Properties

Label 3675.2.a.e.1.1
Level $3675$
Weight $2$
Character 3675.1
Self dual yes
Analytic conductor $29.345$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 3675 = 3 \cdot 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3675.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(29.3450227428\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 525)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 3675.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.00000 q^{3} -1.00000 q^{4} +1.00000 q^{6} +3.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.00000 q^{3} -1.00000 q^{4} +1.00000 q^{6} +3.00000 q^{8} +1.00000 q^{9} +1.00000 q^{12} +3.00000 q^{13} -1.00000 q^{16} -2.00000 q^{17} -1.00000 q^{18} +1.00000 q^{19} -2.00000 q^{23} -3.00000 q^{24} -3.00000 q^{26} -1.00000 q^{27} -8.00000 q^{29} -8.00000 q^{31} -5.00000 q^{32} +2.00000 q^{34} -1.00000 q^{36} -7.00000 q^{37} -1.00000 q^{38} -3.00000 q^{39} +8.00000 q^{43} +2.00000 q^{46} +10.0000 q^{47} +1.00000 q^{48} +2.00000 q^{51} -3.00000 q^{52} +14.0000 q^{53} +1.00000 q^{54} -1.00000 q^{57} +8.00000 q^{58} +10.0000 q^{59} +7.00000 q^{61} +8.00000 q^{62} +7.00000 q^{64} +5.00000 q^{67} +2.00000 q^{68} +2.00000 q^{69} -12.0000 q^{71} +3.00000 q^{72} +11.0000 q^{73} +7.00000 q^{74} -1.00000 q^{76} +3.00000 q^{78} -7.00000 q^{79} +1.00000 q^{81} -14.0000 q^{83} -8.00000 q^{86} +8.00000 q^{87} -6.00000 q^{89} +2.00000 q^{92} +8.00000 q^{93} -10.0000 q^{94} +5.00000 q^{96} -9.00000 q^{97} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107 −0.353553 0.935414i \(-0.615027\pi\)
−0.353553 + 0.935414i \(0.615027\pi\)
\(3\) −1.00000 −0.577350
\(4\) −1.00000 −0.500000
\(5\) 0 0
\(6\) 1.00000 0.408248
\(7\) 0 0
\(8\) 3.00000 1.06066
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) 1.00000 0.288675
\(13\) 3.00000 0.832050 0.416025 0.909353i \(-0.363423\pi\)
0.416025 + 0.909353i \(0.363423\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −1.00000 −0.250000
\(17\) −2.00000 −0.485071 −0.242536 0.970143i \(-0.577979\pi\)
−0.242536 + 0.970143i \(0.577979\pi\)
\(18\) −1.00000 −0.235702
\(19\) 1.00000 0.229416 0.114708 0.993399i \(-0.463407\pi\)
0.114708 + 0.993399i \(0.463407\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −2.00000 −0.417029 −0.208514 0.978019i \(-0.566863\pi\)
−0.208514 + 0.978019i \(0.566863\pi\)
\(24\) −3.00000 −0.612372
\(25\) 0 0
\(26\) −3.00000 −0.588348
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −8.00000 −1.48556 −0.742781 0.669534i \(-0.766494\pi\)
−0.742781 + 0.669534i \(0.766494\pi\)
\(30\) 0 0
\(31\) −8.00000 −1.43684 −0.718421 0.695608i \(-0.755135\pi\)
−0.718421 + 0.695608i \(0.755135\pi\)
\(32\) −5.00000 −0.883883
\(33\) 0 0
\(34\) 2.00000 0.342997
\(35\) 0 0
\(36\) −1.00000 −0.166667
\(37\) −7.00000 −1.15079 −0.575396 0.817875i \(-0.695152\pi\)
−0.575396 + 0.817875i \(0.695152\pi\)
\(38\) −1.00000 −0.162221
\(39\) −3.00000 −0.480384
\(40\) 0 0
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) 0 0
\(43\) 8.00000 1.21999 0.609994 0.792406i \(-0.291172\pi\)
0.609994 + 0.792406i \(0.291172\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 2.00000 0.294884
\(47\) 10.0000 1.45865 0.729325 0.684167i \(-0.239834\pi\)
0.729325 + 0.684167i \(0.239834\pi\)
\(48\) 1.00000 0.144338
\(49\) 0 0
\(50\) 0 0
\(51\) 2.00000 0.280056
\(52\) −3.00000 −0.416025
\(53\) 14.0000 1.92305 0.961524 0.274721i \(-0.0885855\pi\)
0.961524 + 0.274721i \(0.0885855\pi\)
\(54\) 1.00000 0.136083
\(55\) 0 0
\(56\) 0 0
\(57\) −1.00000 −0.132453
\(58\) 8.00000 1.05045
\(59\) 10.0000 1.30189 0.650945 0.759125i \(-0.274373\pi\)
0.650945 + 0.759125i \(0.274373\pi\)
\(60\) 0 0
\(61\) 7.00000 0.896258 0.448129 0.893969i \(-0.352090\pi\)
0.448129 + 0.893969i \(0.352090\pi\)
\(62\) 8.00000 1.01600
\(63\) 0 0
\(64\) 7.00000 0.875000
\(65\) 0 0
\(66\) 0 0
\(67\) 5.00000 0.610847 0.305424 0.952217i \(-0.401202\pi\)
0.305424 + 0.952217i \(0.401202\pi\)
\(68\) 2.00000 0.242536
\(69\) 2.00000 0.240772
\(70\) 0 0
\(71\) −12.0000 −1.42414 −0.712069 0.702109i \(-0.752242\pi\)
−0.712069 + 0.702109i \(0.752242\pi\)
\(72\) 3.00000 0.353553
\(73\) 11.0000 1.28745 0.643726 0.765256i \(-0.277388\pi\)
0.643726 + 0.765256i \(0.277388\pi\)
\(74\) 7.00000 0.813733
\(75\) 0 0
\(76\) −1.00000 −0.114708
\(77\) 0 0
\(78\) 3.00000 0.339683
\(79\) −7.00000 −0.787562 −0.393781 0.919204i \(-0.628833\pi\)
