Properties

Label 324.3.j.a.199.28
Level $324$
Weight $3$
Character 324.199
Analytic conductor $8.828$
Analytic rank $0$
Dimension $204$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [324,3,Mod(19,324)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(324, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([9, 16]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("324.19");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 324 = 2^{2} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 324.j (of order \(18\), degree \(6\), not 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: \(8.82836056527\)
Analytic rank: \(0\)
Dimension: \(204\)
Relative dimension: \(34\) over \(\Q(\zeta_{18})\)
Twist minimal: no (minimal twist has level 108)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 199.28
Character \(\chi\) \(=\) 324.199
Dual form 324.3.j.a.127.28

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.63490 - 1.15200i) q^{2} +(1.34579 - 3.76681i) q^{4} +(7.58012 - 2.75894i) q^{5} +(-9.72462 + 1.71471i) q^{7} +(-2.13913 - 7.70871i) q^{8} +O(q^{10})\) \(q+(1.63490 - 1.15200i) q^{2} +(1.34579 - 3.76681i) q^{4} +(7.58012 - 2.75894i) q^{5} +(-9.72462 + 1.71471i) q^{7} +(-2.13913 - 7.70871i) q^{8} +(9.21444 - 13.2429i) q^{10} +(5.60551 - 15.4010i) q^{11} +(4.71726 + 3.95825i) q^{13} +(-13.9234 + 14.0061i) q^{14} +(-12.3777 - 10.1387i) q^{16} +(-4.02290 + 6.96786i) q^{17} +(-2.87779 + 1.66149i) q^{19} +(-0.191123 - 32.2658i) q^{20} +(-8.57751 - 31.6366i) q^{22} +(19.7154 + 3.47636i) q^{23} +(30.6954 - 25.7565i) q^{25} +(12.2721 + 1.03706i) q^{26} +(-6.62832 + 38.9384i) q^{28} +(-13.6140 + 11.4235i) q^{29} +(26.6424 + 4.69778i) q^{31} +(-31.9160 - 2.31663i) q^{32} +(1.44994 + 16.0261i) q^{34} +(-68.9830 + 39.8273i) q^{35} +(7.47191 - 12.9417i) q^{37} +(-2.79085 + 6.03158i) q^{38} +(-37.4827 - 52.5312i) q^{40} +(-17.2789 - 14.4987i) q^{41} +(-17.9633 + 49.3537i) q^{43} +(-50.4688 - 41.8414i) q^{44} +(36.2375 - 17.0287i) q^{46} +(61.7512 - 10.8884i) q^{47} +(45.5830 - 16.5908i) q^{49} +(20.5124 - 77.4704i) q^{50} +(21.2584 - 12.4420i) q^{52} -18.6838 q^{53} -132.207i q^{55} +(34.0204 + 71.2962i) q^{56} +(-9.09765 + 34.3596i) q^{58} +(-12.4197 - 34.1229i) q^{59} +(15.9855 + 90.6585i) q^{61} +(48.9696 - 23.0117i) q^{62} +(-54.8483 + 32.9798i) q^{64} +(46.6779 + 16.9894i) q^{65} +(3.38288 - 4.03156i) q^{67} +(20.8326 + 24.5308i) q^{68} +(-66.8991 + 144.582i) q^{70} +(-47.7400 - 27.5627i) q^{71} +(26.0555 + 45.1294i) q^{73} +(-2.69305 - 29.7661i) q^{74} +(2.38561 + 13.0761i) q^{76} +(-28.1031 + 159.381i) q^{77} +(38.8945 + 46.3527i) q^{79} +(-121.796 - 42.7032i) q^{80} +(-44.9517 - 3.79865i) q^{82} +(79.5175 + 94.7653i) q^{83} +(-11.2701 + 63.9161i) q^{85} +(27.4873 + 101.382i) q^{86} +(-130.713 - 10.2665i) q^{88} +(87.9969 + 152.415i) q^{89} +(-52.6608 - 30.4037i) q^{91} +(39.6277 - 69.5858i) q^{92} +(88.4135 - 88.9388i) q^{94} +(-17.2300 + 20.5339i) q^{95} +(-36.4756 - 13.2760i) q^{97} +(55.4109 - 79.6359i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8} - 3 q^{10} - 12 q^{13} - 39 q^{14} - 6 q^{16} + 6 q^{17} + 69 q^{20} - 6 q^{22} - 12 q^{25} + 174 q^{26} - 12 q^{28} - 60 q^{29} + 96 q^{32} + 6 q^{34} - 6 q^{37} - 72 q^{38} + 69 q^{40} + 192 q^{41} + 219 q^{44} - 3 q^{46} - 12 q^{49} + 165 q^{50} + 21 q^{52} + 24 q^{53} - 99 q^{56} - 141 q^{58} - 12 q^{61} - 294 q^{62} - 3 q^{64} + 156 q^{65} - 375 q^{68} - 165 q^{70} - 6 q^{73} - 447 q^{74} - 54 q^{76} - 132 q^{77} - 798 q^{80} - 12 q^{82} + 138 q^{85} - 606 q^{86} - 198 q^{88} + 114 q^{89} - 723 q^{92} - 357 q^{94} + 168 q^{97} - 510 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).

\(n\) \(163\) \(245\)
\(\chi(n)\) \(-1\) \(e\left(\frac{7}{9}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.63490 1.15200i 0.817450 0.576000i
\(3\) 0 0
\(4\) 1.34579 3.76681i 0.336448 0.941702i
\(5\) 7.58012 2.75894i 1.51602 0.551788i 0.555873 0.831267i \(-0.312384\pi\)
0.960152 + 0.279480i \(0.0901620\pi\)
\(6\) 0 0
\(7\) −9.72462 + 1.71471i −1.38923 + 0.244959i −0.817711 0.575629i \(-0.804757\pi\)
−0.571520 + 0.820588i \(0.693646\pi\)
\(8\) −2.13913 7.70871i −0.267391 0.963588i
\(9\) 0 0
\(10\) 9.21444 13.2429i 0.921444 1.32429i
\(11\) 5.60551 15.4010i 0.509591 1.40009i −0.372068 0.928205i \(-0.621351\pi\)
0.881660 0.471886i \(-0.156426\pi\)
\(12\) 0 0
\(13\) 4.71726 + 3.95825i 0.362866 + 0.304481i 0.805932 0.592008i \(-0.201665\pi\)
−0.443066 + 0.896489i \(0.646109\pi\)
\(14\) −13.9234 + 14.0061i −0.994530 + 1.00044i
\(15\) 0 0
\(16\) −12.3777 10.1387i −0.773605 0.633668i
\(17\) −4.02290 + 6.96786i −0.236641 + 0.409874i −0.959748 0.280862i \(-0.909380\pi\)
0.723107 + 0.690736i \(0.242713\pi\)
\(18\) 0 0
\(19\) −2.87779 + 1.66149i −0.151462 + 0.0874469i −0.573816 0.818984i \(-0.694537\pi\)
0.422353 + 0.906431i \(0.361204\pi\)
\(20\) −0.191123 32.2658i −0.00955616 1.61329i
\(21\) 0 0
\(22\) −8.57751 31.6366i −0.389887 1.43803i
\(23\) 19.7154 + 3.47636i 0.857193 + 0.151146i 0.584937 0.811079i \(-0.301119\pi\)
0.272256 + 0.962225i \(0.412230\pi\)
\(24\) 0 0
\(25\) 30.6954 25.7565i 1.22782 1.03026i
\(26\) 12.2721 + 1.03706i 0.472005 + 0.0398869i
\(27\) 0 0
\(28\) −6.62832 + 38.9384i −0.236726 + 1.39066i
\(29\) −13.6140 + 11.4235i −0.469449 + 0.393914i −0.846593 0.532240i \(-0.821350\pi\)
0.377145 + 0.926154i \(0.376906\pi\)
\(30\) 0 0
\(31\) 26.6424 + 4.69778i 0.859434 + 0.151541i 0.585962 0.810339i \(-0.300717\pi\)
0.273472 + 0.961880i \(0.411828\pi\)
\(32\) −31.9160 2.31663i −0.997376 0.0723948i
\(33\) 0 0
\(34\) 1.44994 + 16.0261i 0.0426454 + 0.471357i
\(35\) −68.9830 + 39.8273i −1.97094 + 1.13792i
\(36\) 0 0
\(37\) 7.47191 12.9417i 0.201944 0.349776i −0.747211 0.664587i \(-0.768608\pi\)
0.949155 + 0.314810i \(0.101941\pi\)
\(38\) −2.79085 + 6.03158i −0.0734435 + 0.158726i
\(39\) 0 0
\(40\) −37.4827 52.5312i −0.937067 1.31328i
\(41\) −17.2789 14.4987i −0.421436 0.353626i 0.407273 0.913306i \(-0.366480\pi\)
−0.828709 + 0.559680i \(0.810924\pi\)
\(42\) 0 0
\(43\) −17.9633 + 49.3537i −0.417751 + 1.14776i 0.535224 + 0.844710i \(0.320227\pi\)
−0.952975 + 0.303050i \(0.901995\pi\)
\(44\) −50.4688 41.8414i −1.14702 0.950941i
\(45\) 0 0
\(46\) 36.2375 17.0287i 0.787772 0.370189i
\(47\) 61.7512 10.8884i 1.31385 0.231668i 0.527559 0.849518i \(-0.323107\pi\)
0.786296 + 0.617850i \(0.211996\pi\)
\(48\) 0 0
\(49\) 45.5830 16.5908i 0.930265 0.338589i
\(50\) 20.5124 77.4704i 0.410248 1.54941i
\(51\) 0 0
