Properties

Label 2736.3.m.f.1711.2
Level $2736$
Weight $3$
Character 2736.1711
Analytic conductor $74.551$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2736,3,Mod(1711,2736)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2736, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 0, 0]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2736.1711");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 2736.m (of order \(2\), degree \(1\), minimal)

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: no
Analytic conductor: \(74.5506003290\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 2 x^{11} + 50 x^{10} - 136 x^{9} + 2215 x^{8} - 5020 x^{7} + 18282 x^{6} - 12094 x^{5} + 48457 x^{4} - 30372 x^{3} + 89392 x^{2} + 9344 x + 1024 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{16} \)
Twist minimal: no (minimal twist has level 912)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1711.2
Root \(-0.820808 - 1.42168i\) of defining polynomial
Character \(\chi\) \(=\) 2736.1711
Dual form 2736.3.m.f.1711.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-8.90000 q^{5} +2.78940i q^{7} +O(q^{10})\) \(q-8.90000 q^{5} +2.78940i q^{7} -0.270477i q^{11} +7.37703 q^{13} -9.27079 q^{17} +4.35890i q^{19} -23.8911i q^{23} +54.2099 q^{25} +19.2337 q^{29} +6.42293i q^{31} -24.8256i q^{35} +31.6410 q^{37} -17.2511 q^{41} +2.05975i q^{43} +59.4123i q^{47} +41.2193 q^{49} +44.1111 q^{53} +2.40725i q^{55} -54.8364i q^{59} -52.2724 q^{61} -65.6555 q^{65} -42.9738i q^{67} -16.7037i q^{71} -20.3233 q^{73} +0.754469 q^{77} +25.5136i q^{79} +23.6263i q^{83} +82.5100 q^{85} -28.2680 q^{89} +20.5775i q^{91} -38.7942i q^{95} -91.4340 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 10 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 10 q^{5} + 36 q^{13} + 10 q^{17} + 58 q^{25} - 12 q^{29} + 32 q^{37} - 136 q^{41} - 22 q^{49} + 236 q^{53} - 210 q^{61} + 52 q^{65} - 158 q^{73} + 70 q^{77} + 242 q^{85} - 444 q^{89} + 320 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).

\(n\) \(1009\) \(1217\) \(1711\) \(2053\)
\(\chi(n)\) \(1\) \(1\) \(-1\) \(1\)

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
\(5\) −8.90000 −1.78000 −0.890000 0.455961i \(-0.849296\pi\)
−0.890000 + 0.455961i \(0.849296\pi\)
\(6\) 0 0
\(7\) 2.78940i 0.398486i 0.979950 + 0.199243i \(0.0638482\pi\)
−0.979950 + 0.199243i \(0.936152\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) − 0.270477i − 0.0245888i −0.999924 0.0122944i \(-0.996086\pi\)
0.999924 0.0122944i \(-0.00391354\pi\)
\(12\) 0 0
\(13\) 7.37703 0.567464 0.283732 0.958904i \(-0.408427\pi\)
0.283732 + 0.958904i \(0.408427\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −9.27079 −0.545341 −0.272670 0.962108i \(-0.587907\pi\)
−0.272670 + 0.962108i \(0.587907\pi\)
\(18\) 0 0
\(19\) 4.35890i 0.229416i
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) − 23.8911i − 1.03874i −0.854549 0.519372i \(-0.826166\pi\)
0.854549 0.519372i \(-0.173834\pi\)
\(24\) 0 0
\(25\) 54.2099 2.16840
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 19.2337 0.663232 0.331616 0.943415i \(-0.392406\pi\)
0.331616 + 0.943415i \(0.392406\pi\)
\(30\) 0 0
\(31\) 6.42293i 0.207191i 0.994619 + 0.103596i \(0.0330348\pi\)
−0.994619 + 0.103596i \(0.966965\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) − 24.8256i − 0.709304i
\(36\) 0 0
\(37\) 31.6410 0.855161 0.427580 0.903977i \(-0.359366\pi\)
0.427580 + 0.903977i \(0.359366\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −17.2511 −0.420758 −0.210379 0.977620i \(-0.567470\pi\)
−0.210379 + 0.977620i \(0.567470\pi\)
\(42\) 0 0
\(43\) 2.05975i 0.0479012i 0.999713 + 0.0239506i \(0.00762443\pi\)
−0.999713 + 0.0239506i \(0.992376\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 59.4123i 1.26409i 0.774931 + 0.632045i \(0.217784\pi\)
−0.774931 + 0.632045i \(0.782216\pi\)
\(48\) 0 0
\(49\) 41.2193 0.841209
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 44.1111 0.832285 0.416142 0.909299i \(-0.363382\pi\)
0.416142 + 0.909299i \(0.363382\pi\)
\(54\) 0 0
\(55\) 2.40725i 0.0437681i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) − 54.8364i − 0.929431i −0.885460 0.464716i \(-0.846157\pi\)
