Properties

Label 9025.2.a.cv.1.15
Level $9025$
Weight $2$
Character 9025.1
Self dual yes
Analytic conductor $72.065$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $4$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [9025,2,Mod(1,9025)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(9025, 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("9025.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 9025 = 5^{2} \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9025.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: \(72.0649878242\)
Analytic rank: \(0\)
Dimension: \(40\)
Twist minimal: no (minimal twist has level 1805)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) \(=\) 9025.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.937092 q^{2} -1.03012 q^{3} -1.12186 q^{4} +0.965321 q^{6} -1.65832 q^{7} +2.92547 q^{8} -1.93884 q^{9} +O(q^{10})\) \(q-0.937092 q^{2} -1.03012 q^{3} -1.12186 q^{4} +0.965321 q^{6} -1.65832 q^{7} +2.92547 q^{8} -1.93884 q^{9} +4.63847 q^{11} +1.15565 q^{12} -5.55629 q^{13} +1.55400 q^{14} -0.497714 q^{16} +7.23729 q^{17} +1.81688 q^{18} +1.70828 q^{21} -4.34667 q^{22} +4.65440 q^{23} -3.01360 q^{24} +5.20676 q^{26} +5.08762 q^{27} +1.86040 q^{28} +5.69836 q^{29} +6.93959 q^{31} -5.38453 q^{32} -4.77820 q^{33} -6.78201 q^{34} +2.17511 q^{36} -0.159177 q^{37} +5.72367 q^{39} +7.04774 q^{41} -1.60081 q^{42} +3.60620 q^{43} -5.20371 q^{44} -4.36160 q^{46} -7.34488 q^{47} +0.512707 q^{48} -4.24997 q^{49} -7.45531 q^{51} +6.23338 q^{52} +0.175188 q^{53} -4.76757 q^{54} -4.85137 q^{56} -5.33988 q^{58} +1.30720 q^{59} +6.22814 q^{61} -6.50303 q^{62} +3.21523 q^{63} +6.04123 q^{64} +4.47761 q^{66} -1.45987 q^{67} -8.11922 q^{68} -4.79460 q^{69} -10.1796 q^{71} -5.67203 q^{72} +2.72447 q^{73} +0.149163 q^{74} -7.69207 q^{77} -5.36361 q^{78} +2.47593 q^{79} +0.575652 q^{81} -6.60437 q^{82} +5.13444 q^{83} -1.91645 q^{84} -3.37934 q^{86} -5.87001 q^{87} +13.5697 q^{88} -3.66487 q^{89} +9.21412 q^{91} -5.22158 q^{92} -7.14864 q^{93} +6.88283 q^{94} +5.54674 q^{96} +5.45553 q^{97} +3.98261 q^{98} -8.99327 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q + 48 q^{4} + 20 q^{6} + 52 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 40 q + 48 q^{4} + 20 q^{6} + 52 q^{9} + 20 q^{11} + 40 q^{16} + 92 q^{24} + 76 q^{26} + 156 q^{36} + 80 q^{39} + 48 q^{44} + 72 q^{49} + 32 q^{54} + 80 q^{61} + 72 q^{64} + 16 q^{66} + 100 q^{74} + 40 q^{81} + 380 q^{96} + 128 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.937092 −0.662624 −0.331312 0.943521i \(-0.607491\pi\)
−0.331312 + 0.943521i \(0.607491\pi\)
\(3\) −1.03012 −0.594742 −0.297371 0.954762i \(-0.596110\pi\)
−0.297371 + 0.954762i \(0.596110\pi\)
\(4\) −1.12186 −0.560930
\(5\) 0 0
\(6\) 0.965321 0.394091
\(7\) −1.65832 −0.626786 −0.313393 0.949623i \(-0.601466\pi\)
−0.313393 + 0.949623i \(0.601466\pi\)
\(8\) 2.92547 1.03431
\(9\) −1.93884 −0.646282
\(10\) 0 0
\(11\) 4.63847 1.39855 0.699276 0.714852i \(-0.253506\pi\)
0.699276 + 0.714852i \(0.253506\pi\)
\(12\) 1.15565 0.333609
\(13\) −5.55629 −1.54104 −0.770519 0.637416i \(-0.780003\pi\)
−0.770519 + 0.637416i \(0.780003\pi\)
\(14\) 1.55400 0.415324
\(15\) 0 0
\(16\) −0.497714 −0.124428
\(17\) 7.23729 1.75530 0.877651 0.479301i \(-0.159110\pi\)
0.877651 + 0.479301i \(0.159110\pi\)
\(18\) 1.81688 0.428242
\(19\) 0 0
\(20\) 0 0
\(21\) 1.70828 0.372776
\(22\) −4.34667 −0.926714
\(23\) 4.65440 0.970508 0.485254 0.874373i \(-0.338727\pi\)
0.485254 + 0.874373i \(0.338727\pi\)
\(24\) −3.01360 −0.615148
\(25\) 0 0
\(26\) 5.20676 1.02113
\(27\) 5.08762 0.979113
\(28\) 1.86040 0.351583
\(29\) 5.69836 1.05816 0.529079 0.848573i \(-0.322537\pi\)
0.529079 + 0.848573i \(0.322537\pi\)
\(30\) 0 0
\(31\) 6.93959 1.24639 0.623194 0.782067i \(-0.285835\pi\)
0.623194 + 0.782067i \(0.285835\pi\)
\(32\) −5.38453 −0.951860
\(33\) −4.77820 −0.831778
\(34\) −6.78201 −1.16310
\(35\) 0 0
\(36\) 2.17511 0.362518
\(37\) −0.159177 −0.0261685 −0.0130843 0.999914i \(-0.504165\pi\)
−0.0130843 + 0.999914i \(0.504165\pi\)
\(38\) 0 0
\(39\) 5.72367 0.916521
\(40\) 0 0
\(41\) 7.04774 1.10067 0.550336 0.834944i \(-0.314500\pi\)
0.550336 + 0.834944i \(0.314500\pi\)
\(42\) −1.60081 −0.247011
\(43\) 3.60620 0.549940 0.274970 0.961453i \(-0.411332\pi\)
0.274970 + 0.961453i \(0.411332\pi\)
\(44\) −5.20371 −0.784489
\(45\) 0 0
\(46\) −4.36160 −0.643082
\(47\) −7.34488 −1.07136 −0.535681 0.844421i \(-0.679945\pi\)
−0.535681 + 0.844421i \(0.679945\pi\)
\(48\) 0.512707 0.0740029
\(49\) −4.24997 −0.607139
\(50\) 0 0
\(51\) −7.45531 −1.04395
\(52\) 6.23338 0.864414
\(53\) 0.175188 0.0240640 0.0120320 0.999928i \(-0.496170\pi\)
0.0120320 + 0.999928i \(0.496170\pi\)
\(54\) −4.76757 −0.648784
\(55\) 0 0
\(56\) −4.85137 −0.648291
\(57\) 0 0
\(58\) −5.33988 −0.701161
