Properties

Label 2800.2.a.b.1.1
Level $2800$
Weight $2$
Character 2800.1
Self dual yes
Analytic conductor $22.358$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2800 = 2^{4} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2800.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(22.3581125660\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 350)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 2800.1

$q$-expansion

\(f(q)\) \(=\) \(q-3.00000 q^{3} -1.00000 q^{7} +6.00000 q^{9} +O(q^{10})\) \(q-3.00000 q^{3} -1.00000 q^{7} +6.00000 q^{9} +5.00000 q^{11} +6.00000 q^{13} +1.00000 q^{17} +3.00000 q^{19} +3.00000 q^{21} -9.00000 q^{27} -6.00000 q^{29} +4.00000 q^{31} -15.0000 q^{33} -8.00000 q^{37} -18.0000 q^{39} +11.0000 q^{41} -8.00000 q^{43} +2.00000 q^{47} +1.00000 q^{49} -3.00000 q^{51} -4.00000 q^{53} -9.00000 q^{57} -4.00000 q^{59} -2.00000 q^{61} -6.00000 q^{63} +9.00000 q^{67} +10.0000 q^{71} +7.00000 q^{73} -5.00000 q^{77} +2.00000 q^{79} +9.00000 q^{81} +11.0000 q^{83} +18.0000 q^{87} -11.0000 q^{89} -6.00000 q^{91} -12.0000 q^{93} +10.0000 q^{97} +30.0000 q^{99} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −3.00000 −1.73205 −0.866025 0.500000i \(-0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) 6.00000 2.00000
\(10\) 0 0
\(11\) 5.00000 1.50756 0.753778 0.657129i \(-0.228229\pi\)
0.753778 + 0.657129i \(0.228229\pi\)
\(12\) 0 0
\(13\) 6.00000 1.66410 0.832050 0.554700i \(-0.187167\pi\)
0.832050 + 0.554700i \(0.187167\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1.00000 0.242536 0.121268 0.992620i \(-0.461304\pi\)
0.121268 + 0.992620i \(0.461304\pi\)
\(18\) 0 0
\(19\) 3.00000 0.688247 0.344124 0.938924i \(-0.388176\pi\)
0.344124 + 0.938924i \(0.388176\pi\)
\(20\) 0 0
\(21\) 3.00000 0.654654
\(22\) 0 0
\(23\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −9.00000 −1.73205
\(28\) 0 0
\(29\) −6.00000 −1.11417 −0.557086 0.830455i \(-0.688081\pi\)
−0.557086 + 0.830455i \(0.688081\pi\)
\(30\) 0 0
\(31\) 4.00000 0.718421 0.359211 0.933257i \(-0.383046\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(32\) 0 0
\(33\) −15.0000 −2.61116
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −8.00000 −1.31519 −0.657596 0.753371i \(-0.728427\pi\)
−0.657596 + 0.753371i \(0.728427\pi\)
\(38\) 0 0
\(39\) −18.0000 −2.88231
\(40\) 0 0
\(41\) 11.0000 1.71791 0.858956 0.512050i \(-0.171114\pi\)
0.858956 + 0.512050i \(0.171114\pi\)
\(42\) 0 0
\(43\) −8.00000 −1.21999 −0.609994 0.792406i \(-0.708828\pi\)
−0.609994 + 0.792406i \(0.708828\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 2.00000 0.291730 0.145865 0.989305i \(-0.453403\pi\)
0.145865 + 0.989305i \(0.453403\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) −3.00000 −0.420084
\(52\) 0 0
\(53\) −4.00000 −0.549442 −0.274721 0.961524i \(-0.588586\pi\)
−0.274721 + 0.961524i \(0.588586\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −9.00000 −1.19208
\(58\) 0 0
\(59\) −4.00000 −0.520756 −0.260378 0.965507i \(-0.583847\pi\)
−0.260378 + 0.965507i \(0.583847\pi\)
\(60\) 0 0
\(61\) −2.00000 −0.256074 −0.128037 0.991769i \(-0.540868\pi\)
−0.128037 + 0.991769i \(0.540868\pi\)
\(62\) 0 0
\(63\) −6.00000 −0.755929
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 9.00000 1.09952 0.549762 0.835321i \(-0.314718\pi\)
0.549762 + 0.835321i \(0.314718\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 10.0000 1.18678 0.593391 0.804914i \(-0.297789\pi\)
0.593391 + 0.804914i \(0.297789\pi\)
\(72\) 0 0
\(73\) 7.00000 0.819288 0.409644 0.912245i \(-0.365653\pi\)
0.409644 + 0.912245i \(0.365653\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −5.00000 −0.569803
\(78\) 0 0
\(79\) 2.00000 0.225018 0.112509 0.993651i \(-0.464111\pi\)
0.112509 + 0.993651i \(0.464111\pi\)
\(80\) 0 0
\(81\) 9.00000 1.00000
\(82\) 0 0
\(83\) 11.0000 1.20741 0.603703 0.797209i \(-0.293691\pi\)
0.603703 + 0.797209i \(0.293691\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 18.0000 1.92980
\(88\) 0 0
