Properties

Label 8041.2.a.i.1.5
Level 8041
Weight 2
Character 8041.1
Self dual Yes
Analytic conductor 64.208
Analytic rank 0
Dimension 78
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8041 = 11 \cdot 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8041.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2077082653\)
Analytic rank: \(0\)
Dimension: \(78\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Character \(\chi\) = 8041.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.55392 q^{2} +1.24868 q^{3} +4.52253 q^{4} +4.26646 q^{5} -3.18904 q^{6} -0.595052 q^{7} -6.44234 q^{8} -1.44079 q^{9} +O(q^{10})\) \(q-2.55392 q^{2} +1.24868 q^{3} +4.52253 q^{4} +4.26646 q^{5} -3.18904 q^{6} -0.595052 q^{7} -6.44234 q^{8} -1.44079 q^{9} -10.8962 q^{10} +1.00000 q^{11} +5.64721 q^{12} +1.58644 q^{13} +1.51972 q^{14} +5.32746 q^{15} +7.40820 q^{16} -1.00000 q^{17} +3.67967 q^{18} -2.73257 q^{19} +19.2952 q^{20} -0.743032 q^{21} -2.55392 q^{22} -0.638262 q^{23} -8.04445 q^{24} +13.2027 q^{25} -4.05164 q^{26} -5.54514 q^{27} -2.69114 q^{28} -0.508293 q^{29} -13.6059 q^{30} +4.45197 q^{31} -6.03530 q^{32} +1.24868 q^{33} +2.55392 q^{34} -2.53876 q^{35} -6.51601 q^{36} +9.71491 q^{37} +6.97878 q^{38} +1.98096 q^{39} -27.4860 q^{40} +5.39922 q^{41} +1.89765 q^{42} -1.00000 q^{43} +4.52253 q^{44} -6.14707 q^{45} +1.63007 q^{46} +11.5968 q^{47} +9.25050 q^{48} -6.64591 q^{49} -33.7186 q^{50} -1.24868 q^{51} +7.17470 q^{52} +5.13116 q^{53} +14.1619 q^{54} +4.26646 q^{55} +3.83353 q^{56} -3.41212 q^{57} +1.29814 q^{58} +8.62988 q^{59} +24.0936 q^{60} +5.67358 q^{61} -11.3700 q^{62} +0.857344 q^{63} +0.597286 q^{64} +6.76847 q^{65} -3.18904 q^{66} +2.15243 q^{67} -4.52253 q^{68} -0.796988 q^{69} +6.48381 q^{70} +0.352619 q^{71} +9.28206 q^{72} +8.40716 q^{73} -24.8111 q^{74} +16.4860 q^{75} -12.3581 q^{76} -0.595052 q^{77} -5.05921 q^{78} -3.55050 q^{79} +31.6068 q^{80} -2.60176 q^{81} -13.7892 q^{82} -12.3025 q^{83} -3.36038 q^{84} -4.26646 q^{85} +2.55392 q^{86} -0.634697 q^{87} -6.44234 q^{88} -11.1373 q^{89} +15.6991 q^{90} -0.944012 q^{91} -2.88656 q^{92} +5.55911 q^{93} -29.6174 q^{94} -11.6584 q^{95} -7.53618 q^{96} -12.0254 q^{97} +16.9732 q^{98} -1.44079 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 78q + 7q^{2} + 10q^{3} + 91q^{4} + 17q^{5} + 12q^{6} + 11q^{7} + 33q^{8} + 102q^{9} + O(q^{10}) \) \( 78q + 7q^{2} + 10q^{3} + 91q^{4} + 17q^{5} + 12q^{6} + 11q^{7} + 33q^{8} + 102q^{9} + 3q^{10} + 78q^{11} + 31q^{12} - 16q^{13} + 31q^{14} + 38q^{15} + 121q^{16} - 78q^{17} + 11q^{18} + 51q^{20} + 6q^{21} + 7q^{22} + 48q^{23} + 11q^{24} + 101q^{25} + 18q^{26} + 46q^{27} + 27q^{28} + 22q^{29} + 14q^{30} + 56q^{31} + 83q^{32} + 10q^{33} - 7q^{34} + 24q^{35} + 139q^{36} + 53q^{37} + 10q^{38} + 79q^{39} - q^{40} + 23q^{41} + 17q^{42} - 78q^{43} + 91q^{44} + 76q^{45} + 21q^{46} + 57q^{47} + 78q^{48} + 115q^{49} + 58q^{50} - 10q^{51} - 63q^{52} + 22q^{53} - 18q^{54} + 17q^{55} + 111q^{56} - 11q^{57} + 36q^{58} + 71q^{59} + 36q^{60} + 4q^{61} - 5q^{62} + 71q^{63} + 183q^{64} + 47q^{65} + 12q^{66} + 11q^{67} - 91q^{68} + 31q^{69} + 33q^{70} + 159q^{71} + 59q^{72} + 2q^{73} - 4q^{74} + 83q^{75} - 44q^{76} + 11q^{77} + 101q^{78} + 35q^{79} + 85q^{80} + 170q^{81} + 98q^{82} - 32q^{83} + 44q^{84} - 17q^{85} - 7q^{86} - 6q^{87} + 33q^{88} + 50q^{89} - 5q^{90} + 86q^{91} + 106q^{92} + 68q^{93} - q^{94} + 109q^{95} - 50q^{96} + 40q^{97} + 106q^{98} + 102q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.55392 −1.80590 −0.902948 0.429749i \(-0.858602\pi\)
−0.902948 + 0.429749i \(0.858602\pi\)
\(3\) 1.24868 0.720928 0.360464 0.932773i \(-0.382618\pi\)
0.360464 + 0.932773i \(0.382618\pi\)
\(4\) 4.52253 2.26126
\(5\) 4.26646 1.90802 0.954009 0.299777i \(-0.0969123\pi\)
0.954009 + 0.299777i \(0.0969123\pi\)
\(6\) −3.18904 −1.30192
\(7\) −0.595052 −0.224908 −0.112454 0.993657i \(-0.535871\pi\)
−0.112454 + 0.993657i \(0.535871\pi\)
\(8\) −6.44234 −2.27771
\(9\) −1.44079 −0.480263
\(10\) −10.8962 −3.44569
\(11\) 1.00000 0.301511
\(12\) 5.64721 1.63021
\(13\) 1.58644 0.439998 0.219999 0.975500i \(-0.429395\pi\)
0.219999 + 0.975500i \(0.429395\pi\)
\(14\) 1.51972 0.406162
\(15\) 5.32746 1.37554
\(16\) 7.40820 1.85205
\(17\) −1.00000 −0.242536
\(18\) 3.67967 0.867306
\(19\) −2.73257 −0.626895 −0.313448 0.949606i \(-0.601484\pi\)
−0.313448 + 0.949606i \(0.601484\pi\)
\(20\) 19.2952 4.31453
\(21\) −0.743032 −0.162143
\(22\) −2.55392 −0.544498
\(23\) −0.638262 −0.133087 −0.0665435 0.997784i \(-0.521197\pi\)
−0.0665435 + 0.997784i \(0.521197\pi\)
\(24\) −8.04445 −1.64207
\(25\) 13.2027 2.64053
\(26\) −4.05164 −0.794592
\(27\) −5.54514 −1.06716
\(28\) −2.69114 −0.508577
\(29\) −0.508293 −0.0943877 −0.0471938 0.998886i \(-0.515028\pi\)
−0.0471938 + 0.998886i \(0.515028\pi\)
\(30\) −13.6059 −2.48409
\(31\) 4.45197 0.799598 0.399799 0.916603i \(-0.369080\pi\)
0.399799 + 0.916603i \(0.369080\pi\)
\(32\) −6.03530 −1.06690
\(33\) 1.24868 0.217368
\(34\) 2.55392 0.437994
\(35\) −2.53876 −0.429130
\(36\) −6.51601 −1.08600
\(37\) 9.71491 1.59712 0.798561 0.601914i \(-0.205595\pi\)
0.798561 + 0.601914i \(0.205595\pi\)
\(38\) 6.97878 1.13211
\(39\) 1.98096 0.317207
\(40\) −27.4860 −4.34592
