Properties

Label 8042.2.a.a.1.15
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 1.15
Character \(\chi\) = 8042.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-2.04025 q^{3}\) \(+1.00000 q^{4}\) \(+2.67295 q^{5}\) \(-2.04025 q^{6}\) \(+4.19458 q^{7}\) \(+1.00000 q^{8}\) \(+1.16263 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-2.04025 q^{3}\) \(+1.00000 q^{4}\) \(+2.67295 q^{5}\) \(-2.04025 q^{6}\) \(+4.19458 q^{7}\) \(+1.00000 q^{8}\) \(+1.16263 q^{9}\) \(+2.67295 q^{10}\) \(-2.39834 q^{11}\) \(-2.04025 q^{12}\) \(-5.33719 q^{13}\) \(+4.19458 q^{14}\) \(-5.45350 q^{15}\) \(+1.00000 q^{16}\) \(+0.801038 q^{17}\) \(+1.16263 q^{18}\) \(-3.01007 q^{19}\) \(+2.67295 q^{20}\) \(-8.55800 q^{21}\) \(-2.39834 q^{22}\) \(-0.421516 q^{23}\) \(-2.04025 q^{24}\) \(+2.14469 q^{25}\) \(-5.33719 q^{26}\) \(+3.74869 q^{27}\) \(+4.19458 q^{28}\) \(+0.238867 q^{29}\) \(-5.45350 q^{30}\) \(-2.73783 q^{31}\) \(+1.00000 q^{32}\) \(+4.89322 q^{33}\) \(+0.801038 q^{34}\) \(+11.2119 q^{35}\) \(+1.16263 q^{36}\) \(-7.32133 q^{37}\) \(-3.01007 q^{38}\) \(+10.8892 q^{39}\) \(+2.67295 q^{40}\) \(-9.55708 q^{41}\) \(-8.55800 q^{42}\) \(-2.46109 q^{43}\) \(-2.39834 q^{44}\) \(+3.10767 q^{45}\) \(-0.421516 q^{46}\) \(-12.9705 q^{47}\) \(-2.04025 q^{48}\) \(+10.5945 q^{49}\) \(+2.14469 q^{50}\) \(-1.63432 q^{51}\) \(-5.33719 q^{52}\) \(+8.03477 q^{53}\) \(+3.74869 q^{54}\) \(-6.41065 q^{55}\) \(+4.19458 q^{56}\) \(+6.14130 q^{57}\) \(+0.238867 q^{58}\) \(+3.43602 q^{59}\) \(-5.45350 q^{60}\) \(+6.03348 q^{61}\) \(-2.73783 q^{62}\) \(+4.87676 q^{63}\) \(+1.00000 q^{64}\) \(-14.2661 q^{65}\) \(+4.89322 q^{66}\) \(-9.91857 q^{67}\) \(+0.801038 q^{68}\) \(+0.860000 q^{69}\) \(+11.2119 q^{70}\) \(-9.43912 q^{71}\) \(+1.16263 q^{72}\) \(-0.400632 q^{73}\) \(-7.32133 q^{74}\) \(-4.37570 q^{75}\) \(-3.01007 q^{76}\) \(-10.0600 q^{77}\) \(+10.8892 q^{78}\) \(-1.01068 q^{79}\) \(+2.67295 q^{80}\) \(-11.1362 q^{81}\) \(-9.55708 q^{82}\) \(-11.1142 q^{83}\) \(-8.55800 q^{84}\) \(+2.14114 q^{85}\) \(-2.46109 q^{86}\) \(-0.487349 q^{87}\) \(-2.39834 q^{88}\) \(-7.36845 q^{89}\) \(+3.10767 q^{90}\) \(-22.3872 q^{91}\) \(-0.421516 q^{92}\) \(+5.58587 q^{93}\) \(-12.9705 q^{94}\) \(-8.04577 q^{95}\) \(-2.04025 q^{96}\) \(-16.8175 q^{97}\) \(+10.5945 q^{98}\) \(-2.78839 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(67q \) \(\mathstrut +\mathstrut 67q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 67q^{4} \) \(\mathstrut -\mathstrut 20q^{5} \) \(\mathstrut -\mathstrut 11q^{6} \) \(\mathstrut -\mathstrut 40q^{7} \) \(\mathstrut +\mathstrut 67q^{8} \) \(\mathstrut +\mathstrut 24q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(67q \) \(\mathstrut +\mathstrut 67q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 67q^{4} \) \(\mathstrut -\mathstrut 20q^{5} \) \(\mathstrut -\mathstrut 11q^{6} \) \(\mathstrut -\mathstrut 40q^{7} \) \(\mathstrut +\mathstrut 67q^{8} \) \(\mathstrut +\mathstrut 24q^{9} \) \(\mathstrut -\mathstrut 20q^{10} \) \(\mathstrut -\mathstrut 13q^{11} \) \(\mathstrut -\mathstrut 11q^{12} \) \(\mathstrut -\mathstrut 51q^{13} \) \(\mathstrut -\mathstrut 40q^{14} \) \(\mathstrut -\mathstrut 31q^{15} \) \(\mathstrut +\mathstrut 67q^{16} \) \(\mathstrut -\mathstrut 34q^{17} \) \(\mathstrut +\mathstrut 24q^{18} \) \(\mathstrut -\mathstrut 33q^{19} \) \(\mathstrut -\mathstrut 20q^{20} \) \(\mathstrut -\mathstrut 39q^{21} \) \(\mathstrut -\mathstrut 13q^{22} \) \(\mathstrut -\mathstrut 43q^{23} \) \(\mathstrut -\mathstrut 11q^{24} \) \(\mathstrut -\mathstrut 9q^{25} \) \(\mathstrut -\mathstrut 51q^{26} \) \(\mathstrut -\mathstrut 29q^{27} \) \(\mathstrut -\mathstrut 40q^{28} \) \(\mathstrut -\mathstrut 63q^{29} \) \(\mathstrut -\mathstrut 31q^{30} \) \(\mathstrut -\mathstrut 43q^{31} \) \(\mathstrut +\mathstrut 67q^{32} \) \(\mathstrut -\mathstrut 49q^{33} \) \(\mathstrut -\mathstrut 34q^{34} \) \(\mathstrut -\mathstrut 20q^{35} \) \(\mathstrut +\mathstrut 24q^{36} \) \(\mathstrut -\mathstrut 77q^{37} \) \(\mathstrut -\mathstrut 33q^{38} \) \(\mathstrut -\mathstrut 40q^{39} \) \(\mathstrut -\mathstrut 20q^{40} \) \(\mathstrut -\mathstrut 50q^{41} \) \(\mathstrut -\mathstrut 39q^{42} \) \(\mathstrut -\mathstrut 56q^{43} \) \(\mathstrut -\mathstrut 13q^{44} \) \(\mathstrut -\mathstrut 48q^{45} \) \(\mathstrut -\mathstrut 43q^{46} \) \(\mathstrut -\mathstrut 48q^{47} \) \(\mathstrut -\mathstrut 11q^{48} \) \(\mathstrut +\mathstrut q^{49} \) \(\mathstrut -\mathstrut 9q^{50} \) \(\mathstrut -\mathstrut 18q^{51} \) \(\mathstrut -\mathstrut 51q^{52} \) \(\mathstrut -\mathstrut 91q^{53} \) \(\mathstrut -\mathstrut 29q^{54} \) \(\mathstrut -\mathstrut 58q^{55} \) \(\mathstrut -\mathstrut 40q^{56} \) \(\mathstrut -\mathstrut 65q^{57} \) \(\mathstrut -\mathstrut 63q^{58} \) \(\mathstrut -\mathstrut 17q^{59} \) \(\mathstrut -\mathstrut 31q^{60} \) \(\mathstrut -\mathstrut 45q^{61} \) \(\mathstrut -\mathstrut 43q^{62} \) \(\mathstrut -\mathstrut 67q^{63} \) \(\mathstrut +\mathstrut 67q^{64} \) \(\mathstrut -\mathstrut 65q^{65} \) \(\mathstrut -\mathstrut 49q^{66} \) \(\mathstrut -\mathstrut 112q^{67} \) \(\mathstrut -\mathstrut 34q^{68} \) \(\mathstrut -\mathstrut 57q^{69} \) \(\mathstrut -\mathstrut 20q^{70} \) \(\mathstrut -\mathstrut 75q^{71} \) \(\mathstrut +\mathstrut 24q^{72} \) \(\mathstrut -\mathstrut 79q^{73} \) \(\mathstrut -\mathstrut 77q^{74} \) \(\mathstrut -\mathstrut 5q^{75} \) \(\mathstrut -\mathstrut 33q^{76} \) \(\mathstrut -\mathstrut 85q^{77} \) \(\mathstrut -\mathstrut 40q^{78} \) \(\mathstrut -\mathstrut 80q^{79} \) \(\mathstrut -\mathstrut 20q^{80} \) \(\mathstrut -\mathstrut 77q^{81} \) \(\mathstrut -\mathstrut 50q^{82} \) \(\mathstrut -\mathstrut 22q^{83} \) \(\mathstrut -\mathstrut 39q^{84} \) \(\mathstrut -\mathstrut 134q^{85} \) \(\mathstrut -\mathstrut 56q^{86} \) \(\mathstrut -\mathstrut 49q^{87} \) \(\mathstrut -\mathstrut 13q^{88} \) \(\mathstrut -\mathstrut 77q^{89} \) \(\mathstrut -\mathstrut 48q^{90} \) \(\mathstrut -\mathstrut 17q^{91} \) \(\mathstrut -\mathstrut 43q^{92} \) \(\mathstrut -\mathstrut 97q^{93} \) \(\mathstrut -\mathstrut 48q^{94} \) \(\mathstrut -\mathstrut 73q^{95} \) \(\mathstrut -\mathstrut 11q^{96} \) \(\mathstrut -\mathstrut 87q^{97} \) \(\mathstrut +\mathstrut q^{98} \) \(\mathstrut -\mathstrut 44q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −2.04025 −1.17794 −0.588970 0.808155i \(-0.700467\pi\)
