Properties

Label 3381.2.a.bi.1.5
Level $3381$
Weight $2$
Character 3381.1
Self dual yes
Analytic conductor $26.997$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 3381 = 3 \cdot 7^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3381.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(26.9974209234\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Defining polynomial: \(x^{10} - 3 x^{9} - 13 x^{8} + 41 x^{7} + 47 x^{6} - 165 x^{5} - 45 x^{4} + 207 x^{3} + 12 x^{2} - 76 x - 2\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 483)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(-0.0262565\) of defining polynomial
Character \(\chi\) \(=\) 3381.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.0262565 q^{2} -1.00000 q^{3} -1.99931 q^{4} +2.77828 q^{5} +0.0262565 q^{6} +0.105008 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-0.0262565 q^{2} -1.00000 q^{3} -1.99931 q^{4} +2.77828 q^{5} +0.0262565 q^{6} +0.105008 q^{8} +1.00000 q^{9} -0.0729480 q^{10} +0.660156 q^{11} +1.99931 q^{12} +4.12488 q^{13} -2.77828 q^{15} +3.99586 q^{16} +4.12381 q^{17} -0.0262565 q^{18} +4.76829 q^{19} -5.55465 q^{20} -0.0173334 q^{22} +1.00000 q^{23} -0.105008 q^{24} +2.71885 q^{25} -0.108305 q^{26} -1.00000 q^{27} -1.78025 q^{29} +0.0729480 q^{30} -3.62429 q^{31} -0.314933 q^{32} -0.660156 q^{33} -0.108277 q^{34} -1.99931 q^{36} -8.06211 q^{37} -0.125199 q^{38} -4.12488 q^{39} +0.291742 q^{40} -7.99969 q^{41} +12.5842 q^{43} -1.31986 q^{44} +2.77828 q^{45} -0.0262565 q^{46} +11.7622 q^{47} -3.99586 q^{48} -0.0713876 q^{50} -4.12381 q^{51} -8.24691 q^{52} -0.0608257 q^{53} +0.0262565 q^{54} +1.83410 q^{55} -4.76829 q^{57} +0.0467430 q^{58} -8.98717 q^{59} +5.55465 q^{60} +2.71267 q^{61} +0.0951611 q^{62} -7.98346 q^{64} +11.4601 q^{65} +0.0173334 q^{66} -2.68583 q^{67} -8.24477 q^{68} -1.00000 q^{69} +12.4462 q^{71} +0.105008 q^{72} -14.2871 q^{73} +0.211683 q^{74} -2.71885 q^{75} -9.53329 q^{76} +0.108305 q^{78} -6.94797 q^{79} +11.1016 q^{80} +1.00000 q^{81} +0.210044 q^{82} +9.40856 q^{83} +11.4571 q^{85} -0.330417 q^{86} +1.78025 q^{87} +0.0693216 q^{88} -5.92430 q^{89} -0.0729480 q^{90} -1.99931 q^{92} +3.62429 q^{93} -0.308834 q^{94} +13.2477 q^{95} +0.314933 q^{96} +2.53740 q^{97} +0.660156 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q + 3q^{2} - 10q^{3} + 15q^{4} - 5q^{5} - 3q^{6} + 9q^{8} + 10q^{9} + O(q^{10}) \) \( 10q + 3q^{2} - 10q^{3} + 15q^{4} - 5q^{5} - 3q^{6} + 9q^{8} + 10q^{9} + 11q^{10} + 8q^{11} - 15q^{12} + 5q^{15} + 37q^{16} - 11q^{17} + 3q^{18} + q^{19} - 15q^{20} + 6q^{22} + 10q^{23} - 9q^{24} + 21q^{25} + q^{26} - 10q^{27} + 22q^{29} - 11q^{30} - 3q^{31} + 11q^{32} - 8q^{33} - 3q^{34} + 15q^{36} - 3q^{37} + 16q^{38} + 39q^{40} - 26q^{41} + 27q^{43} + 16q^{44} - 5q^{45} + 3q^{46} + 11q^{47} - 37q^{48} + 2q^{50} + 11q^{51} + 29q^{52} + 5q^{53} - 3q^{54} - 18q^{55} - q^{57} + 16q^{58} - 10q^{59} + 15q^{60} + 22q^{61} - 32q^{62} + 69q^{64} - 11q^{65} - 6q^{66} - 2q^{67} - 21q^{68} - 10q^{69} + 27q^{71} + 9q^{72} - 8q^{73} + 14q^{74} - 21q^{75} - 22q^{76} - q^{78} + 21q^{79} - 53q^{80} + 10q^{81} + 36q^{82} - 12q^{83} + 23q^{85} + 18q^{86} - 22q^{87} - 10q^{88} + 6q^{89} + 11q^{90} + 15q^{92} + 3q^{93} + 35q^{94} + 44q^{95} - 11q^{96} + 6q^{97} + 8q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.0262565 −0.0185661 −0.00928307 0.999957i \(-0.502955\pi\)
−0.00928307 + 0.999957i \(0.502955\pi\)
\(3\) −1.00000 −0.577350
\(4\) −1.99931 −0.999655
\(5\) 2.77828 1.24249 0.621243 0.783618i \(-0.286628\pi\)
0.621243 + 0.783618i \(0.286628\pi\)
\(6\) 0.0262565 0.0107192
\(7\) 0 0
\(8\) 0.105008 0.0371259
\(9\) 1.00000 0.333333
\(10\) −0.0729480 −0.0230682
\(11\) 0.660156 0.199045 0.0995223 0.995035i \(-0.468269\pi\)
0.0995223 + 0.995035i \(0.468269\pi\)
\(12\) 1.99931 0.577151
\(13\) 4.12488 1.14404 0.572018 0.820241i \(-0.306161\pi\)
0.572018 + 0.820241i \(0.306161\pi\)
\(14\) 0 0
\(15\) −2.77828 −0.717349
\(16\) 3.99586 0.998966
\(17\) 4.12381 1.00017 0.500085 0.865976i \(-0.333302\pi\)
0.500085 + 0.865976i \(0.333302\pi\)
\(18\) −0.0262565 −0.00618871
\(19\) 4.76829 1.09392 0.546960 0.837159i \(-0.315785\pi\)
0.546960 + 0.837159i \(0.315785\pi\)
\(20\) −5.55465 −1.24206
\(21\) 0 0
\(22\) −0.0173334 −0.00369549
\(23\) 1.00000 0.208514
\(24\) −0.105008 −0.0214346
\(25\) 2.71885 0.543771
\(26\) −0.108305 −0.0212403
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −1.78025 −0.330583 −0.165292 0.986245i \(-0.552857\pi\)
−0.165292 + 0.986245i \(0.552857\pi\)
\(30\) 0.0729480 0.0133184
\(31\) −3.62429 −0.650941 −0.325471 0.945552i \(-0.605523\pi\)
−0.325471 + 0.945552i \(0.605523\pi\)
\(32\) −0.314933 −0.0556728
\(33\) −0.660156 −0.114918
\(34\) −0.108277 −0.0185693
\(35\) 0 0
\(36\) −1.99931 −0.333218
\(37\) −8.06211 −1.32540 −0.662701 0.748884i \(-0.730590\pi\)
−0.662701 + 0.748884i \(0.730590\pi\)
\(38\) −0.125199 −0.0203099
\(39\) −4.12488 −0.660509
\(40\) 0.291742 0.0461284
\(41\) −7.99969 −1.24934 −0.624671 0.780888i \(-0.714767\pi\)
−0.624671 + 0.780888i \(0.714767\pi\)
\(42\) 0 0
\(43\) 12.5842 1.91907 0.959536 0.281585i \(-0.0908601\pi\)
