4267 2.47134
\(401\) −32.3352 −1.61474 −0.807371 0.590044i \(-0.799110\pi\)
−0.807371 + 0.590044i \(0.799110\pi\)
\(402\) −26.2297 −1.30822
\(403\) −35.4985 −1.76831
\(404\) −17.2991 −0.860661
\(405\) 25.4337 1.26381
\(406\) −94.3326 −4.68165
\(407\) −5.22371 −0.258930
\(408\) 33.0863 1.63802
\(409\) −24.2044 −1.19683 −0.598414 0.801187i \(-0.704202\pi\)
−0.598414 + 0.801187i \(0.704202\pi\)
\(410\) −85.5543 −4.22523
\(411\) 17.8816 0.882033
\(412\) −25.7612 −1.26916
\(413\) −64.6204 −3.17976
\(414\) −0.767718 −0.0377313
\(415\) 22.7248 1.11552
\(416\) 12.5029 0.613006
\(417\) 18.0804 0.885402
\(418\) 65.8910 3.22284
\(419\) 24.2859 1.18645 0.593223 0.805038i \(-0.297855\pi\)
0.593223 + 0.805038i \(0.297855\pi\)
\(420\) −116.149 −5.66747
\(421\) −11.4156 −0.556363 −0.278181 0.960529i \(-0.589732\pi\)
−0.278181 + 0.960529i \(0.589732\pi\)
\(422\) −24.7035 −1.20255
\(423\) 2.69042 0.130813
\(424\) 53.2145 2.58433
\(425\) −31.0271 −1.50504
\(426\) 14.9427 0.723978
\(427\) 35.2188 1.70436
\(428\) −29.3114 −1.41682
\(429\) −31.7313 −1.53200
\(430\) −13.3246 −0.642567
\(431\) −6.27698 −0.302352 −0.151176 0.988507i \(-0.548306\pi\)
−0.151176 + 0.988507i \(0.548306\pi\)
\(432\) −32.6889 −1.57274
\(433\) −14.9111 −0.716582 −0.358291 0.933610i \(-0.616640\pi\)
−0.358291 + 0.933610i \(0.616640\pi\)
\(434\) −108.208 −5.19416
\(435\) −45.2492 −2.16953
\(436\) −4.29722 −0.205799
\(437\) 2.67326 0.127879
\(438\) 56.3605 2.69301
\(439\) −29.6766 −1.41639 −0.708195 0.706017i \(-0.750490\pi\)
−0.708195 + 0.706017i \(0.750490\pi\)
\(440\) 110.306 5.25861
\(441\) −8.89025 −0.423345
\(442\) −36.0818 −1.71624
\(443\) 22.5315 1.07051 0.535253 0.844692i \(-0.320216\pi\)
0.535253 + 0.844692i \(0.320216\pi\)
\(444\) −6.69145 −0.317562
\(445\) 10.9556 0.519345
\(446\) 60.6051 2.86973
\(447\) 14.8788 0.703744
\(448\) −17.5349 −0.828446
\(449\) −36.4547 −1.72040 −0.860202 0.509953i \(-0.829663\pi\)
−0.860202 + 0.509953i \(0.829663\pi\)
\(450\) 12.1517 0.572836
\(451\) −48.6189 −2.28937
\(452\) −78.8973 −3.71102
\(453\) −24.1598 −1.13512
\(454\) −20.5406 −0.964019
\(455\) 67.7124 3.17441
\(456\) 45.1214 2.11300
\(457\) 3.45807 0.161762 0.0808808 0.996724i \(-0.474227\pi\)
0.0808808 + 0.996724i \(0.474227\pi\)
\(458\) 35.6585 1.66621
\(459\) 20.5201 0.957796
\(460\) 8.37137 0.390317
\(461\) −4.04873 −0.188568 −0.0942841 0.995545i \(-0.530056\pi\)
−0.0942841 + 0.995545i \(0.530056\pi\)
\(462\) −96.7248 −4.50005
\(463\) 4.48700 0.208528 0.104264 0.994550i \(-0.466751\pi\)
0.104264 + 0.994550i \(0.466751\pi\)
\(464\) 46.5796 2.16240
\(465\) −51.9051 −2.40704
\(466\) 21.2042 0.982264
\(467\) 27.8009 1.28647 0.643235 0.765669i \(-0.277592\pi\)
0.643235 + 0.765669i \(0.277592\pi\)
\(468\) 9.64322 0.445758
\(469\) 31.8080 1.46876
