Properties

Label 2695.2.a.x.1.1
Level $2695$
Weight $2$
Character 2695.1
Self dual yes
Analytic conductor $21.520$
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] = [2695,2,Mod(1,2695)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2695, 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("2695.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2695 = 5 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2695.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: \(21.5196833447\)
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: \( x^{10} - 2x^{9} - 13x^{8} + 24x^{7} + 56x^{6} - 92x^{5} - 86x^{4} + 116x^{3} + 31x^{2} - 22x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-2.29554\) of defining polynomial
Character \(\chi\) \(=\) 2695.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.29554 q^{2} -0.293572 q^{3} +3.26952 q^{4} +1.00000 q^{5} +0.673908 q^{6} -2.91425 q^{8} -2.91382 q^{9} +O(q^{10})\) \(q-2.29554 q^{2} -0.293572 q^{3} +3.26952 q^{4} +1.00000 q^{5} +0.673908 q^{6} -2.91425 q^{8} -2.91382 q^{9} -2.29554 q^{10} -1.00000 q^{11} -0.959841 q^{12} -1.45308 q^{13} -0.293572 q^{15} +0.150739 q^{16} -1.37718 q^{17} +6.68879 q^{18} -3.61374 q^{19} +3.26952 q^{20} +2.29554 q^{22} -5.58209 q^{23} +0.855542 q^{24} +1.00000 q^{25} +3.33562 q^{26} +1.73613 q^{27} +0.104098 q^{29} +0.673908 q^{30} -6.72703 q^{31} +5.48247 q^{32} +0.293572 q^{33} +3.16139 q^{34} -9.52679 q^{36} +0.435179 q^{37} +8.29551 q^{38} +0.426585 q^{39} -2.91425 q^{40} +1.22902 q^{41} +4.44836 q^{43} -3.26952 q^{44} -2.91382 q^{45} +12.8139 q^{46} -0.126494 q^{47} -0.0442527 q^{48} -2.29554 q^{50} +0.404303 q^{51} -4.75089 q^{52} +8.05754 q^{53} -3.98537 q^{54} -1.00000 q^{55} +1.06089 q^{57} -0.238961 q^{58} +11.3961 q^{59} -0.959841 q^{60} +5.32148 q^{61} +15.4422 q^{62} -12.8867 q^{64} -1.45308 q^{65} -0.673908 q^{66} +9.34121 q^{67} -4.50273 q^{68} +1.63875 q^{69} -6.97924 q^{71} +8.49158 q^{72} +14.7242 q^{73} -0.998973 q^{74} -0.293572 q^{75} -11.8152 q^{76} -0.979245 q^{78} -7.63740 q^{79} +0.150739 q^{80} +8.23177 q^{81} -2.82126 q^{82} +8.19774 q^{83} -1.37718 q^{85} -10.2114 q^{86} -0.0305602 q^{87} +2.91425 q^{88} -3.74462 q^{89} +6.68879 q^{90} -18.2508 q^{92} +1.97487 q^{93} +0.290373 q^{94} -3.61374 q^{95} -1.60950 q^{96} -1.39488 q^{97} +2.91382 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + 2 q^{2} + 10 q^{4} + 10 q^{5} + 4 q^{6} + 6 q^{8} + 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q + 2 q^{2} + 10 q^{4} + 10 q^{5} + 4 q^{6} + 6 q^{8} + 10 q^{9} + 2 q^{10} - 10 q^{11} + 4 q^{12} + 8 q^{13} + 6 q^{16} + 28 q^{17} - 10 q^{18} + 8 q^{19} + 10 q^{20} - 2 q^{22} - 8 q^{23} + 32 q^{24} + 10 q^{25} + 12 q^{26} - 8 q^{29} + 4 q^{30} - 4 q^{31} + 14 q^{32} + 20 q^{34} - 22 q^{36} + 28 q^{37} + 24 q^{38} - 24 q^{39} + 6 q^{40} + 44 q^{41} + 20 q^{43} - 10 q^{44} + 10 q^{45} - 12 q^{46} + 12 q^{47} + 16 q^{48} + 2 q^{50} - 4 q^{51} + 36 q^{52} - 8 q^{54} - 10 q^{55} + 12 q^{57} - 8 q^{58} + 16 q^{59} + 4 q^{60} + 16 q^{61} + 36 q^{62} - 34 q^{64} + 8 q^{65} - 4 q^{66} + 20 q^{67} + 8 q^{68} + 4 q^{69} - 4 q^{71} + 10 q^{72} + 20 q^{73} - 16 q^{74} + 4 q^{76} + 52 q^{78} - 20 q^{79} + 6 q^{80} + 10 q^{81} - 32 q^{82} + 16 q^{83} + 28 q^{85} - 20 q^{86} + 20 q^{87} - 6 q^{88} + 44 q^{89} - 10 q^{90} - 24 q^{92} + 16 q^{93} + 24 q^{94} + 8 q^{95} - 4 q^{97} - 10 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.29554 −1.62319 −0.811597 0.584217i \(-0.801402\pi\)
−0.811597 + 0.584217i \(0.801402\pi\)
\(3\) −0.293572 −0.169494 −0.0847470 0.996403i \(-0.527008\pi\)
−0.0847470 + 0.996403i \(0.527008\pi\)
\(4\) 3.26952 1.63476
\(5\) 1.00000 0.447214
\(6\) 0.673908 0.275122
\(7\) 0 0
\(8\) −2.91425 −1.03034
\(9\) −2.91382 −0.971272
\(10\) −2.29554 −0.725915
\(11\) −1.00000 −0.301511
\(12\) −0.959841 −0.277082
\(13\) −1.45308 −0.403013 −0.201507 0.979487i \(-0.564584\pi\)
−0.201507 + 0.979487i \(0.564584\pi\)
\(14\) 0 0
\(15\) −0.293572 −0.0758000
\(16\) 0.150739 0.0376847
\(17\) −1.37718 −0.334016 −0.167008 0.985956i \(-0.553411\pi\)
−0.167008 + 0.985956i \(0.553411\pi\)
\(18\) 6.68879 1.57656
\(19\) −3.61374 −0.829050 −0.414525 0.910038i \(-0.636052\pi\)
−0.414525 + 0.910038i \(0.636052\pi\)
\(20\) 3.26952 0.731088
\(21\) 0 0
\(22\) 2.29554 0.489412
\(23\) −5.58209 −1.16395 −0.581973 0.813208i \(-0.697719\pi\)
−0.581973 + 0.813208i \(0.697719\pi\)
\(24\) 0.855542 0.174637
\(25\) 1.00000 0.200000
\(26\) 3.33562 0.654169
\(27\) 1.73613 0.334119
\(28\) 0 0
\(29\) 0.104098 0.0193304 0.00966522 0.999953i \(-0.496923\pi\)
0.00966522 + 0.999953i \(0.496923\pi\)
\(30\) 0.673908 0.123038
\(31\) −6.72703 −1.20821 −0.604105 0.796905i \(-0.706469\pi\)
−0.604105 + 0.796905i \(0.706469\pi\)
\(32\) 5.48247 0.969173
\(33\) 0.293572 0.0511043
\(34\) 3.16139 0.542173
\(35\) 0 0
\(36\) −9.52679 −1.58780
\(37\) 0.435179 0.0715430 0.0357715 0.999360i \(-0.488611\pi\)
0.0357715 + 0.999360i \(0.488611\pi\)
\(38\) 8.29551 1.34571
\(39\) 0.426585 0.0683083
\(40\) −2.91425 −0.460783
