Properties

Label 2667.2.a.j.1.2
Level $2667$
Weight $2$
Character 2667.1
Self dual yes
Analytic conductor $21.296$
Analytic rank $1$
Dimension $7$
CM no
Inner twists $1$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 2667 = 3 \cdot 7 \cdot 127 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2667.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(21.2961022191\)
Analytic rank: \(1\)
Dimension: \(7\)
Coefficient field: 7.7.118870813.1
Defining polynomial: \(x^{7} - 9 x^{5} - 3 x^{4} + 20 x^{3} + 7 x^{2} - 13 x - 4\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-1.14753\) of defining polynomial
Character \(\chi\) \(=\) 2667.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.15625 q^{2} +1.00000 q^{3} +2.64943 q^{4} -0.239094 q^{5} -2.15625 q^{6} +1.00000 q^{7} -1.40032 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.15625 q^{2} +1.00000 q^{3} +2.64943 q^{4} -0.239094 q^{5} -2.15625 q^{6} +1.00000 q^{7} -1.40032 q^{8} +1.00000 q^{9} +0.515547 q^{10} -3.99784 q^{11} +2.64943 q^{12} -1.61682 q^{13} -2.15625 q^{14} -0.239094 q^{15} -2.27940 q^{16} +4.61421 q^{17} -2.15625 q^{18} -4.17289 q^{19} -0.633462 q^{20} +1.00000 q^{21} +8.62035 q^{22} +5.22408 q^{23} -1.40032 q^{24} -4.94283 q^{25} +3.48627 q^{26} +1.00000 q^{27} +2.64943 q^{28} +9.10130 q^{29} +0.515547 q^{30} -6.57815 q^{31} +7.71560 q^{32} -3.99784 q^{33} -9.94939 q^{34} -0.239094 q^{35} +2.64943 q^{36} -0.353708 q^{37} +8.99781 q^{38} -1.61682 q^{39} +0.334809 q^{40} -7.72038 q^{41} -2.15625 q^{42} -7.33166 q^{43} -10.5920 q^{44} -0.239094 q^{45} -11.2644 q^{46} +3.52396 q^{47} -2.27940 q^{48} +1.00000 q^{49} +10.6580 q^{50} +4.61421 q^{51} -4.28365 q^{52} -0.655025 q^{53} -2.15625 q^{54} +0.955860 q^{55} -1.40032 q^{56} -4.17289 q^{57} -19.6247 q^{58} -11.8415 q^{59} -0.633462 q^{60} -7.05891 q^{61} +14.1842 q^{62} +1.00000 q^{63} -12.0780 q^{64} +0.386572 q^{65} +8.62035 q^{66} -0.167504 q^{67} +12.2250 q^{68} +5.22408 q^{69} +0.515547 q^{70} +6.98566 q^{71} -1.40032 q^{72} -2.79662 q^{73} +0.762683 q^{74} -4.94283 q^{75} -11.0558 q^{76} -3.99784 q^{77} +3.48627 q^{78} +14.2526 q^{79} +0.544990 q^{80} +1.00000 q^{81} +16.6471 q^{82} -6.75526 q^{83} +2.64943 q^{84} -1.10323 q^{85} +15.8089 q^{86} +9.10130 q^{87} +5.59827 q^{88} -11.9943 q^{89} +0.515547 q^{90} -1.61682 q^{91} +13.8408 q^{92} -6.57815 q^{93} -7.59856 q^{94} +0.997714 q^{95} +7.71560 q^{96} -1.79091 q^{97} -2.15625 q^{98} -3.99784 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q - 2q^{2} + 7q^{3} + 4q^{4} - 8q^{5} - 2q^{6} + 7q^{7} - 9q^{8} + 7q^{9} + O(q^{10}) \) \( 7q - 2q^{2} + 7q^{3} + 4q^{4} - 8q^{5} - 2q^{6} + 7q^{7} - 9q^{8} + 7q^{9} - 3q^{11} + 4q^{12} - 23q^{13} - 2q^{14} - 8q^{15} + 2q^{16} + 3q^{17} - 2q^{18} - 9q^{19} - 9q^{20} + 7q^{21} - 19q^{22} + 12q^{23} - 9q^{24} + 3q^{25} + 18q^{26} + 7q^{27} + 4q^{28} - 9q^{29} - 33q^{31} + 10q^{32} - 3q^{33} - 2q^{34} - 8q^{35} + 4q^{36} - 33q^{37} - 3q^{38} - 23q^{39} - 9q^{40} - 3q^{41} - 2q^{42} - 9q^{43} + 2q^{44} - 8q^{45} - 32q^{46} + 11q^{47} + 2q^{48} + 7q^{49} + 29q^{50} + 3q^{51} - 21q^{52} + q^{53} - 2q^{54} - 16q^{55} - 9q^{56} - 9q^{57} - 5q^{58} - 30q^{59} - 9q^{60} - 19q^{61} + 3q^{62} + 7q^{63} - 21q^{64} + 14q^{65} - 19q^{66} - 30q^{67} + 24q^{68} + 12q^{69} + 8q^{71} - 9q^{72} - 20q^{73} - 9q^{74} + 3q^{75} - 42q^{76} - 3q^{77} + 18q^{78} + 8q^{79} + 12q^{80} + 7q^{81} + 10q^{82} - 34q^{83} + 4q^{84} - 28q^{85} + 24q^{86} - 9q^{87} - q^{88} - 12q^{89} - 23q^{91} + 60q^{92} - 33q^{93} - 3q^{94} + 12q^{95} + 10q^{96} + 7q^{97} - 2q^{98} - 3q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.15625 −1.52470 −0.762350 0.647164i \(-0.775955\pi\)
−0.762350 + 0.647164i \(0.775955\pi\)
\(3\) 1.00000 0.577350
\(4\) 2.64943 1.32471
\(5\) −0.239094 −0.106926 −0.0534631 0.998570i \(-0.517026\pi\)
−0.0534631 + 0.998570i \(0.517026\pi\)
\(6\) −2.15625 −0.880286
\(7\) 1.00000 0.377964
\(8\) −1.40032 −0.495090
\(9\) 1.00000 0.333333
\(10\) 0.515547 0.163030
\(11\) −3.99784 −1.20539 −0.602697 0.797970i \(-0.705907\pi\)
−0.602697 + 0.797970i \(0.705907\pi\)
\(12\) 2.64943 0.764823
\(13\) −1.61682 −0.448425 −0.224213 0.974540i \(-0.571981\pi\)
−0.224213 + 0.974540i \(0.571981\pi\)
\(14\) −2.15625 −0.576283
\(15\) −0.239094 −0.0617338
\(16\) −2.27940 −0.569849
\(17\) 4.61421 1.11911 0.559555 0.828793i \(-0.310972\pi\)
0.559555 + 0.828793i \(0.310972\pi\)
\(18\) −2.15625 −0.508234
\(19\) −4.17289 −0.957328 −0.478664 0.877998i \(-0.658879\pi\)
−0.478664 + 0.877998i \(0.658879\pi\)
\(20\) −0.633462 −0.141646
\(21\) 1.00000 0.218218
\(22\) 8.62035 1.83786
\(23\) 5.22408 1.08930 0.544648 0.838665i \(-0.316663\pi\)
0.544648 + 0.838665i \(0.316663\pi\)
\(24\) −1.40032 −0.285840
\(25\) −4.94283 −0.988567
\(26\) 3.48627 0.683714
\(27\) 1.00000 0.192450
\(28\) 2.64943 0.500694
\(29\) 9.10130 1.69007 0.845035 0.534712i \(-0.179580\pi\)
0.845035 + 0.534712i \(0.179580\pi\)
\(30\) 0.515547 0.0941256
\(31\) −6.57815 −1.18147 −0.590736 0.806865i \(-0.701162\pi\)
−0.590736 + 0.806865i \(0.701162\pi\)
\(32\) 7.71560 1.36394
\(33\) −3.99784 −0.695934
\(34\) −9.94939 −1.70631
\(35\) −0.239094 −0.0404143
\(36\) 2.64943 0.441571
\(37\) −0.353708 −0.0581492 −0.0290746 0.999577i \(-0.509256\pi\)
−0.0290746 + 0.999577i \(0.509256\pi\)
\(38\) 8.99781 1.45964
