Properties

Label 5290.2.a.bk.1.4
Level $5290$
Weight $2$
Character 5290.1
Self dual yes
Analytic conductor $42.241$
Analytic rank $0$
Dimension $15$
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] = [5290,2,Mod(1,5290)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5290, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("5290.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 5290 = 2 \cdot 5 \cdot 23^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5290.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: \(42.2408626693\)
Analytic rank: \(0\)
Dimension: \(15\)
Coefficient field: \(\mathbb{Q}[x]/(x^{15} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{15} - 5 x^{14} - 24 x^{13} + 142 x^{12} + 184 x^{11} - 1488 x^{10} - 426 x^{9} + 7165 x^{8} - 206 x^{7} - 16453 x^{6} + 637 x^{5} + 16290 x^{4} + 1068 x^{3} - 4992 x^{2} + \cdots - 32 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 230)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(-1.53931\) of defining polynomial
Character \(\chi\) \(=\) 5290.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.53931 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.53931 q^{6} -3.71769 q^{7} +1.00000 q^{8} -0.630528 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.53931 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.53931 q^{6} -3.71769 q^{7} +1.00000 q^{8} -0.630528 q^{9} -1.00000 q^{10} -5.52957 q^{11} -1.53931 q^{12} +2.56268 q^{13} -3.71769 q^{14} +1.53931 q^{15} +1.00000 q^{16} -5.76605 q^{17} -0.630528 q^{18} -3.65701 q^{19} -1.00000 q^{20} +5.72267 q^{21} -5.52957 q^{22} -1.53931 q^{24} +1.00000 q^{25} +2.56268 q^{26} +5.58850 q^{27} -3.71769 q^{28} +8.55120 q^{29} +1.53931 q^{30} -9.24402 q^{31} +1.00000 q^{32} +8.51172 q^{33} -5.76605 q^{34} +3.71769 q^{35} -0.630528 q^{36} +0.490152 q^{37} -3.65701 q^{38} -3.94475 q^{39} -1.00000 q^{40} -11.3942 q^{41} +5.72267 q^{42} -9.04149 q^{43} -5.52957 q^{44} +0.630528 q^{45} -9.73542 q^{47} -1.53931 q^{48} +6.82119 q^{49} +1.00000 q^{50} +8.87574 q^{51} +2.56268 q^{52} +0.824873 q^{53} +5.58850 q^{54} +5.52957 q^{55} -3.71769 q^{56} +5.62926 q^{57} +8.55120 q^{58} +2.08710 q^{59} +1.53931 q^{60} +9.46716 q^{61} -9.24402 q^{62} +2.34410 q^{63} +1.00000 q^{64} -2.56268 q^{65} +8.51172 q^{66} -1.14674 q^{67} -5.76605 q^{68} +3.71769 q^{70} +2.86767 q^{71} -0.630528 q^{72} -3.21969 q^{73} +0.490152 q^{74} -1.53931 q^{75} -3.65701 q^{76} +20.5572 q^{77} -3.94475 q^{78} +6.94974 q^{79} -1.00000 q^{80} -6.71085 q^{81} -11.3942 q^{82} +9.86488 q^{83} +5.72267 q^{84} +5.76605 q^{85} -9.04149 q^{86} -13.1629 q^{87} -5.52957 q^{88} +3.58473 q^{89} +0.630528 q^{90} -9.52722 q^{91} +14.2294 q^{93} -9.73542 q^{94} +3.65701 q^{95} -1.53931 q^{96} +2.55727 q^{97} +6.82119 q^{98} +3.48655 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 15 q + 15 q^{2} + 5 q^{3} + 15 q^{4} - 15 q^{5} + 5 q^{6} + 4 q^{7} + 15 q^{8} + 28 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 15 q + 15 q^{2} + 5 q^{3} + 15 q^{4} - 15 q^{5} + 5 q^{6} + 4 q^{7} + 15 q^{8} + 28 q^{9} - 15 q^{10} - 7 q^{11} + 5 q^{12} + 17 q^{13} + 4 q^{14} - 5 q^{15} + 15 q^{16} - 2 q^{17} + 28 q^{18} - 18 q^{19} - 15 q^{20} - 7 q^{22} + 5 q^{24} + 15 q^{25} + 17 q^{26} + 29 q^{27} + 4 q^{28} + 35 q^{29} - 5 q^{30} + 19 q^{31} + 15 q^{32} + 21 q^{33} - 2 q^{34} - 4 q^{35} + 28 q^{36} + 12 q^{37} - 18 q^{38} + 26 q^{39} - 15 q^{40} + 27 q^{41} - 12 q^{43} - 7 q^{44} - 28 q^{45} + 40 q^{47} + 5 q^{48} + 29 q^{49} + 15 q^{50} + 27 q^{51} + 17 q^{52} + 20 q^{53} + 29 q^{54} + 7 q^{55} + 4 q^{56} + 11 q^{57} + 35 q^{58} + 15 q^{59} - 5 q^{60} - 28 q^{61} + 19 q^{62} + 51 q^{63} + 15 q^{64} - 17 q^{65} + 21 q^{66} - 4 q^{67} - 2 q^{68} - 4 q^{70} + 22 q^{71} + 28 q^{72} + 48 q^{73} + 12 q^{74} + 5 q^{75} - 18 q^{76} + 45 q^{77} + 26 q^{78} + 2 q^{79} - 15 q^{80} + 79 q^{81} + 27 q^{82} + 29 q^{83} + 2 q^{85} - 12 q^{86} - 7 q^{87} - 7 q^{88} - 20 q^{89} - 28 q^{90} - 6 q^{91} + 63 q^{93} + 40 q^{94} + 18 q^{95} + 5 q^{96} + 22 q^{97} + 29 q^{98} - 23 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −1.53931 −0.888720 −0.444360 0.895848i \(-0.646569\pi\)
−0.444360 + 0.895848i \(0.646569\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) −1.53931 −0.628420
\(7\) −3.71769 −1.40515 −0.702577 0.711608i \(-0.747967\pi\)
−0.702577 + 0.711608i \(0.747967\pi\)
\(8\) 1.00000 0.353553
\(9\) −0.630528 −0.210176
\(10\) −1.00000 −0.316228
\(11\) −5.52957 −1.66723 −0.833614 0.552347i \(-0.813732\pi\)
−0.833614 + 0.552347i \(0.813732\pi\)
\(12\) −1.53931 −0.444360
\(13\) 2.56268 0.710758 0.355379 0.934722i \(-0.384352\pi\)
0.355379 + 0.934722i \(0.384352\pi\)
\(14\) −3.71769 −0.993593
\(15\) 1.53931 0.397448
\(16\) 1.00000 0.250000
\(17\) −5.76605 −1.39847 −0.699237 0.714890i \(-0.746477\pi\)
−0.699237 + 0.714890i \(0.746477\pi\)
\(18\) −0.630528 −0.148617
\(19\) −3.65701 −0.838975 −0.419487 0.907761i \(-0.637790\pi\)
−0.419487 + 0.907761i \(0.637790\pi\)
\(20\) −1.00000 −0.223607
\(21\) 5.72267 1.24879
\(22\) −5.52957 −1.17891
\(23\) 0 0
\(24\) −1.53931 −0.314210
\(25\) 1.00000 0.200000
\(26\) 2.56268 0.502582
\(27\) 5.58850 1.07551
\(28\) −3.71769 −0.702577
\(29\) 8.55120 1.58792 0.793959 0.607971i \(-0.208016\pi\)
0.793959 + 0.607971i \(0.208016\pi\)
