Properties

Label 2736.3.m.f.1711.6
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 1711.6
Root \(0.816029 + 1.41340i\) of defining polynomial
Character \(\chi\) \(=\) 2736.1711
Dual form 2736.3.m.f.1711.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.606930 q^{5} +2.85501i q^{7} +O(q^{10})\) \(q-0.606930 q^{5} +2.85501i q^{7} +2.41768i q^{11} -20.3960 q^{13} -13.5054 q^{17} -4.35890i q^{19} +12.0337i q^{23} -24.6316 q^{25} +24.8131 q^{29} -18.4137i q^{31} -1.73279i q^{35} +1.16584 q^{37} +29.4718 q^{41} -33.7751i q^{43} -13.7717i q^{47} +40.8489 q^{49} +51.7771 q^{53} -1.46736i q^{55} +17.0618i q^{59} +34.7473 q^{61} +12.3789 q^{65} -43.5474i q^{67} -30.7860i q^{71} -64.7947 q^{73} -6.90251 q^{77} -80.1630i q^{79} +128.801i q^{83} +8.19686 q^{85} +163.654 q^{89} -58.2307i q^{91} +2.64555i q^{95} +25.1439 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 10 q^{5}+O(q^{10}) \) 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
\(5\) −0.606930 −0.121386 −0.0606930 0.998156i \(-0.519331\pi\)
−0.0606930 + 0.998156i \(0.519331\pi\)
\(6\) 0 0
\(7\) 2.85501i 0.407859i 0.978986 + 0.203930i \(0.0653713\pi\)
−0.978986 + 0.203930i \(0.934629\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 2.41768i 0.219789i 0.993943 + 0.109895i \(0.0350513\pi\)
−0.993943 + 0.109895i \(0.964949\pi\)
\(12\) 0 0
\(13\) −20.3960 −1.56892 −0.784460 0.620180i \(-0.787060\pi\)
−0.784460 + 0.620180i \(0.787060\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −13.5054 −0.794437 −0.397219 0.917724i \(-0.630025\pi\)
−0.397219 + 0.917724i \(0.630025\pi\)
\(18\) 0 0
\(19\) − 4.35890i − 0.229416i
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 12.0337i 0.523202i 0.965176 + 0.261601i \(0.0842505\pi\)
−0.965176 + 0.261601i \(0.915749\pi\)
\(24\) 0 0
\(25\) −24.6316 −0.985265
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 24.8131 0.855624 0.427812 0.903868i \(-0.359284\pi\)
0.427812 + 0.903868i \(0.359284\pi\)
\(30\) 0 0
\(31\) − 18.4137i − 0.593989i −0.954879 0.296995i \(-0.904016\pi\)
0.954879 0.296995i \(-0.0959844\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) − 1.73279i − 0.0495084i
\(36\) 0 0
\(37\) 1.16584 0.0315091 0.0157545 0.999876i \(-0.494985\pi\)
0.0157545 + 0.999876i \(0.494985\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 29.4718 0.718824 0.359412 0.933179i \(-0.382977\pi\)
0.359412 + 0.933179i \(0.382977\pi\)
\(42\) 0 0
\(43\) − 33.7751i − 0.785468i −0.919652 0.392734i \(-0.871529\pi\)
0.919652 0.392734i \(-0.128471\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) − 13.7717i − 0.293015i −0.989210 0.146508i \(-0.953197\pi\)
0.989210 0.146508i \(-0.0468033\pi\)
\(48\) 0 0
\(49\) 40.8489 0.833651
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 51.7771 0.976927 0.488464 0.872584i \(-0.337558\pi\)
0.488464 + 0.872584i \(0.337558\pi\)
\(54\) 0 0
\(55\) − 1.46736i − 0.0266793i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 17.0618i 0.289182i 0.989491 + 0.144591i \(0.0461867\pi\)
−0.989491 + 0.144591i \(0.953813\pi\)
\(60\) 0 0
\(61\) 34.7473 0.569627 0.284814 0.958583i \(-0.408068\pi\)
0.284814 + 0.958583i \(0.408068\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 12.3789 0.190445
\(66\) 0 0
\(67\) − 43.5474i − 0.649961i −0.945721 0.324980i \(-0.894642\pi\)
0.945721 0.324980i \(-0.105358\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) − 30.7860i − 0.433605i −0.976215 0.216803i \(-0.930437\pi\)
0.976215 0.216803i \(-0.0695628\pi\)
\(72\) 0 0
\(73\) −64.7947 −0.887599 −0.443799 0.896126i \(-0.646370\pi\)
−0.443799 + 0.896126i \(0.646370\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −6.90251 −0.0896430
\(78\) 0 0
\(79\) − 80.1630i − 1.01472i −0.861734 0.507361i \(-0.830621\pi\)
0.861734 0.507361i \(-0.169379\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 128.801i 1.55182i 0.630845 + 0.775909i \(0.282709\pi\)
−0.630845 + 0.775909i \(0.717291\pi\)
\(84\) 0 0
\(85\) 8.19686 0.0964336
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 163.654 1.83881 0.919404 0.393314i \(-0.128671\pi\)
