Properties

Label 5520.2.a.ca.1.3
Level $5520$
Weight $2$
Character 5520.1
Self dual yes
Analytic conductor $44.077$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 5520 = 2^{4} \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5520.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(44.0774219157\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.229.1
Defining polynomial: \( x^{3} - 4x - 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 2760)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(2.11491\) of defining polynomial
Character \(\chi\) \(=\) 5520.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{3} +1.00000 q^{5} +3.58774 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{3} +1.00000 q^{5} +3.58774 q^{7} +1.00000 q^{9} +0.715853 q^{13} -1.00000 q^{15} -1.58774 q^{17} -3.58774 q^{21} -1.00000 q^{23} +1.00000 q^{25} -1.00000 q^{27} +5.58774 q^{29} -4.87189 q^{31} +3.58774 q^{35} +8.15604 q^{37} -0.715853 q^{39} +4.30359 q^{41} -8.45963 q^{43} +1.00000 q^{45} +7.17548 q^{47} +5.87189 q^{49} +1.58774 q^{51} +8.30359 q^{53} +2.30359 q^{59} +6.45963 q^{61} +3.58774 q^{63} +0.715853 q^{65} +6.15604 q^{67} +1.00000 q^{69} +1.01945 q^{71} -5.17548 q^{73} -1.00000 q^{75} -9.89134 q^{79} +1.00000 q^{81} -5.01945 q^{83} -1.58774 q^{85} -5.58774 q^{87} +15.7438 q^{89} +2.56829 q^{91} +4.87189 q^{93} -6.45963 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - 3 q^{3} + 3 q^{5} - q^{7} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q - 3 q^{3} + 3 q^{5} - q^{7} + 3 q^{9} + 4 q^{13} - 3 q^{15} + 7 q^{17} + q^{21} - 3 q^{23} + 3 q^{25} - 3 q^{27} + 5 q^{29} - q^{31} - q^{35} + 9 q^{37} - 4 q^{39} + 3 q^{41} + 3 q^{45} - 2 q^{47} + 4 q^{49} - 7 q^{51} + 15 q^{53} - 3 q^{59} - 6 q^{61} - q^{63} + 4 q^{65} + 3 q^{67} + 3 q^{69} - 5 q^{71} + 8 q^{73} - 3 q^{75} - 8 q^{79} + 3 q^{81} - 7 q^{83} + 7 q^{85} - 5 q^{87} + 20 q^{89} + 4 q^{91} + q^{93} + 6 q^{97}+O(q^{100}) \) 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
\(7\) 3.58774 1.35604 0.678019 0.735044i \(-0.262839\pi\)
0.678019 + 0.735044i \(0.262839\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) 0 0
\(13\) 0.715853 0.198542 0.0992709 0.995060i \(-0.468349\pi\)
0.0992709 + 0.995060i \(0.468349\pi\)
\(14\) 0 0
\(15\) −1.00000 −0.258199
\(16\) 0 0
\(17\) −1.58774 −0.385084 −0.192542 0.981289i \(-0.561673\pi\)
−0.192542 + 0.981289i \(0.561673\pi\)
\(18\) 0 0
\(19\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(20\) 0 0
\(21\) −3.58774 −0.782909
\(22\) 0 0
\(23\) −1.00000 −0.208514
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 5.58774 1.03762 0.518809 0.854890i \(-0.326376\pi\)
0.518809 + 0.854890i \(0.326376\pi\)
\(30\) 0 0
\(31\) −4.87189 −0.875017 −0.437509 0.899214i \(-0.644139\pi\)
−0.437509 + 0.899214i \(0.644139\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 3.58774 0.606439
\(36\) 0 0
\(37\) 8.15604 1.34084 0.670422 0.741980i \(-0.266113\pi\)
0.670422 + 0.741980i \(0.266113\pi\)
\(38\) 0 0
\(39\) −0.715853 −0.114628
\(40\) 0 0
\(41\) 4.30359 0.672108 0.336054 0.941843i \(-0.390907\pi\)
0.336054 + 0.941843i \(0.390907\pi\)
\(42\) 0 0
\(43\) −8.45963 −1.29008 −0.645041 0.764148i \(-0.723160\pi\)
−0.645041 + 0.764148i \(0.723160\pi\)
\(44\) 0 0
\(45\) 1.00000 0.149071
\(46\) 0 0
\(47\) 7.17548 1.04665 0.523326 0.852133i \(-0.324691\pi\)
0.523326 + 0.852133i \(0.324691\pi\)
\(48\) 0 0
\(49\) 5.87189 0.838841
\(50\) 0 0
\(51\) 1.58774 0.222328
\(52\) 0 0
\(53\) 8.30359 1.14059 0.570293 0.821441i \(-0.306830\pi\)
0.570293 + 0.821441i \(0.306830\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 2.30359 0.299902 0.149951 0.988693i \(-0.452088\pi\)
0.149951 + 0.988693i \(0.452088\pi\)
\(60\) 0 0
\(61\) 6.45963 0.827071 0.413535 0.910488i \(-0.364294\pi\)
0.413535 + 0.910488i \(0.364294\pi\)
\(62\) 0 0
\(63\) 3.58774 0.452013
\(64\) 0 0
\(65\) 0.715853 0.0887906
\(66\) 0 0
\(67\) 6.15604 0.752079 0.376040 0.926604i \(-0.377286\pi\)
0.376040 + 0.926604i \(0.377286\pi\)
\(68\) 0 0
\(69\) 1.00000 0.120386
\(70\) 0 0
