Properties

Label 6003.2.a.m.1.6
Level $6003$
Weight $2$
Character 6003.1
Self dual yes
Analytic conductor $47.934$
Analytic rank $1$
Dimension $11$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 6003 = 3^{2} \cdot 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6003.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(47.9341963334\)
Analytic rank: \(1\)
Dimension: \(11\)
Coefficient field: \(\mathbb{Q}[x]/(x^{11} - \cdots)\)
Defining polynomial: \(x^{11} - 2 x^{10} - 18 x^{9} + 30 x^{8} + 124 x^{7} - 152 x^{6} - 408 x^{5} + 285 x^{4} + 634 x^{3} - 93 x^{2} - 369 x - 108\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 2001)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(-0.467085\) of defining polynomial
Character \(\chi\) \(=\) 6003.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.467085 q^{2} -1.78183 q^{4} +0.0105419 q^{5} -1.85912 q^{7} -1.76644 q^{8} +O(q^{10})\) \(q+0.467085 q^{2} -1.78183 q^{4} +0.0105419 q^{5} -1.85912 q^{7} -1.76644 q^{8} +0.00492395 q^{10} +1.01164 q^{11} +2.69792 q^{13} -0.868368 q^{14} +2.73859 q^{16} +3.50932 q^{17} -7.48241 q^{19} -0.0187838 q^{20} +0.472521 q^{22} -1.00000 q^{23} -4.99989 q^{25} +1.26016 q^{26} +3.31264 q^{28} +1.00000 q^{29} +9.06687 q^{31} +4.81203 q^{32} +1.63915 q^{34} -0.0195986 q^{35} -3.80689 q^{37} -3.49493 q^{38} -0.0186215 q^{40} -0.921766 q^{41} +5.98292 q^{43} -1.80257 q^{44} -0.467085 q^{46} +8.75713 q^{47} -3.54367 q^{49} -2.33537 q^{50} -4.80723 q^{52} +9.78399 q^{53} +0.0106645 q^{55} +3.28402 q^{56} +0.467085 q^{58} -13.5157 q^{59} -1.50283 q^{61} +4.23500 q^{62} -3.22954 q^{64} +0.0284411 q^{65} -7.98178 q^{67} -6.25302 q^{68} -0.00915421 q^{70} -3.19615 q^{71} +12.3494 q^{73} -1.77814 q^{74} +13.3324 q^{76} -1.88076 q^{77} +9.57497 q^{79} +0.0288698 q^{80} -0.430543 q^{82} -15.0096 q^{83} +0.0369947 q^{85} +2.79453 q^{86} -1.78699 q^{88} -9.07903 q^{89} -5.01575 q^{91} +1.78183 q^{92} +4.09033 q^{94} -0.0788785 q^{95} +1.28711 q^{97} -1.65520 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11q - 2q^{2} + 18q^{4} - 2q^{5} + 3q^{7} - 18q^{8} + O(q^{10}) \) \( 11q - 2q^{2} + 18q^{4} - 2q^{5} + 3q^{7} - 18q^{8} + 14q^{10} - 11q^{11} - 5q^{13} - 17q^{14} + 20q^{16} - 15q^{17} - 6q^{19} - 21q^{20} - 10q^{22} - 11q^{23} + 3q^{25} + 5q^{26} + 7q^{28} + 11q^{29} + 35q^{31} - 28q^{32} + 28q^{34} - 15q^{35} - 28q^{37} + 2q^{38} - q^{40} - 10q^{41} - 6q^{43} - 18q^{44} + 2q^{46} - 15q^{47} + 22q^{49} - 15q^{50} - 36q^{52} + 7q^{53} - 12q^{55} - 56q^{56} - 2q^{58} + 20q^{59} - 20q^{61} + 11q^{62} + 36q^{64} - 11q^{65} - 39q^{67} - 35q^{68} + 38q^{70} - 49q^{71} - 3q^{73} - 37q^{74} - 18q^{76} - 25q^{77} + 41q^{79} - 51q^{80} - 19q^{82} - 13q^{83} - 62q^{86} - 40q^{88} - 34q^{89} + 2q^{91} - 18q^{92} - 14q^{94} - 25q^{95} - 11q^{97} - 53q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.467085 0.330279 0.165140 0.986270i \(-0.447193\pi\)
0.165140 + 0.986270i \(0.447193\pi\)
\(3\) 0 0
\(4\) −1.78183 −0.890916
\(5\) 0.0105419 0.00471446 0.00235723 0.999997i \(-0.499250\pi\)
0.00235723 + 0.999997i \(0.499250\pi\)
\(6\) 0 0
\(7\) −1.85912 −0.702682 −0.351341 0.936248i \(-0.614274\pi\)
−0.351341 + 0.936248i \(0.614274\pi\)
\(8\) −1.76644 −0.624530
\(9\) 0 0
\(10\) 0.00492395 0.00155709
\(11\) 1.01164 0.305020 0.152510 0.988302i \(-0.451264\pi\)
0.152510 + 0.988302i \(0.451264\pi\)
\(12\) 0 0
\(13\) 2.69792 0.748268 0.374134 0.927375i \(-0.377940\pi\)
0.374134 + 0.927375i \(0.377940\pi\)
\(14\) −0.868368 −0.232081
\(15\) 0 0
\(16\) 2.73859 0.684646
\(17\) 3.50932 0.851135 0.425568 0.904927i \(-0.360074\pi\)
0.425568 + 0.904927i \(0.360074\pi\)
\(18\) 0 0
\(19\) −7.48241 −1.71658 −0.858292 0.513162i \(-0.828474\pi\)
−0.858292 + 0.513162i \(0.828474\pi\)
\(20\) −0.0187838 −0.00420019
\(21\) 0 0
\(22\) 0.472521 0.100742
\(23\) −1.00000 −0.208514
\(24\) 0 0
\(25\) −4.99989 −0.999978
\(26\) 1.26016 0.247137
\(27\) 0 0
\(28\) 3.31264 0.626030
\(29\) 1.00000 0.185695
\(30\) 0 0
\(31\) 9.06687 1.62846 0.814229 0.580544i \(-0.197160\pi\)
0.814229 + 0.580544i \(0.197160\pi\)
\(32\) 4.81203 0.850655
\(33\) 0 0
\(34\) 1.63915 0.281112
\(35\) −0.0195986 −0.00331276
\(36\) 0 0
\(37\) −3.80689 −0.625850 −0.312925 0.949778i \(-0.601309\pi\)
−0.312925 + 0.949778i \(0.601309\pi\)
\(38\) −3.49493 −0.566952
\(39\) 0 0
\(40\) −0.0186215 −0.00294432
\(41\) −0.921766 −0.143956 −0.0719778 0.997406i \(-0.522931\pi\)
−0.0719778 + 0.997406i \(0.522931\pi\)
\(42\) 0 0
\(43\) 5.98292 0.912386 0.456193 0.889881i \(-0.349213\pi\)
0.456193 + 0.889881i \(0.349213\pi\)
\(44\) −1.80257 −0.271747
\(45\) 0 0
\(46\) −0.467085 −0.0688680
\(47\) 8.75713 1.27736 0.638679 0.769473i \(-0.279481\pi\)
