Properties

Label 8015.2.a.l.1.3
Level 8015
Weight 2
Character 8015.1
Self dual Yes
Analytic conductor 64.000
Analytic rank 0
Dimension 62
CM No

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Newspace parameters

Level: \( N \) = \( 8015 = 5 \cdot 7 \cdot 229 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8015.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0000972201\)
Analytic rank: \(0\)
Dimension: \(62\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Character \(\chi\) = 8015.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.61699 q^{2}\) \(+0.399813 q^{3}\) \(+4.84863 q^{4}\) \(-1.00000 q^{5}\) \(-1.04630 q^{6}\) \(-1.00000 q^{7}\) \(-7.45482 q^{8}\) \(-2.84015 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.61699 q^{2}\) \(+0.399813 q^{3}\) \(+4.84863 q^{4}\) \(-1.00000 q^{5}\) \(-1.04630 q^{6}\) \(-1.00000 q^{7}\) \(-7.45482 q^{8}\) \(-2.84015 q^{9}\) \(+2.61699 q^{10}\) \(+1.74534 q^{11}\) \(+1.93854 q^{12}\) \(+4.62721 q^{13}\) \(+2.61699 q^{14}\) \(-0.399813 q^{15}\) \(+9.81192 q^{16}\) \(+5.87048 q^{17}\) \(+7.43264 q^{18}\) \(+7.96108 q^{19}\) \(-4.84863 q^{20}\) \(-0.399813 q^{21}\) \(-4.56754 q^{22}\) \(-1.11824 q^{23}\) \(-2.98053 q^{24}\) \(+1.00000 q^{25}\) \(-12.1094 q^{26}\) \(-2.33497 q^{27}\) \(-4.84863 q^{28}\) \(-5.02093 q^{29}\) \(+1.04630 q^{30}\) \(+4.42471 q^{31}\) \(-10.7680 q^{32}\) \(+0.697810 q^{33}\) \(-15.3630 q^{34}\) \(+1.00000 q^{35}\) \(-13.7708 q^{36}\) \(+3.11946 q^{37}\) \(-20.8341 q^{38}\) \(+1.85002 q^{39}\) \(+7.45482 q^{40}\) \(-4.19477 q^{41}\) \(+1.04630 q^{42}\) \(+11.0065 q^{43}\) \(+8.46252 q^{44}\) \(+2.84015 q^{45}\) \(+2.92641 q^{46}\) \(+11.0169 q^{47}\) \(+3.92293 q^{48}\) \(+1.00000 q^{49}\) \(-2.61699 q^{50}\) \(+2.34709 q^{51}\) \(+22.4356 q^{52}\) \(-4.04621 q^{53}\) \(+6.11058 q^{54}\) \(-1.74534 q^{55}\) \(+7.45482 q^{56}\) \(+3.18294 q^{57}\) \(+13.1397 q^{58}\) \(+4.62878 q^{59}\) \(-1.93854 q^{60}\) \(+3.73455 q^{61}\) \(-11.5794 q^{62}\) \(+2.84015 q^{63}\) \(+8.55599 q^{64}\) \(-4.62721 q^{65}\) \(-1.82616 q^{66}\) \(-3.77666 q^{67}\) \(+28.4638 q^{68}\) \(-0.447085 q^{69}\) \(-2.61699 q^{70}\) \(+8.09433 q^{71}\) \(+21.1728 q^{72}\) \(-0.980406 q^{73}\) \(-8.16358 q^{74}\) \(+0.399813 q^{75}\) \(+38.6003 q^{76}\) \(-1.74534 q^{77}\) \(-4.84147 q^{78}\) \(+16.1440 q^{79}\) \(-9.81192 q^{80}\) \(+7.58690 q^{81}\) \(+10.9777 q^{82}\) \(+3.27280 q^{83}\) \(-1.93854 q^{84}\) \(-5.87048 q^{85}\) \(-28.8038 q^{86}\) \(-2.00743 q^{87}\) \(-13.0112 q^{88}\) \(-18.0829 q^{89}\) \(-7.43264 q^{90}\) \(-4.62721 q^{91}\) \(-5.42192 q^{92}\) \(+1.76905 q^{93}\) \(-28.8311 q^{94}\) \(-7.96108 q^{95}\) \(-4.30520 q^{96}\) \(-12.0081 q^{97}\) \(-2.61699 q^{98}\) \(-4.95704 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(62q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 64q^{4} \) \(\mathstrut -\mathstrut 62q^{5} \) \(\mathstrut +\mathstrut 3q^{6} \) \(\mathstrut -\mathstrut 62q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 69q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(62q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 64q^{4} \) \(\mathstrut -\mathstrut 62q^{5} \) \(\mathstrut +\mathstrut 3q^{6} \) \(\mathstrut -\mathstrut 62q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 69q^{9} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut -\mathstrut 13q^{11} \) \(\mathstrut +\mathstrut 37q^{12} \) \(\mathstrut +\mathstrut 31q^{13} \) \(\mathstrut -\mathstrut 2q^{14} \) \(\mathstrut -\mathstrut 11q^{15} \) \(\mathstrut +\mathstrut 64q^{16} \) \(\mathstrut +\mathstrut 30q^{17} \) \(\mathstrut +\mathstrut 18q^{18} \) \(\mathstrut +\mathstrut 20q^{19} \) \(\mathstrut -\mathstrut 64q^{20} \) \(\mathstrut -\mathstrut 11q^{21} \) \(\mathstrut +\mathstrut 7q^{22} \) \(\mathstrut +\mathstrut 29q^{24} \) \(\mathstrut +\mathstrut 62q^{25} \) \(\mathstrut +\mathstrut 59q^{27} \) \(\mathstrut -\mathstrut 64q^{28} \) \(\mathstrut -\mathstrut 29q^{29} \) \(\mathstrut -\mathstrut 3q^{30} \) \(\mathstrut +\mathstrut 20q^{31} \) \(\mathstrut +\mathstrut 22q^{32} \) \(\mathstrut +\mathstrut 72q^{33} \) \(\mathstrut +\mathstrut 13q^{34} \) \(\mathstrut +\mathstrut 62q^{35} \) \(\mathstrut +\mathstrut 53q^{36} \) \(\mathstrut +\mathstrut 35q^{37} \) \(\mathstrut +\mathstrut 34q^{38} \) \(\mathstrut -\mathstrut 6q^{39} \) \(\mathstrut -\mathstrut 15q^{40} \) \(\mathstrut +\mathstrut 13q^{41} \) \(\mathstrut -\mathstrut 3q^{42} \) \(\mathstrut -\mathstrut 4q^{43} \) \(\mathstrut -\mathstrut 44q^{44} \) \(\mathstrut -\mathstrut 69q^{45} \) \(\mathstrut -\mathstrut 19q^{46} \) \(\mathstrut +\mathstrut 58q^{47} \) \(\mathstrut +\mathstrut 64q^{48} \) \(\mathstrut +\mathstrut 62q^{49} \) \(\mathstrut +\mathstrut 2q^{50} \) \(\mathstrut -\mathstrut 30q^{51} \) \(\mathstrut +\mathstrut 82q^{52} \) \(\mathstrut +\mathstrut 18q^{53} \) \(\mathstrut +\mathstrut 22q^{54} \) \(\mathstrut +\mathstrut 13q^{55} \) \(\mathstrut -\mathstrut 15q^{56} \) \(\mathstrut +\mathstrut 21q^{57} \) \(\mathstrut +\mathstrut 18q^{58} \) \(\mathstrut -\mathstrut 11q^{59} \) \(\mathstrut -\mathstrut 37q^{60} \) \(\mathstrut +\mathstrut 24q^{61} \) \(\mathstrut +\mathstrut 48q^{62} \) \(\mathstrut -\mathstrut 69q^{63} \) \(\mathstrut +\mathstrut 65q^{64} \) \(\mathstrut -\mathstrut 31q^{65} \) \(\mathstrut +\mathstrut 25q^{66} \) \(\mathstrut -\mathstrut 6q^{67} \) \(\mathstrut +\mathstrut 65q^{68} \) \(\mathstrut +\mathstrut 27q^{69} \) \(\mathstrut +\mathstrut 2q^{70} \) \(\mathstrut -\mathstrut 35q^{71} \) \(\mathstrut +\mathstrut 53q^{72} \) \(\mathstrut +\mathstrut 116q^{73} \) \(\mathstrut -\mathstrut 69q^{74} \) \(\mathstrut +\mathstrut 11q^{75} \) \(\mathstrut +\mathstrut 65q^{76} \) \(\mathstrut +\mathstrut 13q^{77} \) \(\mathstrut +\mathstrut 102q^{78} \) \(\mathstrut -\mathstrut 83q^{79} \) \(\mathstrut -\mathstrut 64q^{80} \) \(\mathstrut +\mathstrut 126q^{81} \) \(\mathstrut +\mathstrut 71q^{82} \) \(\mathstrut +\mathstrut 84q^{83} \) \(\mathstrut -\mathstrut 37q^{84} \) \(\mathstrut -\mathstrut 30q^{85} \) \(\mathstrut +\mathstrut 24q^{86} \) \(\mathstrut +\mathstrut 49q^{87} \) \(\mathstrut +\mathstrut 20q^{88} \) \(\mathstrut -\mathstrut 16q^{89} \) \(\mathstrut -\mathstrut 18q^{90} \) \(\mathstrut -\mathstrut 31q^{91} \) \(\mathstrut +\mathstrut 19q^{92} \) \(\mathstrut +\mathstrut 65q^{93} \) \(\mathstrut +\mathstrut 54q^{94} \) \(\mathstrut -\mathstrut 20q^{95} \) \(\mathstrut +\mathstrut 17q^{96} \) \(\mathstrut +\mathstrut 155q^{97} \) \(\mathstrut +\mathstrut 2q^{98} \) \(\mathstrut +\mathstrut 6q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.61699 −1.85049 −0.925245 0.379370i \(-0.876141\pi\)
−0.925245 + 0.379370i \(0.876141\pi\)
\(3\) 0.399813 0.230832 0.115416 0.993317i \(-0.463180\pi\)
0.115416 + 0.993317i \(0.463180\pi\)
\(4\) 4.84863 2.42431
\(5\) −1.00000 −0.447214
\(6\) −1.04630 −0.427152
\(7\) −1.00000 −0.377964
\(8\) −7.45482 −2.63568
\(9\) −2.84015 −0.946717
\(10\) 2.61699 0.827564
\(11\) 1.74534 0.526241 0.263120 0.964763i \(-0.415248\pi\)
0.263120 + 0.964763i \(0.415248\pi\)
\(12\) 1.93854 0.559609
\(13\) 4.62721 1.28336 0.641679 0.766974i \(-0.278238\pi\)
0.641679 + 0.766974i \(0.278238\pi\)
\(14\) 2.61699 0.699419
\(15\) −0.399813 −0.103231
\(16\) 9.81192 2.45298
\(17\) 5.87048 1.42380 0.711901 0.702280i \(-0.247835\pi\)
0.711901 + 0.702280i \(0.247835\pi\)
\(18\) 7.43264 1.75189
\(19\) 7.96108 1.82640 0.913199 0.407514i \(-0.133604\pi\)
0.913199 + 0.407514i \(0.133604\pi\)
\(20\) −4.84863 −1.08419
\(21\) −0.399813 −0.0872462
\(22\) −4.56754 −0.973803
\(23\) −1.11824 −0.233169 −0.116584 0.993181i \(-0.537195\pi\)
−0.116584 + 0.993181i \(0.537195\pi\)
\(24\) −2.98053 −0.608398
\(25\) 1.00000 0.200000
\(26\) −12.1094 −2.37484
\(27\) −2.33497 −0.449364
\(28\) −4.84863 −0.916304
\(29\) −5.02093 −0.932364 −0.466182 0.884689i \(-0.654371\pi\)
−0.466182 + 0.884689i \(0.654371\pi\)
\(30\) 1.04630 0.191028
\(31\) 4.42471 0.794701 0.397350 0.917667i \(-0.369930\pi\)
0.397350 + 0.917667i \(0.369930\pi\)
\(32\) −10.7680 −1.90354
\(33\) 0.697810 0.121473
\(34\) −15.3630 −2.63473
\(35\) 1.00000 0.169031
\(36\) −13.7708 −2.29514
\(37\) 3.11946 0.512836 0.256418 0.966566i \(-0.417458\pi\)
0.256418 + 0.966566i \(0.417458\pi\)
\(38\) −20.8341 −3.37973
\(39\) 1.85002 0.296240
\(40\) 7.45482 1.17871
\(41\) −4.19477 −0.655112 −0.327556 0.944832i \(-0.606225\pi\)
−0.327556 + 0.944832i \(0.606225\pi\)
\(42\) 1.04630 0.161448
\(43\) 11.0065 1.67847 0.839235 0.543768i \(-0.183003\pi\)
0.839235 + 0.543768i \(0.183003\pi\)
\(44\) 8.46252 1.27577
\(45\) 2.84015 0.423385
\(46\) 2.92641 0.431476
\(47\) 11.0169 1.60698 0.803491 0.595317i \(-0.202974\pi\)
0.803491 + 0.595317i \(0.202974\pi\)
\(48\) 3.92293 0.566226
\(49\) 1.00000 0.142857
\(50\) −2.61699 −0.370098
\(51\) 2.34709 0.328659
\(52\) 22.4356 3.11126
\(53\) −4.04621 −0.555790 −0.277895 0.960611i \(-0.589637\pi\)
−0.277895 + 0.960611i \(0.589637\pi\)
\(54\) 6.11058 0.831544
\(55\) −1.74534 −0.235342
\(56\) 7.45482 0.996192
\(57\) 3.18294 0.421591
\(58\) 13.1397 1.72533
\(59\) 4.62878 0.602615 0.301308 0.953527i \(-0.402577\pi\)
0.301308 + 0.953527i \(0.402577\pi\)
\(60\) −1.93854 −0.250265
\(61\) 3.73455 0.478160 0.239080 0.971000i \(-0.423154\pi\)
0.239080 + 0.971000i \(0.423154\pi\)
\(62\) −11.5794 −1.47059
\(63\) 2.84015 0.357825
\(64\) 8.55599 1.06950
\(65\) −4.62721 −0.573935
\(66\) −1.82616 −0.224785
\(67\) −3.77666 −0.461392 −0.230696 0.973026i \(-0.574100\pi\)
−0.230696 + 0.973026i \(0.574100\pi\)
\(68\) 28.4638 3.45174
\(69\) −0.447085 −0.0538228
\(70\) −2.61699 −0.312790
\(71\) 8.09433 0.960620 0.480310 0.877099i \(-0.340524\pi\)
0.480310 + 0.877099i \(0.340524\pi\)
\(72\) 21.1728 2.49524
\(73\) −0.980406 −0.114748 −0.0573739 0.998353i \(-0.518273\pi\)
−0.0573739 + 0.998353i \(0.518273\pi\)
\(74\) −8.16358 −0.948997
\(75\) 0.399813 0.0461664
\(76\) 38.6003 4.42776
\(77\) −1.74534 −0.198900
\(78\) −4.84147 −0.548189
\(79\) 16.1440 1.81634 0.908171 0.418599i \(-0.137479\pi\)
0.908171 + 0.418599i \(0.137479\pi\)
\(80\) −9.81192 −1.09701
\(81\) 7.58690 0.842989
\(82\) 10.9777 1.21228
\(83\) 3.27280 0.359237 0.179618 0.983736i \(-0.442514\pi\)
0.179618 + 0.983736i \(0.442514\pi\)
\(84\) −1.93854 −0.211512
\(85\) −5.87048 −0.636743
\(86\) −28.8038 −3.10599
\(87\) −2.00743 −0.215219
\(88\) −13.0112 −1.38700
\(89\) −18.0829 −1.91678 −0.958391 0.285457i \(-0.907854\pi\)
−0.958391 + 0.285457i \(0.907854\pi\)
\(90\) −7.43264 −0.783469
\(91\) −4.62721 −0.485063
\(92\) −5.42192 −0.565274
\(93\) 1.76905 0.183442
\(94\) −28.8311 −2.97370
\(95\) −7.96108 −0.816790
\(96\) −4.30520 −0.439397
\(97\) −12.0081 −1.21924 −0.609619 0.792694i \(-0.708678\pi\)
−0.609619 + 0.792694i \(0.708678\pi\)
\(98\) −2.61699 −0.264356
\(99\) −4.95704 −0.498201
\(100\) 4.84863 0.484863
\(101\) −17.1467 −1.70616 −0.853081 0.521778i \(-0.825269\pi\)
−0.853081 + 0.521778i \(0.825269\pi\)
\(102\) −6.14231 −0.608180
\(103\) 4.67886 0.461022 0.230511 0.973070i \(-0.425960\pi\)
0.230511 + 0.973070i \(0.425960\pi\)
\(104\) −34.4950 −3.38251
\(105\) 0.399813 0.0390177
\(106\) 10.5889 1.02848
\(107\) 15.6843 1.51626 0.758128 0.652106i \(-0.226114\pi\)
0.758128 + 0.652106i \(0.226114\pi\)
\(108\) −11.3214 −1.08940
