Properties

Label 6240.2.a.bv.1.1
Level $6240$
Weight $2$
Character 6240.1
Self dual yes
Analytic conductor $49.827$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 6240 = 2^{5} \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6240.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(49.8266508613\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{10})^+\)
Defining polynomial: \( x^{2} - x - 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-0.618034\) of defining polynomial
Character \(\chi\) \(=\) 6240.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{3} +1.00000 q^{5} +0.763932 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{3} +1.00000 q^{5} +0.763932 q^{7} +1.00000 q^{9} +6.47214 q^{11} -1.00000 q^{13} +1.00000 q^{15} +5.23607 q^{17} +0.763932 q^{19} +0.763932 q^{21} +7.23607 q^{23} +1.00000 q^{25} +1.00000 q^{27} +9.23607 q^{29} +8.94427 q^{31} +6.47214 q^{33} +0.763932 q^{35} +0.472136 q^{37} -1.00000 q^{39} -12.4721 q^{41} -12.9443 q^{43} +1.00000 q^{45} -4.94427 q^{47} -6.41641 q^{49} +5.23607 q^{51} +0.472136 q^{53} +6.47214 q^{55} +0.763932 q^{57} -6.47214 q^{59} -6.94427 q^{61} +0.763932 q^{63} -1.00000 q^{65} -8.00000 q^{67} +7.23607 q^{69} -4.00000 q^{71} -3.70820 q^{73} +1.00000 q^{75} +4.94427 q^{77} -12.9443 q^{79} +1.00000 q^{81} +8.00000 q^{83} +5.23607 q^{85} +9.23607 q^{87} +2.94427 q^{89} -0.763932 q^{91} +8.94427 q^{93} +0.763932 q^{95} -16.6525 q^{97} +6.47214 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{3} + 2 q^{5} + 6 q^{7} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{3} + 2 q^{5} + 6 q^{7} + 2 q^{9} + 4 q^{11} - 2 q^{13} + 2 q^{15} + 6 q^{17} + 6 q^{19} + 6 q^{21} + 10 q^{23} + 2 q^{25} + 2 q^{27} + 14 q^{29} + 4 q^{33} + 6 q^{35} - 8 q^{37} - 2 q^{39} - 16 q^{41} - 8 q^{43} + 2 q^{45} + 8 q^{47} + 14 q^{49} + 6 q^{51} - 8 q^{53} + 4 q^{55} + 6 q^{57} - 4 q^{59} + 4 q^{61} + 6 q^{63} - 2 q^{65} - 16 q^{67} + 10 q^{69} - 8 q^{71} + 6 q^{73} + 2 q^{75} - 8 q^{77} - 8 q^{79} + 2 q^{81} + 16 q^{83} + 6 q^{85} + 14 q^{87} - 12 q^{89} - 6 q^{91} + 6 q^{95} - 2 q^{97} + 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.00000 0.577350
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) 0.763932 0.288739 0.144370 0.989524i \(-0.453885\pi\)
0.144370 + 0.989524i \(0.453885\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 6.47214 1.95142 0.975711 0.219061i \(-0.0702993\pi\)
0.975711 + 0.219061i \(0.0702993\pi\)
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 1.00000 0.258199
\(16\) 0 0
\(17\) 5.23607 1.26993 0.634967 0.772540i \(-0.281014\pi\)
0.634967 + 0.772540i \(0.281014\pi\)
\(18\) 0 0
\(19\) 0.763932 0.175258 0.0876290 0.996153i \(-0.472071\pi\)
0.0876290 + 0.996153i \(0.472071\pi\)
\(20\) 0 0
\(21\) 0.763932 0.166704
\(22\) 0 0
\(23\) 7.23607 1.50882 0.754412 0.656401i \(-0.227922\pi\)
0.754412 + 0.656401i \(0.227922\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 9.23607 1.71509 0.857547 0.514405i \(-0.171987\pi\)
0.857547 + 0.514405i \(0.171987\pi\)
\(30\) 0 0
\(31\) 8.94427 1.60644 0.803219 0.595683i \(-0.203119\pi\)
0.803219 + 0.595683i \(0.203119\pi\)
\(32\) 0 0
\(33\) 6.47214 1.12665
\(34\) 0 0
\(35\) 0.763932 0.129128
\(36\) 0 0
\(37\) 0.472136 0.0776187 0.0388093 0.999247i \(-0.487644\pi\)
0.0388093 + 0.999247i \(0.487644\pi\)
\(38\) 0 0
\(39\) −1.00000 −0.160128
\(40\) 0 0
\(41\) −12.4721 −1.94782 −0.973910 0.226934i \(-0.927130\pi\)
−0.973910 + 0.226934i \(0.927130\pi\)
\(42\) 0 0
\(43\) −12.9443 −1.97398 −0.986991 0.160773i \(-0.948601\pi\)
−0.986991 + 0.160773i \(0.948601\pi\)
\(44\) 0 0
\(45\) 1.00000 0.149071
\(46\) 0 0
\(47\) −4.94427 −0.721196 −0.360598 0.932721i \(-0.617427\pi\)
−0.360598 + 0.932721i \(0.617427\pi\)
\(48\) 0 0
\(49\) −6.41641 −0.916630
\(50\) 0 0
\(51\) 5.23607 0.733196
\(52\) 0 0
\(53\) 0.472136 0.0648529 0.0324264 0.999474i \(-0.489677\pi\)
0.0324264 + 0.999474i \(0.489677\pi\)
\(54\) 0 0
\(55\) 6.47214 0.872703
\(56\) 0 0
\(57\) 0.763932 0.101185
\(58\) 0 0
\(59\) −6.47214 −0.842600 −0.421300 0.906921i \(-0.638426\pi\)
−0.421300 + 0.906921i \(0.638426\pi\)
\(60\) 0 0
\(61\) −6.94427 −0.889123 −0.444561 0.895748i \(-0.646640\pi\)
