Properties

Label 179.2.a.a.1.1
Level 179
Weight 2
Character 179.1
Self dual yes
Analytic conductor 1.429
Analytic rank 0
Dimension 1
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 179 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 179.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(1.42932219618\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(0\)
Character \(\chi\) = 179.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.00000 q^{2} +2.00000 q^{4} +3.00000 q^{5} -4.00000 q^{7} -3.00000 q^{9} +O(q^{10})\) \(q+2.00000 q^{2} +2.00000 q^{4} +3.00000 q^{5} -4.00000 q^{7} -3.00000 q^{9} +6.00000 q^{10} +4.00000 q^{11} -1.00000 q^{13} -8.00000 q^{14} -4.00000 q^{16} +1.00000 q^{17} -6.00000 q^{18} -3.00000 q^{19} +6.00000 q^{20} +8.00000 q^{22} +6.00000 q^{23} +4.00000 q^{25} -2.00000 q^{26} -8.00000 q^{28} +3.00000 q^{29} -8.00000 q^{31} -8.00000 q^{32} +2.00000 q^{34} -12.0000 q^{35} -6.00000 q^{36} +2.00000 q^{37} -6.00000 q^{38} +12.0000 q^{41} -11.0000 q^{43} +8.00000 q^{44} -9.00000 q^{45} +12.0000 q^{46} +1.00000 q^{47} +9.00000 q^{49} +8.00000 q^{50} -2.00000 q^{52} +12.0000 q^{55} +6.00000 q^{58} -5.00000 q^{59} +14.0000 q^{61} -16.0000 q^{62} +12.0000 q^{63} -8.00000 q^{64} -3.00000 q^{65} -9.00000 q^{67} +2.00000 q^{68} -24.0000 q^{70} +10.0000 q^{73} +4.00000 q^{74} -6.00000 q^{76} -16.0000 q^{77} +10.0000 q^{79} -12.0000 q^{80} +9.00000 q^{81} +24.0000 q^{82} +17.0000 q^{83} +3.00000 q^{85} -22.0000 q^{86} -1.00000 q^{89} -18.0000 q^{90} +4.00000 q^{91} +12.0000 q^{92} +2.00000 q^{94} -9.00000 q^{95} -14.0000 q^{97} +18.0000 q^{98} -12.0000 q^{99} +O(q^{100})\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(3\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(4\) 2.00000 1.00000
\(5\) 3.00000 1.34164 0.670820 0.741620i \(-0.265942\pi\)
0.670820 + 0.741620i \(0.265942\pi\)
\(6\) 0 0
\(7\) −4.00000 −1.51186 −0.755929 0.654654i \(-0.772814\pi\)
−0.755929 + 0.654654i \(0.772814\pi\)
\(8\) 0 0
\(9\) −3.00000 −1.00000
\(10\) 6.00000 1.89737
\(11\) 4.00000 1.20605 0.603023 0.797724i \(-0.293963\pi\)
0.603023 + 0.797724i \(0.293963\pi\)
\(12\) 0 0
\(13\) −1.00000 −0.277350 −0.138675 0.990338i \(-0.544284\pi\)
−0.138675 + 0.990338i \(0.544284\pi\)
\(14\) −8.00000 −2.13809
\(15\) 0 0
\(16\) −4.00000 −1.00000
\(17\) 1.00000 0.242536 0.121268 0.992620i \(-0.461304\pi\)
0.121268 + 0.992620i \(0.461304\pi\)
\(18\) −6.00000 −1.41421
\(19\) −3.00000 −0.688247 −0.344124 0.938924i \(-0.611824\pi\)
−0.344124 + 0.938924i \(0.611824\pi\)
\(20\) 6.00000 1.34164
\(21\) 0 0
\(22\) 8.00000 1.70561
\(23\) 6.00000 1.25109 0.625543 0.780189i \(-0.284877\pi\)
0.625543 + 0.780189i \(0.284877\pi\)
\(24\) 0 0
\(25\) 4.00000 0.800000
\(26\) −2.00000 −0.392232
\(27\) 0 0
\(28\) −8.00000 −1.51186
\(29\) 3.00000 0.557086 0.278543 0.960424i \(-0.410149\pi\)
0.278543 + 0.960424i \(0.410149\pi\)
\(30\) 0 0
\(31\) −8.00000 −1.43684 −0.718421 0.695608i \(-0.755135\pi\)
−0.718421 + 0.695608i \(0.755135\pi\)
\(32\) −8.00000 −1.41421
\(33\) 0 0
\(34\) 2.00000 0.342997
\(35\) −12.0000 −2.02837
\(36\) −6.00000 −1.00000
\(37\) 2.00000 0.328798 0.164399 0.986394i \(-0.447432\pi\)
0.164399 + 0.986394i \(0.447432\pi\)
\(38\) −6.00000 −0.973329
\(39\) 0 0
\(40\) 0 0
\(41\) 12.0000 1.87409 0.937043 0.349215i \(-0.113552\pi\)
0.937043 + 0.349215i \(0.113552\pi\)
\(42\) 0 0
\(43\) −11.0000 −1.67748 −0.838742 0.544529i \(-0.816708\pi\)
−0.838742 + 0.544529i \(0.816708\pi\)
\(44\) 8.00000 1.20605
\(45\) −9.00000 −1.34164
\(46\) 12.0000 1.76930
\(47\) 1.00000 0.145865 0.0729325 0.997337i \(-0.476764\pi\)
0.0729325 + 0.997337i \(0.476764\pi\)
\(48\) 0 0
\(49\) 9.00000 1.28571
\(50\) 8.00000 1.13137
\(51\) 0 0
\(52\) −2.00000 −0.277350
\(53\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(54\) 0 0
\(55\) 12.0000 1.61808
\(56\) 0 0
\(57\) 0 0
\(58\) 6.00000 0.787839
\(59\) −5.00000 −0.650945 −0.325472 0.945552i \(-0.605523\pi\)
−0.325472 + 0.945552i \(0.605523\pi\)
\(60\) 0 0
\(61\) 14.0000 1.79252 0.896258 0.443533i \(-0.146275\pi\)
0.896258 + 0.443533i \(0.146275\pi\)
\(62\) −16.0000 −2.03200
\(63\) 12.0000 1.51186
\(64\) −8.00000 −1.00000
\(65\) −3.00000 −0.372104
\(66\) 0 0
\(67\) −9.00000 −1.09952 −0.549762 0.835321i \(-0.685282\pi\)
−0.549762 + 0.835321i \(0.685282\pi\)
\(68\) 2.00000 0.242536
\(69\) 0 0
\(70\) −24.0000 −2.86855
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) 10.0000 1.17041 0.585206 0.810885i \(-0.301014\pi\)