0.919404 + 0.393314i \(0.128671\pi\)
\(90\) 0 0
\(91\) − 58.2307i − 0.639898i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 2.64555i 0.0278479i
\(96\) 0 0
\(97\) 25.1439 0.259216 0.129608 0.991565i \(-0.458628\pi\)
0.129608 + 0.991565i \(0.458628\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 114.079 1.12950 0.564749 0.825263i \(-0.308973\pi\)
0.564749 + 0.825263i \(0.308973\pi\)
\(102\) 0 0
\(103\) − 67.3211i − 0.653603i −0.945093 0.326802i \(-0.894029\pi\)
0.945093 0.326802i \(-0.105971\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 9.91899i 0.0927008i 0.998925 + 0.0463504i \(0.0147591\pi\)
−0.998925 + 0.0463504i \(0.985241\pi\)
\(108\) 0 0
\(109\) −96.3365 −0.883821 −0.441911 0.897059i \(-0.645699\pi\)
−0.441911 + 0.897059i \(0.645699\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −116.547 −1.03139 −0.515695 0.856772i \(-0.672466\pi\)
−0.515695 + 0.856772i \(0.672466\pi\)
\(114\) 0 0
\(115\) − 7.30359i − 0.0635095i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) − 38.5582i − 0.324018i
\(120\) 0 0
\(121\) 115.155 0.951693
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 30.1229 0.240984
\(126\) 0 0
\(127\) 138.728i 1.09235i 0.837672 + 0.546173i \(0.183916\pi\)
−0.837672 + 0.546173i \(0.816084\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 148.710i 1.13519i 0.823308 + 0.567595i \(0.192126\pi\)
−0.823308 + 0.567595i \(0.807874\pi\)
\(132\) 0 0
\(133\) 12.4447 0.0935693
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −36.4545 −0.266091 −0.133046 0.991110i \(-0.542476\pi\)
−0.133046 + 0.991110i \(0.542476\pi\)
\(138\) 0 0
\(139\) 87.1292i 0.626829i 0.949616 + 0.313415i \(0.101473\pi\)
−0.949616 + 0.313415i \(0.898527\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) − 49.3109i − 0.344832i
\(144\) 0 0
\(145\) −15.0598 −0.103861
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 158.016 1.06051 0.530256 0.847838i \(-0.322096\pi\)
0.530256 + 0.847838i \(0.322096\pi\)
\(150\) 0 0
\(151\) − 205.568i − 1.36138i −0.732573 0.680689i \(-0.761681\pi\)
0.732573 0.680689i \(-0.238319\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 11.1758i 0.0721020i
\(156\) 0 0
\(157\) 26.8308 0.170897 0.0854484 0.996343i \(-0.472768\pi\)
0.0854484 + 0.996343i \(0.472768\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −34.3563 −0.213393
\(162\) 0 0
\(163\) − 134.797i − 0.826973i −0.910510 0.413487i \(-0.864311\pi\)
0.910510 0.413487i \(-0.135689\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) − 75.0890i − 0.449635i −0.974401 0.224817i \(-0.927821\pi\)
0.974401 0.224817i \(-0.0721786\pi\)
\(168\) 0 0
\(169\) 246.995 1.46151
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 217.219 1.25560 0.627800 0.778375i \(-0.283956\pi\)
0.627800 + 0.778375i \(0.283956\pi\)
\(174\) 0 0
\(175\) − 70.3236i − 0.401849i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) − 46.1045i − 0.257567i −0.991673 0.128784i \(-0.958893\pi\)
0.991673 0.128784i \(-0.0411072\pi\)
\(180\) 0 0
\(181\) −148.682 −0.821445 −0.410722 0.911760i \(-0.634723\pi\)
−0.410722 + 0.911760i \(0.634723\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −0.707582 −0.00382477
\(186\) 0 0
\(187\) − 32.6518i − 0.174609i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) − 300.611i − 1.57388i −0.617028 0.786941i \(-0.711664\pi\)
0.617028 0.786941i \(-0.288336\pi\)
\(192\) 0 0
\(193\) 37.3778 0.193667 0.0968337 0.995301i \(-0.469128\pi\)
0.0968337 + 0.995301i \(0.469128\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 118.570 0.601876 0.300938 0.953644i \(-0.402700\pi\)
0.300938 + 0.953644i \(0.402700\pi\)
\(198\) 0 0
\(199\) 117.374i 0.589821i 0.955525 + 0.294910i \(0.0952898\pi\)
−0.955525 + 0.294910i \(0.904710\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 70.8418i 0.348974i
\(204\) 0 0
\(205\) −17.8873 −0.0872552
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 10.5384 0.0504231
\(210\) 0 0
\(211\) 289.759i 1.37326i 0.727005 + 0.686632i \(0.240912\pi\)