−0.444561 + 0.895748i \(0.646640\pi\)
\(62\) 0 0
\(63\) 0.763932 0.0962464
\(64\) 0 0
\(65\) −1.00000 −0.124035
\(66\) 0 0
\(67\) −8.00000 −0.977356 −0.488678 0.872464i \(-0.662521\pi\)
−0.488678 + 0.872464i \(0.662521\pi\)
\(68\) 0 0
\(69\) 7.23607 0.871120
\(70\) 0 0
\(71\) −4.00000 −0.474713 −0.237356 0.971423i \(-0.576281\pi\)
−0.237356 + 0.971423i \(0.576281\pi\)
\(72\) 0 0
\(73\) −3.70820 −0.434012 −0.217006 0.976170i \(-0.569629\pi\)
−0.217006 + 0.976170i \(0.569629\pi\)
\(74\) 0 0
\(75\) 1.00000 0.115470
\(76\) 0 0
\(77\) 4.94427 0.563452
\(78\) 0 0
\(79\) −12.9443 −1.45634 −0.728172 0.685394i \(-0.759630\pi\)
−0.728172 + 0.685394i \(0.759630\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 8.00000 0.878114 0.439057 0.898459i \(-0.355313\pi\)
0.439057 + 0.898459i \(0.355313\pi\)
\(84\) 0 0
\(85\) 5.23607 0.567931
\(86\) 0 0
\(87\) 9.23607 0.990210
\(88\) 0 0
\(89\) 2.94427 0.312092 0.156046 0.987750i \(-0.450125\pi\)
0.156046 + 0.987750i \(0.450125\pi\)
\(90\) 0 0
\(91\) −0.763932 −0.0800818
\(92\) 0 0
\(93\) 8.94427 0.927478
\(94\) 0 0
\(95\) 0.763932 0.0783778
\(96\) 0 0
\(97\) −16.6525 −1.69080 −0.845401 0.534132i \(-0.820639\pi\)
−0.845401 + 0.534132i \(0.820639\pi\)
\(98\) 0 0
\(99\) 6.47214 0.650474
\(100\) 0 0
\(101\) 15.7082 1.56302 0.781512 0.623890i \(-0.214449\pi\)
0.781512 + 0.623890i \(0.214449\pi\)
\(102\) 0 0
\(103\) 4.00000 0.394132 0.197066 0.980390i \(-0.436859\pi\)
0.197066 + 0.980390i \(0.436859\pi\)
\(104\) 0 0
\(105\) 0.763932 0.0745521
\(106\) 0 0
\(107\) −12.0000 −1.16008 −0.580042 0.814587i \(-0.696964\pi\)
−0.580042 + 0.814587i \(0.696964\pi\)
\(108\) 0 0
\(109\) 10.1803 0.975100 0.487550 0.873095i \(-0.337891\pi\)
0.487550 + 0.873095i \(0.337891\pi\)
\(110\) 0 0
\(111\) 0.472136 0.0448132
\(112\) 0 0
\(113\) 6.76393 0.636297 0.318149 0.948041i \(-0.396939\pi\)
0.318149 + 0.948041i \(0.396939\pi\)
\(114\) 0 0
\(115\) 7.23607 0.674767
\(116\) 0 0
\(117\) −1.00000 −0.0924500
\(118\) 0 0
\(119\) 4.00000 0.366679
\(120\) 0 0
\(121\) 30.8885 2.80805
\(122\) 0 0
\(123\) −12.4721 −1.12457
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 4.00000 0.354943 0.177471 0.984126i \(-0.443208\pi\)
0.177471 + 0.984126i \(0.443208\pi\)
\(128\) 0 0
\(129\) −12.9443 −1.13968
\(130\) 0 0
\(131\) 10.6525 0.930711 0.465356 0.885124i \(-0.345926\pi\)
0.465356 + 0.885124i \(0.345926\pi\)
\(132\) 0 0
\(133\) 0.583592 0.0506039
\(134\) 0 0
\(135\) 1.00000 0.0860663
\(136\) 0 0
\(137\) 8.47214 0.723823 0.361912 0.932212i \(-0.382124\pi\)
0.361912 + 0.932212i \(0.382124\pi\)
\(138\) 0 0
\(139\) −2.47214 −0.209684 −0.104842 0.994489i \(-0.533434\pi\)
−0.104842 + 0.994489i \(0.533434\pi\)
\(140\) 0 0
\(141\) −4.94427 −0.416383
\(142\) 0 0
\(143\) −6.47214 −0.541227
\(144\) 0 0
\(145\) 9.23607 0.767014
\(146\) 0 0
\(147\) −6.41641 −0.529216
\(148\) 0 0
\(149\) 4.47214 0.366372 0.183186 0.983078i \(-0.441359\pi\)
0.183186 + 0.983078i \(0.441359\pi\)
\(150\) 0 0
\(151\) −0.944272 −0.0768438 −0.0384219 0.999262i \(-0.512233\pi\)
−0.0384219 + 0.999262i \(0.512233\pi\)
\(152\) 0 0
\(153\) 5.23607 0.423311
\(154\) 0 0
\(155\) 8.94427 0.718421
\(156\) 0 0
\(157\) −13.4164 −1.07075 −0.535373 0.844616i \(-0.679829\pi\)
−0.535373 + 0.844616i \(0.679829\pi\)
\(158\) 0 0
\(159\) 0.472136 0.0374428
\(160\) 0 0
\(161\) 5.52786 0.435657
\(162\) 0 0
\(163\) −1.52786 −0.119672 −0.0598358 0.998208i \(-0.519058\pi\)
−0.0598358 + 0.998208i \(0.519058\pi\)
\(164\) 0 0
\(165\) 6.47214 0.503855
\(166\) 0 0
\(167\) 3.41641 0.264370 0.132185 0.991225i \(-0.457801\pi\)
0.132185 + 0.991225i \(0.457801\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 0.763932 0.0584193
\(172\) 0 0
\(173\) −4.47214 −0.340010 −0.170005 0.985443i \(-0.554378\pi\)
−0.170005 + 0.985443i \(0.554378\pi\)
\(174\) 0 0
\(175\) 0.763932 0.0577478
\(176\) 0 0
\(177\) −6.47214 −0.486476
\(178\) 0 0
\(179\) −16.7639 −1.25300 −0.626498 0.779423i \(-0.715512\pi\)
−0.626498 + 0.779423i \(0.715512\pi\)
\(180\) 0 0
\(181\) 20.4721 1.52168 0.760841 0.648938i \(-0.224787\pi\)
0.760841 + 0.648938i \(0.224787\pi\)
\(182\) 0 0
\(183\) −6.94427 −0.513335
\(184\) 0 0
\(185\) 0.472136 0.0347121
\(186\) 0 0
\(187\) 33.8885 2.47818
\(188\) 0 0
