Properties

Label 1441.2.a.c.1.16
Level $1441$
Weight $2$
Character 1441.1
Self dual yes
Analytic conductor $11.506$
Analytic rank $1$
Dimension $23$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1441 = 11 \cdot 131 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1441.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(11.5064429313\)
Analytic rank: \(1\)
Dimension: \(23\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) \(=\) 1441.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.665447 q^{2} -3.11635 q^{3} -1.55718 q^{4} -0.365961 q^{5} -2.07377 q^{6} -1.41982 q^{7} -2.36711 q^{8} +6.71165 q^{9} +O(q^{10})\) \(q+0.665447 q^{2} -3.11635 q^{3} -1.55718 q^{4} -0.365961 q^{5} -2.07377 q^{6} -1.41982 q^{7} -2.36711 q^{8} +6.71165 q^{9} -0.243528 q^{10} +1.00000 q^{11} +4.85272 q^{12} +2.19271 q^{13} -0.944817 q^{14} +1.14046 q^{15} +1.53917 q^{16} +7.23718 q^{17} +4.46625 q^{18} -2.16873 q^{19} +0.569868 q^{20} +4.42467 q^{21} +0.665447 q^{22} +2.10921 q^{23} +7.37676 q^{24} -4.86607 q^{25} +1.45913 q^{26} -11.5668 q^{27} +2.21092 q^{28} +1.53728 q^{29} +0.758918 q^{30} -6.46030 q^{31} +5.75847 q^{32} -3.11635 q^{33} +4.81595 q^{34} +0.519601 q^{35} -10.4513 q^{36} -5.05934 q^{37} -1.44317 q^{38} -6.83325 q^{39} +0.866272 q^{40} +3.54868 q^{41} +2.94438 q^{42} +3.24433 q^{43} -1.55718 q^{44} -2.45620 q^{45} +1.40357 q^{46} -9.24581 q^{47} -4.79661 q^{48} -4.98410 q^{49} -3.23811 q^{50} -22.5536 q^{51} -3.41444 q^{52} +4.01980 q^{53} -7.69710 q^{54} -0.365961 q^{55} +3.36089 q^{56} +6.75851 q^{57} +1.02298 q^{58} -1.83337 q^{59} -1.77591 q^{60} +11.2639 q^{61} -4.29899 q^{62} -9.52936 q^{63} +0.753605 q^{64} -0.802446 q^{65} -2.07377 q^{66} -7.96789 q^{67} -11.2696 q^{68} -6.57305 q^{69} +0.345766 q^{70} +0.988693 q^{71} -15.8872 q^{72} +0.0955449 q^{73} -3.36672 q^{74} +15.1644 q^{75} +3.37710 q^{76} -1.41982 q^{77} -4.54716 q^{78} -9.70873 q^{79} -0.563278 q^{80} +15.9113 q^{81} +2.36146 q^{82} +9.43070 q^{83} -6.89001 q^{84} -2.64853 q^{85} +2.15893 q^{86} -4.79071 q^{87} -2.36711 q^{88} -5.27112 q^{89} -1.63447 q^{90} -3.11326 q^{91} -3.28443 q^{92} +20.1326 q^{93} -6.15259 q^{94} +0.793670 q^{95} -17.9454 q^{96} -11.5835 q^{97} -3.31665 q^{98} +6.71165 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 23 q - 7 q^{2} - 3 q^{3} + 15 q^{4} - 9 q^{5} - 11 q^{6} - 12 q^{7} - 21 q^{8} + 12 q^{9} + O(q^{10}) \) \( 23 q - 7 q^{2} - 3 q^{3} + 15 q^{4} - 9 q^{5} - 11 q^{6} - 12 q^{7} - 21 q^{8} + 12 q^{9} - 2 q^{10} + 23 q^{11} + 8 q^{12} - 24 q^{13} - 13 q^{14} - 27 q^{15} + 7 q^{16} - 7 q^{17} - 14 q^{18} - 18 q^{19} - 4 q^{20} - 29 q^{21} - 7 q^{22} - 26 q^{23} - 4 q^{24} + 18 q^{25} + 8 q^{26} - 3 q^{27} - 11 q^{28} - 45 q^{29} + 19 q^{30} - 23 q^{31} - 34 q^{32} - 3 q^{33} - 2 q^{34} - 18 q^{35} - 6 q^{36} - 2 q^{37} - 8 q^{38} - 40 q^{39} - 24 q^{40} - 23 q^{41} + 59 q^{42} - 14 q^{43} + 15 q^{44} - 18 q^{45} - 12 q^{46} - 55 q^{47} + 10 q^{48} + 11 q^{49} - 41 q^{50} - 21 q^{51} - 37 q^{52} - 10 q^{53} - 68 q^{54} - 9 q^{55} + 2 q^{56} - 18 q^{57} + 27 q^{58} - 75 q^{59} - 63 q^{60} - 55 q^{61} + 14 q^{62} - 16 q^{63} + 19 q^{64} - 25 q^{65} - 11 q^{66} + 17 q^{67} + 41 q^{68} - 22 q^{69} + 27 q^{70} - 105 q^{71} - 11 q^{72} - 3 q^{73} - 39 q^{74} + 25 q^{75} - 30 q^{76} - 12 q^{77} + 25 q^{78} - 48 q^{79} - 37 q^{80} + 3 q^{81} + 36 q^{82} + 4 q^{83} - 111 q^{84} - 30 q^{85} + 22 q^{86} + 5 q^{87} - 21 q^{88} - 39 q^{89} + 100 q^{90} - 22 q^{91} - 30 q^{92} - 5 q^{93} + 11 q^{94} - 88 q^{95} + 13 q^{96} + 24 q^{97} - 91 q^{98} + 12 q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.665447 0.470542 0.235271 0.971930i \(-0.424402\pi\)
0.235271 + 0.971930i \(0.424402\pi\)
\(3\) −3.11635 −1.79923 −0.899613 0.436687i \(-0.856152\pi\)
−0.899613 + 0.436687i \(0.856152\pi\)
\(4\) −1.55718 −0.778590
\(5\) −0.365961 −0.163663 −0.0818314 0.996646i \(-0.526077\pi\)
−0.0818314 + 0.996646i \(0.526077\pi\)
\(6\) −2.07377 −0.846611
\(7\) −1.41982 −0.536643 −0.268322 0.963329i \(-0.586469\pi\)
−0.268322 + 0.963329i \(0.586469\pi\)
\(8\) −2.36711 −0.836901
\(9\) 6.71165 2.23722
\(10\) −0.243528 −0.0770102
\(11\) 1.00000 0.301511
\(12\) 4.85272 1.40086
\(13\) 2.19271 0.608148 0.304074 0.952648i \(-0.401653\pi\)
0.304074 + 0.952648i \(0.401653\pi\)
\(14\) −0.944817 −0.252513
\(15\) 1.14046 0.294467
\(16\) 1.53917 0.384793
\(17\) 7.23718 1.75527 0.877636 0.479327i \(-0.159119\pi\)
0.877636 + 0.479327i \(0.159119\pi\)
\(18\) 4.46625 1.05270
\(19\) −2.16873 −0.497540 −0.248770 0.968563i \(-0.580026\pi\)
−0.248770 + 0.968563i \(0.580026\pi\)
\(20\) 0.569868 0.127426
\(21\) 4.42467 0.965542
\(22\) 0.665447 0.141874
\(23\) 2.10921 0.439801 0.219901 0.975522i \(-0.429427\pi\)
0.219901 + 0.975522i \(0.429427\pi\)
\(24\) 7.37676 1.50578
\(25\) −4.86607 −0.973214
\(26\) 1.45913 0.286159
\(27\) −11.5668 −2.22603
\(28\) 2.21092 0.417825
\(29\) 1.53728 0.285466 0.142733 0.989761i \(-0.454411\pi\)
0.142733 + 0.989761i \(0.454411\pi\)
\(30\) 0.758918 0.138559
\(31\) −6.46030 −1.16030 −0.580152 0.814508i \(-0.697007\pi\)
−0.580152 + 0.814508i \(0.697007\pi\)
\(32\) 5.75847 1.01796
\(33\) −3.11635 −0.542487
\(34\) 4.81595 0.825929
\(35\) 0.519601 0.0878285
\(36\) −10.4513 −1.74188
\(37\) −5.05934 −0.831751 −0.415875 0.909422i \(-0.636525\pi\)
