Properties

Label 504.2.bm.c.107.10
Level $504$
Weight $2$
Character 504.107
Analytic conductor $4.024$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [504,2,Mod(107,504)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(504, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 3, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("504.107");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 504.bm (of order \(6\), degree \(2\), 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: \(48\)
Relative dimension: \(24\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 107.10
Character \(\chi\) \(=\) 504.107
Dual form 504.2.bm.c.179.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.576030 + 1.29158i) q^{2} +(-1.33638 - 1.48798i) q^{4} +(-1.88256 + 3.26069i) q^{5} +(-2.23426 + 1.41706i) q^{7} +(2.69165 - 0.868922i) q^{8} +O(q^{10})\) \(q+(-0.576030 + 1.29158i) q^{2} +(-1.33638 - 1.48798i) q^{4} +(-1.88256 + 3.26069i) q^{5} +(-2.23426 + 1.41706i) q^{7} +(2.69165 - 0.868922i) q^{8} +(-3.12704 - 4.30974i) q^{10} +(-1.47084 + 0.849192i) q^{11} -5.64222i q^{13} +(-0.543254 - 3.70201i) q^{14} +(-0.428185 + 3.97702i) q^{16} +(2.26012 - 1.30488i) q^{17} +(-1.18076 + 2.04513i) q^{19} +(7.36767 - 1.55630i) q^{20} +(-0.249553 - 2.38888i) q^{22} +(0.653873 - 1.13254i) q^{23} +(-4.58807 - 7.94677i) q^{25} +(7.28740 + 3.25009i) q^{26} +(5.09439 + 1.43081i) q^{28} -6.80944 q^{29} +(4.75107 - 2.74303i) q^{31} +(-4.89000 - 2.84392i) q^{32} +(0.383465 + 3.67078i) q^{34} +(-0.414472 - 9.95295i) q^{35} +(-5.20109 - 3.00285i) q^{37} +(-1.96131 - 2.70311i) q^{38} +(-2.23391 + 10.4124i) q^{40} -6.10456i q^{41} -6.49804 q^{43} +(3.22919 + 1.05375i) q^{44} +(1.08612 + 1.49691i) q^{46} +(-3.53360 + 6.12038i) q^{47} +(2.98386 - 6.33219i) q^{49} +(12.9068 - 1.34830i) q^{50} +(-8.39552 + 7.54014i) q^{52} +(0.488913 + 0.846821i) q^{53} -6.39462i q^{55} +(-4.78253 + 5.75564i) q^{56} +(3.92244 - 8.79496i) q^{58} +(-6.67395 + 3.85320i) q^{59} +(7.64484 + 4.41375i) q^{61} +(0.806095 + 7.71647i) q^{62} +(6.48995 - 4.67767i) q^{64} +(18.3975 + 10.6218i) q^{65} +(6.69828 + 11.6018i) q^{67} +(-4.96201 - 1.61920i) q^{68} +(13.0938 + 5.19787i) q^{70} -9.40544 q^{71} +(-1.09003 - 1.88798i) q^{73} +(6.87442 - 4.98791i) q^{74} +(4.62106 - 0.976124i) q^{76} +(2.08289 - 3.98160i) q^{77} +(-15.0908 - 8.71267i) q^{79} +(-12.1617 - 8.88315i) q^{80} +(7.88456 + 3.51641i) q^{82} +11.8864i q^{83} +9.82605i q^{85} +(3.74307 - 8.39277i) q^{86} +(-3.22111 + 3.56378i) q^{88} +(-9.58642 - 5.53472i) q^{89} +(7.99538 + 12.6062i) q^{91} +(-2.55902 + 0.540552i) q^{92} +(-5.86952 - 8.08946i) q^{94} +(-4.44570 - 7.70018i) q^{95} +15.0631 q^{97} +(6.45976 + 7.50144i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q+O(q^{10}) \) Copy content Toggle raw display \( 48 q - 8 q^{10} - 28 q^{16} - 32 q^{19} + 32 q^{22} + 4 q^{28} + 112 q^{34} - 36 q^{40} - 160 q^{43} + 40 q^{46} + 56 q^{49} - 36 q^{52} + 12 q^{58} - 24 q^{64} + 92 q^{70} + 16 q^{73} - 120 q^{76} + 20 q^{82} - 100 q^{88} - 32 q^{91} - 20 q^{94} + 240 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(73\) \(127\) \(253\) \(281\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.576030 + 1.29158i −0.407315 + 0.913288i
\(3\) 0 0
\(4\) −1.33638 1.48798i −0.668189 0.743991i
\(5\) −1.88256 + 3.26069i −0.841907 + 1.45823i 0.0463738 + 0.998924i \(0.485233\pi\)
−0.888281 + 0.459301i \(0.848100\pi\)
\(6\) 0 0
\(7\) −2.23426 + 1.41706i −0.844472 + 0.535600i
\(8\) 2.69165 0.868922i 0.951642 0.307210i
\(9\) 0 0
\(10\) −3.12704 4.30974i −0.988858 1.36286i
\(11\) −1.47084 + 0.849192i −0.443476 + 0.256041i −0.705071 0.709137i \(-0.749085\pi\)
0.261595 + 0.965178i \(0.415752\pi\)
\(12\) 0 0
\(13\) 5.64222i 1.56487i −0.622733 0.782435i \(-0.713978\pi\)
0.622733 0.782435i \(-0.286022\pi\)
\(14\) −0.543254 3.70201i −0.145191 0.989404i
\(15\) 0 0
\(16\) −0.428185 + 3.97702i −0.107046 + 0.994254i
\(17\) 2.26012 1.30488i 0.548158 0.316479i −0.200220 0.979751i \(-0.564166\pi\)
0.748379 + 0.663271i \(0.230833\pi\)
\(18\) 0 0
\(19\) −1.18076 + 2.04513i −0.270885 + 0.469186i −0.969089 0.246713i \(-0.920649\pi\)
0.698204 + 0.715899i \(0.253983\pi\)
\(20\) 7.36767 1.55630i 1.64746 0.347999i
\(21\) 0 0
\(22\) −0.249553 2.38888i −0.0532048 0.509311i
\(23\) 0.653873 1.13254i 0.136342 0.236151i −0.789767 0.613406i \(-0.789799\pi\)
0.926109 + 0.377255i \(0.123132\pi\)
\(24\) 0 0
\(25\) −4.58807 7.94677i −0.917614 1.58935i
\(26\) 7.28740 + 3.25009i 1.42918 + 0.637395i
\(27\) 0 0
\(28\) 5.09439 + 1.43081i 0.962749 + 0.270398i
\(29\) −6.80944 −1.26448 −0.632241 0.774772i \(-0.717865\pi\)
−0.632241 + 0.774772i \(0.717865\pi\)
\(30\) 0 0
\(31\) 4.75107 2.74303i 0.853317 0.492663i −0.00845183 0.999964i \(-0.502690\pi\)
0.861769 + 0.507302i \(0.169357\pi\)
\(32\) −4.89000 2.84392i −0.864439 0.502739i
\(33\) 0 0
\(34\) 0.383465 + 3.67078i 0.0657637 + 0.629533i
\(35\) −0.414472 9.95295i −0.0700586 1.68236i
\(36\) 0 0
\(37\) −5.20109 3.00285i −0.855054 0.493666i 0.00729899 0.999973i \(-0.497677\pi\)
−0.862353 + 0.506308i \(0.831010\pi\)
\(38\) −1.96131 2.70311i −0.318166 0.438502i
\(39\) 0 0
\(40\) −2.23391 + 10.4124i −0.353212 + 1.64635i
\(41\) 6.10456i 0.953373i −0.879073 0.476686i \(-0.841838\pi\)
0.879073 0.476686i \(-0.158162\pi\)
\(42\) 0 0
\(43\) −6.49804 −0.990943 −0.495471 0.868624i \(-0.665005\pi\)
−0.495471 + 0.868624i \(0.665005\pi\)
\(44\) 3.22919 + 1.05375i 0.486818 + 0.158859i
\(45\) 0 0
\(46\) 1.08612 + 1.49691i 0.160140 + 0.220707i
\(47\) −3.53360 + 6.12038i −0.515429 + 0.892749i 0.484411 + 0.874841i \(0.339034\pi\)
−0.999840 + 0.0179081i \(0.994299\pi\)
\(48\) 0 0
\(49\) 2.98386 6.33219i 0.426266 0.904598i
\(50\) 12.9068 1.34830i 1.82530 0.190678i
\(51\) 0 0
\(52\) −8.39552 + 7.54014i −1.16425 + 1.04563i
\(53\) 0.488913 + 0.846821i 0.0671573 + 0.116320i 0.897649 0.440711i \(-0.145274\pi\)
−0.830492 + 0.557031i \(0.811940\pi\)
\(54\) 0 0
\(55\) 6.39462i 0.862251i
\(56\) −4.78253 + 5.75564i −0.639093 + 0.769130i
\(57\) 0 0
\(58\) 3.92244 8.79496i 0.515042 1.15484i
\(59\) −6.67395 + 3.85320i −0.868874 + 0.501645i −0.866974 0.498354i \(-0.833938\pi\)
−0.00190001 + 0.999998i \(0.500605\pi\)
\(60\) 0 0
\(61\) 7.64484 + 4.41375i 0.978822 + 0.565123i 0.901914 0.431915i \(-0.142162\pi\)
0.0769075 + 0.997038i \(0.475495\pi\)
