Properties

Label 6003.2.a.m.1.2
Level $6003$
Weight $2$
Character 6003.1
Self dual yes
Analytic conductor $47.934$
Analytic rank $1$
Dimension $11$
CM no
Inner twists $1$

Related objects

Downloads

Learn more about

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 1.2
Root \(2.70316\) of defining polynomial
Character \(\chi\) \(=\) 6003.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.70316 q^{2} +5.30708 q^{4} -2.79988 q^{5} +0.880738 q^{7} -8.93955 q^{8} +O(q^{10})\) \(q-2.70316 q^{2} +5.30708 q^{4} -2.79988 q^{5} +0.880738 q^{7} -8.93955 q^{8} +7.56852 q^{10} +5.67616 q^{11} -3.71641 q^{13} -2.38078 q^{14} +13.5509 q^{16} -4.80704 q^{17} +6.68378 q^{19} -14.8592 q^{20} -15.3436 q^{22} -1.00000 q^{23} +2.83932 q^{25} +10.0460 q^{26} +4.67414 q^{28} +1.00000 q^{29} +0.779005 q^{31} -18.7511 q^{32} +12.9942 q^{34} -2.46596 q^{35} -8.14977 q^{37} -18.0673 q^{38} +25.0297 q^{40} -6.06174 q^{41} +9.54562 q^{43} +30.1238 q^{44} +2.70316 q^{46} +7.68018 q^{47} -6.22430 q^{49} -7.67515 q^{50} -19.7233 q^{52} +9.73506 q^{53} -15.8926 q^{55} -7.87341 q^{56} -2.70316 q^{58} -5.14558 q^{59} -7.99562 q^{61} -2.10578 q^{62} +23.5855 q^{64} +10.4055 q^{65} -8.36073 q^{67} -25.5113 q^{68} +6.66589 q^{70} -8.52656 q^{71} -12.6677 q^{73} +22.0301 q^{74} +35.4713 q^{76} +4.99921 q^{77} +15.1051 q^{79} -37.9409 q^{80} +16.3859 q^{82} +0.302272 q^{83} +13.4591 q^{85} -25.8033 q^{86} -50.7423 q^{88} +10.7142 q^{89} -3.27318 q^{91} -5.30708 q^{92} -20.7608 q^{94} -18.7138 q^{95} -0.884027 q^{97} +16.8253 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11q - 2q^{2} + 18q^{4} - 2q^{5} + 3q^{7} - 18q^{8} + O(q^{10}) \) \( 11q - 2q^{2} + 18q^{4} - 2q^{5} + 3q^{7} - 18q^{8} + 14q^{10} - 11q^{11} - 5q^{13} - 17q^{14} + 20q^{16} - 15q^{17} - 6q^{19} - 21q^{20} - 10q^{22} - 11q^{23} + 3q^{25} + 5q^{26} + 7q^{28} + 11q^{29} + 35q^{31} - 28q^{32} + 28q^{34} - 15q^{35} - 28q^{37} + 2q^{38} - q^{40} - 10q^{41} - 6q^{43} - 18q^{44} + 2q^{46} - 15q^{47} + 22q^{49} - 15q^{50} - 36q^{52} + 7q^{53} - 12q^{55} - 56q^{56} - 2q^{58} + 20q^{59} - 20q^{61} + 11q^{62} + 36q^{64} - 11q^{65} - 39q^{67} - 35q^{68} + 38q^{70} - 49q^{71} - 3q^{73} - 37q^{74} - 18q^{76} - 25q^{77} + 41q^{79} - 51q^{80} - 19q^{82} - 13q^{83} - 62q^{86} - 40q^{88} - 34q^{89} + 2q^{91} - 18q^{92} - 14q^{94} - 25q^{95} - 11q^{97} - 53q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.70316 −1.91142 −0.955711 0.294305i \(-0.904912\pi\)
−0.955711 + 0.294305i \(0.904912\pi\)
\(3\) 0 0
\(4\) 5.30708 2.65354
\(5\) −2.79988 −1.25214 −0.626072 0.779765i \(-0.715338\pi\)
−0.626072 + 0.779765i \(0.715338\pi\)
\(6\) 0 0
\(7\) 0.880738 0.332888 0.166444 0.986051i \(-0.446772\pi\)
0.166444 + 0.986051i \(0.446772\pi\)
\(8\) −8.93955 −3.16061
\(9\) 0 0
\(10\) 7.56852 2.39338
\(11\) 5.67616 1.71143 0.855713 0.517451i \(-0.173119\pi\)
0.855713 + 0.517451i \(0.173119\pi\)
\(12\) 0 0
\(13\) −3.71641 −1.03075 −0.515373 0.856966i \(-0.672347\pi\)
−0.515373 + 0.856966i \(0.672347\pi\)
\(14\) −2.38078 −0.636289
\(15\) 0 0
\(16\) 13.5509 3.38772
\(17\) −4.80704 −1.16588 −0.582939 0.812516i \(-0.698097\pi\)
−0.582939 + 0.812516i \(0.698097\pi\)
\(18\) 0 0
\(19\) 6.68378 1.53336 0.766682 0.642027i \(-0.221907\pi\)
0.766682 + 0.642027i \(0.221907\pi\)
\(20\) −14.8592 −3.32261
\(21\) 0 0
\(22\) −15.3436 −3.27126
\(23\) −1.00000 −0.208514
\(24\) 0 0
\(25\) 2.83932 0.567865
\(26\) 10.0460 1.97019
\(27\) 0 0
\(28\) 4.67414 0.883330
\(29\) 1.00000 0.185695
\(30\) 0 0
\(31\) 0.779005 0.139913 0.0699567 0.997550i \(-0.477714\pi\)
0.0699567 + 0.997550i \(0.477714\pi\)
\(32\) −18.7511 −3.31476
\(33\) 0 0
\(34\) 12.9942 2.22849
\(35\) −2.46596 −0.416823
\(36\) 0 0
\(37\) −8.14977 −1.33981 −0.669907 0.742445i \(-0.733666\pi\)
−0.669907 + 0.742445i \(0.733666\pi\)
\(38\) −18.0673 −2.93091
\(39\) 0 0
\(40\) 25.0297 3.95754
\(41\) −6.06174 −0.946686 −0.473343 0.880878i \(-0.656953\pi\)
−0.473343 + 0.880878i \(0.656953\pi\)
\(42\) 0 0
\(43\) 9.54562 1.45569 0.727847 0.685740i \(-0.240521\pi\)
0.727847 + 0.685740i \(0.240521\pi\)
\(44\) 30.1238 4.54133
\(45\) 0 0
\(46\) 2.70316 0.398559
\(47\) 7.68018 1.12027 0.560135 0.828402i \(-0.310749\pi\)
0.560135 + 0.828402i \(0.310749\pi\)
\(48\) 0 0
\(49\) −6.22430 −0.889186
\(50\) −7.67515 −1.08543
\(51\) 0 0
\(52\) −19.7233 −2.73512
\(53\) 9.73506 1.33721 0.668607 0.743616i \(-0.266891\pi\)
0.668607 + 0.743616i \(0.266891\pi\)
\(54\) 0 0
\(55\) −15.8926 −2.14295
\(56\) −7.87341 −1.05213
\(57\) 0 0
\(58\) −2.70316 −0.354942
