Properties

Label 1050.3.q.b.199.4
Level $1050$
Weight $3$
Character 1050.199
Analytic conductor $28.610$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1050,3,Mod(199,1050)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1050, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1050.199");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1050.q (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: \(28.6104277578\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: 16.0.22986704741655040229376.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 31x^{12} + 880x^{8} - 2511x^{4} + 6561 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 199.4
Root \(-0.337183 - 1.25838i\) of defining polynomial
Character \(\chi\) \(=\) 1050.199
Dual form 1050.3.q.b.649.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.22474 + 0.707107i) q^{2} +(0.866025 - 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(5.76140 - 3.97571i) q^{7} +2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+(-1.22474 + 0.707107i) q^{2} +(0.866025 - 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(5.76140 - 3.97571i) q^{7} +2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +(0.647280 - 1.12112i) q^{11} +(-1.73205 - 3.00000i) q^{12} -3.22960 q^{13} +(-4.24500 + 8.94315i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(-15.1826 + 26.2970i) q^{17} +(3.67423 + 2.12132i) q^{18} +(-28.9470 + 16.7125i) q^{19} +(-0.974040 - 12.0852i) q^{21} +1.83078i q^{22} +(-30.9462 + 17.8668i) q^{23} +(4.24264 + 2.44949i) q^{24} +(3.95544 - 2.28367i) q^{26} -5.19615 q^{27} +(-1.12472 - 13.9547i) q^{28} +32.8033 q^{29} +(39.5125 + 22.8125i) q^{31} +(4.89898 + 2.82843i) q^{32} +(-1.12112 - 1.94184i) q^{33} -42.9428i q^{34} -6.00000 q^{36} +(-34.6873 + 20.0267i) q^{37} +(23.6351 - 40.9372i) q^{38} +(-2.79692 + 4.84440i) q^{39} +42.2993i q^{41} +(9.73845 + 14.1125i) q^{42} -55.4597i q^{43} +(-1.29456 - 2.24224i) q^{44} +(25.2675 - 43.7646i) q^{46} +(30.3745 + 52.6102i) q^{47} -6.92820 q^{48} +(17.3875 - 45.8113i) q^{49} +(26.2970 + 45.5477i) q^{51} +(-3.22960 + 5.59383i) q^{52} +(-47.3438 - 27.3340i) q^{53} +(6.36396 - 3.67423i) q^{54} +(11.2450 + 16.2957i) q^{56} +57.8939i q^{57} +(-40.1757 + 23.1954i) q^{58} +(-11.4277 - 6.59780i) q^{59} +(34.1684 - 19.7271i) q^{61} -64.5236 q^{62} +(-18.9713 - 9.00500i) q^{63} -8.00000 q^{64} +(2.74618 + 1.58551i) q^{66} +(-34.7163 - 20.0434i) q^{67} +(30.3651 + 52.5940i) q^{68} +61.8924i q^{69} +46.4480 q^{71} +(7.34847 - 4.24264i) q^{72} +(-68.2001 + 118.126i) q^{73} +(28.3220 - 49.0552i) q^{74} +66.8501i q^{76} +(-0.728012 - 9.03263i) q^{77} -7.91088i q^{78} +(-21.1511 - 36.6348i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-29.9101 - 51.8059i) q^{82} -1.53725 q^{83} +(-21.9062 - 10.3981i) q^{84} +(39.2160 + 67.9240i) q^{86} +(28.4085 - 49.2050i) q^{87} +(3.17101 + 1.83078i) q^{88} +(30.2844 - 17.4847i) q^{89} +(-18.6070 + 12.8400i) q^{91} +71.4672i q^{92} +(68.4376 - 39.5125i) q^{93} +(-74.4020 - 42.9560i) q^{94} +(8.48528 - 4.89898i) q^{96} +150.516 q^{97} +(11.0982 + 68.4020i) q^{98} -3.88368 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 16 q^{4} - 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 16 q^{4} - 24 q^{9} - 8 q^{11} + 32 q^{14} - 32 q^{16} - 144 q^{19} - 144 q^{26} + 48 q^{29} + 192 q^{31} - 96 q^{36} + 24 q^{39} + 16 q^{44} + 64 q^{46} + 528 q^{49} + 48 q^{51} + 80 q^{56} - 624 q^{59} - 408 q^{61} - 128 q^{64} - 72 q^{66} - 128 q^{71} + 32 q^{74} + 288 q^{79} - 72 q^{81} + 352 q^{86} + 672 q^{89} - 592 q^{91} - 72 q^{94} + 48 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.22474 + 0.707107i −0.612372 + 0.353553i
\(3\) 0.866025 1.50000i 0.288675 0.500000i
\(4\) 1.00000 1.73205i 0.250000 0.433013i
\(5\) 0 0
\(6\) 2.44949i 0.408248i
\(7\) 5.76140 3.97571i 0.823057 0.567958i
\(8\) 2.82843i 0.353553i
\(9\) −1.50000 2.59808i −0.166667 0.288675i
\(10\) 0 0
\(11\) 0.647280 1.12112i 0.0588436 0.101920i −0.835103 0.550094i \(-0.814592\pi\)
0.893947 + 0.448174i \(0.147925\pi\)
\(12\) −1.73205 3.00000i −0.144338 0.250000i
\(13\) −3.22960 −0.248431 −0.124215 0.992255i \(-0.539641\pi\)
−0.124215 + 0.992255i \(0.539641\pi\)
\(14\) −4.24500 + 8.94315i −0.303214 + 0.638797i
\(15\) 0 0
\(16\) −2.00000 3.46410i −0.125000 0.216506i
\(17\) −15.1826 + 26.2970i −0.893092 + 1.54688i −0.0569439 + 0.998377i \(0.518136\pi\)
−0.836148 + 0.548504i \(0.815198\pi\)
\(18\) 3.67423 + 2.12132i 0.204124 + 0.117851i
\(19\) −28.9470 + 16.7125i −1.52352 + 0.879607i −0.523912 + 0.851773i \(0.675528\pi\)
−0.999613 + 0.0278345i \(0.991139\pi\)
\(20\) 0 0
\(21\) −0.974040 12.0852i −0.0463829 0.575484i
\(22\) 1.83078i 0.0832175i
\(23\) −30.9462 + 17.8668i −1.34549 + 0.776818i −0.987607 0.156950i \(-0.949834\pi\)
−0.357881 + 0.933767i \(0.616501\pi\)
\(24\) 4.24264 + 2.44949i 0.176777 + 0.102062i
\(25\) 0 0
\(26\) 3.95544 2.28367i 0.152132 0.0878336i
\(27\) −5.19615 −0.192450
\(28\) −1.12472 13.9547i −0.0401687 0.498384i
\(29\) 32.8033 1.13115 0.565574 0.824697i \(-0.308655\pi\)
0.565574 + 0.824697i \(0.308655\pi\)
\(30\) 0 0
\(31\) 39.5125 + 22.8125i 1.27460 + 0.735888i 0.975849 0.218444i \(-0.0700981\pi\)
0.298747 + 0.954332i \(0.403431\pi\)
\(32\) 4.89898 + 2.82843i 0.153093 + 0.0883883i
\(33\) −1.12112 1.94184i −0.0339734 0.0588436i
\(34\) 42.9428i 1.26302i
\(35\) 0 0
\(36\) −6.00000 −0.166667
\(37\) −34.6873 + 20.0267i −0.937494 + 0.541262i −0.889174 0.457570i \(-0.848720\pi\)
−0.0483201 + 0.998832i \(0.515387\pi\)
\(38\) 23.6351 40.9372i 0.621976 1.07729i
\(39\) −2.79692 + 4.84440i −0.0717158 + 0.124215i
\(40\) 0 0
\(41\) 42.2993i 1.03169i 0.856682 + 0.515845i \(0.172522\pi\)
−0.856682 + 0.515845i \(0.827478\pi\)
\(42\) 9.73845 + 14.1125i 0.231868 + 0.336012i
\(43\) 55.4597i 1.28976i −0.764283 0.644881i \(-0.776907\pi\)
0.764283 0.644881i \(-0.223093\pi\)
\(44\) −1.29456 2.24224i −0.0294218 0.0509601i
\(45\) 0 0
\(46\) 25.2675 43.7646i 0.549293 0.951403i
\(47\) 30.3745 + 52.6102i 0.646266 + 1.11937i 0.984008 + 0.178127i \(0.0570037\pi\)
−0.337741 + 0.941239i \(0.609663\pi\)
\(48\) −6.92820 −0.144338
\(49\) 17.3875 45.8113i 0.354847 0.934924i
\(50\) 0 0
\(51\) 26.2970 + 45.5477i 0.515627 + 0.893092i
\(52\) −3.22960 + 5.59383i −0.0621077 + 0.107574i
\(53\) −47.3438 27.3340i −0.893280 0.515735i −0.0182660 0.999833i \(-0.505815\pi\)
−0.875014 + 0.484098i \(0.839148\pi\)
\(54\) 6.36396 3.67423i 0.117851 0.0680414i
\(55\) 0 0
\(56\) 11.2450 + 16.2957i 0.200804 + 0.290995i
\(57\) 57.8939i 1.01568i
\(58\) −40.1757 + 23.1954i −0.692684 + 0.399921i
