Properties

Label 4560.2.a.bp.1.1
Level $4560$
Weight $2$
Character 4560.1
Self dual yes
Analytic conductor $36.412$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 4560 = 2^{4} \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4560.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(36.4117833217\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{7}) \)
Defining polynomial: \(x^{2} - 7\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 2280)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-2.64575\) of defining polynomial
Character \(\chi\) \(=\) 4560.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{3} +1.00000 q^{5} -1.64575 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{3} +1.00000 q^{5} -1.64575 q^{7} +1.00000 q^{9} +0.354249 q^{11} +3.64575 q^{13} +1.00000 q^{15} +1.00000 q^{19} -1.64575 q^{21} -2.00000 q^{23} +1.00000 q^{25} +1.00000 q^{27} +9.64575 q^{29} +2.00000 q^{31} +0.354249 q^{33} -1.64575 q^{35} -6.93725 q^{37} +3.64575 q^{39} +1.64575 q^{41} +4.93725 q^{43} +1.00000 q^{45} -6.00000 q^{47} -4.29150 q^{49} +4.00000 q^{53} +0.354249 q^{55} +1.00000 q^{57} -3.29150 q^{59} +11.2915 q^{61} -1.64575 q^{63} +3.64575 q^{65} -4.00000 q^{67} -2.00000 q^{69} +3.29150 q^{71} -2.00000 q^{73} +1.00000 q^{75} -0.583005 q^{77} +8.00000 q^{79} +1.00000 q^{81} +15.8745 q^{83} +9.64575 q^{87} -12.2288 q^{89} -6.00000 q^{91} +2.00000 q^{93} +1.00000 q^{95} +18.2288 q^{97} +0.354249 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{3} + 2 q^{5} + 2 q^{7} + 2 q^{9} + O(q^{10}) \) \( 2 q + 2 q^{3} + 2 q^{5} + 2 q^{7} + 2 q^{9} + 6 q^{11} + 2 q^{13} + 2 q^{15} + 2 q^{19} + 2 q^{21} - 4 q^{23} + 2 q^{25} + 2 q^{27} + 14 q^{29} + 4 q^{31} + 6 q^{33} + 2 q^{35} + 2 q^{37} + 2 q^{39} - 2 q^{41} - 6 q^{43} + 2 q^{45} - 12 q^{47} + 2 q^{49} + 8 q^{53} + 6 q^{55} + 2 q^{57} + 4 q^{59} + 12 q^{61} + 2 q^{63} + 2 q^{65} - 8 q^{67} - 4 q^{69} - 4 q^{71} - 4 q^{73} + 2 q^{75} + 20 q^{77} + 16 q^{79} + 2 q^{81} + 14 q^{87} + 2 q^{89} - 12 q^{91} + 4 q^{93} + 2 q^{95} + 10 q^{97} + 6 q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.00000 0.577350
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) −1.64575 −0.622036 −0.311018 0.950404i \(-0.600670\pi\)
−0.311018 + 0.950404i \(0.600670\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 0.354249 0.106810 0.0534050 0.998573i \(-0.482993\pi\)
0.0534050 + 0.998573i \(0.482993\pi\)
\(12\) 0 0
\(13\) 3.64575 1.01115 0.505575 0.862783i \(-0.331280\pi\)
0.505575 + 0.862783i \(0.331280\pi\)
\(14\) 0 0
\(15\) 1.00000 0.258199
\(16\) 0 0
\(17\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) −1.64575 −0.359132
\(22\) 0 0
\(23\) −2.00000 −0.417029 −0.208514 0.978019i \(-0.566863\pi\)
−0.208514 + 0.978019i \(0.566863\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 9.64575 1.79117 0.895586 0.444889i \(-0.146757\pi\)
0.895586 + 0.444889i \(0.146757\pi\)
\(30\) 0 0
\(31\) 2.00000 0.359211 0.179605 0.983739i \(-0.442518\pi\)
0.179605 + 0.983739i \(0.442518\pi\)
\(32\) 0 0
\(33\) 0.354249 0.0616668
\(34\) 0 0
\(35\) −1.64575 −0.278183
\(36\) 0 0
\(37\) −6.93725 −1.14048 −0.570239 0.821479i \(-0.693149\pi\)
−0.570239 + 0.821479i \(0.693149\pi\)
\(38\) 0 0
\(39\) 3.64575 0.583787
\(40\) 0 0
\(41\) 1.64575 0.257023 0.128512 0.991708i \(-0.458980\pi\)
0.128512 + 0.991708i \(0.458980\pi\)
\(42\) 0 0
\(43\) 4.93725 0.752924 0.376462 0.926432i \(-0.377141\pi\)
0.376462 + 0.926432i \(0.377141\pi\)
\(44\) 0 0
\(45\) 1.00000 0.149071
\(46\) 0 0
\(47\) −6.00000 −0.875190 −0.437595 0.899172i \(-0.644170\pi\)
−0.437595 + 0.899172i \(0.644170\pi\)
\(48\) 0 0
\(49\) −4.29150 −0.613072
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 4.00000 0.549442 0.274721 0.961524i \(-0.411414\pi\)
0.274721 + 0.961524i \(0.411414\pi\)
\(54\) 0 0
\(55\) 0.354249 0.0477669
\(56\) 0 0
\(57\) 1.00000 0.132453
\(58\) 0 0
\(59\) −3.29150 −0.428517 −0.214259 0.976777i \(-0.568734\pi\)
−0.214259 + 0.976777i \(0.568734\pi\)
\(60\) 0 0
\(61\) 11.2915 1.44573 0.722864 0.690990i \(-0.242825\pi\)
0.722864 + 0.690990i \(0.242825\pi\)
\(62\) 0 0
\(63\) −1.64575 −0.207345
\(64\) 0 0
\(65\) 3.64575 0.452200
\(66\) 0 0