\(89\) −11.0000 −1.16600 −0.582999 0.812473i \(-0.698121\pi\)
−0.582999 + 0.812473i \(0.698121\pi\)
\(90\) 0 0
\(91\) −6.00000 −0.628971
\(92\) 0 0
\(93\) −12.0000 −1.24434
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 10.0000 1.01535 0.507673 0.861550i \(-0.330506\pi\)
0.507673 + 0.861550i \(0.330506\pi\)
\(98\) 0 0
\(99\) 30.0000 3.01511
\(100\) 0 0
\(101\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) 0 0
\(103\) 4.00000 0.394132 0.197066 0.980390i \(-0.436859\pi\)
0.197066 + 0.980390i \(0.436859\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 3.00000 0.290021 0.145010 0.989430i \(-0.453678\pi\)
0.145010 + 0.989430i \(0.453678\pi\)
\(108\) 0 0
\(109\) −18.0000 −1.72409 −0.862044 0.506834i \(-0.830816\pi\)
−0.862044 + 0.506834i \(0.830816\pi\)
\(110\) 0 0
\(111\) 24.0000 2.27798
\(112\) 0 0
\(113\) 1.00000 0.0940721 0.0470360 0.998893i \(-0.485022\pi\)
0.0470360 + 0.998893i \(0.485022\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 36.0000 3.32820
\(118\) 0 0
\(119\) −1.00000 −0.0916698
\(120\) 0 0
\(121\) 14.0000 1.27273
\(122\) 0 0
\(123\) −33.0000 −2.97551
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −14.0000 −1.24230 −0.621150 0.783692i \(-0.713334\pi\)
−0.621150 + 0.783692i \(0.713334\pi\)
\(128\) 0 0
\(129\) 24.0000 2.11308
\(130\) 0 0
\(131\) −8.00000 −0.698963 −0.349482 0.936943i \(-0.613642\pi\)
−0.349482 + 0.936943i \(0.613642\pi\)
\(132\) 0 0
\(133\) −3.00000 −0.260133
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 3.00000 0.256307 0.128154 0.991754i \(-0.459095\pi\)
0.128154 + 0.991754i \(0.459095\pi\)
\(138\) 0 0
\(139\) 11.0000 0.933008 0.466504 0.884519i \(-0.345513\pi\)
0.466504 + 0.884519i \(0.345513\pi\)
\(140\) 0 0
\(141\) −6.00000 −0.505291
\(142\) 0 0
\(143\) 30.0000 2.50873
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −3.00000 −0.247436
\(148\) 0 0
\(149\) 12.0000 0.983078 0.491539 0.870855i \(-0.336434\pi\)
0.491539 + 0.870855i \(0.336434\pi\)
\(150\) 0 0
\(151\) −8.00000 −0.651031 −0.325515 0.945537i \(-0.605538\pi\)
−0.325515 + 0.945537i \(0.605538\pi\)
\(152\) 0 0
\(153\) 6.00000 0.485071
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −4.00000 −0.319235 −0.159617 0.987179i \(-0.551026\pi\)
−0.159617 + 0.987179i \(0.551026\pi\)
\(158\) 0 0
\(159\) 12.0000 0.951662
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −19.0000 −1.48819 −0.744097 0.668071i \(-0.767120\pi\)
−0.744097 + 0.668071i \(0.767120\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 12.0000 0.928588 0.464294 0.885681i \(-0.346308\pi\)
0.464294 + 0.885681i \(0.346308\pi\)
\(168\) 0 0
\(169\) 23.0000 1.76923
\(170\) 0 0
\(171\) 18.0000 1.37649
\(172\) 0 0
\(173\) −2.00000 −0.152057 −0.0760286 0.997106i \(-0.524224\pi\)
−0.0760286 + 0.997106i \(0.524224\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 12.0000 0.901975
\(178\) 0 0
\(179\) −3.00000 −0.224231 −0.112115 0.993695i \(-0.535763\pi\)
−0.112115 + 0.993695i \(0.535763\pi\)
\(180\) 0 0
\(181\) 10.0000 0.743294 0.371647 0.928374i \(-0.378793\pi\)
0.371647 + 0.928374i \(0.378793\pi\)
\(182\) 0 0
\(183\) 6.00000 0.443533
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 5.00000 0.365636
\(188\) 0 0
\(189\) 9.00000 0.654654
\(190\) 0 0
\(191\) 6.00000 0.434145 0.217072 0.976156i \(-0.430349\pi\)
0.217072 + 0.976156i \(0.430349\pi\)
\(192\) 0 0
\(193\) 19.0000 1.36765 0.683825 0.729646i \(-0.260315\pi\)
0.683825 + 0.729646i \(0.260315\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 22.0000 1.56744 0.783718 0.621117i \(-0.213321\pi\)
0.783718 + 0.621117i \(0.213321\pi\)
\(198\) 0 0
\(199\) 10.0000 0.708881 0.354441 0.935079i \(-0.384671\pi\)
0.354441 + 0.935079i \(0.384671\pi\)
\(200\) 0 0
\(201\) −27.0000 −1.90443
\(202\) 0 0
\(203\) 6.00000 0.421117
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 15.0000 1.03757
\(210\) 0 0
\(211\) −1.00000 −0.0688428 −0.0344214 0.999407i \(-0.510959\pi\)
−0.0344214 + 0.999407i \(0.510959\pi\)
\(212\) 0 0
\(213\) −30.0000 −2.05557
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −4.00000 −0.271538