\(71\) 1.01945 0.120986 0.0604930 0.998169i \(-0.480733\pi\)
0.0604930 + 0.998169i \(0.480733\pi\)
\(72\) 0 0
\(73\) −5.17548 −0.605744 −0.302872 0.953031i \(-0.597946\pi\)
−0.302872 + 0.953031i \(0.597946\pi\)
\(74\) 0 0
\(75\) −1.00000 −0.115470
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −9.89134 −1.11286 −0.556431 0.830894i \(-0.687830\pi\)
−0.556431 + 0.830894i \(0.687830\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −5.01945 −0.550956 −0.275478 0.961307i \(-0.588836\pi\)
−0.275478 + 0.961307i \(0.588836\pi\)
\(84\) 0 0
\(85\) −1.58774 −0.172215
\(86\) 0 0
\(87\) −5.58774 −0.599069
\(88\) 0 0
\(89\) 15.7438 1.66884 0.834419 0.551131i \(-0.185804\pi\)
0.834419 + 0.551131i \(0.185804\pi\)
\(90\) 0 0
\(91\) 2.56829 0.269230
\(92\) 0 0
\(93\) 4.87189 0.505191
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −6.45963 −0.655876 −0.327938 0.944699i \(-0.606354\pi\)
−0.327938 + 0.944699i \(0.606354\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 5.58774 0.556001 0.278001 0.960581i \(-0.410328\pi\)
0.278001 + 0.960581i \(0.410328\pi\)
\(102\) 0 0
\(103\) −5.89134 −0.580491 −0.290245 0.956952i \(-0.593737\pi\)
−0.290245 + 0.956952i \(0.593737\pi\)
\(104\) 0 0
\(105\) −3.58774 −0.350128
\(106\) 0 0
\(107\) 0.412259 0.0398545 0.0199273 0.999801i \(-0.493657\pi\)
0.0199273 + 0.999801i \(0.493657\pi\)
\(108\) 0 0
\(109\) 2.14756 0.205699 0.102849 0.994697i \(-0.467204\pi\)
0.102849 + 0.994697i \(0.467204\pi\)
\(110\) 0 0
\(111\) −8.15604 −0.774137
\(112\) 0 0
\(113\) 0.980553 0.0922427 0.0461213 0.998936i \(-0.485314\pi\)
0.0461213 + 0.998936i \(0.485314\pi\)
\(114\) 0 0
\(115\) −1.00000 −0.0932505
\(116\) 0 0
\(117\) 0.715853 0.0661806
\(118\) 0 0
\(119\) −5.69641 −0.522189
\(120\) 0 0
\(121\) −11.0000 −1.00000
\(122\) 0 0
\(123\) −4.30359 −0.388042
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 2.71585 0.240993 0.120496 0.992714i \(-0.461551\pi\)
0.120496 + 0.992714i \(0.461551\pi\)
\(128\) 0 0
\(129\) 8.45963 0.744829
\(130\) 0 0
\(131\) 2.56829 0.224393 0.112196 0.993686i \(-0.464211\pi\)
0.112196 + 0.993686i \(0.464211\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −1.00000 −0.0860663
\(136\) 0 0
\(137\) −6.45963 −0.551883 −0.275942 0.961174i \(-0.588990\pi\)
−0.275942 + 0.961174i \(0.588990\pi\)
\(138\) 0 0
\(139\) −8.04737 −0.682569 −0.341285 0.939960i \(-0.610862\pi\)
−0.341285 + 0.939960i \(0.610862\pi\)
\(140\) 0 0
\(141\) −7.17548 −0.604285
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 5.58774 0.464037
\(146\) 0 0
\(147\) −5.87189 −0.484305
\(148\) 0 0
\(149\) 6.00000 0.491539 0.245770 0.969328i \(-0.420959\pi\)
0.245770 + 0.969328i \(0.420959\pi\)
\(150\) 0 0
\(151\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(152\) 0 0
\(153\) −1.58774 −0.128361
\(154\) 0 0
\(155\) −4.87189 −0.391320
\(156\) 0 0
\(157\) 12.7632 1.01862 0.509308 0.860584i \(-0.329901\pi\)
0.509308 + 0.860584i \(0.329901\pi\)
\(158\) 0 0
\(159\) −8.30359 −0.658518
\(160\) 0 0
\(161\) −3.58774 −0.282754
\(162\) 0 0
\(163\) 16.6072 1.30078 0.650388 0.759602i \(-0.274606\pi\)
0.650388 + 0.759602i \(0.274606\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 15.1755 1.17431 0.587157 0.809473i \(-0.300247\pi\)
0.587157 + 0.809473i \(0.300247\pi\)
\(168\) 0 0
\(169\) −12.4876 −0.960581
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 17.1755 1.30583 0.652914 0.757432i \(-0.273546\pi\)
0.652914 + 0.757432i \(0.273546\pi\)
\(174\) 0 0
\(175\) 3.58774 0.271208
\(176\) 0 0
\(177\) −2.30359 −0.173149
\(178\) 0 0
\(179\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(180\) 0 0
\(181\) −15.0668 −1.11991 −0.559954 0.828524i \(-0.689181\pi\)
−0.559954 + 0.828524i \(0.689181\pi\)
\(182\) 0 0
\(183\) −6.45963 −0.477510
\(184\) 0 0
\(185\) 8.15604 0.599644
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) −3.58774 −0.260970
\(190\) 0 0
\(191\) −4.60719 −0.333364 −0.166682 0.986011i \(-0.553305\pi\)
−0.166682 + 0.986011i \(0.553305\pi\)
\(192\) 0 0
\(193\) −10.6072 −0.763522 −0.381761 0.924261i \(-0.624682\pi\)
−0.381761 + 0.924261i \(0.624682\pi\)
\(194\) 0 0
