Properties

Label 1805.2.a.v.1.3
Level $1805$
Weight $2$
Character 1805.1
Self dual yes
Analytic conductor $14.413$
Analytic rank $0$
Dimension $9$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1805,2,Mod(1,1805)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1805, 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("1805.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1805 = 5 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1805.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: \(14.4129975648\)
Analytic rank: \(0\)
Dimension: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{9} - 3x^{8} - 6x^{7} + 16x^{6} + 12x^{5} - 27x^{4} - 8x^{3} + 15x^{2} - 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 95)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(1.30799\) of defining polynomial
Character \(\chi\) \(=\) 1805.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.307988 q^{2} -1.64392 q^{3} -1.90514 q^{4} +1.00000 q^{5} +0.506308 q^{6} +0.0891959 q^{7} +1.20274 q^{8} -0.297533 q^{9} +O(q^{10})\) \(q-0.307988 q^{2} -1.64392 q^{3} -1.90514 q^{4} +1.00000 q^{5} +0.506308 q^{6} +0.0891959 q^{7} +1.20274 q^{8} -0.297533 q^{9} -0.307988 q^{10} -3.36682 q^{11} +3.13190 q^{12} +0.212870 q^{13} -0.0274713 q^{14} -1.64392 q^{15} +3.43986 q^{16} -2.51423 q^{17} +0.0916368 q^{18} -1.90514 q^{20} -0.146631 q^{21} +1.03694 q^{22} -5.96699 q^{23} -1.97720 q^{24} +1.00000 q^{25} -0.0655615 q^{26} +5.42087 q^{27} -0.169931 q^{28} -4.80823 q^{29} +0.506308 q^{30} +8.06815 q^{31} -3.46491 q^{32} +5.53478 q^{33} +0.774354 q^{34} +0.0891959 q^{35} +0.566844 q^{36} +1.84372 q^{37} -0.349941 q^{39} +1.20274 q^{40} -3.01234 q^{41} +0.0451606 q^{42} -2.44787 q^{43} +6.41428 q^{44} -0.297533 q^{45} +1.83776 q^{46} -7.61831 q^{47} -5.65484 q^{48} -6.99204 q^{49} -0.307988 q^{50} +4.13319 q^{51} -0.405548 q^{52} -8.39967 q^{53} -1.66957 q^{54} -3.36682 q^{55} +0.107279 q^{56} +1.48088 q^{58} +10.4354 q^{59} +3.13190 q^{60} -0.988579 q^{61} -2.48490 q^{62} -0.0265388 q^{63} -5.81256 q^{64} +0.212870 q^{65} -1.70465 q^{66} +9.97964 q^{67} +4.78997 q^{68} +9.80923 q^{69} -0.0274713 q^{70} +6.17719 q^{71} -0.357855 q^{72} +15.7450 q^{73} -0.567844 q^{74} -1.64392 q^{75} -0.300307 q^{77} +0.107778 q^{78} -1.02849 q^{79} +3.43986 q^{80} -8.01887 q^{81} +0.927765 q^{82} +17.9388 q^{83} +0.279353 q^{84} -2.51423 q^{85} +0.753916 q^{86} +7.90434 q^{87} -4.04941 q^{88} +0.656354 q^{89} +0.0916368 q^{90} +0.0189871 q^{91} +11.3680 q^{92} -13.2634 q^{93} +2.34635 q^{94} +5.69603 q^{96} +16.8130 q^{97} +2.15347 q^{98} +1.00174 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9 q + 6 q^{2} + 9 q^{3} + 6 q^{4} + 9 q^{5} + 12 q^{6} + 6 q^{8} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 9 q + 6 q^{2} + 9 q^{3} + 6 q^{4} + 9 q^{5} + 12 q^{6} + 6 q^{8} + 6 q^{9} + 6 q^{10} + 18 q^{12} + 9 q^{13} + 9 q^{15} + 12 q^{16} - 9 q^{17} + 24 q^{18} + 6 q^{20} + 12 q^{21} + 24 q^{22} - 12 q^{23} + 3 q^{24} + 9 q^{25} - 3 q^{26} + 24 q^{27} - 15 q^{28} + 9 q^{29} + 12 q^{30} + 18 q^{31} + 3 q^{32} - 9 q^{33} - 24 q^{34} + 18 q^{36} + 18 q^{37} + 18 q^{39} + 6 q^{40} + 6 q^{41} - 12 q^{43} + 48 q^{44} + 6 q^{45} - 9 q^{46} + 15 q^{47} - 21 q^{48} - 9 q^{49} + 6 q^{50} - 6 q^{51} + 33 q^{52} + 15 q^{53} + 63 q^{54} + 6 q^{58} + 21 q^{59} + 18 q^{60} - 12 q^{61} - 36 q^{62} + 21 q^{63} - 36 q^{64} + 9 q^{65} + 3 q^{66} + 60 q^{67} - 51 q^{68} - 15 q^{69} - 18 q^{71} + 27 q^{73} + 27 q^{74} + 9 q^{75} - 30 q^{77} - 6 q^{78} + 15 q^{79} + 12 q^{80} + 33 q^{81} + 24 q^{82} - 48 q^{84} - 9 q^{85} - 39 q^{86} + 15 q^{87} + 27 q^{88} - 39 q^{89} + 24 q^{90} + 21 q^{91} - 6 q^{92} + 15 q^{93} + 15 q^{94} - 33 q^{96} + 15 q^{97} - 15 q^{98} - 36 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.307988 −0.217781 −0.108890 0.994054i \(-0.534730\pi\)
−0.108890 + 0.994054i \(0.534730\pi\)
\(3\) −1.64392 −0.949117 −0.474558 0.880224i \(-0.657392\pi\)
−0.474558 + 0.880224i \(0.657392\pi\)
\(4\) −1.90514 −0.952572
\(5\) 1.00000 0.447214
\(6\) 0.506308 0.206699
\(7\) 0.0891959 0.0337129 0.0168564 0.999858i \(-0.494634\pi\)
0.0168564 + 0.999858i \(0.494634\pi\)
\(8\) 1.20274 0.425232
\(9\) −0.297533 −0.0991778
\(10\) −0.307988 −0.0973945
\(11\) −3.36682 −1.01513 −0.507567 0.861612i \(-0.669455\pi\)
−0.507567 + 0.861612i \(0.669455\pi\)
\(12\) 3.13190 0.904101
\(13\) 0.212870 0.0590395 0.0295198 0.999564i \(-0.490602\pi\)
0.0295198 + 0.999564i \(0.490602\pi\)
\(14\) −0.0274713 −0.00734201
\(15\) −1.64392 −0.424458
\(16\) 3.43986 0.859964
\(17\) −2.51423 −0.609791 −0.304896 0.952386i \(-0.598622\pi\)
−0.304896 + 0.952386i \(0.598622\pi\)
\(18\) 0.0916368 0.0215990
\(19\) 0 0
\(20\) −1.90514 −0.426003
\(21\) −0.146631 −0.0319975
\(22\) 1.03694 0.221077
\(23\) −5.96699 −1.24420 −0.622101 0.782937i \(-0.713721\pi\)
−0.622101 + 0.782937i \(0.713721\pi\)
\(24\) −1.97720 −0.403595
\(25\) 1.00000 0.200000
\(26\) −0.0655615 −0.0128577
\(27\) 5.42087 1.04325
\(28\) −0.169931 −0.0321139
\(29\) −4.80823 −0.892866 −0.446433 0.894817i \(-0.647306\pi\)
−0.446433 + 0.894817i \(0.647306\pi\)
\(30\) 0.506308 0.0924387
\(31\) 8.06815 1.44908 0.724541 0.689232i \(-0.242052\pi\)
0.724541 + 0.689232i \(0.242052\pi\)
\(32\) −3.46491 −0.612516
\(33\) 5.53478 0.963481
\(34\) 0.774354 0.132801
\(35\) 0.0891959 0.0150769
\(36\) 0.566844 0.0944739
\(37\) 1.84372 0.303106 0.151553 0.988449i \(-0.451573\pi\)
