Properties

Label 8047.2.a.b.1.20
Level 8047
Weight 2
Character 8047.1
Self dual Yes
Analytic conductor 64.256
Analytic rank 1
Dimension 142
CM No

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Newspace parameters

Level: \( N \) = \( 8047 = 13 \cdot 619 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8047.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2556185065\)
Analytic rank: \(1\)
Dimension: \(142\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.20
Character \(\chi\) = 8047.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.15511 q^{2} +1.98414 q^{3} +2.64449 q^{4} -3.20612 q^{5} -4.27605 q^{6} +1.44494 q^{7} -1.38895 q^{8} +0.936828 q^{9} +O(q^{10})\) \(q-2.15511 q^{2} +1.98414 q^{3} +2.64449 q^{4} -3.20612 q^{5} -4.27605 q^{6} +1.44494 q^{7} -1.38895 q^{8} +0.936828 q^{9} +6.90953 q^{10} -1.78531 q^{11} +5.24706 q^{12} +1.00000 q^{13} -3.11400 q^{14} -6.36140 q^{15} -2.29564 q^{16} -1.06140 q^{17} -2.01897 q^{18} +0.795328 q^{19} -8.47856 q^{20} +2.86697 q^{21} +3.84755 q^{22} +2.00280 q^{23} -2.75588 q^{24} +5.27920 q^{25} -2.15511 q^{26} -4.09363 q^{27} +3.82113 q^{28} -6.27710 q^{29} +13.7095 q^{30} +10.4068 q^{31} +7.72526 q^{32} -3.54232 q^{33} +2.28743 q^{34} -4.63265 q^{35} +2.47744 q^{36} -3.52102 q^{37} -1.71402 q^{38} +1.98414 q^{39} +4.45315 q^{40} -7.24903 q^{41} -6.17863 q^{42} +10.4078 q^{43} -4.72125 q^{44} -3.00358 q^{45} -4.31626 q^{46} +6.99850 q^{47} -4.55489 q^{48} -4.91215 q^{49} -11.3773 q^{50} -2.10597 q^{51} +2.64449 q^{52} -6.32045 q^{53} +8.82222 q^{54} +5.72393 q^{55} -2.00695 q^{56} +1.57804 q^{57} +13.5278 q^{58} +1.77323 q^{59} -16.8227 q^{60} +12.1182 q^{61} -22.4279 q^{62} +1.35366 q^{63} -12.0575 q^{64} -3.20612 q^{65} +7.63409 q^{66} -4.99222 q^{67} -2.80686 q^{68} +3.97385 q^{69} +9.98386 q^{70} +7.36867 q^{71} -1.30121 q^{72} +15.3578 q^{73} +7.58817 q^{74} +10.4747 q^{75} +2.10324 q^{76} -2.57967 q^{77} -4.27605 q^{78} -12.0223 q^{79} +7.36011 q^{80} -10.9328 q^{81} +15.6224 q^{82} +6.29160 q^{83} +7.58168 q^{84} +3.40297 q^{85} -22.4299 q^{86} -12.4547 q^{87} +2.47972 q^{88} -12.7667 q^{89} +6.47305 q^{90} +1.44494 q^{91} +5.29640 q^{92} +20.6487 q^{93} -15.0825 q^{94} -2.54992 q^{95} +15.3280 q^{96} +16.0625 q^{97} +10.5862 q^{98} -1.67253 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 142q - 13q^{2} - 26q^{3} + 129q^{4} - 37q^{5} - 15q^{6} - 14q^{7} - 39q^{8} + 98q^{9} + O(q^{10}) \) \( 142q - 13q^{2} - 26q^{3} + 129q^{4} - 37q^{5} - 15q^{6} - 14q^{7} - 39q^{8} + 98q^{9} - 25q^{10} - 25q^{11} - 62q^{12} + 142q^{13} - 57q^{14} - 14q^{15} + 111q^{16} - 141q^{17} - 29q^{18} - 3q^{19} - 87q^{20} - 19q^{21} - 24q^{22} - 69q^{23} - 40q^{24} + 87q^{25} - 13q^{26} - 95q^{27} - 34q^{28} - 147q^{29} - 2q^{30} - 21q^{31} - 66q^{32} - 62q^{33} - 6q^{34} - 59q^{35} + 74q^{36} - 37q^{37} - 76q^{38} - 26q^{39} - 61q^{40} - 97q^{41} - 29q^{42} - 33q^{43} - 57q^{44} - 86q^{45} - q^{46} - 102q^{47} - 141q^{48} + 70q^{49} - 28q^{50} - 13q^{51} + 129q^{52} - 137q^{53} - 29q^{54} - 24q^{55} - 130q^{56} - 65q^{57} - 15q^{58} - 56q^{59} + 11q^{60} - 77q^{61} - 150q^{62} - 32q^{63} + 73q^{64} - 37q^{65} - 32q^{66} - 9q^{67} - 226q^{68} - 113q^{69} + 6q^{70} - 18q^{71} - 82q^{72} - 117q^{73} - 70q^{74} - 83q^{75} + 40q^{76} - 214q^{77} - 15q^{78} - 52q^{79} - 161q^{80} - 10q^{81} - 36q^{82} - 74q^{83} + 53q^{84} + 2q^{85} + 17q^{86} - 49q^{87} - 29q^{88} - 171q^{89} - 57q^{90} - 14q^{91} - 187q^{92} - 39q^{93} + 13q^{94} - 150q^{95} - 47q^{96} - 126q^{97} - 85q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.15511 −1.52389 −0.761946 0.647641i \(-0.775756\pi\)
−0.761946 + 0.647641i \(0.775756\pi\)
\(3\) 1.98414 1.14555 0.572773 0.819714i \(-0.305868\pi\)
0.572773 + 0.819714i \(0.305868\pi\)
\(4\) 2.64449 1.32225
\(5\) −3.20612 −1.43382 −0.716910 0.697166i \(-0.754444\pi\)
−0.716910 + 0.697166i \(0.754444\pi\)
\(6\) −4.27605 −1.74569
\(7\) 1.44494 0.546136 0.273068 0.961995i \(-0.411962\pi\)
0.273068 + 0.961995i \(0.411962\pi\)
\(8\) −1.38895 −0.491069
\(9\) 0.936828 0.312276
\(10\) 6.90953 2.18499
\(11\) −1.78531 −0.538293 −0.269146 0.963099i \(-0.586742\pi\)
−0.269146 + 0.963099i \(0.586742\pi\)
\(12\) 5.24706 1.51469
\(13\) 1.00000 0.277350
\(14\) −3.11400 −0.832252
\(15\) −6.36140 −1.64251
\(16\) −2.29564 −0.573911
\(17\) −1.06140 −0.257427 −0.128714 0.991682i \(-0.541085\pi\)
−0.128714 + 0.991682i \(0.541085\pi\)
\(18\) −2.01897 −0.475875
\(19\) 0.795328 0.182461 0.0912303 0.995830i \(-0.470920\pi\)
0.0912303 + 0.995830i \(0.470920\pi\)
\(20\) −8.47856 −1.89586
\(21\) 2.86697 0.625624
\(22\) 3.84755 0.820300
\(23\) 2.00280 0.417614 0.208807 0.977957i \(-0.433042\pi\)
0.208807 + 0.977957i \(0.433042\pi\)
\(24\) −2.75588 −0.562542
\(25\) 5.27920 1.05584
\(26\) −2.15511 −0.422652
\(27\) −4.09363 −0.787819
\(28\) 3.82113 0.722126
\(29\) −6.27710 −1.16563 −0.582814 0.812605i \(-0.698049\pi\)
−0.582814 + 0.812605i \(0.698049\pi\)
\(30\) 13.7095 2.50300
\(31\) 10.4068 1.86912 0.934561 0.355803i \(-0.115792\pi\)
0.934561 + 0.355803i \(0.115792\pi\)
\(32\) 7.72526 1.36565
\(33\) −3.54232 −0.616639
\(34\) 2.28743 0.392291
\(35\) −4.63265 −0.783060
\(36\) 2.47744 0.412906
\(37\) −3.52102 −0.578852 −0.289426 0.957200i \(-0.593464\pi\)
