Properties

Label 7623.2.a.cr.1.6
Level 7623
Weight 2
Character 7623.1
Self dual yes
Analytic conductor 60.870
Analytic rank 0
Dimension 6
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: \(6\)
Coefficient field: 6.6.3829849.1
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(2.22391\)
Character \(\chi\) = 7623.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.45784 q^{2} +4.04096 q^{4} +2.05098 q^{5} +1.00000 q^{7} +5.01636 q^{8} +O(q^{10})\) \(q+2.45784 q^{2} +4.04096 q^{4} +2.05098 q^{5} +1.00000 q^{7} +5.01636 q^{8} +5.04096 q^{10} +0.206501 q^{13} +2.45784 q^{14} +4.24747 q^{16} +0.813723 q^{17} +6.28843 q^{19} +8.28792 q^{20} -5.11704 q^{23} -0.793499 q^{25} +0.507546 q^{26} +4.04096 q^{28} -3.87979 q^{29} +6.49493 q^{31} +0.406862 q^{32} +2.00000 q^{34} +2.05098 q^{35} +1.79350 q^{37} +15.4559 q^{38} +10.2884 q^{40} -1.82882 q^{41} +10.0819 q^{43} -12.5769 q^{46} +8.79547 q^{47} +1.00000 q^{49} -1.95029 q^{50} +0.834464 q^{52} +3.08686 q^{53} +5.01636 q^{56} -9.53590 q^{58} -2.66333 q^{59} +3.58700 q^{61} +15.9635 q^{62} -7.49493 q^{64} +0.423529 q^{65} +10.2884 q^{67} +3.28823 q^{68} +5.04096 q^{70} +15.5607 q^{71} +7.79350 q^{73} +4.40813 q^{74} +25.4113 q^{76} -12.1639 q^{79} +8.71145 q^{80} -4.49493 q^{82} -14.9484 q^{83} +1.66893 q^{85} +24.7797 q^{86} +5.72940 q^{89} +0.206501 q^{91} -20.6778 q^{92} +21.6178 q^{94} +12.8974 q^{95} -8.49493 q^{97} +2.45784 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 4q^{4} + 6q^{7} + O(q^{10}) \) \( 6q + 4q^{4} + 6q^{7} + 10q^{10} + 4q^{13} + 8q^{16} - 2q^{25} + 4q^{28} + 4q^{31} + 12q^{34} + 8q^{37} + 24q^{40} + 20q^{43} + 6q^{49} - 18q^{52} - 2q^{58} + 16q^{61} - 10q^{64} + 24q^{67} + 10q^{70} + 44q^{73} + 54q^{76} + 8q^{79} + 8q^{82} - 36q^{85} + 4q^{91} + 34q^{94} - 16q^{97} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.45784 1.73795 0.868977 0.494853i \(-0.164778\pi\)
0.868977 + 0.494853i \(0.164778\pi\)
\(3\) 0 0
\(4\) 4.04096 2.02048
\(5\) 2.05098 0.917224 0.458612 0.888637i \(-0.348347\pi\)
0.458612 + 0.888637i \(0.348347\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 5.01636 1.77355
\(9\) 0 0
\(10\) 5.04096 1.59409
\(11\) 0 0
\(12\) 0 0
\(13\) 0.206501 0.0572731 0.0286365 0.999590i \(-0.490883\pi\)
0.0286365 + 0.999590i \(0.490883\pi\)
\(14\) 2.45784 0.656885
\(15\) 0 0
\(16\) 4.24747 1.06187
\(17\) 0.813723 0.197357 0.0986785 0.995119i \(-0.468538\pi\)
0.0986785 + 0.995119i \(0.468538\pi\)
\(18\) 0 0
\(19\) 6.28843 1.44266 0.721332 0.692589i \(-0.243530\pi\)
0.721332 + 0.692589i \(0.243530\pi\)
\(20\) 8.28792 1.85324
\(21\) 0 0
\(22\) 0 0
\(23\) −5.11704 −1.06698 −0.533489 0.845807i \(-0.679119\pi\)
−0.533489 + 0.845807i \(0.679119\pi\)
\(24\) 0 0
\(25\) −0.793499 −0.158700
\(26\) 0.507546 0.0995380
\(27\) 0 0
\(28\) 4.04096 0.763671
\(29\) −3.87979 −0.720459 −0.360230 0.932864i \(-0.617302\pi\)
−0.360230 + 0.932864i \(0.617302\pi\)
\(30\) 0 0
\(31\) 6.49493 1.16652 0.583262 0.812284i \(-0.301776\pi\)
0.583262 + 0.812284i \(0.301776\pi\)
\(32\) 0.406862 0.0719237
\(33\) 0 0
\(34\) 2.00000 0.342997
\(35\) 2.05098 0.346678
\(36\) 0 0
\(37\) 1.79350 0.294849 0.147425 0.989073i \(-0.452902\pi\)
0.147425 + 0.989073i \(0.452902\pi\)
\(38\) 15.4559 2.50728
\(39\) 0 0
\(40\) 10.2884 1.62674
\(41\) −1.82882 −0.285613 −0.142807 0.989751i \(-0.545613\pi\)
−0.142807 + 0.989751i \(0.545613\pi\)
\(42\) 0 0
\(43\) 10.0819 1.53748 0.768740 0.639562i \(-0.220884\pi\)
0.768740 + 0.639562i \(0.220884\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) −12.5769 −1.85436
\(47\) 8.79547 1.28295 0.641475 0.767144i \(-0.278323\pi\)
0.641475 + 0.767144i \(0.278323\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) −1.95029 −0.275813
\(51\) 0 0
\(52\) 0.834464 0.115719
\(53\) 3.08686 0.424013 0.212006 0.977268i \(-0.432000\pi\)
0.212006 + 0.977268i \(0.432000\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 5.01636 0.670339
\(57\) 0 0
\(58\) −9.53590 −1.25212
\(59\) −2.66333 −0.346736 −0.173368 0.984857i \(-0.555465\pi\)
−0.173368 + 0.984857i \(0.555465\pi\)
\(60\) 0 0
\(61\) 3.58700 0.459268 0.229634 0.973277i \(-0.426247\pi\)
0.229634 + 0.973277i \(0.426247\pi\)
\(62\) 15.9635 2.02736
\(63\) 0 0
\(64\) −7.49493 −0.936866
\(65\) 0.423529 0.0525323
\(66\) 0 0
\(67\) 10.2884 1.25693 0.628466 0.777837i \(-0.283683\pi\)
0.628466 + 0.777837i \(0.283683\pi\)
\(68\) 3.28823 0.398756
\(69\) 0 0
