Properties

Label 6240.2.a.bo.1.1
Level $6240$
Weight $2$
Character 6240.1
Self dual yes
Analytic conductor $49.827$
Analytic rank $1$
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: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{33}) \)
Defining polynomial: \( x^{2} - x - 8 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(3.37228\) of defining polynomial
Character \(\chi\) \(=\) 6240.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{3} -1.00000 q^{5} -4.37228 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{3} -1.00000 q^{5} -4.37228 q^{7} +1.00000 q^{9} +4.37228 q^{11} -1.00000 q^{13} -1.00000 q^{15} +0.372281 q^{17} -2.00000 q^{19} -4.37228 q^{21} -2.37228 q^{23} +1.00000 q^{25} +1.00000 q^{27} -2.74456 q^{29} +6.74456 q^{31} +4.37228 q^{33} +4.37228 q^{35} +4.37228 q^{37} -1.00000 q^{39} -0.372281 q^{41} +4.74456 q^{43} -1.00000 q^{45} +2.74456 q^{47} +12.1168 q^{49} +0.372281 q^{51} -7.62772 q^{53} -4.37228 q^{55} -2.00000 q^{57} -2.74456 q^{59} -9.11684 q^{61} -4.37228 q^{63} +1.00000 q^{65} +1.25544 q^{67} -2.37228 q^{69} +4.37228 q^{71} -6.00000 q^{73} +1.00000 q^{75} -19.1168 q^{77} -9.62772 q^{79} +1.00000 q^{81} -14.7446 q^{83} -0.372281 q^{85} -2.74456 q^{87} -13.1168 q^{89} +4.37228 q^{91} +6.74456 q^{93} +2.00000 q^{95} +9.11684 q^{97} +4.37228 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{3} - 2 q^{5} - 3 q^{7} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{3} - 2 q^{5} - 3 q^{7} + 2 q^{9} + 3 q^{11} - 2 q^{13} - 2 q^{15} - 5 q^{17} - 4 q^{19} - 3 q^{21} + q^{23} + 2 q^{25} + 2 q^{27} + 6 q^{29} + 2 q^{31} + 3 q^{33} + 3 q^{35} + 3 q^{37} - 2 q^{39} + 5 q^{41} - 2 q^{43} - 2 q^{45} - 6 q^{47} + 7 q^{49} - 5 q^{51} - 21 q^{53} - 3 q^{55} - 4 q^{57} + 6 q^{59} - q^{61} - 3 q^{63} + 2 q^{65} + 14 q^{67} + q^{69} + 3 q^{71} - 12 q^{73} + 2 q^{75} - 21 q^{77} - 25 q^{79} + 2 q^{81} - 18 q^{83} + 5 q^{85} + 6 q^{87} - 9 q^{89} + 3 q^{91} + 2 q^{93} + 4 q^{95} + q^{97} + 3 q^{99}+O(q^{100}) \) 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
\(7\) −4.37228 −1.65257 −0.826284 0.563254i \(-0.809549\pi\)
−0.826284 + 0.563254i \(0.809549\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 4.37228 1.31829 0.659146 0.752015i \(-0.270918\pi\)
0.659146 + 0.752015i \(0.270918\pi\)
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) −1.00000 −0.258199
\(16\) 0 0
\(17\) 0.372281 0.0902915 0.0451457 0.998980i \(-0.485625\pi\)
0.0451457 + 0.998980i \(0.485625\pi\)
\(18\) 0 0
\(19\) −2.00000 −0.458831 −0.229416 0.973329i \(-0.573682\pi\)
−0.229416 + 0.973329i \(0.573682\pi\)
\(20\) 0 0
\(21\) −4.37228 −0.954110
\(22\) 0 0
\(23\) −2.37228 −0.494655 −0.247327 0.968932i \(-0.579552\pi\)
−0.247327 + 0.968932i \(0.579552\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −2.74456 −0.509652 −0.254826 0.966987i \(-0.582018\pi\)
−0.254826 + 0.966987i \(0.582018\pi\)
\(30\) 0 0
\(31\) 6.74456 1.21136 0.605680 0.795709i \(-0.292901\pi\)
0.605680 + 0.795709i \(0.292901\pi\)
\(32\) 0 0
\(33\) 4.37228 0.761116
\(34\) 0 0
\(35\) 4.37228 0.739050
\(36\) 0 0
\(37\) 4.37228 0.718799 0.359399 0.933184i \(-0.382982\pi\)
0.359399 + 0.933184i \(0.382982\pi\)
\(38\) 0 0
\(39\) −1.00000 −0.160128
\(40\) 0 0
\(41\) −0.372281 −0.0581406 −0.0290703 0.999577i \(-0.509255\pi\)
−0.0290703 + 0.999577i \(0.509255\pi\)
\(42\) 0 0
\(43\) 4.74456 0.723539 0.361770 0.932268i \(-0.382173\pi\)
0.361770 + 0.932268i \(0.382173\pi\)
\(44\) 0 0
\(45\) −1.00000 −0.149071
\(46\) 0 0
\(47\) 2.74456 0.400336 0.200168 0.979762i \(-0.435851\pi\)
0.200168 + 0.979762i \(0.435851\pi\)
\(48\) 0 0
\(49\) 12.1168 1.73098
\(50\) 0 0
\(51\) 0.372281 0.0521298
\(52\) 0 0
\(53\) −7.62772 −1.04775 −0.523874 0.851796i \(-0.675514\pi\)
−0.523874 + 0.851796i \(0.675514\pi\)
\(54\) 0 0
\(55\) −4.37228 −0.589558
\(56\) 0 0
\(57\) −2.00000 −0.264906
\(58\) 0 0
\(59\) −2.74456 −0.357312 −0.178656 0.983912i \(-0.557175\pi\)
−0.178656 + 0.983912i \(0.557175\pi\)
\(60\) 0 0
\(61\) −9.11684 −1.16729 −0.583646 0.812008i \(-0.698374\pi\)
−0.583646 + 0.812008i \(0.698374\pi\)
\(62\) 0 0
\(63\) −4.37228 −0.550856
\(64\) 0 0
\(65\) 1.00000 0.124035
\(66\) 0 0
\(67\) 1.25544 0.153376 0.0766880 0.997055i \(-0.475565\pi\)
