Properties

Label 6027.2.a.y.1.1
Level 6027
Weight 2
Character 6027.1
Self dual Yes
Analytic conductor 48.126
Analytic rank 0
Dimension 7
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6027.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1258372982\)
Analytic rank: \(0\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(2.95889\)
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.95889 q^{2} -1.00000 q^{3} +1.83724 q^{4} +0.513172 q^{5} +1.95889 q^{6} +0.318823 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.95889 q^{2} -1.00000 q^{3} +1.83724 q^{4} +0.513172 q^{5} +1.95889 q^{6} +0.318823 q^{8} +1.00000 q^{9} -1.00525 q^{10} +5.65559 q^{11} -1.83724 q^{12} +0.337188 q^{13} -0.513172 q^{15} -4.29902 q^{16} -4.63097 q^{17} -1.95889 q^{18} +7.43860 q^{19} +0.942822 q^{20} -11.0787 q^{22} +3.51087 q^{23} -0.318823 q^{24} -4.73665 q^{25} -0.660514 q^{26} -1.00000 q^{27} +0.00385180 q^{29} +1.00525 q^{30} -2.90696 q^{31} +7.78366 q^{32} -5.65559 q^{33} +9.07154 q^{34} +1.83724 q^{36} +5.69784 q^{37} -14.5714 q^{38} -0.337188 q^{39} +0.163611 q^{40} -1.00000 q^{41} +6.32365 q^{43} +10.3907 q^{44} +0.513172 q^{45} -6.87741 q^{46} +10.1514 q^{47} +4.29902 q^{48} +9.27858 q^{50} +4.63097 q^{51} +0.619496 q^{52} -1.59568 q^{53} +1.95889 q^{54} +2.90229 q^{55} -7.43860 q^{57} -0.00754524 q^{58} -1.42494 q^{59} -0.942822 q^{60} -2.50182 q^{61} +5.69440 q^{62} -6.64927 q^{64} +0.173036 q^{65} +11.0787 q^{66} +9.61202 q^{67} -8.50821 q^{68} -3.51087 q^{69} +10.3934 q^{71} +0.318823 q^{72} -0.539898 q^{73} -11.1614 q^{74} +4.73665 q^{75} +13.6665 q^{76} +0.660514 q^{78} +7.84764 q^{79} -2.20614 q^{80} +1.00000 q^{81} +1.95889 q^{82} +13.6736 q^{83} -2.37648 q^{85} -12.3873 q^{86} -0.00385180 q^{87} +1.80313 q^{88} -15.4352 q^{89} -1.00525 q^{90} +6.45033 q^{92} +2.90696 q^{93} -19.8854 q^{94} +3.81728 q^{95} -7.78366 q^{96} -2.56452 q^{97} +5.65559 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q + 4q^{2} - 7q^{3} + 8q^{4} - q^{5} - 4q^{6} + 12q^{8} + 7q^{9} + O(q^{10}) \) \( 7q + 4q^{2} - 7q^{3} + 8q^{4} - q^{5} - 4q^{6} + 12q^{8} + 7q^{9} + 3q^{10} + 11q^{11} - 8q^{12} + 7q^{13} + q^{15} + 6q^{16} - 11q^{17} + 4q^{18} - 4q^{19} + 7q^{20} + 6q^{22} + 7q^{23} - 12q^{24} + 2q^{25} + 13q^{26} - 7q^{27} + 4q^{29} - 3q^{30} + 7q^{31} + 18q^{32} - 11q^{33} + 20q^{34} + 8q^{36} - 4q^{38} - 7q^{39} + 9q^{40} - 7q^{41} + q^{43} + 18q^{44} - q^{45} - 17q^{46} - 14q^{47} - 6q^{48} + 19q^{50} + 11q^{51} + 27q^{52} + 23q^{53} - 4q^{54} + 30q^{55} + 4q^{57} - 3q^{58} - 8q^{59} - 7q^{60} + 3q^{61} + 16q^{62} + 6q^{64} + 15q^{65} - 6q^{66} + 3q^{67} - 7q^{69} + 7q^{71} + 12q^{72} + 11q^{73} - 13q^{74} - 2q^{75} + 40q^{76} - 13q^{78} - q^{79} + 43q^{80} + 7q^{81} - 4q^{82} - 10q^{85} - 12q^{86} - 4q^{87} + 10q^{88} - 32q^{89} + 3q^{90} - 19q^{92} - 7q^{93} - 21q^{94} - 8q^{95} - 18q^{96} + 25q^{97} + 11q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.95889 −1.38514 −0.692572 0.721349i \(-0.743522\pi\)
−0.692572 + 0.721349i \(0.743522\pi\)
\(3\) −1.00000 −0.577350
\(4\) 1.83724 0.918621
\(5\) 0.513172 0.229498 0.114749 0.993395i \(-0.463394\pi\)
0.114749 + 0.993395i \(0.463394\pi\)
\(6\) 1.95889 0.799713
\(7\) 0 0
\(8\) 0.318823 0.112721
\(9\) 1.00000 0.333333
\(10\) −1.00525 −0.317887
\(11\) 5.65559 1.70522 0.852612 0.522544i \(-0.175017\pi\)
0.852612 + 0.522544i \(0.175017\pi\)
\(12\) −1.83724 −0.530366
\(13\) 0.337188 0.0935191 0.0467596 0.998906i \(-0.485111\pi\)
0.0467596 + 0.998906i \(0.485111\pi\)
\(14\) 0 0
\(15\) −0.513172 −0.132500
\(16\) −4.29902 −1.07476
\(17\) −4.63097 −1.12317 −0.561587 0.827418i \(-0.689809\pi\)
−0.561587 + 0.827418i \(0.689809\pi\)
\(18\) −1.95889 −0.461714
\(19\) 7.43860 1.70653 0.853266 0.521475i \(-0.174618\pi\)
0.853266 + 0.521475i \(0.174618\pi\)
\(20\) 0.942822 0.210821
\(21\) 0 0
\(22\) −11.0787 −2.36198
\(23\) 3.51087 0.732068 0.366034 0.930602i \(-0.380715\pi\)
0.366034 + 0.930602i \(0.380715\pi\)
\(24\) −0.318823 −0.0650796
\(25\) −4.73665 −0.947331
\(26\) −0.660514 −0.129537
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 0.00385180 0.000715261 0 0.000357630 1.00000i \(-0.499886\pi\)
0.000357630 1.00000i \(0.499886\pi\)
\(30\) 1.00525 0.183532
\(31\) −2.90696 −0.522105 −0.261052 0.965325i \(-0.584070\pi\)
−0.261052 + 0.965325i \(0.584070\pi\)
\(32\) 7.78366 1.37597
\(33\) −5.65559 −0.984512
\(34\) 9.07154 1.55576
\(35\) 0 0
\(36\) 1.83724 0.306207
\(37\) 5.69784 0.936719 0.468360 0.883538i \(-0.344845\pi\)
0.468360 + 0.883538i \(0.344845\pi\)
\(38\) −14.5714 −2.36379
\(39\) −0.337188 −0.0539933
\(40\) 0.163611 0.0258692
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) 6.32365 0.964347 0.482174 0.876076i \(-0.339847\pi\)
0.482174 + 0.876076i \(0.339847\pi\)
\(44\) 10.3907 1.56646
\(45\) 0.513172 0.0764992
\(46\) −6.87741 −1.01402
\(47\) 10.1514 1.48073 0.740365 0.672205i \(-0.234653\pi\)
0.740365 + 0.672205i \(0.234653\pi\)
\(48\) 4.29902 0.620511
\(49\) 0 0