\(30\) 1.53931 0.281038
\(31\) −9.24402 −1.66028 −0.830138 0.557559i \(-0.811738\pi\)
−0.830138 + 0.557559i \(0.811738\pi\)
\(32\) 1.00000 0.176777
\(33\) 8.51172 1.48170
\(34\) −5.76605 −0.988870
\(35\) 3.71769 0.628404
\(36\) −0.630528 −0.105088
\(37\) 0.490152 0.0805805 0.0402903 0.999188i \(-0.487172\pi\)
0.0402903 + 0.999188i \(0.487172\pi\)
\(38\) −3.65701 −0.593245
\(39\) −3.94475 −0.631665
\(40\) −1.00000 −0.158114
\(41\) −11.3942 −1.77947 −0.889735 0.456478i \(-0.849111\pi\)
−0.889735 + 0.456478i \(0.849111\pi\)
\(42\) 5.72267 0.883027
\(43\) −9.04149 −1.37881 −0.689407 0.724374i \(-0.742129\pi\)
−0.689407 + 0.724374i \(0.742129\pi\)
\(44\) −5.52957 −0.833614
\(45\) 0.630528 0.0939935
\(46\) 0 0
\(47\) −9.73542 −1.42006 −0.710028 0.704173i \(-0.751318\pi\)
−0.710028 + 0.704173i \(0.751318\pi\)
\(48\) −1.53931 −0.222180
\(49\) 6.82119 0.974456
\(50\) 1.00000 0.141421
\(51\) 8.87574 1.24285
\(52\) 2.56268 0.355379
\(53\) 0.824873 0.113305 0.0566525 0.998394i \(-0.481957\pi\)
0.0566525 + 0.998394i \(0.481957\pi\)
\(54\) 5.58850 0.760499
\(55\) 5.52957 0.745607
\(56\) −3.71769 −0.496797
\(57\) 5.62926 0.745614
\(58\) 8.55120 1.12283
\(59\) 2.08710 0.271718 0.135859 0.990728i \(-0.456621\pi\)
0.135859 + 0.990728i \(0.456621\pi\)
\(60\) 1.53931 0.198724
\(61\) 9.46716 1.21215 0.606073 0.795409i \(-0.292744\pi\)
0.606073 + 0.795409i \(0.292744\pi\)
\(62\) −9.24402 −1.17399
\(63\) 2.34410 0.295329
\(64\) 1.00000 0.125000
\(65\) −2.56268 −0.317861
\(66\) 8.51172 1.04772
\(67\) −1.14674 −0.140096 −0.0700482 0.997544i \(-0.522315\pi\)
−0.0700482 + 0.997544i \(0.522315\pi\)
\(68\) −5.76605 −0.699237
\(69\) 0 0
\(70\) 3.71769 0.444349
\(71\) 2.86767 0.340330 0.170165 0.985416i \(-0.445570\pi\)
0.170165 + 0.985416i \(0.445570\pi\)
\(72\) −0.630528 −0.0743084
\(73\) −3.21969 −0.376836 −0.188418 0.982089i \(-0.560336\pi\)
−0.188418 + 0.982089i \(0.560336\pi\)
\(74\) 0.490152 0.0569790
\(75\) −1.53931 −0.177744
\(76\) −3.65701 −0.419487
\(77\) 20.5572 2.34271
\(78\) −3.94475 −0.446655
\(79\) 6.94974 0.781907 0.390954 0.920410i \(-0.372145\pi\)
0.390954 + 0.920410i \(0.372145\pi\)
\(80\) −1.00000 −0.111803
\(81\) −6.71085 −0.745650
\(82\) −11.3942 −1.25827
\(83\) 9.86488 1.08281 0.541406 0.840762i \(-0.317892\pi\)
0.541406 + 0.840762i \(0.317892\pi\)
\(84\) 5.72267 0.624394
\(85\) 5.76605 0.625416
\(86\) −9.04149 −0.974969
\(87\) −13.1629 −1.41122
\(88\) −5.52957 −0.589454
\(89\) 3.58473 0.379981 0.189990 0.981786i \(-0.439154\pi\)
0.189990 + 0.981786i \(0.439154\pi\)
\(90\) 0.630528 0.0664635
\(91\) −9.52722 −0.998724
\(92\) 0 0
\(93\) 14.2294 1.47552
\(94\) −9.73542 −1.00413
\(95\) 3.65701 0.375201
\(96\) −1.53931 −0.157105
\(97\) 2.55727 0.259651 0.129826 0.991537i \(-0.458558\pi\)
0.129826 + 0.991537i \(0.458558\pi\)
\(98\) 6.82119 0.689044
\(99\) 3.48655 0.350411
\(100\) 1.00000 0.100000
\(101\) −6.99569 −0.696097 −0.348048 0.937477i \(-0.613156\pi\)
−0.348048 + 0.937477i \(0.613156\pi\)
\(102\) 8.87574 0.878829
\(103\) −1.74044 −0.171491 −0.0857455 0.996317i \(-0.527327\pi\)
−0.0857455 + 0.996317i \(0.527327\pi\)
\(104\) 2.56268 0.251291
\(105\) −5.72267 −0.558475
\(106\) 0.824873 0.0801187
\(107\) 1.08182 0.104584 0.0522919 0.998632i \(-0.483347\pi\)
0.0522919 + 0.998632i \(0.483347\pi\)
\(108\) 5.58850 0.537754
\(109\) 2.33737 0.223880 0.111940 0.993715i \(-0.464294\pi\)
0.111940 + 0.993715i \(0.464294\pi\)
\(110\) 5.52957 0.527224
\(111\) −0.754496 −0.0716136
\(112\) −3.71769 −0.351288
\(113\) 16.0040 1.50553 0.752766 0.658288i \(-0.228719\pi\)
0.752766 + 0.658288i \(0.228719\pi\)
\(114\) 5.62926 0.527229
\(115\) 0 0
\(116\) 8.55120 0.793959
\(117\) −1.61584 −0.149384
\(118\) 2.08710 0.192133
\(119\) 21.4364 1.96507
\(120\) 1.53931 0.140519
\(121\) 19.5762 1.77965
\(122\) 9.46716 0.857117
\(123\) 17.5391 1.58145
\(124\) −9.24402 −0.830138
\(125\) −1.00000 −0.0894427
\(126\) 2.34410 0.208829
\(127\) −2.46423 −0.218665 −0.109332 0.994005i \(-0.534871\pi\)
−0.109332 + 0.994005i \(0.534871\pi\)
\(128\) 1.00000 0.0883883
\(129\) 13.9176 1.22538
\(130\) −2.56268 −0.224762
\(131\) 21.8887 1.91243 0.956214 0.292669i \(-0.0945433\pi\)
0.956214 + 0.292669i \(0.0945433\pi\)
\(132\) 8.51172 0.740850
\(133\) 13.5956 1.17889
\(134\) −1.14674 −0.0990631
\(135\) −5.58850 −0.480982
\(136\) −5.76605 −0.494435
\(137\) 3.01304 0.257421 0.128711 0.991682i \(-0.458916\pi\)
0.128711 + 0.991682i \(0.458916\pi\)
\(138\) 0 0
\(139\) −5.93581 −0.503469 −0.251734 0.967796i \(-0.581001\pi\)
−0.251734 + 0.967796i \(0.581001\pi\)
\(140\) 3.71769 0.314202
\(141\) 14.9858 1.26203
\(142\) 2.86767 0.240650
\(143\) −14.1705 −1.18500
\(144\) −0.630528 −0.0525440
\(145\) −8.55120 −0.710139
\(146\) −3.21969 −0.266463
\(147\) −10.4999 −0.866019
\(148\) 0.490152 0.0402903
\(149\) 1.49328 0.122334 0.0611671 0.998128i \(-0.480518\pi\)
0.0611671 + 0.998128i \(0.480518\pi\)
\(150\) −1.53931 −0.125684
\(151\) −15.6386 −1.27265 −0.636326 0.771420i \(-0.719547\pi\)
−0.636326 + 0.771420i \(0.719547\pi\)
\(152\) −3.65701 −0.296622
\(153\) 3.63566 0.293925
\(154\) 20.5572 1.65655
\(155\) 9.24402 0.742498
\(156\) −3.94475 −0.315833
\(157\) 6.10683 0.487378 0.243689 0.969853i \(-0.421642\pi\)
0.243689 + 0.969853i \(0.421642\pi\)
\(158\) 6.94974 0.552892
\(159\) −1.26973 −0.100696
\(160\) −1.00000 −0.0790569