0.638679 + 0.769473i \(0.279481\pi\)
\(48\) 0 0
\(49\) −3.54367 −0.506239
\(50\) −2.33537 −0.330272
\(51\) 0 0
\(52\) −4.80723 −0.666643
\(53\) 9.78399 1.34393 0.671967 0.740581i \(-0.265449\pi\)
0.671967 + 0.740581i \(0.265449\pi\)
\(54\) 0 0
\(55\) 0.0106645 0.00143800
\(56\) 3.28402 0.438846
\(57\) 0 0
\(58\) 0.467085 0.0613313
\(59\) −13.5157 −1.75960 −0.879799 0.475346i \(-0.842323\pi\)
−0.879799 + 0.475346i \(0.842323\pi\)
\(60\) 0 0
\(61\) −1.50283 −0.192418 −0.0962088 0.995361i \(-0.530672\pi\)
−0.0962088 + 0.995361i \(0.530672\pi\)
\(62\) 4.23500 0.537846
\(63\) 0 0
\(64\) −3.22954 −0.403693
\(65\) 0.0284411 0.00352768
\(66\) 0 0
\(67\) −7.98178 −0.975130 −0.487565 0.873087i \(-0.662115\pi\)
−0.487565 + 0.873087i \(0.662115\pi\)
\(68\) −6.25302 −0.758290
\(69\) 0 0
\(70\) −0.00915421 −0.00109414
\(71\) −3.19615 −0.379313 −0.189656 0.981851i \(-0.560737\pi\)
−0.189656 + 0.981851i \(0.560737\pi\)
\(72\) 0 0
\(73\) 12.3494 1.44539 0.722694 0.691168i \(-0.242903\pi\)
0.722694 + 0.691168i \(0.242903\pi\)
\(74\) −1.77814 −0.206705
\(75\) 0 0
\(76\) 13.3324 1.52933
\(77\) −1.88076 −0.214332
\(78\) 0 0
\(79\) 9.57497 1.07727 0.538634 0.842540i \(-0.318941\pi\)
0.538634 + 0.842540i \(0.318941\pi\)
\(80\) 0.0288698 0.00322774
\(81\) 0 0
\(82\) −0.430543 −0.0475455
\(83\) −15.0096 −1.64752 −0.823760 0.566939i \(-0.808128\pi\)
−0.823760 + 0.566939i \(0.808128\pi\)
\(84\) 0 0
\(85\) 0.0369947 0.00401264
\(86\) 2.79453 0.301342
\(87\) 0 0
\(88\) −1.78699 −0.190494
\(89\) −9.07903 −0.962376 −0.481188 0.876617i \(-0.659795\pi\)
−0.481188 + 0.876617i \(0.659795\pi\)
\(90\) 0 0
\(91\) −5.01575 −0.525794
\(92\) 1.78183 0.185769
\(93\) 0 0
\(94\) 4.09033 0.421885
\(95\) −0.0788785 −0.00809276
\(96\) 0 0
\(97\) 1.28711 0.130686 0.0653432 0.997863i \(-0.479186\pi\)
0.0653432 + 0.997863i \(0.479186\pi\)
\(98\) −1.65520 −0.167200
\(99\) 0 0
\(100\) 8.90896 0.890896
\(101\) −17.9301 −1.78411 −0.892054 0.451929i \(-0.850736\pi\)
−0.892054 + 0.451929i \(0.850736\pi\)
\(102\) 0 0
\(103\) 16.4218 1.61809 0.809044 0.587748i \(-0.199985\pi\)
0.809044 + 0.587748i \(0.199985\pi\)
\(104\) −4.76570 −0.467316
\(105\) 0 0
\(106\) 4.56996 0.443874
\(107\) −3.00179 −0.290194 −0.145097 0.989417i \(-0.546349\pi\)
−0.145097 + 0.989417i \(0.546349\pi\)
\(108\) 0 0
\(109\) −13.8887 −1.33030 −0.665150 0.746710i \(-0.731632\pi\)
−0.665150 + 0.746710i \(0.731632\pi\)
\(110\) 0.00498125 0.000474943 0
\(111\) 0 0
\(112\) −5.09136 −0.481088
\(113\) 2.10899 0.198397 0.0991984 0.995068i \(-0.468372\pi\)
0.0991984 + 0.995068i \(0.468372\pi\)
\(114\) 0 0
\(115\) −0.0105419 −0.000983033 0
\(116\) −1.78183 −0.165439
\(117\) 0 0
\(118\) −6.31300 −0.581159
\(119\) −6.52425 −0.598077
\(120\) 0 0
\(121\) −9.97659 −0.906963
\(122\) −0.701949 −0.0635515
\(123\) 0 0
\(124\) −16.1556 −1.45082
\(125\) −0.105417 −0.00942882
\(126\) 0 0
\(127\) 17.6790 1.56876 0.784380 0.620281i \(-0.212981\pi\)
0.784380 + 0.620281i \(0.212981\pi\)
\(128\) −11.1325 −0.983986
\(129\) 0 0
\(130\) 0.0132844 0.00116512
\(131\) 4.77362 0.417073 0.208536 0.978015i \(-0.433130\pi\)
0.208536 + 0.978015i \(0.433130\pi\)
\(132\) 0 0
\(133\) 13.9107 1.20621
\(134\) −3.72817 −0.322065
\(135\) 0 0
\(136\) −6.19900 −0.531560
\(137\) −3.89537 −0.332804 −0.166402 0.986058i \(-0.553215\pi\)
−0.166402 + 0.986058i \(0.553215\pi\)
\(138\) 0 0
\(139\) 3.17159 0.269011 0.134505 0.990913i \(-0.457055\pi\)
0.134505 + 0.990913i \(0.457055\pi\)
\(140\) 0.0349214 0.00295139
\(141\) 0 0
\(142\) −1.49287 −0.125279
\(143\) 2.72931 0.228237
\(144\) 0 0
\(145\) 0.0105419 0.000875453 0
\(146\) 5.76823 0.477382
\(147\) 0 0
\(148\) 6.78324 0.557579
\(149\) −1.96821 −0.161242 −0.0806211 0.996745i \(-0.525690\pi\)
−0.0806211 + 0.996745i \(0.525690\pi\)
\(150\) 0 0
\(151\) −2.94743 −0.239859 −0.119929 0.992782i \(-0.538267\pi\)
−0.119929 + 0.992782i \(0.538267\pi\)
\(152\) 13.2172 1.07206
\(153\) 0 0
\(154\) −0.878473 −0.0707894
\(155\) 0.0955816 0.00767730
\(156\) 0 0
\(157\) −6.42396 −0.512688 −0.256344 0.966586i \(-0.582518\pi\)
−0.256344 + 0.966586i \(0.582518\pi\)
\(158\) 4.47233 0.355799
\(159\) 0 0
\(160\) 0.0507277 0.00401038
\(161\) 1.85912 0.146519
\(162\) 0 0
\(163\) 12.2619 0.960425 0.480212 0.877152i \(-0.340560\pi\)
0.480212 + 0.877152i \(0.340560\pi\)
\(164\) 1.64243 0.128252
\(165\) 0 0
\(166\) −7.01077 −0.544142
\(167\) −5.89625 −0.456266 −0.228133 0.973630i \(-0.573262\pi\)
−0.228133 + 0.973630i \(0.573262\pi\)
\(168\) 0 0
\(169\) −5.72124 −0.440095
\(170\) 0.0172797 0.00132529
\(171\) 0 0
\(172\) −10.6605 −0.812859
\(173\) 1.40065 0.106490 0.0532449 0.998581i \(-0.483044\pi\)
0.0532449 + 0.998581i \(0.483044\pi\)
\(174\) 0 0