−0.415875 + 0.909422i \(0.636525\pi\)
\(38\) −1.44317 −0.234113
\(39\) −6.83325 −1.09420
\(40\) 0.866272 0.136970
\(41\) 3.54868 0.554211 0.277105 0.960840i \(-0.410625\pi\)
0.277105 + 0.960840i \(0.410625\pi\)
\(42\) 2.94438 0.454328
\(43\) 3.24433 0.494755 0.247378 0.968919i \(-0.420431\pi\)
0.247378 + 0.968919i \(0.420431\pi\)
\(44\) −1.55718 −0.234754
\(45\) −2.45620 −0.366149
\(46\) 1.40357 0.206945
\(47\) −9.24581 −1.34864 −0.674320 0.738440i \(-0.735563\pi\)
−0.674320 + 0.738440i \(0.735563\pi\)
\(48\) −4.79661 −0.692331
\(49\) −4.98410 −0.712014
\(50\) −3.23811 −0.457938
\(51\) −22.5536 −3.15813
\(52\) −3.41444 −0.473498
\(53\) 4.01980 0.552162 0.276081 0.961134i \(-0.410964\pi\)
0.276081 + 0.961134i \(0.410964\pi\)
\(54\) −7.69710 −1.04744
\(55\) −0.365961 −0.0493462
\(56\) 3.36089 0.449117
\(57\) 6.75851 0.895187
\(58\) 1.02298 0.134324
\(59\) −1.83337 −0.238684 −0.119342 0.992853i \(-0.538079\pi\)
−0.119342 + 0.992853i \(0.538079\pi\)
\(60\) −1.77591 −0.229269
\(61\) 11.2639 1.44220 0.721099 0.692832i \(-0.243637\pi\)
0.721099 + 0.692832i \(0.243637\pi\)
\(62\) −4.29899 −0.545972
\(63\) −9.52936 −1.20059
\(64\) 0.753605 0.0942006
\(65\) −0.802446 −0.0995312
\(66\) −2.07377 −0.255263
\(67\) −7.96789 −0.973433 −0.486717 0.873560i \(-0.661806\pi\)
−0.486717 + 0.873560i \(0.661806\pi\)
\(68\) −11.2696 −1.36664
\(69\) −6.57305 −0.791302
\(70\) 0.345766 0.0413270
\(71\) 0.988693 0.117336 0.0586681 0.998278i \(-0.481315\pi\)
0.0586681 + 0.998278i \(0.481315\pi\)
\(72\) −15.8872 −1.87233
\(73\) 0.0955449 0.0111827 0.00559134 0.999984i \(-0.498220\pi\)
0.00559134 + 0.999984i \(0.498220\pi\)
\(74\) −3.36672 −0.391374
\(75\) 15.1644 1.75103
\(76\) 3.37710 0.387380
\(77\) −1.41982 −0.161804
\(78\) −4.54716 −0.514865
\(79\) −9.70873 −1.09232 −0.546159 0.837682i \(-0.683910\pi\)
−0.546159 + 0.837682i \(0.683910\pi\)
\(80\) −0.563278 −0.0629764
\(81\) 15.9113 1.76792
\(82\) 2.36146 0.260779
\(83\) 9.43070 1.03515 0.517577 0.855637i \(-0.326834\pi\)
0.517577 + 0.855637i \(0.326834\pi\)
\(84\) −6.89001 −0.751762
\(85\) −2.64853 −0.287273
\(86\) 2.15893 0.232803
\(87\) −4.79071 −0.513618
\(88\) −2.36711 −0.252335
\(89\) −5.27112 −0.558737 −0.279369 0.960184i \(-0.590125\pi\)
−0.279369 + 0.960184i \(0.590125\pi\)
\(90\) −1.63447 −0.172289
\(91\) −3.11326 −0.326358
\(92\) −3.28443 −0.342425
\(93\) 20.1326 2.08765
\(94\) −6.15259 −0.634591
\(95\) 0.793670 0.0814288
\(96\) −17.9454 −1.83155
\(97\) −11.5835 −1.17613 −0.588065 0.808814i \(-0.700110\pi\)
−0.588065 + 0.808814i \(0.700110\pi\)
\(98\) −3.31665 −0.335033
\(99\) 6.71165 0.674546
\(100\) 7.57735 0.757735
\(101\) −12.0448 −1.19850 −0.599251 0.800561i \(-0.704535\pi\)
−0.599251 + 0.800561i \(0.704535\pi\)
\(102\) −15.0082 −1.48603
\(103\) 8.93384 0.880277 0.440139 0.897930i \(-0.354929\pi\)
0.440139 + 0.897930i \(0.354929\pi\)
\(104\) −5.19039 −0.508960
\(105\) −1.61926 −0.158023
\(106\) 2.67496 0.259815
\(107\) −4.31296 −0.416950 −0.208475 0.978028i \(-0.566850\pi\)
−0.208475 + 0.978028i \(0.566850\pi\)
\(108\) 18.0116 1.73317
\(109\) −6.03330 −0.577885 −0.288943 0.957346i \(-0.593304\pi\)
−0.288943 + 0.957346i \(0.593304\pi\)
\(110\) −0.243528 −0.0232195
\(111\) 15.7667 1.49651
\(112\) −2.18536 −0.206497
\(113\) 0.310798 0.0292374 0.0146187 0.999893i \(-0.495347\pi\)
0.0146187 + 0.999893i \(0.495347\pi\)
\(114\) 4.49743 0.421223
\(115\) −0.771890 −0.0719791
\(116\) −2.39383 −0.222261
\(117\) 14.7167 1.36056
\(118\) −1.22001 −0.112311
\(119\) −10.2755 −0.941955
\(120\) −2.69961 −0.246439
\(121\) 1.00000 0.0909091
\(122\) 7.49554 0.678615
\(123\) −11.0589 −0.997151
\(124\) 10.0599 0.903402
\(125\) 3.61060 0.322942
\(126\) −6.34128 −0.564926
\(127\) −2.98858 −0.265194 −0.132597 0.991170i \(-0.542332\pi\)
−0.132597 + 0.991170i \(0.542332\pi\)
\(128\) −11.0154 −0.973637
\(129\) −10.1105 −0.890177
\(130\) −0.533985 −0.0468336
\(131\) 1.00000 0.0873704
\(132\) 4.85272 0.422375
\(133\) 3.07921 0.267001
\(134\) −5.30221 −0.458041
\(135\) 4.23301 0.364319
\(136\) −17.1312 −1.46899
\(137\) −22.4824 −1.92080 −0.960402 0.278618i \(-0.910124\pi\)
−0.960402 + 0.278618i \(0.910124\pi\)
\(138\) −4.37401 −0.372341
\(139\) 21.4531 1.81963 0.909813 0.415018i \(-0.136225\pi\)
0.909813 + 0.415018i \(0.136225\pi\)
\(140\) −0.809112 −0.0683824
\(141\) 28.8132 2.42651
\(142\) 0.657922 0.0552116
\(143\) 2.19271 0.183363
\(144\) 10.3304 0.860866
\(145\) −0.562586 −0.0467202
\(146\) 0.0635800 0.00526192
\(147\) 15.5322 1.28108
\(148\) 7.87831 0.647593
\(149\) 7.51312 0.615498 0.307749 0.951468i \(-0.400424\pi\)
0.307749 + 0.951468i \(0.400424\pi\)
\(150\) 10.0911 0.823935
\(151\) −10.4765 −0.852566 −0.426283 0.904590i \(-0.640177\pi\)
−0.426283 + 0.904590i \(0.640177\pi\)
\(152\) 5.13362 0.416392
\(153\) 48.5734 3.92693
\(154\) −0.944817 −0.0761355
\(155\) 2.36422 0.189899
\(156\) 10.6406 0.851930
\(157\) 5.16921 0.412548 0.206274 0.978494i \(-0.433866\pi\)
0.206274 + 0.978494i \(0.433866\pi\)
\(158\) −6.46064 −0.513981
\(159\) −12.5271 −0.993465
\(160\) −2.10738 −0.166603
\(161\) −2.99471 −0.236016
\(162\) 10.5881 0.831882
\(163\) −2.38887 −0.187111 −0.0935554 0.995614i \(-0.529823\pi\)
−0.0935554 + 0.995614i \(0.529823\pi\)
\(164\) −5.52594 −0.431503
\(165\) 1.14046 0.0887850
\(166\) 6.27563 0.487083
\(167\) −7.34952 −0.568723 −0.284361 0.958717i \(-0.591782\pi\)