\(70\) 5.04096 0.602511
\(71\) 15.5607 1.84672 0.923361 0.383934i \(-0.125431\pi\)
0.923361 + 0.383934i \(0.125431\pi\)
\(72\) 0 0
\(73\) 7.79350 0.912160 0.456080 0.889939i \(-0.349253\pi\)
0.456080 + 0.889939i \(0.349253\pi\)
\(74\) 4.40813 0.512435
\(75\) 0 0
\(76\) 25.4113 2.91488
\(77\) 0 0
\(78\) 0 0
\(79\) −12.1639 −1.36854 −0.684270 0.729228i \(-0.739879\pi\)
−0.684270 + 0.729228i \(0.739879\pi\)
\(80\) 8.71145 0.973970
\(81\) 0 0
\(82\) −4.49493 −0.496382
\(83\) −14.9484 −1.64080 −0.820400 0.571791i \(-0.806249\pi\)
−0.820400 + 0.571791i \(0.806249\pi\)
\(84\) 0 0
\(85\) 1.66893 0.181021
\(86\) 24.7797 2.67207
\(87\) 0 0
\(88\) 0 0
\(89\) 5.72940 0.607315 0.303657 0.952781i \(-0.401792\pi\)
0.303657 + 0.952781i \(0.401792\pi\)
\(90\) 0 0
\(91\) 0.206501 0.0216472
\(92\) −20.6778 −2.15581
\(93\) 0 0
\(94\) 21.6178 2.22971
\(95\) 12.8974 1.32325
\(96\) 0 0
\(97\) −8.49493 −0.862530 −0.431265 0.902225i \(-0.641933\pi\)
−0.431265 + 0.902225i \(0.641933\pi\)
\(98\) 2.45784 0.248279
\(99\) 0 0
\(100\) −3.20650 −0.320650
\(101\) −10.6451 −1.05922 −0.529612 0.848240i \(-0.677663\pi\)
−0.529612 + 0.848240i \(0.677663\pi\)
\(102\) 0 0
\(103\) −15.7509 −1.55198 −0.775989 0.630746i \(-0.782749\pi\)
−0.775989 + 0.630746i \(0.782749\pi\)
\(104\) 1.03588 0.101577
\(105\) 0 0
\(106\) 7.58700 0.736914
\(107\) 1.43862 0.139077 0.0695384 0.997579i \(-0.477847\pi\)
0.0695384 + 0.997579i \(0.477847\pi\)
\(108\) 0 0
\(109\) −2.49493 −0.238971 −0.119486 0.992836i \(-0.538125\pi\)
−0.119486 + 0.992836i \(0.538125\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 4.24747 0.401348
\(113\) −17.5909 −1.65482 −0.827408 0.561602i \(-0.810185\pi\)
−0.827408 + 0.561602i \(0.810185\pi\)
\(114\) 0 0
\(115\) −10.4949 −0.978657
\(116\) −15.6781 −1.45567
\(117\) 0 0
\(118\) −6.54603 −0.602611
\(119\) 0.813723 0.0745939
\(120\) 0 0
\(121\) 0 0
\(122\) 8.81626 0.798186
\(123\) 0 0
\(124\) 26.2458 2.35694
\(125\) −11.8823 −1.06279
\(126\) 0 0
\(127\) 10.9079 0.967923 0.483961 0.875089i \(-0.339198\pi\)
0.483961 + 0.875089i \(0.339198\pi\)
\(128\) −19.2350 −1.70015
\(129\) 0 0
\(130\) 1.04096 0.0912986
\(131\) 5.72940 0.500580 0.250290 0.968171i \(-0.419474\pi\)
0.250290 + 0.968171i \(0.419474\pi\)
\(132\) 0 0
\(133\) 6.28843 0.545276
\(134\) 25.2873 2.18449
\(135\) 0 0
\(136\) 4.08193 0.350023
\(137\) 6.34175 0.541813 0.270906 0.962606i \(-0.412677\pi\)
0.270906 + 0.962606i \(0.412677\pi\)
\(138\) 0 0
\(139\) −4.16386 −0.353174 −0.176587 0.984285i \(-0.556506\pi\)
−0.176587 + 0.984285i \(0.556506\pi\)
\(140\) 8.28792 0.700457
\(141\) 0 0
\(142\) 38.2458 3.20952
\(143\) 0 0
\(144\) 0 0
\(145\) −7.95736 −0.660823
\(146\) 19.1552 1.58529
\(147\) 0 0
\(148\) 7.24747 0.595738
\(149\) 16.1856 1.32598 0.662990 0.748628i \(-0.269287\pi\)
0.662990 + 0.748628i \(0.269287\pi\)
\(150\) 0 0
\(151\) 1.66893 0.135815 0.0679077 0.997692i \(-0.478368\pi\)
0.0679077 + 0.997692i \(0.478368\pi\)
\(152\) 31.5450 2.55864
\(153\) 0 0
\(154\) 0 0
\(155\) 13.3209 1.06996
\(156\) 0 0
\(157\) −18.5769 −1.48259 −0.741297 0.671177i \(-0.765789\pi\)
−0.741297 + 0.671177i \(0.765789\pi\)
\(158\) −29.8968 −2.37846
\(159\) 0 0
\(160\) 0.834464 0.0659701
\(161\) −5.11704 −0.403280
\(162\) 0 0
\(163\) 10.2884 0.805852 0.402926 0.915233i \(-0.367993\pi\)
0.402926 + 0.915233i \(0.367993\pi\)
\(164\) −7.39018 −0.577076
\(165\) 0 0
\(166\) −36.7407 −2.85163
\(167\) −23.5550 −1.82274 −0.911372 0.411585i \(-0.864975\pi\)
−0.911372 + 0.411585i \(0.864975\pi\)
\(168\) 0 0
\(169\) −12.9574 −0.996720
\(170\) 4.10195 0.314605
\(171\) 0 0
\(172\) 40.7407 3.10645
\(173\) 5.93077 0.450908 0.225454 0.974254i \(-0.427613\pi\)
0.225454 + 0.974254i \(0.427613\pi\)
\(174\) 0 0
\(175\) −0.793499 −0.0599829
\(176\) 0 0
\(177\) 0 0
\(178\) 14.0819 1.05549
\(179\) −16.4078 −1.22638 −0.613188 0.789937i \(-0.710113\pi\)
−0.613188 + 0.789937i \(0.710113\pi\)
\(180\) 0 0
\(181\) −3.50507 −0.260530 −0.130265 0.991479i \(-0.541583\pi\)
−0.130265 + 0.991479i \(0.541583\pi\)
\(182\) 0.507546 0.0376218
\(183\) 0 0
\(184\) −25.6689 −1.89234
\(185\) 3.67842 0.270443
\(186\) 0 0
\(187\) 0 0
\(188\) 35.5422 2.59218
\(189\) 0 0
\(190\) 31.6998 2.29974
\(191\) −18.6476 −1.34929 −0.674647 0.738141i \(-0.735704\pi\)
−0.674647 + 0.738141i \(0.735704\pi\)
\(192\) 0 0
\(193\) 5.50507 0.396264 0.198132 0.980175i \(-0.436513\pi\)
0.198132 + 0.980175i \(0.436513\pi\)
\(194\) −20.8792 −1.49904
