Properties

Label 8007.2.a.j.1.9
Level 8007
Weight 2
Character 8007.1
Self dual Yes
Analytic conductor 63.936
Analytic rank 0
Dimension 64
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: \(0\)
Dimension: \(64\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.32739 q^{2}\) \(-1.00000 q^{3}\) \(+3.41675 q^{4}\) \(+3.32274 q^{5}\) \(+2.32739 q^{6}\) \(+1.34387 q^{7}\) \(-3.29733 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.32739 q^{2}\) \(-1.00000 q^{3}\) \(+3.41675 q^{4}\) \(+3.32274 q^{5}\) \(+2.32739 q^{6}\) \(+1.34387 q^{7}\) \(-3.29733 q^{8}\) \(+1.00000 q^{9}\) \(-7.73332 q^{10}\) \(+6.61253 q^{11}\) \(-3.41675 q^{12}\) \(-5.69091 q^{13}\) \(-3.12770 q^{14}\) \(-3.32274 q^{15}\) \(+0.840683 q^{16}\) \(+1.00000 q^{17}\) \(-2.32739 q^{18}\) \(+3.29674 q^{19}\) \(+11.3530 q^{20}\) \(-1.34387 q^{21}\) \(-15.3899 q^{22}\) \(+9.15661 q^{23}\) \(+3.29733 q^{24}\) \(+6.04060 q^{25}\) \(+13.2450 q^{26}\) \(-1.00000 q^{27}\) \(+4.59166 q^{28}\) \(+2.40186 q^{29}\) \(+7.73332 q^{30}\) \(-0.697480 q^{31}\) \(+4.63807 q^{32}\) \(-6.61253 q^{33}\) \(-2.32739 q^{34}\) \(+4.46532 q^{35}\) \(+3.41675 q^{36}\) \(+8.01191 q^{37}\) \(-7.67281 q^{38}\) \(+5.69091 q^{39}\) \(-10.9562 q^{40}\) \(-10.7539 q^{41}\) \(+3.12770 q^{42}\) \(+8.67047 q^{43}\) \(+22.5934 q^{44}\) \(+3.32274 q^{45}\) \(-21.3110 q^{46}\) \(+2.02538 q^{47}\) \(-0.840683 q^{48}\) \(-5.19402 q^{49}\) \(-14.0588 q^{50}\) \(-1.00000 q^{51}\) \(-19.4444 q^{52}\) \(-4.76109 q^{53}\) \(+2.32739 q^{54}\) \(+21.9717 q^{55}\) \(-4.43118 q^{56}\) \(-3.29674 q^{57}\) \(-5.59007 q^{58}\) \(-2.52293 q^{59}\) \(-11.3530 q^{60}\) \(-10.8784 q^{61}\) \(+1.62331 q^{62}\) \(+1.34387 q^{63}\) \(-12.4760 q^{64}\) \(-18.9094 q^{65}\) \(+15.3899 q^{66}\) \(-11.5508 q^{67}\) \(+3.41675 q^{68}\) \(-9.15661 q^{69}\) \(-10.3925 q^{70}\) \(+11.9722 q^{71}\) \(-3.29733 q^{72}\) \(+6.20046 q^{73}\) \(-18.6468 q^{74}\) \(-6.04060 q^{75}\) \(+11.2641 q^{76}\) \(+8.88636 q^{77}\) \(-13.2450 q^{78}\) \(-2.20634 q^{79}\) \(+2.79337 q^{80}\) \(+1.00000 q^{81}\) \(+25.0285 q^{82}\) \(+13.4909 q^{83}\) \(-4.59166 q^{84}\) \(+3.32274 q^{85}\) \(-20.1796 q^{86}\) \(-2.40186 q^{87}\) \(-21.8037 q^{88}\) \(+13.4090 q^{89}\) \(-7.73332 q^{90}\) \(-7.64783 q^{91}\) \(+31.2859 q^{92}\) \(+0.697480 q^{93}\) \(-4.71386 q^{94}\) \(+10.9542 q^{95}\) \(-4.63807 q^{96}\) \(-7.16444 q^{97}\) \(+12.0885 q^{98}\) \(+6.61253 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(64q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut -\mathstrut 64q^{3} \) \(\mathstrut +\mathstrut 77q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 64q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(64q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut -\mathstrut 64q^{3} \) \(\mathstrut +\mathstrut 77q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 64q^{9} \) \(\mathstrut +\mathstrut 12q^{10} \) \(\mathstrut -\mathstrut 7q^{11} \) \(\mathstrut -\mathstrut 77q^{12} \) \(\mathstrut +\mathstrut 24q^{13} \) \(\mathstrut -\mathstrut 14q^{14} \) \(\mathstrut +\mathstrut 3q^{15} \) \(\mathstrut +\mathstrut 103q^{16} \) \(\mathstrut +\mathstrut 64q^{17} \) \(\mathstrut +\mathstrut 5q^{18} \) \(\mathstrut +\mathstrut 26q^{19} \) \(\mathstrut -\mathstrut 24q^{20} \) \(\mathstrut -\mathstrut 5q^{21} \) \(\mathstrut +\mathstrut 25q^{22} \) \(\mathstrut +\mathstrut 20q^{23} \) \(\mathstrut -\mathstrut 18q^{24} \) \(\mathstrut +\mathstrut 141q^{25} \) \(\mathstrut +\mathstrut 9q^{26} \) \(\mathstrut -\mathstrut 64q^{27} \) \(\mathstrut +\mathstrut 14q^{28} \) \(\mathstrut +\mathstrut 5q^{29} \) \(\mathstrut -\mathstrut 12q^{30} \) \(\mathstrut +\mathstrut 11q^{31} \) \(\mathstrut +\mathstrut 31q^{32} \) \(\mathstrut +\mathstrut 7q^{33} \) \(\mathstrut +\mathstrut 5q^{34} \) \(\mathstrut -\mathstrut 3q^{35} \) \(\mathstrut +\mathstrut 77q^{36} \) \(\mathstrut +\mathstrut 50q^{37} \) \(\mathstrut +\mathstrut 8q^{38} \) \(\mathstrut -\mathstrut 24q^{39} \) \(\mathstrut +\mathstrut 28q^{40} \) \(\mathstrut -\mathstrut 9q^{41} \) \(\mathstrut +\mathstrut 14q^{42} \) \(\mathstrut +\mathstrut 59q^{43} \) \(\mathstrut -\mathstrut 6q^{44} \) \(\mathstrut -\mathstrut 3q^{45} \) \(\mathstrut +\mathstrut 11q^{47} \) \(\mathstrut -\mathstrut 103q^{48} \) \(\mathstrut +\mathstrut 163q^{49} \) \(\mathstrut +\mathstrut 20q^{50} \) \(\mathstrut -\mathstrut 64q^{51} \) \(\mathstrut +\mathstrut 65q^{52} \) \(\mathstrut +\mathstrut 39q^{53} \) \(\mathstrut -\mathstrut 5q^{54} \) \(\mathstrut +\mathstrut 35q^{55} \) \(\mathstrut -\mathstrut 34q^{56} \) \(\mathstrut -\mathstrut 26q^{57} \) \(\mathstrut -\mathstrut 27q^{58} \) \(\mathstrut -\mathstrut 65q^{59} \) \(\mathstrut +\mathstrut 24q^{60} \) \(\mathstrut +\mathstrut 15q^{61} \) \(\mathstrut +\mathstrut 18q^{62} \) \(\mathstrut +\mathstrut 5q^{63} \) \(\mathstrut +\mathstrut 152q^{64} \) \(\mathstrut +\mathstrut 49q^{65} \) \(\mathstrut -\mathstrut 25q^{66} \) \(\mathstrut +\mathstrut 56q^{67} \) \(\mathstrut +\mathstrut 77q^{68} \) \(\mathstrut -\mathstrut 20q^{69} \) \(\mathstrut +\mathstrut 28q^{70} \) \(\mathstrut -\mathstrut 18q^{71} \) \(\mathstrut +\mathstrut 18q^{72} \) \(\mathstrut +\mathstrut 37q^{73} \) \(\mathstrut -\mathstrut 76q^{74} \) \(\mathstrut -\mathstrut 141q^{75} \) \(\mathstrut +\mathstrut 30q^{76} \) \(\mathstrut +\mathstrut 80q^{77} \) \(\mathstrut -\mathstrut 9q^{78} \) \(\mathstrut +\mathstrut 20q^{79} \) \(\mathstrut -\mathstrut 144q^{80} \) \(\mathstrut +\mathstrut 64q^{81} \) \(\mathstrut +\mathstrut 27q^{82} \) \(\mathstrut +\mathstrut 3q^{83} \) \(\mathstrut -\mathstrut 14q^{84} \) \(\mathstrut -\mathstrut 3q^{85} \) \(\mathstrut +\mathstrut 12q^{86} \) \(\mathstrut -\mathstrut 5q^{87} \) \(\mathstrut +\mathstrut 108q^{88} \) \(\mathstrut +\mathstrut 42q^{89} \) \(\mathstrut +\mathstrut 12q^{90} \) \(\mathstrut +\mathstrut 25q^{91} \) \(\mathstrut +\mathstrut 18q^{92} \) \(\mathstrut -\mathstrut 11q^{93} \) \(\mathstrut +\mathstrut 60q^{94} \) \(\mathstrut +\mathstrut 42q^{95} \) \(\mathstrut -\mathstrut 31q^{96} \) \(\mathstrut +\mathstrut 72q^{97} \) \(\mathstrut +\mathstrut 18q^{98} \) \(\mathstrut -\mathstrut 7q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.32739 −1.64571 −0.822857 0.568248i \(-0.807621\pi\)
