Properties

Label 7623.2.a.dc.1.3
Level 7623
Weight 2
Character 7623.1
Self dual yes
Analytic conductor 60.870
Analytic rank 0
Dimension 16
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 7623 = 3^{2} \cdot 7 \cdot 11^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 7623.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(60.8699614608\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 693)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-2.10399\)
Character \(\chi\) = 7623.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.10399 q^{2} +2.42677 q^{4} -3.75046 q^{5} +1.00000 q^{7} -0.897910 q^{8} +O(q^{10})\) \(q-2.10399 q^{2} +2.42677 q^{4} -3.75046 q^{5} +1.00000 q^{7} -0.897910 q^{8} +7.89093 q^{10} +3.46575 q^{13} -2.10399 q^{14} -2.96434 q^{16} +1.52683 q^{17} -5.16008 q^{19} -9.10149 q^{20} -4.87487 q^{23} +9.06597 q^{25} -7.29190 q^{26} +2.42677 q^{28} +10.7274 q^{29} +8.12735 q^{31} +8.03275 q^{32} -3.21244 q^{34} -3.75046 q^{35} +9.25848 q^{37} +10.8568 q^{38} +3.36758 q^{40} -10.8973 q^{41} -0.137677 q^{43} +10.2567 q^{46} -2.73030 q^{47} +1.00000 q^{49} -19.0747 q^{50} +8.41057 q^{52} -2.79394 q^{53} -0.897910 q^{56} -22.5702 q^{58} -4.84485 q^{59} -0.297827 q^{61} -17.0998 q^{62} -10.9721 q^{64} -12.9982 q^{65} +0.816899 q^{67} +3.70527 q^{68} +7.89093 q^{70} +5.72995 q^{71} -2.47516 q^{73} -19.4797 q^{74} -12.5223 q^{76} +11.4243 q^{79} +11.1176 q^{80} +22.9278 q^{82} -10.6460 q^{83} -5.72633 q^{85} +0.289670 q^{86} +8.91589 q^{89} +3.46575 q^{91} -11.8302 q^{92} +5.74451 q^{94} +19.3527 q^{95} +8.08471 q^{97} -2.10399 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 20q^{4} + 16q^{7} + O(q^{10}) \) \( 16q + 20q^{4} + 16q^{7} - 6q^{10} + 32q^{16} + 10q^{19} + 44q^{25} + 20q^{28} + 30q^{31} + 12q^{34} + 38q^{37} - 68q^{40} + 16q^{43} + 80q^{46} + 16q^{49} + 2q^{52} + 18q^{58} - 28q^{61} + 34q^{64} + 52q^{67} - 6q^{70} - 14q^{73} - 14q^{76} + 54q^{79} + 64q^{82} + 30q^{85} - 60q^{94} + 108q^{97} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.10399 −1.48774 −0.743872 0.668322i \(-0.767013\pi\)
−0.743872 + 0.668322i \(0.767013\pi\)
\(3\) 0 0
\(4\) 2.42677 1.21338
\(5\) −3.75046 −1.67726 −0.838629 0.544703i \(-0.816642\pi\)
−0.838629 + 0.544703i \(0.816642\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) −0.897910 −0.317459
\(9\) 0 0
\(10\) 7.89093 2.49533
\(11\) 0 0
\(12\) 0 0
\(13\) 3.46575 0.961227 0.480613 0.876933i \(-0.340414\pi\)
0.480613 + 0.876933i \(0.340414\pi\)
\(14\) −2.10399 −0.562314
\(15\) 0 0
\(16\) −2.96434 −0.741085
\(17\) 1.52683 0.370311 0.185156 0.982709i \(-0.440721\pi\)
0.185156 + 0.982709i \(0.440721\pi\)
\(18\) 0 0
\(19\) −5.16008 −1.18380 −0.591902 0.806010i \(-0.701623\pi\)
−0.591902 + 0.806010i \(0.701623\pi\)
\(20\) −9.10149 −2.03516
\(21\) 0 0
\(22\) 0 0
\(23\) −4.87487 −1.01648 −0.508240 0.861215i \(-0.669704\pi\)
−0.508240 + 0.861215i \(0.669704\pi\)
\(24\) 0 0
\(25\) 9.06597 1.81319
\(26\) −7.29190 −1.43006
\(27\) 0 0
\(28\) 2.42677 0.458616
\(29\) 10.7274 1.99202 0.996010 0.0892450i \(-0.0284454\pi\)
0.996010 + 0.0892450i \(0.0284454\pi\)
\(30\) 0 0
\(31\) 8.12735 1.45971 0.729857 0.683599i \(-0.239586\pi\)
0.729857 + 0.683599i \(0.239586\pi\)
\(32\) 8.03275 1.42000
\(33\) 0 0
\(34\) −3.21244 −0.550929
\(35\) −3.75046 −0.633944
\(36\) 0 0
\(37\) 9.25848 1.52208 0.761042 0.648703i \(-0.224688\pi\)
0.761042 + 0.648703i \(0.224688\pi\)
\(38\) 10.8568 1.76120
\(39\) 0 0
\(40\) 3.36758 0.532461
\(41\) −10.8973 −1.70187 −0.850937 0.525267i \(-0.823965\pi\)
−0.850937 + 0.525267i \(0.823965\pi\)
\(42\) 0 0
\(43\) −0.137677 −0.0209955 −0.0104978 0.999945i \(-0.503342\pi\)
−0.0104978 + 0.999945i \(0.503342\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 10.2567 1.51226
\(47\) −2.73030 −0.398255 −0.199127 0.979974i \(-0.563811\pi\)
−0.199127 + 0.979974i \(0.563811\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) −19.0747 −2.69757
\(51\) 0 0
\(52\) 8.41057 1.16634
\(53\) −2.79394 −0.383777 −0.191889 0.981417i \(-0.561461\pi\)
−0.191889 + 0.981417i \(0.561461\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −0.897910 −0.119988
\(57\) 0 0
\(58\) −22.5702 −2.96362
\(59\) −4.84485 −0.630746 −0.315373 0.948968i \(-0.602130\pi\)
−0.315373 + 0.948968i \(0.602130\pi\)
\(60\) 0 0
\(61\) −0.297827 −0.0381328 −0.0190664 0.999818i \(-0.506069\pi\)
−0.0190664 + 0.999818i \(0.506069\pi\)
\(62\) −17.0998 −2.17168
\(63\) 0 0
\(64\) −10.9721 −1.37152
\(65\) −12.9982 −1.61223