\(189\) 0.763932 0.0555679
\(190\) 0 0
\(191\) −20.9443 −1.51547 −0.757737 0.652560i \(-0.773695\pi\)
−0.757737 + 0.652560i \(0.773695\pi\)
\(192\) 0 0
\(193\) −2.18034 −0.156944 −0.0784721 0.996916i \(-0.525004\pi\)
−0.0784721 + 0.996916i \(0.525004\pi\)
\(194\) 0 0
\(195\) −1.00000 −0.0716115
\(196\) 0 0
\(197\) −9.41641 −0.670891 −0.335446 0.942060i \(-0.608887\pi\)
−0.335446 + 0.942060i \(0.608887\pi\)
\(198\) 0 0
\(199\) −9.88854 −0.700980 −0.350490 0.936566i \(-0.613985\pi\)
−0.350490 + 0.936566i \(0.613985\pi\)
\(200\) 0 0
\(201\) −8.00000 −0.564276
\(202\) 0 0
\(203\) 7.05573 0.495215
\(204\) 0 0
\(205\) −12.4721 −0.871092
\(206\) 0 0
\(207\) 7.23607 0.502941
\(208\) 0 0
\(209\) 4.94427 0.342002
\(210\) 0 0
\(211\) 0.944272 0.0650064 0.0325032 0.999472i \(-0.489652\pi\)
0.0325032 + 0.999472i \(0.489652\pi\)
\(212\) 0 0
\(213\) −4.00000 −0.274075
\(214\) 0 0
\(215\) −12.9443 −0.882792
\(216\) 0 0
\(217\) 6.83282 0.463842
\(218\) 0 0
\(219\) −3.70820 −0.250577
\(220\) 0 0
\(221\) −5.23607 −0.352216
\(222\) 0 0
\(223\) 12.1803 0.815656 0.407828 0.913059i \(-0.366286\pi\)
0.407828 + 0.913059i \(0.366286\pi\)
\(224\) 0 0
\(225\) 1.00000 0.0666667
\(226\) 0 0
\(227\) −21.8885 −1.45279 −0.726397 0.687276i \(-0.758807\pi\)
−0.726397 + 0.687276i \(0.758807\pi\)
\(228\) 0 0
\(229\) −2.76393 −0.182646 −0.0913229 0.995821i \(-0.529110\pi\)
−0.0913229 + 0.995821i \(0.529110\pi\)
\(230\) 0 0
\(231\) 4.94427 0.325309
\(232\) 0 0
\(233\) −10.7639 −0.705169 −0.352584 0.935780i \(-0.614697\pi\)
−0.352584 + 0.935780i \(0.614697\pi\)
\(234\) 0 0
\(235\) −4.94427 −0.322529
\(236\) 0 0
\(237\) −12.9443 −0.840821
\(238\) 0 0
\(239\) −11.0557 −0.715136 −0.357568 0.933887i \(-0.616394\pi\)
−0.357568 + 0.933887i \(0.616394\pi\)
\(240\) 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
\(244\) 0 0
\(245\) −6.41641 −0.409929
\(246\) 0 0
\(247\) −0.763932 −0.0486078
\(248\) 0 0
\(249\) 8.00000 0.506979
\(250\) 0 0
\(251\) −13.7082 −0.865254 −0.432627 0.901573i \(-0.642413\pi\)
−0.432627 + 0.901573i \(0.642413\pi\)
\(252\) 0 0
\(253\) 46.8328 2.94435
\(254\) 0 0
\(255\) 5.23607 0.327895
\(256\) 0 0
\(257\) 19.7082 1.22936 0.614682 0.788775i \(-0.289284\pi\)
0.614682 + 0.788775i \(0.289284\pi\)
\(258\) 0 0
\(259\) 0.360680 0.0224116
\(260\) 0 0
\(261\) 9.23607 0.571698
\(262\) 0 0
\(263\) 18.6525 1.15016 0.575080 0.818097i \(-0.304971\pi\)
0.575080 + 0.818097i \(0.304971\pi\)
\(264\) 0 0
\(265\) 0.472136 0.0290031
\(266\) 0 0
\(267\) 2.94427 0.180187
\(268\) 0 0
\(269\) −2.18034 −0.132938 −0.0664688 0.997789i \(-0.521173\pi\)
−0.0664688 + 0.997789i \(0.521173\pi\)
\(270\) 0 0
\(271\) 21.8885 1.32963 0.664817 0.747006i \(-0.268509\pi\)
0.664817 + 0.747006i \(0.268509\pi\)
\(272\) 0 0
\(273\) −0.763932 −0.0462353
\(274\) 0 0
\(275\) 6.47214 0.390284
\(276\) 0 0
\(277\) −3.52786 −0.211969 −0.105984 0.994368i \(-0.533799\pi\)
−0.105984 + 0.994368i \(0.533799\pi\)
\(278\) 0 0
\(279\) 8.94427 0.535480
\(280\) 0 0
\(281\) 7.88854 0.470591 0.235296 0.971924i \(-0.424394\pi\)
0.235296 + 0.971924i \(0.424394\pi\)
\(282\) 0 0
\(283\) −16.0000 −0.951101 −0.475551 0.879688i \(-0.657751\pi\)
−0.475551 + 0.879688i \(0.657751\pi\)
\(284\) 0 0
\(285\) 0.763932 0.0452514
\(286\) 0 0
\(287\) −9.52786 −0.562412
\(288\) 0 0
\(289\) 10.4164 0.612730
\(290\) 0 0
\(291\) −16.6525 −0.976185
\(292\) 0 0
\(293\) −12.4721 −0.728630 −0.364315 0.931276i \(-0.618697\pi\)
−0.364315 + 0.931276i \(0.618697\pi\)
\(294\) 0 0
\(295\) −6.47214 −0.376822
\(296\) 0 0
\(297\) 6.47214 0.375551
\(298\) 0 0
\(299\) −7.23607 −0.418473
\(300\) 0 0
\(301\) −9.88854 −0.569966
\(302\) 0 0
\(303\) 15.7082 0.902413
\(304\) 0 0
\(305\) −6.94427 −0.397628
\(306\) 0 0
\(307\) −3.05573 −0.174400 −0.0871998 0.996191i \(-0.527792\pi\)
−0.0871998 + 0.996191i \(0.527792\pi\)
\(308\) 0 0
\(309\) 4.00000 0.227552
\(310\) 0 0
\(311\) 20.9443 1.18764 0.593820 0.804598i \(-0.297619\pi\)
0.593820 + 0.804598i \(0.297619\pi\)
\(312\) 0 0
\(313\) 21.4164 1.21053 0.605263 0.796025i \(-0.293068\pi\)
0.605263 + 0.796025i \(0.293068\pi\)
\(314\) 0 0
\(315\) 0.763932 0.0430427
\(316\) 0 0
\(317\) −2.00000 −0.112331 −0.0561656 0.998421i \(-0.517887\pi\)
