Properties

Label 6084.2.a.y.1.2
Level $6084$
Weight $2$
Character 6084.1
Self dual yes
Analytic conductor $48.581$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [6084,2,Mod(1,6084)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6084, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("6084.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6084 = 2^{2} \cdot 3^{2} \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6084.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(48.5809845897\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: \(\Q(\zeta_{14})^+\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - x^{2} - 2x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 2028)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-1.24698\) of defining polynomial
Character \(\chi\) \(=\) 6084.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.554958 q^{5} +1.04892 q^{7} +2.91185 q^{11} -2.75302 q^{17} -4.63102 q^{19} +5.76271 q^{23} -4.69202 q^{25} +2.80194 q^{29} +4.18598 q^{31} -0.582105 q^{35} -0.466812 q^{37} -3.89977 q^{41} +9.19567 q^{43} +11.5211 q^{47} -5.89977 q^{49} -5.62565 q^{53} -1.61596 q^{55} +3.10992 q^{59} +10.9051 q^{61} -8.04892 q^{67} +13.6920 q^{71} -9.36658 q^{73} +3.05429 q^{77} -3.60925 q^{79} +1.65519 q^{83} +1.52781 q^{85} +17.9705 q^{89} +2.57002 q^{95} +1.31767 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - 2 q^{5} - 6 q^{7} + 5 q^{11} - 13 q^{17} + q^{19} - 9 q^{25} + 4 q^{29} - 2 q^{31} + 4 q^{35} + 2 q^{37} + 11 q^{41} - 9 q^{43} + 19 q^{47} + 5 q^{49} - 5 q^{53} - 15 q^{55} + 10 q^{59} + 7 q^{61}+ \cdots - 13 q^{97}+O(q^{100}) \) 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
\(3\) 0 0
\(4\) 0 0
\(5\) −0.554958 −0.248185 −0.124092 0.992271i \(-0.539602\pi\)
−0.124092 + 0.992271i \(0.539602\pi\)
\(6\) 0 0
\(7\) 1.04892 0.396453 0.198227 0.980156i \(-0.436482\pi\)
0.198227 + 0.980156i \(0.436482\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 2.91185 0.877957 0.438979 0.898498i \(-0.355340\pi\)
0.438979 + 0.898498i \(0.355340\pi\)
\(12\) 0 0
\(13\) 0 0
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −2.75302 −0.667706 −0.333853 0.942625i \(-0.608349\pi\)
−0.333853 + 0.942625i \(0.608349\pi\)
\(18\) 0 0
\(19\) −4.63102 −1.06243 −0.531215 0.847237i \(-0.678264\pi\)
−0.531215 + 0.847237i \(0.678264\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 5.76271 1.20161 0.600804 0.799396i \(-0.294847\pi\)
0.600804 + 0.799396i \(0.294847\pi\)
\(24\) 0 0
\(25\) −4.69202 −0.938404
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 2.80194 0.520307 0.260153 0.965567i \(-0.416227\pi\)
0.260153 + 0.965567i \(0.416227\pi\)
\(30\) 0 0
\(31\) 4.18598 0.751824 0.375912 0.926655i \(-0.377329\pi\)
0.375912 + 0.926655i \(0.377329\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −0.582105 −0.0983937
\(36\) 0 0
\(37\) −0.466812 −0.0767434 −0.0383717 0.999264i \(-0.512217\pi\)
−0.0383717 + 0.999264i \(0.512217\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −3.89977 −0.609042 −0.304521 0.952506i \(-0.598496\pi\)
−0.304521 + 0.952506i \(0.598496\pi\)
\(42\) 0 0
\(43\) 9.19567 1.40233 0.701163 0.713001i \(-0.252664\pi\)
0.701163 + 0.713001i \(0.252664\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 11.5211 1.68053 0.840263 0.542179i \(-0.182401\pi\)
0.840263 + 0.542179i \(0.182401\pi\)
\(48\) 0 0
\(49\) −5.89977 −0.842825
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −5.62565 −0.772742 −0.386371 0.922343i \(-0.626272\pi\)
−0.386371 + 0.922343i \(0.626272\pi\)
\(54\) 0 0
\(55\) −1.61596 −0.217896
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 3.10992 0.404877 0.202438 0.979295i \(-0.435113\pi\)
0.202438 + 0.979295i \(0.435113\pi\)
\(60\) 0 0
\(61\) 10.9051 1.39626 0.698131 0.715970i \(-0.254015\pi\)
0.698131 + 0.715970i \(0.254015\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −8.04892 −0.983332 −0.491666 0.870784i \(-0.663612\pi\)
−0.491666 + 0.870784i \(0.663612\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 13.6920 1.62494 0.812472 0.583000i \(-0.198121\pi\)