\(218\) 0 0
\(219\) −21.0000 −1.41905
\(220\) 0 0
\(221\) 6.00000 0.403604
\(222\) 0 0
\(223\) 22.0000 1.47323 0.736614 0.676313i \(-0.236423\pi\)
0.736614 + 0.676313i \(0.236423\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −28.0000 −1.85843 −0.929213 0.369546i \(-0.879513\pi\)
−0.929213 + 0.369546i \(0.879513\pi\)
\(228\) 0 0
\(229\) −14.0000 −0.925146 −0.462573 0.886581i \(-0.653074\pi\)
−0.462573 + 0.886581i \(0.653074\pi\)
\(230\) 0 0
\(231\) 15.0000 0.986928
\(232\) 0 0
\(233\) −6.00000 −0.393073 −0.196537 0.980497i \(-0.562969\pi\)
−0.196537 + 0.980497i \(0.562969\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −6.00000 −0.389742
\(238\) 0 0
\(239\) −4.00000 −0.258738 −0.129369 0.991596i \(-0.541295\pi\)
−0.129369 + 0.991596i \(0.541295\pi\)
\(240\) 0 0
\(241\) −5.00000 −0.322078 −0.161039 0.986948i \(-0.551485\pi\)
−0.161039 + 0.986948i \(0.551485\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 18.0000 1.14531
\(248\) 0 0
\(249\) −33.0000 −2.09129
\(250\) 0 0
\(251\) −27.0000 −1.70422 −0.852112 0.523359i \(-0.824679\pi\)
−0.852112 + 0.523359i \(0.824679\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −2.00000 −0.124757 −0.0623783 0.998053i \(-0.519869\pi\)
−0.0623783 + 0.998053i \(0.519869\pi\)
\(258\) 0 0
\(259\) 8.00000 0.497096
\(260\) 0 0
\(261\) −36.0000 −2.22834
\(262\) 0 0
\(263\) −10.0000 −0.616626 −0.308313 0.951285i \(-0.599764\pi\)
−0.308313 + 0.951285i \(0.599764\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 33.0000 2.01957
\(268\) 0 0
\(269\) 18.0000 1.09748 0.548740 0.835993i \(-0.315108\pi\)
0.548740 + 0.835993i \(0.315108\pi\)
\(270\) 0 0
\(271\) 6.00000 0.364474 0.182237 0.983255i \(-0.441666\pi\)
0.182237 + 0.983255i \(0.441666\pi\)
\(272\) 0 0
\(273\) 18.0000 1.08941
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 30.0000 1.80253 0.901263 0.433273i \(-0.142641\pi\)
0.901263 + 0.433273i \(0.142641\pi\)
\(278\) 0 0
\(279\) 24.0000 1.43684
\(280\) 0 0
\(281\) 14.0000 0.835170 0.417585 0.908638i \(-0.362877\pi\)
0.417585 + 0.908638i \(0.362877\pi\)
\(282\) 0 0
\(283\) −13.0000 −0.772770 −0.386385 0.922338i \(-0.626276\pi\)
−0.386385 + 0.922338i \(0.626276\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −11.0000 −0.649309
\(288\) 0 0
\(289\) −16.0000 −0.941176
\(290\) 0 0
\(291\) −30.0000 −1.75863
\(292\) 0 0
\(293\) 14.0000 0.817889 0.408944 0.912559i \(-0.365897\pi\)
0.408944 + 0.912559i \(0.365897\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −45.0000 −2.61116
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 8.00000 0.461112
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 13.0000 0.741949 0.370975 0.928643i \(-0.379024\pi\)
0.370975 + 0.928643i \(0.379024\pi\)
\(308\) 0 0
\(309\) −12.0000 −0.682656
\(310\) 0 0
\(311\) −6.00000 −0.340229 −0.170114 0.985424i \(-0.554414\pi\)
−0.170114 + 0.985424i \(0.554414\pi\)
\(312\) 0 0
\(313\) 10.0000 0.565233 0.282617 0.959233i \(-0.408798\pi\)
0.282617 + 0.959233i \(0.408798\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −4.00000 −0.224662 −0.112331 0.993671i \(-0.535832\pi\)
−0.112331 + 0.993671i \(0.535832\pi\)
\(318\) 0 0
\(319\) −30.0000 −1.67968
\(320\) 0 0
\(321\) −9.00000 −0.502331
\(322\) 0 0
\(323\) 3.00000 0.166924
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 54.0000 2.98621
\(328\) 0 0
\(329\) −2.00000 −0.110264
\(330\) 0 0
\(331\) 17.0000 0.934405 0.467202 0.884150i \(-0.345262\pi\)
0.467202 + 0.884150i \(0.345262\pi\)
\(332\) 0 0
\(333\) −48.0000 −2.63038
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 29.0000 1.57973 0.789865 0.613280i \(-0.210150\pi\)
0.789865 + 0.613280i \(0.210150\pi\)
\(338\) 0 0
\(339\) −3.00000 −0.162938
\(340\) 0 0
\(341\) 20.0000 1.08306
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 19.0000 1.01997 0.509987 0.860182i \(-0.329650\pi\)
0.509987 + 0.860182i \(0.329650\pi\)
\(348\) 0 0
\(349\) −8.00000 −0.428230 −0.214115 0.976808i \(-0.568687\pi\)
−0.214115 + 0.976808i \(0.568687\pi\)