0.151553 + 0.988449i \(0.451573\pi\)
\(38\) 0 0
\(39\) −0.349941 −0.0560354
\(40\) 1.20274 0.190170
\(41\) −3.01234 −0.470448 −0.235224 0.971941i \(-0.575582\pi\)
−0.235224 + 0.971941i \(0.575582\pi\)
\(42\) 0.0451606 0.00696842
\(43\) −2.44787 −0.373297 −0.186648 0.982427i \(-0.559763\pi\)
−0.186648 + 0.982427i \(0.559763\pi\)
\(44\) 6.41428 0.966989
\(45\) −0.297533 −0.0443537
\(46\) 1.83776 0.270963
\(47\) −7.61831 −1.11125 −0.555623 0.831435i \(-0.687520\pi\)
−0.555623 + 0.831435i \(0.687520\pi\)
\(48\) −5.65484 −0.816206
\(49\) −6.99204 −0.998863
\(50\) −0.307988 −0.0435561
\(51\) 4.13319 0.578763
\(52\) −0.405548 −0.0562394
\(53\) −8.39967 −1.15378 −0.576891 0.816821i \(-0.695734\pi\)
−0.576891 + 0.816821i \(0.695734\pi\)
\(54\) −1.66957 −0.227199
\(55\) −3.36682 −0.453982
\(56\) 0.107279 0.0143358
\(57\) 0 0
\(58\) 1.48088 0.194449
\(59\) 10.4354 1.35858 0.679289 0.733871i \(-0.262288\pi\)
0.679289 + 0.733871i \(0.262288\pi\)
\(60\) 3.13190 0.404326
\(61\) −0.988579 −0.126575 −0.0632873 0.997995i \(-0.520158\pi\)
−0.0632873 + 0.997995i \(0.520158\pi\)
\(62\) −2.48490 −0.315582
\(63\) −0.0265388 −0.00334357
\(64\) −5.81256 −0.726570
\(65\) 0.212870 0.0264033
\(66\) −1.70465 −0.209828
\(67\) 9.97964 1.21921 0.609604 0.792706i \(-0.291329\pi\)
0.609604 + 0.792706i \(0.291329\pi\)
\(68\) 4.78997 0.580870
\(69\) 9.80923 1.18089
\(70\) −0.0274713 −0.00328345
\(71\) 6.17719 0.733097 0.366549 0.930399i \(-0.380539\pi\)
0.366549 + 0.930399i \(0.380539\pi\)
\(72\) −0.357855 −0.0421736
\(73\) 15.7450 1.84281 0.921407 0.388600i \(-0.127041\pi\)
0.921407 + 0.388600i \(0.127041\pi\)
\(74\) −0.567844 −0.0660106
\(75\) −1.64392 −0.189823
\(76\) 0 0
\(77\) −0.300307 −0.0342231
\(78\) 0.107778 0.0122034
\(79\) −1.02849 −0.115715 −0.0578573 0.998325i \(-0.518427\pi\)
−0.0578573 + 0.998325i \(0.518427\pi\)
\(80\) 3.43986 0.384588
\(81\) −8.01887 −0.890986
\(82\) 0.927765 0.102455
\(83\) 17.9388 1.96904 0.984518 0.175284i \(-0.0560842\pi\)
0.984518 + 0.175284i \(0.0560842\pi\)
\(84\) 0.279353 0.0304799
\(85\) −2.51423 −0.272707
\(86\) 0.753916 0.0812968
\(87\) 7.90434 0.847434
\(88\) −4.04941 −0.431668
\(89\) 0.656354 0.0695734 0.0347867 0.999395i \(-0.488925\pi\)
0.0347867 + 0.999395i \(0.488925\pi\)
\(90\) 0.0916368 0.00965937
\(91\) 0.0189871 0.00199039
\(92\) 11.3680 1.18519
\(93\) −13.2634 −1.37535
\(94\) 2.34635 0.242008
\(95\) 0 0
\(96\) 5.69603 0.581349
\(97\) 16.8130 1.70711 0.853553 0.521006i \(-0.174443\pi\)
0.853553 + 0.521006i \(0.174443\pi\)
\(98\) 2.15347 0.217533
\(99\) 1.00174 0.100679
\(100\) −1.90514 −0.190514
\(101\) 3.67973 0.366146 0.183073 0.983099i \(-0.441395\pi\)
0.183073 + 0.983099i \(0.441395\pi\)
\(102\) −1.27298 −0.126043
\(103\) −3.53420 −0.348235 −0.174118 0.984725i \(-0.555707\pi\)
−0.174118 + 0.984725i \(0.555707\pi\)
\(104\) 0.256027 0.0251055
\(105\) −0.146631 −0.0143097
\(106\) 2.58700 0.251272
\(107\) −1.88660 −0.182385 −0.0911923 0.995833i \(-0.529068\pi\)
−0.0911923 + 0.995833i \(0.529068\pi\)
\(108\) −10.3275 −0.993768
\(109\) −13.1599 −1.26049 −0.630244 0.776397i \(-0.717045\pi\)
−0.630244 + 0.776397i \(0.717045\pi\)
\(110\) 1.03694 0.0988685
\(111\) −3.03093 −0.287683
\(112\) 0.306821 0.0289919
\(113\) 12.3456 1.16138 0.580689 0.814125i \(-0.302783\pi\)
0.580689 + 0.814125i \(0.302783\pi\)
\(114\) 0 0
\(115\) −5.96699 −0.556424
\(116\) 9.16037 0.850519
\(117\) −0.0633359 −0.00585541
\(118\) −3.21399 −0.295872
\(119\) −0.224259 −0.0205578
\(120\) −1.97720 −0.180493
\(121\) 0.335489 0.0304990
\(122\) 0.304471 0.0275655
\(123\) 4.95204 0.446510
\(124\) −15.3710 −1.38035
\(125\) 1.00000 0.0894427
\(126\) 0.00817363 0.000728164 0
\(127\) 21.2121 1.88227 0.941134 0.338035i \(-0.109762\pi\)
0.941134 + 0.338035i \(0.109762\pi\)
\(128\) 8.72003 0.770749
\(129\) 4.02410 0.354302
\(130\) −0.0655615 −0.00575012
\(131\) 6.95074 0.607289 0.303645 0.952785i \(-0.401796\pi\)
0.303645 + 0.952785i \(0.401796\pi\)
\(132\) −10.5445 −0.917785
\(133\) 0 0
\(134\) −3.07361 −0.265520
\(135\) 5.42087 0.466555
\(136\) −3.02396 −0.259303
\(137\) 21.0068 1.79474 0.897368 0.441283i \(-0.145477\pi\)
0.897368 + 0.441283i \(0.145477\pi\)
\(138\) −3.02113 −0.257176
\(139\) 15.7214 1.33347 0.666736 0.745294i \(-0.267691\pi\)
0.666736 + 0.745294i \(0.267691\pi\)
\(140\) −0.169931 −0.0143618
\(141\) 12.5239 1.05470
\(142\) −1.90250 −0.159654
\(143\) −0.716695 −0.0599331
\(144\) −1.02347 −0.0852894
\(145\) −4.80823 −0.399302
\(146\) −4.84928 −0.401329
\(147\) 11.4943 0.948038
\(148\) −3.51255 −0.288730
\(149\) −19.5194 −1.59909 −0.799546 0.600605i \(-0.794927\pi\)
−0.799546 + 0.600605i \(0.794927\pi\)
\(150\) 0.506308 0.0413398
\(151\) 11.2284 0.913758 0.456879 0.889529i \(-0.348967\pi\)
0.456879 + 0.889529i \(0.348967\pi\)
\(152\) 0 0
\(153\) 0.748068 0.0604777
\(154\) 0.0924909 0.00745313
\(155\) 8.06815 0.648049
\(156\) 0.666687 0.0533777
\(157\) 4.61281 0.368143 0.184071 0.982913i \(-0.441072\pi\)
0.184071 + 0.982913i \(0.441072\pi\)
\(158\) 0.316764 0.0252004
\(159\) 13.8084 1.09507
\(160\) −3.46491 −0.273925
\(161\) −0.532231 −0.0419456
\(162\) 2.46972 0.194039
\(163\) −0.574735 −0.0450167 −0.0225084 0.999747i \(-0.507165\pi\)
−0.0225084 + 0.999747i \(0.507165\pi\)
\(164\) 5.73894 0.448136
\(165\) 5.53478 0.430882
\(166\) −5.52493 −0.428818
\(167\) 4.12202 0.318971 0.159486 0.987200i \(-0.449016\pi\)
0.159486 + 0.987200i \(0.449016\pi\)