\(41\) 5.39922 0.843216 0.421608 0.906778i \(-0.361466\pi\)
0.421608 + 0.906778i \(0.361466\pi\)
\(42\) 1.89765 0.292813
\(43\) −1.00000 −0.152499
\(44\) 4.52253 0.681797
\(45\) −6.14707 −0.916351
\(46\) 1.63007 0.240341
\(47\) 11.5968 1.69157 0.845786 0.533523i \(-0.179132\pi\)
0.845786 + 0.533523i \(0.179132\pi\)
\(48\) 9.25050 1.33519
\(49\) −6.64591 −0.949416
\(50\) −33.7186 −4.76853
\(51\) −1.24868 −0.174851
\(52\) 7.17470 0.994952
\(53\) 5.13116 0.704819 0.352409 0.935846i \(-0.385362\pi\)
0.352409 + 0.935846i \(0.385362\pi\)
\(54\) 14.1619 1.92719
\(55\) 4.26646 0.575289
\(56\) 3.83353 0.512277
\(57\) −3.41212 −0.451946
\(58\) 1.29814 0.170454
\(59\) 8.62988 1.12352 0.561758 0.827302i \(-0.310125\pi\)
0.561758 + 0.827302i \(0.310125\pi\)
\(60\) 24.0936 3.11047
\(61\) 5.67358 0.726428 0.363214 0.931706i \(-0.381679\pi\)
0.363214 + 0.931706i \(0.381679\pi\)
\(62\) −11.3700 −1.44399
\(63\) 0.857344 0.108015
\(64\) 0.597286 0.0746608
\(65\) 6.76847 0.839525
\(66\) −3.18904 −0.392544
\(67\) 2.15243 0.262962 0.131481 0.991319i \(-0.458027\pi\)
0.131481 + 0.991319i \(0.458027\pi\)
\(68\) −4.52253 −0.548437
\(69\) −0.796988 −0.0959461
\(70\) 6.48381 0.774964
\(71\) 0.352619 0.0418482 0.0209241 0.999781i \(-0.493339\pi\)
0.0209241 + 0.999781i \(0.493339\pi\)
\(72\) 9.28206 1.09390
\(73\) 8.40716 0.983984 0.491992 0.870600i \(-0.336269\pi\)
0.491992 + 0.870600i \(0.336269\pi\)
\(74\) −24.8111 −2.88424
\(75\) 16.4860 1.90364
\(76\) −12.3581 −1.41758
\(77\) −0.595052 −0.0678125
\(78\) −5.05921 −0.572843
\(79\) −3.55050 −0.399462 −0.199731 0.979851i \(-0.564007\pi\)
−0.199731 + 0.979851i \(0.564007\pi\)
\(80\) 31.6068 3.53375
\(81\) −2.60176 −0.289084
\(82\) −13.7892 −1.52276
\(83\) −12.3025 −1.35038 −0.675189 0.737645i \(-0.735938\pi\)
−0.675189 + 0.737645i \(0.735938\pi\)
\(84\) −3.36038 −0.366648
\(85\) −4.26646 −0.462762
\(86\) 2.55392 0.275397
\(87\) −0.634697 −0.0680467
\(88\) −6.44234 −0.686756
\(89\) −11.1373 −1.18056 −0.590278 0.807200i \(-0.700982\pi\)
−0.590278 + 0.807200i \(0.700982\pi\)
\(90\) 15.6991 1.65484
\(91\) −0.944012 −0.0989593
\(92\) −2.88656 −0.300945
\(93\) 5.55911 0.576452
\(94\) −29.6174 −3.05480
\(95\) −11.6584 −1.19613
\(96\) −7.53618 −0.769158
\(97\) −12.0254 −1.22099 −0.610497 0.792019i \(-0.709030\pi\)
−0.610497 + 0.792019i \(0.709030\pi\)
\(98\) 16.9732 1.71455
\(99\) −1.44079 −0.144805
\(100\) 59.7095 5.97095
\(101\) −13.9464 −1.38772 −0.693861 0.720109i \(-0.744092\pi\)
−0.693861 + 0.720109i \(0.744092\pi\)
\(102\) 3.18904 0.315762
\(103\) −1.41604 −0.139527 −0.0697634 0.997564i \(-0.522224\pi\)
−0.0697634 + 0.997564i \(0.522224\pi\)
\(104\) −10.2204 −1.00219
\(105\) −3.17011 −0.309371
\(106\) −13.1046 −1.27283
\(107\) 9.06893 0.876727 0.438364 0.898798i \(-0.355558\pi\)
0.438364 + 0.898798i \(0.355558\pi\)
\(108\) −25.0781 −2.41314
\(109\) −15.4803 −1.48275 −0.741373 0.671094i \(-0.765825\pi\)
−0.741373 + 0.671094i \(0.765825\pi\)
\(110\) −10.8962 −1.03891
\(111\) 12.1309 1.15141
\(112\) −4.40827 −0.416542
\(113\) −6.29118 −0.591825 −0.295912 0.955215i \(-0.595624\pi\)
−0.295912 + 0.955215i \(0.595624\pi\)
\(114\) 8.71429 0.816168
\(115\) −2.72312 −0.253932
\(116\) −2.29877 −0.213435
\(117\) −2.28572 −0.211315
\(118\) −22.0401 −2.02895
\(119\) 0.595052 0.0545483
\(120\) −34.3213 −3.13309
\(121\) 1.00000 0.0909091
\(122\) −14.4899 −1.31185
\(123\) 6.74192 0.607898
\(124\) 20.1342 1.80810
\(125\) 34.9964 3.13017
\(126\) −2.18959 −0.195064
\(127\) 21.8289 1.93700 0.968502 0.249006i \(-0.0801039\pi\)
0.968502 + 0.249006i \(0.0801039\pi\)
\(128\) 10.5452 0.932070
\(129\) −1.24868 −0.109940
\(130\) −17.2861 −1.51610
\(131\) −4.02160 −0.351369 −0.175685 0.984447i \(-0.556214\pi\)
−0.175685 + 0.984447i \(0.556214\pi\)
\(132\) 5.64721 0.491526
\(133\) 1.62602 0.140994
\(134\) −5.49715 −0.474882
\(135\) −23.6581 −2.03617
\(136\) 6.44234 0.552426
\(137\) −10.5552 −0.901790 −0.450895 0.892577i \(-0.648895\pi\)
−0.450895 + 0.892577i \(0.648895\pi\)
\(138\) 2.03545 0.173269
\(139\) 17.3534 1.47190 0.735949 0.677037i \(-0.236737\pi\)
0.735949 + 0.677037i \(0.236737\pi\)
\(140\) −11.4816 −0.970375
\(141\) 14.4808 1.21950
\(142\) −0.900563 −0.0755736
\(143\) 1.58644 0.132664
\(144\) −10.6737 −0.889472
\(145\) −2.16861 −0.180093
\(146\) −21.4712 −1.77697
\(147\) −8.29864 −0.684461
\(148\) 43.9360 3.61151
\(149\) 19.4491 1.59334 0.796668 0.604417i \(-0.206594\pi\)
0.796668 + 0.604417i \(0.206594\pi\)
\(150\) −42.1039 −3.43777
\(151\) −22.1832 −1.80524 −0.902622 0.430434i \(-0.858361\pi\)
−0.902622 + 0.430434i \(0.858361\pi\)
\(152\) 17.6042 1.42789
\(153\) 1.44079 0.116481
\(154\) 1.51972 0.122462
\(155\) 18.9942 1.52565
\(156\) 8.95893 0.717289
\(157\) 9.59826 0.766025 0.383012 0.923743i \(-0.374887\pi\)
0.383012 + 0.923743i \(0.374887\pi\)
\(158\) 9.06769 0.721387
\(159\) 6.40719 0.508123
\(160\) −25.7494 −2.03566
\(161\) 0.379799 0.0299324
\(162\) 6.64469 0.522056
\(163\) −5.44017 −0.426107 −0.213054 0.977041i \(-0.568341\pi\)
−0.213054 + 0.977041i \(0.568341\pi\)
\(164\) 24.4181 1.90673
\(165\) 5.32746 0.414742
\(166\) 31.4197 2.43864
\(167\) −6.29256 −0.486933 −0.243466 0.969909i \(-0.578285\pi\)
−0.243466 + 0.969909i \(0.578285\pi\)
\(168\) 4.78687 0.369315
\(169\) −10.4832 −0.806402