\(52\) 21.2584 12.4420i 0.408815 0.239270i
\(53\) −18.6838 −0.352525 −0.176262 0.984343i \(-0.556401\pi\)
−0.176262 + 0.984343i \(0.556401\pi\)
\(54\) 0 0
\(55\) 132.207i 2.40376i
\(56\) 34.0204 + 71.2962i 0.607507 + 1.27315i
\(57\) 0 0
\(58\) −9.09765 + 34.3596i −0.156856 + 0.592407i
\(59\) −12.4197 34.1229i −0.210504 0.578355i 0.788839 0.614600i \(-0.210683\pi\)
−0.999343 + 0.0362450i \(0.988460\pi\)
\(60\) 0 0
\(61\) 15.9855 + 90.6585i 0.262058 + 1.48621i 0.777283 + 0.629151i \(0.216597\pi\)
−0.515225 + 0.857055i \(0.672292\pi\)
\(62\) 48.9696 23.0117i 0.789832 0.371156i
\(63\) 0 0
\(64\) −54.8483 + 32.9798i −0.857004 + 0.515309i
\(65\) 46.6779 + 16.9894i 0.718122 + 0.261375i
\(66\) 0 0
\(67\) 3.38288 4.03156i 0.0504907 0.0601725i −0.740208 0.672378i \(-0.765273\pi\)
0.790699 + 0.612205i \(0.209717\pi\)
\(68\) 20.8326 + 24.5308i 0.306362 + 0.360747i
\(69\) 0 0
\(70\) −66.8991 + 144.582i −0.955702 + 2.06546i
\(71\) −47.7400 27.5627i −0.672395 0.388207i 0.124589 0.992208i \(-0.460239\pi\)
−0.796983 + 0.604001i \(0.793572\pi\)
\(72\) 0 0
\(73\) 26.0555 + 45.1294i 0.356925 + 0.618211i 0.987445 0.157961i \(-0.0504920\pi\)
−0.630521 + 0.776172i \(0.717159\pi\)
\(74\) −2.69305 29.7661i −0.0363925 0.402244i
\(75\) 0 0
\(76\) 2.38561 + 13.0761i 0.0313896 + 0.172054i
\(77\) −28.1031 + 159.381i −0.364975 + 2.06988i
\(78\) 0 0
\(79\) 38.8945 + 46.3527i 0.492335 + 0.586743i 0.953810 0.300411i \(-0.0971238\pi\)
−0.461474 + 0.887154i \(0.652679\pi\)
\(80\) −121.796 42.7032i −1.52245 0.533790i
\(81\) 0 0
\(82\) −44.9517 3.79865i −0.548191 0.0463250i
\(83\) 79.5175 + 94.7653i 0.958043 + 1.14175i 0.989830 + 0.142256i \(0.0454357\pi\)
−0.0317873 + 0.999495i \(0.510120\pi\)
\(84\) 0 0
\(85\) −11.2701 + 63.9161i −0.132590 + 0.751955i
\(86\) 27.4873 + 101.382i 0.319620 + 1.17886i
\(87\) 0 0
\(88\) −130.713 10.2665i −1.48537 0.116665i
\(89\) 87.9969 + 152.415i 0.988729 + 1.71253i 0.624021 + 0.781407i \(0.285498\pi\)
0.364708 + 0.931122i \(0.381169\pi\)
\(90\) 0 0
\(91\) −52.6608 30.4037i −0.578690 0.334107i
\(92\) 39.6277 69.5858i 0.430736 0.756367i
\(93\) 0 0
\(94\) 88.4135 88.9388i 0.940569 0.946157i
\(95\) −17.2300 + 20.5339i −0.181369 + 0.216147i
\(96\) 0 0
\(97\) −36.4756 13.2760i −0.376037 0.136866i 0.147085 0.989124i \(-0.453011\pi\)
−0.523123 + 0.852257i \(0.675233\pi\)
\(98\) 55.4109 79.6359i 0.565418 0.812612i
\(99\) 0 0
\(100\) −55.7101 150.287i −0.557101 1.50287i
\(101\) −7.21786 40.9345i −0.0714640 0.405292i −0.999465 0.0327141i \(-0.989585\pi\)
0.928001 0.372578i \(-0.121526\pi\)
\(102\) 0 0
\(103\) 27.5704 + 75.7491i 0.267674 + 0.735428i 0.998596 + 0.0529675i \(0.0168680\pi\)
−0.730922 + 0.682461i \(0.760910\pi\)
\(104\) 20.4221 44.8311i 0.196367 0.431069i
\(105\) 0 0
\(106\) −30.5462 + 21.5237i −0.288171 + 0.203054i
\(107\) 17.6548i 0.164998i 0.996591 + 0.0824990i \(0.0262901\pi\)
−0.996591 + 0.0824990i \(0.973710\pi\)
\(108\) 0 0
\(109\) 35.9035 0.329389 0.164695 0.986345i \(-0.447336\pi\)
0.164695 + 0.986345i \(0.447336\pi\)
\(110\) −152.302 216.145i −1.38456 1.96495i
\(111\) 0 0
\(112\) 137.753 + 77.3706i 1.22994 + 0.690809i
\(113\) 150.999 54.9591i 1.33627 0.486364i 0.427636 0.903951i \(-0.359346\pi\)
0.908637 + 0.417587i \(0.137124\pi\)
\(114\) 0 0
\(115\) 159.036 28.0424i 1.38293 0.243847i
\(116\) 24.7085 + 66.6550i 0.213005 + 0.574612i
\(117\) 0 0
\(118\) −59.6146 41.4800i −0.505209 0.351526i
\(119\) 27.1732 74.6579i 0.228347 0.627377i
\(120\) 0 0
\(121\) −113.078 94.8835i −0.934527 0.784161i
\(122\) 130.573 + 129.802i 1.07027 + 1.06395i
\(123\) 0 0
\(124\) 53.5508 94.0348i 0.431862 0.758345i
\(125\) 60.7818 105.277i 0.486254 0.842217i
\(126\) 0 0
\(127\) −191.078 + 110.319i −1.50455 + 0.868653i −0.504565 + 0.863374i \(0.668347\pi\)
−0.999986 + 0.00527883i \(0.998320\pi\)
\(128\) −51.6787 + 117.104i −0.403740 + 0.914874i
\(129\) 0 0
\(130\) 95.8855 25.9971i 0.737581 0.199977i
\(131\) −190.395 33.5717i −1.45339 0.256273i −0.609502 0.792785i \(-0.708630\pi\)
−0.843893 + 0.536512i \(0.819742\pi\)
\(132\) 0 0
\(133\) 25.1364 21.0919i 0.188995 0.158586i
\(134\) 0.886312 10.4883i 0.00661427 0.0782706i
\(135\) 0 0
\(136\) 62.3187 + 16.1062i 0.458225 + 0.118428i
\(137\) −24.6568 + 20.6895i −0.179977 + 0.151018i −0.728325 0.685231i \(-0.759701\pi\)
0.548349 + 0.836250i \(0.315257\pi\)
\(138\) 0 0
\(139\) 15.4986 + 2.73282i 0.111501 + 0.0196606i 0.229120 0.973398i \(-0.426415\pi\)
−0.117619 + 0.993059i \(0.537526\pi\)
\(140\) 57.1852 + 313.445i 0.408466 + 2.23889i
\(141\) 0 0
\(142\) −109.802 + 9.93423i −0.773256 + 0.0699594i
\(143\) 87.4036 50.4625i 0.611214 0.352884i
\(144\) 0 0
\(145\) −71.6791 + 124.152i −0.494338 + 0.856219i
\(146\) 94.5872 + 43.7662i 0.647858 + 0.299768i
\(147\) 0 0
\(148\) −38.6934 45.5621i −0.261442 0.307852i
\(149\) −134.724 113.047i −0.904190 0.758705i 0.0668150 0.997765i \(-0.478716\pi\)
−0.971005 + 0.239060i \(0.923161\pi\)
\(150\) 0 0
\(151\) 75.3614 207.054i 0.499082 1.37122i −0.393082 0.919504i \(-0.628591\pi\)
0.892163 0.451713i \(-0.149187\pi\)
\(152\) 18.9639 + 18.6299i 0.124762 + 0.122565i
\(153\) 0 0
\(154\) 137.661 + 292.946i 0.893901 + 1.90225i
\(155\) 214.914 37.8951i 1.38654 0.244485i
\(156\) 0 0
\(157\) 122.495 44.5844i 0.780221 0.283977i 0.0789561 0.996878i \(-0.474841\pi\)
0.701265 + 0.712901i \(0.252619\pi\)
\(158\) 116.987 + 30.9755i 0.740423 + 0.196047i
\(159\) 0 0
\(160\) −248.319 + 70.4940i −1.55199 + 0.440588i
\(161\) −197.686 −1.22786
\(162\) 0 0
\(163\) 29.1697i 0.178955i −0.995989 0.0894776i \(-0.971480\pi\)
0.995989 0.0894776i \(-0.0285198\pi\)
\(164\) −77.8675 + 45.5739i −0.474802 + 0.277890i
\(165\) 0 0
\(166\) 239.173 + 63.3276i 1.44080 + 0.381491i
\(167\) 3.33963 + 9.17555i 0.0199978 + 0.0549434i 0.949290 0.314402i \(-0.101804\pi\)
−0.929292 + 0.369346i \(0.879582\pi\)
\(168\) 0 0
\(169\) −22.7618 129.088i −0.134685 0.763837i
\(170\) 55.2058 + 117.480i 0.324740 + 0.691057i
\(171\) 0 0
\(172\) 161.731 + 134.084i 0.940297 + 0.779559i
\(173\) −104.706 38.1099i −0.605237 0.220288i 0.0211807 0.999776i \(-0.493257\pi\)
−0.626418 + 0.779487i \(0.715480\pi\)
\(174\) 0 0
\(175\) −254.336 + 303.106i −1.45335 + 1.73203i
\(176\) −225.529 + 133.796i −1.28142 + 0.760206i
\(177\) 0 0
\(178\) 319.448 + 147.811i 1.79465 + 0.830399i
\(179\) −146.156 84.3833i −0.816515 0.471415i 0.0326983 0.999465i \(-0.489590\pi\)
−0.849213 + 0.528050i \(0.822923\pi\)
\(180\) 0 0
\(181\) −97.4396 168.770i −0.538340 0.932433i −0.998994 0.0448526i \(-0.985718\pi\)
