Properties

Label 726.2.a.i.1.1
Level $726$
Weight $2$
Character 726.1
Self dual yes
Analytic conductor $5.797$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 726 = 2 \cdot 3 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 726.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(5.79713918674\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 66)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 726.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -2.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -2.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{12} +4.00000 q^{13} -2.00000 q^{14} +1.00000 q^{16} +6.00000 q^{17} +1.00000 q^{18} +4.00000 q^{19} -2.00000 q^{21} +6.00000 q^{23} +1.00000 q^{24} -5.00000 q^{25} +4.00000 q^{26} +1.00000 q^{27} -2.00000 q^{28} -6.00000 q^{29} +8.00000 q^{31} +1.00000 q^{32} +6.00000 q^{34} +1.00000 q^{36} -10.0000 q^{37} +4.00000 q^{38} +4.00000 q^{39} -6.00000 q^{41} -2.00000 q^{42} -8.00000 q^{43} +6.00000 q^{46} -6.00000 q^{47} +1.00000 q^{48} -3.00000 q^{49} -5.00000 q^{50} +6.00000 q^{51} +4.00000 q^{52} +1.00000 q^{54} -2.00000 q^{56} +4.00000 q^{57} -6.00000 q^{58} -8.00000 q^{61} +8.00000 q^{62} -2.00000 q^{63} +1.00000 q^{64} -4.00000 q^{67} +6.00000 q^{68} +6.00000 q^{69} +6.00000 q^{71} +1.00000 q^{72} -2.00000 q^{73} -10.0000 q^{74} -5.00000 q^{75} +4.00000 q^{76} +4.00000 q^{78} -14.0000 q^{79} +1.00000 q^{81} -6.00000 q^{82} +12.0000 q^{83} -2.00000 q^{84} -8.00000 q^{86} -6.00000 q^{87} -6.00000 q^{89} -8.00000 q^{91} +6.00000 q^{92} +8.00000 q^{93} -6.00000 q^{94} +1.00000 q^{96} +14.0000 q^{97} -3.00000 q^{98} +O(q^{100})\)

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
\(3\) 1.00000 0.577350
\(4\) 1.00000 0.500000
\(5\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(6\) 1.00000 0.408248
\(7\) −2.00000 −0.755929 −0.377964 0.925820i \(-0.623376\pi\)
−0.377964 + 0.925820i \(0.623376\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 0 0
\(12\) 1.00000 0.288675
\(13\) 4.00000 1.10940 0.554700 0.832050i \(-0.312833\pi\)
0.554700 + 0.832050i \(0.312833\pi\)
\(14\) −2.00000 −0.534522
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 6.00000 1.45521 0.727607 0.685994i \(-0.240633\pi\)
0.727607 + 0.685994i \(0.240633\pi\)
\(18\) 1.00000 0.235702
\(19\) 4.00000 0.917663 0.458831 0.888523i \(-0.348268\pi\)
0.458831 + 0.888523i \(0.348268\pi\)
\(20\) 0 0
\(21\) −2.00000 −0.436436
\(22\) 0 0
\(23\) 6.00000 1.25109 0.625543 0.780189i \(-0.284877\pi\)
0.625543 + 0.780189i \(0.284877\pi\)
\(24\) 1.00000 0.204124
\(25\) −5.00000 −1.00000
\(26\) 4.00000 0.784465
\(27\) 1.00000 0.192450
\(28\) −2.00000 −0.377964
\(29\) −6.00000 −1.11417 −0.557086 0.830455i \(-0.688081\pi\)
−0.557086 + 0.830455i \(0.688081\pi\)
\(30\) 0 0
\(31\) 8.00000 1.43684 0.718421 0.695608i \(-0.244865\pi\)
0.718421 + 0.695608i \(0.244865\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) 6.00000 1.02899
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) −10.0000 −1.64399 −0.821995 0.569495i \(-0.807139\pi\)
−0.821995 + 0.569495i \(0.807139\pi\)
\(38\) 4.00000 0.648886
\(39\) 4.00000 0.640513
\(40\) 0 0
\(41\) −6.00000 −0.937043 −0.468521 0.883452i \(-0.655213\pi\)
−0.468521 + 0.883452i \(0.655213\pi\)
\(42\) −2.00000 −0.308607
\(43\) −8.00000 −1.21999 −0.609994 0.792406i \(-0.708828\pi\)
−0.609994 + 0.792406i \(0.708828\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 6.00000 0.884652
\(47\) −6.00000 −0.875190 −0.437595 0.899172i \(-0.644170\pi\)
−0.437595 + 0.899172i \(0.644170\pi\)
\(48\) 1.00000 0.144338
\(49\) −3.00000 −0.428571
\(50\) −5.00000 −0.707107
\(51\) 6.00000 0.840168
\(52\) 4.00000 0.554700
\(53\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(54\) 1.00000 0.136083
\(55\) 0 0
\(56\) −2.00000 −0.267261
\(57\) 4.00000 0.529813
\(58\) −6.00000 −0.787839
\(59\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) 0 0
\(61\) −8.00000 −1.02430 −0.512148 0.858898i \(-0.671150\pi\)
−0.512148 + 0.858898i \(0.671150\pi\)
\(62\) 8.00000 1.01600
\(63\) −2.00000 −0.251976
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) −4.00000 −0.488678 −0.244339 0.969690i \(-0.578571\pi\)
−0.244339 + 0.969690i \(0.578571\pi\)
\(68\) 6.00000 0.727607
\(69\) 6.00000 0.722315
\(70\) 0 0
\(71\) 6.00000 0.712069 0.356034 0.934473i \(-0.384129\pi\)
0.356034 + 0.934473i \(0.384129\pi\)
\(72\) 1.00000 0.117851
\(73\) −2.00000 −0.234082 −0.117041 0.993127i \(-0.537341\pi\)
−0.117041 + 0.993127i \(0.537341\pi\)
\(74\) −10.0000 −1.16248
\(75\) −5.00000 −0.577350
\(76\) 4.00000 0.458831
\(77\) 0 0
\(78\) 4.00000 0.452911
\(79\) −14.0000 −1.57512 −0.787562 0.616236i \(-0.788657\pi\)
−0.787562 + 0.616236i \(0.788657\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) −6.00000 −0.662589