\(170\) 10.8962 0.835701
\(171\) 3.93706 0.301075
\(172\) −4.52253 −0.344840
\(173\) −20.7720 −1.57926 −0.789632 0.613581i \(-0.789728\pi\)
−0.789632 + 0.613581i \(0.789728\pi\)
\(174\) 1.62097 0.122885
\(175\) −7.85628 −0.593879
\(176\) 7.40820 0.558414
\(177\) 10.7760 0.809973
\(178\) 28.4439 2.13196
\(179\) 8.18288 0.611617 0.305808 0.952093i \(-0.401073\pi\)
0.305808 + 0.952093i \(0.401073\pi\)
\(180\) −27.8003 −2.07211
\(181\) 5.18879 0.385679 0.192840 0.981230i \(-0.438230\pi\)
0.192840 + 0.981230i \(0.438230\pi\)
\(182\) 2.41093 0.178710
\(183\) 7.08451 0.523702
\(184\) 4.11191 0.303134
\(185\) 41.4483 3.04734
\(186\) −14.1975 −1.04101
\(187\) −1.00000 −0.0731272
\(188\) 52.4470 3.82509
\(189\) 3.29965 0.240014
\(190\) 29.7747 2.16008
\(191\) 5.34058 0.386431 0.193215 0.981156i \(-0.438108\pi\)
0.193215 + 0.981156i \(0.438108\pi\)
\(192\) 0.745822 0.0538250
\(193\) −6.21263 −0.447195 −0.223597 0.974682i \(-0.571780\pi\)
−0.223597 + 0.974682i \(0.571780\pi\)
\(194\) 30.7120 2.20499
\(195\) 8.45167 0.605237
\(196\) −30.0563 −2.14688
\(197\) −20.5423 −1.46358 −0.731791 0.681530i \(-0.761315\pi\)
−0.731791 + 0.681530i \(0.761315\pi\)
\(198\) 3.67967 0.261502
\(199\) 15.9326 1.12943 0.564717 0.825284i \(-0.308985\pi\)
0.564717 + 0.825284i \(0.308985\pi\)
\(200\) −85.0562 −6.01438
\(201\) 2.68771 0.189576
\(202\) 35.6181 2.50608
\(203\) 0.302461 0.0212286
\(204\) −5.64721 −0.395384
\(205\) 23.0355 1.60887
\(206\) 3.61646 0.251971
\(207\) 0.919602 0.0639167
\(208\) 11.7526 0.814899
\(209\) −2.73257 −0.189016
\(210\) 8.09623 0.558693
\(211\) 19.8004 1.36312 0.681558 0.731764i \(-0.261303\pi\)
0.681558 + 0.731764i \(0.261303\pi\)
\(212\) 23.2058 1.59378
\(213\) 0.440310 0.0301695
\(214\) −23.1614 −1.58328
\(215\) −4.26646 −0.290970
\(216\) 35.7237 2.43069
\(217\) −2.64916 −0.179836
\(218\) 39.5355 2.67768
\(219\) 10.4979 0.709381
\(220\) 19.2952 1.30088
\(221\) −1.58644 −0.106715
\(222\) −30.9813 −2.07933
\(223\) −4.48898 −0.300604 −0.150302 0.988640i \(-0.548025\pi\)
−0.150302 + 0.988640i \(0.548025\pi\)
\(224\) 3.59132 0.239955
\(225\) −19.0223 −1.26815
\(226\) 16.0672 1.06877
\(227\) 18.5039 1.22815 0.614073 0.789249i \(-0.289530\pi\)
0.614073 + 0.789249i \(0.289530\pi\)
\(228\) −15.4314 −1.02197
\(229\) −7.34625 −0.485454 −0.242727 0.970095i \(-0.578042\pi\)
−0.242727 + 0.970095i \(0.578042\pi\)
\(230\) 6.95464 0.458576
\(231\) −0.743032 −0.0488879
\(232\) 3.27460 0.214988
\(233\) 5.20187 0.340786 0.170393 0.985376i \(-0.445496\pi\)
0.170393 + 0.985376i \(0.445496\pi\)
\(234\) 5.83756 0.381613
\(235\) 49.4774 3.22755
\(236\) 39.0289 2.54056
\(237\) −4.43345 −0.287983
\(238\) −1.51972 −0.0985086
\(239\) 19.1790 1.24058 0.620292 0.784371i \(-0.287014\pi\)
0.620292 + 0.784371i \(0.287014\pi\)
\(240\) 39.4669 2.54758
\(241\) 11.0632 0.712642 0.356321 0.934364i \(-0.384031\pi\)
0.356321 + 0.934364i \(0.384031\pi\)
\(242\) −2.55392 −0.164172
\(243\) 13.3866 0.858754
\(244\) 25.6589 1.64264
\(245\) −28.3545 −1.81150
\(246\) −17.2183 −1.09780
\(247\) −4.33505 −0.275833
\(248\) −28.6811 −1.82125
\(249\) −15.3620 −0.973525
\(250\) −89.3781 −5.65277
\(251\) 31.1560 1.96655 0.983275 0.182129i \(-0.0582989\pi\)
0.983275 + 0.182129i \(0.0582989\pi\)
\(252\) 3.87736 0.244251
\(253\) −0.638262 −0.0401272
\(254\) −55.7494 −3.49803
\(255\) −5.32746 −0.333618
\(256\) −28.1261 −1.75788
\(257\) 9.88820 0.616809 0.308405 0.951255i \(-0.400205\pi\)
0.308405 + 0.951255i \(0.400205\pi\)
\(258\) 3.18904 0.198541
\(259\) −5.78088 −0.359206
\(260\) 30.6106 1.89839
\(261\) 0.732343 0.0453309
\(262\) 10.2709 0.634536
\(263\) −6.21163 −0.383026 −0.191513 0.981490i \(-0.561339\pi\)
−0.191513 + 0.981490i \(0.561339\pi\)
\(264\) −8.04445 −0.495102
\(265\) 21.8919 1.34481
\(266\) −4.15274 −0.254621
\(267\) −13.9070 −0.851095
\(268\) 9.73444 0.594626
\(269\) 20.9420 1.27686 0.638429 0.769681i \(-0.279585\pi\)
0.638429 + 0.769681i \(0.279585\pi\)
\(270\) 60.4210 3.67711
\(271\) 23.6343 1.43568 0.717841 0.696207i \(-0.245131\pi\)
0.717841 + 0.696207i \(0.245131\pi\)
\(272\) −7.40820 −0.449188
\(273\) −1.17877 −0.0713425
\(274\) 26.9571 1.62854
\(275\) 13.2027 0.796151
\(276\) −3.60440 −0.216959
\(277\) −14.3862 −0.864384 −0.432192 0.901782i \(-0.642260\pi\)
−0.432192 + 0.901782i \(0.642260\pi\)
\(278\) −44.3193 −2.65809
\(279\) −6.41436 −0.384017
\(280\) 16.3556 0.977434
\(281\) 22.1269 1.31998 0.659989 0.751275i \(-0.270561\pi\)
0.659989 + 0.751275i \(0.270561\pi\)
\(282\) −36.9828 −2.20229
\(283\) 5.55430 0.330169 0.165084 0.986279i \(-0.447210\pi\)
0.165084 + 0.986279i \(0.447210\pi\)
\(284\) 1.59473 0.0946299
\(285\) −14.5577 −0.862322
\(286\) −4.05164 −0.239578
\(287\) −3.21282 −0.189647
\(288\) 8.69559 0.512393
\(289\) 1.00000 0.0588235
\(290\) 5.53847 0.325230
\(291\) −15.0159 −0.880249
\(292\) 38.0216 2.22505
\(293\) −23.8437 −1.39296 −0.696481 0.717575i \(-0.745252\pi\)
−0.696481 + 0.717575i \(0.745252\pi\)
\(294\) 21.1941 1.23607
\(295\) 36.8190 2.14369
\(296\) −62.5868 −3.63778
\(297\) −5.54514 −0.321762
\(298\) −49.6716 −2.87740
\(299\) −1.01256 −0.0585580
\(300\) 74.5582 4.30462
\(301\) 0.595052 0.0342982
\(302\) 56.6542 3.26009
\(303\) −17.4147 −1.00045
\(304\) −20.2434 −1.16104
