Properties

Label 1710.2.a.a.1.1
Level $1710$
Weight $2$
Character 1710.1
Self dual yes
Analytic conductor $13.654$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1710.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(13.6544187456\)
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 \(\chi\) \(=\) 1710.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{5} -4.00000 q^{7} -1.00000 q^{8} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{5} -4.00000 q^{7} -1.00000 q^{8} +1.00000 q^{10} +6.00000 q^{11} +4.00000 q^{14} +1.00000 q^{16} -4.00000 q^{17} -1.00000 q^{19} -1.00000 q^{20} -6.00000 q^{22} +4.00000 q^{23} +1.00000 q^{25} -4.00000 q^{28} +10.0000 q^{29} -2.00000 q^{31} -1.00000 q^{32} +4.00000 q^{34} +4.00000 q^{35} -4.00000 q^{37} +1.00000 q^{38} +1.00000 q^{40} -10.0000 q^{41} -12.0000 q^{43} +6.00000 q^{44} -4.00000 q^{46} +9.00000 q^{49} -1.00000 q^{50} +6.00000 q^{53} -6.00000 q^{55} +4.00000 q^{56} -10.0000 q^{58} -4.00000 q^{59} -10.0000 q^{61} +2.00000 q^{62} +1.00000 q^{64} -8.00000 q^{67} -4.00000 q^{68} -4.00000 q^{70} +6.00000 q^{73} +4.00000 q^{74} -1.00000 q^{76} -24.0000 q^{77} -10.0000 q^{79} -1.00000 q^{80} +10.0000 q^{82} -14.0000 q^{83} +4.00000 q^{85} +12.0000 q^{86} -6.00000 q^{88} -10.0000 q^{89} +4.00000 q^{92} +1.00000 q^{95} -6.00000 q^{97} -9.00000 q^{98} +O(q^{100})\)

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
\(3\) 0 0
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) −4.00000 −1.51186 −0.755929 0.654654i \(-0.772814\pi\)
−0.755929 + 0.654654i \(0.772814\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 1.00000 0.316228
\(11\) 6.00000 1.80907 0.904534 0.426401i \(-0.140219\pi\)
0.904534 + 0.426401i \(0.140219\pi\)
\(12\) 0 0
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) 4.00000 1.06904
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −4.00000 −0.970143 −0.485071 0.874475i \(-0.661206\pi\)
−0.485071 + 0.874475i \(0.661206\pi\)
\(18\) 0 0
\(19\) −1.00000 −0.229416
\(20\) −1.00000 −0.223607
\(21\) 0 0
\(22\) −6.00000 −1.27920
\(23\) 4.00000 0.834058 0.417029 0.908893i \(-0.363071\pi\)
0.417029 + 0.908893i \(0.363071\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) −4.00000 −0.755929
\(29\) 10.0000 1.85695 0.928477 0.371391i \(-0.121119\pi\)
0.928477 + 0.371391i \(0.121119\pi\)
\(30\) 0 0
\(31\) −2.00000 −0.359211 −0.179605 0.983739i \(-0.557482\pi\)
−0.179605 + 0.983739i \(0.557482\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) 4.00000 0.685994
\(35\) 4.00000 0.676123
\(36\) 0 0
\(37\) −4.00000 −0.657596 −0.328798 0.944400i \(-0.606644\pi\)
−0.328798 + 0.944400i \(0.606644\pi\)
\(38\) 1.00000 0.162221
\(39\) 0 0
\(40\) 1.00000 0.158114
\(41\) −10.0000 −1.56174 −0.780869 0.624695i \(-0.785223\pi\)
−0.780869 + 0.624695i \(0.785223\pi\)
\(42\) 0 0
\(43\) −12.0000 −1.82998 −0.914991 0.403473i \(-0.867803\pi\)
−0.914991 + 0.403473i \(0.867803\pi\)
\(44\) 6.00000 0.904534
\(45\) 0 0
\(46\) −4.00000 −0.589768
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 0 0
\(49\) 9.00000 1.28571
\(50\) −1.00000 −0.141421
\(51\) 0 0
\(52\) 0 0
\(53\) 6.00000 0.824163 0.412082 0.911147i \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) 0 0
\(55\) −6.00000 −0.809040
\(56\) 4.00000 0.534522
\(57\) 0 0
\(58\) −10.0000 −1.31306
\(59\) −4.00000 −0.520756 −0.260378 0.965507i \(-0.583847\pi\)
−0.260378 + 0.965507i \(0.583847\pi\)
\(60\) 0 0
\(61\) −10.0000 −1.28037 −0.640184 0.768221i \(-0.721142\pi\)
−0.640184 + 0.768221i \(0.721142\pi\)
\(62\) 2.00000 0.254000
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) −8.00000 −0.977356 −0.488678 0.872464i \(-0.662521\pi\)
−0.488678 + 0.872464i \(0.662521\pi\)
\(68\) −4.00000 −0.485071
\(69\) 0 0
\(70\) −4.00000 −0.478091
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) 6.00000 0.702247 0.351123 0.936329i \(-0.385800\pi\)
0.351123 + 0.936329i \(0.385800\pi\)
\(74\) 4.00000 0.464991
\(75\) 0 0
\(76\) −1.00000 −0.114708
\(77\) −24.0000 −2.73505
\(78\) 0 0
\(79\) −10.0000 −1.12509 −0.562544 0.826767i \(-0.690177\pi\)
−0.562544 + 0.826767i \(0.690177\pi\)
\(80\) −1.00000 −0.111803
\(81\) 0 0
\(82\) 10.0000 1.10432
\(83\) −14.0000 −1.53670 −0.768350 0.640030i \(-0.778922\pi\)
