Properties

Label 8015.2.a.e.1.1
Level 8015
Weight 2
Character 8015.1
Self dual yes
Analytic conductor 64.000
Analytic rank 0
Dimension 1
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 8015 = 5 \cdot 7 \cdot 229 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8015.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(64.0000972201\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 8015.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +2.00000 q^{3} -1.00000 q^{4} -1.00000 q^{5} +2.00000 q^{6} -1.00000 q^{7} -3.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +2.00000 q^{3} -1.00000 q^{4} -1.00000 q^{5} +2.00000 q^{6} -1.00000 q^{7} -3.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -1.00000 q^{11} -2.00000 q^{12} -5.00000 q^{13} -1.00000 q^{14} -2.00000 q^{15} -1.00000 q^{16} +2.00000 q^{17} +1.00000 q^{18} +4.00000 q^{19} +1.00000 q^{20} -2.00000 q^{21} -1.00000 q^{22} -4.00000 q^{23} -6.00000 q^{24} +1.00000 q^{25} -5.00000 q^{26} -4.00000 q^{27} +1.00000 q^{28} -4.00000 q^{29} -2.00000 q^{30} +9.00000 q^{31} +5.00000 q^{32} -2.00000 q^{33} +2.00000 q^{34} +1.00000 q^{35} -1.00000 q^{36} +7.00000 q^{37} +4.00000 q^{38} -10.0000 q^{39} +3.00000 q^{40} +1.00000 q^{41} -2.00000 q^{42} -3.00000 q^{43} +1.00000 q^{44} -1.00000 q^{45} -4.00000 q^{46} +3.00000 q^{47} -2.00000 q^{48} +1.00000 q^{49} +1.00000 q^{50} +4.00000 q^{51} +5.00000 q^{52} -5.00000 q^{53} -4.00000 q^{54} +1.00000 q^{55} +3.00000 q^{56} +8.00000 q^{57} -4.00000 q^{58} +4.00000 q^{59} +2.00000 q^{60} +2.00000 q^{61} +9.00000 q^{62} -1.00000 q^{63} +7.00000 q^{64} +5.00000 q^{65} -2.00000 q^{66} +12.0000 q^{67} -2.00000 q^{68} -8.00000 q^{69} +1.00000 q^{70} +9.00000 q^{71} -3.00000 q^{72} -14.0000 q^{73} +7.00000 q^{74} +2.00000 q^{75} -4.00000 q^{76} +1.00000 q^{77} -10.0000 q^{78} +12.0000 q^{79} +1.00000 q^{80} -11.0000 q^{81} +1.00000 q^{82} +6.00000 q^{83} +2.00000 q^{84} -2.00000 q^{85} -3.00000 q^{86} -8.00000 q^{87} +3.00000 q^{88} +9.00000 q^{89} -1.00000 q^{90} +5.00000 q^{91} +4.00000 q^{92} +18.0000 q^{93} +3.00000 q^{94} -4.00000 q^{95} +10.0000 q^{96} -10.0000 q^{97} +1.00000 q^{98} -1.00000 q^{99} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107 0.353553 0.935414i \(-0.384973\pi\)
0.353553 + 0.935414i \(0.384973\pi\)
\(3\) 2.00000 1.15470 0.577350 0.816497i \(-0.304087\pi\)
0.577350 + 0.816497i \(0.304087\pi\)
\(4\) −1.00000 −0.500000
\(5\) −1.00000 −0.447214
\(6\) 2.00000 0.816497
\(7\) −1.00000 −0.377964
\(8\) −3.00000 −1.06066
\(9\) 1.00000 0.333333
\(10\) −1.00000 −0.316228
\(11\) −1.00000 −0.301511 −0.150756 0.988571i \(-0.548171\pi\)
−0.150756 + 0.988571i \(0.548171\pi\)
\(12\) −2.00000 −0.577350
\(13\) −5.00000 −1.38675 −0.693375 0.720577i \(-0.743877\pi\)
−0.693375 + 0.720577i \(0.743877\pi\)
\(14\) −1.00000 −0.267261
\(15\) −2.00000 −0.516398
\(16\) −1.00000 −0.250000
\(17\) 2.00000 0.485071 0.242536 0.970143i \(-0.422021\pi\)
0.242536 + 0.970143i \(0.422021\pi\)
\(18\) 1.00000 0.235702
\(19\) 4.00000 0.917663 0.458831 0.888523i \(-0.348268\pi\)
0.458831 + 0.888523i \(0.348268\pi\)
\(20\) 1.00000 0.223607
\(21\) −2.00000 −0.436436
\(22\) −1.00000 −0.213201
\(23\) −4.00000 −0.834058 −0.417029 0.908893i \(-0.636929\pi\)
−0.417029 + 0.908893i \(0.636929\pi\)
\(24\) −6.00000 −1.22474
\(25\) 1.00000 0.200000
\(26\) −5.00000 −0.980581
\(27\) −4.00000 −0.769800
\(28\) 1.00000 0.188982
\(29\) −4.00000 −0.742781 −0.371391 0.928477i \(-0.621119\pi\)
−0.371391 + 0.928477i \(0.621119\pi\)
\(30\) −2.00000 −0.365148
\(31\) 9.00000 1.61645 0.808224 0.588875i \(-0.200429\pi\)
0.808224 + 0.588875i \(0.200429\pi\)
\(32\) 5.00000 0.883883
\(33\) −2.00000 −0.348155
\(34\) 2.00000 0.342997
\(35\) 1.00000 0.169031
\(36\) −1.00000 −0.166667
\(37\) 7.00000 1.15079 0.575396 0.817875i \(-0.304848\pi\)
0.575396 + 0.817875i \(0.304848\pi\)
\(38\) 4.00000 0.648886
\(39\) −10.0000 −1.60128
\(40\) 3.00000 0.474342
\(41\) 1.00000 0.156174 0.0780869 0.996947i \(-0.475119\pi\)
0.0780869 + 0.996947i \(0.475119\pi\)
\(42\) −2.00000 −0.308607
\(43\) −3.00000 −0.457496 −0.228748 0.973486i \(-0.573463\pi\)
−0.228748 + 0.973486i \(0.573463\pi\)
\(44\) 1.00000 0.150756
\(45\) −1.00000 −0.149071
\(46\) −4.00000 −0.589768
\(47\) 3.00000 0.437595 0.218797 0.975770i \(-0.429787\pi\)
0.218797 + 0.975770i \(0.429787\pi\)
\(48\) −2.00000 −0.288675
\(49\) 1.00000 0.142857
\(50\) 1.00000 0.141421
\(51\) 4.00000 0.560112
\(52\) 5.00000 0.693375
\(53\) −5.00000 −0.686803 −0.343401 0.939189i \(-0.611579\pi\)
−0.343401 + 0.939189i \(0.611579\pi\)
\(54\) −4.00000 −0.544331
\(55\) 1.00000 0.134840
\(56\) 3.00000 0.400892
\(57\) 8.00000 1.05963
\(58\) −4.00000 −0.525226
\(59\) 4.00000 0.520756 0.260378 0.965507i \(-0.416153\pi\)
0.260378 + 0.965507i \(0.416153\pi\)
\(60\) 2.00000 0.258199
\(61\) 2.00000 0.256074 0.128037 0.991769i \(-0.459132\pi\)
0.128037 + 0.991769i \(0.459132\pi\)
\(62\) 9.00000 1.14300
\(63\) −1.00000 −0.125988
\(64\) 7.00000 0.875000
\(65\) 5.00000 0.620174
\(66\) −2.00000 −0.246183
\(67\) 12.0000 1.46603 0.733017 0.680211i \(-0.238112\pi\)
