Properties

Label 405.3.l.l.28.3
Level $405$
Weight $3$
Character 405.28
Analytic conductor $11.035$
Analytic rank $0$
Dimension $16$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [405,3,Mod(28,405)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(405, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([4, 9]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("405.28");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 405.l (of order \(12\), degree \(4\), 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: \(11.0354507066\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 2 x^{15} + 2 x^{14} - 36 x^{13} - 109 x^{12} + 482 x^{11} - 98 x^{10} + 3204 x^{9} + \cdots + 2560000 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 28.3
Root \(2.05601 + 0.550907i\) of defining polynomial
Character \(\chi\) \(=\) 405.28
Dual form 405.3.l.l.217.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.05601 + 0.550907i) q^{2} +(0.459586 + 0.265342i) q^{4} +(2.92464 - 4.05542i) q^{5} +(-6.15409 - 1.64898i) q^{7} +(-5.22169 - 5.22169i) q^{8} +O(q^{10})\) \(q+(2.05601 + 0.550907i) q^{2} +(0.459586 + 0.265342i) q^{4} +(2.92464 - 4.05542i) q^{5} +(-6.15409 - 1.64898i) q^{7} +(-5.22169 - 5.22169i) q^{8} +(8.24726 - 6.72679i) q^{10} +(-7.02282 - 12.1639i) q^{11} +(-10.6178 + 2.84504i) q^{13} +(-11.7444 - 6.78066i) q^{14} +(-8.92056 - 15.4509i) q^{16} +(-15.7268 + 15.7268i) q^{17} +15.5354i q^{19} +(2.42020 - 1.08778i) q^{20} +(-7.73784 - 28.8780i) q^{22} +(15.4129 - 4.12988i) q^{23} +(-7.89291 - 23.7213i) q^{25} -23.3977 q^{26} +(-2.39079 - 2.39079i) q^{28} +(29.8158 - 17.2141i) q^{29} +(24.7090 - 42.7973i) q^{31} +(-2.18371 - 8.14971i) q^{32} +(-40.9985 + 23.6705i) q^{34} +(-24.6858 + 20.1347i) q^{35} +(22.8392 - 22.8392i) q^{37} +(-8.55854 + 31.9409i) q^{38} +(-36.4477 + 5.90457i) q^{40} +(0.283471 - 0.490987i) q^{41} +(-0.142904 + 0.533325i) q^{43} -7.45379i q^{44} +33.9644 q^{46} +(31.3977 + 8.41300i) q^{47} +(-7.28159 - 4.20403i) q^{49} +(-3.15966 - 53.1196i) q^{50} +(-5.63471 - 1.50982i) q^{52} +(45.4430 + 45.4430i) q^{53} +(-69.8689 - 7.09452i) q^{55} +(23.5242 + 40.7452i) q^{56} +(70.7849 - 18.9668i) q^{58} +(-39.4795 - 22.7935i) q^{59} +(-6.18147 - 10.7066i) q^{61} +(74.3794 - 74.3794i) q^{62} +53.4055i q^{64} +(-19.5155 + 51.3805i) q^{65} +(-31.4421 - 117.344i) q^{67} +(-11.4008 + 3.05483i) q^{68} +(-61.8468 + 27.7977i) q^{70} +48.1581 q^{71} +(-77.4961 - 77.4961i) q^{73} +(59.5400 - 34.3754i) q^{74} +(-4.12219 + 7.13983i) q^{76} +(23.1610 + 86.4381i) q^{77} +(114.870 - 66.3203i) q^{79} +(-88.7492 - 9.01164i) q^{80} +(0.853308 - 0.853308i) q^{82} +(-25.3200 + 94.4956i) q^{83} +(17.7835 + 109.774i) q^{85} +(-0.587625 + 1.01780i) q^{86} +(-26.8450 + 100.187i) q^{88} +119.880i q^{89} +70.0345 q^{91} +(8.17940 + 2.19166i) q^{92} +(59.9193 + 34.5944i) q^{94} +(63.0025 + 45.4354i) q^{95} +(71.5242 + 19.1648i) q^{97} +(-12.6550 - 12.6550i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 2 q^{2} + 2 q^{5} - 26 q^{7} + 72 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 2 q^{2} + 2 q^{5} - 26 q^{7} + 72 q^{8} + 52 q^{10} - 20 q^{11} + 28 q^{13} + 76 q^{16} - 76 q^{17} + 12 q^{20} - 10 q^{22} + 68 q^{23} - 128 q^{25} - 248 q^{26} - 280 q^{28} + 116 q^{31} - 232 q^{32} - 28 q^{35} + 100 q^{37} + 66 q^{38} - 228 q^{40} + 316 q^{41} + 34 q^{43} - 16 q^{46} + 302 q^{47} - 22 q^{50} + 28 q^{52} + 236 q^{53} + 332 q^{55} - 420 q^{56} + 318 q^{58} - 112 q^{61} + 580 q^{62} - 112 q^{65} - 8 q^{67} + 76 q^{68} - 168 q^{70} + 496 q^{71} + 148 q^{73} + 48 q^{76} - 50 q^{77} - 1672 q^{80} + 44 q^{82} + 302 q^{83} - 86 q^{85} - 380 q^{86} + 636 q^{88} - 88 q^{91} + 416 q^{92} - 102 q^{95} + 178 q^{97} + 748 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.05601 + 0.550907i 1.02801 + 0.275453i 0.733135 0.680084i \(-0.238057\pi\)
0.294871 + 0.955537i \(0.404723\pi\)
\(3\) 0 0
\(4\) 0.459586 + 0.265342i 0.114896 + 0.0663355i
\(5\) 2.92464 4.05542i 0.584929 0.811085i
\(6\) 0 0
\(7\) −6.15409 1.64898i −0.879155 0.235569i −0.209113 0.977892i \(-0.567058\pi\)
−0.670043 + 0.742323i \(0.733724\pi\)
\(8\) −5.22169 5.22169i −0.652711 0.652711i
\(9\) 0 0
\(10\) 8.24726 6.72679i 0.824726 0.672679i
\(11\) −7.02282 12.1639i −0.638438 1.10581i −0.985776 0.168067i \(-0.946248\pi\)
0.347338 0.937740i \(-0.387086\pi\)
\(12\) 0 0
\(13\) −10.6178 + 2.84504i −0.816756 + 0.218849i −0.642928 0.765927i \(-0.722280\pi\)
−0.173828 + 0.984776i \(0.555614\pi\)
\(14\) −11.7444 6.78066i −0.838889 0.484333i
\(15\) 0 0
\(16\) −8.92056 15.4509i −0.557535 0.965678i
\(17\) −15.7268 + 15.7268i −0.925105 + 0.925105i −0.997384 0.0722791i \(-0.976973\pi\)
0.0722791 + 0.997384i \(0.476973\pi\)
\(18\) 0 0
\(19\) 15.5354i 0.817651i 0.912613 + 0.408826i \(0.134062\pi\)
−0.912613 + 0.408826i \(0.865938\pi\)
\(20\) 2.42020 1.08778i 0.121010 0.0543892i
\(21\) 0 0
\(22\) −7.73784 28.8780i −0.351720 1.31264i
\(23\) 15.4129 4.12988i 0.670128 0.179560i 0.0923154 0.995730i \(-0.470573\pi\)
0.577812 + 0.816170i \(0.303907\pi\)
\(24\) 0 0
\(25\) −7.89291 23.7213i −0.315716 0.948854i
\(26\) −23.3977 −0.899913
\(27\) 0 0
\(28\) −2.39079 2.39079i −0.0853852 0.0853852i
\(29\) 29.8158 17.2141i 1.02813 0.593591i 0.111681 0.993744i \(-0.464376\pi\)
0.916448 + 0.400153i \(0.131043\pi\)
\(30\) 0 0
\(31\) 24.7090 42.7973i 0.797065 1.38056i −0.124454 0.992225i \(-0.539718\pi\)
0.921519 0.388332i \(-0.126949\pi\)
\(32\) −2.18371 8.14971i −0.0682409 0.254679i
\(33\) 0 0
\(34\) −40.9985 + 23.6705i −1.20584 + 0.696190i
\(35\) −24.6858 + 20.1347i −0.705310 + 0.575278i
\(36\) 0 0
\(37\) 22.8392 22.8392i 0.617276 0.617276i −0.327556 0.944832i \(-0.606225\pi\)
0.944832 + 0.327556i \(0.106225\pi\)
\(38\) −8.55854 + 31.9409i −0.225225 + 0.840550i
\(39\) 0 0
\(40\) −36.4477 + 5.90457i −0.911193 + 0.147614i
\(41\) 0.283471 0.490987i 0.00691393 0.0119753i −0.862548 0.505976i \(-0.831133\pi\)
0.869462 + 0.494000i \(0.164466\pi\)
\(42\) 0 0
\(43\) −0.142904 + 0.533325i −0.00332335 + 0.0124029i −0.967568 0.252612i \(-0.918710\pi\)
0.964244 + 0.265015i \(0.0853770\pi\)
\(44\) 7.45379i 0.169404i
\(45\) 0 0
\(46\) 33.9644 0.738356
\(47\) 31.3977 + 8.41300i 0.668037 + 0.179000i 0.576870 0.816836i \(-0.304274\pi\)
0.0911665 + 0.995836i \(0.470940\pi\)
\(48\) 0 0
\(49\) −7.28159 4.20403i −0.148604 0.0857965i
\(50\) −3.15966 53.1196i −0.0631933 1.06239i
\(51\) 0 0