0.812472 + 0.583000i \(0.198121\pi\)
\(72\) 0 0
\(73\) −9.36658 −1.09628 −0.548138 0.836388i \(-0.684663\pi\)
−0.548138 + 0.836388i \(0.684663\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 3.05429 0.348069
\(78\) 0 0
\(79\) −3.60925 −0.406073 −0.203036 0.979171i \(-0.565081\pi\)
−0.203036 + 0.979171i \(0.565081\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 1.65519 0.181680 0.0908401 0.995865i \(-0.471045\pi\)
0.0908401 + 0.995865i \(0.471045\pi\)
\(84\) 0 0
\(85\) 1.52781 0.165714
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 17.9705 1.90486 0.952432 0.304750i \(-0.0985728\pi\)
0.952432 + 0.304750i \(0.0985728\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 2.57002 0.263679
\(96\) 0 0
\(97\) 1.31767 0.133789 0.0668944 0.997760i \(-0.478691\pi\)
0.0668944 + 0.997760i \(0.478691\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 15.0248 1.49502 0.747509 0.664251i \(-0.231249\pi\)
0.747509 + 0.664251i \(0.231249\pi\)
\(102\) 0 0
\(103\) −9.20775 −0.907267 −0.453633 0.891188i \(-0.649872\pi\)
−0.453633 + 0.891188i \(0.649872\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −7.22952 −0.698904 −0.349452 0.936954i \(-0.613632\pi\)
−0.349452 + 0.936954i \(0.613632\pi\)
\(108\) 0 0
\(109\) 15.5036 1.48498 0.742490 0.669857i \(-0.233645\pi\)
0.742490 + 0.669857i \(0.233645\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −13.8267 −1.30071 −0.650353 0.759632i \(-0.725379\pi\)
−0.650353 + 0.759632i \(0.725379\pi\)
\(114\) 0 0
\(115\) −3.19806 −0.298221
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −2.88769 −0.264714
\(120\) 0 0
\(121\) −2.52111 −0.229191
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 5.37867 0.481083
\(126\) 0 0
\(127\) 7.17629 0.636793 0.318396 0.947958i \(-0.396856\pi\)
0.318396 + 0.947958i \(0.396856\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −13.1304 −1.14720 −0.573602 0.819134i \(-0.694455\pi\)
−0.573602 + 0.819134i \(0.694455\pi\)
\(132\) 0 0
\(133\) −4.85756 −0.421204
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 21.8116 1.86349 0.931747 0.363109i \(-0.118285\pi\)
0.931747 + 0.363109i \(0.118285\pi\)
\(138\) 0 0
\(139\) −2.96615 −0.251585 −0.125793 0.992057i \(-0.540147\pi\)
−0.125793 + 0.992057i \(0.540147\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) −1.55496 −0.129132
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −5.69633 −0.466662 −0.233331 0.972397i \(-0.574963\pi\)
−0.233331 + 0.972397i \(0.574963\pi\)
\(150\) 0 0
\(151\) −19.1468 −1.55814 −0.779070 0.626937i \(-0.784309\pi\)
−0.779070 + 0.626937i \(0.784309\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −2.32304 −0.186591
\(156\) 0 0
\(157\) −8.38404 −0.669119 −0.334560 0.942375i \(-0.608588\pi\)
−0.334560 + 0.942375i \(0.608588\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 6.04461 0.476382
\(162\) 0 0
\(163\) 1.97046 0.154338 0.0771692 0.997018i \(-0.475412\pi\)
0.0771692 + 0.997018i \(0.475412\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 24.7995 1.91905 0.959523 0.281630i \(-0.0908749\pi\)
0.959523 + 0.281630i \(0.0908749\pi\)
\(168\) 0 0
\(169\) 0 0
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 2.57135 0.195496 0.0977481 0.995211i \(-0.468836\pi\)
0.0977481 + 0.995211i \(0.468836\pi\)
\(174\) 0 0
\(175\) −4.92154 −0.372034
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 3.00538 0.224632 0.112316 0.993673i \(-0.464173\pi\)
0.112316 + 0.993673i \(0.464173\pi\)
\(180\) 0 0
\(181\) −14.6843 −1.09147 −0.545736 0.837957i \(-0.683750\pi\)
−0.545736 + 0.837957i \(0.683750\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0.259061 0.0190466
\(186\) 0 0
\(187\) −8.01639 −0.586217
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 17.0804 1.23589 0.617946 0.786220i \(-0.287965\pi\)
0.617946 + 0.786220i \(0.287965\pi\)
\(192\) 0 0
\(193\) 14.9758 1.07798 0.538992 0.842311i \(-0.318805\pi\)
0.538992 + 0.842311i \(0.318805\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 0.192685 0.0137283 0.00686414 0.999976i \(-0.497815\pi\)