\(109\) −10.0647 −0.964022 −0.482011 0.876165i \(-0.660094\pi\)
−0.482011 + 0.876165i \(0.660094\pi\)
\(110\) 4.56754 0.435498
\(111\) 1.24720 0.118379
\(112\) −9.81192 −0.927139
\(113\) 10.3814 0.976602 0.488301 0.872675i \(-0.337617\pi\)
0.488301 + 0.872675i \(0.337617\pi\)
\(114\) −8.32972 −0.780149
\(115\) 1.11824 0.104276
\(116\) −24.3446 −2.26034
\(117\) −13.1420 −1.21498
\(118\) −12.1134 −1.11513
\(119\) −5.87048 −0.538146
\(120\) 2.98053 0.272084
\(121\) −7.95378 −0.723071
\(122\) −9.77326 −0.884830
\(123\) −1.67712 −0.151221
\(124\) 21.4537 1.92660
\(125\) −1.00000 −0.0894427
\(126\) −7.43264 −0.662152
\(127\) −2.59810 −0.230544 −0.115272 0.993334i \(-0.536774\pi\)
−0.115272 + 0.993334i \(0.536774\pi\)
\(128\) −0.854844 −0.0755582
\(129\) 4.40052 0.387445
\(130\) 12.1094 1.06206
\(131\) 5.88602 0.514264 0.257132 0.966376i \(-0.417223\pi\)
0.257132 + 0.966376i \(0.417223\pi\)
\(132\) 3.38342 0.294489
\(133\) −7.96108 −0.690313
\(134\) 9.88346 0.853801
\(135\) 2.33497 0.200962
\(136\) −43.7634 −3.75268
\(137\) −12.3957 −1.05904 −0.529519 0.848298i \(-0.677627\pi\)
−0.529519 + 0.848298i \(0.677627\pi\)
\(138\) 1.17002 0.0995985
\(139\) −0.288058 −0.0244328 −0.0122164 0.999925i \(-0.503889\pi\)
−0.0122164 + 0.999925i \(0.503889\pi\)
\(140\) 4.84863 0.409784
\(141\) 4.40470 0.370943
\(142\) −21.1828 −1.77762
\(143\) 8.07607 0.675355
\(144\) −27.8673 −2.32228
\(145\) 5.02093 0.416966
\(146\) 2.56571 0.212340
\(147\) 0.399813 0.0329760
\(148\) 15.1251 1.24327
\(149\) −7.05276 −0.577785 −0.288892 0.957362i \(-0.593287\pi\)
−0.288892 + 0.957362i \(0.593287\pi\)
\(150\) −1.04630 −0.0854304
\(151\) 4.99633 0.406595 0.203298 0.979117i \(-0.434834\pi\)
0.203298 + 0.979117i \(0.434834\pi\)
\(152\) −59.3484 −4.81379
\(153\) −16.6730 −1.34794
\(154\) 4.56754 0.368063
\(155\) −4.42471 −0.355401
\(156\) 8.97004 0.718178
\(157\) 20.9123 1.66898 0.834491 0.551021i \(-0.185762\pi\)
0.834491 + 0.551021i \(0.185762\pi\)
\(158\) −42.2487 −3.36112
\(159\) −1.61773 −0.128294
\(160\) 10.7680 0.851288
\(161\) 1.11824 0.0881295
\(162\) −19.8548 −1.55994
\(163\) −15.8104 −1.23836 −0.619182 0.785247i \(-0.712536\pi\)
−0.619182 + 0.785247i \(0.712536\pi\)
\(164\) −20.3389 −1.58820
\(165\) −0.697810 −0.0543245
\(166\) −8.56488 −0.664764
\(167\) −1.06983 −0.0827856 −0.0413928 0.999143i \(-0.513179\pi\)
−0.0413928 + 0.999143i \(0.513179\pi\)
\(168\) 2.98053 0.229953
\(169\) 8.41107 0.647006
\(170\) 15.3630 1.17829
\(171\) −22.6107 −1.72908
\(172\) 53.3663 4.06914
\(173\) 17.0568 1.29680 0.648402 0.761298i \(-0.275438\pi\)
0.648402 + 0.761298i \(0.275438\pi\)
\(174\) 5.25342 0.398261
\(175\) −1.00000 −0.0755929
\(176\) 17.1252 1.29086
\(177\) 1.85064 0.139103
\(178\) 47.3227 3.54699
\(179\) −10.9703 −0.819957 −0.409978 0.912095i \(-0.634464\pi\)
−0.409978 + 0.912095i \(0.634464\pi\)
\(180\) 13.7708 1.02642
\(181\) −26.1359 −1.94267 −0.971334 0.237719i \(-0.923600\pi\)
−0.971334 + 0.237719i \(0.923600\pi\)
\(182\) 12.1094 0.897605
\(183\) 1.49312 0.110374
\(184\) 8.33626 0.614557
\(185\) −3.11946 −0.229347
\(186\) −4.62959 −0.339458
\(187\) 10.2460 0.749262
\(188\) 53.4169 3.89583
\(189\) 2.33497 0.169844
\(190\) 20.8341 1.51146
\(191\) 14.8135 1.07187 0.535933 0.844260i \(-0.319960\pi\)
0.535933 + 0.844260i \(0.319960\pi\)
\(192\) 3.42079 0.246874
\(193\) 6.19822 0.446158 0.223079 0.974800i \(-0.428389\pi\)
0.223079 + 0.974800i \(0.428389\pi\)
\(194\) 31.4251 2.25619
\(195\) −1.85002 −0.132482
\(196\) 4.84863 0.346330
\(197\) 27.3227 1.94667 0.973333 0.229398i \(-0.0736759\pi\)
0.973333 + 0.229398i \(0.0736759\pi\)
\(198\) 12.9725 0.921916
\(199\) −6.64068 −0.470745 −0.235373 0.971905i \(-0.575631\pi\)
−0.235373 + 0.971905i \(0.575631\pi\)
\(200\) −7.45482 −0.527135
\(201\) −1.50995 −0.106504
\(202\) 44.8728 3.15724
\(203\) 5.02093 0.352400
\(204\) 11.3802 0.796771
\(205\) 4.19477 0.292975
\(206\) −12.2445 −0.853117
\(207\) 3.17596 0.220745
\(208\) 45.4018 3.14805
\(209\) 13.8948 0.961125
\(210\) −1.04630 −0.0722019
\(211\) −1.42768 −0.0982859 −0.0491429 0.998792i \(-0.515649\pi\)
−0.0491429 + 0.998792i \(0.515649\pi\)
\(212\) −19.6186 −1.34741
\(213\) 3.23622 0.221742
\(214\) −41.0456 −2.80582
\(215\) −11.0065 −0.750635
\(216\) 17.4067 1.18438
\(217\) −4.42471 −0.300369
\(218\) 26.3392 1.78391
\(219\) −0.391979 −0.0264875
\(220\) −8.46252 −0.570543
\(221\) 27.1640 1.82725
\(222\) −3.26390 −0.219059
\(223\) −24.4896 −1.63994 −0.819972 0.572404i \(-0.806011\pi\)
−0.819972 + 0.572404i \(0.806011\pi\)
\(224\) 10.7680 0.719470
\(225\) −2.84015 −0.189343
\(226\) −27.1680 −1.80719
\(227\) 19.5428 1.29710 0.648549 0.761173i \(-0.275376\pi\)
0.648549 + 0.761173i \(0.275376\pi\)
\(228\) 15.4329 1.02207
\(229\) 1.00000 0.0660819
\(230\) −2.92641 −0.192962
\(231\) −0.697810 −0.0459125
\(232\) 37.4301 2.45741
\(233\) −19.9048 −1.30401 −0.652005 0.758215i \(-0.726072\pi\)
−0.652005 + 0.758215i \(0.726072\pi\)
\(234\) 34.3924 2.24830
\(235\) −11.0169 −0.718664
\(236\) 22.4432 1.46093
\(237\) 6.45457 0.419270
\(238\) 15.3630 0.995834
\(239\) −19.7477 −1.27737 −0.638687 0.769467i \(-0.720522\pi\)
−0.638687 + 0.769467i \(0.720522\pi\)
\(240\) −3.92293 −0.253224
\(241\) −7.36370 −0.474337 −0.237169 0.971468i \(-0.576219\pi\)
−0.237169 + 0.971468i \(0.576219\pi\)
\(242\) 20.8149 1.33803
\(243\) 10.0382 0.643953
\(244\) 18.1074 1.15921
\(245\) −1.00000 −0.0638877
\(246\) 4.38900 0.279833
\(247\) 36.8376 2.34392
\(248\) −32.9854 −2.09457
\(249\) 1.30851 0.0829233
\(250\) 2.61699 0.165513
\(251\) −16.6724 −1.05235 −0.526176 0.850375i \(-0.676375\pi\)
−0.526176 + 0.850375i \(0.676375\pi\)