\(66\) 0 0
\(67\) 0.816899 0.0998001 0.0499001 0.998754i \(-0.484110\pi\)
0.0499001 + 0.998754i \(0.484110\pi\)
\(68\) 3.70527 0.449329
\(69\) 0 0
\(70\) 7.89093 0.943146
\(71\) 5.72995 0.680020 0.340010 0.940422i \(-0.389570\pi\)
0.340010 + 0.940422i \(0.389570\pi\)
\(72\) 0 0
\(73\) −2.47516 −0.289695 −0.144848 0.989454i \(-0.546269\pi\)
−0.144848 + 0.989454i \(0.546269\pi\)
\(74\) −19.4797 −2.26447
\(75\) 0 0
\(76\) −12.5223 −1.43641
\(77\) 0 0
\(78\) 0 0
\(79\) 11.4243 1.28533 0.642664 0.766148i \(-0.277829\pi\)
0.642664 + 0.766148i \(0.277829\pi\)
\(80\) 11.1176 1.24299
\(81\) 0 0
\(82\) 22.9278 2.53195
\(83\) −10.6460 −1.16855 −0.584273 0.811557i \(-0.698620\pi\)
−0.584273 + 0.811557i \(0.698620\pi\)
\(84\) 0 0
\(85\) −5.72633 −0.621108
\(86\) 0.289670 0.0312359
\(87\) 0 0
\(88\) 0 0
\(89\) 8.91589 0.945082 0.472541 0.881309i \(-0.343337\pi\)
0.472541 + 0.881309i \(0.343337\pi\)
\(90\) 0 0
\(91\) 3.46575 0.363310
\(92\) −11.8302 −1.23338
\(93\) 0 0
\(94\) 5.74451 0.592501
\(95\) 19.3527 1.98555
\(96\) 0 0
\(97\) 8.08471 0.820878 0.410439 0.911888i \(-0.365375\pi\)
0.410439 + 0.911888i \(0.365375\pi\)
\(98\) −2.10399 −0.212535
\(99\) 0 0
\(100\) 22.0010 2.20010
\(101\) −1.72198 −0.171343 −0.0856715 0.996323i \(-0.527304\pi\)
−0.0856715 + 0.996323i \(0.527304\pi\)
\(102\) 0 0
\(103\) −2.69398 −0.265446 −0.132723 0.991153i \(-0.542372\pi\)
−0.132723 + 0.991153i \(0.542372\pi\)
\(104\) −3.11194 −0.305150
\(105\) 0 0
\(106\) 5.87842 0.570962
\(107\) −4.97994 −0.481429 −0.240715 0.970596i \(-0.577382\pi\)
−0.240715 + 0.970596i \(0.577382\pi\)
\(108\) 0 0
\(109\) 11.2061 1.07335 0.536676 0.843788i \(-0.319680\pi\)
0.536676 + 0.843788i \(0.319680\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −2.96434 −0.280104
\(113\) 16.4261 1.54524 0.772620 0.634869i \(-0.218946\pi\)
0.772620 + 0.634869i \(0.218946\pi\)
\(114\) 0 0
\(115\) 18.2830 1.70490
\(116\) 26.0328 2.41708
\(117\) 0 0
\(118\) 10.1935 0.938388
\(119\) 1.52683 0.139965
\(120\) 0 0
\(121\) 0 0
\(122\) 0.626624 0.0567318
\(123\) 0 0
\(124\) 19.7232 1.77119
\(125\) −15.2493 −1.36394
\(126\) 0 0
\(127\) −19.6058 −1.73973 −0.869865 0.493291i \(-0.835794\pi\)
−0.869865 + 0.493291i \(0.835794\pi\)
\(128\) 7.01975 0.620464
\(129\) 0 0
\(130\) 27.3480 2.39858
\(131\) −13.3659 −1.16778 −0.583891 0.811832i \(-0.698470\pi\)
−0.583891 + 0.811832i \(0.698470\pi\)
\(132\) 0 0
\(133\) −5.16008 −0.447436
\(134\) −1.71875 −0.148477
\(135\) 0 0
\(136\) −1.37096 −0.117559
\(137\) 5.27980 0.451084 0.225542 0.974233i \(-0.427585\pi\)
0.225542 + 0.974233i \(0.427585\pi\)
\(138\) 0 0
\(139\) −21.3757 −1.81306 −0.906531 0.422139i \(-0.861280\pi\)
−0.906531 + 0.422139i \(0.861280\pi\)
\(140\) −9.10149 −0.769217
\(141\) 0 0
\(142\) −12.0557 −1.01170
\(143\) 0 0
\(144\) 0 0
\(145\) −40.2325 −3.34113
\(146\) 5.20770 0.430993
\(147\) 0 0
\(148\) 22.4682 1.84687
\(149\) 10.9966 0.900873 0.450437 0.892808i \(-0.351268\pi\)
0.450437 + 0.892808i \(0.351268\pi\)
\(150\) 0 0
\(151\) −3.54170 −0.288219 −0.144110 0.989562i \(-0.546032\pi\)
−0.144110 + 0.989562i \(0.546032\pi\)
\(152\) 4.63329 0.375810
\(153\) 0 0
\(154\) 0 0
\(155\) −30.4813 −2.44832
\(156\) 0 0
\(157\) 12.7591 1.01828 0.509142 0.860682i \(-0.329963\pi\)
0.509142 + 0.860682i \(0.329963\pi\)
\(158\) −24.0365 −1.91224
\(159\) 0 0
\(160\) −30.1265 −2.38171
\(161\) −4.87487 −0.384194
\(162\) 0 0
\(163\) −16.2850 −1.27554 −0.637769 0.770228i \(-0.720142\pi\)
−0.637769 + 0.770228i \(0.720142\pi\)
\(164\) −26.4452 −2.06503
\(165\) 0 0
\(166\) 22.3990 1.73850
\(167\) −5.66281 −0.438201 −0.219101 0.975702i \(-0.570312\pi\)
−0.219101 + 0.975702i \(0.570312\pi\)
\(168\) 0 0
\(169\) −0.988556 −0.0760427
\(170\) 12.0481 0.924049
\(171\) 0 0
\(172\) −0.334109 −0.0254756
\(173\) 13.4214 1.02041 0.510205 0.860053i \(-0.329570\pi\)
0.510205 + 0.860053i \(0.329570\pi\)
\(174\) 0 0
\(175\) 9.06597 0.685323
\(176\) 0 0
\(177\) 0 0
\(178\) −18.7589 −1.40604
\(179\) 3.80842 0.284654 0.142327 0.989820i \(-0.454541\pi\)
0.142327 + 0.989820i \(0.454541\pi\)
\(180\) 0 0
\(181\) −9.78859 −0.727580 −0.363790 0.931481i \(-0.618517\pi\)
−0.363790 + 0.931481i \(0.618517\pi\)
\(182\) −7.29190 −0.540512
\(183\) 0 0
\(184\) 4.37720 0.322691
\(185\) −34.7236 −2.55293
\(186\) 0 0
\(187\) 0 0
\(188\) −6.62579 −0.483236
\(189\) 0 0
\(190\) −40.7179 −2.95398
\(191\) 8.98965 0.650469 0.325234 0.945633i \(-0.394557\pi\)
0.325234 + 0.945633i \(0.394557\pi\)
\(192\) 0 0