\(195\) 0 0
\(196\) 4.04096 0.288640
\(197\) 18.2366 1.29931 0.649653 0.760231i \(-0.274914\pi\)
0.649653 + 0.760231i \(0.274914\pi\)
\(198\) 0 0
\(199\) −6.90793 −0.489690 −0.244845 0.969562i \(-0.578737\pi\)
−0.244845 + 0.969562i \(0.578737\pi\)
\(200\) −3.98048 −0.281462
\(201\) 0 0
\(202\) −26.1639 −1.84088
\(203\) −3.87979 −0.272308
\(204\) 0 0
\(205\) −3.75086 −0.261971
\(206\) −38.7130 −2.69727
\(207\) 0 0
\(208\) 0.877106 0.0608164
\(209\) 0 0
\(210\) 0 0
\(211\) 7.17400 0.493878 0.246939 0.969031i \(-0.420575\pi\)
0.246939 + 0.969031i \(0.420575\pi\)
\(212\) 12.4739 0.856710
\(213\) 0 0
\(214\) 3.53590 0.241709
\(215\) 20.6778 1.41021
\(216\) 0 0
\(217\) 6.49493 0.440905
\(218\) −6.13214 −0.415321
\(219\) 0 0
\(220\) 0 0
\(221\) 0.168035 0.0113032
\(222\) 0 0
\(223\) 8.16386 0.546692 0.273346 0.961916i \(-0.411870\pi\)
0.273346 + 0.961916i \(0.411870\pi\)
\(224\) 0.406862 0.0271846
\(225\) 0 0
\(226\) −43.2357 −2.87599
\(227\) −3.69921 −0.245525 −0.122763 0.992436i \(-0.539175\pi\)
−0.122763 + 0.992436i \(0.539175\pi\)
\(228\) 0 0
\(229\) −20.2458 −1.33788 −0.668940 0.743317i \(-0.733252\pi\)
−0.668940 + 0.743317i \(0.733252\pi\)
\(230\) −25.7948 −1.70086
\(231\) 0 0
\(232\) −19.4624 −1.27777
\(233\) 13.6903 0.896885 0.448442 0.893812i \(-0.351979\pi\)
0.448442 + 0.893812i \(0.351979\pi\)
\(234\) 0 0
\(235\) 18.0393 1.17675
\(236\) −10.7624 −0.700574
\(237\) 0 0
\(238\) 2.00000 0.129641
\(239\) 16.5966 1.07355 0.536773 0.843726i \(-0.319643\pi\)
0.536773 + 0.843726i \(0.319643\pi\)
\(240\) 0 0
\(241\) −11.9574 −0.770241 −0.385121 0.922866i \(-0.625840\pi\)
−0.385121 + 0.922866i \(0.625840\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 14.4949 0.927943
\(245\) 2.05098 0.131032
\(246\) 0 0
\(247\) 1.29857 0.0826259
\(248\) 32.5809 2.06889
\(249\) 0 0
\(250\) −29.2048 −1.84708
\(251\) −5.54057 −0.349718 −0.174859 0.984594i \(-0.555947\pi\)
−0.174859 + 0.984594i \(0.555947\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 26.8099 1.68220
\(255\) 0 0
\(256\) −32.2868 −2.01792
\(257\) −27.8458 −1.73697 −0.868487 0.495712i \(-0.834907\pi\)
−0.868487 + 0.495712i \(0.834907\pi\)
\(258\) 0 0
\(259\) 1.79350 0.111443
\(260\) 1.71146 0.106141
\(261\) 0 0
\(262\) 14.0819 0.869984
\(263\) −7.16802 −0.441999 −0.220999 0.975274i \(-0.570932\pi\)
−0.220999 + 0.975274i \(0.570932\pi\)
\(264\) 0 0
\(265\) 6.33107 0.388915
\(266\) 15.4559 0.947664
\(267\) 0 0
\(268\) 41.5752 2.53961
\(269\) 11.9031 0.725746 0.362873 0.931839i \(-0.381796\pi\)
0.362873 + 0.931839i \(0.381796\pi\)
\(270\) 0 0
\(271\) 30.2884 1.83989 0.919946 0.392046i \(-0.128233\pi\)
0.919946 + 0.392046i \(0.128233\pi\)
\(272\) 3.45626 0.209567
\(273\) 0 0
\(274\) 15.5870 0.941645
\(275\) 0 0
\(276\) 0 0
\(277\) 28.5769 1.71702 0.858509 0.512799i \(-0.171391\pi\)
0.858509 + 0.512799i \(0.171391\pi\)
\(278\) −10.2341 −0.613800
\(279\) 0 0
\(280\) 10.2884 0.614851
\(281\) 4.72685 0.281980 0.140990 0.990011i \(-0.454971\pi\)
0.140990 + 0.990011i \(0.454971\pi\)
\(282\) 0 0
\(283\) 10.4523 0.621324 0.310662 0.950520i \(-0.399449\pi\)
0.310662 + 0.950520i \(0.399449\pi\)
\(284\) 62.8804 3.73127
\(285\) 0 0
\(286\) 0 0
\(287\) −1.82882 −0.107952
\(288\) 0 0
\(289\) −16.3379 −0.961050
\(290\) −19.5579 −1.14848
\(291\) 0 0
\(292\) 31.4933 1.84300
\(293\) 32.1699 1.87939 0.939693 0.342018i \(-0.111110\pi\)
0.939693 + 0.342018i \(0.111110\pi\)
\(294\) 0 0
\(295\) −5.46243 −0.318035
\(296\) 8.99683 0.522930
\(297\) 0 0
\(298\) 39.7817 2.30449
\(299\) −1.05667 −0.0611091
\(300\) 0 0
\(301\) 10.0819 0.581113
\(302\) 4.10195 0.236041
\(303\) 0 0
\(304\) 26.7099 1.53192
\(305\) 7.35685 0.421252
\(306\) 0 0
\(307\) −24.3277 −1.38846 −0.694228 0.719755i \(-0.744254\pi\)
−0.694228 + 0.719755i \(0.744254\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 32.7407 1.85955
\(311\) −21.6929 −1.23009 −0.615045 0.788492i \(-0.710862\pi\)
−0.615045 + 0.788492i \(0.710862\pi\)
\(312\) 0 0
\(313\) −7.25592 −0.410129 −0.205065 0.978748i \(-0.565740\pi\)
−0.205065 + 0.978748i \(0.565740\pi\)
\(314\) −45.6589 −2.57668
\(315\) 0 0
\(316\) −49.1537 −2.76511
\(317\) −30.9119 −1.73618 −0.868092 0.496403i \(-0.834654\pi\)
−0.868092 + 0.496403i \(0.834654\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −15.3719 −0.859317
\(321\) 0 0
\(322\) −12.5769 −0.700881
\(323\) 5.11704 0.284720
\(324\) 0 0
\(325\) −0.163858 −0.00908923
\(326\) 25.2873 1.40053
