Properties

Label 5077.2.a.c.1.18
Level 5077
Weight 2
Character 5077.1
Self dual Yes
Analytic conductor 40.540
Analytic rank 0
Dimension 216
CM No

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Newspace parameters

Level: \( N \) = \( 5077 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 5077.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(40.5400491062\)
Analytic rank: \(0\)
Dimension: \(216\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) = 5077.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.43502 q^{2} +2.39261 q^{3} +3.92934 q^{4} +2.97521 q^{5} -5.82606 q^{6} +3.62580 q^{7} -4.69798 q^{8} +2.72458 q^{9} +O(q^{10})\) \(q-2.43502 q^{2} +2.39261 q^{3} +3.92934 q^{4} +2.97521 q^{5} -5.82606 q^{6} +3.62580 q^{7} -4.69798 q^{8} +2.72458 q^{9} -7.24469 q^{10} +3.86590 q^{11} +9.40137 q^{12} -2.18560 q^{13} -8.82890 q^{14} +7.11850 q^{15} +3.58101 q^{16} -5.33733 q^{17} -6.63441 q^{18} +6.97449 q^{19} +11.6906 q^{20} +8.67511 q^{21} -9.41356 q^{22} +4.02613 q^{23} -11.2404 q^{24} +3.85185 q^{25} +5.32199 q^{26} -0.658974 q^{27} +14.2470 q^{28} +1.27555 q^{29} -17.3337 q^{30} -1.05636 q^{31} +0.676118 q^{32} +9.24959 q^{33} +12.9965 q^{34} +10.7875 q^{35} +10.7058 q^{36} -8.51792 q^{37} -16.9831 q^{38} -5.22929 q^{39} -13.9774 q^{40} +1.23232 q^{41} -21.1241 q^{42} +4.20610 q^{43} +15.1904 q^{44} +8.10618 q^{45} -9.80372 q^{46} -8.87292 q^{47} +8.56795 q^{48} +6.14640 q^{49} -9.37933 q^{50} -12.7702 q^{51} -8.58796 q^{52} +5.84170 q^{53} +1.60462 q^{54} +11.5019 q^{55} -17.0339 q^{56} +16.6872 q^{57} -3.10600 q^{58} +9.50615 q^{59} +27.9710 q^{60} -7.33471 q^{61} +2.57225 q^{62} +9.87877 q^{63} -8.80838 q^{64} -6.50262 q^{65} -22.5230 q^{66} +1.24804 q^{67} -20.9722 q^{68} +9.63295 q^{69} -26.2678 q^{70} -5.76301 q^{71} -12.8000 q^{72} +4.80385 q^{73} +20.7413 q^{74} +9.21596 q^{75} +27.4051 q^{76} +14.0170 q^{77} +12.7334 q^{78} -13.2199 q^{79} +10.6542 q^{80} -9.75041 q^{81} -3.00072 q^{82} -2.38199 q^{83} +34.0874 q^{84} -15.8797 q^{85} -10.2419 q^{86} +3.05190 q^{87} -18.1619 q^{88} +5.81748 q^{89} -19.7387 q^{90} -7.92455 q^{91} +15.8200 q^{92} -2.52745 q^{93} +21.6058 q^{94} +20.7506 q^{95} +1.61769 q^{96} +19.1223 q^{97} -14.9666 q^{98} +10.5330 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 216q + 25q^{2} + 62q^{3} + 223q^{4} + 46q^{5} + 26q^{6} + 30q^{7} + 75q^{8} + 234q^{9} + O(q^{10}) \) \( 216q + 25q^{2} + 62q^{3} + 223q^{4} + 46q^{5} + 26q^{6} + 30q^{7} + 75q^{8} + 234q^{9} + 24q^{10} + 89q^{11} + 114q^{12} + 34q^{13} + 53q^{14} + 61q^{15} + 229q^{16} + 76q^{17} + 57q^{18} + 54q^{19} + 118q^{20} + 25q^{21} + 26q^{22} + 109q^{23} + 65q^{24} + 232q^{25} + 58q^{26} + 236q^{27} + 57q^{28} + 54q^{29} + 6q^{30} + 77q^{31} + 155q^{32} + 80q^{33} + 28q^{34} + 137q^{35} + 257q^{36} + 42q^{37} + 104q^{38} + 46q^{39} + 47q^{40} + 109q^{41} + 27q^{42} + 68q^{43} + 145q^{44} + 109q^{45} - 7q^{46} + 264q^{47} + 198q^{48} + 222q^{49} + 86q^{50} + 57q^{51} + 68q^{52} + 95q^{53} + 79q^{54} + 50q^{55} + 108q^{56} + 55q^{57} + 38q^{58} + 292q^{59} + 91q^{60} + 16q^{61} + 91q^{62} + 113q^{63} + 231q^{64} + 68q^{65} - 15q^{66} + 152q^{67} + 199q^{68} + 83q^{69} + 24q^{70} + 131q^{71} + 162q^{72} + 71q^{73} + 10q^{74} + 232q^{75} + 60q^{76} + 131q^{77} + 102q^{78} + 10q^{79} + 236q^{80} + 268q^{81} + 54q^{82} + 299q^{83} - 9q^{85} + 35q^{86} + 103q^{87} + 45q^{88} + 134q^{89} + 8q^{90} + 79q^{91} + 206q^{92} + 95q^{93} + 18q^{94} + 119q^{95} + 77q^{96} + 129q^{97} + 150q^{98} + 221q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.43502 −1.72182 −0.860911 0.508756i \(-0.830105\pi\)
−0.860911 + 0.508756i \(0.830105\pi\)
\(3\) 2.39261 1.38137 0.690687 0.723154i \(-0.257308\pi\)
0.690687 + 0.723154i \(0.257308\pi\)
\(4\) 3.92934 1.96467
\(5\) 2.97521 1.33055 0.665276 0.746597i \(-0.268314\pi\)
0.665276 + 0.746597i \(0.268314\pi\)
\(6\) −5.82606 −2.37848
\(7\) 3.62580 1.37042 0.685211 0.728345i \(-0.259710\pi\)
0.685211 + 0.728345i \(0.259710\pi\)
\(8\) −4.69798 −1.66099
\(9\) 2.72458 0.908193
\(10\) −7.24469 −2.29097
\(11\) 3.86590 1.16561 0.582807 0.812611i \(-0.301955\pi\)
0.582807 + 0.812611i \(0.301955\pi\)
\(12\) 9.40137 2.71394
\(13\) −2.18560 −0.606177 −0.303088 0.952962i \(-0.598018\pi\)
−0.303088 + 0.952962i \(0.598018\pi\)
\(14\) −8.82890 −2.35962
\(15\) 7.11850 1.83799
\(16\) 3.58101 0.895252
\(17\) −5.33733 −1.29449 −0.647247 0.762280i \(-0.724080\pi\)
−0.647247 + 0.762280i \(0.724080\pi\)
\(18\) −6.63441 −1.56375
\(19\) 6.97449 1.60006 0.800029 0.599961i \(-0.204817\pi\)
0.800029 + 0.599961i \(0.204817\pi\)
\(20\) 11.6906 2.61409
\(21\) 8.67511 1.89306
\(22\) −9.41356 −2.00698
\(23\) 4.02613 0.839506 0.419753 0.907638i \(-0.362117\pi\)
0.419753 + 0.907638i \(0.362117\pi\)
\(24\) −11.2404 −2.29444
\(25\) 3.85185 0.770369
\(26\) 5.32199 1.04373
\(27\) −0.658974 −0.126820
\(28\) 14.2470 2.69242
\(29\) 1.27555 0.236864 0.118432 0.992962i \(-0.462213\pi\)
0.118432 + 0.992962i \(0.462213\pi\)
\(30\) −17.3337 −3.16469
\(31\) −1.05636 −0.189727 −0.0948636 0.995490i \(-0.530241\pi\)
−0.0948636 + 0.995490i \(0.530241\pi\)
\(32\) 0.676118 0.119522
\(33\) 9.24959 1.61015
\(34\) 12.9965 2.22889
\(35\) 10.7875 1.82342
\(36\) 10.7058 1.78430
