Properties

Label 2001.2.a.l.1.10
Level $2001$
Weight $2$
Character 2001.1
Self dual yes
Analytic conductor $15.978$
Analytic rank $0$
Dimension $11$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2001 = 3 \cdot 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2001.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(15.9780654445\)
Analytic rank: \(0\)
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: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Root \(2.70316\) of defining polynomial
Character \(\chi\) \(=\) 2001.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.70316 q^{2} -1.00000 q^{3} +5.30708 q^{4} +2.79988 q^{5} -2.70316 q^{6} +0.880738 q^{7} +8.93955 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+2.70316 q^{2} -1.00000 q^{3} +5.30708 q^{4} +2.79988 q^{5} -2.70316 q^{6} +0.880738 q^{7} +8.93955 q^{8} +1.00000 q^{9} +7.56852 q^{10} -5.67616 q^{11} -5.30708 q^{12} -3.71641 q^{13} +2.38078 q^{14} -2.79988 q^{15} +13.5509 q^{16} +4.80704 q^{17} +2.70316 q^{18} +6.68378 q^{19} +14.8592 q^{20} -0.880738 q^{21} -15.3436 q^{22} +1.00000 q^{23} -8.93955 q^{24} +2.83932 q^{25} -10.0460 q^{26} -1.00000 q^{27} +4.67414 q^{28} -1.00000 q^{29} -7.56852 q^{30} +0.779005 q^{31} +18.7511 q^{32} +5.67616 q^{33} +12.9942 q^{34} +2.46596 q^{35} +5.30708 q^{36} -8.14977 q^{37} +18.0673 q^{38} +3.71641 q^{39} +25.0297 q^{40} +6.06174 q^{41} -2.38078 q^{42} +9.54562 q^{43} -30.1238 q^{44} +2.79988 q^{45} +2.70316 q^{46} -7.68018 q^{47} -13.5509 q^{48} -6.22430 q^{49} +7.67515 q^{50} -4.80704 q^{51} -19.7233 q^{52} -9.73506 q^{53} -2.70316 q^{54} -15.8926 q^{55} +7.87341 q^{56} -6.68378 q^{57} -2.70316 q^{58} +5.14558 q^{59} -14.8592 q^{60} -7.99562 q^{61} +2.10578 q^{62} +0.880738 q^{63} +23.5855 q^{64} -10.4055 q^{65} +15.3436 q^{66} -8.36073 q^{67} +25.5113 q^{68} -1.00000 q^{69} +6.66589 q^{70} +8.52656 q^{71} +8.93955 q^{72} -12.6677 q^{73} -22.0301 q^{74} -2.83932 q^{75} +35.4713 q^{76} -4.99921 q^{77} +10.0460 q^{78} +15.1051 q^{79} +37.9409 q^{80} +1.00000 q^{81} +16.3859 q^{82} -0.302272 q^{83} -4.67414 q^{84} +13.4591 q^{85} +25.8033 q^{86} +1.00000 q^{87} -50.7423 q^{88} -10.7142 q^{89} +7.56852 q^{90} -3.27318 q^{91} +5.30708 q^{92} -0.779005 q^{93} -20.7608 q^{94} +18.7138 q^{95} -18.7511 q^{96} -0.884027 q^{97} -16.8253 q^{98} -5.67616 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11q + 2q^{2} - 11q^{3} + 18q^{4} + 2q^{5} - 2q^{6} + 3q^{7} + 18q^{8} + 11q^{9} + O(q^{10}) \) \( 11q + 2q^{2} - 11q^{3} + 18q^{4} + 2q^{5} - 2q^{6} + 3q^{7} + 18q^{8} + 11q^{9} + 14q^{10} + 11q^{11} - 18q^{12} - 5q^{13} + 17q^{14} - 2q^{15} + 20q^{16} + 15q^{17} + 2q^{18} - 6q^{19} + 21q^{20} - 3q^{21} - 10q^{22} + 11q^{23} - 18q^{24} + 3q^{25} - 5q^{26} - 11q^{27} + 7q^{28} - 11q^{29} - 14q^{30} + 35q^{31} + 28q^{32} - 11q^{33} + 28q^{34} + 15q^{35} + 18q^{36} - 28q^{37} - 2q^{38} + 5q^{39} - q^{40} + 10q^{41} - 17q^{42} - 6q^{43} + 18q^{44} + 2q^{45} + 2q^{46} + 15q^{47} - 20q^{48} + 22q^{49} + 15q^{50} - 15q^{51} - 36q^{52} - 7q^{53} - 2q^{54} - 12q^{55} + 56q^{56} + 6q^{57} - 2q^{58} - 20q^{59} - 21q^{60} - 20q^{61} - 11q^{62} + 3q^{63} + 36q^{64} + 11q^{65} + 10q^{66} - 39q^{67} + 35q^{68} - 11q^{69} + 38q^{70} + 49q^{71} + 18q^{72} - 3q^{73} + 37q^{74} - 3q^{75} - 18q^{76} + 25q^{77} + 5q^{78} + 41q^{79} + 51q^{80} + 11q^{81} - 19q^{82} + 13q^{83} - 7q^{84} + 62q^{86} + 11q^{87} - 40q^{88} + 34q^{89} + 14q^{90} + 2q^{91} + 18q^{92} - 35q^{93} - 14q^{94} + 25q^{95} - 28q^{96} - 11q^{97} + 53q^{98} + 11q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.70316 1.91142 0.955711 0.294305i \(-0.0950882\pi\)
0.955711 + 0.294305i \(0.0950882\pi\)
\(3\) −1.00000 −0.577350
\(4\) 5.30708 2.65354
\(5\) 2.79988 1.25214 0.626072 0.779765i \(-0.284662\pi\)
0.626072 + 0.779765i \(0.284662\pi\)
\(6\) −2.70316 −1.10356
\(7\) 0.880738 0.332888 0.166444 0.986051i \(-0.446772\pi\)
0.166444 + 0.986051i \(0.446772\pi\)
\(8\) 8.93955 3.16061
\(9\) 1.00000 0.333333
\(10\) 7.56852 2.39338
\(11\) −5.67616 −1.71143 −0.855713 0.517451i \(-0.826881\pi\)
−0.855713 + 0.517451i \(0.826881\pi\)
\(12\) −5.30708 −1.53202
\(13\) −3.71641 −1.03075 −0.515373 0.856966i \(-0.672347\pi\)
−0.515373 + 0.856966i \(0.672347\pi\)
\(14\) 2.38078 0.636289
\(15\) −2.79988 −0.722926
\(16\) 13.5509 3.38772
\(17\) 4.80704 1.16588 0.582939 0.812516i \(-0.301903\pi\)
0.582939 + 0.812516i \(0.301903\pi\)
\(18\) 2.70316 0.637141
\(19\) 6.68378 1.53336 0.766682 0.642027i \(-0.221907\pi\)
0.766682 + 0.642027i \(0.221907\pi\)
\(20\) 14.8592 3.32261
\(21\) −0.880738 −0.192193
\(22\) −15.3436 −3.27126
\(23\) 1.00000 0.208514
\(24\) −8.93955 −1.82478
\(25\) 2.83932 0.567865
\(26\) −10.0460 −1.97019
\(27\) −1.00000 −0.192450
\(28\) 4.67414 0.883330
\(29\) −1.00000 −0.185695
\(30\) −7.56852 −1.38182
\(31\) 0.779005 0.139913 0.0699567 0.997550i \(-0.477714\pi\)
0.0699567 + 0.997550i \(0.477714\pi\)
\(32\) 18.7511 3.31476
\(33\) 5.67616 0.988092
\(34\) 12.9942 2.22849
\(35\) 2.46596 0.416823
\(36\) 5.30708 0.884513
\(37\) −8.14977 −1.33981 −0.669907 0.742445i \(-0.733666\pi\)
−0.669907 + 0.742445i \(0.733666\pi\)
\(38\) 18.0673 2.93091
\(39\) 3.71641 0.595101
\(40\) 25.0297 3.95754
\(41\) 6.06174 0.946686 0.473343 0.880878i \(-0.343047\pi\)