\(62\) 0.806095 + 7.71647i 0.102374 + 0.979993i
\(63\) 0 0
\(64\) 6.48995 4.67767i 0.811244 0.584708i
\(65\) 18.3975 + 10.6218i 2.28193 + 1.31747i
\(66\) 0 0
\(67\) 6.69828 + 11.6018i 0.818325 + 1.41738i 0.906916 + 0.421312i \(0.138430\pi\)
−0.0885910 + 0.996068i \(0.528236\pi\)
\(68\) −4.96201 1.61920i −0.601732 0.196357i
\(69\) 0 0
\(70\) 13.0938 + 5.19787i 1.56501 + 0.621265i
\(71\) −9.40544 −1.11622 −0.558110 0.829767i \(-0.688473\pi\)
−0.558110 + 0.829767i \(0.688473\pi\)
\(72\) 0 0
\(73\) −1.09003 1.88798i −0.127578 0.220971i 0.795160 0.606400i \(-0.207387\pi\)
−0.922738 + 0.385429i \(0.874054\pi\)
\(74\) 6.87442 4.98791i 0.799135 0.579833i
\(75\) 0 0
\(76\) 4.62106 0.976124i 0.530072 0.111969i
\(77\) 2.08289 3.98160i 0.237368 0.453745i
\(78\) 0 0
\(79\) −15.0908 8.71267i −1.69785 0.980252i −0.947800 0.318865i \(-0.896698\pi\)
−0.750045 0.661386i \(-0.769968\pi\)
\(80\) −12.1617 8.88315i −1.35972 0.993167i
\(81\) 0 0
\(82\) 7.88456 + 3.51641i 0.870704 + 0.388323i
\(83\) 11.8864i 1.30471i 0.757915 + 0.652353i \(0.226218\pi\)
−0.757915 + 0.652353i \(0.773782\pi\)
\(84\) 0 0
\(85\) 9.82605i 1.06578i
\(86\) 3.74307 8.39277i 0.403626 0.905016i
\(87\) 0 0
\(88\) −3.22111 + 3.56378i −0.343372 + 0.379900i
\(89\) −9.58642 5.53472i −1.01616 0.586679i −0.103170 0.994664i \(-0.532898\pi\)
−0.912989 + 0.407984i \(0.866232\pi\)
\(90\) 0 0
\(91\) 7.99538 + 12.6062i 0.838144 + 1.32149i
\(92\) −2.55902 + 0.540552i −0.266797 + 0.0563564i
\(93\) 0 0
\(94\) −5.86952 8.08946i −0.605395 0.834364i
\(95\) −4.44570 7.70018i −0.456119 0.790021i
\(96\) 0 0
\(97\) 15.0631 1.52943 0.764715 0.644369i \(-0.222880\pi\)
0.764715 + 0.644369i \(0.222880\pi\)
\(98\) 6.45976 + 7.50144i 0.652534 + 0.757759i
\(99\) 0 0
\(100\) −5.69326 + 17.4469i −0.569326 + 1.74469i
\(101\) −0.777899 1.34736i −0.0774039 0.134067i 0.824725 0.565534i \(-0.191330\pi\)
−0.902129 + 0.431466i \(0.857996\pi\)
\(102\) 0 0
\(103\) 6.94066 + 4.00719i 0.683883 + 0.394840i 0.801317 0.598240i \(-0.204133\pi\)
−0.117433 + 0.993081i \(0.537467\pi\)
\(104\) −4.90265 15.1869i −0.480744 1.48919i
\(105\) 0 0
\(106\) −1.37537 + 0.143677i −0.133588 + 0.0139551i
\(107\) −12.6257 7.28943i −1.22057 0.704696i −0.255530 0.966801i \(-0.582250\pi\)
−0.965039 + 0.262105i \(0.915583\pi\)
\(108\) 0 0
\(109\) −0.655188 + 0.378273i −0.0627556 + 0.0362320i −0.531050 0.847341i \(-0.678202\pi\)
0.468294 + 0.883573i \(0.344869\pi\)
\(110\) 8.25920 + 3.68350i 0.787483 + 0.351208i
\(111\) 0 0
\(112\) −4.67901 9.49246i −0.442125 0.896954i
\(113\) 9.87390i 0.928859i 0.885610 + 0.464429i \(0.153741\pi\)
−0.885610 + 0.464429i \(0.846259\pi\)
\(114\) 0 0
\(115\) 2.46191 + 4.26416i 0.229574 + 0.397635i
\(116\) 9.09999 + 10.1323i 0.844913 + 0.940763i
\(117\) 0 0
\(118\) −1.13234 10.8395i −0.104241 0.997859i
\(119\) −3.20060 + 6.11817i −0.293398 + 0.560852i
\(120\) 0 0
\(121\) −4.05774 + 7.02822i −0.368886 + 0.638929i
\(122\) −10.1044 + 7.33150i −0.914809 + 0.663763i
\(123\) 0 0
\(124\) −10.4308 3.40378i −0.936714 0.305668i
\(125\) 15.7237 1.40637
\(126\) 0 0
\(127\) 4.50847i 0.400062i 0.979790 + 0.200031i \(0.0641043\pi\)
−0.979790 + 0.200031i \(0.935896\pi\)
\(128\) 2.30319 + 11.0768i 0.203575 + 0.979059i
\(129\) 0 0
\(130\) −24.3165 + 17.6435i −2.13270 + 1.54743i
\(131\) −14.0673 8.12176i −1.22907 0.709601i −0.262231 0.965005i \(-0.584458\pi\)
−0.966835 + 0.255404i \(0.917792\pi\)
\(132\) 0 0
\(133\) −0.259961 6.24258i −0.0225414 0.541300i
\(134\) −18.8431 + 1.96843i −1.62779 + 0.170046i
\(135\) 0 0
\(136\) 4.94960 5.47614i 0.424425 0.469575i
\(137\) −3.63470 + 2.09849i −0.310533 + 0.179286i −0.647165 0.762350i \(-0.724046\pi\)
0.336632 + 0.941636i \(0.390712\pi\)
\(138\) 0 0
\(139\) −5.70274 −0.483700 −0.241850 0.970314i \(-0.577754\pi\)
−0.241850 + 0.970314i \(0.577754\pi\)
\(140\) −14.2559 + 13.9176i −1.20485 + 1.17625i
\(141\) 0 0
\(142\) 5.41782 12.1479i 0.454653 1.01943i
\(143\) 4.79133 + 8.29882i 0.400671 + 0.693982i
\(144\) 0 0
\(145\) 12.8192 22.2035i 1.06458 1.84390i
\(146\) 3.06637 0.320326i 0.253775 0.0265104i
\(147\) 0 0
\(148\) 2.48243 + 11.7521i 0.204055 + 0.966015i
\(149\) −6.74195 + 11.6774i −0.552322 + 0.956650i 0.445784 + 0.895140i \(0.352925\pi\)
−0.998106 + 0.0615095i \(0.980409\pi\)
\(150\) 0 0
\(151\) −18.4727 + 10.6652i −1.50329 + 0.867924i −0.503295 + 0.864115i \(0.667879\pi\)
−0.999993 + 0.00380878i \(0.998788\pi\)
\(152\) −1.40113 + 6.53077i −0.113646 + 0.529715i
\(153\) 0 0
\(154\) 3.94276 + 4.98375i 0.317717 + 0.401602i
\(155\) 20.6557i 1.65910i
\(156\) 0 0
\(157\) −7.97251 + 4.60293i −0.636276 + 0.367354i −0.783179 0.621797i \(-0.786403\pi\)
0.146903 + 0.989151i \(0.453070\pi\)
\(158\) 19.9459 14.4723i 1.58681 1.15135i
\(159\) 0 0
\(160\) 18.4789 10.5909i 1.46088 0.837287i
\(161\) 0.143959 + 3.45697i 0.0113456 + 0.272448i
\(162\) 0 0
\(163\) 0.0600325 0.103979i 0.00470211 0.00814429i −0.863665 0.504067i \(-0.831837\pi\)
0.868367 + 0.495922i \(0.165170\pi\)
\(164\) −9.08349 + 8.15801i −0.709301 + 0.637033i
\(165\) 0 0
\(166\) −15.3523 6.84695i −1.19157 0.531426i
\(167\) 12.9810 1.00450 0.502251 0.864722i \(-0.332505\pi\)
0.502251 + 0.864722i \(0.332505\pi\)
\(168\) 0 0
\(169\) −18.8346 −1.44882
\(170\) −12.6912 5.66010i −0.973368 0.434110i
\(171\) 0 0
\(172\) 8.68385 + 9.66898i 0.662137 + 0.737253i
\(173\) 3.44458 5.96618i 0.261886 0.453600i −0.704857 0.709350i \(-0.748989\pi\)
0.966743 + 0.255749i \(0.0823221\pi\)
\(174\) 0 0
\(175\) 21.5120 + 11.2536i 1.62616 + 0.850691i
\(176\) −2.74746 6.21318i −0.207097 0.468336i
\(177\) 0 0
\(178\) 12.6706 9.19350i 0.949704 0.689082i
\(179\) 13.6043 7.85445i 1.01683 0.587070i 0.103649 0.994614i \(-0.466948\pi\)
0.913185 + 0.407544i \(0.133615\pi\)
\(180\) 0 0
\(181\) 15.6714i 1.16485i −0.812886 0.582423i \(-0.802105\pi\)
0.812886 0.582423i \(-0.197895\pi\)
\(182\) −20.8875 + 3.06516i −1.54829 + 0.227205i
\(183\) 0 0
\(184\) 0.775906 3.61657i 0.0572006 0.266617i
\(185\) 19.5827 11.3061i 1.43975 0.831241i
\(186\) 0 0
\(187\) −2.21618 + 3.83854i −0.162063 + 0.280702i
\(188\) 13.8292 2.92120i 1.00860 0.213051i
\(189\) 0 0
\(190\) 12.5063 1.30646i 0.907301 0.0947805i
\(191\) 12.0633 20.8943i 0.872873 1.51186i 0.0138617 0.999904i \(-0.495588\pi\)
0.859011 0.511957i \(-0.171079\pi\)
\(192\) 0 0
\(193\) −4.80306 8.31914i −0.345732 0.598825i 0.639755 0.768579i \(-0.279036\pi\)