\(67\) −4.00000 −0.488678 −0.244339 0.969690i \(-0.578571\pi\)
−0.244339 + 0.969690i \(0.578571\pi\)
\(68\) 0 0
\(69\) −2.00000 −0.240772
\(70\) 0 0
\(71\) 3.29150 0.390629 0.195315 0.980741i \(-0.437427\pi\)
0.195315 + 0.980741i \(0.437427\pi\)
\(72\) 0 0
\(73\) −2.00000 −0.234082 −0.117041 0.993127i \(-0.537341\pi\)
−0.117041 + 0.993127i \(0.537341\pi\)
\(74\) 0 0
\(75\) 1.00000 0.115470
\(76\) 0 0
\(77\) −0.583005 −0.0664396
\(78\) 0 0
\(79\) 8.00000 0.900070 0.450035 0.893011i \(-0.351411\pi\)
0.450035 + 0.893011i \(0.351411\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 15.8745 1.74245 0.871227 0.490881i \(-0.163325\pi\)
0.871227 + 0.490881i \(0.163325\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 9.64575 1.03413
\(88\) 0 0
\(89\) −12.2288 −1.29625 −0.648123 0.761536i \(-0.724446\pi\)
−0.648123 + 0.761536i \(0.724446\pi\)
\(90\) 0 0
\(91\) −6.00000 −0.628971
\(92\) 0 0
\(93\) 2.00000 0.207390
\(94\) 0 0
\(95\) 1.00000 0.102598
\(96\) 0 0
\(97\) 18.2288 1.85085 0.925425 0.378931i \(-0.123708\pi\)
0.925425 + 0.378931i \(0.123708\pi\)
\(98\) 0 0
\(99\) 0.354249 0.0356033
\(100\) 0 0
\(101\) 15.8745 1.57957 0.789786 0.613382i \(-0.210191\pi\)
0.789786 + 0.613382i \(0.210191\pi\)
\(102\) 0 0
\(103\) −14.5830 −1.43691 −0.718453 0.695575i \(-0.755150\pi\)
−0.718453 + 0.695575i \(0.755150\pi\)
\(104\) 0 0
\(105\) −1.64575 −0.160609
\(106\) 0 0
\(107\) −14.5830 −1.40979 −0.704896 0.709311i \(-0.749006\pi\)
−0.704896 + 0.709311i \(0.749006\pi\)
\(108\) 0 0
\(109\) 5.29150 0.506834 0.253417 0.967357i \(-0.418446\pi\)
0.253417 + 0.967357i \(0.418446\pi\)
\(110\) 0 0
\(111\) −6.93725 −0.658455
\(112\) 0 0
\(113\) 17.8745 1.68149 0.840746 0.541430i \(-0.182117\pi\)
0.840746 + 0.541430i \(0.182117\pi\)
\(114\) 0 0
\(115\) −2.00000 −0.186501
\(116\) 0 0
\(117\) 3.64575 0.337050
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −10.8745 −0.988592
\(122\) 0 0
\(123\) 1.64575 0.148392
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 2.58301 0.229205 0.114602 0.993411i \(-0.463441\pi\)
0.114602 + 0.993411i \(0.463441\pi\)
\(128\) 0 0
\(129\) 4.93725 0.434701
\(130\) 0 0
\(131\) −7.64575 −0.668012 −0.334006 0.942571i \(-0.608401\pi\)
−0.334006 + 0.942571i \(0.608401\pi\)
\(132\) 0 0
\(133\) −1.64575 −0.142705
\(134\) 0 0
\(135\) 1.00000 0.0860663
\(136\) 0 0
\(137\) −0.583005 −0.0498095 −0.0249047 0.999690i \(-0.507928\pi\)
−0.0249047 + 0.999690i \(0.507928\pi\)
\(138\) 0 0
\(139\) 17.8745 1.51610 0.758048 0.652199i \(-0.226153\pi\)
0.758048 + 0.652199i \(0.226153\pi\)
\(140\) 0 0
\(141\) −6.00000 −0.505291
\(142\) 0 0
\(143\) 1.29150 0.108001
\(144\) 0 0
\(145\) 9.64575 0.801036
\(146\) 0 0
\(147\) −4.29150 −0.353957
\(148\) 0 0
\(149\) 6.00000 0.491539 0.245770 0.969328i \(-0.420959\pi\)
0.245770 + 0.969328i \(0.420959\pi\)
\(150\) 0 0
\(151\) −6.00000 −0.488273 −0.244137 0.969741i \(-0.578505\pi\)
−0.244137 + 0.969741i \(0.578505\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 2.00000 0.160644
\(156\) 0 0
\(157\) 15.8745 1.26692 0.633462 0.773774i \(-0.281633\pi\)
0.633462 + 0.773774i \(0.281633\pi\)
\(158\) 0 0
\(159\) 4.00000 0.317221
\(160\) 0 0
\(161\) 3.29150 0.259407
\(162\) 0 0
\(163\) −9.64575 −0.755514 −0.377757 0.925905i \(-0.623304\pi\)
−0.377757 + 0.925905i \(0.623304\pi\)
\(164\) 0 0
\(165\) 0.354249 0.0275782
\(166\) 0 0
\(167\) 1.29150 0.0999395 0.0499697 0.998751i \(-0.484088\pi\)
0.0499697 + 0.998751i \(0.484088\pi\)
\(168\) 0 0
\(169\) 0.291503 0.0224233
\(170\) 0 0
\(171\) 1.00000 0.0764719
\(172\) 0 0
\(173\) 8.70850 0.662095 0.331047 0.943614i \(-0.392598\pi\)
0.331047 + 0.943614i \(0.392598\pi\)
\(174\) 0 0
\(175\) −1.64575 −0.124407
\(176\) 0 0
\(177\) −3.29150 −0.247404
\(178\) 0 0
\(179\) 7.29150 0.544992 0.272496 0.962157i \(-0.412151\pi\)
0.272496 + 0.962157i \(0.412151\pi\)
\(180\) 0 0
\(181\) −5.29150 −0.393314 −0.196657 0.980472i \(-0.563009\pi\)
−0.196657 + 0.980472i \(0.563009\pi\)
\(182\) 0 0
\(183\) 11.2915 0.834692
\(184\) 0 0
\(185\) −6.93725 −0.510037
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) −1.64575 −0.119711
\(190\) 0 0
\(191\) −10.9373 −0.791392 −0.395696 0.918382i \(-0.629497\pi\)