−0.393781 + 0.919204i \(0.628833\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −14.0000 −1.53670 −0.768350 0.640030i \(-0.778922\pi\)
−0.768350 + 0.640030i \(0.778922\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −8.00000 −0.862662
\(87\) 8.00000 0.857690
\(88\) 0 0
\(89\) −6.00000 −0.635999 −0.317999 0.948091i \(-0.603011\pi\)
−0.317999 + 0.948091i \(0.603011\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 2.00000 0.208514
\(93\) 8.00000 0.829561
\(94\) −10.0000 −1.03142
\(95\) 0 0
\(96\) 5.00000 0.510310
\(97\) −9.00000 −0.913812 −0.456906 0.889515i \(-0.651042\pi\)
−0.456906 + 0.889515i \(0.651042\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −16.0000 −1.59206 −0.796030 0.605257i \(-0.793070\pi\)
−0.796030 + 0.605257i \(0.793070\pi\)
\(102\) −2.00000 −0.198030
\(103\) 13.0000 1.28093 0.640464 0.767988i \(-0.278742\pi\)
0.640464 + 0.767988i \(0.278742\pi\)
\(104\) 9.00000 0.882523
\(105\) 0 0
\(106\) −14.0000 −1.35980
\(107\) −6.00000 −0.580042 −0.290021 0.957020i \(-0.593662\pi\)
−0.290021 + 0.957020i \(0.593662\pi\)
\(108\) 1.00000 0.0962250
\(109\) −15.0000 −1.43674 −0.718370 0.695662i \(-0.755111\pi\)
−0.718370 + 0.695662i \(0.755111\pi\)
\(110\) 0 0
\(111\) 7.00000 0.664411
\(112\) 0 0
\(113\) 6.00000 0.564433 0.282216 0.959351i \(-0.408930\pi\)
0.282216 + 0.959351i \(0.408930\pi\)
\(114\) 1.00000 0.0936586
\(115\) 0 0
\(116\) 8.00000 0.742781
\(117\) 3.00000 0.277350
\(118\) −10.0000 −0.920575
\(119\) 0 0
\(120\) 0 0
\(121\) −11.0000 −1.00000
\(122\) −7.00000 −0.633750
\(123\) 0 0
\(124\) 8.00000 0.718421
\(125\) 0 0
\(126\) 0 0
\(127\) −11.0000 −0.976092 −0.488046 0.872818i \(-0.662290\pi\)
−0.488046 + 0.872818i \(0.662290\pi\)
\(128\) 3.00000 0.265165
\(129\) −8.00000 −0.704361
\(130\) 0 0
\(131\) 14.0000 1.22319 0.611593 0.791173i \(-0.290529\pi\)
0.611593 + 0.791173i \(0.290529\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −5.00000 −0.431934
\(135\) 0 0
\(136\) −6.00000 −0.514496
\(137\) 10.0000 0.854358 0.427179 0.904167i \(-0.359507\pi\)
0.427179 + 0.904167i \(0.359507\pi\)
\(138\) −2.00000 −0.170251
\(139\) 3.00000 0.254457 0.127228 0.991873i \(-0.459392\pi\)
0.127228 + 0.991873i \(0.459392\pi\)
\(140\) 0 0
\(141\) −10.0000 −0.842152
\(142\) 12.0000 1.00702
\(143\) 0 0
\(144\) −1.00000 −0.0833333
\(145\) 0 0
\(146\) −11.0000 −0.910366
\(147\) 0 0
\(148\) 7.00000 0.575396
\(149\) −4.00000 −0.327693 −0.163846 0.986486i \(-0.552390\pi\)
−0.163846 + 0.986486i \(0.552390\pi\)
\(150\) 0 0
\(151\) −1.00000 −0.0813788 −0.0406894 0.999172i \(-0.512955\pi\)
−0.0406894 + 0.999172i \(0.512955\pi\)
\(152\) 3.00000 0.243332
\(153\) −2.00000 −0.161690
\(154\) 0 0
\(155\) 0 0
\(156\) 3.00000 0.240192
\(157\) −7.00000 −0.558661 −0.279330 0.960195i \(-0.590112\pi\)
−0.279330 + 0.960195i \(0.590112\pi\)
\(158\) 7.00000 0.556890
\(159\) −14.0000 −1.11027
\(160\) 0 0
\(161\) 0 0
\(162\) −1.00000 −0.0785674
\(163\) 9.00000 0.704934 0.352467 0.935824i \(-0.385343\pi\)
0.352467 + 0.935824i \(0.385343\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 14.0000 1.08661
\(167\) −2.00000 −0.154765 −0.0773823 0.997001i \(-0.524656\pi\)
−0.0773823 + 0.997001i \(0.524656\pi\)
\(168\) 0 0
\(169\) −4.00000 −0.307692
\(170\) 0 0
\(171\) 1.00000 0.0764719
\(172\) −8.00000 −0.609994
\(173\) −18.0000 −1.36851 −0.684257 0.729241i \(-0.739873\pi\)
−0.684257 + 0.729241i \(0.739873\pi\)
\(174\) −8.00000 −0.606478
\(175\) 0 0
\(176\) 0 0
\(177\) −10.0000 −0.751646
\(178\) 6.00000 0.449719
\(179\) −12.0000 −0.896922 −0.448461 0.893802i \(-0.648028\pi\)
−0.448461 + 0.893802i \(0.648028\pi\)
\(180\) 0 0
\(181\) 22.0000 1.63525 0.817624 0.575753i \(-0.195291\pi\)
0.817624 + 0.575753i \(0.195291\pi\)
\(182\) 0 0
\(183\) −7.00000 −0.517455
\(184\) −6.00000 −0.442326
\(185\) 0 0
\(186\) −8.00000 −0.586588
\(187\) 0 0
\(188\) −10.0000 −0.729325
\(189\) 0 0
\(190\) 0 0
\(191\) −8.00000 −0.578860 −0.289430 0.957199i \(-0.593466\pi\)
−0.289430 + 0.957199i \(0.593466\pi\)
\(192\) −7.00000 −0.505181
\(193\) −6.00000 −0.431889 −0.215945 0.976406i \(-0.569283\pi\)
−0.215945 + 0.976406i \(0.569283\pi\)
\(194\) 9.00000 0.646162
\(195\) 0 0
\(196\) 0 0
\(197\) −12.0000 −0.854965 −0.427482 0.904024i \(-0.640599\pi\)
−0.427482 + 0.904024i \(0.640599\pi\)
\(198\) 0 0
\(199\) 11.0000 0.779769 0.389885 0.920864i \(-0.372515\pi\)
0.389885 + 0.920864i \(0.372515\pi\)
\(200\) 0 0
\(201\) −5.00000 −0.352673
\(202\) 16.0000 1.12576
\(203\) 0 0
\(204\) −2.00000 −0.140028
\(205\) 0 0