\(195\) −0.715853 −0.0512633
\(196\) 0 0
\(197\) −9.78267 −0.696986 −0.348493 0.937311i \(-0.613307\pi\)
−0.348493 + 0.937311i \(0.613307\pi\)
\(198\) 0 0
\(199\) −2.71585 −0.192522 −0.0962608 0.995356i \(-0.530688\pi\)
−0.0962608 + 0.995356i \(0.530688\pi\)
\(200\) 0 0
\(201\) −6.15604 −0.434213
\(202\) 0 0
\(203\) 20.0474 1.40705
\(204\) 0 0
\(205\) 4.30359 0.300576
\(206\) 0 0
\(207\) −1.00000 −0.0695048
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 13.4791 0.927938 0.463969 0.885851i \(-0.346425\pi\)
0.463969 + 0.885851i \(0.346425\pi\)
\(212\) 0 0
\(213\) −1.01945 −0.0698514
\(214\) 0 0
\(215\) −8.45963 −0.576942
\(216\) 0 0
\(217\) −17.4791 −1.18656
\(218\) 0 0
\(219\) 5.17548 0.349727
\(220\) 0 0
\(221\) −1.13659 −0.0764553
\(222\) 0 0
\(223\) 8.14756 0.545601 0.272800 0.962071i \(-0.412050\pi\)
0.272800 + 0.962071i \(0.412050\pi\)
\(224\) 0 0
\(225\) 1.00000 0.0666667
\(226\) 0 0
\(227\) −18.8106 −1.24850 −0.624252 0.781223i \(-0.714596\pi\)
−0.624252 + 0.781223i \(0.714596\pi\)
\(228\) 0 0
\(229\) 26.7717 1.76912 0.884562 0.466423i \(-0.154457\pi\)
0.884562 + 0.466423i \(0.154457\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −3.74378 −0.245263 −0.122632 0.992452i \(-0.539133\pi\)
−0.122632 + 0.992452i \(0.539133\pi\)
\(234\) 0 0
\(235\) 7.17548 0.468077
\(236\) 0 0
\(237\) 9.89134 0.642511
\(238\) 0 0
\(239\) 19.6825 1.27315 0.636577 0.771213i \(-0.280350\pi\)
0.636577 + 0.771213i \(0.280350\pi\)
\(240\) 0 0
\(241\) −15.7438 −1.01415 −0.507073 0.861903i \(-0.669273\pi\)
−0.507073 + 0.861903i \(0.669273\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) 5.87189 0.375141
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 5.01945 0.318095
\(250\) 0 0
\(251\) −26.6630 −1.68296 −0.841478 0.540291i \(-0.818314\pi\)
−0.841478 + 0.540291i \(0.818314\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 1.58774 0.0994282
\(256\) 0 0
\(257\) −8.35097 −0.520919 −0.260459 0.965485i \(-0.583874\pi\)
−0.260459 + 0.965485i \(0.583874\pi\)
\(258\) 0 0
\(259\) 29.2617 1.81824
\(260\) 0 0
\(261\) 5.58774 0.345873
\(262\) 0 0
\(263\) 3.12811 0.192888 0.0964438 0.995338i \(-0.469253\pi\)
0.0964438 + 0.995338i \(0.469253\pi\)
\(264\) 0 0
\(265\) 8.30359 0.510086
\(266\) 0 0
\(267\) −15.7438 −0.963504
\(268\) 0 0
\(269\) 28.7632 1.75372 0.876862 0.480741i \(-0.159632\pi\)
0.876862 + 0.480741i \(0.159632\pi\)
\(270\) 0 0
\(271\) 15.4402 0.937924 0.468962 0.883218i \(-0.344628\pi\)
0.468962 + 0.883218i \(0.344628\pi\)
\(272\) 0 0
\(273\) −2.56829 −0.155440
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 22.2423 1.33641 0.668205 0.743977i \(-0.267063\pi\)
0.668205 + 0.743977i \(0.267063\pi\)
\(278\) 0 0
\(279\) −4.87189 −0.291672
\(280\) 0 0
\(281\) 30.0947 1.79530 0.897651 0.440707i \(-0.145272\pi\)
0.897651 + 0.440707i \(0.145272\pi\)
\(282\) 0 0
\(283\) 23.8998 1.42070 0.710348 0.703850i \(-0.248537\pi\)
0.710348 + 0.703850i \(0.248537\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 15.4402 0.911405
\(288\) 0 0
\(289\) −14.4791 −0.851710
\(290\) 0 0
\(291\) 6.45963 0.378670
\(292\) 0 0
\(293\) −10.6546 −0.622446 −0.311223 0.950337i \(-0.600739\pi\)
−0.311223 + 0.950337i \(0.600739\pi\)
\(294\) 0 0
\(295\) 2.30359 0.134120
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −0.715853 −0.0413988
\(300\) 0 0
\(301\) −30.3510 −1.74940
\(302\) 0 0
\(303\) −5.58774 −0.321007
\(304\) 0 0
\(305\) 6.45963 0.369877
\(306\) 0 0
\(307\) 6.56829 0.374872 0.187436 0.982277i \(-0.439982\pi\)
0.187436 + 0.982277i \(0.439982\pi\)
\(308\) 0 0
\(309\) 5.89134 0.335146
\(310\) 0 0
\(311\) −22.8106 −1.29347 −0.646735 0.762715i \(-0.723866\pi\)
−0.646735 + 0.762715i \(0.723866\pi\)
\(312\) 0 0
\(313\) 12.7632 0.721420 0.360710 0.932678i \(-0.382534\pi\)
0.360710 + 0.932678i \(0.382534\pi\)
\(314\) 0 0
\(315\) 3.58774 0.202146
\(316\) 0 0
\(317\) 19.2144 1.07919 0.539593 0.841926i \(-0.318578\pi\)
0.539593 + 0.841926i \(0.318578\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) −0.412259 −0.0230100
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) 0.715853 0.0397084