\(327\) 0 0
\(328\) −9.17400 −0.506549
\(329\) 8.79547 0.484910
\(330\) 0 0
\(331\) 20.3277 1.11731 0.558656 0.829399i \(-0.311317\pi\)
0.558656 + 0.829399i \(0.311317\pi\)
\(332\) −60.4059 −3.31521
\(333\) 0 0
\(334\) −57.8944 −3.16784
\(335\) 21.1013 1.15289
\(336\) 0 0
\(337\) −26.8226 −1.46112 −0.730561 0.682847i \(-0.760742\pi\)
−0.730561 + 0.682847i \(0.760742\pi\)
\(338\) −31.8471 −1.73225
\(339\) 0 0
\(340\) 6.74408 0.365749
\(341\) 0 0
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 50.5746 2.72680
\(345\) 0 0
\(346\) 14.5769 0.783657
\(347\) −24.9478 −1.33927 −0.669633 0.742692i \(-0.733549\pi\)
−0.669633 + 0.742692i \(0.733549\pi\)
\(348\) 0 0
\(349\) −19.9574 −1.06829 −0.534146 0.845392i \(-0.679367\pi\)
−0.534146 + 0.845392i \(0.679367\pi\)
\(350\) −1.95029 −0.104247
\(351\) 0 0
\(352\) 0 0
\(353\) 2.89803 0.154247 0.0771234 0.997022i \(-0.475426\pi\)
0.0771234 + 0.997022i \(0.475426\pi\)
\(354\) 0 0
\(355\) 31.9147 1.69386
\(356\) 23.1523 1.22707
\(357\) 0 0
\(358\) −40.3277 −2.13139
\(359\) −26.2392 −1.38485 −0.692425 0.721490i \(-0.743458\pi\)
−0.692425 + 0.721490i \(0.743458\pi\)
\(360\) 0 0
\(361\) 20.5444 1.08128
\(362\) −8.61489 −0.452789
\(363\) 0 0
\(364\) 0.834464 0.0437378
\(365\) 15.9843 0.836655
\(366\) 0 0
\(367\) 23.3379 1.21823 0.609113 0.793083i \(-0.291526\pi\)
0.609113 + 0.793083i \(0.291526\pi\)
\(368\) −21.7345 −1.13299
\(369\) 0 0
\(370\) 9.04096 0.470017
\(371\) 3.08686 0.160262
\(372\) 0 0
\(373\) −2.08193 −0.107798 −0.0538991 0.998546i \(-0.517165\pi\)
−0.0538991 + 0.998546i \(0.517165\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 44.1212 2.27538
\(377\) −0.801181 −0.0412629
\(378\) 0 0
\(379\) −6.45229 −0.331432 −0.165716 0.986174i \(-0.552993\pi\)
−0.165716 + 0.986174i \(0.552993\pi\)
\(380\) 52.1180 2.67360
\(381\) 0 0
\(382\) −45.8328 −2.34501
\(383\) 6.97919 0.356620 0.178310 0.983974i \(-0.442937\pi\)
0.178310 + 0.983974i \(0.442937\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 13.5306 0.688688
\(387\) 0 0
\(388\) −34.3277 −1.74273
\(389\) 8.16232 0.413846 0.206923 0.978357i \(-0.433655\pi\)
0.206923 + 0.978357i \(0.433655\pi\)
\(390\) 0 0
\(391\) −4.16386 −0.210575
\(392\) 5.01636 0.253364
\(393\) 0 0
\(394\) 44.8226 2.25813
\(395\) −24.9478 −1.25526
\(396\) 0 0
\(397\) −27.4198 −1.37616 −0.688080 0.725635i \(-0.741546\pi\)
−0.688080 + 0.725635i \(0.741546\pi\)
\(398\) −16.9786 −0.851059
\(399\) 0 0
\(400\) −3.37036 −0.168518
\(401\) 23.9327 1.19514 0.597571 0.801816i \(-0.296133\pi\)
0.597571 + 0.801816i \(0.296133\pi\)
\(402\) 0 0
\(403\) 1.34121 0.0668104
\(404\) −43.0164 −2.14014
\(405\) 0 0
\(406\) −9.53590 −0.473259
\(407\) 0 0
\(408\) 0 0
\(409\) 23.7509 1.17440 0.587202 0.809440i \(-0.300229\pi\)
0.587202 + 0.809440i \(0.300229\pi\)
\(410\) −9.21899 −0.455294
\(411\) 0 0
\(412\) −63.6487 −3.13574
\(413\) −2.66333 −0.131054
\(414\) 0 0
\(415\) −30.6588 −1.50498
\(416\) 0.0840174 0.00411929
\(417\) 0 0
\(418\) 0 0
\(419\) −22.2844 −1.08867 −0.544333 0.838869i \(-0.683217\pi\)
−0.544333 + 0.838869i \(0.683217\pi\)
\(420\) 0 0
\(421\) 9.38050 0.457177 0.228589 0.973523i \(-0.426589\pi\)
0.228589 + 0.973523i \(0.426589\pi\)
\(422\) 17.6325 0.858337
\(423\) 0 0
\(424\) 15.4848 0.752008
\(425\) −0.645689 −0.0313205
\(426\) 0 0
\(427\) 3.58700 0.173587
\(428\) 5.81342 0.281002
\(429\) 0 0
\(430\) 50.8226 2.45089
\(431\) −5.94331 −0.286279 −0.143140 0.989703i \(-0.545720\pi\)
−0.143140 + 0.989703i \(0.545720\pi\)
\(432\) 0 0
\(433\) −5.42314 −0.260619 −0.130310 0.991473i \(-0.541597\pi\)
−0.130310 + 0.991473i \(0.541597\pi\)
\(434\) 15.9635 0.766272
\(435\) 0 0
\(436\) −10.0819 −0.482837
\(437\) −32.1782 −1.53929
\(438\) 0 0
\(439\) −26.0393 −1.24279 −0.621394 0.783499i \(-0.713433\pi\)
−0.621394 + 0.783499i \(0.713433\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0.413002 0.0196445
\(443\) −7.35685 −0.349534 −0.174767 0.984610i \(-0.555917\pi\)
−0.174767 + 0.984610i \(0.555917\pi\)
\(444\) 0 0
\(445\) 11.7509 0.557044
\(446\) 20.0654 0.950126
\(447\) 0 0
\(448\) −7.49493 −0.354102
\(449\) 11.4172 0.538812 0.269406 0.963027i \(-0.413173\pi\)
0.269406 + 0.963027i \(0.413173\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) −71.0843 −3.34353
\(453\) 0 0
\(454\) −9.09207 −0.426712
\(455\) 0.423529 0.0198553
\(456\) 0 0
\(457\) 11.3209 0.529571 0.264786 0.964307i \(-0.414699\pi\)
0.264786 + 0.964307i \(0.414699\pi\)
