Properties

Label 5077.2.a.c.1.15
Level 5077
Weight 2
Character 5077.1
Self dual Yes
Analytic conductor 40.540
Analytic rank 0
Dimension 216
CM No

Related objects

Downloads

Learn more about

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 1.15
Character \(\chi\) = 5077.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.46105 q^{2} -2.68177 q^{3} +4.05676 q^{4} +2.96431 q^{5} +6.59997 q^{6} +0.509421 q^{7} -5.06178 q^{8} +4.19189 q^{9} +O(q^{10})\) \(q-2.46105 q^{2} -2.68177 q^{3} +4.05676 q^{4} +2.96431 q^{5} +6.59997 q^{6} +0.509421 q^{7} -5.06178 q^{8} +4.19189 q^{9} -7.29531 q^{10} +5.31673 q^{11} -10.8793 q^{12} +5.60467 q^{13} -1.25371 q^{14} -7.94959 q^{15} +4.34378 q^{16} +2.47085 q^{17} -10.3165 q^{18} -0.319690 q^{19} +12.0255 q^{20} -1.36615 q^{21} -13.0847 q^{22} +2.93671 q^{23} +13.5745 q^{24} +3.78712 q^{25} -13.7934 q^{26} -3.19639 q^{27} +2.06660 q^{28} -4.69144 q^{29} +19.5643 q^{30} +7.77911 q^{31} -0.566675 q^{32} -14.2582 q^{33} -6.08088 q^{34} +1.51008 q^{35} +17.0055 q^{36} +9.69240 q^{37} +0.786772 q^{38} -15.0304 q^{39} -15.0047 q^{40} -4.12169 q^{41} +3.36216 q^{42} +2.69266 q^{43} +21.5687 q^{44} +12.4261 q^{45} -7.22738 q^{46} +1.32018 q^{47} -11.6490 q^{48} -6.74049 q^{49} -9.32029 q^{50} -6.62625 q^{51} +22.7368 q^{52} +3.72208 q^{53} +7.86647 q^{54} +15.7604 q^{55} -2.57858 q^{56} +0.857334 q^{57} +11.5459 q^{58} +10.4400 q^{59} -32.2496 q^{60} -2.43738 q^{61} -19.1448 q^{62} +2.13544 q^{63} -7.29294 q^{64} +16.6140 q^{65} +35.0902 q^{66} +9.21258 q^{67} +10.0236 q^{68} -7.87557 q^{69} -3.71638 q^{70} +14.3692 q^{71} -21.2185 q^{72} -6.94100 q^{73} -23.8535 q^{74} -10.1562 q^{75} -1.29690 q^{76} +2.70845 q^{77} +36.9907 q^{78} -9.50471 q^{79} +12.8763 q^{80} -4.00370 q^{81} +10.1437 q^{82} +10.6751 q^{83} -5.54214 q^{84} +7.32436 q^{85} -6.62676 q^{86} +12.5814 q^{87} -26.9121 q^{88} +2.74486 q^{89} -30.5812 q^{90} +2.85513 q^{91} +11.9135 q^{92} -20.8618 q^{93} -3.24902 q^{94} -0.947658 q^{95} +1.51969 q^{96} +15.4084 q^{97} +16.5887 q^{98} +22.2872 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 216q + 25q^{2} + 62q^{3} + 223q^{4} + 46q^{5} + 26q^{6} + 30q^{7} + 75q^{8} + 234q^{9} + O(q^{10}) \) \( 216q + 25q^{2} + 62q^{3} + 223q^{4} + 46q^{5} + 26q^{6} + 30q^{7} + 75q^{8} + 234q^{9} + 24q^{10} + 89q^{11} + 114q^{12} + 34q^{13} + 53q^{14} + 61q^{15} + 229q^{16} + 76q^{17} + 57q^{18} + 54q^{19} + 118q^{20} + 25q^{21} + 26q^{22} + 109q^{23} + 65q^{24} + 232q^{25} + 58q^{26} + 236q^{27} + 57q^{28} + 54q^{29} + 6q^{30} + 77q^{31} + 155q^{32} + 80q^{33} + 28q^{34} + 137q^{35} + 257q^{36} + 42q^{37} + 104q^{38} + 46q^{39} + 47q^{40} + 109q^{41} + 27q^{42} + 68q^{43} + 145q^{44} + 109q^{45} - 7q^{46} + 264q^{47} + 198q^{48} + 222q^{49} + 86q^{50} + 57q^{51} + 68q^{52} + 95q^{53} + 79q^{54} + 50q^{55} + 108q^{56} + 55q^{57} + 38q^{58} + 292q^{59} + 91q^{60} + 16q^{61} + 91q^{62} + 113q^{63} + 231q^{64} + 68q^{65} - 15q^{66} + 152q^{67} + 199q^{68} + 83q^{69} + 24q^{70} + 131q^{71} + 162q^{72} + 71q^{73} + 10q^{74} + 232q^{75} + 60q^{76} + 131q^{77} + 102q^{78} + 10q^{79} + 236q^{80} + 268q^{81} + 54q^{82} + 299q^{83} - 9q^{85} + 35q^{86} + 103q^{87} + 45q^{88} + 134q^{89} + 8q^{90} + 79q^{91} + 206q^{92} + 95q^{93} + 18q^{94} + 119q^{95} + 77q^{96} + 129q^{97} + 150q^{98} + 221q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.46105 −1.74022 −0.870112 0.492854i \(-0.835954\pi\)
−0.870112 + 0.492854i \(0.835954\pi\)
\(3\) −2.68177 −1.54832 −0.774161 0.632989i \(-0.781828\pi\)
−0.774161 + 0.632989i \(0.781828\pi\)
\(4\) 4.05676 2.02838
\(5\) 2.96431 1.32568 0.662839 0.748762i \(-0.269351\pi\)
0.662839 + 0.748762i \(0.269351\pi\)
\(6\) 6.59997 2.69443
\(7\) 0.509421 0.192543 0.0962714 0.995355i \(-0.469308\pi\)
0.0962714 + 0.995355i \(0.469308\pi\)
\(8\) −5.06178 −1.78961
\(9\) 4.19189 1.39730
\(10\) −7.29531 −2.30698
\(11\) 5.31673 1.60305 0.801527 0.597959i \(-0.204021\pi\)
0.801527 + 0.597959i \(0.204021\pi\)
\(12\) −10.8793 −3.14058
\(13\) 5.60467 1.55446 0.777228 0.629219i \(-0.216625\pi\)
0.777228 + 0.629219i \(0.216625\pi\)
\(14\) −1.25371 −0.335068
\(15\) −7.94959 −2.05258
\(16\) 4.34378 1.08594
\(17\) 2.47085 0.599269 0.299634 0.954054i \(-0.403135\pi\)
0.299634 + 0.954054i \(0.403135\pi\)
\(18\) −10.3165 −2.43161
\(19\) −0.319690 −0.0733418 −0.0366709 0.999327i \(-0.511675\pi\)
−0.0366709 + 0.999327i \(0.511675\pi\)
\(20\) 12.0255 2.68898
\(21\) −1.36615 −0.298118
\(22\) −13.0847 −2.78967
\(23\) 2.93671 0.612346 0.306173 0.951976i \(-0.400951\pi\)
0.306173 + 0.951976i \(0.400951\pi\)
\(24\) 13.5745 2.77089
\(25\) 3.78712 0.757424
\(26\) −13.7934 −2.70510
\(27\) −3.19639 −0.615145
\(28\) 2.06660 0.390550
\(29\) −4.69144 −0.871179 −0.435590 0.900145i \(-0.643460\pi\)
−0.435590 + 0.900145i \(0.643460\pi\)
\(30\) 19.5643 3.57194
\(31\) 7.77911 1.39717 0.698585 0.715527i \(-0.253813\pi\)
0.698585 + 0.715527i \(0.253813\pi\)
\(32\) −0.566675 −0.100175
\(33\) −14.2582 −2.48204
\(34\) −6.08088 −1.04286
\(35\) 1.51008 0.255250
\(36\) 17.0055 2.83425
\(37\) 9.69240 1.59342 0.796710 0.604362i \(-0.206572\pi\)
0.796710 + 0.604362i \(0.206572\pi\)
\(38\) 0.786772 0.127631
\(39\) −15.0304 −2.40680
\(40\) −15.0047 −2.37245