\(175\) 9.29540 0.702666
\(176\) 2.77045 0.208831
\(177\) 0 0
\(178\) −4.24068 −0.317853
\(179\) −17.5946 −1.31508 −0.657539 0.753420i \(-0.728403\pi\)
−0.657539 + 0.753420i \(0.728403\pi\)
\(180\) 0 0
\(181\) −21.6515 −1.60934 −0.804672 0.593719i \(-0.797659\pi\)
−0.804672 + 0.593719i \(0.797659\pi\)
\(182\) −2.34279 −0.173659
\(183\) 0 0
\(184\) 1.76644 0.130224
\(185\) −0.0401317 −0.00295054
\(186\) 0 0
\(187\) 3.55016 0.259613
\(188\) −15.6037 −1.13802
\(189\) 0 0
\(190\) −0.0368430 −0.00267287
\(191\) −9.02504 −0.653029 −0.326514 0.945192i \(-0.605874\pi\)
−0.326514 + 0.945192i \(0.605874\pi\)
\(192\) 0 0
\(193\) 2.31723 0.166798 0.0833988 0.996516i \(-0.473422\pi\)
0.0833988 + 0.996516i \(0.473422\pi\)
\(194\) 0.601191 0.0431630
\(195\) 0 0
\(196\) 6.31422 0.451016
\(197\) −21.2889 −1.51677 −0.758384 0.651808i \(-0.774011\pi\)
−0.758384 + 0.651808i \(0.774011\pi\)
\(198\) 0 0
\(199\) −5.92224 −0.419816 −0.209908 0.977721i \(-0.567317\pi\)
−0.209908 + 0.977721i \(0.567317\pi\)
\(200\) 8.83199 0.624516
\(201\) 0 0
\(202\) −8.37487 −0.589254
\(203\) −1.85912 −0.130485
\(204\) 0 0
\(205\) −0.00971712 −0.000678673 0
\(206\) 7.67039 0.534421
\(207\) 0 0
\(208\) 7.38848 0.512299
\(209\) −7.56948 −0.523592
\(210\) 0 0
\(211\) 7.72273 0.531655 0.265828 0.964021i \(-0.414355\pi\)
0.265828 + 0.964021i \(0.414355\pi\)
\(212\) −17.4334 −1.19733
\(213\) 0 0
\(214\) −1.40209 −0.0958452
\(215\) 0.0630710 0.00430141
\(216\) 0 0
\(217\) −16.8564 −1.14429
\(218\) −6.48723 −0.439371
\(219\) 0 0
\(220\) −0.0190024 −0.00128114
\(221\) 9.46786 0.636877
\(222\) 0 0
\(223\) −10.9381 −0.732469 −0.366234 0.930523i \(-0.619353\pi\)
−0.366234 + 0.930523i \(0.619353\pi\)
\(224\) −8.94614 −0.597739
\(225\) 0 0
\(226\) 0.985077 0.0655263
\(227\) −21.4894 −1.42630 −0.713152 0.701010i \(-0.752733\pi\)
−0.713152 + 0.701010i \(0.752733\pi\)
\(228\) 0 0
\(229\) −10.3996 −0.687228 −0.343614 0.939111i \(-0.611651\pi\)
−0.343614 + 0.939111i \(0.611651\pi\)
\(230\) −0.00492395 −0.000324675 0
\(231\) 0 0
\(232\) −1.76644 −0.115972
\(233\) −9.36159 −0.613298 −0.306649 0.951823i \(-0.599208\pi\)
−0.306649 + 0.951823i \(0.599208\pi\)
\(234\) 0 0
\(235\) 0.0923164 0.00602206
\(236\) 24.0827 1.56765
\(237\) 0 0
\(238\) −3.04738 −0.197532
\(239\) −12.7171 −0.822603 −0.411302 0.911499i \(-0.634926\pi\)
−0.411302 + 0.911499i \(0.634926\pi\)
\(240\) 0 0
\(241\) −1.69211 −0.108999 −0.0544993 0.998514i \(-0.517356\pi\)
−0.0544993 + 0.998514i \(0.517356\pi\)
\(242\) −4.65992 −0.299551
\(243\) 0 0
\(244\) 2.67779 0.171428
\(245\) −0.0373568 −0.00238664
\(246\) 0 0
\(247\) −20.1869 −1.28446
\(248\) −16.0161 −1.01702
\(249\) 0 0
\(250\) −0.0492389 −0.00311414
\(251\) −8.84699 −0.558417 −0.279209 0.960230i \(-0.590072\pi\)
−0.279209 + 0.960230i \(0.590072\pi\)
\(252\) 0 0
\(253\) −1.01164 −0.0636011
\(254\) 8.25761 0.518129
\(255\) 0 0
\(256\) 1.25924 0.0787026
\(257\) 4.57937 0.285653 0.142827 0.989748i \(-0.454381\pi\)
0.142827 + 0.989748i \(0.454381\pi\)
\(258\) 0 0
\(259\) 7.07748 0.439773
\(260\) −0.0506772 −0.00314286
\(261\) 0 0
\(262\) 2.22969 0.137750
\(263\) −5.65466 −0.348681 −0.174341 0.984685i \(-0.555779\pi\)
−0.174341 + 0.984685i \(0.555779\pi\)
\(264\) 0 0
\(265\) 0.103141 0.00633593
\(266\) 6.49749 0.398387
\(267\) 0 0
\(268\) 14.2222 0.868759
\(269\) −14.8896 −0.907837 −0.453919 0.891043i \(-0.649974\pi\)
−0.453919 + 0.891043i \(0.649974\pi\)
\(270\) 0 0
\(271\) 11.4241 0.693965 0.346983 0.937872i \(-0.387206\pi\)
0.346983 + 0.937872i \(0.387206\pi\)
\(272\) 9.61057 0.582727
\(273\) 0 0
\(274\) −1.81947 −0.109918
\(275\) −5.05807 −0.305013
\(276\) 0 0
\(277\) −4.30028 −0.258379 −0.129189 0.991620i \(-0.541238\pi\)
−0.129189 + 0.991620i \(0.541238\pi\)
\(278\) 1.48140 0.0888487
\(279\) 0 0
\(280\) 0.0346197 0.00206892
\(281\) −25.7614 −1.53679 −0.768397 0.639973i \(-0.778946\pi\)
−0.768397 + 0.639973i \(0.778946\pi\)
\(282\) 0 0
\(283\) −26.5143 −1.57611 −0.788056 0.615604i \(-0.788912\pi\)
−0.788056 + 0.615604i \(0.788912\pi\)
\(284\) 5.69499 0.337936
\(285\) 0 0
\(286\) 1.27482 0.0753818
\(287\) 1.71367 0.101155
\(288\) 0 0
\(289\) −4.68467 −0.275569
\(290\) 0.00492395 0.000289144 0
\(291\) 0 0
\(292\) −22.0046 −1.28772
\(293\) 9.65842 0.564251 0.282126 0.959377i \(-0.408961\pi\)
0.282126 + 0.959377i \(0.408961\pi\)
\(294\) 0 0
\(295\) −0.142481 −0.00829555
\(296\) 6.72464 0.390862
\(297\) 0 0
\(298\) −0.919323 −0.0532550
\(299\) −2.69792 −0.156025
\(300\) 0 0
\(301\) −11.1230 −0.641117
\(302\) −1.37670 −0.0792203
\(303\) 0 0
\(304\) −20.4912 −1.17525
\(305\) −0.0158426 −0.000907145 0
\(306\) 0 0
\(307\) −9.87759 −0.563744 −0.281872 0.959452i \(-0.590955\pi\)
−0.281872 + 0.959452i \(0.590955\pi\)
