Properties

Label 6026.2.a.i.1.12
Level 6026
Weight 2
Character 6026.1
Self dual Yes
Analytic conductor 48.118
Analytic rank 1
Dimension 25
CM No

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Newspace parameters

Level: \( N \) = \( 6026 = 2 \cdot 23 \cdot 131 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6026.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.117852258\)
Analytic rank: \(1\)
Dimension: \(25\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Character \(\chi\) = 6026.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-0.665355 q^{3}\) \(+1.00000 q^{4}\) \(+0.670202 q^{5}\) \(+0.665355 q^{6}\) \(-3.39786 q^{7}\) \(-1.00000 q^{8}\) \(-2.55730 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-0.665355 q^{3}\) \(+1.00000 q^{4}\) \(+0.670202 q^{5}\) \(+0.665355 q^{6}\) \(-3.39786 q^{7}\) \(-1.00000 q^{8}\) \(-2.55730 q^{9}\) \(-0.670202 q^{10}\) \(-2.66536 q^{11}\) \(-0.665355 q^{12}\) \(+2.25288 q^{13}\) \(+3.39786 q^{14}\) \(-0.445922 q^{15}\) \(+1.00000 q^{16}\) \(+3.18309 q^{17}\) \(+2.55730 q^{18}\) \(+4.73220 q^{19}\) \(+0.670202 q^{20}\) \(+2.26078 q^{21}\) \(+2.66536 q^{22}\) \(+1.00000 q^{23}\) \(+0.665355 q^{24}\) \(-4.55083 q^{25}\) \(-2.25288 q^{26}\) \(+3.69758 q^{27}\) \(-3.39786 q^{28}\) \(-9.07696 q^{29}\) \(+0.445922 q^{30}\) \(+2.40671 q^{31}\) \(-1.00000 q^{32}\) \(+1.77341 q^{33}\) \(-3.18309 q^{34}\) \(-2.27725 q^{35}\) \(-2.55730 q^{36}\) \(+10.0140 q^{37}\) \(-4.73220 q^{38}\) \(-1.49897 q^{39}\) \(-0.670202 q^{40}\) \(+10.3894 q^{41}\) \(-2.26078 q^{42}\) \(-10.8219 q^{43}\) \(-2.66536 q^{44}\) \(-1.71391 q^{45}\) \(-1.00000 q^{46}\) \(+2.12628 q^{47}\) \(-0.665355 q^{48}\) \(+4.54547 q^{49}\) \(+4.55083 q^{50}\) \(-2.11789 q^{51}\) \(+2.25288 q^{52}\) \(+2.74037 q^{53}\) \(-3.69758 q^{54}\) \(-1.78633 q^{55}\) \(+3.39786 q^{56}\) \(-3.14859 q^{57}\) \(+9.07696 q^{58}\) \(+2.19678 q^{59}\) \(-0.445922 q^{60}\) \(+0.869457 q^{61}\) \(-2.40671 q^{62}\) \(+8.68936 q^{63}\) \(+1.00000 q^{64}\) \(+1.50989 q^{65}\) \(-1.77341 q^{66}\) \(-5.55015 q^{67}\) \(+3.18309 q^{68}\) \(-0.665355 q^{69}\) \(+2.27725 q^{70}\) \(+13.2632 q^{71}\) \(+2.55730 q^{72}\) \(+0.381071 q^{73}\) \(-10.0140 q^{74}\) \(+3.02792 q^{75}\) \(+4.73220 q^{76}\) \(+9.05653 q^{77}\) \(+1.49897 q^{78}\) \(-6.31574 q^{79}\) \(+0.670202 q^{80}\) \(+5.21171 q^{81}\) \(-10.3894 q^{82}\) \(-8.49811 q^{83}\) \(+2.26078 q^{84}\) \(+2.13331 q^{85}\) \(+10.8219 q^{86}\) \(+6.03940 q^{87}\) \(+2.66536 q^{88}\) \(+13.3914 q^{89}\) \(+1.71391 q^{90}\) \(-7.65499 q^{91}\) \(+1.00000 q^{92}\) \(-1.60131 q^{93}\) \(-2.12628 q^{94}\) \(+3.17153 q^{95}\) \(+0.665355 q^{96}\) \(+3.23551 q^{97}\) \(-4.54547 q^{98}\) \(+6.81614 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(25q \) \(\mathstrut -\mathstrut 25q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 25q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 11q^{7} \) \(\mathstrut -\mathstrut 25q^{8} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(25q \) \(\mathstrut -\mathstrut 25q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 25q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 11q^{7} \) \(\mathstrut -\mathstrut 25q^{8} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut +\mathstrut 3q^{10} \) \(\mathstrut -\mathstrut 12q^{11} \) \(\mathstrut -\mathstrut 4q^{12} \) \(\mathstrut -\mathstrut 6q^{13} \) \(\mathstrut +\mathstrut 11q^{14} \) \(\mathstrut +\mathstrut 25q^{16} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut -\mathstrut 19q^{18} \) \(\mathstrut -\mathstrut 23q^{19} \) \(\mathstrut -\mathstrut 3q^{20} \) \(\mathstrut -\mathstrut 16q^{21} \) \(\mathstrut +\mathstrut 12q^{22} \) \(\mathstrut +\mathstrut 25q^{23} \) \(\mathstrut +\mathstrut 4q^{24} \) \(\mathstrut +\mathstrut 4q^{25} \) \(\mathstrut +\mathstrut 6q^{26} \) \(\mathstrut -\mathstrut 13q^{27} \) \(\mathstrut -\mathstrut 11q^{28} \) \(\mathstrut -\mathstrut 7q^{29} \) \(\mathstrut -\mathstrut 7q^{31} \) \(\mathstrut -\mathstrut 25q^{32} \) \(\mathstrut +\mathstrut 3q^{33} \) \(\mathstrut -\mathstrut 8q^{34} \) \(\mathstrut -\mathstrut 18q^{35} \) \(\mathstrut +\mathstrut 19q^{36} \) \(\mathstrut -\mathstrut 7q^{37} \) \(\mathstrut +\mathstrut 23q^{38} \) \(\mathstrut -\mathstrut 2q^{39} \) \(\mathstrut +\mathstrut 3q^{40} \) \(\mathstrut -\mathstrut 10q^{41} \) \(\mathstrut +\mathstrut 16q^{42} \) \(\mathstrut -\mathstrut 26q^{43} \) \(\mathstrut -\mathstrut 12q^{44} \) \(\mathstrut +\mathstrut 20q^{45} \) \(\mathstrut -\mathstrut 25q^{46} \) \(\mathstrut -\mathstrut 2q^{47} \) \(\mathstrut -\mathstrut 4q^{48} \) \(\mathstrut +\mathstrut 2q^{49} \) \(\mathstrut -\mathstrut 4q^{50} \) \(\mathstrut -\mathstrut 28q^{51} \) \(\mathstrut -\mathstrut 6q^{52} \) \(\mathstrut +\mathstrut 47q^{53} \) \(\mathstrut +\mathstrut 13q^{54} \) \(\mathstrut -\mathstrut 38q^{55} \) \(\mathstrut +\mathstrut 11q^{56} \) \(\mathstrut -\mathstrut 4q^{57} \) \(\mathstrut +\mathstrut 7q^{58} \) \(\mathstrut -\mathstrut 19q^{59} \) \(\mathstrut -\mathstrut 26q^{61} \) \(\mathstrut +\mathstrut 7q^{62} \) \(\mathstrut -\mathstrut 15q^{63} \) \(\mathstrut +\mathstrut 25q^{64} \) \(\mathstrut +\mathstrut 13q^{65} \) \(\mathstrut -\mathstrut 3q^{66} \) \(\mathstrut -\mathstrut 34q^{67} \) \(\mathstrut +\mathstrut 8q^{68} \) \(\mathstrut -\mathstrut 4q^{69} \) \(\mathstrut +\mathstrut 18q^{70} \) \(\mathstrut -\mathstrut 10q^{71} \) \(\mathstrut -\mathstrut 19q^{72} \) \(\mathstrut -\mathstrut 22q^{73} \) \(\mathstrut +\mathstrut 7q^{74} \) \(\mathstrut -\mathstrut 8q^{75} \) \(\mathstrut -\mathstrut 23q^{76} \) \(\mathstrut +\mathstrut 28q^{77} \) \(\mathstrut +\mathstrut 2q^{78} \) \(\mathstrut -\mathstrut 21q^{79} \) \(\mathstrut -\mathstrut 3q^{80} \) \(\mathstrut -\mathstrut 27q^{81} \) \(\mathstrut +\mathstrut 10q^{82} \) \(\mathstrut -\mathstrut 16q^{83} \) \(\mathstrut -\mathstrut 16q^{84} \) \(\mathstrut -\mathstrut 42q^{85} \) \(\mathstrut +\mathstrut 26q^{86} \) \(\mathstrut -\mathstrut 17q^{87} \) \(\mathstrut +\mathstrut 12q^{88} \) \(\mathstrut +\mathstrut 27q^{89} \) \(\mathstrut -\mathstrut 20q^{90} \) \(\mathstrut -\mathstrut 26q^{91} \) \(\mathstrut +\mathstrut 25q^{92} \) \(\mathstrut -\mathstrut 27q^{93} \) \(\mathstrut +\mathstrut 2q^{94} \) \(\mathstrut +\mathstrut 4q^{96} \) \(\mathstrut +\mathstrut 4q^{97} \) \(\mathstrut -\mathstrut 2q^{98} \) \(\mathstrut -\mathstrut 2q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −0.665355 −0.384143 −0.192071 0.981381i \(-0.561521\pi\)
−0.192071 + 0.981381i \(0.561521\pi\)
\(4\) 1.00000 0.500000
\(5\) 0.670202 0.299723 0.149862 0.988707i \(-0.452117\pi\)
0.149862 + 0.988707i \(0.452117\pi\)
\(6\) 0.665355 0.271630
\(7\) −3.39786 −1.28427 −0.642136 0.766591i \(-0.721951\pi\)
−0.642136 + 0.766591i \(0.721951\pi\)
\(8\) −1.00000 −0.353553
\(9\) −2.55730 −0.852434
\(10\) −0.670202 −0.211936
\(11\) −2.66536 −0.803637 −0.401818 0.915719i \(-0.631622\pi\)
−0.401818 + 0.915719i \(0.631622\pi\)
\(12\) −0.665355 −0.192071
\(13\) 2.25288 0.624837 0.312419 0.949944i \(-0.398861\pi\)
0.312419 + 0.949944i \(0.398861\pi\)
\(14\) 3.39786 0.908117
\(15\) −0.445922 −0.115137
\(16\) 1.00000 0.250000
\(17\) 3.18309 0.772013 0.386007 0.922496i \(-0.373854\pi\)
0.386007 + 0.922496i \(0.373854\pi\)
\(18\) 2.55730 0.602762
\(19\) 4.73220 1.08564 0.542821 0.839849i \(-0.317356\pi\)
0.542821 + 0.839849i \(0.317356\pi\)
\(20\) 0.670202 0.149862
\(21\) 2.26078 0.493343
\(22\) 2.66536 0.568257
\(23\) 1.00000 0.208514
\(24\) 0.665355 0.135815
\(25\) −4.55083 −0.910166
\(26\) −2.25288 −0.441827
\(27\) 3.69758 0.711599
\(28\) −3.39786 −0.642136
\(29\) −9.07696 −1.68555 −0.842775 0.538267i \(-0.819079\pi\)
−0.842775 + 0.538267i \(0.819079\pi\)
\(30\) 0.445922 0.0814139
\(31\) 2.40671 0.432257 0.216129 0.976365i \(-0.430657\pi\)
0.216129 + 0.976365i \(0.430657\pi\)
\(32\) −1.00000 −0.176777
\(33\) 1.77341 0.308711
\(34\) −3.18309 −0.545896
\(35\) −2.27725 −0.384926
\(36\) −2.55730 −0.426217
\(37\) 10.0140 1.64629 0.823147 0.567828i \(-0.192216\pi\)
0.823147 + 0.567828i \(0.192216\pi\)
\(38\) −4.73220 −0.767664
\(39\) −1.49897 −0.240027
\(40\) −0.670202 −0.105968
\(41\) 10.3894 1.62255 0.811274 0.584667i \(-0.198775\pi\)
0.811274 + 0.584667i \(0.198775\pi\)
\(42\) −2.26078 −0.348846
\(43\) −10.8219 −1.65032 −0.825160 0.564899i \(-0.808915\pi\)
−0.825160 + 0.564899i \(0.808915\pi\)
\(44\) −2.66536 −0.401818
\(45\) −1.71391 −0.255495
\(46\) −1.00000 −0.147442
\(47\) 2.12628 0.310149 0.155075 0.987903i \(-0.450438\pi\)
0.155075 + 0.987903i \(0.450438\pi\)
\(48\) −0.665355 −0.0960357
\(49\) 4.54547 0.649352
\(50\) 4.55083 0.643584
\(51\) −2.11789 −0.296563
\(52\) 2.25288 0.312419
\(53\) 2.74037 0.376418 0.188209 0.982129i \(-0.439732\pi\)
0.188209 + 0.982129i \(0.439732\pi\)
\(54\) −3.69758 −0.503177
\(55\) −1.78633 −0.240869
\(56\) 3.39786 0.454058
\(57\) −3.14859 −0.417041
\(58\) 9.07696 1.19186
\(59\) 2.19678 0.285997 0.142998 0.989723i \(-0.454326\pi\)
0.142998 + 0.989723i \(0.454326\pi\)
\(60\) −0.445922 −0.0575683
\(61\) 0.869457 0.111323 0.0556613 0.998450i \(-0.482273\pi\)
0.0556613 + 0.998450i \(0.482273\pi\)
\(62\) −2.40671 −0.305652
\(63\) 8.68936 1.09476
\(64\) 1.00000 0.125000
\(65\) 1.50989 0.187278
\(66\) −1.77341 −0.218292
\(67\) −5.55015 −0.678058 −0.339029 0.940776i \(-0.610099\pi\)
−0.339029 + 0.940776i \(0.610099\pi\)
\(68\) 3.18309 0.386007
\(69\) −0.665355 −0.0800993
\(70\) 2.27725 0.272184
\(71\) 13.2632 1.57405 0.787024 0.616922i \(-0.211621\pi\)
0.787024 + 0.616922i \(0.211621\pi\)
\(72\) 2.55730 0.301381
\(73\) 0.381071 0.0446010 0.0223005 0.999751i \(-0.492901\pi\)
0.0223005 + 0.999751i \(0.492901\pi\)
\(74\) −10.0140 −1.16411
\(75\) 3.02792 0.349634
\(76\) 4.73220 0.542821
\(77\) 9.05653 1.03209
\(78\) 1.49897 0.169725
\(79\) −6.31574 −0.710577 −0.355288 0.934757i \(-0.615617\pi\)
−0.355288 + 0.934757i \(0.615617\pi\)
\(80\) 0.670202 0.0749309
\(81\) 5.21171 0.579079
\(82\) −10.3894 −1.14731
\(83\) −8.49811 −0.932789 −0.466394 0.884577i \(-0.654447\pi\)
−0.466394 + 0.884577i \(0.654447\pi\)
\(84\) 2.26078 0.246672
\(85\) 2.13331 0.231390
\(86\) 10.8219 1.16695
\(87\) 6.03940 0.647492
\(88\) 2.66536 0.284128
\(89\) 13.3914 1.41948 0.709742 0.704462i \(-0.248812\pi\)
0.709742 + 0.704462i \(0.248812\pi\)
\(90\) 1.71391 0.180662
\(91\) −7.65499 −0.802461
\(92\) 1.00000 0.104257
\(93\) −1.60131 −0.166048
\(94\) −2.12628 −0.219309
\(95\) 3.17153 0.325392
\(96\) 0.665355 0.0679075
\(97\) 3.23551 0.328516 0.164258 0.986417i \(-0.447477\pi\)
0.164258 + 0.986417i \(0.447477\pi\)
\(98\) −4.54547 −0.459161
\(99\) 6.81614 0.685047
\(100\) −4.55083 −0.455083
\(101\) −11.9405 −1.18812 −0.594061 0.804420i \(-0.702476\pi\)
−0.594061 + 0.804420i \(0.702476\pi\)
\(102\) 2.11789 0.209702
\(103\) 4.34785 0.428406 0.214203 0.976789i \(-0.431285\pi\)
0.214203 + 0.976789i \(0.431285\pi\)
\(104\) −2.25288 −0.220913
\(105\) 1.51518 0.147867
\(106\) −2.74037 −0.266168
\(107\) −9.12065 −0.881726 −0.440863 0.897574i \(-0.645328\pi\)
−0.440863 + 0.897574i \(0.645328\pi\)
\(108\) 3.69758 0.355800
\(109\) 6.95171 0.665853 0.332926 0.942953i \(-0.391964\pi\)
0.332926 + 0.942953i \(0.391964\pi\)
\(110\) 1.78633 0.170320
\(111\) −6.66287 −0.632412
\(112\) −3.39786 −0.321068
\(113\) −1.13052 −0.106350 −0.0531752 0.998585i \(-0.516934\pi\)