\(41\) 1.22902 0.191940 0.0959702 0.995384i \(-0.469405\pi\)
0.0959702 + 0.995384i \(0.469405\pi\)
\(42\) 0 0
\(43\) 4.44836 0.678368 0.339184 0.940720i \(-0.389849\pi\)
0.339184 + 0.940720i \(0.389849\pi\)
\(44\) −3.26952 −0.492899
\(45\) −2.91382 −0.434366
\(46\) 12.8139 1.88931
\(47\) −0.126494 −0.0184511 −0.00922555 0.999957i \(-0.502937\pi\)
−0.00922555 + 0.999957i \(0.502937\pi\)
\(48\) −0.0442527 −0.00638733
\(49\) 0 0
\(50\) −2.29554 −0.324639
\(51\) 0.404303 0.0566137
\(52\) −4.75089 −0.658831
\(53\) 8.05754 1.10679 0.553394 0.832920i \(-0.313332\pi\)
0.553394 + 0.832920i \(0.313332\pi\)
\(54\) −3.98537 −0.542340
\(55\) −1.00000 −0.134840
\(56\) 0 0
\(57\) 1.06089 0.140519
\(58\) −0.238961 −0.0313771
\(59\) 11.3961 1.48365 0.741826 0.670593i \(-0.233960\pi\)
0.741826 + 0.670593i \(0.233960\pi\)
\(60\) −0.959841 −0.123915
\(61\) 5.32148 0.681346 0.340673 0.940182i \(-0.389345\pi\)
0.340673 + 0.940182i \(0.389345\pi\)
\(62\) 15.4422 1.96116
\(63\) 0 0
\(64\) −12.8867 −1.61084
\(65\) −1.45308 −0.180233
\(66\) −0.673908 −0.0829523
\(67\) 9.34121 1.14121 0.570605 0.821224i \(-0.306709\pi\)
0.570605 + 0.821224i \(0.306709\pi\)
\(68\) −4.50273 −0.546037
\(69\) 1.63875 0.197282
\(70\) 0 0
\(71\) −6.97924 −0.828283 −0.414141 0.910213i \(-0.635918\pi\)
−0.414141 + 0.910213i \(0.635918\pi\)
\(72\) 8.49158 1.00074
\(73\) 14.7242 1.72334 0.861671 0.507468i \(-0.169418\pi\)
0.861671 + 0.507468i \(0.169418\pi\)
\(74\) −0.998973 −0.116128
\(75\) −0.293572 −0.0338988
\(76\) −11.8152 −1.35530
\(77\) 0 0
\(78\) −0.979245 −0.110878
\(79\) −7.63740 −0.859275 −0.429637 0.903002i \(-0.641359\pi\)
−0.429637 + 0.903002i \(0.641359\pi\)
\(80\) 0.150739 0.0168531
\(81\) 8.23177 0.914641
\(82\) −2.82126 −0.311557
\(83\) 8.19774 0.899818 0.449909 0.893074i \(-0.351456\pi\)
0.449909 + 0.893074i \(0.351456\pi\)
\(84\) 0 0
\(85\) −1.37718 −0.149377
\(86\) −10.2114 −1.10112
\(87\) −0.0305602 −0.00327639
\(88\) 2.91425 0.310660
\(89\) −3.74462 −0.396929 −0.198464 0.980108i \(-0.563595\pi\)
−0.198464 + 0.980108i \(0.563595\pi\)
\(90\) 6.68879 0.705061
\(91\) 0 0
\(92\) −18.2508 −1.90278
\(93\) 1.97487 0.204784
\(94\) 0.290373 0.0299497
\(95\) −3.61374 −0.370762
\(96\) −1.60950 −0.164269
\(97\) −1.39488 −0.141629 −0.0708144 0.997490i \(-0.522560\pi\)
−0.0708144 + 0.997490i \(0.522560\pi\)
\(98\) 0 0
\(99\) 2.91382 0.292849
\(100\) 3.26952 0.326952
\(101\) 6.33566 0.630422 0.315211 0.949022i \(-0.397925\pi\)
0.315211 + 0.949022i \(0.397925\pi\)
\(102\) −0.928095 −0.0918951
\(103\) −11.4060 −1.12386 −0.561932 0.827184i \(-0.689942\pi\)
−0.561932 + 0.827184i \(0.689942\pi\)
\(104\) 4.23465 0.415242
\(105\) 0 0
\(106\) −18.4964 −1.79653
\(107\) 12.3939 1.19816 0.599080 0.800689i \(-0.295533\pi\)
0.599080 + 0.800689i \(0.295533\pi\)
\(108\) 5.67632 0.546204
\(109\) −14.7889 −1.41652 −0.708260 0.705951i \(-0.750520\pi\)
−0.708260 + 0.705951i \(0.750520\pi\)
\(110\) 2.29554 0.218872
\(111\) −0.127756 −0.0121261
\(112\) 0 0
\(113\) 9.64437 0.907266 0.453633 0.891189i \(-0.350128\pi\)
0.453633 + 0.891189i \(0.350128\pi\)
\(114\) −2.43533 −0.228090
\(115\) −5.58209 −0.520533
\(116\) 0.340350 0.0316007
\(117\) 4.23402 0.391435
\(118\) −26.1604 −2.40826
\(119\) 0 0
\(120\) 0.855542 0.0781000
\(121\) 1.00000 0.0909091
\(122\) −12.2157 −1.10596
\(123\) −0.360805 −0.0325327
\(124\) −21.9942 −1.97514
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 0.268275 0.0238055 0.0119028 0.999929i \(-0.496211\pi\)
0.0119028 + 0.999929i \(0.496211\pi\)
\(128\) 18.6171 1.64554
\(129\) −1.30591 −0.114979
\(130\) 3.33562 0.292553
\(131\) 10.5415 0.921019 0.460509 0.887655i \(-0.347667\pi\)
0.460509 + 0.887655i \(0.347667\pi\)
\(132\) 0.959841 0.0835434
\(133\) 0 0
\(134\) −21.4432 −1.85241
\(135\) 1.73613 0.149422
\(136\) 4.01345 0.344151
\(137\) −4.98272 −0.425703 −0.212851 0.977085i \(-0.568275\pi\)
−0.212851 + 0.977085i \(0.568275\pi\)
\(138\) −3.76182 −0.320227
\(139\) 5.80701 0.492544 0.246272 0.969201i \(-0.420794\pi\)
0.246272 + 0.969201i \(0.420794\pi\)
\(140\) 0 0
\(141\) 0.0371352 0.00312735
\(142\) 16.0211 1.34446
\(143\) 1.45308 0.121513
\(144\) −0.439225 −0.0366021
\(145\) 0.104098 0.00864484
\(146\) −33.8001 −2.79732
\(147\) 0 0
\(148\) 1.42283 0.116956
\(149\) −8.28793 −0.678974 −0.339487 0.940611i \(-0.610253\pi\)
−0.339487 + 0.940611i \(0.610253\pi\)
\(150\) 0.673908 0.0550243
\(151\) −2.40230 −0.195496 −0.0977480 0.995211i \(-0.531164\pi\)
−0.0977480 + 0.995211i \(0.531164\pi\)
\(152\) 10.5313 0.854205
\(153\) 4.01286 0.324420
\(154\) 0 0
\(155\) −6.72703 −0.540328
\(156\) 1.39473 0.111668
\(157\) −16.0405 −1.28017 −0.640085 0.768304i \(-0.721101\pi\)
−0.640085 + 0.768304i \(0.721101\pi\)
\(158\) 17.5320 1.39477
\(159\) −2.36547 −0.187594
\(160\) 5.48247 0.433427
\(161\) 0 0
\(162\) −18.8964 −1.48464
\(163\) −3.93239 −0.308008 −0.154004 0.988070i \(-0.549217\pi\)
−0.154004 + 0.988070i \(0.549217\pi\)
\(164\) 4.01830 0.313777
\(165\) 0.293572 0.0228546
\(166\) −18.8183 −1.46058
\(167\) 12.2979 0.951642 0.475821 0.879542i \(-0.342151\pi\)