\(39\) −1.61682 −0.258898
\(40\) 0.334809 0.0529380
\(41\) −7.72038 −1.20572 −0.602860 0.797847i \(-0.705972\pi\)
−0.602860 + 0.797847i \(0.705972\pi\)
\(42\) −2.15625 −0.332717
\(43\) −7.33166 −1.11807 −0.559034 0.829145i \(-0.688828\pi\)
−0.559034 + 0.829145i \(0.688828\pi\)
\(44\) −10.5920 −1.59680
\(45\) −0.239094 −0.0356420
\(46\) −11.2644 −1.66085
\(47\) 3.52396 0.514023 0.257011 0.966408i \(-0.417262\pi\)
0.257011 + 0.966408i \(0.417262\pi\)
\(48\) −2.27940 −0.329003
\(49\) 1.00000 0.142857
\(50\) 10.6580 1.50727
\(51\) 4.61421 0.646118
\(52\) −4.28365 −0.594035
\(53\) −0.655025 −0.0899745 −0.0449873 0.998988i \(-0.514325\pi\)
−0.0449873 + 0.998988i \(0.514325\pi\)
\(54\) −2.15625 −0.293429
\(55\) 0.955860 0.128888
\(56\) −1.40032 −0.187126
\(57\) −4.17289 −0.552713
\(58\) −19.6247 −2.57685
\(59\) −11.8415 −1.54163 −0.770814 0.637060i \(-0.780150\pi\)
−0.770814 + 0.637060i \(0.780150\pi\)
\(60\) −0.633462 −0.0817796
\(61\) −7.05891 −0.903801 −0.451901 0.892068i \(-0.649254\pi\)
−0.451901 + 0.892068i \(0.649254\pi\)
\(62\) 14.1842 1.80139
\(63\) 1.00000 0.125988
\(64\) −12.0780 −1.50975
\(65\) 0.386572 0.0479484
\(66\) 8.62035 1.06109
\(67\) −0.167504 −0.0204638 −0.0102319 0.999948i \(-0.503257\pi\)
−0.0102319 + 0.999948i \(0.503257\pi\)
\(68\) 12.2250 1.48250
\(69\) 5.22408 0.628905
\(70\) 0.515547 0.0616197
\(71\) 6.98566 0.829045 0.414523 0.910039i \(-0.363949\pi\)
0.414523 + 0.910039i \(0.363949\pi\)
\(72\) −1.40032 −0.165030
\(73\) −2.79662 −0.327320 −0.163660 0.986517i \(-0.552330\pi\)
−0.163660 + 0.986517i \(0.552330\pi\)
\(74\) 0.762683 0.0886601
\(75\) −4.94283 −0.570749
\(76\) −11.0558 −1.26818
\(77\) −3.99784 −0.455596
\(78\) 3.48627 0.394743
\(79\) 14.2526 1.60354 0.801770 0.597633i \(-0.203892\pi\)
0.801770 + 0.597633i \(0.203892\pi\)
\(80\) 0.544990 0.0609317
\(81\) 1.00000 0.111111
\(82\) 16.6471 1.83836
\(83\) −6.75526 −0.741486 −0.370743 0.928735i \(-0.620897\pi\)
−0.370743 + 0.928735i \(0.620897\pi\)
\(84\) 2.64943 0.289076
\(85\) −1.10323 −0.119662
\(86\) 15.8089 1.70472
\(87\) 9.10130 0.975762
\(88\) 5.59827 0.596778
\(89\) −11.9943 −1.27140 −0.635698 0.771938i \(-0.719288\pi\)
−0.635698 + 0.771938i \(0.719288\pi\)
\(90\) 0.515547 0.0543434
\(91\) −1.61682 −0.169489
\(92\) 13.8408 1.44300
\(93\) −6.57815 −0.682123
\(94\) −7.59856 −0.783731
\(95\) 0.997714 0.102363
\(96\) 7.71560 0.787471
\(97\) −1.79091 −0.181840 −0.0909199 0.995858i \(-0.528981\pi\)
−0.0909199 + 0.995858i \(0.528981\pi\)
\(98\) −2.15625 −0.217814
\(99\) −3.99784 −0.401798
\(100\) −13.0957 −1.30957
\(101\) −11.0925 −1.10375 −0.551873 0.833928i \(-0.686087\pi\)
−0.551873 + 0.833928i \(0.686087\pi\)
\(102\) −9.94939 −0.985137
\(103\) 14.5981 1.43839 0.719197 0.694806i \(-0.244510\pi\)
0.719197 + 0.694806i \(0.244510\pi\)
\(104\) 2.26407 0.222011
\(105\) −0.239094 −0.0233332
\(106\) 1.41240 0.137184
\(107\) 10.6926 1.03369 0.516845 0.856079i \(-0.327106\pi\)
0.516845 + 0.856079i \(0.327106\pi\)
\(108\) 2.64943 0.254941
\(109\) −19.1750 −1.83664 −0.918318 0.395844i \(-0.870452\pi\)
−0.918318 + 0.395844i \(0.870452\pi\)
\(110\) −2.06107 −0.196516
\(111\) −0.353708 −0.0335725
\(112\) −2.27940 −0.215383
\(113\) −13.9603 −1.31327 −0.656636 0.754208i \(-0.728021\pi\)
−0.656636 + 0.754208i \(0.728021\pi\)
\(114\) 8.99781 0.842722
\(115\) −1.24905 −0.116474
\(116\) 24.1132 2.23886
\(117\) −1.61682 −0.149475
\(118\) 25.5332 2.35052
\(119\) 4.61421 0.422984
\(120\) 0.334809 0.0305638
\(121\) 4.98272 0.452974
\(122\) 15.2208 1.37803
\(123\) −7.72038 −0.696123
\(124\) −17.4283 −1.56511
\(125\) 2.37727 0.212630
\(126\) −2.15625 −0.192094
\(127\) −1.00000 −0.0887357
\(128\) 10.6120 0.937978
\(129\) −7.33166 −0.645516
\(130\) −0.833547 −0.0731069
\(131\) −1.23738 −0.108111 −0.0540553 0.998538i \(-0.517215\pi\)
−0.0540553 + 0.998538i \(0.517215\pi\)
\(132\) −10.5920 −0.921913
\(133\) −4.17289 −0.361836
\(134\) 0.361180 0.0312012
\(135\) −0.239094 −0.0205779
\(136\) −6.46139 −0.554059
\(137\) −5.10054 −0.435769 −0.217884 0.975975i \(-0.569916\pi\)
−0.217884 + 0.975975i \(0.569916\pi\)
\(138\) −11.2644 −0.958892
\(139\) 12.5215 1.06206 0.531032 0.847352i \(-0.321805\pi\)
0.531032 + 0.847352i \(0.321805\pi\)
\(140\) −0.633462 −0.0535373
\(141\) 3.52396 0.296771
\(142\) −15.0628 −1.26405
\(143\) 6.46379 0.540529
\(144\) −2.27940 −0.189950
\(145\) −2.17607 −0.180713
\(146\) 6.03022 0.499065
\(147\) 1.00000 0.0824786
\(148\) −0.937122 −0.0770310
\(149\) 9.58767 0.785452 0.392726 0.919655i \(-0.371532\pi\)
0.392726 + 0.919655i \(0.371532\pi\)
\(150\) 10.6580 0.870222
\(151\) −17.1326 −1.39423 −0.697117 0.716957i \(-0.745534\pi\)
−0.697117 + 0.716957i \(0.745534\pi\)
\(152\) 5.84341 0.473963
\(153\) 4.61421 0.373036
\(154\) 8.62035 0.694648
\(155\) 1.57280 0.126330
\(156\) −4.28365 −0.342966
\(157\) 7.98480 0.637257 0.318628 0.947880i \(-0.396778\pi\)
0.318628 + 0.947880i \(0.396778\pi\)
\(158\) −30.7322 −2.44492
\(159\) −0.655025 −0.0519468
\(160\) −1.84476 −0.145841
\(161\) 5.22408 0.411715
\(162\) −2.15625 −0.169411
\(163\) 5.01915 0.393130 0.196565 0.980491i \(-0.437021\pi\)
0.196565 + 0.980491i \(0.437021\pi\)
\(164\) −20.4546 −1.59723
\(165\) 0.955860 0.0744136
\(166\) 14.5661 1.13055
\(167\) 7.58516 0.586958 0.293479 0.955966i \(-0.405187\pi\)
0.293479 + 0.955966i \(0.405187\pi\)