−0.768350 + 0.640030i \(0.778922\pi\)
\(84\) 0 0
\(85\) 4.00000 0.433861
\(86\) 12.0000 1.29399
\(87\) 0 0
\(88\) −6.00000 −0.639602
\(89\) −10.0000 −1.06000 −0.529999 0.847998i \(-0.677808\pi\)
−0.529999 + 0.847998i \(0.677808\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 4.00000 0.417029
\(93\) 0 0
\(94\) 0 0
\(95\) 1.00000 0.102598
\(96\) 0 0
\(97\) −6.00000 −0.609208 −0.304604 0.952479i \(-0.598524\pi\)
−0.304604 + 0.952479i \(0.598524\pi\)
\(98\) −9.00000 −0.909137
\(99\) 0 0
\(100\) 1.00000 0.100000
\(101\) −10.0000 −0.995037 −0.497519 0.867453i \(-0.665755\pi\)
−0.497519 + 0.867453i \(0.665755\pi\)
\(102\) 0 0
\(103\) 18.0000 1.77359 0.886796 0.462160i \(-0.152926\pi\)
0.886796 + 0.462160i \(0.152926\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) −6.00000 −0.582772
\(107\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) 0 0
\(109\) −8.00000 −0.766261 −0.383131 0.923694i \(-0.625154\pi\)
−0.383131 + 0.923694i \(0.625154\pi\)
\(110\) 6.00000 0.572078
\(111\) 0 0
\(112\) −4.00000 −0.377964
\(113\) 2.00000 0.188144 0.0940721 0.995565i \(-0.470012\pi\)
0.0940721 + 0.995565i \(0.470012\pi\)
\(114\) 0 0
\(115\) −4.00000 −0.373002
\(116\) 10.0000 0.928477
\(117\) 0 0
\(118\) 4.00000 0.368230
\(119\) 16.0000 1.46672
\(120\) 0 0
\(121\) 25.0000 2.27273
\(122\) 10.0000 0.905357
\(123\) 0 0
\(124\) −2.00000 −0.179605
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 18.0000 1.59724 0.798621 0.601834i \(-0.205563\pi\)
0.798621 + 0.601834i \(0.205563\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 0 0
\(130\) 0 0
\(131\) 10.0000 0.873704 0.436852 0.899533i \(-0.356093\pi\)
0.436852 + 0.899533i \(0.356093\pi\)
\(132\) 0 0
\(133\) 4.00000 0.346844
\(134\) 8.00000 0.691095
\(135\) 0 0
\(136\) 4.00000 0.342997
\(137\) −12.0000 −1.02523 −0.512615 0.858619i \(-0.671323\pi\)
−0.512615 + 0.858619i \(0.671323\pi\)
\(138\) 0 0
\(139\) −12.0000 −1.01783 −0.508913 0.860818i \(-0.669953\pi\)
−0.508913 + 0.860818i \(0.669953\pi\)
\(140\) 4.00000 0.338062
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) −10.0000 −0.830455
\(146\) −6.00000 −0.496564
\(147\) 0 0
\(148\) −4.00000 −0.328798
\(149\) 10.0000 0.819232 0.409616 0.912258i \(-0.365663\pi\)
0.409616 + 0.912258i \(0.365663\pi\)
\(150\) 0 0
\(151\) −18.0000 −1.46482 −0.732410 0.680864i \(-0.761604\pi\)
−0.732410 + 0.680864i \(0.761604\pi\)
\(152\) 1.00000 0.0811107
\(153\) 0 0
\(154\) 24.0000 1.93398
\(155\) 2.00000 0.160644
\(156\) 0 0
\(157\) −18.0000 −1.43656 −0.718278 0.695756i \(-0.755069\pi\)
−0.718278 + 0.695756i \(0.755069\pi\)
\(158\) 10.0000 0.795557
\(159\) 0 0
\(160\) 1.00000 0.0790569
\(161\) −16.0000 −1.26098
\(162\) 0 0
\(163\) 12.0000 0.939913 0.469956 0.882690i \(-0.344270\pi\)
0.469956 + 0.882690i \(0.344270\pi\)
\(164\) −10.0000 −0.780869
\(165\) 0 0
\(166\) 14.0000 1.08661
\(167\) 8.00000 0.619059 0.309529 0.950890i \(-0.399829\pi\)
0.309529 + 0.950890i \(0.399829\pi\)
\(168\) 0 0
\(169\) −13.0000 −1.00000
\(170\) −4.00000 −0.306786
\(171\) 0 0
\(172\) −12.0000 −0.914991
\(173\) −18.0000 −1.36851 −0.684257 0.729241i \(-0.739873\pi\)
−0.684257 + 0.729241i \(0.739873\pi\)
\(174\) 0 0
\(175\) −4.00000 −0.302372
\(176\) 6.00000 0.452267
\(177\) 0 0
\(178\) 10.0000 0.749532
\(179\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(180\) 0 0
\(181\) −16.0000 −1.18927 −0.594635 0.803996i \(-0.702704\pi\)
−0.594635 + 0.803996i \(0.702704\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −4.00000 −0.294884
\(185\) 4.00000 0.294086
\(186\) 0 0
\(187\) −24.0000 −1.75505
\(188\) 0 0
\(189\) 0 0
\(190\) −1.00000 −0.0725476
\(191\) −16.0000 −1.15772 −0.578860 0.815427i \(-0.696502\pi\)
−0.578860 + 0.815427i \(0.696502\pi\)
\(192\) 0 0
\(193\) −2.00000 −0.143963 −0.0719816 0.997406i \(-0.522932\pi\)
−0.0719816 + 0.997406i \(0.522932\pi\)
\(194\) 6.00000 0.430775
\(195\) 0 0
\(196\) 9.00000 0.642857
\(197\) −10.0000 −0.712470 −0.356235 0.934396i \(-0.615940\pi\)
−0.356235 + 0.934396i \(0.615940\pi\)
\(198\) 0 0
\(199\) 20.0000 1.41776 0.708881 0.705328i \(-0.249200\pi\)
0.708881 + 0.705328i \(0.249200\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 0 0
\(202\) 10.0000 0.703598
\(203\) −40.0000 −2.80745
\(204\) 0 0
\(205\) 10.0000 0.698430