−0.822857 + 0.568248i \(0.807621\pi\)
\(3\) −1.00000 −0.577350
\(4\) 3.41675 1.70838
\(5\) 3.32274 1.48597 0.742987 0.669306i \(-0.233408\pi\)
0.742987 + 0.669306i \(0.233408\pi\)
\(6\) 2.32739 0.950154
\(7\) 1.34387 0.507934 0.253967 0.967213i \(-0.418265\pi\)
0.253967 + 0.967213i \(0.418265\pi\)
\(8\) −3.29733 −1.16578
\(9\) 1.00000 0.333333
\(10\) −7.73332 −2.44549
\(11\) 6.61253 1.99375 0.996876 0.0789778i \(-0.0251656\pi\)
0.996876 + 0.0789778i \(0.0251656\pi\)
\(12\) −3.41675 −0.986331
\(13\) −5.69091 −1.57837 −0.789187 0.614153i \(-0.789498\pi\)
−0.789187 + 0.614153i \(0.789498\pi\)
\(14\) −3.12770 −0.835914
\(15\) −3.32274 −0.857928
\(16\) 0.840683 0.210171
\(17\) 1.00000 0.242536
\(18\) −2.32739 −0.548571
\(19\) 3.29674 0.756324 0.378162 0.925739i \(-0.376556\pi\)
0.378162 + 0.925739i \(0.376556\pi\)
\(20\) 11.3530 2.53860
\(21\) −1.34387 −0.293256
\(22\) −15.3899 −3.28115
\(23\) 9.15661 1.90929 0.954643 0.297753i \(-0.0962372\pi\)
0.954643 + 0.297753i \(0.0962372\pi\)
\(24\) 3.29733 0.673065
\(25\) 6.04060 1.20812
\(26\) 13.2450 2.59755
\(27\) −1.00000 −0.192450
\(28\) 4.59166 0.867742
\(29\) 2.40186 0.446014 0.223007 0.974817i \(-0.428413\pi\)
0.223007 + 0.974817i \(0.428413\pi\)
\(30\) 7.73332 1.41190
\(31\) −0.697480 −0.125271 −0.0626356 0.998036i \(-0.519951\pi\)
−0.0626356 + 0.998036i \(0.519951\pi\)
\(32\) 4.63807 0.819902
\(33\) −6.61253 −1.15109
\(34\) −2.32739 −0.399144
\(35\) 4.46532 0.754777
\(36\) 3.41675 0.569458
\(37\) 8.01191 1.31715 0.658575 0.752515i \(-0.271160\pi\)
0.658575 + 0.752515i \(0.271160\pi\)
\(38\) −7.67281 −1.24469
\(39\) 5.69091 0.911275
\(40\) −10.9562 −1.73232
\(41\) −10.7539 −1.67947 −0.839736 0.542995i \(-0.817290\pi\)
−0.839736 + 0.542995i \(0.817290\pi\)
\(42\) 3.12770 0.482615
\(43\) 8.67047 1.32223 0.661117 0.750283i \(-0.270083\pi\)
0.661117 + 0.750283i \(0.270083\pi\)
\(44\) 22.5934 3.40608
\(45\) 3.32274 0.495325
\(46\) −21.3110 −3.14214
\(47\) 2.02538 0.295432 0.147716 0.989030i \(-0.452808\pi\)
0.147716 + 0.989030i \(0.452808\pi\)
\(48\) −0.840683 −0.121342
\(49\) −5.19402 −0.742003
\(50\) −14.0588 −1.98822
\(51\) −1.00000 −0.140028
\(52\) −19.4444 −2.69646
\(53\) −4.76109 −0.653986 −0.326993 0.945027i \(-0.606035\pi\)
−0.326993 + 0.945027i \(0.606035\pi\)
\(54\) 2.32739 0.316718
\(55\) 21.9717 2.96267
\(56\) −4.43118 −0.592141
\(57\) −3.29674 −0.436664
\(58\) −5.59007 −0.734012
\(59\) −2.52293 −0.328457 −0.164228 0.986422i \(-0.552513\pi\)
−0.164228 + 0.986422i \(0.552513\pi\)
\(60\) −11.3530 −1.46566
\(61\) −10.8784 −1.39283 −0.696416 0.717638i \(-0.745223\pi\)
−0.696416 + 0.717638i \(0.745223\pi\)
\(62\) 1.62331 0.206161
\(63\) 1.34387 0.169311
\(64\) −12.4760 −1.55950
\(65\) −18.9094 −2.34542
\(66\) 15.3899 1.89437
\(67\) −11.5508 −1.41115 −0.705575 0.708635i \(-0.749311\pi\)
−0.705575 + 0.708635i \(0.749311\pi\)
\(68\) 3.41675 0.414342
\(69\) −9.15661 −1.10233
\(70\) −10.3925 −1.24215
\(71\) 11.9722 1.42083 0.710417 0.703781i \(-0.248507\pi\)
0.710417 + 0.703781i \(0.248507\pi\)
\(72\) −3.29733 −0.388594
\(73\) 6.20046 0.725708 0.362854 0.931846i \(-0.381802\pi\)
0.362854 + 0.931846i \(0.381802\pi\)
\(74\) −18.6468 −2.16765
\(75\) −6.04060 −0.697508
\(76\) 11.2641 1.29209
\(77\) 8.88636 1.01269
\(78\) −13.2450 −1.49970
\(79\) −2.20634 −0.248232 −0.124116 0.992268i \(-0.539610\pi\)
−0.124116 + 0.992268i \(0.539610\pi\)
\(80\) 2.79337 0.312308
\(81\) 1.00000 0.111111
\(82\) 25.0285 2.76393
\(83\) 13.4909 1.48082 0.740411 0.672155i \(-0.234631\pi\)
0.740411 + 0.672155i \(0.234631\pi\)
\(84\) −4.59166 −0.500991
\(85\) 3.32274 0.360402
\(86\) −20.1796 −2.17602
\(87\) −2.40186 −0.257507
\(88\) −21.8037 −2.32428
\(89\) 13.4090 1.42135 0.710675 0.703521i \(-0.248390\pi\)
0.710675 + 0.703521i \(0.248390\pi\)
\(90\) −7.73332 −0.815163
\(91\) −7.64783 −0.801710
\(92\) 31.2859 3.26178
\(93\) 0.697480 0.0723253
\(94\) −4.71386 −0.486197
\(95\) 10.9542 1.12388
\(96\) −4.63807 −0.473371
\(97\) −7.16444 −0.727438 −0.363719 0.931509i \(-0.618493\pi\)
−0.363719 + 0.931509i \(0.618493\pi\)
\(98\) 12.0885 1.22112
\(99\) 6.61253 0.664584
\(100\) 20.6392 2.06392
\(101\) −8.47772 −0.843565 −0.421782 0.906697i \(-0.638595\pi\)
−0.421782 + 0.906697i \(0.638595\pi\)
\(102\) 2.32739 0.230446
\(103\) 16.6771 1.64324 0.821622 0.570032i \(-0.193069\pi\)
0.821622 + 0.570032i \(0.193069\pi\)
\(104\) 18.7648 1.84004
\(105\) −4.46532 −0.435771
\(106\) 11.0809 1.07627
\(107\) −5.07153 −0.490283 −0.245142 0.969487i \(-0.578834\pi\)
−0.245142 + 0.969487i \(0.578834\pi\)
\(108\) −3.41675 −0.328777
\(109\) 13.4840 1.29154 0.645768 0.763534i \(-0.276537\pi\)
0.645768 + 0.763534i \(0.276537\pi\)
\(110\) −51.1368 −4.87570
\(111\) −8.01191 −0.760457
\(112\) 1.12977 0.106753
\(113\) 1.05538 0.0992817 0.0496409 0.998767i \(-0.484192\pi\)
0.0496409 + 0.998767i \(0.484192\pi\)
