Properties

Label 4017.2.a.j.1.5
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 1.5
Character \(\chi\) = 4017.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.79927 q^{2} -1.00000 q^{3} +1.23739 q^{4} +1.64720 q^{5} +1.79927 q^{6} +1.60963 q^{7} +1.37215 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.79927 q^{2} -1.00000 q^{3} +1.23739 q^{4} +1.64720 q^{5} +1.79927 q^{6} +1.60963 q^{7} +1.37215 q^{8} +1.00000 q^{9} -2.96376 q^{10} -1.34960 q^{11} -1.23739 q^{12} +1.00000 q^{13} -2.89617 q^{14} -1.64720 q^{15} -4.94365 q^{16} -5.68274 q^{17} -1.79927 q^{18} -1.69316 q^{19} +2.03822 q^{20} -1.60963 q^{21} +2.42830 q^{22} -1.20114 q^{23} -1.37215 q^{24} -2.28674 q^{25} -1.79927 q^{26} -1.00000 q^{27} +1.99174 q^{28} +4.18318 q^{29} +2.96376 q^{30} -9.37738 q^{31} +6.15068 q^{32} +1.34960 q^{33} +10.2248 q^{34} +2.65138 q^{35} +1.23739 q^{36} -0.916122 q^{37} +3.04646 q^{38} -1.00000 q^{39} +2.26020 q^{40} +10.2791 q^{41} +2.89617 q^{42} +10.8850 q^{43} -1.66998 q^{44} +1.64720 q^{45} +2.16117 q^{46} +4.44122 q^{47} +4.94365 q^{48} -4.40908 q^{49} +4.11448 q^{50} +5.68274 q^{51} +1.23739 q^{52} -6.29458 q^{53} +1.79927 q^{54} -2.22305 q^{55} +2.20866 q^{56} +1.69316 q^{57} -7.52669 q^{58} -0.514644 q^{59} -2.03822 q^{60} +13.2649 q^{61} +16.8725 q^{62} +1.60963 q^{63} -1.17946 q^{64} +1.64720 q^{65} -2.42830 q^{66} +3.26458 q^{67} -7.03175 q^{68} +1.20114 q^{69} -4.77057 q^{70} +8.99992 q^{71} +1.37215 q^{72} -13.0859 q^{73} +1.64835 q^{74} +2.28674 q^{75} -2.09510 q^{76} -2.17236 q^{77} +1.79927 q^{78} +6.11519 q^{79} -8.14316 q^{80} +1.00000 q^{81} -18.4949 q^{82} +0.847262 q^{83} -1.99174 q^{84} -9.36059 q^{85} -19.5851 q^{86} -4.18318 q^{87} -1.85185 q^{88} -1.04225 q^{89} -2.96376 q^{90} +1.60963 q^{91} -1.48627 q^{92} +9.37738 q^{93} -7.99097 q^{94} -2.78897 q^{95} -6.15068 q^{96} -1.73211 q^{97} +7.93314 q^{98} -1.34960 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 25q + 6q^{2} - 25q^{3} + 28q^{4} + 7q^{5} - 6q^{6} + 17q^{7} + 21q^{8} + 25q^{9} + O(q^{10}) \) \( 25q + 6q^{2} - 25q^{3} + 28q^{4} + 7q^{5} - 6q^{6} + 17q^{7} + 21q^{8} + 25q^{9} - 6q^{10} + 21q^{11} - 28q^{12} + 25q^{13} + 10q^{14} - 7q^{15} + 30q^{16} + 14q^{17} + 6q^{18} + 12q^{19} + 24q^{20} - 17q^{21} + 3q^{22} + 41q^{23} - 21q^{24} + 30q^{25} + 6q^{26} - 25q^{27} + 14q^{28} + 22q^{29} + 6q^{30} + 14q^{31} + 28q^{32} - 21q^{33} - 11q^{34} + 14q^{35} + 28q^{36} - 6q^{37} + 16q^{38} - 25q^{39} - 34q^{40} + 33q^{41} - 10q^{42} + 35q^{43} + 45q^{44} + 7q^{45} + 3q^{46} + 48q^{47} - 30q^{48} - 4q^{49} + 7q^{50} - 14q^{51} + 28q^{52} + 18q^{53} - 6q^{54} + 10q^{55} + 32q^{56} - 12q^{57} + 33q^{58} + 46q^{59} - 24q^{60} - 19q^{61} + 5q^{62} + 17q^{63} + 29q^{64} + 7q^{65} - 3q^{66} + 16q^{67} + 20q^{68} - 41q^{69} - 43q^{70} + 60q^{71} + 21q^{72} - 14q^{73} - 50q^{74} - 30q^{75} + 59q^{77} - 6q^{78} + 7q^{79} + 32q^{80} + 25q^{81} + 18q^{82} + 23q^{83} - 14q^{84} - 9q^{85} - 9q^{86} - 22q^{87} + 23q^{88} + 10q^{89} - 6q^{90} + 17q^{91} + 69q^{92} - 14q^{93} - 30q^{94} + 81q^{95} - 28q^{96} - 10q^{97} + 55q^{98} + 21q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.79927 −1.27228 −0.636139 0.771574i \(-0.719470\pi\)
−0.636139 + 0.771574i \(0.719470\pi\)
\(3\) −1.00000 −0.577350
\(4\) 1.23739 0.618694
\(5\) 1.64720 0.736649 0.368324 0.929697i \(-0.379932\pi\)
0.368324 + 0.929697i \(0.379932\pi\)
\(6\) 1.79927 0.734551
\(7\) 1.60963 0.608385 0.304192 0.952611i \(-0.401613\pi\)
0.304192 + 0.952611i \(0.401613\pi\)
\(8\) 1.37215 0.485128
\(9\) 1.00000 0.333333
\(10\) −2.96376 −0.937223
\(11\) −1.34960 −0.406919 −0.203459 0.979083i \(-0.565219\pi\)
−0.203459 + 0.979083i \(0.565219\pi\)
\(12\) −1.23739 −0.357203
\(13\) 1.00000 0.277350
\(14\) −2.89617 −0.774035
\(15\) −1.64720 −0.425304
\(16\) −4.94365 −1.23591
\(17\) −5.68274 −1.37827 −0.689133 0.724635i \(-0.742009\pi\)
−0.689133 + 0.724635i \(0.742009\pi\)
\(18\) −1.79927 −0.424093
\(19\) −1.69316 −0.388438 −0.194219 0.980958i \(-0.562217\pi\)
−0.194219 + 0.980958i \(0.562217\pi\)
\(20\) 2.03822 0.455760
\(21\) −1.60963 −0.351251
\(22\) 2.42830 0.517714
\(23\) −1.20114 −0.250454 −0.125227 0.992128i \(-0.539966\pi\)
−0.125227 + 0.992128i \(0.539966\pi\)
\(24\) −1.37215 −0.280089
\(25\) −2.28674 −0.457349
\(26\) −1.79927 −0.352867
\(27\) −1.00000 −0.192450
\(28\) 1.99174 0.376404
\(29\) 4.18318 0.776798 0.388399 0.921491i \(-0.373028\pi\)
0.388399 + 0.921491i \(0.373028\pi\)
\(30\) 2.96376 0.541106
\(31\) −9.37738 −1.68423 −0.842113 0.539300i \(-0.818689\pi\)
−0.842113 + 0.539300i \(0.818689\pi\)
\(32\) 6.15068 1.08730
\(33\) 1.34960 0.234935
\(34\) 10.2248 1.75354
\(35\) 2.65138 0.448166
\(36\) 1.23739 0.206231
\(37\) −0.916122 −0.150610 −0.0753048 0.997161i \(-0.523993\pi\)
−0.0753048 + 0.997161i \(0.523993\pi\)
\(38\) 3.04646 0.494202
\(39\) −1.00000 −0.160128
\(40\) 2.26020 0.357369
\(41\) 10.2791 1.60532 0.802660 0.596437i \(-0.203417\pi\)
0.802660 + 0.596437i \(0.203417\pi\)
\(42\) 2.89617 0.446889
\(43\) 10.8850 1.65995 0.829973 0.557804i \(-0.188356\pi\)
0.829973 + 0.557804i \(0.188356\pi\)
\(44\) −1.66998 −0.251758
\(45\) 1.64720 0.245550
\(46\) 2.16117 0.318648
\(47\) 4.44122 0.647818 0.323909 0.946088i \(-0.395003\pi\)
