Properties

Label 7440.2.a.bp.1.3
Level $7440$
Weight $2$
Character 7440.1
Self dual yes
Analytic conductor $59.409$
Analytic rank $1$
Dimension $3$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [7440,2,Mod(1,7440)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(7440, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 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("7440.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 7440 = 2^{4} \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7440.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: \(59.4086991038\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: 3.3.148.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - x^{2} - 3x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 465)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(2.17009\) of defining polynomial
Character \(\chi\) \(=\) 7440.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{3} +1.00000 q^{5} +1.17009 q^{7} +1.00000 q^{9} -2.00000 q^{11} +0.0917087 q^{13} -1.00000 q^{15} -6.04945 q^{17} -1.17009 q^{21} +1.70928 q^{23} +1.00000 q^{25} -1.00000 q^{27} +7.95774 q^{29} -1.00000 q^{31} +2.00000 q^{33} +1.17009 q^{35} -3.35350 q^{37} -0.0917087 q^{39} -4.68035 q^{41} +0.738205 q^{43} +1.00000 q^{45} +9.12783 q^{47} -5.63090 q^{49} +6.04945 q^{51} +4.97107 q^{53} -2.00000 q^{55} -11.0361 q^{59} -3.26180 q^{61} +1.17009 q^{63} +0.0917087 q^{65} -3.85043 q^{67} -1.70928 q^{69} +1.21953 q^{71} +7.66701 q^{73} -1.00000 q^{75} -2.34017 q^{77} -3.52586 q^{79} +1.00000 q^{81} -12.5464 q^{83} -6.04945 q^{85} -7.95774 q^{87} -5.77432 q^{89} +0.107307 q^{91} +1.00000 q^{93} -12.0000 q^{97} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - 3 q^{3} + 3 q^{5} - 2 q^{7} + 3 q^{9} - 6 q^{11} - 2 q^{13} - 3 q^{15} + 2 q^{21} - 2 q^{23} + 3 q^{25} - 3 q^{27} + 8 q^{29} - 3 q^{31} + 6 q^{33} - 2 q^{35} + 2 q^{39} + 8 q^{41} + 10 q^{43} + 3 q^{45}+ \cdots - 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.00000 −0.577350
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) 1.17009 0.442251 0.221126 0.975245i \(-0.429027\pi\)
0.221126 + 0.975245i \(0.429027\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −2.00000 −0.603023 −0.301511 0.953463i \(-0.597491\pi\)
−0.301511 + 0.953463i \(0.597491\pi\)
\(12\) 0 0
\(13\) 0.0917087 0.0254354 0.0127177 0.999919i \(-0.495952\pi\)
0.0127177 + 0.999919i \(0.495952\pi\)
\(14\) 0 0
\(15\) −1.00000 −0.258199
\(16\) 0 0
\(17\) −6.04945 −1.46721 −0.733603 0.679578i \(-0.762163\pi\)
−0.733603 + 0.679578i \(0.762163\pi\)
\(18\) 0 0
\(19\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(20\) 0 0
\(21\) −1.17009 −0.255334
\(22\) 0 0
\(23\) 1.70928 0.356409 0.178204 0.983994i \(-0.442971\pi\)
0.178204 + 0.983994i \(0.442971\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 7.95774 1.47772 0.738858 0.673862i \(-0.235366\pi\)
0.738858 + 0.673862i \(0.235366\pi\)
\(30\) 0 0
\(31\) −1.00000 −0.179605
\(32\) 0 0
\(33\) 2.00000 0.348155
\(34\) 0 0
\(35\) 1.17009 0.197781
\(36\) 0 0
\(37\) −3.35350 −0.551313 −0.275656 0.961256i \(-0.588895\pi\)
−0.275656 + 0.961256i \(0.588895\pi\)
\(38\) 0 0
\(39\) −0.0917087 −0.0146852
\(40\) 0 0
\(41\) −4.68035 −0.730947 −0.365474 0.930822i \(-0.619093\pi\)
−0.365474 + 0.930822i \(0.619093\pi\)
\(42\) 0 0
\(43\) 0.738205 0.112575 0.0562876 0.998415i \(-0.482074\pi\)
0.0562876 + 0.998415i \(0.482074\pi\)
\(44\) 0 0
\(45\) 1.00000 0.149071
\(46\) 0 0
\(47\) 9.12783 1.33143 0.665715 0.746206i \(-0.268127\pi\)
0.665715 + 0.746206i \(0.268127\pi\)
\(48\) 0 0
\(49\) −5.63090 −0.804414
\(50\) 0 0
\(51\) 6.04945 0.847092
\(52\) 0 0
\(53\) 4.97107 0.682829 0.341415 0.939913i \(-0.389094\pi\)
0.341415 + 0.939913i \(0.389094\pi\)
\(54\) 0 0
\(55\) −2.00000 −0.269680
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −11.0361 −1.43678 −0.718390 0.695641i \(-0.755121\pi\)
−0.718390 + 0.695641i \(0.755121\pi\)
\(60\) 0 0
\(61\) −3.26180 −0.417630 −0.208815 0.977955i \(-0.566961\pi\)
−0.208815 + 0.977955i \(0.566961\pi\)
\(62\) 0 0
\(63\) 1.17009 0.147417
\(64\) 0 0
\(65\) 0.0917087 0.0113751
\(66\) 0 0
\(67\) −3.85043 −0.470405 −0.235203 0.971946i \(-0.575575\pi\)
−0.235203 + 0.971946i \(0.575575\pi\)