\(114\) 7.67281 0.718624
\(115\) 30.4250 2.83715
\(116\) 8.20656 0.761960
\(117\) −5.69091 −0.526125
\(118\) 5.87184 0.540546
\(119\) 1.34387 0.123192
\(120\) 10.9562 1.00016
\(121\) 32.7256 2.97505
\(122\) 25.3182 2.29220
\(123\) 10.7539 0.969643
\(124\) −2.38312 −0.214010
\(125\) 3.45764 0.309261
\(126\) −3.12770 −0.278638
\(127\) 15.6374 1.38759 0.693797 0.720170i \(-0.255936\pi\)
0.693797 + 0.720170i \(0.255936\pi\)
\(128\) 19.7603 1.74658
\(129\) −8.67047 −0.763392
\(130\) 44.0096 3.85990
\(131\) −12.8581 −1.12342 −0.561709 0.827335i \(-0.689856\pi\)
−0.561709 + 0.827335i \(0.689856\pi\)
\(132\) −22.5934 −1.96650
\(133\) 4.43038 0.384163
\(134\) 26.8832 2.32235
\(135\) −3.32274 −0.285976
\(136\) −3.29733 −0.282744
\(137\) 7.89727 0.674709 0.337355 0.941378i \(-0.390468\pi\)
0.337355 + 0.941378i \(0.390468\pi\)
\(138\) 21.3110 1.81411
\(139\) −14.2178 −1.20594 −0.602969 0.797765i \(-0.706016\pi\)
−0.602969 + 0.797765i \(0.706016\pi\)
\(140\) 15.2569 1.28944
\(141\) −2.02538 −0.170568
\(142\) −27.8639 −2.33829
\(143\) −37.6313 −3.14689
\(144\) 0.840683 0.0700569
\(145\) 7.98076 0.662766
\(146\) −14.4309 −1.19431
\(147\) 5.19402 0.428396
\(148\) 27.3747 2.25019
\(149\) −18.3865 −1.50628 −0.753139 0.657861i \(-0.771461\pi\)
−0.753139 + 0.657861i \(0.771461\pi\)
\(150\) 14.0588 1.14790
\(151\) −1.29175 −0.105121 −0.0525606 0.998618i \(-0.516738\pi\)
−0.0525606 + 0.998618i \(0.516738\pi\)
\(152\) −10.8705 −0.881710
\(153\) 1.00000 0.0808452
\(154\) −20.6820 −1.66661
\(155\) −2.31755 −0.186150
\(156\) 19.4444 1.55680
\(157\) −1.00000 −0.0798087
\(158\) 5.13501 0.408519
\(159\) 4.76109 0.377579
\(160\) 15.4111 1.21835
\(161\) 12.3053 0.969791
\(162\) −2.32739 −0.182857
\(163\) 13.7858 1.07979 0.539895 0.841732i \(-0.318464\pi\)
0.539895 + 0.841732i \(0.318464\pi\)
\(164\) −36.7433 −2.86917
\(165\) −21.9717 −1.71050
\(166\) −31.3987 −2.43701
\(167\) 15.9001 1.23039 0.615195 0.788375i \(-0.289077\pi\)
0.615195 + 0.788375i \(0.289077\pi\)
\(168\) 4.43118 0.341873
\(169\) 19.3864 1.49127
\(170\) −7.73332 −0.593118
\(171\) 3.29674 0.252108
\(172\) 29.6248 2.25887
\(173\) −13.1914 −1.00292 −0.501462 0.865180i \(-0.667204\pi\)
−0.501462 + 0.865180i \(0.667204\pi\)
\(174\) 5.59007 0.423782
\(175\) 8.11776 0.613645
\(176\) 5.55904 0.419029
\(177\) 2.52293 0.189635
\(178\) −31.2080 −2.33914
\(179\) −16.0222 −1.19756 −0.598779 0.800914i \(-0.704347\pi\)
−0.598779 + 0.800914i \(0.704347\pi\)
\(180\) 11.3530 0.846201
\(181\) −5.64999 −0.419960 −0.209980 0.977706i \(-0.567340\pi\)
−0.209980 + 0.977706i \(0.567340\pi\)
\(182\) 17.7995 1.31939
\(183\) 10.8784 0.804152
\(184\) −30.1924 −2.22581
\(185\) 26.6215 1.95725
\(186\) −1.62331 −0.119027
\(187\) 6.61253 0.483556
\(188\) 6.92022 0.504709
\(189\) −1.34387 −0.0977520
\(190\) −25.4947 −1.84958
\(191\) 14.3928 1.04143 0.520713 0.853732i \(-0.325666\pi\)
0.520713 + 0.853732i \(0.325666\pi\)
\(192\) 12.4760 0.900375
\(193\) −20.5330 −1.47800 −0.739000 0.673706i \(-0.764701\pi\)
−0.739000 + 0.673706i \(0.764701\pi\)
\(194\) 16.6745 1.19716
\(195\) 18.9094 1.35413
\(196\) −17.7467 −1.26762
\(197\) 12.5215 0.892121 0.446060 0.895003i \(-0.352827\pi\)
0.446060 + 0.895003i \(0.352827\pi\)
\(198\) −15.3899 −1.09372
\(199\) 14.5813 1.03364 0.516822 0.856093i \(-0.327115\pi\)
0.516822 + 0.856093i \(0.327115\pi\)
\(200\) −19.9179 −1.40841
\(201\) 11.5508 0.814728
\(202\) 19.7310 1.38827
\(203\) 3.22778 0.226546
\(204\) −3.41675 −0.239220
\(205\) −35.7323 −2.49565
\(206\) −38.8142 −2.70431
\(207\) 9.15661 0.636429
\(208\) −4.78425 −0.331728
\(209\) 21.7998 1.50792
\(210\) 10.3925 0.717154
\(211\) 3.27818 0.225679 0.112839 0.993613i \(-0.464005\pi\)
0.112839 + 0.993613i \(0.464005\pi\)
\(212\) −16.2674 −1.11725
\(213\) −11.9722 −0.820318
\(214\) 11.8034 0.806866
\(215\) 28.8097 1.96481
\(216\) 3.29733 0.224355
\(217\) −0.937321 −0.0636295
\(218\) −31.3826 −2.12550
\(219\) −6.20046 −0.418988
\(220\) 75.0719 5.06134
\(221\) −5.69091 −0.382812
\(222\) 18.6468 1.25149
\(223\) 4.16671 0.279023 0.139512 0.990220i \(-0.455447\pi\)
0.139512 + 0.990220i \(0.455447\pi\)
\(224\) 6.23295 0.416456
\(225\) 6.04060 0.402707
\(226\) −2.45628 −0.163389
\(227\) 21.9351 1.45588 0.727942 0.685639i \(-0.240477\pi\)
0.727942 + 0.685639i \(0.240477\pi\)
\(228\) −11.2641 −0.745986
\(229\) −4.46636 −0.295145 −0.147573 0.989051i \(-0.547146\pi\)
−0.147573 + 0.989051i \(0.547146\pi\)
\(230\) −70.8110 −4.66914
\(231\) −8.88636 −0.584680
\(232\) −7.91974 −0.519956
\(233\) −6.53994 −0.428446 −0.214223 0.976785i \(-0.568722\pi\)
−0.214223 + 0.976785i \(0.568722\pi\)
\(234\) 13.2450 0.865851
\(235\) 6.72982 0.439005
\(236\) −8.62021 −0.561128
\(237\) 2.20634 0.143317
\(238\) −3.12770 −0.202739
\(239\) −9.55138 −0.617827 −0.308914 0.951090i \(-0.599965\pi\)
−0.308914 + 0.951090i \(0.599965\pi\)
\(240\) −2.79337 −0.180311
\(241\) −16.2977 −1.04983 −0.524913 0.851156i \(-0.675902\pi\)
−0.524913 + 0.851156i \(0.675902\pi\)
\(242\) −76.1652 −4.89608
\(243\) −1.00000 −0.0641500
\(244\) −37.1687 −2.37948
\(245\) −17.2584 −1.10260
\(246\) −25.0285 −1.59576
\(247\) −18.7615 −1.19376
\(248\) 2.29983 0.146039
\(249\) −13.4909 −0.854953
\(250\) −8.04728 −0.508955
\(251\) −23.7998 −1.50223 −0.751115 0.660171i \(-0.770484\pi\)
−0.751115 + 0.660171i \(0.770484\pi\)
\(252\) 4.59166 0.289247
\(253\) 60.5484 3.80664
\(254\) −36.3944 −2.28358
\(255\) −3.32274 −0.208078
\(256\) −21.0381 −1.31488
\(257\) −13.8093 −0.861401 −0.430700 0.902495i \(-0.641733\pi\)
−0.430700 + 0.902495i \(0.641733\pi\)
\(258\) 20.1796 1.25633
