Properties

Label 8027.2.a.f.1.8
Level 8027
Weight 2
Character 8027.1
Self dual Yes
Analytic conductor 64.096
Analytic rank 0
Dimension 176
CM No

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Newspace parameters

Level: \( N \) = \( 8027 = 23 \cdot 349 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8027.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0959177025\)
Analytic rank: \(0\)
Dimension: \(176\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Character \(\chi\) = 8027.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.63094 q^{2} -2.05461 q^{3} +4.92184 q^{4} -2.98457 q^{5} +5.40556 q^{6} +0.228878 q^{7} -7.68717 q^{8} +1.22144 q^{9} +O(q^{10})\) \(q-2.63094 q^{2} -2.05461 q^{3} +4.92184 q^{4} -2.98457 q^{5} +5.40556 q^{6} +0.228878 q^{7} -7.68717 q^{8} +1.22144 q^{9} +7.85221 q^{10} -4.45205 q^{11} -10.1125 q^{12} -3.16946 q^{13} -0.602164 q^{14} +6.13213 q^{15} +10.3808 q^{16} +0.815402 q^{17} -3.21353 q^{18} +2.49505 q^{19} -14.6895 q^{20} -0.470256 q^{21} +11.7131 q^{22} +1.00000 q^{23} +15.7942 q^{24} +3.90763 q^{25} +8.33867 q^{26} +3.65426 q^{27} +1.12650 q^{28} -0.608467 q^{29} -16.1333 q^{30} -3.75357 q^{31} -11.9369 q^{32} +9.14725 q^{33} -2.14527 q^{34} -0.683102 q^{35} +6.01172 q^{36} +8.00206 q^{37} -6.56433 q^{38} +6.51203 q^{39} +22.9429 q^{40} +10.8290 q^{41} +1.23721 q^{42} -0.440332 q^{43} -21.9123 q^{44} -3.64546 q^{45} -2.63094 q^{46} -10.5002 q^{47} -21.3285 q^{48} -6.94761 q^{49} -10.2807 q^{50} -1.67534 q^{51} -15.5996 q^{52} +0.700230 q^{53} -9.61413 q^{54} +13.2874 q^{55} -1.75943 q^{56} -5.12637 q^{57} +1.60084 q^{58} -12.5183 q^{59} +30.1813 q^{60} +8.02118 q^{61} +9.87540 q^{62} +0.279560 q^{63} +10.6437 q^{64} +9.45948 q^{65} -24.0659 q^{66} +15.0315 q^{67} +4.01328 q^{68} -2.05461 q^{69} +1.79720 q^{70} -16.7994 q^{71} -9.38940 q^{72} +3.78320 q^{73} -21.0529 q^{74} -8.02868 q^{75} +12.2802 q^{76} -1.01898 q^{77} -17.1327 q^{78} -3.19883 q^{79} -30.9822 q^{80} -11.1724 q^{81} -28.4905 q^{82} -6.21259 q^{83} -2.31452 q^{84} -2.43362 q^{85} +1.15849 q^{86} +1.25017 q^{87} +34.2237 q^{88} +0.573084 q^{89} +9.59099 q^{90} -0.725421 q^{91} +4.92184 q^{92} +7.71213 q^{93} +27.6254 q^{94} -7.44665 q^{95} +24.5257 q^{96} -8.68164 q^{97} +18.2787 q^{98} -5.43791 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 176q + 19q^{2} + 22q^{3} + 203q^{4} + 28q^{5} + 9q^{6} + 30q^{7} + 51q^{8} + 204q^{9} + O(q^{10}) \) \( 176q + 19q^{2} + 22q^{3} + 203q^{4} + 28q^{5} + 9q^{6} + 30q^{7} + 51q^{8} + 204q^{9} + 18q^{10} + 11q^{11} + 46q^{12} + 87q^{13} - 6q^{14} + 29q^{15} + 257q^{16} + 14q^{17} + 72q^{18} + 34q^{19} + 45q^{20} + 23q^{21} + 62q^{22} + 176q^{23} + 33q^{24} + 272q^{25} + 31q^{26} + 82q^{27} + 80q^{28} + 75q^{29} - 30q^{30} + 73q^{31} + 71q^{32} + 30q^{33} + 23q^{34} + 44q^{35} + 264q^{36} + 236q^{37} - 21q^{38} + 17q^{39} + 43q^{40} + 51q^{41} + 38q^{42} + 51q^{43} + 12q^{44} + 127q^{45} + 19q^{46} + 45q^{47} + 61q^{48} + 268q^{49} + 55q^{50} - 3q^{51} + 166q^{52} + 63q^{53} - 32q^{54} + 11q^{55} - 9q^{56} + 72q^{57} + 98q^{58} + 95q^{59} - 7q^{60} + 73q^{61} + 12q^{62} + 19q^{63} + 365q^{64} + 19q^{65} - 28q^{66} + 138q^{67} + 16q^{68} + 22q^{69} + 100q^{70} + 85q^{71} + 129q^{72} + 118q^{73} - 21q^{74} - 12q^{75} + 52q^{76} + 75q^{77} + 97q^{78} + 74q^{79} + 8q^{80} + 280q^{81} + 67q^{82} + 10q^{83} - 51q^{84} + 169q^{85} - 39q^{86} - 6q^{87} + 159q^{88} + 38q^{89} + 22q^{90} + 90q^{91} + 203q^{92} + 230q^{93} + 63q^{94} + 30q^{95} + 107q^{96} + 161q^{97} + 58q^{98} + 7q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.63094 −1.86035 −0.930177 0.367111i \(-0.880347\pi\)
−0.930177 + 0.367111i \(0.880347\pi\)
\(3\) −2.05461 −1.18623 −0.593116 0.805117i \(-0.702102\pi\)
−0.593116 + 0.805117i \(0.702102\pi\)
\(4\) 4.92184 2.46092
\(5\) −2.98457 −1.33474 −0.667369 0.744727i \(-0.732580\pi\)
−0.667369 + 0.744727i \(0.732580\pi\)
\(6\) 5.40556 2.20681
\(7\) 0.228878 0.0865078 0.0432539 0.999064i \(-0.486228\pi\)
0.0432539 + 0.999064i \(0.486228\pi\)
\(8\) −7.68717 −2.71783
\(9\) 1.22144 0.407146
\(10\) 7.85221 2.48309
\(11\) −4.45205 −1.34234 −0.671172 0.741301i \(-0.734209\pi\)
−0.671172 + 0.741301i \(0.734209\pi\)
\(12\) −10.1125 −2.91922
\(13\) −3.16946 −0.879051 −0.439526 0.898230i \(-0.644853\pi\)
−0.439526 + 0.898230i \(0.644853\pi\)
\(14\) −0.602164 −0.160935
\(15\) 6.13213 1.58331
\(16\) 10.3808 2.59520
\(17\) 0.815402 0.197764 0.0988820 0.995099i \(-0.468473\pi\)
0.0988820 + 0.995099i \(0.468473\pi\)
\(18\) −3.21353 −0.757436
\(19\) 2.49505 0.572405 0.286202 0.958169i \(-0.407607\pi\)
0.286202 + 0.958169i \(0.407607\pi\)
\(20\) −14.6895 −3.28468
\(21\) −0.470256 −0.102618
\(22\) 11.7131 2.49724
\(23\) 1.00000 0.208514
\(24\) 15.7942 3.22397
\(25\) 3.90763 0.781527
\(26\) 8.33867 1.63535
\(27\) 3.65426 0.703262
\(28\) 1.12650 0.212889
\(29\) −0.608467 −0.112990 −0.0564948 0.998403i \(-0.517992\pi\)
−0.0564948 + 0.998403i \(0.517992\pi\)
\(30\) −16.1333 −2.94552
\(31\) −3.75357 −0.674160 −0.337080 0.941476i \(-0.609439\pi\)
−0.337080 + 0.941476i \(0.609439\pi\)
\(32\) −11.9369 −2.11017
\(33\) 9.14725 1.59233
\(34\) −2.14527 −0.367911
\(35\) −0.683102 −0.115465
\(36\) 6.01172 1.00195
\(37\) 8.00206 1.31553 0.657766 0.753223i \(-0.271502\pi\)