0.460653 0.887580i \(-0.347615\pi\)
\(182\) −121.120 + 10.9582i −0.665495 + 0.0602098i
\(183\) 0 0
\(184\) −15.3756 159.417i −0.0835629 0.866396i
\(185\) 20.9326 118.714i 0.113149 0.641700i
\(186\) 0 0
\(187\) 84.7616 + 101.015i 0.453271 + 0.540187i
\(188\) 42.0897 247.258i 0.223882 1.31520i
\(189\) 0 0
\(190\) −4.51425 + 53.4199i −0.0237592 + 0.281157i
\(191\) −19.8733 23.6841i −0.104049 0.124001i 0.711507 0.702679i \(-0.248013\pi\)
−0.815556 + 0.578679i \(0.803569\pi\)
\(192\) 0 0
\(193\) −30.1168 + 170.801i −0.156046 + 0.884979i 0.801778 + 0.597622i \(0.203888\pi\)
−0.957824 + 0.287357i \(0.907223\pi\)
\(194\) −74.9280 + 20.3149i −0.386227 + 0.104716i
\(195\) 0 0
\(196\) −1.14932 194.030i −0.00586386 0.989950i
\(197\) −113.759 197.037i −0.577459 1.00019i −0.995770 0.0918847i \(-0.970711\pi\)
0.418310 0.908304i \(-0.362622\pi\)
\(198\) 0 0
\(199\) −291.449 168.268i −1.46457 0.845570i −0.465352 0.885126i \(-0.654072\pi\)
−0.999217 + 0.0395559i \(0.987406\pi\)
\(200\) −264.211 181.525i −1.32105 0.907626i
\(201\) 0 0
\(202\) −58.9571 58.6089i −0.291867 0.290143i
\(203\) 112.803 134.433i 0.555680 0.662233i
\(204\) 0 0
\(205\) −170.977 62.2305i −0.834033 0.303563i
\(206\) 132.338 + 92.0811i 0.642417 + 0.446995i
\(207\) 0 0
\(208\) −18.2573 96.8207i −0.0877755 0.465484i
\(209\) 9.45717 + 53.6343i 0.0452496 + 0.256623i
\(210\) 0 0
\(211\) 24.6193 + 67.6409i 0.116679 + 0.320573i 0.984261 0.176721i \(-0.0565491\pi\)
−0.867582 + 0.497294i \(0.834327\pi\)
\(212\) −25.1445 + 70.3783i −0.118606 + 0.331973i
\(213\) 0 0
\(214\) 20.3383 + 28.8638i 0.0950388 + 0.134877i
\(215\) 423.667i 1.97054i
\(216\) 0 0
\(217\) −267.143 −1.23107
\(218\) 58.6985 41.3608i 0.269259 0.189728i
\(219\) 0 0
\(220\) −497.997 177.923i −2.26362 0.808740i
\(221\) −46.5575 + 16.9456i −0.210668 + 0.0766767i
\(222\) 0 0
\(223\) 209.915 37.0137i 0.941323 0.165981i 0.318129 0.948048i \(-0.396946\pi\)
0.623195 + 0.782067i \(0.285834\pi\)
\(224\) 314.344 32.1984i 1.40332 0.143743i
\(225\) 0 0
\(226\) 183.555 263.803i 0.812191 1.16727i
\(227\) −55.0033 + 151.120i −0.242305 + 0.665729i 0.757610 + 0.652708i \(0.226367\pi\)
−0.999915 + 0.0130208i \(0.995855\pi\)
\(228\) 0 0
\(229\) 31.3460 + 26.3025i 0.136882 + 0.114858i 0.708658 0.705552i \(-0.249301\pi\)
−0.571776 + 0.820410i \(0.693745\pi\)
\(230\) 227.704 229.057i 0.990016 0.995898i
\(231\) 0 0
\(232\) 117.183 + 80.5100i 0.505097 + 0.347026i
\(233\) 129.017 223.464i 0.553722 0.959075i −0.444280 0.895888i \(-0.646540\pi\)
0.998002 0.0631867i \(-0.0201264\pi\)
\(234\) 0 0
\(235\) 438.041 252.903i 1.86400 1.07618i
\(236\) −145.249 + 0.860367i −0.615462 + 0.00364562i
\(237\) 0 0
\(238\) −41.5803 153.362i −0.174707 0.644377i
\(239\) 175.267 + 30.9043i 0.733335 + 0.129307i 0.527831 0.849350i \(-0.323006\pi\)
0.205504 + 0.978656i \(0.434117\pi\)
\(240\) 0 0
\(241\) 62.2687 52.2496i 0.258376 0.216803i −0.504393 0.863474i \(-0.668284\pi\)
0.762769 + 0.646671i \(0.223839\pi\)
\(242\) −294.177 24.8594i −1.21561 0.102725i
\(243\) 0 0
\(244\) 363.007 + 61.7931i 1.48773 + 0.253250i
\(245\) 299.751 251.521i 1.22347 1.02662i
\(246\) 0 0
\(247\) −20.1518 3.55331i −0.0815864 0.0143859i
\(248\) −20.7778 215.428i −0.0837814 0.868661i
\(249\) 0 0
\(250\) −21.9071 242.138i −0.0876286 0.968552i
\(251\) −369.318 + 213.226i −1.47139 + 0.849506i −0.999483 0.0321430i \(-0.989767\pi\)
−0.471905 + 0.881649i \(0.656433\pi\)
\(252\) 0 0
\(253\) 164.054 284.151i 0.648437 1.12313i
\(254\) −185.306 + 400.482i −0.729551 + 1.57670i
\(255\) 0 0
\(256\) 50.4142 + 250.987i 0.196931 + 0.980417i
\(257\) 60.1598 + 50.4801i 0.234085 + 0.196421i 0.752283 0.658840i \(-0.228953\pi\)
−0.518198 + 0.855261i \(0.673397\pi\)
\(258\) 0 0
\(259\) −50.4701 + 138.665i −0.194865 + 0.535388i
\(260\) 126.815 152.963i 0.487748 0.588318i
\(261\) 0 0
\(262\) −349.951 + 164.448i −1.33569 + 0.627665i
\(263\) −211.922 + 37.3676i −0.805789 + 0.142082i −0.561346 0.827581i \(-0.689716\pi\)
−0.244443 + 0.969664i \(0.578605\pi\)
\(264\) 0 0
\(265\) −141.626 + 51.5475i −0.534436 + 0.194519i
\(266\) 16.7976 63.4403i 0.0631487 0.238497i
\(267\) 0 0
\(268\) −10.6335 18.1683i −0.0396771 0.0677921i
\(269\) −155.433 −0.577816 −0.288908 0.957357i \(-0.593292\pi\)
−0.288908 + 0.957357i \(0.593292\pi\)
\(270\) 0 0
\(271\) 1.75623i 0.00648055i −0.999995 0.00324028i \(-0.998969\pi\)
0.999995 0.00324028i \(-0.00103141\pi\)
\(272\) 120.439 45.4591i 0.442791 0.167129i
\(273\) 0 0
\(274\) −16.4771 + 62.2299i −0.0601353 + 0.227116i
\(275\) −224.613 617.118i −0.816773 2.24407i
\(276\) 0 0
\(277\) 37.9088 + 214.991i 0.136855 + 0.776142i 0.973550 + 0.228474i \(0.0733735\pi\)
−0.836695 + 0.547669i \(0.815515\pi\)
\(278\) 28.4868 13.3865i 0.102471 0.0481528i
\(279\) 0 0
\(280\) 454.581 + 446.574i 1.62350 + 1.59491i
\(281\) −230.978 84.0690i −0.821984 0.299178i −0.103420 0.994638i \(-0.532978\pi\)
−0.718565 + 0.695460i \(0.755201\pi\)
\(282\) 0 0
\(283\) 125.013 148.985i 0.441743 0.526449i −0.498529 0.866873i \(-0.666126\pi\)
0.940272 + 0.340424i \(0.110571\pi\)
\(284\) −168.072 + 142.734i −0.591801 + 0.502584i
\(285\) 0 0
\(286\) 84.7633 183.190i 0.296375 0.640524i
\(287\) 192.891 + 111.366i 0.672095 + 0.388034i
\(288\) 0 0
\(289\) 112.133 + 194.219i 0.388002 + 0.672039i
\(290\) 25.8348 + 285.550i 0.0890855 + 0.984655i
\(291\) 0 0
\(292\) 205.059 37.4112i 0.702258 0.128121i
\(293\) 60.6696 344.075i 0.207064 1.17432i −0.687096 0.726567i \(-0.741115\pi\)
0.894159 0.447749i \(-0.147774\pi\)
\(294\) 0 0
\(295\) −188.286 224.391i −0.638258 0.760647i
\(296\) −115.747 29.9147i −0.391038 0.101063i
\(297\) 0 0
\(298\) −350.491 29.6183i −1.17614 0.0993902i
\(299\) 79.2424 + 94.4375i 0.265025 + 0.315844i
\(300\) 0 0
\(301\) 90.0586 510.748i 0.299198 1.69684i
\(302\) −115.318 425.328i −0.381846 1.40837i
\(303\) 0 0
\(304\) 52.4656 + 8.61155i 0.172584 + 0.0283275i
\(305\) 371.294 + 643.100i 1.21736 + 2.10852i
\(306\) 0 0
\(307\) −44.0218 25.4160i −0.143393 0.0827882i 0.426587 0.904447i \(-0.359716\pi\)
−0.569980 + 0.821658i \(0.693049\pi\)
\(308\) 562.535 + 320.352i 1.82641 + 1.04010i
\(309\) 0 0
\(310\) 307.707 309.536i 0.992605 0.998502i
\(311\) 58.2260 69.3911i 0.187222 0.223122i −0.664266 0.747496i \(-0.731256\pi\)
0.851488 + 0.524373i \(0.175700\pi\)
\(312\) 0 0
\(313\) −369.516 134.493i −1.18056 0.429689i −0.324161 0.946002i \(-0.605082\pi\)
−0.856400 + 0.516313i \(0.827304\pi\)
\(314\) 148.905 214.005i 0.474220 0.681544i
\(315\) 0 0
\(316\) 226.946 84.1271i 0.718182 0.266225i