0.0766880 + 0.997055i \(0.475565\pi\)
\(68\) 0 0
\(69\) −2.37228 −0.285589
\(70\) 0 0
\(71\) 4.37228 0.518894 0.259447 0.965757i \(-0.416460\pi\)
0.259447 + 0.965757i \(0.416460\pi\)
\(72\) 0 0
\(73\) −6.00000 −0.702247 −0.351123 0.936329i \(-0.614200\pi\)
−0.351123 + 0.936329i \(0.614200\pi\)
\(74\) 0 0
\(75\) 1.00000 0.115470
\(76\) 0 0
\(77\) −19.1168 −2.17857
\(78\) 0 0
\(79\) −9.62772 −1.08320 −0.541601 0.840635i \(-0.682182\pi\)
−0.541601 + 0.840635i \(0.682182\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −14.7446 −1.61843 −0.809213 0.587515i \(-0.800106\pi\)
−0.809213 + 0.587515i \(0.800106\pi\)
\(84\) 0 0
\(85\) −0.372281 −0.0403796
\(86\) 0 0
\(87\) −2.74456 −0.294248
\(88\) 0 0
\(89\) −13.1168 −1.39038 −0.695191 0.718825i \(-0.744680\pi\)
−0.695191 + 0.718825i \(0.744680\pi\)
\(90\) 0 0
\(91\) 4.37228 0.458340
\(92\) 0 0
\(93\) 6.74456 0.699379
\(94\) 0 0
\(95\) 2.00000 0.205196
\(96\) 0 0
\(97\) 9.11684 0.925675 0.462838 0.886443i \(-0.346831\pi\)
0.462838 + 0.886443i \(0.346831\pi\)
\(98\) 0 0
\(99\) 4.37228 0.439431
\(100\) 0 0
\(101\) −5.25544 −0.522936 −0.261468 0.965212i \(-0.584207\pi\)
−0.261468 + 0.965212i \(0.584207\pi\)
\(102\) 0 0
\(103\) −8.00000 −0.788263 −0.394132 0.919054i \(-0.628955\pi\)
−0.394132 + 0.919054i \(0.628955\pi\)
\(104\) 0 0
\(105\) 4.37228 0.426691
\(106\) 0 0
\(107\) 1.62772 0.157358 0.0786788 0.996900i \(-0.474930\pi\)
0.0786788 + 0.996900i \(0.474930\pi\)
\(108\) 0 0
\(109\) −9.25544 −0.886510 −0.443255 0.896396i \(-0.646176\pi\)
−0.443255 + 0.896396i \(0.646176\pi\)
\(110\) 0 0
\(111\) 4.37228 0.414999
\(112\) 0 0
\(113\) −2.00000 −0.188144 −0.0940721 0.995565i \(-0.529988\pi\)
−0.0940721 + 0.995565i \(0.529988\pi\)
\(114\) 0 0
\(115\) 2.37228 0.221216
\(116\) 0 0
\(117\) −1.00000 −0.0924500
\(118\) 0 0
\(119\) −1.62772 −0.149213
\(120\) 0 0
\(121\) 8.11684 0.737895
\(122\) 0 0
\(123\) −0.372281 −0.0335675
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −16.0000 −1.41977 −0.709885 0.704317i \(-0.751253\pi\)
−0.709885 + 0.704317i \(0.751253\pi\)
\(128\) 0 0
\(129\) 4.74456 0.417735
\(130\) 0 0
\(131\) 12.0000 1.04844 0.524222 0.851581i \(-0.324356\pi\)
0.524222 + 0.851581i \(0.324356\pi\)
\(132\) 0 0
\(133\) 8.74456 0.758250
\(134\) 0 0
\(135\) −1.00000 −0.0860663
\(136\) 0 0
\(137\) −7.48913 −0.639839 −0.319920 0.947445i \(-0.603656\pi\)
−0.319920 + 0.947445i \(0.603656\pi\)
\(138\) 0 0
\(139\) 3.11684 0.264367 0.132184 0.991225i \(-0.457801\pi\)
0.132184 + 0.991225i \(0.457801\pi\)
\(140\) 0 0
\(141\) 2.74456 0.231134
\(142\) 0 0
\(143\) −4.37228 −0.365629
\(144\) 0 0
\(145\) 2.74456 0.227924
\(146\) 0 0
\(147\) 12.1168 0.999380
\(148\) 0 0
\(149\) −13.1168 −1.07457 −0.537287 0.843400i \(-0.680551\pi\)
−0.537287 + 0.843400i \(0.680551\pi\)
\(150\) 0 0
\(151\) 20.2337 1.64659 0.823297 0.567611i \(-0.192132\pi\)
0.823297 + 0.567611i \(0.192132\pi\)
\(152\) 0 0
\(153\) 0.372281 0.0300972
\(154\) 0 0
\(155\) −6.74456 −0.541736
\(156\) 0 0
\(157\) 2.00000 0.159617 0.0798087 0.996810i \(-0.474569\pi\)
0.0798087 + 0.996810i \(0.474569\pi\)
\(158\) 0 0
\(159\) −7.62772 −0.604917
\(160\) 0 0
\(161\) 10.3723 0.817450
\(162\) 0 0
\(163\) −17.8614 −1.39901 −0.699507 0.714626i \(-0.746597\pi\)
−0.699507 + 0.714626i \(0.746597\pi\)
\(164\) 0 0
\(165\) −4.37228 −0.340382
\(166\) 0 0
\(167\) 2.74456 0.212381 0.106190 0.994346i \(-0.466135\pi\)
0.106190 + 0.994346i \(0.466135\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −2.00000 −0.152944
\(172\) 0 0
\(173\) −11.4891 −0.873502 −0.436751 0.899582i \(-0.643871\pi\)
−0.436751 + 0.899582i \(0.643871\pi\)
\(174\) 0 0
\(175\) −4.37228 −0.330513
\(176\) 0 0
\(177\) −2.74456 −0.206294
\(178\) 0 0
\(179\) 3.25544 0.243323 0.121661 0.992572i \(-0.461178\pi\)
0.121661 + 0.992572i \(0.461178\pi\)
\(180\) 0 0
\(181\) −5.11684 −0.380332 −0.190166 0.981752i \(-0.560903\pi\)
−0.190166 + 0.981752i \(0.560903\pi\)
\(182\) 0 0
\(183\) −9.11684 −0.673936
\(184\) 0 0
\(185\) −4.37228 −0.321457
\(186\) 0 0
\(187\) 1.62772 0.119031
\(188\) 0 0
\(189\) −4.37228 −0.318037
\(190\) 0 0
\(191\) 8.74456 0.632734 0.316367 0.948637i \(-0.397537\pi\)