\(83\) 12.0000 1.31717 0.658586 0.752506i \(-0.271155\pi\)
0.658586 + 0.752506i \(0.271155\pi\)
\(84\) −2.00000 −0.218218
\(85\) 0 0
\(86\) −8.00000 −0.862662
\(87\) −6.00000 −0.643268
\(88\) 0 0
\(89\) −6.00000 −0.635999 −0.317999 0.948091i \(-0.603011\pi\)
−0.317999 + 0.948091i \(0.603011\pi\)
\(90\) 0 0
\(91\) −8.00000 −0.838628
\(92\) 6.00000 0.625543
\(93\) 8.00000 0.829561
\(94\) −6.00000 −0.618853
\(95\) 0 0
\(96\) 1.00000 0.102062
\(97\) 14.0000 1.42148 0.710742 0.703452i \(-0.248359\pi\)
0.710742 + 0.703452i \(0.248359\pi\)
\(98\) −3.00000 −0.303046
\(99\) 0 0
\(100\) −5.00000 −0.500000
\(101\) −6.00000 −0.597022 −0.298511 0.954406i \(-0.596490\pi\)
−0.298511 + 0.954406i \(0.596490\pi\)
\(102\) 6.00000 0.594089
\(103\) −4.00000 −0.394132 −0.197066 0.980390i \(-0.563141\pi\)
−0.197066 + 0.980390i \(0.563141\pi\)
\(104\) 4.00000 0.392232
\(105\) 0 0
\(106\) 0 0
\(107\) 12.0000 1.16008 0.580042 0.814587i \(-0.303036\pi\)
0.580042 + 0.814587i \(0.303036\pi\)
\(108\) 1.00000 0.0962250
\(109\) 4.00000 0.383131 0.191565 0.981480i \(-0.438644\pi\)
0.191565 + 0.981480i \(0.438644\pi\)
\(110\) 0 0
\(111\) −10.0000 −0.949158
\(112\) −2.00000 −0.188982
\(113\) 18.0000 1.69330 0.846649 0.532152i \(-0.178617\pi\)
0.846649 + 0.532152i \(0.178617\pi\)
\(114\) 4.00000 0.374634
\(115\) 0 0
\(116\) −6.00000 −0.557086
\(117\) 4.00000 0.369800
\(118\) 0 0
\(119\) −12.0000 −1.10004
\(120\) 0 0
\(121\) 0 0
\(122\) −8.00000 −0.724286
\(123\) −6.00000 −0.541002
\(124\) 8.00000 0.718421
\(125\) 0 0
\(126\) −2.00000 −0.178174
\(127\) −14.0000 −1.24230 −0.621150 0.783692i \(-0.713334\pi\)
−0.621150 + 0.783692i \(0.713334\pi\)
\(128\) 1.00000 0.0883883
\(129\) −8.00000 −0.704361
\(130\) 0 0
\(131\) 12.0000 1.04844 0.524222 0.851581i \(-0.324356\pi\)
0.524222 + 0.851581i \(0.324356\pi\)
\(132\) 0 0
\(133\) −8.00000 −0.693688
\(134\) −4.00000 −0.345547
\(135\) 0 0
\(136\) 6.00000 0.514496
\(137\) −18.0000 −1.53784 −0.768922 0.639343i \(-0.779207\pi\)
−0.768922 + 0.639343i \(0.779207\pi\)
\(138\) 6.00000 0.510754
\(139\) 4.00000 0.339276 0.169638 0.985506i \(-0.445740\pi\)
0.169638 + 0.985506i \(0.445740\pi\)
\(140\) 0 0
\(141\) −6.00000 −0.505291
\(142\) 6.00000 0.503509
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) −2.00000 −0.165521
\(147\) −3.00000 −0.247436
\(148\) −10.0000 −0.821995
\(149\) 6.00000 0.491539 0.245770 0.969328i \(-0.420959\pi\)
0.245770 + 0.969328i \(0.420959\pi\)
\(150\) −5.00000 −0.408248
\(151\) 10.0000 0.813788 0.406894 0.913475i \(-0.366612\pi\)
0.406894 + 0.913475i \(0.366612\pi\)
\(152\) 4.00000 0.324443
\(153\) 6.00000 0.485071
\(154\) 0 0
\(155\) 0 0
\(156\) 4.00000 0.320256
\(157\) 2.00000 0.159617 0.0798087 0.996810i \(-0.474569\pi\)
0.0798087 + 0.996810i \(0.474569\pi\)
\(158\) −14.0000 −1.11378
\(159\) 0 0
\(160\) 0 0
\(161\) −12.0000 −0.945732
\(162\) 1.00000 0.0785674
\(163\) −4.00000 −0.313304 −0.156652 0.987654i \(-0.550070\pi\)
−0.156652 + 0.987654i \(0.550070\pi\)
\(164\) −6.00000 −0.468521
\(165\) 0 0
\(166\) 12.0000 0.931381
\(167\) −12.0000 −0.928588 −0.464294 0.885681i \(-0.653692\pi\)
−0.464294 + 0.885681i \(0.653692\pi\)
\(168\) −2.00000 −0.154303
\(169\) 3.00000 0.230769
\(170\) 0 0
\(171\) 4.00000 0.305888
\(172\) −8.00000 −0.609994
\(173\) −6.00000 −0.456172 −0.228086 0.973641i \(-0.573247\pi\)
−0.228086 + 0.973641i \(0.573247\pi\)
\(174\) −6.00000 −0.454859
\(175\) 10.0000 0.755929
\(176\) 0 0
\(177\) 0 0
\(178\) −6.00000 −0.449719
\(179\) 24.0000 1.79384 0.896922 0.442189i \(-0.145798\pi\)
0.896922 + 0.442189i \(0.145798\pi\)
\(180\) 0 0
\(181\) −22.0000 −1.63525 −0.817624 0.575753i \(-0.804709\pi\)
−0.817624 + 0.575753i \(0.804709\pi\)
\(182\) −8.00000 −0.592999
\(183\) −8.00000 −0.591377
\(184\) 6.00000 0.442326
\(185\) 0 0
\(186\) 8.00000 0.586588
\(187\) 0 0
\(188\) −6.00000 −0.437595
\(189\) −2.00000 −0.145479
\(190\) 0 0
\(191\) 18.0000 1.30243 0.651217 0.758891i \(-0.274259\pi\)
0.651217 + 0.758891i \(0.274259\pi\)
\(192\) 1.00000 0.0721688
\(193\) −14.0000 −1.00774 −0.503871 0.863779i \(-0.668091\pi\)
−0.503871 + 0.863779i \(0.668091\pi\)
\(194\) 14.0000 1.00514
\(195\) 0 0
\(196\) −3.00000 −0.214286
\(197\) −6.00000 −0.427482 −0.213741 0.976890i \(-0.568565\pi\)
−0.213741 + 0.976890i \(0.568565\pi\)
\(198\) 0 0
\(199\) −4.00000 −0.283552 −0.141776 0.989899i \(-0.545281\pi\)
−0.141776 + 0.989899i \(0.545281\pi\)
\(200\) −5.00000 −0.353553
\(201\) −4.00000 −0.282138
\(202\) −6.00000 −0.422159
\(203\) 12.0000 0.842235
\(204\) 6.00000 0.420084
\(205\) 0 0
\(206\) −4.00000 −0.278693
\(207\) 6.00000 0.417029
\(208\) 4.00000 0.277350
\(209\) 0 0
\(210\) 0 0
\(211\) −8.00000 −0.550743 −0.275371 0.961338i \(-0.588801\pi\)