0.733017 + 0.680211i \(0.238112\pi\)
\(68\) −2.00000 −0.242536
\(69\) −8.00000 −0.963087
\(70\) 1.00000 0.119523
\(71\) 9.00000 1.06810 0.534052 0.845452i \(-0.320669\pi\)
0.534052 + 0.845452i \(0.320669\pi\)
\(72\) −3.00000 −0.353553
\(73\) −14.0000 −1.63858 −0.819288 0.573382i \(-0.805631\pi\)
−0.819288 + 0.573382i \(0.805631\pi\)
\(74\) 7.00000 0.813733
\(75\) 2.00000 0.230940
\(76\) −4.00000 −0.458831
\(77\) 1.00000 0.113961
\(78\) −10.0000 −1.13228
\(79\) 12.0000 1.35011 0.675053 0.737769i \(-0.264121\pi\)
0.675053 + 0.737769i \(0.264121\pi\)
\(80\) 1.00000 0.111803
\(81\) −11.0000 −1.22222
\(82\) 1.00000 0.110432
\(83\) 6.00000 0.658586 0.329293 0.944228i \(-0.393190\pi\)
0.329293 + 0.944228i \(0.393190\pi\)
\(84\) 2.00000 0.218218
\(85\) −2.00000 −0.216930
\(86\) −3.00000 −0.323498
\(87\) −8.00000 −0.857690
\(88\) 3.00000 0.319801
\(89\) 9.00000 0.953998 0.476999 0.878904i \(-0.341725\pi\)
0.476999 + 0.878904i \(0.341725\pi\)
\(90\) −1.00000 −0.105409
\(91\) 5.00000 0.524142
\(92\) 4.00000 0.417029
\(93\) 18.0000 1.86651
\(94\) 3.00000 0.309426
\(95\) −4.00000 −0.410391
\(96\) 10.0000 1.02062
\(97\) −10.0000 −1.01535 −0.507673 0.861550i \(-0.669494\pi\)
−0.507673 + 0.861550i \(0.669494\pi\)
\(98\) 1.00000 0.101015
\(99\) −1.00000 −0.100504
\(100\) −1.00000 −0.100000
\(101\) −14.0000 −1.39305 −0.696526 0.717532i \(-0.745272\pi\)
−0.696526 + 0.717532i \(0.745272\pi\)
\(102\) 4.00000 0.396059
\(103\) 12.0000 1.18240 0.591198 0.806527i \(-0.298655\pi\)
0.591198 + 0.806527i \(0.298655\pi\)
\(104\) 15.0000 1.47087
\(105\) 2.00000 0.195180
\(106\) −5.00000 −0.485643
\(107\) 12.0000 1.16008 0.580042 0.814587i \(-0.303036\pi\)
0.580042 + 0.814587i \(0.303036\pi\)
\(108\) 4.00000 0.384900
\(109\) −2.00000 −0.191565 −0.0957826 0.995402i \(-0.530535\pi\)
−0.0957826 + 0.995402i \(0.530535\pi\)
\(110\) 1.00000 0.0953463
\(111\) 14.0000 1.32882
\(112\) 1.00000 0.0944911
\(113\) 14.0000 1.31701 0.658505 0.752577i \(-0.271189\pi\)
0.658505 + 0.752577i \(0.271189\pi\)
\(114\) 8.00000 0.749269
\(115\) 4.00000 0.373002
\(116\) 4.00000 0.371391
\(117\) −5.00000 −0.462250
\(118\) 4.00000 0.368230
\(119\) −2.00000 −0.183340
\(120\) 6.00000 0.547723
\(121\) −10.0000 −0.909091
\(122\) 2.00000 0.181071
\(123\) 2.00000 0.180334
\(124\) −9.00000 −0.808224
\(125\) −1.00000 −0.0894427
\(126\) −1.00000 −0.0890871
\(127\) 20.0000 1.77471 0.887357 0.461084i \(-0.152539\pi\)
0.887357 + 0.461084i \(0.152539\pi\)
\(128\) −3.00000 −0.265165
\(129\) −6.00000 −0.528271
\(130\) 5.00000 0.438529
\(131\) −9.00000 −0.786334 −0.393167 0.919467i \(-0.628621\pi\)
−0.393167 + 0.919467i \(0.628621\pi\)
\(132\) 2.00000 0.174078
\(133\) −4.00000 −0.346844
\(134\) 12.0000 1.03664
\(135\) 4.00000 0.344265
\(136\) −6.00000 −0.514496
\(137\) −12.0000 −1.02523 −0.512615 0.858619i \(-0.671323\pi\)
−0.512615 + 0.858619i \(0.671323\pi\)
\(138\) −8.00000 −0.681005
\(139\) 19.0000 1.61156 0.805779 0.592216i \(-0.201747\pi\)
0.805779 + 0.592216i \(0.201747\pi\)
\(140\) −1.00000 −0.0845154
\(141\) 6.00000 0.505291
\(142\) 9.00000 0.755263
\(143\) 5.00000 0.418121
\(144\) −1.00000 −0.0833333
\(145\) 4.00000 0.332182
\(146\) −14.0000 −1.15865
\(147\) 2.00000 0.164957
\(148\) −7.00000 −0.575396
\(149\) 7.00000 0.573462 0.286731 0.958011i \(-0.407431\pi\)
0.286731 + 0.958011i \(0.407431\pi\)
\(150\) 2.00000 0.163299
\(151\) −9.00000 −0.732410 −0.366205 0.930534i \(-0.619343\pi\)
−0.366205 + 0.930534i \(0.619343\pi\)
\(152\) −12.0000 −0.973329
\(153\) 2.00000 0.161690
\(154\) 1.00000 0.0805823
\(155\) −9.00000 −0.722897
\(156\) 10.0000 0.800641
\(157\) −1.00000 −0.0798087 −0.0399043 0.999204i \(-0.512705\pi\)
−0.0399043 + 0.999204i \(0.512705\pi\)
\(158\) 12.0000 0.954669
\(159\) −10.0000 −0.793052
\(160\) −5.00000 −0.395285
\(161\) 4.00000 0.315244
\(162\) −11.0000 −0.864242
\(163\) 24.0000 1.87983 0.939913 0.341415i \(-0.110906\pi\)
0.939913 + 0.341415i \(0.110906\pi\)
\(164\) −1.00000 −0.0780869
\(165\) 2.00000 0.155700
\(166\) 6.00000 0.465690
\(167\) −12.0000 −0.928588 −0.464294 0.885681i \(-0.653692\pi\)
−0.464294 + 0.885681i \(0.653692\pi\)
\(168\) 6.00000 0.462910
\(169\) 12.0000 0.923077
\(170\) −2.00000 −0.153393
\(171\) 4.00000 0.305888
\(172\) 3.00000 0.228748
\(173\) 12.0000 0.912343 0.456172 0.889892i \(-0.349220\pi\)
0.456172 + 0.889892i \(0.349220\pi\)
\(174\) −8.00000 −0.606478
\(175\) −1.00000 −0.0755929
\(176\) 1.00000 0.0753778
\(177\) 8.00000 0.601317
\(178\) 9.00000 0.674579
\(179\) −26.0000 −1.94333 −0.971666 0.236360i \(-0.924046\pi\)
−0.971666 + 0.236360i \(0.924046\pi\)
\(180\) 1.00000 0.0745356
\(181\) 12.0000 0.891953 0.445976 0.895045i \(-0.352856\pi\)
0.445976 + 0.895045i \(0.352856\pi\)
\(182\) 5.00000 0.370625
\(183\) 4.00000 0.295689
\(184\) 12.0000 0.884652
\(185\) −7.00000 −0.514650
\(186\) 18.0000 1.31982
\(187\) −2.00000 −0.146254
\(188\) −3.00000 −0.218797
\(189\) 4.00000 0.290957
\(190\) −4.00000 −0.290191
\(191\) −14.0000 −1.01300 −0.506502 0.862239i \(-0.669062\pi\)
−0.506502 + 0.862239i \(0.669062\pi\)
\(192\) 14.0000 1.01036
\(193\) −3.00000 −0.215945 −0.107972 0.994154i \(-0.534436\pi\)