0.959536 + 0.281585i \(0.0908601\pi\)
\(44\) −1.31986 −0.198976
\(45\) 2.77828 0.414162
\(46\) −0.0262565 −0.00387131
\(47\) 11.7622 1.71569 0.857846 0.513908i \(-0.171803\pi\)
0.857846 + 0.513908i \(0.171803\pi\)
\(48\) −3.99586 −0.576753
\(49\) 0 0
\(50\) −0.0713876 −0.0100957
\(51\) −4.12381 −0.577448
\(52\) −8.24691 −1.14364
\(53\) −0.0608257 −0.00835505 −0.00417752 0.999991i \(-0.501330\pi\)
−0.00417752 + 0.999991i \(0.501330\pi\)
\(54\) 0.0262565 0.00357306
\(55\) 1.83410 0.247310
\(56\) 0 0
\(57\) −4.76829 −0.631575
\(58\) 0.0467430 0.00613766
\(59\) −8.98717 −1.17003 −0.585015 0.811022i \(-0.698911\pi\)
−0.585015 + 0.811022i \(0.698911\pi\)
\(60\) 5.55465 0.717102
\(61\) 2.71267 0.347322 0.173661 0.984806i \(-0.444440\pi\)
0.173661 + 0.984806i \(0.444440\pi\)
\(62\) 0.0951611 0.0120855
\(63\) 0 0
\(64\) −7.98346 −0.997932
\(65\) 11.4601 1.42145
\(66\) 0.0173334 0.00213359
\(67\) −2.68583 −0.328126 −0.164063 0.986450i \(-0.552460\pi\)
−0.164063 + 0.986450i \(0.552460\pi\)
\(68\) −8.24477 −0.999825
\(69\) −1.00000 −0.120386
\(70\) 0 0
\(71\) 12.4462 1.47709 0.738545 0.674205i \(-0.235513\pi\)
0.738545 + 0.674205i \(0.235513\pi\)
\(72\) 0.105008 0.0123753
\(73\) −14.2871 −1.67218 −0.836088 0.548596i \(-0.815163\pi\)
−0.836088 + 0.548596i \(0.815163\pi\)
\(74\) 0.211683 0.0246076
\(75\) −2.71885 −0.313946
\(76\) −9.53329 −1.09354
\(77\) 0 0
\(78\) 0.108305 0.0122631
\(79\) −6.94797 −0.781708 −0.390854 0.920453i \(-0.627820\pi\)
−0.390854 + 0.920453i \(0.627820\pi\)
\(80\) 11.1016 1.24120
\(81\) 1.00000 0.111111
\(82\) 0.210044 0.0231955
\(83\) 9.40856 1.03272 0.516362 0.856371i \(-0.327286\pi\)
0.516362 + 0.856371i \(0.327286\pi\)
\(84\) 0 0
\(85\) 11.4571 1.24270
\(86\) −0.330417 −0.0356298
\(87\) 1.78025 0.190862
\(88\) 0.0693216 0.00738971
\(89\) −5.92430 −0.627975 −0.313987 0.949427i \(-0.601665\pi\)
−0.313987 + 0.949427i \(0.601665\pi\)
\(90\) −0.0729480 −0.00768939
\(91\) 0 0
\(92\) −1.99931 −0.208443
\(93\) 3.62429 0.375821
\(94\) −0.308834 −0.0318538
\(95\) 13.2477 1.35918
\(96\) 0.314933 0.0321427
\(97\) 2.53740 0.257634 0.128817 0.991668i \(-0.458882\pi\)
0.128817 + 0.991668i \(0.458882\pi\)
\(98\) 0 0
\(99\) 0.660156 0.0663482
\(100\) −5.43583 −0.543583
\(101\) 6.71178 0.667847 0.333923 0.942600i \(-0.391627\pi\)
0.333923 + 0.942600i \(0.391627\pi\)
\(102\) 0.108277 0.0107210
\(103\) 10.7478 1.05901 0.529507 0.848306i \(-0.322377\pi\)
0.529507 + 0.848306i \(0.322377\pi\)
\(104\) 0.433145 0.0424733
\(105\) 0 0
\(106\) 0.00159707 0.000155121 0
\(107\) −0.484556 −0.0468438 −0.0234219 0.999726i \(-0.507456\pi\)
−0.0234219 + 0.999726i \(0.507456\pi\)
\(108\) 1.99931 0.192384
\(109\) 12.4652 1.19395 0.596975 0.802260i \(-0.296369\pi\)
0.596975 + 0.802260i \(0.296369\pi\)
\(110\) −0.0481570 −0.00459159
\(111\) 8.06211 0.765221
\(112\) 0 0
\(113\) 9.28875 0.873812 0.436906 0.899507i \(-0.356074\pi\)
0.436906 + 0.899507i \(0.356074\pi\)
\(114\) 0.125199 0.0117259
\(115\) 2.77828 0.259076
\(116\) 3.55926 0.330469
\(117\) 4.12488 0.381345
\(118\) 0.235972 0.0217229
\(119\) 0 0
\(120\) −0.291742 −0.0266322
\(121\) −10.5642 −0.960381
\(122\) −0.0712252 −0.00644842
\(123\) 7.99969 0.721308
\(124\) 7.24608 0.650717
\(125\) −6.33767 −0.566858
\(126\) 0 0
\(127\) 2.40074 0.213031 0.106515 0.994311i \(-0.466031\pi\)
0.106515 + 0.994311i \(0.466031\pi\)
\(128\) 0.839484 0.0742006
\(129\) −12.5842 −1.10798
\(130\) −0.300901 −0.0263908
\(131\) −20.1505 −1.76056 −0.880278 0.474458i \(-0.842644\pi\)
−0.880278 + 0.474458i \(0.842644\pi\)
\(132\) 1.31986 0.114879
\(133\) 0 0
\(134\) 0.0705204 0.00609204
\(135\) −2.77828 −0.239116
\(136\) 0.433032 0.0371322
\(137\) 7.00658 0.598613 0.299306 0.954157i \(-0.403245\pi\)
0.299306 + 0.954157i \(0.403245\pi\)
\(138\) 0.0262565 0.00223510
\(139\) −2.88510 −0.244711 −0.122356 0.992486i \(-0.539045\pi\)
−0.122356 + 0.992486i \(0.539045\pi\)
\(140\) 0 0
\(141\) −11.7622 −0.990555
\(142\) −0.326793 −0.0274238
\(143\) 2.72306 0.227714
\(144\) 3.99586 0.332989
\(145\) −4.94603 −0.410745
\(146\) 0.375128 0.0310458
\(147\) 0 0
\(148\) 16.1187 1.32495
\(149\) 19.0608 1.56152 0.780762 0.624829i \(-0.214831\pi\)
0.780762 + 0.624829i \(0.214831\pi\)
\(150\) 0.0713876 0.00582877
\(151\) −5.06290 −0.412013 −0.206006 0.978551i \(-0.566047\pi\)
−0.206006 + 0.978551i \(0.566047\pi\)
\(152\) 0.500708 0.0406128
\(153\) 4.12381 0.333390
\(154\) 0 0
\(155\) −10.0693 −0.808785
\(156\) 8.24691 0.660281
\(157\) −2.74388 −0.218985 −0.109493 0.993988i \(-0.534923\pi\)
−0.109493 + 0.993988i \(0.534923\pi\)
\(158\) 0.182429 0.0145133
\(159\) 0.0608257 0.00482379
\(160\) −0.874973 −0.0691727
\(161\) 0 0
\(162\) −0.0262565 −0.00206290
\(163\) 15.3088 1.19908 0.599539 0.800346i \(-0.295351\pi\)
0.599539 + 0.800346i \(0.295351\pi\)
\(164\) 15.9939 1.24891
\(165\) −1.83410 −0.142785
\(166\) −0.247036 −0.0191737
\(167\) 13.0016 1.00610 0.503049 0.864258i \(-0.332212\pi\)
0.503049 + 0.864258i \(0.332212\pi\)
\(168\) 0 0
\(169\) 4.01461 0.308816
\(170\) −0.300823 −0.0230721
\(171\) 4.76829 0.364640
\(172\) −25.1597 −1.91841
\(173\) −10.4220 −0.792372 −0.396186 0.918170i \(-0.629666\pi\)
