Properties

Label 4017.2.a.j.1.6
Level 4017
Weight 2
Character 4017.1
Self dual Yes
Analytic conductor 32.076
Analytic rank 0
Dimension 25
CM No

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Newspace parameters

Level: \( N \) = \( 4017 = 3 \cdot 13 \cdot 103 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4017.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0759064919\)
Analytic rank: \(0\)
Dimension: \(25\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Character \(\chi\) = 4017.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.55573 q^{2} -1.00000 q^{3} +0.420296 q^{4} -1.90089 q^{5} +1.55573 q^{6} +0.0358686 q^{7} +2.45759 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.55573 q^{2} -1.00000 q^{3} +0.420296 q^{4} -1.90089 q^{5} +1.55573 q^{6} +0.0358686 q^{7} +2.45759 q^{8} +1.00000 q^{9} +2.95727 q^{10} -4.89487 q^{11} -0.420296 q^{12} +1.00000 q^{13} -0.0558019 q^{14} +1.90089 q^{15} -4.66394 q^{16} +0.534376 q^{17} -1.55573 q^{18} +0.251892 q^{19} -0.798937 q^{20} -0.0358686 q^{21} +7.61509 q^{22} +9.05681 q^{23} -2.45759 q^{24} -1.38661 q^{25} -1.55573 q^{26} -1.00000 q^{27} +0.0150754 q^{28} +1.09475 q^{29} -2.95727 q^{30} -0.0390860 q^{31} +2.34065 q^{32} +4.89487 q^{33} -0.831345 q^{34} -0.0681824 q^{35} +0.420296 q^{36} -7.85613 q^{37} -0.391876 q^{38} -1.00000 q^{39} -4.67162 q^{40} +4.76621 q^{41} +0.0558019 q^{42} -12.1897 q^{43} -2.05729 q^{44} -1.90089 q^{45} -14.0900 q^{46} +0.236387 q^{47} +4.66394 q^{48} -6.99871 q^{49} +2.15720 q^{50} -0.534376 q^{51} +0.420296 q^{52} -4.29403 q^{53} +1.55573 q^{54} +9.30461 q^{55} +0.0881505 q^{56} -0.251892 q^{57} -1.70314 q^{58} +13.8587 q^{59} +0.798937 q^{60} -4.97793 q^{61} +0.0608072 q^{62} +0.0358686 q^{63} +5.68646 q^{64} -1.90089 q^{65} -7.61509 q^{66} -8.32506 q^{67} +0.224596 q^{68} -9.05681 q^{69} +0.106073 q^{70} -1.08614 q^{71} +2.45759 q^{72} +7.48444 q^{73} +12.2220 q^{74} +1.38661 q^{75} +0.105869 q^{76} -0.175572 q^{77} +1.55573 q^{78} +1.11032 q^{79} +8.86565 q^{80} +1.00000 q^{81} -7.41494 q^{82} -12.3101 q^{83} -0.0150754 q^{84} -1.01579 q^{85} +18.9638 q^{86} -1.09475 q^{87} -12.0296 q^{88} +12.9144 q^{89} +2.95727 q^{90} +0.0358686 q^{91} +3.80654 q^{92} +0.0390860 q^{93} -0.367754 q^{94} -0.478820 q^{95} -2.34065 q^{96} +19.5036 q^{97} +10.8881 q^{98} -4.89487 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 25q + 6q^{2} - 25q^{3} + 28q^{4} + 7q^{5} - 6q^{6} + 17q^{7} + 21q^{8} + 25q^{9} + O(q^{10}) \) \( 25q + 6q^{2} - 25q^{3} + 28q^{4} + 7q^{5} - 6q^{6} + 17q^{7} + 21q^{8} + 25q^{9} - 6q^{10} + 21q^{11} - 28q^{12} + 25q^{13} + 10q^{14} - 7q^{15} + 30q^{16} + 14q^{17} + 6q^{18} + 12q^{19} + 24q^{20} - 17q^{21} + 3q^{22} + 41q^{23} - 21q^{24} + 30q^{25} + 6q^{26} - 25q^{27} + 14q^{28} + 22q^{29} + 6q^{30} + 14q^{31} + 28q^{32} - 21q^{33} - 11q^{34} + 14q^{35} + 28q^{36} - 6q^{37} + 16q^{38} - 25q^{39} - 34q^{40} + 33q^{41} - 10q^{42} + 35q^{43} + 45q^{44} + 7q^{45} + 3q^{46} + 48q^{47} - 30q^{48} - 4q^{49} + 7q^{50} - 14q^{51} + 28q^{52} + 18q^{53} - 6q^{54} + 10q^{55} + 32q^{56} - 12q^{57} + 33q^{58} + 46q^{59} - 24q^{60} - 19q^{61} + 5q^{62} + 17q^{63} + 29q^{64} + 7q^{65} - 3q^{66} + 16q^{67} + 20q^{68} - 41q^{69} - 43q^{70} + 60q^{71} + 21q^{72} - 14q^{73} - 50q^{74} - 30q^{75} + 59q^{77} - 6q^{78} + 7q^{79} + 32q^{80} + 25q^{81} + 18q^{82} + 23q^{83} - 14q^{84} - 9q^{85} - 9q^{86} - 22q^{87} + 23q^{88} + 10q^{89} - 6q^{90} + 17q^{91} + 69q^{92} - 14q^{93} - 30q^{94} + 81q^{95} - 28q^{96} - 10q^{97} + 55q^{98} + 21q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.55573 −1.10007 −0.550034 0.835142i \(-0.685385\pi\)
−0.550034 + 0.835142i \(0.685385\pi\)
\(3\) −1.00000 −0.577350
\(4\) 0.420296 0.210148
\(5\) −1.90089 −0.850104 −0.425052 0.905169i \(-0.639744\pi\)
−0.425052 + 0.905169i \(0.639744\pi\)
\(6\) 1.55573 0.635124
\(7\) 0.0358686 0.0135571 0.00677853 0.999977i \(-0.497842\pi\)
0.00677853 + 0.999977i \(0.497842\pi\)
\(8\) 2.45759 0.868890
\(9\) 1.00000 0.333333
\(10\) 2.95727 0.935172
\(11\) −4.89487 −1.47586 −0.737929 0.674879i \(-0.764196\pi\)
−0.737929 + 0.674879i \(0.764196\pi\)
\(12\) −0.420296 −0.121329
\(13\) 1.00000 0.277350
\(14\) −0.0558019 −0.0149137
\(15\) 1.90089 0.490808
\(16\) −4.66394 −1.16599
\(17\) 0.534376 0.129605 0.0648026 0.997898i \(-0.479358\pi\)
0.0648026 + 0.997898i \(0.479358\pi\)
\(18\) −1.55573 −0.366689
\(19\) 0.251892 0.0577880 0.0288940 0.999582i \(-0.490801\pi\)
0.0288940 + 0.999582i \(0.490801\pi\)
\(20\) −0.798937 −0.178648
\(21\) −0.0358686 −0.00782718
\(22\) 7.61509 1.62354
\(23\) 9.05681 1.88848 0.944238 0.329265i \(-0.106801\pi\)
0.944238 + 0.329265i \(0.106801\pi\)
\(24\) −2.45759 −0.501654
\(25\) −1.38661 −0.277323
\(26\) −1.55573 −0.305104
\(27\) −1.00000 −0.192450
\(28\) 0.0150754 0.00284899
\(29\) 1.09475 0.203290 0.101645 0.994821i \(-0.467589\pi\)
0.101645 + 0.994821i \(0.467589\pi\)
\(30\) −2.95727 −0.539922
\(31\) −0.0390860 −0.00702004 −0.00351002 0.999994i \(-0.501117\pi\)
−0.00351002 + 0.999994i \(0.501117\pi\)
\(32\) 2.34065 0.413773
\(33\) 4.89487 0.852087
\(34\) −0.831345 −0.142574
\(35\) −0.0681824 −0.0115249
\(36\) 0.420296 0.0700494
\(37\) −7.85613 −1.29154 −0.645770 0.763532i \(-0.723463\pi\)
−0.645770 + 0.763532i \(0.723463\pi\)
\(38\) −0.391876 −0.0635707
\(39\) −1.00000 −0.160128
\(40\) −4.67162 −0.738647