−0.0531752 + 0.998585i \(0.516934\pi\)
\(114\) 3.14859 0.294893
\(115\) 0.670202 0.0624967
\(116\) −9.07696 −0.842775
\(117\) −5.76131 −0.532633
\(118\) −2.19678 −0.202230
\(119\) −10.8157 −0.991475
\(120\) 0.445922 0.0407069
\(121\) −3.89585 −0.354168
\(122\) −0.869457 −0.0787170
\(123\) −6.91262 −0.623290
\(124\) 2.40671 0.216129
\(125\) −6.40098 −0.572521
\(126\) −8.68936 −0.774110
\(127\) −2.61248 −0.231821 −0.115910 0.993260i \(-0.536979\pi\)
−0.115910 + 0.993260i \(0.536979\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 7.20039 0.633959
\(130\) −1.50989 −0.132426
\(131\) 1.00000 0.0873704
\(132\) 1.77341 0.154356
\(133\) −16.0794 −1.39426
\(134\) 5.55015 0.479460
\(135\) 2.47812 0.213283
\(136\) −3.18309 −0.272948
\(137\) 11.4391 0.977310 0.488655 0.872477i \(-0.337488\pi\)
0.488655 + 0.872477i \(0.337488\pi\)
\(138\) 0.665355 0.0566388
\(139\) −0.0220343 −0.00186893 −0.000934464 1.00000i \(-0.500297\pi\)
−0.000934464 1.00000i \(0.500297\pi\)
\(140\) −2.27725 −0.192463
\(141\) −1.41473 −0.119142
\(142\) −13.2632 −1.11302
\(143\) −6.00475 −0.502142
\(144\) −2.55730 −0.213109
\(145\) −6.08340 −0.505199
\(146\) −0.381071 −0.0315376
\(147\) −3.02435 −0.249444
\(148\) 10.0140 0.823147
\(149\) −12.7364 −1.04341 −0.521704 0.853126i \(-0.674704\pi\)
−0.521704 + 0.853126i \(0.674704\pi\)
\(150\) −3.02792 −0.247228
\(151\) 7.42620 0.604335 0.302168 0.953255i \(-0.402290\pi\)
0.302168 + 0.953255i \(0.402290\pi\)
\(152\) −4.73220 −0.383832
\(153\) −8.14013 −0.658091
\(154\) −9.05653 −0.729796
\(155\) 1.61298 0.129558
\(156\) −1.49897 −0.120013
\(157\) 4.52277 0.360956 0.180478 0.983579i \(-0.442235\pi\)
0.180478 + 0.983579i \(0.442235\pi\)
\(158\) 6.31574 0.502454
\(159\) −1.82332 −0.144598
\(160\) −0.670202 −0.0529841
\(161\) −3.39786 −0.267789
\(162\) −5.21171 −0.409470
\(163\) 7.42122 0.581274 0.290637 0.956833i \(-0.406133\pi\)
0.290637 + 0.956833i \(0.406133\pi\)
\(164\) 10.3894 0.811274
\(165\) 1.18854 0.0925280
\(166\) 8.49811 0.659581
\(167\) −4.55293 −0.352317 −0.176158 0.984362i \(-0.556367\pi\)
−0.176158 + 0.984362i \(0.556367\pi\)
\(168\) −2.26078 −0.174423
\(169\) −7.92452 −0.609578
\(170\) −2.13331 −0.163618
\(171\) −12.1017 −0.925438
\(172\) −10.8219 −0.825160
\(173\) −19.1710 −1.45754 −0.728772 0.684756i \(-0.759909\pi\)
−0.728772 + 0.684756i \(0.759909\pi\)
\(174\) −6.03940 −0.457846
\(175\) 15.4631 1.16890
\(176\) −2.66536 −0.200909
\(177\) −1.46164 −0.109864
\(178\) −13.3914 −1.00373
\(179\) −2.38254 −0.178079 −0.0890397 0.996028i \(-0.528380\pi\)
−0.0890397 + 0.996028i \(0.528380\pi\)
\(180\) −1.71391 −0.127747
\(181\) −19.0100 −1.41300 −0.706501 0.707712i \(-0.749727\pi\)
−0.706501 + 0.707712i \(0.749727\pi\)
\(182\) 7.65499 0.567425
\(183\) −0.578498 −0.0427638
\(184\) −1.00000 −0.0737210
\(185\) 6.71141 0.493433
\(186\) 1.60131 0.117414
\(187\) −8.48409 −0.620418
\(188\) 2.12628 0.155075
\(189\) −12.5639 −0.913886
\(190\) −3.17153 −0.230087
\(191\) −7.20331 −0.521213 −0.260607 0.965445i \(-0.583923\pi\)
−0.260607 + 0.965445i \(0.583923\pi\)
\(192\) −0.665355 −0.0480178
\(193\) −14.5057 −1.04414 −0.522072 0.852901i \(-0.674841\pi\)
−0.522072 + 0.852901i \(0.674841\pi\)
\(194\) −3.23551 −0.232296
\(195\) −1.00461 −0.0719416
\(196\) 4.54547 0.324676
\(197\) −1.16500 −0.0830028 −0.0415014 0.999138i \(-0.513214\pi\)
−0.0415014 + 0.999138i \(0.513214\pi\)
\(198\) −6.81614 −0.484402
\(199\) −15.6513 −1.10949 −0.554745 0.832021i \(-0.687184\pi\)
−0.554745 + 0.832021i \(0.687184\pi\)
\(200\) 4.55083 0.321792
\(201\) 3.69282 0.260471
\(202\) 11.9405 0.840129
\(203\) 30.8423 2.16470
\(204\) −2.11789 −0.148282
\(205\) 6.96298 0.486315
\(206\) −4.34785 −0.302929
\(207\) −2.55730 −0.177745
\(208\) 2.25288 0.156209
\(209\) −12.6130 −0.872461
\(210\) −1.51518 −0.104557
\(211\) −20.4743 −1.40951 −0.704754 0.709452i \(-0.748942\pi\)
−0.704754 + 0.709452i \(0.748942\pi\)
\(212\) 2.74037 0.188209
\(213\) −8.82471 −0.604659
\(214\) 9.12065 0.623474
\(215\) −7.25284 −0.494640
\(216\) −3.69758 −0.251588
\(217\) −8.17765 −0.555135
\(218\) −6.95171 −0.470829
\(219\) −0.253547 −0.0171331
\(220\) −1.78633 −0.120434
\(221\) 7.17114 0.482383
\(222\) 6.66287 0.447183
\(223\) −15.6735 −1.04957 −0.524787 0.851233i \(-0.675855\pi\)
−0.524787 + 0.851233i \(0.675855\pi\)
\(224\) 3.39786 0.227029
\(225\) 11.6378 0.775857
\(226\) 1.13052 0.0752011
\(227\) −2.08245 −0.138217 −0.0691084 0.997609i \(-0.522015\pi\)
−0.0691084 + 0.997609i \(0.522015\pi\)
\(228\) −3.14859 −0.208521
\(229\) −0.900940 −0.0595358 −0.0297679 0.999557i \(-0.509477\pi\)
−0.0297679 + 0.999557i \(0.509477\pi\)
\(230\) −0.670202 −0.0441918
\(231\) −6.02581 −0.396469
\(232\) 9.07696 0.595932
\(233\) 10.1771 0.666721 0.333361 0.942799i \(-0.391817\pi\)
0.333361 + 0.942799i \(0.391817\pi\)
\(234\) 5.76131 0.376628
\(235\) 1.42503 0.0929590
\(236\) 2.19678 0.142998
\(237\) 4.20221 0.272963
\(238\) 10.8157 0.701078
\(239\) −11.5389 −0.746391 −0.373196 0.927753i \(-0.621738\pi\)
−0.373196 + 0.927753i \(0.621738\pi\)
\(240\) −0.445922 −0.0287841
\(241\) −5.92932 −0.381941 −0.190971 0.981596i \(-0.561163\pi\)
−0.190971 + 0.981596i \(0.561163\pi\)
\(242\) 3.89585 0.250435
\(243\) −14.5604 −0.934048
\(244\) 0.869457 0.0556613
\(245\) 3.04638 0.194626
\(246\) 6.91262 0.440732
\(247\) 10.6611 0.678350
\(248\) −2.40671 −0.152826
\(249\) 5.65426 0.358324
\(250\) 6.40098 0.404834
\(251\) 17.2997 1.09195 0.545974 0.837802i \(-0.316160\pi\)
0.545974 + 0.837802i \(0.316160\pi\)
\(252\) 8.68936 0.547378
\(253\) −2.66536 −0.167570
\(254\) 2.61248 0.163922
\(255\) −1.41941 −0.0888870
\(256\) 1.00000 0.0625000