\(59\) −5.14558 −0.669898 −0.334949 0.942236i \(-0.608719\pi\)
−0.334949 + 0.942236i \(0.608719\pi\)
\(60\) 0 0
\(61\) −7.99562 −1.02373 −0.511867 0.859065i \(-0.671046\pi\)
−0.511867 + 0.859065i \(0.671046\pi\)
\(62\) −2.10578 −0.267434
\(63\) 0 0
\(64\) 23.5855 2.94819
\(65\) 10.4055 1.29064
\(66\) 0 0
\(67\) −8.36073 −1.02143 −0.510713 0.859751i \(-0.670619\pi\)
−0.510713 + 0.859751i \(0.670619\pi\)
\(68\) −25.5113 −3.09370
\(69\) 0 0
\(70\) 6.66589 0.796726
\(71\) −8.52656 −1.01192 −0.505958 0.862558i \(-0.668861\pi\)
−0.505958 + 0.862558i \(0.668861\pi\)
\(72\) 0 0
\(73\) −12.6677 −1.48264 −0.741321 0.671150i \(-0.765801\pi\)
−0.741321 + 0.671150i \(0.765801\pi\)
\(74\) 22.0301 2.56095
\(75\) 0 0
\(76\) 35.4713 4.06884
\(77\) 4.99921 0.569713
\(78\) 0 0
\(79\) 15.1051 1.69945 0.849726 0.527224i \(-0.176767\pi\)
0.849726 + 0.527224i \(0.176767\pi\)
\(80\) −37.9409 −4.24192
\(81\) 0 0
\(82\) 16.3859 1.80952
\(83\) 0.302272 0.0331786 0.0165893 0.999862i \(-0.494719\pi\)
0.0165893 + 0.999862i \(0.494719\pi\)
\(84\) 0 0
\(85\) 13.4591 1.45985
\(86\) −25.8033 −2.78245
\(87\) 0 0
\(88\) −50.7423 −5.40915
\(89\) 10.7142 1.13570 0.567852 0.823131i \(-0.307775\pi\)
0.567852 + 0.823131i \(0.307775\pi\)
\(90\) 0 0
\(91\) −3.27318 −0.343123
\(92\) −5.30708 −0.553301
\(93\) 0 0
\(94\) −20.7608 −2.14131
\(95\) −18.7138 −1.91999
\(96\) 0 0
\(97\) −0.884027 −0.0897593 −0.0448797 0.998992i \(-0.514290\pi\)
−0.0448797 + 0.998992i \(0.514290\pi\)
\(98\) 16.8253 1.69961
\(99\) 0 0
\(100\) 15.0685 1.50685
\(101\) 1.36093 0.135418 0.0677089 0.997705i \(-0.478431\pi\)
0.0677089 + 0.997705i \(0.478431\pi\)
\(102\) 0 0
\(103\) −5.31264 −0.523470 −0.261735 0.965140i \(-0.584295\pi\)
−0.261735 + 0.965140i \(0.584295\pi\)
\(104\) 33.2230 3.25779
\(105\) 0 0
\(106\) −26.3154 −2.55598
\(107\) −7.83080 −0.757032 −0.378516 0.925595i \(-0.623566\pi\)
−0.378516 + 0.925595i \(0.623566\pi\)
\(108\) 0 0
\(109\) 11.2420 1.07679 0.538393 0.842694i \(-0.319032\pi\)
0.538393 + 0.842694i \(0.319032\pi\)
\(110\) 42.9601 4.09609
\(111\) 0 0
\(112\) 11.9348 1.12773
\(113\) 17.4918 1.64549 0.822745 0.568411i \(-0.192442\pi\)
0.822745 + 0.568411i \(0.192442\pi\)
\(114\) 0 0
\(115\) 2.79988 0.261090
\(116\) 5.30708 0.492750
\(117\) 0 0
\(118\) 13.9093 1.28046
\(119\) −4.23374 −0.388106
\(120\) 0 0
\(121\) 21.2188 1.92898
\(122\) 21.6134 1.95679
\(123\) 0 0
\(124\) 4.13424 0.371266
\(125\) 6.04963 0.541095
\(126\) 0 0
\(127\) 0.206399 0.0183149 0.00915747 0.999958i \(-0.497085\pi\)
0.00915747 + 0.999958i \(0.497085\pi\)
\(128\) −26.2532 −2.32048
\(129\) 0 0
\(130\) −28.1277 −2.46696
\(131\) −9.50384 −0.830354 −0.415177 0.909741i \(-0.636280\pi\)
−0.415177 + 0.909741i \(0.636280\pi\)
\(132\) 0 0
\(133\) 5.88666 0.510438
\(134\) 22.6004 1.95238
\(135\) 0 0
\(136\) 42.9728 3.68488
\(137\) −4.27725 −0.365430 −0.182715 0.983166i \(-0.558489\pi\)
−0.182715 + 0.983166i \(0.558489\pi\)
\(138\) 0 0
\(139\) −9.47109 −0.803327 −0.401663 0.915787i \(-0.631568\pi\)
−0.401663 + 0.915787i \(0.631568\pi\)
\(140\) −13.0870 −1.10606
\(141\) 0 0
\(142\) 23.0487 1.93420
\(143\) −21.0949 −1.76405
\(144\) 0 0
\(145\) −2.79988 −0.232517
\(146\) 34.2428 2.83396
\(147\) 0 0
\(148\) −43.2514 −3.55525
\(149\) 20.3448 1.66671 0.833354 0.552740i \(-0.186418\pi\)
0.833354 + 0.552740i \(0.186418\pi\)
\(150\) 0 0
\(151\) −14.3715 −1.16953 −0.584766 0.811202i \(-0.698814\pi\)
−0.584766 + 0.811202i \(0.698814\pi\)
\(152\) −59.7500 −4.84636
\(153\) 0 0
\(154\) −13.5137 −1.08896
\(155\) −2.18112 −0.175192
\(156\) 0 0
\(157\) −18.9351 −1.51118 −0.755592 0.655043i \(-0.772651\pi\)
−0.755592 + 0.655043i \(0.772651\pi\)
\(158\) −40.8314 −3.24837
\(159\) 0 0
\(160\) 52.5009 4.15056
\(161\) −0.880738 −0.0694119
\(162\) 0 0
\(163\) 12.4920 0.978447 0.489224 0.872158i \(-0.337280\pi\)
0.489224 + 0.872158i \(0.337280\pi\)
\(164\) −32.1701 −2.51207
\(165\) 0 0
\(166\) −0.817089 −0.0634184
\(167\) −8.77674 −0.679165 −0.339582 0.940576i \(-0.610286\pi\)
−0.339582 + 0.940576i \(0.610286\pi\)
\(168\) 0 0
\(169\) 0.811682 0.0624371
\(170\) −36.3822 −2.79038
\(171\) 0 0
\(172\) 50.6593 3.86274
\(173\) −14.7668 −1.12270 −0.561351 0.827578i \(-0.689718\pi\)
−0.561351 + 0.827578i \(0.689718\pi\)
\(174\) 0 0
\(175\) 2.50070 0.189035
\(176\) 76.9170 5.79784
\(177\) 0 0
\(178\) −28.9622 −2.17081
\(179\) 7.96536 0.595359 0.297679 0.954666i \(-0.403787\pi\)
0.297679 + 0.954666i \(0.403787\pi\)
\(180\) 0 0
\(181\) 10.2864 0.764579 0.382289 0.924043i \(-0.375136\pi\)
0.382289 + 0.924043i \(0.375136\pi\)