0.585206 + 0.810885i \(0.301014\pi\)
\(74\) 4.00000 0.464991
\(75\) 0 0
\(76\) −6.00000 −0.688247
\(77\) −16.0000 −1.82337
\(78\) 0 0
\(79\) 10.0000 1.12509 0.562544 0.826767i \(-0.309823\pi\)
0.562544 + 0.826767i \(0.309823\pi\)
\(80\) −12.0000 −1.34164
\(81\) 9.00000 1.00000
\(82\) 24.0000 2.65036
\(83\) 17.0000 1.86599 0.932996 0.359886i \(-0.117184\pi\)
0.932996 + 0.359886i \(0.117184\pi\)
\(84\) 0 0
\(85\) 3.00000 0.325396
\(86\) −22.0000 −2.37232
\(87\) 0 0
\(88\) 0 0
\(89\) −1.00000 −0.106000 −0.0529999 0.998595i \(-0.516878\pi\)
−0.0529999 + 0.998595i \(0.516878\pi\)
\(90\) −18.0000 −1.89737
\(91\) 4.00000 0.419314
\(92\) 12.0000 1.25109
\(93\) 0 0
\(94\) 2.00000 0.206284
\(95\) −9.00000 −0.923381
\(96\) 0 0
\(97\) −14.0000 −1.42148 −0.710742 0.703452i \(-0.751641\pi\)
−0.710742 + 0.703452i \(0.751641\pi\)
\(98\) 18.0000 1.81827
\(99\) −12.0000 −1.20605
\(100\) 8.00000 0.800000
\(101\) 9.00000 0.895533 0.447767 0.894150i \(-0.352219\pi\)
0.447767 + 0.894150i \(0.352219\pi\)
\(102\) 0 0
\(103\) −6.00000 −0.591198 −0.295599 0.955312i \(-0.595519\pi\)
−0.295599 + 0.955312i \(0.595519\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −4.00000 −0.386695 −0.193347 0.981130i \(-0.561934\pi\)
−0.193347 + 0.981130i \(0.561934\pi\)
\(108\) 0 0
\(109\) −14.0000 −1.34096 −0.670478 0.741929i \(-0.733911\pi\)
−0.670478 + 0.741929i \(0.733911\pi\)
\(110\) 24.0000 2.28831
\(111\) 0 0
\(112\) 16.0000 1.51186
\(113\) −4.00000 −0.376288 −0.188144 0.982141i \(-0.560247\pi\)
−0.188144 + 0.982141i \(0.560247\pi\)
\(114\) 0 0
\(115\) 18.0000 1.67851
\(116\) 6.00000 0.557086
\(117\) 3.00000 0.277350
\(118\) −10.0000 −0.920575
\(119\) −4.00000 −0.366679
\(120\) 0 0
\(121\) 5.00000 0.454545
\(122\) 28.0000 2.53500
\(123\) 0 0
\(124\) −16.0000 −1.43684
\(125\) −3.00000 −0.268328
\(126\) 24.0000 2.13809
\(127\) −8.00000 −0.709885 −0.354943 0.934888i \(-0.615500\pi\)
−0.354943 + 0.934888i \(0.615500\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) −6.00000 −0.526235
\(131\) −6.00000 −0.524222 −0.262111 0.965038i \(-0.584419\pi\)
−0.262111 + 0.965038i \(0.584419\pi\)
\(132\) 0 0
\(133\) 12.0000 1.04053
\(134\) −18.0000 −1.55496
\(135\) 0 0
\(136\) 0 0
\(137\) −10.0000 −0.854358 −0.427179 0.904167i \(-0.640493\pi\)
−0.427179 + 0.904167i \(0.640493\pi\)
\(138\) 0 0
\(139\) 7.00000 0.593732 0.296866 0.954919i \(-0.404058\pi\)
0.296866 + 0.954919i \(0.404058\pi\)
\(140\) −24.0000 −2.02837
\(141\) 0 0
\(142\) 0 0
\(143\) −4.00000 −0.334497
\(144\) 12.0000 1.00000
\(145\) 9.00000 0.747409
\(146\) 20.0000 1.65521
\(147\) 0 0
\(148\) 4.00000 0.328798
\(149\) −18.0000 −1.47462 −0.737309 0.675556i \(-0.763904\pi\)
−0.737309 + 0.675556i \(0.763904\pi\)
\(150\) 0 0
\(151\) 21.0000 1.70896 0.854478 0.519488i \(-0.173877\pi\)
0.854478 + 0.519488i \(0.173877\pi\)
\(152\) 0 0
\(153\) −3.00000 −0.242536
\(154\) −32.0000 −2.57863
\(155\) −24.0000 −1.92773
\(156\) 0 0
\(157\) 4.00000 0.319235 0.159617 0.987179i \(-0.448974\pi\)
0.159617 + 0.987179i \(0.448974\pi\)
\(158\) 20.0000 1.59111
\(159\) 0 0
\(160\) −24.0000 −1.89737
\(161\) −24.0000 −1.89146
\(162\) 18.0000 1.41421
\(163\) −20.0000 −1.56652 −0.783260 0.621694i \(-0.786445\pi\)
−0.783260 + 0.621694i \(0.786445\pi\)
\(164\) 24.0000 1.87409
\(165\) 0 0
\(166\) 34.0000 2.63891
\(167\) 10.0000 0.773823 0.386912 0.922117i \(-0.373542\pi\)
0.386912 + 0.922117i \(0.373542\pi\)
\(168\) 0 0
\(169\) −12.0000 −0.923077
\(170\) 6.00000 0.460179
\(171\) 9.00000 0.688247
\(172\) −22.0000 −1.67748
\(173\) −14.0000 −1.06440 −0.532200 0.846619i \(-0.678635\pi\)
−0.532200 + 0.846619i \(0.678635\pi\)
\(174\) 0 0
\(175\) −16.0000 −1.20949
\(176\) −16.0000 −1.20605
\(177\) 0 0
\(178\) −2.00000 −0.149906
\(179\) 1.00000 0.0747435
\(180\) −18.0000 −1.34164
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) 8.00000 0.592999
\(183\) 0 0
\(184\) 0 0
\(185\) 6.00000 0.441129
\(186\) 0 0
\(187\) 4.00000 0.292509
\(188\) 2.00000 0.145865
\(189\) 0 0
\(190\) −18.0000 −1.30586
\(191\) −13.0000 −0.940647 −0.470323 0.882494i \(-0.655863\pi\)
−0.470323 + 0.882494i \(0.655863\pi\)
\(192\) 0 0
\(193\) −6.00000 −0.431889 −0.215945 0.976406i \(-0.569283\pi\)
−0.215945 + 0.976406i \(0.569283\pi\)
\(194\) −28.0000 −2.01028
\(195\) 0 0
\(196\) 18.0000 1.28571
\(197\) −2.00000 −0.142494 −0.0712470 0.997459i \(-0.522698\pi\)
−0.0712470 + 0.997459i \(0.522698\pi\)