0.473343 + 0.880878i \(0.343047\pi\)
\(42\) −2.38078 −0.367362
\(43\) 9.54562 1.45569 0.727847 0.685740i \(-0.240521\pi\)
0.727847 + 0.685740i \(0.240521\pi\)
\(44\) −30.1238 −4.54133
\(45\) 2.79988 0.417381
\(46\) 2.70316 0.398559
\(47\) −7.68018 −1.12027 −0.560135 0.828402i \(-0.689251\pi\)
−0.560135 + 0.828402i \(0.689251\pi\)
\(48\) −13.5509 −1.95590
\(49\) −6.22430 −0.889186
\(50\) 7.67515 1.08543
\(51\) −4.80704 −0.673120
\(52\) −19.7233 −2.73512
\(53\) −9.73506 −1.33721 −0.668607 0.743616i \(-0.733109\pi\)
−0.668607 + 0.743616i \(0.733109\pi\)
\(54\) −2.70316 −0.367854
\(55\) −15.8926 −2.14295
\(56\) 7.87341 1.05213
\(57\) −6.68378 −0.885288
\(58\) −2.70316 −0.354942
\(59\) 5.14558 0.669898 0.334949 0.942236i \(-0.391281\pi\)
0.334949 + 0.942236i \(0.391281\pi\)
\(60\) −14.8592 −1.91831
\(61\) −7.99562 −1.02373 −0.511867 0.859065i \(-0.671046\pi\)
−0.511867 + 0.859065i \(0.671046\pi\)
\(62\) 2.10578 0.267434
\(63\) 0.880738 0.110963
\(64\) 23.5855 2.94819
\(65\) −10.4055 −1.29064
\(66\) 15.3436 1.88866
\(67\) −8.36073 −1.02143 −0.510713 0.859751i \(-0.670619\pi\)
−0.510713 + 0.859751i \(0.670619\pi\)
\(68\) 25.5113 3.09370
\(69\) −1.00000 −0.120386
\(70\) 6.66589 0.796726
\(71\) 8.52656 1.01192 0.505958 0.862558i \(-0.331139\pi\)
0.505958 + 0.862558i \(0.331139\pi\)
\(72\) 8.93955 1.05354
\(73\) −12.6677 −1.48264 −0.741321 0.671150i \(-0.765801\pi\)
−0.741321 + 0.671150i \(0.765801\pi\)
\(74\) −22.0301 −2.56095
\(75\) −2.83932 −0.327857
\(76\) 35.4713 4.06884
\(77\) −4.99921 −0.569713
\(78\) 10.0460 1.13749
\(79\) 15.1051 1.69945 0.849726 0.527224i \(-0.176767\pi\)
0.849726 + 0.527224i \(0.176767\pi\)
\(80\) 37.9409 4.24192
\(81\) 1.00000 0.111111
\(82\) 16.3859 1.80952
\(83\) −0.302272 −0.0331786 −0.0165893 0.999862i \(-0.505281\pi\)
−0.0165893 + 0.999862i \(0.505281\pi\)
\(84\) −4.67414 −0.509991
\(85\) 13.4591 1.45985
\(86\) 25.8033 2.78245
\(87\) 1.00000 0.107211
\(88\) −50.7423 −5.40915
\(89\) −10.7142 −1.13570 −0.567852 0.823131i \(-0.692225\pi\)
−0.567852 + 0.823131i \(0.692225\pi\)
\(90\) 7.56852 0.797792
\(91\) −3.27318 −0.343123
\(92\) 5.30708 0.553301
\(93\) −0.779005 −0.0807791
\(94\) −20.7608 −2.14131
\(95\) 18.7138 1.91999
\(96\) −18.7511 −1.91378
\(97\) −0.884027 −0.0897593 −0.0448797 0.998992i \(-0.514290\pi\)
−0.0448797 + 0.998992i \(0.514290\pi\)
\(98\) −16.8253 −1.69961
\(99\) −5.67616 −0.570475
\(100\) 15.0685 1.50685
\(101\) −1.36093 −0.135418 −0.0677089 0.997705i \(-0.521569\pi\)
−0.0677089 + 0.997705i \(0.521569\pi\)
\(102\) −12.9942 −1.28662
\(103\) −5.31264 −0.523470 −0.261735 0.965140i \(-0.584295\pi\)
−0.261735 + 0.965140i \(0.584295\pi\)
\(104\) −33.2230 −3.25779
\(105\) −2.46596 −0.240653
\(106\) −26.3154 −2.55598
\(107\) 7.83080 0.757032 0.378516 0.925595i \(-0.376434\pi\)
0.378516 + 0.925595i \(0.376434\pi\)
\(108\) −5.30708 −0.510674
\(109\) 11.2420 1.07679 0.538393 0.842694i \(-0.319032\pi\)
0.538393 + 0.842694i \(0.319032\pi\)
\(110\) −42.9601 −4.09609
\(111\) 8.14977 0.773542
\(112\) 11.9348 1.12773
\(113\) −17.4918 −1.64549 −0.822745 0.568411i \(-0.807558\pi\)
−0.822745 + 0.568411i \(0.807558\pi\)
\(114\) −18.0673 −1.69216
\(115\) 2.79988 0.261090
\(116\) −5.30708 −0.492750
\(117\) −3.71641 −0.343582
\(118\) 13.9093 1.28046
\(119\) 4.23374 0.388106
\(120\) −25.0297 −2.28489
\(121\) 21.2188 1.92898
\(122\) −21.6134 −1.95679
\(123\) −6.06174 −0.546569
\(124\) 4.13424 0.371266
\(125\) −6.04963 −0.541095
\(126\) 2.38078 0.212096
\(127\) 0.206399 0.0183149 0.00915747 0.999958i \(-0.497085\pi\)
0.00915747 + 0.999958i \(0.497085\pi\)
\(128\) 26.2532 2.32048
\(129\) −9.54562 −0.840445
\(130\) −28.1277 −2.46696
\(131\) 9.50384 0.830354 0.415177 0.909741i \(-0.363720\pi\)
0.415177 + 0.909741i \(0.363720\pi\)
\(132\) 30.1238 2.62194
\(133\) 5.88666 0.510438
\(134\) −22.6004 −1.95238
\(135\) −2.79988 −0.240975
\(136\) 42.9728 3.68488
\(137\) 4.27725 0.365430 0.182715 0.983166i \(-0.441511\pi\)
0.182715 + 0.983166i \(0.441511\pi\)
\(138\) −2.70316 −0.230108
\(139\) −9.47109 −0.803327 −0.401663 0.915787i \(-0.631568\pi\)
−0.401663 + 0.915787i \(0.631568\pi\)
\(140\) 13.0870 1.10606
\(141\) 7.68018 0.646788
\(142\) 23.0487 1.93420
\(143\) 21.0949 1.76405
\(144\) 13.5509 1.12924
\(145\) −2.79988 −0.232517
\(146\) −34.2428 −2.83396
\(147\) 6.22430 0.513372
\(148\) −43.2514 −3.55525
\(149\) −20.3448 −1.66671 −0.833354 0.552740i \(-0.813582\pi\)
−0.833354 + 0.552740i \(0.813582\pi\)
\(150\) −7.67515 −0.626673
\(151\) −14.3715 −1.16953 −0.584766 0.811202i \(-0.698814\pi\)
−0.584766 + 0.811202i \(0.698814\pi\)
\(152\) 59.7500 4.84636
\(153\) 4.80704 0.388626
\(154\) −13.5137 −1.08896
\(155\) 2.18112 0.175192
\(156\) 19.7233 1.57912
\(157\) −18.9351 −1.51118 −0.755592 0.655043i \(-0.772651\pi\)
−0.755592 + 0.655043i \(0.772651\pi\)
\(158\) 40.8314 3.24837
\(159\) 9.73506 0.772041
\(160\) 52.5009 4.15056
\(161\) 0.880738 0.0694119
\(162\) 2.70316 0.212380
\(163\) 12.4920 0.978447 0.489224 0.872158i \(-0.337280\pi\)
0.489224 + 0.872158i \(0.337280\pi\)
\(164\) 32.1701 2.51207
\(165\) 15.8926 1.23723
\(166\) −0.817089 −0.0634184
\(167\) 8.77674 0.679165 0.339582 0.940576i \(-0.389714\pi\)
0.339582 + 0.940576i \(0.389714\pi\)
\(168\) −7.87341 −0.607447