−0.0561656 + 0.998421i \(0.517887\pi\)
\(318\) 0 0
\(319\) 59.7771 3.34687
\(320\) 0 0
\(321\) −12.0000 −0.669775
\(322\) 0 0
\(323\) 4.00000 0.222566
\(324\) 0 0
\(325\) −1.00000 −0.0554700
\(326\) 0 0
\(327\) 10.1803 0.562974
\(328\) 0 0
\(329\) −3.77709 −0.208238
\(330\) 0 0
\(331\) 13.7082 0.753471 0.376736 0.926321i \(-0.377047\pi\)
0.376736 + 0.926321i \(0.377047\pi\)
\(332\) 0 0
\(333\) 0.472136 0.0258729
\(334\) 0 0
\(335\) −8.00000 −0.437087
\(336\) 0 0
\(337\) 32.4721 1.76887 0.884435 0.466663i \(-0.154544\pi\)
0.884435 + 0.466663i \(0.154544\pi\)
\(338\) 0 0
\(339\) 6.76393 0.367366
\(340\) 0 0
\(341\) 57.8885 3.13484
\(342\) 0 0
\(343\) −10.2492 −0.553406
\(344\) 0 0
\(345\) 7.23607 0.389577
\(346\) 0 0
\(347\) 15.4164 0.827596 0.413798 0.910369i \(-0.364202\pi\)
0.413798 + 0.910369i \(0.364202\pi\)
\(348\) 0 0
\(349\) −23.7082 −1.26907 −0.634536 0.772894i \(-0.718809\pi\)
−0.634536 + 0.772894i \(0.718809\pi\)
\(350\) 0 0
\(351\) −1.00000 −0.0533761
\(352\) 0 0
\(353\) −4.47214 −0.238028 −0.119014 0.992893i \(-0.537973\pi\)
−0.119014 + 0.992893i \(0.537973\pi\)
\(354\) 0 0
\(355\) −4.00000 −0.212298
\(356\) 0 0
\(357\) 4.00000 0.211702
\(358\) 0 0
\(359\) 24.9443 1.31651 0.658254 0.752796i \(-0.271295\pi\)
0.658254 + 0.752796i \(0.271295\pi\)
\(360\) 0 0
\(361\) −18.4164 −0.969285
\(362\) 0 0
\(363\) 30.8885 1.62123
\(364\) 0 0
\(365\) −3.70820 −0.194096
\(366\) 0 0
\(367\) −34.8328 −1.81826 −0.909129 0.416514i \(-0.863252\pi\)
−0.909129 + 0.416514i \(0.863252\pi\)
\(368\) 0 0
\(369\) −12.4721 −0.649273
\(370\) 0 0
\(371\) 0.360680 0.0187256
\(372\) 0 0
\(373\) −5.41641 −0.280451 −0.140225 0.990120i \(-0.544783\pi\)
−0.140225 + 0.990120i \(0.544783\pi\)
\(374\) 0 0
\(375\) 1.00000 0.0516398
\(376\) 0 0
\(377\) −9.23607 −0.475682
\(378\) 0 0
\(379\) −32.7639 −1.68297 −0.841485 0.540280i \(-0.818318\pi\)
−0.841485 + 0.540280i \(0.818318\pi\)
\(380\) 0 0
\(381\) 4.00000 0.204926
\(382\) 0 0
\(383\) −37.3050 −1.90619 −0.953097 0.302665i \(-0.902124\pi\)
−0.953097 + 0.302665i \(0.902124\pi\)
\(384\) 0 0
\(385\) 4.94427 0.251983
\(386\) 0 0
\(387\) −12.9443 −0.657994
\(388\) 0 0
\(389\) 2.76393 0.140137 0.0700685 0.997542i \(-0.477678\pi\)
0.0700685 + 0.997542i \(0.477678\pi\)
\(390\) 0 0
\(391\) 37.8885 1.91611
\(392\) 0 0
\(393\) 10.6525 0.537346
\(394\) 0 0
\(395\) −12.9443 −0.651297
\(396\) 0 0
\(397\) −4.47214 −0.224450 −0.112225 0.993683i \(-0.535798\pi\)
−0.112225 + 0.993683i \(0.535798\pi\)
\(398\) 0 0
\(399\) 0.583592 0.0292161
\(400\) 0 0
\(401\) 5.41641 0.270483 0.135241 0.990813i \(-0.456819\pi\)
0.135241 + 0.990813i \(0.456819\pi\)
\(402\) 0 0
\(403\) −8.94427 −0.445546
\(404\) 0 0
\(405\) 1.00000 0.0496904
\(406\) 0 0
\(407\) 3.05573 0.151467
\(408\) 0 0
\(409\) 16.4721 0.814495 0.407247 0.913318i \(-0.366489\pi\)
0.407247 + 0.913318i \(0.366489\pi\)
\(410\) 0 0
\(411\) 8.47214 0.417900
\(412\) 0 0
\(413\) −4.94427 −0.243292
\(414\) 0 0
\(415\) 8.00000 0.392705
\(416\) 0 0
\(417\) −2.47214 −0.121061
\(418\) 0 0
\(419\) −25.1246 −1.22742 −0.613709 0.789532i \(-0.710323\pi\)
−0.613709 + 0.789532i \(0.710323\pi\)
\(420\) 0 0
\(421\) 27.7082 1.35042 0.675208 0.737628i \(-0.264054\pi\)
0.675208 + 0.737628i \(0.264054\pi\)
\(422\) 0 0
\(423\) −4.94427 −0.240399
\(424\) 0 0
\(425\) 5.23607 0.253987
\(426\) 0 0
\(427\) −5.30495 −0.256725
\(428\) 0 0
\(429\) −6.47214 −0.312478
\(430\) 0 0
\(431\) −25.8885 −1.24701 −0.623504 0.781820i \(-0.714291\pi\)
−0.623504 + 0.781820i \(0.714291\pi\)
\(432\) 0 0
\(433\) −33.4164 −1.60589 −0.802945 0.596053i \(-0.796735\pi\)
−0.802945 + 0.596053i \(0.796735\pi\)
\(434\) 0 0
\(435\) 9.23607 0.442836
\(436\) 0 0
\(437\) 5.52786 0.264434
\(438\) 0 0
\(439\) 13.8885 0.662864 0.331432 0.943479i \(-0.392468\pi\)
0.331432 + 0.943479i \(0.392468\pi\)
\(440\) 0 0
\(441\) −6.41641 −0.305543
\(442\) 0 0
\(443\) −21.5279 −1.02282 −0.511410 0.859337i \(-0.670877\pi\)
−0.511410 + 0.859337i \(0.670877\pi\)
\(444\) 0 0
\(445\) 2.94427 0.139572
\(446\) 0 0
\(447\) 4.47214 0.211525
\(448\) 0 0
\(449\) −24.8328 −1.17193 −0.585967 0.810335i \(-0.699285\pi\)
−0.585967 + 0.810335i \(0.699285\pi\)
\(450\) 0 0
\(451\) −80.7214 −3.80102
\(452\) 0 0