−0.275371 + 0.961338i \(0.588801\pi\)
\(212\) 0 0
\(213\) 6.00000 0.411113
\(214\) 12.0000 0.820303
\(215\) 0 0
\(216\) 1.00000 0.0680414
\(217\) −16.0000 −1.08615
\(218\) 4.00000 0.270914
\(219\) −2.00000 −0.135147
\(220\) 0 0
\(221\) 24.0000 1.61441
\(222\) −10.0000 −0.671156
\(223\) −16.0000 −1.07144 −0.535720 0.844396i \(-0.679960\pi\)
−0.535720 + 0.844396i \(0.679960\pi\)
\(224\) −2.00000 −0.133631
\(225\) −5.00000 −0.333333
\(226\) 18.0000 1.19734
\(227\) 12.0000 0.796468 0.398234 0.917284i \(-0.369623\pi\)
0.398234 + 0.917284i \(0.369623\pi\)
\(228\) 4.00000 0.264906
\(229\) −22.0000 −1.45380 −0.726900 0.686743i \(-0.759040\pi\)
−0.726900 + 0.686743i \(0.759040\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −6.00000 −0.393919
\(233\) 18.0000 1.17922 0.589610 0.807688i \(-0.299282\pi\)
0.589610 + 0.807688i \(0.299282\pi\)
\(234\) 4.00000 0.261488
\(235\) 0 0
\(236\) 0 0
\(237\) −14.0000 −0.909398
\(238\) −12.0000 −0.777844
\(239\) 12.0000 0.776215 0.388108 0.921614i \(-0.373129\pi\)
0.388108 + 0.921614i \(0.373129\pi\)
\(240\) 0 0
\(241\) 10.0000 0.644157 0.322078 0.946713i \(-0.395619\pi\)
0.322078 + 0.946713i \(0.395619\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) −8.00000 −0.512148
\(245\) 0 0
\(246\) −6.00000 −0.382546
\(247\) 16.0000 1.01806
\(248\) 8.00000 0.508001
\(249\) 12.0000 0.760469
\(250\) 0 0
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) −2.00000 −0.125988
\(253\) 0 0
\(254\) −14.0000 −0.878438
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −30.0000 −1.87135 −0.935674 0.352865i \(-0.885208\pi\)
−0.935674 + 0.352865i \(0.885208\pi\)
\(258\) −8.00000 −0.498058
\(259\) 20.0000 1.24274
\(260\) 0 0
\(261\) −6.00000 −0.371391
\(262\) 12.0000 0.741362
\(263\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −8.00000 −0.490511
\(267\) −6.00000 −0.367194
\(268\) −4.00000 −0.244339
\(269\) −24.0000 −1.46331 −0.731653 0.681677i \(-0.761251\pi\)
−0.731653 + 0.681677i \(0.761251\pi\)
\(270\) 0 0
\(271\) −2.00000 −0.121491 −0.0607457 0.998153i \(-0.519348\pi\)
−0.0607457 + 0.998153i \(0.519348\pi\)
\(272\) 6.00000 0.363803
\(273\) −8.00000 −0.484182
\(274\) −18.0000 −1.08742
\(275\) 0 0
\(276\) 6.00000 0.361158
\(277\) 16.0000 0.961347 0.480673 0.876900i \(-0.340392\pi\)
0.480673 + 0.876900i \(0.340392\pi\)
\(278\) 4.00000 0.239904
\(279\) 8.00000 0.478947
\(280\) 0 0
\(281\) 6.00000 0.357930 0.178965 0.983855i \(-0.442725\pi\)
0.178965 + 0.983855i \(0.442725\pi\)
\(282\) −6.00000 −0.357295
\(283\) −8.00000 −0.475551 −0.237775 0.971320i \(-0.576418\pi\)
−0.237775 + 0.971320i \(0.576418\pi\)
\(284\) 6.00000 0.356034
\(285\) 0 0
\(286\) 0 0
\(287\) 12.0000 0.708338
\(288\) 1.00000 0.0589256
\(289\) 19.0000 1.11765
\(290\) 0 0
\(291\) 14.0000 0.820695
\(292\) −2.00000 −0.117041
\(293\) 6.00000 0.350524 0.175262 0.984522i \(-0.443923\pi\)
0.175262 + 0.984522i \(0.443923\pi\)
\(294\) −3.00000 −0.174964
\(295\) 0 0
\(296\) −10.0000 −0.581238
\(297\) 0 0
\(298\) 6.00000 0.347571
\(299\) 24.0000 1.38796
\(300\) −5.00000 −0.288675
\(301\) 16.0000 0.922225
\(302\) 10.0000 0.575435
\(303\) −6.00000 −0.344691
\(304\) 4.00000 0.229416
\(305\) 0 0
\(306\) 6.00000 0.342997
\(307\) −20.0000 −1.14146 −0.570730 0.821138i \(-0.693340\pi\)
−0.570730 + 0.821138i \(0.693340\pi\)
\(308\) 0 0
\(309\) −4.00000 −0.227552
\(310\) 0 0
\(311\) −18.0000 −1.02069 −0.510343 0.859971i \(-0.670482\pi\)
−0.510343 + 0.859971i \(0.670482\pi\)
\(312\) 4.00000 0.226455
\(313\) 26.0000 1.46961 0.734803 0.678280i \(-0.237274\pi\)
0.734803 + 0.678280i \(0.237274\pi\)
\(314\) 2.00000 0.112867
\(315\) 0 0
\(316\) −14.0000 −0.787562
\(317\) 12.0000 0.673987 0.336994 0.941507i \(-0.390590\pi\)
0.336994 + 0.941507i \(0.390590\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 12.0000 0.669775
\(322\) −12.0000 −0.668734
\(323\) 24.0000 1.33540
\(324\) 1.00000 0.0555556
\(325\) −20.0000 −1.10940
\(326\) −4.00000 −0.221540
\(327\) 4.00000 0.221201
\(328\) −6.00000 −0.331295
\(329\) 12.0000 0.661581
\(330\) 0 0
\(331\) −4.00000 −0.219860 −0.109930 0.993939i \(-0.535063\pi\)
−0.109930 + 0.993939i \(0.535063\pi\)
\(332\) 12.0000 0.658586
\(333\) −10.0000 −0.547997
\(334\) −12.0000 −0.656611
\(335\) 0 0
\(336\) −2.00000 −0.109109
\(337\) −2.00000 −0.108947 −0.0544735 0.998515i \(-0.517348\pi\)
−0.0544735 + 0.998515i \(0.517348\pi\)
\(338\) 3.00000 0.163178
\(339\) 18.0000 0.977626
\(340\) 0 0
\(341\) 0 0
\(342\) 4.00000 0.216295
\(343\) 20.0000 1.07990
\(344\) −8.00000 −0.431331
\(345\) 0 0
\(346\) −6.00000 −0.322562
\(347\) −36.0000 −1.93258 −0.966291 0.257454i \(-0.917117\pi\)
−0.966291 + 0.257454i \(0.917117\pi\)
\(348\) −6.00000 −0.321634
\(349\) 4.00000 0.214115 0.107058 0.994253i \(-0.465857\pi\)