−0.395696 + 0.918382i \(0.629497\pi\)
\(192\) 0 0
\(193\) 2.93725 0.211428 0.105714 0.994397i \(-0.466287\pi\)
0.105714 + 0.994397i \(0.466287\pi\)
\(194\) 0 0
\(195\) 3.64575 0.261078
\(196\) 0 0
\(197\) 24.0000 1.70993 0.854965 0.518686i \(-0.173579\pi\)
0.854965 + 0.518686i \(0.173579\pi\)
\(198\) 0 0
\(199\) 23.2915 1.65109 0.825545 0.564336i \(-0.190868\pi\)
0.825545 + 0.564336i \(0.190868\pi\)
\(200\) 0 0
\(201\) −4.00000 −0.282138
\(202\) 0 0
\(203\) −15.8745 −1.11417
\(204\) 0 0
\(205\) 1.64575 0.114944
\(206\) 0 0
\(207\) −2.00000 −0.139010
\(208\) 0 0
\(209\) 0.354249 0.0245039
\(210\) 0 0
\(211\) 10.5830 0.728564 0.364282 0.931289i \(-0.381314\pi\)
0.364282 + 0.931289i \(0.381314\pi\)
\(212\) 0 0
\(213\) 3.29150 0.225530
\(214\) 0 0
\(215\) 4.93725 0.336718
\(216\) 0 0
\(217\) −3.29150 −0.223442
\(218\) 0 0
\(219\) −2.00000 −0.135147
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 1.41699 0.0948890 0.0474445 0.998874i \(-0.484892\pi\)
0.0474445 + 0.998874i \(0.484892\pi\)
\(224\) 0 0
\(225\) 1.00000 0.0666667
\(226\) 0 0
\(227\) −25.2915 −1.67866 −0.839328 0.543625i \(-0.817051\pi\)
−0.839328 + 0.543625i \(0.817051\pi\)
\(228\) 0 0
\(229\) 7.29150 0.481836 0.240918 0.970545i \(-0.422552\pi\)
0.240918 + 0.970545i \(0.422552\pi\)
\(230\) 0 0
\(231\) −0.583005 −0.0383589
\(232\) 0 0
\(233\) 22.0000 1.44127 0.720634 0.693316i \(-0.243851\pi\)
0.720634 + 0.693316i \(0.243851\pi\)
\(234\) 0 0
\(235\) −6.00000 −0.391397
\(236\) 0 0
\(237\) 8.00000 0.519656
\(238\) 0 0
\(239\) 13.0627 0.844959 0.422479 0.906373i \(-0.361160\pi\)
0.422479 + 0.906373i \(0.361160\pi\)
\(240\) 0 0
\(241\) −4.58301 −0.295217 −0.147609 0.989046i \(-0.547158\pi\)
−0.147609 + 0.989046i \(0.547158\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) −4.29150 −0.274174
\(246\) 0 0
\(247\) 3.64575 0.231974
\(248\) 0 0
\(249\) 15.8745 1.00601
\(250\) 0 0
\(251\) 6.22876 0.393156 0.196578 0.980488i \(-0.437017\pi\)
0.196578 + 0.980488i \(0.437017\pi\)
\(252\) 0 0
\(253\) −0.708497 −0.0445428
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −9.87451 −0.615955 −0.307977 0.951394i \(-0.599652\pi\)
−0.307977 + 0.951394i \(0.599652\pi\)
\(258\) 0 0
\(259\) 11.4170 0.709418
\(260\) 0 0
\(261\) 9.64575 0.597057
\(262\) 0 0
\(263\) 1.29150 0.0796375 0.0398187 0.999207i \(-0.487322\pi\)
0.0398187 + 0.999207i \(0.487322\pi\)
\(264\) 0 0
\(265\) 4.00000 0.245718
\(266\) 0 0
\(267\) −12.2288 −0.748388
\(268\) 0 0
\(269\) 4.93725 0.301030 0.150515 0.988608i \(-0.451907\pi\)
0.150515 + 0.988608i \(0.451907\pi\)
\(270\) 0 0
\(271\) −12.7085 −0.771986 −0.385993 0.922502i \(-0.626141\pi\)
−0.385993 + 0.922502i \(0.626141\pi\)
\(272\) 0 0
\(273\) −6.00000 −0.363137
\(274\) 0 0
\(275\) 0.354249 0.0213620
\(276\) 0 0
\(277\) −24.5830 −1.47705 −0.738525 0.674226i \(-0.764477\pi\)
−0.738525 + 0.674226i \(0.764477\pi\)
\(278\) 0 0
\(279\) 2.00000 0.119737
\(280\) 0 0
\(281\) −4.93725 −0.294532 −0.147266 0.989097i \(-0.547047\pi\)
−0.147266 + 0.989097i \(0.547047\pi\)
\(282\) 0 0
\(283\) 3.77124 0.224177 0.112089 0.993698i \(-0.464246\pi\)
0.112089 + 0.993698i \(0.464246\pi\)
\(284\) 0 0
\(285\) 1.00000 0.0592349
\(286\) 0 0
\(287\) −2.70850 −0.159878
\(288\) 0 0
\(289\) −17.0000 −1.00000
\(290\) 0 0
\(291\) 18.2288 1.06859
\(292\) 0 0
\(293\) −17.8745 −1.04424 −0.522120 0.852872i \(-0.674859\pi\)
−0.522120 + 0.852872i \(0.674859\pi\)
\(294\) 0 0
\(295\) −3.29150 −0.191639
\(296\) 0 0
\(297\) 0.354249 0.0205556
\(298\) 0 0
\(299\) −7.29150 −0.421678
\(300\) 0 0
\(301\) −8.12549 −0.468346
\(302\) 0 0
\(303\) 15.8745 0.911967
\(304\) 0 0
\(305\) 11.2915 0.646550
\(306\) 0 0
\(307\) −12.7085 −0.725312 −0.362656 0.931923i \(-0.618130\pi\)
−0.362656 + 0.931923i \(0.618130\pi\)
\(308\) 0 0
\(309\) −14.5830 −0.829598
\(310\) 0 0
\(311\) 4.35425 0.246907 0.123453 0.992350i \(-0.460603\pi\)
0.123453 + 0.992350i \(0.460603\pi\)
\(312\) 0 0
\(313\) −18.7085 −1.05747 −0.528733 0.848788i \(-0.677333\pi\)
−0.528733 + 0.848788i \(0.677333\pi\)
\(314\) 0 0
\(315\) −1.64575 −0.0927276
\(316\) 0 0
\(317\) 22.5830 1.26839 0.634194 0.773174i \(-0.281332\pi\)
0.634194 + 0.773174i \(0.281332\pi\)
\(318\) 0 0