\(68\) 0 0
\(69\) −1.70928 −0.205773
\(70\) 0 0
\(71\) 1.21953 0.144732 0.0723661 0.997378i \(-0.476945\pi\)
0.0723661 + 0.997378i \(0.476945\pi\)
\(72\) 0 0
\(73\) 7.66701 0.897356 0.448678 0.893693i \(-0.351895\pi\)
0.448678 + 0.893693i \(0.351895\pi\)
\(74\) 0 0
\(75\) −1.00000 −0.115470
\(76\) 0 0
\(77\) −2.34017 −0.266687
\(78\) 0 0
\(79\) −3.52586 −0.396690 −0.198345 0.980132i \(-0.563557\pi\)
−0.198345 + 0.980132i \(0.563557\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −12.5464 −1.37714 −0.688572 0.725168i \(-0.741762\pi\)
−0.688572 + 0.725168i \(0.741762\pi\)
\(84\) 0 0
\(85\) −6.04945 −0.656155
\(86\) 0 0
\(87\) −7.95774 −0.853159
\(88\) 0 0
\(89\) −5.77432 −0.612077 −0.306038 0.952019i \(-0.599004\pi\)
−0.306038 + 0.952019i \(0.599004\pi\)
\(90\) 0 0
\(91\) 0.107307 0.0112488
\(92\) 0 0
\(93\) 1.00000 0.103695
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −12.0000 −1.21842 −0.609208 0.793011i \(-0.708512\pi\)
−0.609208 + 0.793011i \(0.708512\pi\)
\(98\) 0 0
\(99\) −2.00000 −0.201008
\(100\) 0 0
\(101\) 13.9421 1.38729 0.693647 0.720315i \(-0.256003\pi\)
0.693647 + 0.720315i \(0.256003\pi\)
\(102\) 0 0
\(103\) −6.77205 −0.667270 −0.333635 0.942702i \(-0.608275\pi\)
−0.333635 + 0.942702i \(0.608275\pi\)
\(104\) 0 0
\(105\) −1.17009 −0.114189
\(106\) 0 0
\(107\) −0.630898 −0.0609912 −0.0304956 0.999535i \(-0.509709\pi\)
−0.0304956 + 0.999535i \(0.509709\pi\)
\(108\) 0 0
\(109\) −11.8660 −1.13656 −0.568280 0.822835i \(-0.692391\pi\)
−0.568280 + 0.822835i \(0.692391\pi\)
\(110\) 0 0
\(111\) 3.35350 0.318301
\(112\) 0 0
\(113\) 3.75872 0.353591 0.176795 0.984248i \(-0.443427\pi\)
0.176795 + 0.984248i \(0.443427\pi\)
\(114\) 0 0
\(115\) 1.70928 0.159391
\(116\) 0 0
\(117\) 0.0917087 0.00847848
\(118\) 0 0
\(119\) −7.07838 −0.648874
\(120\) 0 0
\(121\) −7.00000 −0.636364
\(122\) 0 0
\(123\) 4.68035 0.422013
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 4.18342 0.371218 0.185609 0.982624i \(-0.440574\pi\)
0.185609 + 0.982624i \(0.440574\pi\)
\(128\) 0 0
\(129\) −0.738205 −0.0649953
\(130\) 0 0
\(131\) 0.695944 0.0608049 0.0304025 0.999538i \(-0.490321\pi\)
0.0304025 + 0.999538i \(0.490321\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −1.00000 −0.0860663
\(136\) 0 0
\(137\) 8.20620 0.701103 0.350552 0.936543i \(-0.385994\pi\)
0.350552 + 0.936543i \(0.385994\pi\)
\(138\) 0 0
\(139\) 4.49693 0.381424 0.190712 0.981646i \(-0.438920\pi\)
0.190712 + 0.981646i \(0.438920\pi\)
\(140\) 0 0
\(141\) −9.12783 −0.768702
\(142\) 0 0
\(143\) −0.183417 −0.0153381
\(144\) 0 0
\(145\) 7.95774 0.660854
\(146\) 0 0
\(147\) 5.63090 0.464429
\(148\) 0 0
\(149\) 13.3607 1.09455 0.547275 0.836953i \(-0.315665\pi\)
0.547275 + 0.836953i \(0.315665\pi\)
\(150\) 0 0
\(151\) −13.8660 −1.12840 −0.564201 0.825638i \(-0.690816\pi\)
−0.564201 + 0.825638i \(0.690816\pi\)
\(152\) 0 0
\(153\) −6.04945 −0.489069
\(154\) 0 0
\(155\) −1.00000 −0.0803219
\(156\) 0 0
\(157\) −20.0989 −1.60407 −0.802033 0.597279i \(-0.796248\pi\)
−0.802033 + 0.597279i \(0.796248\pi\)
\(158\) 0 0
\(159\) −4.97107 −0.394232
\(160\) 0 0
\(161\) 2.00000 0.157622
\(162\) 0 0
\(163\) −4.06505 −0.318399 −0.159200 0.987246i \(-0.550891\pi\)
−0.159200 + 0.987246i \(0.550891\pi\)
\(164\) 0 0
\(165\) 2.00000 0.155700
\(166\) 0 0
\(167\) −3.91548 −0.302989 −0.151494 0.988458i \(-0.548409\pi\)
−0.151494 + 0.988458i \(0.548409\pi\)
\(168\) 0 0
\(169\) −12.9916 −0.999353
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 16.0722 1.22195 0.610975 0.791650i \(-0.290778\pi\)
0.610975 + 0.791650i \(0.290778\pi\)
\(174\) 0 0
\(175\) 1.17009 0.0884502
\(176\) 0 0
\(177\) 11.0361 0.829525
\(178\) 0 0
\(179\) −21.9421 −1.64003 −0.820016 0.572340i \(-0.806036\pi\)
−0.820016 + 0.572340i \(0.806036\pi\)
\(180\) 0 0
\(181\) 3.94214 0.293017 0.146509 0.989209i \(-0.453196\pi\)
0.146509 + 0.989209i \(0.453196\pi\)
\(182\) 0 0
\(183\) 3.26180 0.241119
\(184\) 0 0
\(185\) −3.35350 −0.246555
\(186\) 0 0
\(187\) 12.0989 0.884759
\(188\) 0 0
\(189\) −1.17009 −0.0851113
\(190\) 0 0
\(191\) −23.3184 −1.68726 −0.843631 0.536923i \(-0.819587\pi\)
−0.843631 + 0.536923i \(0.819587\pi\)
\(192\) 0 0
\(193\) −10.2557 −0.738218 −0.369109 0.929386i \(-0.620337\pi\)