\(41\) 4.76621 0.744357 0.372179 0.928161i \(-0.378611\pi\)
0.372179 + 0.928161i \(0.378611\pi\)
\(42\) 0.0558019 0.00861042
\(43\) −12.1897 −1.85891 −0.929454 0.368938i \(-0.879721\pi\)
−0.929454 + 0.368938i \(0.879721\pi\)
\(44\) −2.05729 −0.310149
\(45\) −1.90089 −0.283368
\(46\) −14.0900 −2.07745
\(47\) 0.236387 0.0344805 0.0172403 0.999851i \(-0.494512\pi\)
0.0172403 + 0.999851i \(0.494512\pi\)
\(48\) 4.66394 0.673182
\(49\) −6.99871 −0.999816
\(50\) 2.15720 0.305073
\(51\) −0.534376 −0.0748276
\(52\) 0.420296 0.0582846
\(53\) −4.29403 −0.589831 −0.294915 0.955523i \(-0.595292\pi\)
−0.294915 + 0.955523i \(0.595292\pi\)
\(54\) 1.55573 0.211708
\(55\) 9.30461 1.25463
\(56\) 0.0881505 0.0117796
\(57\) −0.251892 −0.0333639
\(58\) −1.70314 −0.223633
\(59\) 13.8587 1.80424 0.902122 0.431481i \(-0.142009\pi\)
0.902122 + 0.431481i \(0.142009\pi\)
\(60\) 0.798937 0.103142
\(61\) −4.97793 −0.637358 −0.318679 0.947863i \(-0.603239\pi\)
−0.318679 + 0.947863i \(0.603239\pi\)
\(62\) 0.0608072 0.00772252
\(63\) 0.0358686 0.00451902
\(64\) 5.68646 0.710808
\(65\) −1.90089 −0.235777
\(66\) −7.61509 −0.937353
\(67\) −8.32506 −1.01707 −0.508534 0.861042i \(-0.669812\pi\)
−0.508534 + 0.861042i \(0.669812\pi\)
\(68\) 0.224596 0.0272363
\(69\) −9.05681 −1.09031
\(70\) 0.106073 0.0126782
\(71\) −1.08614 −0.128901 −0.0644503 0.997921i \(-0.520529\pi\)
−0.0644503 + 0.997921i \(0.520529\pi\)
\(72\) 2.45759 0.289630
\(73\) 7.48444 0.875987 0.437994 0.898978i \(-0.355689\pi\)
0.437994 + 0.898978i \(0.355689\pi\)
\(74\) 12.2220 1.42078
\(75\) 1.38661 0.160112
\(76\) 0.105869 0.0121440
\(77\) −0.175572 −0.0200083
\(78\) 1.55573 0.176152
\(79\) 1.11032 0.124921 0.0624604 0.998047i \(-0.480105\pi\)
0.0624604 + 0.998047i \(0.480105\pi\)
\(80\) 8.86565 0.991210
\(81\) 1.00000 0.111111
\(82\) −7.41494 −0.818843
\(83\) −12.3101 −1.35121 −0.675605 0.737264i \(-0.736118\pi\)
−0.675605 + 0.737264i \(0.736118\pi\)
\(84\) −0.0150754 −0.00164487
\(85\) −1.01579 −0.110178
\(86\) 18.9638 2.04492
\(87\) −1.09475 −0.117370
\(88\) −12.0296 −1.28236
\(89\) 12.9144 1.36893 0.684463 0.729048i \(-0.260037\pi\)
0.684463 + 0.729048i \(0.260037\pi\)
\(90\) 2.95727 0.311724
\(91\) 0.0358686 0.00376005
\(92\) 3.80654 0.396859
\(93\) 0.0390860 0.00405302
\(94\) −0.367754 −0.0379309
\(95\) −0.478820 −0.0491259
\(96\) −2.34065 −0.238892
\(97\) 19.5036 1.98029 0.990146 0.140041i \(-0.0447233\pi\)
0.990146 + 0.140041i \(0.0447233\pi\)
\(98\) 10.8881 1.09987
\(99\) −4.89487 −0.491952
\(100\) −0.582788 −0.0582788
\(101\) −11.1103 −1.10551 −0.552756 0.833343i \(-0.686424\pi\)
−0.552756 + 0.833343i \(0.686424\pi\)
\(102\) 0.831345 0.0823154
\(103\) −1.00000 −0.0985329
\(104\) 2.45759 0.240987
\(105\) 0.0681824 0.00665392
\(106\) 6.68036 0.648854
\(107\) −5.69522 −0.550578 −0.275289 0.961362i \(-0.588774\pi\)
−0.275289 + 0.961362i \(0.588774\pi\)
\(108\) −0.420296 −0.0404430
\(109\) −14.8709 −1.42437 −0.712187 0.701990i \(-0.752295\pi\)
−0.712187 + 0.701990i \(0.752295\pi\)
\(110\) −14.4755 −1.38018
\(111\) 7.85613 0.745671
\(112\) −0.167289 −0.0158074
\(113\) −18.8154 −1.77000 −0.885001 0.465588i \(-0.845843\pi\)
−0.885001 + 0.465588i \(0.845843\pi\)
\(114\) 0.391876 0.0367026
\(115\) −17.2160 −1.60540
\(116\) 0.460119 0.0427210
\(117\) 1.00000 0.0924500
\(118\) −21.5603 −1.98479
\(119\) 0.0191673 0.00175707
\(120\) 4.67162 0.426458
\(121\) 12.9597 1.17816
\(122\) 7.74431 0.701137
\(123\) −4.76621 −0.429755
\(124\) −0.0164277 −0.00147525
\(125\) 12.1403 1.08586
\(126\) −0.0558019 −0.00497123
\(127\) 2.47435 0.219563 0.109781 0.993956i \(-0.464985\pi\)
0.109781 + 0.993956i \(0.464985\pi\)
\(128\) −13.5279 −1.19571
\(129\) 12.1897 1.07324
\(130\) 2.95727 0.259370
\(131\) −15.4870 −1.35310 −0.676551 0.736395i \(-0.736526\pi\)
−0.676551 + 0.736395i \(0.736526\pi\)
\(132\) 2.05729 0.179064
\(133\) 0.00903503 0.000783436 0
\(134\) 12.9515 1.11884
\(135\) 1.90089 0.163603
\(136\) 1.31328 0.112613
\(137\) −0.396590 −0.0338830 −0.0169415 0.999856i \(-0.505393\pi\)
−0.0169415 + 0.999856i \(0.505393\pi\)
\(138\) 14.0900 1.19942
\(139\) −5.42392 −0.460051 −0.230025 0.973185i \(-0.573881\pi\)
−0.230025 + 0.973185i \(0.573881\pi\)
\(140\) −0.0286568 −0.00242194
\(141\) −0.236387 −0.0199073
\(142\) 1.68974 0.141799
\(143\) −4.89487 −0.409329
\(144\) −4.66394 −0.388662
\(145\) −2.08100 −0.172818
\(146\) −11.6438 −0.963645
\(147\) 6.99871 0.577244
\(148\) −3.30190 −0.271414
\(149\) 13.5439 1.10956 0.554781 0.831996i \(-0.312802\pi\)
0.554781 + 0.831996i \(0.312802\pi\)
\(150\) −2.15720 −0.176134
\(151\) −12.0602 −0.981442 −0.490721 0.871317i \(-0.663267\pi\)
−0.490721 + 0.871317i \(0.663267\pi\)
\(152\) 0.619048 0.0502115
\(153\) 0.534376 0.0432017
\(154\) 0.273143 0.0220105
\(155\) 0.0742981 0.00596777
\(156\) −0.420296 −0.0336506
\(157\) −22.4909 −1.79497 −0.897484 0.441047i \(-0.854607\pi\)
−0.897484 + 0.441047i \(0.854607\pi\)
\(158\) −1.72736 −0.137421
\(159\) 4.29403 0.340539
\(160\) −4.44932 −0.351750
\(161\) 0.324855 0.0256022
\(162\) −1.55573 −0.122230
\(163\) −0.477456 −0.0373973 −0.0186986 0.999825i \(-0.505952\pi\)
−0.0186986 + 0.999825i \(0.505952\pi\)
\(164\) 2.00322 0.156425
\(165\) −9.30461 −0.724363
\(166\) 19.1512 1.48642
\(167\) −11.8831 −0.919541 −0.459770 0.888038i \(-0.652068\pi\)
−0.459770 + 0.888038i \(0.652068\pi\)
\(168\) −0.0881505 −0.00680096
\(169\) 1.00000 0.0769231
