Properties

Label 6027.2.a.bd.1.8
Level $6027$
Weight $2$
Character 6027.1
Self dual yes
Analytic conductor $48.126$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [6027,2,Mod(1,6027)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6027, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("6027.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6027.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(48.1258372982\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - 4x^{9} - 11x^{8} + 56x^{7} + 26x^{6} - 266x^{5} + 52x^{4} + 526x^{3} - 255x^{2} - 372x + 239 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Root \(2.13183\) of defining polynomial
Character \(\chi\) \(=\) 6027.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.13183 q^{2} -1.00000 q^{3} +2.54468 q^{4} -2.36072 q^{5} -2.13183 q^{6} +1.16116 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+2.13183 q^{2} -1.00000 q^{3} +2.54468 q^{4} -2.36072 q^{5} -2.13183 q^{6} +1.16116 q^{8} +1.00000 q^{9} -5.03264 q^{10} +4.44436 q^{11} -2.54468 q^{12} +0.290057 q^{13} +2.36072 q^{15} -2.61397 q^{16} -1.80941 q^{17} +2.13183 q^{18} -4.99859 q^{19} -6.00727 q^{20} +9.47459 q^{22} -1.55849 q^{23} -1.16116 q^{24} +0.572989 q^{25} +0.618352 q^{26} -1.00000 q^{27} +8.05686 q^{29} +5.03264 q^{30} +9.92711 q^{31} -7.89484 q^{32} -4.44436 q^{33} -3.85735 q^{34} +2.54468 q^{36} +6.77139 q^{37} -10.6561 q^{38} -0.290057 q^{39} -2.74117 q^{40} -1.00000 q^{41} -6.70057 q^{43} +11.3095 q^{44} -2.36072 q^{45} -3.32244 q^{46} -0.0265330 q^{47} +2.61397 q^{48} +1.22151 q^{50} +1.80941 q^{51} +0.738103 q^{52} -2.59306 q^{53} -2.13183 q^{54} -10.4919 q^{55} +4.99859 q^{57} +17.1758 q^{58} +12.0597 q^{59} +6.00727 q^{60} -1.73842 q^{61} +21.1629 q^{62} -11.6025 q^{64} -0.684744 q^{65} -9.47459 q^{66} +13.8400 q^{67} -4.60437 q^{68} +1.55849 q^{69} -10.2484 q^{71} +1.16116 q^{72} +7.01139 q^{73} +14.4354 q^{74} -0.572989 q^{75} -12.7198 q^{76} -0.618352 q^{78} +14.8949 q^{79} +6.17084 q^{80} +1.00000 q^{81} -2.13183 q^{82} -6.61380 q^{83} +4.27151 q^{85} -14.2844 q^{86} -8.05686 q^{87} +5.16061 q^{88} +13.1333 q^{89} -5.03264 q^{90} -3.96587 q^{92} -9.92711 q^{93} -0.0565637 q^{94} +11.8003 q^{95} +7.89484 q^{96} +4.50954 q^{97} +4.44436 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + 4 q^{2} - 10 q^{3} + 18 q^{4} - 6 q^{5} - 4 q^{6} + 12 q^{8} + 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q + 4 q^{2} - 10 q^{3} + 18 q^{4} - 6 q^{5} - 4 q^{6} + 12 q^{8} + 10 q^{9} - 2 q^{10} - 2 q^{11} - 18 q^{12} + 6 q^{15} + 14 q^{16} - 8 q^{17} + 4 q^{18} - 6 q^{19} - 20 q^{20} + 2 q^{22} - 12 q^{24} + 10 q^{25} - 16 q^{26} - 10 q^{27} + 16 q^{29} + 2 q^{30} - 2 q^{31} + 38 q^{32} + 2 q^{33} + 4 q^{34} + 18 q^{36} + 24 q^{37} + 26 q^{38} - 40 q^{40} - 10 q^{41} + 8 q^{43} - 8 q^{44} - 6 q^{45} + 4 q^{46} + 8 q^{47} - 14 q^{48} + 44 q^{50} + 8 q^{51} + 30 q^{52} + 24 q^{53} - 4 q^{54} + 6 q^{57} - 14 q^{58} - 6 q^{59} + 20 q^{60} + 14 q^{61} + 2 q^{62} + 86 q^{64} + 28 q^{65} - 2 q^{66} + 26 q^{67} + 6 q^{68} + 14 q^{71} + 12 q^{72} + 36 q^{73} + 18 q^{74} - 10 q^{75} + 32 q^{76} + 16 q^{78} + 20 q^{79} - 70 q^{80} + 10 q^{81} - 4 q^{82} - 40 q^{83} + 24 q^{85} - 36 q^{86} - 16 q^{87} + 14 q^{88} - 2 q^{89} - 2 q^{90} + 8 q^{92} + 2 q^{93} + 54 q^{94} - 24 q^{95} - 38 q^{96} - 16 q^{97} - 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.13183 1.50743 0.753714 0.657203i \(-0.228260\pi\)
0.753714 + 0.657203i \(0.228260\pi\)
\(3\) −1.00000 −0.577350
\(4\) 2.54468 1.27234
\(5\) −2.36072 −1.05575 −0.527873 0.849324i \(-0.677010\pi\)
−0.527873 + 0.849324i \(0.677010\pi\)
\(6\) −2.13183 −0.870314
\(7\) 0 0
\(8\) 1.16116 0.410532
\(9\) 1.00000 0.333333
\(10\) −5.03264 −1.59146
\(11\) 4.44436 1.34002 0.670012 0.742350i \(-0.266289\pi\)
0.670012 + 0.742350i \(0.266289\pi\)
\(12\) −2.54468 −0.734586
\(13\) 0.290057 0.0804475 0.0402237 0.999191i \(-0.487193\pi\)
0.0402237 + 0.999191i \(0.487193\pi\)
\(14\) 0 0
\(15\) 2.36072 0.609535
\(16\) −2.61397 −0.653492
\(17\) −1.80941 −0.438847 −0.219423 0.975630i \(-0.570418\pi\)
−0.219423 + 0.975630i \(0.570418\pi\)
\(18\) 2.13183 0.502476
\(19\) −4.99859 −1.14675 −0.573377 0.819291i \(-0.694367\pi\)
−0.573377 + 0.819291i \(0.694367\pi\)
\(20\) −6.00727 −1.34327
\(21\) 0 0
\(22\) 9.47459 2.01999
\(23\) −1.55849 −0.324968 −0.162484 0.986711i \(-0.551951\pi\)
−0.162484 + 0.986711i \(0.551951\pi\)
\(24\) −1.16116 −0.237021
\(25\) 0.572989 0.114598
\(26\) 0.618352 0.121269
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 8.05686 1.49612 0.748060 0.663631i \(-0.230985\pi\)
0.748060 + 0.663631i \(0.230985\pi\)
\(30\) 5.03264 0.918830
\(31\) 9.92711 1.78296 0.891481 0.453058i \(-0.149667\pi\)
0.891481 + 0.453058i \(0.149667\pi\)
\(32\) −7.89484 −1.39562
\(33\) −4.44436 −0.773663
\(34\) −3.85735 −0.661530
\(35\) 0 0
\(36\) 2.54468 0.424113
\(37\) 6.77139 1.11321 0.556605 0.830777i \(-0.312104\pi\)
0.556605 + 0.830777i \(0.312104\pi\)
\(38\) −10.6561 −1.72865
\(39\) −0.290057 −0.0464464