\(41\) −4.12169 −0.643700 −0.321850 0.946791i \(-0.604305\pi\)
−0.321850 + 0.946791i \(0.604305\pi\)
\(42\) 3.36216 0.518792
\(43\) 2.69266 0.410626 0.205313 0.978696i \(-0.434179\pi\)
0.205313 + 0.978696i \(0.434179\pi\)
\(44\) 21.5687 3.25160
\(45\) 12.4261 1.85237
\(46\) −7.22738 −1.06562
\(47\) 1.32018 0.192567 0.0962837 0.995354i \(-0.469304\pi\)
0.0962837 + 0.995354i \(0.469304\pi\)
\(48\) −11.6490 −1.68139
\(49\) −6.74049 −0.962927
\(50\) −9.32029 −1.31809
\(51\) −6.62625 −0.927861
\(52\) 22.7368 3.15303
\(53\) 3.72208 0.511267 0.255634 0.966774i \(-0.417716\pi\)
0.255634 + 0.966774i \(0.417716\pi\)
\(54\) 7.86647 1.07049
\(55\) 15.7604 2.12513
\(56\) −2.57858 −0.344577
\(57\) 0.857334 0.113557
\(58\) 11.5459 1.51605
\(59\) 10.4400 1.35917 0.679584 0.733597i \(-0.262160\pi\)
0.679584 + 0.733597i \(0.262160\pi\)
\(60\) −32.2496 −4.16340
\(61\) −2.43738 −0.312074 −0.156037 0.987751i \(-0.549872\pi\)
−0.156037 + 0.987751i \(0.549872\pi\)
\(62\) −19.1448 −2.43139
\(63\) 2.13544 0.269040
\(64\) −7.29294 −0.911617
\(65\) 16.6140 2.06071
\(66\) 35.0902 4.31931
\(67\) 9.21258 1.12550 0.562748 0.826628i \(-0.309744\pi\)
0.562748 + 0.826628i \(0.309744\pi\)
\(68\) 10.0236 1.21554
\(69\) −7.87557 −0.948108
\(70\) −3.71638 −0.444192
\(71\) 14.3692 1.70531 0.852656 0.522472i \(-0.174990\pi\)
0.852656 + 0.522472i \(0.174990\pi\)
\(72\) −21.2185 −2.50062
\(73\) −6.94100 −0.812383 −0.406191 0.913788i \(-0.633143\pi\)
−0.406191 + 0.913788i \(0.633143\pi\)
\(74\) −23.8535 −2.77291
\(75\) −10.1562 −1.17274
\(76\) −1.29690 −0.148765
\(77\) 2.70845 0.308656
\(78\) 36.9907 4.18837
\(79\) −9.50471 −1.06936 −0.534681 0.845054i \(-0.679568\pi\)
−0.534681 + 0.845054i \(0.679568\pi\)
\(80\) 12.8763 1.43961
\(81\) −4.00370 −0.444856
\(82\) 10.1437 1.12018
\(83\) 10.6751 1.17175 0.585873 0.810403i \(-0.300752\pi\)
0.585873 + 0.810403i \(0.300752\pi\)
\(84\) −5.54214 −0.604697
\(85\) 7.32436 0.794438
\(86\) −6.62676 −0.714582
\(87\) 12.5814 1.34886
\(88\) −26.9121 −2.86884
\(89\) 2.74486 0.290955 0.145477 0.989362i \(-0.453528\pi\)
0.145477 + 0.989362i \(0.453528\pi\)
\(90\) −30.5812 −3.22354
\(91\) 2.85513 0.299299
\(92\) 11.9135 1.24207
\(93\) −20.8618 −2.16327
\(94\) −3.24902 −0.335111
\(95\) −0.947658 −0.0972277
\(96\) 1.51969 0.155103
\(97\) 15.4084 1.56449 0.782243 0.622974i \(-0.214076\pi\)
0.782243 + 0.622974i \(0.214076\pi\)
\(98\) 16.5887 1.67571
\(99\) 22.2872 2.23994
\(100\) 15.3634 1.53634
\(101\) −1.87792 −0.186860 −0.0934302 0.995626i \(-0.529783\pi\)
−0.0934302 + 0.995626i \(0.529783\pi\)
\(102\) 16.3075 1.61469
\(103\) 16.7256 1.64803 0.824014 0.566570i \(-0.191730\pi\)
0.824014 + 0.566570i \(0.191730\pi\)
\(104\) −28.3696 −2.78187
\(105\) −4.04969 −0.395209
\(106\) −9.16023 −0.889720
\(107\) −4.39282 −0.424670 −0.212335 0.977197i \(-0.568107\pi\)
−0.212335 + 0.977197i \(0.568107\pi\)
\(108\) −12.9670 −1.24775
\(109\) 6.47424 0.620120 0.310060 0.950717i \(-0.399651\pi\)
0.310060 + 0.950717i \(0.399651\pi\)
\(110\) −38.7871 −3.69821
\(111\) −25.9928 −2.46713
\(112\) 2.21281 0.209091
\(113\) 11.6682 1.09765 0.548826 0.835937i \(-0.315075\pi\)
0.548826 + 0.835937i \(0.315075\pi\)
\(114\) −2.10994 −0.197614
\(115\) 8.70530 0.811774
\(116\) −19.0321 −1.76708
\(117\) 23.4942 2.17204
\(118\) −25.6933 −2.36526
\(119\) 1.25870 0.115385
\(120\) 40.2391 3.67331
\(121\) 17.2676 1.56978
\(122\) 5.99850 0.543079
\(123\) 11.0534 0.996654
\(124\) 31.5580 2.83399
\(125\) −3.59535 −0.321578
\(126\) −5.25541 −0.468190
\(127\) 11.3220 1.00466 0.502330 0.864676i \(-0.332476\pi\)
0.502330 + 0.864676i \(0.332476\pi\)
\(128\) 19.0816 1.68659
\(129\) −7.22109 −0.635781
\(130\) −40.8878 −3.58610
\(131\) 4.01273 0.350594 0.175297 0.984516i \(-0.443911\pi\)
0.175297 + 0.984516i \(0.443911\pi\)
\(132\) −57.8423 −5.03452
\(133\) −0.162856 −0.0141214
\(134\) −22.6726 −1.95862
\(135\) −9.47508 −0.815485
\(136\) −12.5069 −1.07246
\(137\) −8.85706 −0.756710 −0.378355 0.925661i \(-0.623510\pi\)
−0.378355 + 0.925661i \(0.623510\pi\)
\(138\) 19.3822 1.64992
\(139\) −22.2893 −1.89056 −0.945279 0.326263i \(-0.894210\pi\)
−0.945279 + 0.326263i \(0.894210\pi\)
\(140\) 6.12603 0.517744
\(141\) −3.54041 −0.298156
\(142\) −35.3633 −2.96763
\(143\) 29.7985 2.49188
\(144\) 18.2087 1.51739
\(145\) −13.9069 −1.15490
\(146\) 17.0821 1.41373
\(147\) 18.0765 1.49092
\(148\) 39.3197 3.23206
\(149\) −19.0041 −1.55688 −0.778439 0.627721i \(-0.783988\pi\)
−0.778439 + 0.627721i \(0.783988\pi\)
\(150\) 24.9949 2.04082
\(151\) −15.2888 −1.24418 −0.622091 0.782945i \(-0.713717\pi\)
−0.622091 + 0.782945i \(0.713717\pi\)
\(152\) 1.61820 0.131253
\(153\) 10.3575 0.837358
\(154\) −6.66563 −0.537131
\(155\) 23.0597 1.85220
\(156\) −60.9749 −4.88190
\(157\) −17.9218 −1.43032 −0.715158 0.698963i \(-0.753645\pi\)
−0.715158 + 0.698963i \(0.753645\pi\)
\(158\) 23.3915 1.86093
\(159\) −9.98177 −0.791606
\(160\) −1.67980 −0.132800
\(161\) 1.49602 0.117903
\(162\) 9.85331 0.774149
\(163\) −8.45284 −0.662077 −0.331039 0.943617i \(-0.607399\pi\)
−0.331039 + 0.943617i \(0.607399\pi\)
\(164\) −16.7207 −1.30567
\(165\) −42.2658 −3.29039
\(166\) −26.2720 −2.03910
\(167\) −3.99197 −0.308908 −0.154454 0.988000i \(-0.549362\pi\)
−0.154454 + 0.988000i \(0.549362\pi\)