\(257\) 25.9083 1.61612 0.808059 0.589102i \(-0.200518\pi\)
0.808059 + 0.589102i \(0.200518\pi\)
\(258\) −7.20039 −0.448276
\(259\) −34.0262 −2.11429
\(260\) 1.50989 0.0936392
\(261\) 23.2125 1.43682
\(262\) −1.00000 −0.0617802
\(263\) −15.7746 −0.972704 −0.486352 0.873763i \(-0.661673\pi\)
−0.486352 + 0.873763i \(0.661673\pi\)
\(264\) −1.77341 −0.109146
\(265\) 1.83660 0.112821
\(266\) 16.0794 0.985889
\(267\) −8.91002 −0.545284
\(268\) −5.55015 −0.339029
\(269\) −6.11680 −0.372948 −0.186474 0.982460i \(-0.559706\pi\)
−0.186474 + 0.982460i \(0.559706\pi\)
\(270\) −2.47812 −0.150814
\(271\) −10.2324 −0.621575 −0.310788 0.950479i \(-0.600593\pi\)
−0.310788 + 0.950479i \(0.600593\pi\)
\(272\) 3.18309 0.193003
\(273\) 5.09328 0.308259
\(274\) −11.4391 −0.691063
\(275\) 12.1296 0.731443
\(276\) −0.665355 −0.0400497
\(277\) 23.8901 1.43542 0.717708 0.696344i \(-0.245191\pi\)
0.717708 + 0.696344i \(0.245191\pi\)
\(278\) 0.0220343 0.00132153
\(279\) −6.15467 −0.368471
\(280\) 2.27725 0.136092
\(281\) 22.5490 1.34516 0.672579 0.740025i \(-0.265186\pi\)
0.672579 + 0.740025i \(0.265186\pi\)
\(282\) 1.41473 0.0842458
\(283\) 17.4271 1.03594 0.517968 0.855400i \(-0.326689\pi\)
0.517968 + 0.855400i \(0.326689\pi\)
\(284\) 13.2632 0.787024
\(285\) −2.11019 −0.124997
\(286\) 6.00475 0.355068
\(287\) −35.3016 −2.08379
\(288\) 2.55730 0.150691
\(289\) −6.86792 −0.403995
\(290\) 6.08340 0.357229
\(291\) −2.15276 −0.126197
\(292\) 0.381071 0.0223005
\(293\) −3.30962 −0.193350 −0.0966751 0.995316i \(-0.530821\pi\)
−0.0966751 + 0.995316i \(0.530821\pi\)
\(294\) 3.02435 0.176384
\(295\) 1.47229 0.0857199
\(296\) −10.0140 −0.582053
\(297\) −9.85538 −0.571867
\(298\) 12.7364 0.737801
\(299\) 2.25288 0.130288
\(300\) 3.02792 0.174817
\(301\) 36.7712 2.11946
\(302\) −7.42620 −0.427330
\(303\) 7.94465 0.456408
\(304\) 4.73220 0.271410
\(305\) 0.582712 0.0333660
\(306\) 8.14013 0.465340
\(307\) −13.3594 −0.762461 −0.381230 0.924480i \(-0.624500\pi\)
−0.381230 + 0.924480i \(0.624500\pi\)
\(308\) 9.05653 0.516044
\(309\) −2.89286 −0.164569
\(310\) −1.61298 −0.0916110
\(311\) −19.8616 −1.12625 −0.563124 0.826372i \(-0.690401\pi\)
−0.563124 + 0.826372i \(0.690401\pi\)
\(312\) 1.49897 0.0848623
\(313\) −21.3082 −1.20441 −0.602206 0.798341i \(-0.705711\pi\)
−0.602206 + 0.798341i \(0.705711\pi\)
\(314\) −4.52277 −0.255235
\(315\) 5.82363 0.328124
\(316\) −6.31574 −0.355288
\(317\) 23.6504 1.32834 0.664169 0.747582i \(-0.268785\pi\)
0.664169 + 0.747582i \(0.268785\pi\)
\(318\) 1.82332 0.102246
\(319\) 24.1934 1.35457
\(320\) 0.670202 0.0374654
\(321\) 6.06846 0.338709
\(322\) 3.39786 0.189355
\(323\) 15.0630 0.838130
\(324\) 5.21171 0.289539
\(325\) −10.2525 −0.568706
\(326\) −7.42122 −0.411023
\(327\) −4.62535 −0.255782
\(328\) −10.3894 −0.573657
\(329\) −7.22479 −0.398316
\(330\) −1.18854 −0.0654272
\(331\) 31.6327 1.73869 0.869346 0.494203i \(-0.164540\pi\)
0.869346 + 0.494203i \(0.164540\pi\)
\(332\) −8.49811 −0.466394
\(333\) −25.6089 −1.40336
\(334\) 4.55293 0.249125
\(335\) −3.71972 −0.203230
\(336\) 2.26078 0.123336
\(337\) 3.03332 0.165235 0.0826177 0.996581i \(-0.473672\pi\)
0.0826177 + 0.996581i \(0.473672\pi\)
\(338\) 7.92452 0.431037
\(339\) 0.752197 0.0408537
\(340\) 2.13331 0.115695
\(341\) −6.41474 −0.347378
\(342\) 12.1017 0.654384
\(343\) 8.34017 0.450327
\(344\) 10.8219 0.583476
\(345\) −0.445922 −0.0240076
\(346\) 19.1710 1.03064
\(347\) −25.7632 −1.38304 −0.691520 0.722357i \(-0.743059\pi\)
−0.691520 + 0.722357i \(0.743059\pi\)
\(348\) 6.03940 0.323746
\(349\) 23.9822 1.28374 0.641869 0.766815i \(-0.278159\pi\)
0.641869 + 0.766815i \(0.278159\pi\)
\(350\) −15.4631 −0.826537
\(351\) 8.33021 0.444634
\(352\) 2.66536 0.142064
\(353\) 5.56720 0.296312 0.148156 0.988964i \(-0.452666\pi\)
0.148156 + 0.988964i \(0.452666\pi\)
\(354\) 1.46164 0.0776852
\(355\) 8.88900 0.471779
\(356\) 13.3914 0.709742
\(357\) 7.19628 0.380868
\(358\) 2.38254 0.125921
\(359\) −16.2677 −0.858576 −0.429288 0.903168i \(-0.641235\pi\)
−0.429288 + 0.903168i \(0.641235\pi\)
\(360\) 1.71391 0.0903310
\(361\) 3.39373 0.178618
\(362\) 19.0100 0.999143
\(363\) 2.59212 0.136051
\(364\) −7.65499 −0.401230
\(365\) 0.255394 0.0133680
\(366\) 0.578498 0.0302386
\(367\) −1.48940 −0.0777462 −0.0388731 0.999244i \(-0.512377\pi\)
−0.0388731 + 0.999244i \(0.512377\pi\)
\(368\) 1.00000 0.0521286
\(369\) −26.5688 −1.38311
\(370\) −6.71141 −0.348910
\(371\) −9.31139 −0.483423
\(372\) −1.60131 −0.0830242
\(373\) 6.34579 0.328572 0.164286 0.986413i \(-0.447468\pi\)
0.164286 + 0.986413i \(0.447468\pi\)
\(374\) 8.48409 0.438702
\(375\) 4.25893 0.219930
\(376\) −2.12628 −0.109654
\(377\) −20.4493 −1.05319
\(378\) 12.5639 0.646215
\(379\) −25.9821 −1.33461 −0.667305 0.744784i \(-0.732552\pi\)
−0.667305 + 0.744784i \(0.732552\pi\)
\(380\) 3.17153 0.162696
\(381\) 1.73823 0.0890522
\(382\) 7.20331 0.368553
\(383\) −28.2584 −1.44393 −0.721967 0.691927i \(-0.756762\pi\)
−0.721967 + 0.691927i \(0.756762\pi\)
\(384\) 0.665355 0.0339537
\(385\) 6.06970 0.309341
\(386\) 14.5057 0.738322
\(387\) 27.6748 1.40679
\(388\) 3.23551 0.164258
\(389\) 37.0291 1.87745 0.938726 0.344664i \(-0.112007\pi\)
0.938726 + 0.344664i \(0.112007\pi\)
\(390\) 1.00461 0.0508704
\(391\) 3.18309 0.160976
\(392\) −4.54547 −0.229581
\(393\) −0.665355 −0.0335627
\(394\) 1.16500 0.0586919
\(395\) −4.23282 −0.212977
\(396\) 6.81614 0.342524
\(397\) 13.3645 0.670745 0.335372 0.942086i \(-0.391138\pi\)
0.335372 + 0.942086i \(0.391138\pi\)
\(398\) 15.6513 0.784528
\(399\) 10.6985 0.535594
\(400\) −4.55083 −0.227541
\(401\) −11.3007 −0.564331 −0.282165 0.959366i \(-0.591053\pi\)
−0.282165 + 0.959366i \(0.591053\pi\)