\(168\) −1.40032 −0.108037
\(169\) −10.3859 −0.798915
\(170\) 2.37884 0.182449
\(171\) −4.17289 −0.319109
\(172\) −19.4247 −1.48112
\(173\) −4.01343 −0.305135 −0.152568 0.988293i \(-0.548754\pi\)
−0.152568 + 0.988293i \(0.548754\pi\)
\(174\) −19.6247 −1.48775
\(175\) −4.94283 −0.373643
\(176\) 9.11266 0.686893
\(177\) −11.8415 −0.890059
\(178\) 25.8628 1.93850
\(179\) −24.8302 −1.85590 −0.927948 0.372711i \(-0.878428\pi\)
−0.927948 + 0.372711i \(0.878428\pi\)
\(180\) −0.633462 −0.0472155
\(181\) 7.31346 0.543606 0.271803 0.962353i \(-0.412380\pi\)
0.271803 + 0.962353i \(0.412380\pi\)
\(182\) 3.48627 0.258420
\(183\) −7.05891 −0.521810
\(184\) −7.31540 −0.539299
\(185\) 0.0845694 0.00621767
\(186\) 14.1842 1.04003
\(187\) −18.4469 −1.34897
\(188\) 9.33648 0.680933
\(189\) 1.00000 0.0727393
\(190\) −2.15132 −0.156073
\(191\) −12.4008 −0.897293 −0.448646 0.893709i \(-0.648094\pi\)
−0.448646 + 0.893709i \(0.648094\pi\)
\(192\) −12.0780 −0.871654
\(193\) 16.0448 1.15493 0.577465 0.816415i \(-0.304042\pi\)
0.577465 + 0.816415i \(0.304042\pi\)
\(194\) 3.86166 0.277251
\(195\) 0.386572 0.0276830
\(196\) 2.64943 0.189245
\(197\) 12.1872 0.868304 0.434152 0.900840i \(-0.357048\pi\)
0.434152 + 0.900840i \(0.357048\pi\)
\(198\) 8.62035 0.612622
\(199\) 13.7816 0.976950 0.488475 0.872578i \(-0.337553\pi\)
0.488475 + 0.872578i \(0.337553\pi\)
\(200\) 6.92157 0.489429
\(201\) −0.167504 −0.0118148
\(202\) 23.9183 1.68288
\(203\) 9.10130 0.638786
\(204\) 12.2250 0.855921
\(205\) 1.84590 0.128923
\(206\) −31.4772 −2.19312
\(207\) 5.22408 0.363098
\(208\) 3.68537 0.255535
\(209\) 16.6826 1.15396
\(210\) 0.515547 0.0355761
\(211\) −12.3776 −0.852111 −0.426056 0.904697i \(-0.640097\pi\)
−0.426056 + 0.904697i \(0.640097\pi\)
\(212\) −1.73544 −0.119190
\(213\) 6.98566 0.478649
\(214\) −23.0559 −1.57607
\(215\) 1.75296 0.119551
\(216\) −1.40032 −0.0952800
\(217\) −6.57815 −0.446554
\(218\) 41.3462 2.80032
\(219\) −2.79662 −0.188978
\(220\) 2.53248 0.170740
\(221\) −7.46034 −0.501837
\(222\) 0.762683 0.0511879
\(223\) −16.9298 −1.13370 −0.566852 0.823819i \(-0.691839\pi\)
−0.566852 + 0.823819i \(0.691839\pi\)
\(224\) 7.71560 0.515520
\(225\) −4.94283 −0.329522
\(226\) 30.1019 2.00235
\(227\) −14.4225 −0.957256 −0.478628 0.878018i \(-0.658866\pi\)
−0.478628 + 0.878018i \(0.658866\pi\)
\(228\) −11.0558 −0.732186
\(229\) −16.4164 −1.08483 −0.542414 0.840111i \(-0.682490\pi\)
−0.542414 + 0.840111i \(0.682490\pi\)
\(230\) 2.69326 0.177588
\(231\) −3.99784 −0.263039
\(232\) −12.7448 −0.836736
\(233\) −7.64997 −0.501167 −0.250583 0.968095i \(-0.580622\pi\)
−0.250583 + 0.968095i \(0.580622\pi\)
\(234\) 3.48627 0.227905
\(235\) −0.842559 −0.0549625
\(236\) −31.3731 −2.04221
\(237\) 14.2526 0.925804
\(238\) −9.94939 −0.644923
\(239\) 8.03695 0.519867 0.259933 0.965627i \(-0.416299\pi\)
0.259933 + 0.965627i \(0.416299\pi\)
\(240\) 0.544990 0.0351790
\(241\) −22.8036 −1.46891 −0.734456 0.678657i \(-0.762562\pi\)
−0.734456 + 0.678657i \(0.762562\pi\)
\(242\) −10.7440 −0.690650
\(243\) 1.00000 0.0641500
\(244\) −18.7021 −1.19728
\(245\) −0.239094 −0.0152752
\(246\) 16.6471 1.06138
\(247\) 6.74682 0.429290
\(248\) 9.21155 0.584934
\(249\) −6.75526 −0.428097
\(250\) −5.12600 −0.324197
\(251\) −2.22670 −0.140548 −0.0702739 0.997528i \(-0.522387\pi\)
−0.0702739 + 0.997528i \(0.522387\pi\)
\(252\) 2.64943 0.166898
\(253\) −20.8850 −1.31303
\(254\) 2.15625 0.135295
\(255\) −1.10323 −0.0690869
\(256\) 1.27383 0.0796142
\(257\) 12.7786 0.797110 0.398555 0.917144i \(-0.369512\pi\)
0.398555 + 0.917144i \(0.369512\pi\)
\(258\) 15.8089 0.984219
\(259\) −0.353708 −0.0219783
\(260\) 1.02419 0.0635178
\(261\) 9.10130 0.563356
\(262\) 2.66811 0.164836
\(263\) 1.91222 0.117912 0.0589562 0.998261i \(-0.481223\pi\)
0.0589562 + 0.998261i \(0.481223\pi\)
\(264\) 5.59827 0.344550
\(265\) 0.156612 0.00962063
\(266\) 8.99781 0.551691
\(267\) −11.9943 −0.734041
\(268\) −0.443788 −0.0271087
\(269\) 7.78586 0.474712 0.237356 0.971423i \(-0.423719\pi\)
0.237356 + 0.971423i \(0.423719\pi\)
\(270\) 0.515547 0.0313752
\(271\) −10.3228 −0.627064 −0.313532 0.949578i \(-0.601512\pi\)
−0.313532 + 0.949578i \(0.601512\pi\)
\(272\) −10.5176 −0.637723
\(273\) −1.61682 −0.0978544
\(274\) 10.9981 0.664417
\(275\) 19.7607 1.19161
\(276\) 13.8408 0.833118
\(277\) −13.1278 −0.788776 −0.394388 0.918944i \(-0.629043\pi\)
−0.394388 + 0.918944i \(0.629043\pi\)
\(278\) −26.9996 −1.61933
\(279\) −6.57815 −0.393824
\(280\) 0.334809 0.0200087
\(281\) 18.1404 1.08216 0.541081 0.840970i \(-0.318015\pi\)
0.541081 + 0.840970i \(0.318015\pi\)
\(282\) −7.59856 −0.452487
\(283\) −19.1287 −1.13708 −0.568542 0.822655i \(-0.692492\pi\)
−0.568542 + 0.822655i \(0.692492\pi\)
\(284\) 18.5080 1.09825
\(285\) 0.997714 0.0590995
\(286\) −13.9376 −0.824145
\(287\) −7.72038 −0.455720
\(288\) 7.71560 0.454646
\(289\) 4.29089 0.252406
\(290\) 4.69215 0.275533
\(291\) −1.79091 −0.104985
\(292\) −7.40944 −0.433604
\(293\) −26.6893 −1.55921 −0.779603 0.626274i \(-0.784579\pi\)
−0.779603 + 0.626274i \(0.784579\pi\)
\(294\) −2.15625 −0.125755
\(295\) 2.83122 0.164840
\(296\) 0.495306 0.0287891
\(297\) −3.99784 −0.231978
\(298\) −20.6734 −1.19758
\(299\) −8.44639 −0.488468
\(300\) −13.0957 −0.756079
\(301\) −7.33166 −0.422590
\(302\) 36.9423 2.12579