−0.107972 + 0.994154i \(0.534436\pi\)
\(194\) −10.0000 −0.717958
\(195\) 10.0000 0.716115
\(196\) −1.00000 −0.0714286
\(197\) −6.00000 −0.427482 −0.213741 0.976890i \(-0.568565\pi\)
−0.213741 + 0.976890i \(0.568565\pi\)
\(198\) −1.00000 −0.0710669
\(199\) 12.0000 0.850657 0.425329 0.905039i \(-0.360158\pi\)
0.425329 + 0.905039i \(0.360158\pi\)
\(200\) −3.00000 −0.212132
\(201\) 24.0000 1.69283
\(202\) −14.0000 −0.985037
\(203\) 4.00000 0.280745
\(204\) −4.00000 −0.280056
\(205\) −1.00000 −0.0698430
\(206\) 12.0000 0.836080
\(207\) −4.00000 −0.278019
\(208\) 5.00000 0.346688
\(209\) −4.00000 −0.276686
\(210\) 2.00000 0.138013
\(211\) 8.00000 0.550743 0.275371 0.961338i \(-0.411199\pi\)
0.275371 + 0.961338i \(0.411199\pi\)
\(212\) 5.00000 0.343401
\(213\) 18.0000 1.23334
\(214\) 12.0000 0.820303
\(215\) 3.00000 0.204598
\(216\) 12.0000 0.816497
\(217\) −9.00000 −0.610960
\(218\) −2.00000 −0.135457
\(219\) −28.0000 −1.89206
\(220\) −1.00000 −0.0674200
\(221\) −10.0000 −0.672673
\(222\) 14.0000 0.939618
\(223\) 11.0000 0.736614 0.368307 0.929704i \(-0.379937\pi\)
0.368307 + 0.929704i \(0.379937\pi\)
\(224\) −5.00000 −0.334077
\(225\) 1.00000 0.0666667
\(226\) 14.0000 0.931266
\(227\) 7.00000 0.464606 0.232303 0.972643i \(-0.425374\pi\)
0.232303 + 0.972643i \(0.425374\pi\)
\(228\) −8.00000 −0.529813
\(229\) 1.00000 0.0660819
\(230\) 4.00000 0.263752
\(231\) 2.00000 0.131590
\(232\) 12.0000 0.787839
\(233\) 23.0000 1.50678 0.753390 0.657574i \(-0.228417\pi\)
0.753390 + 0.657574i \(0.228417\pi\)
\(234\) −5.00000 −0.326860
\(235\) −3.00000 −0.195698
\(236\) −4.00000 −0.260378
\(237\) 24.0000 1.55897
\(238\) −2.00000 −0.129641
\(239\) 6.00000 0.388108 0.194054 0.980991i \(-0.437836\pi\)
0.194054 + 0.980991i \(0.437836\pi\)
\(240\) 2.00000 0.129099
\(241\) 20.0000 1.28831 0.644157 0.764894i \(-0.277208\pi\)
0.644157 + 0.764894i \(0.277208\pi\)
\(242\) −10.0000 −0.642824
\(243\) −10.0000 −0.641500
\(244\) −2.00000 −0.128037
\(245\) −1.00000 −0.0638877
\(246\) 2.00000 0.127515
\(247\) −20.0000 −1.27257
\(248\) −27.0000 −1.71450
\(249\) 12.0000 0.760469
\(250\) −1.00000 −0.0632456
\(251\) −3.00000 −0.189358 −0.0946792 0.995508i \(-0.530183\pi\)
−0.0946792 + 0.995508i \(0.530183\pi\)
\(252\) 1.00000 0.0629941
\(253\) 4.00000 0.251478
\(254\) 20.0000 1.25491
\(255\) −4.00000 −0.250490
\(256\) −17.0000 −1.06250
\(257\) 18.0000 1.12281 0.561405 0.827541i \(-0.310261\pi\)
0.561405 + 0.827541i \(0.310261\pi\)
\(258\) −6.00000 −0.373544
\(259\) −7.00000 −0.434959
\(260\) −5.00000 −0.310087
\(261\) −4.00000 −0.247594
\(262\) −9.00000 −0.556022
\(263\) 6.00000 0.369976 0.184988 0.982741i \(-0.440775\pi\)
0.184988 + 0.982741i \(0.440775\pi\)
\(264\) 6.00000 0.369274
\(265\) 5.00000 0.307148
\(266\) −4.00000 −0.245256
\(267\) 18.0000 1.10158
\(268\) −12.0000 −0.733017
\(269\) −6.00000 −0.365826 −0.182913 0.983129i \(-0.558553\pi\)
−0.182913 + 0.983129i \(0.558553\pi\)
\(270\) 4.00000 0.243432
\(271\) −32.0000 −1.94386 −0.971931 0.235267i \(-0.924404\pi\)
−0.971931 + 0.235267i \(0.924404\pi\)
\(272\) −2.00000 −0.121268
\(273\) 10.0000 0.605228
\(274\) −12.0000 −0.724947
\(275\) −1.00000 −0.0603023
\(276\) 8.00000 0.481543
\(277\) 19.0000 1.14160 0.570800 0.821089i \(-0.306633\pi\)
0.570800 + 0.821089i \(0.306633\pi\)
\(278\) 19.0000 1.13954
\(279\) 9.00000 0.538816
\(280\) −3.00000 −0.179284
\(281\) −20.0000 −1.19310 −0.596550 0.802576i \(-0.703462\pi\)
−0.596550 + 0.802576i \(0.703462\pi\)
\(282\) 6.00000 0.357295
\(283\) 27.0000 1.60498 0.802492 0.596663i \(-0.203507\pi\)
0.802492 + 0.596663i \(0.203507\pi\)
\(284\) −9.00000 −0.534052
\(285\) −8.00000 −0.473879
\(286\) 5.00000 0.295656
\(287\) −1.00000 −0.0590281
\(288\) 5.00000 0.294628
\(289\) −13.0000 −0.764706
\(290\) 4.00000 0.234888
\(291\) −20.0000 −1.17242
\(292\) 14.0000 0.819288
\(293\) −22.0000 −1.28525 −0.642627 0.766179i \(-0.722155\pi\)
−0.642627 + 0.766179i \(0.722155\pi\)
\(294\) 2.00000 0.116642
\(295\) −4.00000 −0.232889
\(296\) −21.0000 −1.22060
\(297\) 4.00000 0.232104
\(298\) 7.00000 0.405499
\(299\) 20.0000 1.15663
\(300\) −2.00000 −0.115470
\(301\) 3.00000 0.172917
\(302\) −9.00000 −0.517892
\(303\) −28.0000 −1.60856
\(304\) −4.00000 −0.229416
\(305\) −2.00000 −0.114520
\(306\) 2.00000 0.114332
\(307\) −2.00000 −0.114146 −0.0570730 0.998370i \(-0.518177\pi\)
−0.0570730 + 0.998370i \(0.518177\pi\)
\(308\) −1.00000 −0.0569803
\(309\) 24.0000 1.36531
\(310\) −9.00000 −0.511166
\(311\) −20.0000 −1.13410 −0.567048 0.823685i \(-0.691915\pi\)
−0.567048 + 0.823685i \(0.691915\pi\)
\(312\) 30.0000 1.69842
\(313\) 1.00000 0.0565233 0.0282617 0.999601i \(-0.491003\pi\)
0.0282617 + 0.999601i \(0.491003\pi\)
\(314\) −1.00000 −0.0564333
\(315\) 1.00000 0.0563436
\(316\) −12.0000 −0.675053
\(317\) 4.00000 0.224662 0.112331 0.993671i \(-0.464168\pi\)
0.112331 + 0.993671i \(0.464168\pi\)
\(318\) −10.0000 −0.560772
\(319\) 4.00000 0.223957
\(320\) −7.00000 −0.391312
\(321\) 24.0000 1.33955
\(322\) 4.00000 0.222911
\(323\) 8.00000 0.445132
\(324\) 11.0000 0.611111