\(453\) −0.944272 −0.0443658
\(454\) 0 0
\(455\) −0.763932 −0.0358137
\(456\) 0 0
\(457\) 20.2918 0.949210 0.474605 0.880199i \(-0.342591\pi\)
0.474605 + 0.880199i \(0.342591\pi\)
\(458\) 0 0
\(459\) 5.23607 0.244399
\(460\) 0 0
\(461\) 30.0000 1.39724 0.698620 0.715493i \(-0.253798\pi\)
0.698620 + 0.715493i \(0.253798\pi\)
\(462\) 0 0
\(463\) −5.70820 −0.265283 −0.132641 0.991164i \(-0.542346\pi\)
−0.132641 + 0.991164i \(0.542346\pi\)
\(464\) 0 0
\(465\) 8.94427 0.414781
\(466\) 0 0
\(467\) −8.94427 −0.413892 −0.206946 0.978352i \(-0.566352\pi\)
−0.206946 + 0.978352i \(0.566352\pi\)
\(468\) 0 0
\(469\) −6.11146 −0.282201
\(470\) 0 0
\(471\) −13.4164 −0.618195
\(472\) 0 0
\(473\) −83.7771 −3.85207
\(474\) 0 0
\(475\) 0.763932 0.0350516
\(476\) 0 0
\(477\) 0.472136 0.0216176
\(478\) 0 0
\(479\) −30.8328 −1.40879 −0.704394 0.709810i \(-0.748781\pi\)
−0.704394 + 0.709810i \(0.748781\pi\)
\(480\) 0 0
\(481\) −0.472136 −0.0215275
\(482\) 0 0
\(483\) 5.52786 0.251527
\(484\) 0 0
\(485\) −16.6525 −0.756150
\(486\) 0 0
\(487\) 3.81966 0.173085 0.0865427 0.996248i \(-0.472418\pi\)
0.0865427 + 0.996248i \(0.472418\pi\)
\(488\) 0 0
\(489\) −1.52786 −0.0690924
\(490\) 0 0
\(491\) −18.2918 −0.825497 −0.412749 0.910845i \(-0.635431\pi\)
−0.412749 + 0.910845i \(0.635431\pi\)
\(492\) 0 0
\(493\) 48.3607 2.17806
\(494\) 0 0
\(495\) 6.47214 0.290901
\(496\) 0 0
\(497\) −3.05573 −0.137068
\(498\) 0 0
\(499\) 15.2361 0.682060 0.341030 0.940052i \(-0.389224\pi\)
0.341030 + 0.940052i \(0.389224\pi\)
\(500\) 0 0
\(501\) 3.41641 0.152634
\(502\) 0 0
\(503\) 15.5967 0.695425 0.347712 0.937601i \(-0.386959\pi\)
0.347712 + 0.937601i \(0.386959\pi\)
\(504\) 0 0
\(505\) 15.7082 0.699006
\(506\) 0 0
\(507\) 1.00000 0.0444116
\(508\) 0 0
\(509\) 31.8885 1.41343 0.706717 0.707496i \(-0.250175\pi\)
0.706717 + 0.707496i \(0.250175\pi\)
\(510\) 0 0
\(511\) −2.83282 −0.125316
\(512\) 0 0
\(513\) 0.763932 0.0337284
\(514\) 0 0
\(515\) 4.00000 0.176261
\(516\) 0 0
\(517\) −32.0000 −1.40736
\(518\) 0 0
\(519\) −4.47214 −0.196305
\(520\) 0 0
\(521\) 26.3607 1.15488 0.577441 0.816432i \(-0.304051\pi\)
0.577441 + 0.816432i \(0.304051\pi\)
\(522\) 0 0
\(523\) 10.8328 0.473686 0.236843 0.971548i \(-0.423887\pi\)
0.236843 + 0.971548i \(0.423887\pi\)
\(524\) 0 0
\(525\) 0.763932 0.0333407
\(526\) 0 0
\(527\) 46.8328 2.04007
\(528\) 0 0
\(529\) 29.3607 1.27655
\(530\) 0 0
\(531\) −6.47214 −0.280867
\(532\) 0 0
\(533\) 12.4721 0.540228
\(534\) 0 0
\(535\) −12.0000 −0.518805
\(536\) 0 0
\(537\) −16.7639 −0.723417
\(538\) 0 0
\(539\) −41.5279 −1.78873
\(540\) 0 0
\(541\) −11.1246 −0.478284 −0.239142 0.970985i \(-0.576866\pi\)
−0.239142 + 0.970985i \(0.576866\pi\)
\(542\) 0 0
\(543\) 20.4721 0.878543
\(544\) 0 0
\(545\) 10.1803 0.436078
\(546\) 0 0
\(547\) 29.8885 1.27794 0.638971 0.769231i \(-0.279360\pi\)
0.638971 + 0.769231i \(0.279360\pi\)
\(548\) 0 0
\(549\) −6.94427 −0.296374
\(550\) 0 0
\(551\) 7.05573 0.300584
\(552\) 0 0
\(553\) −9.88854 −0.420504
\(554\) 0 0
\(555\) 0.472136 0.0200411
\(556\) 0 0
\(557\) 31.8885 1.35116 0.675580 0.737286i \(-0.263893\pi\)
0.675580 + 0.737286i \(0.263893\pi\)
\(558\) 0 0
\(559\) 12.9443 0.547484
\(560\) 0 0
\(561\) 33.8885 1.43078
\(562\) 0 0
\(563\) −25.3050 −1.06648 −0.533238 0.845965i \(-0.679025\pi\)
−0.533238 + 0.845965i \(0.679025\pi\)
\(564\) 0 0
\(565\) 6.76393 0.284561
\(566\) 0 0
\(567\) 0.763932 0.0320821
\(568\) 0 0
\(569\) 18.3607 0.769720 0.384860 0.922975i \(-0.374250\pi\)
0.384860 + 0.922975i \(0.374250\pi\)
\(570\) 0 0
\(571\) −25.3050 −1.05898 −0.529490 0.848316i \(-0.677617\pi\)
−0.529490 + 0.848316i \(0.677617\pi\)
\(572\) 0 0
\(573\) −20.9443 −0.874960
\(574\) 0 0
\(575\) 7.23607 0.301765
\(576\) 0 0
\(577\) 41.5967 1.73170 0.865848 0.500308i \(-0.166780\pi\)
0.865848 + 0.500308i \(0.166780\pi\)
\(578\) 0 0
\(579\) −2.18034 −0.0906118
\(580\) 0 0
\(581\) 6.11146 0.253546
\(582\) 0 0
\(583\) 3.05573 0.126555
\(584\) 0 0
\(585\) −1.00000 −0.0413449
\(586\) 0 0
\(587\) 0.944272 0.0389743 0.0194871 0.999810i \(-0.493797\pi\)
0.0194871 + 0.999810i \(0.493797\pi\)
\(588\) 0 0
\(589\) 6.83282 0.281541
\(590\) 0 0
\(591\) −9.41641 −0.387339
\(592\) 0 0