\(470\) −42.9909 −1.98302
\(471\) −16.4609 −0.758480
\(472\) 78.6131 3.61846
\(473\) −7.57209 −0.348165
\(474\) −12.1532 −0.558217
\(475\) −42.3131 −1.94146
\(476\) −75.0547 −3.44013
\(477\) 5.31023 0.243139
\(478\) 0.847293 0.0387543
\(479\) 22.0749 1.00863 0.504314 0.863520i \(-0.331745\pi\)
0.504314 + 0.863520i \(0.331745\pi\)
\(480\) 18.2815 0.834431
\(481\) 3.90099 0.177870
\(482\) 4.24667 0.193430
\(483\) −3.92421 −0.178558
\(484\) 69.9894 3.18134
\(485\) −60.6993 −2.75621
\(486\) −14.7802 −0.670443
\(487\) 9.65733 0.437616 0.218808 0.975768i \(-0.429783\pi\)
0.218808 + 0.975768i \(0.429783\pi\)
\(488\) −42.8449 −1.93950
\(489\) 6.18936 0.279892
\(490\) 142.060 6.41760
\(491\) −10.8227 −0.488421 −0.244210 0.969722i \(-0.578529\pi\)
−0.244210 + 0.969722i \(0.578529\pi\)
\(492\) −62.2797 −2.80778
\(493\) −29.2398 −1.31690
\(494\) −49.2065 −2.21390
\(495\) 11.0073 0.494741
\(496\) 53.4311 2.39913
\(497\) −18.1207 −0.812823
\(498\) 24.2418 1.08630
\(499\) 8.82635 0.395122 0.197561 0.980291i \(-0.436698\pi\)
0.197561 + 0.980291i \(0.436698\pi\)
\(500\) −53.8003 −2.40602
\(501\) 1.86712 0.0834166
\(502\) 33.4172 1.49148
\(503\) −40.2122 −1.79297 −0.896487 0.443071i \(-0.853889\pi\)
−0.896487 + 0.443071i \(0.853889\pi\)
\(504\) 15.7140 0.699959
\(505\) 14.7461 0.656193
\(506\) 6.97141 0.309917
\(507\) 3.45337 0.153370
\(508\) −41.8863 −1.85841
\(509\) −9.29491 −0.411990 −0.205995 0.978553i \(-0.566043\pi\)
−0.205995 + 0.978553i \(0.566043\pi\)
\(510\) −52.7580 −2.33616
\(511\) −68.3469 −3.02349
\(512\) 48.8775 2.16010
\(513\) 27.9842 1.23553
\(514\) 47.0870 2.07692
\(515\) 21.9594 0.967646
\(516\) −9.69967 −0.427004
\(517\) −24.4309 −1.07447
\(518\) 11.8912 0.522470
\(519\) 16.9678 0.744804
\(520\) −82.3746 −3.61237
\(521\) 30.4907 1.33582 0.667911 0.744241i \(-0.267189\pi\)
0.667911 + 0.744241i \(0.267189\pi\)
\(522\) 11.4517 0.501227
\(523\) −29.7316 −1.30007 −0.650037 0.759903i \(-0.725247\pi\)
−0.650037 + 0.759903i \(0.725247\pi\)
\(524\) 68.4868 2.99186
\(525\) 62.1136 2.71086
\(526\) 17.2450 0.751916
\(527\) −33.5408 −1.46106
\(528\) 47.7608 2.07852
\(529\) −22.7172 −0.987703
\(530\) −84.8536 −3.68580
\(531\) 7.84473 0.340432
\(532\) −102.356 −4.43768
\(533\) 36.3079 1.57267
\(534\) 11.6870 0.505745
\(535\) 24.9856 1.08022
\(536\) −38.6956 −1.67140
\(537\) 14.8780 0.642031
\(538\) 13.7366 0.592227
\(539\) 80.7297 3.47727
\(540\) 87.6333 3.77114
\(541\) −38.1722 −1.64115 −0.820575 0.571538i \(-0.806347\pi\)
−0.820575 + 0.571538i \(0.806347\pi\)
\(542\) 5.14263 0.220895
\(543\) −12.4587 −0.534654
\(544\) 11.8134 0.506496
\(545\) 3.66304 0.156907
\(546\) 72.2327 3.09128
\(547\) 19.5715 0.836817 0.418409 0.908259i \(-0.362588\pi\)
0.418409 + 0.908259i \(0.362588\pi\)
\(548\) 49.3469 2.10800
\(549\) −4.27545 −0.182472
