Properties

Label 7623.2.a.cr.1.1
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 1.1
Root \(1.81705\)
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 \(-0.835222\pi\)
−0.868977 + 0.494853i \(0.835222\pi\)
\(3\) 0 0
\(4\) 4.04096 2.02048
\(5\) −2.05098 −0.917224 −0.458612 0.888637i \(-0.651653\pi\)
−0.458612 + 0.888637i \(0.651653\pi\)
\(6\) 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 \(-0.531462\pi\)
−0.0986785 + 0.995119i \(0.531462\pi\)
\(18\) 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 \(-0.320881\pi\)
0.533489 + 0.845807i \(0.320881\pi\)
\(24\) 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 \(-0.382698\pi\)
0.360230 + 0.932864i \(0.382698\pi\)
\(30\) 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 \(-0.454387\pi\)
0.142807 + 0.989751i \(0.454387\pi\)
\(42\) 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 \(-0.721677\pi\)
−0.641475 + 0.767144i \(0.721677\pi\)
\(48\) 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 \(-0.568000\pi\)
−0.212006 + 0.977268i \(0.568000\pi\)
\(54\) 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 \(-0.444535\pi\)
0.173368 + 0.984857i \(0.444535\pi\)
\(60\) 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 \(-0.874569\pi\)
−0.923361 + 0.383934i \(0.874569\pi\)
\(72\) 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 \(-0.193751\pi\)
0.820400 + 0.571791i \(0.193751\pi\)
\(84\) 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 \(-0.598208\pi\)
−0.303657 + 0.952781i \(0.598208\pi\)
\(90\) 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 \(-0.322337\pi\)
0.529612 + 0.848240i \(0.322337\pi\)
\(102\) 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 \(-0.522153\pi\)
−0.0695384 + 0.997579i \(0.522153\pi\)
\(108\) 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 \(-0.189815\pi\)
0.827408 + 0.561602i \(0.189815\pi\)
\(114\) 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 \(-0.580526\pi\)
−0.250290 + 0.968171i \(0.580526\pi\)
\(132\) 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 \(-0.587323\pi\)
−0.270906 + 0.962606i \(0.587323\pi\)
\(138\) 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 \(-0.730713\pi\)
−0.662990 + 0.748628i \(0.730713\pi\)
\(150\) 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 \(-0.135025\pi\)
0.911372 + 0.411585i \(0.135025\pi\)
\(168\) 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 \(-0.572387\pi\)
−0.225454 + 0.974254i \(0.572387\pi\)
\(174\) 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 \(-0.289887\pi\)
0.613188 + 0.789937i \(0.289887\pi\)
\(180\) 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 \(-0.264296\pi\)
0.674647 + 0.738141i \(0.264296\pi\)
\(192\) 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 \(-0.725086\pi\)
−0.649653 + 0.760231i \(0.725086\pi\)
\(198\) 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 \(-0.460825\pi\)
0.122763 + 0.992436i \(0.460825\pi\)
\(228\) 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 \(-0.648021\pi\)
−0.448442 + 0.893812i \(0.648021\pi\)
\(234\) 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 \(-0.680357\pi\)
−0.536773 + 0.843726i \(0.680357\pi\)
\(240\) 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 \(-0.444053\pi\)
0.174859 + 0.984594i \(0.444053\pi\)
\(252\) 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 \(-0.165093\pi\)
0.868487 + 0.495712i \(0.165093\pi\)
\(258\) 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 \(-0.429068\pi\)
0.220999 + 0.975274i \(0.429068\pi\)
\(264\) 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 \(-0.618204\pi\)
−0.362873 + 0.931839i \(0.618204\pi\)
\(270\) 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 \(-0.545029\pi\)
−0.140990 + 0.990011i \(0.545029\pi\)
\(282\) 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 \(-0.888890\pi\)
−0.939693 + 0.342018i \(0.888890\pi\)
\(294\) 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 \(-0.289138\pi\)
0.615045 + 0.788492i \(0.289138\pi\)
\(312\) 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 \(-0.165346\pi\)
0.868092 + 0.496403i \(0.165346\pi\)
\(318\) 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 \(-0.266451\pi\)
0.669633 + 0.742692i \(0.266451\pi\)
\(348\) 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 \(-0.524574\pi\)
−0.0771234 + 0.997022i \(0.524574\pi\)
\(354\) 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 \(-0.256542\pi\)
0.692425 + 0.721490i \(0.256542\pi\)
\(360\) 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 \(-0.557063\pi\)
−0.178310 + 0.983974i \(0.557063\pi\)
\(384\) 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 \(-0.566345\pi\)
−0.206923 + 0.978357i \(0.566345\pi\)
\(390\) 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 \(-0.703867\pi\)
−0.597571 + 0.801816i \(0.703867\pi\)
\(402\) 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 \(-0.316783\pi\)
0.544333 + 0.838869i \(0.316783\pi\)
\(420\) 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 \(-0.454280\pi\)
0.143140 + 0.989703i \(0.454280\pi\)
\(432\) 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 \(-0.444083\pi\)
0.174767 + 0.984610i \(0.444083\pi\)
\(444\) 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 \(-0.586827\pi\)
−0.269406 + 0.963027i \(0.586827\pi\)