\(206\) −13.0000 −0.905753
\(207\) −2.00000 −0.139010
\(208\) −3.00000 −0.208013
\(209\) 0 0
\(210\) 0 0
\(211\) −5.00000 −0.344214 −0.172107 0.985078i \(-0.555058\pi\)
−0.172107 + 0.985078i \(0.555058\pi\)
\(212\) −14.0000 −0.961524
\(213\) 12.0000 0.822226
\(214\) 6.00000 0.410152
\(215\) 0 0
\(216\) −3.00000 −0.204124
\(217\) 0 0
\(218\) 15.0000 1.01593
\(219\) −11.0000 −0.743311
\(220\) 0 0
\(221\) −6.00000 −0.403604
\(222\) −7.00000 −0.469809
\(223\) 15.0000 1.00447 0.502237 0.864730i \(-0.332510\pi\)
0.502237 + 0.864730i \(0.332510\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −6.00000 −0.399114
\(227\) −20.0000 −1.32745 −0.663723 0.747978i \(-0.731025\pi\)
−0.663723 + 0.747978i \(0.731025\pi\)
\(228\) 1.00000 0.0662266
\(229\) 13.0000 0.859064 0.429532 0.903052i \(-0.358679\pi\)
0.429532 + 0.903052i \(0.358679\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −24.0000 −1.57568
\(233\) −24.0000 −1.57229 −0.786146 0.618041i \(-0.787927\pi\)
−0.786146 + 0.618041i \(0.787927\pi\)
\(234\) −3.00000 −0.196116
\(235\) 0 0
\(236\) −10.0000 −0.650945
\(237\) 7.00000 0.454699
\(238\) 0 0
\(239\) −28.0000 −1.81117 −0.905585 0.424165i \(-0.860568\pi\)
−0.905585 + 0.424165i \(0.860568\pi\)
\(240\) 0 0
\(241\) 21.0000 1.35273 0.676364 0.736567i \(-0.263554\pi\)
0.676364 + 0.736567i \(0.263554\pi\)
\(242\) 11.0000 0.707107
\(243\) −1.00000 −0.0641500
\(244\) −7.00000 −0.448129
\(245\) 0 0
\(246\) 0 0
\(247\) 3.00000 0.190885
\(248\) −24.0000 −1.52400
\(249\) 14.0000 0.887214
\(250\) 0 0
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 11.0000 0.690201
\(255\) 0 0
\(256\) −17.0000 −1.06250
\(257\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(258\) 8.00000 0.498058
\(259\) 0 0
\(260\) 0 0
\(261\) −8.00000 −0.495188
\(262\) −14.0000 −0.864923
\(263\) −16.0000 −0.986602 −0.493301 0.869859i \(-0.664210\pi\)
−0.493301 + 0.869859i \(0.664210\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 6.00000 0.367194
\(268\) −5.00000 −0.305424
\(269\) −16.0000 −0.975537 −0.487769 0.872973i \(-0.662189\pi\)
−0.487769 + 0.872973i \(0.662189\pi\)
\(270\) 0 0
\(271\) −12.0000 −0.728948 −0.364474 0.931214i \(-0.618751\pi\)
−0.364474 + 0.931214i \(0.618751\pi\)
\(272\) 2.00000 0.121268
\(273\) 0 0
\(274\) −10.0000 −0.604122
\(275\) 0 0
\(276\) −2.00000 −0.120386
\(277\) −5.00000 −0.300421 −0.150210 0.988654i \(-0.547995\pi\)
−0.150210 + 0.988654i \(0.547995\pi\)
\(278\) −3.00000 −0.179928
\(279\) −8.00000 −0.478947
\(280\) 0 0
\(281\) 6.00000 0.357930 0.178965 0.983855i \(-0.442725\pi\)
0.178965 + 0.983855i \(0.442725\pi\)
\(282\) 10.0000 0.595491
\(283\) 19.0000 1.12943 0.564716 0.825285i \(-0.308986\pi\)
0.564716 + 0.825285i \(0.308986\pi\)
\(284\) 12.0000 0.712069
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −5.00000 −0.294628
\(289\) −13.0000 −0.764706
\(290\) 0 0
\(291\) 9.00000 0.527589
\(292\) −11.0000 −0.643726
\(293\) 16.0000 0.934730 0.467365 0.884064i \(-0.345203\pi\)
0.467365 + 0.884064i \(0.345203\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −21.0000 −1.22060
\(297\) 0 0
\(298\) 4.00000 0.231714
\(299\) −6.00000 −0.346989
\(300\) 0 0
\(301\) 0 0
\(302\) 1.00000 0.0575435
\(303\) 16.0000 0.919176
\(304\) −1.00000 −0.0573539
\(305\) 0 0
\(306\) 2.00000 0.114332
\(307\) 12.0000 0.684876 0.342438 0.939540i \(-0.388747\pi\)
0.342438 + 0.939540i \(0.388747\pi\)
\(308\) 0 0
\(309\) −13.0000 −0.739544
\(310\) 0 0
\(311\) −30.0000 −1.70114 −0.850572 0.525859i \(-0.823744\pi\)
−0.850572 + 0.525859i \(0.823744\pi\)
\(312\) −9.00000 −0.509525
\(313\) −14.0000 −0.791327 −0.395663 0.918396i \(-0.629485\pi\)
−0.395663 + 0.918396i \(0.629485\pi\)
\(314\) 7.00000 0.395033
\(315\) 0 0
\(316\) 7.00000 0.393781
\(317\) −14.0000 −0.786318 −0.393159 0.919470i \(-0.628618\pi\)
−0.393159 + 0.919470i \(0.628618\pi\)
\(318\) 14.0000 0.785081
\(319\) 0 0
\(320\) 0 0
\(321\) 6.00000 0.334887
\(322\) 0 0
\(323\) −2.00000 −0.111283
\(324\) −1.00000 −0.0555556
\(325\) 0 0
\(326\) −9.00000 −0.498464
\(327\) 15.0000 0.829502
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 21.0000 1.15426 0.577132 0.816651i \(-0.304172\pi\)
0.577132 + 0.816651i \(0.304172\pi\)
\(332\) 14.0000 0.768350
\(333\) −7.00000 −0.383598
\(334\) 2.00000 0.109435
\(335\) 0 0
\(336\) 0 0
\(337\) 2.00000 0.108947 0.0544735 0.998515i \(-0.482652\pi\)
0.0544735 + 0.998515i \(0.482652\pi\)
\(338\) 4.00000 0.217571
\(339\) −6.00000 −0.325875