\(550\) −110.346 −4.70516
\(551\) −39.8758 −1.69876
\(552\) 4.77394 0.203192
\(553\) 14.7379 0.626720
\(554\) 24.5995 1.04513
\(555\) 5.70394 0.242119
\(556\) 49.8956 2.11605
\(557\) −25.3215 −1.07291 −0.536453 0.843930i \(-0.680236\pi\)
−0.536453 + 0.843930i \(0.680236\pi\)
\(558\) 13.1362 0.556099
\(559\) 5.65473 0.239170
\(560\) −101.918 −4.30684
\(561\) −29.9814 −1.26581
\(562\) 49.5331 2.08943
\(563\) −6.23855 −0.262923 −0.131462 0.991321i \(-0.541967\pi\)
−0.131462 + 0.991321i \(0.541967\pi\)
\(564\) −31.2954 −1.31777
\(565\) 67.2537 2.82939
\(566\) 78.4455 3.29731
\(567\) −32.9017 −1.38174
\(568\) 22.0445 0.924965
\(569\) 40.2415 1.68701 0.843506 0.537120i \(-0.180488\pi\)
0.843506 + 0.537120i \(0.180488\pi\)
\(570\) −71.9486 −3.01359
\(571\) 13.1388 0.549842 0.274921 0.961467i \(-0.411348\pi\)
0.274921 + 0.961467i \(0.411348\pi\)
\(572\) −87.5672 −3.66137
\(573\) −15.4961 −0.647360
\(574\) 110.676 4.61951
\(575\) −4.47682 −0.186696
\(576\) 2.12869 0.0886953
\(577\) 3.63653 0.151391 0.0756955 0.997131i \(-0.475882\pi\)
0.0756955 + 0.997131i \(0.475882\pi\)
\(578\) 8.56823 0.356391
\(579\) 11.4190 0.474557
\(580\) −124.872 −5.18503
\(581\) −29.3974 −1.21961
\(582\) −64.7514 −2.68403
\(583\) −48.2206 −1.99709
\(584\) 83.1465 3.44063
\(585\) −8.22009 −0.339859
\(586\) −20.3820 −0.841974
\(587\) 21.3888 0.882811 0.441405 0.897308i \(-0.354480\pi\)
0.441405 + 0.897308i \(0.354480\pi\)
\(588\) 103.413 4.26468
\(589\) −45.7412 −1.88473
\(590\) −125.353 −5.16070
\(591\) 8.52066 0.350493
\(592\) −5.87164 −0.241323
\(593\) −40.3708 −1.65783 −0.828916 0.559373i \(-0.811042\pi\)
−0.828916 + 0.559373i \(0.811042\pi\)
\(594\) 72.9782 2.99433
\(595\) 63.9783 2.62285
\(596\) 41.0604 1.68190
\(597\) 7.85887 0.321642
\(598\) −5.20615 −0.212895
\(599\) 14.3270 0.585386 0.292693 0.956207i \(-0.405449\pi\)
0.292693 + 0.956207i \(0.405449\pi\)
\(600\) −75.5635 −3.08487
\(601\) −15.6938 −0.640165 −0.320083 0.947390i \(-0.603711\pi\)
−0.320083 + 0.947390i \(0.603711\pi\)
\(602\) 17.2370 0.702529
\(603\) −3.86140 −0.157249
\(604\) −66.6725 −2.71287
\(605\) −59.6605 −2.42554
\(606\) 15.7305 0.639009
\(607\) −13.3386 −0.541398 −0.270699 0.962664i \(-0.587255\pi\)
−0.270699 + 0.962664i \(0.587255\pi\)
\(608\) 16.1105 0.653367
\(609\) 58.5357 2.37198
\(610\) 68.3186 2.76614
\(611\) 18.2446 0.738099
\(612\) 9.11142 0.368307
\(613\) 21.3728 0.863239 0.431620 0.902056i \(-0.357942\pi\)
0.431620 + 0.902056i \(0.357942\pi\)
\(614\) 7.14016 0.288153
\(615\) 53.0885 2.14074
\(616\) −142.694 −5.74932
\(617\) −40.3810 −1.62568 −0.812840 0.582488i \(-0.802079\pi\)
−0.812840 + 0.582488i \(0.802079\pi\)
\(618\) 23.4253 0.942305
\(619\) −15.6995 −0.631018 −0.315509 0.948923i \(-0.602175\pi\)
−0.315509 + 0.948923i \(0.602175\pi\)
