Properties

Label 392.3.j.e.325.5
Level $392$
Weight $3$
Character 392.325
Analytic conductor $10.681$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [392,3,Mod(117,392)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(392, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 5]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("392.117");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 392 = 2^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 392.j (of order \(6\), degree \(2\), 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: \(10.6812263629\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(14\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 56)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 325.5
Character \(\chi\) \(=\) 392.325
Dual form 392.3.j.e.117.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.33557 + 1.48871i) q^{2} +(-1.70138 + 2.94687i) q^{3} +(-0.432496 - 3.97655i) q^{4} +(2.15858 + 3.73877i) q^{5} +(-2.11472 - 6.46862i) q^{6} +(6.49755 + 4.66711i) q^{8} +(-1.28938 - 2.23327i) q^{9} +O(q^{10})\) \(q+(-1.33557 + 1.48871i) q^{2} +(-1.70138 + 2.94687i) q^{3} +(-0.432496 - 3.97655i) q^{4} +(2.15858 + 3.73877i) q^{5} +(-2.11472 - 6.46862i) q^{6} +(6.49755 + 4.66711i) q^{8} +(-1.28938 - 2.23327i) q^{9} +(-8.44888 - 1.77990i) q^{10} +(15.4899 + 8.94308i) q^{11} +(12.4542 + 5.49111i) q^{12} +3.25607 q^{13} -14.6903 q^{15} +(-15.6259 + 3.43968i) q^{16} +(13.6263 + 7.86717i) q^{17} +(5.04674 + 1.06319i) q^{18} +(0.778522 + 1.34844i) q^{19} +(13.9338 - 10.2007i) q^{20} +(-34.0014 + 11.1157i) q^{22} +(20.7069 + 35.8655i) q^{23} +(-24.8082 + 11.2069i) q^{24} +(3.18105 - 5.50975i) q^{25} +(-4.34871 + 4.84733i) q^{26} -21.8499 q^{27} +3.74374i q^{29} +(19.6199 - 21.8695i) q^{30} +(0.0145172 + 0.00838150i) q^{31} +(15.7488 - 27.8563i) q^{32} +(-52.7082 + 30.4311i) q^{33} +(-29.9109 + 9.77845i) q^{34} +(-8.32306 + 6.09316i) q^{36} +(1.16774 - 0.674194i) q^{37} +(-3.04720 - 0.641947i) q^{38} +(-5.53981 + 9.59523i) q^{39} +(-3.42377 + 34.3672i) q^{40} -70.3018i q^{41} -13.0380i q^{43} +(28.8633 - 65.4641i) q^{44} +(5.56646 - 9.64139i) q^{45} +(-81.0487 - 17.0743i) q^{46} +(-30.9797 + 17.8862i) q^{47} +(16.4493 - 51.8998i) q^{48} +(3.95387 + 12.0943i) q^{50} +(-46.3671 + 26.7701i) q^{51} +(-1.40824 - 12.9479i) q^{52} +(-39.7989 - 22.9779i) q^{53} +(29.1821 - 32.5281i) q^{54} +77.2174i q^{55} -5.29824 q^{57} +(-5.57333 - 5.00004i) q^{58} +(-34.3509 + 59.4974i) q^{59} +(6.35348 + 58.4165i) q^{60} +(-48.0386 - 83.2052i) q^{61} +(-0.0318663 + 0.0104177i) q^{62} +(20.4362 + 60.6495i) q^{64} +(7.02849 + 12.1737i) q^{65} +(25.0926 - 119.110i) q^{66} +(-12.0808 - 6.97484i) q^{67} +(25.3909 - 57.5883i) q^{68} -140.921 q^{69} -75.7095 q^{71} +(2.04511 - 20.5284i) q^{72} +(46.0282 + 26.5744i) q^{73} +(-0.555921 + 2.63886i) q^{74} +(10.8244 + 18.7483i) q^{75} +(5.02543 - 3.67902i) q^{76} +(-6.88567 - 21.0623i) q^{78} +(11.6744 + 20.2206i) q^{79} +(-46.5900 - 50.9968i) q^{80} +(48.7794 - 84.4884i) q^{81} +(104.659 + 93.8931i) q^{82} +102.487 q^{83} +67.9277i q^{85} +(19.4098 + 17.4132i) q^{86} +(-11.0323 - 6.36952i) q^{87} +(58.9078 + 130.401i) q^{88} +(76.6985 - 44.2819i) q^{89} +(6.91880 + 21.1636i) q^{90} +(133.665 - 97.8538i) q^{92} +(-0.0493984 + 0.0285202i) q^{93} +(14.7484 - 70.0080i) q^{94} +(-3.36100 + 5.82143i) q^{95} +(55.2944 + 93.8040i) q^{96} +140.869i q^{97} -46.1241i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q - 2 q^{2} - 4 q^{4} - 20 q^{8} - 32 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 28 q - 2 q^{2} - 4 q^{4} - 20 q^{8} - 32 q^{9} - 24 q^{10} + 18 q^{12} + 28 q^{15} + 16 q^{16} + 6 q^{17} - 42 q^{18} - 92 q^{22} + 30 q^{23} + 30 q^{24} - 32 q^{25} + 30 q^{26} + 22 q^{30} + 6 q^{31} + 88 q^{32} + 6 q^{33} + 256 q^{36} - 6 q^{38} - 20 q^{39} - 102 q^{40} - 42 q^{44} + 68 q^{46} + 294 q^{47} + 400 q^{50} + 168 q^{52} - 330 q^{54} + 124 q^{57} - 22 q^{58} - 62 q^{60} - 520 q^{64} - 52 q^{65} + 306 q^{66} + 456 q^{68} - 136 q^{71} + 96 q^{72} - 234 q^{73} - 138 q^{74} - 956 q^{78} - 162 q^{79} - 276 q^{80} - 18 q^{81} + 642 q^{82} + 168 q^{86} - 48 q^{87} + 50 q^{88} + 150 q^{89} + 1020 q^{92} - 618 q^{94} + 290 q^{95} - 1044 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/392\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(295\) \(297\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.33557 + 1.48871i −0.667786 + 0.744353i
\(3\) −1.70138 + 2.94687i −0.567126 + 0.982291i 0.429722 + 0.902961i \(0.358612\pi\)
−0.996848 + 0.0793303i \(0.974722\pi\)
\(4\) −0.432496 3.97655i −0.108124 0.994137i
\(5\) 2.15858 + 3.73877i 0.431716 + 0.747754i 0.997021 0.0771275i \(-0.0245748\pi\)
−0.565305 + 0.824882i \(0.691242\pi\)
\(6\) −2.11472 6.46862i −0.352453 1.07810i
\(7\) 0 0
\(8\) 6.49755 + 4.66711i 0.812193 + 0.583389i
\(9\) −1.28938 2.23327i −0.143264 0.248141i
\(10\) −8.44888 1.77990i −0.844888 0.177990i
\(11\) 15.4899 + 8.94308i 1.40817 + 0.813007i 0.995212 0.0977432i \(-0.0311624\pi\)
0.412958 + 0.910750i \(0.364496\pi\)
\(12\) 12.4542 + 5.49111i 1.03785 + 0.457592i
\(13\) 3.25607 0.250467 0.125233 0.992127i \(-0.460032\pi\)
0.125233 + 0.992127i \(0.460032\pi\)
\(14\) 0 0
\(15\) −14.6903 −0.979350
\(16\) −15.6259 + 3.43968i −0.976618 + 0.214980i
\(17\) 13.6263 + 7.86717i 0.801550 + 0.462775i 0.844013 0.536323i \(-0.180187\pi\)
−0.0424631 + 0.999098i \(0.513521\pi\)
\(18\) 5.04674 + 1.06319i 0.280375 + 0.0590659i
\(19\) 0.778522 + 1.34844i 0.0409748 + 0.0709705i 0.885786 0.464095i \(-0.153620\pi\)
−0.844811 + 0.535065i \(0.820287\pi\)
\(20\) 13.9338 10.2007i 0.696692 0.510035i
\(21\) 0 0
\(22\) −34.0014 + 11.1157i −1.54552 + 0.505261i
\(23\) 20.7069 + 35.8655i 0.900301 + 1.55937i 0.827103 + 0.562050i \(0.189987\pi\)
0.0731984 + 0.997317i \(0.476679\pi\)
\(24\) −24.8082 + 11.2069i −1.03367 + 0.466956i
\(25\) 3.18105 5.50975i 0.127242 0.220390i
\(26\) −4.34871 + 4.84733i −0.167258 + 0.186436i
\(27\) −21.8499 −0.809257
\(28\) 0 0
\(29\) 3.74374i 0.129095i 0.997915 + 0.0645473i \(0.0205603\pi\)
−0.997915 + 0.0645473i \(0.979440\pi\)
\(30\) 19.6199 21.8695i 0.653996 0.728983i
\(31\) 0.0145172 + 0.00838150i 0.000468296 + 0.000270371i 0.500234 0.865890i \(-0.333247\pi\)
−0.499766 + 0.866161i \(0.666581\pi\)
\(32\) 15.7488 27.8563i 0.492151 0.870510i
\(33\) −52.7082 + 30.4311i −1.59722 + 0.922155i
\(34\) −29.9109 + 9.77845i −0.879732 + 0.287602i
\(35\) 0 0
\(36\) −8.32306 + 6.09316i −0.231196 + 0.169254i
\(37\) 1.16774 0.674194i 0.0315605 0.0182215i −0.484137 0.874992i \(-0.660866\pi\)
0.515697 + 0.856771i \(0.327533\pi\)
\(38\) −3.04720 0.641947i −0.0801895 0.0168933i
\(39\) −5.53981 + 9.59523i −0.142046 + 0.246031i
\(40\) −3.42377 + 34.3672i −0.0855944 + 0.859179i
\(41\) 70.3018i 1.71468i −0.514753 0.857339i \(-0.672116\pi\)
0.514753 0.857339i \(-0.327884\pi\)
\(42\) 0 0
\(43\) 13.0380i 0.303210i −0.988441 0.151605i \(-0.951556\pi\)
0.988441 0.151605i \(-0.0484442\pi\)
\(44\) 28.8633 65.4641i 0.655984 1.48782i
\(45\) 5.56646 9.64139i 0.123699 0.214253i
\(46\) −81.0487 17.0743i −1.76193 0.371181i
\(47\) −30.9797 + 17.8862i −0.659144 + 0.380557i −0.791951 0.610585i \(-0.790934\pi\)
0.132807 + 0.991142i \(0.457601\pi\)
\(48\) 16.4493 51.8998i 0.342693 1.08124i