0.323909 + 0.946088i \(0.395003\pi\)
\(48\) 4.94365 0.713554
\(49\) −4.40908 −0.629868
\(50\) 4.11448 0.581875
\(51\) 5.68274 0.795743
\(52\) 1.23739 0.171595
\(53\) −6.29458 −0.864628 −0.432314 0.901723i \(-0.642303\pi\)
−0.432314 + 0.901723i \(0.642303\pi\)
\(54\) 1.79927 0.244850
\(55\) −2.22305 −0.299756
\(56\) 2.20866 0.295144
\(57\) 1.69316 0.224265
\(58\) −7.52669 −0.988303
\(59\) −0.514644 −0.0670010 −0.0335005 0.999439i \(-0.510666\pi\)
−0.0335005 + 0.999439i \(0.510666\pi\)
\(60\) −2.03822 −0.263133
\(61\) 13.2649 1.69839 0.849196 0.528078i \(-0.177087\pi\)
0.849196 + 0.528078i \(0.177087\pi\)
\(62\) 16.8725 2.14281
\(63\) 1.60963 0.202795
\(64\) −1.17946 −0.147433
\(65\) 1.64720 0.204310
\(66\) −2.42830 −0.298903
\(67\) 3.26458 0.398832 0.199416 0.979915i \(-0.436095\pi\)
0.199416 + 0.979915i \(0.436095\pi\)
\(68\) −7.03175 −0.852725
\(69\) 1.20114 0.144600
\(70\) −4.77057 −0.570192
\(71\) 8.99992 1.06809 0.534047 0.845455i \(-0.320671\pi\)
0.534047 + 0.845455i \(0.320671\pi\)
\(72\) 1.37215 0.161709
\(73\) −13.0859 −1.53158 −0.765792 0.643088i \(-0.777653\pi\)
−0.765792 + 0.643088i \(0.777653\pi\)
\(74\) 1.64835 0.191617
\(75\) 2.28674 0.264050
\(76\) −2.09510 −0.240324
\(77\) −2.17236 −0.247563
\(78\) 1.79927 0.203728
\(79\) 6.11519 0.688012 0.344006 0.938967i \(-0.388216\pi\)
0.344006 + 0.938967i \(0.388216\pi\)
\(80\) −8.14316 −0.910433
\(81\) 1.00000 0.111111
\(82\) −18.4949 −2.04242
\(83\) 0.847262 0.0929990 0.0464995 0.998918i \(-0.485193\pi\)
0.0464995 + 0.998918i \(0.485193\pi\)
\(84\) −1.99174 −0.217317
\(85\) −9.36059 −1.01530
\(86\) −19.5851 −2.11191
\(87\) −4.18318 −0.448484
\(88\) −1.85185 −0.197408
\(89\) −1.04225 −0.110478 −0.0552391 0.998473i \(-0.517592\pi\)
−0.0552391 + 0.998473i \(0.517592\pi\)
\(90\) −2.96376 −0.312408
\(91\) 1.60963 0.168736
\(92\) −1.48627 −0.154955
\(93\) 9.37738 0.972389
\(94\) −7.99097 −0.824206
\(95\) −2.78897 −0.286142
\(96\) −6.15068 −0.627751
\(97\) −1.73211 −0.175870 −0.0879348 0.996126i \(-0.528027\pi\)
−0.0879348 + 0.996126i \(0.528027\pi\)
\(98\) 7.93314 0.801368
\(99\) −1.34960 −0.135640
\(100\) −2.82959 −0.282959
\(101\) −8.16661 −0.812608 −0.406304 0.913738i \(-0.633183\pi\)
−0.406304 + 0.913738i \(0.633183\pi\)
\(102\) −10.2248 −1.01241
\(103\) −1.00000 −0.0985329
\(104\) 1.37215 0.134550
\(105\) −2.65138 −0.258749
\(106\) 11.3257 1.10005
\(107\) 15.5038 1.49881 0.749404 0.662114i \(-0.230340\pi\)
0.749404 + 0.662114i \(0.230340\pi\)
\(108\) −1.23739 −0.119068
\(109\) 17.9030 1.71480 0.857400 0.514650i \(-0.172078\pi\)
0.857400 + 0.514650i \(0.172078\pi\)
\(110\) 3.99988 0.381374
\(111\) 0.916122 0.0869545
\(112\) −7.95747 −0.751910
\(113\) 15.6571 1.47290 0.736448 0.676494i \(-0.236501\pi\)
0.736448 + 0.676494i \(0.236501\pi\)
\(114\) −3.04646 −0.285327
\(115\) −1.97851 −0.184497
\(116\) 5.17622 0.480600
\(117\) 1.00000 0.0924500
\(118\) 0.925986 0.0852439
\(119\) −9.14714 −0.838517
\(120\) −2.26020 −0.206327
\(121\) −9.17859 −0.834417
\(122\) −23.8671 −2.16083
\(123\) −10.2791 −0.926832
\(124\) −11.6035 −1.04202
\(125\) −12.0027 −1.07355
\(126\) −2.89617 −0.258012
\(127\) 19.8321 1.75981 0.879907 0.475146i \(-0.157605\pi\)
0.879907 + 0.475146i \(0.157605\pi\)
\(128\) −10.1792 −0.899721
\(129\) −10.8850 −0.958370
\(130\) −2.96376 −0.259939
\(131\) 13.8163 1.20714 0.603569 0.797311i \(-0.293745\pi\)
0.603569 + 0.797311i \(0.293745\pi\)
\(132\) 1.66998 0.145353
\(133\) −2.72537 −0.236320
\(134\) −5.87388 −0.507426
\(135\) −1.64720 −0.141768
\(136\) −7.79756 −0.668636
\(137\) −1.11420 −0.0951928 −0.0475964 0.998867i \(-0.515156\pi\)
−0.0475964 + 0.998867i \(0.515156\pi\)
\(138\) −2.16117 −0.183971
\(139\) −13.6910 −1.16126 −0.580628 0.814169i \(-0.697193\pi\)
−0.580628 + 0.814169i \(0.697193\pi\)
\(140\) 3.28079 0.277277
\(141\) −4.44122 −0.374018
\(142\) −16.1933 −1.35891
\(143\) −1.34960 −0.112859
\(144\) −4.94365 −0.411971
\(145\) 6.89052 0.572227
\(146\) 23.5450 1.94860
\(147\) 4.40908 0.363654
\(148\) −1.13360 −0.0931812
\(149\) 12.9618 1.06187 0.530937 0.847411i \(-0.321840\pi\)
0.530937 + 0.847411i \(0.321840\pi\)
\(150\) −4.11448 −0.335946
\(151\) −20.7534 −1.68889 −0.844443 0.535646i \(-0.820068\pi\)
−0.844443 + 0.535646i \(0.820068\pi\)
\(152\) −2.32327 −0.188442
\(153\) −5.68274 −0.459422
\(154\) 3.90867 0.314970
\(155\) −15.4464 −1.24068
\(156\) −1.23739 −0.0990703
\(157\) −17.8831 −1.42723 −0.713613 0.700540i \(-0.752942\pi\)
−0.713613 + 0.700540i \(0.752942\pi\)
\(158\) −11.0029 −0.875343
\(159\) 6.29458 0.499193
\(160\) 10.1314 0.800956
\(161\) −1.93339 −0.152373
\(162\) −1.79927 −0.141364
\(163\) 5.93016 0.464486 0.232243 0.972658i \(-0.425394\pi\)
0.232243 + 0.972658i \(0.425394\pi\)
\(164\) 12.7192 0.993202
\(165\) 2.22305 0.173064
\(166\) −1.52446 −0.118321
\(167\) −0.0115586 −0.000894434 0 −0.000447217 1.00000i \(-0.500142\pi\)
−0.000447217 1.00000i \(0.500142\pi\)
\(168\) −2.20866 −0.170402
\(169\) 1.00000 0.0769231
\(170\) 16.8423 1.29174
\(171\) −1.69316 −0.129479
\(172\) 13.4690 1.02700
\(173\) 15.4815 1.17703 0.588517 0.808485i \(-0.299712\pi\)
0.588517 + 0.808485i \(0.299712\pi\)
\(174\) 7.52669 0.570597
\(175\) −3.68082 −0.278244
\(176\) 6.67193 0.502916
\(177\) 0.514644 0.0386830