\(206\) −18.0000 −1.25412
\(207\) 0 0
\(208\) 0 0
\(209\) −6.00000 −0.415029
\(210\) 0 0
\(211\) −4.00000 −0.275371 −0.137686 0.990476i \(-0.543966\pi\)
−0.137686 + 0.990476i \(0.543966\pi\)
\(212\) 6.00000 0.412082
\(213\) 0 0
\(214\) 0 0
\(215\) 12.0000 0.818393
\(216\) 0 0
\(217\) 8.00000 0.543075
\(218\) 8.00000 0.541828
\(219\) 0 0
\(220\) −6.00000 −0.404520
\(221\) 0 0
\(222\) 0 0
\(223\) 14.0000 0.937509 0.468755 0.883328i \(-0.344703\pi\)
0.468755 + 0.883328i \(0.344703\pi\)
\(224\) 4.00000 0.267261
\(225\) 0 0
\(226\) −2.00000 −0.133038
\(227\) 8.00000 0.530979 0.265489 0.964114i \(-0.414466\pi\)
0.265489 + 0.964114i \(0.414466\pi\)
\(228\) 0 0
\(229\) −18.0000 −1.18947 −0.594737 0.803921i \(-0.702744\pi\)
−0.594737 + 0.803921i \(0.702744\pi\)
\(230\) 4.00000 0.263752
\(231\) 0 0
\(232\) −10.0000 −0.656532
\(233\) −4.00000 −0.262049 −0.131024 0.991379i \(-0.541827\pi\)
−0.131024 + 0.991379i \(0.541827\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −4.00000 −0.260378
\(237\) 0 0
\(238\) −16.0000 −1.03713
\(239\) 12.0000 0.776215 0.388108 0.921614i \(-0.373129\pi\)
0.388108 + 0.921614i \(0.373129\pi\)
\(240\) 0 0
\(241\) −22.0000 −1.41714 −0.708572 0.705638i \(-0.750660\pi\)
−0.708572 + 0.705638i \(0.750660\pi\)
\(242\) −25.0000 −1.60706
\(243\) 0 0
\(244\) −10.0000 −0.640184
\(245\) −9.00000 −0.574989
\(246\) 0 0
\(247\) 0 0
\(248\) 2.00000 0.127000
\(249\) 0 0
\(250\) 1.00000 0.0632456
\(251\) −2.00000 −0.126239 −0.0631194 0.998006i \(-0.520105\pi\)
−0.0631194 + 0.998006i \(0.520105\pi\)
\(252\) 0 0
\(253\) 24.0000 1.50887
\(254\) −18.0000 −1.12942
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 6.00000 0.374270 0.187135 0.982334i \(-0.440080\pi\)
0.187135 + 0.982334i \(0.440080\pi\)
\(258\) 0 0
\(259\) 16.0000 0.994192
\(260\) 0 0
\(261\) 0 0
\(262\) −10.0000 −0.617802
\(263\) −20.0000 −1.23325 −0.616626 0.787256i \(-0.711501\pi\)
−0.616626 + 0.787256i \(0.711501\pi\)
\(264\) 0 0
\(265\) −6.00000 −0.368577
\(266\) −4.00000 −0.245256
\(267\) 0 0
\(268\) −8.00000 −0.488678
\(269\) 14.0000 0.853595 0.426798 0.904347i \(-0.359642\pi\)
0.426798 + 0.904347i \(0.359642\pi\)
\(270\) 0 0
\(271\) −4.00000 −0.242983 −0.121491 0.992592i \(-0.538768\pi\)
−0.121491 + 0.992592i \(0.538768\pi\)
\(272\) −4.00000 −0.242536
\(273\) 0 0
\(274\) 12.0000 0.724947
\(275\) 6.00000 0.361814
\(276\) 0 0
\(277\) 10.0000 0.600842 0.300421 0.953807i \(-0.402873\pi\)
0.300421 + 0.953807i \(0.402873\pi\)
\(278\) 12.0000 0.719712
\(279\) 0 0
\(280\) −4.00000 −0.239046
\(281\) 10.0000 0.596550 0.298275 0.954480i \(-0.403589\pi\)
0.298275 + 0.954480i \(0.403589\pi\)
\(282\) 0 0
\(283\) 28.0000 1.66443 0.832214 0.554455i \(-0.187073\pi\)
0.832214 + 0.554455i \(0.187073\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 40.0000 2.36113
\(288\) 0 0
\(289\) −1.00000 −0.0588235
\(290\) 10.0000 0.587220
\(291\) 0 0
\(292\) 6.00000 0.351123
\(293\) −26.0000 −1.51894 −0.759468 0.650545i \(-0.774541\pi\)
−0.759468 + 0.650545i \(0.774541\pi\)
\(294\) 0 0
\(295\) 4.00000 0.232889
\(296\) 4.00000 0.232495
\(297\) 0 0
\(298\) −10.0000 −0.579284
\(299\) 0 0
\(300\) 0 0
\(301\) 48.0000 2.76667
\(302\) 18.0000 1.03578
\(303\) 0 0
\(304\) −1.00000 −0.0573539
\(305\) 10.0000 0.572598
\(306\) 0 0
\(307\) −20.0000 −1.14146 −0.570730 0.821138i \(-0.693340\pi\)
−0.570730 + 0.821138i \(0.693340\pi\)
\(308\) −24.0000 −1.36753
\(309\) 0 0
\(310\) −2.00000 −0.113592
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0 0
\(313\) −14.0000 −0.791327 −0.395663 0.918396i \(-0.629485\pi\)
−0.395663 + 0.918396i \(0.629485\pi\)
\(314\) 18.0000 1.01580
\(315\) 0 0
\(316\) −10.0000 −0.562544
\(317\) 30.0000 1.68497 0.842484 0.538721i \(-0.181092\pi\)
0.842484 + 0.538721i \(0.181092\pi\)
\(318\) 0 0
\(319\) 60.0000 3.35936
\(320\) −1.00000 −0.0559017
\(321\) 0 0
\(322\) 16.0000 0.891645
\(323\) 4.00000 0.222566
\(324\) 0 0
\(325\) 0 0
\(326\) −12.0000 −0.664619
\(327\) 0 0
\(328\) 10.0000 0.552158
\(329\) 0 0
\(330\) 0 0
\(331\) 28.0000 1.53902 0.769510 0.638635i \(-0.220501\pi\)
0.769510 + 0.638635i \(0.220501\pi\)
\(332\) −14.0000 −0.768350
\(333\) 0 0
\(334\) −8.00000 −0.437741
\(335\) 8.00000 0.437087
\(336\) 0 0
\(337\) −26.0000 −1.41631 −0.708155 0.706057i \(-0.750472\pi\)