\(49\) 0 0
\(50\) 3.95387 + 12.0943i 0.0790774 + 0.241886i
\(51\) −46.3671 + 26.7701i −0.909160 + 0.524904i
\(52\) −1.40824 12.9479i −0.0270815 0.248998i
\(53\) −39.7989 22.9779i −0.750923 0.433546i 0.0751042 0.997176i \(-0.476071\pi\)
−0.826027 + 0.563630i \(0.809404\pi\)
\(54\) 29.1821 32.5281i 0.540410 0.602373i
\(55\) 77.2174i 1.40395i
\(56\) 0 0
\(57\) −5.29824 −0.0929516
\(58\) −5.57333 5.00004i −0.0960920 0.0862075i
\(59\) −34.3509 + 59.4974i −0.582218 + 1.00843i 0.412998 + 0.910732i \(0.364482\pi\)
−0.995216 + 0.0976993i \(0.968852\pi\)
\(60\) 6.35348 + 58.4165i 0.105891 + 0.973609i
\(61\) −48.0386 83.2052i −0.787517 1.36402i −0.927484 0.373864i \(-0.878033\pi\)
0.139966 0.990156i \(-0.455301\pi\)
\(62\) −0.0318663 + 0.0104177i −0.000513973 + 0.000168028i
\(63\) 0 0
\(64\) 20.4362 + 60.6495i 0.319316 + 0.947648i
\(65\) 7.02849 + 12.1737i 0.108131 + 0.187288i
\(66\) 25.0926 119.110i 0.380191 1.80470i
\(67\) −12.0808 6.97484i −0.180310 0.104102i 0.407128 0.913371i \(-0.366530\pi\)
−0.587438 + 0.809269i \(0.699864\pi\)
\(68\) 25.3909 57.5883i 0.373395 0.846887i
\(69\) −140.921 −2.04234
\(70\) 0 0
\(71\) −75.7095 −1.06633 −0.533166 0.846011i \(-0.678998\pi\)
−0.533166 + 0.846011i \(0.678998\pi\)
\(72\) 2.04511 20.5284i 0.0284044 0.285117i
\(73\) 46.0282 + 26.5744i 0.630523 + 0.364033i 0.780955 0.624588i \(-0.214733\pi\)
−0.150432 + 0.988620i \(0.548066\pi\)
\(74\) −0.555921 + 2.63886i −0.00751245 + 0.0356602i
\(75\) 10.8244 + 18.7483i 0.144325 + 0.249978i
\(76\) 5.02543 3.67902i 0.0661240 0.0484082i
\(77\) 0 0
\(78\) −6.88567 21.0623i −0.0882778 0.270029i
\(79\) 11.6744 + 20.2206i 0.147777 + 0.255957i 0.930406 0.366532i \(-0.119455\pi\)
−0.782628 + 0.622489i \(0.786122\pi\)
\(80\) −46.5900 50.9968i −0.582374 0.637460i
\(81\) 48.7794 84.4884i 0.602215 1.04307i
\(82\) 104.659 + 93.8931i 1.27633 + 1.14504i
\(83\) 102.487 1.23479 0.617393 0.786655i \(-0.288189\pi\)
0.617393 + 0.786655i \(0.288189\pi\)
\(84\) 0 0
\(85\) 67.9277i 0.799150i
\(86\) 19.4098 + 17.4132i 0.225696 + 0.202480i
\(87\) −11.0323 6.36952i −0.126808 0.0732129i
\(88\) 58.9078 + 130.401i 0.669407 + 1.48183i
\(89\) 76.6985 44.2819i 0.861781 0.497549i −0.00282755 0.999996i \(-0.500900\pi\)
0.864608 + 0.502447i \(0.167567\pi\)
\(90\) 6.91880 + 21.1636i 0.0768755 + 0.235151i
\(91\) 0 0
\(92\) 133.665 97.8538i 1.45288 1.06363i
\(93\) −0.0493984 + 0.0285202i −0.000531166 + 0.000306669i
\(94\) 14.7484 70.0080i 0.156898 0.744766i
\(95\) −3.36100 + 5.82143i −0.0353790 + 0.0612782i
\(96\) 55.2944 + 93.8040i 0.575983 + 0.977125i
\(97\) 140.869i 1.45226i 0.687558 + 0.726130i \(0.258683\pi\)
−0.687558 + 0.726130i \(0.741317\pi\)
\(98\) 0 0
\(99\) 46.1241i 0.465900i
\(100\) −23.2856 10.2667i −0.232856 0.102667i
\(101\) 17.6988 30.6553i 0.175236 0.303518i −0.765007 0.644022i \(-0.777265\pi\)
0.940243 + 0.340504i \(0.110598\pi\)
\(102\) 22.0738 104.780i 0.216410 1.02726i
\(103\) −87.1651 + 50.3248i −0.846263 + 0.488590i −0.859388 0.511324i \(-0.829155\pi\)
0.0131250 + 0.999914i \(0.495822\pi\)
\(104\) 21.1565 + 15.1964i 0.203427 + 0.146119i
\(105\) 0 0
\(106\) 87.3617 28.5603i 0.824167 0.269437i
\(107\) −92.6215 + 53.4751i −0.865622 + 0.499767i −0.865891 0.500233i \(-0.833248\pi\)
0.000269099 1.00000i \(0.499914\pi\)
\(108\) 9.45000 + 86.8873i 0.0875000 + 0.804512i
\(109\) −45.5799 26.3156i −0.418165 0.241427i 0.276127 0.961121i \(-0.410949\pi\)
−0.694292 + 0.719694i \(0.744282\pi\)
\(110\) −114.954 103.129i −1.04504 0.937540i
\(111\) 4.58824i 0.0413355i
\(112\) 0 0
\(113\) 45.4346 0.402076 0.201038 0.979583i \(-0.435568\pi\)
0.201038 + 0.979583i \(0.435568\pi\)
\(114\) 7.07618 7.88753i 0.0620718 0.0691888i
\(115\) −89.3952 + 154.837i −0.777350 + 1.34641i
\(116\) 14.8872 1.61915i 0.128338 0.0139582i
\(117\) −4.19831 7.27168i −0.0358830 0.0621511i
\(118\) −42.6962 130.601i −0.361832 1.10679i
\(119\) 0 0
\(120\) −95.4506 68.5610i −0.795422 0.571342i
\(121\) 99.4572 + 172.265i 0.821961 + 1.42368i
\(122\) 188.027 + 39.6112i 1.54121 + 0.324682i
\(123\) 207.171 + 119.610i 1.68431 + 0.972439i
\(124\) 0.0270508 0.0613532i 0.000218152 0.000494784i
\(125\) 135.395 1.08316
\(126\) 0 0
\(127\) 125.695 0.989723 0.494861 0.868972i \(-0.335219\pi\)
0.494861 + 0.868972i \(0.335219\pi\)
\(128\) −117.583 50.5782i −0.918620 0.395143i
\(129\) 38.4215 + 22.1827i 0.297841 + 0.171959i
\(130\) −27.5101 5.79549i −0.211616 0.0445807i
\(131\) −56.6504 98.1214i −0.432446 0.749018i 0.564638 0.825339i \(-0.309016\pi\)
−0.997083 + 0.0763210i \(0.975683\pi\)
\(132\) 143.807 + 196.436i 1.08945 + 1.48815i
\(133\) 0 0
\(134\) 26.5182 8.66933i 0.197897 0.0646965i
\(135\) −47.1648 81.6919i −0.349369 0.605125i
\(136\) 51.8208 + 114.713i 0.381036 + 0.843477i
\(137\) −39.1679 + 67.8408i −0.285897 + 0.495188i −0.972826 0.231536i \(-0.925625\pi\)
0.686929 + 0.726724i \(0.258958\pi\)
\(138\) 188.211 209.791i 1.36384 1.52022i
\(139\) 149.038 1.07222 0.536109 0.844149i \(-0.319894\pi\)
0.536109 + 0.844149i \(0.319894\pi\)
\(140\) 0 0
\(141\) 121.725i 0.863295i
\(142\) 101.115 112.709i 0.712081 0.793727i
\(143\) 50.4361 + 29.1193i 0.352700 + 0.203631i
\(144\) 27.8294 + 30.4618i 0.193260 + 0.211540i
\(145\) −13.9970 + 8.08117i −0.0965310 + 0.0557322i
\(146\) −101.035 + 33.0305i −0.692023 + 0.226236i
\(147\) 0 0
\(148\) −3.18601 4.35198i −0.0215271 0.0294053i
\(149\) −73.8369 + 42.6298i −0.495550 + 0.286106i −0.726874 0.686771i \(-0.759028\pi\)
0.231324 + 0.972877i \(0.425694\pi\)
\(150\) −42.3675 8.92545i −0.282450 0.0595030i
\(151\) −65.9012 + 114.144i −0.436432 + 0.755922i −0.997411 0.0719076i \(-0.977091\pi\)
0.560979 + 0.827830i \(0.310425\pi\)
\(152\) −1.23483 + 12.3950i −0.00812389 + 0.0815460i
\(153\) 40.5751i 0.265197i
\(154\) 0 0
\(155\) 0.0723686i 0.000466894i
\(156\) 40.5518 + 17.8794i 0.259948 + 0.114612i
\(157\) 122.552 212.267i 0.780589 1.35202i −0.151010 0.988532i \(-0.548253\pi\)
0.931599 0.363487i \(-0.118414\pi\)
\(158\) −45.6946 9.62637i −0.289206 0.0609264i
\(159\) 135.426 78.1883i 0.851737 0.491750i
\(160\) 138.144 1.24885i 0.863397 0.00780534i
\(161\) 0 0
\(162\) 60.6301 + 185.459i 0.374260 + 1.14481i
\(163\) 208.089 120.140i 1.27662 0.737057i 0.300395 0.953815i \(-0.402882\pi\)
0.976225 + 0.216758i \(0.0695482\pi\)
\(164\) −279.559 + 30.4052i −1.70463 + 0.185398i
\(165\) −227.550 131.376i −1.37909 0.796219i
\(166\) −136.879 + 152.573i −0.824573 + 0.919117i
\(167\) 73.1965i 0.438302i −0.975691 0.219151i \(-0.929671\pi\)
0.975691 0.219151i \(-0.0703288\pi\)
\(168\) 0 0
\(169\) −158.398 −0.937266
\(170\) −101.124 90.7224i −0.594850 0.533661i
\(171\) 2.00762 3.47730i 0.0117405 0.0203351i
\(172\) −51.8464 + 5.63890i −0.301433 + 0.0327843i
\(173\) −18.5246 32.0855i −0.107078 0.185465i 0.807507 0.589858i \(-0.200816\pi\)
−0.914585 + 0.404393i \(0.867483\pi\)
\(174\) 24.2168 7.91696i 0.139177 0.0454998i
\(175\) 0 0
\(176\) −272.804 86.4634i −1.55002 0.491269i
\(177\) −116.888 202.455i −0.660382 1.14382i
\(178\) −36.5136 + 173.323i −0.205132 + 0.973726i
\(179\) 205.982 + 118.924i 1.15074 + 0.664379i 0.949067 0.315074i \(-0.102029\pi\)
0.201672 + 0.979453i \(0.435363\pi\)
\(180\) −40.7469 17.9654i −0.226372 0.0998080i
\(181\) −292.553 −1.61631 −0.808157 0.588966i \(-0.799535\pi\)
−0.808157 + 0.588966i \(0.799535\pi\)