\(319\) 3.41699 0.191315
\(320\) 0 0
\(321\) −14.5830 −0.813944
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) 3.64575 0.202230
\(326\) 0 0
\(327\) 5.29150 0.292621
\(328\) 0 0
\(329\) 9.87451 0.544399
\(330\) 0 0
\(331\) −16.5830 −0.911484 −0.455742 0.890112i \(-0.650626\pi\)
−0.455742 + 0.890112i \(0.650626\pi\)
\(332\) 0 0
\(333\) −6.93725 −0.380159
\(334\) 0 0
\(335\) −4.00000 −0.218543
\(336\) 0 0
\(337\) −22.2288 −1.21088 −0.605439 0.795892i \(-0.707002\pi\)
−0.605439 + 0.795892i \(0.707002\pi\)
\(338\) 0 0
\(339\) 17.8745 0.970810
\(340\) 0 0
\(341\) 0.708497 0.0383673
\(342\) 0 0
\(343\) 18.5830 1.00339
\(344\) 0 0
\(345\) −2.00000 −0.107676
\(346\) 0 0
\(347\) −9.29150 −0.498794 −0.249397 0.968401i \(-0.580232\pi\)
−0.249397 + 0.968401i \(0.580232\pi\)
\(348\) 0 0
\(349\) −27.1660 −1.45416 −0.727082 0.686551i \(-0.759124\pi\)
−0.727082 + 0.686551i \(0.759124\pi\)
\(350\) 0 0
\(351\) 3.64575 0.194596
\(352\) 0 0
\(353\) −35.1660 −1.87170 −0.935849 0.352401i \(-0.885365\pi\)
−0.935849 + 0.352401i \(0.885365\pi\)
\(354\) 0 0
\(355\) 3.29150 0.174695
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 10.2288 0.539853 0.269927 0.962881i \(-0.413001\pi\)
0.269927 + 0.962881i \(0.413001\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) −10.8745 −0.570764
\(364\) 0 0
\(365\) −2.00000 −0.104685
\(366\) 0 0
\(367\) −0.228757 −0.0119410 −0.00597050 0.999982i \(-0.501900\pi\)
−0.00597050 + 0.999982i \(0.501900\pi\)
\(368\) 0 0
\(369\) 1.64575 0.0856744
\(370\) 0 0
\(371\) −6.58301 −0.341773
\(372\) 0 0
\(373\) −8.35425 −0.432567 −0.216283 0.976331i \(-0.569393\pi\)
−0.216283 + 0.976331i \(0.569393\pi\)
\(374\) 0 0
\(375\) 1.00000 0.0516398
\(376\) 0 0
\(377\) 35.1660 1.81114
\(378\) 0 0
\(379\) −10.0000 −0.513665 −0.256833 0.966456i \(-0.582679\pi\)
−0.256833 + 0.966456i \(0.582679\pi\)
\(380\) 0 0
\(381\) 2.58301 0.132331
\(382\) 0 0
\(383\) 5.41699 0.276796 0.138398 0.990377i \(-0.455805\pi\)
0.138398 + 0.990377i \(0.455805\pi\)
\(384\) 0 0
\(385\) −0.583005 −0.0297127
\(386\) 0 0
\(387\) 4.93725 0.250975
\(388\) 0 0
\(389\) −6.00000 −0.304212 −0.152106 0.988364i \(-0.548606\pi\)
−0.152106 + 0.988364i \(0.548606\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) −7.64575 −0.385677
\(394\) 0 0
\(395\) 8.00000 0.402524
\(396\) 0 0
\(397\) −14.0000 −0.702640 −0.351320 0.936255i \(-0.614267\pi\)
−0.351320 + 0.936255i \(0.614267\pi\)
\(398\) 0 0
\(399\) −1.64575 −0.0823906
\(400\) 0 0
\(401\) 6.35425 0.317316 0.158658 0.987334i \(-0.449283\pi\)
0.158658 + 0.987334i \(0.449283\pi\)
\(402\) 0 0
\(403\) 7.29150 0.363216
\(404\) 0 0
\(405\) 1.00000 0.0496904
\(406\) 0 0
\(407\) −2.45751 −0.121814
\(408\) 0 0
\(409\) −6.70850 −0.331714 −0.165857 0.986150i \(-0.553039\pi\)
−0.165857 + 0.986150i \(0.553039\pi\)
\(410\) 0 0
\(411\) −0.583005 −0.0287575
\(412\) 0 0
\(413\) 5.41699 0.266553
\(414\) 0 0
\(415\) 15.8745 0.779249
\(416\) 0 0
\(417\) 17.8745 0.875318
\(418\) 0 0
\(419\) 38.9373 1.90221 0.951105 0.308869i \(-0.0999504\pi\)
0.951105 + 0.308869i \(0.0999504\pi\)
\(420\) 0 0
\(421\) −0.583005 −0.0284139 −0.0142070 0.999899i \(-0.504522\pi\)
−0.0142070 + 0.999899i \(0.504522\pi\)
\(422\) 0 0
\(423\) −6.00000 −0.291730
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −18.5830 −0.899295
\(428\) 0 0
\(429\) 1.29150 0.0623543
\(430\) 0 0
\(431\) 32.4575 1.56342 0.781712 0.623640i \(-0.214347\pi\)
0.781712 + 0.623640i \(0.214347\pi\)
\(432\) 0 0
\(433\) −26.2288 −1.26047 −0.630237 0.776403i \(-0.717042\pi\)
−0.630237 + 0.776403i \(0.717042\pi\)
\(434\) 0 0
\(435\) 9.64575 0.462478
\(436\) 0 0
\(437\) −2.00000 −0.0956730
\(438\) 0 0
\(439\) −5.16601 −0.246560 −0.123280 0.992372i \(-0.539341\pi\)
−0.123280 + 0.992372i \(0.539341\pi\)
\(440\) 0 0
\(441\) −4.29150 −0.204357
\(442\) 0 0
\(443\) −8.58301 −0.407791 −0.203895 0.978993i \(-0.565360\pi\)
−0.203895 + 0.978993i \(0.565360\pi\)
\(444\) 0 0
\(445\) −12.2288 −0.579699
\(446\) 0 0
\(447\) 6.00000 0.283790
\(448\) 0 0
\(449\) −2.35425 −0.111104 −0.0555519 0.998456i \(-0.517692\pi\)
−0.0555519 + 0.998456i \(0.517692\pi\)
\(450\) 0 0
\(451\) 0.583005 0.0274526
\(452\) 0 0
\(453\) −6.00000 −0.281905