−0.708155 + 0.706057i \(0.750472\pi\)
\(338\) 13.0000 0.707107
\(339\) 0 0
\(340\) 4.00000 0.216930
\(341\) −12.0000 −0.649836
\(342\) 0 0
\(343\) −8.00000 −0.431959
\(344\) 12.0000 0.646997
\(345\) 0 0
\(346\) 18.0000 0.967686
\(347\) −6.00000 −0.322097 −0.161048 0.986947i \(-0.551488\pi\)
−0.161048 + 0.986947i \(0.551488\pi\)
\(348\) 0 0
\(349\) 10.0000 0.535288 0.267644 0.963518i \(-0.413755\pi\)
0.267644 + 0.963518i \(0.413755\pi\)
\(350\) 4.00000 0.213809
\(351\) 0 0
\(352\) −6.00000 −0.319801
\(353\) −24.0000 −1.27739 −0.638696 0.769460i \(-0.720526\pi\)
−0.638696 + 0.769460i \(0.720526\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −10.0000 −0.529999
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 16.0000 0.840941
\(363\) 0 0
\(364\) 0 0
\(365\) −6.00000 −0.314054
\(366\) 0 0
\(367\) 8.00000 0.417597 0.208798 0.977959i \(-0.433045\pi\)
0.208798 + 0.977959i \(0.433045\pi\)
\(368\) 4.00000 0.208514
\(369\) 0 0
\(370\) −4.00000 −0.207950
\(371\) −24.0000 −1.24602
\(372\) 0 0
\(373\) 12.0000 0.621336 0.310668 0.950518i \(-0.399447\pi\)
0.310668 + 0.950518i \(0.399447\pi\)
\(374\) 24.0000 1.24101
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 20.0000 1.02733 0.513665 0.857991i \(-0.328287\pi\)
0.513665 + 0.857991i \(0.328287\pi\)
\(380\) 1.00000 0.0512989
\(381\) 0 0
\(382\) 16.0000 0.818631
\(383\) 24.0000 1.22634 0.613171 0.789950i \(-0.289894\pi\)
0.613171 + 0.789950i \(0.289894\pi\)
\(384\) 0 0
\(385\) 24.0000 1.22315
\(386\) 2.00000 0.101797
\(387\) 0 0
\(388\) −6.00000 −0.304604
\(389\) 18.0000 0.912636 0.456318 0.889817i \(-0.349168\pi\)
0.456318 + 0.889817i \(0.349168\pi\)
\(390\) 0 0
\(391\) −16.0000 −0.809155
\(392\) −9.00000 −0.454569
\(393\) 0 0
\(394\) 10.0000 0.503793
\(395\) 10.0000 0.503155
\(396\) 0 0
\(397\) 22.0000 1.10415 0.552074 0.833795i \(-0.313837\pi\)
0.552074 + 0.833795i \(0.313837\pi\)
\(398\) −20.0000 −1.00251
\(399\) 0 0
\(400\) 1.00000 0.0500000
\(401\) 6.00000 0.299626 0.149813 0.988714i \(-0.452133\pi\)
0.149813 + 0.988714i \(0.452133\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) −10.0000 −0.497519
\(405\) 0 0
\(406\) 40.0000 1.98517
\(407\) −24.0000 −1.18964
\(408\) 0 0
\(409\) 2.00000 0.0988936 0.0494468 0.998777i \(-0.484254\pi\)
0.0494468 + 0.998777i \(0.484254\pi\)
\(410\) −10.0000 −0.493865
\(411\) 0 0
\(412\) 18.0000 0.886796
\(413\) 16.0000 0.787309
\(414\) 0 0
\(415\) 14.0000 0.687233
\(416\) 0 0
\(417\) 0 0
\(418\) 6.00000 0.293470
\(419\) −26.0000 −1.27018 −0.635092 0.772437i \(-0.719038\pi\)
−0.635092 + 0.772437i \(0.719038\pi\)
\(420\) 0 0
\(421\) 28.0000 1.36464 0.682318 0.731055i \(-0.260972\pi\)
0.682318 + 0.731055i \(0.260972\pi\)
\(422\) 4.00000 0.194717
\(423\) 0 0
\(424\) −6.00000 −0.291386
\(425\) −4.00000 −0.194029
\(426\) 0 0
\(427\) 40.0000 1.93574
\(428\) 0 0
\(429\) 0 0
\(430\) −12.0000 −0.578691
\(431\) 24.0000 1.15604 0.578020 0.816023i \(-0.303826\pi\)
0.578020 + 0.816023i \(0.303826\pi\)
\(432\) 0 0
\(433\) 6.00000 0.288342 0.144171 0.989553i \(-0.453949\pi\)
0.144171 + 0.989553i \(0.453949\pi\)
\(434\) −8.00000 −0.384012
\(435\) 0 0
\(436\) −8.00000 −0.383131
\(437\) −4.00000 −0.191346
\(438\) 0 0
\(439\) 10.0000 0.477274 0.238637 0.971109i \(-0.423299\pi\)
0.238637 + 0.971109i \(0.423299\pi\)
\(440\) 6.00000 0.286039
\(441\) 0 0
\(442\) 0 0
\(443\) −6.00000 −0.285069 −0.142534 0.989790i \(-0.545525\pi\)
−0.142534 + 0.989790i \(0.545525\pi\)
\(444\) 0 0
\(445\) 10.0000 0.474045
\(446\) −14.0000 −0.662919
\(447\) 0 0
\(448\) −4.00000 −0.188982
\(449\) 26.0000 1.22702 0.613508 0.789689i \(-0.289758\pi\)
0.613508 + 0.789689i \(0.289758\pi\)
\(450\) 0 0
\(451\) −60.0000 −2.82529
\(452\) 2.00000 0.0940721
\(453\) 0 0
\(454\) −8.00000 −0.375459
\(455\) 0 0
\(456\) 0 0
\(457\) −38.0000 −1.77757 −0.888783 0.458329i \(-0.848448\pi\)
−0.888783 + 0.458329i \(0.848448\pi\)
\(458\) 18.0000 0.841085
\(459\) 0 0
\(460\) −4.00000 −0.186501
\(461\) 2.00000 0.0931493 0.0465746 0.998915i \(-0.485169\pi\)
0.0465746 + 0.998915i \(0.485169\pi\)
\(462\) 0 0
\(463\) −32.0000 −1.48717 −0.743583 0.668644i \(-0.766875\pi\)
−0.743583 + 0.668644i \(0.766875\pi\)
\(464\) 10.0000 0.464238
\(465\) 0 0
\(466\) 4.00000 0.185296