\(620\) −143.240 −5.75265
\(621\) 2.96079 0.118812
\(622\) −36.5925 −1.46723
\(623\) −14.1725 −0.567809
\(624\) −35.6671 −1.42783
\(625\) 3.77119 0.150847
\(626\) 5.25012 0.209837
\(627\) −40.8870 −1.63287
\(628\) −45.4264 −1.81271
\(629\) 3.68586 0.146965
\(630\) −25.0569 −0.998291
\(631\) −6.34405 −0.252553 −0.126276 0.991995i \(-0.540303\pi\)
−0.126276 + 0.991995i \(0.540303\pi\)
\(632\) −17.9292 −0.713185
\(633\) 15.3291 0.609279
\(634\) −22.2368 −0.883136
\(635\) 35.7048 1.41690
\(636\) −61.7695 −2.44932
\(637\) −60.2878 −2.38869
\(638\) −103.989 −4.11698
\(639\) 2.19980 0.0870226
\(640\) −57.4953 −2.27270
\(641\) −44.0719 −1.74074 −0.870368 0.492402i \(-0.836119\pi\)
−0.870368 + 0.492402i \(0.836119\pi\)
\(642\) 26.6536 1.05193
\(643\) 3.68166 0.145191 0.0725953 0.997361i \(-0.476872\pi\)
0.0725953 + 0.997361i \(0.476872\pi\)
\(644\) −10.8294 −0.426740
\(645\) 8.26821 0.325561
\(646\) −46.4929 −1.82924
\(647\) −50.6441 −1.99103 −0.995513 0.0946247i \(-0.969835\pi\)
−0.995513 + 0.0946247i \(0.969835\pi\)
\(648\) 40.0261 1.57238
\(649\) −71.2356 −2.79624
\(650\) 82.4046 3.23218
\(651\) 67.1459 2.63165
\(652\) 17.0805 0.668923
\(653\) 44.6441 1.74706 0.873530 0.486770i \(-0.161825\pi\)
0.873530 + 0.486770i \(0.161825\pi\)
\(654\) 3.90758 0.152798
\(655\) −58.3797 −2.28108
\(656\) −54.6494 −2.13370
\(657\) 8.29712 0.323701
\(658\) 55.6142 2.16807
\(659\) 31.2563 1.21757 0.608786 0.793335i \(-0.291657\pi\)
0.608786 + 0.793335i \(0.291657\pi\)
\(660\) −128.039 −4.98390
\(661\) −27.3462 −1.06364 −0.531822 0.846856i \(-0.678492\pi\)
−0.531822 + 0.846856i \(0.678492\pi\)
\(662\) 53.7026 2.08721
\(663\) 22.3897 0.869542
\(664\) 35.7630 1.38788
\(665\) 87.2502 3.38342
\(666\) −1.44356 −0.0559367
\(667\) −4.21894 −0.163358
\(668\) 5.15259 0.199360
\(669\) −37.6069 −1.45397
\(670\) 61.7023 2.38377
\(671\) 38.8241 1.49879
\(672\) −23.6494 −0.912297
\(673\) 10.5837 0.407973 0.203987 0.978974i \(-0.434610\pi\)
0.203987 + 0.978974i \(0.434610\pi\)
\(674\) 26.4319 1.01812
\(675\) −46.8643 −1.80381
\(676\) 9.53011 0.366543
\(677\) 8.00730 0.307746 0.153873 0.988091i \(-0.450825\pi\)
0.153873 + 0.988091i \(0.450825\pi\)
\(678\) 71.7434 2.75529
\(679\) 78.5224 3.01341
\(680\) −77.8319 −2.98472
\(681\) 12.7459 0.488426
\(682\) −119.286 −4.56768
\(683\) 13.9415 0.533455 0.266728 0.963772i \(-0.414058\pi\)
0.266728 + 0.963772i \(0.414058\pi\)
\(684\) 12.4257 0.475108
\(685\) −42.0644 −1.60720
\(686\) −100.534 −3.83840
\(687\) −22.1270 −0.844196
\(688\) −8.51131 −0.324491
\(689\) 36.0105 1.37189
\(690\) −7.61232 −0.289796
\(691\) 47.4223 1.80403 0.902015 0.431704i \(-0.142087\pi\)
0.902015 + 0.431704i \(0.142087\pi\)
\(692\) 46.8253 1.78003
\(693\) −14.2394 −0.540908
\(694\) 38.9200 1.47738
\(695\) −42.5321 −1.61334