\(252\) 13.7708 0.867480
\(253\) −1.95171 −0.122703
\(254\) 6.79918 0.426619
\(255\) −2.34709 −0.146981
\(256\) −14.8749 −0.929679
\(257\) −27.6047 −1.72194 −0.860968 0.508659i \(-0.830142\pi\)
−0.860968 + 0.508659i \(0.830142\pi\)
\(258\) −11.5161 −0.716962
\(259\) −3.11946 −0.193834
\(260\) −22.4356 −1.39140
\(261\) 14.2602 0.882684
\(262\) −15.4036 −0.951640
\(263\) 1.22268 0.0753939 0.0376970 0.999289i \(-0.487998\pi\)
0.0376970 + 0.999289i \(0.487998\pi\)
\(264\) −5.20205 −0.320164
\(265\) 4.04621 0.248557
\(266\) 20.8341 1.27742
\(267\) −7.22977 −0.442455
\(268\) −18.3116 −1.11856
\(269\) −8.34156 −0.508594 −0.254297 0.967126i \(-0.581844\pi\)
−0.254297 + 0.967126i \(0.581844\pi\)
\(270\) −6.11058 −0.371878
\(271\) 28.8883 1.75484 0.877418 0.479726i \(-0.159264\pi\)
0.877418 + 0.479726i \(0.159264\pi\)
\(272\) 57.6007 3.49256
\(273\) −1.85002 −0.111968
\(274\) 32.4394 1.95974
\(275\) 1.74534 0.105248
\(276\) −2.16775 −0.130483
\(277\) 3.67855 0.221022 0.110511 0.993875i \(-0.464751\pi\)
0.110511 + 0.993875i \(0.464751\pi\)
\(278\) 0.753845 0.0452126
\(279\) −12.5668 −0.752357
\(280\) −7.45482 −0.445511
\(281\) 5.35347 0.319361 0.159681 0.987169i \(-0.448954\pi\)
0.159681 + 0.987169i \(0.448954\pi\)
\(282\) −11.5270 −0.686426
\(283\) 7.28641 0.433132 0.216566 0.976268i \(-0.430514\pi\)
0.216566 + 0.976268i \(0.430514\pi\)
\(284\) 39.2464 2.32884
\(285\) −3.18294 −0.188541
\(286\) −21.1350 −1.24974
\(287\) 4.19477 0.247609
\(288\) 30.5829 1.80211
\(289\) 17.4626 1.02721
\(290\) −13.1397 −0.771591
\(291\) −4.80099 −0.281439
\(292\) −4.75362 −0.278185
\(293\) 17.2228 1.00617 0.503085 0.864237i \(-0.332198\pi\)
0.503085 + 0.864237i \(0.332198\pi\)
\(294\) −1.04630 −0.0610217
\(295\) −4.62878 −0.269498
\(296\) −23.2550 −1.35167
\(297\) −4.07532 −0.236474
\(298\) 18.4570 1.06918
\(299\) −5.17432 −0.299239
\(300\) 1.93854 0.111922
\(301\) −11.0065 −0.634402
\(302\) −13.0753 −0.752401
\(303\) −6.85547 −0.393837
\(304\) 78.1135 4.48012
\(305\) −3.73455 −0.213840
\(306\) 43.6332 2.49434
\(307\) −16.6755 −0.951724 −0.475862 0.879520i \(-0.657864\pi\)
−0.475862 + 0.879520i \(0.657864\pi\)
\(308\) −8.46252 −0.482197
\(309\) 1.87067 0.106419
\(310\) 11.5794 0.657666
\(311\) −18.4942 −1.04871 −0.524356 0.851499i \(-0.675694\pi\)
−0.524356 + 0.851499i \(0.675694\pi\)
\(312\) −13.7915 −0.780792
\(313\) 14.3145 0.809104 0.404552 0.914515i \(-0.367427\pi\)
0.404552 + 0.914515i \(0.367427\pi\)
\(314\) −54.7272 −3.08844
\(315\) −2.84015 −0.160024
\(316\) 78.2762 4.40338
\(317\) −9.01546 −0.506358 −0.253179 0.967419i \(-0.581476\pi\)
−0.253179 + 0.967419i \(0.581476\pi\)
\(318\) 4.23357 0.237407
\(319\) −8.76325 −0.490648
\(320\) −8.55599 −0.478294
\(321\) 6.27077 0.350000
\(322\) −2.92641 −0.163083
\(323\) 46.7354 2.60043
\(324\) 36.7860 2.04367
\(325\) 4.62721 0.256671
\(326\) 41.3756 2.29158
\(327\) −4.02399 −0.222527
\(328\) 31.2712 1.72666
\(329\) −11.0169 −0.607382
\(330\) 1.82616 0.100527
\(331\) 26.8503 1.47583 0.737913 0.674896i \(-0.235812\pi\)
0.737913 + 0.674896i \(0.235812\pi\)
\(332\) 15.8686 0.870902
\(333\) −8.85972 −0.485510
\(334\) 2.79972 0.153194
\(335\) 3.77666 0.206341
\(336\) −3.92293 −0.214013
\(337\) −0.0243478 −0.00132631 −0.000663153 1.00000i \(-0.500211\pi\)
−0.000663153 1.00000i \(0.500211\pi\)
\(338\) −22.0117 −1.19728
\(339\) 4.15062 0.225431
\(340\) −28.4638 −1.54366
\(341\) 7.72263 0.418204
\(342\) 59.1718 3.19965
\(343\) −1.00000 −0.0539949
\(344\) −82.0513 −4.42391
\(345\) 0.447085 0.0240703
\(346\) −44.6374 −2.39972
\(347\) −15.2660 −0.819520 −0.409760 0.912193i \(-0.634387\pi\)
−0.409760 + 0.912193i \(0.634387\pi\)
\(348\) −9.73328 −0.521759
\(349\) 13.3273 0.713396 0.356698 0.934220i \(-0.383903\pi\)
0.356698 + 0.934220i \(0.383903\pi\)
\(350\) 2.61699 0.139884
\(351\) −10.8044 −0.576695
\(352\) −18.7939 −1.00172
\(353\) −6.19490 −0.329721 −0.164860 0.986317i \(-0.552717\pi\)
−0.164860 + 0.986317i \(0.552717\pi\)
\(354\) −4.84311 −0.257408
\(355\) −8.09433 −0.429603
\(356\) −87.6772 −4.64688
\(357\) −2.34709 −0.124221
\(358\) 28.7091 1.51732
\(359\) −18.2903 −0.965327 −0.482663 0.875806i \(-0.660331\pi\)
−0.482663 + 0.875806i \(0.660331\pi\)
\(360\) −21.1728 −1.11590
\(361\) 44.3788 2.33573
\(362\) 68.3974 3.59489
\(363\) −3.18002 −0.166908
\(364\) −22.4356 −1.17595
\(365\) 0.980406 0.0513168
\(366\) −3.90747 −0.204247
\(367\) 1.92784 0.100632 0.0503162 0.998733i \(-0.483977\pi\)
0.0503162 + 0.998733i \(0.483977\pi\)
\(368\) −10.9721 −0.571958
\(369\) 11.9138 0.620206
\(370\) 8.16358 0.424404
\(371\) 4.04621 0.210069
\(372\) 8.57748 0.444721
\(373\) 21.3939 1.10773 0.553867 0.832605i \(-0.313152\pi\)
0.553867 + 0.832605i \(0.313152\pi\)
\(374\) −26.8137 −1.38650
\(375\) −0.399813 −0.0206462
\(376\) −82.1291 −4.23548
\(377\) −23.2329 −1.19656
\(378\) −6.11058 −0.314294
\(379\) 3.18364 0.163533 0.0817663 0.996652i \(-0.473944\pi\)
0.0817663 + 0.996652i \(0.473944\pi\)
\(380\) −38.6003 −1.98015
\(381\) −1.03875 −0.0532168
\(382\) −38.7667 −1.98348
\(383\) 26.9179 1.37544 0.687719 0.725977i \(-0.258612\pi\)
0.687719 + 0.725977i \(0.258612\pi\)
\(384\) −0.341777 −0.0174412
\(385\) 1.74534 0.0889509
\(386\) −16.2207 −0.825610
\(387\) −31.2600 −1.58904
\(388\) −58.2228 −2.95581
\(389\) −27.8349 −1.41128 −0.705642 0.708569i \(-0.749341\pi\)
−0.705642 + 0.708569i \(0.749341\pi\)
\(390\) 4.84147 0.245157
\(391\) −6.56459 −0.331986
\(392\) −7.45482 −0.376525
\(393\) 2.35330 0.118708
\(394\) −71.5033 −3.60228
\(395\) −16.1440 −0.812293
\(396\) −24.0348 −1.20780
\(397\) −11.3496 −0.569618 −0.284809 0.958584i \(-0.591930\pi\)
−0.284809 + 0.958584i \(0.591930\pi\)
