Properties

Label 504.2.j.a.323.13
Level $504$
Weight $2$
Character 504.323
Analytic conductor $4.024$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [504,2,Mod(323,504)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(504, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("504.323");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 504.j (of order \(2\), degree \(1\), minimal)

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: no
Analytic conductor: \(4.02446026187\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 323.13
Character \(\chi\) \(=\) 504.323
Dual form 504.2.j.a.323.14

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.157273 - 1.40544i) q^{2} +(-1.95053 - 0.442076i) q^{4} -1.81873 q^{5} +1.00000i q^{7} +(-0.928077 + 2.67183i) q^{8} +O(q^{10})\) \(q+(0.157273 - 1.40544i) q^{2} +(-1.95053 - 0.442076i) q^{4} -1.81873 q^{5} +1.00000i q^{7} +(-0.928077 + 2.67183i) q^{8} +(-0.286037 + 2.55612i) q^{10} +2.36894i q^{11} +6.99210i q^{13} +(1.40544 + 0.157273i) q^{14} +(3.60914 + 1.72456i) q^{16} -3.69378i q^{17} +5.53035 q^{19} +(3.54749 + 0.804017i) q^{20} +(3.32941 + 0.372570i) q^{22} -7.60875 q^{23} -1.69222 q^{25} +(9.82698 + 1.09967i) q^{26} +(0.442076 - 1.95053i) q^{28} +5.87055 q^{29} +2.39191i q^{31} +(2.99139 - 4.80120i) q^{32} +(-5.19139 - 0.580932i) q^{34} -1.81873i q^{35} +8.88054i q^{37} +(0.869775 - 7.77259i) q^{38} +(1.68792 - 4.85934i) q^{40} +9.83200i q^{41} -2.88967 q^{43} +(1.04725 - 4.62069i) q^{44} +(-1.19665 + 10.6937i) q^{46} +0.169907 q^{47} -1.00000 q^{49} +(-0.266140 + 2.37831i) q^{50} +(3.09104 - 13.6383i) q^{52} -2.02343 q^{53} -4.30847i q^{55} +(-2.67183 - 0.928077i) q^{56} +(0.923279 - 8.25072i) q^{58} -0.169907i q^{59} +0.420023i q^{61} +(3.36169 + 0.376183i) q^{62} +(-6.27735 - 4.95933i) q^{64} -12.7167i q^{65} -9.76396 q^{67} +(-1.63293 + 7.20483i) q^{68} +(-2.55612 - 0.286037i) q^{70} -12.0101 q^{71} +8.78003 q^{73} +(12.4811 + 1.39667i) q^{74} +(-10.7871 - 2.44484i) q^{76} -2.36894 q^{77} -14.2845i q^{79} +(-6.56405 - 3.13652i) q^{80} +(13.8183 + 1.54631i) q^{82} +10.2248i q^{83} +6.71799i q^{85} +(-0.454467 + 4.06126i) q^{86} +(-6.32941 - 2.19856i) q^{88} +7.42827i q^{89} -6.99210 q^{91} +(14.8411 + 3.36364i) q^{92} +(0.0267217 - 0.238794i) q^{94} -10.0582 q^{95} +4.84384 q^{97} +(-0.157273 + 1.40544i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 8 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 8 q^{4} + 24 q^{10} + 12 q^{16} + 32 q^{19} + 12 q^{22} + 24 q^{25} + 4 q^{28} - 8 q^{40} - 64 q^{43} - 12 q^{46} - 24 q^{49} - 16 q^{52} - 12 q^{58} + 16 q^{64} + 16 q^{67} + 24 q^{70} + 8 q^{76} + 24 q^{82} - 84 q^{88} - 72 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).

\(n\) \(73\) \(127\) \(253\) \(281\)
\(\chi(n)\) \(1\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.157273 1.40544i 0.111209 0.993797i
\(3\) 0 0
\(4\) −1.95053 0.442076i −0.975265 0.221038i
\(5\) −1.81873 −0.813361 −0.406681 0.913570i \(-0.633314\pi\)
−0.406681 + 0.913570i \(0.633314\pi\)
\(6\) 0 0
\(7\) 1.00000i 0.377964i
\(8\) −0.928077 + 2.67183i −0.328125 + 0.944634i
\(9\) 0 0
\(10\) −0.286037 + 2.55612i −0.0904529 + 0.808316i
\(11\) 2.36894i 0.714263i 0.934054 + 0.357131i \(0.116245\pi\)
−0.934054 + 0.357131i \(0.883755\pi\)
\(12\) 0 0
\(13\) 6.99210i 1.93926i 0.244579 + 0.969629i \(0.421350\pi\)
−0.244579 + 0.969629i \(0.578650\pi\)
\(14\) 1.40544 + 0.157273i 0.375620 + 0.0420330i
\(15\) 0 0
\(16\) 3.60914 + 1.72456i 0.902285 + 0.431141i
\(17\) 3.69378i 0.895873i −0.894065 0.447937i \(-0.852159\pi\)
0.894065 0.447937i \(-0.147841\pi\)
\(18\) 0 0
\(19\) 5.53035 1.26875 0.634375 0.773025i \(-0.281258\pi\)
0.634375 + 0.773025i \(0.281258\pi\)
\(20\) 3.54749 + 0.804017i 0.793243 + 0.179784i
\(21\) 0 0
\(22\) 3.32941 + 0.372570i 0.709832 + 0.0794323i
\(23\) −7.60875 −1.58653 −0.793267 0.608874i \(-0.791622\pi\)
−0.793267 + 0.608874i \(0.791622\pi\)
\(24\) 0 0
\(25\) −1.69222 −0.338443
\(26\) 9.82698 + 1.09967i 1.92723 + 0.215663i
\(27\) 0 0
\(28\) 0.442076 1.95053i 0.0835445 0.368616i
\(29\) 5.87055 1.09013 0.545067 0.838392i \(-0.316504\pi\)
0.545067 + 0.838392i \(0.316504\pi\)
\(30\) 0 0
\(31\) 2.39191i 0.429600i 0.976658 + 0.214800i \(0.0689099\pi\)
−0.976658 + 0.214800i \(0.931090\pi\)
\(32\) 2.99139 4.80120i 0.528809 0.848741i
\(33\) 0 0
\(34\) −5.19139 0.580932i −0.890316 0.0996290i
\(35\) 1.81873i 0.307422i
\(36\) 0 0
\(37\) 8.88054i 1.45995i 0.683473 + 0.729976i \(0.260469\pi\)
−0.683473 + 0.729976i \(0.739531\pi\)
\(38\) 0.869775 7.77259i 0.141096 1.26088i
\(39\) 0 0
\(40\) 1.68792 4.85934i 0.266884 0.768329i
\(41\) 9.83200i 1.53550i 0.640749 + 0.767750i \(0.278624\pi\)
−0.640749 + 0.767750i \(0.721376\pi\)
\(42\) 0 0
\(43\) −2.88967 −0.440671 −0.220335 0.975424i \(-0.570715\pi\)
−0.220335 + 0.975424i \(0.570715\pi\)
\(44\) 1.04725 4.62069i 0.157879 0.696596i
\(45\) 0 0
\(46\) −1.19665 + 10.6937i −0.176437 + 1.57669i
\(47\) 0.169907 0.0247835 0.0123917 0.999923i \(-0.496055\pi\)
0.0123917 + 0.999923i \(0.496055\pi\)
\(48\) 0 0
\(49\) −1.00000 −0.142857
\(50\) −0.266140 + 2.37831i −0.0376379 + 0.336344i
\(51\) 0 0
\(52\) 3.09104 13.6383i 0.428650 1.89129i
\(53\) −2.02343 −0.277939 −0.138970 0.990297i \(-0.544379\pi\)
−0.138970 + 0.990297i \(0.544379\pi\)
\(54\) 0 0
\(55\) 4.30847i 0.580954i
\(56\) −2.67183 0.928077i −0.357038 0.124020i
\(57\) 0 0
\(58\) 0.923279 8.25072i 0.121232 1.08337i
\(59\) 0.169907i 0.0221200i −0.999939 0.0110600i \(-0.996479\pi\)
0.999939 0.0110600i \(-0.00352058\pi\)
\(60\) 0 0
\(61\) 0.420023i 0.0537785i 0.999638 + 0.0268892i \(0.00856014\pi\)