\(168\) −0.176358 −0.0136063
\(169\) −12.9547 −0.996514
\(170\) 0.774354 0.0593903
\(171\) 0 0
\(172\) 4.66355 0.355592
\(173\) −6.43458 −0.489212 −0.244606 0.969623i \(-0.578659\pi\)
−0.244606 + 0.969623i \(0.578659\pi\)
\(174\) −2.43444 −0.184555
\(175\) 0.0891959 0.00674258
\(176\) −11.5814 −0.872980
\(177\) −17.1550 −1.28945
\(178\) −0.202149 −0.0151517
\(179\) 3.83032 0.286291 0.143146 0.989702i \(-0.454278\pi\)
0.143146 + 0.989702i \(0.454278\pi\)
\(180\) 0.566844 0.0422500
\(181\) 16.6878 1.24039 0.620195 0.784447i \(-0.287053\pi\)
0.620195 + 0.784447i \(0.287053\pi\)
\(182\) −0.00584781 −0.000433469 0
\(183\) 1.62514 0.120134
\(184\) −7.17672 −0.529075
\(185\) 1.84372 0.135553
\(186\) 4.08496 0.299524
\(187\) 8.46497 0.619020
\(188\) 14.5140 1.05854
\(189\) 0.483520 0.0351709
\(190\) 0 0
\(191\) 7.92694 0.573573 0.286787 0.957994i \(-0.407413\pi\)
0.286787 + 0.957994i \(0.407413\pi\)
\(192\) 9.55538 0.689600
\(193\) −21.2669 −1.53082 −0.765412 0.643540i \(-0.777465\pi\)
−0.765412 + 0.643540i \(0.777465\pi\)
\(194\) −5.17822 −0.371775
\(195\) −0.349941 −0.0250598
\(196\) 13.3208 0.951489
\(197\) 2.88742 0.205720 0.102860 0.994696i \(-0.467201\pi\)
0.102860 + 0.994696i \(0.467201\pi\)
\(198\) −0.308525 −0.0219259
\(199\) 11.6149 0.823355 0.411678 0.911330i \(-0.364943\pi\)
0.411678 + 0.911330i \(0.364943\pi\)
\(200\) 1.20274 0.0850464
\(201\) −16.4057 −1.15717
\(202\) −1.13331 −0.0797396
\(203\) −0.428874 −0.0301011
\(204\) −7.87432 −0.551313
\(205\) −3.01234 −0.210391
\(206\) 1.08849 0.0758389
\(207\) 1.77538 0.123397
\(208\) 0.732242 0.0507719
\(209\) 0 0
\(210\) 0.0451606 0.00311637
\(211\) −23.7001 −1.63158 −0.815790 0.578349i \(-0.803697\pi\)
−0.815790 + 0.578349i \(0.803697\pi\)
\(212\) 16.0026 1.09906
\(213\) −10.1548 −0.695795
\(214\) 0.581051 0.0397198
\(215\) −2.44787 −0.166943
\(216\) 6.51989 0.443623
\(217\) 0.719646 0.0488527
\(218\) 4.05309 0.274510
\(219\) −25.8835 −1.74904
\(220\) 6.41428 0.432451
\(221\) −0.535205 −0.0360018
\(222\) 0.933490 0.0626517
\(223\) −8.81587 −0.590354 −0.295177 0.955443i \(-0.595379\pi\)
−0.295177 + 0.955443i \(0.595379\pi\)
\(224\) −0.309056 −0.0206497
\(225\) −0.297533 −0.0198356
\(226\) −3.80231 −0.252926
\(227\) −1.04512 −0.0693671 −0.0346835 0.999398i \(-0.511042\pi\)
−0.0346835 + 0.999398i \(0.511042\pi\)
\(228\) 0 0
\(229\) −13.4837 −0.891031 −0.445515 0.895274i \(-0.646980\pi\)
−0.445515 + 0.895274i \(0.646980\pi\)
\(230\) 1.83776 0.121178
\(231\) 0.493680 0.0324817
\(232\) −5.78304 −0.379675
\(233\) 11.2178 0.734905 0.367452 0.930042i \(-0.380230\pi\)
0.367452 + 0.930042i \(0.380230\pi\)
\(234\) 0.0195067 0.00127519
\(235\) −7.61831 −0.496964
\(236\) −19.8810 −1.29414
\(237\) 1.69076 0.109827
\(238\) 0.0690692 0.00447709
\(239\) −20.3290 −1.31497 −0.657487 0.753466i \(-0.728380\pi\)
−0.657487 + 0.753466i \(0.728380\pi\)
\(240\) −5.65484 −0.365019
\(241\) −3.84452 −0.247647 −0.123824 0.992304i \(-0.539516\pi\)
−0.123824 + 0.992304i \(0.539516\pi\)
\(242\) −0.103327 −0.00664209
\(243\) −3.08025 −0.197598
\(244\) 1.88339 0.120571
\(245\) −6.99204 −0.446705
\(246\) −1.52517 −0.0972413
\(247\) 0 0
\(248\) 9.70387 0.616197
\(249\) −29.4899 −1.86884
\(250\) −0.307988 −0.0194789
\(251\) −7.93776 −0.501027 −0.250513 0.968113i \(-0.580599\pi\)
−0.250513 + 0.968113i \(0.580599\pi\)
\(252\) 0.0505601 0.00318499
\(253\) 20.0898 1.26303
\(254\) −6.53307 −0.409921
\(255\) 4.13319 0.258831
\(256\) 8.93946 0.558716
\(257\) 24.2278 1.51129 0.755643 0.654984i \(-0.227325\pi\)
0.755643 + 0.654984i \(0.227325\pi\)
\(258\) −1.23938 −0.0771602
\(259\) 0.164452 0.0102186
\(260\) −0.405548 −0.0251510
\(261\) 1.43061 0.0885525
\(262\) −2.14075 −0.132256
\(263\) −12.3772 −0.763212 −0.381606 0.924325i \(-0.624629\pi\)
−0.381606 + 0.924325i \(0.624629\pi\)
\(264\) 6.65689 0.409703
\(265\) −8.39967 −0.515987
\(266\) 0 0
\(267\) −1.07899 −0.0660333
\(268\) −19.0127 −1.16138
\(269\) −24.3788 −1.48640 −0.743202 0.669067i \(-0.766694\pi\)
−0.743202 + 0.669067i \(0.766694\pi\)
\(270\) −1.66957 −0.101607
\(271\) 17.4183 1.05809 0.529043 0.848595i \(-0.322551\pi\)
0.529043 + 0.848595i \(0.322551\pi\)
\(272\) −8.64860 −0.524398
\(273\) −0.0312133 −0.00188911
\(274\) −6.46986 −0.390859
\(275\) −3.36682 −0.203027
\(276\) −18.6880 −1.12489
\(277\) 20.7839 1.24879 0.624393 0.781110i \(-0.285346\pi\)
0.624393 + 0.781110i \(0.285346\pi\)
\(278\) −4.84201 −0.290404
\(279\) −2.40054 −0.143717
\(280\) 0.107279 0.00641117
\(281\) −6.00987 −0.358519 −0.179259 0.983802i \(-0.557370\pi\)
−0.179259 + 0.983802i \(0.557370\pi\)
\(282\) −3.85721 −0.229694
\(283\) 11.5738 0.687993 0.343997 0.938971i \(-0.388219\pi\)
0.343997 + 0.938971i \(0.388219\pi\)
\(284\) −11.7684 −0.698327
\(285\) 0 0
\(286\) 0.220734 0.0130523
\(287\) −0.268688 −0.0158602
\(288\) 1.03093 0.0607480
\(289\) −10.6786 −0.628155
\(290\) 1.48088 0.0869602
\(291\) −27.6393 −1.62024
\(292\) −29.9965 −1.75541
\(293\) 17.4693 1.02057 0.510284 0.860006i \(-0.329540\pi\)
0.510284 + 0.860006i \(0.329540\pi\)
\(294\) −3.54012 −0.206464
\(295\) 10.4354 0.607574
\(296\) 2.21751 0.128890
\(297\) −18.2511 −1.05904
\(298\) 6.01175 0.348251
\(299\) −1.27019 −0.0734571
\(300\) 3.13190 0.180820
\(301\) −0.218340 −0.0125849
\(302\) −3.45823 −0.198999
\(303\) −6.04917 −0.347516
\(304\) 0 0
\(305\) −0.988579 −0.0566059
\(306\) −0.230396 −0.0131709