−0.396186 + 0.918170i \(0.629666\pi\)
\(174\) −0.0467430 −0.00354358
\(175\) 0 0
\(176\) 2.63789 0.198839
\(177\) 8.98717 0.675517
\(178\) 0.155551 0.0116591
\(179\) 19.2231 1.43680 0.718402 0.695628i \(-0.244874\pi\)
0.718402 + 0.695628i \(0.244874\pi\)
\(180\) −5.55465 −0.414019
\(181\) −11.1552 −0.829162 −0.414581 0.910012i \(-0.636072\pi\)
−0.414581 + 0.910012i \(0.636072\pi\)
\(182\) 0 0
\(183\) −2.71267 −0.200526
\(184\) 0.105008 0.00774128
\(185\) −22.3988 −1.64679
\(186\) −0.0951611 −0.00697755
\(187\) 2.72236 0.199078
\(188\) −23.5163 −1.71510
\(189\) 0 0
\(190\) −0.347837 −0.0252347
\(191\) 19.2346 1.39177 0.695884 0.718154i \(-0.255013\pi\)
0.695884 + 0.718154i \(0.255013\pi\)
\(192\) 7.98346 0.576157
\(193\) 17.4527 1.25627 0.628136 0.778104i \(-0.283818\pi\)
0.628136 + 0.778104i \(0.283818\pi\)
\(194\) −0.0666232 −0.00478326
\(195\) −11.4601 −0.820673
\(196\) 0 0
\(197\) −1.16239 −0.0828168 −0.0414084 0.999142i \(-0.513184\pi\)
−0.0414084 + 0.999142i \(0.513184\pi\)
\(198\) −0.0173334 −0.00123183
\(199\) 16.9768 1.20346 0.601728 0.798701i \(-0.294479\pi\)
0.601728 + 0.798701i \(0.294479\pi\)
\(200\) 0.285501 0.0201880
\(201\) 2.68583 0.189444
\(202\) −0.176228 −0.0123993
\(203\) 0 0
\(204\) 8.24477 0.577249
\(205\) −22.2254 −1.55229
\(206\) −0.282200 −0.0196618
\(207\) 1.00000 0.0695048
\(208\) 16.4824 1.14285
\(209\) 3.14782 0.217739
\(210\) 0 0
\(211\) 11.6924 0.804938 0.402469 0.915434i \(-0.368152\pi\)
0.402469 + 0.915434i \(0.368152\pi\)
\(212\) 0.121609 0.00835217
\(213\) −12.4462 −0.852798
\(214\) 0.0127227 0.000869708 0
\(215\) 34.9625 2.38442
\(216\) −0.105008 −0.00714488
\(217\) 0 0
\(218\) −0.327293 −0.0221671
\(219\) 14.2871 0.965431
\(220\) −3.66694 −0.247225
\(221\) 17.0102 1.14423
\(222\) −0.211683 −0.0142072
\(223\) −15.5087 −1.03854 −0.519270 0.854610i \(-0.673796\pi\)
−0.519270 + 0.854610i \(0.673796\pi\)
\(224\) 0 0
\(225\) 2.71885 0.181257
\(226\) −0.243890 −0.0162233
\(227\) −15.3330 −1.01768 −0.508842 0.860860i \(-0.669926\pi\)
−0.508842 + 0.860860i \(0.669926\pi\)
\(228\) 9.53329 0.631358
\(229\) −6.40484 −0.423243 −0.211622 0.977352i \(-0.567874\pi\)
−0.211622 + 0.977352i \(0.567874\pi\)
\(230\) −0.0729480 −0.00481005
\(231\) 0 0
\(232\) −0.186940 −0.0122732
\(233\) −26.1430 −1.71269 −0.856344 0.516406i \(-0.827270\pi\)
−0.856344 + 0.516406i \(0.827270\pi\)
\(234\) −0.108305 −0.00708011
\(235\) 32.6787 2.13172
\(236\) 17.9681 1.16963
\(237\) 6.94797 0.451319
\(238\) 0 0
\(239\) 17.6773 1.14345 0.571724 0.820446i \(-0.306275\pi\)
0.571724 + 0.820446i \(0.306275\pi\)
\(240\) −11.1016 −0.716608
\(241\) 5.75969 0.371014 0.185507 0.982643i \(-0.440607\pi\)
0.185507 + 0.982643i \(0.440607\pi\)
\(242\) 0.277379 0.0178306
\(243\) −1.00000 −0.0641500
\(244\) −5.42347 −0.347202
\(245\) 0 0
\(246\) −0.210044 −0.0133919
\(247\) 19.6686 1.25148
\(248\) −0.380579 −0.0241668
\(249\) −9.40856 −0.596243
\(250\) 0.166405 0.0105244
\(251\) −10.3866 −0.655597 −0.327798 0.944748i \(-0.606307\pi\)
−0.327798 + 0.944748i \(0.606307\pi\)
\(252\) 0 0
\(253\) 0.660156 0.0415037
\(254\) −0.0630349 −0.00395516
\(255\) −11.4571 −0.717471
\(256\) 15.9449 0.996555
\(257\) −2.69848 −0.168327 −0.0841633 0.996452i \(-0.526822\pi\)
−0.0841633 + 0.996452i \(0.526822\pi\)
\(258\) 0.330417 0.0205709
\(259\) 0 0
\(260\) −22.9122 −1.42096
\(261\) −1.78025 −0.110194
\(262\) 0.529081 0.0326867
\(263\) −21.1490 −1.30411 −0.652053 0.758174i \(-0.726092\pi\)
−0.652053 + 0.758174i \(0.726092\pi\)
\(264\) −0.0693216 −0.00426645
\(265\) −0.168991 −0.0103810
\(266\) 0 0
\(267\) 5.92430 0.362561
\(268\) 5.36981 0.328013
\(269\) −28.5411 −1.74018 −0.870090 0.492893i \(-0.835939\pi\)
−0.870090 + 0.492893i \(0.835939\pi\)
\(270\) 0.0729480 0.00443947
\(271\) 15.1472 0.920130 0.460065 0.887885i \(-0.347826\pi\)
0.460065 + 0.887885i \(0.347826\pi\)
\(272\) 16.4782 0.999136
\(273\) 0 0
\(274\) −0.183968 −0.0111139
\(275\) 1.79487 0.108235
\(276\) 1.99931 0.120344
\(277\) 4.23717 0.254587 0.127294 0.991865i \(-0.459371\pi\)
0.127294 + 0.991865i \(0.459371\pi\)
\(278\) 0.0757527 0.00454335
\(279\) −3.62429 −0.216980
\(280\) 0 0
\(281\) 0.762123 0.0454645 0.0227322 0.999742i \(-0.492763\pi\)
0.0227322 + 0.999742i \(0.492763\pi\)
\(282\) 0.308834 0.0183908
\(283\) 17.1714 1.02073 0.510367 0.859957i \(-0.329510\pi\)
0.510367 + 0.859957i \(0.329510\pi\)
\(284\) −24.8838 −1.47658
\(285\) −13.2477 −0.784723
\(286\) −0.0714981 −0.00422777
\(287\) 0 0
\(288\) −0.314933 −0.0185576
\(289\) 0.00578278 0.000340164 0
\(290\) 0.129865 0.00762595
\(291\) −2.53740 −0.148745
\(292\) 28.5643 1.67160
\(293\) −1.15566 −0.0675144 −0.0337572 0.999430i \(-0.510747\pi\)
−0.0337572 + 0.999430i \(0.510747\pi\)
\(294\) 0 0
\(295\) −24.9689 −1.45375
\(296\) −0.846585 −0.0492067
\(297\) −0.660156 −0.0383061
\(298\) −0.500470 −0.0289915
\(299\) 4.12488 0.238548
\(300\) 5.43583 0.313838
\(301\) 0 0
\(302\) 0.132934 0.00764949
\(303\) −6.71178 −0.385581
\(304\) 19.0534 1.09279
\(305\) 7.53656 0.431542
\(306\) −0.108277 −0.00618977
\(307\) 31.0365 1.77135 0.885673 0.464310i \(-0.153698\pi\)