−0.369109 + 0.929386i \(0.620337\pi\)
\(194\) 0 0
\(195\) −0.0917087 −0.00656740
\(196\) 0 0
\(197\) 23.9916 1.70933 0.854665 0.519180i \(-0.173763\pi\)
0.854665 + 0.519180i \(0.173763\pi\)
\(198\) 0 0
\(199\) 16.1217 1.14284 0.571418 0.820659i \(-0.306394\pi\)
0.571418 + 0.820659i \(0.306394\pi\)
\(200\) 0 0
\(201\) 3.85043 0.271589
\(202\) 0 0
\(203\) 9.31124 0.653521
\(204\) 0 0
\(205\) −4.68035 −0.326890
\(206\) 0 0
\(207\) 1.70928 0.118803
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) −18.4391 −1.26940 −0.634699 0.772759i \(-0.718876\pi\)
−0.634699 + 0.772759i \(0.718876\pi\)
\(212\) 0 0
\(213\) −1.21953 −0.0835611
\(214\) 0 0
\(215\) 0.738205 0.0503451
\(216\) 0 0
\(217\) −1.17009 −0.0794306
\(218\) 0 0
\(219\) −7.66701 −0.518089
\(220\) 0 0
\(221\) −0.554787 −0.0373190
\(222\) 0 0
\(223\) 15.2762 1.02297 0.511484 0.859293i \(-0.329096\pi\)
0.511484 + 0.859293i \(0.329096\pi\)
\(224\) 0 0
\(225\) 1.00000 0.0666667
\(226\) 0 0
\(227\) 19.7815 1.31294 0.656472 0.754350i \(-0.272048\pi\)
0.656472 + 0.754350i \(0.272048\pi\)
\(228\) 0 0
\(229\) 25.4329 1.68066 0.840328 0.542079i \(-0.182363\pi\)
0.840328 + 0.542079i \(0.182363\pi\)
\(230\) 0 0
\(231\) 2.34017 0.153972
\(232\) 0 0
\(233\) −16.2062 −1.06170 −0.530852 0.847465i \(-0.678128\pi\)
−0.530852 + 0.847465i \(0.678128\pi\)
\(234\) 0 0
\(235\) 9.12783 0.595434
\(236\) 0 0
\(237\) 3.52586 0.229029
\(238\) 0 0
\(239\) −19.7587 −1.27809 −0.639043 0.769171i \(-0.720669\pi\)
−0.639043 + 0.769171i \(0.720669\pi\)
\(240\) 0 0
\(241\) −8.65368 −0.557433 −0.278716 0.960373i \(-0.589909\pi\)
−0.278716 + 0.960373i \(0.589909\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) −5.63090 −0.359745
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 12.5464 0.795094
\(250\) 0 0
\(251\) 18.9360 1.19523 0.597615 0.801783i \(-0.296115\pi\)
0.597615 + 0.801783i \(0.296115\pi\)
\(252\) 0 0
\(253\) −3.41855 −0.214922
\(254\) 0 0
\(255\) 6.04945 0.378831
\(256\) 0 0
\(257\) −13.1012 −0.817228 −0.408614 0.912707i \(-0.633988\pi\)
−0.408614 + 0.912707i \(0.633988\pi\)
\(258\) 0 0
\(259\) −3.92389 −0.243819
\(260\) 0 0
\(261\) 7.95774 0.492572
\(262\) 0 0
\(263\) −8.49693 −0.523943 −0.261972 0.965076i \(-0.584373\pi\)
−0.261972 + 0.965076i \(0.584373\pi\)
\(264\) 0 0
\(265\) 4.97107 0.305370
\(266\) 0 0
\(267\) 5.77432 0.353383
\(268\) 0 0
\(269\) 21.8010 1.32923 0.664615 0.747186i \(-0.268596\pi\)
0.664615 + 0.747186i \(0.268596\pi\)
\(270\) 0 0
\(271\) −10.3402 −0.628121 −0.314060 0.949403i \(-0.601689\pi\)
−0.314060 + 0.949403i \(0.601689\pi\)
\(272\) 0 0
\(273\) −0.107307 −0.00649452
\(274\) 0 0
\(275\) −2.00000 −0.120605
\(276\) 0 0
\(277\) −0.646496 −0.0388442 −0.0194221 0.999811i \(-0.506183\pi\)
−0.0194221 + 0.999811i \(0.506183\pi\)
\(278\) 0 0
\(279\) −1.00000 −0.0598684
\(280\) 0 0
\(281\) −17.3874 −1.03724 −0.518621 0.855004i \(-0.673555\pi\)
−0.518621 + 0.855004i \(0.673555\pi\)
\(282\) 0 0
\(283\) −2.92881 −0.174100 −0.0870498 0.996204i \(-0.527744\pi\)
−0.0870498 + 0.996204i \(0.527744\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −5.47641 −0.323262
\(288\) 0 0
\(289\) 19.5958 1.15270
\(290\) 0 0
\(291\) 12.0000 0.703452
\(292\) 0 0
\(293\) −31.9916 −1.86897 −0.934484 0.356004i \(-0.884139\pi\)
−0.934484 + 0.356004i \(0.884139\pi\)
\(294\) 0 0
\(295\) −11.0361 −0.642548
\(296\) 0 0
\(297\) 2.00000 0.116052
\(298\) 0 0
\(299\) 0.156755 0.00906540
\(300\) 0 0
\(301\) 0.863763 0.0497865
\(302\) 0 0
\(303\) −13.9421 −0.800955
\(304\) 0 0
\(305\) −3.26180 −0.186770
\(306\) 0 0
\(307\) 5.66701 0.323434 0.161717 0.986837i \(-0.448297\pi\)
0.161717 + 0.986837i \(0.448297\pi\)
\(308\) 0 0
\(309\) 6.77205 0.385249
\(310\) 0 0
\(311\) 16.2401 0.920889 0.460444 0.887689i \(-0.347690\pi\)
0.460444 + 0.887689i \(0.347690\pi\)
\(312\) 0 0
\(313\) 7.42574 0.419728 0.209864 0.977731i \(-0.432698\pi\)
0.209864 + 0.977731i \(0.432698\pi\)
\(314\) 0 0
\(315\) 1.17009 0.0659269
\(316\) 0 0
\(317\) −13.2534 −0.744384 −0.372192 0.928156i \(-0.621394\pi\)
−0.372192 + 0.928156i \(0.621394\pi\)
\(318\) 0 0
\(319\) −15.9155 −0.891096
\(320\) 0 0
\(321\) 0.630898 0.0352133
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) 0.0917087 0.00508709