0.657766 + 0.753223i \(0.271502\pi\)
\(38\) −6.56433 −1.06488
\(39\) 6.51203 1.04276
\(40\) 22.9429 3.62759
\(41\) 10.8290 1.69121 0.845603 0.533812i \(-0.179241\pi\)
0.845603 + 0.533812i \(0.179241\pi\)
\(42\) 1.23721 0.190906
\(43\) −0.440332 −0.0671500 −0.0335750 0.999436i \(-0.510689\pi\)
−0.0335750 + 0.999436i \(0.510689\pi\)
\(44\) −21.9123 −3.30340
\(45\) −3.64546 −0.543434
\(46\) −2.63094 −0.387911
\(47\) −10.5002 −1.53161 −0.765806 0.643071i \(-0.777660\pi\)
−0.765806 + 0.643071i \(0.777660\pi\)
\(48\) −21.3285 −3.07851
\(49\) −6.94761 −0.992516
\(50\) −10.2807 −1.45392
\(51\) −1.67534 −0.234594
\(52\) −15.5996 −2.16327
\(53\) 0.700230 0.0961839 0.0480920 0.998843i \(-0.484686\pi\)
0.0480920 + 0.998843i \(0.484686\pi\)
\(54\) −9.61413 −1.30832
\(55\) 13.2874 1.79168
\(56\) −1.75943 −0.235113
\(57\) −5.12637 −0.679005
\(58\) 1.60084 0.210201
\(59\) −12.5183 −1.62974 −0.814872 0.579641i \(-0.803193\pi\)
−0.814872 + 0.579641i \(0.803193\pi\)
\(60\) 30.1813 3.89639
\(61\) 8.02118 1.02701 0.513503 0.858088i \(-0.328347\pi\)
0.513503 + 0.858088i \(0.328347\pi\)
\(62\) 9.87540 1.25418
\(63\) 0.279560 0.0352213
\(64\) 10.6437 1.33046
\(65\) 9.45948 1.17330
\(66\) −24.0659 −2.96230
\(67\) 15.0315 1.83640 0.918198 0.396122i \(-0.129644\pi\)
0.918198 + 0.396122i \(0.129644\pi\)
\(68\) 4.01328 0.486681
\(69\) −2.05461 −0.247346
\(70\) 1.79720 0.214806
\(71\) −16.7994 −1.99372 −0.996858 0.0792058i \(-0.974762\pi\)
−0.996858 + 0.0792058i \(0.974762\pi\)
\(72\) −9.38940 −1.10655
\(73\) 3.78320 0.442791 0.221395 0.975184i \(-0.428939\pi\)
0.221395 + 0.975184i \(0.428939\pi\)
\(74\) −21.0529 −2.44735
\(75\) −8.02868 −0.927072
\(76\) 12.2802 1.40864
\(77\) −1.01898 −0.116123
\(78\) −17.1327 −1.93990
\(79\) −3.19883 −0.359896 −0.179948 0.983676i \(-0.557593\pi\)
−0.179948 + 0.983676i \(0.557593\pi\)
\(80\) −30.9822 −3.46391
\(81\) −11.1724 −1.24138
\(82\) −28.4905 −3.14624
\(83\) −6.21259 −0.681921 −0.340960 0.940078i \(-0.610752\pi\)
−0.340960 + 0.940078i \(0.610752\pi\)
\(84\) −2.31452 −0.252535
\(85\) −2.43362 −0.263963
\(86\) 1.15849 0.124923
\(87\) 1.25017 0.134032
\(88\) 34.2237 3.64826
\(89\) 0.573084 0.0607468 0.0303734 0.999539i \(-0.490330\pi\)
0.0303734 + 0.999539i \(0.490330\pi\)
\(90\) 9.59099 1.01098
\(91\) −0.725421 −0.0760448
\(92\) 4.92184 0.513137
\(93\) 7.71213 0.799711
\(94\) 27.6254 2.84934
\(95\) −7.44665 −0.764010
\(96\) 24.5257 2.50315
\(97\) −8.68164 −0.881487 −0.440743 0.897633i \(-0.645285\pi\)
−0.440743 + 0.897633i \(0.645285\pi\)
\(98\) 18.2787 1.84643
\(99\) −5.43791 −0.546530
\(100\) 19.2327 1.92327
\(101\) −2.87422 −0.285996 −0.142998 0.989723i \(-0.545674\pi\)
−0.142998 + 0.989723i \(0.545674\pi\)
\(102\) 4.40771 0.436428
\(103\) −4.19722 −0.413564 −0.206782 0.978387i \(-0.566299\pi\)
−0.206782 + 0.978387i \(0.566299\pi\)
\(104\) 24.3642 2.38911
\(105\) 1.40351 0.136969
\(106\) −1.84226 −0.178936
\(107\) −4.71951 −0.456252 −0.228126 0.973632i \(-0.573260\pi\)
−0.228126 + 0.973632i \(0.573260\pi\)
\(108\) 17.9857 1.73067
\(109\) −10.5394 −1.00949 −0.504745 0.863269i \(-0.668413\pi\)
−0.504745 + 0.863269i \(0.668413\pi\)
\(110\) −34.9585 −3.33316
\(111\) −16.4412 −1.56052
\(112\) 2.37594 0.224505
\(113\) −11.7957 −1.10964 −0.554822 0.831969i \(-0.687214\pi\)
−0.554822 + 0.831969i \(0.687214\pi\)
\(114\) 13.4872 1.26319
\(115\) −2.98457 −0.278312
\(116\) −2.99478 −0.278058
\(117\) −3.87131 −0.357902
\(118\) 32.9349 3.03190
\(119\) 0.186628 0.0171081
\(120\) −47.1387 −4.30316
\(121\) 8.82078 0.801889
\(122\) −21.1032 −1.91060
\(123\) −22.2494 −2.00616
\(124\) −18.4744 −1.65905
\(125\) 3.26024 0.291604
\(126\) −0.735506 −0.0655241
\(127\) −9.67470 −0.858491 −0.429245 0.903188i \(-0.641220\pi\)
−0.429245 + 0.903188i \(0.641220\pi\)
\(128\) −4.12899 −0.364954
\(129\) 0.904712 0.0796555
\(130\) −24.8873 −2.18276
\(131\) 10.9994 0.961019 0.480510 0.876989i \(-0.340452\pi\)
0.480510 + 0.876989i \(0.340452\pi\)
\(132\) 45.0213 3.91860
\(133\) 0.571063 0.0495175
\(134\) −39.5471 −3.41635
\(135\) −10.9064 −0.938671
\(136\) −6.26813 −0.537488
\(137\) 15.6571 1.33767 0.668837 0.743409i \(-0.266792\pi\)
0.668837 + 0.743409i \(0.266792\pi\)
\(138\) 5.40556 0.460152
\(139\) −17.2793 −1.46561 −0.732807 0.680437i \(-0.761790\pi\)
−0.732807 + 0.680437i \(0.761790\pi\)
\(140\) −3.36212 −0.284151
\(141\) 21.5739 1.81685
\(142\) 44.1981 3.70902
\(143\) 14.1106 1.17999
\(144\) 12.6795 1.05663
\(145\) 1.81601 0.150811
\(146\) −9.95338 −0.823747
\(147\) 14.2747 1.17735
\(148\) 39.3848 3.23741
\(149\) −8.30005 −0.679967 −0.339983 0.940431i \(-0.610421\pi\)
−0.339983 + 0.940431i \(0.610421\pi\)
\(150\) 21.1230 1.72468
\(151\) 8.26813 0.672851 0.336425 0.941710i \(-0.390782\pi\)
0.336425 + 0.941710i \(0.390782\pi\)
\(152\) −19.1799 −1.55570
\(153\) 0.995963 0.0805189
\(154\) 2.68087 0.216030
\(155\) 11.2028 0.899828
\(156\) 32.0511 2.56614
\(157\) 21.4572 1.71247 0.856235 0.516587i \(-0.172798\pi\)
0.856235 + 0.516587i \(0.172798\pi\)
\(158\) 8.41591 0.669534
\(159\) −1.43870 −0.114096
\(160\) 35.6265 2.81652
\(161\) 0.228878 0.0180381
\(162\) 29.3939 2.30940
\(163\) −5.12274 −0.401244 −0.200622 0.979669i \(-0.564296\pi\)
−0.200622 + 0.979669i \(0.564296\pi\)
\(164\) 53.2986 4.16192
