Properties

Label 8043.2.a.t.1.11
Level 8043
Weight 2
Character 8043.1
Self dual Yes
Analytic conductor 64.224
Analytic rank 0
Dimension 52
CM No

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Newspace parameters

Level: \( N \) = \( 8043 = 3 \cdot 7 \cdot 383 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8043.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2236783457\)
Analytic rank: \(0\)
Dimension: \(52\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) = 8043.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.85290 q^{2}\) \(-1.00000 q^{3}\) \(+1.43325 q^{4}\) \(-3.21014 q^{5}\) \(+1.85290 q^{6}\) \(+1.00000 q^{7}\) \(+1.05014 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.85290 q^{2}\) \(-1.00000 q^{3}\) \(+1.43325 q^{4}\) \(-3.21014 q^{5}\) \(+1.85290 q^{6}\) \(+1.00000 q^{7}\) \(+1.05014 q^{8}\) \(+1.00000 q^{9}\) \(+5.94808 q^{10}\) \(+4.69097 q^{11}\) \(-1.43325 q^{12}\) \(+2.39172 q^{13}\) \(-1.85290 q^{14}\) \(+3.21014 q^{15}\) \(-4.81230 q^{16}\) \(-5.33525 q^{17}\) \(-1.85290 q^{18}\) \(-0.312316 q^{19}\) \(-4.60092 q^{20}\) \(-1.00000 q^{21}\) \(-8.69191 q^{22}\) \(-5.88569 q^{23}\) \(-1.05014 q^{24}\) \(+5.30500 q^{25}\) \(-4.43163 q^{26}\) \(-1.00000 q^{27}\) \(+1.43325 q^{28}\) \(+7.36152 q^{29}\) \(-5.94808 q^{30}\) \(+0.943195 q^{31}\) \(+6.81644 q^{32}\) \(-4.69097 q^{33}\) \(+9.88569 q^{34}\) \(-3.21014 q^{35}\) \(+1.43325 q^{36}\) \(+7.38664 q^{37}\) \(+0.578692 q^{38}\) \(-2.39172 q^{39}\) \(-3.37110 q^{40}\) \(+2.27743 q^{41}\) \(+1.85290 q^{42}\) \(+5.60881 q^{43}\) \(+6.72332 q^{44}\) \(-3.21014 q^{45}\) \(+10.9056 q^{46}\) \(+1.72173 q^{47}\) \(+4.81230 q^{48}\) \(+1.00000 q^{49}\) \(-9.82965 q^{50}\) \(+5.33525 q^{51}\) \(+3.42793 q^{52}\) \(+3.85567 q^{53}\) \(+1.85290 q^{54}\) \(-15.0587 q^{55}\) \(+1.05014 q^{56}\) \(+0.312316 q^{57}\) \(-13.6402 q^{58}\) \(-14.5600 q^{59}\) \(+4.60092 q^{60}\) \(+10.7348 q^{61}\) \(-1.74765 q^{62}\) \(+1.00000 q^{63}\) \(-3.00559 q^{64}\) \(-7.67777 q^{65}\) \(+8.69191 q^{66}\) \(-7.76670 q^{67}\) \(-7.64672 q^{68}\) \(+5.88569 q^{69}\) \(+5.94808 q^{70}\) \(-1.06851 q^{71}\) \(+1.05014 q^{72}\) \(+15.6913 q^{73}\) \(-13.6867 q^{74}\) \(-5.30500 q^{75}\) \(-0.447626 q^{76}\) \(+4.69097 q^{77}\) \(+4.43163 q^{78}\) \(-8.92717 q^{79}\) \(+15.4482 q^{80}\) \(+1.00000 q^{81}\) \(-4.21985 q^{82}\) \(+12.7810 q^{83}\) \(-1.43325 q^{84}\) \(+17.1269 q^{85}\) \(-10.3926 q^{86}\) \(-7.36152 q^{87}\) \(+4.92618 q^{88}\) \(+18.7109 q^{89}\) \(+5.94808 q^{90}\) \(+2.39172 q^{91}\) \(-8.43564 q^{92}\) \(-0.943195 q^{93}\) \(-3.19020 q^{94}\) \(+1.00258 q^{95}\) \(-6.81644 q^{96}\) \(+6.81283 q^{97}\) \(-1.85290 q^{98}\) \(+4.69097 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(52q \) \(\mathstrut +\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut 52q^{3} \) \(\mathstrut +\mathstrut 61q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 3q^{6} \) \(\mathstrut +\mathstrut 52q^{7} \) \(\mathstrut +\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 52q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(52q \) \(\mathstrut +\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut 52q^{3} \) \(\mathstrut +\mathstrut 61q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 3q^{6} \) \(\mathstrut +\mathstrut 52q^{7} \) \(\mathstrut +\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 52q^{9} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut +\mathstrut 9q^{11} \) \(\mathstrut -\mathstrut 61q^{12} \) \(\mathstrut +\mathstrut 44q^{13} \) \(\mathstrut +\mathstrut 3q^{14} \) \(\mathstrut +\mathstrut 7q^{15} \) \(\mathstrut +\mathstrut 95q^{16} \) \(\mathstrut -\mathstrut 6q^{17} \) \(\mathstrut +\mathstrut 3q^{18} \) \(\mathstrut +\mathstrut 7q^{19} \) \(\mathstrut -\mathstrut 21q^{20} \) \(\mathstrut -\mathstrut 52q^{21} \) \(\mathstrut +\mathstrut 19q^{22} \) \(\mathstrut -\mathstrut 4q^{23} \) \(\mathstrut -\mathstrut 24q^{24} \) \(\mathstrut +\mathstrut 83q^{25} \) \(\mathstrut -\mathstrut 5q^{26} \) \(\mathstrut -\mathstrut 52q^{27} \) \(\mathstrut +\mathstrut 61q^{28} \) \(\mathstrut +\mathstrut 31q^{29} \) \(\mathstrut +\mathstrut 2q^{30} \) \(\mathstrut +\mathstrut 11q^{31} \) \(\mathstrut +\mathstrut 71q^{32} \) \(\mathstrut -\mathstrut 9q^{33} \) \(\mathstrut +\mathstrut 17q^{34} \) \(\mathstrut -\mathstrut 7q^{35} \) \(\mathstrut +\mathstrut 61q^{36} \) \(\mathstrut +\mathstrut 71q^{37} \) \(\mathstrut -\mathstrut 8q^{38} \) \(\mathstrut -\mathstrut 44q^{39} \) \(\mathstrut +\mathstrut 20q^{40} \) \(\mathstrut -\mathstrut 25q^{41} \) \(\mathstrut -\mathstrut 3q^{42} \) \(\mathstrut +\mathstrut 75q^{43} \) \(\mathstrut +\mathstrut 14q^{44} \) \(\mathstrut -\mathstrut 7q^{45} \) \(\mathstrut +\mathstrut 36q^{46} \) \(\mathstrut -\mathstrut 20q^{47} \) \(\mathstrut -\mathstrut 95q^{48} \) \(\mathstrut +\mathstrut 52q^{49} \) \(\mathstrut +\mathstrut 26q^{50} \) \(\mathstrut +\mathstrut 6q^{51} \) \(\mathstrut +\mathstrut 88q^{52} \) \(\mathstrut +\mathstrut 70q^{53} \) \(\mathstrut -\mathstrut 3q^{54} \) \(\mathstrut +\mathstrut 12q^{55} \) \(\mathstrut +\mathstrut 24q^{56} \) \(\mathstrut -\mathstrut 7q^{57} \) \(\mathstrut +\mathstrut 48q^{58} \) \(\mathstrut -\mathstrut 27q^{59} \) \(\mathstrut +\mathstrut 21q^{60} \) \(\mathstrut +\mathstrut 59q^{61} \) \(\mathstrut -\mathstrut 23q^{62} \) \(\mathstrut +\mathstrut 52q^{63} \) \(\mathstrut +\mathstrut 138q^{64} \) \(\mathstrut +\mathstrut 44q^{65} \) \(\mathstrut -\mathstrut 19q^{66} \) \(\mathstrut +\mathstrut 65q^{67} \) \(\mathstrut -\mathstrut 8q^{68} \) \(\mathstrut +\mathstrut 4q^{69} \) \(\mathstrut -\mathstrut 