\(40\) −2.74117 −0.433417
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) −6.70057 −1.02183 −0.510914 0.859632i \(-0.670693\pi\)
−0.510914 + 0.859632i \(0.670693\pi\)
\(44\) 11.3095 1.70497
\(45\) −2.36072 −0.351915
\(46\) −3.32244 −0.489866
\(47\) −0.0265330 −0.00387024 −0.00193512 0.999998i \(-0.500616\pi\)
−0.00193512 + 0.999998i \(0.500616\pi\)
\(48\) 2.61397 0.377294
\(49\) 0 0
\(50\) 1.22151 0.172748
\(51\) 1.80941 0.253368
\(52\) 0.738103 0.102356
\(53\) −2.59306 −0.356185 −0.178092 0.984014i \(-0.556993\pi\)
−0.178092 + 0.984014i \(0.556993\pi\)
\(54\) −2.13183 −0.290105
\(55\) −10.4919 −1.41472
\(56\) 0 0
\(57\) 4.99859 0.662079
\(58\) 17.1758 2.25529
\(59\) 12.0597 1.57004 0.785020 0.619470i \(-0.212653\pi\)
0.785020 + 0.619470i \(0.212653\pi\)
\(60\) 6.00727 0.775535
\(61\) −1.73842 −0.222582 −0.111291 0.993788i \(-0.535499\pi\)
−0.111291 + 0.993788i \(0.535499\pi\)
\(62\) 21.1629 2.68769
\(63\) 0 0
\(64\) −11.6025 −1.45031
\(65\) −0.684744 −0.0849320
\(66\) −9.47459 −1.16624
\(67\) 13.8400 1.69082 0.845412 0.534115i \(-0.179355\pi\)
0.845412 + 0.534115i \(0.179355\pi\)
\(68\) −4.60437 −0.558362
\(69\) 1.55849 0.187621
\(70\) 0 0
\(71\) −10.2484 −1.21626 −0.608131 0.793837i \(-0.708080\pi\)
−0.608131 + 0.793837i \(0.708080\pi\)
\(72\) 1.16116 0.136844
\(73\) 7.01139 0.820621 0.410310 0.911946i \(-0.365420\pi\)
0.410310 + 0.911946i \(0.365420\pi\)
\(74\) 14.4354 1.67808
\(75\) −0.572989 −0.0661631
\(76\) −12.7198 −1.45906
\(77\) 0 0
\(78\) −0.618352 −0.0700146
\(79\) 14.8949 1.67580 0.837901 0.545822i \(-0.183783\pi\)
0.837901 + 0.545822i \(0.183783\pi\)
\(80\) 6.17084 0.689921
\(81\) 1.00000 0.111111
\(82\) −2.13183 −0.235421
\(83\) −6.61380 −0.725959 −0.362979 0.931797i \(-0.618240\pi\)
−0.362979 + 0.931797i \(0.618240\pi\)
\(84\) 0 0
\(85\) 4.27151 0.463310
\(86\) −14.2844 −1.54033
\(87\) −8.05686 −0.863786
\(88\) 5.16061 0.550123
\(89\) 13.1333 1.39213 0.696066 0.717978i \(-0.254932\pi\)
0.696066 + 0.717978i \(0.254932\pi\)
\(90\) −5.03264 −0.530487
\(91\) 0 0
\(92\) −3.96587 −0.413470
\(93\) −9.92711 −1.02939
\(94\) −0.0565637 −0.00583410
\(95\) 11.8003 1.21068
\(96\) 7.89484 0.805764
\(97\) 4.50954 0.457874 0.228937 0.973441i \(-0.426475\pi\)
0.228937 + 0.973441i \(0.426475\pi\)
\(98\) 0 0
\(99\) 4.44436 0.446675
\(100\) 1.45807 0.145807
\(101\) −14.8611 −1.47873 −0.739366 0.673304i \(-0.764875\pi\)
−0.739366 + 0.673304i \(0.764875\pi\)
\(102\) 3.85735 0.381934
\(103\) 2.74435 0.270409 0.135205 0.990818i \(-0.456831\pi\)
0.135205 + 0.990818i \(0.456831\pi\)
\(104\) 0.336803 0.0330263
\(105\) 0 0
\(106\) −5.52796 −0.536923
\(107\) 3.07941 0.297698 0.148849 0.988860i \(-0.452443\pi\)
0.148849 + 0.988860i \(0.452443\pi\)
\(108\) −2.54468 −0.244862
\(109\) −10.8608 −1.04027 −0.520137 0.854083i \(-0.674119\pi\)
−0.520137 + 0.854083i \(0.674119\pi\)
\(110\) −22.3668 −2.13259
\(111\) −6.77139 −0.642712
\(112\) 0 0
\(113\) 5.65327 0.531815 0.265907 0.963999i \(-0.414328\pi\)
0.265907 + 0.963999i \(0.414328\pi\)
\(114\) 10.6561 0.998036
\(115\) 3.67916 0.343084
\(116\) 20.5021 1.90357
\(117\) 0.290057 0.0268158
\(118\) 25.7092 2.36672
\(119\) 0 0
\(120\) 2.74117 0.250234
\(121\) 8.75230 0.795664
\(122\) −3.70601 −0.335527
\(123\) 1.00000 0.0901670
\(124\) 25.2613 2.26853
\(125\) 10.4509 0.934759
\(126\) 0 0
\(127\) 1.66494 0.147739 0.0738697 0.997268i \(-0.476465\pi\)
0.0738697 + 0.997268i \(0.476465\pi\)
\(128\) −8.94479 −0.790616
\(129\) 6.70057 0.589952
\(130\) −1.45975 −0.128029
\(131\) 20.1673 1.76202 0.881012 0.473094i \(-0.156863\pi\)
0.881012 + 0.473094i \(0.156863\pi\)
\(132\) −11.3095 −0.984362
\(133\) 0 0
\(134\) 29.5044 2.54879
\(135\) 2.36072 0.203178
\(136\) −2.10102 −0.180161
\(137\) 14.2458 1.21710 0.608551 0.793515i \(-0.291751\pi\)
0.608551 + 0.793515i \(0.291751\pi\)
\(138\) 3.32244 0.282825
\(139\) −11.5913 −0.983159 −0.491580 0.870833i \(-0.663580\pi\)
−0.491580 + 0.870833i \(0.663580\pi\)
\(140\) 0 0
\(141\) 0.0265330 0.00223448
\(142\) −21.8478 −1.83343
\(143\) 1.28912 0.107802
\(144\) −2.61397 −0.217831
\(145\) −19.0200 −1.57952
\(146\) 14.9471 1.23703
\(147\) 0 0
\(148\) 17.2310 1.41638
\(149\) 17.0799 1.39924 0.699619 0.714516i \(-0.253353\pi\)
0.699619 + 0.714516i \(0.253353\pi\)
\(150\) −1.22151 −0.0997361
\(151\) 4.28647 0.348828 0.174414 0.984672i \(-0.444197\pi\)
0.174414 + 0.984672i \(0.444197\pi\)
\(152\) −5.80416 −0.470780
\(153\) −1.80941 −0.146282
\(154\) 0 0
\(155\) −23.4351 −1.88235
\(156\) −0.738103 −0.0590955
\(157\) 5.53484 0.441728 0.220864 0.975305i \(-0.429112\pi\)
0.220864 + 0.975305i \(0.429112\pi\)
\(158\) 31.7532 2.52615
\(159\) 2.59306 0.205643
\(160\) 18.6375 1.47342
\(161\) 0 0
\(162\) 2.13183 0.167492
\(163\) 4.92782 0.385977 0.192988 0.981201i \(-0.438182\pi\)
0.192988 + 0.981201i \(0.438182\pi\)
\(164\) −2.54468 −0.198706
\(165\) 10.4919 0.816791
\(166\) −14.0995 −1.09433
\(167\) 11.0874 0.857966 0.428983 0.903313i \(-0.358872\pi\)
0.428983 + 0.903313i \(0.358872\pi\)
\(168\) 0 0
\(169\) −12.9159 −0.993528