\(340\) 0 0
\(341\) 0 0
\(342\) −1.00000 −0.0540738
\(343\) 0 0
\(344\) 24.0000 1.29399
\(345\) 0 0
\(346\) 18.0000 0.967686
\(347\) −10.0000 −0.536828 −0.268414 0.963304i \(-0.586500\pi\)
−0.268414 + 0.963304i \(0.586500\pi\)
\(348\) −8.00000 −0.428845
\(349\) −22.0000 −1.17763 −0.588817 0.808267i \(-0.700406\pi\)
−0.588817 + 0.808267i \(0.700406\pi\)
\(350\) 0 0
\(351\) −3.00000 −0.160128
\(352\) 0 0
\(353\) −24.0000 −1.27739 −0.638696 0.769460i \(-0.720526\pi\)
−0.638696 + 0.769460i \(0.720526\pi\)
\(354\) 10.0000 0.531494
\(355\) 0 0
\(356\) 6.00000 0.317999
\(357\) 0 0
\(358\) 12.0000 0.634220
\(359\) 30.0000 1.58334 0.791670 0.610949i \(-0.209212\pi\)
0.791670 + 0.610949i \(0.209212\pi\)
\(360\) 0 0
\(361\) −18.0000 −0.947368
\(362\) −22.0000 −1.15629
\(363\) 11.0000 0.577350
\(364\) 0 0
\(365\) 0 0
\(366\) 7.00000 0.365896
\(367\) 8.00000 0.417597 0.208798 0.977959i \(-0.433045\pi\)
0.208798 + 0.977959i \(0.433045\pi\)
\(368\) 2.00000 0.104257
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) −8.00000 −0.414781
\(373\) −11.0000 −0.569558 −0.284779 0.958593i \(-0.591920\pi\)
−0.284779 + 0.958593i \(0.591920\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 30.0000 1.54713
\(377\) −24.0000 −1.23606
\(378\) 0 0
\(379\) 35.0000 1.79783 0.898915 0.438124i \(-0.144357\pi\)
0.898915 + 0.438124i \(0.144357\pi\)
\(380\) 0 0
\(381\) 11.0000 0.563547
\(382\) 8.00000 0.409316
\(383\) −10.0000 −0.510976 −0.255488 0.966812i \(-0.582236\pi\)
−0.255488 + 0.966812i \(0.582236\pi\)
\(384\) −3.00000 −0.153093
\(385\) 0 0
\(386\) 6.00000 0.305392
\(387\) 8.00000 0.406663
\(388\) 9.00000 0.456906
\(389\) −36.0000 −1.82527 −0.912636 0.408773i \(-0.865957\pi\)
−0.912636 + 0.408773i \(0.865957\pi\)
\(390\) 0 0
\(391\) 4.00000 0.202289
\(392\) 0 0
\(393\) −14.0000 −0.706207
\(394\) 12.0000 0.604551
\(395\) 0 0
\(396\) 0 0
\(397\) −14.0000 −0.702640 −0.351320 0.936255i \(-0.614267\pi\)
−0.351320 + 0.936255i \(0.614267\pi\)
\(398\) −11.0000 −0.551380
\(399\) 0 0
\(400\) 0 0
\(401\) −12.0000 −0.599251 −0.299626 0.954057i \(-0.596862\pi\)
−0.299626 + 0.954057i \(0.596862\pi\)
\(402\) 5.00000 0.249377
\(403\) −24.0000 −1.19553
\(404\) 16.0000 0.796030
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 6.00000 0.297044
\(409\) 5.00000 0.247234 0.123617 0.992330i \(-0.460551\pi\)
0.123617 + 0.992330i \(0.460551\pi\)
\(410\) 0 0
\(411\) −10.0000 −0.493264
\(412\) −13.0000 −0.640464
\(413\) 0 0
\(414\) 2.00000 0.0982946
\(415\) 0 0
\(416\) −15.0000 −0.735436
\(417\) −3.00000 −0.146911
\(418\) 0 0
\(419\) 24.0000 1.17248 0.586238 0.810139i \(-0.300608\pi\)
0.586238 + 0.810139i \(0.300608\pi\)
\(420\) 0 0
\(421\) −35.0000 −1.70580 −0.852898 0.522078i \(-0.825157\pi\)
−0.852898 + 0.522078i \(0.825157\pi\)
\(422\) 5.00000 0.243396
\(423\) 10.0000 0.486217
\(424\) 42.0000 2.03970
\(425\) 0 0
\(426\) −12.0000 −0.581402
\(427\) 0 0
\(428\) 6.00000 0.290021
\(429\) 0 0
\(430\) 0 0
\(431\) −2.00000 −0.0963366 −0.0481683 0.998839i \(-0.515338\pi\)
−0.0481683 + 0.998839i \(0.515338\pi\)
\(432\) 1.00000 0.0481125
\(433\) 2.00000 0.0961139 0.0480569 0.998845i \(-0.484697\pi\)
0.0480569 + 0.998845i \(0.484697\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 15.0000 0.718370
\(437\) −2.00000 −0.0956730
\(438\) 11.0000 0.525600
\(439\) −11.0000 −0.525001 −0.262501 0.964932i \(-0.584547\pi\)
−0.262501 + 0.964932i \(0.584547\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 6.00000 0.285391
\(443\) −6.00000 −0.285069 −0.142534 0.989790i \(-0.545525\pi\)
−0.142534 + 0.989790i \(0.545525\pi\)
\(444\) −7.00000 −0.332205
\(445\) 0 0
\(446\) −15.0000 −0.710271
\(447\) 4.00000 0.189194
\(448\) 0 0
\(449\) 6.00000 0.283158 0.141579 0.989927i \(-0.454782\pi\)
0.141579 + 0.989927i \(0.454782\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) −6.00000 −0.282216
\(453\) 1.00000 0.0469841
\(454\) 20.0000 0.938647
\(455\) 0 0
\(456\) −3.00000 −0.140488
\(457\) 3.00000 0.140334 0.0701670 0.997535i \(-0.477647\pi\)
0.0701670 + 0.997535i \(0.477647\pi\)
\(458\) −13.0000 −0.607450
\(459\) 2.00000 0.0933520
\(460\) 0 0
\(461\) −2.00000 −0.0931493 −0.0465746 0.998915i \(-0.514831\pi\)
−0.0465746 + 0.998915i \(0.514831\pi\)
\(462\) 0 0
\(463\) −33.0000 −1.53364 −0.766820 0.641862i \(-0.778162\pi\)
−0.766820 + 0.641862i \(0.778162\pi\)
\(464\) 8.00000 0.371391
\(465\) 0 0
\(466\) 24.0000 1.11178
\(467\) 2.00000 0.0925490 0.0462745 0.998929i \(-0.485265\pi\)
