Properties

Label 2601.2.a.e.1.1
Level $2601$
Weight $2$
Character 2601.1
Self dual yes
Analytic conductor $20.769$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2601 = 3^{2} \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2601.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(20.7690895657\)
Analytic rank: \(1\)
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
Character \(\chi\) \(=\) 2601.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.00000 q^{4} +2.00000 q^{5} -1.00000 q^{7} +3.00000 q^{8} +O(q^{10})\) \(q-1.00000 q^{2} -1.00000 q^{4} +2.00000 q^{5} -1.00000 q^{7} +3.00000 q^{8} -2.00000 q^{10} -6.00000 q^{11} +1.00000 q^{13} +1.00000 q^{14} -1.00000 q^{16} +5.00000 q^{19} -2.00000 q^{20} +6.00000 q^{22} +2.00000 q^{23} -1.00000 q^{25} -1.00000 q^{26} +1.00000 q^{28} +6.00000 q^{29} -7.00000 q^{31} -5.00000 q^{32} -2.00000 q^{35} -7.00000 q^{37} -5.00000 q^{38} +6.00000 q^{40} +6.00000 q^{41} +7.00000 q^{43} +6.00000 q^{44} -2.00000 q^{46} -12.0000 q^{47} -6.00000 q^{49} +1.00000 q^{50} -1.00000 q^{52} +12.0000 q^{53} -12.0000 q^{55} -3.00000 q^{56} -6.00000 q^{58} -6.00000 q^{59} -11.0000 q^{61} +7.00000 q^{62} +7.00000 q^{64} +2.00000 q^{65} -11.0000 q^{67} +2.00000 q^{70} -2.00000 q^{71} +6.00000 q^{73} +7.00000 q^{74} -5.00000 q^{76} +6.00000 q^{77} -2.00000 q^{80} -6.00000 q^{82} +2.00000 q^{83} -7.00000 q^{86} -18.0000 q^{88} +16.0000 q^{89} -1.00000 q^{91} -2.00000 q^{92} +12.0000 q^{94} +10.0000 q^{95} -17.0000 q^{97} +6.00000 q^{98} +O(q^{100})\)

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 \(0.615027\pi\)
\(3\) 0 0
\(4\) −1.00000 −0.500000
\(5\) 2.00000 0.894427 0.447214 0.894427i \(-0.352416\pi\)
0.447214 + 0.894427i \(0.352416\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964 −0.188982 0.981981i \(-0.560519\pi\)
−0.188982 + 0.981981i \(0.560519\pi\)
\(8\) 3.00000 1.06066
\(9\) 0 0
\(10\) −2.00000 −0.632456
\(11\) −6.00000 −1.80907 −0.904534 0.426401i \(-0.859781\pi\)
−0.904534 + 0.426401i \(0.859781\pi\)
\(12\) 0 0
\(13\) 1.00000 0.277350 0.138675 0.990338i \(-0.455716\pi\)
0.138675 + 0.990338i \(0.455716\pi\)
\(14\) 1.00000 0.267261
\(15\) 0 0
\(16\) −1.00000 −0.250000
\(17\) 0 0
\(18\) 0 0
\(19\) 5.00000 1.14708 0.573539 0.819178i \(-0.305570\pi\)
0.573539 + 0.819178i \(0.305570\pi\)
\(20\) −2.00000 −0.447214
\(21\) 0 0
\(22\) 6.00000 1.27920
\(23\) 2.00000 0.417029 0.208514 0.978019i \(-0.433137\pi\)
0.208514 + 0.978019i \(0.433137\pi\)
\(24\) 0 0
\(25\) −1.00000 −0.200000
\(26\) −1.00000 −0.196116
\(27\) 0 0
\(28\) 1.00000 0.188982
\(29\) 6.00000 1.11417 0.557086 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) 0 0
\(31\) −7.00000 −1.25724 −0.628619 0.777714i \(-0.716379\pi\)
−0.628619 + 0.777714i \(0.716379\pi\)
\(32\) −5.00000 −0.883883
\(33\) 0 0
\(34\) 0 0
\(35\) −2.00000 −0.338062
\(36\) 0 0
\(37\) −7.00000 −1.15079 −0.575396 0.817875i \(-0.695152\pi\)
−0.575396 + 0.817875i \(0.695152\pi\)
\(38\) −5.00000 −0.811107
\(39\) 0 0
\(40\) 6.00000 0.948683
\(41\) 6.00000 0.937043 0.468521 0.883452i \(-0.344787\pi\)
0.468521 + 0.883452i \(0.344787\pi\)
\(42\) 0 0
\(43\) 7.00000 1.06749 0.533745 0.845645i \(-0.320784\pi\)
0.533745 + 0.845645i \(0.320784\pi\)
\(44\) 6.00000 0.904534
\(45\) 0 0
\(46\) −2.00000 −0.294884
\(47\) −12.0000 −1.75038 −0.875190 0.483779i \(-0.839264\pi\)
−0.875190 + 0.483779i \(0.839264\pi\)
\(48\) 0 0
\(49\) −6.00000 −0.857143
\(50\) 1.00000 0.141421
\(51\) 0 0
\(52\) −1.00000 −0.138675
\(53\) 12.0000 1.64833 0.824163 0.566352i \(-0.191646\pi\)
0.824163 + 0.566352i \(0.191646\pi\)
\(54\) 0 0
\(55\) −12.0000 −1.61808
\(56\) −3.00000 −0.400892
\(57\) 0 0
\(58\) −6.00000 −0.787839
\(59\) −6.00000 −0.781133 −0.390567 0.920575i \(-0.627721\pi\)
−0.390567 + 0.920575i \(0.627721\pi\)
\(60\) 0 0
\(61\) −11.0000 −1.40841 −0.704203 0.709999i \(-0.748695\pi\)
−0.704203 + 0.709999i \(0.748695\pi\)
\(62\) 7.00000 0.889001
\(63\) 0 0
\(64\) 7.00000 0.875000
\(65\) 2.00000 0.248069
\(66\) 0 0
\(67\) −11.0000 −1.34386 −0.671932 0.740613i \(-0.734535\pi\)
−0.671932 + 0.740613i \(0.734535\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 2.00000 0.239046
\(71\) −2.00000 −0.237356 −0.118678 0.992933i \(-0.537866\pi\)
−0.118678 + 0.992933i \(0.537866\pi\)
\(72\) 0 0
\(73\) 6.00000 0.702247 0.351123 0.936329i \(-0.385800\pi\)
0.351123 + 0.936329i \(0.385800\pi\)