\(50\) 9.27858 1.31219
\(51\) 4.63097 0.648465
\(52\) 0.619496 0.0859087
\(53\) −1.59568 −0.219183 −0.109592 0.993977i \(-0.534954\pi\)
−0.109592 + 0.993977i \(0.534954\pi\)
\(54\) 1.95889 0.266571
\(55\) 2.90229 0.391345
\(56\) 0 0
\(57\) −7.43860 −0.985267
\(58\) −0.00754524 −0.000990739 0
\(59\) −1.42494 −0.185512 −0.0927559 0.995689i \(-0.529568\pi\)
−0.0927559 + 0.995689i \(0.529568\pi\)
\(60\) −0.942822 −0.121718
\(61\) −2.50182 −0.320325 −0.160163 0.987091i \(-0.551202\pi\)
−0.160163 + 0.987091i \(0.551202\pi\)
\(62\) 5.69440 0.723190
\(63\) 0 0
\(64\) −6.64927 −0.831159
\(65\) 0.173036 0.0214624
\(66\) 11.0787 1.36369
\(67\) 9.61202 1.17430 0.587148 0.809480i \(-0.300251\pi\)
0.587148 + 0.809480i \(0.300251\pi\)
\(68\) −8.50821 −1.03177
\(69\) −3.51087 −0.422660
\(70\) 0 0
\(71\) 10.3934 1.23347 0.616733 0.787173i \(-0.288456\pi\)
0.616733 + 0.787173i \(0.288456\pi\)
\(72\) 0.318823 0.0375737
\(73\) −0.539898 −0.0631903 −0.0315951 0.999501i \(-0.510059\pi\)
−0.0315951 + 0.999501i \(0.510059\pi\)
\(74\) −11.1614 −1.29749
\(75\) 4.73665 0.546942
\(76\) 13.6665 1.56766
\(77\) 0 0
\(78\) 0.660514 0.0747884
\(79\) 7.84764 0.882928 0.441464 0.897279i \(-0.354459\pi\)
0.441464 + 0.897279i \(0.354459\pi\)
\(80\) −2.20614 −0.246654
\(81\) 1.00000 0.111111
\(82\) 1.95889 0.216323
\(83\) 13.6736 1.50088 0.750439 0.660940i \(-0.229842\pi\)
0.750439 + 0.660940i \(0.229842\pi\)
\(84\) 0 0
\(85\) −2.37648 −0.257766
\(86\) −12.3873 −1.33576
\(87\) −0.00385180 −0.000412956 0
\(88\) 1.80313 0.192215
\(89\) −15.4352 −1.63613 −0.818066 0.575125i \(-0.804953\pi\)
−0.818066 + 0.575125i \(0.804953\pi\)
\(90\) −1.00525 −0.105962
\(91\) 0 0
\(92\) 6.45033 0.672493
\(93\) 2.90696 0.301437
\(94\) −19.8854 −2.05102
\(95\) 3.81728 0.391645
\(96\) −7.78366 −0.794417
\(97\) −2.56452 −0.260388 −0.130194 0.991489i \(-0.541560\pi\)
−0.130194 + 0.991489i \(0.541560\pi\)
\(98\) 0 0
\(99\) 5.65559 0.568408
\(100\) −8.70238 −0.870238
\(101\) −16.0466 −1.59669 −0.798346 0.602198i \(-0.794292\pi\)
−0.798346 + 0.602198i \(0.794292\pi\)
\(102\) −9.07154 −0.898217
\(103\) 12.2682 1.20882 0.604410 0.796673i \(-0.293409\pi\)
0.604410 + 0.796673i \(0.293409\pi\)
\(104\) 0.107503 0.0105416
\(105\) 0 0
\(106\) 3.12576 0.303600
\(107\) 1.06468 0.102926 0.0514631 0.998675i \(-0.483612\pi\)
0.0514631 + 0.998675i \(0.483612\pi\)
\(108\) −1.83724 −0.176789
\(109\) −7.49782 −0.718161 −0.359081 0.933307i \(-0.616910\pi\)
−0.359081 + 0.933307i \(0.616910\pi\)
\(110\) −5.68526 −0.542069
\(111\) −5.69784 −0.540815
\(112\) 0 0
\(113\) −9.02374 −0.848882 −0.424441 0.905456i \(-0.639529\pi\)
−0.424441 + 0.905456i \(0.639529\pi\)
\(114\) 14.5714 1.36474
\(115\) 1.80168 0.168008
\(116\) 0.00707669 0.000657054 0
\(117\) 0.337188 0.0311730
\(118\) 2.79131 0.256961
\(119\) 0 0
\(120\) −0.163611 −0.0149356
\(121\) 20.9857 1.90779
\(122\) 4.90079 0.443697
\(123\) 1.00000 0.0901670
\(124\) −5.34079 −0.479617
\(125\) −4.99658 −0.446908
\(126\) 0 0
\(127\) 6.16100 0.546700 0.273350 0.961915i \(-0.411868\pi\)
0.273350 + 0.961915i \(0.411868\pi\)
\(128\) −2.54214 −0.224696
\(129\) −6.32365 −0.556766
\(130\) −0.338957 −0.0297285
\(131\) −17.8524 −1.55977 −0.779884 0.625924i \(-0.784722\pi\)
−0.779884 + 0.625924i \(0.784722\pi\)
\(132\) −10.3907 −0.904394
\(133\) 0 0
\(134\) −18.8289 −1.62657
\(135\) −0.513172 −0.0441668
\(136\) −1.47646 −0.126605
\(137\) 13.1730 1.12545 0.562723 0.826646i \(-0.309754\pi\)
0.562723 + 0.826646i \(0.309754\pi\)
\(138\) 6.87741 0.585444
\(139\) 5.82242 0.493851 0.246926 0.969034i \(-0.420580\pi\)
0.246926 + 0.969034i \(0.420580\pi\)
\(140\) 0 0
\(141\) −10.1514 −0.854900
\(142\) −20.3594 −1.70853
\(143\) 1.90700 0.159471
\(144\) −4.29902 −0.358252
\(145\) 0.00197664 0.000164151 0
\(146\) 1.05760 0.0875276
\(147\) 0 0
\(148\) 10.4683 0.860490
\(149\) 12.8687 1.05425 0.527124 0.849788i \(-0.323270\pi\)
0.527124 + 0.849788i \(0.323270\pi\)
\(150\) −9.27858 −0.757593
\(151\) −8.75604 −0.712557 −0.356278 0.934380i \(-0.615954\pi\)
−0.356278 + 0.934380i \(0.615954\pi\)
\(152\) 2.37160 0.192362
\(153\) −4.63097 −0.374391
\(154\) 0 0
\(155\) −1.49177 −0.119822
\(156\) −0.619496 −0.0495994
\(157\) 4.49426 0.358681 0.179341 0.983787i \(-0.442604\pi\)
0.179341 + 0.983787i \(0.442604\pi\)
\(158\) −15.3726 −1.22298
\(159\) 1.59568 0.126546
\(160\) 3.99436 0.315782
\(161\) 0 0
\(162\) −1.95889 −0.153905
\(163\) 9.57653 0.750091 0.375046 0.927006i \(-0.377627\pi\)
0.375046 + 0.927006i \(0.377627\pi\)
\(164\) −1.83724 −0.143465
\(165\) −2.90229 −0.225943
\(166\) −26.7851 −2.07893
\(167\) 6.49269 0.502419 0.251210 0.967933i \(-0.419172\pi\)
0.251210 + 0.967933i \(0.419172\pi\)
\(168\) 0 0
\(169\) −12.8863 −0.991254
\(170\) 4.65526 0.357042
\(171\) 7.43860 0.568844
\(172\) 11.6181 0.885870
\(173\) −0.203823 −0.0154963 −0.00774817 0.999970i \(-0.502466\pi\)
−0.00774817 + 0.999970i \(0.502466\pi\)
\(174\) 0.00754524 0.000572003 0
\(175\) 0 0
\(176\) −24.3135 −1.83270