−0.999638 + 0.0268892i \(0.991440\pi\)
\(62\) 3.36169 + 0.376183i 0.426935 + 0.0477753i
\(63\) 0 0
\(64\) −6.27735 4.95933i −0.784668 0.619916i
\(65\) 12.7167i 1.57732i
\(66\) 0 0
\(67\) −9.76396 −1.19286 −0.596429 0.802666i \(-0.703414\pi\)
−0.596429 + 0.802666i \(0.703414\pi\)
\(68\) −1.63293 + 7.20483i −0.198022 + 0.873714i
\(69\) 0 0
\(70\) −2.55612 0.286037i −0.305515 0.0341880i
\(71\) −12.0101 −1.42534 −0.712670 0.701500i \(-0.752514\pi\)
−0.712670 + 0.701500i \(0.752514\pi\)
\(72\) 0 0
\(73\) 8.78003 1.02762 0.513812 0.857903i \(-0.328233\pi\)
0.513812 + 0.857903i \(0.328233\pi\)
\(74\) 12.4811 + 1.39667i 1.45090 + 0.162359i
\(75\) 0 0
\(76\) −10.7871 2.44484i −1.23737 0.280442i
\(77\) −2.36894 −0.269966
\(78\) 0 0
\(79\) 14.2845i 1.60713i −0.595216 0.803566i \(-0.702933\pi\)
0.595216 0.803566i \(-0.297067\pi\)
\(80\) −6.56405 3.13652i −0.733883 0.350674i
\(81\) 0 0
\(82\) 13.8183 + 1.54631i 1.52598 + 0.170761i
\(83\) 10.2248i 1.12232i 0.827707 + 0.561161i \(0.189645\pi\)
−0.827707 + 0.561161i \(0.810355\pi\)
\(84\) 0 0
\(85\) 6.71799i 0.728669i
\(86\) −0.454467 + 4.06126i −0.0490064 + 0.437937i
\(87\) 0 0
\(88\) −6.32941 2.19856i −0.674717 0.234367i
\(89\) 7.42827i 0.787395i 0.919240 + 0.393698i \(0.128804\pi\)
−0.919240 + 0.393698i \(0.871196\pi\)
\(90\) 0 0
\(91\) −6.99210 −0.732971
\(92\) 14.8411 + 3.36364i 1.54729 + 0.350684i
\(93\) 0 0
\(94\) 0.0267217 0.238794i 0.00275614 0.0246297i
\(95\) −10.0582 −1.03195
\(96\) 0 0
\(97\) 4.84384 0.491818 0.245909 0.969293i \(-0.420914\pi\)
0.245909 + 0.969293i \(0.420914\pi\)
\(98\) −0.157273 + 1.40544i −0.0158870 + 0.141971i
\(99\) 0 0
\(100\) 3.30072 + 0.748088i 0.330072 + 0.0748088i
\(101\) 0.899761 0.0895295 0.0447648 0.998998i \(-0.485746\pi\)
0.0447648 + 0.998998i \(0.485746\pi\)
\(102\) 0 0
\(103\) 13.6119i 1.34122i −0.741810 0.670611i \(-0.766032\pi\)
0.741810 0.670611i \(-0.233968\pi\)
\(104\) −18.6817 6.48921i −1.83189 0.636319i
\(105\) 0 0
\(106\) −0.318230 + 2.84381i −0.0309093 + 0.276215i
\(107\) 9.64387i 0.932308i −0.884704 0.466154i \(-0.845639\pi\)
0.884704 0.466154i \(-0.154361\pi\)
\(108\) 0 0
\(109\) 1.13844i 0.109043i 0.998513 + 0.0545215i \(0.0173633\pi\)
−0.998513 + 0.0545215i \(0.982637\pi\)
\(110\) −6.05530 0.677605i −0.577350 0.0646071i
\(111\) 0 0
\(112\) −1.72456 + 3.60914i −0.162956 + 0.341031i
\(113\) 7.28073i 0.684914i 0.939534 + 0.342457i \(0.111259\pi\)
−0.939534 + 0.342457i \(0.888741\pi\)
\(114\) 0 0
\(115\) 13.8383 1.29043
\(116\) −11.4507 2.59523i −1.06317 0.240961i
\(117\) 0 0
\(118\) −0.238794 0.0267217i −0.0219828 0.00245994i
\(119\) 3.69378 0.338608
\(120\) 0 0
\(121\) 5.38811 0.489829
\(122\) 0.590318 + 0.0660583i 0.0534449 + 0.00598064i
\(123\) 0 0
\(124\) 1.05741 4.66549i 0.0949578 0.418974i
\(125\) 12.1713 1.08864
\(126\) 0 0
\(127\) 5.44445i 0.483117i 0.970386 + 0.241559i \(0.0776586\pi\)
−0.970386 + 0.241559i \(0.922341\pi\)
\(128\) −7.95730 + 8.04247i −0.703333 + 0.710861i
\(129\) 0 0
\(130\) −17.8726 2.00000i −1.56753 0.175412i
\(131\) 6.73222i 0.588197i −0.955775 0.294099i \(-0.904981\pi\)
0.955775 0.294099i \(-0.0950194\pi\)
\(132\) 0 0
\(133\) 5.53035i 0.479542i
\(134\) −1.53561 + 13.7227i −0.132656 + 1.18546i
\(135\) 0 0
\(136\) 9.86915 + 3.42811i 0.846273 + 0.293958i
\(137\) 4.79689i 0.409826i 0.978780 + 0.204913i \(0.0656911\pi\)
−0.978780 + 0.204913i \(0.934309\pi\)
\(138\) 0 0
\(139\) 8.68075 0.736292 0.368146 0.929768i \(-0.379993\pi\)
0.368146 + 0.929768i \(0.379993\pi\)
\(140\) −0.804017 + 3.54749i −0.0679518 + 0.299818i
\(141\) 0 0
\(142\) −1.88887 + 16.8795i −0.158510 + 1.41650i
\(143\) −16.5639 −1.38514
\(144\) 0 0
\(145\) −10.6770 −0.886673
\(146\) 1.38086 12.3398i 0.114281 1.02125i
\(147\) 0 0
\(148\) 3.92587 17.3218i 0.322705 1.42384i
\(149\) −6.20706 −0.508503 −0.254251 0.967138i \(-0.581829\pi\)
−0.254251 + 0.967138i \(0.581829\pi\)
\(150\) 0 0
\(151\) 4.68075i 0.380914i −0.981695 0.190457i \(-0.939003\pi\)
0.981695 0.190457i \(-0.0609970\pi\)
\(152\) −5.13259 + 14.7762i −0.416308 + 1.19850i
\(153\) 0 0
\(154\) −0.372570 + 3.32941i −0.0300226 + 0.268291i
\(155\) 4.35024i 0.349420i
\(156\) 0 0
\(157\) 1.71964i 0.137243i −0.997643 0.0686213i \(-0.978140\pi\)
0.997643 0.0686213i \(-0.0218600\pi\)
\(158\) −20.0760 2.24657i −1.59716 0.178727i
\(159\) 0 0
\(160\) −5.44054 + 8.73210i −0.430113 + 0.690333i
\(161\) 7.60875i 0.599654i
\(162\) 0 0
\(163\) −18.2044 −1.42588 −0.712941 0.701225i \(-0.752637\pi\)
−0.712941 + 0.701225i \(0.752637\pi\)
\(164\) 4.34649 19.1776i 0.339404 1.49752i
\(165\) 0 0
\(166\) 14.3704 + 1.60809i 1.11536 + 0.124812i
\(167\) 8.80889 0.681652 0.340826 0.940126i \(-0.389293\pi\)
0.340826 + 0.940126i \(0.389293\pi\)
\(168\) 0 0
\(169\) −35.8894 −2.76073
\(170\) 9.44175 + 1.05656i 0.724149 + 0.0810343i
\(171\) 0 0
\(172\) 5.63639 + 1.27745i 0.429771 + 0.0974049i
\(173\) 3.74110 0.284430 0.142215 0.989836i \(-0.454578\pi\)
0.142215 + 0.989836i \(0.454578\pi\)
\(174\) 0 0
\(175\) 1.69222i 0.127920i
\(176\) −4.08539 + 8.54984i −0.307948 + 0.644468i
\(177\) 0 0
\(178\) 10.4400 + 1.16827i 0.782511 + 0.0875652i
\(179\) 15.8375i 1.18375i 0.806031 + 0.591873i \(0.201611\pi\)
−0.806031 + 0.591873i \(0.798389\pi\)
\(180\) 0 0
\(181\) 8.14875i 0.605692i −0.953040 0.302846i \(-0.902063\pi\)
0.953040 0.302846i \(-0.0979368\pi\)
\(182\) −1.09967 + 9.82698i −0.0815128 + 0.728424i
\(183\) 0 0
\(184\) 7.06151 20.3293i 0.520581 1.49870i
\(185\) 16.1513i 1.18747i
\(186\) 0 0
\(187\) 8.75035 0.639889
\(188\) −0.331408 0.0751117i −0.0241704 0.00547808i
\(189\) 0 0
\(190\) −1.58189 + 14.1362i −0.114762 + 1.02555i
