Properties

Label 4840.2.a.bh.1.6
Level $4840$
Weight $2$
Character 4840.1
Self dual yes
Analytic conductor $38.648$
Analytic rank $0$
Dimension $8$
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] = [4840,2,Mod(1,4840)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4840, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("4840.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4840 = 2^{3} \cdot 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4840.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: \(38.6475945783\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{7} - 21x^{6} + 15x^{5} + 140x^{4} - 60x^{3} - 295x^{2} + 50x + 100 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 440)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(1.88088\) of defining polynomial
Character \(\chi\) \(=\) 4840.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.88088 q^{3} +1.00000 q^{5} -3.67750 q^{7} +0.537727 q^{9} +O(q^{10})\) \(q+1.88088 q^{3} +1.00000 q^{5} -3.67750 q^{7} +0.537727 q^{9} -2.33434 q^{13} +1.88088 q^{15} +0.320444 q^{17} +4.52846 q^{19} -6.91695 q^{21} -0.780485 q^{23} +1.00000 q^{25} -4.63125 q^{27} -1.52157 q^{29} +4.98712 q^{31} -3.67750 q^{35} +8.86148 q^{37} -4.39063 q^{39} +6.00961 q^{41} +0.236696 q^{43} +0.537727 q^{45} +13.3994 q^{47} +6.52400 q^{49} +0.602718 q^{51} +9.17986 q^{53} +8.51751 q^{57} +6.04683 q^{59} +1.83199 q^{61} -1.97749 q^{63} -2.33434 q^{65} -4.56425 q^{67} -1.46800 q^{69} +12.9744 q^{71} -8.11568 q^{73} +1.88088 q^{75} +11.2338 q^{79} -10.3240 q^{81} -14.0575 q^{83} +0.320444 q^{85} -2.86189 q^{87} -4.85749 q^{89} +8.58454 q^{91} +9.38020 q^{93} +4.52846 q^{95} -5.57068 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + q^{3} + 8 q^{5} + 6 q^{7} + 19 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + q^{3} + 8 q^{5} + 6 q^{7} + 19 q^{9} - 12 q^{13} + q^{15} - 2 q^{17} + 6 q^{19} - 6 q^{21} + 10 q^{23} + 8 q^{25} + 13 q^{27} - 8 q^{29} + 19 q^{31} + 6 q^{35} + 12 q^{37} + 21 q^{39} + 3 q^{41} + 8 q^{43} + 19 q^{45} + 10 q^{47} + 22 q^{49} + 7 q^{51} + 28 q^{53} - 25 q^{57} + 25 q^{59} - 10 q^{61} + 64 q^{63} - 12 q^{65} - 2 q^{67} + 18 q^{69} + 25 q^{71} - 38 q^{73} + q^{75} + 38 q^{79} + 32 q^{81} + 28 q^{83} - 2 q^{85} - 15 q^{87} + 12 q^{89} + 8 q^{91} - 15 q^{93} + 6 q^{95} + 21 q^{97}+O(q^{100}) \) 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
\(3\) 1.88088 1.08593 0.542965 0.839756i \(-0.317302\pi\)
0.542965 + 0.839756i \(0.317302\pi\)
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) −3.67750 −1.38996 −0.694982 0.719027i \(-0.744588\pi\)
−0.694982 + 0.719027i \(0.744588\pi\)
\(8\) 0 0
\(9\) 0.537727 0.179242
\(10\) 0 0
\(11\) 0 0
\(12\) 0 0
\(13\) −2.33434 −0.647430 −0.323715 0.946155i \(-0.604932\pi\)
−0.323715 + 0.946155i \(0.604932\pi\)
\(14\) 0 0
\(15\) 1.88088 0.485642
\(16\) 0 0
\(17\) 0.320444 0.0777191 0.0388595 0.999245i \(-0.487628\pi\)
0.0388595 + 0.999245i \(0.487628\pi\)
\(18\) 0 0
\(19\) 4.52846 1.03890 0.519450 0.854501i \(-0.326137\pi\)
0.519450 + 0.854501i \(0.326137\pi\)
\(20\) 0 0
\(21\) −6.91695 −1.50940
\(22\) 0 0
\(23\) −0.780485 −0.162742 −0.0813712 0.996684i \(-0.525930\pi\)
−0.0813712 + 0.996684i \(0.525930\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −4.63125 −0.891285
\(28\) 0 0
\(29\) −1.52157 −0.282548 −0.141274 0.989971i \(-0.545120\pi\)
−0.141274 + 0.989971i \(0.545120\pi\)
\(30\) 0 0
\(31\) 4.98712 0.895713 0.447857 0.894105i \(-0.352188\pi\)
0.447857 + 0.894105i \(0.352188\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −3.67750 −0.621611
\(36\) 0 0
\(37\) 8.86148 1.45682 0.728410 0.685142i \(-0.240260\pi\)
0.728410 + 0.685142i \(0.240260\pi\)
\(38\) 0 0
\(39\) −4.39063 −0.703063
\(40\) 0 0
\(41\) 6.00961 0.938544 0.469272 0.883054i \(-0.344516\pi\)
0.469272 + 0.883054i \(0.344516\pi\)
\(42\) 0 0
\(43\) 0.236696 0.0360958 0.0180479 0.999837i \(-0.494255\pi\)
0.0180479 + 0.999837i \(0.494255\pi\)
\(44\) 0 0
\(45\) 0.537727 0.0801596
\(46\) 0 0
\(47\) 13.3994 1.95450 0.977251 0.212088i \(-0.0680264\pi\)
0.977251 + 0.212088i \(0.0680264\pi\)
\(48\) 0 0
\(49\) 6.52400 0.932000
\(50\) 0 0
\(51\) 0.602718 0.0843974
\(52\) 0 0
\(53\) 9.17986 1.26095 0.630475 0.776209i \(-0.282860\pi\)