−0.727005 + 0.686632i \(0.759088\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 20.4992i 0.0953449i
\(216\) 0 0
\(217\) 52.5713 0.242264
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 275.456 1.24641
\(222\) 0 0
\(223\) − 79.9420i − 0.358484i −0.983805 0.179242i \(-0.942635\pi\)
0.983805 0.179242i \(-0.0573646\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) − 385.250i − 1.69714i −0.529085 0.848569i \(-0.677465\pi\)
0.529085 0.848569i \(-0.322535\pi\)
\(228\) 0 0
\(229\) 37.4194 0.163404 0.0817018 0.996657i \(-0.473964\pi\)
0.0817018 + 0.996657i \(0.473964\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 36.0574 0.154753 0.0773764 0.997002i \(-0.475346\pi\)
0.0773764 + 0.997002i \(0.475346\pi\)
\(234\) 0 0
\(235\) 8.35848i 0.0355680i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) − 463.070i − 1.93753i −0.247979 0.968765i \(-0.579766\pi\)
0.247979 0.968765i \(-0.420234\pi\)
\(240\) 0 0
\(241\) 429.839 1.78356 0.891781 0.452467i \(-0.149456\pi\)
0.891781 + 0.452467i \(0.149456\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −24.7924 −0.101194
\(246\) 0 0
\(247\) 88.9039i 0.359935i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) − 490.672i − 1.95487i −0.211239 0.977434i \(-0.567750\pi\)
0.211239 0.977434i \(-0.432250\pi\)
\(252\) 0 0
\(253\) −29.0935 −0.114994
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 189.622 0.737828 0.368914 0.929463i \(-0.379730\pi\)
0.368914 + 0.929463i \(0.379730\pi\)
\(258\) 0 0
\(259\) 3.32848i 0.0128513i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 232.128i 0.882615i 0.897356 + 0.441307i \(0.145485\pi\)
−0.897356 + 0.441307i \(0.854515\pi\)
\(264\) 0 0
\(265\) −31.4251 −0.118585
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 95.0653 0.353402 0.176701 0.984265i \(-0.443457\pi\)
0.176701 + 0.984265i \(0.443457\pi\)
\(270\) 0 0
\(271\) 110.876i 0.409137i 0.978852 + 0.204569i \(0.0655791\pi\)
−0.978852 + 0.204569i \(0.934421\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) − 59.5514i − 0.216551i
\(276\) 0 0
\(277\) 119.874 0.432760 0.216380 0.976309i \(-0.430575\pi\)
0.216380 + 0.976309i \(0.430575\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 120.062 0.427266 0.213633 0.976914i \(-0.431470\pi\)
0.213633 + 0.976914i \(0.431470\pi\)
\(282\) 0 0
\(283\) − 26.4929i − 0.0936144i −0.998904 0.0468072i \(-0.985095\pi\)
0.998904 0.0468072i \(-0.0149046\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 84.1424i 0.293179i
\(288\) 0 0
\(289\) −106.603 −0.368869
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 21.7148 0.0741120 0.0370560 0.999313i \(-0.488202\pi\)
0.0370560 + 0.999313i \(0.488202\pi\)
\(294\) 0 0
\(295\) − 10.3553i − 0.0351027i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) − 245.438i − 0.820863i
\(300\) 0 0
\(301\) 96.4285 0.320360
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −21.0892 −0.0691448
\(306\) 0 0
\(307\) − 58.6798i − 0.191139i −0.995423 0.0955697i \(-0.969533\pi\)
0.995423 0.0955697i \(-0.0304673\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 73.7996i 0.237298i 0.992936 + 0.118649i \(0.0378563\pi\)
−0.992936 + 0.118649i \(0.962144\pi\)
\(312\) 0 0
\(313\) 160.115 0.511551 0.255776 0.966736i \(-0.417669\pi\)
0.255776 + 0.966736i \(0.417669\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −75.2978 −0.237532 −0.118766 0.992922i \(-0.537894\pi\)
−0.118766 + 0.992922i \(0.537894\pi\)
\(318\) 0 0
\(319\) 59.9902i 0.188057i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 58.8688i 0.182256i
\(324\) 0 0
\(325\) 502.386 1.54580
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 39.3185 0.119509
\(330\) 0 0
\(331\) 116.291i 0.351333i 0.984450 + 0.175666i \(0.0562080\pi\)
−0.984450 + 0.175666i \(0.943792\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 26.4302i 0.0788962i
\(336\) 0 0
\(337\) 166.131 0.492971 0.246485 0.969147i \(-0.420724\pi\)
0.246485 + 0.969147i \(0.420724\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 44.5184 0.130552