\(37\) −8.51792 −1.40034 −0.700169 0.713978i \(-0.746892\pi\)
−0.700169 + 0.713978i \(0.746892\pi\)
\(38\) −16.9831 −2.75501
\(39\) −5.22929 −0.837357
\(40\) −13.9774 −2.21003
\(41\) 1.23232 0.192455 0.0962277 0.995359i \(-0.469322\pi\)
0.0962277 + 0.995359i \(0.469322\pi\)
\(42\) −21.1241 −3.25952
\(43\) 4.20610 0.641424 0.320712 0.947177i \(-0.396078\pi\)
0.320712 + 0.947177i \(0.396078\pi\)
\(44\) 15.1904 2.29004
\(45\) 8.10618 1.20840
\(46\) −9.80372 −1.44548
\(47\) −8.87292 −1.29425 −0.647124 0.762385i \(-0.724029\pi\)
−0.647124 + 0.762385i \(0.724029\pi\)
\(48\) 8.56795 1.23668
\(49\) 6.14640 0.878057
\(50\) −9.37933 −1.32644
\(51\) −12.7702 −1.78818
\(52\) −8.58796 −1.19094
\(53\) 5.84170 0.802419 0.401209 0.915986i \(-0.368590\pi\)
0.401209 + 0.915986i \(0.368590\pi\)
\(54\) 1.60462 0.218361
\(55\) 11.5019 1.55091
\(56\) −17.0339 −2.27625
\(57\) 16.6872 2.21028
\(58\) −3.10600 −0.407838
\(59\) 9.50615 1.23760 0.618798 0.785550i \(-0.287620\pi\)
0.618798 + 0.785550i \(0.287620\pi\)
\(60\) 27.9710 3.61104
\(61\) −7.33471 −0.939113 −0.469557 0.882902i \(-0.655586\pi\)
−0.469557 + 0.882902i \(0.655586\pi\)
\(62\) 2.57225 0.326676
\(63\) 9.87877 1.24461
\(64\) −8.80838 −1.10105
\(65\) −6.50262 −0.806550
\(66\) −22.5230 −2.77239
\(67\) 1.24804 0.152472 0.0762362 0.997090i \(-0.475710\pi\)
0.0762362 + 0.997090i \(0.475710\pi\)
\(68\) −20.9722 −2.54325
\(69\) 9.63295 1.15967
\(70\) −26.2678 −3.13960
\(71\) −5.76301 −0.683943 −0.341972 0.939710i \(-0.611095\pi\)
−0.341972 + 0.939710i \(0.611095\pi\)
\(72\) −12.8000 −1.50850
\(73\) 4.80385 0.562249 0.281124 0.959671i \(-0.409293\pi\)
0.281124 + 0.959671i \(0.409293\pi\)
\(74\) 20.7413 2.41113
\(75\) 9.21596 1.06417
\(76\) 27.4051 3.14358
\(77\) 14.0170 1.59738
\(78\) 12.7334 1.44178
\(79\) −13.2199 −1.48735 −0.743677 0.668540i \(-0.766920\pi\)
−0.743677 + 0.668540i \(0.766920\pi\)
\(80\) 10.6542 1.19118
\(81\) −9.75041 −1.08338
\(82\) −3.00072 −0.331374
\(83\) −2.38199 −0.261457 −0.130729 0.991418i \(-0.541732\pi\)
−0.130729 + 0.991418i \(0.541732\pi\)
\(84\) 34.0874 3.71924
\(85\) −15.8797 −1.72239
\(86\) −10.2419 −1.10442
\(87\) 3.05190 0.327198
\(88\) −18.1619 −1.93607
\(89\) 5.81748 0.616651 0.308326 0.951281i \(-0.400231\pi\)
0.308326 + 0.951281i \(0.400231\pi\)
\(90\) −19.7387 −2.08065
\(91\) −7.92455 −0.830718
\(92\) 15.8200 1.64935
\(93\) −2.52745 −0.262084
\(94\) 21.6058 2.22846
\(95\) 20.7506 2.12896
\(96\) 1.61769 0.165104
\(97\) 19.1223 1.94158 0.970789 0.239933i \(-0.0771256\pi\)
0.970789 + 0.239933i \(0.0771256\pi\)
\(98\) −14.9666 −1.51186
\(99\) 10.5330 1.05860
\(100\) 15.1352 1.51352
\(101\) 1.57578 0.156796 0.0783981 0.996922i \(-0.475019\pi\)
0.0783981 + 0.996922i \(0.475019\pi\)
\(102\) 31.0956 3.07893
\(103\) 11.2834 1.11179 0.555894 0.831253i \(-0.312376\pi\)
0.555894 + 0.831253i \(0.312376\pi\)
\(104\) 10.2679 1.00685
\(105\) 25.8102 2.51882
\(106\) −14.2247 −1.38162
\(107\) 19.0096 1.83772 0.918862 0.394579i \(-0.129109\pi\)
0.918862 + 0.394579i \(0.129109\pi\)
\(108\) −2.58933 −0.249158
\(109\) −13.3728 −1.28088 −0.640441 0.768007i \(-0.721248\pi\)
−0.640441 + 0.768007i \(0.721248\pi\)
\(110\) −28.0073 −2.67039
\(111\) −20.3800 −1.93439
\(112\) 12.9840 1.22687
\(113\) 8.41050 0.791194 0.395597 0.918424i \(-0.370538\pi\)
0.395597 + 0.918424i \(0.370538\pi\)
\(114\) −40.6338 −3.80570
\(115\) 11.9786 1.11701
\(116\) 5.01208 0.465360
\(117\) −5.95485 −0.550526
\(118\) −23.1477 −2.13092
\(119\) −19.3521 −1.77400
\(120\) −33.4426 −3.05287
\(121\) 3.94520 0.358654
\(122\) 17.8602 1.61699
\(123\) 2.94845 0.265853
\(124\) −4.15078 −0.372751
\(125\) −3.41599 −0.305536
\(126\) −24.0550 −2.14299
\(127\) −19.1208 −1.69669 −0.848347 0.529440i \(-0.822402\pi\)
−0.848347 + 0.529440i \(0.822402\pi\)
\(128\) 20.0964 1.77628
\(129\) 10.0635 0.886046
\(130\) 15.8340 1.38874
\(131\) −9.56606 −0.835791 −0.417895 0.908495i \(-0.637232\pi\)
−0.417895 + 0.908495i \(0.637232\pi\)
\(132\) 36.3448 3.16340
\(133\) 25.2881 2.19276
\(134\) −3.03901 −0.262530
\(135\) −1.96058 −0.168740
\(136\) 25.0747 2.15014
\(137\) 13.6226 1.16386 0.581928 0.813240i \(-0.302298\pi\)
0.581928 + 0.813240i \(0.302298\pi\)
\(138\) −23.4565 −1.99675
\(139\) 13.6917 1.16131 0.580656 0.814149i \(-0.302796\pi\)
0.580656 + 0.814149i \(0.302796\pi\)
\(140\) 42.3877 3.58241
\(141\) −21.2294 −1.78784
\(142\) 14.0331 1.17763
\(143\) −8.44932 −0.706568
\(144\) 9.75674 0.813062
\(145\) 3.79503 0.315160
\(146\) −11.6975 −0.968091
\(147\) 14.7059 1.21292
\(148\) −33.4698 −2.75120
\(149\) −14.6338 −1.19885 −0.599424 0.800431i \(-0.704604\pi\)
−0.599424 + 0.800431i \(0.704604\pi\)
\(150\) −22.4411 −1.83231
\(151\) 5.44621 0.443206 0.221603 0.975137i \(-0.428871\pi\)
0.221603 + 0.975137i \(0.428871\pi\)
\(152\) −32.7660 −2.65767
\(153\) −14.5420 −1.17565
\(154\) −34.1316 −2.75041
\(155\) −3.14288 −0.252442
\(156\) −20.5476 −1.64513
\(157\) 0.631467 0.0503966 0.0251983 0.999682i \(-0.491978\pi\)
0.0251983 + 0.999682i \(0.491978\pi\)
\(158\) 32.1907 2.56096
\(159\) 13.9769 1.10844
\(160\) 2.01159 0.159030
\(161\) 14.5979 1.15048
\(162\) 23.7425 1.86538
\(163\) 14.5819 1.14214 0.571070 0.820902i \(-0.306529\pi\)
0.571070 + 0.820902i \(0.306529\pi\)
\(164\) 4.84218 0.378111