\(307\) 29.6533 1.69240 0.846201 0.532863i \(-0.178884\pi\)
0.846201 + 0.532863i \(0.178884\pi\)
\(308\) 0.572127 0.0326000
\(309\) 5.80994 0.330516
\(310\) −2.48490 −0.141133
\(311\) −11.6224 −0.659045 −0.329522 0.944148i \(-0.606888\pi\)
−0.329522 + 0.944148i \(0.606888\pi\)
\(312\) −0.420887 −0.0238280
\(313\) −0.474863 −0.0268409 −0.0134204 0.999910i \(-0.504272\pi\)
−0.0134204 + 0.999910i \(0.504272\pi\)
\(314\) −1.42069 −0.0801743
\(315\) −0.0265388 −0.00149529
\(316\) 1.95943 0.110226
\(317\) −20.2283 −1.13613 −0.568066 0.822983i \(-0.692308\pi\)
−0.568066 + 0.822983i \(0.692308\pi\)
\(318\) −4.25281 −0.238486
\(319\) 16.1885 0.906379
\(320\) −5.81256 −0.324932
\(321\) 3.10142 0.173104
\(322\) 0.163921 0.00913495
\(323\) 0 0
\(324\) 15.2771 0.848728
\(325\) 0.212870 0.0118079
\(326\) 0.177012 0.00980377
\(327\) 21.6338 1.19635
\(328\) −3.62306 −0.200050
\(329\) −0.679522 −0.0374633
\(330\) −1.70465 −0.0938377
\(331\) −6.01306 −0.330508 −0.165254 0.986251i \(-0.552844\pi\)
−0.165254 + 0.986251i \(0.552844\pi\)
\(332\) −34.1759 −1.87565
\(333\) −0.548568 −0.0300614
\(334\) −1.26953 −0.0694658
\(335\) 9.97964 0.545246
\(336\) −0.504389 −0.0275167
\(337\) −8.86733 −0.483034 −0.241517 0.970397i \(-0.577645\pi\)
−0.241517 + 0.970397i \(0.577645\pi\)
\(338\) 3.98989 0.217022
\(339\) −20.2952 −1.10228
\(340\) 4.78997 0.259773
\(341\) −27.1640 −1.47101
\(342\) 0 0
\(343\) −1.24803 −0.0673874
\(344\) −2.94415 −0.158738
\(345\) 9.80923 0.528111
\(346\) 1.98177 0.106541
\(347\) 19.9712 1.07211 0.536055 0.844183i \(-0.319914\pi\)
0.536055 + 0.844183i \(0.319914\pi\)
\(348\) −15.0589 −0.807241
\(349\) −0.810214 −0.0433698 −0.0216849 0.999765i \(-0.506903\pi\)
−0.0216849 + 0.999765i \(0.506903\pi\)
\(350\) −0.0274713 −0.00146840
\(351\) 1.15394 0.0615928
\(352\) 11.6657 0.621786
\(353\) −20.9503 −1.11507 −0.557536 0.830153i \(-0.688253\pi\)
−0.557536 + 0.830153i \(0.688253\pi\)
\(354\) 5.28354 0.280817
\(355\) 6.17719 0.327851
\(356\) −1.25045 −0.0662736
\(357\) 0.368664 0.0195118
\(358\) −1.17969 −0.0623487
\(359\) 25.7019 1.35649 0.678246 0.734835i \(-0.262740\pi\)
0.678246 + 0.734835i \(0.262740\pi\)
\(360\) −0.357855 −0.0188606
\(361\) 0 0
\(362\) −5.13963 −0.270133
\(363\) −0.551516 −0.0289471
\(364\) −0.0361732 −0.00189599
\(365\) 15.7450 0.824131
\(366\) −0.500525 −0.0261629
\(367\) −24.2860 −1.26772 −0.633858 0.773449i \(-0.718530\pi\)
−0.633858 + 0.773449i \(0.718530\pi\)
\(368\) −20.5256 −1.06997
\(369\) 0.896271 0.0466580
\(370\) −0.567844 −0.0295208
\(371\) −0.749216 −0.0388973
\(372\) 25.2686 1.31012
\(373\) 10.8809 0.563390 0.281695 0.959504i \(-0.409103\pi\)
0.281695 + 0.959504i \(0.409103\pi\)
\(374\) −2.60711 −0.134811
\(375\) −1.64392 −0.0848916
\(376\) −9.16284 −0.472537
\(377\) −1.02353 −0.0527144
\(378\) −0.148918 −0.00765954
\(379\) 19.3318 0.993008 0.496504 0.868034i \(-0.334617\pi\)
0.496504 + 0.868034i \(0.334617\pi\)
\(380\) 0 0
\(381\) −34.8709 −1.78649
\(382\) −2.44140 −0.124913
\(383\) −1.04305 −0.0532973 −0.0266487 0.999645i \(-0.508484\pi\)
−0.0266487 + 0.999645i \(0.508484\pi\)
\(384\) −14.3350 −0.731530
\(385\) −0.300307 −0.0153050
\(386\) 6.54995 0.333384
\(387\) 0.728323 0.0370228
\(388\) −32.0313 −1.62614
\(389\) 26.6031 1.34883 0.674416 0.738352i \(-0.264395\pi\)
0.674416 + 0.738352i \(0.264395\pi\)
\(390\) 0.107778 0.00545753
\(391\) 15.0024 0.758703
\(392\) −8.40960 −0.424749
\(393\) −11.4264 −0.576388
\(394\) −0.889293 −0.0448019
\(395\) −1.02849 −0.0517491
\(396\) −1.90846 −0.0959038
\(397\) −3.69756 −0.185575 −0.0927877 0.995686i \(-0.529578\pi\)
−0.0927877 + 0.995686i \(0.529578\pi\)
\(398\) −3.57724 −0.179311
\(399\) 0 0
\(400\) 3.43986 0.171993
\(401\) −20.2351 −1.01049 −0.505245 0.862976i \(-0.668598\pi\)
−0.505245 + 0.862976i \(0.668598\pi\)
\(402\) 5.05277 0.252009
\(403\) 1.71747 0.0855531
\(404\) −7.01040 −0.348781
\(405\) −8.01887 −0.398461
\(406\) 0.132088 0.00655543
\(407\) −6.20748 −0.307693
\(408\) 4.97115 0.246109
\(409\) 12.4768 0.616939 0.308470 0.951234i \(-0.400183\pi\)
0.308470 + 0.951234i \(0.400183\pi\)
\(410\) 0.927765 0.0458191
\(411\) −34.5335 −1.70341
\(412\) 6.73316 0.331719
\(413\) 0.930798 0.0458016
\(414\) −0.546795 −0.0268735
\(415\) 17.9388 0.880580
\(416\) −0.737576 −0.0361626
\(417\) −25.8447 −1.26562
\(418\) 0 0
\(419\) 28.9962 1.41656 0.708279 0.705933i \(-0.249472\pi\)
0.708279 + 0.705933i \(0.249472\pi\)
\(420\) 0.279353 0.0136310
\(421\) 14.5960 0.711368 0.355684 0.934606i \(-0.384248\pi\)
0.355684 + 0.934606i \(0.384248\pi\)
\(422\) 7.29934 0.355326
\(423\) 2.26670 0.110211
\(424\) −10.1026 −0.490626
\(425\) −2.51423 −0.121958
\(426\) 3.12756 0.151531
\(427\) −0.0881772 −0.00426720
\(428\) 3.59424 0.173734
\(429\) 1.17819 0.0568835
\(430\) 0.753916 0.0363570
\(431\) 13.5081 0.650663 0.325332 0.945600i \(-0.394524\pi\)
0.325332 + 0.945600i \(0.394524\pi\)
\(432\) 18.6470 0.897156
\(433\) 38.0206 1.82715 0.913576 0.406668i \(-0.133310\pi\)
0.913576 + 0.406668i \(0.133310\pi\)
\(434\) −0.221642 −0.0106392
\(435\) 7.90434 0.378984
\(436\) 25.0714 1.20070
\(437\) 0 0
\(438\) 7.97181 0.380908
\(439\) −23.7870 −1.13529 −0.567645 0.823273i \(-0.692146\pi\)
−0.567645 + 0.823273i \(0.692146\pi\)
\(440\) −4.04941 −0.193048
\(441\) 2.08037 0.0990651
\(442\) 0.164837 0.00784049
\(443\) −19.2991 −0.916929 −0.458465 0.888713i \(-0.651600\pi\)
−0.458465 + 0.888713i \(0.651600\pi\)
\(444\) 5.77435 0.274038
