Properties

Label 8042.2.a.a.1.19
Level 8042
Weight 2
Character 8042.1
Self dual Yes
Analytic conductor 64.216
Analytic rank 1
Dimension 67
CM No

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Newspace parameters

Level: \( N \) = \( 8042 = 2 \cdot 4021 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8042.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2156933055\)
Analytic rank: \(1\)
Dimension: \(67\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
Character \(\chi\) = 8042.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-1.55257 q^{3}\) \(+1.00000 q^{4}\) \(+2.63171 q^{5}\) \(-1.55257 q^{6}\) \(-0.882040 q^{7}\) \(+1.00000 q^{8}\) \(-0.589531 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-1.55257 q^{3}\) \(+1.00000 q^{4}\) \(+2.63171 q^{5}\) \(-1.55257 q^{6}\) \(-0.882040 q^{7}\) \(+1.00000 q^{8}\) \(-0.589531 q^{9}\) \(+2.63171 q^{10}\) \(+5.91348 q^{11}\) \(-1.55257 q^{12}\) \(-0.542391 q^{13}\) \(-0.882040 q^{14}\) \(-4.08591 q^{15}\) \(+1.00000 q^{16}\) \(-4.94551 q^{17}\) \(-0.589531 q^{18}\) \(-6.50514 q^{19}\) \(+2.63171 q^{20}\) \(+1.36943 q^{21}\) \(+5.91348 q^{22}\) \(-5.08202 q^{23}\) \(-1.55257 q^{24}\) \(+1.92589 q^{25}\) \(-0.542391 q^{26}\) \(+5.57299 q^{27}\) \(-0.882040 q^{28}\) \(+9.49183 q^{29}\) \(-4.08591 q^{30}\) \(-1.26198 q^{31}\) \(+1.00000 q^{32}\) \(-9.18108 q^{33}\) \(-4.94551 q^{34}\) \(-2.32127 q^{35}\) \(-0.589531 q^{36}\) \(-9.40266 q^{37}\) \(-6.50514 q^{38}\) \(+0.842099 q^{39}\) \(+2.63171 q^{40}\) \(-1.75849 q^{41}\) \(+1.36943 q^{42}\) \(-7.78177 q^{43}\) \(+5.91348 q^{44}\) \(-1.55147 q^{45}\) \(-5.08202 q^{46}\) \(-1.60840 q^{47}\) \(-1.55257 q^{48}\) \(-6.22201 q^{49}\) \(+1.92589 q^{50}\) \(+7.67824 q^{51}\) \(-0.542391 q^{52}\) \(-6.48916 q^{53}\) \(+5.57299 q^{54}\) \(+15.5626 q^{55}\) \(-0.882040 q^{56}\) \(+10.0997 q^{57}\) \(+9.49183 q^{58}\) \(+3.01774 q^{59}\) \(-4.08591 q^{60}\) \(+6.91687 q^{61}\) \(-1.26198 q^{62}\) \(+0.519990 q^{63}\) \(+1.00000 q^{64}\) \(-1.42741 q^{65}\) \(-9.18108 q^{66}\) \(-6.48951 q^{67}\) \(-4.94551 q^{68}\) \(+7.89019 q^{69}\) \(-2.32127 q^{70}\) \(-3.38169 q^{71}\) \(-0.589531 q^{72}\) \(-11.2083 q^{73}\) \(-9.40266 q^{74}\) \(-2.99008 q^{75}\) \(-6.50514 q^{76}\) \(-5.21593 q^{77}\) \(+0.842099 q^{78}\) \(+10.2201 q^{79}\) \(+2.63171 q^{80}\) \(-6.88386 q^{81}\) \(-1.75849 q^{82}\) \(-7.97223 q^{83}\) \(+1.36943 q^{84}\) \(-13.0151 q^{85}\) \(-7.78177 q^{86}\) \(-14.7367 q^{87}\) \(+5.91348 q^{88}\) \(-7.41763 q^{89}\) \(-1.55147 q^{90}\) \(+0.478410 q^{91}\) \(-5.08202 q^{92}\) \(+1.95931 q^{93}\) \(-1.60840 q^{94}\) \(-17.1196 q^{95}\) \(-1.55257 q^{96}\) \(+1.29495 q^{97}\) \(-6.22201 q^{98}\) \(-3.48618 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(67q \) \(\mathstrut +\mathstrut 67q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 67q^{4} \) \(\mathstrut -\mathstrut 20q^{5} \) \(\mathstrut -\mathstrut 11q^{6} \) \(\mathstrut -\mathstrut 40q^{7} \) \(\mathstrut +\mathstrut 67q^{8} \) \(\mathstrut +\mathstrut 24q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(67q \) \(\mathstrut +\mathstrut 67q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 67q^{4} \) \(\mathstrut -\mathstrut 20q^{5} \) \(\mathstrut -\mathstrut 11q^{6} \) \(\mathstrut -\mathstrut 40q^{7} \) \(\mathstrut +\mathstrut 67q^{8} \) \(\mathstrut +\mathstrut 24q^{9} \) \(\mathstrut -\mathstrut 20q^{10} \) \(\mathstrut -\mathstrut 13q^{11} \) \(\mathstrut -\mathstrut 11q^{12} \) \(\mathstrut -\mathstrut 51q^{13} \) \(\mathstrut -\mathstrut 40q^{14} \) \(\mathstrut -\mathstrut 31q^{15} \) \(\mathstrut +\mathstrut 67q^{16} \) \(\mathstrut -\mathstrut 34q^{17} \) \(\mathstrut +\mathstrut 24q^{18} \) \(\mathstrut -\mathstrut 33q^{19} \) \(\mathstrut -\mathstrut 20q^{20} \) \(\mathstrut -\mathstrut 39q^{21} \) \(\mathstrut -\mathstrut 13q^{22} \) \(\mathstrut -\mathstrut 43q^{23} \) \(\mathstrut -\mathstrut 11q^{24} \) \(\mathstrut -\mathstrut 9q^{25} \) \(\mathstrut -\mathstrut 51q^{26} \) \(\mathstrut -\mathstrut 29q^{27} \) \(\mathstrut -\mathstrut 40q^{28} \) \(\mathstrut -\mathstrut 63q^{29} \) \(\mathstrut -\mathstrut 31q^{30} \) \(\mathstrut -\mathstrut 43q^{31} \) \(\mathstrut +\mathstrut 67q^{32} \) \(\mathstrut -\mathstrut 49q^{33} \) \(\mathstrut -\mathstrut 34q^{34} \) \(\mathstrut -\mathstrut 20q^{35} \) \(\mathstrut +\mathstrut 24q^{36} \) \(\mathstrut -\mathstrut 77q^{37} \) \(\mathstrut -\mathstrut 33q^{38} \) \(\mathstrut -\mathstrut 40q^{39} \) \(\mathstrut -\mathstrut 20q^{40} \) \(\mathstrut -\mathstrut 50q^{41} \) \(\mathstrut -\mathstrut 39q^{42} \) \(\mathstrut -\mathstrut 56q^{43} \) \(\mathstrut -\mathstrut 13q^{44} \) \(\mathstrut -\mathstrut 48q^{45} \) \(\mathstrut -\mathstrut 43q^{46} \) \(\mathstrut -\mathstrut 48q^{47} \) \(\mathstrut -\mathstrut 11q^{48} \) \(\mathstrut +\mathstrut q^{49} \) \(\mathstrut -\mathstrut 9q^{50} \) \(\mathstrut -\mathstrut 18q^{51} \) \(\mathstrut -\mathstrut 51q^{52} \) \(\mathstrut -\mathstrut 91q^{53} \) \(\mathstrut -\mathstrut 29q^{54} \) \(\mathstrut -\mathstrut 58q^{55} \) \(\mathstrut -\mathstrut 40q^{56} \) \(\mathstrut -\mathstrut 65q^{57} \) \(\mathstrut -\mathstrut 63q^{58} \) \(\mathstrut -\mathstrut 17q^{59} \) \(\mathstrut -\mathstrut 31q^{60} \) \(\mathstrut -\mathstrut 45q^{61} \) \(\mathstrut -\mathstrut 43q^{62} \) \(\mathstrut -\mathstrut 67q^{63} \) \(\mathstrut +\mathstrut 67q^{64} \) \(\mathstrut -\mathstrut 65q^{65} \) \(\mathstrut -\mathstrut 49q^{66} \) \(\mathstrut -\mathstrut 112q^{67} \) \(\mathstrut -\mathstrut 34q^{68} \) \(\mathstrut -\mathstrut 57q^{69} \) \(\mathstrut -\mathstrut 20q^{70} \) \(\mathstrut -\mathstrut 75q^{71} \) \(\mathstrut +\mathstrut 