−0.284361 + 0.958717i \(0.591782\pi\)
\(168\) −10.4737 −0.808064
\(169\) −8.19203 −0.630156
\(170\) −1.76245 −0.135174
\(171\) −14.5557 −1.11310
\(172\) −5.05200 −0.385212
\(173\) 8.07535 0.613957 0.306979 0.951716i \(-0.400682\pi\)
0.306979 + 0.951716i \(0.400682\pi\)
\(174\) −3.18796 −0.241679
\(175\) 6.90897 0.522269
\(176\) 1.53917 0.116020
\(177\) 5.71342 0.429447
\(178\) −3.50765 −0.262909
\(179\) −9.94824 −0.743566 −0.371783 0.928320i \(-0.621253\pi\)
−0.371783 + 0.928320i \(0.621253\pi\)
\(180\) 3.82475 0.285080
\(181\) −24.0332 −1.78638 −0.893189 0.449682i \(-0.851537\pi\)
−0.893189 + 0.449682i \(0.851537\pi\)
\(182\) −2.07171 −0.153565
\(183\) −35.1024 −2.59484
\(184\) −4.99275 −0.368070
\(185\) 1.85152 0.136127
\(186\) 13.3972 0.982327
\(187\) 7.23718 0.529235
\(188\) 14.3974 1.05004
\(189\) 16.4228 1.19459
\(190\) 0.528145 0.0383157
\(191\) 16.8292 1.21772 0.608858 0.793279i \(-0.291628\pi\)
0.608858 + 0.793279i \(0.291628\pi\)
\(192\) −2.34850 −0.169488
\(193\) 9.26275 0.666747 0.333374 0.942795i \(-0.391813\pi\)
0.333374 + 0.942795i \(0.391813\pi\)
\(194\) −7.70823 −0.553418
\(195\) 2.50070 0.179079
\(196\) 7.76114 0.554367
\(197\) −21.1538 −1.50714 −0.753572 0.657365i \(-0.771671\pi\)
−0.753572 + 0.657365i \(0.771671\pi\)
\(198\) 4.46625 0.317402
\(199\) −24.0321 −1.70359 −0.851796 0.523874i \(-0.824486\pi\)
−0.851796 + 0.523874i \(0.824486\pi\)
\(200\) 11.5185 0.814484
\(201\) 24.8308 1.75143
\(202\) −8.01517 −0.563945
\(203\) −2.18267 −0.153193
\(204\) 35.1200 2.45889
\(205\) −1.29868 −0.0907037
\(206\) 5.94499 0.414207
\(207\) 14.1563 0.983931
\(208\) 3.37496 0.234011
\(209\) −2.16873 −0.150014
\(210\) −1.07753 −0.0743566
\(211\) −15.4107 −1.06091 −0.530457 0.847712i \(-0.677980\pi\)
−0.530457 + 0.847712i \(0.677980\pi\)
\(212\) −6.25956 −0.429908
\(213\) −3.08111 −0.211114
\(214\) −2.87004 −0.196192
\(215\) −1.18730 −0.0809730
\(216\) 27.3800 1.86297
\(217\) 9.17249 0.622669
\(218\) −4.01484 −0.271919
\(219\) −0.297752 −0.0201202
\(220\) 0.569868 0.0384205
\(221\) 15.8690 1.06747
\(222\) 10.4919 0.704170
\(223\) −19.5713 −1.31059 −0.655296 0.755372i \(-0.727456\pi\)
−0.655296 + 0.755372i \(0.727456\pi\)
\(224\) −8.17601 −0.546282
\(225\) −32.6594 −2.17729
\(226\) 0.206819 0.0137574
\(227\) 16.0557 1.06566 0.532828 0.846223i \(-0.321129\pi\)
0.532828 + 0.846223i \(0.321129\pi\)
\(228\) −10.5242 −0.696984
\(229\) 25.5666 1.68949 0.844744 0.535171i \(-0.179753\pi\)
0.844744 + 0.535171i \(0.179753\pi\)
\(230\) −0.513652 −0.0338692
\(231\) 4.42467 0.291122
\(232\) −3.63892 −0.238907
\(233\) 17.4172 1.14104 0.570520 0.821284i \(-0.306742\pi\)
0.570520 + 0.821284i \(0.306742\pi\)
\(234\) 9.79317 0.640200
\(235\) 3.38361 0.220722
\(236\) 2.85488 0.185837
\(237\) 30.2558 1.96533
\(238\) −6.83781 −0.443229
\(239\) −21.7094 −1.40427 −0.702133 0.712046i \(-0.747769\pi\)
−0.702133 + 0.712046i \(0.747769\pi\)
\(240\) 1.75537 0.113309
\(241\) −13.0293 −0.839292 −0.419646 0.907688i \(-0.637846\pi\)
−0.419646 + 0.907688i \(0.637846\pi\)
\(242\) 0.665447 0.0427765
\(243\) −14.8848 −0.954861
\(244\) −17.5400 −1.12288
\(245\) 1.82399 0.116530
\(246\) −7.35913 −0.469201
\(247\) −4.75538 −0.302578
\(248\) 15.2923 0.971060
\(249\) −29.3894 −1.86248
\(250\) 2.40266 0.151958
\(251\) −12.6006 −0.795341 −0.397670 0.917528i \(-0.630181\pi\)
−0.397670 + 0.917528i \(0.630181\pi\)
\(252\) 14.8389 0.934765
\(253\) 2.10921 0.132605
\(254\) −1.98874 −0.124785
\(255\) 8.25374 0.516869
\(256\) −8.83740 −0.552338
\(257\) −4.90794 −0.306149 −0.153074 0.988215i \(-0.548917\pi\)
−0.153074 + 0.988215i \(0.548917\pi\)
\(258\) −6.72797 −0.418865
\(259\) 7.18337 0.446353
\(260\) 1.24955 0.0774940
\(261\) 10.3177 0.638650
\(262\) 0.665447 0.0411114
\(263\) 23.2739 1.43513 0.717565 0.696491i \(-0.245257\pi\)
0.717565 + 0.696491i \(0.245257\pi\)
\(264\) 7.37676 0.454008
\(265\) −1.47109 −0.0903685
\(266\) 2.04905 0.125635
\(267\) 16.4267 1.00530
\(268\) 12.4075 0.757906
\(269\) −20.7709 −1.26642 −0.633212 0.773978i \(-0.718264\pi\)
−0.633212 + 0.773978i \(0.718264\pi\)
\(270\) 2.81684 0.171427
\(271\) −0.703289 −0.0427218 −0.0213609 0.999772i \(-0.506800\pi\)
−0.0213609 + 0.999772i \(0.506800\pi\)
\(272\) 11.1393 0.675417
\(273\) 9.70201 0.587192
\(274\) −14.9609 −0.903819
\(275\) −4.86607 −0.293435
\(276\) 10.2354 0.616100
\(277\) 28.0291 1.68410 0.842051 0.539397i \(-0.181348\pi\)
0.842051 + 0.539397i \(0.181348\pi\)
\(278\) 14.2759 0.856210
\(279\) −43.3593 −2.59585
\(280\) −1.22995 −0.0735038
\(281\) −5.18369 −0.309233 −0.154616 0.987975i \(-0.549414\pi\)
−0.154616 + 0.987975i \(0.549414\pi\)
\(282\) 19.1736 1.14177
\(283\) −10.1603 −0.603965 −0.301983 0.953313i \(-0.597648\pi\)
−0.301983 + 0.953313i \(0.597648\pi\)
\(284\) −1.53957 −0.0913569
\(285\) −2.47335 −0.146509
\(286\) 1.45913 0.0862802
\(287\) −5.03850 −0.297413
\(288\) 38.6488 2.27740
\(289\) 35.3767 2.08098
\(290\) −0.374371 −0.0219838
\(291\) 36.0984 2.11612
\(292\) −0.148781 −0.00870673
\(293\) 28.8594 1.68598 0.842991 0.537928i \(-0.180793\pi\)
0.842991 + 0.537928i \(0.180793\pi\)
\(294\) 10.3359 0.602799
\(295\) 0.670942 0.0390637
\(296\) 11.9760 0.696093
\(297\) −11.5668 −0.671175
\(298\) 4.99958 0.289618
\(299\) 4.62489 0.267464
\(300\) −23.6137 −1.36334
\(301\) −4.60637 −0.265507
