Properties

Label 588.3.d.c.97.8
Level $588$
Weight $3$
Character 588.97
Analytic conductor $16.022$
Analytic rank $0$
Dimension $8$
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] = [588,3,Mod(97,588)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(588, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("588.97");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 588.d (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: \(16.0218395444\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.339738624.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 4x^{6} + 14x^{4} - 8x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{4}\cdot 7^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 97.8
Root \(-0.662827 + 0.382683i\) of defining polynomial
Character \(\chi\) \(=\) 588.97
Dual form 588.3.d.c.97.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.73205i q^{3} +5.82798i q^{5} -3.00000 q^{9} +O(q^{10})\) \(q+1.73205i q^{3} +5.82798i q^{5} -3.00000 q^{9} -6.86137 q^{11} -3.62063i q^{13} -10.0944 q^{15} +9.71521i q^{17} +30.2903i q^{19} -18.1558 q^{23} -8.96538 q^{25} -5.19615i q^{27} -40.4570 q^{29} -55.2124i q^{31} -11.8842i q^{33} +54.9745 q^{37} +6.27112 q^{39} -56.3322i q^{41} -66.0512 q^{43} -17.4839i q^{45} +49.4215i q^{47} -16.8272 q^{51} -81.0162 q^{53} -39.9879i q^{55} -52.4643 q^{57} +34.7914i q^{59} -0.0382805i q^{61} +21.1010 q^{65} -64.0898 q^{67} -31.4467i q^{69} +50.2730 q^{71} +21.3464i q^{73} -15.5285i q^{75} -47.5044 q^{79} +9.00000 q^{81} -33.6039i q^{83} -56.6201 q^{85} -70.0735i q^{87} +156.092i q^{89} +95.6306 q^{93} -176.531 q^{95} -43.7452i q^{97} +20.5841 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 24 q^{9} - 16 q^{23} + 72 q^{25} + 80 q^{29} + 128 q^{37} - 112 q^{43} - 96 q^{51} - 144 q^{53} - 192 q^{57} + 240 q^{65} - 64 q^{67} + 224 q^{71} - 432 q^{79} + 72 q^{81} - 96 q^{85} - 96 q^{93} - 272 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/588\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(295\) \(493\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

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
\(3\) 1.73205i 0.577350i
\(4\) 0 0
\(5\) 5.82798i 1.16560i 0.812617 + 0.582798i \(0.198042\pi\)
−0.812617 + 0.582798i \(0.801958\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −3.00000 −0.333333
\(10\) 0 0
\(11\) −6.86137 −0.623761 −0.311880 0.950121i \(-0.600959\pi\)
−0.311880 + 0.950121i \(0.600959\pi\)
\(12\) 0 0
\(13\) − 3.62063i − 0.278510i −0.990257 0.139255i \(-0.955529\pi\)
0.990257 0.139255i \(-0.0444708\pi\)
\(14\) 0 0
\(15\) −10.0944 −0.672957
\(16\) 0 0
\(17\) 9.71521i 0.571483i 0.958307 + 0.285742i \(0.0922399\pi\)
−0.958307 + 0.285742i \(0.907760\pi\)
\(18\) 0 0
\(19\) 30.2903i 1.59423i 0.603831 + 0.797113i \(0.293640\pi\)
−0.603831 + 0.797113i \(0.706360\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −18.1558 −0.789382 −0.394691 0.918814i \(-0.629148\pi\)
−0.394691 + 0.918814i \(0.629148\pi\)
\(24\) 0 0
\(25\) −8.96538 −0.358615
\(26\) 0 0
\(27\) − 5.19615i − 0.192450i
\(28\) 0 0
\(29\) −40.4570 −1.39507 −0.697534 0.716552i \(-0.745719\pi\)
−0.697534 + 0.716552i \(0.745719\pi\)
\(30\) 0 0
\(31\) − 55.2124i − 1.78104i −0.454940 0.890522i \(-0.650339\pi\)
0.454940 0.890522i \(-0.349661\pi\)
\(32\) 0 0
\(33\) − 11.8842i − 0.360129i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 54.9745 1.48580 0.742899 0.669403i \(-0.233450\pi\)
0.742899 + 0.669403i \(0.233450\pi\)
\(38\) 0 0
\(39\) 6.27112 0.160798
\(40\) 0 0
\(41\) − 56.3322i − 1.37396i −0.726678 0.686978i \(-0.758937\pi\)
0.726678 0.686978i \(-0.241063\pi\)
\(42\) 0 0
\(43\) −66.0512 −1.53608 −0.768038 0.640405i \(-0.778767\pi\)
−0.768038 + 0.640405i \(0.778767\pi\)
\(44\) 0 0
\(45\) − 17.4839i − 0.388532i
\(46\) 0 0
\(47\) 49.4215i 1.05152i 0.850632 + 0.525761i \(0.176219\pi\)
−0.850632 + 0.525761i \(0.823781\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −16.8272 −0.329946
\(52\) 0 0
\(53\) −81.0162 −1.52861 −0.764303 0.644857i \(-0.776917\pi\)
−0.764303 + 0.644857i \(0.776917\pi\)
\(54\) 0 0
\(55\) − 39.9879i − 0.727054i
\(56\) 0 0
\(57\) −52.4643 −0.920426
\(58\) 0 0
\(59\) 34.7914i 0.589685i 0.955546 + 0.294842i \(0.0952671\pi\)
−0.955546 + 0.294842i \(0.904733\pi\)
\(60\) 0 0
\(61\) − 0.0382805i 0 0.000627550i −1.00000 0.000313775i \(-0.999900\pi\)