2q^{70} \) \(\mathstrut -\mathstrut 11q^{71} \) \(\mathstrut +\mathstrut 24q^{72} \) \(\mathstrut +\mathstrut 34q^{73} \) \(\mathstrut +\mathstrut 38q^{74} \) \(\mathstrut -\mathstrut 83q^{75} \) \(\mathstrut +\mathstrut 31q^{76} \) \(\mathstrut +\mathstrut 9q^{77} \) \(\mathstrut +\mathstrut 5q^{78} \) \(\mathstrut +\mathstrut 74q^{79} \) \(\mathstrut -\mathstrut 5q^{80} \) \(\mathstrut +\mathstrut 52q^{81} \) \(\mathstrut +\mathstrut 51q^{82} \) \(\mathstrut -\mathstrut 30q^{83} \) \(\mathstrut -\mathstrut 61q^{84} \) \(\mathstrut +\mathstrut 70q^{85} \) \(\mathstrut +\mathstrut 29q^{86} \) \(\mathstrut -\mathstrut 31q^{87} \) \(\mathstrut +\mathstrut 90q^{88} \) \(\mathstrut -\mathstrut q^{89} \) \(\mathstrut -\mathstrut 2q^{90} \) \(\mathstrut +\mathstrut 44q^{91} \) \(\mathstrut +\mathstrut 34q^{92} \) \(\mathstrut -\mathstrut 11q^{93} \) \(\mathstrut +\mathstrut 27q^{94} \) \(\mathstrut +\mathstrut 9q^{95} \) \(\mathstrut -\mathstrut 71q^{96} \) \(\mathstrut +\mathstrut 73q^{97} \) \(\mathstrut +\mathstrut 3q^{98} \) \(\mathstrut +\mathstrut 9q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.85290 −1.31020 −0.655100 0.755542i \(-0.727373\pi\)
−0.655100 + 0.755542i \(0.727373\pi\)
\(3\) −1.00000 −0.577350
\(4\) 1.43325 0.716623
\(5\) −3.21014 −1.43562 −0.717809 0.696240i \(-0.754855\pi\)
−0.717809 + 0.696240i \(0.754855\pi\)
\(6\) 1.85290 0.756444
\(7\) 1.00000 0.377964
\(8\) 1.05014 0.371281
\(9\) 1.00000 0.333333
\(10\) 5.94808 1.88095
\(11\) 4.69097 1.41438 0.707191 0.707023i \(-0.249962\pi\)
0.707191 + 0.707023i \(0.249962\pi\)
\(12\) −1.43325 −0.413742
\(13\) 2.39172 0.663345 0.331672 0.943395i \(-0.392387\pi\)
0.331672 + 0.943395i \(0.392387\pi\)
\(14\) −1.85290 −0.495209
\(15\) 3.21014 0.828855
\(16\) −4.81230 −1.20307
\(17\) −5.33525 −1.29399 −0.646994 0.762495i \(-0.723974\pi\)
−0.646994 + 0.762495i \(0.723974\pi\)
\(18\) −1.85290 −0.436733
\(19\) −0.312316 −0.0716503 −0.0358252 0.999358i \(-0.511406\pi\)
−0.0358252 + 0.999358i \(0.511406\pi\)
\(20\) −4.60092 −1.02880
\(21\) −1.00000 −0.218218
\(22\) −8.69191 −1.85312
\(23\) −5.88569 −1.22725 −0.613625 0.789597i \(-0.710289\pi\)
−0.613625 + 0.789597i \(0.710289\pi\)
\(24\) −1.05014 −0.214359
\(25\) 5.30500 1.06100
\(26\) −4.43163 −0.869114
\(27\) −1.00000 −0.192450
\(28\) 1.43325 0.270858
\(29\) 7.36152 1.36700 0.683500 0.729951i \(-0.260457\pi\)
0.683500 + 0.729951i \(0.260457\pi\)
\(30\) −5.94808 −1.08597
\(31\) 0.943195 0.169403 0.0847014 0.996406i \(-0.473006\pi\)
0.0847014 + 0.996406i \(0.473006\pi\)
\(32\) 6.81644 1.20499
\(33\) −4.69097 −0.816594
\(34\) 9.88569 1.69538
\(35\) −3.21014 −0.542613
\(36\) 1.43325 0.238874
\(37\) 7.38664 1.21436 0.607178 0.794566i \(-0.292301\pi\)
0.607178 + 0.794566i \(0.292301\pi\)
\(38\) 0.578692 0.0938762
\(39\) −2.39172 −0.382982
\(40\) −3.37110 −0.533017
\(41\) 2.27743 0.355674 0.177837 0.984060i \(-0.443090\pi\)
0.177837 + 0.984060i \(0.443090\pi\)
\(42\) 1.85290 0.285909
\(43\) 5.60881 0.855336 0.427668 0.903936i \(-0.359335\pi\)
0.427668 + 0.903936i \(0.359335\pi\)
\(44\) 6.72332 1.01358
\(45\) −3.21014 −0.478539
\(46\) 10.9056 1.60794
\(47\) 1.72173 0.251140 0.125570 0.992085i \(-0.459924\pi\)
0.125570 + 0.992085i \(0.459924\pi\)
\(48\) 4.81230 0.694595
\(49\) 1.00000 0.142857
\(50\) −9.82965 −1.39012
\(51\) 5.33525 0.747084
\(52\) 3.42793 0.475368
\(53\) 3.85567 0.529617 0.264808 0.964301i \(-0.414691\pi\)
0.264808 + 0.964301i \(0.414691\pi\)
\(54\) 1.85290 0.252148
\(55\) −15.0587 −2.03051
\(56\) 1.05014 0.140331
\(57\) 0.312316 0.0413673
\(58\) −13.6402 −1.79104
\(59\) −14.5600 −1.89556 −0.947778 0.318932i \(-0.896676\pi\)
−0.947778 + 0.318932i \(0.896676\pi\)
\(60\) 4.60092 0.593976
\(61\) 10.7348 1.37445 0.687224 0.726446i \(-0.258829\pi\)
0.687224 + 0.726446i \(0.258829\pi\)
\(62\) −1.74765 −0.221951
\(63\) 1.00000 0.125988
\(64\) −3.00559 −0.375699
\(65\) −7.67777 −0.952310
\(66\) 8.69191 1.06990
\(67\) −7.76670 −0.948853 −0.474426 0.880295i \(-0.657345\pi\)
−0.474426 + 0.880295i \(0.657345\pi\)
\(68\) −7.64672 −0.927301
\(69\) 5.88569 0.708553
\(70\) 5.94808 0.710931
\(71\) −1.06851 −0.126809 −0.0634044 0.997988i \(-0.520196\pi\)
−0.0634044 + 0.997988i \(0.520196\pi\)
\(72\) 1.05014 0.123760
\(73\) 15.6913 1.83653 0.918266 0.395964i \(-0.129589\pi\)
0.918266 + 0.395964i \(0.129589\pi\)
\(74\) −13.6867 −1.59105
\(75\) −5.30500 −0.612569
\(76\) −0.447626 −0.0513463
\(77\) 4.69097 0.534586
\(78\) 4.43163 0.501783
\(79\) −8.92717 −1.00438 −0.502192 0.864756i \(-0.667473\pi\)
−0.502192 + 0.864756i \(0.667473\pi\)
\(80\) 15.4482 1.72716
\(81\) 1.00000 0.111111
\(82\) −4.21985 −0.466004
\(83\) 12.7810 1.40289 0.701447 0.712722i \(-0.252538\pi\)
0.701447 + 0.712722i \(0.252538\pi\)
\(84\) −1.43325 −0.156380
\(85\) 17.1269 1.85767
\(86\) −10.3926 −1.12066
\(87\) −7.36152 −0.789237
\(88\) 4.92618 0.525132
\(89\) 18.7109 1.98335 0.991674 0.128776i \(-0.0411047\pi\)
0.991674 + 0.128776i \(0.0411047\pi\)
\(90\) 5.94808 0.626982
\(91\) 2.39172 0.250721
\(92\) −8.43564 −0.879476
\(93\) −0.943195 −0.0978047
\(94\) −3.19020 −0.329044
\(95\) 1.00258 0.102863
\(96\) −6.81644 −0.695700
\(97\) 6.81283 0.691738 0.345869 0.938283i \(-0.387584\pi\)
0.345869 + 0.938283i \(0.387584\pi\)
\(98\) −1.85290 −0.187171
\(99\) 4.69097 0.471461
\(100\) 7.60337 0.760337
\(101\) −13.6015 −1.35340 −0.676702 0.736257i \(-0.736592\pi\)
−0.676702 + 0.736257i \(0.736592\pi\)
\(102\) −9.88569 −0.978830
\(103\) −4.83718 −0.476621 −0.238311 0.971189i \(-0.576594\pi\)
−0.238311 + 0.971189i \(0.576594\pi\)
\(104\) 2.51165 0.246287
\(105\) 3.21014 0.313278
\(106\) −7.14417 −0.693903
\(107\) −12.9339 −1.25037 −0.625184 0.780477i \(-0.714976\pi\)