−0.289426 + 0.957200i \(0.593464\pi\)
\(38\) −1.71402 −0.278050
\(39\) 1.98414 0.317717
\(40\) 4.45315 0.704104
\(41\) −7.24903 −1.13211 −0.566054 0.824368i \(-0.691531\pi\)
−0.566054 + 0.824368i \(0.691531\pi\)
\(42\) −6.17863 −0.953383
\(43\) 10.4078 1.58717 0.793587 0.608457i \(-0.208211\pi\)
0.793587 + 0.608457i \(0.208211\pi\)
\(44\) −4.72125 −0.711756
\(45\) −3.00358 −0.447748
\(46\) −4.31626 −0.636398
\(47\) 6.99850 1.02084 0.510418 0.859926i \(-0.329491\pi\)
0.510418 + 0.859926i \(0.329491\pi\)
\(48\) −4.55489 −0.657441
\(49\) −4.91215 −0.701736
\(50\) −11.3773 −1.60899
\(51\) −2.10597 −0.294895
\(52\) 2.64449 0.366725
\(53\) −6.32045 −0.868181 −0.434091 0.900869i \(-0.642930\pi\)
−0.434091 + 0.900869i \(0.642930\pi\)
\(54\) 8.82222 1.20055
\(55\) 5.72393 0.771815
\(56\) −2.00695 −0.268190
\(57\) 1.57804 0.209017
\(58\) 13.5278 1.77629
\(59\) 1.77323 0.230855 0.115428 0.993316i \(-0.463176\pi\)
0.115428 + 0.993316i \(0.463176\pi\)
\(60\) −16.8227 −2.17180
\(61\) 12.1182 1.55157 0.775787 0.630995i \(-0.217353\pi\)
0.775787 + 0.630995i \(0.217353\pi\)
\(62\) −22.4279 −2.84834
\(63\) 1.35366 0.170545
\(64\) −12.0575 −1.50719
\(65\) −3.20612 −0.397670
\(66\) 7.63409 0.939691
\(67\) −4.99222 −0.609897 −0.304949 0.952369i \(-0.598639\pi\)
−0.304949 + 0.952369i \(0.598639\pi\)
\(68\) −2.80686 −0.340382
\(69\) 3.97385 0.478396
\(70\) 9.98386 1.19330
\(71\) 7.36867 0.874500 0.437250 0.899340i \(-0.355953\pi\)
0.437250 + 0.899340i \(0.355953\pi\)
\(72\) −1.30121 −0.153349
\(73\) 15.3578 1.79749 0.898747 0.438467i \(-0.144478\pi\)
0.898747 + 0.438467i \(0.144478\pi\)
\(74\) 7.58817 0.882107
\(75\) 10.4747 1.20951
\(76\) 2.10324 0.241258
\(77\) −2.57967 −0.293981
\(78\) −4.27605 −0.484167
\(79\) −12.0223 −1.35262 −0.676308 0.736619i \(-0.736421\pi\)
−0.676308 + 0.736619i \(0.736421\pi\)
\(80\) 7.36011 0.822885
\(81\) −10.9328 −1.21476
\(82\) 15.6224 1.72521
\(83\) 6.29160 0.690592 0.345296 0.938494i \(-0.387778\pi\)
0.345296 + 0.938494i \(0.387778\pi\)
\(84\) 7.58168 0.827229
\(85\) 3.40297 0.369104
\(86\) −22.4299 −2.41868
\(87\) −12.4547 −1.33528
\(88\) 2.47972 0.264339
\(89\) −12.7667 −1.35327 −0.676634 0.736320i \(-0.736562\pi\)
−0.676634 + 0.736320i \(0.736562\pi\)
\(90\) 6.47305 0.682319
\(91\) 1.44494 0.151471
\(92\) 5.29640 0.552188
\(93\) 20.6487 2.14117
\(94\) −15.0825 −1.55564
\(95\) −2.54992 −0.261616
\(96\) 15.3280 1.56441
\(97\) 16.0625 1.63090 0.815452 0.578824i \(-0.196488\pi\)
0.815452 + 0.578824i \(0.196488\pi\)
\(98\) 10.5862 1.06937
\(99\) −1.67253 −0.168096
\(100\) 13.9608 1.39608
\(101\) −12.0055 −1.19459 −0.597294 0.802022i \(-0.703757\pi\)
−0.597294 + 0.802022i \(0.703757\pi\)
\(102\) 4.53859 0.449387
\(103\) −16.5723 −1.63292 −0.816458 0.577405i \(-0.804066\pi\)
−0.816458 + 0.577405i \(0.804066\pi\)
\(104\) −1.38895 −0.136198
\(105\) −9.19184 −0.897032
\(106\) 13.6213 1.32301
\(107\) −11.4089 −1.10294 −0.551469 0.834196i \(-0.685932\pi\)
−0.551469 + 0.834196i \(0.685932\pi\)
\(108\) −10.8256 −1.04169
\(109\) −8.54034 −0.818016 −0.409008 0.912531i \(-0.634125\pi\)
−0.409008 + 0.912531i \(0.634125\pi\)
\(110\) −12.3357 −1.17616
\(111\) −6.98621 −0.663101
\(112\) −3.31707 −0.313433
\(113\) 14.4287 1.35734 0.678668 0.734445i \(-0.262558\pi\)
0.678668 + 0.734445i \(0.262558\pi\)
\(114\) −3.40086 −0.318519
\(115\) −6.42123 −0.598783
\(116\) −16.5998 −1.54125
\(117\) 0.936828 0.0866098
\(118\) −3.82151 −0.351798
\(119\) −1.53366 −0.140590
\(120\) 8.83568 0.806584
\(121\) −7.81265 −0.710241
\(122\) −26.1160 −2.36443
\(123\) −14.3831 −1.29688
\(124\) 27.5208 2.47144
\(125\) −0.895150 −0.0800647
\(126\) −2.91728 −0.259892
\(127\) −0.533754 −0.0473630 −0.0236815 0.999720i \(-0.507539\pi\)
−0.0236815 + 0.999720i \(0.507539\pi\)
\(128\) 10.5347 0.931143
\(129\) 20.6506 1.81818
\(130\) 6.90953 0.606006
\(131\) 6.07953 0.531171 0.265585 0.964087i \(-0.414435\pi\)
0.265585 + 0.964087i \(0.414435\pi\)
\(132\) −9.36765 −0.815349
\(133\) 1.14920 0.0996483
\(134\) 10.7588 0.929418
\(135\) 13.1247 1.12959
\(136\) 1.47423 0.126414
\(137\) −4.98174 −0.425619 −0.212810 0.977094i \(-0.568261\pi\)
−0.212810 + 0.977094i \(0.568261\pi\)
\(138\) −8.56408 −0.729023
\(139\) 2.29173 0.194382 0.0971912 0.995266i \(-0.469014\pi\)
0.0971912 + 0.995266i \(0.469014\pi\)
\(140\) −12.2510 −1.03540
\(141\) 13.8860 1.16942
\(142\) −15.8803 −1.33264
\(143\) −1.78531 −0.149296
\(144\) −2.15062 −0.179219
\(145\) 20.1251 1.67130
\(146\) −33.0977 −2.73919
\(147\) −9.74642 −0.803871
\(148\) −9.31131 −0.765385
\(149\) −3.79949 −0.311266 −0.155633 0.987815i \(-0.549742\pi\)
−0.155633 + 0.987815i \(0.549742\pi\)
\(150\) −22.5741 −1.84317
\(151\) −14.9673 −1.21802 −0.609012 0.793161i \(-0.708434\pi\)
−0.609012 + 0.793161i \(0.708434\pi\)
\(152\) −1.10467 −0.0896007
\(153\) −0.994349 −0.0803883
\(154\) 5.55947 0.447995
\(155\) −33.3655 −2.67999
\(156\) 5.24706 0.420101
\(157\) 4.00970 0.320009 0.160004 0.987116i \(-0.448849\pi\)
0.160004 + 0.987116i \(0.448849\pi\)
\(158\) 25.9094 2.06124
\(159\) −12.5407 −0.994542
\(160\) −24.7681 −1.95809
\(161\) 2.89393 0.228074
\(162\) 23.5615 1.85116
\(163\) 2.41945 0.189506 0.0947530 0.995501i \(-0.469794\pi\)
0.0947530 + 0.995501i \(0.469794\pi\)
\(164\) −19.1700 −1.49693
\(165\) 11.3571 0.884150