\(342\) 0 0
\(343\) 256.520i 0.747871i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) − 180.801i − 0.521040i −0.965468 0.260520i \(-0.916106\pi\)
0.965468 0.260520i \(-0.0838940\pi\)
\(348\) 0 0
\(349\) −55.9774 −0.160394 −0.0801968 0.996779i \(-0.525555\pi\)
−0.0801968 + 0.996779i \(0.525555\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −543.098 −1.53852 −0.769260 0.638936i \(-0.779375\pi\)
−0.769260 + 0.638936i \(0.779375\pi\)
\(354\) 0 0
\(355\) 18.6849i 0.0526336i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) − 127.591i − 0.355408i −0.984084 0.177704i \(-0.943133\pi\)
0.984084 0.177704i \(-0.0568669\pi\)
\(360\) 0 0
\(361\) −19.0000 −0.0526316
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 39.3259 0.107742
\(366\) 0 0
\(367\) − 60.1583i − 0.163919i −0.996636 0.0819595i \(-0.973882\pi\)
0.996636 0.0819595i \(-0.0261178\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 147.824i 0.398449i
\(372\) 0 0
\(373\) −192.929 −0.517235 −0.258617 0.965980i \(-0.583267\pi\)
−0.258617 + 0.965980i \(0.583267\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −506.087 −1.34241
\(378\) 0 0
\(379\) 12.4601i 0.0328763i 0.999865 + 0.0164381i \(0.00523265\pi\)
−0.999865 + 0.0164381i \(0.994767\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) − 586.965i − 1.53255i −0.642515 0.766273i \(-0.722109\pi\)
0.642515 0.766273i \(-0.277891\pi\)
\(384\) 0 0
\(385\) 4.18934 0.0108814
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 164.796 0.423640 0.211820 0.977309i \(-0.432061\pi\)
0.211820 + 0.977309i \(0.432061\pi\)
\(390\) 0 0
\(391\) − 162.520i − 0.415652i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 48.6534i 0.123173i
\(396\) 0 0
\(397\) −278.595 −0.701751 −0.350876 0.936422i \(-0.614116\pi\)
−0.350876 + 0.936422i \(0.614116\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −343.429 −0.856431 −0.428215 0.903677i \(-0.640858\pi\)
−0.428215 + 0.903677i \(0.640858\pi\)
\(402\) 0 0
\(403\) 375.564i 0.931922i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 2.81862i 0.00692536i
\(408\) 0 0
\(409\) 688.882 1.68431 0.842154 0.539236i \(-0.181287\pi\)
0.842154 + 0.539236i \(0.181287\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −48.7115 −0.117946
\(414\) 0 0
\(415\) − 78.1732i − 0.188369i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) − 65.0291i − 0.155201i −0.996985 0.0776004i \(-0.975274\pi\)
0.996985 0.0776004i \(-0.0247258\pi\)
\(420\) 0 0
\(421\) −306.543 −0.728130 −0.364065 0.931374i \(-0.618611\pi\)
−0.364065 + 0.931374i \(0.618611\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 332.661 0.782732
\(426\) 0 0
\(427\) 99.2039i 0.232328i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 521.933i 1.21098i 0.795853 + 0.605491i \(0.207023\pi\)
−0.795853 + 0.605491i \(0.792977\pi\)
\(432\) 0 0
\(433\) 123.944 0.286244 0.143122 0.989705i \(-0.454286\pi\)
0.143122 + 0.989705i \(0.454286\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 52.4535 0.120031
\(438\) 0 0
\(439\) − 513.303i − 1.16925i −0.811302 0.584627i \(-0.801241\pi\)
0.811302 0.584627i \(-0.198759\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 105.258i 0.237602i 0.992918 + 0.118801i \(0.0379051\pi\)
−0.992918 + 0.118801i \(0.962095\pi\)
\(444\) 0 0
\(445\) −99.3266 −0.223206
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 346.829 0.772448 0.386224 0.922405i \(-0.373779\pi\)
0.386224 + 0.922405i \(0.373779\pi\)
\(450\) 0 0
\(451\) 71.2534i 0.157990i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 35.3420i 0.0776747i
\(456\) 0 0
\(457\) −294.201 −0.643765 −0.321883 0.946780i \(-0.604316\pi\)
−0.321883 + 0.946780i \(0.604316\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 692.974 1.50320 0.751598 0.659621i \(-0.229283\pi\)
0.751598 + 0.659621i \(0.229283\pi\)
\(462\) 0 0
\(463\) − 469.144i − 1.01327i −0.862161 0.506635i \(-0.830889\pi\)
0.862161 0.506635i \(-0.169111\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 445.537i 0.954041i 0.878892 + 0.477020i \(0.158283\pi\)