\(59\) −11.4277 6.59780i −0.193690 0.111827i 0.400019 0.916507i \(-0.369004\pi\)
−0.593709 + 0.804680i \(0.702337\pi\)
\(60\) 0 0
\(61\) 34.1684 19.7271i 0.560137 0.323395i −0.193064 0.981186i \(-0.561842\pi\)
0.753200 + 0.657791i \(0.228509\pi\)
\(62\) −64.5236 −1.04070
\(63\) −18.9713 9.00500i −0.301132 0.142937i
\(64\) −8.00000 −0.125000
\(65\) 0 0
\(66\) 2.74618 + 1.58551i 0.0416087 + 0.0240228i
\(67\) −34.7163 20.0434i −0.518153 0.299156i 0.218026 0.975943i \(-0.430038\pi\)
−0.736179 + 0.676787i \(0.763372\pi\)
\(68\) 30.3651 + 52.5940i 0.446546 + 0.773440i
\(69\) 61.8924i 0.896992i
\(70\) 0 0
\(71\) 46.4480 0.654198 0.327099 0.944990i \(-0.393929\pi\)
0.327099 + 0.944990i \(0.393929\pi\)
\(72\) 7.34847 4.24264i 0.102062 0.0589256i
\(73\) −68.2001 + 118.126i −0.934247 + 1.61816i −0.158277 + 0.987395i \(0.550594\pi\)
−0.775970 + 0.630769i \(0.782739\pi\)
\(74\) 28.3220 49.0552i 0.382730 0.662908i
\(75\) 0 0
\(76\) 66.8501i 0.879607i
\(77\) −0.728012 9.03263i −0.00945470 0.117307i
\(78\) 7.91088i 0.101422i
\(79\) −21.1511 36.6348i −0.267736 0.463732i 0.700541 0.713612i \(-0.252942\pi\)
−0.968277 + 0.249880i \(0.919609\pi\)
\(80\) 0 0
\(81\) −4.50000 + 7.79423i −0.0555556 + 0.0962250i
\(82\) −29.9101 51.8059i −0.364758 0.631779i
\(83\) −1.53725 −0.0185211 −0.00926054 0.999957i \(-0.502948\pi\)
−0.00926054 + 0.999957i \(0.502948\pi\)
\(84\) −21.9062 10.3981i −0.260788 0.123787i
\(85\) 0 0
\(86\) 39.2160 + 67.9240i 0.456000 + 0.789814i
\(87\) 28.4085 49.2050i 0.326534 0.565574i
\(88\) 3.17101 + 1.83078i 0.0360342 + 0.0208044i
\(89\) 30.2844 17.4847i 0.340274 0.196457i −0.320119 0.947377i \(-0.603723\pi\)
0.660393 + 0.750920i \(0.270390\pi\)
\(90\) 0 0
\(91\) −18.6070 + 12.8400i −0.204473 + 0.141098i
\(92\) 71.4672i 0.776818i
\(93\) 68.4376 39.5125i 0.735888 0.424865i
\(94\) −74.4020 42.9560i −0.791511 0.456979i
\(95\) 0 0
\(96\) 8.48528 4.89898i 0.0883883 0.0510310i
\(97\) 150.516 1.55172 0.775858 0.630907i \(-0.217317\pi\)
0.775858 + 0.630907i \(0.217317\pi\)
\(98\) 11.0982 + 68.4020i 0.113247 + 0.697979i
\(99\) −3.88368 −0.0392291
\(100\) 0 0
\(101\) 103.806 + 59.9325i 1.02778 + 0.593391i 0.916349 0.400381i \(-0.131122\pi\)
0.111434 + 0.993772i \(0.464456\pi\)
\(102\) −64.4142 37.1895i −0.631511 0.364603i
\(103\) −49.8245 86.2986i −0.483733 0.837851i 0.516092 0.856533i \(-0.327386\pi\)
−0.999825 + 0.0186825i \(0.994053\pi\)
\(104\) 9.13469i 0.0878336i
\(105\) 0 0
\(106\) 77.3122 0.729360
\(107\) −40.6950 + 23.4953i −0.380327 + 0.219582i −0.677961 0.735098i \(-0.737136\pi\)
0.297634 + 0.954680i \(0.403803\pi\)
\(108\) −5.19615 + 9.00000i −0.0481125 + 0.0833333i
\(109\) −29.0802 + 50.3683i −0.266791 + 0.462095i −0.968031 0.250830i \(-0.919297\pi\)
0.701241 + 0.712925i \(0.252630\pi\)
\(110\) 0 0
\(111\) 69.3746i 0.624996i
\(112\) −25.2951 12.0067i −0.225849 0.107202i
\(113\) 211.102i 1.86816i 0.357068 + 0.934078i \(0.383776\pi\)
−0.357068 + 0.934078i \(0.616224\pi\)
\(114\) −40.9372 70.9053i −0.359098 0.621976i
\(115\) 0 0
\(116\) 32.8033 56.8170i 0.282787 0.489802i
\(117\) 4.84440 + 8.39075i 0.0414052 + 0.0717158i
\(118\) 18.6614 0.158148
\(119\) 17.0762 + 211.869i 0.143498 + 1.78041i
\(120\) 0 0
\(121\) 59.6621 + 103.338i 0.493075 + 0.854031i
\(122\) −27.8983 + 48.3213i −0.228675 + 0.396077i
\(123\) 63.4490 + 36.6323i 0.515845 + 0.297823i
\(124\) 79.0250 45.6251i 0.637298 0.367944i
\(125\) 0 0
\(126\) 29.6025 2.38590i 0.234940 0.0189357i
\(127\) 90.2615i 0.710720i 0.934729 + 0.355360i \(0.115642\pi\)
−0.934729 + 0.355360i \(0.884358\pi\)
\(128\) 9.79796 5.65685i 0.0765466 0.0441942i
\(129\) −83.1896 48.0296i −0.644881 0.372322i
\(130\) 0 0
\(131\) −174.806 + 100.924i −1.33440 + 0.770414i −0.985970 0.166923i \(-0.946617\pi\)
−0.348426 + 0.937336i \(0.613284\pi\)
\(132\) −4.48449 −0.0339734
\(133\) −100.331 + 211.372i −0.754368 + 1.58927i
\(134\) 56.6914 0.423070
\(135\) 0 0
\(136\) −74.3791 42.9428i −0.546905 0.315756i
\(137\) 0.00352554 + 0.00203547i 2.57339e−5 + 1.48575e-5i 0.500013 0.866018i \(-0.333329\pi\)
−0.499987 + 0.866033i \(0.666662\pi\)
\(138\) −43.7646 75.8024i −0.317134 0.549293i
\(139\) 115.950i 0.834169i −0.908868 0.417085i \(-0.863052\pi\)
0.908868 0.417085i \(-0.136948\pi\)
\(140\) 0 0
\(141\) 105.220 0.746244
\(142\) −56.8870 + 32.8437i −0.400613 + 0.231294i
\(143\) −2.09046 + 3.62078i −0.0146186 + 0.0253201i
\(144\) −6.00000 + 10.3923i −0.0416667 + 0.0721688i
\(145\) 0 0
\(146\) 192.899i 1.32123i
\(147\) −53.6589 65.7550i −0.365027 0.447313i
\(148\) 80.1068i 0.541262i
\(149\) −2.59675 4.49770i −0.0174278 0.0301859i 0.857180 0.515017i \(-0.172214\pi\)
−0.874608 + 0.484831i \(0.838881\pi\)
\(150\) 0 0
\(151\) 80.3710 139.207i 0.532258 0.921899i −0.467032 0.884240i \(-0.654677\pi\)
0.999291 0.0376583i \(-0.0119898\pi\)
\(152\) −47.2702 81.8744i −0.310988 0.538647i
\(153\) 91.0954 0.595395
\(154\) 7.27866 + 10.5479i 0.0472640 + 0.0684928i
\(155\) 0 0
\(156\) 5.59383 + 9.68881i 0.0358579 + 0.0621077i
\(157\) 47.6157 82.4728i 0.303285 0.525305i −0.673593 0.739102i \(-0.735250\pi\)
0.976878 + 0.213798i \(0.0685833\pi\)
\(158\) 51.8095 + 29.9122i 0.327908 + 0.189318i
\(159\) −82.0019 + 47.3438i −0.515735 + 0.297760i
\(160\) 0 0
\(161\) −107.260 + 225.971i −0.666214 + 1.40355i
\(162\) 12.7279i 0.0785674i
\(163\) −213.473 + 123.249i −1.30965 + 0.756128i −0.982038 0.188683i \(-0.939578\pi\)
−0.327615 + 0.944811i \(0.606245\pi\)
\(164\) 73.2645 + 42.2993i 0.446735 + 0.257923i
\(165\) 0 0
\(166\) 1.88274 1.08700i 0.0113418 0.00654819i
\(167\) 14.9445 0.0894879 0.0447439 0.998998i \(-0.485753\pi\)
0.0447439 + 0.998998i \(0.485753\pi\)
\(168\) 34.1820 2.75500i 0.203464 0.0163988i
\(169\) −158.570 −0.938282
\(170\) 0 0
\(171\) 86.8409 + 50.1376i 0.507841 + 0.293202i
\(172\) −96.0591 55.4597i −0.558483 0.322440i
\(173\) −83.8331 145.203i −0.484584 0.839325i 0.515259 0.857035i \(-0.327696\pi\)
−0.999843 + 0.0177099i \(0.994362\pi\)
\(174\) 80.3513i 0.461789i
\(175\) 0 0
\(176\) −5.17824 −0.0294218
\(177\) −19.7934 + 11.4277i −0.111827 + 0.0645635i
\(178\) −24.7271 + 42.8286i −0.138916 + 0.240610i
\(179\) 33.4724 57.9759i 0.186997 0.323888i −0.757251 0.653124i \(-0.773458\pi\)
0.944248 + 0.329236i \(0.106791\pi\)
\(180\) 0 0
\(181\) 24.9109i 0.137629i −0.997629 0.0688146i \(-0.978078\pi\)
0.997629 0.0688146i \(-0.0219217\pi\)
\(182\) 13.7097 28.8828i 0.0753278 0.158697i
\(183\) 68.3367i 0.373425i
\(184\) −50.5350 87.5291i −0.274647 0.475702i
\(185\) 0 0
\(186\) −55.8791 + 96.7854i −0.300425 + 0.520352i
\(187\) 19.6547 + 34.0430i 0.105106 + 0.182048i
\(188\) 121.498 0.646266