\(398\) 17.3786 0.871110
\(399\) −3.18294 −0.159346
\(400\) 9.81192 0.490596
\(401\) 12.1063 0.604557 0.302279 0.953220i \(-0.402253\pi\)
0.302279 + 0.953220i \(0.402253\pi\)
\(402\) 3.95153 0.197084
\(403\) 20.4740 1.01989
\(404\) −83.1380 −4.13627
\(405\) −7.58690 −0.376996
\(406\) −13.1397 −0.652113
\(407\) 5.44452 0.269875
\(408\) −17.4971 −0.866238
\(409\) 34.3705 1.69951 0.849755 0.527177i \(-0.176750\pi\)
0.849755 + 0.527177i \(0.176750\pi\)
\(410\) −10.9777 −0.542148
\(411\) −4.95596 −0.244460
\(412\) 22.6861 1.11766
\(413\) −4.62878 −0.227767
\(414\) −8.31146 −0.408486
\(415\) −3.27280 −0.160656
\(416\) −49.8260 −2.44292
\(417\) −0.115169 −0.00563986
\(418\) −36.3626 −1.77855
\(419\) −34.4905 −1.68497 −0.842485 0.538719i \(-0.818908\pi\)
−0.842485 + 0.538719i \(0.818908\pi\)
\(420\) 1.93854 0.0945911
\(421\) −4.21410 −0.205383 −0.102691 0.994713i \(-0.532745\pi\)
−0.102691 + 0.994713i \(0.532745\pi\)
\(422\) 3.73623 0.181877
\(423\) −31.2897 −1.52136
\(424\) 30.1638 1.46488
\(425\) 5.87048 0.284760
\(426\) −8.46914 −0.410331
\(427\) −3.73455 −0.180727
\(428\) 76.0472 3.67588
\(429\) 3.22891 0.155893
\(430\) 28.8038 1.38904
\(431\) 2.04410 0.0984606 0.0492303 0.998787i \(-0.484323\pi\)
0.0492303 + 0.998787i \(0.484323\pi\)
\(432\) −22.9105 −1.10228
\(433\) 12.4201 0.596873 0.298437 0.954429i \(-0.403535\pi\)
0.298437 + 0.954429i \(0.403535\pi\)
\(434\) 11.5794 0.555829
\(435\) 2.00743 0.0962490
\(436\) −48.7999 −2.33709
\(437\) −8.90238 −0.425859
\(438\) 1.02580 0.0490148
\(439\) −19.1695 −0.914912 −0.457456 0.889232i \(-0.651239\pi\)
−0.457456 + 0.889232i \(0.651239\pi\)
\(440\) 13.0112 0.620286
\(441\) −2.84015 −0.135245
\(442\) −71.0877 −3.38130
\(443\) 13.1937 0.626853 0.313426 0.949613i \(-0.398523\pi\)
0.313426 + 0.949613i \(0.398523\pi\)
\(444\) 6.04720 0.286987
\(445\) 18.0829 0.857211
\(446\) 64.0889 3.03470
\(447\) −2.81978 −0.133371
\(448\) −8.55599 −0.404233
\(449\) 37.3597 1.76311 0.881556 0.472080i \(-0.156497\pi\)
0.881556 + 0.472080i \(0.156497\pi\)
\(450\) 7.43264 0.350378
\(451\) −7.32131 −0.344747
\(452\) 50.3356 2.36759
\(453\) 1.99759 0.0938552
\(454\) −51.1432 −2.40027
\(455\) 4.62721 0.216927
\(456\) −23.7282 −1.11118
\(457\) 9.80953 0.458870 0.229435 0.973324i \(-0.426312\pi\)
0.229435 + 0.973324i \(0.426312\pi\)
\(458\) −2.61699 −0.122284
\(459\) −13.7074 −0.639805
\(460\) 5.42192 0.252798
\(461\) −19.4924 −0.907852 −0.453926 0.891039i \(-0.649977\pi\)
−0.453926 + 0.891039i \(0.649977\pi\)
\(462\) 1.82616 0.0849607
\(463\) 26.3337 1.22383 0.611915 0.790923i \(-0.290399\pi\)
0.611915 + 0.790923i \(0.290399\pi\)
\(464\) −49.2650 −2.28707
\(465\) −1.76905 −0.0820379
\(466\) 52.0907 2.41306
\(467\) −20.7782 −0.961501 −0.480750 0.876858i \(-0.659636\pi\)
−0.480750 + 0.876858i \(0.659636\pi\)
\(468\) −63.7205 −2.94548
\(469\) 3.77666 0.174390
\(470\) 28.8311 1.32988
\(471\) 8.36100 0.385254
\(472\) −34.5067 −1.58830
\(473\) 19.2101 0.883280
\(474\) −16.8915 −0.775854
\(475\) 7.96108 0.365280
\(476\) −28.4638 −1.30463
\(477\) 11.4919 0.526176
\(478\) 51.6796 2.36377
\(479\) −41.0377 −1.87506 −0.937530 0.347905i \(-0.886893\pi\)
−0.937530 + 0.347905i \(0.886893\pi\)
\(480\) 4.30520 0.196504
\(481\) 14.4344 0.658151
\(482\) 19.2707 0.877756
\(483\) 0.447085 0.0203431
\(484\) −38.5649 −1.75295
\(485\) 12.0081 0.545260
\(486\) −26.2699 −1.19163
\(487\) −5.20716 −0.235959 −0.117980 0.993016i \(-0.537642\pi\)
−0.117980 + 0.993016i \(0.537642\pi\)
\(488\) −27.8404 −1.26027
\(489\) −6.32119 −0.285854
\(490\) 2.61699 0.118223
\(491\) 22.6705 1.02311 0.511553 0.859252i \(-0.329071\pi\)
0.511553 + 0.859252i \(0.329071\pi\)
\(492\) −8.13173 −0.366607
\(493\) −29.4753 −1.32750
\(494\) −96.4036 −4.33740
\(495\) 4.95704 0.222802
\(496\) 43.4149 1.94939
\(497\) −8.09433 −0.363080
\(498\) −3.42435 −0.153449
\(499\) 31.3705 1.40434 0.702168 0.712011i \(-0.252215\pi\)
0.702168 + 0.712011i \(0.252215\pi\)
\(500\) −4.84863 −0.216837
\(501\) −0.427730 −0.0191095
\(502\) 43.6315 1.94737
\(503\) 32.8822 1.46615 0.733073 0.680150i \(-0.238085\pi\)
0.733073 + 0.680150i \(0.238085\pi\)
\(504\) −21.1728 −0.943112
\(505\) 17.1467 0.763019
\(506\) 5.10760 0.227060
\(507\) 3.36285 0.149350
\(508\) −12.5972 −0.558910
\(509\) −31.4170 −1.39253 −0.696266 0.717784i \(-0.745157\pi\)
−0.696266 + 0.717784i \(0.745157\pi\)
\(510\) 6.14231 0.271986
\(511\) 0.980406 0.0433706
\(512\) 40.6370 1.79592
\(513\) −18.5888 −0.820718
\(514\) 72.2413 3.18643
\(515\) −4.67886 −0.206175
\(516\) 21.3365 0.939287
\(517\) 19.2283 0.845660
\(518\) 8.16358 0.358687
\(519\) 6.81952 0.299344
\(520\) 34.4950 1.51271
\(521\) 34.2747 1.50160 0.750800 0.660529i \(-0.229668\pi\)
0.750800 + 0.660529i \(0.229668\pi\)
\(522\) −37.3188 −1.63340
\(523\) 13.2657 0.580070 0.290035 0.957016i \(-0.406333\pi\)
0.290035 + 0.957016i \(0.406333\pi\)
\(524\) 28.5391 1.24674
\(525\) −0.399813 −0.0174492
\(526\) −3.19975 −0.139516
\(527\) 25.9752 1.13150
\(528\) 6.84686 0.297971
\(529\) −21.7495 −0.945632
\(530\) −10.5889 −0.459952
\(531\) −13.1464 −0.570506
\(532\) −38.6003 −1.67354
\(533\) −19.4101 −0.840743
\(534\) 18.9202 0.818758
\(535\) −15.6843 −0.678090
\(536\) 28.1543 1.21608
\(537\) −4.38605 −0.189272
\(538\) 21.8298 0.941148
\(539\) 1.74534 0.0751773
\(540\) 11.3214 0.487194
\(541\) 4.00772 0.172306 0.0861528 0.996282i \(-0.472543\pi\)
0.0861528 + 0.996282i \(0.472543\pi\)
\(542\) −75.6002 −3.24731
\(543\) −10.4495 −0.448430
\(544\) −63.2136 −2.71026
\(545\) 10.0647 0.431124
\(546\) 4.84147 0.207196
\(547\) −45.1572 −1.93078 −0.965390 0.260810i \(-0.916011\pi\)
−0.965390 + 0.260810i \(0.916011\pi\)