\(198\) −24.0000 −1.70561
\(199\) 17.0000 1.20510 0.602549 0.798082i \(-0.294152\pi\)
0.602549 + 0.798082i \(0.294152\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 18.0000 1.26648
\(203\) −12.0000 −0.842235
\(204\) 0 0
\(205\) 36.0000 2.51435
\(206\) −12.0000 −0.836080
\(207\) −18.0000 −1.25109
\(208\) 4.00000 0.277350
\(209\) −12.0000 −0.830057
\(210\) 0 0
\(211\) −8.00000 −0.550743 −0.275371 0.961338i \(-0.588801\pi\)
−0.275371 + 0.961338i \(0.588801\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) −8.00000 −0.546869
\(215\) −33.0000 −2.25058
\(216\) 0 0
\(217\) 32.0000 2.17230
\(218\) −28.0000 −1.89640
\(219\) 0 0
\(220\) 24.0000 1.61808
\(221\) −1.00000 −0.0672673
\(222\) 0 0
\(223\) −26.0000 −1.74109 −0.870544 0.492090i \(-0.836233\pi\)
−0.870544 + 0.492090i \(0.836233\pi\)
\(224\) 32.0000 2.13809
\(225\) −12.0000 −0.800000
\(226\) −8.00000 −0.532152
\(227\) 21.0000 1.39382 0.696909 0.717159i \(-0.254558\pi\)
0.696909 + 0.717159i \(0.254558\pi\)
\(228\) 0 0
\(229\) 8.00000 0.528655 0.264327 0.964433i \(-0.414850\pi\)
0.264327 + 0.964433i \(0.414850\pi\)
\(230\) 36.0000 2.37377
\(231\) 0 0
\(232\) 0 0
\(233\) 24.0000 1.57229 0.786146 0.618041i \(-0.212073\pi\)
0.786146 + 0.618041i \(0.212073\pi\)
\(234\) 6.00000 0.392232
\(235\) 3.00000 0.195698
\(236\) −10.0000 −0.650945
\(237\) 0 0
\(238\) −8.00000 −0.518563
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 0 0
\(241\) 4.00000 0.257663 0.128831 0.991667i \(-0.458877\pi\)
0.128831 + 0.991667i \(0.458877\pi\)
\(242\) 10.0000 0.642824
\(243\) 0 0
\(244\) 28.0000 1.79252
\(245\) 27.0000 1.72497
\(246\) 0 0
\(247\) 3.00000 0.190885
\(248\) 0 0
\(249\) 0 0
\(250\) −6.00000 −0.379473
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 24.0000 1.51186
\(253\) 24.0000 1.50887
\(254\) −16.0000 −1.00393
\(255\) 0 0
\(256\) 16.0000 1.00000
\(257\) −6.00000 −0.374270 −0.187135 0.982334i \(-0.559920\pi\)
−0.187135 + 0.982334i \(0.559920\pi\)
\(258\) 0 0
\(259\) −8.00000 −0.497096
\(260\) −6.00000 −0.372104
\(261\) −9.00000 −0.557086
\(262\) −12.0000 −0.741362
\(263\) −4.00000 −0.246651 −0.123325 0.992366i \(-0.539356\pi\)
−0.123325 + 0.992366i \(0.539356\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 24.0000 1.47153
\(267\) 0 0
\(268\) −18.0000 −1.09952
\(269\) 18.0000 1.09748 0.548740 0.835993i \(-0.315108\pi\)
0.548740 + 0.835993i \(0.315108\pi\)
\(270\) 0 0
\(271\) 10.0000 0.607457 0.303728 0.952759i \(-0.401768\pi\)
0.303728 + 0.952759i \(0.401768\pi\)
\(272\) −4.00000 −0.242536
\(273\) 0 0
\(274\) −20.0000 −1.20824
\(275\) 16.0000 0.964836
\(276\) 0 0
\(277\) −14.0000 −0.841178 −0.420589 0.907251i \(-0.638177\pi\)
−0.420589 + 0.907251i \(0.638177\pi\)
\(278\) 14.0000 0.839664
\(279\) 24.0000 1.43684
\(280\) 0 0
\(281\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(282\) 0 0
\(283\) −2.00000 −0.118888 −0.0594438 0.998232i \(-0.518933\pi\)
−0.0594438 + 0.998232i \(0.518933\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) −8.00000 −0.473050
\(287\) −48.0000 −2.83335
\(288\) 24.0000 1.41421
\(289\) −16.0000 −0.941176
\(290\) 18.0000 1.05700
\(291\) 0 0
\(292\) 20.0000 1.17041
\(293\) −8.00000 −0.467365 −0.233682 0.972313i \(-0.575078\pi\)
−0.233682 + 0.972313i \(0.575078\pi\)
\(294\) 0 0
\(295\) −15.0000 −0.873334
\(296\) 0 0
\(297\) 0 0
\(298\) −36.0000 −2.08542
\(299\) −6.00000 −0.346989
\(300\) 0 0
\(301\) 44.0000 2.53612
\(302\) 42.0000 2.41683
\(303\) 0 0
\(304\) 12.0000 0.688247
\(305\) 42.0000 2.40491
\(306\) −6.00000 −0.342997
\(307\) 6.00000 0.342438 0.171219 0.985233i \(-0.445229\pi\)
0.171219 + 0.985233i \(0.445229\pi\)
\(308\) −32.0000 −1.82337
\(309\) 0 0
\(310\) −48.0000 −2.72622
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0 0
\(313\) −8.00000 −0.452187 −0.226093 0.974106i \(-0.572595\pi\)
−0.226093 + 0.974106i \(0.572595\pi\)
\(314\) 8.00000 0.451466
\(315\) 36.0000 2.02837
\(316\) 20.0000 1.12509
\(317\) 29.0000 1.62880 0.814401 0.580302i \(-0.197066\pi\)
0.814401 + 0.580302i \(0.197066\pi\)
\(318\) 0 0
\(319\) 12.0000 0.671871
\(320\) −24.0000 −1.34164
\(321\) 0 0
\(322\) −48.0000 −2.67494
\(323\) −3.00000 −0.166924
\(324\) 18.0000 1.00000
\(325\) −4.00000 −0.221880
\(326\) −40.0000 −2.21540
\(327\) 0 0
\(328\) 0 0
\(329\) −4.00000 −0.220527
\(330\) 0 0
\(331\) 20.0000 1.09930 0.549650 0.835395i \(-0.314761\pi\)
0.549650 + 0.835395i \(0.314761\pi\)
\(332\) 34.0000 1.86599