\(305\) 24.2061 1.38604
\(306\) −3.67967 −0.210353
\(307\) −16.2035 −0.924780 −0.462390 0.886677i \(-0.653008\pi\)
−0.462390 + 0.886677i \(0.653008\pi\)
\(308\) −2.69114 −0.153342
\(309\) −1.76819 −0.100589
\(310\) −48.5096 −2.75516
\(311\) −7.70219 −0.436751 −0.218376 0.975865i \(-0.570076\pi\)
−0.218376 + 0.975865i \(0.570076\pi\)
\(312\) −12.7620 −0.722506
\(313\) 4.43924 0.250921 0.125460 0.992099i \(-0.459959\pi\)
0.125460 + 0.992099i \(0.459959\pi\)
\(314\) −24.5132 −1.38336
\(315\) 3.65782 0.206095
\(316\) −16.0572 −0.903289
\(317\) 13.8184 0.776116 0.388058 0.921635i \(-0.373146\pi\)
0.388058 + 0.921635i \(0.373146\pi\)
\(318\) −16.3635 −0.917618
\(319\) −0.508293 −0.0284590
\(320\) 2.54830 0.142454
\(321\) 11.3242 0.632057
\(322\) −0.969978 −0.0540548
\(323\) 2.73257 0.152044
\(324\) −11.7665 −0.653696
\(325\) 20.9452 1.16183
\(326\) 13.8938 0.769506
\(327\) −19.3300 −1.06895
\(328\) −34.7836 −1.92060
\(329\) −6.90072 −0.380449
\(330\) −13.6059 −0.748981
\(331\) −20.3626 −1.11923 −0.559614 0.828753i \(-0.689051\pi\)
−0.559614 + 0.828753i \(0.689051\pi\)
\(332\) −55.6385 −3.05356
\(333\) −13.9971 −0.767039
\(334\) 16.0707 0.879350
\(335\) 9.18327 0.501736
\(336\) −5.50453 −0.300297
\(337\) 7.51500 0.409368 0.204684 0.978828i \(-0.434383\pi\)
0.204684 + 0.978828i \(0.434383\pi\)
\(338\) 26.7733 1.45628
\(339\) −7.85569 −0.426663
\(340\) −19.2952 −1.04643
\(341\) 4.45197 0.241088
\(342\) −10.0550 −0.543710
\(343\) 8.12003 0.438440
\(344\) 6.44234 0.347348
\(345\) −3.40032 −0.183067
\(346\) 53.0500 2.85199
\(347\) −15.2044 −0.816213 −0.408107 0.912934i \(-0.633811\pi\)
−0.408107 + 0.912934i \(0.633811\pi\)
\(348\) −2.87044 −0.153872
\(349\) 25.2028 1.34908 0.674538 0.738240i \(-0.264343\pi\)
0.674538 + 0.738240i \(0.264343\pi\)
\(350\) 20.0643 1.07248
\(351\) −8.79701 −0.469550
\(352\) −6.03530 −0.321682
\(353\) −1.73988 −0.0926047 −0.0463024 0.998927i \(-0.514744\pi\)
−0.0463024 + 0.998927i \(0.514744\pi\)
\(354\) −27.5211 −1.46273
\(355\) 1.50444 0.0798472
\(356\) −50.3689 −2.66955
\(357\) 0.743032 0.0393254
\(358\) −20.8984 −1.10452
\(359\) −1.08977 −0.0575157 −0.0287578 0.999586i \(-0.509155\pi\)
−0.0287578 + 0.999586i \(0.509155\pi\)
\(360\) 39.6015 2.08718
\(361\) −11.5330 −0.607003
\(362\) −13.2518 −0.696497
\(363\) 1.24868 0.0655389
\(364\) −4.26932 −0.223773
\(365\) 35.8688 1.87746
\(366\) −18.0933 −0.945752
\(367\) 16.1938 0.845311 0.422655 0.906290i \(-0.361098\pi\)
0.422655 + 0.906290i \(0.361098\pi\)
\(368\) −4.72838 −0.246484
\(369\) −7.77914 −0.404966
\(370\) −105.856 −5.50318
\(371\) −3.05330 −0.158520
\(372\) 25.1412 1.30351
\(373\) 13.8301 0.716096 0.358048 0.933703i \(-0.383442\pi\)
0.358048 + 0.933703i \(0.383442\pi\)
\(374\) 2.55392 0.132060
\(375\) 43.6994 2.25663
\(376\) −74.7108 −3.85291
\(377\) −0.806375 −0.0415304
\(378\) −8.42705 −0.433440
\(379\) 9.47920 0.486914 0.243457 0.969912i \(-0.421719\pi\)
0.243457 + 0.969912i \(0.421719\pi\)
\(380\) −52.7255 −2.70476
\(381\) 27.2574 1.39644
\(382\) −13.6394 −0.697854
\(383\) 28.8688 1.47513 0.737563 0.675278i \(-0.235977\pi\)
0.737563 + 0.675278i \(0.235977\pi\)
\(384\) 13.1676 0.671955
\(385\) −2.53876 −0.129387
\(386\) 15.8666 0.807587
\(387\) 1.44079 0.0732394
\(388\) −54.3852 −2.76099
\(389\) 9.35289 0.474210 0.237105 0.971484i \(-0.423801\pi\)
0.237105 + 0.971484i \(0.423801\pi\)
\(390\) −21.5849 −1.09300
\(391\) 0.638262 0.0322783
\(392\) 42.8153 2.16250
\(393\) −5.02171 −0.253312
\(394\) 52.4636 2.64308
\(395\) −15.1480 −0.762181
\(396\) −6.51601 −0.327442
\(397\) −28.0321 −1.40689 −0.703446 0.710748i \(-0.748356\pi\)
−0.703446 + 0.710748i \(0.748356\pi\)
\(398\) −40.6908 −2.03964
\(399\) 2.03039 0.101647
\(400\) 97.8081 4.89040
\(401\) 11.4546 0.572017 0.286008 0.958227i \(-0.407671\pi\)
0.286008 + 0.958227i \(0.407671\pi\)
\(402\) −6.86421 −0.342355
\(403\) 7.06277 0.351822
\(404\) −63.0732 −3.13801
\(405\) −11.1003 −0.551578
\(406\) −0.772462 −0.0383366
\(407\) 9.71491 0.481550
\(408\) 8.04445 0.398260
\(409\) −19.6097 −0.969636 −0.484818 0.874615i \(-0.661114\pi\)
−0.484818 + 0.874615i \(0.661114\pi\)
\(410\) −58.8310 −2.90546
\(411\) −13.1801 −0.650126
\(412\) −6.40409 −0.315507
\(413\) −5.13523 −0.252688
\(414\) −2.34859 −0.115427
\(415\) −52.4882 −2.57655
\(416\) −9.57462 −0.469434
\(417\) 21.6689 1.06113
\(418\) 6.97878 0.341343
\(419\) 13.6030 0.664550 0.332275 0.943182i \(-0.392184\pi\)
0.332275 + 0.943182i \(0.392184\pi\)
\(420\) −14.3369 −0.699570
\(421\) −20.7130 −1.00949 −0.504745 0.863268i \(-0.668414\pi\)
−0.504745 + 0.863268i \(0.668414\pi\)
\(422\) −50.5687 −2.46165
\(423\) −16.7086 −0.812399
\(424\) −33.0567 −1.60537
\(425\) −13.2027 −0.640424
\(426\) −1.12452 −0.0544831
\(427\) −3.37608 −0.163380
\(428\) 41.0145 1.98251
\(429\) 1.98096 0.0956415
\(430\) 10.8962 0.525462
\(431\) 24.4660 1.17849 0.589243 0.807956i \(-0.299426\pi\)
0.589243 + 0.807956i \(0.299426\pi\)
\(432\) −41.0795 −1.97644
\(433\) −35.1203 −1.68777 −0.843886 0.536523i \(-0.819738\pi\)
−0.843886 + 0.536523i \(0.819738\pi\)
\(434\) 6.76574 0.324766
\(435\) −2.70791 −0.129834
\(436\) −70.0101 −3.35288
\(437\) 1.74410 0.0834315
\(438\) −26.8108 −1.28107
\(439\) 29.2098 1.39411 0.697055 0.717018i \(-0.254493\pi\)