0.885460 0.464716i \(-0.153843\pi\)
\(60\) 0 0
\(61\) −52.2724 −0.856925 −0.428462 0.903560i \(-0.640945\pi\)
−0.428462 + 0.903560i \(0.640945\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −65.6555 −1.01009
\(66\) 0 0
\(67\) − 42.9738i − 0.641399i −0.947181 0.320700i \(-0.896082\pi\)
0.947181 0.320700i \(-0.103918\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) − 16.7037i − 0.235263i −0.993057 0.117631i \(-0.962470\pi\)
0.993057 0.117631i \(-0.0375301\pi\)
\(72\) 0 0
\(73\) −20.3233 −0.278401 −0.139201 0.990264i \(-0.544453\pi\)
−0.139201 + 0.990264i \(0.544453\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0.754469 0.00979830
\(78\) 0 0
\(79\) 25.5136i 0.322957i 0.986876 + 0.161478i \(0.0516262\pi\)
−0.986876 + 0.161478i \(0.948374\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 23.6263i 0.284655i 0.989820 + 0.142327i \(0.0454586\pi\)
−0.989820 + 0.142327i \(0.954541\pi\)
\(84\) 0 0
\(85\) 82.5100 0.970706
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −28.2680 −0.317617 −0.158809 0.987309i \(-0.550765\pi\)
−0.158809 + 0.987309i \(0.550765\pi\)
\(90\) 0 0
\(91\) 20.5775i 0.226126i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) − 38.7942i − 0.408360i
\(96\) 0 0
\(97\) −91.4340 −0.942619 −0.471309 0.881968i \(-0.656218\pi\)
−0.471309 + 0.881968i \(0.656218\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −147.437 −1.45977 −0.729887 0.683567i \(-0.760428\pi\)
−0.729887 + 0.683567i \(0.760428\pi\)
\(102\) 0 0
\(103\) 103.703i 1.00683i 0.864045 + 0.503415i \(0.167923\pi\)
−0.864045 + 0.503415i \(0.832077\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) − 111.378i − 1.04092i −0.853887 0.520459i \(-0.825761\pi\)
0.853887 0.520459i \(-0.174239\pi\)
\(108\) 0 0
\(109\) 60.1516 0.551849 0.275925 0.961179i \(-0.411016\pi\)
0.275925 + 0.961179i \(0.411016\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 74.8741 0.662602 0.331301 0.943525i \(-0.392512\pi\)
0.331301 + 0.943525i \(0.392512\pi\)
\(114\) 0 0
\(115\) 212.631i 1.84896i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) − 25.8599i − 0.217310i
\(120\) 0 0
\(121\) 120.927 0.999395
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −259.968 −2.07975
\(126\) 0 0
\(127\) 168.857i 1.32958i 0.747030 + 0.664790i \(0.231479\pi\)
−0.747030 + 0.664790i \(0.768521\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) − 118.259i − 0.902744i −0.892336 0.451372i \(-0.850935\pi\)
0.892336 0.451372i \(-0.149065\pi\)
\(132\) 0 0
\(133\) −12.1587 −0.0914189
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −85.7018 −0.625560 −0.312780 0.949826i \(-0.601260\pi\)
−0.312780 + 0.949826i \(0.601260\pi\)
\(138\) 0 0
\(139\) − 85.7838i − 0.617149i −0.951200 0.308575i \(-0.900148\pi\)
0.951200 0.308575i \(-0.0998520\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) − 1.99532i − 0.0139533i
\(144\) 0 0
\(145\) −171.180 −1.18055
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −16.3400 −0.109665 −0.0548323 0.998496i \(-0.517462\pi\)
−0.0548323 + 0.998496i \(0.517462\pi\)
\(150\) 0 0
\(151\) 49.9011i 0.330471i 0.986254 + 0.165235i \(0.0528383\pi\)
−0.986254 + 0.165235i \(0.947162\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) − 57.1641i − 0.368801i
\(156\) 0 0
\(157\) −294.055 −1.87296 −0.936481 0.350718i \(-0.885938\pi\)
−0.936481 + 0.350718i \(0.885938\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 66.6418 0.413924
\(162\) 0 0
\(163\) − 33.7956i − 0.207335i −0.994612 0.103668i \(-0.966942\pi\)
0.994612 0.103668i \(-0.0330578\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 274.855i 1.64584i 0.568157 + 0.822920i \(0.307657\pi\)
−0.568157 + 0.822920i \(0.692343\pi\)
\(168\) 0 0
\(169\) −114.579 −0.677985
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −272.490 −1.57509 −0.787543 0.616260i \(-0.788647\pi\)
−0.787543 + 0.616260i \(0.788647\pi\)
\(174\) 0 0
\(175\) 151.213i 0.864075i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 319.797i 1.78657i 0.449486 + 0.893287i \(0.351607\pi\)
−0.449486 + 0.893287i \(0.648393\pi\)
\(180\) 0 0
\(181\) −245.785 −1.35793 −0.678963 0.734172i \(-0.737570\pi\)