\(168\) 6.91515 0.533515
\(169\) 18.4123 1.41633
\(170\) −18.0256 −1.38250
\(171\) −1.34011 −0.102480
\(172\) 10.9235 0.832906
\(173\) −24.4672 −1.86021 −0.930104 0.367295i \(-0.880284\pi\)
−0.930104 + 0.367295i \(0.880284\pi\)
\(174\) −30.9634 −2.34733
\(175\) 1.92924 0.145837
\(176\) 23.0947 1.74083
\(177\) −27.9976 −2.10443
\(178\) −6.75523 −0.506326
\(179\) −21.6767 −1.62019 −0.810097 0.586295i \(-0.800586\pi\)
−0.810097 + 0.586295i \(0.800586\pi\)
\(180\) 50.4096 3.75731
\(181\) 9.54699 0.709622 0.354811 0.934938i \(-0.384545\pi\)
0.354811 + 0.934938i \(0.384545\pi\)
\(182\) −7.02662 −0.520848
\(183\) 6.53649 0.483191
\(184\) −14.8650 −1.09586
\(185\) 28.7312 2.11236
\(186\) 51.3419 3.76457
\(187\) 13.1368 0.960660
\(188\) 5.35564 0.390600
\(189\) −1.62831 −0.118442
\(190\) 2.33223 0.169198
\(191\) 15.2925 1.10652 0.553262 0.833007i \(-0.313383\pi\)
0.553262 + 0.833007i \(0.313383\pi\)
\(192\) 19.5580 1.41148
\(193\) −18.8934 −1.35998 −0.679988 0.733223i \(-0.738015\pi\)
−0.679988 + 0.733223i \(0.738015\pi\)
\(194\) −37.9208 −2.72256
\(195\) −44.5549 −3.19064
\(196\) −27.3445 −1.95318
\(197\) −6.46157 −0.460368 −0.230184 0.973147i \(-0.573933\pi\)
−0.230184 + 0.973147i \(0.573933\pi\)
\(198\) −54.8498 −3.89800
\(199\) 1.41100 0.100023 0.0500115 0.998749i \(-0.484074\pi\)
0.0500115 + 0.998749i \(0.484074\pi\)
\(200\) −19.1696 −1.35549
\(201\) −24.7060 −1.74263
\(202\) 4.62166 0.325179
\(203\) −2.38992 −0.167739
\(204\) −26.8811 −1.88205
\(205\) −12.2180 −0.853340
\(206\) −41.1626 −2.86794
\(207\) 12.3104 0.855629
\(208\) 24.3454 1.68805
\(209\) −1.69970 −0.117571
\(210\) 9.96647 0.687752
\(211\) −1.23071 −0.0847255 −0.0423628 0.999102i \(-0.513489\pi\)
−0.0423628 + 0.999102i \(0.513489\pi\)
\(212\) 15.0996 1.03704
\(213\) −38.5350 −2.64037
\(214\) 10.8109 0.739021
\(215\) 7.98186 0.544358
\(216\) 16.1794 1.10087
\(217\) 3.96284 0.269015
\(218\) −15.9334 −1.07915
\(219\) 18.6142 1.25783
\(220\) 63.9362 4.31058
\(221\) 13.8483 0.931537
\(222\) 63.9695 4.29335
\(223\) −26.0748 −1.74610 −0.873050 0.487631i \(-0.837861\pi\)
−0.873050 + 0.487631i \(0.837861\pi\)
\(224\) −0.288676 −0.0192880
\(225\) 15.8752 1.05835
\(226\) −28.7160 −1.91016
\(227\) −0.882142 −0.0585498 −0.0292749 0.999571i \(-0.509320\pi\)
−0.0292749 + 0.999571i \(0.509320\pi\)
\(228\) 3.47800 0.230336
\(229\) −8.38820 −0.554308 −0.277154 0.960826i \(-0.589391\pi\)
−0.277154 + 0.960826i \(0.589391\pi\)
\(230\) −21.4242 −1.41267
\(231\) −7.26344 −0.477899
\(232\) 23.7471 1.55907
\(233\) 20.2085 1.32390 0.661950 0.749548i \(-0.269729\pi\)
0.661950 + 0.749548i \(0.269729\pi\)
\(234\) −57.8203 −3.77983
\(235\) 3.91341 0.255283
\(236\) 42.3525 2.75691
\(237\) 25.4894 1.65572
\(238\) −3.09772 −0.200796
\(239\) −3.90841 −0.252814 −0.126407 0.991978i \(-0.540345\pi\)
−0.126407 + 0.991978i \(0.540345\pi\)
\(240\) −34.5313 −2.22898
\(241\) −10.4128 −0.670747 −0.335374 0.942085i \(-0.608863\pi\)
−0.335374 + 0.942085i \(0.608863\pi\)
\(242\) −42.4964 −2.73177
\(243\) 20.3262 1.30392
\(244\) −9.88785 −0.633005
\(245\) −19.9809 −1.27653
\(246\) −27.2030 −1.73440
\(247\) −1.79176 −0.114007
\(248\) −39.3762 −2.50039
\(249\) −28.6282 −1.81424
\(250\) 8.84832 0.559617
\(251\) 1.63860 0.103428 0.0517138 0.998662i \(-0.483532\pi\)
0.0517138 + 0.998662i \(0.483532\pi\)
\(252\) 8.66295 0.545715
\(253\) 15.6137 0.981623
\(254\) −27.8639 −1.74833
\(255\) −19.6423 −1.23005
\(256\) −32.3749 −2.02343
\(257\) −4.13934 −0.258205 −0.129102 0.991631i \(-0.541210\pi\)
−0.129102 + 0.991631i \(0.541210\pi\)
\(258\) 17.7714 1.10640
\(259\) 4.93751 0.306802
\(260\) 67.3989 4.17990
\(261\) −19.6660 −1.21730
\(262\) −9.87552 −0.610111
\(263\) −4.24519 −0.261770 −0.130885 0.991398i \(-0.541782\pi\)
−0.130885 + 0.991398i \(0.541782\pi\)
\(264\) 72.1721 4.44189
\(265\) 11.0334 0.677776
\(266\) 0.400798 0.0245745
\(267\) −7.36108 −0.450491
\(268\) 37.3732 2.28293
\(269\) −1.69124 −0.103117 −0.0515583 0.998670i \(-0.516419\pi\)
−0.0515583 + 0.998670i \(0.516419\pi\)
\(270\) 23.3186 1.41913
\(271\) 3.83364 0.232877 0.116439 0.993198i \(-0.462852\pi\)
0.116439 + 0.993198i \(0.462852\pi\)
\(272\) 10.7328 0.650773
\(273\) −7.65682 −0.463412
\(274\) 21.7977 1.31684
\(275\) 20.1351 1.21419
\(276\) −31.9493 −1.92312
\(277\) −7.02152 −0.421882 −0.210941 0.977499i \(-0.567653\pi\)
−0.210941 + 0.977499i \(0.567653\pi\)
\(278\) 54.8552 3.28999
\(279\) 32.6092 1.95226
\(280\) −7.64369 −0.456798
\(281\) −23.5195 −1.40305 −0.701527 0.712642i \(-0.747498\pi\)
−0.701527 + 0.712642i \(0.747498\pi\)
\(282\) 8.71312 0.518859
\(283\) −14.7623 −0.877529 −0.438764 0.898602i \(-0.644584\pi\)
−0.438764 + 0.898602i \(0.644584\pi\)
\(284\) 58.2925 3.45902
\(285\) 2.54140 0.150540
\(286\) −73.3356 −4.33642
\(287\) −2.09967 −0.123940
\(288\) −2.37544 −0.139974
\(289\) −10.8949 −0.640877
\(290\) 34.2255 2.00979
\(291\) −41.3218 −2.42233
\(292\) −28.1580 −1.64782
\(293\) 12.2059 0.713076 0.356538 0.934281i \(-0.383957\pi\)
0.356538 + 0.934281i \(0.383957\pi\)
\(294\) −44.4870 −2.59454
\(295\) 30.9473 1.80182
\(296\) −49.0608 −2.85160
\(297\) −16.9943 −0.986111
\(298\) 46.7700 2.70932
\(299\) 16.4593 0.951864
\(300\) −41.2012 −2.37875
\(301\) 1.37169 0.0790631