\(170\) 1.58030 0.121203
\(171\) 0.251892 0.0192627
\(172\) −5.12327 −0.390646
\(173\) −5.75389 −0.437460 −0.218730 0.975785i \(-0.570191\pi\)
−0.218730 + 0.975785i \(0.570191\pi\)
\(174\) 1.70314 0.129114
\(175\) −0.0497359 −0.00375968
\(176\) 22.8294 1.72083
\(177\) −13.8587 −1.04168
\(178\) −20.0914 −1.50591
\(179\) 6.33310 0.473358 0.236679 0.971588i \(-0.423941\pi\)
0.236679 + 0.971588i \(0.423941\pi\)
\(180\) −0.798937 −0.0595493
\(181\) 1.06556 0.0792022 0.0396011 0.999216i \(-0.487391\pi\)
0.0396011 + 0.999216i \(0.487391\pi\)
\(182\) −0.0558019 −0.00413631
\(183\) 4.97793 0.367979
\(184\) 22.2579 1.64088
\(185\) 14.9336 1.09794
\(186\) −0.0608072 −0.00445860
\(187\) −2.61570 −0.191279
\(188\) 0.0993524 0.00724602
\(189\) −0.0358686 −0.00260906
\(190\) 0.744914 0.0540417
\(191\) 6.58878 0.476747 0.238374 0.971174i \(-0.423386\pi\)
0.238374 + 0.971174i \(0.423386\pi\)
\(192\) −5.68646 −0.410385
\(193\) −4.43314 −0.319104 −0.159552 0.987190i \(-0.551005\pi\)
−0.159552 + 0.987190i \(0.551005\pi\)
\(194\) −30.3424 −2.17845
\(195\) 1.90089 0.136126
\(196\) −2.94153 −0.210109
\(197\) 14.1993 1.01165 0.505827 0.862635i \(-0.331187\pi\)
0.505827 + 0.862635i \(0.331187\pi\)
\(198\) 7.61509 0.541181
\(199\) 18.5251 1.31321 0.656606 0.754234i \(-0.271992\pi\)
0.656606 + 0.754234i \(0.271992\pi\)
\(200\) −3.40773 −0.240963
\(201\) 8.32506 0.587204
\(202\) 17.2846 1.21614
\(203\) 0.0392672 0.00275602
\(204\) −0.224596 −0.0157249
\(205\) −9.06005 −0.632782
\(206\) 1.55573 0.108393
\(207\) 9.05681 0.629492
\(208\) −4.66394 −0.323386
\(209\) −1.23298 −0.0852869
\(210\) −0.106073 −0.00731976
\(211\) 19.0545 1.31177 0.655884 0.754861i \(-0.272296\pi\)
0.655884 + 0.754861i \(0.272296\pi\)
\(212\) −1.80477 −0.123952
\(213\) 1.08614 0.0744209
\(214\) 8.86023 0.605673
\(215\) 23.1712 1.58027
\(216\) −2.45759 −0.167218
\(217\) −0.00140196 −9.51712e−5 0
\(218\) 23.1351 1.56691
\(219\) −7.48444 −0.505751
\(220\) 3.91069 0.263659
\(221\) 0.534376 0.0359460
\(222\) −12.2220 −0.820288
\(223\) 25.1849 1.68651 0.843253 0.537516i \(-0.180637\pi\)
0.843253 + 0.537516i \(0.180637\pi\)
\(224\) 0.0839560 0.00560954
\(225\) −1.38661 −0.0924408
\(226\) 29.2717 1.94712
\(227\) 29.0343 1.92707 0.963536 0.267580i \(-0.0862238\pi\)
0.963536 + 0.267580i \(0.0862238\pi\)
\(228\) −0.105869 −0.00701137
\(229\) 1.96397 0.129783 0.0648913 0.997892i \(-0.479330\pi\)
0.0648913 + 0.997892i \(0.479330\pi\)
\(230\) 26.7835 1.76605
\(231\) 0.175572 0.0115518
\(232\) 2.69045 0.176637
\(233\) 7.21438 0.472630 0.236315 0.971677i \(-0.424060\pi\)
0.236315 + 0.971677i \(0.424060\pi\)
\(234\) −1.55573 −0.101701
\(235\) −0.449345 −0.0293121
\(236\) 5.82474 0.379158
\(237\) −1.11032 −0.0721230
\(238\) −0.0298192 −0.00193289
\(239\) −13.4023 −0.866920 −0.433460 0.901173i \(-0.642707\pi\)
−0.433460 + 0.901173i \(0.642707\pi\)
\(240\) −8.86565 −0.572275
\(241\) −11.8626 −0.764137 −0.382069 0.924134i \(-0.624788\pi\)
−0.382069 + 0.924134i \(0.624788\pi\)
\(242\) −20.1618 −1.29605
\(243\) −1.00000 −0.0641500
\(244\) −2.09220 −0.133940
\(245\) 13.3038 0.849948
\(246\) 7.41494 0.472759
\(247\) 0.251892 0.0160275
\(248\) −0.0960574 −0.00609965
\(249\) 12.3101 0.780122
\(250\) −18.8870 −1.19452
\(251\) 1.30407 0.0823120 0.0411560 0.999153i \(-0.486896\pi\)
0.0411560 + 0.999153i \(0.486896\pi\)
\(252\) 0.0150754 0.000949664 0
\(253\) −44.3319 −2.78712
\(254\) −3.84942 −0.241534
\(255\) 1.01579 0.0636113
\(256\) 9.67284 0.604553
\(257\) 19.9765 1.24610 0.623049 0.782183i \(-0.285894\pi\)
0.623049 + 0.782183i \(0.285894\pi\)
\(258\) −18.9638 −1.18064
\(259\) −0.281789 −0.0175095
\(260\) −0.798937 −0.0495480
\(261\) 1.09475 0.0677633
\(262\) 24.0935 1.48850
\(263\) 26.2345 1.61769 0.808845 0.588022i \(-0.200093\pi\)
0.808845 + 0.588022i \(0.200093\pi\)
\(264\) 12.0296 0.740370
\(265\) 8.16249 0.501418
\(266\) −0.0140561 −0.000861833 0
\(267\) −12.9144 −0.790350
\(268\) −3.49899 −0.213735
\(269\) −1.20388 −0.0734021 −0.0367011 0.999326i \(-0.511685\pi\)
−0.0367011 + 0.999326i \(0.511685\pi\)
\(270\) −2.95727 −0.179974
\(271\) 26.2188 1.59268 0.796340 0.604849i \(-0.206767\pi\)
0.796340 + 0.604849i \(0.206767\pi\)
\(272\) −2.49230 −0.151118
\(273\) −0.0358686 −0.00217087
\(274\) 0.616987 0.0372736
\(275\) 6.78728 0.409289
\(276\) −3.80654 −0.229127
\(277\) −5.26115 −0.316112 −0.158056 0.987430i \(-0.550523\pi\)
−0.158056 + 0.987430i \(0.550523\pi\)
\(278\) 8.43816 0.506087
\(279\) −0.0390860 −0.00234001
\(280\) −0.167565 −0.0100139
\(281\) −7.49919 −0.447364 −0.223682 0.974662i \(-0.571808\pi\)
−0.223682 + 0.974662i \(0.571808\pi\)
\(282\) 0.367754 0.0218994
\(283\) −9.16187 −0.544617 −0.272308 0.962210i \(-0.587787\pi\)
−0.272308 + 0.962210i \(0.587787\pi\)
\(284\) −0.456499 −0.0270882
\(285\) 0.478820 0.0283628
\(286\) 7.61509 0.450290
\(287\) 0.170958 0.0100913
\(288\) 2.34065 0.137924
\(289\) −16.7144 −0.983202
\(290\) 3.23748 0.190111
\(291\) −19.5036 −1.14332
\(292\) 3.14568 0.184087
\(293\) 9.32109 0.544544 0.272272 0.962220i \(-0.412225\pi\)
0.272272 + 0.962220i \(0.412225\pi\)
\(294\) −10.8881 −0.635007
\(295\) −26.3438 −1.53380
\(296\) −19.3072 −1.12221
\(297\) 4.89487 0.284029
\(298\) −21.0707 −1.22059
\(299\) 9.05681 0.523769
\(300\) 0.582788 0.0336473
\(301\) −0.437227 −0.0252013
\(302\) 18.7624 1.07965
\(303\) 11.1103 0.638267
\(304\) −1.17481 −0.0673800