0.630475 + 0.776209i \(0.282860\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 8.51751 1.12817
\(58\) 0 0
\(59\) 6.04683 0.787231 0.393615 0.919275i \(-0.371224\pi\)
0.393615 + 0.919275i \(0.371224\pi\)
\(60\) 0 0
\(61\) 1.83199 0.234562 0.117281 0.993099i \(-0.462582\pi\)
0.117281 + 0.993099i \(0.462582\pi\)
\(62\) 0 0
\(63\) −1.97749 −0.249141
\(64\) 0 0
\(65\) −2.33434 −0.289539
\(66\) 0 0
\(67\) −4.56425 −0.557612 −0.278806 0.960347i \(-0.589939\pi\)
−0.278806 + 0.960347i \(0.589939\pi\)
\(68\) 0 0
\(69\) −1.46800 −0.176727
\(70\) 0 0
\(71\) 12.9744 1.53978 0.769890 0.638177i \(-0.220311\pi\)
0.769890 + 0.638177i \(0.220311\pi\)
\(72\) 0 0
\(73\) −8.11568 −0.949869 −0.474934 0.880021i \(-0.657528\pi\)
−0.474934 + 0.880021i \(0.657528\pi\)
\(74\) 0 0
\(75\) 1.88088 0.217186
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 11.2338 1.26390 0.631950 0.775009i \(-0.282255\pi\)
0.631950 + 0.775009i \(0.282255\pi\)
\(80\) 0 0
\(81\) −10.3240 −1.14711
\(82\) 0 0
\(83\) −14.0575 −1.54301 −0.771507 0.636220i \(-0.780497\pi\)
−0.771507 + 0.636220i \(0.780497\pi\)
\(84\) 0 0
\(85\) 0.320444 0.0347570
\(86\) 0 0
\(87\) −2.86189 −0.306827
\(88\) 0 0
\(89\) −4.85749 −0.514893 −0.257447 0.966293i \(-0.582881\pi\)
−0.257447 + 0.966293i \(0.582881\pi\)
\(90\) 0 0
\(91\) 8.58454 0.899904
\(92\) 0 0
\(93\) 9.38020 0.972681
\(94\) 0 0
\(95\) 4.52846 0.464610
\(96\) 0 0
\(97\) −5.57068 −0.565617 −0.282809 0.959176i \(-0.591266\pi\)
−0.282809 + 0.959176i \(0.591266\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −2.50083 −0.248842 −0.124421 0.992230i \(-0.539707\pi\)
−0.124421 + 0.992230i \(0.539707\pi\)
\(102\) 0 0
\(103\) 9.80665 0.966278 0.483139 0.875544i \(-0.339497\pi\)
0.483139 + 0.875544i \(0.339497\pi\)
\(104\) 0 0
\(105\) −6.91695 −0.675025
\(106\) 0 0
\(107\) 13.2084 1.27690 0.638452 0.769661i \(-0.279575\pi\)
0.638452 + 0.769661i \(0.279575\pi\)
\(108\) 0 0
\(109\) 10.6945 1.02435 0.512173 0.858882i \(-0.328841\pi\)
0.512173 + 0.858882i \(0.328841\pi\)
\(110\) 0 0
\(111\) 16.6674 1.58200
\(112\) 0 0
\(113\) −18.8367 −1.77201 −0.886005 0.463675i \(-0.846530\pi\)
−0.886005 + 0.463675i \(0.846530\pi\)
\(114\) 0 0
\(115\) −0.780485 −0.0727806
\(116\) 0 0
\(117\) −1.25524 −0.116047
\(118\) 0 0
\(119\) −1.17843 −0.108027
\(120\) 0 0
\(121\) 0 0
\(122\) 0 0
\(123\) 11.3034 1.01919
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 7.30297 0.648033 0.324017 0.946051i \(-0.394967\pi\)
0.324017 + 0.946051i \(0.394967\pi\)
\(128\) 0 0
\(129\) 0.445198 0.0391975
\(130\) 0 0
\(131\) −5.45982 −0.477027 −0.238513 0.971139i \(-0.576660\pi\)
−0.238513 + 0.971139i \(0.576660\pi\)
\(132\) 0 0
\(133\) −16.6534 −1.44403
\(134\) 0 0
\(135\) −4.63125 −0.398595
\(136\) 0 0
\(137\) 20.5698 1.75740 0.878699 0.477377i \(-0.158412\pi\)
0.878699 + 0.477377i \(0.158412\pi\)
\(138\) 0 0
\(139\) −9.49138 −0.805048 −0.402524 0.915409i \(-0.631867\pi\)
−0.402524 + 0.915409i \(0.631867\pi\)
\(140\) 0 0
\(141\) 25.2027 2.12245
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) −1.52157 −0.126359
\(146\) 0 0
\(147\) 12.2709 1.01209
\(148\) 0 0
\(149\) 21.5816 1.76804 0.884018 0.467452i \(-0.154828\pi\)
0.884018 + 0.467452i \(0.154828\pi\)
\(150\) 0 0
\(151\) 23.8130 1.93787 0.968936 0.247310i \(-0.0795465\pi\)
0.968936 + 0.247310i \(0.0795465\pi\)
\(152\) 0 0
\(153\) 0.172311 0.0139306
\(154\) 0 0
\(155\) 4.98712 0.400575
\(156\) 0 0
\(157\) 10.7734 0.859808 0.429904 0.902875i \(-0.358547\pi\)
0.429904 + 0.902875i \(0.358547\pi\)
\(158\) 0 0
\(159\) 17.2663 1.36930
\(160\) 0 0
\(161\) 2.87023 0.226206
\(162\) 0 0
\(163\) 3.34342 0.261877 0.130939 0.991390i \(-0.458201\pi\)
0.130939 + 0.991390i \(0.458201\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −11.4630 −0.887032 −0.443516 0.896266i \(-0.646269\pi\)
−0.443516 + 0.896266i \(0.646269\pi\)
\(168\) 0 0
\(169\) −7.55085 −0.580835
\(170\) 0 0
\(171\) 2.43508 0.186215
\(172\) 0 0
\(173\) −14.3879 −1.09389 −0.546945 0.837168i \(-0.684209\pi\)
−0.546945 + 0.837168i \(0.684209\pi\)
\(174\) 0 0
\(175\) −3.67750 −0.277993
\(176\) 0 0
\(177\) 11.3734 0.854877
\(178\) 0 0
\(179\) −12.3747 −0.924927 −0.462464 0.886638i \(-0.653034\pi\)
−0.462464 + 0.886638i \(0.653034\pi\)
\(180\) 0 0
\(181\) −11.9220 −0.886153 −0.443076 0.896484i \(-0.646113\pi\)