−0.588970 + 0.808155i \(0.700467\pi\)
\(4\) 1.00000 0.500000
\(5\) 2.67295 1.19538 0.597691 0.801727i \(-0.296085\pi\)
0.597691 + 0.801727i \(0.296085\pi\)
\(6\) −2.04025 −0.832930
\(7\) 4.19458 1.58540 0.792701 0.609611i \(-0.208674\pi\)
0.792701 + 0.609611i \(0.208674\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.16263 0.387544
\(10\) 2.67295 0.845262
\(11\) −2.39834 −0.723127 −0.361563 0.932348i \(-0.617757\pi\)
−0.361563 + 0.932348i \(0.617757\pi\)
\(12\) −2.04025 −0.588970
\(13\) −5.33719 −1.48027 −0.740135 0.672458i \(-0.765238\pi\)
−0.740135 + 0.672458i \(0.765238\pi\)
\(14\) 4.19458 1.12105
\(15\) −5.45350 −1.40809
\(16\) 1.00000 0.250000
\(17\) 0.801038 0.194280 0.0971401 0.995271i \(-0.469030\pi\)
0.0971401 + 0.995271i \(0.469030\pi\)
\(18\) 1.16263 0.274035
\(19\) −3.01007 −0.690557 −0.345278 0.938500i \(-0.612216\pi\)
−0.345278 + 0.938500i \(0.612216\pi\)
\(20\) 2.67295 0.597691
\(21\) −8.55800 −1.86751
\(22\) −2.39834 −0.511328
\(23\) −0.421516 −0.0878922 −0.0439461 0.999034i \(-0.513993\pi\)
−0.0439461 + 0.999034i \(0.513993\pi\)
\(24\) −2.04025 −0.416465
\(25\) 2.14469 0.428937
\(26\) −5.33719 −1.04671
\(27\) 3.74869 0.721436
\(28\) 4.19458 0.792701
\(29\) 0.238867 0.0443564 0.0221782 0.999754i \(-0.492940\pi\)
0.0221782 + 0.999754i \(0.492940\pi\)
\(30\) −5.45350 −0.995669
\(31\) −2.73783 −0.491729 −0.245865 0.969304i \(-0.579072\pi\)
−0.245865 + 0.969304i \(0.579072\pi\)
\(32\) 1.00000 0.176777
\(33\) 4.89322 0.851800
\(34\) 0.801038 0.137377
\(35\) 11.2119 1.89516
\(36\) 1.16263 0.193772
\(37\) −7.32133 −1.20362 −0.601809 0.798640i \(-0.705553\pi\)
−0.601809 + 0.798640i \(0.705553\pi\)
\(38\) −3.01007 −0.488297
\(39\) 10.8892 1.74367
\(40\) 2.67295 0.422631
\(41\) −9.55708 −1.49257 −0.746283 0.665629i \(-0.768163\pi\)
−0.746283 + 0.665629i \(0.768163\pi\)
\(42\) −8.55800 −1.32053
\(43\) −2.46109 −0.375313 −0.187657 0.982235i \(-0.560089\pi\)
−0.187657 + 0.982235i \(0.560089\pi\)
\(44\) −2.39834 −0.361563
\(45\) 3.10767 0.463264
\(46\) −0.421516 −0.0621492
\(47\) −12.9705 −1.89194 −0.945969 0.324256i \(-0.894886\pi\)
−0.945969 + 0.324256i \(0.894886\pi\)
\(48\) −2.04025 −0.294485
\(49\) 10.5945 1.51350
\(50\) 2.14469 0.303304
\(51\) −1.63432 −0.228851
\(52\) −5.33719 −0.740135
\(53\) 8.03477 1.10366 0.551830 0.833956i \(-0.313930\pi\)
0.551830 + 0.833956i \(0.313930\pi\)
\(54\) 3.74869 0.510133
\(55\) −6.41065 −0.864412
\(56\) 4.19458 0.560524
\(57\) 6.14130 0.813435
\(58\) 0.238867 0.0313647
\(59\) 3.43602 0.447332 0.223666 0.974666i \(-0.428198\pi\)
0.223666 + 0.974666i \(0.428198\pi\)
\(60\) −5.45350 −0.704044
\(61\) 6.03348 0.772508 0.386254 0.922392i \(-0.373769\pi\)
0.386254 + 0.922392i \(0.373769\pi\)
\(62\) −2.73783 −0.347705
\(63\) 4.87676 0.614413
\(64\) 1.00000 0.125000
\(65\) −14.2661 −1.76949
\(66\) 4.89322 0.602314
\(67\) −9.91857 −1.21175 −0.605873 0.795561i \(-0.707176\pi\)
−0.605873 + 0.795561i \(0.707176\pi\)
\(68\) 0.801038 0.0971401
\(69\) 0.860000 0.103532
\(70\) 11.2119 1.34008
\(71\) −9.43912 −1.12022 −0.560109 0.828419i \(-0.689241\pi\)
−0.560109 + 0.828419i \(0.689241\pi\)
\(72\) 1.16263 0.137018
\(73\) −0.400632 −0.0468905 −0.0234452 0.999725i \(-0.507464\pi\)
−0.0234452 + 0.999725i \(0.507464\pi\)
\(74\) −7.32133 −0.851087
\(75\) −4.37570 −0.505263
\(76\) −3.01007 −0.345278
\(77\) −10.0600 −1.14645
\(78\) 10.8892 1.23296
\(79\) −1.01068 −0.113711 −0.0568553 0.998382i \(-0.518107\pi\)
−0.0568553 + 0.998382i \(0.518107\pi\)
\(80\) 2.67295 0.298845
\(81\) −11.1362 −1.23735
\(82\) −9.55708 −1.05540
\(83\) −11.1142 −1.21994 −0.609971 0.792423i \(-0.708819\pi\)
−0.609971 + 0.792423i \(0.708819\pi\)
\(84\) −8.55800 −0.933754
\(85\) 2.14114 0.232239
\(86\) −2.46109 −0.265386
\(87\) −0.487349 −0.0522492
\(88\) −2.39834 −0.255664
\(89\) −7.36845 −0.781054 −0.390527 0.920592i \(-0.627707\pi\)
−0.390527 + 0.920592i \(0.627707\pi\)
\(90\) 3.10767 0.327577
\(91\) −22.3872 −2.34682
\(92\) −0.421516 −0.0439461
\(93\) 5.58587 0.579228
\(94\) −12.9705 −1.33780
\(95\) −8.04577 −0.825479
\(96\) −2.04025 −0.208232
\(97\) −16.8175 −1.70756 −0.853779 0.520635i \(-0.825695\pi\)
−0.853779 + 0.520635i \(0.825695\pi\)
\(98\) 10.5945 1.07020
\(99\) −2.78839 −0.280244
\(100\) 2.14469 0.214469
\(101\) 10.1920 1.01414 0.507070 0.861905i \(-0.330729\pi\)
0.507070 + 0.861905i \(0.330729\pi\)
\(102\) −1.63432 −0.161822
\(103\) 10.7986 1.06402 0.532011 0.846737i \(-0.321436\pi\)
0.532011 + 0.846737i \(0.321436\pi\)
\(104\) −5.33719 −0.523354
\(105\) −22.8751 −2.23239
\(106\) 8.03477 0.780406
\(107\) −7.01385 −0.678055 −0.339027 0.940777i \(-0.610098\pi\)
−0.339027 + 0.940777i \(0.610098\pi\)
\(108\) 3.74869 0.360718
\(109\) −14.5679 −1.39535 −0.697676 0.716414i \(-0.745782\pi\)
−0.697676 + 0.716414i \(0.745782\pi\)
\(110\) −6.41065 −0.611232
\(111\) 14.9374 1.41779
\(112\) 4.19458 0.396350