\(326\) 0 0
\(327\) −2.14756 −0.118760
\(328\) 0 0
\(329\) 25.7438 1.41930
\(330\) 0 0
\(331\) −15.2229 −0.836724 −0.418362 0.908280i \(-0.637396\pi\)
−0.418362 + 0.908280i \(0.637396\pi\)
\(332\) 0 0
\(333\) 8.15604 0.446948
\(334\) 0 0
\(335\) 6.15604 0.336340
\(336\) 0 0
\(337\) 14.2423 0.775828 0.387914 0.921696i \(-0.373196\pi\)
0.387914 + 0.921696i \(0.373196\pi\)
\(338\) 0 0
\(339\) −0.980553 −0.0532563
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −4.04737 −0.218538
\(344\) 0 0
\(345\) 1.00000 0.0538382
\(346\) 0 0
\(347\) 12.0000 0.644194 0.322097 0.946707i \(-0.395612\pi\)
0.322097 + 0.946707i \(0.395612\pi\)
\(348\) 0 0
\(349\) −11.4791 −0.614461 −0.307230 0.951635i \(-0.599402\pi\)
−0.307230 + 0.951635i \(0.599402\pi\)
\(350\) 0 0
\(351\) −0.715853 −0.0382094
\(352\) 0 0
\(353\) 17.7827 0.946476 0.473238 0.880935i \(-0.343085\pi\)
0.473238 + 0.880935i \(0.343085\pi\)
\(354\) 0 0
\(355\) 1.01945 0.0541066
\(356\) 0 0
\(357\) 5.69641 0.301486
\(358\) 0 0
\(359\) −20.6072 −1.08761 −0.543803 0.839213i \(-0.683016\pi\)
−0.543803 + 0.839213i \(0.683016\pi\)
\(360\) 0 0
\(361\) −19.0000 −1.00000
\(362\) 0 0
\(363\) 11.0000 0.577350
\(364\) 0 0
\(365\) −5.17548 −0.270897
\(366\) 0 0
\(367\) 10.7632 0.561836 0.280918 0.959732i \(-0.409361\pi\)
0.280918 + 0.959732i \(0.409361\pi\)
\(368\) 0 0
\(369\) 4.30359 0.224036
\(370\) 0 0
\(371\) 29.7911 1.54668
\(372\) 0 0
\(373\) −11.5962 −0.600429 −0.300215 0.953872i \(-0.597058\pi\)
−0.300215 + 0.953872i \(0.597058\pi\)
\(374\) 0 0
\(375\) −1.00000 −0.0516398
\(376\) 0 0
\(377\) 4.00000 0.206010
\(378\) 0 0
\(379\) −0.919260 −0.0472192 −0.0236096 0.999721i \(-0.507516\pi\)
−0.0236096 + 0.999721i \(0.507516\pi\)
\(380\) 0 0
\(381\) −2.71585 −0.139137
\(382\) 0 0
\(383\) 3.12811 0.159839 0.0799195 0.996801i \(-0.474534\pi\)
0.0799195 + 0.996801i \(0.474534\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −8.45963 −0.430027
\(388\) 0 0
\(389\) 11.4317 0.579610 0.289805 0.957086i \(-0.406409\pi\)
0.289805 + 0.957086i \(0.406409\pi\)
\(390\) 0 0
\(391\) 1.58774 0.0802955
\(392\) 0 0
\(393\) −2.56829 −0.129553
\(394\) 0 0
\(395\) −9.89134 −0.497687
\(396\) 0 0
\(397\) −2.14756 −0.107783 −0.0538914 0.998547i \(-0.517162\pi\)
−0.0538914 + 0.998547i \(0.517162\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −16.6461 −0.831266 −0.415633 0.909532i \(-0.636440\pi\)
−0.415633 + 0.909532i \(0.636440\pi\)
\(402\) 0 0
\(403\) −3.48755 −0.173727
\(404\) 0 0
\(405\) 1.00000 0.0496904
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 2.26470 0.111982 0.0559911 0.998431i \(-0.482168\pi\)
0.0559911 + 0.998431i \(0.482168\pi\)
\(410\) 0 0
\(411\) 6.45963 0.318630
\(412\) 0 0
\(413\) 8.26470 0.406679
\(414\) 0 0
\(415\) −5.01945 −0.246395
\(416\) 0 0
\(417\) 8.04737 0.394081
\(418\) 0 0
\(419\) 11.7827 0.575621 0.287811 0.957687i \(-0.407073\pi\)
0.287811 + 0.957687i \(0.407073\pi\)
\(420\) 0 0
\(421\) −20.4985 −0.999037 −0.499518 0.866303i \(-0.666490\pi\)
−0.499518 + 0.866303i \(0.666490\pi\)
\(422\) 0 0
\(423\) 7.17548 0.348884
\(424\) 0 0
\(425\) −1.58774 −0.0770168
\(426\) 0 0
\(427\) 23.1755 1.12154
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 16.9193 0.814972 0.407486 0.913211i \(-0.366406\pi\)
0.407486 + 0.913211i \(0.366406\pi\)
\(432\) 0 0
\(433\) 17.0753 0.820586 0.410293 0.911954i \(-0.365426\pi\)
0.410293 + 0.911954i \(0.365426\pi\)
\(434\) 0 0
\(435\) −5.58774 −0.267912
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 22.0558 1.05267 0.526334 0.850278i \(-0.323566\pi\)
0.526334 + 0.850278i \(0.323566\pi\)
\(440\) 0 0
\(441\) 5.87189 0.279614
\(442\) 0 0
\(443\) 12.8245 0.609311 0.304656 0.952463i \(-0.401459\pi\)
0.304656 + 0.952463i \(0.401459\pi\)
\(444\) 0 0
\(445\) 15.7438 0.746327
\(446\) 0 0
\(447\) −6.00000 −0.283790
\(448\) 0 0
\(449\) 10.5598 0.498349 0.249174 0.968459i \(-0.419841\pi\)
0.249174 + 0.968459i \(0.419841\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 2.56829 0.120404
\(456\) 0 0
\(457\) −6.72433 −0.314551 −0.157275 0.987555i \(-0.550271\pi\)