\(52\) −5.63471 1.50982i −0.108360 0.0290349i
\(53\) 45.4430 + 45.4430i 0.857415 + 0.857415i 0.991033 0.133618i \(-0.0426594\pi\)
−0.133618 + 0.991033i \(0.542659\pi\)
\(54\) 0 0
\(55\) −69.8689 7.09452i −1.27034 0.128991i
\(56\) 23.5242 + 40.7452i 0.420076 + 0.727593i
\(57\) 0 0
\(58\) 70.7849 18.9668i 1.22043 0.327013i
\(59\) −39.4795 22.7935i −0.669145 0.386331i 0.126608 0.991953i \(-0.459591\pi\)
−0.795753 + 0.605622i \(0.792924\pi\)
\(60\) 0 0
\(61\) −6.18147 10.7066i −0.101336 0.175518i 0.810900 0.585185i \(-0.198978\pi\)
−0.912235 + 0.409667i \(0.865645\pi\)
\(62\) 74.3794 74.3794i 1.19967 1.19967i
\(63\) 0 0
\(64\) 53.4055i 0.834461i
\(65\) −19.5155 + 51.3805i −0.300239 + 0.790469i
\(66\) 0 0
\(67\) −31.4421 117.344i −0.469286 1.75140i −0.642275 0.766475i \(-0.722009\pi\)
0.172989 0.984924i \(-0.444657\pi\)
\(68\) −11.4008 + 3.05483i −0.167659 + 0.0449240i
\(69\) 0 0
\(70\) −61.8468 + 27.7977i −0.883525 + 0.397110i
\(71\) 48.1581 0.678282 0.339141 0.940735i \(-0.389864\pi\)
0.339141 + 0.940735i \(0.389864\pi\)
\(72\) 0 0
\(73\) −77.4961 77.4961i −1.06159 1.06159i −0.997974 0.0636162i \(-0.979737\pi\)
−0.0636162 0.997974i \(-0.520263\pi\)
\(74\) 59.5400 34.3754i 0.804594 0.464533i
\(75\) 0 0
\(76\) −4.12219 + 7.13983i −0.0542393 + 0.0939452i
\(77\) 23.1610 + 86.4381i 0.300792 + 1.12257i
\(78\) 0 0
\(79\) 114.870 66.3203i 1.45405 0.839497i 0.455344 0.890316i \(-0.349516\pi\)
0.998708 + 0.0508186i \(0.0161830\pi\)
\(80\) −88.7492 9.01164i −1.10937 0.112645i
\(81\) 0 0
\(82\) 0.853308 0.853308i 0.0104062 0.0104062i
\(83\) −25.3200 + 94.4956i −0.305060 + 1.13850i 0.627833 + 0.778348i \(0.283942\pi\)
−0.932893 + 0.360153i \(0.882724\pi\)
\(84\) 0 0
\(85\) 17.7835 + 109.774i 0.209218 + 1.29146i
\(86\) −0.587625 + 1.01780i −0.00683285 + 0.0118348i
\(87\) 0 0
\(88\) −26.8450 + 100.187i −0.305057 + 1.13849i
\(89\) 119.880i 1.34697i 0.739202 + 0.673484i \(0.235203\pi\)
−0.739202 + 0.673484i \(0.764797\pi\)
\(90\) 0 0
\(91\) 70.0345 0.769610
\(92\) 8.17940 + 2.19166i 0.0889065 + 0.0238224i
\(93\) 0 0
\(94\) 59.9193 + 34.5944i 0.637440 + 0.368026i
\(95\) 63.0025 + 45.4354i 0.663184 + 0.478268i
\(96\) 0 0
\(97\) 71.5242 + 19.1648i 0.737362 + 0.197576i 0.607906 0.794009i \(-0.292010\pi\)
0.129457 + 0.991585i \(0.458677\pi\)
\(98\) −12.6550 12.6550i −0.129133 0.129133i
\(99\) 0 0
\(100\) 2.66680 12.9963i 0.0266680 0.129963i
\(101\) −90.3436 156.480i −0.894491 1.54930i −0.834433 0.551109i \(-0.814205\pi\)
−0.0600581 0.998195i \(-0.519129\pi\)
\(102\) 0 0
\(103\) −76.0198 + 20.3694i −0.738056 + 0.197761i −0.608214 0.793773i \(-0.708114\pi\)
−0.129842 + 0.991535i \(0.541447\pi\)
\(104\) 70.2989 + 40.5871i 0.675951 + 0.390260i
\(105\) 0 0
\(106\) 68.3965 + 118.466i 0.645250 + 1.11761i
\(107\) 61.3219 61.3219i 0.573102 0.573102i −0.359892 0.932994i \(-0.617187\pi\)
0.932994 + 0.359892i \(0.117187\pi\)
\(108\) 0 0
\(109\) 202.258i 1.85557i 0.373110 + 0.927787i \(0.378291\pi\)
−0.373110 + 0.927787i \(0.621709\pi\)
\(110\) −139.743 53.0777i −1.27039 0.482524i
\(111\) 0 0
\(112\) 29.4197 + 109.796i 0.262676 + 0.980319i
\(113\) −108.734 + 29.1353i −0.962252 + 0.257835i −0.705553 0.708657i \(-0.749301\pi\)
−0.256699 + 0.966491i \(0.582635\pi\)
\(114\) 0 0
\(115\) 28.3289 74.5844i 0.246339 0.648560i
\(116\) 18.2705 0.157505
\(117\) 0 0
\(118\) −68.6133 68.6133i −0.581469 0.581469i
\(119\) 122.717 70.8509i 1.03124 0.595385i
\(120\) 0 0
\(121\) −38.1399 + 66.0603i −0.315206 + 0.545953i
\(122\) −6.81083 25.4184i −0.0558265 0.208347i
\(123\) 0 0
\(124\) 22.7118 13.1127i 0.183160 0.105747i
\(125\) −119.284 37.3674i −0.954272 0.298939i
\(126\) 0 0
\(127\) 8.86658 8.86658i 0.0698156 0.0698156i −0.671337 0.741152i \(-0.734280\pi\)
0.741152 + 0.671337i \(0.234280\pi\)
\(128\) −38.1563 + 142.401i −0.298096 + 1.11251i
\(129\) 0 0
\(130\) −68.4301 + 94.8877i −0.526385 + 0.729906i
\(131\) −11.4127 + 19.7674i −0.0871198 + 0.150896i −0.906293 0.422651i \(-0.861100\pi\)
0.819173 + 0.573547i \(0.194433\pi\)
\(132\) 0 0
\(133\) 25.6176 95.6060i 0.192613 0.718842i
\(134\) 258.582i 1.92971i
\(135\) 0 0
\(136\) 164.241 1.20765
\(137\) −80.6238 21.6031i −0.588495 0.157687i −0.0477295 0.998860i \(-0.515199\pi\)
−0.540765 + 0.841174i \(0.681865\pi\)
\(138\) 0 0
\(139\) 101.699 + 58.7157i 0.731644 + 0.422415i 0.819023 0.573760i \(-0.194516\pi\)
−0.0873791 + 0.996175i \(0.527849\pi\)
\(140\) −16.6879 + 2.70345i −0.119199 + 0.0193103i
\(141\) 0 0
\(142\) 99.0135 + 26.5306i 0.697278 + 0.186835i
\(143\) 109.174 + 109.174i 0.763453 + 0.763453i
\(144\) 0 0
\(145\) 17.3899 171.261i 0.119930 1.18111i
\(146\) −116.640 202.026i −0.798903 1.38374i
\(147\) 0 0
\(148\) 16.5568 4.43637i 0.111870 0.0299755i
\(149\) −94.4712 54.5429i −0.634035 0.366060i 0.148278 0.988946i \(-0.452627\pi\)
−0.782313 + 0.622886i \(0.785960\pi\)
\(150\) 0 0
\(151\) −94.5773 163.813i −0.626340 1.08485i −0.988280 0.152651i \(-0.951219\pi\)
0.361940 0.932201i \(-0.382114\pi\)
\(152\) 81.1208 81.1208i 0.533690 0.533690i
\(153\) 0 0
\(154\) 190.477i 1.23687i
\(155\) −101.296 225.372i −0.653522 1.45402i
\(156\) 0 0
\(157\) 31.7599 + 118.529i 0.202292 + 0.754965i 0.990258 + 0.139246i \(0.0444677\pi\)
−0.787966 + 0.615719i \(0.788866\pi\)
\(158\) 272.711 73.0726i 1.72602 0.462485i
\(159\) 0 0
\(160\) −39.4371 14.9792i −0.246482 0.0936197i
\(161\) −101.663 −0.631445
\(162\) 0 0
\(163\) −55.2937 55.2937i −0.339225 0.339225i 0.516851 0.856076i \(-0.327104\pi\)
−0.856076 + 0.516851i \(0.827104\pi\)
\(164\) 0.260559 0.150434i 0.00158877 0.000917278i
\(165\) 0 0
\(166\) −104.117 + 180.335i −0.627208 + 1.08636i
\(167\) 34.4299 + 128.494i 0.206167 + 0.769426i 0.989091 + 0.147308i \(0.0470608\pi\)
−0.782924 + 0.622118i \(0.786272\pi\)
\(168\) 0 0
\(169\) −41.7142 + 24.0837i −0.246830 + 0.142507i
\(170\) −23.9122 + 235.494i −0.140660 + 1.38526i
\(171\) 0 0
\(172\) −0.207190 + 0.207190i −0.00120459 + 0.00120459i
\(173\) −8.52392 + 31.8117i −0.0492712 + 0.183883i −0.986176 0.165703i \(-0.947011\pi\)
0.936905 + 0.349585i \(0.113678\pi\)
\(174\) 0 0
\(175\) 9.45755 + 158.998i 0.0540432 + 0.908563i
\(176\) −125.295 + 217.017i −0.711903 + 1.23305i
\(177\) 0 0
\(178\) −66.0428 + 246.475i −0.371027 + 1.38469i
\(179\) 133.416i 0.745343i −0.927963 0.372672i \(-0.878442\pi\)
0.927963 0.372672i \(-0.121558\pi\)
\(180\) 0 0
\(181\) −118.379 −0.654028 −0.327014 0.945020i \(-0.606042\pi\)