\(178\) 1.87529 0.140559
\(179\) 8.52693 0.637333 0.318666 0.947867i \(-0.396765\pi\)
0.318666 + 0.947867i \(0.396765\pi\)
\(180\) 2.03822 0.151920
\(181\) 4.29033 0.318898 0.159449 0.987206i \(-0.449028\pi\)
0.159449 + 0.987206i \(0.449028\pi\)
\(182\) −2.89617 −0.214679
\(183\) −13.2649 −0.980567
\(184\) −1.64814 −0.121502
\(185\) −1.50903 −0.110946
\(186\) −16.8725 −1.23715
\(187\) 7.66941 0.560843
\(188\) 5.49551 0.400801
\(189\) −1.60963 −0.117084
\(190\) 5.01812 0.364053
\(191\) 4.70275 0.340279 0.170139 0.985420i \(-0.445578\pi\)
0.170139 + 0.985420i \(0.445578\pi\)
\(192\) 1.17946 0.0851205
\(193\) 2.56339 0.184517 0.0922584 0.995735i \(-0.470591\pi\)
0.0922584 + 0.995735i \(0.470591\pi\)
\(194\) 3.11655 0.223755
\(195\) −1.64720 −0.117958
\(196\) −5.45574 −0.389695
\(197\) 1.06613 0.0759585 0.0379793 0.999279i \(-0.487908\pi\)
0.0379793 + 0.999279i \(0.487908\pi\)
\(198\) 2.42830 0.172571
\(199\) 19.4636 1.37974 0.689869 0.723934i \(-0.257668\pi\)
0.689869 + 0.723934i \(0.257668\pi\)
\(200\) −3.13775 −0.221873
\(201\) −3.26458 −0.230266
\(202\) 14.6940 1.03386
\(203\) 6.73340 0.472592
\(204\) 7.03175 0.492321
\(205\) 16.9316 1.18256
\(206\) 1.79927 0.125361
\(207\) −1.20114 −0.0834848
\(208\) −4.94365 −0.342780
\(209\) 2.28509 0.158063
\(210\) 4.77057 0.329200
\(211\) 1.10109 0.0758021 0.0379010 0.999281i \(-0.487933\pi\)
0.0379010 + 0.999281i \(0.487933\pi\)
\(212\) −7.78884 −0.534940
\(213\) −8.99992 −0.616664
\(214\) −27.8956 −1.90690
\(215\) 17.9297 1.22280
\(216\) −1.37215 −0.0933629
\(217\) −15.0942 −1.02466
\(218\) −32.2125 −2.18170
\(219\) 13.0859 0.884260
\(220\) −2.75078 −0.185457
\(221\) −5.68274 −0.382262
\(222\) −1.64835 −0.110630
\(223\) −19.1148 −1.28002 −0.640010 0.768366i \(-0.721070\pi\)
−0.640010 + 0.768366i \(0.721070\pi\)
\(224\) 9.90035 0.661495
\(225\) −2.28674 −0.152450
\(226\) −28.1714 −1.87394
\(227\) 28.4833 1.89050 0.945250 0.326347i \(-0.105818\pi\)
0.945250 + 0.326347i \(0.105818\pi\)
\(228\) 2.09510 0.138751
\(229\) −1.78837 −0.118179 −0.0590895 0.998253i \(-0.518820\pi\)
−0.0590895 + 0.998253i \(0.518820\pi\)
\(230\) 3.55988 0.234731
\(231\) 2.17236 0.142931
\(232\) 5.73995 0.376846
\(233\) −8.78256 −0.575365 −0.287682 0.957726i \(-0.592885\pi\)
−0.287682 + 0.957726i \(0.592885\pi\)
\(234\) −1.79927 −0.117622
\(235\) 7.31556 0.477214
\(236\) −0.636814 −0.0414531
\(237\) −6.11519 −0.397224
\(238\) 16.4582 1.06683
\(239\) 19.8477 1.28384 0.641921 0.766771i \(-0.278138\pi\)
0.641921 + 0.766771i \(0.278138\pi\)
\(240\) 8.14316 0.525639
\(241\) −26.5702 −1.71154 −0.855769 0.517358i \(-0.826915\pi\)
−0.855769 + 0.517358i \(0.826915\pi\)
\(242\) 16.5148 1.06161
\(243\) −1.00000 −0.0641500
\(244\) 16.4138 1.05078
\(245\) −7.26261 −0.463991
\(246\) 18.4949 1.17919
\(247\) −1.69316 −0.107733
\(248\) −12.8672 −0.817065
\(249\) −0.847262 −0.0536930
\(250\) 21.5961 1.36586
\(251\) −5.57862 −0.352119 −0.176060 0.984379i \(-0.556335\pi\)
−0.176060 + 0.984379i \(0.556335\pi\)
\(252\) 1.99174 0.125468
\(253\) 1.62105 0.101915
\(254\) −35.6834 −2.23897
\(255\) 9.36059 0.586183
\(256\) 20.6741 1.29213
\(257\) −6.43309 −0.401285 −0.200643 0.979665i \(-0.564303\pi\)
−0.200643 + 0.979665i \(0.564303\pi\)
\(258\) 19.5851 1.21931
\(259\) −1.47462 −0.0916286
\(260\) 2.03822 0.126405
\(261\) 4.18318 0.258933
\(262\) −24.8594 −1.53582
\(263\) 10.4800 0.646224 0.323112 0.946361i \(-0.395271\pi\)
0.323112 + 0.946361i \(0.395271\pi\)
\(264\) 1.85185 0.113973
\(265\) −10.3684 −0.636927
\(266\) 4.90369 0.300665
\(267\) 1.04225 0.0637846
\(268\) 4.03955 0.246755
\(269\) −15.3651 −0.936826 −0.468413 0.883510i \(-0.655174\pi\)
−0.468413 + 0.883510i \(0.655174\pi\)
\(270\) 2.96376 0.180369
\(271\) 20.0219 1.21625 0.608123 0.793843i \(-0.291923\pi\)
0.608123 + 0.793843i \(0.291923\pi\)
\(272\) 28.0935 1.70342
\(273\) −1.60963 −0.0974195
\(274\) 2.00476 0.121112
\(275\) 3.08618 0.186104
\(276\) 1.48627 0.0894631
\(277\) 14.1549 0.850488 0.425244 0.905079i \(-0.360188\pi\)
0.425244 + 0.905079i \(0.360188\pi\)
\(278\) 24.6339 1.47744
\(279\) −9.37738 −0.561409
\(280\) 3.63809 0.217418
\(281\) 26.0328 1.55298 0.776492 0.630127i \(-0.216997\pi\)
0.776492 + 0.630127i \(0.216997\pi\)
\(282\) 7.99097 0.475855
\(283\) 12.7178 0.755994 0.377997 0.925807i \(-0.376613\pi\)
0.377997 + 0.925807i \(0.376613\pi\)
\(284\) 11.1364 0.660823
\(285\) 2.78897 0.165204
\(286\) 2.42830 0.143588
\(287\) 16.5455 0.976653
\(288\) 6.15068 0.362432
\(289\) 15.2935 0.899619
\(290\) −12.3979 −0.728032
\(291\) 1.73211 0.101538
\(292\) −16.1923 −0.947581
\(293\) 20.8978 1.22086 0.610431 0.792070i \(-0.290996\pi\)
0.610431 + 0.792070i \(0.290996\pi\)
\(294\) −7.93314 −0.462670
\(295\) −0.847720 −0.0493562
\(296\) −1.25706 −0.0730649
\(297\) 1.34960 0.0783116
\(298\) −23.3219 −1.35100
\(299\) −1.20114 −0.0694635
\(300\) 2.82959 0.163366
\(301\) 17.5209 1.00989
\(302\) 37.3410 2.14873
\(303\) 8.16661 0.469160
\(304\) 8.37040 0.480075
\(305\) 21.8498 1.25112
\(306\) 10.2248 0.584513
\(307\) −9.00311 −0.513835 −0.256917 0.966433i \(-0.582707\pi\)
−0.256917 + 0.966433i \(0.582707\pi\)
\(308\) −2.68805 −0.153166
\(309\) 1.00000 0.0568880
\(310\) 27.7923 1.57850