−0.878892 + 0.477020i \(0.841717\pi\)
\(468\) 0 0
\(469\) 124.328 0.265092
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 81.6575 0.172637
\(474\) 0 0
\(475\) 107.367i 0.226035i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) − 783.725i − 1.63617i −0.575097 0.818085i \(-0.695036\pi\)
0.575097 0.818085i \(-0.304964\pi\)
\(480\) 0 0
\(481\) −23.7784 −0.0494352
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −15.2606 −0.0314652
\(486\) 0 0
\(487\) − 89.5516i − 0.183884i −0.995764 0.0919421i \(-0.970693\pi\)
0.995764 0.0919421i \(-0.0293075\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 877.757i 1.78769i 0.448374 + 0.893846i \(0.352003\pi\)
−0.448374 + 0.893846i \(0.647997\pi\)
\(492\) 0 0
\(493\) −335.112 −0.679740
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 87.8943 0.176850
\(498\) 0 0
\(499\) 511.990i 1.02603i 0.858379 + 0.513016i \(0.171472\pi\)
−0.858379 + 0.513016i \(0.828528\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) − 497.093i − 0.988256i −0.869389 0.494128i \(-0.835487\pi\)
0.869389 0.494128i \(-0.164513\pi\)
\(504\) 0 0
\(505\) −69.2382 −0.137105
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 939.366 1.84551 0.922756 0.385384i \(-0.125931\pi\)
0.922756 + 0.385384i \(0.125931\pi\)
\(510\) 0 0
\(511\) − 184.990i − 0.362015i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 40.8592i 0.0793383i
\(516\) 0 0
\(517\) 33.2956 0.0644016
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 381.461 0.732171 0.366086 0.930581i \(-0.380698\pi\)
0.366086 + 0.930581i \(0.380698\pi\)
\(522\) 0 0
\(523\) − 535.503i − 1.02391i −0.859014 0.511953i \(-0.828922\pi\)
0.859014 0.511953i \(-0.171078\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 248.685i 0.471887i
\(528\) 0 0
\(529\) 384.191 0.726259
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −601.105 −1.12778
\(534\) 0 0
\(535\) − 6.02014i − 0.0112526i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 98.7596i 0.183227i
\(540\) 0 0
\(541\) −236.065 −0.436350 −0.218175 0.975910i \(-0.570010\pi\)
−0.218175 + 0.975910i \(0.570010\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 58.4696 0.107284
\(546\) 0 0
\(547\) 351.582i 0.642745i 0.946953 + 0.321373i \(0.104144\pi\)
−0.946953 + 0.321373i \(0.895856\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) − 108.158i − 0.196294i
\(552\) 0 0
\(553\) 228.866 0.413863
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 91.0821 0.163523 0.0817613 0.996652i \(-0.473945\pi\)
0.0817613 + 0.996652i \(0.473945\pi\)
\(558\) 0 0
\(559\) 688.876i 1.23234i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 278.239i 0.494207i 0.968989 + 0.247103i \(0.0794788\pi\)
−0.968989 + 0.247103i \(0.920521\pi\)
\(564\) 0 0
\(565\) 70.7360 0.125196
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −189.085 −0.332312 −0.166156 0.986100i \(-0.553135\pi\)
−0.166156 + 0.986100i \(0.553135\pi\)
\(570\) 0 0
\(571\) − 590.253i − 1.03372i −0.856071 0.516859i \(-0.827101\pi\)
0.856071 0.516859i \(-0.172899\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) − 296.409i − 0.515493i
\(576\) 0 0
\(577\) −266.414 −0.461723 −0.230861 0.972987i \(-0.574154\pi\)
−0.230861 + 0.972987i \(0.574154\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −367.728 −0.632923
\(582\) 0 0
\(583\) 125.181i 0.214718i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 495.542i 0.844194i 0.906551 + 0.422097i \(0.138706\pi\)
−0.906551 + 0.422097i \(0.861294\pi\)
\(588\) 0 0
\(589\) −80.2633 −0.136270
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −468.331 −0.789765 −0.394883 0.918732i \(-0.629215\pi\)
−0.394883 + 0.918732i \(0.629215\pi\)
\(594\) 0 0
\(595\) 23.4021i 0.0393313i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) − 164.789i − 0.275107i −0.990494 0.137553i \(-0.956076\pi\)
0.990494 0.137553i \(-0.0439239\pi\)
\(600\) 0 0
\(601\) −1051.90 −1.75024 −0.875121 0.483904i \(-0.839218\pi\)
−0.875121 + 0.483904i \(0.839218\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −69.8910 −0.115522