\(59\) 1.30720 0.170183 0.0850915 0.996373i \(-0.472882\pi\)
0.0850915 + 0.996373i \(0.472882\pi\)
\(60\) 0 0
\(61\) 6.22814 0.797431 0.398716 0.917075i \(-0.369456\pi\)
0.398716 + 0.917075i \(0.369456\pi\)
\(62\) −6.50303 −0.825886
\(63\) 3.21523 0.405080
\(64\) 6.04123 0.755154
\(65\) 0 0
\(66\) 4.47761 0.551156
\(67\) −1.45987 −0.178352 −0.0891760 0.996016i \(-0.528423\pi\)
−0.0891760 + 0.996016i \(0.528423\pi\)
\(68\) −8.11922 −0.984600
\(69\) −4.79460 −0.577202
\(70\) 0 0
\(71\) −10.1796 −1.20810 −0.604050 0.796946i \(-0.706447\pi\)
−0.604050 + 0.796946i \(0.706447\pi\)
\(72\) −5.67203 −0.668455
\(73\) 2.72447 0.318875 0.159437 0.987208i \(-0.449032\pi\)
0.159437 + 0.987208i \(0.449032\pi\)
\(74\) 0.149163 0.0173399
\(75\) 0 0
\(76\) 0 0
\(77\) −7.69207 −0.876593
\(78\) −5.36361 −0.607309
\(79\) 2.47593 0.278564 0.139282 0.990253i \(-0.455521\pi\)
0.139282 + 0.990253i \(0.455521\pi\)
\(80\) 0 0
\(81\) 0.575652 0.0639614
\(82\) −6.60437 −0.729331
\(83\) 5.13444 0.563578 0.281789 0.959476i \(-0.409072\pi\)
0.281789 + 0.959476i \(0.409072\pi\)
\(84\) −1.91645 −0.209101
\(85\) 0 0
\(86\) −3.37934 −0.364403
\(87\) −5.87001 −0.629331
\(88\) 13.5697 1.44653
\(89\) −3.66487 −0.388476 −0.194238 0.980954i \(-0.562223\pi\)
−0.194238 + 0.980954i \(0.562223\pi\)
\(90\) 0 0
\(91\) 9.21412 0.965902
\(92\) −5.22158 −0.544387
\(93\) −7.14864 −0.741279
\(94\) 6.88283 0.709910
\(95\) 0 0
\(96\) 5.54674 0.566111
\(97\) 5.45553 0.553925 0.276962 0.960881i \(-0.410672\pi\)
0.276962 + 0.960881i \(0.410672\pi\)
\(98\) 3.98261 0.402305
\(99\) −8.99327 −0.903858
\(100\) 0 0
\(101\) 12.6577 1.25949 0.629746 0.776801i \(-0.283159\pi\)
0.629746 + 0.776801i \(0.283159\pi\)
\(102\) 6.98631 0.691747
\(103\) −12.5555 −1.23713 −0.618566 0.785733i \(-0.712286\pi\)
−0.618566 + 0.785733i \(0.712286\pi\)
\(104\) −16.2548 −1.59391
\(105\) 0 0
\(106\) −0.164167 −0.0159454
\(107\) −8.39376 −0.811455 −0.405728 0.913994i \(-0.632982\pi\)
−0.405728 + 0.913994i \(0.632982\pi\)
\(108\) −5.70760 −0.549214
\(109\) −5.69743 −0.545715 −0.272858 0.962054i \(-0.587969\pi\)
−0.272858 + 0.962054i \(0.587969\pi\)
\(110\) 0 0
\(111\) 0.163972 0.0155635
\(112\) 0.825369 0.0779901
\(113\) −12.6186 −1.18706 −0.593529 0.804813i \(-0.702266\pi\)
−0.593529 + 0.804813i \(0.702266\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −6.39275 −0.593552
\(117\) 10.7728 0.995945
\(118\) −1.22497 −0.112767
\(119\) −12.0018 −1.10020
\(120\) 0 0
\(121\) 10.5154 0.955947
\(122\) −5.83634 −0.528397
\(123\) −7.26004 −0.654616
\(124\) −7.78524 −0.699136
\(125\) 0 0
\(126\) −3.01296 −0.268416
\(127\) −2.29831 −0.203942 −0.101971 0.994787i \(-0.532515\pi\)
−0.101971 + 0.994787i \(0.532515\pi\)
\(128\) 5.10788 0.451477
\(129\) −3.71483 −0.327073
\(130\) 0 0
\(131\) −2.12308 −0.185494 −0.0927472 0.995690i \(-0.529565\pi\)
−0.0927472 + 0.995690i \(0.529565\pi\)
\(132\) 5.36047 0.466569
\(133\) 0 0
\(134\) 1.36804 0.118180
\(135\) 0 0
\(136\) 21.1725 1.81552
\(137\) −0.0104664 −0.000894205 0 −0.000447103 1.00000i \(-0.500142\pi\)
−0.000447103 1.00000i \(0.500142\pi\)
\(138\) 4.49298 0.382468
\(139\) 18.2404 1.54713 0.773564 0.633719i \(-0.218472\pi\)
0.773564 + 0.633719i \(0.218472\pi\)
\(140\) 0 0
\(141\) 7.56614 0.637184
\(142\) 9.53925 0.800516
\(143\) −25.7727 −2.15522
\(144\) 0.964990 0.0804158
\(145\) 0 0
\(146\) −2.55307 −0.211294
\(147\) 4.37800 0.361091
\(148\) 0.178574 0.0146787
\(149\) 4.58418 0.375550 0.187775 0.982212i \(-0.439872\pi\)
0.187775 + 0.982212i \(0.439872\pi\)
\(150\) 0 0
\(151\) 21.1633 1.72224 0.861122 0.508398i \(-0.169762\pi\)
0.861122 + 0.508398i \(0.169762\pi\)
\(152\) 0 0
\(153\) −14.0320 −1.13442
\(154\) 7.20818 0.580852
\(155\) 0 0
\(156\) −6.42115 −0.514104
\(157\) 6.03786 0.481874 0.240937 0.970541i \(-0.422545\pi\)
0.240937 + 0.970541i \(0.422545\pi\)
\(158\) −2.32017 −0.184583
\(159\) −0.180466 −0.0143119
\(160\) 0 0
\(161\) −7.71848 −0.608301
\(162\) −0.539439 −0.0423823
\(163\) 0.710826 0.0556762 0.0278381 0.999612i \(-0.491138\pi\)
0.0278381 + 0.999612i \(0.491138\pi\)
\(164\) −7.90657 −0.617399
\(165\) 0 0
\(166\) −4.81144 −0.373440
\(167\) −18.9237 −1.46436 −0.732181 0.681111i \(-0.761497\pi\)
−0.732181 + 0.681111i \(0.761497\pi\)
\(168\) 4.99751 0.385566
\(169\) 17.8724 1.37480
\(170\) 0 0
\(171\) 0 0
\(172\) −4.04565 −0.308478
\(173\) 8.75776 0.665840 0.332920 0.942955i \(-0.391966\pi\)
0.332920 + 0.942955i \(0.391966\pi\)
\(174\) 5.50074 0.417010
\(175\) 0 0
\(176\) −2.30863 −0.174020
\(177\) −1.34658 −0.101215
\(178\) 3.43432 0.257413
\(179\) 7.40606 0.553555 0.276778 0.960934i \(-0.410733\pi\)
0.276778 + 0.960934i \(0.410733\pi\)
\(180\) 0 0
\(181\) −18.4532 −1.37161 −0.685807 0.727783i \(-0.740551\pi\)
−0.685807 + 0.727783i \(0.740551\pi\)
\(182\) −8.63448 −0.640030
\(183\) −6.41575 −0.474266
\(184\) 13.6163 1.00381