−0.678963 + 0.734172i \(0.737570\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −281.604 −1.52219
\(186\) 0 0
\(187\) 2.50754i 0.0134093i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 336.257i 1.76051i 0.474504 + 0.880253i \(0.342627\pi\)
−0.474504 + 0.880253i \(0.657373\pi\)
\(192\) 0 0
\(193\) −329.129 −1.70533 −0.852665 0.522458i \(-0.825015\pi\)
−0.852665 + 0.522458i \(0.825015\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −276.972 −1.40595 −0.702973 0.711216i \(-0.748145\pi\)
−0.702973 + 0.711216i \(0.748145\pi\)
\(198\) 0 0
\(199\) 235.145i 1.18163i 0.806806 + 0.590816i \(0.201194\pi\)
−0.806806 + 0.590816i \(0.798806\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 53.6505i 0.264288i
\(204\) 0 0
\(205\) 153.534 0.748948
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 1.17898 0.00564107
\(210\) 0 0
\(211\) − 147.521i − 0.699154i −0.936908 0.349577i \(-0.886325\pi\)
0.936908 0.349577i \(-0.113675\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) − 18.3318i − 0.0852640i
\(216\) 0 0
\(217\) −17.9161 −0.0825628
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −68.3909 −0.309461
\(222\) 0 0
\(223\) − 420.735i − 1.88670i −0.331794 0.943352i \(-0.607654\pi\)
0.331794 0.943352i \(-0.392346\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 257.749i 1.13546i 0.823215 + 0.567730i \(0.192178\pi\)
−0.823215 + 0.567730i \(0.807822\pi\)
\(228\) 0 0
\(229\) 155.183 0.677654 0.338827 0.940849i \(-0.389970\pi\)
0.338827 + 0.940849i \(0.389970\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 334.053 1.43370 0.716852 0.697225i \(-0.245582\pi\)
0.716852 + 0.697225i \(0.245582\pi\)
\(234\) 0 0
\(235\) − 528.769i − 2.25008i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 447.085i 1.87065i 0.353793 + 0.935324i \(0.384892\pi\)
−0.353793 + 0.935324i \(0.615108\pi\)
\(240\) 0 0
\(241\) −321.663 −1.33470 −0.667351 0.744744i \(-0.732572\pi\)
−0.667351 + 0.744744i \(0.732572\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −366.851 −1.49735
\(246\) 0 0
\(247\) 32.1557i 0.130185i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) − 231.428i − 0.922024i −0.887394 0.461012i \(-0.847487\pi\)
0.887394 0.461012i \(-0.152513\pi\)
\(252\) 0 0
\(253\) −6.46200 −0.0255415
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 383.148 1.49085 0.745424 0.666590i \(-0.232247\pi\)
0.745424 + 0.666590i \(0.232247\pi\)
\(258\) 0 0
\(259\) 88.2592i 0.340769i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 211.078i 0.802579i 0.915951 + 0.401289i \(0.131438\pi\)
−0.915951 + 0.401289i \(0.868562\pi\)
\(264\) 0 0
\(265\) −392.589 −1.48147
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 250.597 0.931586 0.465793 0.884894i \(-0.345769\pi\)
0.465793 + 0.884894i \(0.345769\pi\)
\(270\) 0 0
\(271\) 180.019i 0.664275i 0.943231 + 0.332138i \(0.107770\pi\)
−0.943231 + 0.332138i \(0.892230\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) − 14.6626i − 0.0533184i
\(276\) 0 0
\(277\) 464.791 1.67795 0.838974 0.544172i \(-0.183156\pi\)
0.838974 + 0.544172i \(0.183156\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −216.576 −0.770734 −0.385367 0.922763i \(-0.625925\pi\)
−0.385367 + 0.922763i \(0.625925\pi\)
\(282\) 0 0
\(283\) − 70.7228i − 0.249904i −0.992163 0.124952i \(-0.960122\pi\)
0.992163 0.124952i \(-0.0398777\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) − 48.1201i − 0.167666i
\(288\) 0 0
\(289\) −203.052 −0.702604
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −378.264 −1.29100 −0.645502 0.763758i \(-0.723352\pi\)
−0.645502 + 0.763758i \(0.723352\pi\)
\(294\) 0 0
\(295\) 488.044i 1.65439i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) − 176.245i − 0.589449i
\(300\) 0 0
\(301\) −5.74546 −0.0190879
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 465.224 1.52533
\(306\) 0 0
\(307\) − 122.269i − 0.398270i −0.979972 0.199135i \(-0.936187\pi\)
0.979972 0.199135i \(-0.0638132\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 280.599i 0.902249i 0.892461 + 0.451125i \(0.148977\pi\)
−0.892461 + 0.451125i \(0.851023\pi\)
\(312\) 0 0
\(313\) 405.043 1.29407 0.647033 0.762462i \(-0.276009\pi\)