\(177\) 1.42494 0.107105
\(178\) 30.2359 2.26628
\(179\) −17.2933 −1.29256 −0.646282 0.763098i \(-0.723677\pi\)
−0.646282 + 0.763098i \(0.723677\pi\)
\(180\) 0.942822 0.0702738
\(181\) 9.90127 0.735955 0.367978 0.929835i \(-0.380050\pi\)
0.367978 + 0.929835i \(0.380050\pi\)
\(182\) 0 0
\(183\) 2.50182 0.184940
\(184\) 1.11935 0.0825195
\(185\) 2.92397 0.214975
\(186\) −5.69440 −0.417534
\(187\) −26.1908 −1.91526
\(188\) 18.6505 1.36023
\(189\) 0 0
\(190\) −7.47763 −0.542484
\(191\) −25.6289 −1.85444 −0.927222 0.374513i \(-0.877810\pi\)
−0.927222 + 0.374513i \(0.877810\pi\)
\(192\) 6.64927 0.479870
\(193\) −14.1502 −1.01855 −0.509277 0.860603i \(-0.670087\pi\)
−0.509277 + 0.860603i \(0.670087\pi\)
\(194\) 5.02361 0.360674
\(195\) −0.173036 −0.0123913
\(196\) 0 0
\(197\) −13.9750 −0.995676 −0.497838 0.867270i \(-0.665873\pi\)
−0.497838 + 0.867270i \(0.665873\pi\)
\(198\) −11.0787 −0.787327
\(199\) −5.25791 −0.372723 −0.186362 0.982481i \(-0.559670\pi\)
−0.186362 + 0.982481i \(0.559670\pi\)
\(200\) −1.51016 −0.106784
\(201\) −9.61202 −0.677980
\(202\) 31.4334 2.21165
\(203\) 0 0
\(204\) 8.50821 0.595694
\(205\) −0.513172 −0.0358415
\(206\) −24.0320 −1.67439
\(207\) 3.51087 0.244023
\(208\) −1.44958 −0.100510
\(209\) 42.0697 2.91002
\(210\) 0 0
\(211\) 2.92311 0.201235 0.100618 0.994925i \(-0.467918\pi\)
0.100618 + 0.994925i \(0.467918\pi\)
\(212\) −2.93165 −0.201346
\(213\) −10.3934 −0.712141
\(214\) −2.08558 −0.142567
\(215\) 3.24512 0.221315
\(216\) −0.318823 −0.0216932
\(217\) 0 0
\(218\) 14.6874 0.994756
\(219\) 0.539898 0.0364829
\(220\) 5.33221 0.359498
\(221\) −1.56151 −0.105038
\(222\) 11.1614 0.749106
\(223\) 20.3713 1.36416 0.682082 0.731275i \(-0.261075\pi\)
0.682082 + 0.731275i \(0.261075\pi\)
\(224\) 0 0
\(225\) −4.73665 −0.315777
\(226\) 17.6765 1.17582
\(227\) −9.00865 −0.597925 −0.298962 0.954265i \(-0.596641\pi\)
−0.298962 + 0.954265i \(0.596641\pi\)
\(228\) −13.6665 −0.905087
\(229\) 16.7740 1.10846 0.554230 0.832364i \(-0.313013\pi\)
0.554230 + 0.832364i \(0.313013\pi\)
\(230\) −3.52930 −0.232715
\(231\) 0 0
\(232\) 0.00122804 8.06250e−5 0
\(233\) 20.9774 1.37428 0.687138 0.726527i \(-0.258867\pi\)
0.687138 + 0.726527i \(0.258867\pi\)
\(234\) −0.660514 −0.0431791
\(235\) 5.20940 0.339824
\(236\) −2.61797 −0.170415
\(237\) −7.84764 −0.509759
\(238\) 0 0
\(239\) −13.3300 −0.862246 −0.431123 0.902293i \(-0.641882\pi\)
−0.431123 + 0.902293i \(0.641882\pi\)
\(240\) 2.20614 0.142406
\(241\) 7.33366 0.472403 0.236201 0.971704i \(-0.424098\pi\)
0.236201 + 0.971704i \(0.424098\pi\)
\(242\) −41.1086 −2.64256
\(243\) −1.00000 −0.0641500
\(244\) −4.59645 −0.294258
\(245\) 0 0
\(246\) −1.95889 −0.124894
\(247\) 2.50821 0.159593
\(248\) −0.926806 −0.0588522
\(249\) −13.6736 −0.866532
\(250\) 9.78774 0.619031
\(251\) −26.5835 −1.67794 −0.838969 0.544179i \(-0.816841\pi\)
−0.838969 + 0.544179i \(0.816841\pi\)
\(252\) 0 0
\(253\) 19.8561 1.24834
\(254\) −12.0687 −0.757258
\(255\) 2.37648 0.148821
\(256\) 18.2783 1.14239
\(257\) 26.5995 1.65923 0.829615 0.558336i \(-0.188560\pi\)
0.829615 + 0.558336i \(0.188560\pi\)
\(258\) 12.3873 0.771201
\(259\) 0 0
\(260\) 0.317908 0.0197158
\(261\) 0.00385180 0.000238420 0
\(262\) 34.9708 2.16050
\(263\) −6.28864 −0.387774 −0.193887 0.981024i \(-0.562110\pi\)
−0.193887 + 0.981024i \(0.562110\pi\)
\(264\) −1.80313 −0.110975
\(265\) −0.818858 −0.0503020
\(266\) 0 0
\(267\) 15.4352 0.944621
\(268\) 17.6596 1.07873
\(269\) −12.8076 −0.780894 −0.390447 0.920625i \(-0.627680\pi\)
−0.390447 + 0.920625i \(0.627680\pi\)
\(270\) 1.00525 0.0611774
\(271\) 9.34578 0.567716 0.283858 0.958866i \(-0.408386\pi\)
0.283858 + 0.958866i \(0.408386\pi\)
\(272\) 19.9086 1.20714
\(273\) 0 0
\(274\) −25.8044 −1.55890
\(275\) −26.7886 −1.61541
\(276\) −6.45033 −0.388264
\(277\) −26.2243 −1.57567 −0.787833 0.615888i \(-0.788797\pi\)
−0.787833 + 0.615888i \(0.788797\pi\)
\(278\) −11.4055 −0.684055
\(279\) −2.90696 −0.174035
\(280\) 0 0
\(281\) 2.90948 0.173565 0.0867826 0.996227i \(-0.472341\pi\)
0.0867826 + 0.996227i \(0.472341\pi\)
\(282\) 19.8854 1.18416
\(283\) 2.90496 0.172682 0.0863411 0.996266i \(-0.472483\pi\)
0.0863411 + 0.996266i \(0.472483\pi\)
\(284\) 19.0951 1.13309
\(285\) −3.81728 −0.226116
\(286\) −3.73559 −0.220890
\(287\) 0 0
\(288\) 7.78366 0.458657
\(289\) 4.44585 0.261520
\(290\) −0.00387201 −0.000227372 0
\(291\) 2.56452 0.150335
\(292\) −0.991924 −0.0580479
\(293\) 11.7862 0.688560 0.344280 0.938867i \(-0.388123\pi\)
0.344280 + 0.938867i \(0.388123\pi\)
\(294\) 0 0
\(295\) −0.731242 −0.0425745
\(296\) 1.81661 0.105588
\(297\) −5.65559 −0.328171
\(298\) −25.2084 −1.46028
\(299\) 1.18382 0.0684624
\(300\) 8.70238 0.502432
\(301\) 0 0
\(302\) 17.1521 0.986993
\(303\) 16.0466 0.921851
\(304\) −31.9787 −1.83411
\(305\) −1.28387 −0.0735139
\(306\) 9.07154 0.518586
\(307\) −9.97122 −0.569088 −0.284544 0.958663i \(-0.591842\pi\)
−0.284544 + 0.958663i \(0.591842\pi\)
\(308\) 0 0
\(309\) −12.2682 −0.697913