0.885673 + 0.464310i \(0.153698\pi\)
\(308\) 0 0
\(309\) −10.7478 −0.611422
\(310\) 0.264384 0.0150160
\(311\) 17.6141 0.998801 0.499401 0.866371i \(-0.333554\pi\)
0.499401 + 0.866371i \(0.333554\pi\)
\(312\) −0.433145 −0.0245220
\(313\) 15.7406 0.889713 0.444856 0.895602i \(-0.353255\pi\)
0.444856 + 0.895602i \(0.353255\pi\)
\(314\) 0.0720446 0.00406571
\(315\) 0 0
\(316\) 13.8912 0.781438
\(317\) −5.22139 −0.293263 −0.146631 0.989191i \(-0.546843\pi\)
−0.146631 + 0.989191i \(0.546843\pi\)
\(318\) −0.00159707 −8.95592e−5 0
\(319\) −1.17524 −0.0658008
\(320\) −22.1803 −1.23992
\(321\) 0.484556 0.0270453
\(322\) 0 0
\(323\) 19.6635 1.09411
\(324\) −1.99931 −0.111073
\(325\) 11.2149 0.622093
\(326\) −0.401955 −0.0222623
\(327\) −12.4652 −0.689328
\(328\) −0.840030 −0.0463829
\(329\) 0 0
\(330\) 0.0481570 0.00265096
\(331\) −13.9449 −0.766483 −0.383241 0.923648i \(-0.625192\pi\)
−0.383241 + 0.923648i \(0.625192\pi\)
\(332\) −18.8106 −1.03237
\(333\) −8.06211 −0.441801
\(334\) −0.341378 −0.0186793
\(335\) −7.46199 −0.407692
\(336\) 0 0
\(337\) 9.28645 0.505865 0.252933 0.967484i \(-0.418605\pi\)
0.252933 + 0.967484i \(0.418605\pi\)
\(338\) −0.105410 −0.00573353
\(339\) −9.28875 −0.504496
\(340\) −22.9063 −1.24227
\(341\) −2.39260 −0.129566
\(342\) −0.125199 −0.00676996
\(343\) 0 0
\(344\) 1.32144 0.0712473
\(345\) −2.77828 −0.149578
\(346\) 0.273646 0.0147113
\(347\) 7.67494 0.412013 0.206006 0.978551i \(-0.433953\pi\)
0.206006 + 0.978551i \(0.433953\pi\)
\(348\) −3.55926 −0.190797
\(349\) 5.71924 0.306144 0.153072 0.988215i \(-0.451083\pi\)
0.153072 + 0.988215i \(0.451083\pi\)
\(350\) 0 0
\(351\) −4.12488 −0.220170
\(352\) −0.207905 −0.0110814
\(353\) 13.4196 0.714253 0.357127 0.934056i \(-0.383757\pi\)
0.357127 + 0.934056i \(0.383757\pi\)
\(354\) −0.235972 −0.0125417
\(355\) 34.5790 1.83526
\(356\) 11.8445 0.627758
\(357\) 0 0
\(358\) −0.504732 −0.0266759
\(359\) 17.8658 0.942922 0.471461 0.881887i \(-0.343727\pi\)
0.471461 + 0.881887i \(0.343727\pi\)
\(360\) 0.291742 0.0153761
\(361\) 3.73658 0.196662
\(362\) 0.292897 0.0153943
\(363\) 10.5642 0.554476
\(364\) 0 0
\(365\) −39.6935 −2.07765
\(366\) 0.0712252 0.00372300
\(367\) 26.1522 1.36513 0.682566 0.730824i \(-0.260864\pi\)
0.682566 + 0.730824i \(0.260864\pi\)
\(368\) 3.99586 0.208299
\(369\) −7.99969 −0.416447
\(370\) 0.588114 0.0305746
\(371\) 0 0
\(372\) −7.24608 −0.375692
\(373\) 20.1300 1.04229 0.521147 0.853467i \(-0.325504\pi\)
0.521147 + 0.853467i \(0.325504\pi\)
\(374\) −0.0714795 −0.00369612
\(375\) 6.33767 0.327276
\(376\) 1.23512 0.0636966
\(377\) −7.34330 −0.378199
\(378\) 0 0
\(379\) 8.04896 0.413447 0.206724 0.978399i \(-0.433720\pi\)
0.206724 + 0.978399i \(0.433720\pi\)
\(380\) −26.4862 −1.35871
\(381\) −2.40074 −0.122993
\(382\) −0.505034 −0.0258398
\(383\) 20.0694 1.02550 0.512749 0.858539i \(-0.328627\pi\)
0.512749 + 0.858539i \(0.328627\pi\)
\(384\) −0.839484 −0.0428397
\(385\) 0 0
\(386\) −0.458246 −0.0233241
\(387\) 12.5842 0.639691
\(388\) −5.07305 −0.257545
\(389\) 12.4516 0.631322 0.315661 0.948872i \(-0.397774\pi\)
0.315661 + 0.948872i \(0.397774\pi\)
\(390\) 0.300901 0.0152367
\(391\) 4.12381 0.208550
\(392\) 0 0
\(393\) 20.1505 1.01646
\(394\) 0.0305203 0.00153759
\(395\) −19.3034 −0.971261
\(396\) −1.31986 −0.0663253
\(397\) −6.93528 −0.348072 −0.174036 0.984739i \(-0.555681\pi\)
−0.174036 + 0.984739i \(0.555681\pi\)
\(398\) −0.445752 −0.0223435
\(399\) 0 0
\(400\) 10.8642 0.543208
\(401\) −14.4161 −0.719908 −0.359954 0.932970i \(-0.617208\pi\)
−0.359954 + 0.932970i \(0.617208\pi\)
\(402\) −0.0705204 −0.00351724
\(403\) −14.9497 −0.744700
\(404\) −13.4189 −0.667617
\(405\) 2.77828 0.138054
\(406\) 0 0
\(407\) −5.32225 −0.263814
\(408\) −0.433032 −0.0214383
\(409\) 24.0265 1.18803 0.594016 0.804453i \(-0.297541\pi\)
0.594016 + 0.804453i \(0.297541\pi\)
\(410\) 0.583561 0.0288200
\(411\) −7.00658 −0.345609
\(412\) −21.4882 −1.05865
\(413\) 0 0
\(414\) −0.0262565 −0.00129044
\(415\) 26.1396 1.28314
\(416\) −1.29906 −0.0636917
\(417\) 2.88510 0.141284
\(418\) −0.0826506 −0.00404257
\(419\) 31.8946 1.55815 0.779076 0.626930i \(-0.215689\pi\)
0.779076 + 0.626930i \(0.215689\pi\)
\(420\) 0 0
\(421\) −18.8400 −0.918205 −0.459102 0.888383i \(-0.651829\pi\)
−0.459102 + 0.888383i \(0.651829\pi\)
\(422\) −0.307002 −0.0149446
\(423\) 11.7622 0.571897
\(424\) −0.00638717 −0.000310189 0
\(425\) 11.2120 0.543863
\(426\) 0.326793 0.0158332
\(427\) 0 0
\(428\) 0.968777 0.0468276
\(429\) −2.72306 −0.131471
\(430\) −0.917992 −0.0442695
\(431\) −36.3431 −1.75058 −0.875292 0.483595i \(-0.839331\pi\)
−0.875292 + 0.483595i \(0.839331\pi\)
\(432\) −3.99586 −0.192251
\(433\) 21.5486 1.03556 0.517780 0.855514i \(-0.326759\pi\)
0.517780 + 0.855514i \(0.326759\pi\)
\(434\) 0 0
\(435\) 4.94603 0.237144
\(436\) −24.9218 −1.19354
\(437\) 4.76829 0.228098
\(438\) −0.375128 −0.0179243
\(439\) −10.7375 −0.512473 −0.256237 0.966614i \(-0.582483\pi\)
−0.256237 + 0.966614i \(0.582483\pi\)
\(440\) 0.192595 0.00918160
\(441\) 0 0
\(442\) −0.446628 −0.0212439
\(443\) −33.9531 −1.61316 −0.806580 0.591125i \(-0.798684\pi\)