0.475821 + 0.879542i \(0.342151\pi\)
\(168\) 0 0
\(169\) −10.8885 −0.837580
\(170\) 3.16139 0.242467
\(171\) 10.5298 0.805233
\(172\) 14.5440 1.10897
\(173\) 11.3383 0.862033 0.431017 0.902344i \(-0.358155\pi\)
0.431017 + 0.902344i \(0.358155\pi\)
\(174\) 0.0701522 0.00531822
\(175\) 0 0
\(176\) −0.150739 −0.0113624
\(177\) −3.34559 −0.251470
\(178\) 8.59594 0.644293
\(179\) −25.3377 −1.89383 −0.946913 0.321488i \(-0.895817\pi\)
−0.946913 + 0.321488i \(0.895817\pi\)
\(180\) −9.52679 −0.710085
\(181\) 3.52411 0.261945 0.130972 0.991386i \(-0.458190\pi\)
0.130972 + 0.991386i \(0.458190\pi\)
\(182\) 0 0
\(183\) −1.56224 −0.115484
\(184\) 16.2676 1.19926
\(185\) 0.435179 0.0319950
\(186\) −4.53340 −0.332405
\(187\) 1.37718 0.100710
\(188\) −0.413576 −0.0301632
\(189\) 0 0
\(190\) 8.29551 0.601819
\(191\) 10.3942 0.752100 0.376050 0.926599i \(-0.377282\pi\)
0.376050 + 0.926599i \(0.377282\pi\)
\(192\) 3.78318 0.273028
\(193\) 6.33141 0.455745 0.227872 0.973691i \(-0.426823\pi\)
0.227872 + 0.973691i \(0.426823\pi\)
\(194\) 3.20201 0.229891
\(195\) 0.426585 0.0305484
\(196\) 0 0
\(197\) 25.7530 1.83483 0.917413 0.397937i \(-0.130274\pi\)
0.917413 + 0.397937i \(0.130274\pi\)
\(198\) −6.68879 −0.475352
\(199\) −8.00340 −0.567346 −0.283673 0.958921i \(-0.591553\pi\)
−0.283673 + 0.958921i \(0.591553\pi\)
\(200\) −2.91425 −0.206068
\(201\) −2.74232 −0.193428
\(202\) −14.5438 −1.02330
\(203\) 0 0
\(204\) 1.32188 0.0925499
\(205\) 1.22902 0.0858383
\(206\) 26.1829 1.82425
\(207\) 16.2652 1.13051
\(208\) −0.219036 −0.0151874
\(209\) 3.61374 0.249968
\(210\) 0 0
\(211\) 12.5161 0.861643 0.430821 0.902437i \(-0.358224\pi\)
0.430821 + 0.902437i \(0.358224\pi\)
\(212\) 26.3443 1.80933
\(213\) 2.04891 0.140389
\(214\) −28.4507 −1.94485
\(215\) 4.44836 0.303375
\(216\) −5.05952 −0.344257
\(217\) 0 0
\(218\) 33.9486 2.29929
\(219\) −4.32263 −0.292096
\(220\) −3.26952 −0.220431
\(221\) 2.00116 0.134613
\(222\) 0.293271 0.0196830
\(223\) −17.1800 −1.15046 −0.575229 0.817992i \(-0.695087\pi\)
−0.575229 + 0.817992i \(0.695087\pi\)
\(224\) 0 0
\(225\) −2.91382 −0.194254
\(226\) −22.1391 −1.47267
\(227\) 21.9004 1.45358 0.726789 0.686861i \(-0.241012\pi\)
0.726789 + 0.686861i \(0.241012\pi\)
\(228\) 3.46862 0.229715
\(229\) 12.9430 0.855296 0.427648 0.903945i \(-0.359342\pi\)
0.427648 + 0.903945i \(0.359342\pi\)
\(230\) 12.8139 0.844926
\(231\) 0 0
\(232\) −0.303366 −0.0199170
\(233\) −2.46926 −0.161767 −0.0808833 0.996724i \(-0.525774\pi\)
−0.0808833 + 0.996724i \(0.525774\pi\)
\(234\) −9.71938 −0.635376
\(235\) −0.126494 −0.00825158
\(236\) 37.2600 2.42542
\(237\) 2.24213 0.145642
\(238\) 0 0
\(239\) −15.2734 −0.987957 −0.493978 0.869474i \(-0.664458\pi\)
−0.493978 + 0.869474i \(0.664458\pi\)
\(240\) −0.0442527 −0.00285650
\(241\) −4.64559 −0.299248 −0.149624 0.988743i \(-0.547806\pi\)
−0.149624 + 0.988743i \(0.547806\pi\)
\(242\) −2.29554 −0.147563
\(243\) −7.62501 −0.489145
\(244\) 17.3987 1.11384
\(245\) 0 0
\(246\) 0.828245 0.0528070
\(247\) 5.25108 0.334118
\(248\) 19.6042 1.24487
\(249\) −2.40663 −0.152514
\(250\) −2.29554 −0.145183
\(251\) 25.2788 1.59558 0.797791 0.602935i \(-0.206002\pi\)
0.797791 + 0.602935i \(0.206002\pi\)
\(252\) 0 0
\(253\) 5.58209 0.350943
\(254\) −0.615837 −0.0386410
\(255\) 0.404303 0.0253184
\(256\) −16.9630 −1.06019
\(257\) 30.7280 1.91676 0.958378 0.285501i \(-0.0921600\pi\)
0.958378 + 0.285501i \(0.0921600\pi\)
\(258\) 2.99778 0.186634
\(259\) 0 0
\(260\) −4.75089 −0.294638
\(261\) −0.303321 −0.0187751
\(262\) −24.1986 −1.49499
\(263\) −17.7003 −1.09145 −0.545725 0.837965i \(-0.683746\pi\)
−0.545725 + 0.837965i \(0.683746\pi\)
\(264\) −0.855542 −0.0526550
\(265\) 8.05754 0.494971
\(266\) 0 0
\(267\) 1.09932 0.0672770
\(268\) 30.5413 1.86561
\(269\) 18.4815 1.12683 0.563417 0.826173i \(-0.309486\pi\)
0.563417 + 0.826173i \(0.309486\pi\)
\(270\) −3.98537 −0.242542
\(271\) 27.4033 1.66463 0.832316 0.554302i \(-0.187015\pi\)
0.832316 + 0.554302i \(0.187015\pi\)
\(272\) −0.207595 −0.0125873
\(273\) 0 0
\(274\) 11.4381 0.690999
\(275\) −1.00000 −0.0603023
\(276\) 5.35792 0.322509
\(277\) −9.27239 −0.557124 −0.278562 0.960418i \(-0.589858\pi\)
−0.278562 + 0.960418i \(0.589858\pi\)
\(278\) −13.3302 −0.799495
\(279\) 19.6013 1.17350
\(280\) 0 0
\(281\) 22.8183 1.36122 0.680612 0.732644i \(-0.261714\pi\)
0.680612 + 0.732644i \(0.261714\pi\)
\(282\) −0.0852456 −0.00507630
\(283\) 22.9802 1.36603 0.683015 0.730404i \(-0.260668\pi\)
0.683015 + 0.730404i \(0.260668\pi\)
\(284\) −22.8188 −1.35405
\(285\) 1.06089 0.0628420
\(286\) −3.33562 −0.197239
\(287\) 0 0
\(288\) −15.9749 −0.941330
\(289\) −15.1034 −0.888433
\(290\) −0.238961 −0.0140323
\(291\) 0.409499 0.0240052
\(292\) 48.1412 2.81725
\(293\) 7.46806 0.436289 0.218144 0.975917i \(-0.430000\pi\)
0.218144 + 0.975917i \(0.430000\pi\)
\(294\) 0 0
\(295\) 11.3961 0.663509
\(296\) −1.26822 −0.0737138
\(297\) −1.73613 −0.100741
\(298\) 19.0253 1.10211
\(299\) 8.11125 0.469086
\(300\) −0.959841 −0.0554165
\(301\) 0 0
\(302\) 5.51458 0.317328
\(303\) −1.85997 −0.106853