\(445\) 0.656354 0.0311142
\(446\) 2.71518 0.128568
\(447\) 32.0883 1.51772
\(448\) −0.518457 −0.0244948
\(449\) −26.4136 −1.24654 −0.623268 0.782008i \(-0.714195\pi\)
−0.623268 + 0.782008i \(0.714195\pi\)
\(450\) 0.0916368 0.00431980
\(451\) 10.1420 0.477569
\(452\) −23.5202 −1.10630
\(453\) −18.4586 −0.867263
\(454\) 0.321885 0.0151068
\(455\) 0.0189871 0.000890130 0
\(456\) 0 0
\(457\) −38.4641 −1.79927 −0.899637 0.436638i \(-0.856169\pi\)
−0.899637 + 0.436638i \(0.856169\pi\)
\(458\) 4.15283 0.194049
\(459\) −13.6293 −0.636163
\(460\) 11.3680 0.530034
\(461\) 33.9836 1.58277 0.791387 0.611315i \(-0.209359\pi\)
0.791387 + 0.611315i \(0.209359\pi\)
\(462\) −0.152048 −0.00707389
\(463\) −5.39446 −0.250702 −0.125351 0.992112i \(-0.540006\pi\)
−0.125351 + 0.992112i \(0.540006\pi\)
\(464\) −16.5396 −0.767833
\(465\) −13.2634 −0.615074
\(466\) −3.45496 −0.160048
\(467\) 22.4289 1.03788 0.518942 0.854809i \(-0.326326\pi\)
0.518942 + 0.854809i \(0.326326\pi\)
\(468\) 0.120664 0.00557770
\(469\) 0.890143 0.0411030
\(470\) 2.34635 0.108229
\(471\) −7.58309 −0.349410
\(472\) 12.5511 0.577711
\(473\) 8.24155 0.378947
\(474\) −0.520734 −0.0239181
\(475\) 0 0
\(476\) 0.427246 0.0195828
\(477\) 2.49918 0.114430
\(478\) 6.26109 0.286376
\(479\) −28.7406 −1.31319 −0.656597 0.754242i \(-0.728005\pi\)
−0.656597 + 0.754242i \(0.728005\pi\)
\(480\) 5.69603 0.259987
\(481\) 0.392473 0.0178952
\(482\) 1.18407 0.0539328
\(483\) 0.874943 0.0398113
\(484\) −0.639154 −0.0290525
\(485\) 16.8130 0.763441
\(486\) 0.948682 0.0430331
\(487\) −34.4441 −1.56081 −0.780406 0.625273i \(-0.784988\pi\)
−0.780406 + 0.625273i \(0.784988\pi\)
\(488\) −1.18900 −0.0538236
\(489\) 0.944817 0.0427261
\(490\) 2.15347 0.0972838
\(491\) −19.3862 −0.874887 −0.437444 0.899246i \(-0.644116\pi\)
−0.437444 + 0.899246i \(0.644116\pi\)
\(492\) −9.43434 −0.425333
\(493\) 12.0890 0.544462
\(494\) 0 0
\(495\) 1.00174 0.0450249
\(496\) 27.7533 1.24616
\(497\) 0.550980 0.0247148
\(498\) 9.08254 0.406998
\(499\) 11.2685 0.504445 0.252223 0.967669i \(-0.418838\pi\)
0.252223 + 0.967669i \(0.418838\pi\)
\(500\) −1.90514 −0.0852006
\(501\) −6.77626 −0.302741
\(502\) 2.44474 0.109114
\(503\) 10.5918 0.472266 0.236133 0.971721i \(-0.424120\pi\)
0.236133 + 0.971721i \(0.424120\pi\)
\(504\) −0.0319192 −0.00142179
\(505\) 3.67973 0.163746
\(506\) −6.18742 −0.275064
\(507\) 21.2964 0.945808
\(508\) −40.4120 −1.79299
\(509\) −2.17937 −0.0965988 −0.0482994 0.998833i \(-0.515380\pi\)
−0.0482994 + 0.998833i \(0.515380\pi\)
\(510\) −1.27298 −0.0563683
\(511\) 1.40439 0.0621266
\(512\) −20.1933 −0.892426
\(513\) 0 0
\(514\) −7.46186 −0.329129
\(515\) −3.53420 −0.155735
\(516\) −7.66649 −0.337498
\(517\) 25.6495 1.12806
\(518\) −0.0506494 −0.00222541
\(519\) 10.5779 0.464319
\(520\) 0.256027 0.0112275
\(521\) −11.4473 −0.501517 −0.250759 0.968050i \(-0.580680\pi\)
−0.250759 + 0.968050i \(0.580680\pi\)
\(522\) −0.440611 −0.0192850
\(523\) −9.75228 −0.426437 −0.213219 0.977004i \(-0.568395\pi\)
−0.213219 + 0.977004i \(0.568395\pi\)
\(524\) −13.2422 −0.578486
\(525\) −0.146631 −0.00639949
\(526\) 3.81204 0.166213
\(527\) −20.2852 −0.883637
\(528\) 19.0388 0.828560
\(529\) 12.6049 0.548040
\(530\) 2.58700 0.112372
\(531\) −3.10489 −0.134741
\(532\) 0 0
\(533\) −0.641237 −0.0277750
\(534\) 0.332317 0.0143808
\(535\) −1.88660 −0.0815649
\(536\) 12.0029 0.518446
\(537\) −6.29673 −0.271724
\(538\) 7.50840 0.323710
\(539\) 23.5410 1.01398
\(540\) −10.3275 −0.444427
\(541\) 22.8160 0.980938 0.490469 0.871459i \(-0.336825\pi\)
0.490469 + 0.871459i \(0.336825\pi\)
\(542\) −5.36463 −0.230430
\(543\) −27.4333 −1.17728
\(544\) 8.71160 0.373507
\(545\) −13.1599 −0.563707
\(546\) 0.00961333 0.000411412 0
\(547\) 30.9172 1.32192 0.660962 0.750419i \(-0.270148\pi\)
0.660962 + 0.750419i \(0.270148\pi\)
\(548\) −40.0210 −1.70961
\(549\) 0.294135 0.0125534
\(550\) 1.03694 0.0442153
\(551\) 0 0
\(552\) 11.7979 0.502154
\(553\) −0.0917374 −0.00390107
\(554\) −6.40121 −0.271961
\(555\) −3.03093 −0.128656
\(556\) −29.9515 −1.27023
\(557\) −9.82887 −0.416463 −0.208231 0.978080i \(-0.566771\pi\)
−0.208231 + 0.978080i \(0.566771\pi\)
\(558\) 0.739339 0.0312987
\(559\) −0.521078 −0.0220393
\(560\) 0.306821 0.0129656
\(561\) −13.9157 −0.587522
\(562\) 1.85097 0.0780785
\(563\) 33.4193 1.40846 0.704228 0.709974i \(-0.251293\pi\)
0.704228 + 0.709974i \(0.251293\pi\)
\(564\) −23.8598 −1.00468
\(565\) 12.3456 0.519384
\(566\) −3.56461 −0.149832
\(567\) −0.715251 −0.0300377
\(568\) 7.42954 0.311736
\(569\) 37.6326 1.57764 0.788820 0.614624i \(-0.210692\pi\)
0.788820 + 0.614624i \(0.210692\pi\)
\(570\) 0 0
\(571\) −2.75232 −0.115181 −0.0575904 0.998340i \(-0.518342\pi\)
−0.0575904 + 0.998340i \(0.518342\pi\)
\(572\) 1.36541 0.0570905
\(573\) −13.0312 −0.544388
\(574\) 0.0827528 0.00345404
\(575\) −5.96699 −0.248840
\(576\) 1.72943 0.0720596
\(577\) 0.0370999 0.00154449 0.000772245 1.00000i \(-0.499754\pi\)
0.000772245 1.00000i \(0.499754\pi\)
\(578\) 3.28889 0.136800
\(579\) 34.9610 1.45293
\(580\) 9.16037 0.380363
\(581\) 1.60006 0.0663819
\(582\) 8.51257 0.352857
\(583\) 28.2802 1.17125
\(584\) 18.9371 0.783624
\(585\) −0.0633359 −0.00261862
\(586\) −5.38035 −0.222260
\(587\) −3.60678 −0.148868 −0.0744340 0.997226i \(-0.523715\pi\)
−0.0744340 + 0.997226i \(0.523715\pi\)
\(588\) −21.8984 −0.903074
\(589\) 0 0
\(590\) −3.21399 −0.132318
\(591\) −4.74669 −0.195253