\(161\) 0 0
\(162\) −6.71085 −0.527254
\(163\) 16.4053 1.28496 0.642479 0.766303i \(-0.277906\pi\)
0.642479 + 0.766303i \(0.277906\pi\)
\(164\) −11.3942 −0.889735
\(165\) −8.51172 −0.662637
\(166\) 9.86488 0.765663
\(167\) −14.3536 −1.11071 −0.555357 0.831612i \(-0.687418\pi\)
−0.555357 + 0.831612i \(0.687418\pi\)
\(168\) 5.72267 0.441513
\(169\) −6.43269 −0.494823
\(170\) 5.76605 0.442236
\(171\) 2.30584 0.176332
\(172\) −9.04149 −0.689407
\(173\) −10.4022 −0.790863 −0.395432 0.918495i \(-0.629405\pi\)
−0.395432 + 0.918495i \(0.629405\pi\)
\(174\) −13.1629 −0.997880
\(175\) −3.71769 −0.281031
\(176\) −5.52957 −0.416807
\(177\) −3.21270 −0.241481
\(178\) 3.58473 0.268687
\(179\) −12.6474 −0.945310 −0.472655 0.881248i \(-0.656704\pi\)
−0.472655 + 0.881248i \(0.656704\pi\)
\(180\) 0.630528 0.0469968
\(181\) −4.07323 −0.302761 −0.151380 0.988476i \(-0.548372\pi\)
−0.151380 + 0.988476i \(0.548372\pi\)
\(182\) −9.52722 −0.706205
\(183\) −14.5729 −1.07726
\(184\) 0 0
\(185\) −0.490152 −0.0360367
\(186\) 14.2294 1.04335
\(187\) 31.8838 2.33157
\(188\) −9.73542 −0.710028
\(189\) −20.7763 −1.51125
\(190\) 3.65701 0.265307
\(191\) −6.14225 −0.444438 −0.222219 0.974997i \(-0.571330\pi\)
−0.222219 + 0.974997i \(0.571330\pi\)
\(192\) −1.53931 −0.111090
\(193\) 6.53510 0.470406 0.235203 0.971946i \(-0.424424\pi\)
0.235203 + 0.971946i \(0.424424\pi\)
\(194\) 2.55727 0.183601
\(195\) 3.94475 0.282489
\(196\) 6.82119 0.487228
\(197\) 4.45551 0.317442 0.158721 0.987323i \(-0.449263\pi\)
0.158721 + 0.987323i \(0.449263\pi\)
\(198\) 3.48655 0.247778
\(199\) −15.1131 −1.07134 −0.535671 0.844427i \(-0.679941\pi\)
−0.535671 + 0.844427i \(0.679941\pi\)
\(200\) 1.00000 0.0707107
\(201\) 1.76518 0.124507
\(202\) −6.99569 −0.492215
\(203\) −31.7907 −2.23127
\(204\) 8.87574 0.621426
\(205\) 11.3942 0.795803
\(206\) −1.74044 −0.121262
\(207\) 0 0
\(208\) 2.56268 0.177690
\(209\) 20.2217 1.39876
\(210\) −5.72267 −0.394902
\(211\) −8.59548 −0.591737 −0.295868 0.955229i \(-0.595609\pi\)
−0.295868 + 0.955229i \(0.595609\pi\)
\(212\) 0.824873 0.0566525
\(213\) −4.41424 −0.302459
\(214\) 1.08182 0.0739520
\(215\) 9.04149 0.616624
\(216\) 5.58850 0.380250
\(217\) 34.3664 2.33294
\(218\) 2.33737 0.158307
\(219\) 4.95609 0.334902
\(220\) 5.52957 0.372804
\(221\) −14.7765 −0.993976
\(222\) −0.754496 −0.0506384
\(223\) 1.23633 0.0827906 0.0413953 0.999143i \(-0.486820\pi\)
0.0413953 + 0.999143i \(0.486820\pi\)
\(224\) −3.71769 −0.248398
\(225\) −0.630528 −0.0420352
\(226\) 16.0040 1.06457
\(227\) 21.1727 1.40528 0.702640 0.711545i \(-0.252004\pi\)
0.702640 + 0.711545i \(0.252004\pi\)
\(228\) 5.62926 0.372807
\(229\) −11.2218 −0.741557 −0.370779 0.928721i \(-0.620909\pi\)
−0.370779 + 0.928721i \(0.620909\pi\)
\(230\) 0 0
\(231\) −31.6439 −2.08202
\(232\) 8.55120 0.561414
\(233\) 1.43374 0.0939276 0.0469638 0.998897i \(-0.485045\pi\)
0.0469638 + 0.998897i \(0.485045\pi\)
\(234\) −1.61584 −0.105631
\(235\) 9.73542 0.635068
\(236\) 2.08710 0.135859
\(237\) −10.6978 −0.694897
\(238\) 21.4364 1.38951
\(239\) −6.91805 −0.447491 −0.223746 0.974648i \(-0.571828\pi\)
−0.223746 + 0.974648i \(0.571828\pi\)
\(240\) 1.53931 0.0993620
\(241\) −16.4852 −1.06191 −0.530953 0.847401i \(-0.678166\pi\)
−0.530953 + 0.847401i \(0.678166\pi\)
\(242\) 19.5762 1.25840
\(243\) −6.43544 −0.412834
\(244\) 9.46716 0.606073
\(245\) −6.82119 −0.435790
\(246\) 17.5391 1.11825
\(247\) −9.37172 −0.596308
\(248\) −9.24402 −0.586996
\(249\) −15.1851 −0.962316
\(250\) −1.00000 −0.0632456
\(251\) 21.1825 1.33703 0.668513 0.743701i \(-0.266931\pi\)
0.668513 + 0.743701i \(0.266931\pi\)
\(252\) 2.34410 0.147665
\(253\) 0 0
\(254\) −2.46423 −0.154619
\(255\) −8.87574 −0.555820
\(256\) 1.00000 0.0625000
\(257\) 0.629630 0.0392752 0.0196376 0.999807i \(-0.493749\pi\)
0.0196376 + 0.999807i \(0.493749\pi\)
\(258\) 13.9176 0.866475
\(259\) −1.82223 −0.113228
\(260\) −2.56268 −0.158930
\(261\) −5.39177 −0.333742
\(262\) 21.8887 1.35229
\(263\) 26.2962 1.62149 0.810747 0.585397i \(-0.199061\pi\)
0.810747 + 0.585397i \(0.199061\pi\)
\(264\) 8.51172 0.523860
\(265\) −0.824873 −0.0506715
\(266\) 13.5956 0.833600
\(267\) −5.51801 −0.337697
\(268\) −1.14674 −0.0700482
\(269\) 26.6135 1.62266 0.811328 0.584591i \(-0.198745\pi\)
0.811328 + 0.584591i \(0.198745\pi\)
\(270\) −5.58850 −0.340106
\(271\) 9.82645 0.596914 0.298457 0.954423i \(-0.403528\pi\)
0.298457 + 0.954423i \(0.403528\pi\)
\(272\) −5.76605 −0.349618
\(273\) 14.6653 0.887587
\(274\) 3.01304 0.182024
\(275\) −5.52957 −0.333446
\(276\) 0 0
\(277\) 11.7531 0.706178 0.353089 0.935590i \(-0.385131\pi\)
0.353089 + 0.935590i \(0.385131\pi\)
\(278\) −5.93581 −0.356006
\(279\) 5.82861 0.348950
\(280\) 3.71769 0.222174
\(281\) −14.7365 −0.879103 −0.439552 0.898217i \(-0.644863\pi\)
−0.439552 + 0.898217i \(0.644863\pi\)
\(282\) 14.9858 0.892392
\(283\) −2.06989 −0.123042 −0.0615211 0.998106i \(-0.519595\pi\)
−0.0615211 + 0.998106i \(0.519595\pi\)
\(284\) 2.86767 0.170165
\(285\) −5.62926 −0.333449
\(286\) −14.1705 −0.837919
\(287\) 42.3599 2.50043
\(288\) −0.630528 −0.0371542
\(289\) 16.2474 0.955727
\(290\) −8.55120 −0.502144
\(291\) −3.93642 −0.230757
\(292\) −3.21969 −0.188418
\(293\) −20.4438 −1.19434 −0.597169 0.802115i \(-0.703708\pi\)
−0.597169 + 0.802115i \(0.703708\pi\)
