Properties

Label 8007.2.a.e.1.18
Level 8007
Weight 2
Character 8007.1
Self dual Yes
Analytic conductor 63.936
Analytic rank 1
Dimension 46
CM No

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Newspace parameters

Level: \( N \) = \( 8007 = 3 \cdot 17 \cdot 157 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8007.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9362168984\)
Analytic rank: \(1\)
Dimension: \(46\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-0.938469 q^{2}\) \(+1.00000 q^{3}\) \(-1.11928 q^{4}\) \(-3.16176 q^{5}\) \(-0.938469 q^{6}\) \(+3.19339 q^{7}\) \(+2.92734 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-0.938469 q^{2}\) \(+1.00000 q^{3}\) \(-1.11928 q^{4}\) \(-3.16176 q^{5}\) \(-0.938469 q^{6}\) \(+3.19339 q^{7}\) \(+2.92734 q^{8}\) \(+1.00000 q^{9}\) \(+2.96721 q^{10}\) \(-3.89690 q^{11}\) \(-1.11928 q^{12}\) \(+3.99640 q^{13}\) \(-2.99690 q^{14}\) \(-3.16176 q^{15}\) \(-0.508669 q^{16}\) \(-1.00000 q^{17}\) \(-0.938469 q^{18}\) \(-2.61070 q^{19}\) \(+3.53888 q^{20}\) \(+3.19339 q^{21}\) \(+3.65712 q^{22}\) \(-2.63739 q^{23}\) \(+2.92734 q^{24}\) \(+4.99672 q^{25}\) \(-3.75050 q^{26}\) \(+1.00000 q^{27}\) \(-3.57429 q^{28}\) \(-8.17474 q^{29}\) \(+2.96721 q^{30}\) \(+9.36114 q^{31}\) \(-5.37732 q^{32}\) \(-3.89690 q^{33}\) \(+0.938469 q^{34}\) \(-10.0967 q^{35}\) \(-1.11928 q^{36}\) \(+6.64774 q^{37}\) \(+2.45006 q^{38}\) \(+3.99640 q^{39}\) \(-9.25556 q^{40}\) \(+0.367288 q^{41}\) \(-2.99690 q^{42}\) \(+5.19918 q^{43}\) \(+4.36171 q^{44}\) \(-3.16176 q^{45}\) \(+2.47511 q^{46}\) \(-8.99268 q^{47}\) \(-0.508669 q^{48}\) \(+3.19775 q^{49}\) \(-4.68927 q^{50}\) \(-1.00000 q^{51}\) \(-4.47307 q^{52}\) \(+10.5866 q^{53}\) \(-0.938469 q^{54}\) \(+12.3211 q^{55}\) \(+9.34815 q^{56}\) \(-2.61070 q^{57}\) \(+7.67174 q^{58}\) \(+5.79433 q^{59}\) \(+3.53888 q^{60}\) \(-8.59133 q^{61}\) \(-8.78514 q^{62}\) \(+3.19339 q^{63}\) \(+6.06378 q^{64}\) \(-12.6357 q^{65}\) \(+3.65712 q^{66}\) \(-13.3867 q^{67}\) \(+1.11928 q^{68}\) \(-2.63739 q^{69}\) \(+9.47547 q^{70}\) \(-11.1243 q^{71}\) \(+2.92734 q^{72}\) \(-8.17971 q^{73}\) \(-6.23870 q^{74}\) \(+4.99672 q^{75}\) \(+2.92210 q^{76}\) \(-12.4443 q^{77}\) \(-3.75050 q^{78}\) \(+6.91010 q^{79}\) \(+1.60829 q^{80}\) \(+1.00000 q^{81}\) \(-0.344688 q^{82}\) \(+4.30590 q^{83}\) \(-3.57429 q^{84}\) \(+3.16176 q^{85}\) \(-4.87927 q^{86}\) \(-8.17474 q^{87}\) \(-11.4076 q^{88}\) \(-0.653746 q^{89}\) \(+2.96721 q^{90}\) \(+12.7621 q^{91}\) \(+2.95197 q^{92}\) \(+9.36114 q^{93}\) \(+8.43935 q^{94}\) \(+8.25441 q^{95}\) \(-5.37732 q^{96}\) \(+17.7265 q^{97}\) \(-3.00099 q^{98}\) \(-3.89690 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(46q \) \(\mathstrut -\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 46q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut q^{7} \) \(\mathstrut -\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 46q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(46q \) \(\mathstrut -\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 46q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut q^{7} \) \(\mathstrut -\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 46q^{9} \) \(\mathstrut -\mathstrut 10q^{10} \) \(\mathstrut -\mathstrut 25q^{11} \) \(\mathstrut +\mathstrut 43q^{12} \) \(\mathstrut -\mathstrut 8q^{13} \) \(\mathstrut -\mathstrut 28q^{14} \) \(\mathstrut -\mathstrut 19q^{15} \) \(\mathstrut +\mathstrut 33q^{16} \) \(\mathstrut -\mathstrut 46q^{17} \) \(\mathstrut -\mathstrut 5q^{18} \) \(\mathstrut -\mathstrut 2q^{19} \) \(\mathstrut -\mathstrut 56q^{20} \) \(\mathstrut +\mathstrut q^{21} \) \(\mathstrut -\mathstrut 19q^{22} \) \(\mathstrut -\mathstrut 64q^{23} \) \(\mathstrut -\mathstrut 18q^{24} \) \(\mathstrut +\mathstrut 11q^{25} \) \(\mathstrut -\mathstrut 13q^{26} \) \(\mathstrut +\mathstrut 46q^{27} \) \(\mathstrut -\mathstrut 38q^{28} \) \(\mathstrut -\mathstrut 51q^{29} \) \(\mathstrut -\mathstrut 10q^{30} \) \(\mathstrut -\mathstrut 19q^{31} \) \(\mathstrut -\mathstrut 61q^{32} \) \(\mathstrut -\mathstrut 25q^{33} \) \(\mathstrut +\mathstrut 5q^{34} \) \(\mathstrut -\mathstrut 39q^{35} \) \(\mathstrut +\mathstrut 43q^{36} \) \(\mathstrut -\mathstrut 46q^{37} \) \(\mathstrut -\mathstrut 48q^{38} \) \(\mathstrut -\mathstrut 8q^{39} \) \(\mathstrut -\mathstrut 10q^{40} \) \(\mathstrut -\mathstrut 53q^{41} \) \(\mathstrut -\mathstrut 28q^{42} \) \(\mathstrut -\mathstrut 33q^{43} \) \(\mathstrut -\mathstrut 62q^{44} \) \(\mathstrut -\mathstrut 19q^{45} \) \(\mathstrut +\mathstrut 2q^{46} \) \(\mathstrut -\mathstrut 45q^{47} \) \(\mathstrut +\mathstrut 33q^{48} \) \(\mathstrut +\mathstrut 21q^{49} \) \(\mathstrut -\mathstrut 60q^{50} \) \(\mathstrut -\mathstrut 46q^{51} \) \(\mathstrut -\mathstrut 63q^{52} \) \(\mathstrut -\mathstrut 47q^{53} \) \(\mathstrut -\mathstrut 5q^{54} \) \(\mathstrut +\mathstrut 5q^{55} \) \(\mathstrut -\mathstrut 82q^{56} \) \(\mathstrut -\mathstrut 2q^{57} \) \(\mathstrut -\mathstrut 21q^{58} \) \(\mathstrut -\mathstrut 65q^{59} \) \(\mathstrut -\mathstrut 56q^{60} \) \(\mathstrut -\mathstrut 37q^{61} \) \(\mathstrut -\mathstrut 46q^{62} \) \(\mathstrut +\mathstrut q^{63} \) \(\mathstrut +\mathstrut 74q^{64} \) \(\mathstrut -\mathstrut 85q^{65} \) \(\mathstrut -\mathstrut 19q^{66} \) \(\mathstrut -\mathstrut 52q^{67} \) \(\mathstrut -\mathstrut 43q^{68} \) \(\mathstrut -\mathstrut 64q^{69} \) \(\mathstrut -\mathstrut 20q^{70} \) \(\mathstrut -\mathstrut 48q^{71} \) \(\mathstrut -\mathstrut 18q^{72} \) \(\mathstrut -\mathstrut 39q^{73} \) \(\mathstrut -\mathstrut 16q^{74} \) \(\mathstrut +\mathstrut 