\(454\) 0 0
\(455\) −6.00000 −0.281284
\(456\) 0 0
\(457\) 9.29150 0.434638 0.217319 0.976101i \(-0.430269\pi\)
0.217319 + 0.976101i \(0.430269\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −6.00000 −0.279448 −0.139724 0.990190i \(-0.544622\pi\)
−0.139724 + 0.990190i \(0.544622\pi\)
\(462\) 0 0
\(463\) 7.77124 0.361160 0.180580 0.983560i \(-0.442202\pi\)
0.180580 + 0.983560i \(0.442202\pi\)
\(464\) 0 0
\(465\) 2.00000 0.0927478
\(466\) 0 0
\(467\) 0.583005 0.0269783 0.0134891 0.999909i \(-0.495706\pi\)
0.0134891 + 0.999909i \(0.495706\pi\)
\(468\) 0 0
\(469\) 6.58301 0.303975
\(470\) 0 0
\(471\) 15.8745 0.731459
\(472\) 0 0
\(473\) 1.74902 0.0804198
\(474\) 0 0
\(475\) 1.00000 0.0458831
\(476\) 0 0
\(477\) 4.00000 0.183147
\(478\) 0 0
\(479\) 13.5203 0.617756 0.308878 0.951102i \(-0.400046\pi\)
0.308878 + 0.951102i \(0.400046\pi\)
\(480\) 0 0
\(481\) −25.2915 −1.15319
\(482\) 0 0
\(483\) 3.29150 0.149769
\(484\) 0 0
\(485\) 18.2288 0.827725
\(486\) 0 0
\(487\) −3.29150 −0.149152 −0.0745761 0.997215i \(-0.523760\pi\)
−0.0745761 + 0.997215i \(0.523760\pi\)
\(488\) 0 0
\(489\) −9.64575 −0.436196
\(490\) 0 0
\(491\) 32.8118 1.48077 0.740387 0.672181i \(-0.234642\pi\)
0.740387 + 0.672181i \(0.234642\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0.354249 0.0159223
\(496\) 0 0
\(497\) −5.41699 −0.242985
\(498\) 0 0
\(499\) −19.2915 −0.863606 −0.431803 0.901968i \(-0.642122\pi\)
−0.431803 + 0.901968i \(0.642122\pi\)
\(500\) 0 0
\(501\) 1.29150 0.0577001
\(502\) 0 0
\(503\) 1.29150 0.0575853 0.0287926 0.999585i \(-0.490834\pi\)
0.0287926 + 0.999585i \(0.490834\pi\)
\(504\) 0 0
\(505\) 15.8745 0.706406
\(506\) 0 0
\(507\) 0.291503 0.0129461
\(508\) 0 0
\(509\) 34.3542 1.52273 0.761363 0.648326i \(-0.224531\pi\)
0.761363 + 0.648326i \(0.224531\pi\)
\(510\) 0 0
\(511\) 3.29150 0.145608
\(512\) 0 0
\(513\) 1.00000 0.0441511
\(514\) 0 0
\(515\) −14.5830 −0.642604
\(516\) 0 0
\(517\) −2.12549 −0.0934790
\(518\) 0 0
\(519\) 8.70850 0.382261
\(520\) 0 0
\(521\) 26.8118 1.17464 0.587322 0.809353i \(-0.300182\pi\)
0.587322 + 0.809353i \(0.300182\pi\)
\(522\) 0 0
\(523\) −6.12549 −0.267849 −0.133925 0.990992i \(-0.542758\pi\)
−0.133925 + 0.990992i \(0.542758\pi\)
\(524\) 0 0
\(525\) −1.64575 −0.0718265
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −19.0000 −0.826087
\(530\) 0 0
\(531\) −3.29150 −0.142839
\(532\) 0 0
\(533\) 6.00000 0.259889
\(534\) 0 0
\(535\) −14.5830 −0.630478
\(536\) 0 0
\(537\) 7.29150 0.314652
\(538\) 0 0
\(539\) −1.52026 −0.0654822
\(540\) 0 0
\(541\) −26.0000 −1.11783 −0.558914 0.829226i \(-0.688782\pi\)
−0.558914 + 0.829226i \(0.688782\pi\)
\(542\) 0 0
\(543\) −5.29150 −0.227080
\(544\) 0 0
\(545\) 5.29150 0.226663
\(546\) 0 0
\(547\) 40.4575 1.72984 0.864919 0.501911i \(-0.167370\pi\)
0.864919 + 0.501911i \(0.167370\pi\)
\(548\) 0 0
\(549\) 11.2915 0.481910
\(550\) 0 0
\(551\) 9.64575 0.410923
\(552\) 0 0
\(553\) −13.1660 −0.559876
\(554\) 0 0
\(555\) −6.93725 −0.294470
\(556\) 0 0
\(557\) −10.0000 −0.423714 −0.211857 0.977301i \(-0.567951\pi\)
−0.211857 + 0.977301i \(0.567951\pi\)
\(558\) 0 0
\(559\) 18.0000 0.761319
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 3.87451 0.163291 0.0816455 0.996661i \(-0.473982\pi\)
0.0816455 + 0.996661i \(0.473982\pi\)
\(564\) 0 0
\(565\) 17.8745 0.751986
\(566\) 0 0
\(567\) −1.64575 −0.0691151
\(568\) 0 0
\(569\) 0.479741 0.0201118 0.0100559 0.999949i \(-0.496799\pi\)
0.0100559 + 0.999949i \(0.496799\pi\)
\(570\) 0 0
\(571\) −13.8745 −0.580630 −0.290315 0.956931i \(-0.593760\pi\)
−0.290315 + 0.956931i \(0.593760\pi\)
\(572\) 0 0
\(573\) −10.9373 −0.456910
\(574\) 0 0
\(575\) −2.00000 −0.0834058
\(576\) 0 0
\(577\) 27.8745 1.16043 0.580215 0.814463i \(-0.302968\pi\)
0.580215 + 0.814463i \(0.302968\pi\)
\(578\) 0 0
\(579\) 2.93725 0.122068
\(580\) 0 0
\(581\) −26.1255 −1.08387
\(582\) 0 0
\(583\) 1.41699 0.0586859
\(584\) 0 0
\(585\) 3.64575 0.150733
\(586\) 0 0
\(587\) −36.5830 −1.50994 −0.754971 0.655758i \(-0.772349\pi\)
−0.754971 + 0.655758i \(0.772349\pi\)
\(588\) 0 0
\(589\) 2.00000 0.0824086
\(590\) 0 0
\(591\) 24.0000 0.987228
\(592\) 0 0