\(326\) 0 0
\(327\) 11.8660 0.656193
\(328\) 0 0
\(329\) 10.6803 0.588827
\(330\) 0 0
\(331\) −3.62475 −0.199235 −0.0996173 0.995026i \(-0.531762\pi\)
−0.0996173 + 0.995026i \(0.531762\pi\)
\(332\) 0 0
\(333\) −3.35350 −0.183771
\(334\) 0 0
\(335\) −3.85043 −0.210372
\(336\) 0 0
\(337\) 13.3268 0.725959 0.362980 0.931797i \(-0.381759\pi\)
0.362980 + 0.931797i \(0.381759\pi\)
\(338\) 0 0
\(339\) −3.75872 −0.204146
\(340\) 0 0
\(341\) 2.00000 0.108306
\(342\) 0 0
\(343\) −14.7792 −0.798004
\(344\) 0 0
\(345\) −1.70928 −0.0920243
\(346\) 0 0
\(347\) −16.2290 −0.871218 −0.435609 0.900136i \(-0.643467\pi\)
−0.435609 + 0.900136i \(0.643467\pi\)
\(348\) 0 0
\(349\) 2.38962 0.127913 0.0639567 0.997953i \(-0.479628\pi\)
0.0639567 + 0.997953i \(0.479628\pi\)
\(350\) 0 0
\(351\) −0.0917087 −0.00489505
\(352\) 0 0
\(353\) −36.2062 −1.92706 −0.963531 0.267597i \(-0.913770\pi\)
−0.963531 + 0.267597i \(0.913770\pi\)
\(354\) 0 0
\(355\) 1.21953 0.0647262
\(356\) 0 0
\(357\) 7.07838 0.374627
\(358\) 0 0
\(359\) −0.382433 −0.0201841 −0.0100920 0.999949i \(-0.503212\pi\)
−0.0100920 + 0.999949i \(0.503212\pi\)
\(360\) 0 0
\(361\) −19.0000 −1.00000
\(362\) 0 0
\(363\) 7.00000 0.367405
\(364\) 0 0
\(365\) 7.66701 0.401310
\(366\) 0 0
\(367\) 7.63317 0.398448 0.199224 0.979954i \(-0.436158\pi\)
0.199224 + 0.979954i \(0.436158\pi\)
\(368\) 0 0
\(369\) −4.68035 −0.243649
\(370\) 0 0
\(371\) 5.81658 0.301982
\(372\) 0 0
\(373\) −17.5486 −0.908634 −0.454317 0.890840i \(-0.650117\pi\)
−0.454317 + 0.890840i \(0.650117\pi\)
\(374\) 0 0
\(375\) −1.00000 −0.0516398
\(376\) 0 0
\(377\) 0.729794 0.0375863
\(378\) 0 0
\(379\) −7.68649 −0.394828 −0.197414 0.980320i \(-0.563254\pi\)
−0.197414 + 0.980320i \(0.563254\pi\)
\(380\) 0 0
\(381\) −4.18342 −0.214323
\(382\) 0 0
\(383\) 5.92389 0.302697 0.151348 0.988480i \(-0.451638\pi\)
0.151348 + 0.988480i \(0.451638\pi\)
\(384\) 0 0
\(385\) −2.34017 −0.119266
\(386\) 0 0
\(387\) 0.738205 0.0375251
\(388\) 0 0
\(389\) −28.7636 −1.45837 −0.729187 0.684314i \(-0.760102\pi\)
−0.729187 + 0.684314i \(0.760102\pi\)
\(390\) 0 0
\(391\) −10.3402 −0.522925
\(392\) 0 0
\(393\) −0.695944 −0.0351057
\(394\) 0 0
\(395\) −3.52586 −0.177405
\(396\) 0 0
\(397\) 9.41855 0.472704 0.236352 0.971668i \(-0.424048\pi\)
0.236352 + 0.971668i \(0.424048\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 13.9721 0.697734 0.348867 0.937172i \(-0.386566\pi\)
0.348867 + 0.937172i \(0.386566\pi\)
\(402\) 0 0
\(403\) −0.0917087 −0.00456834
\(404\) 0 0
\(405\) 1.00000 0.0496904
\(406\) 0 0
\(407\) 6.70701 0.332454
\(408\) 0 0
\(409\) 4.73820 0.234289 0.117145 0.993115i \(-0.462626\pi\)
0.117145 + 0.993115i \(0.462626\pi\)
\(410\) 0 0
\(411\) −8.20620 −0.404782
\(412\) 0 0
\(413\) −12.9132 −0.635418
\(414\) 0 0
\(415\) −12.5464 −0.615877
\(416\) 0 0
\(417\) −4.49693 −0.220216
\(418\) 0 0
\(419\) −30.3123 −1.48085 −0.740426 0.672138i \(-0.765376\pi\)
−0.740426 + 0.672138i \(0.765376\pi\)
\(420\) 0 0
\(421\) −33.9916 −1.65665 −0.828324 0.560249i \(-0.810706\pi\)
−0.828324 + 0.560249i \(0.810706\pi\)
\(422\) 0 0
\(423\) 9.12783 0.443810
\(424\) 0 0
\(425\) −6.04945 −0.293441
\(426\) 0 0
\(427\) −3.81658 −0.184697
\(428\) 0 0
\(429\) 0.183417 0.00885548
\(430\) 0 0
\(431\) −16.6381 −0.801428 −0.400714 0.916203i \(-0.631238\pi\)
−0.400714 + 0.916203i \(0.631238\pi\)
\(432\) 0 0
\(433\) −32.8976 −1.58096 −0.790479 0.612489i \(-0.790168\pi\)
−0.790479 + 0.612489i \(0.790168\pi\)
\(434\) 0 0
\(435\) −7.95774 −0.381544
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 28.5113 1.36077 0.680385 0.732855i \(-0.261813\pi\)
0.680385 + 0.732855i \(0.261813\pi\)
\(440\) 0 0
\(441\) −5.63090 −0.268138
\(442\) 0 0
\(443\) 20.0494 0.952578 0.476289 0.879289i \(-0.341982\pi\)
0.476289 + 0.879289i \(0.341982\pi\)
\(444\) 0 0
\(445\) −5.77432 −0.273729
\(446\) 0 0
\(447\) −13.3607 −0.631939
\(448\) 0 0
\(449\) −31.7308 −1.49747 −0.748735 0.662869i \(-0.769339\pi\)
−0.748735 + 0.662869i \(0.769339\pi\)
\(450\) 0 0
\(451\) 9.36069 0.440778
\(452\) 0 0
\(453\) 13.8660 0.651483
\(454\) 0 0
\(455\) 0.107307 0.00503064
\(456\) 0 0
\(457\) −38.7864 −1.81435 −0.907176 0.420751i \(-0.861767\pi\)
−0.907176 + 0.420751i \(0.861767\pi\)