\(593\) −6.00000 −0.246390 −0.123195 0.992382i \(-0.539314\pi\)
−0.123195 + 0.992382i \(0.539314\pi\)
\(594\) 0 0
\(595\) 4.00000 0.163984
\(596\) 0 0
\(597\) −9.88854 −0.404711
\(598\) 0 0
\(599\) −16.0000 −0.653742 −0.326871 0.945069i \(-0.605994\pi\)
−0.326871 + 0.945069i \(0.605994\pi\)
\(600\) 0 0
\(601\) −2.36068 −0.0962941 −0.0481471 0.998840i \(-0.515332\pi\)
−0.0481471 + 0.998840i \(0.515332\pi\)
\(602\) 0 0
\(603\) −8.00000 −0.325785
\(604\) 0 0
\(605\) 30.8885 1.25580
\(606\) 0 0
\(607\) −0.944272 −0.0383268 −0.0191634 0.999816i \(-0.506100\pi\)
−0.0191634 + 0.999816i \(0.506100\pi\)
\(608\) 0 0
\(609\) 7.05573 0.285913
\(610\) 0 0
\(611\) 4.94427 0.200024
\(612\) 0 0
\(613\) −2.58359 −0.104350 −0.0521752 0.998638i \(-0.516615\pi\)
−0.0521752 + 0.998638i \(0.516615\pi\)
\(614\) 0 0
\(615\) −12.4721 −0.502925
\(616\) 0 0
\(617\) −9.41641 −0.379090 −0.189545 0.981872i \(-0.560701\pi\)
−0.189545 + 0.981872i \(0.560701\pi\)
\(618\) 0 0
\(619\) −34.6525 −1.39280 −0.696400 0.717654i \(-0.745216\pi\)
−0.696400 + 0.717654i \(0.745216\pi\)
\(620\) 0 0
\(621\) 7.23607 0.290373
\(622\) 0 0
\(623\) 2.24922 0.0901132
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 4.94427 0.197455
\(628\) 0 0
\(629\) 2.47214 0.0985705
\(630\) 0 0
\(631\) 23.4164 0.932192 0.466096 0.884734i \(-0.345660\pi\)
0.466096 + 0.884734i \(0.345660\pi\)
\(632\) 0 0
\(633\) 0.944272 0.0375314
\(634\) 0 0
\(635\) 4.00000 0.158735
\(636\) 0 0
\(637\) 6.41641 0.254227
\(638\) 0 0
\(639\) −4.00000 −0.158238
\(640\) 0 0
\(641\) 26.0000 1.02694 0.513469 0.858108i \(-0.328360\pi\)
0.513469 + 0.858108i \(0.328360\pi\)
\(642\) 0 0
\(643\) −8.00000 −0.315489 −0.157745 0.987480i \(-0.550422\pi\)
−0.157745 + 0.987480i \(0.550422\pi\)
\(644\) 0 0
\(645\) −12.9443 −0.509680
\(646\) 0 0
\(647\) 29.7082 1.16795 0.583975 0.811772i \(-0.301497\pi\)
0.583975 + 0.811772i \(0.301497\pi\)
\(648\) 0 0
\(649\) −41.8885 −1.64427
\(650\) 0 0
\(651\) 6.83282 0.267799
\(652\) 0 0
\(653\) 26.0000 1.01746 0.508729 0.860927i \(-0.330115\pi\)
0.508729 + 0.860927i \(0.330115\pi\)
\(654\) 0 0
\(655\) 10.6525 0.416227
\(656\) 0 0
\(657\) −3.70820 −0.144671
\(658\) 0 0
\(659\) −26.2918 −1.02418 −0.512091 0.858931i \(-0.671129\pi\)
−0.512091 + 0.858931i \(0.671129\pi\)
\(660\) 0 0
\(661\) −27.1246 −1.05503 −0.527513 0.849547i \(-0.676875\pi\)
−0.527513 + 0.849547i \(0.676875\pi\)
\(662\) 0 0
\(663\) −5.23607 −0.203352
\(664\) 0 0
\(665\) 0.583592 0.0226307
\(666\) 0 0
\(667\) 66.8328 2.58778
\(668\) 0 0
\(669\) 12.1803 0.470919
\(670\) 0 0
\(671\) −44.9443 −1.73505
\(672\) 0 0
\(673\) 5.05573 0.194884 0.0974420 0.995241i \(-0.468934\pi\)
0.0974420 + 0.995241i \(0.468934\pi\)
\(674\) 0 0
\(675\) 1.00000 0.0384900
\(676\) 0 0
\(677\) −30.0000 −1.15299 −0.576497 0.817099i \(-0.695581\pi\)
−0.576497 + 0.817099i \(0.695581\pi\)
\(678\) 0 0
\(679\) −12.7214 −0.488201
\(680\) 0 0
\(681\) −21.8885 −0.838771
\(682\) 0 0
\(683\) −49.8885 −1.90893 −0.954466 0.298320i \(-0.903574\pi\)
−0.954466 + 0.298320i \(0.903574\pi\)
\(684\) 0 0
\(685\) 8.47214 0.323704
\(686\) 0 0
\(687\) −2.76393 −0.105451
\(688\) 0 0
\(689\) −0.472136 −0.0179869
\(690\) 0 0
\(691\) 21.7082 0.825819 0.412909 0.910772i \(-0.364513\pi\)
0.412909 + 0.910772i \(0.364513\pi\)
\(692\) 0 0
\(693\) 4.94427 0.187817
\(694\) 0 0
\(695\) −2.47214 −0.0937735
\(696\) 0 0
\(697\) −65.3050 −2.47360
\(698\) 0 0
\(699\) −10.7639 −0.407129
\(700\) 0 0
\(701\) 18.7639 0.708704 0.354352 0.935112i \(-0.384701\pi\)
0.354352 + 0.935112i \(0.384701\pi\)
\(702\) 0 0
\(703\) 0.360680 0.0136033
\(704\) 0 0
\(705\) −4.94427 −0.186212
\(706\) 0 0
\(707\) 12.0000 0.451306
\(708\) 0 0
\(709\) −44.6525 −1.67696 −0.838479 0.544933i \(-0.816555\pi\)
−0.838479 + 0.544933i \(0.816555\pi\)
\(710\) 0 0
\(711\) −12.9443 −0.485448
\(712\) 0 0
\(713\) 64.7214 2.42383
\(714\) 0 0
\(715\) −6.47214 −0.242044
\(716\) 0 0
\(717\) −11.0557 −0.412884
\(718\) 0 0
\(719\) 25.5279 0.952029 0.476014 0.879438i \(-0.342081\pi\)
0.476014 + 0.879438i \(0.342081\pi\)
\(720\) 0 0
\(721\) 3.05573 0.113801
\(722\) 0 0
\(723\) 10.0000 0.371904
\(724\) 0 0
\(725\) 9.23607 0.343019
\(726\) 0 0
\(727\) −5.52786 −0.205017 −0.102509 0.994732i \(-0.532687\pi\)