0.0462745 + 0.998929i \(0.485265\pi\)
\(468\) −3.00000 −0.138675
\(469\) 0 0
\(470\) 0 0
\(471\) 7.00000 0.322543
\(472\) 30.0000 1.38086
\(473\) 0 0
\(474\) −7.00000 −0.321521
\(475\) 0 0
\(476\) 0 0
\(477\) 14.0000 0.641016
\(478\) 28.0000 1.28069
\(479\) 2.00000 0.0913823 0.0456912 0.998956i \(-0.485451\pi\)
0.0456912 + 0.998956i \(0.485451\pi\)
\(480\) 0 0
\(481\) −21.0000 −0.957518
\(482\) −21.0000 −0.956524
\(483\) 0 0
\(484\) 11.0000 0.500000
\(485\) 0 0
\(486\) 1.00000 0.0453609
\(487\) −8.00000 −0.362515 −0.181257 0.983436i \(-0.558017\pi\)
−0.181257 + 0.983436i \(0.558017\pi\)
\(488\) 21.0000 0.950625
\(489\) −9.00000 −0.406994
\(490\) 0 0
\(491\) −6.00000 −0.270776 −0.135388 0.990793i \(-0.543228\pi\)
−0.135388 + 0.990793i \(0.543228\pi\)
\(492\) 0 0
\(493\) 16.0000 0.720604
\(494\) −3.00000 −0.134976
\(495\) 0 0
\(496\) 8.00000 0.359211
\(497\) 0 0
\(498\) −14.0000 −0.627355
\(499\) −19.0000 −0.850557 −0.425278 0.905063i \(-0.639824\pi\)
−0.425278 + 0.905063i \(0.639824\pi\)
\(500\) 0 0
\(501\) 2.00000 0.0893534
\(502\) 0 0
\(503\) −40.0000 −1.78351 −0.891756 0.452517i \(-0.850526\pi\)
−0.891756 + 0.452517i \(0.850526\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 4.00000 0.177646
\(508\) 11.0000 0.488046
\(509\) −8.00000 −0.354594 −0.177297 0.984157i \(-0.556735\pi\)
−0.177297 + 0.984157i \(0.556735\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 11.0000 0.486136
\(513\) −1.00000 −0.0441511
\(514\) 0 0
\(515\) 0 0
\(516\) 8.00000 0.352180
\(517\) 0 0
\(518\) 0 0
\(519\) 18.0000 0.790112
\(520\) 0 0
\(521\) 34.0000 1.48957 0.744784 0.667306i \(-0.232553\pi\)
0.744784 + 0.667306i \(0.232553\pi\)
\(522\) 8.00000 0.350150
\(523\) 16.0000 0.699631 0.349816 0.936819i \(-0.386244\pi\)
0.349816 + 0.936819i \(0.386244\pi\)
\(524\) −14.0000 −0.611593
\(525\) 0 0
\(526\) 16.0000 0.697633
\(527\) 16.0000 0.696971
\(528\) 0 0
\(529\) −19.0000 −0.826087
\(530\) 0 0
\(531\) 10.0000 0.433963
\(532\) 0 0
\(533\) 0 0
\(534\) −6.00000 −0.259645
\(535\) 0 0
\(536\) 15.0000 0.647901
\(537\) 12.0000 0.517838
\(538\) 16.0000 0.689809
\(539\) 0 0
\(540\) 0 0
\(541\) −3.00000 −0.128980 −0.0644900 0.997918i \(-0.520542\pi\)
−0.0644900 + 0.997918i \(0.520542\pi\)
\(542\) 12.0000 0.515444
\(543\) −22.0000 −0.944110
\(544\) 10.0000 0.428746
\(545\) 0 0
\(546\) 0 0
\(547\) 12.0000 0.513083 0.256541 0.966533i \(-0.417417\pi\)
0.256541 + 0.966533i \(0.417417\pi\)
\(548\) −10.0000 −0.427179
\(549\) 7.00000 0.298753
\(550\) 0 0
\(551\) −8.00000 −0.340811
\(552\) 6.00000 0.255377
\(553\) 0 0
\(554\) 5.00000 0.212430
\(555\) 0 0
\(556\) −3.00000 −0.127228
\(557\) 4.00000 0.169485 0.0847427 0.996403i \(-0.472993\pi\)
0.0847427 + 0.996403i \(0.472993\pi\)
\(558\) 8.00000 0.338667
\(559\) 24.0000 1.01509
\(560\) 0 0
\(561\) 0 0
\(562\) −6.00000 −0.253095
\(563\) −28.0000 −1.18006 −0.590030 0.807382i \(-0.700884\pi\)
−0.590030 + 0.807382i \(0.700884\pi\)
\(564\) 10.0000 0.421076
\(565\) 0 0
\(566\) −19.0000 −0.798630
\(567\) 0 0
\(568\) −36.0000 −1.51053
\(569\) 12.0000 0.503066 0.251533 0.967849i \(-0.419065\pi\)
0.251533 + 0.967849i \(0.419065\pi\)
\(570\) 0 0
\(571\) −3.00000 −0.125546 −0.0627730 0.998028i \(-0.519994\pi\)
−0.0627730 + 0.998028i \(0.519994\pi\)
\(572\) 0 0
\(573\) 8.00000 0.334205
\(574\) 0 0
\(575\) 0 0
\(576\) 7.00000 0.291667
\(577\) 2.00000 0.0832611 0.0416305 0.999133i \(-0.486745\pi\)
0.0416305 + 0.999133i \(0.486745\pi\)
\(578\) 13.0000 0.540729
\(579\) 6.00000 0.249351
\(580\) 0 0
\(581\) 0 0
\(582\) −9.00000 −0.373062
\(583\) 0 0
\(584\) 33.0000 1.36555
\(585\) 0 0
\(586\) −16.0000 −0.660954
\(587\) 6.00000 0.247647 0.123823 0.992304i \(-0.460484\pi\)
0.123823 + 0.992304i \(0.460484\pi\)
\(588\) 0 0
\(589\) −8.00000 −0.329634
\(590\) 0 0
\(591\) 12.0000 0.493614
\(592\) 7.00000 0.287698
\(593\) −42.0000 −1.72473 −0.862367 0.506284i \(-0.831019\pi\)
−0.862367 + 0.506284i \(0.831019\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 4.00000 0.163846
\(597\) −11.0000 −0.450200
\(598\) 6.00000 0.245358
\(599\) 26.0000 1.06233 0.531166 0.847268i \(-0.321754\pi\)
0.531166 + 0.847268i \(0.321754\pi\)
\(600\) 0 0
\(601\) −45.0000 −1.83559 −0.917794 0.397057i \(-0.870032\pi\)
−0.917794 + 0.397057i \(0.870032\pi\)
\(602\) 0 0
\(603\) 5.00000 0.203616
\(604\) 1.00000 0.0406894
\(605\) 0 0
\(606\) −16.0000 −0.649956
\(607\) 43.0000 1.74532 0.872658 0.488332i \(-0.162394\pi\)