24q^{72} \) \(\mathstrut -\mathstrut 79q^{73} \) \(\mathstrut -\mathstrut 77q^{74} \) \(\mathstrut -\mathstrut 5q^{75} \) \(\mathstrut -\mathstrut 33q^{76} \) \(\mathstrut -\mathstrut 85q^{77} \) \(\mathstrut -\mathstrut 40q^{78} \) \(\mathstrut -\mathstrut 80q^{79} \) \(\mathstrut -\mathstrut 20q^{80} \) \(\mathstrut -\mathstrut 77q^{81} \) \(\mathstrut -\mathstrut 50q^{82} \) \(\mathstrut -\mathstrut 22q^{83} \) \(\mathstrut -\mathstrut 39q^{84} \) \(\mathstrut -\mathstrut 134q^{85} \) \(\mathstrut -\mathstrut 56q^{86} \) \(\mathstrut -\mathstrut 49q^{87} \) \(\mathstrut -\mathstrut 13q^{88} \) \(\mathstrut -\mathstrut 77q^{89} \) \(\mathstrut -\mathstrut 48q^{90} \) \(\mathstrut -\mathstrut 17q^{91} \) \(\mathstrut -\mathstrut 43q^{92} \) \(\mathstrut -\mathstrut 97q^{93} \) \(\mathstrut -\mathstrut 48q^{94} \) \(\mathstrut -\mathstrut 73q^{95} \) \(\mathstrut -\mathstrut 11q^{96} \) \(\mathstrut -\mathstrut 87q^{97} \) \(\mathstrut +\mathstrut q^{98} \) \(\mathstrut -\mathstrut 44q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −1.55257 −0.896376 −0.448188 0.893939i \(-0.647930\pi\)
−0.448188 + 0.893939i \(0.647930\pi\)
\(4\) 1.00000 0.500000
\(5\) 2.63171 1.17694 0.588468 0.808521i \(-0.299731\pi\)
0.588468 + 0.808521i \(0.299731\pi\)
\(6\) −1.55257 −0.633833
\(7\) −0.882040 −0.333380 −0.166690 0.986009i \(-0.553308\pi\)
−0.166690 + 0.986009i \(0.553308\pi\)
\(8\) 1.00000 0.353553
\(9\) −0.589531 −0.196510
\(10\) 2.63171 0.832219
\(11\) 5.91348 1.78298 0.891491 0.453039i \(-0.149660\pi\)
0.891491 + 0.453039i \(0.149660\pi\)
\(12\) −1.55257 −0.448188
\(13\) −0.542391 −0.150432 −0.0752160 0.997167i \(-0.523965\pi\)
−0.0752160 + 0.997167i \(0.523965\pi\)
\(14\) −0.882040 −0.235735
\(15\) −4.08591 −1.05498
\(16\) 1.00000 0.250000
\(17\) −4.94551 −1.19946 −0.599731 0.800202i \(-0.704726\pi\)
−0.599731 + 0.800202i \(0.704726\pi\)
\(18\) −0.589531 −0.138954
\(19\) −6.50514 −1.49238 −0.746191 0.665732i \(-0.768119\pi\)
−0.746191 + 0.665732i \(0.768119\pi\)
\(20\) 2.63171 0.588468
\(21\) 1.36943 0.298834
\(22\) 5.91348 1.26076
\(23\) −5.08202 −1.05968 −0.529838 0.848099i \(-0.677747\pi\)
−0.529838 + 0.848099i \(0.677747\pi\)
\(24\) −1.55257 −0.316917
\(25\) 1.92589 0.385178
\(26\) −0.542391 −0.106372
\(27\) 5.57299 1.07252
\(28\) −0.882040 −0.166690
\(29\) 9.49183 1.76259 0.881295 0.472567i \(-0.156673\pi\)
0.881295 + 0.472567i \(0.156673\pi\)
\(30\) −4.08591 −0.745981
\(31\) −1.26198 −0.226658 −0.113329 0.993558i \(-0.536151\pi\)
−0.113329 + 0.993558i \(0.536151\pi\)
\(32\) 1.00000 0.176777
\(33\) −9.18108 −1.59822
\(34\) −4.94551 −0.848147
\(35\) −2.32127 −0.392367
\(36\) −0.589531 −0.0982552
\(37\) −9.40266 −1.54579 −0.772894 0.634535i \(-0.781191\pi\)
−0.772894 + 0.634535i \(0.781191\pi\)
\(38\) −6.50514 −1.05527
\(39\) 0.842099 0.134844
\(40\) 2.63171 0.416110
\(41\) −1.75849 −0.274630 −0.137315 0.990527i \(-0.543847\pi\)
−0.137315 + 0.990527i \(0.543847\pi\)
\(42\) 1.36943 0.211307
\(43\) −7.78177 −1.18671 −0.593354 0.804942i \(-0.702197\pi\)
−0.593354 + 0.804942i \(0.702197\pi\)
\(44\) 5.91348 0.891491
\(45\) −1.55147 −0.231280
\(46\) −5.08202 −0.749303
\(47\) −1.60840 −0.234609 −0.117305 0.993096i \(-0.537425\pi\)
−0.117305 + 0.993096i \(0.537425\pi\)
\(48\) −1.55257 −0.224094
\(49\) −6.22201 −0.888858
\(50\) 1.92589 0.272362
\(51\) 7.67824 1.07517
\(52\) −0.542391 −0.0752160
\(53\) −6.48916 −0.891354 −0.445677 0.895194i \(-0.647037\pi\)
−0.445677 + 0.895194i \(0.647037\pi\)
\(54\) 5.57299 0.758388
\(55\) 15.5626 2.09846
\(56\) −0.882040 −0.117868
\(57\) 10.0997 1.33773
\(58\) 9.49183 1.24634
\(59\) 3.01774 0.392876 0.196438 0.980516i \(-0.437063\pi\)
0.196438 + 0.980516i \(0.437063\pi\)
\(60\) −4.08591 −0.527488
\(61\) 6.91687 0.885615 0.442807 0.896617i \(-0.353983\pi\)
0.442807 + 0.896617i \(0.353983\pi\)
\(62\) −1.26198 −0.160272
\(63\) 0.519990 0.0655126
\(64\) 1.00000 0.125000
\(65\) −1.42741 −0.177049
\(66\) −9.18108 −1.13011
\(67\) −6.48951 −0.792820 −0.396410 0.918074i \(-0.629744\pi\)
−0.396410 + 0.918074i \(0.629744\pi\)
\(68\) −4.94551 −0.599731
\(69\) 7.89019 0.949867
\(70\) −2.32127 −0.277445
\(71\) −3.38169 −0.401332 −0.200666 0.979660i \(-0.564311\pi\)
−0.200666 + 0.979660i \(0.564311\pi\)
\(72\) −0.589531 −0.0694769
\(73\) −11.2083 −1.31183 −0.655916 0.754834i \(-0.727717\pi\)
−0.655916 + 0.754834i \(0.727717\pi\)
\(74\) −9.40266 −1.09304
\(75\) −2.99008 −0.345264
\(76\) −6.50514 −0.746191
\(77\) −5.21593 −0.594410
\(78\) 0.842099 0.0953489
\(79\) 10.2201 1.14985 0.574927 0.818205i \(-0.305030\pi\)
0.574927 + 0.818205i \(0.305030\pi\)
\(80\) 2.63171 0.294234
\(81\) −6.88386 −0.764873
\(82\) −1.75849 −0.194193
\(83\) −7.97223 −0.875066 −0.437533 0.899202i \(-0.644148\pi\)
−0.437533 + 0.899202i \(0.644148\pi\)
\(84\) 1.36943 0.149417
\(85\) −13.0151 −1.41169
\(86\) −7.78177 −0.839129
\(87\) −14.7367 −1.57994
\(88\) 5.91348 0.630379
\(89\) −7.41763 −0.786267 −0.393134 0.919481i \(-0.628609\pi\)
−0.393134 + 0.919481i \(0.628609\pi\)
\(90\) −1.55147 −0.163540
\(91\) 0.478410 0.0501510
\(92\) −5.08202 −0.529838
\(93\) 1.95931 0.203171
\(94\) −1.60840 −0.165894
\(95\) −17.1196 −1.75644
\(96\) −1.55257 −0.158458
\(97\) 1.29495 0.131482 0.0657410 0.997837i \(-0.479059\pi\)
0.0657410 + 0.997837i \(0.479059\pi\)
\(98\) −6.22201 −0.628517
\(99\) −3.48618 −0.350375
\(100\) 1.92589 0.192589
\(101\) 8.20757 0.816684 0.408342 0.912829i \(-0.366107\pi\)
0.408342 + 0.912829i \(0.366107\pi\)
\(102\) 7.67824 0.760259
\(103\) 0.559554 0.0551345 0.0275673 0.999620i \(-0.491224\pi\)
0.0275673 + 0.999620i \(0.491224\pi\)
\(104\) −0.542391 −0.0531858
\(105\) 3.60393 0.351708
\(106\) −6.48916 −0.630283