\(325\) −5.00000 −0.277350
\(326\) 24.0000 1.32924
\(327\) −4.00000 −0.221201
\(328\) −3.00000 −0.165647
\(329\) −3.00000 −0.165395
\(330\) 2.00000 0.110096
\(331\) −32.0000 −1.75888 −0.879440 0.476011i \(-0.842082\pi\)
−0.879440 + 0.476011i \(0.842082\pi\)
\(332\) −6.00000 −0.329293
\(333\) 7.00000 0.383598
\(334\) −12.0000 −0.656611
\(335\) −12.0000 −0.655630
\(336\) 2.00000 0.109109
\(337\) 1.00000 0.0544735 0.0272367 0.999629i \(-0.491329\pi\)
0.0272367 + 0.999629i \(0.491329\pi\)
\(338\) 12.0000 0.652714
\(339\) 28.0000 1.52075
\(340\) 2.00000 0.108465
\(341\) −9.00000 −0.487377
\(342\) 4.00000 0.216295
\(343\) −1.00000 −0.0539949
\(344\) 9.00000 0.485247
\(345\) 8.00000 0.430706
\(346\) 12.0000 0.645124
\(347\) 33.0000 1.77153 0.885766 0.464131i \(-0.153633\pi\)
0.885766 + 0.464131i \(0.153633\pi\)
\(348\) 8.00000 0.428845
\(349\) −33.0000 −1.76645 −0.883225 0.468950i \(-0.844632\pi\)
−0.883225 + 0.468950i \(0.844632\pi\)
\(350\) −1.00000 −0.0534522
\(351\) 20.0000 1.06752
\(352\) −5.00000 −0.266501
\(353\) 2.00000 0.106449 0.0532246 0.998583i \(-0.483050\pi\)
0.0532246 + 0.998583i \(0.483050\pi\)
\(354\) 8.00000 0.425195
\(355\) −9.00000 −0.477670
\(356\) −9.00000 −0.476999
\(357\) −4.00000 −0.211702
\(358\) −26.0000 −1.37414
\(359\) 21.0000 1.10834 0.554169 0.832404i \(-0.313036\pi\)
0.554169 + 0.832404i \(0.313036\pi\)
\(360\) 3.00000 0.158114
\(361\) −3.00000 −0.157895
\(362\) 12.0000 0.630706
\(363\) −20.0000 −1.04973
\(364\) −5.00000 −0.262071
\(365\) 14.0000 0.732793
\(366\) 4.00000 0.209083
\(367\) 10.0000 0.521996 0.260998 0.965339i \(-0.415948\pi\)
0.260998 + 0.965339i \(0.415948\pi\)
\(368\) 4.00000 0.208514
\(369\) 1.00000 0.0520579
\(370\) −7.00000 −0.363913
\(371\) 5.00000 0.259587
\(372\) −18.0000 −0.933257
\(373\) 35.0000 1.81223 0.906116 0.423030i \(-0.139034\pi\)
0.906116 + 0.423030i \(0.139034\pi\)
\(374\) −2.00000 −0.103418
\(375\) −2.00000 −0.103280
\(376\) −9.00000 −0.464140
\(377\) 20.0000 1.03005
\(378\) 4.00000 0.205738
\(379\) 28.0000 1.43826 0.719132 0.694874i \(-0.244540\pi\)
0.719132 + 0.694874i \(0.244540\pi\)
\(380\) 4.00000 0.205196
\(381\) 40.0000 2.04926
\(382\) −14.0000 −0.716302
\(383\) 2.00000 0.102195 0.0510976 0.998694i \(-0.483728\pi\)
0.0510976 + 0.998694i \(0.483728\pi\)
\(384\) −6.00000 −0.306186
\(385\) −1.00000 −0.0509647
\(386\) −3.00000 −0.152696
\(387\) −3.00000 −0.152499
\(388\) 10.0000 0.507673
\(389\) −20.0000 −1.01404 −0.507020 0.861934i \(-0.669253\pi\)
−0.507020 + 0.861934i \(0.669253\pi\)
\(390\) 10.0000 0.506370
\(391\) −8.00000 −0.404577
\(392\) −3.00000 −0.151523
\(393\) −18.0000 −0.907980
\(394\) −6.00000 −0.302276
\(395\) −12.0000 −0.603786
\(396\) 1.00000 0.0502519
\(397\) −22.0000 −1.10415 −0.552074 0.833795i \(-0.686163\pi\)
−0.552074 + 0.833795i \(0.686163\pi\)
\(398\) 12.0000 0.601506
\(399\) −8.00000 −0.400501
\(400\) −1.00000 −0.0500000
\(401\) 38.0000 1.89763 0.948815 0.315833i \(-0.102284\pi\)
0.948815 + 0.315833i \(0.102284\pi\)
\(402\) 24.0000 1.19701
\(403\) −45.0000 −2.24161
\(404\) 14.0000 0.696526
\(405\) 11.0000 0.546594
\(406\) 4.00000 0.198517
\(407\) −7.00000 −0.346977
\(408\) −12.0000 −0.594089
\(409\) −4.00000 −0.197787 −0.0988936 0.995098i \(-0.531530\pi\)
−0.0988936 + 0.995098i \(0.531530\pi\)
\(410\) −1.00000 −0.0493865
\(411\) −24.0000 −1.18383
\(412\) −12.0000 −0.591198
\(413\) −4.00000 −0.196827
\(414\) −4.00000 −0.196589
\(415\) −6.00000 −0.294528
\(416\) −25.0000 −1.22573
\(417\) 38.0000 1.86087
\(418\) −4.00000 −0.195646
\(419\) 1.00000 0.0488532 0.0244266 0.999702i \(-0.492224\pi\)
0.0244266 + 0.999702i \(0.492224\pi\)
\(420\) −2.00000 −0.0975900
\(421\) 6.00000 0.292422 0.146211 0.989253i \(-0.453292\pi\)
0.146211 + 0.989253i \(0.453292\pi\)
\(422\) 8.00000 0.389434
\(423\) 3.00000 0.145865
\(424\) 15.0000 0.728464
\(425\) 2.00000 0.0970143
\(426\) 18.0000 0.872103
\(427\) −2.00000 −0.0967868
\(428\) −12.0000 −0.580042
\(429\) 10.0000 0.482805
\(430\) 3.00000 0.144673
\(431\) −4.00000 −0.192673 −0.0963366 0.995349i \(-0.530713\pi\)
−0.0963366 + 0.995349i \(0.530713\pi\)
\(432\) 4.00000 0.192450
\(433\) −18.0000 −0.865025 −0.432512 0.901628i \(-0.642373\pi\)
−0.432512 + 0.901628i \(0.642373\pi\)
\(434\) −9.00000 −0.432014
\(435\) 8.00000 0.383571
\(436\) 2.00000 0.0957826
\(437\) −16.0000 −0.765384
\(438\) −28.0000 −1.33789
\(439\) 30.0000 1.43182 0.715911 0.698192i \(-0.246012\pi\)
0.715911 + 0.698192i \(0.246012\pi\)
\(440\) −3.00000 −0.143019
\(441\) 1.00000 0.0476190
\(442\) −10.0000 −0.475651
\(443\) 32.0000 1.52037 0.760183 0.649709i \(-0.225109\pi\)
0.760183 + 0.649709i \(0.225109\pi\)
\(444\) −14.0000 −0.664411
\(445\) −9.00000 −0.426641
\(446\) 11.0000 0.520865
\(447\) 14.0000 0.662177
\(448\) −7.00000 −0.330719
\(449\) −25.0000 −1.17982 −0.589911 0.807468i \(-0.700837\pi\)
−0.589911 + 0.807468i \(0.700837\pi\)
\(450\) 1.00000 0.0471405
\(451\) −1.00000 −0.0470882
\(452\) −14.0000 −0.658505
\(453\) −18.0000 −0.845714
\(454\) 7.00000 0.328526
\(455\) −5.00000 −0.234404
\(456\) −24.0000 −1.12390
\(457\) −34.0000 −1.59045 −0.795226 0.606313i \(-0.792648\pi\)