0.00686414 + 0.999976i \(0.497815\pi\)
\(198\) 0 0
\(199\) 11.8726 0.841628 0.420814 0.907147i \(-0.361744\pi\)
0.420814 + 0.907147i \(0.361744\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 2.93900 0.206277
\(204\) 0 0
\(205\) 2.16421 0.151155
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −13.4849 −0.932767
\(210\) 0 0
\(211\) 6.03385 0.415387 0.207694 0.978194i \(-0.433404\pi\)
0.207694 + 0.978194i \(0.433404\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −5.10321 −0.348036
\(216\) 0 0
\(217\) 4.39075 0.298063
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −8.52648 −0.570976 −0.285488 0.958382i \(-0.592156\pi\)
−0.285488 + 0.958382i \(0.592156\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 11.0000 0.730096 0.365048 0.930989i \(-0.381053\pi\)
0.365048 + 0.930989i \(0.381053\pi\)
\(228\) 0 0
\(229\) 17.9119 1.18365 0.591824 0.806067i \(-0.298408\pi\)
0.591824 + 0.806067i \(0.298408\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −22.8159 −1.49472 −0.747361 0.664418i \(-0.768679\pi\)
−0.747361 + 0.664418i \(0.768679\pi\)
\(234\) 0 0
\(235\) −6.39373 −0.417081
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 8.34481 0.539781 0.269891 0.962891i \(-0.413012\pi\)
0.269891 + 0.962891i \(0.413012\pi\)
\(240\) 0 0
\(241\) 3.75541 0.241907 0.120954 0.992658i \(-0.461405\pi\)
0.120954 + 0.992658i \(0.461405\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 3.27413 0.209176
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 30.3086 1.91306 0.956530 0.291634i \(-0.0941989\pi\)
0.956530 + 0.291634i \(0.0941989\pi\)
\(252\) 0 0
\(253\) 16.7802 1.05496
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 20.8412 1.30004 0.650018 0.759919i \(-0.274761\pi\)
0.650018 + 0.759919i \(0.274761\pi\)
\(258\) 0 0
\(259\) −0.489647 −0.0304252
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −8.58642 −0.529461 −0.264731 0.964322i \(-0.585283\pi\)
−0.264731 + 0.964322i \(0.585283\pi\)
\(264\) 0 0
\(265\) 3.12200 0.191783
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −14.8267 −0.903999 −0.452000 0.892018i \(-0.649289\pi\)
−0.452000 + 0.892018i \(0.649289\pi\)
\(270\) 0 0
\(271\) 7.23490 0.439489 0.219744 0.975557i \(-0.429478\pi\)
0.219744 + 0.975557i \(0.429478\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −13.6625 −0.823879
\(276\) 0 0
\(277\) 11.2054 0.673265 0.336632 0.941636i \(-0.390712\pi\)
0.336632 + 0.941636i \(0.390712\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −12.3002 −0.733769 −0.366884 0.930267i \(-0.619576\pi\)
−0.366884 + 0.930267i \(0.619576\pi\)
\(282\) 0 0
\(283\) 24.3521 1.44758 0.723791 0.690019i \(-0.242398\pi\)
0.723791 + 0.690019i \(0.242398\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −4.09054 −0.241457
\(288\) 0 0
\(289\) −9.42088 −0.554169
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 6.20237 0.362347 0.181173 0.983451i \(-0.442011\pi\)
0.181173 + 0.983451i \(0.442011\pi\)
\(294\) 0 0
\(295\) −1.72587 −0.100484
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 9.64550 0.555957
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −6.05190 −0.346531
\(306\) 0 0
\(307\) 26.4795 1.51126 0.755632 0.654996i \(-0.227330\pi\)
0.755632 + 0.654996i \(0.227330\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −15.5308 −0.880671 −0.440335 0.897833i \(-0.645140\pi\)
−0.440335 + 0.897833i \(0.645140\pi\)
\(312\) 0 0
\(313\) 16.9681 0.959092 0.479546 0.877517i \(-0.340801\pi\)
0.479546 + 0.877517i \(0.340801\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 25.5066 1.43260 0.716298 0.697795i \(-0.245835\pi\)
0.716298 + 0.697795i \(0.245835\pi\)
\(318\) 0 0
\(319\) 8.15883 0.456807
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 12.7493 0.709390
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 12.0847 0.666250
\(330\) 0 0
\(331\) −10.6136 −0.583374 −0.291687 0.956514i \(-0.594217\pi\)
−0.291687 + 0.956514i \(0.594217\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 4.46681 0.244048