\(294\) −10.4999 −0.612368
\(295\) −2.08710 −0.121516
\(296\) 0.490152 0.0284895
\(297\) −30.9020 −1.79312
\(298\) 1.49328 0.0865033
\(299\) 0 0
\(300\) −1.53931 −0.0888720
\(301\) 33.6134 1.93745
\(302\) −15.6386 −0.899901
\(303\) 10.7685 0.618636
\(304\) −3.65701 −0.209744
\(305\) −9.46716 −0.542088
\(306\) 3.63566 0.207837
\(307\) −9.37242 −0.534912 −0.267456 0.963570i \(-0.586183\pi\)
−0.267456 + 0.963570i \(0.586183\pi\)
\(308\) 20.5572 1.17136
\(309\) 2.67908 0.152408
\(310\) 9.24402 0.525025
\(311\) 7.48356 0.424354 0.212177 0.977231i \(-0.431945\pi\)
0.212177 + 0.977231i \(0.431945\pi\)
\(312\) −3.94475 −0.223327
\(313\) −2.78633 −0.157492 −0.0787462 0.996895i \(-0.525092\pi\)
−0.0787462 + 0.996895i \(0.525092\pi\)
\(314\) 6.10683 0.344628
\(315\) −2.34410 −0.132075
\(316\) 6.94974 0.390954
\(317\) 15.8539 0.890442 0.445221 0.895421i \(-0.353125\pi\)
0.445221 + 0.895421i \(0.353125\pi\)
\(318\) −1.26973 −0.0712032
\(319\) −47.2845 −2.64742
\(320\) −1.00000 −0.0559017
\(321\) −1.66526 −0.0929458
\(322\) 0 0
\(323\) 21.0865 1.17328
\(324\) −6.71085 −0.372825
\(325\) 2.56268 0.142152
\(326\) 16.4053 0.908603
\(327\) −3.59794 −0.198967
\(328\) −11.3942 −0.629137
\(329\) 36.1932 1.99540
\(330\) −8.51172 −0.468555
\(331\) −10.9915 −0.604149 −0.302074 0.953284i \(-0.597679\pi\)
−0.302074 + 0.953284i \(0.597679\pi\)
\(332\) 9.86488 0.541406
\(333\) −0.309055 −0.0169361
\(334\) −14.3536 −0.785394
\(335\) 1.14674 0.0626530
\(336\) 5.72267 0.312197
\(337\) 24.4167 1.33006 0.665030 0.746817i \(-0.268419\pi\)
0.665030 + 0.746817i \(0.268419\pi\)
\(338\) −6.43269 −0.349892
\(339\) −24.6351 −1.33800
\(340\) 5.76605 0.312708
\(341\) 51.1155 2.76806
\(342\) 2.30584 0.124686
\(343\) 0.664752 0.0358932
\(344\) −9.04149 −0.487484
\(345\) 0 0
\(346\) −10.4022 −0.559225
\(347\) 23.9579 1.28613 0.643063 0.765813i \(-0.277663\pi\)
0.643063 + 0.765813i \(0.277663\pi\)
\(348\) −13.1629 −0.705608
\(349\) −5.85393 −0.313354 −0.156677 0.987650i \(-0.550078\pi\)
−0.156677 + 0.987650i \(0.550078\pi\)
\(350\) −3.71769 −0.198719
\(351\) 14.3215 0.764426
\(352\) −5.52957 −0.294727
\(353\) −13.8742 −0.738452 −0.369226 0.929340i \(-0.620377\pi\)
−0.369226 + 0.929340i \(0.620377\pi\)
\(354\) −3.21270 −0.170753
\(355\) −2.86767 −0.152200
\(356\) 3.58473 0.189990
\(357\) −32.9972 −1.74640
\(358\) −12.6474 −0.668435
\(359\) −19.9793 −1.05447 −0.527234 0.849720i \(-0.676771\pi\)
−0.527234 + 0.849720i \(0.676771\pi\)
\(360\) 0.630528 0.0332317
\(361\) −5.62631 −0.296121
\(362\) −4.07323 −0.214084
\(363\) −30.1338 −1.58161
\(364\) −9.52722 −0.499362
\(365\) 3.21969 0.168526
\(366\) −14.5729 −0.761737
\(367\) 5.43074 0.283482 0.141741 0.989904i \(-0.454730\pi\)
0.141741 + 0.989904i \(0.454730\pi\)
\(368\) 0 0
\(369\) 7.18434 0.374002
\(370\) −0.490152 −0.0254818
\(371\) −3.06662 −0.159211
\(372\) 14.2294 0.737760
\(373\) −30.6865 −1.58889 −0.794444 0.607337i \(-0.792238\pi\)
−0.794444 + 0.607337i \(0.792238\pi\)
\(374\) 31.8838 1.64867
\(375\) 1.53931 0.0794896
\(376\) −9.73542 −0.502066
\(377\) 21.9140 1.12863
\(378\) −20.7763 −1.06862
\(379\) 11.4897 0.590188 0.295094 0.955468i \(-0.404649\pi\)
0.295094 + 0.955468i \(0.404649\pi\)
\(380\) 3.65701 0.187600
\(381\) 3.79321 0.194332
\(382\) −6.14225 −0.314265
\(383\) −10.6061 −0.541944 −0.270972 0.962587i \(-0.587345\pi\)
−0.270972 + 0.962587i \(0.587345\pi\)
\(384\) −1.53931 −0.0785525
\(385\) −20.5572 −1.04769
\(386\) 6.53510 0.332628
\(387\) 5.70091 0.289794
\(388\) 2.55727 0.129826
\(389\) −36.6757 −1.85953 −0.929766 0.368152i \(-0.879991\pi\)
−0.929766 + 0.368152i \(0.879991\pi\)
\(390\) 3.94475 0.199750
\(391\) 0 0
\(392\) 6.82119 0.344522
\(393\) −33.6935 −1.69961
\(394\) 4.45551 0.224466
\(395\) −6.94974 −0.349680
\(396\) 3.48655 0.175206
\(397\) −4.28172 −0.214893 −0.107447 0.994211i \(-0.534268\pi\)
−0.107447 + 0.994211i \(0.534268\pi\)
\(398\) −15.1131 −0.757553
\(399\) −20.9278 −1.04770
\(400\) 1.00000 0.0500000
\(401\) 27.0327 1.34995 0.674975 0.737840i \(-0.264154\pi\)
0.674975 + 0.737840i \(0.264154\pi\)
\(402\) 1.76518 0.0880394
\(403\) −23.6894 −1.18005
\(404\) −6.99569 −0.348048
\(405\) 6.71085 0.333465
\(406\) −31.7907 −1.57775
\(407\) −2.71033 −0.134346
\(408\) 8.87574 0.439414
\(409\) −26.7573 −1.32306 −0.661532 0.749917i \(-0.730094\pi\)
−0.661532 + 0.749917i \(0.730094\pi\)
\(410\) 11.3942 0.562718
\(411\) −4.63800 −0.228776
\(412\) −1.74044 −0.0857455
\(413\) −7.75919 −0.381805
\(414\) 0 0
\(415\) −9.86488 −0.484248
\(416\) 2.56268 0.125646
\(417\) 9.13705 0.447443
\(418\) 20.2217 0.989075
\(419\) −4.58163 −0.223827 −0.111914 0.993718i \(-0.535698\pi\)
−0.111914 + 0.993718i \(0.535698\pi\)
\(420\) −5.72267 −0.279238
\(421\) −14.5615 −0.709686 −0.354843 0.934926i \(-0.615466\pi\)
−0.354843 + 0.934926i \(0.615466\pi\)
\(422\) −8.59548 −0.418421
\(423\) 6.13845 0.298462
\(424\) 0.824873 0.0400594
\(425\) −5.76605 −0.279695
\(426\) −4.41424 −0.213870
\(427\) −35.1959 −1.70325
\(428\) 1.08182 0.0522919
\(429\) 21.8128 1.05313
\(430\) 9.04149 0.436019
\(431\) −8.19202 −0.394596 −0.197298 0.980344i \(-0.563217\pi\)
−0.197298 + 0.980344i \(0.563217\pi\)
\(432\) 5.58850 0.268877
\(433\) 4.11382 0.197697 0.0988487 0.995102i \(-0.468484\pi\)
0.0988487 + 0.995102i \(0.468484\pi\)
\(434\) 34.3664 1.64964