\(304\) −0.544732 −0.0312425
\(305\) 5.32148 0.304707
\(306\) −9.21169 −0.526597
\(307\) −15.3016 −0.873311 −0.436655 0.899629i \(-0.643837\pi\)
−0.436655 + 0.899629i \(0.643837\pi\)
\(308\) 0 0
\(309\) 3.34847 0.190488
\(310\) 15.4422 0.877058
\(311\) −22.5435 −1.27833 −0.639163 0.769072i \(-0.720719\pi\)
−0.639163 + 0.769072i \(0.720719\pi\)
\(312\) −1.24318 −0.0703809
\(313\) 8.51249 0.481154 0.240577 0.970630i \(-0.422663\pi\)
0.240577 + 0.970630i \(0.422663\pi\)
\(314\) 36.8217 2.07797
\(315\) 0 0
\(316\) −24.9707 −1.40471
\(317\) −19.7133 −1.10721 −0.553605 0.832779i \(-0.686748\pi\)
−0.553605 + 0.832779i \(0.686748\pi\)
\(318\) 5.43004 0.304501
\(319\) −0.104098 −0.00582835
\(320\) −12.8867 −0.720390
\(321\) −3.63849 −0.203081
\(322\) 0 0
\(323\) 4.97679 0.276916
\(324\) 26.9140 1.49522
\(325\) −1.45308 −0.0806026
\(326\) 9.02697 0.499957
\(327\) 4.34161 0.240092
\(328\) −3.58166 −0.197764
\(329\) 0 0
\(330\) −0.673908 −0.0370974
\(331\) 14.8302 0.815140 0.407570 0.913174i \(-0.366376\pi\)
0.407570 + 0.913174i \(0.366376\pi\)
\(332\) 26.8027 1.47099
\(333\) −1.26803 −0.0694877
\(334\) −28.2304 −1.54470
\(335\) 9.34121 0.510365
\(336\) 0 0
\(337\) 5.99144 0.326374 0.163187 0.986595i \(-0.447823\pi\)
0.163187 + 0.986595i \(0.447823\pi\)
\(338\) 24.9951 1.35956
\(339\) −2.83132 −0.153776
\(340\) −4.50273 −0.244195
\(341\) 6.72703 0.364289
\(342\) −24.1716 −1.30705
\(343\) 0 0
\(344\) −12.9636 −0.698951
\(345\) 1.63875 0.0882272
\(346\) −26.0275 −1.39925
\(347\) −11.7269 −0.629535 −0.314767 0.949169i \(-0.601926\pi\)
−0.314767 + 0.949169i \(0.601926\pi\)
\(348\) −0.0999172 −0.00535612
\(349\) 27.8798 1.49237 0.746186 0.665738i \(-0.231883\pi\)
0.746186 + 0.665738i \(0.231883\pi\)
\(350\) 0 0
\(351\) −2.52275 −0.134654
\(352\) −5.48247 −0.292217
\(353\) 22.0207 1.17204 0.586021 0.810296i \(-0.300693\pi\)
0.586021 + 0.810296i \(0.300693\pi\)
\(354\) 7.67995 0.408185
\(355\) −6.97924 −0.370419
\(356\) −12.2431 −0.648884
\(357\) 0 0
\(358\) 58.1638 3.07405
\(359\) −17.8613 −0.942682 −0.471341 0.881951i \(-0.656230\pi\)
−0.471341 + 0.881951i \(0.656230\pi\)
\(360\) 8.49158 0.447546
\(361\) −5.94086 −0.312677
\(362\) −8.08975 −0.425188
\(363\) −0.293572 −0.0154085
\(364\) 0 0
\(365\) 14.7242 0.770702
\(366\) 3.58619 0.187453
\(367\) 4.37925 0.228595 0.114298 0.993447i \(-0.463538\pi\)
0.114298 + 0.993447i \(0.463538\pi\)
\(368\) −0.841439 −0.0438630
\(369\) −3.58113 −0.186426
\(370\) −0.998973 −0.0519341
\(371\) 0 0
\(372\) 6.45688 0.334774
\(373\) −7.46212 −0.386374 −0.193187 0.981162i \(-0.561882\pi\)
−0.193187 + 0.981162i \(0.561882\pi\)
\(374\) −3.16139 −0.163471
\(375\) −0.293572 −0.0151600
\(376\) 0.368636 0.0190110
\(377\) −0.151263 −0.00779042
\(378\) 0 0
\(379\) −11.4780 −0.589588 −0.294794 0.955561i \(-0.595251\pi\)
−0.294794 + 0.955561i \(0.595251\pi\)
\(380\) −11.8152 −0.606108
\(381\) −0.0787580 −0.00403489
\(382\) −23.8604 −1.22081
\(383\) 24.7310 1.26369 0.631847 0.775093i \(-0.282297\pi\)
0.631847 + 0.775093i \(0.282297\pi\)
\(384\) −5.46547 −0.278908
\(385\) 0 0
\(386\) −14.5340 −0.739763
\(387\) −12.9617 −0.658880
\(388\) −4.56060 −0.231529
\(389\) −28.4414 −1.44204 −0.721019 0.692916i \(-0.756326\pi\)
−0.721019 + 0.692916i \(0.756326\pi\)
\(390\) −0.979245 −0.0495860
\(391\) 7.68757 0.388777
\(392\) 0 0
\(393\) −3.09470 −0.156107
\(394\) −59.1172 −2.97828
\(395\) −7.63740 −0.384279
\(396\) 9.52679 0.478739
\(397\) 23.1144 1.16008 0.580038 0.814589i \(-0.303038\pi\)
0.580038 + 0.814589i \(0.303038\pi\)
\(398\) 18.3722 0.920913
\(399\) 0 0
\(400\) 0.150739 0.00753695
\(401\) 2.84597 0.142121 0.0710606 0.997472i \(-0.477362\pi\)
0.0710606 + 0.997472i \(0.477362\pi\)
\(402\) 6.29512 0.313972
\(403\) 9.77494 0.486925
\(404\) 20.7146 1.03059
\(405\) 8.23177 0.409040
\(406\) 0 0
\(407\) −0.435179 −0.0215710
\(408\) −1.17824 −0.0583315
\(409\) −27.0904 −1.33953 −0.669767 0.742571i \(-0.733606\pi\)
−0.669767 + 0.742571i \(0.733606\pi\)
\(410\) −2.82126 −0.139332
\(411\) 1.46279 0.0721540
\(412\) −37.2921 −1.83725
\(413\) 0 0
\(414\) −37.3375 −1.83504
\(415\) 8.19774 0.402411
\(416\) −7.96649 −0.390589
\(417\) −1.70478 −0.0834833
\(418\) −8.29551 −0.405747
\(419\) 7.34341 0.358749 0.179375 0.983781i \(-0.442593\pi\)
0.179375 + 0.983781i \(0.442593\pi\)
\(420\) 0 0
\(421\) 32.3775 1.57798 0.788991 0.614404i \(-0.210604\pi\)
0.788991 + 0.614404i \(0.210604\pi\)
\(422\) −28.7312 −1.39861
\(423\) 0.368581 0.0179210
\(424\) −23.4817 −1.14037
\(425\) −1.37718 −0.0668032
\(426\) −4.70336 −0.227879
\(427\) 0 0
\(428\) 40.5220 1.95871
\(429\) −0.426585 −0.0205957
\(430\) −10.2114 −0.492437
\(431\) 35.9538 1.73183 0.865916 0.500190i \(-0.166736\pi\)
0.865916 + 0.500190i \(0.166736\pi\)
\(432\) 0.261703 0.0125912
\(433\) −15.9908 −0.768468 −0.384234 0.923236i \(-0.625534\pi\)
−0.384234 + 0.923236i \(0.625534\pi\)
\(434\) 0 0
\(435\) −0.0305602 −0.00146525
\(436\) −48.3527 −2.31567
\(437\) 20.1723 0.964970
\(438\) 9.92278 0.474129
\(439\) 17.5823 0.839157 0.419578 0.907719i \(-0.362178\pi\)