0.647033 + 0.762462i \(0.276009\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 150.448 0.474598 0.237299 0.971437i \(-0.423738\pi\)
0.237299 + 0.971437i \(0.423738\pi\)
\(318\) 0 0
\(319\) − 5.20228i − 0.0163081i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) − 40.4104i − 0.125110i
\(324\) 0 0
\(325\) 399.908 1.23049
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −165.725 −0.503722
\(330\) 0 0
\(331\) − 411.544i − 1.24334i −0.783281 0.621668i \(-0.786456\pi\)
0.783281 0.621668i \(-0.213544\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 382.466i 1.14169i
\(336\) 0 0
\(337\) −293.791 −0.871783 −0.435892 0.899999i \(-0.643567\pi\)
−0.435892 + 0.899999i \(0.643567\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 1.73726 0.00509460
\(342\) 0 0
\(343\) 251.657i 0.733695i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) − 332.604i − 0.958512i −0.877675 0.479256i \(-0.840907\pi\)
0.877675 0.479256i \(-0.159093\pi\)
\(348\) 0 0
\(349\) −4.98236 −0.0142761 −0.00713806 0.999975i \(-0.502272\pi\)
−0.00713806 + 0.999975i \(0.502272\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −357.751 −1.01346 −0.506730 0.862105i \(-0.669146\pi\)
−0.506730 + 0.862105i \(0.669146\pi\)
\(354\) 0 0
\(355\) 148.662i 0.418768i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 379.442i 1.05694i 0.848952 + 0.528471i \(0.177234\pi\)
−0.848952 + 0.528471i \(0.822766\pi\)
\(360\) 0 0
\(361\) −19.0000 −0.0526316
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 180.877 0.495554
\(366\) 0 0
\(367\) − 317.133i − 0.864124i −0.901844 0.432062i \(-0.857786\pi\)
0.901844 0.432062i \(-0.142214\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 123.043i 0.331653i
\(372\) 0 0
\(373\) −619.617 −1.66117 −0.830586 0.556891i \(-0.811994\pi\)
−0.830586 + 0.556891i \(0.811994\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 141.888 0.376360
\(378\) 0 0
\(379\) − 503.578i − 1.32870i −0.747421 0.664351i \(-0.768708\pi\)
0.747421 0.664351i \(-0.231292\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) − 357.174i − 0.932568i −0.884635 0.466284i \(-0.845593\pi\)
0.884635 0.466284i \(-0.154407\pi\)
\(384\) 0 0
\(385\) −6.71477 −0.0174410
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −340.019 −0.874084 −0.437042 0.899441i \(-0.643974\pi\)
−0.437042 + 0.899441i \(0.643974\pi\)
\(390\) 0 0
\(391\) 221.489i 0.566469i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) − 227.071i − 0.574863i
\(396\) 0 0
\(397\) 294.916 0.742862 0.371431 0.928460i \(-0.378867\pi\)
0.371431 + 0.928460i \(0.378867\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −55.5356 −0.138493 −0.0692463 0.997600i \(-0.522059\pi\)
−0.0692463 + 0.997600i \(0.522059\pi\)
\(402\) 0 0
\(403\) 47.3822i 0.117574i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) − 8.55816i − 0.0210274i
\(408\) 0 0
\(409\) −275.415 −0.673386 −0.336693 0.941615i \(-0.609308\pi\)
−0.336693 + 0.941615i \(0.609308\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 152.961 0.370365
\(414\) 0 0
\(415\) − 210.274i − 0.506685i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 33.9969i 0.0811381i 0.999177 + 0.0405691i \(0.0129171\pi\)
−0.999177 + 0.0405691i \(0.987083\pi\)
\(420\) 0 0
\(421\) 148.897 0.353675 0.176838 0.984240i \(-0.443413\pi\)
0.176838 + 0.984240i \(0.443413\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −502.569 −1.18252
\(426\) 0 0
\(427\) − 145.809i − 0.341472i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) − 307.522i − 0.713508i −0.934198 0.356754i \(-0.883884\pi\)
0.934198 0.356754i \(-0.116116\pi\)
\(432\) 0 0
\(433\) 151.782 0.350535 0.175268 0.984521i \(-0.443921\pi\)
0.175268 + 0.984521i \(0.443921\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 104.139 0.238304
\(438\) 0 0
\(439\) − 316.456i − 0.720857i −0.932787 0.360428i \(-0.882630\pi\)
0.932787 0.360428i \(-0.117370\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 671.256i 1.51525i 0.652689 + 0.757626i \(0.273641\pi\)
−0.652689 + 0.757626i \(0.726359\pi\)
\(444\) 0 0
\(445\) 251.585 0.565359
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 756.843 1.68562 0.842809 0.538212i \(-0.180900\pi\)
0.842809 + 0.538212i \(0.180900\pi\)