\(467\) 10.0000 0.462745 0.231372 0.972865i \(-0.425678\pi\)
0.231372 + 0.972865i \(0.425678\pi\)
\(468\) 0 0
\(469\) 32.0000 1.47762
\(470\) 0 0
\(471\) 0 0
\(472\) 4.00000 0.184115
\(473\) −72.0000 −3.31056
\(474\) 0 0
\(475\) −1.00000 −0.0458831
\(476\) 16.0000 0.733359
\(477\) 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
\(481\) 0 0
\(482\) 22.0000 1.00207
\(483\) 0 0
\(484\) 25.0000 1.13636
\(485\) 6.00000 0.272446
\(486\) 0 0
\(487\) −2.00000 −0.0906287 −0.0453143 0.998973i \(-0.514429\pi\)
−0.0453143 + 0.998973i \(0.514429\pi\)
\(488\) 10.0000 0.452679
\(489\) 0 0
\(490\) 9.00000 0.406579
\(491\) 26.0000 1.17336 0.586682 0.809818i \(-0.300434\pi\)
0.586682 + 0.809818i \(0.300434\pi\)
\(492\) 0 0
\(493\) −40.0000 −1.80151
\(494\) 0 0
\(495\) 0 0
\(496\) −2.00000 −0.0898027
\(497\) 0 0
\(498\) 0 0
\(499\) −36.0000 −1.61158 −0.805791 0.592200i \(-0.798259\pi\)
−0.805791 + 0.592200i \(0.798259\pi\)
\(500\) −1.00000 −0.0447214
\(501\) 0 0
\(502\) 2.00000 0.0892644
\(503\) 28.0000 1.24846 0.624229 0.781241i \(-0.285413\pi\)
0.624229 + 0.781241i \(0.285413\pi\)
\(504\) 0 0
\(505\) 10.0000 0.444994
\(506\) −24.0000 −1.06693
\(507\) 0 0
\(508\) 18.0000 0.798621
\(509\) 18.0000 0.797836 0.398918 0.916987i \(-0.369386\pi\)
0.398918 + 0.916987i \(0.369386\pi\)
\(510\) 0 0
\(511\) −24.0000 −1.06170
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −6.00000 −0.264649
\(515\) −18.0000 −0.793175
\(516\) 0 0
\(517\) 0 0
\(518\) −16.0000 −0.703000
\(519\) 0 0
\(520\) 0 0
\(521\) −42.0000 −1.84005 −0.920027 0.391856i \(-0.871833\pi\)
−0.920027 + 0.391856i \(0.871833\pi\)
\(522\) 0 0
\(523\) −16.0000 −0.699631 −0.349816 0.936819i \(-0.613756\pi\)
−0.349816 + 0.936819i \(0.613756\pi\)
\(524\) 10.0000 0.436852
\(525\) 0 0
\(526\) 20.0000 0.872041
\(527\) 8.00000 0.348485
\(528\) 0 0
\(529\) −7.00000 −0.304348
\(530\) 6.00000 0.260623
\(531\) 0 0
\(532\) 4.00000 0.173422
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 8.00000 0.345547
\(537\) 0 0
\(538\) −14.0000 −0.603583
\(539\) 54.0000 2.32594
\(540\) 0 0
\(541\) −22.0000 −0.945854 −0.472927 0.881102i \(-0.656803\pi\)
−0.472927 + 0.881102i \(0.656803\pi\)
\(542\) 4.00000 0.171815
\(543\) 0 0
\(544\) 4.00000 0.171499
\(545\) 8.00000 0.342682
\(546\) 0 0
\(547\) 4.00000 0.171028 0.0855138 0.996337i \(-0.472747\pi\)
0.0855138 + 0.996337i \(0.472747\pi\)
\(548\) −12.0000 −0.512615
\(549\) 0 0
\(550\) −6.00000 −0.255841
\(551\) −10.0000 −0.426014
\(552\) 0 0
\(553\) 40.0000 1.70097
\(554\) −10.0000 −0.424859
\(555\) 0 0
\(556\) −12.0000 −0.508913
\(557\) −22.0000 −0.932170 −0.466085 0.884740i \(-0.654336\pi\)
−0.466085 + 0.884740i \(0.654336\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 4.00000 0.169031
\(561\) 0 0
\(562\) −10.0000 −0.421825
\(563\) 4.00000 0.168580 0.0842900 0.996441i \(-0.473138\pi\)
0.0842900 + 0.996441i \(0.473138\pi\)
\(564\) 0 0
\(565\) −2.00000 −0.0841406
\(566\) −28.0000 −1.17693
\(567\) 0 0
\(568\) 0 0
\(569\) 34.0000 1.42535 0.712677 0.701492i \(-0.247483\pi\)
0.712677 + 0.701492i \(0.247483\pi\)
\(570\) 0 0
\(571\) −20.0000 −0.836974 −0.418487 0.908223i \(-0.637439\pi\)
−0.418487 + 0.908223i \(0.637439\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) −40.0000 −1.66957
\(575\) 4.00000 0.166812
\(576\) 0 0
\(577\) −2.00000 −0.0832611 −0.0416305 0.999133i \(-0.513255\pi\)
−0.0416305 + 0.999133i \(0.513255\pi\)
\(578\) 1.00000 0.0415945
\(579\) 0 0
\(580\) −10.0000 −0.415227
\(581\) 56.0000 2.32327
\(582\) 0 0
\(583\) 36.0000 1.49097
\(584\) −6.00000 −0.248282
\(585\) 0 0
\(586\) 26.0000 1.07405
\(587\) −42.0000 −1.73353 −0.866763 0.498721i \(-0.833803\pi\)
−0.866763 + 0.498721i \(0.833803\pi\)
\(588\) 0 0
\(589\) 2.00000 0.0824086
\(590\) −4.00000 −0.164677
\(591\) 0 0
\(592\) −4.00000 −0.164399
\(593\) 44.0000 1.80686 0.903432 0.428732i \(-0.141040\pi\)
0.903432 + 0.428732i \(0.141040\pi\)
\(594\) 0 0
\(595\) −16.0000 −0.655936
\(596\) 10.0000 0.409616
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) 0 0
\(601\) 26.0000 1.06056 0.530281 0.847822i \(-0.322086\pi\)
0.530281 + 0.847822i \(0.322086\pi\)
\(602\) −48.0000 −1.95633
\(603\) 0 0
\(604\) −18.0000 −0.732410
\(605\) −25.0000 −1.01639
\(606\) 0 0