\(74\) 7.00000 0.813733
\(75\) 0 0
\(76\) −5.00000 −0.573539
\(77\) 6.00000 0.683763
\(78\) 0 0
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) −2.00000 −0.223607
\(81\) 0 0
\(82\) −6.00000 −0.662589
\(83\) 2.00000 0.219529 0.109764 0.993958i \(-0.464990\pi\)
0.109764 + 0.993958i \(0.464990\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −7.00000 −0.754829
\(87\) 0 0
\(88\) −18.0000 −1.91881
\(89\) 16.0000 1.69600 0.847998 0.529999i \(-0.177808\pi\)
0.847998 + 0.529999i \(0.177808\pi\)
\(90\) 0 0
\(91\) −1.00000 −0.104828
\(92\) −2.00000 −0.208514
\(93\) 0 0
\(94\) 12.0000 1.23771
\(95\) 10.0000 1.02598
\(96\) 0 0
\(97\) −17.0000 −1.72609 −0.863044 0.505128i \(-0.831445\pi\)
−0.863044 + 0.505128i \(0.831445\pi\)
\(98\) 6.00000 0.606092
\(99\) 0 0
\(100\) 1.00000 0.100000
\(101\) −4.00000 −0.398015 −0.199007 0.979998i \(-0.563772\pi\)
−0.199007 + 0.979998i \(0.563772\pi\)
\(102\) 0 0
\(103\) −7.00000 −0.689730 −0.344865 0.938652i \(-0.612075\pi\)
−0.344865 + 0.938652i \(0.612075\pi\)
\(104\) 3.00000 0.294174
\(105\) 0 0
\(106\) −12.0000 −1.16554
\(107\) 16.0000 1.54678 0.773389 0.633932i \(-0.218560\pi\)
0.773389 + 0.633932i \(0.218560\pi\)
\(108\) 0 0
\(109\) −6.00000 −0.574696 −0.287348 0.957826i \(-0.592774\pi\)
−0.287348 + 0.957826i \(0.592774\pi\)
\(110\) 12.0000 1.14416
\(111\) 0 0
\(112\) 1.00000 0.0944911
\(113\) −4.00000 −0.376288 −0.188144 0.982141i \(-0.560247\pi\)
−0.188144 + 0.982141i \(0.560247\pi\)
\(114\) 0 0
\(115\) 4.00000 0.373002
\(116\) −6.00000 −0.557086
\(117\) 0 0
\(118\) 6.00000 0.552345
\(119\) 0 0
\(120\) 0 0
\(121\) 25.0000 2.27273
\(122\) 11.0000 0.995893
\(123\) 0 0
\(124\) 7.00000 0.628619
\(125\) −12.0000 −1.07331
\(126\) 0 0
\(127\) 5.00000 0.443678 0.221839 0.975083i \(-0.428794\pi\)
0.221839 + 0.975083i \(0.428794\pi\)
\(128\) 3.00000 0.265165
\(129\) 0 0
\(130\) −2.00000 −0.175412
\(131\) −10.0000 −0.873704 −0.436852 0.899533i \(-0.643907\pi\)
−0.436852 + 0.899533i \(0.643907\pi\)
\(132\) 0 0
\(133\) −5.00000 −0.433555
\(134\) 11.0000 0.950255
\(135\) 0 0
\(136\) 0 0
\(137\) −6.00000 −0.512615 −0.256307 0.966595i \(-0.582506\pi\)
−0.256307 + 0.966595i \(0.582506\pi\)
\(138\) 0 0
\(139\) −13.0000 −1.10265 −0.551323 0.834292i \(-0.685877\pi\)
−0.551323 + 0.834292i \(0.685877\pi\)
\(140\) 2.00000 0.169031
\(141\) 0 0
\(142\) 2.00000 0.167836
\(143\) −6.00000 −0.501745
\(144\) 0 0
\(145\) 12.0000 0.996546
\(146\) −6.00000 −0.496564
\(147\) 0 0
\(148\) 7.00000 0.575396
\(149\) 14.0000 1.14692 0.573462 0.819232i \(-0.305600\pi\)
0.573462 + 0.819232i \(0.305600\pi\)
\(150\) 0 0
\(151\) 5.00000 0.406894 0.203447 0.979086i \(-0.434786\pi\)
0.203447 + 0.979086i \(0.434786\pi\)
\(152\) 15.0000 1.21666
\(153\) 0 0
\(154\) −6.00000 −0.483494
\(155\) −14.0000 −1.12451
\(156\) 0 0
\(157\) −17.0000 −1.35675 −0.678374 0.734717i \(-0.737315\pi\)
−0.678374 + 0.734717i \(0.737315\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) −10.0000 −0.790569
\(161\) −2.00000 −0.157622
\(162\) 0 0
\(163\) −12.0000 −0.939913 −0.469956 0.882690i \(-0.655730\pi\)
−0.469956 + 0.882690i \(0.655730\pi\)
\(164\) −6.00000 −0.468521
\(165\) 0 0
\(166\) −2.00000 −0.155230
\(167\) −8.00000 −0.619059 −0.309529 0.950890i \(-0.600171\pi\)
−0.309529 + 0.950890i \(0.600171\pi\)
\(168\) 0 0
\(169\) −12.0000 −0.923077
\(170\) 0 0
\(171\) 0 0
\(172\) −7.00000 −0.533745
\(173\) −16.0000 −1.21646 −0.608229 0.793762i \(-0.708120\pi\)
−0.608229 + 0.793762i \(0.708120\pi\)
\(174\) 0 0
\(175\) 1.00000 0.0755929
\(176\) 6.00000 0.452267
\(177\) 0 0
\(178\) −16.0000 −1.19925
\(179\) −18.0000 −1.34538 −0.672692 0.739923i \(-0.734862\pi\)
−0.672692 + 0.739923i \(0.734862\pi\)
\(180\) 0 0
\(181\) −13.0000 −0.966282 −0.483141 0.875542i \(-0.660504\pi\)
−0.483141 + 0.875542i \(0.660504\pi\)
\(182\) 1.00000 0.0741249
\(183\) 0 0
\(184\) 6.00000 0.442326
\(185\) −14.0000 −1.02930
\(186\) 0 0
\(187\) 0 0
\(188\) 12.0000 0.875190
\(189\) 0 0
\(190\) −10.0000 −0.725476
\(191\) −10.0000 −0.723575 −0.361787 0.932261i \(-0.617833\pi\)
−0.361787 + 0.932261i \(0.617833\pi\)
\(192\) 0 0
\(193\) 1.00000 0.0719816 0.0359908 0.999352i \(-0.488541\pi\)
0.0359908 + 0.999352i \(0.488541\pi\)
\(194\) 17.0000 1.22053
\(195\) 0 0
\(196\) 6.00000 0.428571
\(197\) −12.0000 −0.854965 −0.427482 0.904024i \(-0.640599\pi\)
−0.427482 + 0.904024i \(0.640599\pi\)