\(458\) 0 0
\(459\) 6.04945 0.282364
\(460\) 0 0
\(461\) −0.324575 −0.0151169 −0.00755847 0.999971i \(-0.502406\pi\)
−0.00755847 + 0.999971i \(0.502406\pi\)
\(462\) 0 0
\(463\) −16.8371 −0.782486 −0.391243 0.920287i \(-0.627955\pi\)
−0.391243 + 0.920287i \(0.627955\pi\)
\(464\) 0 0
\(465\) 1.00000 0.0463739
\(466\) 0 0
\(467\) 31.0700 1.43775 0.718873 0.695141i \(-0.244658\pi\)
0.718873 + 0.695141i \(0.244658\pi\)
\(468\) 0 0
\(469\) −4.50534 −0.208037
\(470\) 0 0
\(471\) 20.0989 0.926108
\(472\) 0 0
\(473\) −1.47641 −0.0678854
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 4.97107 0.227610
\(478\) 0 0
\(479\) 30.3123 1.38500 0.692502 0.721416i \(-0.256508\pi\)
0.692502 + 0.721416i \(0.256508\pi\)
\(480\) 0 0
\(481\) −0.307546 −0.0140229
\(482\) 0 0
\(483\) −2.00000 −0.0910032
\(484\) 0 0
\(485\) −12.0000 −0.544892
\(486\) 0 0
\(487\) −5.92777 −0.268613 −0.134306 0.990940i \(-0.542881\pi\)
−0.134306 + 0.990940i \(0.542881\pi\)
\(488\) 0 0
\(489\) 4.06505 0.183828
\(490\) 0 0
\(491\) 11.1194 0.501812 0.250906 0.968011i \(-0.419271\pi\)
0.250906 + 0.968011i \(0.419271\pi\)
\(492\) 0 0
\(493\) −48.1399 −2.16811
\(494\) 0 0
\(495\) −2.00000 −0.0898933
\(496\) 0 0
\(497\) 1.42696 0.0640080
\(498\) 0 0
\(499\) 0.482553 0.0216020 0.0108010 0.999942i \(-0.496562\pi\)
0.0108010 + 0.999942i \(0.496562\pi\)
\(500\) 0 0
\(501\) 3.91548 0.174931
\(502\) 0 0
\(503\) −28.1795 −1.25646 −0.628232 0.778026i \(-0.716221\pi\)
−0.628232 + 0.778026i \(0.716221\pi\)
\(504\) 0 0
\(505\) 13.9421 0.620417
\(506\) 0 0
\(507\) 12.9916 0.576977
\(508\) 0 0
\(509\) −30.8359 −1.36678 −0.683388 0.730055i \(-0.739494\pi\)
−0.683388 + 0.730055i \(0.739494\pi\)
\(510\) 0 0
\(511\) 8.97107 0.396857
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −6.77205 −0.298412
\(516\) 0 0
\(517\) −18.2557 −0.802883
\(518\) 0 0
\(519\) −16.0722 −0.705493
\(520\) 0 0
\(521\) −29.0472 −1.27258 −0.636290 0.771450i \(-0.719532\pi\)
−0.636290 + 0.771450i \(0.719532\pi\)
\(522\) 0 0
\(523\) −16.5958 −0.725685 −0.362842 0.931851i \(-0.618194\pi\)
−0.362842 + 0.931851i \(0.618194\pi\)
\(524\) 0 0
\(525\) −1.17009 −0.0510668
\(526\) 0 0
\(527\) 6.04945 0.263518
\(528\) 0 0
\(529\) −20.0784 −0.872973
\(530\) 0 0
\(531\) −11.0361 −0.478927
\(532\) 0 0
\(533\) −0.429229 −0.0185920
\(534\) 0 0
\(535\) −0.630898 −0.0272761
\(536\) 0 0
\(537\) 21.9421 0.946873
\(538\) 0 0
\(539\) 11.2618 0.485080
\(540\) 0 0
\(541\) −11.6370 −0.500315 −0.250158 0.968205i \(-0.580482\pi\)
−0.250158 + 0.968205i \(0.580482\pi\)
\(542\) 0 0
\(543\) −3.94214 −0.169173
\(544\) 0 0
\(545\) −11.8660 −0.508285
\(546\) 0 0
\(547\) 12.9821 0.555076 0.277538 0.960715i \(-0.410482\pi\)
0.277538 + 0.960715i \(0.410482\pi\)
\(548\) 0 0
\(549\) −3.26180 −0.139210
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) −4.12556 −0.175437
\(554\) 0 0
\(555\) 3.35350 0.142348
\(556\) 0 0
\(557\) 45.9337 1.94627 0.973137 0.230225i \(-0.0739464\pi\)
0.973137 + 0.230225i \(0.0739464\pi\)
\(558\) 0 0
\(559\) 0.0676998 0.00286340
\(560\) 0 0
\(561\) −12.0989 −0.510816
\(562\) 0 0
\(563\) 20.2017 0.851399 0.425699 0.904865i \(-0.360028\pi\)
0.425699 + 0.904865i \(0.360028\pi\)
\(564\) 0 0
\(565\) 3.75872 0.158131
\(566\) 0 0
\(567\) 1.17009 0.0491390
\(568\) 0 0
\(569\) 21.1883 0.888261 0.444131 0.895962i \(-0.353513\pi\)
0.444131 + 0.895962i \(0.353513\pi\)
\(570\) 0 0
\(571\) −0.299135 −0.0125184 −0.00625921 0.999980i \(-0.501992\pi\)
−0.00625921 + 0.999980i \(0.501992\pi\)
\(572\) 0 0
\(573\) 23.3184 0.974141
\(574\) 0 0
\(575\) 1.70928 0.0712817
\(576\) 0 0
\(577\) 19.7009 0.820158 0.410079 0.912050i \(-0.365501\pi\)
0.410079 + 0.912050i \(0.365501\pi\)
\(578\) 0 0
\(579\) 10.2557 0.426210
\(580\) 0 0
\(581\) −14.6803 −0.609043
\(582\) 0 0
\(583\) −9.94214 −0.411761
\(584\) 0 0
\(585\) 0.0917087 0.00379169
\(586\) 0 0
\(587\) 13.6598 0.563801 0.281901 0.959444i \(-0.409035\pi\)
0.281901 + 0.959444i \(0.409035\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) −23.9916 −0.986882
\(592\) 0 0
\(593\) 36.4846 1.49824 0.749122 0.662432i \(-0.230476\pi\)
0.749122 + 0.662432i \(0.230476\pi\)
\(594\) 0 0
\(595\) −7.07838 −0.290185
\(596\) 0 0
\(597\) −16.1217 −0.659817
\(598\) 0 0