\(303\) −11.0925 −0.637249
\(304\) 9.51168 0.545532
\(305\) 1.68774 0.0966400
\(306\) −9.94939 −0.568769
\(307\) 9.45867 0.539835 0.269917 0.962883i \(-0.413004\pi\)
0.269917 + 0.962883i \(0.413004\pi\)
\(308\) −10.5920 −0.603534
\(309\) 14.5981 0.830458
\(310\) −3.39135 −0.192616
\(311\) 1.98631 0.112633 0.0563167 0.998413i \(-0.482064\pi\)
0.0563167 + 0.998413i \(0.482064\pi\)
\(312\) 2.26407 0.128178
\(313\) −20.0441 −1.13296 −0.566480 0.824075i \(-0.691695\pi\)
−0.566480 + 0.824075i \(0.691695\pi\)
\(314\) −17.2173 −0.971626
\(315\) −0.239094 −0.0134714
\(316\) 37.7611 2.12423
\(317\) −27.2490 −1.53046 −0.765228 0.643760i \(-0.777374\pi\)
−0.765228 + 0.643760i \(0.777374\pi\)
\(318\) 1.41240 0.0792034
\(319\) −36.3855 −2.03720
\(320\) 2.88778 0.161432
\(321\) 10.6926 0.596801
\(322\) −11.2644 −0.627742
\(323\) −19.2546 −1.07135
\(324\) 2.64943 0.147190
\(325\) 7.99168 0.443298
\(326\) −10.8226 −0.599406
\(327\) −19.1750 −1.06038
\(328\) 10.8110 0.596940
\(329\) 3.52396 0.194282
\(330\) −2.06107 −0.113458
\(331\) 34.0423 1.87113 0.935567 0.353150i \(-0.114889\pi\)
0.935567 + 0.353150i \(0.114889\pi\)
\(332\) −17.8976 −0.982256
\(333\) −0.353708 −0.0193831
\(334\) −16.3555 −0.894935
\(335\) 0.0400491 0.00218812
\(336\) −2.27940 −0.124351
\(337\) −13.1131 −0.714318 −0.357159 0.934044i \(-0.616255\pi\)
−0.357159 + 0.934044i \(0.616255\pi\)
\(338\) 22.3946 1.21811
\(339\) −13.9603 −0.758218
\(340\) −2.92292 −0.158518
\(341\) 26.2984 1.42414
\(342\) 8.99781 0.486546
\(343\) 1.00000 0.0539949
\(344\) 10.2667 0.553543
\(345\) −1.24905 −0.0672464
\(346\) 8.65396 0.465240
\(347\) −8.22380 −0.441477 −0.220738 0.975333i \(-0.570847\pi\)
−0.220738 + 0.975333i \(0.570847\pi\)
\(348\) 24.1132 1.29260
\(349\) −22.6433 −1.21207 −0.606035 0.795438i \(-0.707241\pi\)
−0.606035 + 0.795438i \(0.707241\pi\)
\(350\) 10.6580 0.569694
\(351\) −1.61682 −0.0862995
\(352\) −30.8457 −1.64408
\(353\) −22.9217 −1.22000 −0.610000 0.792401i \(-0.708831\pi\)
−0.610000 + 0.792401i \(0.708831\pi\)
\(354\) 25.5332 1.35707
\(355\) −1.67023 −0.0886466
\(356\) −31.7781 −1.68423
\(357\) 4.61421 0.244210
\(358\) 53.5402 2.82969
\(359\) 22.9728 1.21246 0.606230 0.795289i \(-0.292681\pi\)
0.606230 + 0.795289i \(0.292681\pi\)
\(360\) 0.334809 0.0176460
\(361\) −1.58696 −0.0835240
\(362\) −15.7697 −0.828836
\(363\) 4.98272 0.261525
\(364\) −4.28365 −0.224524
\(365\) 0.668655 0.0349990
\(366\) 15.2208 0.795604
\(367\) −2.80411 −0.146373 −0.0731866 0.997318i \(-0.523317\pi\)
−0.0731866 + 0.997318i \(0.523317\pi\)
\(368\) −11.9077 −0.620734
\(369\) −7.72038 −0.401907
\(370\) −0.182353 −0.00948008
\(371\) −0.655025 −0.0340072
\(372\) −17.4283 −0.903617
\(373\) −35.2417 −1.82475 −0.912374 0.409358i \(-0.865753\pi\)
−0.912374 + 0.409358i \(0.865753\pi\)
\(374\) 39.7761 2.05677
\(375\) 2.37727 0.122762
\(376\) −4.93469 −0.254487
\(377\) −14.7152 −0.757870
\(378\) −2.15625 −0.110906
\(379\) −8.26039 −0.424308 −0.212154 0.977236i \(-0.568048\pi\)
−0.212154 + 0.977236i \(0.568048\pi\)
\(380\) 2.64337 0.135602
\(381\) −1.00000 −0.0512316
\(382\) 26.7393 1.36810
\(383\) −6.69505 −0.342101 −0.171050 0.985262i \(-0.554716\pi\)
−0.171050 + 0.985262i \(0.554716\pi\)
\(384\) 10.6120 0.541542
\(385\) 0.955860 0.0487151
\(386\) −34.5966 −1.76092
\(387\) −7.33166 −0.372689
\(388\) −4.74489 −0.240885
\(389\) −13.4050 −0.679658 −0.339829 0.940487i \(-0.610369\pi\)
−0.339829 + 0.940487i \(0.610369\pi\)
\(390\) −0.833547 −0.0422083
\(391\) 24.1050 1.21904
\(392\) −1.40032 −0.0707271
\(393\) −1.23738 −0.0624176
\(394\) −26.2787 −1.32390
\(395\) −3.40771 −0.171460
\(396\) −10.5920 −0.532267
\(397\) 1.27937 0.0642097 0.0321048 0.999485i \(-0.489779\pi\)
0.0321048 + 0.999485i \(0.489779\pi\)
\(398\) −29.7165 −1.48956
\(399\) −4.17289 −0.208906
\(400\) 11.2667 0.563334
\(401\) −25.8637 −1.29157 −0.645785 0.763519i \(-0.723470\pi\)
−0.645785 + 0.763519i \(0.723470\pi\)
\(402\) 0.361180 0.0180140
\(403\) 10.6357 0.529802
\(404\) −29.3888 −1.46215
\(405\) −0.239094 −0.0118807
\(406\) −19.6247 −0.973958
\(407\) 1.41407 0.0700927
\(408\) −6.46139 −0.319886
\(409\) −8.40634 −0.415667 −0.207833 0.978164i \(-0.566641\pi\)
−0.207833 + 0.978164i \(0.566641\pi\)
\(410\) −3.98022 −0.196569
\(411\) −5.10054 −0.251591
\(412\) 38.6766 1.90546
\(413\) −11.8415 −0.582681
\(414\) −11.2644 −0.553616
\(415\) 1.61514 0.0792843
\(416\) −12.4747 −0.611625
\(417\) 12.5215 0.613183
\(418\) −35.9718 −1.75944
\(419\) 12.0193 0.587183 0.293592 0.955931i \(-0.405149\pi\)
0.293592 + 0.955931i \(0.405149\pi\)
\(420\) −0.633462 −0.0309098
\(421\) 27.5197 1.34123 0.670614 0.741807i \(-0.266031\pi\)
0.670614 + 0.741807i \(0.266031\pi\)
\(422\) 26.6893 1.29922
\(423\) 3.52396 0.171341
\(424\) 0.917247 0.0445455
\(425\) −22.8073 −1.10631
\(426\) −15.0628 −0.729797
\(427\) −7.05891 −0.341605
\(428\) 28.3292 1.36934
\(429\) 6.46379 0.312075
\(430\) −3.77981 −0.182279
\(431\) 35.4733 1.70869 0.854345 0.519707i \(-0.173959\pi\)
0.854345 + 0.519707i \(0.173959\pi\)
\(432\) −2.27940 −0.109668
\(433\) 26.5237 1.27465 0.637323 0.770597i \(-0.280042\pi\)
0.637323 + 0.770597i \(0.280042\pi\)
\(434\) 14.1842 0.680862
\(435\) −2.17607 −0.104334
\(436\) −50.8028 −2.43301
\(437\) −21.7995 −1.04281
\(438\) 6.03022 0.288135
\(439\) −32.6301 −1.55735 −0.778674 0.627428i \(-0.784108\pi\)