\(198\) 0 0
\(199\) −16.0000 −1.13421 −0.567105 0.823646i \(-0.691937\pi\)
−0.567105 + 0.823646i \(0.691937\pi\)
\(200\) −3.00000 −0.212132
\(201\) 0 0
\(202\) 4.00000 0.281439
\(203\) −6.00000 −0.421117
\(204\) 0 0
\(205\) 12.0000 0.838116
\(206\) 7.00000 0.487713
\(207\) 0 0
\(208\) −1.00000 −0.0693375
\(209\) −30.0000 −2.07514
\(210\) 0 0
\(211\) 1.00000 0.0688428 0.0344214 0.999407i \(-0.489041\pi\)
0.0344214 + 0.999407i \(0.489041\pi\)
\(212\) −12.0000 −0.824163
\(213\) 0 0
\(214\) −16.0000 −1.09374
\(215\) 14.0000 0.954792
\(216\) 0 0
\(217\) 7.00000 0.475191
\(218\) 6.00000 0.406371
\(219\) 0 0
\(220\) 12.0000 0.809040
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(224\) 5.00000 0.334077
\(225\) 0 0
\(226\) 4.00000 0.266076
\(227\) −18.0000 −1.19470 −0.597351 0.801980i \(-0.703780\pi\)
−0.597351 + 0.801980i \(0.703780\pi\)
\(228\) 0 0
\(229\) 6.00000 0.396491 0.198246 0.980152i \(-0.436476\pi\)
0.198246 + 0.980152i \(0.436476\pi\)
\(230\) −4.00000 −0.263752
\(231\) 0 0
\(232\) 18.0000 1.18176
\(233\) 12.0000 0.786146 0.393073 0.919507i \(-0.371412\pi\)
0.393073 + 0.919507i \(0.371412\pi\)
\(234\) 0 0
\(235\) −24.0000 −1.56559
\(236\) 6.00000 0.390567
\(237\) 0 0
\(238\) 0 0
\(239\) 20.0000 1.29369 0.646846 0.762620i \(-0.276088\pi\)
0.646846 + 0.762620i \(0.276088\pi\)
\(240\) 0 0
\(241\) 18.0000 1.15948 0.579741 0.814801i \(-0.303154\pi\)
0.579741 + 0.814801i \(0.303154\pi\)
\(242\) −25.0000 −1.60706
\(243\) 0 0
\(244\) 11.0000 0.704203
\(245\) −12.0000 −0.766652
\(246\) 0 0
\(247\) 5.00000 0.318142
\(248\) −21.0000 −1.33350
\(249\) 0 0
\(250\) 12.0000 0.758947
\(251\) −6.00000 −0.378717 −0.189358 0.981908i \(-0.560641\pi\)
−0.189358 + 0.981908i \(0.560641\pi\)
\(252\) 0 0
\(253\) −12.0000 −0.754434
\(254\) −5.00000 −0.313728
\(255\) 0 0
\(256\) −17.0000 −1.06250
\(257\) −24.0000 −1.49708 −0.748539 0.663090i \(-0.769245\pi\)
−0.748539 + 0.663090i \(0.769245\pi\)
\(258\) 0 0
\(259\) 7.00000 0.434959
\(260\) −2.00000 −0.124035
\(261\) 0 0
\(262\) 10.0000 0.617802
\(263\) −16.0000 −0.986602 −0.493301 0.869859i \(-0.664210\pi\)
−0.493301 + 0.869859i \(0.664210\pi\)
\(264\) 0 0
\(265\) 24.0000 1.47431
\(266\) 5.00000 0.306570
\(267\) 0 0
\(268\) 11.0000 0.671932
\(269\) 14.0000 0.853595 0.426798 0.904347i \(-0.359642\pi\)
0.426798 + 0.904347i \(0.359642\pi\)
\(270\) 0 0
\(271\) −13.0000 −0.789694 −0.394847 0.918747i \(-0.629202\pi\)
−0.394847 + 0.918747i \(0.629202\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 6.00000 0.362473
\(275\) 6.00000 0.361814
\(276\) 0 0
\(277\) −5.00000 −0.300421 −0.150210 0.988654i \(-0.547995\pi\)
−0.150210 + 0.988654i \(0.547995\pi\)
\(278\) 13.0000 0.779688
\(279\) 0 0
\(280\) −6.00000 −0.358569
\(281\) 18.0000 1.07379 0.536895 0.843649i \(-0.319597\pi\)
0.536895 + 0.843649i \(0.319597\pi\)
\(282\) 0 0
\(283\) −11.0000 −0.653882 −0.326941 0.945045i \(-0.606018\pi\)
−0.326941 + 0.945045i \(0.606018\pi\)
\(284\) 2.00000 0.118678
\(285\) 0 0
\(286\) 6.00000 0.354787
\(287\) −6.00000 −0.354169
\(288\) 0 0
\(289\) 0 0
\(290\) −12.0000 −0.704664
\(291\) 0 0
\(292\) −6.00000 −0.351123
\(293\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(294\) 0 0
\(295\) −12.0000 −0.698667
\(296\) −21.0000 −1.22060
\(297\) 0 0
\(298\) −14.0000 −0.810998
\(299\) 2.00000 0.115663
\(300\) 0 0
\(301\) −7.00000 −0.403473
\(302\) −5.00000 −0.287718
\(303\) 0 0
\(304\) −5.00000 −0.286770
\(305\) −22.0000 −1.25972
\(306\) 0 0
\(307\) 12.0000 0.684876 0.342438 0.939540i \(-0.388747\pi\)
0.342438 + 0.939540i \(0.388747\pi\)
\(308\) −6.00000 −0.341882
\(309\) 0 0
\(310\) 14.0000 0.795147
\(311\) −4.00000 −0.226819 −0.113410 0.993548i \(-0.536177\pi\)
−0.113410 + 0.993548i \(0.536177\pi\)
\(312\) 0 0
\(313\) 1.00000 0.0565233 0.0282617 0.999601i \(-0.491003\pi\)
0.0282617 + 0.999601i \(0.491003\pi\)
\(314\) 17.0000 0.959366
\(315\) 0 0
\(316\) 0 0
\(317\) −2.00000 −0.112331 −0.0561656 0.998421i \(-0.517887\pi\)
−0.0561656 + 0.998421i \(0.517887\pi\)
\(318\) 0 0
\(319\) −36.0000 −2.01561
\(320\) 14.0000 0.782624
\(321\) 0 0
\(322\) 2.00000 0.111456
\(323\) 0 0
\(324\) 0 0
\(325\) −1.00000 −0.0554700
\(326\) 12.0000 0.664619
\(327\) 0 0
\(328\) 18.0000 0.993884
\(329\) 12.0000 0.661581
\(330\) 0 0
\(331\) 19.0000 1.04433 0.522167 0.852843i \(-0.325124\pi\)
0.522167 + 0.852843i \(0.325124\pi\)