\(170\) 9.10611 0.698407
\(171\) −4.99859 −0.382251
\(172\) −17.0508 −1.30011
\(173\) 15.4355 1.17354 0.586768 0.809755i \(-0.300400\pi\)
0.586768 + 0.809755i \(0.300400\pi\)
\(174\) −17.1758 −1.30209
\(175\) 0 0
\(176\) −11.6174 −0.875695
\(177\) −12.0597 −0.906463
\(178\) 27.9980 2.09854
\(179\) 3.64551 0.272478 0.136239 0.990676i \(-0.456498\pi\)
0.136239 + 0.990676i \(0.456498\pi\)
\(180\) −6.00727 −0.447755
\(181\) −3.63738 −0.270364 −0.135182 0.990821i \(-0.543162\pi\)
−0.135182 + 0.990821i \(0.543162\pi\)
\(182\) 0 0
\(183\) 1.73842 0.128508
\(184\) −1.80966 −0.133410
\(185\) −15.9853 −1.17527
\(186\) −21.1629 −1.55174
\(187\) −8.04167 −0.588065
\(188\) −0.0675180 −0.00492426
\(189\) 0 0
\(190\) 25.1561 1.82501
\(191\) −10.3820 −0.751212 −0.375606 0.926779i \(-0.622565\pi\)
−0.375606 + 0.926779i \(0.622565\pi\)
\(192\) 11.6025 0.837337
\(193\) 19.0283 1.36969 0.684844 0.728690i \(-0.259870\pi\)
0.684844 + 0.728690i \(0.259870\pi\)
\(194\) 9.61354 0.690212
\(195\) 0.684744 0.0490355
\(196\) 0 0
\(197\) 7.16377 0.510398 0.255199 0.966889i \(-0.417859\pi\)
0.255199 + 0.966889i \(0.417859\pi\)
\(198\) 9.47459 0.673330
\(199\) 4.63169 0.328332 0.164166 0.986433i \(-0.447507\pi\)
0.164166 + 0.986433i \(0.447507\pi\)
\(200\) 0.665332 0.0470461
\(201\) −13.8400 −0.976197
\(202\) −31.6812 −2.22908
\(203\) 0 0
\(204\) 4.60437 0.322370
\(205\) 2.36072 0.164880
\(206\) 5.85048 0.407622
\(207\) −1.55849 −0.108323
\(208\) −0.758201 −0.0525718
\(209\) −22.2155 −1.53668
\(210\) 0 0
\(211\) −1.15161 −0.0792801 −0.0396401 0.999214i \(-0.512621\pi\)
−0.0396401 + 0.999214i \(0.512621\pi\)
\(212\) −6.59852 −0.453188
\(213\) 10.2484 0.702209
\(214\) 6.56477 0.448759
\(215\) 15.8182 1.07879
\(216\) −1.16116 −0.0790069
\(217\) 0 0
\(218\) −23.1533 −1.56814
\(219\) −7.01139 −0.473786
\(220\) −26.6984 −1.80001
\(221\) −0.524833 −0.0353041
\(222\) −14.4354 −0.968842
\(223\) 21.3568 1.43016 0.715080 0.699043i \(-0.246390\pi\)
0.715080 + 0.699043i \(0.246390\pi\)
\(224\) 0 0
\(225\) 0.572989 0.0381993
\(226\) 12.0518 0.801672
\(227\) 0.453953 0.0301299 0.0150650 0.999887i \(-0.495204\pi\)
0.0150650 + 0.999887i \(0.495204\pi\)
\(228\) 12.7198 0.842389
\(229\) −18.5024 −1.22268 −0.611338 0.791370i \(-0.709368\pi\)
−0.611338 + 0.791370i \(0.709368\pi\)
\(230\) 7.84333 0.517174
\(231\) 0 0
\(232\) 9.35530 0.614206
\(233\) −0.886114 −0.0580513 −0.0290256 0.999579i \(-0.509240\pi\)
−0.0290256 + 0.999579i \(0.509240\pi\)
\(234\) 0.618352 0.0404229
\(235\) 0.0626370 0.00408598
\(236\) 30.6881 1.99762
\(237\) −14.8949 −0.967525
\(238\) 0 0
\(239\) −10.3105 −0.666930 −0.333465 0.942763i \(-0.608218\pi\)
−0.333465 + 0.942763i \(0.608218\pi\)
\(240\) −6.17084 −0.398326
\(241\) 10.7928 0.695227 0.347614 0.937638i \(-0.386992\pi\)
0.347614 + 0.937638i \(0.386992\pi\)
\(242\) 18.6584 1.19941
\(243\) −1.00000 −0.0641500
\(244\) −4.42373 −0.283200
\(245\) 0 0
\(246\) 2.13183 0.135920
\(247\) −1.44988 −0.0922535
\(248\) 11.5270 0.731963
\(249\) 6.61380 0.419133
\(250\) 22.2795 1.40908
\(251\) 13.9975 0.883513 0.441756 0.897135i \(-0.354356\pi\)
0.441756 + 0.897135i \(0.354356\pi\)
\(252\) 0 0
\(253\) −6.92650 −0.435465
\(254\) 3.54936 0.222707
\(255\) −4.27151 −0.267492
\(256\) 4.13624 0.258515
\(257\) −8.45313 −0.527292 −0.263646 0.964620i \(-0.584925\pi\)
−0.263646 + 0.964620i \(0.584925\pi\)
\(258\) 14.2844 0.889311
\(259\) 0 0
\(260\) −1.74245 −0.108062
\(261\) 8.05686 0.498707
\(262\) 42.9931 2.65612
\(263\) −29.3309 −1.80862 −0.904310 0.426875i \(-0.859614\pi\)
−0.904310 + 0.426875i \(0.859614\pi\)
\(264\) −5.16061 −0.317614
\(265\) 6.12149 0.376040
\(266\) 0 0
\(267\) −13.1333 −0.803748
\(268\) 35.2183 2.15130
\(269\) −1.45573 −0.0887573 −0.0443787 0.999015i \(-0.514131\pi\)
−0.0443787 + 0.999015i \(0.514131\pi\)
\(270\) 5.03264 0.306277
\(271\) −30.5158 −1.85370 −0.926850 0.375432i \(-0.877494\pi\)
−0.926850 + 0.375432i \(0.877494\pi\)
\(272\) 4.72974 0.286783
\(273\) 0 0
\(274\) 30.3696 1.83469
\(275\) 2.54657 0.153564
\(276\) 3.96587 0.238717
\(277\) 29.2660 1.75842 0.879211 0.476433i \(-0.158071\pi\)
0.879211 + 0.476433i \(0.158071\pi\)
\(278\) −24.7106 −1.48204
\(279\) 9.92711 0.594321
\(280\) 0 0
\(281\) −12.6815 −0.756512 −0.378256 0.925701i \(-0.623476\pi\)
−0.378256 + 0.925701i \(0.623476\pi\)
\(282\) 0.0565637 0.00336832
\(283\) 26.4622 1.57301 0.786506 0.617583i \(-0.211888\pi\)
0.786506 + 0.617583i \(0.211888\pi\)
\(284\) −26.0789 −1.54750
\(285\) −11.8003 −0.698987
\(286\) 2.74818 0.162503
\(287\) 0 0
\(288\) −7.89484 −0.465208
\(289\) −13.7260 −0.807414
\(290\) −40.5472 −2.38102
\(291\) −4.50954 −0.264354
\(292\) 17.8417 1.04411
\(293\) −2.35974 −0.137857 −0.0689287 0.997622i \(-0.521958\pi\)
−0.0689287 + 0.997622i \(0.521958\pi\)
\(294\) 0 0
\(295\) −28.4696 −1.65756
\(296\) 7.86267 0.457008
\(297\) −4.44436 −0.257888
\(298\) 36.4113 2.10925
\(299\) −0.452053 −0.0261429
\(300\) −1.45807 −0.0841819
\(301\) 0 0
\(302\) 9.13800 0.525833
\(303\) 14.8611 0.853747
\(304\) 13.0661 0.749395