−0.985486 + 0.169754i \(0.945703\pi\)
\(194\) −8.67682 + 19.4553i −0.622959 + 1.39681i
\(195\) 0 0
\(196\) −13.4097 + 4.02227i −0.957839 + 0.287305i
\(197\) −2.05305 −0.146274 −0.0731371 0.997322i \(-0.523301\pi\)
−0.0731371 + 0.997322i \(0.523301\pi\)
\(198\) 0 0
\(199\) 8.62103 4.97735i 0.611128 0.352835i −0.162279 0.986745i \(-0.551884\pi\)
0.773407 + 0.633910i \(0.218551\pi\)
\(200\) −19.2546 17.4032i −1.36151 1.23060i
\(201\) 0 0
\(202\) 2.18832 0.228602i 0.153970 0.0160844i
\(203\) 15.2141 9.64941i 1.06782 0.677256i
\(204\) 0 0
\(205\) 19.9051 + 11.4922i 1.39023 + 0.802651i
\(206\) −9.17365 + 6.65618i −0.639159 + 0.463758i
\(207\) 0 0
\(208\) 22.4392 + 2.41591i 1.55588 + 0.167514i
\(209\) 4.01076i 0.277430i
\(210\) 0 0
\(211\) −13.9757 −0.962128 −0.481064 0.876685i \(-0.659750\pi\)
−0.481064 + 0.876685i \(0.659750\pi\)
\(212\) 0.606683 1.85917i 0.0416672 0.127688i
\(213\) 0 0
\(214\) 16.6877 12.1082i 1.14075 0.827698i
\(215\) 12.2330 21.1881i 0.834281 1.44502i
\(216\) 0 0
\(217\) −6.72808 + 12.8612i −0.456732 + 0.873076i
\(218\) −0.111163 1.06413i −0.00752893 0.0720718i
\(219\) 0 0
\(220\) −9.51509 + 8.54564i −0.641507 + 0.576147i
\(221\) −7.36241 12.7521i −0.495249 0.857796i
\(222\) 0 0
\(223\) 15.8817i 1.06352i 0.846896 + 0.531759i \(0.178469\pi\)
−0.846896 + 0.531759i \(0.821531\pi\)
\(224\) 14.9556 0.575385i 0.999261 0.0384446i
\(225\) 0 0
\(226\) −12.7530 5.68767i −0.848315 0.378338i
\(227\) 0.620059 0.357991i 0.0411548 0.0237607i −0.479281 0.877661i \(-0.659103\pi\)
0.520436 + 0.853901i \(0.325769\pi\)
\(228\) 0 0
\(229\) 3.89913 + 2.25117i 0.257662 + 0.148761i 0.623268 0.782009i \(-0.285805\pi\)
−0.365606 + 0.930770i \(0.619138\pi\)
\(230\) −6.92565 + 0.723483i −0.456664 + 0.0477051i
\(231\) 0 0
\(232\) −18.3286 + 5.91687i −1.20333 + 0.388462i
\(233\) 6.69604 + 3.86596i 0.438672 + 0.253267i 0.703034 0.711156i \(-0.251828\pi\)
−0.264362 + 0.964423i \(0.585161\pi\)
\(234\) 0 0
\(235\) −13.3044 23.0440i −0.867886 1.50322i
\(236\) 14.6524 + 4.78138i 0.953791 + 0.311241i
\(237\) 0 0
\(238\) −6.05849 7.65809i −0.392713 0.496400i
\(239\) 21.3788 1.38288 0.691440 0.722433i \(-0.256976\pi\)
0.691440 + 0.722433i \(0.256976\pi\)
\(240\) 0 0
\(241\) 4.25688 + 7.37313i 0.274210 + 0.474945i 0.969935 0.243362i \(-0.0782504\pi\)
−0.695726 + 0.718308i \(0.744917\pi\)
\(242\) −6.74015 9.28939i −0.433273 0.597144i
\(243\) 0 0
\(244\) −3.64882 17.2738i −0.233592 1.10584i
\(245\) 15.0300 + 21.6502i 0.960232 + 1.38318i
\(246\) 0 0
\(247\) 11.5391 + 6.66209i 0.734215 + 0.423899i
\(248\) 10.4047 11.5116i 0.660701 0.730986i
\(249\) 0 0
\(250\) −9.05731 + 20.3084i −0.572835 + 1.28442i
\(251\) 0.778871i 0.0491619i 0.999698 + 0.0245810i \(0.00782515\pi\)
−0.999698 + 0.0245810i \(0.992175\pi\)
\(252\) 0 0
\(253\) 2.22106i 0.139637i
\(254\) −5.82307 2.59702i −0.365372 0.162951i
\(255\) 0 0
\(256\) −15.6333 3.40580i −0.977082 0.212862i
\(257\) −10.6901 6.17195i −0.666832 0.384996i 0.128043 0.991769i \(-0.459130\pi\)
−0.794875 + 0.606773i \(0.792464\pi\)
\(258\) 0 0
\(259\) 15.8758 0.661120i 0.986476 0.0410800i
\(260\) −8.78098 41.5700i −0.544573 2.57806i
\(261\) 0 0
\(262\) 18.5931 13.4907i 1.14869 0.833460i
\(263\) 1.01432 + 1.75686i 0.0625458 + 0.108333i 0.895603 0.444855i \(-0.146745\pi\)
−0.833057 + 0.553187i \(0.813411\pi\)
\(264\) 0 0
\(265\) −3.68163 −0.226161
\(266\) 8.21256 + 3.26015i 0.503544 + 0.199893i
\(267\) 0 0
\(268\) 8.31178 25.4713i 0.507723 1.55590i
\(269\) −13.1346 22.7498i −0.800833 1.38708i −0.919069 0.394097i \(-0.871057\pi\)
0.118236 0.992986i \(-0.462276\pi\)
\(270\) 0 0
\(271\) −7.01591 4.05064i −0.426186 0.246059i 0.271535 0.962429i \(-0.412469\pi\)
−0.697720 + 0.716370i \(0.745802\pi\)
\(272\) 4.22177 + 9.54724i 0.255983 + 0.578887i
\(273\) 0 0
\(274\) −0.616685 5.90331i −0.0372553 0.356632i
\(275\) 13.4967 + 7.79231i 0.813880 + 0.469894i
\(276\) 0 0
\(277\) −8.45693 + 4.88261i −0.508127 + 0.293368i −0.732064 0.681236i \(-0.761443\pi\)
0.223936 + 0.974604i \(0.428109\pi\)
\(278\) 3.28495 7.36557i 0.197018 0.441758i
\(279\) 0 0
\(280\) −9.76395 26.4297i −0.583508 1.57948i
\(281\) 1.88752i 0.112600i −0.998414 0.0562999i \(-0.982070\pi\)
0.998414 0.0562999i \(-0.0179303\pi\)
\(282\) 0 0
\(283\) 3.28892 + 5.69657i 0.195506 + 0.338626i 0.947066 0.321038i \(-0.104032\pi\)
−0.751560 + 0.659664i \(0.770698\pi\)
\(284\) 12.5692 + 13.9951i 0.745847 + 0.830458i
\(285\) 0 0
\(286\) −13.4786 + 1.40803i −0.797005 + 0.0832585i
\(287\) 8.65056 + 13.6392i 0.510626 + 0.805097i
\(288\) 0 0
\(289\) −5.09459 + 8.82408i −0.299682 + 0.519064i
\(290\) 21.2934 + 29.3469i 1.25039 + 1.72331i
\(291\) 0 0
\(292\) −1.35259 + 4.14500i −0.0791546 + 0.242567i
\(293\) 14.1311 0.825545 0.412772 0.910834i \(-0.364560\pi\)
0.412772 + 0.910834i \(0.364560\pi\)
\(294\) 0 0
\(295\) 29.0156i 1.68935i
\(296\) −16.6088 3.56328i −0.965364 0.207111i
\(297\) 0 0
\(298\) −11.1988 15.4343i −0.648728 0.894087i
\(299\) −6.39004 3.68929i −0.369546 0.213357i
\(300\) 0 0
\(301\) 14.5183 9.20814i 0.836823 0.530749i
\(302\) −3.13419 30.0025i −0.180353 1.72645i
\(303\) 0 0
\(304\) −7.62795 5.57159i −0.437493 0.319553i
\(305\) −28.7838 + 16.6183i −1.64815 + 0.951562i
\(306\) 0 0
\(307\) −17.5973 −1.00433 −0.502167 0.864771i \(-0.667464\pi\)
−0.502167 + 0.864771i \(0.667464\pi\)
\(308\) −8.70808 + 2.22162i −0.496189 + 0.126588i
\(309\) 0 0
\(310\) −26.6785 11.8983i −1.51524 0.675778i
\(311\) 5.44683 + 9.43418i 0.308861 + 0.534963i 0.978114 0.208072i \(-0.0667188\pi\)
−0.669252 + 0.743035i \(0.733385\pi\)
\(312\) 0 0
\(313\) −1.76535 + 3.05768i −0.0997835 + 0.172830i −0.911595 0.411090i \(-0.865148\pi\)
0.811811 + 0.583920i \(0.198482\pi\)
\(314\) −1.35267 12.9486i −0.0763354 0.730732i
\(315\) 0 0
\(316\) 7.20270 + 34.0982i 0.405183 + 1.91818i
\(317\) 8.09426 14.0197i 0.454619 0.787423i −0.544047 0.839055i \(-0.683109\pi\)
0.998666 + 0.0516316i \(0.0164422\pi\)
\(318\) 0 0
\(319\) 10.0156 5.78252i 0.560767 0.323759i
\(320\) 3.03470 + 29.9677i 0.169645 + 1.67525i
\(321\) 0 0
\(322\) −4.54790 1.80539i −0.253444 0.100610i
\(323\) 6.16298i 0.342918i
\(324\) 0 0
\(325\) −44.8374 + 25.8869i −2.48713 + 1.43595i
\(326\) 0.0997175 + 0.137432i 0.00552284 + 0.00761167i
\(327\) 0 0
\(328\) −5.30439 16.4313i −0.292886 0.907269i
\(329\) −0.777972 18.6819i −0.0428910 1.02996i