\(185\) 0 0
\(186\) 6.69893 0.491189
\(187\) 33.5700 2.45488
\(188\) 8.23993 0.600958
\(189\) −8.43691 −0.613695
\(190\) 0 0
\(191\) 4.89265 0.354020 0.177010 0.984209i \(-0.443358\pi\)
0.177010 + 0.984209i \(0.443358\pi\)
\(192\) −6.22321 −0.449122
\(193\) −9.38838 −0.675790 −0.337895 0.941184i \(-0.609715\pi\)
−0.337895 + 0.941184i \(0.609715\pi\)
\(194\) −5.11233 −0.367044
\(195\) 0 0
\(196\) 4.76787 0.340562
\(197\) −5.93272 −0.422689 −0.211344 0.977412i \(-0.567784\pi\)
−0.211344 + 0.977412i \(0.567784\pi\)
\(198\) 8.42752 0.598918
\(199\) 6.01622 0.426478 0.213239 0.977000i \(-0.431599\pi\)
0.213239 + 0.977000i \(0.431599\pi\)
\(200\) 0 0
\(201\) 1.50385 0.106074
\(202\) −11.8615 −0.834570
\(203\) −9.44970 −0.663239
\(204\) 8.36380 0.585583
\(205\) 0 0
\(206\) 11.7657 0.819753
\(207\) −9.02415 −0.627222
\(208\) 2.76545 0.191749
\(209\) 0 0
\(210\) 0 0
\(211\) −1.67907 −0.115592 −0.0577959 0.998328i \(-0.518407\pi\)
−0.0577959 + 0.998328i \(0.518407\pi\)
\(212\) −0.196537 −0.0134982
\(213\) 10.4863 0.718509
\(214\) 7.86572 0.537690
\(215\) 0 0
\(216\) 14.8837 1.01271
\(217\) −11.5081 −0.781219
\(218\) 5.33902 0.361604
\(219\) −2.80654 −0.189648
\(220\) 0 0
\(221\) −40.2125 −2.70499
\(222\) −0.153657 −0.0103128
\(223\) 20.3605 1.36344 0.681719 0.731614i \(-0.261233\pi\)
0.681719 + 0.731614i \(0.261233\pi\)
\(224\) 8.92928 0.596613
\(225\) 0 0
\(226\) 11.8248 0.786573
\(227\) −17.9725 −1.19287 −0.596437 0.802660i \(-0.703417\pi\)
−0.596437 + 0.802660i \(0.703417\pi\)
\(228\) 0 0
\(229\) −2.44953 −0.161870 −0.0809348 0.996719i \(-0.525791\pi\)
−0.0809348 + 0.996719i \(0.525791\pi\)
\(230\) 0 0
\(231\) 7.92379 0.521347
\(232\) 16.6704 1.09446
\(233\) −21.4829 −1.40739 −0.703695 0.710502i \(-0.748468\pi\)
−0.703695 + 0.710502i \(0.748468\pi\)
\(234\) −10.0951 −0.659937
\(235\) 0 0
\(236\) −1.46649 −0.0954607
\(237\) −2.55051 −0.165674
\(238\) 11.2467 0.729018
\(239\) −1.79620 −0.116187 −0.0580933 0.998311i \(-0.518502\pi\)
−0.0580933 + 0.998311i \(0.518502\pi\)
\(240\) 0 0
\(241\) −17.2978 −1.11425 −0.557125 0.830429i \(-0.688095\pi\)
−0.557125 + 0.830429i \(0.688095\pi\)
\(242\) −9.85391 −0.633433
\(243\) −15.8559 −1.01715
\(244\) −6.98709 −0.447303
\(245\) 0 0
\(246\) 6.80332 0.433764
\(247\) 0 0
\(248\) 20.3016 1.28915
\(249\) −5.28911 −0.335184
\(250\) 0 0
\(251\) −3.50798 −0.221422 −0.110711 0.993853i \(-0.535313\pi\)
−0.110711 + 0.993853i \(0.535313\pi\)
\(252\) −3.60703 −0.227222
\(253\) 21.5893 1.35731
\(254\) 2.15373 0.135137
\(255\) 0 0
\(256\) −16.8690 −1.05431
\(257\) 0.0821166 0.00512229 0.00256115 0.999997i \(-0.499185\pi\)
0.00256115 + 0.999997i \(0.499185\pi\)
\(258\) 3.48114 0.216726
\(259\) 0.263966 0.0164021
\(260\) 0 0
\(261\) −11.0482 −0.683868
\(262\) 1.98952 0.122913
\(263\) 24.2253 1.49380 0.746898 0.664939i \(-0.231542\pi\)
0.746898 + 0.664939i \(0.231542\pi\)
\(264\) −13.9785 −0.860316
\(265\) 0 0
\(266\) 0 0
\(267\) 3.77527 0.231043
\(268\) 1.63777 0.100043
\(269\) 14.4267 0.879611 0.439806 0.898093i \(-0.355047\pi\)
0.439806 + 0.898093i \(0.355047\pi\)
\(270\) 0 0
\(271\) −25.8909 −1.57276 −0.786382 0.617741i \(-0.788048\pi\)
−0.786382 + 0.617741i \(0.788048\pi\)
\(272\) −3.60210 −0.218409
\(273\) −9.49169 −0.574463
\(274\) 0.00980798 0.000592522 0
\(275\) 0 0
\(276\) 5.37887 0.323770
\(277\) 26.2297 1.57599 0.787994 0.615683i \(-0.211120\pi\)
0.787994 + 0.615683i \(0.211120\pi\)
\(278\) −17.0929 −1.02516
\(279\) −13.4548 −0.805517
\(280\) 0 0
\(281\) 20.6414 1.23136 0.615682 0.787994i \(-0.288880\pi\)
0.615682 + 0.787994i \(0.288880\pi\)
\(282\) −7.09017 −0.422213
\(283\) −20.8771 −1.24102 −0.620508 0.784200i \(-0.713073\pi\)
−0.620508 + 0.784200i \(0.713073\pi\)
\(284\) 11.4201 0.677659
\(285\) 0 0
\(286\) 24.1514 1.42810
\(287\) −11.6874 −0.689886
\(288\) 10.4398 0.615170
\(289\) 35.3784 2.08108
\(290\) 0 0
\(291\) −5.61987 −0.329443
\(292\) −3.05647 −0.178866
\(293\) 6.62626 0.387110 0.193555 0.981089i \(-0.437998\pi\)
0.193555 + 0.981089i \(0.437998\pi\)
\(294\) −4.10259 −0.239268
\(295\) 0 0
\(296\) −0.465667 −0.0270663
\(297\) 23.5988 1.36934
\(298\) −4.29580 −0.248849
\(299\) −25.8612 −1.49559
\(300\) 0 0
\(301\) −5.98023 −0.344695
\(302\) −19.8319 −1.14120
\(303\) −13.0390 −0.749074
\(304\) 0 0
\(305\) 0 0
\(306\) 13.1493 0.751693
\(307\) −11.4661 −0.654405 −0.327203 0.944954i \(-0.606106\pi\)
−0.327203 + 0.944954i \(0.606106\pi\)
\(308\) 8.62942 0.491707
\(309\) 12.9337 0.735774
\(310\) 0 0
\(311\) 26.4613 1.50048 0.750240 0.661165i \(-0.229938\pi\)
0.750240 + 0.661165i \(0.229938\pi\)
\(312\) 16.7444 0.947966
\(313\) −18.3102 −1.03495 −0.517477 0.855697i \(-0.673129\pi\)
−0.517477 + 0.855697i \(0.673129\pi\)
\(314\) −5.65803 −0.319301
\(315\) 0 0
\(316\) −2.77764 −0.156255
\(317\) −10.5284 −0.591333 −0.295666 0.955291i \(-0.595542\pi\)