\(458\) −49.7609 −2.32517
\(459\) 0 0
\(460\) −42.4096 −1.97736
\(461\) −0.604106 −0.0281360 −0.0140680 0.999901i \(-0.504478\pi\)
−0.0140680 + 0.999901i \(0.504478\pi\)
\(462\) 0 0
\(463\) −34.8653 −1.62033 −0.810164 0.586204i \(-0.800622\pi\)
−0.810164 + 0.586204i \(0.800622\pi\)
\(464\) −16.4793 −0.765031
\(465\) 0 0
\(466\) 33.6487 1.55874
\(467\) 28.4582 1.31689 0.658443 0.752630i \(-0.271215\pi\)
0.658443 + 0.752630i \(0.271215\pi\)
\(468\) 0 0
\(469\) 10.2884 0.475076
\(470\) 44.3376 2.04514
\(471\) 0 0
\(472\) −13.3602 −0.614954
\(473\) 0 0
\(474\) 0 0
\(475\) −4.98986 −0.228951
\(476\) 3.28823 0.150716
\(477\) 0 0
\(478\) 40.7918 1.86577
\(479\) 30.1064 1.37560 0.687798 0.725902i \(-0.258577\pi\)
0.687798 + 0.725902i \(0.258577\pi\)
\(480\) 0 0
\(481\) 0.370359 0.0168869
\(482\) −29.3892 −1.33864
\(483\) 0 0
\(484\) 0 0
\(485\) −17.4229 −0.791133
\(486\) 0 0
\(487\) −33.1537 −1.50234 −0.751169 0.660110i \(-0.770510\pi\)
−0.751169 + 0.660110i \(0.770510\pi\)
\(488\) 17.9937 0.814535
\(489\) 0 0
\(490\) 5.04096 0.227728
\(491\) −10.8257 −0.488555 −0.244277 0.969705i \(-0.578551\pi\)
−0.244277 + 0.969705i \(0.578551\pi\)
\(492\) 0 0
\(493\) −3.15708 −0.142188
\(494\) 3.19167 0.143600
\(495\) 0 0
\(496\) 27.5870 1.23869
\(497\) 15.5607 0.697995
\(498\) 0 0
\(499\) 38.8653 1.73985 0.869925 0.493185i \(-0.164167\pi\)
0.869925 + 0.493185i \(0.164167\pi\)
\(500\) −48.0161 −2.14734
\(501\) 0 0
\(502\) −13.6178 −0.607793
\(503\) 10.4437 0.465662 0.232831 0.972517i \(-0.425201\pi\)
0.232831 + 0.972517i \(0.425201\pi\)
\(504\) 0 0
\(505\) −21.8328 −0.971546
\(506\) 0 0
\(507\) 0 0
\(508\) 44.0786 1.95567
\(509\) −41.7999 −1.85275 −0.926374 0.376605i \(-0.877092\pi\)
−0.926374 + 0.376605i \(0.877092\pi\)
\(510\) 0 0
\(511\) 7.79350 0.344764
\(512\) −40.8855 −1.80690
\(513\) 0 0
\(514\) −68.4405 −3.01878
\(515\) −32.3046 −1.42351
\(516\) 0 0
\(517\) 0 0
\(518\) 4.40813 0.193682
\(519\) 0 0
\(520\) 2.12457 0.0931686
\(521\) 27.8874 1.22177 0.610884 0.791720i \(-0.290814\pi\)
0.610884 + 0.791720i \(0.290814\pi\)
\(522\) 0 0
\(523\) −30.6161 −1.33875 −0.669375 0.742924i \(-0.733438\pi\)
−0.669375 + 0.742924i \(0.733438\pi\)
\(524\) 23.1523 1.01141
\(525\) 0 0
\(526\) −17.6178 −0.768174
\(527\) 5.28508 0.230222
\(528\) 0 0
\(529\) 3.18413 0.138441
\(530\) 15.5607 0.675916
\(531\) 0 0
\(532\) 25.4113 1.10172
\(533\) −0.377652 −0.0163579
\(534\) 0 0
\(535\) 2.95058 0.127565
\(536\) 51.6105 2.22923
\(537\) 0 0
\(538\) 29.2559 1.26131
\(539\) 0 0
\(540\) 0 0
\(541\) −16.7407 −0.719740 −0.359870 0.933003i \(-0.617179\pi\)
−0.359870 + 0.933003i \(0.617179\pi\)
\(542\) 74.4440 3.19765
\(543\) 0 0
\(544\) 0.331073 0.0141946
\(545\) −5.11704 −0.219190
\(546\) 0 0
\(547\) 21.4029 0.915120 0.457560 0.889179i \(-0.348723\pi\)
0.457560 + 0.889179i \(0.348723\pi\)
\(548\) 25.6268 1.09472
\(549\) 0 0
\(550\) 0 0
\(551\) −24.3978 −1.03938
\(552\) 0 0
\(553\) −12.1639 −0.517260
\(554\) 70.2373 2.98410
\(555\) 0 0
\(556\) −16.8260 −0.713582
\(557\) −7.53742 −0.319371 −0.159685 0.987168i \(-0.551048\pi\)
−0.159685 + 0.987168i \(0.551048\pi\)
\(558\) 0 0
\(559\) 2.08193 0.0880562
\(560\) 8.71145 0.368126
\(561\) 0 0
\(562\) 11.6178 0.490068
\(563\) −14.9900 −0.631752 −0.315876 0.948800i \(-0.602298\pi\)
−0.315876 + 0.948800i \(0.602298\pi\)
\(564\) 0 0
\(565\) −36.0786 −1.51784
\(566\) 25.6900 1.07983
\(567\) 0 0
\(568\) 78.0583 3.27525
\(569\) −17.8339 −0.747635 −0.373818 0.927502i \(-0.621951\pi\)
−0.373818 + 0.927502i \(0.621951\pi\)
\(570\) 0 0
\(571\) −16.4130 −0.686863 −0.343431 0.939178i \(-0.611589\pi\)
−0.343431 + 0.939178i \(0.611589\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) −4.49493 −0.187615
\(575\) 4.06037 0.169329
\(576\) 0 0
\(577\) 25.2357 1.05057 0.525287 0.850925i \(-0.323958\pi\)
0.525287 + 0.850925i \(0.323958\pi\)
\(578\) −40.1558 −1.67026
\(579\) 0 0
\(580\) −32.1554 −1.33518
\(581\) −14.9484 −0.620164
\(582\) 0 0
\(583\) 0 0
\(584\) 39.0950 1.61776
\(585\) 0 0
\(586\) 79.0684 3.26629
\(587\) −30.4883 −1.25839 −0.629194 0.777248i \(-0.716615\pi\)
−0.629194 + 0.777248i \(0.716615\pi\)
\(588\) 0 0
\(589\) 40.8429 1.68290
\(590\) −13.4258 −0.552730
\(591\) 0 0
\(592\) 7.61783 0.313091
\(593\) 36.2719 1.48951 0.744754 0.667340i \(-0.232567\pi\)
0.744754 + 0.667340i \(0.232567\pi\)
\(594\) 0 0
\(595\) 1.66893 0.0684193
\(596\) 65.4056 2.67912
\(597\) 0 0