\(450\) 0 0
\(451\) 4.66602i 0.0103459i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) − 183.139i − 0.402504i
\(456\) 0 0
\(457\) −454.168 −0.993803 −0.496902 0.867807i \(-0.665529\pi\)
−0.496902 + 0.867807i \(0.665529\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −599.386 −1.30019 −0.650093 0.759855i \(-0.725270\pi\)
−0.650093 + 0.759855i \(0.725270\pi\)
\(462\) 0 0
\(463\) − 277.842i − 0.600091i −0.953925 0.300046i \(-0.902998\pi\)
0.953925 0.300046i \(-0.0970019\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 377.100i 0.807494i 0.914871 + 0.403747i \(0.132292\pi\)
−0.914871 + 0.403747i \(0.867708\pi\)
\(468\) 0 0
\(469\) 119.871 0.255588
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0.557116 0.00117783
\(474\) 0 0
\(475\) 236.296i 0.497465i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 65.7826i 0.137333i 0.997640 + 0.0686666i \(0.0218745\pi\)
−0.997640 + 0.0686666i \(0.978126\pi\)
\(480\) 0 0
\(481\) 233.416 0.485273
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 813.762 1.67786
\(486\) 0 0
\(487\) − 77.8127i − 0.159780i −0.996804 0.0798898i \(-0.974543\pi\)
0.996804 0.0798898i \(-0.0254568\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 450.685i 0.917892i 0.888464 + 0.458946i \(0.151773\pi\)
−0.888464 + 0.458946i \(0.848227\pi\)
\(492\) 0 0
\(493\) −178.312 −0.361687
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 46.5932 0.0937488
\(498\) 0 0
\(499\) − 851.013i − 1.70544i −0.522371 0.852718i \(-0.674952\pi\)
0.522371 0.852718i \(-0.325048\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) − 245.544i − 0.488159i −0.969755 0.244080i \(-0.921514\pi\)
0.969755 0.244080i \(-0.0784858\pi\)
\(504\) 0 0
\(505\) 1312.19 2.59840
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 509.002 1.00000 0.500002 0.866024i \(-0.333333\pi\)
0.500002 + 0.866024i \(0.333333\pi\)
\(510\) 0 0
\(511\) − 56.6898i − 0.110939i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) − 922.961i − 1.79216i
\(516\) 0 0
\(517\) 16.0697 0.0310825
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 47.7953 0.0917376 0.0458688 0.998947i \(-0.485394\pi\)
0.0458688 + 0.998947i \(0.485394\pi\)
\(522\) 0 0
\(523\) 375.574i 0.718114i 0.933316 + 0.359057i \(0.116902\pi\)
−0.933316 + 0.359057i \(0.883098\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) − 59.5457i − 0.112990i
\(528\) 0 0
\(529\) −41.7843 −0.0789873
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −127.262 −0.238765
\(534\) 0 0
\(535\) 991.266i 1.85283i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) − 11.1489i − 0.0206844i
\(540\) 0 0
\(541\) 220.703 0.407953 0.203977 0.978976i \(-0.434613\pi\)
0.203977 + 0.978976i \(0.434613\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −535.349 −0.982291
\(546\) 0 0
\(547\) 746.194i 1.36416i 0.731279 + 0.682079i \(0.238924\pi\)
−0.731279 + 0.682079i \(0.761076\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 83.8378i 0.152156i
\(552\) 0 0
\(553\) −71.1676 −0.128694
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −173.653 −0.311764 −0.155882 0.987776i \(-0.549822\pi\)
−0.155882 + 0.987776i \(0.549822\pi\)
\(558\) 0 0
\(559\) 15.1948i 0.0271822i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) − 623.274i − 1.10706i −0.832830 0.553530i \(-0.813281\pi\)
0.832830 0.553530i \(-0.186719\pi\)
\(564\) 0 0
\(565\) −666.379 −1.17943
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −789.796 −1.38804 −0.694021 0.719955i \(-0.744162\pi\)
−0.694021 + 0.719955i \(0.744162\pi\)
\(570\) 0 0
\(571\) 1017.55i 1.78205i 0.453950 + 0.891027i \(0.350015\pi\)
−0.453950 + 0.891027i \(0.649985\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) − 1295.13i − 2.25241i
\(576\) 0 0
\(577\) −250.762 −0.434596 −0.217298 0.976105i \(-0.569724\pi\)
−0.217298 + 0.976105i \(0.569724\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −65.9033 −0.113431
\(582\) 0 0
\(583\) − 11.9311i − 0.0204649i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 378.322i 0.644501i 0.946654 + 0.322250i \(0.104439\pi\)
−0.946654 + 0.322250i \(0.895561\pi\)
\(588\) 0 0
\(589\) −27.9969 −0.0475330