1.00000 0.000313775i \(-9.98776e-5\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 21.1010 0.324630
\(66\) 0 0
\(67\) −64.0898 −0.956565 −0.478282 0.878206i \(-0.658740\pi\)
−0.478282 + 0.878206i \(0.658740\pi\)
\(68\) 0 0
\(69\) − 31.4467i − 0.455750i
\(70\) 0 0
\(71\) 50.2730 0.708070 0.354035 0.935232i \(-0.384809\pi\)
0.354035 + 0.935232i \(0.384809\pi\)
\(72\) 0 0
\(73\) 21.3464i 0.292416i 0.989254 + 0.146208i \(0.0467069\pi\)
−0.989254 + 0.146208i \(0.953293\pi\)
\(74\) 0 0
\(75\) − 15.5285i − 0.207047i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −47.5044 −0.601321 −0.300660 0.953731i \(-0.597207\pi\)
−0.300660 + 0.953731i \(0.597207\pi\)
\(80\) 0 0
\(81\) 9.00000 0.111111
\(82\) 0 0
\(83\) − 33.6039i − 0.404866i −0.979296 0.202433i \(-0.935115\pi\)
0.979296 0.202433i \(-0.0648849\pi\)
\(84\) 0 0
\(85\) −56.6201 −0.666119
\(86\) 0 0
\(87\) − 70.0735i − 0.805443i
\(88\) 0 0
\(89\) 156.092i 1.75384i 0.480636 + 0.876920i \(0.340406\pi\)
−0.480636 + 0.876920i \(0.659594\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 95.6306 1.02829
\(94\) 0 0
\(95\) −176.531 −1.85822
\(96\) 0 0
\(97\) − 43.7452i − 0.450981i −0.974245 0.225491i \(-0.927601\pi\)
0.974245 0.225491i \(-0.0723985\pi\)
\(98\) 0 0
\(99\) 20.5841 0.207920
\(100\) 0 0
\(101\) 169.746i 1.68066i 0.542077 + 0.840329i \(0.317638\pi\)
−0.542077 + 0.840329i \(0.682362\pi\)
\(102\) 0 0
\(103\) − 59.7216i − 0.579822i −0.957054 0.289911i \(-0.906374\pi\)
0.957054 0.289911i \(-0.0936257\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −57.7678 −0.539886 −0.269943 0.962876i \(-0.587005\pi\)
−0.269943 + 0.962876i \(0.587005\pi\)
\(108\) 0 0
\(109\) 179.846 1.64996 0.824980 0.565162i \(-0.191186\pi\)
0.824980 + 0.565162i \(0.191186\pi\)
\(110\) 0 0
\(111\) 95.2187i 0.857826i
\(112\) 0 0
\(113\) 96.6900 0.855664 0.427832 0.903858i \(-0.359278\pi\)
0.427832 + 0.903858i \(0.359278\pi\)
\(114\) 0 0
\(115\) − 105.812i − 0.920101i
\(116\) 0 0
\(117\) 10.8619i 0.0928367i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −73.9216 −0.610922
\(122\) 0 0
\(123\) 97.5702 0.793254
\(124\) 0 0
\(125\) 93.4495i 0.747596i
\(126\) 0 0
\(127\) −136.454 −1.07444 −0.537221 0.843441i \(-0.680526\pi\)
−0.537221 + 0.843441i \(0.680526\pi\)
\(128\) 0 0
\(129\) − 114.404i − 0.886853i
\(130\) 0 0
\(131\) − 26.5364i − 0.202568i −0.994858 0.101284i \(-0.967705\pi\)
0.994858 0.101284i \(-0.0322950\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 30.2831 0.224319
\(136\) 0 0
\(137\) 210.866 1.53917 0.769583 0.638546i \(-0.220464\pi\)
0.769583 + 0.638546i \(0.220464\pi\)
\(138\) 0 0
\(139\) 83.7490i 0.602511i 0.953543 + 0.301256i \(0.0974057\pi\)
−0.953543 + 0.301256i \(0.902594\pi\)
\(140\) 0 0
\(141\) −85.6006 −0.607096
\(142\) 0 0
\(143\) 24.8425i 0.173724i
\(144\) 0 0
\(145\) − 235.783i − 1.62609i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 7.99481 0.0536564 0.0268282 0.999640i \(-0.491459\pi\)
0.0268282 + 0.999640i \(0.491459\pi\)
\(150\) 0 0
\(151\) 60.8831 0.403199 0.201600 0.979468i \(-0.435386\pi\)
0.201600 + 0.979468i \(0.435386\pi\)
\(152\) 0 0
\(153\) − 29.1456i − 0.190494i
\(154\) 0 0
\(155\) 321.777 2.07598
\(156\) 0 0
\(157\) 29.1758i 0.185833i 0.995674 + 0.0929166i \(0.0296190\pi\)
−0.995674 + 0.0929166i \(0.970381\pi\)
\(158\) 0 0
\(159\) − 140.324i − 0.882542i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −62.4556 −0.383163 −0.191582 0.981477i \(-0.561362\pi\)
−0.191582 + 0.981477i \(0.561362\pi\)
\(164\) 0 0
\(165\) 69.2612 0.419765
\(166\) 0 0
\(167\) 141.404i 0.846730i 0.905959 + 0.423365i \(0.139151\pi\)
−0.905959 + 0.423365i \(0.860849\pi\)
\(168\) 0 0
\(169\) 155.891 0.922432
\(170\) 0 0
\(171\) − 90.8708i − 0.531408i
\(172\) 0 0
\(173\) 243.848i 1.40953i 0.709443 + 0.704763i \(0.248946\pi\)
−0.709443 + 0.704763i \(0.751054\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −60.2605 −0.340455
\(178\) 0 0
\(179\) −286.642 −1.60135 −0.800676 0.599098i \(-0.795526\pi\)
−0.800676 + 0.599098i \(0.795526\pi\)
\(180\) 0 0
\(181\) 214.838i 1.18695i 0.804852 + 0.593475i \(0.202245\pi\)
−0.804852 + 0.593475i \(0.797755\pi\)
\(182\) 0 0
\(183\) 0.0663038 0.000362316 0
\(184\) 0 0
\(185\) 320.391i 1.73184i
\(186\) 0 0
\(187\) − 66.6597i − 0.356469i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −45.3249 −0.237303 −0.118652 0.992936i \(-0.537857\pi\)