\(182\) 8.84794 0.655853
\(183\) 0 0
\(184\) 8.93955 0.659033
\(185\) 22.8184 1.67764
\(186\) 0 0
\(187\) −27.2855 −1.99531
\(188\) 40.7593 2.97268
\(189\) 0 0
\(190\) 50.5863 3.66992
\(191\) −23.0537 −1.66811 −0.834054 0.551683i \(-0.813986\pi\)
−0.834054 + 0.551683i \(0.813986\pi\)
\(192\) 0 0
\(193\) 5.67387 0.408414 0.204207 0.978928i \(-0.434538\pi\)
0.204207 + 0.978928i \(0.434538\pi\)
\(194\) 2.38967 0.171568
\(195\) 0 0
\(196\) −33.0328 −2.35949
\(197\) −7.96762 −0.567669 −0.283835 0.958873i \(-0.591607\pi\)
−0.283835 + 0.958873i \(0.591607\pi\)
\(198\) 0 0
\(199\) −6.95306 −0.492889 −0.246445 0.969157i \(-0.579262\pi\)
−0.246445 + 0.969157i \(0.579262\pi\)
\(200\) −25.3823 −1.79480
\(201\) 0 0
\(202\) −3.67882 −0.258841
\(203\) 0.880738 0.0618157
\(204\) 0 0
\(205\) 16.9722 1.18539
\(206\) 14.3609 1.00057
\(207\) 0 0
\(208\) −50.3607 −3.49188
\(209\) 37.9382 2.62424
\(210\) 0 0
\(211\) 5.75864 0.396441 0.198221 0.980157i \(-0.436484\pi\)
0.198221 + 0.980157i \(0.436484\pi\)
\(212\) 51.6647 3.54835
\(213\) 0 0
\(214\) 21.1679 1.44701
\(215\) −26.7266 −1.82274
\(216\) 0 0
\(217\) 0.686100 0.0465755
\(218\) −30.3889 −2.05819
\(219\) 0 0
\(220\) −84.3430 −5.68640
\(221\) 17.8649 1.20172
\(222\) 0 0
\(223\) 12.0916 0.809713 0.404856 0.914380i \(-0.367322\pi\)
0.404856 + 0.914380i \(0.367322\pi\)
\(224\) −16.5148 −1.10344
\(225\) 0 0
\(226\) −47.2831 −3.14523
\(227\) 27.0451 1.79505 0.897523 0.440968i \(-0.145365\pi\)
0.897523 + 0.440968i \(0.145365\pi\)
\(228\) 0 0
\(229\) −5.32014 −0.351565 −0.175782 0.984429i \(-0.556245\pi\)
−0.175782 + 0.984429i \(0.556245\pi\)
\(230\) −7.56852 −0.499054
\(231\) 0 0
\(232\) −8.93955 −0.586911
\(233\) −23.8743 −1.56406 −0.782028 0.623244i \(-0.785814\pi\)
−0.782028 + 0.623244i \(0.785814\pi\)
\(234\) 0 0
\(235\) −21.5036 −1.40274
\(236\) −27.3080 −1.77760
\(237\) 0 0
\(238\) 11.4445 0.741836
\(239\) 8.24781 0.533506 0.266753 0.963765i \(-0.414049\pi\)
0.266753 + 0.963765i \(0.414049\pi\)
\(240\) 0 0
\(241\) 10.5594 0.680192 0.340096 0.940391i \(-0.389540\pi\)
0.340096 + 0.940391i \(0.389540\pi\)
\(242\) −57.3577 −3.68709
\(243\) 0 0
\(244\) −42.4334 −2.71652
\(245\) 17.4273 1.11339
\(246\) 0 0
\(247\) −24.8396 −1.58051
\(248\) −6.96396 −0.442212
\(249\) 0 0
\(250\) −16.3531 −1.03426
\(251\) 15.9674 1.00785 0.503927 0.863746i \(-0.331888\pi\)
0.503927 + 0.863746i \(0.331888\pi\)
\(252\) 0 0
\(253\) −5.67616 −0.356857
\(254\) −0.557929 −0.0350076
\(255\) 0 0
\(256\) 23.7956 1.48722
\(257\) 5.13834 0.320521 0.160260 0.987075i \(-0.448767\pi\)
0.160260 + 0.987075i \(0.448767\pi\)
\(258\) 0 0
\(259\) −7.17782 −0.446008
\(260\) 55.2227 3.42477
\(261\) 0 0
\(262\) 25.6904 1.58716
\(263\) −22.1102 −1.36337 −0.681687 0.731644i \(-0.738754\pi\)
−0.681687 + 0.731644i \(0.738754\pi\)
\(264\) 0 0
\(265\) −27.2570 −1.67438
\(266\) −15.9126 −0.975663
\(267\) 0 0
\(268\) −44.3710 −2.71039
\(269\) −20.1023 −1.22566 −0.612828 0.790216i \(-0.709968\pi\)
−0.612828 + 0.790216i \(0.709968\pi\)
\(270\) 0 0
\(271\) 6.90145 0.419233 0.209617 0.977784i \(-0.432778\pi\)
0.209617 + 0.977784i \(0.432778\pi\)
\(272\) −65.1397 −3.94967
\(273\) 0 0
\(274\) 11.5621 0.698491
\(275\) 16.1165 0.971859
\(276\) 0 0
\(277\) 24.5794 1.47683 0.738416 0.674345i \(-0.235574\pi\)
0.738416 + 0.674345i \(0.235574\pi\)
\(278\) 25.6019 1.53550
\(279\) 0 0
\(280\) 22.0446 1.31742
\(281\) 17.2690 1.03018 0.515090 0.857136i \(-0.327759\pi\)
0.515090 + 0.857136i \(0.327759\pi\)
\(282\) 0 0
\(283\) −7.22081 −0.429232 −0.214616 0.976698i \(-0.568850\pi\)
−0.214616 + 0.976698i \(0.568850\pi\)
\(284\) −45.2511 −2.68516
\(285\) 0 0
\(286\) 57.0229 3.37184
\(287\) −5.33881 −0.315140
\(288\) 0 0
\(289\) 6.10760 0.359271
\(290\) 7.56852 0.444439
\(291\) 0 0
\(292\) −67.2285 −3.93425
\(293\) 18.2359 1.06535 0.532677 0.846319i \(-0.321186\pi\)
0.532677 + 0.846319i \(0.321186\pi\)
\(294\) 0 0
\(295\) 14.4070 0.838809
\(296\) 72.8553 4.23463
\(297\) 0 0
\(298\) −54.9951 −3.18578
\(299\) 3.71641 0.214925
\(300\) 0 0
\(301\) 8.40720 0.484583
\(302\) 38.8484 2.23547
\(303\) 0 0
\(304\) 90.5712 5.19461
\(305\) 22.3868 1.28186
\(306\) 0 0
\(307\) −14.8966 −0.850193 −0.425097 0.905148i \(-0.639760\pi\)
−0.425097 + 0.905148i \(0.639760\pi\)
\(308\) 26.5312 1.51175
\(309\) 0 0
\(310\) 5.89592 0.334866
\(311\) 1.07620 0.0610259 0.0305129 0.999534i \(-0.490286\pi\)
0.0305129 + 0.999534i \(0.490286\pi\)
\(312\) 0 0
\(313\) −24.6270 −1.39200 −0.696000 0.718042i \(-0.745039\pi\)
−0.696000 + 0.718042i \(0.745039\pi\)