\(308\) 3.35119 0.190952
\(309\) 0 0
\(310\) 0.0446448 0.00253565
\(311\) 24.0414 1.36326 0.681632 0.731695i \(-0.261270\pi\)
0.681632 + 0.731695i \(0.261270\pi\)
\(312\) 0 0
\(313\) −16.8236 −0.950924 −0.475462 0.879736i \(-0.657719\pi\)
−0.475462 + 0.879736i \(0.657719\pi\)
\(314\) −3.00054 −0.169330
\(315\) 0 0
\(316\) −17.0610 −0.959755
\(317\) −7.39291 −0.415227 −0.207614 0.978211i \(-0.566570\pi\)
−0.207614 + 0.978211i \(0.566570\pi\)
\(318\) 0 0
\(319\) 1.01164 0.0566408
\(320\) −0.0340454 −0.00190319
\(321\) 0 0
\(322\) 0.868368 0.0483923
\(323\) −26.2582 −1.46104
\(324\) 0 0
\(325\) −13.4893 −0.748251
\(326\) 5.72735 0.317208
\(327\) 0 0
\(328\) 1.62824 0.0899046
\(329\) −16.2806 −0.897577
\(330\) 0 0
\(331\) 6.93138 0.380983 0.190492 0.981689i \(-0.438992\pi\)
0.190492 + 0.981689i \(0.438992\pi\)
\(332\) 26.7446 1.46780
\(333\) 0 0
\(334\) −2.75405 −0.150695
\(335\) −0.0841428 −0.00459721
\(336\) 0 0
\(337\) 4.06977 0.221694 0.110847 0.993837i \(-0.464644\pi\)
0.110847 + 0.993837i \(0.464644\pi\)
\(338\) −2.67231 −0.145354
\(339\) 0 0
\(340\) −0.0659184 −0.00357493
\(341\) 9.17238 0.496712
\(342\) 0 0
\(343\) 19.6020 1.05841
\(344\) −10.5685 −0.569813
\(345\) 0 0
\(346\) 0.654225 0.0351714
\(347\) −7.42107 −0.398384 −0.199192 0.979960i \(-0.563832\pi\)
−0.199192 + 0.979960i \(0.563832\pi\)
\(348\) 0 0
\(349\) 24.6446 1.31919 0.659597 0.751619i \(-0.270727\pi\)
0.659597 + 0.751619i \(0.270727\pi\)
\(350\) 4.34174 0.232076
\(351\) 0 0
\(352\) 4.86803 0.259467
\(353\) 21.7155 1.15580 0.577901 0.816107i \(-0.303872\pi\)
0.577901 + 0.816107i \(0.303872\pi\)
\(354\) 0 0
\(355\) −0.0336933 −0.00178826
\(356\) 16.1773 0.857396
\(357\) 0 0
\(358\) −8.21816 −0.434343
\(359\) 11.8532 0.625587 0.312794 0.949821i \(-0.398735\pi\)
0.312794 + 0.949821i \(0.398735\pi\)
\(360\) 0 0
\(361\) 36.9865 1.94666
\(362\) −10.1131 −0.531533
\(363\) 0 0
\(364\) 8.93723 0.468438
\(365\) 0.130186 0.00681423
\(366\) 0 0
\(367\) −11.8459 −0.618349 −0.309174 0.951005i \(-0.600053\pi\)
−0.309174 + 0.951005i \(0.600053\pi\)
\(368\) −2.73859 −0.142759
\(369\) 0 0
\(370\) −0.0187449 −0.000974503 0
\(371\) −18.1896 −0.944358
\(372\) 0 0
\(373\) −34.5101 −1.78687 −0.893434 0.449195i \(-0.851711\pi\)
−0.893434 + 0.449195i \(0.851711\pi\)
\(374\) 1.65823 0.0857449
\(375\) 0 0
\(376\) −15.4689 −0.797749
\(377\) 2.69792 0.138950
\(378\) 0 0
\(379\) −3.08382 −0.158405 −0.0792027 0.996859i \(-0.525237\pi\)
−0.0792027 + 0.996859i \(0.525237\pi\)
\(380\) 0.140548 0.00720997
\(381\) 0 0
\(382\) −4.21546 −0.215682
\(383\) 24.4060 1.24709 0.623544 0.781788i \(-0.285692\pi\)
0.623544 + 0.781788i \(0.285692\pi\)
\(384\) 0 0
\(385\) −0.0198266 −0.00101046
\(386\) 1.08234 0.0550898
\(387\) 0 0
\(388\) −2.29342 −0.116431
\(389\) 0.324732 0.0164645 0.00823227 0.999966i \(-0.497380\pi\)
0.00823227 + 0.999966i \(0.497380\pi\)
\(390\) 0 0
\(391\) −3.50932 −0.177474
\(392\) 6.25967 0.316161
\(393\) 0 0
\(394\) −9.94371 −0.500957
\(395\) 0.100938 0.00507874
\(396\) 0 0
\(397\) 6.99747 0.351193 0.175596 0.984462i \(-0.443815\pi\)
0.175596 + 0.984462i \(0.443815\pi\)
\(398\) −2.76619 −0.138657
\(399\) 0 0
\(400\) −13.6926 −0.684631
\(401\) −18.5106 −0.924374 −0.462187 0.886782i \(-0.652935\pi\)
−0.462187 + 0.886782i \(0.652935\pi\)
\(402\) 0 0
\(403\) 24.4617 1.21852
\(404\) 31.9483 1.58949
\(405\) 0 0
\(406\) −0.868368 −0.0430964
\(407\) −3.85119 −0.190897
\(408\) 0 0
\(409\) −10.9316 −0.540533 −0.270266 0.962786i \(-0.587112\pi\)
−0.270266 + 0.962786i \(0.587112\pi\)
\(410\) −0.00453872 −0.000224152 0
\(411\) 0 0
\(412\) −29.2609 −1.44158
\(413\) 25.1274 1.23644
\(414\) 0 0
\(415\) −0.158229 −0.00776717
\(416\) 12.9825 0.636517
\(417\) 0 0
\(418\) −3.53560 −0.172932
\(419\) −25.7158 −1.25630 −0.628150 0.778092i \(-0.716188\pi\)
−0.628150 + 0.778092i \(0.716188\pi\)
\(420\) 0 0
\(421\) 34.0277 1.65841 0.829204 0.558945i \(-0.188794\pi\)
0.829204 + 0.558945i \(0.188794\pi\)
\(422\) 3.60718 0.175595
\(423\) 0 0
\(424\) −17.2828 −0.839328
\(425\) −17.5462 −0.851116
\(426\) 0 0
\(427\) 2.79394 0.135208
\(428\) 5.34869 0.258539
\(429\) 0 0
\(430\) 0.0294596 0.00142067
\(431\) 34.2245 1.64854 0.824269 0.566199i \(-0.191587\pi\)
0.824269 + 0.566199i \(0.191587\pi\)
\(432\) 0 0
\(433\) 9.01368 0.433170 0.216585 0.976264i \(-0.430508\pi\)
0.216585 + 0.976264i \(0.430508\pi\)
\(434\) −7.87338 −0.377934
\(435\) 0 0
\(436\) 24.7474 1.18519
\(437\) 7.48241 0.357932
\(438\) 0 0
\(439\) 29.1400 1.39078 0.695389 0.718633i \(-0.255232\pi\)
0.695389 + 0.718633i \(0.255232\pi\)
\(440\) −0.0188382 −0.000898077 0
\(441\) 0 0
\(442\) 4.42230 0.210347
\(443\) 40.2151 1.91068 0.955338 0.295516i \(-0.0954917\pi\)