−0.778674 + 0.627428i \(0.784108\pi\)
\(440\) −1.33851 −0.0638111
\(441\) 1.00000 0.0476190
\(442\) 16.0864 0.765151
\(443\) 16.0947 0.764681 0.382340 0.924022i \(-0.375118\pi\)
0.382340 + 0.924022i \(0.375118\pi\)
\(444\) −0.937122 −0.0444739
\(445\) 2.86777 0.135945
\(446\) 36.5050 1.72856
\(447\) 9.58767 0.453481
\(448\) −12.0780 −0.570632
\(449\) 33.1478 1.56434 0.782171 0.623064i \(-0.214112\pi\)
0.782171 + 0.623064i \(0.214112\pi\)
\(450\) 10.6580 0.502423
\(451\) 30.8648 1.45337
\(452\) −36.9867 −1.73971
\(453\) −17.1326 −0.804962
\(454\) 31.0986 1.45953
\(455\) 0.386572 0.0181228
\(456\) 5.84341 0.273643
\(457\) −20.7795 −0.972026 −0.486013 0.873952i \(-0.661549\pi\)
−0.486013 + 0.873952i \(0.661549\pi\)
\(458\) 35.3980 1.65404
\(459\) 4.61421 0.215373
\(460\) −3.30925 −0.154295
\(461\) 26.0027 1.21106 0.605532 0.795821i \(-0.292960\pi\)
0.605532 + 0.795821i \(0.292960\pi\)
\(462\) 8.62035 0.401055
\(463\) 1.40695 0.0653867 0.0326934 0.999465i \(-0.489592\pi\)
0.0326934 + 0.999465i \(0.489592\pi\)
\(464\) −20.7455 −0.963084
\(465\) 1.57280 0.0729367
\(466\) 16.4953 0.764129
\(467\) −4.52880 −0.209568 −0.104784 0.994495i \(-0.533415\pi\)
−0.104784 + 0.994495i \(0.533415\pi\)
\(468\) −4.28365 −0.198012
\(469\) −0.167504 −0.00773460
\(470\) 1.81677 0.0838013
\(471\) 7.98480 0.367920
\(472\) 16.5819 0.763244
\(473\) 29.3108 1.34771
\(474\) −30.7322 −1.41157
\(475\) 20.6259 0.946382
\(476\) 12.2250 0.560332
\(477\) −0.655025 −0.0299915
\(478\) −17.3297 −0.792641
\(479\) 1.74794 0.0798653 0.0399327 0.999202i \(-0.487286\pi\)
0.0399327 + 0.999202i \(0.487286\pi\)
\(480\) −1.84476 −0.0842012
\(481\) 0.571882 0.0260756
\(482\) 49.1704 2.23965
\(483\) 5.22408 0.237704
\(484\) 13.2013 0.600061
\(485\) 0.428197 0.0194434
\(486\) −2.15625 −0.0978096
\(487\) −25.2382 −1.14365 −0.571827 0.820375i \(-0.693765\pi\)
−0.571827 + 0.820375i \(0.693765\pi\)
\(488\) 9.88477 0.447463
\(489\) 5.01915 0.226974
\(490\) 0.515547 0.0232900
\(491\) −27.1705 −1.22619 −0.613093 0.790010i \(-0.710075\pi\)
−0.613093 + 0.790010i \(0.710075\pi\)
\(492\) −20.4546 −0.922163
\(493\) 41.9953 1.89137
\(494\) −14.5478 −0.654539
\(495\) 0.955860 0.0429627
\(496\) 14.9942 0.673260
\(497\) 6.98566 0.313350
\(498\) 14.5661 0.652720
\(499\) −18.9409 −0.847909 −0.423955 0.905683i \(-0.639358\pi\)
−0.423955 + 0.905683i \(0.639358\pi\)
\(500\) 6.29841 0.281673
\(501\) 7.58516 0.338880
\(502\) 4.80132 0.214293
\(503\) −2.52810 −0.112722 −0.0563611 0.998410i \(-0.517950\pi\)
−0.0563611 + 0.998410i \(0.517950\pi\)
\(504\) −1.40032 −0.0623754
\(505\) 2.65216 0.118019
\(506\) 45.0334 2.00198
\(507\) −10.3859 −0.461254
\(508\) −2.64943 −0.117549
\(509\) 34.9093 1.54733 0.773663 0.633598i \(-0.218422\pi\)
0.773663 + 0.633598i \(0.218422\pi\)
\(510\) 2.37884 0.105337
\(511\) −2.79662 −0.123715
\(512\) −23.9707 −1.05937
\(513\) −4.17289 −0.184238
\(514\) −27.5540 −1.21535
\(515\) −3.49032 −0.153802
\(516\) −19.4247 −0.855124
\(517\) −14.0882 −0.619600
\(518\) 0.762683 0.0335104
\(519\) −4.01343 −0.176170
\(520\) −0.541327 −0.0237387
\(521\) 8.56576 0.375273 0.187636 0.982239i \(-0.439917\pi\)
0.187636 + 0.982239i \(0.439917\pi\)
\(522\) −19.6247 −0.858950
\(523\) 2.00260 0.0875675 0.0437838 0.999041i \(-0.486059\pi\)
0.0437838 + 0.999041i \(0.486059\pi\)
\(524\) −3.27835 −0.143215
\(525\) −4.94283 −0.215723
\(526\) −4.12322 −0.179781
\(527\) −30.3530 −1.32220
\(528\) 9.11266 0.396578
\(529\) 4.29098 0.186564
\(530\) −0.337696 −0.0146686
\(531\) −11.8415 −0.513876
\(532\) −11.0558 −0.479328
\(533\) 12.4825 0.540676
\(534\) 25.8628 1.11919
\(535\) −2.55653 −0.110528
\(536\) 0.234559 0.0101314
\(537\) −24.8302 −1.07150
\(538\) −16.7883 −0.723794
\(539\) −3.99784 −0.172199
\(540\) −0.633462 −0.0272599
\(541\) −14.8542 −0.638632 −0.319316 0.947648i \(-0.603453\pi\)
−0.319316 + 0.947648i \(0.603453\pi\)
\(542\) 22.2585 0.956085
\(543\) 7.31346 0.313851
\(544\) 35.6014 1.52640
\(545\) 4.58464 0.196384
\(546\) 3.48627 0.149199
\(547\) 9.86356 0.421735 0.210868 0.977515i \(-0.432371\pi\)
0.210868 + 0.977515i \(0.432371\pi\)
\(548\) −13.5135 −0.577268
\(549\) −7.05891 −0.301267
\(550\) −42.6090 −1.81685
\(551\) −37.9788 −1.61795
\(552\) −7.31540 −0.311364
\(553\) 14.2526 0.606081
\(554\) 28.3069 1.20265
\(555\) 0.0845694 0.00358977
\(556\) 33.1749 1.40693
\(557\) −1.50087 −0.0635939 −0.0317970 0.999494i \(-0.510123\pi\)
−0.0317970 + 0.999494i \(0.510123\pi\)
\(558\) 14.1842 0.600463
\(559\) 11.8540 0.501370
\(560\) 0.544990 0.0230300
\(561\) −18.4469 −0.778827
\(562\) −39.1152 −1.64997
\(563\) 40.5430 1.70868 0.854341 0.519713i \(-0.173961\pi\)
0.854341 + 0.519713i \(0.173961\pi\)
\(564\) 9.33648 0.393137
\(565\) 3.33782 0.140423
\(566\) 41.2463 1.73371
\(567\) 1.00000 0.0419961
\(568\) −9.78219 −0.410452
\(569\) 3.51593 0.147396 0.0736978 0.997281i \(-0.476520\pi\)
0.0736978 + 0.997281i \(0.476520\pi\)
\(570\) −2.15132 −0.0901090
\(571\) −39.7252 −1.66245 −0.831224 0.555937i \(-0.812359\pi\)
−0.831224 + 0.555937i \(0.812359\pi\)
\(572\) 17.1253 0.716046
\(573\) −12.4008 −0.518052
\(574\) 16.6471 0.694836
\(575\) −25.8217 −1.07684
\(576\) −12.0780 −0.503250
\(577\) 34.1969 1.42364 0.711818 0.702364i \(-0.247872\pi\)
0.711818 + 0.702364i \(0.247872\pi\)
\(578\) −9.25225 −0.384843
\(579\) 16.0448 0.666799