\(169\) 0.811682 0.0624371
\(170\) 36.3822 2.79038
\(171\) 6.68378 0.511121
\(172\) 50.6593 3.86274
\(173\) 14.7668 1.12270 0.561351 0.827578i \(-0.310282\pi\)
0.561351 + 0.827578i \(0.310282\pi\)
\(174\) 2.70316 0.204926
\(175\) 2.50070 0.189035
\(176\) −76.9170 −5.79784
\(177\) −5.14558 −0.386766
\(178\) −28.9622 −2.17081
\(179\) −7.96536 −0.595359 −0.297679 0.954666i \(-0.596213\pi\)
−0.297679 + 0.954666i \(0.596213\pi\)
\(180\) 14.8592 1.10754
\(181\) 10.2864 0.764579 0.382289 0.924043i \(-0.375136\pi\)
0.382289 + 0.924043i \(0.375136\pi\)
\(182\) −8.84794 −0.655853
\(183\) 7.99562 0.591053
\(184\) 8.93955 0.659033
\(185\) −22.8184 −1.67764
\(186\) −2.10578 −0.154403
\(187\) −27.2855 −1.99531
\(188\) −40.7593 −2.97268
\(189\) −0.880738 −0.0640643
\(190\) 50.5863 3.66992
\(191\) 23.0537 1.66811 0.834054 0.551683i \(-0.186014\pi\)
0.834054 + 0.551683i \(0.186014\pi\)
\(192\) −23.5855 −1.70214
\(193\) 5.67387 0.408414 0.204207 0.978928i \(-0.434538\pi\)
0.204207 + 0.978928i \(0.434538\pi\)
\(194\) −2.38967 −0.171568
\(195\) 10.4055 0.745153
\(196\) −33.0328 −2.35949
\(197\) 7.96762 0.567669 0.283835 0.958873i \(-0.408393\pi\)
0.283835 + 0.958873i \(0.408393\pi\)
\(198\) −15.3436 −1.09042
\(199\) −6.95306 −0.492889 −0.246445 0.969157i \(-0.579262\pi\)
−0.246445 + 0.969157i \(0.579262\pi\)
\(200\) 25.3823 1.79480
\(201\) 8.36073 0.589721
\(202\) −3.67882 −0.258841
\(203\) −0.880738 −0.0618157
\(204\) −25.5113 −1.78615
\(205\) 16.9722 1.18539
\(206\) −14.3609 −1.00057
\(207\) 1.00000 0.0695048
\(208\) −50.3607 −3.49188
\(209\) −37.9382 −2.62424
\(210\) −6.66589 −0.459990
\(211\) 5.75864 0.396441 0.198221 0.980157i \(-0.436484\pi\)
0.198221 + 0.980157i \(0.436484\pi\)
\(212\) −51.6647 −3.54835
\(213\) −8.52656 −0.584230
\(214\) 21.1679 1.44701
\(215\) 26.7266 1.82274
\(216\) −8.93955 −0.608260
\(217\) 0.686100 0.0465755
\(218\) 30.3889 2.05819
\(219\) 12.6677 0.856004
\(220\) −84.3430 −5.68640
\(221\) −17.8649 −1.20172
\(222\) 22.0301 1.47857
\(223\) 12.0916 0.809713 0.404856 0.914380i \(-0.367322\pi\)
0.404856 + 0.914380i \(0.367322\pi\)
\(224\) 16.5148 1.10344
\(225\) 2.83932 0.189288
\(226\) −47.2831 −3.14523
\(227\) −27.0451 −1.79505 −0.897523 0.440968i \(-0.854635\pi\)
−0.897523 + 0.440968i \(0.854635\pi\)
\(228\) −35.4713 −2.34914
\(229\) −5.32014 −0.351565 −0.175782 0.984429i \(-0.556245\pi\)
−0.175782 + 0.984429i \(0.556245\pi\)
\(230\) 7.56852 0.499054
\(231\) 4.99921 0.328924
\(232\) −8.93955 −0.586911
\(233\) 23.8743 1.56406 0.782028 0.623244i \(-0.214186\pi\)
0.782028 + 0.623244i \(0.214186\pi\)
\(234\) −10.0460 −0.656730
\(235\) −21.5036 −1.40274
\(236\) 27.3080 1.77760
\(237\) −15.1051 −0.981179
\(238\) 11.4445 0.741836
\(239\) −8.24781 −0.533506 −0.266753 0.963765i \(-0.585951\pi\)
−0.266753 + 0.963765i \(0.585951\pi\)
\(240\) −37.9409 −2.44907
\(241\) 10.5594 0.680192 0.340096 0.940391i \(-0.389540\pi\)
0.340096 + 0.940391i \(0.389540\pi\)
\(242\) 57.3577 3.68709
\(243\) −1.00000 −0.0641500
\(244\) −42.4334 −2.71652
\(245\) −17.4273 −1.11339
\(246\) −16.3859 −1.04472
\(247\) −24.8396 −1.58051
\(248\) 6.96396 0.442212
\(249\) 0.302272 0.0191557
\(250\) −16.3531 −1.03426
\(251\) −15.9674 −1.00785 −0.503927 0.863746i \(-0.668112\pi\)
−0.503927 + 0.863746i \(0.668112\pi\)
\(252\) 4.67414 0.294443
\(253\) −5.67616 −0.356857
\(254\) 0.557929 0.0350076
\(255\) −13.4591 −0.842843
\(256\) 23.7956 1.48722
\(257\) −5.13834 −0.320521 −0.160260 0.987075i \(-0.551233\pi\)
−0.160260 + 0.987075i \(0.551233\pi\)
\(258\) −25.8033 −1.60645
\(259\) −7.17782 −0.446008
\(260\) −55.2227 −3.42477
\(261\) −1.00000 −0.0618984
\(262\) 25.6904 1.58716
\(263\) 22.1102 1.36337 0.681687 0.731644i \(-0.261246\pi\)
0.681687 + 0.731644i \(0.261246\pi\)
\(264\) 50.7423 3.12297
\(265\) −27.2570 −1.67438
\(266\) 15.9126 0.975663
\(267\) 10.7142 0.655699
\(268\) −44.3710 −2.71039
\(269\) 20.1023 1.22566 0.612828 0.790216i \(-0.290032\pi\)
0.612828 + 0.790216i \(0.290032\pi\)
\(270\) −7.56852 −0.460606
\(271\) 6.90145 0.419233 0.209617 0.977784i \(-0.432778\pi\)
0.209617 + 0.977784i \(0.432778\pi\)
\(272\) 65.1397 3.94967
\(273\) 3.27318 0.198102
\(274\) 11.5621 0.698491
\(275\) −16.1165 −0.971859
\(276\) −5.30708 −0.319448
\(277\) 24.5794 1.47683 0.738416 0.674345i \(-0.235574\pi\)
0.738416 + 0.674345i \(0.235574\pi\)
\(278\) −25.6019 −1.53550
\(279\) 0.779005 0.0466378
\(280\) 22.0446 1.31742
\(281\) −17.2690 −1.03018 −0.515090 0.857136i \(-0.672241\pi\)
−0.515090 + 0.857136i \(0.672241\pi\)
\(282\) 20.7608 1.23629
\(283\) −7.22081 −0.429232 −0.214616 0.976698i \(-0.568850\pi\)
−0.214616 + 0.976698i \(0.568850\pi\)
\(284\) 45.2511 2.68516
\(285\) −18.7138 −1.10851
\(286\) 57.0229 3.37184
\(287\) 5.33881 0.315140
\(288\) 18.7511 1.10492
\(289\) 6.10760 0.359271
\(290\) −7.56852 −0.444439
\(291\) 0.884027 0.0518226
\(292\) −67.2285 −3.93425
\(293\) −18.2359 −1.06535 −0.532677 0.846319i \(-0.678814\pi\)
−0.532677 + 0.846319i \(0.678814\pi\)
\(294\) 16.8253 0.981270
\(295\) 14.4070 0.838809
\(296\) −72.8553 −4.23463
\(297\) 5.67616 0.329364
\(298\) −54.9951 −3.18578
\(299\) −3.71641 −0.214925
\(300\) −15.0685 −0.869981
\(301\) 8.40720 0.484583
\(302\) −38.8484 −2.23547
\(303\) 1.36093 0.0781835
\(304\) 90.5712 5.19461