−0.443076 + 0.896484i \(0.646113\pi\)
\(182\) 0 0
\(183\) 3.44576 0.254718
\(184\) 0 0
\(185\) 8.86148 0.651509
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 17.0314 1.23885
\(190\) 0 0
\(191\) 0.537459 0.0388892 0.0194446 0.999811i \(-0.493810\pi\)
0.0194446 + 0.999811i \(0.493810\pi\)
\(192\) 0 0
\(193\) −7.19252 −0.517729 −0.258864 0.965914i \(-0.583348\pi\)
−0.258864 + 0.965914i \(0.583348\pi\)
\(194\) 0 0
\(195\) −4.39063 −0.314419
\(196\) 0 0
\(197\) −21.9556 −1.56427 −0.782135 0.623108i \(-0.785870\pi\)
−0.782135 + 0.623108i \(0.785870\pi\)
\(198\) 0 0
\(199\) −25.3774 −1.79895 −0.899477 0.436968i \(-0.856052\pi\)
−0.899477 + 0.436968i \(0.856052\pi\)
\(200\) 0 0
\(201\) −8.58483 −0.605527
\(202\) 0 0
\(203\) 5.59556 0.392731
\(204\) 0 0
\(205\) 6.00961 0.419730
\(206\) 0 0
\(207\) −0.419688 −0.0291703
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 22.1234 1.52304 0.761518 0.648144i \(-0.224455\pi\)
0.761518 + 0.648144i \(0.224455\pi\)
\(212\) 0 0
\(213\) 24.4034 1.67209
\(214\) 0 0
\(215\) 0.236696 0.0161426
\(216\) 0 0
\(217\) −18.3401 −1.24501
\(218\) 0 0
\(219\) −15.2647 −1.03149
\(220\) 0 0
\(221\) −0.748025 −0.0503176
\(222\) 0 0
\(223\) −20.3283 −1.36128 −0.680641 0.732617i \(-0.738298\pi\)
−0.680641 + 0.732617i \(0.738298\pi\)
\(224\) 0 0
\(225\) 0.537727 0.0358485
\(226\) 0 0
\(227\) 20.0768 1.33254 0.666272 0.745708i \(-0.267889\pi\)
0.666272 + 0.745708i \(0.267889\pi\)
\(228\) 0 0
\(229\) 26.3280 1.73980 0.869900 0.493228i \(-0.164183\pi\)
0.869900 + 0.493228i \(0.164183\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −5.42781 −0.355587 −0.177794 0.984068i \(-0.556896\pi\)
−0.177794 + 0.984068i \(0.556896\pi\)
\(234\) 0 0
\(235\) 13.3994 0.874079
\(236\) 0 0
\(237\) 21.1295 1.37251
\(238\) 0 0
\(239\) −0.634170 −0.0410211 −0.0205105 0.999790i \(-0.506529\pi\)
−0.0205105 + 0.999790i \(0.506529\pi\)
\(240\) 0 0
\(241\) 22.9844 1.48055 0.740277 0.672302i \(-0.234694\pi\)
0.740277 + 0.672302i \(0.234694\pi\)
\(242\) 0 0
\(243\) −5.52456 −0.354401
\(244\) 0 0
\(245\) 6.52400 0.416803
\(246\) 0 0
\(247\) −10.5710 −0.672614
\(248\) 0 0
\(249\) −26.4406 −1.67560
\(250\) 0 0
\(251\) −7.71649 −0.487061 −0.243530 0.969893i \(-0.578306\pi\)
−0.243530 + 0.969893i \(0.578306\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0.602718 0.0377437
\(256\) 0 0
\(257\) 5.26088 0.328165 0.164082 0.986447i \(-0.447534\pi\)
0.164082 + 0.986447i \(0.447534\pi\)
\(258\) 0 0
\(259\) −32.5881 −2.02493
\(260\) 0 0
\(261\) −0.818188 −0.0506446
\(262\) 0 0
\(263\) −8.57705 −0.528884 −0.264442 0.964402i \(-0.585188\pi\)
−0.264442 + 0.964402i \(0.585188\pi\)
\(264\) 0 0
\(265\) 9.17986 0.563914
\(266\) 0 0
\(267\) −9.13638 −0.559138
\(268\) 0 0
\(269\) −20.7056 −1.26244 −0.631222 0.775602i \(-0.717446\pi\)
−0.631222 + 0.775602i \(0.717446\pi\)
\(270\) 0 0
\(271\) 0.609048 0.0369970 0.0184985 0.999829i \(-0.494111\pi\)
0.0184985 + 0.999829i \(0.494111\pi\)
\(272\) 0 0
\(273\) 16.1465 0.977232
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −0.287731 −0.0172881 −0.00864404 0.999963i \(-0.502752\pi\)
−0.00864404 + 0.999963i \(0.502752\pi\)
\(278\) 0 0
\(279\) 2.68171 0.160550
\(280\) 0 0
\(281\) −27.2485 −1.62551 −0.812756 0.582605i \(-0.802034\pi\)
−0.812756 + 0.582605i \(0.802034\pi\)
\(282\) 0 0
\(283\) 25.0168 1.48709 0.743546 0.668685i \(-0.233143\pi\)
0.743546 + 0.668685i \(0.233143\pi\)
\(284\) 0 0
\(285\) 8.51751 0.504534
\(286\) 0 0
\(287\) −22.1003 −1.30454
\(288\) 0 0
\(289\) −16.8973 −0.993960
\(290\) 0 0
\(291\) −10.4778 −0.614220
\(292\) 0 0
\(293\) 7.29288 0.426055 0.213027 0.977046i \(-0.431668\pi\)
0.213027 + 0.977046i \(0.431668\pi\)
\(294\) 0 0
\(295\) 6.04683 0.352060
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 1.82192 0.105364
\(300\) 0 0
\(301\) −0.870450 −0.0501719
\(302\) 0 0
\(303\) −4.70377 −0.270225
\(304\) 0 0
\(305\) 1.83199 0.104899
\(306\) 0 0
\(307\) −27.8261 −1.58812 −0.794059 0.607841i \(-0.792036\pi\)
−0.794059 + 0.607841i \(0.792036\pi\)
\(308\) 0 0
\(309\) 18.4452 1.04931
\(310\) 0 0
\(311\) 9.76469 0.553705 0.276852 0.960912i \(-0.410709\pi\)
0.276852 + 0.960912i \(0.410709\pi\)
\(312\) 0 0
\(313\) −7.34068 −0.414920 −0.207460 0.978244i \(-0.566520\pi\)