\(305\) 4.10393 0.234990
\(306\) −3.85735 −0.220510
\(307\) 10.3588 0.591205 0.295603 0.955311i \(-0.404480\pi\)
0.295603 + 0.955311i \(0.404480\pi\)
\(308\) 0 0
\(309\) −2.74435 −0.156121
\(310\) −49.9596 −2.83751
\(311\) 4.07018 0.230799 0.115399 0.993319i \(-0.463185\pi\)
0.115399 + 0.993319i \(0.463185\pi\)
\(312\) −0.336803 −0.0190677
\(313\) 17.4202 0.984649 0.492324 0.870412i \(-0.336147\pi\)
0.492324 + 0.870412i \(0.336147\pi\)
\(314\) 11.7993 0.665874
\(315\) 0 0
\(316\) 37.9026 2.13219
\(317\) −28.1622 −1.58175 −0.790873 0.611980i \(-0.790373\pi\)
−0.790873 + 0.611980i \(0.790373\pi\)
\(318\) 5.52796 0.309993
\(319\) 35.8075 2.00484
\(320\) 27.3902 1.53116
\(321\) −3.07941 −0.171876
\(322\) 0 0
\(323\) 9.04450 0.503249
\(324\) 2.54468 0.141371
\(325\) 0.166200 0.00921911
\(326\) 10.5052 0.581832
\(327\) 10.8608 0.600602
\(328\) −1.16116 −0.0641143
\(329\) 0 0
\(330\) 22.3668 1.23125
\(331\) −9.65052 −0.530441 −0.265220 0.964188i \(-0.585445\pi\)
−0.265220 + 0.964188i \(0.585445\pi\)
\(332\) −16.8300 −0.923666
\(333\) 6.77139 0.371070
\(334\) 23.6363 1.29332
\(335\) −32.6723 −1.78508
\(336\) 0 0
\(337\) 8.72939 0.475520 0.237760 0.971324i \(-0.423587\pi\)
0.237760 + 0.971324i \(0.423587\pi\)
\(338\) −27.5344 −1.49767
\(339\) −5.65327 −0.307043
\(340\) 10.8696 0.589488
\(341\) 44.1196 2.38921
\(342\) −10.6561 −0.576217
\(343\) 0 0
\(344\) −7.78044 −0.419493
\(345\) −3.67916 −0.198080
\(346\) 32.9057 1.76902
\(347\) 31.1565 1.67257 0.836284 0.548296i \(-0.184723\pi\)
0.836284 + 0.548296i \(0.184723\pi\)
\(348\) −20.5021 −1.09903
\(349\) −5.77148 −0.308940 −0.154470 0.987997i \(-0.549367\pi\)
−0.154470 + 0.987997i \(0.549367\pi\)
\(350\) 0 0
\(351\) −0.290057 −0.0154821
\(352\) −35.0875 −1.87017
\(353\) 5.70652 0.303727 0.151864 0.988401i \(-0.451473\pi\)
0.151864 + 0.988401i \(0.451473\pi\)
\(354\) −25.7092 −1.36643
\(355\) 24.1936 1.28406
\(356\) 33.4201 1.77126
\(357\) 0 0
\(358\) 7.77159 0.410741
\(359\) 14.2254 0.750789 0.375394 0.926865i \(-0.377507\pi\)
0.375394 + 0.926865i \(0.377507\pi\)
\(360\) −2.74117 −0.144472
\(361\) 5.98587 0.315046
\(362\) −7.75426 −0.407555
\(363\) −8.75230 −0.459377
\(364\) 0 0
\(365\) −16.5519 −0.866367
\(366\) 3.70601 0.193716
\(367\) 13.5717 0.708438 0.354219 0.935163i \(-0.384747\pi\)
0.354219 + 0.935163i \(0.384747\pi\)
\(368\) 4.07385 0.212364
\(369\) −1.00000 −0.0520579
\(370\) −34.0779 −1.77163
\(371\) 0 0
\(372\) −25.2613 −1.30974
\(373\) −5.56422 −0.288104 −0.144052 0.989570i \(-0.546013\pi\)
−0.144052 + 0.989570i \(0.546013\pi\)
\(374\) −17.1434 −0.886466
\(375\) −10.4509 −0.539683
\(376\) −0.0308091 −0.00158886
\(377\) 2.33695 0.120359
\(378\) 0 0
\(379\) −24.0210 −1.23388 −0.616939 0.787011i \(-0.711627\pi\)
−0.616939 + 0.787011i \(0.711627\pi\)
\(380\) 30.0279 1.54040
\(381\) −1.66494 −0.0852974
\(382\) −22.1325 −1.13240
\(383\) −22.6618 −1.15797 −0.578983 0.815340i \(-0.696550\pi\)
−0.578983 + 0.815340i \(0.696550\pi\)
\(384\) 8.94479 0.456462
\(385\) 0 0
\(386\) 40.5650 2.06471
\(387\) −6.70057 −0.340609
\(388\) 11.4753 0.582571
\(389\) 14.8536 0.753106 0.376553 0.926395i \(-0.377109\pi\)
0.376553 + 0.926395i \(0.377109\pi\)
\(390\) 1.45975 0.0739175
\(391\) 2.81996 0.142611
\(392\) 0 0
\(393\) −20.1673 −1.01731
\(394\) 15.2719 0.769388
\(395\) −35.1625 −1.76922
\(396\) 11.3095 0.568322
\(397\) 31.7430 1.59313 0.796567 0.604551i \(-0.206647\pi\)
0.796567 + 0.604551i \(0.206647\pi\)
\(398\) 9.87395 0.494936
\(399\) 0 0
\(400\) −1.49778 −0.0748888
\(401\) −14.5053 −0.724360 −0.362180 0.932108i \(-0.617968\pi\)
−0.362180 + 0.932108i \(0.617968\pi\)
\(402\) −29.5044 −1.47155
\(403\) 2.87943 0.143435
\(404\) −37.8167 −1.88145
\(405\) −2.36072 −0.117305
\(406\) 0 0
\(407\) 30.0945 1.49173
\(408\) 2.10102 0.104016
\(409\) −14.3986 −0.711965 −0.355982 0.934493i \(-0.615854\pi\)
−0.355982 + 0.934493i \(0.615854\pi\)
\(410\) 5.03264 0.248544
\(411\) −14.2458 −0.702694
\(412\) 6.98350 0.344052
\(413\) 0 0
\(414\) −3.32244 −0.163289
\(415\) 15.6133 0.766428
\(416\) −2.28996 −0.112274
\(417\) 11.5913 0.567627
\(418\) −47.3596 −2.31643
\(419\) −30.8227 −1.50579 −0.752893 0.658143i \(-0.771342\pi\)
−0.752893 + 0.658143i \(0.771342\pi\)
\(420\) 0 0
\(421\) −0.694209 −0.0338337 −0.0169168 0.999857i \(-0.505385\pi\)
−0.0169168 + 0.999857i \(0.505385\pi\)
\(422\) −2.45503 −0.119509
\(423\) −0.0265330 −0.00129008
\(424\) −3.01096 −0.146225
\(425\) −1.03677 −0.0502909
\(426\) 21.8478 1.05853
\(427\) 0 0
\(428\) 7.83612 0.378773
\(429\) −1.28912 −0.0622392
\(430\) 33.7215 1.62620
\(431\) −19.6946 −0.948657 −0.474328 0.880348i \(-0.657309\pi\)
−0.474328 + 0.880348i \(0.657309\pi\)
\(432\) 2.61397 0.125765
\(433\) −21.8904 −1.05199 −0.525993 0.850489i \(-0.676306\pi\)
−0.525993 + 0.850489i \(0.676306\pi\)
\(434\) 0 0
\(435\) 19.0200 0.911938
\(436\) −27.6372 −1.32358
\(437\) 7.79027 0.372659
\(438\) −14.9471 −0.714198
\(439\) −3.09324 −0.147632 −0.0738161 0.997272i \(-0.523518\pi\)
−0.0738161 + 0.997272i \(0.523518\pi\)