−0.295666 + 0.955291i \(0.595542\pi\)
\(318\) 0.169113 0.00948338
\(319\) 26.4317 1.47989
\(320\) 0 0
\(321\) 8.64661 0.482607
\(322\) 7.23292 0.403075
\(323\) 0 0
\(324\) −0.645801 −0.0358778
\(325\) 0 0
\(326\) −0.666109 −0.0368924
\(327\) 5.86906 0.324560
\(328\) 20.6179 1.13843
\(329\) 12.1802 0.671515
\(330\) 0 0
\(331\) −25.7708 −1.41649 −0.708245 0.705967i \(-0.750513\pi\)
−0.708245 + 0.705967i \(0.750513\pi\)
\(332\) −5.76012 −0.316128
\(333\) 0.308619 0.0169122
\(334\) 17.7333 0.970321
\(335\) 0 0
\(336\) −0.850233 −0.0463840
\(337\) −16.6242 −0.905579 −0.452789 0.891618i \(-0.649571\pi\)
−0.452789 + 0.891618i \(0.649571\pi\)
\(338\) −16.7481 −0.910976
\(339\) 12.9987 0.705994
\(340\) 0 0
\(341\) 32.1891 1.74314
\(342\) 0 0
\(343\) 18.6561 1.00733
\(344\) 10.5498 0.568808
\(345\) 0 0
\(346\) −8.20683 −0.441202
\(347\) −9.54628 −0.512471 −0.256236 0.966614i \(-0.582482\pi\)
−0.256236 + 0.966614i \(0.582482\pi\)
\(348\) 6.58533 0.353011
\(349\) 32.0012 1.71298 0.856492 0.516160i \(-0.172639\pi\)
0.856492 + 0.516160i \(0.172639\pi\)
\(350\) 0 0
\(351\) −28.2683 −1.50885
\(352\) −24.9760 −1.33123
\(353\) −18.7280 −0.996789 −0.498394 0.866950i \(-0.666077\pi\)
−0.498394 + 0.866950i \(0.666077\pi\)
\(354\) 1.26187 0.0670675
\(355\) 0 0
\(356\) 4.11147 0.217908
\(357\) 12.3633 0.654335
\(358\) −6.94016 −0.366799
\(359\) −9.87122 −0.520983 −0.260492 0.965476i \(-0.583885\pi\)
−0.260492 + 0.965476i \(0.583885\pi\)
\(360\) 0 0
\(361\) 0 0
\(362\) 17.2923 0.908864
\(363\) −10.8322 −0.568542
\(364\) −10.3369 −0.541803
\(365\) 0 0
\(366\) 6.01215 0.314260
\(367\) 34.1527 1.78276 0.891379 0.453258i \(-0.149738\pi\)
0.891379 + 0.453258i \(0.149738\pi\)
\(368\) −2.31656 −0.120759
\(369\) −13.6645 −0.711344
\(370\) 0 0
\(371\) −0.290518 −0.0150830
\(372\) 8.01977 0.415806
\(373\) 9.81800 0.508357 0.254178 0.967157i \(-0.418195\pi\)
0.254178 + 0.967157i \(0.418195\pi\)
\(374\) −31.4581 −1.62666
\(375\) 0 0
\(376\) −21.4872 −1.10812
\(377\) −31.6617 −1.63066
\(378\) 7.90616 0.406649
\(379\) 6.07203 0.311899 0.155950 0.987765i \(-0.450156\pi\)
0.155950 + 0.987765i \(0.450156\pi\)
\(380\) 0 0
\(381\) 2.36754 0.121293
\(382\) −4.58486 −0.234582
\(383\) −26.4785 −1.35299 −0.676494 0.736448i \(-0.736501\pi\)
−0.676494 + 0.736448i \(0.736501\pi\)
\(384\) −5.26175 −0.268513
\(385\) 0 0
\(386\) 8.79777 0.447795
\(387\) −6.99186 −0.355416
\(388\) −6.12033 −0.310713
\(389\) 31.4368 1.59391 0.796954 0.604040i \(-0.206443\pi\)
0.796954 + 0.604040i \(0.206443\pi\)
\(390\) 0 0
\(391\) 33.6852 1.70353
\(392\) −12.4332 −0.627969
\(393\) 2.18704 0.110321
\(394\) 5.55950 0.280084
\(395\) 0 0
\(396\) 10.0892 0.507001
\(397\) 14.6216 0.733839 0.366919 0.930253i \(-0.380413\pi\)
0.366919 + 0.930253i \(0.380413\pi\)
\(398\) −5.63775 −0.282595
\(399\) 0 0
\(400\) 0 0
\(401\) 28.2233 1.40940 0.704701 0.709504i \(-0.251081\pi\)
0.704701 + 0.709504i \(0.251081\pi\)
\(402\) −1.40925 −0.0702868
\(403\) −38.5584 −1.92073
\(404\) −14.2002 −0.706487
\(405\) 0 0
\(406\) 8.85524 0.439478
\(407\) −0.738337 −0.0365980
\(408\) −21.8103 −1.07977
\(409\) −13.1999 −0.652692 −0.326346 0.945250i \(-0.605817\pi\)
−0.326346 + 0.945250i \(0.605817\pi\)
\(410\) 0 0
\(411\) 0.0107817 0.000531822 0
\(412\) 14.0855 0.693943
\(413\) −2.16776 −0.106668
\(414\) 8.45646 0.415612
\(415\) 0 0
\(416\) 29.9181 1.46685
\(417\) −18.7898 −0.920142
\(418\) 0 0
\(419\) 12.6114 0.616109 0.308054 0.951369i \(-0.400322\pi\)
0.308054 + 0.951369i \(0.400322\pi\)
\(420\) 0 0
\(421\) 6.35565 0.309755 0.154878 0.987934i \(-0.450502\pi\)
0.154878 + 0.987934i \(0.450502\pi\)
\(422\) 1.57344 0.0765938
\(423\) 14.2406 0.692401
\(424\) 0.512508 0.0248896
\(425\) 0 0
\(426\) −9.82661 −0.476101
\(427\) −10.3283 −0.499819
\(428\) 9.41662 0.455169
\(429\) 26.5491 1.28180
\(430\) 0 0
\(431\) −26.4091 −1.27208 −0.636041 0.771656i \(-0.719429\pi\)
−0.636041 + 0.771656i \(0.719429\pi\)
\(432\) −2.53218 −0.121830
\(433\) 16.0552 0.771566 0.385783 0.922590i \(-0.373931\pi\)
0.385783 + 0.922590i \(0.373931\pi\)
\(434\) 10.7841 0.517654
\(435\) 0 0
\(436\) 6.39172 0.306108
\(437\) 0 0
\(438\) 2.62998 0.125665
\(439\) −25.1024 −1.19807 −0.599036 0.800722i \(-0.704449\pi\)
−0.599036 + 0.800722i \(0.704449\pi\)
\(440\) 0 0
\(441\) 8.24004 0.392383
\(442\) 37.6828 1.79239
\(443\) −37.7165 −1.79197 −0.895983 0.444088i \(-0.853528\pi\)
−0.895983 + 0.444088i \(0.853528\pi\)
\(444\) −0.183953 −0.00873004
\(445\) 0 0
\(446\) −19.0796 −0.903446
\(447\) −4.72227 −0.223356
\(448\) −10.0183 −0.473320
\(449\) 33.7311 1.59187 0.795934 0.605384i \(-0.206980\pi\)
0.795934 + 0.605384i \(0.206980\pi\)
\(450\) 0 0
\(451\) 32.6907 1.53935
\(452\) 14.1563 0.665856
\(453\) −21.8008 −1.02429
\(454\) 16.8418 0.790427
\(455\) 0 0
\(456\) 0 0
\(457\) −7.84620 −0.367030 −0.183515 0.983017i \(-0.558748\pi\)