\(113\) 3.92168 0.368920 0.184460 0.982840i \(-0.440946\pi\)
0.184460 + 0.982840i \(0.440946\pi\)
\(114\) 6.14130 0.575185
\(115\) −1.12669 −0.105065
\(116\) 0.238867 0.0221782
\(117\) −6.20519 −0.573670
\(118\) 3.43602 0.316311
\(119\) 3.36002 0.308012
\(120\) −5.45350 −0.497835
\(121\) −5.24797 −0.477088
\(122\) 6.03348 0.546246
\(123\) 19.4989 1.75815
\(124\) −2.73783 −0.245865
\(125\) −7.63212 −0.682638
\(126\) 4.87676 0.434456
\(127\) 7.63448 0.677450 0.338725 0.940885i \(-0.390004\pi\)
0.338725 + 0.940885i \(0.390004\pi\)
\(128\) 1.00000 0.0883883
\(129\) 5.02125 0.442097
\(130\) −14.2661 −1.25122
\(131\) 21.4281 1.87219 0.936093 0.351753i \(-0.114414\pi\)
0.936093 + 0.351753i \(0.114414\pi\)
\(132\) 4.89322 0.425900
\(133\) −12.6260 −1.09481
\(134\) −9.91857 −0.856834
\(135\) 10.0201 0.862392
\(136\) 0.801038 0.0686885
\(137\) −11.1135 −0.949491 −0.474745 0.880123i \(-0.657460\pi\)
−0.474745 + 0.880123i \(0.657460\pi\)
\(138\) 0.860000 0.0732081
\(139\) 14.4888 1.22892 0.614462 0.788947i \(-0.289373\pi\)
0.614462 + 0.788947i \(0.289373\pi\)
\(140\) 11.2119 0.947580
\(141\) 26.4631 2.22859
\(142\) −9.43912 −0.792113
\(143\) 12.8004 1.07042
\(144\) 1.16263 0.0968861
\(145\) 0.638480 0.0530229
\(146\) −0.400632 −0.0331566
\(147\) −21.6154 −1.78281
\(148\) −7.32133 −0.601809
\(149\) 4.23832 0.347217 0.173608 0.984815i \(-0.444457\pi\)
0.173608 + 0.984815i \(0.444457\pi\)
\(150\) −4.37570 −0.357275
\(151\) −3.74351 −0.304643 −0.152321 0.988331i \(-0.548675\pi\)
−0.152321 + 0.988331i \(0.548675\pi\)
\(152\) −3.01007 −0.244149
\(153\) 0.931314 0.0752922
\(154\) −10.0600 −0.810660
\(155\) −7.31810 −0.587804
\(156\) 10.8892 0.871835
\(157\) 6.92682 0.552820 0.276410 0.961040i \(-0.410855\pi\)
0.276410 + 0.961040i \(0.410855\pi\)
\(158\) −1.01068 −0.0804056
\(159\) −16.3930 −1.30005
\(160\) 2.67295 0.211316
\(161\) −1.76808 −0.139344
\(162\) −11.1362 −0.874941
\(163\) 12.6789 0.993089 0.496544 0.868011i \(-0.334602\pi\)
0.496544 + 0.868011i \(0.334602\pi\)
\(164\) −9.55708 −0.746283
\(165\) 13.0794 1.01823
\(166\) −11.1142 −0.862630
\(167\) 18.9367 1.46537 0.732685 0.680568i \(-0.238267\pi\)
0.732685 + 0.680568i \(0.238267\pi\)
\(168\) −8.55800 −0.660264
\(169\) 15.4856 1.19120
\(170\) 2.14114 0.164218
\(171\) −3.49960 −0.267621
\(172\) −2.46109 −0.187657
\(173\) −12.5582 −0.954779 −0.477390 0.878692i \(-0.658417\pi\)
−0.477390 + 0.878692i \(0.658417\pi\)
\(174\) −0.487349 −0.0369458
\(175\) 8.99605 0.680038
\(176\) −2.39834 −0.180782
\(177\) −7.01036 −0.526931
\(178\) −7.36845 −0.552288
\(179\) 22.5167 1.68298 0.841488 0.540276i \(-0.181680\pi\)
0.841488 + 0.540276i \(0.181680\pi\)
\(180\) 3.10767 0.231632
\(181\) −3.08568 −0.229357 −0.114678 0.993403i \(-0.536584\pi\)
−0.114678 + 0.993403i \(0.536584\pi\)
\(182\) −22.3872 −1.65945
\(183\) −12.3098 −0.909969
\(184\) −0.421516 −0.0310746
\(185\) −19.5696 −1.43878
\(186\) 5.58587 0.409576
\(187\) −1.92116 −0.140489
\(188\) −12.9705 −0.945969
\(189\) 15.7242 1.14377
\(190\) −8.04577 −0.583702
\(191\) −7.37115 −0.533358 −0.266679 0.963785i \(-0.585926\pi\)
−0.266679 + 0.963785i \(0.585926\pi\)
\(192\) −2.04025 −0.147243
\(193\) 24.3783 1.75479 0.877395 0.479768i \(-0.159279\pi\)
0.877395 + 0.479768i \(0.159279\pi\)
\(194\) −16.8175 −1.20743
\(195\) 29.1064 2.08435
\(196\) 10.5945 0.756748
\(197\) −1.53694 −0.109502 −0.0547511 0.998500i \(-0.517437\pi\)
−0.0547511 + 0.998500i \(0.517437\pi\)
\(198\) −2.78839 −0.198162
\(199\) −24.3425 −1.72560 −0.862798 0.505549i \(-0.831290\pi\)
−0.862798 + 0.505549i \(0.831290\pi\)
\(200\) 2.14469 0.151652
\(201\) 20.2364 1.42736
\(202\) 10.1920 0.717105
\(203\) 1.00194 0.0703227
\(204\) −1.63432 −0.114425
\(205\) −25.5456 −1.78419
\(206\) 10.7986 0.752377
\(207\) −0.490069 −0.0340621
\(208\) −5.33719 −0.370067
\(209\) 7.21916 0.499360
\(210\) −22.8751 −1.57853
\(211\) −1.08059 −0.0743909 −0.0371954 0.999308i \(-0.511842\pi\)
−0.0371954 + 0.999308i \(0.511842\pi\)
\(212\) 8.03477 0.551830
\(213\) 19.2582 1.31955
\(214\) −7.01385 −0.479457
\(215\) −6.57839 −0.448642
\(216\) 3.74869 0.255066
\(217\) −11.4840 −0.779588
\(218\) −14.5679 −0.986662
\(219\) 0.817391 0.0552342
\(220\) −6.41065 −0.432206
\(221\) −4.27529 −0.287587
\(222\) 14.9374 1.00253
\(223\) 23.1324 1.54906 0.774531 0.632536i \(-0.217986\pi\)
0.774531 + 0.632536i \(0.217986\pi\)
\(224\) 4.19458 0.280262
\(225\) 2.49348 0.166232
\(226\) 3.92168 0.260866
\(227\) −18.6940 −1.24076 −0.620381 0.784300i \(-0.713022\pi\)
−0.620381 + 0.784300i \(0.713022\pi\)
\(228\) 6.14130 0.406718
\(229\) 14.9675 0.989084 0.494542 0.869154i \(-0.335336\pi\)
0.494542 + 0.869154i \(0.335336\pi\)
\(230\) −1.12669 −0.0742920
\(231\) 20.5250 1.35045
\(232\) 0.238867 0.0156824
\(233\) 5.44756 0.356882 0.178441 0.983951i \(-0.442895\pi\)
0.178441 + 0.983951i \(0.442895\pi\)
\(234\) −6.20519 −0.405646
\(235\) −34.6695 −2.26159
\(236\) 3.43602 0.223666
\(237\) 2.06205 0.133944
\(238\) 3.36002 0.217797
\(239\) −19.3347 −1.25066 −0.625329 0.780361i \(-0.715035\pi\)
−0.625329 + 0.780361i \(0.715035\pi\)
\(240\) −5.45350 −0.352022
\(241\) 9.45825 0.609260 0.304630 0.952471i \(-0.401467\pi\)
0.304630 + 0.952471i \(0.401467\pi\)
\(242\) −5.24797 −0.337352
\(243\) 11.4746 0.736093
\(244\) 6.03348 0.386254
\(245\) 28.3186 1.80921
\(246\) 19.4989 1.24320
\(247\) 16.0653 1.02221
\(248\) −2.73783 −0.173853
\(249\) 22.6758 1.43702
\(250\) −7.63212 −0.482698
\(251\) −15.5320 −0.980373 −0.490187 0.871618i \(-0.663071\pi\)
−0.490187 + 0.871618i \(0.663071\pi\)
\(252\) 4.87676 0.307207
\(253\) 1.01094 0.0635572
\(254\) 7.63448 0.479030
\(255\) −4.36846 −0.273564