\(302\) 37.6264 2.16516
\(303\) 5.03616 0.289320
\(304\) −1.38866 −0.0796451
\(305\) −7.22513 −0.413710
\(306\) −25.4904 −1.45719
\(307\) −5.64330 −0.322080 −0.161040 0.986948i \(-0.551485\pi\)
−0.161040 + 0.986948i \(0.551485\pi\)
\(308\) 10.9875 0.626072
\(309\) −44.8544 −2.55168
\(310\) −56.7510 −3.22324
\(311\) 12.0814 0.685071 0.342536 0.939505i \(-0.388714\pi\)
0.342536 + 0.939505i \(0.388714\pi\)
\(312\) 76.0809 4.30723
\(313\) −23.9734 −1.35505 −0.677527 0.735498i \(-0.736948\pi\)
−0.677527 + 0.735498i \(0.736948\pi\)
\(314\) 44.1064 2.48907
\(315\) 6.33009 0.356660
\(316\) −38.5583 −2.16907
\(317\) 6.47460 0.363650 0.181825 0.983331i \(-0.441800\pi\)
0.181825 + 0.983331i \(0.441800\pi\)
\(318\) 24.5656 1.37757
\(319\) −24.9431 −1.39655
\(320\) −21.6185 −1.20851
\(321\) 11.7805 0.657526
\(322\) −3.68177 −0.205177
\(323\) −0.789905 −0.0439515
\(324\) −16.2421 −0.902337
\(325\) 21.2256 1.17738
\(326\) 20.8028 1.15216
\(327\) −17.3624 −0.960144
\(328\) 20.8631 1.15197
\(329\) 0.672525 0.0370775
\(330\) 104.018 5.72601
\(331\) −18.2953 −1.00560 −0.502800 0.864403i \(-0.667697\pi\)
−0.502800 + 0.864403i \(0.667697\pi\)
\(332\) 43.3063 2.37674
\(333\) 40.6295 2.22648
\(334\) 9.82442 0.537568
\(335\) 27.3089 1.49205
\(336\) −5.93425 −0.323740
\(337\) −7.08664 −0.386034 −0.193017 0.981195i \(-0.561827\pi\)
−0.193017 + 0.981195i \(0.561827\pi\)
\(338\) −45.3137 −2.46474
\(339\) −31.2914 −1.69952
\(340\) 29.7132 1.61142
\(341\) 41.3594 2.23974
\(342\) 3.29806 0.178339
\(343\) −6.99969 −0.377948
\(344\) −13.6296 −0.734861
\(345\) −23.3456 −1.25689
\(346\) 60.2150 3.23718
\(347\) 18.5704 0.996911 0.498456 0.866915i \(-0.333901\pi\)
0.498456 + 0.866915i \(0.333901\pi\)
\(348\) 51.0396 2.73601
\(349\) −4.54374 −0.243221 −0.121610 0.992578i \(-0.538806\pi\)
−0.121610 + 0.992578i \(0.538806\pi\)
\(350\) −4.74795 −0.253788
\(351\) −17.9147 −0.956216
\(352\) −3.01286 −0.160586
\(353\) −20.2356 −1.07703 −0.538515 0.842616i \(-0.681015\pi\)
−0.538515 + 0.842616i \(0.681015\pi\)
\(354\) 68.9035 3.66218
\(355\) 42.5948 2.26070
\(356\) 11.1352 0.590166
\(357\) −3.37555 −0.178653
\(358\) 53.3475 2.81950
\(359\) 26.4774 1.39743 0.698713 0.715402i \(-0.253756\pi\)
0.698713 + 0.715402i \(0.253756\pi\)
\(360\) −62.8981 −3.31502
\(361\) −18.8978 −0.994621
\(362\) −23.4956 −1.23490
\(363\) −46.3077 −2.43052
\(364\) 11.5826 0.607093
\(365\) −20.5753 −1.07696
\(366\) −16.0866 −0.840860
\(367\) −14.0100 −0.731316 −0.365658 0.930749i \(-0.619156\pi\)
−0.365658 + 0.930749i \(0.619156\pi\)
\(368\) 12.7564 0.664973
\(369\) −17.2777 −0.899441
\(370\) −70.7090 −3.67599
\(371\) 1.89611 0.0984409
\(372\) −84.6313 −4.38793
\(373\) −34.7395 −1.79874 −0.899371 0.437186i \(-0.855975\pi\)
−0.899371 + 0.437186i \(0.855975\pi\)
\(374\) −32.3304 −1.67176
\(375\) 9.64189 0.497905
\(376\) −6.68245 −0.344621
\(377\) −26.2940 −1.35421
\(378\) 4.00734 0.206115
\(379\) −5.38103 −0.276405 −0.138202 0.990404i \(-0.544132\pi\)
−0.138202 + 0.990404i \(0.544132\pi\)
\(380\) −3.84442 −0.197215
\(381\) −30.3629 −1.55554
\(382\) −37.6355 −1.92560
\(383\) −19.2637 −0.984331 −0.492166 0.870502i \(-0.663795\pi\)
−0.492166 + 0.870502i \(0.663795\pi\)
\(384\) −51.1725 −2.61139
\(385\) 8.02868 0.409179
\(386\) 46.4975 2.36666
\(387\) 11.2873 0.573767
\(388\) 62.5081 3.17337
\(389\) 31.2113 1.58248 0.791238 0.611509i \(-0.209437\pi\)
0.791238 + 0.611509i \(0.209437\pi\)
\(390\) 109.652 5.55243
\(391\) 7.25616 0.366960
\(392\) 34.1189 1.72326
\(393\) −10.7612 −0.542831
\(394\) 15.9022 0.801143
\(395\) −28.1749 −1.41763
\(396\) 90.4136 4.54346
\(397\) 21.0148 1.05470 0.527352 0.849647i \(-0.323185\pi\)
0.527352 + 0.849647i \(0.323185\pi\)
\(398\) −3.47253 −0.174062
\(399\) 0.436744 0.0218645
\(400\) 16.4504 0.822520
\(401\) −12.7336 −0.635883 −0.317942 0.948110i \(-0.602992\pi\)
−0.317942 + 0.948110i \(0.602992\pi\)
\(402\) 60.8028 3.03257
\(403\) 43.5994 2.17184
\(404\) −7.61828 −0.379024
\(405\) −11.8682 −0.589736
\(406\) 5.88170 0.291904
\(407\) 51.5318 2.55434
\(408\) 33.5407 1.66051
\(409\) 15.3529 0.759153 0.379576 0.925160i \(-0.376070\pi\)
0.379576 + 0.925160i \(0.376070\pi\)
\(410\) 30.0690 1.48500
\(411\) 23.7526 1.17163
\(412\) 67.8519 3.34282
\(413\) 5.31834 0.261698
\(414\) −30.2964 −1.48899
\(415\) 31.6443 1.55336
\(416\) −3.17603 −0.155718
\(417\) 59.7749 2.92719
\(418\) 4.18305 0.204600
\(419\) −10.5882 −0.517267 −0.258634 0.965975i \(-0.583272\pi\)
−0.258634 + 0.965975i \(0.583272\pi\)
\(420\) −16.4286 −0.801634
\(421\) −19.4982 −0.950285 −0.475143 0.879909i \(-0.657604\pi\)
−0.475143 + 0.879909i \(0.657604\pi\)
\(422\) 3.02883 0.147441
\(423\) 5.53404 0.269074
\(424\) −18.8404 −0.914970
\(425\) 9.35741 0.453901
\(426\) 94.8364 4.59484
\(427\) −1.24165 −0.0600876
\(428\) −17.8206 −0.861392
\(429\) −79.9128 −3.85822
\(430\) −19.6437 −0.947306
\(431\) 19.0229 0.916299 0.458149 0.888875i \(-0.348512\pi\)
0.458149 + 0.888875i \(0.348512\pi\)
\(432\) −13.8844 −0.668013
\(433\) 16.0641 0.771993 0.385996 0.922500i \(-0.373858\pi\)
0.385996 + 0.922500i \(0.373858\pi\)
\(434\) −9.75274 −0.468146
\(435\) 37.2951 1.78816
\(436\) 26.2644 1.25784
\(437\) −0.938834 −0.0449105
\(438\) −45.8104 −2.18890