0.107058 + 0.994253i \(0.465857\pi\)
\(350\) 10.0000 0.534522
\(351\) 4.00000 0.213504
\(352\) 0 0
\(353\) −6.00000 −0.319348 −0.159674 0.987170i \(-0.551044\pi\)
−0.159674 + 0.987170i \(0.551044\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −6.00000 −0.317999
\(357\) −12.0000 −0.635107
\(358\) 24.0000 1.26844
\(359\) 12.0000 0.633336 0.316668 0.948536i \(-0.397436\pi\)
0.316668 + 0.948536i \(0.397436\pi\)
\(360\) 0 0
\(361\) −3.00000 −0.157895
\(362\) −22.0000 −1.15629
\(363\) 0 0
\(364\) −8.00000 −0.419314
\(365\) 0 0
\(366\) −8.00000 −0.418167
\(367\) 8.00000 0.417597 0.208798 0.977959i \(-0.433045\pi\)
0.208798 + 0.977959i \(0.433045\pi\)
\(368\) 6.00000 0.312772
\(369\) −6.00000 −0.312348
\(370\) 0 0
\(371\) 0 0
\(372\) 8.00000 0.414781
\(373\) −20.0000 −1.03556 −0.517780 0.855514i \(-0.673242\pi\)
−0.517780 + 0.855514i \(0.673242\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −6.00000 −0.309426
\(377\) −24.0000 −1.23606
\(378\) −2.00000 −0.102869
\(379\) 20.0000 1.02733 0.513665 0.857991i \(-0.328287\pi\)
0.513665 + 0.857991i \(0.328287\pi\)
\(380\) 0 0
\(381\) −14.0000 −0.717242
\(382\) 18.0000 0.920960
\(383\) 6.00000 0.306586 0.153293 0.988181i \(-0.451012\pi\)
0.153293 + 0.988181i \(0.451012\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) −14.0000 −0.712581
\(387\) −8.00000 −0.406663
\(388\) 14.0000 0.710742
\(389\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(390\) 0 0
\(391\) 36.0000 1.82060
\(392\) −3.00000 −0.151523
\(393\) 12.0000 0.605320
\(394\) −6.00000 −0.302276
\(395\) 0 0
\(396\) 0 0
\(397\) 26.0000 1.30490 0.652451 0.757831i \(-0.273741\pi\)
0.652451 + 0.757831i \(0.273741\pi\)
\(398\) −4.00000 −0.200502
\(399\) −8.00000 −0.400501
\(400\) −5.00000 −0.250000
\(401\) 30.0000 1.49813 0.749064 0.662497i \(-0.230503\pi\)
0.749064 + 0.662497i \(0.230503\pi\)
\(402\) −4.00000 −0.199502
\(403\) 32.0000 1.59403
\(404\) −6.00000 −0.298511
\(405\) 0 0
\(406\) 12.0000 0.595550
\(407\) 0 0
\(408\) 6.00000 0.297044
\(409\) 34.0000 1.68119 0.840596 0.541663i \(-0.182205\pi\)
0.840596 + 0.541663i \(0.182205\pi\)
\(410\) 0 0
\(411\) −18.0000 −0.887875
\(412\) −4.00000 −0.197066
\(413\) 0 0
\(414\) 6.00000 0.294884
\(415\) 0 0
\(416\) 4.00000 0.196116
\(417\) 4.00000 0.195881
\(418\) 0 0
\(419\) 24.0000 1.17248 0.586238 0.810139i \(-0.300608\pi\)
0.586238 + 0.810139i \(0.300608\pi\)
\(420\) 0 0
\(421\) −10.0000 −0.487370 −0.243685 0.969854i \(-0.578356\pi\)
−0.243685 + 0.969854i \(0.578356\pi\)
\(422\) −8.00000 −0.389434
\(423\) −6.00000 −0.291730
\(424\) 0 0
\(425\) −30.0000 −1.45521
\(426\) 6.00000 0.290701
\(427\) 16.0000 0.774294
\(428\) 12.0000 0.580042
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) 1.00000 0.0481125
\(433\) 26.0000 1.24948 0.624740 0.780833i \(-0.285205\pi\)
0.624740 + 0.780833i \(0.285205\pi\)
\(434\) −16.0000 −0.768025
\(435\) 0 0
\(436\) 4.00000 0.191565
\(437\) 24.0000 1.14808
\(438\) −2.00000 −0.0955637
\(439\) 10.0000 0.477274 0.238637 0.971109i \(-0.423299\pi\)
0.238637 + 0.971109i \(0.423299\pi\)
\(440\) 0 0
\(441\) −3.00000 −0.142857
\(442\) 24.0000 1.14156
\(443\) −24.0000 −1.14027 −0.570137 0.821549i \(-0.693110\pi\)
−0.570137 + 0.821549i \(0.693110\pi\)
\(444\) −10.0000 −0.474579
\(445\) 0 0
\(446\) −16.0000 −0.757622
\(447\) 6.00000 0.283790
\(448\) −2.00000 −0.0944911
\(449\) 6.00000 0.283158 0.141579 0.989927i \(-0.454782\pi\)
0.141579 + 0.989927i \(0.454782\pi\)
\(450\) −5.00000 −0.235702
\(451\) 0 0
\(452\) 18.0000 0.846649
\(453\) 10.0000 0.469841
\(454\) 12.0000 0.563188
\(455\) 0 0
\(456\) 4.00000 0.187317
\(457\) 10.0000 0.467780 0.233890 0.972263i \(-0.424854\pi\)
0.233890 + 0.972263i \(0.424854\pi\)
\(458\) −22.0000 −1.02799
\(459\) 6.00000 0.280056
\(460\) 0 0
\(461\) −42.0000 −1.95614 −0.978068 0.208288i \(-0.933211\pi\)
−0.978068 + 0.208288i \(0.933211\pi\)
\(462\) 0 0
\(463\) −4.00000 −0.185896 −0.0929479 0.995671i \(-0.529629\pi\)
−0.0929479 + 0.995671i \(0.529629\pi\)
\(464\) −6.00000 −0.278543
\(465\) 0 0
\(466\) 18.0000 0.833834
\(467\) −12.0000 −0.555294 −0.277647 0.960683i \(-0.589555\pi\)
−0.277647 + 0.960683i \(0.589555\pi\)
\(468\) 4.00000 0.184900
\(469\) 8.00000 0.369406
\(470\) 0 0
\(471\) 2.00000 0.0921551
\(472\) 0 0
\(473\) 0 0
\(474\) −14.0000 −0.643041
\(475\) −20.0000 −0.917663
\(476\) −12.0000 −0.550019
\(477\) 0 0
\(478\) 12.0000 0.548867
\(479\) 24.0000 1.09659 0.548294 0.836286i \(-0.315277\pi\)
0.548294 + 0.836286i \(0.315277\pi\)
\(480\) 0 0
\(481\) −40.0000 −1.82384
\(482\) 10.0000 0.455488
\(483\) −12.0000 −0.546019
\(484\) 0 0
\(485\) 0 0
\(486\) 1.00000 0.0453609
\(487\) 20.0000 0.906287 0.453143 0.891438i \(-0.350303\pi\)
0.453143 + 0.891438i \(0.350303\pi\)
\(488\) −8.00000 −0.362143