\(256\) 1.00000 0.0625000
\(257\) 9.63121 0.600779 0.300389 0.953817i \(-0.402883\pi\)
0.300389 + 0.953817i \(0.402883\pi\)
\(258\) 5.02125 0.312610
\(259\) −30.7099 −1.90822
\(260\) −14.2661 −0.884744
\(261\) 0.277714 0.0171901
\(262\) 21.4281 1.32384
\(263\) −0.0567599 −0.00349997 −0.00174998 0.999998i \(-0.500557\pi\)
−0.00174998 + 0.999998i \(0.500557\pi\)
\(264\) 4.89322 0.301157
\(265\) 21.4766 1.31930
\(266\) −12.6260 −0.774147
\(267\) 15.0335 0.920035
\(268\) −9.91857 −0.605873
\(269\) −2.65267 −0.161736 −0.0808682 0.996725i \(-0.525769\pi\)
−0.0808682 + 0.996725i \(0.525769\pi\)
\(270\) 10.0201 0.609803
\(271\) −3.48178 −0.211503 −0.105752 0.994393i \(-0.533725\pi\)
−0.105752 + 0.994393i \(0.533725\pi\)
\(272\) 0.801038 0.0485701
\(273\) 45.6757 2.76442
\(274\) −11.1135 −0.671391
\(275\) −5.14369 −0.310176
\(276\) 0.860000 0.0517659
\(277\) 5.86663 0.352492 0.176246 0.984346i \(-0.443605\pi\)
0.176246 + 0.984346i \(0.443605\pi\)
\(278\) 14.4888 0.868980
\(279\) −3.18310 −0.190567
\(280\) 11.2119 0.670040
\(281\) −11.2021 −0.668264 −0.334132 0.942526i \(-0.608443\pi\)
−0.334132 + 0.942526i \(0.608443\pi\)
\(282\) 26.4631 1.57585
\(283\) 19.5530 1.16231 0.581154 0.813794i \(-0.302602\pi\)
0.581154 + 0.813794i \(0.302602\pi\)
\(284\) −9.43912 −0.560109
\(285\) 16.4154 0.972365
\(286\) 12.8004 0.756903
\(287\) −40.0879 −2.36631
\(288\) 1.16263 0.0685088
\(289\) −16.3583 −0.962255
\(290\) 0.638480 0.0374928
\(291\) 34.3120 2.01140
\(292\) −0.400632 −0.0234452
\(293\) −15.1528 −0.885237 −0.442618 0.896710i \(-0.645950\pi\)
−0.442618 + 0.896710i \(0.645950\pi\)
\(294\) −21.6154 −1.26064
\(295\) 9.18433 0.534732
\(296\) −7.32133 −0.425544
\(297\) −8.99064 −0.521690
\(298\) 4.23832 0.245519
\(299\) 2.24971 0.130104
\(300\) −4.37570 −0.252631
\(301\) −10.3232 −0.595022
\(302\) −3.74351 −0.215415
\(303\) −20.7942 −1.19460
\(304\) −3.01007 −0.172639
\(305\) 16.1272 0.923442
\(306\) 0.931314 0.0532397
\(307\) −19.2004 −1.09582 −0.547912 0.836536i \(-0.684577\pi\)
−0.547912 + 0.836536i \(0.684577\pi\)
\(308\) −10.0600 −0.573223
\(309\) −22.0320 −1.25336
\(310\) −7.31810 −0.415640
\(311\) 31.8211 1.80441 0.902205 0.431308i \(-0.141948\pi\)
0.902205 + 0.431308i \(0.141948\pi\)
\(312\) 10.8892 0.616480
\(313\) −3.36399 −0.190144 −0.0950719 0.995470i \(-0.530308\pi\)
−0.0950719 + 0.995470i \(0.530308\pi\)
\(314\) 6.92682 0.390903
\(315\) 13.0353 0.734458
\(316\) −1.01068 −0.0568553
\(317\) −8.00488 −0.449599 −0.224800 0.974405i \(-0.572173\pi\)
−0.224800 + 0.974405i \(0.572173\pi\)
\(318\) −16.3930 −0.919272
\(319\) −0.572883 −0.0320753
\(320\) 2.67295 0.149423
\(321\) 14.3100 0.798708
\(322\) −1.76808 −0.0985314
\(323\) −2.41118 −0.134162
\(324\) −11.1362 −0.618677
\(325\) −11.4466 −0.634943
\(326\) 12.6789 0.702220
\(327\) 29.7222 1.64364
\(328\) −9.55708 −0.527702
\(329\) −54.4057 −2.99948
\(330\) 13.0794 0.719995
\(331\) −1.21229 −0.0666335 −0.0333168 0.999445i \(-0.510607\pi\)
−0.0333168 + 0.999445i \(0.510607\pi\)
\(332\) −11.1142 −0.609971
\(333\) −8.51202 −0.466456
\(334\) 18.9367 1.03617
\(335\) −26.5119 −1.44850
\(336\) −8.55800 −0.466877
\(337\) 33.2630 1.81195 0.905975 0.423331i \(-0.139139\pi\)
0.905975 + 0.423331i \(0.139139\pi\)
\(338\) 15.4856 0.842305
\(339\) −8.00122 −0.434566
\(340\) 2.14114 0.116120
\(341\) 6.56625 0.355582
\(342\) −3.49960 −0.189237
\(343\) 15.0773 0.814098
\(344\) −2.46109 −0.132693
\(345\) 2.29874 0.123760
\(346\) −12.5582 −0.675131
\(347\) −3.24867 −0.174398 −0.0871988 0.996191i \(-0.527792\pi\)
−0.0871988 + 0.996191i \(0.527792\pi\)
\(348\) −0.487349 −0.0261246
\(349\) −9.62179 −0.515043 −0.257521 0.966273i \(-0.582906\pi\)
−0.257521 + 0.966273i \(0.582906\pi\)
\(350\) 8.99605 0.480859
\(351\) −20.0075 −1.06792
\(352\) −2.39834 −0.127832
\(353\) −3.20686 −0.170684 −0.0853419 0.996352i \(-0.527198\pi\)
−0.0853419 + 0.996352i \(0.527198\pi\)
\(354\) −7.01036 −0.372596
\(355\) −25.2303 −1.33909
\(356\) −7.36845 −0.390527
\(357\) −6.85528 −0.362820
\(358\) 22.5167 1.19004
\(359\) −19.9591 −1.05340 −0.526701 0.850050i \(-0.676571\pi\)
−0.526701 + 0.850050i \(0.676571\pi\)
\(360\) 3.10767 0.163788
\(361\) −9.93949 −0.523131
\(362\) −3.08568 −0.162180
\(363\) 10.7072 0.561981
\(364\) −22.3872 −1.17341
\(365\) −1.07087 −0.0560520
\(366\) −12.3098 −0.643445
\(367\) 14.0355 0.732647 0.366324 0.930488i \(-0.380616\pi\)
0.366324 + 0.930488i \(0.380616\pi\)
\(368\) −0.421516 −0.0219731
\(369\) −11.1114 −0.578435
\(370\) −19.5696 −1.01737
\(371\) 33.7025 1.74974
\(372\) 5.58587 0.289614
\(373\) −8.72325 −0.451673 −0.225836 0.974165i \(-0.572511\pi\)
−0.225836 + 0.974165i \(0.572511\pi\)
\(374\) −1.92116 −0.0993409
\(375\) 15.5715 0.804107
\(376\) −12.9705 −0.668901
\(377\) −1.27488 −0.0656595
\(378\) 15.7242 0.808765
\(379\) 31.6337 1.62491 0.812457 0.583021i \(-0.198130\pi\)
0.812457 + 0.583021i \(0.198130\pi\)
\(380\) −8.04577 −0.412739
\(381\) −15.5763 −0.797996
\(382\) −7.37115 −0.377141
\(383\) −14.2137 −0.726287 −0.363144 0.931733i \(-0.618297\pi\)
−0.363144 + 0.931733i \(0.618297\pi\)
\(384\) −2.04025 −0.104116
\(385\) −26.8900 −1.37044
\(386\) 24.3783 1.24082
\(387\) −2.86135 −0.145451
\(388\) −16.8175 −0.853779
\(389\) −14.0417 −0.711943 −0.355971 0.934497i \(-0.615850\pi\)
−0.355971 + 0.934497i \(0.615850\pi\)
\(390\) 29.1064 1.47386
\(391\) −0.337651 −0.0170757
\(392\) 10.5945 0.535102
\(393\) −43.7188 −2.20532
\(394\) −1.53694 −0.0774298
\(395\) −2.70151 −0.135928
\(396\) −2.78839 −0.140122
\(397\) −9.38410 −0.470974 −0.235487 0.971877i \(-0.575669\pi\)
−0.235487 + 0.971877i \(0.575669\pi\)
\(398\) −24.3425 −1.22018
\(399\) 25.7602 1.28962
\(400\) 2.14469 0.107234