\(332\) −2.00000 −0.109764
\(333\) 0 0
\(334\) 8.00000 0.437741
\(335\) −22.0000 −1.20199
\(336\) 0 0
\(337\) 14.0000 0.762629 0.381314 0.924445i \(-0.375472\pi\)
0.381314 + 0.924445i \(0.375472\pi\)
\(338\) 12.0000 0.652714
\(339\) 0 0
\(340\) 0 0
\(341\) 42.0000 2.27443
\(342\) 0 0
\(343\) 13.0000 0.701934
\(344\) 21.0000 1.13224
\(345\) 0 0
\(346\) 16.0000 0.860165
\(347\) −26.0000 −1.39575 −0.697877 0.716218i \(-0.745872\pi\)
−0.697877 + 0.716218i \(0.745872\pi\)
\(348\) 0 0
\(349\) −30.0000 −1.60586 −0.802932 0.596071i \(-0.796728\pi\)
−0.802932 + 0.596071i \(0.796728\pi\)
\(350\) −1.00000 −0.0534522
\(351\) 0 0
\(352\) 30.0000 1.59901
\(353\) 24.0000 1.27739 0.638696 0.769460i \(-0.279474\pi\)
0.638696 + 0.769460i \(0.279474\pi\)
\(354\) 0 0
\(355\) −4.00000 −0.212298
\(356\) −16.0000 −0.847998
\(357\) 0 0
\(358\) 18.0000 0.951330
\(359\) −12.0000 −0.633336 −0.316668 0.948536i \(-0.602564\pi\)
−0.316668 + 0.948536i \(0.602564\pi\)
\(360\) 0 0
\(361\) 6.00000 0.315789
\(362\) 13.0000 0.683265
\(363\) 0 0
\(364\) 1.00000 0.0524142
\(365\) 12.0000 0.628109
\(366\) 0 0
\(367\) −7.00000 −0.365397 −0.182699 0.983169i \(-0.558483\pi\)
−0.182699 + 0.983169i \(0.558483\pi\)
\(368\) −2.00000 −0.104257
\(369\) 0 0
\(370\) 14.0000 0.727825
\(371\) −12.0000 −0.623009
\(372\) 0 0
\(373\) −6.00000 −0.310668 −0.155334 0.987862i \(-0.549645\pi\)
−0.155334 + 0.987862i \(0.549645\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −36.0000 −1.85656
\(377\) 6.00000 0.309016
\(378\) 0 0
\(379\) −25.0000 −1.28416 −0.642082 0.766636i \(-0.721929\pi\)
−0.642082 + 0.766636i \(0.721929\pi\)
\(380\) −10.0000 −0.512989
\(381\) 0 0
\(382\) 10.0000 0.511645
\(383\) 18.0000 0.919757 0.459879 0.887982i \(-0.347893\pi\)
0.459879 + 0.887982i \(0.347893\pi\)
\(384\) 0 0
\(385\) 12.0000 0.611577
\(386\) −1.00000 −0.0508987
\(387\) 0 0
\(388\) 17.0000 0.863044
\(389\) 30.0000 1.52106 0.760530 0.649303i \(-0.224939\pi\)
0.760530 + 0.649303i \(0.224939\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −18.0000 −0.909137
\(393\) 0 0
\(394\) 12.0000 0.604551
\(395\) 0 0
\(396\) 0 0
\(397\) −30.0000 −1.50566 −0.752828 0.658217i \(-0.771311\pi\)
−0.752828 + 0.658217i \(0.771311\pi\)
\(398\) 16.0000 0.802008
\(399\) 0 0
\(400\) 1.00000 0.0500000
\(401\) 2.00000 0.0998752 0.0499376 0.998752i \(-0.484098\pi\)
0.0499376 + 0.998752i \(0.484098\pi\)
\(402\) 0 0
\(403\) −7.00000 −0.348695
\(404\) 4.00000 0.199007
\(405\) 0 0
\(406\) 6.00000 0.297775
\(407\) 42.0000 2.08186
\(408\) 0 0
\(409\) 5.00000 0.247234 0.123617 0.992330i \(-0.460551\pi\)
0.123617 + 0.992330i \(0.460551\pi\)
\(410\) −12.0000 −0.592638
\(411\) 0 0
\(412\) 7.00000 0.344865
\(413\) 6.00000 0.295241
\(414\) 0 0
\(415\) 4.00000 0.196352
\(416\) −5.00000 −0.245145
\(417\) 0 0
\(418\) 30.0000 1.46735
\(419\) −2.00000 −0.0977064 −0.0488532 0.998806i \(-0.515557\pi\)
−0.0488532 + 0.998806i \(0.515557\pi\)
\(420\) 0 0
\(421\) 13.0000 0.633581 0.316791 0.948495i \(-0.397395\pi\)
0.316791 + 0.948495i \(0.397395\pi\)
\(422\) −1.00000 −0.0486792
\(423\) 0 0
\(424\) 36.0000 1.74831
\(425\) 0 0
\(426\) 0 0
\(427\) 11.0000 0.532327
\(428\) −16.0000 −0.773389
\(429\) 0 0
\(430\) −14.0000 −0.675140
\(431\) −12.0000 −0.578020 −0.289010 0.957326i \(-0.593326\pi\)
−0.289010 + 0.957326i \(0.593326\pi\)
\(432\) 0 0
\(433\) −1.00000 −0.0480569 −0.0240285 0.999711i \(-0.507649\pi\)
−0.0240285 + 0.999711i \(0.507649\pi\)
\(434\) −7.00000 −0.336011
\(435\) 0 0
\(436\) 6.00000 0.287348
\(437\) 10.0000 0.478365
\(438\) 0 0
\(439\) −1.00000 −0.0477274 −0.0238637 0.999715i \(-0.507597\pi\)
−0.0238637 + 0.999715i \(0.507597\pi\)
\(440\) −36.0000 −1.71623
\(441\) 0 0
\(442\) 0 0
\(443\) −26.0000 −1.23530 −0.617649 0.786454i \(-0.711915\pi\)
−0.617649 + 0.786454i \(0.711915\pi\)
\(444\) 0 0
\(445\) 32.0000 1.51695
\(446\) 0 0
\(447\) 0 0
\(448\) −7.00000 −0.330719
\(449\) 20.0000 0.943858 0.471929 0.881636i \(-0.343558\pi\)
0.471929 + 0.881636i \(0.343558\pi\)
\(450\) 0 0
\(451\) −36.0000 −1.69517
\(452\) 4.00000 0.188144
\(453\) 0 0
\(454\) 18.0000 0.844782
\(455\) −2.00000 −0.0937614
\(456\) 0 0
\(457\) 18.0000 0.842004 0.421002 0.907060i \(-0.361678\pi\)
0.421002 + 0.907060i \(0.361678\pi\)
\(458\) −6.00000 −0.280362
\(459\) 0 0
\(460\) −4.00000 −0.186501
\(461\) 40.0000 1.86299 0.931493 0.363760i \(-0.118507\pi\)
0.931493 + 0.363760i \(0.118507\pi\)