\(165\) −27.3006 −2.12535
\(166\) 16.3449 1.26861
\(167\) 22.3880 1.73244 0.866220 0.499663i \(-0.166543\pi\)
0.866220 + 0.499663i \(0.166543\pi\)
\(168\) 3.61494 0.278899
\(169\) −2.95449 −0.227269
\(170\) 6.40271 0.491065
\(171\) 3.04755 0.233052
\(172\) −2.16724 −0.165251
\(173\) −0.230581 −0.0175308 −0.00876538 0.999962i \(-0.502790\pi\)
−0.00876538 + 0.999962i \(0.502790\pi\)
\(174\) −3.28911 −0.249347
\(175\) 0.894372 0.0676082
\(176\) −46.2159 −3.48365
\(177\) 25.7203 1.93325
\(178\) −1.50775 −0.113010
\(179\) −13.1701 −0.984379 −0.492190 0.870488i \(-0.663803\pi\)
−0.492190 + 0.870488i \(0.663803\pi\)
\(180\) −17.9424 −1.33735
\(181\) −22.5609 −1.67694 −0.838470 0.544948i \(-0.816549\pi\)
−0.838470 + 0.544948i \(0.816549\pi\)
\(182\) 1.90854 0.141470
\(183\) −16.4804 −1.21827
\(184\) −7.68717 −0.566706
\(185\) −23.8827 −1.75589
\(186\) −20.2901 −1.48775
\(187\) −3.63021 −0.265468
\(188\) −51.6803 −3.76917
\(189\) 0.836380 0.0608377
\(190\) 19.5917 1.42133
\(191\) −11.5402 −0.835021 −0.417511 0.908672i \(-0.637097\pi\)
−0.417511 + 0.908672i \(0.637097\pi\)
\(192\) −21.8686 −1.57823
\(193\) −1.13217 −0.0814954 −0.0407477 0.999169i \(-0.512974\pi\)
−0.0407477 + 0.999169i \(0.512974\pi\)
\(194\) 22.8408 1.63988
\(195\) −19.4356 −1.39181
\(196\) −34.1950 −2.44250
\(197\) 3.69105 0.262977 0.131488 0.991318i \(-0.458024\pi\)
0.131488 + 0.991318i \(0.458024\pi\)
\(198\) 14.3068 1.01674
\(199\) −3.35641 −0.237930 −0.118965 0.992898i \(-0.537958\pi\)
−0.118965 + 0.992898i \(0.537958\pi\)
\(200\) −30.0387 −2.12405
\(201\) −30.8840 −2.17839
\(202\) 7.56191 0.532054
\(203\) −0.139265 −0.00977447
\(204\) −8.24573 −0.577317
\(205\) −32.3199 −2.25732
\(206\) 11.0426 0.769376
\(207\) 1.22144 0.0848958
\(208\) −32.9016 −2.28131
\(209\) −11.1081 −0.768364
\(210\) −3.69255 −0.254810
\(211\) 25.5631 1.75984 0.879920 0.475122i \(-0.157596\pi\)
0.879920 + 0.475122i \(0.157596\pi\)
\(212\) 3.44642 0.236701
\(213\) 34.5162 2.36501
\(214\) 12.4167 0.848790
\(215\) 1.31420 0.0896277
\(216\) −28.0909 −1.91134
\(217\) −0.859109 −0.0583201
\(218\) 27.7285 1.87801
\(219\) −7.77303 −0.525252
\(220\) 65.3986 4.40918
\(221\) −2.58439 −0.173845
\(222\) 43.2557 2.90313
\(223\) −23.6936 −1.58664 −0.793321 0.608804i \(-0.791650\pi\)
−0.793321 + 0.608804i \(0.791650\pi\)
\(224\) −2.73210 −0.182546
\(225\) 4.77293 0.318196
\(226\) 31.0337 2.06433
\(227\) −6.21504 −0.412506 −0.206253 0.978499i \(-0.566127\pi\)
−0.206253 + 0.978499i \(0.566127\pi\)
\(228\) −25.2312 −1.67097
\(229\) −17.7950 −1.17593 −0.587964 0.808887i \(-0.700070\pi\)
−0.587964 + 0.808887i \(0.700070\pi\)
\(230\) 7.85221 0.517759
\(231\) 2.09361 0.137749
\(232\) 4.67739 0.307086
\(233\) −17.0964 −1.12002 −0.560012 0.828485i \(-0.689203\pi\)
−0.560012 + 0.828485i \(0.689203\pi\)
\(234\) 10.1852 0.665825
\(235\) 31.3386 2.04430
\(236\) −61.6130 −4.01067
\(237\) 6.57235 0.426920
\(238\) −0.491006 −0.0318272
\(239\) −6.87581 −0.444759 −0.222380 0.974960i \(-0.571382\pi\)
−0.222380 + 0.974960i \(0.571382\pi\)
\(240\) 63.6564 4.10900
\(241\) −20.7952 −1.33953 −0.669767 0.742571i \(-0.733606\pi\)
−0.669767 + 0.742571i \(0.733606\pi\)
\(242\) −23.2069 −1.49180
\(243\) 11.9922 0.769300
\(244\) 39.4789 2.52738
\(245\) 20.7356 1.32475
\(246\) 58.5369 3.73217
\(247\) −7.90798 −0.503173
\(248\) 28.8543 1.83225
\(249\) 12.7645 0.808916
\(250\) −8.57748 −0.542488
\(251\) −6.31715 −0.398735 −0.199368 0.979925i \(-0.563889\pi\)
−0.199368 + 0.979925i \(0.563889\pi\)
\(252\) 1.37595 0.0866768
\(253\) −4.45205 −0.279898
\(254\) 25.4535 1.59710
\(255\) 5.00015 0.313122
\(256\) −10.4242 −0.651512
\(257\) −30.5067 −1.90295 −0.951477 0.307719i \(-0.900434\pi\)
−0.951477 + 0.307719i \(0.900434\pi\)
\(258\) −2.38024 −0.148187
\(259\) 1.83150 0.113804
\(260\) 46.5580 2.88740
\(261\) −0.743205 −0.0460032
\(262\) −28.9387 −1.78784
\(263\) 5.22419 0.322137 0.161069 0.986943i \(-0.448506\pi\)
0.161069 + 0.986943i \(0.448506\pi\)
\(264\) −70.3165 −4.32768
\(265\) −2.08988 −0.128380
\(266\) −1.50243 −0.0921200
\(267\) −1.17747 −0.0720597
\(268\) 73.9828 4.51922
\(269\) −15.4095 −0.939534 −0.469767 0.882790i \(-0.655662\pi\)
−0.469767 + 0.882790i \(0.655662\pi\)
\(270\) 28.6940 1.74626
\(271\) 22.6210 1.37413 0.687063 0.726598i \(-0.258900\pi\)
0.687063 + 0.726598i \(0.258900\pi\)
\(272\) 8.46453 0.513237
\(273\) 1.49046 0.0902067
\(274\) −41.1928 −2.48855
\(275\) −17.3970 −1.04908
\(276\) −10.1125 −0.608699
\(277\) −9.40141 −0.564876 −0.282438 0.959286i \(-0.591143\pi\)
−0.282438 + 0.959286i \(0.591143\pi\)
\(278\) 45.4608 2.72656
\(279\) −4.58475 −0.274482
\(280\) 5.25112 0.313814
\(281\) 7.07424 0.422014 0.211007 0.977485i \(-0.432326\pi\)
0.211007 + 0.977485i \(0.432326\pi\)
\(282\) −56.7595 −3.37998
\(283\) −1.32472 −0.0787466 −0.0393733 0.999225i \(-0.512536\pi\)
−0.0393733 + 0.999225i \(0.512536\pi\)
\(284\) −82.6837 −4.90637
\(285\) 15.3000 0.906293
\(286\) −37.1242 −2.19520
\(287\) 2.47852 0.146303
\(288\) −14.5802 −0.859146
\(289\) −16.3351 −0.960889
\(290\) −4.77781 −0.280563
\(291\) 17.8374 1.04565
\(292\) 18.6203 1.08967
\(293\) 31.7535 1.85506 0.927529 0.373751i \(-0.121929\pi\)
0.927529 + 0.373751i \(0.121929\pi\)
\(294\) −37.5558 −2.19030
\(295\) 37.3617 2.17528
\(296\) −61.5132 −3.57538