\(592\) 6.34214 0.260660
\(593\) 17.8435 0.732744 0.366372 0.930469i \(-0.380600\pi\)
0.366372 + 0.930469i \(0.380600\pi\)
\(594\) 5.62113 0.230638
\(595\) −0.224259 −0.00919373
\(596\) 37.1873 1.52325
\(597\) −19.0939 −0.781460
\(598\) 0.391204 0.0159975
\(599\) −21.9448 −0.896642 −0.448321 0.893873i \(-0.647978\pi\)
−0.448321 + 0.893873i \(0.647978\pi\)
\(600\) −1.97720 −0.0807190
\(601\) 10.2808 0.419362 0.209681 0.977770i \(-0.432757\pi\)
0.209681 + 0.977770i \(0.432757\pi\)
\(602\) 0.0672462 0.00274075
\(603\) −2.96928 −0.120918
\(604\) −21.3918 −0.870420
\(605\) 0.335489 0.0136396
\(606\) 1.86307 0.0756822
\(607\) 32.2616 1.30946 0.654729 0.755864i \(-0.272783\pi\)
0.654729 + 0.755864i \(0.272783\pi\)
\(608\) 0 0
\(609\) 0.705034 0.0285694
\(610\) 0.304471 0.0123277
\(611\) −1.62171 −0.0656074
\(612\) −1.42518 −0.0576094
\(613\) −16.3957 −0.662215 −0.331108 0.943593i \(-0.607422\pi\)
−0.331108 + 0.943593i \(0.607422\pi\)
\(614\) −9.13287 −0.368573
\(615\) 4.95204 0.199685
\(616\) −0.361190 −0.0145528
\(617\) −12.7768 −0.514377 −0.257188 0.966361i \(-0.582796\pi\)
−0.257188 + 0.966361i \(0.582796\pi\)
\(618\) −1.78939 −0.0719799
\(619\) 4.28207 0.172111 0.0860555 0.996290i \(-0.472574\pi\)
0.0860555 + 0.996290i \(0.472574\pi\)
\(620\) −15.3710 −0.617313
\(621\) −32.3463 −1.29801
\(622\) 3.57956 0.143527
\(623\) 0.0585441 0.00234552
\(624\) −1.20375 −0.0481884
\(625\) 1.00000 0.0400000
\(626\) 0.146252 0.00584542
\(627\) 0 0
\(628\) −8.78807 −0.350682
\(629\) −4.63554 −0.184831
\(630\) 0.00817363 0.000325645 0
\(631\) −22.7879 −0.907170 −0.453585 0.891213i \(-0.649855\pi\)
−0.453585 + 0.891213i \(0.649855\pi\)
\(632\) −1.23701 −0.0492055
\(633\) 38.9610 1.54856
\(634\) 6.23007 0.247428
\(635\) 21.2121 0.841776
\(636\) −26.3069 −1.04314
\(637\) −1.48840 −0.0589724
\(638\) −4.98585 −0.197392
\(639\) −1.83792 −0.0727069
\(640\) 8.72003 0.344689
\(641\) −31.3626 −1.23875 −0.619373 0.785097i \(-0.712613\pi\)
−0.619373 + 0.785097i \(0.712613\pi\)
\(642\) −0.955200 −0.0376987
\(643\) −11.1490 −0.439674 −0.219837 0.975537i \(-0.570553\pi\)
−0.219837 + 0.975537i \(0.570553\pi\)
\(644\) 1.01398 0.0399562
\(645\) 4.02410 0.158449
\(646\) 0 0
\(647\) −17.5536 −0.690102 −0.345051 0.938584i \(-0.612138\pi\)
−0.345051 + 0.938584i \(0.612138\pi\)
\(648\) −9.64461 −0.378876
\(649\) −35.1342 −1.37914
\(650\) −0.0655615 −0.00257153
\(651\) −1.18304 −0.0463669
\(652\) 1.09495 0.0428816
\(653\) −2.09533 −0.0819966 −0.0409983 0.999159i \(-0.513054\pi\)
−0.0409983 + 0.999159i \(0.513054\pi\)
\(654\) −6.66294 −0.260542
\(655\) 6.95074 0.271588
\(656\) −10.3620 −0.404569
\(657\) −4.68466 −0.182766
\(658\) 0.209285 0.00815878
\(659\) −13.0001 −0.506411 −0.253205 0.967413i \(-0.581485\pi\)
−0.253205 + 0.967413i \(0.581485\pi\)
\(660\) −10.5445 −0.410446
\(661\) 38.0961 1.48177 0.740884 0.671633i \(-0.234407\pi\)
0.740884 + 0.671633i \(0.234407\pi\)
\(662\) 1.85195 0.0719782
\(663\) 0.879833 0.0341699
\(664\) 21.5756 0.837298
\(665\) 0 0
\(666\) 0.168953 0.00654678
\(667\) 28.6906 1.11091
\(668\) −7.85304 −0.303843
\(669\) 14.4926 0.560315
\(670\) −3.07361 −0.118744
\(671\) 3.32837 0.128490
\(672\) 0.508063 0.0195989
\(673\) 33.9497 1.30867 0.654333 0.756207i \(-0.272950\pi\)
0.654333 + 0.756207i \(0.272950\pi\)
\(674\) 2.73103 0.105196
\(675\) 5.42087 0.208650
\(676\) 24.6805 0.949251
\(677\) −16.5562 −0.636307 −0.318153 0.948039i \(-0.603063\pi\)
−0.318153 + 0.948039i \(0.603063\pi\)
\(678\) 6.25068 0.240056
\(679\) 1.49965 0.0575515
\(680\) −3.02396 −0.115964
\(681\) 1.71809 0.0658374
\(682\) 8.36620 0.320358
\(683\) 5.33328 0.204072 0.102036 0.994781i \(-0.467464\pi\)
0.102036 + 0.994781i \(0.467464\pi\)
\(684\) 0 0
\(685\) 21.0068 0.802630
\(686\) 0.384380 0.0146757
\(687\) 22.1662 0.845692
\(688\) −8.42033 −0.321022
\(689\) −1.78804 −0.0681188
\(690\) −3.02113 −0.115012
\(691\) −14.1302 −0.537538 −0.268769 0.963205i \(-0.586617\pi\)
−0.268769 + 0.963205i \(0.586617\pi\)
\(692\) 12.2588 0.466009
\(693\) 0.0893513 0.00339417
\(694\) −6.15089 −0.233485
\(695\) 15.7214 0.596347
\(696\) 9.50685 0.360356
\(697\) 7.57372 0.286875
\(698\) 0.249536 0.00944510
\(699\) −18.4412 −0.697510
\(700\) −0.169931 −0.00642279
\(701\) −38.1622 −1.44137 −0.720683 0.693265i \(-0.756172\pi\)
−0.720683 + 0.693265i \(0.756172\pi\)
\(702\) −0.355400 −0.0134137
\(703\) 0 0
\(704\) 19.5699 0.737567
\(705\) 12.5239 0.471677
\(706\) 6.45245 0.242841
\(707\) 0.328216 0.0123438
\(708\) 32.6827 1.22829
\(709\) 33.1675 1.24563 0.622816 0.782368i \(-0.285988\pi\)
0.622816 + 0.782368i \(0.285988\pi\)
\(710\) −1.90250 −0.0713996
\(711\) 0.306011 0.0114763
\(712\) 0.789422 0.0295849
\(713\) −48.1425 −1.80295
\(714\) −0.113544 −0.00424928
\(715\) −0.716695 −0.0268029
\(716\) −7.29730 −0.272713
\(717\) 33.4192 1.24806
\(718\) −7.91587 −0.295418
\(719\) 42.3410 1.57905 0.789527 0.613716i \(-0.210326\pi\)
0.789527 + 0.613716i \(0.210326\pi\)
\(720\) −1.02347 −0.0381426
\(721\) −0.315236 −0.0117400
\(722\) 0 0
\(723\) 6.32007 0.235046
\(724\) −31.7926 −1.18156
\(725\) −4.80823 −0.178573
\(726\) 0.169861 0.00630412
\(727\) −4.20162 −0.155829 −0.0779147 0.996960i \(-0.524826\pi\)
−0.0779147 + 0.996960i \(0.524826\pi\)
\(728\) 0.0228365 0.000846379 0
\(729\) 29.1203 1.07853
\(730\) −4.84928 −0.179480
\(731\) 6.15452 0.227633
\(732\) −3.09613 −0.114436
\(733\) 16.9357 0.625536 0.312768 0.949830i \(-0.398744\pi\)