\(580\) −5.76533 −0.239392
\(581\) −6.75526 −0.280256
\(582\) 3.86166 0.160071
\(583\) 2.61868 0.108455
\(584\) 3.91618 0.162053
\(585\) 0.386572 0.0159828
\(586\) 57.5489 2.37732
\(587\) −14.5520 −0.600625 −0.300313 0.953841i \(-0.597091\pi\)
−0.300313 + 0.953841i \(0.597091\pi\)
\(588\) 2.64943 0.109260
\(589\) 27.4499 1.13105
\(590\) −6.10483 −0.251332
\(591\) 12.1872 0.501315
\(592\) 0.806240 0.0331363
\(593\) −22.6700 −0.930947 −0.465473 0.885062i \(-0.654116\pi\)
−0.465473 + 0.885062i \(0.654116\pi\)
\(594\) 8.62035 0.353697
\(595\) −1.10323 −0.0452280
\(596\) 25.4018 1.04050
\(597\) 13.7816 0.564042
\(598\) 18.2126 0.744767
\(599\) 19.5665 0.799466 0.399733 0.916632i \(-0.369103\pi\)
0.399733 + 0.916632i \(0.369103\pi\)
\(600\) 6.92157 0.282572
\(601\) 7.31719 0.298475 0.149237 0.988801i \(-0.452318\pi\)
0.149237 + 0.988801i \(0.452318\pi\)
\(602\) 15.8089 0.644323
\(603\) −0.167504 −0.00682127
\(604\) −45.3917 −1.84696
\(605\) −1.19134 −0.0484348
\(606\) 23.9183 0.971613
\(607\) 25.1482 1.02074 0.510368 0.859956i \(-0.329509\pi\)
0.510368 + 0.859956i \(0.329509\pi\)
\(608\) −32.1964 −1.30574
\(609\) 9.10130 0.368803
\(610\) −3.63920 −0.147347
\(611\) −5.69762 −0.230501
\(612\) 12.2250 0.494166
\(613\) 40.8861 1.65137 0.825686 0.564129i \(-0.190788\pi\)
0.825686 + 0.564129i \(0.190788\pi\)
\(614\) −20.3953 −0.823087
\(615\) 1.84590 0.0744338
\(616\) 5.59827 0.225561
\(617\) 23.3040 0.938185 0.469092 0.883149i \(-0.344581\pi\)
0.469092 + 0.883149i \(0.344581\pi\)
\(618\) −31.4772 −1.26620
\(619\) 36.2218 1.45588 0.727939 0.685642i \(-0.240478\pi\)
0.727939 + 0.685642i \(0.240478\pi\)
\(620\) 4.16701 0.167351
\(621\) 5.22408 0.209635
\(622\) −4.28299 −0.171732
\(623\) −11.9943 −0.480543
\(624\) 3.68537 0.147533
\(625\) 24.1458 0.965831
\(626\) 43.2202 1.72743
\(627\) 16.6826 0.666237
\(628\) 21.1551 0.844182
\(629\) −1.63208 −0.0650753
\(630\) 0.515547 0.0205399
\(631\) 44.1474 1.75748 0.878741 0.477299i \(-0.158384\pi\)
0.878741 + 0.477299i \(0.158384\pi\)
\(632\) −19.9582 −0.793896
\(633\) −12.3776 −0.491967
\(634\) 58.7557 2.33349
\(635\) 0.239094 0.00948816
\(636\) −1.73544 −0.0688146
\(637\) −1.61682 −0.0640608
\(638\) 78.4564 3.10612
\(639\) 6.98566 0.276348
\(640\) −2.53727 −0.100294
\(641\) 20.5976 0.813557 0.406779 0.913527i \(-0.366652\pi\)
0.406779 + 0.913527i \(0.366652\pi\)
\(642\) −23.0559 −0.909943
\(643\) −3.13591 −0.123668 −0.0618342 0.998086i \(-0.519695\pi\)
−0.0618342 + 0.998086i \(0.519695\pi\)
\(644\) 13.8408 0.545404
\(645\) 1.75296 0.0690226
\(646\) 41.5178 1.63349
\(647\) 6.98764 0.274712 0.137356 0.990522i \(-0.456139\pi\)
0.137356 + 0.990522i \(0.456139\pi\)
\(648\) −1.40032 −0.0550100
\(649\) 47.3403 1.85827
\(650\) −17.2321 −0.675897
\(651\) −6.57815 −0.257818
\(652\) 13.2979 0.520784
\(653\) 18.7511 0.733786 0.366893 0.930263i \(-0.380422\pi\)
0.366893 + 0.930263i \(0.380422\pi\)
\(654\) 41.3462 1.61677
\(655\) 0.295851 0.0115598
\(656\) 17.5978 0.687079
\(657\) −2.79662 −0.109107
\(658\) −7.59856 −0.296223
\(659\) 28.0273 1.09179 0.545895 0.837854i \(-0.316190\pi\)
0.545895 + 0.837854i \(0.316190\pi\)
\(660\) 2.53248 0.0985766
\(661\) −46.8900 −1.82381 −0.911905 0.410401i \(-0.865389\pi\)
−0.911905 + 0.410401i \(0.865389\pi\)
\(662\) −73.4038 −2.85292
\(663\) −7.46034 −0.289736
\(664\) 9.45956 0.367102
\(665\) 0.997714 0.0386897
\(666\) 0.762683 0.0295534
\(667\) 47.5459 1.84098
\(668\) 20.0963 0.777550
\(669\) −16.9298 −0.654545
\(670\) −0.0863560 −0.00333622
\(671\) 28.2204 1.08944
\(672\) 7.71560 0.297636
\(673\) 30.2264 1.16514 0.582571 0.812780i \(-0.302047\pi\)
0.582571 + 0.812780i \(0.302047\pi\)
\(674\) 28.2752 1.08912
\(675\) −4.94283 −0.190250
\(676\) −27.5166 −1.05833
\(677\) −4.66520 −0.179298 −0.0896491 0.995973i \(-0.528575\pi\)
−0.0896491 + 0.995973i \(0.528575\pi\)
\(678\) 30.1019 1.15606
\(679\) −1.79091 −0.0687290
\(680\) 1.54488 0.0592434
\(681\) −14.4225 −0.552672
\(682\) −56.7060 −2.17138
\(683\) −34.8003 −1.33160 −0.665798 0.746132i \(-0.731909\pi\)
−0.665798 + 0.746132i \(0.731909\pi\)
\(684\) −11.0558 −0.422728
\(685\) 1.21951 0.0465951
\(686\) −2.15625 −0.0823261
\(687\) −16.4164 −0.626326
\(688\) 16.7118 0.637130
\(689\) 1.05906 0.0403469
\(690\) 2.69326 0.102531
\(691\) 36.6726 1.39509 0.697546 0.716540i \(-0.254275\pi\)
0.697546 + 0.716540i \(0.254275\pi\)
\(692\) −10.6333 −0.404216
\(693\) −3.99784 −0.151865
\(694\) 17.7326 0.673120
\(695\) −2.99383 −0.113562
\(696\) −12.7448 −0.483090
\(697\) −35.6234 −1.34933
\(698\) 48.8247 1.84804
\(699\) −7.64997 −0.289349
\(700\) −13.0957 −0.494970
\(701\) −11.0457 −0.417192 −0.208596 0.978002i \(-0.566889\pi\)
−0.208596 + 0.978002i \(0.566889\pi\)
\(702\) 3.48627 0.131581
\(703\) 1.47598 0.0556678
\(704\) 48.2859 1.81984
\(705\) −0.842559 −0.0317326
\(706\) 49.4250 1.86014
\(707\) −11.0925 −0.417177
\(708\) −31.3731 −1.17907
\(709\) −7.73369 −0.290445 −0.145222 0.989399i \(-0.546390\pi\)
−0.145222 + 0.989399i \(0.546390\pi\)
\(710\) 3.60144 0.135160
\(711\) 14.2526 0.534513
\(712\) 16.7960 0.629455
\(713\) −34.3648 −1.28697
\(714\) −9.94939 −0.372347
\(715\) −1.54545 −0.0577967
\(716\) −65.7857 −2.45853
\(717\) 8.03695 0.300145
\(718\) −49.5353 −1.84864
\(719\) −50.9775 −1.90114 −0.950571 0.310509i \(-0.899501\pi\)
−0.950571 + 0.310509i \(0.899501\pi\)