\(189\) −29.9371 + 20.6584i −0.158397 + 0.109304i
\(190\) 0 0
\(191\) 6.80231 + 11.7819i 0.0356142 + 0.0616856i 0.883283 0.468840i \(-0.155328\pi\)
−0.847669 + 0.530526i \(0.821995\pi\)
\(192\) −6.92820 + 12.0000i −0.0360844 + 0.0625000i
\(193\) −157.978 91.2089i −0.818541 0.472585i 0.0313718 0.999508i \(-0.490012\pi\)
−0.849913 + 0.526923i \(0.823346\pi\)
\(194\) −184.344 + 106.431i −0.950228 + 0.548615i
\(195\) 0 0
\(196\) −61.9600 75.9273i −0.316122 0.387384i
\(197\) 286.679i 1.45522i 0.685989 + 0.727612i \(0.259370\pi\)
−0.685989 + 0.727612i \(0.740630\pi\)
\(198\) 4.75652 2.74618i 0.0240228 0.0138696i
\(199\) 2.74117 + 1.58262i 0.0137747 + 0.00795285i 0.506872 0.862022i \(-0.330802\pi\)
−0.493097 + 0.869974i \(0.664135\pi\)
\(200\) 0 0
\(201\) −60.1303 + 34.7163i −0.299156 + 0.172718i
\(202\) −169.515 −0.839181
\(203\) 188.993 130.416i 0.931000 0.642445i
\(204\) 105.188 0.515627
\(205\) 0 0
\(206\) 122.045 + 70.4625i 0.592450 + 0.342051i
\(207\) 92.8387 + 53.6004i 0.448496 + 0.258939i
\(208\) 6.45920 + 11.1877i 0.0310539 + 0.0537869i
\(209\) 43.2708i 0.207037i
\(210\) 0 0
\(211\) −179.324 −0.849878 −0.424939 0.905222i \(-0.639705\pi\)
−0.424939 + 0.905222i \(0.639705\pi\)
\(212\) −94.6877 + 54.6679i −0.446640 + 0.257868i
\(213\) 40.2252 69.6720i 0.188851 0.327099i
\(214\) 33.2273 57.5514i 0.155268 0.268932i
\(215\) 0 0
\(216\) 14.6969i 0.0680414i
\(217\) 318.343 25.6578i 1.46702 0.118239i
\(218\) 82.2512i 0.377299i
\(219\) 118.126 + 204.600i 0.539388 + 0.934247i
\(220\) 0 0
\(221\) 49.0336 84.9288i 0.221872 0.384293i
\(222\) −49.0552 84.9661i −0.220969 0.382730i
\(223\) 71.3345 0.319886 0.159943 0.987126i \(-0.448869\pi\)
0.159943 + 0.987126i \(0.448869\pi\)
\(224\) 39.4700 3.18120i 0.176205 0.0142018i
\(225\) 0 0
\(226\) −149.271 258.546i −0.660493 1.14401i
\(227\) 71.2698 123.443i 0.313964 0.543802i −0.665253 0.746618i \(-0.731676\pi\)
0.979217 + 0.202817i \(0.0650096\pi\)
\(228\) 100.275 + 57.8939i 0.439804 + 0.253921i
\(229\) −109.001 + 62.9320i −0.475989 + 0.274812i −0.718743 0.695276i \(-0.755282\pi\)
0.242755 + 0.970088i \(0.421949\pi\)
\(230\) 0 0
\(231\) −14.1794 6.73047i −0.0613828 0.0291362i
\(232\) 92.7817i 0.399921i
\(233\) −142.258 + 82.1326i −0.610549 + 0.352500i −0.773180 0.634186i \(-0.781335\pi\)
0.162631 + 0.986687i \(0.448002\pi\)
\(234\) −11.8663 6.85102i −0.0507108 0.0292779i
\(235\) 0 0
\(236\) −22.8555 + 13.1956i −0.0968452 + 0.0559136i
\(237\) −73.2697 −0.309155
\(238\) −170.728 247.411i −0.717344 1.03954i
\(239\) 50.4246 0.210982 0.105491 0.994420i \(-0.466359\pi\)
0.105491 + 0.994420i \(0.466359\pi\)
\(240\) 0 0
\(241\) −169.006 97.5757i −0.701270 0.404879i 0.106550 0.994307i \(-0.466020\pi\)
−0.807820 + 0.589429i \(0.799353\pi\)
\(242\) −146.142 84.3749i −0.603891 0.348657i
\(243\) 7.79423 + 13.5000i 0.0320750 + 0.0555556i
\(244\) 78.9084i 0.323395i
\(245\) 0 0
\(246\) −103.612 −0.421186
\(247\) 93.4872 53.9748i 0.378491 0.218522i
\(248\) −64.5236 + 111.758i −0.260176 + 0.450638i
\(249\) −1.33130 + 2.30587i −0.00534657 + 0.00926054i
\(250\) 0 0
\(251\) 328.725i 1.30966i 0.755775 + 0.654832i \(0.227260\pi\)
−0.755775 + 0.654832i \(0.772740\pi\)
\(252\) −34.5684 + 23.8542i −0.137176 + 0.0946597i
\(253\) 46.2593i 0.182843i
\(254\) −63.8245 110.547i −0.251278 0.435225i
\(255\) 0 0
\(256\) −8.00000 + 13.8564i −0.0312500 + 0.0541266i
\(257\) −201.596 349.175i −0.784420 1.35866i −0.929345 0.369213i \(-0.879627\pi\)
0.144924 0.989443i \(-0.453706\pi\)
\(258\) 135.848 0.526543
\(259\) −120.227 + 253.288i −0.464197 + 0.977947i
\(260\) 0 0
\(261\) −49.2050 85.2255i −0.188525 0.326534i
\(262\) 142.728 247.213i 0.544765 0.943560i
\(263\) 431.240 + 248.977i 1.63970 + 0.946679i 0.980937 + 0.194326i \(0.0622519\pi\)
0.658759 + 0.752354i \(0.271081\pi\)
\(264\) 5.49235 3.17101i 0.0208044 0.0120114i
\(265\) 0 0
\(266\) −26.5830 329.822i −0.0999360 1.23993i
\(267\) 60.5688i 0.226849i
\(268\) −69.4325 + 40.0869i −0.259077 + 0.149578i
\(269\) 155.357 + 89.6952i 0.577534 + 0.333439i 0.760153 0.649745i \(-0.225124\pi\)
−0.182619 + 0.983184i \(0.558457\pi\)
\(270\) 0 0
\(271\) −126.057 + 72.7792i −0.465156 + 0.268558i −0.714210 0.699932i \(-0.753214\pi\)
0.249054 + 0.968490i \(0.419880\pi\)
\(272\) 121.461 0.446546
\(273\) 3.14576 + 39.0303i 0.0115229 + 0.142968i
\(274\) −0.00575719 −2.10116e−5
\(275\) 0 0
\(276\) 107.201 + 61.8924i 0.388409 + 0.224248i
\(277\) 185.057 + 106.843i 0.668076 + 0.385714i 0.795347 0.606154i \(-0.207288\pi\)
−0.127271 + 0.991868i \(0.540622\pi\)
\(278\) 81.9887 + 142.009i 0.294923 + 0.510822i
\(279\) 136.875i 0.490592i
\(280\) 0 0
\(281\) −349.479 −1.24370 −0.621849 0.783137i \(-0.713618\pi\)
−0.621849 + 0.783137i \(0.713618\pi\)
\(282\) −128.868 + 74.4020i −0.456979 + 0.263837i
\(283\) −47.1253 + 81.6234i −0.166521 + 0.288422i −0.937194 0.348808i \(-0.886587\pi\)
0.770674 + 0.637230i \(0.219920\pi\)
\(284\) 46.4480 80.4503i 0.163549 0.283276i
\(285\) 0 0
\(286\) 5.91271i 0.0206738i
\(287\) 168.170 + 243.703i 0.585957 + 0.849140i
\(288\) 16.9706i 0.0589256i
\(289\) −316.521 548.230i −1.09523 1.89699i
\(290\) 0 0
\(291\) 130.351 225.775i 0.447942 0.775858i
\(292\) 136.400 + 236.252i 0.467124 + 0.809082i
\(293\) 195.931 0.668707 0.334354 0.942448i \(-0.391482\pi\)
0.334354 + 0.942448i \(0.391482\pi\)
\(294\) 112.214 + 42.5905i 0.381681 + 0.144866i
\(295\) 0 0
\(296\) −56.6441 98.1104i −0.191365 0.331454i
\(297\) −3.36337 + 5.82552i −0.0113245 + 0.0196145i
\(298\) 6.36070 + 3.67235i 0.0213446 + 0.0123233i
\(299\) 99.9440 57.7027i 0.334261 0.192986i
\(300\) 0 0
\(301\) −220.492 319.526i −0.732531 1.06155i
\(302\) 227.324i 0.752727i
\(303\) 179.797 103.806i 0.593391 0.342594i
\(304\) 115.788 + 66.8501i 0.380881 + 0.219902i
\(305\) 0 0
\(306\) −111.569 + 64.4142i −0.364603 + 0.210504i
\(307\) 452.419 1.47368 0.736839 0.676069i \(-0.236318\pi\)
0.736839 + 0.676069i \(0.236318\pi\)
\(308\) −16.3730 7.77168i −0.0531590 0.0252327i
\(309\) −172.597 −0.558567
\(310\) 0 0
\(311\) −56.8889 32.8448i −0.182922 0.105610i 0.405743 0.913987i \(-0.367013\pi\)
−0.588665 + 0.808377i \(0.700346\pi\)
\(312\) −13.7020 7.91088i −0.0439168 0.0253554i
\(313\) −177.290 307.075i −0.566422 0.981071i −0.996916 0.0784776i \(-0.974994\pi\)
0.430494 0.902593i \(-0.358339\pi\)
\(314\) 134.678i 0.428909i
\(315\) 0 0
\(316\) −84.6045 −0.267736
\(317\) 116.792 67.4299i 0.368429 0.212713i −0.304343 0.952563i \(-0.598437\pi\)
0.672772 + 0.739850i \(0.265104\pi\)
\(318\) 66.9543 115.968i 0.210548 0.364680i
\(319\) 21.2329 36.7765i 0.0665609 0.115287i
\(320\) 0 0
\(321\) 81.3900i 0.253551i