\(489\) −4.00000 −0.180886
\(490\) 0 0
\(491\) −12.0000 −0.541552 −0.270776 0.962642i \(-0.587280\pi\)
−0.270776 + 0.962642i \(0.587280\pi\)
\(492\) −6.00000 −0.270501
\(493\) −36.0000 −1.62136
\(494\) 16.0000 0.719874
\(495\) 0 0
\(496\) 8.00000 0.359211
\(497\) −12.0000 −0.538274
\(498\) 12.0000 0.537733
\(499\) −4.00000 −0.179065 −0.0895323 0.995984i \(-0.528537\pi\)
−0.0895323 + 0.995984i \(0.528537\pi\)
\(500\) 0 0
\(501\) −12.0000 −0.536120
\(502\) 0 0
\(503\) −12.0000 −0.535054 −0.267527 0.963550i \(-0.586206\pi\)
−0.267527 + 0.963550i \(0.586206\pi\)
\(504\) −2.00000 −0.0890871
\(505\) 0 0
\(506\) 0 0
\(507\) 3.00000 0.133235
\(508\) −14.0000 −0.621150
\(509\) 24.0000 1.06378 0.531891 0.846813i \(-0.321482\pi\)
0.531891 + 0.846813i \(0.321482\pi\)
\(510\) 0 0
\(511\) 4.00000 0.176950
\(512\) 1.00000 0.0441942
\(513\) 4.00000 0.176604
\(514\) −30.0000 −1.32324
\(515\) 0 0
\(516\) −8.00000 −0.352180
\(517\) 0 0
\(518\) 20.0000 0.878750
\(519\) −6.00000 −0.263371
\(520\) 0 0
\(521\) −18.0000 −0.788594 −0.394297 0.918983i \(-0.629012\pi\)
−0.394297 + 0.918983i \(0.629012\pi\)
\(522\) −6.00000 −0.262613
\(523\) 16.0000 0.699631 0.349816 0.936819i \(-0.386244\pi\)
0.349816 + 0.936819i \(0.386244\pi\)
\(524\) 12.0000 0.524222
\(525\) 10.0000 0.436436
\(526\) 0 0
\(527\) 48.0000 2.09091
\(528\) 0 0
\(529\) 13.0000 0.565217
\(530\) 0 0
\(531\) 0 0
\(532\) −8.00000 −0.346844
\(533\) −24.0000 −1.03956
\(534\) −6.00000 −0.259645
\(535\) 0 0
\(536\) −4.00000 −0.172774
\(537\) 24.0000 1.03568
\(538\) −24.0000 −1.03471
\(539\) 0 0
\(540\) 0 0
\(541\) −20.0000 −0.859867 −0.429934 0.902861i \(-0.641463\pi\)
−0.429934 + 0.902861i \(0.641463\pi\)
\(542\) −2.00000 −0.0859074
\(543\) −22.0000 −0.944110
\(544\) 6.00000 0.257248
\(545\) 0 0
\(546\) −8.00000 −0.342368
\(547\) 28.0000 1.19719 0.598597 0.801050i \(-0.295725\pi\)
0.598597 + 0.801050i \(0.295725\pi\)
\(548\) −18.0000 −0.768922
\(549\) −8.00000 −0.341432
\(550\) 0 0
\(551\) −24.0000 −1.02243
\(552\) 6.00000 0.255377
\(553\) 28.0000 1.19068
\(554\) 16.0000 0.679775
\(555\) 0 0
\(556\) 4.00000 0.169638
\(557\) −18.0000 −0.762684 −0.381342 0.924434i \(-0.624538\pi\)
−0.381342 + 0.924434i \(0.624538\pi\)
\(558\) 8.00000 0.338667
\(559\) −32.0000 −1.35346
\(560\) 0 0
\(561\) 0 0
\(562\) 6.00000 0.253095
\(563\) 12.0000 0.505740 0.252870 0.967500i \(-0.418626\pi\)
0.252870 + 0.967500i \(0.418626\pi\)
\(564\) −6.00000 −0.252646
\(565\) 0 0
\(566\) −8.00000 −0.336265
\(567\) −2.00000 −0.0839921
\(568\) 6.00000 0.251754
\(569\) −18.0000 −0.754599 −0.377300 0.926091i \(-0.623147\pi\)
−0.377300 + 0.926091i \(0.623147\pi\)
\(570\) 0 0
\(571\) 28.0000 1.17176 0.585882 0.810397i \(-0.300748\pi\)
0.585882 + 0.810397i \(0.300748\pi\)
\(572\) 0 0
\(573\) 18.0000 0.751961
\(574\) 12.0000 0.500870
\(575\) −30.0000 −1.25109
\(576\) 1.00000 0.0416667
\(577\) −34.0000 −1.41544 −0.707719 0.706494i \(-0.750276\pi\)
−0.707719 + 0.706494i \(0.750276\pi\)
\(578\) 19.0000 0.790296
\(579\) −14.0000 −0.581820
\(580\) 0 0
\(581\) −24.0000 −0.995688
\(582\) 14.0000 0.580319
\(583\) 0 0
\(584\) −2.00000 −0.0827606
\(585\) 0 0
\(586\) 6.00000 0.247858
\(587\) 24.0000 0.990586 0.495293 0.868726i \(-0.335061\pi\)
0.495293 + 0.868726i \(0.335061\pi\)
\(588\) −3.00000 −0.123718
\(589\) 32.0000 1.31854
\(590\) 0 0
\(591\) −6.00000 −0.246807
\(592\) −10.0000 −0.410997
\(593\) 30.0000 1.23195 0.615976 0.787765i \(-0.288762\pi\)
0.615976 + 0.787765i \(0.288762\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 6.00000 0.245770
\(597\) −4.00000 −0.163709
\(598\) 24.0000 0.981433
\(599\) 30.0000 1.22577 0.612883 0.790173i \(-0.290010\pi\)
0.612883 + 0.790173i \(0.290010\pi\)
\(600\) −5.00000 −0.204124
\(601\) 22.0000 0.897399 0.448699 0.893683i \(-0.351887\pi\)
0.448699 + 0.893683i \(0.351887\pi\)
\(602\) 16.0000 0.652111
\(603\) −4.00000 −0.162893
\(604\) 10.0000 0.406894
\(605\) 0 0
\(606\) −6.00000 −0.243733
\(607\) −14.0000 −0.568242 −0.284121 0.958788i \(-0.591702\pi\)
−0.284121 + 0.958788i \(0.591702\pi\)
\(608\) 4.00000 0.162221
\(609\) 12.0000 0.486265
\(610\) 0 0
\(611\) −24.0000 −0.970936
\(612\) 6.00000 0.242536
\(613\) 16.0000 0.646234 0.323117 0.946359i \(-0.395269\pi\)
0.323117 + 0.946359i \(0.395269\pi\)
\(614\) −20.0000 −0.807134
\(615\) 0 0
\(616\) 0 0
\(617\) −30.0000 −1.20775 −0.603877 0.797077i \(-0.706378\pi\)
−0.603877 + 0.797077i \(0.706378\pi\)
\(618\) −4.00000 −0.160904
\(619\) 44.0000 1.76851 0.884255 0.467005i \(-0.154667\pi\)
0.884255 + 0.467005i \(0.154667\pi\)
\(620\) 0 0
\(621\) 6.00000 0.240772
\(622\) −18.0000 −0.721734
\(623\) 12.0000 0.480770
\(624\) 4.00000 0.160128
\(625\) 25.0000 1.00000
\(626\) 26.0000 1.03917
\(627\) 0 0
\(628\) 2.00000 0.0798087