\(462\) 0 0
\(463\) 41.0000 1.90543 0.952716 0.303863i \(-0.0982765\pi\)
0.952716 + 0.303863i \(0.0982765\pi\)
\(464\) −6.00000 −0.278543
\(465\) 0 0
\(466\) −12.0000 −0.555889
\(467\) −12.0000 −0.555294 −0.277647 0.960683i \(-0.589555\pi\)
−0.277647 + 0.960683i \(0.589555\pi\)
\(468\) 0 0
\(469\) 11.0000 0.507933
\(470\) 24.0000 1.10704
\(471\) 0 0
\(472\) −18.0000 −0.828517
\(473\) −42.0000 −1.93116
\(474\) 0 0
\(475\) −5.00000 −0.229416
\(476\) 0 0
\(477\) 0 0
\(478\) −20.0000 −0.914779
\(479\) 6.00000 0.274147 0.137073 0.990561i \(-0.456230\pi\)
0.137073 + 0.990561i \(0.456230\pi\)
\(480\) 0 0
\(481\) −7.00000 −0.319173
\(482\) −18.0000 −0.819878
\(483\) 0 0
\(484\) −25.0000 −1.13636
\(485\) −34.0000 −1.54386
\(486\) 0 0
\(487\) −5.00000 −0.226572 −0.113286 0.993562i \(-0.536138\pi\)
−0.113286 + 0.993562i \(0.536138\pi\)
\(488\) −33.0000 −1.49384
\(489\) 0 0
\(490\) 12.0000 0.542105
\(491\) −4.00000 −0.180517 −0.0902587 0.995918i \(-0.528769\pi\)
−0.0902587 + 0.995918i \(0.528769\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) −5.00000 −0.224961
\(495\) 0 0
\(496\) 7.00000 0.314309
\(497\) 2.00000 0.0897123
\(498\) 0 0
\(499\) 13.0000 0.581960 0.290980 0.956729i \(-0.406019\pi\)
0.290980 + 0.956729i \(0.406019\pi\)
\(500\) 12.0000 0.536656
\(501\) 0 0
\(502\) 6.00000 0.267793
\(503\) −6.00000 −0.267527 −0.133763 0.991013i \(-0.542706\pi\)
−0.133763 + 0.991013i \(0.542706\pi\)
\(504\) 0 0
\(505\) −8.00000 −0.355995
\(506\) 12.0000 0.533465
\(507\) 0 0
\(508\) −5.00000 −0.221839
\(509\) 28.0000 1.24108 0.620539 0.784176i \(-0.286914\pi\)
0.620539 + 0.784176i \(0.286914\pi\)
\(510\) 0 0
\(511\) −6.00000 −0.265424
\(512\) 11.0000 0.486136
\(513\) 0 0
\(514\) 24.0000 1.05859
\(515\) −14.0000 −0.616914
\(516\) 0 0
\(517\) 72.0000 3.16656
\(518\) −7.00000 −0.307562
\(519\) 0 0
\(520\) 6.00000 0.263117
\(521\) −14.0000 −0.613351 −0.306676 0.951814i \(-0.599217\pi\)
−0.306676 + 0.951814i \(0.599217\pi\)
\(522\) 0 0
\(523\) −36.0000 −1.57417 −0.787085 0.616844i \(-0.788411\pi\)
−0.787085 + 0.616844i \(0.788411\pi\)
\(524\) 10.0000 0.436852
\(525\) 0 0
\(526\) 16.0000 0.697633
\(527\) 0 0
\(528\) 0 0
\(529\) −19.0000 −0.826087
\(530\) −24.0000 −1.04249
\(531\) 0 0
\(532\) 5.00000 0.216777
\(533\) 6.00000 0.259889
\(534\) 0 0
\(535\) 32.0000 1.38348
\(536\) −33.0000 −1.42538
\(537\) 0 0
\(538\) −14.0000 −0.603583
\(539\) 36.0000 1.55063
\(540\) 0 0
\(541\) 30.0000 1.28980 0.644900 0.764267i \(-0.276899\pi\)
0.644900 + 0.764267i \(0.276899\pi\)
\(542\) 13.0000 0.558398
\(543\) 0 0
\(544\) 0 0
\(545\) −12.0000 −0.514024
\(546\) 0 0
\(547\) 41.0000 1.75303 0.876517 0.481371i \(-0.159861\pi\)
0.876517 + 0.481371i \(0.159861\pi\)
\(548\) 6.00000 0.256307
\(549\) 0 0
\(550\) −6.00000 −0.255841
\(551\) 30.0000 1.27804
\(552\) 0 0
\(553\) 0 0
\(554\) 5.00000 0.212430
\(555\) 0 0
\(556\) 13.0000 0.551323
\(557\) −12.0000 −0.508456 −0.254228 0.967144i \(-0.581821\pi\)
−0.254228 + 0.967144i \(0.581821\pi\)
\(558\) 0 0
\(559\) 7.00000 0.296068
\(560\) 2.00000 0.0845154
\(561\) 0 0
\(562\) −18.0000 −0.759284
\(563\) 32.0000 1.34864 0.674320 0.738440i \(-0.264437\pi\)
0.674320 + 0.738440i \(0.264437\pi\)
\(564\) 0 0
\(565\) −8.00000 −0.336563
\(566\) 11.0000 0.462364
\(567\) 0 0
\(568\) −6.00000 −0.251754
\(569\) −20.0000 −0.838444 −0.419222 0.907884i \(-0.637697\pi\)
−0.419222 + 0.907884i \(0.637697\pi\)
\(570\) 0 0
\(571\) 23.0000 0.962520 0.481260 0.876578i \(-0.340179\pi\)
0.481260 + 0.876578i \(0.340179\pi\)
\(572\) 6.00000 0.250873
\(573\) 0 0
\(574\) 6.00000 0.250435
\(575\) −2.00000 −0.0834058
\(576\) 0 0
\(577\) −5.00000 −0.208153 −0.104076 0.994569i \(-0.533189\pi\)
−0.104076 + 0.994569i \(0.533189\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) −12.0000 −0.498273
\(581\) −2.00000 −0.0829740
\(582\) 0 0
\(583\) −72.0000 −2.98194
\(584\) 18.0000 0.744845
\(585\) 0 0
\(586\) 0 0
\(587\) 34.0000 1.40333 0.701665 0.712507i \(-0.252440\pi\)
0.701665 + 0.712507i \(0.252440\pi\)
\(588\) 0 0
\(589\) −35.0000 −1.44215
\(590\) 12.0000 0.494032
\(591\) 0 0
\(592\) 7.00000 0.287698
\(593\) −6.00000 −0.246390 −0.123195 0.992382i \(-0.539314\pi\)
−0.123195 + 0.992382i \(0.539314\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −14.0000 −0.573462
\(597\) 0 0
\(598\) −2.00000 −0.0817861
\(599\) 6.00000 0.245153 0.122577 0.992459i \(-0.460884\pi\)