\(401\) −30.7776 −1.53696 −0.768479 0.639875i \(-0.778986\pi\)
−0.768479 + 0.639875i \(0.778986\pi\)
\(402\) 20.2364 1.00930
\(403\) 14.6123 0.727892
\(404\) 10.1920 0.507070
\(405\) −29.7665 −1.47911
\(406\) 1.00194 0.0497257
\(407\) 17.5590 0.870369
\(408\) −1.63432 −0.0809109
\(409\) −3.48340 −0.172243 −0.0861215 0.996285i \(-0.527447\pi\)
−0.0861215 + 0.996285i \(0.527447\pi\)
\(410\) −25.5456 −1.26161
\(411\) 22.6744 1.11844
\(412\) 10.7986 0.532011
\(413\) 14.4127 0.709201
\(414\) −0.490069 −0.0240856
\(415\) −29.7078 −1.45830
\(416\) −5.33719 −0.261677
\(417\) −29.5608 −1.44760
\(418\) 7.21916 0.353101
\(419\) 29.5874 1.44544 0.722720 0.691141i \(-0.242892\pi\)
0.722720 + 0.691141i \(0.242892\pi\)
\(420\) −22.8751 −1.11619
\(421\) −6.68560 −0.325836 −0.162918 0.986640i \(-0.552091\pi\)
−0.162918 + 0.986640i \(0.552091\pi\)
\(422\) −1.08059 −0.0526023
\(423\) −15.0799 −0.733210
\(424\) 8.03477 0.390203
\(425\) 1.71798 0.0833340
\(426\) 19.2582 0.933062
\(427\) 25.3079 1.22473
\(428\) −7.01385 −0.339027
\(429\) −26.1160 −1.26089
\(430\) −6.57839 −0.317238
\(431\) 9.98406 0.480915 0.240458 0.970660i \(-0.422703\pi\)
0.240458 + 0.970660i \(0.422703\pi\)
\(432\) 3.74869 0.180359
\(433\) −30.0644 −1.44480 −0.722401 0.691475i \(-0.756961\pi\)
−0.722401 + 0.691475i \(0.756961\pi\)
\(434\) −11.4840 −0.551252
\(435\) −1.30266 −0.0624578
\(436\) −14.5679 −0.697676
\(437\) 1.26879 0.0606946
\(438\) 0.817391 0.0390565
\(439\) −36.2268 −1.72901 −0.864506 0.502622i \(-0.832369\pi\)
−0.864506 + 0.502622i \(0.832369\pi\)
\(440\) −6.41065 −0.305616
\(441\) 12.3175 0.586547
\(442\) −4.27529 −0.203355
\(443\) −19.9284 −0.946827 −0.473413 0.880840i \(-0.656978\pi\)
−0.473413 + 0.880840i \(0.656978\pi\)
\(444\) 14.9374 0.708896
\(445\) −19.6955 −0.933657
\(446\) 23.1324 1.09535
\(447\) −8.64724 −0.409000
\(448\) 4.19458 0.198175
\(449\) 3.12974 0.147701 0.0738507 0.997269i \(-0.476471\pi\)
0.0738507 + 0.997269i \(0.476471\pi\)
\(450\) 2.49348 0.117544
\(451\) 22.9211 1.07931
\(452\) 3.92168 0.184460
\(453\) 7.63771 0.358851
\(454\) −18.6940 −0.877352
\(455\) −59.8401 −2.80535
\(456\) 6.14130 0.287593
\(457\) 10.8299 0.506601 0.253301 0.967388i \(-0.418484\pi\)
0.253301 + 0.967388i \(0.418484\pi\)
\(458\) 14.9675 0.699388
\(459\) 3.00285 0.140161
\(460\) −1.12669 −0.0525324
\(461\) 31.1707 1.45177 0.725883 0.687819i \(-0.241432\pi\)
0.725883 + 0.687819i \(0.241432\pi\)
\(462\) 20.5250 0.954909
\(463\) 6.78995 0.315556 0.157778 0.987475i \(-0.449567\pi\)
0.157778 + 0.987475i \(0.449567\pi\)
\(464\) 0.238867 0.0110891
\(465\) 14.9308 0.692398
\(466\) 5.44756 0.252354
\(467\) 37.4714 1.73397 0.866984 0.498336i \(-0.166055\pi\)
0.866984 + 0.498336i \(0.166055\pi\)
\(468\) −6.20519 −0.286835
\(469\) −41.6042 −1.92110
\(470\) −34.6695 −1.59918
\(471\) −14.1325 −0.651190
\(472\) 3.43602 0.158156
\(473\) 5.90254 0.271399
\(474\) 2.06205 0.0947130
\(475\) −6.45565 −0.296206
\(476\) 3.36002 0.154006
\(477\) 9.34149 0.427718
\(478\) −19.3347 −0.884349
\(479\) 6.84565 0.312786 0.156393 0.987695i \(-0.450013\pi\)
0.156393 + 0.987695i \(0.450013\pi\)
\(480\) −5.45350 −0.248917
\(481\) 39.0753 1.78168
\(482\) 9.45825 0.430812
\(483\) 3.60734 0.164139
\(484\) −5.24797 −0.238544
\(485\) −44.9524 −2.04118
\(486\) 11.4746 0.520496
\(487\) −28.9894 −1.31364 −0.656818 0.754049i \(-0.728098\pi\)
−0.656818 + 0.754049i \(0.728098\pi\)
\(488\) 6.03348 0.273123
\(489\) −25.8682 −1.16980
\(490\) 28.3186 1.27930
\(491\) 30.4910 1.37604 0.688020 0.725692i \(-0.258480\pi\)
0.688020 + 0.725692i \(0.258480\pi\)
\(492\) 19.4989 0.879077
\(493\) 0.191341 0.00861758
\(494\) 16.0653 0.722812
\(495\) −7.45324 −0.334998
\(496\) −2.73783 −0.122932
\(497\) −39.5931 −1.77599
\(498\) 22.6758 1.01613
\(499\) 28.2435 1.26435 0.632176 0.774825i \(-0.282162\pi\)
0.632176 + 0.774825i \(0.282162\pi\)
\(500\) −7.63212 −0.341319
\(501\) −38.6358 −1.72612
\(502\) −15.5320 −0.693228
\(503\) −2.11175 −0.0941585 −0.0470792 0.998891i \(-0.514991\pi\)
−0.0470792 + 0.998891i \(0.514991\pi\)
\(504\) 4.87676 0.217228
\(505\) 27.2427 1.21228
\(506\) 1.01094 0.0449417
\(507\) −31.5945 −1.40316
\(508\) 7.63448 0.338725
\(509\) −10.3413 −0.458371 −0.229186 0.973383i \(-0.573606\pi\)
−0.229186 + 0.973383i \(0.573606\pi\)
\(510\) −4.36846 −0.193439
\(511\) −1.68048 −0.0743402
\(512\) 1.00000 0.0441942
\(513\) −11.2838 −0.498193
\(514\) 9.63121 0.424815
\(515\) 28.8643 1.27191
\(516\) 5.02125 0.221048
\(517\) 31.1076 1.36811
\(518\) −30.7099 −1.34931
\(519\) 25.6218 1.12467
\(520\) −14.2661 −0.625608
\(521\) −7.62420 −0.334022 −0.167011 0.985955i \(-0.553412\pi\)
−0.167011 + 0.985955i \(0.553412\pi\)
\(522\) 0.277714 0.0121552
\(523\) −26.0289 −1.13816 −0.569081 0.822281i \(-0.692701\pi\)
−0.569081 + 0.822281i \(0.692701\pi\)
\(524\) 21.4281 0.936093
\(525\) −18.3542 −0.801044
\(526\) −0.0567599 −0.00247485
\(527\) −2.19311 −0.0955333
\(528\) 4.89322 0.212950
\(529\) −22.8223 −0.992275
\(530\) 21.4766 0.932883
\(531\) 3.99483 0.173361
\(532\) −12.6260 −0.547405
\(533\) 51.0079 2.20940
\(534\) 15.0335 0.650563
\(535\) −18.7477 −0.810534
\(536\) −9.91857 −0.428417
\(537\) −45.9397 −1.98245
\(538\) −2.65267 −0.114365
\(539\) −25.4092 −1.09445
\(540\) 10.0201 0.431196
\(541\) 3.80091 0.163414 0.0817069 0.996656i \(-0.473963\pi\)
0.0817069 + 0.996656i \(0.473963\pi\)
\(542\) −3.48178 −0.149555
\(543\) 6.29556 0.270168
\(544\) 0.801038 0.0343442
\(545\) −38.9393 −1.66798
\(546\) 45.6757 1.95474
\(547\) 1.55100 0.0663159 0.0331580 0.999450i \(-0.489444\pi\)
0.0331580 + 0.999450i \(0.489444\pi\)
\(548\) −11.1135 −0.474745
\(549\) 7.01472 0.299381