\(439\) −1.14929 −0.0548524 −0.0274262 0.999624i \(-0.508731\pi\)
−0.0274262 + 0.999624i \(0.508731\pi\)
\(440\) −79.7758 −3.80316
\(441\) −28.2554 −1.34550
\(442\) −34.0813 −1.62108
\(443\) −37.8723 −1.79937 −0.899683 0.436544i \(-0.856202\pi\)
−0.899683 + 0.436544i \(0.856202\pi\)
\(444\) −105.446 −5.00427
\(445\) 8.13661 0.385712
\(446\) 64.1714 3.03860
\(447\) 50.9647 2.41055
\(448\) −3.71517 −0.175525
\(449\) −2.93782 −0.138645 −0.0693223 0.997594i \(-0.522084\pi\)
−0.0693223 + 0.997594i \(0.522084\pi\)
\(450\) −39.0697 −1.84176
\(451\) −21.9139 −1.03189
\(452\) 47.3351 2.22646
\(453\) 41.0010 1.92639
\(454\) 2.17099 0.101890
\(455\) 8.46350 0.396775
\(456\) −4.33964 −0.203222
\(457\) −10.1951 −0.476909 −0.238454 0.971154i \(-0.576641\pi\)
−0.238454 + 0.971154i \(0.576641\pi\)
\(458\) 20.6438 0.964619
\(459\) −7.89779 −0.368637
\(460\) 35.3153 1.64658
\(461\) 7.01973 0.326941 0.163471 0.986548i \(-0.447731\pi\)
0.163471 + 0.986548i \(0.447731\pi\)
\(462\) 17.8757 0.831652
\(463\) 23.9219 1.11175 0.555873 0.831267i \(-0.312384\pi\)
0.555873 + 0.831267i \(0.312384\pi\)
\(464\) −20.3786 −0.946052
\(465\) −61.8408 −2.86780
\(466\) −49.7340 −2.30388
\(467\) 10.9429 0.506377 0.253188 0.967417i \(-0.418521\pi\)
0.253188 + 0.967417i \(0.418521\pi\)
\(468\) 95.3103 4.40572
\(469\) 4.69308 0.216706
\(470\) −9.63109 −0.444249
\(471\) 48.0622 2.21459
\(472\) −52.8449 −2.43238
\(473\) 14.3161 0.658256
\(474\) −62.7308 −2.88132
\(475\) −1.21070 −0.0555509
\(476\) 5.10625 0.234045
\(477\) 15.6026 0.714393
\(478\) 9.61879 0.439953
\(479\) −16.1452 −0.737691 −0.368845 0.929491i \(-0.620247\pi\)
−0.368845 + 0.929491i \(0.620247\pi\)
\(480\) 4.50484 0.205617
\(481\) 54.3227 2.47690
\(482\) 25.6264 1.16725
\(483\) −4.01198 −0.182551
\(484\) 70.0504 3.18411
\(485\) 45.6752 2.07401
\(486\) −50.0237 −2.26912
\(487\) 1.95910 0.0887754 0.0443877 0.999014i \(-0.485866\pi\)
0.0443877 + 0.999014i \(0.485866\pi\)
\(488\) 12.3375 0.558491
\(489\) 22.6686 1.02511
\(490\) 49.1739 2.22145
\(491\) 36.9414 1.66714 0.833571 0.552413i \(-0.186293\pi\)
0.833571 + 0.552413i \(0.186293\pi\)
\(492\) 44.8411 2.02159
\(493\) −11.5918 −0.522071
\(494\) 4.40960 0.198397
\(495\) 66.0660 2.96945
\(496\) 33.7907 1.51725
\(497\) 7.31998 0.328346
\(498\) 70.4554 3.15718
\(499\) −14.7958 −0.662351 −0.331176 0.943569i \(-0.607445\pi\)
−0.331176 + 0.943569i \(0.607445\pi\)
\(500\) −14.5855 −0.652281
\(501\) 10.7055 0.478288
\(502\) −4.03268 −0.179987
\(503\) −4.57140 −0.203829 −0.101914 0.994793i \(-0.532497\pi\)
−0.101914 + 0.994793i \(0.532497\pi\)
\(504\) −10.8091 −0.481477
\(505\) −5.56674 −0.247717
\(506\) −38.4260 −1.70824
\(507\) −49.3777 −2.19294
\(508\) 45.9304 2.03783
\(509\) −20.2486 −0.897502 −0.448751 0.893657i \(-0.648131\pi\)
−0.448751 + 0.893657i \(0.648131\pi\)
\(510\) 48.3405 2.14055
\(511\) −3.53589 −0.156418
\(512\) 41.5130 1.83463
\(513\) 1.02185 0.0451159
\(514\) 10.1871 0.449334
\(515\) 49.5800 2.18475
\(516\) −29.2942 −1.28961
\(517\) 7.01902 0.308696
\(518\) −12.1514 −0.533904
\(519\) 65.6155 2.88020
\(520\) −84.0963 −3.68787
\(521\) 26.8344 1.17563 0.587817 0.808994i \(-0.299987\pi\)
0.587817 + 0.808994i \(0.299987\pi\)
\(522\) 48.3991 2.11837
\(523\) −5.53034 −0.241825 −0.120912 0.992663i \(-0.538582\pi\)
−0.120912 + 0.992663i \(0.538582\pi\)
\(524\) 16.2787 0.711137
\(525\) −5.17377 −0.225802
\(526\) 10.4476 0.455538
\(527\) 19.2210 0.837281
\(528\) −61.9346 −2.69536
\(529\) −14.3758 −0.625033
\(530\) −27.1537 −1.17948
\(531\) 43.7633 1.89916
\(532\) −0.660669 −0.0286436
\(533\) −23.1007 −1.00060
\(534\) 18.1160 0.783955
\(535\) −13.0217 −0.562976
\(536\) −46.6321 −2.01420
\(537\) 58.1320 2.50858
\(538\) 4.16222 0.179446
\(539\) −35.8373 −1.54362
\(540\) −38.4381 −1.65411
\(541\) −15.0879 −0.648681 −0.324340 0.945940i \(-0.605142\pi\)
−0.324340 + 0.945940i \(0.605142\pi\)
\(542\) −9.43478 −0.405259
\(543\) −25.6028 −1.09872
\(544\) −1.40017 −0.0600318
\(545\) 19.1916 0.822079
\(546\) 18.8438 0.806440
\(547\) −18.5017 −0.791077 −0.395539 0.918449i \(-0.629442\pi\)
−0.395539 + 0.918449i \(0.629442\pi\)
\(548\) −35.9310 −1.53490
\(549\) −10.2172 −0.436061
\(550\) −49.5534 −2.11297
\(551\) 1.49981 0.0638939
\(552\) 39.8644 1.69674
\(553\) −4.84189 −0.205898
\(554\) 17.2803 0.734169
\(555\) −77.0506 −3.27062
\(556\) −90.4225 −3.83477
\(557\) 23.6808 1.00339 0.501694 0.865045i \(-0.332710\pi\)
0.501694 + 0.865045i \(0.332710\pi\)
\(558\) −80.2529 −3.39737
\(559\) 15.0915 0.638300
\(560\) 6.55945 0.277187
\(561\) −35.2300 −1.48741
\(562\) 57.8826 2.44163
\(563\) 34.5619 1.45661 0.728305 0.685254i \(-0.240309\pi\)
0.728305 + 0.685254i \(0.240309\pi\)
\(564\) −14.3626 −0.604774
\(565\) 34.5881 1.45513
\(566\) 36.3308 1.52710
\(567\) −2.03957 −0.0856538
\(568\) −72.7339 −3.05185
\(569\) 27.7347 1.16270 0.581349 0.813654i \(-0.302525\pi\)
0.581349 + 0.813654i \(0.302525\pi\)
\(570\) −6.25451 −0.261973
\(571\) 10.3937 0.434965 0.217482 0.976064i \(-0.430216\pi\)
0.217482 + 0.976064i \(0.430216\pi\)
\(572\) 120.885 5.05447
\(573\) −41.0109 −1.71326
\(574\) 5.16740 0.215683
\(575\) 11.1217 0.463805
\(576\) −30.5712 −1.27380
\(577\) 42.8693 1.78467 0.892337 0.451370i \(-0.149065\pi\)
0.892337 + 0.451370i \(0.149065\pi\)