\(302\) −6.97156 −0.401168
\(303\) 37.5358 2.15638
\(304\) −3.33805 −0.191450
\(305\) −4.12216 −0.236034
\(306\) 32.3230 1.84778
\(307\) 9.72158 0.554840 0.277420 0.960749i \(-0.410521\pi\)
0.277420 + 0.960749i \(0.410521\pi\)
\(308\) 2.21092 0.125979
\(309\) −27.8410 −1.58382
\(310\) 1.57326 0.0893553
\(311\) −7.37275 −0.418070 −0.209035 0.977908i \(-0.567032\pi\)
−0.209035 + 0.977908i \(0.567032\pi\)
\(312\) 16.1751 0.915734
\(313\) −5.34412 −0.302068 −0.151034 0.988529i \(-0.548260\pi\)
−0.151034 + 0.988529i \(0.548260\pi\)
\(314\) 3.43984 0.194121
\(315\) 3.48738 0.196491
\(316\) 15.1182 0.850468
\(317\) −9.54283 −0.535979 −0.267989 0.963422i \(-0.586359\pi\)
−0.267989 + 0.963422i \(0.586359\pi\)
\(318\) −8.33613 −0.467467
\(319\) 1.53728 0.0860713
\(320\) −0.275790 −0.0154171
\(321\) 13.4407 0.750187
\(322\) −1.99282 −0.111056
\(323\) −15.6955 −0.873318
\(324\) −24.7768 −1.37649
\(325\) −10.6699 −0.591858
\(326\) −1.58967 −0.0880435
\(327\) 18.8019 1.03975
\(328\) −8.40013 −0.463820
\(329\) 13.1274 0.723738
\(330\) 0.758918 0.0417771
\(331\) −9.17761 −0.504447 −0.252223 0.967669i \(-0.581162\pi\)
−0.252223 + 0.967669i \(0.581162\pi\)
\(332\) −14.6853 −0.805961
\(333\) −33.9565 −1.86081
\(334\) −4.89071 −0.267608
\(335\) 2.91594 0.159315
\(336\) 6.81034 0.371534
\(337\) −28.6772 −1.56215 −0.781073 0.624440i \(-0.785327\pi\)
−0.781073 + 0.624440i \(0.785327\pi\)
\(338\) −5.45136 −0.296515
\(339\) −0.968556 −0.0526047
\(340\) 4.12423 0.223668
\(341\) −6.46030 −0.349845
\(342\) −9.68606 −0.523762
\(343\) 17.0153 0.918740
\(344\) −7.67969 −0.414061
\(345\) 2.40548 0.129507
\(346\) 5.37371 0.288893
\(347\) −10.5212 −0.564807 −0.282403 0.959296i \(-0.591132\pi\)
−0.282403 + 0.959296i \(0.591132\pi\)
\(348\) 7.46001 0.399898
\(349\) 7.05897 0.377858 0.188929 0.981991i \(-0.439498\pi\)
0.188929 + 0.981991i \(0.439498\pi\)
\(350\) 4.59755 0.245749
\(351\) −25.3626 −1.35376
\(352\) 5.75847 0.306927
\(353\) 4.58192 0.243871 0.121936 0.992538i \(-0.461090\pi\)
0.121936 + 0.992538i \(0.461090\pi\)
\(354\) 3.80198 0.202073
\(355\) −0.361823 −0.0192036
\(356\) 8.20808 0.435028
\(357\) 32.0221 1.69479
\(358\) −6.62002 −0.349879
\(359\) −20.2730 −1.06997 −0.534984 0.844862i \(-0.679682\pi\)
−0.534984 + 0.844862i \(0.679682\pi\)
\(360\) 5.81412 0.306431
\(361\) −14.2966 −0.752454
\(362\) −15.9928 −0.840565
\(363\) −3.11635 −0.163566
\(364\) 4.84791 0.254099
\(365\) −0.0349657 −0.00183019
\(366\) −23.3588 −1.22098
\(367\) −1.26832 −0.0662059 −0.0331029 0.999452i \(-0.510539\pi\)
−0.0331029 + 0.999452i \(0.510539\pi\)
\(368\) 3.24644 0.169233
\(369\) 23.8175 1.23989
\(370\) 1.23209 0.0640533
\(371\) −5.70741 −0.296314
\(372\) −31.3501 −1.62543
\(373\) −14.1984 −0.735166 −0.367583 0.929991i \(-0.619815\pi\)
−0.367583 + 0.929991i \(0.619815\pi\)
\(374\) 4.81595 0.249027
\(375\) −11.2519 −0.581046
\(376\) 21.8859 1.12868
\(377\) 3.37081 0.173606
\(378\) 10.9285 0.562103
\(379\) −6.47018 −0.332351 −0.166175 0.986096i \(-0.553142\pi\)
−0.166175 + 0.986096i \(0.553142\pi\)
\(380\) −1.23589 −0.0633997
\(381\) 9.31348 0.477144
\(382\) 11.1989 0.572986
\(383\) −3.21670 −0.164366 −0.0821830 0.996617i \(-0.526189\pi\)
−0.0821830 + 0.996617i \(0.526189\pi\)
\(384\) 34.3280 1.75179
\(385\) 0.519601 0.0264813
\(386\) 6.16386 0.313732
\(387\) 21.7748 1.10687
\(388\) 18.0377 0.915723
\(389\) −17.5018 −0.887379 −0.443689 0.896181i \(-0.646331\pi\)
−0.443689 + 0.896181i \(0.646331\pi\)
\(390\) 1.66409 0.0842642
\(391\) 15.2647 0.771971
\(392\) 11.7979 0.595886
\(393\) −3.11635 −0.157199
\(394\) −14.0767 −0.709175
\(395\) 3.55302 0.178772
\(396\) −10.4513 −0.525195
\(397\) 6.70272 0.336400 0.168200 0.985753i \(-0.446205\pi\)
0.168200 + 0.985753i \(0.446205\pi\)
\(398\) −15.9921 −0.801611
\(399\) −9.59590 −0.480396
\(400\) −7.48973 −0.374486
\(401\) −6.71574 −0.335368 −0.167684 0.985841i \(-0.553629\pi\)
−0.167684 + 0.985841i \(0.553629\pi\)
\(402\) 16.5236 0.824120
\(403\) −14.1656 −0.705637
\(404\) 18.7559 0.933142
\(405\) −5.82292 −0.289343
\(406\) −1.45245 −0.0720839
\(407\) −5.05934 −0.250782
\(408\) 53.3869 2.64305
\(409\) −5.64545 −0.279150 −0.139575 0.990212i \(-0.544574\pi\)
−0.139575 + 0.990212i \(0.544574\pi\)
\(410\) −0.864202 −0.0426799
\(411\) 70.0632 3.45596
\(412\) −13.9116 −0.685376
\(413\) 2.60306 0.128088
\(414\) 9.42026 0.462981
\(415\) −3.45127 −0.169416
\(416\) 12.6266 0.619072
\(417\) −66.8554 −3.27392
\(418\) −1.44317 −0.0705878
\(419\) −23.1568 −1.13128 −0.565642 0.824651i \(-0.691372\pi\)
−0.565642 + 0.824651i \(0.691372\pi\)
\(420\) 2.52148 0.123036
\(421\) −17.6397 −0.859706 −0.429853 0.902899i \(-0.641435\pi\)
−0.429853 + 0.902899i \(0.641435\pi\)
\(422\) −10.2550 −0.499205
\(423\) −62.0546 −3.01720
\(424\) −9.51533 −0.462105
\(425\) −35.2166 −1.70826
\(426\) −2.05032 −0.0993382
\(427\) −15.9928 −0.773946
\(428\) 6.71606 0.324633
\(429\) −6.83325 −0.329912
\(430\) −0.790083 −0.0381012
\(431\) 5.75725 0.277317 0.138658 0.990340i \(-0.455721\pi\)
0.138658 + 0.990340i \(0.455721\pi\)
\(432\) −17.8033 −0.856563
\(433\) 33.9978 1.63383 0.816914 0.576759i \(-0.195683\pi\)
0.816914 + 0.576759i \(0.195683\pi\)
\(434\) 6.10380 0.292992
\(435\) 1.75322 0.0840603
\(436\) 9.39494 0.449936
\(437\) −4.57431 −0.218819
\(438\) −0.198138 −0.00946739