\(548\) −60.1022 −2.56744
\(549\) −10.6067 −0.452682
\(550\) −4.56754 −0.194761
\(551\) −39.9721 −1.70287
\(552\) 3.33294 0.141859
\(553\) −16.1440 −0.686513
\(554\) −9.62671 −0.409000
\(555\) −1.24720 −0.0529406
\(556\) −1.39669 −0.0592327
\(557\) −3.57824 −0.151615 −0.0758073 0.997122i \(-0.524153\pi\)
−0.0758073 + 0.997122i \(0.524153\pi\)
\(558\) 32.8872 1.39223
\(559\) 50.9293 2.15408
\(560\) 9.81192 0.414629
\(561\) 4.09648 0.172954
\(562\) −14.0100 −0.590975
\(563\) 36.3504 1.53199 0.765994 0.642848i \(-0.222247\pi\)
0.765994 + 0.642848i \(0.222247\pi\)
\(564\) 21.3567 0.899281
\(565\) −10.3814 −0.436750
\(566\) −19.0684 −0.801507
\(567\) −7.58690 −0.318620
\(568\) −60.3418 −2.53188
\(569\) 32.3304 1.35536 0.677681 0.735356i \(-0.262985\pi\)
0.677681 + 0.735356i \(0.262985\pi\)
\(570\) 8.32972 0.348893
\(571\) 38.8893 1.62747 0.813734 0.581237i \(-0.197431\pi\)
0.813734 + 0.581237i \(0.197431\pi\)
\(572\) 39.1579 1.63727
\(573\) 5.92262 0.247421
\(574\) −10.9777 −0.458198
\(575\) −1.11824 −0.0466337
\(576\) −24.3003 −1.01251
\(577\) −3.75212 −0.156203 −0.0781015 0.996945i \(-0.524886\pi\)
−0.0781015 + 0.996945i \(0.524886\pi\)
\(578\) −45.6993 −1.90084
\(579\) 2.47813 0.102987
\(580\) 24.3446 1.01086
\(581\) −3.27280 −0.135779
\(582\) 12.5641 0.520800
\(583\) −7.06203 −0.292480
\(584\) 7.30875 0.302438
\(585\) 13.1420 0.543354
\(586\) −45.0720 −1.86191
\(587\) 15.5047 0.639946 0.319973 0.947427i \(-0.396326\pi\)
0.319973 + 0.947427i \(0.396326\pi\)
\(588\) 1.93854 0.0799441
\(589\) 35.2255 1.45144
\(590\) 12.1134 0.498703
\(591\) 10.9240 0.449352
\(592\) 30.6079 1.25798
\(593\) −19.3929 −0.796370 −0.398185 0.917305i \(-0.630360\pi\)
−0.398185 + 0.917305i \(0.630360\pi\)
\(594\) 10.6651 0.437592
\(595\) 5.87048 0.240666
\(596\) −34.1962 −1.40073
\(597\) −2.65503 −0.108663
\(598\) 13.5411 0.553738
\(599\) 1.58856 0.0649067 0.0324534 0.999473i \(-0.489668\pi\)
0.0324534 + 0.999473i \(0.489668\pi\)
\(600\) −2.98053 −0.121680
\(601\) 0.541877 0.0221036 0.0110518 0.999939i \(-0.496482\pi\)
0.0110518 + 0.999939i \(0.496482\pi\)
\(602\) 28.8038 1.17396
\(603\) 10.7263 0.436807
\(604\) 24.2253 0.985714
\(605\) 7.95378 0.323367
\(606\) 17.9407 0.728791
\(607\) 29.7086 1.20583 0.602917 0.797804i \(-0.294005\pi\)
0.602917 + 0.797804i \(0.294005\pi\)
\(608\) −85.7253 −3.47662
\(609\) 2.00743 0.0813452
\(610\) 9.77326 0.395708
\(611\) 50.9776 2.06233
\(612\) −80.8414 −3.26782
\(613\) 13.8927 0.561121 0.280560 0.959836i \(-0.409480\pi\)
0.280560 + 0.959836i \(0.409480\pi\)
\(614\) 43.6397 1.76115
\(615\) 1.67712 0.0676280
\(616\) 13.0112 0.524237
\(617\) 9.63940 0.388068 0.194034 0.980995i \(-0.437843\pi\)
0.194034 + 0.980995i \(0.437843\pi\)
\(618\) −4.89552 −0.196927
\(619\) −16.2902 −0.654759 −0.327380 0.944893i \(-0.606166\pi\)
−0.327380 + 0.944893i \(0.606166\pi\)
\(620\) −21.4537 −0.861603
\(621\) 2.61105 0.104778
\(622\) 48.3992 1.94063
\(623\) 18.0829 0.724476
\(624\) 18.1522 0.726670
\(625\) 1.00000 0.0400000
\(626\) −37.4609 −1.49724
\(627\) 5.55532 0.221858
\(628\) 101.396 4.04614
\(629\) 18.3127 0.730176
\(630\) 7.43264 0.296123
\(631\) −15.4851 −0.616452 −0.308226 0.951313i \(-0.599735\pi\)
−0.308226 + 0.951313i \(0.599735\pi\)
\(632\) −120.351 −4.78729
\(633\) −0.570806 −0.0226875
\(634\) 23.5933 0.937011
\(635\) 2.59810 0.103102
\(636\) −7.84375 −0.311025
\(637\) 4.62721 0.183337
\(638\) 22.9333 0.907939
\(639\) −22.9891 −0.909435
\(640\) 0.854844 0.0337907
\(641\) 4.01235 0.158478 0.0792391 0.996856i \(-0.474751\pi\)
0.0792391 + 0.996856i \(0.474751\pi\)
\(642\) −16.4105 −0.647672
\(643\) 31.5934 1.24592 0.622961 0.782253i \(-0.285929\pi\)
0.622961 + 0.782253i \(0.285929\pi\)
\(644\) 5.42192 0.213653
\(645\) −4.40052 −0.173270
\(646\) −122.306 −4.81206
\(647\) −36.8732 −1.44963 −0.724817 0.688942i \(-0.758076\pi\)
−0.724817 + 0.688942i \(0.758076\pi\)
\(648\) −56.5590 −2.22185
\(649\) 8.07880 0.317121
\(650\) −12.1094 −0.474968
\(651\) −1.76905 −0.0693347
\(652\) −76.6586 −3.00218
\(653\) −48.5667 −1.90056 −0.950281 0.311394i \(-0.899204\pi\)
−0.950281 + 0.311394i \(0.899204\pi\)
\(654\) 10.5307 0.411784
\(655\) −5.88602 −0.229986
\(656\) −41.1587 −1.60698
\(657\) 2.78450 0.108634
\(658\) 28.8311 1.12395
\(659\) −43.7606 −1.70467 −0.852335 0.522996i \(-0.824814\pi\)
−0.852335 + 0.522996i \(0.824814\pi\)
\(660\) −3.38342 −0.131699
\(661\) −40.1405 −1.56129 −0.780643 0.624977i \(-0.785108\pi\)
−0.780643 + 0.624977i \(0.785108\pi\)
\(662\) −70.2669 −2.73100
\(663\) 10.8605 0.421786
\(664\) −24.3982 −0.946832
\(665\) 7.96108 0.308718
\(666\) 23.1858 0.898431
\(667\) 5.61460 0.217398
\(668\) −5.18718 −0.200698
\(669\) −9.79124 −0.378551
\(670\) −9.88346 −0.381831
\(671\) 6.51807 0.251627
\(672\) 4.30520 0.166077
\(673\) −3.67180 −0.141537 −0.0707687 0.997493i \(-0.522545\pi\)
−0.0707687 + 0.997493i \(0.522545\pi\)
\(674\) 0.0637178 0.00245432
\(675\) −2.33497 −0.0898728
\(676\) 40.7822 1.56854
\(677\) 26.9689 1.03650 0.518250 0.855229i \(-0.326584\pi\)
0.518250 + 0.855229i \(0.326584\pi\)
\(678\) −10.8621 −0.417157
\(679\) 12.0081 0.460829
\(680\) 43.7634 1.67825
\(681\) 7.81344 0.299412
\(682\) −20.2100 −0.773882
\(683\) 42.0721 1.60984 0.804921 0.593381i \(-0.202207\pi\)
0.804921 + 0.593381i \(0.202207\pi\)
\(684\) −109.631 −4.19183
\(685\) 12.3957 0.473616
\(686\) 2.61699 0.0999171
\(687\) 0.399813 0.0152538
\(688\) 107.995 4.11726
\(689\) −18.7227 −0.713277
\(690\) −1.17002 −0.0445418
\(691\) 39.4007 1.49887 0.749436 0.662077i \(-0.230325\pi\)
0.749436 + 0.662077i \(0.230325\pi\)
\(692\) 82.7020 3.14386
\(693\) 4.95704 0.188302