\(314\) 51.1846 2.88851
\(315\) 0 0
\(316\) 80.1637 4.50956
\(317\) −10.3442 −0.580988 −0.290494 0.956877i \(-0.593820\pi\)
−0.290494 + 0.956877i \(0.593820\pi\)
\(318\) 0 0
\(319\) 5.67616 0.317804
\(320\) −66.0367 −3.69156
\(321\) 0 0
\(322\) 2.38078 0.132676
\(323\) −32.1292 −1.78771
\(324\) 0 0
\(325\) −10.5521 −0.585324
\(326\) −33.7678 −1.87023
\(327\) 0 0
\(328\) 54.1893 2.99210
\(329\) 6.76423 0.372924
\(330\) 0 0
\(331\) −14.0821 −0.774025 −0.387012 0.922075i \(-0.626493\pi\)
−0.387012 + 0.922075i \(0.626493\pi\)
\(332\) 1.60418 0.0880408
\(333\) 0 0
\(334\) 23.7249 1.29817
\(335\) 23.4090 1.27897
\(336\) 0 0
\(337\) −0.569964 −0.0310479 −0.0155240 0.999879i \(-0.504942\pi\)
−0.0155240 + 0.999879i \(0.504942\pi\)
\(338\) −2.19411 −0.119344
\(339\) 0 0
\(340\) 71.4286 3.87376
\(341\) 4.42176 0.239452
\(342\) 0 0
\(343\) −11.6471 −0.628887
\(344\) −85.3336 −4.60088
\(345\) 0 0
\(346\) 39.9171 2.14596
\(347\) 12.4225 0.666877 0.333438 0.942772i \(-0.391791\pi\)
0.333438 + 0.942772i \(0.391791\pi\)
\(348\) 0 0
\(349\) −28.4638 −1.52363 −0.761816 0.647793i \(-0.775692\pi\)
−0.761816 + 0.647793i \(0.775692\pi\)
\(350\) −6.75980 −0.361326
\(351\) 0 0
\(352\) −106.434 −5.67297
\(353\) −27.0042 −1.43729 −0.718644 0.695378i \(-0.755237\pi\)
−0.718644 + 0.695378i \(0.755237\pi\)
\(354\) 0 0
\(355\) 23.8733 1.26706
\(356\) 56.8611 3.01363
\(357\) 0 0
\(358\) −21.5316 −1.13798
\(359\) −14.0693 −0.742551 −0.371276 0.928523i \(-0.621079\pi\)
−0.371276 + 0.928523i \(0.621079\pi\)
\(360\) 0 0
\(361\) 25.6729 1.35120
\(362\) −27.8057 −1.46143
\(363\) 0 0
\(364\) −17.3710 −0.910489
\(365\) 35.4680 1.85648
\(366\) 0 0
\(367\) 34.8397 1.81862 0.909310 0.416120i \(-0.136610\pi\)
0.909310 + 0.416120i \(0.136610\pi\)
\(368\) −13.5509 −0.706389
\(369\) 0 0
\(370\) −61.6817 −3.20668
\(371\) 8.57404 0.445142
\(372\) 0 0
\(373\) 22.0794 1.14323 0.571613 0.820523i \(-0.306318\pi\)
0.571613 + 0.820523i \(0.306318\pi\)
\(374\) 73.7571 3.81389
\(375\) 0 0
\(376\) −68.6574 −3.54073
\(377\) −3.71641 −0.191405
\(378\) 0 0
\(379\) −7.46769 −0.383590 −0.191795 0.981435i \(-0.561431\pi\)
−0.191795 + 0.981435i \(0.561431\pi\)
\(380\) −99.3154 −5.09477
\(381\) 0 0
\(382\) 62.3178 3.18846
\(383\) 30.9640 1.58218 0.791092 0.611697i \(-0.209513\pi\)
0.791092 + 0.611697i \(0.209513\pi\)
\(384\) 0 0
\(385\) −13.9972 −0.713363
\(386\) −15.3374 −0.780652
\(387\) 0 0
\(388\) −4.69160 −0.238180
\(389\) 20.5067 1.03973 0.519864 0.854249i \(-0.325982\pi\)
0.519864 + 0.854249i \(0.325982\pi\)
\(390\) 0 0
\(391\) 4.80704 0.243102
\(392\) 55.6425 2.81037
\(393\) 0 0
\(394\) 21.5378 1.08506
\(395\) −42.2924 −2.12796
\(396\) 0 0
\(397\) −18.4473 −0.925843 −0.462922 0.886399i \(-0.653199\pi\)
−0.462922 + 0.886399i \(0.653199\pi\)
\(398\) 18.7952 0.942120
\(399\) 0 0
\(400\) 38.4754 1.92377
\(401\) 15.7291 0.785475 0.392738 0.919651i \(-0.371528\pi\)
0.392738 + 0.919651i \(0.371528\pi\)
\(402\) 0 0
\(403\) −2.89510 −0.144215
\(404\) 7.22257 0.359336
\(405\) 0 0
\(406\) −2.38078 −0.118156
\(407\) −46.2594 −2.29299
\(408\) 0 0
\(409\) −7.14903 −0.353497 −0.176748 0.984256i \(-0.556558\pi\)
−0.176748 + 0.984256i \(0.556558\pi\)
\(410\) −45.8785 −2.26578
\(411\) 0 0
\(412\) −28.1946 −1.38905
\(413\) −4.53191 −0.223001
\(414\) 0 0
\(415\) −0.846325 −0.0415444
\(416\) 69.6869 3.41668
\(417\) 0 0
\(418\) −102.553 −5.01603
\(419\) 14.7980 0.722928 0.361464 0.932386i \(-0.382277\pi\)
0.361464 + 0.932386i \(0.382277\pi\)
\(420\) 0 0
\(421\) 6.98352 0.340356 0.170178 0.985413i \(-0.445566\pi\)
0.170178 + 0.985413i \(0.445566\pi\)
\(422\) −15.5665 −0.757767
\(423\) 0 0
\(424\) −87.0271 −4.22641
\(425\) −13.6487 −0.662061
\(426\) 0 0
\(427\) −7.04205 −0.340789
\(428\) −41.5586 −2.00881
\(429\) 0 0
\(430\) 72.2463 3.48402
\(431\) −18.2431 −0.878737 −0.439368 0.898307i \(-0.644798\pi\)
−0.439368 + 0.898307i \(0.644798\pi\)
\(432\) 0 0
\(433\) −6.54148 −0.314364 −0.157182 0.987570i \(-0.550241\pi\)
−0.157182 + 0.987570i \(0.550241\pi\)
\(434\) −1.85464 −0.0890255
\(435\) 0 0
\(436\) 59.6620 2.85729
\(437\) −6.68378 −0.319728
\(438\) 0 0
\(439\) −24.9232 −1.18952 −0.594760 0.803904i \(-0.702753\pi\)
−0.594760 + 0.803904i \(0.702753\pi\)
\(440\) 142.072 6.77303
\(441\) 0 0
\(442\) −48.2917 −2.29700
\(443\) 31.7227 1.50719 0.753594 0.657340i \(-0.228318\pi\)
0.753594 + 0.657340i \(0.228318\pi\)
\(444\) 0 0
\(445\) −29.9985 −1.42207
\(446\) −32.6855 −1.54770
\(447\) 0 0
\(448\) 20.7727 0.981417
\(449\) −27.6235 −1.30363 −0.651816 0.758377i \(-0.725992\pi\)