\(440\) −12.1827 −0.580790
\(441\) 0 0
\(442\) −1.11885 −0.0532184
\(443\) −28.9415 −1.37505 −0.687526 0.726159i \(-0.741303\pi\)
−0.687526 + 0.726159i \(0.741303\pi\)
\(444\) −17.2310 −0.817748
\(445\) −31.0041 −1.46974
\(446\) 45.5290 2.15586
\(447\) −17.0799 −0.807851
\(448\) 0 0
\(449\) −25.2696 −1.19255 −0.596274 0.802781i \(-0.703353\pi\)
−0.596274 + 0.802781i \(0.703353\pi\)
\(450\) 1.22151 0.0575827
\(451\) −4.44436 −0.209277
\(452\) 14.3857 0.676649
\(453\) −4.28647 −0.201396
\(454\) 0.967749 0.0454187
\(455\) 0 0
\(456\) 5.80416 0.271805
\(457\) −10.0789 −0.471473 −0.235736 0.971817i \(-0.575750\pi\)
−0.235736 + 0.971817i \(0.575750\pi\)
\(458\) −39.4440 −1.84310
\(459\) 1.80941 0.0844561
\(460\) 9.36229 0.436519
\(461\) −0.973232 −0.0453279 −0.0226640 0.999743i \(-0.507215\pi\)
−0.0226640 + 0.999743i \(0.507215\pi\)
\(462\) 0 0
\(463\) 13.9337 0.647553 0.323776 0.946134i \(-0.395047\pi\)
0.323776 + 0.946134i \(0.395047\pi\)
\(464\) −21.0604 −0.977702
\(465\) 23.4351 1.08678
\(466\) −1.88904 −0.0875081
\(467\) −2.67442 −0.123758 −0.0618788 0.998084i \(-0.519709\pi\)
−0.0618788 + 0.998084i \(0.519709\pi\)
\(468\) 0.738103 0.0341188
\(469\) 0 0
\(470\) 0.133531 0.00615933
\(471\) −5.53484 −0.255032
\(472\) 14.0033 0.644552
\(473\) −29.7797 −1.36927
\(474\) −31.7532 −1.45847
\(475\) −2.86414 −0.131416
\(476\) 0 0
\(477\) −2.59306 −0.118728
\(478\) −21.9801 −1.00535
\(479\) −7.15536 −0.326937 −0.163468 0.986549i \(-0.552268\pi\)
−0.163468 + 0.986549i \(0.552268\pi\)
\(480\) −18.6375 −0.850681
\(481\) 1.96409 0.0895549
\(482\) 23.0084 1.04801
\(483\) 0 0
\(484\) 22.2718 1.01235
\(485\) −10.6457 −0.483398
\(486\) −2.13183 −0.0967016
\(487\) 38.5585 1.74725 0.873625 0.486599i \(-0.161763\pi\)
0.873625 + 0.486599i \(0.161763\pi\)
\(488\) −2.01859 −0.0913772
\(489\) −4.92782 −0.222844
\(490\) 0 0
\(491\) −40.3676 −1.82176 −0.910882 0.412667i \(-0.864597\pi\)
−0.910882 + 0.412667i \(0.864597\pi\)
\(492\) 2.54468 0.114723
\(493\) −14.5782 −0.656568
\(494\) −3.09089 −0.139066
\(495\) −10.4919 −0.471575
\(496\) −25.9491 −1.16515
\(497\) 0 0
\(498\) 14.0995 0.631812
\(499\) 12.9878 0.581414 0.290707 0.956812i \(-0.406110\pi\)
0.290707 + 0.956812i \(0.406110\pi\)
\(500\) 26.5942 1.18933
\(501\) −11.0874 −0.495347
\(502\) 29.8402 1.33183
\(503\) 28.4964 1.27059 0.635296 0.772269i \(-0.280878\pi\)
0.635296 + 0.772269i \(0.280878\pi\)
\(504\) 0 0
\(505\) 35.0828 1.56116
\(506\) −14.7661 −0.656433
\(507\) 12.9159 0.573614
\(508\) 4.23674 0.187975
\(509\) 3.91314 0.173447 0.0867235 0.996232i \(-0.472360\pi\)
0.0867235 + 0.996232i \(0.472360\pi\)
\(510\) −9.10611 −0.403225
\(511\) 0 0
\(512\) 26.7073 1.18031
\(513\) 4.99859 0.220693
\(514\) −18.0206 −0.794854
\(515\) −6.47864 −0.285483
\(516\) 17.0508 0.750620
\(517\) −0.117922 −0.00518621
\(518\) 0 0
\(519\) −15.4355 −0.677542
\(520\) −0.795097 −0.0348673
\(521\) −29.5289 −1.29369 −0.646843 0.762624i \(-0.723911\pi\)
−0.646843 + 0.762624i \(0.723911\pi\)
\(522\) 17.1758 0.751765
\(523\) 38.8288 1.69786 0.848932 0.528502i \(-0.177246\pi\)
0.848932 + 0.528502i \(0.177246\pi\)
\(524\) 51.3193 2.24189
\(525\) 0 0
\(526\) −62.5284 −2.72637
\(527\) −17.9622 −0.782447
\(528\) 11.6174 0.505582
\(529\) −20.5711 −0.894396
\(530\) 13.0500 0.566854
\(531\) 12.0597 0.523347
\(532\) 0 0
\(533\) −0.290057 −0.0125638
\(534\) −27.9980 −1.21159
\(535\) −7.26963 −0.314293
\(536\) 16.0704 0.694137
\(537\) −3.64551 −0.157315
\(538\) −3.10336 −0.133795
\(539\) 0 0
\(540\) 6.00727 0.258512
\(541\) −23.2651 −1.00025 −0.500123 0.865954i \(-0.666712\pi\)
−0.500123 + 0.865954i \(0.666712\pi\)
\(542\) −65.0543 −2.79432
\(543\) 3.63738 0.156095
\(544\) 14.2850 0.612465
\(545\) 25.6392 1.09826
\(546\) 0 0
\(547\) −8.34737 −0.356908 −0.178454 0.983948i \(-0.557110\pi\)
−0.178454 + 0.983948i \(0.557110\pi\)
\(548\) 36.2510 1.54857
\(549\) −1.73842 −0.0741941
\(550\) 5.42884 0.231486
\(551\) −40.2729 −1.71568
\(552\) 1.80966 0.0770243
\(553\) 0 0
\(554\) 62.3899 2.65069
\(555\) 15.9853 0.678540
\(556\) −29.4961 −1.25091
\(557\) −8.69009 −0.368211 −0.184106 0.982906i \(-0.558939\pi\)
−0.184106 + 0.982906i \(0.558939\pi\)
\(558\) 21.1629 0.895896
\(559\) −1.94355 −0.0822034
\(560\) 0 0
\(561\) 8.04167 0.339519
\(562\) −27.0347 −1.14039
\(563\) −35.6405 −1.50207 −0.751034 0.660263i \(-0.770445\pi\)
−0.751034 + 0.660263i \(0.770445\pi\)
\(564\) 0.0675180 0.00284302
\(565\) −13.3458 −0.561461
\(566\) 56.4127 2.37120
\(567\) 0 0
\(568\) −11.9000 −0.499315
\(569\) −2.01831 −0.0846120 −0.0423060 0.999105i \(-0.513470\pi\)
−0.0423060 + 0.999105i \(0.513470\pi\)
\(570\) −25.1561 −1.05367
\(571\) 45.5386 1.90573 0.952866 0.303392i \(-0.0981193\pi\)
0.952866 + 0.303392i \(0.0981193\pi\)
\(572\) 3.28039 0.137160
\(573\) 10.3820 0.433713
\(574\) 0 0
\(575\) −0.893000 −0.0372407
\(576\) −11.6025 −0.483437
\(577\) −12.2375 −0.509454 −0.254727 0.967013i \(-0.581986\pi\)
−0.254727 + 0.967013i \(0.581986\pi\)
\(578\) −29.2615 −1.21712
\(579\) −19.0283 −0.790789
\(580\) −48.3997 −2.00969