\(402\) −3.69282 −0.184181
\(403\) 5.42203 0.270090
\(404\) −11.9405 −0.594061
\(405\) 3.49290 0.173563
\(406\) −30.8423 −1.53068
\(407\) −26.6910 −1.32302
\(408\) 2.11789 0.104851
\(409\) −1.51058 −0.0746936 −0.0373468 0.999302i \(-0.511891\pi\)
−0.0373468 + 0.999302i \(0.511891\pi\)
\(410\) −6.96298 −0.343877
\(411\) −7.61108 −0.375427
\(412\) 4.34785 0.214203
\(413\) −7.46436 −0.367297
\(414\) 2.55730 0.125685
\(415\) −5.69545 −0.279579
\(416\) −2.25288 −0.110457
\(417\) 0.0146607 0.000717935 0
\(418\) 12.6130 0.616923
\(419\) 31.3682 1.53244 0.766218 0.642581i \(-0.222136\pi\)
0.766218 + 0.642581i \(0.222136\pi\)
\(420\) 1.51518 0.0739333
\(421\) −33.4032 −1.62797 −0.813987 0.580884i \(-0.802707\pi\)
−0.813987 + 0.580884i \(0.802707\pi\)
\(422\) 20.4743 0.996672
\(423\) −5.43753 −0.264382
\(424\) −2.74037 −0.133084
\(425\) −14.4857 −0.702660
\(426\) 8.82471 0.427559
\(427\) −2.95430 −0.142968
\(428\) −9.12065 −0.440863
\(429\) 3.99529 0.192894
\(430\) 7.25284 0.349763
\(431\) −29.8622 −1.43841 −0.719206 0.694797i \(-0.755494\pi\)
−0.719206 + 0.694797i \(0.755494\pi\)
\(432\) 3.69758 0.177900
\(433\) −25.3290 −1.21723 −0.608617 0.793464i \(-0.708276\pi\)
−0.608617 + 0.793464i \(0.708276\pi\)
\(434\) 8.17765 0.392540
\(435\) 4.04762 0.194068
\(436\) 6.95171 0.332926
\(437\) 4.73220 0.226372
\(438\) 0.253547 0.0121150
\(439\) −5.73920 −0.273917 −0.136959 0.990577i \(-0.543733\pi\)
−0.136959 + 0.990577i \(0.543733\pi\)
\(440\) 1.78633 0.0851600
\(441\) −11.6241 −0.553530
\(442\) −7.17114 −0.341096
\(443\) −14.6720 −0.697089 −0.348545 0.937292i \(-0.613324\pi\)
−0.348545 + 0.937292i \(0.613324\pi\)
\(444\) −6.66287 −0.316206
\(445\) 8.97493 0.425453
\(446\) 15.6735 0.742161
\(447\) 8.47424 0.400818
\(448\) −3.39786 −0.160534
\(449\) −3.29391 −0.155449 −0.0777247 0.996975i \(-0.524766\pi\)
−0.0777247 + 0.996975i \(0.524766\pi\)
\(450\) −11.6378 −0.548614
\(451\) −27.6914 −1.30394
\(452\) −1.13052 −0.0531752
\(453\) −4.94106 −0.232151
\(454\) 2.08245 0.0977341
\(455\) −5.13039 −0.240516
\(456\) 3.14859 0.147446
\(457\) 4.46826 0.209016 0.104508 0.994524i \(-0.466673\pi\)
0.104508 + 0.994524i \(0.466673\pi\)
\(458\) 0.900940 0.0420982
\(459\) 11.7697 0.549364
\(460\) 0.670202 0.0312483
\(461\) −21.9946 −1.02439 −0.512195 0.858869i \(-0.671168\pi\)
−0.512195 + 0.858869i \(0.671168\pi\)
\(462\) 6.02581 0.280346
\(463\) 4.28775 0.199268 0.0996342 0.995024i \(-0.468233\pi\)
0.0996342 + 0.995024i \(0.468233\pi\)
\(464\) −9.07696 −0.421387
\(465\) −1.07320 −0.0497686
\(466\) −10.1771 −0.471443
\(467\) −39.0018 −1.80479 −0.902393 0.430913i \(-0.858192\pi\)
−0.902393 + 0.430913i \(0.858192\pi\)
\(468\) −5.76131 −0.266316
\(469\) 18.8586 0.870811
\(470\) −1.42503 −0.0657319
\(471\) −3.00925 −0.138659
\(472\) −2.19678 −0.101115
\(473\) 28.8442 1.32626
\(474\) −4.20221 −0.193014
\(475\) −21.5354 −0.988114
\(476\) −10.8157 −0.495737
\(477\) −7.00795 −0.320872
\(478\) 11.5389 0.527778
\(479\) 15.6867 0.716746 0.358373 0.933579i \(-0.383332\pi\)
0.358373 + 0.933579i \(0.383332\pi\)
\(480\) 0.445922 0.0203535
\(481\) 22.5604 1.02867
\(482\) 5.92932 0.270073
\(483\) 2.26078 0.102869
\(484\) −3.89585 −0.177084
\(485\) 2.16844 0.0984639
\(486\) 14.5604 0.660472
\(487\) −9.11804 −0.413178 −0.206589 0.978428i \(-0.566236\pi\)
−0.206589 + 0.978428i \(0.566236\pi\)
\(488\) −0.869457 −0.0393585
\(489\) −4.93774 −0.223292
\(490\) −3.04638 −0.137621
\(491\) −27.2290 −1.22883 −0.614413 0.788985i \(-0.710607\pi\)
−0.614413 + 0.788985i \(0.710607\pi\)
\(492\) −6.91262 −0.311645
\(493\) −28.8928 −1.30127
\(494\) −10.6611 −0.479666
\(495\) 4.56819 0.205325
\(496\) 2.40671 0.108064
\(497\) −45.0664 −2.02150
\(498\) −5.65426 −0.253373
\(499\) 0.612110 0.0274018 0.0137009 0.999906i \(-0.495639\pi\)
0.0137009 + 0.999906i \(0.495639\pi\)
\(500\) −6.40098 −0.286261
\(501\) 3.02932 0.135340
\(502\) −17.2997 −0.772123
\(503\) −8.18722 −0.365050 −0.182525 0.983201i \(-0.558427\pi\)
−0.182525 + 0.983201i \(0.558427\pi\)
\(504\) −8.68936 −0.387055
\(505\) −8.00253 −0.356108
\(506\) 2.66536 0.118490
\(507\) 5.27261 0.234165
\(508\) −2.61248 −0.115910
\(509\) −12.1602 −0.538991 −0.269496 0.963002i \(-0.586857\pi\)
−0.269496 + 0.963002i \(0.586857\pi\)
\(510\) 1.41941 0.0628526
\(511\) −1.29483 −0.0572797
\(512\) −1.00000 −0.0441942
\(513\) 17.4977 0.772542
\(514\) −25.9083 −1.14277
\(515\) 2.91394 0.128403
\(516\) 7.20039 0.316979
\(517\) −5.66729 −0.249247
\(518\) 34.0262 1.49503
\(519\) 12.7555 0.559905
\(520\) −1.50989 −0.0662129
\(521\) −35.6658 −1.56255 −0.781273 0.624189i \(-0.785429\pi\)
−0.781273 + 0.624189i \(0.785429\pi\)
\(522\) −23.2125 −1.01599
\(523\) −21.5639 −0.942925 −0.471462 0.881886i \(-0.656274\pi\)
−0.471462 + 0.881886i \(0.656274\pi\)
\(524\) 1.00000 0.0436852
\(525\) −10.2884 −0.449024
\(526\) 15.7746 0.687805
\(527\) 7.66077 0.333708
\(528\) 1.77341 0.0771778
\(529\) 1.00000 0.0434783
\(530\) −1.83660 −0.0797768
\(531\) −5.61784 −0.243793
\(532\) −16.0794 −0.697129
\(533\) 23.4060 1.01383
\(534\) 8.91002 0.385574
\(535\) −6.11267 −0.264274
\(536\) 5.55015 0.239730
\(537\) 1.58524 0.0684079
\(538\) 6.11680 0.263714
\(539\) −12.1153 −0.521843
\(540\) 2.47812 0.106641
\(541\) 6.48935 0.278999 0.139500 0.990222i \(-0.455451\pi\)
0.139500 + 0.990222i \(0.455451\pi\)
\(542\) 10.2324 0.439520
\(543\) 12.6484 0.542794
\(544\) −3.18309 −0.136474
\(545\) 4.65905 0.199572
\(546\) −5.09328 −0.217972
\(547\) −32.1280 −1.37369 −0.686847 0.726802i \(-0.741006\pi\)
−0.686847 + 0.726802i \(0.741006\pi\)
\(548\) 11.4391 0.488655
\(549\) −2.22347 −0.0948952
\(550\) −12.1296 −0.517208
\(551\) −42.9540 −1.82990