\(191\) 21.8014 1.57750 0.788748 0.614717i \(-0.210730\pi\)
0.788748 + 0.614717i \(0.210730\pi\)
\(192\) 0 0
\(193\) 18.2130 1.31100 0.655501 0.755194i \(-0.272458\pi\)
0.655501 + 0.755194i \(0.272458\pi\)
\(194\) 0.761805 6.80774i 0.0546944 0.488767i
\(195\) 0 0
\(196\) 1.95053 + 0.442076i 0.139324 + 0.0315768i
\(197\) 12.1692 0.867022 0.433511 0.901148i \(-0.357274\pi\)
0.433511 + 0.901148i \(0.357274\pi\)
\(198\) 0 0
\(199\) 19.9646i 1.41525i −0.706588 0.707625i \(-0.749766\pi\)
0.706588 0.707625i \(-0.250234\pi\)
\(200\) 1.57051 4.52131i 0.111052 0.319705i
\(201\) 0 0
\(202\) 0.141508 1.26456i 0.00995647 0.0889742i
\(203\) 5.87055i 0.412032i
\(204\) 0 0
\(205\) 17.8818i 1.24892i
\(206\) −19.1307 2.14078i −1.33290 0.149156i
\(207\) 0 0
\(208\) −12.0583 + 25.2354i −0.836094 + 1.74976i
\(209\) 13.1011i 0.906221i
\(210\) 0 0
\(211\) −0.750003 −0.0516323 −0.0258162 0.999667i \(-0.508218\pi\)
−0.0258162 + 0.999667i \(0.508218\pi\)
\(212\) 3.94676 + 0.894508i 0.271064 + 0.0614351i
\(213\) 0 0
\(214\) −13.5539 1.51672i −0.926525 0.103681i
\(215\) 5.25553 0.358424
\(216\) 0 0
\(217\) −2.39191 −0.162373
\(218\) 1.60001 + 0.179046i 0.108367 + 0.0121265i
\(219\) 0 0
\(220\) −1.90467 + 8.40380i −0.128413 + 0.566584i
\(221\) 25.8273 1.73733
\(222\) 0 0
\(223\) 11.6042i 0.777078i −0.921432 0.388539i \(-0.872980\pi\)
0.921432 0.388539i \(-0.127020\pi\)
\(224\) 4.80120 + 2.99139i 0.320794 + 0.199871i
\(225\) 0 0
\(226\) 10.2326 + 1.14506i 0.680665 + 0.0761684i
\(227\) 5.59958i 0.371657i −0.982582 0.185829i \(-0.940503\pi\)
0.982582 0.185829i \(-0.0594970\pi\)
\(228\) 0 0
\(229\) 23.4718i 1.55106i 0.631310 + 0.775531i \(0.282518\pi\)
−0.631310 + 0.775531i \(0.717482\pi\)
\(230\) 2.17639 19.4489i 0.143507 1.28242i
\(231\) 0 0
\(232\) −5.44833 + 15.6851i −0.357700 + 1.02978i
\(233\) 16.9709i 1.11180i −0.831248 0.555901i \(-0.812373\pi\)
0.831248 0.555901i \(-0.187627\pi\)
\(234\) 0 0
\(235\) −0.309015 −0.0201579
\(236\) −0.0751117 + 0.331408i −0.00488936 + 0.0215729i
\(237\) 0 0
\(238\) 0.580932 5.19139i 0.0376562 0.336508i
\(239\) 15.4661 1.00042 0.500211 0.865904i \(-0.333256\pi\)
0.500211 + 0.865904i \(0.333256\pi\)
\(240\) 0 0
\(241\) 25.5683 1.64700 0.823500 0.567316i \(-0.192018\pi\)
0.823500 + 0.567316i \(0.192018\pi\)
\(242\) 0.847405 7.57268i 0.0544732 0.486790i
\(243\) 0 0
\(244\) 0.185682 0.819268i 0.0118871 0.0524483i
\(245\) 1.81873 0.116194
\(246\) 0 0
\(247\) 38.6688i 2.46043i
\(248\) −6.39078 2.21988i −0.405815 0.140962i
\(249\) 0 0
\(250\) 1.91422 17.1061i 0.121066 1.08189i
\(251\) 21.8041i 1.37626i 0.725586 + 0.688131i \(0.241569\pi\)
−0.725586 + 0.688131i \(0.758431\pi\)
\(252\) 0 0
\(253\) 18.0247i 1.13320i
\(254\) 7.65186 + 0.856265i 0.480120 + 0.0537269i
\(255\) 0 0
\(256\) 10.0518 + 12.4484i 0.628235 + 0.778024i
\(257\) 2.98714i 0.186333i −0.995651 0.0931664i \(-0.970301\pi\)
0.995651 0.0931664i \(-0.0296989\pi\)
\(258\) 0 0
\(259\) −8.88054 −0.551810
\(260\) −5.62177 + 24.8044i −0.348647 + 1.53830i
\(261\) 0 0
\(262\) −9.46174 1.05880i −0.584549 0.0654127i
\(263\) 25.7673 1.58888 0.794441 0.607342i \(-0.207764\pi\)
0.794441 + 0.607342i \(0.207764\pi\)
\(264\) 0 0
\(265\) 3.68007 0.226065
\(266\) 7.77259 + 0.869775i 0.476568 + 0.0533293i
\(267\) 0 0
\(268\) 19.0449 + 4.31641i 1.16335 + 0.263667i
\(269\) 17.9674 1.09549 0.547744 0.836646i \(-0.315487\pi\)
0.547744 + 0.836646i \(0.315487\pi\)
\(270\) 0 0
\(271\) 4.90908i 0.298205i 0.988822 + 0.149103i \(0.0476385\pi\)
−0.988822 + 0.149103i \(0.952362\pi\)
\(272\) 6.37016 13.3314i 0.386248 0.808333i
\(273\) 0 0
\(274\) 6.74174 + 0.754420i 0.407284 + 0.0455762i
\(275\) 4.00876i 0.241737i
\(276\) 0 0
\(277\) 3.72578i 0.223860i 0.993716 + 0.111930i \(0.0357033\pi\)
−0.993716 + 0.111930i \(0.964297\pi\)
\(278\) 1.36525 12.2003i 0.0818821 0.731725i
\(279\) 0 0
\(280\) 4.85934 + 1.68792i 0.290401 + 0.100873i
\(281\) 16.9316i 1.01006i −0.863103 0.505028i \(-0.831482\pi\)
0.863103 0.505028i \(-0.168518\pi\)
\(282\) 0 0
\(283\) −10.1986 −0.606244 −0.303122 0.952952i \(-0.598029\pi\)
−0.303122 + 0.952952i \(0.598029\pi\)
\(284\) 23.4261 + 5.30938i 1.39008 + 0.315054i
\(285\) 0 0
\(286\) −2.60505 + 23.2796i −0.154040 + 1.37655i
\(287\) −9.83200 −0.580365
\(288\) 0 0
\(289\) 3.35598 0.197411
\(290\) −1.67920 + 15.0058i −0.0986058 + 0.881173i
\(291\) 0 0
\(292\) −17.1257 3.88144i −1.00221 0.227144i
\(293\) −30.0240 −1.75402 −0.877010 0.480472i \(-0.840465\pi\)
−0.877010 + 0.480472i \(0.840465\pi\)
\(294\) 0 0
\(295\) 0.309015i 0.0179915i
\(296\) −23.7273 8.24183i −1.37912 0.479047i
\(297\) 0 0
\(298\) −0.976203 + 8.72367i −0.0565499 + 0.505348i
\(299\) 53.2011i 3.07670i
\(300\) 0 0
\(301\) 2.88967i 0.166558i
\(302\) −6.57853 0.736156i −0.378552 0.0423610i
\(303\) 0 0
\(304\) 19.9598 + 9.53745i 1.14477 + 0.547010i
\(305\) 0.763909i 0.0437413i
\(306\) 0 0
\(307\) 30.1978 1.72348 0.861738 0.507353i \(-0.169376\pi\)
0.861738 + 0.507353i \(0.169376\pi\)
\(308\) 4.62069 + 1.04725i 0.263288 + 0.0596727i
\(309\) 0 0
\(310\) −6.11401 0.684175i −0.347252 0.0388586i
\(311\) 21.8076 1.23659 0.618297 0.785945i \(-0.287823\pi\)
0.618297 + 0.785945i \(0.287823\pi\)
\(312\) 0 0
\(313\) −31.6447 −1.78866 −0.894331 0.447406i \(-0.852348\pi\)
−0.894331 + 0.447406i \(0.852348\pi\)
\(314\) −2.41686 0.270453i −0.136391 0.0152626i
\(315\) 0 0
\(316\) −6.31483 + 27.8624i −0.355237 + 1.56738i
\(317\) −5.63931 −0.316735 −0.158368 0.987380i \(-0.550623\pi\)
−0.158368 + 0.987380i \(0.550623\pi\)
\(318\) 0 0
\(319\) 13.9070i 0.778642i
\(320\) 11.4168 + 9.01968i 0.638219 + 0.504216i
\(321\) 0 0