\(165\) 27.5194 2.14239
\(166\) 5.80020 0.450183
\(167\) −12.9680 −1.00350 −0.501748 0.865014i \(-0.667309\pi\)
−0.501748 + 0.865014i \(0.667309\pi\)
\(168\) −40.7555 −3.14435
\(169\) −8.22314 −0.632549
\(170\) 38.6673 2.96565
\(171\) 19.0026 1.45316
\(172\) 16.5272 1.26018
\(173\) 22.7625 1.73060 0.865302 0.501251i \(-0.167127\pi\)
0.865302 + 0.501251i \(0.167127\pi\)
\(174\) −7.43145 −0.563377
\(175\) 13.9660 1.05573
\(176\) 13.8438 1.04352
\(177\) 22.7445 1.70958
\(178\) −14.1657 −1.06176
\(179\) 8.04535 0.601338 0.300669 0.953729i \(-0.402790\pi\)
0.300669 + 0.953729i \(0.402790\pi\)
\(180\) 31.8519 2.37410
\(181\) 9.67121 0.718855 0.359428 0.933173i \(-0.382972\pi\)
0.359428 + 0.933173i \(0.382972\pi\)
\(182\) 19.2965 1.43035
\(183\) −17.5491 −1.29727
\(184\) −18.9147 −1.39441
\(185\) −25.3426 −1.86322
\(186\) 6.15439 0.451262
\(187\) −20.6336 −1.50888
\(188\) −34.8647 −2.54277
\(189\) −2.38931 −0.173796
\(190\) −50.5281 −3.66569
\(191\) 7.50880 0.543318 0.271659 0.962394i \(-0.412428\pi\)
0.271659 + 0.962394i \(0.412428\pi\)
\(192\) −21.0750 −1.52096
\(193\) −14.5882 −1.05008 −0.525041 0.851077i \(-0.675950\pi\)
−0.525041 + 0.851077i \(0.675950\pi\)
\(194\) −46.5633 −3.34305
\(195\) −15.5582 −1.11415
\(196\) 24.1513 1.72509
\(197\) −5.58894 −0.398196 −0.199098 0.979980i \(-0.563801\pi\)
−0.199098 + 0.979980i \(0.563801\pi\)
\(198\) −25.6480 −1.82272
\(199\) −1.62205 −0.114984 −0.0574922 0.998346i \(-0.518310\pi\)
−0.0574922 + 0.998346i \(0.518310\pi\)
\(200\) −18.0959 −1.27957
\(201\) 2.98607 0.210621
\(202\) −3.83707 −0.269975
\(203\) 4.62490 0.324604
\(204\) −50.1782 −3.51318
\(205\) 3.66639 0.256072
\(206\) −27.4754 −1.91430
\(207\) 10.9695 0.762434
\(208\) −7.82666 −0.542681
\(209\) 26.9627 1.86505
\(210\) −62.8485 −4.33696
\(211\) −12.4747 −0.858794 −0.429397 0.903116i \(-0.641274\pi\)
−0.429397 + 0.903116i \(0.641274\pi\)
\(212\) 22.9540 1.57649
\(213\) −13.7886 −0.944781
\(214\) −46.2887 −3.16423
\(215\) 12.5140 0.853448
\(216\) 3.09584 0.210646
\(217\) −3.83013 −0.260006
\(218\) 32.5631 2.20545
\(219\) 11.4937 0.776675
\(220\) 45.1946 3.04702
\(221\) 11.6653 0.784692
\(222\) 49.6259 3.33067
\(223\) 10.5911 0.709235 0.354617 0.935012i \(-0.384611\pi\)
0.354617 + 0.935012i \(0.384611\pi\)
\(224\) 2.45147 0.163795
\(225\) 10.4947 0.699644
\(226\) −20.4798 −1.36229
\(227\) 1.52010 0.100892 0.0504461 0.998727i \(-0.483936\pi\)
0.0504461 + 0.998727i \(0.483936\pi\)
\(228\) 65.5698 4.34246
\(229\) 3.51289 0.232138 0.116069 0.993241i \(-0.462971\pi\)
0.116069 + 0.993241i \(0.462971\pi\)
\(230\) −29.1681 −1.92329
\(231\) 33.5371 2.20658
\(232\) −5.99252 −0.393428
\(233\) 25.5923 1.67661 0.838304 0.545204i \(-0.183548\pi\)
0.838304 + 0.545204i \(0.183548\pi\)
\(234\) 14.5002 0.947907
\(235\) −26.3988 −1.72207
\(236\) 37.3529 2.43146
\(237\) −31.6300 −2.05459
\(238\) 47.1228 3.05452
\(239\) −23.1730 −1.49893 −0.749467 0.662042i \(-0.769690\pi\)
−0.749467 + 0.662042i \(0.769690\pi\)
\(240\) 25.4914 1.64546
\(241\) −7.22448 −0.465370 −0.232685 0.972552i \(-0.574751\pi\)
−0.232685 + 0.972552i \(0.574751\pi\)
\(242\) −9.60664 −0.617538
\(243\) −21.3520 −1.36973
\(244\) −28.8205 −1.84505
\(245\) 18.2868 1.16830
\(246\) −7.17955 −0.457751
\(247\) −15.2435 −0.969919
\(248\) 4.96273 0.315134
\(249\) −5.69917 −0.361170
\(250\) 8.31802 0.526078
\(251\) −15.3812 −0.970852 −0.485426 0.874278i \(-0.661336\pi\)
−0.485426 + 0.874278i \(0.661336\pi\)
\(252\) 38.8170 2.44524
\(253\) 15.5646 0.978539
\(254\) 46.5595 2.92140
\(255\) −37.9938 −2.37927
\(256\) −31.3183 −1.95740
\(257\) −6.35474 −0.396398 −0.198199 0.980162i \(-0.563509\pi\)
−0.198199 + 0.980162i \(0.563509\pi\)
\(258\) −24.5050 −1.52561
\(259\) −30.8842 −1.91905
\(260\) −25.5510 −1.58460
\(261\) 3.47535 0.215118
\(262\) 23.2936 1.43908
\(263\) 10.8471 0.668860 0.334430 0.942421i \(-0.391456\pi\)
0.334430 + 0.942421i \(0.391456\pi\)
\(264\) −43.4544 −2.67443
\(265\) 17.3802 1.06766
\(266\) −61.5771 −3.77553
\(267\) 13.9189 0.851826
\(268\) 4.90397 0.299558
\(269\) 13.8113 0.842088 0.421044 0.907040i \(-0.361664\pi\)
0.421044 + 0.907040i \(0.361664\pi\)
\(270\) 4.77406 0.290540
\(271\) −0.140142 −0.00851304 −0.00425652 0.999991i \(-0.501355\pi\)
−0.00425652 + 0.999991i \(0.501355\pi\)
\(272\) −19.1130 −1.15890
\(273\) −18.9603 −1.14753
\(274\) −33.1713 −2.00395
\(275\) 14.8909 0.897953
\(276\) 37.8511 2.27837
\(277\) −20.1103 −1.20831 −0.604157 0.796866i \(-0.706490\pi\)
−0.604157 + 0.796866i \(0.706490\pi\)
\(278\) −33.3395 −1.99957
\(279\) −2.87813 −0.172309
\(280\) −50.6794 −3.02867
\(281\) −14.1427 −0.843682 −0.421841 0.906670i \(-0.638616\pi\)
−0.421841 + 0.906670i \(0.638616\pi\)
\(282\) 51.6942 3.07834
\(283\) −16.9198 −1.00578 −0.502889 0.864351i \(-0.667729\pi\)
−0.502889 + 0.864351i \(0.667729\pi\)
\(284\) −22.6448 −1.34372
\(285\) 49.6480 2.94089
\(286\) 20.5743 1.21658
\(287\) 4.46813 0.263745
\(288\) 1.84214 0.108549
\(289\) 11.4871 0.675714
\(290\) −9.24099 −0.542650
\(291\) 45.7523 2.68205
\(292\) 18.8760 1.10463
\(293\) 17.8455 1.04255 0.521273 0.853390i \(-0.325457\pi\)
0.521273 + 0.853390i \(0.325457\pi\)
\(294\) −35.8093 −2.08844
\(295\) 28.2828 1.64669
\(296\) 40.0170 2.32594
\(297\) −2.54753 −0.147823