\(581\) 0 0
\(582\) −9.61354 −0.398494
\(583\) −11.5245 −0.477296
\(584\) 8.14134 0.336891
\(585\) −0.684744 −0.0283107
\(586\) −5.03055 −0.207810
\(587\) 19.8859 0.820777 0.410389 0.911911i \(-0.365393\pi\)
0.410389 + 0.911911i \(0.365393\pi\)
\(588\) 0 0
\(589\) −49.6215 −2.04462
\(590\) −60.6921 −2.49866
\(591\) −7.16377 −0.294678
\(592\) −17.7002 −0.727473
\(593\) 9.29758 0.381806 0.190903 0.981609i \(-0.438858\pi\)
0.190903 + 0.981609i \(0.438858\pi\)
\(594\) −9.47459 −0.388747
\(595\) 0 0
\(596\) 43.4628 1.78031
\(597\) −4.63169 −0.189562
\(598\) −0.963698 −0.0394085
\(599\) −14.3452 −0.586127 −0.293063 0.956093i \(-0.594675\pi\)
−0.293063 + 0.956093i \(0.594675\pi\)
\(600\) −0.665332 −0.0271621
\(601\) −24.4136 −0.995851 −0.497925 0.867220i \(-0.665905\pi\)
−0.497925 + 0.867220i \(0.665905\pi\)
\(602\) 0 0
\(603\) 13.8400 0.563608
\(604\) 10.9077 0.443827
\(605\) −20.6617 −0.840018
\(606\) 31.6812 1.28696
\(607\) 6.54301 0.265573 0.132786 0.991145i \(-0.457608\pi\)
0.132786 + 0.991145i \(0.457608\pi\)
\(608\) 39.4631 1.60044
\(609\) 0 0
\(610\) 8.74886 0.354231
\(611\) −0.00769610 −0.000311351 0
\(612\) −4.60437 −0.186121
\(613\) −4.74967 −0.191837 −0.0959186 0.995389i \(-0.530579\pi\)
−0.0959186 + 0.995389i \(0.530579\pi\)
\(614\) 22.0830 0.891199
\(615\) −2.36072 −0.0951933
\(616\) 0 0
\(617\) −40.3997 −1.62643 −0.813216 0.581962i \(-0.802285\pi\)
−0.813216 + 0.581962i \(0.802285\pi\)
\(618\) −5.85048 −0.235341
\(619\) −26.1618 −1.05153 −0.525766 0.850629i \(-0.676221\pi\)
−0.525766 + 0.850629i \(0.676221\pi\)
\(620\) −59.6348 −2.39499
\(621\) 1.55849 0.0625402
\(622\) 8.67691 0.347913
\(623\) 0 0
\(624\) 0.758201 0.0303523
\(625\) −27.5366 −1.10147
\(626\) 37.1369 1.48429
\(627\) 22.2155 0.887202
\(628\) 14.0844 0.562028
\(629\) −12.2522 −0.488528
\(630\) 0 0
\(631\) −28.0225 −1.11556 −0.557778 0.829990i \(-0.688346\pi\)
−0.557778 + 0.829990i \(0.688346\pi\)
\(632\) 17.2953 0.687970
\(633\) 1.15161 0.0457724
\(634\) −60.0369 −2.38437
\(635\) −3.93045 −0.155975
\(636\) 6.59852 0.261648
\(637\) 0 0
\(638\) 76.3354 3.02215
\(639\) −10.2484 −0.405421
\(640\) 21.1161 0.834689
\(641\) 0.737870 0.0291441 0.0145721 0.999894i \(-0.495361\pi\)
0.0145721 + 0.999894i \(0.495361\pi\)
\(642\) −6.56477 −0.259091
\(643\) 34.8978 1.37624 0.688118 0.725599i \(-0.258437\pi\)
0.688118 + 0.725599i \(0.258437\pi\)
\(644\) 0 0
\(645\) −15.8182 −0.622839
\(646\) 19.2813 0.758612
\(647\) −11.0952 −0.436197 −0.218098 0.975927i \(-0.569985\pi\)
−0.218098 + 0.975927i \(0.569985\pi\)
\(648\) 1.16116 0.0456147
\(649\) 53.5976 2.10389
\(650\) 0.354309 0.0138971
\(651\) 0 0
\(652\) 12.5397 0.491093
\(653\) −5.40616 −0.211559 −0.105780 0.994390i \(-0.533734\pi\)
−0.105780 + 0.994390i \(0.533734\pi\)
\(654\) 23.1533 0.905365
\(655\) −47.6093 −1.86025
\(656\) 2.61397 0.102058
\(657\) 7.01139 0.273540
\(658\) 0 0
\(659\) −27.2471 −1.06140 −0.530698 0.847561i \(-0.678070\pi\)
−0.530698 + 0.847561i \(0.678070\pi\)
\(660\) 26.6984 1.03924
\(661\) 37.0310 1.44034 0.720169 0.693799i \(-0.244064\pi\)
0.720169 + 0.693799i \(0.244064\pi\)
\(662\) −20.5732 −0.799601
\(663\) 0.524833 0.0203828
\(664\) −7.67968 −0.298029
\(665\) 0 0
\(666\) 14.4354 0.559361
\(667\) −12.5566 −0.486192
\(668\) 28.2138 1.09162
\(669\) −21.3568 −0.825703
\(670\) −69.6516 −2.69088
\(671\) −7.72617 −0.298266
\(672\) 0 0
\(673\) 37.1780 1.43311 0.716554 0.697532i \(-0.245719\pi\)
0.716554 + 0.697532i \(0.245719\pi\)
\(674\) 18.6095 0.716813
\(675\) −0.572989 −0.0220544
\(676\) −32.8667 −1.26411
\(677\) 13.6605 0.525017 0.262508 0.964930i \(-0.415450\pi\)
0.262508 + 0.964930i \(0.415450\pi\)
\(678\) −12.0518 −0.462846
\(679\) 0 0
\(680\) 4.95991 0.190204
\(681\) −0.453953 −0.0173955
\(682\) 94.0553 3.60156
\(683\) −24.8142 −0.949489 −0.474744 0.880124i \(-0.657459\pi\)
−0.474744 + 0.880124i \(0.657459\pi\)
\(684\) −12.7198 −0.486354
\(685\) −33.6303 −1.28495
\(686\) 0 0
\(687\) 18.5024 0.705912
\(688\) 17.5151 0.667756
\(689\) −0.752138 −0.0286542
\(690\) −7.84333 −0.298591
\(691\) 4.35305 0.165598 0.0827989 0.996566i \(-0.473614\pi\)
0.0827989 + 0.996566i \(0.473614\pi\)
\(692\) 39.2783 1.49314
\(693\) 0 0
\(694\) 66.4202 2.52128
\(695\) 27.3637 1.03797
\(696\) −9.35530 −0.354612
\(697\) 1.80941 0.0685363
\(698\) −12.3038 −0.465705
\(699\) 0.886114 0.0335159
\(700\) 0 0
\(701\) 0.411635 0.0155472 0.00777361 0.999970i \(-0.497526\pi\)
0.00777361 + 0.999970i \(0.497526\pi\)
\(702\) −0.618352 −0.0233382
\(703\) −33.8474 −1.27658
\(704\) −51.5656 −1.94345
\(705\) −0.0626370 −0.00235904
\(706\) 12.1653 0.457847
\(707\) 0 0
\(708\) −30.6881 −1.15333
\(709\) −15.0664 −0.565831 −0.282915 0.959145i \(-0.591302\pi\)
−0.282915 + 0.959145i \(0.591302\pi\)
\(710\) 51.5765 1.93563
\(711\) 14.8949 0.558601
\(712\) 15.2499 0.571515
\(713\) −15.4713 −0.579406
\(714\) 0 0
\(715\) −3.04325 −0.113811
\(716\) 9.27665 0.346685
\(717\) 10.3105 0.385052
\(718\) 30.3261 1.13176
\(719\) −35.8607 −1.33738 −0.668688 0.743543i \(-0.733144\pi\)