\(182\) 0 0
\(183\) 326.927 1.78649
\(184\) −32.8437 + 329.679i −0.178499 + 1.79173i
\(185\) 5.04132 + 2.91061i 0.0272504 + 0.0157330i
\(186\) 0.0235169 0.111631i 0.000126435 0.000600164i
\(187\) 140.713 + 243.723i 0.752478 + 1.30333i
\(188\) 84.5238 + 115.457i 0.449595 + 0.614132i
\(189\) 0 0
\(190\) −4.17754 12.7785i −0.0219871 0.0672552i
\(191\) −70.6135 122.306i −0.369704 0.640346i 0.619815 0.784748i \(-0.287208\pi\)
−0.989519 + 0.144402i \(0.953874\pi\)
\(192\) −213.496 42.9648i −1.11196 0.223775i
\(193\) 32.9799 57.1229i 0.170880 0.295973i −0.767848 0.640633i \(-0.778672\pi\)
0.938728 + 0.344659i \(0.112006\pi\)
\(194\) −209.713 188.141i −1.08099 0.969798i
\(195\) −47.8325 −0.245295
\(196\) 0 0
\(197\) 199.421i 1.01229i −0.862448 0.506145i \(-0.831070\pi\)
0.862448 0.506145i \(-0.168930\pi\)
\(198\) 68.6652 + 61.6020i 0.346794 + 0.311121i
\(199\) −58.6230 33.8460i −0.294588 0.170080i 0.345421 0.938448i \(-0.387736\pi\)
−0.640009 + 0.768367i \(0.721069\pi\)
\(200\) 46.3836 20.9535i 0.231918 0.104768i
\(201\) 41.1079 23.7337i 0.204517 0.118078i
\(202\) 21.9987 + 67.2907i 0.108904 + 0.333122i
\(203\) 0 0
\(204\) 126.506 + 172.803i 0.620128 + 0.847075i
\(205\) 262.842 151.752i 1.28216 0.740254i
\(206\) 41.4964 196.976i 0.201439 0.956193i
\(207\) 53.3982 92.4884i 0.257962 0.446804i
\(208\) −50.8790 + 11.1998i −0.244611 + 0.0538454i
\(209\) 27.8495i 0.133251i
\(210\) 0 0
\(211\) 62.1464i 0.294533i −0.989097 0.147266i \(-0.952953\pi\)
0.989097 0.147266i \(-0.0470475\pi\)
\(212\) −74.1600 + 168.200i −0.349811 + 0.793398i
\(213\) 128.811 223.106i 0.604744 1.04745i
\(214\) 44.0940 209.306i 0.206047 0.978066i
\(215\) 48.7463 28.1437i 0.226727 0.130901i
\(216\) −141.971 101.976i −0.657273 0.472111i
\(217\) 0 0
\(218\) 100.051 32.7088i 0.458952 0.150040i
\(219\) −156.623 + 90.4261i −0.715172 + 0.412905i
\(220\) 307.059 33.3962i 1.39572 0.151801i
\(221\) 44.3683 + 25.6161i 0.200762 + 0.115910i
\(222\) −6.83054 6.12792i −0.0307682 0.0276033i
\(223\) 115.525i 0.518050i −0.965871 0.259025i \(-0.916599\pi\)
0.965871 0.259025i \(-0.0834012\pi\)
\(224\) 0 0
\(225\) −16.4063 −0.0729171
\(226\) −60.6812 + 67.6388i −0.268501 + 0.299287i
\(227\) 28.2532 48.9360i 0.124463 0.215577i −0.797060 0.603901i \(-0.793612\pi\)
0.921523 + 0.388324i \(0.126946\pi\)
\(228\) 2.29147 + 21.0687i 0.0100503 + 0.0924067i
\(229\) 59.1696 + 102.485i 0.258383 + 0.447532i 0.965809 0.259255i \(-0.0834771\pi\)
−0.707426 + 0.706787i \(0.750144\pi\)
\(230\) −111.113 339.879i −0.483101 1.47774i
\(231\) 0 0
\(232\) −17.4724 + 24.3251i −0.0753123 + 0.104850i
\(233\) 12.3403 + 21.3740i 0.0529625 + 0.0917337i 0.891291 0.453431i \(-0.149800\pi\)
−0.838329 + 0.545165i \(0.816467\pi\)
\(234\) 16.4325 + 3.46180i 0.0702245 + 0.0147940i
\(235\) −133.745 77.2175i −0.569126 0.328585i
\(236\) 251.451 + 110.866i 1.06547 + 0.469769i
\(237\) −79.4503 −0.335233
\(238\) 0 0
\(239\) −251.189 −1.05100 −0.525499 0.850794i \(-0.676121\pi\)
−0.525499 + 0.850794i \(0.676121\pi\)
\(240\) 229.548 50.5298i 0.956452 0.210541i
\(241\) −97.3782 56.2213i −0.404059 0.233283i 0.284175 0.958772i \(-0.408280\pi\)
−0.688234 + 0.725489i \(0.741614\pi\)
\(242\) −389.284 82.0096i −1.60861 0.338883i
\(243\) 67.6598 + 117.190i 0.278436 + 0.482265i
\(244\) −310.093 + 227.014i −1.27087 + 0.930384i
\(245\) 0 0
\(246\) −454.755 + 148.668i −1.84860 + 0.604343i
\(247\) 2.53492 + 4.39061i 0.0102628 + 0.0177758i
\(248\) 0.0552087 + 0.122212i 0.000222616 + 0.000492792i
\(249\) −174.370 + 302.017i −0.700280 + 1.21292i
\(250\) −180.830 + 201.564i −0.723321 + 0.806256i
\(251\) 121.248 0.483059 0.241529 0.970394i \(-0.422351\pi\)
0.241529 + 0.970394i \(0.422351\pi\)
\(252\) 0 0
\(253\) 740.735i 2.92781i
\(254\) −167.874 + 187.123i −0.660923 + 0.736704i
\(255\) −200.174 115.571i −0.784998 0.453219i
\(256\) 232.337 107.496i 0.907567 0.419907i
\(257\) 90.7377 52.3874i 0.353065 0.203842i −0.312969 0.949763i \(-0.601324\pi\)
0.666034 + 0.745921i \(0.267990\pi\)
\(258\) −84.3381 + 27.5718i −0.326892 + 0.106867i
\(259\) 0 0
\(260\) 45.3695 33.2142i 0.174498 0.127747i
\(261\) 8.36079 4.82710i 0.0320337 0.0184946i
\(262\) 221.735 + 46.7123i 0.846315 + 0.178291i
\(263\) 52.3392 90.6542i 0.199008 0.344693i −0.749199 0.662345i \(-0.769561\pi\)
0.948207 + 0.317653i \(0.102895\pi\)
\(264\) −484.500 48.2675i −1.83523 0.182831i
\(265\) 198.399i 0.748675i
\(266\) 0 0
\(267\) 301.361i 1.12869i
\(268\) −22.5109 + 51.0564i −0.0839959 + 0.190509i
\(269\) −152.466 + 264.079i −0.566789 + 0.981707i 0.430092 + 0.902785i \(0.358481\pi\)
−0.996881 + 0.0789222i \(0.974852\pi\)
\(270\) 184.607 + 38.8908i 0.683731 + 0.144040i
\(271\) −88.8942 + 51.3231i −0.328023 + 0.189384i −0.654963 0.755661i \(-0.727316\pi\)
0.326940 + 0.945045i \(0.393982\pi\)
\(272\) −239.984 76.0613i −0.882295 0.279637i
\(273\) 0 0
\(274\) −48.6835 148.916i −0.177677 0.543488i
\(275\) 98.5482 56.8968i 0.358357 0.206898i
\(276\) 60.9479 + 560.381i 0.220826 + 2.03036i
\(277\) −14.4235 8.32739i −0.0520703 0.0300628i 0.473739 0.880665i \(-0.342904\pi\)
−0.525809 + 0.850603i \(0.676237\pi\)
\(278\) −199.051 + 221.874i −0.716012 + 0.798109i
\(279\) 0.0432277i 0.000154938i
\(280\) 0 0
\(281\) 75.8291 0.269855 0.134927 0.990856i \(-0.456920\pi\)
0.134927 + 0.990856i \(0.456920\pi\)
\(282\) 181.212 + 162.572i 0.642596 + 0.576496i
\(283\) 43.6656 75.6311i 0.154296 0.267248i −0.778507 0.627636i \(-0.784023\pi\)
0.932802 + 0.360389i \(0.117356\pi\)
\(284\) 32.7441 + 301.063i 0.115296 + 1.06008i
\(285\) −11.4367 19.8089i −0.0401287 0.0695050i
\(286\) −110.711 + 36.1936i −0.387102 + 0.126551i
\(287\) 0 0
\(288\) −82.5169 + 0.745975i −0.286517 + 0.00259019i
\(289\) −20.7152 35.8798i −0.0716789 0.124151i
\(290\) 6.66350 31.6304i 0.0229776 0.109070i
\(291\) −415.124 239.672i −1.42654 0.823614i
\(292\) 85.7673 194.527i 0.293724 0.666187i
\(293\) 27.5057 0.0938760 0.0469380 0.998898i \(-0.485054\pi\)
0.0469380 + 0.998898i \(0.485054\pi\)
\(294\) 0 0
\(295\) −296.597 −1.00541
\(296\) 10.7340 + 1.06935i 0.0362634 + 0.00361268i
\(297\) −338.452 195.406i −1.13957 0.657931i
\(298\) 35.1513 166.857i 0.117957 0.559922i
\(299\) 67.4232 + 116.780i 0.225496 + 0.390570i
\(300\) 69.8722 51.1522i 0.232907 0.170507i
\(301\) 0 0
\(302\) −81.9115 250.555i −0.271230 0.829654i
\(303\) 60.2248 + 104.312i 0.198762 + 0.344266i
\(304\) −16.8033 18.3927i −0.0552740 0.0605023i
\(305\) 207.390 359.211i 0.679968 1.17774i
\(306\) 60.4044 + 54.1909i 0.197400 + 0.177095i
\(307\) 247.996 0.807805 0.403902 0.914802i \(-0.367654\pi\)
0.403902 + 0.914802i \(0.367654\pi\)
\(308\) 0 0
\(309\) 342.486i 1.10837i
\(310\) −0.107736 0.0966534i −0.000347534 0.000311785i
\(311\) −378.484 218.518i −1.21699 0.702630i −0.252717 0.967540i \(-0.581324\pi\)
−0.964273 + 0.264910i \(0.914658\pi\)
\(312\) −80.7771 + 36.4905i −0.258901 + 0.116957i
\(313\) 71.7330 41.4151i 0.229179 0.132317i −0.381014 0.924569i \(-0.624425\pi\)
0.610193 + 0.792253i \(0.291092\pi\)
\(314\) 152.326 + 465.943i 0.485114 + 1.48389i
\(315\) 0 0
\(316\) 75.3593 55.1691i 0.238479 0.174586i
\(317\) 211.775 122.268i 0.668059 0.385704i −0.127282 0.991867i \(-0.540625\pi\)
0.795341 + 0.606162i \(0.207292\pi\)
\(318\) −64.4718 + 306.036i −0.202742 + 0.962377i