−0.157275 + 0.987555i \(0.550271\pi\)
\(458\) 0 0
\(459\) 1.58774 0.0741094
\(460\) 0 0
\(461\) 8.81060 0.410350 0.205175 0.978725i \(-0.434224\pi\)
0.205175 + 0.978725i \(0.434224\pi\)
\(462\) 0 0
\(463\) 14.1087 0.655685 0.327843 0.944732i \(-0.393678\pi\)
0.327843 + 0.944732i \(0.393678\pi\)
\(464\) 0 0
\(465\) 4.87189 0.225928
\(466\) 0 0
\(467\) 11.2757 0.521776 0.260888 0.965369i \(-0.415985\pi\)
0.260888 + 0.965369i \(0.415985\pi\)
\(468\) 0 0
\(469\) 22.0863 1.01985
\(470\) 0 0
\(471\) −12.7632 −0.588098
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 8.30359 0.380195
\(478\) 0 0
\(479\) 10.9582 0.500691 0.250345 0.968157i \(-0.419456\pi\)
0.250345 + 0.968157i \(0.419456\pi\)
\(480\) 0 0
\(481\) 5.83852 0.266214
\(482\) 0 0
\(483\) 3.58774 0.163248
\(484\) 0 0
\(485\) −6.45963 −0.293317
\(486\) 0 0
\(487\) −24.7717 −1.12251 −0.561256 0.827642i \(-0.689682\pi\)
−0.561256 + 0.827642i \(0.689682\pi\)
\(488\) 0 0
\(489\) −16.6072 −0.751003
\(490\) 0 0
\(491\) 0.559817 0.0252642 0.0126321 0.999920i \(-0.495979\pi\)
0.0126321 + 0.999920i \(0.495979\pi\)
\(492\) 0 0
\(493\) −8.87189 −0.399570
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 3.65751 0.164062
\(498\) 0 0
\(499\) −5.77419 −0.258488 −0.129244 0.991613i \(-0.541255\pi\)
−0.129244 + 0.991613i \(0.541255\pi\)
\(500\) 0 0
\(501\) −15.1755 −0.677991
\(502\) 0 0
\(503\) 5.69641 0.253990 0.126995 0.991903i \(-0.459467\pi\)
0.126995 + 0.991903i \(0.459467\pi\)
\(504\) 0 0
\(505\) 5.58774 0.248651
\(506\) 0 0
\(507\) 12.4876 0.554592
\(508\) 0 0
\(509\) −31.3789 −1.39084 −0.695422 0.718601i \(-0.744783\pi\)
−0.695422 + 0.718601i \(0.744783\pi\)
\(510\) 0 0
\(511\) −18.5683 −0.821413
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −5.89134 −0.259603
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) −17.1755 −0.753920
\(520\) 0 0
\(521\) 13.1755 0.577228 0.288614 0.957445i \(-0.406806\pi\)
0.288614 + 0.957445i \(0.406806\pi\)
\(522\) 0 0
\(523\) 24.4596 1.06954 0.534772 0.844996i \(-0.320397\pi\)
0.534772 + 0.844996i \(0.320397\pi\)
\(524\) 0 0
\(525\) −3.58774 −0.156582
\(526\) 0 0
\(527\) 7.73530 0.336955
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 2.30359 0.0999675
\(532\) 0 0
\(533\) 3.08074 0.133442
\(534\) 0 0
\(535\) 0.412259 0.0178235
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −27.8385 −1.19687 −0.598436 0.801171i \(-0.704211\pi\)
−0.598436 + 0.801171i \(0.704211\pi\)
\(542\) 0 0
\(543\) 15.0668 0.646579
\(544\) 0 0
\(545\) 2.14756 0.0919913
\(546\) 0 0
\(547\) −1.13659 −0.0485970 −0.0242985 0.999705i \(-0.507735\pi\)
−0.0242985 + 0.999705i \(0.507735\pi\)
\(548\) 0 0
\(549\) 6.45963 0.275690
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) −35.4876 −1.50908
\(554\) 0 0
\(555\) −8.15604 −0.346204
\(556\) 0 0
\(557\) −11.4791 −0.486384 −0.243192 0.969978i \(-0.578195\pi\)
−0.243192 + 0.969978i \(0.578195\pi\)
\(558\) 0 0
\(559\) −6.05585 −0.256135
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 31.5877 1.33126 0.665632 0.746280i \(-0.268162\pi\)
0.665632 + 0.746280i \(0.268162\pi\)
\(564\) 0 0
\(565\) 0.980553 0.0412522
\(566\) 0 0
\(567\) 3.58774 0.150671
\(568\) 0 0
\(569\) 13.0807 0.548373 0.274187 0.961677i \(-0.411591\pi\)
0.274187 + 0.961677i \(0.411591\pi\)
\(570\) 0 0
\(571\) 43.5823 1.82386 0.911931 0.410343i \(-0.134591\pi\)
0.911931 + 0.410343i \(0.134591\pi\)
\(572\) 0 0
\(573\) 4.60719 0.192468
\(574\) 0 0
\(575\) −1.00000 −0.0417029
\(576\) 0 0
\(577\) 7.52645 0.313330 0.156665 0.987652i \(-0.449926\pi\)
0.156665 + 0.987652i \(0.449926\pi\)
\(578\) 0 0
\(579\) 10.6072 0.440820
\(580\) 0 0
\(581\) −18.0085 −0.747118
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0.715853 0.0295969
\(586\) 0 0
\(587\) −6.95815 −0.287194 −0.143597 0.989636i \(-0.545867\pi\)
−0.143597 + 0.989636i \(0.545867\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 9.78267 0.402405
\(592\) 0 0
\(593\) 6.00000 0.246390 0.123195 0.992382i \(-0.460686\pi\)
0.123195 + 0.992382i \(0.460686\pi\)
\(594\) 0 0
\(595\) −5.69641 −0.233530
\(596\) 0 0