\(305\) 9.46250 0.541821
\(306\) −0.831345 −0.0475248
\(307\) 21.8385 1.24639 0.623194 0.782067i \(-0.285835\pi\)
0.623194 + 0.782067i \(0.285835\pi\)
\(308\) −0.0737923 −0.00420471
\(309\) 1.00000 0.0568880
\(310\) −0.115588 −0.00656495
\(311\) 31.0320 1.75966 0.879831 0.475287i \(-0.157656\pi\)
0.879831 + 0.475287i \(0.157656\pi\)
\(312\) −2.45759 −0.139134
\(313\) 18.5465 1.04831 0.524155 0.851623i \(-0.324381\pi\)
0.524155 + 0.851623i \(0.324381\pi\)
\(314\) 34.9898 1.97459
\(315\) −0.0681824 −0.00384164
\(316\) 0.466663 0.0262519
\(317\) 31.9655 1.79536 0.897682 0.440644i \(-0.145250\pi\)
0.897682 + 0.440644i \(0.145250\pi\)
\(318\) −6.68036 −0.374616
\(319\) −5.35865 −0.300027
\(320\) −10.8094 −0.604261
\(321\) 5.69522 0.317876
\(322\) −0.505387 −0.0281641
\(323\) 0.134605 0.00748963
\(324\) 0.420296 0.0233498
\(325\) −1.38661 −0.0769154
\(326\) 0.742793 0.0411395
\(327\) 14.8709 0.822363
\(328\) 11.7134 0.646765
\(329\) 0.00847887 0.000467455 0
\(330\) 14.4755 0.796848
\(331\) 7.25012 0.398502 0.199251 0.979948i \(-0.436149\pi\)
0.199251 + 0.979948i \(0.436149\pi\)
\(332\) −5.17389 −0.283954
\(333\) −7.85613 −0.430513
\(334\) 18.4869 1.01156
\(335\) 15.8250 0.864614
\(336\) 0.167289 0.00912638
\(337\) −18.0727 −0.984484 −0.492242 0.870458i \(-0.663823\pi\)
−0.492242 + 0.870458i \(0.663823\pi\)
\(338\) −1.55573 −0.0846206
\(339\) 18.8154 1.02191
\(340\) −0.426933 −0.0231537
\(341\) 0.191320 0.0103606
\(342\) −0.391876 −0.0211902
\(343\) −0.502115 −0.0271116
\(344\) −29.9573 −1.61519
\(345\) 17.2160 0.926879
\(346\) 8.95150 0.481235
\(347\) 35.4091 1.90086 0.950431 0.310936i \(-0.100643\pi\)
0.950431 + 0.310936i \(0.100643\pi\)
\(348\) −0.460119 −0.0246650
\(349\) −5.28216 −0.282748 −0.141374 0.989956i \(-0.545152\pi\)
−0.141374 + 0.989956i \(0.545152\pi\)
\(350\) 0.0773756 0.00413590
\(351\) −1.00000 −0.0533761
\(352\) −11.4572 −0.610669
\(353\) −26.5517 −1.41321 −0.706603 0.707610i \(-0.749773\pi\)
−0.706603 + 0.707610i \(0.749773\pi\)
\(354\) 21.5603 1.14592
\(355\) 2.06463 0.109579
\(356\) 5.42788 0.287677
\(357\) −0.0191673 −0.00101444
\(358\) −9.85260 −0.520726
\(359\) 0.438112 0.0231227 0.0115613 0.999933i \(-0.496320\pi\)
0.0115613 + 0.999933i \(0.496320\pi\)
\(360\) −4.67162 −0.246216
\(361\) −18.9366 −0.996661
\(362\) −1.65772 −0.0871277
\(363\) −12.9597 −0.680208
\(364\) 0.0150754 0.000790168 0
\(365\) −14.2271 −0.744681
\(366\) −7.74431 −0.404802
\(367\) −3.56264 −0.185968 −0.0929842 0.995668i \(-0.529641\pi\)
−0.0929842 + 0.995668i \(0.529641\pi\)
\(368\) −42.2404 −2.20194
\(369\) 4.76621 0.248119
\(370\) −23.2327 −1.20781
\(371\) −0.154021 −0.00799638
\(372\) 0.0164277 0.000851735 0
\(373\) 34.4069 1.78152 0.890761 0.454472i \(-0.150172\pi\)
0.890761 + 0.454472i \(0.150172\pi\)
\(374\) 4.06932 0.210420
\(375\) −12.1403 −0.626920
\(376\) 0.580942 0.0299598
\(377\) 1.09475 0.0563825
\(378\) 0.0558019 0.00287014
\(379\) 23.6696 1.21583 0.607913 0.794004i \(-0.292007\pi\)
0.607913 + 0.794004i \(0.292007\pi\)
\(380\) −0.201246 −0.0103237
\(381\) −2.47435 −0.126765
\(382\) −10.2504 −0.524454
\(383\) 32.0837 1.63940 0.819700 0.572793i \(-0.194140\pi\)
0.819700 + 0.572793i \(0.194140\pi\)
\(384\) 13.5279 0.690343
\(385\) 0.333744 0.0170091
\(386\) 6.89676 0.351036
\(387\) −12.1897 −0.619636
\(388\) 8.19729 0.416154
\(389\) −27.2417 −1.38121 −0.690604 0.723233i \(-0.742655\pi\)
−0.690604 + 0.723233i \(0.742655\pi\)
\(390\) −2.95727 −0.149747
\(391\) 4.83974 0.244756
\(392\) −17.2000 −0.868731
\(393\) 15.4870 0.781214
\(394\) −22.0902 −1.11289
\(395\) −2.11060 −0.106196
\(396\) −2.05729 −0.103383
\(397\) −3.20402 −0.160805 −0.0804026 0.996762i \(-0.525621\pi\)
−0.0804026 + 0.996762i \(0.525621\pi\)
\(398\) −28.8201 −1.44462
\(399\) −0.00903503 −0.000452317 0
\(400\) 6.46708 0.323354
\(401\) 5.76770 0.288025 0.144013 0.989576i \(-0.453999\pi\)
0.144013 + 0.989576i \(0.453999\pi\)
\(402\) −12.9515 −0.645964
\(403\) −0.0390860 −0.00194701
\(404\) −4.66960 −0.232321
\(405\) −1.90089 −0.0944560
\(406\) −0.0610891 −0.00303180
\(407\) 38.4547 1.90613
\(408\) −1.31328 −0.0650170
\(409\) 32.2722 1.59576 0.797879 0.602818i \(-0.205956\pi\)
0.797879 + 0.602818i \(0.205956\pi\)
\(410\) 14.0950 0.696102
\(411\) 0.396590 0.0195624
\(412\) −0.420296 −0.0207065
\(413\) 0.497091 0.0244603
\(414\) −14.0900 −0.692483
\(415\) 23.4002 1.14867
\(416\) 2.34065 0.114760
\(417\) 5.42392 0.265611
\(418\) 1.91818 0.0938213
\(419\) 30.3398 1.48220 0.741098 0.671397i \(-0.234306\pi\)
0.741098 + 0.671397i \(0.234306\pi\)
\(420\) 0.0286568 0.00139831
\(421\) 8.42042 0.410386 0.205193 0.978721i \(-0.434218\pi\)
0.205193 + 0.978721i \(0.434218\pi\)
\(422\) −29.6437 −1.44303
\(423\) 0.236387 0.0114935
\(424\) −10.5530 −0.512498
\(425\) −0.740973 −0.0359424
\(426\) −1.68974 −0.0818679
\(427\) −0.178551 −0.00864071
\(428\) −2.39368 −0.115703
\(429\) 4.89487 0.236326
\(430\) −36.0482 −1.73840
\(431\) −33.7404 −1.62522 −0.812610 0.582808i \(-0.801954\pi\)
−0.812610 + 0.582808i \(0.801954\pi\)
\(432\) 4.66394 0.224394
\(433\) 30.1503 1.44893 0.724466 0.689311i \(-0.242087\pi\)
0.724466 + 0.689311i \(0.242087\pi\)
\(434\) 0.00218107 0.000104695 0
\(435\) 2.08100 0.0997763
\(436\) −6.25018 −0.299329
\(437\) 2.28134 0.109131
\(438\) 11.6438 0.556361
\(439\) −26.8258 −1.28033 −0.640163 0.768239i \(-0.721133\pi\)