\(333\) −6.00000 −0.328798
\(334\) 20.0000 1.09435
\(335\) −27.0000 −1.47517
\(336\) 0 0
\(337\) −34.0000 −1.85210 −0.926049 0.377403i \(-0.876817\pi\)
−0.926049 + 0.377403i \(0.876817\pi\)
\(338\) −24.0000 −1.30543
\(339\) 0 0
\(340\) 6.00000 0.325396
\(341\) −32.0000 −1.73290
\(342\) 18.0000 0.973329
\(343\) −8.00000 −0.431959
\(344\) 0 0
\(345\) 0 0
\(346\) −28.0000 −1.50529
\(347\) 15.0000 0.805242 0.402621 0.915367i \(-0.368099\pi\)
0.402621 + 0.915367i \(0.368099\pi\)
\(348\) 0 0
\(349\) −18.0000 −0.963518 −0.481759 0.876304i \(-0.660002\pi\)
−0.481759 + 0.876304i \(0.660002\pi\)
\(350\) −32.0000 −1.71047
\(351\) 0 0
\(352\) −32.0000 −1.70561
\(353\) −24.0000 −1.27739 −0.638696 0.769460i \(-0.720526\pi\)
−0.638696 + 0.769460i \(0.720526\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −2.00000 −0.106000
\(357\) 0 0
\(358\) 2.00000 0.105703
\(359\) 32.0000 1.68890 0.844448 0.535638i \(-0.179929\pi\)
0.844448 + 0.535638i \(0.179929\pi\)
\(360\) 0 0
\(361\) −10.0000 −0.526316
\(362\) 4.00000 0.210235
\(363\) 0 0
\(364\) 8.00000 0.419314
\(365\) 30.0000 1.57027
\(366\) 0 0
\(367\) −11.0000 −0.574195 −0.287098 0.957901i \(-0.592690\pi\)
−0.287098 + 0.957901i \(0.592690\pi\)
\(368\) −24.0000 −1.25109
\(369\) −36.0000 −1.87409
\(370\) 12.0000 0.623850
\(371\) 0 0
\(372\) 0 0
\(373\) 37.0000 1.91579 0.957894 0.287123i \(-0.0926989\pi\)
0.957894 + 0.287123i \(0.0926989\pi\)
\(374\) 8.00000 0.413670
\(375\) 0 0
\(376\) 0 0
\(377\) −3.00000 −0.154508
\(378\) 0 0
\(379\) −18.0000 −0.924598 −0.462299 0.886724i \(-0.652975\pi\)
−0.462299 + 0.886724i \(0.652975\pi\)
\(380\) −18.0000 −0.923381
\(381\) 0 0
\(382\) −26.0000 −1.33028
\(383\) 21.0000 1.07305 0.536525 0.843884i \(-0.319737\pi\)
0.536525 + 0.843884i \(0.319737\pi\)
\(384\) 0 0
\(385\) −48.0000 −2.44631
\(386\) −12.0000 −0.610784
\(387\) 33.0000 1.67748
\(388\) −28.0000 −1.42148
\(389\) 15.0000 0.760530 0.380265 0.924878i \(-0.375833\pi\)
0.380265 + 0.924878i \(0.375833\pi\)
\(390\) 0 0
\(391\) 6.00000 0.303433
\(392\) 0 0
\(393\) 0 0
\(394\) −4.00000 −0.201517
\(395\) 30.0000 1.50946
\(396\) −24.0000 −1.20605
\(397\) −13.0000 −0.652451 −0.326226 0.945292i \(-0.605777\pi\)
−0.326226 + 0.945292i \(0.605777\pi\)
\(398\) 34.0000 1.70427
\(399\) 0 0
\(400\) −16.0000 −0.800000
\(401\) 22.0000 1.09863 0.549314 0.835616i \(-0.314889\pi\)
0.549314 + 0.835616i \(0.314889\pi\)
\(402\) 0 0
\(403\) 8.00000 0.398508
\(404\) 18.0000 0.895533
\(405\) 27.0000 1.34164
\(406\) −24.0000 −1.19110
\(407\) 8.00000 0.396545
\(408\) 0 0
\(409\) −17.0000 −0.840596 −0.420298 0.907386i \(-0.638074\pi\)
−0.420298 + 0.907386i \(0.638074\pi\)
\(410\) 72.0000 3.55583
\(411\) 0 0
\(412\) −12.0000 −0.591198
\(413\) 20.0000 0.984136
\(414\) −36.0000 −1.76930
\(415\) 51.0000 2.50349
\(416\) 8.00000 0.392232
\(417\) 0 0
\(418\) −24.0000 −1.17388
\(419\) 11.0000 0.537385 0.268693 0.963226i \(-0.413408\pi\)
0.268693 + 0.963226i \(0.413408\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(422\) −16.0000 −0.778868
\(423\) −3.00000 −0.145865
\(424\) 0 0
\(425\) 4.00000 0.194029
\(426\) 0 0
\(427\) −56.0000 −2.71003
\(428\) −8.00000 −0.386695
\(429\) 0 0
\(430\) −66.0000 −3.18280
\(431\) −22.0000 −1.05970 −0.529851 0.848091i \(-0.677752\pi\)
−0.529851 + 0.848091i \(0.677752\pi\)
\(432\) 0 0
\(433\) −21.0000 −1.00920 −0.504598 0.863355i \(-0.668359\pi\)
−0.504598 + 0.863355i \(0.668359\pi\)
\(434\) 64.0000 3.07210
\(435\) 0 0
\(436\) −28.0000 −1.34096
\(437\) −18.0000 −0.861057
\(438\) 0 0
\(439\) 27.0000 1.28864 0.644320 0.764756i \(-0.277141\pi\)
0.644320 + 0.764756i \(0.277141\pi\)
\(440\) 0 0
\(441\) −27.0000 −1.28571
\(442\) −2.00000 −0.0951303
\(443\) 3.00000 0.142534 0.0712672 0.997457i \(-0.477296\pi\)
0.0712672 + 0.997457i \(0.477296\pi\)
\(444\) 0 0
\(445\) −3.00000 −0.142214
\(446\) −52.0000 −2.46227
\(447\) 0 0
\(448\) 32.0000 1.51186
\(449\) 8.00000 0.377543 0.188772 0.982021i \(-0.439549\pi\)
0.188772 + 0.982021i \(0.439549\pi\)
\(450\) −24.0000 −1.13137
\(451\) 48.0000 2.26023
\(452\) −8.00000 −0.376288
\(453\) 0 0
\(454\) 42.0000 1.97116
\(455\) 12.0000 0.562569
\(456\) 0 0
\(457\) −8.00000 −0.374224 −0.187112 0.982339i \(-0.559913\pi\)
−0.187112 + 0.982339i \(0.559913\pi\)
\(458\) 16.0000 0.747631
\(459\) 0 0
\(460\) 36.0000 1.67851
\(461\) 42.0000 1.95614 0.978068 0.208288i \(-0.0667892\pi\)
0.978068 + 0.208288i \(0.0667892\pi\)
\(462\) 0 0