\(450\) 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 \(-0.495522\pi\)
0.0140680 + 0.999901i \(0.495522\pi\)
\(462\) 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 \(-0.728785\pi\)
−0.658443 + 0.752630i \(0.728785\pi\)
\(468\) 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 \(-0.741423\pi\)
−0.687798 + 0.725902i \(0.741423\pi\)
\(480\) 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 \(-0.421449\pi\)
0.244277 + 0.969705i \(0.421449\pi\)
\(492\) 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 \(-0.574799\pi\)
−0.232831 + 0.972517i \(0.574799\pi\)
\(504\) 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 \(-0.122908\pi\)
0.926374 + 0.376605i \(0.122908\pi\)
\(510\) 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 \(-0.709186\pi\)
−0.610884 + 0.791720i \(0.709186\pi\)
\(522\) 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 \(-0.448952\pi\)
0.159685 + 0.987168i \(0.448952\pi\)
\(558\) 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 \(-0.397702\pi\)
0.315876 + 0.948800i \(0.397702\pi\)
\(564\) 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 \(-0.378049\pi\)
0.373818 + 0.927502i \(0.378049\pi\)
\(570\) 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 \(-0.283385\pi\)
0.629194 + 0.777248i \(0.283385\pi\)
\(588\) 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 \(-0.767433\pi\)
−0.744754 + 0.667340i \(0.767433\pi\)
\(594\) 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 \(-0.513206\pi\)
−0.0414755 + 0.999140i \(0.513206\pi\)
\(600\) 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 \(-0.294451\pi\)
0.601800 + 0.798647i \(0.294451\pi\)
\(618\) 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 \(-0.501056\pi\)
−0.00331849 + 0.999994i \(0.501056\pi\)
\(642\) 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 \(-0.271958\pi\)
0.656686 + 0.754164i \(0.271958\pi\)
\(648\) 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 \(-0.469128\pi\)
0.0968348 + 0.995300i \(0.469128\pi\)
\(654\) 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 \(-0.580827\pi\)
−0.251206 + 0.967934i \(0.580827\pi\)
\(660\) 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 \(-0.536612\pi\)
−0.114768 + 0.993392i \(0.536612\pi\)
\(678\) 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 \(-0.526033\pi\)
−0.0816932 + 0.996658i \(0.526033\pi\)
\(684\) 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 \(-0.638456\pi\)
−0.421384 + 0.906882i \(0.638456\pi\)
\(702\) 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 \(-0.623544\pi\)
−0.378454 + 0.925620i \(0.623544\pi\)
\(720\) 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 \(-0.362843\pi\)
0.417682 + 0.908593i \(0.362843\pi\)
\(744\) 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 \(-0.125432\pi\)
0.923359 + 0.383938i \(0.125432\pi\)
\(762\) 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 \(-0.281485\pi\)
0.633824 + 0.773478i \(0.281485\pi\)
\(774\) 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 \(-0.430184\pi\)
0.217580 + 0.976043i \(0.430184\pi\)
\(798\) 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 \(-0.305510\pi\)
0.573693 + 0.819070i \(0.305510\pi\)
\(810\) 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 \(-0.546973\pi\)
−0.147036 + 0.989131i \(0.546973\pi\)
\(822\) 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 \(-0.496726\pi\)
0.0102853 + 0.999947i \(0.496726\pi\)
\(828\) 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 \(-0.267499\pi\)
0.667185 + 0.744892i \(0.267499\pi\)
\(840\) 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 \(-0.480972\pi\)
0.0597421 + 0.998214i \(0.480972\pi\)
\(858\) 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 \(-0.323644\pi\)
0.526126 + 0.850406i \(0.323644\pi\)
\(864\) 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 \(-0.559655\pi\)
−0.186316 + 0.982490i \(0.559655\pi\)
\(882\) 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 \(-0.363672\pi\)
0.415313 + 0.909679i \(0.363672\pi\)
\(888\) 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 \(-0.201113\pi\)
0.806957 + 0.590610i \(0.201113\pi\)
\(912\) 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 \(-0.570912\pi\)
−0.220938 + 0.975288i \(0.570912\pi\)
\(930\) 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 \(-0.680727\pi\)
−0.537753 + 0.843103i \(0.680727\pi\)
\(942\) 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 \(-0.391630\pi\)
0.333914 + 0.942603i \(0.391630\pi\)
\(948\) 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 \(-0.860588\pi\)
−0.905613 + 0.424106i \(0.860588\pi\)
\(954\) 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 \(-0.299809\pi\)
0.588271 + 0.808664i \(0.299809\pi\)
\(972\) 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 \(-0.425251\pi\)
0.232678 + 0.972554i \(0.425251\pi\)
\(978\) 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 \(-0.409269\pi\)
0.281195 + 0.959651i \(0.409269\pi\)
\(984\) 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.1.1 yes 6
3.2 odd 2 inner 7623.2.a.cr.1.6 yes 6
11.10 odd 2 7623.2.a.cq.1.6 yes 6
33.32 even 2 7623.2.a.cq.1.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
7623.2.a.cq.1.1 6 33.32 even 2
7623.2.a.cq.1.6 yes 6 11.10 odd 2
7623.2.a.cr.1.1 yes 6 1.1 even 1 trivial
7623.2.a.cr.1.6 yes 6 3.2 odd 2 inner