\(193\) −5.84941 −0.421049 −0.210525 0.977589i \(-0.567517\pi\)
−0.210525 + 0.977589i \(0.567517\pi\)
\(194\) −17.0101 −1.22126
\(195\) 0 0
\(196\) 2.42677 0.173340
\(197\) 6.19555 0.441414 0.220707 0.975340i \(-0.429163\pi\)
0.220707 + 0.975340i \(0.429163\pi\)
\(198\) 0 0
\(199\) −18.8634 −1.33719 −0.668596 0.743626i \(-0.733105\pi\)
−0.668596 + 0.743626i \(0.733105\pi\)
\(200\) −8.14043 −0.575615
\(201\) 0 0
\(202\) 3.62302 0.254914
\(203\) 10.7274 0.752913
\(204\) 0 0
\(205\) 40.8700 2.85448
\(206\) 5.66810 0.394915
\(207\) 0 0
\(208\) −10.2737 −0.712351
\(209\) 0 0
\(210\) 0 0
\(211\) 0.640180 0.0440718 0.0220359 0.999757i \(-0.492985\pi\)
0.0220359 + 0.999757i \(0.492985\pi\)
\(212\) −6.78024 −0.465669
\(213\) 0 0
\(214\) 10.4777 0.716243
\(215\) 0.516352 0.0352149
\(216\) 0 0
\(217\) 8.12735 0.551720
\(218\) −23.5775 −1.59687
\(219\) 0 0
\(220\) 0 0
\(221\) 5.29163 0.355953
\(222\) 0 0
\(223\) −16.7123 −1.11914 −0.559568 0.828785i \(-0.689033\pi\)
−0.559568 + 0.828785i \(0.689033\pi\)
\(224\) 8.03275 0.536711
\(225\) 0 0
\(226\) −34.5604 −2.29892
\(227\) 9.32634 0.619011 0.309506 0.950898i \(-0.399836\pi\)
0.309506 + 0.950898i \(0.399836\pi\)
\(228\) 0 0
\(229\) 21.3716 1.41228 0.706138 0.708074i \(-0.250436\pi\)
0.706138 + 0.708074i \(0.250436\pi\)
\(230\) −38.4672 −2.53646
\(231\) 0 0
\(232\) −9.63220 −0.632385
\(233\) −17.1164 −1.12133 −0.560666 0.828042i \(-0.689455\pi\)
−0.560666 + 0.828042i \(0.689455\pi\)
\(234\) 0 0
\(235\) 10.2399 0.667976
\(236\) −11.7573 −0.765336
\(237\) 0 0
\(238\) −3.21244 −0.208231
\(239\) 3.37044 0.218016 0.109008 0.994041i \(-0.465233\pi\)
0.109008 + 0.994041i \(0.465233\pi\)
\(240\) 0 0
\(241\) 5.77583 0.372054 0.186027 0.982545i \(-0.440439\pi\)
0.186027 + 0.982545i \(0.440439\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) −0.722755 −0.0462697
\(245\) −3.75046 −0.239608
\(246\) 0 0
\(247\) −17.8836 −1.13790
\(248\) −7.29763 −0.463400
\(249\) 0 0
\(250\) 32.0843 2.02919
\(251\) 11.7616 0.742383 0.371191 0.928556i \(-0.378949\pi\)
0.371191 + 0.928556i \(0.378949\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 41.2503 2.58827
\(255\) 0 0
\(256\) 7.17482 0.448426
\(257\) −14.2660 −0.889891 −0.444945 0.895558i \(-0.646777\pi\)
−0.444945 + 0.895558i \(0.646777\pi\)
\(258\) 0 0
\(259\) 9.25848 0.575294
\(260\) −31.5435 −1.95625
\(261\) 0 0
\(262\) 28.1216 1.73736
\(263\) −4.85285 −0.299239 −0.149620 0.988744i \(-0.547805\pi\)
−0.149620 + 0.988744i \(0.547805\pi\)
\(264\) 0 0
\(265\) 10.4786 0.643693
\(266\) 10.8568 0.665670
\(267\) 0 0
\(268\) 1.98242 0.121096
\(269\) −6.35465 −0.387450 −0.193725 0.981056i \(-0.562057\pi\)
−0.193725 + 0.981056i \(0.562057\pi\)
\(270\) 0 0
\(271\) −15.2155 −0.924273 −0.462137 0.886809i \(-0.652917\pi\)
−0.462137 + 0.886809i \(0.652917\pi\)
\(272\) −4.52605 −0.274432
\(273\) 0 0
\(274\) −11.1086 −0.671098
\(275\) 0 0
\(276\) 0 0
\(277\) −0.379296 −0.0227897 −0.0113948 0.999935i \(-0.503627\pi\)
−0.0113948 + 0.999935i \(0.503627\pi\)
\(278\) 44.9742 2.69737
\(279\) 0 0
\(280\) 3.36758 0.201251
\(281\) 5.04347 0.300868 0.150434 0.988620i \(-0.451933\pi\)
0.150434 + 0.988620i \(0.451933\pi\)
\(282\) 0 0
\(283\) −32.1351 −1.91023 −0.955116 0.296233i \(-0.904270\pi\)
−0.955116 + 0.296233i \(0.904270\pi\)
\(284\) 13.9052 0.825125
\(285\) 0 0
\(286\) 0 0
\(287\) −10.8973 −0.643248
\(288\) 0 0
\(289\) −14.6688 −0.862870
\(290\) 84.6488 4.97075
\(291\) 0 0
\(292\) −6.00663 −0.351511
\(293\) 26.8246 1.56711 0.783554 0.621324i \(-0.213405\pi\)
0.783554 + 0.621324i \(0.213405\pi\)
\(294\) 0 0
\(295\) 18.1704 1.05792
\(296\) −8.31328 −0.483200
\(297\) 0 0
\(298\) −23.1366 −1.34027
\(299\) −16.8951 −0.977069
\(300\) 0 0
\(301\) −0.137677 −0.00793556
\(302\) 7.45169 0.428797
\(303\) 0 0
\(304\) 15.2962 0.877300
\(305\) 1.11699 0.0639585
\(306\) 0 0
\(307\) −5.75200 −0.328284 −0.164142 0.986437i \(-0.552486\pi\)
−0.164142 + 0.986437i \(0.552486\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 64.1323 3.64247
\(311\) 17.8807 1.01392 0.506960 0.861970i \(-0.330769\pi\)
0.506960 + 0.861970i \(0.330769\pi\)
\(312\) 0 0
\(313\) 19.5005 1.10223 0.551117 0.834428i \(-0.314202\pi\)
0.551117 + 0.834428i \(0.314202\pi\)
\(314\) −26.8449 −1.51495
\(315\) 0 0
\(316\) 27.7240 1.55960
\(317\) −17.5109 −0.983508 −0.491754 0.870734i \(-0.663644\pi\)
−0.491754 + 0.870734i \(0.663644\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 41.1506 2.30039
\(321\) 0 0
\(322\) 10.2567 0.571582