\(322\) −10.6937 1.19665i −0.595934 0.0666867i
\(323\) 20.4279i 1.13664i
\(324\) 0 0
\(325\) 11.8321i 0.656329i
\(326\) −2.86306 + 25.5853i −0.158570 + 1.41704i
\(327\) 0 0
\(328\) −26.2694 9.12486i −1.45049 0.503836i
\(329\) 0.169907i 0.00936727i
\(330\) 0 0
\(331\) −5.48698 −0.301592 −0.150796 0.988565i \(-0.548184\pi\)
−0.150796 + 0.988565i \(0.548184\pi\)
\(332\) 4.52015 19.9438i 0.248075 1.09456i
\(333\) 0 0
\(334\) 1.38540 12.3804i 0.0758057 0.677424i
\(335\) 17.7580 0.970224
\(336\) 0 0
\(337\) −5.06316 −0.275808 −0.137904 0.990446i \(-0.544036\pi\)
−0.137904 + 0.990446i \(0.544036\pi\)
\(338\) −5.64444 + 50.4405i −0.307017 + 2.74360i
\(339\) 0 0
\(340\) 2.96986 13.1037i 0.161063 0.710645i
\(341\) −5.66630 −0.306847
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) 2.68184 7.72071i 0.144595 0.416273i
\(345\) 0 0
\(346\) 0.588373 5.25789i 0.0316311 0.282666i
\(347\) 31.2066i 1.67526i 0.546241 + 0.837628i \(0.316058\pi\)
−0.546241 + 0.837628i \(0.683942\pi\)
\(348\) 0 0
\(349\) 10.6407i 0.569583i −0.958590 0.284791i \(-0.908076\pi\)
0.958590 0.284791i \(-0.0919243\pi\)
\(350\) −2.37831 0.266140i −0.127126 0.0142258i
\(351\) 0 0
\(352\) 11.3738 + 7.08644i 0.606224 + 0.377708i
\(353\) 29.5238i 1.57139i 0.618613 + 0.785696i \(0.287695\pi\)
−0.618613 + 0.785696i \(0.712305\pi\)
\(354\) 0 0
\(355\) 21.8432 1.15932
\(356\) 3.28386 14.4891i 0.174044 0.767919i
\(357\) 0 0
\(358\) 22.2586 + 2.49080i 1.17640 + 0.131643i
\(359\) −21.6557 −1.14294 −0.571471 0.820622i \(-0.693627\pi\)
−0.571471 + 0.820622i \(0.693627\pi\)
\(360\) 0 0
\(361\) 11.5848 0.609727
\(362\) −11.4526 1.28158i −0.601935 0.0673582i
\(363\) 0 0
\(364\) 13.6383 + 3.09104i 0.714841 + 0.162014i
\(365\) −15.9685 −0.835830
\(366\) 0 0
\(367\) 13.2680i 0.692585i 0.938127 + 0.346292i \(0.112559\pi\)
−0.938127 + 0.346292i \(0.887441\pi\)
\(368\) −27.4610 13.1218i −1.43151 0.684020i
\(369\) 0 0
\(370\) −22.6997 2.54017i −1.18010 0.132057i
\(371\) 2.02343i 0.105051i
\(372\) 0 0
\(373\) 2.38377i 0.123427i −0.998094 0.0617135i \(-0.980343\pi\)
0.998094 0.0617135i \(-0.0196565\pi\)
\(374\) 1.37619 12.2981i 0.0711613 0.635920i
\(375\) 0 0
\(376\) −0.157687 + 0.453962i −0.00813207 + 0.0234113i
\(377\) 41.0475i 2.11405i
\(378\) 0 0
\(379\) −4.33792 −0.222824 −0.111412 0.993774i \(-0.535537\pi\)
−0.111412 + 0.993774i \(0.535537\pi\)
\(380\) 19.6189 + 4.44650i 1.00643 + 0.228101i
\(381\) 0 0
\(382\) 3.42877 30.6406i 0.175431 1.56771i
\(383\) −28.5614 −1.45942 −0.729709 0.683758i \(-0.760344\pi\)
−0.729709 + 0.683758i \(0.760344\pi\)
\(384\) 0 0
\(385\) 4.30847 0.219580
\(386\) 2.86441 25.5973i 0.145795 1.30287i
\(387\) 0 0
\(388\) −9.44806 2.14135i −0.479653 0.108710i
\(389\) −25.5023 −1.29302 −0.646510 0.762906i \(-0.723772\pi\)
−0.646510 + 0.762906i \(0.723772\pi\)
\(390\) 0 0
\(391\) 28.1051i 1.42133i
\(392\) 0.928077 2.67183i 0.0468750 0.134948i
\(393\) 0 0
\(394\) 1.91389 17.1031i 0.0964205 0.861644i
\(395\) 25.9797i 1.30718i
\(396\) 0 0
\(397\) 25.9062i 1.30020i −0.759850 0.650099i \(-0.774728\pi\)
0.759850 0.650099i \(-0.225272\pi\)
\(398\) −28.0590 3.13989i −1.40647 0.157388i
\(399\) 0 0
\(400\) −6.10744 2.91834i −0.305372 0.145917i
\(401\) 4.65113i 0.232266i −0.993234 0.116133i \(-0.962950\pi\)
0.993234 0.116133i \(-0.0370499\pi\)
\(402\) 0 0
\(403\) −16.7245 −0.833105
\(404\) −1.75501 0.397762i −0.0873150 0.0197894i
\(405\) 0 0
\(406\) 8.25072 + 0.923279i 0.409476 + 0.0458216i
\(407\) −21.0375 −1.04279
\(408\) 0 0
\(409\) 18.1415 0.897041 0.448521 0.893773i \(-0.351951\pi\)
0.448521 + 0.893773i \(0.351951\pi\)
\(410\) −25.1318 2.81232i −1.24117 0.138890i
\(411\) 0 0
\(412\) −6.01749 + 26.5504i −0.296461 + 1.30805i
\(413\) 0.169907 0.00836057
\(414\) 0 0
\(415\) 18.5962i 0.912853i
\(416\) 33.5705 + 20.9161i 1.64593 + 1.02550i
\(417\) 0 0
\(418\) 18.4128 + 2.06045i 0.900600 + 0.100780i
\(419\) 8.21628i 0.401392i −0.979654 0.200696i \(-0.935680\pi\)
0.979654 0.200696i \(-0.0643203\pi\)
\(420\) 0 0
\(421\) 14.8382i 0.723171i 0.932339 + 0.361586i \(0.117765\pi\)
−0.932339 + 0.361586i \(0.882235\pi\)
\(422\) −0.117955 + 1.05408i −0.00574197 + 0.0513121i
\(423\) 0 0
\(424\) 1.87790 5.40625i 0.0911987 0.262551i
\(425\) 6.25068i 0.303202i
\(426\) 0 0
\(427\) −0.420023 −0.0203264
\(428\) −4.26332 + 18.8107i −0.206075 + 0.909247i
\(429\) 0 0
\(430\) 0.826553 7.38634i 0.0398599 0.356201i
\(431\) 13.1807 0.634893 0.317447 0.948276i \(-0.397175\pi\)
0.317447 + 0.948276i \(0.397175\pi\)
\(432\) 0 0
\(433\) −7.66377 −0.368297 −0.184149 0.982898i \(-0.558953\pi\)
−0.184149 + 0.982898i \(0.558953\pi\)
\(434\) −0.376183 + 3.36169i −0.0180574 + 0.161366i
\(435\) 0 0
\(436\) 0.503278 2.22057i 0.0241026 0.106346i
\(437\) −42.0791 −2.01292
\(438\) 0 0
\(439\) 23.3466i 1.11427i 0.830422 + 0.557135i \(0.188099\pi\)
−0.830422 + 0.557135i \(0.811901\pi\)
\(440\) 11.5115 + 3.99859i 0.548789 + 0.190625i
\(441\) 0 0
\(442\) 4.06193 36.2987i 0.193206 1.72655i
\(443\) 14.8435i 0.705236i 0.935767 + 0.352618i \(0.114709\pi\)
−0.935767 + 0.352618i \(0.885291\pi\)
\(444\) 0 0
\(445\) 13.5100i 0.640437i
\(446\) −16.3091 1.82503i −0.772257 0.0864178i
\(447\) 0 0
\(448\) 4.95933 6.27735i 0.234306 0.296577i
\(449\) 4.06073i 0.191638i −0.995399 0.0958189i \(-0.969453\pi\)
0.995399 0.0958189i \(-0.0305470\pi\)
\(450\) 0 0
\(451\) −23.2914 −1.09675
\(452\) 3.21863 14.2013i 0.151392 0.667972i
\(453\) 0 0
\(454\) −7.86989 0.880663i −0.369352 0.0413316i
\(455\) 12.7167 0.596170
\(456\) 0 0
\(457\) 23.0425 1.07788 0.538940 0.842344i \(-0.318825\pi\)
0.538940 + 0.842344i \(0.318825\pi\)
\(458\) 32.9883 + 3.69148i 1.54144 + 0.172492i