\(439\) −11.9364 −0.569693 −0.284846 0.958573i \(-0.591943\pi\)
−0.284846 + 0.958573i \(0.591943\pi\)
\(440\) 0.866272 0.0412979
\(441\) −33.4515 −1.59293
\(442\) 10.5600 0.502287
\(443\) 14.3092 0.679849 0.339924 0.940453i \(-0.389599\pi\)
0.339924 + 0.940453i \(0.389599\pi\)
\(444\) −24.5516 −1.16517
\(445\) 1.92902 0.0914446
\(446\) −13.0237 −0.616688
\(447\) −23.4135 −1.10742
\(448\) −1.06999 −0.0505521
\(449\) 0.159024 0.00750479 0.00375239 0.999993i \(-0.498806\pi\)
0.00375239 + 0.999993i \(0.498806\pi\)
\(450\) −21.7331 −1.02451
\(451\) 3.54868 0.167101
\(452\) −0.483969 −0.0227640
\(453\) 32.6485 1.53396
\(454\) 10.6842 0.501436
\(455\) 1.13933 0.0534127
\(456\) −15.9982 −0.749183
\(457\) −2.36060 −0.110424 −0.0552121 0.998475i \(-0.517584\pi\)
−0.0552121 + 0.998475i \(0.517584\pi\)
\(458\) 17.0132 0.794975
\(459\) −83.7111 −3.90730
\(460\) 1.20197 0.0560423
\(461\) −30.6098 −1.42564 −0.712821 0.701346i \(-0.752583\pi\)
−0.712821 + 0.701346i \(0.752583\pi\)
\(462\) 2.94438 0.136985
\(463\) −24.0291 −1.11673 −0.558365 0.829596i \(-0.688571\pi\)
−0.558365 + 0.829596i \(0.688571\pi\)
\(464\) 2.36614 0.109846
\(465\) −7.36774 −0.341671
\(466\) 11.5902 0.536907
\(467\) −34.1262 −1.57917 −0.789586 0.613640i \(-0.789705\pi\)
−0.789586 + 0.613640i \(0.789705\pi\)
\(468\) −22.9165 −1.05932
\(469\) 11.3130 0.522386
\(470\) 2.25161 0.103859
\(471\) −16.1091 −0.742268
\(472\) 4.33979 0.199755
\(473\) 3.24433 0.149174
\(474\) 20.1336 0.924769
\(475\) 10.5532 0.484213
\(476\) 16.0008 0.733397
\(477\) 26.9795 1.23531
\(478\) −14.4465 −0.660766
\(479\) 1.01642 0.0464412 0.0232206 0.999730i \(-0.492608\pi\)
0.0232206 + 0.999730i \(0.492608\pi\)
\(480\) 6.56732 0.299756
\(481\) −11.0937 −0.505827
\(482\) −8.67032 −0.394922
\(483\) 9.33258 0.424647
\(484\) −1.55718 −0.0707809
\(485\) 4.23913 0.192489
\(486\) −9.90505 −0.449302
\(487\) −2.07316 −0.0939441 −0.0469720 0.998896i \(-0.514957\pi\)
−0.0469720 + 0.998896i \(0.514957\pi\)
\(488\) −26.6630 −1.20698
\(489\) 7.44456 0.336655
\(490\) 1.21377 0.0548324
\(491\) −5.20467 −0.234883 −0.117442 0.993080i \(-0.537469\pi\)
−0.117442 + 0.993080i \(0.537469\pi\)
\(492\) 17.2208 0.776372
\(493\) 11.1256 0.501071
\(494\) −3.16445 −0.142375
\(495\) −2.45620 −0.110398
\(496\) −9.94353 −0.446478
\(497\) −1.40377 −0.0629677
\(498\) −19.5571 −0.876373
\(499\) −3.13953 −0.140545 −0.0702723 0.997528i \(-0.522387\pi\)
−0.0702723 + 0.997528i \(0.522387\pi\)
\(500\) −5.62236 −0.251439
\(501\) 22.9037 1.02326
\(502\) −8.38501 −0.374241
\(503\) 6.13363 0.273485 0.136742 0.990607i \(-0.456337\pi\)
0.136742 + 0.990607i \(0.456337\pi\)
\(504\) 22.5571 1.00477
\(505\) 4.40793 0.196150
\(506\) 1.40357 0.0623962
\(507\) 25.5293 1.13379
\(508\) 4.65376 0.206477
\(509\) −13.4114 −0.594452 −0.297226 0.954807i \(-0.596061\pi\)
−0.297226 + 0.954807i \(0.596061\pi\)
\(510\) 5.49242 0.243209
\(511\) −0.135657 −0.00600111
\(512\) 16.1501 0.713739
\(513\) 25.0852 1.10754
\(514\) −3.26597 −0.144056
\(515\) −3.26944 −0.144069
\(516\) 15.7438 0.693083
\(517\) −9.24581 −0.406630
\(518\) 4.78015 0.210028
\(519\) −25.1656 −1.10465
\(520\) 1.89948 0.0832978
\(521\) −35.2552 −1.54456 −0.772279 0.635283i \(-0.780883\pi\)
−0.772279 + 0.635283i \(0.780883\pi\)
\(522\) 6.86588 0.300511
\(523\) 36.1668 1.58146 0.790731 0.612163i \(-0.209700\pi\)
0.790731 + 0.612163i \(0.209700\pi\)
\(524\) −1.55718 −0.0680258
\(525\) −21.5308 −0.939680
\(526\) 15.4875 0.675289
\(527\) −46.7543 −2.03665
\(528\) −4.79661 −0.208746
\(529\) −18.5512 −0.806575
\(530\) −0.978933 −0.0425221
\(531\) −12.3049 −0.533988
\(532\) −4.79488 −0.207885
\(533\) 7.78122 0.337042
\(534\) 10.9311 0.473033
\(535\) 1.57838 0.0682392
\(536\) 18.8609 0.814667
\(537\) 31.0022 1.33784
\(538\) −13.8219 −0.595906
\(539\) −4.98410 −0.214680
\(540\) −6.59155 −0.283655
\(541\) −9.03229 −0.388328 −0.194164 0.980969i \(-0.562199\pi\)
−0.194164 + 0.980969i \(0.562199\pi\)
\(542\) −0.468001 −0.0201024
\(543\) 74.8961 3.21410
\(544\) 41.6750 1.78680
\(545\) 2.20795 0.0945783
\(546\) 6.45617 0.276299
\(547\) 37.0223 1.58296 0.791479 0.611196i \(-0.209311\pi\)
0.791479 + 0.611196i \(0.209311\pi\)
\(548\) 35.0092 1.49552
\(549\) 75.5996 3.22651
\(550\) −3.23811 −0.138074
\(551\) −3.33394 −0.142031
\(552\) 15.5592 0.662242
\(553\) 13.7847 0.586185
\(554\) 18.6518 0.792441
\(555\) −5.77000 −0.244923
\(556\) −33.4063 −1.41674
\(557\) −0.0245232 −0.00103908 −0.000519541 1.00000i \(-0.500165\pi\)
−0.000519541 1.00000i \(0.500165\pi\)
\(558\) −28.8533 −1.22146
\(559\) 7.11386 0.300884
\(560\) 0.799755 0.0337958
\(561\) −22.5536 −0.952213
\(562\) −3.44947 −0.145507
\(563\) 1.16649 0.0491615 0.0245808 0.999698i \(-0.492175\pi\)
0.0245808 + 0.999698i \(0.492175\pi\)
\(564\) −44.8673 −1.88926
\(565\) −0.113740 −0.00478508
\(566\) −6.76112 −0.284191
\(567\) −22.5913 −0.948744
\(568\) −2.34035 −0.0981988
\(569\) 4.83680 0.202769 0.101385 0.994847i \(-0.467673\pi\)
0.101385 + 0.994847i \(0.467673\pi\)
\(570\) −1.64589 −0.0689385
\(571\) −31.9414 −1.33671 −0.668354 0.743843i \(-0.733001\pi\)
−0.668354 + 0.743843i \(0.733001\pi\)
\(572\) −3.41444 −0.142765
\(573\) −52.4456 −2.19095
\(574\) −3.35285 −0.139945
\(575\) −10.2636 −0.428021
\(576\) 5.05793 0.210747
\(577\) 28.9575 1.20552 0.602759 0.797923i \(-0.294068\pi\)
0.602759 + 0.797923i \(0.294068\pi\)