\(317\) −14.4192 81.7755i −0.0454865 0.257967i 0.953581 0.301136i \(-0.0973658\pi\)
−0.999068 + 0.0431689i \(0.986255\pi\)
\(318\) 0 0
\(319\) 99.6201 + 273.704i 0.312289 + 0.858006i
\(320\) −324.767 + 401.314i −1.01490 + 1.25411i
\(321\) 0 0
\(322\) −323.197 + 227.734i −1.00372 + 0.707249i
\(323\) 26.7360i 0.0827740i
\(324\) 0 0
\(325\) 246.749 0.759226
\(326\) −33.6035 47.6895i −0.103078 0.146287i
\(327\) 0 0
\(328\) −74.8044 + 164.212i −0.228062 + 0.500647i
\(329\) −581.836 + 211.771i −1.76850 + 0.643681i
\(330\) 0 0
\(331\) −315.054 + 55.5524i −0.951823 + 0.167832i −0.627937 0.778264i \(-0.716101\pi\)
−0.323886 + 0.946096i \(0.604989\pi\)
\(332\) 463.977 171.993i 1.39752 0.518051i
\(333\) 0 0
\(334\) 16.0302 + 11.1539i 0.0479946 + 0.0333948i
\(335\) 14.5198 39.8929i 0.0433427 0.119083i
\(336\) 0 0
\(337\) −152.931 128.324i −0.453801 0.380784i 0.387043 0.922062i \(-0.373496\pi\)
−0.840844 + 0.541278i \(0.817941\pi\)
\(338\) −185.923 184.825i −0.550068 0.546819i
\(339\) 0 0
\(340\) 225.593 + 128.470i 0.663508 + 0.377854i
\(341\) 221.695 383.987i 0.650132 1.12606i
\(342\) 0 0
\(343\) 4.20414 2.42726i 0.0122570 0.00707657i
\(344\) 418.879 + 32.8998i 1.21767 + 0.0956388i
\(345\) 0 0
\(346\) −215.086 + 58.3155i −0.621637 + 0.168542i
\(347\) 11.0840 + 1.95441i 0.0319425 + 0.00563232i 0.189597 0.981862i \(-0.439282\pi\)
−0.157654 + 0.987494i \(0.550393\pi\)
\(348\) 0 0
\(349\) 499.117 418.808i 1.43013 1.20002i 0.484499 0.874792i \(-0.339002\pi\)
0.945634 0.325233i \(-0.105443\pi\)
\(350\) −66.6358 + 788.542i −0.190388 + 2.25298i
\(351\) 0 0
\(352\) −214.584 + 478.553i −0.609614 + 1.35953i
\(353\) −298.966 + 250.862i −0.846928 + 0.710657i −0.959111 0.283031i \(-0.908660\pi\)
0.112183 + 0.993688i \(0.464216\pi\)
\(354\) 0 0
\(355\) −437.919 77.2169i −1.23357 0.217512i
\(356\) 692.544 126.348i 1.94535 0.354911i
\(357\) 0 0
\(358\) −336.160 + 30.4137i −0.938995 + 0.0849544i
\(359\) 254.033 146.666i 0.707613 0.408540i −0.102564 0.994726i \(-0.532705\pi\)
0.810176 + 0.586186i \(0.199371\pi\)
\(360\) 0 0
\(361\) −174.979 + 303.072i −0.484706 + 0.839536i
\(362\) −353.727 163.672i −0.977147 0.452133i
\(363\) 0 0
\(364\) −185.395 + 157.446i −0.509328 + 0.432544i
\(365\) 322.013 + 270.201i 0.882228 + 0.740277i
\(366\) 0 0
\(367\) 83.0666 228.224i 0.226340 0.621863i −0.773591 0.633686i \(-0.781541\pi\)
0.999930 + 0.0118229i \(0.00376345\pi\)
\(368\) −208.786 242.918i −0.567353 0.660103i
\(369\) 0 0
\(370\) −102.536 218.200i −0.277125 0.589731i
\(371\) 181.693 32.0374i 0.489738 0.0863541i
\(372\) 0 0
\(373\) −245.752 + 89.4465i −0.658853 + 0.239803i −0.649741 0.760155i \(-0.725123\pi\)
−0.00911216 + 0.999958i \(0.502901\pi\)
\(374\) 254.946 + 67.5039i 0.681674 + 0.180492i
\(375\) 0 0
\(376\) −216.029 452.730i −0.574545 1.20407i
\(377\) −109.438 −0.290286
\(378\) 0 0
\(379\) 691.822i 1.82539i 0.408643 + 0.912694i \(0.366002\pi\)
−0.408643 + 0.912694i \(0.633998\pi\)
\(380\) 54.1594 + 92.5366i 0.142525 + 0.243517i
\(381\) 0 0
\(382\) −59.7750 15.8271i −0.156479 0.0414321i
\(383\) 51.3904 + 141.194i 0.134179 + 0.368653i 0.988526 0.151049i \(-0.0482652\pi\)
−0.854348 + 0.519702i \(0.826043\pi\)
\(384\) 0 0
\(385\) 226.696 + 1285.66i 0.588822 + 3.33938i
\(386\) 147.525 + 313.937i 0.382188 + 0.813308i
\(387\) 0 0
\(388\) −99.0969 + 119.530i −0.255405 + 0.308067i
\(389\) 488.180 + 177.683i 1.25496 + 0.456768i 0.882075 0.471109i \(-0.156146\pi\)
0.372886 + 0.927877i \(0.378368\pi\)
\(390\) 0 0
\(391\) −103.536 + 123.389i −0.264798 + 0.315574i
\(392\) −225.402 315.896i −0.575004 0.805856i
\(393\) 0 0
\(394\) −412.972 191.085i −1.04815 0.484988i
\(395\) 422.709 + 244.051i 1.07015 + 0.617851i
\(396\) 0 0
\(397\) −24.3799 42.2272i −0.0614103 0.106366i 0.833686 0.552239i \(-0.186226\pi\)
−0.895096 + 0.445873i \(0.852893\pi\)
\(398\) −670.336 + 60.6478i −1.68426 + 0.152381i
\(399\) 0 0
\(400\) −641.075 + 7.59494i −1.60269 + 0.0189874i
\(401\) −56.2085 + 318.774i −0.140171 + 0.794948i 0.830948 + 0.556350i \(0.187799\pi\)
−0.971119 + 0.238597i \(0.923312\pi\)
\(402\) 0 0
\(403\) 107.084 + 127.618i 0.265718 + 0.316670i
\(404\) −163.906 27.9011i −0.405709 0.0690621i
\(405\) 0 0
\(406\) 29.5543 349.734i 0.0727939 0.861414i
\(407\) −157.432 187.620i −0.386810 0.460982i
\(408\) 0 0
\(409\) −115.513 + 655.106i −0.282427 + 1.60173i 0.431905 + 0.901919i \(0.357842\pi\)
−0.714333 + 0.699806i \(0.753270\pi\)
\(410\) −351.219 + 95.2247i −0.856633 + 0.232255i
\(411\) 0 0
\(412\) 322.436 1.90992i 0.782613 0.00463572i
\(413\) 179.288 + 310.536i 0.434112 + 0.751904i
\(414\) 0 0
\(415\) 864.204 + 498.949i 2.08242 + 1.20229i
\(416\) −141.386 137.260i −0.339871 0.329951i
\(417\) 0 0
\(418\) 77.2482 + 76.7920i 0.184804 + 0.183713i
\(419\) 152.424 181.652i 0.363781 0.433537i −0.552845 0.833284i \(-0.686458\pi\)
0.916625 + 0.399747i \(0.130902\pi\)
\(420\) 0 0
\(421\) −580.285 211.207i −1.37835 0.501678i −0.456672 0.889635i \(-0.650959\pi\)
−0.921678 + 0.387957i \(0.873181\pi\)
\(422\) 118.172 + 82.2247i 0.280029 + 0.194845i
\(423\) 0 0
\(424\) 39.9671 + 144.028i 0.0942619 + 0.339689i
\(425\) 55.9833 + 317.497i 0.131725 + 0.747051i
\(426\) 0 0
\(427\) −310.907 854.209i −0.728118 2.00049i
\(428\) 66.5022 + 23.7597i 0.155379 + 0.0555132i
\(429\) 0 0
\(430\) 488.064 + 692.652i 1.13503 + 1.61082i
\(431\) 366.813i 0.851075i −0.904941 0.425538i \(-0.860085\pi\)
0.904941 0.425538i \(-0.139915\pi\)
\(432\) 0 0
\(433\) 485.644 1.12158 0.560790 0.827958i \(-0.310497\pi\)
0.560790 + 0.827958i \(0.310497\pi\)
\(434\) −436.752 + 307.749i −1.00634 + 0.709098i
\(435\) 0 0
\(436\) 48.3186 135.241i 0.110822 0.310187i
\(437\) −62.5127 + 22.7528i −0.143050 + 0.0520659i
\(438\) 0 0
\(439\) 645.820 113.875i 1.47112 0.259397i 0.620094 0.784528i \(-0.287095\pi\)
0.851022 + 0.525130i \(0.175983\pi\)
\(440\) −1019.14 + 282.807i −2.31623 + 0.642743i
\(441\) 0 0
\(442\) −56.5956 + 81.3386i −0.128044 + 0.184024i
\(443\) −89.5630 + 246.072i −0.202174 + 0.555468i −0.998798 0.0490061i \(-0.984395\pi\)
0.796625 + 0.604474i \(0.206617\pi\)
\(444\) 0 0
\(445\) 1087.53 + 912.547i 2.44389 + 2.05067i
\(446\) 300.550 302.336i 0.673880 0.677883i
\(447\) 0 0
\(448\) 476.827 414.765i 1.06435 0.925815i
\(449\) −302.012 + 523.100i −0.672633 + 1.16503i 0.304522 + 0.952505i \(0.401503\pi\)
−0.977155 + 0.212529i \(0.931830\pi\)
\(450\) 0 0
\(451\) −320.151 + 184.839i −0.709869 + 0.409843i
\(452\) −3.80724 642.747i −0.00842311 1.42201i
\(453\) 0 0