\(107\) 0.00863711 0.000834981 0 0.000417490 1.00000i \(-0.499867\pi\)
0.000417490 1.00000i \(0.499867\pi\)
\(108\) 5.57299 0.536261
\(109\) −7.33424 −0.702493 −0.351247 0.936283i \(-0.614242\pi\)
−0.351247 + 0.936283i \(0.614242\pi\)
\(110\) 15.5626 1.48383
\(111\) 14.5983 1.38561
\(112\) −0.882040 −0.0833450
\(113\) −13.1405 −1.23615 −0.618076 0.786118i \(-0.712088\pi\)
−0.618076 + 0.786118i \(0.712088\pi\)
\(114\) 10.0997 0.945921
\(115\) −13.3744 −1.24717
\(116\) 9.49183 0.881295
\(117\) 0.319756 0.0295615
\(118\) 3.01774 0.277805
\(119\) 4.36214 0.399876
\(120\) −4.08591 −0.372991
\(121\) 23.9693 2.17902
\(122\) 6.91687 0.626224
\(123\) 2.73018 0.246172
\(124\) −1.26198 −0.113329
\(125\) −8.09016 −0.723606
\(126\) 0.519990 0.0463244
\(127\) −5.95706 −0.528604 −0.264302 0.964440i \(-0.585141\pi\)
−0.264302 + 0.964440i \(0.585141\pi\)
\(128\) 1.00000 0.0883883
\(129\) 12.0817 1.06374
\(130\) −1.42741 −0.125193
\(131\) −2.48326 −0.216963 −0.108482 0.994098i \(-0.534599\pi\)
−0.108482 + 0.994098i \(0.534599\pi\)
\(132\) −9.18108 −0.799111
\(133\) 5.73779 0.497530
\(134\) −6.48951 −0.560608
\(135\) 14.6665 1.26229
\(136\) −4.94551 −0.424074
\(137\) −6.15230 −0.525627 −0.262813 0.964847i \(-0.584650\pi\)
−0.262813 + 0.964847i \(0.584650\pi\)
\(138\) 7.89019 0.671657
\(139\) −0.266066 −0.0225674 −0.0112837 0.999936i \(-0.503592\pi\)
−0.0112837 + 0.999936i \(0.503592\pi\)
\(140\) −2.32127 −0.196183
\(141\) 2.49715 0.210298
\(142\) −3.38169 −0.283785
\(143\) −3.20742 −0.268218
\(144\) −0.589531 −0.0491276
\(145\) 24.9797 2.07445
\(146\) −11.2083 −0.927605
\(147\) 9.66009 0.796751
\(148\) −9.40266 −0.772894
\(149\) 21.3333 1.74769 0.873846 0.486203i \(-0.161618\pi\)
0.873846 + 0.486203i \(0.161618\pi\)
\(150\) −2.99008 −0.244139
\(151\) 15.0180 1.22215 0.611075 0.791573i \(-0.290737\pi\)
0.611075 + 0.791573i \(0.290737\pi\)
\(152\) −6.50514 −0.527636
\(153\) 2.91553 0.235707
\(154\) −5.21593 −0.420311
\(155\) −3.32116 −0.266762
\(156\) 0.842099 0.0674218
\(157\) 10.0160 0.799361 0.399681 0.916655i \(-0.369121\pi\)
0.399681 + 0.916655i \(0.369121\pi\)
\(158\) 10.2201 0.813070
\(159\) 10.0749 0.798988
\(160\) 2.63171 0.208055
\(161\) 4.48255 0.353274
\(162\) −6.88386 −0.540847
\(163\) 10.0724 0.788929 0.394464 0.918911i \(-0.370930\pi\)
0.394464 + 0.918911i \(0.370930\pi\)
\(164\) −1.75849 −0.137315
\(165\) −24.1619 −1.88100
\(166\) −7.97223 −0.618765
\(167\) 19.4175 1.50257 0.751284 0.659979i \(-0.229435\pi\)
0.751284 + 0.659979i \(0.229435\pi\)
\(168\) 1.36943 0.105654
\(169\) −12.7058 −0.977370
\(170\) −13.0151 −0.998215
\(171\) 3.83498 0.293268
\(172\) −7.78177 −0.593354
\(173\) −0.00547070 −0.000415929 0 −0.000207965 1.00000i \(-0.500066\pi\)
−0.000207965 1.00000i \(0.500066\pi\)
\(174\) −14.7367 −1.11719
\(175\) −1.69871 −0.128411
\(176\) 5.91348 0.445745
\(177\) −4.68524 −0.352165
\(178\) −7.41763 −0.555975
\(179\) −21.0505 −1.57339 −0.786694 0.617343i \(-0.788209\pi\)
−0.786694 + 0.617343i \(0.788209\pi\)
\(180\) −1.55147 −0.115640
\(181\) 15.3500 1.14096 0.570478 0.821313i \(-0.306758\pi\)
0.570478 + 0.821313i \(0.306758\pi\)
\(182\) 0.478410 0.0354621
\(183\) −10.7389 −0.793844
\(184\) −5.08202 −0.374652
\(185\) −24.7451 −1.81929
\(186\) 1.95931 0.143664
\(187\) −29.2452 −2.13862
\(188\) −1.60840 −0.117305
\(189\) −4.91560 −0.357558
\(190\) −17.1196 −1.24199
\(191\) −0.740802 −0.0536026 −0.0268013 0.999641i \(-0.508532\pi\)
−0.0268013 + 0.999641i \(0.508532\pi\)
\(192\) −1.55257 −0.112047
\(193\) −6.69960 −0.482247 −0.241124 0.970494i \(-0.577516\pi\)
−0.241124 + 0.970494i \(0.577516\pi\)
\(194\) 1.29495 0.0929719
\(195\) 2.21616 0.158702
\(196\) −6.22201 −0.444429
\(197\) −14.5701 −1.03807 −0.519037 0.854752i \(-0.673709\pi\)
−0.519037 + 0.854752i \(0.673709\pi\)
\(198\) −3.48618 −0.247752
\(199\) 18.2544 1.29402 0.647010 0.762481i \(-0.276019\pi\)
0.647010 + 0.762481i \(0.276019\pi\)
\(200\) 1.92589 0.136181
\(201\) 10.0754 0.710664
\(202\) 8.20757 0.577483
\(203\) −8.37218 −0.587612
\(204\) 7.67824 0.537584
\(205\) −4.62783 −0.323222
\(206\) 0.559554 0.0389860
\(207\) 2.99601 0.208237
\(208\) −0.542391 −0.0376080
\(209\) −38.4680 −2.66089
\(210\) 3.60393 0.248695
\(211\) 2.29284 0.157846 0.0789229 0.996881i \(-0.474852\pi\)
0.0789229 + 0.996881i \(0.474852\pi\)
\(212\) −6.48916 −0.445677
\(213\) 5.25030 0.359745
\(214\) 0.00863711 0.000590420 0
\(215\) −20.4793 −1.39668
\(216\) 5.57299 0.379194
\(217\) 1.11312 0.0755633
\(218\) −7.33424 −0.496738
\(219\) 17.4016 1.17589
\(220\) 15.5626 1.04923
\(221\) 2.68240 0.180438
\(222\) 14.5983 0.979772
\(223\) 2.95621 0.197962 0.0989812 0.995089i \(-0.468442\pi\)
0.0989812 + 0.995089i \(0.468442\pi\)
\(224\) −0.882040 −0.0589338
\(225\) −1.13537 −0.0756915
\(226\) −13.1405 −0.874092
\(227\) 17.2714 1.14634 0.573171 0.819436i \(-0.305713\pi\)
0.573171 + 0.819436i \(0.305713\pi\)
\(228\) 10.0997 0.668867
\(229\) −12.4178 −0.820593 −0.410297 0.911952i \(-0.634575\pi\)
−0.410297 + 0.911952i \(0.634575\pi\)
\(230\) −13.3744 −0.881882
\(231\) 8.09808 0.532815
\(232\) 9.49183 0.623169
\(233\) −9.05913 −0.593483 −0.296742 0.954958i \(-0.595900\pi\)
−0.296742 + 0.954958i \(0.595900\pi\)
\(234\) 0.319756 0.0209031
\(235\) −4.23284 −0.276120
\(236\) 3.01774 0.196438
\(237\) −15.8674 −1.03070
\(238\) 4.36214 0.282755
\(239\) 11.5170 0.744973 0.372487 0.928038i \(-0.378505\pi\)
0.372487 + 0.928038i \(0.378505\pi\)
\(240\) −4.08591 −0.263744
\(241\) −2.75272 −0.177319 −0.0886593 0.996062i \(-0.528258\pi\)
−0.0886593 + 0.996062i \(0.528258\pi\)
\(242\) 23.9693 1.54080
\(243\) −6.03132 −0.386909
\(244\) 6.91687 0.442807
\(245\) −16.3745 −1.04613
\(246\) 2.73018 0.174070
\(247\) 3.52833 0.224502
\(248\) −1.26198 −0.0801358
\(249\) 12.3774 0.784388