0.697055 + 0.717018i \(0.254493\pi\)
\(440\) −27.4860 −1.31034
\(441\) 9.57536 0.455970
\(442\) 4.05164 0.192717
\(443\) 30.2757 1.43844 0.719220 0.694783i \(-0.244499\pi\)
0.719220 + 0.694783i \(0.244499\pi\)
\(444\) 54.8621 2.60364
\(445\) −47.5170 −2.25252
\(446\) 11.4645 0.542860
\(447\) 24.2858 1.14868
\(448\) −0.355416 −0.0167918
\(449\) −9.82167 −0.463513 −0.231757 0.972774i \(-0.574447\pi\)
−0.231757 + 0.972774i \(0.574447\pi\)
\(450\) 48.5814 2.29015
\(451\) 5.39922 0.254239
\(452\) −28.4520 −1.33827
\(453\) −27.6998 −1.30145
\(454\) −47.2575 −2.21790
\(455\) −4.02759 −0.188816
\(456\) 21.9820 1.02940
\(457\) 19.5742 0.915643 0.457822 0.889044i \(-0.348630\pi\)
0.457822 + 0.889044i \(0.348630\pi\)
\(458\) 18.7618 0.876679
\(459\) 5.54514 0.258825
\(460\) −12.3154 −0.574208
\(461\) −1.20202 −0.0559836 −0.0279918 0.999608i \(-0.508911\pi\)
−0.0279918 + 0.999608i \(0.508911\pi\)
\(462\) 1.89765 0.0882865
\(463\) 14.1508 0.657643 0.328821 0.944392i \(-0.393349\pi\)
0.328821 + 0.944392i \(0.393349\pi\)
\(464\) −3.76554 −0.174811
\(465\) 23.7177 1.09988
\(466\) −13.2852 −0.615424
\(467\) −19.5043 −0.902552 −0.451276 0.892384i \(-0.649031\pi\)
−0.451276 + 0.892384i \(0.649031\pi\)
\(468\) −10.3372 −0.477839
\(469\) −1.28081 −0.0591423
\(470\) −126.362 −5.82862
\(471\) 11.9852 0.552249
\(472\) −55.5967 −2.55904
\(473\) −1.00000 −0.0459800
\(474\) 11.3227 0.520068
\(475\) −36.0773 −1.65534
\(476\) 2.69114 0.123348
\(477\) −7.39292 −0.338498
\(478\) −48.9816 −2.24037
\(479\) −9.90090 −0.452384 −0.226192 0.974083i \(-0.572628\pi\)
−0.226192 + 0.974083i \(0.572628\pi\)
\(480\) −32.1528 −1.46757
\(481\) 15.4121 0.702731
\(482\) −28.2545 −1.28696
\(483\) 0.474249 0.0215791
\(484\) 4.52253 0.205569
\(485\) −51.3059 −2.32968
\(486\) −34.1885 −1.55082
\(487\) −24.3005 −1.10116 −0.550580 0.834783i \(-0.685593\pi\)
−0.550580 + 0.834783i \(0.685593\pi\)
\(488\) −36.5512 −1.65459
\(489\) −6.79305 −0.307193
\(490\) 72.4153 3.27139
\(491\) 23.3672 1.05454 0.527272 0.849696i \(-0.323215\pi\)
0.527272 + 0.849696i \(0.323215\pi\)
\(492\) 30.4905 1.37462
\(493\) 0.508293 0.0228924
\(494\) 11.0714 0.498126
\(495\) −6.14707 −0.276290
\(496\) 32.9811 1.48090
\(497\) −0.209827 −0.00941202
\(498\) 39.2333 1.75809
\(499\) −15.4943 −0.693619 −0.346809 0.937936i \(-0.612735\pi\)
−0.346809 + 0.937936i \(0.612735\pi\)
\(500\) 158.272 7.07814
\(501\) −7.85741 −0.351043
\(502\) −79.5701 −3.55139
\(503\) 1.57361 0.0701640 0.0350820 0.999384i \(-0.488831\pi\)
0.0350820 + 0.999384i \(0.488831\pi\)
\(504\) −5.52331 −0.246028
\(505\) −59.5019 −2.64780
\(506\) 1.63007 0.0724656
\(507\) −13.0902 −0.581357
\(508\) 98.7219 4.38008
\(509\) −6.85295 −0.303752 −0.151876 0.988400i \(-0.548531\pi\)
−0.151876 + 0.988400i \(0.548531\pi\)
\(510\) 13.6059 0.602480
\(511\) −5.00270 −0.221306
\(512\) 50.7417 2.24249
\(513\) 15.1525 0.668999
\(514\) −25.2537 −1.11389
\(515\) −6.04149 −0.266220
\(516\) −5.64721 −0.248604
\(517\) 11.5968 0.510028
\(518\) 14.7639 0.648689
\(519\) −25.9376 −1.13853
\(520\) −43.6048 −1.91220
\(521\) 2.96156 0.129748 0.0648742 0.997893i \(-0.479335\pi\)
0.0648742 + 0.997893i \(0.479335\pi\)
\(522\) −1.87035 −0.0818630
\(523\) 1.03749 0.0453661 0.0226830 0.999743i \(-0.492779\pi\)
0.0226830 + 0.999743i \(0.492779\pi\)
\(524\) −18.1878 −0.794538
\(525\) −9.81000 −0.428144
\(526\) 15.8640 0.691705
\(527\) −4.45197 −0.193931
\(528\) 9.25050 0.402576
\(529\) −22.5926 −0.982288
\(530\) −55.9102 −2.42858
\(531\) −12.4338 −0.539583
\(532\) 7.35373 0.318825
\(533\) 8.56552 0.371014
\(534\) 35.5175 1.53699
\(535\) 38.6922 1.67281
\(536\) −13.8667 −0.598951
\(537\) 10.2178 0.440932
\(538\) −53.4843 −2.30587
\(539\) −6.64591 −0.286260
\(540\) −106.994 −4.60431
\(541\) −33.4088 −1.43636 −0.718178 0.695859i \(-0.755024\pi\)
−0.718178 + 0.695859i \(0.755024\pi\)
\(542\) −60.3602 −2.59269
\(543\) 6.47915 0.278047
\(544\) 6.03530 0.258761
\(545\) −66.0461 −2.82911
\(546\) 3.01049 0.128837
\(547\) −34.8133 −1.48851 −0.744254 0.667896i \(-0.767195\pi\)
−0.744254 + 0.667896i \(0.767195\pi\)
\(548\) −47.7361 −2.03919
\(549\) −8.17444 −0.348876
\(550\) −33.7186 −1.43777
\(551\) 1.38895 0.0591712
\(552\) 5.13447 0.218538
\(553\) 2.11273 0.0898424
\(554\) 36.7413 1.56099
\(555\) 51.7558 2.19691
\(556\) 78.4813 3.32835
\(557\) 2.39432 0.101450 0.0507252 0.998713i \(-0.483847\pi\)
0.0507252 + 0.998713i \(0.483847\pi\)
\(558\) 16.3818 0.693496
\(559\) −1.58644 −0.0670991
\(560\) −18.8077 −0.794770
\(561\) −1.24868 −0.0527195
\(562\) −56.5104 −2.38375
\(563\) −11.6365 −0.490418 −0.245209 0.969470i \(-0.578857\pi\)
−0.245209 + 0.969470i \(0.578857\pi\)
\(564\) 65.4897 2.75761
\(565\) −26.8411 −1.12921
\(566\) −14.1853 −0.596251
\(567\) 1.54818 0.0650175
\(568\) −2.27170 −0.0953182
\(569\) 18.2554 0.765305 0.382653 0.923892i \(-0.375011\pi\)
0.382653 + 0.923892i \(0.375011\pi\)
\(570\) 37.1792 1.55726
\(571\) 46.6660 1.95291 0.976455 0.215722i \(-0.0692104\pi\)
0.976455 + 0.215722i \(0.0692104\pi\)
\(572\) 7.17470 0.299989
\(573\) 6.66869 0.278589
\(574\) 8.20529 0.342482
\(575\) −8.42677 −0.351421
\(576\) −0.860564 −0.0358568
\(577\) 3.14319 0.130853 0.0654264 0.997857i \(-0.479159\pi\)
0.0654264 + 0.997857i \(0.479159\pi\)