\(606\) 0 0
\(607\) − 984.361i − 1.62168i −0.585267 0.810841i \(-0.699010\pi\)
0.585267 0.810841i \(-0.300990\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 280.888i 0.459718i
\(612\) 0 0
\(613\) −449.217 −0.732817 −0.366408 0.930454i \(-0.619413\pi\)
−0.366408 + 0.930454i \(0.619413\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 314.644 0.509958 0.254979 0.966947i \(-0.417931\pi\)
0.254979 + 0.966947i \(0.417931\pi\)
\(618\) 0 0
\(619\) − 132.283i − 0.213704i −0.994275 0.106852i \(-0.965923\pi\)
0.994275 0.106852i \(-0.0340771\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 467.234i 0.749975i
\(624\) 0 0
\(625\) 597.508 0.956013
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −15.7451 −0.0250320
\(630\) 0 0
\(631\) − 521.872i − 0.827055i −0.910492 0.413528i \(-0.864297\pi\)
0.910492 0.413528i \(-0.135703\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) − 84.1982i − 0.132596i
\(636\) 0 0
\(637\) −833.152 −1.30793
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 514.200 0.802184 0.401092 0.916038i \(-0.368631\pi\)
0.401092 + 0.916038i \(0.368631\pi\)
\(642\) 0 0
\(643\) − 216.096i − 0.336075i −0.985781 0.168037i \(-0.946257\pi\)
0.985781 0.168037i \(-0.0537429\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 48.2451i 0.0745674i 0.999305 + 0.0372837i \(0.0118705\pi\)
−0.999305 + 0.0372837i \(0.988129\pi\)
\(648\) 0 0
\(649\) −41.2499 −0.0635591
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −693.988 −1.06277 −0.531384 0.847131i \(-0.678328\pi\)
−0.531384 + 0.847131i \(0.678328\pi\)
\(654\) 0 0
\(655\) − 90.2566i − 0.137796i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 1059.76i 1.60814i 0.594537 + 0.804068i \(0.297335\pi\)
−0.594537 + 0.804068i \(0.702665\pi\)
\(660\) 0 0
\(661\) −174.231 −0.263588 −0.131794 0.991277i \(-0.542074\pi\)
−0.131794 + 0.991277i \(0.542074\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −7.55307 −0.0113580
\(666\) 0 0
\(667\) 298.592i 0.447665i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 84.0078i 0.125198i
\(672\) 0 0
\(673\) −512.636 −0.761718 −0.380859 0.924633i \(-0.624372\pi\)
−0.380859 + 0.924633i \(0.624372\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 483.929 0.714814 0.357407 0.933949i \(-0.383661\pi\)
0.357407 + 0.933949i \(0.383661\pi\)
\(678\) 0 0
\(679\) 71.7862i 0.105723i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 961.587i 1.40789i 0.710256 + 0.703944i \(0.248579\pi\)
−0.710256 + 0.703944i \(0.751421\pi\)
\(684\) 0 0
\(685\) 22.1254 0.0322998
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −1056.04 −1.53272
\(690\) 0 0
\(691\) 98.7795i 0.142952i 0.997442 + 0.0714758i \(0.0227709\pi\)
−0.997442 + 0.0714758i \(0.977229\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) − 52.8814i − 0.0760883i
\(696\) 0 0
\(697\) −398.029 −0.571061
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −1135.85 −1.62033 −0.810166 0.586201i \(-0.800623\pi\)
−0.810166 + 0.586201i \(0.800623\pi\)
\(702\) 0 0
\(703\) − 5.08176i − 0.00722868i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 325.698i 0.460676i
\(708\) 0 0
\(709\) −494.337 −0.697232 −0.348616 0.937266i \(-0.613348\pi\)
−0.348616 + 0.937266i \(0.613348\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 221.584 0.310777
\(714\) 0 0
\(715\) 29.9283i 0.0418578i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) − 355.276i − 0.494126i −0.968999 0.247063i \(-0.920535\pi\)
0.968999 0.247063i \(-0.0794654\pi\)
\(720\) 0 0
\(721\) 192.203 0.266578
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −611.187 −0.843017
\(726\) 0 0
\(727\) − 596.808i − 0.820919i −0.911879 0.410459i \(-0.865368\pi\)
0.911879 0.410459i \(-0.134632\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 456.148i 0.624005i
\(732\) 0 0
\(733\) 1042.13 1.42173 0.710865 0.703329i \(-0.248304\pi\)
0.710865 + 0.703329i \(0.248304\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 105.284 0.142854
\(738\) 0 0