\(350\) 0 0
\(351\) −54.0000 −2.88231
\(352\) 0 0
\(353\) 18.0000 0.958043 0.479022 0.877803i \(-0.340992\pi\)
0.479022 + 0.877803i \(0.340992\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 3.00000 0.158777
\(358\) 0 0
\(359\) −26.0000 −1.37223 −0.686114 0.727494i \(-0.740685\pi\)
−0.686114 + 0.727494i \(0.740685\pi\)
\(360\) 0 0
\(361\) −10.0000 −0.526316
\(362\) 0 0
\(363\) −42.0000 −2.20443
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −8.00000 −0.417597 −0.208798 0.977959i \(-0.566955\pi\)
−0.208798 + 0.977959i \(0.566955\pi\)
\(368\) 0 0
\(369\) 66.0000 3.43582
\(370\) 0 0
\(371\) 4.00000 0.207670
\(372\) 0 0
\(373\) 4.00000 0.207112 0.103556 0.994624i \(-0.466978\pi\)
0.103556 + 0.994624i \(0.466978\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −36.0000 −1.85409
\(378\) 0 0
\(379\) −9.00000 −0.462299 −0.231149 0.972918i \(-0.574249\pi\)
−0.231149 + 0.972918i \(0.574249\pi\)
\(380\) 0 0
\(381\) 42.0000 2.15173
\(382\) 0 0
\(383\) −6.00000 −0.306586 −0.153293 0.988181i \(-0.548988\pi\)
−0.153293 + 0.988181i \(0.548988\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −48.0000 −2.43998
\(388\) 0 0
\(389\) 8.00000 0.405616 0.202808 0.979219i \(-0.434993\pi\)
0.202808 + 0.979219i \(0.434993\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 24.0000 1.21064
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −10.0000 −0.501886 −0.250943 0.968002i \(-0.580741\pi\)
−0.250943 + 0.968002i \(0.580741\pi\)
\(398\) 0 0
\(399\) 9.00000 0.450564
\(400\) 0 0
\(401\) 37.0000 1.84769 0.923846 0.382765i \(-0.125028\pi\)
0.923846 + 0.382765i \(0.125028\pi\)
\(402\) 0 0
\(403\) 24.0000 1.19553
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −40.0000 −1.98273
\(408\) 0 0
\(409\) −21.0000 −1.03838 −0.519192 0.854658i \(-0.673767\pi\)
−0.519192 + 0.854658i \(0.673767\pi\)
\(410\) 0 0
\(411\) −9.00000 −0.443937
\(412\) 0 0
\(413\) 4.00000 0.196827
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −33.0000 −1.61602
\(418\) 0 0
\(419\) 39.0000 1.90527 0.952637 0.304109i \(-0.0983586\pi\)
0.952637 + 0.304109i \(0.0983586\pi\)
\(420\) 0 0
\(421\) 20.0000 0.974740 0.487370 0.873195i \(-0.337956\pi\)
0.487370 + 0.873195i \(0.337956\pi\)
\(422\) 0 0
\(423\) 12.0000 0.583460
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 2.00000 0.0967868
\(428\) 0 0
\(429\) −90.0000 −4.34524
\(430\) 0 0
\(431\) 36.0000 1.73406 0.867029 0.498257i \(-0.166026\pi\)
0.867029 + 0.498257i \(0.166026\pi\)
\(432\) 0 0
\(433\) 1.00000 0.0480569 0.0240285 0.999711i \(-0.492351\pi\)
0.0240285 + 0.999711i \(0.492351\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) −28.0000 −1.33637 −0.668184 0.743996i \(-0.732928\pi\)
−0.668184 + 0.743996i \(0.732928\pi\)
\(440\) 0 0
\(441\) 6.00000 0.285714
\(442\) 0 0
\(443\) 37.0000 1.75792 0.878962 0.476893i \(-0.158237\pi\)
0.878962 + 0.476893i \(0.158237\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −36.0000 −1.70274
\(448\) 0 0
\(449\) 33.0000 1.55737 0.778683 0.627417i \(-0.215888\pi\)
0.778683 + 0.627417i \(0.215888\pi\)
\(450\) 0 0
\(451\) 55.0000 2.58985
\(452\) 0 0
\(453\) 24.0000 1.12762
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −25.0000 −1.16945 −0.584725 0.811231i \(-0.698798\pi\)
−0.584725 + 0.811231i \(0.698798\pi\)
\(458\) 0 0
\(459\) −9.00000 −0.420084
\(460\) 0 0
\(461\) −38.0000 −1.76984 −0.884918 0.465746i \(-0.845786\pi\)
−0.884918 + 0.465746i \(0.845786\pi\)
\(462\) 0 0
\(463\) 8.00000 0.371792 0.185896 0.982569i \(-0.440481\pi\)
0.185896 + 0.982569i \(0.440481\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −4.00000 −0.185098 −0.0925490 0.995708i \(-0.529501\pi\)
−0.0925490 + 0.995708i \(0.529501\pi\)
\(468\) 0 0
\(469\) −9.00000 −0.415581
\(470\) 0 0
\(471\) 12.0000 0.552931
\(472\) 0 0
\(473\) −40.0000 −1.83920
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −24.0000 −1.09888
\(478\) 0 0
\(479\) 6.00000 0.274147 0.137073 0.990561i \(-0.456230\pi\)
0.137073 + 0.990561i \(0.456230\pi\)
\(480\) 0 0
\(481\) −48.0000 −2.18861