\(166\) −13.5591 −1.05239
\(167\) 18.1432 1.40396 0.701982 0.712195i \(-0.252299\pi\)
0.701982 + 0.712195i \(0.252299\pi\)
\(168\) −3.98208 −0.307224
\(169\) 1.00000 0.0769231
\(170\) −7.33377 −0.562475
\(171\) 0.745086 0.0569781
\(172\) 27.5233 2.09864
\(173\) −12.9664 −0.985821 −0.492910 0.870080i \(-0.664067\pi\)
−0.492910 + 0.870080i \(0.664067\pi\)
\(174\) 26.8412 2.03482
\(175\) 7.62812 0.576632
\(176\) 4.09845 0.308932
\(177\) 3.51835 0.264455
\(178\) 27.5136 2.06223
\(179\) 3.30127 0.246748 0.123374 0.992360i \(-0.460628\pi\)
0.123374 + 0.992360i \(0.460628\pi\)
\(180\) −7.94296 −0.592033
\(181\) 6.96513 0.517714 0.258857 0.965916i \(-0.416654\pi\)
0.258857 + 0.965916i \(0.416654\pi\)
\(182\) −3.11400 −0.230825
\(183\) 24.0442 1.77740
\(184\) −2.78180 −0.205077
\(185\) 11.2888 0.829969
\(186\) −44.5001 −3.26291
\(187\) 1.89493 0.138571
\(188\) 18.5075 1.34980
\(189\) −5.91505 −0.430256
\(190\) 5.49534 0.398674
\(191\) −11.0142 −0.796956 −0.398478 0.917178i \(-0.630462\pi\)
−0.398478 + 0.917178i \(0.630462\pi\)
\(192\) −23.9238 −1.72655
\(193\) −25.6542 −1.84663 −0.923315 0.384042i \(-0.874532\pi\)
−0.923315 + 0.384042i \(0.874532\pi\)
\(194\) −34.6165 −2.48532
\(195\) −6.36140 −0.455550
\(196\) −12.9901 −0.927868
\(197\) 8.47097 0.603532 0.301766 0.953382i \(-0.402424\pi\)
0.301766 + 0.953382i \(0.402424\pi\)
\(198\) 3.60449 0.256160
\(199\) −16.1683 −1.14614 −0.573070 0.819506i \(-0.694248\pi\)
−0.573070 + 0.819506i \(0.694248\pi\)
\(200\) −7.33256 −0.518490
\(201\) −9.90529 −0.698666
\(202\) 25.8731 1.82042
\(203\) −9.07003 −0.636591
\(204\) −5.56922 −0.389923
\(205\) 23.2412 1.62324
\(206\) 35.7151 2.48839
\(207\) 1.87628 0.130411
\(208\) −2.29564 −0.159174
\(209\) −1.41991 −0.0982172
\(210\) 19.8094 1.36698
\(211\) 13.8361 0.952516 0.476258 0.879305i \(-0.341993\pi\)
0.476258 + 0.879305i \(0.341993\pi\)
\(212\) −16.7144 −1.14795
\(213\) 14.6205 1.00178
\(214\) 24.5874 1.68076
\(215\) −33.3686 −2.27572
\(216\) 5.68586 0.386873
\(217\) 15.0372 1.02079
\(218\) 18.4054 1.24657
\(219\) 30.4721 2.05911
\(220\) 15.1369 1.02053
\(221\) −1.06140 −0.0713974
\(222\) 15.0560 1.01049
\(223\) −4.24439 −0.284225 −0.142113 0.989851i \(-0.545389\pi\)
−0.142113 + 0.989851i \(0.545389\pi\)
\(224\) 11.1625 0.745828
\(225\) 4.94571 0.329714
\(226\) −31.0954 −2.06843
\(227\) 9.14520 0.606988 0.303494 0.952833i \(-0.401847\pi\)
0.303494 + 0.952833i \(0.401847\pi\)
\(228\) 4.17313 0.276372
\(229\) −3.28239 −0.216906 −0.108453 0.994102i \(-0.534590\pi\)
−0.108453 + 0.994102i \(0.534590\pi\)
\(230\) 13.8384 0.912480
\(231\) −5.11844 −0.336769
\(232\) 8.71859 0.572404
\(233\) −0.470381 −0.0308157 −0.0154078 0.999881i \(-0.504905\pi\)
−0.0154078 + 0.999881i \(0.504905\pi\)
\(234\) −2.01897 −0.131984
\(235\) −22.4380 −1.46370
\(236\) 4.68930 0.305247
\(237\) −23.8540 −1.54948
\(238\) 3.30520 0.214244
\(239\) 22.9218 1.48269 0.741345 0.671124i \(-0.234188\pi\)
0.741345 + 0.671124i \(0.234188\pi\)
\(240\) 14.6035 0.942653
\(241\) 4.50551 0.290225 0.145113 0.989415i \(-0.453646\pi\)
0.145113 + 0.989415i \(0.453646\pi\)
\(242\) 16.8371 1.08233
\(243\) −9.41144 −0.603744
\(244\) 32.0464 2.05156
\(245\) 15.7489 1.00616
\(246\) 30.9972 1.97631
\(247\) 0.795328 0.0506055
\(248\) −14.4546 −0.917867
\(249\) 12.4834 0.791105
\(250\) 1.92915 0.122010
\(251\) 30.3983 1.91873 0.959363 0.282176i \(-0.0910561\pi\)
0.959363 + 0.282176i \(0.0910561\pi\)
\(252\) 3.57974 0.225503
\(253\) −3.57564 −0.224798
\(254\) 1.15030 0.0721761
\(255\) 6.75199 0.422826
\(256\) 1.41160 0.0882253
\(257\) −28.1035 −1.75305 −0.876523 0.481360i \(-0.840143\pi\)
−0.876523 + 0.481360i \(0.840143\pi\)
\(258\) −44.5042 −2.77071
\(259\) −5.08766 −0.316132
\(260\) −8.47856 −0.525818
\(261\) −5.88057 −0.363998
\(262\) −13.1020 −0.809447
\(263\) −21.3141 −1.31428 −0.657142 0.753767i \(-0.728235\pi\)
−0.657142 + 0.753767i \(0.728235\pi\)
\(264\) 4.92012 0.302812
\(265\) 20.2641 1.24482
\(266\) −2.47665 −0.151853
\(267\) −25.3310 −1.55023
\(268\) −13.2019 −0.806435
\(269\) −14.2474 −0.868676 −0.434338 0.900750i \(-0.643018\pi\)
−0.434338 + 0.900750i \(0.643018\pi\)
\(270\) −28.2851 −1.72138
\(271\) −7.52736 −0.457254 −0.228627 0.973514i \(-0.573424\pi\)
−0.228627 + 0.973514i \(0.573424\pi\)
\(272\) 2.43659 0.147740
\(273\) 2.86697 0.173517
\(274\) 10.7362 0.648597
\(275\) −9.42503 −0.568351
\(276\) 10.5088 0.632557
\(277\) 16.2655 0.977299 0.488649 0.872480i \(-0.337490\pi\)
0.488649 + 0.872480i \(0.337490\pi\)
\(278\) −4.93894 −0.296218
\(279\) 9.74942 0.583682
\(280\) 6.43452 0.384536
\(281\) −15.4849 −0.923751 −0.461875 0.886945i \(-0.652823\pi\)
−0.461875 + 0.886945i \(0.652823\pi\)
\(282\) −29.9259 −1.78206
\(283\) −24.8749 −1.47866 −0.739330 0.673344i \(-0.764857\pi\)
−0.739330 + 0.673344i \(0.764857\pi\)
\(284\) 19.4864 1.15630
\(285\) −5.05940 −0.299693
\(286\) 3.84755 0.227510
\(287\) −10.4744 −0.618285
\(288\) 7.23725 0.426459
\(289\) −15.8734 −0.933731
\(290\) −43.3719 −2.54688
\(291\) 31.8704 1.86828
\(292\) 40.6136 2.37673
\(293\) 1.79886 0.105090 0.0525451 0.998619i \(-0.483267\pi\)
0.0525451 + 0.998619i \(0.483267\pi\)
\(294\) 21.0046 1.22501
\(295\) −5.68519 −0.331005
\(296\) 4.89052 0.284256
\(297\) 7.30842 0.424077
\(298\) 8.18831 0.474336