\(720\) 0.544990 0.0203106
\(721\) 14.5981 0.543662
\(722\) 3.42188 0.127349
\(723\) −22.8036 −0.848076
\(724\) 19.3765 0.720121
\(725\) −44.9862 −1.67075
\(726\) −10.7440 −0.398747
\(727\) −6.89848 −0.255850 −0.127925 0.991784i \(-0.540832\pi\)
−0.127925 + 0.991784i \(0.540832\pi\)
\(728\) 2.26407 0.0839122
\(729\) 1.00000 0.0370370
\(730\) −1.44179 −0.0533630
\(731\) −33.8298 −1.25124
\(732\) −18.7021 −0.691248
\(733\) 6.77021 0.250063 0.125032 0.992153i \(-0.460097\pi\)
0.125032 + 0.992153i \(0.460097\pi\)
\(734\) 6.04636 0.223175
\(735\) −0.239094 −0.00881912
\(736\) 40.3069 1.48573
\(737\) 0.669652 0.0246670
\(738\) 16.6471 0.612788
\(739\) 10.2163 0.375814 0.187907 0.982187i \(-0.439830\pi\)
0.187907 + 0.982187i \(0.439830\pi\)
\(740\) 0.224060 0.00823662
\(741\) 6.74682 0.247851
\(742\) 1.41240 0.0518508
\(743\) 3.12087 0.114493 0.0572467 0.998360i \(-0.481768\pi\)
0.0572467 + 0.998360i \(0.481768\pi\)
\(744\) 9.21155 0.337712
\(745\) −2.29235 −0.0839854
\(746\) 75.9901 2.78219
\(747\) −6.75526 −0.247162
\(748\) −48.8736 −1.78699
\(749\) 10.6926 0.390698
\(750\) −5.12600 −0.187175
\(751\) 17.9651 0.655557 0.327778 0.944755i \(-0.393700\pi\)
0.327778 + 0.944755i \(0.393700\pi\)
\(752\) −8.03251 −0.292916
\(753\) −2.22670 −0.0811454
\(754\) 31.7296 1.15552
\(755\) 4.09631 0.149080
\(756\) 2.64943 0.0963587
\(757\) −41.8801 −1.52216 −0.761080 0.648658i \(-0.775330\pi\)
−0.761080 + 0.648658i \(0.775330\pi\)
\(758\) 17.8115 0.646942
\(759\) −20.8850 −0.758078
\(760\) −1.39712 −0.0506790
\(761\) 47.4903 1.72152 0.860761 0.509010i \(-0.169988\pi\)
0.860761 + 0.509010i \(0.169988\pi\)
\(762\) 2.15625 0.0781128
\(763\) −19.1750 −0.694183
\(764\) −32.8551 −1.18866
\(765\) −1.10323 −0.0398873
\(766\) 14.4362 0.521602
\(767\) 19.1455 0.691305
\(768\) 1.27383 0.0459653
\(769\) 44.5562 1.60674 0.803369 0.595481i \(-0.203039\pi\)
0.803369 + 0.595481i \(0.203039\pi\)
\(770\) −2.06107 −0.0742760
\(771\) 12.7786 0.460212
\(772\) 42.5095 1.52995
\(773\) 28.7248 1.03316 0.516580 0.856239i \(-0.327205\pi\)
0.516580 + 0.856239i \(0.327205\pi\)
\(774\) 15.8089 0.568239
\(775\) 32.5147 1.16796
\(776\) 2.50786 0.0900270
\(777\) −0.353708 −0.0126892
\(778\) 28.9045 1.03628
\(779\) 32.2163 1.15427
\(780\) 1.02419 0.0366720
\(781\) −27.9275 −0.999326
\(782\) −51.9764 −1.85867
\(783\) 9.10130 0.325254
\(784\) −2.27940 −0.0814070
\(785\) −1.90912 −0.0681394
\(786\) 2.66811 0.0951682
\(787\) −6.88490 −0.245420 −0.122710 0.992443i \(-0.539159\pi\)
−0.122710 + 0.992443i \(0.539159\pi\)
\(788\) 32.2891 1.15025
\(789\) 1.91222 0.0680767
\(790\) 7.34788 0.261426
\(791\) −13.9603 −0.496370
\(792\) 5.59827 0.198926
\(793\) 11.4130 0.405287
\(794\) −2.75864 −0.0979006
\(795\) 0.156612 0.00555447
\(796\) 36.5132 1.29418
\(797\) 19.8500 0.703123 0.351562 0.936165i \(-0.385651\pi\)
0.351562 + 0.936165i \(0.385651\pi\)
\(798\) 8.99781 0.318519
\(799\) 16.2603 0.575248
\(800\) −38.1370 −1.34834
\(801\) −11.9943 −0.423799
\(802\) 55.7686 1.96926
\(803\) 11.1804 0.394549
\(804\) −0.443788 −0.0156512
\(805\) −1.24905 −0.0440231
\(806\) −22.9332 −0.807789
\(807\) 7.78586 0.274075
\(808\) 15.5331 0.546454
\(809\) −18.8305 −0.662046 −0.331023 0.943623i \(-0.607394\pi\)
−0.331023 + 0.943623i \(0.607394\pi\)
\(810\) 0.515547 0.0181145
\(811\) −47.7100 −1.67533 −0.837663 0.546188i \(-0.816078\pi\)
−0.837663 + 0.546188i \(0.816078\pi\)
\(812\) 24.1132 0.846208
\(813\) −10.3228 −0.362036
\(814\) −3.04908 −0.106870
\(815\) −1.20005 −0.0420359
\(816\) −10.5176 −0.368190
\(817\) 30.5942 1.07036
\(818\) 18.1262 0.633768
\(819\) −1.61682 −0.0564963
\(820\) 4.89057 0.170786
\(821\) 25.1137 0.876475 0.438238 0.898859i \(-0.355603\pi\)
0.438238 + 0.898859i \(0.355603\pi\)
\(822\) 10.9981 0.383601
\(823\) 43.0088 1.49919 0.749597 0.661895i \(-0.230247\pi\)
0.749597 + 0.661895i \(0.230247\pi\)
\(824\) −20.4421 −0.712134
\(825\) 19.7607 0.687978
\(826\) 25.5332 0.888413
\(827\) 13.8440 0.481403 0.240701 0.970599i \(-0.422623\pi\)
0.240701 + 0.970599i \(0.422623\pi\)
\(828\) 13.8408 0.481001
\(829\) 12.5853 0.437105 0.218553 0.975825i \(-0.429867\pi\)
0.218553 + 0.975825i \(0.429867\pi\)
\(830\) −3.48266 −0.120885
\(831\) −13.1278 −0.455400
\(832\) 19.5280 0.677010
\(833\) 4.61421 0.159873
\(834\) −26.9996 −0.934920
\(835\) −1.81357 −0.0627611
\(836\) 44.1992 1.52866
\(837\) −6.57815 −0.227374
\(838\) −25.9167 −0.895279
\(839\) −4.46813 −0.154257 −0.0771284 0.997021i \(-0.524575\pi\)
−0.0771284 + 0.997021i \(0.524575\pi\)
\(840\) 0.334809 0.0115520
\(841\) 53.8337 1.85633
\(842\) −59.3394 −2.04497
\(843\) 18.1404 0.624787
\(844\) −32.7936 −1.12880
\(845\) 2.48320 0.0854248
\(846\) −7.59856 −0.261244
\(847\) 4.98272 0.171208
\(848\) 1.49306 0.0512719
\(849\) −19.1287 −0.656495
\(850\) 49.1782 1.68680
\(851\) −1.84780 −0.0633416
\(852\) 18.5080 0.634073
\(853\) −20.9580 −0.717589 −0.358795 0.933416i \(-0.616812\pi\)
−0.358795 + 0.933416i \(0.616812\pi\)
\(854\) 15.2208 0.520845
\(855\) 0.997714 0.0341211
\(856\) −14.9731 −0.511769
\(857\) −3.36198 −0.114843 −0.0574216 0.998350i \(-0.518288\pi\)
−0.0574216 + 0.998350i \(0.518288\pi\)
\(858\) −13.9376 −0.475820
\(859\) 31.0025 1.05779 0.528895 0.848687i \(-0.322607\pi\)
0.528895 + 0.848687i \(0.322607\pi\)
\(860\) 4.64432 0.158370
\(861\) −7.72038 −0.263110