−0.183515 + 0.983017i \(0.558748\pi\)
\(458\) 2.29543 0.107259
\(459\) 36.8206 1.71864
\(460\) 0 0
\(461\) −3.23991 −0.150898 −0.0754489 0.997150i \(-0.524039\pi\)
−0.0754489 + 0.997150i \(0.524039\pi\)
\(462\) −7.42532 −0.345457
\(463\) 14.0731 0.654031 0.327015 0.945019i \(-0.393957\pi\)
0.327015 + 0.945019i \(0.393957\pi\)
\(464\) −2.83615 −0.131665
\(465\) 0 0
\(466\) 20.1314 0.932570
\(467\) −16.9146 −0.782717 −0.391358 0.920238i \(-0.627995\pi\)
−0.391358 + 0.920238i \(0.627995\pi\)
\(468\) −12.0856 −0.558655
\(469\) 2.42094 0.111789
\(470\) 0 0
\(471\) −6.21974 −0.286591
\(472\) 3.82417 0.176022
\(473\) 16.7272 0.769120
\(474\) 2.39006 0.109779
\(475\) 0 0
\(476\) 13.4643 0.617134
\(477\) −0.339663 −0.0155521
\(478\) 1.68321 0.0769880
\(479\) −6.92210 −0.316279 −0.158139 0.987417i \(-0.550550\pi\)
−0.158139 + 0.987417i \(0.550550\pi\)
\(480\) 0 0
\(481\) 0.884433 0.0403267
\(482\) 16.2096 0.738328
\(483\) 7.95099 0.361783
\(484\) −11.7968 −0.536219
\(485\) 0 0
\(486\) 14.8584 0.673990
\(487\) 41.6119 1.88562 0.942808 0.333337i \(-0.108175\pi\)
0.942808 + 0.333337i \(0.108175\pi\)
\(488\) 18.2202 0.824791
\(489\) −0.732239 −0.0331130
\(490\) 0 0
\(491\) −1.77453 −0.0800832 −0.0400416 0.999198i \(-0.512749\pi\)
−0.0400416 + 0.999198i \(0.512749\pi\)
\(492\) 8.14474 0.367193
\(493\) 41.2407 1.85739
\(494\) 0 0
\(495\) 0 0
\(496\) −3.45393 −0.155086
\(497\) 16.8811 0.757221
\(498\) 4.95638 0.222101
\(499\) 27.2650 1.22055 0.610275 0.792190i \(-0.291059\pi\)
0.610275 + 0.792190i \(0.291059\pi\)
\(500\) 0 0
\(501\) 19.4938 0.870918
\(502\) 3.28730 0.146719
\(503\) −0.427240 −0.0190497 −0.00952484 0.999955i \(-0.503032\pi\)
−0.00952484 + 0.999955i \(0.503032\pi\)
\(504\) 9.40604 0.418978
\(505\) 0 0
\(506\) −20.2311 −0.899384
\(507\) −18.4108 −0.817652
\(508\) 2.57838 0.114397
\(509\) 13.0601 0.578878 0.289439 0.957196i \(-0.406531\pi\)
0.289439 + 0.957196i \(0.406531\pi\)
\(510\) 0 0
\(511\) −4.51804 −0.199866
\(512\) 5.59205 0.247136
\(513\) 0 0
\(514\) −0.0769508 −0.00339415
\(515\) 0 0
\(516\) 4.16752 0.183465
\(517\) −34.0690 −1.49835
\(518\) −0.247361 −0.0108684
\(519\) −9.02158 −0.396003
\(520\) 0 0
\(521\) 9.51301 0.416773 0.208386 0.978047i \(-0.433179\pi\)
0.208386 + 0.978047i \(0.433179\pi\)
\(522\) 10.3532 0.453147
\(523\) −4.22384 −0.184696 −0.0923478 0.995727i \(-0.529437\pi\)
−0.0923478 + 0.995727i \(0.529437\pi\)
\(524\) 2.38180 0.104049
\(525\) 0 0
\(526\) −22.7013 −0.989824
\(527\) 50.2238 2.18779
\(528\) 2.37818 0.103497
\(529\) −1.33661 −0.0581133
\(530\) 0 0
\(531\) −2.53446 −0.109986
\(532\) 0 0
\(533\) −39.1593 −1.69618
\(534\) −3.53778 −0.153095
\(535\) 0 0
\(536\) −4.27082 −0.184471
\(537\) −7.62916 −0.329223
\(538\) −13.5191 −0.582852
\(539\) −19.7134 −0.849115
\(540\) 0 0
\(541\) −2.84642 −0.122377 −0.0611887 0.998126i \(-0.519489\pi\)
−0.0611887 + 0.998126i \(0.519489\pi\)
\(542\) 24.2622 1.04215
\(543\) 19.0091 0.815757
\(544\) −38.9694 −1.67080
\(545\) 0 0
\(546\) 8.89458 0.380653
\(547\) 42.2483 1.80641 0.903203 0.429213i \(-0.141209\pi\)
0.903203 + 0.429213i \(0.141209\pi\)
\(548\) 0.0117418 0.000501586 0
\(549\) −12.0754 −0.515365
\(550\) 0 0
\(551\) 0 0
\(552\) −14.0265 −0.597006
\(553\) −4.10588 −0.174600
\(554\) −24.5796 −1.04429
\(555\) 0 0
\(556\) −20.4631 −0.867829
\(557\) 0.534205 0.0226350 0.0113175 0.999936i \(-0.496397\pi\)
0.0113175 + 0.999936i \(0.496397\pi\)
\(558\) 12.6084 0.533755
\(559\) −20.0371 −0.847479
\(560\) 0 0
\(561\) −34.5812 −1.46002
\(562\) −19.3429 −0.815932
\(563\) 20.5002 0.863980 0.431990 0.901879i \(-0.357812\pi\)
0.431990 + 0.901879i \(0.357812\pi\)
\(564\) −8.48815 −0.357415
\(565\) 0 0
\(566\) 19.5638 0.822327
\(567\) −0.954616 −0.0400901
\(568\) −29.7802 −1.24955
\(569\) 15.6118 0.654479 0.327239 0.944941i \(-0.393882\pi\)
0.327239 + 0.944941i \(0.393882\pi\)
\(570\) 0 0
\(571\) 41.7485 1.74712 0.873561 0.486715i \(-0.161805\pi\)
0.873561 + 0.486715i \(0.161805\pi\)
\(572\) 28.9134 1.20893
\(573\) −5.04004 −0.210551
\(574\) 10.9522 0.457135
\(575\) 0 0
\(576\) −11.7130 −0.488042
\(577\) 16.5613 0.689455 0.344727 0.938703i \(-0.387971\pi\)
0.344727 + 0.938703i \(0.387971\pi\)
\(578\) −33.1528 −1.37897
\(579\) 9.67119 0.401921
\(580\) 0 0
\(581\) −8.51455 −0.353243
\(582\) 5.26633 0.218296
\(583\) 0.812606 0.0336547
\(584\) 7.97034 0.329815
\(585\) 0 0
\(586\) −6.20942 −0.256509
\(587\) 10.7958 0.445591 0.222795 0.974865i \(-0.428482\pi\)
0.222795 + 0.974865i \(0.428482\pi\)
\(588\) −4.91150 −0.202547
\(589\) 0 0
\(590\) 0 0
\(591\) 6.11143 0.251391
\(592\) 0.0792245 0.00325611
\(593\) −8.68450 −0.356630 −0.178315 0.983973i \(-0.557065\pi\)
−0.178315 + 0.983973i \(0.557065\pi\)
\(594\) −22.1142 −0.907358
\(595\) 0 0
\(596\) −5.14280 −0.210657
\(597\) −6.19745 −0.253645