\(454\) 84.1658 + 310.430i 0.185387 + 0.683767i
\(455\) −483.057 85.1760i −1.06166 0.187200i
\(456\) 0 0
\(457\) 308.359 258.744i 0.674747 0.566180i −0.239719 0.970842i \(-0.577055\pi\)
0.914466 + 0.404662i \(0.132611\pi\)
\(458\) 81.5480 + 6.89123i 0.178052 + 0.0150463i
\(459\) 0 0
\(460\) 108.400 636.799i 0.235651 1.38435i
\(461\) −163.353 + 137.069i −0.354344 + 0.297330i −0.802532 0.596609i \(-0.796514\pi\)
0.448187 + 0.893940i \(0.352070\pi\)
\(462\) 0 0
\(463\) −121.366 21.4001i −0.262130 0.0462206i 0.0410384 0.999158i \(-0.486933\pi\)
−0.303169 + 0.952937i \(0.598045\pi\)
\(464\) 284.329 3.36851i 0.612779 0.00725971i
\(465\) 0 0
\(466\) −46.5008 513.970i −0.0997871 1.10294i
\(467\) 161.897 93.4714i 0.346675 0.200153i −0.316545 0.948578i \(-0.602523\pi\)
0.663220 + 0.748425i \(0.269189\pi\)
\(468\) 0 0
\(469\) −25.9842 + 45.0060i −0.0554035 + 0.0959616i
\(470\) 424.809 918.094i 0.903848 1.95339i
\(471\) 0 0
\(472\) −236.476 + 168.733i −0.501009 + 0.357486i
\(473\) 659.403 + 553.305i 1.39409 + 1.16978i
\(474\) 0 0
\(475\) −45.5406 + 125.122i −0.0958749 + 0.263414i
\(476\) −244.652 202.830i −0.513975 0.426114i
\(477\) 0 0
\(478\) 322.146 151.382i 0.673945 0.316699i
\(479\) −507.526 + 89.4906i −1.05955 + 0.186828i −0.676158 0.736756i \(-0.736356\pi\)
−0.383395 + 0.923584i \(0.625245\pi\)
\(480\) 0 0
\(481\) 86.4735 31.4738i 0.179779 0.0654340i
\(482\) 41.6115 157.156i 0.0863308 0.326051i
\(483\) 0 0
\(484\) −509.587 + 298.249i −1.05287 + 0.616216i
\(485\) −313.118 −0.645603
\(486\) 0 0
\(487\) 318.498i 0.654000i −0.945024 0.327000i \(-0.893962\pi\)
0.945024 0.327000i \(-0.106038\pi\)
\(488\) 664.665 317.158i 1.36202 0.649914i
\(489\) 0 0
\(490\) 200.311 756.525i 0.408798 1.54393i
\(491\) 288.906 + 793.764i 0.588404 + 1.61663i 0.773422 + 0.633892i \(0.218544\pi\)
−0.185018 + 0.982735i \(0.559234\pi\)
\(492\) 0 0
\(493\) −24.8297 140.816i −0.0503644 0.285631i
\(494\) −37.0396 + 17.4056i −0.0749790 + 0.0352340i
\(495\) 0 0
\(496\) −282.143 328.267i −0.568836 0.661829i
\(497\) 511.515 + 186.176i 1.02921 + 0.374600i
\(498\) 0 0
\(499\) 159.217 189.747i 0.319072 0.380255i −0.582539 0.812802i \(-0.697941\pi\)
0.901611 + 0.432548i \(0.142385\pi\)
\(500\) −314.759 370.634i −0.629518 0.741269i
\(501\) 0 0
\(502\) −358.162 + 774.058i −0.713470 + 1.54195i
\(503\) −602.610 347.917i −1.19803 0.691684i −0.237915 0.971286i \(-0.576464\pi\)
−0.960116 + 0.279602i \(0.909797\pi\)
\(504\) 0 0
\(505\) −167.648 290.375i −0.331977 0.575000i
\(506\) −59.1290 653.549i −0.116856 1.29160i
\(507\) 0 0
\(508\) 158.399 + 868.220i 0.311809 + 1.70909i
\(509\) 107.678 610.672i 0.211548 1.19975i −0.675249 0.737590i \(-0.735964\pi\)
0.886797 0.462159i \(-0.152925\pi\)
\(510\) 0 0
\(511\) −330.764 394.189i −0.647287 0.771407i
\(512\) 371.559 + 352.261i 0.725701 + 0.688010i
\(513\) 0 0
\(514\) 156.508 + 13.2258i 0.304491 + 0.0257310i
\(515\) 417.974 + 498.122i 0.811601 + 0.967228i
\(516\) 0 0
\(517\) 178.454 1012.06i 0.345173 1.95757i
\(518\) 77.2291 + 284.846i 0.149091 + 0.549895i
\(519\) 0 0
\(520\) 31.1160 396.169i 0.0598386 0.761863i
\(521\) −492.557 853.134i −0.945408 1.63749i −0.754933 0.655802i \(-0.772331\pi\)
−0.190475 0.981692i \(-0.561003\pi\)
\(522\) 0 0
\(523\) −257.700 148.783i −0.492735 0.284481i 0.232973 0.972483i \(-0.425154\pi\)
−0.725708 + 0.688002i \(0.758488\pi\)
\(524\) −382.690 + 671.999i −0.730324 + 1.28244i
\(525\) 0 0
\(526\) −303.424 + 305.227i −0.576852 + 0.580279i
\(527\) −139.913 + 166.742i −0.265490 + 0.316399i
\(528\) 0 0
\(529\) −120.484 43.8526i −0.227758 0.0828972i
\(530\) −172.161 + 247.428i −0.324832 + 0.466845i
\(531\) 0 0
\(532\) −45.6209 123.069i −0.0857536 0.231333i
\(533\) −24.1194 136.788i −0.0452522 0.256638i
\(534\) 0 0
\(535\) 48.7084 + 133.825i 0.0910438 + 0.250141i
\(536\) −38.3145 17.4536i −0.0714823 0.0325627i
\(537\) 0 0
\(538\) −254.117 + 179.058i −0.472336 + 0.332822i
\(539\) 795.023i 1.47500i
\(540\) 0 0
\(541\) −454.094 −0.839361 −0.419680 0.907672i \(-0.637858\pi\)
−0.419680 + 0.907672i \(0.637858\pi\)
\(542\) −2.02318 2.87126i −0.00373280 0.00529752i
\(543\) 0 0
\(544\) 144.537 213.067i 0.265693 0.391667i
\(545\) 272.153 99.0554i 0.499362 0.181753i
\(546\) 0 0
\(547\) −487.249 + 85.9151i −0.890765 + 0.157066i −0.600258 0.799807i \(-0.704935\pi\)
−0.290508 + 0.956873i \(0.593824\pi\)
\(548\) 44.7505 + 120.721i 0.0816614 + 0.220294i
\(549\) 0 0
\(550\) −1078.14 750.172i −1.96025 1.36395i
\(551\) 20.1981 55.4940i 0.0366573 0.100715i
\(552\) 0 0
\(553\) −457.716 384.069i −0.827695 0.694519i
\(554\) 309.647 + 307.818i 0.558930 + 0.555629i
\(555\) 0 0
\(556\) 31.1519 54.7024i 0.0560285 0.0983856i
\(557\) −16.2577 + 28.1591i −0.0291879 + 0.0505550i −0.880250 0.474509i \(-0.842625\pi\)
0.851062 + 0.525064i \(0.175959\pi\)
\(558\) 0 0
\(559\) −280.092 + 161.711i −0.501058 + 0.289286i
\(560\) 1257.65 + 206.426i 2.24580 + 0.368618i
\(561\) 0 0
\(562\) −474.473 + 128.642i −0.844257 + 0.228900i
\(563\) 141.933 + 25.0265i 0.252100 + 0.0444521i 0.298270 0.954482i \(-0.403590\pi\)
−0.0461697 + 0.998934i \(0.514701\pi\)
\(564\) 0 0
\(565\) 992.961 833.193i 1.75745 1.47468i
\(566\) 32.7534 387.591i 0.0578682 0.684790i
\(567\) 0 0
\(568\) −110.351 + 426.974i −0.194280 + 0.751715i
\(569\) −138.945 + 116.589i −0.244191 + 0.204901i −0.756666 0.653801i \(-0.773173\pi\)
0.512475 + 0.858702i \(0.328729\pi\)
\(570\) 0 0
\(571\) 845.424 + 149.071i 1.48060 + 0.261070i 0.854819 0.518927i \(-0.173668\pi\)
0.625783 + 0.779997i \(0.284779\pi\)
\(572\) −72.4554 397.145i −0.126670 0.694309i
\(573\) 0 0
\(574\) 443.651 40.1388i 0.772912 0.0699283i
\(575\) 694.712 401.092i 1.20819 0.697552i
\(576\) 0 0
\(577\) 340.538 589.830i 0.590188 1.02224i −0.404019 0.914751i \(-0.632387\pi\)
0.994207 0.107484i \(-0.0342796\pi\)
\(578\) 407.066 + 188.352i 0.704267 + 0.325869i
\(579\) 0 0
\(580\) 371.191 + 437.084i 0.639984 + 0.753593i
\(581\) −935.773 785.207i −1.61062 1.35147i
\(582\) 0 0
\(583\) −104.732 + 287.749i −0.179644 + 0.493567i
\(584\) 292.153 297.392i 0.500263 0.509232i
\(585\) 0 0
\(586\) −297.185 632.419i −0.507142 1.07921i
\(587\) −542.437 + 95.6463i −0.924084 + 0.162941i −0.615392 0.788221i \(-0.711002\pi\)
−0.308692 + 0.951162i \(0.599891\pi\)
\(588\) 0 0
\(589\) −84.4766 + 30.7470i −0.143424 + 0.0522020i
\(590\) −566.327 149.951i −0.959877 0.254154i
\(591\) 0 0
\(592\) −223.697 + 84.4333i −0.377867 + 0.142624i
\(593\) 815.019 1.37440 0.687200 0.726468i \(-0.258840\pi\)