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −34.0000 −1.54069 −0.770344 0.637629i \(-0.779915\pi\)
−0.770344 + 0.637629i \(0.779915\pi\)
\(488\) 0 0
\(489\) 57.0000 2.57763
\(490\) 0 0
\(491\) 12.0000 0.541552 0.270776 0.962642i \(-0.412720\pi\)
0.270776 + 0.962642i \(0.412720\pi\)
\(492\) 0 0
\(493\) −6.00000 −0.270226
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −10.0000 −0.448561
\(498\) 0 0
\(499\) −36.0000 −1.61158 −0.805791 0.592200i \(-0.798259\pi\)
−0.805791 + 0.592200i \(0.798259\pi\)
\(500\) 0 0
\(501\) −36.0000 −1.60836
\(502\) 0 0
\(503\) −30.0000 −1.33763 −0.668817 0.743427i \(-0.733199\pi\)
−0.668817 + 0.743427i \(0.733199\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −69.0000 −3.06440
\(508\) 0 0
\(509\) −14.0000 −0.620539 −0.310270 0.950649i \(-0.600419\pi\)
−0.310270 + 0.950649i \(0.600419\pi\)
\(510\) 0 0
\(511\) −7.00000 −0.309662
\(512\) 0 0
\(513\) −27.0000 −1.19208
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 10.0000 0.439799
\(518\) 0 0
\(519\) 6.00000 0.263371
\(520\) 0 0
\(521\) 11.0000 0.481919 0.240959 0.970535i \(-0.422538\pi\)
0.240959 + 0.970535i \(0.422538\pi\)
\(522\) 0 0
\(523\) 13.0000 0.568450 0.284225 0.958758i \(-0.408264\pi\)
0.284225 + 0.958758i \(0.408264\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 4.00000 0.174243
\(528\) 0 0
\(529\) −23.0000 −1.00000
\(530\) 0 0
\(531\) −24.0000 −1.04151
\(532\) 0 0
\(533\) 66.0000 2.85878
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 9.00000 0.388379
\(538\) 0 0
\(539\) 5.00000 0.215365
\(540\) 0 0
\(541\) −42.0000 −1.80572 −0.902861 0.429934i \(-0.858537\pi\)
−0.902861 + 0.429934i \(0.858537\pi\)
\(542\) 0 0
\(543\) −30.0000 −1.28742
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 27.0000 1.15444 0.577218 0.816590i \(-0.304138\pi\)
0.577218 + 0.816590i \(0.304138\pi\)
\(548\) 0 0
\(549\) −12.0000 −0.512148
\(550\) 0 0
\(551\) −18.0000 −0.766826
\(552\) 0 0
\(553\) −2.00000 −0.0850487
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −4.00000 −0.169485 −0.0847427 0.996403i \(-0.527007\pi\)
−0.0847427 + 0.996403i \(0.527007\pi\)
\(558\) 0 0
\(559\) −48.0000 −2.03018
\(560\) 0 0
\(561\) −15.0000 −0.633300
\(562\) 0 0
\(563\) 20.0000 0.842900 0.421450 0.906852i \(-0.361521\pi\)
0.421450 + 0.906852i \(0.361521\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −9.00000 −0.377964
\(568\) 0 0
\(569\) 21.0000 0.880366 0.440183 0.897908i \(-0.354914\pi\)
0.440183 + 0.897908i \(0.354914\pi\)
\(570\) 0 0
\(571\) −12.0000 −0.502184 −0.251092 0.967963i \(-0.580790\pi\)
−0.251092 + 0.967963i \(0.580790\pi\)
\(572\) 0 0
\(573\) −18.0000 −0.751961
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −13.0000 −0.541197 −0.270599 0.962692i \(-0.587222\pi\)
−0.270599 + 0.962692i \(0.587222\pi\)
\(578\) 0 0
\(579\) −57.0000 −2.36884
\(580\) 0 0
\(581\) −11.0000 −0.456357
\(582\) 0 0
\(583\) −20.0000 −0.828315
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −13.0000 −0.536567 −0.268284 0.963340i \(-0.586456\pi\)
−0.268284 + 0.963340i \(0.586456\pi\)
\(588\) 0 0
\(589\) 12.0000 0.494451
\(590\) 0 0
\(591\) −66.0000 −2.71488
\(592\) 0 0
\(593\) 39.0000 1.60154 0.800769 0.598973i \(-0.204424\pi\)
0.800769 + 0.598973i \(0.204424\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −30.0000 −1.22782
\(598\) 0 0
\(599\) 24.0000 0.980613 0.490307 0.871550i \(-0.336885\pi\)
0.490307 + 0.871550i \(0.336885\pi\)
\(600\) 0 0
\(601\) 21.0000 0.856608 0.428304 0.903635i \(-0.359111\pi\)
0.428304 + 0.903635i \(0.359111\pi\)
\(602\) 0 0
\(603\) 54.0000 2.19905
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 28.0000 1.13648 0.568242 0.822861i \(-0.307624\pi\)
0.568242 + 0.822861i \(0.307624\pi\)
\(608\) 0 0
\(609\) −18.0000 −0.729397
\(610\) 0 0
\(611\) 12.0000 0.485468
\(612\) 0 0
\(613\) −18.0000 −0.727013 −0.363507 0.931592i \(-0.618421\pi\)
−0.363507 + 0.931592i \(0.618421\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −14.0000 −0.563619 −0.281809 0.959470i \(-0.590935\pi\)