\(305\) −22.3868 −1.28186
\(306\) 12.9942 0.742828
\(307\) −14.8966 −0.850193 −0.425097 0.905148i \(-0.639760\pi\)
−0.425097 + 0.905148i \(0.639760\pi\)
\(308\) −26.5312 −1.51175
\(309\) 5.31264 0.302226
\(310\) 5.89592 0.334866
\(311\) −1.07620 −0.0610259 −0.0305129 0.999534i \(-0.509714\pi\)
−0.0305129 + 0.999534i \(0.509714\pi\)
\(312\) 33.2230 1.88088
\(313\) −24.6270 −1.39200 −0.696000 0.718042i \(-0.745039\pi\)
−0.696000 + 0.718042i \(0.745039\pi\)
\(314\) −51.1846 −2.88851
\(315\) 2.46596 0.138941
\(316\) 80.1637 4.50956
\(317\) 10.3442 0.580988 0.290494 0.956877i \(-0.406180\pi\)
0.290494 + 0.956877i \(0.406180\pi\)
\(318\) 26.3154 1.47570
\(319\) 5.67616 0.317804
\(320\) 66.0367 3.69156
\(321\) −7.83080 −0.437073
\(322\) 2.38078 0.132676
\(323\) 32.1292 1.78771
\(324\) 5.30708 0.294838
\(325\) −10.5521 −0.585324
\(326\) 33.7678 1.87023
\(327\) −11.2420 −0.621683
\(328\) 54.1893 2.99210
\(329\) −6.76423 −0.372924
\(330\) 42.9601 2.36488
\(331\) −14.0821 −0.774025 −0.387012 0.922075i \(-0.626493\pi\)
−0.387012 + 0.922075i \(0.626493\pi\)
\(332\) −1.60418 −0.0880408
\(333\) −8.14977 −0.446605
\(334\) 23.7249 1.29817
\(335\) −23.4090 −1.27897
\(336\) −11.9348 −0.651096
\(337\) −0.569964 −0.0310479 −0.0155240 0.999879i \(-0.504942\pi\)
−0.0155240 + 0.999879i \(0.504942\pi\)
\(338\) 2.19411 0.119344
\(339\) 17.4918 0.950024
\(340\) 71.4286 3.87376
\(341\) −4.42176 −0.239452
\(342\) 18.0673 0.976969
\(343\) −11.6471 −0.628887
\(344\) 85.3336 4.60088
\(345\) −2.79988 −0.150740
\(346\) 39.9171 2.14596
\(347\) −12.4225 −0.666877 −0.333438 0.942772i \(-0.608209\pi\)
−0.333438 + 0.942772i \(0.608209\pi\)
\(348\) 5.30708 0.284489
\(349\) −28.4638 −1.52363 −0.761816 0.647793i \(-0.775692\pi\)
−0.761816 + 0.647793i \(0.775692\pi\)
\(350\) 6.75980 0.361326
\(351\) 3.71641 0.198367
\(352\) −106.434 −5.67297
\(353\) 27.0042 1.43729 0.718644 0.695378i \(-0.244763\pi\)
0.718644 + 0.695378i \(0.244763\pi\)
\(354\) −13.9093 −0.739273
\(355\) 23.8733 1.26706
\(356\) −56.8611 −3.01363
\(357\) −4.23374 −0.224073
\(358\) −21.5316 −1.13798
\(359\) 14.0693 0.742551 0.371276 0.928523i \(-0.378921\pi\)
0.371276 + 0.928523i \(0.378921\pi\)
\(360\) 25.0297 1.31918
\(361\) 25.6729 1.35120
\(362\) 27.8057 1.46143
\(363\) −21.2188 −1.11370
\(364\) −17.3710 −0.910489
\(365\) −35.4680 −1.85648
\(366\) 21.6134 1.12975
\(367\) 34.8397 1.81862 0.909310 0.416120i \(-0.136610\pi\)
0.909310 + 0.416120i \(0.136610\pi\)
\(368\) 13.5509 0.706389
\(369\) 6.06174 0.315562
\(370\) −61.6817 −3.20668
\(371\) −8.57404 −0.445142
\(372\) −4.13424 −0.214350
\(373\) 22.0794 1.14323 0.571613 0.820523i \(-0.306318\pi\)
0.571613 + 0.820523i \(0.306318\pi\)
\(374\) −73.7571 −3.81389
\(375\) 6.04963 0.312402
\(376\) −68.6574 −3.54073
\(377\) 3.71641 0.191405
\(378\) −2.38078 −0.122454
\(379\) −7.46769 −0.383590 −0.191795 0.981435i \(-0.561431\pi\)
−0.191795 + 0.981435i \(0.561431\pi\)
\(380\) 99.3154 5.09477
\(381\) −0.206399 −0.0105741
\(382\) 62.3178 3.18846
\(383\) −30.9640 −1.58218 −0.791092 0.611697i \(-0.790487\pi\)
−0.791092 + 0.611697i \(0.790487\pi\)
\(384\) −26.2532 −1.33973
\(385\) −13.9972 −0.713363
\(386\) 15.3374 0.780652
\(387\) 9.54562 0.485231
\(388\) −4.69160 −0.238180
\(389\) −20.5067 −1.03973 −0.519864 0.854249i \(-0.674018\pi\)
−0.519864 + 0.854249i \(0.674018\pi\)
\(390\) 28.1277 1.42430
\(391\) 4.80704 0.243102
\(392\) −55.6425 −2.81037
\(393\) −9.50384 −0.479405
\(394\) 21.5378 1.08506
\(395\) 42.2924 2.12796
\(396\) −30.1238 −1.51378
\(397\) −18.4473 −0.925843 −0.462922 0.886399i \(-0.653199\pi\)
−0.462922 + 0.886399i \(0.653199\pi\)
\(398\) −18.7952 −0.942120
\(399\) −5.88666 −0.294701
\(400\) 38.4754 1.92377
\(401\) −15.7291 −0.785475 −0.392738 0.919651i \(-0.628472\pi\)
−0.392738 + 0.919651i \(0.628472\pi\)
\(402\) 22.6004 1.12721
\(403\) −2.89510 −0.144215
\(404\) −7.22257 −0.359336
\(405\) 2.79988 0.139127
\(406\) −2.38078 −0.118156
\(407\) 46.2594 2.29299
\(408\) −42.9728 −2.12747
\(409\) −7.14903 −0.353497 −0.176748 0.984256i \(-0.556558\pi\)
−0.176748 + 0.984256i \(0.556558\pi\)
\(410\) 45.8785 2.26578
\(411\) −4.27725 −0.210981
\(412\) −28.1946 −1.38905
\(413\) 4.53191 0.223001
\(414\) 2.70316 0.132853
\(415\) −0.846325 −0.0415444
\(416\) −69.6869 −3.41668
\(417\) 9.47109 0.463801
\(418\) −102.553 −5.01603
\(419\) −14.7980 −0.722928 −0.361464 0.932386i \(-0.617723\pi\)
−0.361464 + 0.932386i \(0.617723\pi\)
\(420\) −13.0870 −0.638582
\(421\) 6.98352 0.340356 0.170178 0.985413i \(-0.445566\pi\)
0.170178 + 0.985413i \(0.445566\pi\)
\(422\) 15.5665 0.757767
\(423\) −7.68018 −0.373423
\(424\) −87.0271 −4.22641
\(425\) 13.6487 0.662061
\(426\) −23.0487 −1.11671
\(427\) −7.04205 −0.340789
\(428\) 41.5586 2.00881
\(429\) −21.0949 −1.01847
\(430\) 72.2463 3.48402
\(431\) 18.2431 0.878737 0.439368 0.898307i \(-0.355202\pi\)
0.439368 + 0.898307i \(0.355202\pi\)
\(432\) −13.5509 −0.651968
\(433\) −6.54148 −0.314364 −0.157182 0.987570i \(-0.550241\pi\)
−0.157182 + 0.987570i \(0.550241\pi\)
\(434\) 1.85464 0.0890255
\(435\) 2.79988 0.134244
\(436\) 59.6620 2.85729
\(437\) 6.68378 0.319728
\(438\) 34.2428 1.63619
\(439\) −24.9232 −1.18952 −0.594760 0.803904i \(-0.702753\pi\)
−0.594760 + 0.803904i \(0.702753\pi\)