−0.806580 + 0.591125i \(0.798684\pi\)
\(444\) −16.1187 −0.764957
\(445\) −16.4594 −0.780250
\(446\) 0.407204 0.0192817
\(447\) −19.0608 −0.901546
\(448\) 0 0
\(449\) 6.94219 0.327622 0.163811 0.986492i \(-0.447621\pi\)
0.163811 + 0.986492i \(0.447621\pi\)
\(450\) −0.0713876 −0.00336524
\(451\) −5.28104 −0.248675
\(452\) −18.5711 −0.873511
\(453\) 5.06290 0.237876
\(454\) 0.402590 0.0188945
\(455\) 0 0
\(456\) −0.500708 −0.0234478
\(457\) −39.5509 −1.85011 −0.925057 0.379829i \(-0.875983\pi\)
−0.925057 + 0.379829i \(0.875983\pi\)
\(458\) 0.168169 0.00785800
\(459\) −4.12381 −0.192483
\(460\) −5.55465 −0.258987
\(461\) −4.90582 −0.228487 −0.114243 0.993453i \(-0.536444\pi\)
−0.114243 + 0.993453i \(0.536444\pi\)
\(462\) 0 0
\(463\) −0.772106 −0.0358828 −0.0179414 0.999839i \(-0.505711\pi\)
−0.0179414 + 0.999839i \(0.505711\pi\)
\(464\) −7.11362 −0.330242
\(465\) 10.0693 0.466952
\(466\) 0.686425 0.0317980
\(467\) −19.1977 −0.888365 −0.444182 0.895936i \(-0.646506\pi\)
−0.444182 + 0.895936i \(0.646506\pi\)
\(468\) −8.24691 −0.381214
\(469\) 0 0
\(470\) −0.858027 −0.0395778
\(471\) 2.74388 0.126431
\(472\) −0.943724 −0.0434384
\(473\) 8.30754 0.381981
\(474\) −0.182429 −0.00837926
\(475\) 12.9643 0.594842
\(476\) 0 0
\(477\) −0.0608257 −0.00278502
\(478\) −0.464143 −0.0212294
\(479\) −18.2104 −0.832056 −0.416028 0.909352i \(-0.636578\pi\)
−0.416028 + 0.909352i \(0.636578\pi\)
\(480\) 0.874973 0.0399369
\(481\) −33.2552 −1.51631
\(482\) −0.151229 −0.00688830
\(483\) 0 0
\(484\) 21.1211 0.960050
\(485\) 7.04961 0.320106
\(486\) 0.0262565 0.00119102
\(487\) −28.8813 −1.30873 −0.654367 0.756177i \(-0.727065\pi\)
−0.654367 + 0.756177i \(0.727065\pi\)
\(488\) 0.284852 0.0128946
\(489\) −15.3088 −0.692288
\(490\) 0 0
\(491\) −23.6817 −1.06874 −0.534369 0.845251i \(-0.679451\pi\)
−0.534369 + 0.845251i \(0.679451\pi\)
\(492\) −15.9939 −0.721059
\(493\) −7.34139 −0.330640
\(494\) −0.516429 −0.0232352
\(495\) 1.83410 0.0824367
\(496\) −14.4822 −0.650268
\(497\) 0 0
\(498\) 0.247036 0.0110699
\(499\) 25.3699 1.13571 0.567856 0.823128i \(-0.307773\pi\)
0.567856 + 0.823128i \(0.307773\pi\)
\(500\) 12.6710 0.566663
\(501\) −13.0016 −0.580871
\(502\) 0.272716 0.0121719
\(503\) −29.2636 −1.30480 −0.652400 0.757874i \(-0.726238\pi\)
−0.652400 + 0.757874i \(0.726238\pi\)
\(504\) 0 0
\(505\) 18.6472 0.829790
\(506\) −0.0173334 −0.000770563 0
\(507\) −4.01461 −0.178295
\(508\) −4.79982 −0.212957
\(509\) −40.6862 −1.80338 −0.901692 0.432379i \(-0.857674\pi\)
−0.901692 + 0.432379i \(0.857674\pi\)
\(510\) 0.300823 0.0133207
\(511\) 0 0
\(512\) −2.09762 −0.0927028
\(513\) −4.76829 −0.210525
\(514\) 0.0708526 0.00312518
\(515\) 29.8605 1.31581
\(516\) 25.1597 1.10760
\(517\) 7.76488 0.341499
\(518\) 0 0
\(519\) 10.4220 0.457476
\(520\) 1.20340 0.0527725
\(521\) −33.7965 −1.48065 −0.740326 0.672248i \(-0.765329\pi\)
−0.740326 + 0.672248i \(0.765329\pi\)
\(522\) 0.0467430 0.00204589
\(523\) 12.8567 0.562186 0.281093 0.959681i \(-0.409303\pi\)
0.281093 + 0.959681i \(0.409303\pi\)
\(524\) 40.2871 1.75995
\(525\) 0 0
\(526\) 0.555300 0.0242122
\(527\) −14.9459 −0.651052
\(528\) −2.63789 −0.114800
\(529\) 1.00000 0.0434783
\(530\) 0.00443711 0.000192736 0
\(531\) −8.98717 −0.390010
\(532\) 0 0
\(533\) −32.9977 −1.42929
\(534\) −0.155551 −0.00673137
\(535\) −1.34623 −0.0582027
\(536\) −0.282033 −0.0121820
\(537\) −19.2231 −0.829539
\(538\) 0.749388 0.0323084
\(539\) 0 0
\(540\) 5.55465 0.239034
\(541\) −11.5066 −0.494706 −0.247353 0.968925i \(-0.579561\pi\)
−0.247353 + 0.968925i \(0.579561\pi\)
\(542\) −0.397714 −0.0170833
\(543\) 11.1552 0.478717
\(544\) −1.29872 −0.0556823
\(545\) 34.6319 1.48347
\(546\) 0 0
\(547\) 8.26280 0.353292 0.176646 0.984274i \(-0.443475\pi\)
0.176646 + 0.984274i \(0.443475\pi\)
\(548\) −14.0083 −0.598406
\(549\) 2.71267 0.115774
\(550\) −0.0471269 −0.00200950
\(551\) −8.48873 −0.361632
\(552\) −0.105008 −0.00446943
\(553\) 0 0
\(554\) −0.111253 −0.00472670
\(555\) 22.3988 0.950776
\(556\) 5.76822 0.244627
\(557\) −22.6003 −0.957604 −0.478802 0.877923i \(-0.658929\pi\)
−0.478802 + 0.877923i \(0.658929\pi\)
\(558\) 0.0951611 0.00402849
\(559\) 51.9083 2.19549
\(560\) 0 0
\(561\) −2.72236 −0.114938
\(562\) −0.0200107 −0.000844100 0
\(563\) −10.1504 −0.427786 −0.213893 0.976857i \(-0.568614\pi\)
−0.213893 + 0.976857i \(0.568614\pi\)
\(564\) 23.5163 0.990213
\(565\) 25.8068 1.08570
\(566\) −0.450860 −0.0189511
\(567\) 0 0
\(568\) 1.30695 0.0548382
\(569\) 36.5753 1.53332 0.766659 0.642055i \(-0.221918\pi\)
0.766659 + 0.642055i \(0.221918\pi\)
\(570\) 0.347837 0.0145693
\(571\) 8.14486 0.340852 0.170426 0.985371i \(-0.445486\pi\)
0.170426 + 0.985371i \(0.445486\pi\)
\(572\) −5.44425 −0.227635
\(573\) −19.2346 −0.803538
\(574\) 0 0
\(575\) 2.71885 0.113384
\(576\) −7.98346 −0.332644
\(577\) −7.31887 −0.304689 −0.152344 0.988327i \(-0.548682\pi\)
−0.152344 + 0.988327i \(0.548682\pi\)
\(578\) −0.000151836 0 −6.31553e−6 0
\(579\) −17.4527 −0.725309
\(580\) 9.88864 0.410604
\(581\) 0 0
\(582\) 0.0666232 0.00276162
\(583\) −0.0401544 −0.00166303
\(584\) −1.50025 −0.0620810
\(585\) 11.4601 0.473816