−0.118652 + 0.992936i \(0.537857\pi\)
\(192\) 0 0
\(193\) 314.031 1.62710 0.813551 0.581494i \(-0.197532\pi\)
0.813551 + 0.581494i \(0.197532\pi\)
\(194\) 0 0
\(195\) 36.5480i 0.187425i
\(196\) 0 0
\(197\) 259.231 1.31590 0.657948 0.753063i \(-0.271425\pi\)
0.657948 + 0.753063i \(0.271425\pi\)
\(198\) 0 0
\(199\) − 73.5255i − 0.369475i −0.982788 0.184737i \(-0.940857\pi\)
0.982788 0.184737i \(-0.0591435\pi\)
\(200\) 0 0
\(201\) − 111.007i − 0.552273i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 328.303 1.60148
\(206\) 0 0
\(207\) 54.4673 0.263127
\(208\) 0 0
\(209\) − 207.833i − 0.994415i
\(210\) 0 0
\(211\) 263.537 1.24899 0.624496 0.781028i \(-0.285304\pi\)
0.624496 + 0.781028i \(0.285304\pi\)
\(212\) 0 0
\(213\) 87.0754i 0.408805i
\(214\) 0 0
\(215\) − 384.945i − 1.79044i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −36.9730 −0.168827
\(220\) 0 0
\(221\) 35.1752 0.159164
\(222\) 0 0
\(223\) 191.042i 0.856689i 0.903616 + 0.428344i \(0.140903\pi\)
−0.903616 + 0.428344i \(0.859097\pi\)
\(224\) 0 0
\(225\) 26.8961 0.119538
\(226\) 0 0
\(227\) 431.405i 1.90046i 0.311547 + 0.950231i \(0.399153\pi\)
−0.311547 + 0.950231i \(0.600847\pi\)
\(228\) 0 0
\(229\) − 34.8689i − 0.152266i −0.997098 0.0761329i \(-0.975743\pi\)
0.997098 0.0761329i \(-0.0242573\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −350.771 −1.50546 −0.752728 0.658332i \(-0.771262\pi\)
−0.752728 + 0.658332i \(0.771262\pi\)
\(234\) 0 0
\(235\) −288.028 −1.22565
\(236\) 0 0
\(237\) − 82.2800i − 0.347173i
\(238\) 0 0
\(239\) 167.400 0.700419 0.350209 0.936671i \(-0.386110\pi\)
0.350209 + 0.936671i \(0.386110\pi\)
\(240\) 0 0
\(241\) − 82.0658i − 0.340522i −0.985399 0.170261i \(-0.945539\pi\)
0.985399 0.170261i \(-0.0544611\pi\)
\(242\) 0 0
\(243\) 15.5885i 0.0641500i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 109.670 0.444008
\(248\) 0 0
\(249\) 58.2037 0.233750
\(250\) 0 0
\(251\) 232.918i 0.927959i 0.885846 + 0.463979i \(0.153579\pi\)
−0.885846 + 0.463979i \(0.846421\pi\)
\(252\) 0 0
\(253\) 124.574 0.492385
\(254\) 0 0
\(255\) − 98.0689i − 0.384584i
\(256\) 0 0
\(257\) 37.3589i 0.145365i 0.997355 + 0.0726827i \(0.0231560\pi\)
−0.997355 + 0.0726827i \(0.976844\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 121.371 0.465023
\(262\) 0 0
\(263\) 3.37261 0.0128236 0.00641181 0.999979i \(-0.497959\pi\)
0.00641181 + 0.999979i \(0.497959\pi\)
\(264\) 0 0
\(265\) − 472.161i − 1.78174i
\(266\) 0 0
\(267\) −270.359 −1.01258
\(268\) 0 0
\(269\) − 87.2686i − 0.324419i −0.986756 0.162209i \(-0.948138\pi\)
0.986756 0.162209i \(-0.0518620\pi\)
\(270\) 0 0
\(271\) 92.0075i 0.339511i 0.985486 + 0.169756i \(0.0542978\pi\)
−0.985486 + 0.169756i \(0.945702\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 61.5148 0.223690
\(276\) 0 0
\(277\) 152.481 0.550474 0.275237 0.961376i \(-0.411244\pi\)
0.275237 + 0.961376i \(0.411244\pi\)
\(278\) 0 0
\(279\) 165.637i 0.593681i
\(280\) 0 0
\(281\) −219.880 −0.782491 −0.391245 0.920286i \(-0.627956\pi\)
−0.391245 + 0.920286i \(0.627956\pi\)
\(282\) 0 0
\(283\) − 387.389i − 1.36887i −0.729076 0.684433i \(-0.760050\pi\)
0.729076 0.684433i \(-0.239950\pi\)
\(284\) 0 0
\(285\) − 305.761i − 1.07285i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 194.615 0.673407
\(290\) 0 0
\(291\) 75.7689 0.260374
\(292\) 0 0
\(293\) 14.8794i 0.0507828i 0.999678 + 0.0253914i \(0.00808320\pi\)
−0.999678 + 0.0253914i \(0.991917\pi\)
\(294\) 0 0
\(295\) −202.764 −0.687335
\(296\) 0 0
\(297\) 35.6527i 0.120043i
\(298\) 0 0
\(299\) 65.7354i 0.219851i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −294.009 −0.970328
\(304\) 0 0
\(305\) 0.223098 0.000731470 0
\(306\) 0 0
\(307\) 453.211i 1.47626i 0.674660 + 0.738128i \(0.264290\pi\)
−0.674660 + 0.738128i \(0.735710\pi\)
\(308\) 0 0
\(309\) 103.441 0.334760
\(310\) 0 0
\(311\) − 435.246i − 1.39950i −0.714386 0.699752i \(-0.753294\pi\)
0.714386 0.699752i \(-0.246706\pi\)
\(312\) 0 0
\(313\) − 54.9405i − 0.175529i −0.996141 0.0877644i \(-0.972028\pi\)
0.996141 0.0877644i \(-0.0279723\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 433.691 1.36811 0.684055 0.729430i \(-0.260215\pi\)
0.684055 + 0.729430i \(0.260215\pi\)
\(318\) 0 0
\(319\) 277.590 0.870189
\(320\) 0 0
\(321\) − 100.057i − 0.311703i
\(322\) 0 0
\(323\) −294.277 −0.911073