−0.625184 + 0.780477i \(0.714976\pi\)
\(108\) −1.43325 −0.137914
\(109\) 5.11701 0.490121 0.245061 0.969508i \(-0.421192\pi\)
0.245061 + 0.969508i \(0.421192\pi\)
\(110\) 27.9023 2.66038
\(111\) −7.38664 −0.701109
\(112\) −4.81230 −0.454719
\(113\) 13.5759 1.27711 0.638554 0.769577i \(-0.279533\pi\)
0.638554 + 0.769577i \(0.279533\pi\)
\(114\) −0.578692 −0.0541995
\(115\) 18.8939 1.76186
\(116\) 10.5509 0.979623
\(117\) 2.39172 0.221115
\(118\) 26.9783 2.48356
\(119\) −5.33525 −0.489081
\(120\) 3.37110 0.307738
\(121\) 11.0052 1.00048
\(122\) −19.8905 −1.80080
\(123\) −2.27743 −0.205349
\(124\) 1.35183 0.121398
\(125\) −0.979095 −0.0875729
\(126\) −1.85290 −0.165070
\(127\) 17.8346 1.58256 0.791282 0.611451i \(-0.209414\pi\)
0.791282 + 0.611451i \(0.209414\pi\)
\(128\) −8.06380 −0.712746
\(129\) −5.60881 −0.493828
\(130\) 14.2262 1.24772
\(131\) −21.6482 −1.89142 −0.945708 0.325018i \(-0.894630\pi\)
−0.945708 + 0.325018i \(0.894630\pi\)
\(132\) −6.72332 −0.585190
\(133\) −0.312316 −0.0270813
\(134\) 14.3909 1.24319
\(135\) 3.21014 0.276285
\(136\) −5.60276 −0.480433
\(137\) −2.09823 −0.179264 −0.0896320 0.995975i \(-0.528569\pi\)
−0.0896320 + 0.995975i \(0.528569\pi\)
\(138\) −10.9056 −0.928346
\(139\) −18.1952 −1.54330 −0.771650 0.636048i \(-0.780568\pi\)
−0.771650 + 0.636048i \(0.780568\pi\)
\(140\) −4.60092 −0.388849
\(141\) −1.72173 −0.144996
\(142\) 1.97985 0.166145
\(143\) 11.2195 0.938223
\(144\) −4.81230 −0.401025
\(145\) −23.6315 −1.96249
\(146\) −29.0745 −2.40622
\(147\) −1.00000 −0.0824786
\(148\) 10.5869 0.870235
\(149\) −17.8336 −1.46098 −0.730492 0.682922i \(-0.760709\pi\)
−0.730492 + 0.682922i \(0.760709\pi\)
\(150\) 9.82965 0.802587
\(151\) 9.35590 0.761372 0.380686 0.924704i \(-0.375688\pi\)
0.380686 + 0.924704i \(0.375688\pi\)
\(152\) −0.327976 −0.0266024
\(153\) −5.33525 −0.431329
\(154\) −8.69191 −0.700414
\(155\) −3.02779 −0.243198
\(156\) −3.42793 −0.274454
\(157\) −23.3467 −1.86327 −0.931635 0.363396i \(-0.881617\pi\)
−0.931635 + 0.363396i \(0.881617\pi\)
\(158\) 16.5412 1.31594
\(159\) −3.85567 −0.305774
\(160\) −21.8817 −1.72990
\(161\) −5.88569 −0.463857
\(162\) −1.85290 −0.145578
\(163\) 18.9277 1.48254 0.741268 0.671210i \(-0.234225\pi\)
0.741268 + 0.671210i \(0.234225\pi\)
\(164\) 3.26411 0.254884
\(165\) 15.0587 1.17232
\(166\) −23.6819 −1.83807
\(167\) 6.43574 0.498012 0.249006 0.968502i \(-0.419896\pi\)
0.249006 + 0.968502i \(0.419896\pi\)
\(168\) −1.05014 −0.0810201
\(169\) −7.27966 −0.559973
\(170\) −31.7345 −2.43392
\(171\) −0.312316 −0.0238834
\(172\) 8.03881 0.612953
\(173\) −15.7641 −1.19852 −0.599261 0.800554i \(-0.704539\pi\)
−0.599261 + 0.800554i \(0.704539\pi\)
\(174\) 13.6402 1.03406
\(175\) 5.30500 0.401020
\(176\) −22.5744 −1.70161
\(177\) 14.5600 1.09440
\(178\) −34.6694 −2.59858
\(179\) −7.14886 −0.534331 −0.267166 0.963651i \(-0.586087\pi\)
−0.267166 + 0.963651i \(0.586087\pi\)
\(180\) −4.60092 −0.342932
\(181\) −9.10549 −0.676806 −0.338403 0.941001i \(-0.609887\pi\)
−0.338403 + 0.941001i \(0.609887\pi\)
\(182\) −4.43163 −0.328494
\(183\) −10.7348 −0.793538
\(184\) −6.18079 −0.455654
\(185\) −23.7122 −1.74335
\(186\) 1.74765 0.128144
\(187\) −25.0275 −1.83019
\(188\) 2.46766 0.179973
\(189\) −1.00000 −0.0727393
\(190\) −1.85768 −0.134770
\(191\) −19.5972 −1.41800 −0.709001 0.705207i \(-0.750854\pi\)
−0.709001 + 0.705207i \(0.750854\pi\)
\(192\) 3.00559 0.216910
\(193\) −5.18417 −0.373165 −0.186582 0.982439i \(-0.559741\pi\)
−0.186582 + 0.982439i \(0.559741\pi\)
\(194\) −12.6235 −0.906314
\(195\) 7.67777 0.549817
\(196\) 1.43325 0.102375
\(197\) 16.7284 1.19185 0.595926 0.803040i \(-0.296785\pi\)
0.595926 + 0.803040i \(0.296785\pi\)
\(198\) −8.69191 −0.617707
\(199\) 20.7020 1.46752 0.733762 0.679406i \(-0.237763\pi\)
0.733762 + 0.679406i \(0.237763\pi\)
\(200\) 5.57099 0.393929
\(201\) 7.76670 0.547820
\(202\) 25.2023 1.77323
\(203\) 7.36152 0.516677
\(204\) 7.64672 0.535378
\(205\) −7.31086 −0.510613
\(206\) 8.96281 0.624469
\(207\) −5.88569 −0.409083
\(208\) −11.5097 −0.798053
\(209\) −1.46507 −0.101341
\(210\) −5.94808 −0.410456
\(211\) 16.8083 1.15713 0.578567 0.815635i \(-0.303612\pi\)
0.578567 + 0.815635i \(0.303612\pi\)
\(212\) 5.52612 0.379535
\(213\) 1.06851 0.0732131
\(214\) 23.9653 1.63823
\(215\) −18.0051 −1.22794
\(216\) −1.05014 −0.0714530
\(217\) 0.943195 0.0640282
\(218\) −9.48132 −0.642156
\(219\) −15.6913 −1.06032
\(220\) −21.5828 −1.45511
\(221\) −12.7604 −0.858360
\(222\) 13.6867 0.918592
\(223\) −21.3467 −1.42948 −0.714739 0.699392i \(-0.753454\pi\)
−0.714739 + 0.699392i \(0.753454\pi\)
\(224\) 6.81644 0.455442
\(225\) 5.30500 0.353667
\(226\) −25.1547 −1.67327
\(227\) 3.72777 0.247421 0.123711 0.992318i \(-0.460521\pi\)
0.123711 + 0.992318i \(0.460521\pi\)
\(228\) 0.447626 0.0296448
\(229\) −14.4009 −0.951640 −0.475820 0.879543i \(-0.657849\pi\)
−0.475820 + 0.879543i \(0.657849\pi\)
\(230\) −35.0085 −2.30839
\(231\) −4.69097 −0.308643
\(232\) 7.73062 0.507540
\(233\) 26.9701 1.76687 0.883435 0.468553i \(-0.155225\pi\)
0.883435 + 0.468553i \(0.155225\pi\)
\(234\) −4.43163 −0.289705
\(235\) −5.52699 −0.360541
\(236\) −20.8681 −1.35840
\(237\) 8.92717 0.579882
\(238\) 9.88569 0.640794
\(239\) −8.73652 −0.565119 −0.282559 0.959250i \(-0.591183\pi\)
−0.282559 + 0.959250i \(0.591183\pi\)
\(240\) −15.4482 −0.997174
\(241\) −6.09077 −0.392341 −0.196171 0.980570i \(-0.562851\pi\)
−0.196171 + 0.980570i \(0.562851\pi\)
\(242\) −20.3916 −1.31082
\(243\) −1.00000 −0.0641500
\(244\) 15.3856 0.984961
\(245\) −3.21014 −0.205088
\(246\) 4.21985 0.269048
\(247\) −0.746975 −0.0475289
\(248\) 0.990486 0.0628959