−0.668688 + 0.743543i \(0.733144\pi\)
\(720\) 6.17084 0.229974
\(721\) 0 0
\(722\) 12.7608 0.474909
\(723\) −10.7928 −0.401390
\(724\) −9.25596 −0.343995
\(725\) 4.61649 0.171452
\(726\) −18.6584 −0.692477
\(727\) 27.2538 1.01079 0.505394 0.862889i \(-0.331347\pi\)
0.505394 + 0.862889i \(0.331347\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −35.2858 −1.30599
\(731\) 12.1241 0.448426
\(732\) 4.42373 0.163506
\(733\) −50.8127 −1.87681 −0.938405 0.345538i \(-0.887697\pi\)
−0.938405 + 0.345538i \(0.887697\pi\)
\(734\) 28.9325 1.06792
\(735\) 0 0
\(736\) 12.3041 0.453534
\(737\) 61.5098 2.26574
\(738\) −2.13183 −0.0784736
\(739\) 6.60828 0.243090 0.121545 0.992586i \(-0.461215\pi\)
0.121545 + 0.992586i \(0.461215\pi\)
\(740\) −40.6776 −1.49534
\(741\) 1.44988 0.0532626
\(742\) 0 0
\(743\) 26.8065 0.983434 0.491717 0.870755i \(-0.336369\pi\)
0.491717 + 0.870755i \(0.336369\pi\)
\(744\) −11.5270 −0.422599
\(745\) −40.3208 −1.47724
\(746\) −11.8619 −0.434297
\(747\) −6.61380 −0.241986
\(748\) −20.4635 −0.748218
\(749\) 0 0
\(750\) −22.2795 −0.813534
\(751\) 20.8690 0.761522 0.380761 0.924674i \(-0.375662\pi\)
0.380761 + 0.924674i \(0.375662\pi\)
\(752\) 0.0693564 0.00252917
\(753\) −13.9975 −0.510096
\(754\) 4.98197 0.181433
\(755\) −10.1191 −0.368273
\(756\) 0 0
\(757\) −12.8198 −0.465942 −0.232971 0.972484i \(-0.574845\pi\)
−0.232971 + 0.972484i \(0.574845\pi\)
\(758\) −51.2086 −1.85998
\(759\) 6.92650 0.251416
\(760\) 13.7020 0.497023
\(761\) −36.2182 −1.31291 −0.656454 0.754366i \(-0.727944\pi\)
−0.656454 + 0.754366i \(0.727944\pi\)
\(762\) −3.54936 −0.128580
\(763\) 0 0
\(764\) −26.4188 −0.955797
\(765\) 4.27151 0.154437
\(766\) −48.3111 −1.74555
\(767\) 3.49801 0.126306
\(768\) −4.13624 −0.149254
\(769\) 14.7160 0.530671 0.265336 0.964156i \(-0.414517\pi\)
0.265336 + 0.964156i \(0.414517\pi\)
\(770\) 0 0
\(771\) 8.45313 0.304432
\(772\) 48.4209 1.74271
\(773\) −33.6972 −1.21200 −0.606002 0.795463i \(-0.707228\pi\)
−0.606002 + 0.795463i \(0.707228\pi\)
\(774\) −14.2844 −0.513444
\(775\) 5.68813 0.204324
\(776\) 5.23629 0.187972
\(777\) 0 0
\(778\) 31.6652 1.13525
\(779\) 4.99859 0.179093
\(780\) 1.74245 0.0623898
\(781\) −45.5476 −1.62982
\(782\) 6.01165 0.214976
\(783\) −8.05686 −0.287929
\(784\) 0 0
\(785\) −13.0662 −0.466353
\(786\) −42.9931 −1.53351
\(787\) −44.9121 −1.60094 −0.800472 0.599370i \(-0.795418\pi\)
−0.800472 + 0.599370i \(0.795418\pi\)
\(788\) 18.2295 0.649399
\(789\) 29.3309 1.04421
\(790\) −74.9604 −2.66697
\(791\) 0 0
\(792\) 5.16061 0.183374
\(793\) −0.504243 −0.0179062
\(794\) 67.6704 2.40153
\(795\) −6.12149 −0.217107
\(796\) 11.7862 0.417749
\(797\) −22.6417 −0.802009 −0.401004 0.916076i \(-0.631339\pi\)
−0.401004 + 0.916076i \(0.631339\pi\)
\(798\) 0 0
\(799\) 0.0480091 0.00169844
\(800\) −4.52366 −0.159936
\(801\) 13.1333 0.464044
\(802\) −30.9228 −1.09192
\(803\) 31.1611 1.09965
\(804\) −35.2183 −1.24205
\(805\) 0 0
\(806\) 6.13845 0.216218
\(807\) 1.45573 0.0512441
\(808\) −17.2561 −0.607067
\(809\) 21.5559 0.757864 0.378932 0.925425i \(-0.376291\pi\)
0.378932 + 0.925425i \(0.376291\pi\)
\(810\) −5.03264 −0.176829
\(811\) −21.0625 −0.739603 −0.369801 0.929111i \(-0.620574\pi\)
−0.369801 + 0.929111i \(0.620574\pi\)
\(812\) 0 0
\(813\) 30.5158 1.07023
\(814\) 64.1561 2.24867
\(815\) −11.6332 −0.407493
\(816\) −4.72974 −0.165574
\(817\) 33.4934 1.17179
\(818\) −30.6953 −1.07324
\(819\) 0 0
\(820\) 6.00727 0.209783
\(821\) 31.9922 1.11653 0.558267 0.829661i \(-0.311467\pi\)
0.558267 + 0.829661i \(0.311467\pi\)
\(822\) −30.3696 −1.05926
\(823\) 30.9541 1.07899 0.539495 0.841989i \(-0.318615\pi\)
0.539495 + 0.841989i \(0.318615\pi\)
\(824\) 3.18663 0.111012
\(825\) −2.54657 −0.0886601
\(826\) 0 0
\(827\) −5.33182 −0.185405 −0.0927027 0.995694i \(-0.529551\pi\)
−0.0927027 + 0.995694i \(0.529551\pi\)
\(828\) −3.96587 −0.137823
\(829\) 25.4635 0.884383 0.442191 0.896921i \(-0.354201\pi\)
0.442191 + 0.896921i \(0.354201\pi\)
\(830\) 33.2849 1.15533
\(831\) −29.2660 −1.01523
\(832\) −3.36539 −0.116674
\(833\) 0 0
\(834\) 24.7106 0.855657
\(835\) −26.1741 −0.905793
\(836\) −56.5313 −1.95518
\(837\) −9.92711 −0.343131
\(838\) −65.7086 −2.26987
\(839\) −20.2282 −0.698356 −0.349178 0.937056i \(-0.613539\pi\)
−0.349178 + 0.937056i \(0.613539\pi\)
\(840\) 0 0
\(841\) 35.9129 1.23838
\(842\) −1.47993 −0.0510018
\(843\) 12.6815 0.436773
\(844\) −2.93048 −0.100871
\(845\) 30.4907 1.04891
\(846\) −0.0565637 −0.00194470
\(847\) 0 0
\(848\) 6.77819 0.232764
\(849\) −26.4622 −0.908179
\(850\) −2.21022 −0.0758099
\(851\) −10.5532 −0.361758
\(852\) 26.0789 0.893448
\(853\) 4.47575 0.153247 0.0766233 0.997060i \(-0.475586\pi\)
0.0766233 + 0.997060i \(0.475586\pi\)
\(854\) 0 0
\(855\) 11.8003 0.403560
\(856\) 3.57569 0.122215
\(857\) 6.14745 0.209993 0.104997 0.994473i \(-0.466517\pi\)
0.104997 + 0.994473i \(0.466517\pi\)
\(858\) −2.74818 −0.0938212
\(859\) −8.71423 −0.297326 −0.148663 0.988888i \(-0.547497\pi\)
−0.148663 + 0.988888i \(0.547497\pi\)
\(860\) 40.2521 1.37259
\(861\) 0 0