\(578\) 23.5413 0.979190
\(579\) −28.8660 −1.19963
\(580\) 0.876048 0.0363759
\(581\) −13.3899 −0.555508
\(582\) 24.0215 0.995725
\(583\) 4.01980 0.166483
\(584\) −0.226166 −0.00935880
\(585\) −5.38574 −0.222673
\(586\) 19.2044 0.793325
\(587\) 9.83039 0.405744 0.202872 0.979205i \(-0.434973\pi\)
0.202872 + 0.979205i \(0.434973\pi\)
\(588\) −24.1865 −0.997433
\(589\) 14.0106 0.577298
\(590\) 0.446476 0.0183811
\(591\) 65.9227 2.71170
\(592\) −7.78720 −0.320052
\(593\) −28.1565 −1.15625 −0.578124 0.815949i \(-0.696215\pi\)
−0.578124 + 0.815949i \(0.696215\pi\)
\(594\) −7.69710 −0.315816
\(595\) 3.76044 0.154163
\(596\) −11.6993 −0.479221
\(597\) 74.8925 3.06515
\(598\) 3.07762 0.125853
\(599\) −39.2750 −1.60473 −0.802366 0.596833i \(-0.796426\pi\)
−0.802366 + 0.596833i \(0.796426\pi\)
\(600\) −35.8959 −1.46544
\(601\) 26.3119 1.07329 0.536643 0.843809i \(-0.319692\pi\)
0.536643 + 0.843809i \(0.319692\pi\)
\(602\) −3.06529 −0.124932
\(603\) −53.4777 −2.17778
\(604\) 16.3138 0.663800
\(605\) −0.365961 −0.0148784
\(606\) 24.9781 1.01467
\(607\) 34.1539 1.38626 0.693132 0.720810i \(-0.256230\pi\)
0.693132 + 0.720810i \(0.256230\pi\)
\(608\) −12.4885 −0.506477
\(609\) 6.80197 0.275630
\(610\) −2.74308 −0.111064
\(611\) −20.2734 −0.820172
\(612\) −75.6376 −3.05747
\(613\) −37.0422 −1.49612 −0.748059 0.663632i \(-0.769014\pi\)
−0.748059 + 0.663632i \(0.769014\pi\)
\(614\) 6.46919 0.261075
\(615\) 4.04714 0.163197
\(616\) 3.36089 0.135414
\(617\) 34.0143 1.36936 0.684682 0.728842i \(-0.259941\pi\)
0.684682 + 0.728842i \(0.259941\pi\)
\(618\) −18.5267 −0.745253
\(619\) 37.0134 1.48769 0.743846 0.668351i \(-0.232999\pi\)
0.743846 + 0.668351i \(0.232999\pi\)
\(620\) −3.68152 −0.147853
\(621\) −24.3969 −0.979013
\(622\) −4.90617 −0.196720
\(623\) 7.48406 0.299843
\(624\) −10.5176 −0.421039
\(625\) 23.0090 0.920361
\(626\) −3.55623 −0.142135
\(627\) 6.75851 0.269909
\(628\) −8.04940 −0.321206
\(629\) −36.6153 −1.45995
\(630\) 2.32066 0.0924575
\(631\) −39.2780 −1.56363 −0.781816 0.623510i \(-0.785706\pi\)
−0.781816 + 0.623510i \(0.785706\pi\)
\(632\) 22.9817 0.914162
\(633\) 48.0251 1.90883
\(634\) −6.35024 −0.252200
\(635\) 1.09371 0.0434024
\(636\) 19.5070 0.773502
\(637\) −10.9287 −0.433010
\(638\) 1.02298 0.0405001
\(639\) 6.63576 0.262507
\(640\) 4.03123 0.159348
\(641\) 26.7369 1.05604 0.528021 0.849231i \(-0.322934\pi\)
0.528021 + 0.849231i \(0.322934\pi\)
\(642\) 8.94407 0.352994
\(643\) 39.4468 1.55563 0.777815 0.628493i \(-0.216328\pi\)
0.777815 + 0.628493i \(0.216328\pi\)
\(644\) 4.66331 0.183760
\(645\) 3.70004 0.145689
\(646\) −10.4445 −0.410933
\(647\) 7.39287 0.290644 0.145322 0.989384i \(-0.453578\pi\)
0.145322 + 0.989384i \(0.453578\pi\)
\(648\) −37.6639 −1.47958
\(649\) −1.83337 −0.0719660
\(650\) −7.10023 −0.278494
\(651\) −28.5847 −1.12032
\(652\) 3.71990 0.145683
\(653\) −34.7265 −1.35895 −0.679477 0.733697i \(-0.737793\pi\)
−0.679477 + 0.733697i \(0.737793\pi\)
\(654\) 12.5116 0.489244
\(655\) −0.365961 −0.0142993
\(656\) 5.46204 0.213257
\(657\) 0.641264 0.0250181
\(658\) 8.73560 0.340549
\(659\) −1.23081 −0.0479455 −0.0239728 0.999713i \(-0.507631\pi\)
−0.0239728 + 0.999713i \(0.507631\pi\)
\(660\) −1.77591 −0.0691272
\(661\) 22.9260 0.891717 0.445859 0.895103i \(-0.352898\pi\)
0.445859 + 0.895103i \(0.352898\pi\)
\(662\) −6.10721 −0.237363
\(663\) −49.4534 −1.92061
\(664\) −22.3235 −0.866322
\(665\) −1.12687 −0.0436982
\(666\) −22.5963 −0.875588
\(667\) 3.24246 0.125548
\(668\) 11.4445 0.442802
\(669\) 60.9911 2.35805
\(670\) 1.94040 0.0749643
\(671\) 11.2639 0.434839
\(672\) 25.4793 0.982886
\(673\) 23.4705 0.904723 0.452361 0.891835i \(-0.350582\pi\)
0.452361 + 0.891835i \(0.350582\pi\)
\(674\) −19.0831 −0.735055
\(675\) 56.2850 2.16641
\(676\) 12.7565 0.490634
\(677\) 21.5108 0.826726 0.413363 0.910566i \(-0.364354\pi\)
0.413363 + 0.910566i \(0.364354\pi\)
\(678\) −0.644522 −0.0247527
\(679\) 16.4466 0.631162
\(680\) 6.26936 0.240419
\(681\) −50.0353 −1.91736
\(682\) −4.29899 −0.164617
\(683\) 16.3042 0.623864 0.311932 0.950104i \(-0.399024\pi\)
0.311932 + 0.950104i \(0.399024\pi\)
\(684\) 22.6659 0.866653
\(685\) 8.22770 0.314364
\(686\) 11.3228 0.432306
\(687\) −79.6745 −3.03977
\(688\) 4.99358 0.190378
\(689\) 8.81425 0.335796
\(690\) 1.60072 0.0609384
\(691\) 42.8764 1.63109 0.815547 0.578691i \(-0.196436\pi\)
0.815547 + 0.578691i \(0.196436\pi\)
\(692\) −12.5748 −0.478021
\(693\) −9.52936 −0.361991
\(694\) −7.00129 −0.265765
\(695\) −7.85100 −0.297805
\(696\) 11.3402 0.429848
\(697\) 25.6824 0.972791
\(698\) 4.69737 0.177798
\(699\) −54.2782 −2.05299
\(700\) −10.7585 −0.406633
\(701\) 38.3257 1.44754 0.723771 0.690041i \(-0.242407\pi\)
0.723771 + 0.690041i \(0.242407\pi\)
\(702\) −16.8775 −0.637000
\(703\) 10.9723 0.413829
\(704\) 0.753605 0.0284026
\(705\) −10.5445 −0.397129
\(706\) 3.04903 0.114752
\(707\) 17.1015 0.643168
\(708\) −8.89683 −0.334363
\(709\) −8.81025 −0.330876 −0.165438 0.986220i \(-0.552904\pi\)
−0.165438 + 0.986220i \(0.552904\pi\)
\(710\) −0.240774 −0.00903609
\(711\) −65.1616 −2.44375
\(712\) 12.4773 0.467608
\(713\) −13.6262 −0.510304
\(714\) 21.3090 0.797470
\(715\) −0.802446 −0.0300098
\(716\) 15.4912 0.578934
\(717\) 67.6542 2.52659
\(718\) −13.4906 −0.503464
\(719\) −26.1964 −0.976962 −0.488481 0.872575i \(-0.662449\pi\)