\(250\) −8.09016 −0.511667
\(251\) 1.12731 0.0711555 0.0355777 0.999367i \(-0.488673\pi\)
0.0355777 + 0.999367i \(0.488673\pi\)
\(252\) 0.519990 0.0327563
\(253\) −30.0524 −1.88938
\(254\) −5.95706 −0.373779
\(255\) 20.2069 1.26540
\(256\) 1.00000 0.0625000
\(257\) 0.288177 0.0179760 0.00898799 0.999960i \(-0.497139\pi\)
0.00898799 + 0.999960i \(0.497139\pi\)
\(258\) 12.0817 0.752175
\(259\) 8.29352 0.515334
\(260\) −1.42741 −0.0885245
\(261\) −5.59573 −0.346367
\(262\) −2.48326 −0.153416
\(263\) −28.6909 −1.76916 −0.884579 0.466391i \(-0.845554\pi\)
−0.884579 + 0.466391i \(0.845554\pi\)
\(264\) −9.18108 −0.565057
\(265\) −17.0776 −1.04907
\(266\) 5.73779 0.351807
\(267\) 11.5164 0.704791
\(268\) −6.48951 −0.396410
\(269\) 7.36450 0.449021 0.224511 0.974472i \(-0.427922\pi\)
0.224511 + 0.974472i \(0.427922\pi\)
\(270\) 14.6665 0.892574
\(271\) −2.69132 −0.163486 −0.0817430 0.996653i \(-0.526049\pi\)
−0.0817430 + 0.996653i \(0.526049\pi\)
\(272\) −4.94551 −0.299865
\(273\) −0.742765 −0.0449542
\(274\) −6.15230 −0.371674
\(275\) 11.3887 0.686766
\(276\) 7.89019 0.474934
\(277\) 14.8917 0.894755 0.447377 0.894345i \(-0.352358\pi\)
0.447377 + 0.894345i \(0.352358\pi\)
\(278\) −0.266066 −0.0159576
\(279\) 0.743976 0.0445407
\(280\) −2.32127 −0.138723
\(281\) −11.3827 −0.679037 −0.339518 0.940599i \(-0.610264\pi\)
−0.339518 + 0.940599i \(0.610264\pi\)
\(282\) 2.49715 0.148703
\(283\) −21.5999 −1.28398 −0.641991 0.766712i \(-0.721891\pi\)
−0.641991 + 0.766712i \(0.721891\pi\)
\(284\) −3.38169 −0.200666
\(285\) 26.5794 1.57443
\(286\) −3.20742 −0.189659
\(287\) 1.55106 0.0915561
\(288\) −0.589531 −0.0347385
\(289\) 7.45804 0.438708
\(290\) 24.9797 1.46686
\(291\) −2.01050 −0.117857
\(292\) −11.2083 −0.655916
\(293\) −5.88354 −0.343720 −0.171860 0.985121i \(-0.554978\pi\)
−0.171860 + 0.985121i \(0.554978\pi\)
\(294\) 9.66009 0.563388
\(295\) 7.94181 0.462390
\(296\) −9.40266 −0.546518
\(297\) 32.9558 1.91229
\(298\) 21.3333 1.23580
\(299\) 2.75644 0.159409
\(300\) −2.99008 −0.172632
\(301\) 6.86383 0.395625
\(302\) 15.0180 0.864190
\(303\) −12.7428 −0.732056
\(304\) −6.50514 −0.373095
\(305\) 18.2032 1.04231
\(306\) 2.91553 0.166670
\(307\) 27.9241 1.59371 0.796857 0.604168i \(-0.206495\pi\)
0.796857 + 0.604168i \(0.206495\pi\)
\(308\) −5.21593 −0.297205
\(309\) −0.868746 −0.0494212
\(310\) −3.32116 −0.188629
\(311\) −0.221177 −0.0125418 −0.00627089 0.999980i \(-0.501996\pi\)
−0.00627089 + 0.999980i \(0.501996\pi\)
\(312\) 0.842099 0.0476744
\(313\) 15.9954 0.904115 0.452058 0.891989i \(-0.350690\pi\)
0.452058 + 0.891989i \(0.350690\pi\)
\(314\) 10.0160 0.565234
\(315\) 1.36846 0.0771041
\(316\) 10.2201 0.574927
\(317\) −10.4611 −0.587555 −0.293778 0.955874i \(-0.594912\pi\)
−0.293778 + 0.955874i \(0.594912\pi\)
\(318\) 10.0749 0.564970
\(319\) 56.1298 3.14266
\(320\) 2.63171 0.147117
\(321\) −0.0134097 −0.000748456 0
\(322\) 4.48255 0.249803
\(323\) 32.1712 1.79005
\(324\) −6.88386 −0.382437
\(325\) −1.04459 −0.0579432
\(326\) 10.0724 0.557857
\(327\) 11.3869 0.629698
\(328\) −1.75849 −0.0970963
\(329\) 1.41867 0.0782140
\(330\) −24.1619 −1.33007
\(331\) −3.16315 −0.173862 −0.0869311 0.996214i \(-0.527706\pi\)
−0.0869311 + 0.996214i \(0.527706\pi\)
\(332\) −7.97223 −0.437533
\(333\) 5.54316 0.303763
\(334\) 19.4175 1.06248
\(335\) −17.0785 −0.933098
\(336\) 1.36943 0.0747084
\(337\) −29.8037 −1.62351 −0.811755 0.583999i \(-0.801487\pi\)
−0.811755 + 0.583999i \(0.801487\pi\)
\(338\) −12.7058 −0.691105
\(339\) 20.4015 1.10806
\(340\) −13.0151 −0.705845
\(341\) −7.46269 −0.404127
\(342\) 3.83498 0.207372
\(343\) 11.6623 0.629707
\(344\) −7.78177 −0.419565
\(345\) 20.7647 1.11793
\(346\) −0.00547070 −0.000294107 0
\(347\) −5.26729 −0.282763 −0.141382 0.989955i \(-0.545154\pi\)
−0.141382 + 0.989955i \(0.545154\pi\)
\(348\) −14.7367 −0.789971
\(349\) −24.9944 −1.33792 −0.668960 0.743298i \(-0.733260\pi\)
−0.668960 + 0.743298i \(0.733260\pi\)
\(350\) −1.69871 −0.0908000
\(351\) −3.02274 −0.161342
\(352\) 5.91348 0.315190
\(353\) −22.8772 −1.21763 −0.608814 0.793313i \(-0.708355\pi\)
−0.608814 + 0.793313i \(0.708355\pi\)
\(354\) −4.68524 −0.249018
\(355\) −8.89962 −0.472343
\(356\) −7.41763 −0.393134
\(357\) −6.77251 −0.358439
\(358\) −21.0505 −1.11255
\(359\) 0.243368 0.0128445 0.00642223 0.999979i \(-0.497956\pi\)
0.00642223 + 0.999979i \(0.497956\pi\)
\(360\) −1.55147 −0.0817699
\(361\) 23.3168 1.22720
\(362\) 15.3500 0.806778
\(363\) −37.2139 −1.95322
\(364\) 0.478410 0.0250755
\(365\) −29.4970 −1.54394
\(366\) −10.7389 −0.561332
\(367\) −10.2883 −0.537046 −0.268523 0.963273i \(-0.586536\pi\)
−0.268523 + 0.963273i \(0.586536\pi\)
\(368\) −5.08202 −0.264919
\(369\) 1.03668 0.0539676
\(370\) −24.7451 −1.28643
\(371\) 5.72370 0.297160
\(372\) 1.95931 0.101585
\(373\) −29.5349 −1.52926 −0.764629 0.644471i \(-0.777078\pi\)
−0.764629 + 0.644471i \(0.777078\pi\)
\(374\) −29.2452 −1.51223
\(375\) 12.5605 0.648623
\(376\) −1.60840 −0.0829469
\(377\) −5.14828 −0.265150
\(378\) −4.91560 −0.252831
\(379\) −31.9775 −1.64257 −0.821286 0.570517i \(-0.806743\pi\)
−0.821286 + 0.570517i \(0.806743\pi\)
\(380\) −17.1196 −0.878218
\(381\) 9.24874 0.473827
\(382\) −0.740802 −0.0379027
\(383\) 18.6199 0.951432 0.475716 0.879599i \(-0.342189\pi\)
0.475716 + 0.879599i \(0.342189\pi\)
\(384\) −1.55257 −0.0792292
\(385\) −13.7268 −0.699583
\(386\) −6.69960 −0.341000
\(387\) 4.58759 0.233201
\(388\) 1.29495 0.0657410
\(389\) −23.6433 −1.19876 −0.599381 0.800464i \(-0.704587\pi\)
−0.599381 + 0.800464i \(0.704587\pi\)
\(390\) 2.21616 0.112220
\(391\) 25.1332 1.27104
\(392\) −6.22201 −0.314259
\(393\) 3.85542 0.194480
\(394\) −14.5701 −0.734029
\(395\) 26.8964 1.35330