\(463\) −16.0000 −0.743583 −0.371792 0.928316i \(-0.621256\pi\)
−0.371792 + 0.928316i \(0.621256\pi\)
\(464\) −12.0000 −0.557086
\(465\) 0 0
\(466\) 48.0000 2.22356
\(467\) 16.0000 0.740392 0.370196 0.928954i \(-0.379291\pi\)
0.370196 + 0.928954i \(0.379291\pi\)
\(468\) 6.00000 0.277350
\(469\) 36.0000 1.66233
\(470\) 6.00000 0.276759
\(471\) 0 0
\(472\) 0 0
\(473\) −44.0000 −2.02312
\(474\) 0 0
\(475\) −12.0000 −0.550598
\(476\) −8.00000 −0.366679
\(477\) 0 0
\(478\) 0 0
\(479\) 33.0000 1.50781 0.753904 0.656984i \(-0.228168\pi\)
0.753904 + 0.656984i \(0.228168\pi\)
\(480\) 0 0
\(481\) −2.00000 −0.0911922
\(482\) 8.00000 0.364390
\(483\) 0 0
\(484\) 10.0000 0.454545
\(485\) −42.0000 −1.90712
\(486\) 0 0
\(487\) 27.0000 1.22349 0.611743 0.791056i \(-0.290469\pi\)
0.611743 + 0.791056i \(0.290469\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 54.0000 2.43947
\(491\) −6.00000 −0.270776 −0.135388 0.990793i \(-0.543228\pi\)
−0.135388 + 0.990793i \(0.543228\pi\)
\(492\) 0 0
\(493\) 3.00000 0.135113
\(494\) 6.00000 0.269953
\(495\) −36.0000 −1.61808
\(496\) 32.0000 1.43684
\(497\) 0 0
\(498\) 0 0
\(499\) −28.0000 −1.25345 −0.626726 0.779240i \(-0.715605\pi\)
−0.626726 + 0.779240i \(0.715605\pi\)
\(500\) −6.00000 −0.268328
\(501\) 0 0
\(502\) 0 0
\(503\) 40.0000 1.78351 0.891756 0.452517i \(-0.149474\pi\)
0.891756 + 0.452517i \(0.149474\pi\)
\(504\) 0 0
\(505\) 27.0000 1.20148
\(506\) 48.0000 2.13386
\(507\) 0 0
\(508\) −16.0000 −0.709885
\(509\) −15.0000 −0.664863 −0.332432 0.943127i \(-0.607869\pi\)
−0.332432 + 0.943127i \(0.607869\pi\)
\(510\) 0 0
\(511\) −40.0000 −1.76950
\(512\) 32.0000 1.41421
\(513\) 0 0
\(514\) −12.0000 −0.529297
\(515\) −18.0000 −0.793175
\(516\) 0 0
\(517\) 4.00000 0.175920
\(518\) −16.0000 −0.703000
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(522\) −18.0000 −0.787839
\(523\) −16.0000 −0.699631 −0.349816 0.936819i \(-0.613756\pi\)
−0.349816 + 0.936819i \(0.613756\pi\)
\(524\) −12.0000 −0.524222
\(525\) 0 0
\(526\) −8.00000 −0.348817
\(527\) −8.00000 −0.348485
\(528\) 0 0
\(529\) 13.0000 0.565217
\(530\) 0 0
\(531\) 15.0000 0.650945
\(532\) 24.0000 1.04053
\(533\) −12.0000 −0.519778
\(534\) 0 0
\(535\) −12.0000 −0.518805
\(536\) 0 0
\(537\) 0 0
\(538\) 36.0000 1.55207
\(539\) 36.0000 1.55063
\(540\) 0 0
\(541\) −18.0000 −0.773880 −0.386940 0.922105i \(-0.626468\pi\)
−0.386940 + 0.922105i \(0.626468\pi\)
\(542\) 20.0000 0.859074
\(543\) 0 0
\(544\) −8.00000 −0.342997
\(545\) −42.0000 −1.79908
\(546\) 0 0
\(547\) −28.0000 −1.19719 −0.598597 0.801050i \(-0.704275\pi\)
−0.598597 + 0.801050i \(0.704275\pi\)
\(548\) −20.0000 −0.854358
\(549\) −42.0000 −1.79252
\(550\) 32.0000 1.36448
\(551\) −9.00000 −0.383413
\(552\) 0 0
\(553\) −40.0000 −1.70097
\(554\) −28.0000 −1.18961
\(555\) 0 0
\(556\) 14.0000 0.593732
\(557\) −29.0000 −1.22877 −0.614385 0.789007i \(-0.710596\pi\)
−0.614385 + 0.789007i \(0.710596\pi\)
\(558\) 48.0000 2.03200
\(559\) 11.0000 0.465250
\(560\) 48.0000 2.02837
\(561\) 0 0
\(562\) 0 0
\(563\) −38.0000 −1.60151 −0.800755 0.598993i \(-0.795568\pi\)
−0.800755 + 0.598993i \(0.795568\pi\)
\(564\) 0 0
\(565\) −12.0000 −0.504844
\(566\) −4.00000 −0.168133
\(567\) −36.0000 −1.51186
\(568\) 0 0
\(569\) 8.00000 0.335377 0.167689 0.985840i \(-0.446370\pi\)
0.167689 + 0.985840i \(0.446370\pi\)
\(570\) 0 0
\(571\) 18.0000 0.753277 0.376638 0.926360i \(-0.377080\pi\)
0.376638 + 0.926360i \(0.377080\pi\)
\(572\) −8.00000 −0.334497
\(573\) 0 0
\(574\) −96.0000 −4.00696
\(575\) 24.0000 1.00087
\(576\) 24.0000 1.00000
\(577\) 32.0000 1.33218 0.666089 0.745873i \(-0.267967\pi\)
0.666089 + 0.745873i \(0.267967\pi\)
\(578\) −32.0000 −1.33102
\(579\) 0 0
\(580\) 18.0000 0.747409
\(581\) −68.0000 −2.82112
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 9.00000 0.372104
\(586\) −16.0000 −0.660954
\(587\) −34.0000 −1.40333 −0.701665 0.712507i \(-0.747560\pi\)
−0.701665 + 0.712507i \(0.747560\pi\)
\(588\) 0 0
\(589\) 24.0000 0.988903
\(590\) −30.0000 −1.23508
\(591\) 0 0
\(592\) −8.00000 −0.328798
\(593\) 26.0000 1.06769 0.533846 0.845582i \(-0.320746\pi\)
0.533846 + 0.845582i \(0.320746\pi\)
\(594\) 0 0
\(595\) −12.0000 −0.491952
\(596\) −36.0000 −1.47462
\(597\) 0 0
\(598\) −12.0000 −0.490716
\(599\) 20.0000 0.817178 0.408589 0.912719i \(-0.366021\pi\)
0.408589 + 0.912719i \(0.366021\pi\)
\(600\) 0 0
\(601\) 7.00000 0.285536 0.142768 0.989756i \(-0.454400\pi\)