\(336\) 0 0
\(337\) 29.2717 1.59453 0.797266 0.603628i \(-0.206279\pi\)
0.797266 + 0.603628i \(0.206279\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 12.1890 0.660069
\(342\) 0 0
\(343\) −13.5308 −0.730594
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 34.8146 1.86895 0.934473 0.356034i \(-0.115871\pi\)
0.934473 + 0.356034i \(0.115871\pi\)
\(348\) 0 0
\(349\) 30.1957 1.61634 0.808169 0.588951i \(-0.200459\pi\)
0.808169 + 0.588951i \(0.200459\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −24.9691 −1.32897 −0.664486 0.747300i \(-0.731350\pi\)
−0.664486 + 0.747300i \(0.731350\pi\)
\(354\) 0 0
\(355\) −7.59850 −0.403286
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −14.1661 −0.747660 −0.373830 0.927497i \(-0.621956\pi\)
−0.373830 + 0.927497i \(0.621956\pi\)
\(360\) 0 0
\(361\) 2.44637 0.128756
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 5.19806 0.272079
\(366\) 0 0
\(367\) 8.78687 0.458671 0.229335 0.973347i \(-0.426345\pi\)
0.229335 + 0.973347i \(0.426345\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −5.90084 −0.306356
\(372\) 0 0
\(373\) −18.3260 −0.948886 −0.474443 0.880286i \(-0.657350\pi\)
−0.474443 + 0.880286i \(0.657350\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 4.77586 0.245319 0.122660 0.992449i \(-0.460858\pi\)
0.122660 + 0.992449i \(0.460858\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 6.19029 0.316309 0.158155 0.987414i \(-0.449446\pi\)
0.158155 + 0.987414i \(0.449446\pi\)
\(384\) 0 0
\(385\) −1.69501 −0.0863855
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −24.8780 −1.26136 −0.630682 0.776041i \(-0.717225\pi\)
−0.630682 + 0.776041i \(0.717225\pi\)
\(390\) 0 0
\(391\) −15.8649 −0.802320
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 2.00298 0.100781
\(396\) 0 0
\(397\) 4.62027 0.231885 0.115942 0.993256i \(-0.463011\pi\)
0.115942 + 0.993256i \(0.463011\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −1.64848 −0.0823212 −0.0411606 0.999153i \(-0.513106\pi\)
−0.0411606 + 0.999153i \(0.513106\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −1.35929 −0.0673774
\(408\) 0 0
\(409\) 34.8049 1.72099 0.860496 0.509457i \(-0.170154\pi\)
0.860496 + 0.509457i \(0.170154\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 3.26205 0.160515
\(414\) 0 0
\(415\) −0.918559 −0.0450903
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −21.6353 −1.05696 −0.528478 0.848947i \(-0.677237\pi\)
−0.528478 + 0.848947i \(0.677237\pi\)
\(420\) 0 0
\(421\) 35.1008 1.71071 0.855355 0.518043i \(-0.173339\pi\)
0.855355 + 0.518043i \(0.173339\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 12.9172 0.626578
\(426\) 0 0
\(427\) 11.4386 0.553553
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −20.0925 −0.967820 −0.483910 0.875118i \(-0.660784\pi\)
−0.483910 + 0.875118i \(0.660784\pi\)
\(432\) 0 0
\(433\) −18.6939 −0.898373 −0.449187 0.893438i \(-0.648286\pi\)
−0.449187 + 0.893438i \(0.648286\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −26.6872 −1.27662
\(438\) 0 0
\(439\) 1.35019 0.0644411 0.0322206 0.999481i \(-0.489742\pi\)
0.0322206 + 0.999481i \(0.489742\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 0.400436 0.0190253 0.00951265 0.999955i \(-0.496972\pi\)
0.00951265 + 0.999955i \(0.496972\pi\)
\(444\) 0 0
\(445\) −9.97285 −0.472759
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 35.7904 1.68906 0.844528 0.535512i \(-0.179881\pi\)
0.844528 + 0.535512i \(0.179881\pi\)
\(450\) 0 0
\(451\) −11.3556 −0.534713
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −5.17092 −0.241885 −0.120943 0.992660i \(-0.538592\pi\)
−0.120943 + 0.992660i \(0.538592\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −20.8780 −0.972386 −0.486193 0.873852i \(-0.661615\pi\)
−0.486193 + 0.873852i \(0.661615\pi\)
\(462\) 0 0
\(463\) 30.7198 1.42767 0.713834 0.700315i \(-0.246957\pi\)
0.713834 + 0.700315i \(0.246957\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −15.2741 −0.706802 −0.353401 0.935472i \(-0.614975\pi\)
−0.353401 + 0.935472i \(0.614975\pi\)