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −414.449 −0.698903 −0.349451 0.936955i \(-0.613632\pi\)
−0.349451 + 0.936955i \(0.613632\pi\)
\(594\) 0 0
\(595\) 230.153i 0.386812i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 538.060i 0.898263i 0.893466 + 0.449132i \(0.148267\pi\)
−0.893466 + 0.449132i \(0.851733\pi\)
\(600\) 0 0
\(601\) −21.9493 −0.0365213 −0.0182606 0.999833i \(-0.505813\pi\)
−0.0182606 + 0.999833i \(0.505813\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −1076.25 −1.77892
\(606\) 0 0
\(607\) − 1096.78i − 1.80689i −0.428703 0.903446i \(-0.641029\pi\)
0.428703 0.903446i \(-0.358971\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 438.286i 0.717326i
\(612\) 0 0
\(613\) −681.420 −1.11162 −0.555808 0.831311i \(-0.687591\pi\)
−0.555808 + 0.831311i \(0.687591\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 146.398 0.237273 0.118637 0.992938i \(-0.462148\pi\)
0.118637 + 0.992938i \(0.462148\pi\)
\(618\) 0 0
\(619\) 1171.04i 1.89183i 0.324414 + 0.945915i \(0.394833\pi\)
−0.324414 + 0.945915i \(0.605167\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) − 78.8506i − 0.126566i
\(624\) 0 0
\(625\) 958.470 1.53355
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −293.337 −0.466354
\(630\) 0 0
\(631\) − 0.379351i 0 0.000601190i −1.00000 0.000300595i \(-0.999904\pi\)
1.00000 0.000300595i \(-9.56824e-5\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) − 1502.82i − 2.36665i
\(636\) 0 0
\(637\) 304.076 0.477356
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 122.649 0.191340 0.0956700 0.995413i \(-0.469501\pi\)
0.0956700 + 0.995413i \(0.469501\pi\)
\(642\) 0 0
\(643\) 1158.37i 1.80150i 0.434335 + 0.900751i \(0.356983\pi\)
−0.434335 + 0.900751i \(0.643017\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) − 179.547i − 0.277507i −0.990327 0.138754i \(-0.955690\pi\)
0.990327 0.138754i \(-0.0443097\pi\)
\(648\) 0 0
\(649\) −14.8320 −0.0228536
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 266.762 0.408517 0.204259 0.978917i \(-0.434522\pi\)
0.204259 + 0.978917i \(0.434522\pi\)
\(654\) 0 0
\(655\) 1052.51i 1.60688i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) − 40.1621i − 0.0609441i −0.999536 0.0304720i \(-0.990299\pi\)
0.999536 0.0304720i \(-0.00970105\pi\)
\(660\) 0 0
\(661\) −90.7035 −0.137222 −0.0686108 0.997644i \(-0.521857\pi\)
−0.0686108 + 0.997644i \(0.521857\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 108.212 0.162726
\(666\) 0 0
\(667\) − 459.515i − 0.688927i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 14.1385i 0.0210708i
\(672\) 0 0
\(673\) −760.379 −1.12983 −0.564917 0.825147i \(-0.691092\pi\)
−0.564917 + 0.825147i \(0.691092\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 191.850 0.283382 0.141691 0.989911i \(-0.454746\pi\)
0.141691 + 0.989911i \(0.454746\pi\)
\(678\) 0 0
\(679\) − 255.046i − 0.375620i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) − 1243.23i − 1.82024i −0.414342 0.910121i \(-0.635988\pi\)
0.414342 0.910121i \(-0.364012\pi\)
\(684\) 0 0
\(685\) 762.746 1.11350
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 325.409 0.472291
\(690\) 0 0
\(691\) − 245.587i − 0.355409i −0.984084 0.177704i \(-0.943133\pi\)
0.984084 0.177704i \(-0.0568671\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 763.475i 1.09853i
\(696\) 0 0
\(697\) 159.931 0.229456
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −511.775 −0.730064 −0.365032 0.930995i \(-0.618942\pi\)
−0.365032 + 0.930995i \(0.618942\pi\)
\(702\) 0 0
\(703\) 137.920i 0.196187i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) − 411.261i − 0.581699i
\(708\) 0 0
\(709\) −813.026 −1.14672 −0.573361 0.819303i \(-0.694361\pi\)
−0.573361 + 0.819303i \(0.694361\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 153.451 0.215219
\(714\) 0 0
\(715\) 17.7583i 0.0248368i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) − 156.564i − 0.217753i −0.994055 0.108877i \(-0.965275\pi\)
0.994055 0.108877i \(-0.0347253\pi\)
\(720\) 0 0
\(721\) −289.270 −0.401207
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 1042.66 1.43815
\(726\) 0 0
\(727\) 759.958i 1.04533i 0.852537 + 0.522667i \(0.175063\pi\)