−0.640163 + 0.768239i \(0.721133\pi\)
\(440\) 22.8669 1.09014
\(441\) −6.99871 −0.333272
\(442\) −0.831345 −0.0395430
\(443\) 2.45757 0.116763 0.0583813 0.998294i \(-0.481406\pi\)
0.0583813 + 0.998294i \(0.481406\pi\)
\(444\) 3.30190 0.156701
\(445\) −24.5489 −1.16373
\(446\) −39.1809 −1.85527
\(447\) −13.5439 −0.640606
\(448\) 0.203966 0.00963647
\(449\) −17.3572 −0.819138 −0.409569 0.912279i \(-0.634321\pi\)
−0.409569 + 0.912279i \(0.634321\pi\)
\(450\) 2.15720 0.101691
\(451\) −23.3300 −1.09857
\(452\) −7.90803 −0.371963
\(453\) 12.0602 0.566636
\(454\) −45.1695 −2.11991
\(455\) −0.0681824 −0.00319644
\(456\) −0.619048 −0.0289896
\(457\) −10.0498 −0.470108 −0.235054 0.971982i \(-0.575527\pi\)
−0.235054 + 0.971982i \(0.575527\pi\)
\(458\) −3.05540 −0.142770
\(459\) −0.534376 −0.0249425
\(460\) −7.23582 −0.337372
\(461\) −8.90788 −0.414881 −0.207441 0.978248i \(-0.566513\pi\)
−0.207441 + 0.978248i \(0.566513\pi\)
\(462\) −0.273143 −0.0127078
\(463\) 12.1778 0.565949 0.282975 0.959127i \(-0.408679\pi\)
0.282975 + 0.959127i \(0.408679\pi\)
\(464\) −5.10585 −0.237033
\(465\) −0.0742981 −0.00344549
\(466\) −11.2236 −0.519925
\(467\) −30.3265 −1.40334 −0.701671 0.712501i \(-0.747562\pi\)
−0.701671 + 0.712501i \(0.747562\pi\)
\(468\) 0.420296 0.0194282
\(469\) −0.298608 −0.0137885
\(470\) 0.699060 0.0322452
\(471\) 22.4909 1.03633
\(472\) 34.0589 1.56769
\(473\) 59.6668 2.74348
\(474\) 1.72736 0.0793402
\(475\) −0.349277 −0.0160259
\(476\) 0.00805596 0.000369244 0
\(477\) −4.29403 −0.196610
\(478\) 20.8503 0.953670
\(479\) −28.8604 −1.31867 −0.659333 0.751851i \(-0.729161\pi\)
−0.659333 + 0.751851i \(0.729161\pi\)
\(480\) 4.44932 0.203083
\(481\) −7.85613 −0.358209
\(482\) 18.4550 0.840602
\(483\) −0.324855 −0.0147814
\(484\) 5.44691 0.247587
\(485\) −37.0742 −1.68345
\(486\) 1.55573 0.0705694
\(487\) −29.7213 −1.34680 −0.673400 0.739278i \(-0.735167\pi\)
−0.673400 + 0.739278i \(0.735167\pi\)
\(488\) −12.2337 −0.553794
\(489\) 0.477456 0.0215913
\(490\) −20.6971 −0.935000
\(491\) 27.1608 1.22575 0.612875 0.790180i \(-0.290013\pi\)
0.612875 + 0.790180i \(0.290013\pi\)
\(492\) −2.00322 −0.0903122
\(493\) 0.585008 0.0263474
\(494\) −0.391876 −0.0176313
\(495\) 9.30461 0.418211
\(496\) 0.182295 0.00818527
\(497\) −0.0389582 −0.00174752
\(498\) −19.1512 −0.858186
\(499\) −0.717096 −0.0321016 −0.0160508 0.999871i \(-0.505109\pi\)
−0.0160508 + 0.999871i \(0.505109\pi\)
\(500\) 5.10250 0.228191
\(501\) 11.8831 0.530897
\(502\) −2.02878 −0.0905488
\(503\) −32.0236 −1.42786 −0.713931 0.700216i \(-0.753087\pi\)
−0.713931 + 0.700216i \(0.753087\pi\)
\(504\) 0.0881505 0.00392654
\(505\) 21.1194 0.939800
\(506\) 68.9684 3.06602
\(507\) −1.00000 −0.0444116
\(508\) 1.03996 0.0461407
\(509\) 28.3129 1.25495 0.627473 0.778638i \(-0.284089\pi\)
0.627473 + 0.778638i \(0.284089\pi\)
\(510\) −1.58030 −0.0699767
\(511\) 0.268457 0.0118758
\(512\) 12.0075 0.530661
\(513\) −0.251892 −0.0111213
\(514\) −31.0780 −1.37079
\(515\) 1.90089 0.0837633
\(516\) 5.12327 0.225539
\(517\) −1.15708 −0.0508884
\(518\) 0.438387 0.0192616
\(519\) 5.75389 0.252568
\(520\) −4.67162 −0.204864
\(521\) −20.5538 −0.900480 −0.450240 0.892908i \(-0.648662\pi\)
−0.450240 + 0.892908i \(0.648662\pi\)
\(522\) −1.70314 −0.0745442
\(523\) 14.8844 0.650851 0.325425 0.945568i \(-0.394492\pi\)
0.325425 + 0.945568i \(0.394492\pi\)
\(524\) −6.50911 −0.284352
\(525\) 0.0497359 0.00217065
\(526\) −40.8139 −1.77957
\(527\) −0.0208866 −0.000909834 0
\(528\) −22.8294 −0.993521
\(529\) 59.0258 2.56634
\(530\) −12.6986 −0.551593
\(531\) 13.8587 0.601415
\(532\) 0.00379739 0.000164638 0
\(533\) 4.76621 0.206448
\(534\) 20.0914 0.869438
\(535\) 10.8260 0.468049
\(536\) −20.4596 −0.883720
\(537\) −6.33310 −0.273294
\(538\) 1.87292 0.0807473
\(539\) 34.2578 1.47559
\(540\) 0.798937 0.0343808
\(541\) −1.01832 −0.0437808 −0.0218904 0.999760i \(-0.506968\pi\)
−0.0218904 + 0.999760i \(0.506968\pi\)
\(542\) −40.7894 −1.75206
\(543\) −1.06556 −0.0457274
\(544\) 1.25079 0.0536271
\(545\) 28.2680 1.21087
\(546\) 0.0558019 0.00238810
\(547\) −4.97328 −0.212642 −0.106321 0.994332i \(-0.533907\pi\)
−0.106321 + 0.994332i \(0.533907\pi\)
\(548\) −0.166685 −0.00712045
\(549\) −4.97793 −0.212453
\(550\) −10.5592 −0.450245
\(551\) 0.275759 0.0117477
\(552\) −22.2579 −0.947361
\(553\) 0.0398257 0.00169356
\(554\) 8.18493 0.347744
\(555\) −14.9336 −0.633898
\(556\) −2.27965 −0.0966788
\(557\) 38.8606 1.64658 0.823288 0.567624i \(-0.192137\pi\)
0.823288 + 0.567624i \(0.192137\pi\)
\(558\) 0.0608072 0.00257417
\(559\) −12.1897 −0.515568
\(560\) 0.317999 0.0134379
\(561\) 2.61570 0.110435
\(562\) 11.6667 0.492131
\(563\) 18.8758 0.795520 0.397760 0.917489i \(-0.369788\pi\)
0.397760 + 0.917489i \(0.369788\pi\)
\(564\) −0.0993524 −0.00418349
\(565\) 35.7660 1.50469
\(566\) 14.2534 0.599115
\(567\) 0.0358686 0.00150634
\(568\) −2.66928 −0.112001
\(569\) 45.2348 1.89634 0.948170 0.317764i \(-0.102932\pi\)
0.948170 + 0.317764i \(0.102932\pi\)
\(570\) −0.744914 −0.0312010
\(571\) −43.7121 −1.82930 −0.914648 0.404251i \(-0.867532\pi\)
−0.914648 + 0.404251i \(0.867532\pi\)
\(572\) −2.05729 −0.0860197
\(573\) −6.58878 −0.275250
\(574\) −0.265964 −0.0111011
\(575\) −12.5583 −0.523717
\(576\) 5.68646 0.236936
\(577\) 21.8607 0.910074 0.455037 0.890473i \(-0.349626\pi\)
0.455037 + 0.890473i \(0.349626\pi\)
\(578\) 26.0032 1.08159