\(696\) −71.2107 −2.69924
\(697\) 34.3056 1.29942
\(698\) 36.5800 1.38457
\(699\) −13.1577 −0.497670
\(700\) 171.412 6.47876
\(701\) −18.2394 −0.688892 −0.344446 0.938806i \(-0.611933\pi\)
−0.344446 + 0.938806i \(0.611933\pi\)
\(702\) −54.4991 −2.05694
\(703\) 5.02658 0.189581
\(704\) −19.3300 −0.728525
\(705\) 26.6769 1.00471
\(706\) −55.6758 −2.09539
\(707\) −19.0760 −0.717426
\(708\) −91.2512 −3.42943
\(709\) 21.8973 0.822372 0.411186 0.911552i \(-0.365115\pi\)
0.411186 + 0.911552i \(0.365115\pi\)
\(710\) −35.1511 −1.31920
\(711\) −1.78914 −0.0670980
\(712\) 17.2413 0.646147
\(713\) −4.83952 −0.181241
\(714\) 68.2493 2.55417
\(715\) 74.6442 2.79153
\(716\) 41.0580 1.53441
\(717\) −0.525766 −0.0196351
\(718\) 38.4991 1.43677
\(719\) −11.2021 −0.417770 −0.208885 0.977940i \(-0.566983\pi\)
−0.208885 + 0.977940i \(0.566983\pi\)
\(720\) 12.3726 0.461100
\(721\) −28.4073 −1.05794
\(722\) −15.7254 −0.585241
\(723\) −2.63516 −0.0980027
\(724\) −34.3817 −1.27778
\(725\) 66.7787 2.48010
\(726\) −63.6432 −2.36202
\(727\) −30.8841 −1.14543 −0.572715 0.819755i \(-0.694110\pi\)
−0.572715 + 0.819755i \(0.694110\pi\)
\(728\) 106.562 3.94946
\(729\) 30.0014 1.11116
\(730\) −132.582 −4.90707
\(731\) 5.34288 0.197614
\(732\) 49.7328 1.83818
\(733\) 51.2138 1.89162 0.945812 0.324713i \(-0.105268\pi\)
0.945812 + 0.324713i \(0.105268\pi\)
\(734\) −51.6658 −1.90702
\(735\) −88.1514 −3.25151
\(736\) 1.70453 0.0628297
\(737\) 35.0643 1.29161
\(738\) −13.4357 −0.494574
\(739\) 18.0742 0.664872 0.332436 0.943126i \(-0.392130\pi\)
0.332436 + 0.943126i \(0.392130\pi\)
\(740\) 15.7409 0.578646
\(741\) 30.5338 1.12169
\(742\) 109.769 4.02975
\(743\) 40.4259 1.48308 0.741542 0.670906i \(-0.234095\pi\)
0.741542 + 0.670906i \(0.234095\pi\)
\(744\) −81.6854 −2.99473
\(745\) −35.0008 −1.28233
\(746\) 76.1759 2.78900
\(747\) 3.56876 0.130574
\(748\) −82.7381 −3.02520
\(749\) −32.3221 −1.18103
\(750\) 48.9221 1.78638
\(751\) 17.7809 0.648834 0.324417 0.945914i \(-0.394832\pi\)
0.324417 + 0.945914i \(0.394832\pi\)
\(752\) −27.4612 −1.00141
\(753\) −20.7362 −0.755668
\(754\) 77.6579 2.82813
\(755\) 56.8331 2.06837
\(756\) −113.365 −4.12304
\(757\) −28.6166 −1.04009 −0.520043 0.854140i \(-0.674084\pi\)
−0.520043 + 0.854140i \(0.674084\pi\)
\(758\) −38.3102 −1.39149
\(759\) −4.32593 −0.157021
\(760\) −106.143 −3.85021
\(761\) −4.05011 −0.146816 −0.0734082 0.997302i \(-0.523388\pi\)
−0.0734082 + 0.997302i \(0.523388\pi\)
\(762\) 38.0884 1.37980
\(763\) −4.73862 −0.171549
\(764\) −42.7639 −1.54714
\(765\) −7.76677 −0.280808
\(766\) 21.9799 0.794165
\(767\) 53.1978 1.92086
\(768\) −49.8093 −1.79734
\(769\) 14.7109 0.530487 0.265244 0.964181i \(-0.414548\pi\)
0.265244 + 0.964181i \(0.414548\pi\)
\(770\) 227.534 8.19976
\(771\) −29.2186 −1.05228