0.312768 + 0.949830i \(0.398744\pi\)
\(734\) 7.47979 0.276084
\(735\) 11.4943 0.423975
\(736\) 20.6751 0.762094
\(737\) −33.5997 −1.23766
\(738\) −0.276041 −0.0101612
\(739\) 20.8465 0.766852 0.383426 0.923572i \(-0.374744\pi\)
0.383426 + 0.923572i \(0.374744\pi\)
\(740\) −3.51255 −0.129124
\(741\) 0 0
\(742\) 0.230750 0.00847109
\(743\) 45.3499 1.66373 0.831863 0.554981i \(-0.187274\pi\)
0.831863 + 0.554981i \(0.187274\pi\)
\(744\) −15.9524 −0.584842
\(745\) −19.5194 −0.715136
\(746\) −3.35118 −0.122695
\(747\) −5.33738 −0.195285
\(748\) −16.1270 −0.589661
\(749\) −0.168277 −0.00614871
\(750\) 0.506308 0.0184877
\(751\) −8.67683 −0.316622 −0.158311 0.987389i \(-0.550605\pi\)
−0.158311 + 0.987389i \(0.550605\pi\)
\(752\) −26.2059 −0.955631
\(753\) 13.0490 0.475533
\(754\) 0.315235 0.0114802
\(755\) 11.2284 0.408645
\(756\) −0.921174 −0.0335028
\(757\) 10.0763 0.366229 0.183114 0.983092i \(-0.441382\pi\)
0.183114 + 0.983092i \(0.441382\pi\)
\(758\) −5.95397 −0.216258
\(759\) −33.0259 −1.19877
\(760\) 0 0
\(761\) 4.52014 0.163855 0.0819275 0.996638i \(-0.473892\pi\)
0.0819275 + 0.996638i \(0.473892\pi\)
\(762\) 10.7398 0.389063
\(763\) −1.17381 −0.0424947
\(764\) −15.1020 −0.546370
\(765\) 0.748068 0.0270465
\(766\) 0.321247 0.0116071
\(767\) 2.22139 0.0802097
\(768\) −14.6957 −0.530287
\(769\) −39.5765 −1.42717 −0.713583 0.700571i \(-0.752929\pi\)
−0.713583 + 0.700571i \(0.752929\pi\)
\(770\) 0.0924909 0.00333314
\(771\) −39.8284 −1.43439
\(772\) 40.5165 1.45822
\(773\) −23.4986 −0.845187 −0.422593 0.906319i \(-0.638880\pi\)
−0.422593 + 0.906319i \(0.638880\pi\)
\(774\) −0.224315 −0.00806284
\(775\) 8.06815 0.289816
\(776\) 20.2217 0.725917
\(777\) −0.270346 −0.00969861
\(778\) −8.19345 −0.293749
\(779\) 0 0
\(780\) 0.666687 0.0238712
\(781\) −20.7975 −0.744192
\(782\) −4.62056 −0.165231
\(783\) −26.0648 −0.931480
\(784\) −24.0516 −0.858987
\(785\) 4.61281 0.164638
\(786\) 3.51921 0.125526
\(787\) 7.52483 0.268231 0.134116 0.990966i \(-0.457181\pi\)
0.134116 + 0.990966i \(0.457181\pi\)
\(788\) −5.50096 −0.195963
\(789\) 20.3471 0.724377
\(790\) 0.316764 0.0112700
\(791\) 1.10118 0.0391534
\(792\) 1.20483 0.0428119
\(793\) −0.210439 −0.00747290
\(794\) 1.13881 0.0404147
\(795\) 13.8084 0.489732
\(796\) −22.1280 −0.784305
\(797\) −18.7858 −0.665426 −0.332713 0.943028i \(-0.607964\pi\)
−0.332713 + 0.943028i \(0.607964\pi\)
\(798\) 0 0
\(799\) 19.1542 0.677627
\(800\) −3.46491 −0.122503
\(801\) −0.195287 −0.00690014
\(802\) 6.23216 0.220065
\(803\) −53.0106 −1.87070
\(804\) 31.2552 1.10229
\(805\) −0.532231 −0.0187587
\(806\) −0.528960 −0.0186318
\(807\) 40.0768 1.41077
\(808\) 4.42575 0.155697
\(809\) −19.4930 −0.685338 −0.342669 0.939456i \(-0.611331\pi\)
−0.342669 + 0.939456i \(0.611331\pi\)
\(810\) 2.46972 0.0867771
\(811\) 15.2060 0.533954 0.266977 0.963703i \(-0.413975\pi\)
0.266977 + 0.963703i \(0.413975\pi\)
\(812\) 0.817067 0.0286734
\(813\) −28.6342 −1.00425
\(814\) 1.91183 0.0670096
\(815\) −0.574735 −0.0201321
\(816\) 14.2176 0.497715
\(817\) 0 0
\(818\) −3.84272 −0.134357
\(819\) −0.00564930 −0.000197403 0
\(820\) 5.73894 0.200412
\(821\) −26.7664 −0.934154 −0.467077 0.884217i \(-0.654693\pi\)
−0.467077 + 0.884217i \(0.654693\pi\)
\(822\) 10.6359 0.370970
\(823\) 27.6484 0.963763 0.481881 0.876236i \(-0.339954\pi\)
0.481881 + 0.876236i \(0.339954\pi\)
\(824\) −4.25072 −0.148081
\(825\) 5.53478 0.192696
\(826\) −0.286675 −0.00997469
\(827\) 12.8221 0.445869 0.222935 0.974833i \(-0.428436\pi\)
0.222935 + 0.974833i \(0.428436\pi\)
\(828\) −3.38235 −0.117545
\(829\) 45.4531 1.57865 0.789326 0.613974i \(-0.210430\pi\)
0.789326 + 0.613974i \(0.210430\pi\)
\(830\) −5.52493 −0.191773
\(831\) −34.1671 −1.18524
\(832\) −1.23732 −0.0428963
\(833\) 17.5796 0.609098
\(834\) 7.95986 0.275628
\(835\) 4.12202 0.142648
\(836\) 0 0
\(837\) 43.7364 1.51175
\(838\) −8.93049 −0.308499
\(839\) 23.3132 0.804859 0.402430 0.915451i \(-0.368166\pi\)
0.402430 + 0.915451i \(0.368166\pi\)
\(840\) −0.176358 −0.00608494
\(841\) −5.88093 −0.202791
\(842\) −4.49541 −0.154922
\(843\) 9.87974 0.340276
\(844\) 45.1520 1.55420
\(845\) −12.9547 −0.445655
\(846\) −0.698118 −0.0240018
\(847\) 0.0299242 0.00102821
\(848\) −28.8937 −0.992212
\(849\) −19.0264 −0.652986
\(850\) 0.774354 0.0265601
\(851\) −11.0015 −0.377125
\(852\) 19.3463 0.662794
\(853\) −45.7832 −1.56759 −0.783793 0.621022i \(-0.786718\pi\)
−0.783793 + 0.621022i \(0.786718\pi\)
\(854\) 0.0271576 0.000929312 0
\(855\) 0 0
\(856\) −2.26909 −0.0775558
\(857\) 6.44896 0.220292 0.110146 0.993915i \(-0.464868\pi\)
0.110146 + 0.993915i \(0.464868\pi\)
\(858\) −0.362868 −0.0123881
\(859\) −14.5369 −0.495993 −0.247997 0.968761i \(-0.579772\pi\)
−0.247997 + 0.968761i \(0.579772\pi\)
\(860\) 4.66355 0.159026
\(861\) 0.441702 0.0150531
\(862\) −4.16034 −0.141702
\(863\) −4.57136 −0.155611 −0.0778054 0.996969i \(-0.524791\pi\)
−0.0778054 + 0.996969i \(0.524791\pi\)
\(864\) −18.7829 −0.639006
\(865\) −6.43458 −0.218782
\(866\) −11.7099 −0.397918
\(867\) 17.5548 0.596192
\(868\) −1.37103 −0.0465357
\(869\) 3.46275 0.117466
\(870\) −2.43444 −0.0825353
\(871\) 2.12437 0.0719814
\(872\) −15.8279 −0.536000
\(873\) −5.00244 −0.169307
\(874\) 0 0
\(875\) 0.0891959 0.00301537
\(876\) 49.3118 1.66609
\(877\) 32.9569 1.11288 0.556438 0.830889i \(-0.312168\pi\)
0.556438 + 0.830889i \(0.312168\pi\)
\(878\) 7.32611 0.247244