\(586\) 0.0303436 0.00125348
\(587\) −46.8386 −1.93324 −0.966618 0.256223i \(-0.917522\pi\)
−0.966618 + 0.256223i \(0.917522\pi\)
\(588\) 0 0
\(589\) −17.2816 −0.712078
\(590\) 0.655596 0.0269905
\(591\) 1.16239 0.0478143
\(592\) −32.2151 −1.32403
\(593\) −16.0755 −0.660143 −0.330072 0.943956i \(-0.607073\pi\)
−0.330072 + 0.943956i \(0.607073\pi\)
\(594\) 0.0173334 0.000711197 0
\(595\) 0 0
\(596\) −38.1085 −1.56099
\(597\) −16.9768 −0.694816
\(598\) −0.108305 −0.00442891
\(599\) −27.5797 −1.12688 −0.563439 0.826158i \(-0.690522\pi\)
−0.563439 + 0.826158i \(0.690522\pi\)
\(600\) −0.285501 −0.0116555
\(601\) −32.9659 −1.34471 −0.672353 0.740231i \(-0.734716\pi\)
−0.672353 + 0.740231i \(0.734716\pi\)
\(602\) 0 0
\(603\) −2.68583 −0.109375
\(604\) 10.1223 0.411871
\(605\) −29.3503 −1.19326
\(606\) 0.176228 0.00715876
\(607\) −36.8404 −1.49531 −0.747653 0.664090i \(-0.768819\pi\)
−0.747653 + 0.664090i \(0.768819\pi\)
\(608\) −1.50169 −0.0609017
\(609\) 0 0
\(610\) −0.197884 −0.00801208
\(611\) 48.5176 1.96281
\(612\) −8.24477 −0.333275
\(613\) 22.1316 0.893887 0.446943 0.894562i \(-0.352513\pi\)
0.446943 + 0.894562i \(0.352513\pi\)
\(614\) −0.814909 −0.0328871
\(615\) 22.2254 0.896214
\(616\) 0 0
\(617\) 25.5349 1.02800 0.513998 0.857792i \(-0.328164\pi\)
0.513998 + 0.857792i \(0.328164\pi\)
\(618\) 0.282200 0.0113517
\(619\) 30.3835 1.22121 0.610607 0.791933i \(-0.290925\pi\)
0.610607 + 0.791933i \(0.290925\pi\)
\(620\) 20.1316 0.808506
\(621\) −1.00000 −0.0401286
\(622\) −0.462483 −0.0185439
\(623\) 0 0
\(624\) −16.4824 −0.659826
\(625\) −31.2021 −1.24808
\(626\) −0.413294 −0.0165185
\(627\) −3.14782 −0.125712
\(628\) 5.48586 0.218910
\(629\) −33.2466 −1.32563
\(630\) 0 0
\(631\) −23.5164 −0.936175 −0.468087 0.883682i \(-0.655057\pi\)
−0.468087 + 0.883682i \(0.655057\pi\)
\(632\) −0.729592 −0.0290216
\(633\) −11.6924 −0.464731
\(634\) 0.137095 0.00544475
\(635\) 6.66992 0.264688
\(636\) −0.121609 −0.00482213
\(637\) 0 0
\(638\) 0.0308577 0.00122167
\(639\) 12.4462 0.492363
\(640\) 2.33232 0.0921932
\(641\) 21.6111 0.853586 0.426793 0.904349i \(-0.359643\pi\)
0.426793 + 0.904349i \(0.359643\pi\)
\(642\) −0.0127227 −0.000502126 0
\(643\) −12.5132 −0.493472 −0.246736 0.969083i \(-0.579358\pi\)
−0.246736 + 0.969083i \(0.579358\pi\)
\(644\) 0 0
\(645\) −34.9625 −1.37665
\(646\) −0.516295 −0.0203133
\(647\) 18.8434 0.740811 0.370405 0.928870i \(-0.379219\pi\)
0.370405 + 0.928870i \(0.379219\pi\)
\(648\) 0.105008 0.00412510
\(649\) −5.93294 −0.232888
\(650\) −0.294465 −0.0115499
\(651\) 0 0
\(652\) −30.6071 −1.19866
\(653\) 32.6635 1.27822 0.639111 0.769115i \(-0.279303\pi\)
0.639111 + 0.769115i \(0.279303\pi\)
\(654\) 0.327293 0.0127982
\(655\) −55.9837 −2.18747
\(656\) −31.9657 −1.24805
\(657\) −14.2871 −0.557392
\(658\) 0 0
\(659\) −31.3480 −1.22114 −0.610571 0.791961i \(-0.709060\pi\)
−0.610571 + 0.791961i \(0.709060\pi\)
\(660\) 3.66694 0.142735
\(661\) 37.9924 1.47773 0.738866 0.673852i \(-0.235362\pi\)
0.738866 + 0.673852i \(0.235362\pi\)
\(662\) 0.366145 0.0142306
\(663\) −17.0102 −0.660621
\(664\) 0.987973 0.0383408
\(665\) 0 0
\(666\) 0.211683 0.00820253
\(667\) −1.78025 −0.0689314
\(668\) −25.9943 −1.00575
\(669\) 15.5087 0.599601
\(670\) 0.195926 0.00756927
\(671\) 1.79079 0.0691325
\(672\) 0 0
\(673\) 10.3170 0.397691 0.198845 0.980031i \(-0.436281\pi\)
0.198845 + 0.980031i \(0.436281\pi\)
\(674\) −0.243830 −0.00939197
\(675\) −2.71885 −0.104649
\(676\) −8.02645 −0.308710
\(677\) −27.3198 −1.04999 −0.524993 0.851106i \(-0.675932\pi\)
−0.524993 + 0.851106i \(0.675932\pi\)
\(678\) 0.243890 0.00936654
\(679\) 0 0
\(680\) 1.20309 0.0461362
\(681\) 15.3330 0.587560
\(682\) 0.0628212 0.00240555
\(683\) −21.3082 −0.815337 −0.407669 0.913130i \(-0.633658\pi\)
−0.407669 + 0.913130i \(0.633658\pi\)
\(684\) −9.53329 −0.364514
\(685\) 19.4663 0.743768
\(686\) 0 0
\(687\) 6.40484 0.244360
\(688\) 50.2848 1.91709
\(689\) −0.250898 −0.00955847
\(690\) 0.0729480 0.00277708
\(691\) −20.6702 −0.786332 −0.393166 0.919467i \(-0.628620\pi\)
−0.393166 + 0.919467i \(0.628620\pi\)
\(692\) 20.8369 0.792099
\(693\) 0 0
\(694\) −0.201517 −0.00764949
\(695\) −8.01563 −0.304050
\(696\) 0.186940 0.00708594
\(697\) −32.9892 −1.24955
\(698\) −0.150167 −0.00568391
\(699\) 26.1430 0.988821
\(700\) 0 0
\(701\) −1.93401 −0.0730465 −0.0365232 0.999333i \(-0.511628\pi\)
−0.0365232 + 0.999333i \(0.511628\pi\)
\(702\) 0.108305 0.00408770
\(703\) −38.4425 −1.44988
\(704\) −5.27033 −0.198633
\(705\) −32.6787 −1.23075
\(706\) −0.352352 −0.0132609
\(707\) 0 0
\(708\) −17.9681 −0.675284
\(709\) 25.3329 0.951396 0.475698 0.879609i \(-0.342196\pi\)
0.475698 + 0.879609i \(0.342196\pi\)
\(710\) −0.907923 −0.0340737
\(711\) −6.94797 −0.260569
\(712\) −0.622098 −0.0233141
\(713\) −3.62429 −0.135731
\(714\) 0 0
\(715\) 7.56544 0.282931
\(716\) −38.4330 −1.43631
\(717\) −17.6773 −0.660170
\(718\) −0.469094 −0.0175064
\(719\) −11.7275 −0.437361 −0.218681 0.975796i \(-0.570175\pi\)
−0.218681 + 0.975796i \(0.570175\pi\)
\(720\) 11.1016 0.413734
\(721\) 0 0
\(722\) −0.0981095 −0.00365126
\(723\) −5.75969 −0.214205