\(772\) 31.5124 1.13416
\(773\) −8.56342 −0.308005 −0.154002 0.988070i \(-0.549216\pi\)
−0.154002 + 0.988070i \(0.549216\pi\)
\(774\) −2.09253 −0.0752143
\(775\) 76.6014 2.75161
\(776\) −95.5253 −3.42916
\(777\) −7.37878 −0.264712
\(778\) −38.6749 −1.38656
\(779\) 46.7842 1.67622
\(780\) 95.6175 3.42366
\(781\) −19.9757 −0.714787
\(782\) −4.91905 −0.175905
\(783\) −44.1648 −1.57832
\(784\) 90.7432 3.24083
\(785\) 38.7225 1.38206
\(786\) −62.2769 −2.22134
\(787\) −21.5824 −0.769330 −0.384665 0.923056i \(-0.625683\pi\)
−0.384665 + 0.923056i \(0.625683\pi\)
\(788\) 23.5141 0.837654
\(789\) −10.7009 −0.380963
\(790\) 28.5891 1.01716
\(791\) −87.0014 −3.09341
\(792\) 17.3227 0.615535
\(793\) −28.9933 −1.02958
\(794\) −66.3440 −2.35446
\(795\) 52.6537 1.86743
\(796\) 21.6877 0.768702
\(797\) 11.3298 0.401320 0.200660 0.979661i \(-0.435691\pi\)
0.200660 + 0.979661i \(0.435691\pi\)
\(798\) 93.0748 3.29481
\(799\) 17.2385 0.609854
\(800\) −26.9798 −0.953879
\(801\) 1.72050 0.0607908
\(802\) 81.1428 2.86525
\(803\) −75.3436 −2.65882
\(804\) 44.9165 1.58408
\(805\) 9.23126 0.325359
\(806\) 89.0808 3.13774
\(807\) −8.52389 −0.300055
\(808\) 23.2066 0.816406
\(809\) −14.5982 −0.513244 −0.256622 0.966512i \(-0.582610\pi\)
−0.256622 + 0.966512i \(0.582610\pi\)
\(810\) −63.8239 −2.24254
\(811\) 3.90842 0.137243 0.0686216 0.997643i \(-0.478140\pi\)
0.0686216 + 0.997643i \(0.478140\pi\)
\(812\) 161.538 5.66887
\(813\) −3.19112 −0.111918
\(814\) 13.1085 0.459453
\(815\) −14.5598 −0.510006
\(816\) −33.7002 −1.17974
\(817\) 7.28634 0.254917
\(818\) 60.7390 2.12369
\(819\) 10.6337 0.371573
\(820\) 146.506 5.11621
\(821\) 19.8006 0.691047 0.345524 0.938410i \(-0.387701\pi\)
0.345524 + 0.938410i \(0.387701\pi\)
\(822\) −44.8725 −1.56511
\(823\) −3.83510 −0.133683 −0.0668416 0.997764i \(-0.521292\pi\)
−0.0668416 + 0.997764i \(0.521292\pi\)
\(824\) 34.5585 1.20390
\(825\) 68.4722 2.38390
\(826\) 162.160 5.64227
\(827\) 37.7819 1.31381 0.656903 0.753975i \(-0.271866\pi\)
0.656903 + 0.753975i \(0.271866\pi\)
\(828\) 1.31466 0.0456877
\(829\) −31.4880 −1.09362 −0.546811 0.837256i \(-0.684158\pi\)
−0.546811 + 0.837256i \(0.684158\pi\)
\(830\) −57.0262 −1.97941
\(831\) −15.2646 −0.529522
\(832\) 14.4353 0.500455
\(833\) −56.9631 −1.97365
\(834\) −45.3715 −1.57109
\(835\) −4.39218 −0.151998
\(836\) −112.834 −3.90244
\(837\) −50.6611 −1.75110
\(838\) −60.9438 −2.10527
\(839\) 46.3153 1.59898 0.799490 0.600679i \(-0.205103\pi\)
0.799490 + 0.600679i \(0.205103\pi\)
\(840\) 155.813 5.37605
\(841\) 33.9321 1.17007
\(842\) 28.6466 0.987228
\(843\) −30.7365 −1.05862
\(844\) 42.3031 1.45613
\(845\) −8.12367 −0.279463
\(846\) −6.75141 −0.232118
\(847\) 77.1785 2.65188
\(848\) −54.2018 −1.86130
\(849\) −48.6773 −1.67060
\(850\) 77.8602 2.67058