0.316367 + 0.948637i \(0.397537\pi\)
\(192\) 0 0
\(193\) −21.1168 −1.52002 −0.760012 0.649909i \(-0.774807\pi\)
−0.760012 + 0.649909i \(0.774807\pi\)
\(194\) 0 0
\(195\) 1.00000 0.0716115
\(196\) 0 0
\(197\) 3.48913 0.248590 0.124295 0.992245i \(-0.460333\pi\)
0.124295 + 0.992245i \(0.460333\pi\)
\(198\) 0 0
\(199\) 8.00000 0.567105 0.283552 0.958957i \(-0.408487\pi\)
0.283552 + 0.958957i \(0.408487\pi\)
\(200\) 0 0
\(201\) 1.25544 0.0885517
\(202\) 0 0
\(203\) 12.0000 0.842235
\(204\) 0 0
\(205\) 0.372281 0.0260013
\(206\) 0 0
\(207\) −2.37228 −0.164885
\(208\) 0 0
\(209\) −8.74456 −0.604874
\(210\) 0 0
\(211\) −21.4891 −1.47937 −0.739686 0.672952i \(-0.765026\pi\)
−0.739686 + 0.672952i \(0.765026\pi\)
\(212\) 0 0
\(213\) 4.37228 0.299584
\(214\) 0 0
\(215\) −4.74456 −0.323576
\(216\) 0 0
\(217\) −29.4891 −2.00185
\(218\) 0 0
\(219\) −6.00000 −0.405442
\(220\) 0 0
\(221\) −0.372281 −0.0250424
\(222\) 0 0
\(223\) −20.2337 −1.35495 −0.677474 0.735547i \(-0.736925\pi\)
−0.677474 + 0.735547i \(0.736925\pi\)
\(224\) 0 0
\(225\) 1.00000 0.0666667
\(226\) 0 0
\(227\) 14.0000 0.929213 0.464606 0.885517i \(-0.346196\pi\)
0.464606 + 0.885517i \(0.346196\pi\)
\(228\) 0 0
\(229\) 24.2337 1.60141 0.800704 0.599061i \(-0.204459\pi\)
0.800704 + 0.599061i \(0.204459\pi\)
\(230\) 0 0
\(231\) −19.1168 −1.25780
\(232\) 0 0
\(233\) −16.3723 −1.07258 −0.536292 0.844033i \(-0.680175\pi\)
−0.536292 + 0.844033i \(0.680175\pi\)
\(234\) 0 0
\(235\) −2.74456 −0.179036
\(236\) 0 0
\(237\) −9.62772 −0.625388
\(238\) 0 0
\(239\) −14.6060 −0.944782 −0.472391 0.881389i \(-0.656609\pi\)
−0.472391 + 0.881389i \(0.656609\pi\)
\(240\) 0 0
\(241\) 6.74456 0.434455 0.217228 0.976121i \(-0.430299\pi\)
0.217228 + 0.976121i \(0.430299\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) −12.1168 −0.774117
\(246\) 0 0
\(247\) 2.00000 0.127257
\(248\) 0 0
\(249\) −14.7446 −0.934399
\(250\) 0 0
\(251\) 18.9783 1.19790 0.598948 0.800788i \(-0.295585\pi\)
0.598948 + 0.800788i \(0.295585\pi\)
\(252\) 0 0
\(253\) −10.3723 −0.652100
\(254\) 0 0
\(255\) −0.372281 −0.0233132
\(256\) 0 0
\(257\) −14.0000 −0.873296 −0.436648 0.899632i \(-0.643834\pi\)
−0.436648 + 0.899632i \(0.643834\pi\)
\(258\) 0 0
\(259\) −19.1168 −1.18786
\(260\) 0 0
\(261\) −2.74456 −0.169884
\(262\) 0 0
\(263\) −2.51087 −0.154827 −0.0774136 0.996999i \(-0.524666\pi\)
−0.0774136 + 0.996999i \(0.524666\pi\)
\(264\) 0 0
\(265\) 7.62772 0.468567
\(266\) 0 0
\(267\) −13.1168 −0.802738
\(268\) 0 0
\(269\) 25.7228 1.56835 0.784174 0.620541i \(-0.213087\pi\)
0.784174 + 0.620541i \(0.213087\pi\)
\(270\) 0 0
\(271\) −3.48913 −0.211949 −0.105975 0.994369i \(-0.533796\pi\)
−0.105975 + 0.994369i \(0.533796\pi\)
\(272\) 0 0
\(273\) 4.37228 0.264623
\(274\) 0 0
\(275\) 4.37228 0.263658
\(276\) 0 0
\(277\) −21.2554 −1.27712 −0.638558 0.769574i \(-0.720469\pi\)
−0.638558 + 0.769574i \(0.720469\pi\)
\(278\) 0 0
\(279\) 6.74456 0.403786
\(280\) 0 0
\(281\) 3.48913 0.208144 0.104072 0.994570i \(-0.466813\pi\)
0.104072 + 0.994570i \(0.466813\pi\)
\(282\) 0 0
\(283\) −25.4891 −1.51517 −0.757586 0.652736i \(-0.773621\pi\)
−0.757586 + 0.652736i \(0.773621\pi\)
\(284\) 0 0
\(285\) 2.00000 0.118470
\(286\) 0 0
\(287\) 1.62772 0.0960812
\(288\) 0 0
\(289\) −16.8614 −0.991847
\(290\) 0 0
\(291\) 9.11684 0.534439
\(292\) 0 0
\(293\) −2.74456 −0.160339 −0.0801695 0.996781i \(-0.525546\pi\)
−0.0801695 + 0.996781i \(0.525546\pi\)
\(294\) 0 0
\(295\) 2.74456 0.159795
\(296\) 0 0
\(297\) 4.37228 0.253705
\(298\) 0 0
\(299\) 2.37228 0.137193
\(300\) 0 0
\(301\) −20.7446 −1.19570
\(302\) 0 0
\(303\) −5.25544 −0.301917
\(304\) 0 0
\(305\) 9.11684 0.522029
\(306\) 0 0
\(307\) 9.11684 0.520326 0.260163 0.965565i \(-0.416224\pi\)
0.260163 + 0.965565i \(0.416224\pi\)
\(308\) 0 0
\(309\) −8.00000 −0.455104
\(310\) 0 0
\(311\) −31.7228 −1.79884 −0.899418 0.437090i \(-0.856009\pi\)
−0.899418 + 0.437090i \(0.856009\pi\)
\(312\) 0 0
\(313\) −28.9783 −1.63795 −0.818974 0.573831i \(-0.805457\pi\)
−0.818974 + 0.573831i \(0.805457\pi\)
\(314\) 0 0
\(315\) 4.37228 0.246350
\(316\) 0 0
\(317\) −6.00000 −0.336994 −0.168497 0.985702i \(-0.553891\pi\)
−0.168497 + 0.985702i \(0.553891\pi\)
\(318\) 0 0