\(330\) 0 0
\(331\) 5.79835 10.0430i 0.318706 0.552016i −0.661512 0.749935i \(-0.730085\pi\)
0.980218 + 0.197919i \(0.0634183\pi\)
\(332\) 17.6868 15.8848i 0.970690 0.871791i
\(333\) 0 0
\(334\) −7.47747 + 16.7661i −0.409149 + 0.917400i
\(335\) −50.4397 −2.75581
\(336\) 0 0
\(337\) 2.81073 0.153110 0.0765550 0.997065i \(-0.475608\pi\)
0.0765550 + 0.997065i \(0.475608\pi\)
\(338\) 10.8493 24.3265i 0.590124 1.32319i
\(339\) 0 0
\(340\) 14.6210 13.1313i 0.792935 0.712146i
\(341\) −4.65872 + 8.06914i −0.252284 + 0.436968i
\(342\) 0 0
\(343\) 2.30639 + 18.3761i 0.124533 + 0.992215i
\(344\) −17.4905 + 5.64629i −0.943022 + 0.304428i
\(345\) 0 0
\(346\) 5.72164 + 7.88566i 0.307597 + 0.423936i
\(347\) −18.7883 + 10.8474i −1.00861 + 0.582320i −0.910784 0.412884i \(-0.864522\pi\)
−0.0978242 + 0.995204i \(0.531188\pi\)
\(348\) 0 0
\(349\) 7.44465i 0.398503i −0.979948 0.199251i \(-0.936149\pi\)
0.979948 0.199251i \(-0.0638511\pi\)
\(350\) −26.9265 + 21.3022i −1.43928 + 1.13865i
\(351\) 0 0
\(352\) 9.60747 + 0.0304086i 0.512080 + 0.00162078i
\(353\) 13.0365 7.52665i 0.693865 0.400603i −0.111193 0.993799i \(-0.535467\pi\)
0.805058 + 0.593196i \(0.202134\pi\)
\(354\) 0 0
\(355\) 17.7063 30.6682i 0.939754 1.62770i
\(356\) 4.57551 + 21.6609i 0.242502 + 1.14803i
\(357\) 0 0
\(358\) 2.30819 + 22.0955i 0.121992 + 1.16778i
\(359\) −9.01876 + 15.6210i −0.475992 + 0.824442i −0.999622 0.0275035i \(-0.991244\pi\)
0.523630 + 0.851946i \(0.324578\pi\)
\(360\) 0 0
\(361\) 6.71162 + 11.6249i 0.353243 + 0.611835i
\(362\) 20.2409 + 9.02720i 1.06384 + 0.474459i
\(363\) 0 0
\(364\) 8.07294 28.7436i 0.423137 1.50658i
\(365\) 8.20816 0.429635
\(366\) 0 0
\(367\) −3.38897 + 1.95662i −0.176903 + 0.102135i −0.585837 0.810429i \(-0.699234\pi\)
0.408934 + 0.912564i \(0.365901\pi\)
\(368\) 4.22416 + 3.08540i 0.220199 + 0.160838i
\(369\) 0 0
\(370\) 3.32253 + 31.8054i 0.172730 + 1.65348i
\(371\) −2.29236 1.19920i −0.119013 0.0622594i
\(372\) 0 0
\(373\) 15.8513 + 9.15178i 0.820752 + 0.473861i 0.850676 0.525691i \(-0.176193\pi\)
−0.0299239 + 0.999552i \(0.509527\pi\)
\(374\) −3.68121 5.07351i −0.190351 0.262345i
\(375\) 0 0
\(376\) −4.19308 + 19.5443i −0.216242 + 1.00792i
\(377\) 38.4203i 1.97875i
\(378\) 0 0
\(379\) 25.8073 1.32563 0.662816 0.748783i \(-0.269361\pi\)
0.662816 + 0.748783i \(0.269361\pi\)
\(380\) −5.51659 + 16.9055i −0.282995 + 0.867232i
\(381\) 0 0
\(382\) 20.0379 + 27.6166i 1.02523 + 1.41299i
\(383\) −7.37665 + 12.7767i −0.376929 + 0.652860i −0.990614 0.136691i \(-0.956353\pi\)
0.613685 + 0.789551i \(0.289687\pi\)
\(384\) 0 0
\(385\) 9.06159 + 14.2873i 0.461822 + 0.728147i
\(386\) 13.5116 1.41148i 0.687721 0.0718423i
\(387\) 0 0
\(388\) −20.1300 22.4137i −1.02195 1.13788i
\(389\) 8.70264 + 15.0734i 0.441242 + 0.764253i 0.997782 0.0665677i \(-0.0212049\pi\)
−0.556540 + 0.830821i \(0.687872\pi\)
\(390\) 0 0
\(391\) 3.41290i 0.172598i
\(392\) 2.52933 19.6368i 0.127750 0.991806i
\(393\) 0 0
\(394\) 1.18262 2.65169i 0.0595796 0.133590i
\(395\) 56.8186 32.8042i 2.85886 1.65056i
\(396\) 0 0
\(397\) 10.0273 + 5.78926i 0.503255 + 0.290554i 0.730057 0.683387i \(-0.239494\pi\)
−0.226802 + 0.973941i \(0.572827\pi\)
\(398\) 1.46270 + 14.0019i 0.0733184 + 0.701851i
\(399\) 0 0
\(400\) 33.5690 14.8441i 1.67845 0.742207i
\(401\) −31.1453 17.9818i −1.55532 0.897967i −0.997694 0.0678773i \(-0.978377\pi\)
−0.557630 0.830089i \(-0.688289\pi\)
\(402\) 0 0
\(403\) −15.4768 26.8065i −0.770953 1.33533i
\(404\) −0.965282 + 2.95809i −0.0480246 + 0.147170i
\(405\) 0 0
\(406\) 3.69926 + 25.2086i 0.183591 + 1.25108i
\(407\) 10.2000 0.505595
\(408\) 0 0
\(409\) 12.1615 + 21.0644i 0.601349 + 1.04157i 0.992617 + 0.121290i \(0.0387031\pi\)
−0.391268 + 0.920277i \(0.627964\pi\)
\(410\) −26.3091 + 19.0892i −1.29931 + 0.942751i
\(411\) 0 0
\(412\) −3.31272 15.6827i −0.163206 0.772631i
\(413\) 9.45111 18.0665i 0.465059 0.888993i
\(414\) 0 0
\(415\) −38.7580 22.3769i −1.90256 1.09844i
\(416\) −16.0460 + 27.5905i −0.786720 + 1.35273i
\(417\) 0 0
\(418\) 5.18024 + 2.31032i 0.253374 + 0.113001i
\(419\) 6.92954i 0.338530i 0.985571 + 0.169265i \(0.0541394\pi\)
−0.985571 + 0.169265i \(0.945861\pi\)
\(420\) 0 0
\(421\) 12.6192i 0.615024i −0.951544 0.307512i \(-0.900504\pi\)
0.951544 0.307512i \(-0.0994965\pi\)
\(422\) 8.05043 18.0508i 0.391889 0.878700i
\(423\) 0 0
\(424\) 2.05180 + 1.85452i 0.0996444 + 0.0900634i
\(425\) −20.7391 11.9737i −1.00600 0.580812i
\(426\) 0 0
\(427\) −23.3352 + 0.971750i −1.12927 + 0.0470263i
\(428\) 6.02612 + 28.5282i 0.291284 + 1.37896i
\(429\) 0 0
\(430\) 20.3197 + 28.0049i 0.979902 + 1.35052i
\(431\) −11.1759 19.3571i −0.538322 0.932401i −0.998995 0.0448306i \(-0.985725\pi\)
0.460673 0.887570i \(-0.347608\pi\)
\(432\) 0 0
\(433\) −32.2813 −1.55134 −0.775671 0.631138i \(-0.782588\pi\)
−0.775671 + 0.631138i \(0.782588\pi\)
\(434\) −12.7358 16.0983i −0.611336 0.772745i
\(435\) 0 0
\(436\) 1.43844 + 0.469393i 0.0688889 + 0.0224798i
\(437\) 1.54413 + 2.67451i 0.0738658 + 0.127939i
\(438\) 0 0
\(439\) −2.42798 1.40180i −0.115881 0.0669041i 0.440939 0.897537i \(-0.354645\pi\)
−0.556820 + 0.830633i \(0.687979\pi\)
\(440\) −5.55643 17.2121i −0.264892 0.820554i
\(441\) 0 0
\(442\) 20.7113 2.16359i 0.985137 0.102912i
\(443\) 16.2066 + 9.35689i 0.769999 + 0.444559i 0.832874 0.553462i \(-0.186694\pi\)
−0.0628752 + 0.998021i \(0.520027\pi\)
\(444\) 0 0
\(445\) 36.0940 20.8389i 1.71102 0.987859i
\(446\) −20.5126 9.14834i −0.971298 0.433187i
\(447\) 0 0
\(448\) −7.87170 + 19.6478i −0.371903 + 0.928272i
\(449\) 13.8950i 0.655747i 0.944722 + 0.327874i \(0.106332\pi\)
−0.944722 + 0.327874i \(0.893668\pi\)
\(450\) 0 0
\(451\) 5.18395 + 8.97886i 0.244103 + 0.422798i
\(452\) 14.6922 13.1953i 0.691063 0.620653i
\(453\) 0 0
\(454\) 0.105203 + 1.00707i 0.00493742 + 0.0472642i
\(455\) −56.1567 + 2.33854i −2.63267 + 0.109633i
\(456\) 0 0
\(457\) 2.88922 5.00428i 0.135152 0.234090i −0.790503 0.612458i \(-0.790181\pi\)
0.925656 + 0.378367i \(0.123514\pi\)
\(458\) −5.15359 + 3.73932i −0.240811 + 0.174727i
\(459\) 0 0
\(460\) 3.05494 9.36181i 0.142438 0.436496i
\(461\) −15.4222 −0.718285 −0.359142 0.933283i \(-0.616931\pi\)
−0.359142 + 0.933283i \(0.616931\pi\)
\(462\) 0 0
\(463\) 11.5902i 0.538644i −0.963050 0.269322i \(-0.913200\pi\)
0.963050 0.269322i \(-0.0867996\pi\)