−0.651816 + 0.758377i \(0.725992\pi\)
\(450\) 0 0
\(451\) −34.4074 −1.62018
\(452\) 92.8303 4.36637
\(453\) 0 0
\(454\) −73.1072 −3.43109
\(455\) 9.16452 0.429639
\(456\) 0 0
\(457\) 3.37558 0.157903 0.0789516 0.996878i \(-0.474843\pi\)
0.0789516 + 0.996878i \(0.474843\pi\)
\(458\) 14.3812 0.671989
\(459\) 0 0
\(460\) 14.8592 0.692812
\(461\) −39.9849 −1.86228 −0.931140 0.364661i \(-0.881185\pi\)
−0.931140 + 0.364661i \(0.881185\pi\)
\(462\) 0 0
\(463\) 9.18722 0.426966 0.213483 0.976947i \(-0.431519\pi\)
0.213483 + 0.976947i \(0.431519\pi\)
\(464\) 13.5509 0.629085
\(465\) 0 0
\(466\) 64.5360 2.98957
\(467\) −13.0823 −0.605378 −0.302689 0.953089i \(-0.597884\pi\)
−0.302689 + 0.953089i \(0.597884\pi\)
\(468\) 0 0
\(469\) −7.36362 −0.340020
\(470\) 58.1276 2.68123
\(471\) 0 0
\(472\) 45.9992 2.11729
\(473\) 54.1825 2.49131
\(474\) 0 0
\(475\) 18.9774 0.870743
\(476\) −22.4688 −1.02986
\(477\) 0 0
\(478\) −22.2951 −1.01976
\(479\) −41.5385 −1.89794 −0.948972 0.315361i \(-0.897875\pi\)
−0.948972 + 0.315361i \(0.897875\pi\)
\(480\) 0 0
\(481\) 30.2879 1.38101
\(482\) −28.5438 −1.30013
\(483\) 0 0
\(484\) 112.610 5.11862
\(485\) 2.47517 0.112392
\(486\) 0 0
\(487\) 22.4277 1.01630 0.508148 0.861270i \(-0.330330\pi\)
0.508148 + 0.861270i \(0.330330\pi\)
\(488\) 71.4773 3.23563
\(489\) 0 0
\(490\) −47.1088 −2.12816
\(491\) −13.8826 −0.626513 −0.313256 0.949669i \(-0.601420\pi\)
−0.313256 + 0.949669i \(0.601420\pi\)
\(492\) 0 0
\(493\) −4.80704 −0.216498
\(494\) 67.1455 3.02102
\(495\) 0 0
\(496\) 10.5562 0.473988
\(497\) −7.50967 −0.336855
\(498\) 0 0
\(499\) −10.9367 −0.489592 −0.244796 0.969575i \(-0.578721\pi\)
−0.244796 + 0.969575i \(0.578721\pi\)
\(500\) 32.1059 1.43582
\(501\) 0 0
\(502\) −43.1625 −1.92644
\(503\) 3.54058 0.157867 0.0789334 0.996880i \(-0.474849\pi\)
0.0789334 + 0.996880i \(0.474849\pi\)
\(504\) 0 0
\(505\) −3.81044 −0.169563
\(506\) 15.3436 0.682105
\(507\) 0 0
\(508\) 1.09537 0.0485994
\(509\) −12.3607 −0.547878 −0.273939 0.961747i \(-0.588327\pi\)
−0.273939 + 0.961747i \(0.588327\pi\)
\(510\) 0 0
\(511\) −11.1569 −0.493554
\(512\) −11.8168 −0.522233
\(513\) 0 0
\(514\) −13.8898 −0.612651
\(515\) 14.8748 0.655460
\(516\) 0 0
\(517\) 43.5939 1.91726
\(518\) 19.4028 0.852509
\(519\) 0 0
\(520\) −93.0205 −4.07922
\(521\) −34.5365 −1.51307 −0.756535 0.653953i \(-0.773109\pi\)
−0.756535 + 0.653953i \(0.773109\pi\)
\(522\) 0 0
\(523\) 31.4234 1.37405 0.687024 0.726634i \(-0.258917\pi\)
0.687024 + 0.726634i \(0.258917\pi\)
\(524\) −50.4376 −2.20338
\(525\) 0 0
\(526\) 59.7675 2.60599
\(527\) −3.74471 −0.163122
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 73.6801 3.20046
\(531\) 0 0
\(532\) 31.2409 1.35447
\(533\) 22.5279 0.975792
\(534\) 0 0
\(535\) 21.9253 0.947913
\(536\) 74.7412 3.22833
\(537\) 0 0
\(538\) 54.3396 2.34275
\(539\) −35.3301 −1.52178
\(540\) 0 0
\(541\) 28.3717 1.21980 0.609898 0.792480i \(-0.291210\pi\)
0.609898 + 0.792480i \(0.291210\pi\)
\(542\) −18.6557 −0.801332
\(543\) 0 0
\(544\) 90.1374 3.86461
\(545\) −31.4762 −1.34829
\(546\) 0 0
\(547\) 20.4656 0.875046 0.437523 0.899207i \(-0.355856\pi\)
0.437523 + 0.899207i \(0.355856\pi\)
\(548\) −22.6997 −0.969682
\(549\) 0 0
\(550\) −43.5653 −1.85763
\(551\) 6.68378 0.284738
\(552\) 0 0
\(553\) 13.3036 0.565727
\(554\) −66.4420 −2.82285
\(555\) 0 0
\(556\) −50.2638 −2.13166
\(557\) −33.3630 −1.41363 −0.706817 0.707396i \(-0.749870\pi\)
−0.706817 + 0.707396i \(0.749870\pi\)
\(558\) 0 0
\(559\) −35.4754 −1.50045
\(560\) −33.4160 −1.41208
\(561\) 0 0
\(562\) −46.6808 −1.96911
\(563\) −21.5508 −0.908257 −0.454129 0.890936i \(-0.650049\pi\)
−0.454129 + 0.890936i \(0.650049\pi\)
\(564\) 0 0
\(565\) −48.9749 −2.06039
\(566\) 19.5190 0.820445
\(567\) 0 0
\(568\) 76.2236 3.19827
\(569\) −12.9510 −0.542934 −0.271467 0.962448i \(-0.587509\pi\)
−0.271467 + 0.962448i \(0.587509\pi\)
\(570\) 0 0
\(571\) 3.76335 0.157491 0.0787456 0.996895i \(-0.474909\pi\)
0.0787456 + 0.996895i \(0.474909\pi\)
\(572\) −111.952 −4.68096
\(573\) 0 0
\(574\) 14.4317 0.602366
\(575\) −2.83932 −0.118408
\(576\) 0 0
\(577\) 9.05091 0.376794 0.188397 0.982093i \(-0.439671\pi\)
0.188397 + 0.982093i \(0.439671\pi\)
\(578\) −16.5098 −0.686718
\(579\) 0 0
\(580\) −14.8592 −0.616993
\(581\) 0.266222 0.0110448
\(582\) 0 0
\(583\) 55.2578 2.28854
\(584\) 113.244 4.68605
\(585\) 0 0
\(586\) −49.2946 −2.03634
\(587\) 7.59812 0.313608 0.156804 0.987630i \(-0.449881\pi\)
0.156804 + 0.987630i \(0.449881\pi\)
\(588\) 0 0
\(589\) 5.20670 0.214538