\(396\) −3.48618 −0.175187
\(397\) 4.67201 0.234481 0.117241 0.993104i \(-0.462595\pi\)
0.117241 + 0.993104i \(0.462595\pi\)
\(398\) 18.2544 0.915010
\(399\) −8.90832 −0.445974
\(400\) 1.92589 0.0962945
\(401\) 14.7675 0.737454 0.368727 0.929538i \(-0.379794\pi\)
0.368727 + 0.929538i \(0.379794\pi\)
\(402\) 10.0754 0.502516
\(403\) 0.684486 0.0340967
\(404\) 8.20757 0.408342
\(405\) −18.1163 −0.900207
\(406\) −8.37218 −0.415504
\(407\) −55.6024 −2.75611
\(408\) 7.67824 0.380129
\(409\) −23.0521 −1.13985 −0.569927 0.821695i \(-0.693029\pi\)
−0.569927 + 0.821695i \(0.693029\pi\)
\(410\) −4.62783 −0.228552
\(411\) 9.55187 0.471159
\(412\) 0.559554 0.0275673
\(413\) −2.66177 −0.130977
\(414\) 2.99601 0.147246
\(415\) −20.9806 −1.02990
\(416\) −0.542391 −0.0265929
\(417\) 0.413086 0.0202289
\(418\) −38.4680 −1.88153
\(419\) −39.7993 −1.94432 −0.972161 0.234314i \(-0.924716\pi\)
−0.972161 + 0.234314i \(0.924716\pi\)
\(420\) 3.60393 0.175854
\(421\) −9.88650 −0.481838 −0.240919 0.970545i \(-0.577449\pi\)
−0.240919 + 0.970545i \(0.577449\pi\)
\(422\) 2.29284 0.111614
\(423\) 0.948203 0.0461032
\(424\) −6.48916 −0.315141
\(425\) −9.52451 −0.462006
\(426\) 5.25030 0.254378
\(427\) −6.10096 −0.295246
\(428\) 0.00863711 0.000417490 0
\(429\) 4.97973 0.240424
\(430\) −20.4793 −0.987601
\(431\) 6.91554 0.333110 0.166555 0.986032i \(-0.446736\pi\)
0.166555 + 0.986032i \(0.446736\pi\)
\(432\) 5.57299 0.268131
\(433\) 2.07242 0.0995942 0.0497971 0.998759i \(-0.484143\pi\)
0.0497971 + 0.998759i \(0.484143\pi\)
\(434\) 1.11312 0.0534313
\(435\) −38.7828 −1.85949
\(436\) −7.33424 −0.351247
\(437\) 33.0593 1.58144
\(438\) 17.4016 0.831482
\(439\) 13.0518 0.622930 0.311465 0.950258i \(-0.399180\pi\)
0.311465 + 0.950258i \(0.399180\pi\)
\(440\) 15.5626 0.741916
\(441\) 3.66807 0.174670
\(442\) 2.68240 0.127589
\(443\) 23.0493 1.09510 0.547552 0.836771i \(-0.315560\pi\)
0.547552 + 0.836771i \(0.315560\pi\)
\(444\) 14.5983 0.692803
\(445\) −19.5210 −0.925386
\(446\) 2.95621 0.139981
\(447\) −33.1214 −1.56659
\(448\) −0.882040 −0.0416725
\(449\) −1.94533 −0.0918059 −0.0459030 0.998946i \(-0.514617\pi\)
−0.0459030 + 0.998946i \(0.514617\pi\)
\(450\) −1.13537 −0.0535220
\(451\) −10.3988 −0.489660
\(452\) −13.1405 −0.618076
\(453\) −23.3165 −1.09551
\(454\) 17.2714 0.810586
\(455\) 1.25904 0.0590245
\(456\) 10.0997 0.472960
\(457\) 36.3128 1.69864 0.849320 0.527878i \(-0.177012\pi\)
0.849320 + 0.527878i \(0.177012\pi\)
\(458\) −12.4178 −0.580247
\(459\) −27.5613 −1.28645
\(460\) −13.3744 −0.623585
\(461\) 6.56578 0.305799 0.152899 0.988242i \(-0.451139\pi\)
0.152899 + 0.988242i \(0.451139\pi\)
\(462\) 8.09808 0.376757
\(463\) −18.5160 −0.860509 −0.430255 0.902708i \(-0.641576\pi\)
−0.430255 + 0.902708i \(0.641576\pi\)
\(464\) 9.49183 0.440647
\(465\) 5.15633 0.239119
\(466\) −9.05913 −0.419656
\(467\) −29.8689 −1.38217 −0.691085 0.722774i \(-0.742867\pi\)
−0.691085 + 0.722774i \(0.742867\pi\)
\(468\) 0.319756 0.0147807
\(469\) 5.72401 0.264310
\(470\) −4.23284 −0.195246
\(471\) −15.5505 −0.716528
\(472\) 3.01774 0.138903
\(473\) −46.0173 −2.11588
\(474\) −15.8674 −0.728816
\(475\) −12.5282 −0.574833
\(476\) 4.36214 0.199938
\(477\) 3.82556 0.175160
\(478\) 11.5170 0.526776
\(479\) 31.0213 1.41740 0.708699 0.705511i \(-0.249282\pi\)
0.708699 + 0.705511i \(0.249282\pi\)
\(480\) −4.08591 −0.186495
\(481\) 5.09991 0.232536
\(482\) −2.75272 −0.125383
\(483\) −6.95946 −0.316666
\(484\) 23.9693 1.08951
\(485\) 3.40793 0.154746
\(486\) −6.03132 −0.273586
\(487\) 19.7355 0.894299 0.447150 0.894459i \(-0.352439\pi\)
0.447150 + 0.894459i \(0.352439\pi\)
\(488\) 6.91687 0.313112
\(489\) −15.6380 −0.707177
\(490\) −16.3745 −0.739725
\(491\) −20.3203 −0.917040 −0.458520 0.888684i \(-0.651620\pi\)
−0.458520 + 0.888684i \(0.651620\pi\)
\(492\) 2.73018 0.123086
\(493\) −46.9419 −2.11416
\(494\) 3.52833 0.158747
\(495\) −9.17462 −0.412368
\(496\) −1.26198 −0.0566646
\(497\) 2.98278 0.133796
\(498\) 12.3774 0.554646
\(499\) −7.99526 −0.357917 −0.178958 0.983857i \(-0.557273\pi\)
−0.178958 + 0.983857i \(0.557273\pi\)
\(500\) −8.09016 −0.361803
\(501\) −30.1469 −1.34687
\(502\) 1.12731 0.0503145
\(503\) 42.6353 1.90101 0.950507 0.310704i \(-0.100565\pi\)
0.950507 + 0.310704i \(0.100565\pi\)
\(504\) 0.519990 0.0231622
\(505\) 21.5999 0.961185
\(506\) −30.0524 −1.33599
\(507\) 19.7266 0.876091
\(508\) −5.95706 −0.264302
\(509\) 22.6908 1.00575 0.502876 0.864359i \(-0.332275\pi\)
0.502876 + 0.864359i \(0.332275\pi\)
\(510\) 20.2069 0.894776
\(511\) 9.88616 0.437338
\(512\) 1.00000 0.0441942
\(513\) −36.2531 −1.60061
\(514\) 0.288177 0.0127109
\(515\) 1.47258 0.0648898
\(516\) 12.0817 0.531868
\(517\) −9.51125 −0.418304
\(518\) 8.29352 0.364396
\(519\) 0.00849363 0.000372829 0
\(520\) −1.42741 −0.0625963
\(521\) −3.94159 −0.172684 −0.0863420 0.996266i \(-0.527518\pi\)
−0.0863420 + 0.996266i \(0.527518\pi\)
\(522\) −5.59573 −0.244919
\(523\) 15.8239 0.691932 0.345966 0.938247i \(-0.387551\pi\)
0.345966 + 0.938247i \(0.387551\pi\)
\(524\) −2.48326 −0.108482
\(525\) 2.63737 0.115104
\(526\) −28.6909 −1.25098
\(527\) 6.24113 0.271868
\(528\) −9.18108 −0.399555
\(529\) 2.82696 0.122911
\(530\) −17.0776 −0.741802
\(531\) −1.77905 −0.0772042
\(532\) 5.73779 0.248765
\(533\) 0.953788 0.0413132
\(534\) 11.5164 0.498362
\(535\) 0.0227303 0.000982719 0
\(536\) −6.48951 −0.280304
\(537\) 32.6823 1.41035
\(538\) 7.36450 0.317506
\(539\) −36.7937 −1.58482
\(540\) 14.6665 0.631145
\(541\) 6.35580 0.273257 0.136629 0.990622i \(-0.456373\pi\)
0.136629 + 0.990622i \(0.456373\pi\)
\(542\) −2.69132 −0.115602
\(543\) −23.8319 −1.02273
\(544\) −4.94551 −0.212037
\(545\) −19.3016 −0.826789
\(546\) −0.742765 −0.0317874