\(311\) −9.44741 −0.535713 −0.267857 0.963459i \(-0.586315\pi\)
−0.267857 + 0.963459i \(0.586315\pi\)
\(312\) −1.37215 −0.0776826
\(313\) −28.1141 −1.58910 −0.794552 0.607196i \(-0.792294\pi\)
−0.794552 + 0.607196i \(0.792294\pi\)
\(314\) 32.1766 1.81583
\(315\) 2.65138 0.149389
\(316\) 7.56686 0.425669
\(317\) −0.636062 −0.0357248 −0.0178624 0.999840i \(-0.505686\pi\)
−0.0178624 + 0.999840i \(0.505686\pi\)
\(318\) −11.3257 −0.635113
\(319\) −5.64561 −0.316094
\(320\) −1.94281 −0.108606
\(321\) −15.5038 −0.865337
\(322\) 3.47870 0.193860
\(323\) 9.62180 0.535371
\(324\) 1.23739 0.0687438
\(325\) −2.28674 −0.126846
\(326\) −10.6700 −0.590955
\(327\) −17.9030 −0.990040
\(328\) 14.1044 0.778786
\(329\) 7.14874 0.394123
\(330\) −3.99988 −0.220186
\(331\) −22.1606 −1.21806 −0.609029 0.793148i \(-0.708441\pi\)
−0.609029 + 0.793148i \(0.708441\pi\)
\(332\) 1.04839 0.0575379
\(333\) −0.916122 −0.0502032
\(334\) 0.0207972 0.00113797
\(335\) 5.37741 0.293799
\(336\) 7.95747 0.434115
\(337\) 9.51276 0.518193 0.259096 0.965851i \(-0.416575\pi\)
0.259096 + 0.965851i \(0.416575\pi\)
\(338\) −1.79927 −0.0978676
\(339\) −15.6571 −0.850377
\(340\) −11.5827 −0.628159
\(341\) 12.6557 0.685344
\(342\) 3.04646 0.164734
\(343\) −18.3644 −0.991587
\(344\) 14.9358 0.805286
\(345\) 1.97851 0.106519
\(346\) −27.8554 −1.49752
\(347\) 11.8048 0.633714 0.316857 0.948473i \(-0.397373\pi\)
0.316857 + 0.948473i \(0.397373\pi\)
\(348\) −5.17622 −0.277474
\(349\) −12.5318 −0.670810 −0.335405 0.942074i \(-0.608873\pi\)
−0.335405 + 0.942074i \(0.608873\pi\)
\(350\) 6.62281 0.354004
\(351\) −1.00000 −0.0533761
\(352\) −8.30094 −0.442442
\(353\) 19.7268 1.04995 0.524976 0.851117i \(-0.324074\pi\)
0.524976 + 0.851117i \(0.324074\pi\)
\(354\) −0.925986 −0.0492156
\(355\) 14.8246 0.786810
\(356\) −1.28967 −0.0683522
\(357\) 9.14714 0.484118
\(358\) −15.3423 −0.810865
\(359\) 2.82840 0.149277 0.0746387 0.997211i \(-0.476220\pi\)
0.0746387 + 0.997211i \(0.476220\pi\)
\(360\) 2.26020 0.119123
\(361\) −16.1332 −0.849116
\(362\) −7.71949 −0.405727
\(363\) 9.17859 0.481751
\(364\) 1.99174 0.104396
\(365\) −21.5550 −1.12824
\(366\) 23.8671 1.24755
\(367\) 33.4629 1.74675 0.873375 0.487048i \(-0.161926\pi\)
0.873375 + 0.487048i \(0.161926\pi\)
\(368\) 5.93800 0.309539
\(369\) 10.2791 0.535107
\(370\) 2.71516 0.141155
\(371\) −10.1320 −0.526026
\(372\) 11.6035 0.601611
\(373\) 12.4943 0.646932 0.323466 0.946240i \(-0.395152\pi\)
0.323466 + 0.946240i \(0.395152\pi\)
\(374\) −13.7994 −0.713549
\(375\) 12.0027 0.619817
\(376\) 6.09401 0.314275
\(377\) 4.18318 0.215445
\(378\) 2.89617 0.148963
\(379\) −17.6173 −0.904940 −0.452470 0.891780i \(-0.649457\pi\)
−0.452470 + 0.891780i \(0.649457\pi\)
\(380\) −3.45104 −0.177035
\(381\) −19.8321 −1.01603
\(382\) −8.46153 −0.432930
\(383\) 22.6631 1.15803 0.579016 0.815316i \(-0.303437\pi\)
0.579016 + 0.815316i \(0.303437\pi\)
\(384\) 10.1792 0.519454
\(385\) −3.57830 −0.182367
\(386\) −4.61224 −0.234757
\(387\) 10.8850 0.553315
\(388\) −2.14330 −0.108809
\(389\) 30.6139 1.55218 0.776092 0.630620i \(-0.217199\pi\)
0.776092 + 0.630620i \(0.217199\pi\)
\(390\) 2.96376 0.150076
\(391\) 6.82575 0.345193
\(392\) −6.04991 −0.305566
\(393\) −13.8163 −0.696941
\(394\) −1.91826 −0.0966404
\(395\) 10.0729 0.506823
\(396\) −1.66998 −0.0839194
\(397\) −6.72243 −0.337389 −0.168695 0.985668i \(-0.553955\pi\)
−0.168695 + 0.985668i \(0.553955\pi\)
\(398\) −35.0204 −1.75541
\(399\) 2.72537 0.136439
\(400\) 11.3049 0.565243
\(401\) 18.9050 0.944070 0.472035 0.881580i \(-0.343520\pi\)
0.472035 + 0.881580i \(0.343520\pi\)
\(402\) 5.87388 0.292962
\(403\) −9.37738 −0.467121
\(404\) −10.1053 −0.502756
\(405\) 1.64720 0.0818498
\(406\) −12.1152 −0.601269
\(407\) 1.23640 0.0612859
\(408\) 7.79756 0.386037
\(409\) 34.1838 1.69028 0.845140 0.534545i \(-0.179517\pi\)
0.845140 + 0.534545i \(0.179517\pi\)
\(410\) −30.4647 −1.50454
\(411\) 1.11420 0.0549596
\(412\) −1.23739 −0.0609617
\(413\) −0.828389 −0.0407624
\(414\) 2.16117 0.106216
\(415\) 1.39561 0.0685076
\(416\) 6.15068 0.301562
\(417\) 13.6910 0.670452
\(418\) −4.11150 −0.201100
\(419\) 5.35227 0.261475 0.130738 0.991417i \(-0.458265\pi\)
0.130738 + 0.991417i \(0.458265\pi\)
\(420\) −3.28079 −0.160086
\(421\) −15.9053 −0.775179 −0.387589 0.921832i \(-0.626692\pi\)
−0.387589 + 0.921832i \(0.626692\pi\)
\(422\) −1.98116 −0.0964414
\(423\) 4.44122 0.215939
\(424\) −8.63711 −0.419455
\(425\) 12.9950 0.630349
\(426\) 16.1933 0.784569
\(427\) 21.3516 1.03328
\(428\) 19.1842 0.927303
\(429\) 1.34960 0.0651592
\(430\) −32.2605 −1.55574
\(431\) −8.73882 −0.420934 −0.210467 0.977601i \(-0.567498\pi\)
−0.210467 + 0.977601i \(0.567498\pi\)
\(432\) 4.94365 0.237851
\(433\) 13.1340 0.631182 0.315591 0.948895i \(-0.397797\pi\)
0.315591 + 0.948895i \(0.397797\pi\)
\(434\) 27.1585 1.30365
\(435\) −6.89052 −0.330375
\(436\) 22.1530 1.06094
\(437\) 2.03372 0.0972860
\(438\) −23.5450 −1.12503
\(439\) −18.9325 −0.903600 −0.451800 0.892119i \(-0.649218\pi\)
−0.451800 + 0.892119i \(0.649218\pi\)
\(440\) −3.05036 −0.145420
\(441\) −4.40908 −0.209956
\(442\) 10.2248 0.486344
\(443\) −28.6223 −1.35989 −0.679943 0.733265i \(-0.737995\pi\)
−0.679943 + 0.733265i \(0.737995\pi\)
\(444\) 1.13360 0.0537982