\(319\) −12.0000 −0.671871
\(320\) 0 0
\(321\) 1.62772 0.0908504
\(322\) 0 0
\(323\) −0.744563 −0.0414286
\(324\) 0 0
\(325\) −1.00000 −0.0554700
\(326\) 0 0
\(327\) −9.25544 −0.511827
\(328\) 0 0
\(329\) −12.0000 −0.661581
\(330\) 0 0
\(331\) 22.0000 1.20923 0.604615 0.796518i \(-0.293327\pi\)
0.604615 + 0.796518i \(0.293327\pi\)
\(332\) 0 0
\(333\) 4.37228 0.239600
\(334\) 0 0
\(335\) −1.25544 −0.0685919
\(336\) 0 0
\(337\) −26.0000 −1.41631 −0.708155 0.706057i \(-0.750472\pi\)
−0.708155 + 0.706057i \(0.750472\pi\)
\(338\) 0 0
\(339\) −2.00000 −0.108625
\(340\) 0 0
\(341\) 29.4891 1.59693
\(342\) 0 0
\(343\) −22.3723 −1.20799
\(344\) 0 0
\(345\) 2.37228 0.127719
\(346\) 0 0
\(347\) 35.1168 1.88517 0.942585 0.333965i \(-0.108387\pi\)
0.942585 + 0.333965i \(0.108387\pi\)
\(348\) 0 0
\(349\) 20.9783 1.12294 0.561470 0.827497i \(-0.310236\pi\)
0.561470 + 0.827497i \(0.310236\pi\)
\(350\) 0 0
\(351\) −1.00000 −0.0533761
\(352\) 0 0
\(353\) −9.25544 −0.492617 −0.246309 0.969191i \(-0.579218\pi\)
−0.246309 + 0.969191i \(0.579218\pi\)
\(354\) 0 0
\(355\) −4.37228 −0.232057
\(356\) 0 0
\(357\) −1.62772 −0.0861480
\(358\) 0 0
\(359\) 9.25544 0.488483 0.244242 0.969714i \(-0.421461\pi\)
0.244242 + 0.969714i \(0.421461\pi\)
\(360\) 0 0
\(361\) −15.0000 −0.789474
\(362\) 0 0
\(363\) 8.11684 0.426024
\(364\) 0 0
\(365\) 6.00000 0.314054
\(366\) 0 0
\(367\) 24.7446 1.29166 0.645828 0.763483i \(-0.276512\pi\)
0.645828 + 0.763483i \(0.276512\pi\)
\(368\) 0 0
\(369\) −0.372281 −0.0193802
\(370\) 0 0
\(371\) 33.3505 1.73147
\(372\) 0 0
\(373\) −15.4891 −0.801997 −0.400998 0.916079i \(-0.631337\pi\)
−0.400998 + 0.916079i \(0.631337\pi\)
\(374\) 0 0
\(375\) −1.00000 −0.0516398
\(376\) 0 0
\(377\) 2.74456 0.141352
\(378\) 0 0
\(379\) −8.23369 −0.422936 −0.211468 0.977385i \(-0.567824\pi\)
−0.211468 + 0.977385i \(0.567824\pi\)
\(380\) 0 0
\(381\) −16.0000 −0.819705
\(382\) 0 0
\(383\) 27.4891 1.40463 0.702314 0.711867i \(-0.252150\pi\)
0.702314 + 0.711867i \(0.252150\pi\)
\(384\) 0 0
\(385\) 19.1168 0.974285
\(386\) 0 0
\(387\) 4.74456 0.241180
\(388\) 0 0
\(389\) −17.2554 −0.874885 −0.437443 0.899246i \(-0.644116\pi\)
−0.437443 + 0.899246i \(0.644116\pi\)
\(390\) 0 0
\(391\) −0.883156 −0.0446631
\(392\) 0 0
\(393\) 12.0000 0.605320
\(394\) 0 0
\(395\) 9.62772 0.484423
\(396\) 0 0
\(397\) −14.6060 −0.733053 −0.366526 0.930408i \(-0.619453\pi\)
−0.366526 + 0.930408i \(0.619453\pi\)
\(398\) 0 0
\(399\) 8.74456 0.437776
\(400\) 0 0
\(401\) 11.4891 0.573740 0.286870 0.957970i \(-0.407385\pi\)
0.286870 + 0.957970i \(0.407385\pi\)
\(402\) 0 0
\(403\) −6.74456 −0.335971
\(404\) 0 0
\(405\) −1.00000 −0.0496904
\(406\) 0 0
\(407\) 19.1168 0.947587
\(408\) 0 0
\(409\) −28.2337 −1.39607 −0.698033 0.716066i \(-0.745941\pi\)
−0.698033 + 0.716066i \(0.745941\pi\)
\(410\) 0 0
\(411\) −7.48913 −0.369411
\(412\) 0 0
\(413\) 12.0000 0.590481
\(414\) 0 0
\(415\) 14.7446 0.723782
\(416\) 0 0
\(417\) 3.11684 0.152633
\(418\) 0 0
\(419\) −0.744563 −0.0363743 −0.0181871 0.999835i \(-0.505789\pi\)
−0.0181871 + 0.999835i \(0.505789\pi\)
\(420\) 0 0
\(421\) 13.2554 0.646030 0.323015 0.946394i \(-0.395303\pi\)
0.323015 + 0.946394i \(0.395303\pi\)
\(422\) 0 0
\(423\) 2.74456 0.133445
\(424\) 0 0
\(425\) 0.372281 0.0180583
\(426\) 0 0
\(427\) 39.8614 1.92903
\(428\) 0 0
\(429\) −4.37228 −0.211096
\(430\) 0 0
\(431\) −20.2337 −0.974622 −0.487311 0.873228i \(-0.662022\pi\)
−0.487311 + 0.873228i \(0.662022\pi\)
\(432\) 0 0
\(433\) −23.4891 −1.12882 −0.564408 0.825496i \(-0.690895\pi\)
−0.564408 + 0.825496i \(0.690895\pi\)
\(434\) 0 0
\(435\) 2.74456 0.131592
\(436\) 0 0
\(437\) 4.74456 0.226963
\(438\) 0 0
\(439\) 7.11684 0.339668 0.169834 0.985473i \(-0.445677\pi\)
0.169834 + 0.985473i \(0.445677\pi\)
\(440\) 0 0
\(441\) 12.1168 0.576993
\(442\) 0 0
\(443\) −15.8614 −0.753598 −0.376799 0.926295i \(-0.622975\pi\)
−0.376799 + 0.926295i \(0.622975\pi\)
\(444\) 0 0
\(445\) 13.1168 0.621798
\(446\) 0 0
\(447\) −13.1168 −0.620405
\(448\) 0 0
\(449\) 1.11684 0.0527071 0.0263536 0.999653i \(-0.491610\pi\)
0.0263536 + 0.999653i \(0.491610\pi\)
\(450\) 0 0
\(451\) −1.62772 −0.0766463
\(452\) 0 0
\(453\) 20.2337 0.950662
\(454\) 0 0