\(599\) −37.1038 −1.51602 −0.758010 0.652242i \(-0.773828\pi\)
−0.758010 + 0.652242i \(0.773828\pi\)
\(600\) 0 0
\(601\) −26.8638 −1.09580 −0.547898 0.836545i \(-0.684572\pi\)
−0.547898 + 0.836545i \(0.684572\pi\)
\(602\) 0 0
\(603\) −3.85043 −0.156802
\(604\) 0 0
\(605\) −7.00000 −0.284590
\(606\) 0 0
\(607\) −6.88777 −0.279566 −0.139783 0.990182i \(-0.544641\pi\)
−0.139783 + 0.990182i \(0.544641\pi\)
\(608\) 0 0
\(609\) −9.31124 −0.377311
\(610\) 0 0
\(611\) 0.837101 0.0338655
\(612\) 0 0
\(613\) 28.4729 1.15001 0.575005 0.818150i \(-0.305000\pi\)
0.575005 + 0.818150i \(0.305000\pi\)
\(614\) 0 0
\(615\) 4.68035 0.188730
\(616\) 0 0
\(617\) 5.20394 0.209503 0.104751 0.994498i \(-0.466595\pi\)
0.104751 + 0.994498i \(0.466595\pi\)
\(618\) 0 0
\(619\) −14.0494 −0.564695 −0.282348 0.959312i \(-0.591113\pi\)
−0.282348 + 0.959312i \(0.591113\pi\)
\(620\) 0 0
\(621\) −1.70928 −0.0685909
\(622\) 0 0
\(623\) −6.75646 −0.270692
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 20.2868 0.808890
\(630\) 0 0
\(631\) 3.15061 0.125424 0.0627120 0.998032i \(-0.480025\pi\)
0.0627120 + 0.998032i \(0.480025\pi\)
\(632\) 0 0
\(633\) 18.4391 0.732887
\(634\) 0 0
\(635\) 4.18342 0.166014
\(636\) 0 0
\(637\) −0.516403 −0.0204606
\(638\) 0 0
\(639\) 1.21953 0.0482441
\(640\) 0 0
\(641\) 4.19448 0.165672 0.0828360 0.996563i \(-0.473602\pi\)
0.0828360 + 0.996563i \(0.473602\pi\)
\(642\) 0 0
\(643\) 38.0722 1.50142 0.750711 0.660631i \(-0.229711\pi\)
0.750711 + 0.660631i \(0.229711\pi\)
\(644\) 0 0
\(645\) −0.738205 −0.0290668
\(646\) 0 0
\(647\) 5.20847 0.204766 0.102383 0.994745i \(-0.467353\pi\)
0.102383 + 0.994745i \(0.467353\pi\)
\(648\) 0 0
\(649\) 22.0722 0.866411
\(650\) 0 0
\(651\) 1.17009 0.0458593
\(652\) 0 0
\(653\) 25.6658 1.00438 0.502190 0.864757i \(-0.332528\pi\)
0.502190 + 0.864757i \(0.332528\pi\)
\(654\) 0 0
\(655\) 0.695944 0.0271928
\(656\) 0 0
\(657\) 7.66701 0.299119
\(658\) 0 0
\(659\) 11.9721 0.466367 0.233184 0.972433i \(-0.425086\pi\)
0.233184 + 0.972433i \(0.425086\pi\)
\(660\) 0 0
\(661\) 36.9504 1.43720 0.718601 0.695422i \(-0.244783\pi\)
0.718601 + 0.695422i \(0.244783\pi\)
\(662\) 0 0
\(663\) 0.554787 0.0215462
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 13.6020 0.526670
\(668\) 0 0
\(669\) −15.2762 −0.590611
\(670\) 0 0
\(671\) 6.52359 0.251840
\(672\) 0 0
\(673\) −20.8853 −0.805070 −0.402535 0.915405i \(-0.631871\pi\)
−0.402535 + 0.915405i \(0.631871\pi\)
\(674\) 0 0
\(675\) −1.00000 −0.0384900
\(676\) 0 0
\(677\) −31.1110 −1.19569 −0.597847 0.801611i \(-0.703977\pi\)
−0.597847 + 0.801611i \(0.703977\pi\)
\(678\) 0 0
\(679\) −14.0410 −0.538846
\(680\) 0 0
\(681\) −19.7815 −0.758029
\(682\) 0 0
\(683\) −27.1545 −1.03904 −0.519519 0.854459i \(-0.673889\pi\)
−0.519519 + 0.854459i \(0.673889\pi\)
\(684\) 0 0
\(685\) 8.20620 0.313543
\(686\) 0 0
\(687\) −25.4329 −0.970327
\(688\) 0 0
\(689\) 0.455891 0.0173680
\(690\) 0 0
\(691\) −42.3234 −1.61006 −0.805028 0.593237i \(-0.797850\pi\)
−0.805028 + 0.593237i \(0.797850\pi\)
\(692\) 0 0
\(693\) −2.34017 −0.0888958
\(694\) 0 0
\(695\) 4.49693 0.170578
\(696\) 0 0
\(697\) 28.3135 1.07245
\(698\) 0 0
\(699\) 16.2062 0.612975
\(700\) 0 0
\(701\) −8.69472 −0.328395 −0.164198 0.986427i \(-0.552503\pi\)
−0.164198 + 0.986427i \(0.552503\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) −9.12783 −0.343774
\(706\) 0 0
\(707\) 16.3135 0.613533
\(708\) 0 0
\(709\) −31.3074 −1.17577 −0.587886 0.808943i \(-0.700040\pi\)
−0.587886 + 0.808943i \(0.700040\pi\)
\(710\) 0 0
\(711\) −3.52586 −0.132230
\(712\) 0 0
\(713\) −1.70928 −0.0640129
\(714\) 0 0
\(715\) −0.183417 −0.00685942
\(716\) 0 0
\(717\) 19.7587 0.737903
\(718\) 0 0
\(719\) −20.5236 −0.765401 −0.382700 0.923873i \(-0.625006\pi\)
−0.382700 + 0.923873i \(0.625006\pi\)
\(720\) 0 0
\(721\) −7.92389 −0.295101
\(722\) 0 0
\(723\) 8.65368 0.321834
\(724\) 0 0
\(725\) 7.95774 0.295543
\(726\) 0 0
\(727\) −31.7971 −1.17929 −0.589645 0.807663i \(-0.700732\pi\)
−0.589645 + 0.807663i \(0.700732\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −4.46573 −0.165171
\(732\) 0 0
\(733\) 10.1978 0.376664 0.188332 0.982105i \(-0.439692\pi\)
0.188332 + 0.982105i \(0.439692\pi\)
\(734\) 0 0