\(249\) −12.7810 −0.809961
\(250\) 1.81417 0.114738
\(251\) −25.2040 −1.59086 −0.795431 0.606044i \(-0.792756\pi\)
−0.795431 + 0.606044i \(0.792756\pi\)
\(252\) 1.43325 0.0902860
\(253\) −27.6096 −1.73580
\(254\) −33.0458 −2.07347
\(255\) −17.1269 −1.07253
\(256\) 20.9526 1.30954
\(257\) 7.18529 0.448206 0.224103 0.974565i \(-0.428055\pi\)
0.224103 + 0.974565i \(0.428055\pi\)
\(258\) 10.3926 0.647014
\(259\) 7.38664 0.458983
\(260\) −11.0041 −0.682447
\(261\) 7.36152 0.455666
\(262\) 40.1121 2.47813
\(263\) 1.08053 0.0666282 0.0333141 0.999445i \(-0.489394\pi\)
0.0333141 + 0.999445i \(0.489394\pi\)
\(264\) −4.92618 −0.303185
\(265\) −12.3772 −0.760327
\(266\) 0.578692 0.0354819
\(267\) −18.7109 −1.14509
\(268\) −11.1316 −0.679970
\(269\) −2.00098 −0.122002 −0.0610009 0.998138i \(-0.519429\pi\)
−0.0610009 + 0.998138i \(0.519429\pi\)
\(270\) −5.94808 −0.361988
\(271\) 22.8381 1.38732 0.693659 0.720304i \(-0.255998\pi\)
0.693659 + 0.720304i \(0.255998\pi\)
\(272\) 25.6748 1.55676
\(273\) −2.39172 −0.144754
\(274\) 3.88782 0.234872
\(275\) 24.8856 1.50066
\(276\) 8.43564 0.507766
\(277\) 17.6647 1.06137 0.530686 0.847569i \(-0.321934\pi\)
0.530686 + 0.847569i \(0.321934\pi\)
\(278\) 33.7140 2.02203
\(279\) 0.943195 0.0564676
\(280\) −3.37110 −0.201462
\(281\) −8.23815 −0.491447 −0.245724 0.969340i \(-0.579026\pi\)
−0.245724 + 0.969340i \(0.579026\pi\)
\(282\) 3.19020 0.189973
\(283\) 19.0525 1.13255 0.566277 0.824215i \(-0.308383\pi\)
0.566277 + 0.824215i \(0.308383\pi\)
\(284\) −1.53144 −0.0908741
\(285\) −1.00258 −0.0593877
\(286\) −20.7887 −1.22926
\(287\) 2.27743 0.134432
\(288\) 6.81644 0.401662
\(289\) 11.4649 0.674405
\(290\) 43.7868 2.57125
\(291\) −6.81283 −0.399375
\(292\) 22.4895 1.31610
\(293\) 14.1130 0.824490 0.412245 0.911073i \(-0.364745\pi\)
0.412245 + 0.911073i \(0.364745\pi\)
\(294\) 1.85290 0.108063
\(295\) 46.7398 2.72129
\(296\) 7.75701 0.450867
\(297\) −4.69097 −0.272198
\(298\) 33.0439 1.91418
\(299\) −14.0769 −0.814090
\(300\) −7.60337 −0.438981
\(301\) 5.60881 0.323287
\(302\) −17.3356 −0.997550
\(303\) 13.6015 0.781389
\(304\) 1.50296 0.0862007
\(305\) −34.4601 −1.97318
\(306\) 9.88569 0.565128
\(307\) 3.92129 0.223800 0.111900 0.993719i \(-0.464306\pi\)
0.111900 + 0.993719i \(0.464306\pi\)
\(308\) 6.72332 0.383097
\(309\) 4.83718 0.275177
\(310\) 5.61019 0.318638
\(311\) −2.79178 −0.158307 −0.0791536 0.996862i \(-0.525222\pi\)
−0.0791536 + 0.996862i \(0.525222\pi\)
\(312\) −2.51165 −0.142194
\(313\) 3.95575 0.223592 0.111796 0.993731i \(-0.464340\pi\)
0.111796 + 0.993731i \(0.464340\pi\)
\(314\) 43.2591 2.44125
\(315\) −3.21014 −0.180871
\(316\) −12.7948 −0.719765
\(317\) 5.47919 0.307742 0.153871 0.988091i \(-0.450826\pi\)
0.153871 + 0.988091i \(0.450826\pi\)
\(318\) 7.14417 0.400625
\(319\) 34.5327 1.93346
\(320\) 9.64838 0.539361
\(321\) 12.9339 0.721901
\(322\) 10.9056 0.607745
\(323\) 1.66629 0.0927147
\(324\) 1.43325 0.0796248
\(325\) 12.6881 0.703809
\(326\) −35.0713 −1.94242
\(327\) −5.11701 −0.282971
\(328\) 2.39162 0.132055
\(329\) 1.72173 0.0949220
\(330\) −27.9023 −1.53597
\(331\) 2.77529 0.152544 0.0762719 0.997087i \(-0.475698\pi\)
0.0762719 + 0.997087i \(0.475698\pi\)
\(332\) 18.3183 1.00535
\(333\) 7.38664 0.404785
\(334\) −11.9248 −0.652496
\(335\) 24.9322 1.36219
\(336\) 4.81230 0.262532
\(337\) −26.2917 −1.43220 −0.716101 0.697997i \(-0.754075\pi\)
−0.716101 + 0.697997i \(0.754075\pi\)
\(338\) 13.4885 0.733677
\(339\) −13.5759 −0.737339
\(340\) 24.5471 1.33125
\(341\) 4.42450 0.239600
\(342\) 0.578692 0.0312921
\(343\) 1.00000 0.0539949
\(344\) 5.89004 0.317570
\(345\) −18.8939 −1.01721
\(346\) 29.2093 1.57030
\(347\) −30.0569 −1.61354 −0.806769 0.590867i \(-0.798786\pi\)
−0.806769 + 0.590867i \(0.798786\pi\)
\(348\) −10.5509 −0.565586
\(349\) −10.6376 −0.569417 −0.284708 0.958614i \(-0.591897\pi\)
−0.284708 + 0.958614i \(0.591897\pi\)
\(350\) −9.82965 −0.525417
\(351\) −2.39172 −0.127661
\(352\) 31.9757 1.70431
\(353\) −22.0385 −1.17299 −0.586495 0.809953i \(-0.699493\pi\)
−0.586495 + 0.809953i \(0.699493\pi\)
\(354\) −26.9783 −1.43388
\(355\) 3.43007 0.182049
\(356\) 26.8173 1.42131
\(357\) 5.33525 0.282371
\(358\) 13.2461 0.700080
\(359\) 2.56691 0.135476 0.0677382 0.997703i \(-0.478422\pi\)
0.0677382 + 0.997703i \(0.478422\pi\)
\(360\) −3.37110 −0.177672
\(361\) −18.9025 −0.994866
\(362\) 16.8716 0.886750
\(363\) −11.0052 −0.577625
\(364\) 3.42793 0.179672
\(365\) −50.3714 −2.63656
\(366\) 19.8905 1.03969
\(367\) 5.51924 0.288102 0.144051 0.989570i \(-0.453987\pi\)
0.144051 + 0.989570i \(0.453987\pi\)
\(368\) 28.3237 1.47647
\(369\) 2.27743 0.118558
\(370\) 43.9363 2.28414
\(371\) 3.85567 0.200176
\(372\) −1.35183 −0.0700891
\(373\) −4.48940 −0.232453 −0.116226 0.993223i \(-0.537080\pi\)
−0.116226 + 0.993223i \(0.537080\pi\)
\(374\) 46.3735 2.39792
\(375\) 0.979095 0.0505602
\(376\) 1.80806 0.0932434
\(377\) 17.6067 0.906792
\(378\) 1.85290 0.0953030
\(379\) 31.9282 1.64004 0.820021 0.572334i \(-0.193962\pi\)
0.820021 + 0.572334i \(0.193962\pi\)
\(380\) 1.43694 0.0737136
\(381\) −17.8346 −0.913694
\(382\) 36.3117 1.85787
\(383\) −1.00000 −0.0510976
\(384\) 8.06380 0.411504
\(385\) −15.0587 −0.767462
\(386\) 9.60576 0.488920
\(387\) 5.60881 0.285112
\(388\) 9.76445 0.495715
\(389\) 25.8081 1.30852 0.654260 0.756270i \(-0.272980\pi\)
0.654260 + 0.756270i \(0.272980\pi\)
\(390\) −14.2262 −0.720369
\(391\) 31.4016 1.58805
\(392\) 1.05014 0.0530401
\(393\) 21.6482 1.09201
\(394\) −30.9961 −1.56156
\(395\) 28.6575 1.44191
\(396\) 6.72332 0.337859
\(397\) −9.61054 −0.482339 −0.241170 0.970483i \(-0.577531\pi\)
−0.241170 + 0.970483i \(0.577531\pi\)