\(299\) 2.00280 0.115825
\(300\) 27.7003 1.59928
\(301\) 15.0386 0.866813
\(302\) 32.2562 1.85614
\(303\) −23.8206 −1.36846
\(304\) −1.82579 −0.104716
\(305\) −38.8523 −2.22468
\(306\) 2.14293 0.122503
\(307\) −21.8289 −1.24584 −0.622920 0.782286i \(-0.714054\pi\)
−0.622920 + 0.782286i \(0.714054\pi\)
\(308\) −6.82192 −0.388715
\(309\) −32.8818 −1.87058
\(310\) 71.9064 4.08401
\(311\) −9.37801 −0.531778 −0.265889 0.964004i \(-0.585666\pi\)
−0.265889 + 0.964004i \(0.585666\pi\)
\(312\) −2.75588 −0.156021
\(313\) 27.7292 1.56735 0.783674 0.621172i \(-0.213343\pi\)
0.783674 + 0.621172i \(0.213343\pi\)
\(314\) −8.64134 −0.487659
\(315\) −4.34000 −0.244531
\(316\) −31.7929 −1.78849
\(317\) −5.37862 −0.302094 −0.151047 0.988527i \(-0.548264\pi\)
−0.151047 + 0.988527i \(0.548264\pi\)
\(318\) 27.0266 1.51557
\(319\) 11.2066 0.627449
\(320\) 38.6578 2.16104
\(321\) −22.6369 −1.26347
\(322\) −6.23673 −0.347560
\(323\) −0.844160 −0.0469703
\(324\) −28.9118 −1.60621
\(325\) 5.27920 0.292837
\(326\) −5.21418 −0.288787
\(327\) −16.9453 −0.937075
\(328\) 10.0686 0.555943
\(329\) 10.1124 0.557515
\(330\) −24.4758 −1.34735
\(331\) −5.26321 −0.289292 −0.144646 0.989483i \(-0.546204\pi\)
−0.144646 + 0.989483i \(0.546204\pi\)
\(332\) 16.6381 0.913133
\(333\) −3.29859 −0.180762
\(334\) −39.1006 −2.13949
\(335\) 16.0057 0.874483
\(336\) −6.58154 −0.359052
\(337\) 25.8015 1.40550 0.702749 0.711438i \(-0.251956\pi\)
0.702749 + 0.711438i \(0.251956\pi\)
\(338\) −2.15511 −0.117222
\(339\) 28.6286 1.55489
\(340\) 8.99913 0.488047
\(341\) −18.5795 −1.00613
\(342\) −1.60574 −0.0868285
\(343\) −17.2123 −0.929379
\(344\) −14.4559 −0.779412
\(345\) −12.7406 −0.685933
\(346\) 27.9441 1.50228
\(347\) −5.79355 −0.311014 −0.155507 0.987835i \(-0.549701\pi\)
−0.155507 + 0.987835i \(0.549701\pi\)
\(348\) −32.9363 −1.76557
\(349\) −5.69565 −0.304881 −0.152440 0.988313i \(-0.548713\pi\)
−0.152440 + 0.988313i \(0.548713\pi\)
\(350\) −16.4394 −0.878725
\(351\) −4.09363 −0.218502
\(352\) −13.7920 −0.735118
\(353\) 11.2156 0.596949 0.298474 0.954418i \(-0.403522\pi\)
0.298474 + 0.954418i \(0.403522\pi\)
\(354\) −7.58242 −0.403001
\(355\) −23.6248 −1.25388
\(356\) −33.7614 −1.78935
\(357\) −3.04300 −0.161052
\(358\) −7.11459 −0.376018
\(359\) −29.7593 −1.57064 −0.785319 0.619091i \(-0.787501\pi\)
−0.785319 + 0.619091i \(0.787501\pi\)
\(360\) 4.17183 0.219875
\(361\) −18.3675 −0.966708
\(362\) −15.0106 −0.788941
\(363\) −15.5014 −0.813614
\(364\) 3.82113 0.200282
\(365\) −49.2389 −2.57728
\(366\) −51.8179 −2.70856
\(367\) −12.3699 −0.645702 −0.322851 0.946450i \(-0.604641\pi\)
−0.322851 + 0.946450i \(0.604641\pi\)
\(368\) −4.59772 −0.239673
\(369\) −6.79110 −0.353530
\(370\) −24.3286 −1.26478
\(371\) −9.13267 −0.474145
\(372\) 54.6052 2.83115
\(373\) −3.68423 −0.190762 −0.0953811 0.995441i \(-0.530407\pi\)
−0.0953811 + 0.995441i \(0.530407\pi\)
\(374\) −4.08378 −0.211167
\(375\) −1.77611 −0.0917178
\(376\) −9.72058 −0.501301
\(377\) −6.27710 −0.323287
\(378\) 12.7476 0.655664
\(379\) −30.5241 −1.56792 −0.783959 0.620812i \(-0.786803\pi\)
−0.783959 + 0.620812i \(0.786803\pi\)
\(380\) −6.74323 −0.345920
\(381\) −1.05905 −0.0542565
\(382\) 23.7367 1.21448
\(383\) −0.249694 −0.0127588 −0.00637939 0.999980i \(-0.502031\pi\)
−0.00637939 + 0.999980i \(0.502031\pi\)
\(384\) 20.9023 1.06667
\(385\) 8.27073 0.421516
\(386\) 55.2876 2.81407
\(387\) 9.75032 0.495637
\(388\) 42.4773 2.15646
\(389\) −26.7589 −1.35673 −0.678364 0.734726i \(-0.737311\pi\)
−0.678364 + 0.734726i \(0.737311\pi\)
\(390\) 13.7095 0.694208
\(391\) −2.12577 −0.107505
\(392\) 6.82274 0.344600
\(393\) 12.0627 0.608481
\(394\) −18.2559 −0.919717
\(395\) 38.5449 1.93941
\(396\) −4.42300 −0.222264
\(397\) 8.45450 0.424319 0.212160 0.977235i \(-0.431950\pi\)
0.212160 + 0.977235i \(0.431950\pi\)
\(398\) 34.8444 1.74659
\(399\) 2.28018 0.114152
\(400\) −12.1192 −0.605958
\(401\) −1.61347 −0.0805728 −0.0402864 0.999188i \(-0.512827\pi\)
−0.0402864 + 0.999188i \(0.512827\pi\)
\(402\) 21.3470 1.06469
\(403\) 10.4068 0.518401
\(404\) −31.7484 −1.57954
\(405\) 35.0520 1.74175
\(406\) 19.5469 0.970097
\(407\) 6.28612 0.311592
\(408\) 2.92509 0.144813
\(409\) −30.1802 −1.49231 −0.746157 0.665771i \(-0.768103\pi\)
−0.746157 + 0.665771i \(0.768103\pi\)
\(410\) −50.0874 −2.47364
\(411\) −9.88450 −0.487566
\(412\) −43.8253 −2.15912
\(413\) 2.56221 0.126078
\(414\) −4.04360 −0.198732
\(415\) −20.1716 −0.990185
\(416\) 7.72526 0.378762
\(417\) 4.54713 0.222674
\(418\) 3.06006 0.149672
\(419\) −1.08788 −0.0531464 −0.0265732 0.999647i \(-0.508460\pi\)
−0.0265732 + 0.999647i \(0.508460\pi\)
\(420\) −24.3078 −1.18610
\(421\) 32.5833 1.58801 0.794007 0.607908i \(-0.207991\pi\)
0.794007 + 0.607908i \(0.207991\pi\)
\(422\) −29.8183 −1.45153
\(423\) 6.55640 0.318783
\(424\) 8.77881 0.426337
\(425\) −5.60334 −0.271802
\(426\) −31.5088 −1.52660
\(427\) 17.5100 0.847370
\(428\) −30.1707 −1.45836
\(429\) −3.54232 −0.171025
\(430\) 71.9130 3.46795
\(431\) −16.0729 −0.774205 −0.387103 0.922037i \(-0.626524\pi\)
−0.387103 + 0.922037i \(0.626524\pi\)
\(432\) 9.39751 0.452138
\(433\) −2.24522 −0.107898 −0.0539491 0.998544i \(-0.517181\pi\)
−0.0539491 + 0.998544i \(0.517181\pi\)
\(434\) −32.4069 −1.55558
\(435\) 39.9312 1.91455