\(598\) −2.59714 −0.106205
\(599\) 2.03018 0.0829511 0.0414755 0.999140i \(-0.486794\pi\)
0.0414755 + 0.999140i \(0.486794\pi\)
\(600\) 0 0
\(601\) 28.7834 1.17410 0.587049 0.809551i \(-0.300290\pi\)
0.587049 + 0.809551i \(0.300290\pi\)
\(602\) 24.7797 1.00995
\(603\) 0 0
\(604\) 6.74408 0.274413
\(605\) 0 0
\(606\) 0 0
\(607\) 23.4422 0.951488 0.475744 0.879584i \(-0.342179\pi\)
0.475744 + 0.879584i \(0.342179\pi\)
\(608\) 2.55852 0.103762
\(609\) 0 0
\(610\) 18.0819 0.732116
\(611\) 1.81627 0.0734785
\(612\) 0 0
\(613\) 30.2458 1.22162 0.610808 0.791779i \(-0.290845\pi\)
0.610808 + 0.791779i \(0.290845\pi\)
\(614\) −59.7936 −2.41307
\(615\) 0 0
\(616\) 0 0
\(617\) −29.8968 −1.20360 −0.601800 0.798647i \(-0.705549\pi\)
−0.601800 + 0.798647i \(0.705549\pi\)
\(618\) 0 0
\(619\) 23.0718 0.927334 0.463667 0.886010i \(-0.346533\pi\)
0.463667 + 0.886010i \(0.346533\pi\)
\(620\) 53.8295 2.16184
\(621\) 0 0
\(622\) −53.3176 −2.13784
\(623\) 5.72940 0.229543
\(624\) 0 0
\(625\) −20.4029 −0.816115
\(626\) −17.8339 −0.712785
\(627\) 0 0
\(628\) −75.0684 −2.99556
\(629\) 1.45941 0.0581906
\(630\) 0 0
\(631\) −24.3277 −0.968471 −0.484236 0.874938i \(-0.660902\pi\)
−0.484236 + 0.874938i \(0.660902\pi\)
\(632\) −61.0183 −2.42718
\(633\) 0 0
\(634\) −75.9764 −3.01741
\(635\) 22.3719 0.887802
\(636\) 0 0
\(637\) 0.206501 0.00818187
\(638\) 0 0
\(639\) 0 0
\(640\) −39.4506 −1.55942
\(641\) 0.168035 0.00663697 0.00331849 0.999994i \(-0.498944\pi\)
0.00331849 + 0.999994i \(0.498944\pi\)
\(642\) 0 0
\(643\) 11.2357 0.443091 0.221545 0.975150i \(-0.428890\pi\)
0.221545 + 0.975150i \(0.428890\pi\)
\(644\) −20.6778 −0.814819
\(645\) 0 0
\(646\) 12.5769 0.494830
\(647\) −33.4072 −1.31337 −0.656686 0.754164i \(-0.728042\pi\)
−0.656686 + 0.754164i \(0.728042\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) −0.402737 −0.0157967
\(651\) 0 0
\(652\) 41.5752 1.62821
\(653\) −4.94901 −0.193670 −0.0968348 0.995300i \(-0.530872\pi\)
−0.0968348 + 0.995300i \(0.530872\pi\)
\(654\) 0 0
\(655\) 11.7509 0.459144
\(656\) −7.76783 −0.303283
\(657\) 0 0
\(658\) 21.6178 0.842751
\(659\) 12.8974 0.502412 0.251206 0.967934i \(-0.419173\pi\)
0.251206 + 0.967934i \(0.419173\pi\)
\(660\) 0 0
\(661\) 25.8978 1.00731 0.503654 0.863906i \(-0.331989\pi\)
0.503654 + 0.863906i \(0.331989\pi\)
\(662\) 49.9622 1.94184
\(663\) 0 0
\(664\) −74.9865 −2.91004
\(665\) 12.8974 0.500140
\(666\) 0 0
\(667\) 19.8531 0.768714
\(668\) −95.1851 −3.68282
\(669\) 0 0
\(670\) 51.8636 2.00367
\(671\) 0 0
\(672\) 0 0
\(673\) 47.0718 1.81448 0.907242 0.420609i \(-0.138183\pi\)
0.907242 + 0.420609i \(0.138183\pi\)
\(674\) −65.9257 −2.53936
\(675\) 0 0
\(676\) −52.3602 −2.01385
\(677\) 5.97235 0.229536 0.114768 0.993392i \(-0.463388\pi\)
0.114768 + 0.993392i \(0.463388\pi\)
\(678\) 0 0
\(679\) −8.49493 −0.326006
\(680\) 8.37194 0.321049
\(681\) 0 0
\(682\) 0 0
\(683\) 4.26999 0.163386 0.0816932 0.996658i \(-0.473967\pi\)
0.0816932 + 0.996658i \(0.473967\pi\)
\(684\) 0 0
\(685\) 13.0068 0.496964
\(686\) 2.45784 0.0938407
\(687\) 0 0
\(688\) 42.8226 1.63260
\(689\) 0.637440 0.0242845
\(690\) 0 0
\(691\) −19.3379 −0.735647 −0.367823 0.929896i \(-0.619897\pi\)
−0.367823 + 0.929896i \(0.619897\pi\)
\(692\) 23.9660 0.911051
\(693\) 0 0
\(694\) −61.3176 −2.32758
\(695\) −8.53997 −0.323940
\(696\) 0 0
\(697\) −1.48815 −0.0563677
\(698\) −49.0519 −1.85664
\(699\) 0 0
\(700\) −3.20650 −0.121194
\(701\) 22.3135 0.842769 0.421384 0.906882i \(-0.361544\pi\)
0.421384 + 0.906882i \(0.361544\pi\)
\(702\) 0 0
\(703\) 11.2783 0.425369
\(704\) 0 0
\(705\) 0 0
\(706\) 7.12289 0.268074
\(707\) −10.6451 −0.400349
\(708\) 0 0
\(709\) 15.0325 0.564558 0.282279 0.959332i \(-0.408910\pi\)
0.282279 + 0.959332i \(0.408910\pi\)
\(710\) 78.4412 2.94384
\(711\) 0 0
\(712\) 28.7407 1.07710
\(713\) −33.2348 −1.24465
\(714\) 0 0
\(715\) 0 0
\(716\) −66.3034 −2.47787
\(717\) 0 0
\(718\) −64.4916 −2.40680
\(719\) 20.2958 0.756907 0.378454 0.925620i \(-0.376456\pi\)
0.378454 + 0.925620i \(0.376456\pi\)
\(720\) 0 0
\(721\) −15.7509 −0.586593
\(722\) 50.4947 1.87922
\(723\) 0 0
\(724\) −14.1639 −0.526396
\(725\) 3.07861 0.114337
\(726\) 0 0
\(727\) −26.9865 −1.00087 −0.500437 0.865773i \(-0.666827\pi\)
−0.500437 + 0.865773i \(0.666827\pi\)
\(728\) 1.03588 0.0383924
\(729\) 0 0
\(730\) 39.2868 1.45407
\(731\) 8.20390 0.303432
\(732\) 0 0
\(733\) −4.41300 −0.162998 −0.0814990 0.996673i \(-0.525971\pi\)