0.419578 + 0.907719i \(0.362178\pi\)
\(440\) 2.91425 0.138931
\(441\) 0 0
\(442\) −4.59376 −0.218503
\(443\) 4.62095 0.219548 0.109774 0.993957i \(-0.464987\pi\)
0.109774 + 0.993957i \(0.464987\pi\)
\(444\) −0.417703 −0.0198233
\(445\) −3.74462 −0.177512
\(446\) 39.4375 1.86742
\(447\) 2.43311 0.115082
\(448\) 0 0
\(449\) 14.2318 0.671642 0.335821 0.941926i \(-0.390986\pi\)
0.335821 + 0.941926i \(0.390986\pi\)
\(450\) 6.68879 0.315313
\(451\) −1.22902 −0.0578722
\(452\) 31.5325 1.48316
\(453\) 0.705247 0.0331354
\(454\) −50.2732 −2.35944
\(455\) 0 0
\(456\) −3.09171 −0.144783
\(457\) −39.2810 −1.83749 −0.918745 0.394852i \(-0.870796\pi\)
−0.918745 + 0.394852i \(0.870796\pi\)
\(458\) −29.7112 −1.38831
\(459\) −2.39097 −0.111601
\(460\) −18.2508 −0.850947
\(461\) 2.04093 0.0950556 0.0475278 0.998870i \(-0.484866\pi\)
0.0475278 + 0.998870i \(0.484866\pi\)
\(462\) 0 0
\(463\) 17.9813 0.835660 0.417830 0.908525i \(-0.362791\pi\)
0.417830 + 0.908525i \(0.362791\pi\)
\(464\) 0.0156916 0.000728462 0
\(465\) 1.97487 0.0915823
\(466\) 5.66829 0.262579
\(467\) −8.06125 −0.373030 −0.186515 0.982452i \(-0.559719\pi\)
−0.186515 + 0.982452i \(0.559719\pi\)
\(468\) 13.8432 0.639904
\(469\) 0 0
\(470\) 0.290373 0.0133939
\(471\) 4.70904 0.216981
\(472\) −33.2112 −1.52867
\(473\) −4.44836 −0.204536
\(474\) −5.14690 −0.236405
\(475\) −3.61374 −0.165810
\(476\) 0 0
\(477\) −23.4782 −1.07499
\(478\) 35.0609 1.60365
\(479\) 15.0626 0.688226 0.344113 0.938928i \(-0.388180\pi\)
0.344113 + 0.938928i \(0.388180\pi\)
\(480\) −1.60950 −0.0734633
\(481\) −0.632352 −0.0288328
\(482\) 10.6641 0.485739
\(483\) 0 0
\(484\) 3.26952 0.148615
\(485\) −1.39488 −0.0633383
\(486\) 17.5036 0.793977
\(487\) −40.3416 −1.82805 −0.914025 0.405657i \(-0.867043\pi\)
−0.914025 + 0.405657i \(0.867043\pi\)
\(488\) −15.5081 −0.702020
\(489\) 1.15444 0.0522055
\(490\) 0 0
\(491\) −14.3021 −0.645444 −0.322722 0.946494i \(-0.604598\pi\)
−0.322722 + 0.946494i \(0.604598\pi\)
\(492\) −1.17966 −0.0531833
\(493\) −0.143361 −0.00645668
\(494\) −12.0541 −0.542339
\(495\) 2.91382 0.130966
\(496\) −1.01403 −0.0455311
\(497\) 0 0
\(498\) 5.52452 0.247560
\(499\) 24.6179 1.10205 0.551025 0.834489i \(-0.314237\pi\)
0.551025 + 0.834489i \(0.314237\pi\)
\(500\) 3.26952 0.146218
\(501\) −3.61033 −0.161298
\(502\) −58.0285 −2.58994
\(503\) 6.42927 0.286667 0.143333 0.989674i \(-0.454218\pi\)
0.143333 + 0.989674i \(0.454218\pi\)
\(504\) 0 0
\(505\) 6.33566 0.281933
\(506\) −12.8139 −0.569649
\(507\) 3.19657 0.141965
\(508\) 0.877131 0.0389164
\(509\) −34.7891 −1.54200 −0.771001 0.636834i \(-0.780244\pi\)
−0.771001 + 0.636834i \(0.780244\pi\)
\(510\) −0.928095 −0.0410967
\(511\) 0 0
\(512\) 1.70500 0.0753512
\(513\) −6.27393 −0.277001
\(514\) −70.5374 −3.11127
\(515\) −11.4060 −0.502607
\(516\) −4.26971 −0.187964
\(517\) 0.126494 0.00556322
\(518\) 0 0
\(519\) −3.32860 −0.146109
\(520\) 4.23465 0.185702
\(521\) −12.8010 −0.560821 −0.280410 0.959880i \(-0.590471\pi\)
−0.280410 + 0.959880i \(0.590471\pi\)
\(522\) 0.696287 0.0304757
\(523\) 2.71397 0.118674 0.0593368 0.998238i \(-0.481101\pi\)
0.0593368 + 0.998238i \(0.481101\pi\)
\(524\) 34.4658 1.50565
\(525\) 0 0
\(526\) 40.6319 1.77163
\(527\) 9.26435 0.403562
\(528\) 0.0442527 0.00192585
\(529\) 8.15976 0.354772
\(530\) −18.4964 −0.803434
\(531\) −33.2063 −1.44103
\(532\) 0 0
\(533\) −1.78587 −0.0773545
\(534\) −2.52353 −0.109204
\(535\) 12.3939 0.535833
\(536\) −27.2226 −1.17584
\(537\) 7.43844 0.320992
\(538\) −42.4250 −1.82907
\(539\) 0 0
\(540\) 5.67632 0.244270
\(541\) 18.3714 0.789848 0.394924 0.918714i \(-0.370771\pi\)
0.394924 + 0.918714i \(0.370771\pi\)
\(542\) −62.9055 −2.70202
\(543\) −1.03458 −0.0443981
\(544\) −7.55037 −0.323719
\(545\) −14.7889 −0.633487
\(546\) 0 0
\(547\) 7.58542 0.324329 0.162165 0.986764i \(-0.448152\pi\)
0.162165 + 0.986764i \(0.448152\pi\)
\(548\) −16.2911 −0.695923
\(549\) −15.5058 −0.661772
\(550\) 2.29554 0.0978823
\(551\) −0.376182 −0.0160259
\(552\) −4.77572 −0.203268
\(553\) 0 0
\(554\) 21.2852 0.904321
\(555\) −0.127756 −0.00542296
\(556\) 18.9862 0.805193
\(557\) 24.4867 1.03754 0.518768 0.854915i \(-0.326391\pi\)
0.518768 + 0.854915i \(0.326391\pi\)
\(558\) −44.9957 −1.90482
\(559\) −6.46384 −0.273391
\(560\) 0 0
\(561\) −0.404303 −0.0170697
\(562\) −52.3804 −2.20953
\(563\) −5.29195 −0.223029 −0.111514 0.993763i \(-0.535570\pi\)
−0.111514 + 0.993763i \(0.535570\pi\)
\(564\) 0.121415 0.00511247
\(565\) 9.64437 0.405741
\(566\) −52.7521 −2.21733
\(567\) 0 0
\(568\) 20.3392 0.853415
\(569\) 38.2666 1.60422 0.802111 0.597176i \(-0.203710\pi\)
0.802111 + 0.597176i \(0.203710\pi\)
\(570\) −2.43533 −0.102005
\(571\) −28.8958 −1.20925 −0.604627 0.796509i \(-0.706678\pi\)
−0.604627 + 0.796509i \(0.706678\pi\)
\(572\) 4.75089 0.198645
\(573\) −3.05146 −0.127476
\(574\) 0 0
\(575\) −5.58209 −0.232789
\(576\) 37.5495 1.56456
\(577\) 26.4403 1.10073 0.550363 0.834925i \(-0.314489\pi\)
0.550363 + 0.834925i \(0.314489\pi\)
\(578\) 34.6704 1.44210
\(579\) −1.85873 −0.0772460
\(580\) 0.340350 0.0141322