\(436\) −22.5849 −1.08162
\(437\) 1.59289 0.0761981
\(438\) −65.6707 −3.13787
\(439\) 13.3023 0.634885 0.317443 0.948278i \(-0.397176\pi\)
0.317443 + 0.948278i \(0.397176\pi\)
\(440\) −7.95027 −0.379014
\(441\) −4.60184 −0.219135
\(442\) 2.28743 0.108802
\(443\) −13.9235 −0.661523 −0.330762 0.943714i \(-0.607306\pi\)
−0.330762 + 0.943714i \(0.607306\pi\)
\(444\) −18.4750 −0.876783
\(445\) 40.9316 1.94034
\(446\) 9.14711 0.433128
\(447\) −7.53873 −0.356570
\(448\) −17.4224 −0.823129
\(449\) −10.9141 −0.515068 −0.257534 0.966269i \(-0.582910\pi\)
−0.257534 + 0.966269i \(0.582910\pi\)
\(450\) −10.6585 −0.502448
\(451\) 12.9418 0.609405
\(452\) 38.1565 1.79473
\(453\) −29.6973 −1.39530
\(454\) −19.7089 −0.924984
\(455\) −4.63265 −0.217182
\(456\) −2.19183 −0.102642
\(457\) −28.6280 −1.33916 −0.669580 0.742740i \(-0.733526\pi\)
−0.669580 + 0.742740i \(0.733526\pi\)
\(458\) 7.07390 0.330542
\(459\) 4.34497 0.202806
\(460\) −16.9809 −0.791738
\(461\) −14.8945 −0.693705 −0.346853 0.937920i \(-0.612750\pi\)
−0.346853 + 0.937920i \(0.612750\pi\)
\(462\) 11.0308 0.513199
\(463\) 10.5295 0.489347 0.244673 0.969606i \(-0.421319\pi\)
0.244673 + 0.969606i \(0.421319\pi\)
\(464\) 14.4100 0.668967
\(465\) −66.2021 −3.07005
\(466\) 1.01372 0.0469597
\(467\) 18.9886 0.878686 0.439343 0.898319i \(-0.355211\pi\)
0.439343 + 0.898319i \(0.355211\pi\)
\(468\) 2.47744 0.114520
\(469\) −7.21346 −0.333087
\(470\) 48.3564 2.23051
\(471\) 7.95582 0.366585
\(472\) −2.46293 −0.113366
\(473\) −18.5812 −0.854364
\(474\) 51.4079 2.36124
\(475\) 4.19869 0.192649
\(476\) −4.05574 −0.185895
\(477\) −5.92118 −0.271112
\(478\) −49.3991 −2.25946
\(479\) −13.3420 −0.609610 −0.304805 0.952415i \(-0.598591\pi\)
−0.304805 + 0.952415i \(0.598591\pi\)
\(480\) −49.1435 −2.24308
\(481\) −3.52102 −0.160545
\(482\) −9.70986 −0.442272
\(483\) 5.74198 0.261269
\(484\) −20.6605 −0.939114
\(485\) −51.4984 −2.33842
\(486\) 20.2827 0.920041
\(487\) −2.21402 −0.100327 −0.0501634 0.998741i \(-0.515974\pi\)
−0.0501634 + 0.998741i \(0.515974\pi\)
\(488\) −16.8316 −0.761929
\(489\) 4.80054 0.217088
\(490\) −33.9407 −1.53328
\(491\) 0.0656429 0.00296242 0.00148121 0.999999i \(-0.499529\pi\)
0.00148121 + 0.999999i \(0.499529\pi\)
\(492\) −38.0360 −1.71480
\(493\) 6.66251 0.300064
\(494\) −1.71402 −0.0771173
\(495\) 5.36234 0.241019
\(496\) −23.8904 −1.07271
\(497\) 10.6473 0.477596
\(498\) −26.9032 −1.20556
\(499\) −34.9872 −1.56624 −0.783121 0.621869i \(-0.786374\pi\)
−0.783121 + 0.621869i \(0.786374\pi\)
\(500\) −2.36722 −0.105865
\(501\) 35.9987 1.60831
\(502\) −65.5117 −2.92393
\(503\) 24.7479 1.10345 0.551727 0.834025i \(-0.313969\pi\)
0.551727 + 0.834025i \(0.313969\pi\)
\(504\) −1.88017 −0.0837494
\(505\) 38.4909 1.71282
\(506\) 7.70588 0.342568
\(507\) 1.98414 0.0881189
\(508\) −1.41151 −0.0626256
\(509\) 25.9601 1.15066 0.575330 0.817921i \(-0.304874\pi\)
0.575330 + 0.817921i \(0.304874\pi\)
\(510\) −14.5513 −0.644341
\(511\) 22.1911 0.981676
\(512\) −24.1115 −1.06559
\(513\) −3.25578 −0.143746
\(514\) 60.5660 2.67145
\(515\) 53.1327 2.34131
\(516\) 54.6103 2.40408
\(517\) −12.4945 −0.549509
\(518\) 10.9645 0.481750
\(519\) −25.7273 −1.12930
\(520\) 4.45315 0.195283
\(521\) 1.54924 0.0678734 0.0339367 0.999424i \(-0.489196\pi\)
0.0339367 + 0.999424i \(0.489196\pi\)
\(522\) 12.6733 0.554694
\(523\) 31.4091 1.37342 0.686711 0.726930i \(-0.259054\pi\)
0.686711 + 0.726930i \(0.259054\pi\)
\(524\) 16.0773 0.702339
\(525\) 15.1353 0.660559
\(526\) 45.9342 2.00283
\(527\) −11.0458 −0.481163
\(528\) 8.13191 0.353896
\(529\) −18.9888 −0.825599
\(530\) −43.6714 −1.89696
\(531\) 1.66121 0.0720905
\(532\) 3.03905 0.131760
\(533\) −7.24903 −0.313990
\(534\) 54.5910 2.36238
\(535\) 36.5782 1.58141
\(536\) 6.93396 0.299501
\(537\) 6.55019 0.282662
\(538\) 30.7046 1.32377
\(539\) 8.76973 0.377739
\(540\) 34.7081 1.49360
\(541\) 15.5046 0.666593 0.333297 0.942822i \(-0.391839\pi\)
0.333297 + 0.942822i \(0.391839\pi\)
\(542\) 16.2223 0.696806
\(543\) 13.8198 0.593066
\(544\) −8.19959 −0.351554
\(545\) 27.3813 1.17289
\(546\) −6.17863 −0.264421
\(547\) 1.07613 0.0460121 0.0230060 0.999735i \(-0.492676\pi\)
0.0230060 + 0.999735i \(0.492676\pi\)
\(548\) −13.1742 −0.562773
\(549\) 11.3527 0.484519
\(550\) 20.3120 0.866105
\(551\) −4.99235 −0.212681
\(552\) −5.51949 −0.234925
\(553\) −17.3715 −0.738711
\(554\) −35.0539 −1.48930
\(555\) 22.3986 0.950768
\(556\) 6.06048 0.257021
\(557\) −23.9714 −1.01570 −0.507851 0.861445i \(-0.669560\pi\)
−0.507851 + 0.861445i \(0.669560\pi\)
\(558\) −21.0111 −0.889469
\(559\) 10.4078 0.440203
\(560\) 10.6349 0.449407
\(561\) 3.75982 0.158740
\(562\) 33.3716 1.40770
\(563\) −35.5533 −1.49839 −0.749197 0.662347i \(-0.769560\pi\)
−0.749197 + 0.662347i \(0.769560\pi\)
\(564\) 36.7215 1.54625
\(565\) −46.2600 −1.94617
\(566\) 53.6081 2.25332
\(567\) −15.7973 −0.663424
\(568\) −10.2347 −0.429439
\(569\) −5.73879 −0.240583 −0.120291 0.992739i \(-0.538383\pi\)
−0.120291 + 0.992739i \(0.538383\pi\)
\(570\) 10.9036 0.456700
\(571\) 47.5790 1.99112 0.995559 0.0941359i \(-0.0300088\pi\)
0.995559 + 0.0941359i \(0.0300088\pi\)
\(572\) −4.72125 −0.197405
\(573\) −21.8537 −0.912950
\(574\) 22.5735 0.942199
\(575\) 10.5732 0.440933
\(576\) −11.2958 −0.470659