\(862\) −76.4894 −2.60524
\(863\) 8.87723 0.302185 0.151092 0.988520i \(-0.451721\pi\)
0.151092 + 0.988520i \(0.451721\pi\)
\(864\) 7.71560 0.262490
\(865\) 0.959586 0.0326269
\(866\) −57.1917 −1.94345
\(867\) 4.29089 0.145726
\(868\) −17.4283 −0.591556
\(869\) −56.9795 −1.93290
\(870\) 4.69215 0.159079
\(871\) 0.270823 0.00917650
\(872\) 26.8513 0.909299
\(873\) −1.79091 −0.0606133
\(874\) 47.0053 1.58998
\(875\) 2.37727 0.0803665
\(876\) −7.40944 −0.250342
\(877\) −19.3103 −0.652061 −0.326030 0.945359i \(-0.605711\pi\)
−0.326030 + 0.945359i \(0.605711\pi\)
\(878\) 70.3587 2.37449
\(879\) −26.6893 −0.900208
\(880\) −2.17878 −0.0734468
\(881\) 3.30078 0.111206 0.0556030 0.998453i \(-0.482292\pi\)
0.0556030 + 0.998453i \(0.482292\pi\)
\(882\) −2.15625 −0.0726048
\(883\) 51.9315 1.74764 0.873818 0.486253i \(-0.161637\pi\)
0.873818 + 0.486253i \(0.161637\pi\)
\(884\) −19.7656 −0.664790
\(885\) 2.83122 0.0951706
\(886\) −34.7042 −1.16591
\(887\) 9.29948 0.312246 0.156123 0.987738i \(-0.450100\pi\)
0.156123 + 0.987738i \(0.450100\pi\)
\(888\) 0.495306 0.0166214
\(889\) −1.00000 −0.0335389
\(890\) −6.18364 −0.207276
\(891\) −3.99784 −0.133933
\(892\) −44.8543 −1.50183
\(893\) −14.7051 −0.492088
\(894\) −20.6734 −0.691423
\(895\) 5.93675 0.198444
\(896\) 10.6120 0.354522
\(897\) −8.44639 −0.282017
\(898\) −71.4750 −2.38515
\(899\) −59.8698 −1.99677
\(900\) −13.0957 −0.436522
\(901\) −3.02242 −0.100691
\(902\) −66.5524 −2.21595
\(903\) −7.33166 −0.243982
\(904\) 19.5489 0.650187
\(905\) −1.74861 −0.0581256
\(906\) 36.9423 1.22733
\(907\) −31.2600 −1.03797 −0.518985 0.854783i \(-0.673690\pi\)
−0.518985 + 0.854783i \(0.673690\pi\)
\(908\) −38.2114 −1.26809
\(909\) −11.0925 −0.367916
\(910\) −0.833547 −0.0276318
\(911\) −30.7338 −1.01826 −0.509128 0.860691i \(-0.670032\pi\)
−0.509128 + 0.860691i \(0.670032\pi\)
\(912\) 9.51168 0.314963
\(913\) 27.0065 0.893783
\(914\) 44.8059 1.48205
\(915\) 1.68774 0.0557951
\(916\) −43.4941 −1.43709
\(917\) −1.23738 −0.0408619
\(918\) −9.94939 −0.328379
\(919\) 7.17530 0.236691 0.118346 0.992972i \(-0.462241\pi\)
0.118346 + 0.992972i \(0.462241\pi\)
\(920\) 1.74907 0.0576651
\(921\) 9.45867 0.311674
\(922\) −56.0683 −1.84651
\(923\) −11.2946 −0.371765
\(924\) −10.5920 −0.348450
\(925\) 1.74832 0.0574844
\(926\) −3.03375 −0.0996952
\(927\) 14.5981 0.479465
\(928\) 70.2220 2.30515
\(929\) 23.3488 0.766051 0.383025 0.923738i \(-0.374882\pi\)
0.383025 + 0.923738i \(0.374882\pi\)
\(930\) −3.39135 −0.111207
\(931\) −4.17289 −0.136761
\(932\) −20.2680 −0.663902
\(933\) 1.98631 0.0650289
\(934\) 9.76524 0.319529
\(935\) 4.41053 0.144240
\(936\) 2.26407 0.0740036
\(937\) −54.8510 −1.79191 −0.895953 0.444150i \(-0.853506\pi\)
−0.895953 + 0.444150i \(0.853506\pi\)
\(938\) 0.361180 0.0117929
\(939\) −20.0441 −0.654115
\(940\) −2.23230 −0.0728095
\(941\) −2.79391 −0.0910788 −0.0455394 0.998963i \(-0.514501\pi\)
−0.0455394 + 0.998963i \(0.514501\pi\)
\(942\) −17.2173 −0.560969
\(943\) −40.3319 −1.31339
\(944\) 26.9914 0.878495
\(945\) −0.239094 −0.00777773
\(946\) −63.2014 −2.05486
\(947\) 6.53039 0.212209 0.106105 0.994355i \(-0.466162\pi\)
0.106105 + 0.994355i \(0.466162\pi\)
\(948\) 37.7611 1.22642
\(949\) 4.52163 0.146778
\(950\) −44.4747 −1.44295
\(951\) −27.2490 −0.883609
\(952\) −6.46139 −0.209415
\(953\) 19.4446 0.629873 0.314937 0.949113i \(-0.398017\pi\)
0.314937 + 0.949113i \(0.398017\pi\)
\(954\) 1.41240 0.0457281
\(955\) 2.96497 0.0959440
\(956\) 21.2933 0.688674
\(957\) −36.3855 −1.17618
\(958\) −3.76899 −0.121771
\(959\) −5.10054 −0.164705
\(960\) 2.88778 0.0932026
\(961\) 12.2721 0.395874
\(962\) −1.23312 −0.0397574
\(963\) 10.6926 0.344563
\(964\) −60.4165 −1.94589
\(965\) −3.83622 −0.123492
\(966\) −11.2644 −0.362427
\(967\) −4.67554 −0.150355 −0.0751777 0.997170i \(-0.523952\pi\)
−0.0751777 + 0.997170i \(0.523952\pi\)
\(968\) −6.97742 −0.224263
\(969\) −19.2546 −0.618547
\(970\) −0.923301 −0.0296454
\(971\) 4.75185 0.152494 0.0762470 0.997089i \(-0.475706\pi\)
0.0762470 + 0.997089i \(0.475706\pi\)
\(972\) 2.64943 0.0849804
\(973\) 12.5215 0.401422
\(974\) 54.4200 1.74373
\(975\) 7.99168 0.255938
\(976\) 16.0901 0.515030
\(977\) −37.3562 −1.19513 −0.597565 0.801821i \(-0.703865\pi\)
−0.597565 + 0.801821i \(0.703865\pi\)
\(978\) −10.8226 −0.346067
\(979\) 47.9514 1.53253
\(980\) −0.633462 −0.0202352
\(981\) −19.1750 −0.612212
\(982\) 58.5864 1.86957
\(983\) 45.4192 1.44865 0.724324 0.689459i \(-0.242152\pi\)
0.724324 + 0.689459i \(0.242152\pi\)
\(984\) 10.8110 0.344643
\(985\) −2.91389 −0.0928444
\(986\) −90.5524 −2.88378
\(987\) 3.52396 0.112169
\(988\) 17.8752 0.568686
\(989\) −38.3011 −1.21791
\(990\) −2.06107 −0.0655053
\(991\) −8.11368 −0.257739 −0.128870 0.991662i \(-0.541135\pi\)
−0.128870 + 0.991662i \(0.541135\pi\)
\(992\) −50.7544 −1.61145
\(993\) 34.0423 1.08030
\(994\) −15.0628 −0.477764
\(995\) −3.29509 −0.104461
\(996\) −17.8976 −0.567106
\(997\) −33.0431 −1.04648 −0.523242 0.852184i \(-0.675278\pi\)
−0.523242 + 0.852184i \(0.675278\pi\)
\(998\) 40.8413 1.29281
\(999\) −0.353708 −0.0111908
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 2667.2.a.j.1.2 7
3.2 odd 2 8001.2.a.l.1.6 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2667.2.a.j.1.2 7 1.1 even 1 trivial
8001.2.a.l.1.6 7 3.2 odd 2