\(319\) −33.4806 + 57.9900i −0.104955 + 0.181787i
\(320\) −182.641 + 207.323i −0.570755 + 0.647885i
\(321\) 363.925i 1.13372i
\(322\) 0 0
\(323\) 24.4991i 0.0758485i
\(324\) −357.069 157.433i −1.10207 0.485904i
\(325\) 10.3577 17.9401i 0.0318699 0.0552004i
\(326\) −99.0643 + 470.240i −0.303878 + 1.44245i
\(327\) 155.097 89.5456i 0.474304 0.273840i
\(328\) 328.106 456.789i 1.00032 1.39265i
\(329\) 0 0
\(330\) 499.490 163.293i 1.51361 0.494828i
\(331\) 66.2919 38.2736i 0.200278 0.115630i −0.396507 0.918032i \(-0.629778\pi\)
0.596785 + 0.802401i \(0.296445\pi\)
\(332\) −44.3253 407.546i −0.133510 1.22755i
\(333\) −3.01132 1.73858i −0.00904299 0.00522097i
\(334\) 108.968 + 97.7592i 0.326252 + 0.292692i
\(335\) 60.2230i 0.179770i
\(336\) 0 0
\(337\) −38.2520 −0.113507 −0.0567537 0.998388i \(-0.518075\pi\)
−0.0567537 + 0.998388i \(0.518075\pi\)
\(338\) 211.552 235.808i 0.625893 0.697657i
\(339\) −77.3015 + 133.890i −0.228028 + 0.394956i
\(340\) 270.118 29.3785i 0.794465 0.0864072i
\(341\) 0.149913 + 0.259656i 0.000439627 + 0.000761456i
\(342\) 2.49536 + 7.63294i 0.00729637 + 0.0223185i
\(343\) 0 0
\(344\) 60.8500 84.7153i 0.176889 0.246265i
\(345\) −304.190 526.873i −0.881711 1.52717i
\(346\) 72.5068 + 15.2748i 0.209557 + 0.0441469i
\(347\) 208.395 + 120.317i 0.600561 + 0.346734i 0.769262 0.638933i \(-0.220624\pi\)
−0.168701 + 0.985667i \(0.553957\pi\)
\(348\) −20.5573 + 46.6254i −0.0590727 + 0.133981i
\(349\) 430.367 1.23314 0.616572 0.787298i \(-0.288521\pi\)
0.616572 + 0.787298i \(0.288521\pi\)
\(350\) 0 0
\(351\) −71.1449 −0.202692
\(352\) 493.068 290.648i 1.40076 0.825703i
\(353\) 265.950 + 153.546i 0.753399 + 0.434975i 0.826921 0.562318i \(-0.190090\pi\)
−0.0735214 + 0.997294i \(0.523424\pi\)
\(354\) 457.509 + 96.3822i 1.29240 + 0.272266i
\(355\) −163.425 283.061i −0.460353 0.797354i
\(356\) −209.261 285.844i −0.587811 0.802931i
\(357\) 0 0
\(358\) −452.147 + 147.816i −1.26298 + 0.412893i
\(359\) −230.880 399.896i −0.643120 1.11392i −0.984732 0.174075i \(-0.944306\pi\)
0.341613 0.939841i \(-0.389027\pi\)
\(360\) 81.1657 36.6661i 0.225460 0.101850i
\(361\) 179.288 310.536i 0.496642 0.860209i
\(362\) 390.726 435.526i 1.07935 1.20311i
\(363\) −676.858 −1.86462
\(364\) 0 0
\(365\) 229.452i 0.628635i
\(366\) −436.635 + 486.699i −1.19299 + 1.32978i
\(367\) 542.949 + 313.471i 1.47942 + 0.854146i 0.999729 0.0232895i \(-0.00741394\pi\)
0.479695 + 0.877435i \(0.340747\pi\)
\(368\) −446.930 489.205i −1.21448 1.32936i
\(369\) −157.003 + 90.6457i −0.425482 + 0.245652i
\(370\) −11.0661 + 3.61772i −0.0299083 + 0.00977762i
\(371\) 0 0
\(372\) 0.134777 + 0.184100i 0.000362303 + 0.000494894i
\(373\) −357.317 + 206.297i −0.957953 + 0.553075i −0.895543 0.444976i \(-0.853212\pi\)
−0.0624108 + 0.998051i \(0.519879\pi\)
\(374\) −550.765 116.028i −1.47263 0.310236i
\(375\) −230.359 + 398.993i −0.614290 + 1.06398i
\(376\) −284.769 28.3697i −0.757364 0.0754512i
\(377\) 12.1899i 0.0323339i
\(378\) 0 0
\(379\) 327.118i 0.863107i −0.902087 0.431554i \(-0.857966\pi\)
0.902087 0.431554i \(-0.142034\pi\)
\(380\) 24.6028 + 10.8475i 0.0647443 + 0.0285459i
\(381\) −213.854 + 370.407i −0.561298 + 0.972196i
\(382\) 276.387 + 58.2259i 0.723527 + 0.152424i
\(383\) 215.523 124.432i 0.562724 0.324889i −0.191514 0.981490i \(-0.561340\pi\)
0.754238 + 0.656601i \(0.228006\pi\)
\(384\) 349.102 260.451i 0.909119 0.678257i
\(385\) 0 0
\(386\) 40.9922 + 125.389i 0.106197 + 0.324842i
\(387\) −29.1175 + 16.8110i −0.0752390 + 0.0434392i
\(388\) 560.173 60.9253i 1.44375 0.157024i
\(389\) 326.728 + 188.637i 0.839918 + 0.484927i 0.857236 0.514923i \(-0.172179\pi\)
−0.0173181 + 0.999850i \(0.505513\pi\)
\(390\) 63.8837 71.2086i 0.163804 0.182586i
\(391\) 651.620i 1.66655i
\(392\) 0 0
\(393\) 385.535 0.981005
\(394\) 296.880 + 266.341i 0.753502 + 0.675994i
\(395\) −50.4003 + 87.2958i −0.127596 + 0.221002i
\(396\) −183.415 + 19.9485i −0.463168 + 0.0503749i
\(397\) 335.874 + 581.752i 0.846031 + 1.46537i 0.884723 + 0.466118i \(0.154348\pi\)
−0.0386913 + 0.999251i \(0.512319\pi\)
\(398\) 128.682 42.0687i 0.323322 0.105700i
\(399\) 0 0
\(400\) −30.7550 + 97.0365i −0.0768876 + 0.242591i
\(401\) 235.200 + 407.378i 0.586534 + 1.01591i 0.994682 + 0.102991i \(0.0328411\pi\)
−0.408149 + 0.912915i \(0.633826\pi\)
\(402\) −19.5701 + 92.8957i −0.0486819 + 0.231084i
\(403\) 0.0472689 + 0.0272907i 0.000117293 + 6.77189e-5i
\(404\) −129.557 57.1220i −0.320685 0.141391i
\(405\) 421.177 1.03994
\(406\) 0 0
\(407\) 24.1175 0.0592567
\(408\) −426.211 42.4606i −1.04464 0.104070i
\(409\) 57.7400 + 33.3362i 0.141174 + 0.0815067i 0.568923 0.822391i \(-0.307360\pi\)
−0.427750 + 0.903897i \(0.640693\pi\)
\(410\) −125.130 + 593.971i −0.305196 + 1.44871i
\(411\) −133.279 230.846i −0.324279 0.561669i
\(412\) 237.818 + 324.851i 0.577227 + 0.788474i
\(413\) 0 0
\(414\) 66.3709 + 203.019i 0.160316 + 0.490384i
\(415\) 221.227 + 383.177i 0.533077 + 0.923317i
\(416\) 51.2793 90.7021i 0.123267 0.218034i
\(417\) −253.571 + 439.197i −0.608083 + 1.05323i
\(418\) −41.4598 37.1950i −0.0991860 0.0889833i
\(419\) −437.380 −1.04387 −0.521933 0.852986i \(-0.674789\pi\)
−0.521933 + 0.852986i \(0.674789\pi\)
\(420\) 0 0
\(421\) 703.800i 1.67173i −0.548933 0.835867i \(-0.684966\pi\)
0.548933 0.835867i \(-0.315034\pi\)
\(422\) 92.5178 + 83.0010i 0.219236 + 0.196685i
\(423\) 79.8893 + 46.1241i 0.188864 + 0.109040i
\(424\) −151.355 335.046i −0.356969 0.790203i
\(425\) 86.6923 50.0518i 0.203982 0.117769i
\(426\) 160.104 + 489.736i 0.375832 + 1.14961i
\(427\) 0 0
\(428\) 252.705 + 345.186i 0.590431 + 0.806510i
\(429\) −171.622 + 99.0858i −0.400051 + 0.230969i
\(430\) −23.2065 + 110.157i −0.0539686 + 0.256179i
\(431\) 274.869 476.087i 0.637747 1.10461i −0.348178 0.937428i \(-0.613200\pi\)
0.985926 0.167183i \(-0.0534670\pi\)
\(432\) 341.425 75.1568i 0.790335 0.173974i
\(433\) 355.012i 0.819890i 0.912110 + 0.409945i \(0.134452\pi\)
−0.912110 + 0.409945i \(0.865548\pi\)
\(434\) 0 0
\(435\) 54.9965i 0.126429i
\(436\) −84.9321 + 192.632i −0.194798 + 0.441817i
\(437\) −32.2416 + 55.8441i −0.0737794 + 0.127790i
\(438\) 74.5628 353.936i 0.170235 0.808073i
\(439\) −477.032 + 275.415i −1.08663 + 0.627369i −0.932678 0.360709i \(-0.882535\pi\)
−0.153956 + 0.988078i \(0.549201\pi\)
\(440\) −360.382 + 501.724i −0.819050 + 1.14028i
\(441\) 0 0
\(442\) −97.3919 + 31.8393i −0.220344 + 0.0720347i
\(443\) 234.027 135.116i 0.528278 0.305001i −0.212037 0.977262i \(-0.568010\pi\)
0.740315 + 0.672260i \(0.234676\pi\)
\(444\) 18.2454 1.98439i 0.0410932 0.00446936i
\(445\) 331.120 + 191.172i 0.744089 + 0.429600i
\(446\) 171.983 + 154.292i 0.385612 + 0.345947i
\(447\) 290.117i 0.649032i
\(448\) 0 0
\(449\) 455.397 1.01425 0.507124 0.861873i \(-0.330709\pi\)
0.507124 + 0.861873i \(0.330709\pi\)
\(450\) 21.9118 24.4242i 0.0486930 0.0542761i
\(451\) 628.714 1088.96i 1.39404 2.41456i
\(452\) −19.6503 180.673i −0.0434741 0.399719i
\(453\) −224.246 388.405i −0.495024 0.857406i
\(454\) 35.1171 + 107.418i 0.0773505 + 0.236604i
\(455\) 0 0
\(456\) −34.4256 24.7275i −0.0754947 0.0542269i
\(457\) 84.3172 + 146.042i 0.184501 + 0.319566i 0.943408 0.331633i \(-0.107600\pi\)
−0.758907 + 0.651199i \(0.774266\pi\)
\(458\) −231.595 48.7896i −0.505666 0.106528i