\(851\) 0.531824 0.0182307
\(852\) −25.5884 −0.876645
\(853\) −27.6240 −0.945828 −0.472914 0.881109i \(-0.656798\pi\)
−0.472914 + 0.881109i \(0.656798\pi\)
\(854\) −88.3789 −3.02426
\(855\) −10.5919 −0.362236
\(856\) 39.3211 1.34397
\(857\) 48.9285 1.67137 0.835683 0.549212i \(-0.185072\pi\)
0.835683 + 0.549212i \(0.185072\pi\)
\(858\) 79.6272 2.71843
\(859\) 26.3969 0.900650 0.450325 0.892865i \(-0.351308\pi\)
0.450325 + 0.892865i \(0.351308\pi\)
\(860\) 22.8174 0.778066
\(861\) −68.6768 −2.34050
\(862\) 15.7516 0.536503
\(863\) 35.0054 1.19160 0.595799 0.803134i \(-0.296835\pi\)
0.595799 + 0.803134i \(0.296835\pi\)
\(864\) 17.8433 0.607043
\(865\) −39.9149 −1.35715
\(866\) 37.4183 1.27153
\(867\) −5.31679 −0.180568
\(868\) 185.299 6.28947
\(869\) 16.2466 0.551130
\(870\) 113.549 3.84969
\(871\) −26.1855 −0.887261
\(872\) 5.76470 0.195217
\(873\) −9.53238 −0.322622
\(874\) −6.70834 −0.226913
\(875\) −59.3265 −2.00560
\(876\) −96.5135 −3.26089
\(877\) 7.59709 0.256535 0.128268 0.991740i \(-0.459058\pi\)
0.128268 + 0.991740i \(0.459058\pi\)
\(878\) 74.4713 2.51329
\(879\) 12.6475 0.426591
\(880\) −112.352 −3.78738
\(881\) 28.6671 0.965818 0.482909 0.875670i \(-0.339580\pi\)
0.482909 + 0.875670i \(0.339580\pi\)
\(882\) 22.3094 0.751197
\(883\) −35.0356 −1.17904 −0.589521 0.807753i \(-0.700683\pi\)
−0.589521 + 0.807753i \(0.700683\pi\)
\(884\) 61.7876 2.07814
\(885\) 77.7845 2.61470
\(886\) −56.5412 −1.89954
\(887\) −51.1100 −1.71611 −0.858053 0.513561i \(-0.828326\pi\)
−0.858053 + 0.513561i \(0.828326\pi\)
\(888\) 8.97655 0.301233
\(889\) −46.1888 −1.54912
\(890\) −27.4923 −0.921543
\(891\) −36.2699 −1.21509
\(892\) −103.782 −3.47488
\(893\) 23.5089 0.786697
\(894\) −37.3373 −1.24875
\(895\) −34.9987 −1.16988
\(896\) 74.3776 2.48478
\(897\) 3.23054 0.107865
\(898\) 91.4804 3.05274
\(899\) 72.1890 2.40764
\(900\) −20.8089 −0.693630
\(901\) 34.0246 1.13352
\(902\) 122.005 4.06234
\(903\) −10.6960 −0.355940
\(904\) 105.840 3.52020
\(905\) 29.3077 0.974220
\(906\) 60.6271 2.01420
\(907\) −29.1580 −0.968175 −0.484087 0.875020i \(-0.660848\pi\)
−0.484087 + 0.875020i \(0.660848\pi\)
\(908\) 35.1744 1.16730
\(909\) 2.31577 0.0768092
\(910\) −169.919 −5.63277
\(911\) 15.0994 0.500264 0.250132 0.968212i \(-0.419526\pi\)
0.250132 + 0.968212i \(0.419526\pi\)
\(912\) −45.9585 −1.52184
\(913\) −32.4069 −1.07251
\(914\) −8.67776 −0.287035
\(915\) −42.3933 −1.40148
\(916\) −61.0627 −2.01757
\(917\) 75.5216 2.49394
\(918\) −51.4936 −1.69954
\(919\) −45.0741 −1.48686 −0.743428 0.668816i \(-0.766801\pi\)
−0.743428 + 0.668816i \(0.766801\pi\)
\(920\) −11.2302 −0.370247
\(921\) −4.43064 −0.145995
\(922\) 10.1600 0.334602
\(923\) 14.9176 0.491018
\(924\) 165.635 5.44898
\(925\) −8.41787 −0.276778
\(926\) −11.2598 −0.370019