\(440\) −142.072 −6.77303
\(441\) −6.22430 −0.296395
\(442\) −48.2917 −2.29700
\(443\) −31.7227 −1.50719 −0.753594 0.657340i \(-0.771682\pi\)
−0.753594 + 0.657340i \(0.771682\pi\)
\(444\) 43.2514 2.05262
\(445\) −29.9985 −1.42207
\(446\) 32.6855 1.54770
\(447\) 20.3448 0.962274
\(448\) 20.7727 0.981417
\(449\) 27.6235 1.30363 0.651816 0.758377i \(-0.274008\pi\)
0.651816 + 0.758377i \(0.274008\pi\)
\(450\) 7.67515 0.361810
\(451\) −34.4074 −1.62018
\(452\) −92.8303 −4.36637
\(453\) 14.3715 0.675230
\(454\) −73.1072 −3.43109
\(455\) −9.16452 −0.429639
\(456\) −59.7500 −2.79805
\(457\) 3.37558 0.157903 0.0789516 0.996878i \(-0.474843\pi\)
0.0789516 + 0.996878i \(0.474843\pi\)
\(458\) −14.3812 −0.671989
\(459\) −4.80704 −0.224373
\(460\) 14.8592 0.692812
\(461\) 39.9849 1.86228 0.931140 0.364661i \(-0.118815\pi\)
0.931140 + 0.364661i \(0.118815\pi\)
\(462\) 13.5137 0.628713
\(463\) 9.18722 0.426966 0.213483 0.976947i \(-0.431519\pi\)
0.213483 + 0.976947i \(0.431519\pi\)
\(464\) −13.5509 −0.629085
\(465\) −2.18112 −0.101147
\(466\) 64.5360 2.98957
\(467\) 13.0823 0.605378 0.302689 0.953089i \(-0.402116\pi\)
0.302689 + 0.953089i \(0.402116\pi\)
\(468\) −19.7233 −0.911708
\(469\) −7.36362 −0.340020
\(470\) −58.1276 −2.68123
\(471\) 18.9351 0.872482
\(472\) 45.9992 2.11729
\(473\) −54.1825 −2.49131
\(474\) −40.8314 −1.87545
\(475\) 18.9774 0.870743
\(476\) 22.4688 1.02986
\(477\) −9.73506 −0.445738
\(478\) −22.2951 −1.01976
\(479\) 41.5385 1.89794 0.948972 0.315361i \(-0.102125\pi\)
0.948972 + 0.315361i \(0.102125\pi\)
\(480\) −52.5009 −2.39633
\(481\) 30.2879 1.38101
\(482\) 28.5438 1.30013
\(483\) −0.880738 −0.0400750
\(484\) 112.610 5.11862
\(485\) −2.47517 −0.112392
\(486\) −2.70316 −0.122618
\(487\) 22.4277 1.01630 0.508148 0.861270i \(-0.330330\pi\)
0.508148 + 0.861270i \(0.330330\pi\)
\(488\) −71.4773 −3.23563
\(489\) −12.4920 −0.564907
\(490\) −47.1088 −2.12816
\(491\) 13.8826 0.626513 0.313256 0.949669i \(-0.398580\pi\)
0.313256 + 0.949669i \(0.398580\pi\)
\(492\) −32.1701 −1.45034
\(493\) −4.80704 −0.216498
\(494\) −67.1455 −3.02102
\(495\) −15.8926 −0.714317
\(496\) 10.5562 0.473988
\(497\) 7.50967 0.336855
\(498\) 0.817089 0.0366146
\(499\) −10.9367 −0.489592 −0.244796 0.969575i \(-0.578721\pi\)
−0.244796 + 0.969575i \(0.578721\pi\)
\(500\) −32.1059 −1.43582
\(501\) −8.77674 −0.392116
\(502\) −43.1625 −1.92644
\(503\) −3.54058 −0.157867 −0.0789334 0.996880i \(-0.525151\pi\)
−0.0789334 + 0.996880i \(0.525151\pi\)
\(504\) 7.87341 0.350709
\(505\) −3.81044 −0.169563
\(506\) −15.3436 −0.682105
\(507\) −0.811682 −0.0360481
\(508\) 1.09537 0.0485994
\(509\) 12.3607 0.547878 0.273939 0.961747i \(-0.411673\pi\)
0.273939 + 0.961747i \(0.411673\pi\)
\(510\) −36.3822 −1.61103
\(511\) −11.1569 −0.493554
\(512\) 11.8168 0.522233
\(513\) −6.68378 −0.295096
\(514\) −13.8898 −0.612651
\(515\) −14.8748 −0.655460
\(516\) −50.6593 −2.23015
\(517\) 43.5939 1.91726
\(518\) −19.4028 −0.852509
\(519\) −14.7668 −0.648192
\(520\) −93.0205 −4.07922
\(521\) 34.5365 1.51307 0.756535 0.653953i \(-0.226891\pi\)
0.756535 + 0.653953i \(0.226891\pi\)
\(522\) −2.70316 −0.118314
\(523\) 31.4234 1.37405 0.687024 0.726634i \(-0.258917\pi\)
0.687024 + 0.726634i \(0.258917\pi\)
\(524\) 50.4376 2.20338
\(525\) −2.50070 −0.109140
\(526\) 59.7675 2.60599
\(527\) 3.74471 0.163122
\(528\) 76.9170 3.34738
\(529\) 1.00000 0.0434783
\(530\) −73.6801 −3.20046
\(531\) 5.14558 0.223299
\(532\) 31.2409 1.35447
\(533\) −22.5279 −0.975792
\(534\) 28.9622 1.25332
\(535\) 21.9253 0.947913
\(536\) −74.7412 −3.22833
\(537\) 7.96536 0.343730
\(538\) 54.3396 2.34275
\(539\) 35.3301 1.52178
\(540\) −14.8592 −0.639437
\(541\) 28.3717 1.21980 0.609898 0.792480i \(-0.291210\pi\)
0.609898 + 0.792480i \(0.291210\pi\)
\(542\) 18.6557 0.801332
\(543\) −10.2864 −0.441430
\(544\) 90.1374 3.86461
\(545\) 31.4762 1.34829
\(546\) 8.84794 0.378657
\(547\) 20.4656 0.875046 0.437523 0.899207i \(-0.355856\pi\)
0.437523 + 0.899207i \(0.355856\pi\)
\(548\) 22.6997 0.969682
\(549\) −7.99562 −0.341245
\(550\) −43.5653 −1.85763
\(551\) −6.68378 −0.284738
\(552\) −8.93955 −0.380493
\(553\) 13.3036 0.565727
\(554\) 66.4420 2.82285
\(555\) 22.8184 0.968586
\(556\) −50.2638 −2.13166
\(557\) 33.3630 1.41363 0.706817 0.707396i \(-0.250130\pi\)
0.706817 + 0.707396i \(0.250130\pi\)
\(558\) 2.10578 0.0891446
\(559\) −35.4754 −1.50045
\(560\) 33.4160 1.41208
\(561\) 27.2855 1.15199
\(562\) −46.6808 −1.96911
\(563\) 21.5508 0.908257 0.454129 0.890936i \(-0.349951\pi\)
0.454129 + 0.890936i \(0.349951\pi\)
\(564\) 40.7593 1.71628
\(565\) −48.9749 −2.06039
\(566\) −19.5190 −0.820445
\(567\) 0.880738 0.0369875
\(568\) 76.2236 3.19827
\(569\) 12.9510 0.542934 0.271467 0.962448i \(-0.412491\pi\)
0.271467 + 0.962448i \(0.412491\pi\)
\(570\) −50.5863 −2.11883
\(571\) 3.76335 0.157491 0.0787456 0.996895i \(-0.474909\pi\)
0.0787456 + 0.996895i \(0.474909\pi\)
\(572\) 111.952 4.68096
\(573\) −23.0537 −0.963082
\(574\) 14.4317 0.602366
\(575\) 2.83932 0.118408
\(576\) 23.5855 0.982731
\(577\) 9.05091 0.376794 0.188397 0.982093i \(-0.439671\pi\)
0.188397 + 0.982093i \(0.439671\pi\)
\(578\) 16.5098 0.686718
\(579\) −5.67387 −0.235798
\(580\) −14.8592 −0.616993
\(581\) −0.266222 −0.0110448