\(459\) −297.735 171.897i −0.648659 0.374504i
\(460\) 654.380 + 288.518i 1.42257 + 0.627213i
\(461\) 265.062 0.574971 0.287485 0.957785i \(-0.407181\pi\)
0.287485 + 0.957785i \(0.407181\pi\)
\(462\) 0 0
\(463\) 97.4735 0.210526 0.105263 0.994444i \(-0.466432\pi\)
0.105263 + 0.994444i \(0.466432\pi\)
\(464\) −12.8773 58.4993i −0.0277528 0.126076i
\(465\) −0.213261 0.123126i −0.000458626 0.000264788i
\(466\) −48.3009 10.1754i −0.103650 0.0218357i
\(467\) −37.0997 64.2586i −0.0794427 0.137599i 0.823567 0.567219i \(-0.191981\pi\)
−0.903010 + 0.429620i \(0.858647\pi\)
\(468\) −27.1005 + 19.8398i −0.0579070 + 0.0423926i
\(469\) 0 0
\(470\) 293.580 95.9770i 0.624638 0.204206i
\(471\) 417.016 + 722.293i 0.885385 + 1.53353i
\(472\) −500.877 + 226.268i −1.06118 + 0.479382i
\(473\) 116.600 201.958i 0.246512 0.426972i
\(474\) 106.112 118.278i 0.223864 0.249532i
\(475\) 9.90608 0.0208549
\(476\) 0 0
\(477\) 118.509i 0.248447i
\(478\) 335.480 373.946i 0.701842 0.782314i
\(479\) 475.220 + 274.368i 0.992108 + 0.572794i 0.905904 0.423484i \(-0.139193\pi\)
0.0862043 + 0.996277i \(0.472526\pi\)
\(480\) −231.354 + 409.216i −0.481988 + 0.852534i
\(481\) 3.80224 2.19522i 0.00790486 0.00456387i
\(482\) 213.753 69.8799i 0.443470 0.144979i
\(483\) 0 0
\(484\) 642.006 470.001i 1.32646 0.971076i
\(485\) −526.678 + 304.078i −1.08593 + 0.626964i
\(486\) −264.827 55.7904i −0.544911 0.114795i
\(487\) −283.938 + 491.795i −0.583034 + 1.00985i 0.412083 + 0.911146i \(0.364801\pi\)
−0.995117 + 0.0986990i \(0.968532\pi\)
\(488\) 76.1951 764.831i 0.156137 1.56728i
\(489\) 817.617i 1.67202i
\(490\) 0 0
\(491\) 78.8005i 0.160490i 0.996775 + 0.0802449i \(0.0255702\pi\)
−0.996775 + 0.0802449i \(0.974430\pi\)
\(492\) 386.035 875.555i 0.784623 1.77958i
\(493\) −29.4527 + 51.0135i −0.0597417 + 0.103476i
\(494\) −9.92190 2.09022i −0.0200848 0.00423122i
\(495\) 172.447 99.5626i 0.348379 0.201136i
\(496\) −0.255674 0.0810339i −0.000515471 0.000163375i
\(497\) 0 0
\(498\) −216.732 662.951i −0.435204 1.33123i
\(499\) −290.932 + 167.970i −0.583030 + 0.336612i −0.762337 0.647181i \(-0.775948\pi\)
0.179307 + 0.983793i \(0.442615\pi\)
\(500\) −58.5579 538.406i −0.117116 1.07681i
\(501\) 215.701 + 124.535i 0.430541 + 0.248573i
\(502\) −161.935 + 180.502i −0.322580 + 0.359566i
\(503\) 274.052i 0.544836i −0.962179 0.272418i \(-0.912177\pi\)
0.962179 0.272418i \(-0.0878233\pi\)
\(504\) 0 0
\(505\) 152.817 0.302609
\(506\) −1102.74 989.304i −2.17932 1.95515i
\(507\) 269.495 466.779i 0.531548 0.920669i
\(508\) −54.3625 499.832i −0.107013 0.983921i
\(509\) −168.009 291.000i −0.330076 0.571709i 0.652450 0.757831i \(-0.273741\pi\)
−0.982526 + 0.186123i \(0.940408\pi\)
\(510\) 439.398 143.648i 0.861566 0.281663i
\(511\) 0 0
\(512\) −150.273 + 489.451i −0.293501 + 0.955959i
\(513\) −17.0106 29.4633i −0.0331591 0.0574333i
\(514\) −43.1972 + 205.049i −0.0840412 + 0.398928i
\(515\) −376.306 217.260i −0.730691 0.421865i
\(516\) 71.5933 162.379i 0.138747 0.314688i
\(517\) −639.829 −1.23758
\(518\) 0 0
\(519\) 126.069 0.242908
\(520\) −11.1480 + 111.902i −0.0214385 + 0.215196i
\(521\) 547.572 + 316.141i 1.05100 + 0.606796i 0.922930 0.384969i \(-0.125788\pi\)
0.128072 + 0.991765i \(0.459121\pi\)
\(522\) −3.98029 + 18.8937i −0.00762508 + 0.0361948i
\(523\) −389.623 674.847i −0.744977 1.29034i −0.950206 0.311624i \(-0.899127\pi\)
0.205229 0.978714i \(-0.434206\pi\)
\(524\) −365.683 + 267.710i −0.697869 + 0.510897i
\(525\) 0 0
\(526\) 65.0547 + 198.993i 0.123678 + 0.378314i
\(527\) 0.131877 + 0.228418i 0.000250242 + 0.000433431i
\(528\) 718.940 656.813i 1.36163 1.24396i
\(529\) −593.054 + 1027.20i −1.12109 + 1.94178i
\(530\) 295.358 + 264.976i 0.557279 + 0.499955i
\(531\) 177.165 0.333644
\(532\) 0 0
\(533\) 228.907i 0.429470i
\(534\) −448.638 402.489i −0.840146 0.753725i
\(535\) −399.862 230.861i −0.747406 0.431515i
\(536\) −45.9431 101.702i −0.0857146 0.189742i
\(537\) −700.908 + 404.669i −1.30523 + 0.753574i
\(538\) −189.507 579.674i −0.352243 1.07746i
\(539\) 0 0
\(540\) −304.453 + 222.885i −0.563802 + 0.412750i
\(541\) 583.617 336.952i 1.07878 0.622831i 0.148209 0.988956i \(-0.452649\pi\)
0.930566 + 0.366125i \(0.119316\pi\)
\(542\) 42.3195 200.883i 0.0780803 0.370633i
\(543\) 497.743 862.117i 0.916655 1.58769i
\(544\) 433.749 255.681i 0.797333 0.470002i
\(545\) 227.217i 0.416913i
\(546\) 0 0
\(547\) 52.5329i 0.0960382i −0.998846 0.0480191i \(-0.984709\pi\)
0.998846 0.0480191i \(-0.0152908\pi\)
\(548\) 286.712 + 126.412i 0.523198 + 0.230679i
\(549\) −123.880 + 214.566i −0.225646 + 0.390831i
\(550\) −46.9155 + 222.699i −0.0853009 + 0.404907i
\(551\) −5.04821 + 2.91458i −0.00916190 + 0.00528963i
\(552\) −915.643 657.695i −1.65877 1.19148i
\(553\) 0 0
\(554\) 31.6606 10.3505i 0.0571491 0.0186832i
\(555\) −17.1544 + 9.90409i −0.0309088 + 0.0178452i
\(556\) −64.4585 592.658i −0.115933 1.06593i
\(557\) 678.123 + 391.515i 1.21746 + 0.702899i 0.964373 0.264546i \(-0.0852220\pi\)
0.253083 + 0.967445i \(0.418555\pi\)
\(558\) 0.0643534 + 0.0577337i 0.000115329 + 0.000103465i
\(559\) 42.4528i 0.0759441i
\(560\) 0 0
\(561\) −957.628 −1.70700
\(562\) −101.275 + 112.887i −0.180205 + 0.200867i
\(563\) −446.202 + 772.844i −0.792543 + 1.37272i 0.131845 + 0.991270i \(0.457910\pi\)
−0.924388 + 0.381454i \(0.875423\pi\)
\(564\) −484.044 + 52.6454i −0.858234 + 0.0933429i
\(565\) 98.0743 + 169.870i 0.173583 + 0.300654i
\(566\) 54.2739 + 166.016i 0.0958903 + 0.293315i
\(567\) 0 0
\(568\) −491.926 353.345i −0.866067 0.622085i
\(569\) 148.722 + 257.593i 0.261373 + 0.452712i 0.966607 0.256263i \(-0.0824912\pi\)
−0.705234 + 0.708975i \(0.749158\pi\)
\(570\) 44.7642 + 9.43036i 0.0785337 + 0.0165445i
\(571\) −218.885 126.373i −0.383335 0.221319i 0.295933 0.955209i \(-0.404369\pi\)
−0.679268 + 0.733890i \(0.737703\pi\)
\(572\) 93.9808 213.155i 0.164302 0.372649i
\(573\) 480.561 0.838676
\(574\) 0 0
\(575\) 263.479 0.458225
\(576\) 109.097 123.840i 0.189404 0.215000i
\(577\) −764.454 441.358i −1.32488 0.764918i −0.340375 0.940290i \(-0.610554\pi\)
−0.984502 + 0.175371i \(0.943887\pi\)
\(578\) 81.0811 + 17.0812i 0.140279 + 0.0295522i
\(579\) 112.223 + 194.375i 0.193821 + 0.335709i
\(580\) 38.1888 + 52.1647i 0.0658428 + 0.0899391i
\(581\) 0 0
\(582\) 911.229 297.899i 1.56568 0.511853i
\(583\) −410.987 711.850i −0.704951 1.22101i
\(584\) 175.045 + 387.487i 0.299734 + 0.663504i
\(585\) 18.1248 31.3930i 0.0309825 0.0536633i
\(586\) −36.7358 + 40.9479i −0.0626890 + 0.0698769i
\(587\) 66.7814 0.113767 0.0568836 0.998381i \(-0.481884\pi\)
0.0568836 + 0.998381i \(0.481884\pi\)
\(588\) 0 0
\(589\) 0.0261007i 4.43136e-5i
\(590\) 396.126 441.545i 0.671400 0.748382i
\(591\) 587.670 + 339.291i 0.994365 + 0.574097i
\(592\) −15.9279 + 14.5515i −0.0269053 + 0.0245803i
\(593\) 311.911 180.082i 0.525989 0.303680i −0.213393 0.976967i \(-0.568451\pi\)
0.739381 + 0.673287i \(0.235118\pi\)
\(594\) 742.929 242.878i 1.25072 0.408886i
\(595\) 0 0
\(596\) 201.454 + 275.179i 0.338009 + 0.461710i
\(597\) 199.480 115.170i 0.334137 0.192914i
\(598\) −263.900 55.5952i −0.441305 0.0929686i
\(599\) 99.0219 171.511i 0.165312 0.286329i −0.771454 0.636285i \(-0.780470\pi\)
0.936766 + 0.349956i \(0.113804\pi\)
\(600\) −17.1688 + 172.337i −0.0286146 + 0.287228i