\(593\) −15.4170 −0.633100 −0.316550 0.948576i \(-0.602525\pi\)
−0.316550 + 0.948576i \(0.602525\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 23.2915 0.953258
\(598\) 0 0
\(599\) 5.41699 0.221332 0.110666 0.993858i \(-0.464702\pi\)
0.110666 + 0.993858i \(0.464702\pi\)
\(600\) 0 0
\(601\) −15.8745 −0.647535 −0.323767 0.946137i \(-0.604950\pi\)
−0.323767 + 0.946137i \(0.604950\pi\)
\(602\) 0 0
\(603\) −4.00000 −0.162893
\(604\) 0 0
\(605\) −10.8745 −0.442112
\(606\) 0 0
\(607\) 12.4575 0.505635 0.252817 0.967514i \(-0.418643\pi\)
0.252817 + 0.967514i \(0.418643\pi\)
\(608\) 0 0
\(609\) −15.8745 −0.643268
\(610\) 0 0
\(611\) −21.8745 −0.884948
\(612\) 0 0
\(613\) −14.4575 −0.583933 −0.291967 0.956428i \(-0.594310\pi\)
−0.291967 + 0.956428i \(0.594310\pi\)
\(614\) 0 0
\(615\) 1.64575 0.0663631
\(616\) 0 0
\(617\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(618\) 0 0
\(619\) 37.8745 1.52231 0.761153 0.648573i \(-0.224634\pi\)
0.761153 + 0.648573i \(0.224634\pi\)
\(620\) 0 0
\(621\) −2.00000 −0.0802572
\(622\) 0 0
\(623\) 20.1255 0.806311
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0.354249 0.0141473
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) −37.1660 −1.47956 −0.739778 0.672851i \(-0.765069\pi\)
−0.739778 + 0.672851i \(0.765069\pi\)
\(632\) 0 0
\(633\) 10.5830 0.420637
\(634\) 0 0
\(635\) 2.58301 0.102503
\(636\) 0 0
\(637\) −15.6458 −0.619907
\(638\) 0 0
\(639\) 3.29150 0.130210
\(640\) 0 0
\(641\) −20.2288 −0.798988 −0.399494 0.916736i \(-0.630814\pi\)
−0.399494 + 0.916736i \(0.630814\pi\)
\(642\) 0 0
\(643\) −44.9373 −1.77215 −0.886076 0.463540i \(-0.846579\pi\)
−0.886076 + 0.463540i \(0.846579\pi\)
\(644\) 0 0
\(645\) 4.93725 0.194404
\(646\) 0 0
\(647\) 25.2915 0.994312 0.497156 0.867661i \(-0.334378\pi\)
0.497156 + 0.867661i \(0.334378\pi\)
\(648\) 0 0
\(649\) −1.16601 −0.0457699
\(650\) 0 0
\(651\) −3.29150 −0.129004
\(652\) 0 0
\(653\) −4.00000 −0.156532 −0.0782660 0.996933i \(-0.524938\pi\)
−0.0782660 + 0.996933i \(0.524938\pi\)
\(654\) 0 0
\(655\) −7.64575 −0.298744
\(656\) 0 0
\(657\) −2.00000 −0.0780274
\(658\) 0 0
\(659\) −13.1660 −0.512875 −0.256437 0.966561i \(-0.582549\pi\)
−0.256437 + 0.966561i \(0.582549\pi\)
\(660\) 0 0
\(661\) −5.29150 −0.205816 −0.102908 0.994691i \(-0.532815\pi\)
−0.102908 + 0.994691i \(0.532815\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −1.64575 −0.0638195
\(666\) 0 0
\(667\) −19.2915 −0.746970
\(668\) 0 0
\(669\) 1.41699 0.0547842
\(670\) 0 0
\(671\) 4.00000 0.154418
\(672\) 0 0
\(673\) 9.52026 0.366979 0.183490 0.983022i \(-0.441261\pi\)
0.183490 + 0.983022i \(0.441261\pi\)
\(674\) 0 0
\(675\) 1.00000 0.0384900
\(676\) 0 0
\(677\) −4.00000 −0.153732 −0.0768662 0.997041i \(-0.524491\pi\)
−0.0768662 + 0.997041i \(0.524491\pi\)
\(678\) 0 0
\(679\) −30.0000 −1.15129
\(680\) 0 0
\(681\) −25.2915 −0.969172
\(682\) 0 0
\(683\) −8.00000 −0.306111 −0.153056 0.988218i \(-0.548911\pi\)
−0.153056 + 0.988218i \(0.548911\pi\)
\(684\) 0 0
\(685\) −0.583005 −0.0222755
\(686\) 0 0
\(687\) 7.29150 0.278188
\(688\) 0 0
\(689\) 14.5830 0.555568
\(690\) 0 0
\(691\) −31.2915 −1.19038 −0.595192 0.803583i \(-0.702924\pi\)
−0.595192 + 0.803583i \(0.702924\pi\)
\(692\) 0 0
\(693\) −0.583005 −0.0221465
\(694\) 0 0
\(695\) 17.8745 0.678019
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 22.0000 0.832116
\(700\) 0 0
\(701\) −10.0000 −0.377695 −0.188847 0.982006i \(-0.560475\pi\)
−0.188847 + 0.982006i \(0.560475\pi\)
\(702\) 0 0
\(703\) −6.93725 −0.261643
\(704\) 0 0
\(705\) −6.00000 −0.225973
\(706\) 0 0
\(707\) −26.1255 −0.982550
\(708\) 0 0
\(709\) −32.4575 −1.21897 −0.609484 0.792799i \(-0.708623\pi\)
−0.609484 + 0.792799i \(0.708623\pi\)
\(710\) 0 0
\(711\) 8.00000 0.300023
\(712\) 0 0
\(713\) −4.00000 −0.149801
\(714\) 0 0
\(715\) 1.29150 0.0482995
\(716\) 0 0
\(717\) 13.0627 0.487837
\(718\) 0 0
\(719\) 7.64575 0.285138 0.142569 0.989785i \(-0.454464\pi\)
0.142569 + 0.989785i \(0.454464\pi\)
\(720\) 0 0
\(721\) 24.0000 0.893807
\(722\) 0 0
\(723\) −4.58301 −0.170444
\(724\) 0 0
\(725\) 9.64575 0.358234
\(726\) 0 0
\(727\) 39.9778 1.48269 0.741347 0.671122i \(-0.234187\pi\)