0.872658 + 0.488332i \(0.162394\pi\)
\(608\) −5.00000 −0.202777
\(609\) 0 0
\(610\) 0 0
\(611\) 30.0000 1.21367
\(612\) 2.00000 0.0808452
\(613\) −6.00000 −0.242338 −0.121169 0.992632i \(-0.538664\pi\)
−0.121169 + 0.992632i \(0.538664\pi\)
\(614\) −12.0000 −0.484281
\(615\) 0 0
\(616\) 0 0
\(617\) 24.0000 0.966204 0.483102 0.875564i \(-0.339510\pi\)
0.483102 + 0.875564i \(0.339510\pi\)
\(618\) 13.0000 0.522937
\(619\) −12.0000 −0.482321 −0.241160 0.970485i \(-0.577528\pi\)
−0.241160 + 0.970485i \(0.577528\pi\)
\(620\) 0 0
\(621\) 2.00000 0.0802572
\(622\) 30.0000 1.20289
\(623\) 0 0
\(624\) 3.00000 0.120096
\(625\) 0 0
\(626\) 14.0000 0.559553
\(627\) 0 0
\(628\) 7.00000 0.279330
\(629\) 14.0000 0.558217
\(630\) 0 0
\(631\) 45.0000 1.79142 0.895711 0.444637i \(-0.146667\pi\)
0.895711 + 0.444637i \(0.146667\pi\)
\(632\) −21.0000 −0.835335
\(633\) 5.00000 0.198732
\(634\) 14.0000 0.556011
\(635\) 0 0
\(636\) 14.0000 0.555136
\(637\) 0 0
\(638\) 0 0
\(639\) −12.0000 −0.474713
\(640\) 0 0
\(641\) 24.0000 0.947943 0.473972 0.880540i \(-0.342820\pi\)
0.473972 + 0.880540i \(0.342820\pi\)
\(642\) −6.00000 −0.236801
\(643\) 29.0000 1.14365 0.571824 0.820376i \(-0.306236\pi\)
0.571824 + 0.820376i \(0.306236\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 2.00000 0.0786889
\(647\) −12.0000 −0.471769 −0.235884 0.971781i \(-0.575799\pi\)
−0.235884 + 0.971781i \(0.575799\pi\)
\(648\) 3.00000 0.117851
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) −9.00000 −0.352467
\(653\) −44.0000 −1.72185 −0.860927 0.508729i \(-0.830115\pi\)
−0.860927 + 0.508729i \(0.830115\pi\)
\(654\) −15.0000 −0.586546
\(655\) 0 0
\(656\) 0 0
\(657\) 11.0000 0.429151
\(658\) 0 0
\(659\) −24.0000 −0.934907 −0.467454 0.884018i \(-0.654829\pi\)
−0.467454 + 0.884018i \(0.654829\pi\)
\(660\) 0 0
\(661\) 11.0000 0.427850 0.213925 0.976850i \(-0.431375\pi\)
0.213925 + 0.976850i \(0.431375\pi\)
\(662\) −21.0000 −0.816188
\(663\) 6.00000 0.233021
\(664\) −42.0000 −1.62992
\(665\) 0 0
\(666\) 7.00000 0.271244
\(667\) 16.0000 0.619522
\(668\) 2.00000 0.0773823
\(669\) −15.0000 −0.579934
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 1.00000 0.0385472 0.0192736 0.999814i \(-0.493865\pi\)
0.0192736 + 0.999814i \(0.493865\pi\)
\(674\) −2.00000 −0.0770371
\(675\) 0 0
\(676\) 4.00000 0.153846
\(677\) 14.0000 0.538064 0.269032 0.963131i \(-0.413296\pi\)
0.269032 + 0.963131i \(0.413296\pi\)
\(678\) 6.00000 0.230429
\(679\) 0 0
\(680\) 0 0
\(681\) 20.0000 0.766402
\(682\) 0 0
\(683\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(684\) −1.00000 −0.0382360
\(685\) 0 0
\(686\) 0 0
\(687\) −13.0000 −0.495981
\(688\) −8.00000 −0.304997
\(689\) 42.0000 1.60007
\(690\) 0 0
\(691\) −15.0000 −0.570627 −0.285313 0.958434i \(-0.592098\pi\)
−0.285313 + 0.958434i \(0.592098\pi\)
\(692\) 18.0000 0.684257
\(693\) 0 0
\(694\) 10.0000 0.379595
\(695\) 0 0
\(696\) 24.0000 0.909718
\(697\) 0 0
\(698\) 22.0000 0.832712
\(699\) 24.0000 0.907763
\(700\) 0 0
\(701\) 34.0000 1.28416 0.642081 0.766637i \(-0.278071\pi\)
0.642081 + 0.766637i \(0.278071\pi\)
\(702\) 3.00000 0.113228
\(703\) −7.00000 −0.264010
\(704\) 0 0
\(705\) 0 0
\(706\) 24.0000 0.903252
\(707\) 0 0
\(708\) 10.0000 0.375823
\(709\) 1.00000 0.0375558 0.0187779 0.999824i \(-0.494022\pi\)
0.0187779 + 0.999824i \(0.494022\pi\)
\(710\) 0 0
\(711\) −7.00000 −0.262521
\(712\) −18.0000 −0.674579
\(713\) 16.0000 0.599205
\(714\) 0 0
\(715\) 0 0
\(716\) 12.0000 0.448461
\(717\) 28.0000 1.04568
\(718\) −30.0000 −1.11959
\(719\) −4.00000 −0.149175 −0.0745874 0.997214i \(-0.523764\pi\)
−0.0745874 + 0.997214i \(0.523764\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 18.0000 0.669891
\(723\) −21.0000 −0.780998
\(724\) −22.0000 −0.817624
\(725\) 0 0
\(726\) −11.0000 −0.408248
\(727\) −43.0000 −1.59478 −0.797391 0.603463i \(-0.793787\pi\)
−0.797391 + 0.603463i \(0.793787\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −16.0000 −0.591781
\(732\) 7.00000 0.258727
\(733\) 31.0000 1.14501 0.572506 0.819901i \(-0.305971\pi\)
0.572506 + 0.819901i \(0.305971\pi\)
\(734\) −8.00000 −0.295285
\(735\) 0 0
\(736\) 10.0000 0.368605
\(737\) 0 0
\(738\) 0 0
\(739\) −49.0000 −1.80249 −0.901247 0.433306i \(-0.857347\pi\)
−0.901247 + 0.433306i \(0.857347\pi\)
\(740\) 0 0
\(741\) −3.00000 −0.110208
\(742\) 0 0
\(743\) −6.00000 −0.220119 −0.110059 0.993925i \(-0.535104\pi\)
−0.110059 + 0.993925i \(0.535104\pi\)
\(744\) 24.0000 0.879883