−0.795226 + 0.606313i \(0.792648\pi\)
\(458\) 1.00000 0.0467269
\(459\) −8.00000 −0.373408
\(460\) −4.00000 −0.186501
\(461\) −6.00000 −0.279448 −0.139724 0.990190i \(-0.544622\pi\)
−0.139724 + 0.990190i \(0.544622\pi\)
\(462\) 2.00000 0.0930484
\(463\) −23.0000 −1.06890 −0.534450 0.845200i \(-0.679481\pi\)
−0.534450 + 0.845200i \(0.679481\pi\)
\(464\) 4.00000 0.185695
\(465\) −18.0000 −0.834730
\(466\) 23.0000 1.06545
\(467\) −24.0000 −1.11059 −0.555294 0.831654i \(-0.687394\pi\)
−0.555294 + 0.831654i \(0.687394\pi\)
\(468\) 5.00000 0.231125
\(469\) −12.0000 −0.554109
\(470\) −3.00000 −0.138380
\(471\) −2.00000 −0.0921551
\(472\) −12.0000 −0.552345
\(473\) 3.00000 0.137940
\(474\) 24.0000 1.10236
\(475\) 4.00000 0.183533
\(476\) 2.00000 0.0916698
\(477\) −5.00000 −0.228934
\(478\) 6.00000 0.274434
\(479\) 17.0000 0.776750 0.388375 0.921501i \(-0.373037\pi\)
0.388375 + 0.921501i \(0.373037\pi\)
\(480\) −10.0000 −0.456435
\(481\) −35.0000 −1.59586
\(482\) 20.0000 0.910975
\(483\) 8.00000 0.364013
\(484\) 10.0000 0.454545
\(485\) 10.0000 0.454077
\(486\) −10.0000 −0.453609
\(487\) 20.0000 0.906287 0.453143 0.891438i \(-0.350303\pi\)
0.453143 + 0.891438i \(0.350303\pi\)
\(488\) −6.00000 −0.271607
\(489\) 48.0000 2.17064
\(490\) −1.00000 −0.0451754
\(491\) −24.0000 −1.08310 −0.541552 0.840667i \(-0.682163\pi\)
−0.541552 + 0.840667i \(0.682163\pi\)
\(492\) −2.00000 −0.0901670
\(493\) −8.00000 −0.360302
\(494\) −20.0000 −0.899843
\(495\) 1.00000 0.0449467
\(496\) −9.00000 −0.404112
\(497\) −9.00000 −0.403705
\(498\) 12.0000 0.537733
\(499\) −10.0000 −0.447661 −0.223831 0.974628i \(-0.571856\pi\)
−0.223831 + 0.974628i \(0.571856\pi\)
\(500\) 1.00000 0.0447214
\(501\) −24.0000 −1.07224
\(502\) −3.00000 −0.133897
\(503\) −36.0000 −1.60516 −0.802580 0.596544i \(-0.796540\pi\)
−0.802580 + 0.596544i \(0.796540\pi\)
\(504\) 3.00000 0.133631
\(505\) 14.0000 0.622992
\(506\) 4.00000 0.177822
\(507\) 24.0000 1.06588
\(508\) −20.0000 −0.887357
\(509\) −38.0000 −1.68432 −0.842160 0.539227i \(-0.818716\pi\)
−0.842160 + 0.539227i \(0.818716\pi\)
\(510\) −4.00000 −0.177123
\(511\) 14.0000 0.619324
\(512\) −11.0000 −0.486136
\(513\) −16.0000 −0.706417
\(514\) 18.0000 0.793946
\(515\) −12.0000 −0.528783
\(516\) 6.00000 0.264135
\(517\) −3.00000 −0.131940
\(518\) −7.00000 −0.307562
\(519\) 24.0000 1.05348
\(520\) −15.0000 −0.657794
\(521\) 27.0000 1.18289 0.591446 0.806345i \(-0.298557\pi\)
0.591446 + 0.806345i \(0.298557\pi\)
\(522\) −4.00000 −0.175075
\(523\) 21.0000 0.918266 0.459133 0.888368i \(-0.348160\pi\)
0.459133 + 0.888368i \(0.348160\pi\)
\(524\) 9.00000 0.393167
\(525\) −2.00000 −0.0872872
\(526\) 6.00000 0.261612
\(527\) 18.0000 0.784092
\(528\) 2.00000 0.0870388
\(529\) −7.00000 −0.304348
\(530\) 5.00000 0.217186
\(531\) 4.00000 0.173585
\(532\) 4.00000 0.173422
\(533\) −5.00000 −0.216574
\(534\) 18.0000 0.778936
\(535\) −12.0000 −0.518805
\(536\) −36.0000 −1.55496
\(537\) −52.0000 −2.24397
\(538\) −6.00000 −0.258678
\(539\) −1.00000 −0.0430730
\(540\) −4.00000 −0.172133
\(541\) −19.0000 −0.816874 −0.408437 0.912787i \(-0.633926\pi\)
−0.408437 + 0.912787i \(0.633926\pi\)
\(542\) −32.0000 −1.37452
\(543\) 24.0000 1.02994
\(544\) 10.0000 0.428746
\(545\) 2.00000 0.0856706
\(546\) 10.0000 0.427960
\(547\) 2.00000 0.0855138 0.0427569 0.999086i \(-0.486386\pi\)
0.0427569 + 0.999086i \(0.486386\pi\)
\(548\) 12.0000 0.512615
\(549\) 2.00000 0.0853579
\(550\) −1.00000 −0.0426401
\(551\) −16.0000 −0.681623
\(552\) 24.0000 1.02151
\(553\) −12.0000 −0.510292
\(554\) 19.0000 0.807233
\(555\) −14.0000 −0.594267
\(556\) −19.0000 −0.805779
\(557\) 18.0000 0.762684 0.381342 0.924434i \(-0.375462\pi\)
0.381342 + 0.924434i \(0.375462\pi\)
\(558\) 9.00000 0.381000
\(559\) 15.0000 0.634432
\(560\) −1.00000 −0.0422577
\(561\) −4.00000 −0.168880
\(562\) −20.0000 −0.843649
\(563\) 20.0000 0.842900 0.421450 0.906852i \(-0.361521\pi\)
0.421450 + 0.906852i \(0.361521\pi\)
\(564\) −6.00000 −0.252646
\(565\) −14.0000 −0.588984
\(566\) 27.0000 1.13489
\(567\) 11.0000 0.461957
\(568\) −27.0000 −1.13289
\(569\) 11.0000 0.461144 0.230572 0.973055i \(-0.425940\pi\)
0.230572 + 0.973055i \(0.425940\pi\)
\(570\) −8.00000 −0.335083
\(571\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(572\) −5.00000 −0.209061
\(573\) −28.0000 −1.16972
\(574\) −1.00000 −0.0417392
\(575\) −4.00000 −0.166812
\(576\) 7.00000 0.291667
\(577\) 3.00000 0.124892 0.0624458 0.998048i \(-0.480110\pi\)
0.0624458 + 0.998048i \(0.480110\pi\)
\(578\) −13.0000 −0.540729
\(579\) −6.00000 −0.249351
\(580\) −4.00000 −0.166091
\(581\) −6.00000 −0.248922
\(582\) −20.0000 −0.829027
\(583\) 5.00000 0.207079
\(584\) 42.0000 1.73797
\(585\) 5.00000 0.206725
\(586\) −22.0000 −0.908812
\(587\) 12.0000 0.495293 0.247647 0.968850i \(-0.420343\pi\)
0.247647 + 0.968850i \(0.420343\pi\)
\(588\) −2.00000 −0.0824786
\(589\) 36.0000 1.48335
\(590\) −4.00000 −0.164677
\(591\) −12.0000 −0.493614
\(592\) −7.00000 −0.287698
\(593\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(594\) 4.00000 0.164122