\(298\) 35.6337 2.06420
\(299\) −8.79952 −0.508889
\(300\) 36.2126 2.09074
\(301\) 15.2505 0.879021
\(302\) −13.2616 −0.763122
\(303\) 3.77023 0.216594
\(304\) 24.9757 1.43246
\(305\) −21.8223 −1.24954
\(306\) 35.4101 2.02426
\(307\) −30.8644 −1.76153 −0.880763 0.473557i \(-0.842970\pi\)
−0.880763 + 0.473557i \(0.842970\pi\)
\(308\) 55.0774 3.13833
\(309\) 26.9968 1.53579
\(310\) 7.65297 0.434660
\(311\) −27.9464 −1.58469 −0.792347 0.610070i \(-0.791141\pi\)
−0.792347 + 0.610070i \(0.791141\pi\)
\(312\) 24.5671 1.39084
\(313\) −15.5951 −0.881486 −0.440743 0.897633i \(-0.645285\pi\)
−0.440743 + 0.897633i \(0.645285\pi\)
\(314\) −1.53764 −0.0867739
\(315\) 29.3914 1.65602
\(316\) −51.9454 −2.92216
\(317\) −4.57734 −0.257089 −0.128545 0.991704i \(-0.541031\pi\)
−0.128545 + 0.991704i \(0.541031\pi\)
\(318\) −34.0341 −1.90854
\(319\) 4.93116 0.276092
\(320\) −26.2067 −1.46500
\(321\) 45.4825 2.53858
\(322\) −35.5463 −1.98092
\(323\) −37.2252 −2.07127
\(324\) −38.3126 −2.12848
\(325\) −8.41860 −0.466980
\(326\) −35.5071 −1.96656
\(327\) −31.9959 −1.76938
\(328\) −5.78939 −0.319666
\(329\) −32.1714 −1.77367
\(330\) −67.0105 −3.68880
\(331\) 9.24139 0.507953 0.253976 0.967210i \(-0.418261\pi\)
0.253976 + 0.967210i \(0.418261\pi\)
\(332\) −9.35964 −0.513677
\(333\) −23.2077 −1.27178
\(334\) 31.5774 1.72784
\(335\) 3.71318 0.202873
\(336\) 31.0656 1.69477
\(337\) 27.6687 1.50721 0.753606 0.657326i \(-0.228313\pi\)
0.753606 + 0.657326i \(0.228313\pi\)
\(338\) 20.0235 1.08914
\(339\) 20.1231 1.09293
\(340\) −62.3965 −3.38393
\(341\) −4.08377 −0.221148
\(342\) −46.2717 −2.50209
\(343\) −3.09499 −0.167114
\(344\) −19.7601 −1.06540
\(345\) 28.6600 1.54300
\(346\) −55.4273 −2.97979
\(347\) 5.50791 0.295680 0.147840 0.989011i \(-0.452768\pi\)
0.147840 + 0.989011i \(0.452768\pi\)
\(348\) 11.9919 0.642836
\(349\) −28.3536 −1.51773 −0.758866 0.651247i \(-0.774246\pi\)
−0.758866 + 0.651247i \(0.774246\pi\)
\(350\) −34.0076 −1.81778
\(351\) 1.44026 0.0768751
\(352\) 2.61380 0.139316
\(353\) −25.0867 −1.33523 −0.667615 0.744506i \(-0.732685\pi\)
−0.667615 + 0.744506i \(0.732685\pi\)
\(354\) −55.3834 −2.94359
\(355\) −17.1461 −0.910022
\(356\) 22.8588 1.21152
\(357\) −46.3020 −2.45056
\(358\) −19.5906 −1.03540
\(359\) −16.2633 −0.858343 −0.429171 0.903223i \(-0.641194\pi\)
−0.429171 + 0.903223i \(0.641194\pi\)
\(360\) −38.0827 −2.00713
\(361\) 29.6436 1.56019
\(362\) −23.5496 −1.23774
\(363\) 9.43931 0.495436
\(364\) −31.1382 −1.63209
\(365\) 14.2925 0.748101
\(366\) 42.7324 2.23366
\(367\) −31.9483 −1.66769 −0.833843 0.552001i \(-0.813864\pi\)
−0.833843 + 0.552001i \(0.813864\pi\)
\(368\) 14.4176 0.751569
\(369\) 3.35754 0.174787
\(370\) 61.7097 3.20813
\(371\) 21.1808 1.09965
\(372\) −9.93119 −0.514908
\(373\) −25.7708 −1.33436 −0.667181 0.744896i \(-0.732499\pi\)
−0.667181 + 0.744896i \(0.732499\pi\)
\(374\) 50.2433 2.59802
\(375\) −8.17313 −0.422059
\(376\) 41.6848 2.14973
\(377\) −2.78785 −0.143582
\(378\) 5.81801 0.299246
\(379\) −31.8836 −1.63775 −0.818875 0.573972i \(-0.805402\pi\)
−0.818875 + 0.573972i \(0.805402\pi\)
\(380\) 81.5359 4.18270
\(381\) −45.7485 −2.34377
\(382\) −18.2841 −0.935496
\(383\) −2.43471 −0.124408 −0.0622039 0.998063i \(-0.519813\pi\)
−0.0622039 + 0.998063i \(0.519813\pi\)
\(384\) 48.0827 2.45371
\(385\) 41.7034 2.12540
\(386\) 35.5226 1.80805
\(387\) 11.4598 0.582537
\(388\) 75.1381 3.81456
\(389\) −7.09833 −0.359900 −0.179950 0.983676i \(-0.557594\pi\)
−0.179950 + 0.983676i \(0.557594\pi\)
\(390\) 37.8846 1.91836
\(391\) −21.4888 −1.08674
\(392\) −28.8756 −1.45844
\(393\) −22.8879 −1.15454
\(394\) 13.6092 0.685622
\(395\) −39.3319 −1.97900
\(396\) 41.3875 2.07980
\(397\) −17.1690 −0.861689 −0.430844 0.902426i \(-0.641784\pi\)
−0.430844 + 0.902426i \(0.641784\pi\)
\(398\) 3.94974 0.197983
\(399\) 60.5045 3.02901
\(400\) 13.7935 0.689675
\(401\) −19.1715 −0.957379 −0.478690 0.877984i \(-0.658888\pi\)
−0.478690 + 0.877984i \(0.658888\pi\)
\(402\) −7.27116 −0.362652
\(403\) 2.30877 0.115008
\(404\) 6.19178 0.308053
\(405\) −29.0095 −1.44149
\(406\) −11.2617 −0.558910
\(407\) −32.9294 −1.63225
\(408\) 59.9939 2.97014
\(409\) 3.90390 0.193035 0.0965177 0.995331i \(-0.469230\pi\)
0.0965177 + 0.995331i \(0.469230\pi\)
\(410\) −8.92775 −0.440910
\(411\) 32.5935 1.60772
\(412\) 44.3363 2.18429
\(413\) 34.4674 1.69603
\(414\) −26.7110 −1.31277
\(415\) −7.08691 −0.347883
\(416\) −1.47772 −0.0724514
\(417\) 32.7588 1.60420
\(418\) −65.6548 −3.21128
\(419\) −2.01086 −0.0982369 −0.0491185 0.998793i \(-0.515641\pi\)
−0.0491185 + 0.998793i \(0.515641\pi\)
\(420\) 101.417 4.94865
\(421\) 1.54727 0.0754094 0.0377047 0.999289i \(-0.487995\pi\)
0.0377047 + 0.999289i \(0.487995\pi\)
\(422\) 30.3762 1.47869
\(423\) −24.1750 −1.17543
\(424\) −27.4442 −1.33281
\(425\) −20.5586 −0.997238
\(426\) 33.5756 1.62674
\(427\) −26.5942 −1.28698
\(428\) 74.6950 3.61052
\(429\) −20.2159 −0.976034
\(430\) −30.4719 −1.46948
\(431\) −7.10285 −0.342132 −0.171066 0.985260i \(-0.554721\pi\)
−0.171066 + 0.985260i \(0.554721\pi\)
\(432\) −2.35979 −0.113536
\(433\) 27.9140 1.34146 0.670729 0.741702i \(-0.265981\pi\)
0.670729 + 0.741702i \(0.265981\pi\)
\(434\) 9.32646 0.447684
\(435\) 9.08003 0.435354