\(323\) −7.87859 −0.438376
\(324\) 0 0
\(325\) 31.4204 1.74289
\(326\) 34.2634 1.89767
\(327\) 0 0
\(328\) 9.78481 0.540276
\(329\) −2.73030 −0.150526
\(330\) 0 0
\(331\) −17.6231 −0.968652 −0.484326 0.874888i \(-0.660935\pi\)
−0.484326 + 0.874888i \(0.660935\pi\)
\(332\) −25.8352 −1.41789
\(333\) 0 0
\(334\) 11.9145 0.651931
\(335\) −3.06375 −0.167391
\(336\) 0 0
\(337\) 1.60109 0.0872167 0.0436084 0.999049i \(-0.486115\pi\)
0.0436084 + 0.999049i \(0.486115\pi\)
\(338\) 2.07991 0.113132
\(339\) 0 0
\(340\) −13.8965 −0.753641
\(341\) 0 0
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0.123621 0.00666522
\(345\) 0 0
\(346\) −28.2384 −1.51811
\(347\) 3.44462 0.184917 0.0924585 0.995717i \(-0.470527\pi\)
0.0924585 + 0.995717i \(0.470527\pi\)
\(348\) 0 0
\(349\) 3.39745 0.181862 0.0909308 0.995857i \(-0.471016\pi\)
0.0909308 + 0.995857i \(0.471016\pi\)
\(350\) −19.0747 −1.01959
\(351\) 0 0
\(352\) 0 0
\(353\) 10.4083 0.553977 0.276989 0.960873i \(-0.410664\pi\)
0.276989 + 0.960873i \(0.410664\pi\)
\(354\) 0 0
\(355\) −21.4900 −1.14057
\(356\) 21.6368 1.14675
\(357\) 0 0
\(358\) −8.01286 −0.423493
\(359\) 22.9948 1.21362 0.606811 0.794846i \(-0.292449\pi\)
0.606811 + 0.794846i \(0.292449\pi\)
\(360\) 0 0
\(361\) 7.62647 0.401393
\(362\) 20.5951 1.08245
\(363\) 0 0
\(364\) 8.41057 0.440834
\(365\) 9.28299 0.485894
\(366\) 0 0
\(367\) 19.6357 1.02498 0.512488 0.858695i \(-0.328724\pi\)
0.512488 + 0.858695i \(0.328724\pi\)
\(368\) 14.4508 0.753298
\(369\) 0 0
\(370\) 73.0580 3.79810
\(371\) −2.79394 −0.145054
\(372\) 0 0
\(373\) −31.9047 −1.65196 −0.825981 0.563698i \(-0.809378\pi\)
−0.825981 + 0.563698i \(0.809378\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 2.45156 0.126430
\(377\) 37.1784 1.91478
\(378\) 0 0
\(379\) −1.71958 −0.0883287 −0.0441644 0.999024i \(-0.514063\pi\)
−0.0441644 + 0.999024i \(0.514063\pi\)
\(380\) 46.9645 2.40923
\(381\) 0 0
\(382\) −18.9141 −0.967731
\(383\) 8.68039 0.443547 0.221774 0.975098i \(-0.428815\pi\)
0.221774 + 0.975098i \(0.428815\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 12.3071 0.626414
\(387\) 0 0
\(388\) 19.6197 0.996039
\(389\) −26.8018 −1.35890 −0.679452 0.733720i \(-0.737782\pi\)
−0.679452 + 0.733720i \(0.737782\pi\)
\(390\) 0 0
\(391\) −7.44311 −0.376414
\(392\) −0.897910 −0.0453513
\(393\) 0 0
\(394\) −13.0354 −0.656712
\(395\) −42.8462 −2.15583
\(396\) 0 0
\(397\) −17.8714 −0.896938 −0.448469 0.893798i \(-0.648031\pi\)
−0.448469 + 0.893798i \(0.648031\pi\)
\(398\) 39.6884 1.98940
\(399\) 0 0
\(400\) −26.8746 −1.34373
\(401\) −28.9136 −1.44388 −0.721938 0.691958i \(-0.756748\pi\)
−0.721938 + 0.691958i \(0.756748\pi\)
\(402\) 0 0
\(403\) 28.1674 1.40312
\(404\) −4.17883 −0.207905
\(405\) 0 0
\(406\) −22.5702 −1.12014
\(407\) 0 0
\(408\) 0 0
\(409\) 27.6583 1.36761 0.683807 0.729663i \(-0.260323\pi\)
0.683807 + 0.729663i \(0.260323\pi\)
\(410\) −85.9899 −4.24674
\(411\) 0 0
\(412\) −6.53766 −0.322087
\(413\) −4.84485 −0.238399
\(414\) 0 0
\(415\) 39.9273 1.95995
\(416\) 27.8395 1.36495
\(417\) 0 0
\(418\) 0 0
\(419\) −4.51003 −0.220330 −0.110165 0.993913i \(-0.535138\pi\)
−0.110165 + 0.993913i \(0.535138\pi\)
\(420\) 0 0
\(421\) 35.9445 1.75183 0.875914 0.482467i \(-0.160259\pi\)
0.875914 + 0.482467i \(0.160259\pi\)
\(422\) −1.34693 −0.0655676
\(423\) 0 0
\(424\) 2.50871 0.121834
\(425\) 13.8422 0.671446
\(426\) 0 0
\(427\) −0.297827 −0.0144128
\(428\) −12.0851 −0.584158
\(429\) 0 0
\(430\) −1.08640 −0.0523907
\(431\) −22.2209 −1.07034 −0.535172 0.844743i \(-0.679753\pi\)
−0.535172 + 0.844743i \(0.679753\pi\)
\(432\) 0 0
\(433\) 25.4892 1.22493 0.612467 0.790496i \(-0.290177\pi\)
0.612467 + 0.790496i \(0.290177\pi\)
\(434\) −17.0998 −0.820819
\(435\) 0 0
\(436\) 27.1946 1.30239
\(437\) 25.1547 1.20331
\(438\) 0 0
\(439\) 11.1407 0.531715 0.265857 0.964012i \(-0.414345\pi\)
0.265857 + 0.964012i \(0.414345\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −11.1335 −0.529567
\(443\) 13.8512 0.658092 0.329046 0.944314i \(-0.393273\pi\)
0.329046 + 0.944314i \(0.393273\pi\)
\(444\) 0 0
\(445\) −33.4387 −1.58515
\(446\) 35.1624 1.66499
\(447\) 0 0
\(448\) −10.9721 −0.518385
\(449\) 10.6878 0.504390 0.252195 0.967676i \(-0.418848\pi\)
0.252195 + 0.967676i \(0.418848\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 39.8624 1.87497
\(453\) 0 0
\(454\) −19.6225 −0.920930
\(455\) −12.9982 −0.609364
\(456\) 0 0
\(457\) 31.3778 1.46779 0.733895 0.679263i \(-0.237700\pi\)
0.733895 + 0.679263i \(0.237700\pi\)