\(310\) 2.92221 0.165970
\(311\) −23.9202 −1.35639 −0.678194 0.734883i \(-0.737237\pi\)
−0.678194 + 0.734883i \(0.737237\pi\)
\(312\) −0.107503 −0.00608619
\(313\) 19.0421 1.07632 0.538160 0.842842i \(-0.319119\pi\)
0.538160 + 0.842842i \(0.319119\pi\)
\(314\) −8.80376 −0.496825
\(315\) 0 0
\(316\) 14.4180 0.811077
\(317\) −13.4871 −0.757510 −0.378755 0.925497i \(-0.623648\pi\)
−0.378755 + 0.925497i \(0.623648\pi\)
\(318\) −3.12576 −0.175284
\(319\) 0.0217842 0.00121968
\(320\) −3.41222 −0.190749
\(321\) −1.06468 −0.0594245
\(322\) 0 0
\(323\) −34.4479 −1.91673
\(324\) 1.83724 0.102069
\(325\) −1.59714 −0.0885936
\(326\) −18.7593 −1.03898
\(327\) 7.49782 0.414631
\(328\) −0.318823 −0.0176041
\(329\) 0 0
\(330\) 5.68526 0.312963
\(331\) 6.88877 0.378641 0.189320 0.981915i \(-0.439371\pi\)
0.189320 + 0.981915i \(0.439371\pi\)
\(332\) 25.1218 1.37874
\(333\) 5.69784 0.312240
\(334\) −12.7184 −0.695922
\(335\) 4.93262 0.269498
\(336\) 0 0
\(337\) 32.2680 1.75775 0.878875 0.477051i \(-0.158294\pi\)
0.878875 + 0.477051i \(0.158294\pi\)
\(338\) 25.2428 1.37303
\(339\) 9.02374 0.490102
\(340\) −4.36618 −0.236789
\(341\) −16.4406 −0.890306
\(342\) −14.5714 −0.787931
\(343\) 0 0
\(344\) 2.01613 0.108702
\(345\) −1.80168 −0.0969993
\(346\) 0.399266 0.0214646
\(347\) 8.81735 0.473340 0.236670 0.971590i \(-0.423944\pi\)
0.236670 + 0.971590i \(0.423944\pi\)
\(348\) −0.00707669 −0.000379350 0
\(349\) −16.4848 −0.882410 −0.441205 0.897406i \(-0.645449\pi\)
−0.441205 + 0.897406i \(0.645449\pi\)
\(350\) 0 0
\(351\) −0.337188 −0.0179978
\(352\) 44.0212 2.34634
\(353\) 10.5079 0.559281 0.279640 0.960105i \(-0.409785\pi\)
0.279640 + 0.960105i \(0.409785\pi\)
\(354\) −2.79131 −0.148356
\(355\) 5.33358 0.283077
\(356\) −28.3583 −1.50299
\(357\) 0 0
\(358\) 33.8757 1.79039
\(359\) −10.6446 −0.561800 −0.280900 0.959737i \(-0.590633\pi\)
−0.280900 + 0.959737i \(0.590633\pi\)
\(360\) 0.163611 0.00862308
\(361\) 36.3328 1.91225
\(362\) −19.3955 −1.01940
\(363\) −20.9857 −1.10146
\(364\) 0 0
\(365\) −0.277061 −0.0145020
\(366\) −4.90079 −0.256168
\(367\) 26.4608 1.38124 0.690621 0.723217i \(-0.257337\pi\)
0.690621 + 0.723217i \(0.257337\pi\)
\(368\) −15.0933 −0.786794
\(369\) −1.00000 −0.0520579
\(370\) −5.72774 −0.297771
\(371\) 0 0
\(372\) 5.34079 0.276907
\(373\) −28.8140 −1.49193 −0.745966 0.665984i \(-0.768012\pi\)
−0.745966 + 0.665984i \(0.768012\pi\)
\(374\) 51.3049 2.65291
\(375\) 4.99658 0.258022
\(376\) 3.23650 0.166910
\(377\) 0.00129878 6.68906e−5 0
\(378\) 0 0
\(379\) 35.6547 1.83146 0.915728 0.401798i \(-0.131615\pi\)
0.915728 + 0.401798i \(0.131615\pi\)
\(380\) 7.01328 0.359774
\(381\) −6.16100 −0.315638
\(382\) 50.2042 2.56867
\(383\) −37.6215 −1.92237 −0.961185 0.275904i \(-0.911023\pi\)
−0.961185 + 0.275904i \(0.911023\pi\)
\(384\) 2.54214 0.129728
\(385\) 0 0
\(386\) 27.7187 1.41084
\(387\) 6.32365 0.321449
\(388\) −4.71165 −0.239198
\(389\) −3.09403 −0.156873 −0.0784367 0.996919i \(-0.524993\pi\)
−0.0784367 + 0.996919i \(0.524993\pi\)
\(390\) 0.338957 0.0171638
\(391\) −16.2587 −0.822240
\(392\) 0 0
\(393\) 17.8524 0.900533
\(394\) 27.3754 1.37915
\(395\) 4.02719 0.202630
\(396\) 10.3907 0.522152
\(397\) 28.0868 1.40964 0.704818 0.709388i \(-0.251029\pi\)
0.704818 + 0.709388i \(0.251029\pi\)
\(398\) 10.2997 0.516275
\(399\) 0 0
\(400\) 20.3630 1.01815
\(401\) −6.78324 −0.338739 −0.169369 0.985553i \(-0.554173\pi\)
−0.169369 + 0.985553i \(0.554173\pi\)
\(402\) 18.8289 0.939099
\(403\) −0.980191 −0.0488268
\(404\) −29.4814 −1.46676
\(405\) 0.513172 0.0254997
\(406\) 0 0
\(407\) 32.2246 1.59732
\(408\) 1.47646 0.0730957
\(409\) 22.9474 1.13468 0.567338 0.823485i \(-0.307973\pi\)
0.567338 + 0.823485i \(0.307973\pi\)
\(410\) 1.00525 0.0496456
\(411\) −13.1730 −0.649776
\(412\) 22.5396 1.11045
\(413\) 0 0
\(414\) −6.87741 −0.338006
\(415\) 7.01693 0.344448
\(416\) 2.62456 0.128680
\(417\) −5.82242 −0.285125
\(418\) −82.4098 −4.03080
\(419\) 1.76985 0.0864631 0.0432315 0.999065i \(-0.486235\pi\)
0.0432315 + 0.999065i \(0.486235\pi\)
\(420\) 0 0
\(421\) −36.4308 −1.77553 −0.887764 0.460299i \(-0.847742\pi\)
−0.887764 + 0.460299i \(0.847742\pi\)
\(422\) −5.72605 −0.278740
\(423\) 10.1514 0.493577
\(424\) −0.508740 −0.0247066
\(425\) 21.9353 1.06402
\(426\) 20.3594 0.986418
\(427\) 0 0
\(428\) 1.95607 0.0945502
\(429\) −1.90700 −0.0920707
\(430\) −6.35683 −0.306553
\(431\) 32.7586 1.57793 0.788963 0.614440i \(-0.210618\pi\)
0.788963 + 0.614440i \(0.210618\pi\)
\(432\) 4.29902 0.206837
\(433\) −15.2131 −0.731097 −0.365548 0.930792i \(-0.619119\pi\)
−0.365548 + 0.930792i \(0.619119\pi\)
\(434\) 0 0
\(435\) −0.00197664 −9.47724e−5 0
\(436\) −13.7753 −0.659718
\(437\) 26.1160 1.24930
\(438\) −1.05760 −0.0505341
\(439\) 12.8477 0.613186 0.306593 0.951841i \(-0.400811\pi\)
0.306593 + 0.951841i \(0.400811\pi\)
\(440\) 0.925319 0.0441128
\(441\) 0 0
\(442\) 3.05882 0.145493
\(443\) −25.4783 −1.21051 −0.605254 0.796032i \(-0.706929\pi\)