\(436\) −52.5462 −2.51651
\(437\) 28.0802 1.34326
\(438\) −27.9875 −1.33730
\(439\) −8.94710 −0.427022 −0.213511 0.976941i \(-0.568490\pi\)
−0.213511 + 0.976941i \(0.568490\pi\)
\(440\) −54.0354 −2.57604
\(441\) 16.7463 0.797445
\(442\) −28.4052 −1.35110
\(443\) −8.85279 −0.420609 −0.210304 0.977636i \(-0.567445\pi\)
−0.210304 + 0.977636i \(0.567445\pi\)
\(444\) −80.0801 −3.80043
\(445\) 17.3082 0.820487
\(446\) −25.7896 −1.22118
\(447\) −35.0130 −1.65606
\(448\) −31.9374 −1.50890
\(449\) 20.1869 0.952678 0.476339 0.879262i \(-0.341964\pi\)
0.476339 + 0.879262i \(0.341964\pi\)
\(450\) −25.5547 −1.20466
\(451\) 4.76401 0.224329
\(452\) 33.0477 1.55443
\(453\) 13.0306 0.612233
\(454\) −3.70147 −0.173718
\(455\) −23.5772 −1.10531
\(456\) −78.3963 −3.67124
\(457\) −18.2974 −0.855917 −0.427959 0.903798i \(-0.640767\pi\)
−0.427959 + 0.903798i \(0.640767\pi\)
\(458\) −8.55396 −0.399700
\(459\) 3.51717 0.164167
\(460\) 47.0678 2.19455
\(461\) 39.7046 1.84923 0.924614 0.380904i \(-0.124387\pi\)
0.924614 + 0.380904i \(0.124387\pi\)
\(462\) −81.6637 −3.79934
\(463\) 39.1184 1.81798 0.908992 0.416813i \(-0.136853\pi\)
0.908992 + 0.416813i \(0.136853\pi\)
\(464\) 4.56777 0.212053
\(465\) −7.51967 −0.348717
\(466\) −62.3178 −2.88682
\(467\) 18.1117 0.838109 0.419055 0.907961i \(-0.362362\pi\)
0.419055 + 0.907961i \(0.362362\pi\)
\(468\) −23.3986 −1.08160
\(469\) 4.52514 0.208952
\(470\) 64.2816 2.96509
\(471\) 1.51085 0.0696165
\(472\) −44.6597 −2.05563
\(473\) 16.2604 0.747652
\(474\) 77.0198 3.53764
\(475\) 26.8647 1.23264
\(476\) −76.0408 −3.48533
\(477\) 15.9162 0.728751
\(478\) 56.4267 2.58090
\(479\) 2.27339 0.103874 0.0519369 0.998650i \(-0.483461\pi\)
0.0519369 + 0.998650i \(0.483461\pi\)
\(480\) 4.81295 0.219680
\(481\) 18.6168 0.848852
\(482\) 17.5918 0.801284
\(483\) 34.9271 1.58924
\(484\) 15.5020 0.704636
\(485\) 56.8929 2.58337
\(486\) 51.9926 2.35843
\(487\) −6.85428 −0.310597 −0.155299 0.987868i \(-0.549634\pi\)
−0.155299 + 0.987868i \(0.549634\pi\)
\(488\) 34.4583 1.55985
\(489\) 34.8887 1.57772
\(490\) −44.5288 −2.01160
\(491\) −17.5114 −0.790280 −0.395140 0.918621i \(-0.629304\pi\)
−0.395140 + 0.918621i \(0.629304\pi\)
\(492\) 11.5855 0.522313
\(493\) −6.80805 −0.306619
\(494\) 37.1182 1.67003
\(495\) 31.3377 1.40853
\(496\) −3.78282 −0.169854
\(497\) −20.8955 −0.937291
\(498\) 13.8776 0.621871
\(499\) 0.947905 0.0424341 0.0212170 0.999775i \(-0.493246\pi\)
0.0212170 + 0.999775i \(0.493246\pi\)
\(500\) −13.4226 −0.600276
\(501\) −31.0274 −1.38620
\(502\) 37.4536 1.67163
\(503\) −7.22953 −0.322349 −0.161174 0.986926i \(-0.551528\pi\)
−0.161174 + 0.986926i \(0.551528\pi\)
\(504\) −46.4102 −2.06728
\(505\) 4.68828 0.208626
\(506\) −37.9002 −1.68487
\(507\) −19.6748 −0.873787
\(508\) −75.1319 −3.33344
\(509\) −0.278015 −0.0123228 −0.00616141 0.999981i \(-0.501961\pi\)
−0.00616141 + 0.999981i \(0.501961\pi\)
\(510\) 92.5159 4.09667
\(511\) 17.4178 0.770518
\(512\) 36.0682 1.59400
\(513\) −4.59601 −0.202919
\(514\) 15.4739 0.682526
\(515\) 33.5705 1.47929
\(516\) 39.5431 1.74079
\(517\) −34.3018 −1.50859
\(518\) 75.2038 3.30427
\(519\) 54.4619 2.39061
\(520\) 30.5491 1.33967
\(521\) 31.9828 1.40119 0.700596 0.713558i \(-0.252918\pi\)
0.700596 + 0.713558i \(0.252918\pi\)
\(522\) −8.46255 −0.370396
\(523\) 25.1888 1.10143 0.550714 0.834694i \(-0.314356\pi\)
0.550714 + 0.834694i \(0.314356\pi\)
\(524\) −37.5883 −1.64205
\(525\) 33.4152 1.45836
\(526\) −26.4129 −1.15166
\(527\) 5.63812 0.245601
\(528\) 33.1229 1.44149
\(529\) −6.79028 −0.295230
\(530\) −42.3213 −1.83832
\(531\) 25.9003 1.12398
\(532\) 99.3654 4.30804
\(533\) −2.69335 −0.116662
\(534\) −33.8930 −1.46669
\(535\) 56.5574 2.44519
\(536\) −5.86327 −0.253255
\(537\) 19.2494 0.830672
\(538\) −33.6307 −1.44992
\(539\) 23.7614 1.02347
\(540\) −7.70379 −0.331518
\(541\) 32.6938 1.40561 0.702807 0.711380i \(-0.251930\pi\)
0.702807 + 0.711380i \(0.251930\pi\)
\(542\) 0.341250 0.0146579
\(543\) 23.1394 0.993007
\(544\) −3.60867 −0.154720
\(545\) −39.7868 −1.70428
\(546\) 46.1689 1.97585
\(547\) −18.7171 −0.800287 −0.400144 0.916452i \(-0.631040\pi\)
−0.400144 + 0.916452i \(0.631040\pi\)
\(548\) 53.5277 2.28659
\(549\) −19.9840 −0.852896
\(550\) −36.2596 −1.54611
\(551\) 8.89634 0.378997
\(552\) −45.2554 −1.92620
\(553\) −47.9326 −2.03830
\(554\) 48.9691 2.08050
\(555\) −60.6348 −2.57381
\(556\) 53.7991 2.28159
\(557\) 13.1985 0.559239 0.279619 0.960111i \(-0.409792\pi\)
0.279619 + 0.960111i \(0.409792\pi\)
\(558\) 7.00830 0.296685
\(559\) −9.19286 −0.388816
\(560\) 38.6301 1.63242
\(561\) −49.3682 −2.08433
\(562\) 34.4377 1.45267
\(563\) −11.5093 −0.485059 −0.242530 0.970144i \(-0.577977\pi\)
−0.242530 + 0.970144i \(0.577977\pi\)
\(564\) −83.4176 −3.51251
\(565\) 25.0230 1.05272
\(566\) 41.2001 1.73177
\(567\) −35.3530 −1.48469
\(568\) 27.0745 1.13602
\(569\) 28.6722 1.20200 0.601000 0.799249i \(-0.294769\pi\)
0.601000 + 0.799249i \(0.294769\pi\)
\(570\) −120.894 −5.06369
\(571\) −23.0367 −0.964058 −0.482029 0.876155i \(-0.660100\pi\)
−0.482029 + 0.876155i \(0.660100\pi\)
\(572\) −33.2002 −1.38817
\(573\) 17.9656 0.750525
\(574\) −10.8800 −0.454122
\(575\) 15.5080 0.646730
\(576\) −23.9991 −0.999963