\(595\) 2.00000 0.0819920
\(596\) −7.00000 −0.286731
\(597\) 24.0000 0.982255
\(598\) 20.0000 0.817861
\(599\) 46.0000 1.87951 0.939755 0.341850i \(-0.111053\pi\)
0.939755 + 0.341850i \(0.111053\pi\)
\(600\) −6.00000 −0.244949
\(601\) −10.0000 −0.407909 −0.203954 0.978980i \(-0.565379\pi\)
−0.203954 + 0.978980i \(0.565379\pi\)
\(602\) 3.00000 0.122271
\(603\) 12.0000 0.488678
\(604\) 9.00000 0.366205
\(605\) 10.0000 0.406558
\(606\) −28.0000 −1.13742
\(607\) −34.0000 −1.38002 −0.690009 0.723801i \(-0.742393\pi\)
−0.690009 + 0.723801i \(0.742393\pi\)
\(608\) 20.0000 0.811107
\(609\) 8.00000 0.324176
\(610\) −2.00000 −0.0809776
\(611\) −15.0000 −0.606835
\(612\) −2.00000 −0.0808452
\(613\) −6.00000 −0.242338 −0.121169 0.992632i \(-0.538664\pi\)
−0.121169 + 0.992632i \(0.538664\pi\)
\(614\) −2.00000 −0.0807134
\(615\) −2.00000 −0.0806478
\(616\) −3.00000 −0.120873
\(617\) 41.0000 1.65060 0.825299 0.564696i \(-0.191007\pi\)
0.825299 + 0.564696i \(0.191007\pi\)
\(618\) 24.0000 0.965422
\(619\) 42.0000 1.68812 0.844061 0.536247i \(-0.180158\pi\)
0.844061 + 0.536247i \(0.180158\pi\)
\(620\) 9.00000 0.361449
\(621\) 16.0000 0.642058
\(622\) −20.0000 −0.801927
\(623\) −9.00000 −0.360577
\(624\) 10.0000 0.400320
\(625\) 1.00000 0.0400000
\(626\) 1.00000 0.0399680
\(627\) −8.00000 −0.319489
\(628\) 1.00000 0.0399043
\(629\) 14.0000 0.558217
\(630\) 1.00000 0.0398410
\(631\) 7.00000 0.278666 0.139333 0.990246i \(-0.455504\pi\)
0.139333 + 0.990246i \(0.455504\pi\)
\(632\) −36.0000 −1.43200
\(633\) 16.0000 0.635943
\(634\) 4.00000 0.158860
\(635\) −20.0000 −0.793676
\(636\) 10.0000 0.396526
\(637\) −5.00000 −0.198107
\(638\) 4.00000 0.158362
\(639\) 9.00000 0.356034
\(640\) 3.00000 0.118585
\(641\) 42.0000 1.65890 0.829450 0.558581i \(-0.188654\pi\)
0.829450 + 0.558581i \(0.188654\pi\)
\(642\) 24.0000 0.947204
\(643\) 42.0000 1.65632 0.828159 0.560493i \(-0.189388\pi\)
0.828159 + 0.560493i \(0.189388\pi\)
\(644\) −4.00000 −0.157622
\(645\) 6.00000 0.236250
\(646\) 8.00000 0.314756
\(647\) 45.0000 1.76913 0.884566 0.466415i \(-0.154454\pi\)
0.884566 + 0.466415i \(0.154454\pi\)
\(648\) 33.0000 1.29636
\(649\) −4.00000 −0.157014
\(650\) −5.00000 −0.196116
\(651\) −18.0000 −0.705476
\(652\) −24.0000 −0.939913
\(653\) 6.00000 0.234798 0.117399 0.993085i \(-0.462544\pi\)
0.117399 + 0.993085i \(0.462544\pi\)
\(654\) −4.00000 −0.156412
\(655\) 9.00000 0.351659
\(656\) −1.00000 −0.0390434
\(657\) −14.0000 −0.546192
\(658\) −3.00000 −0.116952
\(659\) −24.0000 −0.934907 −0.467454 0.884018i \(-0.654829\pi\)
−0.467454 + 0.884018i \(0.654829\pi\)
\(660\) −2.00000 −0.0778499
\(661\) −20.0000 −0.777910 −0.388955 0.921257i \(-0.627164\pi\)
−0.388955 + 0.921257i \(0.627164\pi\)
\(662\) −32.0000 −1.24372
\(663\) −20.0000 −0.776736
\(664\) −18.0000 −0.698535
\(665\) 4.00000 0.155113
\(666\) 7.00000 0.271244
\(667\) 16.0000 0.619522
\(668\) 12.0000 0.464294
\(669\) 22.0000 0.850569
\(670\) −12.0000 −0.463600
\(671\) −2.00000 −0.0772091
\(672\) −10.0000 −0.385758
\(673\) 22.0000 0.848038 0.424019 0.905653i \(-0.360619\pi\)
0.424019 + 0.905653i \(0.360619\pi\)
\(674\) 1.00000 0.0385186
\(675\) −4.00000 −0.153960
\(676\) −12.0000 −0.461538
\(677\) −30.0000 −1.15299 −0.576497 0.817099i \(-0.695581\pi\)
−0.576497 + 0.817099i \(0.695581\pi\)
\(678\) 28.0000 1.07533
\(679\) 10.0000 0.383765
\(680\) 6.00000 0.230089
\(681\) 14.0000 0.536481
\(682\) −9.00000 −0.344628
\(683\) −19.0000 −0.727015 −0.363507 0.931591i \(-0.618421\pi\)
−0.363507 + 0.931591i \(0.618421\pi\)
\(684\) −4.00000 −0.152944
\(685\) 12.0000 0.458496
\(686\) −1.00000 −0.0381802
\(687\) 2.00000 0.0763048
\(688\) 3.00000 0.114374
\(689\) 25.0000 0.952424
\(690\) 8.00000 0.304555
\(691\) 50.0000 1.90209 0.951045 0.309053i \(-0.100012\pi\)
0.951045 + 0.309053i \(0.100012\pi\)
\(692\) −12.0000 −0.456172
\(693\) 1.00000 0.0379869
\(694\) 33.0000 1.25266
\(695\) −19.0000 −0.720711
\(696\) 24.0000 0.909718
\(697\) 2.00000 0.0757554
\(698\) −33.0000 −1.24907
\(699\) 46.0000 1.73988
\(700\) 1.00000 0.0377964
\(701\) −17.0000 −0.642081 −0.321041 0.947065i \(-0.604033\pi\)
−0.321041 + 0.947065i \(0.604033\pi\)
\(702\) 20.0000 0.754851
\(703\) 28.0000 1.05604
\(704\) −7.00000 −0.263822
\(705\) −6.00000 −0.225973
\(706\) 2.00000 0.0752710
\(707\) 14.0000 0.526524
\(708\) −8.00000 −0.300658
\(709\) 34.0000 1.27690 0.638448 0.769665i \(-0.279577\pi\)
0.638448 + 0.769665i \(0.279577\pi\)
\(710\) −9.00000 −0.337764
\(711\) 12.0000 0.450035
\(712\) −27.0000 −1.01187
\(713\) −36.0000 −1.34821
\(714\) −4.00000 −0.149696
\(715\) −5.00000 −0.186989
\(716\) 26.0000 0.971666
\(717\) 12.0000 0.448148
\(718\) 21.0000 0.783713
\(719\) −41.0000 −1.52904 −0.764521 0.644599i \(-0.777024\pi\)
−0.764521 + 0.644599i \(0.777024\pi\)
\(720\) 1.00000 0.0372678
\(721\) −12.0000 −0.446903
\(722\) −3.00000 −0.111648
\(723\) 40.0000 1.48762
\(724\) −12.0000 −0.445976
\(725\) −4.00000 −0.148556
\(726\) −20.0000 −0.742270
\(727\) −16.0000 −0.593407 −0.296704 0.954970i \(-0.595887\pi\)
−0.296704 + 0.954970i \(0.595887\pi\)
\(728\) −15.0000 −0.555937
\(729\) 13.0000 0.481481