−0.605254 + 0.796032i \(0.706929\pi\)
\(444\) −10.4683 −0.496804
\(445\) −7.92093 −0.375488
\(446\) −39.9051 −1.88956
\(447\) −12.8687 −0.608670
\(448\) 0 0
\(449\) −24.5659 −1.15934 −0.579668 0.814853i \(-0.696818\pi\)
−0.579668 + 0.814853i \(0.696818\pi\)
\(450\) 9.27858 0.437396
\(451\) −5.65559 −0.266311
\(452\) −16.5788 −0.779801
\(453\) 8.75604 0.411395
\(454\) 17.6469 0.828211
\(455\) 0 0
\(456\) −2.37160 −0.111060
\(457\) −19.2097 −0.898592 −0.449296 0.893383i \(-0.648325\pi\)
−0.449296 + 0.893383i \(0.648325\pi\)
\(458\) −32.8585 −1.53538
\(459\) 4.63097 0.216155
\(460\) 3.31013 0.154336
\(461\) −2.22690 −0.103717 −0.0518586 0.998654i \(-0.516515\pi\)
−0.0518586 + 0.998654i \(0.516515\pi\)
\(462\) 0 0
\(463\) −21.7689 −1.01169 −0.505844 0.862625i \(-0.668819\pi\)
−0.505844 + 0.862625i \(0.668819\pi\)
\(464\) −0.0165590 −0.000768731 0
\(465\) 1.49177 0.0691792
\(466\) −41.0924 −1.90357
\(467\) 15.6865 0.725885 0.362942 0.931812i \(-0.381772\pi\)
0.362942 + 0.931812i \(0.381772\pi\)
\(468\) 0.619496 0.0286362
\(469\) 0 0
\(470\) −10.2046 −0.470705
\(471\) −4.49426 −0.207085
\(472\) −0.454306 −0.0209111
\(473\) 35.7640 1.64443
\(474\) 15.3726 0.706089
\(475\) −35.2341 −1.61665
\(476\) 0 0
\(477\) −1.59568 −0.0730611
\(478\) 26.1120 1.19433
\(479\) 18.7627 0.857290 0.428645 0.903473i \(-0.358991\pi\)
0.428645 + 0.903473i \(0.358991\pi\)
\(480\) −3.99436 −0.182317
\(481\) 1.92124 0.0876012
\(482\) −14.3658 −0.654345
\(483\) 0 0
\(484\) 38.5558 1.75254
\(485\) −1.31604 −0.0597584
\(486\) 1.95889 0.0888570
\(487\) 38.4308 1.74147 0.870733 0.491756i \(-0.163645\pi\)
0.870733 + 0.491756i \(0.163645\pi\)
\(488\) −0.797640 −0.0361074
\(489\) −9.57653 −0.433066
\(490\) 0 0
\(491\) 36.8009 1.66080 0.830402 0.557165i \(-0.188111\pi\)
0.830402 + 0.557165i \(0.188111\pi\)
\(492\) 1.83724 0.0828293
\(493\) −0.0178375 −0.000803363 0
\(494\) −4.91330 −0.221060
\(495\) 2.90229 0.130448
\(496\) 12.4971 0.561135
\(497\) 0 0
\(498\) 26.7851 1.20027
\(499\) −9.91559 −0.443883 −0.221941 0.975060i \(-0.571239\pi\)
−0.221941 + 0.975060i \(0.571239\pi\)
\(500\) −9.17993 −0.410539
\(501\) −6.49269 −0.290072
\(502\) 52.0742 2.32418
\(503\) 27.2048 1.21300 0.606501 0.795083i \(-0.292573\pi\)
0.606501 + 0.795083i \(0.292573\pi\)
\(504\) 0 0
\(505\) −8.23465 −0.366437
\(506\) −38.8958 −1.72913
\(507\) 12.8863 0.572301
\(508\) 11.3193 0.502211
\(509\) 18.0939 0.801999 0.401000 0.916078i \(-0.368663\pi\)
0.401000 + 0.916078i \(0.368663\pi\)
\(510\) −4.65526 −0.206139
\(511\) 0 0
\(512\) −30.7209 −1.35768
\(513\) −7.43860 −0.328422
\(514\) −52.1054 −2.29827
\(515\) 6.29569 0.277421
\(516\) −11.6181 −0.511457
\(517\) 57.4120 2.52498
\(518\) 0 0
\(519\) 0.203823 0.00894682
\(520\) 0.0551678 0.00241927
\(521\) −23.3651 −1.02365 −0.511823 0.859091i \(-0.671029\pi\)
−0.511823 + 0.859091i \(0.671029\pi\)
\(522\) −0.00754524 −0.000330246 0
\(523\) −37.3684 −1.63401 −0.817004 0.576633i \(-0.804366\pi\)
−0.817004 + 0.576633i \(0.804366\pi\)
\(524\) −32.7991 −1.43284
\(525\) 0 0
\(526\) 12.3187 0.537123
\(527\) 13.4620 0.586415
\(528\) 24.3135 1.05811
\(529\) −10.6738 −0.464077
\(530\) 1.60405 0.0696755
\(531\) −1.42494 −0.0618373
\(532\) 0 0
\(533\) −0.337188 −0.0146052
\(534\) −30.2359 −1.30844
\(535\) 0.546362 0.0236213
\(536\) 3.06454 0.132368
\(537\) 17.2933 0.746263
\(538\) 25.0887 1.08165
\(539\) 0 0
\(540\) −0.942822 −0.0405726
\(541\) 31.1517 1.33931 0.669657 0.742670i \(-0.266441\pi\)
0.669657 + 0.742670i \(0.266441\pi\)
\(542\) −18.3073 −0.786367
\(543\) −9.90127 −0.424904
\(544\) −36.0459 −1.54545
\(545\) −3.84767 −0.164816
\(546\) 0 0
\(547\) 9.48991 0.405759 0.202880 0.979204i \(-0.434970\pi\)
0.202880 + 0.979204i \(0.434970\pi\)
\(548\) 24.2020 1.03386
\(549\) −2.50182 −0.106775
\(550\) 52.4758 2.23758
\(551\) 0.0286520 0.00122062
\(552\) −1.11935 −0.0476427
\(553\) 0 0
\(554\) 51.3705 2.18252
\(555\) −2.92397 −0.124116
\(556\) 10.6972 0.453662
\(557\) −17.2459 −0.730730 −0.365365 0.930864i \(-0.619056\pi\)
−0.365365 + 0.930864i \(0.619056\pi\)
\(558\) 5.69440 0.241063
\(559\) 2.13226 0.0901849
\(560\) 0 0
\(561\) 26.1908 1.10578
\(562\) −5.69935 −0.240413
\(563\) 40.4074 1.70297 0.851485 0.524378i \(-0.175702\pi\)
0.851485 + 0.524378i \(0.175702\pi\)
\(564\) −18.6505 −0.785329
\(565\) −4.63073 −0.194816
\(566\) −5.69050 −0.239190
\(567\) 0 0
\(568\) 3.31365 0.139038
\(569\) 13.6338 0.571560 0.285780 0.958295i \(-0.407747\pi\)
0.285780 + 0.958295i \(0.407747\pi\)
\(570\) 7.47763 0.313204
\(571\) 17.1020 0.715697 0.357849 0.933780i \(-0.383510\pi\)
0.357849 + 0.933780i \(0.383510\pi\)
\(572\) 3.50362 0.146494
\(573\) 25.6289 1.07066
\(574\) 0 0
\(575\) −16.6298 −0.693510
\(576\) −6.64927 −0.277053
\(577\) 13.9866 0.582270 0.291135 0.956682i \(-0.405967\pi\)
0.291135 + 0.956682i \(0.405967\pi\)
\(578\) −8.70891 −0.362243
\(579\) 14.1502 0.588062
\(580\) 0.00363156 0.000150792 0
\(581\) 0 0
\(582\) −5.02361 −0.208236
\(583\) −9.02450 −0.373757