\(578\) −2.55392 −0.106229
\(579\) −7.75761 −0.322395
\(580\) −9.80761 −0.407239
\(581\) 7.32064 0.303712
\(582\) 38.3495 1.58964
\(583\) 5.13116 0.212511
\(584\) −54.1618 −2.24123
\(585\) −9.75193 −0.403193
\(586\) 60.8950 2.51555
\(587\) 26.0128 1.07366 0.536832 0.843689i \(-0.319621\pi\)
0.536832 + 0.843689i \(0.319621\pi\)
\(588\) −37.5308 −1.54775
\(589\) −12.1653 −0.501264
\(590\) −94.0331 −3.87128
\(591\) −25.6509 −1.05514
\(592\) 71.9700 2.95795
\(593\) 18.3272 0.752606 0.376303 0.926497i \(-0.377195\pi\)
0.376303 + 0.926497i \(0.377195\pi\)
\(594\) 14.1619 0.581068
\(595\) 2.53876 0.104079
\(596\) 87.9593 3.60295
\(597\) 19.8948 0.814241
\(598\) 2.58601 0.105750
\(599\) −12.2063 −0.498735 −0.249368 0.968409i \(-0.580223\pi\)
−0.249368 + 0.968409i \(0.580223\pi\)
\(600\) −106.208 −4.33593
\(601\) 43.2061 1.76241 0.881206 0.472732i \(-0.156732\pi\)
0.881206 + 0.472732i \(0.156732\pi\)
\(602\) −1.51972 −0.0619391
\(603\) −3.10120 −0.126291
\(604\) −100.324 −4.08213
\(605\) 4.26646 0.173456
\(606\) 44.4758 1.80671
\(607\) −0.416530 −0.0169065 −0.00845323 0.999964i \(-0.502691\pi\)
−0.00845323 + 0.999964i \(0.502691\pi\)
\(608\) 16.4919 0.668834
\(609\) 0.377678 0.0153043
\(610\) −61.8206 −2.50304
\(611\) 18.3976 0.744289
\(612\) 6.51601 0.263394
\(613\) −34.2794 −1.38453 −0.692266 0.721642i \(-0.743387\pi\)
−0.692266 + 0.721642i \(0.743387\pi\)
\(614\) 41.3824 1.67006
\(615\) 28.7641 1.15988
\(616\) 3.83353 0.154457
\(617\) 36.2627 1.45988 0.729941 0.683511i \(-0.239548\pi\)
0.729941 + 0.683511i \(0.239548\pi\)
\(618\) 4.51582 0.181653
\(619\) 12.5451 0.504229 0.252115 0.967697i \(-0.418874\pi\)
0.252115 + 0.967697i \(0.418874\pi\)
\(620\) 85.9016 3.44989
\(621\) 3.53925 0.142025
\(622\) 19.6708 0.788728
\(623\) 6.62729 0.265517
\(624\) 14.6753 0.587483
\(625\) 83.2972 3.33189
\(626\) −11.3375 −0.453137
\(627\) −3.41212 −0.136267
\(628\) 43.4084 1.73218
\(629\) −9.71491 −0.387359
\(630\) −9.34181 −0.372186
\(631\) −44.7652 −1.78208 −0.891038 0.453928i \(-0.850022\pi\)
−0.891038 + 0.453928i \(0.850022\pi\)
\(632\) 22.8735 0.909859
\(633\) 24.7244 0.982708
\(634\) −35.2910 −1.40159
\(635\) 93.1322 3.69584
\(636\) 28.9767 1.14900
\(637\) −10.5433 −0.417741
\(638\) 1.29814 0.0513939
\(639\) −0.508050 −0.0200982
\(640\) 44.9905 1.77841
\(641\) 10.3472 0.408690 0.204345 0.978899i \(-0.434493\pi\)
0.204345 + 0.978899i \(0.434493\pi\)
\(642\) −28.9212 −1.14143
\(643\) 33.5277 1.32220 0.661101 0.750297i \(-0.270089\pi\)
0.661101 + 0.750297i \(0.270089\pi\)
\(644\) 1.71765 0.0676850
\(645\) −5.32746 −0.209768
\(646\) −6.97878 −0.274577
\(647\) 49.0109 1.92682 0.963408 0.268040i \(-0.0863759\pi\)
0.963408 + 0.268040i \(0.0863759\pi\)
\(648\) 16.7614 0.658451
\(649\) 8.62988 0.338753
\(650\) −53.4925 −2.09815
\(651\) −3.30796 −0.129649
\(652\) −24.6033 −0.963541
\(653\) 0.500721 0.0195947 0.00979737 0.999952i \(-0.496881\pi\)
0.00979737 + 0.999952i \(0.496881\pi\)
\(654\) 49.3674 1.93042
\(655\) −17.1580 −0.670419
\(656\) 39.9985 1.56168
\(657\) −12.1129 −0.472571
\(658\) 17.6239 0.687051
\(659\) −17.1235 −0.667035 −0.333518 0.942744i \(-0.608236\pi\)
−0.333518 + 0.942744i \(0.608236\pi\)
\(660\) 24.0936 0.937841
\(661\) −4.75895 −0.185102 −0.0925508 0.995708i \(-0.529502\pi\)
−0.0925508 + 0.995708i \(0.529502\pi\)
\(662\) 52.0045 2.02121
\(663\) −1.98096 −0.0769340
\(664\) 79.2571 3.07577
\(665\) 6.93736 0.269019
\(666\) 35.7476 1.38519
\(667\) 0.324424 0.0125618
\(668\) −28.4583 −1.10108
\(669\) −5.60531 −0.216714
\(670\) −23.4534 −0.906083
\(671\) 5.67358 0.219026
\(672\) 4.48442 0.172990
\(673\) −6.84253 −0.263760 −0.131880 0.991266i \(-0.542101\pi\)
−0.131880 + 0.991266i \(0.542101\pi\)
\(674\) −19.1927 −0.739276
\(675\) −73.2107 −2.81788
\(676\) −47.4107 −1.82349
\(677\) 12.6953 0.487920 0.243960 0.969785i \(-0.421553\pi\)
0.243960 + 0.969785i \(0.421553\pi\)
\(678\) 20.0628 0.770509
\(679\) 7.15574 0.274612
\(680\) 27.4860 1.05404
\(681\) 23.1055 0.885404
\(682\) −11.3700 −0.435380
\(683\) 34.5924 1.32364 0.661820 0.749663i \(-0.269784\pi\)
0.661820 + 0.749663i \(0.269784\pi\)
\(684\) 17.8055 0.680809
\(685\) −45.0333 −1.72063
\(686\) −20.7379 −0.791778
\(687\) −9.17314 −0.349977
\(688\) −7.40820 −0.282435
\(689\) 8.14025 0.310119
\(690\) 8.68415 0.330600
\(691\) −12.0188 −0.457218 −0.228609 0.973518i \(-0.573418\pi\)
−0.228609 + 0.973518i \(0.573418\pi\)
\(692\) −93.9418 −3.57113
\(693\) 0.857344 0.0325678
\(694\) 38.8308 1.47400
\(695\) 74.0376 2.80841
\(696\) 4.08894 0.154991
\(697\) −5.39922 −0.204510
\(698\) −64.3661 −2.43629
\(699\) 6.49549 0.245682
\(700\) −35.5302 −1.34292
\(701\) −4.43916 −0.167665 −0.0838325 0.996480i \(-0.526716\pi\)
−0.0838325 + 0.996480i \(0.526716\pi\)
\(702\) 22.4669 0.847959
\(703\) −26.5467 −1.00123
\(704\) 0.597286 0.0225111
\(705\) 61.7816 2.32683
\(706\) 4.44353 0.167235
\(707\) 8.29885 0.312111
\(708\) 48.7347 1.83156
\(709\) 25.3573 0.952314 0.476157 0.879360i \(-0.342029\pi\)
0.476157 + 0.879360i \(0.342029\pi\)
\(710\) −3.84221 −0.144196
\(711\) 5.11552 0.191847
\(712\) 71.7506 2.68897
\(713\) −2.84153 −0.106416
\(714\) −1.89765 −0.0710176
\(715\) 6.76847 0.253126
\(716\) 37.0073 1.38303
\(717\) 23.9485 0.894372
\(718\) 2.78318 0.103867