\(297\) −16.2690 −0.944020
\(298\) 21.8369 1.26498
\(299\) −3.16946 −0.183295
\(300\) −39.5159 −2.28145
\(301\) −0.100782 −0.00580900
\(302\) −21.7529 −1.25174
\(303\) 5.90542 0.339258
\(304\) 25.9007 1.48550
\(305\) −23.9397 −1.37079
\(306\) −2.62032 −0.149794
\(307\) −4.30086 −0.245463 −0.122732 0.992440i \(-0.539165\pi\)
−0.122732 + 0.992440i \(0.539165\pi\)
\(308\) −5.01524 −0.285770
\(309\) 8.62366 0.490583
\(310\) −29.4738 −1.67400
\(311\) −13.9944 −0.793547 −0.396774 0.917916i \(-0.629870\pi\)
−0.396774 + 0.917916i \(0.629870\pi\)
\(312\) −50.0591 −2.83404
\(313\) 9.97013 0.563545 0.281773 0.959481i \(-0.409078\pi\)
0.281773 + 0.959481i \(0.409078\pi\)
\(314\) −56.4525 −3.18580
\(315\) −0.834367 −0.0470112
\(316\) −15.7441 −0.885675
\(317\) −22.8673 −1.28435 −0.642177 0.766556i \(-0.721969\pi\)
−0.642177 + 0.766556i \(0.721969\pi\)
\(318\) 3.78514 0.212260
\(319\) 2.70893 0.151671
\(320\) −31.7667 −1.77581
\(321\) 9.69677 0.541221
\(322\) −0.602164 −0.0335573
\(323\) 2.03447 0.113201
\(324\) −54.9887 −3.05493
\(325\) −12.3851 −0.687002
\(326\) 13.4776 0.746456
\(327\) 21.6544 1.19749
\(328\) −83.2444 −4.59640
\(329\) −2.40327 −0.132496
\(330\) 71.8261 3.95390
\(331\) 26.6590 1.46531 0.732655 0.680600i \(-0.238281\pi\)
0.732655 + 0.680600i \(0.238281\pi\)
\(332\) −30.5774 −1.67815
\(333\) 9.77403 0.535613
\(334\) −58.9016 −3.22295
\(335\) −44.8626 −2.45111
\(336\) −4.88163 −0.266315
\(337\) −19.7403 −1.07532 −0.537660 0.843161i \(-0.680692\pi\)
−0.537660 + 0.843161i \(0.680692\pi\)
\(338\) 7.77309 0.422801
\(339\) 24.2356 1.31629
\(340\) −11.9779 −0.649592
\(341\) 16.7111 0.904956
\(342\) −8.01793 −0.433560
\(343\) −3.19230 −0.172368
\(344\) 3.38491 0.182502
\(345\) 6.13213 0.330143
\(346\) 0.606645 0.0326134
\(347\) −13.8804 −0.745138 −0.372569 0.928004i \(-0.621523\pi\)
−0.372569 + 0.928004i \(0.621523\pi\)
\(348\) 6.15311 0.329841
\(349\) −1.00000 −0.0535288
\(350\) −2.35304 −0.125775
\(351\) −11.5820 −0.618204
\(352\) 53.1437 2.83257
\(353\) 9.75402 0.519154 0.259577 0.965722i \(-0.416417\pi\)
0.259577 + 0.965722i \(0.416417\pi\)
\(354\) −67.6684 −3.59654
\(355\) 50.1388 2.66109
\(356\) 2.82062 0.149493
\(357\) −0.383448 −0.0202942
\(358\) 34.6497 1.83129
\(359\) −16.4800 −0.869782 −0.434891 0.900483i \(-0.643213\pi\)
−0.434891 + 0.900483i \(0.643213\pi\)
\(360\) 28.0233 1.47696
\(361\) −12.7747 −0.672353
\(362\) 59.3564 3.11970
\(363\) −18.1233 −0.951226
\(364\) −3.57040 −0.187140
\(365\) −11.2912 −0.591010
\(366\) 43.3590 2.26641
\(367\) −7.70470 −0.402182 −0.201091 0.979573i \(-0.564449\pi\)
−0.201091 + 0.979573i \(0.564449\pi\)
\(368\) 10.3808 0.541137
\(369\) 13.2270 0.688568
\(370\) 62.8339 3.26658
\(371\) 0.160267 0.00832066
\(372\) 37.9578 1.96802
\(373\) 12.6023 0.652525 0.326262 0.945279i \(-0.394211\pi\)
0.326262 + 0.945279i \(0.394211\pi\)
\(374\) 9.55087 0.493864
\(375\) −6.69853 −0.345910
\(376\) 80.7169 4.16266
\(377\) 1.92852 0.0993236
\(378\) −2.20046 −0.113180
\(379\) 10.9700 0.563489 0.281745 0.959489i \(-0.409087\pi\)
0.281745 + 0.959489i \(0.409087\pi\)
\(380\) −36.6512 −1.88017
\(381\) 19.8778 1.01837
\(382\) 30.3616 1.55344
\(383\) 24.1547 1.23425 0.617123 0.786867i \(-0.288298\pi\)
0.617123 + 0.786867i \(0.288298\pi\)
\(384\) 8.48347 0.432920
\(385\) 3.04121 0.154994
\(386\) 2.97867 0.151610
\(387\) −0.537838 −0.0273399
\(388\) −42.7296 −2.16927
\(389\) 7.28676 0.369454 0.184727 0.982790i \(-0.440860\pi\)
0.184727 + 0.982790i \(0.440860\pi\)
\(390\) 51.1338 2.58926
\(391\) 0.815402 0.0412367
\(392\) 53.4075 2.69749
\(393\) −22.5995 −1.13999
\(394\) −9.71093 −0.489230
\(395\) 9.54711 0.480367
\(396\) −26.7645 −1.34497
\(397\) −10.8698 −0.545542 −0.272771 0.962079i \(-0.587940\pi\)
−0.272771 + 0.962079i \(0.587940\pi\)
\(398\) 8.83052 0.442634
\(399\) −1.17331 −0.0587392
\(400\) 40.5644 2.02822
\(401\) −19.8380 −0.990663 −0.495331 0.868704i \(-0.664953\pi\)
−0.495331 + 0.868704i \(0.664953\pi\)
\(402\) 81.2540 4.05258
\(403\) 11.8968 0.592622
\(404\) −14.1465 −0.703813
\(405\) 33.3448 1.65692
\(406\) 0.366397 0.0181840
\(407\) −35.6256 −1.76590
\(408\) 12.8786 0.637586
\(409\) 16.4458 0.813193 0.406597 0.913608i \(-0.366715\pi\)
0.406597 + 0.913608i \(0.366715\pi\)
\(410\) 85.0316 4.19941
\(411\) −32.1692 −1.58679
\(412\) −20.6580 −1.01775
\(413\) −2.86516 −0.140986
\(414\) −3.21353 −0.157936
\(415\) 18.5419 0.910186
\(416\) 37.8336 1.85494
\(417\) 35.5023 1.73856
\(418\) 29.2248 1.42943
\(419\) 14.1447 0.691012 0.345506 0.938417i \(-0.387707\pi\)
0.345506 + 0.938417i \(0.387707\pi\)
\(420\) 6.90785 0.337069
\(421\) 2.57159 0.125332 0.0626658 0.998035i \(-0.480040\pi\)
0.0626658 + 0.998035i \(0.480040\pi\)
\(422\) −67.2551 −3.27393
\(423\) −12.8254 −0.623590
\(424\) −5.38278 −0.261411
\(425\) 3.18629 0.154558
\(426\) −90.8100 −4.39976
\(427\) 1.83587 0.0888441
\(428\) −23.2286 −1.12280
\(429\) −28.9919 −1.39974
\(430\) −3.45758 −0.166739
\(431\) −39.6491 −1.90983 −0.954915 0.296879i \(-0.904054\pi\)
−0.954915 + 0.296879i \(0.904054\pi\)
\(432\) 37.9341 1.82511
\(433\) −30.4796 −1.46476 −0.732379 0.680897i \(-0.761590\pi\)
−0.732379 + 0.680897i \(0.761590\pi\)
\(434\) 2.26026 0.108496
\(435\) −3.73120 −0.178897
\(436\) −51.8731 −2.48427
\(437\) 2.49505 0.119355