\(590\) −38.9445 −1.60332
\(591\) 0 0
\(592\) −110.437 −4.53892
\(593\) −7.95422 −0.326641 −0.163320 0.986573i \(-0.552220\pi\)
−0.163320 + 0.986573i \(0.552220\pi\)
\(594\) 0 0
\(595\) 11.8540 0.485965
\(596\) 107.971 4.42267
\(597\) 0 0
\(598\) −10.0460 −0.410813
\(599\) −31.2856 −1.27830 −0.639148 0.769084i \(-0.720713\pi\)
−0.639148 + 0.769084i \(0.720713\pi\)
\(600\) 0 0
\(601\) 14.4217 0.588274 0.294137 0.955763i \(-0.404968\pi\)
0.294137 + 0.955763i \(0.404968\pi\)
\(602\) −22.7260 −0.926242
\(603\) 0 0
\(604\) −76.2704 −3.10340
\(605\) −59.4100 −2.41536
\(606\) 0 0
\(607\) −27.1287 −1.10112 −0.550560 0.834796i \(-0.685586\pi\)
−0.550560 + 0.834796i \(0.685586\pi\)
\(608\) −125.328 −5.08274
\(609\) 0 0
\(610\) −60.5150 −2.45018
\(611\) −28.5427 −1.15471
\(612\) 0 0
\(613\) −7.58210 −0.306238 −0.153119 0.988208i \(-0.548932\pi\)
−0.153119 + 0.988208i \(0.548932\pi\)
\(614\) 40.2679 1.62508
\(615\) 0 0
\(616\) −44.6907 −1.80064
\(617\) −40.3076 −1.62272 −0.811361 0.584546i \(-0.801273\pi\)
−0.811361 + 0.584546i \(0.801273\pi\)
\(618\) 0 0
\(619\) 7.17677 0.288459 0.144229 0.989544i \(-0.453930\pi\)
0.144229 + 0.989544i \(0.453930\pi\)
\(620\) −11.5754 −0.464878
\(621\) 0 0
\(622\) −2.90915 −0.116646
\(623\) 9.43642 0.378062
\(624\) 0 0
\(625\) −31.1349 −1.24539
\(626\) 66.5707 2.66070
\(627\) 0 0
\(628\) −100.490 −4.00998
\(629\) 39.1762 1.56206
\(630\) 0 0
\(631\) −13.8537 −0.551506 −0.275753 0.961229i \(-0.588927\pi\)
−0.275753 + 0.961229i \(0.588927\pi\)
\(632\) −135.033 −5.37131
\(633\) 0 0
\(634\) 27.9620 1.11051
\(635\) −0.577892 −0.0229329
\(636\) 0 0
\(637\) 23.1320 0.916525
\(638\) −15.3436 −0.607457
\(639\) 0 0
\(640\) 73.5058 2.90557
\(641\) 2.14458 0.0847056 0.0423528 0.999103i \(-0.486515\pi\)
0.0423528 + 0.999103i \(0.486515\pi\)
\(642\) 0 0
\(643\) −48.1250 −1.89786 −0.948932 0.315481i \(-0.897834\pi\)
−0.948932 + 0.315481i \(0.897834\pi\)
\(644\) −4.67414 −0.184187
\(645\) 0 0
\(646\) 86.8503 3.41708
\(647\) −14.6607 −0.576370 −0.288185 0.957575i \(-0.593052\pi\)
−0.288185 + 0.957575i \(0.593052\pi\)
\(648\) 0 0
\(649\) −29.2071 −1.14648
\(650\) 28.5240 1.11880
\(651\) 0 0
\(652\) 66.2959 2.59635
\(653\) −30.0473 −1.17584 −0.587921 0.808918i \(-0.700053\pi\)
−0.587921 + 0.808918i \(0.700053\pi\)
\(654\) 0 0
\(655\) 26.6096 1.03972
\(656\) −82.1421 −3.20711
\(657\) 0 0
\(658\) −18.2848 −0.712816
\(659\) −17.5722 −0.684516 −0.342258 0.939606i \(-0.611192\pi\)
−0.342258 + 0.939606i \(0.611192\pi\)
\(660\) 0 0
\(661\) −22.2147 −0.864052 −0.432026 0.901861i \(-0.642201\pi\)
−0.432026 + 0.901861i \(0.642201\pi\)
\(662\) 38.0663 1.47949
\(663\) 0 0
\(664\) −2.70218 −0.104865
\(665\) −16.4819 −0.639142
\(666\) 0 0
\(667\) −1.00000 −0.0387202
\(668\) −46.5788 −1.80219
\(669\) 0 0
\(670\) −63.2784 −2.44466
\(671\) −45.3844 −1.75205
\(672\) 0 0
\(673\) 28.1597 1.08547 0.542737 0.839902i \(-0.317388\pi\)
0.542737 + 0.839902i \(0.317388\pi\)
\(674\) 1.54070 0.0593457
\(675\) 0 0
\(676\) 4.30766 0.165679
\(677\) −0.245245 −0.00942553 −0.00471277 0.999989i \(-0.501500\pi\)
−0.00471277 + 0.999989i \(0.501500\pi\)
\(678\) 0 0
\(679\) −0.778596 −0.0298798
\(680\) −120.319 −4.61401
\(681\) 0 0
\(682\) −11.9527 −0.457693
\(683\) −28.9636 −1.10826 −0.554131 0.832430i \(-0.686949\pi\)
−0.554131 + 0.832430i \(0.686949\pi\)
\(684\) 0 0
\(685\) 11.9758 0.457571
\(686\) 31.4841 1.20207
\(687\) 0 0
\(688\) 129.352 4.93149
\(689\) −36.1795 −1.37833
\(690\) 0 0
\(691\) −35.3723 −1.34563 −0.672813 0.739813i \(-0.734914\pi\)
−0.672813 + 0.739813i \(0.734914\pi\)
\(692\) −78.3687 −2.97913
\(693\) 0 0
\(694\) −33.5801 −1.27468
\(695\) 26.5179 1.00588
\(696\) 0 0
\(697\) 29.1390 1.10372
\(698\) 76.9422 2.91231
\(699\) 0 0
\(700\) 13.2714 0.501612
\(701\) −19.9823 −0.754722 −0.377361 0.926066i \(-0.623168\pi\)
−0.377361 + 0.926066i \(0.623168\pi\)
\(702\) 0 0
\(703\) −54.4712 −2.05442
\(704\) 133.875 5.04561
\(705\) 0 0
\(706\) 72.9966 2.74726
\(707\) 1.19862 0.0450789
\(708\) 0 0
\(709\) −13.0449 −0.489911 −0.244956 0.969534i \(-0.578773\pi\)
−0.244956 + 0.969534i \(0.578773\pi\)
\(710\) −64.5334 −2.42190
\(711\) 0 0
\(712\) −95.7803 −3.58952
\(713\) −0.779005 −0.0291740
\(714\) 0 0
\(715\) 59.0632 2.20884
\(716\) 42.2727 1.57981
\(717\) 0 0
\(718\) 38.0317 1.41933
\(719\) −8.19259 −0.305532 −0.152766 0.988262i \(-0.548818\pi\)
−0.152766 + 0.988262i \(0.548818\pi\)
\(720\) 0 0
\(721\) −4.67905 −0.174257
\(722\) −69.3978 −2.58272
\(723\) 0 0
\(724\) 54.5905 2.02884
\(725\) 2.83932 0.105450
\(726\) 0 0