\(578\) 26.8129 1.11527
\(579\) 50.6677 2.10568
\(580\) −56.4169 −2.34258
\(581\) 5.43812 0.225611
\(582\) 101.695 4.21539
\(583\) 19.7893 0.819589
\(584\) 35.1338 1.45385
\(585\) 69.6440 2.87943
\(586\) −30.0393 −1.24091
\(587\) −34.8919 −1.44014 −0.720072 0.693900i \(-0.755891\pi\)
−0.720072 + 0.693900i \(0.755891\pi\)
\(588\) 73.3318 3.02415
\(589\) −2.48690 −0.102471
\(590\) −76.1628 −3.13557
\(591\) 17.3284 0.712797
\(592\) 42.1016 1.73037
\(593\) −37.5188 −1.54071 −0.770357 0.637613i \(-0.779922\pi\)
−0.770357 + 0.637613i \(0.779922\pi\)
\(594\) 41.8239 1.71605
\(595\) 3.73118 0.152963
\(596\) −77.0951 −3.15794
\(597\) −3.78397 −0.154868
\(598\) −40.5071 −1.65646
\(599\) 5.69171 0.232557 0.116278 0.993217i \(-0.462903\pi\)
0.116278 + 0.993217i \(0.462903\pi\)
\(600\) 51.4084 2.09874
\(601\) −40.1689 −1.63852 −0.819262 0.573420i \(-0.805616\pi\)
−0.819262 + 0.573420i \(0.805616\pi\)
\(602\) −3.37581 −0.137588
\(603\) 38.6182 1.57265
\(604\) −62.0229 −2.52367
\(605\) 51.1864 2.08102
\(606\) −12.3942 −0.503481
\(607\) −37.9715 −1.54121 −0.770607 0.637311i \(-0.780047\pi\)
−0.770607 + 0.637311i \(0.780047\pi\)
\(608\) 0.181160 0.00734702
\(609\) 6.40921 0.259714
\(610\) 17.7814 0.719948
\(611\) 7.39915 0.299338
\(612\) 42.0180 1.69848
\(613\) −17.9997 −0.727002 −0.363501 0.931594i \(-0.618419\pi\)
−0.363501 + 0.931594i \(0.618419\pi\)
\(614\) 13.8884 0.560491
\(615\) 32.7658 1.32124
\(616\) −13.7096 −0.552375
\(617\) −3.67067 −0.147775 −0.0738877 0.997267i \(-0.523541\pi\)
−0.0738877 + 0.997267i \(0.523541\pi\)
\(618\) 110.389 4.44049
\(619\) −17.6426 −0.709116 −0.354558 0.935034i \(-0.615369\pi\)
−0.354558 + 0.935034i \(0.615369\pi\)
\(620\) 93.5476 3.75696
\(621\) −9.38685 −0.376681
\(622\) −29.7328 −1.19218
\(623\) 1.39829 0.0560212
\(624\) −65.2889 −2.61365
\(625\) −29.5933 −1.18373
\(626\) 58.9996 2.35810
\(627\) 4.55821 0.182037
\(628\) −72.7044 −2.90122
\(629\) 23.9485 0.954887
\(630\) −15.5787 −0.620669
\(631\) −15.9504 −0.634974 −0.317487 0.948263i \(-0.602839\pi\)
−0.317487 + 0.948263i \(0.602839\pi\)
\(632\) 48.1108 1.91374
\(633\) 3.30048 0.131182
\(634\) −15.9343 −0.632832
\(635\) 33.5618 1.33186
\(636\) −40.4936 −1.60568
\(637\) −37.7782 −1.49683
\(638\) 61.3862 2.43030
\(639\) 60.2343 2.38283
\(640\) 56.5638 2.23588
\(641\) −14.4039 −0.568919 −0.284459 0.958688i \(-0.591814\pi\)
−0.284459 + 0.958688i \(0.591814\pi\)
\(642\) −28.9925 −1.14424
\(643\) −16.4388 −0.648284 −0.324142 0.946008i \(-0.605076\pi\)
−0.324142 + 0.946008i \(0.605076\pi\)
\(644\) 6.06899 0.239152
\(645\) −21.4055 −0.842842
\(646\) 1.94399 0.0764854
\(647\) 27.2832 1.07261 0.536306 0.844023i \(-0.319819\pi\)
0.536306 + 0.844023i \(0.319819\pi\)
\(648\) 20.2659 0.796119
\(649\) 55.5065 2.17882
\(650\) −52.2372 −2.04891
\(651\) −10.6274 −0.416522
\(652\) −34.2911 −1.34294
\(653\) −10.4856 −0.410334 −0.205167 0.978727i \(-0.565774\pi\)
−0.205167 + 0.978727i \(0.565774\pi\)
\(654\) 42.7298 1.67087
\(655\) 11.8950 0.464775
\(656\) −17.9037 −0.699022
\(657\) −29.0959 −1.13514
\(658\) −1.65512 −0.0645231
\(659\) −10.8763 −0.423682 −0.211841 0.977304i \(-0.567946\pi\)
−0.211841 + 0.977304i \(0.567946\pi\)
\(660\) −171.462 −6.67416
\(661\) 4.85508 0.188841 0.0944203 0.995532i \(-0.469900\pi\)
0.0944203 + 0.995532i \(0.469900\pi\)
\(662\) 45.0256 1.74997
\(663\) −37.1380 −1.44232
\(664\) −54.0351 −2.09697
\(665\) −0.482757 −0.0187205
\(666\) −99.9912 −3.87458
\(667\) −13.7774 −0.533463
\(668\) −16.1944 −0.626582
\(669\) 69.9267 2.70352
\(670\) −67.2086 −2.59650
\(671\) −12.9589 −0.500271
\(672\) 0.774163 0.0298640
\(673\) 1.59932 0.0616491 0.0308245 0.999525i \(-0.490187\pi\)
0.0308245 + 0.999525i \(0.490187\pi\)
\(674\) 17.4406 0.671786
\(675\) −12.1051 −0.465926
\(676\) 74.6944 2.87286
\(677\) −10.6034 −0.407523 −0.203762 0.979021i \(-0.565317\pi\)
−0.203762 + 0.979021i \(0.565317\pi\)
\(678\) 77.0098 2.95754
\(679\) 7.84935 0.301231
\(680\) −37.0743 −1.42174
\(681\) 2.36570 0.0906539
\(682\) −101.788 −3.89765
\(683\) 47.4960 1.81739 0.908693 0.417466i \(-0.137082\pi\)
0.908693 + 0.417466i \(0.137082\pi\)
\(684\) −5.43648 −0.207869
\(685\) −26.2551 −1.00315
\(686\) 17.2266 0.657714
\(687\) 22.4952 0.858246
\(688\) 11.6963 0.445917
\(689\) 20.8611 0.794743
\(690\) 57.4547 2.18726
\(691\) −37.7516 −1.43614 −0.718069 0.695972i \(-0.754974\pi\)
−0.718069 + 0.695972i \(0.754974\pi\)
\(692\) −99.2577 −3.77321
\(693\) 11.3535 0.431285
\(694\) −45.7026 −1.73485
\(695\) −66.0725 −2.50627
\(696\) −63.6842 −2.41394
\(697\) −10.1841 −0.385750
\(698\) 11.1824 0.423259
\(699\) −54.1945 −2.04982
\(700\) 7.82645 0.295812
\(701\) −34.3860 −1.29874 −0.649371 0.760471i \(-0.724968\pi\)
−0.649371 + 0.760471i \(0.724968\pi\)
\(702\) 44.0890 1.66403
\(703\) −3.09856 −0.116864
\(704\) −38.7745 −1.46137
\(705\) −10.4949 −0.395259
\(706\) 49.8007 1.87427
\(707\) −0.956653 −0.0359786
\(708\) −113.580 −4.26858
\(709\) 13.0658 0.490698 0.245349 0.969435i \(-0.421098\pi\)
0.245349 + 0.969435i \(0.421098\pi\)
\(710\) −104.828 −3.93412
\(711\) −39.8427 −1.49422
\(712\) −13.8939 −0.520695
\(713\) 22.8450 0.855551
\(714\) 8.30739 0.310896
\(715\) 88.3319 3.30343
\(716\) −87.9373 −3.28637
\(717\) 10.4815 0.391438