\(455\) −4.37228 −0.204976
\(456\) 0 0
\(457\) −8.37228 −0.391639 −0.195819 0.980640i \(-0.562737\pi\)
−0.195819 + 0.980640i \(0.562737\pi\)
\(458\) 0 0
\(459\) 0.372281 0.0173766
\(460\) 0 0
\(461\) −9.86141 −0.459291 −0.229646 0.973274i \(-0.573757\pi\)
−0.229646 + 0.973274i \(0.573757\pi\)
\(462\) 0 0
\(463\) −1.39403 −0.0647861 −0.0323931 0.999475i \(-0.510313\pi\)
−0.0323931 + 0.999475i \(0.510313\pi\)
\(464\) 0 0
\(465\) −6.74456 −0.312772
\(466\) 0 0
\(467\) −2.37228 −0.109776 −0.0548880 0.998493i \(-0.517480\pi\)
−0.0548880 + 0.998493i \(0.517480\pi\)
\(468\) 0 0
\(469\) −5.48913 −0.253464
\(470\) 0 0
\(471\) 2.00000 0.0921551
\(472\) 0 0
\(473\) 20.7446 0.953836
\(474\) 0 0
\(475\) −2.00000 −0.0917663
\(476\) 0 0
\(477\) −7.62772 −0.349249
\(478\) 0 0
\(479\) 40.0951 1.83199 0.915996 0.401188i \(-0.131403\pi\)
0.915996 + 0.401188i \(0.131403\pi\)
\(480\) 0 0
\(481\) −4.37228 −0.199359
\(482\) 0 0
\(483\) 10.3723 0.471955
\(484\) 0 0
\(485\) −9.11684 −0.413975
\(486\) 0 0
\(487\) 32.8397 1.48811 0.744053 0.668120i \(-0.232901\pi\)
0.744053 + 0.668120i \(0.232901\pi\)
\(488\) 0 0
\(489\) −17.8614 −0.807721
\(490\) 0 0
\(491\) 4.74456 0.214119 0.107060 0.994253i \(-0.465856\pi\)
0.107060 + 0.994253i \(0.465856\pi\)
\(492\) 0 0
\(493\) −1.02175 −0.0460173
\(494\) 0 0
\(495\) −4.37228 −0.196519
\(496\) 0 0
\(497\) −19.1168 −0.857508
\(498\) 0 0
\(499\) 8.97825 0.401922 0.200961 0.979599i \(-0.435594\pi\)
0.200961 + 0.979599i \(0.435594\pi\)
\(500\) 0 0
\(501\) 2.74456 0.122618
\(502\) 0 0
\(503\) 18.5109 0.825359 0.412680 0.910876i \(-0.364593\pi\)
0.412680 + 0.910876i \(0.364593\pi\)
\(504\) 0 0
\(505\) 5.25544 0.233864
\(506\) 0 0
\(507\) 1.00000 0.0444116
\(508\) 0 0
\(509\) −37.1168 −1.64518 −0.822588 0.568638i \(-0.807470\pi\)
−0.822588 + 0.568638i \(0.807470\pi\)
\(510\) 0 0
\(511\) 26.2337 1.16051
\(512\) 0 0
\(513\) −2.00000 −0.0883022
\(514\) 0 0
\(515\) 8.00000 0.352522
\(516\) 0 0
\(517\) 12.0000 0.527759
\(518\) 0 0
\(519\) −11.4891 −0.504317
\(520\) 0 0
\(521\) 31.4891 1.37956 0.689782 0.724017i \(-0.257706\pi\)
0.689782 + 0.724017i \(0.257706\pi\)
\(522\) 0 0
\(523\) 43.7228 1.91187 0.955933 0.293586i \(-0.0948488\pi\)
0.955933 + 0.293586i \(0.0948488\pi\)
\(524\) 0 0
\(525\) −4.37228 −0.190822
\(526\) 0 0
\(527\) 2.51087 0.109375
\(528\) 0 0
\(529\) −17.3723 −0.755317
\(530\) 0 0
\(531\) −2.74456 −0.119104
\(532\) 0 0
\(533\) 0.372281 0.0161253
\(534\) 0 0
\(535\) −1.62772 −0.0703724
\(536\) 0 0
\(537\) 3.25544 0.140482
\(538\) 0 0
\(539\) 52.9783 2.28193
\(540\) 0 0
\(541\) −15.4891 −0.665930 −0.332965 0.942939i \(-0.608049\pi\)
−0.332965 + 0.942939i \(0.608049\pi\)
\(542\) 0 0
\(543\) −5.11684 −0.219585
\(544\) 0 0
\(545\) 9.25544 0.396459
\(546\) 0 0
\(547\) −12.0000 −0.513083 −0.256541 0.966533i \(-0.582583\pi\)
−0.256541 + 0.966533i \(0.582583\pi\)
\(548\) 0 0
\(549\) −9.11684 −0.389097
\(550\) 0 0
\(551\) 5.48913 0.233845
\(552\) 0 0
\(553\) 42.0951 1.79007
\(554\) 0 0
\(555\) −4.37228 −0.185593
\(556\) 0 0
\(557\) 14.7446 0.624747 0.312374 0.949959i \(-0.398876\pi\)
0.312374 + 0.949959i \(0.398876\pi\)
\(558\) 0 0
\(559\) −4.74456 −0.200674
\(560\) 0 0
\(561\) 1.62772 0.0687223
\(562\) 0 0
\(563\) 31.1168 1.31142 0.655709 0.755013i \(-0.272370\pi\)
0.655709 + 0.755013i \(0.272370\pi\)
\(564\) 0 0
\(565\) 2.00000 0.0841406
\(566\) 0 0
\(567\) −4.37228 −0.183619
\(568\) 0 0
\(569\) −8.97825 −0.376388 −0.188194 0.982132i \(-0.560263\pi\)
−0.188194 + 0.982132i \(0.560263\pi\)
\(570\) 0 0
\(571\) −16.6060 −0.694938 −0.347469 0.937691i \(-0.612959\pi\)
−0.347469 + 0.937691i \(0.612959\pi\)
\(572\) 0 0
\(573\) 8.74456 0.365309
\(574\) 0 0
\(575\) −2.37228 −0.0989310
\(576\) 0 0
\(577\) −9.86141 −0.410536 −0.205268 0.978706i \(-0.565807\pi\)
−0.205268 + 0.978706i \(0.565807\pi\)
\(578\) 0 0
\(579\) −21.1168 −0.877586
\(580\) 0 0
\(581\) 64.4674 2.67456
\(582\) 0 0
\(583\) −33.3505 −1.38124
\(584\) 0 0
\(585\) 1.00000 0.0413449
\(586\) 0 0
\(587\) 20.5109 0.846574 0.423287 0.905996i \(-0.360876\pi\)
0.423287 + 0.905996i \(0.360876\pi\)
\(588\) 0 0
\(589\) −13.4891 −0.555810
\(590\) 0 0
\(591\) 3.48913 0.143523
\(592\) 0 0
\(593\) −29.7228 −1.22057 −0.610285 0.792182i \(-0.708945\pi\)