\(445\) −1.71679 −0.0813836
\(446\) 34.3927 1.62854
\(447\) −12.9618 −0.613073
\(448\) −1.89851 −0.0896960
\(449\) −3.34029 −0.157638 −0.0788191 0.996889i \(-0.525115\pi\)
−0.0788191 + 0.996889i \(0.525115\pi\)
\(450\) 4.11448 0.193958
\(451\) −13.8726 −0.653235
\(452\) 19.3739 0.911272
\(453\) 20.7534 0.975078
\(454\) −51.2492 −2.40524
\(455\) 2.65138 0.124299
\(456\) 2.32327 0.108797
\(457\) 6.51875 0.304934 0.152467 0.988309i \(-0.451278\pi\)
0.152467 + 0.988309i \(0.451278\pi\)
\(458\) 3.21777 0.150357
\(459\) 5.68274 0.265248
\(460\) −2.44818 −0.114147
\(461\) 24.1888 1.12659 0.563293 0.826257i \(-0.309534\pi\)
0.563293 + 0.826257i \(0.309534\pi\)
\(462\) −3.90867 −0.181848
\(463\) −22.0758 −1.02595 −0.512974 0.858404i \(-0.671456\pi\)
−0.512974 + 0.858404i \(0.671456\pi\)
\(464\) −20.6802 −0.960053
\(465\) 15.4464 0.716309
\(466\) 15.8022 0.732025
\(467\) 12.0070 0.555617 0.277809 0.960636i \(-0.410392\pi\)
0.277809 + 0.960636i \(0.410392\pi\)
\(468\) 1.23739 0.0571983
\(469\) 5.25479 0.242643
\(470\) −13.1627 −0.607150
\(471\) 17.8831 0.824009
\(472\) −0.706168 −0.0325040
\(473\) −14.6904 −0.675463
\(474\) 11.0029 0.505380
\(475\) 3.87183 0.177652
\(476\) −11.3186 −0.518785
\(477\) −6.29458 −0.288209
\(478\) −35.7115 −1.63341
\(479\) −22.3156 −1.01963 −0.509814 0.860285i \(-0.670286\pi\)
−0.509814 + 0.860285i \(0.670286\pi\)
\(480\) −10.1314 −0.462432
\(481\) −0.916122 −0.0417716
\(482\) 47.8071 2.17755
\(483\) 1.93339 0.0879724
\(484\) −11.3575 −0.516249
\(485\) −2.85313 −0.129554
\(486\) 1.79927 0.0816167
\(487\) 2.39871 0.108696 0.0543480 0.998522i \(-0.482692\pi\)
0.0543480 + 0.998522i \(0.482692\pi\)
\(488\) 18.2014 0.823937
\(489\) −5.93016 −0.268171
\(490\) 13.0674 0.590326
\(491\) 13.0322 0.588136 0.294068 0.955784i \(-0.404991\pi\)
0.294068 + 0.955784i \(0.404991\pi\)
\(492\) −12.7192 −0.573425
\(493\) −23.7719 −1.07063
\(494\) 3.04646 0.137067
\(495\) −2.22305 −0.0999188
\(496\) 46.3585 2.08156
\(497\) 14.4866 0.649812
\(498\) 1.52446 0.0683125
\(499\) 19.9733 0.894130 0.447065 0.894502i \(-0.352469\pi\)
0.447065 + 0.894502i \(0.352469\pi\)
\(500\) −14.8520 −0.664201
\(501\) 0.0115586 0.000516402 0
\(502\) 10.0375 0.447994
\(503\) −15.7952 −0.704275 −0.352138 0.935948i \(-0.614545\pi\)
−0.352138 + 0.935948i \(0.614545\pi\)
\(504\) 2.20866 0.0983815
\(505\) −13.4520 −0.598607
\(506\) −2.91672 −0.129664
\(507\) −1.00000 −0.0444116
\(508\) 24.5400 1.08879
\(509\) −3.81576 −0.169131 −0.0845654 0.996418i \(-0.526950\pi\)
−0.0845654 + 0.996418i \(0.526950\pi\)
\(510\) −16.8423 −0.745788
\(511\) −21.0635 −0.931792
\(512\) −16.8400 −0.744228
\(513\) 1.69316 0.0747550
\(514\) 11.5749 0.510547
\(515\) −1.64720 −0.0725841
\(516\) −13.4690 −0.592937
\(517\) −5.99386 −0.263610
\(518\) 2.65325 0.116577
\(519\) −15.4815 −0.679561
\(520\) 2.26020 0.0991163
\(521\) 5.83741 0.255741 0.127871 0.991791i \(-0.459186\pi\)
0.127871 + 0.991791i \(0.459186\pi\)
\(522\) −7.52669 −0.329434
\(523\) 35.2019 1.53927 0.769637 0.638482i \(-0.220437\pi\)
0.769637 + 0.638482i \(0.220437\pi\)
\(524\) 17.0962 0.746849
\(525\) 3.68082 0.160644
\(526\) −18.8564 −0.822177
\(527\) 53.2892 2.32131
\(528\) −6.67193 −0.290359
\(529\) −21.5573 −0.937273
\(530\) 18.6556 0.810349
\(531\) −0.514644 −0.0223337
\(532\) −3.37234 −0.146210
\(533\) 10.2791 0.445236
\(534\) −1.87529 −0.0811518
\(535\) 25.5378 1.10409
\(536\) 4.47949 0.193485
\(537\) −8.52693 −0.367964
\(538\) 27.6460 1.19190
\(539\) 5.95048 0.256305
\(540\) −2.03822 −0.0877110
\(541\) −3.35919 −0.144423 −0.0722114 0.997389i \(-0.523006\pi\)
−0.0722114 + 0.997389i \(0.523006\pi\)
\(542\) −36.0250 −1.54740
\(543\) −4.29033 −0.184116
\(544\) −34.9527 −1.49858
\(545\) 29.4898 1.26321
\(546\) 2.89617 0.123945
\(547\) 17.9689 0.768296 0.384148 0.923272i \(-0.374495\pi\)
0.384148 + 0.923272i \(0.374495\pi\)
\(548\) −1.37870 −0.0588952
\(549\) 13.2649 0.566131
\(550\) −5.55289 −0.236776
\(551\) −7.08281 −0.301738
\(552\) 1.64814 0.0701494
\(553\) 9.84322 0.418576
\(554\) −25.4686 −1.08206
\(555\) 1.50903 0.0640549
\(556\) −16.9411 −0.718462
\(557\) −3.74880 −0.158842 −0.0794208 0.996841i \(-0.525307\pi\)
−0.0794208 + 0.996841i \(0.525307\pi\)
\(558\) 16.8725 0.714269
\(559\) 10.8850 0.460386
\(560\) −13.1075 −0.553893
\(561\) −7.66941 −0.323803
\(562\) −46.8401 −1.97583
\(563\) 6.19386 0.261040 0.130520 0.991446i \(-0.458335\pi\)
0.130520 + 0.991446i \(0.458335\pi\)
\(564\) −5.49551 −0.231403
\(565\) 25.7903 1.08501
\(566\) −22.8828 −0.961836
\(567\) 1.60963 0.0675983
\(568\) 12.3492 0.518162
\(569\) −39.1979 −1.64326 −0.821630 0.570021i \(-0.806935\pi\)
−0.821630 + 0.570021i \(0.806935\pi\)
\(570\) −5.01812 −0.210186
\(571\) 34.2869 1.43486 0.717431 0.696630i \(-0.245318\pi\)
0.717431 + 0.696630i \(0.245318\pi\)
\(572\) −1.66998 −0.0698252
\(573\) −4.70275 −0.196460
\(574\) −29.7700 −1.24257
\(575\) 2.74669 0.114545
\(576\) −1.17946 −0.0491444
\(577\) 27.5803 1.14818 0.574092 0.818790i \(-0.305355\pi\)
0.574092 + 0.818790i \(0.305355\pi\)
\(578\) −27.5172 −1.14457
\(579\) −2.56339 −0.106531
\(580\) 8.52625 0.354033
\(581\) 1.36378 0.0565792
\(582\) −3.11655 −0.129185
\(583\) 8.49516 0.351833
\(584\) −17.9557 −0.743014
\(585\) 1.64720 0.0681032