\(322\) −28.4190 352.601i −0.0882576 1.09504i
\(323\) 1014.96i 3.14228i
\(324\) 9.00000 + 15.5885i 0.0277778 + 0.0481125i
\(325\) 0 0
\(326\) 174.300 301.897i 0.534664 0.926064i
\(327\) 50.3683 + 87.2405i 0.154032 + 0.266791i
\(328\) −119.641 −0.364758
\(329\) 384.162 + 182.348i 1.16767 + 0.554250i
\(330\) 0 0
\(331\) 90.2612 + 156.337i 0.272692 + 0.472317i 0.969550 0.244892i \(-0.0787525\pi\)
−0.696858 + 0.717209i \(0.745419\pi\)
\(332\) −1.53725 + 2.66259i −0.00463027 + 0.00801986i
\(333\) 104.062 + 60.0801i 0.312498 + 0.180421i
\(334\) −18.3032 + 10.5673i −0.0547999 + 0.0316387i
\(335\) 0 0
\(336\) −39.9162 + 27.5445i −0.118798 + 0.0819777i
\(337\) 5.84677i 0.0173495i −0.999962 0.00867473i \(-0.997239\pi\)
0.999962 0.00867473i \(-0.00276129\pi\)
\(338\) 194.207 112.126i 0.574578 0.331733i
\(339\) 316.653 + 182.819i 0.934078 + 0.539290i
\(340\) 0 0
\(341\) 51.1513 29.5322i 0.150004 0.0866047i
\(342\) −141.811 −0.414651
\(343\) −81.9559 333.065i −0.238938 0.971035i
\(344\) 156.864 0.456000
\(345\) 0 0
\(346\) 205.348 + 118.558i 0.593492 + 0.342653i
\(347\) −339.718 196.136i −0.979014 0.565234i −0.0770414 0.997028i \(-0.524547\pi\)
−0.901972 + 0.431794i \(0.857881\pi\)
\(348\) −56.8170 98.4099i −0.163267 0.282787i
\(349\) 230.853i 0.661471i −0.943724 0.330735i \(-0.892703\pi\)
0.943724 0.330735i \(-0.107297\pi\)
\(350\) 0 0
\(351\) 16.7815 0.0478106
\(352\) 6.34202 3.66157i 0.0180171 0.0104022i
\(353\) −62.8188 + 108.805i −0.177957 + 0.308230i −0.941181 0.337904i \(-0.890282\pi\)
0.763224 + 0.646134i \(0.223615\pi\)
\(354\) 16.1613 27.9921i 0.0456533 0.0790738i
\(355\) 0 0
\(356\) 69.9388i 0.196457i
\(357\) 332.592 + 157.870i 0.931630 + 0.442212i
\(358\) 94.6743i 0.264453i
\(359\) 215.984 + 374.096i 0.601628 + 1.04205i 0.992575 + 0.121637i \(0.0388143\pi\)
−0.390947 + 0.920413i \(0.627852\pi\)
\(360\) 0 0
\(361\) 378.118 654.919i 1.04742 1.81418i
\(362\) 17.6147 + 30.5095i 0.0486593 + 0.0842803i
\(363\) 206.675 0.569354
\(364\) 3.63241 + 45.0683i 0.00997916 + 0.123814i
\(365\) 0 0
\(366\) 48.3213 + 83.6950i 0.132026 + 0.228675i
\(367\) 236.049 408.849i 0.643185 1.11403i −0.341532 0.939870i \(-0.610946\pi\)
0.984717 0.174159i \(-0.0557208\pi\)
\(368\) 123.785 + 71.4672i 0.336372 + 0.194204i
\(369\) 109.897 63.4490i 0.297823 0.171948i
\(370\) 0 0
\(371\) −381.439 + 30.7432i −1.02814 + 0.0828658i
\(372\) 158.050i 0.424865i
\(373\) −75.7963 + 43.7610i −0.203207 + 0.117322i −0.598151 0.801384i \(-0.704098\pi\)
0.394943 + 0.918705i \(0.370764\pi\)
\(374\) −48.1441 27.7960i −0.128728 0.0743209i
\(375\) 0 0
\(376\) −148.804 + 85.9121i −0.395756 + 0.228490i
\(377\) −105.942 −0.281012
\(378\) 22.0577 46.4700i 0.0583536 0.122936i
\(379\) 359.658 0.948965 0.474483 0.880265i \(-0.342635\pi\)
0.474483 + 0.880265i \(0.342635\pi\)
\(380\) 0 0
\(381\) 135.392 + 78.1687i 0.355360 + 0.205167i
\(382\) −16.6622 9.61992i −0.0436183 0.0251830i
\(383\) −242.085 419.304i −0.632077 1.09479i −0.987126 0.159942i \(-0.948869\pi\)
0.355050 0.934847i \(-0.384464\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 0 0
\(386\) 257.978 0.668336
\(387\) −144.089 + 83.1896i −0.372322 + 0.214960i
\(388\) 150.516 260.702i 0.387929 0.671913i
\(389\) −179.791 + 311.407i −0.462188 + 0.800533i −0.999070 0.0431246i \(-0.986269\pi\)
0.536882 + 0.843657i \(0.319602\pi\)
\(390\) 0 0
\(391\) 1085.06i 2.77508i
\(392\) 129.574 + 49.1793i 0.330546 + 0.125457i
\(393\) 349.612i 0.889597i
\(394\) −202.713 351.109i −0.514499 0.891139i
\(395\) 0 0
\(396\) −3.88368 + 6.72673i −0.00980727 + 0.0169867i
\(397\) 90.6969 + 157.092i 0.228456 + 0.395697i 0.957351 0.288929i \(-0.0932991\pi\)
−0.728895 + 0.684626i \(0.759966\pi\)
\(398\) −4.47632 −0.0112470
\(399\) 230.169 + 333.550i 0.576865 + 0.835965i
\(400\) 0 0
\(401\) 132.742 + 229.916i 0.331027 + 0.573355i 0.982713 0.185133i \(-0.0592716\pi\)
−0.651687 + 0.758488i \(0.725938\pi\)
\(402\) 49.0962 85.0371i 0.122130 0.211535i
\(403\) −127.610 73.6754i −0.316649 0.182817i
\(404\) 207.612 119.865i 0.513891 0.296695i
\(405\) 0 0
\(406\) −139.250 + 293.365i −0.342980 + 0.722574i
\(407\) 51.8516i 0.127399i
\(408\) −128.828 + 74.3791i −0.315756 + 0.182302i
\(409\) 492.567 + 284.384i 1.20432 + 0.695315i 0.961513 0.274759i \(-0.0885981\pi\)
0.242808 + 0.970074i \(0.421931\pi\)
\(410\) 0 0
\(411\) 0.00610642 0.00352554i 1.48575e−5 8.57797e-6i
\(412\) −199.298 −0.483733
\(413\) −92.0707 + 7.42071i −0.222931 + 0.0179678i
\(414\) −151.605 −0.366195
\(415\) 0 0
\(416\) −15.8218 9.13469i −0.0380331 0.0219584i
\(417\) −173.924 100.415i −0.417085 0.240804i
\(418\) −30.5970 52.9956i −0.0731987 0.126784i
\(419\) 556.041i 1.32707i −0.748146 0.663534i \(-0.769056\pi\)
0.748146 0.663534i \(-0.230944\pi\)
\(420\) 0 0
\(421\) −476.267 −1.13128 −0.565638 0.824654i \(-0.691370\pi\)
−0.565638 + 0.824654i \(0.691370\pi\)
\(422\) 219.627 126.801i 0.520442 0.300477i
\(423\) 91.1235 157.831i 0.215422 0.373122i
\(424\) 77.3122 133.909i 0.182340 0.315822i
\(425\) 0 0
\(426\) 113.774i 0.267075i
\(427\) 118.428 249.499i 0.277350 0.584307i
\(428\) 93.9810i 0.219582i
\(429\) 3.62078 + 6.27137i 0.00844004 + 0.0146186i
\(430\) 0 0
\(431\) −229.808 + 398.039i −0.533196 + 0.923523i 0.466052 + 0.884757i \(0.345676\pi\)
−0.999248 + 0.0387660i \(0.987657\pi\)
\(432\) 10.3923 + 18.0000i 0.0240563 + 0.0416667i
\(433\) −65.9185 −0.152237 −0.0761183 0.997099i \(-0.524253\pi\)
−0.0761183 + 0.997099i \(0.524253\pi\)
\(434\) −371.746 + 256.527i −0.856559 + 0.591076i
\(435\) 0 0
\(436\) 58.1604 + 100.737i 0.133395 + 0.231047i
\(437\) 597.199 1034.38i 1.36659 2.36700i
\(438\) −289.348 167.055i −0.660613 0.381405i
\(439\) 307.619 177.604i 0.700727 0.404565i −0.106891 0.994271i \(-0.534090\pi\)
0.807618 + 0.589706i \(0.200756\pi\)
\(440\) 0 0
\(441\) −145.102 + 23.5429i −0.329031 + 0.0533852i
\(442\) 138.688i 0.313774i
\(443\) 656.650 379.117i 1.48228 0.855795i 0.482482 0.875906i \(-0.339735\pi\)
0.999798 + 0.0201113i \(0.00640205\pi\)
\(444\) 120.160 + 69.3746i 0.270631 + 0.156249i
\(445\) 0 0
\(446\) −87.3666 + 50.4411i −0.195889 + 0.113097i
\(447\) −8.99539 −0.0201239
\(448\) −46.0912 + 31.8057i −0.102882 + 0.0709948i
\(449\) −668.104 −1.48798 −0.743992 0.668189i \(-0.767070\pi\)
−0.743992 + 0.668189i \(0.767070\pi\)
\(450\) 0 0
\(451\) 47.4227 + 27.3795i 0.105150 + 0.0607084i
\(452\) 365.639 + 211.102i 0.808936 + 0.467039i
\(453\) −139.207 241.113i −0.307300 0.532258i
\(454\) 201.581i 0.444012i
\(455\) 0 0
\(456\) −163.749 −0.359098
\(457\) −645.475 + 372.665i −1.41242 + 0.815460i −0.995616 0.0935379i \(-0.970182\pi\)