\(550\) −5.14369 −0.219327
\(551\) −0.719005 −0.0306306
\(552\) 0.860000 0.0366040
\(553\) −4.23938 −0.180277
\(554\) 5.86663 0.249249
\(555\) 39.9269 1.69480
\(556\) 14.4888 0.614462
\(557\) −11.9035 −0.504366 −0.252183 0.967680i \(-0.581149\pi\)
−0.252183 + 0.967680i \(0.581149\pi\)
\(558\) −3.18310 −0.134751
\(559\) 13.1353 0.555565
\(560\) 11.2119 0.473790
\(561\) 3.91966 0.165488
\(562\) −11.2021 −0.472534
\(563\) 30.6587 1.29211 0.646055 0.763291i \(-0.276418\pi\)
0.646055 + 0.763291i \(0.276418\pi\)
\(564\) 26.4631 1.11430
\(565\) 10.4825 0.441001
\(566\) 19.5530 0.821875
\(567\) −46.7116 −1.96170
\(568\) −9.43912 −0.396057
\(569\) 14.3386 0.601105 0.300553 0.953765i \(-0.402829\pi\)
0.300553 + 0.953765i \(0.402829\pi\)
\(570\) 16.4154 0.687566
\(571\) −34.5427 −1.44557 −0.722783 0.691076i \(-0.757137\pi\)
−0.722783 + 0.691076i \(0.757137\pi\)
\(572\) 12.8004 0.535211
\(573\) 15.0390 0.628264
\(574\) −40.0879 −1.67324
\(575\) −0.904020 −0.0377002
\(576\) 1.16263 0.0484431
\(577\) −40.0807 −1.66858 −0.834290 0.551326i \(-0.814122\pi\)
−0.834290 + 0.551326i \(0.814122\pi\)
\(578\) −16.3583 −0.680417
\(579\) −49.7380 −2.06704
\(580\) 0.638480 0.0265114
\(581\) −46.6194 −1.93410
\(582\) 34.3120 1.42228
\(583\) −19.2701 −0.798086
\(584\) −0.400632 −0.0165783
\(585\) −16.5862 −0.685755
\(586\) −15.1528 −0.625957
\(587\) 39.1026 1.61394 0.806969 0.590594i \(-0.201106\pi\)
0.806969 + 0.590594i \(0.201106\pi\)
\(588\) −21.6154 −0.891405
\(589\) 8.24106 0.339567
\(590\) 9.18433 0.378113
\(591\) 3.13574 0.128987
\(592\) −7.32133 −0.300905
\(593\) 11.9437 0.490471 0.245235 0.969464i \(-0.421135\pi\)
0.245235 + 0.969464i \(0.421135\pi\)
\(594\) −8.99064 −0.368890
\(595\) 8.98117 0.368192
\(596\) 4.23832 0.173608
\(597\) 49.6649 2.03265
\(598\) 2.24971 0.0919976
\(599\) −31.8588 −1.30171 −0.650857 0.759200i \(-0.725590\pi\)
−0.650857 + 0.759200i \(0.725590\pi\)
\(600\) −4.37570 −0.178637
\(601\) −11.2253 −0.457888 −0.228944 0.973440i \(-0.573527\pi\)
−0.228944 + 0.973440i \(0.573527\pi\)
\(602\) −10.3232 −0.420744
\(603\) −11.5317 −0.469605
\(604\) −3.74351 −0.152321
\(605\) −14.0276 −0.570302
\(606\) −20.7942 −0.844707
\(607\) −1.67512 −0.0679910 −0.0339955 0.999422i \(-0.510823\pi\)
−0.0339955 + 0.999422i \(0.510823\pi\)
\(608\) −3.01007 −0.122074
\(609\) −2.04422 −0.0828360
\(610\) 16.1272 0.652972
\(611\) 69.2259 2.80058
\(612\) 0.931314 0.0376461
\(613\) 10.4102 0.420463 0.210231 0.977652i \(-0.432578\pi\)
0.210231 + 0.977652i \(0.432578\pi\)
\(614\) −19.2004 −0.774864
\(615\) 52.1196 2.10166
\(616\) −10.0600 −0.405330
\(617\) 19.3567 0.779271 0.389636 0.920969i \(-0.372601\pi\)
0.389636 + 0.920969i \(0.372601\pi\)
\(618\) −22.0320 −0.886256
\(619\) 19.3738 0.778699 0.389349 0.921090i \(-0.372700\pi\)
0.389349 + 0.921090i \(0.372700\pi\)
\(620\) −7.31810 −0.293902
\(621\) −1.58014 −0.0634086
\(622\) 31.8211 1.27591
\(623\) −30.9075 −1.23828
\(624\) 10.8892 0.435918
\(625\) −31.1238 −1.24495
\(626\) −3.36399 −0.134452
\(627\) −14.7289 −0.588217
\(628\) 6.92682 0.276410
\(629\) −5.86466 −0.233839
\(630\) 13.0353 0.519341
\(631\) 2.89056 0.115071 0.0575357 0.998343i \(-0.481676\pi\)
0.0575357 + 0.998343i \(0.481676\pi\)
\(632\) −1.01068 −0.0402028
\(633\) 2.20468 0.0876280
\(634\) −8.00488 −0.317915
\(635\) 20.4066 0.809812
\(636\) −16.3930 −0.650023
\(637\) −56.5447 −2.24038
\(638\) −0.572883 −0.0226807
\(639\) −10.9742 −0.434134
\(640\) 2.67295 0.105658
\(641\) −14.9793 −0.591648 −0.295824 0.955243i \(-0.595594\pi\)
−0.295824 + 0.955243i \(0.595594\pi\)
\(642\) 14.3100 0.564772
\(643\) −14.0359 −0.553523 −0.276762 0.960939i \(-0.589261\pi\)
−0.276762 + 0.960939i \(0.589261\pi\)
\(644\) −1.76808 −0.0696722
\(645\) 13.4216 0.528474
\(646\) −2.41118 −0.0948666
\(647\) −12.3248 −0.484539 −0.242269 0.970209i \(-0.577892\pi\)
−0.242269 + 0.970209i \(0.577892\pi\)
\(648\) −11.1362 −0.437471
\(649\) −8.24075 −0.323478
\(650\) −11.4466 −0.448972
\(651\) 23.4304 0.918308
\(652\) 12.6789 0.496544
\(653\) −36.3293 −1.42167 −0.710837 0.703357i \(-0.751684\pi\)
−0.710837 + 0.703357i \(0.751684\pi\)
\(654\) 29.7222 1.16223
\(655\) 57.2765 2.23798
\(656\) −9.55708 −0.373141
\(657\) −0.465788 −0.0181721
\(658\) −54.4057 −2.12095
\(659\) −4.39841 −0.171338 −0.0856688 0.996324i \(-0.527303\pi\)
−0.0856688 + 0.996324i \(0.527303\pi\)
\(660\) 13.0794 0.509113
\(661\) −26.4084 −1.02717 −0.513584 0.858039i \(-0.671682\pi\)
−0.513584 + 0.858039i \(0.671682\pi\)
\(662\) −1.21229 −0.0471170
\(663\) 8.72268 0.338761
\(664\) −11.1142 −0.431315
\(665\) −33.7486 −1.30872
\(666\) −8.51202 −0.329834
\(667\) −0.100686 −0.00389858
\(668\) 18.9367 0.732685
\(669\) −47.1960 −1.82470
\(670\) −26.5119 −1.02424
\(671\) −14.4703 −0.558621
\(672\) −8.55800 −0.330132
\(673\) −31.4133 −1.21089 −0.605447 0.795886i \(-0.707006\pi\)
−0.605447 + 0.795886i \(0.707006\pi\)
\(674\) 33.2630 1.28124
\(675\) 8.03977 0.309451
\(676\) 15.4856 0.595599
\(677\) 22.4385 0.862382 0.431191 0.902261i \(-0.358093\pi\)
0.431191 + 0.902261i \(0.358093\pi\)
\(678\) −8.00122 −0.307285
\(679\) −70.5423 −2.70717
\(680\) 2.14114 0.0821089
\(681\) 38.1405 1.46155
\(682\) 6.56625 0.251435
\(683\) −30.9126 −1.18284 −0.591418 0.806365i \(-0.701432\pi\)
−0.591418 + 0.806365i \(0.701432\pi\)
\(684\) −3.49960 −0.133811
\(685\) −29.7059 −1.13500
\(686\) 15.0773 0.575654
\(687\) −30.5376 −1.16508
\(688\) −2.46109 −0.0938283
\(689\) −42.8831 −1.63372
\(690\) 2.29874 0.0875116
\(691\) −6.42503 −0.244420 −0.122210 0.992504i \(-0.538998\pi\)
−0.122210 + 0.992504i \(0.538998\pi\)
\(692\) −12.5582 −0.477390
\(693\) −11.6961 −0.444299
\(694\) −3.24867 −0.123318