\(547\) −8.82179 −0.377193 −0.188596 0.982055i \(-0.560394\pi\)
−0.188596 + 0.982055i \(0.560394\pi\)
\(548\) −6.15230 −0.262813
\(549\) −4.07771 −0.174033
\(550\) 11.3887 0.485617
\(551\) −61.7457 −2.63045
\(552\) 7.89019 0.335829
\(553\) −9.01456 −0.383338
\(554\) 14.8917 0.632687
\(555\) 38.4184 1.63077
\(556\) −0.266066 −0.0112837
\(557\) −14.5363 −0.615922 −0.307961 0.951399i \(-0.599647\pi\)
−0.307961 + 0.951399i \(0.599647\pi\)
\(558\) 0.743976 0.0314950
\(559\) 4.22076 0.178519
\(560\) −2.32127 −0.0980917
\(561\) 45.4051 1.91701
\(562\) −11.3827 −0.480152
\(563\) 34.8655 1.46941 0.734704 0.678388i \(-0.237321\pi\)
0.734704 + 0.678388i \(0.237321\pi\)
\(564\) 2.49715 0.105149
\(565\) −34.5819 −1.45487
\(566\) −21.5999 −0.907912
\(567\) 6.07184 0.254993
\(568\) −3.38169 −0.141892
\(569\) 26.8211 1.12440 0.562200 0.827001i \(-0.309955\pi\)
0.562200 + 0.827001i \(0.309955\pi\)
\(570\) 26.5794 1.11329
\(571\) −12.0883 −0.505878 −0.252939 0.967482i \(-0.581397\pi\)
−0.252939 + 0.967482i \(0.581397\pi\)
\(572\) −3.20742 −0.134109
\(573\) 1.15015 0.0480480
\(574\) 1.55106 0.0647399
\(575\) −9.78742 −0.408164
\(576\) −0.589531 −0.0245638
\(577\) 33.8792 1.41041 0.705205 0.709003i \(-0.250855\pi\)
0.705205 + 0.709003i \(0.250855\pi\)
\(578\) 7.45804 0.310214
\(579\) 10.4016 0.432275
\(580\) 24.9797 1.03723
\(581\) 7.03183 0.291729
\(582\) −2.01050 −0.0833377
\(583\) −38.3735 −1.58927
\(584\) −11.2083 −0.463802
\(585\) 0.841505 0.0347920
\(586\) −5.88354 −0.243047
\(587\) −44.5269 −1.83782 −0.918911 0.394465i \(-0.870930\pi\)
−0.918911 + 0.394465i \(0.870930\pi\)
\(588\) 9.66009 0.398375
\(589\) 8.20935 0.338260
\(590\) 7.94181 0.326959
\(591\) 22.6210 0.930504
\(592\) −9.40266 −0.386447
\(593\) 3.97893 0.163395 0.0816976 0.996657i \(-0.473966\pi\)
0.0816976 + 0.996657i \(0.473966\pi\)
\(594\) 32.9558 1.35219
\(595\) 11.4799 0.470629
\(596\) 21.3333 0.873846
\(597\) −28.3412 −1.15993
\(598\) 2.75644 0.112719
\(599\) 12.5086 0.511090 0.255545 0.966797i \(-0.417745\pi\)
0.255545 + 0.966797i \(0.417745\pi\)
\(600\) −2.99008 −0.122069
\(601\) −32.0039 −1.30546 −0.652732 0.757589i \(-0.726377\pi\)
−0.652732 + 0.757589i \(0.726377\pi\)
\(602\) 6.86383 0.279749
\(603\) 3.82577 0.155797
\(604\) 15.0180 0.611075
\(605\) 63.0801 2.56457
\(606\) −12.7428 −0.517642
\(607\) 27.9887 1.13603 0.568013 0.823020i \(-0.307712\pi\)
0.568013 + 0.823020i \(0.307712\pi\)
\(608\) −6.50514 −0.263818
\(609\) 12.9984 0.526721
\(610\) 18.2032 0.737026
\(611\) 0.872382 0.0352928
\(612\) 2.91553 0.117853
\(613\) −33.7759 −1.36420 −0.682098 0.731261i \(-0.738932\pi\)
−0.682098 + 0.731261i \(0.738932\pi\)
\(614\) 27.9241 1.12693
\(615\) 7.18503 0.289728
\(616\) −5.21593 −0.210156
\(617\) −18.2996 −0.736714 −0.368357 0.929684i \(-0.620080\pi\)
−0.368357 + 0.929684i \(0.620080\pi\)
\(618\) −0.868746 −0.0349461
\(619\) 5.98223 0.240446 0.120223 0.992747i \(-0.461639\pi\)
0.120223 + 0.992747i \(0.461639\pi\)
\(620\) −3.32116 −0.133381
\(621\) −28.3221 −1.13653
\(622\) −0.221177 −0.00886838
\(623\) 6.54265 0.262126
\(624\) 0.842099 0.0337109
\(625\) −30.9204 −1.23682
\(626\) 15.9954 0.639306
\(627\) 59.7242 2.38516
\(628\) 10.0160 0.399681
\(629\) 46.5009 1.85411
\(630\) 1.36846 0.0545209
\(631\) 27.0906 1.07846 0.539229 0.842159i \(-0.318716\pi\)
0.539229 + 0.842159i \(0.318716\pi\)
\(632\) 10.2201 0.406535
\(633\) −3.55979 −0.141489
\(634\) −10.4611 −0.415464
\(635\) −15.6772 −0.622132
\(636\) 10.0749 0.399494
\(637\) 3.37476 0.133713
\(638\) 56.1298 2.22220
\(639\) 1.99361 0.0788660
\(640\) 2.63171 0.104027
\(641\) −19.7405 −0.779701 −0.389851 0.920878i \(-0.627473\pi\)
−0.389851 + 0.920878i \(0.627473\pi\)
\(642\) −0.0134097 −0.000529239 0
\(643\) −7.04426 −0.277798 −0.138899 0.990307i \(-0.544356\pi\)
−0.138899 + 0.990307i \(0.544356\pi\)
\(644\) 4.48255 0.176637
\(645\) 31.7956 1.25195
\(646\) 32.1712 1.26576
\(647\) −2.08754 −0.0820696 −0.0410348 0.999158i \(-0.513065\pi\)
−0.0410348 + 0.999158i \(0.513065\pi\)
\(648\) −6.88386 −0.270424
\(649\) 17.8453 0.700491
\(650\) −1.04459 −0.0409720
\(651\) −1.72819 −0.0677331
\(652\) 10.0724 0.394464
\(653\) 4.67434 0.182921 0.0914606 0.995809i \(-0.470846\pi\)
0.0914606 + 0.995809i \(0.470846\pi\)
\(654\) 11.3869 0.445264
\(655\) −6.53520 −0.255352
\(656\) −1.75849 −0.0686575
\(657\) 6.60764 0.257789
\(658\) 1.41867 0.0553057
\(659\) −21.7121 −0.845784 −0.422892 0.906180i \(-0.638985\pi\)
−0.422892 + 0.906180i \(0.638985\pi\)
\(660\) −24.1619 −0.940502
\(661\) 9.91003 0.385455 0.192728 0.981252i \(-0.438267\pi\)
0.192728 + 0.981252i \(0.438267\pi\)
\(662\) −3.16315 −0.122939
\(663\) −4.16460 −0.161740
\(664\) −7.97223 −0.309383
\(665\) 15.1002 0.585561
\(666\) 5.54316 0.214793
\(667\) −48.2377 −1.86777
\(668\) 19.4175 0.751284
\(669\) −4.58972 −0.177449
\(670\) −17.0785 −0.659800
\(671\) 40.9028 1.57903
\(672\) 1.36943 0.0528268
\(673\) 26.9480 1.03877 0.519384 0.854541i \(-0.326161\pi\)
0.519384 + 0.854541i \(0.326161\pi\)
\(674\) −29.8037 −1.14799
\(675\) 10.7330 0.413112
\(676\) −12.7058 −0.488685
\(677\) −27.5716 −1.05966 −0.529831 0.848103i \(-0.677744\pi\)
−0.529831 + 0.848103i \(0.677744\pi\)
\(678\) 20.4015 0.783515
\(679\) −1.14220 −0.0438335
\(680\) −13.0151 −0.499108
\(681\) −26.8150 −1.02755
\(682\) −7.46269 −0.285761
\(683\) −43.6122 −1.66878 −0.834388 0.551178i \(-0.814178\pi\)
−0.834388 + 0.551178i \(0.814178\pi\)
\(684\) 3.83498 0.146634
\(685\) −16.1911 −0.618629
\(686\) 11.6623 0.445270
\(687\) 19.2795 0.735560
\(688\) −7.78177 −0.296677
\(689\) 3.51966 0.134088
\(690\) 20.7647 0.790498
\(691\) 9.32740 0.354831 0.177416 0.984136i \(-0.443226\pi\)
0.177416 + 0.984136i \(0.443226\pi\)