\(579\) 4.43314 0.184235
\(580\) −0.874636 −0.0363173
\(581\) −0.441547 −0.0183185
\(582\) 30.3424 1.25773
\(583\) 21.0187 0.870506
\(584\) 18.3937 0.761137
\(585\) −1.90089 −0.0785922
\(586\) −14.5011 −0.599035
\(587\) 40.3603 1.66585 0.832924 0.553388i \(-0.186665\pi\)
0.832924 + 0.553388i \(0.186665\pi\)
\(588\) 2.94153 0.121307
\(589\) −0.00984545 −0.000405675 0
\(590\) 40.9838 1.68728
\(591\) −14.1993 −0.584079
\(592\) 36.6405 1.50592
\(593\) −25.0594 −1.02906 −0.514532 0.857471i \(-0.672034\pi\)
−0.514532 + 0.857471i \(0.672034\pi\)
\(594\) −7.61509 −0.312451
\(595\) −0.0364350 −0.00149369
\(596\) 5.69246 0.233172
\(597\) −18.5251 −0.758183
\(598\) −14.0900 −0.576181
\(599\) 25.6823 1.04935 0.524675 0.851303i \(-0.324187\pi\)
0.524675 + 0.851303i \(0.324187\pi\)
\(600\) 3.40773 0.139120
\(601\) −18.3879 −0.750057 −0.375029 0.927013i \(-0.622367\pi\)
−0.375029 + 0.927013i \(0.622367\pi\)
\(602\) 0.680207 0.0277232
\(603\) −8.32506 −0.339023
\(604\) −5.06884 −0.206248
\(605\) −24.6350 −1.00155
\(606\) −17.2846 −0.702137
\(607\) −3.58164 −0.145374 −0.0726872 0.997355i \(-0.523157\pi\)
−0.0726872 + 0.997355i \(0.523157\pi\)
\(608\) 0.589592 0.0239111
\(609\) −0.0392672 −0.00159119
\(610\) −14.7211 −0.596039
\(611\) 0.236387 0.00956318
\(612\) 0.224596 0.00907876
\(613\) −42.2637 −1.70701 −0.853507 0.521081i \(-0.825529\pi\)
−0.853507 + 0.521081i \(0.825529\pi\)
\(614\) −33.9748 −1.37111
\(615\) 9.06005 0.365337
\(616\) −0.431485 −0.0173850
\(617\) −24.0812 −0.969473 −0.484737 0.874660i \(-0.661085\pi\)
−0.484737 + 0.874660i \(0.661085\pi\)
\(618\) −1.55573 −0.0625806
\(619\) −30.3097 −1.21825 −0.609124 0.793075i \(-0.708479\pi\)
−0.609124 + 0.793075i \(0.708479\pi\)
\(620\) 0.0312272 0.00125412
\(621\) −9.05681 −0.363437
\(622\) −48.2774 −1.93575
\(623\) 0.463223 0.0185586
\(624\) 4.66394 0.186707
\(625\) −16.1442 −0.645770
\(626\) −28.8533 −1.15321
\(627\) 1.23298 0.0492404
\(628\) −9.45283 −0.377209
\(629\) −4.19812 −0.167390
\(630\) 0.106073 0.00422606
\(631\) 26.8025 1.06699 0.533496 0.845802i \(-0.320878\pi\)
0.533496 + 0.845802i \(0.320878\pi\)
\(632\) 2.72871 0.108542
\(633\) −19.0545 −0.757350
\(634\) −49.7298 −1.97502
\(635\) −4.70346 −0.186651
\(636\) 1.80477 0.0715636
\(637\) −6.99871 −0.277299
\(638\) 8.33662 0.330050
\(639\) −1.08614 −0.0429669
\(640\) 25.7151 1.01648
\(641\) 24.3105 0.960207 0.480103 0.877212i \(-0.340599\pi\)
0.480103 + 0.877212i \(0.340599\pi\)
\(642\) −8.86023 −0.349685
\(643\) 42.2245 1.66517 0.832585 0.553897i \(-0.186860\pi\)
0.832585 + 0.553897i \(0.186860\pi\)
\(644\) 0.136535 0.00538025
\(645\) −23.1712 −0.912367
\(646\) −0.209409 −0.00823910
\(647\) −10.5044 −0.412969 −0.206484 0.978450i \(-0.566202\pi\)
−0.206484 + 0.978450i \(0.566202\pi\)
\(648\) 2.45759 0.0965434
\(649\) −67.8363 −2.66281
\(650\) 2.15720 0.0846122
\(651\) 0.00140196 5.49471e−5 0
\(652\) −0.200673 −0.00785896
\(653\) 4.46492 0.174726 0.0873628 0.996177i \(-0.472156\pi\)
0.0873628 + 0.996177i \(0.472156\pi\)
\(654\) −23.1351 −0.904654
\(655\) 29.4390 1.15028
\(656\) −22.2294 −0.867910
\(657\) 7.48444 0.291996
\(658\) −0.0131908 −0.000514232 0
\(659\) −3.42365 −0.133367 −0.0666833 0.997774i \(-0.521242\pi\)
−0.0666833 + 0.997774i \(0.521242\pi\)
\(660\) −3.91069 −0.152223
\(661\) 21.8750 0.850837 0.425419 0.904997i \(-0.360127\pi\)
0.425419 + 0.904997i \(0.360127\pi\)
\(662\) −11.2792 −0.438380
\(663\) −0.534376 −0.0207534
\(664\) −30.2532 −1.17405
\(665\) −0.0171746 −0.000666003 0
\(666\) 12.2220 0.473593
\(667\) 9.91494 0.383908
\(668\) −4.99442 −0.193240
\(669\) −25.1849 −0.973705
\(670\) −24.6195 −0.951133
\(671\) 24.3663 0.940650
\(672\) −0.0839560 −0.00323867
\(673\) 6.84061 0.263686 0.131843 0.991271i \(-0.457910\pi\)
0.131843 + 0.991271i \(0.457910\pi\)
\(674\) 28.1163 1.08300
\(675\) 1.38661 0.0533707
\(676\) 0.420296 0.0161652
\(677\) 4.03421 0.155047 0.0775236 0.996991i \(-0.475299\pi\)
0.0775236 + 0.996991i \(0.475299\pi\)
\(678\) −29.2717 −1.12417
\(679\) 0.699568 0.0268469
\(680\) −2.49640 −0.0957326
\(681\) −29.0343 −1.11260
\(682\) −0.297643 −0.0113973
\(683\) −30.7886 −1.17809 −0.589046 0.808099i \(-0.700496\pi\)
−0.589046 + 0.808099i \(0.700496\pi\)
\(684\) 0.105869 0.00404801
\(685\) 0.753875 0.0288041
\(686\) 0.781155 0.0298246
\(687\) −1.96397 −0.0749300
\(688\) 56.8519 2.16746
\(689\) −4.29403 −0.163590
\(690\) −26.7835 −1.01963
\(691\) 39.0616 1.48597 0.742986 0.669307i \(-0.233409\pi\)
0.742986 + 0.669307i \(0.233409\pi\)
\(692\) −2.41834 −0.0919314
\(693\) −0.175572 −0.00666943
\(694\) −55.0870 −2.09108
\(695\) 10.3103 0.391091
\(696\) −2.69045 −0.101981
\(697\) 2.54695 0.0964726
\(698\) 8.21761 0.311041
\(699\) −7.21438 −0.272873
\(700\) −0.0209038 −0.000790090 0
\(701\) 8.50990 0.321415 0.160707 0.987002i \(-0.448622\pi\)
0.160707 + 0.987002i \(0.448622\pi\)
\(702\) 1.55573 0.0587172
\(703\) −1.97890 −0.0746355
\(704\) −27.8345 −1.04905
\(705\) 0.449345 0.0169233
\(706\) 41.3073 1.55462
\(707\) −0.398509 −0.0149875
\(708\) −5.82474 −0.218907
\(709\) 0.789559 0.0296525 0.0148262 0.999890i \(-0.495280\pi\)
0.0148262 + 0.999890i \(0.495280\pi\)
\(710\) −3.21200 −0.120544
\(711\) 1.11032 0.0416402
\(712\) 31.7384 1.18945
\(713\) −0.353994 −0.0132572
\(714\) 0.0298192 0.00111596
\(715\) 9.30461 0.347973
\(716\) 2.66178 0.0994753
\(717\) 13.4023 0.500517
\(718\) −0.681584 −0.0254365