−0.416802 + 0.908997i \(0.636849\pi\)
\(458\) 88.9993 154.151i 0.194322 0.336575i
\(459\) 78.8909 136.643i 0.171876 0.297697i
\(460\) 0 0
\(461\) 592.937i 1.28620i −0.765783 0.643099i \(-0.777648\pi\)
0.765783 0.643099i \(-0.222352\pi\)
\(462\) 22.1253 1.78326i 0.0478903 0.00385987i
\(463\) 529.829i 1.14434i 0.820136 + 0.572169i \(0.193898\pi\)
−0.820136 + 0.572169i \(0.806102\pi\)
\(464\) −65.6066 113.634i −0.141394 0.244901i
\(465\) 0 0
\(466\) 116.153 201.183i 0.249255 0.431723i
\(467\) −83.6375 144.864i −0.179095 0.310202i 0.762476 0.647017i \(-0.223984\pi\)
−0.941571 + 0.336815i \(0.890650\pi\)
\(468\) 19.3776 0.0414052
\(469\) −279.701 + 22.5434i −0.596378 + 0.0480669i
\(470\) 0 0
\(471\) −82.4728 142.847i −0.175102 0.303285i
\(472\) 18.6614 32.3225i 0.0395369 0.0684799i
\(473\) −62.1771 35.8980i −0.131453 0.0758943i
\(474\) 89.7367 51.8095i 0.189318 0.109303i
\(475\) 0 0
\(476\) 384.044 + 182.292i 0.806815 + 0.382966i
\(477\) 164.004i 0.343824i
\(478\) −61.7573 + 35.6556i −0.129199 + 0.0745933i
\(479\) −221.195 127.707i −0.461785 0.266612i 0.251009 0.967985i \(-0.419237\pi\)
−0.712795 + 0.701373i \(0.752571\pi\)
\(480\) 0 0
\(481\) 112.026 64.6783i 0.232902 0.134466i
\(482\) 275.986 0.572585
\(483\) 246.066 + 356.587i 0.509454 + 0.738276i
\(484\) 238.648 0.493075
\(485\) 0 0
\(486\) −19.0919 11.0227i −0.0392837 0.0226805i
\(487\) −525.531 303.415i −1.07912 0.623030i −0.148460 0.988918i \(-0.547432\pi\)
−0.930659 + 0.365889i \(0.880765\pi\)
\(488\) 55.7967 + 96.6427i 0.114337 + 0.198038i
\(489\) 426.947i 0.873102i
\(490\) 0 0
\(491\) 707.855 1.44166 0.720830 0.693112i \(-0.243761\pi\)
0.720830 + 0.693112i \(0.243761\pi\)
\(492\) 126.898 73.2645i 0.257923 0.148912i
\(493\) −498.038 + 862.628i −1.01022 + 1.74975i
\(494\) −76.3319 + 132.211i −0.154518 + 0.267633i
\(495\) 0 0
\(496\) 182.500i 0.367944i
\(497\) 267.606 184.664i 0.538442 0.371557i
\(498\) 3.76548i 0.00756120i
\(499\) 330.115 + 571.776i 0.661553 + 1.14584i 0.980208 + 0.197972i \(0.0634357\pi\)
−0.318655 + 0.947871i \(0.603231\pi\)
\(500\) 0 0
\(501\) 12.9423 22.4167i 0.0258329 0.0447439i
\(502\) −232.444 402.605i −0.463036 0.802002i
\(503\) −254.083 −0.505136 −0.252568 0.967579i \(-0.581275\pi\)
−0.252568 + 0.967579i \(0.581275\pi\)
\(504\) 25.4700 53.6589i 0.0505357 0.106466i
\(505\) 0 0
\(506\) −32.7103 56.6559i −0.0646448 0.111968i
\(507\) −137.325 + 237.855i −0.270859 + 0.469141i
\(508\) 156.337 + 90.2615i 0.307751 + 0.177680i
\(509\) −222.003 + 128.174i −0.436156 + 0.251815i −0.701966 0.712211i \(-0.747694\pi\)
0.265810 + 0.964026i \(0.414361\pi\)
\(510\) 0 0
\(511\) 76.7063 + 951.715i 0.150110 + 1.86246i
\(512\) 22.6274i 0.0441942i
\(513\) 150.413 86.8409i 0.293202 0.169280i
\(514\) 493.807 + 285.100i 0.960715 + 0.554669i
\(515\) 0 0
\(516\) −166.379 + 96.0591i −0.322440 + 0.186161i
\(517\) 78.6433 0.152115
\(518\) −31.8545 395.227i −0.0614952 0.762986i
\(519\) −290.406 −0.559550
\(520\) 0 0
\(521\) 164.700 + 95.0898i 0.316124 + 0.182514i 0.649663 0.760222i \(-0.274910\pi\)
−0.333540 + 0.942736i \(0.608243\pi\)
\(522\) 120.527 + 69.5863i 0.230895 + 0.133307i
\(523\) 173.610 + 300.701i 0.331950 + 0.574954i 0.982894 0.184171i \(-0.0589602\pi\)
−0.650944 + 0.759126i \(0.725627\pi\)
\(524\) 403.697i 0.770414i
\(525\) 0 0
\(526\) −704.212 −1.33881
\(527\) −1199.80 + 692.706i −2.27666 + 1.31443i
\(528\) −4.48449 + 7.76736i −0.00849335 + 0.0147109i
\(529\) 373.946 647.693i 0.706891 1.22437i
\(530\) 0 0
\(531\) 39.5868i 0.0745515i
\(532\) 265.777 + 385.151i 0.499580 + 0.723967i
\(533\) 136.610i 0.256304i
\(534\) 42.8286 + 74.1813i 0.0802033 + 0.138916i
\(535\) 0 0
\(536\) 56.6914 98.1924i 0.105768 0.183195i
\(537\) −57.9759 100.417i −0.107963 0.186997i
\(538\) −253.696 −0.471554
\(539\) −40.1055 49.1462i −0.0744072 0.0911804i
\(540\) 0 0
\(541\) −216.672 375.287i −0.400503 0.693691i 0.593284 0.804993i \(-0.297831\pi\)
−0.993787 + 0.111302i \(0.964498\pi\)
\(542\) 102.925 178.272i 0.189899 0.328915i
\(543\) −37.3663 21.5735i −0.0688146 0.0397301i
\(544\) −148.758 + 85.8856i −0.273452 + 0.157878i
\(545\) 0 0
\(546\) −31.4513 45.5777i −0.0576032 0.0834757i
\(547\) 718.061i 1.31272i 0.754446 + 0.656362i \(0.227906\pi\)
−0.754446 + 0.656362i \(0.772094\pi\)
\(548\) 0.00705109 0.00407095i 1.28670e−5 7.42874e-6i
\(549\) −102.505 59.1813i −0.186712 0.107798i
\(550\) 0 0
\(551\) −949.556 + 548.226i −1.72333 + 0.994966i
\(552\) −175.058 −0.317134
\(553\) −267.510 126.977i −0.483742 0.229615i
\(554\) −302.197 −0.545482
\(555\) 0 0
\(556\) −200.830 115.950i −0.361206 0.208542i
\(557\) −858.396 495.595i −1.54111 0.889758i −0.998769 0.0495971i \(-0.984206\pi\)
−0.542337 0.840161i \(-0.682460\pi\)
\(558\) 96.7854 + 167.637i 0.173451 + 0.300425i
\(559\) 179.113i 0.320417i
\(560\) 0 0
\(561\) 68.0860 0.121365
\(562\) 428.023 247.119i 0.761606 0.439713i
\(563\) −290.108 + 502.481i −0.515289 + 0.892506i 0.484554 + 0.874762i \(0.338982\pi\)
−0.999843 + 0.0177449i \(0.994351\pi\)
\(564\) 105.220 182.247i 0.186561 0.323133i
\(565\) 0 0
\(566\) 133.291i 0.235496i
\(567\) 5.06126 + 62.7964i 0.00892639 + 0.110752i
\(568\) 131.375i 0.231294i
\(569\) −106.770 184.931i −0.187645 0.325010i 0.756820 0.653624i \(-0.226752\pi\)
−0.944465 + 0.328613i \(0.893419\pi\)
\(570\) 0 0
\(571\) 378.751 656.016i 0.663311 1.14889i −0.316429 0.948616i \(-0.602484\pi\)
0.979740 0.200273i \(-0.0641828\pi\)
\(572\) 4.18091 + 7.24156i 0.00730929 + 0.0126601i
\(573\) 23.5639 0.0411237
\(574\) −378.289 179.560i −0.659040 0.312823i
\(575\) 0 0
\(576\) 12.0000 + 20.7846i 0.0208333 + 0.0360844i
\(577\) 90.7836 157.242i 0.157337 0.272516i −0.776570 0.630031i \(-0.783042\pi\)
0.933908 + 0.357514i \(0.116376\pi\)
\(578\) 775.314 + 447.628i 1.34137 + 0.774442i
\(579\) −273.627 + 157.978i −0.472585 + 0.272847i
\(580\) 0 0
\(581\) −8.85671 + 6.11165i −0.0152439 + 0.0105192i
\(582\) 368.689i 0.633486i
\(583\) −61.2894 + 35.3855i −0.105128 + 0.0606955i
\(584\) −334.111 192.899i −0.572107 0.330306i
\(585\) 0 0
\(586\) −239.966 + 138.544i −0.409498 + 0.236424i
\(587\) −156.397 −0.266434 −0.133217 0.991087i \(-0.542531\pi\)
−0.133217 + 0.991087i \(0.542531\pi\)
\(588\) −167.550 + 27.1850i −0.284949 + 0.0462329i
\(589\) −1525.02 −2.58917
\(590\) 0 0
\(591\) 430.019 + 248.271i 0.727612 + 0.420087i
\(592\) 138.749 + 80.1068i 0.234373 + 0.135316i
\(593\) 105.889 + 183.404i 0.178564 + 0.309282i 0.941389 0.337323i \(-0.109521\pi\)
−0.762825 + 0.646605i \(0.776188\pi\)
\(594\) 9.51303i 0.0160152i
\(595\) 0 0
\(596\) −10.3870 −0.0174278
\(597\) 4.74785 2.74117i 0.00795285 0.00459158i