\(694\) 39.9508 1.51651
\(695\) 0.288058 0.0109267
\(696\) 14.9650 0.567248
\(697\) −24.6253 −0.932750
\(698\) −34.8775 −1.32013
\(699\) −7.95821 −0.301007
\(700\) −4.84863 −0.183261
\(701\) 12.3263 0.465558 0.232779 0.972530i \(-0.425218\pi\)
0.232779 + 0.972530i \(0.425218\pi\)
\(702\) 28.2749 1.06717
\(703\) 24.8343 0.936642
\(704\) 14.9331 0.562814
\(705\) −4.40470 −0.165891
\(706\) 16.2120 0.610145
\(707\) 17.1467 0.644869
\(708\) 8.97307 0.337229
\(709\) 14.7548 0.554128 0.277064 0.960851i \(-0.410639\pi\)
0.277064 + 0.960851i \(0.410639\pi\)
\(710\) 21.1828 0.794975
\(711\) −45.8514 −1.71956
\(712\) 134.805 5.05202
\(713\) −4.94787 −0.185299
\(714\) 6.14231 0.229870
\(715\) −8.07607 −0.302028
\(716\) −53.1908 −1.98783
\(717\) −7.89539 −0.294859
\(718\) 47.8656 1.78633
\(719\) 21.2135 0.791130 0.395565 0.918438i \(-0.370549\pi\)
0.395565 + 0.918438i \(0.370549\pi\)
\(720\) 27.8673 1.03855
\(721\) −4.67886 −0.174250
\(722\) −116.139 −4.32224
\(723\) −2.94410 −0.109492
\(724\) −126.723 −4.70963
\(725\) −5.02093 −0.186473
\(726\) 8.32207 0.308861
\(727\) 6.23478 0.231235 0.115618 0.993294i \(-0.463115\pi\)
0.115618 + 0.993294i \(0.463115\pi\)
\(728\) 34.4950 1.27847
\(729\) −18.7473 −0.694344
\(730\) −2.56571 −0.0949612
\(731\) 64.6133 2.38981
\(732\) 7.23957 0.267582
\(733\) −45.2162 −1.67010 −0.835049 0.550175i \(-0.814561\pi\)
−0.835049 + 0.550175i \(0.814561\pi\)
\(734\) −5.04513 −0.186219
\(735\) −0.399813 −0.0147473
\(736\) 12.0412 0.443846
\(737\) −6.59156 −0.242803
\(738\) −31.1782 −1.14768
\(739\) 47.6842 1.75409 0.877046 0.480406i \(-0.159511\pi\)
0.877046 + 0.480406i \(0.159511\pi\)
\(740\) −15.1251 −0.556009
\(741\) 14.7281 0.541052
\(742\) −10.5889 −0.388730
\(743\) −24.3019 −0.891550 −0.445775 0.895145i \(-0.647072\pi\)
−0.445775 + 0.895145i \(0.647072\pi\)
\(744\) −13.1880 −0.483495
\(745\) 7.05276 0.258393
\(746\) −55.9875 −2.04985
\(747\) −9.29525 −0.340095
\(748\) 49.6791 1.81645
\(749\) −15.6843 −0.573091
\(750\) 1.04630 0.0382056
\(751\) −7.15359 −0.261038 −0.130519 0.991446i \(-0.541664\pi\)
−0.130519 + 0.991446i \(0.541664\pi\)
\(752\) 108.097 3.94189
\(753\) −6.66584 −0.242917
\(754\) 60.8002 2.21421
\(755\) −4.99633 −0.181835
\(756\) 11.3214 0.411754
\(757\) 20.6426 0.750266 0.375133 0.926971i \(-0.377597\pi\)
0.375133 + 0.926971i \(0.377597\pi\)
\(758\) −8.33154 −0.302615
\(759\) −0.780318 −0.0283237
\(760\) 59.3484 2.15279
\(761\) 15.4737 0.560921 0.280461 0.959866i \(-0.409513\pi\)
0.280461 + 0.959866i \(0.409513\pi\)
\(762\) 2.71840 0.0984772
\(763\) 10.0647 0.364366
\(764\) 71.8251 2.59854
\(765\) 16.6730 0.602815
\(766\) −70.4437 −2.54524
\(767\) 21.4183 0.773371
\(768\) −5.94716 −0.214600
\(769\) 6.69276 0.241347 0.120673 0.992692i \(-0.461495\pi\)
0.120673 + 0.992692i \(0.461495\pi\)
\(770\) −4.56754 −0.164603
\(771\) −11.0367 −0.397478
\(772\) 30.0528 1.08163
\(773\) 16.9051 0.608033 0.304017 0.952667i \(-0.401672\pi\)
0.304017 + 0.952667i \(0.401672\pi\)
\(774\) 81.8071 2.94050
\(775\) 4.42471 0.158940
\(776\) 89.5182 3.21352
\(777\) −1.24720 −0.0447430
\(778\) 72.8435 2.61157
\(779\) −33.3949 −1.19650
\(780\) −8.97004 −0.321179
\(781\) 14.1274 0.505518
\(782\) 17.1795 0.614336
\(783\) 11.7237 0.418971
\(784\) 9.81192 0.350426
\(785\) −20.9123 −0.746392
\(786\) −6.15857 −0.219669
\(787\) −24.1160 −0.859642 −0.429821 0.902914i \(-0.641423\pi\)
−0.429821 + 0.902914i \(0.641423\pi\)
\(788\) 132.478 4.71933
\(789\) 0.488845 0.0174033
\(790\) 42.2487 1.50314
\(791\) −10.3814 −0.369121
\(792\) 36.9538 1.31310
\(793\) 17.2805 0.613650
\(794\) 29.7016 1.05407
\(795\) 1.61773 0.0573749
\(796\) −32.1982 −1.14123
\(797\) −15.4285 −0.546504 −0.273252 0.961942i \(-0.588099\pi\)
−0.273252 + 0.961942i \(0.588099\pi\)
\(798\) 8.32972 0.294869
\(799\) 64.6746 2.28802
\(800\) −10.7680 −0.380708
\(801\) 51.3581 1.81465
\(802\) −31.6819 −1.11873
\(803\) −1.71115 −0.0603850
\(804\) −7.32120 −0.258199
\(805\) −1.11824 −0.0394127
\(806\) −53.5803 −1.88729
\(807\) −3.33506 −0.117400
\(808\) 127.826 4.49689
\(809\) −9.75800 −0.343073 −0.171536 0.985178i \(-0.554873\pi\)
−0.171536 + 0.985178i \(0.554873\pi\)
\(810\) 19.8548 0.697628
\(811\) −51.4393 −1.80628 −0.903139 0.429348i \(-0.858743\pi\)
−0.903139 + 0.429348i \(0.858743\pi\)
\(812\) 24.3446 0.854329
\(813\) 11.5499 0.405072
\(814\) −14.2483 −0.499401
\(815\) 15.8104 0.553813
\(816\) 23.0295 0.806193
\(817\) 87.6234 3.06556
\(818\) −89.9471 −3.14493
\(819\) 13.1420 0.459218
\(820\) 20.3389 0.710264
\(821\) 46.1717 1.61140 0.805701 0.592322i \(-0.201789\pi\)
0.805701 + 0.592322i \(0.201789\pi\)
\(822\) 12.9697 0.452370
\(823\) −36.3201 −1.26604 −0.633019 0.774136i \(-0.718184\pi\)
−0.633019 + 0.774136i \(0.718184\pi\)
\(824\) −34.8801 −1.21511
\(825\) 0.697810 0.0242946
\(826\) 12.1134 0.421481
\(827\) −8.67073 −0.301511 −0.150755 0.988571i \(-0.548171\pi\)
−0.150755 + 0.988571i \(0.548171\pi\)
\(828\) 15.3991 0.535154
\(829\) −18.2959 −0.635444 −0.317722 0.948184i \(-0.602918\pi\)
−0.317722 + 0.948184i \(0.602918\pi\)
\(830\) 8.56488 0.297291
\(831\) 1.47073 0.0510190
\(832\) 39.5904 1.37255
\(833\) 5.87048 0.203400
\(834\) 0.301397 0.0104365
\(835\) 1.06983 0.0370228
\(836\) 67.3708 2.33007
\(837\) −10.3315 −0.357110
\(838\) 90.2612 3.11802
\(839\) 10.3271 0.356531 0.178265 0.983982i \(-0.442951\pi\)
0.178265 + 0.983982i \(0.442951\pi\)
\(840\) −2.98053 −0.102838
\(841\) −3.79024 −0.130698
\(842\) 11.0282 0.380058
\(843\) 2.14039 0.0737188
\(844\) −6.92231 −0.238276
\(845\) −8.41107 −0.289350
\(846\) 81.8847 2.81525
\(847\) 7.95378 0.273295
\(848\) −39.7011 −1.36334
\(849\) 2.91320 0.0999807