−0.281809 + 0.959470i \(0.590935\pi\)
\(618\) 0 0
\(619\) 4.00000 0.160774 0.0803868 0.996764i \(-0.474384\pi\)
0.0803868 + 0.996764i \(0.474384\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 11.0000 0.440706
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −45.0000 −1.79713
\(628\) 0 0
\(629\) −8.00000 −0.318981
\(630\) 0 0
\(631\) 16.0000 0.636950 0.318475 0.947931i \(-0.396829\pi\)
0.318475 + 0.947931i \(0.396829\pi\)
\(632\) 0 0
\(633\) 3.00000 0.119239
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 6.00000 0.237729
\(638\) 0 0
\(639\) 60.0000 2.37356
\(640\) 0 0
\(641\) 2.00000 0.0789953 0.0394976 0.999220i \(-0.487424\pi\)
0.0394976 + 0.999220i \(0.487424\pi\)
\(642\) 0 0
\(643\) 16.0000 0.630978 0.315489 0.948929i \(-0.397831\pi\)
0.315489 + 0.948929i \(0.397831\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −8.00000 −0.314512 −0.157256 0.987558i \(-0.550265\pi\)
−0.157256 + 0.987558i \(0.550265\pi\)
\(648\) 0 0
\(649\) −20.0000 −0.785069
\(650\) 0 0
\(651\) 12.0000 0.470317
\(652\) 0 0
\(653\) 28.0000 1.09572 0.547862 0.836569i \(-0.315442\pi\)
0.547862 + 0.836569i \(0.315442\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 42.0000 1.63858
\(658\) 0 0
\(659\) −1.00000 −0.0389545 −0.0194772 0.999810i \(-0.506200\pi\)
−0.0194772 + 0.999810i \(0.506200\pi\)
\(660\) 0 0
\(661\) −50.0000 −1.94477 −0.972387 0.233373i \(-0.925024\pi\)
−0.972387 + 0.233373i \(0.925024\pi\)
\(662\) 0 0
\(663\) −18.0000 −0.699062
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) −66.0000 −2.55171
\(670\) 0 0
\(671\) −10.0000 −0.386046
\(672\) 0 0
\(673\) −34.0000 −1.31060 −0.655302 0.755367i \(-0.727459\pi\)
−0.655302 + 0.755367i \(0.727459\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 48.0000 1.84479 0.922395 0.386248i \(-0.126229\pi\)
0.922395 + 0.386248i \(0.126229\pi\)
\(678\) 0 0
\(679\) −10.0000 −0.383765
\(680\) 0 0
\(681\) 84.0000 3.21889
\(682\) 0 0
\(683\) −13.0000 −0.497431 −0.248716 0.968577i \(-0.580008\pi\)
−0.248716 + 0.968577i \(0.580008\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 42.0000 1.60240
\(688\) 0 0
\(689\) −24.0000 −0.914327
\(690\) 0 0
\(691\) −49.0000 −1.86405 −0.932024 0.362397i \(-0.881959\pi\)
−0.932024 + 0.362397i \(0.881959\pi\)
\(692\) 0 0
\(693\) −30.0000 −1.13961
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 11.0000 0.416655
\(698\) 0 0
\(699\) 18.0000 0.680823
\(700\) 0 0
\(701\) −32.0000 −1.20862 −0.604312 0.796748i \(-0.706552\pi\)
−0.604312 + 0.796748i \(0.706552\pi\)
\(702\) 0 0
\(703\) −24.0000 −0.905177
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 4.00000 0.150223 0.0751116 0.997175i \(-0.476069\pi\)
0.0751116 + 0.997175i \(0.476069\pi\)
\(710\) 0 0
\(711\) 12.0000 0.450035
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 12.0000 0.448148
\(718\) 0 0
\(719\) 48.0000 1.79010 0.895049 0.445968i \(-0.147140\pi\)
0.895049 + 0.445968i \(0.147140\pi\)
\(720\) 0 0
\(721\) −4.00000 −0.148968
\(722\) 0 0
\(723\) 15.0000 0.557856
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 6.00000 0.222528 0.111264 0.993791i \(-0.464510\pi\)
0.111264 + 0.993791i \(0.464510\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) −8.00000 −0.295891
\(732\) 0 0
\(733\) −40.0000 −1.47743 −0.738717 0.674016i \(-0.764568\pi\)
−0.738717 + 0.674016i \(0.764568\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 45.0000 1.65760
\(738\) 0 0
\(739\) −4.00000 −0.147142 −0.0735712 0.997290i \(-0.523440\pi\)
−0.0735712 + 0.997290i \(0.523440\pi\)
\(740\) 0 0
\(741\) −54.0000 −1.98374
\(742\) 0 0
\(743\) −24.0000 −0.880475 −0.440237 0.897881i \(-0.645106\pi\)
−0.440237 + 0.897881i \(0.645106\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 66.0000 2.41481
\(748\) 0 0
\(749\) −3.00000 −0.109618
\(750\) 0 0
\(751\) −50.0000 −1.82453 −0.912263 0.409605i \(-0.865667\pi\)
−0.912263 + 0.409605i \(0.865667\pi\)
\(752\) 0 0
\(753\) 81.0000 2.95180
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 2.00000 0.0726912 0.0363456 0.999339i \(-0.488428\pi\)