\(582\) 2.38967 0.0990549
\(583\) 55.2578 2.28854
\(584\) −113.244 −4.68605
\(585\) −10.4055 −0.430214
\(586\) −49.2946 −2.03634
\(587\) −7.59812 −0.313608 −0.156804 0.987630i \(-0.550119\pi\)
−0.156804 + 0.987630i \(0.550119\pi\)
\(588\) 33.0328 1.36225
\(589\) 5.20670 0.214538
\(590\) 38.9445 1.60332
\(591\) −7.96762 −0.327744
\(592\) −110.437 −4.53892
\(593\) 7.95422 0.326641 0.163320 0.986573i \(-0.447780\pi\)
0.163320 + 0.986573i \(0.447780\pi\)
\(594\) 15.3436 0.629554
\(595\) 11.8540 0.485965
\(596\) −107.971 −4.42267
\(597\) 6.95306 0.284570
\(598\) −10.0460 −0.410813
\(599\) 31.2856 1.27830 0.639148 0.769084i \(-0.279287\pi\)
0.639148 + 0.769084i \(0.279287\pi\)
\(600\) −25.3823 −1.03623
\(601\) 14.4217 0.588274 0.294137 0.955763i \(-0.404968\pi\)
0.294137 + 0.955763i \(0.404968\pi\)
\(602\) 22.7260 0.926242
\(603\) −8.36073 −0.340475
\(604\) −76.2704 −3.10340
\(605\) 59.4100 2.41536
\(606\) 3.67882 0.149442
\(607\) −27.1287 −1.10112 −0.550560 0.834796i \(-0.685586\pi\)
−0.550560 + 0.834796i \(0.685586\pi\)
\(608\) 125.328 5.08274
\(609\) 0.880738 0.0356893
\(610\) −60.5150 −2.45018
\(611\) 28.5427 1.15471
\(612\) 25.5113 1.03123
\(613\) −7.58210 −0.306238 −0.153119 0.988208i \(-0.548932\pi\)
−0.153119 + 0.988208i \(0.548932\pi\)
\(614\) −40.2679 −1.62508
\(615\) −16.9722 −0.684383
\(616\) −44.6907 −1.80064
\(617\) 40.3076 1.62272 0.811361 0.584546i \(-0.198727\pi\)
0.811361 + 0.584546i \(0.198727\pi\)
\(618\) 14.3609 0.577681
\(619\) 7.17677 0.288459 0.144229 0.989544i \(-0.453930\pi\)
0.144229 + 0.989544i \(0.453930\pi\)
\(620\) 11.5754 0.464878
\(621\) −1.00000 −0.0401286
\(622\) −2.90915 −0.116646
\(623\) −9.43642 −0.378062
\(624\) 50.3607 2.01604
\(625\) −31.1349 −1.24539
\(626\) −66.5707 −2.66070
\(627\) 37.9382 1.51510
\(628\) −100.490 −4.00998
\(629\) −39.1762 −1.56206
\(630\) 6.66589 0.265575
\(631\) −13.8537 −0.551506 −0.275753 0.961229i \(-0.588927\pi\)
−0.275753 + 0.961229i \(0.588927\pi\)
\(632\) 135.033 5.37131
\(633\) −5.75864 −0.228885
\(634\) 27.9620 1.11051
\(635\) 0.577892 0.0229329
\(636\) 51.6647 2.04864
\(637\) 23.1320 0.916525
\(638\) 15.3436 0.607457
\(639\) 8.52656 0.337305
\(640\) 73.5058 2.90557
\(641\) −2.14458 −0.0847056 −0.0423528 0.999103i \(-0.513485\pi\)
−0.0423528 + 0.999103i \(0.513485\pi\)
\(642\) −21.1679 −0.835431
\(643\) −48.1250 −1.89786 −0.948932 0.315481i \(-0.897834\pi\)
−0.948932 + 0.315481i \(0.897834\pi\)
\(644\) 4.67414 0.184187
\(645\) −26.7266 −1.05236
\(646\) 86.8503 3.41708
\(647\) 14.6607 0.576370 0.288185 0.957575i \(-0.406948\pi\)
0.288185 + 0.957575i \(0.406948\pi\)
\(648\) 8.93955 0.351179
\(649\) −29.2071 −1.14648
\(650\) −28.5240 −1.11880
\(651\) −0.686100 −0.0268904
\(652\) 66.2959 2.59635
\(653\) 30.0473 1.17584 0.587921 0.808918i \(-0.299947\pi\)
0.587921 + 0.808918i \(0.299947\pi\)
\(654\) −30.3889 −1.18830
\(655\) 26.6096 1.03972
\(656\) 82.1421 3.20711
\(657\) −12.6677 −0.494214
\(658\) −18.2848 −0.712816
\(659\) 17.5722 0.684516 0.342258 0.939606i \(-0.388808\pi\)
0.342258 + 0.939606i \(0.388808\pi\)
\(660\) 84.3430 3.28305
\(661\) −22.2147 −0.864052 −0.432026 0.901861i \(-0.642201\pi\)
−0.432026 + 0.901861i \(0.642201\pi\)
\(662\) −38.0663 −1.47949
\(663\) 17.8649 0.693815
\(664\) −2.70218 −0.104865
\(665\) 16.4819 0.639142
\(666\) −22.0301 −0.853650
\(667\) −1.00000 −0.0387202
\(668\) 46.5788 1.80219
\(669\) −12.0916 −0.467488
\(670\) −63.2784 −2.44466
\(671\) 45.3844 1.75205
\(672\) −16.5148 −0.637074
\(673\) 28.1597 1.08547 0.542737 0.839902i \(-0.317388\pi\)
0.542737 + 0.839902i \(0.317388\pi\)
\(674\) −1.54070 −0.0593457
\(675\) −2.83932 −0.109286
\(676\) 4.30766 0.165679
\(677\) 0.245245 0.00942553 0.00471277 0.999989i \(-0.498500\pi\)
0.00471277 + 0.999989i \(0.498500\pi\)
\(678\) 47.2831 1.81590
\(679\) −0.778596 −0.0298798
\(680\) 120.319 4.61401
\(681\) 27.0451 1.03637
\(682\) −11.9527 −0.457693
\(683\) 28.9636 1.10826 0.554131 0.832430i \(-0.313051\pi\)
0.554131 + 0.832430i \(0.313051\pi\)
\(684\) 35.4713 1.35628
\(685\) 11.9758 0.457571
\(686\) −31.4841 −1.20207
\(687\) 5.32014 0.202976
\(688\) 129.352 4.93149
\(689\) 36.1795 1.37833
\(690\) −7.56852 −0.288129
\(691\) −35.3723 −1.34563 −0.672813 0.739813i \(-0.734914\pi\)
−0.672813 + 0.739813i \(0.734914\pi\)
\(692\) 78.3687 2.97913
\(693\) −4.99921 −0.189904
\(694\) −33.5801 −1.27468
\(695\) −26.5179 −1.00588
\(696\) 8.93955 0.338853
\(697\) 29.1390 1.10372
\(698\) −76.9422 −2.91231
\(699\) −23.8743 −0.903008
\(700\) 13.2714 0.501612
\(701\) 19.9823 0.754722 0.377361 0.926066i \(-0.376832\pi\)
0.377361 + 0.926066i \(0.376832\pi\)
\(702\) 10.0460 0.379164
\(703\) −54.4712 −2.05442
\(704\) −133.875 −5.04561
\(705\) 21.5036 0.809872
\(706\) 72.9966 2.74726
\(707\) −1.19862 −0.0450789
\(708\) −27.3080 −1.02630
\(709\) −13.0449 −0.489911 −0.244956 0.969534i \(-0.578773\pi\)
−0.244956 + 0.969534i \(0.578773\pi\)
\(710\) 64.5334 2.42190
\(711\) 15.1051 0.566484
\(712\) −95.7803 −3.58952
\(713\) 0.779005 0.0291740
\(714\) −11.4445 −0.428299
\(715\) 59.0632 2.20884
\(716\) −42.2727 −1.57981
\(717\) 8.24781 0.308020
\(718\) 38.0317 1.41933
\(719\) 8.19259 0.305532 0.152766 0.988262i \(-0.451182\pi\)
0.152766 + 0.988262i \(0.451182\pi\)
\(720\) 37.9409 1.41397