0.122577 + 0.992459i \(0.460884\pi\)
\(600\) 0 0
\(601\) −19.0000 −0.775026 −0.387513 0.921864i \(-0.626666\pi\)
−0.387513 + 0.921864i \(0.626666\pi\)
\(602\) 7.00000 0.285299
\(603\) 0 0
\(604\) −5.00000 −0.203447
\(605\) 50.0000 2.03279
\(606\) 0 0
\(607\) 31.0000 1.25825 0.629126 0.777304i \(-0.283413\pi\)
0.629126 + 0.777304i \(0.283413\pi\)
\(608\) −25.0000 −1.01388
\(609\) 0 0
\(610\) 22.0000 0.890754
\(611\) −12.0000 −0.485468
\(612\) 0 0
\(613\) 19.0000 0.767403 0.383701 0.923457i \(-0.374649\pi\)
0.383701 + 0.923457i \(0.374649\pi\)
\(614\) −12.0000 −0.484281
\(615\) 0 0
\(616\) 18.0000 0.725241
\(617\) 24.0000 0.966204 0.483102 0.875564i \(-0.339510\pi\)
0.483102 + 0.875564i \(0.339510\pi\)
\(618\) 0 0
\(619\) −24.0000 −0.964641 −0.482321 0.875995i \(-0.660206\pi\)
−0.482321 + 0.875995i \(0.660206\pi\)
\(620\) 14.0000 0.562254
\(621\) 0 0
\(622\) 4.00000 0.160385
\(623\) −16.0000 −0.641026
\(624\) 0 0
\(625\) −19.0000 −0.760000
\(626\) −1.00000 −0.0399680
\(627\) 0 0
\(628\) 17.0000 0.678374
\(629\) 0 0
\(630\) 0 0
\(631\) −17.0000 −0.676759 −0.338380 0.941010i \(-0.609879\pi\)
−0.338380 + 0.941010i \(0.609879\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 2.00000 0.0794301
\(635\) 10.0000 0.396838
\(636\) 0 0
\(637\) −6.00000 −0.237729
\(638\) 36.0000 1.42525
\(639\) 0 0
\(640\) 6.00000 0.237171
\(641\) −30.0000 −1.18493 −0.592464 0.805597i \(-0.701845\pi\)
−0.592464 + 0.805597i \(0.701845\pi\)
\(642\) 0 0
\(643\) −17.0000 −0.670415 −0.335207 0.942144i \(-0.608806\pi\)
−0.335207 + 0.942144i \(0.608806\pi\)
\(644\) 2.00000 0.0788110
\(645\) 0 0
\(646\) 0 0
\(647\) −4.00000 −0.157256 −0.0786281 0.996904i \(-0.525054\pi\)
−0.0786281 + 0.996904i \(0.525054\pi\)
\(648\) 0 0
\(649\) 36.0000 1.41312
\(650\) 1.00000 0.0392232
\(651\) 0 0
\(652\) 12.0000 0.469956
\(653\) −24.0000 −0.939193 −0.469596 0.882881i \(-0.655601\pi\)
−0.469596 + 0.882881i \(0.655601\pi\)
\(654\) 0 0
\(655\) −20.0000 −0.781465
\(656\) −6.00000 −0.234261
\(657\) 0 0
\(658\) −12.0000 −0.467809
\(659\) −20.0000 −0.779089 −0.389545 0.921008i \(-0.627368\pi\)
−0.389545 + 0.921008i \(0.627368\pi\)
\(660\) 0 0
\(661\) −25.0000 −0.972387 −0.486194 0.873851i \(-0.661615\pi\)
−0.486194 + 0.873851i \(0.661615\pi\)
\(662\) −19.0000 −0.738456
\(663\) 0 0
\(664\) 6.00000 0.232845
\(665\) −10.0000 −0.387783
\(666\) 0 0
\(667\) 12.0000 0.464642
\(668\) 8.00000 0.309529
\(669\) 0 0
\(670\) 22.0000 0.849934
\(671\) 66.0000 2.54790
\(672\) 0 0
\(673\) 1.00000 0.0385472 0.0192736 0.999814i \(-0.493865\pi\)
0.0192736 + 0.999814i \(0.493865\pi\)
\(674\) −14.0000 −0.539260
\(675\) 0 0
\(676\) 12.0000 0.461538
\(677\) 42.0000 1.61419 0.807096 0.590421i \(-0.201038\pi\)
0.807096 + 0.590421i \(0.201038\pi\)
\(678\) 0 0
\(679\) 17.0000 0.652400
\(680\) 0 0
\(681\) 0 0
\(682\) −42.0000 −1.60826
\(683\) 28.0000 1.07139 0.535695 0.844411i \(-0.320050\pi\)
0.535695 + 0.844411i \(0.320050\pi\)
\(684\) 0 0
\(685\) −12.0000 −0.458496
\(686\) −13.0000 −0.496342
\(687\) 0 0
\(688\) −7.00000 −0.266872
\(689\) 12.0000 0.457164
\(690\) 0 0
\(691\) 35.0000 1.33146 0.665731 0.746191i \(-0.268120\pi\)
0.665731 + 0.746191i \(0.268120\pi\)
\(692\) 16.0000 0.608229
\(693\) 0 0
\(694\) 26.0000 0.986947
\(695\) −26.0000 −0.986236
\(696\) 0 0
\(697\) 0 0
\(698\) 30.0000 1.13552
\(699\) 0 0
\(700\) −1.00000 −0.0377964
\(701\) 6.00000 0.226617 0.113308 0.993560i \(-0.463855\pi\)
0.113308 + 0.993560i \(0.463855\pi\)
\(702\) 0 0
\(703\) −35.0000 −1.32005
\(704\) −42.0000 −1.58293
\(705\) 0 0
\(706\) −24.0000 −0.903252
\(707\) 4.00000 0.150435
\(708\) 0 0
\(709\) −41.0000 −1.53979 −0.769894 0.638172i \(-0.779691\pi\)
−0.769894 + 0.638172i \(0.779691\pi\)
\(710\) 4.00000 0.150117
\(711\) 0 0
\(712\) 48.0000 1.79888
\(713\) −14.0000 −0.524304
\(714\) 0 0
\(715\) −12.0000 −0.448775
\(716\) 18.0000 0.672692
\(717\) 0 0
\(718\) 12.0000 0.447836
\(719\) 32.0000 1.19340 0.596699 0.802465i \(-0.296479\pi\)
0.596699 + 0.802465i \(0.296479\pi\)
\(720\) 0 0
\(721\) 7.00000 0.260694
\(722\) −6.00000 −0.223297
\(723\) 0 0
\(724\) 13.0000 0.483141
\(725\) −6.00000 −0.222834
\(726\) 0 0
\(727\) 13.0000 0.482143 0.241072 0.970507i \(-0.422501\pi\)
0.241072 + 0.970507i \(0.422501\pi\)
\(728\) −3.00000 −0.111187
\(729\) 0 0
\(730\) −12.0000 −0.444140
\(731\) 0 0
\(732\) 0 0