−0.327014 + 0.945020i \(0.606042\pi\)
\(182\) 143.992 + 38.5825i 0.791163 + 0.211992i
\(183\) 0 0
\(184\) −102.046 58.9166i −0.554600 0.320199i
\(185\) −25.8261 159.419i −0.139600 0.861726i
\(186\) 0 0
\(187\) 301.745 + 80.8524i 1.61361 + 0.432366i
\(188\) 12.1976 + 12.1976i 0.0648810 + 0.0648810i
\(189\) 0 0
\(190\) 104.503 + 128.124i 0.550017 + 0.674339i
\(191\) 71.3161 + 123.523i 0.373383 + 0.646718i 0.990084 0.140480i \(-0.0448644\pi\)
−0.616701 + 0.787198i \(0.711531\pi\)
\(192\) 0 0
\(193\) 172.858 46.3171i 0.895636 0.239985i 0.218495 0.975838i \(-0.429885\pi\)
0.677141 + 0.735853i \(0.263219\pi\)
\(194\) 136.496 + 78.8063i 0.703590 + 0.406218i
\(195\) 0 0
\(196\) −2.23101 3.86422i −0.0113827 0.0197154i
\(197\) 45.6222 45.6222i 0.231585 0.231585i −0.581769 0.813354i \(-0.697639\pi\)
0.813354 + 0.581769i \(0.197639\pi\)
\(198\) 0 0
\(199\) 328.469i 1.65060i −0.564694 0.825300i \(-0.691006\pi\)
0.564694 0.825300i \(-0.308994\pi\)
\(200\) −82.6511 + 165.080i −0.413256 + 0.825398i
\(201\) 0 0
\(202\) −99.5418 371.495i −0.492781 1.83908i
\(203\) −211.875 + 56.7716i −1.04372 + 0.279663i
\(204\) 0 0
\(205\) −1.16211 2.58556i −0.00566881 0.0126125i
\(206\) −167.519 −0.813200
\(207\) 0 0
\(208\) 138.675 + 138.675i 0.666708 + 0.666708i
\(209\) 188.970 109.102i 0.904164 0.522019i
\(210\) 0 0
\(211\) 146.953 254.531i 0.696461 1.20631i −0.273225 0.961950i \(-0.588090\pi\)
0.969686 0.244356i \(-0.0785764\pi\)
\(212\) 8.82702 + 32.9429i 0.0416369 + 0.155391i
\(213\) 0 0
\(214\) 159.861 92.2959i 0.747015 0.431289i
\(215\) 1.74492 + 2.13932i 0.00811589 + 0.00995034i
\(216\) 0 0
\(217\) −222.634 + 222.634i −1.02596 + 1.02596i
\(218\) −111.425 + 415.844i −0.511124 + 1.90754i
\(219\) 0 0
\(220\) −30.2283 21.7997i −0.137401 0.0990895i
\(221\) 122.241 211.728i 0.553127 0.958044i
\(222\) 0 0
\(223\) −45.2387 + 168.833i −0.202864 + 0.757099i 0.787226 + 0.616665i \(0.211516\pi\)
−0.990090 + 0.140434i \(0.955150\pi\)
\(224\) 53.7550i 0.239977i
\(225\) 0 0
\(226\) −239.610 −1.06022
\(227\) 174.790 + 46.8349i 0.770002 + 0.206321i 0.622372 0.782721i \(-0.286169\pi\)
0.147629 + 0.989043i \(0.452836\pi\)
\(228\) 0 0
\(229\) −255.131 147.300i −1.11411 0.643232i −0.174219 0.984707i \(-0.555740\pi\)
−0.939891 + 0.341475i \(0.889073\pi\)
\(230\) 99.3337 137.740i 0.431886 0.598869i
\(231\) 0 0
\(232\) −245.575 65.8017i −1.05851 0.283628i
\(233\) 297.567 + 297.567i 1.27711 + 1.27711i 0.942278 + 0.334832i \(0.108680\pi\)
0.334832 + 0.942278i \(0.391320\pi\)
\(234\) 0 0
\(235\) 125.945 102.726i 0.535938 0.437132i
\(236\) −12.0962 20.9512i −0.0512549 0.0887761i
\(237\) 0 0
\(238\) 291.340 78.0644i 1.22412 0.328002i
\(239\) −7.15486 4.13086i −0.0299366 0.0172839i 0.484957 0.874538i \(-0.338835\pi\)
−0.514894 + 0.857254i \(0.672169\pi\)
\(240\) 0 0
\(241\) −90.0470 155.966i −0.373639 0.647162i 0.616483 0.787368i \(-0.288557\pi\)
−0.990122 + 0.140206i \(0.955223\pi\)
\(242\) −114.809 + 114.809i −0.474418 + 0.474418i
\(243\) 0 0
\(244\) 6.56081i 0.0268886i
\(245\) −38.3452 + 17.2346i −0.156511 + 0.0703454i
\(246\) 0 0
\(247\) −44.1987 164.952i −0.178942 0.667822i
\(248\) −352.497 + 94.4512i −1.42136 + 0.380852i
\(249\) 0 0
\(250\) −224.663 142.542i −0.898654 0.570169i
\(251\) 162.440 0.647170 0.323585 0.946199i \(-0.395112\pi\)
0.323585 + 0.946199i \(0.395112\pi\)
\(252\) 0 0
\(253\) −158.478 158.478i −0.626394 0.626394i
\(254\) 23.1145 13.3451i 0.0910018 0.0525399i
\(255\) 0 0
\(256\) −50.0886 + 86.7560i −0.195659 + 0.338891i
\(257\) −45.7352 170.686i −0.177958 0.664148i −0.996029 0.0890309i \(-0.971623\pi\)
0.818071 0.575117i \(-0.195044\pi\)
\(258\) 0 0
\(259\) −178.216 + 102.893i −0.688093 + 0.397270i
\(260\) −22.6025 + 18.4355i −0.0869326 + 0.0709056i
\(261\) 0 0
\(262\) −34.3546 + 34.3546i −0.131124 + 0.131124i
\(263\) 23.4884 87.6600i 0.0893096 0.333308i −0.906786 0.421592i \(-0.861472\pi\)
0.996095 + 0.0882837i \(0.0281382\pi\)
\(264\) 0 0
\(265\) 317.195 51.3860i 1.19696 0.193909i
\(266\) 105.340 182.454i 0.396015 0.685918i
\(267\) 0 0
\(268\) 16.6858 62.2724i 0.0622606 0.232360i
\(269\) 415.479i 1.54453i −0.635301 0.772265i \(-0.719124\pi\)
0.635301 0.772265i \(-0.280876\pi\)
\(270\) 0 0
\(271\) 164.446 0.606811 0.303405 0.952862i \(-0.401876\pi\)
0.303405 + 0.952862i \(0.401876\pi\)
\(272\) 383.284 + 102.701i 1.40913 + 0.377576i
\(273\) 0 0
\(274\) −153.862 88.8323i −0.561541 0.324206i
\(275\) −233.113 + 262.599i −0.847684 + 0.954905i
\(276\) 0 0
\(277\) −299.886 80.3543i −1.08262 0.290088i −0.326952 0.945041i \(-0.606022\pi\)
−0.755669 + 0.654953i \(0.772688\pi\)
\(278\) 176.747 + 176.747i 0.635779 + 0.635779i
\(279\) 0 0
\(280\) 234.039 + 23.7644i 0.835854 + 0.0848730i
\(281\) 221.587 + 383.800i 0.788566 + 1.36584i 0.926845 + 0.375443i \(0.122509\pi\)
−0.138279 + 0.990393i \(0.544157\pi\)
\(282\) 0 0
\(283\) 15.2414 4.08392i 0.0538565 0.0144308i −0.231790 0.972766i \(-0.574458\pi\)
0.285647 + 0.958335i \(0.407792\pi\)
\(284\) 22.1328 + 12.7784i 0.0779322 + 0.0449942i
\(285\) 0 0
\(286\) 164.318 + 284.607i 0.574539 + 0.995130i
\(287\) −2.55414 + 2.55414i −0.00889943 + 0.00889943i
\(288\) 0 0
\(289\) 205.664i 0.711640i
\(290\) 130.103 342.534i 0.448629 1.18115i
\(291\) 0 0
\(292\) −15.0531 56.1791i −0.0515518 0.192394i
\(293\) 335.831 89.9857i 1.14618 0.307119i 0.364748 0.931106i \(-0.381155\pi\)
0.781434 + 0.623988i \(0.214489\pi\)
\(294\) 0 0
\(295\) −207.901 + 93.4433i −0.704749 + 0.316757i
\(296\) −238.518 −0.805805
\(297\) 0 0
\(298\) −164.186 164.186i −0.550959 0.550959i
\(299\) −151.902 + 87.7008i −0.508034 + 0.293314i
\(300\) 0 0
\(301\) 1.75889 3.04648i 0.00584348 0.0101212i
\(302\) −104.207 388.904i −0.345055 1.28776i
\(303\) 0 0
\(304\) 240.035 138.584i 0.789588 0.455869i
\(305\) −61.4985 6.24459i −0.201634 0.0204741i
\(306\) 0 0
\(307\) 48.6485 48.6485i 0.158464 0.158464i −0.623422 0.781886i \(-0.714258\pi\)
0.781886 + 0.623422i \(0.214258\pi\)
\(308\) −12.2912 + 45.8713i −0.0399064 + 0.148933i
\(309\) 0 0
\(310\) −84.1066 519.173i −0.271311 1.67475i
\(311\) 155.769 269.800i 0.500866 0.867525i −0.499134 0.866525i \(-0.666348\pi\)
1.00000 0.000999981i \(-0.000318304\pi\)
\(312\) 0 0
\(313\) 26.8749 100.298i 0.0858623 0.320442i −0.909614 0.415455i \(-0.863622\pi\)
0.995476 + 0.0950125i \(0.0302891\pi\)
\(314\) 261.195i 0.831830i
\(315\) 0 0
\(316\) 70.3902 0.222754