\(695\) 38.7279 1.46903
\(696\) −0.487349 −0.0184729
\(697\) −7.65559 −0.289976
\(698\) −9.62179 −0.364190
\(699\) −11.1144 −0.420386
\(700\) 8.99605 0.340019
\(701\) 12.7870 0.482958 0.241479 0.970406i \(-0.422367\pi\)
0.241479 + 0.970406i \(0.422367\pi\)
\(702\) −20.0075 −0.755134
\(703\) 22.0377 0.831167
\(704\) −2.39834 −0.0903908
\(705\) 70.7346 2.66402
\(706\) −3.20686 −0.120692
\(707\) 42.7510 1.60782
\(708\) −7.01036 −0.263465
\(709\) −14.1053 −0.529736 −0.264868 0.964285i \(-0.585328\pi\)
−0.264868 + 0.964285i \(0.585328\pi\)
\(710\) −25.2303 −0.946878
\(711\) −1.17505 −0.0440679
\(712\) −7.36845 −0.276144
\(713\) 1.15404 0.0432192
\(714\) −6.85528 −0.256553
\(715\) 34.2149 1.27956
\(716\) 22.5167 0.841488
\(717\) 39.4477 1.47320
\(718\) −19.9591 −0.744868
\(719\) 6.06752 0.226280 0.113140 0.993579i \(-0.463909\pi\)
0.113140 + 0.993579i \(0.463909\pi\)
\(720\) 3.10767 0.115816
\(721\) 45.2958 1.68690
\(722\) −9.93949 −0.369910
\(723\) −19.2972 −0.717672
\(724\) −3.08568 −0.114678
\(725\) 0.512294 0.0190261
\(726\) 10.7072 0.397381
\(727\) 28.4746 1.05606 0.528032 0.849224i \(-0.322930\pi\)
0.528032 + 0.849224i \(0.322930\pi\)
\(728\) −22.3872 −0.829727
\(729\) 9.99755 0.370280
\(730\) −1.07087 −0.0396347
\(731\) −1.97143 −0.0729159
\(732\) −12.3098 −0.454984
\(733\) −32.0738 −1.18467 −0.592337 0.805690i \(-0.701795\pi\)
−0.592337 + 0.805690i \(0.701795\pi\)
\(734\) 14.0355 0.518060
\(735\) −57.7770 −2.13114
\(736\) −0.421516 −0.0155373
\(737\) 23.7881 0.876246
\(738\) −11.1114 −0.409016
\(739\) 15.0996 0.555449 0.277724 0.960661i \(-0.410420\pi\)
0.277724 + 0.960661i \(0.410420\pi\)
\(740\) −19.5696 −0.719392
\(741\) −32.7773 −1.20410
\(742\) 33.7025 1.23726
\(743\) 16.4345 0.602924 0.301462 0.953478i \(-0.402525\pi\)
0.301462 + 0.953478i \(0.402525\pi\)
\(744\) 5.58587 0.204788
\(745\) 11.3288 0.415056
\(746\) −8.72325 −0.319381
\(747\) −12.9218 −0.472782
\(748\) −1.92116 −0.0702446
\(749\) −29.4201 −1.07499
\(750\) 15.5715 0.568590
\(751\) −3.26334 −0.119081 −0.0595404 0.998226i \(-0.518964\pi\)
−0.0595404 + 0.998226i \(0.518964\pi\)
\(752\) −12.9705 −0.472985
\(753\) 31.6893 1.15482
\(754\) −1.27488 −0.0464283
\(755\) −10.0062 −0.364164
\(756\) 15.7242 0.571883
\(757\) −30.7109 −1.11621 −0.558103 0.829771i \(-0.688471\pi\)
−0.558103 + 0.829771i \(0.688471\pi\)
\(758\) 31.6337 1.14899
\(759\) −2.06257 −0.0748666
\(760\) −8.04577 −0.291851
\(761\) −41.6871 −1.51115 −0.755577 0.655059i \(-0.772644\pi\)
−0.755577 + 0.655059i \(0.772644\pi\)
\(762\) −15.5763 −0.564269
\(763\) −61.1062 −2.21219
\(764\) −7.37115 −0.266679
\(765\) 2.48936 0.0900030
\(766\) −14.2137 −0.513563
\(767\) −18.3387 −0.662172
\(768\) −2.04025 −0.0736213
\(769\) 6.83008 0.246299 0.123150 0.992388i \(-0.460701\pi\)
0.123150 + 0.992388i \(0.460701\pi\)
\(770\) −26.8900 −0.969048
\(771\) −19.6501 −0.707682
\(772\) 24.3783 0.877395
\(773\) −13.6397 −0.490587 −0.245294 0.969449i \(-0.578884\pi\)
−0.245294 + 0.969449i \(0.578884\pi\)
\(774\) −2.86135 −0.102849
\(775\) −5.87179 −0.210921
\(776\) −16.8175 −0.603713
\(777\) 62.6559 2.24777
\(778\) −14.0417 −0.503420
\(779\) 28.7675 1.03070
\(780\) 29.1064 1.04218
\(781\) 22.6382 0.810059
\(782\) −0.337651 −0.0120744
\(783\) 0.895438 0.0320003
\(784\) 10.5945 0.378374
\(785\) 18.5151 0.660831
\(786\) −43.7188 −1.55940
\(787\) −15.2235 −0.542660 −0.271330 0.962486i \(-0.587464\pi\)
−0.271330 + 0.962486i \(0.587464\pi\)
\(788\) −1.53694 −0.0547511
\(789\) 0.115805 0.00412275
\(790\) −2.70151 −0.0961153
\(791\) 16.4498 0.584887
\(792\) −2.78839 −0.0990811
\(793\) −32.2018 −1.14352
\(794\) −9.38410 −0.333029
\(795\) −43.8177 −1.55405
\(796\) −24.3425 −0.862798
\(797\) 44.0125 1.55900 0.779501 0.626401i \(-0.215473\pi\)
0.779501 + 0.626401i \(0.215473\pi\)
\(798\) 25.7602 0.911900
\(799\) −10.3898 −0.367566
\(800\) 2.14469 0.0758261
\(801\) −8.56680 −0.302693
\(802\) −30.7776 −1.08679
\(803\) 0.960852 0.0339077
\(804\) 20.2364 0.713682
\(805\) −4.72600 −0.166570
\(806\) 14.6123 0.514697
\(807\) 5.41213 0.190516
\(808\) 10.1920 0.358552
\(809\) 39.5341 1.38995 0.694973 0.719036i \(-0.255416\pi\)
0.694973 + 0.719036i \(0.255416\pi\)
\(810\) −29.7665 −1.04589
\(811\) 41.9015 1.47136 0.735680 0.677329i \(-0.236863\pi\)
0.735680 + 0.677329i \(0.236863\pi\)
\(812\) 1.00194 0.0351614
\(813\) 7.10372 0.249138
\(814\) 17.5590 0.615444
\(815\) 33.8901 1.18712
\(816\) −1.63432 −0.0572127
\(817\) 7.40806 0.259175
\(818\) −3.48340 −0.121794
\(819\) −26.0282 −0.909498
\(820\) −25.5456 −0.892093
\(821\) 22.5847 0.788211 0.394105 0.919065i \(-0.371054\pi\)
0.394105 + 0.919065i \(0.371054\pi\)
\(822\) 22.6744 0.790859
\(823\) −16.9816 −0.591940 −0.295970 0.955197i \(-0.595643\pi\)
−0.295970 + 0.955197i \(0.595643\pi\)
\(824\) 10.7986 0.376189
\(825\) 10.4944 0.365369
\(826\) 14.4127 0.501481
\(827\) 27.4384 0.954127 0.477063 0.878869i \(-0.341701\pi\)
0.477063 + 0.878869i \(0.341701\pi\)
\(828\) −0.490069 −0.0170311
\(829\) −5.21012 −0.180955 −0.0904774 0.995899i \(-0.528839\pi\)
−0.0904774 + 0.995899i \(0.528839\pi\)
\(830\) −29.7078 −1.03117
\(831\) −11.9694 −0.415214
\(832\) −5.33719 −0.185034
\(833\) 8.48658 0.294043
\(834\) −29.5608 −1.02361
\(835\) 50.6171 1.75168
\(836\) 7.21916 0.249680
\(837\) −10.2633 −0.354751
\(838\) 29.5874 1.02208
\(839\) −28.1121 −0.970538 −0.485269 0.874365i \(-0.661278\pi\)
−0.485269 + 0.874365i \(0.661278\pi\)
\(840\) −22.8751 −0.789267
\(841\) −28.9429 −0.998033
\(842\) −6.68560 −0.230401
\(843\) 22.8552 0.787175
\(844\) −1.08059 −0.0371954
\(845\) 41.3923 1.42394
\(846\) −15.0799 −0.518458
\(847\) −22.0130 −0.756376
\(848\) 8.03477 0.275915