\(577\) −17.8774 −0.744245 −0.372123 0.928184i \(-0.621370\pi\)
−0.372123 + 0.928184i \(0.621370\pi\)
\(578\) −27.9714 −1.16346
\(579\) −34.9039 −1.45055
\(580\) 14.9120 0.619185
\(581\) −8.63661 −0.358307
\(582\) −111.408 −4.61800
\(583\) 22.5834 0.935310
\(584\) −22.5684 −0.933887
\(585\) −17.7169 −0.732503
\(586\) −43.4543 −1.79508
\(587\) 36.3205 1.49911 0.749555 0.661942i \(-0.230268\pi\)
0.749555 + 0.661942i \(0.230268\pi\)
\(588\) 57.7845 2.38299
\(589\) −7.36755 −0.303575
\(590\) −68.8691 −2.83530
\(591\) −13.3722 −0.550057
\(592\) −30.5027 −1.25365
\(593\) 16.9232 0.694952 0.347476 0.937689i \(-0.387039\pi\)
0.347476 + 0.937689i \(0.387039\pi\)
\(594\) 6.20329 0.254524
\(595\) −57.5764 −2.36040
\(596\) −57.5012 −2.35534
\(597\) −3.88094 −0.158836
\(598\) 21.4270 0.876216
\(599\) 30.5568 1.24852 0.624258 0.781218i \(-0.285401\pi\)
0.624258 + 0.781218i \(0.285401\pi\)
\(600\) −43.2964 −1.76757
\(601\) −36.4012 −1.48484 −0.742419 0.669936i \(-0.766322\pi\)
−0.742419 + 0.669936i \(0.766322\pi\)
\(602\) −37.1352 −1.51352
\(603\) 3.40039 0.138474
\(604\) 21.4000 0.870753
\(605\) 11.7378 0.477208
\(606\) −9.18060 −0.372937
\(607\) 8.22180 0.333713 0.166856 0.985981i \(-0.446638\pi\)
0.166856 + 0.985981i \(0.446638\pi\)
\(608\) 4.71558 0.191242
\(609\) 11.0656 0.448399
\(610\) 53.1377 2.15148
\(611\) 19.3927 0.784544
\(612\) −57.1404 −2.30976
\(613\) −15.2003 −0.613934 −0.306967 0.951720i \(-0.599314\pi\)
−0.306967 + 0.951720i \(0.599314\pi\)
\(614\) 75.1556 3.03303
\(615\) 8.77225 0.353731
\(616\) −65.8514 −2.65323
\(617\) 6.11397 0.246139 0.123070 0.992398i \(-0.460726\pi\)
0.123070 + 0.992398i \(0.460726\pi\)
\(618\) −65.7378 −2.64436
\(619\) −30.0068 −1.20607 −0.603037 0.797713i \(-0.706043\pi\)
−0.603037 + 0.797713i \(0.706043\pi\)
\(620\) −12.3494 −0.495964
\(621\) −2.65311 −0.106466
\(622\) 68.0501 2.72856
\(623\) 21.0930 0.845073
\(624\) −18.7261 −0.749645
\(625\) −29.4225 −1.17690
\(626\) 37.9744 1.51776
\(627\) 64.5112 2.57633
\(628\) 2.48125 0.0990125
\(629\) 45.4630 1.81273
\(630\) −71.5686 −2.85136
\(631\) −5.92911 −0.236034 −0.118017 0.993012i \(-0.537654\pi\)
−0.118017 + 0.993012i \(0.537654\pi\)
\(632\) 62.1067 2.47047
\(633\) −29.8471 −1.18631
\(634\) 11.1459 0.442661
\(635\) −56.8882 −2.25754
\(636\) 54.9199 2.17772
\(637\) −13.4336 −0.532258
\(638\) −12.0075 −0.475381
\(639\) −15.7018 −0.621153
\(640\) 59.7908 2.36344
\(641\) 35.7446 1.41183 0.705914 0.708297i \(-0.250536\pi\)
0.705914 + 0.708297i \(0.250536\pi\)
\(642\) −110.751 −4.37099
\(643\) 22.6249 0.892238 0.446119 0.894974i \(-0.352806\pi\)
0.446119 + 0.894974i \(0.352806\pi\)
\(644\) 57.3601 2.26031
\(645\) 29.9411 1.17893
\(646\) 90.6442 3.56635
\(647\) −10.5516 −0.414826 −0.207413 0.978253i \(-0.566504\pi\)
−0.207413 + 0.978253i \(0.566504\pi\)
\(648\) 45.8072 1.79948
\(649\) 36.7498 1.44256
\(650\) 20.4995 0.804056
\(651\) −9.16401 −0.359166
\(652\) 57.2970 2.24392
\(653\) 50.6682 1.98280 0.991399 0.130874i \(-0.0417784\pi\)
0.991399 + 0.130874i \(0.0417784\pi\)
\(654\) 77.9107 3.04655
\(655\) −28.4610 −1.11206
\(656\) 4.41293 0.172296
\(657\) 13.0885 0.510630
\(658\) 78.3381 3.05394
\(659\) 35.1648 1.36982 0.684912 0.728625i \(-0.259840\pi\)
0.684912 + 0.728625i \(0.259840\pi\)
\(660\) 108.133 4.20908
\(661\) 3.39076 0.131885 0.0659427 0.997823i \(-0.478995\pi\)
0.0659427 + 0.997823i \(0.478995\pi\)
\(662\) −22.5030 −0.874604
\(663\) 27.9105 1.08395
\(664\) 11.1905 0.434277
\(665\) 75.2373 2.91758
\(666\) 56.5114 2.18977
\(667\) 5.13554 0.198849
\(668\) −50.9557 −1.97154
\(669\) 25.3404 0.979718
\(670\) −9.04167 −0.349310
\(671\) −28.3553 −1.09464
\(672\) 5.86540 0.226263
\(673\) −32.2711 −1.24396 −0.621980 0.783033i \(-0.713672\pi\)
−0.621980 + 0.783033i \(0.713672\pi\)
\(674\) −67.3740 −2.59515
\(675\) −2.53827 −0.0976979
\(676\) −32.3115 −1.24275
\(677\) 2.07821 0.0798722 0.0399361 0.999202i \(-0.487285\pi\)
0.0399361 + 0.999202i \(0.487285\pi\)
\(678\) −49.0001 −1.88184
\(679\) 69.3337 2.66078
\(680\) 74.6023 2.86087
\(681\) 3.63699 0.139370
\(682\) 9.94407 0.380778
\(683\) −31.7398 −1.21449 −0.607244 0.794515i \(-0.707725\pi\)
−0.607244 + 0.794515i \(0.707725\pi\)
\(684\) 74.6674 2.85498
\(685\) 40.5300 1.54857
\(686\) 7.53637 0.287740
\(687\) 8.40497 0.320670
\(688\) 15.0621 0.574236
\(689\) −12.7676 −0.486408
\(690\) −69.7878 −2.65678
\(691\) −36.2489 −1.37897 −0.689487 0.724298i \(-0.742164\pi\)
−0.689487 + 0.724298i \(0.742164\pi\)
\(692\) 89.4416 3.40006
\(693\) 38.1904 1.45073
\(694\) −13.4119 −0.509108
\(695\) 40.7355 1.54519
\(696\) −14.3378 −0.543471
\(697\) −6.57728 −0.249132
\(698\) 69.0416 2.61326
\(699\) 61.2324 2.31602
\(700\) 54.8771 2.07416
\(701\) −6.37857 −0.240915 −0.120458 0.992718i \(-0.538436\pi\)
−0.120458 + 0.992718i \(0.538436\pi\)
\(702\) −3.50705 −0.132365
\(703\) −59.4082 −2.24062
\(704\) −34.0523 −1.28340
\(705\) −63.1619 −2.37882
\(706\) 61.0867 2.29903
\(707\) 5.71347 0.214877
\(708\) 89.3708 3.35876
\(709\) −8.49080 −0.318879 −0.159439 0.987208i \(-0.550969\pi\)
−0.159439 + 0.987208i \(0.550969\pi\)
\(710\) 41.7512 1.56690
\(711\) −36.0186 −1.35080
\(712\) −27.3304 −1.02425
\(713\) −4.25303 −0.159277
\(714\) 112.746 4.21943
\(715\) −25.1385 −0.940126
\(716\) 31.6129 1.18143