\(598\) 24.2343 0.991015
\(599\) −3.05376 −0.124773 −0.0623865 0.998052i \(-0.519871\pi\)
−0.0623865 + 0.998052i \(0.519871\pi\)
\(600\) 0 0
\(601\) −14.6668 −0.598273 −0.299136 0.954210i \(-0.596699\pi\)
−0.299136 + 0.954210i \(0.596699\pi\)
\(602\) 5.60403 0.228403
\(603\) 2.83047 0.115266
\(604\) −23.7422 −0.966058
\(605\) 0 0
\(606\) 12.2188 0.496354
\(607\) 15.6370 0.634687 0.317343 0.948311i \(-0.397209\pi\)
0.317343 + 0.948311i \(0.397209\pi\)
\(608\) 0 0
\(609\) 9.73436 0.394456
\(610\) 0 0
\(611\) 40.8103 1.65101
\(612\) 15.7419 0.636329
\(613\) −35.3890 −1.42935 −0.714674 0.699458i \(-0.753425\pi\)
−0.714674 + 0.699458i \(0.753425\pi\)
\(614\) 10.7448 0.433625
\(615\) 0 0
\(616\) −22.5029 −0.906668
\(617\) 48.2113 1.94091 0.970456 0.241278i \(-0.0775666\pi\)
0.970456 + 0.241278i \(0.0775666\pi\)
\(618\) −12.1201 −0.487542
\(619\) −19.3969 −0.779627 −0.389814 0.920894i \(-0.627461\pi\)
−0.389814 + 0.920894i \(0.627461\pi\)
\(620\) 0 0
\(621\) 23.6798 0.950238
\(622\) −24.7966 −0.994254
\(623\) 6.07754 0.243491
\(624\) −2.84875 −0.114041
\(625\) 0 0
\(626\) 17.1584 0.685786
\(627\) 0 0
\(628\) −6.77363 −0.270297
\(629\) −1.15201 −0.0459336
\(630\) 0 0
\(631\) −12.5878 −0.501111 −0.250556 0.968102i \(-0.580613\pi\)
−0.250556 + 0.968102i \(0.580613\pi\)
\(632\) 7.24325 0.288121
\(633\) 1.72965 0.0687473
\(634\) 9.86606 0.391831
\(635\) 0 0
\(636\) 0.202457 0.00802794
\(637\) 23.6141 0.935625
\(638\) −24.7689 −0.980610
\(639\) 19.7367 0.780773
\(640\) 0 0
\(641\) −37.9593 −1.49930 −0.749652 0.661832i \(-0.769779\pi\)
−0.749652 + 0.661832i \(0.769779\pi\)
\(642\) −8.10267 −0.319787
\(643\) 1.82578 0.0720018 0.0360009 0.999352i \(-0.488538\pi\)
0.0360009 + 0.999352i \(0.488538\pi\)
\(644\) 8.65905 0.341214
\(645\) 0 0
\(646\) 0 0
\(647\) 4.37469 0.171987 0.0859933 0.996296i \(-0.472594\pi\)
0.0859933 + 0.996296i \(0.472594\pi\)
\(648\) 1.68405 0.0661558
\(649\) 6.06341 0.238010
\(650\) 0 0
\(651\) 11.8547 0.464624
\(652\) −0.797447 −0.0312304
\(653\) 4.65542 0.182181 0.0910904 0.995843i \(-0.470965\pi\)
0.0910904 + 0.995843i \(0.470965\pi\)
\(654\) −5.49985 −0.215061
\(655\) 0 0
\(656\) −3.50776 −0.136955
\(657\) −5.28231 −0.206083
\(658\) −11.4139 −0.444962
\(659\) −22.1482 −0.862772 −0.431386 0.902168i \(-0.641975\pi\)
−0.431386 + 0.902168i \(0.641975\pi\)
\(660\) 0 0
\(661\) 37.3989 1.45465 0.727325 0.686294i \(-0.240763\pi\)
0.727325 + 0.686294i \(0.240763\pi\)
\(662\) 24.1496 0.938600
\(663\) 41.4239 1.60877
\(664\) 15.0206 0.582914
\(665\) 0 0
\(666\) −0.289204 −0.0112064
\(667\) 26.5224 1.02695
\(668\) 21.2297 0.821403
\(669\) −20.9738 −0.810894
\(670\) 0 0
\(671\) 28.8890 1.11525
\(672\) −9.19827 −0.354831
\(673\) 3.41423 0.131609 0.0658044 0.997833i \(-0.479039\pi\)
0.0658044 + 0.997833i \(0.479039\pi\)
\(674\) 15.5784 0.600058
\(675\) 0 0
\(676\) −20.0503 −0.771166
\(677\) −17.9024 −0.688046 −0.344023 0.938961i \(-0.611790\pi\)
−0.344023 + 0.938961i \(0.611790\pi\)
\(678\) −12.1810 −0.467808
\(679\) −9.04701 −0.347193
\(680\) 0 0
\(681\) 18.5139 0.709453
\(682\) −30.1641 −1.15504
\(683\) 20.3014 0.776813 0.388407 0.921488i \(-0.373026\pi\)
0.388407 + 0.921488i \(0.373026\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −17.4824 −0.667483
\(687\) 2.52332 0.0962707
\(688\) −1.79485 −0.0684282
\(689\) −0.973397 −0.0370835
\(690\) 0 0
\(691\) 19.6152 0.746198 0.373099 0.927791i \(-0.378295\pi\)
0.373099 + 0.927791i \(0.378295\pi\)
\(692\) −9.82498 −0.373490
\(693\) 14.9137 0.566526
\(694\) 8.94574 0.339576
\(695\) 0 0
\(696\) −17.1725 −0.650923
\(697\) 51.0065 1.93201
\(698\) −29.9881 −1.13506
\(699\) 22.1300 0.837035
\(700\) 0 0
\(701\) 5.53697 0.209128 0.104564 0.994518i \(-0.466655\pi\)
0.104564 + 0.994518i \(0.466655\pi\)
\(702\) 26.4900 0.999801
\(703\) 0 0
\(704\) 28.0221 1.05612
\(705\) 0 0
\(706\) 17.5498 0.660496
\(707\) −20.9906 −0.789433
\(708\) 1.51067 0.0567745
\(709\) −10.8727 −0.408331 −0.204166 0.978936i \(-0.565448\pi\)
−0.204166 + 0.978936i \(0.565448\pi\)
\(710\) 0 0
\(711\) −4.80044 −0.180031
\(712\) −10.7215 −0.401804
\(713\) 32.2996 1.20963
\(714\) −11.5855 −0.433578
\(715\) 0 0
\(716\) −8.30856 −0.310505
\(717\) 1.85031 0.0691011
\(718\) 9.25024 0.345216
\(719\) 19.8622 0.740733 0.370367 0.928886i \(-0.379232\pi\)
0.370367 + 0.928886i \(0.379232\pi\)
\(720\) 0 0
\(721\) 20.8211 0.775417
\(722\) 0 0
\(723\) 17.8189 0.662691
\(724\) 20.7019 0.769379
\(725\) 0 0
\(726\) 10.1507 0.376730
\(727\) −23.4155 −0.868434 −0.434217 0.900808i \(-0.642975\pi\)
−0.434217 + 0.900808i \(0.642975\pi\)
\(728\) 26.9556 0.999042
\(729\) 14.6065 0.540983
\(730\) 0 0
\(731\) 26.0991 0.965310
\(732\) 7.19757 0.266030
\(733\) 21.7404 0.802999 0.401499 0.915859i \(-0.368489\pi\)
0.401499 + 0.915859i \(0.368489\pi\)
\(734\) −32.0043 −1.18130
\(735\) 0 0
\(736\) −25.0617 −0.923788