\(607\) 22.0000 0.892952 0.446476 0.894795i \(-0.352679\pi\)
0.446476 + 0.894795i \(0.352679\pi\)
\(608\) 1.00000 0.0405554
\(609\) 0 0
\(610\) −10.0000 −0.404888
\(611\) 0 0
\(612\) 0 0
\(613\) 14.0000 0.565455 0.282727 0.959200i \(-0.408761\pi\)
0.282727 + 0.959200i \(0.408761\pi\)
\(614\) 20.0000 0.807134
\(615\) 0 0
\(616\) 24.0000 0.966988
\(617\) −8.00000 −0.322068 −0.161034 0.986949i \(-0.551483\pi\)
−0.161034 + 0.986949i \(0.551483\pi\)
\(618\) 0 0
\(619\) −20.0000 −0.803868 −0.401934 0.915669i \(-0.631662\pi\)
−0.401934 + 0.915669i \(0.631662\pi\)
\(620\) 2.00000 0.0803219
\(621\) 0 0
\(622\) 0 0
\(623\) 40.0000 1.60257
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 14.0000 0.559553
\(627\) 0 0
\(628\) −18.0000 −0.718278
\(629\) 16.0000 0.637962
\(630\) 0 0
\(631\) −36.0000 −1.43314 −0.716569 0.697517i \(-0.754288\pi\)
−0.716569 + 0.697517i \(0.754288\pi\)
\(632\) 10.0000 0.397779
\(633\) 0 0
\(634\) −30.0000 −1.19145
\(635\) −18.0000 −0.714308
\(636\) 0 0
\(637\) 0 0
\(638\) −60.0000 −2.37542
\(639\) 0 0
\(640\) 1.00000 0.0395285
\(641\) −42.0000 −1.65890 −0.829450 0.558581i \(-0.811346\pi\)
−0.829450 + 0.558581i \(0.811346\pi\)
\(642\) 0 0
\(643\) 28.0000 1.10421 0.552106 0.833774i \(-0.313824\pi\)
0.552106 + 0.833774i \(0.313824\pi\)
\(644\) −16.0000 −0.630488
\(645\) 0 0
\(646\) −4.00000 −0.157378
\(647\) 12.0000 0.471769 0.235884 0.971781i \(-0.424201\pi\)
0.235884 + 0.971781i \(0.424201\pi\)
\(648\) 0 0
\(649\) −24.0000 −0.942082
\(650\) 0 0
\(651\) 0 0
\(652\) 12.0000 0.469956
\(653\) 42.0000 1.64359 0.821794 0.569785i \(-0.192974\pi\)
0.821794 + 0.569785i \(0.192974\pi\)
\(654\) 0 0
\(655\) −10.0000 −0.390732
\(656\) −10.0000 −0.390434
\(657\) 0 0
\(658\) 0 0
\(659\) 36.0000 1.40236 0.701180 0.712984i \(-0.252657\pi\)
0.701180 + 0.712984i \(0.252657\pi\)
\(660\) 0 0
\(661\) −40.0000 −1.55582 −0.777910 0.628376i \(-0.783720\pi\)
−0.777910 + 0.628376i \(0.783720\pi\)
\(662\) −28.0000 −1.08825
\(663\) 0 0
\(664\) 14.0000 0.543305
\(665\) −4.00000 −0.155113
\(666\) 0 0
\(667\) 40.0000 1.54881
\(668\) 8.00000 0.309529
\(669\) 0 0
\(670\) −8.00000 −0.309067
\(671\) −60.0000 −2.31627
\(672\) 0 0
\(673\) −10.0000 −0.385472 −0.192736 0.981251i \(-0.561736\pi\)
−0.192736 + 0.981251i \(0.561736\pi\)
\(674\) 26.0000 1.00148
\(675\) 0 0
\(676\) −13.0000 −0.500000
\(677\) −2.00000 −0.0768662 −0.0384331 0.999261i \(-0.512237\pi\)
−0.0384331 + 0.999261i \(0.512237\pi\)
\(678\) 0 0
\(679\) 24.0000 0.921035
\(680\) −4.00000 −0.153393
\(681\) 0 0
\(682\) 12.0000 0.459504
\(683\) −36.0000 −1.37750 −0.688751 0.724998i \(-0.741841\pi\)
−0.688751 + 0.724998i \(0.741841\pi\)
\(684\) 0 0
\(685\) 12.0000 0.458496
\(686\) 8.00000 0.305441
\(687\) 0 0
\(688\) −12.0000 −0.457496
\(689\) 0 0
\(690\) 0 0
\(691\) 28.0000 1.06517 0.532585 0.846376i \(-0.321221\pi\)
0.532585 + 0.846376i \(0.321221\pi\)
\(692\) −18.0000 −0.684257
\(693\) 0 0
\(694\) 6.00000 0.227757
\(695\) 12.0000 0.455186
\(696\) 0 0
\(697\) 40.0000 1.51511
\(698\) −10.0000 −0.378506
\(699\) 0 0
\(700\) −4.00000 −0.151186
\(701\) 30.0000 1.13308 0.566542 0.824033i \(-0.308281\pi\)
0.566542 + 0.824033i \(0.308281\pi\)
\(702\) 0 0
\(703\) 4.00000 0.150863
\(704\) 6.00000 0.226134
\(705\) 0 0
\(706\) 24.0000 0.903252
\(707\) 40.0000 1.50435
\(708\) 0 0
\(709\) −34.0000 −1.27690 −0.638448 0.769665i \(-0.720423\pi\)
−0.638448 + 0.769665i \(0.720423\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 10.0000 0.374766
\(713\) −8.00000 −0.299602
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −16.0000 −0.596699 −0.298350 0.954457i \(-0.596436\pi\)
−0.298350 + 0.954457i \(0.596436\pi\)
\(720\) 0 0
\(721\) −72.0000 −2.68142
\(722\) −1.00000 −0.0372161
\(723\) 0 0
\(724\) −16.0000 −0.594635
\(725\) 10.0000 0.371391
\(726\) 0 0
\(727\) −28.0000 −1.03846 −0.519231 0.854634i \(-0.673782\pi\)
−0.519231 + 0.854634i \(0.673782\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 6.00000 0.222070
\(731\) 48.0000 1.77534
\(732\) 0 0
\(733\) −18.0000 −0.664845 −0.332423 0.943131i \(-0.607866\pi\)
−0.332423 + 0.943131i \(0.607866\pi\)
\(734\) −8.00000 −0.295285
\(735\) 0 0
\(736\) −4.00000 −0.147442
\(737\) −48.0000 −1.76810
\(738\) 0 0
\(739\) −4.00000 −0.147142 −0.0735712 0.997290i \(-0.523440\pi\)