\(459\) 0 0
\(460\) −26.9920 6.11757i −1.25851 0.285233i
\(461\) 27.1646 1.26518 0.632592 0.774485i \(-0.281991\pi\)
0.632592 + 0.774485i \(0.281991\pi\)
\(462\) 0 0
\(463\) 16.8894i 0.784917i 0.919770 + 0.392459i \(0.128375\pi\)
−0.919770 + 0.392459i \(0.871625\pi\)
\(464\) 21.1876 + 10.1241i 0.983611 + 0.470002i
\(465\) 0 0
\(466\) −23.8516 2.66907i −1.10491 0.123642i
\(467\) 12.0923i 0.559566i −0.960063 0.279783i \(-0.909737\pi\)
0.960063 0.279783i \(-0.0902625\pi\)
\(468\) 0 0
\(469\) 9.76396i 0.450858i
\(470\) −0.0485997 + 0.434302i −0.00224174 + 0.0200329i
\(471\) 0 0
\(472\) 0.453962 + 0.157687i 0.0208953 + 0.00725812i
\(473\) 6.84546i 0.314755i
\(474\) 0 0
\(475\) −9.35856 −0.429400
\(476\) −7.20483 1.63293i −0.330233 0.0748453i
\(477\) 0 0
\(478\) 2.43240 21.7367i 0.111256 0.994216i
\(479\) 6.77258 0.309447 0.154724 0.987958i \(-0.450551\pi\)
0.154724 + 0.987958i \(0.450551\pi\)
\(480\) 0 0
\(481\) −62.0936 −2.83123
\(482\) 4.02120 35.9348i 0.183161 1.63678i
\(483\) 0 0
\(484\) −10.5097 2.38195i −0.477713 0.108271i
\(485\) −8.80965 −0.400026
\(486\) 0 0
\(487\) 6.15599i 0.278955i 0.990225 + 0.139477i \(0.0445422\pi\)
−0.990225 + 0.139477i \(0.955458\pi\)
\(488\) −1.12223 0.389814i −0.0508010 0.0176461i
\(489\) 0 0
\(490\) 0.286037 2.55612i 0.0129218 0.115474i
\(491\) 29.4205i 1.32773i −0.747853 0.663864i \(-0.768915\pi\)
0.747853 0.663864i \(-0.231085\pi\)
\(492\) 0 0
\(493\) 21.6845i 0.976622i
\(494\) 54.3467 + 6.08155i 2.44517 + 0.273622i
\(495\) 0 0
\(496\) −4.12500 + 8.63274i −0.185218 + 0.387621i
\(497\) 12.0101i 0.538728i
\(498\) 0 0
\(499\) −15.1862 −0.679827 −0.339913 0.940457i \(-0.610398\pi\)
−0.339913 + 0.940457i \(0.610398\pi\)
\(500\) −23.7406 5.38066i −1.06171 0.240630i
\(501\) 0 0
\(502\) 30.6444 + 3.42919i 1.36773 + 0.153052i
\(503\) −38.0202 −1.69524 −0.847619 0.530605i \(-0.821965\pi\)
−0.847619 + 0.530605i \(0.821965\pi\)
\(504\) 0 0
\(505\) −1.63642 −0.0728199
\(506\) −25.3326 2.83480i −1.12617 0.126022i
\(507\) 0 0
\(508\) 2.40686 10.6196i 0.106787 0.471167i
\(509\) 0.855999 0.0379415 0.0189707 0.999820i \(-0.493961\pi\)
0.0189707 + 0.999820i \(0.493961\pi\)
\(510\) 0 0
\(511\) 8.78003i 0.388405i
\(512\) 19.0763 12.1694i 0.843063 0.537815i
\(513\) 0 0
\(514\) −4.19825 0.469797i −0.185177 0.0207218i
\(515\) 24.7564i 1.09090i
\(516\) 0 0
\(517\) 0.402499i 0.0177019i
\(518\) −1.39667 + 12.4811i −0.0613661 + 0.548387i
\(519\) 0 0
\(520\) 33.9770 + 11.8021i 1.48999 + 0.517557i
\(521\) 8.80793i 0.385883i −0.981210 0.192941i \(-0.938197\pi\)
0.981210 0.192941i \(-0.0618027\pi\)
\(522\) 0 0
\(523\) 29.4892 1.28947 0.644736 0.764405i \(-0.276967\pi\)
0.644736 + 0.764405i \(0.276967\pi\)
\(524\) −2.97615 + 13.1314i −0.130014 + 0.573648i
\(525\) 0 0
\(526\) 4.05250 36.2145i 0.176697 1.57903i
\(527\) 8.83519 0.384867
\(528\) 0 0
\(529\) 34.8931 1.51709
\(530\) 0.578775 5.17212i 0.0251404 0.224663i
\(531\) 0 0
\(532\) 2.44484 10.7871i 0.105997 0.467681i
\(533\) −68.7463 −2.97773
\(534\) 0 0
\(535\) 17.5396i 0.758303i
\(536\) 9.06171 26.0876i 0.391406 1.12681i
\(537\) 0 0
\(538\) 2.82578 25.2521i 0.121828 1.08869i
\(539\) 2.36894i 0.102038i
\(540\) 0 0
\(541\) 9.02347i 0.387949i 0.981007 + 0.193975i \(0.0621379\pi\)
−0.981007 + 0.193975i \(0.937862\pi\)
\(542\) 6.89942 + 0.772065i 0.296356 + 0.0331631i
\(543\) 0 0
\(544\) −17.7346 11.0496i −0.760365 0.473746i
\(545\) 2.07052i 0.0886914i
\(546\) 0 0
\(547\) 23.0161 0.984097 0.492048 0.870568i \(-0.336248\pi\)
0.492048 + 0.870568i \(0.336248\pi\)
\(548\) 2.12059 9.35647i 0.0905870 0.399689i
\(549\) 0 0
\(550\) −5.63408 0.630470i −0.240238 0.0268833i
\(551\) 32.4662 1.38311
\(552\) 0 0
\(553\) 14.2845 0.607439
\(554\) 5.23636 + 0.585964i 0.222472 + 0.0248952i
\(555\) 0 0
\(556\) −16.9321 3.83755i −0.718080 0.162748i
\(557\) −14.6781 −0.621930 −0.310965 0.950421i \(-0.600652\pi\)
−0.310965 + 0.950421i \(0.600652\pi\)
\(558\) 0 0
\(559\) 20.2049i 0.854574i
\(560\) 3.13652 6.56405i 0.132542 0.277382i
\(561\) 0 0
\(562\) −23.7964 2.66289i −1.00379 0.112327i
\(563\) 22.3172i 0.940556i 0.882518 + 0.470278i \(0.155846\pi\)
−0.882518 + 0.470278i \(0.844154\pi\)
\(564\) 0 0
\(565\) 13.2417i 0.557082i
\(566\) −1.60396 + 14.3335i −0.0674196 + 0.602484i
\(567\) 0 0
\(568\) 11.1463 32.0890i 0.467689 1.34642i
\(569\) 19.5564i 0.819847i −0.912120 0.409923i \(-0.865555\pi\)
0.912120 0.409923i \(-0.134445\pi\)
\(570\) 0 0
\(571\) 22.2399 0.930709 0.465355 0.885124i \(-0.345927\pi\)
0.465355 + 0.885124i \(0.345927\pi\)
\(572\) 32.3083 + 7.32249i 1.35088 + 0.306169i
\(573\) 0 0
\(574\) −1.54631 + 13.8183i −0.0645416 + 0.576765i
\(575\) 12.8757 0.536952
\(576\) 0 0
\(577\) −41.9160 −1.74499 −0.872493 0.488627i \(-0.837498\pi\)
−0.872493 + 0.488627i \(0.837498\pi\)
\(578\) 0.527806 4.71664i 0.0219538 0.196186i
\(579\) 0 0
\(580\) 20.8257 + 4.72002i 0.864741 + 0.195988i
\(581\) −10.2248 −0.424197
\(582\) 0 0
\(583\) 4.79338i 0.198522i
\(584\) −8.14854 + 23.4587i −0.337189 + 0.970729i
\(585\) 0 0
\(586\) −4.72196 + 42.1969i −0.195062 + 1.74314i
\(587\) 9.70280i 0.400478i 0.979747 + 0.200239i \(0.0641718\pi\)
−0.979747 + 0.200239i \(0.935828\pi\)
\(588\) 0 0
\(589\) 13.2281i 0.545055i
\(590\) 0.434302 + 0.0485997i 0.0178799 + 0.00200082i
\(591\) 0 0
\(592\) −15.3151 + 32.0511i −0.629445 + 1.31729i
\(593\) 19.0205i 0.781077i 0.920587 + 0.390538i \(0.127711\pi\)
−0.920587 + 0.390538i \(0.872289\pi\)
\(594\) 0 0
\(595\) −6.71799 −0.275411
\(596\) 12.1071 + 2.74399i 0.495925 + 0.112398i
\(597\) 0 0
\(598\) −74.7711 8.36710i −3.05762 0.342156i
\(599\) −22.2207 −0.907914 −0.453957 0.891024i \(-0.649988\pi\)