11q^{75} \) \(\mathstrut +\mathstrut 42q^{76} \) \(\mathstrut -\mathstrut 78q^{77} \) \(\mathstrut -\mathstrut 13q^{78} \) \(\mathstrut -\mathstrut 26q^{79} \) \(\mathstrut -\mathstrut 78q^{80} \) \(\mathstrut +\mathstrut 46q^{81} \) \(\mathstrut +\mathstrut 3q^{82} \) \(\mathstrut -\mathstrut 47q^{83} \) \(\mathstrut -\mathstrut 38q^{84} \) \(\mathstrut +\mathstrut 19q^{85} \) \(\mathstrut -\mathstrut 6q^{86} \) \(\mathstrut -\mathstrut 51q^{87} \) \(\mathstrut -\mathstrut 58q^{88} \) \(\mathstrut -\mathstrut 58q^{89} \) \(\mathstrut -\mathstrut 10q^{90} \) \(\mathstrut -\mathstrut 43q^{91} \) \(\mathstrut -\mathstrut 68q^{92} \) \(\mathstrut -\mathstrut 19q^{93} \) \(\mathstrut -\mathstrut 78q^{95} \) \(\mathstrut -\mathstrut 61q^{96} \) \(\mathstrut -\mathstrut 44q^{97} \) \(\mathstrut -\mathstrut 4q^{98} \) \(\mathstrut -\mathstrut 25q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.938469 −0.663598 −0.331799 0.943350i \(-0.607656\pi\)
−0.331799 + 0.943350i \(0.607656\pi\)
\(3\) 1.00000 0.577350
\(4\) −1.11928 −0.559638
\(5\) −3.16176 −1.41398 −0.706991 0.707223i \(-0.749948\pi\)
−0.706991 + 0.707223i \(0.749948\pi\)
\(6\) −0.938469 −0.383128
\(7\) 3.19339 1.20699 0.603494 0.797367i \(-0.293775\pi\)
0.603494 + 0.797367i \(0.293775\pi\)
\(8\) 2.92734 1.03497
\(9\) 1.00000 0.333333
\(10\) 2.96721 0.938315
\(11\) −3.89690 −1.17496 −0.587480 0.809239i \(-0.699880\pi\)
−0.587480 + 0.809239i \(0.699880\pi\)
\(12\) −1.11928 −0.323107
\(13\) 3.99640 1.10840 0.554201 0.832383i \(-0.313024\pi\)
0.554201 + 0.832383i \(0.313024\pi\)
\(14\) −2.99690 −0.800955
\(15\) −3.16176 −0.816363
\(16\) −0.508669 −0.127167
\(17\) −1.00000 −0.242536
\(18\) −0.938469 −0.221199
\(19\) −2.61070 −0.598936 −0.299468 0.954106i \(-0.596809\pi\)
−0.299468 + 0.954106i \(0.596809\pi\)
\(20\) 3.53888 0.791318
\(21\) 3.19339 0.696855
\(22\) 3.65712 0.779701
\(23\) −2.63739 −0.549934 −0.274967 0.961454i \(-0.588667\pi\)
−0.274967 + 0.961454i \(0.588667\pi\)
\(24\) 2.92734 0.597542
\(25\) 4.99672 0.999344
\(26\) −3.75050 −0.735533
\(27\) 1.00000 0.192450
\(28\) −3.57429 −0.675477
\(29\) −8.17474 −1.51801 −0.759005 0.651084i \(-0.774314\pi\)
−0.759005 + 0.651084i \(0.774314\pi\)
\(30\) 2.96721 0.541736
\(31\) 9.36114 1.68131 0.840656 0.541570i \(-0.182170\pi\)
0.840656 + 0.541570i \(0.182170\pi\)
\(32\) −5.37732 −0.950584
\(33\) −3.89690 −0.678364
\(34\) 0.938469 0.160946
\(35\) −10.0967 −1.70666
\(36\) −1.11928 −0.186546
\(37\) 6.64774 1.09288 0.546441 0.837498i \(-0.315982\pi\)
0.546441 + 0.837498i \(0.315982\pi\)
\(38\) 2.45006 0.397453
\(39\) 3.99640 0.639936
\(40\) −9.25556 −1.46343
\(41\) 0.367288 0.0573607 0.0286804 0.999589i \(-0.490870\pi\)
0.0286804 + 0.999589i \(0.490870\pi\)
\(42\) −2.99690 −0.462432
\(43\) 5.19918 0.792868 0.396434 0.918063i \(-0.370248\pi\)
0.396434 + 0.918063i \(0.370248\pi\)
\(44\) 4.36171 0.657552
\(45\) −3.16176 −0.471327
\(46\) 2.47511 0.364935
\(47\) −8.99268 −1.31172 −0.655859 0.754884i \(-0.727693\pi\)
−0.655859 + 0.754884i \(0.727693\pi\)
\(48\) −0.508669 −0.0734200
\(49\) 3.19775 0.456821
\(50\) −4.68927 −0.663162
\(51\) −1.00000 −0.140028
\(52\) −4.47307 −0.620304
\(53\) 10.5866 1.45418 0.727090 0.686543i \(-0.240872\pi\)
0.727090 + 0.686543i \(0.240872\pi\)
\(54\) −0.938469 −0.127709
\(55\) 12.3211 1.66137
\(56\) 9.34815 1.24920
\(57\) −2.61070 −0.345796
\(58\) 7.67174 1.00735
\(59\) 5.79433 0.754358 0.377179 0.926140i \(-0.376894\pi\)
0.377179 + 0.926140i \(0.376894\pi\)
\(60\) 3.53888 0.456868
\(61\) −8.59133 −1.10001 −0.550004 0.835162i \(-0.685374\pi\)
−0.550004 + 0.835162i \(0.685374\pi\)
\(62\) −8.78514 −1.11571
\(63\) 3.19339 0.402330
\(64\) 6.06378 0.757973
\(65\) −12.6357 −1.56726
\(66\) 3.65712 0.450161
\(67\) −13.3867 −1.63545 −0.817723 0.575612i \(-0.804764\pi\)
−0.817723 + 0.575612i \(0.804764\pi\)
\(68\) 1.11928 0.135732
\(69\) −2.63739 −0.317504
\(70\) 9.47547 1.13254
\(71\) −11.1243 −1.32021 −0.660103 0.751175i \(-0.729487\pi\)
−0.660103 + 0.751175i \(0.729487\pi\)
\(72\) 2.92734 0.344991
\(73\) −8.17971 −0.957362 −0.478681 0.877989i \(-0.658885\pi\)
−0.478681 + 0.877989i \(0.658885\pi\)
\(74\) −6.23870 −0.725234
\(75\) 4.99672 0.576972
\(76\) 2.92210 0.335187
\(77\) −12.4443 −1.41816
\(78\) −3.75050 −0.424660
\(79\) 6.91010 0.777447 0.388724 0.921354i \(-0.372916\pi\)
0.388724 + 0.921354i \(0.372916\pi\)
\(80\) 1.60829 0.179812
\(81\) 1.00000 0.111111
\(82\) −0.344688 −0.0380645
\(83\) 4.30590 0.472634 0.236317 0.971676i \(-0.424060\pi\)
0.236317 + 0.971676i \(0.424060\pi\)
\(84\) −3.57429 −0.389987
\(85\) 3.16176 0.342941
\(86\) −4.87927 −0.526145
\(87\) −8.17474 −0.876424
\(88\) −11.4076 −1.21605
\(89\) −0.653746 −0.0692970 −0.0346485 0.999400i \(-0.511031\pi\)
−0.0346485 + 0.999400i \(0.511031\pi\)
\(90\) 2.96721 0.312772
\(91\) 12.7621 1.33783
\(92\) 2.95197 0.307764
\(93\) 9.36114 0.970706
\(94\) 8.43935 0.870453
\(95\) 8.25441 0.846885
\(96\) −5.37732 −0.548820
\(97\) 17.7265 1.79985 0.899926 0.436043i \(-0.143620\pi\)
0.899926 + 0.436043i \(0.143620\pi\)
\(98\) −3.00099 −0.303146
\(99\) −3.89690 −0.391653
\(100\) −5.59271 −0.559271
\(101\) 4.42409 0.440214 0.220107 0.975476i \(-0.429359\pi\)
0.220107 + 0.975476i \(0.429359\pi\)
\(102\) 0.938469 0.0929223
\(103\) −4.43823 −0.437312 −0.218656 0.975802i \(-0.570167\pi\)
−0.218656 + 0.975802i \(0.570167\pi\)
\(104\) 11.6988 1.14717
\(105\) −10.0967 −0.985340
\(106\) −9.93518 −0.964990
\(107\) −7.01299 −0.677971 −0.338986 0.940792i \(-0.610084\pi\)
−0.338986 + 0.940792i \(0.610084\pi\)
\(108\) −1.11928 −0.107702
\(109\) −2.69617 −0.258246 −0.129123 0.991629i \(-0.541216\pi\)