\(259\) 10.7669 0.669025
\(260\) −64.6087 −4.00686
\(261\) 2.40186 0.148671
\(262\) 29.9259 1.84883
\(263\) −18.3375 −1.13074 −0.565368 0.824839i \(-0.691266\pi\)
−0.565368 + 0.824839i \(0.691266\pi\)
\(264\) 21.8037 1.34193
\(265\) −15.8199 −0.971806
\(266\) −10.3112 −0.632222
\(267\) −13.4090 −0.820617
\(268\) −39.4661 −2.41077
\(269\) 6.94847 0.423656 0.211828 0.977307i \(-0.432058\pi\)
0.211828 + 0.977307i \(0.432058\pi\)
\(270\) 7.73332 0.470635
\(271\) 17.5830 1.06809 0.534046 0.845456i \(-0.320671\pi\)
0.534046 + 0.845456i \(0.320671\pi\)
\(272\) 0.840683 0.0509739
\(273\) 7.64783 0.462867
\(274\) −18.3800 −1.11038
\(275\) 39.9436 2.40869
\(276\) −31.2859 −1.88319
\(277\) 18.1426 1.09008 0.545042 0.838409i \(-0.316514\pi\)
0.545042 + 0.838409i \(0.316514\pi\)
\(278\) 33.0904 1.98463
\(279\) −0.697480 −0.0417571
\(280\) −14.7236 −0.879906
\(281\) −2.37433 −0.141641 −0.0708204 0.997489i \(-0.522562\pi\)
−0.0708204 + 0.997489i \(0.522562\pi\)
\(282\) 4.71386 0.280706
\(283\) 25.0080 1.48657 0.743287 0.668973i \(-0.233266\pi\)
0.743287 + 0.668973i \(0.233266\pi\)
\(284\) 40.9059 2.42732
\(285\) −10.9542 −0.648872
\(286\) 87.5828 5.17888
\(287\) −14.4518 −0.853061
\(288\) 4.63807 0.273301
\(289\) 1.00000 0.0588235
\(290\) −18.5744 −1.09072
\(291\) 7.16444 0.419987
\(292\) 21.1854 1.23978
\(293\) −7.01012 −0.409535 −0.204768 0.978811i \(-0.565644\pi\)
−0.204768 + 0.978811i \(0.565644\pi\)
\(294\) −12.0885 −0.705017
\(295\) −8.38303 −0.488079
\(296\) −26.4179 −1.53551
\(297\) −6.61253 −0.383698
\(298\) 42.7925 2.47890
\(299\) −52.1095 −3.01357
\(300\) −20.6392 −1.19161
\(301\) 11.6520 0.671608
\(302\) 3.00641 0.172999
\(303\) 8.47772 0.487032
\(304\) 2.77152 0.158957
\(305\) −36.1460 −2.06971
\(306\) −2.32739 −0.133048
\(307\) −23.0077 −1.31312 −0.656560 0.754273i \(-0.727989\pi\)
−0.656560 + 0.754273i \(0.727989\pi\)
\(308\) 30.3625 1.73006
\(309\) −16.6771 −0.948728
\(310\) 5.39384 0.306349
\(311\) 5.75350 0.326251 0.163126 0.986605i \(-0.447842\pi\)
0.163126 + 0.986605i \(0.447842\pi\)
\(312\) −18.7648 −1.06235
\(313\) −6.84090 −0.386670 −0.193335 0.981133i \(-0.561930\pi\)
−0.193335 + 0.981133i \(0.561930\pi\)
\(314\) 2.32739 0.131342
\(315\) 4.46532 0.251592
\(316\) −7.53850 −0.424074
\(317\) 10.4124 0.584819 0.292409 0.956293i \(-0.405543\pi\)
0.292409 + 0.956293i \(0.405543\pi\)
\(318\) −11.0809 −0.621387
\(319\) 15.8824 0.889243
\(320\) −41.4544 −2.31737
\(321\) 5.07153 0.283065
\(322\) −28.6392 −1.59600
\(323\) 3.29674 0.183436
\(324\) 3.41675 0.189819
\(325\) −34.3765 −1.90687
\(326\) −32.0850 −1.77703
\(327\) −13.4840 −0.745668
\(328\) 35.4591 1.95790
\(329\) 2.72184 0.150060
\(330\) 51.1368 2.81499
\(331\) −35.5826 −1.95580 −0.977899 0.209080i \(-0.932953\pi\)
−0.977899 + 0.209080i \(0.932953\pi\)
\(332\) 46.0951 2.52980
\(333\) 8.01191 0.439050
\(334\) −37.0058 −2.02487
\(335\) −38.3802 −2.09693
\(336\) −1.12977 −0.0616338
\(337\) 1.72703 0.0940772 0.0470386 0.998893i \(-0.485022\pi\)
0.0470386 + 0.998893i \(0.485022\pi\)
\(338\) −45.1198 −2.45420
\(339\) −1.05538 −0.0573203
\(340\) 11.3530 0.615701
\(341\) −4.61211 −0.249760
\(342\) −7.67281 −0.414898
\(343\) −16.3871 −0.884823
\(344\) −28.5894 −1.54144
\(345\) −30.4250 −1.63803
\(346\) 30.7016 1.65053
\(347\) 9.72179 0.521893 0.260947 0.965353i \(-0.415965\pi\)
0.260947 + 0.965353i \(0.415965\pi\)
\(348\) −8.20656 −0.439918
\(349\) −4.86787 −0.260571 −0.130285 0.991477i \(-0.541589\pi\)
−0.130285 + 0.991477i \(0.541589\pi\)
\(350\) −18.8932 −1.00988
\(351\) 5.69091 0.303758
\(352\) 30.6694 1.63468
\(353\) 19.9469 1.06167 0.530833 0.847476i \(-0.321879\pi\)
0.530833 + 0.847476i \(0.321879\pi\)
\(354\) −5.87184 −0.312085
\(355\) 39.7803 2.11132
\(356\) 45.8152 2.42820
\(357\) −1.34387 −0.0711250
\(358\) 37.2900 1.97084
\(359\) −31.0406 −1.63826 −0.819130 0.573608i \(-0.805543\pi\)
−0.819130 + 0.573608i \(0.805543\pi\)
\(360\) −10.9562 −0.577441
\(361\) −8.13149 −0.427973
\(362\) 13.1497 0.691135
\(363\) −32.7256 −1.71765
\(364\) −26.1307 −1.36962
\(365\) 20.6025 1.07838
\(366\) −25.3182 −1.32340
\(367\) 1.74313 0.0909906 0.0454953 0.998965i \(-0.485513\pi\)
0.0454953 + 0.998965i \(0.485513\pi\)
\(368\) 7.69781 0.401276
\(369\) −10.7539 −0.559824
\(370\) −61.9586 −3.22107
\(371\) −6.39827 −0.332182
\(372\) 2.38312 0.123559
\(373\) 14.3852 0.744836 0.372418 0.928065i \(-0.378529\pi\)
0.372418 + 0.928065i \(0.378529\pi\)
\(374\) −15.3899 −0.795795
\(375\) −3.45764 −0.178552
\(376\) −6.67836 −0.344410
\(377\) −13.6688 −0.703978
\(378\) 3.12770 0.160872
\(379\) 19.6571 1.00972 0.504859 0.863202i \(-0.331544\pi\)
0.504859 + 0.863202i \(0.331544\pi\)
\(380\) 37.4278 1.92001
\(381\) −15.6374 −0.801128
\(382\) −33.4976 −1.71389
\(383\) −25.1687 −1.28606 −0.643031 0.765840i \(-0.722323\pi\)
−0.643031 + 0.765840i \(0.722323\pi\)
\(384\) −19.7603 −1.00839
\(385\) 29.5271 1.50484
\(386\) 47.7884 2.43236
\(387\) 8.67047 0.440745
\(388\) −24.4791 −1.24274
\(389\) −8.73440 −0.442852 −0.221426 0.975177i \(-0.571071\pi\)
−0.221426 + 0.975177i \(0.571071\pi\)
\(390\) −44.0096 −2.22851
\(391\) 9.15661 0.463070
\(392\) 17.1264 0.865015
\(393\) 12.8581 0.648606
\(394\) −29.1425 −1.46818
\(395\) −7.33108 −0.368867
\(396\) 22.5934 1.13536
\(397\) 16.0492 0.805487 0.402744 0.915313i \(-0.368057\pi\)
0.402744 + 0.915313i \(0.368057\pi\)
\(398\) −33.9365 −1.70108
\(399\) −4.43038 −0.221797
\(400\) 5.07823 0.253911
\(401\) −15.3628 −0.767180 −0.383590 0.923503i \(-0.625312\pi\)
−0.383590 + 0.923503i \(0.625312\pi\)
\(402\) −26.8832 −1.34081
\(403\) 3.96930 0.197725