\(552\) 0.665355 0.0283194
\(553\) 21.4600 0.912573
\(554\) −23.8901 −1.01499
\(555\) −4.46547 −0.189549
\(556\) −0.0220343 −0.000934464 0
\(557\) 11.9182 0.504992 0.252496 0.967598i \(-0.418749\pi\)
0.252496 + 0.967598i \(0.418749\pi\)
\(558\) 6.15467 0.260548
\(559\) −24.3804 −1.03118
\(560\) −2.27725 −0.0962315
\(561\) 5.64493 0.238329
\(562\) −22.5490 −0.951171
\(563\) 1.59951 0.0674115 0.0337058 0.999432i \(-0.489269\pi\)
0.0337058 + 0.999432i \(0.489269\pi\)
\(564\) −1.41473 −0.0595708
\(565\) −0.757676 −0.0318757
\(566\) −17.4271 −0.732517
\(567\) −17.7087 −0.743694
\(568\) −13.2632 −0.556510
\(569\) 29.7103 1.24552 0.622761 0.782412i \(-0.286011\pi\)
0.622761 + 0.782412i \(0.286011\pi\)
\(570\) 2.11019 0.0883863
\(571\) −38.5184 −1.61194 −0.805972 0.591953i \(-0.798357\pi\)
−0.805972 + 0.591953i \(0.798357\pi\)
\(572\) −6.00475 −0.251071
\(573\) 4.79276 0.200220
\(574\) 35.3016 1.47346
\(575\) −4.55083 −0.189783
\(576\) −2.55730 −0.106554
\(577\) −16.1198 −0.671077 −0.335539 0.942026i \(-0.608918\pi\)
−0.335539 + 0.942026i \(0.608918\pi\)
\(578\) 6.86792 0.285668
\(579\) 9.65145 0.401101
\(580\) −6.08340 −0.252599
\(581\) 28.8754 1.19795
\(582\) 2.15276 0.0892347
\(583\) −7.30407 −0.302504
\(584\) −0.381071 −0.0157688
\(585\) −3.86124 −0.159643
\(586\) 3.30962 0.136719
\(587\) −3.12478 −0.128974 −0.0644868 0.997919i \(-0.520541\pi\)
−0.0644868 + 0.997919i \(0.520541\pi\)
\(588\) −3.02435 −0.124722
\(589\) 11.3890 0.469276
\(590\) −1.47229 −0.0606131
\(591\) 0.775139 0.0318849
\(592\) 10.0140 0.411573
\(593\) 27.6055 1.13362 0.566811 0.823848i \(-0.308177\pi\)
0.566811 + 0.823848i \(0.308177\pi\)
\(594\) 9.85538 0.404371
\(595\) −7.24871 −0.297168
\(596\) −12.7364 −0.521704
\(597\) 10.4137 0.426202
\(598\) −2.25288 −0.0921273
\(599\) −9.21585 −0.376550 −0.188275 0.982116i \(-0.560290\pi\)
−0.188275 + 0.982116i \(0.560290\pi\)
\(600\) −3.02792 −0.123614
\(601\) −10.8477 −0.442487 −0.221243 0.975219i \(-0.571012\pi\)
−0.221243 + 0.975219i \(0.571012\pi\)
\(602\) −36.7712 −1.49868
\(603\) 14.1934 0.578000
\(604\) 7.42620 0.302168
\(605\) −2.61101 −0.106152
\(606\) −7.94465 −0.322729
\(607\) 9.39050 0.381149 0.190574 0.981673i \(-0.438965\pi\)
0.190574 + 0.981673i \(0.438965\pi\)
\(608\) −4.73220 −0.191916
\(609\) −20.5210 −0.831555
\(610\) −0.582712 −0.0235933
\(611\) 4.79025 0.193793
\(612\) −8.14013 −0.329045
\(613\) 28.5696 1.15391 0.576957 0.816774i \(-0.304240\pi\)
0.576957 + 0.816774i \(0.304240\pi\)
\(614\) 13.3594 0.539141
\(615\) −4.63285 −0.186815
\(616\) −9.05653 −0.364898
\(617\) 32.4045 1.30455 0.652277 0.757980i \(-0.273814\pi\)
0.652277 + 0.757980i \(0.273814\pi\)
\(618\) 2.89286 0.116368
\(619\) −39.0485 −1.56949 −0.784746 0.619817i \(-0.787207\pi\)
−0.784746 + 0.619817i \(0.787207\pi\)
\(620\) 1.61298 0.0647788
\(621\) 3.69758 0.148379
\(622\) 19.8616 0.796378
\(623\) −45.5021 −1.82300
\(624\) −1.49897 −0.0600067
\(625\) 18.4642 0.738568
\(626\) 21.3082 0.851648
\(627\) 8.39214 0.335150
\(628\) 4.52277 0.180478
\(629\) 31.8755 1.27096
\(630\) −5.82363 −0.232019
\(631\) 0.580118 0.0230941 0.0115471 0.999933i \(-0.496324\pi\)
0.0115471 + 0.999933i \(0.496324\pi\)
\(632\) 6.31574 0.251227
\(633\) 13.6227 0.541452
\(634\) −23.6504 −0.939277
\(635\) −1.75089 −0.0694820
\(636\) −1.82332 −0.0722992
\(637\) 10.2404 0.405740
\(638\) −24.1934 −0.957825
\(639\) −33.9179 −1.34177
\(640\) −0.670202 −0.0264921
\(641\) −30.3791 −1.19990 −0.599952 0.800036i \(-0.704814\pi\)
−0.599952 + 0.800036i \(0.704814\pi\)
\(642\) −6.06846 −0.239503
\(643\) 13.2016 0.520620 0.260310 0.965525i \(-0.416175\pi\)
0.260310 + 0.965525i \(0.416175\pi\)
\(644\) −3.39786 −0.133895
\(645\) 4.82571 0.190012
\(646\) −15.0630 −0.592647
\(647\) 35.2463 1.38567 0.692837 0.721094i \(-0.256361\pi\)
0.692837 + 0.721094i \(0.256361\pi\)
\(648\) −5.21171 −0.204735
\(649\) −5.85522 −0.229837
\(650\) 10.2525 0.402136
\(651\) 5.44104 0.213251
\(652\) 7.42122 0.290637
\(653\) 19.8954 0.778566 0.389283 0.921118i \(-0.372723\pi\)
0.389283 + 0.921118i \(0.372723\pi\)
\(654\) 4.62535 0.180866
\(655\) 0.670202 0.0261870
\(656\) 10.3894 0.405637
\(657\) −0.974513 −0.0380194
\(658\) 7.22479 0.281652
\(659\) 23.2928 0.907360 0.453680 0.891165i \(-0.350111\pi\)
0.453680 + 0.891165i \(0.350111\pi\)
\(660\) 1.18854 0.0462640
\(661\) −37.5728 −1.46141 −0.730706 0.682693i \(-0.760809\pi\)
−0.730706 + 0.682693i \(0.760809\pi\)
\(662\) −31.6327 −1.22944
\(663\) −4.77135 −0.185304
\(664\) 8.49811 0.329791
\(665\) −10.7764 −0.417892
\(666\) 25.6089 0.992324
\(667\) −9.07696 −0.351461
\(668\) −4.55293 −0.176158
\(669\) 10.4284 0.403187
\(670\) 3.71972 0.143705
\(671\) −2.31742 −0.0894629
\(672\) −2.26078 −0.0872116
\(673\) −29.8570 −1.15090 −0.575452 0.817836i \(-0.695174\pi\)
−0.575452 + 0.817836i \(0.695174\pi\)
\(674\) −3.03332 −0.116839
\(675\) −16.8270 −0.647673
\(676\) −7.92452 −0.304789
\(677\) −35.7525 −1.37408 −0.687040 0.726620i \(-0.741090\pi\)
−0.687040 + 0.726620i \(0.741090\pi\)
\(678\) −0.752197 −0.0288879
\(679\) −10.9938 −0.421903
\(680\) −2.13331 −0.0818089
\(681\) 1.38557 0.0530950
\(682\) 6.41474 0.245633
\(683\) 14.0646 0.538166 0.269083 0.963117i \(-0.413279\pi\)
0.269083 + 0.963117i \(0.413279\pi\)
\(684\) −12.1017 −0.462719
\(685\) 7.66652 0.292923
\(686\) −8.34017 −0.318429
\(687\) 0.599445 0.0228702
\(688\) −10.8219 −0.412580
\(689\) 6.17373 0.235200
\(690\) 0.445922 0.0169760
\(691\) −16.8164 −0.639725 −0.319862 0.947464i \(-0.603637\pi\)
−0.319862 + 0.947464i \(0.603637\pi\)
\(692\) −19.1710 −0.728772
\(693\) −23.1603 −0.879787
\(694\) 25.7632 0.977957
\(695\) −0.0147675 −0.000560161 0
\(696\) −6.03940 −0.228923