\(739\) − 463.422i − 0.627094i −0.949573 0.313547i \(-0.898483\pi\)
0.949573 0.313547i \(-0.101517\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 516.160i 0.694697i 0.937736 + 0.347349i \(0.112918\pi\)
−0.937736 + 0.347349i \(0.887082\pi\)
\(744\) 0 0
\(745\) −95.9049 −0.128731
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −28.3188 −0.0378089
\(750\) 0 0
\(751\) 141.566i 0.188504i 0.995548 + 0.0942520i \(0.0300459\pi\)
−0.995548 + 0.0942520i \(0.969954\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 124.765i 0.165252i
\(756\) 0 0
\(757\) 714.786 0.944235 0.472118 0.881536i \(-0.343490\pi\)
0.472118 + 0.881536i \(0.343490\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 528.806 0.694883 0.347442 0.937702i \(-0.387050\pi\)
0.347442 + 0.937702i \(0.387050\pi\)
\(762\) 0 0
\(763\) − 275.042i − 0.360474i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) − 347.991i − 0.453704i
\(768\) 0 0
\(769\) 305.574 0.397366 0.198683 0.980064i \(-0.436334\pi\)
0.198683 + 0.980064i \(0.436334\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −79.5350 −0.102891 −0.0514456 0.998676i \(-0.516383\pi\)
−0.0514456 + 0.998676i \(0.516383\pi\)
\(774\) 0 0
\(775\) 453.559i 0.585237i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) − 128.465i − 0.164910i
\(780\) 0 0
\(781\) 74.4306 0.0953017
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −16.2844 −0.0207445
\(786\) 0 0
\(787\) 333.127i 0.423287i 0.977347 + 0.211644i \(0.0678816\pi\)
−0.977347 + 0.211644i \(0.932118\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) − 332.744i − 0.420662i
\(792\) 0 0
\(793\) −708.704 −0.893699
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −1014.86 −1.27336 −0.636678 0.771130i \(-0.719692\pi\)
−0.636678 + 0.771130i \(0.719692\pi\)
\(798\) 0 0
\(799\) 185.993i 0.232782i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) − 156.653i − 0.195085i
\(804\) 0 0
\(805\) 20.8519 0.0259029
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −423.473 −0.523452 −0.261726 0.965142i \(-0.584292\pi\)
−0.261726 + 0.965142i \(0.584292\pi\)
\(810\) 0 0
\(811\) 265.825i 0.327774i 0.986479 + 0.163887i \(0.0524033\pi\)
−0.986479 + 0.163887i \(0.947597\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 81.8122i 0.100383i
\(816\) 0 0
\(817\) −147.222 −0.180199
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −437.207 −0.532529 −0.266265 0.963900i \(-0.585790\pi\)
−0.266265 + 0.963900i \(0.585790\pi\)
\(822\) 0 0
\(823\) − 138.346i − 0.168100i −0.996462 0.0840500i \(-0.973214\pi\)
0.996462 0.0840500i \(-0.0267855\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 927.025i 1.12095i 0.828172 + 0.560475i \(0.189381\pi\)
−0.828172 + 0.560475i \(0.810619\pi\)
\(828\) 0 0
\(829\) −1330.94 −1.60547 −0.802737 0.596333i \(-0.796624\pi\)
−0.802737 + 0.596333i \(0.796624\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −551.682 −0.662283
\(834\) 0 0
\(835\) 45.5738i 0.0545794i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) − 248.602i − 0.296308i −0.988964 0.148154i \(-0.952667\pi\)
0.988964 0.148154i \(-0.0473331\pi\)
\(840\) 0 0
\(841\) −225.310 −0.267907
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −149.909 −0.177407
\(846\) 0 0
\(847\) 328.769i 0.388156i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 14.0293i 0.0164856i
\(852\) 0 0
\(853\) 955.871 1.12060 0.560300 0.828290i \(-0.310686\pi\)
0.560300 + 0.828290i \(0.310686\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −990.079 −1.15528 −0.577642 0.816290i \(-0.696027\pi\)
−0.577642 + 0.816290i \(0.696027\pi\)
\(858\) 0 0
\(859\) 187.142i 0.217861i 0.994049 + 0.108930i \(0.0347425\pi\)
−0.994049 + 0.108930i \(0.965257\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 423.878i 0.491168i 0.969375 + 0.245584i \(0.0789797\pi\)
−0.969375 + 0.245584i \(0.921020\pi\)
\(864\) 0 0
\(865\) −131.837 −0.152412
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 193.809 0.223025
\(870\) 0 0
\(871\) 888.190i 1.01974i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 86.0014i 0.0982873i