\(398\) −38.3587 −1.92275
\(399\) 0.312316 0.0156354
\(400\) −25.5292 −1.27646
\(401\) −11.7868 −0.588606 −0.294303 0.955712i \(-0.595087\pi\)
−0.294303 + 0.955712i \(0.595087\pi\)
\(402\) −14.3909 −0.717754
\(403\) 2.25586 0.112372
\(404\) −19.4944 −0.969881
\(405\) −3.21014 −0.159513
\(406\) −13.6402 −0.676950
\(407\) 34.6505 1.71756
\(408\) 5.60276 0.277378
\(409\) 20.1698 0.997333 0.498667 0.866794i \(-0.333823\pi\)
0.498667 + 0.866794i \(0.333823\pi\)
\(410\) 13.5463 0.669005
\(411\) 2.09823 0.103498
\(412\) −6.93286 −0.341558
\(413\) −14.5600 −0.716453
\(414\) 10.9056 0.535981
\(415\) −41.0287 −2.01402
\(416\) 16.3030 0.799322
\(417\) 18.1952 0.891024
\(418\) 2.71463 0.132777
\(419\) 10.2205 0.499303 0.249651 0.968336i \(-0.419684\pi\)
0.249651 + 0.968336i \(0.419684\pi\)
\(420\) 4.60092 0.224502
\(421\) 8.76855 0.427353 0.213677 0.976904i \(-0.431456\pi\)
0.213677 + 0.976904i \(0.431456\pi\)
\(422\) −31.1442 −1.51608
\(423\) 1.72173 0.0837134
\(424\) 4.04899 0.196636
\(425\) −28.3035 −1.37292
\(426\) −1.97985 −0.0959238
\(427\) 10.7348 0.519492
\(428\) −18.5375 −0.896043
\(429\) −11.2195 −0.541683
\(430\) 33.3616 1.60884
\(431\) 20.8702 1.00528 0.502642 0.864495i \(-0.332362\pi\)
0.502642 + 0.864495i \(0.332362\pi\)
\(432\) 4.81230 0.231532
\(433\) −4.67650 −0.224738 −0.112369 0.993667i \(-0.535844\pi\)
−0.112369 + 0.993667i \(0.535844\pi\)
\(434\) −1.74765 −0.0838897
\(435\) 23.6315 1.13304
\(436\) 7.33394 0.351232
\(437\) 1.83820 0.0879329
\(438\) 29.0745 1.38923
\(439\) −25.5135 −1.21769 −0.608847 0.793288i \(-0.708368\pi\)
−0.608847 + 0.793288i \(0.708368\pi\)
\(440\) −15.8137 −0.753890
\(441\) 1.00000 0.0476190
\(442\) 23.6439 1.12462
\(443\) −28.1711 −1.33845 −0.669224 0.743060i \(-0.733373\pi\)
−0.669224 + 0.743060i \(0.733373\pi\)
\(444\) −10.5869 −0.502431
\(445\) −60.0645 −2.84733
\(446\) 39.5533 1.87290
\(447\) 17.8336 0.843499
\(448\) −3.00559 −0.142001
\(449\) −32.6607 −1.54135 −0.770677 0.637226i \(-0.780082\pi\)
−0.770677 + 0.637226i \(0.780082\pi\)
\(450\) −9.82965 −0.463374
\(451\) 10.6834 0.503059
\(452\) 19.4575 0.915205
\(453\) −9.35590 −0.439578
\(454\) −6.90720 −0.324171
\(455\) −7.67777 −0.359939
\(456\) 0.327976 0.0153589
\(457\) 24.4618 1.14428 0.572138 0.820158i \(-0.306114\pi\)
0.572138 + 0.820158i \(0.306114\pi\)
\(458\) 26.6835 1.24684
\(459\) 5.33525 0.249028
\(460\) 27.0796 1.26259
\(461\) 26.0424 1.21292 0.606459 0.795115i \(-0.292590\pi\)
0.606459 + 0.795115i \(0.292590\pi\)
\(462\) 8.69191 0.404384
\(463\) 29.2747 1.36051 0.680256 0.732975i \(-0.261869\pi\)
0.680256 + 0.732975i \(0.261869\pi\)
\(464\) −35.4258 −1.64460
\(465\) 3.02779 0.140410
\(466\) −49.9730 −2.31495
\(467\) 7.39736 0.342309 0.171155 0.985244i \(-0.445250\pi\)
0.171155 + 0.985244i \(0.445250\pi\)
\(468\) 3.42793 0.158456
\(469\) −7.76670 −0.358633
\(470\) 10.2410 0.472381
\(471\) 23.3467 1.07576
\(472\) −15.2901 −0.703783
\(473\) 26.3108 1.20977
\(474\) −16.5412 −0.759761
\(475\) −1.65684 −0.0760210
\(476\) −7.64672 −0.350487
\(477\) 3.85567 0.176539
\(478\) 16.1879 0.740418
\(479\) −27.2961 −1.24719 −0.623596 0.781746i \(-0.714329\pi\)
−0.623596 + 0.781746i \(0.714329\pi\)
\(480\) 21.8817 0.998759
\(481\) 17.6668 0.805537
\(482\) 11.2856 0.514045
\(483\) 5.88569 0.267808
\(484\) 15.7732 0.716964
\(485\) −21.8701 −0.993071
\(486\) 1.85290 0.0840493
\(487\) −3.17351 −0.143805 −0.0719026 0.997412i \(-0.522907\pi\)
−0.0719026 + 0.997412i \(0.522907\pi\)
\(488\) 11.2730 0.510306
\(489\) −18.9277 −0.855942
\(490\) 5.94808 0.268707
\(491\) 21.4652 0.968711 0.484355 0.874871i \(-0.339054\pi\)
0.484355 + 0.874871i \(0.339054\pi\)
\(492\) −3.26411 −0.147158
\(493\) −39.2755 −1.76888
\(494\) 1.38407 0.0622723
\(495\) −15.0587 −0.676837
\(496\) −4.53893 −0.203804
\(497\) −1.06851 −0.0479292
\(498\) 23.6819 1.06121
\(499\) 42.1584 1.88727 0.943634 0.330990i \(-0.107383\pi\)
0.943634 + 0.330990i \(0.107383\pi\)
\(500\) −1.40328 −0.0627568
\(501\) −6.43574 −0.287528
\(502\) 46.7005 2.08435
\(503\) −24.3838 −1.08722 −0.543610 0.839338i \(-0.682943\pi\)
−0.543610 + 0.839338i \(0.682943\pi\)
\(504\) 1.05014 0.0467769
\(505\) 43.6629 1.94297
\(506\) 51.1579 2.27425
\(507\) 7.27966 0.323301
\(508\) 25.5614 1.13410
\(509\) −11.0516 −0.489854 −0.244927 0.969541i \(-0.578764\pi\)
−0.244927 + 0.969541i \(0.578764\pi\)
\(510\) 31.7345 1.40523
\(511\) 15.6913 0.694144
\(512\) −22.6956 −1.00301
\(513\) 0.312316 0.0137891
\(514\) −13.3136 −0.587240
\(515\) 15.5280 0.684246
\(516\) −8.03881 −0.353889
\(517\) 8.07659 0.355208
\(518\) −13.6867 −0.601360
\(519\) 15.7641 0.691966
\(520\) −8.06273 −0.353574
\(521\) 38.0117 1.66532 0.832662 0.553781i \(-0.186816\pi\)
0.832662 + 0.553781i \(0.186816\pi\)
\(522\) −13.6402 −0.597014
\(523\) 16.8756 0.737917 0.368959 0.929446i \(-0.379714\pi\)
0.368959 + 0.929446i \(0.379714\pi\)
\(524\) −31.0272 −1.35543
\(525\) −5.30500 −0.231529
\(526\) −2.00211 −0.0872962
\(527\) −5.03218 −0.219205
\(528\) 22.5744 0.982423
\(529\) 11.6413 0.506144
\(530\) 22.9338 0.996181
\(531\) −14.5600 −0.631852
\(532\) −0.447626 −0.0194071
\(533\) 5.44698 0.235935
\(534\) 34.6694 1.50029
\(535\) 41.5197 1.79505
\(536\) −8.15612 −0.352291
\(537\) 7.14886 0.308496
\(538\) 3.70762 0.159847
\(539\) 4.69097 0.202055
\(540\) 4.60092 0.197992
\(541\) 31.3415 1.34748 0.673739 0.738970i \(-0.264687\pi\)
0.673739 + 0.738970i \(0.264687\pi\)
\(542\) −42.3168 −1.81766
\(543\) 9.10549 0.390754
\(544\) −36.3674 −1.55924
\(545\) −16.4263 −0.703627
\(546\) 4.43163 0.189656
\(547\) 17.4234 0.744970 0.372485 0.928038i \(-0.378506\pi\)
0.372485 + 0.928038i \(0.378506\pi\)
\(548\) −3.00728 −0.128465