−0.207460 + 0.978244i \(0.566520\pi\)
\(314\) 0 0
\(315\) −1.97749 −0.111419
\(316\) 0 0
\(317\) −7.85302 −0.441070 −0.220535 0.975379i \(-0.570780\pi\)
−0.220535 + 0.975379i \(0.570780\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 24.8435 1.38663
\(322\) 0 0
\(323\) 1.45112 0.0807423
\(324\) 0 0
\(325\) −2.33434 −0.129486
\(326\) 0 0
\(327\) 20.1151 1.11237
\(328\) 0 0
\(329\) −49.2762 −2.71669
\(330\) 0 0
\(331\) 19.0888 1.04922 0.524608 0.851344i \(-0.324212\pi\)
0.524608 + 0.851344i \(0.324212\pi\)
\(332\) 0 0
\(333\) 4.76506 0.261124
\(334\) 0 0
\(335\) −4.56425 −0.249372
\(336\) 0 0
\(337\) −7.76848 −0.423176 −0.211588 0.977359i \(-0.567864\pi\)
−0.211588 + 0.977359i \(0.567864\pi\)
\(338\) 0 0
\(339\) −35.4297 −1.92428
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 1.75050 0.0945179
\(344\) 0 0
\(345\) −1.46800 −0.0790346
\(346\) 0 0
\(347\) 16.8673 0.905485 0.452743 0.891641i \(-0.350446\pi\)
0.452743 + 0.891641i \(0.350446\pi\)
\(348\) 0 0
\(349\) −0.916586 −0.0490637 −0.0245319 0.999699i \(-0.507810\pi\)
−0.0245319 + 0.999699i \(0.507810\pi\)
\(350\) 0 0
\(351\) 10.8109 0.577044
\(352\) 0 0
\(353\) 5.60398 0.298270 0.149135 0.988817i \(-0.452351\pi\)
0.149135 + 0.988817i \(0.452351\pi\)
\(354\) 0 0
\(355\) 12.9744 0.688610
\(356\) 0 0
\(357\) −2.21649 −0.117309
\(358\) 0 0
\(359\) 2.77506 0.146462 0.0732311 0.997315i \(-0.476669\pi\)
0.0732311 + 0.997315i \(0.476669\pi\)
\(360\) 0 0
\(361\) 1.50693 0.0793120
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −8.11568 −0.424794
\(366\) 0 0
\(367\) 28.6677 1.49644 0.748222 0.663449i \(-0.230908\pi\)
0.748222 + 0.663449i \(0.230908\pi\)
\(368\) 0 0
\(369\) 3.23153 0.168227
\(370\) 0 0
\(371\) −33.7589 −1.75268
\(372\) 0 0
\(373\) −17.0173 −0.881122 −0.440561 0.897723i \(-0.645220\pi\)
−0.440561 + 0.897723i \(0.645220\pi\)
\(374\) 0 0
\(375\) 1.88088 0.0971285
\(376\) 0 0
\(377\) 3.55186 0.182930
\(378\) 0 0
\(379\) 0.848376 0.0435781 0.0217891 0.999763i \(-0.493064\pi\)
0.0217891 + 0.999763i \(0.493064\pi\)
\(380\) 0 0
\(381\) 13.7360 0.703718
\(382\) 0 0
\(383\) −30.7454 −1.57102 −0.785509 0.618850i \(-0.787599\pi\)
−0.785509 + 0.618850i \(0.787599\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0.127278 0.00646991
\(388\) 0 0
\(389\) −26.3829 −1.33766 −0.668832 0.743413i \(-0.733206\pi\)
−0.668832 + 0.743413i \(0.733206\pi\)
\(390\) 0 0
\(391\) −0.250102 −0.0126482
\(392\) 0 0
\(393\) −10.2693 −0.518017
\(394\) 0 0
\(395\) 11.2338 0.565233
\(396\) 0 0
\(397\) 16.7272 0.839516 0.419758 0.907636i \(-0.362115\pi\)
0.419758 + 0.907636i \(0.362115\pi\)
\(398\) 0 0
\(399\) −31.3231 −1.56812
\(400\) 0 0
\(401\) −5.83932 −0.291602 −0.145801 0.989314i \(-0.546576\pi\)
−0.145801 + 0.989314i \(0.546576\pi\)
\(402\) 0 0
\(403\) −11.6416 −0.579911
\(404\) 0 0
\(405\) −10.3240 −0.513005
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 36.3522 1.79750 0.898751 0.438459i \(-0.144476\pi\)
0.898751 + 0.438459i \(0.144476\pi\)
\(410\) 0 0
\(411\) 38.6894 1.90841
\(412\) 0 0
\(413\) −22.2372 −1.09422
\(414\) 0 0
\(415\) −14.0575 −0.690057
\(416\) 0 0
\(417\) −17.8522 −0.874226
\(418\) 0 0
\(419\) −8.37243 −0.409020 −0.204510 0.978864i \(-0.565560\pi\)
−0.204510 + 0.978864i \(0.565560\pi\)
\(420\) 0 0
\(421\) 22.0147 1.07293 0.536465 0.843923i \(-0.319759\pi\)
0.536465 + 0.843923i \(0.319759\pi\)
\(422\) 0 0
\(423\) 7.20521 0.350330
\(424\) 0 0
\(425\) 0.320444 0.0155438
\(426\) 0 0
\(427\) −6.73714 −0.326033
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 3.24452 0.156283 0.0781414 0.996942i \(-0.475101\pi\)
0.0781414 + 0.996942i \(0.475101\pi\)
\(432\) 0 0
\(433\) −27.6170 −1.32719 −0.663595 0.748092i \(-0.730970\pi\)
−0.663595 + 0.748092i \(0.730970\pi\)
\(434\) 0 0
\(435\) −2.86189 −0.137217
\(436\) 0 0
\(437\) −3.53439 −0.169073
\(438\) 0 0
\(439\) 14.5936 0.696516 0.348258 0.937399i \(-0.386773\pi\)
0.348258 + 0.937399i \(0.386773\pi\)
\(440\) 0 0
\(441\) 3.50813 0.167054
\(442\) 0 0
\(443\) 24.0251 1.14147 0.570734 0.821135i \(-0.306659\pi\)
0.570734 + 0.821135i \(0.306659\pi\)
\(444\) 0 0
\(445\) −4.85749 −0.230267
\(446\) 0 0
\(447\) 40.5926 1.91996
\(448\) 0 0
\(449\) 9.26951 0.437455 0.218728 0.975786i \(-0.429809\pi\)