\(438\) 20.4503 0.977155
\(439\) −15.9366 −0.760615 −0.380307 0.924860i \(-0.624182\pi\)
−0.380307 + 0.924860i \(0.624182\pi\)
\(440\) −102.143 −4.86947
\(441\) −8.48608 −0.404099
\(442\) 6.79937 0.323413
\(443\) −2.43015 −0.115460 −0.0577298 0.998332i \(-0.518386\pi\)
−0.0577298 + 0.998332i \(0.518386\pi\)
\(444\) −80.9207 −3.84032
\(445\) −1.71041 −0.0810810
\(446\) 62.3364 2.95172
\(447\) 17.0534 0.806598
\(448\) 2.43610 0.115095
\(449\) −19.9848 −0.943143 −0.471571 0.881828i \(-0.656313\pi\)
−0.471571 + 0.881828i \(0.656313\pi\)
\(450\) −12.5573 −0.591957
\(451\) −48.2113 −2.27018
\(452\) −58.0564 −2.73074
\(453\) −16.9878 −0.798157
\(454\) 16.3514 0.767408
\(455\) 2.16507 0.101500
\(456\) 39.4073 1.84542
\(457\) 0.626530 0.0293078 0.0146539 0.999893i \(-0.495335\pi\)
0.0146539 + 0.999893i \(0.495335\pi\)
\(458\) 46.8176 2.18764
\(459\) 2.97969 0.139080
\(460\) −14.6895 −0.684904
\(461\) 19.4873 0.907616 0.453808 0.891099i \(-0.350065\pi\)
0.453808 + 0.891099i \(0.350065\pi\)
\(462\) −5.50815 −0.256262
\(463\) 38.4685 1.78778 0.893892 0.448283i \(-0.147964\pi\)
0.893892 + 0.448283i \(0.147964\pi\)
\(464\) −6.31638 −0.293230
\(465\) −23.0174 −1.06740
\(466\) 44.9796 2.08364
\(467\) −33.6159 −1.55556 −0.777778 0.628539i \(-0.783653\pi\)
−0.777778 + 0.628539i \(0.783653\pi\)
\(468\) −19.0539 −0.880768
\(469\) 3.44039 0.158863
\(470\) −82.4498 −3.80313
\(471\) −44.0862 −2.03139
\(472\) 96.2303 4.42936
\(473\) 1.96038 0.0901384
\(474\) −17.2915 −0.794223
\(475\) 9.74976 0.447350
\(476\) 0.918551 0.0421017
\(477\) 0.855287 0.0391609
\(478\) 18.0898 0.827410
\(479\) 17.9263 0.819072 0.409536 0.912294i \(-0.365691\pi\)
0.409536 + 0.912294i \(0.365691\pi\)
\(480\) −73.1986 −3.34105
\(481\) −25.3623 −1.15642
\(482\) 54.7108 2.49201
\(483\) −0.470256 −0.0213974
\(484\) 43.4144 1.97338
\(485\) 25.9109 1.17655
\(486\) −31.5507 −1.43117
\(487\) −0.128777 −0.00583546 −0.00291773 0.999996i \(-0.500929\pi\)
−0.00291773 + 0.999996i \(0.500929\pi\)
\(488\) −61.6602 −2.79122
\(489\) 10.5253 0.475969
\(490\) −54.5541 −2.46450
\(491\) −15.6854 −0.707872 −0.353936 0.935270i \(-0.615157\pi\)
−0.353936 + 0.935270i \(0.615157\pi\)
\(492\) −109.508 −4.93700
\(493\) −0.496145 −0.0223453
\(494\) 20.8054 0.936080
\(495\) 16.2298 0.729475
\(496\) −38.9650 −1.74958
\(497\) −3.84500 −0.172472
\(498\) −33.5826 −1.50487
\(499\) −3.37144 −0.150926 −0.0754632 0.997149i \(-0.524044\pi\)
−0.0754632 + 0.997149i \(0.524044\pi\)
\(500\) 16.0464 0.717615
\(501\) −45.9988 −2.05507
\(502\) 16.6200 0.741789
\(503\) −30.0034 −1.33779 −0.668894 0.743358i \(-0.733232\pi\)
−0.668894 + 0.743358i \(0.733232\pi\)
\(504\) −2.14903 −0.0957254
\(505\) 8.57831 0.381730
\(506\) 11.7131 0.520710
\(507\) 6.07035 0.269594
\(508\) −47.6173 −2.11268
\(509\) −28.6795 −1.27120 −0.635598 0.772020i \(-0.719246\pi\)
−0.635598 + 0.772020i \(0.719246\pi\)
\(510\) −13.1551 −0.582517
\(511\) 0.865893 0.0383048
\(512\) 35.6834 1.57700
\(513\) 9.11757 0.402550
\(514\) 80.2612 3.54017
\(515\) 12.5269 0.552000
\(516\) 4.45285 0.196026
\(517\) 46.7475 2.05595
\(518\) −4.81856 −0.211715
\(519\) 0.473755 0.0207955
\(520\) −72.7166 −3.18883
\(521\) −40.1973 −1.76108 −0.880538 0.473975i \(-0.842819\pi\)
−0.880538 + 0.473975i \(0.842819\pi\)
\(522\) 1.95533 0.0855823
\(523\) −17.7048 −0.774175 −0.387087 0.922043i \(-0.626519\pi\)
−0.387087 + 0.922043i \(0.626519\pi\)
\(524\) 54.1371 2.36499
\(525\) −1.83759 −0.0801990
\(526\) −13.7445 −0.599289
\(527\) −3.06067 −0.133325
\(528\) 94.9558 4.13242
\(529\) 1.00000 0.0434783
\(530\) 5.49835 0.238833
\(531\) −15.2903 −0.663544
\(532\) 2.81068 0.121858
\(533\) −34.3222 −1.48666
\(534\) 3.09784 0.134057
\(535\) 14.0857 0.608977
\(536\) −115.550 −4.99100
\(537\) 27.0595 1.16770
\(538\) 40.5415 1.74787
\(539\) 30.9312 1.33230
\(540\) −53.6794 −2.30999
\(541\) 5.59650 0.240612 0.120306 0.992737i \(-0.461612\pi\)
0.120306 + 0.992737i \(0.461612\pi\)
\(542\) −59.5144 −2.55636
\(543\) 46.3540 1.98924
\(544\) −9.73337 −0.417315
\(545\) 31.4555 1.34740
\(546\) −3.92131 −0.167817
\(547\) −22.2762 −0.952462 −0.476231 0.879320i \(-0.657997\pi\)
−0.476231 + 0.879320i \(0.657997\pi\)
\(548\) 77.0616 3.29191
\(549\) 9.79737 0.418142
\(550\) 45.7704 1.95166
\(551\) −1.51816 −0.0646757
\(552\) 15.7942 0.672244
\(553\) −0.732141 −0.0311338
\(554\) 24.7345 1.05087
\(555\) 49.0697 2.08289
\(556\) −85.0460 −3.60675
\(557\) 39.0311 1.65380 0.826900 0.562349i \(-0.190102\pi\)
0.826900 + 0.562349i \(0.190102\pi\)
\(558\) 12.0622 0.510633
\(559\) 1.39562 0.0590283
\(560\) −7.09114 −0.299655
\(561\) 7.45869 0.314906
\(562\) −18.6119 −0.785095
\(563\) −33.2073 −1.39952 −0.699761 0.714377i \(-0.746710\pi\)
−0.699761 + 0.714377i \(0.746710\pi\)
\(564\) 106.183 4.47111
\(565\) 35.2050 1.48108
\(566\) 3.48526 0.146497
\(567\) −2.55712 −0.107389
\(568\) 129.140 5.41857
\(569\) 32.7635 1.37352 0.686759 0.726885i \(-0.259033\pi\)
0.686759 + 0.726885i \(0.259033\pi\)
\(570\) −40.2533 −1.68603
\(571\) 41.6595 1.74339 0.871697 0.490044i \(-0.163019\pi\)
0.871697 + 0.490044i \(0.163019\pi\)
\(572\) 69.4502 2.90386
\(573\) 23.7107 0.990529
\(574\) −6.52084 −0.272175
\(575\) 3.90763 0.162960
\(576\) 13.0006 0.541690
\(577\) −23.0819 −0.960914 −0.480457 0.877018i \(-0.659529\pi\)