\(468\) 0 0
\(469\) −8.44265 −0.389845
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 26.7764 1.23118
\(474\) 0 0
\(475\) 21.7289 0.996988
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 3.05861 0.139751 0.0698756 0.997556i \(-0.477740\pi\)
0.0698756 + 0.997556i \(0.477740\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −0.731250 −0.0332044
\(486\) 0 0
\(487\) −15.1521 −0.686608 −0.343304 0.939224i \(-0.611546\pi\)
−0.343304 + 0.939224i \(0.611546\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −23.4795 −1.05961 −0.529807 0.848118i \(-0.677736\pi\)
−0.529807 + 0.848118i \(0.677736\pi\)
\(492\) 0 0
\(493\) −7.71379 −0.347412
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 14.3618 0.644215
\(498\) 0 0
\(499\) −38.0689 −1.70420 −0.852099 0.523381i \(-0.824670\pi\)
−0.852099 + 0.523381i \(0.824670\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 11.1274 0.496145 0.248073 0.968741i \(-0.420203\pi\)
0.248073 + 0.968741i \(0.420203\pi\)
\(504\) 0 0
\(505\) −8.33811 −0.371041
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 26.7633 1.18626 0.593131 0.805106i \(-0.297892\pi\)
0.593131 + 0.805106i \(0.297892\pi\)
\(510\) 0 0
\(511\) −9.82477 −0.434622
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 5.10992 0.225170
\(516\) 0 0
\(517\) 33.5478 1.47543
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −20.5797 −0.901614 −0.450807 0.892622i \(-0.648864\pi\)
−0.450807 + 0.892622i \(0.648864\pi\)
\(522\) 0 0
\(523\) −6.77479 −0.296241 −0.148120 0.988969i \(-0.547322\pi\)
−0.148120 + 0.988969i \(0.547322\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −11.5241 −0.501997
\(528\) 0 0
\(529\) 10.2088 0.443862
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 4.01208 0.173457
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −17.1793 −0.739964
\(540\) 0 0
\(541\) −1.94331 −0.0835495 −0.0417748 0.999127i \(-0.513301\pi\)
−0.0417748 + 0.999127i \(0.513301\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −8.60388 −0.368550
\(546\) 0 0
\(547\) −39.1323 −1.67318 −0.836588 0.547833i \(-0.815453\pi\)
−0.836588 + 0.547833i \(0.815453\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −12.9758 −0.552789
\(552\) 0 0
\(553\) −3.78581 −0.160989
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −24.4989 −1.03805 −0.519025 0.854759i \(-0.673705\pi\)
−0.519025 + 0.854759i \(0.673705\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 21.8267 0.919885 0.459943 0.887949i \(-0.347870\pi\)
0.459943 + 0.887949i \(0.347870\pi\)
\(564\) 0 0
\(565\) 7.67324 0.322815
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 11.5627 0.484735 0.242367 0.970185i \(-0.422076\pi\)
0.242367 + 0.970185i \(0.422076\pi\)
\(570\) 0 0
\(571\) 24.7614 1.03623 0.518116 0.855310i \(-0.326634\pi\)
0.518116 + 0.855310i \(0.326634\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −27.0388 −1.12759
\(576\) 0 0
\(577\) −13.5090 −0.562388 −0.281194 0.959651i \(-0.590730\pi\)
−0.281194 + 0.959651i \(0.590730\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 1.73615 0.0720278
\(582\) 0 0
\(583\) −16.3811 −0.678434
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −6.70304 −0.276664 −0.138332 0.990386i \(-0.544174\pi\)
−0.138332 + 0.990386i \(0.544174\pi\)
\(588\) 0 0
\(589\) −19.3854 −0.798760
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −16.0194 −0.657837 −0.328918 0.944358i \(-0.606684\pi\)
−0.328918 + 0.944358i \(0.606684\pi\)
\(594\) 0 0
\(595\) 1.60255 0.0656980
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −19.8243 −0.809999 −0.404999 0.914317i \(-0.632728\pi\)
−0.404999 + 0.914317i \(0.632728\pi\)
\(600\) 0 0
\(601\) 29.1909 1.19072 0.595360 0.803459i \(-0.297009\pi\)
0.595360 + 0.803459i \(0.297009\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 1.39911 0.0568818
\(606\) 0 0
\(607\) −6.36227 −0.258237 −0.129118 0.991629i \(-0.541215\pi\)
−0.129118 + 0.991629i \(0.541215\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −30.7711 −1.24283 −0.621416 0.783481i \(-0.713442\pi\)