0.218728 + 0.975786i \(0.429809\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 44.7895 2.10439
\(454\) 0 0
\(455\) 8.58454 0.402449
\(456\) 0 0
\(457\) −8.93524 −0.417973 −0.208986 0.977919i \(-0.567016\pi\)
−0.208986 + 0.977919i \(0.567016\pi\)
\(458\) 0 0
\(459\) −1.48406 −0.0692698
\(460\) 0 0
\(461\) −11.9953 −0.558678 −0.279339 0.960193i \(-0.590115\pi\)
−0.279339 + 0.960193i \(0.590115\pi\)
\(462\) 0 0
\(463\) 0.787889 0.0366163 0.0183082 0.999832i \(-0.494172\pi\)
0.0183082 + 0.999832i \(0.494172\pi\)
\(464\) 0 0
\(465\) 9.38020 0.434996
\(466\) 0 0
\(467\) −12.1038 −0.560096 −0.280048 0.959986i \(-0.590350\pi\)
−0.280048 + 0.959986i \(0.590350\pi\)
\(468\) 0 0
\(469\) 16.7850 0.775060
\(470\) 0 0
\(471\) 20.2634 0.933690
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 4.52846 0.207780
\(476\) 0 0
\(477\) 4.93626 0.226016
\(478\) 0 0
\(479\) −8.44837 −0.386016 −0.193008 0.981197i \(-0.561824\pi\)
−0.193008 + 0.981197i \(0.561824\pi\)
\(480\) 0 0
\(481\) −20.6857 −0.943188
\(482\) 0 0
\(483\) 5.39857 0.245644
\(484\) 0 0
\(485\) −5.57068 −0.252952
\(486\) 0 0
\(487\) −4.54679 −0.206035 −0.103017 0.994680i \(-0.532850\pi\)
−0.103017 + 0.994680i \(0.532850\pi\)
\(488\) 0 0
\(489\) 6.28860 0.284380
\(490\) 0 0
\(491\) 15.8830 0.716788 0.358394 0.933570i \(-0.383324\pi\)
0.358394 + 0.933570i \(0.383324\pi\)
\(492\) 0 0
\(493\) −0.487577 −0.0219594
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −47.7134 −2.14024
\(498\) 0 0
\(499\) 4.19713 0.187890 0.0939448 0.995577i \(-0.470052\pi\)
0.0939448 + 0.995577i \(0.470052\pi\)
\(500\) 0 0
\(501\) −21.5605 −0.963254
\(502\) 0 0
\(503\) 10.9721 0.489224 0.244612 0.969621i \(-0.421339\pi\)
0.244612 + 0.969621i \(0.421339\pi\)
\(504\) 0 0
\(505\) −2.50083 −0.111286
\(506\) 0 0
\(507\) −14.2023 −0.630745
\(508\) 0 0
\(509\) 15.3788 0.681651 0.340826 0.940127i \(-0.389293\pi\)
0.340826 + 0.940127i \(0.389293\pi\)
\(510\) 0 0
\(511\) 29.8454 1.32028
\(512\) 0 0
\(513\) −20.9724 −0.925955
\(514\) 0 0
\(515\) 9.80665 0.432133
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) −27.0619 −1.18789
\(520\) 0 0
\(521\) 11.8490 0.519113 0.259556 0.965728i \(-0.416424\pi\)
0.259556 + 0.965728i \(0.416424\pi\)
\(522\) 0 0
\(523\) 37.9145 1.65789 0.828943 0.559334i \(-0.188943\pi\)
0.828943 + 0.559334i \(0.188943\pi\)
\(524\) 0 0
\(525\) −6.91695 −0.301881
\(526\) 0 0
\(527\) 1.59809 0.0696140
\(528\) 0 0
\(529\) −22.3908 −0.973515
\(530\) 0 0
\(531\) 3.25155 0.141105
\(532\) 0 0
\(533\) −14.0285 −0.607641
\(534\) 0 0
\(535\) 13.2084 0.571049
\(536\) 0 0
\(537\) −23.2754 −1.00441
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −28.5341 −1.22678 −0.613389 0.789781i \(-0.710194\pi\)
−0.613389 + 0.789781i \(0.710194\pi\)
\(542\) 0 0
\(543\) −22.4238 −0.962299
\(544\) 0 0
\(545\) 10.6945 0.458102
\(546\) 0 0
\(547\) 32.3868 1.38476 0.692379 0.721534i \(-0.256563\pi\)
0.692379 + 0.721534i \(0.256563\pi\)
\(548\) 0 0
\(549\) 0.985110 0.0420435
\(550\) 0 0
\(551\) −6.89035 −0.293539
\(552\) 0 0
\(553\) −41.3122 −1.75678
\(554\) 0 0
\(555\) 16.6674 0.707493
\(556\) 0 0
\(557\) −2.22631 −0.0943317 −0.0471659 0.998887i \(-0.515019\pi\)
−0.0471659 + 0.998887i \(0.515019\pi\)
\(558\) 0 0
\(559\) −0.552530 −0.0233695
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0.381215 0.0160663 0.00803315 0.999968i \(-0.497443\pi\)
0.00803315 + 0.999968i \(0.497443\pi\)
\(564\) 0 0
\(565\) −18.8367 −0.792467
\(566\) 0 0
\(567\) 37.9666 1.59445
\(568\) 0 0
\(569\) 34.2147 1.43436 0.717178 0.696890i \(-0.245433\pi\)
0.717178 + 0.696890i \(0.245433\pi\)
\(570\) 0 0
\(571\) 31.9104 1.33541 0.667704 0.744427i \(-0.267277\pi\)
0.667704 + 0.744427i \(0.267277\pi\)
\(572\) 0 0
\(573\) 1.01090 0.0422309
\(574\) 0 0
\(575\) −0.780485 −0.0325485
\(576\) 0 0
\(577\) −5.38137 −0.224029 −0.112015 0.993707i \(-0.535730\pi\)
−0.112015 + 0.993707i \(0.535730\pi\)
\(578\) 0 0
\(579\) −13.5283 −0.562217
\(580\) 0 0
\(581\) 51.6966 2.14473
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) −1.25524 −0.0518977
\(586\) 0 0
\(587\) 12.5991 0.520022 0.260011 0.965606i \(-0.416274\pi\)
0.260011 + 0.965606i \(0.416274\pi\)
\(588\) 0 0
\(589\) 22.5840 0.930556
\(590\) 0 0
\(591\) −41.2959 −1.69869
\(592\) 0 0
\(593\) −11.6814 −0.479696 −0.239848 0.970810i \(-0.577098\pi\)