\(735\) 5.63090 0.207699
\(736\) 0 0
\(737\) 7.70086 0.283665
\(738\) 0 0
\(739\) −41.3835 −1.52232 −0.761158 0.648567i \(-0.775369\pi\)
−0.761158 + 0.648567i \(0.775369\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 23.8987 0.876757 0.438378 0.898791i \(-0.355553\pi\)
0.438378 + 0.898791i \(0.355553\pi\)
\(744\) 0 0
\(745\) 13.3607 0.489498
\(746\) 0 0
\(747\) −12.5464 −0.459048
\(748\) 0 0
\(749\) −0.738205 −0.0269734
\(750\) 0 0
\(751\) −51.6475 −1.88465 −0.942323 0.334706i \(-0.891363\pi\)
−0.942323 + 0.334706i \(0.891363\pi\)
\(752\) 0 0
\(753\) −18.9360 −0.690066
\(754\) 0 0
\(755\) −13.8660 −0.504637
\(756\) 0 0
\(757\) −0.687534 −0.0249888 −0.0124944 0.999922i \(-0.503977\pi\)
−0.0124944 + 0.999922i \(0.503977\pi\)
\(758\) 0 0
\(759\) 3.41855 0.124086
\(760\) 0 0
\(761\) −32.1555 −1.16564 −0.582819 0.812602i \(-0.698050\pi\)
−0.582819 + 0.812602i \(0.698050\pi\)
\(762\) 0 0
\(763\) −13.8843 −0.502645
\(764\) 0 0
\(765\) −6.04945 −0.218718
\(766\) 0 0
\(767\) −1.01211 −0.0365451
\(768\) 0 0
\(769\) −34.2206 −1.23403 −0.617013 0.786953i \(-0.711657\pi\)
−0.617013 + 0.786953i \(0.711657\pi\)
\(770\) 0 0
\(771\) 13.1012 0.471827
\(772\) 0 0
\(773\) 9.20781 0.331182 0.165591 0.986195i \(-0.447047\pi\)
0.165591 + 0.986195i \(0.447047\pi\)
\(774\) 0 0
\(775\) −1.00000 −0.0359211
\(776\) 0 0
\(777\) 3.92389 0.140769
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) −2.43907 −0.0872768
\(782\) 0 0
\(783\) −7.95774 −0.284386
\(784\) 0 0
\(785\) −20.0989 −0.717360
\(786\) 0 0
\(787\) 35.4908 1.26511 0.632555 0.774515i \(-0.282006\pi\)
0.632555 + 0.774515i \(0.282006\pi\)
\(788\) 0 0
\(789\) 8.49693 0.302499
\(790\) 0 0
\(791\) 4.39803 0.156376
\(792\) 0 0
\(793\) −0.299135 −0.0106226
\(794\) 0 0
\(795\) −4.97107 −0.176306
\(796\) 0 0
\(797\) 6.89884 0.244369 0.122185 0.992507i \(-0.461010\pi\)
0.122185 + 0.992507i \(0.461010\pi\)
\(798\) 0 0
\(799\) −55.2183 −1.95348
\(800\) 0 0
\(801\) −5.77432 −0.204026
\(802\) 0 0
\(803\) −15.3340 −0.541126
\(804\) 0 0
\(805\) 2.00000 0.0704907
\(806\) 0 0
\(807\) −21.8010 −0.767431
\(808\) 0 0
\(809\) 56.2278 1.97686 0.988432 0.151668i \(-0.0484644\pi\)
0.988432 + 0.151668i \(0.0484644\pi\)
\(810\) 0 0
\(811\) −34.7070 −1.21873 −0.609364 0.792891i \(-0.708575\pi\)
−0.609364 + 0.792891i \(0.708575\pi\)
\(812\) 0 0
\(813\) 10.3402 0.362646
\(814\) 0 0
\(815\) −4.06505 −0.142392
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0.107307 0.00374962
\(820\) 0 0
\(821\) 31.2651 1.09116 0.545580 0.838059i \(-0.316309\pi\)
0.545580 + 0.838059i \(0.316309\pi\)
\(822\) 0 0
\(823\) 44.5523 1.55300 0.776499 0.630119i \(-0.216994\pi\)
0.776499 + 0.630119i \(0.216994\pi\)
\(824\) 0 0
\(825\) 2.00000 0.0696311
\(826\) 0 0
\(827\) 2.97107 0.103314 0.0516571 0.998665i \(-0.483550\pi\)
0.0516571 + 0.998665i \(0.483550\pi\)
\(828\) 0 0
\(829\) −30.2823 −1.05175 −0.525874 0.850562i \(-0.676262\pi\)
−0.525874 + 0.850562i \(0.676262\pi\)
\(830\) 0 0
\(831\) 0.646496 0.0224267
\(832\) 0 0
\(833\) 34.0638 1.18024
\(834\) 0 0
\(835\) −3.91548 −0.135501
\(836\) 0 0
\(837\) 1.00000 0.0345651
\(838\) 0 0
\(839\) 47.8687 1.65261 0.826305 0.563223i \(-0.190439\pi\)
0.826305 + 0.563223i \(0.190439\pi\)
\(840\) 0 0
\(841\) 34.3256 1.18364
\(842\) 0 0
\(843\) 17.3874 0.598852
\(844\) 0 0
\(845\) −12.9916 −0.446924
\(846\) 0 0
\(847\) −8.19061 −0.281433
\(848\) 0 0
\(849\) 2.92881 0.100517
\(850\) 0 0
\(851\) −5.73206 −0.196493
\(852\) 0 0
\(853\) −47.8531 −1.63846 −0.819229 0.573466i \(-0.805598\pi\)
−0.819229 + 0.573466i \(0.805598\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 3.13170 0.106977 0.0534884 0.998568i \(-0.482966\pi\)
0.0534884 + 0.998568i \(0.482966\pi\)
\(858\) 0 0
\(859\) 18.4703 0.630197 0.315099 0.949059i \(-0.397962\pi\)
0.315099 + 0.949059i \(0.397962\pi\)
\(860\) 0 0
\(861\) 5.47641 0.186636
\(862\) 0 0
\(863\) 47.9130 1.63098 0.815489 0.578772i \(-0.196468\pi\)
0.815489 + 0.578772i \(0.196468\pi\)
\(864\) 0 0
\(865\) 16.0722 0.546472
\(866\) 0 0
\(867\) −19.5958 −0.665509
\(868\) 0 0
\(869\) 7.05172 0.239213
\(870\) 0 0
\(871\) −0.353118 −0.0119650
\(872\) 0 0
\(873\) −12.0000 −0.406138
\(874\) 0 0
\(875\) 1.17009 0.0395561
\(876\) 0 0