\(718\) −65.1623 −2.43183
\(719\) 50.0741 1.86745 0.933725 0.357992i \(-0.116538\pi\)
0.933725 + 0.357992i \(0.116538\pi\)
\(720\) 53.9760 2.01157
\(721\) 8.52039 0.317316
\(722\) 46.5084 1.73086
\(723\) 27.9247 1.03853
\(724\) 38.7298 1.43938
\(725\) −17.7671 −0.659852
\(726\) 113.965 4.22966
\(727\) −27.2266 −1.00978 −0.504889 0.863184i \(-0.668467\pi\)
−0.504889 + 0.863184i \(0.668467\pi\)
\(728\) −14.4521 −0.535629
\(729\) −42.4990 −1.57404
\(730\) 50.6367 1.87415
\(731\) 6.65315 0.246076
\(732\) 26.5169 0.980095
\(733\) −34.3850 −1.27004 −0.635020 0.772496i \(-0.719008\pi\)
−0.635020 + 0.772496i \(0.719008\pi\)
\(734\) 34.4793 1.27265
\(735\) 53.5842 1.97648
\(736\) −1.66416 −0.0613417
\(737\) 48.9808 1.80423
\(738\) 42.5212 1.56523
\(739\) 3.27467 0.120461 0.0602303 0.998185i \(-0.480816\pi\)
0.0602303 + 0.998185i \(0.480816\pi\)
\(740\) 116.556 4.28467
\(741\) 4.80508 0.176519
\(742\) −4.66641 −0.171309
\(743\) −2.94932 −0.108200 −0.0541000 0.998536i \(-0.517229\pi\)
−0.0541000 + 0.998536i \(0.517229\pi\)
\(744\) 105.598 3.87141
\(745\) −56.3340 −2.06392
\(746\) 85.4956 3.13021
\(747\) 44.7489 1.63728
\(748\) 53.2930 1.94858
\(749\) −2.23779 −0.0817672
\(750\) −23.7292 −0.866467
\(751\) −23.8675 −0.870937 −0.435469 0.900204i \(-0.643417\pi\)
−0.435469 + 0.900204i \(0.643417\pi\)
\(752\) 5.73455 0.209117
\(753\) −4.39436 −0.160139
\(754\) 64.7108 2.35663
\(755\) −45.3206 −1.64939
\(756\) −6.60564 −0.240245
\(757\) −16.5062 −0.599930 −0.299965 0.953950i \(-0.596975\pi\)
−0.299965 + 0.953950i \(0.596975\pi\)
\(758\) 13.2430 0.481006
\(759\) −41.8723 −1.51987
\(760\) 4.79684 0.174000
\(761\) 36.7709 1.33294 0.666472 0.745530i \(-0.267804\pi\)
0.666472 + 0.745530i \(0.267804\pi\)
\(762\) 74.7245 2.70698
\(763\) 3.29811 0.119400
\(764\) 62.0379 2.24445
\(765\) 30.7029 1.11007
\(766\) 47.4090 1.71296
\(767\) 58.5126 2.11277
\(768\) 86.8221 3.13292
\(769\) −3.78764 −0.136586 −0.0682929 0.997665i \(-0.521755\pi\)
−0.0682929 + 0.997665i \(0.521755\pi\)
\(770\) −19.7590 −0.712064
\(771\) 11.1007 0.399784
\(772\) −76.6459 −2.75855
\(773\) −4.39803 −0.158186 −0.0790931 0.996867i \(-0.525202\pi\)
−0.0790931 + 0.996867i \(0.525202\pi\)
\(774\) −27.7787 −0.998484
\(775\) 29.4604 1.05825
\(776\) −77.9940 −2.79982
\(777\) −13.2413 −0.475028
\(778\) −76.8125 −2.75386
\(779\) 1.31766 0.0472101
\(780\) −180.748 −6.47183
\(781\) 76.3972 2.73371
\(782\) −17.8578 −0.638592
\(783\) 14.9957 0.535902
\(784\) −29.2792 −1.04569
\(785\) −53.1258 −1.89614
\(786\) 26.4839 0.944648
\(787\) 13.1167 0.467559 0.233779 0.972290i \(-0.424891\pi\)
0.233779 + 0.972290i \(0.424891\pi\)
\(788\) −26.2130 −0.933800
\(789\) 11.3846 0.405304
\(790\) 69.3397 2.46700
\(791\) 5.94402 0.211345
\(792\) −112.813 −4.00863
\(793\) −13.6607 −0.485106
\(794\) −51.7185 −1.83542
\(795\) −29.5891 −1.04942
\(796\) 5.72408 0.202885
\(797\) −19.4415 −0.688655 −0.344327 0.938850i \(-0.611893\pi\)
−0.344327 + 0.938850i \(0.611893\pi\)
\(798\) −1.07485 −0.0380492
\(799\) 3.26196 0.115400
\(800\) −2.14607 −0.0758750
\(801\) 11.5062 0.406550
\(802\) 31.3379 1.10658
\(803\) −36.9034 −1.30229
\(804\) −100.226 −3.53471
\(805\) 4.43466 0.156301
\(806\) −107.300 −3.77949
\(807\) 4.53551 0.159657
\(808\) 9.50564 0.334407
\(809\) −14.4970 −0.509689 −0.254844 0.966982i \(-0.582024\pi\)
−0.254844 + 0.966982i \(0.582024\pi\)
\(810\) 29.2082 1.02627
\(811\) 2.15502 0.0756731 0.0378366 0.999284i \(-0.487953\pi\)
0.0378366 + 0.999284i \(0.487953\pi\)
\(812\) −9.69532 −0.340239
\(813\) −10.2810 −0.360569
\(814\) −126.822 −4.44512
\(815\) −25.0568 −0.877702
\(816\) −28.7830 −1.00760
\(817\) −0.860814 −0.0301161
\(818\) −37.7843 −1.32110
\(819\) 11.9684 0.418211
\(820\) −49.5653 −1.73090
\(821\) 40.8637 1.42615 0.713076 0.701086i \(-0.247301\pi\)
0.713076 + 0.701086i \(0.247301\pi\)
\(822\) −58.4563 −2.03890
\(823\) 7.54146 0.262879 0.131439 0.991324i \(-0.458040\pi\)
0.131439 + 0.991324i \(0.458040\pi\)
\(824\) −84.6616 −2.94933
\(825\) −53.9977 −1.87996
\(826\) −13.0887 −0.455414
\(827\) −44.6275 −1.55185 −0.775925 0.630825i \(-0.782717\pi\)
−0.775925 + 0.630825i \(0.782717\pi\)
\(828\) 49.9402 1.73554
\(829\) −12.5652 −0.436408 −0.218204 0.975903i \(-0.570020\pi\)
−0.218204 + 0.975903i \(0.570020\pi\)
\(830\) −77.8782 −2.70319
\(831\) 18.8301 0.653209
\(832\) −40.8745 −1.41707
\(833\) −16.6547 −0.577052
\(834\) −147.109 −5.09397
\(835\) −11.8334 −0.409512
\(836\) −6.89528 −0.238478
\(837\) −24.8651 −0.859462
\(838\) 26.0581 0.900161
\(839\) −52.3631 −1.80778 −0.903888 0.427769i \(-0.859300\pi\)
−0.903888 + 0.427769i \(0.859300\pi\)
\(840\) 20.4986 0.707270
\(841\) −6.99037 −0.241047
\(842\) 47.9861 1.65371
\(843\) 63.0739 2.17238
\(844\) −4.99269 −0.171855
\(845\) 54.5799 1.87760
\(846\) −13.6195 −0.468249
\(847\) 8.79646 0.302250
\(848\) 16.1679 0.555208
\(849\) 39.5892 1.35870
\(850\) −23.0290 −0.789889
\(851\) 28.4637 0.975724
\(852\) −156.327 −5.35568
\(853\) −29.6640 −1.01568 −0.507838 0.861453i \(-0.669555\pi\)
−0.507838 + 0.861453i \(0.669555\pi\)
\(854\) 3.05576 0.104566
\(855\) −3.97248 −0.135856
\(856\) 22.2355 0.759994
\(857\) 23.9074 0.816662 0.408331 0.912834i \(-0.366111\pi\)
0.408331 + 0.912834i \(0.366111\pi\)
\(858\) 196.669 6.71417