\(719\) 13.9187 0.519080 0.259540 0.965732i \(-0.416429\pi\)
0.259540 + 0.965732i \(0.416429\pi\)
\(720\) −45.5387 −1.69713
\(721\) 0.842618 0.0313808
\(722\) 29.4545 1.09618
\(723\) 13.8144 0.513763
\(724\) 23.4664 0.872123
\(725\) −6.71083 −0.249234
\(726\) −3.18904 −0.118356
\(727\) −48.9187 −1.81430 −0.907148 0.420812i \(-0.861745\pi\)
−0.907148 + 0.420812i \(0.861745\pi\)
\(728\) 6.08165 0.225401
\(729\) 24.5210 0.908184
\(730\) −91.6062 −3.39050
\(731\) 1.00000 0.0369863
\(732\) 32.0399 1.18423
\(733\) −40.9840 −1.51378 −0.756890 0.653543i \(-0.773282\pi\)
−0.756890 + 0.653543i \(0.773282\pi\)
\(734\) −41.3578 −1.52654
\(735\) −35.4058 −1.30596
\(736\) 3.85210 0.141990
\(737\) 2.15243 0.0792859
\(738\) 19.8673 0.731326
\(739\) 0.342822 0.0126109 0.00630546 0.999980i \(-0.497993\pi\)
0.00630546 + 0.999980i \(0.497993\pi\)
\(740\) 187.451 6.89083
\(741\) −5.41311 −0.198856
\(742\) 7.79791 0.286270
\(743\) −20.4319 −0.749574 −0.374787 0.927111i \(-0.622284\pi\)
−0.374787 + 0.927111i \(0.622284\pi\)
\(744\) −35.8137 −1.31299
\(745\) 82.9790 3.04012
\(746\) −35.3211 −1.29320
\(747\) 17.7254 0.648537
\(748\) −4.52253 −0.165360
\(749\) −5.39649 −0.197183
\(750\) −111.605 −4.07524
\(751\) 9.27015 0.338273 0.169136 0.985593i \(-0.445902\pi\)
0.169136 + 0.985593i \(0.445902\pi\)
\(752\) 85.9117 3.13288
\(753\) 38.9040 1.41774
\(754\) 2.05942 0.0749996
\(755\) −94.6438 −3.44444
\(756\) 14.9227 0.542735
\(757\) 32.0377 1.16443 0.582215 0.813035i \(-0.302186\pi\)
0.582215 + 0.813035i \(0.302186\pi\)
\(758\) −24.2092 −0.879316
\(759\) −0.796988 −0.0289288
\(760\) 75.1075 2.72443
\(761\) −2.99035 −0.108400 −0.0542000 0.998530i \(-0.517261\pi\)
−0.0542000 + 0.998530i \(0.517261\pi\)
\(762\) −69.6134 −2.52183
\(763\) 9.21159 0.333482
\(764\) 24.1529 0.873822
\(765\) 6.14707 0.222248
\(766\) −73.7287 −2.66393
\(767\) 13.6908 0.494345
\(768\) −35.1206 −1.26731
\(769\) 55.1837 1.98997 0.994987 0.100007i \(-0.0318866\pi\)
0.994987 + 0.100007i \(0.0318866\pi\)
\(770\) 6.48381 0.233660
\(771\) 12.3472 0.444675
\(772\) −28.0968 −1.01123
\(773\) 3.11539 0.112053 0.0560264 0.998429i \(-0.482157\pi\)
0.0560264 + 0.998429i \(0.482157\pi\)
\(774\) −3.67967 −0.132263
\(775\) 58.7780 2.11137
\(776\) 77.4718 2.78107
\(777\) −7.21849 −0.258962
\(778\) −23.8866 −0.856375
\(779\) −14.7538 −0.528608
\(780\) 38.2229 1.36860
\(781\) 0.352619 0.0126177
\(782\) −1.63007 −0.0582913
\(783\) 2.81856 0.100727
\(784\) −49.2343 −1.75837
\(785\) 40.9506 1.46159
\(786\) 12.8251 0.457455
\(787\) 17.7449 0.632537 0.316269 0.948670i \(-0.397570\pi\)
0.316269 + 0.948670i \(0.397570\pi\)
\(788\) −92.9033 −3.30954
\(789\) −7.75636 −0.276134
\(790\) 38.6870 1.37642
\(791\) 3.74358 0.133106
\(792\) 9.28206 0.329824
\(793\) 9.00078 0.319627
\(794\) 71.5920 2.54070
\(795\) 27.3360 0.969509
\(796\) 72.0558 2.55395
\(797\) 35.7188 1.26522 0.632612 0.774469i \(-0.281983\pi\)
0.632612 + 0.774469i \(0.281983\pi\)
\(798\) −5.18546 −0.183563
\(799\) −11.5968 −0.410266
\(800\) −79.6821 −2.81719
\(801\) 16.0466 0.566977
\(802\) −29.2542 −1.03300
\(803\) 8.40716 0.296682
\(804\) 12.1552 0.428682
\(805\) 1.62040 0.0571115
\(806\) −18.0378 −0.635354
\(807\) 26.1500 0.920522
\(808\) 89.8478 3.16083
\(809\) −13.8715 −0.487695 −0.243848 0.969814i \(-0.578410\pi\)
−0.243848 + 0.969814i \(0.578410\pi\)
\(810\) 28.3493 0.996093
\(811\) −46.5306 −1.63391 −0.816955 0.576701i \(-0.804340\pi\)
−0.816955 + 0.576701i \(0.804340\pi\)
\(812\) 1.36789 0.0480034
\(813\) 29.5118 1.03502
\(814\) −24.8111 −0.869630
\(815\) −23.2103 −0.813020
\(816\) −9.25050 −0.323832
\(817\) 2.73257 0.0956006
\(818\) 50.0816 1.75106
\(819\) 1.36012 0.0475265
\(820\) 104.179 3.63809
\(821\) −8.74519 −0.305209 −0.152605 0.988287i \(-0.548766\pi\)
−0.152605 + 0.988287i \(0.548766\pi\)
\(822\) 33.6609 1.17406
\(823\) −40.8917 −1.42540 −0.712698 0.701471i \(-0.752527\pi\)
−0.712698 + 0.701471i \(0.752527\pi\)
\(824\) 9.12263 0.317802
\(825\) 16.4860 0.573968
\(826\) 13.1150 0.456329
\(827\) −25.2317 −0.877393 −0.438696 0.898635i \(-0.644560\pi\)
−0.438696 + 0.898635i \(0.644560\pi\)
\(828\) 4.15892 0.144533
\(829\) −7.05098 −0.244891 −0.122445 0.992475i \(-0.539074\pi\)
−0.122445 + 0.992475i \(0.539074\pi\)
\(830\) 134.051 4.65298
\(831\) −17.9638 −0.623158
\(832\) 0.947557 0.0328506
\(833\) 6.64591 0.230267
\(834\) −55.3408 −1.91629
\(835\) −26.8469 −0.929076
\(836\) −12.3581 −0.427415
\(837\) −24.6868 −0.853301
\(838\) −34.7410 −1.20011
\(839\) −32.1303 −1.10926 −0.554630 0.832097i \(-0.687140\pi\)
−0.554630 + 0.832097i \(0.687140\pi\)
\(840\) 20.4230 0.704659
\(841\) −28.7416 −0.991091
\(842\) 52.8995 1.82304
\(843\) 27.6295 0.951609
\(844\) 89.5479 3.08237
\(845\) −44.7262 −1.53863
\(846\) 42.6725 1.46711
\(847\) −0.595052 −0.0204462
\(848\) 38.0127 1.30536
\(849\) 6.93557 0.238028
\(850\) 33.7186 1.15654
\(851\) −6.20066 −0.212556
\(852\) 1.99131 0.0682213
\(853\) −27.8399 −0.953221 −0.476610 0.879115i \(-0.658135\pi\)
−0.476610 + 0.879115i \(0.658135\pi\)
\(854\) 8.62224 0.295047
\(855\) 16.7973 0.574456
\(856\) −58.4252 −1.99693
\(857\) 30.5580 1.04384 0.521921 0.852994i \(-0.325215\pi\)
0.521921 + 0.852994i \(0.325215\pi\)
\(858\) −5.05921 −0.172719