\(721\) −4.67905 −0.174257
\(722\) 69.3978 2.58272
\(723\) −10.5594 −0.392709
\(724\) 54.5905 2.02884
\(725\) −2.83932 −0.105450
\(726\) −57.3577 −2.12874
\(727\) −28.0803 −1.04144 −0.520721 0.853727i \(-0.674337\pi\)
−0.520721 + 0.853727i \(0.674337\pi\)
\(728\) −29.2608 −1.08448
\(729\) 1.00000 0.0370370
\(730\) −95.8758 −3.54852
\(731\) 45.8862 1.69716
\(732\) 42.4334 1.56838
\(733\) −32.2797 −1.19228 −0.596140 0.802881i \(-0.703300\pi\)
−0.596140 + 0.802881i \(0.703300\pi\)
\(734\) 94.1774 3.47615
\(735\) 17.4273 0.642815
\(736\) 18.7511 0.691176
\(737\) 47.4568 1.74809
\(738\) 16.3859 0.603172
\(739\) 2.56275 0.0942721 0.0471361 0.998888i \(-0.484991\pi\)
0.0471361 + 0.998888i \(0.484991\pi\)
\(740\) −121.099 −4.45168
\(741\) 24.8396 0.912507
\(742\) −23.1770 −0.850855
\(743\) 35.8227 1.31421 0.657104 0.753800i \(-0.271781\pi\)
0.657104 + 0.753800i \(0.271781\pi\)
\(744\) −6.96396 −0.255311
\(745\) −56.9629 −2.08696
\(746\) 59.6841 2.18519
\(747\) −0.302272 −0.0110595
\(748\) −144.806 −5.29464
\(749\) 6.89689 0.252007
\(750\) 16.3531 0.597132
\(751\) −42.9765 −1.56824 −0.784118 0.620612i \(-0.786884\pi\)
−0.784118 + 0.620612i \(0.786884\pi\)
\(752\) −104.073 −3.79516
\(753\) 15.9674 0.581885
\(754\) 10.0460 0.365855
\(755\) −40.2383 −1.46442
\(756\) −4.67414 −0.169997
\(757\) −32.0132 −1.16354 −0.581769 0.813354i \(-0.697639\pi\)
−0.581769 + 0.813354i \(0.697639\pi\)
\(758\) −20.1864 −0.733202
\(759\) 5.67616 0.206031
\(760\) 167.293 6.06834
\(761\) 11.4559 0.415278 0.207639 0.978206i \(-0.433422\pi\)
0.207639 + 0.978206i \(0.433422\pi\)
\(762\) −0.557929 −0.0202116
\(763\) 9.90124 0.358449
\(764\) 122.348 4.42639
\(765\) 13.4591 0.486616
\(766\) −83.7005 −3.02422
\(767\) −19.1231 −0.690495
\(768\) −23.7956 −0.858648
\(769\) −0.0983888 −0.00354799 −0.00177400 0.999998i \(-0.500565\pi\)
−0.00177400 + 0.999998i \(0.500565\pi\)
\(770\) −37.8366 −1.36354
\(771\) 5.13834 0.185053
\(772\) 30.1117 1.08374
\(773\) 12.4020 0.446070 0.223035 0.974810i \(-0.428404\pi\)
0.223035 + 0.974810i \(0.428404\pi\)
\(774\) 25.8033 0.927482
\(775\) 2.21185 0.0794519
\(776\) −7.90281 −0.283694
\(777\) 7.17782 0.257503
\(778\) −55.4328 −1.98736
\(779\) 40.5153 1.45161
\(780\) 55.2227 1.97729
\(781\) −48.3981 −1.73182
\(782\) 12.9942 0.464671
\(783\) 1.00000 0.0357371
\(784\) −84.3449 −3.01232
\(785\) −53.0159 −1.89222
\(786\) −25.6904 −0.916346
\(787\) 26.7197 0.952455 0.476227 0.879322i \(-0.342004\pi\)
0.476227 + 0.879322i \(0.342004\pi\)
\(788\) 42.2848 1.50633
\(789\) −22.1102 −0.787145
\(790\) 114.323 4.06743
\(791\) −15.4057 −0.547763
\(792\) −50.7423 −1.80305
\(793\) 29.7150 1.05521
\(794\) −49.8660 −1.76968
\(795\) 27.2570 0.966706
\(796\) −36.9004 −1.30790
\(797\) 20.2834 0.718474 0.359237 0.933246i \(-0.383037\pi\)
0.359237 + 0.933246i \(0.383037\pi\)
\(798\) −15.9126 −0.563299
\(799\) −36.9189 −1.30610
\(800\) 53.2406 1.88234
\(801\) −10.7142 −0.378568
\(802\) −42.5184 −1.50138
\(803\) 71.9039 2.53743
\(804\) 44.3710 1.56485
\(805\) 2.46596 0.0869137
\(806\) −7.82592 −0.275656
\(807\) −20.1023 −0.707633
\(808\) −12.1661 −0.428003
\(809\) 35.7621 1.25733 0.628665 0.777676i \(-0.283602\pi\)
0.628665 + 0.777676i \(0.283602\pi\)
\(810\) 7.56852 0.265931
\(811\) 26.4097 0.927370 0.463685 0.886000i \(-0.346527\pi\)
0.463685 + 0.886000i \(0.346527\pi\)
\(812\) −4.67414 −0.164030
\(813\) −6.90145 −0.242045
\(814\) 125.047 4.38288
\(815\) 34.9760 1.22516
\(816\) −65.1397 −2.28034
\(817\) 63.8008 2.23211
\(818\) −19.3250 −0.675682
\(819\) −3.27318 −0.114374
\(820\) 90.0725 3.14547
\(821\) 21.8673 0.763172 0.381586 0.924333i \(-0.375378\pi\)
0.381586 + 0.924333i \(0.375378\pi\)
\(822\) −11.5621 −0.403274
\(823\) −33.6657 −1.17351 −0.586756 0.809764i \(-0.699595\pi\)
−0.586756 + 0.809764i \(0.699595\pi\)
\(824\) −47.4927 −1.65449
\(825\) 16.1165 0.561103
\(826\) 12.2505 0.426249
\(827\) −49.4034 −1.71793 −0.858963 0.512038i \(-0.828891\pi\)
−0.858963 + 0.512038i \(0.828891\pi\)
\(828\) 5.30708 0.184434
\(829\) 3.54310 0.123057 0.0615285 0.998105i \(-0.480402\pi\)
0.0615285 + 0.998105i \(0.480402\pi\)
\(830\) −2.28775 −0.0794090
\(831\) −24.5794 −0.852650
\(832\) −87.6535 −3.03884
\(833\) −29.9204 −1.03668
\(834\) 25.6019 0.886520
\(835\) 24.5738 0.850412
\(836\) −201.341 −6.96351
\(837\) −0.779005 −0.0269264
\(838\) −40.0013 −1.38182
\(839\) −27.3924 −0.945691 −0.472846 0.881145i \(-0.656773\pi\)
−0.472846 + 0.881145i \(0.656773\pi\)
\(840\) −22.0446 −0.760611
\(841\) 1.00000 0.0344828
\(842\) 18.8776 0.650564
\(843\) 17.2690 0.594775
\(844\) 30.5615 1.05197
\(845\) 2.27261 0.0781802
\(846\) −20.7608 −0.713770
\(847\) 18.6882 0.642133
\(848\) −131.919 −4.53011
\(849\) 7.22081 0.247817
\(850\) 36.8947 1.26548
\(851\) −8.14977 −0.279371
\(852\) −45.2511 −1.55028
\(853\) 18.4109 0.630376 0.315188 0.949029i \(-0.397932\pi\)
0.315188 + 0.949029i \(0.397932\pi\)
\(854\) −19.0358 −0.651391
\(855\) 18.7138 0.639997
\(856\) 70.0039 2.39268
\(857\) 40.3861 1.37956 0.689782 0.724018i \(-0.257707\pi\)
0.689782 + 0.724018i \(0.257707\pi\)
\(858\) −57.0229 −1.94673
\(859\) 38.5166 1.31417 0.657085 0.753816i \(-0.271789\pi\)
0.657085 + 0.753816i \(0.271789\pi\)
\(860\) 141.840 4.83670
\(861\) −5.33881 −0.181946