\(586\) −37.6008 −1.55328
\(587\) −12.1931 −0.503263 −0.251631 0.967823i \(-0.580967\pi\)
−0.251631 + 0.967823i \(0.580967\pi\)
\(588\) 5.45574 0.224991
\(589\) 15.8774 0.654218
\(590\) 1.52528 0.0627948
\(591\) −1.06613 −0.0438547
\(592\) 4.52898 0.186140
\(593\) −35.4511 −1.45580 −0.727902 0.685682i \(-0.759504\pi\)
−0.727902 + 0.685682i \(0.759504\pi\)
\(594\) −2.42830 −0.0996342
\(595\) −15.0671 −0.617692
\(596\) 16.0388 0.656975
\(597\) −19.4636 −0.796592
\(598\) 2.16117 0.0883770
\(599\) −17.3043 −0.707035 −0.353518 0.935428i \(-0.615015\pi\)
−0.353518 + 0.935428i \(0.615015\pi\)
\(600\) 3.13775 0.128098
\(601\) 8.97454 0.366079 0.183039 0.983106i \(-0.441406\pi\)
0.183039 + 0.983106i \(0.441406\pi\)
\(602\) −31.5248 −1.28486
\(603\) 3.26458 0.132944
\(604\) −25.6800 −1.04490
\(605\) −15.1189 −0.614672
\(606\) −14.6940 −0.596902
\(607\) −16.1776 −0.656628 −0.328314 0.944569i \(-0.606480\pi\)
−0.328314 + 0.944569i \(0.606480\pi\)
\(608\) −10.4141 −0.422348
\(609\) −6.73340 −0.272851
\(610\) −39.3139 −1.59177
\(611\) 4.44122 0.179672
\(612\) −7.03175 −0.284242
\(613\) 28.6950 1.15898 0.579491 0.814979i \(-0.303251\pi\)
0.579491 + 0.814979i \(0.303251\pi\)
\(614\) 16.1991 0.653741
\(615\) −16.9316 −0.682750
\(616\) −2.98080 −0.120100
\(617\) 18.3455 0.738564 0.369282 0.929317i \(-0.379604\pi\)
0.369282 + 0.929317i \(0.379604\pi\)
\(618\) −1.79927 −0.0723774
\(619\) 10.8276 0.435196 0.217598 0.976038i \(-0.430178\pi\)
0.217598 + 0.976038i \(0.430178\pi\)
\(620\) −19.1132 −0.767603
\(621\) 1.20114 0.0482000
\(622\) 16.9985 0.681577
\(623\) −1.67764 −0.0672132
\(624\) 4.94365 0.197904
\(625\) −8.33708 −0.333483
\(626\) 50.5850 2.02178
\(627\) −2.28509 −0.0912576
\(628\) −22.1283 −0.883016
\(629\) 5.20608 0.207580
\(630\) −4.77057 −0.190064
\(631\) 45.2379 1.80089 0.900446 0.434968i \(-0.143240\pi\)
0.900446 + 0.434968i \(0.143240\pi\)
\(632\) 8.39094 0.333774
\(633\) −1.10109 −0.0437643
\(634\) 1.14445 0.0454519
\(635\) 32.6674 1.29636
\(636\) 7.78884 0.308848
\(637\) −4.40908 −0.174694
\(638\) 10.1580 0.402159
\(639\) 8.99992 0.356031
\(640\) −16.7671 −0.662778
\(641\) 2.35661 0.0930806 0.0465403 0.998916i \(-0.485180\pi\)
0.0465403 + 0.998916i \(0.485180\pi\)
\(642\) 27.8956 1.10095
\(643\) −1.27910 −0.0504427 −0.0252213 0.999682i \(-0.508029\pi\)
−0.0252213 + 0.999682i \(0.508029\pi\)
\(644\) −2.39236 −0.0942720
\(645\) −17.9297 −0.705982
\(646\) −17.3123 −0.681142
\(647\) 42.0542 1.65332 0.826660 0.562702i \(-0.190238\pi\)
0.826660 + 0.562702i \(0.190238\pi\)
\(648\) 1.37215 0.0539031
\(649\) 0.694562 0.0272640
\(650\) 4.11448 0.161383
\(651\) 15.0942 0.591587
\(652\) 7.33790 0.287374
\(653\) −31.2300 −1.22212 −0.611061 0.791583i \(-0.709257\pi\)
−0.611061 + 0.791583i \(0.709257\pi\)
\(654\) 32.2125 1.25961
\(655\) 22.7582 0.889236
\(656\) −50.8161 −1.98403
\(657\) −13.0859 −0.510528
\(658\) −12.8625 −0.501434
\(659\) 4.87132 0.189760 0.0948798 0.995489i \(-0.469753\pi\)
0.0948798 + 0.995489i \(0.469753\pi\)
\(660\) 2.75078 0.107074
\(661\) 23.5754 0.916976 0.458488 0.888701i \(-0.348391\pi\)
0.458488 + 0.888701i \(0.348391\pi\)
\(662\) 39.8731 1.54971
\(663\) 5.68274 0.220699
\(664\) 1.16257 0.0451164
\(665\) −4.48923 −0.174085
\(666\) 1.64835 0.0638725
\(667\) −5.02458 −0.194552
\(668\) −0.0143025 −0.000553381 0
\(669\) 19.1148 0.739020
\(670\) −9.67543 −0.373795
\(671\) −17.9022 −0.691108
\(672\) −9.90035 −0.381914
\(673\) 23.8325 0.918677 0.459339 0.888261i \(-0.348086\pi\)
0.459339 + 0.888261i \(0.348086\pi\)
\(674\) −17.1161 −0.659286
\(675\) 2.28674 0.0880168
\(676\) 1.23739 0.0475918
\(677\) −36.5920 −1.40635 −0.703173 0.711019i \(-0.748234\pi\)
−0.703173 + 0.711019i \(0.748234\pi\)
\(678\) 28.1714 1.08192
\(679\) −2.78807 −0.106996
\(680\) −12.8441 −0.492549
\(681\) −28.4833 −1.09148
\(682\) −22.7711 −0.871949
\(683\) 39.0622 1.49467 0.747337 0.664446i \(-0.231332\pi\)
0.747337 + 0.664446i \(0.231332\pi\)
\(684\) −2.09510 −0.0801081
\(685\) −1.83531 −0.0701237
\(686\) 33.0427 1.26158
\(687\) 1.78837 0.0682307
\(688\) −53.8115 −2.05155
\(689\) −6.29458 −0.239805
\(690\) −3.55988 −0.135522
\(691\) −34.7407 −1.32160 −0.660799 0.750563i \(-0.729782\pi\)
−0.660799 + 0.750563i \(0.729782\pi\)
\(692\) 19.1566 0.728224
\(693\) −2.17236 −0.0825211
\(694\) −21.2400 −0.806260
\(695\) −22.5518 −0.855438
\(696\) −5.73995 −0.217572
\(697\) −58.4133 −2.21256
\(698\) 22.5481 0.853458
\(699\) 8.78256 0.332187
\(700\) −4.55461 −0.172148
\(701\) −40.6136 −1.53395 −0.766976 0.641675i \(-0.778240\pi\)
−0.766976 + 0.641675i \(0.778240\pi\)
\(702\) 1.79927 0.0679092
\(703\) 1.55114 0.0585025
\(704\) 1.59180 0.0599933
\(705\) −7.31556 −0.275520
\(706\) −35.4939 −1.33583
\(707\) −13.1453 −0.494379
\(708\) 0.636814 0.0239329
\(709\) −29.9697 −1.12553 −0.562767 0.826616i \(-0.690263\pi\)
−0.562767 + 0.826616i \(0.690263\pi\)
\(710\) −26.6736 −1.00104
\(711\) 6.11519 0.229337
\(712\) −1.43012 −0.0535960
\(713\) 11.2635 0.421822
\(714\) −16.4582 −0.615933
\(715\) −2.22305 −0.0831374
\(716\) 10.5511 0.394314
\(717\) −19.8477 −0.741227
\(718\) −5.08907 −0.189922
\(719\) −48.9396 −1.82514 −0.912570 0.408921i \(-0.865905\pi\)
−0.912570 + 0.408921i \(0.865905\pi\)