\(724\) 22.3028 0.828876
\(725\) −4.84023 −0.179762
\(726\) −0.277379 −0.0102945
\(727\) 13.4547 0.499007 0.249503 0.968374i \(-0.419733\pi\)
0.249503 + 0.968374i \(0.419733\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 1.04221 0.0385740
\(731\) 51.8948 1.91940
\(732\) 5.42347 0.200457
\(733\) 20.7942 0.768051 0.384025 0.923323i \(-0.374538\pi\)
0.384025 + 0.923323i \(0.374538\pi\)
\(734\) −0.686664 −0.0253452
\(735\) 0 0
\(736\) −0.314933 −0.0116086
\(737\) −1.77307 −0.0653117
\(738\) 0.210044 0.00773182
\(739\) −23.3524 −0.859034 −0.429517 0.903059i \(-0.641316\pi\)
−0.429517 + 0.903059i \(0.641316\pi\)
\(740\) 44.7822 1.64623
\(741\) −19.6686 −0.722544
\(742\) 0 0
\(743\) 6.11578 0.224366 0.112183 0.993688i \(-0.464216\pi\)
0.112183 + 0.993688i \(0.464216\pi\)
\(744\) 0.380579 0.0139527
\(745\) 52.9564 1.94017
\(746\) −0.528544 −0.0193514
\(747\) 9.40856 0.344241
\(748\) −5.44284 −0.199010
\(749\) 0 0
\(750\) −0.166405 −0.00607625
\(751\) 24.5032 0.894136 0.447068 0.894500i \(-0.352468\pi\)
0.447068 + 0.894500i \(0.352468\pi\)
\(752\) 47.0001 1.71392
\(753\) 10.3866 0.378509
\(754\) 0.192809 0.00702170
\(755\) −14.0662 −0.511920
\(756\) 0 0
\(757\) 23.0058 0.836160 0.418080 0.908410i \(-0.362703\pi\)
0.418080 + 0.908410i \(0.362703\pi\)
\(758\) −0.211337 −0.00767612
\(759\) −0.660156 −0.0239621
\(760\) 1.39111 0.0504608
\(761\) −10.6470 −0.385953 −0.192976 0.981203i \(-0.561814\pi\)
−0.192976 + 0.981203i \(0.561814\pi\)
\(762\) 0.0630349 0.00228351
\(763\) 0 0
\(764\) −38.4560 −1.39129
\(765\) 11.4571 0.414232
\(766\) −0.526952 −0.0190395
\(767\) −37.0710 −1.33856
\(768\) −15.9449 −0.575361
\(769\) 17.0235 0.613883 0.306942 0.951728i \(-0.400694\pi\)
0.306942 + 0.951728i \(0.400694\pi\)
\(770\) 0 0
\(771\) 2.69848 0.0971834
\(772\) −34.8933 −1.25584
\(773\) −7.84327 −0.282103 −0.141051 0.990002i \(-0.545048\pi\)
−0.141051 + 0.990002i \(0.545048\pi\)
\(774\) −0.330417 −0.0118766
\(775\) −9.85391 −0.353963
\(776\) 0.266447 0.00956488
\(777\) 0 0
\(778\) −0.326936 −0.0117212
\(779\) −38.1448 −1.36668
\(780\) 22.9122 0.820390
\(781\) 8.21642 0.294007
\(782\) −0.108277 −0.00387197
\(783\) 1.78025 0.0636208
\(784\) 0 0
\(785\) −7.62327 −0.272086
\(786\) −0.529081 −0.0188717
\(787\) −40.9580 −1.45999 −0.729997 0.683450i \(-0.760479\pi\)
−0.729997 + 0.683450i \(0.760479\pi\)
\(788\) 2.32398 0.0827883
\(789\) 21.1490 0.752926
\(790\) 0.506840 0.0180326
\(791\) 0 0
\(792\) 0.0693216 0.00246324
\(793\) 11.1894 0.397348
\(794\) 0.182096 0.00646235
\(795\) 0.168991 0.00599349
\(796\) −33.9420 −1.20304
\(797\) −11.8092 −0.418303 −0.209151 0.977883i \(-0.567070\pi\)
−0.209151 + 0.977883i \(0.567070\pi\)
\(798\) 0 0
\(799\) 48.5050 1.71598
\(800\) −0.856257 −0.0302733
\(801\) −5.92430 −0.209325
\(802\) 0.378517 0.0133659
\(803\) −9.43170 −0.332837
\(804\) −5.36981 −0.189378
\(805\) 0 0
\(806\) 0.392528 0.0138262
\(807\) 28.5411 1.00469
\(808\) 0.704789 0.0247944
\(809\) 13.0478 0.458736 0.229368 0.973340i \(-0.426334\pi\)
0.229368 + 0.973340i \(0.426334\pi\)
\(810\) −0.0729480 −0.00256313
\(811\) −51.3449 −1.80296 −0.901481 0.432818i \(-0.857519\pi\)
−0.901481 + 0.432818i \(0.857519\pi\)
\(812\) 0 0
\(813\) −15.1472 −0.531237
\(814\) 0.139744 0.00489801
\(815\) 42.5322 1.48984
\(816\) −16.4782 −0.576851
\(817\) 60.0051 2.09931
\(818\) −0.630851 −0.0220572
\(819\) 0 0
\(820\) 44.4355 1.55175
\(821\) 56.3021 1.96496 0.982479 0.186374i \(-0.0596737\pi\)
0.982479 + 0.186374i \(0.0596737\pi\)
\(822\) 0.183968 0.00641663
\(823\) −13.5565 −0.472551 −0.236276 0.971686i \(-0.575927\pi\)
−0.236276 + 0.971686i \(0.575927\pi\)
\(824\) 1.12860 0.0393168
\(825\) −1.79487 −0.0624893
\(826\) 0 0
\(827\) 3.80574 0.132339 0.0661693 0.997808i \(-0.478922\pi\)
0.0661693 + 0.997808i \(0.478922\pi\)
\(828\) −1.99931 −0.0694808
\(829\) −38.8924 −1.35079 −0.675395 0.737457i \(-0.736027\pi\)
−0.675395 + 0.737457i \(0.736027\pi\)
\(830\) −0.686335 −0.0238230
\(831\) −4.23717 −0.146986
\(832\) −32.9308 −1.14167
\(833\) 0 0
\(834\) −0.0757527 −0.00262310
\(835\) 36.1222 1.25006
\(836\) −6.29346 −0.217664
\(837\) 3.62429 0.125274
\(838\) −0.837440 −0.0289289
\(839\) 5.77279 0.199299 0.0996495 0.995023i \(-0.468228\pi\)
0.0996495 + 0.995023i \(0.468228\pi\)
\(840\) 0 0
\(841\) −25.8307 −0.890715
\(842\) 0.494672 0.0170475
\(843\) −0.762123 −0.0262489
\(844\) −23.3767 −0.804661
\(845\) 11.1537 0.383700
\(846\) −0.308834 −0.0106179
\(847\) 0 0
\(848\) −0.243051 −0.00834641
\(849\) −17.1714 −0.589321
\(850\) −0.294388 −0.0100974
\(851\) −8.06211 −0.276365
\(852\) 24.8838 0.852504
\(853\) 6.63846 0.227296 0.113648 0.993521i \(-0.463746\pi\)
0.113648 + 0.993521i \(0.463746\pi\)
\(854\) 0 0
\(855\) 13.2477 0.453060
\(856\) −0.0508822 −0.00173912
\(857\) −25.7842 −0.880770 −0.440385 0.897809i \(-0.645158\pi\)
−0.440385 + 0.897809i \(0.645158\pi\)
\(858\) 0.0714981 0.00244090
\(859\) 21.1070 0.720162 0.360081 0.932921i \(-0.382749\pi\)
0.360081 + 0.932921i \(0.382749\pi\)
\(860\) −69.9008 −2.38360
\(861\) 0 0
\(862\) 0.954242 0.0325016
\(863\) 12.4548 0.423965 0.211982 0.977273i \(-0.432008\pi\)