\(464\) 2.91570 27.0813i 0.135358 1.25722i
\(465\) 0 0
\(466\) −8.85033 + 6.42159i −0.409984 + 0.297474i
\(467\) −1.98153 1.14404i −0.0916943 0.0529397i 0.453452 0.891281i \(-0.350192\pi\)
−0.545146 + 0.838341i \(0.683526\pi\)
\(468\) 0 0
\(469\) −31.4061 16.4295i −1.45020 0.758643i
\(470\) 37.4270 3.90978i 1.72638 0.180345i
\(471\) 0 0
\(472\) −14.6158 + 16.1706i −0.672746 + 0.744313i
\(473\) 9.55761 5.51809i 0.439459 0.253722i
\(474\) 0 0
\(475\) 21.6696 0.994270
\(476\) 13.3809 3.41376i 0.613314 0.156469i
\(477\) 0 0
\(478\) −12.3148 + 27.6125i −0.563268 + 1.26297i
\(479\) 9.42948 + 16.3323i 0.430844 + 0.746244i 0.996946 0.0780912i \(-0.0248825\pi\)
−0.566102 + 0.824335i \(0.691549\pi\)
\(480\) 0 0
\(481\) −16.9427 + 29.3457i −0.772522 + 1.33805i
\(482\) −11.9751 + 1.25097i −0.545451 + 0.0569802i
\(483\) 0 0
\(484\) 15.8806 3.35451i 0.721843 0.152478i
\(485\) −28.3573 + 49.1162i −1.28764 + 2.23025i
\(486\) 0 0
\(487\) −26.9019 + 15.5318i −1.21904 + 0.703813i −0.964713 0.263305i \(-0.915187\pi\)
−0.254327 + 0.967118i \(0.581854\pi\)
\(488\) 24.4124 + 5.23750i 1.10510 + 0.237090i
\(489\) 0 0
\(490\) −36.6207 + 6.94136i −1.65436 + 0.313579i
\(491\) 7.52948i 0.339801i −0.985461 0.169900i \(-0.945655\pi\)
0.985461 0.169900i \(-0.0543446\pi\)
\(492\) 0 0
\(493\) −15.3901 + 8.88549i −0.693136 + 0.400182i
\(494\) −15.2515 + 11.0661i −0.686198 + 0.497889i
\(495\) 0 0
\(496\) 8.87474 + 20.0696i 0.398487 + 0.901151i
\(497\) 21.0142 13.3281i 0.942617 0.597848i
\(498\) 0 0
\(499\) −0.883277 + 1.52988i −0.0395409 + 0.0684869i −0.885119 0.465366i \(-0.845923\pi\)
0.845578 + 0.533852i \(0.179256\pi\)
\(500\) −21.0128 23.3966i −0.939720 1.04633i
\(501\) 0 0
\(502\) −1.00598 0.448653i −0.0448990 0.0200244i
\(503\) 16.9584 0.756136 0.378068 0.925778i \(-0.376589\pi\)
0.378068 + 0.925778i \(0.376589\pi\)
\(504\) 0 0
\(505\) 5.85777 0.260667
\(506\) −2.86868 1.27940i −0.127528 0.0568760i
\(507\) 0 0
\(508\) 6.70853 6.02503i 0.297643 0.267317i
\(509\) 5.13114 8.88739i 0.227434 0.393927i −0.729613 0.683860i \(-0.760300\pi\)
0.957047 + 0.289934i \(0.0936332\pi\)
\(510\) 0 0
\(511\) 5.11079 + 2.67361i 0.226088 + 0.118273i
\(512\) 13.4041 18.2299i 0.592385 0.805655i
\(513\) 0 0
\(514\) 14.1294 10.2520i 0.623223 0.452195i
\(515\) −26.1324 + 15.0876i −1.15153 + 0.664837i
\(516\) 0 0
\(517\) 12.0028i 0.527884i
\(518\) −8.29107 + 20.8858i −0.364289 + 0.917669i
\(519\) 0 0
\(520\) 58.7492 + 12.6042i 2.57632 + 0.552730i
\(521\) −32.7368 + 18.9006i −1.43423 + 0.828051i −0.997440 0.0715138i \(-0.977217\pi\)
−0.436787 + 0.899565i \(0.643884\pi\)
\(522\) 0 0
\(523\) 19.6691 34.0679i 0.860070 1.48968i −0.0117911 0.999930i \(-0.503753\pi\)
0.871861 0.489754i \(-0.162913\pi\)
\(524\) 6.71420 + 31.7856i 0.293311 + 1.38856i
\(525\) 0 0
\(526\) −2.85341 + 0.298080i −0.124415 + 0.0129969i
\(527\) 7.15864 12.3991i 0.311835 0.540114i
\(528\) 0 0
\(529\) 10.6449 + 18.4375i 0.462822 + 0.801631i
\(530\) 2.12073 4.75514i 0.0921186 0.206550i
\(531\) 0 0
\(532\) −8.94144 + 8.72926i −0.387661 + 0.378461i
\(533\) −34.4433 −1.49190
\(534\) 0 0
\(535\) 47.5372 27.4456i 2.05521 1.18658i
\(536\) 28.1104 + 25.4076i 1.21419 + 1.09744i
\(537\) 0 0
\(538\) 36.9493 3.85988i 1.59300 0.166411i
\(539\) 0.988451 + 11.8475i 0.0425756 + 0.510309i
\(540\) 0 0
\(541\) 12.8385 + 7.41231i 0.551970 + 0.318680i 0.749916 0.661533i \(-0.230094\pi\)
−0.197946 + 0.980213i \(0.563427\pi\)
\(542\) 9.27311 6.72834i 0.398314 0.289007i
\(543\) 0 0
\(544\) −14.7629 0.0467261i −0.632956 0.00200337i
\(545\) 2.84849i 0.122016i
\(546\) 0 0
\(547\) −16.2017 −0.692736 −0.346368 0.938099i \(-0.612585\pi\)
−0.346368 + 0.938099i \(0.612585\pi\)
\(548\) 7.97986 + 2.60399i 0.340883 + 0.111237i
\(549\) 0 0
\(550\) −17.8389 + 12.9435i −0.760654 + 0.551912i
\(551\) 8.04030 13.9262i 0.342528 0.593277i
\(552\) 0 0
\(553\) 46.0632 1.91822i 1.95881 0.0815708i
\(554\) −1.43485 13.7354i −0.0609611 0.583560i
\(555\) 0 0
\(556\) 7.62102 + 8.48558i 0.323203 + 0.359869i
\(557\) −1.17534 2.03574i −0.0498006 0.0862572i 0.840051 0.542508i \(-0.182525\pi\)
−0.889851 + 0.456251i \(0.849192\pi\)
\(558\) 0 0
\(559\) 36.6634i 1.55070i
\(560\) 39.7605 + 2.61334i 1.68019 + 0.110434i
\(561\) 0 0
\(562\) 2.43789 + 1.08727i 0.102836 + 0.0458636i
\(563\) −6.40537 + 3.69814i −0.269954 + 0.155858i −0.628867 0.777513i \(-0.716481\pi\)
0.358913 + 0.933371i \(0.383148\pi\)
\(564\) 0 0
\(565\) −32.1957 18.5882i −1.35449 0.782012i
\(566\) −9.25211 + 0.966515i −0.388895 + 0.0406257i
\(567\) 0 0
\(568\) −25.3161 + 8.17260i −1.06224 + 0.342914i
\(569\) −30.2952 17.4909i −1.27004 0.733258i −0.295045 0.955483i \(-0.595334\pi\)
−0.974995 + 0.222226i \(0.928668\pi\)
\(570\) 0 0
\(571\) 16.4081 + 28.4197i 0.686659 + 1.18933i 0.972912 + 0.231174i \(0.0742567\pi\)
−0.286254 + 0.958154i \(0.592410\pi\)
\(572\) 5.94548 18.2198i 0.248593 0.761807i
\(573\) 0 0
\(574\) −22.5992 + 3.31633i −0.943271 + 0.138421i
\(575\) −12.0001 −0.500437
\(576\) 0 0
\(577\) 4.58139 + 7.93520i 0.190726 + 0.330347i 0.945491 0.325648i \(-0.105583\pi\)
−0.754765 + 0.655995i \(0.772249\pi\)
\(578\) −8.46241 11.6630i −0.351990 0.485118i
\(579\) 0 0
\(580\) −50.1697 + 10.5975i −2.08318 + 0.440038i
\(581\) −16.8438 26.5574i −0.698800 1.10179i
\(582\) 0 0
\(583\) −1.43823 0.830362i −0.0595653 0.0343901i
\(584\) −4.57447 4.13463i −0.189293 0.171092i
\(585\) 0 0
\(586\) −8.13991 + 18.2514i −0.336257 + 0.753960i
\(587\) 17.4528i 0.720354i −0.932884 0.360177i \(-0.882716\pi\)
0.932884 0.360177i \(-0.117284\pi\)
\(588\) 0 0
\(589\) 12.9554i 0.533819i
\(590\) 37.4760 + 16.7138i 1.54286 + 0.688098i
\(591\) 0 0
\(592\) 14.1694 19.3990i 0.582359 0.797296i
\(593\) −17.0385 9.83721i −0.699689 0.403966i 0.107542 0.994200i \(-0.465702\pi\)
−0.807232 + 0.590235i \(0.799035\pi\)
\(594\) 0 0
\(595\) −13.9241 21.9540i −0.570834 0.900025i
\(596\) 26.3856 5.57352i 1.08079 0.228300i
\(597\) 0 0
\(598\) 8.44589 6.12813i 0.345378 0.250598i
\(599\) −2.68048 4.64273i −0.109521 0.189697i 0.806055 0.591841i \(-0.201598\pi\)
−0.915576 + 0.402144i \(0.868265\pi\)
\(600\) 0 0
\(601\) 12.4609 0.508291 0.254145 0.967166i \(-0.418206\pi\)
0.254145 + 0.967166i \(0.418206\pi\)
\(602\) 3.53009 + 24.0558i 0.143876 + 0.980442i
\(603\) 0 0
\(604\) 40.5562 + 13.2343i 1.65021 + 0.538496i
\(605\) −15.2779 26.4621i −0.621135 1.07584i