−0.480457 + 0.877018i \(0.659529\pi\)
\(578\) 42.9767 1.78759
\(579\) 2.32617 0.0966725
\(580\) 8.93811 0.371135
\(581\) −1.42193 −0.0589915
\(582\) −46.9291 −1.94527
\(583\) −3.11746 −0.129112
\(584\) −29.0821 −1.20343
\(585\) 11.5542 0.477706
\(586\) −83.5414 −3.45107
\(587\) 9.00552 0.371698 0.185849 0.982578i \(-0.440497\pi\)
0.185849 + 0.982578i \(0.440497\pi\)
\(588\) 70.2576 2.89737
\(589\) −9.36535 −0.385892
\(590\) −98.2963 −4.04679
\(591\) −7.58369 −0.311951
\(592\) 83.0678 3.41407
\(593\) −25.9986 −1.06763 −0.533816 0.845600i \(-0.679243\pi\)
−0.533816 + 0.845600i \(0.679243\pi\)
\(594\) 42.8026 1.75621
\(595\) −0.557003 −0.0228349
\(596\) −40.8515 −1.67334
\(597\) 6.89613 0.282240
\(598\) 8.33867 0.340993
\(599\) 18.5189 0.756661 0.378330 0.925671i \(-0.376498\pi\)
0.378330 + 0.925671i \(0.376498\pi\)
\(600\) 61.7178 2.51962
\(601\) 35.6404 1.45380 0.726901 0.686743i \(-0.240960\pi\)
0.726901 + 0.686743i \(0.240960\pi\)
\(602\) 0.265152 0.0108068
\(603\) 18.3601 0.747681
\(604\) 40.6944 1.65583
\(605\) −26.3262 −1.07031
\(606\) −15.5368 −0.631139
\(607\) −44.7603 −1.81676 −0.908381 0.418142i \(-0.862681\pi\)
−0.908381 + 0.418142i \(0.862681\pi\)
\(608\) −29.7832 −1.20787
\(609\) 0.286135 0.0115948
\(610\) 62.9840 2.55015
\(611\) 33.2800 1.34637
\(612\) 4.90197 0.198150
\(613\) 25.3292 1.02304 0.511518 0.859272i \(-0.329083\pi\)
0.511518 + 0.859272i \(0.329083\pi\)
\(614\) 11.3153 0.456649
\(615\) 66.4049 2.67770
\(616\) 7.83305 0.315603
\(617\) 12.2873 0.494669 0.247334 0.968930i \(-0.420445\pi\)
0.247334 + 0.968930i \(0.420445\pi\)
\(618\) −22.6883 −0.912658
\(619\) −8.52472 −0.342637 −0.171319 0.985216i \(-0.554803\pi\)
−0.171319 + 0.985216i \(0.554803\pi\)
\(620\) 55.1382 2.21440
\(621\) 3.65426 0.146640
\(622\) 36.8183 1.47628
\(623\) 0.131166 0.00525507
\(624\) 67.6000 2.70617
\(625\) −29.2686 −1.17074
\(626\) −26.2308 −1.04839
\(627\) 22.8229 0.911458
\(628\) 105.609 4.21425
\(629\) 6.52490 0.260165
\(630\) 2.19517 0.0874576
\(631\) −27.3594 −1.08916 −0.544581 0.838708i \(-0.683311\pi\)
−0.544581 + 0.838708i \(0.683311\pi\)
\(632\) 24.5899 0.978134
\(633\) −52.5224 −2.08758
\(634\) 60.1624 2.38935
\(635\) 28.8748 1.14586
\(636\) −7.08105 −0.280782
\(637\) 22.0202 0.872473
\(638\) −7.12702 −0.282162
\(639\) −20.5194 −0.811734
\(640\) 12.3232 0.487119
\(641\) 46.9265 1.85348 0.926742 0.375699i \(-0.122597\pi\)
0.926742 + 0.375699i \(0.122597\pi\)
\(642\) −25.5116 −1.00686
\(643\) 20.9496 0.826171 0.413086 0.910692i \(-0.364451\pi\)
0.413086 + 0.910692i \(0.364451\pi\)
\(644\) 1.12650 0.0443903
\(645\) −2.70017 −0.106319
\(646\) −5.35257 −0.210594
\(647\) 19.8076 0.778718 0.389359 0.921086i \(-0.372697\pi\)
0.389359 + 0.921086i \(0.372697\pi\)
\(648\) 85.8842 3.37385
\(649\) 55.7321 2.18768
\(650\) 32.5845 1.27807
\(651\) 1.76514 0.0691812
\(652\) −25.2133 −0.987429
\(653\) 1.13530 0.0444278 0.0222139 0.999753i \(-0.492929\pi\)
0.0222139 + 0.999753i \(0.492929\pi\)
\(654\) −56.9713 −2.22775
\(655\) −32.8283 −1.28271
\(656\) 112.414 4.38902
\(657\) 4.62095 0.180280
\(658\) 6.32285 0.246490
\(659\) −41.2185 −1.60564 −0.802822 0.596218i \(-0.796669\pi\)
−0.802822 + 0.596218i \(0.796669\pi\)
\(660\) −134.369 −5.23030
\(661\) 14.1319 0.549668 0.274834 0.961492i \(-0.411377\pi\)
0.274834 + 0.961492i \(0.411377\pi\)
\(662\) −70.1381 −2.72599
\(663\) 5.30992 0.206220
\(664\) 47.7573 1.85334
\(665\) −1.70438 −0.0660929
\(666\) −25.7149 −0.996431
\(667\) −0.608467 −0.0235599
\(668\) 110.190 4.26339
\(669\) 48.6812 1.88213
\(670\) 118.031 4.55993
\(671\) −35.7107 −1.37860
\(672\) 5.61340 0.216542
\(673\) 9.93640 0.383020 0.191510 0.981491i \(-0.438662\pi\)
0.191510 + 0.981491i \(0.438662\pi\)
\(674\) 51.9354 2.00048
\(675\) 14.2795 0.549618
\(676\) −14.5415 −0.559290
\(677\) 15.6518 0.601546 0.300773 0.953696i \(-0.402755\pi\)
0.300773 + 0.953696i \(0.402755\pi\)
\(678\) −63.7623 −2.44877
\(679\) −1.98704 −0.0762555
\(680\) 18.7077 0.717406
\(681\) 12.7695 0.489328
\(682\) −43.9658 −1.68354
\(683\) 27.4149 1.04900 0.524501 0.851410i \(-0.324252\pi\)
0.524501 + 0.851410i \(0.324252\pi\)
\(684\) 14.9996 0.573523
\(685\) −46.7296 −1.78545
\(686\) 8.39875 0.320666
\(687\) 36.5619 1.39492
\(688\) −4.57100 −0.174268
\(689\) −2.21935 −0.0845506
\(690\) −16.1333 −0.614183
\(691\) −15.2052 −0.578434 −0.289217 0.957264i \(-0.593395\pi\)
−0.289217 + 0.957264i \(0.593395\pi\)
\(692\) −1.13488 −0.0431418
\(693\) −1.24462 −0.0472791
\(694\) 36.5184 1.38622
\(695\) 51.5713 1.95621
\(696\) −9.61023 −0.364275
\(697\) 8.83000 0.334460
\(698\) 2.63094 0.0995825
\(699\) 35.1265 1.32861
\(700\) 4.40195 0.166378
\(701\) 23.8884 0.902252 0.451126 0.892460i \(-0.351022\pi\)
0.451126 + 0.892460i \(0.351022\pi\)
\(702\) 30.4716 1.15008
\(703\) 19.9656 0.753016
\(704\) −47.3861 −1.78593
\(705\) −64.3886 −2.42502
\(706\) −25.6622 −0.965811
\(707\) −0.657847 −0.0247409
\(708\) 126.591 4.75758
\(709\) −9.91002 −0.372178 −0.186089 0.982533i \(-0.559581\pi\)
−0.186089 + 0.982533i \(0.559581\pi\)
\(710\) −131.912 −4.95057
\(711\) −3.90717 −0.146530
\(712\) −4.40539 −0.165099
\(713\) −3.75357 −0.140572
\(714\) 1.00883 0.0377544
\(715\) −42.1141 −1.57498
\(716\) −64.8210 −2.42248
\(717\) 14.1271 0.527588