\(717\) −55.4438 −2.07059
\(718\) 39.6015 1.47791
\(719\) −47.3743 −1.76676 −0.883382 0.468653i \(-0.844739\pi\)
−0.883382 + 0.468653i \(0.844739\pi\)
\(720\) 29.0283 1.08182
\(721\) 40.9114 1.52362
\(722\) −72.1827 −2.68636
\(723\) −17.2854 −0.642850
\(724\) 38.0014 1.41231
\(725\) 4.91324 0.182473
\(726\) −22.9849 −0.853051
\(727\) 34.2286 1.26947 0.634734 0.772730i \(-0.281110\pi\)
0.634734 + 0.772730i \(0.281110\pi\)
\(728\) 37.2293 1.37981
\(729\) −21.8358 −0.808732
\(730\) −34.8024 −1.28810
\(731\) −22.4494 −0.830319
\(732\) −68.9563 −2.54870
\(733\) −6.53757 −0.241471 −0.120735 0.992685i \(-0.538525\pi\)
−0.120735 + 0.992685i \(0.538525\pi\)
\(734\) 77.7948 2.87146
\(735\) 43.7532 1.61386
\(736\) 2.72214 0.100339
\(737\) 4.82480 0.177724
\(738\) −8.17569 −0.300951
\(739\) 1.73943 0.0639858 0.0319929 0.999488i \(-0.489815\pi\)
0.0319929 + 0.999488i \(0.489815\pi\)
\(740\) −99.5794 −3.66061
\(741\) −36.4717 −1.33982
\(742\) −51.5757 −1.89340
\(743\) −34.2926 −1.25807 −0.629036 0.777376i \(-0.716550\pi\)
−0.629036 + 0.777376i \(0.716550\pi\)
\(744\) 11.8739 0.435318
\(745\) −43.5386 −1.59513
\(746\) 62.7525 2.29753
\(747\) −6.48992 −0.237454
\(748\) −81.0764 −2.96445
\(749\) 68.9248 2.51846
\(750\) 19.9018 0.726710
\(751\) 29.6568 1.08219 0.541096 0.840961i \(-0.318010\pi\)
0.541096 + 0.840961i \(0.318010\pi\)
\(752\) −31.7740 −1.15868
\(753\) −36.8012 −1.34111
\(754\) 6.78848 0.247222
\(755\) 16.2036 0.589709
\(756\) −9.38838 −0.341452
\(757\) 25.2425 0.917455 0.458727 0.888577i \(-0.348305\pi\)
0.458727 + 0.888577i \(0.348305\pi\)
\(758\) 77.6373 2.81991
\(759\) 37.2401 1.35173
\(760\) −97.4856 −3.53617
\(761\) −9.70283 −0.351727 −0.175864 0.984415i \(-0.556272\pi\)
−0.175864 + 0.984415i \(0.556272\pi\)
\(762\) 111.399 4.03555
\(763\) −48.4870 −1.75535
\(764\) 29.5046 1.06744
\(765\) −43.2654 −1.56426
\(766\) 5.92857 0.214208
\(767\) −20.7767 −0.750202
\(768\) −74.9326 −2.70390
\(769\) 23.9716 0.864436 0.432218 0.901769i \(-0.357731\pi\)
0.432218 + 0.901769i \(0.357731\pi\)
\(770\) −101.549 −3.65956
\(771\) −15.2044 −0.547573
\(772\) −57.3219 −2.06306
\(773\) −12.1885 −0.438389 −0.219194 0.975681i \(-0.570343\pi\)
−0.219194 + 0.975681i \(0.570343\pi\)
\(774\) −27.9050 −1.00302
\(775\) −4.06892 −0.146160
\(776\) −89.8363 −3.22493
\(777\) −73.8939 −2.65093
\(778\) 17.2846 0.619683
\(779\) 8.59478 0.307940
\(780\) −61.1335 −2.18893
\(781\) −22.2792 −0.797213
\(782\) 52.3257 1.87116
\(783\) −0.840556 −0.0300390
\(784\) 22.0103 0.786082
\(785\) 1.87874 0.0670553
\(786\) 55.7324 1.98791
\(787\) −34.7676 −1.23933 −0.619666 0.784866i \(-0.712732\pi\)
−0.619666 + 0.784866i \(0.712732\pi\)
\(788\) −21.9608 −0.782322
\(789\) 25.9528 0.923946
\(790\) 95.7740 3.40749
\(791\) 30.4948 1.08427
\(792\) −49.4836 −1.75832
\(793\) 16.0308 0.569269
\(794\) 41.8070 1.48367
\(795\) 41.5841 1.47484
\(796\) −6.37360 −0.225906
\(797\) −16.3193 −0.578061 −0.289030 0.957320i \(-0.593333\pi\)
−0.289030 + 0.957320i \(0.593333\pi\)
\(798\) −147.330 −5.21542
\(799\) 47.3577 1.67540
\(800\) 2.60430 0.0920760
\(801\) 15.8502 0.560038
\(802\) 46.6830 1.64844
\(803\) 18.5712 0.655364
\(804\) 11.7333 0.413801
\(805\) 43.4318 1.53077
\(806\) −5.62192 −0.198024
\(807\) 33.0450 1.16324
\(808\) −7.40299 −0.260436
\(809\) 13.0347 0.458274 0.229137 0.973394i \(-0.426410\pi\)
0.229137 + 0.973394i \(0.426410\pi\)
\(810\) 70.6387 2.48199
\(811\) −17.6821 −0.620904 −0.310452 0.950589i \(-0.600480\pi\)
−0.310452 + 0.950589i \(0.600480\pi\)
\(812\) 18.1728 0.637739
\(813\) −0.335306 −0.0117597
\(814\) 80.1839 2.81044
\(815\) 43.3840 1.51968
\(816\) −45.7300 −1.60087
\(817\) 29.3354 1.02632
\(818\) −9.50609 −0.332373
\(819\) −21.5911 −0.754453
\(820\) 14.4065 0.503097
\(821\) −35.1270 −1.22594 −0.612970 0.790106i \(-0.710025\pi\)
−0.612970 + 0.790106i \(0.710025\pi\)
\(822\) −79.3660 −2.76821
\(823\) 56.5437 1.97099 0.985495 0.169703i \(-0.0542807\pi\)
0.985495 + 0.169703i \(0.0542807\pi\)
\(824\) −53.0092 −1.84666
\(825\) 35.6280 1.24041
\(826\) −83.9288 −2.92026
\(827\) 31.3054 1.08860 0.544298 0.838892i \(-0.316796\pi\)
0.544298 + 0.838892i \(0.316796\pi\)
\(828\) 43.1029 1.49793
\(829\) 17.4882 0.607389 0.303695 0.952769i \(-0.401780\pi\)
0.303695 + 0.952769i \(0.401780\pi\)
\(830\) 17.2568 0.598992
\(831\) −48.1162 −1.66913
\(832\) 19.2516 0.667429
\(833\) −32.8054 −1.13664
\(834\) −79.7684 −2.76215
\(835\) −38.5825 −1.33520
\(836\) 105.946 3.66420
\(837\) 0.696111 0.0240611
\(838\) 4.89649 0.169146
\(839\) −49.4807 −1.70826 −0.854132 0.520056i \(-0.825911\pi\)
−0.854132 + 0.520056i \(0.825911\pi\)
\(840\) −121.256 −4.18373
\(841\) −27.3730 −0.943895
\(842\) −3.76764 −0.129842
\(843\) −33.8379 −1.16544
\(844\) −49.0173 −1.68724
\(845\) −24.4655 −0.841640
\(846\) 58.8666 2.02388
\(847\) 14.3045 0.491508
\(848\) 20.9192 0.718367
\(849\) −40.4824 −1.38935
\(850\) 50.0606 1.71707
\(851\) −34.2942 −1.17559
\(852\) −54.1801 −1.85618
\(853\) −33.0821 −1.13271 −0.566354 0.824162i \(-0.691647\pi\)
−0.566354 + 0.824162i \(0.691647\pi\)
\(854\) 64.7574 2.21595
\(855\) 56.5365 1.93351
\(856\) −89.3065 −3.05243
\(857\) 45.2819 1.54680 0.773400 0.633919i \(-0.218555\pi\)
0.773400 + 0.633919i \(0.218555\pi\)