−0.852537 + 0.522667i \(0.824937\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) − 19.0955i − 0.0261224i
\(732\) 0 0
\(733\) 655.205 0.893868 0.446934 0.894567i \(-0.352516\pi\)
0.446934 + 0.894567i \(0.352516\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −11.6234 −0.0157713
\(738\) 0 0
\(739\) − 322.374i − 0.436230i −0.975923 0.218115i \(-0.930009\pi\)
0.975923 0.218115i \(-0.0699908\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 1325.78i 1.78436i 0.451680 + 0.892180i \(0.350825\pi\)
−0.451680 + 0.892180i \(0.649175\pi\)
\(744\) 0 0
\(745\) 145.426 0.195203
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 310.678 0.414791
\(750\) 0 0
\(751\) − 1165.72i − 1.55222i −0.630599 0.776109i \(-0.717191\pi\)
0.630599 0.776109i \(-0.282809\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) − 444.119i − 0.588237i
\(756\) 0 0
\(757\) 959.947 1.26809 0.634047 0.773295i \(-0.281393\pi\)
0.634047 + 0.773295i \(0.281393\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −542.826 −0.713306 −0.356653 0.934237i \(-0.616082\pi\)
−0.356653 + 0.934237i \(0.616082\pi\)
\(762\) 0 0
\(763\) 167.787i 0.219904i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) − 404.530i − 0.527418i
\(768\) 0 0
\(769\) −951.457 −1.23727 −0.618633 0.785680i \(-0.712313\pi\)
−0.618633 + 0.785680i \(0.712313\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 881.670 1.14058 0.570291 0.821443i \(-0.306830\pi\)
0.570291 + 0.821443i \(0.306830\pi\)
\(774\) 0 0
\(775\) 348.187i 0.449273i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) − 75.1956i − 0.0965284i
\(780\) 0 0
\(781\) −4.51796 −0.00578484
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 2617.09 3.33387
\(786\) 0 0
\(787\) 652.411i 0.828985i 0.910053 + 0.414493i \(0.136041\pi\)
−0.910053 + 0.414493i \(0.863959\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 208.854i 0.264037i
\(792\) 0 0
\(793\) −385.615 −0.486274
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −584.554 −0.733442 −0.366721 0.930331i \(-0.619520\pi\)
−0.366721 + 0.930331i \(0.619520\pi\)
\(798\) 0 0
\(799\) − 550.799i − 0.689360i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 5.49699i 0.00684556i
\(804\) 0 0
\(805\) −593.112 −0.736785
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 917.370 1.13396 0.566978 0.823733i \(-0.308112\pi\)
0.566978 + 0.823733i \(0.308112\pi\)
\(810\) 0 0
\(811\) − 677.208i − 0.835028i −0.908671 0.417514i \(-0.862901\pi\)
0.908671 0.417514i \(-0.137099\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 300.781i 0.369056i
\(816\) 0 0
\(817\) −8.97824 −0.0109893
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 304.673 0.371100 0.185550 0.982635i \(-0.440593\pi\)
0.185550 + 0.982635i \(0.440593\pi\)
\(822\) 0 0
\(823\) 1510.65i 1.83554i 0.397112 + 0.917770i \(0.370013\pi\)
−0.397112 + 0.917770i \(0.629987\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 278.384i 0.336620i 0.985734 + 0.168310i \(0.0538309\pi\)
−0.985734 + 0.168310i \(0.946169\pi\)
\(828\) 0 0
\(829\) 361.034 0.435505 0.217752 0.976004i \(-0.430127\pi\)
0.217752 + 0.976004i \(0.430127\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −382.135 −0.458746
\(834\) 0 0
\(835\) − 2446.21i − 2.92959i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 568.835i 0.677991i 0.940788 + 0.338996i \(0.110087\pi\)
−0.940788 + 0.338996i \(0.889913\pi\)
\(840\) 0 0
\(841\) −471.064 −0.560124
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 1019.76 1.20681
\(846\) 0 0
\(847\) 337.313i 0.398245i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) − 755.937i − 0.888293i
\(852\) 0 0
\(853\) 24.6871 0.0289415 0.0144708 0.999895i \(-0.495394\pi\)
0.0144708 + 0.999895i \(0.495394\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −689.321 −0.804342 −0.402171 0.915565i \(-0.631744\pi\)
−0.402171 + 0.915565i \(0.631744\pi\)
\(858\) 0 0
\(859\) 466.648i 0.543246i 0.962404 + 0.271623i \(0.0875603\pi\)
−0.962404 + 0.271623i \(0.912440\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) − 739.477i − 0.856868i −0.903573 0.428434i \(-0.859066\pi\)
0.903573 0.428434i \(-0.140934\pi\)
\(864\) 0 0
\(865\) 2425.16 2.80365