−0.102509 + 0.994732i \(0.532687\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −67.7771 −2.50683
\(732\) 0 0
\(733\) −7.52786 −0.278048 −0.139024 0.990289i \(-0.544397\pi\)
−0.139024 + 0.990289i \(0.544397\pi\)
\(734\) 0 0
\(735\) −6.41641 −0.236673
\(736\) 0 0
\(737\) −51.7771 −1.90723
\(738\) 0 0
\(739\) 20.1803 0.742346 0.371173 0.928564i \(-0.378956\pi\)
0.371173 + 0.928564i \(0.378956\pi\)
\(740\) 0 0
\(741\) −0.763932 −0.0280637
\(742\) 0 0
\(743\) −20.5836 −0.755139 −0.377569 0.925981i \(-0.623240\pi\)
−0.377569 + 0.925981i \(0.623240\pi\)
\(744\) 0 0
\(745\) 4.47214 0.163846
\(746\) 0 0
\(747\) 8.00000 0.292705
\(748\) 0 0
\(749\) −9.16718 −0.334962
\(750\) 0 0
\(751\) 20.0000 0.729810 0.364905 0.931045i \(-0.381101\pi\)
0.364905 + 0.931045i \(0.381101\pi\)
\(752\) 0 0
\(753\) −13.7082 −0.499555
\(754\) 0 0
\(755\) −0.944272 −0.0343656
\(756\) 0 0
\(757\) −26.9443 −0.979306 −0.489653 0.871917i \(-0.662877\pi\)
−0.489653 + 0.871917i \(0.662877\pi\)
\(758\) 0 0
\(759\) 46.8328 1.69992
\(760\) 0 0
\(761\) −2.58359 −0.0936551 −0.0468276 0.998903i \(-0.514911\pi\)
−0.0468276 + 0.998903i \(0.514911\pi\)
\(762\) 0 0
\(763\) 7.77709 0.281549
\(764\) 0 0
\(765\) 5.23607 0.189310
\(766\) 0 0
\(767\) 6.47214 0.233695
\(768\) 0 0
\(769\) 32.8328 1.18398 0.591991 0.805945i \(-0.298342\pi\)
0.591991 + 0.805945i \(0.298342\pi\)
\(770\) 0 0
\(771\) 19.7082 0.709774
\(772\) 0 0
\(773\) −46.3607 −1.66748 −0.833739 0.552159i \(-0.813804\pi\)
−0.833739 + 0.552159i \(0.813804\pi\)
\(774\) 0 0
\(775\) 8.94427 0.321288
\(776\) 0 0
\(777\) 0.360680 0.0129393
\(778\) 0 0
\(779\) −9.52786 −0.341371
\(780\) 0 0
\(781\) −25.8885 −0.926365
\(782\) 0 0
\(783\) 9.23607 0.330070
\(784\) 0 0
\(785\) −13.4164 −0.478852
\(786\) 0 0
\(787\) 32.3607 1.15353 0.576767 0.816909i \(-0.304314\pi\)
0.576767 + 0.816909i \(0.304314\pi\)
\(788\) 0 0
\(789\) 18.6525 0.664046
\(790\) 0 0
\(791\) 5.16718 0.183724
\(792\) 0 0
\(793\) 6.94427 0.246598
\(794\) 0 0
\(795\) 0.472136 0.0167449
\(796\) 0 0
\(797\) −18.5836 −0.658265 −0.329132 0.944284i \(-0.606756\pi\)
−0.329132 + 0.944284i \(0.606756\pi\)
\(798\) 0 0
\(799\) −25.8885 −0.915871
\(800\) 0 0
\(801\) 2.94427 0.104031
\(802\) 0 0
\(803\) −24.0000 −0.846942
\(804\) 0 0
\(805\) 5.52786 0.194832
\(806\) 0 0
\(807\) −2.18034 −0.0767516
\(808\) 0 0
\(809\) −46.7214 −1.64264 −0.821318 0.570471i \(-0.806761\pi\)
−0.821318 + 0.570471i \(0.806761\pi\)
\(810\) 0 0
\(811\) 5.70820 0.200442 0.100221 0.994965i \(-0.468045\pi\)
0.100221 + 0.994965i \(0.468045\pi\)
\(812\) 0 0
\(813\) 21.8885 0.767665
\(814\) 0 0
\(815\) −1.52786 −0.0535187
\(816\) 0 0
\(817\) −9.88854 −0.345956
\(818\) 0 0
\(819\) −0.763932 −0.0266939
\(820\) 0 0
\(821\) 51.3050 1.79056 0.895278 0.445509i \(-0.146977\pi\)
0.895278 + 0.445509i \(0.146977\pi\)
\(822\) 0 0
\(823\) 47.7771 1.66540 0.832702 0.553721i \(-0.186793\pi\)
0.832702 + 0.553721i \(0.186793\pi\)
\(824\) 0 0
\(825\) 6.47214 0.225331
\(826\) 0 0
\(827\) 3.05573 0.106258 0.0531290 0.998588i \(-0.483081\pi\)
0.0531290 + 0.998588i \(0.483081\pi\)
\(828\) 0 0
\(829\) −43.8885 −1.52431 −0.762156 0.647393i \(-0.775859\pi\)
−0.762156 + 0.647393i \(0.775859\pi\)
\(830\) 0 0
\(831\) −3.52786 −0.122380
\(832\) 0 0
\(833\) −33.5967 −1.16406
\(834\) 0 0
\(835\) 3.41641 0.118230
\(836\) 0 0
\(837\) 8.94427 0.309159
\(838\) 0 0
\(839\) −17.8885 −0.617581 −0.308791 0.951130i \(-0.599924\pi\)
−0.308791 + 0.951130i \(0.599924\pi\)
\(840\) 0 0
\(841\) 56.3050 1.94155
\(842\) 0 0
\(843\) 7.88854 0.271696
\(844\) 0 0
\(845\) 1.00000 0.0344010
\(846\) 0 0
\(847\) 23.5967 0.810794
\(848\) 0 0
\(849\) −16.0000 −0.549119
\(850\) 0 0
\(851\) 3.41641 0.117113
\(852\) 0 0
\(853\) −17.4164 −0.596326 −0.298163 0.954515i \(-0.596374\pi\)
−0.298163 + 0.954515i \(0.596374\pi\)
\(854\) 0 0
\(855\) 0.763932 0.0261259
\(856\) 0 0
\(857\) −19.1246 −0.653284 −0.326642 0.945148i \(-0.605917\pi\)
−0.326642 + 0.945148i \(0.605917\pi\)
\(858\) 0 0
\(859\) 16.9443 0.578131 0.289066 0.957309i \(-0.406655\pi\)
0.289066 + 0.957309i \(0.406655\pi\)
\(860\) 0 0
\(861\) −9.52786 −0.324709
\(862\) 0 0
\(863\) 27.4164 0.933265 0.466633 0.884451i \(-0.345467\pi\)