−0.610285 + 0.792182i \(0.708945\pi\)
\(594\) 0 0
\(595\) 1.62772 0.0667300
\(596\) 0 0
\(597\) 8.00000 0.327418
\(598\) 0 0
\(599\) −20.0000 −0.817178 −0.408589 0.912719i \(-0.633979\pi\)
−0.408589 + 0.912719i \(0.633979\pi\)
\(600\) 0 0
\(601\) −13.8614 −0.565419 −0.282709 0.959206i \(-0.591233\pi\)
−0.282709 + 0.959206i \(0.591233\pi\)
\(602\) 0 0
\(603\) 1.25544 0.0511254
\(604\) 0 0
\(605\) −8.11684 −0.329997
\(606\) 0 0
\(607\) −43.7228 −1.77465 −0.887327 0.461141i \(-0.847440\pi\)
−0.887327 + 0.461141i \(0.847440\pi\)
\(608\) 0 0
\(609\) 12.0000 0.486265
\(610\) 0 0
\(611\) −2.74456 −0.111033
\(612\) 0 0
\(613\) −3.35053 −0.135327 −0.0676634 0.997708i \(-0.521554\pi\)
−0.0676634 + 0.997708i \(0.521554\pi\)
\(614\) 0 0
\(615\) 0.372281 0.0150118
\(616\) 0 0
\(617\) 22.4674 0.904502 0.452251 0.891891i \(-0.350621\pi\)
0.452251 + 0.891891i \(0.350621\pi\)
\(618\) 0 0
\(619\) −1.25544 −0.0504603 −0.0252301 0.999682i \(-0.508032\pi\)
−0.0252301 + 0.999682i \(0.508032\pi\)
\(620\) 0 0
\(621\) −2.37228 −0.0951964
\(622\) 0 0
\(623\) 57.3505 2.29770
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −8.74456 −0.349224
\(628\) 0 0
\(629\) 1.62772 0.0649014
\(630\) 0 0
\(631\) 36.2337 1.44244 0.721220 0.692706i \(-0.243582\pi\)
0.721220 + 0.692706i \(0.243582\pi\)
\(632\) 0 0
\(633\) −21.4891 −0.854116
\(634\) 0 0
\(635\) 16.0000 0.634941
\(636\) 0 0
\(637\) −12.1168 −0.480087
\(638\) 0 0
\(639\) 4.37228 0.172965
\(640\) 0 0
\(641\) 40.9783 1.61854 0.809272 0.587434i \(-0.199862\pi\)
0.809272 + 0.587434i \(0.199862\pi\)
\(642\) 0 0
\(643\) −2.88316 −0.113701 −0.0568503 0.998383i \(-0.518106\pi\)
−0.0568503 + 0.998383i \(0.518106\pi\)
\(644\) 0 0
\(645\) −4.74456 −0.186817
\(646\) 0 0
\(647\) −24.6060 −0.967360 −0.483680 0.875245i \(-0.660700\pi\)
−0.483680 + 0.875245i \(0.660700\pi\)
\(648\) 0 0
\(649\) −12.0000 −0.471041
\(650\) 0 0
\(651\) −29.4891 −1.15577
\(652\) 0 0
\(653\) −4.51087 −0.176524 −0.0882621 0.996097i \(-0.528131\pi\)
−0.0882621 + 0.996097i \(0.528131\pi\)
\(654\) 0 0
\(655\) −12.0000 −0.468879
\(656\) 0 0
\(657\) −6.00000 −0.234082
\(658\) 0 0
\(659\) −22.9783 −0.895106 −0.447553 0.894258i \(-0.647704\pi\)
−0.447553 + 0.894258i \(0.647704\pi\)
\(660\) 0 0
\(661\) 16.5109 0.642199 0.321099 0.947046i \(-0.395948\pi\)
0.321099 + 0.947046i \(0.395948\pi\)
\(662\) 0 0
\(663\) −0.372281 −0.0144582
\(664\) 0 0
\(665\) −8.74456 −0.339100
\(666\) 0 0
\(667\) 6.51087 0.252102
\(668\) 0 0
\(669\) −20.2337 −0.782280
\(670\) 0 0
\(671\) −39.8614 −1.53883
\(672\) 0 0
\(673\) 4.23369 0.163197 0.0815983 0.996665i \(-0.473998\pi\)
0.0815983 + 0.996665i \(0.473998\pi\)
\(674\) 0 0
\(675\) 1.00000 0.0384900
\(676\) 0 0
\(677\) 1.86141 0.0715397 0.0357698 0.999360i \(-0.488612\pi\)
0.0357698 + 0.999360i \(0.488612\pi\)
\(678\) 0 0
\(679\) −39.8614 −1.52974
\(680\) 0 0
\(681\) 14.0000 0.536481
\(682\) 0 0
\(683\) 2.00000 0.0765279 0.0382639 0.999268i \(-0.487817\pi\)
0.0382639 + 0.999268i \(0.487817\pi\)
\(684\) 0 0
\(685\) 7.48913 0.286145
\(686\) 0 0
\(687\) 24.2337 0.924573
\(688\) 0 0
\(689\) 7.62772 0.290593
\(690\) 0 0
\(691\) −28.9783 −1.10238 −0.551192 0.834378i \(-0.685827\pi\)
−0.551192 + 0.834378i \(0.685827\pi\)
\(692\) 0 0
\(693\) −19.1168 −0.726189
\(694\) 0 0
\(695\) −3.11684 −0.118229
\(696\) 0 0
\(697\) −0.138593 −0.00524960
\(698\) 0 0
\(699\) −16.3723 −0.619257
\(700\) 0 0
\(701\) −28.2337 −1.06637 −0.533186 0.845998i \(-0.679005\pi\)
−0.533186 + 0.845998i \(0.679005\pi\)
\(702\) 0 0
\(703\) −8.74456 −0.329807
\(704\) 0 0
\(705\) −2.74456 −0.103366
\(706\) 0 0
\(707\) 22.9783 0.864186
\(708\) 0 0
\(709\) 35.2119 1.32241 0.661206 0.750204i \(-0.270045\pi\)
0.661206 + 0.750204i \(0.270045\pi\)
\(710\) 0 0
\(711\) −9.62772 −0.361068
\(712\) 0 0
\(713\) −16.0000 −0.599205
\(714\) 0 0
\(715\) 4.37228 0.163514
\(716\) 0 0
\(717\) −14.6060 −0.545470
\(718\) 0 0
\(719\) 20.4674 0.763304 0.381652 0.924306i \(-0.375355\pi\)
0.381652 + 0.924306i \(0.375355\pi\)
\(720\) 0 0
\(721\) 34.9783 1.30266
\(722\) 0 0
\(723\) 6.74456 0.250833
\(724\) 0 0
\(725\) −2.74456 −0.101930
\(726\) 0 0
\(727\) −30.2337 −1.12131 −0.560653 0.828051i \(-0.689450\pi\)