0.0363456 + 0.999339i \(0.488428\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 27.0000 0.978749 0.489375 0.872074i \(-0.337225\pi\)
0.489375 + 0.872074i \(0.337225\pi\)
\(762\) 0 0
\(763\) 18.0000 0.651644
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −24.0000 −0.866590
\(768\) 0 0
\(769\) 19.0000 0.685158 0.342579 0.939489i \(-0.388700\pi\)
0.342579 + 0.939489i \(0.388700\pi\)
\(770\) 0 0
\(771\) 6.00000 0.216085
\(772\) 0 0
\(773\) −36.0000 −1.29483 −0.647415 0.762138i \(-0.724150\pi\)
−0.647415 + 0.762138i \(0.724150\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −24.0000 −0.860995
\(778\) 0 0
\(779\) 33.0000 1.18235
\(780\) 0 0
\(781\) 50.0000 1.78914
\(782\) 0 0
\(783\) 54.0000 1.92980
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 52.0000 1.85360 0.926800 0.375555i \(-0.122548\pi\)
0.926800 + 0.375555i \(0.122548\pi\)
\(788\) 0 0
\(789\) 30.0000 1.06803
\(790\) 0 0
\(791\) −1.00000 −0.0355559
\(792\) 0 0
\(793\) −12.0000 −0.426132
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −42.0000 −1.48772 −0.743858 0.668338i \(-0.767006\pi\)
−0.743858 + 0.668338i \(0.767006\pi\)
\(798\) 0 0
\(799\) 2.00000 0.0707549
\(800\) 0 0
\(801\) −66.0000 −2.33200
\(802\) 0 0
\(803\) 35.0000 1.23512
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −54.0000 −1.90089
\(808\) 0 0
\(809\) 6.00000 0.210949 0.105474 0.994422i \(-0.466364\pi\)
0.105474 + 0.994422i \(0.466364\pi\)
\(810\) 0 0
\(811\) 28.0000 0.983213 0.491606 0.870817i \(-0.336410\pi\)
0.491606 + 0.870817i \(0.336410\pi\)
\(812\) 0 0
\(813\) −18.0000 −0.631288
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −24.0000 −0.839654
\(818\) 0 0
\(819\) −36.0000 −1.25794
\(820\) 0 0
\(821\) −24.0000 −0.837606 −0.418803 0.908077i \(-0.637550\pi\)
−0.418803 + 0.908077i \(0.637550\pi\)
\(822\) 0 0
\(823\) 10.0000 0.348578 0.174289 0.984695i \(-0.444237\pi\)
0.174289 + 0.984695i \(0.444237\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 41.0000 1.42571 0.712855 0.701312i \(-0.247402\pi\)
0.712855 + 0.701312i \(0.247402\pi\)
\(828\) 0 0
\(829\) −4.00000 −0.138926 −0.0694629 0.997585i \(-0.522129\pi\)
−0.0694629 + 0.997585i \(0.522129\pi\)
\(830\) 0 0
\(831\) −90.0000 −3.12207
\(832\) 0 0
\(833\) 1.00000 0.0346479
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −36.0000 −1.24434
\(838\) 0 0
\(839\) −2.00000 −0.0690477 −0.0345238 0.999404i \(-0.510991\pi\)
−0.0345238 + 0.999404i \(0.510991\pi\)
\(840\) 0 0
\(841\) 7.00000 0.241379
\(842\) 0 0
\(843\) −42.0000 −1.44656
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −14.0000 −0.481046
\(848\) 0 0
\(849\) 39.0000 1.33848
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 34.0000 1.16414 0.582069 0.813139i \(-0.302243\pi\)
0.582069 + 0.813139i \(0.302243\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −3.00000 −0.102478 −0.0512390 0.998686i \(-0.516317\pi\)
−0.0512390 + 0.998686i \(0.516317\pi\)
\(858\) 0 0
\(859\) 51.0000 1.74010 0.870049 0.492966i \(-0.164087\pi\)
0.870049 + 0.492966i \(0.164087\pi\)
\(860\) 0 0
\(861\) 33.0000 1.12464
\(862\) 0 0
\(863\) 4.00000 0.136162 0.0680808 0.997680i \(-0.478312\pi\)
0.0680808 + 0.997680i \(0.478312\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 48.0000 1.63017
\(868\) 0 0
\(869\) 10.0000 0.339227
\(870\) 0 0
\(871\) 54.0000 1.82972
\(872\) 0 0
\(873\) 60.0000 2.03069
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −32.0000 −1.08056 −0.540282 0.841484i \(-0.681682\pi\)
−0.540282 + 0.841484i \(0.681682\pi\)
\(878\) 0 0
\(879\) −42.0000 −1.41662
\(880\) 0 0
\(881\) 26.0000 0.875962 0.437981 0.898984i \(-0.355694\pi\)
0.437981 + 0.898984i \(0.355694\pi\)
\(882\) 0 0
\(883\) 15.0000 0.504790 0.252395 0.967624i \(-0.418782\pi\)
0.252395 + 0.967624i \(0.418782\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −34.0000 −1.14161 −0.570804 0.821086i \(-0.693368\pi\)
−0.570804 + 0.821086i \(0.693368\pi\)
\(888\) 0 0
\(889\) 14.0000 0.469545
\(890\) 0 0
\(891\) 45.0000 1.50756
\(892\) 0 0