0.687200 + 0.726468i \(0.258840\pi\)
\(594\) 0 0
\(595\) 640.885i 1.07712i
\(596\) −607.138 + 355.343i −1.01869 + 0.596212i
\(597\) 0 0
\(598\) 238.345 + 63.1085i 0.398571 + 0.105533i
\(599\) 261.738 + 719.120i 0.436959 + 1.20053i 0.941461 + 0.337123i \(0.109454\pi\)
−0.504502 + 0.863411i \(0.668324\pi\)
\(600\) 0 0
\(601\) −13.1717 74.7002i −0.0219162 0.124293i 0.971887 0.235449i \(-0.0756559\pi\)
−0.993803 + 0.111156i \(0.964545\pi\)
\(602\) −441.145 938.769i −0.732798 1.55942i
\(603\) 0 0
\(604\) −678.511 562.523i −1.12336 0.931329i
\(605\) −1118.92 407.254i −1.84946 0.673147i
\(606\) 0 0
\(607\) 741.278 883.420i 1.22122 1.45539i 0.371264 0.928527i \(-0.378925\pi\)
0.849952 0.526860i \(-0.176631\pi\)
\(608\) 95.6966 46.3614i 0.157396 0.0762523i
\(609\) 0 0
\(610\) 1347.88 + 623.673i 2.20964 + 1.02241i
\(611\) 334.395 + 193.063i 0.547291 + 0.315979i
\(612\) 0 0
\(613\) 582.872 + 1009.56i 0.950852 + 1.64692i 0.743587 + 0.668639i \(0.233123\pi\)
0.207265 + 0.978285i \(0.433544\pi\)
\(614\) −101.250 + 9.16050i −0.164903 + 0.0149194i
\(615\) 0 0
\(616\) 1288.73 124.297i 2.09210 0.201781i
\(617\) −55.5811 + 315.216i −0.0900828 + 0.510885i 0.906061 + 0.423147i \(0.139075\pi\)
−0.996144 + 0.0877375i \(0.972036\pi\)
\(618\) 0 0
\(619\) 4.81103 + 5.73357i 0.00777227 + 0.00926263i 0.769917 0.638145i \(-0.220298\pi\)
−0.762144 + 0.647407i \(0.775853\pi\)
\(620\) 146.486 860.538i 0.236267 1.38797i
\(621\) 0 0
\(622\) 15.2552 180.524i 0.0245260 0.290231i
\(623\) −1117.08 1331.29i −1.79307 2.13690i
\(624\) 0 0
\(625\) −3.67192 + 20.8245i −0.00587507 + 0.0333192i
\(626\) −759.056 + 205.800i −1.21255 + 0.328754i
\(627\) 0 0
\(628\) −3.08855 521.415i −0.00491807 0.830279i
\(629\) 60.1174 + 104.126i 0.0955762 + 0.165543i
\(630\) 0 0
\(631\) 519.028 + 299.661i 0.822549 + 0.474899i 0.851295 0.524688i \(-0.175818\pi\)
−0.0287456 + 0.999587i \(0.509151\pi\)
\(632\) 274.119 398.980i 0.433732 0.631298i
\(633\) 0 0
\(634\) −117.779 117.084i −0.185772 0.184675i
\(635\) −1144.03 + 1363.40i −1.80162 + 2.14709i
\(636\) 0 0
\(637\) 280.697 + 102.165i 0.440655 + 0.160385i
\(638\) 478.176 + 332.716i 0.749492 + 0.521499i
\(639\) 0 0
\(640\) −68.6482 + 1030.24i −0.107263 + 1.60975i
\(641\) −65.6070 372.076i −0.102351 0.580462i −0.992245 0.124295i \(-0.960333\pi\)
0.889894 0.456167i \(-0.150778\pi\)
\(642\) 0 0
\(643\) 240.323 + 660.282i 0.373753 + 1.02688i 0.973898 + 0.226986i \(0.0728872\pi\)
−0.600145 + 0.799891i \(0.704891\pi\)
\(644\) −266.044 + 744.645i −0.413112 + 1.15628i
\(645\) 0 0
\(646\) −30.7999 43.7107i −0.0476778 0.0676636i
\(647\) 1201.08i 1.85638i 0.372111 + 0.928188i \(0.378634\pi\)
−0.372111 + 0.928188i \(0.621366\pi\)
\(648\) 0 0
\(649\) −595.146 −0.917021
\(650\) 403.409 284.254i 0.620629 0.437314i
\(651\) 0 0
\(652\) −109.877 39.2564i −0.168523 0.0602091i
\(653\) 567.170 206.433i 0.868560 0.316130i 0.130976 0.991386i \(-0.458189\pi\)
0.737584 + 0.675256i \(0.235967\pi\)
\(654\) 0 0
\(655\) −1535.84 + 270.809i −2.34479 + 0.413450i
\(656\) 66.8747 + 354.645i 0.101943 + 0.540617i
\(657\) 0 0
\(658\) −707.283 + 1016.50i −1.07490 + 1.54483i
\(659\) 288.066 791.455i 0.437126 1.20099i −0.504227 0.863571i \(-0.668223\pi\)
0.941353 0.337423i \(-0.109555\pi\)
\(660\) 0 0
\(661\) −660.176 553.953i −0.998753 0.838053i −0.0119415 0.999929i \(-0.503801\pi\)
−0.986811 + 0.161876i \(0.948246\pi\)
\(662\) −451.084 + 453.764i −0.681396 + 0.685445i
\(663\) 0 0
\(664\) 560.420 815.692i 0.844006 1.22845i
\(665\) 132.345 229.229i 0.199016 0.344705i
\(666\) 0 0
\(667\) −308.118 + 177.892i −0.461947 + 0.266705i
\(668\) 39.0570 0.231350i 0.0584685 0.000346332i
\(669\) 0 0
\(670\) −22.2181 81.9476i −0.0331614 0.122310i
\(671\) 1485.84 + 261.994i 2.21437 + 0.390452i
\(672\) 0 0
\(673\) −909.054 + 762.787i −1.35075 + 1.13341i −0.372027 + 0.928222i \(0.621337\pi\)
−0.978722 + 0.205191i \(0.934218\pi\)
\(674\) −397.856 33.6209i −0.590291 0.0498826i
\(675\) 0 0
\(676\) −516.884 87.9869i −0.764621 0.130158i
\(677\) 125.669 105.449i 0.185627 0.155759i −0.545239 0.838281i \(-0.683561\pi\)
0.730866 + 0.682521i \(0.239117\pi\)
\(678\) 0 0
\(679\) 377.476 + 66.5592i 0.555930 + 0.0980254i
\(680\) 516.819 49.8466i 0.760028 0.0733038i
\(681\) 0 0
\(682\) −79.9040 883.173i −0.117161 1.29497i
\(683\) 640.955 370.056i 0.938441 0.541809i 0.0489695 0.998800i \(-0.484406\pi\)
0.889471 + 0.456991i \(0.151073\pi\)
\(684\) 0 0
\(685\) −129.820 + 224.856i −0.189519 + 0.328256i
\(686\) 4.07714 8.81150i 0.00594336 0.0128448i
\(687\) 0 0
\(688\) 722.725 428.761i 1.05047 0.623199i
\(689\) −88.1363 73.9551i −0.127919 0.107337i
\(690\) 0 0
\(691\) −347.369 + 954.389i −0.502705 + 1.38117i 0.385918 + 0.922533i \(0.373885\pi\)
−0.888623 + 0.458638i \(0.848338\pi\)
\(692\) −284.465 + 343.120i −0.411077 + 0.495838i
\(693\) 0 0
\(694\) 20.3728 9.57353i 0.0293556 0.0137947i
\(695\) 125.021 22.0445i 0.179886 0.0317188i
\(696\) 0 0
\(697\) 170.536 62.0700i 0.244671 0.0890530i
\(698\) 333.538 1259.69i 0.477848 1.80472i
\(699\) 0 0
\(700\) 799.458 + 1365.95i 1.14208 + 1.95136i
\(701\) −418.263 −0.596666 −0.298333 0.954462i \(-0.596431\pi\)
−0.298333 + 0.954462i \(0.596431\pi\)
\(702\) 0 0
\(703\) 49.6580i 0.0706373i
\(704\) 200.470 + 1029.59i 0.284758 + 1.46248i
\(705\) 0 0
\(706\) −199.786 + 754.542i −0.282983 + 1.06876i
\(707\) 140.382 + 385.696i 0.198560 + 0.545539i
\(708\) 0 0
\(709\) 175.990 + 998.089i 0.248223 + 1.40774i 0.812887 + 0.582421i \(0.197894\pi\)
−0.564665 + 0.825320i \(0.690994\pi\)
\(710\) −804.907 + 378.241i −1.13367 + 0.532733i
\(711\) 0 0
\(712\) 986.686 1004.38i 1.38580 1.41064i
\(713\) 508.936 + 185.238i 0.713796 + 0.259800i
\(714\) 0 0
\(715\) 523.307 623.653i 0.731898 0.872242i
\(716\) −514.551 + 436.980i −0.718647 + 0.610307i
\(717\) 0 0
\(718\) 246.359 532.430i 0.343119 0.741546i
\(719\) −982.339 567.154i −1.36626 0.788809i −0.375809 0.926697i \(-0.622635\pi\)
−0.990448 + 0.137888i \(0.955968\pi\)
\(720\) 0 0
\(721\) −398.000 689.356i −0.552011 0.956110i
\(722\) 63.0664 + 697.068i 0.0873496 + 0.965469i
\(723\) 0 0
\(724\) −766.859 + 139.906i −1.05920 + 0.193241i
\(725\) −123.658 + 701.298i −0.170562 + 0.967308i
\(726\) 0 0
\(727\) 81.1979 + 96.7678i 0.111689 + 0.133106i 0.818992 0.573804i \(-0.194533\pi\)
−0.707303 + 0.706910i \(0.750089\pi\)
\(728\) −121.725 + 470.984i −0.167205 + 0.646955i
\(729\) 0 0
\(730\) 837.731 + 70.7925i 1.14758 + 0.0969761i
\(731\) −271.625 323.710i −0.371580 0.442832i
\(732\) 0 0