\(601\) 373.907i 0.622141i 0.950387 + 0.311071i \(0.100688\pi\)
−0.950387 + 0.311071i \(0.899312\pi\)
\(602\) 0 0
\(603\) 35.9728i 0.0596565i
\(604\) 482.402 + 212.692i 0.798679 + 0.352140i
\(605\) −429.373 + 743.696i −0.709708 + 1.22925i
\(606\) −235.725 49.6597i −0.388986 0.0819466i
\(607\) −200.164 + 115.565i −0.329760 + 0.190387i −0.655735 0.754992i \(-0.727641\pi\)
0.325975 + 0.945379i \(0.394308\pi\)
\(608\) 49.8234 0.450416i 0.0819463 0.000740816i
\(609\) 0 0
\(610\) 257.775 + 788.495i 0.422581 + 1.29261i
\(611\) −100.872 + 58.2386i −0.165094 + 0.0953168i
\(612\) −161.349 + 17.5486i −0.263642 + 0.0286741i
\(613\) −444.718 256.758i −0.725479 0.418855i 0.0912873 0.995825i \(-0.470902\pi\)
−0.816766 + 0.576969i \(0.804235\pi\)
\(614\) −331.217 + 369.193i −0.539441 + 0.601292i
\(615\) 1032.75i 1.67927i
\(616\) 0 0
\(617\) −1119.01 −1.81363 −0.906815 0.421529i \(-0.861493\pi\)
−0.906815 + 0.421529i \(0.861493\pi\)
\(618\) 509.862 + 457.415i 0.825019 + 0.740154i
\(619\) −64.1019 + 111.028i −0.103557 + 0.179366i −0.913148 0.407629i \(-0.866356\pi\)
0.809591 + 0.586995i \(0.199689\pi\)
\(620\) 0.287777 0.0312991i 0.000464157 5.04824e-5i
\(621\) −452.445 783.658i −0.728575 1.26193i
\(622\) 830.802 271.605i 1.33569 0.436665i
\(623\) 0 0
\(624\) 53.5599 168.989i 0.0858332 0.270816i
\(625\) 212.735 + 368.469i 0.340377 + 0.589550i
\(626\) −34.1497 + 162.102i −0.0545522 + 0.258949i
\(627\) −82.0690 47.3826i −0.130892 0.0755703i
\(628\) −897.094 395.531i −1.42849 0.629827i
\(629\) 21.2160 0.0337297
\(630\) 0 0
\(631\) 313.995 0.497615 0.248808 0.968553i \(-0.419961\pi\)
0.248808 + 0.968553i \(0.419961\pi\)
\(632\) −18.5170 + 185.870i −0.0292991 + 0.294098i
\(633\) 183.138 + 105.735i 0.289317 + 0.167037i
\(634\) −100.819 + 478.569i −0.159020 + 0.754840i
\(635\) 271.322 + 469.944i 0.427279 + 0.740070i
\(636\) −369.491 504.713i −0.580961 0.793573i
\(637\) 0 0
\(638\) −41.6145 127.293i −0.0652264 0.199518i
\(639\) 97.6183 + 169.080i 0.152767 + 0.264601i
\(640\) −64.7127 548.795i −0.101114 0.857492i
\(641\) 115.594 200.215i 0.180334 0.312348i −0.761660 0.647977i \(-0.775615\pi\)
0.941994 + 0.335629i \(0.108949\pi\)
\(642\) 541.778 + 486.048i 0.843891 + 0.757085i
\(643\) −637.869 −0.992020 −0.496010 0.868317i \(-0.665202\pi\)
−0.496010 + 0.868317i \(0.665202\pi\)
\(644\) 0 0
\(645\) 191.532i 0.296949i
\(646\) −36.4719 32.7203i −0.0564581 0.0506505i
\(647\) 586.461 + 338.594i 0.906432 + 0.523329i 0.879281 0.476303i \(-0.158023\pi\)
0.0271505 + 0.999631i \(0.491357\pi\)
\(648\) 711.263 321.309i 1.09763 0.495847i
\(649\) −1064.18 + 614.405i −1.63972 + 0.946695i
\(650\) 12.8741 + 39.3799i 0.0198063 + 0.0605845i
\(651\) 0 0
\(652\) −567.742 775.517i −0.870769 1.18944i
\(653\) −916.022 + 528.865i −1.40279 + 0.809901i −0.994678 0.103031i \(-0.967146\pi\)
−0.408112 + 0.912932i \(0.633813\pi\)
\(654\) −73.8367 + 350.489i −0.112900 + 0.535916i
\(655\) 244.569 423.606i 0.373388 0.646726i
\(656\) 241.816 + 1098.53i 0.368622 + 1.67459i
\(657\) 137.058i 0.208612i
\(658\) 0 0
\(659\) 644.502i 0.978000i 0.872284 + 0.489000i \(0.162638\pi\)
−0.872284 + 0.489000i \(0.837362\pi\)
\(660\) −424.009 + 961.684i −0.642438 + 1.45710i
\(661\) −560.069 + 970.068i −0.847306 + 1.46758i 0.0362979 + 0.999341i \(0.488443\pi\)
−0.883604 + 0.468236i \(0.844890\pi\)
\(662\) −31.5593 + 149.806i −0.0476727 + 0.226294i
\(663\) −150.975 + 87.1652i −0.227714 + 0.131471i
\(664\) 665.916 + 478.319i 1.00289 + 0.720360i
\(665\) 0 0
\(666\) 6.61007 2.16096i 0.00992503 0.00324469i
\(667\) −134.271 + 77.5214i −0.201306 + 0.116224i
\(668\) −291.070 + 31.6572i −0.435733 + 0.0473910i
\(669\) 340.438 + 196.552i 0.508876 + 0.293800i
\(670\) 89.6544 + 80.4322i 0.133813 + 0.120048i
\(671\) 1718.45i 2.56103i
\(672\) 0 0
\(673\) −307.811 −0.457371 −0.228686 0.973500i \(-0.573443\pi\)
−0.228686 + 0.973500i \(0.573443\pi\)
\(674\) 51.0883 56.9460i 0.0757987 0.0844897i
\(675\) −69.5058 + 120.388i −0.102972 + 0.178352i
\(676\) 68.5065 + 629.878i 0.101341 + 0.931772i
\(677\) 507.773 + 879.488i 0.750033 + 1.29910i 0.947806 + 0.318848i \(0.103296\pi\)
−0.197773 + 0.980248i \(0.563371\pi\)
\(678\) −96.0814 293.899i −0.141713 0.433479i
\(679\) 0 0
\(680\) −317.026 + 441.364i −0.466215 + 0.649064i
\(681\) 96.1388 + 166.517i 0.141173 + 0.244519i
\(682\) −0.586772 0.123614i −0.000860369 0.000181252i
\(683\) −840.220 485.102i −1.23019 0.710251i −0.263121 0.964763i \(-0.584752\pi\)
−0.967070 + 0.254512i \(0.918085\pi\)
\(684\) −14.6959 6.47948i −0.0214853 0.00947293i
\(685\) −338.188 −0.493706
\(686\) 0 0
\(687\) −402.680 −0.586143
\(688\) 44.8467 + 203.731i 0.0651842 + 0.296121i
\(689\) −129.588 74.8177i −0.188081 0.108589i
\(690\) 1190.63 + 250.827i 1.72555 + 0.363517i
\(691\) −274.581 475.588i −0.397367 0.688260i 0.596033 0.802960i \(-0.296743\pi\)
−0.993400 + 0.114700i \(0.963409\pi\)
\(692\) −119.578 + 87.5407i −0.172800 + 0.126504i
\(693\) 0 0
\(694\) −457.442 + 149.547i −0.659138 + 0.215485i
\(695\) 321.711 + 557.221i 0.462894 + 0.801756i
\(696\) −41.9559 92.8754i −0.0602814 0.133442i
\(697\) 553.076 957.956i 0.793510 1.37440i
\(698\) −574.786 + 640.691i −0.823476 + 0.917895i
\(699\) −83.9818 −0.120146
\(700\) 0 0
\(701\) 452.665i 0.645742i −0.946443 0.322871i \(-0.895352\pi\)
0.946443 0.322871i \(-0.104648\pi\)
\(702\) 95.0191 105.914i 0.135355 0.150874i
\(703\) 1.81822 + 1.04975i 0.00258637 + 0.00149324i
\(704\) −225.839 + 1122.21i −0.320794 + 1.59406i
\(705\) 455.100 262.752i 0.645533 0.372698i
\(706\) −583.781 + 190.849i −0.826885 + 0.270325i
\(707\) 0 0
\(708\) −754.520 + 552.371i −1.06571 + 0.780185i
\(709\) −609.174 + 351.707i −0.859202 + 0.496060i −0.863745 0.503929i \(-0.831887\pi\)
0.00454321 + 0.999990i \(0.498554\pi\)
\(710\) 639.660 + 134.756i 0.900930 + 0.189797i
\(711\) 30.1054 52.1442i 0.0423424 0.0733392i
\(712\) 705.020 + 70.2365i 0.990197 + 0.0986468i
\(713\) 0.694220i 0.000973661i
\(714\) 0 0
\(715\) 251.425i 0.351644i
\(716\) 383.820 870.533i 0.536062 1.21583i
\(717\) 427.367 740.221i 0.596049 1.03239i
\(718\) 903.684 + 190.377i 1.25861 + 0.265149i
\(719\) −54.1160 + 31.2439i −0.0752656 + 0.0434546i −0.537161 0.843480i \(-0.680503\pi\)
0.461895 + 0.886935i \(0.347170\pi\)
\(720\) −53.8176 + 169.802i −0.0747467 + 0.235836i
\(721\) 0 0
\(722\) 222.845 + 681.650i 0.308649 + 0.944113i
\(723\) 331.354 191.307i 0.458305 0.264602i
\(724\) 126.528 + 1163.35i 0.174762 + 1.60684i
\(725\) 20.6271 + 11.9090i 0.0284511 + 0.0164263i
\(726\) 903.992 1007.64i 1.24517 1.38794i
\(727\) 889.995i 1.22420i −0.790779 0.612101i \(-0.790324\pi\)
0.790779 0.612101i \(-0.209676\pi\)
\(728\) 0 0
\(729\) 417.569 0.572797
\(730\) −341.586 306.449i −0.467927 0.419794i
\(731\) 102.573 177.661i 0.140318 0.243038i
\(732\) −141.395 1300.04i −0.193162 1.77601i
\(733\) 456.127 + 790.035i 0.622274 + 1.07781i 0.989061 + 0.147505i \(0.0471243\pi\)
−0.366787 + 0.930305i \(0.619542\pi\)
\(734\) −1191.81 + 389.628i −1.62372 + 0.530828i
\(735\) 0 0
\(736\) 1325.19 11.9801i 1.80053 0.0162773i
\(737\) −124.753 216.079i −0.169271 0.293187i
\(738\) 74.7438 354.795i 0.101279 0.480752i
\(739\) 1081.52 + 624.415i 1.46349 + 0.844946i 0.999171 0.0407224i \(-0.0129659\pi\)
0.464319 + 0.885668i \(0.346299\pi\)