−0.129123 + 0.991629i \(0.541216\pi\)
\(110\) −11.5629 −1.10248
\(111\) 6.64774 0.630976
\(112\) −1.62438 −0.153489
\(113\) 3.47775 0.327159 0.163579 0.986530i \(-0.447696\pi\)
0.163579 + 0.986530i \(0.447696\pi\)
\(114\) 2.45006 0.229469
\(115\) 8.33879 0.777596
\(116\) 9.14979 0.849537
\(117\) 3.99640 0.369467
\(118\) −5.43780 −0.500590
\(119\) −3.19339 −0.292738
\(120\) −9.25556 −0.844913
\(121\) 4.18585 0.380532
\(122\) 8.06270 0.729962
\(123\) 0.367288 0.0331172
\(124\) −10.4777 −0.940926
\(125\) 0.0103688 0.000927417 0
\(126\) −2.99690 −0.266985
\(127\) −15.2780 −1.35571 −0.677853 0.735197i \(-0.737090\pi\)
−0.677853 + 0.735197i \(0.737090\pi\)
\(128\) 5.06396 0.447595
\(129\) 5.19918 0.457762
\(130\) 11.8582 1.04003
\(131\) 13.0166 1.13727 0.568633 0.822591i \(-0.307472\pi\)
0.568633 + 0.822591i \(0.307472\pi\)
\(132\) 4.36171 0.379638
\(133\) −8.33699 −0.722909
\(134\) 12.5630 1.08528
\(135\) −3.16176 −0.272121
\(136\) −2.92734 −0.251018
\(137\) −8.48559 −0.724973 −0.362486 0.931989i \(-0.618072\pi\)
−0.362486 + 0.931989i \(0.618072\pi\)
\(138\) 2.47511 0.210695
\(139\) −16.1044 −1.36596 −0.682980 0.730437i \(-0.739316\pi\)
−0.682980 + 0.730437i \(0.739316\pi\)
\(140\) 11.3010 0.955112
\(141\) −8.99268 −0.757320
\(142\) 10.4398 0.876086
\(143\) −15.5736 −1.30233
\(144\) −0.508669 −0.0423891
\(145\) 25.8466 2.14644
\(146\) 7.67640 0.635303
\(147\) 3.19775 0.263746
\(148\) −7.44066 −0.611618
\(149\) −7.77400 −0.636871 −0.318436 0.947945i \(-0.603157\pi\)
−0.318436 + 0.947945i \(0.603157\pi\)
\(150\) −4.68927 −0.382877
\(151\) −6.12281 −0.498267 −0.249134 0.968469i \(-0.580146\pi\)
−0.249134 + 0.968469i \(0.580146\pi\)
\(152\) −7.64242 −0.619882
\(153\) −1.00000 −0.0808452
\(154\) 11.6786 0.941090
\(155\) −29.5977 −2.37734
\(156\) −4.47307 −0.358133
\(157\) 1.00000 0.0798087
\(158\) −6.48492 −0.515912
\(159\) 10.5866 0.839571
\(160\) 17.0018 1.34411
\(161\) −8.42222 −0.663764
\(162\) −0.938469 −0.0737331
\(163\) 18.3261 1.43541 0.717705 0.696347i \(-0.245192\pi\)
0.717705 + 0.696347i \(0.245192\pi\)
\(164\) −0.411097 −0.0321013
\(165\) 12.3211 0.959194
\(166\) −4.04095 −0.313639
\(167\) 7.02150 0.543340 0.271670 0.962390i \(-0.412424\pi\)
0.271670 + 0.962390i \(0.412424\pi\)
\(168\) 9.34815 0.721226
\(169\) 2.97121 0.228555
\(170\) −2.96721 −0.227575
\(171\) −2.61070 −0.199645
\(172\) −5.81932 −0.443719
\(173\) 7.26500 0.552348 0.276174 0.961108i \(-0.410933\pi\)
0.276174 + 0.961108i \(0.410933\pi\)
\(174\) 7.67174 0.581593
\(175\) 15.9565 1.20620
\(176\) 1.98223 0.149416
\(177\) 5.79433 0.435529
\(178\) 0.613521 0.0459853
\(179\) 23.1191 1.72800 0.864001 0.503490i \(-0.167951\pi\)
0.864001 + 0.503490i \(0.167951\pi\)
\(180\) 3.53888 0.263773
\(181\) −9.53173 −0.708488 −0.354244 0.935153i \(-0.615262\pi\)
−0.354244 + 0.935153i \(0.615262\pi\)
\(182\) −11.9768 −0.887780
\(183\) −8.59133 −0.635089
\(184\) −7.72054 −0.569166
\(185\) −21.0186 −1.54531
\(186\) −8.78514 −0.644158
\(187\) 3.89690 0.284970
\(188\) 10.0653 0.734087
\(189\) 3.19339 0.232285
\(190\) −7.74651 −0.561991
\(191\) 21.7974 1.57720 0.788601 0.614906i \(-0.210806\pi\)
0.788601 + 0.614906i \(0.210806\pi\)
\(192\) 6.06378 0.437616
\(193\) 3.66453 0.263779 0.131889 0.991264i \(-0.457896\pi\)
0.131889 + 0.991264i \(0.457896\pi\)
\(194\) −16.6358 −1.19438
\(195\) −12.6357 −0.904858
\(196\) −3.57916 −0.255655
\(197\) 11.3572 0.809168 0.404584 0.914501i \(-0.367416\pi\)
0.404584 + 0.914501i \(0.367416\pi\)
\(198\) 3.65712 0.259900
\(199\) −6.77838 −0.480506 −0.240253 0.970710i \(-0.577230\pi\)
−0.240253 + 0.970710i \(0.577230\pi\)
\(200\) 14.6271 1.03429
\(201\) −13.3867 −0.944225
\(202\) −4.15187 −0.292125
\(203\) −26.1051 −1.83222
\(204\) 1.11928 0.0783650
\(205\) −1.16128 −0.0811070
\(206\) 4.16514 0.290199
\(207\) −2.63739 −0.183311
\(208\) −2.03284 −0.140952
\(209\) 10.1736 0.703726
\(210\) 9.47547 0.653870
\(211\) −0.321094 −0.0221050 −0.0110525 0.999939i \(-0.503518\pi\)
−0.0110525 + 0.999939i \(0.503518\pi\)
\(212\) −11.8493 −0.813814
\(213\) −11.1243 −0.762221
\(214\) 6.58147 0.449900
\(215\) −16.4386 −1.12110
\(216\) 2.92734 0.199181
\(217\) 29.8938 2.02932
\(218\) 2.53027 0.171371
\(219\) −8.17971 −0.552733
\(220\) −13.7907 −0.929767
\(221\) −3.99640 −0.268827
\(222\) −6.23870 −0.418714
\(223\) 5.06897 0.339444 0.169722 0.985492i \(-0.445713\pi\)
0.169722 + 0.985492i \(0.445713\pi\)
\(224\) −17.1719 −1.14734
\(225\) 4.99672 0.333115
\(226\) −3.26376 −0.217102
\(227\) −12.3705 −0.821061 −0.410530 0.911847i \(-0.634656\pi\)
−0.410530 + 0.911847i \(0.634656\pi\)
\(228\) 2.92210 0.193521
\(229\) 4.56787 0.301853 0.150927 0.988545i \(-0.451774\pi\)
0.150927 + 0.988545i \(0.451774\pi\)
\(230\) −7.82569 −0.516011
\(231\) −12.4443 −0.818777
\(232\) −23.9303 −1.57110
\(233\) −26.2130 −1.71727 −0.858636 0.512585i \(-0.828688\pi\)
−0.858636 + 0.512585i \(0.828688\pi\)
\(234\) −3.75050 −0.245178
\(235\) 28.4327 1.85474
\(236\) −6.48546 −0.422167
\(237\) 6.91010 0.448859
\(238\) 2.99690 0.194260
\(239\) 14.5206 0.939262 0.469631 0.882863i \(-0.344387\pi\)
0.469631 + 0.882863i \(0.344387\pi\)
\(240\) 1.60829 0.103815
\(241\) −17.0645 −1.09922 −0.549611 0.835421i \(-0.685224\pi\)
−0.549611 + 0.835421i \(0.685224\pi\)
\(242\) −3.92829 −0.252520
\(243\) 1.00000 0.0641500
\(244\) 9.61607 0.615606
\(245\) −10.1105 −0.645937
\(246\) −0.344688 −0.0219765
\(247\) −10.4334 −0.663862
\(248\) 27.4033 1.74011
\(249\) 4.30590 0.272875
\(250\) −0.00973083 −0.000615432 0
\(251\) 12.1258 0.765375 0.382687 0.923878i \(-0.374999\pi\)
0.382687 + 0.923878i \(0.374999\pi\)
\(252\) −3.57429 −0.225159
\(253\) 10.2776 0.646150
\(254\) 14.3380 0.899644