\(927\) 3.44856 0.113266
\(928\) −25.4256 −0.834638
\(929\) 42.2910 1.38752 0.693761 0.720205i \(-0.255952\pi\)
0.693761 + 0.720205i \(0.255952\pi\)
\(930\) 130.252 4.27113
\(931\) −77.6832 −2.54597
\(932\) −36.3107 −1.18940
\(933\) 22.7065 0.743379
\(934\) −69.7642 −2.28275
\(935\) 70.5277 2.30650
\(936\) −12.9363 −0.422837
\(937\) −6.96123 −0.227413 −0.113707 0.993514i \(-0.536272\pi\)
−0.113707 + 0.993514i \(0.536272\pi\)
\(938\) −79.8199 −2.60621
\(939\) −3.25783 −0.106315
\(940\) 73.6189 2.40118
\(941\) 29.0893 0.948284 0.474142 0.880448i \(-0.342758\pi\)
0.474142 + 0.880448i \(0.342758\pi\)
\(942\) 41.3075 1.34587
\(943\) 4.94986 0.161190
\(944\) −80.0715 −2.60611
\(945\) 96.6347 3.14353
\(946\) 19.0016 0.617795
\(947\) −18.5406 −0.602488 −0.301244 0.953547i \(-0.597402\pi\)
−0.301244 + 0.953547i \(0.597402\pi\)
\(948\) 20.8116 0.675929
\(949\) 56.2656 1.82646
\(950\) 106.182 3.44499
\(951\) 13.7985 0.447446
\(952\) 100.686 3.26324
\(953\) 53.3908 1.72950 0.864749 0.502205i \(-0.167478\pi\)
0.864749 + 0.502205i \(0.167478\pi\)
\(954\) −13.3256 −0.431433
\(955\) 36.4529 1.17959
\(956\) −1.45093 −0.0469264
\(957\) 64.5280 2.08589
\(958\) −55.3954 −1.78974
\(959\) 54.4157 1.75717
\(960\) 21.1070 0.681226
\(961\) 51.8075 1.67121
\(962\) −9.78925 −0.315618
\(963\) 3.92381 0.126443
\(964\) −7.27213 −0.234219
\(965\) −26.8619 −0.864715
\(966\) 9.84751 0.316838
\(967\) −40.8793 −1.31459 −0.657295 0.753634i \(-0.728299\pi\)
−0.657295 + 0.753634i \(0.728299\pi\)
\(968\) −93.8904 −3.01775
\(969\) 28.8500 0.926794
\(970\) 152.320 4.89071
\(971\) −33.3048 −1.06880 −0.534402 0.845231i \(-0.679463\pi\)
−0.534402 + 0.845231i \(0.679463\pi\)
\(972\) 25.3100 0.811820
\(973\) 55.0208 1.76389
\(974\) −24.2344 −0.776519
\(975\) −51.1341 −1.63760
\(976\) 43.6398 1.39687
\(977\) −28.1602 −0.900923 −0.450462 0.892796i \(-0.648741\pi\)
−0.450462 + 0.892796i \(0.648741\pi\)
\(978\) −15.5317 −0.496650
\(979\) −15.6233 −0.499324
\(980\) −243.267 −7.77088
\(981\) 0.575254 0.0183664
\(982\) 27.1587 0.866669
\(983\) −46.1640 −1.47240 −0.736201 0.676763i \(-0.763382\pi\)
−0.736201 + 0.676763i \(0.763382\pi\)
\(984\) 83.5479 2.66341
\(985\) −20.0439 −0.638652
\(986\) 73.3752 2.33674
\(987\) −34.5100 −1.09847
\(988\) 84.2627 2.68075
\(989\) 0.770911 0.0245135
\(990\) −27.6220 −0.877884
\(991\) 7.13537 0.226662 0.113331 0.993557i \(-0.463848\pi\)
0.113331 + 0.993557i \(0.463848\pi\)
\(992\) −29.1656 −0.926009
\(993\) −33.3238 −1.05750
\(994\) 45.4725 1.44230
\(995\) −18.4871 −0.586080
\(996\) −41.5125 −1.31537
\(997\) −48.3396 −1.53093 −0.765465 0.643478i \(-0.777491\pi\)
−0.765465 + 0.643478i \(0.777491\pi\)
\(998\) −22.1491 −0.701117
\(999\) 5.56724 0.176140
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 \(a_p\))