\(733\) −1.34916 + 7.65145i −0.00184060 + 0.0104385i −0.985714 0.168426i \(-0.946131\pi\)
0.983874 + 0.178865i \(0.0572425\pi\)
\(734\) −127.108 468.815i −0.173172 0.638713i
\(735\) 0 0
\(736\) −621.185 156.625i −0.844001 0.212806i
\(737\) −43.1273 74.6986i −0.0585173 0.101355i
\(738\) 0 0
\(739\) −859.244 496.085i −1.16271 0.671292i −0.210759 0.977538i \(-0.567594\pi\)
−0.951952 + 0.306246i \(0.900927\pi\)
\(740\) −419.004 238.614i −0.566221 0.322451i
\(741\) 0 0
\(742\) 260.143 261.688i 0.350596 0.352679i
\(743\) 376.614 448.831i 0.506883 0.604080i −0.450544 0.892754i \(-0.648770\pi\)
0.957427 + 0.288674i \(0.0932144\pi\)
\(744\) 0 0
\(745\) −1333.12 485.215i −1.78942 0.651295i
\(746\) −298.738 + 429.343i −0.400453 + 0.575526i
\(747\) 0 0
\(748\) 494.576 183.336i 0.661197 0.245101i
\(749\) −30.2729 171.686i −0.0404177 0.229220i
\(750\) 0 0
\(751\) −46.8479 128.714i −0.0623807 0.171390i 0.904587 0.426290i \(-0.140180\pi\)
−0.966967 + 0.254900i \(0.917957\pi\)
\(752\) −874.731 491.302i −1.16321 0.653328i
\(753\) 0 0
\(754\) −178.920 + 126.072i −0.237294 + 0.167205i
\(755\) 1777.41i 2.35418i
\(756\) 0 0
\(757\) 906.432 1.19740 0.598700 0.800973i \(-0.295684\pi\)
0.598700 + 0.800973i \(0.295684\pi\)
\(758\) 796.979 + 1131.06i 1.05142 + 1.49216i
\(759\) 0 0
\(760\) 195.147 + 88.8964i 0.256773 + 0.116969i
\(761\) −109.794 + 39.9619i −0.144276 + 0.0525123i −0.413149 0.910663i \(-0.635571\pi\)
0.268873 + 0.963176i \(0.413349\pi\)
\(762\) 0 0
\(763\) −349.147 + 61.5641i −0.457598 + 0.0806869i
\(764\) −115.959 + 42.9851i −0.151779 + 0.0562632i
\(765\) 0 0
\(766\) 246.674 + 171.636i 0.322028 + 0.224068i
\(767\) 76.4800 210.127i 0.0997131 0.273960i
\(768\) 0 0
\(769\) 382.761 + 321.174i 0.497738 + 0.417652i 0.856790 0.515666i \(-0.172455\pi\)
−0.359052 + 0.933318i \(0.616900\pi\)
\(770\) 1851.71 + 1840.77i 2.40481 + 2.39061i
\(771\) 0 0
\(772\) 602.843 + 343.307i 0.780885 + 0.444698i
\(773\) −203.400 + 352.299i −0.263131 + 0.455756i −0.967072 0.254502i \(-0.918088\pi\)
0.703942 + 0.710258i \(0.251422\pi\)
\(774\) 0 0
\(775\) 938.799 542.016i 1.21135 0.699375i
\(776\) −24.3151 + 309.579i −0.0313339 + 0.398942i
\(777\) 0 0
\(778\) 1002.82 271.889i 1.28897 0.349472i
\(779\) 73.8143 + 13.0154i 0.0947552 + 0.0167079i
\(780\) 0 0
\(781\) −692.100 + 580.741i −0.886172 + 0.743587i
\(782\) −27.1264 + 321.003i −0.0346884 + 0.410489i
\(783\) 0 0
\(784\) −732.421 256.795i −0.934210 0.327545i
\(785\) 805.519 675.911i 1.02614 0.861033i
\(786\) 0 0
\(787\) 546.498 + 96.3624i 0.694407 + 0.122443i 0.509702 0.860351i \(-0.329756\pi\)
0.184706 + 0.982794i \(0.440867\pi\)
\(788\) −895.298 + 163.339i −1.13617 + 0.207283i
\(789\) 0 0
\(790\) 972.234 87.9617i 1.23068 0.111344i
\(791\) −1374.17 + 793.376i −1.73725 + 1.00300i
\(792\) 0 0
\(793\) −283.441 + 490.934i −0.357429 + 0.619085i
\(794\) −88.5044 40.9516i −0.111467 0.0515763i
\(795\) 0 0
\(796\) −1026.06 + 871.380i −1.28903 + 1.09470i
\(797\) −185.771 155.880i −0.233088 0.195584i 0.518761 0.854919i \(-0.326393\pi\)
−0.751849 + 0.659335i \(0.770838\pi\)
\(798\) 0 0
\(799\) −172.550 + 474.076i −0.215957 + 0.593337i
\(800\) −1039.34 + 750.935i −1.29918 + 0.938669i
\(801\) 0 0
\(802\) 275.333 + 585.916i 0.343307 + 0.730568i
\(803\) 841.093 148.307i 1.04744 0.184692i
\(804\) 0 0
\(805\) −1498.48 + 545.404i −1.86147 + 0.677520i
\(806\) 322.088 + 85.2816i 0.399613 + 0.105808i
\(807\) 0 0
\(808\) −300.112 + 143.205i −0.371426 + 0.177233i
\(809\) 358.925 0.443666 0.221833 0.975085i \(-0.428796\pi\)
0.221833 + 0.975085i \(0.428796\pi\)
\(810\) 0 0
\(811\) 474.238i 0.584757i 0.956303 + 0.292379i \(0.0944468\pi\)
−0.956303 + 0.292379i \(0.905553\pi\)
\(812\) −354.575 605.826i −0.436669 0.746092i
\(813\) 0 0
\(814\) −473.523 125.378i −0.581724 0.154027i
\(815\) −80.4774 221.110i −0.0987453 0.271300i
\(816\) 0 0
\(817\) −30.3062 171.875i −0.0370945 0.210374i
\(818\) 565.830 + 1204.10i 0.691724 + 1.47201i
\(819\) 0 0
\(820\) −464.510 + 560.288i −0.566475 + 0.683278i
\(821\) −721.915 262.755i −0.879311 0.320043i −0.137380 0.990518i \(-0.543868\pi\)
−0.741932 + 0.670475i \(0.766090\pi\)
\(822\) 0 0
\(823\) −541.613 + 645.469i −0.658096 + 0.784288i −0.987111 0.160037i \(-0.948839\pi\)
0.329015 + 0.944325i \(0.393283\pi\)
\(824\) 524.951 374.569i 0.637076 0.454574i
\(825\) 0 0
\(826\) 650.856 + 301.156i 0.787961 + 0.364595i
\(827\) 99.9028 + 57.6789i 0.120801 + 0.0697447i 0.559183 0.829044i \(-0.311115\pi\)
−0.438382 + 0.898789i \(0.644448\pi\)
\(828\) 0 0
\(829\) −612.938 1061.64i −0.739370 1.28063i −0.952779 0.303663i \(-0.901790\pi\)
0.213410 0.976963i \(-0.431543\pi\)
\(830\) 1987.68 179.833i 2.39479 0.216666i
\(831\) 0 0
\(832\) −389.276 61.5288i −0.467879 0.0739529i
\(833\) −67.7728 + 384.359i −0.0813600 + 0.461415i
\(834\) 0 0
\(835\) 50.6296 + 60.3380i 0.0606342 + 0.0722610i
\(836\) 214.757 + 36.5572i 0.256887 + 0.0437288i
\(837\) 0 0
\(838\) 39.9350 472.575i 0.0476551 0.563932i
\(839\) 787.091 + 938.019i 0.938130 + 1.11802i 0.992832 + 0.119517i \(0.0381347\pi\)
−0.0547020 + 0.998503i \(0.517421\pi\)
\(840\) 0 0
\(841\) −91.1935 + 517.184i −0.108435 + 0.614963i
\(842\) −1192.02 + 323.187i −1.41570 + 0.383833i
\(843\) 0 0
\(844\) 287.923 1.70548i 0.341141 0.00202071i
\(845\) −528.684 915.707i −0.625661 1.08368i
\(846\) 0 0
\(847\) 1262.34 + 728.810i 1.49036 + 0.860460i
\(848\) 231.262 + 189.429i 0.272715 + 0.223384i
\(849\) 0 0
\(850\) 457.283 + 454.583i 0.537980 + 0.534803i
\(851\) 192.302 229.177i 0.225972 0.269303i
\(852\) 0 0
\(853\) 243.051 + 88.4635i 0.284937 + 0.103709i 0.480535 0.876976i \(-0.340442\pi\)
−0.195598 + 0.980684i \(0.562665\pi\)
\(854\) −1492.35 1038.38i −1.74748 1.21590i
\(855\) 0 0
\(856\) 136.095 37.7658i 0.158990 0.0441189i
\(857\) −0.150722 0.854790i −0.000175872 0.000997421i 0.984720 0.174147i \(-0.0557167\pi\)
−0.984896 + 0.173149i \(0.944606\pi\)
\(858\) 0 0
\(859\) −550.181 1511.61i −0.640490 1.75973i −0.650182 0.759778i \(-0.725307\pi\)
0.00969236 0.999953i \(-0.496915\pi\)
\(860\) 1595.87 + 570.167i 1.85566 + 0.662985i
\(861\) 0 0
\(862\) −422.569 599.703i −0.490219 0.695711i
\(863\) 847.738i 0.982316i 0.871071 + 0.491158i \(0.163426\pi\)
−0.871071 + 0.491158i \(0.836574\pi\)
\(864\) 0 0
\(865\) −898.828 −1.03911
\(866\) 793.979 559.462i 0.916835 0.646030i
\(867\) 0 0
\(868\) −359.519 + 1006.28i −0.414192 + 1.15930i
\(869\) 931.901 339.184i 1.07238 0.390315i
\(870\) 0 0
\(871\) 31.9158 5.62762i 0.0366427 0.00646110i
\(872\) −76.8021 276.769i −0.0880758 0.317396i