\(435\) 13.1629 0.631115
\(436\) 2.33737 0.111940
\(437\) 0 0
\(438\) 4.95609 0.236811
\(439\) −7.79137 −0.371862 −0.185931 0.982563i \(-0.559530\pi\)
−0.185931 + 0.982563i \(0.559530\pi\)
\(440\) 5.52957 0.263612
\(441\) −4.30095 −0.204807
\(442\) −14.7765 −0.702847
\(443\) 36.6224 1.73998 0.869991 0.493068i \(-0.164124\pi\)
0.869991 + 0.493068i \(0.164124\pi\)
\(444\) −0.754496 −0.0358068
\(445\) −3.58473 −0.169932
\(446\) 1.23633 0.0585418
\(447\) −2.29862 −0.108721
\(448\) −3.71769 −0.175644
\(449\) 3.52535 0.166371 0.0831857 0.996534i \(-0.473491\pi\)
0.0831857 + 0.996534i \(0.473491\pi\)
\(450\) −0.630528 −0.0297234
\(451\) 63.0048 2.96678
\(452\) 16.0040 0.752766
\(453\) 24.0727 1.13103
\(454\) 21.1727 0.993683
\(455\) 9.52722 0.446643
\(456\) 5.62926 0.263614
\(457\) 30.5111 1.42725 0.713624 0.700529i \(-0.247052\pi\)
0.713624 + 0.700529i \(0.247052\pi\)
\(458\) −11.2218 −0.524360
\(459\) −32.2236 −1.50407
\(460\) 0 0
\(461\) −6.50868 −0.303139 −0.151570 0.988447i \(-0.548433\pi\)
−0.151570 + 0.988447i \(0.548433\pi\)
\(462\) −31.6439 −1.47221
\(463\) 4.72959 0.219803 0.109901 0.993942i \(-0.464946\pi\)
0.109901 + 0.993942i \(0.464946\pi\)
\(464\) 8.55120 0.396980
\(465\) −14.2294 −0.659873
\(466\) 1.43374 0.0664169
\(467\) 26.7107 1.23602 0.618011 0.786169i \(-0.287939\pi\)
0.618011 + 0.786169i \(0.287939\pi\)
\(468\) −1.61584 −0.0746921
\(469\) 4.26321 0.196857
\(470\) 9.73542 0.449061
\(471\) −9.40030 −0.433143
\(472\) 2.08710 0.0960667
\(473\) 49.9956 2.29880
\(474\) −10.6978 −0.491366
\(475\) −3.65701 −0.167795
\(476\) 21.4364 0.982535
\(477\) −0.520105 −0.0238140
\(478\) −6.91805 −0.316424
\(479\) −8.12800 −0.371378 −0.185689 0.982609i \(-0.559452\pi\)
−0.185689 + 0.982609i \(0.559452\pi\)
\(480\) 1.53931 0.0702595
\(481\) 1.25610 0.0572733
\(482\) −16.4852 −0.750881
\(483\) 0 0
\(484\) 19.5762 0.889826
\(485\) −2.55727 −0.116120
\(486\) −6.43544 −0.291917
\(487\) −7.40083 −0.335364 −0.167682 0.985841i \(-0.553628\pi\)
−0.167682 + 0.985841i \(0.553628\pi\)
\(488\) 9.46716 0.428558
\(489\) −25.2527 −1.14197
\(490\) −6.82119 −0.308150
\(491\) −25.9839 −1.17264 −0.586318 0.810081i \(-0.699423\pi\)
−0.586318 + 0.810081i \(0.699423\pi\)
\(492\) 17.5391 0.790725
\(493\) −49.3067 −2.22066
\(494\) −9.37172 −0.421654
\(495\) −3.48655 −0.156709
\(496\) −9.24402 −0.415069
\(497\) −10.6611 −0.478216
\(498\) −15.1851 −0.680460
\(499\) −34.5272 −1.54565 −0.772824 0.634620i \(-0.781157\pi\)
−0.772824 + 0.634620i \(0.781157\pi\)
\(500\) −1.00000 −0.0447214
\(501\) 22.0946 0.987115
\(502\) 21.1825 0.945420
\(503\) −6.49298 −0.289508 −0.144754 0.989468i \(-0.546239\pi\)
−0.144754 + 0.989468i \(0.546239\pi\)
\(504\) 2.34410 0.104415
\(505\) 6.99569 0.311304
\(506\) 0 0
\(507\) 9.90190 0.439759
\(508\) −2.46423 −0.109332
\(509\) 29.0414 1.28724 0.643620 0.765345i \(-0.277432\pi\)
0.643620 + 0.765345i \(0.277432\pi\)
\(510\) −8.87574 −0.393024
\(511\) 11.9698 0.529512
\(512\) 1.00000 0.0441942
\(513\) −20.4372 −0.902324
\(514\) 0.629630 0.0277718
\(515\) 1.74044 0.0766931
\(516\) 13.9176 0.612690
\(517\) 53.8327 2.36756
\(518\) −1.82223 −0.0800643
\(519\) 16.0122 0.702857
\(520\) −2.56268 −0.112381
\(521\) −30.2264 −1.32424 −0.662121 0.749397i \(-0.730343\pi\)
−0.662121 + 0.749397i \(0.730343\pi\)
\(522\) −5.39177 −0.235991
\(523\) −15.3474 −0.671094 −0.335547 0.942024i \(-0.608921\pi\)
−0.335547 + 0.942024i \(0.608921\pi\)
\(524\) 21.8887 0.956214
\(525\) 5.72267 0.249758
\(526\) 26.2962 1.14657
\(527\) 53.3015 2.32185
\(528\) 8.51172 0.370425
\(529\) 0 0
\(530\) −0.824873 −0.0358302
\(531\) −1.31598 −0.0571085
\(532\) 13.5956 0.589444
\(533\) −29.1995 −1.26477
\(534\) −5.51801 −0.238788
\(535\) −1.08182 −0.0467713
\(536\) −1.14674 −0.0495316
\(537\) 19.4682 0.840116
\(538\) 26.6135 1.14739
\(539\) −37.7183 −1.62464
\(540\) −5.58850 −0.240491
\(541\) 12.3830 0.532386 0.266193 0.963920i \(-0.414234\pi\)
0.266193 + 0.963920i \(0.414234\pi\)
\(542\) 9.82645 0.422082
\(543\) 6.26995 0.269070
\(544\) −5.76605 −0.247217
\(545\) −2.33737 −0.100122
\(546\) 14.6653 0.627619
\(547\) −13.3181 −0.569439 −0.284720 0.958611i \(-0.591901\pi\)
−0.284720 + 0.958611i \(0.591901\pi\)
\(548\) 3.01304 0.128711
\(549\) −5.96931 −0.254764
\(550\) −5.52957 −0.235782
\(551\) −31.2718 −1.33222
\(552\) 0 0
\(553\) −25.8370 −1.09870
\(554\) 11.7531 0.499343
\(555\) 0.754496 0.0320266
\(556\) −5.93581 −0.251734
\(557\) 20.8720 0.884375 0.442188 0.896923i \(-0.354203\pi\)
0.442188 + 0.896923i \(0.354203\pi\)
\(558\) 5.82861 0.246745
\(559\) −23.1704 −0.980004
\(560\) 3.71769 0.157101
\(561\) −49.0790 −2.07212
\(562\) −14.7365 −0.621620
\(563\) 2.67269 0.112641 0.0563203 0.998413i \(-0.482063\pi\)
0.0563203 + 0.998413i \(0.482063\pi\)
\(564\) 14.9858 0.631017
\(565\) −16.0040 −0.673294
\(566\) −2.06989 −0.0870040
\(567\) 24.9488 1.04775
\(568\) 2.86767 0.120325
\(569\) −17.1915 −0.720704 −0.360352 0.932816i \(-0.617343\pi\)
−0.360352 + 0.932816i \(0.617343\pi\)
\(570\) −5.62926 −0.235784
\(571\) −26.3607 −1.10316 −0.551581 0.834121i \(-0.685975\pi\)
−0.551581 + 0.834121i \(0.685975\pi\)
\(572\) −14.1705 −0.592498
\(573\) 9.45483 0.394981
\(574\) 42.3599 1.76807
\(575\) 0 0
\(576\) −0.630528 −0.0262720
\(577\) 14.4867 0.603087 0.301544 0.953452i \(-0.402498\pi\)
0.301544 + 0.953452i \(0.402498\pi\)