\(404\) −28.9663 −1.44113
\(405\) 3.32274 0.165108
\(406\) −7.51231 −0.372830
\(407\) 52.9790 2.62607
\(408\) 3.29733 0.163242
\(409\) −1.99130 −0.0984634 −0.0492317 0.998787i \(-0.515677\pi\)
−0.0492317 + 0.998787i \(0.515677\pi\)
\(410\) 83.1630 4.10713
\(411\) −7.89727 −0.389544
\(412\) 56.9815 2.80728
\(413\) −3.39048 −0.166834
\(414\) −21.3110 −1.04738
\(415\) 44.8268 2.20046
\(416\) −26.3948 −1.29411
\(417\) 14.2178 0.696248
\(418\) −50.7367 −2.48161
\(419\) 12.9930 0.634748 0.317374 0.948300i \(-0.397199\pi\)
0.317374 + 0.948300i \(0.397199\pi\)
\(420\) −15.2569 −0.744460
\(421\) −6.93314 −0.337901 −0.168950 0.985625i \(-0.554038\pi\)
−0.168950 + 0.985625i \(0.554038\pi\)
\(422\) −7.62960 −0.371403
\(423\) 2.02538 0.0984774
\(424\) 15.6989 0.762405
\(425\) 6.04060 0.293012
\(426\) 27.8639 1.35001
\(427\) −14.6191 −0.707467
\(428\) −17.3281 −0.837588
\(429\) 37.6313 1.81686
\(430\) −67.0515 −3.23351
\(431\) 15.8071 0.761400 0.380700 0.924699i \(-0.375683\pi\)
0.380700 + 0.924699i \(0.375683\pi\)
\(432\) −0.840683 −0.0404474
\(433\) 19.7601 0.949608 0.474804 0.880092i \(-0.342519\pi\)
0.474804 + 0.880092i \(0.342519\pi\)
\(434\) 2.18151 0.104716
\(435\) −7.98076 −0.382648
\(436\) 46.0716 2.20643
\(437\) 30.1870 1.44404
\(438\) 14.4309 0.689534
\(439\) −13.9659 −0.666555 −0.333278 0.942829i \(-0.608155\pi\)
−0.333278 + 0.942829i \(0.608155\pi\)
\(440\) −72.4481 −3.45383
\(441\) −5.19402 −0.247334
\(442\) 13.2450 0.629999
\(443\) −11.5698 −0.549698 −0.274849 0.961487i \(-0.588628\pi\)
−0.274849 + 0.961487i \(0.588628\pi\)
\(444\) −27.3747 −1.29915
\(445\) 44.5546 2.11209
\(446\) −9.69756 −0.459193
\(447\) 18.3865 0.869650
\(448\) −16.7660 −0.792121
\(449\) −39.4676 −1.86259 −0.931295 0.364265i \(-0.881320\pi\)
−0.931295 + 0.364265i \(0.881320\pi\)
\(450\) −14.0588 −0.662740
\(451\) −71.1103 −3.34845
\(452\) 3.60597 0.169610
\(453\) 1.29175 0.0606917
\(454\) −51.0516 −2.39597
\(455\) −25.4117 −1.19132
\(456\) 10.8705 0.509056
\(457\) −30.1436 −1.41006 −0.705030 0.709178i \(-0.749066\pi\)
−0.705030 + 0.709178i \(0.749066\pi\)
\(458\) 10.3950 0.485724
\(459\) −1.00000 −0.0466760
\(460\) 103.955 4.84692
\(461\) −1.31904 −0.0614339 −0.0307170 0.999528i \(-0.509779\pi\)
−0.0307170 + 0.999528i \(0.509779\pi\)
\(462\) 20.6820 0.962216
\(463\) 29.1315 1.35386 0.676929 0.736048i \(-0.263310\pi\)
0.676929 + 0.736048i \(0.263310\pi\)
\(464\) 2.01920 0.0937392
\(465\) 2.31755 0.107474
\(466\) 15.2210 0.705099
\(467\) −29.3480 −1.35806 −0.679032 0.734108i \(-0.737600\pi\)
−0.679032 + 0.734108i \(0.737600\pi\)
\(468\) −19.4444 −0.898818
\(469\) −15.5227 −0.716771
\(470\) −15.6629 −0.722476
\(471\) 1.00000 0.0460776
\(472\) 8.31893 0.382910
\(473\) 57.3337 2.63621
\(474\) −5.13501 −0.235859
\(475\) 19.9143 0.913731
\(476\) 4.59166 0.210458
\(477\) −4.76109 −0.217995
\(478\) 22.2298 1.01677
\(479\) 25.5498 1.16740 0.583700 0.811969i \(-0.301604\pi\)
0.583700 + 0.811969i \(0.301604\pi\)
\(480\) −15.4111 −0.703417
\(481\) −45.5950 −2.07895
\(482\) 37.9311 1.72771
\(483\) −12.3053 −0.559909
\(484\) 111.815 5.08250
\(485\) −23.8056 −1.08095
\(486\) 2.32739 0.105573
\(487\) −38.5443 −1.74661 −0.873305 0.487174i \(-0.838028\pi\)
−0.873305 + 0.487174i \(0.838028\pi\)
\(488\) 35.8696 1.62374
\(489\) −13.7858 −0.623417
\(490\) 40.1670 1.81456
\(491\) −11.9324 −0.538503 −0.269251 0.963070i \(-0.586776\pi\)
−0.269251 + 0.963070i \(0.586776\pi\)
\(492\) 36.7433 1.65651
\(493\) 2.40186 0.108174
\(494\) 43.6653 1.96459
\(495\) 21.9717 0.987555
\(496\) −0.586360 −0.0263283
\(497\) 16.0890 0.721690
\(498\) 31.3987 1.40701
\(499\) −30.4419 −1.36276 −0.681382 0.731928i \(-0.738621\pi\)
−0.681382 + 0.731928i \(0.738621\pi\)
\(500\) 11.8139 0.528333
\(501\) −15.9001 −0.710366
\(502\) 55.3915 2.47224
\(503\) −13.9165 −0.620504 −0.310252 0.950654i \(-0.600413\pi\)
−0.310252 + 0.950654i \(0.600413\pi\)
\(504\) −4.43118 −0.197380
\(505\) −28.1693 −1.25352
\(506\) −140.920 −6.26465
\(507\) −19.3864 −0.860982
\(508\) 53.4291 2.37053
\(509\) 33.7056 1.49397 0.746987 0.664838i \(-0.231500\pi\)
0.746987 + 0.664838i \(0.231500\pi\)
\(510\) 7.73332 0.342437
\(511\) 8.33259 0.368612
\(512\) 9.44317 0.417333
\(513\) −3.29674 −0.145555
\(514\) 32.1397 1.41762
\(515\) 55.4137 2.44182
\(516\) −29.6248 −1.30416
\(517\) 13.3929 0.589019
\(518\) −25.0589 −1.10102
\(519\) 13.1914 0.579039
\(520\) 62.3506 2.73426
\(521\) 38.3145 1.67859 0.839293 0.543679i \(-0.182969\pi\)
0.839293 + 0.543679i \(0.182969\pi\)
\(522\) −5.59007 −0.244671
\(523\) −19.0674 −0.833761 −0.416880 0.908961i \(-0.636877\pi\)
−0.416880 + 0.908961i \(0.636877\pi\)
\(524\) −43.9330 −1.91922
\(525\) −8.11776 −0.354288
\(526\) 42.6785 1.86087
\(527\) −0.697480 −0.0303827
\(528\) −5.55904 −0.241926
\(529\) 60.8436 2.64537
\(530\) 36.8190 1.59931
\(531\) −2.52293 −0.109486
\(532\) 15.1375 0.656294
\(533\) 61.1993 2.65083
\(534\) 31.2080 1.35050
\(535\) −16.8514 −0.728548
\(536\) 38.0867 1.64510
\(537\) 16.0222 0.691411
\(538\) −16.1718 −0.697216
\(539\) −34.3456 −1.47937
\(540\) −11.3530 −0.488554
\(541\) 3.55653 0.152907 0.0764536 0.997073i \(-0.475640\pi\)
0.0764536 + 0.997073i \(0.475640\pi\)
\(542\) −40.9225 −1.75777
\(543\) 5.64999 0.242464
\(544\) 4.63807 0.198855
\(545\) 44.8039 1.91919
\(546\) −17.7995 −0.761748
\(547\) 31.7365 1.35696 0.678478 0.734621i \(-0.262640\pi\)
0.678478 + 0.734621i \(0.262640\pi\)
\(548\) 26.9830 1.15266
\(549\) −10.8784 −0.464277
\(550\) −92.9645 −3.96402
\(551\) 7.91832 0.337332
\(552\) 30.1924 1.28507
\(553\) −2.96502 −0.126086