\(720\) −8.14316 −0.303478
\(721\) −1.60963 −0.0599459
\(722\) 29.0281 1.08031
\(723\) 26.5702 0.988157
\(724\) 5.30881 0.197300
\(725\) −9.56587 −0.355267
\(726\) −16.5148 −0.612921
\(727\) −36.5346 −1.35499 −0.677497 0.735525i \(-0.736935\pi\)
−0.677497 + 0.735525i \(0.736935\pi\)
\(728\) 2.20866 0.0818583
\(729\) 1.00000 0.0370370
\(730\) 38.7833 1.43543
\(731\) −61.8566 −2.28785
\(732\) −16.4138 −0.606671
\(733\) 27.3143 1.00888 0.504439 0.863447i \(-0.331699\pi\)
0.504439 + 0.863447i \(0.331699\pi\)
\(734\) −60.2090 −2.22235
\(735\) 7.26261 0.267886
\(736\) −7.38781 −0.272318
\(737\) −4.40587 −0.162292
\(738\) −18.4949 −0.680805
\(739\) 22.5737 0.830386 0.415193 0.909733i \(-0.363714\pi\)
0.415193 + 0.909733i \(0.363714\pi\)
\(740\) −1.86726 −0.0686418
\(741\) 1.69316 0.0621999
\(742\) 18.2302 0.669252
\(743\) 16.9299 0.621097 0.310549 0.950558i \(-0.399487\pi\)
0.310549 + 0.950558i \(0.399487\pi\)
\(744\) 12.8672 0.471733
\(745\) 21.3507 0.782228
\(746\) −22.4807 −0.823077
\(747\) 0.847262 0.0309997
\(748\) 9.49003 0.346990
\(749\) 24.9554 0.911851
\(750\) −21.5961 −0.788580
\(751\) −34.1315 −1.24547 −0.622737 0.782431i \(-0.713980\pi\)
−0.622737 + 0.782431i \(0.713980\pi\)
\(752\) −21.9558 −0.800646
\(753\) 5.57862 0.203296
\(754\) −7.52669 −0.274106
\(755\) −34.1849 −1.24412
\(756\) −1.99174 −0.0724390
\(757\) 19.0415 0.692075 0.346037 0.938221i \(-0.387527\pi\)
0.346037 + 0.938221i \(0.387527\pi\)
\(758\) 31.6984 1.15134
\(759\) −1.62105 −0.0588404
\(760\) −3.82688 −0.138816
\(761\) −23.7317 −0.860274 −0.430137 0.902764i \(-0.641535\pi\)
−0.430137 + 0.902764i \(0.641535\pi\)
\(762\) 35.6834 1.29267
\(763\) 28.8174 1.04326
\(764\) 5.81912 0.210529
\(765\) −9.36059 −0.338433
\(766\) −40.7772 −1.47334
\(767\) −0.514644 −0.0185827
\(768\) −20.6741 −0.746011
\(769\) 30.4111 1.09665 0.548326 0.836264i \(-0.315265\pi\)
0.548326 + 0.836264i \(0.315265\pi\)
\(770\) 6.43835 0.232022
\(771\) 6.43309 0.231682
\(772\) 3.17190 0.114159
\(773\) 39.3672 1.41594 0.707970 0.706243i \(-0.249611\pi\)
0.707970 + 0.706243i \(0.249611\pi\)
\(774\) −19.5851 −0.703971
\(775\) 21.4437 0.770279
\(776\) −2.37672 −0.0853192
\(777\) 1.47462 0.0529018
\(778\) −55.0827 −1.97481
\(779\) −17.4041 −0.623568
\(780\) −2.03822 −0.0729800
\(781\) −12.1463 −0.434628
\(782\) −12.2814 −0.439182
\(783\) −4.18318 −0.149495
\(784\) 21.7969 0.778461
\(785\) −29.4570 −1.05136
\(786\) 24.8594 0.886704
\(787\) −9.50619 −0.338859 −0.169430 0.985542i \(-0.554193\pi\)
−0.169430 + 0.985542i \(0.554193\pi\)
\(788\) 1.31921 0.0469951
\(789\) −10.4800 −0.373097
\(790\) −18.1239 −0.644821
\(791\) 25.2022 0.896088
\(792\) −1.85185 −0.0658026
\(793\) 13.2649 0.471049
\(794\) 12.0955 0.429253
\(795\) 10.3684 0.367730
\(796\) 24.0840 0.853636
\(797\) 39.3523 1.39393 0.696965 0.717105i \(-0.254533\pi\)
0.696965 + 0.717105i \(0.254533\pi\)
\(798\) −4.90369 −0.173589
\(799\) −25.2383 −0.892866
\(800\) −14.0650 −0.497274
\(801\) −1.04225 −0.0368261
\(802\) −34.0153 −1.20112
\(803\) 17.6606 0.623231
\(804\) −4.03955 −0.142464
\(805\) −3.18468 −0.112245
\(806\) 16.8725 0.594308
\(807\) 15.3651 0.540877
\(808\) −11.2058 −0.394219
\(809\) −9.71594 −0.341594 −0.170797 0.985306i \(-0.554634\pi\)
−0.170797 + 0.985306i \(0.554634\pi\)
\(810\) −2.96376 −0.104136
\(811\) 12.6189 0.443109 0.221554 0.975148i \(-0.428887\pi\)
0.221554 + 0.975148i \(0.428887\pi\)
\(812\) 8.33182 0.292390
\(813\) −20.0219 −0.702200
\(814\) −2.22462 −0.0779727
\(815\) 9.76813 0.342163
\(816\) −28.0935 −0.983468
\(817\) −18.4301 −0.644786
\(818\) −61.5060 −2.15051
\(819\) 1.60963 0.0562452
\(820\) 20.9510 0.731641
\(821\) −43.7419 −1.52660 −0.763301 0.646043i \(-0.776423\pi\)
−0.763301 + 0.646043i \(0.776423\pi\)
\(822\) −2.00476 −0.0699240
\(823\) −1.10056 −0.0383630 −0.0191815 0.999816i \(-0.506106\pi\)
−0.0191815 + 0.999816i \(0.506106\pi\)
\(824\) −1.37215 −0.0478011
\(825\) −3.08618 −0.107447
\(826\) 1.49050 0.0518611
\(827\) −39.0030 −1.35627 −0.678133 0.734939i \(-0.737211\pi\)
−0.678133 + 0.734939i \(0.737211\pi\)
\(828\) −1.48627 −0.0516515
\(829\) −29.3859 −1.02062 −0.510308 0.859992i \(-0.670468\pi\)
−0.510308 + 0.859992i \(0.670468\pi\)
\(830\) −2.51108 −0.0871608
\(831\) −14.1549 −0.491029
\(832\) −1.17946 −0.0408906
\(833\) 25.0556 0.868126
\(834\) −24.6339 −0.853002
\(835\) −0.0190393 −0.000658884 0
\(836\) 2.82754 0.0977925
\(837\) 9.37738 0.324130
\(838\) −9.63020 −0.332670
\(839\) −14.1572 −0.488760 −0.244380 0.969680i \(-0.578584\pi\)
−0.244380 + 0.969680i \(0.578584\pi\)
\(840\) −3.63809 −0.125526
\(841\) −11.5010 −0.396585
\(842\) 28.6181 0.986244
\(843\) −26.0328 −0.896616
\(844\) 1.36247 0.0468983
\(845\) 1.64720 0.0566653
\(846\) −7.99097 −0.274735
\(847\) −14.7742 −0.507647
\(848\) 31.1182 1.06860
\(849\) −12.7178 −0.436474
\(850\) −23.3815 −0.801979
\(851\) 1.10039 0.0377208
\(852\) −11.1364 −0.381526
\(853\) 19.9896 0.684430 0.342215 0.939622i \(-0.388823\pi\)
0.342215 + 0.939622i \(0.388823\pi\)
\(854\) −38.4174 −1.31462
\(855\) −2.78897 −0.0953808
\(856\) 21.2735 0.727113
\(857\) 33.7798 1.15390 0.576948 0.816781i \(-0.304244\pi\)
0.576948 + 0.816781i \(0.304244\pi\)
\(858\) −2.42830 −0.0829007
\(859\) −5.95894 −0.203317 −0.101658 0.994819i \(-0.532415\pi\)