\(850\) −15.3630 −0.526946
\(851\) −3.48829 −0.119577
\(852\) 15.6912 0.537572
\(853\) −16.3801 −0.560843 −0.280421 0.959877i \(-0.590474\pi\)
−0.280421 + 0.959877i \(0.590474\pi\)
\(854\) 9.77326 0.334434
\(855\) 22.6107 0.773269
\(856\) −116.923 −3.99636
\(857\) −25.9394 −0.886073 −0.443036 0.896504i \(-0.646099\pi\)
−0.443036 + 0.896504i \(0.646099\pi\)
\(858\) −8.45003 −0.288479
\(859\) −37.2587 −1.27125 −0.635625 0.771998i \(-0.719258\pi\)
−0.635625 + 0.771998i \(0.719258\pi\)
\(860\) −53.3663 −1.81977
\(861\) 1.67712 0.0571561
\(862\) −5.34937 −0.182200
\(863\) 44.4899 1.51445 0.757227 0.653152i \(-0.226554\pi\)
0.757227 + 0.653152i \(0.226554\pi\)
\(864\) 25.1430 0.855382
\(865\) −17.0568 −0.579948
\(866\) −32.5033 −1.10451
\(867\) 6.98175 0.237113
\(868\) −21.4537 −0.728188
\(869\) 28.1768 0.955833
\(870\) −5.25342 −0.178108
\(871\) −17.4754 −0.592131
\(872\) 75.0304 2.54085
\(873\) 34.1048 1.15427
\(874\) 23.2974 0.788047
\(875\) 1.00000 0.0338062
\(876\) −1.90056 −0.0642139
\(877\) −23.6685 −0.799229 −0.399614 0.916683i \(-0.630856\pi\)
−0.399614 + 0.916683i \(0.630856\pi\)
\(878\) 50.1664 1.69303
\(879\) 6.88591 0.232256
\(880\) −17.1252 −0.577290
\(881\) −34.2932 −1.15537 −0.577683 0.816261i \(-0.696043\pi\)
−0.577683 + 0.816261i \(0.696043\pi\)
\(882\) 7.43264 0.250270
\(883\) 33.5949 1.13056 0.565279 0.824900i \(-0.308769\pi\)
0.565279 + 0.824900i \(0.308769\pi\)
\(884\) 131.708 4.42981
\(885\) −1.85064 −0.0622087
\(886\) −34.5278 −1.15998
\(887\) −57.5722 −1.93308 −0.966542 0.256508i \(-0.917428\pi\)
−0.966542 + 0.256508i \(0.917428\pi\)
\(888\) −9.29764 −0.312008
\(889\) 2.59810 0.0871373
\(890\) −47.3227 −1.58626
\(891\) 13.2418 0.443615
\(892\) −118.741 −3.97574
\(893\) 87.7065 2.93499
\(894\) 7.37933 0.246802
\(895\) 10.9703 0.366696
\(896\) 0.854844 0.0285583
\(897\) −2.06876 −0.0690738
\(898\) −97.7698 −3.26262
\(899\) −22.2162 −0.740950
\(900\) −13.7708 −0.459027
\(901\) −23.7532 −0.791335
\(902\) 19.1598 0.637951
\(903\) −4.40052 −0.146440
\(904\) −77.3916 −2.57401
\(905\) 26.1359 0.868787
\(906\) −5.22768 −0.173678
\(907\) 6.19626 0.205743 0.102872 0.994695i \(-0.467197\pi\)
0.102872 + 0.994695i \(0.467197\pi\)
\(908\) 94.7555 3.14457
\(909\) 48.6993 1.61525
\(910\) −12.1094 −0.401421
\(911\) 16.2533 0.538497 0.269248 0.963071i \(-0.413225\pi\)
0.269248 + 0.963071i \(0.413225\pi\)
\(912\) 31.2308 1.03415
\(913\) 5.71216 0.189045
\(914\) −25.6714 −0.849135
\(915\) −1.49312 −0.0493610
\(916\) 4.84863 0.160203
\(917\) −5.88602 −0.194373
\(918\) 35.8720 1.18395
\(919\) −46.2406 −1.52534 −0.762668 0.646791i \(-0.776111\pi\)
−0.762668 + 0.646791i \(0.776111\pi\)
\(920\) −8.33626 −0.274838
\(921\) −6.66709 −0.219688
\(922\) 51.0114 1.67997
\(923\) 37.4542 1.23282
\(924\) −3.38342 −0.111306
\(925\) 3.11946 0.102567
\(926\) −68.9150 −2.26469
\(927\) −13.2887 −0.436457
\(928\) 54.0656 1.77479
\(929\) 22.9290 0.752278 0.376139 0.926563i \(-0.377252\pi\)
0.376139 + 0.926563i \(0.377252\pi\)
\(930\) 4.62959 0.151810
\(931\) 7.96108 0.260914
\(932\) −96.5111 −3.16133
\(933\) −7.39423 −0.242076
\(934\) 54.3763 1.77925
\(935\) −10.2460 −0.335080
\(936\) 97.9710 3.20228
\(937\) 7.64838 0.249862 0.124931 0.992165i \(-0.460129\pi\)
0.124931 + 0.992165i \(0.460129\pi\)
\(938\) −9.88346 −0.322706
\(939\) 5.72312 0.186767
\(940\) −53.4169 −1.74227
\(941\) −12.2603 −0.399674 −0.199837 0.979829i \(-0.564041\pi\)
−0.199837 + 0.979829i \(0.564041\pi\)
\(942\) −21.8806 −0.712909
\(943\) 4.69075 0.152752
\(944\) 45.4172 1.47820
\(945\) −2.33497 −0.0759564
\(946\) −50.2725 −1.63450
\(947\) 25.8125 0.838792 0.419396 0.907803i \(-0.362242\pi\)
0.419396 + 0.907803i \(0.362242\pi\)
\(948\) 31.2958 1.01644
\(949\) −4.53654 −0.147262
\(950\) −20.8341 −0.675946
\(951\) −3.60449 −0.116884
\(952\) 43.7634 1.41838
\(953\) −5.59674 −0.181296 −0.0906481 0.995883i \(-0.528894\pi\)
−0.0906481 + 0.995883i \(0.528894\pi\)
\(954\) −30.0740 −0.973683
\(955\) −14.8135 −0.479353
\(956\) −95.7493 −3.09676
\(957\) −3.50366 −0.113257
\(958\) 107.395 3.46978
\(959\) 12.3957 0.400278
\(960\) −3.42079 −0.110406
\(961\) −11.4220 −0.368451
\(962\) −37.7746 −1.21790
\(963\) −44.5457 −1.43547
\(964\) −35.7038 −1.14994
\(965\) −6.19822 −0.199528
\(966\) −1.17002 −0.0376447
\(967\) −18.3100 −0.588811 −0.294405 0.955681i \(-0.595122\pi\)
−0.294405 + 0.955681i \(0.595122\pi\)
\(968\) 59.2940 1.90578
\(969\) 18.6854 0.600261
\(970\) −31.4251 −1.00900
\(971\) 48.9631 1.57130 0.785650 0.618671i \(-0.212329\pi\)
0.785650 + 0.618671i \(0.212329\pi\)
\(972\) 48.6716 1.56114
\(973\) 0.288058 0.00923472
\(974\) 13.6271 0.436640
\(975\) 1.85002 0.0592479
\(976\) 36.6431 1.17292
\(977\) −58.9481 −1.88592 −0.942958 0.332912i \(-0.891969\pi\)
−0.942958 + 0.332912i \(0.891969\pi\)
\(978\) 16.5425 0.528970
\(979\) −31.5609 −1.00869
\(980\) −4.84863 −0.154884
\(981\) 28.5852 0.912656
\(982\) −59.3284 −1.89325
\(983\) −32.4578 −1.03524 −0.517621 0.855610i \(-0.673182\pi\)
−0.517621 + 0.855610i \(0.673182\pi\)
\(984\) 12.5026 0.398569
\(985\) −27.3227 −0.870575
\(986\) 77.1365 2.45653
\(987\) −4.40470 −0.140203
\(988\) 178.612 5.68240
\(989\) −12.3079 −0.391367
\(990\) −12.9725 −0.412293
\(991\) 57.7768 1.83534 0.917670 0.397343i \(-0.130068\pi\)
0.917670 + 0.397343i \(0.130068\pi\)
\(992\) −47.6454 −1.51274
\(993\) 10.7351 0.340668
\(994\) 21.1828 0.671877
\(995\) 6.64068 0.210524
\(996\) 6.34446 0.201032
\(997\) 30.7798 0.974806 0.487403 0.873177i \(-0.337944\pi\)
0.487403 + 0.873177i \(0.337944\pi\)
\(998\) −82.0963 −2.59871
\(999\) −7.28382 −0.230450
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 \(a_p\))