\(858\) 49.2262 1.68056
\(859\) 21.1811 0.722689 0.361345 0.932432i \(-0.382318\pi\)
0.361345 + 0.932432i \(0.382318\pi\)
\(860\) 49.1717 1.67674
\(861\) 10.6905 0.364331
\(862\) 17.2956 0.589091
\(863\) 30.3164 1.03198 0.515991 0.856594i \(-0.327424\pi\)
0.515991 + 0.856594i \(0.327424\pi\)
\(864\) −0.445544 −0.0151577
\(865\) 67.7232 2.30266
\(866\) −67.9711 −2.30975
\(867\) 27.4842 0.933414
\(868\) −15.0499 −0.510826
\(869\) −51.1068 −1.73368
\(870\) −22.1101 −0.749602
\(871\) −2.72772 −0.0924253
\(872\) 62.8251 2.12753
\(873\) 52.1003 1.76333
\(874\) −68.3760 −2.31285
\(875\) −12.3857 −0.418713
\(876\) 45.1628 1.52591
\(877\) 42.5199 1.43579 0.717897 0.696149i \(-0.245105\pi\)
0.717897 + 0.696149i \(0.245105\pi\)
\(878\) 21.7864 0.735256
\(879\) 42.6974 1.44015
\(880\) 41.1882 1.38845
\(881\) −43.1458 −1.45362 −0.726810 0.686839i \(-0.758998\pi\)
−0.726810 + 0.686839i \(0.758998\pi\)
\(882\) −40.7777 −1.37306
\(883\) 17.9940 0.605547 0.302773 0.953063i \(-0.402087\pi\)
0.302773 + 0.953063i \(0.402087\pi\)
\(884\) 45.8368 1.54166
\(885\) 67.6696 2.27469
\(886\) 21.5567 0.724213
\(887\) −33.8644 −1.13706 −0.568528 0.822664i \(-0.692487\pi\)
−0.568528 + 0.822664i \(0.692487\pi\)
\(888\) 95.7450 3.21299
\(889\) −69.3280 −2.32519
\(890\) −42.1458 −1.41273
\(891\) −37.6941 −1.26280
\(892\) 41.6161 1.39341
\(893\) −61.8841 −2.07087
\(894\) 85.2574 2.85144
\(895\) 23.9366 0.800112
\(896\) 72.8653 2.43426
\(897\) −21.0538 −0.702966
\(898\) −49.1555 −1.64034
\(899\) −1.34744 −0.0449396
\(900\) 41.2370 1.37457
\(901\) −31.1791 −1.03873
\(902\) −11.6005 −0.386254
\(903\) 36.4884 1.21426
\(904\) −39.5124 −1.31416
\(905\) 28.7738 0.956474
\(906\) −31.7299 −1.05416
\(907\) 28.5992 0.949619 0.474810 0.880089i \(-0.342517\pi\)
0.474810 + 0.880089i \(0.342517\pi\)
\(908\) 5.97297 0.198220
\(909\) 4.29335 0.142401
\(910\) 57.4109 1.90315
\(911\) 21.3574 0.707602 0.353801 0.935321i \(-0.384889\pi\)
0.353801 + 0.935321i \(0.384889\pi\)
\(912\) 59.7571 1.97876
\(913\) −9.20854 −0.304758
\(914\) 44.5546 1.47374
\(915\) −52.2122 −1.72608
\(916\) 13.8033 0.456074
\(917\) −34.6846 −1.14539
\(918\) −8.56438 −0.282667
\(919\) −23.4921 −0.774933 −0.387466 0.921884i \(-0.626650\pi\)
−0.387466 + 0.921884i \(0.626650\pi\)
\(920\) −56.2750 −1.85533
\(921\) −73.8465 −2.43333
\(922\) −96.6817 −3.18404
\(923\) 12.5956 0.414591
\(924\) 131.779 4.33520
\(925\) −32.8097 −1.07878
\(926\) −95.2541 −3.13024
\(927\) 30.7426 1.00972
\(928\) 0.862424 0.0283105
\(929\) 6.57180 0.215614 0.107807 0.994172i \(-0.465617\pi\)
0.107807 + 0.994172i \(0.465617\pi\)
\(930\) 18.3106 0.600427
\(931\) 42.8680 1.40494
\(932\) 100.561 3.29398
\(933\) −66.8648 −2.18906
\(934\) −44.1024 −1.44307
\(935\) −61.3892 −2.00764
\(936\) 27.9757 0.914415
\(937\) 19.3674 0.632706 0.316353 0.948642i \(-0.397542\pi\)
0.316353 + 0.948642i \(0.397542\pi\)
\(938\) −11.0188 −0.359777
\(939\) −37.3129 −1.21766
\(940\) −103.730 −3.38329
\(941\) −28.7492 −0.937199 −0.468599 0.883411i \(-0.655241\pi\)
−0.468599 + 0.883411i \(0.655241\pi\)
\(942\) −3.67896 −0.119867
\(943\) 4.96146 0.161567
\(944\) 34.0416 1.10796
\(945\) −7.10867 −0.231245
\(946\) −39.5943 −1.28732
\(947\) −1.29786 −0.0421748 −0.0210874 0.999778i \(-0.506713\pi\)
−0.0210874 + 0.999778i \(0.506713\pi\)
\(948\) −124.285 −4.03659
\(949\) −10.4993 −0.340822
\(950\) −65.4161 −2.12238
\(951\) −10.9518 −0.355136
\(952\) 90.9156 2.94659
\(953\) 4.47948 0.145104 0.0725522 0.997365i \(-0.476886\pi\)
0.0725522 + 0.997365i \(0.476886\pi\)
\(954\) −38.7562 −1.25478
\(955\) 22.3402 0.722913
\(956\) −91.0543 −2.94491
\(957\) 11.7983 0.381386
\(958\) −5.53576 −0.178852
\(959\) 49.3927 1.59498
\(960\) −62.7025 −2.02371
\(961\) −29.8841 −0.964004
\(962\) −45.3323 −1.46157
\(963\) 51.7931 1.66901
\(964\) −28.3874 −0.914297
\(965\) −43.4029 −1.39719
\(966\) −85.0483 −2.73639
\(967\) 27.9357 0.898351 0.449176 0.893443i \(-0.351718\pi\)
0.449176 + 0.893443i \(0.351718\pi\)
\(968\) −18.5344 −0.595719
\(969\) −89.0654 −2.86119
\(970\) −138.535 −4.44810
\(971\) 50.9471 1.63497 0.817485 0.575950i \(-0.195368\pi\)
0.817485 + 0.575950i \(0.195368\pi\)
\(972\) −83.8991 −2.69107
\(973\) 49.6432 1.59149
\(974\) 16.6903 0.534793
\(975\) −20.1424 −0.645074
\(976\) −26.2657 −0.840743
\(977\) −24.6332 −0.788086 −0.394043 0.919092i \(-0.628924\pi\)
−0.394043 + 0.919092i \(0.628924\pi\)
\(978\) −84.9547 −2.71655
\(979\) 22.4898 0.718777
\(980\) 71.8549 2.29532
\(981\) −36.4352 −1.16329
\(982\) 42.6407 1.36072
\(983\) 50.3525 1.60599 0.802997 0.595983i \(-0.203237\pi\)
0.802997 + 0.595983i \(0.203237\pi\)
\(984\) −13.8518 −0.441578
\(985\) −16.6283 −0.529820
\(986\) 16.5778 0.527944
\(987\) −76.9736 −2.45010
\(988\) −59.8967 −1.90557
\(989\) 16.9343 0.538479
\(990\) −76.3080 −2.42523
\(991\) 33.7978 1.07362 0.536812 0.843702i \(-0.319629\pi\)
0.536812 + 0.843702i \(0.319629\pi\)
\(992\) −0.714221 −0.0226765
\(993\) 22.1110 0.701672
\(994\) 50.8810 1.61385
\(995\) −4.82595 −0.152993
\(996\) −22.3940 −0.709580
\(997\) −28.0884 −0.889567 −0.444784 0.895638i \(-0.646719\pi\)
−0.444784 + 0.895638i \(0.646719\pi\)
\(998\) −2.30817 −0.0730638
\(999\) 5.61309 0.177590
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 \(a_p\))