\(629\) −60.0000 −2.39236
\(630\) 0 0
\(631\) −16.0000 −0.636950 −0.318475 0.947931i \(-0.603171\pi\)
−0.318475 + 0.947931i \(0.603171\pi\)
\(632\) −14.0000 −0.556890
\(633\) −8.00000 −0.317971
\(634\) 12.0000 0.476581
\(635\) 0 0
\(636\) 0 0
\(637\) −12.0000 −0.475457
\(638\) 0 0
\(639\) 6.00000 0.237356
\(640\) 0 0
\(641\) 6.00000 0.236986 0.118493 0.992955i \(-0.462194\pi\)
0.118493 + 0.992955i \(0.462194\pi\)
\(642\) 12.0000 0.473602
\(643\) −4.00000 −0.157745 −0.0788723 0.996885i \(-0.525132\pi\)
−0.0788723 + 0.996885i \(0.525132\pi\)
\(644\) −12.0000 −0.472866
\(645\) 0 0
\(646\) 24.0000 0.944267
\(647\) 6.00000 0.235884 0.117942 0.993020i \(-0.462370\pi\)
0.117942 + 0.993020i \(0.462370\pi\)
\(648\) 1.00000 0.0392837
\(649\) 0 0
\(650\) −20.0000 −0.784465
\(651\) −16.0000 −0.627089
\(652\) −4.00000 −0.156652
\(653\) −36.0000 −1.40879 −0.704394 0.709809i \(-0.748781\pi\)
−0.704394 + 0.709809i \(0.748781\pi\)
\(654\) 4.00000 0.156412
\(655\) 0 0
\(656\) −6.00000 −0.234261
\(657\) −2.00000 −0.0780274
\(658\) 12.0000 0.467809
\(659\) −36.0000 −1.40236 −0.701180 0.712984i \(-0.747343\pi\)
−0.701180 + 0.712984i \(0.747343\pi\)
\(660\) 0 0
\(661\) −22.0000 −0.855701 −0.427850 0.903850i \(-0.640729\pi\)
−0.427850 + 0.903850i \(0.640729\pi\)
\(662\) −4.00000 −0.155464
\(663\) 24.0000 0.932083
\(664\) 12.0000 0.465690
\(665\) 0 0
\(666\) −10.0000 −0.387492
\(667\) −36.0000 −1.39393
\(668\) −12.0000 −0.464294
\(669\) −16.0000 −0.618596
\(670\) 0 0
\(671\) 0 0
\(672\) −2.00000 −0.0771517
\(673\) −14.0000 −0.539660 −0.269830 0.962908i \(-0.586968\pi\)
−0.269830 + 0.962908i \(0.586968\pi\)
\(674\) −2.00000 −0.0770371
\(675\) −5.00000 −0.192450
\(676\) 3.00000 0.115385
\(677\) −30.0000 −1.15299 −0.576497 0.817099i \(-0.695581\pi\)
−0.576497 + 0.817099i \(0.695581\pi\)
\(678\) 18.0000 0.691286
\(679\) −28.0000 −1.07454
\(680\) 0 0
\(681\) 12.0000 0.459841
\(682\) 0 0
\(683\) −24.0000 −0.918334 −0.459167 0.888350i \(-0.651852\pi\)
−0.459167 + 0.888350i \(0.651852\pi\)
\(684\) 4.00000 0.152944
\(685\) 0 0
\(686\) 20.0000 0.763604
\(687\) −22.0000 −0.839352
\(688\) −8.00000 −0.304997
\(689\) 0 0
\(690\) 0 0
\(691\) 20.0000 0.760836 0.380418 0.924815i \(-0.375780\pi\)
0.380418 + 0.924815i \(0.375780\pi\)
\(692\) −6.00000 −0.228086
\(693\) 0 0
\(694\) −36.0000 −1.36654
\(695\) 0 0
\(696\) −6.00000 −0.227429
\(697\) −36.0000 −1.36360
\(698\) 4.00000 0.151402
\(699\) 18.0000 0.680823
\(700\) 10.0000 0.377964
\(701\) 6.00000 0.226617 0.113308 0.993560i \(-0.463855\pi\)
0.113308 + 0.993560i \(0.463855\pi\)
\(702\) 4.00000 0.150970
\(703\) −40.0000 −1.50863
\(704\) 0 0
\(705\) 0 0
\(706\) −6.00000 −0.225813
\(707\) 12.0000 0.451306
\(708\) 0 0
\(709\) 26.0000 0.976450 0.488225 0.872718i \(-0.337644\pi\)
0.488225 + 0.872718i \(0.337644\pi\)
\(710\) 0 0
\(711\) −14.0000 −0.525041
\(712\) −6.00000 −0.224860
\(713\) 48.0000 1.79761
\(714\) −12.0000 −0.449089
\(715\) 0 0
\(716\) 24.0000 0.896922
\(717\) 12.0000 0.448148
\(718\) 12.0000 0.447836
\(719\) 30.0000 1.11881 0.559406 0.828894i \(-0.311029\pi\)
0.559406 + 0.828894i \(0.311029\pi\)
\(720\) 0 0
\(721\) 8.00000 0.297936
\(722\) −3.00000 −0.111648
\(723\) 10.0000 0.371904
\(724\) −22.0000 −0.817624
\(725\) 30.0000 1.11417
\(726\) 0 0
\(727\) −28.0000 −1.03846 −0.519231 0.854634i \(-0.673782\pi\)
−0.519231 + 0.854634i \(0.673782\pi\)
\(728\) −8.00000 −0.296500
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −48.0000 −1.77534
\(732\) −8.00000 −0.295689
\(733\) 4.00000 0.147743 0.0738717 0.997268i \(-0.476464\pi\)
0.0738717 + 0.997268i \(0.476464\pi\)
\(734\) 8.00000 0.295285
\(735\) 0 0
\(736\) 6.00000 0.221163
\(737\) 0 0
\(738\) −6.00000 −0.220863
\(739\) −8.00000 −0.294285 −0.147142 0.989115i \(-0.547008\pi\)
−0.147142 + 0.989115i \(0.547008\pi\)
\(740\) 0 0
\(741\) 16.0000 0.587775
\(742\) 0 0
\(743\) −36.0000 −1.32071 −0.660356 0.750953i \(-0.729595\pi\)
−0.660356 + 0.750953i \(0.729595\pi\)
\(744\) 8.00000 0.293294
\(745\) 0 0
\(746\) −20.0000 −0.732252
\(747\) 12.0000 0.439057
\(748\) 0 0
\(749\) −24.0000 −0.876941
\(750\) 0 0
\(751\) 8.00000 0.291924 0.145962 0.989290i \(-0.453372\pi\)
0.145962 + 0.989290i \(0.453372\pi\)
\(752\) −6.00000 −0.218797
\(753\) 0 0
\(754\) −24.0000 −0.874028
\(755\) 0 0
\(756\) −2.00000 −0.0727393
\(757\) −34.0000 −1.23575 −0.617876 0.786276i \(-0.712006\pi\)
−0.617876 + 0.786276i \(0.712006\pi\)
\(758\) 20.0000 0.726433
\(759\) 0 0
\(760\) 0 0
\(761\) −18.0000 −0.652499 −0.326250 0.945284i \(-0.605785\pi\)
−0.326250 + 0.945284i \(0.605785\pi\)
\(762\) −14.0000 −0.507166
\(763\) −8.00000 −0.289619
\(764\) 18.0000 0.651217
\(765\) 0 0
\(766\) 6.00000 0.216789
\(767\) 0 0
\(768\) 1.00000 0.0360844
\(769\) 34.0000 1.22607 0.613036 0.790055i \(-0.289948\pi\)