\(730\) 14.0000 0.518163
\(731\) −6.00000 −0.221918
\(732\) −4.00000 −0.147844
\(733\) −28.0000 −1.03420 −0.517102 0.855924i \(-0.672989\pi\)
−0.517102 + 0.855924i \(0.672989\pi\)
\(734\) 10.0000 0.369107
\(735\) −2.00000 −0.0737711
\(736\) −20.0000 −0.737210
\(737\) −12.0000 −0.442026
\(738\) 1.00000 0.0368105
\(739\) −30.0000 −1.10357 −0.551784 0.833987i \(-0.686053\pi\)
−0.551784 + 0.833987i \(0.686053\pi\)
\(740\) 7.00000 0.257325
\(741\) −40.0000 −1.46944
\(742\) 5.00000 0.183556
\(743\) 8.00000 0.293492 0.146746 0.989174i \(-0.453120\pi\)
0.146746 + 0.989174i \(0.453120\pi\)
\(744\) −54.0000 −1.97974
\(745\) −7.00000 −0.256460
\(746\) 35.0000 1.28144
\(747\) 6.00000 0.219529
\(748\) 2.00000 0.0731272
\(749\) −12.0000 −0.438470
\(750\) −2.00000 −0.0730297
\(751\) 29.0000 1.05823 0.529113 0.848552i \(-0.322525\pi\)
0.529113 + 0.848552i \(0.322525\pi\)
\(752\) −3.00000 −0.109399
\(753\) −6.00000 −0.218652
\(754\) 20.0000 0.728357
\(755\) 9.00000 0.327544
\(756\) −4.00000 −0.145479
\(757\) −3.00000 −0.109037 −0.0545184 0.998513i \(-0.517362\pi\)
−0.0545184 + 0.998513i \(0.517362\pi\)
\(758\) 28.0000 1.01701
\(759\) 8.00000 0.290382
\(760\) 12.0000 0.435286
\(761\) −47.0000 −1.70375 −0.851874 0.523746i \(-0.824534\pi\)
−0.851874 + 0.523746i \(0.824534\pi\)
\(762\) 40.0000 1.44905
\(763\) 2.00000 0.0724049
\(764\) 14.0000 0.506502
\(765\) −2.00000 −0.0723102
\(766\) 2.00000 0.0722629
\(767\) −20.0000 −0.722158
\(768\) −34.0000 −1.22687
\(769\) 14.0000 0.504853 0.252426 0.967616i \(-0.418771\pi\)
0.252426 + 0.967616i \(0.418771\pi\)
\(770\) −1.00000 −0.0360375
\(771\) 36.0000 1.29651
\(772\) 3.00000 0.107972
\(773\) 1.00000 0.0359675 0.0179838 0.999838i \(-0.494275\pi\)
0.0179838 + 0.999838i \(0.494275\pi\)
\(774\) −3.00000 −0.107833
\(775\) 9.00000 0.323290
\(776\) 30.0000 1.07694
\(777\) −14.0000 −0.502247
\(778\) −20.0000 −0.717035
\(779\) 4.00000 0.143315
\(780\) −10.0000 −0.358057
\(781\) −9.00000 −0.322045
\(782\) −8.00000 −0.286079
\(783\) 16.0000 0.571793
\(784\) −1.00000 −0.0357143
\(785\) 1.00000 0.0356915
\(786\) −18.0000 −0.642039
\(787\) 22.0000 0.784215 0.392108 0.919919i \(-0.371746\pi\)
0.392108 + 0.919919i \(0.371746\pi\)
\(788\) 6.00000 0.213741
\(789\) 12.0000 0.427211
\(790\) −12.0000 −0.426941
\(791\) −14.0000 −0.497783
\(792\) 3.00000 0.106600
\(793\) −10.0000 −0.355110
\(794\) −22.0000 −0.780751
\(795\) 10.0000 0.354663
\(796\) −12.0000 −0.425329
\(797\) 15.0000 0.531327 0.265664 0.964066i \(-0.414409\pi\)
0.265664 + 0.964066i \(0.414409\pi\)
\(798\) −8.00000 −0.283197
\(799\) 6.00000 0.212265
\(800\) 5.00000 0.176777
\(801\) 9.00000 0.317999
\(802\) 38.0000 1.34183
\(803\) 14.0000 0.494049
\(804\) −24.0000 −0.846415
\(805\) −4.00000 −0.140981
\(806\) −45.0000 −1.58506
\(807\) −12.0000 −0.422420
\(808\) 42.0000 1.47755
\(809\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(810\) 11.0000 0.386501
\(811\) 4.00000 0.140459 0.0702295 0.997531i \(-0.477627\pi\)
0.0702295 + 0.997531i \(0.477627\pi\)
\(812\) −4.00000 −0.140372
\(813\) −64.0000 −2.24458
\(814\) −7.00000 −0.245350
\(815\) −24.0000 −0.840683
\(816\) −4.00000 −0.140028
\(817\) −12.0000 −0.419827
\(818\) −4.00000 −0.139857
\(819\) 5.00000 0.174714
\(820\) 1.00000 0.0349215
\(821\) −10.0000 −0.349002 −0.174501 0.984657i \(-0.555831\pi\)
−0.174501 + 0.984657i \(0.555831\pi\)
\(822\) −24.0000 −0.837096
\(823\) −8.00000 −0.278862 −0.139431 0.990232i \(-0.544527\pi\)
−0.139431 + 0.990232i \(0.544527\pi\)
\(824\) −36.0000 −1.25412
\(825\) −2.00000 −0.0696311
\(826\) −4.00000 −0.139178
\(827\) 24.0000 0.834562 0.417281 0.908778i \(-0.362983\pi\)
0.417281 + 0.908778i \(0.362983\pi\)
\(828\) 4.00000 0.139010
\(829\) −42.0000 −1.45872 −0.729360 0.684130i \(-0.760182\pi\)
−0.729360 + 0.684130i \(0.760182\pi\)
\(830\) −6.00000 −0.208263
\(831\) 38.0000 1.31821
\(832\) −35.0000 −1.21341
\(833\) 2.00000 0.0692959
\(834\) 38.0000 1.31583
\(835\) 12.0000 0.415277
\(836\) 4.00000 0.138343
\(837\) −36.0000 −1.24434
\(838\) 1.00000 0.0345444
\(839\) −5.00000 −0.172619 −0.0863096 0.996268i \(-0.527507\pi\)
−0.0863096 + 0.996268i \(0.527507\pi\)
\(840\) −6.00000 −0.207020
\(841\) −13.0000 −0.448276
\(842\) 6.00000 0.206774
\(843\) −40.0000 −1.37767
\(844\) −8.00000 −0.275371
\(845\) −12.0000 −0.412813
\(846\) 3.00000 0.103142
\(847\) 10.0000 0.343604
\(848\) 5.00000 0.171701
\(849\) 54.0000 1.85328
\(850\) 2.00000 0.0685994
\(851\) −28.0000 −0.959828
\(852\) −18.0000 −0.616670
\(853\) −47.0000 −1.60925 −0.804625 0.593784i \(-0.797633\pi\)
−0.804625 + 0.593784i \(0.797633\pi\)
\(854\) −2.00000 −0.0684386
\(855\) −4.00000 −0.136797
\(856\) −36.0000 −1.23045
\(857\) 39.0000 1.33221 0.666107 0.745856i \(-0.267959\pi\)
0.666107 + 0.745856i \(0.267959\pi\)
\(858\) 10.0000 0.341394
\(859\) 50.0000 1.70598 0.852989 0.521929i \(-0.174787\pi\)
0.852989 + 0.521929i \(0.174787\pi\)
\(860\) −3.00000 −0.102299
\(861\) −2.00000 −0.0681598
\(862\) −4.00000 −0.136241
\(863\) 24.0000 0.816970 0.408485 0.912765i \(-0.366057\pi\)
0.408485 + 0.912765i \(0.366057\pi\)
\(864\) −20.0000 −0.680414