\(578\) 16.2474 0.675801
\(579\) −10.0595 −0.418060
\(580\) −8.55120 −0.355069
\(581\) −36.6745 −1.52152
\(582\) −3.93642 −0.163170
\(583\) −4.56119 −0.188905
\(584\) −3.21969 −0.133232
\(585\) 1.61584 0.0668067
\(586\) −20.4438 −0.844525
\(587\) 9.94004 0.410269 0.205135 0.978734i \(-0.434237\pi\)
0.205135 + 0.978734i \(0.434237\pi\)
\(588\) −10.4999 −0.433010
\(589\) 33.8054 1.39293
\(590\) −2.08710 −0.0859246
\(591\) −6.85841 −0.282117
\(592\) 0.490152 0.0201451
\(593\) 17.2518 0.708445 0.354222 0.935161i \(-0.384746\pi\)
0.354222 + 0.935161i \(0.384746\pi\)
\(594\) −30.9020 −1.26793
\(595\) −21.4364 −0.878806
\(596\) 1.49328 0.0611671
\(597\) 23.2638 0.952123
\(598\) 0 0
\(599\) −7.22276 −0.295114 −0.147557 0.989054i \(-0.547141\pi\)
−0.147557 + 0.989054i \(0.547141\pi\)
\(600\) −1.53931 −0.0628420
\(601\) −23.4338 −0.955886 −0.477943 0.878391i \(-0.658618\pi\)
−0.477943 + 0.878391i \(0.658618\pi\)
\(602\) 33.6134 1.36998
\(603\) 0.723050 0.0294449
\(604\) −15.6386 −0.636326
\(605\) −19.5762 −0.795884
\(606\) 10.7685 0.437441
\(607\) 32.4537 1.31726 0.658628 0.752468i \(-0.271137\pi\)
0.658628 + 0.752468i \(0.271137\pi\)
\(608\) −3.65701 −0.148311
\(609\) 48.9357 1.98297
\(610\) −9.46716 −0.383314
\(611\) −24.9487 −1.00932
\(612\) 3.63566 0.146963
\(613\) −5.76585 −0.232881 −0.116440 0.993198i \(-0.537148\pi\)
−0.116440 + 0.993198i \(0.537148\pi\)
\(614\) −9.37242 −0.378240
\(615\) −17.5391 −0.707246
\(616\) 20.5572 0.828274
\(617\) −1.34969 −0.0543365 −0.0271682 0.999631i \(-0.508649\pi\)
−0.0271682 + 0.999631i \(0.508649\pi\)
\(618\) 2.67908 0.107768
\(619\) 14.7990 0.594822 0.297411 0.954750i \(-0.403877\pi\)
0.297411 + 0.954750i \(0.403877\pi\)
\(620\) 9.24402 0.371249
\(621\) 0 0
\(622\) 7.48356 0.300064
\(623\) −13.3269 −0.533931
\(624\) −3.94475 −0.157916
\(625\) 1.00000 0.0400000
\(626\) −2.78633 −0.111364
\(627\) −31.1274 −1.24311
\(628\) 6.10683 0.243689
\(629\) −2.82624 −0.112690
\(630\) −2.34410 −0.0933914
\(631\) −15.8874 −0.632469 −0.316235 0.948681i \(-0.602419\pi\)
−0.316235 + 0.948681i \(0.602419\pi\)
\(632\) 6.94974 0.276446
\(633\) 13.2311 0.525889
\(634\) 15.8539 0.629637
\(635\) 2.46423 0.0977899
\(636\) −1.26973 −0.0503482
\(637\) 17.4805 0.692603
\(638\) −47.2845 −1.87201
\(639\) −1.80815 −0.0715292
\(640\) −1.00000 −0.0395285
\(641\) −17.0653 −0.674040 −0.337020 0.941498i \(-0.609419\pi\)
−0.337020 + 0.941498i \(0.609419\pi\)
\(642\) −1.66526 −0.0657226
\(643\) 40.2129 1.58584 0.792920 0.609326i \(-0.208560\pi\)
0.792920 + 0.609326i \(0.208560\pi\)
\(644\) 0 0
\(645\) −13.9176 −0.548007
\(646\) 21.0865 0.829637
\(647\) −44.6393 −1.75495 −0.877475 0.479622i \(-0.840774\pi\)
−0.877475 + 0.479622i \(0.840774\pi\)
\(648\) −6.71085 −0.263627
\(649\) −11.5408 −0.453015
\(650\) 2.56268 0.100516
\(651\) −52.9005 −2.07333
\(652\) 16.4053 0.642479
\(653\) −21.1084 −0.826034 −0.413017 0.910723i \(-0.635525\pi\)
−0.413017 + 0.910723i \(0.635525\pi\)
\(654\) −3.59794 −0.140691
\(655\) −21.8887 −0.855264
\(656\) −11.3942 −0.444867
\(657\) 2.03010 0.0792018
\(658\) 36.1932 1.41096
\(659\) −15.9775 −0.622394 −0.311197 0.950345i \(-0.600730\pi\)
−0.311197 + 0.950345i \(0.600730\pi\)
\(660\) −8.51172 −0.331318
\(661\) 13.4394 0.522734 0.261367 0.965240i \(-0.415827\pi\)
0.261367 + 0.965240i \(0.415827\pi\)
\(662\) −10.9915 −0.427198
\(663\) 22.7456 0.883367
\(664\) 9.86488 0.382832
\(665\) −13.5956 −0.527215
\(666\) −0.309055 −0.0119756
\(667\) 0 0
\(668\) −14.3536 −0.555357
\(669\) −1.90309 −0.0735777
\(670\) 1.14674 0.0443024
\(671\) −52.3494 −2.02092
\(672\) 5.72267 0.220757
\(673\) 33.0607 1.27440 0.637198 0.770700i \(-0.280093\pi\)
0.637198 + 0.770700i \(0.280093\pi\)
\(674\) 24.4167 0.940495
\(675\) 5.58850 0.215102
\(676\) −6.43269 −0.247411
\(677\) 30.4215 1.16919 0.584596 0.811324i \(-0.301253\pi\)
0.584596 + 0.811324i \(0.301253\pi\)
\(678\) −24.6351 −0.946107
\(679\) −9.50712 −0.364850
\(680\) 5.76605 0.221118
\(681\) −32.5913 −1.24890
\(682\) 51.1155 1.95731
\(683\) −47.2669 −1.80862 −0.904309 0.426879i \(-0.859613\pi\)
−0.904309 + 0.426879i \(0.859613\pi\)
\(684\) 2.30584 0.0881661
\(685\) −3.01304 −0.115122
\(686\) 0.664752 0.0253803
\(687\) 17.2738 0.659037
\(688\) −9.04149 −0.344704
\(689\) 2.11388 0.0805325
\(690\) 0 0
\(691\) −16.7843 −0.638507 −0.319253 0.947669i \(-0.603432\pi\)
−0.319253 + 0.947669i \(0.603432\pi\)
\(692\) −10.4022 −0.395432
\(693\) −12.9619 −0.492382
\(694\) 23.9579 0.909428
\(695\) 5.93581 0.225158
\(696\) −13.1629 −0.498940
\(697\) 65.6993 2.48854
\(698\) −5.85393 −0.221575
\(699\) −2.20697 −0.0834754
\(700\) −3.71769 −0.140515
\(701\) −12.8024 −0.483540 −0.241770 0.970334i \(-0.577728\pi\)
−0.241770 + 0.970334i \(0.577728\pi\)
\(702\) 14.3215 0.540531
\(703\) −1.79249 −0.0676050
\(704\) −5.52957 −0.208404
\(705\) −14.9858 −0.564398
\(706\) −13.8742 −0.522164
\(707\) 26.0078 0.978123
\(708\) −3.21270 −0.120740
\(709\) −25.6434 −0.963060 −0.481530 0.876430i \(-0.659919\pi\)
−0.481530 + 0.876430i \(0.659919\pi\)
\(710\) −2.86767 −0.107622
\(711\) −4.38201 −0.164338
\(712\) 3.58473 0.134343
\(713\) 0 0
\(714\) −32.9972 −1.23489
\(715\) 14.1705 0.529947
\(716\) −12.6474 −0.472655
\(717\) 10.6490 0.397695
\(718\) −19.9793 −0.745622
\(719\) 38.7793 1.44622 0.723112 0.690730i \(-0.242711\pi\)