\(317\) 277.411 + 74.3321i 0.875114 + 0.234486i 0.668298 0.743894i \(-0.267023\pi\)
0.206816 + 0.978380i \(0.433690\pi\)
\(318\) 0 0
\(319\) −418.781 241.783i −1.31279 0.757942i
\(320\) 216.582 + 156.192i 0.676818 + 0.488100i
\(321\) 0 0
\(322\) −209.020 56.0067i −0.649130 0.173934i
\(323\) −244.322 244.322i −0.756413 0.756413i
\(324\) 0 0
\(325\) 151.294 + 229.414i 0.465519 + 0.705888i
\(326\) −83.2228 144.146i −0.255285 0.442166i
\(327\) 0 0
\(328\) −4.04398 + 1.08358i −0.0123292 + 0.00330360i
\(329\) −179.352 103.549i −0.545141 0.314738i
\(330\) 0 0
\(331\) −196.224 339.870i −0.592822 1.02680i −0.993850 0.110732i \(-0.964680\pi\)
0.401028 0.916066i \(-0.368653\pi\)
\(332\) −36.7104 + 36.7104i −0.110573 + 0.110573i
\(333\) 0 0
\(334\) 283.153i 0.847764i
\(335\) −567.835 215.677i −1.69503 0.643813i
\(336\) 0 0
\(337\) 129.126 + 481.905i 0.383164 + 1.42999i 0.841041 + 0.540971i \(0.181943\pi\)
−0.457878 + 0.889015i \(0.651390\pi\)
\(338\) −99.0328 + 26.5358i −0.292997 + 0.0785082i
\(339\) 0 0
\(340\) −20.9546 + 55.1693i −0.0616312 + 0.162263i
\(341\) −694.108 −2.03551
\(342\) 0 0
\(343\) 258.629 + 258.629i 0.754021 + 0.754021i
\(344\) 3.53106 2.03866i 0.0102647 0.00592633i
\(345\) 0 0
\(346\) −35.0506 + 60.7094i −0.101302 + 0.175461i
\(347\) 10.1941 + 38.0448i 0.0293777 + 0.109639i 0.979058 0.203582i \(-0.0652584\pi\)
−0.949680 + 0.313221i \(0.898592\pi\)
\(348\) 0 0
\(349\) −64.7685 + 37.3941i −0.185583 + 0.107147i −0.589913 0.807467i \(-0.700838\pi\)
0.404330 + 0.914613i \(0.367505\pi\)
\(350\) −68.1485 + 332.113i −0.194710 + 0.948894i
\(351\) 0 0
\(352\) −83.7963 + 83.7963i −0.238058 + 0.238058i
\(353\) 10.9753 40.9602i 0.0310914 0.116035i −0.948636 0.316369i \(-0.897536\pi\)
0.979728 + 0.200334i \(0.0642029\pi\)
\(354\) 0 0
\(355\) 140.845 195.301i 0.396747 0.550144i
\(356\) −31.8092 + 55.0952i −0.0893518 + 0.154762i
\(357\) 0 0
\(358\) 73.5000 274.306i 0.205307 0.766217i
\(359\) 138.605i 0.386086i 0.981190 + 0.193043i \(0.0618357\pi\)
−0.981190 + 0.193043i \(0.938164\pi\)
\(360\) 0 0
\(361\) 119.652 0.331447
\(362\) −243.389 65.2158i −0.672344 0.180154i
\(363\) 0 0
\(364\) 32.1868 + 18.5831i 0.0884254 + 0.0510524i
\(365\) −540.928 + 87.6309i −1.48199 + 0.240085i
\(366\) 0 0
\(367\) 239.063 + 64.0568i 0.651399 + 0.174542i 0.569361 0.822087i \(-0.307191\pi\)
0.0820377 + 0.996629i \(0.473857\pi\)
\(368\) −201.302 201.302i −0.547017 0.547017i
\(369\) 0 0
\(370\) 34.7264 341.996i 0.0938552 0.924313i
\(371\) −204.726 354.595i −0.551821 0.955782i
\(372\) 0 0
\(373\) −229.403 + 61.4683i −0.615021 + 0.164794i −0.552864 0.833272i \(-0.686465\pi\)
−0.0621579 + 0.998066i \(0.519798\pi\)
\(374\) 575.849 + 332.467i 1.53970 + 0.888949i
\(375\) 0 0
\(376\) −120.019 207.879i −0.319200 0.552870i
\(377\) −267.604 + 267.604i −0.709824 + 0.709824i
\(378\) 0 0
\(379\) 589.803i 1.55621i −0.628134 0.778105i \(-0.716181\pi\)
0.628134 0.778105i \(-0.283819\pi\)
\(380\) 16.8991 + 37.5987i 0.0444714 + 0.0989439i
\(381\) 0 0
\(382\) 78.5771 + 293.254i 0.205699 + 0.767680i
\(383\) −28.3616 + 7.59948i −0.0740513 + 0.0198420i −0.295654 0.955295i \(-0.595538\pi\)
0.221603 + 0.975137i \(0.428871\pi\)
\(384\) 0 0
\(385\) 418.281 + 158.873i 1.08644 + 0.412657i
\(386\) 380.914 0.986823
\(387\) 0 0
\(388\) 27.7862 + 27.7862i 0.0716140 + 0.0716140i
\(389\) 218.171 125.961i 0.560852 0.323808i −0.192636 0.981270i \(-0.561704\pi\)
0.753487 + 0.657463i \(0.228370\pi\)
\(390\) 0 0
\(391\) −177.446 + 307.346i −0.453827 + 0.786051i
\(392\) 16.0701 + 59.9743i 0.0409950 + 0.152996i
\(393\) 0 0
\(394\) 118.933 68.6662i 0.301861 0.174280i
\(395\) 66.9974 659.810i 0.169614 1.67040i
\(396\) 0 0
\(397\) −471.289 + 471.289i −1.18713 + 1.18713i −0.209269 + 0.977858i \(0.567108\pi\)
−0.977858 + 0.209269i \(0.932892\pi\)
\(398\) 180.956 675.337i 0.454663 1.69683i
\(399\) 0 0
\(400\) −296.106 + 333.560i −0.740265 + 0.833899i
\(401\) 22.2961 38.6179i 0.0556012 0.0963041i −0.836885 0.547379i \(-0.815626\pi\)
0.892486 + 0.451075i \(0.148959\pi\)
\(402\) 0 0
\(403\) −140.596 + 524.713i −0.348874 + 1.30202i
\(404\) 95.8878i 0.237346i
\(405\) 0 0
\(406\) −466.893 −1.14998
\(407\) −438.209 117.418i −1.07668 0.288496i
\(408\) 0 0
\(409\) −20.0292 11.5639i −0.0489712 0.0282735i 0.475315 0.879816i \(-0.342334\pi\)
−0.524286 + 0.851542i \(0.675668\pi\)
\(410\) −0.964902 5.95615i −0.00235342 0.0145272i
\(411\) 0 0
\(412\) −40.3425 10.8097i −0.0979186 0.0262372i
\(413\) 205.374 + 205.374i 0.497275 + 0.497275i
\(414\) 0 0
\(415\) 309.168 + 379.049i 0.744982 + 0.913372i
\(416\) 46.3725 + 80.3195i 0.111472 + 0.193076i
\(417\) 0 0
\(418\) 448.630 120.210i 1.07328 0.287584i
\(419\) 263.471 + 152.115i 0.628810 + 0.363043i 0.780291 0.625417i \(-0.215071\pi\)
−0.151481 + 0.988460i \(0.548404\pi\)
\(420\) 0 0
\(421\) −124.207 215.133i −0.295029 0.511005i 0.679963 0.733246i \(-0.261996\pi\)
−0.974992 + 0.222242i \(0.928663\pi\)
\(422\) 442.360 442.360i 1.04825 1.04825i
\(423\) 0 0
\(424\) 474.578i 1.11929i
\(425\) 497.191 + 248.930i 1.16986 + 0.585719i
\(426\) 0 0
\(427\) 20.3863 + 76.0826i 0.0477430 + 0.178179i
\(428\) 44.4539 11.9114i 0.103864 0.0278304i
\(429\) 0 0
\(430\) 2.40900 + 5.35976i 0.00560233 + 0.0124646i
\(431\) 553.040 1.28316 0.641578 0.767058i \(-0.278280\pi\)
0.641578 + 0.767058i \(0.278280\pi\)
\(432\) 0 0
\(433\) 257.444 + 257.444i 0.594560 + 0.594560i 0.938860 0.344300i \(-0.111884\pi\)
−0.344300 + 0.938860i \(0.611884\pi\)
\(434\) −580.388 + 335.087i −1.33730 + 0.772090i
\(435\) 0 0
\(436\) −53.6674 + 92.9547i −0.123090 + 0.213199i
\(437\) 64.1593 + 239.446i 0.146818 + 0.547931i
\(438\) 0 0
\(439\) 12.1098 6.99162i 0.0275851 0.0159262i −0.486144 0.873879i \(-0.661597\pi\)
0.513729 + 0.857952i \(0.328264\pi\)
\(440\) 327.788 + 401.879i 0.744973 + 0.913361i
\(441\) 0 0
\(442\) 367.971 367.971i 0.832514 0.832514i
\(443\) −10.8984 + 40.6733i −0.0246013 + 0.0918133i −0.977135 0.212620i \(-0.931800\pi\)
0.952534 + 0.304433i \(0.0984671\pi\)
\(444\) 0 0
\(445\) 486.165 + 350.607i 1.09251 + 0.787881i
\(446\) −186.022 + 322.200i −0.417091 + 0.722422i
\(447\) 0 0
\(448\) 88.0648 328.662i 0.196573 0.733621i
\(449\) 254.042i 0.565795i −0.959150 0.282898i \(-0.908704\pi\)
0.959150 0.282898i \(-0.0912957\pi\)
\(450\) 0 0
\(451\) −7.96307 −0.0176565
\(452\) −57.7036 15.4616i −0.127663 0.0342072i
\(453\) 0 0
\(454\) 333.569 + 192.586i 0.734734 + 0.424199i