\(549\) 10.7348 0.458149
\(550\) −46.1106 −1.96616
\(551\) −2.29912 −0.0979459
\(552\) 6.18079 0.263072
\(553\) −8.92717 −0.379622
\(554\) −32.7310 −1.39061
\(555\) 23.7122 1.00652
\(556\) −26.0782 −1.10596
\(557\) −0.331868 −0.0140617 −0.00703085 0.999975i \(-0.502238\pi\)
−0.00703085 + 0.999975i \(0.502238\pi\)
\(558\) −1.74765 −0.0739838
\(559\) 13.4147 0.567383
\(560\) 15.4482 0.652804
\(561\) 25.0275 1.05666
\(562\) 15.2645 0.643894
\(563\) −43.0228 −1.81319 −0.906597 0.421997i \(-0.861329\pi\)
−0.906597 + 0.421997i \(0.861329\pi\)
\(564\) −2.46766 −0.103907
\(565\) −43.5804 −1.83344
\(566\) −35.3024 −1.48387
\(567\) 1.00000 0.0419961
\(568\) −1.12209 −0.0470817
\(569\) 41.3196 1.73221 0.866104 0.499864i \(-0.166617\pi\)
0.866104 + 0.499864i \(0.166617\pi\)
\(570\) 1.85768 0.0778097
\(571\) 2.11330 0.0884388 0.0442194 0.999022i \(-0.485920\pi\)
0.0442194 + 0.999022i \(0.485920\pi\)
\(572\) 16.0803 0.672352
\(573\) 19.5972 0.818684
\(574\) −4.21985 −0.176133
\(575\) −31.2236 −1.30211
\(576\) −3.00559 −0.125233
\(577\) −32.0184 −1.33294 −0.666472 0.745530i \(-0.732196\pi\)
−0.666472 + 0.745530i \(0.732196\pi\)
\(578\) −21.2433 −0.883605
\(579\) 5.18417 0.215447
\(580\) −33.8697 −1.40636
\(581\) 12.7810 0.530244
\(582\) 12.6235 0.523261
\(583\) 18.0868 0.749080
\(584\) 16.4781 0.681869
\(585\) −7.67777 −0.317437
\(586\) −26.1500 −1.08025
\(587\) 43.7137 1.80426 0.902128 0.431469i \(-0.142005\pi\)
0.902128 + 0.431469i \(0.142005\pi\)
\(588\) −1.43325 −0.0591061
\(589\) −0.294575 −0.0121378
\(590\) −86.6042 −3.56544
\(591\) −16.7284 −0.688116
\(592\) −35.5467 −1.46096
\(593\) 23.8069 0.977633 0.488816 0.872387i \(-0.337429\pi\)
0.488816 + 0.872387i \(0.337429\pi\)
\(594\) 8.69191 0.356634
\(595\) 17.1269 0.702134
\(596\) −25.5599 −1.04697
\(597\) −20.7020 −0.847276
\(598\) 26.0832 1.06662
\(599\) 26.4572 1.08101 0.540506 0.841340i \(-0.318233\pi\)
0.540506 + 0.841340i \(0.318233\pi\)
\(600\) −5.57099 −0.227435
\(601\) −42.2007 −1.72140 −0.860702 0.509109i \(-0.829975\pi\)
−0.860702 + 0.509109i \(0.829975\pi\)
\(602\) −10.3926 −0.423570
\(603\) −7.76670 −0.316284
\(604\) 13.4093 0.545617
\(605\) −35.3283 −1.43630
\(606\) −25.2023 −1.02377
\(607\) 24.0184 0.974879 0.487439 0.873157i \(-0.337931\pi\)
0.487439 + 0.873157i \(0.337931\pi\)
\(608\) −2.12889 −0.0863377
\(609\) −7.36152 −0.298304
\(610\) 63.8513 2.58526
\(611\) 4.11790 0.166593
\(612\) −7.64672 −0.309100
\(613\) 43.6832 1.76435 0.882173 0.470925i \(-0.156080\pi\)
0.882173 + 0.470925i \(0.156080\pi\)
\(614\) −7.26576 −0.293222
\(615\) 7.31086 0.294802
\(616\) 4.92618 0.198481
\(617\) −3.55895 −0.143278 −0.0716389 0.997431i \(-0.522823\pi\)
−0.0716389 + 0.997431i \(0.522823\pi\)
\(618\) −8.96281 −0.360537
\(619\) −37.1304 −1.49240 −0.746199 0.665723i \(-0.768123\pi\)
−0.746199 + 0.665723i \(0.768123\pi\)
\(620\) −4.33956 −0.174281
\(621\) 5.88569 0.236184
\(622\) 5.17289 0.207414
\(623\) 18.7109 0.749635
\(624\) 11.5097 0.460756
\(625\) −23.3820 −0.935279
\(626\) −7.32961 −0.292950
\(627\) 1.46507 0.0585092
\(628\) −33.4616 −1.33526
\(629\) −39.4096 −1.57136
\(630\) 5.94808 0.236977
\(631\) −43.8209 −1.74448 −0.872240 0.489077i \(-0.837334\pi\)
−0.872240 + 0.489077i \(0.837334\pi\)
\(632\) −9.37477 −0.372908
\(633\) −16.8083 −0.668071
\(634\) −10.1524 −0.403204
\(635\) −57.2515 −2.27196
\(636\) −5.52612 −0.219125
\(637\) 2.39172 0.0947636
\(638\) −63.9857 −2.53322
\(639\) −1.06851 −0.0422696
\(640\) 25.8859 1.02323
\(641\) 27.9201 1.10278 0.551389 0.834248i \(-0.314098\pi\)
0.551389 + 0.834248i \(0.314098\pi\)
\(642\) −23.9653 −0.945834
\(643\) −4.19824 −0.165562 −0.0827812 0.996568i \(-0.526380\pi\)
−0.0827812 + 0.996568i \(0.526380\pi\)
\(644\) −8.43564 −0.332411
\(645\) 18.0051 0.708949
\(646\) −3.08747 −0.121475
\(647\) −37.2669 −1.46511 −0.732557 0.680706i \(-0.761673\pi\)
−0.732557 + 0.680706i \(0.761673\pi\)
\(648\) 1.05014 0.0412534
\(649\) −68.3008 −2.68104
\(650\) −23.5098 −0.922130
\(651\) −0.943195 −0.0369667
\(652\) 27.1281 1.06242
\(653\) −21.1806 −0.828862 −0.414431 0.910081i \(-0.636019\pi\)
−0.414431 + 0.910081i \(0.636019\pi\)
\(654\) 9.48132 0.370749
\(655\) 69.4939 2.71535
\(656\) −10.9597 −0.427903
\(657\) 15.6913 0.612177
\(658\) −3.19020 −0.124367
\(659\) 2.13751 0.0832657 0.0416328 0.999133i \(-0.486744\pi\)
0.0416328 + 0.999133i \(0.486744\pi\)
\(660\) 21.5828 0.840109
\(661\) 18.8595 0.733551 0.366775 0.930310i \(-0.380462\pi\)
0.366775 + 0.930310i \(0.380462\pi\)
\(662\) −5.14234 −0.199863
\(663\) 12.7604 0.495575
\(664\) 13.4218 0.520867
\(665\) 1.00258 0.0388784
\(666\) −13.6867 −0.530350
\(667\) −43.3276 −1.67765
\(668\) 9.22399 0.356887
\(669\) 21.3467 0.825309
\(670\) −46.1969 −1.78474
\(671\) 50.3566 1.94399
\(672\) −6.81644 −0.262950
\(673\) −14.0290 −0.540777 −0.270389 0.962751i \(-0.587152\pi\)
−0.270389 + 0.962751i \(0.587152\pi\)
\(674\) 48.7160 1.87647
\(675\) −5.30500 −0.204190
\(676\) −10.4335 −0.401290
\(677\) 34.0790 1.30976 0.654881 0.755732i \(-0.272719\pi\)
0.654881 + 0.755732i \(0.272719\pi\)
\(678\) 25.1547 0.966061
\(679\) 6.81283 0.261452
\(680\) 17.9856 0.689718
\(681\) −3.72777 −0.142849
\(682\) −8.19817 −0.313924
\(683\) 36.4699 1.39548 0.697740 0.716351i \(-0.254189\pi\)
0.697740 + 0.716351i \(0.254189\pi\)
\(684\) −0.447626 −0.0171154
\(685\) 6.73562 0.257355
\(686\) −1.85290 −0.0707441
\(687\) 14.4009 0.549429
\(688\) −26.9913 −1.02903
\(689\) 9.22169 0.351318
\(690\) 35.0085 1.33275
\(691\) −7.13401 −0.271390 −0.135695 0.990751i \(-0.543327\pi\)
−0.135695 + 0.990751i \(0.543327\pi\)
\(692\) −22.5938 −0.858888
\(693\) 4.69097 0.178195
\(694\) 55.6924 2.11406
\(695\) 58.4092 2.21559