\(597\) 2.71585 0.111152
\(598\) 0 0
\(599\) −29.5962 −1.20927 −0.604634 0.796503i \(-0.706681\pi\)
−0.604634 + 0.796503i \(0.706681\pi\)
\(600\) 0 0
\(601\) −10.7771 −0.439609 −0.219804 0.975544i \(-0.570542\pi\)
−0.219804 + 0.975544i \(0.570542\pi\)
\(602\) 0 0
\(603\) 6.15604 0.250693
\(604\) 0 0
\(605\) −11.0000 −0.447214
\(606\) 0 0
\(607\) 5.28415 0.214477 0.107238 0.994233i \(-0.465799\pi\)
0.107238 + 0.994233i \(0.465799\pi\)
\(608\) 0 0
\(609\) −20.0474 −0.812360
\(610\) 0 0
\(611\) 5.13659 0.207804
\(612\) 0 0
\(613\) −33.9472 −1.37111 −0.685557 0.728019i \(-0.740441\pi\)
−0.685557 + 0.728019i \(0.740441\pi\)
\(614\) 0 0
\(615\) −4.30359 −0.173538
\(616\) 0 0
\(617\) 1.37041 0.0551707 0.0275854 0.999619i \(-0.491218\pi\)
0.0275854 + 0.999619i \(0.491218\pi\)
\(618\) 0 0
\(619\) −6.35097 −0.255267 −0.127633 0.991821i \(-0.540738\pi\)
−0.127633 + 0.991821i \(0.540738\pi\)
\(620\) 0 0
\(621\) 1.00000 0.0401286
\(622\) 0 0
\(623\) 56.4846 2.26301
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −12.9497 −0.516337
\(630\) 0 0
\(631\) −5.57926 −0.222107 −0.111053 0.993814i \(-0.535422\pi\)
−0.111053 + 0.993814i \(0.535422\pi\)
\(632\) 0 0
\(633\) −13.4791 −0.535745
\(634\) 0 0
\(635\) 2.71585 0.107775
\(636\) 0 0
\(637\) 4.20341 0.166545
\(638\) 0 0
\(639\) 1.01945 0.0403287
\(640\) 0 0
\(641\) −26.0947 −1.03068 −0.515340 0.856986i \(-0.672334\pi\)
−0.515340 + 0.856986i \(0.672334\pi\)
\(642\) 0 0
\(643\) 31.0753 1.22549 0.612745 0.790281i \(-0.290065\pi\)
0.612745 + 0.790281i \(0.290065\pi\)
\(644\) 0 0
\(645\) 8.45963 0.333098
\(646\) 0 0
\(647\) 2.86341 0.112572 0.0562862 0.998415i \(-0.482074\pi\)
0.0562862 + 0.998415i \(0.482074\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 17.4791 0.685059
\(652\) 0 0
\(653\) 15.2313 0.596048 0.298024 0.954558i \(-0.403672\pi\)
0.298024 + 0.954558i \(0.403672\pi\)
\(654\) 0 0
\(655\) 2.56829 0.100352
\(656\) 0 0
\(657\) −5.17548 −0.201915
\(658\) 0 0
\(659\) −20.7019 −0.806433 −0.403216 0.915105i \(-0.632108\pi\)
−0.403216 + 0.915105i \(0.632108\pi\)
\(660\) 0 0
\(661\) 33.9472 1.32039 0.660196 0.751093i \(-0.270473\pi\)
0.660196 + 0.751093i \(0.270473\pi\)
\(662\) 0 0
\(663\) 1.13659 0.0441415
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −5.58774 −0.216358
\(668\) 0 0
\(669\) −8.14756 −0.315003
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −44.0558 −1.69823 −0.849114 0.528209i \(-0.822864\pi\)
−0.849114 + 0.528209i \(0.822864\pi\)
\(674\) 0 0
\(675\) −1.00000 −0.0384900
\(676\) 0 0
\(677\) −28.0085 −1.07645 −0.538227 0.842800i \(-0.680906\pi\)
−0.538227 + 0.842800i \(0.680906\pi\)
\(678\) 0 0
\(679\) −23.1755 −0.889393
\(680\) 0 0
\(681\) 18.8106 0.720824
\(682\) 0 0
\(683\) 3.90526 0.149430 0.0747152 0.997205i \(-0.476195\pi\)
0.0747152 + 0.997205i \(0.476195\pi\)
\(684\) 0 0
\(685\) −6.45963 −0.246810
\(686\) 0 0
\(687\) −26.7717 −1.02140
\(688\) 0 0
\(689\) 5.94415 0.226454
\(690\) 0 0
\(691\) −48.4068 −1.84148 −0.920741 0.390174i \(-0.872415\pi\)
−0.920741 + 0.390174i \(0.872415\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −8.04737 −0.305254
\(696\) 0 0
\(697\) −6.83299 −0.258818
\(698\) 0 0
\(699\) 3.74378 0.141603
\(700\) 0 0
\(701\) −19.2144 −0.725717 −0.362858 0.931844i \(-0.618199\pi\)
−0.362858 + 0.931844i \(0.618199\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) −7.17548 −0.270244
\(706\) 0 0
\(707\) 20.0474 0.753959
\(708\) 0 0
\(709\) 14.4596 0.543043 0.271521 0.962432i \(-0.412473\pi\)
0.271521 + 0.962432i \(0.412473\pi\)
\(710\) 0 0
\(711\) −9.89134 −0.370954
\(712\) 0 0
\(713\) 4.87189 0.182454
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −19.6825 −0.735056
\(718\) 0 0
\(719\) −34.2338 −1.27671 −0.638353 0.769744i \(-0.720384\pi\)
−0.638353 + 0.769744i \(0.720384\pi\)
\(720\) 0 0
\(721\) −21.1366 −0.787168
\(722\) 0 0
\(723\) 15.7438 0.585517
\(724\) 0 0
\(725\) 5.58774 0.207524
\(726\) 0 0
\(727\) −22.4512 −0.832667 −0.416334 0.909212i \(-0.636685\pi\)
−0.416334 + 0.909212i \(0.636685\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 13.4317 0.496790