\(255\) 3.16176 0.197997
\(256\) −16.8799 −1.05500
\(257\) −4.73637 −0.295446 −0.147723 0.989029i \(-0.547194\pi\)
−0.147723 + 0.989029i \(0.547194\pi\)
\(258\) −4.87927 −0.303770
\(259\) 21.2288 1.31910
\(260\) 14.1428 0.877098
\(261\) −8.17474 −0.506004
\(262\) −12.2157 −0.754687
\(263\) 0.820477 0.0505928 0.0252964 0.999680i \(-0.491947\pi\)
0.0252964 + 0.999680i \(0.491947\pi\)
\(264\) −11.4076 −0.702088
\(265\) −33.4722 −2.05618
\(266\) 7.82401 0.479721
\(267\) −0.653746 −0.0400086
\(268\) 14.9834 0.915258
\(269\) −21.8863 −1.33443 −0.667214 0.744866i \(-0.732514\pi\)
−0.667214 + 0.744866i \(0.732514\pi\)
\(270\) 2.96721 0.180579
\(271\) −30.4449 −1.84940 −0.924698 0.380703i \(-0.875682\pi\)
−0.924698 + 0.380703i \(0.875682\pi\)
\(272\) 0.508669 0.0308426
\(273\) 12.7621 0.772396
\(274\) 7.96346 0.481090
\(275\) −19.4717 −1.17419
\(276\) 2.95197 0.177687
\(277\) −14.7706 −0.887481 −0.443741 0.896155i \(-0.646349\pi\)
−0.443741 + 0.896155i \(0.646349\pi\)
\(278\) 15.1135 0.906448
\(279\) 9.36114 0.560437
\(280\) −29.5566 −1.76635
\(281\) 4.52998 0.270236 0.135118 0.990830i \(-0.456859\pi\)
0.135118 + 0.990830i \(0.456859\pi\)
\(282\) 8.43935 0.502556
\(283\) 23.1198 1.37433 0.687164 0.726503i \(-0.258856\pi\)
0.687164 + 0.726503i \(0.258856\pi\)
\(284\) 12.4511 0.738838
\(285\) 8.25441 0.488949
\(286\) 14.6153 0.864222
\(287\) 1.17289 0.0692338
\(288\) −5.37732 −0.316861
\(289\) 1.00000 0.0588235
\(290\) −24.2562 −1.42437
\(291\) 17.7265 1.03914
\(292\) 9.15535 0.535776
\(293\) 10.0891 0.589413 0.294706 0.955588i \(-0.404778\pi\)
0.294706 + 0.955588i \(0.404778\pi\)
\(294\) −3.00099 −0.175021
\(295\) −18.3203 −1.06665
\(296\) 19.4602 1.13110
\(297\) −3.89690 −0.226121
\(298\) 7.29566 0.422626
\(299\) −10.5401 −0.609547
\(300\) −5.59271 −0.322895
\(301\) 16.6030 0.956982
\(302\) 5.74607 0.330649
\(303\) 4.42409 0.254157
\(304\) 1.32798 0.0761650
\(305\) 27.1637 1.55539
\(306\) 0.938469 0.0536487
\(307\) −1.13614 −0.0648432 −0.0324216 0.999474i \(-0.510322\pi\)
−0.0324216 + 0.999474i \(0.510322\pi\)
\(308\) 13.9286 0.793658
\(309\) −4.43823 −0.252482
\(310\) 27.7765 1.57760
\(311\) −16.6346 −0.943262 −0.471631 0.881796i \(-0.656335\pi\)
−0.471631 + 0.881796i \(0.656335\pi\)
\(312\) 11.6988 0.662316
\(313\) −21.6848 −1.22570 −0.612849 0.790200i \(-0.709977\pi\)
−0.612849 + 0.790200i \(0.709977\pi\)
\(314\) −0.938469 −0.0529609
\(315\) −10.0967 −0.568887
\(316\) −7.73431 −0.435089
\(317\) 23.3728 1.31275 0.656373 0.754436i \(-0.272090\pi\)
0.656373 + 0.754436i \(0.272090\pi\)
\(318\) −9.93518 −0.557137
\(319\) 31.8562 1.78360
\(320\) −19.1722 −1.07176
\(321\) −7.01299 −0.391427
\(322\) 7.90399 0.440472
\(323\) 2.61070 0.145263
\(324\) −1.11928 −0.0621820
\(325\) 19.9689 1.10767
\(326\) −17.1985 −0.952535
\(327\) −2.69617 −0.149098
\(328\) 1.07518 0.0593668
\(329\) −28.7172 −1.58323
\(330\) −11.5629 −0.636519
\(331\) −31.4738 −1.72996 −0.864978 0.501809i \(-0.832668\pi\)
−0.864978 + 0.501809i \(0.832668\pi\)
\(332\) −4.81949 −0.264504
\(333\) 6.64774 0.364294
\(334\) −6.58946 −0.360559
\(335\) 42.3255 2.31249
\(336\) −1.62438 −0.0886171
\(337\) 28.1301 1.53234 0.766172 0.642636i \(-0.222159\pi\)
0.766172 + 0.642636i \(0.222159\pi\)
\(338\) −2.78839 −0.151668
\(339\) 3.47775 0.188885
\(340\) −3.53888 −0.191923
\(341\) −36.4795 −1.97547
\(342\) 2.45006 0.132484
\(343\) −12.1421 −0.655610
\(344\) 15.2198 0.820596
\(345\) 8.33879 0.448945
\(346\) −6.81798 −0.366537
\(347\) 3.22192 0.172962 0.0864810 0.996254i \(-0.472438\pi\)
0.0864810 + 0.996254i \(0.472438\pi\)
\(348\) 9.14979 0.490480
\(349\) −14.1179 −0.755714 −0.377857 0.925864i \(-0.623339\pi\)
−0.377857 + 0.925864i \(0.623339\pi\)
\(350\) −14.9747 −0.800430
\(351\) 3.99640 0.213312
\(352\) 20.9549 1.11690
\(353\) −2.75038 −0.146388 −0.0731941 0.997318i \(-0.523319\pi\)
−0.0731941 + 0.997318i \(0.523319\pi\)
\(354\) −5.43780 −0.289016
\(355\) 35.1722 1.86675
\(356\) 0.731723 0.0387812
\(357\) −3.19339 −0.169012
\(358\) −21.6966 −1.14670
\(359\) −20.4598 −1.07983 −0.539913 0.841721i \(-0.681543\pi\)
−0.539913 + 0.841721i \(0.681543\pi\)
\(360\) −9.25556 −0.487811
\(361\) −12.1842 −0.641276
\(362\) 8.94523 0.470151
\(363\) 4.18585 0.219700
\(364\) −14.2843 −0.748700
\(365\) 25.8623 1.35369
\(366\) 8.06270 0.421444
\(367\) −5.34969 −0.279252 −0.139626 0.990204i \(-0.544590\pi\)
−0.139626 + 0.990204i \(0.544590\pi\)
\(368\) 1.34156 0.0699335
\(369\) 0.367288 0.0191202
\(370\) 19.7253 1.02547
\(371\) 33.8071 1.75518
\(372\) −10.4777 −0.543244
\(373\) 11.3104 0.585632 0.292816 0.956169i \(-0.405408\pi\)
0.292816 + 0.956169i \(0.405408\pi\)
\(374\) −3.65712 −0.189105
\(375\) 0.0103688 0.000535444 0
\(376\) −26.3247 −1.35759
\(377\) −32.6695 −1.68257
\(378\) −2.99690 −0.154144
\(379\) 21.2526 1.09167 0.545836 0.837892i \(-0.316212\pi\)
0.545836 + 0.837892i \(0.316212\pi\)
\(380\) −9.23896 −0.473949
\(381\) −15.2780 −0.782718
\(382\) −20.4561 −1.04663
\(383\) −7.00071 −0.357720 −0.178860 0.983875i \(-0.557241\pi\)
−0.178860 + 0.983875i \(0.557241\pi\)
\(384\) 5.06396 0.258419
\(385\) 39.3460 2.00526
\(386\) −3.43905 −0.175043
\(387\) 5.19918 0.264289
\(388\) −19.8408 −1.00727
\(389\) −32.5726 −1.65150 −0.825748 0.564039i \(-0.809247\pi\)
−0.825748 + 0.564039i \(0.809247\pi\)
\(390\) 11.8582 0.600462
\(391\) 2.63739 0.133378
\(392\) 9.36091 0.472797
\(393\) 13.0166 0.656601
\(394\) −10.6584 −0.536962
\(395\) −21.8481 −1.09930
\(396\) 4.36171 0.219184
\(397\) −32.0993 −1.61102 −0.805508 0.592585i \(-0.798108\pi\)
−0.805508 + 0.592585i \(0.798108\pi\)
\(398\) 6.36130 0.318863
\(399\) −8.33699 −0.417372
\(400\) −2.54168 −0.127084