\(737\) −6.77159 −0.249435
\(738\) 12.8049 0.471353
\(739\) 12.2347 0.450060 0.225030 0.974352i \(-0.427752\pi\)
0.225030 + 0.974352i \(0.427752\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0.272242 0.00999433
\(743\) 50.4338 1.85024 0.925119 0.379677i \(-0.123965\pi\)
0.925119 + 0.379677i \(0.123965\pi\)
\(744\) −20.9131 −0.766712
\(745\) 0 0
\(746\) −9.20037 −0.336849
\(747\) −9.95489 −0.364230
\(748\) −37.6608 −1.37701
\(749\) 13.9195 0.508609
\(750\) 0 0
\(751\) 22.2970 0.813628 0.406814 0.913511i \(-0.366640\pi\)
0.406814 + 0.913511i \(0.366640\pi\)
\(752\) 3.65565 0.133308
\(753\) 3.61365 0.131689
\(754\) 29.6700 1.08052
\(755\) 0 0
\(756\) 9.46502 0.344240
\(757\) −32.4795 −1.18049 −0.590244 0.807225i \(-0.700968\pi\)
−0.590244 + 0.807225i \(0.700968\pi\)
\(758\) −5.69005 −0.206672
\(759\) −22.2396 −0.807248
\(760\) 0 0
\(761\) −30.6378 −1.11062 −0.555310 0.831644i \(-0.687400\pi\)
−0.555310 + 0.831644i \(0.687400\pi\)
\(762\) −2.21861 −0.0803716
\(763\) 9.44817 0.342047
\(764\) −5.48887 −0.198580
\(765\) 0 0
\(766\) 24.8128 0.896522
\(767\) −7.26319 −0.262259
\(768\) 17.3772 0.627045
\(769\) −46.4253 −1.67414 −0.837070 0.547096i \(-0.815733\pi\)
−0.837070 + 0.547096i \(0.815733\pi\)
\(770\) 0 0
\(771\) −0.0845903 −0.00304644
\(772\) 10.5324 0.379071
\(773\) 19.6866 0.708078 0.354039 0.935231i \(-0.384808\pi\)
0.354039 + 0.935231i \(0.384808\pi\)
\(774\) 6.55201 0.235507
\(775\) 0 0
\(776\) 15.9600 0.572930
\(777\) −0.271918 −0.00975500
\(778\) −29.4591 −1.05616
\(779\) 0 0
\(780\) 0 0
\(781\) −47.2179 −1.68959
\(782\) −31.5661 −1.12880
\(783\) 28.9911 1.03606
\(784\) 2.11527 0.0755454
\(785\) 0 0
\(786\) −2.04945 −0.0731016
\(787\) 16.9130 0.602882 0.301441 0.953485i \(-0.402532\pi\)
0.301441 + 0.953485i \(0.402532\pi\)
\(788\) 6.65567 0.237099
\(789\) −24.9550 −0.888423
\(790\) 0 0
\(791\) 20.9257 0.744032
\(792\) −26.3095 −0.934869
\(793\) −34.6054 −1.22887
\(794\) −13.7018 −0.486259
\(795\) 0 0
\(796\) −6.74935 −0.239224
\(797\) 25.3986 0.899664 0.449832 0.893113i \(-0.351484\pi\)
0.449832 + 0.893113i \(0.351484\pi\)
\(798\) 0 0
\(799\) −53.1571 −1.88056
\(800\) 0 0
\(801\) 7.10562 0.251065
\(802\) −26.4478 −0.933903
\(803\) 12.6374 0.445963
\(804\) −1.68711 −0.0594998
\(805\) 0 0
\(806\) 36.1328 1.27272
\(807\) −14.8613 −0.523142
\(808\) 37.0298 1.30270
\(809\) 23.9338 0.841468 0.420734 0.907184i \(-0.361773\pi\)
0.420734 + 0.907184i \(0.361773\pi\)
\(810\) 0 0
\(811\) −41.5106 −1.45763 −0.728817 0.684709i \(-0.759929\pi\)
−0.728817 + 0.684709i \(0.759929\pi\)
\(812\) 10.6012 0.372030
\(813\) 26.6709 0.935389
\(814\) 0.691890 0.0242507
\(815\) 0 0
\(816\) 3.71061 0.129897
\(817\) 0 0
\(818\) 12.3695 0.432489
\(819\) −17.8647 −0.624245
\(820\) 0 0
\(821\) −0.396510 −0.0138383 −0.00691915 0.999976i \(-0.502202\pi\)
−0.00691915 + 0.999976i \(0.502202\pi\)
\(822\) −0.0101034 −0.000352398 0
\(823\) 47.7970 1.66610 0.833050 0.553198i \(-0.186593\pi\)
0.833050 + 0.553198i \(0.186593\pi\)
\(824\) −36.7307 −1.27958
\(825\) 0 0
\(826\) 2.03139 0.0706810
\(827\) −13.1333 −0.456691 −0.228346 0.973580i \(-0.573332\pi\)
−0.228346 + 0.973580i \(0.573332\pi\)
\(828\) 10.1238 0.351827
\(829\) −3.12517 −0.108542 −0.0542708 0.998526i \(-0.517283\pi\)
−0.0542708 + 0.998526i \(0.517283\pi\)
\(830\) 0 0
\(831\) −27.0198 −0.937307
\(832\) −33.5669 −1.16372
\(833\) −30.7583 −1.06571
\(834\) 17.6078 0.609708
\(835\) 0 0
\(836\) 0 0
\(837\) 35.3060 1.22035
\(838\) −11.8181 −0.408249
\(839\) 26.7440 0.923304 0.461652 0.887061i \(-0.347257\pi\)
0.461652 + 0.887061i \(0.347257\pi\)
\(840\) 0 0
\(841\) 3.47126 0.119699
\(842\) −5.95583 −0.205251
\(843\) −21.2632 −0.732345
\(844\) 1.88368 0.0648388
\(845\) 0 0
\(846\) −13.3447 −0.458802
\(847\) −17.4379 −0.599174
\(848\) −0.0871936 −0.00299424
\(849\) 21.5060 0.738085
\(850\) 0 0
\(851\) −0.740872 −0.0253968
\(852\) −11.7641 −0.403033
\(853\) −1.50616 −0.0515698 −0.0257849 0.999668i \(-0.508209\pi\)
−0.0257849 + 0.999668i \(0.508209\pi\)
\(854\) 9.67852 0.331192
\(855\) 0 0
\(856\) −24.5557 −0.839296
\(857\) 11.1639 0.381353 0.190677 0.981653i \(-0.438932\pi\)
0.190677 + 0.981653i \(0.438932\pi\)
\(858\) −24.8789 −0.849353
\(859\) −15.0137 −0.512261 −0.256130 0.966642i \(-0.582448\pi\)
−0.256130 + 0.966642i \(0.582448\pi\)
\(860\) 0 0
\(861\) 12.0395 0.410304
\(862\) 24.7477 0.842911
\(863\) 16.5470 0.563267 0.281633 0.959522i \(-0.409124\pi\)
0.281633 + 0.959522i \(0.409124\pi\)
\(864\) −27.3945 −0.931979
\(865\) 0 0
\(866\) −15.0452 −0.511258
\(867\) −36.4441 −1.23771
\(868\) 12.9104 0.438209
\(869\) 11.4845 0.389586
\(870\) 0 0
\(871\) 8.11149 0.274847
\(872\) −16.6677 −0.564438
\(873\) −10.5774 −0.357991
\(874\) 0 0
\(875\) 0 0
\(876\) 3.14854 0.106379
\(877\) −38.8103 −1.31053 −0.655265 0.755399i \(-0.727443\pi\)