−0.488481 + 0.872575i \(0.662449\pi\)
\(720\) −3.78052 −0.140892
\(721\) −12.6845 −0.472395
\(722\) −9.51364 −0.354061
\(723\) 40.6039 1.51008
\(724\) 37.4241 1.39086
\(725\) −7.48053 −0.277820
\(726\) −2.07377 −0.0769647
\(727\) −44.4398 −1.64818 −0.824090 0.566459i \(-0.808313\pi\)
−0.824090 + 0.566459i \(0.808313\pi\)
\(728\) 7.36944 0.273130
\(729\) −1.34762 −0.0499120
\(730\) −0.0232678 −0.000861181 0
\(731\) 23.4798 0.868430
\(732\) 54.6607 2.02032
\(733\) −3.28824 −0.121454 −0.0607270 0.998154i \(-0.519342\pi\)
−0.0607270 + 0.998154i \(0.519342\pi\)
\(734\) −0.844001 −0.0311526
\(735\) −5.68419 −0.209664
\(736\) 12.1458 0.447701
\(737\) −7.96789 −0.293501
\(738\) 15.8493 0.583420
\(739\) −10.8177 −0.397936 −0.198968 0.980006i \(-0.563759\pi\)
−0.198968 + 0.980006i \(0.563759\pi\)
\(740\) −2.88316 −0.105987
\(741\) 14.8194 0.544406
\(742\) −3.79798 −0.139428
\(743\) 15.7090 0.576307 0.288153 0.957584i \(-0.406959\pi\)
0.288153 + 0.957584i \(0.406959\pi\)
\(744\) −47.6561 −1.74716
\(745\) −2.74951 −0.100734
\(746\) −9.44829 −0.345926
\(747\) 63.2956 2.31586
\(748\) −11.2696 −0.412057
\(749\) 6.12364 0.223753
\(750\) −7.48754 −0.273406
\(751\) 24.3807 0.889665 0.444832 0.895614i \(-0.353263\pi\)
0.444832 + 0.895614i \(0.353263\pi\)
\(752\) −14.2309 −0.518948
\(753\) 39.2678 1.43100
\(754\) 2.24310 0.0816887
\(755\) 3.83400 0.139533
\(756\) −25.5733 −0.930093
\(757\) −26.1515 −0.950492 −0.475246 0.879853i \(-0.657641\pi\)
−0.475246 + 0.879853i \(0.657641\pi\)
\(758\) −4.30556 −0.156385
\(759\) −6.57305 −0.238587
\(760\) −1.87871 −0.0681478
\(761\) 31.0390 1.12516 0.562581 0.826742i \(-0.309808\pi\)
0.562581 + 0.826742i \(0.309808\pi\)
\(762\) 6.19762 0.224516
\(763\) 8.56622 0.310118
\(764\) −26.2061 −0.948102
\(765\) −17.7760 −0.642692
\(766\) −2.14055 −0.0773410
\(767\) −4.02004 −0.145155
\(768\) 27.5405 0.993781
\(769\) −15.9241 −0.574236 −0.287118 0.957895i \(-0.592697\pi\)
−0.287118 + 0.957895i \(0.592697\pi\)
\(770\) 0.345766 0.0124606
\(771\) 15.2949 0.550831
\(772\) −14.4238 −0.519123
\(773\) −47.4778 −1.70766 −0.853829 0.520553i \(-0.825726\pi\)
−0.853829 + 0.520553i \(0.825726\pi\)
\(774\) 14.4900 0.520831
\(775\) 31.4363 1.12923
\(776\) 27.4196 0.984304
\(777\) −22.3859 −0.803091
\(778\) −11.6465 −0.417549
\(779\) −7.69612 −0.275742
\(780\) −3.89405 −0.139429
\(781\) 0.988693 0.0353782
\(782\) 10.1579 0.363245
\(783\) −17.7815 −0.635458
\(784\) −7.67139 −0.273978
\(785\) −1.89173 −0.0675188
\(786\) −2.07377 −0.0739688
\(787\) −17.6803 −0.630234 −0.315117 0.949053i \(-0.602044\pi\)
−0.315117 + 0.949053i \(0.602044\pi\)
\(788\) 32.9403 1.17345
\(789\) −72.5297 −2.58212
\(790\) 2.36434 0.0841196
\(791\) −0.441278 −0.0156901
\(792\) −15.8872 −0.564529
\(793\) 24.6985 0.877070
\(794\) 4.46030 0.158290
\(795\) 4.58444 0.162593
\(796\) 37.4224 1.32640
\(797\) 3.28027 0.116193 0.0580965 0.998311i \(-0.481497\pi\)
0.0580965 + 0.998311i \(0.481497\pi\)
\(798\) −6.38556 −0.226046
\(799\) −66.9135 −2.36723
\(800\) −28.0211 −0.990696
\(801\) −35.3779 −1.25002
\(802\) −4.46897 −0.157805
\(803\) 0.0955449 0.00337171
\(804\) −38.6660 −1.36364
\(805\) 1.09595 0.0386271
\(806\) −9.42642 −0.332032
\(807\) 64.7295 2.27858
\(808\) 28.5114 1.00303
\(809\) −38.1115 −1.33993 −0.669964 0.742394i \(-0.733690\pi\)
−0.669964 + 0.742394i \(0.733690\pi\)
\(810\) −3.87484 −0.136148
\(811\) 28.1301 0.987781 0.493891 0.869524i \(-0.335574\pi\)
0.493891 + 0.869524i \(0.335574\pi\)
\(812\) 3.39881 0.119275
\(813\) 2.19170 0.0768662
\(814\) −3.36672 −0.118004
\(815\) 0.874234 0.0306231
\(816\) −34.7139 −1.21523
\(817\) −7.03605 −0.246160
\(818\) −3.75675 −0.131352
\(819\) −20.8951 −0.730134
\(820\) 2.02228 0.0706210
\(821\) 0.430043 0.0150086 0.00750431 0.999972i \(-0.497611\pi\)
0.00750431 + 0.999972i \(0.497611\pi\)
\(822\) 46.6233 1.62617
\(823\) 10.7802 0.375772 0.187886 0.982191i \(-0.439836\pi\)
0.187886 + 0.982191i \(0.439836\pi\)
\(824\) −21.1474 −0.736705
\(825\) 15.1644 0.527956
\(826\) 1.73220 0.0602708
\(827\) 28.2268 0.981543 0.490772 0.871288i \(-0.336715\pi\)
0.490772 + 0.871288i \(0.336715\pi\)
\(828\) −22.0439 −0.766079
\(829\) 1.13211 0.0393197 0.0196598 0.999807i \(-0.493742\pi\)
0.0196598 + 0.999807i \(0.493742\pi\)
\(830\) −2.29664 −0.0797174
\(831\) −87.3484 −3.03008
\(832\) 1.65244 0.0572879
\(833\) −36.0708 −1.24978
\(834\) −44.4887 −1.54052
\(835\) 2.68964 0.0930788
\(836\) 3.37710 0.116799
\(837\) 74.7251 2.58288
\(838\) −15.4096 −0.532317
\(839\) 43.6279 1.50620 0.753102 0.657904i \(-0.228557\pi\)
0.753102 + 0.657904i \(0.228557\pi\)
\(840\) 3.83297 0.132250
\(841\) −26.6368 −0.918509
\(842\) −11.7383 −0.404528
\(843\) 16.1542 0.556380
\(844\) 23.9972 0.826018
\(845\) 2.99797 0.103133
\(846\) −41.2940 −1.41972
\(847\) −1.41982 −0.0487857
\(848\) 6.18717 0.212468
\(849\) 31.6630 1.08667
\(850\) −23.4348 −0.803806
\(851\) −10.6712 −0.365805
\(852\) 4.79785 0.164372
\(853\) 18.7367 0.641532 0.320766 0.947158i \(-0.396060\pi\)
0.320766 + 0.947158i \(0.396060\pi\)
\(854\) −10.6424 −0.364174
\(855\) 5.32683 0.182174
\(856\) 10.2093 0.348946
\(857\) −1.72759 −0.0590135 −0.0295067 0.999565i \(-0.509394\pi\)
−0.0295067 + 0.999565i \(0.509394\pi\)
\(858\) −4.54716 −0.155238
\(859\) 51.8781 1.77006 0.885029 0.465537i \(-0.154139\pi\)