\(324\) 0 0
\(325\) 32.4603i 0.0998780i
\(326\) 0 0
\(327\) 311.502i 0.952605i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −576.548 −1.74184 −0.870919 0.491427i \(-0.836475\pi\)
−0.870919 + 0.491427i \(0.836475\pi\)
\(332\) 0 0
\(333\) −164.924 −0.495266
\(334\) 0 0
\(335\) − 373.514i − 1.11497i
\(336\) 0 0
\(337\) −301.108 −0.893495 −0.446747 0.894660i \(-0.647418\pi\)
−0.446747 + 0.894660i \(0.647418\pi\)
\(338\) 0 0
\(339\) 167.472i 0.494018i
\(340\) 0 0
\(341\) 378.832i 1.11095i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 183.271 0.531220
\(346\) 0 0
\(347\) −252.112 −0.726547 −0.363273 0.931683i \(-0.618341\pi\)
−0.363273 + 0.931683i \(0.618341\pi\)
\(348\) 0 0
\(349\) − 406.452i − 1.16462i −0.812967 0.582309i \(-0.802149\pi\)
0.812967 0.582309i \(-0.197851\pi\)
\(350\) 0 0
\(351\) −18.8134 −0.0535993
\(352\) 0 0
\(353\) 134.429i 0.380819i 0.981705 + 0.190410i \(0.0609816\pi\)
−0.981705 + 0.190410i \(0.939018\pi\)
\(354\) 0 0
\(355\) 292.990i 0.825324i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −116.676 −0.325003 −0.162501 0.986708i \(-0.551956\pi\)
−0.162501 + 0.986708i \(0.551956\pi\)
\(360\) 0 0
\(361\) −556.501 −1.54155
\(362\) 0 0
\(363\) − 128.036i − 0.352716i
\(364\) 0 0
\(365\) −124.406 −0.340839
\(366\) 0 0
\(367\) 419.148i 1.14209i 0.820918 + 0.571046i \(0.193462\pi\)
−0.820918 + 0.571046i \(0.806538\pi\)
\(368\) 0 0
\(369\) 168.997i 0.457985i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −126.992 −0.340462 −0.170231 0.985404i \(-0.554451\pi\)
−0.170231 + 0.985404i \(0.554451\pi\)
\(374\) 0 0
\(375\) −161.859 −0.431625
\(376\) 0 0
\(377\) 146.480i 0.388541i
\(378\) 0 0
\(379\) −366.675 −0.967479 −0.483740 0.875212i \(-0.660722\pi\)
−0.483740 + 0.875212i \(0.660722\pi\)
\(380\) 0 0
\(381\) − 236.346i − 0.620329i
\(382\) 0 0
\(383\) 258.364i 0.674579i 0.941401 + 0.337290i \(0.109510\pi\)
−0.941401 + 0.337290i \(0.890490\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 198.154 0.512025
\(388\) 0 0
\(389\) 542.395 1.39433 0.697166 0.716910i \(-0.254444\pi\)
0.697166 + 0.716910i \(0.254444\pi\)
\(390\) 0 0
\(391\) − 176.387i − 0.451118i
\(392\) 0 0
\(393\) 45.9623 0.116953
\(394\) 0 0
\(395\) − 276.855i − 0.700898i
\(396\) 0 0
\(397\) 404.764i 1.01956i 0.860306 + 0.509778i \(0.170273\pi\)
−0.860306 + 0.509778i \(0.829727\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −473.436 −1.18064 −0.590319 0.807170i \(-0.700998\pi\)
−0.590319 + 0.807170i \(0.700998\pi\)
\(402\) 0 0
\(403\) −199.904 −0.496039
\(404\) 0 0
\(405\) 52.4518i 0.129511i
\(406\) 0 0
\(407\) −377.201 −0.926783
\(408\) 0 0
\(409\) 403.658i 0.986938i 0.869763 + 0.493469i \(0.164271\pi\)
−0.869763 + 0.493469i \(0.835729\pi\)
\(410\) 0 0
\(411\) 365.230i 0.888638i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 195.843 0.471911
\(416\) 0 0
\(417\) −145.058 −0.347860
\(418\) 0 0
\(419\) − 454.684i − 1.08517i −0.840003 0.542583i \(-0.817447\pi\)
0.840003 0.542583i \(-0.182553\pi\)
\(420\) 0 0
\(421\) −180.928 −0.429758 −0.214879 0.976641i \(-0.568936\pi\)
−0.214879 + 0.976641i \(0.568936\pi\)
\(422\) 0 0
\(423\) − 148.265i − 0.350507i
\(424\) 0 0
\(425\) − 87.1006i − 0.204943i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −43.0285 −0.100299
\(430\) 0 0
\(431\) −807.892 −1.87446 −0.937229 0.348714i \(-0.886618\pi\)
−0.937229 + 0.348714i \(0.886618\pi\)
\(432\) 0 0
\(433\) − 166.000i − 0.383372i −0.981456 0.191686i \(-0.938604\pi\)
0.981456 0.191686i \(-0.0613955\pi\)
\(434\) 0 0
\(435\) 408.387 0.938822
\(436\) 0 0
\(437\) − 549.944i − 1.25845i
\(438\) 0 0
\(439\) 29.2895i 0.0667186i 0.999443 + 0.0333593i \(0.0106206\pi\)
−0.999443 + 0.0333593i \(0.989379\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 822.751 1.85723 0.928613 0.371049i \(-0.121002\pi\)
0.928613 + 0.371049i \(0.121002\pi\)
\(444\) 0 0
\(445\) −909.701 −2.04427
\(446\) 0 0
\(447\) 13.8474i 0.0309786i
\(448\) 0 0
\(449\) −428.131 −0.953522 −0.476761 0.879033i \(-0.658189\pi\)
−0.476761 + 0.879033i \(0.658189\pi\)
\(450\) 0 0
\(451\) 386.516i 0.857020i
\(452\) 0 0
\(453\) 105.453i 0.232787i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −187.311 −0.409871 −0.204935 0.978775i \(-0.565698\pi\)
−0.204935 + 0.978775i \(0.565698\pi\)
\(458\) 0 0
\(459\) 50.4817 0.109982
\(460\) 0 0
\(461\) 182.821i 0.396576i 0.980144 + 0.198288i \(0.0635381\pi\)