−0.621416 + 0.783481i \(0.713442\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 12.0242 0.484075 0.242037 0.970267i \(-0.422184\pi\)
0.242037 + 0.970267i \(0.422184\pi\)
\(618\) 0 0
\(619\) −9.02715 −0.362832 −0.181416 0.983406i \(-0.558068\pi\)
−0.181416 + 0.983406i \(0.558068\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 18.8495 0.755190
\(624\) 0 0
\(625\) 20.4752 0.819007
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 1.28514 0.0512420
\(630\) 0 0
\(631\) −15.5526 −0.619138 −0.309569 0.950877i \(-0.600185\pi\)
−0.309569 + 0.950877i \(0.600185\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −3.98254 −0.158042
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 19.4209 0.767079 0.383539 0.923525i \(-0.374705\pi\)
0.383539 + 0.923525i \(0.374705\pi\)
\(642\) 0 0
\(643\) 26.8267 1.05794 0.528971 0.848640i \(-0.322578\pi\)
0.528971 + 0.848640i \(0.322578\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −5.08815 −0.200036 −0.100018 0.994986i \(-0.531890\pi\)
−0.100018 + 0.994986i \(0.531890\pi\)
\(648\) 0 0
\(649\) 9.05562 0.355464
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 19.7157 0.771535 0.385768 0.922596i \(-0.373937\pi\)
0.385768 + 0.922596i \(0.373937\pi\)
\(654\) 0 0
\(655\) 7.28680 0.284719
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −9.42519 −0.367153 −0.183577 0.983005i \(-0.558768\pi\)
−0.183577 + 0.983005i \(0.558768\pi\)
\(660\) 0 0
\(661\) 29.9946 1.16666 0.583328 0.812237i \(-0.301750\pi\)
0.583328 + 0.812237i \(0.301750\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 2.69574 0.104536
\(666\) 0 0
\(667\) 16.1468 0.625205
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 31.7542 1.22586
\(672\) 0 0
\(673\) −47.7294 −1.83984 −0.919918 0.392112i \(-0.871745\pi\)
−0.919918 + 0.392112i \(0.871745\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 42.9124 1.64926 0.824630 0.565673i \(-0.191384\pi\)
0.824630 + 0.565673i \(0.191384\pi\)
\(678\) 0 0
\(679\) 1.38212 0.0530411
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0.970460 0.0371336 0.0185668 0.999828i \(-0.494090\pi\)
0.0185668 + 0.999828i \(0.494090\pi\)
\(684\) 0 0
\(685\) −12.1045 −0.462491
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) −1.16660 −0.0443797 −0.0221898 0.999754i \(-0.507064\pi\)
−0.0221898 + 0.999754i \(0.507064\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 1.64609 0.0624397
\(696\) 0 0
\(697\) 10.7362 0.406661
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 17.3274 0.654445 0.327223 0.944947i \(-0.393887\pi\)
0.327223 + 0.944947i \(0.393887\pi\)
\(702\) 0 0
\(703\) 2.16182 0.0815345
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 15.7597 0.592705
\(708\) 0 0
\(709\) −16.4601 −0.618172 −0.309086 0.951034i \(-0.600023\pi\)
−0.309086 + 0.951034i \(0.600023\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 24.1226 0.903398
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −14.1715 −0.528508 −0.264254 0.964453i \(-0.585126\pi\)
−0.264254 + 0.964453i \(0.585126\pi\)
\(720\) 0 0
\(721\) −9.65817 −0.359689
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −13.1468 −0.488258
\(726\) 0 0
\(727\) −37.8810 −1.40493 −0.702464 0.711719i \(-0.747917\pi\)
−0.702464 + 0.711719i \(0.747917\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −25.3159 −0.936341
\(732\) 0 0
\(733\) −0.377338 −0.0139373 −0.00696865 0.999976i \(-0.502218\pi\)
−0.00696865 + 0.999976i \(0.502218\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −23.4373 −0.863323
\(738\) 0 0
\(739\) −1.12631 −0.0414320 −0.0207160 0.999785i \(-0.506595\pi\)
−0.0207160 + 0.999785i \(0.506595\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −22.7047 −0.832954 −0.416477 0.909146i \(-0.636735\pi\)
−0.416477 + 0.909146i \(0.636735\pi\)
\(744\) 0 0
\(745\) 3.16123 0.115818
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −7.58317 −0.277083
\(750\) 0 0
\(751\) 13.9282 0.508249 0.254124 0.967172i \(-0.418213\pi\)
0.254124 + 0.967172i \(0.418213\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 10.6256 0.386707