\(458\) −44.9656 −2.10111
\(459\) 0 0
\(460\) 44.3686 2.06870
\(461\) 41.1844 1.91815 0.959075 0.283151i \(-0.0913797\pi\)
0.959075 + 0.283151i \(0.0913797\pi\)
\(462\) 0 0
\(463\) 35.6274 1.65575 0.827874 0.560915i \(-0.189550\pi\)
0.827874 + 0.560915i \(0.189550\pi\)
\(464\) −31.7995 −1.47626
\(465\) 0 0
\(466\) 36.0127 1.66826
\(467\) 6.45945 0.298908 0.149454 0.988769i \(-0.452248\pi\)
0.149454 + 0.988769i \(0.452248\pi\)
\(468\) 0 0
\(469\) 0.816899 0.0377209
\(470\) −21.5446 −0.993777
\(471\) 0 0
\(472\) 4.35024 0.200236
\(473\) 0 0
\(474\) 0 0
\(475\) −46.7812 −2.14647
\(476\) 3.70527 0.169831
\(477\) 0 0
\(478\) −7.09137 −0.324352
\(479\) −6.80306 −0.310840 −0.155420 0.987849i \(-0.549673\pi\)
−0.155420 + 0.987849i \(0.549673\pi\)
\(480\) 0 0
\(481\) 32.0876 1.46307
\(482\) −12.1523 −0.553521
\(483\) 0 0
\(484\) 0 0
\(485\) −30.3214 −1.37682
\(486\) 0 0
\(487\) 26.7244 1.21100 0.605499 0.795846i \(-0.292974\pi\)
0.605499 + 0.795846i \(0.292974\pi\)
\(488\) 0.267422 0.0121056
\(489\) 0 0
\(490\) 7.89093 0.356476
\(491\) −6.09257 −0.274954 −0.137477 0.990505i \(-0.543899\pi\)
−0.137477 + 0.990505i \(0.543899\pi\)
\(492\) 0 0
\(493\) 16.3789 0.737667
\(494\) 37.6268 1.69291
\(495\) 0 0
\(496\) −24.0922 −1.08177
\(497\) 5.72995 0.257023
\(498\) 0 0
\(499\) 1.49552 0.0669488 0.0334744 0.999440i \(-0.489343\pi\)
0.0334744 + 0.999440i \(0.489343\pi\)
\(500\) −37.0064 −1.65498
\(501\) 0 0
\(502\) −24.7462 −1.10448
\(503\) 14.3833 0.641321 0.320660 0.947194i \(-0.396095\pi\)
0.320660 + 0.947194i \(0.396095\pi\)
\(504\) 0 0
\(505\) 6.45820 0.287386
\(506\) 0 0
\(507\) 0 0
\(508\) −47.5786 −2.11096
\(509\) −2.78397 −0.123397 −0.0616986 0.998095i \(-0.519652\pi\)
−0.0616986 + 0.998095i \(0.519652\pi\)
\(510\) 0 0
\(511\) −2.47516 −0.109495
\(512\) −29.1352 −1.28761
\(513\) 0 0
\(514\) 30.0156 1.32393
\(515\) 10.1037 0.445221
\(516\) 0 0
\(517\) 0 0
\(518\) −19.4797 −0.855890
\(519\) 0 0
\(520\) 11.6712 0.511816
\(521\) 40.5289 1.77560 0.887801 0.460227i \(-0.152232\pi\)
0.887801 + 0.460227i \(0.152232\pi\)
\(522\) 0 0
\(523\) 0.895277 0.0391477 0.0195739 0.999808i \(-0.493769\pi\)
0.0195739 + 0.999808i \(0.493769\pi\)
\(524\) −32.4358 −1.41697
\(525\) 0 0
\(526\) 10.2103 0.445192
\(527\) 12.4091 0.540549
\(528\) 0 0
\(529\) 0.764354 0.0332328
\(530\) −22.0468 −0.957651
\(531\) 0 0
\(532\) −12.5223 −0.542911
\(533\) −37.7674 −1.63589
\(534\) 0 0
\(535\) 18.6771 0.807481
\(536\) −0.733502 −0.0316825
\(537\) 0 0
\(538\) 13.3701 0.576426
\(539\) 0 0
\(540\) 0 0
\(541\) −2.86106 −0.123007 −0.0615033 0.998107i \(-0.519589\pi\)
−0.0615033 + 0.998107i \(0.519589\pi\)
\(542\) 32.0131 1.37508
\(543\) 0 0
\(544\) 12.2647 0.525844
\(545\) −42.0281 −1.80029
\(546\) 0 0
\(547\) 26.7191 1.14243 0.571214 0.820801i \(-0.306473\pi\)
0.571214 + 0.820801i \(0.306473\pi\)
\(548\) 12.8128 0.547338
\(549\) 0 0
\(550\) 0 0
\(551\) −55.3540 −2.35816
\(552\) 0 0
\(553\) 11.4243 0.485809
\(554\) 0.798034 0.0339052
\(555\) 0 0
\(556\) −51.8738 −2.19994
\(557\) −11.4407 −0.484756 −0.242378 0.970182i \(-0.577927\pi\)
−0.242378 + 0.970182i \(0.577927\pi\)
\(558\) 0 0
\(559\) −0.477154 −0.0201814
\(560\) 11.1176 0.469806
\(561\) 0 0
\(562\) −10.6114 −0.447615
\(563\) 12.2142 0.514769 0.257385 0.966309i \(-0.417139\pi\)
0.257385 + 0.966309i \(0.417139\pi\)
\(564\) 0 0
\(565\) −61.6056 −2.59177
\(566\) 67.6118 2.84194
\(567\) 0 0
\(568\) −5.14498 −0.215879
\(569\) 20.3769 0.854243 0.427121 0.904194i \(-0.359528\pi\)
0.427121 + 0.904194i \(0.359528\pi\)
\(570\) 0 0
\(571\) −20.3621 −0.852129 −0.426065 0.904693i \(-0.640100\pi\)
−0.426065 + 0.904693i \(0.640100\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 22.9278 0.956989
\(575\) −44.1954 −1.84308
\(576\) 0 0
\(577\) 6.04479 0.251648 0.125824 0.992053i \(-0.459843\pi\)
0.125824 + 0.992053i \(0.459843\pi\)
\(578\) 30.8629 1.28373
\(579\) 0 0
\(580\) −97.6349 −4.05407
\(581\) −10.6460 −0.441669
\(582\) 0 0
\(583\) 0 0
\(584\) 2.22247 0.0919665
\(585\) 0 0
\(586\) −56.4386 −2.33146
\(587\) 36.5418 1.50824 0.754120 0.656736i \(-0.228064\pi\)
0.754120 + 0.656736i \(0.228064\pi\)
\(588\) 0 0
\(589\) −41.9378 −1.72802
\(590\) −38.2304 −1.57392
\(591\) 0 0
\(592\) −27.4453 −1.12799
\(593\) 15.6666 0.643349 0.321675 0.946850i \(-0.395754\pi\)
0.321675 + 0.946850i \(0.395754\pi\)
\(594\) 0 0
\(595\) −5.72633 −0.234757
\(596\) 26.6861 1.09310
\(597\) 0 0
\(598\) 35.5471 1.45363
\(599\) 28.4274 1.16151 0.580756 0.814078i \(-0.302757\pi\)