\(732\) 0 0
\(733\) −5.27567 −0.194861 −0.0974306 0.995242i \(-0.531062\pi\)
−0.0974306 + 0.995242i \(0.531062\pi\)
\(734\) 0 0
\(735\) −5.87189 −0.216588
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 3.34544 0.123064 0.0615320 0.998105i \(-0.480401\pi\)
0.0615320 + 0.998105i \(0.480401\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 13.1366 0.481935 0.240967 0.970533i \(-0.422535\pi\)
0.240967 + 0.970533i \(0.422535\pi\)
\(744\) 0 0
\(745\) 6.00000 0.219823
\(746\) 0 0
\(747\) −5.01945 −0.183652
\(748\) 0 0
\(749\) 1.47908 0.0540443
\(750\) 0 0
\(751\) −11.2453 −0.410345 −0.205173 0.978726i \(-0.565776\pi\)
−0.205173 + 0.978726i \(0.565776\pi\)
\(752\) 0 0
\(753\) 26.6630 0.971655
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −17.2926 −0.628511 −0.314256 0.949338i \(-0.601755\pi\)
−0.314256 + 0.949338i \(0.601755\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −11.6964 −0.423994 −0.211997 0.977270i \(-0.567997\pi\)
−0.211997 + 0.977270i \(0.567997\pi\)
\(762\) 0 0
\(763\) 7.70488 0.278936
\(764\) 0 0
\(765\) −1.58774 −0.0574049
\(766\) 0 0
\(767\) 1.64903 0.0595432
\(768\) 0 0
\(769\) −37.5653 −1.35464 −0.677320 0.735688i \(-0.736859\pi\)
−0.677320 + 0.735688i \(0.736859\pi\)
\(770\) 0 0
\(771\) 8.35097 0.300753
\(772\) 0 0
\(773\) 33.7827 1.21508 0.607539 0.794290i \(-0.292157\pi\)
0.607539 + 0.794290i \(0.292157\pi\)
\(774\) 0 0
\(775\) −4.87189 −0.175003
\(776\) 0 0
\(777\) −29.2617 −1.04976
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) −5.58774 −0.199690
\(784\) 0 0
\(785\) 12.7632 0.455539
\(786\) 0 0
\(787\) 38.6406 1.37739 0.688695 0.725051i \(-0.258184\pi\)
0.688695 + 0.725051i \(0.258184\pi\)
\(788\) 0 0
\(789\) −3.12811 −0.111364
\(790\) 0 0
\(791\) 3.51797 0.125085
\(792\) 0 0
\(793\) 4.62414 0.164208
\(794\) 0 0
\(795\) −8.30359 −0.294498
\(796\) 0 0
\(797\) −33.7353 −1.19497 −0.597483 0.801882i \(-0.703832\pi\)
−0.597483 + 0.801882i \(0.703832\pi\)
\(798\) 0 0
\(799\) −11.3928 −0.403049
\(800\) 0 0
\(801\) 15.7438 0.556279
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) −3.58774 −0.126451
\(806\) 0 0
\(807\) −28.7632 −1.01251
\(808\) 0 0
\(809\) 38.0474 1.33767 0.668837 0.743409i \(-0.266792\pi\)
0.668837 + 0.743409i \(0.266792\pi\)
\(810\) 0 0
\(811\) −24.1421 −0.847744 −0.423872 0.905722i \(-0.639329\pi\)
−0.423872 + 0.905722i \(0.639329\pi\)
\(812\) 0 0
\(813\) −15.4402 −0.541511
\(814\) 0 0
\(815\) 16.6072 0.581724
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 2.56829 0.0897435
\(820\) 0 0
\(821\) −4.18645 −0.146108 −0.0730541 0.997328i \(-0.523275\pi\)
−0.0730541 + 0.997328i \(0.523275\pi\)
\(822\) 0 0
\(823\) −9.59622 −0.334503 −0.167252 0.985914i \(-0.553489\pi\)
−0.167252 + 0.985914i \(0.553489\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 36.2897 1.26192 0.630958 0.775817i \(-0.282662\pi\)
0.630958 + 0.775817i \(0.282662\pi\)
\(828\) 0 0
\(829\) −49.9248 −1.73396 −0.866980 0.498343i \(-0.833942\pi\)
−0.866980 + 0.498343i \(0.833942\pi\)
\(830\) 0 0
\(831\) −22.2423 −0.771577
\(832\) 0 0
\(833\) −9.32304 −0.323024
\(834\) 0 0
\(835\) 15.1755 0.525169
\(836\) 0 0
\(837\) 4.87189 0.168397
\(838\) 0 0
\(839\) −49.3091 −1.70234 −0.851170 0.524890i \(-0.824106\pi\)
−0.851170 + 0.524890i \(0.824106\pi\)
\(840\) 0 0
\(841\) 2.22285 0.0766502
\(842\) 0 0
\(843\) −30.0947 −1.03652
\(844\) 0 0
\(845\) −12.4876 −0.429585
\(846\) 0 0
\(847\) −39.4652 −1.35604
\(848\) 0 0
\(849\) −23.8998 −0.820239
\(850\) 0 0
\(851\) −8.15604 −0.279585
\(852\) 0 0
\(853\) 28.2982 0.968910 0.484455 0.874816i \(-0.339018\pi\)
0.484455 + 0.874816i \(0.339018\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −20.8634 −0.712681 −0.356340 0.934356i \(-0.615976\pi\)
−0.356340 + 0.934356i \(0.615976\pi\)
\(858\) 0 0
\(859\) 5.77419 0.197013 0.0985065 0.995136i \(-0.468593\pi\)
0.0985065 + 0.995136i \(0.468593\pi\)
\(860\) 0 0
\(861\) −15.4402 −0.526200
\(862\) 0 0
\(863\) 12.6072 0.429154 0.214577 0.976707i \(-0.431163\pi\)
0.214577 + 0.976707i \(0.431163\pi\)
\(864\) 0 0
\(865\) 17.1755 0.583984