−0.0735712 + 0.997290i \(0.523440\pi\)
\(740\) 4.00000 0.147043
\(741\) 0 0
\(742\) 24.0000 0.881068
\(743\) −8.00000 −0.293492 −0.146746 0.989174i \(-0.546880\pi\)
−0.146746 + 0.989174i \(0.546880\pi\)
\(744\) 0 0
\(745\) −10.0000 −0.366372
\(746\) −12.0000 −0.439351
\(747\) 0 0
\(748\) −24.0000 −0.877527
\(749\) 0 0
\(750\) 0 0
\(751\) 46.0000 1.67856 0.839282 0.543696i \(-0.182976\pi\)
0.839282 + 0.543696i \(0.182976\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 18.0000 0.655087
\(756\) 0 0
\(757\) −26.0000 −0.944986 −0.472493 0.881334i \(-0.656646\pi\)
−0.472493 + 0.881334i \(0.656646\pi\)
\(758\) −20.0000 −0.726433
\(759\) 0 0
\(760\) −1.00000 −0.0362738
\(761\) −24.0000 −0.869999 −0.435000 0.900431i \(-0.643252\pi\)
−0.435000 + 0.900431i \(0.643252\pi\)
\(762\) 0 0
\(763\) 32.0000 1.15848
\(764\) −16.0000 −0.578860
\(765\) 0 0
\(766\) −24.0000 −0.867155
\(767\) 0 0
\(768\) 0 0
\(769\) −14.0000 −0.504853 −0.252426 0.967616i \(-0.581229\pi\)
−0.252426 + 0.967616i \(0.581229\pi\)
\(770\) −24.0000 −0.864900
\(771\) 0 0
\(772\) −2.00000 −0.0719816
\(773\) −30.0000 −1.07903 −0.539513 0.841978i \(-0.681391\pi\)
−0.539513 + 0.841978i \(0.681391\pi\)
\(774\) 0 0
\(775\) −2.00000 −0.0718421
\(776\) 6.00000 0.215387
\(777\) 0 0
\(778\) −18.0000 −0.645331
\(779\) 10.0000 0.358287
\(780\) 0 0
\(781\) 0 0
\(782\) 16.0000 0.572159
\(783\) 0 0
\(784\) 9.00000 0.321429
\(785\) 18.0000 0.642448
\(786\) 0 0
\(787\) −52.0000 −1.85360 −0.926800 0.375555i \(-0.877452\pi\)
−0.926800 + 0.375555i \(0.877452\pi\)
\(788\) −10.0000 −0.356235
\(789\) 0 0
\(790\) −10.0000 −0.355784
\(791\) −8.00000 −0.284447
\(792\) 0 0
\(793\) 0 0
\(794\) −22.0000 −0.780751
\(795\) 0 0
\(796\) 20.0000 0.708881
\(797\) 2.00000 0.0708436 0.0354218 0.999372i \(-0.488723\pi\)
0.0354218 + 0.999372i \(0.488723\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −1.00000 −0.0353553
\(801\) 0 0
\(802\) −6.00000 −0.211867
\(803\) 36.0000 1.27041
\(804\) 0 0
\(805\) 16.0000 0.563926
\(806\) 0 0
\(807\) 0 0
\(808\) 10.0000 0.351799
\(809\) −36.0000 −1.26569 −0.632846 0.774277i \(-0.718114\pi\)
−0.632846 + 0.774277i \(0.718114\pi\)
\(810\) 0 0
\(811\) 20.0000 0.702295 0.351147 0.936320i \(-0.385792\pi\)
0.351147 + 0.936320i \(0.385792\pi\)
\(812\) −40.0000 −1.40372
\(813\) 0 0
\(814\) 24.0000 0.841200
\(815\) −12.0000 −0.420342
\(816\) 0 0
\(817\) 12.0000 0.419827
\(818\) −2.00000 −0.0699284
\(819\) 0 0
\(820\) 10.0000 0.349215
\(821\) −50.0000 −1.74501 −0.872506 0.488603i \(-0.837507\pi\)
−0.872506 + 0.488603i \(0.837507\pi\)
\(822\) 0 0
\(823\) −16.0000 −0.557725 −0.278862 0.960331i \(-0.589957\pi\)
−0.278862 + 0.960331i \(0.589957\pi\)
\(824\) −18.0000 −0.627060
\(825\) 0 0
\(826\) −16.0000 −0.556711
\(827\) 36.0000 1.25184 0.625921 0.779886i \(-0.284723\pi\)
0.625921 + 0.779886i \(0.284723\pi\)
\(828\) 0 0
\(829\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(830\) −14.0000 −0.485947
\(831\) 0 0
\(832\) 0 0
\(833\) −36.0000 −1.24733
\(834\) 0 0
\(835\) −8.00000 −0.276851
\(836\) −6.00000 −0.207514
\(837\) 0 0
\(838\) 26.0000 0.898155
\(839\) 24.0000 0.828572 0.414286 0.910147i \(-0.364031\pi\)
0.414286 + 0.910147i \(0.364031\pi\)
\(840\) 0 0
\(841\) 71.0000 2.44828
\(842\) −28.0000 −0.964944
\(843\) 0 0
\(844\) −4.00000 −0.137686
\(845\) 13.0000 0.447214
\(846\) 0 0
\(847\) −100.000 −3.43604
\(848\) 6.00000 0.206041
\(849\) 0 0
\(850\) 4.00000 0.137199
\(851\) −16.0000 −0.548473
\(852\) 0 0
\(853\) 2.00000 0.0684787 0.0342393 0.999414i \(-0.489099\pi\)
0.0342393 + 0.999414i \(0.489099\pi\)
\(854\) −40.0000 −1.36877
\(855\) 0 0
\(856\) 0 0
\(857\) −30.0000 −1.02478 −0.512390 0.858753i \(-0.671240\pi\)
−0.512390 + 0.858753i \(0.671240\pi\)
\(858\) 0 0
\(859\) −28.0000 −0.955348 −0.477674 0.878537i \(-0.658520\pi\)
−0.477674 + 0.878537i \(0.658520\pi\)
\(860\) 12.0000 0.409197
\(861\) 0 0
\(862\) −24.0000 −0.817443
\(863\) 48.0000 1.63394 0.816970 0.576681i \(-0.195652\pi\)
0.816970 + 0.576681i \(0.195652\pi\)
\(864\) 0 0
\(865\) 18.0000 0.612018
\(866\) −6.00000 −0.203888
\(867\) 0 0
\(868\) 8.00000 0.271538
\(869\) −60.0000 −2.03536
\(870\) 0 0
\(871\) 0 0
\(872\) 8.00000 0.270914
\(873\) 0 0
\(874\) 4.00000 0.135302
\(875\) 4.00000 0.135225