0.741347 + 0.671122i \(0.234187\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) −32.5830 −1.20348 −0.601740 0.798692i \(-0.705526\pi\)
−0.601740 + 0.798692i \(0.705526\pi\)
\(734\) 0 0
\(735\) −4.29150 −0.158294
\(736\) 0 0
\(737\) −1.41699 −0.0521957
\(738\) 0 0
\(739\) 10.5830 0.389302 0.194651 0.980873i \(-0.437643\pi\)
0.194651 + 0.980873i \(0.437643\pi\)
\(740\) 0 0
\(741\) 3.64575 0.133930
\(742\) 0 0
\(743\) 31.7490 1.16476 0.582379 0.812917i \(-0.302122\pi\)
0.582379 + 0.812917i \(0.302122\pi\)
\(744\) 0 0
\(745\) 6.00000 0.219823
\(746\) 0 0
\(747\) 15.8745 0.580818
\(748\) 0 0
\(749\) 24.0000 0.876941
\(750\) 0 0
\(751\) −36.3320 −1.32577 −0.662887 0.748719i \(-0.730669\pi\)
−0.662887 + 0.748719i \(0.730669\pi\)
\(752\) 0 0
\(753\) 6.22876 0.226989
\(754\) 0 0
\(755\) −6.00000 −0.218362
\(756\) 0 0
\(757\) −19.8745 −0.722351 −0.361176 0.932498i \(-0.617625\pi\)
−0.361176 + 0.932498i \(0.617625\pi\)
\(758\) 0 0
\(759\) −0.708497 −0.0257168
\(760\) 0 0
\(761\) −11.1660 −0.404768 −0.202384 0.979306i \(-0.564869\pi\)
−0.202384 + 0.979306i \(0.564869\pi\)
\(762\) 0 0
\(763\) −8.70850 −0.315269
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −12.0000 −0.433295
\(768\) 0 0
\(769\) 21.7490 0.784290 0.392145 0.919904i \(-0.371733\pi\)
0.392145 + 0.919904i \(0.371733\pi\)
\(770\) 0 0
\(771\) −9.87451 −0.355622
\(772\) 0 0
\(773\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(774\) 0 0
\(775\) 2.00000 0.0718421
\(776\) 0 0
\(777\) 11.4170 0.409582
\(778\) 0 0
\(779\) 1.64575 0.0589652
\(780\) 0 0
\(781\) 1.16601 0.0417231
\(782\) 0 0
\(783\) 9.64575 0.344711
\(784\) 0 0
\(785\) 15.8745 0.566585
\(786\) 0 0
\(787\) −11.2915 −0.402499 −0.201249 0.979540i \(-0.564500\pi\)
−0.201249 + 0.979540i \(0.564500\pi\)
\(788\) 0 0
\(789\) 1.29150 0.0459787
\(790\) 0 0
\(791\) −29.4170 −1.04595
\(792\) 0 0
\(793\) 41.1660 1.46185
\(794\) 0 0
\(795\) 4.00000 0.141865
\(796\) 0 0
\(797\) 39.2915 1.39178 0.695888 0.718150i \(-0.255011\pi\)
0.695888 + 0.718150i \(0.255011\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) −12.2288 −0.432082
\(802\) 0 0
\(803\) −0.708497 −0.0250023
\(804\) 0 0
\(805\) 3.29150 0.116010
\(806\) 0 0
\(807\) 4.93725 0.173800
\(808\) 0 0
\(809\) −8.58301 −0.301762 −0.150881 0.988552i \(-0.548211\pi\)
−0.150881 + 0.988552i \(0.548211\pi\)
\(810\) 0 0
\(811\) −5.41699 −0.190216 −0.0951082 0.995467i \(-0.530320\pi\)
−0.0951082 + 0.995467i \(0.530320\pi\)
\(812\) 0 0
\(813\) −12.7085 −0.445706
\(814\) 0 0
\(815\) −9.64575 −0.337876
\(816\) 0 0
\(817\) 4.93725 0.172733
\(818\) 0 0
\(819\) −6.00000 −0.209657
\(820\) 0 0
\(821\) 14.7085 0.513330 0.256665 0.966500i \(-0.417376\pi\)
0.256665 + 0.966500i \(0.417376\pi\)
\(822\) 0 0
\(823\) 43.2693 1.50827 0.754136 0.656718i \(-0.228056\pi\)
0.754136 + 0.656718i \(0.228056\pi\)
\(824\) 0 0
\(825\) 0.354249 0.0123334
\(826\) 0 0
\(827\) −22.7085 −0.789652 −0.394826 0.918756i \(-0.629195\pi\)
−0.394826 + 0.918756i \(0.629195\pi\)
\(828\) 0 0
\(829\) −27.8745 −0.968122 −0.484061 0.875034i \(-0.660839\pi\)
−0.484061 + 0.875034i \(0.660839\pi\)
\(830\) 0 0
\(831\) −24.5830 −0.852775
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 1.29150 0.0446943
\(836\) 0 0
\(837\) 2.00000 0.0691301
\(838\) 0 0
\(839\) 28.7085 0.991127 0.495564 0.868572i \(-0.334962\pi\)
0.495564 + 0.868572i \(0.334962\pi\)
\(840\) 0 0
\(841\) 64.0405 2.20829
\(842\) 0 0
\(843\) −4.93725 −0.170048
\(844\) 0 0
\(845\) 0.291503 0.0100280
\(846\) 0 0
\(847\) 17.8967 0.614939
\(848\) 0 0
\(849\) 3.77124 0.129429
\(850\) 0 0
\(851\) 13.8745 0.475612
\(852\) 0 0
\(853\) −45.2915 −1.55075 −0.775376 0.631500i \(-0.782440\pi\)
−0.775376 + 0.631500i \(0.782440\pi\)
\(854\) 0 0
\(855\) 1.00000 0.0341993
\(856\) 0 0
\(857\) −23.7490 −0.811251 −0.405625 0.914039i \(-0.632946\pi\)
−0.405625 + 0.914039i \(0.632946\pi\)
\(858\) 0 0
\(859\) −2.83399 −0.0966945 −0.0483472 0.998831i \(-0.515395\pi\)
−0.0483472 + 0.998831i \(0.515395\pi\)
\(860\) 0 0
\(861\) −2.70850 −0.0923053
\(862\) 0 0
\(863\) −1.16601 −0.0396915 −0.0198457 0.999803i \(-0.506318\pi\)
−0.0198457 + 0.999803i \(0.506318\pi\)
\(864\) 0 0
\(865\) 8.70850 0.296098
\(866\) 0 0
\(867\) −17.0000 −0.577350