\(745\) 0 0
\(746\) 11.0000 0.402739
\(747\) −14.0000 −0.512233
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 23.0000 0.839282 0.419641 0.907690i \(-0.362156\pi\)
0.419641 + 0.907690i \(0.362156\pi\)
\(752\) −10.0000 −0.364662
\(753\) 0 0
\(754\) 24.0000 0.874028
\(755\) 0 0
\(756\) 0 0
\(757\) 43.0000 1.56286 0.781431 0.623992i \(-0.214490\pi\)
0.781431 + 0.623992i \(0.214490\pi\)
\(758\) −35.0000 −1.27126
\(759\) 0 0
\(760\) 0 0
\(761\) −6.00000 −0.217500 −0.108750 0.994069i \(-0.534685\pi\)
−0.108750 + 0.994069i \(0.534685\pi\)
\(762\) −11.0000 −0.398488
\(763\) 0 0
\(764\) 8.00000 0.289430
\(765\) 0 0
\(766\) 10.0000 0.361315
\(767\) 30.0000 1.08324
\(768\) 17.0000 0.613435
\(769\) −10.0000 −0.360609 −0.180305 0.983611i \(-0.557708\pi\)
−0.180305 + 0.983611i \(0.557708\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 6.00000 0.215945
\(773\) −48.0000 −1.72644 −0.863220 0.504828i \(-0.831556\pi\)
−0.863220 + 0.504828i \(0.831556\pi\)
\(774\) −8.00000 −0.287554
\(775\) 0 0
\(776\) −27.0000 −0.969244
\(777\) 0 0
\(778\) 36.0000 1.29066
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) −4.00000 −0.143040
\(783\) 8.00000 0.285897
\(784\) 0 0
\(785\) 0 0
\(786\) 14.0000 0.499363
\(787\) 17.0000 0.605985 0.302992 0.952993i \(-0.402014\pi\)
0.302992 + 0.952993i \(0.402014\pi\)
\(788\) 12.0000 0.427482
\(789\) 16.0000 0.569615
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 21.0000 0.745732
\(794\) 14.0000 0.496841
\(795\) 0 0
\(796\) −11.0000 −0.389885
\(797\) −30.0000 −1.06265 −0.531327 0.847167i \(-0.678307\pi\)
−0.531327 + 0.847167i \(0.678307\pi\)
\(798\) 0 0
\(799\) −20.0000 −0.707549
\(800\) 0 0
\(801\) −6.00000 −0.212000
\(802\) 12.0000 0.423735
\(803\) 0 0
\(804\) 5.00000 0.176336
\(805\) 0 0
\(806\) 24.0000 0.845364
\(807\) 16.0000 0.563227
\(808\) −48.0000 −1.68863
\(809\) −6.00000 −0.210949 −0.105474 0.994422i \(-0.533636\pi\)
−0.105474 + 0.994422i \(0.533636\pi\)
\(810\) 0 0
\(811\) 3.00000 0.105344 0.0526721 0.998612i \(-0.483226\pi\)
0.0526721 + 0.998612i \(0.483226\pi\)
\(812\) 0 0
\(813\) 12.0000 0.420858
\(814\) 0 0
\(815\) 0 0
\(816\) −2.00000 −0.0700140
\(817\) 8.00000 0.279885
\(818\) −5.00000 −0.174821
\(819\) 0 0
\(820\) 0 0
\(821\) −48.0000 −1.67521 −0.837606 0.546275i \(-0.816045\pi\)
−0.837606 + 0.546275i \(0.816045\pi\)
\(822\) 10.0000 0.348790
\(823\) −5.00000 −0.174289 −0.0871445 0.996196i \(-0.527774\pi\)
−0.0871445 + 0.996196i \(0.527774\pi\)
\(824\) 39.0000 1.35863
\(825\) 0 0
\(826\) 0 0
\(827\) 24.0000 0.834562 0.417281 0.908778i \(-0.362983\pi\)
0.417281 + 0.908778i \(0.362983\pi\)
\(828\) 2.00000 0.0695048
\(829\) −15.0000 −0.520972 −0.260486 0.965478i \(-0.583883\pi\)
−0.260486 + 0.965478i \(0.583883\pi\)
\(830\) 0 0
\(831\) 5.00000 0.173448
\(832\) 21.0000 0.728044
\(833\) 0 0
\(834\) 3.00000 0.103882
\(835\) 0 0
\(836\) 0 0
\(837\) 8.00000 0.276520
\(838\) −24.0000 −0.829066
\(839\) −42.0000 −1.45000 −0.725001 0.688748i \(-0.758161\pi\)
−0.725001 + 0.688748i \(0.758161\pi\)
\(840\) 0 0
\(841\) 35.0000 1.20690
\(842\) 35.0000 1.20618
\(843\) −6.00000 −0.206651
\(844\) 5.00000 0.172107
\(845\) 0 0
\(846\) −10.0000 −0.343807
\(847\) 0 0
\(848\) −14.0000 −0.480762
\(849\) −19.0000 −0.652078
\(850\) 0 0
\(851\) 14.0000 0.479914
\(852\) −12.0000 −0.411113
\(853\) 6.00000 0.205436 0.102718 0.994711i \(-0.467246\pi\)
0.102718 + 0.994711i \(0.467246\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −18.0000 −0.615227
\(857\) −18.0000 −0.614868 −0.307434 0.951569i \(-0.599470\pi\)
−0.307434 + 0.951569i \(0.599470\pi\)
\(858\) 0 0
\(859\) −52.0000 −1.77422 −0.887109 0.461561i \(-0.847290\pi\)
−0.887109 + 0.461561i \(0.847290\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 2.00000 0.0681203
\(863\) −6.00000 −0.204242 −0.102121 0.994772i \(-0.532563\pi\)
−0.102121 + 0.994772i \(0.532563\pi\)
\(864\) 5.00000 0.170103
\(865\) 0 0
\(866\) −2.00000 −0.0679628
\(867\) 13.0000 0.441503
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 15.0000 0.508256
\(872\) −45.0000 −1.52389
\(873\) −9.00000 −0.304604
\(874\) 2.00000 0.0676510
\(875\) 0 0
\(876\) 11.0000 0.371656
\(877\) −23.0000 −0.776655 −0.388327 0.921521i \(-0.626947\pi\)
−0.388327 + 0.921521i \(0.626947\pi\)
\(878\) 11.0000 0.371232
\(879\) −16.0000 −0.539667
\(880\) 0 0
\(881\) 12.0000 0.404290 0.202145 0.979356i \(-0.435209\pi\)
0.202145 + 0.979356i \(0.435209\pi\)
\(882\) 0 0