−0.980144 + 0.198288i \(0.936462\pi\)
\(462\) 0 0
\(463\) 232.389 0.501920 0.250960 0.967997i \(-0.419254\pi\)
0.250960 + 0.967997i \(0.419254\pi\)
\(464\) 0 0
\(465\) 557.333i 1.19857i
\(466\) 0 0
\(467\) − 448.927i − 0.961299i −0.876913 0.480650i \(-0.840401\pi\)
0.876913 0.480650i \(-0.159599\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −50.5340 −0.107291
\(472\) 0 0
\(473\) 453.202 0.958144
\(474\) 0 0
\(475\) − 271.564i − 0.571713i
\(476\) 0 0
\(477\) 243.049 0.509536
\(478\) 0 0
\(479\) − 631.644i − 1.31867i −0.751848 0.659336i \(-0.770837\pi\)
0.751848 0.659336i \(-0.229163\pi\)
\(480\) 0 0
\(481\) − 199.043i − 0.413810i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 254.946 0.525662
\(486\) 0 0
\(487\) 701.535 1.44052 0.720262 0.693702i \(-0.244022\pi\)
0.720262 + 0.693702i \(0.244022\pi\)
\(488\) 0 0
\(489\) − 108.176i − 0.221219i
\(490\) 0 0
\(491\) −414.789 −0.844785 −0.422392 0.906413i \(-0.638810\pi\)
−0.422392 + 0.906413i \(0.638810\pi\)
\(492\) 0 0
\(493\) − 393.048i − 0.797258i
\(494\) 0 0
\(495\) 119.964i 0.242351i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −612.340 −1.22713 −0.613567 0.789643i \(-0.710266\pi\)
−0.613567 + 0.789643i \(0.710266\pi\)
\(500\) 0 0
\(501\) −244.919 −0.488860
\(502\) 0 0
\(503\) − 467.449i − 0.929323i −0.885488 0.464661i \(-0.846176\pi\)
0.885488 0.464661i \(-0.153824\pi\)
\(504\) 0 0
\(505\) −989.279 −1.95897
\(506\) 0 0
\(507\) 270.011i 0.532566i
\(508\) 0 0
\(509\) 62.5666i 0.122921i 0.998110 + 0.0614603i \(0.0195758\pi\)
−0.998110 + 0.0614603i \(0.980424\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 157.393 0.306809
\(514\) 0 0
\(515\) 348.057 0.675838
\(516\) 0 0
\(517\) − 339.099i − 0.655898i
\(518\) 0 0
\(519\) −422.357 −0.813790
\(520\) 0 0
\(521\) − 712.575i − 1.36771i −0.729620 0.683853i \(-0.760303\pi\)
0.729620 0.683853i \(-0.239697\pi\)
\(522\) 0 0
\(523\) − 280.114i − 0.535590i −0.963476 0.267795i \(-0.913705\pi\)
0.963476 0.267795i \(-0.0862950\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 536.400 1.01784
\(528\) 0 0
\(529\) −199.368 −0.376876
\(530\) 0 0
\(531\) − 104.374i − 0.196562i
\(532\) 0 0
\(533\) −203.958 −0.382660
\(534\) 0 0
\(535\) − 336.670i − 0.629289i
\(536\) 0 0
\(537\) − 496.478i − 0.924541i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 633.002 1.17006 0.585030 0.811012i \(-0.301083\pi\)
0.585030 + 0.811012i \(0.301083\pi\)
\(542\) 0 0
\(543\) −372.110 −0.685286
\(544\) 0 0
\(545\) 1048.14i 1.92319i
\(546\) 0 0
\(547\) 1047.16 1.91438 0.957189 0.289465i \(-0.0934773\pi\)
0.957189 + 0.289465i \(0.0934773\pi\)
\(548\) 0 0
\(549\) 0.114842i 0 0.000209183i
\(550\) 0 0
\(551\) − 1225.45i − 2.22405i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −554.933 −0.999879
\(556\) 0 0
\(557\) 681.732 1.22393 0.611967 0.790883i \(-0.290378\pi\)
0.611967 + 0.790883i \(0.290378\pi\)
\(558\) 0 0
\(559\) 239.147i 0.427812i
\(560\) 0 0
\(561\) 115.458 0.205807
\(562\) 0 0
\(563\) 201.588i 0.358061i 0.983844 + 0.179031i \(0.0572961\pi\)
−0.983844 + 0.179031i \(0.942704\pi\)
\(564\) 0 0
\(565\) 563.508i 0.997359i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −684.800 −1.20352 −0.601758 0.798679i \(-0.705533\pi\)
−0.601758 + 0.798679i \(0.705533\pi\)
\(570\) 0 0
\(571\) −25.0602 −0.0438884 −0.0219442 0.999759i \(-0.506986\pi\)
−0.0219442 + 0.999759i \(0.506986\pi\)
\(572\) 0 0
\(573\) − 78.5050i − 0.137007i
\(574\) 0 0
\(575\) 162.773 0.283084
\(576\) 0 0
\(577\) 1019.96i 1.76770i 0.467773 + 0.883849i \(0.345056\pi\)
−0.467773 + 0.883849i \(0.654944\pi\)
\(578\) 0 0
\(579\) 543.917i 0.939408i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 555.882 0.953485
\(584\) 0 0
\(585\) −63.3029 −0.108210
\(586\) 0 0
\(587\) − 581.810i − 0.991158i −0.868563 0.495579i \(-0.834956\pi\)
0.868563 0.495579i \(-0.165044\pi\)
\(588\) 0 0
\(589\) 1672.40 2.83939
\(590\) 0 0
\(591\) 449.002i 0.759733i
\(592\) 0 0
\(593\) − 143.863i − 0.242602i −0.992616 0.121301i \(-0.961293\pi\)
0.992616 0.121301i \(-0.0387066\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 127.350 0.213316
\(598\) 0 0
\(599\) 710.736 1.18654 0.593269 0.805005i \(-0.297837\pi\)
0.593269 + 0.805005i \(0.297837\pi\)
\(600\) 0 0
\(601\) 914.930i 1.52235i 0.648549 + 0.761173i \(0.275376\pi\)
−0.648549 + 0.761173i \(0.724624\pi\)