\(877\) 44.8104 1.51314 0.756571 0.653912i \(-0.226873\pi\)
0.756571 + 0.653912i \(0.226873\pi\)
\(878\) 0 0
\(879\) 31.9916 1.07905
\(880\) 0 0
\(881\) −24.4501 −0.823746 −0.411873 0.911241i \(-0.635125\pi\)
−0.411873 + 0.911241i \(0.635125\pi\)
\(882\) 0 0
\(883\) −39.8043 −1.33952 −0.669761 0.742577i \(-0.733603\pi\)
−0.669761 + 0.742577i \(0.733603\pi\)
\(884\) 0 0
\(885\) 11.0361 0.370975
\(886\) 0 0
\(887\) −16.9588 −0.569420 −0.284710 0.958614i \(-0.591897\pi\)
−0.284710 + 0.958614i \(0.591897\pi\)
\(888\) 0 0
\(889\) 4.89496 0.164172
\(890\) 0 0
\(891\) −2.00000 −0.0670025
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) −21.9421 −0.733445
\(896\) 0 0
\(897\) −0.156755 −0.00523391
\(898\) 0 0
\(899\) −7.95774 −0.265405
\(900\) 0 0
\(901\) −30.0722 −1.00185
\(902\) 0 0
\(903\) −0.863763 −0.0287442
\(904\) 0 0
\(905\) 3.94214 0.131041
\(906\) 0 0
\(907\) 3.72487 0.123682 0.0618412 0.998086i \(-0.480303\pi\)
0.0618412 + 0.998086i \(0.480303\pi\)
\(908\) 0 0
\(909\) 13.9421 0.462432
\(910\) 0 0
\(911\) 56.5523 1.87366 0.936831 0.349781i \(-0.113744\pi\)
0.936831 + 0.349781i \(0.113744\pi\)
\(912\) 0 0
\(913\) 25.0928 0.830449
\(914\) 0 0
\(915\) 3.26180 0.107832
\(916\) 0 0
\(917\) 0.814315 0.0268911
\(918\) 0 0
\(919\) 40.9770 1.35171 0.675854 0.737036i \(-0.263775\pi\)
0.675854 + 0.737036i \(0.263775\pi\)
\(920\) 0 0
\(921\) −5.66701 −0.186734
\(922\) 0 0
\(923\) 0.111842 0.00368132
\(924\) 0 0
\(925\) −3.35350 −0.110263
\(926\) 0 0
\(927\) −6.77205 −0.222423
\(928\) 0 0
\(929\) 40.2713 1.32126 0.660628 0.750713i \(-0.270290\pi\)
0.660628 + 0.750713i \(0.270290\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −16.2401 −0.531675
\(934\) 0 0
\(935\) 12.0989 0.395676
\(936\) 0 0
\(937\) −28.9405 −0.945446 −0.472723 0.881211i \(-0.656729\pi\)
−0.472723 + 0.881211i \(0.656729\pi\)
\(938\) 0 0
\(939\) −7.42574 −0.242330
\(940\) 0 0
\(941\) 45.7431 1.49118 0.745592 0.666403i \(-0.232167\pi\)
0.745592 + 0.666403i \(0.232167\pi\)
\(942\) 0 0
\(943\) −8.00000 −0.260516
\(944\) 0 0
\(945\) −1.17009 −0.0380629
\(946\) 0 0
\(947\) 57.7093 1.87530 0.937650 0.347582i \(-0.112997\pi\)
0.937650 + 0.347582i \(0.112997\pi\)
\(948\) 0 0
\(949\) 0.703132 0.0228246
\(950\) 0 0
\(951\) 13.2534 0.429770
\(952\) 0 0
\(953\) −3.89269 −0.126097 −0.0630483 0.998010i \(-0.520082\pi\)
−0.0630483 + 0.998010i \(0.520082\pi\)
\(954\) 0 0
\(955\) −23.3184 −0.754567
\(956\) 0 0
\(957\) 15.9155 0.514474
\(958\) 0 0
\(959\) 9.60197 0.310064
\(960\) 0 0
\(961\) 1.00000 0.0322581
\(962\) 0 0
\(963\) −0.630898 −0.0203304
\(964\) 0 0
\(965\) −10.2557 −0.330141
\(966\) 0 0
\(967\) −23.1317 −0.743865 −0.371933 0.928260i \(-0.621305\pi\)
−0.371933 + 0.928260i \(0.621305\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 3.51414 0.112774 0.0563870 0.998409i \(-0.482042\pi\)
0.0563870 + 0.998409i \(0.482042\pi\)
\(972\) 0 0
\(973\) 5.26180 0.168685
\(974\) 0 0
\(975\) −0.0917087 −0.00293703
\(976\) 0 0
\(977\) 37.5174 1.20029 0.600145 0.799891i \(-0.295110\pi\)
0.600145 + 0.799891i \(0.295110\pi\)
\(978\) 0 0
\(979\) 11.5486 0.369096
\(980\) 0 0
\(981\) −11.8660 −0.378853
\(982\) 0 0
\(983\) −56.2434 −1.79388 −0.896942 0.442147i \(-0.854217\pi\)
−0.896942 + 0.442147i \(0.854217\pi\)
\(984\) 0 0
\(985\) 23.9916 0.764436
\(986\) 0 0
\(987\) −10.6803 −0.339959
\(988\) 0 0
\(989\) 1.26180 0.0401228
\(990\) 0 0
\(991\) −61.4284 −1.95134 −0.975669 0.219251i \(-0.929639\pi\)
−0.975669 + 0.219251i \(0.929639\pi\)
\(992\) 0 0
\(993\) 3.62475 0.115028
\(994\) 0 0
\(995\) 16.1217 0.511092
\(996\) 0 0
\(997\) 49.6307 1.57182 0.785910 0.618340i \(-0.212195\pi\)
0.785910 + 0.618340i \(0.212195\pi\)
\(998\) 0 0
\(999\) 3.35350 0.106100
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 7440.2.a.bp.1.3 3
4.3 odd 2 465.2.a.f.1.3 3
12.11 even 2 1395.2.a.i.1.1 3
20.3 even 4 2325.2.c.o.1024.1 6
20.7 even 4 2325.2.c.o.1024.6 6
20.19 odd 2 2325.2.a.q.1.1 3
60.59 even 2 6975.2.a.be.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
465.2.a.f.1.3 3 4.3 odd 2
1395.2.a.i.1.1 3 12.11 even 2
2325.2.a.q.1.1 3 20.19 odd 2
2325.2.c.o.1024.1 6 20.3 even 4
2325.2.c.o.1024.6 6 20.7 even 4
6975.2.a.be.1.3 3 60.59 even 2
7440.2.a.bp.1.3 3 1.1 even 1 trivial