0.613036 + 0.790055i \(0.289948\pi\)
\(770\) 0 0
\(771\) −30.0000 −1.08042
\(772\) −14.0000 −0.503871
\(773\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(774\) −8.00000 −0.287554
\(775\) −40.0000 −1.43684
\(776\) 14.0000 0.502571
\(777\) 20.0000 0.717496
\(778\) 0 0
\(779\) −24.0000 −0.859889
\(780\) 0 0
\(781\) 0 0
\(782\) 36.0000 1.28736
\(783\) −6.00000 −0.214423
\(784\) −3.00000 −0.107143
\(785\) 0 0
\(786\) 12.0000 0.428026
\(787\) −32.0000 −1.14068 −0.570338 0.821410i \(-0.693188\pi\)
−0.570338 + 0.821410i \(0.693188\pi\)
\(788\) −6.00000 −0.213741
\(789\) 0 0
\(790\) 0 0
\(791\) −36.0000 −1.28001
\(792\) 0 0
\(793\) −32.0000 −1.13635
\(794\) 26.0000 0.922705
\(795\) 0 0
\(796\) −4.00000 −0.141776
\(797\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(798\) −8.00000 −0.283197
\(799\) −36.0000 −1.27359
\(800\) −5.00000 −0.176777
\(801\) −6.00000 −0.212000
\(802\) 30.0000 1.05934
\(803\) 0 0
\(804\) −4.00000 −0.141069
\(805\) 0 0
\(806\) 32.0000 1.12715
\(807\) −24.0000 −0.844840
\(808\) −6.00000 −0.211079
\(809\) 42.0000 1.47664 0.738321 0.674450i \(-0.235619\pi\)
0.738321 + 0.674450i \(0.235619\pi\)
\(810\) 0 0
\(811\) −8.00000 −0.280918 −0.140459 0.990086i \(-0.544858\pi\)
−0.140459 + 0.990086i \(0.544858\pi\)
\(812\) 12.0000 0.421117
\(813\) −2.00000 −0.0701431
\(814\) 0 0
\(815\) 0 0
\(816\) 6.00000 0.210042
\(817\) −32.0000 −1.11954
\(818\) 34.0000 1.18878
\(819\) −8.00000 −0.279543
\(820\) 0 0
\(821\) 18.0000 0.628204 0.314102 0.949389i \(-0.398297\pi\)
0.314102 + 0.949389i \(0.398297\pi\)
\(822\) −18.0000 −0.627822
\(823\) 8.00000 0.278862 0.139431 0.990232i \(-0.455473\pi\)
0.139431 + 0.990232i \(0.455473\pi\)
\(824\) −4.00000 −0.139347
\(825\) 0 0
\(826\) 0 0
\(827\) 12.0000 0.417281 0.208640 0.977992i \(-0.433096\pi\)
0.208640 + 0.977992i \(0.433096\pi\)
\(828\) 6.00000 0.208514
\(829\) 14.0000 0.486240 0.243120 0.969996i \(-0.421829\pi\)
0.243120 + 0.969996i \(0.421829\pi\)
\(830\) 0 0
\(831\) 16.0000 0.555034
\(832\) 4.00000 0.138675
\(833\) −18.0000 −0.623663
\(834\) 4.00000 0.138509
\(835\) 0 0
\(836\) 0 0
\(837\) 8.00000 0.276520
\(838\) 24.0000 0.829066
\(839\) 18.0000 0.621429 0.310715 0.950503i \(-0.399432\pi\)
0.310715 + 0.950503i \(0.399432\pi\)
\(840\) 0 0
\(841\) 7.00000 0.241379
\(842\) −10.0000 −0.344623
\(843\) 6.00000 0.206651
\(844\) −8.00000 −0.275371
\(845\) 0 0
\(846\) −6.00000 −0.206284
\(847\) 0 0
\(848\) 0 0
\(849\) −8.00000 −0.274559
\(850\) −30.0000 −1.02899
\(851\) −60.0000 −2.05677
\(852\) 6.00000 0.205557
\(853\) −8.00000 −0.273915 −0.136957 0.990577i \(-0.543732\pi\)
−0.136957 + 0.990577i \(0.543732\pi\)
\(854\) 16.0000 0.547509
\(855\) 0 0
\(856\) 12.0000 0.410152
\(857\) −54.0000 −1.84460 −0.922302 0.386469i \(-0.873695\pi\)
−0.922302 + 0.386469i \(0.873695\pi\)
\(858\) 0 0
\(859\) 20.0000 0.682391 0.341196 0.939992i \(-0.389168\pi\)
0.341196 + 0.939992i \(0.389168\pi\)
\(860\) 0 0
\(861\) 12.0000 0.408959
\(862\) 0 0
\(863\) 42.0000 1.42970 0.714848 0.699280i \(-0.246496\pi\)
0.714848 + 0.699280i \(0.246496\pi\)
\(864\) 1.00000 0.0340207
\(865\) 0 0
\(866\) 26.0000 0.883516
\(867\) 19.0000 0.645274
\(868\) −16.0000 −0.543075
\(869\) 0 0
\(870\) 0 0
\(871\) −16.0000 −0.542139
\(872\) 4.00000 0.135457
\(873\) 14.0000 0.473828
\(874\) 24.0000 0.811812
\(875\) 0 0
\(876\) −2.00000 −0.0675737
\(877\) 52.0000 1.75592 0.877958 0.478738i \(-0.158906\pi\)
0.877958 + 0.478738i \(0.158906\pi\)
\(878\) 10.0000 0.337484
\(879\) 6.00000 0.202375
\(880\) 0 0
\(881\) −30.0000 −1.01073 −0.505363 0.862907i \(-0.668641\pi\)
−0.505363 + 0.862907i \(0.668641\pi\)
\(882\) −3.00000 −0.101015
\(883\) −28.0000 −0.942275 −0.471138 0.882060i \(-0.656156\pi\)
−0.471138 + 0.882060i \(0.656156\pi\)
\(884\) 24.0000 0.807207
\(885\) 0 0
\(886\) −24.0000 −0.806296
\(887\) 36.0000 1.20876 0.604381 0.796696i \(-0.293421\pi\)
0.604381 + 0.796696i \(0.293421\pi\)
\(888\) −10.0000 −0.335578
\(889\) 28.0000 0.939090
\(890\) 0 0
\(891\) 0 0
\(892\) −16.0000 −0.535720
\(893\) −24.0000 −0.803129
\(894\) 6.00000 0.200670
\(895\) 0 0
\(896\) −2.00000 −0.0668153
\(897\) 24.0000 0.801337
\(898\) 6.00000 0.200223
\(899\) −48.0000 −1.60089
\(900\) −5.00000 −0.166667
\(901\) 0 0
\(902\) 0 0
\(903\) 16.0000 0.532447
\(904\) 18.0000 0.598671
\(905\) 0 0
\(906\) 10.0000 0.332228
\(907\) 20.0000 0.664089 0.332045 0.943264i \(-0.392262\pi\)
0.332045 + 0.943264i \(0.392262\pi\)
\(908\) 12.0000 0.398234
\(909\) −6.00000 −0.199007
\(910\) 0 0
\(911\) −42.0000 −1.39152 −0.695761 0.718273i \(-0.744933\pi\)
−0.695761 + 0.718273i \(0.744933\pi\)
\(912\) 4.00000 0.132453
\(913\) 0 0
\(914\) 10.0000 0.330771
\(915\) 0 0
\(916\) −22.0000 −0.726900
\(917\) −24.0000 −0.792550