\(697\) 33.0703 1.25263
\(698\) −23.9822 −0.907739
\(699\) −6.77135 −0.256116
\(700\) 15.4631 0.584450
\(701\) −10.7148 −0.404693 −0.202347 0.979314i \(-0.564857\pi\)
−0.202347 + 0.979314i \(0.564857\pi\)
\(702\) −8.33021 −0.314404
\(703\) 47.3883 1.78729
\(704\) −2.66536 −0.100455
\(705\) −0.948153 −0.0357095
\(706\) −5.56720 −0.209524
\(707\) 40.5721 1.52587
\(708\) −1.46164 −0.0549318
\(709\) −26.3019 −0.987788 −0.493894 0.869522i \(-0.664427\pi\)
−0.493894 + 0.869522i \(0.664427\pi\)
\(710\) −8.88900 −0.333598
\(711\) 16.1513 0.605720
\(712\) −13.3914 −0.501863
\(713\) 2.40671 0.0901318
\(714\) −7.19628 −0.269314
\(715\) −4.02439 −0.150504
\(716\) −2.38254 −0.0890397
\(717\) 7.67748 0.286721
\(718\) 16.2677 0.607105
\(719\) 46.0316 1.71669 0.858345 0.513074i \(-0.171493\pi\)
0.858345 + 0.513074i \(0.171493\pi\)
\(720\) −1.71391 −0.0638736
\(721\) −14.7734 −0.550190
\(722\) −3.39373 −0.126302
\(723\) 3.94510 0.146720
\(724\) −19.0100 −0.706501
\(725\) 41.3077 1.53413
\(726\) −2.59212 −0.0962027
\(727\) 9.59565 0.355883 0.177941 0.984041i \(-0.443056\pi\)
0.177941 + 0.984041i \(0.443056\pi\)
\(728\) 7.65499 0.283713
\(729\) −5.94731 −0.220271
\(730\) −0.255394 −0.00945257
\(731\) −34.4470 −1.27407
\(732\) −0.578498 −0.0213819
\(733\) 19.9457 0.736710 0.368355 0.929685i \(-0.379921\pi\)
0.368355 + 0.929685i \(0.379921\pi\)
\(734\) 1.48940 0.0549749
\(735\) −2.02692 −0.0747642
\(736\) −1.00000 −0.0368605
\(737\) 14.7931 0.544913
\(738\) 26.5688 0.978010
\(739\) 13.3186 0.489934 0.244967 0.969531i \(-0.421223\pi\)
0.244967 + 0.969531i \(0.421223\pi\)
\(740\) 6.71141 0.246716
\(741\) −7.09341 −0.260583
\(742\) 9.31139 0.341832
\(743\) −3.66185 −0.134340 −0.0671702 0.997742i \(-0.521397\pi\)
−0.0671702 + 0.997742i \(0.521397\pi\)
\(744\) 1.60131 0.0587070
\(745\) −8.53598 −0.312734
\(746\) −6.34579 −0.232336
\(747\) 21.7322 0.795141
\(748\) −8.48409 −0.310209
\(749\) 30.9907 1.13238
\(750\) −4.25893 −0.155514
\(751\) −14.0114 −0.511283 −0.255641 0.966772i \(-0.582287\pi\)
−0.255641 + 0.966772i \(0.582287\pi\)
\(752\) 2.12628 0.0775373
\(753\) −11.5104 −0.419464
\(754\) 20.4493 0.744721
\(755\) 4.97705 0.181133
\(756\) −12.5639 −0.456943
\(757\) −9.44368 −0.343236 −0.171618 0.985164i \(-0.554900\pi\)
−0.171618 + 0.985164i \(0.554900\pi\)
\(758\) 25.9821 0.943712
\(759\) 1.77341 0.0643707
\(760\) −3.17153 −0.115044
\(761\) −34.1167 −1.23673 −0.618364 0.785892i \(-0.712204\pi\)
−0.618364 + 0.785892i \(0.712204\pi\)
\(762\) −1.73823 −0.0629694
\(763\) −23.6209 −0.855135
\(764\) −7.20331 −0.260607
\(765\) −5.45553 −0.197245
\(766\) 28.2584 1.02102
\(767\) 4.94909 0.178701
\(768\) −0.665355 −0.0240089
\(769\) −16.7212 −0.602984 −0.301492 0.953469i \(-0.597485\pi\)
−0.301492 + 0.953469i \(0.597485\pi\)
\(770\) −6.06970 −0.218737
\(771\) −17.2382 −0.620820
\(772\) −14.5057 −0.522072
\(773\) 43.9077 1.57925 0.789624 0.613590i \(-0.210275\pi\)
0.789624 + 0.613590i \(0.210275\pi\)
\(774\) −27.6748 −0.994751
\(775\) −10.9525 −0.393426
\(776\) −3.23551 −0.116148
\(777\) 22.6395 0.812188
\(778\) −37.0291 −1.32756
\(779\) 49.1646 1.76150
\(780\) −1.00461 −0.0359708
\(781\) −35.3511 −1.26496
\(782\) −3.18309 −0.113827
\(783\) −33.5628 −1.19944
\(784\) 4.54547 0.162338
\(785\) 3.03117 0.108187
\(786\) 0.665355 0.0237324
\(787\) 17.7914 0.634194 0.317097 0.948393i \(-0.397292\pi\)
0.317097 + 0.948393i \(0.397292\pi\)
\(788\) −1.16500 −0.0415014
\(789\) 10.4957 0.373657
\(790\) 4.23282 0.150597
\(791\) 3.84135 0.136583
\(792\) −6.81614 −0.242201
\(793\) 1.95879 0.0695585
\(794\) −13.3645 −0.474288
\(795\) −1.22199 −0.0433395
\(796\) −15.6513 −0.554745
\(797\) 3.81395 0.135097 0.0675484 0.997716i \(-0.478482\pi\)
0.0675484 + 0.997716i \(0.478482\pi\)
\(798\) −10.6985 −0.378722
\(799\) 6.76813 0.239439
\(800\) 4.55083 0.160896
\(801\) −34.2458 −1.21002
\(802\) 11.3007 0.399042
\(803\) −1.01569 −0.0358430
\(804\) 3.69282 0.130236
\(805\) −2.27725 −0.0802626
\(806\) −5.42203 −0.190983
\(807\) 4.06984 0.143265
\(808\) 11.9405 0.420064
\(809\) −31.2612 −1.09909 −0.549543 0.835466i \(-0.685198\pi\)
−0.549543 + 0.835466i \(0.685198\pi\)
\(810\) −3.49290 −0.122728
\(811\) −27.1488 −0.953323 −0.476661 0.879087i \(-0.658153\pi\)
−0.476661 + 0.879087i \(0.658153\pi\)
\(812\) 30.8423 1.08235
\(813\) 6.80819 0.238774
\(814\) 26.6910 0.935518
\(815\) 4.97371 0.174222
\(816\) −2.11789 −0.0741408
\(817\) −51.2113 −1.79166
\(818\) 1.51058 0.0528163
\(819\) 19.5761 0.684045
\(820\) 6.96298 0.243158
\(821\) −19.1189 −0.667255 −0.333627 0.942705i \(-0.608273\pi\)
−0.333627 + 0.942705i \(0.608273\pi\)
\(822\) 7.61108 0.265467
\(823\) −38.3991 −1.33851 −0.669255 0.743033i \(-0.733387\pi\)
−0.669255 + 0.743033i \(0.733387\pi\)
\(824\) −4.34785 −0.151464
\(825\) −8.07049 −0.280978
\(826\) 7.46436 0.259718
\(827\) 6.30986 0.219415 0.109708 0.993964i \(-0.465009\pi\)
0.109708 + 0.993964i \(0.465009\pi\)
\(828\) −2.55730 −0.0888724
\(829\) −3.56625 −0.123861 −0.0619304 0.998080i \(-0.519726\pi\)
−0.0619304 + 0.998080i \(0.519726\pi\)
\(830\) 5.69545 0.197692
\(831\) −15.8954 −0.551405
\(832\) 2.25288 0.0781047
\(833\) 14.4686 0.501309
\(834\) −0.0146607 −0.000507657 0
\(835\) −3.05138 −0.105598
\(836\) −12.6130 −0.436231
\(837\) 8.89898 0.307594
\(838\) −31.3682 −1.08360
\(839\) −23.7059 −0.818419 −0.409209 0.912441i \(-0.634195\pi\)
−0.409209 + 0.912441i \(0.634195\pi\)
\(840\) −1.51518 −0.0522787
\(841\) 53.3912 1.84108
\(842\) 33.4032 1.15115
\(843\) −15.0031 −0.516733
\(844\) −20.4743 −0.704754
\(845\) −5.31103 −0.182705
\(846\) 5.43753 0.186946
\(847\) 13.2376 0.454848
\(848\) 2.74037 0.0941046
\(849\) −11.5952 −0.397947
\(850\) 14.4857 0.496856