\(602\) 0 0
\(603\) 192.269 0.318855
\(604\) 0 0
\(605\) − 430.814i − 0.712089i
\(606\) 0 0
\(607\) 622.481i 1.02550i 0.858537 + 0.512752i \(0.171374\pi\)
−0.858537 + 0.512752i \(0.828626\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 178.937 0.292859
\(612\) 0 0
\(613\) −345.019 −0.562837 −0.281419 0.959585i \(-0.590805\pi\)
−0.281419 + 0.959585i \(0.590805\pi\)
\(614\) 0 0
\(615\) 568.637i 0.924614i
\(616\) 0 0
\(617\) −854.311 −1.38462 −0.692310 0.721600i \(-0.743407\pi\)
−0.692310 + 0.721600i \(0.743407\pi\)
\(618\) 0 0
\(619\) 49.2180i 0.0795121i 0.999209 + 0.0397561i \(0.0126581\pi\)
−0.999209 + 0.0397561i \(0.987342\pi\)
\(620\) 0 0
\(621\) 94.3402i 0.151917i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −768.756 −1.23001
\(626\) 0 0
\(627\) 359.977 0.574126
\(628\) 0 0
\(629\) 534.089i 0.849109i
\(630\) 0 0
\(631\) 457.699 0.725355 0.362677 0.931915i \(-0.381863\pi\)
0.362677 + 0.931915i \(0.381863\pi\)
\(632\) 0 0
\(633\) 456.460i 0.721106i
\(634\) 0 0
\(635\) − 795.252i − 1.25237i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −150.819 −0.236023
\(640\) 0 0
\(641\) −323.931 −0.505353 −0.252677 0.967551i \(-0.581311\pi\)
−0.252677 + 0.967551i \(0.581311\pi\)
\(642\) 0 0
\(643\) − 117.018i − 0.181987i −0.995851 0.0909935i \(-0.970996\pi\)
0.995851 0.0909935i \(-0.0290043\pi\)
\(644\) 0 0
\(645\) 666.745 1.03371
\(646\) 0 0
\(647\) 539.247i 0.833458i 0.909031 + 0.416729i \(0.136824\pi\)
−0.909031 + 0.416729i \(0.863176\pi\)
\(648\) 0 0
\(649\) − 238.717i − 0.367822i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −797.906 −1.22191 −0.610954 0.791666i \(-0.709214\pi\)
−0.610954 + 0.791666i \(0.709214\pi\)
\(654\) 0 0
\(655\) 154.654 0.236112
\(656\) 0 0
\(657\) − 64.0391i − 0.0974720i
\(658\) 0 0
\(659\) 295.186 0.447929 0.223965 0.974597i \(-0.428100\pi\)
0.223965 + 0.974597i \(0.428100\pi\)
\(660\) 0 0
\(661\) − 1032.24i − 1.56163i −0.624759 0.780817i \(-0.714803\pi\)
0.624759 0.780817i \(-0.285197\pi\)
\(662\) 0 0
\(663\) 60.9252i 0.0918933i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 734.528 1.10124
\(668\) 0 0
\(669\) −330.894 −0.494609
\(670\) 0 0
\(671\) 0.262657i 0 0.000391441i
\(672\) 0 0
\(673\) 418.188 0.621379 0.310689 0.950512i \(-0.399440\pi\)
0.310689 + 0.950512i \(0.399440\pi\)
\(674\) 0 0
\(675\) 46.5855i 0.0690155i
\(676\) 0 0
\(677\) 465.460i 0.687534i 0.939055 + 0.343767i \(0.111703\pi\)
−0.939055 + 0.343767i \(0.888297\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −747.215 −1.09723
\(682\) 0 0
\(683\) 1259.41 1.84394 0.921969 0.387263i \(-0.126580\pi\)
0.921969 + 0.387263i \(0.126580\pi\)
\(684\) 0 0
\(685\) 1228.92i 1.79405i
\(686\) 0 0
\(687\) 60.3947 0.0879107
\(688\) 0 0
\(689\) 293.330i 0.425732i
\(690\) 0 0
\(691\) 458.874i 0.664073i 0.943267 + 0.332036i \(0.107736\pi\)
−0.943267 + 0.332036i \(0.892264\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −488.088 −0.702285
\(696\) 0 0
\(697\) 547.279 0.785192
\(698\) 0 0
\(699\) − 607.553i − 0.869175i
\(700\) 0 0
\(701\) 822.907 1.17390 0.586952 0.809622i \(-0.300328\pi\)
0.586952 + 0.809622i \(0.300328\pi\)
\(702\) 0 0
\(703\) 1665.19i 2.36870i
\(704\) 0 0
\(705\) − 498.879i − 0.707629i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 285.908 0.403255 0.201627 0.979462i \(-0.435377\pi\)
0.201627 + 0.979462i \(0.435377\pi\)
\(710\) 0 0
\(711\) 142.513 0.200440
\(712\) 0 0
\(713\) 1002.42i 1.40592i
\(714\) 0 0
\(715\) −144.782 −0.202492
\(716\) 0 0
\(717\) 289.945i 0.404387i
\(718\) 0 0
\(719\) − 699.242i − 0.972520i −0.873814 0.486260i \(-0.838361\pi\)
0.873814 0.486260i \(-0.161639\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 142.142 0.196600
\(724\) 0 0
\(725\) 362.712 0.500293
\(726\) 0 0
\(727\) − 216.138i − 0.297302i −0.988890 0.148651i \(-0.952507\pi\)
0.988890 0.148651i \(-0.0474930\pi\)
\(728\) 0 0
\(729\) −27.0000 −0.0370370
\(730\) 0 0
\(731\) − 641.702i − 0.877841i
\(732\) 0 0
\(733\) − 727.188i − 0.992071i −0.868302 0.496035i \(-0.834789\pi\)
0.868302 0.496035i \(-0.165211\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 439.744 0.596668
\(738\) 0 0
\(739\) 396.413 0.536418 0.268209 0.963361i \(-0.413568\pi\)
0.268209 + 0.963361i \(0.413568\pi\)
\(740\) 0 0
\(741\) 189.954i 0.256348i
\(742\) 0 0
\(743\) 739.481 0.995263 0.497632 0.867388i \(-0.334203\pi\)