\(584\) −0.172132 −0.00712288
\(585\) 0.173036 0.00715414
\(586\) −23.0879 −0.953754
\(587\) −12.3410 −0.509366 −0.254683 0.967025i \(-0.581971\pi\)
−0.254683 + 0.967025i \(0.581971\pi\)
\(588\) 0 0
\(589\) −21.6237 −0.890989
\(590\) 1.43242 0.0589718
\(591\) 13.9750 0.574854
\(592\) −24.4952 −1.00674
\(593\) −0.617404 −0.0253538 −0.0126769 0.999920i \(-0.504035\pi\)
−0.0126769 + 0.999920i \(0.504035\pi\)
\(594\) 11.0787 0.454563
\(595\) 0 0
\(596\) 23.6430 0.968455
\(597\) 5.25791 0.215192
\(598\) −2.31898 −0.0948301
\(599\) 23.8114 0.972906 0.486453 0.873707i \(-0.338290\pi\)
0.486453 + 0.873707i \(0.338290\pi\)
\(600\) 1.51016 0.0616519
\(601\) −19.7114 −0.804047 −0.402023 0.915629i \(-0.631693\pi\)
−0.402023 + 0.915629i \(0.631693\pi\)
\(602\) 0 0
\(603\) 9.61202 0.391432
\(604\) −16.0870 −0.654570
\(605\) 10.7693 0.437833
\(606\) −31.4334 −1.27690
\(607\) 18.1517 0.736753 0.368376 0.929677i \(-0.379914\pi\)
0.368376 + 0.929677i \(0.379914\pi\)
\(608\) 57.8996 2.34814
\(609\) 0 0
\(610\) 2.51495 0.101827
\(611\) 3.42292 0.138477
\(612\) −8.50821 −0.343924
\(613\) 31.2630 1.26270 0.631351 0.775497i \(-0.282501\pi\)
0.631351 + 0.775497i \(0.282501\pi\)
\(614\) 19.5325 0.788268
\(615\) 0.513172 0.0206931
\(616\) 0 0
\(617\) −12.3896 −0.498785 −0.249393 0.968402i \(-0.580231\pi\)
−0.249393 + 0.968402i \(0.580231\pi\)
\(618\) 24.0320 0.966709
\(619\) 32.7938 1.31809 0.659047 0.752102i \(-0.270960\pi\)
0.659047 + 0.752102i \(0.270960\pi\)
\(620\) −2.74074 −0.110071
\(621\) −3.51087 −0.140887
\(622\) 46.8569 1.87879
\(623\) 0 0
\(624\) 1.44958 0.0580296
\(625\) 21.1192 0.844767
\(626\) −37.3013 −1.49086
\(627\) −42.0697 −1.68010
\(628\) 8.25705 0.329492
\(629\) −26.3865 −1.05210
\(630\) 0 0
\(631\) −42.1403 −1.67758 −0.838790 0.544455i \(-0.816737\pi\)
−0.838790 + 0.544455i \(0.816737\pi\)
\(632\) 2.50201 0.0995247
\(633\) −2.92311 −0.116183
\(634\) 26.4197 1.04926
\(635\) 3.16165 0.125466
\(636\) 2.93165 0.116247
\(637\) 0 0
\(638\) −0.0426728 −0.00168943
\(639\) 10.3934 0.411155
\(640\) −1.30456 −0.0515671
\(641\) 10.0868 0.398404 0.199202 0.979958i \(-0.436165\pi\)
0.199202 + 0.979958i \(0.436165\pi\)
\(642\) 2.08558 0.0823114
\(643\) −26.4450 −1.04289 −0.521444 0.853286i \(-0.674606\pi\)
−0.521444 + 0.853286i \(0.674606\pi\)
\(644\) 0 0
\(645\) −3.24512 −0.127777
\(646\) 67.4796 2.65495
\(647\) 17.7110 0.696292 0.348146 0.937440i \(-0.386811\pi\)
0.348146 + 0.937440i \(0.386811\pi\)
\(648\) 0.318823 0.0125246
\(649\) −8.05890 −0.316339
\(650\) 3.12862 0.122715
\(651\) 0 0
\(652\) 17.5944 0.689050
\(653\) −41.1025 −1.60846 −0.804232 0.594315i \(-0.797423\pi\)
−0.804232 + 0.594315i \(0.797423\pi\)
\(654\) −14.6874 −0.574323
\(655\) −9.16134 −0.357963
\(656\) 4.29902 0.167849
\(657\) −0.539898 −0.0210634
\(658\) 0 0
\(659\) 39.6534 1.54468 0.772339 0.635211i \(-0.219087\pi\)
0.772339 + 0.635211i \(0.219087\pi\)
\(660\) −5.33221 −0.207556
\(661\) 41.9575 1.63196 0.815979 0.578082i \(-0.196199\pi\)
0.815979 + 0.578082i \(0.196199\pi\)
\(662\) −13.4943 −0.524472
\(663\) 1.56151 0.0606439
\(664\) 4.35948 0.169181
\(665\) 0 0
\(666\) −11.1614 −0.432497
\(667\) 0.0135232 0.000523619 0
\(668\) 11.9286 0.461533
\(669\) −20.3713 −0.787601
\(670\) −9.66245 −0.373293
\(671\) −14.1493 −0.546227
\(672\) 0 0
\(673\) −27.1875 −1.04800 −0.524000 0.851718i \(-0.675561\pi\)
−0.524000 + 0.851718i \(0.675561\pi\)
\(674\) −63.2094 −2.43474
\(675\) 4.73665 0.182314
\(676\) −23.6753 −0.910587
\(677\) 17.9846 0.691206 0.345603 0.938381i \(-0.387674\pi\)
0.345603 + 0.938381i \(0.387674\pi\)
\(678\) −17.6765 −0.678862
\(679\) 0 0
\(680\) −0.757679 −0.0290556
\(681\) 9.00865 0.345212
\(682\) 32.2052 1.23320
\(683\) −31.4508 −1.20343 −0.601716 0.798710i \(-0.705516\pi\)
−0.601716 + 0.798710i \(0.705516\pi\)
\(684\) 13.6665 0.522552
\(685\) 6.76002 0.258287
\(686\) 0 0
\(687\) −16.7740 −0.639970
\(688\) −27.1855 −1.03644
\(689\) −0.538044 −0.0204978
\(690\) 3.52930 0.134358
\(691\) 42.5967 1.62045 0.810227 0.586117i \(-0.199344\pi\)
0.810227 + 0.586117i \(0.199344\pi\)
\(692\) −0.374471 −0.0142353
\(693\) 0 0
\(694\) −17.2722 −0.655644
\(695\) 2.98791 0.113338
\(696\) −0.00122804 −4.65489e−5 0
\(697\) 4.63097 0.175410
\(698\) 32.2918 1.22226
\(699\) −20.9774 −0.793439
\(700\) 0 0
\(701\) 18.0204 0.680619 0.340310 0.940313i \(-0.389468\pi\)
0.340310 + 0.940313i \(0.389468\pi\)
\(702\) 0.660514 0.0249295
\(703\) 42.3840 1.59854
\(704\) −37.6056 −1.41731
\(705\) −5.20940 −0.196197
\(706\) −20.5839 −0.774684
\(707\) 0 0
\(708\) 2.61797 0.0983892
\(709\) −8.47808 −0.318401 −0.159201 0.987246i \(-0.550892\pi\)
−0.159201 + 0.987246i \(0.550892\pi\)
\(710\) −10.4479 −0.392103
\(711\) 7.84764 0.294309
\(712\) −4.92111 −0.184427
\(713\) −10.2060 −0.382216
\(714\) 0 0
\(715\) 0.978618 0.0365982
\(716\) −31.7721 −1.18738
\(717\) 13.3300 0.497818
\(718\) 20.8516 0.778173
\(719\) 7.37205 0.274931 0.137466 0.990507i \(-0.456104\pi\)
0.137466 + 0.990507i \(0.456104\pi\)