−0.453957 + 0.891024i \(0.649988\pi\)
\(600\) 0 0
\(601\) 7.60754 0.310318 0.155159 0.987889i \(-0.450411\pi\)
0.155159 + 0.987889i \(0.450411\pi\)
\(602\) −4.06126 0.454467i −0.165525 0.0185227i
\(603\) 0 0
\(604\) −2.06925 + 9.12995i −0.0841965 + 0.371493i
\(605\) −9.79953 −0.398408
\(606\) 0 0
\(607\) 14.1339i 0.573678i 0.957979 + 0.286839i \(0.0926045\pi\)
−0.957979 + 0.286839i \(0.907396\pi\)
\(608\) 16.5435 26.5524i 0.670926 1.07684i
\(609\) 0 0
\(610\) −1.07363 0.120142i −0.0434700 0.00486442i
\(611\) 1.18801i 0.0480615i
\(612\) 0 0
\(613\) 17.3711i 0.701611i −0.936448 0.350806i \(-0.885908\pi\)
0.936448 0.350806i \(-0.114092\pi\)
\(614\) 4.74929 42.4412i 0.191666 1.71279i
\(615\) 0 0
\(616\) 2.19856 6.32941i 0.0885825 0.255019i
\(617\) 26.9441i 1.08473i 0.840143 + 0.542365i \(0.182471\pi\)
−0.840143 + 0.542365i \(0.817529\pi\)
\(618\) 0 0
\(619\) 11.4286 0.459355 0.229678 0.973267i \(-0.426233\pi\)
0.229678 + 0.973267i \(0.426233\pi\)
\(620\) −1.92314 + 8.48528i −0.0772350 + 0.340777i
\(621\) 0 0
\(622\) 3.42974 30.6493i 0.137520 1.22892i
\(623\) −7.42827 −0.297607
\(624\) 0 0
\(625\) −13.6753 −0.547013
\(626\) −4.97685 + 44.4747i −0.198915 + 1.77757i
\(627\) 0 0
\(628\) −0.760213 + 3.35422i −0.0303358 + 0.133848i
\(629\) 32.8028 1.30793
\(630\) 0 0
\(631\) 42.8774i 1.70692i −0.521156 0.853462i \(-0.674499\pi\)
0.521156 0.853462i \(-0.325501\pi\)
\(632\) 38.1658 + 13.2571i 1.51815 + 0.527340i
\(633\) 0 0
\(634\) −0.886911 + 7.92572i −0.0352237 + 0.314771i
\(635\) 9.90200i 0.392949i
\(636\) 0 0
\(637\) 6.99210i 0.277037i
\(638\) 19.5455 + 2.18719i 0.773813 + 0.0865919i
\(639\) 0 0
\(640\) 14.4722 14.6271i 0.572064 0.578187i
\(641\) 6.41036i 0.253194i −0.991954 0.126597i \(-0.959594\pi\)
0.991954 0.126597i \(-0.0404055\pi\)
\(642\) 0 0
\(643\) 23.5994 0.930668 0.465334 0.885135i \(-0.345934\pi\)
0.465334 + 0.885135i \(0.345934\pi\)
\(644\) −3.36364 + 14.8411i −0.132546 + 0.584821i
\(645\) 0 0
\(646\) −28.7102 3.21276i −1.12959 0.126404i
\(647\) 5.87058 0.230796 0.115398 0.993319i \(-0.463186\pi\)
0.115398 + 0.993319i \(0.463186\pi\)
\(648\) 0 0
\(649\) 0.402499 0.0157995
\(650\) −16.6294 1.86088i −0.652258 0.0729896i
\(651\) 0 0
\(652\) 35.5083 + 8.04774i 1.39061 + 0.315174i
\(653\) 34.2268 1.33940 0.669699 0.742633i \(-0.266423\pi\)
0.669699 + 0.742633i \(0.266423\pi\)
\(654\) 0 0
\(655\) 12.2441i 0.478417i
\(656\) −16.9559 + 35.4850i −0.662017 + 1.38546i
\(657\) 0 0
\(658\) 0.238794 + 0.0267217i 0.00930916 + 0.00104172i
\(659\) 11.1474i 0.434241i −0.976145 0.217120i \(-0.930334\pi\)
0.976145 0.217120i \(-0.0696664\pi\)
\(660\) 0 0
\(661\) 49.2293i 1.91480i 0.288768 + 0.957399i \(0.406754\pi\)
−0.288768 + 0.957399i \(0.593246\pi\)
\(662\) −0.862954 + 7.71163i −0.0335397 + 0.299721i
\(663\) 0 0
\(664\) −27.3190 9.48943i −1.06018 0.368261i
\(665\) 10.0582i 0.390041i
\(666\) 0 0
\(667\) −44.6676 −1.72954
\(668\) −17.1820 3.89419i −0.664792 0.150671i
\(669\) 0 0
\(670\) 2.79286 24.9579i 0.107897 0.964206i
\(671\) −0.995011 −0.0384120
\(672\) 0 0
\(673\) −16.3489 −0.630202 −0.315101 0.949058i \(-0.602038\pi\)
−0.315101 + 0.949058i \(0.602038\pi\)
\(674\) −0.796297 + 7.11597i −0.0306722 + 0.274097i
\(675\) 0 0
\(676\) 70.0034 + 15.8658i 2.69244 + 0.610225i
\(677\) −32.1693 −1.23637 −0.618184 0.786034i \(-0.712131\pi\)
−0.618184 + 0.786034i \(0.712131\pi\)
\(678\) 0 0
\(679\) 4.84384i 0.185890i
\(680\) −17.9493 6.23482i −0.688326 0.239094i
\(681\) 0 0
\(682\) −0.891155 + 7.96365i −0.0341241 + 0.304944i
\(683\) 18.0796i 0.691798i −0.938272 0.345899i \(-0.887574\pi\)
0.938272 0.345899i \(-0.112426\pi\)
\(684\) 0 0
\(685\) 8.72425i 0.333336i
\(686\) −1.40544 0.157273i −0.0536600 0.00600471i
\(687\) 0 0
\(688\) −10.4292 4.98342i −0.397610 0.189991i
\(689\) 14.1480i 0.538996i
\(690\) 0 0
\(691\) 10.8603 0.413146 0.206573 0.978431i \(-0.433769\pi\)
0.206573 + 0.978431i \(0.433769\pi\)
\(692\) −7.29712 1.65385i −0.277395 0.0628699i
\(693\) 0 0
\(694\) 43.8590 + 4.90795i 1.66486 + 0.186303i
\(695\) −15.7880 −0.598871
\(696\) 0 0
\(697\) 36.3173 1.37561
\(698\) −14.9549 1.67349i −0.566050 0.0633426i
\(699\) 0 0
\(700\) −0.748088 + 3.30072i −0.0282751 + 0.124755i
\(701\) 48.4528 1.83004 0.915018 0.403414i \(-0.132176\pi\)
0.915018 + 0.403414i \(0.132176\pi\)
\(702\) 0 0
\(703\) 49.1125i 1.85231i
\(704\) 11.7484 14.8707i 0.442783 0.560459i
\(705\) 0 0
\(706\) 41.4939 + 4.64329i 1.56164 + 0.174752i
\(707\) 0.899761i 0.0338390i
\(708\) 0 0
\(709\) 24.1866i 0.908348i 0.890913 + 0.454174i \(0.150066\pi\)
−0.890913 + 0.454174i \(0.849934\pi\)
\(710\) 3.43534 30.6993i 0.128926 1.15212i
\(711\) 0 0
\(712\) −19.8471 6.89401i −0.743800 0.258364i
\(713\) 18.1995i 0.681575i
\(714\) 0 0
\(715\) 30.1252 1.12662
\(716\) 7.00135 30.8914i 0.261653 1.15447i
\(717\) 0 0
\(718\) −3.40585 + 30.4358i −0.127105 + 1.13585i
\(719\) −40.8996 −1.52530 −0.762650 0.646812i \(-0.776102\pi\)
−0.762650 + 0.646812i \(0.776102\pi\)
\(720\) 0 0
\(721\) 13.6119 0.506934
\(722\) 1.82198 16.2818i 0.0678069 0.605945i
\(723\) 0 0
\(724\) −3.60237 + 15.8944i −0.133881 + 0.590710i
\(725\) −9.93425 −0.368949
\(726\) 0 0
\(727\) 27.9812i 1.03777i 0.854845 + 0.518883i \(0.173652\pi\)
−0.854845 + 0.518883i \(0.826348\pi\)
\(728\) 6.48921 18.6817i 0.240506 0.692390i
\(729\) 0 0
\(730\) −2.51141 + 22.4428i −0.0929516 + 0.830645i
\(731\) 10.6738i 0.394785i
\(732\) 0 0
\(733\) 17.8163i 0.658062i 0.944319 + 0.329031i \(0.106722\pi\)
−0.944319 + 0.329031i \(0.893278\pi\)
\(734\) 18.6474 + 2.08670i 0.688288 + 0.0770215i
\(735\) 0 0