\(740\) 9.39382 21.3059i 0.0126944 0.0287917i
\(741\) −17.2514 −0.0232813
\(742\) 0 0
\(743\) −305.880 −0.411682 −0.205841 0.978585i \(-0.565993\pi\)
−0.205841 + 0.978585i \(0.565993\pi\)
\(744\) −0.454075 0.0452365i −0.000610316 6.08018e-5i
\(745\) −318.766 184.040i −0.427874 0.247033i
\(746\) 170.106 807.464i 0.228025 1.08239i
\(747\) −132.145 228.882i −0.176901 0.306401i
\(748\) 908.318 664.963i 1.21433 0.888988i
\(749\) 0 0
\(750\) −286.323 875.820i −0.381764 1.16776i
\(751\) −258.895 448.420i −0.344734 0.597097i 0.640571 0.767899i \(-0.278698\pi\)
−0.985305 + 0.170802i \(0.945364\pi\)
\(752\) 422.564 386.048i 0.561920 0.513362i
\(753\) −206.288 + 357.302i −0.273955 + 0.474504i
\(754\) −18.1472 16.2805i −0.0240678 0.0215921i
\(755\) −569.012 −0.753659
\(756\) 0 0
\(757\) 939.898i 1.24161i 0.783965 + 0.620804i \(0.213194\pi\)
−0.783965 + 0.620804i \(0.786806\pi\)
\(758\) 486.982 + 436.889i 0.642457 + 0.576371i
\(759\) −2182.85 1260.27i −2.87596 1.66044i
\(760\) −49.0075 + 22.1388i −0.0644836 + 0.0291301i
\(761\) 976.757 563.931i 1.28352 0.741039i 0.306028 0.952022i \(-0.401000\pi\)
0.977490 + 0.210983i \(0.0676665\pi\)
\(762\) −265.809 813.072i −0.348831 1.06702i
\(763\) 0 0
\(764\) −455.816 + 333.695i −0.596618 + 0.436773i
\(765\) 151.701 87.5846i 0.198302 0.114490i
\(766\) −102.603 + 487.039i −0.133947 + 0.635821i
\(767\) −111.849 + 193.728i −0.145826 + 0.252579i
\(768\) −78.5156 + 867.560i −0.102234 + 1.12964i
\(769\) 300.115i 0.390267i −0.980777 0.195133i \(-0.937486\pi\)
0.980777 0.195133i \(-0.0625139\pi\)
\(770\) 0 0
\(771\) 356.524i 0.462417i
\(772\) −241.416 106.441i −0.312714 0.137877i
\(773\) 375.120 649.727i 0.485278 0.840527i −0.514579 0.857443i \(-0.672052\pi\)
0.999857 + 0.0169165i \(0.00538495\pi\)
\(774\) 13.8619 65.7997i 0.0179094 0.0850125i
\(775\) 0.0923598 0.0533240i 0.000119174 6.88051e-5i
\(776\) −657.452 + 915.304i −0.847231 + 1.17952i
\(777\) 0 0
\(778\) −717.194 + 234.465i −0.921843 + 0.301369i
\(779\) 94.7977 54.7315i 0.121691 0.0702586i
\(780\) 20.6874 + 190.208i 0.0265222 + 0.243857i
\(781\) −1172.73 677.076i −1.50158 0.866935i
\(782\) −970.071 870.285i −1.24050 1.11290i
\(783\) 81.8005i 0.104471i
\(784\) 0 0
\(785\) 1058.16 1.34797
\(786\) −514.910 + 573.949i −0.655102 + 0.730215i
\(787\) 144.776 250.760i 0.183960 0.318627i −0.759266 0.650781i \(-0.774442\pi\)
0.943225 + 0.332153i \(0.107775\pi\)
\(788\) −793.009 + 86.2489i −1.00636 + 0.109453i
\(789\) 178.098 + 308.474i 0.225726 + 0.390969i
\(790\) −62.6447 191.621i −0.0792971 0.242558i
\(791\) 0 0
\(792\) 215.266 299.693i 0.271801 0.378401i
\(793\) −156.417 270.922i −0.197247 0.341642i
\(794\) −1314.64 276.952i −1.65572 0.348807i
\(795\) 584.657 + 337.552i 0.735417 + 0.424593i
\(796\) −109.236 + 247.756i −0.137231 + 0.311251i
\(797\) 1086.57 1.36332 0.681659 0.731670i \(-0.261259\pi\)
0.681659 + 0.731670i \(0.261259\pi\)
\(798\) 0 0
\(799\) −562.854 −0.704448
\(800\) −103.383 175.384i −0.129229 0.219231i
\(801\) −197.787 114.192i −0.246925 0.142562i
\(802\) −920.593 193.939i −1.14787 0.241819i
\(803\) 475.313 + 823.267i 0.591922 + 1.02524i
\(804\) −112.157 153.203i −0.139499 0.190551i
\(805\) 0 0
\(806\) −0.103759 + 0.0339208i −0.000128733 + 4.20854e-5i
\(807\) −518.806 898.598i −0.642882 1.11350i
\(808\) 258.070 116.582i 0.319394 0.144284i
\(809\) −90.9745 + 157.572i −0.112453 + 0.194774i −0.916759 0.399441i \(-0.869204\pi\)
0.804306 + 0.594216i \(0.202537\pi\)
\(810\) −562.513 + 627.010i −0.694460 + 0.774086i
\(811\) 1005.31 1.23960 0.619799 0.784760i \(-0.287214\pi\)
0.619799 + 0.784760i \(0.287214\pi\)
\(812\) 0 0
\(813\) 349.280i 0.429619i
\(814\) −32.2106 + 35.9039i −0.0395708 + 0.0441079i
\(815\) 898.355 + 518.665i 1.10228 + 0.636399i
\(816\) 632.447 577.795i 0.775058 0.708082i
\(817\) 17.5810 10.1504i 0.0215190 0.0124240i
\(818\) −126.744 + 41.4351i −0.154944 + 0.0506541i
\(819\) 0 0
\(820\) −717.128 979.573i −0.874546 1.19460i
\(821\) 851.009 491.330i 1.03655 0.598453i 0.117697 0.993050i \(-0.462449\pi\)
0.918855 + 0.394596i \(0.129115\pi\)
\(822\) 521.665 + 109.898i 0.634629 + 0.133696i
\(823\) −742.505 + 1286.06i −0.902194 + 1.56265i −0.0775532 + 0.996988i \(0.524711\pi\)
−0.824641 + 0.565657i \(0.808623\pi\)
\(824\) −801.231 79.8213i −0.972367 0.0968705i
\(825\) 387.212i 0.469348i
\(826\) 0 0
\(827\) 708.113i 0.856243i −0.903721 0.428121i \(-0.859176\pi\)
0.903721 0.428121i \(-0.140824\pi\)
\(828\) −390.879 172.340i −0.472076 0.208140i
\(829\) 75.0164 129.932i 0.0904902 0.156734i −0.817227 0.576316i \(-0.804490\pi\)
0.907718 + 0.419582i \(0.137823\pi\)
\(830\) −865.902 182.418i −1.04326 0.219780i
\(831\) 49.0796 28.3361i 0.0590609 0.0340988i
\(832\) 66.5417 + 197.479i 0.0799780 + 0.237354i
\(833\) 0 0
\(834\) −315.174 964.072i −0.377907 1.15596i
\(835\) 273.665 158.001i 0.327743 0.189222i
\(836\) 110.745 12.0448i 0.132470 0.0144077i
\(837\) −0.317199 0.183135i −0.000378972 0.000218799i
\(838\) 584.152 651.130i 0.697079 0.777005i
\(839\) 1106.41i 1.31873i 0.751824 + 0.659364i \(0.229174\pi\)
−0.751824 + 0.659364i \(0.770826\pi\)
\(840\) 0 0
\(841\) 826.984 0.983335
\(842\) 1047.75 + 939.975i 1.24436 + 1.11636i
\(843\) −129.014 + 223.459i −0.153042 + 0.265076i
\(844\) −247.128 + 26.8781i −0.292806 + 0.0318461i
\(845\) −341.915 592.214i −0.404633 0.700845i
\(846\) −175.363 + 57.3297i −0.207285 + 0.0677656i
\(847\) 0 0
\(848\) 700.931 + 222.155i 0.826569 + 0.261975i
\(849\) 148.584 + 257.354i 0.175010 + 0.303126i
\(850\) −41.2713 + 195.907i −0.0485544 + 0.230479i
\(851\) 48.3606 + 27.9210i 0.0568279 + 0.0328096i
\(852\) −942.904 415.729i −1.10669 0.487945i
\(853\) −1243.82 −1.45817 −0.729086 0.684423i \(-0.760054\pi\)
−0.729086 + 0.684423i \(0.760054\pi\)
\(854\) 0 0
\(855\) 17.3344 0.0202742
\(856\) −851.386 84.8180i −0.994610 0.0990864i
\(857\) −245.650 141.826i −0.286639 0.165491i 0.349786 0.936830i \(-0.386254\pi\)
−0.636425 + 0.771339i \(0.719588\pi\)
\(858\) 81.7033 387.831i 0.0952253 0.452017i
\(859\) −455.900 789.641i −0.530733 0.919256i −0.999357 0.0358586i \(-0.988583\pi\)
0.468624 0.883398i \(-0.344750\pi\)
\(860\) −132.997 181.670i −0.154648 0.211244i
\(861\) 0 0
\(862\) 341.647 + 1045.05i 0.396342 + 1.21235i
\(863\) 436.908 + 756.747i 0.506266 + 0.876879i 0.999974 + 0.00725099i \(0.00230808\pi\)
−0.493707 + 0.869628i \(0.664359\pi\)
\(864\) −344.111 + 608.659i −0.398276 + 0.704466i
\(865\) 79.9735 138.518i 0.0924550 0.160137i
\(866\) −528.509 474.145i −0.610288 0.547511i
\(867\) 140.978 0.162604
\(868\) 0 0
\(869\) 417.620i 0.480575i
\(870\) 81.8737 + 73.4518i 0.0941077 + 0.0844274i
\(871\) −39.3358 22.7105i −0.0451617 0.0260741i
\(872\) −173.340 383.713i −0.198784 0.440038i
\(873\) 314.599 181.634i 0.360365 0.208057i
\(874\) −40.0745 122.582i −0.0458518 0.140254i
\(875\) 0 0
\(876\) 427.323 + 583.709i 0.487811 + 0.666334i
\(877\) 549.476 317.240i 0.626540 0.361733i −0.152871 0.988246i \(-0.548852\pi\)
0.779411 + 0.626513i \(0.215518\pi\)
\(878\) 227.099 1078.00i 0.258655 1.22779i
\(879\) −46.7975 + 81.0557i −0.0532395 + 0.0922136i
\(880\) −265.603 1206.59i −0.301822 1.37113i
\(881\) 670.044i 0.760549i −0.924874 0.380274i \(-0.875830\pi\)
0.924874 0.380274i \(-0.124170\pi\)
\(882\) 0 0
\(883\) 875.514i 0.991522i −0.868459 0.495761i \(-0.834889\pi\)