\(455\) 204.826 284.019i 0.450167 0.624219i
\(456\) 0 0
\(457\) 325.593 + 87.2425i 0.712458 + 0.190903i 0.596804 0.802387i \(-0.296437\pi\)
0.115654 + 0.993290i \(0.463104\pi\)
\(458\) −443.404 443.404i −0.968131 0.968131i
\(459\) 0 0
\(460\) 32.8100 26.7611i 0.0713260 0.0581763i
\(461\) 289.085 + 500.709i 0.627082 + 1.08614i 0.988134 + 0.153592i \(0.0490841\pi\)
−0.361053 + 0.932545i \(0.617583\pi\)
\(462\) 0 0
\(463\) −270.741 + 72.5447i −0.584753 + 0.156684i −0.539054 0.842271i \(-0.681218\pi\)
−0.0456989 + 0.998955i \(0.514551\pi\)
\(464\) −531.946 307.119i −1.14644 0.661895i
\(465\) 0 0
\(466\) 447.869 + 775.732i 0.961092 + 1.66466i
\(467\) −377.215 + 377.215i −0.807740 + 0.807740i −0.984291 0.176551i \(-0.943506\pi\)
0.176551 + 0.984291i \(0.443506\pi\)
\(468\) 0 0
\(469\) 773.991i 1.65030i
\(470\) 315.538 141.822i 0.671357 0.301748i
\(471\) 0 0
\(472\) 87.1292 + 325.170i 0.184596 + 0.688920i
\(473\) 7.49089 2.00718i 0.0158370 0.00424351i
\(474\) 0 0
\(475\) 368.520 122.619i 0.775831 0.258146i
\(476\) 75.1988 0.157981
\(477\) 0 0
\(478\) −12.4348 12.4348i −0.0260141 0.0260141i
\(479\) −603.903 + 348.664i −1.26076 + 0.727899i −0.973221 0.229871i \(-0.926170\pi\)
−0.287537 + 0.957770i \(0.592836\pi\)
\(480\) 0 0
\(481\) −177.524 + 307.481i −0.369074 + 0.639254i
\(482\) −99.2150 370.276i −0.205840 0.768206i
\(483\) 0 0
\(484\) −35.0571 + 20.2402i −0.0724321 + 0.0418187i
\(485\) 286.904 234.010i 0.591555 0.482496i
\(486\) 0 0
\(487\) 369.496 369.496i 0.758718 0.758718i −0.217371 0.976089i \(-0.569748\pi\)
0.976089 + 0.217371i \(0.0697481\pi\)
\(488\) −23.6289 + 88.1843i −0.0484199 + 0.180706i
\(489\) 0 0
\(490\) −88.3328 + 14.3100i −0.180271 + 0.0292041i
\(491\) −55.5151 + 96.1550i −0.113065 + 0.195835i −0.917005 0.398876i \(-0.869400\pi\)
0.803939 + 0.594711i \(0.202734\pi\)
\(492\) 0 0
\(493\) −198.183 + 739.629i −0.401994 + 1.50026i
\(494\) 363.493i 0.735815i
\(495\) 0 0
\(496\) −881.673 −1.77757
\(497\) −296.369 79.4118i −0.596316 0.159782i
\(498\) 0 0
\(499\) 362.119 + 209.069i 0.725689 + 0.418977i 0.816843 0.576860i \(-0.195722\pi\)
−0.0911538 + 0.995837i \(0.529055\pi\)
\(500\) −44.9061 48.8246i −0.0898122 0.0976492i
\(501\) 0 0
\(502\) 333.978 + 89.4891i 0.665295 + 0.178265i
\(503\) 496.065 + 496.065i 0.986213 + 0.986213i 0.999906 0.0136937i \(-0.00435898\pi\)
−0.0136937 + 0.999906i \(0.504359\pi\)
\(504\) 0 0
\(505\) −898.814 91.2661i −1.77983 0.180725i
\(506\) −238.526 413.138i −0.471394 0.816479i
\(507\) 0 0
\(508\) 6.42763 1.72228i 0.0126528 0.00339031i
\(509\) 416.912 + 240.704i 0.819081 + 0.472897i 0.850099 0.526622i \(-0.176542\pi\)
−0.0310184 + 0.999519i \(0.509875\pi\)
\(510\) 0 0
\(511\) 349.128 + 604.708i 0.683225 + 1.18338i
\(512\) 266.203 266.203i 0.519927 0.519927i
\(513\) 0 0
\(514\) 376.129i 0.731768i
\(515\) −139.724 + 367.866i −0.271309 + 0.714302i
\(516\) 0 0
\(517\) −118.166 441.001i −0.228561 0.853000i
\(518\) −423.099 + 113.369i −0.816793 + 0.218859i
\(519\) 0 0
\(520\) 370.197 166.389i 0.711917 0.319979i
\(521\) 504.810 0.968925 0.484463 0.874812i \(-0.339015\pi\)
0.484463 + 0.874812i \(0.339015\pi\)
\(522\) 0 0
\(523\) 389.397 + 389.397i 0.744545 + 0.744545i 0.973449 0.228904i \(-0.0735143\pi\)
−0.228904 + 0.973449i \(0.573514\pi\)
\(524\) −10.4902 + 6.05653i −0.0200195 + 0.0115583i
\(525\) 0 0
\(526\) 96.5850 167.290i 0.183622 0.318042i
\(527\) 284.470 + 1061.66i 0.539792 + 2.01453i
\(528\) 0 0
\(529\) −237.625 + 137.193i −0.449196 + 0.259343i
\(530\) 680.466 + 69.0949i 1.28390 + 0.130368i
\(531\) 0 0
\(532\) 37.1418 37.1418i 0.0698153 0.0698153i
\(533\) −1.61297 + 6.01970i −0.00302622 + 0.0112940i
\(534\) 0 0
\(535\) −69.3414 428.031i −0.129610 0.800058i
\(536\) −448.551 + 776.913i −0.836849 + 1.44946i
\(537\) 0 0
\(538\) 228.890 854.229i 0.425446 1.58779i
\(539\) 118.096i 0.219103i
\(540\) 0 0
\(541\) −110.976 −0.205131 −0.102565 0.994726i \(-0.532705\pi\)
−0.102565 + 0.994726i \(0.532705\pi\)
\(542\) 338.102 + 90.5942i 0.623805 + 0.167148i
\(543\) 0 0
\(544\) 162.512 + 93.8261i 0.298735 + 0.172474i
\(545\) 820.240 + 591.531i 1.50503 + 1.08538i
\(546\) 0 0
\(547\) 210.140 + 56.3070i 0.384169 + 0.102938i 0.445734 0.895165i \(-0.352943\pi\)
−0.0615654 + 0.998103i \(0.519609\pi\)
\(548\) −31.3213 31.3213i −0.0571557 0.0571557i
\(549\) 0 0
\(550\) −623.951 + 411.483i −1.13446 + 0.748151i
\(551\) 267.428 + 463.199i 0.485350 + 0.840651i
\(552\) 0 0
\(553\) −816.282 + 218.722i −1.47610 + 0.395519i
\(554\) −572.302 330.419i −1.03304 0.596424i
\(555\) 0 0
\(556\) 31.1595 + 53.9698i 0.0560422 + 0.0970680i
\(557\) −416.448 + 416.448i −0.747662 + 0.747662i −0.974040 0.226378i \(-0.927312\pi\)
0.226378 + 0.974040i \(0.427312\pi\)
\(558\) 0 0
\(559\) 6.06932i 0.0108575i
\(560\) 531.310 + 201.804i 0.948769 + 0.360365i
\(561\) 0 0
\(562\) 244.148 + 911.171i 0.434426 + 1.62130i
\(563\) 739.834 198.238i 1.31409 0.352110i 0.467331 0.884082i \(-0.345216\pi\)
0.846762 + 0.531972i \(0.178549\pi\)
\(564\) 0 0
\(565\) −199.854 + 526.175i −0.353723 + 0.931283i
\(566\) 33.5864 0.0593398
\(567\) 0 0
\(568\) −251.466 251.466i −0.442722 0.442722i
\(569\) −1.55238 + 0.896268i −0.00272826 + 0.00157516i −0.501364 0.865237i \(-0.667168\pi\)
0.498635 + 0.866812i \(0.333835\pi\)
\(570\) 0 0
\(571\) 454.163 786.634i 0.795382 1.37764i −0.127214 0.991875i \(-0.540603\pi\)
0.922596 0.385767i \(-0.126063\pi\)
\(572\) 21.2063 + 79.1431i 0.0370740 + 0.138362i
\(573\) 0 0
\(574\) −6.65843 + 3.84424i −0.0116000 + 0.00669729i
\(575\) −219.619 333.019i −0.381947 0.579163i
\(576\) 0 0
\(577\) −518.888 + 518.888i −0.899286 + 0.899286i −0.995373 0.0960874i \(-0.969367\pi\)
0.0960874 + 0.995373i \(0.469367\pi\)
\(578\) 113.302 422.848i 0.196024 0.731570i
\(579\) 0 0
\(580\) 53.4348 74.0947i 0.0921290 0.127749i
\(581\) 311.643 539.782i 0.536391 0.929057i
\(582\) 0 0
\(583\) 233.625 871.901i 0.400729 1.49554i
\(584\) 809.321i 1.38582i
\(585\) 0 0
\(586\) 740.047 1.26288
\(587\) −475.752 127.477i −0.810481 0.217168i −0.170301 0.985392i \(-0.554474\pi\)
−0.640181 + 0.768224i \(0.721141\pi\)
\(588\) 0 0
\(589\) 664.872 + 383.864i 1.12881 + 0.651721i
\(590\) −478.926 + 77.5864i −0.811738 + 0.131502i
\(591\) 0 0
\(592\) −556.624 149.147i −0.940243 0.251937i
\(593\) −528.279 528.279i −0.890858 0.890858i 0.103746 0.994604i \(-0.466917\pi\)
−0.994604 + 0.103746i \(0.966917\pi\)
\(594\) 0 0
\(595\) 71.5743 704.884i 0.120293 1.18468i