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 6.90085 0.00794114
\(870\) 0 0
\(871\) − 317.019i − 0.363971i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) − 725.156i − 0.828749i
\(876\) 0 0
\(877\) 692.804 0.789970 0.394985 0.918688i \(-0.370750\pi\)
0.394985 + 0.918688i \(0.370750\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 347.623 0.394577 0.197289 0.980345i \(-0.436786\pi\)
0.197289 + 0.980345i \(0.436786\pi\)
\(882\) 0 0
\(883\) 783.477i 0.887290i 0.896203 + 0.443645i \(0.146315\pi\)
−0.896203 + 0.443645i \(0.853685\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 539.971i 0.608761i 0.952551 + 0.304380i \(0.0984494\pi\)
−0.952551 + 0.304380i \(0.901551\pi\)
\(888\) 0 0
\(889\) −471.009 −0.529819
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −258.972 −0.290002
\(894\) 0 0
\(895\) − 2846.19i − 3.18010i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 123.537i 0.137416i
\(900\) 0 0
\(901\) −408.945 −0.453879
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 2187.48 2.41711
\(906\) 0 0
\(907\) − 364.840i − 0.402250i −0.979566 0.201125i \(-0.935540\pi\)
0.979566 0.201125i \(-0.0644597\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 140.980i 0.154753i 0.997002 + 0.0773764i \(0.0246543\pi\)
−0.997002 + 0.0773764i \(0.975346\pi\)
\(912\) 0 0
\(913\) 6.39039 0.00699933
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 329.873 0.359730
\(918\) 0 0
\(919\) − 1653.67i − 1.79943i −0.436482 0.899713i \(-0.643776\pi\)
0.436482 0.899713i \(-0.356224\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) − 123.223i − 0.133503i
\(924\) 0 0
\(925\) 1715.25 1.85433
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −819.652 −0.882295 −0.441148 0.897435i \(-0.645428\pi\)
−0.441148 + 0.897435i \(0.645428\pi\)
\(930\) 0 0
\(931\) 179.671i 0.192987i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) − 22.3171i − 0.0238685i
\(936\) 0 0
\(937\) −609.090 −0.650043 −0.325021 0.945707i \(-0.605371\pi\)
−0.325021 + 0.945707i \(0.605371\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −707.610 −0.751977 −0.375988 0.926624i \(-0.622697\pi\)
−0.375988 + 0.926624i \(0.622697\pi\)
\(942\) 0 0
\(943\) 412.147i 0.437059i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 479.473i 0.506307i 0.967426 + 0.253154i \(0.0814678\pi\)
−0.967426 + 0.253154i \(0.918532\pi\)
\(948\) 0 0
\(949\) −149.925 −0.157983
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −743.165 −0.779816 −0.389908 0.920854i \(-0.627493\pi\)
−0.389908 + 0.920854i \(0.627493\pi\)
\(954\) 0 0
\(955\) − 2992.68i − 3.13370i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) − 239.056i − 0.249277i
\(960\) 0 0
\(961\) 919.746 0.957072
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 2929.24 3.03549
\(966\) 0 0
\(967\) 1097.27i 1.13471i 0.823473 + 0.567355i \(0.192033\pi\)
−0.823473 + 0.567355i \(0.807967\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) − 1062.93i − 1.09468i −0.836910 0.547340i \(-0.815640\pi\)
0.836910 0.547340i \(-0.184360\pi\)
\(972\) 0 0
\(973\) 239.285 0.245925
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 685.421 0.701556 0.350778 0.936459i \(-0.385917\pi\)
0.350778 + 0.936459i \(0.385917\pi\)
\(978\) 0 0
\(979\) 7.64584i 0.00780985i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) − 747.688i − 0.760619i −0.924859 0.380309i \(-0.875818\pi\)
0.924859 0.380309i \(-0.124182\pi\)
\(984\) 0 0
\(985\) 2465.05 2.50258
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 49.2097 0.0497570
\(990\) 0 0
\(991\) 514.441i 0.519113i 0.965728 + 0.259556i \(0.0835763\pi\)
−0.965728 + 0.259556i \(0.916424\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) − 2092.79i − 2.10330i
\(996\) 0 0
\(997\) 329.890 0.330883 0.165442 0.986220i \(-0.447095\pi\)
0.165442 + 0.986220i \(0.447095\pi\)
\(998\) 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 2736.3.m.f.1711.2 12
3.2 odd 2 912.3.m.a.799.12 yes 12
4.3 odd 2 inner 2736.3.m.f.1711.1 12
12.11 even 2 912.3.m.a.799.6 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
912.3.m.a.799.6 12 12.11 even 2
912.3.m.a.799.12 yes 12 3.2 odd 2
2736.3.m.f.1711.1 12 4.3 odd 2 inner
2736.3.m.f.1711.2 12 1.1 even 1 trivial