0.955338 + 0.295516i \(0.0954917\pi\)
\(444\) 0 0
\(445\) −0.0957099 −0.00453708
\(446\) −5.10902 −0.241919
\(447\) 0 0
\(448\) 6.00411 0.283667
\(449\) −5.94087 −0.280367 −0.140183 0.990126i \(-0.544769\pi\)
−0.140183 + 0.990126i \(0.544769\pi\)
\(450\) 0 0
\(451\) −0.932492 −0.0439093
\(452\) −3.75786 −0.176755
\(453\) 0 0
\(454\) −10.0374 −0.471078
\(455\) −0.0528754 −0.00247883
\(456\) 0 0
\(457\) 9.12815 0.426997 0.213498 0.976943i \(-0.431514\pi\)
0.213498 + 0.976943i \(0.431514\pi\)
\(458\) −4.85752 −0.226977
\(459\) 0 0
\(460\) 0.0187838 0.000875799 0
\(461\) −29.1021 −1.35542 −0.677709 0.735330i \(-0.737027\pi\)
−0.677709 + 0.735330i \(0.737027\pi\)
\(462\) 0 0
\(463\) −19.7693 −0.918760 −0.459380 0.888240i \(-0.651928\pi\)
−0.459380 + 0.888240i \(0.651928\pi\)
\(464\) 2.73859 0.127136
\(465\) 0 0
\(466\) −4.37266 −0.202560
\(467\) −17.0583 −0.789366 −0.394683 0.918817i \(-0.629146\pi\)
−0.394683 + 0.918817i \(0.629146\pi\)
\(468\) 0 0
\(469\) 14.8391 0.685206
\(470\) 0.0431196 0.00198896
\(471\) 0 0
\(472\) 23.8747 1.09892
\(473\) 6.05254 0.278296
\(474\) 0 0
\(475\) 37.4112 1.71654
\(476\) 11.6251 0.532836
\(477\) 0 0
\(478\) −5.93999 −0.271689
\(479\) 17.3642 0.793392 0.396696 0.917950i \(-0.370157\pi\)
0.396696 + 0.917950i \(0.370157\pi\)
\(480\) 0 0
\(481\) −10.2707 −0.468303
\(482\) −0.790362 −0.0360000
\(483\) 0 0
\(484\) 17.7766 0.808027
\(485\) 0.0135685 0.000616116 0
\(486\) 0 0
\(487\) 39.5581 1.79255 0.896274 0.443500i \(-0.146263\pi\)
0.896274 + 0.443500i \(0.146263\pi\)
\(488\) 2.65465 0.120171
\(489\) 0 0
\(490\) −0.0174488 −0.000788258 0
\(491\) −8.63557 −0.389718 −0.194859 0.980831i \(-0.562425\pi\)
−0.194859 + 0.980831i \(0.562425\pi\)
\(492\) 0 0
\(493\) 3.50932 0.158052
\(494\) −9.42902 −0.424232
\(495\) 0 0
\(496\) 24.8304 1.11492
\(497\) 5.94202 0.266536
\(498\) 0 0
\(499\) −39.3668 −1.76230 −0.881150 0.472837i \(-0.843230\pi\)
−0.881150 + 0.472837i \(0.843230\pi\)
\(500\) 0.187836 0.00840028
\(501\) 0 0
\(502\) −4.13230 −0.184434
\(503\) 34.5468 1.54037 0.770183 0.637823i \(-0.220165\pi\)
0.770183 + 0.637823i \(0.220165\pi\)
\(504\) 0 0
\(505\) −0.189016 −0.00841111
\(506\) −0.472521 −0.0210061
\(507\) 0 0
\(508\) −31.5010 −1.39763
\(509\) 4.87692 0.216165 0.108083 0.994142i \(-0.465529\pi\)
0.108083 + 0.994142i \(0.465529\pi\)
\(510\) 0 0
\(511\) −22.9590 −1.01565
\(512\) 22.8532 1.00998
\(513\) 0 0
\(514\) 2.13896 0.0943454
\(515\) 0.173116 0.00762841
\(516\) 0 0
\(517\) 8.85904 0.389620
\(518\) 3.30579 0.145248
\(519\) 0 0
\(520\) −0.0502394 −0.00220314
\(521\) −28.3250 −1.24094 −0.620470 0.784230i \(-0.713058\pi\)
−0.620470 + 0.784230i \(0.713058\pi\)
\(522\) 0 0
\(523\) 9.04905 0.395687 0.197844 0.980234i \(-0.436606\pi\)
0.197844 + 0.980234i \(0.436606\pi\)
\(524\) −8.50578 −0.371577
\(525\) 0 0
\(526\) −2.64121 −0.115162
\(527\) 31.8185 1.38604
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0.0481759 0.00209263
\(531\) 0 0
\(532\) −24.7865 −1.07463
\(533\) −2.48685 −0.107717
\(534\) 0 0
\(535\) −0.0316445 −0.00136811
\(536\) 14.0993 0.608998
\(537\) 0 0
\(538\) −6.95473 −0.299840
\(539\) −3.58491 −0.154413
\(540\) 0 0
\(541\) −42.1779 −1.81337 −0.906685 0.421808i \(-0.861396\pi\)
−0.906685 + 0.421808i \(0.861396\pi\)
\(542\) 5.33604 0.229202
\(543\) 0 0
\(544\) 16.8870 0.724022
\(545\) −0.146413 −0.00627165
\(546\) 0 0
\(547\) −31.3645 −1.34105 −0.670525 0.741887i \(-0.733931\pi\)
−0.670525 + 0.741887i \(0.733931\pi\)
\(548\) 6.94089 0.296500
\(549\) 0 0
\(550\) −2.36255 −0.100740
\(551\) −7.48241 −0.318761
\(552\) 0 0
\(553\) −17.8010 −0.756977
\(554\) −2.00860 −0.0853372
\(555\) 0 0
\(556\) −5.65124 −0.239666
\(557\) 39.1429 1.65854 0.829269 0.558850i \(-0.188757\pi\)
0.829269 + 0.558850i \(0.188757\pi\)
\(558\) 0 0
\(559\) 16.1414 0.682709
\(560\) −0.0536724 −0.00226807
\(561\) 0 0
\(562\) −12.0328 −0.507571
\(563\) −18.0039 −0.758775 −0.379388 0.925238i \(-0.623865\pi\)
−0.379388 + 0.925238i \(0.623865\pi\)
\(564\) 0 0
\(565\) 0.0222326 0.000935334 0
\(566\) −12.3844 −0.520557
\(567\) 0 0
\(568\) 5.64580 0.236892
\(569\) −41.1091 −1.72338 −0.861691 0.507433i \(-0.830594\pi\)
−0.861691 + 0.507433i \(0.830594\pi\)
\(570\) 0 0
\(571\) −32.4790 −1.35920 −0.679601 0.733582i \(-0.737847\pi\)
−0.679601 + 0.733582i \(0.737847\pi\)
\(572\) −4.86317 −0.203340
\(573\) 0 0
\(574\) 0.800432 0.0334094
\(575\) 4.99989 0.208510
\(576\) 0 0
\(577\) 7.17376 0.298647 0.149324 0.988788i \(-0.452290\pi\)
0.149324 + 0.988788i \(0.452290\pi\)
\(578\) −2.18814 −0.0910147
\(579\) 0 0
\(580\) −0.0187838 −0.000779955 0
\(581\) 27.9047 1.15768
\(582\) 0 0
\(583\) 9.89785 0.409927
\(584\) −21.8145 −0.902689