\(879\) −28.7181 −0.968639
\(880\) −11.5814 −0.390408
\(881\) −16.2413 −0.547184 −0.273592 0.961846i \(-0.588212\pi\)
−0.273592 + 0.961846i \(0.588212\pi\)
\(882\) −0.640729 −0.0215745
\(883\) −28.5141 −0.959575 −0.479787 0.877385i \(-0.659286\pi\)
−0.479787 + 0.877385i \(0.659286\pi\)
\(884\) 1.01964 0.0342943
\(885\) −17.1550 −0.576659
\(886\) 5.94391 0.199689
\(887\) 38.6352 1.29724 0.648622 0.761111i \(-0.275346\pi\)
0.648622 + 0.761111i \(0.275346\pi\)
\(888\) −3.64541 −0.122332
\(889\) 1.89203 0.0634567
\(890\) −0.202149 −0.00677606
\(891\) 26.9981 0.904471
\(892\) 16.7955 0.562355
\(893\) 0 0
\(894\) −9.88282 −0.330531
\(895\) 3.83032 0.128033
\(896\) 0.777791 0.0259842
\(897\) 2.08809 0.0697193
\(898\) 8.13508 0.271471
\(899\) −38.7935 −1.29384
\(900\) 0.566844 0.0188948
\(901\) 21.1187 0.703566
\(902\) −3.12362 −0.104005
\(903\) 0.358933 0.0119446
\(904\) 14.8486 0.493855
\(905\) 16.6878 0.554720
\(906\) 5.68505 0.188873
\(907\) 28.6565 0.951522 0.475761 0.879575i \(-0.342173\pi\)
0.475761 + 0.879575i \(0.342173\pi\)
\(908\) 1.99110 0.0660771
\(909\) −1.09484 −0.0363136
\(910\) −0.00584781 −0.000193853 0
\(911\) −47.5952 −1.57690 −0.788450 0.615099i \(-0.789116\pi\)
−0.788450 + 0.615099i \(0.789116\pi\)
\(912\) 0 0
\(913\) −60.3966 −1.99884
\(914\) 11.8465 0.391847
\(915\) 1.62514 0.0537256
\(916\) 25.6885 0.848770
\(917\) 0.619978 0.0204735
\(918\) 4.19768 0.138544
\(919\) −27.2196 −0.897891 −0.448945 0.893559i \(-0.648200\pi\)
−0.448945 + 0.893559i \(0.648200\pi\)
\(920\) −7.17672 −0.236610
\(921\) −48.7476 −1.60629
\(922\) −10.4666 −0.344698
\(923\) 1.31494 0.0432817
\(924\) −0.940530 −0.0309412
\(925\) 1.84372 0.0606212
\(926\) 1.66143 0.0545980
\(927\) 1.05154 0.0345372
\(928\) 16.6601 0.546894
\(929\) −32.2399 −1.05776 −0.528879 0.848697i \(-0.677387\pi\)
−0.528879 + 0.848697i \(0.677387\pi\)
\(930\) 4.08496 0.133951
\(931\) 0 0
\(932\) −21.3716 −0.700049
\(933\) 19.1062 0.625510
\(934\) −6.90783 −0.226031
\(935\) 8.46497 0.276834
\(936\) −0.0761765 −0.00248991
\(937\) 18.1725 0.593668 0.296834 0.954929i \(-0.404069\pi\)
0.296834 + 0.954929i \(0.404069\pi\)
\(938\) −0.274154 −0.00895144
\(939\) 0.780637 0.0254751
\(940\) 14.5140 0.473394
\(941\) 23.5571 0.767939 0.383970 0.923346i \(-0.374557\pi\)
0.383970 + 0.923346i \(0.374557\pi\)
\(942\) 2.33550 0.0760948
\(943\) 17.9746 0.585333
\(944\) 35.8964 1.16833
\(945\) 0.483520 0.0157289
\(946\) −2.53830 −0.0825273
\(947\) −8.43157 −0.273989 −0.136995 0.990572i \(-0.543744\pi\)
−0.136995 + 0.990572i \(0.543744\pi\)
\(948\) −3.22114 −0.104618
\(949\) 3.35164 0.108799
\(950\) 0 0
\(951\) 33.2536 1.07832
\(952\) −0.269725 −0.00874184
\(953\) 50.0741 1.62206 0.811029 0.585005i \(-0.198908\pi\)
0.811029 + 0.585005i \(0.198908\pi\)
\(954\) −0.769719 −0.0249206
\(955\) 7.92694 0.256510
\(956\) 38.7296 1.25261
\(957\) −26.6125 −0.860260
\(958\) 8.85178 0.285988
\(959\) 1.87372 0.0605057
\(960\) 9.55538 0.308398
\(961\) 34.0950 1.09984
\(962\) −0.120877 −0.00389723
\(963\) 0.561327 0.0180885
\(964\) 7.32436 0.235902
\(965\) −21.2669 −0.684605
\(966\) −0.269472 −0.00867013
\(967\) −6.00845 −0.193219 −0.0966094 0.995322i \(-0.530800\pi\)
−0.0966094 + 0.995322i \(0.530800\pi\)
\(968\) 0.403505 0.0129692
\(969\) 0 0
\(970\) −5.17822 −0.166263
\(971\) 35.9725 1.15441 0.577206 0.816599i \(-0.304143\pi\)
0.577206 + 0.816599i \(0.304143\pi\)
\(972\) 5.86832 0.188227
\(973\) 1.40228 0.0449552
\(974\) 10.6084 0.339915
\(975\) −0.349941 −0.0112071
\(976\) −3.40057 −0.108850
\(977\) 33.6347 1.07607 0.538035 0.842922i \(-0.319167\pi\)
0.538035 + 0.842922i \(0.319167\pi\)
\(978\) −0.290993 −0.00930492
\(979\) −2.20983 −0.0706264
\(980\) 13.3208 0.425519
\(981\) 3.91550 0.125012
\(982\) 5.97072 0.190533
\(983\) 45.0395 1.43654 0.718268 0.695766i \(-0.244935\pi\)
0.718268 + 0.695766i \(0.244935\pi\)
\(984\) 5.95601 0.189871
\(985\) 2.88742 0.0920010
\(986\) −3.72327 −0.118573
\(987\) 1.11708 0.0355570
\(988\) 0 0
\(989\) 14.6064 0.464457
\(990\) −0.308525 −0.00980556
\(991\) −6.12993 −0.194724 −0.0973619 0.995249i \(-0.531040\pi\)
−0.0973619 + 0.995249i \(0.531040\pi\)
\(992\) −27.9554 −0.887586
\(993\) 9.88498 0.313690
\(994\) −0.169695 −0.00538241
\(995\) 11.6149 0.368216
\(996\) 56.1824 1.78021
\(997\) −44.9173 −1.42255 −0.711273 0.702916i \(-0.751881\pi\)
−0.711273 + 0.702916i \(0.751881\pi\)
\(998\) −3.47055 −0.109858
\(999\) 9.99458 0.316214
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 1805.2.a.v.1.3 9
5.4 even 2 9025.2.a.cc.1.7 9
19.9 even 9 95.2.k.a.81.3 yes 18
19.17 even 9 95.2.k.a.61.3 18
19.18 odd 2 1805.2.a.s.1.7 9
57.17 odd 18 855.2.bs.c.631.1 18
57.47 odd 18 855.2.bs.c.271.1 18
95.9 even 18 475.2.l.c.176.1 18
95.17 odd 36 475.2.u.b.99.3 36
95.28 odd 36 475.2.u.b.24.3 36
95.47 odd 36 475.2.u.b.24.4 36
95.74 even 18 475.2.l.c.251.1 18
95.93 odd 36 475.2.u.b.99.4 36
95.94 odd 2 9025.2.a.cf.1.3 9
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
95.2.k.a.61.3 18 19.17 even 9
95.2.k.a.81.3 yes 18 19.9 even 9
475.2.l.c.176.1 18 95.9 even 18
475.2.l.c.251.1 18 95.74 even 18
475.2.u.b.24.3 36 95.28 odd 36
475.2.u.b.24.4 36 95.47 odd 36
475.2.u.b.99.3 36 95.17 odd 36
475.2.u.b.99.4 36 95.93 odd 36
855.2.bs.c.271.1 18 57.47 odd 18
855.2.bs.c.631.1 18 57.17 odd 18
1805.2.a.s.1.7 9 19.18 odd 2
1805.2.a.v.1.3 9 1.1 even 1 trivial
9025.2.a.cc.1.7 9 5.4 even 2
9025.2.a.cf.1.3 9 95.94 odd 2