0.211982 + 0.977273i \(0.432008\pi\)
\(864\) 0.314933 0.0107142
\(865\) −28.9553 −0.984511
\(866\) −0.565791 −0.0192264
\(867\) −0.00578278 −0.000196394 0
\(868\) 0 0
\(869\) −4.58675 −0.155595
\(870\) −0.129865 −0.00440285
\(871\) −11.0787 −0.375388
\(872\) 1.30894 0.0443265
\(873\) 2.53740 0.0858779
\(874\) −0.125199 −0.00423490
\(875\) 0 0
\(876\) −28.5643 −0.965098
\(877\) −45.9072 −1.55018 −0.775088 0.631854i \(-0.782294\pi\)
−0.775088 + 0.631854i \(0.782294\pi\)
\(878\) 0.281929 0.00951465
\(879\) 1.15566 0.0389794
\(880\) 7.32881 0.247054
\(881\) 17.7656 0.598539 0.299269 0.954169i \(-0.403257\pi\)
0.299269 + 0.954169i \(0.403257\pi\)
\(882\) 0 0
\(883\) 8.07698 0.271812 0.135906 0.990722i \(-0.456605\pi\)
0.135906 + 0.990722i \(0.456605\pi\)
\(884\) −34.0087 −1.14384
\(885\) 24.9689 0.839320
\(886\) 0.891489 0.0299502
\(887\) −51.6718 −1.73497 −0.867484 0.497464i \(-0.834265\pi\)
−0.867484 + 0.497464i \(0.834265\pi\)
\(888\) 0.846585 0.0284095
\(889\) 0 0
\(890\) 0.432166 0.0144862
\(891\) 0.660156 0.0221161
\(892\) 31.0067 1.03818
\(893\) 56.0855 1.87683
\(894\) 0.500470 0.0167382
\(895\) 53.4073 1.78521
\(896\) 0 0
\(897\) −4.12488 −0.137726
\(898\) −0.182278 −0.00608268
\(899\) 6.45212 0.215190
\(900\) −5.43583 −0.181194
\(901\) −0.250833 −0.00835647
\(902\) 0.138662 0.00461693
\(903\) 0 0
\(904\) 0.975392 0.0324411
\(905\) −30.9924 −1.03022
\(906\) −0.132934 −0.00441643
\(907\) 38.7795 1.28765 0.643826 0.765172i \(-0.277346\pi\)
0.643826 + 0.765172i \(0.277346\pi\)
\(908\) 30.6553 1.01733
\(909\) 6.71178 0.222616
\(910\) 0 0
\(911\) 9.13030 0.302500 0.151250 0.988496i \(-0.451670\pi\)
0.151250 + 0.988496i \(0.451670\pi\)
\(912\) −19.0534 −0.630922
\(913\) 6.21112 0.205558
\(914\) 1.03847 0.0343495
\(915\) −7.53656 −0.249151
\(916\) 12.8053 0.423098
\(917\) 0 0
\(918\) 0.108277 0.00357366
\(919\) 3.74922 0.123675 0.0618377 0.998086i \(-0.480304\pi\)
0.0618377 + 0.998086i \(0.480304\pi\)
\(920\) 0.291742 0.00961843
\(921\) −31.0365 −1.02269
\(922\) 0.128810 0.00424212
\(923\) 51.3389 1.68984
\(924\) 0 0
\(925\) −21.9197 −0.720715
\(926\) 0.0202728 0.000666206 0
\(927\) 10.7478 0.353004
\(928\) 0.560658 0.0184045
\(929\) 44.4320 1.45777 0.728883 0.684638i \(-0.240040\pi\)
0.728883 + 0.684638i \(0.240040\pi\)
\(930\) −0.264384 −0.00866950
\(931\) 0 0
\(932\) 52.2681 1.71210
\(933\) −17.6141 −0.576658
\(934\) 0.504065 0.0164935
\(935\) 7.56347 0.247352
\(936\) 0.433145 0.0141578
\(937\) 59.8482 1.95516 0.977579 0.210571i \(-0.0675324\pi\)
0.977579 + 0.210571i \(0.0675324\pi\)
\(938\) 0 0
\(939\) −15.7406 −0.513676
\(940\) −65.3348 −2.13099
\(941\) 21.7078 0.707654 0.353827 0.935311i \(-0.384880\pi\)
0.353827 + 0.935311i \(0.384880\pi\)
\(942\) −0.0720446 −0.00234734
\(943\) −7.99969 −0.260506
\(944\) −35.9115 −1.16882
\(945\) 0 0
\(946\) −0.218127 −0.00709191
\(947\) 16.5648 0.538285 0.269143 0.963100i \(-0.413260\pi\)
0.269143 + 0.963100i \(0.413260\pi\)
\(948\) −13.8912 −0.451164
\(949\) −58.9324 −1.91303
\(950\) −0.340396 −0.0110439
\(951\) 5.22139 0.169315
\(952\) 0 0
\(953\) 51.8971 1.68111 0.840555 0.541726i \(-0.182229\pi\)
0.840555 + 0.541726i \(0.182229\pi\)
\(954\) 0.00159707 5.17070e−5 0
\(955\) 53.4392 1.72925
\(956\) −35.3424 −1.14305
\(957\) 1.17524 0.0379901
\(958\) 0.478142 0.0154481
\(959\) 0 0
\(960\) 22.1803 0.715866
\(961\) −17.8645 −0.576276
\(962\) 0.873165 0.0281520
\(963\) −0.484556 −0.0156146
\(964\) −11.5154 −0.370886
\(965\) 48.4885 1.56090
\(966\) 0 0
\(967\) −1.28492 −0.0413202 −0.0206601 0.999787i \(-0.506577\pi\)
−0.0206601 + 0.999787i \(0.506577\pi\)
\(968\) −1.10932 −0.0356550
\(969\) −19.6635 −0.631683
\(970\) −0.185098 −0.00594314
\(971\) −50.4972 −1.62053 −0.810266 0.586063i \(-0.800677\pi\)
−0.810266 + 0.586063i \(0.800677\pi\)
\(972\) 1.99931 0.0641279
\(973\) 0 0
\(974\) 0.758321 0.0242982
\(975\) −11.2149 −0.359165
\(976\) 10.8395 0.346963
\(977\) −5.77501 −0.184759 −0.0923794 0.995724i \(-0.529447\pi\)
−0.0923794 + 0.995724i \(0.529447\pi\)
\(978\) 0.401955 0.0128531
\(979\) −3.91096 −0.124995
\(980\) 0 0
\(981\) 12.4652 0.397983
\(982\) 0.621797 0.0198423
\(983\) 44.3068 1.41317 0.706584 0.707629i \(-0.250235\pi\)
0.706584 + 0.707629i \(0.250235\pi\)
\(984\) 0.840030 0.0267792
\(985\) −3.22945 −0.102899
\(986\) 0.192759 0.00613870
\(987\) 0 0
\(988\) −39.3237 −1.25105
\(989\) 12.5842 0.400154
\(990\) −0.0481570 −0.00153053
\(991\) 9.45792 0.300441 0.150220 0.988653i \(-0.452002\pi\)
0.150220 + 0.988653i \(0.452002\pi\)
\(992\) 1.14141 0.0362397
\(993\) 13.9449 0.442529
\(994\) 0 0
\(995\) 47.1665 1.49528
\(996\) 18.8106 0.596038
\(997\) −33.4467 −1.05927 −0.529635 0.848226i \(-0.677671\pi\)
−0.529635 + 0.848226i \(0.677671\pi\)
\(998\) −0.666124 −0.0210858
\(999\) 8.06211 0.255074
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 3381.2.a.bi.1.5 10
7.2 even 3 483.2.i.h.277.6 20
7.4 even 3 483.2.i.h.415.6 yes 20
7.6 odd 2 3381.2.a.bj.1.5 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
483.2.i.h.277.6 20 7.2 even 3
483.2.i.h.415.6 yes 20 7.4 even 3
3381.2.a.bi.1.5 10 1.1 even 1 trivial
3381.2.a.bj.1.5 10 7.6 odd 2