\(865\) −12.0000 −0.408012
\(866\) −18.0000 −0.611665
\(867\) −26.0000 −0.883006
\(868\) 9.00000 0.305480
\(869\) −12.0000 −0.407072
\(870\) 8.00000 0.271225
\(871\) −60.0000 −2.03302
\(872\) 6.00000 0.203186
\(873\) −10.0000 −0.338449
\(874\) −16.0000 −0.541208
\(875\) 1.00000 0.0338062
\(876\) 28.0000 0.946032
\(877\) 2.00000 0.0675352 0.0337676 0.999430i \(-0.489249\pi\)
0.0337676 + 0.999430i \(0.489249\pi\)
\(878\) 30.0000 1.01245
\(879\) −44.0000 −1.48408
\(880\) −1.00000 −0.0337100
\(881\) 53.0000 1.78562 0.892808 0.450438i \(-0.148732\pi\)
0.892808 + 0.450438i \(0.148732\pi\)
\(882\) 1.00000 0.0336718
\(883\) −33.0000 −1.11054 −0.555269 0.831671i \(-0.687385\pi\)
−0.555269 + 0.831671i \(0.687385\pi\)
\(884\) 10.0000 0.336336
\(885\) −8.00000 −0.268917
\(886\) 32.0000 1.07506
\(887\) 3.00000 0.100730 0.0503651 0.998731i \(-0.483962\pi\)
0.0503651 + 0.998731i \(0.483962\pi\)
\(888\) −42.0000 −1.40943
\(889\) −20.0000 −0.670778
\(890\) −9.00000 −0.301681
\(891\) 11.0000 0.368514
\(892\) −11.0000 −0.368307
\(893\) 12.0000 0.401565
\(894\) 14.0000 0.468230
\(895\) 26.0000 0.869084
\(896\) 3.00000 0.100223
\(897\) 40.0000 1.33556
\(898\) −25.0000 −0.834261
\(899\) −36.0000 −1.20067
\(900\) −1.00000 −0.0333333
\(901\) −10.0000 −0.333148
\(902\) −1.00000 −0.0332964
\(903\) 6.00000 0.199667
\(904\) −42.0000 −1.39690
\(905\) −12.0000 −0.398893
\(906\) −18.0000 −0.598010
\(907\) −12.0000 −0.398453 −0.199227 0.979953i \(-0.563843\pi\)
−0.199227 + 0.979953i \(0.563843\pi\)
\(908\) −7.00000 −0.232303
\(909\) −14.0000 −0.464351
\(910\) −5.00000 −0.165748
\(911\) −7.00000 −0.231920 −0.115960 0.993254i \(-0.536994\pi\)
−0.115960 + 0.993254i \(0.536994\pi\)
\(912\) −8.00000 −0.264906
\(913\) −6.00000 −0.198571
\(914\) −34.0000 −1.12462
\(915\) −4.00000 −0.132236
\(916\) −1.00000 −0.0330409
\(917\) 9.00000 0.297206
\(918\) −8.00000 −0.264039
\(919\) −55.0000 −1.81428 −0.907141 0.420826i \(-0.861740\pi\)
−0.907141 + 0.420826i \(0.861740\pi\)
\(920\) −12.0000 −0.395628
\(921\) −4.00000 −0.131804
\(922\) −6.00000 −0.197599
\(923\) −45.0000 −1.48119
\(924\) −2.00000 −0.0657952
\(925\) 7.00000 0.230159
\(926\) −23.0000 −0.755827
\(927\) 12.0000 0.394132
\(928\) −20.0000 −0.656532
\(929\) 30.0000 0.984268 0.492134 0.870519i \(-0.336217\pi\)
0.492134 + 0.870519i \(0.336217\pi\)
\(930\) −18.0000 −0.590243
\(931\) 4.00000 0.131095
\(932\) −23.0000 −0.753390
\(933\) −40.0000 −1.30954
\(934\) −24.0000 −0.785304
\(935\) 2.00000 0.0654070
\(936\) 15.0000 0.490290
\(937\) −43.0000 −1.40475 −0.702374 0.711808i \(-0.747877\pi\)
−0.702374 + 0.711808i \(0.747877\pi\)
\(938\) −12.0000 −0.391814
\(939\) 2.00000 0.0652675
\(940\) 3.00000 0.0978492
\(941\) 24.0000 0.782378 0.391189 0.920310i \(-0.372064\pi\)
0.391189 + 0.920310i \(0.372064\pi\)
\(942\) −2.00000 −0.0651635
\(943\) −4.00000 −0.130258
\(944\) −4.00000 −0.130189
\(945\) −4.00000 −0.130120
\(946\) 3.00000 0.0975384
\(947\) 38.0000 1.23483 0.617417 0.786636i \(-0.288179\pi\)
0.617417 + 0.786636i \(0.288179\pi\)
\(948\) −24.0000 −0.779484
\(949\) 70.0000 2.27230
\(950\) 4.00000 0.129777
\(951\) 8.00000 0.259418
\(952\) 6.00000 0.194461
\(953\) −2.00000 −0.0647864 −0.0323932 0.999475i \(-0.510313\pi\)
−0.0323932 + 0.999475i \(0.510313\pi\)
\(954\) −5.00000 −0.161881
\(955\) 14.0000 0.453029
\(956\) −6.00000 −0.194054
\(957\) 8.00000 0.258603
\(958\) 17.0000 0.549245
\(959\) 12.0000 0.387500
\(960\) −14.0000 −0.451848
\(961\) 50.0000 1.61290
\(962\) −35.0000 −1.12845
\(963\) 12.0000 0.386695
\(964\) −20.0000 −0.644157
\(965\) 3.00000 0.0965734
\(966\) 8.00000 0.257396
\(967\) −1.00000 −0.0321578 −0.0160789 0.999871i \(-0.505118\pi\)
−0.0160789 + 0.999871i \(0.505118\pi\)
\(968\) 30.0000 0.964237
\(969\) 16.0000 0.513994
\(970\) 10.0000 0.321081
\(971\) 2.00000 0.0641831 0.0320915 0.999485i \(-0.489783\pi\)
0.0320915 + 0.999485i \(0.489783\pi\)
\(972\) 10.0000 0.320750
\(973\) −19.0000 −0.609112
\(974\) 20.0000 0.640841
\(975\) −10.0000 −0.320256
\(976\) −2.00000 −0.0640184
\(977\) 59.0000 1.88758 0.943789 0.330550i \(-0.107234\pi\)
0.943789 + 0.330550i \(0.107234\pi\)
\(978\) 48.0000 1.53487
\(979\) −9.00000 −0.287641
\(980\) 1.00000 0.0319438
\(981\) −2.00000 −0.0638551
\(982\) −24.0000 −0.765871
\(983\) −20.0000 −0.637901 −0.318950 0.947771i \(-0.603330\pi\)
−0.318950 + 0.947771i \(0.603330\pi\)
\(984\) −6.00000 −0.191273
\(985\) 6.00000 0.191176
\(986\) −8.00000 −0.254772
\(987\) −6.00000 −0.190982
\(988\) 20.0000 0.636285
\(989\) 12.0000 0.381578
\(990\) 1.00000 0.0317821
\(991\) −25.0000 −0.794151 −0.397076 0.917786i \(-0.629975\pi\)
−0.397076 + 0.917786i \(0.629975\pi\)
\(992\) 45.0000 1.42875
\(993\) −64.0000 −2.03098
\(994\) −9.00000 −0.285463
\(995\) −12.0000 −0.380426
\(996\) −12.0000 −0.380235
\(997\) 40.0000 1.26681 0.633406 0.773819i \(-0.281656\pi\)
0.633406 + 0.773819i \(0.281656\pi\)
\(998\) −10.0000 −0.316544
\(999\) −28.0000 −0.885881
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 8015.2.a.e.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8015.2.a.e.1.1 1 1.1 even 1 trivial