\(733\) 37.0000 1.36663 0.683313 0.730125i \(-0.260538\pi\)
0.683313 + 0.730125i \(0.260538\pi\)
\(734\) 7.00000 0.258375
\(735\) 0 0
\(736\) −10.0000 −0.368605
\(737\) 66.0000 2.43114
\(738\) 0 0
\(739\) 19.0000 0.698926 0.349463 0.936950i \(-0.386364\pi\)
0.349463 + 0.936950i \(0.386364\pi\)
\(740\) 14.0000 0.514650
\(741\) 0 0
\(742\) 12.0000 0.440534
\(743\) 30.0000 1.10059 0.550297 0.834969i \(-0.314515\pi\)
0.550297 + 0.834969i \(0.314515\pi\)
\(744\) 0 0
\(745\) 28.0000 1.02584
\(746\) 6.00000 0.219676
\(747\) 0 0
\(748\) 0 0
\(749\) −16.0000 −0.584627
\(750\) 0 0
\(751\) −17.0000 −0.620339 −0.310169 0.950681i \(-0.600386\pi\)
−0.310169 + 0.950681i \(0.600386\pi\)
\(752\) 12.0000 0.437595
\(753\) 0 0
\(754\) −6.00000 −0.218507
\(755\) 10.0000 0.363937
\(756\) 0 0
\(757\) 13.0000 0.472493 0.236247 0.971693i \(-0.424083\pi\)
0.236247 + 0.971693i \(0.424083\pi\)
\(758\) 25.0000 0.908041
\(759\) 0 0
\(760\) 30.0000 1.08821
\(761\) −34.0000 −1.23250 −0.616250 0.787551i \(-0.711349\pi\)
−0.616250 + 0.787551i \(0.711349\pi\)
\(762\) 0 0
\(763\) 6.00000 0.217215
\(764\) 10.0000 0.361787
\(765\) 0 0
\(766\) −18.0000 −0.650366
\(767\) −6.00000 −0.216647
\(768\) 0 0
\(769\) 22.0000 0.793340 0.396670 0.917961i \(-0.370166\pi\)
0.396670 + 0.917961i \(0.370166\pi\)
\(770\) −12.0000 −0.432450
\(771\) 0 0
\(772\) −1.00000 −0.0359908
\(773\) 4.00000 0.143870 0.0719350 0.997409i \(-0.477083\pi\)
0.0719350 + 0.997409i \(0.477083\pi\)
\(774\) 0 0
\(775\) 7.00000 0.251447
\(776\) −51.0000 −1.83079
\(777\) 0 0
\(778\) −30.0000 −1.07555
\(779\) 30.0000 1.07486
\(780\) 0 0
\(781\) 12.0000 0.429394
\(782\) 0 0
\(783\) 0 0
\(784\) 6.00000 0.214286
\(785\) −34.0000 −1.21351
\(786\) 0 0
\(787\) 35.0000 1.24762 0.623808 0.781578i \(-0.285585\pi\)
0.623808 + 0.781578i \(0.285585\pi\)
\(788\) 12.0000 0.427482
\(789\) 0 0
\(790\) 0 0
\(791\) 4.00000 0.142224
\(792\) 0 0
\(793\) −11.0000 −0.390621
\(794\) 30.0000 1.06466
\(795\) 0 0
\(796\) 16.0000 0.567105
\(797\) 16.0000 0.566749 0.283375 0.959009i \(-0.408546\pi\)
0.283375 + 0.959009i \(0.408546\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 5.00000 0.176777
\(801\) 0 0
\(802\) −2.00000 −0.0706225
\(803\) −36.0000 −1.27041
\(804\) 0 0
\(805\) −4.00000 −0.140981
\(806\) 7.00000 0.246564
\(807\) 0 0
\(808\) −12.0000 −0.422159
\(809\) 10.0000 0.351581 0.175791 0.984428i \(-0.443752\pi\)
0.175791 + 0.984428i \(0.443752\pi\)
\(810\) 0 0
\(811\) 23.0000 0.807639 0.403820 0.914839i \(-0.367682\pi\)
0.403820 + 0.914839i \(0.367682\pi\)
\(812\) 6.00000 0.210559
\(813\) 0 0
\(814\) −42.0000 −1.47210
\(815\) −24.0000 −0.840683
\(816\) 0 0
\(817\) 35.0000 1.22449
\(818\) −5.00000 −0.174821
\(819\) 0 0
\(820\) −12.0000 −0.419058
\(821\) −18.0000 −0.628204 −0.314102 0.949389i \(-0.601703\pi\)
−0.314102 + 0.949389i \(0.601703\pi\)
\(822\) 0 0
\(823\) −11.0000 −0.383436 −0.191718 0.981450i \(-0.561406\pi\)
−0.191718 + 0.981450i \(0.561406\pi\)
\(824\) −21.0000 −0.731570
\(825\) 0 0
\(826\) −6.00000 −0.208767
\(827\) 18.0000 0.625921 0.312961 0.949766i \(-0.398679\pi\)
0.312961 + 0.949766i \(0.398679\pi\)
\(828\) 0 0
\(829\) 17.0000 0.590434 0.295217 0.955430i \(-0.404608\pi\)
0.295217 + 0.955430i \(0.404608\pi\)
\(830\) −4.00000 −0.138842
\(831\) 0 0
\(832\) 7.00000 0.242681
\(833\) 0 0
\(834\) 0 0
\(835\) −16.0000 −0.553703
\(836\) 30.0000 1.03757
\(837\) 0 0
\(838\) 2.00000 0.0690889
\(839\) −20.0000 −0.690477 −0.345238 0.938515i \(-0.612202\pi\)
−0.345238 + 0.938515i \(0.612202\pi\)
\(840\) 0 0
\(841\) 7.00000 0.241379
\(842\) −13.0000 −0.448010
\(843\) 0 0
\(844\) −1.00000 −0.0344214
\(845\) −24.0000 −0.825625
\(846\) 0 0
\(847\) −25.0000 −0.859010
\(848\) −12.0000 −0.412082
\(849\) 0 0
\(850\) 0 0
\(851\) −14.0000 −0.479914
\(852\) 0 0
\(853\) 13.0000 0.445112 0.222556 0.974920i \(-0.428560\pi\)
0.222556 + 0.974920i \(0.428560\pi\)
\(854\) −11.0000 −0.376412
\(855\) 0 0
\(856\) 48.0000 1.64061
\(857\) 32.0000 1.09310 0.546550 0.837427i \(-0.315941\pi\)
0.546550 + 0.837427i \(0.315941\pi\)
\(858\) 0 0
\(859\) −11.0000 −0.375315 −0.187658 0.982235i \(-0.560090\pi\)
−0.187658 + 0.982235i \(0.560090\pi\)
\(860\) −14.0000 −0.477396
\(861\) 0 0
\(862\) 12.0000 0.408722
\(863\) 4.00000 0.136162 0.0680808 0.997680i \(-0.478312\pi\)
0.0680808 + 0.997680i \(0.478312\pi\)
\(864\) 0 0
\(865\) −32.0000 −1.08803
\(866\) 1.00000 0.0339814