−0.239848 + 0.970810i \(0.577098\pi\)
\(594\) 0 0
\(595\) −1.17843 −0.0483110
\(596\) 0 0
\(597\) −47.7319 −1.95354
\(598\) 0 0
\(599\) −14.6795 −0.599788 −0.299894 0.953973i \(-0.596951\pi\)
−0.299894 + 0.953973i \(0.596951\pi\)
\(600\) 0 0
\(601\) −36.1956 −1.47645 −0.738225 0.674554i \(-0.764336\pi\)
−0.738225 + 0.674554i \(0.764336\pi\)
\(602\) 0 0
\(603\) −2.45432 −0.0999477
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 12.4459 0.505163 0.252582 0.967576i \(-0.418720\pi\)
0.252582 + 0.967576i \(0.418720\pi\)
\(608\) 0 0
\(609\) 10.5246 0.426479
\(610\) 0 0
\(611\) −31.2787 −1.26540
\(612\) 0 0
\(613\) −20.0072 −0.808085 −0.404042 0.914740i \(-0.632395\pi\)
−0.404042 + 0.914740i \(0.632395\pi\)
\(614\) 0 0
\(615\) 11.3034 0.455797
\(616\) 0 0
\(617\) 27.8583 1.12153 0.560767 0.827973i \(-0.310506\pi\)
0.560767 + 0.827973i \(0.310506\pi\)
\(618\) 0 0
\(619\) −37.5555 −1.50948 −0.754742 0.656022i \(-0.772238\pi\)
−0.754742 + 0.656022i \(0.772238\pi\)
\(620\) 0 0
\(621\) 3.61462 0.145050
\(622\) 0 0
\(623\) 17.8634 0.715683
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 2.83961 0.113223
\(630\) 0 0
\(631\) −38.8856 −1.54801 −0.774006 0.633178i \(-0.781750\pi\)
−0.774006 + 0.633178i \(0.781750\pi\)
\(632\) 0 0
\(633\) 41.6115 1.65391
\(634\) 0 0
\(635\) 7.30297 0.289809
\(636\) 0 0
\(637\) −15.2292 −0.603404
\(638\) 0 0
\(639\) 6.97669 0.275994
\(640\) 0 0
\(641\) 46.8601 1.85086 0.925432 0.378913i \(-0.123702\pi\)
0.925432 + 0.378913i \(0.123702\pi\)
\(642\) 0 0
\(643\) −3.63734 −0.143443 −0.0717213 0.997425i \(-0.522849\pi\)
−0.0717213 + 0.997425i \(0.522849\pi\)
\(644\) 0 0
\(645\) 0.445198 0.0175297
\(646\) 0 0
\(647\) 3.24879 0.127723 0.0638616 0.997959i \(-0.479658\pi\)
0.0638616 + 0.997959i \(0.479658\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) −34.4957 −1.35199
\(652\) 0 0
\(653\) −1.47102 −0.0575655 −0.0287828 0.999586i \(-0.509163\pi\)
−0.0287828 + 0.999586i \(0.509163\pi\)
\(654\) 0 0
\(655\) −5.45982 −0.213333
\(656\) 0 0
\(657\) −4.36402 −0.170257
\(658\) 0 0
\(659\) 35.5658 1.38545 0.692723 0.721203i \(-0.256411\pi\)
0.692723 + 0.721203i \(0.256411\pi\)
\(660\) 0 0
\(661\) −17.9956 −0.699949 −0.349975 0.936759i \(-0.613810\pi\)
−0.349975 + 0.936759i \(0.613810\pi\)
\(662\) 0 0
\(663\) −1.40695 −0.0546414
\(664\) 0 0
\(665\) −16.6534 −0.645791
\(666\) 0 0
\(667\) 1.18756 0.0459825
\(668\) 0 0
\(669\) −38.2351 −1.47826
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −50.2103 −1.93547 −0.967733 0.251979i \(-0.918919\pi\)
−0.967733 + 0.251979i \(0.918919\pi\)
\(674\) 0 0
\(675\) −4.63125 −0.178257
\(676\) 0 0
\(677\) 37.5334 1.44252 0.721262 0.692662i \(-0.243562\pi\)
0.721262 + 0.692662i \(0.243562\pi\)
\(678\) 0 0
\(679\) 20.4862 0.786187
\(680\) 0 0
\(681\) 37.7622 1.44705
\(682\) 0 0
\(683\) 25.4543 0.973983 0.486992 0.873407i \(-0.338094\pi\)
0.486992 + 0.873407i \(0.338094\pi\)
\(684\) 0 0
\(685\) 20.5698 0.785932
\(686\) 0 0
\(687\) 49.5198 1.88930
\(688\) 0 0
\(689\) −21.4289 −0.816377
\(690\) 0 0
\(691\) 13.5637 0.515988 0.257994 0.966147i \(-0.416939\pi\)
0.257994 + 0.966147i \(0.416939\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −9.49138 −0.360029
\(696\) 0 0
\(697\) 1.92574 0.0729427
\(698\) 0 0
\(699\) −10.2091 −0.386143
\(700\) 0 0
\(701\) −18.3908 −0.694609 −0.347305 0.937752i \(-0.612903\pi\)
−0.347305 + 0.937752i \(0.612903\pi\)
\(702\) 0 0
\(703\) 40.1289 1.51349
\(704\) 0 0
\(705\) 25.2027 0.949188
\(706\) 0 0
\(707\) 9.19680 0.345881
\(708\) 0 0
\(709\) 18.5923 0.698247 0.349124 0.937077i \(-0.386479\pi\)
0.349124 + 0.937077i \(0.386479\pi\)
\(710\) 0 0
\(711\) 6.04071 0.226544
\(712\) 0 0
\(713\) −3.89237 −0.145770
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −1.19280 −0.0445460
\(718\) 0 0
\(719\) 27.1222 1.01149 0.505743 0.862684i \(-0.331218\pi\)
0.505743 + 0.862684i \(0.331218\pi\)
\(720\) 0 0
\(721\) −36.0639 −1.34309
\(722\) 0 0
\(723\) 43.2310 1.60778
\(724\) 0 0
\(725\) −1.52157 −0.0565096
\(726\) 0 0
\(727\) −5.23140 −0.194022 −0.0970109 0.995283i \(-0.530928\pi\)
−0.0970109 + 0.995283i \(0.530928\pi\)
\(728\) 0 0
\(729\) 20.5810 0.762261
\(730\) 0 0
\(731\) 0.0758479 0.00280533
\(732\) 0 0
\(733\) 4.09384 0.151210 0.0756048 0.997138i \(-0.475911\pi\)