\(876\) 0 0
\(877\) 4.00000 0.135070 0.0675352 0.997717i \(-0.478487\pi\)
0.0675352 + 0.997717i \(0.478487\pi\)
\(878\) −10.0000 −0.337484
\(879\) 0 0
\(880\) −6.00000 −0.202260
\(881\) 20.0000 0.673817 0.336909 0.941537i \(-0.390619\pi\)
0.336909 + 0.941537i \(0.390619\pi\)
\(882\) 0 0
\(883\) 20.0000 0.673054 0.336527 0.941674i \(-0.390748\pi\)
0.336527 + 0.941674i \(0.390748\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 6.00000 0.201574
\(887\) 16.0000 0.537227 0.268614 0.963248i \(-0.413434\pi\)
0.268614 + 0.963248i \(0.413434\pi\)
\(888\) 0 0
\(889\) −72.0000 −2.41480
\(890\) −10.0000 −0.335201
\(891\) 0 0
\(892\) 14.0000 0.468755
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 4.00000 0.133631
\(897\) 0 0
\(898\) −26.0000 −0.867631
\(899\) −20.0000 −0.667037
\(900\) 0 0
\(901\) −24.0000 −0.799556
\(902\) 60.0000 1.99778
\(903\) 0 0
\(904\) −2.00000 −0.0665190
\(905\) 16.0000 0.531858
\(906\) 0 0
\(907\) 32.0000 1.06254 0.531271 0.847202i \(-0.321714\pi\)
0.531271 + 0.847202i \(0.321714\pi\)
\(908\) 8.00000 0.265489
\(909\) 0 0
\(910\) 0 0
\(911\) −32.0000 −1.06021 −0.530104 0.847933i \(-0.677847\pi\)
−0.530104 + 0.847933i \(0.677847\pi\)
\(912\) 0 0
\(913\) −84.0000 −2.77999
\(914\) 38.0000 1.25693
\(915\) 0 0
\(916\) −18.0000 −0.594737
\(917\) −40.0000 −1.32092
\(918\) 0 0
\(919\) −52.0000 −1.71532 −0.857661 0.514216i \(-0.828083\pi\)
−0.857661 + 0.514216i \(0.828083\pi\)
\(920\) 4.00000 0.131876
\(921\) 0 0
\(922\) −2.00000 −0.0658665
\(923\) 0 0
\(924\) 0 0
\(925\) −4.00000 −0.131519
\(926\) 32.0000 1.05159
\(927\) 0 0
\(928\) −10.0000 −0.328266
\(929\) 36.0000 1.18112 0.590561 0.806993i \(-0.298907\pi\)
0.590561 + 0.806993i \(0.298907\pi\)
\(930\) 0 0
\(931\) −9.00000 −0.294963
\(932\) −4.00000 −0.131024
\(933\) 0 0
\(934\) −10.0000 −0.327210
\(935\) 24.0000 0.784884
\(936\) 0 0
\(937\) 14.0000 0.457360 0.228680 0.973502i \(-0.426559\pi\)
0.228680 + 0.973502i \(0.426559\pi\)
\(938\) −32.0000 −1.04484
\(939\) 0 0
\(940\) 0 0
\(941\) 50.0000 1.62995 0.814977 0.579494i \(-0.196750\pi\)
0.814977 + 0.579494i \(0.196750\pi\)
\(942\) 0 0
\(943\) −40.0000 −1.30258
\(944\) −4.00000 −0.130189
\(945\) 0 0
\(946\) 72.0000 2.34092
\(947\) 38.0000 1.23483 0.617417 0.786636i \(-0.288179\pi\)
0.617417 + 0.786636i \(0.288179\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 1.00000 0.0324443
\(951\) 0 0
\(952\) −16.0000 −0.518563
\(953\) −34.0000 −1.10137 −0.550684 0.834714i \(-0.685633\pi\)
−0.550684 + 0.834714i \(0.685633\pi\)
\(954\) 0 0
\(955\) 16.0000 0.517748
\(956\) 12.0000 0.388108
\(957\) 0 0
\(958\) −24.0000 −0.775405
\(959\) 48.0000 1.55000
\(960\) 0 0
\(961\) −27.0000 −0.870968
\(962\) 0 0
\(963\) 0 0
\(964\) −22.0000 −0.708572
\(965\) 2.00000 0.0643823
\(966\) 0 0
\(967\) 12.0000 0.385894 0.192947 0.981209i \(-0.438195\pi\)
0.192947 + 0.981209i \(0.438195\pi\)
\(968\) −25.0000 −0.803530
\(969\) 0 0
\(970\) −6.00000 −0.192648
\(971\) 60.0000 1.92549 0.962746 0.270408i \(-0.0871586\pi\)
0.962746 + 0.270408i \(0.0871586\pi\)
\(972\) 0 0
\(973\) 48.0000 1.53881
\(974\) 2.00000 0.0640841
\(975\) 0 0
\(976\) −10.0000 −0.320092
\(977\) 18.0000 0.575871 0.287936 0.957650i \(-0.407031\pi\)
0.287936 + 0.957650i \(0.407031\pi\)
\(978\) 0 0
\(979\) −60.0000 −1.91761
\(980\) −9.00000 −0.287494
\(981\) 0 0
\(982\) −26.0000 −0.829693
\(983\) 24.0000 0.765481 0.382741 0.923856i \(-0.374980\pi\)
0.382741 + 0.923856i \(0.374980\pi\)
\(984\) 0 0
\(985\) 10.0000 0.318626
\(986\) 40.0000 1.27386
\(987\) 0 0
\(988\) 0 0
\(989\) −48.0000 −1.52631
\(990\) 0 0
\(991\) −34.0000 −1.08005 −0.540023 0.841650i \(-0.681584\pi\)
−0.540023 + 0.841650i \(0.681584\pi\)
\(992\) 2.00000 0.0635001
\(993\) 0 0
\(994\) 0 0
\(995\) −20.0000 −0.634043
\(996\) 0 0
\(997\) −10.0000 −0.316703 −0.158352 0.987383i \(-0.550618\pi\)
−0.158352 + 0.987383i \(0.550618\pi\)
\(998\) 36.0000 1.13956
\(999\) 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 1710.2.a.a.1.1 1
3.2 odd 2 1710.2.a.p.1.1 yes 1
5.4 even 2 8550.2.a.bl.1.1 1
15.14 odd 2 8550.2.a.q.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1710.2.a.a.1.1 1 1.1 even 1 trivial
1710.2.a.p.1.1 yes 1 3.2 odd 2
8550.2.a.q.1.1 1 15.14 odd 2
8550.2.a.bl.1.1 1 5.4 even 2