\(867\) 0 0
\(868\) −7.00000 −0.237595
\(869\) 0 0
\(870\) 0 0
\(871\) −11.0000 −0.372721
\(872\) −18.0000 −0.609557
\(873\) 0 0
\(874\) −10.0000 −0.338255
\(875\) 12.0000 0.405674
\(876\) 0 0
\(877\) 54.0000 1.82345 0.911725 0.410801i \(-0.134751\pi\)
0.911725 + 0.410801i \(0.134751\pi\)
\(878\) 1.00000 0.0337484
\(879\) 0 0
\(880\) 12.0000 0.404520
\(881\) −32.0000 −1.07811 −0.539054 0.842271i \(-0.681218\pi\)
−0.539054 + 0.842271i \(0.681218\pi\)
\(882\) 0 0
\(883\) −36.0000 −1.21150 −0.605748 0.795656i \(-0.707126\pi\)
−0.605748 + 0.795656i \(0.707126\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 26.0000 0.873487
\(887\) −48.0000 −1.61168 −0.805841 0.592132i \(-0.798286\pi\)
−0.805841 + 0.592132i \(0.798286\pi\)
\(888\) 0 0
\(889\) −5.00000 −0.167695
\(890\) −32.0000 −1.07264
\(891\) 0 0
\(892\) 0 0
\(893\) −60.0000 −2.00782
\(894\) 0 0
\(895\) −36.0000 −1.20335
\(896\) −3.00000 −0.100223
\(897\) 0 0
\(898\) −20.0000 −0.667409
\(899\) −42.0000 −1.40078
\(900\) 0 0
\(901\) 0 0
\(902\) 36.0000 1.19867
\(903\) 0 0
\(904\) −12.0000 −0.399114
\(905\) −26.0000 −0.864269
\(906\) 0 0
\(907\) −11.0000 −0.365249 −0.182625 0.983183i \(-0.558459\pi\)
−0.182625 + 0.983183i \(0.558459\pi\)
\(908\) 18.0000 0.597351
\(909\) 0 0
\(910\) 2.00000 0.0662994
\(911\) −50.0000 −1.65657 −0.828287 0.560304i \(-0.810684\pi\)
−0.828287 + 0.560304i \(0.810684\pi\)
\(912\) 0 0
\(913\) −12.0000 −0.397142
\(914\) −18.0000 −0.595387
\(915\) 0 0
\(916\) −6.00000 −0.198246
\(917\) 10.0000 0.330229
\(918\) 0 0
\(919\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(920\) 12.0000 0.395628
\(921\) 0 0
\(922\) −40.0000 −1.31733
\(923\) −2.00000 −0.0658308
\(924\) 0 0
\(925\) 7.00000 0.230159
\(926\) −41.0000 −1.34734
\(927\) 0 0
\(928\) −30.0000 −0.984798
\(929\) 12.0000 0.393707 0.196854 0.980433i \(-0.436928\pi\)
0.196854 + 0.980433i \(0.436928\pi\)
\(930\) 0 0
\(931\) −30.0000 −0.983210
\(932\) −12.0000 −0.393073
\(933\) 0 0
\(934\) 12.0000 0.392652
\(935\) 0 0
\(936\) 0 0
\(937\) −17.0000 −0.555366 −0.277683 0.960673i \(-0.589566\pi\)
−0.277683 + 0.960673i \(0.589566\pi\)
\(938\) −11.0000 −0.359163
\(939\) 0 0
\(940\) 24.0000 0.782794
\(941\) −36.0000 −1.17357 −0.586783 0.809744i \(-0.699606\pi\)
−0.586783 + 0.809744i \(0.699606\pi\)
\(942\) 0 0
\(943\) 12.0000 0.390774
\(944\) 6.00000 0.195283
\(945\) 0 0
\(946\) 42.0000 1.36554
\(947\) 28.0000 0.909878 0.454939 0.890523i \(-0.349661\pi\)
0.454939 + 0.890523i \(0.349661\pi\)
\(948\) 0 0
\(949\) 6.00000 0.194768
\(950\) 5.00000 0.162221
\(951\) 0 0
\(952\) 0 0
\(953\) −34.0000 −1.10137 −0.550684 0.834714i \(-0.685633\pi\)
−0.550684 + 0.834714i \(0.685633\pi\)
\(954\) 0 0
\(955\) −20.0000 −0.647185
\(956\) −20.0000 −0.646846
\(957\) 0 0
\(958\) −6.00000 −0.193851
\(959\) 6.00000 0.193750
\(960\) 0 0
\(961\) 18.0000 0.580645
\(962\) 7.00000 0.225689
\(963\) 0 0
\(964\) −18.0000 −0.579741
\(965\) 2.00000 0.0643823
\(966\) 0 0
\(967\) 48.0000 1.54358 0.771788 0.635880i \(-0.219363\pi\)
0.771788 + 0.635880i \(0.219363\pi\)
\(968\) 75.0000 2.41059
\(969\) 0 0
\(970\) 34.0000 1.09167
\(971\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(972\) 0 0
\(973\) 13.0000 0.416761
\(974\) 5.00000 0.160210
\(975\) 0 0
\(976\) 11.0000 0.352101
\(977\) −18.0000 −0.575871 −0.287936 0.957650i \(-0.592969\pi\)
−0.287936 + 0.957650i \(0.592969\pi\)
\(978\) 0 0
\(979\) −96.0000 −3.06817
\(980\) 12.0000 0.383326
\(981\) 0 0
\(982\) 4.00000 0.127645
\(983\) 36.0000 1.14822 0.574111 0.818778i \(-0.305348\pi\)
0.574111 + 0.818778i \(0.305348\pi\)
\(984\) 0 0
\(985\) −24.0000 −0.764704
\(986\) 0 0
\(987\) 0 0
\(988\) −5.00000 −0.159071
\(989\) 14.0000 0.445174
\(990\) 0 0
\(991\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(992\) 35.0000 1.11125
\(993\) 0 0
\(994\) −2.00000 −0.0634361
\(995\) −32.0000 −1.01447
\(996\) 0 0
\(997\) 29.0000 0.918439 0.459220 0.888323i \(-0.348129\pi\)
0.459220 + 0.888323i \(0.348129\pi\)
\(998\) −13.0000 −0.411508
\(999\) 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 2601.2.a.e.1.1 yes 1
3.2 odd 2 2601.2.a.h.1.1 yes 1
17.16 even 2 2601.2.a.d.1.1 1
51.50 odd 2 2601.2.a.k.1.1 yes 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2601.2.a.d.1.1 1 17.16 even 2
2601.2.a.e.1.1 yes 1 1.1 even 1 trivial
2601.2.a.h.1.1 yes 1 3.2 odd 2
2601.2.a.k.1.1 yes 1 51.50 odd 2