0.497632 + 0.867388i \(0.334203\pi\)
\(744\) 0 0
\(745\) 46.5936i 0.0625417i
\(746\) 0 0
\(747\) 100.812i 0.134955i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −748.332 −0.996448 −0.498224 0.867048i \(-0.666014\pi\)
−0.498224 + 0.867048i \(0.666014\pi\)
\(752\) 0 0
\(753\) −403.425 −0.535757
\(754\) 0 0
\(755\) 354.825i 0.469967i
\(756\) 0 0
\(757\) 199.145 0.263071 0.131536 0.991311i \(-0.458009\pi\)
0.131536 + 0.991311i \(0.458009\pi\)
\(758\) 0 0
\(759\) 215.768i 0.284279i
\(760\) 0 0
\(761\) − 981.456i − 1.28969i −0.764312 0.644846i \(-0.776921\pi\)
0.764312 0.644846i \(-0.223079\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 169.860 0.222040
\(766\) 0 0
\(767\) 125.967 0.164233
\(768\) 0 0
\(769\) − 724.214i − 0.941760i −0.882197 0.470880i \(-0.843936\pi\)
0.882197 0.470880i \(-0.156064\pi\)
\(770\) 0 0
\(771\) −64.7075 −0.0839268
\(772\) 0 0
\(773\) − 1404.90i − 1.81746i −0.417383 0.908731i \(-0.637053\pi\)
0.417383 0.908731i \(-0.362947\pi\)
\(774\) 0 0
\(775\) 495.000i 0.638709i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 1706.32 2.19039
\(780\) 0 0
\(781\) −344.942 −0.441667
\(782\) 0 0
\(783\) 210.221i 0.268481i
\(784\) 0 0
\(785\) −170.036 −0.216607
\(786\) 0 0
\(787\) − 255.814i − 0.325049i −0.986704 0.162525i \(-0.948036\pi\)
0.986704 0.162525i \(-0.0519637\pi\)
\(788\) 0 0
\(789\) 5.84154i 0.00740372i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −0.138600 −0.000174779 0
\(794\) 0 0
\(795\) 817.807 1.02869
\(796\) 0 0
\(797\) − 474.641i − 0.595534i −0.954639 0.297767i \(-0.903758\pi\)
0.954639 0.297767i \(-0.0962418\pi\)
\(798\) 0 0
\(799\) −480.141 −0.600927
\(800\) 0 0
\(801\) − 468.276i − 0.584614i
\(802\) 0 0
\(803\) − 146.465i − 0.182398i
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 151.154 0.187303
\(808\) 0 0
\(809\) 467.727 0.578155 0.289077 0.957306i \(-0.406651\pi\)
0.289077 + 0.957306i \(0.406651\pi\)
\(810\) 0 0
\(811\) 1567.70i 1.93305i 0.256571 + 0.966525i \(0.417407\pi\)
−0.256571 + 0.966525i \(0.582593\pi\)
\(812\) 0 0
\(813\) −159.362 −0.196017
\(814\) 0 0
\(815\) − 363.990i − 0.446614i
\(816\) 0 0
\(817\) − 2000.71i − 2.44885i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −438.250 −0.533801 −0.266900 0.963724i \(-0.585999\pi\)
−0.266900 + 0.963724i \(0.585999\pi\)
\(822\) 0 0
\(823\) 937.213 1.13878 0.569388 0.822069i \(-0.307180\pi\)
0.569388 + 0.822069i \(0.307180\pi\)
\(824\) 0 0
\(825\) 106.547i 0.129148i
\(826\) 0 0
\(827\) −1160.31 −1.40303 −0.701516 0.712654i \(-0.747493\pi\)
−0.701516 + 0.712654i \(0.747493\pi\)
\(828\) 0 0
\(829\) − 254.599i − 0.307116i −0.988140 0.153558i \(-0.950927\pi\)
0.988140 0.153558i \(-0.0490732\pi\)
\(830\) 0 0
\(831\) 264.105i 0.317816i
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) −824.100 −0.986946
\(836\) 0 0
\(837\) −286.892 −0.342762
\(838\) 0 0
\(839\) − 129.902i − 0.154829i −0.996999 0.0774146i \(-0.975333\pi\)
0.996999 0.0774146i \(-0.0246665\pi\)
\(840\) 0 0
\(841\) 795.767 0.946215
\(842\) 0 0
\(843\) − 380.843i − 0.451771i
\(844\) 0 0
\(845\) 908.530i 1.07518i
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 670.978 0.790315
\(850\) 0 0
\(851\) −998.106 −1.17286
\(852\) 0 0
\(853\) − 1229.45i − 1.44133i −0.693284 0.720665i \(-0.743837\pi\)
0.693284 0.720665i \(-0.256163\pi\)
\(854\) 0 0
\(855\) 529.594 0.619408
\(856\) 0 0
\(857\) 668.190i 0.779685i 0.920881 + 0.389843i \(0.127471\pi\)
−0.920881 + 0.389843i \(0.872529\pi\)
\(858\) 0 0
\(859\) − 19.3907i − 0.0225736i −0.999936 0.0112868i \(-0.996407\pi\)
0.999936 0.0112868i \(-0.00359278\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 92.9711 0.107730 0.0538651 0.998548i \(-0.482846\pi\)
0.0538651 + 0.998548i \(0.482846\pi\)
\(864\) 0 0
\(865\) −1421.14 −1.64294
\(866\) 0 0
\(867\) 337.082i 0.388792i
\(868\) 0 0
\(869\) 325.945 0.375080
\(870\) 0 0
\(871\) 232.046i 0.266413i
\(872\) 0 0
\(873\) 131.236i 0.150327i
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 312.308 0.356110 0.178055 0.984021i \(-0.443020\pi\)
0.178055 + 0.984021i \(0.443020\pi\)
\(878\) 0 0
\(879\) −25.7718 −0.0293195
\(880\) 0 0
\(881\) − 772.018i − 0.876298i −0.898902 0.438149i \(-0.855634\pi\)
0.898902 0.438149i \(-0.144366\pi\)
\(882\) 0 0
\(883\) −959.154 −1.08624 −0.543122 0.839654i \(-0.682758\pi\)
−0.543122 + 0.839654i \(0.682758\pi\)