\(719\) −47.0102 −1.75318 −0.876591 0.481235i \(-0.840188\pi\)
−0.876591 + 0.481235i \(0.840188\pi\)
\(720\) 8.86565 0.330403
\(721\) −0.0358686 −0.00133582
\(722\) 29.4602 1.09639
\(723\) 11.8626 0.441175
\(724\) 0.447849 0.0166442
\(725\) −1.51799 −0.0563769
\(726\) 20.1618 0.748275
\(727\) −38.8714 −1.44166 −0.720831 0.693111i \(-0.756240\pi\)
−0.720831 + 0.693111i \(0.756240\pi\)
\(728\) 0.0881505 0.00326707
\(729\) 1.00000 0.0370370
\(730\) 22.1335 0.819199
\(731\) −6.51387 −0.240924
\(732\) 2.09220 0.0773300
\(733\) 16.1652 0.597075 0.298538 0.954398i \(-0.403501\pi\)
0.298538 + 0.954398i \(0.403501\pi\)
\(734\) 5.54251 0.204578
\(735\) −13.3038 −0.490718
\(736\) 21.1988 0.781399
\(737\) 40.7500 1.50105
\(738\) −7.41494 −0.272948
\(739\) −43.6800 −1.60680 −0.803398 0.595443i \(-0.796977\pi\)
−0.803398 + 0.595443i \(0.796977\pi\)
\(740\) 6.27655 0.230731
\(741\) −0.251892 −0.00925349
\(742\) 0.239615 0.00879656
\(743\) −13.1409 −0.482092 −0.241046 0.970514i \(-0.577490\pi\)
−0.241046 + 0.970514i \(0.577490\pi\)
\(744\) 0.0960574 0.00352163
\(745\) −25.7456 −0.943244
\(746\) −53.5279 −1.95979
\(747\) −12.3101 −0.450403
\(748\) −1.09937 −0.0401969
\(749\) −0.204280 −0.00746422
\(750\) 18.8870 0.689654
\(751\) −23.7021 −0.864900 −0.432450 0.901658i \(-0.642351\pi\)
−0.432450 + 0.901658i \(0.642351\pi\)
\(752\) −1.10249 −0.0402038
\(753\) −1.30407 −0.0475229
\(754\) −1.70314 −0.0620245
\(755\) 22.9250 0.834328
\(756\) −0.0150754 −0.000548289 0
\(757\) 19.5982 0.712309 0.356155 0.934427i \(-0.384088\pi\)
0.356155 + 0.934427i \(0.384088\pi\)
\(758\) −36.8235 −1.33749
\(759\) 44.3319 1.60914
\(760\) −1.17674 −0.0426850
\(761\) −34.3378 −1.24474 −0.622372 0.782722i \(-0.713831\pi\)
−0.622372 + 0.782722i \(0.713831\pi\)
\(762\) 3.84942 0.139450
\(763\) −0.533399 −0.0193103
\(764\) 2.76924 0.100188
\(765\) −1.01579 −0.0367260
\(766\) −49.9136 −1.80345
\(767\) 13.8587 0.500407
\(768\) −9.67284 −0.349039
\(769\) 21.9549 0.791715 0.395858 0.918312i \(-0.370447\pi\)
0.395858 + 0.918312i \(0.370447\pi\)
\(770\) −0.519215 −0.0187112
\(771\) −19.9765 −0.719435
\(772\) −1.86323 −0.0670591
\(773\) −37.6754 −1.35509 −0.677546 0.735481i \(-0.736956\pi\)
−0.677546 + 0.735481i \(0.736956\pi\)
\(774\) 18.9638 0.681641
\(775\) 0.0541971 0.00194682
\(776\) 47.9319 1.72066
\(777\) 0.281789 0.0101091
\(778\) 42.3807 1.51942
\(779\) 1.20057 0.0430150
\(780\) 0.798937 0.0286065
\(781\) 5.31649 0.190239
\(782\) −7.52933 −0.269248
\(783\) −1.09475 −0.0391232
\(784\) 32.6416 1.16577
\(785\) 42.7527 1.52591
\(786\) −24.0935 −0.859388
\(787\) 28.6748 1.02215 0.511073 0.859537i \(-0.329248\pi\)
0.511073 + 0.859537i \(0.329248\pi\)
\(788\) 5.96789 0.212597
\(789\) −26.2345 −0.933974
\(790\) 3.28352 0.116822
\(791\) −0.674882 −0.0239960
\(792\) −12.0296 −0.427453
\(793\) −4.97793 −0.176771
\(794\) 4.98459 0.176897
\(795\) −8.16249 −0.289494
\(796\) 7.78604 0.275969
\(797\) 8.48894 0.300694 0.150347 0.988633i \(-0.451961\pi\)
0.150347 + 0.988633i \(0.451961\pi\)
\(798\) 0.0140561 0.000497579 0
\(799\) 0.126319 0.00446886
\(800\) −3.24558 −0.114748
\(801\) 12.9144 0.456309
\(802\) −8.97299 −0.316847
\(803\) −36.6353 −1.29283
\(804\) 3.49899 0.123400
\(805\) −0.617515 −0.0217645
\(806\) 0.0608072 0.00214184
\(807\) 1.20388 0.0423787
\(808\) −27.3045 −0.960568
\(809\) 26.8291 0.943262 0.471631 0.881796i \(-0.343665\pi\)
0.471631 + 0.881796i \(0.343665\pi\)
\(810\) 2.95727 0.103908
\(811\) 21.9442 0.770567 0.385283 0.922798i \(-0.374104\pi\)
0.385283 + 0.922798i \(0.374104\pi\)
\(812\) 0.0165038 0.000579171 0
\(813\) −26.2188 −0.919534
\(814\) −59.8251 −2.09687
\(815\) 0.907592 0.0317916
\(816\) 2.49230 0.0872479
\(817\) −3.07048 −0.107423
\(818\) −50.2068 −1.75544
\(819\) 0.0358686 0.00125335
\(820\) −3.80791 −0.132978
\(821\) 14.0185 0.489248 0.244624 0.969618i \(-0.421335\pi\)
0.244624 + 0.969618i \(0.421335\pi\)
\(822\) −0.616987 −0.0215199
\(823\) 36.5432 1.27381 0.636907 0.770941i \(-0.280213\pi\)
0.636907 + 0.770941i \(0.280213\pi\)
\(824\) −2.45759 −0.0856143
\(825\) −6.78728 −0.236303
\(826\) −0.773340 −0.0269079
\(827\) 47.9632 1.66784 0.833921 0.551883i \(-0.186091\pi\)
0.833921 + 0.551883i \(0.186091\pi\)
\(828\) 3.80654 0.132286
\(829\) −40.0084 −1.38955 −0.694775 0.719227i \(-0.744496\pi\)
−0.694775 + 0.719227i \(0.744496\pi\)
\(830\) −36.4044 −1.26361
\(831\) 5.26115 0.182507
\(832\) 5.68646 0.197143
\(833\) −3.73994 −0.129581
\(834\) −8.43816 −0.292189
\(835\) 22.5885 0.781706
\(836\) −0.518216 −0.0179229
\(837\) 0.0390860 0.00135101
\(838\) −47.2005 −1.63051
\(839\) −9.88436 −0.341246 −0.170623 0.985336i \(-0.554578\pi\)
−0.170623 + 0.985336i \(0.554578\pi\)
\(840\) 0.167565 0.00578152
\(841\) −27.8015 −0.958673
\(842\) −13.0999 −0.451453
\(843\) 7.49919 0.258286
\(844\) 8.00855 0.275666
\(845\) −1.90089 −0.0653926
\(846\) −0.367754 −0.0126436
\(847\) 0.464847 0.0159723
\(848\) 20.0271 0.687735
\(849\) 9.16187 0.314435
\(850\) 1.15275 0.0395391
\(851\) −71.1514 −2.43904
\(852\) 0.456499 0.0156394
\(853\) −8.22993 −0.281787 −0.140894 0.990025i \(-0.544998\pi\)
−0.140894 + 0.990025i \(0.544998\pi\)
\(854\) 0.277778 0.00950536
\(855\) −0.478820 −0.0163753
\(856\) −13.9965 −0.478392
\(857\) −22.8180 −0.779447 −0.389724 0.920932i \(-0.627429\pi\)
−0.389724 + 0.920932i \(0.627429\pi\)
\(858\) −7.61509 −0.259975