0.580756 + 0.814078i \(0.302757\pi\)
\(600\) 0 0
\(601\) −12.3125 −0.502239 −0.251120 0.967956i \(-0.580799\pi\)
−0.251120 + 0.967956i \(0.580799\pi\)
\(602\) 0.289670 0.0118061
\(603\) 0 0
\(604\) −8.59487 −0.349720
\(605\) 0 0
\(606\) 0 0
\(607\) −33.5574 −1.36205 −0.681026 0.732259i \(-0.738466\pi\)
−0.681026 + 0.732259i \(0.738466\pi\)
\(608\) −41.4497 −1.68101
\(609\) 0 0
\(610\) −2.35013 −0.0951539
\(611\) −9.46254 −0.382813
\(612\) 0 0
\(613\) −5.38046 −0.217315 −0.108657 0.994079i \(-0.534655\pi\)
−0.108657 + 0.994079i \(0.534655\pi\)
\(614\) 12.1021 0.488402
\(615\) 0 0
\(616\) 0 0
\(617\) −29.3058 −1.17981 −0.589904 0.807473i \(-0.700834\pi\)
−0.589904 + 0.807473i \(0.700834\pi\)
\(618\) 0 0
\(619\) 3.35835 0.134984 0.0674918 0.997720i \(-0.478500\pi\)
0.0674918 + 0.997720i \(0.478500\pi\)
\(620\) −73.9710 −2.97075
\(621\) 0 0
\(622\) −37.6207 −1.50845
\(623\) 8.91589 0.357207
\(624\) 0 0
\(625\) 11.8620 0.474478
\(626\) −41.0289 −1.63984
\(627\) 0 0
\(628\) 30.9633 1.23557
\(629\) 14.1361 0.563645
\(630\) 0 0
\(631\) −31.1413 −1.23972 −0.619858 0.784714i \(-0.712810\pi\)
−0.619858 + 0.784714i \(0.712810\pi\)
\(632\) −10.2580 −0.408040
\(633\) 0 0
\(634\) 36.8426 1.46321
\(635\) 73.5306 2.91797
\(636\) 0 0
\(637\) 3.46575 0.137318
\(638\) 0 0
\(639\) 0 0
\(640\) −26.3273 −1.04068
\(641\) 21.2928 0.841017 0.420508 0.907289i \(-0.361852\pi\)
0.420508 + 0.907289i \(0.361852\pi\)
\(642\) 0 0
\(643\) 22.7558 0.897399 0.448700 0.893683i \(-0.351887\pi\)
0.448700 + 0.893683i \(0.351887\pi\)
\(644\) −11.8302 −0.466174
\(645\) 0 0
\(646\) 16.5765 0.652192
\(647\) 43.0823 1.69374 0.846870 0.531799i \(-0.178484\pi\)
0.846870 + 0.531799i \(0.178484\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) −66.1082 −2.59298
\(651\) 0 0
\(652\) −39.5198 −1.54772
\(653\) 35.7629 1.39951 0.699756 0.714382i \(-0.253292\pi\)
0.699756 + 0.714382i \(0.253292\pi\)
\(654\) 0 0
\(655\) 50.1282 1.95867
\(656\) 32.3033 1.26123
\(657\) 0 0
\(658\) 5.74451 0.223944
\(659\) 16.6988 0.650495 0.325247 0.945629i \(-0.394552\pi\)
0.325247 + 0.945629i \(0.394552\pi\)
\(660\) 0 0
\(661\) 36.5422 1.42133 0.710664 0.703532i \(-0.248395\pi\)
0.710664 + 0.703532i \(0.248395\pi\)
\(662\) 37.0787 1.44111
\(663\) 0 0
\(664\) 9.55912 0.370966
\(665\) 19.3527 0.750466
\(666\) 0 0
\(667\) −52.2944 −2.02485
\(668\) −13.7423 −0.531706
\(669\) 0 0
\(670\) 6.44609 0.249034
\(671\) 0 0
\(672\) 0 0
\(673\) 28.6689 1.10510 0.552552 0.833478i \(-0.313654\pi\)
0.552552 + 0.833478i \(0.313654\pi\)
\(674\) −3.36867 −0.129756
\(675\) 0 0
\(676\) −2.39899 −0.0922690
\(677\) 10.9806 0.422019 0.211010 0.977484i \(-0.432325\pi\)
0.211010 + 0.977484i \(0.432325\pi\)
\(678\) 0 0
\(679\) 8.08471 0.310263
\(680\) 5.14173 0.197176
\(681\) 0 0
\(682\) 0 0
\(683\) 25.3941 0.971679 0.485840 0.874048i \(-0.338514\pi\)
0.485840 + 0.874048i \(0.338514\pi\)
\(684\) 0 0
\(685\) −19.8017 −0.756584
\(686\) −2.10399 −0.0803306
\(687\) 0 0
\(688\) 0.408121 0.0155595
\(689\) −9.68310 −0.368897
\(690\) 0 0
\(691\) −26.5965 −1.01178 −0.505889 0.862599i \(-0.668835\pi\)
−0.505889 + 0.862599i \(0.668835\pi\)
\(692\) 32.5706 1.23815
\(693\) 0 0
\(694\) −7.24744 −0.275109
\(695\) 80.1687 3.04097
\(696\) 0 0
\(697\) −16.6384 −0.630224
\(698\) −7.14820 −0.270563
\(699\) 0 0
\(700\) 22.0010 0.831559
\(701\) −45.1579 −1.70559 −0.852796 0.522245i \(-0.825095\pi\)
−0.852796 + 0.522245i \(0.825095\pi\)
\(702\) 0 0
\(703\) −47.7745 −1.80185
\(704\) 0 0
\(705\) 0 0
\(706\) −21.8989 −0.824177
\(707\) −1.72198 −0.0647615
\(708\) 0 0
\(709\) 42.7235 1.60452 0.802258 0.596978i \(-0.203632\pi\)
0.802258 + 0.596978i \(0.203632\pi\)
\(710\) 45.2146 1.69687
\(711\) 0 0
\(712\) −8.00567 −0.300025
\(713\) −39.6198 −1.48377
\(714\) 0 0
\(715\) 0 0
\(716\) 9.24214 0.345395
\(717\) 0 0
\(718\) −48.3809 −1.80556
\(719\) −15.4401 −0.575819 −0.287909 0.957658i \(-0.592960\pi\)
−0.287909 + 0.957658i \(0.592960\pi\)
\(720\) 0 0
\(721\) −2.69398 −0.100329
\(722\) −16.0460 −0.597171
\(723\) 0 0
\(724\) −23.7546 −0.882834
\(725\) 97.2539 3.61192
\(726\) 0 0
\(727\) 14.8932 0.552357 0.276178 0.961106i \(-0.410932\pi\)
0.276178 + 0.961106i \(0.410932\pi\)
\(728\) −3.11194 −0.115336
\(729\) 0 0
\(730\) −19.5313 −0.722886
\(731\) −0.210209 −0.00777488
\(732\) 0 0
\(733\) −7.38664 −0.272832 −0.136416 0.990652i \(-0.543558\pi\)
−0.136416 + 0.990652i \(0.543558\pi\)
\(734\) −41.3133 −1.52490
\(735\) 0 0
\(736\) −39.1586 −1.44341