\(401\) −33.7957 −1.68768 −0.843839 0.536596i \(-0.819710\pi\)
−0.843839 + 0.536596i \(0.819710\pi\)
\(402\) 12.5630 0.626586
\(403\) 37.4109 1.86357
\(404\) −4.95178 −0.246360
\(405\) −3.16176 −0.157109
\(406\) 24.4989 1.21586
\(407\) −25.9056 −1.28409
\(408\) −2.92734 −0.144925
\(409\) −21.7914 −1.07751 −0.538757 0.842461i \(-0.681106\pi\)
−0.538757 + 0.842461i \(0.681106\pi\)
\(410\) 1.08982 0.0538224
\(411\) −8.48559 −0.418563
\(412\) 4.96760 0.244736
\(413\) 18.5036 0.910501
\(414\) 2.47511 0.121645
\(415\) −13.6142 −0.668295
\(416\) −21.4899 −1.05363
\(417\) −16.1044 −0.788637
\(418\) −9.54765 −0.466991
\(419\) −35.1932 −1.71930 −0.859650 0.510883i \(-0.829319\pi\)
−0.859650 + 0.510883i \(0.829319\pi\)
\(420\) 11.3010 0.551434
\(421\) −26.1770 −1.27579 −0.637895 0.770124i \(-0.720194\pi\)
−0.637895 + 0.770124i \(0.720194\pi\)
\(422\) 0.301337 0.0146689
\(423\) −8.99268 −0.437239
\(424\) 30.9906 1.50504
\(425\) −4.99672 −0.242377
\(426\) 10.4398 0.505808
\(427\) −27.4355 −1.32770
\(428\) 7.84947 0.379418
\(429\) −15.5736 −0.751900
\(430\) 15.4271 0.743960
\(431\) 7.91517 0.381260 0.190630 0.981662i \(-0.438947\pi\)
0.190630 + 0.981662i \(0.438947\pi\)
\(432\) −0.508669 −0.0244733
\(433\) −19.3800 −0.931345 −0.465673 0.884957i \(-0.654188\pi\)
−0.465673 + 0.884957i \(0.654188\pi\)
\(434\) −28.0544 −1.34665
\(435\) 25.8466 1.23925
\(436\) 3.01775 0.144524
\(437\) 6.88544 0.329375
\(438\) 7.67640 0.366793
\(439\) −16.6192 −0.793190 −0.396595 0.917994i \(-0.629808\pi\)
−0.396595 + 0.917994i \(0.629808\pi\)
\(440\) 36.0680 1.71947
\(441\) 3.19775 0.152274
\(442\) 3.75050 0.178393
\(443\) −26.8218 −1.27434 −0.637171 0.770723i \(-0.719895\pi\)
−0.637171 + 0.770723i \(0.719895\pi\)
\(444\) −7.44066 −0.353118
\(445\) 2.06699 0.0979846
\(446\) −4.75707 −0.225254
\(447\) −7.77400 −0.367698
\(448\) 19.3640 0.914865
\(449\) −28.1842 −1.33010 −0.665048 0.746800i \(-0.731589\pi\)
−0.665048 + 0.746800i \(0.731589\pi\)
\(450\) −4.68927 −0.221054
\(451\) −1.43129 −0.0673966
\(452\) −3.89256 −0.183091
\(453\) −6.12281 −0.287675
\(454\) 11.6094 0.544854
\(455\) −40.3506 −1.89166
\(456\) −7.64242 −0.357889
\(457\) −31.2171 −1.46027 −0.730136 0.683302i \(-0.760543\pi\)
−0.730136 + 0.683302i \(0.760543\pi\)
\(458\) −4.28680 −0.200309
\(459\) −1.00000 −0.0466760
\(460\) −9.33341 −0.435172
\(461\) −11.1046 −0.517194 −0.258597 0.965985i \(-0.583260\pi\)
−0.258597 + 0.965985i \(0.583260\pi\)
\(462\) 11.6786 0.543339
\(463\) −31.2253 −1.45116 −0.725581 0.688137i \(-0.758429\pi\)
−0.725581 + 0.688137i \(0.758429\pi\)
\(464\) 4.15823 0.193041
\(465\) −29.5977 −1.37256
\(466\) 24.6001 1.13958
\(467\) −5.84983 −0.270698 −0.135349 0.990798i \(-0.543216\pi\)
−0.135349 + 0.990798i \(0.543216\pi\)
\(468\) −4.47307 −0.206768
\(469\) −42.7490 −1.97396
\(470\) −26.6832 −1.23080
\(471\) 1.00000 0.0460776
\(472\) 16.9620 0.780740
\(473\) −20.2607 −0.931588
\(474\) −6.48492 −0.297862
\(475\) −13.0449 −0.598543
\(476\) 3.57429 0.163827
\(477\) 10.5866 0.484726
\(478\) −13.6272 −0.623292
\(479\) −11.6305 −0.531412 −0.265706 0.964054i \(-0.585605\pi\)
−0.265706 + 0.964054i \(0.585605\pi\)
\(480\) 17.0018 0.776022
\(481\) 26.5670 1.21135
\(482\) 16.0145 0.729441
\(483\) −8.42222 −0.383224
\(484\) −4.68512 −0.212960
\(485\) −56.0469 −2.54496
\(486\) −0.938469 −0.0425698
\(487\) −13.6357 −0.617894 −0.308947 0.951079i \(-0.599976\pi\)
−0.308947 + 0.951079i \(0.599976\pi\)
\(488\) −25.1498 −1.13848
\(489\) 18.3261 0.828735
\(490\) 9.48840 0.428642
\(491\) 17.2416 0.778101 0.389050 0.921216i \(-0.372803\pi\)
0.389050 + 0.921216i \(0.372803\pi\)
\(492\) −0.411097 −0.0185337
\(493\) 8.17474 0.368172
\(494\) 9.79143 0.440537
\(495\) 12.3211 0.553791
\(496\) −4.76172 −0.213808
\(497\) −35.5241 −1.59347
\(498\) −4.04095 −0.181079
\(499\) 9.47865 0.424323 0.212161 0.977235i \(-0.431950\pi\)
0.212161 + 0.977235i \(0.431950\pi\)
\(500\) −0.0116056 −0.000519018 0
\(501\) 7.02150 0.313697
\(502\) −11.3797 −0.507901
\(503\) 20.6318 0.919928 0.459964 0.887938i \(-0.347862\pi\)
0.459964 + 0.887938i \(0.347862\pi\)
\(504\) 9.34815 0.416400
\(505\) −13.9879 −0.622454
\(506\) −9.64525 −0.428784
\(507\) 2.97121 0.131956
\(508\) 17.1003 0.758705
\(509\) −19.1511 −0.848858 −0.424429 0.905461i \(-0.639525\pi\)
−0.424429 + 0.905461i \(0.639525\pi\)
\(510\) −2.96721 −0.131390
\(511\) −26.1210 −1.15553
\(512\) 5.71337 0.252498
\(513\) −2.61070 −0.115265
\(514\) 4.44493 0.196058
\(515\) 14.0326 0.618351
\(516\) −5.81932 −0.256181
\(517\) 35.0436 1.54122
\(518\) −19.9226 −0.875349
\(519\) 7.26500 0.318898
\(520\) −36.9889 −1.62207
\(521\) 1.14721 0.0502601 0.0251301 0.999684i \(-0.492000\pi\)
0.0251301 + 0.999684i \(0.492000\pi\)
\(522\) 7.67174 0.335783
\(523\) −3.21216 −0.140458 −0.0702289 0.997531i \(-0.522373\pi\)
−0.0702289 + 0.997531i \(0.522373\pi\)
\(524\) −14.5692 −0.636457
\(525\) 15.9565 0.696398
\(526\) −0.769992 −0.0335732
\(527\) −9.36114 −0.407778
\(528\) 1.98223 0.0862656
\(529\) −16.0442 −0.697573
\(530\) 31.4126 1.36448
\(531\) 5.79433 0.251453
\(532\) 9.33140 0.404567
\(533\) 1.46783 0.0635788
\(534\) 0.613521 0.0265496
\(535\) 22.1734 0.958639
\(536\) −39.1875 −1.69264
\(537\) 23.1191 0.997663
\(538\) 20.5396 0.885524
\(539\) −12.4613 −0.536747
\(540\) 3.53888 0.152289
\(541\) −22.0075 −0.946176 −0.473088 0.881015i \(-0.656861\pi\)
−0.473088 + 0.881015i \(0.656861\pi\)
\(542\) 28.5716 1.22725
\(543\) −9.53173 −0.409046
\(544\) 5.37732 0.230551
\(545\) 8.52463 0.365155
\(546\) −11.9768 −0.512560
\(547\) −13.7768 −0.589053 −0.294526 0.955643i \(-0.595162\pi\)
−0.294526 + 0.955643i \(0.595162\pi\)
\(548\) 9.49771 0.405722