\(859\) −18.3811 −0.627156 −0.313578 0.949563i \(-0.601528\pi\)
−0.313578 + 0.949563i \(0.601528\pi\)
\(860\) −19.2952 −0.657960
\(861\) −4.01179 −0.136721
\(862\) −62.4843 −2.12822
\(863\) 15.7089 0.534738 0.267369 0.963594i \(-0.413846\pi\)
0.267369 + 0.963594i \(0.413846\pi\)
\(864\) 33.4666 1.13856
\(865\) −88.6227 −3.01326
\(866\) 89.6945 3.04794
\(867\) 1.24868 0.0424075
\(868\) −11.9809 −0.406657
\(869\) −3.55050 −0.120442
\(870\) 6.91580 0.234467
\(871\) 3.41470 0.115703
\(872\) 99.7295 3.37727
\(873\) 17.3261 0.586398
\(874\) −4.45429 −0.150669
\(875\) −20.8247 −0.704002
\(876\) 47.4770 1.60410
\(877\) 28.9421 0.977307 0.488653 0.872478i \(-0.337488\pi\)
0.488653 + 0.872478i \(0.337488\pi\)
\(878\) −74.5997 −2.51762
\(879\) −29.7732 −1.00423
\(880\) 31.6068 1.06546
\(881\) 31.9419 1.07615 0.538074 0.842897i \(-0.319152\pi\)
0.538074 + 0.842897i \(0.319152\pi\)
\(882\) −24.4547 −0.823434
\(883\) −57.2850 −1.92780 −0.963898 0.266273i \(-0.914208\pi\)
−0.963898 + 0.266273i \(0.914208\pi\)
\(884\) −7.17470 −0.241311
\(885\) 45.9753 1.54544
\(886\) −77.3217 −2.59767
\(887\) 25.5219 0.856943 0.428471 0.903555i \(-0.359052\pi\)
0.428471 + 0.903555i \(0.359052\pi\)
\(888\) −78.1511 −2.62258
\(889\) −12.9893 −0.435649
\(890\) 121.355 4.06782
\(891\) −2.60176 −0.0871622
\(892\) −20.3015 −0.679745
\(893\) −31.6892 −1.06044
\(894\) −62.0242 −2.07440
\(895\) 34.9119 1.16698
\(896\) −6.27492 −0.209631
\(897\) −1.26437 −0.0422161
\(898\) 25.0838 0.837057
\(899\) −2.26291 −0.0754722
\(900\) −86.0288 −2.86763
\(901\) −5.13116 −0.170944
\(902\) −13.7892 −0.459130
\(903\) 0.743032 0.0247265
\(904\) 40.5300 1.34801
\(905\) 22.1377 0.735884
\(906\) 70.7432 2.35029
\(907\) −35.4369 −1.17666 −0.588332 0.808620i \(-0.700215\pi\)
−0.588332 + 0.808620i \(0.700215\pi\)
\(908\) 83.6843 2.77716
\(909\) 20.0939 0.666472
\(910\) 10.2862 0.340983
\(911\) −20.2300 −0.670250 −0.335125 0.942174i \(-0.608779\pi\)
−0.335125 + 0.942174i \(0.608779\pi\)
\(912\) −25.2777 −0.837027
\(913\) −12.3025 −0.407154
\(914\) −49.9911 −1.65356
\(915\) 30.2258 0.999233
\(916\) −33.2236 −1.09774
\(917\) 2.39306 0.0790259
\(918\) −14.1619 −0.467411
\(919\) 17.9108 0.590822 0.295411 0.955370i \(-0.404543\pi\)
0.295411 + 0.955370i \(0.404543\pi\)
\(920\) 17.5433 0.578385
\(921\) −20.2330 −0.666700
\(922\) 3.06987 0.101101
\(923\) 0.559408 0.0184131
\(924\) −3.36038 −0.110548
\(925\) 128.263 4.21726
\(926\) −36.1400 −1.18764
\(927\) 2.04022 0.0670096
\(928\) 3.06770 0.100702
\(929\) −38.8923 −1.27601 −0.638007 0.770031i \(-0.720241\pi\)
−0.638007 + 0.770031i \(0.720241\pi\)
\(930\) −60.5732 −1.98627
\(931\) 18.1604 0.595184
\(932\) 23.5256 0.770607
\(933\) −9.61760 −0.314866
\(934\) 49.8126 1.62992
\(935\) −4.26646 −0.139528
\(936\) 14.7254 0.481315
\(937\) 32.2995 1.05518 0.527589 0.849500i \(-0.323096\pi\)
0.527589 + 0.849500i \(0.323096\pi\)
\(938\) 3.27109 0.106805
\(939\) 5.54321 0.180896
\(940\) 223.763 7.29834
\(941\) 30.8418 1.00541 0.502707 0.864457i \(-0.332337\pi\)
0.502707 + 0.864457i \(0.332337\pi\)
\(942\) −30.6093 −0.997304
\(943\) −3.44612 −0.112221
\(944\) 63.9319 2.08081
\(945\) 14.0778 0.457951
\(946\) 2.55392 0.0830352
\(947\) −4.39935 −0.142960 −0.0714799 0.997442i \(-0.522772\pi\)
−0.0714799 + 0.997442i \(0.522772\pi\)
\(948\) −20.0504 −0.651206
\(949\) 13.3374 0.432951
\(950\) 92.1386 2.98937
\(951\) 17.2548 0.559524
\(952\) −3.83353 −0.124245
\(953\) −19.2614 −0.623940 −0.311970 0.950092i \(-0.600989\pi\)
−0.311970 + 0.950092i \(0.600989\pi\)
\(954\) 18.8809 0.611293
\(955\) 22.7854 0.737317
\(956\) 86.7374 2.80529
\(957\) −0.634697 −0.0205168
\(958\) 25.2861 0.816958
\(959\) 6.28088 0.202820
\(960\) 3.18202 0.102699
\(961\) −11.1799 −0.360643
\(962\) −39.3613 −1.26906
\(963\) −13.0664 −0.421060
\(964\) 50.0335 1.61147
\(965\) −26.5059 −0.853256
\(966\) −1.21120 −0.0389696
\(967\) −17.6122 −0.566371 −0.283185 0.959065i \(-0.591391\pi\)
−0.283185 + 0.959065i \(0.591391\pi\)
\(968\) −6.44234 −0.207065
\(969\) 3.41212 0.109613
\(970\) 131.031 4.20716
\(971\) −15.8140 −0.507496 −0.253748 0.967270i \(-0.581663\pi\)
−0.253748 + 0.967270i \(0.581663\pi\)
\(972\) 60.5415 1.94187
\(973\) −10.3262 −0.331042
\(974\) 62.0616 1.98858
\(975\) 26.1539 0.837596
\(976\) 42.0310 1.34538
\(977\) −30.3631 −0.971401 −0.485701 0.874125i \(-0.661435\pi\)
−0.485701 + 0.874125i \(0.661435\pi\)
\(978\) 17.3489 0.554758
\(979\) −11.1373 −0.355951
\(980\) −128.234 −4.09629
\(981\) 22.3039 0.712108
\(982\) −59.6779 −1.90440
\(983\) −2.59855 −0.0828810 −0.0414405 0.999141i \(-0.513195\pi\)
−0.0414405 + 0.999141i \(0.513195\pi\)
\(984\) −43.4338 −1.38462
\(985\) −87.6431 −2.79254
\(986\) −1.29814 −0.0413413
\(987\) −8.61681 −0.274276
\(988\) −19.6054 −0.623731
\(989\) 0.638262 0.0202956
\(990\) 15.6991 0.498952
\(991\) −42.3759 −1.34611 −0.673057 0.739591i \(-0.735019\pi\)
−0.673057 + 0.739591i \(0.735019\pi\)
\(992\) −26.8690 −0.853091
\(993\) −25.4264 −0.806883
\(994\) 0.535882 0.0169971
\(995\) 67.9760 2.15498
\(996\) −69.4749 −2.20140
\(997\) 4.92344 0.155927 0.0779634 0.996956i \(-0.475158\pi\)
0.0779634 + 0.996956i \(0.475158\pi\)
\(998\) 39.5712 1.25260
\(999\) −53.8705 −1.70439
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 \(a_p\))