\(585\) 0 0
\(586\) 4.51131 0.186360
\(587\) −3.16686 −0.130710 −0.0653552 0.997862i \(-0.520818\pi\)
−0.0653552 + 0.997862i \(0.520818\pi\)
\(588\) 0 0
\(589\) −67.8421 −2.79538
\(590\) −0.0665507 −0.00273985
\(591\) 0 0
\(592\) −10.4255 −0.428486
\(593\) −1.38330 −0.0568054 −0.0284027 0.999597i \(-0.509042\pi\)
−0.0284027 + 0.999597i \(0.509042\pi\)
\(594\) 0 0
\(595\) −0.0687777 −0.00281961
\(596\) 3.50702 0.143653
\(597\) 0 0
\(598\) −1.26016 −0.0515317
\(599\) 0.353620 0.0144485 0.00722427 0.999974i \(-0.497700\pi\)
0.00722427 + 0.999974i \(0.497700\pi\)
\(600\) 0 0
\(601\) −1.76477 −0.0719863 −0.0359931 0.999352i \(-0.511459\pi\)
−0.0359931 + 0.999352i \(0.511459\pi\)
\(602\) −5.19537 −0.211748
\(603\) 0 0
\(604\) 5.25183 0.213694
\(605\) −0.105172 −0.00427584
\(606\) 0 0
\(607\) −34.2574 −1.39047 −0.695233 0.718785i \(-0.744699\pi\)
−0.695233 + 0.718785i \(0.744699\pi\)
\(608\) −36.0056 −1.46022
\(609\) 0 0
\(610\) −0.00739985 −0.000299611 0
\(611\) 23.6260 0.955806
\(612\) 0 0
\(613\) 10.3428 0.417743 0.208871 0.977943i \(-0.433021\pi\)
0.208871 + 0.977943i \(0.433021\pi\)
\(614\) −4.61368 −0.186193
\(615\) 0 0
\(616\) 3.32224 0.133857
\(617\) −33.9967 −1.36866 −0.684328 0.729174i \(-0.739904\pi\)
−0.684328 + 0.729174i \(0.739904\pi\)
\(618\) 0 0
\(619\) 22.6908 0.912022 0.456011 0.889974i \(-0.349278\pi\)
0.456011 + 0.889974i \(0.349278\pi\)
\(620\) −0.170310 −0.00683983
\(621\) 0 0
\(622\) 11.2294 0.450258
\(623\) 16.8790 0.676244
\(624\) 0 0
\(625\) 24.9983 0.999933
\(626\) −7.85804 −0.314070
\(627\) 0 0
\(628\) 11.4464 0.456762
\(629\) −13.3596 −0.532683
\(630\) 0 0
\(631\) 44.0926 1.75530 0.877649 0.479304i \(-0.159111\pi\)
0.877649 + 0.479304i \(0.159111\pi\)
\(632\) −16.9136 −0.672786
\(633\) 0 0
\(634\) −3.45312 −0.137141
\(635\) 0.186370 0.00739586
\(636\) 0 0
\(637\) −9.56053 −0.378802
\(638\) 0.472521 0.0187073
\(639\) 0 0
\(640\) −0.117358 −0.00463896
\(641\) −35.7799 −1.41322 −0.706611 0.707603i \(-0.749777\pi\)
−0.706611 + 0.707603i \(0.749777\pi\)
\(642\) 0 0
\(643\) 14.1099 0.556438 0.278219 0.960518i \(-0.410256\pi\)
0.278219 + 0.960518i \(0.410256\pi\)
\(644\) −3.31264 −0.130536
\(645\) 0 0
\(646\) −12.2648 −0.482553
\(647\) −31.5829 −1.24165 −0.620826 0.783948i \(-0.713203\pi\)
−0.620826 + 0.783948i \(0.713203\pi\)
\(648\) 0 0
\(649\) −13.6730 −0.536713
\(650\) −6.30065 −0.247132
\(651\) 0 0
\(652\) −21.8486 −0.855657
\(653\) −40.0535 −1.56742 −0.783708 0.621130i \(-0.786674\pi\)
−0.783708 + 0.621130i \(0.786674\pi\)
\(654\) 0 0
\(655\) 0.0503228 0.00196627
\(656\) −2.52433 −0.0985587
\(657\) 0 0
\(658\) −7.60441 −0.296451
\(659\) −2.01244 −0.0783933 −0.0391967 0.999232i \(-0.512480\pi\)
−0.0391967 + 0.999232i \(0.512480\pi\)
\(660\) 0 0
\(661\) −22.8081 −0.887134 −0.443567 0.896241i \(-0.646287\pi\)
−0.443567 + 0.896241i \(0.646287\pi\)
\(662\) 3.23755 0.125831
\(663\) 0 0
\(664\) 26.5136 1.02893
\(665\) 0.146645 0.00568664
\(666\) 0 0
\(667\) −1.00000 −0.0387202
\(668\) 10.5061 0.406494
\(669\) 0 0
\(670\) −0.0393019 −0.00151836
\(671\) −1.52032 −0.0586912
\(672\) 0 0
\(673\) 5.35191 0.206301 0.103150 0.994666i \(-0.467108\pi\)
0.103150 + 0.994666i \(0.467108\pi\)
\(674\) 1.90093 0.0732211
\(675\) 0 0
\(676\) 10.1943 0.392088
\(677\) 30.9706 1.19030 0.595149 0.803615i \(-0.297093\pi\)
0.595149 + 0.803615i \(0.297093\pi\)
\(678\) 0 0
\(679\) −2.39290 −0.0918309
\(680\) −0.0653489 −0.00250602
\(681\) 0 0
\(682\) 4.28428 0.164054
\(683\) 48.6419 1.86123 0.930615 0.365999i \(-0.119273\pi\)
0.930615 + 0.365999i \(0.119273\pi\)
\(684\) 0 0
\(685\) −0.0410644 −0.00156899
\(686\) 9.15579 0.349570
\(687\) 0 0
\(688\) 16.3847 0.624662
\(689\) 26.3964 1.00562
\(690\) 0 0
\(691\) 49.3224 1.87631 0.938156 0.346213i \(-0.112532\pi\)
0.938156 + 0.346213i \(0.112532\pi\)
\(692\) −2.49573 −0.0948734
\(693\) 0 0
\(694\) −3.46627 −0.131578
\(695\) 0.0334344 0.00126824
\(696\) 0 0
\(697\) −3.23477 −0.122526
\(698\) 11.5111 0.435703
\(699\) 0 0
\(700\) −16.5628 −0.626016
\(701\) −24.7023 −0.932993 −0.466497 0.884523i \(-0.654484\pi\)
−0.466497 + 0.884523i \(0.654484\pi\)
\(702\) 0 0
\(703\) 28.4848 1.07432
\(704\) −3.26712 −0.123134
\(705\) 0 0
\(706\) 10.1430 0.381737
\(707\) 33.3342 1.25366
\(708\) 0 0
\(709\) 21.9049 0.822655 0.411328 0.911488i \(-0.365065\pi\)
0.411328 + 0.911488i \(0.365065\pi\)
\(710\) −0.0157377 −0.000590624 0
\(711\) 0 0
\(712\) 16.0376 0.601033
\(713\) −9.06687 −0.339557
\(714\) 0 0
\(715\) 0.0287720 0.00107601
\(716\) 31.3505 1.17162
\(717\) 0 0
\(718\) 5.53645 0.206618
\(719\) −24.6474 −0.919194 −0.459597 0.888128i \(-0.652006\pi\)
−0.459597 + 0.888128i \(0.652006\pi\)
\(720\) 0 0
\(721\) −30.5301 −1.13700