−0.560653 + 0.828051i \(0.689450\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 1.76631 0.0653294
\(732\) 0 0
\(733\) −6.60597 −0.243997 −0.121999 0.992530i \(-0.538930\pi\)
−0.121999 + 0.992530i \(0.538930\pi\)
\(734\) 0 0
\(735\) −12.1168 −0.446937
\(736\) 0 0
\(737\) 5.48913 0.202195
\(738\) 0 0
\(739\) 47.9565 1.76411 0.882054 0.471148i \(-0.156160\pi\)
0.882054 + 0.471148i \(0.156160\pi\)
\(740\) 0 0
\(741\) 2.00000 0.0734718
\(742\) 0 0
\(743\) −38.0000 −1.39408 −0.697042 0.717030i \(-0.745501\pi\)
−0.697042 + 0.717030i \(0.745501\pi\)
\(744\) 0 0
\(745\) 13.1168 0.480564
\(746\) 0 0
\(747\) −14.7446 −0.539475
\(748\) 0 0
\(749\) −7.11684 −0.260044
\(750\) 0 0
\(751\) −38.8397 −1.41728 −0.708640 0.705571i \(-0.750691\pi\)
−0.708640 + 0.705571i \(0.750691\pi\)
\(752\) 0 0
\(753\) 18.9783 0.691606
\(754\) 0 0
\(755\) −20.2337 −0.736379
\(756\) 0 0
\(757\) 2.74456 0.0997528 0.0498764 0.998755i \(-0.484117\pi\)
0.0498764 + 0.998755i \(0.484117\pi\)
\(758\) 0 0
\(759\) −10.3723 −0.376490
\(760\) 0 0
\(761\) 8.51087 0.308519 0.154259 0.988030i \(-0.450701\pi\)
0.154259 + 0.988030i \(0.450701\pi\)
\(762\) 0 0
\(763\) 40.4674 1.46502
\(764\) 0 0
\(765\) −0.372281 −0.0134599
\(766\) 0 0
\(767\) 2.74456 0.0991004
\(768\) 0 0
\(769\) 39.9565 1.44087 0.720434 0.693523i \(-0.243943\pi\)
0.720434 + 0.693523i \(0.243943\pi\)
\(770\) 0 0
\(771\) −14.0000 −0.504198
\(772\) 0 0
\(773\) 49.7228 1.78841 0.894203 0.447662i \(-0.147743\pi\)
0.894203 + 0.447662i \(0.147743\pi\)
\(774\) 0 0
\(775\) 6.74456 0.242272
\(776\) 0 0
\(777\) −19.1168 −0.685813
\(778\) 0 0
\(779\) 0.744563 0.0266767
\(780\) 0 0
\(781\) 19.1168 0.684054
\(782\) 0 0
\(783\) −2.74456 −0.0980827
\(784\) 0 0
\(785\) −2.00000 −0.0713831
\(786\) 0 0
\(787\) 22.7446 0.810756 0.405378 0.914149i \(-0.367140\pi\)
0.405378 + 0.914149i \(0.367140\pi\)
\(788\) 0 0
\(789\) −2.51087 −0.0893895
\(790\) 0 0
\(791\) 8.74456 0.310921
\(792\) 0 0
\(793\) 9.11684 0.323749
\(794\) 0 0
\(795\) 7.62772 0.270527
\(796\) 0 0
\(797\) 36.0951 1.27855 0.639277 0.768977i \(-0.279234\pi\)
0.639277 + 0.768977i \(0.279234\pi\)
\(798\) 0 0
\(799\) 1.02175 0.0361469
\(800\) 0 0
\(801\) −13.1168 −0.463461
\(802\) 0 0
\(803\) −26.2337 −0.925767
\(804\) 0 0
\(805\) −10.3723 −0.365575
\(806\) 0 0
\(807\) 25.7228 0.905486
\(808\) 0 0
\(809\) 40.9783 1.44072 0.720359 0.693601i \(-0.243977\pi\)
0.720359 + 0.693601i \(0.243977\pi\)
\(810\) 0 0
\(811\) −44.9783 −1.57940 −0.789700 0.613493i \(-0.789764\pi\)
−0.789700 + 0.613493i \(0.789764\pi\)
\(812\) 0 0
\(813\) −3.48913 −0.122369
\(814\) 0 0
\(815\) 17.8614 0.625658
\(816\) 0 0
\(817\) −9.48913 −0.331982
\(818\) 0 0
\(819\) 4.37228 0.152780
\(820\) 0 0
\(821\) 15.6277 0.545411 0.272706 0.962098i \(-0.412082\pi\)
0.272706 + 0.962098i \(0.412082\pi\)
\(822\) 0 0
\(823\) 10.9783 0.382678 0.191339 0.981524i \(-0.438717\pi\)
0.191339 + 0.981524i \(0.438717\pi\)
\(824\) 0 0
\(825\) 4.37228 0.152223
\(826\) 0 0
\(827\) 37.2554 1.29550 0.647749 0.761854i \(-0.275710\pi\)
0.647749 + 0.761854i \(0.275710\pi\)
\(828\) 0 0
\(829\) 4.51087 0.156669 0.0783346 0.996927i \(-0.475040\pi\)
0.0783346 + 0.996927i \(0.475040\pi\)
\(830\) 0 0
\(831\) −21.2554 −0.737343
\(832\) 0 0
\(833\) 4.51087 0.156293
\(834\) 0 0
\(835\) −2.74456 −0.0949795
\(836\) 0 0
\(837\) 6.74456 0.233126
\(838\) 0 0
\(839\) −53.5842 −1.84993 −0.924966 0.380049i \(-0.875907\pi\)
−0.924966 + 0.380049i \(0.875907\pi\)
\(840\) 0 0
\(841\) −21.4674 −0.740254
\(842\) 0 0
\(843\) 3.48913 0.120172
\(844\) 0 0
\(845\) −1.00000 −0.0344010
\(846\) 0 0
\(847\) −35.4891 −1.21942
\(848\) 0 0
\(849\) −25.4891 −0.874785
\(850\) 0 0
\(851\) −10.3723 −0.355557
\(852\) 0 0
\(853\) 49.1168 1.68173 0.840864 0.541246i \(-0.182047\pi\)
0.840864 + 0.541246i \(0.182047\pi\)
\(854\) 0 0
\(855\) 2.00000 0.0683986
\(856\) 0 0
\(857\) −28.8397 −0.985144 −0.492572 0.870272i \(-0.663943\pi\)
−0.492572 + 0.870272i \(0.663943\pi\)
\(858\) 0 0
\(859\) −1.35053 −0.0460796 −0.0230398 0.999735i \(-0.507334\pi\)
−0.0230398 + 0.999735i \(0.507334\pi\)
\(860\) 0 0
\(861\) 1.62772 0.0554725
\(862\) 0 0
\(863\) 11.4891 0.391094 0.195547 0.980694i \(-0.437352\pi\)