\(727\) −28.0803 −1.04144 −0.520721 0.853727i \(-0.674337\pi\)
−0.520721 + 0.853727i \(0.674337\pi\)
\(728\) 29.2608 1.08448
\(729\) 0 0
\(730\) −95.8758 −3.54852
\(731\) −45.8862 −1.69716
\(732\) 0 0
\(733\) −32.2797 −1.19228 −0.596140 0.802881i \(-0.703300\pi\)
−0.596140 + 0.802881i \(0.703300\pi\)
\(734\) −94.1774 −3.47615
\(735\) 0 0
\(736\) 18.7511 0.691176
\(737\) −47.4568 −1.74809
\(738\) 0 0
\(739\) 2.56275 0.0942721 0.0471361 0.998888i \(-0.484991\pi\)
0.0471361 + 0.998888i \(0.484991\pi\)
\(740\) 121.099 4.45168
\(741\) 0 0
\(742\) −23.1770 −0.850855
\(743\) −35.8227 −1.31421 −0.657104 0.753800i \(-0.728219\pi\)
−0.657104 + 0.753800i \(0.728219\pi\)
\(744\) 0 0
\(745\) −56.9629 −2.08696
\(746\) −59.6841 −2.18519
\(747\) 0 0
\(748\) −144.806 −5.29464
\(749\) −6.89689 −0.252007
\(750\) 0 0
\(751\) −42.9765 −1.56824 −0.784118 0.620612i \(-0.786884\pi\)
−0.784118 + 0.620612i \(0.786884\pi\)
\(752\) 104.073 3.79516
\(753\) 0 0
\(754\) 10.0460 0.365855
\(755\) 40.2383 1.46442
\(756\) 0 0
\(757\) −32.0132 −1.16354 −0.581769 0.813354i \(-0.697639\pi\)
−0.581769 + 0.813354i \(0.697639\pi\)
\(758\) 20.1864 0.733202
\(759\) 0 0
\(760\) 167.293 6.06834
\(761\) −11.4559 −0.415278 −0.207639 0.978206i \(-0.566578\pi\)
−0.207639 + 0.978206i \(0.566578\pi\)
\(762\) 0 0
\(763\) 9.90124 0.358449
\(764\) −122.348 −4.42639
\(765\) 0 0
\(766\) −83.7005 −3.02422
\(767\) 19.1231 0.690495
\(768\) 0 0
\(769\) −0.0983888 −0.00354799 −0.00177400 0.999998i \(-0.500565\pi\)
−0.00177400 + 0.999998i \(0.500565\pi\)
\(770\) 37.8366 1.36354
\(771\) 0 0
\(772\) 30.1117 1.08374
\(773\) −12.4020 −0.446070 −0.223035 0.974810i \(-0.571596\pi\)
−0.223035 + 0.974810i \(0.571596\pi\)
\(774\) 0 0
\(775\) 2.21185 0.0794519
\(776\) 7.90281 0.283694
\(777\) 0 0
\(778\) −55.4328 −1.98736
\(779\) −40.5153 −1.45161
\(780\) 0 0
\(781\) −48.3981 −1.73182
\(782\) −12.9942 −0.464671
\(783\) 0 0
\(784\) −84.3449 −3.01232
\(785\) 53.0159 1.89222
\(786\) 0 0
\(787\) 26.7197 0.952455 0.476227 0.879322i \(-0.342004\pi\)
0.476227 + 0.879322i \(0.342004\pi\)
\(788\) −42.2848 −1.50633
\(789\) 0 0
\(790\) 114.323 4.06743
\(791\) 15.4057 0.547763
\(792\) 0 0
\(793\) 29.7150 1.05521
\(794\) 49.8660 1.76968
\(795\) 0 0
\(796\) −36.9004 −1.30790
\(797\) −20.2834 −0.718474 −0.359237 0.933246i \(-0.616963\pi\)
−0.359237 + 0.933246i \(0.616963\pi\)
\(798\) 0 0
\(799\) −36.9189 −1.30610
\(800\) −53.2406 −1.88234
\(801\) 0 0
\(802\) −42.5184 −1.50138
\(803\) −71.9039 −2.53743
\(804\) 0 0
\(805\) 2.46596 0.0869137
\(806\) 7.82592 0.275656
\(807\) 0 0
\(808\) −12.1661 −0.428003
\(809\) −35.7621 −1.25733 −0.628665 0.777676i \(-0.716398\pi\)
−0.628665 + 0.777676i \(0.716398\pi\)
\(810\) 0 0
\(811\) 26.4097 0.927370 0.463685 0.886000i \(-0.346527\pi\)
0.463685 + 0.886000i \(0.346527\pi\)
\(812\) 4.67414 0.164030
\(813\) 0 0
\(814\) 125.047 4.38288
\(815\) −34.9760 −1.22516
\(816\) 0 0
\(817\) 63.8008 2.23211
\(818\) 19.3250 0.675682
\(819\) 0 0
\(820\) 90.0725 3.14547
\(821\) −21.8673 −0.763172 −0.381586 0.924333i \(-0.624622\pi\)
−0.381586 + 0.924333i \(0.624622\pi\)
\(822\) 0 0
\(823\) −33.6657 −1.17351 −0.586756 0.809764i \(-0.699595\pi\)
−0.586756 + 0.809764i \(0.699595\pi\)
\(824\) 47.4927 1.65449
\(825\) 0 0
\(826\) 12.2505 0.426249
\(827\) 49.4034 1.71793 0.858963 0.512038i \(-0.171109\pi\)
0.858963 + 0.512038i \(0.171109\pi\)
\(828\) 0 0
\(829\) 3.54310 0.123057 0.0615285 0.998105i \(-0.480402\pi\)
0.0615285 + 0.998105i \(0.480402\pi\)
\(830\) 2.28775 0.0794090
\(831\) 0 0
\(832\) −87.6535 −3.03884
\(833\) 29.9204 1.03668
\(834\) 0 0
\(835\) 24.5738 0.850412
\(836\) 201.341 6.96351
\(837\) 0 0
\(838\) −40.0013 −1.38182
\(839\) 27.3924 0.945691 0.472846 0.881145i \(-0.343227\pi\)
0.472846 + 0.881145i \(0.343227\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) −18.8776 −0.650564
\(843\) 0 0
\(844\) 30.5615 1.05197
\(845\) −2.27261 −0.0781802
\(846\) 0 0
\(847\) 18.6882 0.642133
\(848\) 131.919 4.53011
\(849\) 0 0
\(850\) 36.8947 1.26548
\(851\) 8.14977 0.279371
\(852\) 0 0
\(853\) 18.4109 0.630376 0.315188 0.949029i \(-0.397932\pi\)
0.315188 + 0.949029i \(0.397932\pi\)
\(854\) 19.0358 0.651391
\(855\) 0 0
\(856\) 70.0039 2.39268
\(857\) −40.3861 −1.37956 −0.689782 0.724018i \(-0.742293\pi\)
−0.689782 + 0.724018i \(0.742293\pi\)
\(858\) 0 0
\(859\) 38.5166 1.31417 0.657085 0.753816i \(-0.271789\pi\)
0.657085 + 0.753816i \(0.271789\pi\)
\(860\) −141.840 −4.83670
\(861\) 0 0
\(862\) 49.3139 1.67964
\(863\) −22.4884 −0.765513 −0.382756 0.923849i \(-0.625025\pi\)