\(549\) −8.59133 −0.366669
\(550\) 18.2736 0.779190
\(551\) 21.3418 0.909191
\(552\) −7.72054 −0.328608
\(553\) 22.0667 0.938370
\(554\) 13.8618 0.588930
\(555\) −21.0186 −0.892188
\(556\) 18.0253 0.764443
\(557\) −2.29854 −0.0973923 −0.0486961 0.998814i \(-0.515507\pi\)
−0.0486961 + 0.998814i \(0.515507\pi\)
\(558\) −8.78514 −0.371905
\(559\) 20.7780 0.878816
\(560\) 5.13589 0.217031
\(561\) 3.89690 0.164527
\(562\) −4.25125 −0.179328
\(563\) −5.41074 −0.228035 −0.114018 0.993479i \(-0.536372\pi\)
−0.114018 + 0.993479i \(0.536372\pi\)
\(564\) 10.0653 0.423825
\(565\) −10.9958 −0.462597
\(566\) −21.6972 −0.912000
\(567\) 3.19339 0.134110
\(568\) −32.5645 −1.36638
\(569\) 41.5767 1.74299 0.871493 0.490408i \(-0.163152\pi\)
0.871493 + 0.490408i \(0.163152\pi\)
\(570\) −7.74651 −0.324465
\(571\) −26.5040 −1.10916 −0.554579 0.832131i \(-0.687121\pi\)
−0.554579 + 0.832131i \(0.687121\pi\)
\(572\) 17.4311 0.728832
\(573\) 21.7974 0.910598
\(574\) −1.10072 −0.0459434
\(575\) −13.1783 −0.549573
\(576\) 6.06378 0.252658
\(577\) 40.9331 1.70407 0.852033 0.523488i \(-0.175370\pi\)
0.852033 + 0.523488i \(0.175370\pi\)
\(578\) −0.938469 −0.0390352
\(579\) 3.66453 0.152293
\(580\) −28.9294 −1.20123
\(581\) 13.7504 0.570464
\(582\) −16.6358 −0.689574
\(583\) −41.2549 −1.70860
\(584\) −23.9448 −0.990843
\(585\) −12.6357 −0.522420
\(586\) −9.46832 −0.391133
\(587\) −2.78441 −0.114925 −0.0574625 0.998348i \(-0.518301\pi\)
−0.0574625 + 0.998348i \(0.518301\pi\)
\(588\) −3.57916 −0.147602
\(589\) −24.4392 −1.00700
\(590\) 17.1930 0.707825
\(591\) 11.3572 0.467173
\(592\) −3.38150 −0.138979
\(593\) 13.5205 0.555222 0.277611 0.960694i \(-0.410457\pi\)
0.277611 + 0.960694i \(0.410457\pi\)
\(594\) 3.65712 0.150054
\(595\) 10.0967 0.413926
\(596\) 8.70125 0.356417
\(597\) −6.77838 −0.277421
\(598\) 9.89152 0.404494
\(599\) 13.9623 0.570483 0.285241 0.958456i \(-0.407926\pi\)
0.285241 + 0.958456i \(0.407926\pi\)
\(600\) 14.6271 0.597150
\(601\) −35.0318 −1.42898 −0.714488 0.699647i \(-0.753341\pi\)
−0.714488 + 0.699647i \(0.753341\pi\)
\(602\) −15.5814 −0.635051
\(603\) −13.3867 −0.545149
\(604\) 6.85311 0.278849
\(605\) −13.2346 −0.538065
\(606\) −4.15187 −0.168658
\(607\) −7.49108 −0.304054 −0.152027 0.988376i \(-0.548580\pi\)
−0.152027 + 0.988376i \(0.548580\pi\)
\(608\) 14.0386 0.569339
\(609\) −26.1051 −1.05783
\(610\) −25.4923 −1.03215
\(611\) −35.9384 −1.45391
\(612\) 1.11928 0.0452441
\(613\) 45.0264 1.81860 0.909301 0.416140i \(-0.136617\pi\)
0.909301 + 0.416140i \(0.136617\pi\)
\(614\) 1.06624 0.0430298
\(615\) −1.16128 −0.0468272
\(616\) −36.4288 −1.46776
\(617\) −27.3417 −1.10074 −0.550368 0.834922i \(-0.685513\pi\)
−0.550368 + 0.834922i \(0.685513\pi\)
\(618\) 4.16514 0.167546
\(619\) −0.00114521 −4.60299e−5 0 −2.30149e−5 1.00000i \(-0.500007\pi\)
−2.30149e−5 1.00000i \(0.500007\pi\)
\(620\) 33.1280 1.33045
\(621\) −2.63739 −0.105835
\(622\) 15.6111 0.625946
\(623\) −2.08767 −0.0836406
\(624\) −2.03284 −0.0813789
\(625\) −25.0164 −1.00066
\(626\) 20.3505 0.813371
\(627\) 10.1736 0.406296
\(628\) −1.11928 −0.0446640
\(629\) −6.64774 −0.265063
\(630\) 9.47547 0.377512
\(631\) −19.2656 −0.766949 −0.383475 0.923551i \(-0.625273\pi\)
−0.383475 + 0.923551i \(0.625273\pi\)
\(632\) 20.2282 0.804636
\(633\) −0.321094 −0.0127623
\(634\) −21.9346 −0.871136
\(635\) 48.3055 1.91694
\(636\) −11.8493 −0.469856
\(637\) 12.7795 0.506342
\(638\) −29.8960 −1.18359
\(639\) −11.1243 −0.440069
\(640\) −16.0110 −0.632892
\(641\) 30.9125 1.22097 0.610486 0.792027i \(-0.290974\pi\)
0.610486 + 0.792027i \(0.290974\pi\)
\(642\) 6.58147 0.259750
\(643\) −8.79402 −0.346802 −0.173401 0.984851i \(-0.555476\pi\)
−0.173401 + 0.984851i \(0.555476\pi\)
\(644\) 9.42678 0.371467
\(645\) −16.4386 −0.647268
\(646\) −2.45006 −0.0963964
\(647\) 7.62021 0.299581 0.149791 0.988718i \(-0.452140\pi\)
0.149791 + 0.988718i \(0.452140\pi\)
\(648\) 2.92734 0.114997
\(649\) −22.5800 −0.886341
\(650\) −18.7402 −0.735051
\(651\) 29.8938 1.17163
\(652\) −20.5120 −0.803311
\(653\) −25.8874 −1.01305 −0.506526 0.862225i \(-0.669070\pi\)
−0.506526 + 0.862225i \(0.669070\pi\)
\(654\) 2.53027 0.0989413
\(655\) −41.1554 −1.60807
\(656\) −0.186828 −0.00729441
\(657\) −8.17971 −0.319121
\(658\) 26.9502 1.05063
\(659\) −31.3890 −1.22274 −0.611371 0.791344i \(-0.709382\pi\)
−0.611371 + 0.791344i \(0.709382\pi\)
\(660\) −13.7907 −0.536801
\(661\) 23.3594 0.908576 0.454288 0.890855i \(-0.349894\pi\)
0.454288 + 0.890855i \(0.349894\pi\)
\(662\) 29.5372 1.14800
\(663\) −3.99640 −0.155207
\(664\) 12.6048 0.489163
\(665\) 26.3596 1.02218
\(666\) −6.23870 −0.241745
\(667\) 21.5600 0.834805
\(668\) −7.85899 −0.304074
\(669\) 5.06897 0.195978
\(670\) −39.7212 −1.53456
\(671\) 33.4796 1.29246
\(672\) −17.1719 −0.662420
\(673\) −34.9821 −1.34846 −0.674231 0.738520i \(-0.735525\pi\)
−0.674231 + 0.738520i \(0.735525\pi\)
\(674\) −26.3992 −1.01686
\(675\) 4.99672 0.192324
\(676\) −3.32561 −0.127908
\(677\) −6.96778 −0.267794 −0.133897 0.990995i \(-0.542749\pi\)
−0.133897 + 0.990995i \(0.542749\pi\)
\(678\) −3.26376 −0.125344
\(679\) 56.6076 2.17240
\(680\) 9.25556 0.354934
\(681\) −12.3705 −0.474040
\(682\) 34.2348 1.31092
\(683\) 24.1975 0.925890 0.462945 0.886387i \(-0.346793\pi\)
0.462945 + 0.886387i \(0.346793\pi\)
\(684\) 2.92210 0.111729
\(685\) 26.8294 1.02510
\(686\) 11.3950 0.435062
\(687\) 4.56787 0.174275
\(688\) −2.64466 −0.100827
\(689\) 42.3082 1.61182
\(690\) −7.82569 −0.297919
\(691\) −32.2655 −1.22744 −0.613719 0.789525i \(-0.710327\pi\)
−0.613719 + 0.789525i \(0.710327\pi\)
\(692\) −8.13154 −0.309115
\(693\) −12.4443 −0.472721