\(577\) 17.6140 0.733282 0.366641 0.930362i \(-0.380508\pi\)
0.366641 + 0.930362i \(0.380508\pi\)
\(578\) 34.2090 1.42291
\(579\) −50.9017 −2.11540
\(580\) 53.2208 2.20987
\(581\) 9.09097 0.377157
\(582\) −68.6842 −2.84705
\(583\) 11.2840 0.467336
\(584\) −21.3312 −0.882693
\(585\) −3.00358 −0.124183
\(586\) −3.87673 −0.160146
\(587\) −18.9106 −0.780523 −0.390262 0.920704i \(-0.627615\pi\)
−0.390262 + 0.920704i \(0.627615\pi\)
\(588\) −25.7743 −1.06292
\(589\) 8.27684 0.341041
\(590\) 12.2522 0.504415
\(591\) 16.8076 0.691373
\(592\) 8.08300 0.332209
\(593\) 24.1298 0.990890 0.495445 0.868639i \(-0.335005\pi\)
0.495445 + 0.868639i \(0.335005\pi\)
\(594\) −15.7504 −0.646248
\(595\) 4.91709 0.201581
\(596\) −10.0477 −0.411571
\(597\) −32.0802 −1.31296
\(598\) −4.31626 −0.176505
\(599\) −8.71567 −0.356113 −0.178056 0.984020i \(-0.556981\pi\)
−0.178056 + 0.984020i \(0.556981\pi\)
\(600\) −14.5488 −0.593954
\(601\) −23.9910 −0.978612 −0.489306 0.872112i \(-0.662750\pi\)
−0.489306 + 0.872112i \(0.662750\pi\)
\(602\) −32.4099 −1.32093
\(603\) −4.67686 −0.190456
\(604\) −39.5810 −1.61053
\(605\) 25.0483 1.01836
\(606\) 51.3359 2.08538
\(607\) 25.4497 1.03297 0.516486 0.856296i \(-0.327240\pi\)
0.516486 + 0.856296i \(0.327240\pi\)
\(608\) 6.14412 0.249177
\(609\) −17.9963 −0.729245
\(610\) 83.7309 3.39017
\(611\) 6.99850 0.283129
\(612\) −2.62955 −0.106293
\(613\) 24.9852 1.00914 0.504571 0.863370i \(-0.331651\pi\)
0.504571 + 0.863370i \(0.331651\pi\)
\(614\) 47.0436 1.89853
\(615\) 46.1140 1.85950
\(616\) 3.58304 0.144365
\(617\) 26.7234 1.07585 0.537923 0.842994i \(-0.319209\pi\)
0.537923 + 0.842994i \(0.319209\pi\)
\(618\) 70.8639 2.85056
\(619\) 1.00000 0.0401934
\(620\) −88.2349 −3.54360
\(621\) −8.19874 −0.329004
\(622\) 20.2106 0.810373
\(623\) −18.4471 −0.739068
\(624\) −4.55489 −0.182341
\(625\) −23.5260 −0.941042
\(626\) −59.7595 −2.38847
\(627\) −2.81731 −0.112512
\(628\) 10.6036 0.423131
\(629\) 3.73720 0.149012
\(630\) 9.35316 0.372639
\(631\) −11.4253 −0.454835 −0.227417 0.973797i \(-0.573028\pi\)
−0.227417 + 0.973797i \(0.573028\pi\)
\(632\) 16.6984 0.664227
\(633\) 27.4528 1.09115
\(634\) 11.5915 0.460358
\(635\) 1.71128 0.0679101
\(636\) −33.1638 −1.31503
\(637\) −4.91215 −0.194626
\(638\) −24.1514 −0.956165
\(639\) 6.90318 0.273085
\(640\) −33.7755 −1.33509
\(641\) −46.9163 −1.85308 −0.926542 0.376191i \(-0.877234\pi\)
−0.926542 + 0.376191i \(0.877234\pi\)
\(642\) 48.7849 1.92539
\(643\) −2.14213 −0.0844774 −0.0422387 0.999108i \(-0.513449\pi\)
−0.0422387 + 0.999108i \(0.513449\pi\)
\(644\) 7.65298 0.301570
\(645\) −66.2082 −2.60695
\(646\) 1.81926 0.0715777
\(647\) 37.3190 1.46716 0.733581 0.679602i \(-0.237847\pi\)
0.733581 + 0.679602i \(0.237847\pi\)
\(648\) 15.1852 0.596530
\(649\) −3.16578 −0.124268
\(650\) −11.3773 −0.446252
\(651\) 29.8361 1.16937
\(652\) 6.39822 0.250574
\(653\) −0.221600 −0.00867188 −0.00433594 0.999991i \(-0.501380\pi\)
−0.00433594 + 0.999991i \(0.501380\pi\)
\(654\) 36.5189 1.42800
\(655\) −19.4917 −0.761604
\(656\) 16.6412 0.649729
\(657\) 14.3876 0.561315
\(658\) −21.7933 −0.849593
\(659\) −43.6436 −1.70011 −0.850056 0.526692i \(-0.823432\pi\)
−0.850056 + 0.526692i \(0.823432\pi\)
\(660\) 30.0338 1.16906
\(661\) −3.92641 −0.152720 −0.0763598 0.997080i \(-0.524330\pi\)
−0.0763598 + 0.997080i \(0.524330\pi\)
\(662\) 11.3428 0.440850
\(663\) −2.10597 −0.0817890
\(664\) −8.73872 −0.339128
\(665\) −3.68447 −0.142878
\(666\) 7.10882 0.275461
\(667\) −12.5718 −0.486782
\(668\) 47.9796 1.85639
\(669\) −8.42147 −0.325593
\(670\) −34.4940 −1.33262
\(671\) −21.6348 −0.835200
\(672\) 22.1481 0.854381
\(673\) −30.4414 −1.17343 −0.586715 0.809794i \(-0.699579\pi\)
−0.586715 + 0.809794i \(0.699579\pi\)
\(674\) −55.6050 −2.14183
\(675\) −21.6111 −0.831811
\(676\) 2.64449 0.101711
\(677\) −7.03644 −0.270432 −0.135216 0.990816i \(-0.543173\pi\)
−0.135216 + 0.990816i \(0.543173\pi\)
\(678\) −61.6977 −2.36948
\(679\) 23.2094 0.890695
\(680\) −4.72656 −0.181255
\(681\) 18.1454 0.695333
\(682\) 40.0408 1.53324
\(683\) −4.09008 −0.156502 −0.0782512 0.996934i \(-0.524934\pi\)
−0.0782512 + 0.996934i \(0.524934\pi\)
\(684\) 1.97037 0.0753391
\(685\) 15.9721 0.610261
\(686\) 37.0944 1.41627
\(687\) −6.51273 −0.248476
\(688\) −23.8926 −0.910897
\(689\) −6.32045 −0.240790
\(690\) 27.4575 1.04529
\(691\) 25.0542 0.953107 0.476554 0.879145i \(-0.341886\pi\)
0.476554 + 0.879145i \(0.341886\pi\)
\(692\) −34.2897 −1.30350
\(693\) −2.41671 −0.0918032
\(694\) 12.4857 0.473952
\(695\) −7.34757 −0.278709
\(696\) 17.2989 0.655715
\(697\) 7.69411 0.291435
\(698\) 12.2747 0.464606
\(699\) −0.933303 −0.0353008
\(700\) 20.1725 0.762450
\(701\) −10.3232 −0.389903 −0.194951 0.980813i \(-0.562455\pi\)
−0.194951 + 0.980813i \(0.562455\pi\)
\(702\) 8.82222 0.332973
\(703\) −2.80036 −0.105618
\(704\) 21.5264 0.811308
\(705\) −44.5203 −1.67673
\(706\) −24.1709 −0.909685
\(707\) −17.3472 −0.652407
\(708\) 9.30424 0.349675
\(709\) 4.04652 0.151970 0.0759851 0.997109i \(-0.475790\pi\)
0.0759851 + 0.997109i \(0.475790\pi\)
\(710\) 50.9141 1.91077
\(711\) −11.2628 −0.422389
\(712\) 17.7323 0.664547
\(713\) 20.8428 0.780571
\(714\) 6.55799 0.245427
\(715\) 5.72393 0.214063
\(716\) 8.73018 0.326262
\(717\) 45.4802 1.69849