\(581\) 0 0
\(582\) −0.940022 −0.0389652
\(583\) −8.05754 −0.333709
\(584\) −42.9101 −1.77563
\(585\) 4.23402 0.175055
\(586\) −17.1433 −0.708182
\(587\) −29.7315 −1.22715 −0.613576 0.789636i \(-0.710269\pi\)
−0.613576 + 0.789636i \(0.710269\pi\)
\(588\) 0 0
\(589\) 24.3098 1.00167
\(590\) −26.1604 −1.07700
\(591\) −7.56036 −0.310992
\(592\) 0.0655984 0.00269608
\(593\) −6.72955 −0.276349 −0.138175 0.990408i \(-0.544124\pi\)
−0.138175 + 0.990408i \(0.544124\pi\)
\(594\) 3.98537 0.163522
\(595\) 0 0
\(596\) −27.0976 −1.10996
\(597\) 2.34957 0.0961617
\(598\) −18.6197 −0.761418
\(599\) 15.2411 0.622736 0.311368 0.950289i \(-0.399213\pi\)
0.311368 + 0.950289i \(0.399213\pi\)
\(600\) 0.855542 0.0349274
\(601\) 20.2186 0.824736 0.412368 0.911017i \(-0.364702\pi\)
0.412368 + 0.911017i \(0.364702\pi\)
\(602\) 0 0
\(603\) −27.2186 −1.10843
\(604\) −7.85436 −0.319590
\(605\) 1.00000 0.0406558
\(606\) 4.26965 0.173443
\(607\) −40.0956 −1.62743 −0.813715 0.581264i \(-0.802559\pi\)
−0.813715 + 0.581264i \(0.802559\pi\)
\(608\) −19.8122 −0.803492
\(609\) 0 0
\(610\) −12.2157 −0.494599
\(611\) 0.183807 0.00743604
\(612\) 13.1201 0.530350
\(613\) −10.0274 −0.405002 −0.202501 0.979282i \(-0.564907\pi\)
−0.202501 + 0.979282i \(0.564907\pi\)
\(614\) 35.1256 1.41755
\(615\) −0.360805 −0.0145491
\(616\) 0 0
\(617\) −31.1046 −1.25222 −0.626112 0.779733i \(-0.715355\pi\)
−0.626112 + 0.779733i \(0.715355\pi\)
\(618\) −7.68657 −0.309199
\(619\) −15.6172 −0.627710 −0.313855 0.949471i \(-0.601621\pi\)
−0.313855 + 0.949471i \(0.601621\pi\)
\(620\) −21.9942 −0.883308
\(621\) −9.69125 −0.388896
\(622\) 51.7496 2.07497
\(623\) 0 0
\(624\) 0.0643030 0.00257418
\(625\) 1.00000 0.0400000
\(626\) −19.5408 −0.781007
\(627\) −1.06089 −0.0423680
\(628\) −52.4448 −2.09277
\(629\) −0.599321 −0.0238965
\(630\) 0 0
\(631\) −4.02267 −0.160140 −0.0800699 0.996789i \(-0.525514\pi\)
−0.0800699 + 0.996789i \(0.525514\pi\)
\(632\) 22.2573 0.885347
\(633\) −3.67437 −0.146043
\(634\) 45.2528 1.79722
\(635\) 0.268275 0.0106462
\(636\) −7.73395 −0.306671
\(637\) 0 0
\(638\) 0.238961 0.00946054
\(639\) 20.3362 0.804488
\(640\) 18.6171 0.735906
\(641\) 27.6129 1.09064 0.545321 0.838227i \(-0.316408\pi\)
0.545321 + 0.838227i \(0.316408\pi\)
\(642\) 8.35232 0.329640
\(643\) −30.9004 −1.21859 −0.609296 0.792942i \(-0.708548\pi\)
−0.609296 + 0.792942i \(0.708548\pi\)
\(644\) 0 0
\(645\) −1.30591 −0.0514203
\(646\) −11.4244 −0.449488
\(647\) 42.4760 1.66990 0.834952 0.550323i \(-0.185495\pi\)
0.834952 + 0.550323i \(0.185495\pi\)
\(648\) −23.9894 −0.942393
\(649\) −11.3961 −0.447338
\(650\) 3.33562 0.130834
\(651\) 0 0
\(652\) −12.8570 −0.503520
\(653\) 38.7082 1.51477 0.757385 0.652969i \(-0.226477\pi\)
0.757385 + 0.652969i \(0.226477\pi\)
\(654\) −9.96636 −0.389716
\(655\) 10.5415 0.411892
\(656\) 0.185261 0.00723322
\(657\) −42.9037 −1.67383
\(658\) 0 0
\(659\) −14.7649 −0.575160 −0.287580 0.957757i \(-0.592851\pi\)
−0.287580 + 0.957757i \(0.592851\pi\)
\(660\) 0.959841 0.0373618
\(661\) −28.2032 −1.09698 −0.548489 0.836158i \(-0.684797\pi\)
−0.548489 + 0.836158i \(0.684797\pi\)
\(662\) −34.0433 −1.32313
\(663\) −0.587486 −0.0228161
\(664\) −23.8902 −0.927121
\(665\) 0 0
\(666\) 2.91082 0.112792
\(667\) −0.581083 −0.0224996
\(668\) 40.2084 1.55571
\(669\) 5.04357 0.194996
\(670\) −21.4432 −0.828422
\(671\) −5.32148 −0.205434
\(672\) 0 0
\(673\) 11.9087 0.459048 0.229524 0.973303i \(-0.426283\pi\)
0.229524 + 0.973303i \(0.426283\pi\)
\(674\) −13.7536 −0.529769
\(675\) 1.73613 0.0668237
\(676\) −35.6004 −1.36924
\(677\) 10.1493 0.390069 0.195035 0.980796i \(-0.437518\pi\)
0.195035 + 0.980796i \(0.437518\pi\)
\(678\) 6.49941 0.249608
\(679\) 0 0
\(680\) 4.01345 0.153909
\(681\) −6.42933 −0.246373
\(682\) −15.4422 −0.591312
\(683\) 6.84024 0.261735 0.130867 0.991400i \(-0.458224\pi\)
0.130867 + 0.991400i \(0.458224\pi\)
\(684\) 34.4274 1.31636
\(685\) −4.98272 −0.190380
\(686\) 0 0
\(687\) −3.79970 −0.144967
\(688\) 0.670540 0.0255641
\(689\) −11.7083 −0.446050
\(690\) −3.76182 −0.143210
\(691\) 25.7899 0.981094 0.490547 0.871415i \(-0.336797\pi\)
0.490547 + 0.871415i \(0.336797\pi\)
\(692\) 37.0708 1.40922
\(693\) 0 0
\(694\) 26.9197 1.02186
\(695\) 5.80701 0.220272
\(696\) 0.0890599 0.00337581
\(697\) −1.69258 −0.0641111
\(698\) −63.9993 −2.42241
\(699\) 0.724906 0.0274184
\(700\) 0 0
\(701\) −25.6370 −0.968298 −0.484149 0.874986i \(-0.660871\pi\)
−0.484149 + 0.874986i \(0.660871\pi\)
\(702\) 5.79107 0.218570
\(703\) −1.57263 −0.0593127
\(704\) 12.8867 0.485687
\(705\) 0.0371352 0.00139859
\(706\) −50.5495 −1.90245
\(707\) 0 0
\(708\) −10.9385 −0.411094
\(709\) 35.1596 1.32045 0.660223 0.751069i \(-0.270462\pi\)
0.660223 + 0.751069i \(0.270462\pi\)
\(710\) 16.0211 0.601263
\(711\) 22.2540 0.834589
\(712\) 10.9128 0.408973
\(713\) 37.5509 1.40629
\(714\) 0 0
\(715\) 1.45308 0.0543423
\(716\) −82.8421 −3.09596
\(717\) 4.48386 0.167453
\(718\) 41.0013 1.53016
\(719\) −44.8159 −1.67135 −0.835676 0.549222i \(-0.814924\pi\)
−0.835676 + 0.549222i \(0.814924\pi\)