0.195547 + 0.980694i \(0.437352\pi\)
\(864\) 0 0
\(865\) 11.4891 0.390642
\(866\) 0 0
\(867\) −16.8614 −0.572643
\(868\) 0 0
\(869\) −42.0951 −1.42798
\(870\) 0 0
\(871\) −1.25544 −0.0425389
\(872\) 0 0
\(873\) 9.11684 0.308558
\(874\) 0 0
\(875\) 4.37228 0.147810
\(876\) 0 0
\(877\) −15.4891 −0.523031 −0.261515 0.965199i \(-0.584222\pi\)
−0.261515 + 0.965199i \(0.584222\pi\)
\(878\) 0 0
\(879\) −2.74456 −0.0925718
\(880\) 0 0
\(881\) −21.7228 −0.731860 −0.365930 0.930642i \(-0.619249\pi\)
−0.365930 + 0.930642i \(0.619249\pi\)
\(882\) 0 0
\(883\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(884\) 0 0
\(885\) 2.74456 0.0922575
\(886\) 0 0
\(887\) −52.6060 −1.76634 −0.883168 0.469057i \(-0.844594\pi\)
−0.883168 + 0.469057i \(0.844594\pi\)
\(888\) 0 0
\(889\) 69.9565 2.34627
\(890\) 0 0
\(891\) 4.37228 0.146477
\(892\) 0 0
\(893\) −5.48913 −0.183687
\(894\) 0 0
\(895\) −3.25544 −0.108817
\(896\) 0 0
\(897\) 2.37228 0.0792082
\(898\) 0 0
\(899\) −18.5109 −0.617372
\(900\) 0 0
\(901\) −2.83966 −0.0946027
\(902\) 0 0
\(903\) −20.7446 −0.690336
\(904\) 0 0
\(905\) 5.11684 0.170090
\(906\) 0 0
\(907\) 11.2554 0.373731 0.186865 0.982386i \(-0.440167\pi\)
0.186865 + 0.982386i \(0.440167\pi\)
\(908\) 0 0
\(909\) −5.25544 −0.174312
\(910\) 0 0
\(911\) −27.7228 −0.918498 −0.459249 0.888308i \(-0.651881\pi\)
−0.459249 + 0.888308i \(0.651881\pi\)
\(912\) 0 0
\(913\) −64.4674 −2.13356
\(914\) 0 0
\(915\) 9.11684 0.301394
\(916\) 0 0
\(917\) −52.4674 −1.73263
\(918\) 0 0
\(919\) −3.11684 −0.102815 −0.0514076 0.998678i \(-0.516371\pi\)
−0.0514076 + 0.998678i \(0.516371\pi\)
\(920\) 0 0
\(921\) 9.11684 0.300410
\(922\) 0 0
\(923\) −4.37228 −0.143915
\(924\) 0 0
\(925\) 4.37228 0.143760
\(926\) 0 0
\(927\) −8.00000 −0.262754
\(928\) 0 0
\(929\) 47.3505 1.55352 0.776760 0.629796i \(-0.216862\pi\)
0.776760 + 0.629796i \(0.216862\pi\)
\(930\) 0 0
\(931\) −24.2337 −0.794227
\(932\) 0 0
\(933\) −31.7228 −1.03856
\(934\) 0 0
\(935\) −1.62772 −0.0532321
\(936\) 0 0
\(937\) −17.2554 −0.563711 −0.281855 0.959457i \(-0.590950\pi\)
−0.281855 + 0.959457i \(0.590950\pi\)
\(938\) 0 0
\(939\) −28.9783 −0.945669
\(940\) 0 0
\(941\) 9.39403 0.306237 0.153118 0.988208i \(-0.451068\pi\)
0.153118 + 0.988208i \(0.451068\pi\)
\(942\) 0 0
\(943\) 0.883156 0.0287595
\(944\) 0 0
\(945\) 4.37228 0.142230
\(946\) 0 0
\(947\) −53.7228 −1.74576 −0.872878 0.487938i \(-0.837749\pi\)
−0.872878 + 0.487938i \(0.837749\pi\)
\(948\) 0 0
\(949\) 6.00000 0.194768
\(950\) 0 0
\(951\) −6.00000 −0.194563
\(952\) 0 0
\(953\) 58.3288 1.88945 0.944727 0.327857i \(-0.106326\pi\)
0.944727 + 0.327857i \(0.106326\pi\)
\(954\) 0 0
\(955\) −8.74456 −0.282967
\(956\) 0 0
\(957\) −12.0000 −0.387905
\(958\) 0 0
\(959\) 32.7446 1.05738
\(960\) 0 0
\(961\) 14.4891 0.467391
\(962\) 0 0
\(963\) 1.62772 0.0524525
\(964\) 0 0
\(965\) 21.1168 0.679775
\(966\) 0 0
\(967\) −17.2554 −0.554897 −0.277449 0.960740i \(-0.589489\pi\)
−0.277449 + 0.960740i \(0.589489\pi\)
\(968\) 0 0
\(969\) −0.744563 −0.0239188
\(970\) 0 0
\(971\) −29.2119 −0.937456 −0.468728 0.883343i \(-0.655288\pi\)
−0.468728 + 0.883343i \(0.655288\pi\)
\(972\) 0 0
\(973\) −13.6277 −0.436885
\(974\) 0 0
\(975\) −1.00000 −0.0320256
\(976\) 0 0
\(977\) −22.0000 −0.703842 −0.351921 0.936030i \(-0.614471\pi\)
−0.351921 + 0.936030i \(0.614471\pi\)
\(978\) 0 0
\(979\) −57.3505 −1.83293
\(980\) 0 0
\(981\) −9.25544 −0.295503
\(982\) 0 0
\(983\) 52.2337 1.66600 0.832998 0.553276i \(-0.186623\pi\)
0.832998 + 0.553276i \(0.186623\pi\)
\(984\) 0 0
\(985\) −3.48913 −0.111173
\(986\) 0 0
\(987\) −12.0000 −0.381964
\(988\) 0 0
\(989\) −11.2554 −0.357902
\(990\) 0 0
\(991\) −39.8614 −1.26624 −0.633120 0.774054i \(-0.718226\pi\)
−0.633120 + 0.774054i \(0.718226\pi\)
\(992\) 0 0
\(993\) 22.0000 0.698149
\(994\) 0 0
\(995\) −8.00000 −0.253617
\(996\) 0 0
\(997\) 53.7228 1.70142 0.850709 0.525636i \(-0.176173\pi\)
0.850709 + 0.525636i \(0.176173\pi\)
\(998\) 0 0
\(999\) 4.37228 0.138333
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.bo.1.1 yes 2
4.3 odd 2 6240.2.a.bk.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6240.2.a.bk.1.2 2 4.3 odd 2
6240.2.a.bo.1.1 yes 2 1.1 even 1 trivial