\(849\) −39.8931 −1.36913
\(850\) 1.71798 0.0589261
\(851\) 3.08606 0.105789
\(852\) 19.2582 0.659775
\(853\) 33.5853 1.14994 0.574969 0.818175i \(-0.305014\pi\)
0.574969 + 0.818175i \(0.305014\pi\)
\(854\) 25.3079 0.866018
\(855\) −9.35428 −0.319910
\(856\) −7.01385 −0.239729
\(857\) −1.17386 −0.0400983 −0.0200491 0.999799i \(-0.506382\pi\)
−0.0200491 + 0.999799i \(0.506382\pi\)
\(858\) −26.1160 −0.891587
\(859\) 30.1159 1.02754 0.513771 0.857927i \(-0.328248\pi\)
0.513771 + 0.857927i \(0.328248\pi\)
\(860\) −6.57839 −0.224321
\(861\) 81.7895 2.78738
\(862\) 9.98406 0.340058
\(863\) −19.8174 −0.674593 −0.337296 0.941398i \(-0.609512\pi\)
−0.337296 + 0.941398i \(0.609512\pi\)
\(864\) 3.74869 0.127533
\(865\) −33.5674 −1.14133
\(866\) −30.0644 −1.02163
\(867\) 33.3752 1.13348
\(868\) −11.4840 −0.389794
\(869\) 2.42396 0.0822272
\(870\) −1.30266 −0.0441643
\(871\) 52.9373 1.79371
\(872\) −14.5679 −0.493331
\(873\) −19.5526 −0.661755
\(874\) 1.26879 0.0429175
\(875\) −32.0135 −1.08225
\(876\) 0.817391 0.0276171
\(877\) 21.6564 0.731285 0.365642 0.930755i \(-0.380849\pi\)
0.365642 + 0.930755i \(0.380849\pi\)
\(878\) −36.2268 −1.22260
\(879\) 30.9156 1.04276
\(880\) −6.41065 −0.216103
\(881\) −31.7939 −1.07116 −0.535582 0.844484i \(-0.679908\pi\)
−0.535582 + 0.844484i \(0.679908\pi\)
\(882\) 12.3175 0.414752
\(883\) 52.6894 1.77314 0.886569 0.462596i \(-0.153082\pi\)
0.886569 + 0.462596i \(0.153082\pi\)
\(884\) −4.27529 −0.143794
\(885\) −18.7384 −0.629883
\(886\) −19.9284 −0.669508
\(887\) −5.01236 −0.168298 −0.0841492 0.996453i \(-0.526817\pi\)
−0.0841492 + 0.996453i \(0.526817\pi\)
\(888\) 14.9374 0.501265
\(889\) 32.0234 1.07403
\(890\) −19.6955 −0.660195
\(891\) 26.7084 0.894763
\(892\) 23.1324 0.774531
\(893\) 39.0420 1.30649
\(894\) −8.64724 −0.289207
\(895\) 60.1860 2.01180
\(896\) 4.19458 0.140131
\(897\) −4.58998 −0.153255
\(898\) 3.12974 0.104441
\(899\) −0.653977 −0.0218114
\(900\) 2.49348 0.0831161
\(901\) 6.43616 0.214419
\(902\) 22.9211 0.763190
\(903\) 21.0620 0.700901
\(904\) 3.92168 0.130433
\(905\) −8.24787 −0.274169
\(906\) 7.63771 0.253746
\(907\) −40.8132 −1.35518 −0.677590 0.735440i \(-0.736976\pi\)
−0.677590 + 0.735440i \(0.736976\pi\)
\(908\) −18.6940 −0.620381
\(909\) 11.8495 0.393024
\(910\) −59.8401 −1.98368
\(911\) −15.3199 −0.507570 −0.253785 0.967261i \(-0.581676\pi\)
−0.253785 + 0.967261i \(0.581676\pi\)
\(912\) 6.14130 0.203359
\(913\) 26.6556 0.882173
\(914\) 10.8299 0.358221
\(915\) −32.9036 −1.08776
\(916\) 14.9675 0.494542
\(917\) 89.8820 2.96817
\(918\) 3.00285 0.0991087
\(919\) 47.7432 1.57490 0.787452 0.616376i \(-0.211400\pi\)
0.787452 + 0.616376i \(0.211400\pi\)
\(920\) −1.12669 −0.0371460
\(921\) 39.1736 1.29081
\(922\) 31.1707 1.02655
\(923\) 50.3784 1.65822
\(924\) 20.5250 0.675223
\(925\) −15.7019 −0.516277
\(926\) 6.78995 0.223132
\(927\) 12.5549 0.412356
\(928\) 0.238867 0.00784118
\(929\) 16.8886 0.554097 0.277048 0.960856i \(-0.410644\pi\)
0.277048 + 0.960856i \(0.410644\pi\)
\(930\) 14.9308 0.489600
\(931\) −31.8901 −1.04516
\(932\) 5.44756 0.178441
\(933\) −64.9231 −2.12549
\(934\) 37.4714 1.22610
\(935\) −5.13518 −0.167938
\(936\) −6.20519 −0.202823
\(937\) 30.2579 0.988481 0.494240 0.869325i \(-0.335446\pi\)
0.494240 + 0.869325i \(0.335446\pi\)
\(938\) −41.6042 −1.35843
\(939\) 6.86339 0.223978
\(940\) −34.6695 −1.13079
\(941\) −60.1500 −1.96083 −0.980417 0.196932i \(-0.936902\pi\)
−0.980417 + 0.196932i \(0.936902\pi\)
\(942\) −14.1325 −0.460461
\(943\) 4.02846 0.131185
\(944\) 3.43602 0.111833
\(945\) 42.0300 1.36724
\(946\) 5.90254 0.191908
\(947\) 30.5954 0.994216 0.497108 0.867689i \(-0.334395\pi\)
0.497108 + 0.867689i \(0.334395\pi\)
\(948\) 2.06205 0.0669722
\(949\) 2.13825 0.0694105
\(950\) −6.45565 −0.209449
\(951\) 16.3320 0.529601
\(952\) 3.36002 0.108899
\(953\) −18.8637 −0.611055 −0.305527 0.952183i \(-0.598833\pi\)
−0.305527 + 0.952183i \(0.598833\pi\)
\(954\) 9.34149 0.302442
\(955\) −19.7028 −0.637566
\(956\) −19.3347 −0.625329
\(957\) 1.16883 0.0377828
\(958\) 6.84565 0.221173
\(959\) −46.6165 −1.50532
\(960\) −5.45350 −0.176011
\(961\) −23.5043 −0.758202
\(962\) 39.0753 1.25984
\(963\) −8.15454 −0.262776
\(964\) 9.45825 0.304630
\(965\) 65.1622 2.09764
\(966\) 3.60734 0.116064
\(967\) 29.8978 0.961450 0.480725 0.876871i \(-0.340374\pi\)
0.480725 + 0.876871i \(0.340374\pi\)
\(968\) −5.24797 −0.168676
\(969\) 4.91942 0.158034
\(970\) −44.9524 −1.44334
\(971\) −41.1553 −1.32074 −0.660368 0.750942i \(-0.729600\pi\)
−0.660368 + 0.750942i \(0.729600\pi\)
\(972\) 11.4746 0.368047
\(973\) 60.7744 1.94834
\(974\) −28.9894 −0.928881
\(975\) 23.3540 0.747925
\(976\) 6.03348 0.193127
\(977\) 15.3161 0.490005 0.245002 0.969522i \(-0.421211\pi\)
0.245002 + 0.969522i \(0.421211\pi\)
\(978\) −25.8682 −0.827173
\(979\) 17.6720 0.564801
\(980\) 28.3186 0.904603
\(981\) −16.9371 −0.540761
\(982\) 30.4910 0.973007
\(983\) 53.5638 1.70842 0.854210 0.519928i \(-0.174041\pi\)
0.854210 + 0.519928i \(0.174041\pi\)
\(984\) 19.4989 0.621601
\(985\) −4.10816 −0.130897
\(986\) 0.191341 0.00609355
\(987\) 111.001 3.53321
\(988\) 16.0653 0.511105
\(989\) 1.03739 0.0329871
\(990\) −7.45324 −0.236879
\(991\) −0.354954 −0.0112755 −0.00563775 0.999984i \(-0.501795\pi\)
−0.00563775 + 0.999984i \(0.501795\pi\)
\(992\) −2.73783 −0.0869263
\(993\) 2.47338 0.0784904
\(994\) −39.5931 −1.25582
\(995\) −65.0665 −2.06275
\(996\) 22.6758 0.718510
\(997\) 6.46381 0.204711 0.102355 0.994748i \(-0.467362\pi\)
0.102355 + 0.994748i \(0.467362\pi\)
\(998\) 28.2435 0.894032
\(999\) −27.4454 −0.868334
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 \(a_p\))