0.723112 + 0.690730i \(0.242711\pi\)
\(720\) 0.630528 0.0234984
\(721\) 6.47042 0.240971
\(722\) −5.62631 −0.209389
\(723\) 25.3758 0.943737
\(724\) −4.07323 −0.151380
\(725\) 8.55120 0.317584
\(726\) −30.1338 −1.11837
\(727\) −22.2487 −0.825159 −0.412579 0.910922i \(-0.635372\pi\)
−0.412579 + 0.910922i \(0.635372\pi\)
\(728\) −9.52722 −0.353102
\(729\) 30.0387 1.11254
\(730\) 3.21969 0.119166
\(731\) 52.1337 1.92823
\(732\) −14.5729 −0.538629
\(733\) 3.98219 0.147086 0.0735428 0.997292i \(-0.476569\pi\)
0.0735428 + 0.997292i \(0.476569\pi\)
\(734\) 5.43074 0.200452
\(735\) 10.4999 0.387295
\(736\) 0 0
\(737\) 6.34097 0.233573
\(738\) 7.18434 0.264459
\(739\) −46.1521 −1.69773 −0.848867 0.528606i \(-0.822715\pi\)
−0.848867 + 0.528606i \(0.822715\pi\)
\(740\) −0.490152 −0.0180184
\(741\) 14.4260 0.529951
\(742\) −3.06662 −0.112579
\(743\) 46.1168 1.69186 0.845931 0.533292i \(-0.179045\pi\)
0.845931 + 0.533292i \(0.179045\pi\)
\(744\) 14.2294 0.521675
\(745\) −1.49328 −0.0547095
\(746\) −30.6865 −1.12351
\(747\) −6.22008 −0.227581
\(748\) 31.8838 1.16579
\(749\) −4.02188 −0.146956
\(750\) 1.53931 0.0562076
\(751\) 48.1341 1.75644 0.878219 0.478259i \(-0.158732\pi\)
0.878219 + 0.478259i \(0.158732\pi\)
\(752\) −9.73542 −0.355014
\(753\) −32.6064 −1.18824
\(754\) 21.9140 0.798059
\(755\) 15.6386 0.569147
\(756\) −20.7763 −0.755627
\(757\) 16.9349 0.615511 0.307755 0.951466i \(-0.400422\pi\)
0.307755 + 0.951466i \(0.400422\pi\)
\(758\) 11.4897 0.417326
\(759\) 0 0
\(760\) 3.65701 0.132654
\(761\) 19.3763 0.702390 0.351195 0.936302i \(-0.385775\pi\)
0.351195 + 0.936302i \(0.385775\pi\)
\(762\) 3.79321 0.137413
\(763\) −8.68962 −0.314585
\(764\) −6.14225 −0.222219
\(765\) −3.63566 −0.131447
\(766\) −10.6061 −0.383213
\(767\) 5.34857 0.193126
\(768\) −1.53931 −0.0555450
\(769\) 35.5736 1.28282 0.641408 0.767200i \(-0.278351\pi\)
0.641408 + 0.767200i \(0.278351\pi\)
\(770\) −20.5572 −0.740831
\(771\) −0.969195 −0.0349047
\(772\) 6.53510 0.235203
\(773\) −10.4461 −0.375721 −0.187860 0.982196i \(-0.560155\pi\)
−0.187860 + 0.982196i \(0.560155\pi\)
\(774\) 5.70091 0.204915
\(775\) −9.24402 −0.332055
\(776\) 2.55727 0.0918005
\(777\) 2.80498 0.100628
\(778\) −36.6757 −1.31489
\(779\) 41.6685 1.49293
\(780\) 3.94475 0.141245
\(781\) −15.8570 −0.567408
\(782\) 0 0
\(783\) 47.7884 1.70782
\(784\) 6.82119 0.243614
\(785\) −6.10683 −0.217962
\(786\) −33.6935 −1.20181
\(787\) 7.02667 0.250474 0.125237 0.992127i \(-0.460031\pi\)
0.125237 + 0.992127i \(0.460031\pi\)
\(788\) 4.45551 0.158721
\(789\) −40.4780 −1.44105
\(790\) −6.94974 −0.247261
\(791\) −59.4979 −2.11550
\(792\) 3.48655 0.123889
\(793\) 24.2613 0.861543
\(794\) −4.28172 −0.151953
\(795\) 1.26973 0.0450328
\(796\) −15.1131 −0.535671
\(797\) −47.1489 −1.67010 −0.835049 0.550175i \(-0.814561\pi\)
−0.835049 + 0.550175i \(0.814561\pi\)
\(798\) −20.9278 −0.740837
\(799\) 56.1349 1.98591
\(800\) 1.00000 0.0353553
\(801\) −2.26027 −0.0798628
\(802\) 27.0327 0.954559
\(803\) 17.8035 0.628271
\(804\) 1.76518 0.0622533
\(805\) 0 0
\(806\) −23.6894 −0.834424
\(807\) −40.9664 −1.44209
\(808\) −6.99569 −0.246107
\(809\) 24.3207 0.855070 0.427535 0.903999i \(-0.359382\pi\)
0.427535 + 0.903999i \(0.359382\pi\)
\(810\) 6.71085 0.235795
\(811\) −47.9783 −1.68475 −0.842373 0.538894i \(-0.818842\pi\)
−0.842373 + 0.538894i \(0.818842\pi\)
\(812\) −31.7907 −1.11563
\(813\) −15.1259 −0.530490
\(814\) −2.71033 −0.0949971
\(815\) −16.4053 −0.574651
\(816\) 8.87574 0.310713
\(817\) 33.0648 1.15679
\(818\) −26.7573 −0.935548
\(819\) 6.00718 0.209908
\(820\) 11.3942 0.397901
\(821\) 35.9961 1.25627 0.628137 0.778103i \(-0.283818\pi\)
0.628137 + 0.778103i \(0.283818\pi\)
\(822\) −4.63800 −0.161769
\(823\) −26.6789 −0.929967 −0.464984 0.885319i \(-0.653940\pi\)
−0.464984 + 0.885319i \(0.653940\pi\)
\(824\) −1.74044 −0.0606312
\(825\) 8.51172 0.296340
\(826\) −7.75919 −0.269977
\(827\) −1.18494 −0.0412043 −0.0206021 0.999788i \(-0.506558\pi\)
−0.0206021 + 0.999788i \(0.506558\pi\)
\(828\) 0 0
\(829\) 11.1131 0.385974 0.192987 0.981201i \(-0.438182\pi\)
0.192987 + 0.981201i \(0.438182\pi\)
\(830\) −9.86488 −0.342415
\(831\) −18.0917 −0.627595
\(832\) 2.56268 0.0888448
\(833\) −39.3314 −1.36275
\(834\) 9.13705 0.316390
\(835\) 14.3536 0.496727
\(836\) 20.2217 0.699381
\(837\) −51.6603 −1.78564
\(838\) −4.58163 −0.158270
\(839\) −24.1312 −0.833103 −0.416552 0.909112i \(-0.636761\pi\)
−0.416552 + 0.909112i \(0.636761\pi\)
\(840\) −5.72267 −0.197451
\(841\) 44.1231 1.52149
\(842\) −14.5615 −0.501824
\(843\) 22.6840 0.781277
\(844\) −8.59548 −0.295868
\(845\) 6.43269 0.221291
\(846\) 6.13845 0.211044
\(847\) −72.7781 −2.50068
\(848\) 0.824873 0.0283263
\(849\) 3.18620 0.109350
\(850\) −5.76605 −0.197774
\(851\) 0 0
\(852\) −4.41424 −0.151229
\(853\) −48.2825 −1.65316 −0.826581 0.562818i \(-0.809717\pi\)
−0.826581 + 0.562818i \(0.809717\pi\)
\(854\) −35.1959 −1.20438
\(855\) −2.30584 −0.0788582
\(856\) 1.08182 0.0369760
\(857\) −21.2639 −0.726362 −0.363181 0.931719i \(-0.618309\pi\)
−0.363181 + 0.931719i \(0.618309\pi\)
\(858\) 21.8128 0.744676
\(859\) 5.40004 0.184247 0.0921236 0.995748i \(-0.470635\pi\)
0.0921236 + 0.995748i \(0.470635\pi\)
\(860\) 9.04149 0.308312
\(861\) −65.2050 −2.22218
\(862\) −8.19202 −0.279021