\(876\) 0 0
\(877\) 510.331 0.581906 0.290953 0.956737i \(-0.406028\pi\)
0.290953 + 0.956737i \(0.406028\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −224.398 −0.254708 −0.127354 0.991857i \(-0.540648\pi\)
−0.127354 + 0.991857i \(0.540648\pi\)
\(882\) 0 0
\(883\) − 213.961i − 0.242312i −0.992633 0.121156i \(-0.961340\pi\)
0.992633 0.121156i \(-0.0386601\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) − 1124.46i − 1.26771i −0.773451 0.633856i \(-0.781471\pi\)
0.773451 0.633856i \(-0.218529\pi\)
\(888\) 0 0
\(889\) −396.070 −0.445523
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −60.0296 −0.0672224
\(894\) 0 0
\(895\) 27.9822i 0.0312651i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) − 456.900i − 0.508232i
\(900\) 0 0
\(901\) −699.273 −0.776107
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 90.2393 0.0997120
\(906\) 0 0
\(907\) 1546.70i 1.70529i 0.522489 + 0.852646i \(0.325003\pi\)
−0.522489 + 0.852646i \(0.674997\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 833.914i 0.915383i 0.889111 + 0.457692i \(0.151324\pi\)
−0.889111 + 0.457692i \(0.848676\pi\)
\(912\) 0 0
\(913\) −311.400 −0.341073
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −424.569 −0.462998
\(918\) 0 0
\(919\) − 931.367i − 1.01346i −0.862106 0.506729i \(-0.830855\pi\)
0.862106 0.506729i \(-0.169145\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 627.909i 0.680292i
\(924\) 0 0
\(925\) −28.7165 −0.0310448
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −1462.78 −1.57457 −0.787286 0.616587i \(-0.788515\pi\)
−0.787286 + 0.616587i \(0.788515\pi\)
\(930\) 0 0
\(931\) − 178.056i − 0.191253i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 19.8174i 0.0211951i
\(936\) 0 0
\(937\) −1683.57 −1.79677 −0.898383 0.439212i \(-0.855258\pi\)
−0.898383 + 0.439212i \(0.855258\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 415.814 0.441885 0.220942 0.975287i \(-0.429087\pi\)
0.220942 + 0.975287i \(0.429087\pi\)
\(942\) 0 0
\(943\) 354.653i 0.376091i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 987.972i 1.04327i 0.853170 + 0.521633i \(0.174677\pi\)
−0.853170 + 0.521633i \(0.825323\pi\)
\(948\) 0 0
\(949\) 1321.55 1.39257
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 887.756 0.931538 0.465769 0.884906i \(-0.345778\pi\)
0.465769 + 0.884906i \(0.345778\pi\)
\(954\) 0 0
\(955\) 182.450i 0.191047i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) − 104.078i − 0.108528i
\(960\) 0 0
\(961\) 621.937 0.647177
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −22.6857 −0.0235085
\(966\) 0 0
\(967\) − 1635.00i − 1.69080i −0.534136 0.845399i \(-0.679363\pi\)
0.534136 0.845399i \(-0.320637\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) − 549.534i − 0.565947i −0.959128 0.282973i \(-0.908679\pi\)
0.959128 0.282973i \(-0.0913208\pi\)
\(972\) 0 0
\(973\) −248.755 −0.255658
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −527.248 −0.539660 −0.269830 0.962908i \(-0.586967\pi\)
−0.269830 + 0.962908i \(0.586967\pi\)
\(978\) 0 0
\(979\) 395.663i 0.404150i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 32.1942i 0.0327509i 0.999866 + 0.0163755i \(0.00521270\pi\)
−0.999866 + 0.0163755i \(0.994787\pi\)
\(984\) 0 0
\(985\) −71.9635 −0.0730594
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 406.438 0.410959
\(990\) 0 0
\(991\) 1854.35i 1.87119i 0.353069 + 0.935597i \(0.385138\pi\)
−0.353069 + 0.935597i \(0.614862\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) − 71.2380i − 0.0715960i
\(996\) 0 0
\(997\) 535.802 0.537415 0.268707 0.963222i \(-0.413404\pi\)
0.268707 + 0.963222i \(0.413404\pi\)
\(998\) 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.1711.6 12
3.2 odd 2 912.3.m.a.799.10 yes 12
4.3 odd 2 inner 2736.3.m.f.1711.5 12
12.11 even 2 912.3.m.a.799.4 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
912.3.m.a.799.4 12 12.11 even 2
912.3.m.a.799.10 yes 12 3.2 odd 2
2736.3.m.f.1711.5 12 4.3 odd 2 inner
2736.3.m.f.1711.6 12 1.1 even 1 trivial