\(554\) −42.2250 −1.79397
\(555\) −26.6215 −1.13002
\(556\) −48.5786 −2.06019
\(557\) 4.64363 0.196757 0.0983785 0.995149i \(-0.468634\pi\)
0.0983785 + 0.995149i \(0.468634\pi\)
\(558\) 1.62331 0.0687202
\(559\) −49.3429 −2.08698
\(560\) 3.75392 0.158632
\(561\) −6.61253 −0.279181
\(562\) 5.52600 0.233100
\(563\) −42.4376 −1.78853 −0.894266 0.447535i \(-0.852302\pi\)
−0.894266 + 0.447535i \(0.852302\pi\)
\(564\) −6.92022 −0.291394
\(565\) 3.50675 0.147530
\(566\) −58.2035 −2.44647
\(567\) 1.34387 0.0564371
\(568\) −39.4762 −1.65638
\(569\) −26.7428 −1.12112 −0.560559 0.828114i \(-0.689414\pi\)
−0.560559 + 0.828114i \(0.689414\pi\)
\(570\) 25.4947 1.06786
\(571\) −12.1029 −0.506492 −0.253246 0.967402i \(-0.581498\pi\)
−0.253246 + 0.967402i \(0.581498\pi\)
\(572\) −128.577 −5.37607
\(573\) −14.3928 −0.601267
\(574\) 33.6349 1.40389
\(575\) 55.3114 2.30665
\(576\) −12.4760 −0.519832
\(577\) 6.35422 0.264530 0.132265 0.991214i \(-0.457775\pi\)
0.132265 + 0.991214i \(0.457775\pi\)
\(578\) −2.32739 −0.0968067
\(579\) 20.5330 0.853323
\(580\) 27.2683 1.13225
\(581\) 18.1300 0.752160
\(582\) −16.6745 −0.691178
\(583\) −31.4828 −1.30389
\(584\) −20.4450 −0.846019
\(585\) −18.9094 −0.781808
\(586\) 16.3153 0.673978
\(587\) −4.33028 −0.178730 −0.0893648 0.995999i \(-0.528484\pi\)
−0.0893648 + 0.995999i \(0.528484\pi\)
\(588\) 17.7467 0.731861
\(589\) −2.29941 −0.0947457
\(590\) 19.5106 0.803238
\(591\) −12.5215 −0.515066
\(592\) 6.73547 0.276826
\(593\) 1.81519 0.0745410 0.0372705 0.999305i \(-0.488134\pi\)
0.0372705 + 0.999305i \(0.488134\pi\)
\(594\) 15.3899 0.631457
\(595\) 4.46532 0.183060
\(596\) −62.8220 −2.57329
\(597\) −14.5813 −0.596775
\(598\) 121.279 4.95947
\(599\) 13.4305 0.548756 0.274378 0.961622i \(-0.411528\pi\)
0.274378 + 0.961622i \(0.411528\pi\)
\(600\) 19.9179 0.813144
\(601\) −18.5674 −0.757379 −0.378689 0.925524i \(-0.623625\pi\)
−0.378689 + 0.925524i \(0.623625\pi\)
\(602\) −27.1187 −1.10527
\(603\) −11.5508 −0.470384
\(604\) −4.41359 −0.179586
\(605\) 108.738 4.42085
\(606\) −19.7310 −0.801516
\(607\) 6.45040 0.261814 0.130907 0.991395i \(-0.458211\pi\)
0.130907 + 0.991395i \(0.458211\pi\)
\(608\) 15.2905 0.620112
\(609\) −3.22778 −0.130796
\(610\) 84.1258 3.40616
\(611\) −11.5263 −0.466303
\(612\) 3.41675 0.138114
\(613\) −48.2329 −1.94811 −0.974054 0.226315i \(-0.927332\pi\)
−0.974054 + 0.226315i \(0.927332\pi\)
\(614\) 53.5480 2.16102
\(615\) 35.7323 1.44087
\(616\) −29.3013 −1.18058
\(617\) 27.5600 1.10952 0.554762 0.832009i \(-0.312809\pi\)
0.554762 + 0.832009i \(0.312809\pi\)
\(618\) 38.8142 1.56133
\(619\) 11.5015 0.462285 0.231142 0.972920i \(-0.425754\pi\)
0.231142 + 0.972920i \(0.425754\pi\)
\(620\) −7.91848 −0.318014
\(621\) −9.15661 −0.367442
\(622\) −13.3907 −0.536916
\(623\) 18.0199 0.721952
\(624\) 4.78425 0.191523
\(625\) −18.7142 −0.748566
\(626\) 15.9214 0.636349
\(627\) −21.7998 −0.870600
\(628\) −3.41675 −0.136343
\(629\) 8.01191 0.319456
\(630\) −10.3925 −0.414049
\(631\) 12.3845 0.493017 0.246509 0.969141i \(-0.420717\pi\)
0.246509 + 0.969141i \(0.420717\pi\)
\(632\) 7.27503 0.289385
\(633\) −3.27818 −0.130296
\(634\) −24.2337 −0.962444
\(635\) 51.9590 2.06193
\(636\) 16.2674 0.645046
\(637\) 29.5587 1.17116
\(638\) −36.9645 −1.46344
\(639\) 11.9722 0.473611
\(640\) 65.6584 2.59538
\(641\) 10.1901 0.402485 0.201243 0.979541i \(-0.435502\pi\)
0.201243 + 0.979541i \(0.435502\pi\)
\(642\) −11.8034 −0.465844
\(643\) −22.1714 −0.874354 −0.437177 0.899376i \(-0.644022\pi\)
−0.437177 + 0.899376i \(0.644022\pi\)
\(644\) 42.0440 1.65677
\(645\) −28.8097 −1.13438
\(646\) −7.67281 −0.301883
\(647\) −0.718734 −0.0282564 −0.0141282 0.999900i \(-0.504497\pi\)
−0.0141282 + 0.999900i \(0.504497\pi\)
\(648\) −3.29733 −0.129531
\(649\) −16.6829 −0.654862
\(650\) 80.0076 3.13816
\(651\) 0.937321 0.0367365
\(652\) 47.1028 1.84469
\(653\) −5.19193 −0.203176 −0.101588 0.994827i \(-0.532392\pi\)
−0.101588 + 0.994827i \(0.532392\pi\)
\(654\) 31.3826 1.22716
\(655\) −42.7242 −1.66937
\(656\) −9.04059 −0.352976
\(657\) 6.20046 0.241903
\(658\) −6.33480 −0.246956
\(659\) −13.0414 −0.508021 −0.254011 0.967201i \(-0.581750\pi\)
−0.254011 + 0.967201i \(0.581750\pi\)
\(660\) −75.0719 −2.92217
\(661\) 26.3710 1.02571 0.512857 0.858474i \(-0.328587\pi\)
0.512857 + 0.858474i \(0.328587\pi\)
\(662\) 82.8147 3.21868
\(663\) 5.69091 0.221017
\(664\) −44.4841 −1.72632
\(665\) 14.7210 0.570856
\(666\) −18.6468 −0.722550
\(667\) 21.9929 0.851569
\(668\) 54.3268 2.10197
\(669\) −4.16671 −0.161094
\(670\) 89.3257 3.45095
\(671\) −71.9335 −2.77696
\(672\) −6.23295 −0.240441
\(673\) −14.3105 −0.551628 −0.275814 0.961211i \(-0.588947\pi\)
−0.275814 + 0.961211i \(0.588947\pi\)
\(674\) −4.01947 −0.154824
\(675\) −6.04060 −0.232503
\(676\) 66.2387 2.54764
\(677\) −1.46380 −0.0562583 −0.0281291 0.999604i \(-0.508955\pi\)
−0.0281291 + 0.999604i \(0.508955\pi\)
\(678\) 2.45628 0.0943329
\(679\) −9.62805 −0.369491
\(680\) −10.9562 −0.420150
\(681\) −21.9351 −0.840555
\(682\) 10.7342 0.411033
\(683\) 16.2029 0.619988 0.309994 0.950739i \(-0.399673\pi\)
0.309994 + 0.950739i \(0.399673\pi\)
\(684\) 11.2641 0.430695
\(685\) 26.2406 1.00260
\(686\) 38.1393 1.45617
\(687\) 4.46636 0.170402
\(688\) 7.28912 0.277895
\(689\) 27.0949 1.03223
\(690\) 70.8110 2.69573
\(691\) 43.6737 1.66143 0.830713 0.556701i \(-0.187933\pi\)
0.830713 + 0.556701i \(0.187933\pi\)
\(692\) −45.0718 −1.71337
\(693\) 8.88636 0.337565
\(694\) −22.6264 −0.858887
\(695\) −47.2420 −1.79199
\(696\) 7.91974 0.300197
\(697\) −10.7539 −0.407332
\(698\) 11.3294 0.428825