\(694\) −3.02368 −0.114777
\(695\) 50.9183 1.93144
\(696\) −23.9303 −0.907074
\(697\) −0.367288 −0.0139120
\(698\) 13.2492 0.501490
\(699\) −26.2130 −0.991468
\(700\) −17.8597 −0.675034
\(701\) −7.90448 −0.298548 −0.149274 0.988796i \(-0.547694\pi\)
−0.149274 + 0.988796i \(0.547694\pi\)
\(702\) −3.75050 −0.141553
\(703\) −17.3553 −0.654566
\(704\) −23.6300 −0.890588
\(705\) 28.4327 1.07084
\(706\) 2.58115 0.0971428
\(707\) 14.1279 0.531333
\(708\) −6.48546 −0.243738
\(709\) −19.3028 −0.724931 −0.362466 0.931997i \(-0.618065\pi\)
−0.362466 + 0.931997i \(0.618065\pi\)
\(710\) −33.0080 −1.23877
\(711\) 6.91010 0.259149
\(712\) −1.91374 −0.0717204
\(713\) −24.6890 −0.924610
\(714\) 2.99690 0.112156
\(715\) 49.2399 1.84147
\(716\) −25.8767 −0.967056
\(717\) 14.5206 0.542283
\(718\) 19.2009 0.716570
\(719\) −43.6511 −1.62791 −0.813957 0.580926i \(-0.802691\pi\)
−0.813957 + 0.580926i \(0.802691\pi\)
\(720\) 1.60829 0.0599374
\(721\) −14.1730 −0.527830
\(722\) 11.4345 0.425549
\(723\) −17.0645 −0.634636
\(724\) 10.6686 0.396497
\(725\) −40.8469 −1.51702
\(726\) −3.92829 −0.145792
\(727\) 10.6095 0.393484 0.196742 0.980455i \(-0.436964\pi\)
0.196742 + 0.980455i \(0.436964\pi\)
\(728\) 37.3590 1.38462
\(729\) 1.00000 0.0370370
\(730\) −24.2709 −0.898307
\(731\) −5.19918 −0.192299
\(732\) 9.61607 0.355420
\(733\) −14.4560 −0.533943 −0.266972 0.963704i \(-0.586023\pi\)
−0.266972 + 0.963704i \(0.586023\pi\)
\(734\) 5.02052 0.185311
\(735\) −10.1105 −0.372932
\(736\) 14.1821 0.522758
\(737\) 52.1667 1.92158
\(738\) −0.344688 −0.0126882
\(739\) 25.0656 0.922051 0.461026 0.887387i \(-0.347482\pi\)
0.461026 + 0.887387i \(0.347482\pi\)
\(740\) 23.5256 0.864817
\(741\) −10.4334 −0.383281
\(742\) −31.7269 −1.16473
\(743\) 39.2069 1.43836 0.719180 0.694824i \(-0.244518\pi\)
0.719180 + 0.694824i \(0.244518\pi\)
\(744\) 27.4033 1.00465
\(745\) 24.5795 0.900524
\(746\) −10.6145 −0.388624
\(747\) 4.30590 0.157545
\(748\) −4.36171 −0.159480
\(749\) −22.3952 −0.818303
\(750\) −0.00973083 −0.000355320 0
\(751\) 3.99017 0.145603 0.0728016 0.997346i \(-0.476806\pi\)
0.0728016 + 0.997346i \(0.476806\pi\)
\(752\) 4.57430 0.166807
\(753\) 12.1258 0.441889
\(754\) 30.6593 1.11655
\(755\) 19.3589 0.704541
\(756\) −3.57429 −0.129996
\(757\) 11.8841 0.431936 0.215968 0.976400i \(-0.430709\pi\)
0.215968 + 0.976400i \(0.430709\pi\)
\(758\) −19.9449 −0.724431
\(759\) 10.2776 0.373055
\(760\) 24.1635 0.876502
\(761\) 14.8864 0.539633 0.269816 0.962912i \(-0.413037\pi\)
0.269816 + 0.962912i \(0.413037\pi\)
\(762\) 14.3380 0.519410
\(763\) −8.60991 −0.311700
\(764\) −24.3973 −0.882662
\(765\) 3.16176 0.114314
\(766\) 6.56995 0.237382
\(767\) 23.1565 0.836132
\(768\) −16.8799 −0.609102
\(769\) 49.8262 1.79678 0.898389 0.439201i \(-0.144738\pi\)
0.898389 + 0.439201i \(0.144738\pi\)
\(770\) −36.9250 −1.33068
\(771\) −4.73637 −0.170576
\(772\) −4.10162 −0.147621
\(773\) 21.2647 0.764838 0.382419 0.923989i \(-0.375091\pi\)
0.382419 + 0.923989i \(0.375091\pi\)
\(774\) −4.87927 −0.175382
\(775\) 46.7750 1.68021
\(776\) 51.8915 1.86280
\(777\) 21.2288 0.761580
\(778\) 30.5684 1.09593
\(779\) −0.958879 −0.0343554
\(780\) 14.1428 0.506393
\(781\) 43.3501 1.55119
\(782\) −2.47511 −0.0885097
\(783\) −8.17474 −0.292141
\(784\) −1.62660 −0.0580927
\(785\) −3.16176 −0.112848
\(786\) −12.2157 −0.435719
\(787\) 16.9550 0.604380 0.302190 0.953248i \(-0.402282\pi\)
0.302190 + 0.953248i \(0.402282\pi\)
\(788\) −12.7119 −0.452841
\(789\) 0.820477 0.0292097
\(790\) 20.5037 0.729490
\(791\) 11.1058 0.394877
\(792\) −11.4076 −0.405350
\(793\) −34.3344 −1.21925
\(794\) 30.1242 1.06907
\(795\) −33.4722 −1.18714
\(796\) 7.58688 0.268910
\(797\) 47.3156 1.67600 0.838001 0.545668i \(-0.183724\pi\)
0.838001 + 0.545668i \(0.183724\pi\)
\(798\) 7.82401 0.276967
\(799\) 8.99268 0.318138
\(800\) −26.8690 −0.949961
\(801\) −0.653746 −0.0230990
\(802\) 31.7162 1.11994
\(803\) 31.8755 1.12486
\(804\) 14.9834 0.528424
\(805\) 26.6290 0.938549
\(806\) −35.1089 −1.23666
\(807\) −21.8863 −0.770433
\(808\) 12.9508 0.455609
\(809\) −3.49688 −0.122944 −0.0614718 0.998109i \(-0.519579\pi\)
−0.0614718 + 0.998109i \(0.519579\pi\)
\(810\) 2.96721 0.104257
\(811\) 36.6303 1.28626 0.643132 0.765755i \(-0.277635\pi\)
0.643132 + 0.765755i \(0.277635\pi\)
\(812\) 29.2189 1.02538
\(813\) −30.4449 −1.06775
\(814\) 24.3116 0.852121
\(815\) −57.9427 −2.02964
\(816\) 0.508669 0.0178070
\(817\) −13.5735 −0.474877
\(818\) 20.4505 0.715036
\(819\) 12.7621 0.445943
\(820\) 1.29979 0.0453906
\(821\) −31.6148 −1.10337 −0.551683 0.834054i \(-0.686014\pi\)
−0.551683 + 0.834054i \(0.686014\pi\)
\(822\) 7.96346 0.277758
\(823\) −26.5119 −0.924146 −0.462073 0.886842i \(-0.652894\pi\)
−0.462073 + 0.886842i \(0.652894\pi\)
\(824\) −12.9922 −0.452605
\(825\) −19.4717 −0.677919
\(826\) −17.3650 −0.604207
\(827\) 39.6677 1.37938 0.689690 0.724105i \(-0.257747\pi\)
0.689690 + 0.724105i \(0.257747\pi\)
\(828\) 2.95197 0.102588
\(829\) 36.5725 1.27022 0.635108 0.772423i \(-0.280955\pi\)
0.635108 + 0.772423i \(0.280955\pi\)
\(830\) 12.7765 0.443479
\(831\) −14.7706 −0.512387
\(832\) 24.2333 0.840139
\(833\) −3.19775 −0.110795
\(834\) 15.1135 0.523338
\(835\) −22.2003 −0.768272
\(836\) −11.3871 −0.393832
\(837\) 9.36114 0.323569
\(838\) 33.0277 1.14092
\(839\) −46.3732 −1.60098 −0.800490 0.599346i \(-0.795427\pi\)
−0.800490 + 0.599346i \(0.795427\pi\)
\(840\) −29.5566 −1.01980
\(841\) 37.8263 1.30436
\(842\) 24.5663 0.846611
\(843\) 4.52998 0.156021
\(844\) 0.359393 0.0123708
\(845\) −9.39426 −0.323172
\(846\) 8.43935 0.290151
\(847\) 13.3671 0.459297
\(848\) −5.38507 −0.184924
\(849\) 23.1198 0.793468