0.142768 + 0.989756i \(0.454400\pi\)
\(602\) 88.0000 3.58661
\(603\) 27.0000 1.09952
\(604\) 42.0000 1.70896
\(605\) 15.0000 0.609837
\(606\) 0 0
\(607\) 1.00000 0.0405887 0.0202944 0.999794i \(-0.493540\pi\)
0.0202944 + 0.999794i \(0.493540\pi\)
\(608\) 24.0000 0.973329
\(609\) 0 0
\(610\) 84.0000 3.40106
\(611\) −1.00000 −0.0404557
\(612\) −6.00000 −0.242536
\(613\) 31.0000 1.25208 0.626039 0.779792i \(-0.284675\pi\)
0.626039 + 0.779792i \(0.284675\pi\)
\(614\) 12.0000 0.484281
\(615\) 0 0
\(616\) 0 0
\(617\) −13.0000 −0.523360 −0.261680 0.965155i \(-0.584277\pi\)
−0.261680 + 0.965155i \(0.584277\pi\)
\(618\) 0 0
\(619\) 35.0000 1.40677 0.703384 0.710810i \(-0.251671\pi\)
0.703384 + 0.710810i \(0.251671\pi\)
\(620\) −48.0000 −1.92773
\(621\) 0 0
\(622\) 0 0
\(623\) 4.00000 0.160257
\(624\) 0 0
\(625\) −29.0000 −1.16000
\(626\) −16.0000 −0.639489
\(627\) 0 0
\(628\) 8.00000 0.319235
\(629\) 2.00000 0.0797452
\(630\) 72.0000 2.86855
\(631\) 18.0000 0.716569 0.358284 0.933613i \(-0.383362\pi\)
0.358284 + 0.933613i \(0.383362\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 58.0000 2.30347
\(635\) −24.0000 −0.952411
\(636\) 0 0
\(637\) −9.00000 −0.356593
\(638\) 24.0000 0.950169
\(639\) 0 0
\(640\) 0 0
\(641\) 28.0000 1.10593 0.552967 0.833203i \(-0.313496\pi\)
0.552967 + 0.833203i \(0.313496\pi\)
\(642\) 0 0
\(643\) −19.0000 −0.749287 −0.374643 0.927169i \(-0.622235\pi\)
−0.374643 + 0.927169i \(0.622235\pi\)
\(644\) −48.0000 −1.89146
\(645\) 0 0
\(646\) −6.00000 −0.236067
\(647\) 32.0000 1.25805 0.629025 0.777385i \(-0.283454\pi\)
0.629025 + 0.777385i \(0.283454\pi\)
\(648\) 0 0
\(649\) −20.0000 −0.785069
\(650\) −8.00000 −0.313786
\(651\) 0 0
\(652\) −40.0000 −1.56652
\(653\) 1.00000 0.0391330 0.0195665 0.999809i \(-0.493771\pi\)
0.0195665 + 0.999809i \(0.493771\pi\)
\(654\) 0 0
\(655\) −18.0000 −0.703318
\(656\) −48.0000 −1.87409
\(657\) −30.0000 −1.17041
\(658\) −8.00000 −0.311872
\(659\) −42.0000 −1.63609 −0.818044 0.575156i \(-0.804941\pi\)
−0.818044 + 0.575156i \(0.804941\pi\)
\(660\) 0 0
\(661\) 29.0000 1.12797 0.563985 0.825785i \(-0.309268\pi\)
0.563985 + 0.825785i \(0.309268\pi\)
\(662\) 40.0000 1.55464
\(663\) 0 0
\(664\) 0 0
\(665\) 36.0000 1.39602
\(666\) −12.0000 −0.464991
\(667\) 18.0000 0.696963
\(668\) 20.0000 0.773823
\(669\) 0 0
\(670\) −54.0000 −2.08620
\(671\) 56.0000 2.16186
\(672\) 0 0
\(673\) −18.0000 −0.693849 −0.346925 0.937893i \(-0.612774\pi\)
−0.346925 + 0.937893i \(0.612774\pi\)
\(674\) −68.0000 −2.61926
\(675\) 0 0
\(676\) −24.0000 −0.923077
\(677\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(678\) 0 0
\(679\) 56.0000 2.14908
\(680\) 0 0
\(681\) 0 0
\(682\) −64.0000 −2.45069
\(683\) 9.00000 0.344375 0.172188 0.985064i \(-0.444916\pi\)
0.172188 + 0.985064i \(0.444916\pi\)
\(684\) 18.0000 0.688247
\(685\) −30.0000 −1.14624
\(686\) −16.0000 −0.610883
\(687\) 0 0
\(688\) 44.0000 1.67748
\(689\) 0 0
\(690\) 0 0
\(691\) −10.0000 −0.380418 −0.190209 0.981744i \(-0.560917\pi\)
−0.190209 + 0.981744i \(0.560917\pi\)
\(692\) −28.0000 −1.06440
\(693\) 48.0000 1.82337
\(694\) 30.0000 1.13878
\(695\) 21.0000 0.796575
\(696\) 0 0
\(697\) 12.0000 0.454532
\(698\) −36.0000 −1.36262
\(699\) 0 0
\(700\) −32.0000 −1.20949
\(701\) 34.0000 1.28416 0.642081 0.766637i \(-0.278071\pi\)
0.642081 + 0.766637i \(0.278071\pi\)
\(702\) 0 0
\(703\) −6.00000 −0.226294
\(704\) −32.0000 −1.20605
\(705\) 0 0
\(706\) −48.0000 −1.80650
\(707\) −36.0000 −1.35392
\(708\) 0 0
\(709\) 31.0000 1.16423 0.582115 0.813107i \(-0.302225\pi\)
0.582115 + 0.813107i \(0.302225\pi\)
\(710\) 0 0
\(711\) −30.0000 −1.12509
\(712\) 0 0
\(713\) −48.0000 −1.79761
\(714\) 0 0
\(715\) −12.0000 −0.448775
\(716\) 2.00000 0.0747435
\(717\) 0 0
\(718\) 64.0000 2.38846
\(719\) 19.0000 0.708580 0.354290 0.935136i \(-0.384723\pi\)
0.354290 + 0.935136i \(0.384723\pi\)
\(720\) 36.0000 1.34164
\(721\) 24.0000 0.893807
\(722\) −20.0000 −0.744323
\(723\) 0 0
\(724\) 4.00000 0.148659
\(725\) 12.0000 0.445669
\(726\) 0 0
\(727\) −24.0000 −0.890111 −0.445055 0.895503i \(-0.646816\pi\)
−0.445055 + 0.895503i \(0.646816\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 60.0000 2.22070
\(731\) −11.0000 −0.406850
\(732\) 0 0
\(733\) −13.0000 −0.480166 −0.240083 0.970752i \(-0.577175\pi\)
−0.240083 + 0.970752i \(0.577175\pi\)
\(734\) −22.0000 −0.812035
\(735\) 0 0
\(736\) −48.0000 −1.76930
\(737\) −36.0000 −1.32608