\(699\) 6.53994 0.247363
\(700\) 27.7364 1.04834
\(701\) 34.9340 1.31944 0.659720 0.751512i \(-0.270675\pi\)
0.659720 + 0.751512i \(0.270675\pi\)
\(702\) −13.2450 −0.499899
\(703\) 26.4132 0.996192
\(704\) −82.4977 −3.10925
\(705\) −6.72982 −0.253460
\(706\) −46.4242 −1.74720
\(707\) −11.3929 −0.428475
\(708\) 8.62021 0.323967
\(709\) −26.1764 −0.983076 −0.491538 0.870856i \(-0.663565\pi\)
−0.491538 + 0.870856i \(0.663565\pi\)
\(710\) −92.5844 −3.47463
\(711\) −2.20634 −0.0827441
\(712\) −44.2139 −1.65699
\(713\) −6.38656 −0.239178
\(714\) 3.12770 0.117051
\(715\) −125.039 −4.67619
\(716\) −54.7440 −2.04588
\(717\) 9.55138 0.356703
\(718\) 72.2436 2.69611
\(719\) −48.8397 −1.82141 −0.910707 0.413052i \(-0.864463\pi\)
−0.910707 + 0.413052i \(0.864463\pi\)
\(720\) 2.79337 0.104103
\(721\) 22.4118 0.834660
\(722\) 18.9252 0.704322
\(723\) 16.2977 0.606117
\(724\) −19.3046 −0.717450
\(725\) 14.5087 0.538839
\(726\) 76.1652 2.82675
\(727\) −0.921621 −0.0341810 −0.0170905 0.999854i \(-0.505440\pi\)
−0.0170905 + 0.999854i \(0.505440\pi\)
\(728\) 25.2174 0.934620
\(729\) 1.00000 0.0370370
\(730\) −47.9501 −1.77471
\(731\) 8.67047 0.320689
\(732\) 37.1687 1.37379
\(733\) −20.1621 −0.744706 −0.372353 0.928091i \(-0.621449\pi\)
−0.372353 + 0.928091i \(0.621449\pi\)
\(734\) −4.05695 −0.149745
\(735\) 17.2584 0.636585
\(736\) 42.4690 1.56543
\(737\) −76.3798 −2.81349
\(738\) 25.0285 0.921310
\(739\) −11.2639 −0.414351 −0.207176 0.978304i \(-0.566427\pi\)
−0.207176 + 0.978304i \(0.566427\pi\)
\(740\) 90.9590 3.34372
\(741\) 18.7615 0.689219
\(742\) 14.8913 0.546676
\(743\) 34.4926 1.26541 0.632705 0.774393i \(-0.281945\pi\)
0.632705 + 0.774393i \(0.281945\pi\)
\(744\) −2.29983 −0.0843157
\(745\) −61.0935 −2.23829
\(746\) −33.4799 −1.22579
\(747\) 13.4909 0.493607
\(748\) 22.5934 0.826095
\(749\) −6.81546 −0.249032
\(750\) 8.04728 0.293845
\(751\) 12.3314 0.449979 0.224990 0.974361i \(-0.427765\pi\)
0.224990 + 0.974361i \(0.427765\pi\)
\(752\) 1.70270 0.0620912
\(753\) 23.7998 0.867313
\(754\) 31.8126 1.15855
\(755\) −4.29215 −0.156207
\(756\) −4.59166 −0.166997
\(757\) 3.84629 0.139796 0.0698978 0.997554i \(-0.477733\pi\)
0.0698978 + 0.997554i \(0.477733\pi\)
\(758\) −45.7498 −1.66171
\(759\) −60.5484 −2.19777
\(760\) −36.1197 −1.31020
\(761\) 16.7457 0.607030 0.303515 0.952827i \(-0.401840\pi\)
0.303515 + 0.952827i \(0.401840\pi\)
\(762\) 36.3944 1.31843
\(763\) 18.1207 0.656015
\(764\) 49.1766 1.77915
\(765\) 3.32274 0.120134
\(766\) 58.5775 2.11649
\(767\) 14.3577 0.518428
\(768\) 21.0381 0.759146
\(769\) −27.3621 −0.986702 −0.493351 0.869830i \(-0.664228\pi\)
−0.493351 + 0.869830i \(0.664228\pi\)
\(770\) −68.7210 −2.47653
\(771\) 13.8093 0.497330
\(772\) −70.1562 −2.52498
\(773\) 6.73634 0.242289 0.121145 0.992635i \(-0.461343\pi\)
0.121145 + 0.992635i \(0.461343\pi\)
\(774\) −20.1796 −0.725340
\(775\) −4.21320 −0.151343
\(776\) 23.6235 0.848036
\(777\) −10.7669 −0.386262
\(778\) 20.3284 0.728807
\(779\) −35.4527 −1.27023
\(780\) 64.6087 2.31336
\(781\) 79.1662 2.83279
\(782\) −21.3110 −0.762081
\(783\) −2.40186 −0.0858355
\(784\) −4.36653 −0.155947
\(785\) −3.32274 −0.118594
\(786\) −29.9259 −1.06742
\(787\) −13.9835 −0.498457 −0.249228 0.968445i \(-0.580177\pi\)
−0.249228 + 0.968445i \(0.580177\pi\)
\(788\) 42.7829 1.52408
\(789\) 18.3375 0.652831
\(790\) 17.0623 0.607049
\(791\) 1.41829 0.0504286
\(792\) −21.8037 −0.774761
\(793\) 61.9078 2.19841
\(794\) −37.3528 −1.32560
\(795\) 15.8199 0.561072
\(796\) 49.8208 1.76585
\(797\) −14.7852 −0.523720 −0.261860 0.965106i \(-0.584336\pi\)
−0.261860 + 0.965106i \(0.584336\pi\)
\(798\) 10.3112 0.365014
\(799\) 2.02538 0.0716528
\(800\) 28.0167 0.990540
\(801\) 13.4090 0.473783
\(802\) 35.7552 1.26256
\(803\) 41.0007 1.44688
\(804\) 39.4661 1.39186
\(805\) 40.8872 1.44108
\(806\) −9.23811 −0.325399
\(807\) −6.94847 −0.244598
\(808\) 27.9539 0.983414
\(809\) 7.68490 0.270187 0.135093 0.990833i \(-0.456867\pi\)
0.135093 + 0.990833i \(0.456867\pi\)
\(810\) −7.73332 −0.271721
\(811\) 40.3889 1.41825 0.709123 0.705085i \(-0.249091\pi\)
0.709123 + 0.705085i \(0.249091\pi\)
\(812\) 11.0285 0.387025
\(813\) −17.5830 −0.616663
\(814\) −123.303 −4.32176
\(815\) 45.8067 1.60454
\(816\) −0.840683 −0.0294298
\(817\) 28.5843 1.00004
\(818\) 4.63453 0.162043
\(819\) −7.64783 −0.267237
\(820\) −122.088 −4.26351
\(821\) 47.1690 1.64621 0.823104 0.567890i \(-0.192240\pi\)
0.823104 + 0.567890i \(0.192240\pi\)
\(822\) 18.3800 0.641078
\(823\) −47.1418 −1.64326 −0.821630 0.570022i \(-0.806935\pi\)
−0.821630 + 0.570022i \(0.806935\pi\)
\(824\) −54.9900 −1.91567
\(825\) −39.9436 −1.39066
\(826\) 7.89097 0.274562
\(827\) −2.32575 −0.0808742 −0.0404371 0.999182i \(-0.512875\pi\)
−0.0404371 + 0.999182i \(0.512875\pi\)
\(828\) 31.2859 1.08726
\(829\) −1.25975 −0.0437529 −0.0218765 0.999761i \(-0.506964\pi\)
−0.0218765 + 0.999761i \(0.506964\pi\)
\(830\) −104.330 −3.62133
\(831\) −18.1426 −0.629360
\(832\) 70.9996 2.46147
\(833\) −5.19402 −0.179962
\(834\) −33.0904 −1.14583
\(835\) 52.8320 1.82833
\(836\) 74.4845 2.57610
\(837\) 0.697480 0.0241084
\(838\) −30.2397 −1.04461
\(839\) 39.2346 1.35453 0.677264 0.735740i \(-0.263166\pi\)
0.677264 + 0.735740i \(0.263166\pi\)
\(840\) 14.7236 0.508014
\(841\) −23.2311 −0.801071
\(842\) 16.1361 0.556088
\(843\) 2.37433 0.0817764
\(844\) 11.2007 0.385544
\(845\) 64.4161 2.21598
\(846\) −4.71386 −0.162066
\(847\) 43.9788 1.51113
\(848\) −4.00257 −0.137449
\(849\) −25.0080 −0.858274
\(850\) −14.0588 −0.482214
\(851\) 73.3619 2.51481