\(883\) −31.0000 −1.04323 −0.521617 0.853180i \(-0.674671\pi\)
−0.521617 + 0.853180i \(0.674671\pi\)
\(884\) 6.00000 0.201802
\(885\) 0 0
\(886\) 6.00000 0.201574
\(887\) −58.0000 −1.94745 −0.973725 0.227728i \(-0.926870\pi\)
−0.973725 + 0.227728i \(0.926870\pi\)
\(888\) 21.0000 0.704714
\(889\) 0 0
\(890\) 0 0
\(891\) 0 0
\(892\) −15.0000 −0.502237
\(893\) 10.0000 0.334637
\(894\) −4.00000 −0.133780
\(895\) 0 0
\(896\) 0 0
\(897\) 6.00000 0.200334
\(898\) −6.00000 −0.200223
\(899\) 64.0000 2.13452
\(900\) 0 0
\(901\) −28.0000 −0.932815
\(902\) 0 0
\(903\) 0 0
\(904\) 18.0000 0.598671
\(905\) 0 0
\(906\) −1.00000 −0.0332228
\(907\) −1.00000 −0.0332045 −0.0166022 0.999862i \(-0.505285\pi\)
−0.0166022 + 0.999862i \(0.505285\pi\)
\(908\) 20.0000 0.663723
\(909\) −16.0000 −0.530687
\(910\) 0 0
\(911\) 54.0000 1.78910 0.894550 0.446968i \(-0.147496\pi\)
0.894550 + 0.446968i \(0.147496\pi\)
\(912\) 1.00000 0.0331133
\(913\) 0 0
\(914\) −3.00000 −0.0992312
\(915\) 0 0
\(916\) −13.0000 −0.429532
\(917\) 0 0
\(918\) −2.00000 −0.0660098
\(919\) 24.0000 0.791687 0.395843 0.918318i \(-0.370452\pi\)
0.395843 + 0.918318i \(0.370452\pi\)
\(920\) 0 0
\(921\) −12.0000 −0.395413
\(922\) 2.00000 0.0658665
\(923\) −36.0000 −1.18495
\(924\) 0 0
\(925\) 0 0
\(926\) 33.0000 1.08445
\(927\) 13.0000 0.426976
\(928\) 40.0000 1.31306
\(929\) −44.0000 −1.44359 −0.721797 0.692105i \(-0.756683\pi\)
−0.721797 + 0.692105i \(0.756683\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 24.0000 0.786146
\(933\) 30.0000 0.982156
\(934\) −2.00000 −0.0654420
\(935\) 0 0
\(936\) 9.00000 0.294174
\(937\) −22.0000 −0.718709 −0.359354 0.933201i \(-0.617003\pi\)
−0.359354 + 0.933201i \(0.617003\pi\)
\(938\) 0 0
\(939\) 14.0000 0.456873
\(940\) 0 0
\(941\) 42.0000 1.36916 0.684580 0.728937i \(-0.259985\pi\)
0.684580 + 0.728937i \(0.259985\pi\)
\(942\) −7.00000 −0.228072
\(943\) 0 0
\(944\) −10.0000 −0.325472
\(945\) 0 0
\(946\) 0 0
\(947\) 22.0000 0.714904 0.357452 0.933932i \(-0.383646\pi\)
0.357452 + 0.933932i \(0.383646\pi\)
\(948\) −7.00000 −0.227349
\(949\) 33.0000 1.07123
\(950\) 0 0
\(951\) 14.0000 0.453981
\(952\) 0 0
\(953\) 20.0000 0.647864 0.323932 0.946080i \(-0.394995\pi\)
0.323932 + 0.946080i \(0.394995\pi\)
\(954\) −14.0000 −0.453267
\(955\) 0 0
\(956\) 28.0000 0.905585
\(957\) 0 0
\(958\) −2.00000 −0.0646171
\(959\) 0 0
\(960\) 0 0
\(961\) 33.0000 1.06452
\(962\) 21.0000 0.677067
\(963\) −6.00000 −0.193347
\(964\) −21.0000 −0.676364
\(965\) 0 0
\(966\) 0 0
\(967\) 23.0000 0.739630 0.369815 0.929105i \(-0.379421\pi\)
0.369815 + 0.929105i \(0.379421\pi\)
\(968\) −33.0000 −1.06066
\(969\) 2.00000 0.0642493
\(970\) 0 0
\(971\) 8.00000 0.256732 0.128366 0.991727i \(-0.459027\pi\)
0.128366 + 0.991727i \(0.459027\pi\)
\(972\) 1.00000 0.0320750
\(973\) 0 0
\(974\) 8.00000 0.256337
\(975\) 0 0
\(976\) −7.00000 −0.224065
\(977\) 40.0000 1.27971 0.639857 0.768494i \(-0.278994\pi\)
0.639857 + 0.768494i \(0.278994\pi\)
\(978\) 9.00000 0.287788
\(979\) 0 0
\(980\) 0 0
\(981\) −15.0000 −0.478913
\(982\) 6.00000 0.191468
\(983\) 22.0000 0.701691 0.350846 0.936433i \(-0.385894\pi\)
0.350846 + 0.936433i \(0.385894\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) −16.0000 −0.509544
\(987\) 0 0
\(988\) −3.00000 −0.0954427
\(989\) −16.0000 −0.508770
\(990\) 0 0
\(991\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(992\) 40.0000 1.27000
\(993\) −21.0000 −0.666415
\(994\) 0 0
\(995\) 0 0
\(996\) −14.0000 −0.443607
\(997\) 37.0000 1.17180 0.585901 0.810383i \(-0.300741\pi\)
0.585901 + 0.810383i \(0.300741\pi\)
\(998\) 19.0000 0.601434
\(999\) 7.00000 0.221470
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 3675.2.a.e.1.1 1
5.4 even 2 3675.2.a.m.1.1 1
7.2 even 3 525.2.i.d.151.1 yes 2
7.4 even 3 525.2.i.d.226.1 yes 2
7.6 odd 2 3675.2.a.g.1.1 1
35.2 odd 12 525.2.r.c.424.1 4
35.4 even 6 525.2.i.b.226.1 yes 2
35.9 even 6 525.2.i.b.151.1 2
35.18 odd 12 525.2.r.c.499.1 4
35.23 odd 12 525.2.r.c.424.2 4
35.32 odd 12 525.2.r.c.499.2 4
35.34 odd 2 3675.2.a.k.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
525.2.i.b.151.1 2 35.9 even 6
525.2.i.b.226.1 yes 2 35.4 even 6
525.2.i.d.151.1 yes 2 7.2 even 3
525.2.i.d.226.1 yes 2 7.4 even 3
525.2.r.c.424.1 4 35.2 odd 12
525.2.r.c.424.2 4 35.23 odd 12
525.2.r.c.499.1 4 35.18 odd 12
525.2.r.c.499.2 4 35.32 odd 12
3675.2.a.e.1.1 1 1.1 even 1 trivial
3675.2.a.g.1.1 1 7.6 odd 2
3675.2.a.k.1.1 1 35.34 odd 2
3675.2.a.m.1.1 1 5.4 even 2