\(722\) 17.2758 0.642941
\(723\) 0 0
\(724\) 38.5793 1.43379
\(725\) −4.99989 −0.185691
\(726\) 0 0
\(727\) 1.09130 0.0404741 0.0202370 0.999795i \(-0.493558\pi\)
0.0202370 + 0.999795i \(0.493558\pi\)
\(728\) 8.86002 0.328374
\(729\) 0 0
\(730\) 0.0608078 0.00225060
\(731\) 20.9960 0.776564
\(732\) 0 0
\(733\) −11.3513 −0.419271 −0.209635 0.977780i \(-0.567228\pi\)
−0.209635 + 0.977780i \(0.567228\pi\)
\(734\) −5.53303 −0.204228
\(735\) 0 0
\(736\) −4.81203 −0.177374
\(737\) −8.07467 −0.297434
\(738\) 0 0
\(739\) 37.8330 1.39171 0.695854 0.718183i \(-0.255026\pi\)
0.695854 + 0.718183i \(0.255026\pi\)
\(740\) 0.0715080 0.00262868
\(741\) 0 0
\(742\) −8.49611 −0.311902
\(743\) −19.9697 −0.732618 −0.366309 0.930493i \(-0.619379\pi\)
−0.366309 + 0.930493i \(0.619379\pi\)
\(744\) 0 0
\(745\) −0.0207486 −0.000760170 0
\(746\) −16.1192 −0.590165
\(747\) 0 0
\(748\) −6.32578 −0.231294
\(749\) 5.58070 0.203914
\(750\) 0 0
\(751\) −10.9630 −0.400046 −0.200023 0.979791i \(-0.564102\pi\)
−0.200023 + 0.979791i \(0.564102\pi\)
\(752\) 23.9821 0.874539
\(753\) 0 0
\(754\) 1.26016 0.0458922
\(755\) −0.0310714 −0.00113080
\(756\) 0 0
\(757\) 30.3461 1.10295 0.551474 0.834192i \(-0.314066\pi\)
0.551474 + 0.834192i \(0.314066\pi\)
\(758\) −1.44041 −0.0523180
\(759\) 0 0
\(760\) 0.139334 0.00505417
\(761\) 53.4315 1.93689 0.968446 0.249223i \(-0.0801753\pi\)
0.968446 + 0.249223i \(0.0801753\pi\)
\(762\) 0 0
\(763\) 25.8208 0.934777
\(764\) 16.0811 0.581793
\(765\) 0 0
\(766\) 11.3997 0.411887
\(767\) −36.4643 −1.31665
\(768\) 0 0
\(769\) 40.3898 1.45649 0.728246 0.685315i \(-0.240336\pi\)
0.728246 + 0.685315i \(0.240336\pi\)
\(770\) −0.00926074 −0.000333734 0
\(771\) 0 0
\(772\) −4.12891 −0.148603
\(773\) −21.5543 −0.775255 −0.387627 0.921816i \(-0.626705\pi\)
−0.387627 + 0.921816i \(0.626705\pi\)
\(774\) 0 0
\(775\) −45.3333 −1.62842
\(776\) −2.27360 −0.0816176
\(777\) 0 0
\(778\) 0.151677 0.00543790
\(779\) 6.89703 0.247112
\(780\) 0 0
\(781\) −3.23334 −0.115698
\(782\) −1.63915 −0.0586160
\(783\) 0 0
\(784\) −9.70464 −0.346594
\(785\) −0.0677205 −0.00241705
\(786\) 0 0
\(787\) −28.6203 −1.02020 −0.510101 0.860114i \(-0.670392\pi\)
−0.510101 + 0.860114i \(0.670392\pi\)
\(788\) 37.9331 1.35131
\(789\) 0 0
\(790\) 0.0471466 0.00167740
\(791\) −3.92086 −0.139410
\(792\) 0 0
\(793\) −4.05451 −0.143980
\(794\) 3.26841 0.115992
\(795\) 0 0
\(796\) 10.5524 0.374021
\(797\) 41.4204 1.46719 0.733593 0.679589i \(-0.237842\pi\)
0.733593 + 0.679589i \(0.237842\pi\)
\(798\) 0 0
\(799\) 30.7316 1.08721
\(800\) −24.0596 −0.850636
\(801\) 0 0
\(802\) −8.64602 −0.305302
\(803\) 12.4931 0.440872
\(804\) 0 0
\(805\) 0.0195986 0.000690759 0
\(806\) 11.4257 0.402453
\(807\) 0 0
\(808\) 31.6723 1.11423
\(809\) −16.4746 −0.579215 −0.289608 0.957145i \(-0.593525\pi\)
−0.289608 + 0.957145i \(0.593525\pi\)
\(810\) 0 0
\(811\) −20.4990 −0.719816 −0.359908 0.932988i \(-0.617192\pi\)
−0.359908 + 0.932988i \(0.617192\pi\)
\(812\) 3.31264 0.116251
\(813\) 0 0
\(814\) −1.79884 −0.0630492
\(815\) 0.129263 0.00452788
\(816\) 0 0
\(817\) −44.7667 −1.56619
\(818\) −5.10599 −0.178527
\(819\) 0 0
\(820\) 0.0173143 0.000604640 0
\(821\) −13.5365 −0.472427 −0.236213 0.971701i \(-0.575906\pi\)
−0.236213 + 0.971701i \(0.575906\pi\)
\(822\) 0 0
\(823\) 5.32001 0.185444 0.0927219 0.995692i \(-0.470443\pi\)
0.0927219 + 0.995692i \(0.470443\pi\)
\(824\) −29.0081 −1.01055
\(825\) 0 0
\(826\) 11.7366 0.408370
\(827\) −2.86383 −0.0995851 −0.0497926 0.998760i \(-0.515856\pi\)
−0.0497926 + 0.998760i \(0.515856\pi\)
\(828\) 0 0
\(829\) −50.6084 −1.75770 −0.878852 0.477095i \(-0.841690\pi\)
−0.878852 + 0.477095i \(0.841690\pi\)
\(830\) −0.0739066 −0.00256533
\(831\) 0 0
\(832\) −8.71304 −0.302070
\(833\) −12.4359 −0.430877
\(834\) 0 0
\(835\) −0.0621574 −0.00215105
\(836\) 13.4875 0.466476
\(837\) 0 0
\(838\) −12.0115 −0.414930
\(839\) 19.9598 0.689089 0.344545 0.938770i \(-0.388033\pi\)
0.344545 + 0.938770i \(0.388033\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) 15.8938 0.547738
\(843\) 0 0
\(844\) −13.7606 −0.473660
\(845\) −0.0603125 −0.00207481
\(846\) 0 0
\(847\) 18.5477 0.637306
\(848\) 26.7943 0.920120
\(849\) 0 0
\(850\) −8.19558 −0.281106
\(851\) 3.80689 0.130499
\(852\) 0 0
\(853\) 2.93688 0.100557 0.0502784 0.998735i \(-0.483989\pi\)
0.0502784 + 0.998735i \(0.483989\pi\)
\(854\) 1.30501 0.0446565
\(855\) 0 0
\(856\) 5.30248 0.181235
\(857\) 36.5423 1.24826 0.624131 0.781320i \(-0.285453\pi\)
0.624131 + 0.781320i \(0.285453\pi\)
\(858\) 0 0
\(859\) 15.2091 0.518929 0.259464 0.965753i \(-0.416454\pi\)
0.259464 + 0.965753i \(0.416454\pi\)
\(860\) −0.112382 −0.00383219
\(861\) 0 0