−0.655265 + 0.755399i \(0.727443\pi\)
\(878\) 23.5232 0.793871
\(879\) −6.82587 −0.230231
\(880\) 0 0
\(881\) −6.88434 −0.231939 −0.115970 0.993253i \(-0.536998\pi\)
−0.115970 + 0.993253i \(0.536998\pi\)
\(882\) −7.72167 −0.260002
\(883\) 38.0406 1.28017 0.640083 0.768306i \(-0.278900\pi\)
0.640083 + 0.768306i \(0.278900\pi\)
\(884\) 45.1128 1.51731
\(885\) 0 0
\(886\) 35.3438 1.18740
\(887\) 23.7860 0.798657 0.399329 0.916808i \(-0.369243\pi\)
0.399329 + 0.916808i \(0.369243\pi\)
\(888\) 0.479695 0.0160975
\(889\) 3.81133 0.127828
\(890\) 0 0
\(891\) 2.67015 0.0894533
\(892\) −22.8416 −0.764793
\(893\) 0 0
\(894\) 4.42520 0.148001
\(895\) 0 0
\(896\) −8.47050 −0.282980
\(897\) 26.6402 0.889491
\(898\) −31.6091 −1.05481
\(899\) 39.5443 1.31888
\(900\) 0 0
\(901\) 1.26789 0.0422395
\(902\) −30.6342 −1.02001
\(903\) 6.16038 0.205005
\(904\) −36.9153 −1.22779
\(905\) 0 0
\(906\) 20.4294 0.678720
\(907\) −55.4867 −1.84241 −0.921203 0.389082i \(-0.872792\pi\)
−0.921203 + 0.389082i \(0.872792\pi\)
\(908\) 20.1626 0.669118
\(909\) −24.5414 −0.813987
\(910\) 0 0
\(911\) −56.4481 −1.87021 −0.935105 0.354370i \(-0.884695\pi\)
−0.935105 + 0.354370i \(0.884695\pi\)
\(912\) 0 0
\(913\) 23.8160 0.788193
\(914\) 7.35261 0.243203
\(915\) 0 0
\(916\) 2.74803 0.0907974
\(917\) 3.52075 0.116265
\(918\) −34.5043 −1.13881
\(919\) −2.23921 −0.0738646 −0.0369323 0.999318i \(-0.511759\pi\)
−0.0369323 + 0.999318i \(0.511759\pi\)
\(920\) 0 0
\(921\) 11.8115 0.389202
\(922\) 3.03610 0.0999885
\(923\) 56.5611 1.86173
\(924\) −8.88938 −0.292439
\(925\) 0 0
\(926\) −13.1878 −0.433376
\(927\) 24.3432 0.799535
\(928\) −30.6830 −1.00722
\(929\) −0.843663 −0.0276797 −0.0138399 0.999904i \(-0.504406\pi\)
−0.0138399 + 0.999904i \(0.504406\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 24.1008 0.789447
\(933\) −27.2584 −0.892399
\(934\) 15.8506 0.518647
\(935\) 0 0
\(936\) 31.5155 1.03012
\(937\) 22.1652 0.724106 0.362053 0.932158i \(-0.382076\pi\)
0.362053 + 0.932158i \(0.382076\pi\)
\(938\) −2.26864 −0.0740738
\(939\) 18.8618 0.615531
\(940\) 0 0
\(941\) −44.7326 −1.45824 −0.729121 0.684385i \(-0.760071\pi\)
−0.729121 + 0.684385i \(0.760071\pi\)
\(942\) 5.82847 0.189902
\(943\) 32.8029 1.06821
\(944\) −0.650612 −0.0211756
\(945\) 0 0
\(946\) −15.6750 −0.509637
\(947\) 21.5903 0.701589 0.350795 0.936452i \(-0.385912\pi\)
0.350795 + 0.936452i \(0.385912\pi\)
\(948\) 2.86132 0.0929312
\(949\) −15.1379 −0.491398
\(950\) 0 0
\(951\) 10.8455 0.351691
\(952\) −35.1107 −1.13795
\(953\) 53.5274 1.73392 0.866962 0.498374i \(-0.166070\pi\)
0.866962 + 0.498374i \(0.166070\pi\)
\(954\) 0.318295 0.0103052
\(955\) 0 0
\(956\) 2.01509 0.0651725
\(957\) −27.2279 −0.880153
\(958\) 6.48664 0.209574
\(959\) 0.0173567 0.000560476 0
\(960\) 0 0
\(961\) 17.1579 0.553482
\(962\) −0.828795 −0.0267214
\(963\) 16.2742 0.524429
\(964\) 19.4057 0.625015
\(965\) 0 0
\(966\) −7.45081 −0.239726
\(967\) 28.9670 0.931515 0.465757 0.884912i \(-0.345782\pi\)
0.465757 + 0.884912i \(0.345782\pi\)
\(968\) 30.7625 0.988745
\(969\) 0 0
\(970\) 0 0
\(971\) −17.6259 −0.565642 −0.282821 0.959173i \(-0.591270\pi\)
−0.282821 + 0.959173i \(0.591270\pi\)
\(972\) 17.7880 0.570552
\(973\) −30.2484 −0.969718
\(974\) −38.9942 −1.24945
\(975\) 0 0
\(976\) −3.09983 −0.0992232
\(977\) −11.3082 −0.361782 −0.180891 0.983503i \(-0.557898\pi\)
−0.180891 + 0.983503i \(0.557898\pi\)
\(978\) 0.686175 0.0219415
\(979\) −16.9994 −0.543303
\(980\) 0 0
\(981\) 11.0464 0.352686
\(982\) 1.66289 0.0530650
\(983\) 18.4503 0.588474 0.294237 0.955733i \(-0.404935\pi\)
0.294237 + 0.955733i \(0.404935\pi\)
\(984\) −21.2390 −0.677075
\(985\) 0 0
\(986\) −38.6463 −1.23075
\(987\) −12.5471 −0.399378
\(988\) 0 0
\(989\) 16.7847 0.533721
\(990\) 0 0
\(991\) 13.6693 0.434218 0.217109 0.976147i \(-0.430337\pi\)
0.217109 + 0.976147i \(0.430337\pi\)
\(992\) −37.3665 −1.18639
\(993\) 26.5471 0.842446
\(994\) −15.8191 −0.501753
\(995\) 0 0
\(996\) 5.93364 0.188015
\(997\) −43.6905 −1.38369 −0.691846 0.722045i \(-0.743202\pi\)
−0.691846 + 0.722045i \(0.743202\pi\)
\(998\) −25.5498 −0.808765
\(999\) −0.809832 −0.0256219
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 9025.2.a.cv.1.15 40
5.2 odd 4 1805.2.b.m.1084.15 40
5.3 odd 4 1805.2.b.m.1084.26 yes 40
5.4 even 2 inner 9025.2.a.cv.1.26 40
19.18 odd 2 inner 9025.2.a.cv.1.25 40
95.18 even 4 1805.2.b.m.1084.16 yes 40
95.37 even 4 1805.2.b.m.1084.25 yes 40
95.94 odd 2 inner 9025.2.a.cv.1.16 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1805.2.b.m.1084.15 40 5.2 odd 4
1805.2.b.m.1084.16 yes 40 95.18 even 4
1805.2.b.m.1084.25 yes 40 95.37 even 4
1805.2.b.m.1084.26 yes 40 5.3 odd 4
9025.2.a.cv.1.15 40 1.1 even 1 trivial
9025.2.a.cv.1.16 40 95.94 odd 2 inner
9025.2.a.cv.1.25 40 19.18 odd 2 inner
9025.2.a.cv.1.26 40 5.4 even 2 inner