\(720\) −2.20614 −0.0822180
\(721\) 0 0
\(722\) −71.1719 −2.64874
\(723\) −7.33366 −0.272742
\(724\) 18.1910 0.676064
\(725\) −0.0182446 −0.000677589 0
\(726\) 41.1086 1.52568
\(727\) 20.2474 0.750934 0.375467 0.926836i \(-0.377482\pi\)
0.375467 + 0.926836i \(0.377482\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0.542731 0.0200874
\(731\) −29.2846 −1.08313
\(732\) 4.59645 0.169890
\(733\) −3.10316 −0.114618 −0.0573090 0.998356i \(-0.518252\pi\)
−0.0573090 + 0.998356i \(0.518252\pi\)
\(734\) −51.8337 −1.91322
\(735\) 0 0
\(736\) 27.3275 1.00730
\(737\) 54.3616 2.00244
\(738\) 1.95889 0.0721077
\(739\) 29.8501 1.09805 0.549026 0.835805i \(-0.314999\pi\)
0.549026 + 0.835805i \(0.314999\pi\)
\(740\) 5.37205 0.197480
\(741\) −2.50821 −0.0921413
\(742\) 0 0
\(743\) 24.7526 0.908084 0.454042 0.890980i \(-0.349982\pi\)
0.454042 + 0.890980i \(0.349982\pi\)
\(744\) 0.926806 0.0339784
\(745\) 6.60388 0.241947
\(746\) 56.4434 2.06654
\(747\) 13.6736 0.500292
\(748\) −48.1189 −1.75940
\(749\) 0 0
\(750\) −9.78774 −0.357398
\(751\) 49.0314 1.78918 0.894591 0.446886i \(-0.147467\pi\)
0.894591 + 0.446886i \(0.147467\pi\)
\(752\) −43.6410 −1.59142
\(753\) 26.5835 0.968758
\(754\) −0.00254416 −9.26530e−5 0
\(755\) −4.49336 −0.163530
\(756\) 0 0
\(757\) 37.5453 1.36461 0.682304 0.731069i \(-0.260978\pi\)
0.682304 + 0.731069i \(0.260978\pi\)
\(758\) −69.8435 −2.53683
\(759\) −19.8561 −0.720729
\(760\) 1.21704 0.0441467
\(761\) 30.7380 1.11425 0.557126 0.830428i \(-0.311904\pi\)
0.557126 + 0.830428i \(0.311904\pi\)
\(762\) 12.0687 0.437203
\(763\) 0 0
\(764\) −47.0865 −1.70353
\(765\) −2.37648 −0.0859219
\(766\) 73.6964 2.66276
\(767\) −0.480474 −0.0173489
\(768\) −18.2783 −0.659562
\(769\) −16.6161 −0.599191 −0.299595 0.954066i \(-0.596852\pi\)
−0.299595 + 0.954066i \(0.596852\pi\)
\(770\) 0 0
\(771\) −26.5995 −0.957957
\(772\) −25.9974 −0.935665
\(773\) 15.0910 0.542785 0.271393 0.962469i \(-0.412516\pi\)
0.271393 + 0.962469i \(0.412516\pi\)
\(774\) −12.3873 −0.445253
\(775\) 13.7692 0.494606
\(776\) −0.817630 −0.0293512
\(777\) 0 0
\(778\) 6.06085 0.217292
\(779\) −7.43860 −0.266516
\(780\) −0.317908 −0.0113829
\(781\) 58.7806 2.10334
\(782\) 31.8490 1.13892
\(783\) −0.00385180 −0.000137652 0
\(784\) 0 0
\(785\) 2.30633 0.0823165
\(786\) −34.9708 −1.24737
\(787\) −13.5486 −0.482954 −0.241477 0.970407i \(-0.577632\pi\)
−0.241477 + 0.970407i \(0.577632\pi\)
\(788\) −25.6754 −0.914649
\(789\) 6.28864 0.223882
\(790\) −7.88882 −0.280671
\(791\) 0 0
\(792\) 1.80313 0.0640716
\(793\) −0.843584 −0.0299566
\(794\) −55.0189 −1.95255
\(795\) 0.818858 0.0290419
\(796\) −9.66006 −0.342392
\(797\) 30.4556 1.07879 0.539396 0.842052i \(-0.318653\pi\)
0.539396 + 0.842052i \(0.318653\pi\)
\(798\) 0 0
\(799\) −47.0107 −1.66312
\(800\) −36.8685 −1.30350
\(801\) −15.4352 −0.545377
\(802\) 13.2876 0.469202
\(803\) −3.05344 −0.107754
\(804\) −17.6596 −0.622807
\(805\) 0 0
\(806\) 1.92008 0.0676321
\(807\) 12.8076 0.450850
\(808\) −5.11602 −0.179981
\(809\) 36.5584 1.28533 0.642663 0.766149i \(-0.277830\pi\)
0.642663 + 0.766149i \(0.277830\pi\)
\(810\) −1.00525 −0.0353208
\(811\) 42.8439 1.50445 0.752226 0.658905i \(-0.228980\pi\)
0.752226 + 0.658905i \(0.228980\pi\)
\(812\) 0 0
\(813\) −9.34578 −0.327771
\(814\) −63.1245 −2.21251
\(815\) 4.91441 0.172144
\(816\) −19.9086 −0.696942
\(817\) 47.0391 1.64569
\(818\) −44.9514 −1.57169
\(819\) 0 0
\(820\) −0.942822 −0.0329248
\(821\) −38.0887 −1.32931 −0.664653 0.747152i \(-0.731421\pi\)
−0.664653 + 0.747152i \(0.731421\pi\)
\(822\) 25.8044 0.900033
\(823\) 23.4658 0.817965 0.408982 0.912542i \(-0.365884\pi\)
0.408982 + 0.912542i \(0.365884\pi\)
\(824\) 3.91139 0.136260
\(825\) 26.7886 0.932658
\(826\) 0 0
\(827\) 22.1287 0.769492 0.384746 0.923023i \(-0.374289\pi\)
0.384746 + 0.923023i \(0.374289\pi\)
\(828\) 6.45033 0.224164
\(829\) −8.56171 −0.297360 −0.148680 0.988885i \(-0.547503\pi\)
−0.148680 + 0.988885i \(0.547503\pi\)
\(830\) −13.7454 −0.477109
\(831\) 26.2243 0.909712
\(832\) −2.24206 −0.0777293
\(833\) 0 0
\(834\) 11.4055 0.394939
\(835\) 3.33187 0.115304
\(836\) 77.2922 2.67321
\(837\) 2.90696 0.100479
\(838\) −3.46695 −0.119764
\(839\) 5.19195 0.179246 0.0896231 0.995976i \(-0.471434\pi\)
0.0896231 + 0.995976i \(0.471434\pi\)
\(840\) 0 0
\(841\) −29.0000 −0.999999
\(842\) 71.3638 2.45936
\(843\) −2.90948 −0.100208
\(844\) 5.37047 0.184859
\(845\) −6.61289 −0.227490
\(846\) −19.8854 −0.683674
\(847\) 0 0
\(848\) 6.85986 0.235569
\(849\) −2.90496 −0.0996981
\(850\) −42.9688 −1.47382
\(851\) 20.0044 0.685742
\(852\) −19.0951 −0.654188
\(853\) −10.7872 −0.369348 −0.184674 0.982800i \(-0.559123\pi\)
−0.184674 + 0.982800i \(0.559123\pi\)
\(854\) 0 0
\(855\) 3.81728 0.130548
\(856\) 0.339444 0.0116020
\(857\) −33.0347 −1.12844 −0.564221 0.825624i \(-0.690824\pi\)
−0.564221 + 0.825624i \(0.690824\pi\)
\(858\) 3.73559 0.127531
\(859\) −30.0052 −1.02377 −0.511883 0.859055i \(-0.671052\pi\)