\(696\) −7.73062 −0.293028
\(697\) −12.1506 −0.460238
\(698\) 19.7104 0.746050
\(699\) −26.9701 −1.02010
\(700\) 7.60337 0.287380
\(701\) −12.1932 −0.460533 −0.230266 0.973128i \(-0.573960\pi\)
−0.230266 + 0.973128i \(0.573960\pi\)
\(702\) 4.43163 0.167261
\(703\) −2.30697 −0.0870090
\(704\) −14.0992 −0.531382
\(705\) 5.52699 0.208159
\(706\) 40.8352 1.53685
\(707\) −13.6015 −0.511539
\(708\) 20.8681 0.784272
\(709\) 19.9645 0.749782 0.374891 0.927069i \(-0.377680\pi\)
0.374891 + 0.927069i \(0.377680\pi\)
\(710\) −6.35558 −0.238521
\(711\) −8.92717 −0.334795
\(712\) 19.6490 0.736378
\(713\) −5.55135 −0.207900
\(714\) −9.88569 −0.369963
\(715\) −36.0162 −1.34693
\(716\) −10.2461 −0.382914
\(717\) 8.73652 0.326271
\(718\) −4.75624 −0.177501
\(719\) 1.07483 0.0400843 0.0200422 0.999799i \(-0.493620\pi\)
0.0200422 + 0.999799i \(0.493620\pi\)
\(720\) 15.4482 0.575719
\(721\) −4.83718 −0.180146
\(722\) 35.0244 1.30347
\(723\) 6.09077 0.226518
\(724\) −13.0504 −0.485014
\(725\) 39.0528 1.45039
\(726\) 20.3916 0.756804
\(727\) −21.8309 −0.809665 −0.404832 0.914391i \(-0.632670\pi\)
−0.404832 + 0.914391i \(0.632670\pi\)
\(728\) 2.51165 0.0930878
\(729\) 1.00000 0.0370370
\(730\) 93.3333 3.45442
\(731\) −29.9244 −1.10679
\(732\) −15.3856 −0.568667
\(733\) 43.6954 1.61393 0.806964 0.590601i \(-0.201109\pi\)
0.806964 + 0.590601i \(0.201109\pi\)
\(734\) −10.2266 −0.377471
\(735\) 3.21014 0.118408
\(736\) −40.1194 −1.47882
\(737\) −36.4334 −1.34204
\(738\) −4.21985 −0.155335
\(739\) −10.7849 −0.396729 −0.198364 0.980128i \(-0.563563\pi\)
−0.198364 + 0.980128i \(0.563563\pi\)
\(740\) −33.9853 −1.24933
\(741\) 0.746975 0.0274408
\(742\) −7.14417 −0.262271
\(743\) 0.991731 0.0363831 0.0181915 0.999835i \(-0.494209\pi\)
0.0181915 + 0.999835i \(0.494209\pi\)
\(744\) −0.990486 −0.0363130
\(745\) 57.2483 2.09741
\(746\) 8.31843 0.304559
\(747\) 12.7810 0.467631
\(748\) −35.8706 −1.31156
\(749\) −12.9339 −0.472595
\(750\) −1.81417 −0.0662440
\(751\) −31.0574 −1.13330 −0.566651 0.823958i \(-0.691761\pi\)
−0.566651 + 0.823958i \(0.691761\pi\)
\(752\) −8.28548 −0.302140
\(753\) 25.2040 0.918485
\(754\) −32.6235 −1.18808
\(755\) −30.0337 −1.09304
\(756\) −1.43325 −0.0521266
\(757\) −22.7351 −0.826322 −0.413161 0.910658i \(-0.635575\pi\)
−0.413161 + 0.910658i \(0.635575\pi\)
\(758\) −59.1598 −2.14878
\(759\) 27.6096 1.00216
\(760\) 1.05285 0.0381908
\(761\) 36.9060 1.33784 0.668920 0.743334i \(-0.266757\pi\)
0.668920 + 0.743334i \(0.266757\pi\)
\(762\) 33.0458 1.19712
\(763\) 5.11701 0.185248
\(764\) −28.0876 −1.01617
\(765\) 17.1269 0.619224
\(766\) 1.85290 0.0669481
\(767\) −34.8236 −1.25741
\(768\) −20.9526 −0.756063
\(769\) −41.7437 −1.50532 −0.752659 0.658411i \(-0.771229\pi\)
−0.752659 + 0.658411i \(0.771229\pi\)
\(770\) 27.9023 1.00553
\(771\) −7.18529 −0.258772
\(772\) −7.43019 −0.267418
\(773\) 12.5894 0.452808 0.226404 0.974033i \(-0.427303\pi\)
0.226404 + 0.974033i \(0.427303\pi\)
\(774\) −10.3926 −0.373554
\(775\) 5.00365 0.179736
\(776\) 7.15442 0.256829
\(777\) −7.38664 −0.264994
\(778\) −47.8198 −1.71442
\(779\) −0.711278 −0.0254842
\(780\) 11.0041 0.394011
\(781\) −5.01235 −0.179356
\(782\) −58.1841 −2.08066
\(783\) −7.36152 −0.263079
\(784\) −4.81230 −0.171868
\(785\) 74.9462 2.67494
\(786\) −40.1121 −1.43075
\(787\) −6.94407 −0.247530 −0.123765 0.992312i \(-0.539497\pi\)
−0.123765 + 0.992312i \(0.539497\pi\)
\(788\) 23.9760 0.854108
\(789\) −1.08053 −0.0384678
\(790\) −53.0995 −1.88919
\(791\) 13.5759 0.482702
\(792\) 4.92618 0.175044
\(793\) 25.6746 0.911733
\(794\) 17.8074 0.631960
\(795\) 12.3772 0.438975
\(796\) 29.6710 1.05166
\(797\) −1.86467 −0.0660499 −0.0330249 0.999455i \(-0.510514\pi\)
−0.0330249 + 0.999455i \(0.510514\pi\)
\(798\) −0.578692 −0.0204855
\(799\) −9.18586 −0.324972
\(800\) 36.1612 1.27849
\(801\) 18.7109 0.661116
\(802\) 21.8398 0.771191
\(803\) 73.6077 2.59756
\(804\) 11.1316 0.392581
\(805\) 18.8939 0.665922
\(806\) −4.17989 −0.147230
\(807\) 2.00098 0.0704377
\(808\) −14.2835 −0.502493
\(809\) 8.82350 0.310218 0.155109 0.987897i \(-0.450427\pi\)
0.155109 + 0.987897i \(0.450427\pi\)
\(810\) 5.94808 0.208994
\(811\) −46.5161 −1.63340 −0.816701 0.577061i \(-0.804200\pi\)
−0.816701 + 0.577061i \(0.804200\pi\)
\(812\) 10.5509 0.370263
\(813\) −22.8381 −0.800968
\(814\) −64.2040 −2.25035
\(815\) −60.7607 −2.12835
\(816\) −25.6748 −0.898798
\(817\) −1.75172 −0.0612851
\(818\) −37.3727 −1.30671
\(819\) 2.39172 0.0835736
\(820\) −10.4783 −0.365917
\(821\) 35.3062 1.23220 0.616098 0.787670i \(-0.288713\pi\)
0.616098 + 0.787670i \(0.288713\pi\)
\(822\) −3.88782 −0.135603
\(823\) 31.8375 1.10979 0.554893 0.831922i \(-0.312759\pi\)
0.554893 + 0.831922i \(0.312759\pi\)
\(824\) −5.07971 −0.176960
\(825\) −24.8856 −0.866406
\(826\) 26.9783 0.938696
\(827\) 1.29171 0.0449172 0.0224586 0.999748i \(-0.492851\pi\)
0.0224586 + 0.999748i \(0.492851\pi\)
\(828\) −8.43564 −0.293159
\(829\) 53.0048 1.84093 0.920467 0.390821i \(-0.127809\pi\)
0.920467 + 0.390821i \(0.127809\pi\)
\(830\) 76.0221 2.63877
\(831\) −17.6647 −0.612783
\(832\) −7.18855 −0.249218
\(833\) −5.33525 −0.184855
\(834\) −33.7140 −1.16742
\(835\) −20.6596 −0.714956
\(836\) −2.09980 −0.0726232
\(837\) −0.943195 −0.0326016
\(838\) −18.9375 −0.654186
\(839\) 4.78091 0.165055 0.0825277 0.996589i \(-0.473701\pi\)
0.0825277 + 0.996589i \(0.473701\pi\)
\(840\) 3.37110 0.116314
\(841\) 25.1919 0.868686
\(842\) −16.2473 −0.559918
\(843\) 8.23815 0.283737
\(844\) 24.0905 0.829228
\(845\) 23.3687 0.803908
\(846\) −3.19020 −0.109681
\(847\) 11.0052 0.378144
\(848\) −18.5546 −0.637168
\(849\) −19.0525 −0.653880
\(850\) 52.4436 1.79880