0.0756048 + 0.997138i \(0.475911\pi\)
\(734\) 0 0
\(735\) 12.2709 0.452619
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) −20.0800 −0.738656 −0.369328 0.929299i \(-0.620412\pi\)
−0.369328 + 0.929299i \(0.620412\pi\)
\(740\) 0 0
\(741\) −19.8828 −0.730412
\(742\) 0 0
\(743\) 34.0552 1.24936 0.624682 0.780880i \(-0.285229\pi\)
0.624682 + 0.780880i \(0.285229\pi\)
\(744\) 0 0
\(745\) 21.5816 0.790690
\(746\) 0 0
\(747\) −7.55912 −0.276574
\(748\) 0 0
\(749\) −48.5739 −1.77485
\(750\) 0 0
\(751\) −21.7522 −0.793748 −0.396874 0.917873i \(-0.629905\pi\)
−0.396874 + 0.917873i \(0.629905\pi\)
\(752\) 0 0
\(753\) −14.5138 −0.528913
\(754\) 0 0
\(755\) 23.8130 0.866643
\(756\) 0 0
\(757\) −23.6837 −0.860797 −0.430399 0.902639i \(-0.641627\pi\)
−0.430399 + 0.902639i \(0.641627\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −34.8826 −1.26449 −0.632247 0.774767i \(-0.717867\pi\)
−0.632247 + 0.774767i \(0.717867\pi\)
\(762\) 0 0
\(763\) −39.3290 −1.42381
\(764\) 0 0
\(765\) 0.172311 0.00622993
\(766\) 0 0
\(767\) −14.1154 −0.509677
\(768\) 0 0
\(769\) 4.67665 0.168644 0.0843222 0.996439i \(-0.473128\pi\)
0.0843222 + 0.996439i \(0.473128\pi\)
\(770\) 0 0
\(771\) 9.89511 0.356364
\(772\) 0 0
\(773\) 51.8575 1.86518 0.932592 0.360933i \(-0.117542\pi\)
0.932592 + 0.360933i \(0.117542\pi\)
\(774\) 0 0
\(775\) 4.98712 0.179143
\(776\) 0 0
\(777\) −61.2945 −2.19893
\(778\) 0 0
\(779\) 27.2143 0.975053
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 7.04676 0.251831
\(784\) 0 0
\(785\) 10.7734 0.384518
\(786\) 0 0
\(787\) −42.0650 −1.49945 −0.749727 0.661747i \(-0.769815\pi\)
−0.749727 + 0.661747i \(0.769815\pi\)
\(788\) 0 0
\(789\) −16.1324 −0.574330
\(790\) 0 0
\(791\) 69.2720 2.46303
\(792\) 0 0
\(793\) −4.27649 −0.151863
\(794\) 0 0
\(795\) 17.2663 0.612371
\(796\) 0 0
\(797\) −14.7933 −0.524006 −0.262003 0.965067i \(-0.584383\pi\)
−0.262003 + 0.965067i \(0.584383\pi\)
\(798\) 0 0
\(799\) 4.29375 0.151902
\(800\) 0 0
\(801\) −2.61201 −0.0922907
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 2.87023 0.101162
\(806\) 0 0
\(807\) −38.9449 −1.37093
\(808\) 0 0
\(809\) 32.2134 1.13256 0.566281 0.824212i \(-0.308382\pi\)
0.566281 + 0.824212i \(0.308382\pi\)
\(810\) 0 0
\(811\) 39.7933 1.39733 0.698666 0.715448i \(-0.253777\pi\)
0.698666 + 0.715448i \(0.253777\pi\)
\(812\) 0 0
\(813\) 1.14555 0.0401761
\(814\) 0 0
\(815\) 3.34342 0.117115
\(816\) 0 0
\(817\) 1.07187 0.0375000
\(818\) 0 0
\(819\) 4.61614 0.161301
\(820\) 0 0
\(821\) 21.2122 0.740312 0.370156 0.928970i \(-0.379304\pi\)
0.370156 + 0.928970i \(0.379304\pi\)
\(822\) 0 0
\(823\) 7.36759 0.256818 0.128409 0.991721i \(-0.459013\pi\)
0.128409 + 0.991721i \(0.459013\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 22.7215 0.790105 0.395053 0.918658i \(-0.370726\pi\)
0.395053 + 0.918658i \(0.370726\pi\)
\(828\) 0 0
\(829\) −54.9754 −1.90937 −0.954687 0.297611i \(-0.903810\pi\)
−0.954687 + 0.297611i \(0.903810\pi\)
\(830\) 0 0
\(831\) −0.541189 −0.0187736
\(832\) 0 0
\(833\) 2.09058 0.0724341
\(834\) 0 0
\(835\) −11.4630 −0.396693
\(836\) 0 0
\(837\) −23.0966 −0.798335
\(838\) 0 0
\(839\) −19.0212 −0.656686 −0.328343 0.944559i \(-0.606490\pi\)
−0.328343 + 0.944559i \(0.606490\pi\)
\(840\) 0 0
\(841\) −26.6848 −0.920167
\(842\) 0 0
\(843\) −51.2514 −1.76519
\(844\) 0 0
\(845\) −7.55085 −0.259757
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 47.0536 1.61488
\(850\) 0 0
\(851\) −6.91625 −0.237086
\(852\) 0 0
\(853\) −19.2192 −0.658051 −0.329026 0.944321i \(-0.606720\pi\)
−0.329026 + 0.944321i \(0.606720\pi\)
\(854\) 0 0
\(855\) 2.43508 0.0832778
\(856\) 0 0
\(857\) 10.4481 0.356900 0.178450 0.983949i \(-0.442892\pi\)
0.178450 + 0.983949i \(0.442892\pi\)
\(858\) 0 0
\(859\) 5.96939 0.203673 0.101836 0.994801i \(-0.467528\pi\)
0.101836 + 0.994801i \(0.467528\pi\)
\(860\) 0 0
\(861\) −41.5682 −1.41664
\(862\) 0 0
\(863\) 20.6871 0.704198 0.352099 0.935963i \(-0.385468\pi\)
0.352099 + 0.935963i \(0.385468\pi\)
\(864\) 0 0
\(865\) −14.3879 −0.489203
\(866\) 0 0
\(867\) −31.7819 −1.07937
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 10.6545 0.361014
\(872\) 0 0
\(873\) −2.99551 −0.101383
\(874\) 0 0
\(875\) −3.67750 −0.124322
\(876\) 0 0
\(877\) 38.2883 1.29290 0.646451 0.762955i \(-0.276252\pi\)