\(606\) 0 0
\(607\) 10.6807 + 6.16649i 0.433515 + 0.250290i 0.700843 0.713315i \(-0.252807\pi\)
−0.267328 + 0.963606i \(0.586141\pi\)
\(608\) 11.5901 6.64273i 0.470041 0.269398i
\(609\) 0 0
\(610\) −4.88363 46.7493i −0.197732 1.89282i
\(611\) 34.5325 + 19.9373i 1.39704 + 0.806579i
\(612\) 0 0
\(613\) 3.55744 2.05389i 0.143683 0.0829557i −0.426435 0.904518i \(-0.640231\pi\)
0.570118 + 0.821563i \(0.306897\pi\)
\(614\) 10.1366 22.7284i 0.409080 0.917245i
\(615\) 0 0
\(616\) 2.14672 12.5269i 0.0864937 0.504725i
\(617\) 36.1255i 1.45436i 0.686447 + 0.727180i \(0.259169\pi\)
−0.686447 + 0.727180i \(0.740831\pi\)
\(618\) 0 0
\(619\) −0.802674 1.39027i −0.0322622 0.0558798i 0.849443 0.527680i \(-0.176938\pi\)
−0.881706 + 0.471800i \(0.843604\pi\)
\(620\) 30.7353 27.6038i 1.23436 1.10860i
\(621\) 0 0
\(622\) −15.3226 + 1.60066i −0.614379 + 0.0641807i
\(623\) 29.2616 1.21855i 1.17234 0.0488201i
\(624\) 0 0
\(625\) −6.66043 + 11.5362i −0.266417 + 0.461448i
\(626\) −2.93235 4.04141i −0.117200 0.161527i
\(627\) 0 0
\(628\) 17.5034 + 5.71170i 0.698461 + 0.227922i
\(629\) −15.6734 −0.624940
\(630\) 0 0
\(631\) 8.98270i 0.357596i −0.983886 0.178798i \(-0.942779\pi\)
0.983886 0.178798i \(-0.0572208\pi\)
\(632\) −48.1897 10.3387i −1.91688 0.411253i
\(633\) 0 0
\(634\) 13.4450 + 18.5302i 0.533971 + 0.735927i
\(635\) −14.7007 8.48748i −0.583381 0.336815i
\(636\) 0 0
\(637\) −35.7276 16.8356i −1.41558 0.667050i
\(638\) 1.69931 + 16.2669i 0.0672764 + 0.644014i
\(639\) 0 0
\(640\) −40.4539 13.3427i −1.59908 0.527418i
\(641\) 34.1214 19.7000i 1.34772 0.778104i 0.359790 0.933033i \(-0.382848\pi\)
0.987926 + 0.154929i \(0.0495149\pi\)
\(642\) 0 0
\(643\) 40.0002 1.57745 0.788726 0.614745i \(-0.210741\pi\)
0.788726 + 0.614745i \(0.210741\pi\)
\(644\) 4.95153 4.83403i 0.195118 0.190488i
\(645\) 0 0
\(646\) −7.96001 3.55006i −0.313182 0.139675i
\(647\) 19.8854 + 34.4425i 0.781775 + 1.35407i 0.930907 + 0.365257i \(0.119019\pi\)
−0.149132 + 0.988817i \(0.547648\pi\)
\(648\) 0 0
\(649\) 6.54422 11.3349i 0.256883 0.444935i
\(650\) −7.60739 72.8229i −0.298386 2.85635i
\(651\) 0 0
\(652\) −0.234946 + 0.0496284i −0.00920118 + 0.00194360i
\(653\) −1.64003 + 2.84061i −0.0641792 + 0.111162i −0.896330 0.443388i \(-0.853776\pi\)
0.832150 + 0.554550i \(0.187110\pi\)
\(654\) 0 0
\(655\) 52.9651 30.5794i 2.06952 1.19484i
\(656\) 24.2780 + 2.61388i 0.947895 + 0.102055i
\(657\) 0 0
\(658\) 24.5773 + 9.75650i 0.958124 + 0.380348i
\(659\) 16.7484i 0.652425i 0.945297 + 0.326212i \(0.105772\pi\)
−0.945297 + 0.326212i \(0.894228\pi\)
\(660\) 0 0
\(661\) 4.50164 2.59902i 0.175093 0.101090i −0.409892 0.912134i \(-0.634434\pi\)
0.584985 + 0.811044i \(0.301100\pi\)
\(662\) 9.63141 + 13.2742i 0.374335 + 0.515915i
\(663\) 0 0
\(664\) 10.3284 + 31.9941i 0.400819 + 1.24161i
\(665\) 20.8445 + 10.9044i 0.808315 + 0.422854i
\(666\) 0 0
\(667\) −4.45251 + 7.71197i −0.172402 + 0.298609i
\(668\) −17.3476 19.3156i −0.671198 0.747341i
\(669\) 0 0
\(670\) 29.0548 65.1471i 1.12248 2.51685i
\(671\) −14.9925 −0.578779
\(672\) 0 0
\(673\) −29.9571 −1.15476 −0.577380 0.816475i \(-0.695925\pi\)
−0.577380 + 0.816475i \(0.695925\pi\)
\(674\) −1.61906 + 3.63029i −0.0623640 + 0.139833i
\(675\) 0 0
\(676\) 25.1702 + 28.0256i 0.968083 + 1.07791i
\(677\) −15.2704 + 26.4492i −0.586891 + 1.01652i 0.407746 + 0.913095i \(0.366315\pi\)
−0.994637 + 0.103429i \(0.967018\pi\)
\(678\) 0 0
\(679\) −33.6550 + 21.3454i −1.29156 + 0.819162i
\(680\) 8.53807 + 26.4483i 0.327420 + 1.01425i
\(681\) 0 0
\(682\) −7.73841 10.6652i −0.296319 0.408391i
\(683\) 11.1942 6.46296i 0.428333 0.247298i −0.270303 0.962775i \(-0.587124\pi\)
0.698636 + 0.715477i \(0.253791\pi\)
\(684\) 0 0
\(685\) 15.8022i 0.603770i
\(686\) −25.0628 7.60629i −0.956902 0.290409i
\(687\) 0 0
\(688\) 2.78237 25.8428i 0.106077 0.985249i
\(689\) 4.77795 2.75855i 0.182025 0.105092i
\(690\) 0 0
\(691\) −8.33676 + 14.4397i −0.317145 + 0.549312i −0.979891 0.199533i \(-0.936058\pi\)
0.662746 + 0.748844i \(0.269391\pi\)
\(692\) −13.4808 + 2.84761i −0.512464 + 0.108250i
\(693\) 0 0
\(694\) −3.18774 30.5151i −0.121005 1.15834i
\(695\) 10.7358 18.5949i 0.407231 0.705344i
\(696\) 0 0
\(697\) −7.96571 13.7970i −0.301723 0.522599i
\(698\) 9.61539 + 4.28834i 0.363948 + 0.162316i
\(699\) 0 0
\(700\) −12.0031 47.0486i −0.453674 1.77827i
\(701\) −24.5914 −0.928805 −0.464403 0.885624i \(-0.653731\pi\)
−0.464403 + 0.885624i \(0.653731\pi\)
\(702\) 0 0
\(703\) 12.2825 7.09128i 0.463242 0.267453i
\(704\) −5.57347 + 12.3913i −0.210058 + 0.467016i
\(705\) 0 0
\(706\) 2.21186 + 21.1734i 0.0832444 + 0.796870i
\(707\) 3.64733 + 1.90803i 0.137172 + 0.0717587i
\(708\) 0 0
\(709\) −4.59843 2.65490i −0.172698 0.0997070i 0.411160 0.911563i \(-0.365124\pi\)
−0.583857 + 0.811856i \(0.698457\pi\)
\(710\) 29.4112 + 40.5350i 1.10378 + 1.52125i
\(711\) 0 0
\(712\) −30.6125 6.56768i −1.14725 0.246134i
\(713\) 7.17437i 0.268682i
\(714\) 0 0
\(715\) −36.0799 −1.34931
\(716\) −29.8678 9.74646i −1.11621 0.364242i
\(717\) 0 0
\(718\) −14.9807 20.6466i −0.559075 0.770525i
\(719\) −5.16456 + 8.94528i −0.192606 + 0.333603i −0.946113 0.323837i \(-0.895027\pi\)
0.753507 + 0.657439i \(0.228360\pi\)
\(720\) 0 0
\(721\) −21.1857 + 0.882240i −0.788997 + 0.0328563i
\(722\) −18.8806 + 1.97235i −0.702663 + 0.0734031i
\(723\) 0 0
\(724\) −23.3188 + 20.9429i −0.866636 + 0.778338i
\(725\) 31.2422 + 54.1131i 1.16031 + 2.00971i
\(726\) 0 0
\(727\) 28.6727i 1.06341i 0.846929 + 0.531706i \(0.178449\pi\)
−0.846929 + 0.531706i \(0.821551\pi\)
\(728\) 32.4746 + 26.9841i 1.20359 + 1.00010i
\(729\) 0 0
\(730\) −4.72815 + 10.6015i −0.174997 + 0.392380i
\(731\) −14.6863 + 8.47916i −0.543193 + 0.313613i
\(732\) 0 0
\(733\) 33.6091 + 19.4042i 1.24138 + 0.716710i 0.969375 0.245586i \(-0.0789803\pi\)
0.272004 + 0.962296i \(0.412314\pi\)
\(734\) −0.574993 5.50421i −0.0212234 0.203164i
\(735\) 0 0
\(736\) −6.41830 + 3.67857i −0.236582 + 0.135594i
\(737\) −19.7042 11.3763i −0.725815 0.419050i
\(738\) 0 0
\(739\) −5.59773 9.69556i −0.205916 0.356657i 0.744508 0.667613i \(-0.232684\pi\)
−0.950424 + 0.310956i \(0.899351\pi\)
\(740\) −42.9932 14.0295i −1.58046 0.515736i
\(741\) 0 0
\(742\) 2.86934 2.27000i 0.105337 0.0833343i
\(743\) −6.68201 −0.245139 −0.122570 0.992460i \(-0.539113\pi\)
−0.122570 + 0.992460i \(0.539113\pi\)