\(859\) 8.09768 0.276289 0.138145 0.990412i \(-0.455886\pi\)
0.138145 + 0.990412i \(0.455886\pi\)
\(860\) 9.73878 0.332090
\(861\) −0.170958 −0.00582622
\(862\) 52.4910 1.78785
\(863\) 4.85749 0.165351 0.0826755 0.996577i \(-0.473654\pi\)
0.0826755 + 0.996577i \(0.473654\pi\)
\(864\) −2.34065 −0.0796306
\(865\) 10.9375 0.371887
\(866\) −46.9057 −1.59392
\(867\) 16.7144 0.567652
\(868\) −0.000589238 0 −2.00000e−5 0
\(869\) −5.43487 −0.184365
\(870\) −3.23748 −0.109761
\(871\) −8.32506 −0.282084
\(872\) −36.5466 −1.23762
\(873\) 19.5036 0.660097
\(874\) −3.54915 −0.120052
\(875\) 0.435454 0.0147210
\(876\) −3.14568 −0.106283
\(877\) 26.9048 0.908510 0.454255 0.890872i \(-0.349906\pi\)
0.454255 + 0.890872i \(0.349906\pi\)
\(878\) 41.7337 1.40845
\(879\) −9.32109 −0.314393
\(880\) −43.3962 −1.46288
\(881\) −18.5516 −0.625018 −0.312509 0.949915i \(-0.601169\pi\)
−0.312509 + 0.949915i \(0.601169\pi\)
\(882\) 10.8881 0.366622
\(883\) −1.72428 −0.0580267 −0.0290133 0.999579i \(-0.509237\pi\)
−0.0290133 + 0.999579i \(0.509237\pi\)
\(884\) 0.224596 0.00755399
\(885\) 26.3438 0.885537
\(886\) −3.82331 −0.128447
\(887\) 48.2328 1.61950 0.809749 0.586777i \(-0.199603\pi\)
0.809749 + 0.586777i \(0.199603\pi\)
\(888\) 19.3072 0.647906
\(889\) 0.0887514 0.00297663
\(890\) 38.1915 1.28018
\(891\) −4.89487 −0.163984
\(892\) 10.5851 0.354416
\(893\) 0.0595439 0.00199256
\(894\) 21.0707 0.704710
\(895\) −12.0385 −0.402404
\(896\) −0.485228 −0.0162103
\(897\) −9.05681 −0.302398
\(898\) 27.0032 0.901107
\(899\) −0.0427893 −0.00142710
\(900\) −0.582788 −0.0194263
\(901\) −2.29463 −0.0764452
\(902\) 36.2951 1.20850
\(903\) 0.437227 0.0145500
\(904\) −46.2406 −1.53794
\(905\) −2.02551 −0.0673301
\(906\) −18.7624 −0.623337
\(907\) 34.3124 1.13932 0.569661 0.821879i \(-0.307074\pi\)
0.569661 + 0.821879i \(0.307074\pi\)
\(908\) 12.2030 0.404970
\(909\) −11.1103 −0.368504
\(910\) 0.106073 0.00351630
\(911\) −27.6516 −0.916140 −0.458070 0.888916i \(-0.651459\pi\)
−0.458070 + 0.888916i \(0.651459\pi\)
\(912\) 1.17481 0.0389019
\(913\) 60.2563 1.99419
\(914\) 15.6347 0.517151
\(915\) −9.46250 −0.312820
\(916\) 0.825448 0.0272736
\(917\) −0.555496 −0.0183441
\(918\) 0.831345 0.0274385
\(919\) 48.3144 1.59375 0.796873 0.604147i \(-0.206486\pi\)
0.796873 + 0.604147i \(0.206486\pi\)
\(920\) −42.3099 −1.39492
\(921\) −21.8385 −0.719603
\(922\) 13.8583 0.456397
\(923\) −1.08614 −0.0357506
\(924\) 0.0737923 0.00242759
\(925\) 10.8934 0.358173
\(926\) −18.9453 −0.622582
\(927\) −1.00000 −0.0328443
\(928\) 2.56243 0.0841158
\(929\) 20.0230 0.656935 0.328467 0.944515i \(-0.393468\pi\)
0.328467 + 0.944515i \(0.393468\pi\)
\(930\) 0.115588 0.00379028
\(931\) −1.76292 −0.0577774
\(932\) 3.03218 0.0993222
\(933\) −31.0320 −1.01594
\(934\) 47.1798 1.54377
\(935\) 4.97216 0.162607
\(936\) 2.45759 0.0803289
\(937\) −31.1058 −1.01618 −0.508090 0.861304i \(-0.669648\pi\)
−0.508090 + 0.861304i \(0.669648\pi\)
\(938\) 0.464554 0.0151682
\(939\) −18.5465 −0.605242
\(940\) −0.188858 −0.00615987
\(941\) −6.22850 −0.203043 −0.101522 0.994833i \(-0.532371\pi\)
−0.101522 + 0.994833i \(0.532371\pi\)
\(942\) −34.9898 −1.14003
\(943\) 43.1667 1.40570
\(944\) −64.6360 −2.10372
\(945\) 0.0681824 0.00221797
\(946\) −92.8254 −3.01802
\(947\) −5.73933 −0.186503 −0.0932515 0.995643i \(-0.529726\pi\)
−0.0932515 + 0.995643i \(0.529726\pi\)
\(948\) −0.466663 −0.0151565
\(949\) 7.48444 0.242955
\(950\) 0.543381 0.0176296
\(951\) −31.9655 −1.03655
\(952\) 0.0471055 0.00152670
\(953\) −16.8709 −0.546502 −0.273251 0.961943i \(-0.588099\pi\)
−0.273251 + 0.961943i \(0.588099\pi\)
\(954\) 6.68036 0.216285
\(955\) −12.5246 −0.405285
\(956\) −5.63292 −0.182182
\(957\) 5.35865 0.173221
\(958\) 44.8990 1.45062
\(959\) −0.0142252 −0.000459354 0
\(960\) 10.8094 0.348870
\(961\) −30.9985 −0.999951
\(962\) 12.2220 0.394053
\(963\) −5.69522 −0.183526
\(964\) −4.98580 −0.160582
\(965\) 8.42691 0.271272
\(966\) 0.505387 0.0162606
\(967\) −1.69416 −0.0544806 −0.0272403 0.999629i \(-0.508672\pi\)
−0.0272403 + 0.999629i \(0.508672\pi\)
\(968\) 31.8497 1.02369
\(969\) −0.134605 −0.00432414
\(970\) 57.6775 1.85191
\(971\) 42.3831 1.36014 0.680069 0.733148i \(-0.261950\pi\)
0.680069 + 0.733148i \(0.261950\pi\)
\(972\) −0.420296 −0.0134810
\(973\) −0.194549 −0.00623694
\(974\) 46.2383 1.48157
\(975\) 1.38661 0.0444071
\(976\) 23.2168 0.743151
\(977\) 50.4319 1.61346 0.806729 0.590921i \(-0.201236\pi\)
0.806729 + 0.590921i \(0.201236\pi\)
\(978\) −0.742793 −0.0237519
\(979\) −63.2144 −2.02034
\(980\) 5.59153 0.178615
\(981\) −14.8709 −0.474791
\(982\) −42.2549 −1.34841
\(983\) −30.4746 −0.971988 −0.485994 0.873962i \(-0.661542\pi\)
−0.485994 + 0.873962i \(0.661542\pi\)
\(984\) −11.7134 −0.373410
\(985\) −26.9912 −0.860012
\(986\) −0.910115 −0.0289840
\(987\) −0.00847887 −0.000269885 0
\(988\) 0.105869 0.00336815
\(989\) −110.400 −3.51050
\(990\) −14.4755 −0.460060
\(991\) 23.1748 0.736170 0.368085 0.929792i \(-0.380013\pi\)
0.368085 + 0.929792i \(0.380013\pi\)
\(992\) −0.0914866 −0.00290470
\(993\) −7.25012 −0.230075
\(994\) 0.0606085 0.00192238
\(995\) −35.2142 −1.11637
\(996\) 5.17389 0.163941
\(997\) 36.6688 1.16131 0.580656 0.814149i \(-0.302796\pi\)
0.580656 + 0.814149i \(0.302796\pi\)
\(998\) 1.11561 0.0353139
\(999\) 7.85613 0.248557
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 \(a_p\))