\(736\) −22.7608 + 36.5312i −0.838973 + 1.34656i
\(737\) 23.1303i 0.852014i
\(738\) 0 0
\(739\) −39.6052 −1.45690 −0.728450 0.685099i \(-0.759759\pi\)
−0.728450 + 0.685099i \(0.759759\pi\)
\(740\) −7.14011 + 31.5036i −0.262476 + 1.15810i
\(741\) 0 0
\(742\) −2.84381 0.318230i −0.104399 0.0116826i
\(743\) 37.2631 1.36705 0.683525 0.729927i \(-0.260446\pi\)
0.683525 + 0.729927i \(0.260446\pi\)
\(744\) 0 0
\(745\) 11.2890 0.413596
\(746\) −3.35025 0.374903i −0.122661 0.0137262i
\(747\) 0 0
\(748\) −17.0678 3.86832i −0.624062 0.141440i
\(749\) 9.64387 0.352379
\(750\) 0 0
\(751\) 10.2637i 0.374529i 0.982310 + 0.187264i \(0.0599621\pi\)
−0.982310 + 0.187264i \(0.940038\pi\)
\(752\) 0.613217 + 0.293015i 0.0223617 + 0.0106852i
\(753\) 0 0
\(754\) 57.6898 + 6.45566i 2.10094 + 0.235101i
\(755\) 8.51303i 0.309821i
\(756\) 0 0
\(757\) 18.9330i 0.688132i 0.938945 + 0.344066i \(0.111804\pi\)
−0.938945 + 0.344066i \(0.888196\pi\)
\(758\) −0.682238 + 6.09669i −0.0247800 + 0.221442i
\(759\) 0 0
\(760\) 9.33481 26.8739i 0.338609 0.974818i
\(761\) 41.0983i 1.48981i 0.667170 + 0.744905i \(0.267505\pi\)
−0.667170 + 0.744905i \(0.732495\pi\)
\(762\) 0 0
\(763\) −1.13844 −0.0412144
\(764\) −42.5243 9.63788i −1.53848 0.348686i
\(765\) 0 0
\(766\) −4.49193 + 40.1413i −0.162300 + 1.45037i
\(767\) 1.18801 0.0428964
\(768\) 0 0
\(769\) 24.3838 0.879301 0.439651 0.898169i \(-0.355102\pi\)
0.439651 + 0.898169i \(0.355102\pi\)
\(770\) 0.677605 6.05530i 0.0244192 0.218218i
\(771\) 0 0
\(772\) −35.5250 8.05153i −1.27857 0.289781i
\(773\) 27.1940 0.978102 0.489051 0.872255i \(-0.337343\pi\)
0.489051 + 0.872255i \(0.337343\pi\)
\(774\) 0 0
\(775\) 4.04763i 0.145395i
\(776\) −4.49546 + 12.9419i −0.161378 + 0.464588i
\(777\) 0 0
\(778\) −4.01083 + 35.8420i −0.143795 + 1.28500i
\(779\) 54.3744i 1.94817i
\(780\) 0 0
\(781\) 28.4513i 1.01807i
\(782\) 39.5000 + 4.42017i 1.41252 + 0.158065i
\(783\) 0 0
\(784\) −3.60914 1.72456i −0.128898 0.0615916i
\(785\) 3.12757i 0.111628i
\(786\) 0 0
\(787\) −40.8769 −1.45710 −0.728552 0.684990i \(-0.759807\pi\)
−0.728552 + 0.684990i \(0.759807\pi\)
\(788\) −23.7365 5.37972i −0.845577 0.191645i
\(789\) 0 0
\(790\) 36.5129 + 4.08590i 1.29907 + 0.145370i
\(791\) −7.28073 −0.258873
\(792\) 0 0
\(793\) −2.93684 −0.104290
\(794\) −36.4097 4.07435i −1.29213 0.144593i
\(795\) 0 0
\(796\) −8.82585 + 38.9415i −0.312824 + 1.38024i
\(797\) −21.8622 −0.774398 −0.387199 0.921996i \(-0.626557\pi\)
−0.387199 + 0.921996i \(0.626557\pi\)
\(798\) 0 0
\(799\) 0.627599i 0.0222028i
\(800\) −5.06209 + 8.12468i −0.178972 + 0.287251i
\(801\) 0 0
\(802\) −6.53689 0.731496i −0.230825 0.0258300i
\(803\) 20.7994i 0.733994i
\(804\) 0 0
\(805\) 13.8383i 0.487735i
\(806\) −2.63031 + 23.5053i −0.0926486 + 0.827938i
\(807\) 0 0
\(808\) −0.835047 + 2.40401i −0.0293769 + 0.0845727i
\(809\) 15.7533i 0.553855i −0.960891 0.276928i \(-0.910684\pi\)
0.960891 0.276928i \(-0.0893163\pi\)
\(810\) 0 0
\(811\) 35.0976 1.23244 0.616221 0.787573i \(-0.288663\pi\)
0.616221 + 0.787573i \(0.288663\pi\)
\(812\) 2.59523 11.4507i 0.0910747 0.401841i
\(813\) 0 0
\(814\) −3.30863 + 29.5670i −0.115967 + 1.03632i
\(815\) 33.1090 1.15976
\(816\) 0 0
\(817\) −15.9809 −0.559101
\(818\) 2.85317 25.4969i 0.0997588 0.891477i
\(819\) 0 0
\(820\) −7.90510 + 34.8789i −0.276058 + 1.21803i
\(821\) −13.6689 −0.477047 −0.238524 0.971137i \(-0.576663\pi\)
−0.238524 + 0.971137i \(0.576663\pi\)
\(822\) 0 0
\(823\) 50.4577i 1.75885i −0.476041 0.879423i \(-0.657929\pi\)
0.476041 0.879423i \(-0.342071\pi\)
\(824\) 36.3687 + 12.6329i 1.26696 + 0.440088i
\(825\) 0 0
\(826\) 0.0267217 0.238794i 0.000929769 0.00830871i
\(827\) 27.4214i 0.953535i −0.879029 0.476768i \(-0.841808\pi\)
0.879029 0.476768i \(-0.158192\pi\)
\(828\) 0 0
\(829\) 0.0571961i 0.00198650i 1.00000 0.000993251i \(0.000316162\pi\)
−1.00000 0.000993251i \(0.999684\pi\)
\(830\) −26.1359 2.92468i −0.907190 0.101517i
\(831\) 0 0
\(832\) 34.6761 43.8918i 1.20218 1.52167i
\(833\) 3.69378i 0.127982i
\(834\) 0 0
\(835\) −16.0210 −0.554429
\(836\) 5.79167 25.5541i 0.200309 0.883806i
\(837\) 0 0
\(838\) −11.5475 1.29220i −0.398902 0.0446383i
\(839\) 24.4761 0.845010 0.422505 0.906361i \(-0.361151\pi\)
0.422505 + 0.906361i \(0.361151\pi\)
\(840\) 0 0
\(841\) 5.46339 0.188393
\(842\) 20.8543 + 2.33365i 0.718686 + 0.0804230i
\(843\) 0 0
\(844\) 1.46290 + 0.331558i 0.0503552 + 0.0114127i
\(845\) 65.2732 2.24547
\(846\) 0 0
\(847\) 5.38811i 0.185138i
\(848\) −7.30283 3.48953i −0.250780 0.119831i
\(849\) 0 0
\(850\) 8.78496 + 0.983062i 0.301322 + 0.0337188i
\(851\) 67.5699i 2.31626i
\(852\) 0 0
\(853\) 38.5932i 1.32141i 0.750648 + 0.660703i \(0.229742\pi\)
−0.750648 + 0.660703i \(0.770258\pi\)
\(854\) −0.0660583 + 0.590318i −0.00226047 + 0.0202003i
\(855\) 0 0
\(856\) 25.7668 + 8.95025i 0.880690 + 0.305913i
\(857\) 9.45790i 0.323076i 0.986867 + 0.161538i \(0.0516454\pi\)
−0.986867 + 0.161538i \(0.948355\pi\)
\(858\) 0 0
\(859\) −2.27620 −0.0776631 −0.0388315 0.999246i \(-0.512364\pi\)
−0.0388315 + 0.999246i \(0.512364\pi\)
\(860\) −10.2511 2.32334i −0.349559 0.0792254i
\(861\) 0 0
\(862\) 2.07297 18.5247i 0.0706057 0.630955i
\(863\) −11.3263 −0.385553 −0.192776 0.981243i \(-0.561749\pi\)
−0.192776 + 0.981243i \(0.561749\pi\)
\(864\) 0 0
\(865\) −6.80405 −0.231345
\(866\) −1.20530 + 10.7710i −0.0409579 + 0.366013i
\(867\) 0 0
\(868\) 4.66549 + 1.05741i 0.158357 + 0.0358907i
\(869\) 33.8392 1.14791
\(870\) 0 0
\(871\) 68.2706i 2.31326i
\(872\) −3.04172 1.05656i −0.103006 0.0357797i
\(873\) 0 0
\(874\) −6.61790 + 59.1397i −0.223854 + 2.00043i
\(875\) 12.1713i 0.411467i
\(876\) 0 0