\(852\) −40.9059 −1.40141
\(853\) 0.193812 0.00663599 0.00331800 0.999994i \(-0.498944\pi\)
0.00331800 + 0.999994i \(0.498944\pi\)
\(854\) 34.0243 1.16429
\(855\) 10.9542 0.374626
\(856\) 16.7225 0.571564
\(857\) 11.1660 0.381424 0.190712 0.981646i \(-0.438920\pi\)
0.190712 + 0.981646i \(0.438920\pi\)
\(858\) −87.5828 −2.99003
\(859\) 37.7779 1.28897 0.644483 0.764619i \(-0.277073\pi\)
0.644483 + 0.764619i \(0.277073\pi\)
\(860\) 98.4356 3.35663
\(861\) 14.4518 0.492515
\(862\) −36.7892 −1.25305
\(863\) 36.3519 1.23743 0.618716 0.785615i \(-0.287653\pi\)
0.618716 + 0.785615i \(0.287653\pi\)
\(864\) −4.63807 −0.157790
\(865\) −43.8316 −1.49032
\(866\) −45.9894 −1.56278
\(867\) −1.00000 −0.0339618
\(868\) −3.20259 −0.108703
\(869\) −14.5895 −0.494914
\(870\) 18.5744 0.629729
\(871\) 65.7344 2.22732
\(872\) −44.4613 −1.50565
\(873\) −7.16444 −0.242479
\(874\) −70.2569 −2.37648
\(875\) 4.64661 0.157084
\(876\) −21.1854 −0.715789
\(877\) 1.64946 0.0556984 0.0278492 0.999612i \(-0.491134\pi\)
0.0278492 + 0.999612i \(0.491134\pi\)
\(878\) 32.5041 1.09696
\(879\) 7.01012 0.236445
\(880\) 18.4713 0.622666
\(881\) −16.5085 −0.556186 −0.278093 0.960554i \(-0.589702\pi\)
−0.278093 + 0.960554i \(0.589702\pi\)
\(882\) 12.0885 0.407042
\(883\) −6.45829 −0.217339 −0.108669 0.994078i \(-0.534659\pi\)
−0.108669 + 0.994078i \(0.534659\pi\)
\(884\) −19.4444 −0.653987
\(885\) 8.38303 0.281792
\(886\) 26.9274 0.904645
\(887\) 0.737297 0.0247560 0.0123780 0.999923i \(-0.496060\pi\)
0.0123780 + 0.999923i \(0.496060\pi\)
\(888\) 26.4179 0.886527
\(889\) 21.0146 0.704807
\(890\) −103.696 −3.47590
\(891\) 6.61253 0.221528
\(892\) 14.2366 0.476677
\(893\) 6.67716 0.223443
\(894\) −42.7925 −1.43120
\(895\) −53.2377 −1.77954
\(896\) 26.5552 0.887148
\(897\) 52.1095 1.73988
\(898\) 91.8565 3.06529
\(899\) −1.67525 −0.0558728
\(900\) 20.6392 0.687974
\(901\) −4.76109 −0.158615
\(902\) 165.501 5.51059
\(903\) −11.6520 −0.387753
\(904\) −3.47994 −0.115741
\(905\) −18.7734 −0.624050
\(906\) −3.00641 −0.0998812
\(907\) 5.40099 0.179337 0.0896685 0.995972i \(-0.471419\pi\)
0.0896685 + 0.995972i \(0.471419\pi\)
\(908\) 74.9468 2.48720
\(909\) −8.47772 −0.281188
\(910\) 59.1431 1.96057
\(911\) 50.3897 1.66949 0.834743 0.550639i \(-0.185616\pi\)
0.834743 + 0.550639i \(0.185616\pi\)
\(912\) −2.77152 −0.0917740
\(913\) 89.2091 2.95239
\(914\) 70.1560 2.32055
\(915\) 36.1460 1.19495
\(916\) −15.2604 −0.504219
\(917\) −17.2796 −0.570622
\(918\) 2.32739 0.0768154
\(919\) −51.5149 −1.69932 −0.849659 0.527332i \(-0.823192\pi\)
−0.849659 + 0.527332i \(0.823192\pi\)
\(920\) −100.321 −3.30750
\(921\) 23.0077 0.758131
\(922\) 3.06993 0.101103
\(923\) −68.1324 −2.24261
\(924\) −30.3625 −0.998852
\(925\) 48.3967 1.59127
\(926\) −67.8005 −2.22806
\(927\) 16.6771 0.547748
\(928\) 11.1400 0.365688
\(929\) 9.22204 0.302565 0.151283 0.988491i \(-0.451660\pi\)
0.151283 + 0.988491i \(0.451660\pi\)
\(930\) −5.39384 −0.176871
\(931\) −17.1233 −0.561195
\(932\) −22.3453 −0.731946
\(933\) −5.75350 −0.188361
\(934\) 68.3043 2.23499
\(935\) 21.9717 0.718552
\(936\) 18.7648 0.613347
\(937\) 6.78658 0.221708 0.110854 0.993837i \(-0.464641\pi\)
0.110854 + 0.993837i \(0.464641\pi\)
\(938\) 36.1274 1.17960
\(939\) 6.84090 0.223244
\(940\) 22.9941 0.749985
\(941\) −42.1257 −1.37326 −0.686630 0.727008i \(-0.740911\pi\)
−0.686630 + 0.727008i \(0.740911\pi\)
\(942\) −2.32739 −0.0758305
\(943\) −98.4690 −3.20659
\(944\) −2.12098 −0.0690321
\(945\) −4.46532 −0.145257
\(946\) −133.438 −4.33844
\(947\) −11.0615 −0.359450 −0.179725 0.983717i \(-0.557521\pi\)
−0.179725 + 0.983717i \(0.557521\pi\)
\(948\) 7.53850 0.244839
\(949\) −35.2862 −1.14544
\(950\) −46.3484 −1.50374
\(951\) −10.4124 −0.337645
\(952\) −4.43118 −0.143615
\(953\) −3.12289 −0.101160 −0.0505802 0.998720i \(-0.516107\pi\)
−0.0505802 + 0.998720i \(0.516107\pi\)
\(954\) 11.0809 0.358758
\(955\) 47.8235 1.54753
\(956\) −32.6347 −1.05548
\(957\) −15.8824 −0.513404
\(958\) −59.4644 −1.92121
\(959\) 10.6129 0.342708
\(960\) 41.4544 1.33793
\(961\) −30.5135 −0.984307
\(962\) 106.117 3.42137
\(963\) −5.07153 −0.163428
\(964\) −55.6851 −1.79350
\(965\) −68.2259 −2.19627
\(966\) 28.6392 0.921451
\(967\) 7.84030 0.252127 0.126064 0.992022i \(-0.459766\pi\)
0.126064 + 0.992022i \(0.459766\pi\)
\(968\) −107.907 −3.46826
\(969\) −3.29674 −0.105907
\(970\) 55.4049 1.77894
\(971\) 29.7540 0.954851 0.477425 0.878672i \(-0.341570\pi\)
0.477425 + 0.878672i \(0.341570\pi\)
\(972\) −3.41675 −0.109592
\(973\) −19.1068 −0.612537
\(974\) 89.7077 2.87442
\(975\) 34.3765 1.10093
\(976\) −9.14526 −0.292733
\(977\) −12.4161 −0.397227 −0.198614 0.980078i \(-0.563644\pi\)
−0.198614 + 0.980078i \(0.563644\pi\)
\(978\) 32.0850 1.02597
\(979\) 88.6673 2.83382
\(980\) −58.9676 −1.88365
\(981\) 13.4840 0.430512
\(982\) 27.7714 0.886221
\(983\) 0.206575 0.00658871 0.00329436 0.999995i \(-0.498951\pi\)
0.00329436 + 0.999995i \(0.498951\pi\)
\(984\) −35.4591 −1.13039
\(985\) 41.6057 1.32567
\(986\) −5.59007 −0.178024
\(987\) −2.72184 −0.0866372
\(988\) −64.1032 −2.03940
\(989\) 79.3921 2.52452
\(990\) −51.1368 −1.62523
\(991\) 10.2608 0.325944 0.162972 0.986631i \(-0.447892\pi\)
0.162972 + 0.986631i \(0.447892\pi\)
\(992\) −3.23496 −0.102710
\(993\) 35.5826 1.12918
\(994\) −37.4454 −1.18769
\(995\) 48.4500 1.53597
\(996\) −46.0951 −1.46058
\(997\) −10.8776 −0.344497 −0.172248 0.985054i \(-0.555103\pi\)
−0.172248 + 0.985054i \(0.555103\pi\)
\(998\) 70.8501 2.24272
\(999\) −8.01191 −0.253486
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 \(a_p\))