\(851\) 10.0140 0.343276
\(852\) −8.82471 −0.302330
\(853\) −13.6342 −0.466827 −0.233414 0.972378i \(-0.574990\pi\)
−0.233414 + 0.972378i \(0.574990\pi\)
\(854\) 2.95430 0.101094
\(855\) −8.11056 −0.277375
\(856\) 9.12065 0.311737
\(857\) 33.9476 1.15963 0.579815 0.814748i \(-0.303125\pi\)
0.579815 + 0.814748i \(0.303125\pi\)
\(858\) −3.99529 −0.136397
\(859\) −35.5735 −1.21375 −0.606876 0.794797i \(-0.707577\pi\)
−0.606876 + 0.794797i \(0.707577\pi\)
\(860\) −7.25284 −0.247320
\(861\) 23.4881 0.800473
\(862\) 29.8622 1.01711
\(863\) −0.895710 −0.0304903 −0.0152452 0.999884i \(-0.504853\pi\)
−0.0152452 + 0.999884i \(0.504853\pi\)
\(864\) −3.69758 −0.125794
\(865\) −12.8484 −0.436860
\(866\) 25.3290 0.860715
\(867\) 4.56960 0.155192
\(868\) −8.17765 −0.277568
\(869\) 16.8337 0.571046
\(870\) −4.04762 −0.137227
\(871\) −12.5038 −0.423676
\(872\) −6.95171 −0.235414
\(873\) −8.27417 −0.280038
\(874\) −4.73220 −0.160069
\(875\) 21.7497 0.735273
\(876\) −0.253547 −0.00856657
\(877\) −34.8547 −1.17696 −0.588480 0.808512i \(-0.700273\pi\)
−0.588480 + 0.808512i \(0.700273\pi\)
\(878\) 5.73920 0.193689
\(879\) 2.20207 0.0742741
\(880\) −1.78633 −0.0602172
\(881\) −48.2420 −1.62531 −0.812657 0.582742i \(-0.801980\pi\)
−0.812657 + 0.582742i \(0.801980\pi\)
\(882\) 11.6241 0.391405
\(883\) 26.9038 0.905386 0.452693 0.891666i \(-0.350463\pi\)
0.452693 + 0.891666i \(0.350463\pi\)
\(884\) 7.17114 0.241191
\(885\) −0.979593 −0.0329287
\(886\) 14.6720 0.492917
\(887\) 3.29742 0.110717 0.0553583 0.998467i \(-0.482370\pi\)
0.0553583 + 0.998467i \(0.482370\pi\)
\(888\) 6.66287 0.223591
\(889\) 8.87686 0.297720
\(890\) −8.97493 −0.300840
\(891\) −13.8911 −0.465369
\(892\) −15.6735 −0.524787
\(893\) 10.0620 0.336711
\(894\) −8.47424 −0.283421
\(895\) −1.59678 −0.0533746
\(896\) 3.39786 0.113515
\(897\) −1.49897 −0.0500490
\(898\) 3.29391 0.109919
\(899\) −21.8456 −0.728591
\(900\) 11.6378 0.387928
\(901\) 8.72284 0.290600
\(902\) 27.6914 0.922024
\(903\) −24.4659 −0.814175
\(904\) 1.13052 0.0376005
\(905\) −12.7405 −0.423510
\(906\) 4.94106 0.164156
\(907\) 19.4964 0.647366 0.323683 0.946166i \(-0.395079\pi\)
0.323683 + 0.946166i \(0.395079\pi\)
\(908\) −2.08245 −0.0691084
\(909\) 30.5354 1.01280
\(910\) 5.13039 0.170071
\(911\) 43.3798 1.43724 0.718618 0.695405i \(-0.244775\pi\)
0.718618 + 0.695405i \(0.244775\pi\)
\(912\) −3.14859 −0.104260
\(913\) 22.6505 0.749623
\(914\) −4.46826 −0.147797
\(915\) −0.387710 −0.0128173
\(916\) −0.900940 −0.0297679
\(917\) −3.39786 −0.112207
\(918\) −11.7697 −0.388459
\(919\) −13.9411 −0.459874 −0.229937 0.973206i \(-0.573852\pi\)
−0.229937 + 0.973206i \(0.573852\pi\)
\(920\) −0.670202 −0.0220959
\(921\) 8.88874 0.292894
\(922\) 21.9946 0.724353
\(923\) 29.8804 0.983524
\(924\) −6.02581 −0.198234
\(925\) −45.5721 −1.49840
\(926\) −4.28775 −0.140904
\(927\) −11.1188 −0.365188
\(928\) 9.07696 0.297966
\(929\) 41.2786 1.35431 0.677154 0.735842i \(-0.263213\pi\)
0.677154 + 0.735842i \(0.263213\pi\)
\(930\) 1.07320 0.0351917
\(931\) 21.5101 0.704964
\(932\) 10.1771 0.333361
\(933\) 13.2150 0.432640
\(934\) 39.0018 1.27618
\(935\) −5.68605 −0.185954
\(936\) 5.76131 0.188314
\(937\) −7.35757 −0.240361 −0.120181 0.992752i \(-0.538347\pi\)
−0.120181 + 0.992752i \(0.538347\pi\)
\(938\) −18.8586 −0.615756
\(939\) 14.1775 0.462666
\(940\) 1.42503 0.0464795
\(941\) 10.3822 0.338451 0.169225 0.985577i \(-0.445873\pi\)
0.169225 + 0.985577i \(0.445873\pi\)
\(942\) 3.00925 0.0980466
\(943\) 10.3894 0.338324
\(944\) 2.19678 0.0714991
\(945\) −8.42032 −0.273913
\(946\) −28.8442 −0.937806
\(947\) 15.7911 0.513141 0.256570 0.966526i \(-0.417407\pi\)
0.256570 + 0.966526i \(0.417407\pi\)
\(948\) 4.20221 0.136481
\(949\) 0.858508 0.0278684
\(950\) 21.5354 0.698702
\(951\) −15.7359 −0.510272
\(952\) 10.8157 0.350539
\(953\) 30.8900 1.00063 0.500313 0.865845i \(-0.333218\pi\)
0.500313 + 0.865845i \(0.333218\pi\)
\(954\) 7.00795 0.226891
\(955\) −4.82767 −0.156220
\(956\) −11.5389 −0.373196
\(957\) −16.0972 −0.520348
\(958\) −15.6867 −0.506816
\(959\) −38.8686 −1.25513
\(960\) −0.445922 −0.0143921
\(961\) −25.2078 −0.813154
\(962\) −22.5604 −0.727377
\(963\) 23.3243 0.751614
\(964\) −5.92932 −0.190971
\(965\) −9.72176 −0.312955
\(966\) −2.26078 −0.0727395
\(967\) 37.0403 1.19114 0.595568 0.803305i \(-0.296927\pi\)
0.595568 + 0.803305i \(0.296927\pi\)
\(968\) 3.89585 0.125217
\(969\) −10.0223 −0.321961
\(970\) −2.16844 −0.0696245
\(971\) −53.6435 −1.72150 −0.860750 0.509028i \(-0.830005\pi\)
−0.860750 + 0.509028i \(0.830005\pi\)
\(972\) −14.5604 −0.467024
\(973\) 0.0748696 0.00240021
\(974\) 9.11804 0.292161
\(975\) 6.82154 0.218464
\(976\) 0.869457 0.0278307
\(977\) −38.9609 −1.24647 −0.623235 0.782034i \(-0.714182\pi\)
−0.623235 + 0.782034i \(0.714182\pi\)
\(978\) 4.93774 0.157892
\(979\) −35.6929 −1.14075
\(980\) 3.04638 0.0973130
\(981\) −17.7776 −0.567596
\(982\) 27.2290 0.868911
\(983\) 48.9246 1.56045 0.780227 0.625497i \(-0.215104\pi\)
0.780227 + 0.625497i \(0.215104\pi\)
\(984\) 6.91262 0.220366
\(985\) −0.780785 −0.0248779
\(986\) 28.8928 0.920134
\(987\) 4.80705 0.153010
\(988\) 10.6611 0.339175
\(989\) −10.8219 −0.344116
\(990\) −4.56819 −0.145187
\(991\) 14.4871 0.460199 0.230100 0.973167i \(-0.426095\pi\)
0.230100 + 0.973167i \(0.426095\pi\)
\(992\) −2.40671 −0.0764130
\(993\) −21.0470 −0.667906
\(994\) 45.0664 1.42942
\(995\) −10.4895 −0.332540
\(996\) 5.65426 0.179162
\(997\) 21.6914 0.686972 0.343486 0.939158i \(-0.388392\pi\)
0.343486 + 0.939158i \(0.388392\pi\)
\(998\) −0.612110 −0.0193760
\(999\) 37.0276 1.17150
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 \(a_p\))