\(873\) 0 0
\(874\) −75.9908 + 109.213i −0.0869461 + 0.124958i
\(875\) −410.559 + 1128.00i −0.469211 + 1.28915i
\(876\) 0 0
\(877\) −242.653 203.610i −0.276685 0.232167i 0.493876 0.869532i \(-0.335580\pi\)
−0.770561 + 0.637366i \(0.780024\pi\)
\(878\) 924.666 930.159i 1.05315 1.05941i
\(879\) 0 0
\(880\) −1340.40 + 1636.41i −1.52318 + 1.85956i
\(881\) −383.212 + 663.743i −0.434974 + 0.753397i −0.997294 0.0735229i \(-0.976576\pi\)
0.562319 + 0.826920i \(0.309909\pi\)
\(882\) 0 0
\(883\) −233.975 + 135.085i −0.264977 + 0.152985i −0.626603 0.779339i \(-0.715555\pi\)
0.361626 + 0.932323i \(0.382222\pi\)
\(884\) 1.17389 + 198.178i 0.00132793 + 0.224184i
\(885\) 0 0
\(886\) 137.049 + 505.480i 0.154683 + 0.570520i
\(887\) 172.336 + 30.3875i 0.194291 + 0.0342588i 0.269947 0.962875i \(-0.412994\pi\)
−0.0756557 + 0.997134i \(0.524105\pi\)
\(888\) 0 0
\(889\) 1668.99 1400.45i 1.87738 1.57531i
\(890\) 2829.26 + 239.087i 3.17894 + 0.268637i
\(891\) 0 0
\(892\) 143.079 840.523i 0.160402 0.942290i
\(893\) −159.616 + 133.933i −0.178741 + 0.149981i
\(894\) 0 0
\(895\) −1340.69 236.400i −1.49798 0.264134i
\(896\) 301.756 1227.40i 0.336781 1.36987i
\(897\) 0 0
\(898\) 108.852 + 1203.13i 0.121216 + 1.33979i
\(899\) −416.376 + 240.395i −0.463154 + 0.267402i
\(900\) 0 0
\(901\) 75.1630 130.186i 0.0834218 0.144491i
\(902\) −310.480 + 671.008i −0.344213 + 0.743911i
\(903\) 0 0
\(904\) −746.669 1046.44i −0.825962 1.15757i
\(905\) −1204.23 1010.47i −1.33064 1.11654i
\(906\) 0 0
\(907\) 67.1004 184.357i 0.0739805 0.203260i −0.897190 0.441644i \(-0.854395\pi\)
0.971171 + 0.238384i \(0.0766177\pi\)
\(908\) 495.218 + 410.564i 0.545395 + 0.452163i
\(909\) 0 0
\(910\) −887.872 + 417.227i −0.975684 + 0.458492i
\(911\) −272.275 + 48.0095i −0.298875 + 0.0526998i −0.321075 0.947054i \(-0.604044\pi\)
0.0221996 + 0.999754i \(0.492933\pi\)
\(912\) 0 0
\(913\) 1905.22 693.442i 2.08677 0.759520i
\(914\) 206.063 778.251i 0.225452 0.851478i
\(915\) 0 0
\(916\) 141.262 82.6769i 0.154216 0.0902586i
\(917\) 1909.08 2.08188
\(918\) 0 0
\(919\) 1081.67i 1.17701i 0.808494 + 0.588504i \(0.200283\pi\)
−0.808494 + 0.588504i \(0.799717\pi\)
\(920\) −556.370 1165.98i −0.604750 1.26737i
\(921\) 0 0
\(922\) −109.162 + 412.277i −0.118396 + 0.447155i
\(923\) −116.102 318.987i −0.125787 0.345598i
\(924\) 0 0
\(925\) −103.980 589.702i −0.112411 0.637515i
\(926\) −223.075 + 104.827i −0.240901 + 0.113204i
\(927\) 0 0
\(928\) 460.969 333.054i 0.496734 0.358895i
\(929\) 664.820 + 241.975i 0.715630 + 0.260468i 0.674069 0.738668i \(-0.264545\pi\)
0.0415604 + 0.999136i \(0.486767\pi\)
\(930\) 0 0
\(931\) −103.612 + 123.481i −0.111292 + 0.132632i
\(932\) −668.117 786.720i −0.716864 0.844120i
\(933\) 0 0
\(934\) 157.007 339.322i 0.168101 0.363300i
\(935\) 921.198 + 531.854i 0.985238 + 0.568828i
\(936\) 0 0
\(937\) 426.668 + 739.011i 0.455355 + 0.788699i 0.998709 0.0508055i \(-0.0161789\pi\)
−0.543353 + 0.839504i \(0.682846\pi\)
\(938\) 9.36531 + 103.514i 0.00998434 + 0.110356i
\(939\) 0 0
\(940\) −363.125 1990.37i −0.386303 2.11742i
\(941\) 122.045 692.150i 0.129697 0.735548i −0.848710 0.528859i \(-0.822620\pi\)
0.978407 0.206689i \(-0.0662688\pi\)
\(942\) 0 0
\(943\) −290.258 345.916i −0.307802 0.366825i
\(944\) −192.234 + 548.283i −0.203638 + 0.580808i
\(945\) 0 0
\(946\) 1715.47 + 144.966i 1.81339 + 0.153241i
\(947\) 143.597 + 171.133i 0.151634 + 0.180710i 0.836514 0.547946i \(-0.184590\pi\)
−0.684880 + 0.728656i \(0.740145\pi\)
\(948\) 0 0
\(949\) −55.7231 + 316.021i −0.0587177 + 0.333004i
\(950\) 69.6860 + 257.024i 0.0733536 + 0.270552i
\(951\) 0 0
\(952\) −633.642 49.7678i −0.665591 0.0522771i
\(953\) −386.808 669.970i −0.405884 0.703012i 0.588540 0.808468i \(-0.299703\pi\)
−0.994424 + 0.105456i \(0.966370\pi\)
\(954\) 0 0
\(955\) −215.985 124.699i −0.226163 0.130575i
\(956\) 352.283 618.606i 0.368497 0.647078i
\(957\) 0 0
\(958\) −726.661 + 730.978i −0.758519 + 0.763025i
\(959\) 204.301 243.477i 0.213036 0.253886i
\(960\) 0 0
\(961\) −215.294 78.3605i −0.224031 0.0815406i
\(962\) 105.118 151.074i 0.109270 0.157041i
\(963\) 0 0
\(964\) −113.014 304.871i −0.117234 0.316256i
\(965\) 242.940 + 1377.78i 0.251752 + 1.42775i
\(966\) 0 0
\(967\) −401.660 1103.55i −0.415367 1.14121i −0.954297 0.298861i \(-0.903393\pi\)
0.538929 0.842351i \(-0.318829\pi\)
\(968\) −489.541 + 1074.65i −0.505724 + 1.11018i
\(969\) 0 0
\(970\) −511.916 + 360.711i −0.527748 + 0.371867i
\(971\) 1571.76i 1.61870i −0.587324 0.809352i \(-0.699819\pi\)
0.587324 0.809352i \(-0.300181\pi\)
\(972\) 0 0
\(973\) −155.404 −0.159716
\(974\) −366.910 520.712i −0.376704 0.534612i
\(975\) 0 0
\(976\) 721.294 1284.22i 0.739031 1.31579i
\(977\) 1382.71 503.263i 1.41526 0.515111i 0.482588 0.875847i \(-0.339697\pi\)
0.932668 + 0.360736i \(0.117475\pi\)
\(978\) 0 0
\(979\) 2840.61 500.877i 2.90154 0.511621i
\(980\) −544.029 1467.60i −0.555132 1.49755i
\(981\) 0 0
\(982\) 1386.75 + 964.904i 1.41217 + 0.982591i
\(983\) −1.95433 + 5.36948i −0.00198813 + 0.00546233i −0.940683 0.339288i \(-0.889814\pi\)
0.938695 + 0.344750i \(0.112036\pi\)
\(984\) 0 0
\(985\) −1405.92 1179.71i −1.42733 1.19768i
\(986\) −202.814 201.616i −0.205694 0.204479i
\(987\) 0 0
\(988\) −40.5048 + 71.1261i −0.0409968 + 0.0719900i
\(989\) −525.725 + 910.583i −0.531573 + 0.920711i
\(990\) 0 0
\(991\) 1320.59 762.444i 1.33258 0.769368i 0.346889 0.937906i \(-0.387238\pi\)
0.985695 + 0.168538i \(0.0539047\pi\)
\(992\) −839.438 211.655i −0.846208 0.213362i
\(993\) 0 0
\(994\) 1050.75 284.886i 1.05709 0.286606i
\(995\) −2673.46 471.404i −2.68690 0.473773i
\(996\) 0 0
\(997\) 629.178 527.943i 0.631071 0.529532i −0.270190 0.962807i \(-0.587087\pi\)
0.901262 + 0.433275i \(0.142642\pi\)
\(998\) 41.7147 493.635i 0.0417983 0.494624i
\(999\) 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 324.3.j.a.199.28 204
3.2 odd 2 108.3.j.a.103.7 yes 204
4.3 odd 2 inner 324.3.j.a.199.26 204
12.11 even 2 108.3.j.a.103.9 yes 204
27.11 odd 18 108.3.j.a.43.9 yes 204
27.16 even 9 inner 324.3.j.a.127.26 204
108.11 even 18 108.3.j.a.43.7 204
108.43 odd 18 inner 324.3.j.a.127.28 204
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
108.3.j.a.43.7 204 108.11 even 18
108.3.j.a.43.9 yes 204 27.11 odd 18
108.3.j.a.103.7 yes 204 3.2 odd 2
108.3.j.a.103.9 yes 204 12.11 even 2
324.3.j.a.127.26 204 27.16 even 9 inner
324.3.j.a.127.28 204 108.43 odd 18 inner
324.3.j.a.199.26 204 4.3 odd 2 inner
324.3.j.a.199.28 204 1.1 even 1 trivial