\(851\) −43.4754 −1.49032
\(852\) 1.53144 0.0524662
\(853\) 30.0506 1.02891 0.514457 0.857516i \(-0.327994\pi\)
0.514457 + 0.857516i \(0.327994\pi\)
\(854\) −19.8905 −0.680639
\(855\) 1.00258 0.0342875
\(856\) −13.5824 −0.464238
\(857\) 32.6428 1.11506 0.557529 0.830157i \(-0.311749\pi\)
0.557529 + 0.830157i \(0.311749\pi\)
\(858\) 20.7887 0.709713
\(859\) 41.5308 1.41701 0.708506 0.705705i \(-0.249370\pi\)
0.708506 + 0.705705i \(0.249370\pi\)
\(860\) −25.8057 −0.879967
\(861\) −2.27743 −0.0776145
\(862\) −38.6705 −1.31712
\(863\) 25.8555 0.880132 0.440066 0.897965i \(-0.354955\pi\)
0.440066 + 0.897965i \(0.354955\pi\)
\(864\) −6.81644 −0.231900
\(865\) 50.6049 1.72062
\(866\) 8.66509 0.294452
\(867\) −11.4649 −0.389368
\(868\) 1.35183 0.0458841
\(869\) −41.8771 −1.42058
\(870\) −43.7868 −1.48451
\(871\) −18.5758 −0.629417
\(872\) 5.37358 0.181972
\(873\) 6.81283 0.230579
\(874\) −3.40600 −0.115210
\(875\) −0.979095 −0.0330994
\(876\) −22.4895 −0.759851
\(877\) −16.7193 −0.564569 −0.282285 0.959331i \(-0.591092\pi\)
−0.282285 + 0.959331i \(0.591092\pi\)
\(878\) 47.2741 1.59542
\(879\) −14.1130 −0.476019
\(880\) 72.4669 2.44286
\(881\) −2.58708 −0.0871611 −0.0435805 0.999050i \(-0.513877\pi\)
−0.0435805 + 0.999050i \(0.513877\pi\)
\(882\) −1.85290 −0.0623905
\(883\) −13.5192 −0.454957 −0.227478 0.973783i \(-0.573048\pi\)
−0.227478 + 0.973783i \(0.573048\pi\)
\(884\) −18.2889 −0.615121
\(885\) −46.7398 −1.57114
\(886\) 52.1983 1.75363
\(887\) 0.778491 0.0261392 0.0130696 0.999915i \(-0.495840\pi\)
0.0130696 + 0.999915i \(0.495840\pi\)
\(888\) −7.75701 −0.260308
\(889\) 17.8346 0.598153
\(890\) 111.294 3.73057
\(891\) 4.69097 0.157154
\(892\) −30.5950 −1.02440
\(893\) −0.537725 −0.0179943
\(894\) −33.0439 −1.10515
\(895\) 22.9489 0.767096
\(896\) −8.06380 −0.269393
\(897\) 14.0769 0.470015
\(898\) 60.5171 2.01948
\(899\) 6.94334 0.231573
\(900\) 7.60337 0.253446
\(901\) −20.5709 −0.685318
\(902\) −19.7952 −0.659108
\(903\) −5.60881 −0.186650
\(904\) 14.2565 0.474166
\(905\) 29.2299 0.971635
\(906\) 17.3356 0.575935
\(907\) 4.86748 0.161622 0.0808110 0.996729i \(-0.474249\pi\)
0.0808110 + 0.996729i \(0.474249\pi\)
\(908\) 5.34282 0.177308
\(909\) −13.6015 −0.451135
\(910\) 14.2262 0.471592
\(911\) 3.21058 0.106371 0.0531856 0.998585i \(-0.483063\pi\)
0.0531856 + 0.998585i \(0.483063\pi\)
\(912\) −1.50296 −0.0497680
\(913\) 59.9552 1.98423
\(914\) −45.3253 −1.49923
\(915\) 34.4601 1.13922
\(916\) −20.6401 −0.681967
\(917\) −21.6482 −0.714888
\(918\) −9.88569 −0.326277
\(919\) −5.49041 −0.181112 −0.0905559 0.995891i \(-0.528864\pi\)
−0.0905559 + 0.995891i \(0.528864\pi\)
\(920\) 19.8412 0.654146
\(921\) −3.92129 −0.129211
\(922\) −48.2541 −1.58916
\(923\) −2.55558 −0.0841180
\(924\) −6.72332 −0.221181
\(925\) 39.1861 1.28843
\(926\) −54.2432 −1.78254
\(927\) −4.83718 −0.158874
\(928\) 50.1793 1.64722
\(929\) 1.43430 0.0470580 0.0235290 0.999723i \(-0.492510\pi\)
0.0235290 + 0.999723i \(0.492510\pi\)
\(930\) −5.61019 −0.183965
\(931\) −0.312316 −0.0102358
\(932\) 38.6548 1.26618
\(933\) 2.79178 0.0913987
\(934\) −13.7066 −0.448493
\(935\) 80.3418 2.62746
\(936\) 2.51165 0.0820957
\(937\) 37.0831 1.21145 0.605726 0.795673i \(-0.292883\pi\)
0.605726 + 0.795673i \(0.292883\pi\)
\(938\) 14.3909 0.469880
\(939\) −3.95575 −0.129091
\(940\) −7.92154 −0.258372
\(941\) −19.0673 −0.621575 −0.310787 0.950479i \(-0.600593\pi\)
−0.310787 + 0.950479i \(0.600593\pi\)
\(942\) −43.2591 −1.40946
\(943\) −13.4042 −0.436502
\(944\) 70.0672 2.28049
\(945\) 3.21014 0.104426
\(946\) −48.7513 −1.58504
\(947\) 29.0946 0.945447 0.472724 0.881211i \(-0.343271\pi\)
0.472724 + 0.881211i \(0.343271\pi\)
\(948\) 12.7948 0.415557
\(949\) 37.5294 1.21825
\(950\) 3.06996 0.0996027
\(951\) −5.47919 −0.177675
\(952\) −5.60276 −0.181586
\(953\) −13.9007 −0.450288 −0.225144 0.974325i \(-0.572285\pi\)
−0.225144 + 0.974325i \(0.572285\pi\)
\(954\) −7.14417 −0.231301
\(955\) 62.9097 2.03571
\(956\) −12.5216 −0.404977
\(957\) −34.5327 −1.11628
\(958\) 50.5771 1.63407
\(959\) −2.09823 −0.0677554
\(960\) −9.64838 −0.311400
\(961\) −30.1104 −0.971303
\(962\) −32.7349 −1.05541
\(963\) −12.9339 −0.416790
\(964\) −8.72957 −0.281161
\(965\) 16.6419 0.535722
\(966\) −10.9056 −0.350882
\(967\) −17.9285 −0.576542 −0.288271 0.957549i \(-0.593080\pi\)
−0.288271 + 0.957549i \(0.593080\pi\)
\(968\) 11.5570 0.371457
\(969\) −1.66629 −0.0535288
\(970\) 40.5232 1.30112
\(971\) −58.9141 −1.89064 −0.945322 0.326139i \(-0.894252\pi\)
−0.945322 + 0.326139i \(0.894252\pi\)
\(972\) −1.43325 −0.0459714
\(973\) −18.1952 −0.583312
\(974\) 5.88019 0.188414
\(975\) −12.6881 −0.406344
\(976\) −51.6590 −1.65356
\(977\) 0.0288918 0.000924330 0 0.000462165 1.00000i \(-0.499853\pi\)
0.000462165 1.00000i \(0.499853\pi\)
\(978\) 35.0713 1.12146
\(979\) 87.7722 2.80521
\(980\) −4.60092 −0.146971
\(981\) 5.11701 0.163374
\(982\) −39.7729 −1.26920
\(983\) 55.3085 1.76407 0.882034 0.471185i \(-0.156174\pi\)
0.882034 + 0.471185i \(0.156174\pi\)
\(984\) −2.39162 −0.0762420
\(985\) −53.7006 −1.71104
\(986\) 72.7737 2.31759
\(987\) −1.72173 −0.0548033
\(988\) −1.07060 −0.0340603
\(989\) −33.0117 −1.04971
\(990\) 27.9023 0.886792
\(991\) −40.3241 −1.28094 −0.640468 0.767985i \(-0.721260\pi\)
−0.640468 + 0.767985i \(0.721260\pi\)
\(992\) 6.42923 0.204128
\(993\) −2.77529 −0.0880712
\(994\) 1.97985 0.0627969
\(995\) −66.4563 −2.10681
\(996\) −18.3183 −0.580436
\(997\) −31.5092 −0.997906 −0.498953 0.866629i \(-0.666282\pi\)
−0.498953 + 0.866629i \(0.666282\pi\)
\(998\) −78.1154 −2.47270
\(999\) −7.38664 −0.233703
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 \(a_p\))