−0.101658 + 0.994819i \(0.532415\pi\)
\(860\) 22.1860 0.756537
\(861\) −16.5455 −0.563871
\(862\) 15.7235 0.535545
\(863\) 46.9730 1.59898 0.799489 0.600681i \(-0.205104\pi\)
0.799489 + 0.600681i \(0.205104\pi\)
\(864\) −6.15068 −0.209250
\(865\) 25.5010 0.867061
\(866\) −23.6318 −0.803040
\(867\) −15.2935 −0.519395
\(868\) −18.6773 −0.633950
\(869\) −8.25304 −0.279965
\(870\) 12.3979 0.420330
\(871\) 3.26458 0.110616
\(872\) 24.5656 0.831897
\(873\) −1.73211 −0.0586232
\(874\) −3.65922 −0.123775
\(875\) −19.3200 −0.653134
\(876\) 16.1923 0.547086
\(877\) −39.2526 −1.32547 −0.662733 0.748856i \(-0.730604\pi\)
−0.662733 + 0.748856i \(0.730604\pi\)
\(878\) 34.0648 1.14963
\(879\) −20.8978 −0.704865
\(880\) 10.9900 0.370472
\(881\) −48.1487 −1.62217 −0.811086 0.584927i \(-0.801123\pi\)
−0.811086 + 0.584927i \(0.801123\pi\)
\(882\) 7.93314 0.267123
\(883\) 39.4323 1.32700 0.663501 0.748175i \(-0.269070\pi\)
0.663501 + 0.748175i \(0.269070\pi\)
\(884\) −7.03175 −0.236503
\(885\) 0.847720 0.0284958
\(886\) 51.4993 1.73015
\(887\) 30.6038 1.02757 0.513787 0.857918i \(-0.328242\pi\)
0.513787 + 0.857918i \(0.328242\pi\)
\(888\) 1.25706 0.0421840
\(889\) 31.9224 1.07064
\(890\) 3.08897 0.103543
\(891\) −1.34960 −0.0452132
\(892\) −23.6524 −0.791941
\(893\) −7.51971 −0.251637
\(894\) 23.3219 0.780000
\(895\) 14.0455 0.469490
\(896\) −16.3848 −0.547376
\(897\) 1.20114 0.0401048
\(898\) 6.01010 0.200560
\(899\) −39.2273 −1.30830
\(900\) −2.82959 −0.0943196
\(901\) 35.7705 1.19169
\(902\) 24.9606 0.831098
\(903\) −17.5209 −0.583058
\(904\) 21.4839 0.714543
\(905\) 7.06702 0.234916
\(906\) −37.3410 −1.24057
\(907\) 23.0357 0.764889 0.382444 0.923979i \(-0.375082\pi\)
0.382444 + 0.923979i \(0.375082\pi\)
\(908\) 35.2448 1.16964
\(909\) −8.16661 −0.270869
\(910\) −4.77057 −0.158143
\(911\) −49.5471 −1.64157 −0.820785 0.571238i \(-0.806463\pi\)
−0.820785 + 0.571238i \(0.806463\pi\)
\(912\) −8.37040 −0.277172
\(913\) −1.14346 −0.0378431
\(914\) −11.7290 −0.387962
\(915\) −21.8498 −0.722333
\(916\) −2.21291 −0.0731166
\(917\) 22.2392 0.734404
\(918\) −10.2248 −0.337469
\(919\) 57.5631 1.89883 0.949416 0.314020i \(-0.101676\pi\)
0.949416 + 0.314020i \(0.101676\pi\)
\(920\) −2.71481 −0.0895046
\(921\) 9.00311 0.296663
\(922\) −43.5223 −1.43333
\(923\) 8.99992 0.296236
\(924\) 2.68805 0.0884304
\(925\) 2.09494 0.0688811
\(926\) 39.7203 1.30529
\(927\) −1.00000 −0.0328443
\(928\) 25.7294 0.844610
\(929\) 13.9139 0.456501 0.228250 0.973602i \(-0.426700\pi\)
0.228250 + 0.973602i \(0.426700\pi\)
\(930\) −27.7923 −0.911345
\(931\) 7.46528 0.244665
\(932\) −10.8674 −0.355975
\(933\) 9.44741 0.309294
\(934\) −21.6039 −0.706900
\(935\) 12.6330 0.413144
\(936\) 1.37215 0.0448501
\(937\) −39.1940 −1.28041 −0.640205 0.768204i \(-0.721151\pi\)
−0.640205 + 0.768204i \(0.721151\pi\)
\(938\) −9.45480 −0.308710
\(939\) 28.1141 0.917470
\(940\) 9.05218 0.295250
\(941\) −52.1472 −1.69995 −0.849975 0.526823i \(-0.823383\pi\)
−0.849975 + 0.526823i \(0.823383\pi\)
\(942\) −32.1766 −1.04837
\(943\) −12.3466 −0.402059
\(944\) 2.54422 0.0828073
\(945\) −2.65138 −0.0862496
\(946\) 26.4320 0.859378
\(947\) 22.9919 0.747137 0.373569 0.927603i \(-0.378134\pi\)
0.373569 + 0.927603i \(0.378134\pi\)
\(948\) −7.56686 −0.245760
\(949\) −13.0859 −0.424785
\(950\) −6.96648 −0.226023
\(951\) 0.636062 0.0206257
\(952\) −12.5512 −0.406788
\(953\) −15.2248 −0.493180 −0.246590 0.969120i \(-0.579310\pi\)
−0.246590 + 0.969120i \(0.579310\pi\)
\(954\) 11.3257 0.366683
\(955\) 7.74635 0.250666
\(956\) 24.5593 0.794305
\(957\) 5.64561 0.182497
\(958\) 40.1520 1.29725
\(959\) −1.79346 −0.0579139
\(960\) 1.94281 0.0627039
\(961\) 56.9352 1.83662
\(962\) 1.64835 0.0531451
\(963\) 15.5038 0.499602
\(964\) −32.8777 −1.05892
\(965\) 4.22240 0.135924
\(966\) −3.47870 −0.111925
\(967\) 54.9687 1.76767 0.883837 0.467794i \(-0.154951\pi\)
0.883837 + 0.467794i \(0.154951\pi\)
\(968\) −12.5944 −0.404799
\(969\) −9.62180 −0.309097
\(970\) 5.13357 0.164829
\(971\) 15.4111 0.494565 0.247283 0.968943i \(-0.420462\pi\)
0.247283 + 0.968943i \(0.420462\pi\)
\(972\) −1.23739 −0.0396892
\(973\) −22.0375 −0.706491
\(974\) −4.31594 −0.138292
\(975\) 2.28674 0.0732344
\(976\) −65.5768 −2.09906
\(977\) 10.8355 0.346660 0.173330 0.984864i \(-0.444547\pi\)
0.173330 + 0.984864i \(0.444547\pi\)
\(978\) 10.6700 0.341188
\(979\) 1.40662 0.0449557
\(980\) −8.98667 −0.287069
\(981\) 17.9030 0.571600
\(982\) −23.4486 −0.748274
\(983\) −10.4095 −0.332011 −0.166005 0.986125i \(-0.553087\pi\)
−0.166005 + 0.986125i \(0.553087\pi\)
\(984\) −14.1044 −0.449632
\(985\) 1.75612 0.0559547
\(986\) 42.7722 1.36215
\(987\) −7.14874 −0.227547
\(988\) −2.09510 −0.0666540
\(989\) −13.0744 −0.415740
\(990\) 3.99988 0.127125
\(991\) 24.1474 0.767068 0.383534 0.923527i \(-0.374707\pi\)
0.383534 + 0.923527i \(0.374707\pi\)
\(992\) −57.6773 −1.83125
\(993\) 22.1606 0.703246
\(994\) −26.0653 −0.826742
\(995\) 32.0604 1.01638
\(996\) −1.04839 −0.0332195
\(997\) −42.8259 −1.35631 −0.678155 0.734919i \(-0.737220\pi\)
−0.678155 + 0.734919i \(0.737220\pi\)
\(998\) −35.9375 −1.13758
\(999\) 0.916122 0.0289848
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 \(a_p\))