\(596\) −28.9451 50.1343i −0.0485655 0.0841180i
\(597\) 0 0
\(598\) −360.628 + 96.6300i −0.603057 + 0.161589i
\(599\) −448.466 258.922i −0.748690 0.432257i 0.0765301 0.997067i \(-0.475616\pi\)
−0.825221 + 0.564811i \(0.808949\pi\)
\(600\) 0 0
\(601\) 51.0959 + 88.5006i 0.0850181 + 0.147256i 0.905399 0.424562i \(-0.139572\pi\)
−0.820381 + 0.571818i \(0.806239\pi\)
\(602\) 5.29462 5.29462i 0.00879506 0.00879506i
\(603\) 0 0
\(604\) 100.381i 0.166194i
\(605\) 156.357 + 347.876i 0.258441 + 0.575002i
\(606\) 0 0
\(607\) −230.837 861.496i −0.380292 1.41927i −0.845456 0.534044i \(-0.820671\pi\)
0.465164 0.885224i \(-0.345995\pi\)
\(608\) 126.609 33.9247i 0.208238 0.0557973i
\(609\) 0 0
\(610\) −123.001 46.7189i −0.201642 0.0765883i
\(611\) −357.311 −0.584797
\(612\) 0 0
\(613\) −91.7462 91.7462i −0.149668 0.149668i 0.628302 0.777970i \(-0.283750\pi\)
−0.777970 + 0.628302i \(0.783750\pi\)
\(614\) 126.823 73.2212i 0.206552 0.119253i
\(615\) 0 0
\(616\) 330.413 572.292i 0.536385 0.929045i
\(617\) −212.585 793.378i −0.344546 1.28586i −0.893142 0.449776i \(-0.851504\pi\)
0.548595 0.836088i \(-0.315163\pi\)
\(618\) 0 0
\(619\) −1035.69 + 597.954i −1.67316 + 0.965999i −0.707308 + 0.706906i \(0.750090\pi\)
−0.965852 + 0.259093i \(0.916576\pi\)
\(620\) 13.2466 130.456i 0.0213654 0.210413i
\(621\) 0 0
\(622\) 468.898 468.898i 0.753856 0.753856i
\(623\) 197.680 737.753i 0.317304 1.18419i
\(624\) 0 0
\(625\) −500.404 + 374.461i −0.800646 + 0.599137i
\(626\) 110.510 191.409i 0.176534 0.305766i
\(627\) 0 0
\(628\) −16.8545 + 62.9017i −0.0268383 + 0.100162i
\(629\) 718.375i 1.14209i
\(630\) 0 0
\(631\) 1072.92 1.70034 0.850171 0.526507i \(-0.176499\pi\)
0.850171 + 0.526507i \(0.176499\pi\)
\(632\) −946.119 253.512i −1.49702 0.401126i
\(633\) 0 0
\(634\) 529.410 + 305.655i 0.835032 + 0.482106i
\(635\) −10.0261 61.8894i −0.0157892 0.0974636i
\(636\) 0 0
\(637\) 89.2753 + 23.9212i 0.140150 + 0.0375530i
\(638\) −727.819 727.819i −1.14078 1.14078i
\(639\) 0 0
\(640\) 465.904 + 571.213i 0.727974 + 0.892520i
\(641\) −108.538 187.994i −0.169327 0.293282i 0.768857 0.639421i \(-0.220826\pi\)
−0.938183 + 0.346139i \(0.887493\pi\)
\(642\) 0 0
\(643\) −384.240 + 102.957i −0.597573 + 0.160119i −0.544912 0.838493i \(-0.683437\pi\)
−0.0526611 + 0.998612i \(0.516770\pi\)
\(644\) −46.7227 26.9754i −0.0725508 0.0418872i
\(645\) 0 0
\(646\) −367.730 636.926i −0.569241 0.985954i
\(647\) 308.718 308.718i 0.477154 0.477154i −0.427067 0.904220i \(-0.640453\pi\)
0.904220 + 0.427067i \(0.140453\pi\)
\(648\) 0 0
\(649\) 640.299i 0.986593i
\(650\) 184.676 + 555.026i 0.284117 + 0.853886i
\(651\) 0 0
\(652\) −10.7405 40.0839i −0.0164731 0.0614784i
\(653\) 337.252 90.3665i 0.516466 0.138387i 0.00883466 0.999961i \(-0.497188\pi\)
0.507632 + 0.861574i \(0.330521\pi\)
\(654\) 0 0
\(655\) 46.7869 + 104.096i 0.0714304 + 0.158925i
\(656\) −10.1149 −0.0154190
\(657\) 0 0
\(658\) −311.703 311.703i −0.473713 0.473713i
\(659\) 366.440 211.564i 0.556054 0.321038i −0.195506 0.980703i \(-0.562635\pi\)
0.751560 + 0.659664i \(0.229302\pi\)
\(660\) 0 0
\(661\) −223.082 + 386.390i −0.337492 + 0.584554i −0.983960 0.178387i \(-0.942912\pi\)
0.646468 + 0.762941i \(0.276245\pi\)
\(662\) −216.202 806.878i −0.326590 1.21885i
\(663\) 0 0
\(664\) 625.640 361.213i 0.942228 0.543996i
\(665\) −312.801 383.504i −0.470377 0.576697i
\(666\) 0 0
\(667\) 388.456 388.456i 0.582393 0.582393i
\(668\) −18.2714 + 68.1897i −0.0273524 + 0.102080i
\(669\) 0 0
\(670\) −1048.66 756.260i −1.56516 1.12875i
\(671\) −86.8227 + 150.381i −0.129393 + 0.224115i
\(672\) 0 0
\(673\) 127.705 476.600i 0.189754 0.708172i −0.803808 0.594888i \(-0.797196\pi\)
0.993563 0.113284i \(-0.0361370\pi\)
\(674\) 1061.94i 1.57558i
\(675\) 0 0
\(676\) −25.5617 −0.0378131
\(677\) −794.165 212.796i −1.17307 0.314322i −0.380893 0.924619i \(-0.624383\pi\)
−0.792172 + 0.610297i \(0.791050\pi\)
\(678\) 0 0
\(679\) −408.563 235.884i −0.601714 0.347399i
\(680\) 480.346 666.066i 0.706391 0.979508i
\(681\) 0 0
\(682\) −1427.09 382.389i −2.09251 0.560687i
\(683\) −702.491 702.491i −1.02854 1.02854i −0.999581 0.0289564i \(-0.990782\pi\)
−0.0289564 0.999581i \(-0.509218\pi\)
\(684\) 0 0
\(685\) −323.405 + 263.782i −0.472125 + 0.385083i
\(686\) 389.264 + 674.226i 0.567441 + 0.982836i
\(687\) 0 0
\(688\) 9.51511 2.54957i 0.0138301 0.00370577i
\(689\) −611.793 353.219i −0.887944 0.512655i
\(690\) 0 0
\(691\) −79.1995 137.178i −0.114616 0.198520i 0.803010 0.595965i \(-0.203230\pi\)
−0.917626 + 0.397445i \(0.869897\pi\)
\(692\) −12.3585 + 12.3585i −0.0178590 + 0.0178590i
\(693\) 0 0
\(694\) 83.8365i 0.120802i
\(695\) 535.549 240.708i 0.770574 0.346343i
\(696\) 0 0
\(697\) 3.26355 + 12.1797i 0.00468228 + 0.0174745i
\(698\) −153.766 + 41.2014i −0.220295 + 0.0590277i
\(699\) 0 0
\(700\) −37.8424 + 75.5829i −0.0540606 + 0.107976i
\(701\) 567.989 0.810255 0.405128 0.914260i \(-0.367227\pi\)
0.405128 + 0.914260i \(0.367227\pi\)
\(702\) 0 0
\(703\) 354.816 + 354.816i 0.504716 + 0.504716i
\(704\) 649.618 375.057i 0.922753 0.532752i
\(705\) 0 0
\(706\) 45.1305 78.1684i 0.0639243 0.110720i
\(707\) 297.950 + 1111.97i 0.421429 + 1.57279i
\(708\) 0 0
\(709\) 175.177 101.139i 0.247077 0.142650i −0.371348 0.928494i \(-0.621104\pi\)
0.618425 + 0.785844i \(0.287771\pi\)
\(710\) 397.172 323.949i 0.559397 0.456266i
\(711\) 0 0
\(712\) 625.977 625.977i 0.879181 0.879181i
\(713\) 204.091 761.677i 0.286242 1.06827i
\(714\) 0 0
\(715\) 762.040 123.451i 1.06579 0.172659i
\(716\) 35.4010 61.3163i 0.0494427 0.0856373i
\(717\) 0 0
\(718\) −76.3584 + 284.974i −0.106349 + 0.396899i
\(719\) 842.936i 1.17237i 0.810176 + 0.586186i \(0.199371\pi\)
−0.810176 + 0.586186i \(0.800629\pi\)
\(720\) 0 0
\(721\) 501.421 0.695452
\(722\) 246.006 + 65.9172i 0.340729 + 0.0912981i
\(723\) 0 0
\(724\) −54.4053 31.4109i −0.0751455 0.0433852i
\(725\) −643.675 571.400i −0.887828 0.788138i
\(726\) 0 0
\(727\) −638.604 171.114i −0.878410 0.235369i −0.208689 0.977982i \(-0.566920\pi\)
−0.669721 + 0.742613i \(0.733586\pi\)
\(728\) −365.698 365.698i −0.502333 0.502333i
\(729\) 0 0
\(730\) −1160.43 117.831i −1.58963 0.161412i
\(731\) −6.14007 10.6349i −0.00839955 0.0145485i
\(732\) 0 0
\(733\) −211.707 + 56.7266i −0.288822 + 0.0773896i −0.400321 0.916375i \(-0.631101\pi\)
0.111499 + 0.993765i \(0.464435\pi\)
\(734\) 456.228 + 263.403i 0.621564 + 0.358860i