\(850\) 4.68927 0.160841
\(851\) −17.5327 −0.601012
\(852\) 12.4511 0.426568
\(853\) 42.1101 1.44182 0.720911 0.693027i \(-0.243723\pi\)
0.720911 + 0.693027i \(0.243723\pi\)
\(854\) 25.7473 0.881056
\(855\) 8.25441 0.282295
\(856\) −20.5294 −0.701681
\(857\) 13.0924 0.447229 0.223615 0.974678i \(-0.428214\pi\)
0.223615 + 0.974678i \(0.428214\pi\)
\(858\) 14.6153 0.498959
\(859\) −44.8238 −1.52937 −0.764684 0.644406i \(-0.777105\pi\)
−0.764684 + 0.644406i \(0.777105\pi\)
\(860\) 18.3993 0.627410
\(861\) 1.17289 0.0399721
\(862\) −7.42814 −0.253004
\(863\) 5.07199 0.172653 0.0863263 0.996267i \(-0.472487\pi\)
0.0863263 + 0.996267i \(0.472487\pi\)
\(864\) −5.37732 −0.182940
\(865\) −22.9702 −0.781010
\(866\) 18.1876 0.618039
\(867\) 1.00000 0.0339618
\(868\) −33.4594 −1.13569
\(869\) −26.9280 −0.913470
\(870\) −24.2562 −0.822362
\(871\) −53.4986 −1.81273
\(872\) −7.89261 −0.267277
\(873\) 17.7265 0.599951
\(874\) −6.46177 −0.218573
\(875\) 0.0331118 0.00111938
\(876\) 9.15535 0.309331
\(877\) 39.2280 1.32463 0.662317 0.749223i \(-0.269573\pi\)
0.662317 + 0.749223i \(0.269573\pi\)
\(878\) 15.5966 0.526359
\(879\) 10.0891 0.340298
\(880\) −6.26734 −0.211272
\(881\) 27.9967 0.943232 0.471616 0.881804i \(-0.343671\pi\)
0.471616 + 0.881804i \(0.343671\pi\)
\(882\) −3.00099 −0.101049
\(883\) 50.0321 1.68371 0.841857 0.539701i \(-0.181463\pi\)
0.841857 + 0.539701i \(0.181463\pi\)
\(884\) 4.47307 0.150446
\(885\) −18.3203 −0.615830
\(886\) 25.1714 0.845650
\(887\) −52.7111 −1.76986 −0.884932 0.465720i \(-0.845796\pi\)
−0.884932 + 0.465720i \(0.845796\pi\)
\(888\) 19.4602 0.653042
\(889\) −48.7888 −1.63632
\(890\) −1.93980 −0.0650224
\(891\) −3.89690 −0.130551
\(892\) −5.67358 −0.189966
\(893\) 23.4772 0.785635
\(894\) 7.29566 0.244003
\(895\) −73.0970 −2.44336
\(896\) 16.1712 0.540242
\(897\) −10.5401 −0.351922
\(898\) 26.4500 0.882649
\(899\) −76.5249 −2.55225
\(900\) −5.59271 −0.186424
\(901\) −10.5866 −0.352690
\(902\) 1.34322 0.0447242
\(903\) 16.6030 0.552514
\(904\) 10.1806 0.338600
\(905\) 30.1370 1.00179
\(906\) 5.74607 0.190900
\(907\) −31.8539 −1.05769 −0.528846 0.848718i \(-0.677375\pi\)
−0.528846 + 0.848718i \(0.677375\pi\)
\(908\) 13.8460 0.459497
\(909\) 4.42409 0.146738
\(910\) 37.8678 1.25530
\(911\) −7.88328 −0.261185 −0.130592 0.991436i \(-0.541688\pi\)
−0.130592 + 0.991436i \(0.541688\pi\)
\(912\) 1.32798 0.0439739
\(913\) −16.7797 −0.555326
\(914\) 29.2962 0.969034
\(915\) 27.1637 0.898005
\(916\) −5.11271 −0.168929
\(917\) 41.5671 1.37267
\(918\) 0.938469 0.0309741
\(919\) 8.67506 0.286164 0.143082 0.989711i \(-0.454299\pi\)
0.143082 + 0.989711i \(0.454299\pi\)
\(920\) 24.4105 0.804790
\(921\) −1.13614 −0.0374372
\(922\) 10.4214 0.343209
\(923\) −44.4570 −1.46332
\(924\) 13.9286 0.458219
\(925\) 33.2169 1.09216
\(926\) 29.3040 0.962988
\(927\) −4.43823 −0.145771
\(928\) 43.9582 1.44300
\(929\) 0.0643093 0.00210992 0.00105496 0.999999i \(-0.499664\pi\)
0.00105496 + 0.999999i \(0.499664\pi\)
\(930\) 27.7765 0.910828
\(931\) −8.34837 −0.273607
\(932\) 29.3396 0.961051
\(933\) −16.6346 −0.544592
\(934\) 5.48989 0.179635
\(935\) −12.3211 −0.402942
\(936\) 11.6988 0.382388
\(937\) 19.3821 0.633185 0.316593 0.948562i \(-0.397461\pi\)
0.316593 + 0.948562i \(0.397461\pi\)
\(938\) 40.1186 1.30992
\(939\) −21.6848 −0.707657
\(940\) −31.8240 −1.03799
\(941\) 25.3346 0.825885 0.412942 0.910757i \(-0.364501\pi\)
0.412942 + 0.910757i \(0.364501\pi\)
\(942\) −0.938469 −0.0305770
\(943\) −0.968681 −0.0315446
\(944\) −2.94740 −0.0959296
\(945\) −10.0967 −0.328447
\(946\) 19.0140 0.618200
\(947\) 54.7938 1.78056 0.890280 0.455413i \(-0.150508\pi\)
0.890280 + 0.455413i \(0.150508\pi\)
\(948\) −7.73431 −0.251199
\(949\) −32.6894 −1.06114
\(950\) 12.2423 0.397192
\(951\) 23.3728 0.757915
\(952\) −9.34815 −0.302975
\(953\) 46.8870 1.51882 0.759410 0.650612i \(-0.225488\pi\)
0.759410 + 0.650612i \(0.225488\pi\)
\(954\) −9.93518 −0.321663
\(955\) −68.9180 −2.23013
\(956\) −16.2526 −0.525647
\(957\) 31.8562 1.02976
\(958\) 10.9149 0.352644
\(959\) −27.0978 −0.875034
\(960\) −19.1722 −0.618781
\(961\) 56.6310 1.82681
\(962\) −24.9323 −0.803851
\(963\) −7.01299 −0.225990
\(964\) 19.0999 0.615167
\(965\) −11.5864 −0.372978
\(966\) 7.90399 0.254307
\(967\) 19.3935 0.623652 0.311826 0.950139i \(-0.399059\pi\)
0.311826 + 0.950139i \(0.399059\pi\)
\(968\) 12.2534 0.393840
\(969\) 2.61070 0.0838678
\(970\) 52.5983 1.68883
\(971\) −11.5844 −0.371761 −0.185881 0.982572i \(-0.559514\pi\)
−0.185881 + 0.982572i \(0.559514\pi\)
\(972\) −1.11928 −0.0359008
\(973\) −51.4277 −1.64870
\(974\) 12.7967 0.410033
\(975\) 19.9689 0.639516
\(976\) 4.37014 0.139885
\(977\) 28.4649 0.910674 0.455337 0.890319i \(-0.349519\pi\)
0.455337 + 0.890319i \(0.349519\pi\)
\(978\) −17.1985 −0.549947
\(979\) 2.54759 0.0814212
\(980\) 11.3165 0.361491
\(981\) −2.69617 −0.0860820
\(982\) −16.1807 −0.516346
\(983\) −35.7667 −1.14078 −0.570390 0.821374i \(-0.693208\pi\)
−0.570390 + 0.821374i \(0.693208\pi\)
\(984\) 1.07518 0.0342754
\(985\) −35.9088 −1.14415
\(986\) −7.67174 −0.244318
\(987\) −28.7172 −0.914077
\(988\) 11.6779 0.371522
\(989\) −13.7123 −0.436025
\(990\) −11.5629 −0.367494
\(991\) 1.18549 0.0376582 0.0188291 0.999823i \(-0.494006\pi\)
0.0188291 + 0.999823i \(0.494006\pi\)
\(992\) −50.3378 −1.59823
\(993\) −31.4738 −0.998791
\(994\) 33.3383 1.05743
\(995\) 21.4316 0.679427
\(996\) −4.81949 −0.152711
\(997\) −9.92711 −0.314395 −0.157197 0.987567i \(-0.550246\pi\)
−0.157197 + 0.987567i \(0.550246\pi\)
\(998\) −8.89542 −0.281580
\(999\) 6.64774 0.210325
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 \(a_p\))