−0.382756 + 0.923849i \(0.625025\pi\)
\(864\) 0 0
\(865\) 41.3454 1.40578
\(866\) 17.6827 0.600882
\(867\) 0 0
\(868\) 3.64118 0.123590
\(869\) 85.7387 2.90849
\(870\) 0 0
\(871\) 31.0719 1.05283
\(872\) −100.498 −3.40330
\(873\) 0 0
\(874\) 18.0673 0.611136
\(875\) 5.32814 0.180124
\(876\) 0 0
\(877\) −2.78341 −0.0939892 −0.0469946 0.998895i \(-0.514964\pi\)
−0.0469946 + 0.998895i \(0.514964\pi\)
\(878\) 67.3714 2.27367
\(879\) 0 0
\(880\) −215.358 −7.25973
\(881\) 0.347005 0.0116909 0.00584544 0.999983i \(-0.498139\pi\)
0.00584544 + 0.999983i \(0.498139\pi\)
\(882\) 0 0
\(883\) −31.9999 −1.07688 −0.538442 0.842663i \(-0.680987\pi\)
−0.538442 + 0.842663i \(0.680987\pi\)
\(884\) 94.8104 3.18882
\(885\) 0 0
\(886\) −85.7514 −2.88087
\(887\) −54.2012 −1.81990 −0.909949 0.414721i \(-0.863879\pi\)
−0.909949 + 0.414721i \(0.863879\pi\)
\(888\) 0 0
\(889\) 0.181783 0.00609682
\(890\) 81.0907 2.71817
\(891\) 0 0
\(892\) 64.1710 2.14860
\(893\) 51.3326 1.71778
\(894\) 0 0
\(895\) −22.3020 −0.745475
\(896\) −23.1222 −0.772459
\(897\) 0 0
\(898\) 74.6706 2.49179
\(899\) 0.779005 0.0259813
\(900\) 0 0
\(901\) −46.7968 −1.55903
\(902\) 93.0088 3.09685
\(903\) 0 0
\(904\) −156.369 −5.20075
\(905\) −28.8005 −0.957363
\(906\) 0 0
\(907\) −8.16651 −0.271164 −0.135582 0.990766i \(-0.543290\pi\)
−0.135582 + 0.990766i \(0.543290\pi\)
\(908\) 143.530 4.76322
\(909\) 0 0
\(910\) −24.7732 −0.821222
\(911\) −21.0259 −0.696618 −0.348309 0.937380i \(-0.613244\pi\)
−0.348309 + 0.937380i \(0.613244\pi\)
\(912\) 0 0
\(913\) 1.71574 0.0567828
\(914\) −9.12474 −0.301820
\(915\) 0 0
\(916\) −28.2344 −0.932890
\(917\) −8.37039 −0.276415
\(918\) 0 0
\(919\) −12.9335 −0.426638 −0.213319 0.976983i \(-0.568427\pi\)
−0.213319 + 0.976983i \(0.568427\pi\)
\(920\) −25.0297 −0.825204
\(921\) 0 0
\(922\) 108.085 3.55961
\(923\) 31.6882 1.04303
\(924\) 0 0
\(925\) −23.1398 −0.760833
\(926\) −24.8345 −0.816113
\(927\) 0 0
\(928\) −18.7511 −0.615536
\(929\) 13.5273 0.443817 0.221909 0.975067i \(-0.428771\pi\)
0.221909 + 0.975067i \(0.428771\pi\)
\(930\) 0 0
\(931\) −41.6018 −1.36344
\(932\) −126.703 −4.15028
\(933\) 0 0
\(934\) 35.3636 1.15713
\(935\) 76.3961 2.49842
\(936\) 0 0
\(937\) −4.15878 −0.135862 −0.0679308 0.997690i \(-0.521640\pi\)
−0.0679308 + 0.997690i \(0.521640\pi\)
\(938\) 19.9050 0.649923
\(939\) 0 0
\(940\) −114.121 −3.72222
\(941\) 46.9661 1.53105 0.765525 0.643406i \(-0.222479\pi\)
0.765525 + 0.643406i \(0.222479\pi\)
\(942\) 0 0
\(943\) 6.06174 0.197398
\(944\) −69.7273 −2.26943
\(945\) 0 0
\(946\) −146.464 −4.76195
\(947\) 6.09656 0.198112 0.0990558 0.995082i \(-0.468418\pi\)
0.0990558 + 0.995082i \(0.468418\pi\)
\(948\) 0 0
\(949\) 47.0783 1.52823
\(950\) −51.2990 −1.66436
\(951\) 0 0
\(952\) 37.8478 1.22665
\(953\) 9.32474 0.302058 0.151029 0.988529i \(-0.451741\pi\)
0.151029 + 0.988529i \(0.451741\pi\)
\(954\) 0 0
\(955\) 64.5476 2.08871
\(956\) 43.7717 1.41568
\(957\) 0 0
\(958\) 112.285 3.62777
\(959\) −3.76713 −0.121647
\(960\) 0 0
\(961\) −30.3932 −0.980424
\(962\) −81.8730 −2.63969
\(963\) 0 0
\(964\) 56.0396 1.80492
\(965\) −15.8862 −0.511393
\(966\) 0 0
\(967\) −43.6266 −1.40294 −0.701468 0.712701i \(-0.747472\pi\)
−0.701468 + 0.712701i \(0.747472\pi\)
\(968\) −189.686 −6.09675
\(969\) 0 0
\(970\) −6.69078 −0.214828
\(971\) −19.3929 −0.622347 −0.311173 0.950353i \(-0.600722\pi\)
−0.311173 + 0.950353i \(0.600722\pi\)
\(972\) 0 0
\(973\) −8.34155 −0.267418
\(974\) −60.6256 −1.94257
\(975\) 0 0
\(976\) −108.348 −3.46813
\(977\) 58.1111 1.85914 0.929569 0.368649i \(-0.120180\pi\)
0.929569 + 0.368649i \(0.120180\pi\)
\(978\) 0 0
\(979\) 60.8155 1.94367
\(980\) 92.4879 2.95442
\(981\) 0 0
\(982\) 37.5269 1.19753
\(983\) −30.4731 −0.971942 −0.485971 0.873975i \(-0.661534\pi\)
−0.485971 + 0.873975i \(0.661534\pi\)
\(984\) 0 0
\(985\) 22.3084 0.710804
\(986\) 12.9942 0.413819
\(987\) 0 0
\(988\) −131.826 −4.19394
\(989\) −9.54562 −0.303533
\(990\) 0 0
\(991\) 11.8870 0.377603 0.188802 0.982015i \(-0.439540\pi\)
0.188802 + 0.982015i \(0.439540\pi\)
\(992\) −14.6072 −0.463780
\(993\) 0 0
\(994\) 20.2998 0.643872
\(995\) 19.4677 0.617168
\(996\) 0 0
\(997\) −33.6336 −1.06519 −0.532593 0.846371i \(-0.678782\pi\)
−0.532593 + 0.846371i \(0.678782\pi\)
\(998\) 29.5635 0.935818
\(999\) 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.1.2 11
3.2 odd 2 2001.2.a.l.1.10 11
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2001.2.a.l.1.10 11 3.2 odd 2
6003.2.a.m.1.2 11 1.1 even 1 trivial