\(884\) 0 0
\(885\) − 351.197i − 0.396833i
\(886\) 0 0
\(887\) 554.964i 0.625664i 0.949808 + 0.312832i \(0.101278\pi\)
−0.949808 + 0.312832i \(0.898722\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −61.7523 −0.0693068
\(892\) 0 0
\(893\) −1496.99 −1.67636
\(894\) 0 0
\(895\) − 1670.54i − 1.86653i
\(896\) 0 0
\(897\) −113.857 −0.126931
\(898\) 0 0
\(899\) 2233.73i 2.48468i
\(900\) 0 0
\(901\) − 787.089i − 0.873573i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −1252.07 −1.38351
\(906\) 0 0
\(907\) 573.116 0.631881 0.315940 0.948779i \(-0.397680\pi\)
0.315940 + 0.948779i \(0.397680\pi\)
\(908\) 0 0
\(909\) − 509.239i − 0.560219i
\(910\) 0 0
\(911\) 726.088 0.797023 0.398511 0.917163i \(-0.369527\pi\)
0.398511 + 0.917163i \(0.369527\pi\)
\(912\) 0 0
\(913\) 230.569i 0.252540i
\(914\) 0 0
\(915\) 0.386417i 0 0.000422314i
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 784.533 0.853681 0.426840 0.904327i \(-0.359627\pi\)
0.426840 + 0.904327i \(0.359627\pi\)
\(920\) 0 0
\(921\) −784.984 −0.852317
\(922\) 0 0
\(923\) − 182.020i − 0.197205i
\(924\) 0 0
\(925\) −492.868 −0.532830
\(926\) 0 0
\(927\) 179.165i 0.193274i
\(928\) 0 0
\(929\) 159.109i 0.171269i 0.996327 + 0.0856347i \(0.0272918\pi\)
−0.996327 + 0.0856347i \(0.972708\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 753.868 0.808004
\(934\) 0 0
\(935\) 388.491 0.415499
\(936\) 0 0
\(937\) 728.876i 0.777883i 0.921262 + 0.388941i \(0.127159\pi\)
−0.921262 + 0.388941i \(0.872841\pi\)
\(938\) 0 0
\(939\) 95.1597 0.101342
\(940\) 0 0
\(941\) − 323.245i − 0.343513i −0.985139 0.171756i \(-0.945056\pi\)
0.985139 0.171756i \(-0.0549442\pi\)
\(942\) 0 0
\(943\) 1022.75i 1.08458i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 673.049 0.710717 0.355359 0.934730i \(-0.384359\pi\)
0.355359 + 0.934730i \(0.384359\pi\)
\(948\) 0 0
\(949\) 77.2873 0.0814408
\(950\) 0 0
\(951\) 751.175i 0.789879i
\(952\) 0 0
\(953\) −195.034 −0.204653 −0.102326 0.994751i \(-0.532629\pi\)
−0.102326 + 0.994751i \(0.532629\pi\)
\(954\) 0 0
\(955\) − 264.153i − 0.276600i
\(956\) 0 0
\(957\) 480.800i 0.502404i
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −2087.40 −2.17212
\(962\) 0 0
\(963\) 173.303 0.179962
\(964\) 0 0
\(965\) 1830.16i 1.89654i
\(966\) 0 0
\(967\) −731.573 −0.756538 −0.378269 0.925696i \(-0.623481\pi\)
−0.378269 + 0.925696i \(0.623481\pi\)
\(968\) 0 0
\(969\) − 509.702i − 0.526008i
\(970\) 0 0
\(971\) 498.822i 0.513720i 0.966449 + 0.256860i \(0.0826879\pi\)
−0.966449 + 0.256860i \(0.917312\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) −56.2230 −0.0576646
\(976\) 0 0
\(977\) −180.705 −0.184959 −0.0924794 0.995715i \(-0.529479\pi\)
−0.0924794 + 0.995715i \(0.529479\pi\)
\(978\) 0 0
\(979\) − 1071.00i − 1.09398i
\(980\) 0 0
\(981\) −539.537 −0.549987
\(982\) 0 0
\(983\) − 326.658i − 0.332307i −0.986100 0.166153i \(-0.946865\pi\)
0.986100 0.166153i \(-0.0531347\pi\)
\(984\) 0 0
\(985\) 1510.80i 1.53380i
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 1199.21 1.21255
\(990\) 0 0
\(991\) −1646.75 −1.66171 −0.830854 0.556491i \(-0.812147\pi\)
−0.830854 + 0.556491i \(0.812147\pi\)
\(992\) 0 0
\(993\) − 998.611i − 1.00565i
\(994\) 0 0
\(995\) 428.505 0.430659
\(996\) 0 0
\(997\) 140.158i 0.140580i 0.997527 + 0.0702900i \(0.0223925\pi\)
−0.997527 + 0.0702900i \(0.977608\pi\)
\(998\) 0 0
\(999\) − 285.656i − 0.285942i
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 588.3.d.c.97.8 yes 8
3.2 odd 2 1764.3.d.h.685.1 8
4.3 odd 2 2352.3.f.j.97.4 8
7.2 even 3 588.3.m.e.325.4 8
7.3 odd 6 588.3.m.e.313.4 8
7.4 even 3 588.3.m.f.313.1 8
7.5 odd 6 588.3.m.f.325.1 8
7.6 odd 2 inner 588.3.d.c.97.1 8
21.2 odd 6 1764.3.z.m.325.1 8
21.5 even 6 1764.3.z.l.325.4 8
21.11 odd 6 1764.3.z.l.901.4 8
21.17 even 6 1764.3.z.m.901.1 8
21.20 even 2 1764.3.d.h.685.8 8
28.27 even 2 2352.3.f.j.97.5 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
588.3.d.c.97.1 8 7.6 odd 2 inner
588.3.d.c.97.8 yes 8 1.1 even 1 trivial
588.3.m.e.313.4 8 7.3 odd 6
588.3.m.e.325.4 8 7.2 even 3
588.3.m.f.313.1 8 7.4 even 3
588.3.m.f.325.1 8 7.5 odd 6
1764.3.d.h.685.1 8 3.2 odd 2
1764.3.d.h.685.8 8 21.20 even 2
1764.3.z.l.325.4 8 21.5 even 6
1764.3.z.l.901.4 8 21.11 odd 6
1764.3.z.m.325.1 8 21.2 odd 6
1764.3.z.m.901.1 8 21.17 even 6
2352.3.f.j.97.4 8 4.3 odd 2
2352.3.f.j.97.5 8 28.27 even 2