\(737\) 0 0
\(738\) 0 0
\(739\) 34.8552 1.28217 0.641084 0.767471i \(-0.278485\pi\)
0.641084 + 0.767471i \(0.278485\pi\)
\(740\) −84.2660 −3.09768
\(741\) 0 0
\(742\) 5.87842 0.215803
\(743\) −3.33330 −0.122287 −0.0611434 0.998129i \(-0.519475\pi\)
−0.0611434 + 0.998129i \(0.519475\pi\)
\(744\) 0 0
\(745\) −41.2422 −1.51100
\(746\) 67.1271 2.45770
\(747\) 0 0
\(748\) 0 0
\(749\) −4.97994 −0.181963
\(750\) 0 0
\(751\) 51.2589 1.87046 0.935232 0.354036i \(-0.115191\pi\)
0.935232 + 0.354036i \(0.115191\pi\)
\(752\) 8.09353 0.295141
\(753\) 0 0
\(754\) −78.2228 −2.84871
\(755\) 13.2830 0.483418
\(756\) 0 0
\(757\) 4.07426 0.148081 0.0740407 0.997255i \(-0.476411\pi\)
0.0740407 + 0.997255i \(0.476411\pi\)
\(758\) 3.61797 0.131411
\(759\) 0 0
\(760\) −17.3770 −0.630330
\(761\) 6.01136 0.217912 0.108956 0.994047i \(-0.465249\pi\)
0.108956 + 0.994047i \(0.465249\pi\)
\(762\) 0 0
\(763\) 11.2061 0.405689
\(764\) 21.8158 0.789267
\(765\) 0 0
\(766\) −18.2634 −0.659885
\(767\) −16.7910 −0.606290
\(768\) 0 0
\(769\) 43.2310 1.55895 0.779474 0.626434i \(-0.215486\pi\)
0.779474 + 0.626434i \(0.215486\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −14.1951 −0.510894
\(773\) −9.64530 −0.346917 −0.173459 0.984841i \(-0.555494\pi\)
−0.173459 + 0.984841i \(0.555494\pi\)
\(774\) 0 0
\(775\) 73.6823 2.64675
\(776\) −7.25935 −0.260595
\(777\) 0 0
\(778\) 56.3906 2.02170
\(779\) 56.2311 2.01469
\(780\) 0 0
\(781\) 0 0
\(782\) 15.6602 0.560008
\(783\) 0 0
\(784\) −2.96434 −0.105869
\(785\) −47.8524 −1.70793
\(786\) 0 0
\(787\) −24.1192 −0.859757 −0.429879 0.902887i \(-0.641444\pi\)
−0.429879 + 0.902887i \(0.641444\pi\)
\(788\) 15.0351 0.535605
\(789\) 0 0
\(790\) 90.1480 3.20732
\(791\) 16.4261 0.584046
\(792\) 0 0
\(793\) −1.03219 −0.0366543
\(794\) 37.6011 1.33441
\(795\) 0 0
\(796\) −45.7771 −1.62253
\(797\) −42.4069 −1.50213 −0.751066 0.660228i \(-0.770460\pi\)
−0.751066 + 0.660228i \(0.770460\pi\)
\(798\) 0 0
\(799\) −4.16871 −0.147478
\(800\) 72.8247 2.57474
\(801\) 0 0
\(802\) 60.8338 2.14812
\(803\) 0 0
\(804\) 0 0
\(805\) 18.2830 0.644392
\(806\) −59.2638 −2.08748
\(807\) 0 0
\(808\) 1.54618 0.0543944
\(809\) −3.46232 −0.121729 −0.0608643 0.998146i \(-0.519386\pi\)
−0.0608643 + 0.998146i \(0.519386\pi\)
\(810\) 0 0
\(811\) 15.7547 0.553224 0.276612 0.960982i \(-0.410788\pi\)
0.276612 + 0.960982i \(0.410788\pi\)
\(812\) 26.0328 0.913571
\(813\) 0 0
\(814\) 0 0
\(815\) 61.0762 2.13941
\(816\) 0 0
\(817\) 0.710424 0.0248546
\(818\) −58.1927 −2.03466
\(819\) 0 0
\(820\) 99.1819 3.46358
\(821\) 7.93147 0.276810 0.138405 0.990376i \(-0.455802\pi\)
0.138405 + 0.990376i \(0.455802\pi\)
\(822\) 0 0
\(823\) 32.9402 1.14822 0.574111 0.818777i \(-0.305348\pi\)
0.574111 + 0.818777i \(0.305348\pi\)
\(824\) 2.41895 0.0842682
\(825\) 0 0
\(826\) 10.1935 0.354677
\(827\) 30.1775 1.04937 0.524687 0.851295i \(-0.324182\pi\)
0.524687 + 0.851295i \(0.324182\pi\)
\(828\) 0 0
\(829\) −21.7848 −0.756619 −0.378309 0.925679i \(-0.623494\pi\)
−0.378309 + 0.925679i \(0.623494\pi\)
\(830\) −84.0065 −2.91591
\(831\) 0 0
\(832\) −38.0267 −1.31834
\(833\) 1.52683 0.0529016
\(834\) 0 0
\(835\) 21.2381 0.734976
\(836\) 0 0
\(837\) 0 0
\(838\) 9.48906 0.327794
\(839\) −13.4974 −0.465982 −0.232991 0.972479i \(-0.574851\pi\)
−0.232991 + 0.972479i \(0.574851\pi\)
\(840\) 0 0
\(841\) 86.0761 2.96814
\(842\) −75.6268 −2.60627
\(843\) 0 0
\(844\) 1.55357 0.0534760
\(845\) 3.70754 0.127543
\(846\) 0 0
\(847\) 0 0
\(848\) 8.28218 0.284411
\(849\) 0 0
\(850\) −29.1239 −0.998940
\(851\) −45.1339 −1.54717
\(852\) 0 0
\(853\) 22.5171 0.770971 0.385485 0.922714i \(-0.374034\pi\)
0.385485 + 0.922714i \(0.374034\pi\)
\(854\) 0.626624 0.0214426
\(855\) 0 0
\(856\) 4.47154 0.152834
\(857\) 12.2772 0.419383 0.209691 0.977768i \(-0.432754\pi\)
0.209691 + 0.977768i \(0.432754\pi\)
\(858\) 0 0
\(859\) −46.4901 −1.58622 −0.793110 0.609078i \(-0.791540\pi\)
−0.793110 + 0.609078i \(0.791540\pi\)
\(860\) 1.25306 0.0427291
\(861\) 0 0
\(862\) 46.7526 1.59240
\(863\) 54.4619 1.85391 0.926953 0.375178i \(-0.122419\pi\)
0.926953 + 0.375178i \(0.122419\pi\)
\(864\) 0 0
\(865\) −50.3364 −1.71149
\(866\) −53.6290 −1.82239
\(867\) 0 0
\(868\) 19.7232 0.669448
\(869\) 0 0
\(870\) 0 0
\(871\) 2.83117 0.0959306
\(872\) −10.0621 −0.340746
\(873\) 0 0
\(874\) −52.9253 −1.79022
\(875\) −15.2493 −0.515519
\(876\) 0 0
\(877\) −29.4571 −0.994697 −0.497348 0.867551i \(-0.665693\pi\)
−0.497348 + 0.867551i \(0.665693\pi\)