\(692\) −0.00547070 −0.000207965 0
\(693\) 3.07495 0.116808
\(694\) −5.26729 −0.199944
\(695\) −0.700208 −0.0265604
\(696\) −14.7367 −0.558594
\(697\) 8.69662 0.329408
\(698\) −24.9944 −0.946052
\(699\) 14.0649 0.531984
\(700\) −1.69871 −0.0642053
\(701\) −8.74867 −0.330433 −0.165216 0.986257i \(-0.552832\pi\)
−0.165216 + 0.986257i \(0.552832\pi\)
\(702\) −3.02274 −0.114086
\(703\) 61.1656 2.30690
\(704\) 5.91348 0.222873
\(705\) 6.57178 0.247507
\(706\) −22.8772 −0.860993
\(707\) −7.23941 −0.272266
\(708\) −4.68524 −0.176082
\(709\) −41.2119 −1.54775 −0.773873 0.633341i \(-0.781683\pi\)
−0.773873 + 0.633341i \(0.781683\pi\)
\(710\) −8.89962 −0.333997
\(711\) −6.02509 −0.225958
\(712\) −7.41763 −0.277987
\(713\) 6.41341 0.240184
\(714\) −6.77251 −0.253455
\(715\) −8.44099 −0.315675
\(716\) −21.0505 −0.786694
\(717\) −17.8809 −0.667776
\(718\) 0.243368 0.00908240
\(719\) 37.0291 1.38095 0.690475 0.723356i \(-0.257401\pi\)
0.690475 + 0.723356i \(0.257401\pi\)
\(720\) −1.55147 −0.0578200
\(721\) −0.493549 −0.0183807
\(722\) 23.3168 0.867762
\(723\) 4.27379 0.158944
\(724\) 15.3500 0.570478
\(725\) 18.2802 0.678911
\(726\) −37.2139 −1.38114
\(727\) 47.1436 1.74846 0.874230 0.485512i \(-0.161367\pi\)
0.874230 + 0.485512i \(0.161367\pi\)
\(728\) 0.478410 0.0177311
\(729\) 30.0156 1.11169
\(730\) −29.4970 −1.09173
\(731\) 38.4848 1.42341
\(732\) −10.7389 −0.396922
\(733\) 27.9809 1.03350 0.516748 0.856137i \(-0.327142\pi\)
0.516748 + 0.856137i \(0.327142\pi\)
\(734\) −10.2883 −0.379749
\(735\) 25.4225 0.937725
\(736\) −5.08202 −0.187326
\(737\) −38.3756 −1.41358
\(738\) 1.03668 0.0381609
\(739\) 20.7881 0.764703 0.382351 0.924017i \(-0.375114\pi\)
0.382351 + 0.924017i \(0.375114\pi\)
\(740\) −24.7451 −0.909646
\(741\) −5.47797 −0.201238
\(742\) 5.72370 0.210124
\(743\) −48.8925 −1.79369 −0.896845 0.442344i \(-0.854147\pi\)
−0.896845 + 0.442344i \(0.854147\pi\)
\(744\) 1.95931 0.0718318
\(745\) 56.1430 2.05692
\(746\) −29.5349 −1.08135
\(747\) 4.69988 0.171960
\(748\) −29.2452 −1.06931
\(749\) −0.00761827 −0.000278366 0
\(750\) 12.5605 0.458646
\(751\) −37.6155 −1.37261 −0.686304 0.727315i \(-0.740768\pi\)
−0.686304 + 0.727315i \(0.740768\pi\)
\(752\) −1.60840 −0.0586523
\(753\) −1.75023 −0.0637820
\(754\) −5.14828 −0.187489
\(755\) 39.5231 1.43839
\(756\) −4.91560 −0.178779
\(757\) 20.9612 0.761847 0.380923 0.924607i \(-0.375606\pi\)
0.380923 + 0.924607i \(0.375606\pi\)
\(758\) −31.9775 −1.16147
\(759\) 46.6585 1.69360
\(760\) −17.1196 −0.620994
\(761\) −44.1859 −1.60174 −0.800869 0.598840i \(-0.795628\pi\)
−0.800869 + 0.598840i \(0.795628\pi\)
\(762\) 9.24874 0.335047
\(763\) 6.46910 0.234197
\(764\) −0.740802 −0.0268013
\(765\) 7.67283 0.277412
\(766\) 18.6199 0.672764
\(767\) −1.63679 −0.0591012
\(768\) −1.55257 −0.0560235
\(769\) −28.5036 −1.02787 −0.513934 0.857830i \(-0.671812\pi\)
−0.513934 + 0.857830i \(0.671812\pi\)
\(770\) −13.7268 −0.494680
\(771\) −0.447414 −0.0161132
\(772\) −6.69960 −0.241124
\(773\) 32.6834 1.17554 0.587769 0.809028i \(-0.300006\pi\)
0.587769 + 0.809028i \(0.300006\pi\)
\(774\) 4.58759 0.164898
\(775\) −2.43043 −0.0873038
\(776\) 1.29495 0.0464859
\(777\) −12.8763 −0.461933
\(778\) −23.6433 −0.847653
\(779\) 11.4392 0.409853
\(780\) 2.21616 0.0793512
\(781\) −19.9975 −0.715568
\(782\) 25.1332 0.898761
\(783\) 52.8979 1.89042
\(784\) −6.22201 −0.222214
\(785\) 26.3591 0.940797
\(786\) 3.85542 0.137518
\(787\) −5.16397 −0.184076 −0.0920378 0.995756i \(-0.529338\pi\)
−0.0920378 + 0.995756i \(0.529338\pi\)
\(788\) −14.5701 −0.519037
\(789\) 44.5446 1.58583
\(790\) 26.8964 0.956931
\(791\) 11.5904 0.412108
\(792\) −3.48618 −0.123876
\(793\) −3.75165 −0.133225
\(794\) 4.67201 0.165803
\(795\) 26.5141 0.940358
\(796\) 18.2544 0.647010
\(797\) −16.2077 −0.574105 −0.287052 0.957915i \(-0.592675\pi\)
−0.287052 + 0.957915i \(0.592675\pi\)
\(798\) −8.90832 −0.315351
\(799\) 7.95436 0.281405
\(800\) 1.92589 0.0680905
\(801\) 4.37292 0.154510
\(802\) 14.7675 0.521459
\(803\) −66.2800 −2.33897
\(804\) 10.0754 0.355332
\(805\) 11.7968 0.415781
\(806\) 0.684486 0.0241100
\(807\) −11.4339 −0.402492
\(808\) 8.20757 0.288741
\(809\) 26.0475 0.915783 0.457891 0.889008i \(-0.348605\pi\)
0.457891 + 0.889008i \(0.348605\pi\)
\(810\) −18.1163 −0.636542
\(811\) −42.0203 −1.47553 −0.737766 0.675056i \(-0.764119\pi\)
−0.737766 + 0.675056i \(0.764119\pi\)
\(812\) −8.37218 −0.293806
\(813\) 4.17846 0.146545
\(814\) −55.6024 −1.94886
\(815\) 26.5075 0.928518
\(816\) 7.67824 0.268792
\(817\) 50.6215 1.77102
\(818\) −23.0521 −0.805999
\(819\) −0.282038 −0.00985520
\(820\) −4.62783 −0.161611
\(821\) −53.1911 −1.85638 −0.928191 0.372104i \(-0.878636\pi\)
−0.928191 + 0.372104i \(0.878636\pi\)
\(822\) 9.55187 0.333160
\(823\) 21.7285 0.757407 0.378703 0.925518i \(-0.376370\pi\)
0.378703 + 0.925518i \(0.376370\pi\)
\(824\) 0.559554 0.0194930
\(825\) −17.6818 −0.615600
\(826\) −2.66177 −0.0926147
\(827\) 4.42385 0.153832 0.0769162 0.997038i \(-0.475493\pi\)
0.0769162 + 0.997038i \(0.475493\pi\)
\(828\) 2.99601 0.104119
\(829\) 30.9185 1.07384 0.536922 0.843632i \(-0.319587\pi\)
0.536922 + 0.843632i \(0.319587\pi\)
\(830\) −20.9806 −0.728247
\(831\) −23.1204 −0.802036
\(832\) −0.542391 −0.0188040
\(833\) 30.7710 1.06615
\(834\) 0.413086 0.0143040
\(835\) 51.1011 1.76843
\(836\) −38.4680 −1.33044
\(837\) −7.03300 −0.243096
\(838\) −39.7993 −1.37484
\(839\) −10.8624 −0.375010 −0.187505 0.982264i \(-0.560040\pi\)
−0.187505 + 0.982264i \(0.560040\pi\)
\(840\) 3.60393 0.124348
\(841\) 61.0949 2.10672
\(842\) −9.88650 −0.340711
\(843\) 17.6725 0.608672
\(844\) 2.29284 0.0789229
\(845\) −33.4380 −1.15030
\(846\) 0.948203 0.0325999
\(847\) −21.1419 −0.726443
\(848\) −6.48916 −0.222839