\(598\) −81.6039 + 141.342i −0.136461 + 0.236358i
\(599\) 264.528 458.175i 0.441616 0.764901i −0.556194 0.831053i \(-0.687739\pi\)
0.997810 + 0.0661519i \(0.0210722\pi\)
\(600\) 0 0
\(601\) 899.473i 1.49663i 0.663345 + 0.748314i \(0.269136\pi\)
−0.663345 + 0.748314i \(0.730864\pi\)
\(602\) 495.985 + 235.427i 0.823895 + 0.391074i
\(603\) 120.261i 0.199437i
\(604\) −160.742 278.413i −0.266129 0.460949i
\(605\) 0 0
\(606\) −146.804 + 254.272i −0.242251 + 0.419591i
\(607\) 268.038 + 464.255i 0.441578 + 0.764835i 0.997807 0.0661939i \(-0.0210856\pi\)
−0.556229 + 0.831029i \(0.687752\pi\)
\(608\) −189.081 −0.310988
\(609\) −31.9517 396.433i −0.0524659 0.650958i
\(610\) 0 0
\(611\) −98.0976 169.910i −0.160552 0.278085i
\(612\) 91.0954 157.782i 0.148849 0.257813i
\(613\) 717.977 + 414.524i 1.17125 + 0.676222i 0.953974 0.299888i \(-0.0969495\pi\)
0.217276 + 0.976110i \(0.430283\pi\)
\(614\) −554.098 + 319.908i −0.902439 + 0.521024i
\(615\) 0 0
\(616\) 25.5481 2.05913i 0.0414742 0.00334274i
\(617\) 404.320i 0.655300i 0.944799 + 0.327650i \(0.106257\pi\)
−0.944799 + 0.327650i \(0.893743\pi\)
\(618\) 211.388 122.045i 0.342051 0.197483i
\(619\) 346.662 + 200.145i 0.560036 + 0.323337i 0.753160 0.657838i \(-0.228529\pi\)
−0.193124 + 0.981174i \(0.561862\pi\)
\(620\) 0 0
\(621\) 160.801 92.8387i 0.258939 0.149499i
\(622\) 92.8991 0.149355
\(623\) 104.966 221.138i 0.168485 0.354957i
\(624\) 22.3753 0.0358579
\(625\) 0 0
\(626\) 434.270 + 250.726i 0.693722 + 0.400521i
\(627\) 64.9061 + 37.4736i 0.103519 + 0.0597665i
\(628\) −95.2314 164.946i −0.151642 0.262652i
\(629\) 1216.23i 1.93359i
\(630\) 0 0
\(631\) 334.639 0.530331 0.265165 0.964203i \(-0.414573\pi\)
0.265165 + 0.964203i \(0.414573\pi\)
\(632\) 103.619 59.8244i 0.163954 0.0946589i
\(633\) −155.299 + 268.987i −0.245339 + 0.424939i
\(634\) −95.3603 + 165.169i −0.150411 + 0.260519i
\(635\) 0 0
\(636\) 189.375i 0.297760i
\(637\) −56.1547 + 147.952i −0.0881550 + 0.232264i
\(638\) 60.0558i 0.0941313i
\(639\) −69.6720 120.676i −0.109033 0.188851i
\(640\) 0 0
\(641\) 36.0084 62.3683i 0.0561753 0.0972984i −0.836570 0.547860i \(-0.815443\pi\)
0.892746 + 0.450561i \(0.148776\pi\)
\(642\) −57.5514 99.6819i −0.0896439 0.155268i
\(643\) 1254.20 1.95054 0.975269 0.221020i \(-0.0709386\pi\)
0.975269 + 0.221020i \(0.0709386\pi\)
\(644\) 284.133 + 411.751i 0.441200 + 0.639366i
\(645\) 0 0
\(646\) 717.683 + 1243.06i 1.11096 + 1.92425i
\(647\) −73.1699 + 126.734i −0.113091 + 0.195879i −0.917015 0.398853i \(-0.869409\pi\)
0.803924 + 0.594732i \(0.202742\pi\)
\(648\) −22.0454 12.7279i −0.0340207 0.0196419i
\(649\) −14.7939 + 8.54125i −0.0227949 + 0.0131606i
\(650\) 0 0
\(651\) 237.207 499.735i 0.364373 0.767642i
\(652\) 492.996i 0.756128i
\(653\) −687.082 + 396.687i −1.05219 + 0.607484i −0.923262 0.384170i \(-0.874488\pi\)
−0.128930 + 0.991654i \(0.541154\pi\)
\(654\) −123.377 71.2316i −0.188649 0.108917i
\(655\) 0 0
\(656\) 146.529 84.5986i 0.223368 0.128961i
\(657\) 409.200 0.622832
\(658\) −599.441 + 48.3137i −0.911004 + 0.0734251i
\(659\) −35.5649 −0.0539680 −0.0269840 0.999636i \(-0.508590\pi\)
−0.0269840 + 0.999636i \(0.508590\pi\)
\(660\) 0 0
\(661\) 193.509 + 111.723i 0.292752 + 0.169021i 0.639182 0.769055i \(-0.279273\pi\)
−0.346430 + 0.938076i \(0.612606\pi\)
\(662\) −221.094 127.649i −0.333979 0.192823i
\(663\) −84.9288 147.101i −0.128098 0.221872i
\(664\) 4.34800i 0.00654819i
\(665\) 0 0
\(666\) −169.932 −0.255154
\(667\) −1015.14 + 586.090i −1.52195 + 0.878696i
\(668\) 14.9445 25.8846i 0.0223720 0.0387494i
\(669\) 61.7775 107.002i 0.0923431 0.159943i
\(670\) 0 0
\(671\) 51.0759i 0.0761190i
\(672\) 29.4102 61.9600i 0.0437652 0.0922024i
\(673\) 216.920i 0.322318i −0.986928 0.161159i \(-0.948477\pi\)
0.986928 0.161159i \(-0.0515232\pi\)
\(674\) 4.13429 + 7.16080i 0.00613396 + 0.0106243i
\(675\) 0 0
\(676\) −158.570 + 274.651i −0.234571 + 0.406288i
\(677\) 23.4825 + 40.6729i 0.0346861 + 0.0600781i 0.882847 0.469660i \(-0.155624\pi\)
−0.848161 + 0.529738i \(0.822290\pi\)
\(678\) −517.091 −0.762672
\(679\) 867.186 598.410i 1.27715 0.881310i
\(680\) 0 0
\(681\) −123.443 213.809i −0.181267 0.313964i
\(682\) −41.7648 + 72.3388i −0.0612388 + 0.106069i
\(683\) 51.1993 + 29.5599i 0.0749623 + 0.0432795i 0.537013 0.843574i \(-0.319553\pi\)
−0.462050 + 0.886854i \(0.652886\pi\)
\(684\) 173.682 100.275i 0.253921 0.146601i
\(685\) 0 0
\(686\) 335.888 + 349.968i 0.489632 + 0.510157i
\(687\) 218.003i 0.317326i
\(688\) −192.118 + 110.919i −0.279242 + 0.161220i
\(689\) 152.902 + 88.2779i 0.221918 + 0.128125i
\(690\) 0 0
\(691\) 916.389 529.078i 1.32618 0.765669i 0.341472 0.939892i \(-0.389075\pi\)
0.984706 + 0.174222i \(0.0557412\pi\)
\(692\) −335.332 −0.484584
\(693\) −22.3754 + 15.4404i −0.0322878 + 0.0222805i
\(694\) 554.757 0.799361
\(695\) 0 0
\(696\) 139.173 + 80.3513i 0.199961 + 0.115447i
\(697\) −1112.34 642.212i −1.59590 0.921395i
\(698\) 163.238 + 282.736i 0.233865 + 0.405066i
\(699\) 284.516i 0.407032i
\(700\) 0 0
\(701\) −394.358 −0.562565 −0.281283 0.959625i \(-0.590760\pi\)
−0.281283 + 0.959625i \(0.590760\pi\)
\(702\) −20.5531 + 11.8663i −0.0292779 + 0.0169036i
\(703\) 669.394 1159.42i 0.952197 1.64925i
\(704\) −5.17824 + 8.96898i −0.00735546 + 0.0127400i
\(705\) 0 0
\(706\) 177.678i 0.251669i
\(707\) 836.342 67.4075i 1.18295 0.0953430i
\(708\) 45.7109i 0.0645635i
\(709\) −20.7217 35.8911i −0.0292267 0.0506221i 0.851042 0.525097i \(-0.175971\pi\)
−0.880269 + 0.474475i \(0.842638\pi\)
\(710\) 0 0
\(711\) −63.4534 + 109.905i −0.0892453 + 0.154577i
\(712\) 49.4542 + 85.6572i 0.0694581 + 0.120305i
\(713\) −1630.35 −2.28660
\(714\) −518.971 + 41.8280i −0.726850 + 0.0585826i
\(715\) 0 0
\(716\) −66.9449 115.952i −0.0934984 0.161944i
\(717\) 43.6690 75.6369i 0.0609051 0.105491i
\(718\) −529.052 305.448i −0.736841 0.425415i
\(719\) −556.327 + 321.195i −0.773751 + 0.446725i −0.834211 0.551445i \(-0.814077\pi\)
0.0604602 + 0.998171i \(0.480743\pi\)
\(720\) 0 0
\(721\) −630.157 299.113i −0.874004 0.414859i
\(722\) 1069.48i 1.48127i
\(723\) −292.727 + 169.006i −0.404879 + 0.233757i
\(724\) −43.1469 24.9109i −0.0595952 0.0344073i
\(725\) 0 0
\(726\) −253.125 + 146.142i −0.348657 + 0.201297i
\(727\) −979.168 −1.34686 −0.673431 0.739250i \(-0.735180\pi\)
−0.673431 + 0.739250i \(0.735180\pi\)
\(728\) −36.3169 52.6286i −0.0498858 0.0722921i
\(729\) 27.0000 0.0370370
\(730\) 0 0
\(731\) 1458.42 + 842.021i 1.99511 + 1.15188i
\(732\) −118.363 68.3367i −0.161698 0.0933562i
\(733\) 618.862 + 1071.90i 0.844286 + 1.46235i 0.886240 + 0.463227i \(0.153308\pi\)