−0.0814990 + 0.996673i \(0.525971\pi\)
\(734\) 57.3607 2.11722
\(735\) 0 0
\(736\) −2.08193 −0.0767409
\(737\) 0 0
\(738\) 0 0
\(739\) −36.1808 −1.33093 −0.665466 0.746428i \(-0.731767\pi\)
−0.665466 + 0.746428i \(0.731767\pi\)
\(740\) 14.8644 0.546425
\(741\) 0 0
\(742\) 7.58700 0.278527
\(743\) −22.7703 −0.835363 −0.417682 0.908593i \(-0.637157\pi\)
−0.417682 + 0.908593i \(0.637157\pi\)
\(744\) 0 0
\(745\) 33.1964 1.21622
\(746\) −5.11704 −0.187348
\(747\) 0 0
\(748\) 0 0
\(749\) 1.43862 0.0525661
\(750\) 0 0
\(751\) −15.0291 −0.548421 −0.274211 0.961670i \(-0.588417\pi\)
−0.274211 + 0.961670i \(0.588417\pi\)
\(752\) 37.3584 1.36232
\(753\) 0 0
\(754\) −1.96917 −0.0717130
\(755\) 3.42293 0.124573
\(756\) 0 0
\(757\) 23.6094 0.858097 0.429048 0.903281i \(-0.358849\pi\)
0.429048 + 0.903281i \(0.358849\pi\)
\(758\) −15.8587 −0.576013
\(759\) 0 0
\(760\) 64.6981 2.34685
\(761\) −50.9440 −1.84672 −0.923359 0.383938i \(-0.874568\pi\)
−0.923359 + 0.383938i \(0.874568\pi\)
\(762\) 0 0
\(763\) −2.49493 −0.0903226
\(764\) −75.3543 −2.72622
\(765\) 0 0
\(766\) 17.1537 0.619789
\(767\) −0.549981 −0.0198586
\(768\) 0 0
\(769\) 17.3602 0.626026 0.313013 0.949749i \(-0.398662\pi\)
0.313013 + 0.949749i \(0.398662\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 22.2458 0.800643
\(773\) −35.2442 −1.26765 −0.633824 0.773478i \(-0.718515\pi\)
−0.633824 + 0.773478i \(0.718515\pi\)
\(774\) 0 0
\(775\) −5.15372 −0.185127
\(776\) −42.6136 −1.52974
\(777\) 0 0
\(778\) 20.0617 0.719245
\(779\) −11.5004 −0.412044
\(780\) 0 0
\(781\) 0 0
\(782\) −10.2341 −0.365970
\(783\) 0 0
\(784\) 4.24747 0.151695
\(785\) −38.1007 −1.35987
\(786\) 0 0
\(787\) 29.8754 1.06494 0.532472 0.846448i \(-0.321263\pi\)
0.532472 + 0.846448i \(0.321263\pi\)
\(788\) 73.6935 2.62522
\(789\) 0 0
\(790\) −61.3176 −2.18158
\(791\) −17.5909 −0.625462
\(792\) 0 0
\(793\) 0.740719 0.0263037
\(794\) −67.3934 −2.39170
\(795\) 0 0
\(796\) −27.9147 −0.989411
\(797\) −12.2851 −0.435159 −0.217580 0.976043i \(-0.569816\pi\)
−0.217580 + 0.976043i \(0.569816\pi\)
\(798\) 0 0
\(799\) 7.15708 0.253199
\(800\) −0.322844 −0.0114143
\(801\) 0 0
\(802\) 58.8226 2.07710
\(803\) 0 0
\(804\) 0 0
\(805\) −10.4949 −0.369898
\(806\) 3.29648 0.116113
\(807\) 0 0
\(808\) −53.3995 −1.87859
\(809\) −32.6350 −1.14739 −0.573693 0.819070i \(-0.694490\pi\)
−0.573693 + 0.819070i \(0.694490\pi\)
\(810\) 0 0
\(811\) 13.8754 0.487232 0.243616 0.969872i \(-0.421666\pi\)
0.243616 + 0.969872i \(0.421666\pi\)
\(812\) −15.6781 −0.550193
\(813\) 0 0
\(814\) 0 0
\(815\) 21.1013 0.739147
\(816\) 0 0
\(817\) 63.3995 2.21807
\(818\) 58.3757 2.04106
\(819\) 0 0
\(820\) −15.1571 −0.529308
\(821\) 8.42606 0.294072 0.147036 0.989131i \(-0.453027\pi\)
0.147036 + 0.989131i \(0.453027\pi\)
\(822\) 0 0
\(823\) 39.4422 1.37487 0.687433 0.726247i \(-0.258737\pi\)
0.687433 + 0.726247i \(0.258737\pi\)
\(824\) −79.0120 −2.75251
\(825\) 0 0
\(826\) −6.54603 −0.227766
\(827\) −0.591563 −0.0205707 −0.0102853 0.999947i \(-0.503274\pi\)
−0.0102853 + 0.999947i \(0.503274\pi\)
\(828\) 0 0
\(829\) 23.5667 0.818506 0.409253 0.912421i \(-0.365789\pi\)
0.409253 + 0.912421i \(0.365789\pi\)
\(830\) −75.3543 −2.61559
\(831\) 0 0
\(832\) −1.54771 −0.0536572
\(833\) 0.813723 0.0281938
\(834\) 0 0
\(835\) −48.3108 −1.67186
\(836\) 0 0
\(837\) 0 0
\(838\) −54.7715 −1.89205
\(839\) −38.6507 −1.33437 −0.667185 0.744892i \(-0.732501\pi\)
−0.667185 + 0.744892i \(0.732501\pi\)
\(840\) 0 0
\(841\) −13.9472 −0.480939
\(842\) 23.0557 0.794553
\(843\) 0 0
\(844\) 28.9899 0.997872
\(845\) −26.5752 −0.914216
\(846\) 0 0
\(847\) 0 0
\(848\) 13.1113 0.450245
\(849\) 0 0
\(850\) −1.58700 −0.0544336
\(851\) −9.17741 −0.314598
\(852\) 0 0
\(853\) 38.3927 1.31454 0.657271 0.753654i \(-0.271711\pi\)
0.657271 + 0.753654i \(0.271711\pi\)
\(854\) 8.81626 0.301686
\(855\) 0 0
\(856\) 7.21664 0.246660
\(857\) −3.49785 −0.119484 −0.0597421 0.998214i \(-0.519028\pi\)
−0.0597421 + 0.998214i \(0.519028\pi\)
\(858\) 0 0
\(859\) −31.1740 −1.06364 −0.531822 0.846856i \(-0.678492\pi\)
−0.531822 + 0.846856i \(0.678492\pi\)
\(860\) 83.5582 2.84931
\(861\) 0 0
\(862\) −14.6077 −0.497540
\(863\) −30.9119 −1.05225 −0.526126 0.850406i \(-0.676356\pi\)
−0.526126 + 0.850406i \(0.676356\pi\)
\(864\) 0 0
\(865\) 12.1639 0.413584
\(866\) −13.3292 −0.452944
\(867\) 0 0
\(868\) 26.2458 0.890840
\(869\) 0 0
\(870\) 0 0
\(871\) 2.12457 0.0719884