\(738\) −72.0000 −2.65036
\(739\) 4.00000 0.147142 0.0735712 0.997290i \(-0.476560\pi\)
0.0735712 + 0.997290i \(0.476560\pi\)
\(740\) 12.0000 0.441129
\(741\) 0 0
\(742\) 0 0
\(743\) −33.0000 −1.21065 −0.605326 0.795977i \(-0.706957\pi\)
−0.605326 + 0.795977i \(0.706957\pi\)
\(744\) 0 0
\(745\) −54.0000 −1.97841
\(746\) 74.0000 2.70933
\(747\) −51.0000 −1.86599
\(748\) 8.00000 0.292509
\(749\) 16.0000 0.584627
\(750\) 0 0
\(751\) −30.0000 −1.09472 −0.547358 0.836899i \(-0.684366\pi\)
−0.547358 + 0.836899i \(0.684366\pi\)
\(752\) −4.00000 −0.145865
\(753\) 0 0
\(754\) −6.00000 −0.218507
\(755\) 63.0000 2.29280
\(756\) 0 0
\(757\) 44.0000 1.59921 0.799604 0.600528i \(-0.205043\pi\)
0.799604 + 0.600528i \(0.205043\pi\)
\(758\) −36.0000 −1.30758
\(759\) 0 0
\(760\) 0 0
\(761\) −35.0000 −1.26875 −0.634375 0.773026i \(-0.718742\pi\)
−0.634375 + 0.773026i \(0.718742\pi\)
\(762\) 0 0
\(763\) 56.0000 2.02734
\(764\) −26.0000 −0.940647
\(765\) −9.00000 −0.325396
\(766\) 42.0000 1.51752
\(767\) 5.00000 0.180540
\(768\) 0 0
\(769\) −14.0000 −0.504853 −0.252426 0.967616i \(-0.581229\pi\)
−0.252426 + 0.967616i \(0.581229\pi\)
\(770\) −96.0000 −3.45960
\(771\) 0 0
\(772\) −12.0000 −0.431889
\(773\) 26.0000 0.935155 0.467578 0.883952i \(-0.345127\pi\)
0.467578 + 0.883952i \(0.345127\pi\)
\(774\) 66.0000 2.37232
\(775\) −32.0000 −1.14947
\(776\) 0 0
\(777\) 0 0
\(778\) 30.0000 1.07555
\(779\) −36.0000 −1.28983
\(780\) 0 0
\(781\) 0 0
\(782\) 12.0000 0.429119
\(783\) 0 0
\(784\) −36.0000 −1.28571
\(785\) 12.0000 0.428298
\(786\) 0 0
\(787\) 26.0000 0.926800 0.463400 0.886149i \(-0.346629\pi\)
0.463400 + 0.886149i \(0.346629\pi\)
\(788\) −4.00000 −0.142494
\(789\) 0 0
\(790\) 60.0000 2.13470
\(791\) 16.0000 0.568895
\(792\) 0 0
\(793\) −14.0000 −0.497155
\(794\) −26.0000 −0.922705
\(795\) 0 0
\(796\) 34.0000 1.20510
\(797\) 6.00000 0.212531 0.106265 0.994338i \(-0.466111\pi\)
0.106265 + 0.994338i \(0.466111\pi\)
\(798\) 0 0
\(799\) 1.00000 0.0353775
\(800\) −32.0000 −1.13137
\(801\) 3.00000 0.106000
\(802\) 44.0000 1.55369
\(803\) 40.0000 1.41157
\(804\) 0 0
\(805\) −72.0000 −2.53767
\(806\) 16.0000 0.563576
\(807\) 0 0
\(808\) 0 0
\(809\) 41.0000 1.44148 0.720742 0.693204i \(-0.243801\pi\)
0.720742 + 0.693204i \(0.243801\pi\)
\(810\) 54.0000 1.89737
\(811\) −19.0000 −0.667180 −0.333590 0.942718i \(-0.608260\pi\)
−0.333590 + 0.942718i \(0.608260\pi\)
\(812\) −24.0000 −0.842235
\(813\) 0 0
\(814\) 16.0000 0.560800
\(815\) −60.0000 −2.10171
\(816\) 0 0
\(817\) 33.0000 1.15452
\(818\) −34.0000 −1.18878
\(819\) −12.0000 −0.419314
\(820\) 72.0000 2.51435
\(821\) −42.0000 −1.46581 −0.732905 0.680331i \(-0.761836\pi\)
−0.732905 + 0.680331i \(0.761836\pi\)
\(822\) 0 0
\(823\) −7.00000 −0.244005 −0.122002 0.992530i \(-0.538932\pi\)
−0.122002 + 0.992530i \(0.538932\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 40.0000 1.39178
\(827\) 8.00000 0.278187 0.139094 0.990279i \(-0.455581\pi\)
0.139094 + 0.990279i \(0.455581\pi\)
\(828\) −36.0000 −1.25109
\(829\) 30.0000 1.04194 0.520972 0.853574i \(-0.325570\pi\)
0.520972 + 0.853574i \(0.325570\pi\)
\(830\) 102.000 3.54047
\(831\) 0 0
\(832\) 8.00000 0.277350
\(833\) 9.00000 0.311832
\(834\) 0 0
\(835\) 30.0000 1.03819
\(836\) −24.0000 −0.830057
\(837\) 0 0
\(838\) 22.0000 0.759977
\(839\) 30.0000 1.03572 0.517858 0.855467i \(-0.326730\pi\)
0.517858 + 0.855467i \(0.326730\pi\)
\(840\) 0 0
\(841\) −20.0000 −0.689655
\(842\) 0 0
\(843\) 0 0
\(844\) −16.0000 −0.550743
\(845\) −36.0000 −1.23844
\(846\) −6.00000 −0.206284
\(847\) −20.0000 −0.687208
\(848\) 0 0
\(849\) 0 0
\(850\) 8.00000 0.274398
\(851\) 12.0000 0.411355
\(852\) 0 0
\(853\) −8.00000 −0.273915 −0.136957 0.990577i \(-0.543732\pi\)
−0.136957 + 0.990577i \(0.543732\pi\)
\(854\) −112.000 −3.83256
\(855\) 27.0000 0.923381
\(856\) 0 0
\(857\) −5.00000 −0.170797 −0.0853984 0.996347i \(-0.527216\pi\)
−0.0853984 + 0.996347i \(0.527216\pi\)
\(858\) 0 0
\(859\) 16.0000 0.545913 0.272956 0.962026i \(-0.411998\pi\)
0.272956 + 0.962026i \(0.411998\pi\)
\(860\) −66.0000 −2.25058
\(861\) 0 0
\(862\) −44.0000 −1.49865
\(863\) 33.0000 1.12333 0.561667 0.827364i \(-0.310160\pi\)
0.561667 + 0.827364i \(0.310160\pi\)
\(864\) 0 0
\(865\) −42.0000 −1.42804
\(866\) −42.0000 −1.42722
\(867\) 0 0
\(868\) 64.0000 2.17230
\(869\) 40.0000 1.35691
\(870\) 0 0
\(871\) 9.00000 0.304953
\(872\) 0 0
\(873\) 42.0000 1.42148
\(874\) −36.0000 −1.21772