\(863\) −42.7775 −1.45616 −0.728082 0.685490i \(-0.759588\pi\)
−0.728082 + 0.685490i \(0.759588\pi\)
\(864\) 5.58850 0.190125
\(865\) 10.4022 0.353685
\(866\) 4.11382 0.139793
\(867\) −25.0097 −0.849374
\(868\) 34.3664 1.16647
\(869\) −38.4291 −1.30362
\(870\) 13.1629 0.446266
\(871\) −2.93872 −0.0995747
\(872\) 2.33737 0.0791535
\(873\) −1.61243 −0.0545724
\(874\) 0 0
\(875\) 3.71769 0.125681
\(876\) 4.95609 0.167451
\(877\) 15.4981 0.523334 0.261667 0.965158i \(-0.415728\pi\)
0.261667 + 0.965158i \(0.415728\pi\)
\(878\) −7.79137 −0.262946
\(879\) 31.4693 1.06143
\(880\) 5.52957 0.186402
\(881\) −6.24048 −0.210247 −0.105124 0.994459i \(-0.533524\pi\)
−0.105124 + 0.994459i \(0.533524\pi\)
\(882\) −4.30095 −0.144821
\(883\) 14.4886 0.487582 0.243791 0.969828i \(-0.421609\pi\)
0.243791 + 0.969828i \(0.421609\pi\)
\(884\) −14.7765 −0.496988
\(885\) 3.21270 0.107994
\(886\) 36.6224 1.23035
\(887\) −1.33272 −0.0447483 −0.0223741 0.999750i \(-0.507123\pi\)
−0.0223741 + 0.999750i \(0.507123\pi\)
\(888\) −0.754496 −0.0253192
\(889\) 9.16122 0.307258
\(890\) −3.58473 −0.120160
\(891\) 37.1081 1.24317
\(892\) 1.23633 0.0413953
\(893\) 35.6025 1.19139
\(894\) −2.29862 −0.0768772
\(895\) 12.6474 0.422755
\(896\) −3.71769 −0.124199
\(897\) 0 0
\(898\) 3.52535 0.117642
\(899\) −79.0475 −2.63638
\(900\) −0.630528 −0.0210176
\(901\) −4.75626 −0.158454
\(902\) 63.0048 2.09783
\(903\) −51.7414 −1.72185
\(904\) 16.0040 0.532286
\(905\) 4.07323 0.135399
\(906\) 24.0727 0.799761
\(907\) 26.5828 0.882667 0.441334 0.897343i \(-0.354506\pi\)
0.441334 + 0.897343i \(0.354506\pi\)
\(908\) 21.1727 0.702640
\(909\) 4.41097 0.146303
\(910\) 9.52722 0.315824
\(911\) −10.9950 −0.364282 −0.182141 0.983272i \(-0.558303\pi\)
−0.182141 + 0.983272i \(0.558303\pi\)
\(912\) 5.62926 0.186404
\(913\) −54.5486 −1.80529
\(914\) 30.5111 1.00922
\(915\) 14.5729 0.481765
\(916\) −11.2218 −0.370779
\(917\) −81.3755 −2.68725
\(918\) −32.2236 −1.06354
\(919\) −29.3494 −0.968148 −0.484074 0.875027i \(-0.660844\pi\)
−0.484074 + 0.875027i \(0.660844\pi\)
\(920\) 0 0
\(921\) 14.4271 0.475388
\(922\) −6.50868 −0.214352
\(923\) 7.34892 0.241893
\(924\) −31.6439 −1.04101
\(925\) 0.490152 0.0161161
\(926\) 4.72959 0.155424
\(927\) 1.09740 0.0360433
\(928\) 8.55120 0.280707
\(929\) 51.1379 1.67778 0.838889 0.544302i \(-0.183205\pi\)
0.838889 + 0.544302i \(0.183205\pi\)
\(930\) −14.2294 −0.466601
\(931\) −24.9451 −0.817544
\(932\) 1.43374 0.0469638
\(933\) −11.5195 −0.377132
\(934\) 26.7107 0.874000
\(935\) −31.8838 −1.04271
\(936\) −1.61584 −0.0528153
\(937\) 49.6173 1.62093 0.810464 0.585788i \(-0.199215\pi\)
0.810464 + 0.585788i \(0.199215\pi\)
\(938\) 4.26321 0.139199
\(939\) 4.28902 0.139967
\(940\) 9.73542 0.317534
\(941\) 19.5044 0.635824 0.317912 0.948120i \(-0.397018\pi\)
0.317912 + 0.948120i \(0.397018\pi\)
\(942\) −9.40030 −0.306278
\(943\) 0 0
\(944\) 2.08710 0.0679294
\(945\) 20.7763 0.675853
\(946\) 49.9956 1.62550
\(947\) 39.8475 1.29487 0.647435 0.762121i \(-0.275842\pi\)
0.647435 + 0.762121i \(0.275842\pi\)
\(948\) −10.6978 −0.347449
\(949\) −8.25101 −0.267839
\(950\) −3.65701 −0.118649
\(951\) −24.4040 −0.791354
\(952\) 21.4364 0.694757
\(953\) −33.7408 −1.09297 −0.546486 0.837469i \(-0.684035\pi\)
−0.546486 + 0.837469i \(0.684035\pi\)
\(954\) −0.520105 −0.0168390
\(955\) 6.14225 0.198759
\(956\) −6.91805 −0.223746
\(957\) 72.7854 2.35282
\(958\) −8.12800 −0.262604
\(959\) −11.2015 −0.361717
\(960\) 1.53931 0.0496810
\(961\) 54.4519 1.75651
\(962\) 1.25610 0.0404983
\(963\) −0.682120 −0.0219810
\(964\) −16.4852 −0.530953
\(965\) −6.53510 −0.210372
\(966\) 0 0
\(967\) 12.3031 0.395642 0.197821 0.980238i \(-0.436614\pi\)
0.197821 + 0.980238i \(0.436614\pi\)
\(968\) 19.5762 0.629202
\(969\) −32.4586 −1.04272
\(970\) −2.55727 −0.0821089
\(971\) −18.1012 −0.580896 −0.290448 0.956891i \(-0.593804\pi\)
−0.290448 + 0.956891i \(0.593804\pi\)
\(972\) −6.43544 −0.206417
\(973\) 22.0675 0.707451
\(974\) −7.40083 −0.237138
\(975\) −3.94475 −0.126333
\(976\) 9.46716 0.303036
\(977\) 40.8441 1.30672 0.653359 0.757048i \(-0.273359\pi\)
0.653359 + 0.757048i \(0.273359\pi\)
\(978\) −25.2527 −0.807494
\(979\) −19.8220 −0.633515
\(980\) −6.82119 −0.217895
\(981\) −1.47378 −0.0470541
\(982\) −25.9839 −0.829179
\(983\) 7.99453 0.254986 0.127493 0.991839i \(-0.459307\pi\)
0.127493 + 0.991839i \(0.459307\pi\)
\(984\) 17.5391 0.559127
\(985\) −4.45551 −0.141965
\(986\) −49.3067 −1.57024
\(987\) −55.7126 −1.77335
\(988\) −9.37172 −0.298154
\(989\) 0 0
\(990\) −3.48655 −0.110810
\(991\) 6.88475 0.218701 0.109351 0.994003i \(-0.465123\pi\)
0.109351 + 0.994003i \(0.465123\pi\)
\(992\) −9.24402 −0.293498
\(993\) 16.9194 0.536919
\(994\) −10.6611 −0.338150
\(995\) 15.1131 0.479118
\(996\) −15.1851 −0.481158
\(997\) −26.7299 −0.846544 −0.423272 0.906003i \(-0.639119\pi\)
−0.423272 + 0.906003i \(0.639119\pi\)
\(998\) −34.5272 −1.09294
\(999\) 2.73922 0.0866650
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 5290.2.a.bk.1.4 15
23.9 even 11 230.2.g.d.81.3 yes 30
23.18 even 11 230.2.g.d.71.3 30
23.22 odd 2 5290.2.a.bl.1.4 15
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
230.2.g.d.71.3 30 23.18 even 11
230.2.g.d.81.3 yes 30 23.9 even 11
5290.2.a.bk.1.4 15 1.1 even 1 trivial
5290.2.a.bl.1.4 15 23.22 odd 2