\(744\) 0 0
\(745\) −25.3843 43.9668i −0.930007 1.61082i
\(746\) −20.9511 + 15.2016i −0.767076 + 0.556572i
\(747\) 0 0
\(748\) 8.67335 1.83210i 0.317129 0.0669883i
\(749\) 38.5387 1.60487i 1.40817 0.0586407i
\(750\) 0 0
\(751\) −43.2883 24.9925i −1.57961 0.911990i −0.994913 0.100741i \(-0.967879\pi\)
−0.584701 0.811249i \(-0.698788\pi\)
\(752\) −22.8278 16.6738i −0.832444 0.608032i
\(753\) 0 0
\(754\) −49.6231 22.1313i −1.80717 0.805973i
\(755\) 80.3117i 2.92284i
\(756\) 0 0
\(757\) 32.8378i 1.19351i 0.802424 + 0.596755i \(0.203543\pi\)
−0.802424 + 0.596755i \(0.796457\pi\)
\(758\) −14.8658 + 33.3323i −0.539949 + 1.21068i
\(759\) 0 0
\(760\) −18.6571 16.8632i −0.676765 0.611693i
\(761\) 28.7157 + 16.5790i 1.04094 + 0.600988i 0.920100 0.391683i \(-0.128107\pi\)
0.120842 + 0.992672i \(0.461440\pi\)
\(762\) 0 0
\(763\) 0.927825 1.77360i 0.0335895 0.0642088i
\(764\) −47.2116 + 9.97268i −1.70806 + 0.360799i
\(765\) 0 0
\(766\) −12.2530 16.8873i −0.442721 0.610165i
\(767\) 21.7406 + 37.6559i 0.785008 + 1.35967i
\(768\) 0 0
\(769\) −48.1183 −1.73519 −0.867596 0.497270i \(-0.834336\pi\)
−0.867596 + 0.497270i \(0.834336\pi\)
\(770\) −23.6730 + 3.47391i −0.853114 + 0.125191i
\(771\) 0 0
\(772\) −5.96004 + 18.2644i −0.214506 + 0.657350i
\(773\) 14.2293 + 24.6458i 0.511791 + 0.886449i 0.999907 + 0.0136695i \(0.00435128\pi\)
−0.488115 + 0.872779i \(0.662315\pi\)
\(774\) 0 0
\(775\) −43.5965 25.1704i −1.56603 0.904148i
\(776\) 40.5447 13.0887i 1.45547 0.469857i
\(777\) 0 0
\(778\) −24.4816 + 2.55745i −0.877707 + 0.0916890i
\(779\) 12.4847 + 7.20802i 0.447309 + 0.258254i
\(780\) 0 0
\(781\) 13.8339 7.98703i 0.495017 0.285798i
\(782\) 4.40804 + 1.96593i 0.157631 + 0.0703016i
\(783\) 0 0
\(784\) 23.9056 + 14.5782i 0.853770 + 0.520650i
\(785\) 34.6612i 1.23711i
\(786\) 0 0
\(787\) −11.0597 19.1559i −0.394234 0.682834i 0.598769 0.800922i \(-0.295657\pi\)
−0.993003 + 0.118088i \(0.962323\pi\)
\(788\) 2.74366 + 3.05491i 0.0977388 + 0.108827i
\(789\) 0 0
\(790\) 9.64020 + 92.2823i 0.342983 + 3.28326i
\(791\) −13.9920 22.0609i −0.497497 0.784395i
\(792\) 0 0
\(793\) 24.9033 43.1339i 0.884344 1.53173i
\(794\) −13.2533 + 9.61629i −0.470343 + 0.341270i
\(795\) 0 0
\(796\) −18.9272 6.17631i −0.670856 0.218914i
\(797\) 25.7820 0.913247 0.456623 0.889660i \(-0.349059\pi\)
0.456623 + 0.889660i \(0.349059\pi\)
\(798\) 0 0
\(799\) 18.4437i 0.652490i
\(800\) −0.164293 + 51.9078i −0.00580864 + 1.83522i
\(801\) 0 0
\(802\) 41.1656 29.8688i 1.45361 1.05470i
\(803\) 3.20652 + 1.85128i 0.113156 + 0.0653304i
\(804\) 0 0
\(805\) −11.5431 6.03856i −0.406842 0.212831i
\(806\) 43.5380 4.54816i 1.53356 0.160202i
\(807\) 0 0
\(808\) −3.26458 2.95069i −0.114848 0.103805i
\(809\) 2.56573 1.48132i 0.0902062 0.0520806i −0.454218 0.890890i \(-0.650081\pi\)
0.544425 + 0.838810i \(0.316748\pi\)
\(810\) 0 0
\(811\) −51.9174 −1.82307 −0.911533 0.411228i \(-0.865100\pi\)
−0.911533 + 0.411228i \(0.865100\pi\)
\(812\) −34.6899 9.74302i −1.21738 0.341913i
\(813\) 0 0
\(814\) −5.87550 + 13.1741i −0.205936 + 0.461754i
\(815\) 0.226030 + 0.391495i 0.00791747 + 0.0137135i
\(816\) 0 0
\(817\) 7.67262 13.2894i 0.268431 0.464936i
\(818\) −34.2118 + 3.57391i −1.19619 + 0.124959i
\(819\) 0 0
\(820\) −9.50053 44.9764i −0.331773 1.57064i
\(821\) 10.7741 18.6612i 0.376017 0.651281i −0.614462 0.788947i \(-0.710627\pi\)
0.990479 + 0.137666i \(0.0439601\pi\)
\(822\) 0 0
\(823\) −30.0162 + 17.3299i −1.04630 + 0.604082i −0.921611 0.388114i \(-0.873127\pi\)
−0.124689 + 0.992196i \(0.539793\pi\)
\(824\) 22.1638 + 4.75506i 0.772111 + 0.165650i
\(825\) 0 0
\(826\) 17.8903 + 22.6137i 0.622481 + 0.786833i
\(827\) 40.6029i 1.41190i −0.708260 0.705951i \(-0.750520\pi\)
0.708260 0.705951i \(-0.249480\pi\)
\(828\) 0 0
\(829\) 28.2837 16.3296i 0.982334 0.567151i 0.0793604 0.996846i \(-0.474712\pi\)
0.902974 + 0.429695i \(0.141379\pi\)
\(830\) 51.2275 37.1694i 1.77813 1.29017i
\(831\) 0 0
\(832\) −26.3924 36.6177i −0.914992 1.26949i
\(833\) −1.51886 18.2050i −0.0526256 0.630767i
\(834\) 0 0
\(835\) −24.4376 + 42.3271i −0.845697 + 1.46479i
\(836\) −5.96795 + 5.35990i −0.206406 + 0.185376i
\(837\) 0 0
\(838\) −8.95008 3.99162i −0.309175 0.137888i
\(839\) −35.4704 −1.22458 −0.612288 0.790635i \(-0.709751\pi\)
−0.612288 + 0.790635i \(0.709751\pi\)
\(840\) 0 0
\(841\) 17.3685 0.598913
\(842\) 16.2988 + 7.26906i 0.561694 + 0.250508i
\(843\) 0 0
\(844\) 18.6768 + 20.7956i 0.642884 + 0.715815i
\(845\) 35.4573 61.4138i 1.21977 2.11270i
\(846\) 0 0
\(847\) −0.893370 21.4530i −0.0306965 0.737133i
\(848\) −3.57717 + 1.58182i −0.122840 + 0.0543198i
\(849\) 0 0
\(850\) 27.4115 19.8891i 0.940205 0.682190i
\(851\) −6.80170 + 3.92697i −0.233159 + 0.134615i
\(852\) 0 0
\(853\) 2.87597i 0.0984714i −0.998787 0.0492357i \(-0.984321\pi\)
0.998787 0.0492357i \(-0.0156786\pi\)
\(854\) 12.1867 30.6991i 0.417019 1.05050i
\(855\) 0 0
\(856\) −40.3178 8.64987i −1.37803 0.295647i
\(857\) 5.76468 3.32824i 0.196918 0.113691i −0.398299 0.917256i \(-0.630399\pi\)
0.595217 + 0.803565i \(0.297066\pi\)
\(858\) 0 0
\(859\) 10.2685 17.7855i 0.350355 0.606833i −0.635956 0.771725i \(-0.719394\pi\)
0.986312 + 0.164892i \(0.0527276\pi\)
\(860\) −47.8754 + 10.1129i −1.63254 + 0.344847i
\(861\) 0 0
\(862\) 31.4390 3.28425i 1.07082 0.111862i
\(863\) 15.7546 27.2877i 0.536292 0.928886i −0.462807 0.886459i \(-0.653158\pi\)
0.999100 0.0424266i \(-0.0135089\pi\)
\(864\) 0 0
\(865\) 12.9692 + 22.4634i 0.440968 + 0.763778i
\(866\) 18.5950 41.6940i 0.631884 1.41682i
\(867\) 0 0
\(868\) 28.1285 7.17618i 0.954744 0.243575i
\(869\) 29.5949 1.00394
\(870\) 0 0
\(871\) 65.4596 37.7931i 2.21801 1.28057i
\(872\) −1.43485 + 1.58749i −0.0485900 + 0.0537590i
\(873\) 0 0
\(874\) −4.34383 + 0.453775i −0.146932 + 0.0153492i
\(875\) −35.1308 + 22.2815i −1.18764 + 0.753251i
\(876\) 0 0
\(877\) 48.3067 + 27.8899i 1.63120 + 0.941774i 0.983723 + 0.179689i \(0.0575091\pi\)
0.647477 + 0.762085i \(0.275824\pi\)
\(878\) 3.20913 2.32847i 0.108303 0.0785819i
\(879\) 0 0
\(880\) 25.4315 + 2.73808i 0.857297 + 0.0923008i
\(881\) 21.9485i 0.739464i 0.929138 + 0.369732i \(0.120550\pi\)
−0.929138 + 0.369732i \(0.879450\pi\)
\(882\) 0 0
\(883\) 33.4287 1.12497 0.562483 0.826809i \(-0.309846\pi\)
0.562483 + 0.826809i \(0.309846\pi\)
\(884\) −9.13589 + 27.9967i −0.307273 + 0.941631i