\(849\) 33.5354 1.15093
\(850\) −9.52451 −0.326688
\(851\) 47.7845 1.63803
\(852\) 5.25030 0.179872
\(853\) 37.7761 1.29343 0.646714 0.762733i \(-0.276143\pi\)
0.646714 + 0.762733i \(0.276143\pi\)
\(854\) −6.10096 −0.208770
\(855\) 10.0926 0.345158
\(856\) 0.00863711 0.000295210 0
\(857\) −45.5128 −1.55469 −0.777343 0.629077i \(-0.783433\pi\)
−0.777343 + 0.629077i \(0.783433\pi\)
\(858\) 4.97973 0.170005
\(859\) 27.2305 0.929094 0.464547 0.885549i \(-0.346217\pi\)
0.464547 + 0.885549i \(0.346217\pi\)
\(860\) −20.4793 −0.698340
\(861\) −2.40812 −0.0820687
\(862\) 6.91554 0.235544
\(863\) 1.49875 0.0510181 0.0255091 0.999675i \(-0.491879\pi\)
0.0255091 + 0.999675i \(0.491879\pi\)
\(864\) 5.57299 0.189597
\(865\) −0.0143973 −0.000489522 0
\(866\) 2.07242 0.0704237
\(867\) −11.5791 −0.393248
\(868\) 1.11312 0.0377816
\(869\) 60.4365 2.05017
\(870\) −38.7828 −1.31486
\(871\) 3.51985 0.119266
\(872\) −7.33424 −0.248369
\(873\) −0.763412 −0.0258376
\(874\) 33.0593 1.11825
\(875\) 7.13585 0.241236
\(876\) 17.4016 0.587947
\(877\) −13.4100 −0.452823 −0.226412 0.974032i \(-0.572699\pi\)
−0.226412 + 0.974032i \(0.572699\pi\)
\(878\) 13.0518 0.440478
\(879\) 9.13460 0.308102
\(880\) 15.5626 0.524614
\(881\) −46.6340 −1.57114 −0.785570 0.618773i \(-0.787630\pi\)
−0.785570 + 0.618773i \(0.787630\pi\)
\(882\) 3.66807 0.123510
\(883\) 37.6874 1.26828 0.634141 0.773218i \(-0.281354\pi\)
0.634141 + 0.773218i \(0.281354\pi\)
\(884\) 2.68240 0.0902188
\(885\) −12.3302 −0.414475
\(886\) 23.0493 0.774356
\(887\) −5.27908 −0.177254 −0.0886271 0.996065i \(-0.528248\pi\)
−0.0886271 + 0.996065i \(0.528248\pi\)
\(888\) 14.5983 0.489886
\(889\) 5.25436 0.176226
\(890\) −19.5210 −0.654347
\(891\) −40.7076 −1.36376
\(892\) 2.95621 0.0989812
\(893\) 10.4629 0.350127
\(894\) −33.1214 −1.10775
\(895\) −55.3988 −1.85178
\(896\) −0.882040 −0.0294669
\(897\) −4.27956 −0.142890
\(898\) −1.94533 −0.0649166
\(899\) −11.9785 −0.399505
\(900\) −1.13537 −0.0378458
\(901\) 32.0922 1.06915
\(902\) −10.3988 −0.346242
\(903\) −10.6566 −0.354628
\(904\) −13.1405 −0.437046
\(905\) 40.3967 1.34283
\(906\) −23.3165 −0.774639
\(907\) 49.7010 1.65030 0.825148 0.564917i \(-0.191092\pi\)
0.825148 + 0.564917i \(0.191092\pi\)
\(908\) 17.2714 0.573171
\(909\) −4.83862 −0.160487
\(910\) 1.25904 0.0417367
\(911\) 58.0575 1.92353 0.961766 0.273872i \(-0.0883044\pi\)
0.961766 + 0.273872i \(0.0883044\pi\)
\(912\) 10.0997 0.334434
\(913\) −47.1436 −1.56023
\(914\) 36.3128 1.20112
\(915\) −28.2617 −0.934303
\(916\) −12.4178 −0.410297
\(917\) 2.19033 0.0723311
\(918\) −27.5613 −0.909658
\(919\) −23.3875 −0.771482 −0.385741 0.922607i \(-0.626054\pi\)
−0.385741 + 0.922607i \(0.626054\pi\)
\(920\) −13.3744 −0.440941
\(921\) −43.3541 −1.42857
\(922\) 6.56578 0.216232
\(923\) 1.83420 0.0603733
\(924\) 8.09808 0.266407
\(925\) −18.1085 −0.595404
\(926\) −18.5160 −0.608472
\(927\) −0.329875 −0.0108345
\(928\) 9.49183 0.311585
\(929\) 36.0194 1.18176 0.590879 0.806760i \(-0.298781\pi\)
0.590879 + 0.806760i \(0.298781\pi\)
\(930\) 5.15633 0.169083
\(931\) 40.4750 1.32651
\(932\) −9.05913 −0.296742
\(933\) 0.343392 0.0112422
\(934\) −29.8689 −0.977342
\(935\) −76.9648 −2.51702
\(936\) 0.319756 0.0104516
\(937\) 53.8068 1.75779 0.878897 0.477012i \(-0.158280\pi\)
0.878897 + 0.477012i \(0.158280\pi\)
\(938\) 5.72401 0.186895
\(939\) −24.8340 −0.810427
\(940\) −4.23284 −0.138060
\(941\) −7.32756 −0.238872 −0.119436 0.992842i \(-0.538109\pi\)
−0.119436 + 0.992842i \(0.538109\pi\)
\(942\) −15.5505 −0.506662
\(943\) 8.93668 0.291018
\(944\) 3.01774 0.0982190
\(945\) −12.9364 −0.420822
\(946\) −46.0173 −1.49615
\(947\) −35.9251 −1.16741 −0.583705 0.811966i \(-0.698397\pi\)
−0.583705 + 0.811966i \(0.698397\pi\)
\(948\) −15.8674 −0.515351
\(949\) 6.07927 0.197342
\(950\) −12.5282 −0.406468
\(951\) 16.2416 0.526670
\(952\) 4.36214 0.141378
\(953\) 47.8518 1.55007 0.775036 0.631917i \(-0.217732\pi\)
0.775036 + 0.631917i \(0.217732\pi\)
\(954\) 3.82556 0.123857
\(955\) −1.94958 −0.0630868
\(956\) 11.5170 0.372487
\(957\) −87.1453 −2.81701
\(958\) 31.0213 1.00225
\(959\) 5.42658 0.175233
\(960\) −4.08591 −0.131872
\(961\) −29.4074 −0.948626
\(962\) 5.09991 0.164428
\(963\) −0.00509184 −0.000164082 0
\(964\) −2.75272 −0.0886593
\(965\) −17.6314 −0.567574
\(966\) −6.95946 −0.223917
\(967\) 35.0205 1.12618 0.563092 0.826394i \(-0.309612\pi\)
0.563092 + 0.826394i \(0.309612\pi\)
\(968\) 23.9693 0.770401
\(969\) −49.9480 −1.60456
\(970\) 3.40793 0.109422
\(971\) 12.7728 0.409897 0.204949 0.978773i \(-0.434297\pi\)
0.204949 + 0.978773i \(0.434297\pi\)
\(972\) −6.03132 −0.193455
\(973\) 0.234681 0.00752352
\(974\) 19.7355 0.632365
\(975\) 1.62179 0.0519388
\(976\) 6.91687 0.221404
\(977\) −11.3687 −0.363716 −0.181858 0.983325i \(-0.558211\pi\)
−0.181858 + 0.983325i \(0.558211\pi\)
\(978\) −15.6380 −0.500049
\(979\) −43.8640 −1.40190
\(980\) −16.3745 −0.523064
\(981\) 4.32377 0.138047
\(982\) −20.3203 −0.648445
\(983\) −43.0587 −1.37336 −0.686679 0.726961i \(-0.740932\pi\)
−0.686679 + 0.726961i \(0.740932\pi\)
\(984\) 2.73018 0.0870348
\(985\) −38.3442 −1.22175
\(986\) −46.9419 −1.49494
\(987\) −2.20259 −0.0701092
\(988\) 3.52833 0.112251
\(989\) 39.5471 1.25752
\(990\) −9.17462 −0.291588
\(991\) 56.8558 1.80608 0.903042 0.429551i \(-0.141328\pi\)
0.903042 + 0.429551i \(0.141328\pi\)
\(992\) −1.26198 −0.0400679
\(993\) 4.91100 0.155846
\(994\) 2.98278 0.0946082
\(995\) 48.0403 1.52298
\(996\) 12.3774 0.392194
\(997\) 14.4490 0.457604 0.228802 0.973473i \(-0.426519\pi\)
0.228802 + 0.973473i \(0.426519\pi\)
\(998\) −7.99526 −0.253085
\(999\) −52.4009 −1.65789
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 \(a_p\))