\(875\) 12.0000 0.405674
\(876\) 0 0
\(877\) 5.00000 0.168838 0.0844190 0.996430i \(-0.473097\pi\)
0.0844190 + 0.996430i \(0.473097\pi\)
\(878\) 54.0000 1.82241
\(879\) 0 0
\(880\) −48.0000 −1.61808
\(881\) −18.0000 −0.606435 −0.303218 0.952921i \(-0.598061\pi\)
−0.303218 + 0.952921i \(0.598061\pi\)
\(882\) −54.0000 −1.81827
\(883\) −10.0000 −0.336527 −0.168263 0.985742i \(-0.553816\pi\)
−0.168263 + 0.985742i \(0.553816\pi\)
\(884\) −2.00000 −0.0672673
\(885\) 0 0
\(886\) 6.00000 0.201574
\(887\) −15.0000 −0.503651 −0.251825 0.967773i \(-0.581031\pi\)
−0.251825 + 0.967773i \(0.581031\pi\)
\(888\) 0 0
\(889\) 32.0000 1.07325
\(890\) −6.00000 −0.201120
\(891\) 36.0000 1.20605
\(892\) −52.0000 −1.74109
\(893\) −3.00000 −0.100391
\(894\) 0 0
\(895\) 3.00000 0.100279
\(896\) 0 0
\(897\) 0 0
\(898\) 16.0000 0.533927
\(899\) −24.0000 −0.800445
\(900\) −24.0000 −0.800000
\(901\) 0 0
\(902\) 96.0000 3.19645
\(903\) 0 0
\(904\) 0 0
\(905\) 6.00000 0.199447
\(906\) 0 0
\(907\) 43.0000 1.42779 0.713896 0.700252i \(-0.246929\pi\)
0.713896 + 0.700252i \(0.246929\pi\)
\(908\) 42.0000 1.39382
\(909\) −27.0000 −0.895533
\(910\) 24.0000 0.795592
\(911\) −27.0000 −0.894550 −0.447275 0.894397i \(-0.647605\pi\)
−0.447275 + 0.894397i \(0.647605\pi\)
\(912\) 0 0
\(913\) 68.0000 2.25047
\(914\) −16.0000 −0.529233
\(915\) 0 0
\(916\) 16.0000 0.528655
\(917\) 24.0000 0.792550
\(918\) 0 0
\(919\) −14.0000 −0.461817 −0.230909 0.972975i \(-0.574170\pi\)
−0.230909 + 0.972975i \(0.574170\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 84.0000 2.76639
\(923\) 0 0
\(924\) 0 0
\(925\) 8.00000 0.263038
\(926\) −32.0000 −1.05159
\(927\) 18.0000 0.591198
\(928\) −24.0000 −0.787839
\(929\) 4.00000 0.131236 0.0656179 0.997845i \(-0.479098\pi\)
0.0656179 + 0.997845i \(0.479098\pi\)
\(930\) 0 0
\(931\) −27.0000 −0.884889
\(932\) 48.0000 1.57229
\(933\) 0 0
\(934\) 32.0000 1.04707
\(935\) 12.0000 0.392442
\(936\) 0 0
\(937\) 53.0000 1.73143 0.865717 0.500533i \(-0.166863\pi\)
0.865717 + 0.500533i \(0.166863\pi\)
\(938\) 72.0000 2.35088
\(939\) 0 0
\(940\) 6.00000 0.195698
\(941\) −46.0000 −1.49956 −0.749779 0.661689i \(-0.769840\pi\)
−0.749779 + 0.661689i \(0.769840\pi\)
\(942\) 0 0
\(943\) 72.0000 2.34464
\(944\) 20.0000 0.650945
\(945\) 0 0
\(946\) −88.0000 −2.86113
\(947\) 7.00000 0.227469 0.113735 0.993511i \(-0.463719\pi\)
0.113735 + 0.993511i \(0.463719\pi\)
\(948\) 0 0
\(949\) −10.0000 −0.324614
\(950\) −24.0000 −0.778663
\(951\) 0 0
\(952\) 0 0
\(953\) −52.0000 −1.68445 −0.842223 0.539130i \(-0.818753\pi\)
−0.842223 + 0.539130i \(0.818753\pi\)
\(954\) 0 0
\(955\) −39.0000 −1.26201
\(956\) 0 0
\(957\) 0 0
\(958\) 66.0000 2.13236
\(959\) 40.0000 1.29167
\(960\) 0 0
\(961\) 33.0000 1.06452
\(962\) −4.00000 −0.128965
\(963\) 12.0000 0.386695
\(964\) 8.00000 0.257663
\(965\) −18.0000 −0.579441
\(966\) 0 0
\(967\) −8.00000 −0.257263 −0.128631 0.991692i \(-0.541058\pi\)
−0.128631 + 0.991692i \(0.541058\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) −84.0000 −2.69708
\(971\) 20.0000 0.641831 0.320915 0.947108i \(-0.396010\pi\)
0.320915 + 0.947108i \(0.396010\pi\)
\(972\) 0 0
\(973\) −28.0000 −0.897639
\(974\) 54.0000 1.73027
\(975\) 0 0
\(976\) −56.0000 −1.79252
\(977\) 54.0000 1.72761 0.863807 0.503824i \(-0.168074\pi\)
0.863807 + 0.503824i \(0.168074\pi\)
\(978\) 0 0
\(979\) −4.00000 −0.127841
\(980\) 54.0000 1.72497
\(981\) 42.0000 1.34096
\(982\) −12.0000 −0.382935
\(983\) −5.00000 −0.159475 −0.0797376 0.996816i \(-0.525408\pi\)
−0.0797376 + 0.996816i \(0.525408\pi\)
\(984\) 0 0
\(985\) −6.00000 −0.191176
\(986\) 6.00000 0.191079
\(987\) 0 0
\(988\) 6.00000 0.190885
\(989\) −66.0000 −2.09868
\(990\) −72.0000 −2.28831
\(991\) −20.0000 −0.635321 −0.317660 0.948205i \(-0.602897\pi\)
−0.317660 + 0.948205i \(0.602897\pi\)
\(992\) 64.0000 2.03200
\(993\) 0 0
\(994\) 0 0
\(995\) 51.0000 1.61681
\(996\) 0 0
\(997\) −26.0000 −0.823428 −0.411714 0.911313i \(-0.635070\pi\)
−0.411714 + 0.911313i \(0.635070\pi\)
\(998\) −56.0000 −1.77265
\(999\) 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 179.2.a.a.1.1 1
3.2 odd 2 1611.2.a.a.1.1 1
4.3 odd 2 2864.2.a.b.1.1 1
5.4 even 2 4475.2.a.a.1.1 1
7.6 odd 2 8771.2.a.b.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
179.2.a.a.1.1 1 1.1 even 1 trivial
1611.2.a.a.1.1 1 3.2 odd 2
2864.2.a.b.1.1 1 4.3 odd 2
4475.2.a.a.1.1 1 5.4 even 2
8771.2.a.b.1.1 1 7.6 odd 2