\(862\) −41.9855 −1.43003
\(863\) 43.6551 1.48604 0.743019 0.669270i \(-0.233393\pi\)
0.743019 + 0.669270i \(0.233393\pi\)
\(864\) 7.89484 0.268588
\(865\) −36.4388 −1.23896
\(866\) −46.6665 −1.58579
\(867\) 13.7260 0.466160
\(868\) 0 0
\(869\) 66.1980 2.24561
\(870\) 40.5472 1.37468
\(871\) 4.01439 0.136022
\(872\) −12.6111 −0.427066
\(873\) 4.50954 0.152625
\(874\) 16.6075 0.561757
\(875\) 0 0
\(876\) −17.8417 −0.602816
\(877\) −8.85811 −0.299117 −0.149559 0.988753i \(-0.547785\pi\)
−0.149559 + 0.988753i \(0.547785\pi\)
\(878\) −6.59425 −0.222545
\(879\) 2.35974 0.0795920
\(880\) 27.4254 0.924510
\(881\) 17.2141 0.579957 0.289978 0.957033i \(-0.406352\pi\)
0.289978 + 0.957033i \(0.406352\pi\)
\(882\) 0 0
\(883\) 29.4313 0.990441 0.495221 0.868767i \(-0.335087\pi\)
0.495221 + 0.868767i \(0.335087\pi\)
\(884\) −1.33553 −0.0449188
\(885\) 28.4696 0.956994
\(886\) −61.6983 −2.07279
\(887\) −48.1948 −1.61822 −0.809111 0.587656i \(-0.800051\pi\)
−0.809111 + 0.587656i \(0.800051\pi\)
\(888\) −7.86267 −0.263854
\(889\) 0 0
\(890\) −66.0954 −2.21552
\(891\) 4.44436 0.148892
\(892\) 54.3463 1.81965
\(893\) 0.132628 0.00443821
\(894\) −36.4113 −1.21778
\(895\) −8.60602 −0.287667
\(896\) 0 0
\(897\) 0.452053 0.0150936
\(898\) −53.8704 −1.79768
\(899\) 79.9813 2.66753
\(900\) 1.45807 0.0486025
\(901\) 4.69192 0.156311
\(902\) −9.47459 −0.315469
\(903\) 0 0
\(904\) 6.56435 0.218327
\(905\) 8.58683 0.285436
\(906\) −9.13800 −0.303590
\(907\) 4.87399 0.161838 0.0809190 0.996721i \(-0.474214\pi\)
0.0809190 + 0.996721i \(0.474214\pi\)
\(908\) 1.15517 0.0383355
\(909\) −14.8611 −0.492911
\(910\) 0 0
\(911\) 3.16921 0.105001 0.0525003 0.998621i \(-0.483281\pi\)
0.0525003 + 0.998621i \(0.483281\pi\)
\(912\) −13.0661 −0.432663
\(913\) −29.3941 −0.972802
\(914\) −21.4865 −0.710711
\(915\) −4.10393 −0.135672
\(916\) −47.0828 −1.55566
\(917\) 0 0
\(918\) 3.85735 0.127311
\(919\) 5.06669 0.167135 0.0835673 0.996502i \(-0.473369\pi\)
0.0835673 + 0.996502i \(0.473369\pi\)
\(920\) 4.27210 0.140847
\(921\) −10.3588 −0.341332
\(922\) −2.07476 −0.0683286
\(923\) −2.97263 −0.0978452
\(924\) 0 0
\(925\) 3.87993 0.127571
\(926\) 29.7042 0.976139
\(927\) 2.74435 0.0901364
\(928\) −63.6076 −2.08802
\(929\) 28.7365 0.942814 0.471407 0.881916i \(-0.343746\pi\)
0.471407 + 0.881916i \(0.343746\pi\)
\(930\) 49.9596 1.63824
\(931\) 0 0
\(932\) −2.25488 −0.0738609
\(933\) −4.07018 −0.133252
\(934\) −5.70140 −0.186556
\(935\) 18.9841 0.620847
\(936\) 0.336803 0.0110088
\(937\) 8.98878 0.293651 0.146825 0.989162i \(-0.453094\pi\)
0.146825 + 0.989162i \(0.453094\pi\)
\(938\) 0 0
\(939\) −17.4202 −0.568487
\(940\) 0.159391 0.00519876
\(941\) −41.6826 −1.35881 −0.679406 0.733762i \(-0.737763\pi\)
−0.679406 + 0.733762i \(0.737763\pi\)
\(942\) −11.7993 −0.384442
\(943\) 1.55849 0.0507515
\(944\) −31.5237 −1.02601
\(945\) 0 0
\(946\) −63.4852 −2.06408
\(947\) −49.3593 −1.60396 −0.801981 0.597349i \(-0.796221\pi\)
−0.801981 + 0.597349i \(0.796221\pi\)
\(948\) −37.9026 −1.23102
\(949\) 2.03371 0.0660169
\(950\) −6.10584 −0.198100
\(951\) 28.1622 0.913222
\(952\) 0 0
\(953\) 7.39228 0.239460 0.119730 0.992807i \(-0.461797\pi\)
0.119730 + 0.992807i \(0.461797\pi\)
\(954\) −5.52796 −0.178974
\(955\) 24.5089 0.793089
\(956\) −26.2369 −0.848561
\(957\) −35.8075 −1.15749
\(958\) −15.2540 −0.492834
\(959\) 0 0
\(960\) −27.3902 −0.884015
\(961\) 67.5475 2.17895
\(962\) 4.18710 0.134998
\(963\) 3.07941 0.0992327
\(964\) 27.4643 0.884565
\(965\) −44.9205 −1.44604
\(966\) 0 0
\(967\) −42.9143 −1.38003 −0.690016 0.723795i \(-0.742396\pi\)
−0.690016 + 0.723795i \(0.742396\pi\)
\(968\) 10.1628 0.326646
\(969\) −9.04450 −0.290551
\(970\) −22.6949 −0.728688
\(971\) 28.9224 0.928165 0.464083 0.885792i \(-0.346384\pi\)
0.464083 + 0.885792i \(0.346384\pi\)
\(972\) −2.54468 −0.0816206
\(973\) 0 0
\(974\) 82.1999 2.63385
\(975\) −0.166200 −0.00532265
\(976\) 4.54418 0.145456
\(977\) 22.2031 0.710339 0.355169 0.934802i \(-0.384423\pi\)
0.355169 + 0.934802i \(0.384423\pi\)
\(978\) −10.5052 −0.335921
\(979\) 58.3693 1.86549
\(980\) 0 0
\(981\) −10.8608 −0.346758
\(982\) −86.0566 −2.74618
\(983\) 32.9506 1.05096 0.525480 0.850806i \(-0.323886\pi\)
0.525480 + 0.850806i \(0.323886\pi\)
\(984\) 1.16116 0.0370164
\(985\) −16.9117 −0.538850
\(986\) −31.0781 −0.989728
\(987\) 0 0
\(988\) −3.68947 −0.117378
\(989\) 10.4428 0.332062
\(990\) −22.3668 −0.710865
\(991\) −24.4004 −0.775104 −0.387552 0.921848i \(-0.626679\pi\)
−0.387552 + 0.921848i \(0.626679\pi\)
\(992\) −78.3730 −2.48834
\(993\) 9.65052 0.306250
\(994\) 0 0
\(995\) −10.9341 −0.346635
\(996\) 16.8300 0.533279
\(997\) −4.47325 −0.141669 −0.0708346 0.997488i \(-0.522566\pi\)
−0.0708346 + 0.997488i \(0.522566\pi\)
\(998\) 27.6877 0.876440
\(999\) −6.77139 −0.214237
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 6027.2.a.bd.1.8 10
7.6 odd 2 6027.2.a.be.1.8 yes 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6027.2.a.bd.1.8 10 1.1 even 1 trivial
6027.2.a.be.1.8 yes 10 7.6 odd 2