\(735\) 0 0
\(736\) −67.3148 116.593i −0.0914603 0.158414i
\(737\) −1206.54 + 1206.54i −1.63710 + 1.63710i
\(738\) 0 0
\(739\) 311.453i 0.421451i 0.977545 + 0.210726i \(0.0675827\pi\)
−0.977545 + 0.210726i \(0.932417\pi\)
\(740\) 30.4313 80.1195i 0.0411234 0.108270i
\(741\) 0 0
\(742\) −225.569 841.836i −0.304002 1.13455i
\(743\) −44.6785 + 11.9716i −0.0601326 + 0.0161125i −0.288760 0.957402i \(-0.593243\pi\)
0.228627 + 0.973514i \(0.426576\pi\)
\(744\) 0 0
\(745\) −497.489 + 223.602i −0.667771 + 0.300137i
\(746\) −505.519 −0.677639
\(747\) 0 0
\(748\) 117.224 + 117.224i 0.156717 + 0.156717i
\(749\) −478.499 + 276.262i −0.638851 + 0.368841i
\(750\) 0 0
\(751\) 503.153 871.487i 0.669978 1.16044i −0.307932 0.951408i \(-0.599637\pi\)
0.977910 0.209027i \(-0.0670297\pi\)
\(752\) −150.097 560.170i −0.199597 0.744907i
\(753\) 0 0
\(754\) −697.621 + 402.772i −0.925227 + 0.534180i
\(755\) −940.935 95.5430i −1.24627 0.126547i
\(756\) 0 0
\(757\) 511.251 511.251i 0.675364 0.675364i −0.283583 0.958948i \(-0.591523\pi\)
0.958948 + 0.283583i \(0.0915233\pi\)
\(758\) 324.927 1212.64i 0.428663 1.59979i
\(759\) 0 0
\(760\) −91.7297 566.229i −0.120697 0.745038i
\(761\) 268.202 464.540i 0.352434 0.610434i −0.634241 0.773135i \(-0.718687\pi\)
0.986675 + 0.162701i \(0.0520207\pi\)
\(762\) 0 0
\(763\) 333.519 1244.71i 0.437116 1.63134i
\(764\) 75.6926i 0.0990741i
\(765\) 0 0
\(766\) −62.4985 −0.0815907
\(767\) 484.036 + 129.697i 0.631076 + 0.169096i
\(768\) 0 0
\(769\) 397.833 + 229.689i 0.517338 + 0.298685i 0.735845 0.677150i \(-0.236785\pi\)
−0.218507 + 0.975835i \(0.570119\pi\)
\(770\) 772.466 + 557.078i 1.00320 + 0.723478i
\(771\) 0 0
\(772\) 91.7328 + 24.5797i 0.118825 + 0.0318390i
\(773\) 229.707 + 229.707i 0.297163 + 0.297163i 0.839902 0.542739i \(-0.182613\pi\)
−0.542739 + 0.839902i \(0.682613\pi\)
\(774\) 0 0
\(775\) −1210.24 248.336i −1.56159 0.320434i
\(776\) −273.404 473.549i −0.352325 0.610244i
\(777\) 0 0
\(778\) 517.956 138.786i 0.665753 0.178388i
\(779\) 7.62766 + 4.40383i 0.00979161 + 0.00565319i
\(780\) 0 0
\(781\) −338.205 585.789i −0.433041 0.750049i
\(782\) −534.151 + 534.151i −0.683057 + 0.683057i
\(783\) 0 0
\(784\) 150.009i 0.191338i
\(785\) 573.573 + 217.857i 0.730667 + 0.277525i
\(786\) 0 0
\(787\) −111.429 415.860i −0.141587 0.528411i −0.999884 0.0152567i \(-0.995143\pi\)
0.858296 0.513154i \(-0.171523\pi\)
\(788\) 33.0728 8.86183i 0.0419705 0.0112460i
\(789\) 0 0
\(790\) 501.241 1319.67i 0.634483 1.67047i
\(791\) 717.205 0.906707
\(792\) 0 0
\(793\) 96.0946 + 96.0946i 0.121179 + 0.121179i
\(794\) −1228.61 + 709.340i −1.54737 + 0.893375i
\(795\) 0 0
\(796\) 87.1567 150.960i 0.109493 0.189648i
\(797\) −16.9281 63.1765i −0.0212398 0.0792679i 0.954492 0.298235i \(-0.0963979\pi\)
−0.975732 + 0.218967i \(0.929731\pi\)
\(798\) 0 0
\(799\) −626.095 + 361.476i −0.783598 + 0.452411i
\(800\) −176.086 + 116.125i −0.220108 + 0.145157i
\(801\) 0 0
\(802\) 67.1159 67.1159i 0.0836856 0.0836856i
\(803\) −398.412 + 1486.89i −0.496155 + 1.85167i
\(804\) 0 0
\(805\) −297.327 + 412.285i −0.369351 + 0.512156i
\(806\) −578.135 + 1001.36i −0.717290 + 1.24238i
\(807\) 0 0
\(808\) −345.342 + 1288.83i −0.427403 + 1.59509i
\(809\) 108.424i 0.134022i −0.997752 0.0670111i \(-0.978654\pi\)
0.997752 0.0670111i \(-0.0213463\pi\)
\(810\) 0 0
\(811\) −182.633 −0.225195 −0.112597 0.993641i \(-0.535917\pi\)
−0.112597 + 0.993641i \(0.535917\pi\)
\(812\) −112.438 30.1278i −0.138471 0.0371032i
\(813\) 0 0
\(814\) −836.277 482.825i −1.02737 0.593151i
\(815\) −385.954 + 62.5249i −0.473563 + 0.0767176i
\(816\) 0 0
\(817\) −8.28541 2.22007i −0.0101413 0.00271734i
\(818\) −34.8097 34.8097i −0.0425546 0.0425546i
\(819\) 0 0
\(820\) 0.151970 1.49664i 0.000185329 0.00182517i
\(821\) 307.529 + 532.656i 0.374579 + 0.648789i 0.990264 0.139203i \(-0.0444541\pi\)
−0.615685 + 0.787992i \(0.711121\pi\)
\(822\) 0 0
\(823\) −1036.95 + 277.850i −1.25996 + 0.337606i −0.826177 0.563410i \(-0.809489\pi\)
−0.433785 + 0.901016i \(0.642822\pi\)
\(824\) 503.314 + 290.589i 0.610818 + 0.352656i
\(825\) 0 0
\(826\) 309.110 + 535.395i 0.374225 + 0.648177i
\(827\) 850.244 850.244i 1.02811 1.02811i 0.0285125 0.999593i \(-0.490923\pi\)
0.999593 0.0285125i \(-0.00907704\pi\)
\(828\) 0 0
\(829\) 76.6013i 0.0924021i −0.998932 0.0462010i \(-0.985289\pi\)
0.998932 0.0462010i \(-0.0147115\pi\)
\(830\) 426.831 + 949.653i 0.514255 + 1.14416i
\(831\) 0 0
\(832\) −151.941 567.051i −0.182621 0.681551i
\(833\) 180.632 48.4002i 0.216845 0.0581034i
\(834\) 0 0
\(835\) 621.793 + 236.172i 0.744662 + 0.282841i
\(836\) 115.797 0.138514
\(837\) 0 0
\(838\) 457.899 + 457.899i 0.546419 + 0.546419i
\(839\) −15.6364 + 9.02767i −0.0186369 + 0.0107600i −0.509290 0.860595i \(-0.670092\pi\)
0.490653 + 0.871355i \(0.336758\pi\)
\(840\) 0 0
\(841\) 172.153 298.177i 0.204700 0.354551i
\(842\) −136.853 510.742i −0.162533 0.606582i
\(843\) 0 0
\(844\) 135.075 77.9857i 0.160042 0.0924002i
\(845\) −24.3296 + 239.605i −0.0287925 + 0.283556i
\(846\) 0 0
\(847\) 343.649 343.649i 0.405725 0.405725i
\(848\) 296.756 1107.51i 0.349949 1.30603i
\(849\) 0 0
\(850\) 885.093 + 785.710i 1.04129 + 0.924364i
\(851\) 257.696 446.343i 0.302816 0.524492i
\(852\) 0 0
\(853\) −54.1951 + 202.259i −0.0635347 + 0.237115i −0.990390 0.138305i \(-0.955835\pi\)
0.926855 + 0.375420i \(0.122501\pi\)
\(854\) 167.658i 0.196321i
\(855\) 0 0
\(856\) −640.407 −0.748139
\(857\) 374.050 + 100.226i 0.436464 + 0.116950i 0.470359 0.882475i \(-0.344124\pi\)
−0.0338947 + 0.999425i \(0.510791\pi\)
\(858\) 0 0
\(859\) 330.468 + 190.796i 0.384712 + 0.222114i 0.679866 0.733336i \(-0.262038\pi\)
−0.295154 + 0.955450i \(0.595371\pi\)
\(860\) 0.234286 + 1.44620i 0.000272426 + 0.00168163i
\(861\) 0 0
\(862\) 1137.06 + 304.673i 1.31909 + 0.353449i
\(863\) 653.316 + 653.316i 0.757029 + 0.757029i 0.975781 0.218752i \(-0.0701984\pi\)
−0.218752 + 0.975781i \(0.570198\pi\)
\(864\) 0 0
\(865\) 104.080 + 127.606i 0.120324 + 0.147521i
\(866\) 387.481 + 671.136i 0.447437 + 0.774984i
\(867\) 0 0
\(868\) −161.393 + 43.2452i −0.185937 + 0.0498216i
\(869\) −1613.42 931.510i −1.85664 1.07193i
\(870\) 0 0
\(871\) 667.695 + 1156.48i 0.766584 + 1.32776i
\(872\) 1056.13 1056.13i 1.21115 1.21115i
\(873\) 0 0
\(874\) 527.649i 0.603717i
\(875\) 672.466 + 426.660i 0.768533 + 0.487611i
\(876\) 0 0
\(877\) 32.4798 + 121.216i 0.0370351 + 0.138217i 0.981968 0.189047i \(-0.0605400\pi\)