\(862\) 15.9858 0.544478
\(863\) 11.0986 0.377802 0.188901 0.981996i \(-0.439507\pi\)
0.188901 + 0.981996i \(0.439507\pi\)
\(864\) 0 0
\(865\) 0.0147655 0.000502042 0
\(866\) 4.21016 0.143067
\(867\) 0 0
\(868\) 30.0353 1.01946
\(869\) 9.68639 0.328588
\(870\) 0 0
\(871\) −21.5342 −0.729658
\(872\) 24.5336 0.830813
\(873\) 0 0
\(874\) 3.49493 0.118218
\(875\) 0.195984 0.00662546
\(876\) 0 0
\(877\) −23.3671 −0.789051 −0.394526 0.918885i \(-0.629091\pi\)
−0.394526 + 0.918885i \(0.629091\pi\)
\(878\) 13.6109 0.459345
\(879\) 0 0
\(880\) 0.0292057 0.000984525 0
\(881\) −45.1791 −1.52212 −0.761061 0.648680i \(-0.775321\pi\)
−0.761061 + 0.648680i \(0.775321\pi\)
\(882\) 0 0
\(883\) 25.5241 0.858955 0.429478 0.903077i \(-0.358698\pi\)
0.429478 + 0.903077i \(0.358698\pi\)
\(884\) −16.8701 −0.567404
\(885\) 0 0
\(886\) 18.7839 0.631056
\(887\) −15.3894 −0.516725 −0.258362 0.966048i \(-0.583183\pi\)
−0.258362 + 0.966048i \(0.583183\pi\)
\(888\) 0 0
\(889\) −32.8674 −1.10234
\(890\) −0.0447047 −0.00149850
\(891\) 0 0
\(892\) 19.4898 0.652568
\(893\) −65.5245 −2.19269
\(894\) 0 0
\(895\) −0.185479 −0.00619989
\(896\) 20.6967 0.691429
\(897\) 0 0
\(898\) −2.77489 −0.0925994
\(899\) 9.06687 0.302397
\(900\) 0 0
\(901\) 34.3352 1.14387
\(902\) −0.435553 −0.0145023
\(903\) 0 0
\(904\) −3.72539 −0.123905
\(905\) −0.228247 −0.00758719
\(906\) 0 0
\(907\) −15.7921 −0.524368 −0.262184 0.965018i \(-0.584443\pi\)
−0.262184 + 0.965018i \(0.584443\pi\)
\(908\) 38.2905 1.27072
\(909\) 0 0
\(910\) −0.0246973 −0.000818708 0
\(911\) −2.70731 −0.0896972 −0.0448486 0.998994i \(-0.514281\pi\)
−0.0448486 + 0.998994i \(0.514281\pi\)
\(912\) 0 0
\(913\) −15.1843 −0.502526
\(914\) 4.26363 0.141028
\(915\) 0 0
\(916\) 18.5304 0.612262
\(917\) −8.87473 −0.293069
\(918\) 0 0
\(919\) 23.0679 0.760940 0.380470 0.924793i \(-0.375762\pi\)
0.380470 + 0.924793i \(0.375762\pi\)
\(920\) 0.0186215 0.000613934 0
\(921\) 0 0
\(922\) −13.5932 −0.447667
\(923\) −8.62294 −0.283828
\(924\) 0 0
\(925\) 19.0340 0.625836
\(926\) −9.23397 −0.303447
\(927\) 0 0
\(928\) 4.81203 0.157963
\(929\) 27.9038 0.915494 0.457747 0.889083i \(-0.348657\pi\)
0.457747 + 0.889083i \(0.348657\pi\)
\(930\) 0 0
\(931\) 26.5152 0.869000
\(932\) 16.6808 0.546397
\(933\) 0 0
\(934\) −7.96770 −0.260711
\(935\) 0.0374252 0.00122394
\(936\) 0 0
\(937\) −50.2667 −1.64214 −0.821070 0.570827i \(-0.806623\pi\)
−0.821070 + 0.570827i \(0.806623\pi\)
\(938\) 6.93113 0.226309
\(939\) 0 0
\(940\) −0.164492 −0.00536515
\(941\) 0.205558 0.00670099 0.00335050 0.999994i \(-0.498934\pi\)
0.00335050 + 0.999994i \(0.498934\pi\)
\(942\) 0 0
\(943\) 0.921766 0.0300168
\(944\) −37.0140 −1.20470
\(945\) 0 0
\(946\) 2.82705 0.0919154
\(947\) −12.3180 −0.400283 −0.200141 0.979767i \(-0.564140\pi\)
−0.200141 + 0.979767i \(0.564140\pi\)
\(948\) 0 0
\(949\) 33.3177 1.08154
\(950\) 17.4742 0.566939
\(951\) 0 0
\(952\) 11.5247 0.373517
\(953\) 12.5356 0.406068 0.203034 0.979172i \(-0.434920\pi\)
0.203034 + 0.979172i \(0.434920\pi\)
\(954\) 0 0
\(955\) −0.0951406 −0.00307868
\(956\) 22.6598 0.732870
\(957\) 0 0
\(958\) 8.11057 0.262041
\(959\) 7.24197 0.233855
\(960\) 0 0
\(961\) 51.2081 1.65188
\(962\) −4.79729 −0.154671
\(963\) 0 0
\(964\) 3.01506 0.0971086
\(965\) 0.0244279 0.000786361 0
\(966\) 0 0
\(967\) −33.5440 −1.07870 −0.539351 0.842081i \(-0.681330\pi\)
−0.539351 + 0.842081i \(0.681330\pi\)
\(968\) 17.6230 0.566426
\(969\) 0 0
\(970\) 0.00633767 0.000203490 0
\(971\) 22.4426 0.720216 0.360108 0.932911i \(-0.382740\pi\)
0.360108 + 0.932911i \(0.382740\pi\)
\(972\) 0 0
\(973\) −5.89637 −0.189029
\(974\) 18.4770 0.592042
\(975\) 0 0
\(976\) −4.11563 −0.131738
\(977\) 7.78408 0.249035 0.124517 0.992217i \(-0.460262\pi\)
0.124517 + 0.992217i \(0.460262\pi\)
\(978\) 0 0
\(979\) −9.18469 −0.293544
\(980\) 0.0665636 0.00212630
\(981\) 0 0
\(982\) −4.03355 −0.128716
\(983\) −33.4760 −1.06772 −0.533859 0.845574i \(-0.679259\pi\)
−0.533859 + 0.845574i \(0.679259\pi\)
\(984\) 0 0
\(985\) −0.224424 −0.00715074
\(986\) 1.63915 0.0522012
\(987\) 0 0
\(988\) 35.9697 1.14435
\(989\) −5.98292 −0.190246
\(990\) 0 0
\(991\) 2.35201 0.0747140 0.0373570 0.999302i \(-0.488106\pi\)
0.0373570 + 0.999302i \(0.488106\pi\)
\(992\) 43.6300 1.38526
\(993\) 0 0
\(994\) 2.77543 0.0880314
\(995\) −0.0624314 −0.00197921
\(996\) 0 0
\(997\) 28.4195 0.900055 0.450028 0.893015i \(-0.351414\pi\)
0.450028 + 0.893015i \(0.351414\pi\)
\(998\) −18.3876 −0.582051
\(999\) 0 0
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 6003.2.a.m.1.6 11
3.2 odd 2 2001.2.a.l.1.6 11
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2001.2.a.l.1.6 11 3.2 odd 2
6003.2.a.m.1.6 11 1.1 even 1 trivial