−0.0419537 + 0.999120i \(0.513358\pi\)
\(734\) 667.647i 0.909601i
\(735\) 0 0
\(736\) −202.140 −0.274647
\(737\) −44.9423 + 25.9474i −0.0609800 + 0.0352068i
\(738\) −89.7304 + 155.418i −0.121586 + 0.210593i
\(739\) −477.274 + 826.662i −0.645837 + 1.11862i 0.338271 + 0.941049i \(0.390158\pi\)
−0.984108 + 0.177574i \(0.943175\pi\)
\(740\) 0 0
\(741\) 186.974i 0.252327i
\(742\) 445.426 307.370i 0.600305 0.414246i
\(743\) 401.194i 0.539964i −0.962865 0.269982i \(-0.912982\pi\)
0.962865 0.269982i \(-0.0870178\pi\)
\(744\) 111.758 + 193.571i 0.150213 + 0.260176i
\(745\) 0 0
\(746\) 61.8874 107.192i 0.0829590 0.143689i
\(747\) 2.30587 + 3.99389i 0.00308685 + 0.00534657i
\(748\) 78.6190 0.105106
\(749\) −141.050 + 297.157i −0.188318 + 0.396738i
\(750\) 0 0
\(751\) 420.870 + 728.968i 0.560412 + 0.970662i 0.997460 + 0.0712243i \(0.0226906\pi\)
−0.437048 + 0.899438i \(0.643976\pi\)
\(752\) 121.498 210.441i 0.161567 0.279841i
\(753\) 493.088 + 284.685i 0.654832 + 0.378067i
\(754\) 129.751 74.9120i 0.172084 0.0993528i
\(755\) 0 0
\(756\) 5.84424 + 72.5110i 0.00773048 + 0.0959140i
\(757\) 1287.18i 1.70037i −0.526487 0.850183i \(-0.676491\pi\)
0.526487 0.850183i \(-0.323509\pi\)
\(758\) −440.489 + 254.317i −0.581120 + 0.335510i
\(759\) 69.3890 + 40.0617i 0.0914216 + 0.0527823i
\(760\) 0 0
\(761\) −1237.18 + 714.288i −1.62573 + 0.938618i −0.640387 + 0.768052i \(0.721226\pi\)
−0.985346 + 0.170565i \(0.945441\pi\)
\(762\) −221.095 −0.290150
\(763\) 32.7072 + 405.807i 0.0428666 + 0.531857i
\(764\) 27.2092 0.0356142
\(765\) 0 0
\(766\) 592.986 + 342.361i 0.774133 + 0.446946i
\(767\) 36.9070 + 21.3083i 0.0481187 + 0.0277813i
\(768\) 13.8564 + 24.0000i 0.0180422 + 0.0312500i
\(769\) 1030.04i 1.33945i −0.742608 0.669726i \(-0.766411\pi\)
0.742608 0.669726i \(-0.233589\pi\)
\(770\) 0 0
\(771\) −698.349 −0.905771
\(772\) −315.957 + 182.418i −0.409271 + 0.236293i
\(773\) −374.310 + 648.324i −0.484231 + 0.838712i −0.999836 0.0181142i \(-0.994234\pi\)
0.515605 + 0.856826i \(0.327567\pi\)
\(774\) 117.648 203.772i 0.152000 0.263271i
\(775\) 0 0
\(776\) 425.725i 0.548615i
\(777\) 275.813 + 399.695i 0.354972 + 0.514408i
\(778\) 508.526i 0.653632i
\(779\) −706.929 1224.44i −0.907482 1.57181i
\(780\) 0 0
\(781\) 30.0649 52.0739i 0.0384954 0.0666759i
\(782\) 767.250 + 1328.92i 0.981139 + 1.69938i
\(783\) −170.451 −0.217690
\(784\) −193.470 + 31.3905i −0.246773 + 0.0400389i
\(785\) 0 0
\(786\) −247.213 428.185i −0.314520 0.544765i
\(787\) 80.7880 139.929i 0.102653 0.177800i −0.810124 0.586259i \(-0.800600\pi\)
0.912777 + 0.408458i \(0.133934\pi\)
\(788\) 496.543 + 286.679i 0.630131 + 0.363806i
\(789\) 746.930 431.240i 0.946679 0.546566i
\(790\) 0 0
\(791\) 839.279 + 1216.24i 1.06103 + 1.53760i
\(792\) 10.9847i 0.0138696i
\(793\) −110.350 + 63.7107i −0.139155 + 0.0803414i
\(794\) −222.161 128.265i −0.279800 0.161543i
\(795\) 0 0
\(796\) 5.48235 3.16523i 0.00688737 0.00397643i
\(797\) −1350.55 −1.69454 −0.847269 0.531164i \(-0.821755\pi\)
−0.847269 + 0.531164i \(0.821755\pi\)
\(798\) −517.754 245.760i −0.648815 0.307969i
\(799\) −1844.65 −2.30870
\(800\) 0 0
\(801\) −90.8531 52.4541i −0.113425 0.0654857i
\(802\) −325.150 187.725i −0.405423 0.234071i
\(803\) 88.2891 + 152.921i 0.109949 + 0.190437i
\(804\) 138.865i 0.172718i
\(805\) 0 0
\(806\) 208.386 0.258543
\(807\) 269.085 155.357i 0.333439 0.192511i
\(808\) −169.515 + 293.608i −0.209795 + 0.363376i
\(809\) 644.079 1115.58i 0.796142 1.37896i −0.125969 0.992034i \(-0.540204\pi\)
0.922111 0.386925i \(-0.126463\pi\)
\(810\) 0 0
\(811\) 1097.00i 1.35265i 0.736605 + 0.676323i \(0.236428\pi\)
−0.736605 + 0.676323i \(0.763572\pi\)
\(812\) −36.8947 457.762i −0.0454368 0.563746i
\(813\) 252.114i 0.310104i
\(814\) −36.6646 63.5049i −0.0450425 0.0780159i
\(815\) 0 0
\(816\) 105.188 182.191i 0.128907 0.223273i
\(817\) 926.873 + 1605.39i 1.13448 + 1.96498i
\(818\) −804.359 −0.983324
\(819\) 61.2697 + 29.0826i 0.0748104 + 0.0355099i
\(820\) 0 0
\(821\) −448.083 776.103i −0.545778 0.945315i −0.998558 0.0536923i \(-0.982901\pi\)
0.452780 0.891622i \(-0.350432\pi\)
\(822\) −0.00498587 + 0.00863579i −6.06554e−6 + 1.05058e-5i
\(823\) −46.8742 27.0628i −0.0569553 0.0328832i 0.471252 0.881999i \(-0.343802\pi\)
−0.528207 + 0.849115i \(0.677136\pi\)
\(824\) 244.089 140.925i 0.296225 0.171026i
\(825\) 0 0
\(826\) 107.516 74.1923i 0.130164 0.0898212i
\(827\) 977.965i 1.18255i −0.806472 0.591273i \(-0.798626\pi\)
0.806472 0.591273i \(-0.201374\pi\)
\(828\) 185.677 107.201i 0.224248 0.129470i
\(829\) 667.395 + 385.321i 0.805061 + 0.464802i 0.845238 0.534391i \(-0.179459\pi\)
−0.0401771 + 0.999193i \(0.512792\pi\)
\(830\) 0 0
\(831\) 320.528 185.057i 0.385714 0.222692i
\(832\) 25.8368 0.0310539
\(833\) 940.712 + 1152.77i 1.12931 + 1.38388i
\(834\) 284.017 0.340548
\(835\) 0 0
\(836\) 74.9472 + 43.2708i 0.0896497 + 0.0517593i
\(837\) −205.313 118.537i −0.245296 0.141622i
\(838\) 393.181 + 681.009i 0.469189 + 0.812659i
\(839\) 148.387i 0.176862i −0.996082 0.0884308i \(-0.971815\pi\)
0.996082 0.0884308i \(-0.0281852\pi\)
\(840\) 0 0
\(841\) 235.056 0.279496
\(842\) 583.306 336.772i 0.692762 0.399966i
\(843\) −302.658 + 524.218i −0.359024 + 0.621849i
\(844\) −179.324 + 310.599i −0.212470 + 0.368008i
\(845\) 0 0
\(846\) 257.736i 0.304653i
\(847\) 754.578 + 358.171i 0.890883 + 0.422870i
\(848\) 218.672i 0.257868i
\(849\) 81.6234 + 141.376i 0.0961407 + 0.166521i
\(850\) 0 0
\(851\) 715.627 1239.50i 0.840924 1.45652i
\(852\) −80.4503 139.344i −0.0944253 0.163549i
\(853\) 59.1817 0.0693807 0.0346903 0.999398i \(-0.488956\pi\)
0.0346903 + 0.999398i \(0.488956\pi\)
\(854\) 31.3780 + 389.314i 0.0367423 + 0.455872i
\(855\) 0 0
\(856\) −66.4546 115.103i −0.0776339 0.134466i
\(857\) −128.218 + 222.080i −0.149613 + 0.259137i −0.931084 0.364804i \(-0.881136\pi\)
0.781472 + 0.623941i \(0.214469\pi\)
\(858\) −8.86906 5.12055i −0.0103369 0.00596801i
\(859\) −26.1614 + 15.1043i −0.0304556 + 0.0175836i −0.515151 0.857100i \(-0.672264\pi\)
0.484695 + 0.874683i \(0.338931\pi\)
\(860\) 0 0
\(861\) 511.194 41.2012i 0.593721 0.0478528i
\(862\) 649.994i 0.754054i
\(863\) 1114.24 643.310i 1.29113 0.745434i 0.312275 0.949992i \(-0.398909\pi\)
0.978855 + 0.204558i \(0.0655756\pi\)
\(864\) −25.4558 14.6969i −0.0294628 0.0170103i
\(865\) 0 0
\(866\) 80.7333 46.6114i 0.0932255 0.0538238i
\(867\) −1096.46 −1.26466
\(868\) 273.903 577.045i 0.315556 0.664798i
\(869\) −54.7628 −0.0630182
\(870\) 0 0
\(871\) 112.120 + 64.7323i 0.128725 + 0.0743196i
\(872\) −142.463 82.2512i −0.163375 0.0943247i