\(885\) 0 0
\(886\) −21.4207 + 15.5423i −0.719643 + 0.522155i
\(887\) 6.18309 10.7094i 0.207608 0.359587i −0.743353 0.668900i \(-0.766766\pi\)
0.950960 + 0.309313i \(0.100099\pi\)
\(888\) 0 0
\(889\) −6.38880 10.0731i −0.214273 0.337841i
\(890\) 6.12394 + 58.6223i 0.205275 + 1.96502i
\(891\) 0 0
\(892\) 23.6317 21.2240i 0.791248 0.710631i
\(893\) −8.34466 14.4534i −0.279243 0.483664i
\(894\) 0 0
\(895\) 59.1460i 1.97703i
\(896\) −20.8425 21.4847i −0.696298 0.717753i
\(897\) 0 0
\(898\) −17.9466 8.00396i −0.598886 0.267096i
\(899\) −32.3521 + 18.6785i −1.07900 + 0.622963i
\(900\) 0 0
\(901\) 2.21000 + 1.27594i 0.0736257 + 0.0425078i
\(902\) −14.5831 + 1.52341i −0.485563 + 0.0507240i
\(903\) 0 0
\(904\) 8.57965 + 26.5771i 0.285355 + 0.883941i
\(905\) 51.0996 + 29.5024i 1.69861 + 0.980692i
\(906\) 0 0
\(907\) −6.85914 11.8804i −0.227754 0.394481i 0.729388 0.684100i \(-0.239805\pi\)
−0.957142 + 0.289619i \(0.906471\pi\)
\(908\) −1.36132 0.444225i −0.0451769 0.0147421i
\(909\) 0 0
\(910\) 29.3275 73.8782i 0.972198 2.44904i
\(911\) −9.02706 −0.299080 −0.149540 0.988756i \(-0.547779\pi\)
−0.149540 + 0.988756i \(0.547779\pi\)
\(912\) 0 0
\(913\) −10.0939 17.4831i −0.334058 0.578606i
\(914\) 4.79917 + 6.61429i 0.158742 + 0.218781i
\(915\) 0 0
\(916\) −1.86102 8.81025i −0.0614899 0.291099i
\(917\) 42.9391 1.78812i 1.41797 0.0590489i
\(918\) 0 0
\(919\) 37.8104 + 21.8298i 1.24725 + 0.720100i 0.970560 0.240860i \(-0.0774294\pi\)
0.276689 + 0.960959i \(0.410763\pi\)
\(920\) 10.3318 + 9.33840i 0.340630 + 0.307878i
\(921\) 0 0
\(922\) 8.88367 19.9191i 0.292568 0.656001i
\(923\) 53.0675i 1.74674i
\(924\) 0 0
\(925\) 55.1092i 1.81198i
\(926\) 14.9698 + 6.67633i 0.491937 + 0.219398i
\(927\) 0 0
\(928\) 33.2982 + 19.3655i 1.09307 + 0.635703i
\(929\) 43.0944 + 24.8806i 1.41388 + 0.816304i 0.995751 0.0920830i \(-0.0293525\pi\)
0.418129 + 0.908387i \(0.362686\pi\)
\(930\) 0 0
\(931\) 9.42695 + 13.5792i 0.308956 + 0.445039i
\(932\) −3.19596 15.1300i −0.104687 0.495599i
\(933\) 0 0
\(934\) 2.61904 1.90031i 0.0856977 0.0621802i
\(935\) −8.34421 14.4526i −0.272885 0.472650i
\(936\) 0 0
\(937\) 40.5415 1.32443 0.662216 0.749313i \(-0.269616\pi\)
0.662216 + 0.749313i \(0.269616\pi\)
\(938\) 39.3109 31.0998i 1.28355 1.01544i
\(939\) 0 0
\(940\) −16.5093 + 50.5922i −0.538472 + 1.65014i
\(941\) −27.1914 47.0968i −0.886414 1.53531i −0.844085 0.536209i \(-0.819856\pi\)
−0.0423286 0.999104i \(-0.513478\pi\)
\(942\) 0 0
\(943\) −6.91367 3.99161i −0.225140 0.129985i
\(944\) −12.4666 28.1923i −0.405752 0.917581i
\(945\) 0 0
\(946\) 1.62160 + 15.5230i 0.0527229 + 0.504698i
\(947\) −12.3501 7.13032i −0.401323 0.231704i 0.285732 0.958310i \(-0.407763\pi\)
−0.687055 + 0.726606i \(0.741097\pi\)
\(948\) 0 0
\(949\) −10.6524 + 6.15016i −0.345791 + 0.199643i
\(950\) −12.4823 + 27.9881i −0.404981 + 0.908055i
\(951\) 0 0
\(952\) −3.29867 + 19.2490i −0.106910 + 0.623865i
\(953\) 3.31610i 0.107419i −0.998557 0.0537095i \(-0.982896\pi\)
0.998557 0.0537095i \(-0.0171045\pi\)
\(954\) 0 0
\(955\) 45.4200 + 78.6697i 1.46976 + 2.54569i
\(956\) −28.5702 31.8113i −0.924026 1.02885i
\(957\) 0 0
\(958\) −26.5263 + 2.77105i −0.857025 + 0.0895285i
\(959\) 5.14717 9.83919i 0.166211 0.317724i
\(960\) 0 0
\(961\) −0.451578 + 0.782157i −0.0145670 + 0.0252309i
\(962\) −28.1429 38.7870i −0.907363 1.25054i
\(963\) 0 0
\(964\) 5.28229 16.1875i 0.170131 0.521363i
\(965\) 36.1682 1.16430
\(966\) 0 0
\(967\) 18.6637i 0.600185i −0.953910 0.300092i \(-0.902982\pi\)
0.953910 0.300092i \(-0.0970175\pi\)
\(968\) −4.81505 + 22.4434i −0.154762 + 0.721357i
\(969\) 0 0
\(970\) −47.1031 64.9182i −1.51239 2.08440i
\(971\) 4.93811 + 2.85102i 0.158472 + 0.0914936i 0.577139 0.816646i \(-0.304169\pi\)
−0.418667 + 0.908140i \(0.637503\pi\)
\(972\) 0 0
\(973\) 12.7414 8.08115i 0.408471 0.259070i
\(974\) −4.56434 43.6928i −0.146251 1.40001i
\(975\) 0 0
\(976\) −20.8270 + 28.5138i −0.666655 + 0.912703i
\(977\) −3.52730 + 2.03649i −0.112848 + 0.0651530i −0.555362 0.831609i \(-0.687420\pi\)
0.442514 + 0.896762i \(0.354087\pi\)
\(978\) 0 0
\(979\) 18.8002 0.600856
\(980\) 12.1293 51.2972i 0.387456 1.63863i
\(981\) 0 0
\(982\) 9.72496 + 4.33721i 0.310336 + 0.138406i
\(983\) 13.6318 + 23.6109i 0.434786 + 0.753071i 0.997278 0.0737313i \(-0.0234907\pi\)
−0.562492 + 0.826803i \(0.690157\pi\)
\(984\) 0 0
\(985\) 3.86500 6.69438i 0.123149 0.213301i
\(986\) −2.61118 24.9959i −0.0831570 0.796033i
\(987\) 0 0
\(988\) −5.50750 26.0730i −0.175217 0.829494i
\(989\) −4.24890 + 7.35930i −0.135107 + 0.234012i
\(990\) 0 0
\(991\) 7.91978 4.57249i 0.251580 0.145250i −0.368907 0.929466i \(-0.620268\pi\)
0.620488 + 0.784216i \(0.286935\pi\)
\(992\) −31.0337 0.0982246i −0.985320 0.00311863i
\(993\) 0 0
\(994\) 5.10955 + 34.8190i 0.162065 + 1.10439i
\(995\) 37.4807i 1.18822i
\(996\) 0 0
\(997\) −40.5025 + 23.3841i −1.28273 + 0.740583i −0.977346 0.211647i \(-0.932117\pi\)
−0.305381 + 0.952230i \(0.598784\pi\)
\(998\) −1.46718 2.02208i −0.0464426 0.0640080i
\(999\) 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.bm.c.107.10 yes 48
3.2 odd 2 inner 504.2.bm.c.107.15 yes 48
4.3 odd 2 2016.2.bu.c.1871.1 48
7.4 even 3 inner 504.2.bm.c.179.8 yes 48
8.3 odd 2 inner 504.2.bm.c.107.17 yes 48
8.5 even 2 2016.2.bu.c.1871.23 48
12.11 even 2 2016.2.bu.c.1871.24 48
21.11 odd 6 inner 504.2.bm.c.179.17 yes 48
24.5 odd 2 2016.2.bu.c.1871.2 48
24.11 even 2 inner 504.2.bm.c.107.8 48
28.11 odd 6 2016.2.bu.c.431.2 48
56.11 odd 6 inner 504.2.bm.c.179.15 yes 48
56.53 even 6 2016.2.bu.c.431.24 48
84.11 even 6 2016.2.bu.c.431.23 48
168.11 even 6 inner 504.2.bm.c.179.10 yes 48
168.53 odd 6 2016.2.bu.c.431.1 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
504.2.bm.c.107.8 48 24.11 even 2 inner
504.2.bm.c.107.10 yes 48 1.1 even 1 trivial
504.2.bm.c.107.15 yes 48 3.2 odd 2 inner
504.2.bm.c.107.17 yes 48 8.3 odd 2 inner
504.2.bm.c.179.8 yes 48 7.4 even 3 inner
504.2.bm.c.179.10 yes 48 168.11 even 6 inner
504.2.bm.c.179.15 yes 48 56.11 odd 6 inner
504.2.bm.c.179.17 yes 48 21.11 odd 6 inner
2016.2.bu.c.431.1 48 168.53 odd 6
2016.2.bu.c.431.2 48 28.11 odd 6
2016.2.bu.c.431.23 48 84.11 even 6
2016.2.bu.c.431.24 48 56.53 even 6
2016.2.bu.c.1871.1 48 4.3 odd 2
2016.2.bu.c.1871.2 48 24.5 odd 2
2016.2.bu.c.1871.23 48 8.5 even 2
2016.2.bu.c.1871.24 48 12.11 even 2