\(866\) 0 0
\(867\) 14.4791 0.491735
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 4.40682 0.149319
\(872\) 0 0
\(873\) −6.45963 −0.218625
\(874\) 0 0
\(875\) 3.58774 0.121288
\(876\) 0 0
\(877\) 2.16451 0.0730904 0.0365452 0.999332i \(-0.488365\pi\)
0.0365452 + 0.999332i \(0.488365\pi\)
\(878\) 0 0
\(879\) 10.6546 0.359369
\(880\) 0 0
\(881\) 32.4288 1.09255 0.546276 0.837605i \(-0.316045\pi\)
0.546276 + 0.837605i \(0.316045\pi\)
\(882\) 0 0
\(883\) 4.82452 0.162358 0.0811790 0.996700i \(-0.474131\pi\)
0.0811790 + 0.996700i \(0.474131\pi\)
\(884\) 0 0
\(885\) −2.30359 −0.0774345
\(886\) 0 0
\(887\) 47.7996 1.60495 0.802477 0.596683i \(-0.203515\pi\)
0.802477 + 0.596683i \(0.203515\pi\)
\(888\) 0 0
\(889\) 9.74378 0.326796
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0.715853 0.0239016
\(898\) 0 0
\(899\) −27.2229 −0.907933
\(900\) 0 0
\(901\) −13.1840 −0.439221
\(902\) 0 0
\(903\) 30.3510 1.01002
\(904\) 0 0
\(905\) −15.0668 −0.500838
\(906\) 0 0
\(907\) −21.6266 −0.718101 −0.359050 0.933318i \(-0.616899\pi\)
−0.359050 + 0.933318i \(0.616899\pi\)
\(908\) 0 0
\(909\) 5.58774 0.185334
\(910\) 0 0
\(911\) −46.3510 −1.53568 −0.767838 0.640644i \(-0.778667\pi\)
−0.767838 + 0.640644i \(0.778667\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) −6.45963 −0.213549
\(916\) 0 0
\(917\) 9.21438 0.304286
\(918\) 0 0
\(919\) −50.8106 −1.67609 −0.838043 0.545603i \(-0.816300\pi\)
−0.838043 + 0.545603i \(0.816300\pi\)
\(920\) 0 0
\(921\) −6.56829 −0.216433
\(922\) 0 0
\(923\) 0.729774 0.0240208
\(924\) 0 0
\(925\) 8.15604 0.268169
\(926\) 0 0
\(927\) −5.89134 −0.193497
\(928\) 0 0
\(929\) 8.91078 0.292353 0.146177 0.989259i \(-0.453303\pi\)
0.146177 + 0.989259i \(0.453303\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 22.8106 0.746785
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 3.81355 0.124583 0.0622916 0.998058i \(-0.480159\pi\)
0.0622916 + 0.998058i \(0.480159\pi\)
\(938\) 0 0
\(939\) −12.7632 −0.416512
\(940\) 0 0
\(941\) −37.4876 −1.22206 −0.611030 0.791608i \(-0.709244\pi\)
−0.611030 + 0.791608i \(0.709244\pi\)
\(942\) 0 0
\(943\) −4.30359 −0.140144
\(944\) 0 0
\(945\) −3.58774 −0.116709
\(946\) 0 0
\(947\) −34.6461 −1.12585 −0.562923 0.826509i \(-0.690323\pi\)
−0.562923 + 0.826509i \(0.690323\pi\)
\(948\) 0 0
\(949\) −3.70488 −0.120266
\(950\) 0 0
\(951\) −19.2144 −0.623069
\(952\) 0 0
\(953\) 13.3230 0.431576 0.215788 0.976440i \(-0.430768\pi\)
0.215788 + 0.976440i \(0.430768\pi\)
\(954\) 0 0
\(955\) −4.60719 −0.149085
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −23.1755 −0.748375
\(960\) 0 0
\(961\) −7.26470 −0.234345
\(962\) 0 0
\(963\) 0.412259 0.0132848
\(964\) 0 0
\(965\) −10.6072 −0.341457
\(966\) 0 0
\(967\) −22.9332 −0.737481 −0.368741 0.929532i \(-0.620211\pi\)
−0.368741 + 0.929532i \(0.620211\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −39.5653 −1.26971 −0.634856 0.772630i \(-0.718941\pi\)
−0.634856 + 0.772630i \(0.718941\pi\)
\(972\) 0 0
\(973\) −28.8719 −0.925590
\(974\) 0 0
\(975\) −0.715853 −0.0229256
\(976\) 0 0
\(977\) −47.1142 −1.50732 −0.753658 0.657267i \(-0.771713\pi\)
−0.753658 + 0.657267i \(0.771713\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 2.14756 0.0685663
\(982\) 0 0
\(983\) 47.3006 1.50866 0.754328 0.656498i \(-0.227963\pi\)
0.754328 + 0.656498i \(0.227963\pi\)
\(984\) 0 0
\(985\) −9.78267 −0.311702
\(986\) 0 0
\(987\) −25.7438 −0.819433
\(988\) 0 0
\(989\) 8.45963 0.269001
\(990\) 0 0
\(991\) 18.3983 0.584442 0.292221 0.956351i \(-0.405606\pi\)
0.292221 + 0.956351i \(0.405606\pi\)
\(992\) 0 0
\(993\) 15.2229 0.483083
\(994\) 0 0
\(995\) −2.71585 −0.0860983
\(996\) 0 0
\(997\) −17.4178 −0.551627 −0.275813 0.961211i \(-0.588947\pi\)
−0.275813 + 0.961211i \(0.588947\pi\)
\(998\) 0 0
\(999\) −8.15604 −0.258046
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 5520.2.a.ca.1.3 3
4.3 odd 2 2760.2.a.t.1.1 3
12.11 even 2 8280.2.a.bh.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2760.2.a.t.1.1 3 4.3 odd 2
5520.2.a.ca.1.3 3 1.1 even 1 trivial
8280.2.a.bh.1.1 3 12.11 even 2