\(756\) 0 0
\(757\) 1.16660 0.0424009 0.0212005 0.999775i \(-0.493251\pi\)
0.0212005 + 0.999775i \(0.493251\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0.821789 0.0297898 0.0148949 0.999889i \(-0.495259\pi\)
0.0148949 + 0.999889i \(0.495259\pi\)
\(762\) 0 0
\(763\) 16.2620 0.588726
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 33.7017 1.21531 0.607657 0.794199i \(-0.292109\pi\)
0.607657 + 0.794199i \(0.292109\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −0.764037 −0.0274805 −0.0137403 0.999906i \(-0.504374\pi\)
−0.0137403 + 0.999906i \(0.504374\pi\)
\(774\) 0 0
\(775\) −19.6407 −0.705515
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 18.0599 0.647064
\(780\) 0 0
\(781\) 39.8692 1.42663
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 4.65279 0.166065
\(786\) 0 0
\(787\) −12.1739 −0.433953 −0.216976 0.976177i \(-0.569619\pi\)
−0.216976 + 0.976177i \(0.569619\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −14.5031 −0.515669
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −38.2887 −1.35626 −0.678128 0.734944i \(-0.737209\pi\)
−0.678128 + 0.734944i \(0.737209\pi\)
\(798\) 0 0
\(799\) −31.7178 −1.12210
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −27.2741 −0.962483
\(804\) 0 0
\(805\) −3.35450 −0.118231
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 29.9638 1.05347 0.526735 0.850030i \(-0.323416\pi\)
0.526735 + 0.850030i \(0.323416\pi\)
\(810\) 0 0
\(811\) 46.3521 1.62764 0.813821 0.581115i \(-0.197383\pi\)
0.813821 + 0.581115i \(0.197383\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −1.09352 −0.0383044
\(816\) 0 0
\(817\) −42.5854 −1.48987
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 48.3105 1.68605 0.843024 0.537876i \(-0.180773\pi\)
0.843024 + 0.537876i \(0.180773\pi\)
\(822\) 0 0
\(823\) −5.31229 −0.185175 −0.0925874 0.995705i \(-0.529514\pi\)
−0.0925874 + 0.995705i \(0.529514\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 22.0968 0.768380 0.384190 0.923254i \(-0.374481\pi\)
0.384190 + 0.923254i \(0.374481\pi\)
\(828\) 0 0
\(829\) −1.61655 −0.0561450 −0.0280725 0.999606i \(-0.508937\pi\)
−0.0280725 + 0.999606i \(0.508937\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 16.2422 0.562759
\(834\) 0 0
\(835\) −13.7627 −0.476278
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −41.0823 −1.41832 −0.709159 0.705048i \(-0.750925\pi\)
−0.709159 + 0.705048i \(0.750925\pi\)
\(840\) 0 0
\(841\) −21.1491 −0.729281
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −2.64443 −0.0908638
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −2.69010 −0.0922155
\(852\) 0 0
\(853\) −35.0441 −1.19989 −0.599944 0.800042i \(-0.704811\pi\)
−0.599944 + 0.800042i \(0.704811\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 3.76079 0.128466 0.0642331 0.997935i \(-0.479540\pi\)
0.0642331 + 0.997935i \(0.479540\pi\)
\(858\) 0 0
\(859\) 7.11662 0.242816 0.121408 0.992603i \(-0.461259\pi\)
0.121408 + 0.992603i \(0.461259\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −57.5900 −1.96039 −0.980193 0.198044i \(-0.936541\pi\)
−0.980193 + 0.198044i \(0.936541\pi\)
\(864\) 0 0
\(865\) −1.42699 −0.0485192
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −10.5096 −0.356514
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 5.64178 0.190727
\(876\) 0 0
\(877\) −19.2150 −0.648846 −0.324423 0.945912i \(-0.605170\pi\)
−0.324423 + 0.945912i \(0.605170\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 11.1444 0.375463 0.187731 0.982220i \(-0.439887\pi\)
0.187731 + 0.982220i \(0.439887\pi\)
\(882\) 0 0
\(883\) −4.28919 −0.144343 −0.0721714 0.997392i \(-0.522993\pi\)
−0.0721714 + 0.997392i \(0.522993\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 33.1739 1.11387 0.556935 0.830556i \(-0.311977\pi\)
0.556935 + 0.830556i \(0.311977\pi\)
\(888\) 0 0
\(889\) 7.52734 0.252459
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −53.3545 −1.78544
\(894\) 0 0
\(895\) −1.66786 −0.0557504
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 11.7289 0.391179