\(877\) 33.2328i 1.12219i −0.827751 0.561096i \(-0.810380\pi\)
0.827751 0.561096i \(-0.189620\pi\)
\(878\) 32.8122 + 3.67178i 1.10736 + 0.123917i
\(879\) 0 0
\(880\) 7.43023 15.5499i 0.250473 0.524186i
\(881\) 3.87015i 0.130389i 0.997873 + 0.0651943i \(0.0207667\pi\)
−0.997873 + 0.0651943i \(0.979233\pi\)
\(882\) 0 0
\(883\) 44.6838 1.50373 0.751865 0.659317i \(-0.229154\pi\)
0.751865 + 0.659317i \(0.229154\pi\)
\(884\) −50.3769 11.4176i −1.69436 0.384016i
\(885\) 0 0
\(886\) 20.8617 + 2.33448i 0.700862 + 0.0784284i
\(887\) 8.13586 0.273176 0.136588 0.990628i \(-0.456386\pi\)
0.136588 + 0.990628i \(0.456386\pi\)
\(888\) 0 0
\(889\) −5.44445 −0.182601
\(890\) −18.9876 2.12476i −0.636464 0.0712222i
\(891\) 0 0
\(892\) −5.12995 + 22.6344i −0.171764 + 0.757857i
\(893\) 0.939645 0.0314440
\(894\) 0 0
\(895\) 28.8041i 0.962814i
\(896\) −8.04247 7.95730i −0.268680 0.265835i
\(897\) 0 0
\(898\) −5.70712 0.638643i −0.190449 0.0213118i
\(899\) 14.0418i 0.468322i
\(900\) 0 0
\(901\) 7.47409i 0.248998i
\(902\) −3.66311 + 32.7348i −0.121968 + 1.08995i
\(903\) 0 0
\(904\) −19.4529 6.75708i −0.646993 0.224737i
\(905\) 14.8204i 0.492646i
\(906\) 0 0
\(907\) −30.7597 −1.02136 −0.510679 0.859771i \(-0.670606\pi\)
−0.510679 + 0.859771i \(0.670606\pi\)
\(908\) −2.47544 + 10.9222i −0.0821504 + 0.362465i
\(909\) 0 0
\(910\) 2.00000 17.8726i 0.0662994 0.592472i
\(911\) 11.5179 0.381606 0.190803 0.981628i \(-0.438891\pi\)
0.190803 + 0.981628i \(0.438891\pi\)
\(912\) 0 0
\(913\) −24.2220 −0.801632
\(914\) 3.62395 32.3848i 0.119870 1.07119i
\(915\) 0 0
\(916\) 10.3763 45.7825i 0.342843 1.51270i
\(917\) 6.73222 0.222318
\(918\) 0 0
\(919\) 16.5397i 0.545595i 0.962071 + 0.272797i \(0.0879489\pi\)
−0.962071 + 0.272797i \(0.912051\pi\)
\(920\) −12.8430 + 36.9735i −0.423421 + 1.21898i
\(921\) 0 0
\(922\) 4.27226 38.1783i 0.140699 1.25734i
\(923\) 83.9760i 2.76410i
\(924\) 0 0
\(925\) 15.0278i 0.494111i
\(926\) 23.7371 + 2.65625i 0.780048 + 0.0872897i
\(927\) 0 0
\(928\) 17.5611 28.1857i 0.576473 0.925242i
\(929\) 49.8949i 1.63700i 0.574509 + 0.818499i \(0.305193\pi\)
−0.574509 + 0.818499i \(0.694807\pi\)
\(930\) 0 0
\(931\) −5.53035 −0.181250
\(932\) −7.50244 + 33.1023i −0.245750 + 1.08430i
\(933\) 0 0
\(934\) −16.9950 1.90180i −0.556095 0.0622286i
\(935\) −15.9145 −0.520461
\(936\) 0 0
\(937\) −11.6763 −0.381447 −0.190724 0.981644i \(-0.561083\pi\)
−0.190724 + 0.981644i \(0.561083\pi\)
\(938\) −13.7227 1.53561i −0.448061 0.0501393i
\(939\) 0 0
\(940\) 0.602743 + 0.136608i 0.0196593 + 0.00445566i
\(941\) 38.1741 1.24444 0.622219 0.782843i \(-0.286231\pi\)
0.622219 + 0.782843i \(0.286231\pi\)
\(942\) 0 0
\(943\) 74.8093i 2.43612i
\(944\) 0.293015 0.613217i 0.00953684 0.0199585i
\(945\) 0 0
\(946\) −9.62089 1.07661i −0.312802 0.0350035i
\(947\) 35.3693i 1.14935i −0.818382 0.574675i \(-0.805129\pi\)
0.818382 0.574675i \(-0.194871\pi\)
\(948\) 0 0
\(949\) 61.3908i 1.99283i
\(950\) −1.47185 + 13.1529i −0.0477530 + 0.426736i
\(951\) 0 0
\(952\) −3.42811 + 9.86915i −0.111106 + 0.319861i
\(953\) 8.21631i 0.266152i 0.991106 + 0.133076i \(0.0424855\pi\)
−0.991106 + 0.133076i \(0.957514\pi\)
\(954\) 0 0
\(955\) −39.6509 −1.28307
\(956\) −30.1672 6.83720i −0.975676 0.221131i
\(957\) 0 0
\(958\) 1.06514 9.51846i 0.0344132 0.307528i
\(959\) −4.79689 −0.154900
\(960\) 0 0
\(961\) 25.2788 0.815444
\(962\) −9.76565 + 87.2689i −0.314857 + 2.81366i
\(963\) 0 0
\(964\) −49.8718 11.3031i −1.60626 0.364049i
\(965\) −33.1246 −1.06632
\(966\) 0 0
\(967\) 17.5083i 0.563028i −0.959557 0.281514i \(-0.909163\pi\)
0.959557 0.281514i \(-0.0908366\pi\)
\(968\) −5.00059 + 14.3961i −0.160725 + 0.462709i
\(969\) 0 0
\(970\) −1.38552 + 12.3814i −0.0444863 + 0.397544i
\(971\) 25.6587i 0.823428i −0.911313 0.411714i \(-0.864930\pi\)
0.911313 0.411714i \(-0.135070\pi\)
\(972\) 0 0
\(973\) 8.68075i 0.278292i
\(974\) 8.65189 + 0.968171i 0.277224 + 0.0310222i
\(975\) 0 0
\(976\) −0.724357 + 1.51592i −0.0231861 + 0.0485235i
\(977\) 47.1792i 1.50940i −0.656072 0.754698i \(-0.727783\pi\)
0.656072 0.754698i \(-0.272217\pi\)
\(978\) 0 0
\(979\) −17.5971 −0.562407
\(980\) −3.54749 0.804017i −0.113320 0.0256834i
\(981\) 0 0
\(982\) −41.3488 4.62705i −1.31949 0.147655i
\(983\) −28.1932 −0.899225 −0.449612 0.893224i \(-0.648438\pi\)
−0.449612 + 0.893224i \(0.648438\pi\)
\(984\) 0 0
\(985\) −22.1326 −0.705202
\(986\) −30.4763 3.41039i −0.970564 0.108609i
\(987\) 0 0
\(988\) 17.0945 75.4246i 0.543849 2.39958i
\(989\) 21.9868 0.699139
\(990\) 0 0
\(991\) 23.1846i 0.736482i −0.929730 0.368241i \(-0.879960\pi\)
0.929730 0.368241i \(-0.120040\pi\)
\(992\) 11.4841 + 7.15515i 0.364619 + 0.227176i
\(993\) 0 0
\(994\) −16.8795 1.88887i −0.535386 0.0599112i
\(995\) 36.3102i 1.15111i
\(996\) 0 0
\(997\) 9.32007i 0.295169i 0.989049 + 0.147585i \(0.0471499\pi\)
−0.989049 + 0.147585i \(0.952850\pi\)
\(998\) −2.38837 + 21.3433i −0.0756027 + 0.675610i
\(999\) 0 0
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 504.2.j.a.323.13 yes 24
3.2 odd 2 inner 504.2.j.a.323.12 yes 24
4.3 odd 2 2016.2.j.a.1583.7 24
8.3 odd 2 inner 504.2.j.a.323.11 24
8.5 even 2 2016.2.j.a.1583.17 24
12.11 even 2 2016.2.j.a.1583.18 24
24.5 odd 2 2016.2.j.a.1583.8 24
24.11 even 2 inner 504.2.j.a.323.14 yes 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
504.2.j.a.323.11 24 8.3 odd 2 inner
504.2.j.a.323.12 yes 24 3.2 odd 2 inner
504.2.j.a.323.13 yes 24 1.1 even 1 trivial
504.2.j.a.323.14 yes 24 24.11 even 2 inner
2016.2.j.a.1583.7 24 4.3 odd 2
2016.2.j.a.1583.8 24 24.5 odd 2
2016.2.j.a.1583.17 24 8.5 even 2
2016.2.j.a.1583.18 24 12.11 even 2