0.646451 + 0.762955i \(0.276252\pi\)
\(878\) 0 0
\(879\) 13.7171 0.462665
\(880\) 0 0
\(881\) 41.8177 1.40888 0.704438 0.709766i \(-0.251199\pi\)
0.704438 + 0.709766i \(0.251199\pi\)
\(882\) 0 0
\(883\) 45.7598 1.53994 0.769970 0.638080i \(-0.220271\pi\)
0.769970 + 0.638080i \(0.220271\pi\)
\(884\) 0 0
\(885\) 11.3734 0.382313
\(886\) 0 0
\(887\) 22.4995 0.755458 0.377729 0.925916i \(-0.376705\pi\)
0.377729 + 0.925916i \(0.376705\pi\)
\(888\) 0 0
\(889\) −26.8566 −0.900743
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 60.6785 2.03053
\(894\) 0 0
\(895\) −12.3747 −0.413640
\(896\) 0 0
\(897\) 3.42682 0.114418
\(898\) 0 0
\(899\) −7.58824 −0.253082
\(900\) 0 0
\(901\) 2.94163 0.0979999
\(902\) 0 0
\(903\) −1.63722 −0.0544832
\(904\) 0 0
\(905\) −11.9220 −0.396300
\(906\) 0 0
\(907\) −21.0041 −0.697429 −0.348714 0.937229i \(-0.613382\pi\)
−0.348714 + 0.937229i \(0.613382\pi\)
\(908\) 0 0
\(909\) −1.34476 −0.0446030
\(910\) 0 0
\(911\) 6.95297 0.230362 0.115181 0.993345i \(-0.463255\pi\)
0.115181 + 0.993345i \(0.463255\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 3.44576 0.113913
\(916\) 0 0
\(917\) 20.0785 0.663050
\(918\) 0 0
\(919\) 12.1861 0.401981 0.200990 0.979593i \(-0.435584\pi\)
0.200990 + 0.979593i \(0.435584\pi\)
\(920\) 0 0
\(921\) −52.3376 −1.72458
\(922\) 0 0
\(923\) −30.2867 −0.996899
\(924\) 0 0
\(925\) 8.86148 0.291364
\(926\) 0 0
\(927\) 5.27330 0.173198
\(928\) 0 0
\(929\) −5.95040 −0.195226 −0.0976132 0.995224i \(-0.531121\pi\)
−0.0976132 + 0.995224i \(0.531121\pi\)
\(930\) 0 0
\(931\) 29.5436 0.968254
\(932\) 0 0
\(933\) 18.3663 0.601284
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −55.7339 −1.82075 −0.910374 0.413786i \(-0.864206\pi\)
−0.910374 + 0.413786i \(0.864206\pi\)
\(938\) 0 0
\(939\) −13.8070 −0.450573
\(940\) 0 0
\(941\) −42.6191 −1.38934 −0.694671 0.719328i \(-0.744450\pi\)
−0.694671 + 0.719328i \(0.744450\pi\)
\(942\) 0 0
\(943\) −4.69041 −0.152741
\(944\) 0 0
\(945\) 17.0314 0.554032
\(946\) 0 0
\(947\) −48.4409 −1.57412 −0.787059 0.616878i \(-0.788397\pi\)
−0.787059 + 0.616878i \(0.788397\pi\)
\(948\) 0 0
\(949\) 18.9448 0.614973
\(950\) 0 0
\(951\) −14.7706 −0.478971
\(952\) 0 0
\(953\) 11.7840 0.381720 0.190860 0.981617i \(-0.438872\pi\)
0.190860 + 0.981617i \(0.438872\pi\)
\(954\) 0 0
\(955\) 0.537459 0.0173918
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −75.6455 −2.44272
\(960\) 0 0
\(961\) −6.12864 −0.197698
\(962\) 0 0
\(963\) 7.10252 0.228876
\(964\) 0 0
\(965\) −7.19252 −0.231535
\(966\) 0 0
\(967\) −6.15437 −0.197911 −0.0989556 0.995092i \(-0.531550\pi\)
−0.0989556 + 0.995092i \(0.531550\pi\)
\(968\) 0 0
\(969\) 2.72938 0.0876804
\(970\) 0 0
\(971\) 34.5095 1.10746 0.553731 0.832696i \(-0.313204\pi\)
0.553731 + 0.832696i \(0.313204\pi\)
\(972\) 0 0
\(973\) 34.9045 1.11899
\(974\) 0 0
\(975\) −4.39063 −0.140613
\(976\) 0 0
\(977\) −40.2624 −1.28811 −0.644055 0.764979i \(-0.722749\pi\)
−0.644055 + 0.764979i \(0.722749\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 5.75072 0.183606
\(982\) 0 0
\(983\) −2.81279 −0.0897141 −0.0448570 0.998993i \(-0.514283\pi\)
−0.0448570 + 0.998993i \(0.514283\pi\)
\(984\) 0 0
\(985\) −21.9556 −0.699563
\(986\) 0 0
\(987\) −92.6829 −2.95013
\(988\) 0 0
\(989\) −0.184738 −0.00587432
\(990\) 0 0
\(991\) 42.1576 1.33918 0.669591 0.742730i \(-0.266470\pi\)
0.669591 + 0.742730i \(0.266470\pi\)
\(992\) 0 0
\(993\) 35.9039 1.13937
\(994\) 0 0
\(995\) −25.3774 −0.804517
\(996\) 0 0
\(997\) −61.7812 −1.95663 −0.978314 0.207126i \(-0.933589\pi\)
−0.978314 + 0.207126i \(0.933589\pi\)
\(998\) 0 0
\(999\) −41.0398 −1.29844
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 4840.2.a.bh.1.6 8
4.3 odd 2 9680.2.a.de.1.3 8
11.7 odd 10 440.2.y.d.401.2 yes 16
11.8 odd 10 440.2.y.d.361.2 16
11.10 odd 2 4840.2.a.bg.1.6 8
44.7 even 10 880.2.bo.k.401.3 16
44.19 even 10 880.2.bo.k.801.3 16
44.43 even 2 9680.2.a.df.1.3 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
440.2.y.d.361.2 16 11.8 odd 10
440.2.y.d.401.2 yes 16 11.7 odd 10
880.2.bo.k.401.3 16 44.7 even 10
880.2.bo.k.801.3 16 44.19 even 10
4840.2.a.bg.1.6 8 11.10 odd 2
4840.2.a.bh.1.6 8 1.1 even 1 trivial
9680.2.a.de.1.3 8 4.3 odd 2
9680.2.a.df.1.3 8 44.43 even 2