\(918\) 6.00000 0.198030
\(919\) −2.00000 −0.0659739 −0.0329870 0.999456i \(-0.510502\pi\)
−0.0329870 + 0.999456i \(0.510502\pi\)
\(920\) 0 0
\(921\) −20.0000 −0.659022
\(922\) −42.0000 −1.38320
\(923\) 24.0000 0.789970
\(924\) 0 0
\(925\) 50.0000 1.64399
\(926\) −4.00000 −0.131448
\(927\) −4.00000 −0.131377
\(928\) −6.00000 −0.196960
\(929\) 30.0000 0.984268 0.492134 0.870519i \(-0.336217\pi\)
0.492134 + 0.870519i \(0.336217\pi\)
\(930\) 0 0
\(931\) −12.0000 −0.393284
\(932\) 18.0000 0.589610
\(933\) −18.0000 −0.589294
\(934\) −12.0000 −0.392652
\(935\) 0 0
\(936\) 4.00000 0.130744
\(937\) 22.0000 0.718709 0.359354 0.933201i \(-0.382997\pi\)
0.359354 + 0.933201i \(0.382997\pi\)
\(938\) 8.00000 0.261209
\(939\) 26.0000 0.848478
\(940\) 0 0
\(941\) 18.0000 0.586783 0.293392 0.955992i \(-0.405216\pi\)
0.293392 + 0.955992i \(0.405216\pi\)
\(942\) 2.00000 0.0651635
\(943\) −36.0000 −1.17232
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 12.0000 0.389948 0.194974 0.980808i \(-0.437538\pi\)
0.194974 + 0.980808i \(0.437538\pi\)
\(948\) −14.0000 −0.454699
\(949\) −8.00000 −0.259691
\(950\) −20.0000 −0.648886
\(951\) 12.0000 0.389127
\(952\) −12.0000 −0.388922
\(953\) 42.0000 1.36051 0.680257 0.732974i \(-0.261868\pi\)
0.680257 + 0.732974i \(0.261868\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 12.0000 0.388108
\(957\) 0 0
\(958\) 24.0000 0.775405
\(959\) 36.0000 1.16250
\(960\) 0 0
\(961\) 33.0000 1.06452
\(962\) −40.0000 −1.28965
\(963\) 12.0000 0.386695
\(964\) 10.0000 0.322078
\(965\) 0 0
\(966\) −12.0000 −0.386094
\(967\) −14.0000 −0.450210 −0.225105 0.974335i \(-0.572272\pi\)
−0.225105 + 0.974335i \(0.572272\pi\)
\(968\) 0 0
\(969\) 24.0000 0.770991
\(970\) 0 0
\(971\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(972\) 1.00000 0.0320750
\(973\) −8.00000 −0.256468
\(974\) 20.0000 0.640841
\(975\) −20.0000 −0.640513
\(976\) −8.00000 −0.256074
\(977\) 54.0000 1.72761 0.863807 0.503824i \(-0.168074\pi\)
0.863807 + 0.503824i \(0.168074\pi\)
\(978\) −4.00000 −0.127906
\(979\) 0 0
\(980\) 0 0
\(981\) 4.00000 0.127710
\(982\) −12.0000 −0.382935
\(983\) 30.0000 0.956851 0.478426 0.878128i \(-0.341208\pi\)
0.478426 + 0.878128i \(0.341208\pi\)
\(984\) −6.00000 −0.191273
\(985\) 0 0
\(986\) −36.0000 −1.14647
\(987\) 12.0000 0.381964
\(988\) 16.0000 0.509028
\(989\) −48.0000 −1.52631
\(990\) 0 0
\(991\) 56.0000 1.77890 0.889449 0.457034i \(-0.151088\pi\)
0.889449 + 0.457034i \(0.151088\pi\)
\(992\) 8.00000 0.254000
\(993\) −4.00000 −0.126936
\(994\) −12.0000 −0.380617
\(995\) 0 0
\(996\) 12.0000 0.380235
\(997\) −44.0000 −1.39349 −0.696747 0.717317i \(-0.745370\pi\)
−0.696747 + 0.717317i \(0.745370\pi\)
\(998\) −4.00000 −0.126618
\(999\) −10.0000 −0.316386
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 726.2.a.i.1.1 1
3.2 odd 2 2178.2.a.b.1.1 1
4.3 odd 2 5808.2.a.l.1.1 1
11.2 odd 10 726.2.e.k.565.1 4
11.3 even 5 726.2.e.b.493.1 4
11.4 even 5 726.2.e.b.511.1 4
11.5 even 5 726.2.e.b.487.1 4
11.6 odd 10 726.2.e.k.487.1 4
11.7 odd 10 726.2.e.k.511.1 4
11.8 odd 10 726.2.e.k.493.1 4
11.9 even 5 726.2.e.b.565.1 4
11.10 odd 2 66.2.a.a.1.1 1
33.32 even 2 198.2.a.e.1.1 1
44.43 even 2 528.2.a.d.1.1 1
55.32 even 4 1650.2.c.d.199.1 2
55.43 even 4 1650.2.c.d.199.2 2
55.54 odd 2 1650.2.a.m.1.1 1
77.76 even 2 3234.2.a.d.1.1 1
88.21 odd 2 2112.2.a.i.1.1 1
88.43 even 2 2112.2.a.v.1.1 1
99.32 even 6 1782.2.e.f.1189.1 2
99.43 odd 6 1782.2.e.s.595.1 2
99.65 even 6 1782.2.e.f.595.1 2
99.76 odd 6 1782.2.e.s.1189.1 2
132.131 odd 2 1584.2.a.h.1.1 1
165.32 odd 4 4950.2.c.r.199.2 2
165.98 odd 4 4950.2.c.r.199.1 2
165.164 even 2 4950.2.a.g.1.1 1
231.230 odd 2 9702.2.a.bu.1.1 1
264.131 odd 2 6336.2.a.bf.1.1 1
264.197 even 2 6336.2.a.bj.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
66.2.a.a.1.1 1 11.10 odd 2
198.2.a.e.1.1 1 33.32 even 2
528.2.a.d.1.1 1 44.43 even 2
726.2.a.i.1.1 1 1.1 even 1 trivial
726.2.e.b.487.1 4 11.5 even 5
726.2.e.b.493.1 4 11.3 even 5
726.2.e.b.511.1 4 11.4 even 5
726.2.e.b.565.1 4 11.9 even 5
726.2.e.k.487.1 4 11.6 odd 10
726.2.e.k.493.1 4 11.8 odd 10
726.2.e.k.511.1 4 11.7 odd 10
726.2.e.k.565.1 4 11.2 odd 10
1584.2.a.h.1.1 1 132.131 odd 2
1650.2.a.m.1.1 1 55.54 odd 2
1650.2.c.d.199.1 2 55.32 even 4
1650.2.c.d.199.2 2 55.43 even 4
1782.2.e.f.595.1 2 99.65 even 6
1782.2.e.f.1189.1 2 99.32 even 6
1782.2.e.s.595.1 2 99.43 odd 6
1782.2.e.s.1189.1 2 99.76 odd 6
2112.2.a.i.1.1 1 88.21 odd 2
2112.2.a.v.1.1 1 88.43 even 2
2178.2.a.b.1.1 1 3.2 odd 2
3234.2.a.d.1.1 1 77.76 even 2
4950.2.a.g.1.1 1 165.164 even 2
4950.2.c.r.199.1 2 165.98 odd 4
4950.2.c.r.199.2 2 165.32 odd 4
5808.2.a.l.1.1 1 4.3 odd 2
6336.2.a.bf.1.1 1 264.131 odd 2
6336.2.a.bj.1.1 1 264.197 even 2
9702.2.a.bu.1.1 1 231.230 odd 2