0.885029 + 0.465537i \(0.154139\pi\)
\(860\) 1.84884 0.0630448
\(861\) 15.7017 0.535114
\(862\) 3.83114 0.130489
\(863\) −54.0944 −1.84139 −0.920697 0.390278i \(-0.872379\pi\)
−0.920697 + 0.390278i \(0.872379\pi\)
\(864\) −66.6071 −2.26602
\(865\) −2.95527 −0.100482
\(866\) 22.6237 0.768784
\(867\) −110.246 −3.74416
\(868\) −14.2832 −0.484804
\(869\) −9.70873 −0.329346
\(870\) 1.16667 0.0395539
\(871\) −17.4713 −0.591991
\(872\) 14.2815 0.483633
\(873\) −77.7447 −2.63126
\(874\) −3.04396 −0.102963
\(875\) −5.12642 −0.173305
\(876\) 0.463653 0.0156654
\(877\) 3.12871 0.105649 0.0528246 0.998604i \(-0.483178\pi\)
0.0528246 + 0.998604i \(0.483178\pi\)
\(878\) −7.94303 −0.268064
\(879\) −89.9359 −3.03346
\(880\) −0.563278 −0.0189881
\(881\) 54.7043 1.84303 0.921517 0.388339i \(-0.126951\pi\)
0.921517 + 0.388339i \(0.126951\pi\)
\(882\) −22.2602 −0.749540
\(883\) 3.65628 0.123044 0.0615218 0.998106i \(-0.480405\pi\)
0.0615218 + 0.998106i \(0.480405\pi\)
\(884\) −24.7109 −0.831118
\(885\) −2.09089 −0.0702845
\(886\) 9.52198 0.319897
\(887\) 34.8731 1.17092 0.585462 0.810699i \(-0.300913\pi\)
0.585462 + 0.810699i \(0.300913\pi\)
\(888\) −37.3216 −1.25243
\(889\) 4.24326 0.142314
\(890\) 1.28366 0.0430285
\(891\) 15.9113 0.533049
\(892\) 30.4761 1.02041
\(893\) 20.0516 0.671002
\(894\) −15.5804 −0.521088
\(895\) 3.64067 0.121694
\(896\) 15.6400 0.522496
\(897\) −14.4128 −0.481229
\(898\) 0.105822 0.00353132
\(899\) −9.93131 −0.331228
\(900\) 50.8566 1.69522
\(901\) 29.0920 0.969196
\(902\) 2.36146 0.0786279
\(903\) 14.3551 0.477707
\(904\) −0.735694 −0.0244688
\(905\) 8.79524 0.292364
\(906\) 21.7258 0.721792
\(907\) 56.3977 1.87265 0.936327 0.351129i \(-0.114202\pi\)
0.936327 + 0.351129i \(0.114202\pi\)
\(908\) −25.0017 −0.829710
\(909\) −80.8404 −2.68131
\(910\) 0.758165 0.0251329
\(911\) −34.2745 −1.13556 −0.567782 0.823179i \(-0.692198\pi\)
−0.567782 + 0.823179i \(0.692198\pi\)
\(912\) 10.4025 0.344462
\(913\) 9.43070 0.312111
\(914\) −1.57085 −0.0519592
\(915\) 12.8461 0.424679
\(916\) −39.8118 −1.31542
\(917\) −1.41982 −0.0468867
\(918\) −55.7052 −1.83855
\(919\) −27.2707 −0.899577 −0.449788 0.893135i \(-0.648501\pi\)
−0.449788 + 0.893135i \(0.648501\pi\)
\(920\) 1.82715 0.0602394
\(921\) −30.2959 −0.998282
\(922\) −20.3692 −0.670824
\(923\) 2.16791 0.0713578
\(924\) −6.89001 −0.226665
\(925\) 24.6191 0.809472
\(926\) −15.9901 −0.525468
\(927\) 59.9608 1.96937
\(928\) 8.85239 0.290594
\(929\) 56.6923 1.86001 0.930007 0.367542i \(-0.119801\pi\)
0.930007 + 0.367542i \(0.119801\pi\)
\(930\) −4.90284 −0.160770
\(931\) 10.8091 0.354255
\(932\) −27.1217 −0.888402
\(933\) 22.9761 0.752204
\(934\) −22.7092 −0.743067
\(935\) −2.64853 −0.0866161
\(936\) −34.8361 −1.13865
\(937\) 13.4732 0.440152 0.220076 0.975483i \(-0.429370\pi\)
0.220076 + 0.975483i \(0.429370\pi\)
\(938\) 7.52820 0.245805
\(939\) 16.6542 0.543488
\(940\) −5.26889 −0.171852
\(941\) −41.2558 −1.34490 −0.672451 0.740142i \(-0.734758\pi\)
−0.672451 + 0.740142i \(0.734758\pi\)
\(942\) −10.7197 −0.349268
\(943\) 7.48492 0.243743
\(944\) −2.82187 −0.0918441
\(945\) −6.01012 −0.195509
\(946\) 2.15893 0.0701927
\(947\) 11.7440 0.381627 0.190814 0.981626i \(-0.438887\pi\)
0.190814 + 0.981626i \(0.438887\pi\)
\(948\) −47.1138 −1.53018
\(949\) 0.209502 0.00680072
\(950\) 7.02258 0.227842
\(951\) 29.7388 0.964347
\(952\) 24.3233 0.788323
\(953\) −30.8804 −1.00031 −0.500157 0.865935i \(-0.666724\pi\)
−0.500157 + 0.865935i \(0.666724\pi\)
\(954\) 17.9534 0.581264
\(955\) −6.15883 −0.199295
\(956\) 33.8055 1.09335
\(957\) −4.79071 −0.154862
\(958\) 0.676371 0.0218526
\(959\) 31.9211 1.03079
\(960\) 0.859459 0.0277389
\(961\) 10.7355 0.346307
\(962\) −7.38224 −0.238013
\(963\) −28.9471 −0.932807
\(964\) 20.2890 0.653465
\(965\) −3.38981 −0.109122
\(966\) 6.21033 0.199814
\(967\) 39.3097 1.26411 0.632057 0.774922i \(-0.282211\pi\)
0.632057 + 0.774922i \(0.282211\pi\)
\(968\) −2.36711 −0.0760819
\(969\) 48.9126 1.57130
\(970\) 2.82091 0.0905740
\(971\) −16.5858 −0.532262 −0.266131 0.963937i \(-0.585745\pi\)
−0.266131 + 0.963937i \(0.585745\pi\)
\(972\) 23.1783 0.743446
\(973\) −30.4596 −0.976490
\(974\) −1.37958 −0.0442046
\(975\) 33.2511 1.06489
\(976\) 17.3371 0.554948
\(977\) −59.5742 −1.90595 −0.952974 0.303051i \(-0.901995\pi\)
−0.952974 + 0.303051i \(0.901995\pi\)
\(978\) 4.95396 0.158410
\(979\) −5.27112 −0.168466
\(980\) −2.84028 −0.0907294
\(981\) −40.4934 −1.29285
\(982\) −3.46343 −0.110522
\(983\) −26.7673 −0.853743 −0.426872 0.904312i \(-0.640384\pi\)
−0.426872 + 0.904312i \(0.640384\pi\)
\(984\) 26.1778 0.834517
\(985\) 7.74147 0.246664
\(986\) 7.40348 0.235775
\(987\) −40.9097 −1.30217
\(988\) 7.40499 0.235584
\(989\) 6.84297 0.217594
\(990\) −1.63447 −0.0519470
\(991\) 9.70997 0.308447 0.154224 0.988036i \(-0.450712\pi\)
0.154224 + 0.988036i \(0.450712\pi\)
\(992\) −37.2014 −1.18115
\(993\) 28.6007 0.907614
\(994\) −0.934134 −0.0296289
\(995\) 8.79482 0.278815
\(996\) 45.7646 1.45011
\(997\) −49.2587 −1.56004 −0.780020 0.625755i \(-0.784791\pi\)
−0.780020 + 0.625755i \(0.784791\pi\)
\(998\) −2.08919 −0.0661321
\(999\) 58.5205 1.85151
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 1441.2.a.c.1.16 23
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1441.2.a.c.1.16 23 1.1 even 1 trivial