\(900\) 0 0
\(901\) 15.4875 0.515964
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 8.14914 0.270887
\(906\) 0 0
\(907\) −40.6282 −1.34904 −0.674518 0.738259i \(-0.735648\pi\)
−0.674518 + 0.738259i \(0.735648\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −46.2731 −1.53309 −0.766547 0.642188i \(-0.778027\pi\)
−0.766547 + 0.642188i \(0.778027\pi\)
\(912\) 0 0
\(913\) 4.81966 0.159507
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −13.7727 −0.454813
\(918\) 0 0
\(919\) 50.4674 1.66477 0.832383 0.554201i \(-0.186976\pi\)
0.832383 + 0.554201i \(0.186976\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 2.19029 0.0720164
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 17.9250 0.588100 0.294050 0.955790i \(-0.404997\pi\)
0.294050 + 0.955790i \(0.404997\pi\)
\(930\) 0 0
\(931\) 27.3220 0.895442
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 4.44876 0.145490
\(936\) 0 0
\(937\) 5.85325 0.191217 0.0956086 0.995419i \(-0.469520\pi\)
0.0956086 + 0.995419i \(0.469520\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −56.7958 −1.85149 −0.925745 0.378147i \(-0.876561\pi\)
−0.925745 + 0.378147i \(0.876561\pi\)
\(942\) 0 0
\(943\) −22.4733 −0.731830
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −6.14974 −0.199840 −0.0999198 0.994995i \(-0.531859\pi\)
−0.0999198 + 0.994995i \(0.531859\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −48.9778 −1.58655 −0.793273 0.608867i \(-0.791624\pi\)
−0.793273 + 0.608867i \(0.791624\pi\)
\(954\) 0 0
\(955\) −9.47889 −0.306730
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 22.8786 0.738788
\(960\) 0 0
\(961\) −13.4776 −0.434760
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −8.31096 −0.267539
\(966\) 0 0
\(967\) −54.2616 −1.74493 −0.872467 0.488673i \(-0.837481\pi\)
−0.872467 + 0.488673i \(0.837481\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 36.3142 1.16538 0.582689 0.812695i \(-0.302000\pi\)
0.582689 + 0.812695i \(0.302000\pi\)
\(972\) 0 0
\(973\) −3.11124 −0.0997419
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 49.7375 1.59124 0.795621 0.605794i \(-0.207144\pi\)
0.795621 + 0.605794i \(0.207144\pi\)
\(978\) 0 0
\(979\) 52.3274 1.67239
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −10.9981 −0.350784 −0.175392 0.984499i \(-0.556119\pi\)
−0.175392 + 0.984499i \(0.556119\pi\)
\(984\) 0 0
\(985\) −0.106932 −0.00340715
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 52.9920 1.68505
\(990\) 0 0
\(991\) 6.73078 0.213810 0.106905 0.994269i \(-0.465906\pi\)
0.106905 + 0.994269i \(0.465906\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −6.58881 −0.208879
\(996\) 0 0
\(997\) 43.3497 1.37290 0.686450 0.727177i \(-0.259168\pi\)
0.686450 + 0.727177i \(0.259168\pi\)
\(998\) 0 0
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 6084.2.a.y.1.2 3
3.2 odd 2 2028.2.a.j.1.2 yes 3
12.11 even 2 8112.2.a.co.1.2 3
13.5 odd 4 6084.2.b.r.4393.4 6
13.8 odd 4 6084.2.b.r.4393.3 6
13.12 even 2 6084.2.a.bb.1.2 3
39.2 even 12 2028.2.q.j.1837.3 12
39.5 even 4 2028.2.b.f.337.3 6
39.8 even 4 2028.2.b.f.337.4 6
39.11 even 12 2028.2.q.j.1837.4 12
39.17 odd 6 2028.2.i.l.2005.2 6
39.20 even 12 2028.2.q.j.361.4 12
39.23 odd 6 2028.2.i.l.529.2 6
39.29 odd 6 2028.2.i.m.529.2 6
39.32 even 12 2028.2.q.j.361.3 12
39.35 odd 6 2028.2.i.m.2005.2 6
39.38 odd 2 2028.2.a.i.1.2 3
156.155 even 2 8112.2.a.ch.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2028.2.a.i.1.2 3 39.38 odd 2
2028.2.a.j.1.2 yes 3 3.2 odd 2
2028.2.b.f.337.3 6 39.5 even 4
2028.2.b.f.337.4 6 39.8 even 4
2028.2.i.l.529.2 6 39.23 odd 6
2028.2.i.l.2005.2 6 39.17 odd 6
2028.2.i.m.529.2 6 39.29 odd 6
2028.2.i.m.2005.2 6 39.35 odd 6
2028.2.q.j.361.3 12 39.32 even 12
2028.2.q.j.361.4 12 39.20 even 12
2028.2.q.j.1837.3 12 39.2 even 12
2028.2.q.j.1837.4 12 39.11 even 12
6084.2.a.y.1.2 3 1.1 even 1 trivial
6084.2.a.bb.1.2 3 13.12 even 2
6084.2.b.r.4393.3 6 13.8 odd 4
6084.2.b.r.4393.4 6 13.5 odd 4
8112.2.a.ch.1.2 3 156.155 even 2
8112.2.a.co.1.2 3 12.11 even 2