\(878\) −23.4398 −0.791056
\(879\) 0 0
\(880\) 0 0
\(881\) −29.9763 −1.00993 −0.504964 0.863141i \(-0.668494\pi\)
−0.504964 + 0.863141i \(0.668494\pi\)
\(882\) 0 0
\(883\) 30.2544 1.01814 0.509071 0.860725i \(-0.329989\pi\)
0.509071 + 0.860725i \(0.329989\pi\)
\(884\) 12.8415 0.431908
\(885\) 0 0
\(886\) −29.1428 −0.979073
\(887\) 47.3156 1.58870 0.794352 0.607458i \(-0.207811\pi\)
0.794352 + 0.607458i \(0.207811\pi\)
\(888\) 0 0
\(889\) −19.6058 −0.657556
\(890\) 70.3546 2.35829
\(891\) 0 0
\(892\) −40.5567 −1.35794
\(893\) 14.0886 0.471456
\(894\) 0 0
\(895\) −14.2833 −0.477439
\(896\) 7.01975 0.234513
\(897\) 0 0
\(898\) −22.4871 −0.750404
\(899\) 87.1849 2.90778
\(900\) 0 0
\(901\) −4.26588 −0.142117
\(902\) 0 0
\(903\) 0 0
\(904\) −14.7492 −0.490551
\(905\) 36.7118 1.22034
\(906\) 0 0
\(907\) −49.6479 −1.64853 −0.824265 0.566204i \(-0.808411\pi\)
−0.824265 + 0.566204i \(0.808411\pi\)
\(908\) 22.6328 0.751097
\(909\) 0 0
\(910\) 27.3480 0.906578
\(911\) −21.5478 −0.713909 −0.356954 0.934122i \(-0.616185\pi\)
−0.356954 + 0.934122i \(0.616185\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) −66.0185 −2.18370
\(915\) 0 0
\(916\) 51.8639 1.71363
\(917\) −13.3659 −0.441380
\(918\) 0 0
\(919\) 44.2085 1.45830 0.729151 0.684353i \(-0.239915\pi\)
0.729151 + 0.684353i \(0.239915\pi\)
\(920\) −16.4165 −0.541236
\(921\) 0 0
\(922\) −86.6516 −2.85372
\(923\) 19.8586 0.653654
\(924\) 0 0
\(925\) 83.9371 2.75983
\(926\) −74.9597 −2.46333
\(927\) 0 0
\(928\) 86.1702 2.82868
\(929\) 1.70847 0.0560532 0.0280266 0.999607i \(-0.491078\pi\)
0.0280266 + 0.999607i \(0.491078\pi\)
\(930\) 0 0
\(931\) −5.16008 −0.169115
\(932\) −41.5375 −1.36061
\(933\) 0 0
\(934\) −13.5906 −0.444698
\(935\) 0 0
\(936\) 0 0
\(937\) −33.3716 −1.09020 −0.545101 0.838371i \(-0.683509\pi\)
−0.545101 + 0.838371i \(0.683509\pi\)
\(938\) −1.71875 −0.0561191
\(939\) 0 0
\(940\) 24.8498 0.810511
\(941\) −22.2132 −0.724128 −0.362064 0.932153i \(-0.617928\pi\)
−0.362064 + 0.932153i \(0.617928\pi\)
\(942\) 0 0
\(943\) 53.1230 1.72992
\(944\) 14.3618 0.467436
\(945\) 0 0
\(946\) 0 0
\(947\) 16.6969 0.542578 0.271289 0.962498i \(-0.412550\pi\)
0.271289 + 0.962498i \(0.412550\pi\)
\(948\) 0 0
\(949\) −8.57829 −0.278463
\(950\) 98.4270 3.19339
\(951\) 0 0
\(952\) −1.37096 −0.0444330
\(953\) −19.0864 −0.618269 −0.309135 0.951018i \(-0.600039\pi\)
−0.309135 + 0.951018i \(0.600039\pi\)
\(954\) 0 0
\(955\) −33.7154 −1.09100
\(956\) 8.17927 0.264537
\(957\) 0 0
\(958\) 14.3136 0.462450
\(959\) 5.27980 0.170494
\(960\) 0 0
\(961\) 35.0538 1.13077
\(962\) −67.5119 −2.17667
\(963\) 0 0
\(964\) 14.0166 0.451444
\(965\) 21.9380 0.706208
\(966\) 0 0
\(967\) 36.9443 1.18805 0.594024 0.804447i \(-0.297538\pi\)
0.594024 + 0.804447i \(0.297538\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 63.7959 2.04836
\(971\) −31.3049 −1.00462 −0.502310 0.864687i \(-0.667516\pi\)
−0.502310 + 0.864687i \(0.667516\pi\)
\(972\) 0 0
\(973\) −21.3757 −0.685273
\(974\) −56.2278 −1.80165
\(975\) 0 0
\(976\) 0.882859 0.0282596
\(977\) −44.7409 −1.43139 −0.715695 0.698413i \(-0.753890\pi\)
−0.715695 + 0.698413i \(0.753890\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) −9.10149 −0.290737
\(981\) 0 0
\(982\) 12.8187 0.409061
\(983\) 57.2232 1.82514 0.912568 0.408926i \(-0.134097\pi\)
0.912568 + 0.408926i \(0.134097\pi\)
\(984\) 0 0
\(985\) −23.2362 −0.740366
\(986\) −34.4610 −1.09746
\(987\) 0 0
\(988\) −43.3993 −1.38071
\(989\) 0.671156 0.0213415
\(990\) 0 0
\(991\) −26.9663 −0.856614 −0.428307 0.903633i \(-0.640890\pi\)
−0.428307 + 0.903633i \(0.640890\pi\)
\(992\) 65.2850 2.07280
\(993\) 0 0
\(994\) −12.0557 −0.382385
\(995\) 70.7466 2.24282
\(996\) 0 0
\(997\) 25.3305 0.802224 0.401112 0.916029i \(-0.368624\pi\)
0.401112 + 0.916029i \(0.368624\pi\)
\(998\) −3.14656 −0.0996027
\(999\) 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 7623.2.a.dc.1.3 16
3.2 odd 2 inner 7623.2.a.dc.1.14 16
11.5 even 5 693.2.m.k.190.7 yes 32
11.9 even 5 693.2.m.k.631.7 yes 32
11.10 odd 2 7623.2.a.db.1.14 16
33.5 odd 10 693.2.m.k.190.2 32
33.20 odd 10 693.2.m.k.631.2 yes 32
33.32 even 2 7623.2.a.db.1.3 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
693.2.m.k.190.2 32 33.5 odd 10
693.2.m.k.190.7 yes 32 11.5 even 5
693.2.m.k.631.2 yes 32 33.20 odd 10
693.2.m.k.631.7 yes 32 11.9 even 5
7623.2.a.db.1.3 16 33.32 even 2
7623.2.a.db.1.14 16 11.10 odd 2
7623.2.a.dc.1.3 16 1.1 even 1 trivial
7623.2.a.dc.1.14 16 3.2 odd 2 inner