\(718\) 43.3579 1.61810
\(719\) −51.1979 −1.90936 −0.954680 0.297633i \(-0.903803\pi\)
−0.954680 + 0.297633i \(0.903803\pi\)
\(720\) −37.8428 −1.41032
\(721\) −0.960651 −0.0357765
\(722\) 33.6095 1.25081
\(723\) 42.7260 1.58900
\(724\) −111.041 −4.12681
\(725\) −2.37767 −0.0883044
\(726\) 47.6813 1.76962
\(727\) 31.7496 1.17753 0.588764 0.808305i \(-0.299615\pi\)
0.588764 + 0.808305i \(0.299615\pi\)
\(728\) 5.57644 0.206676
\(729\) 8.87787 0.328810
\(730\) 29.7065 1.09949
\(731\) −0.359048 −0.0132799
\(732\) −81.1139 −2.99806
\(733\) −3.16313 −0.116833 −0.0584165 0.998292i \(-0.518605\pi\)
−0.0584165 + 0.998292i \(0.518605\pi\)
\(734\) 20.2706 0.748201
\(735\) −42.6037 −1.57146
\(736\) −11.9369 −0.440000
\(737\) −66.9212 −2.46508
\(738\) −34.7993 −1.28098
\(739\) −26.8997 −0.989521 −0.494760 0.869029i \(-0.664744\pi\)
−0.494760 + 0.869029i \(0.664744\pi\)
\(740\) −117.547 −4.32110
\(741\) 16.2479 0.596880
\(742\) −0.421653 −0.0154794
\(743\) 32.0968 1.17752 0.588760 0.808308i \(-0.299616\pi\)
0.588760 + 0.808308i \(0.299616\pi\)
\(744\) −59.2845 −2.17347
\(745\) 24.7720 0.907578
\(746\) −33.1560 −1.21393
\(747\) −7.58830 −0.277641
\(748\) −17.8673 −0.653294
\(749\) −1.08019 −0.0394694
\(750\) 17.6234 0.643516
\(751\) 26.3161 0.960289 0.480145 0.877189i \(-0.340584\pi\)
0.480145 + 0.877189i \(0.340584\pi\)
\(752\) −109.001 −3.97484
\(753\) 12.9793 0.472992
\(754\) −5.07380 −0.184777
\(755\) −24.6768 −0.898080
\(756\) 4.11652 0.149717
\(757\) −7.12245 −0.258870 −0.129435 0.991588i \(-0.541316\pi\)
−0.129435 + 0.991588i \(0.541316\pi\)
\(758\) −28.8613 −1.04829
\(759\) 9.14725 0.332024
\(760\) 57.2437 2.07645
\(761\) 24.8606 0.901196 0.450598 0.892727i \(-0.351211\pi\)
0.450598 + 0.892727i \(0.351211\pi\)
\(762\) −52.2972 −1.89453
\(763\) −2.41223 −0.0873287
\(764\) −56.7991 −2.05492
\(765\) −2.97252 −0.107472
\(766\) −63.5494 −2.29613
\(767\) 39.6763 1.43263
\(768\) 21.4177 0.772844
\(769\) −10.8611 −0.391661 −0.195831 0.980638i \(-0.562740\pi\)
−0.195831 + 0.980638i \(0.562740\pi\)
\(770\) −8.00122 −0.288344
\(771\) 62.6795 2.25735
\(772\) −5.57236 −0.200554
\(773\) 37.4718 1.34777 0.673884 0.738837i \(-0.264625\pi\)
0.673884 + 0.738837i \(0.264625\pi\)
\(774\) 1.41502 0.0508618
\(775\) −14.6676 −0.526875
\(776\) 66.7372 2.39573
\(777\) −3.76302 −0.134998
\(778\) −19.1710 −0.687315
\(779\) 27.0190 0.968055
\(780\) −95.6587 −3.42513
\(781\) 74.7916 2.67625
\(782\) −2.14527 −0.0767148
\(783\) −2.22350 −0.0794613
\(784\) −72.1218 −2.57578
\(785\) −64.0404 −2.28570
\(786\) 59.4578 2.12079
\(787\) 17.8744 0.637155 0.318577 0.947897i \(-0.396795\pi\)
0.318577 + 0.947897i \(0.396795\pi\)
\(788\) 18.1668 0.647164
\(789\) −10.7337 −0.382129
\(790\) −25.1178 −0.893653
\(791\) −2.69977 −0.0959928
\(792\) 41.8021 1.48537
\(793\) −25.4228 −0.902791
\(794\) 28.5979 1.01490
\(795\) 4.29390 0.152289
\(796\) −16.5197 −0.585526
\(797\) −35.6080 −1.26130 −0.630649 0.776068i \(-0.717211\pi\)
−0.630649 + 0.776068i \(0.717211\pi\)
\(798\) 3.08692 0.109276
\(799\) −8.56189 −0.302898
\(800\) −46.6450 −1.64915
\(801\) 0.699986 0.0247328
\(802\) 52.1926 1.84298
\(803\) −16.8430 −0.594378
\(804\) −152.006 −5.36084
\(805\) −0.683102 −0.0240762
\(806\) −31.2997 −1.10249
\(807\) 31.6606 1.11451
\(808\) 22.0947 0.777287
\(809\) 26.1925 0.920881 0.460440 0.887691i \(-0.347692\pi\)
0.460440 + 0.887691i \(0.347692\pi\)
\(810\) −87.7280 −3.08245
\(811\) −31.0296 −1.08960 −0.544798 0.838567i \(-0.683394\pi\)
−0.544798 + 0.838567i \(0.683394\pi\)
\(812\) −0.685439 −0.0240542
\(813\) −46.4774 −1.63003
\(814\) 93.7288 3.28519
\(815\) 15.2892 0.535556
\(816\) −17.3913 −0.608818
\(817\) −1.09865 −0.0384370
\(818\) −43.2679 −1.51283
\(819\) −0.886057 −0.0309613
\(820\) −159.073 −5.55508
\(821\) 20.9002 0.729422 0.364711 0.931121i \(-0.381168\pi\)
0.364711 + 0.931121i \(0.381168\pi\)
\(822\) 84.6353 2.95199
\(823\) 16.2708 0.567165 0.283583 0.958948i \(-0.408477\pi\)
0.283583 + 0.958948i \(0.408477\pi\)
\(824\) 32.2647 1.12400
\(825\) 35.7441 1.24445
\(826\) 7.53807 0.262283
\(827\) 23.9242 0.831928 0.415964 0.909381i \(-0.363444\pi\)
0.415964 + 0.909381i \(0.363444\pi\)
\(828\) 6.01172 0.208922
\(829\) −1.51181 −0.0525075 −0.0262537 0.999655i \(-0.508358\pi\)
−0.0262537 + 0.999655i \(0.508358\pi\)
\(830\) −48.7826 −1.69327
\(831\) 19.3163 0.670074
\(832\) −33.7347 −1.16954
\(833\) −5.66510 −0.196284
\(834\) −93.4045 −3.23433
\(835\) −66.8186 −2.31235
\(836\) −54.6723 −1.89088
\(837\) −13.7165 −0.474112
\(838\) −37.2137 −1.28553
\(839\) 19.9387 0.688360 0.344180 0.938904i \(-0.388157\pi\)
0.344180 + 0.938904i \(0.388157\pi\)
\(840\) −10.7890 −0.372257
\(841\) −28.6298 −0.987233
\(842\) −6.76570 −0.233161
\(843\) −14.5348 −0.500606
\(844\) 125.818 4.33082
\(845\) 8.81789 0.303344
\(846\) 33.7427 1.16010
\(847\) 2.01888 0.0693697
\(848\) 7.26894 0.249617
\(849\) 2.72179 0.0934117
\(850\) −8.38294 −0.287533
\(851\) 8.00206 0.274307
\(852\) 169.883 5.82010
\(853\) 43.3645 1.48477 0.742385 0.669973i \(-0.233694\pi\)
0.742385 + 0.669973i \(0.233694\pi\)
\(854\) −4.83007 −0.165281
\(855\) −9.09563 −0.311064
\(856\) 36.2797 1.24001
\(857\) 48.0809 1.64241 0.821206 0.570632i \(-0.193302\pi\)
0.821206 + 0.570632i \(0.193302\pi\)