\(718\) 64.1346 2.39348
\(719\) −35.8604 −1.33737 −0.668684 0.743546i \(-0.733142\pi\)
−0.668684 + 0.743546i \(0.733142\pi\)
\(720\) 6.89516 0.256967
\(721\) −23.9460 −0.891794
\(722\) 39.5839 1.47316
\(723\) 8.93958 0.332466
\(724\) 18.4192 0.684546
\(725\) −33.1381 −1.23072
\(726\) 33.4073 1.23986
\(727\) 35.7101 1.32441 0.662206 0.749322i \(-0.269620\pi\)
0.662206 + 0.749322i \(0.269620\pi\)
\(728\) −2.00695 −0.0743826
\(729\) 14.1249 0.523143
\(730\) 106.115 3.92750
\(731\) −11.0468 −0.408582
\(732\) 63.5847 2.35016
\(733\) −29.2357 −1.07985 −0.539923 0.841715i \(-0.681546\pi\)
−0.539923 + 0.841715i \(0.681546\pi\)
\(734\) 26.6584 0.983980
\(735\) 31.2482 1.15261
\(736\) 15.4722 0.570313
\(737\) 8.91269 0.328303
\(738\) 14.6355 0.538742
\(739\) 15.1785 0.558348 0.279174 0.960240i \(-0.409939\pi\)
0.279174 + 0.960240i \(0.409939\pi\)
\(740\) 29.8532 1.09742
\(741\) 1.57804 0.0579709
\(742\) 19.6819 0.722545
\(743\) −19.6363 −0.720385 −0.360193 0.932878i \(-0.617289\pi\)
−0.360193 + 0.932878i \(0.617289\pi\)
\(744\) −28.6800 −1.05146
\(745\) 12.1816 0.446300
\(746\) 7.93992 0.290701
\(747\) 5.89415 0.215656
\(748\) 5.01113 0.183225
\(749\) −16.4851 −0.602354
\(750\) 3.82770 0.139768
\(751\) −25.8769 −0.944262 −0.472131 0.881529i \(-0.656515\pi\)
−0.472131 + 0.881529i \(0.656515\pi\)
\(752\) −16.0661 −0.585869
\(753\) 60.3147 2.19799
\(754\) 13.5278 0.492655
\(755\) 47.9870 1.74643
\(756\) −15.6423 −0.568905
\(757\) 22.7535 0.826991 0.413496 0.910506i \(-0.364308\pi\)
0.413496 + 0.910506i \(0.364308\pi\)
\(758\) 65.7828 2.38934
\(759\) −7.09458 −0.257517
\(760\) 3.54171 0.128471
\(761\) −18.2672 −0.662186 −0.331093 0.943598i \(-0.607417\pi\)
−0.331093 + 0.943598i \(0.607417\pi\)
\(762\) 2.28236 0.0826811
\(763\) −12.3403 −0.446748
\(764\) −29.1268 −1.05377
\(765\) 3.18800 0.115262
\(766\) 0.538118 0.0194430
\(767\) 1.77323 0.0640277
\(768\) 2.80083 0.101066
\(769\) −37.9425 −1.36824 −0.684122 0.729368i \(-0.739814\pi\)
−0.684122 + 0.729368i \(0.739814\pi\)
\(770\) −17.8243 −0.642344
\(771\) −55.7613 −2.00820
\(772\) −67.8424 −2.44170
\(773\) 38.3058 1.37776 0.688882 0.724873i \(-0.258102\pi\)
0.688882 + 0.724873i \(0.258102\pi\)
\(774\) −21.0130 −0.755297
\(775\) 54.9398 1.97349
\(776\) −22.3101 −0.800886
\(777\) −10.0946 −0.362143
\(778\) 57.6683 2.06751
\(779\) −5.76535 −0.206565
\(780\) −16.8227 −0.602349
\(781\) −13.1554 −0.470737
\(782\) 4.58127 0.163826
\(783\) 25.6961 0.918305
\(784\) 11.2765 0.402734
\(785\) −12.8556 −0.458835
\(786\) −25.9964 −0.927259
\(787\) −1.44271 −0.0514271 −0.0257135 0.999669i \(-0.508186\pi\)
−0.0257135 + 0.999669i \(0.508186\pi\)
\(788\) 22.4014 0.798017
\(789\) −42.2903 −1.50557
\(790\) −83.0686 −2.95545
\(791\) 20.8486 0.741289
\(792\) 2.32307 0.0825467
\(793\) 12.1182 0.430329
\(794\) −18.2204 −0.646617
\(795\) 40.2070 1.42599
\(796\) −42.7569 −1.51548
\(797\) −4.73650 −0.167775 −0.0838877 0.996475i \(-0.526734\pi\)
−0.0838877 + 0.996475i \(0.526734\pi\)
\(798\) −4.91403 −0.173955
\(799\) −7.42820 −0.262791
\(800\) 40.7832 1.44190
\(801\) −11.9602 −0.422593
\(802\) 3.47720 0.122784
\(803\) −27.4185 −0.967578
\(804\) −26.1945 −0.923808
\(805\) −9.27829 −0.327017
\(806\) −22.4279 −0.789987
\(807\) −28.2688 −0.995109
\(808\) 16.6750 0.586625
\(809\) −53.6218 −1.88524 −0.942622 0.333863i \(-0.891648\pi\)
−0.942622 + 0.333863i \(0.891648\pi\)
\(810\) −75.5408 −2.65423
\(811\) −34.1003 −1.19742 −0.598711 0.800965i \(-0.704320\pi\)
−0.598711 + 0.800965i \(0.704320\pi\)
\(812\) −23.9856 −0.841731
\(813\) −14.9354 −0.523806
\(814\) −13.5473 −0.474832
\(815\) −7.75704 −0.271717
\(816\) 4.83455 0.169243
\(817\) 8.27761 0.289597
\(818\) 65.0415 2.27412
\(819\) 1.35366 0.0473007
\(820\) 61.4613 2.14632
\(821\) −1.52946 −0.0533784 −0.0266892 0.999644i \(-0.508496\pi\)
−0.0266892 + 0.999644i \(0.508496\pi\)
\(822\) 21.3022 0.742998
\(823\) −51.7188 −1.80281 −0.901403 0.432982i \(-0.857461\pi\)
−0.901403 + 0.432982i \(0.857461\pi\)
\(824\) 23.0181 0.801874
\(825\) −18.7006 −0.651072
\(826\) −5.52184 −0.192130
\(827\) 4.07925 0.141849 0.0709247 0.997482i \(-0.477405\pi\)
0.0709247 + 0.997482i \(0.477405\pi\)
\(828\) 4.96182 0.172435
\(829\) 8.70954 0.302495 0.151247 0.988496i \(-0.451671\pi\)
0.151247 + 0.988496i \(0.451671\pi\)
\(830\) 43.4720 1.50894
\(831\) 32.2731 1.11954
\(832\) −12.0575 −0.418018
\(833\) 5.21375 0.180646
\(834\) −9.79956 −0.339331
\(835\) −58.1693 −2.01303
\(836\) −3.75494 −0.129867
\(837\) −42.6017 −1.47253
\(838\) 2.34450 0.0809894
\(839\) −18.8791 −0.651779 −0.325890 0.945408i \(-0.605664\pi\)
−0.325890 + 0.945408i \(0.605664\pi\)
\(840\) 12.7670 0.440504
\(841\) 10.4020 0.358690
\(842\) −70.2206 −2.41996
\(843\) −30.7242 −1.05820
\(844\) 36.5895 1.25946
\(845\) −3.20612 −0.110294
\(846\) −14.1297 −0.485791
\(847\) −11.2888 −0.387888
\(848\) 14.5095 0.498259
\(849\) −49.3554 −1.69387
\(850\) 12.0758 0.414197
\(851\) −7.05191 −0.241736
\(852\) 38.6638 1.32460
\(853\) 46.2514 1.58362 0.791809 0.610769i \(-0.209140\pi\)
0.791809 + 0.610769i \(0.209140\pi\)
\(854\) −37.7360 −1.29130
\(855\) −2.38883 −0.0816964
\(856\) 15.8464 0.541618
\(857\) −25.9528 −0.886532 −0.443266 0.896390i \(-0.646180\pi\)
−0.443266 + 0.896390i \(0.646180\pi\)
\(858\) 7.63409 0.260623