0.466633 + 0.884451i \(0.345467\pi\)
\(864\) 0 0
\(865\) −4.47214 −0.152057
\(866\) 0 0
\(867\) 10.4164 0.353760
\(868\) 0 0
\(869\) −83.7771 −2.84194
\(870\) 0 0
\(871\) 8.00000 0.271070
\(872\) 0 0
\(873\) −16.6525 −0.563601
\(874\) 0 0
\(875\) 0.763932 0.0258256
\(876\) 0 0
\(877\) −38.0000 −1.28317 −0.641584 0.767052i \(-0.721723\pi\)
−0.641584 + 0.767052i \(0.721723\pi\)
\(878\) 0 0
\(879\) −12.4721 −0.420675
\(880\) 0 0
\(881\) 6.58359 0.221807 0.110903 0.993831i \(-0.464626\pi\)
0.110903 + 0.993831i \(0.464626\pi\)
\(882\) 0 0
\(883\) 21.8885 0.736608 0.368304 0.929705i \(-0.379939\pi\)
0.368304 + 0.929705i \(0.379939\pi\)
\(884\) 0 0
\(885\) −6.47214 −0.217558
\(886\) 0 0
\(887\) 14.0689 0.472387 0.236193 0.971706i \(-0.424100\pi\)
0.236193 + 0.971706i \(0.424100\pi\)
\(888\) 0 0
\(889\) 3.05573 0.102486
\(890\) 0 0
\(891\) 6.47214 0.216825
\(892\) 0 0
\(893\) −3.77709 −0.126395
\(894\) 0 0
\(895\) −16.7639 −0.560356
\(896\) 0 0
\(897\) −7.23607 −0.241605
\(898\) 0 0
\(899\) 82.6099 2.75519
\(900\) 0 0
\(901\) 2.47214 0.0823588
\(902\) 0 0
\(903\) −9.88854 −0.329070
\(904\) 0 0
\(905\) 20.4721 0.680517
\(906\) 0 0
\(907\) 24.0000 0.796907 0.398453 0.917189i \(-0.369547\pi\)
0.398453 + 0.917189i \(0.369547\pi\)
\(908\) 0 0
\(909\) 15.7082 0.521008
\(910\) 0 0
\(911\) 54.4721 1.80474 0.902371 0.430960i \(-0.141825\pi\)
0.902371 + 0.430960i \(0.141825\pi\)
\(912\) 0 0
\(913\) 51.7771 1.71357
\(914\) 0 0
\(915\) −6.94427 −0.229571
\(916\) 0 0
\(917\) 8.13777 0.268733
\(918\) 0 0
\(919\) 15.7771 0.520438 0.260219 0.965550i \(-0.416205\pi\)
0.260219 + 0.965550i \(0.416205\pi\)
\(920\) 0 0
\(921\) −3.05573 −0.100690
\(922\) 0 0
\(923\) 4.00000 0.131662
\(924\) 0 0
\(925\) 0.472136 0.0155237
\(926\) 0 0
\(927\) 4.00000 0.131377
\(928\) 0 0
\(929\) 47.8885 1.57117 0.785586 0.618752i \(-0.212362\pi\)
0.785586 + 0.618752i \(0.212362\pi\)
\(930\) 0 0
\(931\) −4.90170 −0.160647
\(932\) 0 0
\(933\) 20.9443 0.685685
\(934\) 0 0
\(935\) 33.8885 1.10827
\(936\) 0 0
\(937\) −54.0000 −1.76410 −0.882052 0.471153i \(-0.843838\pi\)
−0.882052 + 0.471153i \(0.843838\pi\)
\(938\) 0 0
\(939\) 21.4164 0.698898
\(940\) 0 0
\(941\) 15.5279 0.506194 0.253097 0.967441i \(-0.418551\pi\)
0.253097 + 0.967441i \(0.418551\pi\)
\(942\) 0 0
\(943\) −90.2492 −2.93892
\(944\) 0 0
\(945\) 0.763932 0.0248507
\(946\) 0 0
\(947\) 1.88854 0.0613694 0.0306847 0.999529i \(-0.490231\pi\)
0.0306847 + 0.999529i \(0.490231\pi\)
\(948\) 0 0
\(949\) 3.70820 0.120373
\(950\) 0 0
\(951\) −2.00000 −0.0648544
\(952\) 0 0
\(953\) 42.1803 1.36636 0.683178 0.730252i \(-0.260597\pi\)
0.683178 + 0.730252i \(0.260597\pi\)
\(954\) 0 0
\(955\) −20.9443 −0.677741
\(956\) 0 0
\(957\) 59.7771 1.93232
\(958\) 0 0
\(959\) 6.47214 0.208996
\(960\) 0 0
\(961\) 49.0000 1.58065
\(962\) 0 0
\(963\) −12.0000 −0.386695
\(964\) 0 0
\(965\) −2.18034 −0.0701876
\(966\) 0 0
\(967\) 0.763932 0.0245664 0.0122832 0.999925i \(-0.496090\pi\)
0.0122832 + 0.999925i \(0.496090\pi\)
\(968\) 0 0
\(969\) 4.00000 0.128499
\(970\) 0 0
\(971\) −60.5410 −1.94285 −0.971427 0.237339i \(-0.923725\pi\)
−0.971427 + 0.237339i \(0.923725\pi\)
\(972\) 0 0
\(973\) −1.88854 −0.0605439
\(974\) 0 0
\(975\) −1.00000 −0.0320256
\(976\) 0 0
\(977\) 13.7771 0.440768 0.220384 0.975413i \(-0.429269\pi\)
0.220384 + 0.975413i \(0.429269\pi\)
\(978\) 0 0
\(979\) 19.0557 0.609024
\(980\) 0 0
\(981\) 10.1803 0.325033
\(982\) 0 0
\(983\) 19.4164 0.619287 0.309644 0.950853i \(-0.399790\pi\)
0.309644 + 0.950853i \(0.399790\pi\)
\(984\) 0 0
\(985\) −9.41641 −0.300032
\(986\) 0 0
\(987\) −3.77709 −0.120226
\(988\) 0 0
\(989\) −93.6656 −2.97839
\(990\) 0 0
\(991\) −27.0557 −0.859454 −0.429727 0.902959i \(-0.641390\pi\)
−0.429727 + 0.902959i \(0.641390\pi\)
\(992\) 0 0
\(993\) 13.7082 0.435017
\(994\) 0 0
\(995\) −9.88854 −0.313488
\(996\) 0 0
\(997\) −16.4721 −0.521678 −0.260839 0.965382i \(-0.583999\pi\)
−0.260839 + 0.965382i \(0.583999\pi\)
\(998\) 0 0
\(999\) 0.472136 0.0149377
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 6240.2.a.bv.1.1 yes 2
4.3 odd 2 6240.2.a.bl.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6240.2.a.bl.1.2 2 4.3 odd 2
6240.2.a.bv.1.1 yes 2 1.1 even 1 trivial