\(872\) −12.5155 −0.423827
\(873\) 0 0
\(874\) −79.0887 −2.67522
\(875\) −11.8823 −0.401696
\(876\) 0 0
\(877\) 26.5118 0.895242 0.447621 0.894223i \(-0.352271\pi\)
0.447621 + 0.894223i \(0.352271\pi\)
\(878\) −64.0003 −2.15991
\(879\) 0 0
\(880\) 0 0
\(881\) 11.0604 0.372633 0.186316 0.982490i \(-0.440345\pi\)
0.186316 + 0.982490i \(0.440345\pi\)
\(882\) 0 0
\(883\) 17.8754 0.601556 0.300778 0.953694i \(-0.402754\pi\)
0.300778 + 0.953694i \(0.402754\pi\)
\(884\) 0.679023 0.0228380
\(885\) 0 0
\(886\) −18.0819 −0.607474
\(887\) −24.7382 −0.830626 −0.415313 0.909679i \(-0.636328\pi\)
−0.415313 + 0.909679i \(0.636328\pi\)
\(888\) 0 0
\(889\) 10.9079 0.365840
\(890\) 28.8817 0.968117
\(891\) 0 0
\(892\) 32.9899 1.10458
\(893\) 55.3097 1.85087
\(894\) 0 0
\(895\) −33.6520 −1.12486
\(896\) −19.2350 −0.642598
\(897\) 0 0
\(898\) 28.0617 0.936430
\(899\) −25.1990 −0.840433
\(900\) 0 0
\(901\) 2.51185 0.0836818
\(902\) 0 0
\(903\) 0 0
\(904\) −88.2424 −2.93490
\(905\) −7.18881 −0.238964
\(906\) 0 0
\(907\) 25.3176 0.840656 0.420328 0.907372i \(-0.361915\pi\)
0.420328 + 0.907372i \(0.361915\pi\)
\(908\) −14.9484 −0.496080
\(909\) 0 0
\(910\) 1.04096 0.0345076
\(911\) −48.7124 −1.61391 −0.806957 0.590610i \(-0.798887\pi\)
−0.806957 + 0.590610i \(0.798887\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 27.8250 0.920370
\(915\) 0 0
\(916\) −81.8125 −2.70316
\(917\) 5.72940 0.189201
\(918\) 0 0
\(919\) 37.0068 1.22074 0.610371 0.792116i \(-0.291021\pi\)
0.610371 + 0.792116i \(0.291021\pi\)
\(920\) −52.6463 −1.73570
\(921\) 0 0
\(922\) −1.48479 −0.0488991
\(923\) 3.21331 0.105767
\(924\) 0 0
\(925\) −1.42314 −0.0467925
\(926\) −85.6932 −2.81605
\(927\) 0 0
\(928\) −1.57854 −0.0518181
\(929\) 13.4682 0.441877 0.220938 0.975288i \(-0.429088\pi\)
0.220938 + 0.975288i \(0.429088\pi\)
\(930\) 0 0
\(931\) 6.28843 0.206095
\(932\) 55.3222 1.81214
\(933\) 0 0
\(934\) 69.9455 2.28869
\(935\) 0 0
\(936\) 0 0
\(937\) −54.7204 −1.78764 −0.893819 0.448427i \(-0.851984\pi\)
−0.893819 + 0.448427i \(0.851984\pi\)
\(938\) 25.2873 0.825659
\(939\) 0 0
\(940\) 72.8961 2.37761
\(941\) 32.9919 1.07551 0.537753 0.843103i \(-0.319273\pi\)
0.537753 + 0.843103i \(0.319273\pi\)
\(942\) 0 0
\(943\) 9.35813 0.304743
\(944\) −11.3124 −0.368187
\(945\) 0 0
\(946\) 0 0
\(947\) −20.5513 −0.667829 −0.333914 0.942603i \(-0.608370\pi\)
−0.333914 + 0.942603i \(0.608370\pi\)
\(948\) 0 0
\(949\) 1.60937 0.0522422
\(950\) −12.2643 −0.397905
\(951\) 0 0
\(952\) 4.08193 0.132296
\(953\) 55.9138 1.81123 0.905613 0.424106i \(-0.139412\pi\)
0.905613 + 0.424106i \(0.139412\pi\)
\(954\) 0 0
\(955\) −38.2458 −1.23760
\(956\) 67.0664 2.16908
\(957\) 0 0
\(958\) 73.9966 2.39072
\(959\) 6.34175 0.204786
\(960\) 0 0
\(961\) 11.1841 0.360778
\(962\) 0.910283 0.0293487
\(963\) 0 0
\(964\) −48.3193 −1.55626
\(965\) 11.2908 0.363462
\(966\) 0 0
\(967\) 28.9046 0.929509 0.464754 0.885440i \(-0.346143\pi\)
0.464754 + 0.885440i \(0.346143\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) −42.8226 −1.37495
\(971\) −36.6621 −1.17654 −0.588271 0.808664i \(-0.700191\pi\)
−0.588271 + 0.808664i \(0.700191\pi\)
\(972\) 0 0
\(973\) −4.16386 −0.133487
\(974\) −81.4865 −2.61099
\(975\) 0 0
\(976\) 15.2357 0.487681
\(977\) −14.5457 −0.465357 −0.232678 0.972554i \(-0.574749\pi\)
−0.232678 + 0.972554i \(0.574749\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 8.28792 0.264748
\(981\) 0 0
\(982\) −26.6077 −0.849085
\(983\) −17.6325 −0.562390 −0.281195 0.959651i \(-0.590731\pi\)
−0.281195 + 0.959651i \(0.590731\pi\)
\(984\) 0 0
\(985\) 37.4029 1.19175
\(986\) −7.75958 −0.247115
\(987\) 0 0
\(988\) 5.24747 0.166944
\(989\) −51.5897 −1.64046
\(990\) 0 0
\(991\) 15.1144 0.480126 0.240063 0.970757i \(-0.422832\pi\)
0.240063 + 0.970757i \(0.422832\pi\)
\(992\) 2.64254 0.0839007
\(993\) 0 0
\(994\) 38.2458 1.21308
\(995\) −14.1680 −0.449156
\(996\) 0 0
\(997\) −24.5769 −0.778357 −0.389178 0.921162i \(-0.627241\pi\)
−0.389178 + 0.921162i \(0.627241\pi\)
\(998\) 95.5246 3.02378
\(999\) 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.cr.1.6 yes 6
3.2 odd 2 inner 7623.2.a.cr.1.1 yes 6
11.10 odd 2 7623.2.a.cq.1.1 6
33.32 even 2 7623.2.a.cq.1.6 yes 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
7623.2.a.cq.1.1 6 11.10 odd 2
7623.2.a.cq.1.6 yes 6 33.32 even 2
7623.2.a.cr.1.1 yes 6 3.2 odd 2 inner
7623.2.a.cr.1.6 yes 6 1.1 even 1 trivial