\(893\) 6.00000 0.200782
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −24.0000 −0.800445
\(900\) 0 0
\(901\) −4.00000 −0.133259
\(902\) 0 0
\(903\) −24.0000 −0.798670
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −4.00000 −0.132818 −0.0664089 0.997792i \(-0.521154\pi\)
−0.0664089 + 0.997792i \(0.521154\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 12.0000 0.397578 0.198789 0.980042i \(-0.436299\pi\)
0.198789 + 0.980042i \(0.436299\pi\)
\(912\) 0 0
\(913\) 55.0000 1.82023
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 8.00000 0.264183
\(918\) 0 0
\(919\) 34.0000 1.12156 0.560778 0.827966i \(-0.310502\pi\)
0.560778 + 0.827966i \(0.310502\pi\)
\(920\) 0 0
\(921\) −39.0000 −1.28509
\(922\) 0 0
\(923\) 60.0000 1.97492
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 24.0000 0.788263
\(928\) 0 0
\(929\) 46.0000 1.50921 0.754606 0.656179i \(-0.227828\pi\)
0.754606 + 0.656179i \(0.227828\pi\)
\(930\) 0 0
\(931\) 3.00000 0.0983210
\(932\) 0 0
\(933\) 18.0000 0.589294
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 7.00000 0.228680 0.114340 0.993442i \(-0.463525\pi\)
0.114340 + 0.993442i \(0.463525\pi\)
\(938\) 0 0
\(939\) −30.0000 −0.979013
\(940\) 0 0
\(941\) 56.0000 1.82555 0.912774 0.408465i \(-0.133936\pi\)
0.912774 + 0.408465i \(0.133936\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −4.00000 −0.129983 −0.0649913 0.997886i \(-0.520702\pi\)
−0.0649913 + 0.997886i \(0.520702\pi\)
\(948\) 0 0
\(949\) 42.0000 1.36338
\(950\) 0 0
\(951\) 12.0000 0.389127
\(952\) 0 0
\(953\) −9.00000 −0.291539 −0.145769 0.989319i \(-0.546566\pi\)
−0.145769 + 0.989319i \(0.546566\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 90.0000 2.90929
\(958\) 0 0
\(959\) −3.00000 −0.0968751
\(960\) 0 0
\(961\) −15.0000 −0.483871
\(962\) 0 0
\(963\) 18.0000 0.580042
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −2.00000 −0.0643157 −0.0321578 0.999483i \(-0.510238\pi\)
−0.0321578 + 0.999483i \(0.510238\pi\)
\(968\) 0 0
\(969\) −9.00000 −0.289122
\(970\) 0 0
\(971\) 51.0000 1.63667 0.818334 0.574743i \(-0.194898\pi\)
0.818334 + 0.574743i \(0.194898\pi\)
\(972\) 0 0
\(973\) −11.0000 −0.352644
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −21.0000 −0.671850 −0.335925 0.941889i \(-0.609049\pi\)
−0.335925 + 0.941889i \(0.609049\pi\)
\(978\) 0 0
\(979\) −55.0000 −1.75781
\(980\) 0 0
\(981\) −108.000 −3.44817
\(982\) 0 0
\(983\) −4.00000 −0.127580 −0.0637901 0.997963i \(-0.520319\pi\)
−0.0637901 + 0.997963i \(0.520319\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 6.00000 0.190982
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) −4.00000 −0.127064 −0.0635321 0.997980i \(-0.520237\pi\)
−0.0635321 + 0.997980i \(0.520237\pi\)
\(992\) 0 0
\(993\) −51.0000 −1.61844
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 58.0000 1.83688 0.918439 0.395562i \(-0.129450\pi\)
0.918439 + 0.395562i \(0.129450\pi\)
\(998\) 0 0
\(999\) 72.0000 2.27798
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 2800.2.a.b.1.1 1
4.3 odd 2 350.2.a.c.1.1 1
5.2 odd 4 2800.2.g.a.449.2 2
5.3 odd 4 2800.2.g.a.449.1 2
5.4 even 2 2800.2.a.bg.1.1 1
12.11 even 2 3150.2.a.bq.1.1 1
20.3 even 4 350.2.c.a.99.2 2
20.7 even 4 350.2.c.a.99.1 2
20.19 odd 2 350.2.a.d.1.1 yes 1
28.27 even 2 2450.2.a.a.1.1 1
60.23 odd 4 3150.2.g.v.2899.1 2
60.47 odd 4 3150.2.g.v.2899.2 2
60.59 even 2 3150.2.a.j.1.1 1
140.27 odd 4 2450.2.c.r.99.1 2
140.83 odd 4 2450.2.c.r.99.2 2
140.139 even 2 2450.2.a.bg.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
350.2.a.c.1.1 1 4.3 odd 2
350.2.a.d.1.1 yes 1 20.19 odd 2
350.2.c.a.99.1 2 20.7 even 4
350.2.c.a.99.2 2 20.3 even 4
2450.2.a.a.1.1 1 28.27 even 2
2450.2.a.bg.1.1 1 140.139 even 2
2450.2.c.r.99.1 2 140.27 odd 4
2450.2.c.r.99.2 2 140.83 odd 4
2800.2.a.b.1.1 1 1.1 even 1 trivial
2800.2.a.bg.1.1 1 5.4 even 2
2800.2.g.a.449.1 2 5.3 odd 4
2800.2.g.a.449.2 2 5.2 odd 4
3150.2.a.j.1.1 1 60.59 even 2
3150.2.a.bq.1.1 1 12.11 even 2
3150.2.g.v.2899.1 2 60.23 odd 4
3150.2.g.v.2899.2 2 60.47 odd 4