\(858\) 76.2759 2.60402
\(859\) −16.5351 −0.564169 −0.282084 0.959390i \(-0.591026\pi\)
−0.282084 + 0.959390i \(0.591026\pi\)
\(860\) 6.46828 0.220566
\(861\) −5.09241 −0.173549
\(862\) 104.314 3.55296
\(863\) 0.918753 0.0312747 0.0156374 0.999878i \(-0.495022\pi\)
0.0156374 + 0.999878i \(0.495022\pi\)
\(864\) −43.6205 −1.48400
\(865\) 0.688185 0.0233990
\(866\) 80.1900 2.72497
\(867\) 33.5624 1.13984
\(868\) −4.22839 −0.143521
\(869\) 14.2413 0.483104
\(870\) 9.81656 0.332812
\(871\) −47.6419 −1.61429
\(872\) 81.0180 2.74362
\(873\) −10.6041 −0.358894
\(874\) −6.56433 −0.222042
\(875\) 0.746197 0.0252261
\(876\) −38.2576 −1.29260
\(877\) −14.4453 −0.487782 −0.243891 0.969803i \(-0.578424\pi\)
−0.243891 + 0.969803i \(0.578424\pi\)
\(878\) 41.9283 1.41501
\(879\) −65.2411 −2.20053
\(880\) 137.934 4.64977
\(881\) 32.9166 1.10899 0.554494 0.832188i \(-0.312912\pi\)
0.554494 + 0.832188i \(0.312912\pi\)
\(882\) 22.3264 0.751768
\(883\) 49.2930 1.65884 0.829420 0.558625i \(-0.188671\pi\)
0.829420 + 0.558625i \(0.188671\pi\)
\(884\) −12.7199 −0.427818
\(885\) −76.7638 −2.58039
\(886\) 6.39356 0.214796
\(887\) −42.2438 −1.41841 −0.709204 0.705003i \(-0.750946\pi\)
−0.709204 + 0.705003i \(0.750946\pi\)
\(888\) 126.386 4.24123
\(889\) −2.21433 −0.0742661
\(890\) 4.49997 0.150839
\(891\) 49.7401 1.66636
\(892\) −116.616 −3.90460
\(893\) −26.1986 −0.876702
\(894\) −44.8664 −1.50056
\(895\) 39.3070 1.31389
\(896\) −0.945035 −0.0315714
\(897\) 6.51203 0.217430
\(898\) 52.5789 1.75458
\(899\) 2.28392 0.0761731
\(900\) 23.4916 0.783053
\(901\) 0.570969 0.0190217
\(902\) 126.841 4.22334
\(903\) 0.207069 0.00689082
\(904\) 90.6754 3.01582
\(905\) 67.3346 2.23828
\(906\) 44.6939 1.48485
\(907\) −42.6787 −1.41712 −0.708561 0.705650i \(-0.750655\pi\)
−0.708561 + 0.705650i \(0.750655\pi\)
\(908\) −30.5894 −1.01514
\(909\) −3.51069 −0.116442
\(910\) −5.69616 −0.188826
\(911\) 20.8112 0.689507 0.344753 0.938693i \(-0.387963\pi\)
0.344753 + 0.938693i \(0.387963\pi\)
\(912\) −53.2158 −1.76215
\(913\) 27.6588 0.915373
\(914\) −1.64836 −0.0545230
\(915\) 49.1869 1.62607
\(916\) −87.5841 −2.89386
\(917\) 2.51751 0.0831356
\(918\) −7.83938 −0.258738
\(919\) 0.198263 0.00654009 0.00327005 0.999995i \(-0.498959\pi\)
0.00327005 + 0.999995i \(0.498959\pi\)
\(920\) 22.9429 0.756404
\(921\) 8.83661 0.291176
\(922\) −51.2700 −1.68849
\(923\) 53.2450 1.75258
\(924\) 10.3044 0.338989
\(925\) 31.2691 1.02812
\(926\) −101.208 −3.32591
\(927\) −5.12664 −0.168381
\(928\) 7.26321 0.238427
\(929\) 13.5423 0.444309 0.222155 0.975011i \(-0.428691\pi\)
0.222155 + 0.975011i \(0.428691\pi\)
\(930\) 60.5573 1.98575
\(931\) −17.3347 −0.568121
\(932\) −84.1457 −2.75629
\(933\) 28.7530 0.941331
\(934\) 88.4413 2.89389
\(935\) 10.8346 0.354330
\(936\) 29.7594 0.972716
\(937\) −49.2146 −1.60777 −0.803885 0.594785i \(-0.797237\pi\)
−0.803885 + 0.594785i \(0.797237\pi\)
\(938\) −9.05146 −0.295541
\(939\) −20.4848 −0.668495
\(940\) 154.243 5.03086
\(941\) 25.0294 0.815935 0.407968 0.912996i \(-0.366238\pi\)
0.407968 + 0.912996i \(0.366238\pi\)
\(942\) 115.988 3.77910
\(943\) 10.8290 0.352641
\(944\) −129.950 −4.22951
\(945\) −2.49623 −0.0812024
\(946\) −5.15764 −0.167689
\(947\) −48.9624 −1.59106 −0.795532 0.605912i \(-0.792808\pi\)
−0.795532 + 0.605912i \(0.792808\pi\)
\(948\) 32.3480 1.05062
\(949\) −11.9907 −0.389236
\(950\) −25.6510 −0.832229
\(951\) 46.9834 1.52354
\(952\) −1.43464 −0.0464969
\(953\) 38.3680 1.24286 0.621431 0.783469i \(-0.286552\pi\)
0.621431 + 0.783469i \(0.286552\pi\)
\(954\) −2.25021 −0.0728532
\(955\) 34.4426 1.11454
\(956\) −33.8416 −1.09452
\(957\) −5.56580 −0.179917
\(958\) −47.1629 −1.52377
\(959\) 3.58356 0.115719
\(960\) 65.2683 2.10652
\(961\) −16.9107 −0.545508
\(962\) 66.7265 2.15135
\(963\) −5.76459 −0.185761
\(964\) −102.350 −3.29648
\(965\) 3.37904 0.108775
\(966\) 1.23721 0.0398067
\(967\) −25.1060 −0.807356 −0.403678 0.914901i \(-0.632268\pi\)
−0.403678 + 0.914901i \(0.632268\pi\)
\(968\) −67.8068 −2.17939
\(969\) −4.18005 −0.134283
\(970\) −68.1700 −2.18881
\(971\) −6.37105 −0.204457 −0.102228 0.994761i \(-0.532597\pi\)
−0.102228 + 0.994761i \(0.532597\pi\)
\(972\) 59.0237 1.89318
\(973\) −3.95486 −0.126787
\(974\) 0.338806 0.0108560
\(975\) 25.4466 0.814944
\(976\) 83.2662 2.66529
\(977\) 42.7400 1.36737 0.683686 0.729776i \(-0.260376\pi\)
0.683686 + 0.729776i \(0.260376\pi\)
\(978\) −27.6913 −0.885470
\(979\) −2.55140 −0.0815431
\(980\) 102.057 3.26010
\(981\) −12.8732 −0.411010
\(982\) 41.2673 1.31689
\(983\) −4.74542 −0.151356 −0.0756778 0.997132i \(-0.524112\pi\)
−0.0756778 + 0.997132i \(0.524112\pi\)
\(984\) 171.035 5.45240
\(985\) −11.0162 −0.351005
\(986\) 1.30533 0.0415701
\(987\) 4.93779 0.157171
\(988\) −38.9218 −1.23827
\(989\) −0.440332 −0.0140017
\(990\) −42.6996 −1.35708
\(991\) −27.5281 −0.874460 −0.437230 0.899350i \(-0.644041\pi\)
−0.437230 + 0.899350i \(0.644041\pi\)
\(992\) 44.8060 1.42259
\(993\) −54.7739 −1.73820
\(994\) 10.1160 0.320859
\(995\) 10.0174 0.317574
\(996\) 62.8247 1.99068
\(997\) −17.2609 −0.546660 −0.273330 0.961920i \(-0.588125\pi\)
−0.273330 + 0.961920i \(0.588125\pi\)
\(998\) 8.87005 0.280776
\(999\) 29.2416 0.925163
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 \(a_p\))