\(868\) 0 0
\(869\) 2.83399 0.0961365
\(870\) 0 0
\(871\) −14.5830 −0.494126
\(872\) 0 0
\(873\) 18.2288 0.616950
\(874\) 0 0
\(875\) −1.64575 −0.0556365
\(876\) 0 0
\(877\) −16.8118 −0.567693 −0.283846 0.958870i \(-0.591611\pi\)
−0.283846 + 0.958870i \(0.591611\pi\)
\(878\) 0 0
\(879\) −17.8745 −0.602892
\(880\) 0 0
\(881\) −38.7085 −1.30412 −0.652061 0.758166i \(-0.726095\pi\)
−0.652061 + 0.758166i \(0.726095\pi\)
\(882\) 0 0
\(883\) −25.6458 −0.863048 −0.431524 0.902101i \(-0.642024\pi\)
−0.431524 + 0.902101i \(0.642024\pi\)
\(884\) 0 0
\(885\) −3.29150 −0.110643
\(886\) 0 0
\(887\) −43.7490 −1.46895 −0.734474 0.678637i \(-0.762571\pi\)
−0.734474 + 0.678637i \(0.762571\pi\)
\(888\) 0 0
\(889\) −4.25098 −0.142573
\(890\) 0 0
\(891\) 0.354249 0.0118678
\(892\) 0 0
\(893\) −6.00000 −0.200782
\(894\) 0 0
\(895\) 7.29150 0.243728
\(896\) 0 0
\(897\) −7.29150 −0.243456
\(898\) 0 0
\(899\) 19.2915 0.643408
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) −8.12549 −0.270399
\(904\) 0 0
\(905\) −5.29150 −0.175895
\(906\) 0 0
\(907\) −53.8745 −1.78887 −0.894437 0.447194i \(-0.852423\pi\)
−0.894437 + 0.447194i \(0.852423\pi\)
\(908\) 0 0
\(909\) 15.8745 0.526524
\(910\) 0 0
\(911\) −23.7490 −0.786840 −0.393420 0.919359i \(-0.628708\pi\)
−0.393420 + 0.919359i \(0.628708\pi\)
\(912\) 0 0
\(913\) 5.62352 0.186111
\(914\) 0 0
\(915\) 11.2915 0.373286
\(916\) 0 0
\(917\) 12.5830 0.415527
\(918\) 0 0
\(919\) −18.5830 −0.612997 −0.306498 0.951871i \(-0.599157\pi\)
−0.306498 + 0.951871i \(0.599157\pi\)
\(920\) 0 0
\(921\) −12.7085 −0.418759
\(922\) 0 0
\(923\) 12.0000 0.394985
\(924\) 0 0
\(925\) −6.93725 −0.228096
\(926\) 0 0
\(927\) −14.5830 −0.478969
\(928\) 0 0
\(929\) −15.8745 −0.520826 −0.260413 0.965497i \(-0.583859\pi\)
−0.260413 + 0.965497i \(0.583859\pi\)
\(930\) 0 0
\(931\) −4.29150 −0.140648
\(932\) 0 0
\(933\) 4.35425 0.142552
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 17.2915 0.564889 0.282444 0.959284i \(-0.408855\pi\)
0.282444 + 0.959284i \(0.408855\pi\)
\(938\) 0 0
\(939\) −18.7085 −0.610529
\(940\) 0 0
\(941\) −16.2288 −0.529042 −0.264521 0.964380i \(-0.585214\pi\)
−0.264521 + 0.964380i \(0.585214\pi\)
\(942\) 0 0
\(943\) −3.29150 −0.107186
\(944\) 0 0
\(945\) −1.64575 −0.0535363
\(946\) 0 0
\(947\) −26.7085 −0.867910 −0.433955 0.900935i \(-0.642882\pi\)
−0.433955 + 0.900935i \(0.642882\pi\)
\(948\) 0 0
\(949\) −7.29150 −0.236692
\(950\) 0 0
\(951\) 22.5830 0.732304
\(952\) 0 0
\(953\) −28.7085 −0.929959 −0.464980 0.885321i \(-0.653938\pi\)
−0.464980 + 0.885321i \(0.653938\pi\)
\(954\) 0 0
\(955\) −10.9373 −0.353921
\(956\) 0 0
\(957\) 3.41699 0.110456
\(958\) 0 0
\(959\) 0.959482 0.0309833
\(960\) 0 0
\(961\) −27.0000 −0.870968
\(962\) 0 0
\(963\) −14.5830 −0.469931
\(964\) 0 0
\(965\) 2.93725 0.0945535
\(966\) 0 0
\(967\) −51.5203 −1.65678 −0.828390 0.560152i \(-0.810743\pi\)
−0.828390 + 0.560152i \(0.810743\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 11.7490 0.377044 0.188522 0.982069i \(-0.439630\pi\)
0.188522 + 0.982069i \(0.439630\pi\)
\(972\) 0 0
\(973\) −29.4170 −0.943066
\(974\) 0 0
\(975\) 3.64575 0.116757
\(976\) 0 0
\(977\) −50.3320 −1.61026 −0.805132 0.593096i \(-0.797906\pi\)
−0.805132 + 0.593096i \(0.797906\pi\)
\(978\) 0 0
\(979\) −4.33202 −0.138452
\(980\) 0 0
\(981\) 5.29150 0.168945
\(982\) 0 0
\(983\) −33.2915 −1.06183 −0.530917 0.847424i \(-0.678152\pi\)
−0.530917 + 0.847424i \(0.678152\pi\)
\(984\) 0 0
\(985\) 24.0000 0.764704
\(986\) 0 0
\(987\) 9.87451 0.314309
\(988\) 0 0
\(989\) −9.87451 −0.313991
\(990\) 0 0
\(991\) 3.74902 0.119091 0.0595457 0.998226i \(-0.481035\pi\)
0.0595457 + 0.998226i \(0.481035\pi\)
\(992\) 0 0
\(993\) −16.5830 −0.526246
\(994\) 0 0
\(995\) 23.2915 0.738390
\(996\) 0 0
\(997\) −53.2915 −1.68776 −0.843879 0.536533i \(-0.819734\pi\)
−0.843879 + 0.536533i \(0.819734\pi\)
\(998\) 0 0
\(999\) −6.93725 −0.219485
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 4560.2.a.bp.1.1 2
4.3 odd 2 2280.2.a.n.1.2 2
12.11 even 2 6840.2.a.w.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2280.2.a.n.1.2 2 4.3 odd 2
4560.2.a.bp.1.1 2 1.1 even 1 trivial
6840.2.a.w.1.2 2 12.11 even 2