\(862\) 49.3139 1.67964
\(863\) 22.4884 0.765513 0.382756 0.923849i \(-0.374975\pi\)
0.382756 + 0.923849i \(0.374975\pi\)
\(864\) −18.7511 −0.637927
\(865\) 41.3454 1.40578
\(866\) −17.6827 −0.600882
\(867\) −6.10760 −0.207425
\(868\) 3.64118 0.123590
\(869\) −85.7387 −2.90849
\(870\) 7.56852 0.256597
\(871\) 31.0719 1.05283
\(872\) 100.498 3.40330
\(873\) −0.884027 −0.0299198
\(874\) 18.0673 0.611136
\(875\) −5.32814 −0.180124
\(876\) 67.2285 2.27144
\(877\) −2.78341 −0.0939892 −0.0469946 0.998895i \(-0.514964\pi\)
−0.0469946 + 0.998895i \(0.514964\pi\)
\(878\) −67.3714 −2.27367
\(879\) 18.2359 0.615082
\(880\) −215.358 −7.25973
\(881\) −0.347005 −0.0116909 −0.00584544 0.999983i \(-0.501861\pi\)
−0.00584544 + 0.999983i \(0.501861\pi\)
\(882\) −16.8253 −0.566537
\(883\) −31.9999 −1.07688 −0.538442 0.842663i \(-0.680987\pi\)
−0.538442 + 0.842663i \(0.680987\pi\)
\(884\) −94.8104 −3.18882
\(885\) −14.4070 −0.484287
\(886\) −85.7514 −2.88087
\(887\) 54.2012 1.81990 0.909949 0.414721i \(-0.136121\pi\)
0.909949 + 0.414721i \(0.136121\pi\)
\(888\) 72.8553 2.44486
\(889\) 0.181783 0.00609682
\(890\) −81.0907 −2.71817
\(891\) −5.67616 −0.190158
\(892\) 64.1710 2.14860
\(893\) −51.3326 −1.71778
\(894\) 54.9951 1.83931
\(895\) −22.3020 −0.745475
\(896\) 23.1222 0.772459
\(897\) 3.71641 0.124087
\(898\) 74.6706 2.49179
\(899\) −0.779005 −0.0259813
\(900\) 15.0685 0.502284
\(901\) −46.7968 −1.55903
\(902\) −93.0088 −3.09685
\(903\) −8.40720 −0.279774
\(904\) −156.369 −5.20075
\(905\) 28.8005 0.957363
\(906\) 38.8484 1.29065
\(907\) −8.16651 −0.271164 −0.135582 0.990766i \(-0.543290\pi\)
−0.135582 + 0.990766i \(0.543290\pi\)
\(908\) −143.530 −4.76322
\(909\) −1.36093 −0.0451392
\(910\) −24.7732 −0.821222
\(911\) 21.0259 0.696618 0.348309 0.937380i \(-0.386756\pi\)
0.348309 + 0.937380i \(0.386756\pi\)
\(912\) −90.5712 −2.99911
\(913\) 1.71574 0.0567828
\(914\) 9.12474 0.301820
\(915\) 22.3868 0.740084
\(916\) −28.2344 −0.932890
\(917\) 8.37039 0.276415
\(918\) −12.9942 −0.428872
\(919\) −12.9335 −0.426638 −0.213319 0.976983i \(-0.568427\pi\)
−0.213319 + 0.976983i \(0.568427\pi\)
\(920\) 25.0297 0.825204
\(921\) 14.8966 0.490859
\(922\) 108.085 3.55961
\(923\) −31.6882 −1.04303
\(924\) 26.5312 0.872812
\(925\) −23.1398 −0.760833
\(926\) 24.8345 0.816113
\(927\) −5.31264 −0.174490
\(928\) −18.7511 −0.615536
\(929\) −13.5273 −0.443817 −0.221909 0.975067i \(-0.571229\pi\)
−0.221909 + 0.975067i \(0.571229\pi\)
\(930\) −5.89592 −0.193335
\(931\) −41.6018 −1.36344
\(932\) 126.703 4.15028
\(933\) 1.07620 0.0352333
\(934\) 35.3636 1.15713
\(935\) −76.3961 −2.49842
\(936\) −33.2230 −1.08593
\(937\) −4.15878 −0.135862 −0.0679308 0.997690i \(-0.521640\pi\)
−0.0679308 + 0.997690i \(0.521640\pi\)
\(938\) −19.9050 −0.649923
\(939\) 24.6270 0.803671
\(940\) −114.121 −3.72222
\(941\) −46.9661 −1.53105 −0.765525 0.643406i \(-0.777521\pi\)
−0.765525 + 0.643406i \(0.777521\pi\)
\(942\) 51.1846 1.66768
\(943\) 6.06174 0.197398
\(944\) 69.7273 2.26943
\(945\) −2.46596 −0.0802177
\(946\) −146.464 −4.76195
\(947\) −6.09656 −0.198112 −0.0990558 0.995082i \(-0.531582\pi\)
−0.0990558 + 0.995082i \(0.531582\pi\)
\(948\) −80.1637 −2.60360
\(949\) 47.0783 1.52823
\(950\) 51.2990 1.66436
\(951\) −10.3442 −0.335433
\(952\) 37.8478 1.22665
\(953\) −9.32474 −0.302058 −0.151029 0.988529i \(-0.548259\pi\)
−0.151029 + 0.988529i \(0.548259\pi\)
\(954\) −26.3154 −0.851994
\(955\) 64.5476 2.08871
\(956\) −43.7717 −1.41568
\(957\) −5.67616 −0.183484
\(958\) 112.285 3.62777
\(959\) 3.76713 0.121647
\(960\) −66.0367 −2.13132
\(961\) −30.3932 −0.980424
\(962\) 81.8730 2.63969
\(963\) 7.83080 0.252344
\(964\) 56.0396 1.80492
\(965\) 15.8862 0.511393
\(966\) −2.38078 −0.0766002
\(967\) −43.6266 −1.40294 −0.701468 0.712701i \(-0.747472\pi\)
−0.701468 + 0.712701i \(0.747472\pi\)
\(968\) 189.686 6.09675
\(969\) −32.1292 −1.03214
\(970\) −6.69078 −0.214828
\(971\) 19.3929 0.622347 0.311173 0.950353i \(-0.399278\pi\)
0.311173 + 0.950353i \(0.399278\pi\)
\(972\) −5.30708 −0.170225
\(973\) −8.34155 −0.267418
\(974\) 60.6256 1.94257
\(975\) 10.5521 0.337937
\(976\) −108.348 −3.46813
\(977\) −58.1111 −1.85914 −0.929569 0.368649i \(-0.879820\pi\)
−0.929569 + 0.368649i \(0.879820\pi\)
\(978\) −33.7678 −1.07978
\(979\) 60.8155 1.94367
\(980\) −92.4879 −2.95442
\(981\) 11.2420 0.358929
\(982\) 37.5269 1.19753
\(983\) 30.4731 0.971942 0.485971 0.873975i \(-0.338466\pi\)
0.485971 + 0.873975i \(0.338466\pi\)
\(984\) −54.1893 −1.72749
\(985\) 22.3084 0.710804
\(986\) −12.9942 −0.413819
\(987\) 6.76423 0.215308
\(988\) −131.826 −4.19394
\(989\) 9.54562 0.303533
\(990\) −42.9601 −1.36536
\(991\) 11.8870 0.377603 0.188802 0.982015i \(-0.439540\pi\)
0.188802 + 0.982015i \(0.439540\pi\)
\(992\) 14.6072 0.463780
\(993\) 14.0821 0.446883
\(994\) 20.2998 0.643872
\(995\) −19.4677 −0.617168
\(996\) 1.60418 0.0508304
\(997\) −33.6336 −1.06519 −0.532593 0.846371i \(-0.678782\pi\)
−0.532593 + 0.846371i \(0.678782\pi\)
\(998\) −29.5635 −0.935818
\(999\) 8.14977 0.257847
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 2001.2.a.l.1.10 11
3.2 odd 2 6003.2.a.m.1.2 11
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2001.2.a.l.1.10 11 1.1 even 1 trivial
6003.2.a.m.1.2 11 3.2 odd 2