\(720\) −0.439225 −0.0163690
\(721\) 0 0
\(722\) 13.6375 0.507535
\(723\) 1.36381 0.0507208
\(724\) 11.5222 0.428217
\(725\) 0.104098 0.00386609
\(726\) 0.673908 0.0250111
\(727\) −39.1944 −1.45364 −0.726819 0.686829i \(-0.759002\pi\)
−0.726819 + 0.686829i \(0.759002\pi\)
\(728\) 0 0
\(729\) −22.4568 −0.831734
\(730\) −33.8001 −1.25100
\(731\) −6.12620 −0.226586
\(732\) −5.10778 −0.188789
\(733\) 18.2423 0.673796 0.336898 0.941541i \(-0.390622\pi\)
0.336898 + 0.941541i \(0.390622\pi\)
\(734\) −10.0528 −0.371055
\(735\) 0 0
\(736\) −30.6037 −1.12807
\(737\) −9.34121 −0.344088
\(738\) 8.22065 0.302606
\(739\) −46.9095 −1.72559 −0.862797 0.505550i \(-0.831290\pi\)
−0.862797 + 0.505550i \(0.831290\pi\)
\(740\) 1.42283 0.0523042
\(741\) −1.54157 −0.0566310
\(742\) 0 0
\(743\) 9.95770 0.365312 0.182656 0.983177i \(-0.441530\pi\)
0.182656 + 0.983177i \(0.441530\pi\)
\(744\) −5.75526 −0.210998
\(745\) −8.28793 −0.303646
\(746\) 17.1296 0.627160
\(747\) −23.8867 −0.873968
\(748\) 4.50273 0.164636
\(749\) 0 0
\(750\) 0.673908 0.0246076
\(751\) 8.46961 0.309060 0.154530 0.987988i \(-0.450614\pi\)
0.154530 + 0.987988i \(0.450614\pi\)
\(752\) −0.0190676 −0.000695325 0
\(753\) −7.42114 −0.270441
\(754\) 0.347230 0.0126454
\(755\) −2.40230 −0.0874285
\(756\) 0 0
\(757\) 20.4472 0.743167 0.371584 0.928399i \(-0.378815\pi\)
0.371584 + 0.928399i \(0.378815\pi\)
\(758\) 26.3484 0.957016
\(759\) −1.63875 −0.0594827
\(760\) 10.5313 0.382012
\(761\) 52.8243 1.91488 0.957439 0.288635i \(-0.0932015\pi\)
0.957439 + 0.288635i \(0.0932015\pi\)
\(762\) 0.180792 0.00654942
\(763\) 0 0
\(764\) 33.9842 1.22951
\(765\) 4.01286 0.145085
\(766\) −56.7711 −2.05122
\(767\) −16.5596 −0.597931
\(768\) 4.97985 0.179695
\(769\) 15.4979 0.558870 0.279435 0.960165i \(-0.409853\pi\)
0.279435 + 0.960165i \(0.409853\pi\)
\(770\) 0 0
\(771\) −9.02087 −0.324879
\(772\) 20.7007 0.745035
\(773\) −25.4616 −0.915790 −0.457895 0.889006i \(-0.651396\pi\)
−0.457895 + 0.889006i \(0.651396\pi\)
\(774\) 29.7541 1.06949
\(775\) −6.72703 −0.241642
\(776\) 4.06503 0.145926
\(777\) 0 0
\(778\) 65.2885 2.34071
\(779\) −4.44136 −0.159128
\(780\) 1.39473 0.0499394
\(781\) 6.97924 0.249737
\(782\) −17.6471 −0.631061
\(783\) 0.180727 0.00645866
\(784\) 0 0
\(785\) −16.0405 −0.572510
\(786\) 7.10403 0.253392
\(787\) −31.9072 −1.13737 −0.568684 0.822556i \(-0.692547\pi\)
−0.568684 + 0.822556i \(0.692547\pi\)
\(788\) 84.2001 2.99950
\(789\) 5.19632 0.184994
\(790\) 17.5320 0.623760
\(791\) 0 0
\(792\) −8.49158 −0.301735
\(793\) −7.73256 −0.274591
\(794\) −53.0600 −1.88303
\(795\) −2.36547 −0.0838945
\(796\) −26.1673 −0.927475
\(797\) −28.8682 −1.02256 −0.511281 0.859413i \(-0.670829\pi\)
−0.511281 + 0.859413i \(0.670829\pi\)
\(798\) 0 0
\(799\) 0.174206 0.00616296
\(800\) 5.48247 0.193835
\(801\) 10.9111 0.385526
\(802\) −6.53306 −0.230690
\(803\) −14.7242 −0.519607
\(804\) −8.96608 −0.316209
\(805\) 0 0
\(806\) −22.4388 −0.790374
\(807\) −5.42564 −0.190992
\(808\) −18.4637 −0.649551
\(809\) 37.4007 1.31494 0.657469 0.753482i \(-0.271627\pi\)
0.657469 + 0.753482i \(0.271627\pi\)
\(810\) −18.8964 −0.663951
\(811\) −28.2722 −0.992771 −0.496386 0.868102i \(-0.665340\pi\)
−0.496386 + 0.868102i \(0.665340\pi\)
\(812\) 0 0
\(813\) −8.04484 −0.282145
\(814\) 0.998973 0.0350140
\(815\) −3.93239 −0.137745
\(816\) 0.0609441 0.00213347
\(817\) −16.0752 −0.562401
\(818\) 62.1872 2.17433
\(819\) 0 0
\(820\) 4.01830 0.140325
\(821\) −11.4769 −0.400548 −0.200274 0.979740i \(-0.564183\pi\)
−0.200274 + 0.979740i \(0.564183\pi\)
\(822\) −3.35790 −0.117120
\(823\) −28.5492 −0.995164 −0.497582 0.867417i \(-0.665779\pi\)
−0.497582 + 0.867417i \(0.665779\pi\)
\(824\) 33.2398 1.15796
\(825\) 0.293572 0.0102209
\(826\) 0 0
\(827\) 36.3199 1.26297 0.631483 0.775390i \(-0.282446\pi\)
0.631483 + 0.775390i \(0.282446\pi\)
\(828\) 53.1794 1.84811
\(829\) 29.2920 1.01735 0.508677 0.860957i \(-0.330135\pi\)
0.508677 + 0.860957i \(0.330135\pi\)
\(830\) −18.8183 −0.653192
\(831\) 2.72212 0.0944291
\(832\) 18.7255 0.649190
\(833\) 0 0
\(834\) 3.91339 0.135510
\(835\) 12.2979 0.425587
\(836\) 11.8152 0.408638
\(837\) −11.6790 −0.403686
\(838\) −16.8571 −0.582320
\(839\) −3.32507 −0.114794 −0.0573971 0.998351i \(-0.518280\pi\)
−0.0573971 + 0.998351i \(0.518280\pi\)
\(840\) 0 0
\(841\) −28.9892 −0.999626
\(842\) −74.3240 −2.56137
\(843\) −6.69881 −0.230719
\(844\) 40.9216 1.40858
\(845\) −10.8885 −0.374577
\(846\) −0.846095 −0.0290893
\(847\) 0 0
\(848\) 1.21458 0.0417090
\(849\) −6.74634 −0.231534
\(850\) 3.16139 0.108435
\(851\) −2.42921 −0.0832722
\(852\) 6.69896 0.229503
\(853\) 27.1154 0.928415 0.464208 0.885726i \(-0.346339\pi\)
0.464208 + 0.885726i \(0.346339\pi\)
\(854\) 0 0
\(855\) 10.5298 0.360111
\(856\) −36.1188 −1.23451
\(857\) 55.1107 1.88255 0.941273 0.337648i \(-0.109631\pi\)
0.941273 + 0.337648i \(0.109631\pi\)
\(858\) 0.979245 0.0334309
\(859\) 23.9506 0.817185 0.408592 0.912717i \(-0.366020\pi\)
0.408592 + 0.912717i \(0.366020\pi\)
\(860\) 14.5440 0.495946
\(861\) 0 0