\(873\) −225.775 391.053i −0.258619 0.447942i
\(874\) 1689.13i 1.93265i
\(875\) 0 0
\(876\) 472.504 0.539388
\(877\) −264.177 + 152.523i −0.301228 + 0.173914i −0.642994 0.765871i \(-0.722308\pi\)
0.341767 + 0.939785i \(0.388975\pi\)
\(878\) −251.170 + 435.039i −0.286071 + 0.495489i
\(879\) 169.681 293.897i 0.193039 0.334354i
\(880\) 0 0
\(881\) 515.564i 0.585204i −0.956234 0.292602i \(-0.905479\pi\)
0.956234 0.292602i \(-0.0945210\pi\)
\(882\) 161.066 131.437i 0.182615 0.149022i
\(883\) 951.802i 1.07792i −0.842332 0.538960i \(-0.818818\pi\)
0.842332 0.538960i \(-0.181182\pi\)
\(884\) −98.0673 169.858i −0.110936 0.192147i
\(885\) 0 0
\(886\) −536.152 + 928.643i −0.605138 + 1.04813i
\(887\) −608.088 1053.24i −0.685556 1.18742i −0.973262 0.229699i \(-0.926226\pi\)
0.287706 0.957719i \(-0.407108\pi\)
\(888\) −196.221 −0.220969
\(889\) 358.853 + 520.033i 0.403659 + 0.584963i
\(890\) 0 0
\(891\) 5.82552 + 10.0901i 0.00653818 + 0.0113245i
\(892\) 71.3345 123.555i 0.0799715 0.138515i
\(893\) −1758.50 1015.27i −1.96920 1.13692i
\(894\) 11.0171 6.36070i 0.0123233 0.00711488i
\(895\) 0 0
\(896\) 33.9600 71.5452i 0.0379018 0.0798496i
\(897\) 199.888i 0.222841i
\(898\) 818.257 472.421i 0.911200 0.526081i
\(899\) 1296.14 + 748.327i 1.44176 + 0.832399i
\(900\) 0 0
\(901\) 1437.60 830.000i 1.59556 0.921198i
\(902\) −77.4409 −0.0858547
\(903\) −670.240 + 54.0200i −0.742237 + 0.0598228i
\(904\) −597.086 −0.660493
\(905\) 0 0
\(906\) 340.985 + 196.868i 0.376363 + 0.217294i
\(907\) −1188.52 686.190i −1.31038 0.756549i −0.328222 0.944601i \(-0.606449\pi\)
−0.982159 + 0.188052i \(0.939783\pi\)
\(908\) −142.540 246.886i −0.156982 0.271901i
\(909\) 359.595i 0.395594i
\(910\) 0 0
\(911\) −317.135 −0.348118 −0.174059 0.984735i \(-0.555688\pi\)
−0.174059 + 0.984735i \(0.555688\pi\)
\(912\) 200.550 115.788i 0.219902 0.126960i
\(913\) −0.995031 + 1.72344i −0.00108985 + 0.00188767i
\(914\) 527.028 912.839i 0.576617 0.998730i
\(915\) 0 0
\(916\) 251.728i 0.274812i
\(917\) −605.882 + 1276.44i −0.660721 + 1.39198i
\(918\) 223.137i 0.243069i
\(919\) 451.409 + 781.863i 0.491195 + 0.850775i 0.999949 0.0101370i \(-0.00322675\pi\)
−0.508753 + 0.860912i \(0.669893\pi\)
\(920\) 0 0
\(921\) 391.806 678.628i 0.425414 0.736839i
\(922\) 419.270 + 726.197i 0.454740 + 0.787632i
\(923\) −150.009 −0.162523
\(924\) −25.8369 + 17.8290i −0.0279621 + 0.0192955i
\(925\) 0 0
\(926\) −374.645 648.905i −0.404585 0.700761i
\(927\) −149.474 + 258.896i −0.161244 + 0.279284i
\(928\) 160.703 + 92.7817i 0.173171 + 0.0999803i
\(929\) 291.968 168.568i 0.314282 0.181451i −0.334559 0.942375i \(-0.608587\pi\)
0.648841 + 0.760924i \(0.275254\pi\)
\(930\) 0 0
\(931\) 262.307 + 1616.69i 0.281748 + 1.73651i
\(932\) 328.530i 0.352500i
\(933\) −98.5344 + 56.8889i −0.105610 + 0.0609741i
\(934\) 204.869 + 118.281i 0.219346 + 0.126640i
\(935\) 0 0
\(936\) −23.7326 + 13.7020i −0.0253554 + 0.0146389i
\(937\) 1577.72 1.68380 0.841900 0.539634i \(-0.181438\pi\)
0.841900 + 0.539634i \(0.181438\pi\)
\(938\) 326.622 225.388i 0.348211 0.240286i
\(939\) −614.150 −0.654047
\(940\) 0 0
\(941\) −711.530 410.802i −0.756142 0.436559i 0.0717667 0.997421i \(-0.477136\pi\)
−0.827909 + 0.560863i \(0.810470\pi\)
\(942\) 202.016 + 116.634i 0.214455 + 0.123815i
\(943\) −755.753 1309.00i −0.801435 1.38813i
\(944\) 52.7824i 0.0559136i
\(945\) 0 0
\(946\) 101.535 0.107331
\(947\) 354.357 204.588i 0.374189 0.216038i −0.301098 0.953593i \(-0.597353\pi\)
0.675287 + 0.737555i \(0.264020\pi\)
\(948\) −73.2697 + 126.907i −0.0772887 + 0.133868i
\(949\) 220.259 381.500i 0.232096 0.402002i
\(950\) 0 0
\(951\) 233.584i 0.245619i
\(952\) −599.256 + 48.2988i −0.629470 + 0.0507340i
\(953\) 820.950i 0.861437i −0.902486 0.430719i \(-0.858260\pi\)
0.902486 0.430719i \(-0.141740\pi\)
\(954\) −115.968 200.863i −0.121560 0.210548i
\(955\) 0 0
\(956\) 50.4246 87.3380i 0.0527454 0.0913577i
\(957\) −36.7765 63.6988i −0.0384289 0.0665609i
\(958\) 361.210 0.377046
\(959\) 0.0284045 0.00228935i 2.96189e−5 2.38722e-6i
\(960\) 0 0
\(961\) 560.324 + 970.510i 0.583063 + 1.00990i
\(962\) −91.4689 + 158.429i −0.0950820 + 0.164687i
\(963\) 122.085 + 70.4858i 0.126776 + 0.0731940i
\(964\) −338.012 + 195.151i −0.350635 + 0.202439i
\(965\) 0 0
\(966\) −553.514 262.733i −0.572995 0.271981i
\(967\) 1627.11i 1.68263i 0.540543 + 0.841317i \(0.318219\pi\)
−0.540543 + 0.841317i \(0.681781\pi\)
\(968\) −292.283 + 168.750i −0.301945 + 0.174328i
\(969\) −1522.44 878.978i −1.57114 0.907098i
\(970\) 0 0
\(971\) 1074.33 620.263i 1.10641 0.638788i 0.168515 0.985699i \(-0.446103\pi\)
0.937898 + 0.346911i \(0.112769\pi\)
\(972\) 31.1769 0.0320750
\(973\) −460.981 668.032i −0.473773 0.686569i
\(974\) 858.188 0.881097
\(975\) 0 0
\(976\) −136.673 78.9084i −0.140034 0.0808488i
\(977\) −622.459 359.377i −0.637113 0.367837i 0.146389 0.989227i \(-0.453235\pi\)
−0.783502 + 0.621390i \(0.786568\pi\)
\(978\) −301.897 522.901i −0.308688 0.534664i
\(979\) 45.2700i 0.0462410i
\(980\) 0 0
\(981\) 174.481 0.177860
\(982\) −866.941 + 500.529i −0.882832 + 0.509704i
\(983\) −201.047 + 348.223i −0.204524 + 0.354246i −0.949981 0.312308i \(-0.898898\pi\)
0.745457 + 0.666554i \(0.232231\pi\)
\(984\) −103.612 + 179.461i −0.105296 + 0.182379i
\(985\) 0 0
\(986\) 1408.66i 1.42867i
\(987\) 606.217 418.325i 0.614202 0.423835i
\(988\) 215.899i 0.218522i
\(989\) 990.889 + 1716.27i 1.00191 + 1.73536i
\(990\) 0 0
\(991\) 298.270 516.618i 0.300979 0.521310i −0.675379 0.737471i \(-0.736020\pi\)
0.976358 + 0.216160i \(0.0693534\pi\)
\(992\) 129.047 + 223.516i 0.130088 + 0.225319i
\(993\) 312.674 0.314878
\(994\) −197.172 + 415.392i −0.198362 + 0.417899i
\(995\) 0 0
\(996\) 2.66259 + 4.61175i 0.00267329 + 0.00463027i
\(997\) 680.693 1178.99i 0.682741 1.18254i −0.291400 0.956601i \(-0.594121\pi\)
0.974141 0.225941i \(-0.0725457\pi\)
\(998\) −808.613 466.853i −0.810234 0.467789i
\(999\) 180.240 104.062i 0.180421 0.104166i
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 1050.3.q.b.199.4 16
5.2 odd 4 1050.3.p.c.451.2 8
5.3 odd 4 1050.3.p.d.451.3 yes 8
5.4 even 2 inner 1050.3.q.b.199.5 16
7.5 odd 6 inner 1050.3.q.b.649.5 16
35.12 even 12 1050.3.p.c.901.2 yes 8
35.19 odd 6 inner 1050.3.q.b.649.4 16
35.33 even 12 1050.3.p.d.901.3 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1050.3.p.c.451.2 8 5.2 odd 4
1050.3.p.c.901.2 yes 8 35.12 even 12
1050.3.p.d.451.3 yes 8 5.3 odd 4
1050.3.p.d.901.3 yes 8 35.33 even 12
1050.3.q.b.199.4 16 1.1 even 1 trivial
1050.3.q.b.199.5 16 5.4 even 2 inner
1050.3.q.b.649.4 16 35.19 odd 6 inner
1050.3.q.b.649.5 16 7.5 odd 6 inner