\(859\) −44.9547 −1.53383 −0.766916 0.641747i \(-0.778210\pi\)
−0.766916 + 0.641747i \(0.778210\pi\)
\(860\) −88.2431 −3.00907
\(861\) −20.7827 −0.708274
\(862\) 34.6389 1.17981
\(863\) −14.1731 −0.482459 −0.241230 0.970468i \(-0.577551\pi\)
−0.241230 + 0.970468i \(0.577551\pi\)
\(864\) −31.6244 −1.07588
\(865\) 41.5720 1.41349
\(866\) 4.83869 0.164425
\(867\) −31.4952 −1.06963
\(868\) 39.7659 1.34974
\(869\) 21.4636 0.728103
\(870\) −86.0560 −2.91757
\(871\) −4.99222 −0.169155
\(872\) 11.8621 0.401702
\(873\) 15.0479 0.509293
\(874\) −3.43284 −0.116118
\(875\) −1.29344 −0.0437262
\(876\) 80.5832 2.72265
\(877\) 37.3884 1.26252 0.631258 0.775573i \(-0.282539\pi\)
0.631258 + 0.775573i \(0.282539\pi\)
\(878\) −28.6679 −0.967496
\(879\) 3.56919 0.120386
\(880\) −13.1401 −0.442953
\(881\) 32.6995 1.10167 0.550837 0.834613i \(-0.314309\pi\)
0.550837 + 0.834613i \(0.314309\pi\)
\(882\) 9.91747 0.333939
\(883\) −3.81884 −0.128514 −0.0642570 0.997933i \(-0.520468\pi\)
−0.0642570 + 0.997933i \(0.520468\pi\)
\(884\) −2.80686 −0.0944050
\(885\) −11.2802 −0.379181
\(886\) 30.0065 1.00809
\(887\) 10.6807 0.358622 0.179311 0.983792i \(-0.442613\pi\)
0.179311 + 0.983792i \(0.442613\pi\)
\(888\) 9.70350 0.325628
\(889\) −0.771242 −0.0258666
\(890\) −88.2119 −2.95687
\(891\) 19.5186 0.653896
\(892\) −11.2242 −0.375816
\(893\) 5.56610 0.186262
\(894\) 16.2468 0.543374
\(895\) −10.5843 −0.353793
\(896\) 15.2220 0.508531
\(897\) 3.97385 0.132683
\(898\) 23.5211 0.784908
\(899\) −65.3248 −2.17870
\(900\) 13.0789 0.435963
\(901\) 6.70852 0.223493
\(902\) −27.8910 −0.928668
\(903\) 29.8388 0.992974
\(904\) −20.0407 −0.666545
\(905\) −22.3310 −0.742309
\(906\) 64.0010 2.12629
\(907\) 44.5948 1.48075 0.740374 0.672195i \(-0.234649\pi\)
0.740374 + 0.672195i \(0.234649\pi\)
\(908\) 24.1844 0.802588
\(909\) −11.2471 −0.373041
\(910\) 9.98386 0.330962
\(911\) −4.95396 −0.164132 −0.0820660 0.996627i \(-0.526152\pi\)
−0.0820660 + 0.996627i \(0.526152\pi\)
\(912\) −3.62263 −0.119957
\(913\) −11.2325 −0.371741
\(914\) 61.6964 2.04074
\(915\) −77.0886 −2.54847
\(916\) −8.68025 −0.286803
\(917\) 8.78455 0.290091
\(918\) −9.36389 −0.309054
\(919\) −30.8533 −1.01776 −0.508878 0.860838i \(-0.669940\pi\)
−0.508878 + 0.860838i \(0.669940\pi\)
\(920\) 8.91878 0.294043
\(921\) −43.3116 −1.42717
\(922\) 32.0992 1.05713
\(923\) 7.36867 0.242543
\(924\) −13.5357 −0.445291
\(925\) −18.5882 −0.611175
\(926\) −22.6922 −0.745712
\(927\) −15.5254 −0.509921
\(928\) −48.4923 −1.59184
\(929\) −54.5545 −1.78988 −0.894938 0.446190i \(-0.852780\pi\)
−0.894938 + 0.446190i \(0.852780\pi\)
\(930\) 142.673 4.67842
\(931\) −3.90677 −0.128039
\(932\) −1.24392 −0.0407459
\(933\) −18.6073 −0.609177
\(934\) −40.9224 −1.33902
\(935\) −6.07538 −0.198686
\(936\) −1.30121 −0.0425314
\(937\) 41.4863 1.35530 0.677649 0.735385i \(-0.262999\pi\)
0.677649 + 0.735385i \(0.262999\pi\)
\(938\) 15.5458 0.507588
\(939\) 55.0188 1.79547
\(940\) −59.3372 −1.93537
\(941\) 28.4939 0.928873 0.464437 0.885606i \(-0.346257\pi\)
0.464437 + 0.885606i \(0.346257\pi\)
\(942\) −17.1457 −0.558636
\(943\) −14.5184 −0.472784
\(944\) −4.07071 −0.132490
\(945\) 18.9643 0.616910
\(946\) 40.0445 1.30196
\(947\) −53.0786 −1.72482 −0.862411 0.506208i \(-0.831047\pi\)
−0.862411 + 0.506208i \(0.831047\pi\)
\(948\) −63.0817 −2.04880
\(949\) 15.3578 0.498535
\(950\) −9.04864 −0.293577
\(951\) −10.6720 −0.346062
\(952\) 2.13018 0.0690394
\(953\) −24.5554 −0.795426 −0.397713 0.917510i \(-0.630196\pi\)
−0.397713 + 0.917510i \(0.630196\pi\)
\(954\) 12.7608 0.413146
\(955\) 35.3127 1.14269
\(956\) 60.6166 1.96048
\(957\) 22.2355 0.718772
\(958\) 28.7534 0.928979
\(959\) −7.19832 −0.232446
\(960\) 76.7026 2.47557
\(961\) 77.3022 2.49362
\(962\) 7.58817 0.244653
\(963\) −10.6882 −0.344421
\(964\) 11.9148 0.383749
\(965\) 82.2505 2.64774
\(966\) −12.3746 −0.398146
\(967\) −53.4093 −1.71753 −0.858763 0.512373i \(-0.828767\pi\)
−0.858763 + 0.512373i \(0.828767\pi\)
\(968\) 10.8514 0.348777
\(969\) −1.67493 −0.0538067
\(970\) 110.985 3.56350
\(971\) 43.7089 1.40269 0.701343 0.712824i \(-0.252584\pi\)
0.701343 + 0.712824i \(0.252584\pi\)
\(972\) −24.8885 −0.798298
\(973\) 3.31142 0.106159
\(974\) 4.77145 0.152887
\(975\) 10.4747 0.335459
\(976\) −27.8190 −0.890465
\(977\) 10.5564 0.337728 0.168864 0.985639i \(-0.445990\pi\)
0.168864 + 0.985639i \(0.445990\pi\)
\(978\) −10.3457 −0.330818
\(979\) 22.7926 0.728454
\(980\) 41.6480 1.33040
\(981\) −8.00083 −0.255447
\(982\) −0.141468 −0.00451441
\(983\) −8.85818 −0.282532 −0.141266 0.989972i \(-0.545117\pi\)
−0.141266 + 0.989972i \(0.545117\pi\)
\(984\) 19.9775 0.636858
\(985\) −27.1589 −0.865356
\(986\) −14.3584 −0.457266
\(987\) 20.0645 0.638659
\(988\) 2.10324 0.0669129
\(989\) 20.8448 0.662826
\(990\) −11.5564 −0.367287
\(991\) −6.95532 −0.220943 −0.110471 0.993879i \(-0.535236\pi\)
−0.110471 + 0.993879i \(0.535236\pi\)
\(992\) 80.3955 2.55256
\(993\) −10.4430 −0.331397
\(994\) −22.9460 −0.727804
\(995\) 51.8375 1.64336
\(996\) 33.0123 1.04604
\(997\) −28.0571 −0.888578 −0.444289 0.895883i \(-0.646544\pi\)
−0.444289 + 0.895883i \(0.646544\pi\)
\(998\) 75.4012 2.38678
\(999\) 14.4137 0.456031
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 \(a_p\))