\(862\) −82.5335 −2.81110
\(863\) 0.309183 0.0105247 0.00526235 0.999986i \(-0.498325\pi\)
0.00526235 + 0.999986i \(0.498325\pi\)
\(864\) 9.51829 0.323819
\(865\) 11.3383 0.385513
\(866\) 36.7075 1.24737
\(867\) 4.43393 0.150584
\(868\) 0 0
\(869\) 7.63740 0.259081
\(870\) 0.0701522 0.00237838
\(871\) −13.5736 −0.459923
\(872\) 43.0986 1.45950
\(873\) 4.06443 0.137560
\(874\) −46.3063 −1.56633
\(875\) 0 0
\(876\) −14.1329 −0.477507
\(877\) −28.4555 −0.960873 −0.480437 0.877029i \(-0.659522\pi\)
−0.480437 + 0.877029i \(0.659522\pi\)
\(878\) −40.3609 −1.36212
\(879\) −2.19241 −0.0739483
\(880\) −0.150739 −0.00508141
\(881\) 37.5430 1.26486 0.632428 0.774619i \(-0.282059\pi\)
0.632428 + 0.774619i \(0.282059\pi\)
\(882\) 0 0
\(883\) −2.90495 −0.0977592 −0.0488796 0.998805i \(-0.515565\pi\)
−0.0488796 + 0.998805i \(0.515565\pi\)
\(884\) 6.54285 0.220060
\(885\) −3.34559 −0.112461
\(886\) −10.6076 −0.356370
\(887\) −56.7508 −1.90550 −0.952752 0.303749i \(-0.901762\pi\)
−0.952752 + 0.303749i \(0.901762\pi\)
\(888\) 0.372314 0.0124940
\(889\) 0 0
\(890\) 8.59594 0.288137
\(891\) −8.23177 −0.275775
\(892\) −56.1705 −1.88073
\(893\) 0.457118 0.0152969
\(894\) −5.58530 −0.186800
\(895\) −25.3377 −0.846945
\(896\) 0 0
\(897\) −2.38124 −0.0795072
\(898\) −32.6698 −1.09021
\(899\) −0.700268 −0.0233552
\(900\) −9.52679 −0.317560
\(901\) −11.0967 −0.369685
\(902\) 2.82126 0.0939378
\(903\) 0 0
\(904\) −28.1061 −0.934794
\(905\) 3.52411 0.117145
\(906\) −1.61893 −0.0537852
\(907\) −2.60141 −0.0863784 −0.0431892 0.999067i \(-0.513752\pi\)
−0.0431892 + 0.999067i \(0.513752\pi\)
\(908\) 71.6037 2.37625
\(909\) −18.4610 −0.612311
\(910\) 0 0
\(911\) −18.8906 −0.625872 −0.312936 0.949774i \(-0.601313\pi\)
−0.312936 + 0.949774i \(0.601313\pi\)
\(912\) 0.159918 0.00529542
\(913\) −8.19774 −0.271305
\(914\) 90.1714 2.98260
\(915\) −1.56224 −0.0516460
\(916\) 42.3174 1.39821
\(917\) 0 0
\(918\) 5.48858 0.181150
\(919\) 2.85576 0.0942028 0.0471014 0.998890i \(-0.485002\pi\)
0.0471014 + 0.998890i \(0.485002\pi\)
\(920\) 16.2676 0.536327
\(921\) 4.49214 0.148021
\(922\) −4.68505 −0.154294
\(923\) 10.1414 0.333809
\(924\) 0 0
\(925\) 0.435179 0.0143086
\(926\) −41.2768 −1.35644
\(927\) 33.2349 1.09158
\(928\) 0.570712 0.0187345
\(929\) −4.55208 −0.149349 −0.0746744 0.997208i \(-0.523792\pi\)
−0.0746744 + 0.997208i \(0.523792\pi\)
\(930\) −4.53340 −0.148656
\(931\) 0 0
\(932\) −8.07330 −0.264450
\(933\) 6.61815 0.216668
\(934\) 18.5050 0.605501
\(935\) 1.37718 0.0450387
\(936\) −12.3390 −0.403312
\(937\) 39.5112 1.29078 0.645388 0.763855i \(-0.276696\pi\)
0.645388 + 0.763855i \(0.276696\pi\)
\(938\) 0 0
\(939\) −2.49903 −0.0815527
\(940\) −0.413576 −0.0134894
\(941\) −35.4567 −1.15585 −0.577927 0.816088i \(-0.696138\pi\)
−0.577927 + 0.816088i \(0.696138\pi\)
\(942\) −10.8098 −0.352203
\(943\) −6.86049 −0.223408
\(944\) 1.71784 0.0559110
\(945\) 0 0
\(946\) 10.2114 0.332001
\(947\) 8.35366 0.271457 0.135729 0.990746i \(-0.456662\pi\)
0.135729 + 0.990746i \(0.456662\pi\)
\(948\) 7.33069 0.238090
\(949\) −21.3956 −0.694529
\(950\) 8.29551 0.269142
\(951\) 5.78728 0.187665
\(952\) 0 0
\(953\) −11.3306 −0.367033 −0.183517 0.983017i \(-0.558748\pi\)
−0.183517 + 0.983017i \(0.558748\pi\)
\(954\) 53.8952 1.74492
\(955\) 10.3942 0.336350
\(956\) −49.9369 −1.61507
\(957\) 0.0305602 0.000987869 0
\(958\) −34.5768 −1.11713
\(959\) 0 0
\(960\) 3.78318 0.122102
\(961\) 14.2529 0.459772
\(962\) 1.45159 0.0468012
\(963\) −36.1134 −1.16374
\(964\) −15.1889 −0.489200
\(965\) 6.33141 0.203815
\(966\) 0 0
\(967\) 25.7910 0.829383 0.414692 0.909962i \(-0.363889\pi\)
0.414692 + 0.909962i \(0.363889\pi\)
\(968\) −2.91425 −0.0936675
\(969\) −1.46105 −0.0469356
\(970\) 3.20201 0.102810
\(971\) 25.8433 0.829349 0.414675 0.909970i \(-0.363895\pi\)
0.414675 + 0.909970i \(0.363895\pi\)
\(972\) −24.9302 −0.799635
\(973\) 0 0
\(974\) 92.6058 2.96728
\(975\) 0.426585 0.0136617
\(976\) 0.802154 0.0256763
\(977\) 23.7974 0.761345 0.380673 0.924710i \(-0.375692\pi\)
0.380673 + 0.924710i \(0.375692\pi\)
\(978\) −2.65007 −0.0847398
\(979\) 3.74462 0.119679
\(980\) 0 0
\(981\) 43.0922 1.37583
\(982\) 32.8311 1.04768
\(983\) −54.2199 −1.72935 −0.864674 0.502334i \(-0.832475\pi\)
−0.864674 + 0.502334i \(0.832475\pi\)
\(984\) 1.05148 0.0335198
\(985\) 25.7530 0.820559
\(986\) 0.329093 0.0104804
\(987\) 0 0
\(988\) 17.1685 0.546203
\(989\) −24.8311 −0.789584
\(990\) −6.68879 −0.212584
\(991\) −42.1179 −1.33792 −0.668959 0.743299i \(-0.733260\pi\)
−0.668959 + 0.743299i \(0.733260\pi\)
\(992\) −36.8807 −1.17096
\(993\) −4.35372 −0.138161
\(994\) 0 0
\(995\) −8.00340 −0.253725
\(996\) −7.86852 −0.249324
\(997\) 20.6025 0.652487 0.326244 0.945286i \(-0.394217\pi\)
0.326244 + 0.945286i \(0.394217\pi\)
\(998\) −56.5116 −1.78884
\(999\) 0.755528 0.0239038
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 2695.2.a.x.1.1 yes 10
7.6 odd 2 2695.2.a.w.1.1 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2695.2.a.w.1.1 10 7.6 odd 2
2695.2.a.x.1.1 yes 10 1.1 even 1 trivial