\(859\) −57.0716 −1.94726 −0.973630 0.228135i \(-0.926737\pi\)
−0.973630 + 0.228135i \(0.926737\pi\)
\(860\) 32.3805 1.10417
\(861\) 5.63085 0.191899
\(862\) −46.8162 −1.59457
\(863\) 10.2580 0.349188 0.174594 0.984641i \(-0.444139\pi\)
0.174594 + 0.984641i \(0.444139\pi\)
\(864\) 1.81131 0.0616222
\(865\) −72.5284 −2.46604
\(866\) −39.5346 −1.34344
\(867\) 29.2176 0.992283
\(868\) 16.0763 0.545665
\(869\) −50.5339 −1.71425
\(870\) −91.7850 −3.11180
\(871\) 51.6335 1.74953
\(872\) −32.7712 −1.10977
\(873\) 64.5904 2.18605
\(874\) 2.31052 0.0781544
\(875\) −1.83154 −0.0619175
\(876\) 75.5132 2.55135
\(877\) 16.1061 0.543865 0.271932 0.962316i \(-0.412337\pi\)
0.271932 + 0.962316i \(0.412337\pi\)
\(878\) 2.82845 0.0954555
\(879\) −32.7334 −1.10407
\(880\) 68.4597 2.30778
\(881\) 28.6462 0.965115 0.482558 0.875864i \(-0.339708\pi\)
0.482558 + 0.875864i \(0.339708\pi\)
\(882\) 69.5380 2.34147
\(883\) 48.8402 1.64360 0.821801 0.569775i \(-0.192969\pi\)
0.821801 + 0.569775i \(0.192969\pi\)
\(884\) 56.1792 1.88951
\(885\) −82.9936 −2.78980
\(886\) 93.2055 3.13130
\(887\) 29.9247 1.00477 0.502387 0.864643i \(-0.332455\pi\)
0.502387 + 0.864643i \(0.332455\pi\)
\(888\) 131.570 4.41520
\(889\) 5.76764 0.193440
\(890\) −20.0246 −0.671226
\(891\) −21.2866 −0.713128
\(892\) −105.779 −3.54175
\(893\) −0.422047 −0.0141232
\(894\) −125.427 −4.19489
\(895\) −64.2565 −2.14786
\(896\) 9.72057 0.324741
\(897\) −44.1400 −1.47379
\(898\) 7.23013 0.241273
\(899\) −36.4953 −1.21718
\(900\) 64.4019 2.14673
\(901\) 9.19671 0.306387
\(902\) 53.9312 1.79571
\(903\) −3.67857 −0.122415
\(904\) −59.0619 −1.96437
\(905\) 28.3002 0.940731
\(906\) −100.905 −3.35236
\(907\) 19.2573 0.639428 0.319714 0.947514i \(-0.396413\pi\)
0.319714 + 0.947514i \(0.396413\pi\)
\(908\) −3.57864 −0.118761
\(909\) −7.87206 −0.261100
\(910\) −20.8291 −0.690477
\(911\) −41.9884 −1.39114 −0.695568 0.718460i \(-0.744847\pi\)
−0.695568 + 0.718460i \(0.744847\pi\)
\(912\) 3.72407 0.123316
\(913\) 56.7566 1.87837
\(914\) 25.0907 0.829928
\(915\) 19.3762 0.640556
\(916\) −34.0289 −1.12435
\(917\) 2.04417 0.0675043
\(918\) 19.4369 0.641512
\(919\) −24.7889 −0.817709 −0.408855 0.912600i \(-0.634072\pi\)
−0.408855 + 0.912600i \(0.634072\pi\)
\(920\) −44.0644 −1.45276
\(921\) 15.1340 0.498683
\(922\) −17.2759 −0.568951
\(923\) 80.5348 2.65083
\(924\) −29.4660 −0.969361
\(925\) 36.7063 1.20690
\(926\) −58.8730 −1.93469
\(927\) 70.1122 2.30279
\(928\) 2.65853 0.0872704
\(929\) −6.21733 −0.203984 −0.101992 0.994785i \(-0.532522\pi\)
−0.101992 + 0.994785i \(0.532522\pi\)
\(930\) 152.193 4.99061
\(931\) 2.15486 0.0706228
\(932\) 81.9809 2.68537
\(933\) −32.3994 −1.06071
\(934\) −26.9310 −0.881209
\(935\) 38.9416 1.27353
\(936\) −118.923 −3.88710
\(937\) 29.2969 0.957089 0.478545 0.878063i \(-0.341165\pi\)
0.478545 + 0.878063i \(0.341165\pi\)
\(938\) −11.5499 −0.377117
\(939\) 64.2910 2.09806
\(940\) 15.8758 0.517810
\(941\) 23.8796 0.778451 0.389226 0.921142i \(-0.372743\pi\)
0.389226 + 0.921142i \(0.372743\pi\)
\(942\) −118.283 −3.85388
\(943\) −12.1042 −0.394167
\(944\) 45.3489 1.47598
\(945\) −4.82680 −0.157016
\(946\) −35.2327 −1.14551
\(947\) 20.8510 0.677566 0.338783 0.940865i \(-0.389985\pi\)
0.338783 + 0.940865i \(0.389985\pi\)
\(948\) 103.405 3.35842
\(949\) −38.9020 −1.26281
\(950\) 2.97960 0.0966710
\(951\) −17.3634 −0.563047
\(952\) −6.37127 −0.206494
\(953\) −26.0475 −0.843762 −0.421881 0.906651i \(-0.638630\pi\)
−0.421881 + 0.906651i \(0.638630\pi\)
\(954\) −38.3987 −1.24320
\(955\) 45.3316 1.46690
\(956\) −15.8555 −0.512803
\(957\) 66.8917 2.16230
\(958\) 39.7340 1.28375
\(959\) −4.51197 −0.145699
\(960\) 57.9759 1.87116
\(961\) 29.5146 0.952083
\(962\) −133.691 −4.31036
\(963\) −18.4142 −0.593391
\(964\) −42.2422 −1.36053
\(965\) −56.0058 −1.80289
\(966\) 9.87367 0.317680
\(967\) −11.7108 −0.376594 −0.188297 0.982112i \(-0.560297\pi\)
−0.188297 + 0.982112i \(0.560297\pi\)
\(968\) −87.4048 −2.80930
\(969\) 2.11834 0.0680510
\(970\) −112.409 −3.60923
\(971\) 51.0813 1.63928 0.819639 0.572881i \(-0.194174\pi\)
0.819639 + 0.572881i \(0.194174\pi\)
\(972\) 82.4584 2.64485
\(973\) −11.3547 −0.364013
\(974\) −4.82144 −0.154489
\(975\) −56.9221 −1.82297
\(976\) −10.5874 −0.338895
\(977\) −56.4145 −1.80486 −0.902429 0.430838i \(-0.858218\pi\)
−0.902429 + 0.430838i \(0.858218\pi\)
\(978\) −55.7885 −1.78392
\(979\) 14.5937 0.466416
\(980\) −81.0577 −2.58929
\(981\) 27.1393 0.866492
\(982\) −90.9145 −2.90120
\(983\) −8.57607 −0.273534 −0.136767 0.990603i \(-0.543671\pi\)
−0.136767 + 0.990603i \(0.543671\pi\)
\(984\) −55.9501 −1.78362
\(985\) −19.1541 −0.610299
\(986\) 28.5281 0.908520
\(987\) −1.80356 −0.0574079
\(988\) −7.26872 −0.231249
\(989\) 7.90754 0.251445
\(990\) −162.592 −5.16750
\(991\) −60.0564 −1.90776 −0.953878 0.300195i \(-0.902948\pi\)
−0.953878 + 0.300195i \(0.902948\pi\)
\(992\) −4.40823 −0.139961
\(993\) 49.0638 1.55699
\(994\) −18.0148 −0.571395
\(995\) 4.18263 0.132598
\(996\) −116.138 −3.67996
\(997\) 46.5701 1.47489 0.737445 0.675407i \(-0.236032\pi\)
0.737445 + 0.675407i \(0.236032\pi\)
\(998\) 36.4132 1.15264
\(999\) −30.9807 −0.980185
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 \(a_p\))