−0.511883 + 0.859055i \(0.671052\pi\)
\(860\) 5.96207 0.203305
\(861\) 0 0
\(862\) −64.1704 −2.18565
\(863\) −22.4627 −0.764639 −0.382320 0.924030i \(-0.624875\pi\)
−0.382320 + 0.924030i \(0.624875\pi\)
\(864\) −7.78366 −0.264806
\(865\) −0.104596 −0.00355637
\(866\) 29.8008 1.01267
\(867\) −4.44585 −0.150989
\(868\) 0 0
\(869\) 44.3830 1.50559
\(870\) 0.00387201 0.000131273 0
\(871\) 3.24106 0.109819
\(872\) −2.39048 −0.0809519
\(873\) −2.56452 −0.0867960
\(874\) −51.1583 −1.73046
\(875\) 0 0
\(876\) 0.991924 0.0335140
\(877\) −39.4229 −1.33122 −0.665608 0.746302i \(-0.731828\pi\)
−0.665608 + 0.746302i \(0.731828\pi\)
\(878\) −25.1671 −0.849350
\(879\) −11.7862 −0.397540
\(880\) −12.4770 −0.420600
\(881\) 43.8734 1.47813 0.739066 0.673633i \(-0.235267\pi\)
0.739066 + 0.673633i \(0.235267\pi\)
\(882\) 0 0
\(883\) 17.4922 0.588658 0.294329 0.955704i \(-0.404904\pi\)
0.294329 + 0.955704i \(0.404904\pi\)
\(884\) −2.86887 −0.0964904
\(885\) 0.731242 0.0245804
\(886\) 49.9091 1.67673
\(887\) −35.3835 −1.18806 −0.594030 0.804443i \(-0.702464\pi\)
−0.594030 + 0.804443i \(0.702464\pi\)
\(888\) −1.81661 −0.0609613
\(889\) 0 0
\(890\) 15.5162 0.520105
\(891\) 5.65559 0.189469
\(892\) 37.4271 1.25315
\(893\) 75.5120 2.52691
\(894\) 25.2084 0.843095
\(895\) −8.87446 −0.296640
\(896\) 0 0
\(897\) −1.18382 −0.0395268
\(898\) 48.1218 1.60585
\(899\) −0.0111970 −0.000373441 0
\(900\) −8.70238 −0.290079
\(901\) 7.38953 0.246181
\(902\) 11.0787 0.368879
\(903\) 0 0
\(904\) −2.87698 −0.0956869
\(905\) 5.08106 0.168900
\(906\) −17.1521 −0.569841
\(907\) −23.1267 −0.767910 −0.383955 0.923352i \(-0.625438\pi\)
−0.383955 + 0.923352i \(0.625438\pi\)
\(908\) −16.5511 −0.549266
\(909\) −16.0466 −0.532231
\(910\) 0 0
\(911\) 37.9418 1.25707 0.628534 0.777782i \(-0.283655\pi\)
0.628534 + 0.777782i \(0.283655\pi\)
\(912\) 31.9787 1.05892
\(913\) 77.3325 2.55933
\(914\) 37.6296 1.24468
\(915\) 1.28387 0.0424433
\(916\) 30.8180 1.01825
\(917\) 0 0
\(918\) −9.07154 −0.299406
\(919\) 26.5698 0.876456 0.438228 0.898864i \(-0.355606\pi\)
0.438228 + 0.898864i \(0.355606\pi\)
\(920\) 0.574419 0.0189380
\(921\) 9.97122 0.328563
\(922\) 4.36225 0.143663
\(923\) 3.50452 0.115353
\(924\) 0 0
\(925\) −26.9887 −0.887383
\(926\) 42.6429 1.40133
\(927\) 12.2682 0.402940
\(928\) 0.0299811 0.000984177 0
\(929\) 38.3519 1.25828 0.629142 0.777290i \(-0.283406\pi\)
0.629142 + 0.777290i \(0.283406\pi\)
\(930\) −2.92221 −0.0958230
\(931\) 0 0
\(932\) 38.5406 1.26244
\(933\) 23.9202 0.783111
\(934\) −30.7281 −1.00545
\(935\) −13.4404 −0.439548
\(936\) 0.107503 0.00351386
\(937\) 29.1402 0.951969 0.475985 0.879454i \(-0.342092\pi\)
0.475985 + 0.879454i \(0.342092\pi\)
\(938\) 0 0
\(939\) −19.0421 −0.621414
\(940\) 9.57093 0.312169
\(941\) −39.2714 −1.28021 −0.640105 0.768287i \(-0.721109\pi\)
−0.640105 + 0.768287i \(0.721109\pi\)
\(942\) 8.80376 0.286842
\(943\) −3.51087 −0.114330
\(944\) 6.12587 0.199380
\(945\) 0 0
\(946\) −70.0576 −2.27777
\(947\) −30.3126 −0.985028 −0.492514 0.870305i \(-0.663922\pi\)
−0.492514 + 0.870305i \(0.663922\pi\)
\(948\) −14.4180 −0.468275
\(949\) −0.182047 −0.00590950
\(950\) 69.0196 2.23929
\(951\) 13.4871 0.437348
\(952\) 0 0
\(953\) 52.1968 1.69082 0.845410 0.534118i \(-0.179356\pi\)
0.845410 + 0.534118i \(0.179356\pi\)
\(954\) 3.12576 0.101200
\(955\) −13.1520 −0.425590
\(956\) −24.4904 −0.792077
\(957\) −0.0217842 −0.000704183 0
\(958\) −36.7540 −1.18747
\(959\) 0 0
\(960\) 3.41222 0.110129
\(961\) −22.5496 −0.727407
\(962\) −3.76350 −0.121340
\(963\) 1.06468 0.0343087
\(964\) 13.4737 0.433959
\(965\) −7.26149 −0.233756
\(966\) 0 0
\(967\) −50.5470 −1.62548 −0.812741 0.582625i \(-0.802026\pi\)
−0.812741 + 0.582625i \(0.802026\pi\)
\(968\) 6.69073 0.215048
\(969\) 34.4479 1.10663
\(970\) 2.57798 0.0827739
\(971\) 30.5794 0.981339 0.490669 0.871346i \(-0.336752\pi\)
0.490669 + 0.871346i \(0.336752\pi\)
\(972\) −1.83724 −0.0589296
\(973\) 0 0
\(974\) −75.2816 −2.41218
\(975\) 1.59714 0.0511495
\(976\) 10.7554 0.344272
\(977\) −21.3420 −0.682792 −0.341396 0.939919i \(-0.610900\pi\)
−0.341396 + 0.939919i \(0.610900\pi\)
\(978\) 18.7593 0.599858
\(979\) −87.2953 −2.78997
\(980\) 0 0
\(981\) −7.49782 −0.239387
\(982\) −72.0889 −2.30045
\(983\) −10.2173 −0.325880 −0.162940 0.986636i \(-0.552098\pi\)
−0.162940 + 0.986636i \(0.552098\pi\)
\(984\) 0.318823 0.0101637
\(985\) −7.17157 −0.228505
\(986\) 0.0349418 0.00111277
\(987\) 0 0
\(988\) 4.60819 0.146606
\(989\) 22.2015 0.705968
\(990\) −5.68526 −0.180690
\(991\) −5.79546 −0.184099 −0.0920495 0.995754i \(-0.529342\pi\)
−0.0920495 + 0.995754i \(0.529342\pi\)
\(992\) −22.6268 −0.718401
\(993\) −6.88877 −0.218608
\(994\) 0 0
\(995\) −2.69821 −0.0855391
\(996\) −25.1218 −0.796015
\(997\) −0.874723 −0.0277028 −0.0138514 0.999904i \(-0.504409\pi\)
−0.0138514 + 0.999904i \(0.504409\pi\)
\(998\) 19.4235 0.614841
\(999\) −5.69784 −0.180272
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 \(a_p\))