−0.944933 + 0.327264i \(0.893873\pi\)
\(878\) 28.7497 7.70346i 0.0327445 0.00877387i
\(879\) 0 0
\(880\) 513.653 + 1142.82i 0.583697 + 1.29866i
\(881\) 515.743 0.585406 0.292703 0.956203i \(-0.405445\pi\)
0.292703 + 0.956203i \(0.405445\pi\)
\(882\) 0 0
\(883\) 61.1931 + 61.1931i 0.0693014 + 0.0693014i 0.740908 0.671607i \(-0.234395\pi\)
−0.671607 + 0.740908i \(0.734395\pi\)
\(884\) 112.360 64.8714i 0.127105 0.0733839i
\(885\) 0 0
\(886\) −44.8144 + 77.6208i −0.0505806 + 0.0876081i
\(887\) 106.220 + 396.418i 0.119752 + 0.446920i 0.999598 0.0283378i \(-0.00902139\pi\)
−0.879846 + 0.475258i \(0.842355\pi\)
\(888\) 0 0
\(889\) −69.1866 + 39.9449i −0.0778252 + 0.0449324i
\(890\) 806.409 + 988.684i 0.906077 + 1.11088i
\(891\) 0 0
\(892\) −65.5895 + 65.5895i −0.0735309 + 0.0735309i
\(893\) −130.699 + 487.775i −0.146360 + 0.546221i
\(894\) 0 0
\(895\) −541.060 390.196i −0.604536 0.435973i
\(896\) 469.634 813.431i 0.524146 0.907847i
\(897\) 0 0
\(898\) 139.954 522.314i 0.155850 0.581641i
\(899\) 1701.38i 1.89252i
\(900\) 0 0
\(901\) −1429.35 −1.58640
\(902\) −16.3722 4.38691i −0.0181510 0.00486354i
\(903\) 0 0
\(904\) 719.913 + 415.642i 0.796364 + 0.459781i
\(905\) −346.217 + 480.077i −0.382560 + 0.530472i
\(906\) 0 0
\(907\) 190.103 + 50.9379i 0.209595 + 0.0561609i 0.362089 0.932144i \(-0.382064\pi\)
−0.152494 + 0.988304i \(0.548730\pi\)
\(908\) 67.9039 + 67.9039i 0.0747840 + 0.0747840i
\(909\) 0 0
\(910\) 577.593 471.107i 0.634718 0.517700i
\(911\) −439.391 761.048i −0.482318 0.835399i 0.517476 0.855698i \(-0.326872\pi\)
−0.999794 + 0.0202989i \(0.993538\pi\)
\(912\) 0 0
\(913\) 1327.25 355.636i 1.45372 0.389524i
\(914\) 621.361 + 358.743i 0.679826 + 0.392498i
\(915\) 0 0
\(916\) −78.1698 135.394i −0.0853382 0.147810i
\(917\) 102.831 102.831i 0.112138 0.112138i
\(918\) 0 0
\(919\) 922.414i 1.00372i −0.864950 0.501858i \(-0.832650\pi\)
0.864950 0.501858i \(-0.167350\pi\)
\(920\) −537.381 + 241.532i −0.584110 + 0.262534i
\(921\) 0 0
\(922\) 318.517 + 1188.72i 0.345464 + 1.28929i
\(923\) −511.334 + 137.012i −0.553991 + 0.148442i
\(924\) 0 0
\(925\) −722.045 361.509i −0.780589 0.390821i
\(926\) −596.611 −0.644289
\(927\) 0 0
\(928\) −205.399 205.399i −0.221335 0.221335i
\(929\) −64.0110 + 36.9568i −0.0689031 + 0.0397812i −0.534056 0.845449i \(-0.679333\pi\)
0.465153 + 0.885230i \(0.345999\pi\)
\(930\) 0 0
\(931\) 65.3111 113.122i 0.0701516 0.121506i
\(932\) 57.8005 + 215.714i 0.0620177 + 0.231453i
\(933\) 0 0
\(934\) −983.368 + 567.748i −1.05286 + 0.607867i
\(935\) 1210.39 987.240i 1.29453 1.05587i
\(936\) 0 0
\(937\) −732.726 + 732.726i −0.781992 + 0.781992i −0.980167 0.198175i \(-0.936499\pi\)
0.198175 + 0.980167i \(0.436499\pi\)
\(938\) −426.397 + 1591.33i −0.454581 + 1.69652i
\(939\) 0 0
\(940\) 85.1403 13.7928i 0.0905748 0.0146732i
\(941\) −374.739 + 649.067i −0.398235 + 0.689763i −0.993508 0.113760i \(-0.963710\pi\)
0.595273 + 0.803523i \(0.297044\pi\)
\(942\) 0 0
\(943\) 2.34141 8.73825i 0.00248293 0.00926644i
\(944\) 813.324i 0.861572i
\(945\) 0 0
\(946\) 16.5071 0.0174494
\(947\) −426.171 114.192i −0.450022 0.120583i 0.0266874 0.999644i \(-0.491504\pi\)
−0.476710 + 0.879061i \(0.658171\pi\)
\(948\) 0 0
\(949\) 1043.32 + 602.361i 1.09939 + 0.634732i
\(950\) 825.233 49.0865i 0.868666 0.0516700i
\(951\) 0 0
\(952\) −1010.75 270.830i −1.06171 0.284485i
\(953\) −838.669 838.669i −0.880030 0.880030i 0.113507 0.993537i \(-0.463792\pi\)
−0.993537 + 0.113507i \(0.963792\pi\)
\(954\) 0 0
\(955\) 709.513 + 72.0443i 0.742946 + 0.0754391i
\(956\) −2.19218 3.79697i −0.00229307 0.00397172i
\(957\) 0 0
\(958\) −1433.71 + 384.162i −1.49657 + 0.401005i
\(959\) 460.543 + 265.894i 0.480232 + 0.277262i
\(960\) 0 0
\(961\) −740.572 1282.71i −0.770627 1.33476i
\(962\) −534.386 + 534.386i −0.555495 + 0.555495i
\(963\) 0 0
\(964\) 95.5730i 0.0991421i
\(965\) 317.712 836.472i 0.329235 0.866810i
\(966\) 0 0
\(967\) 356.813 + 1331.65i 0.368990 + 1.37709i 0.861930 + 0.507027i \(0.169255\pi\)
−0.492940 + 0.870063i \(0.664078\pi\)
\(968\) 544.101 145.791i 0.562088 0.150611i
\(969\) 0 0
\(970\) 718.797 323.071i 0.741027 0.333062i
\(971\) 1716.72 1.76800 0.883998 0.467491i \(-0.154842\pi\)
0.883998 + 0.467491i \(0.154842\pi\)
\(972\) 0 0
\(973\) −529.041 529.041i −0.543721 0.543721i
\(974\) 963.246 556.130i 0.988958 0.570975i
\(975\) 0 0
\(976\) −110.284 + 191.018i −0.112996 + 0.195715i
\(977\) 308.607 + 1151.74i 0.315872 + 1.17885i 0.923175 + 0.384380i \(0.125585\pi\)
−0.607303 + 0.794470i \(0.707749\pi\)
\(978\) 0 0
\(979\) 1458.21 841.897i 1.48949 0.859956i
\(980\) −22.1960 2.25379i −0.0226489 0.00229978i
\(981\) 0 0
\(982\) −167.112 + 167.112i −0.170175 + 0.170175i
\(983\) 102.104 381.057i 0.103870 0.387647i −0.894345 0.447378i \(-0.852358\pi\)
0.998214 + 0.0597315i \(0.0190245\pi\)
\(984\) 0 0
\(985\) −51.5886 318.446i −0.0523742 0.323295i
\(986\) −814.933 + 1411.51i −0.826505 + 1.43155i
\(987\) 0 0
\(988\) 23.4556 87.5373i 0.0237404 0.0886005i
\(989\) 8.81029i 0.00890828i
\(990\) 0 0
\(991\) 567.310 0.572462 0.286231 0.958161i \(-0.407598\pi\)
0.286231 + 0.958161i \(0.407598\pi\)
\(992\) −402.743 107.915i −0.405991 0.108785i
\(993\) 0 0
\(994\) −565.590 326.543i −0.569004 0.328514i
\(995\) −1332.08 960.656i −1.33878 0.965484i
\(996\) 0 0
\(997\) 1648.08 + 441.602i 1.65304 + 0.442931i 0.960462 0.278411i \(-0.0898079\pi\)
0.692579 + 0.721342i \(0.256475\pi\)
\(998\) 629.343 + 629.343i 0.630604 + 0.630604i
\(999\) 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 405.3.l.l.28.3 16
3.2 odd 2 405.3.l.k.28.2 16
5.2 odd 4 inner 405.3.l.l.352.2 16
9.2 odd 6 405.3.l.k.298.3 16
9.4 even 3 405.3.g.c.163.2 yes 8
9.5 odd 6 405.3.g.e.163.3 yes 8
9.7 even 3 inner 405.3.l.l.298.2 16
15.2 even 4 405.3.l.k.352.3 16
45.2 even 12 405.3.l.k.217.2 16
45.7 odd 12 inner 405.3.l.l.217.3 16
45.22 odd 12 405.3.g.c.82.2 8
45.32 even 12 405.3.g.e.82.3 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
405.3.g.c.82.2 8 45.22 odd 12
405.3.g.c.163.2 yes 8 9.4 even 3
405.3.g.e.82.3 yes 8 45.32 even 12
405.3.g.e.163.3 yes 8 9.5 odd 6
405.3.l.k.28.2 16 3.2 odd 2
405.3.l.k.217.2 16 45.2 even 12
405.3.l.k.298.3 16 9.2 odd 6
405.3.l.k.352.3 16 15.2 even 4
405.3.l.l.28.3 16 1.1 even 1 trivial
405.3.l.l.217.3 16 45.7 odd 12 inner
405.3.l.l.298.2 16 9.7 even 3 inner
405.3.l.l.352.2 16 5.2 odd 4 inner