0.868459 0.495761i \(-0.165111\pi\)
\(884\) 82.6744 187.512i 0.0935231 0.212117i
\(885\) 504.623 874.033i 0.570196 0.987608i
\(886\) −111.412 + 528.854i −0.125748 + 0.596901i
\(887\) −854.152 + 493.145i −0.962967 + 0.555969i −0.897085 0.441858i \(-0.854319\pi\)
−0.0658820 + 0.997827i \(0.520986\pi\)
\(888\) −21.4138 + 29.8123i −0.0241146 + 0.0335724i
\(889\) 0 0
\(890\) −726.833 + 237.616i −0.816667 + 0.266985i
\(891\) 1511.17 872.476i 1.69604 0.979210i
\(892\) −459.392 + 49.9642i −0.515013 + 0.0560136i
\(893\) −48.2368 27.8495i −0.0540166 0.0311865i
\(894\) 431.900 + 387.473i 0.483109 + 0.433415i
\(895\) 1026.83i 1.14729i
\(896\) 0 0
\(897\) −458.850 −0.511538
\(898\) −608.216 + 677.953i −0.677301 + 0.754959i
\(899\) −0.0313782 + 0.0543486i −3.49034e−5 + 6.04545e-5i
\(900\) 7.09567 + 65.2406i 0.00788408 + 0.0724896i
\(901\) −361.543 626.210i −0.401268 0.695017i
\(902\) 781.457 + 2390.36i 0.866360 + 2.65007i
\(903\) 0 0
\(904\) 295.213 + 212.048i 0.326564 + 0.234567i
\(905\) −631.499 1093.79i −0.697789 1.20861i
\(906\) 877.718 + 184.907i 0.968783 + 0.204091i
\(907\) −750.592 433.355i −0.827555 0.477789i 0.0254599 0.999676i \(-0.491895\pi\)
−0.853015 + 0.521887i \(0.825228\pi\)
\(908\) −206.816 91.1856i −0.227771 0.100425i
\(909\) −91.2820 −0.100420
\(910\) 0 0
\(911\) −128.713 −0.141288 −0.0706438 0.997502i \(-0.522505\pi\)
−0.0706438 + 0.997502i \(0.522505\pi\)
\(912\) 82.7898 18.2243i 0.0907782 0.0199827i
\(913\) 1587.51 + 916.552i 1.73879 + 1.00389i
\(914\) −330.025 69.5255i −0.361077 0.0760673i
\(915\) 705.699 + 1222.31i 0.771256 + 1.33585i
\(916\) 381.945 279.615i 0.416971 0.305257i
\(917\) 0 0
\(918\) 653.550 213.659i 0.711929 0.232743i
\(919\) −430.087 744.933i −0.467995 0.810591i 0.531336 0.847161i \(-0.321690\pi\)
−0.999331 + 0.0365701i \(0.988357\pi\)
\(920\) −1303.49 + 588.844i −1.41684 + 0.640047i
\(921\) −421.935 + 730.813i −0.458127 + 0.793500i
\(922\) −354.009 + 394.599i −0.383957 + 0.427982i
\(923\) −246.515 −0.267081
\(924\) 0 0
\(925\) 8.57859i 0.00927415i
\(926\) −130.183 + 145.109i −0.140586 + 0.156706i
\(927\) 224.778 + 129.776i 0.242479 + 0.139995i
\(928\) 104.287 + 58.9595i 0.112378 + 0.0635340i
\(929\) −202.025 + 116.639i −0.217465 + 0.125554i −0.604776 0.796396i \(-0.706737\pi\)
0.387311 + 0.921949i \(0.373404\pi\)
\(930\) 0.468124 0.153039i 0.000503360 0.000164558i
\(931\) 0 0
\(932\) 79.6575 58.3158i 0.0854694 0.0625706i
\(933\) 1287.89 743.563i 1.38037 0.796960i
\(934\) 145.212 + 30.5914i 0.155473 + 0.0327531i
\(935\) −607.483 + 1052.19i −0.649714 + 1.12534i
\(936\) 6.65903 66.8420i 0.00711435 0.0714124i
\(937\) 1426.29i 1.52219i −0.648641 0.761095i \(-0.724662\pi\)
0.648641 0.761095i \(-0.275338\pi\)
\(938\) 0 0
\(939\) 281.851i 0.300161i
\(940\) −249.215 + 565.238i −0.265123 + 0.601317i
\(941\) 635.425 1100.59i 0.675265 1.16959i −0.301126 0.953584i \(-0.597362\pi\)
0.976391 0.216010i \(-0.0693043\pi\)
\(942\) −1632.24 343.860i −1.73274 0.365031i
\(943\) 2521.41 1455.73i 2.67381 1.54373i
\(944\) 332.111 1047.86i 0.351812 1.11002i
\(945\) 0 0
\(946\) 144.928 + 443.312i 0.153200 + 0.468618i
\(947\) −1413.50 + 816.086i −1.49261 + 0.861759i −0.999964 0.00847064i \(-0.997304\pi\)
−0.492646 + 0.870230i \(0.663970\pi\)
\(948\) 34.3619 + 315.938i 0.0362467 + 0.333268i
\(949\) 149.871 + 86.5280i 0.157925 + 0.0911781i
\(950\) −13.2303 + 14.7472i −0.0139266 + 0.0155234i
\(951\) 832.098i 0.874972i
\(952\) 0 0
\(953\) 95.9158 0.100646 0.0503231 0.998733i \(-0.483975\pi\)
0.0503231 + 0.998733i \(0.483975\pi\)
\(954\) −176.425 158.277i −0.184932 0.165909i
\(955\) 304.850 528.015i 0.319215 0.552896i
\(956\) 108.638 + 998.864i 0.113638 + 1.04484i
\(957\) −113.926 197.326i −0.119045 0.206192i
\(958\) −1043.14 + 341.024i −1.08888 + 0.355975i
\(959\) 0 0
\(960\) −300.213 890.957i −0.312722 0.928080i
\(961\) −480.500 832.250i −0.500000 0.866025i
\(962\) −1.81012 + 8.59229i −0.00188162 + 0.00893170i
\(963\) 238.849 + 137.899i 0.248025 + 0.143198i
\(964\) −181.451 + 411.545i −0.188227 + 0.426914i
\(965\) 284.759 0.295087
\(966\) 0 0
\(967\) 1419.97 1.46843 0.734216 0.678916i \(-0.237550\pi\)
0.734216 + 0.678916i \(0.237550\pi\)
\(968\) −157.751 + 1583.48i −0.162966 + 1.63582i
\(969\) −72.1956 41.6822i −0.0745053 0.0430157i
\(970\) 250.734 1190.19i 0.258488 1.22700i
\(971\) 329.817 + 571.261i 0.339668 + 0.588322i 0.984370 0.176112i \(-0.0563520\pi\)
−0.644702 + 0.764434i \(0.723019\pi\)
\(972\) 436.750 319.737i 0.449332 0.328948i
\(973\) 0 0
\(974\) −352.919 1079.53i −0.362340 1.10834i
\(975\) 35.2448 + 61.0459i 0.0361486 + 0.0626111i
\(976\) 1036.85 + 1134.92i 1.06234 + 1.16283i
\(977\) 957.151 1657.83i 0.979683 1.69686i 0.316160 0.948706i \(-0.397606\pi\)
0.663523 0.748156i \(-0.269060\pi\)
\(978\) −1217.19 1091.99i −1.24457 1.11655i
\(979\) 1584.07 1.61804
\(980\) 0 0
\(981\) 135.723i 0.138352i
\(982\) −117.311 105.244i −0.119461 0.107173i
\(983\) −193.655 111.806i −0.197004 0.113740i 0.398253 0.917275i \(-0.369616\pi\)
−0.595257 + 0.803535i \(0.702950\pi\)
\(984\) 787.867 + 1744.06i 0.800678 + 1.77242i
\(985\) 745.591 430.467i 0.756945 0.437022i
\(986\) −36.6080 111.979i −0.0371278 0.113569i
\(987\) 0 0
\(988\) 16.3631 11.9792i 0.0165619 0.0121247i
\(989\) 467.616 269.978i 0.472816 0.272981i
\(990\) −82.0964 + 389.697i −0.0829257 + 0.393633i
\(991\) 736.371 1275.43i 0.743058 1.28701i −0.208038 0.978121i \(-0.566708\pi\)
0.951096 0.308894i \(-0.0999589\pi\)
\(992\) 0.462106 0.272396i 0.000465833 0.000274593i
\(993\) 260.472i 0.262308i
\(994\) 0 0
\(995\) 292.237i 0.293706i
\(996\) 1276.40 + 562.768i 1.28153 + 0.565029i
\(997\) 53.4480 92.5746i 0.0536088 0.0928532i −0.837976 0.545708i \(-0.816261\pi\)
0.891584 + 0.452854i \(0.149594\pi\)
\(998\) 138.503 657.448i 0.138781 0.658765i
\(999\) −25.5150 + 14.7311i −0.0255405 + 0.0147458i
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 392.3.j.e.325.5 28
7.2 even 3 56.3.j.a.5.14 yes 28
7.3 odd 6 392.3.h.a.293.9 28
7.4 even 3 392.3.h.a.293.10 28
7.5 odd 6 inner 392.3.j.e.117.14 28
7.6 odd 2 56.3.j.a.45.5 yes 28
8.5 even 2 inner 392.3.j.e.325.14 28
28.3 even 6 1568.3.h.a.881.22 28
28.11 odd 6 1568.3.h.a.881.8 28
28.23 odd 6 224.3.n.a.145.11 28
28.27 even 2 224.3.n.a.17.4 28
56.3 even 6 1568.3.h.a.881.7 28
56.5 odd 6 inner 392.3.j.e.117.5 28
56.11 odd 6 1568.3.h.a.881.21 28
56.13 odd 2 56.3.j.a.45.14 yes 28
56.27 even 2 224.3.n.a.17.11 28
56.37 even 6 56.3.j.a.5.5 28
56.45 odd 6 392.3.h.a.293.12 28
56.51 odd 6 224.3.n.a.145.4 28
56.53 even 6 392.3.h.a.293.11 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
56.3.j.a.5.5 28 56.37 even 6
56.3.j.a.5.14 yes 28 7.2 even 3
56.3.j.a.45.5 yes 28 7.6 odd 2
56.3.j.a.45.14 yes 28 56.13 odd 2
224.3.n.a.17.4 28 28.27 even 2
224.3.n.a.17.11 28 56.27 even 2
224.3.n.a.145.4 28 56.51 odd 6
224.3.n.a.145.11 28 28.23 odd 6
392.3.h.a.293.9 28 7.3 odd 6
392.3.h.a.293.10 28 7.4 even 3
392.3.h.a.293.11 28 56.53 even 6
392.3.h.a.293.12 28 56.45 odd 6
392.3.j.e.117.5 28 56.5 odd 6 inner
392.3.j.e.117.14 28 7.5 odd 6 inner
392.3.j.e.325.5 28 1.1 even 1 trivial
392.3.j.e.325.14 28 8.5 even 2 inner
1568.3.h.a.881.7 28 56.3 even 6
1568.3.h.a.881.8 28 28.11 odd 6
1568.3.h.a.881.21 28 56.11 odd 6
1568.3.h.a.881.22 28 28.3 even 6