Properties

Label 540.2.n.d.359.7
Level $540$
Weight $2$
Character 540.359
Analytic conductor $4.312$
Analytic rank $0$
Dimension $48$
Inner twists $8$

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [540,2,Mod(179,540)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(540, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 5, 3])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("540.179"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: \( N \) \(=\) \( 540 = 2^{2} \cdot 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 540.n (of order \(6\), degree \(2\), not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [48,0,0,-2,18,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.31192170915\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 180)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 359.7
Character \(\chi\) \(=\) 540.359
Dual form 540.2.n.d.179.7

$q$-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.937387 - 1.05892i) q^{2} +(-0.242609 + 1.98523i) q^{4} +(-0.520093 - 2.17474i) q^{5} +(-0.550457 + 0.953419i) q^{7} +(2.32961 - 1.60403i) q^{8} +(-1.81534 + 2.58931i) q^{10} +(-2.84126 + 4.92120i) q^{11} +(-2.07548 + 1.19828i) q^{13} +(1.52558 - 0.310835i) q^{14} +(-3.88228 - 0.963271i) q^{16} -1.29175 q^{17} -2.78362i q^{19} +(4.44354 - 0.504891i) q^{20} +(7.87450 - 1.60442i) q^{22} +(-1.82546 + 1.05393i) q^{23} +(-4.45901 + 2.26214i) q^{25} +(3.21441 + 1.07451i) q^{26} +(-1.75921 - 1.32409i) q^{28} +(5.51723 + 3.18537i) q^{29} +(-2.78385 + 1.60725i) q^{31} +(2.61918 + 5.01397i) q^{32} +(1.21087 + 1.36785i) q^{34} +(2.35973 + 0.701235i) q^{35} +6.51687i q^{37} +(-2.94763 + 2.60933i) q^{38} +(-4.69996 - 4.23206i) q^{40} +(-6.35642 + 3.66988i) q^{41} +(-2.25473 + 3.90530i) q^{43} +(-9.08040 - 6.83448i) q^{44} +(2.82719 + 0.945071i) q^{46} +(8.09628 + 4.67439i) q^{47} +(2.89400 + 5.01255i) q^{49} +(6.57523 + 2.60122i) q^{50} +(-1.87533 - 4.41103i) q^{52} -11.5954 q^{53} +(12.1801 + 3.61952i) q^{55} +(0.246959 + 3.10404i) q^{56} +(-1.79874 - 8.82821i) q^{58} +(-3.66237 - 6.34341i) q^{59} +(2.48990 - 4.31263i) q^{61} +(4.31149 + 1.44124i) q^{62} +(2.85419 - 7.47353i) q^{64} +(3.68540 + 3.89043i) q^{65} +(-1.85016 - 3.20457i) q^{67} +(0.313389 - 2.56441i) q^{68} +(-1.46943 - 3.15608i) q^{70} +12.6950 q^{71} +9.86891i q^{73} +(6.90082 - 6.10883i) q^{74} +(5.52614 + 0.675333i) q^{76} +(-3.12798 - 5.41781i) q^{77} +(0.975531 + 0.563223i) q^{79} +(-0.0757197 + 8.94395i) q^{80} +(9.84453 + 3.29082i) q^{82} +(-9.98138 - 5.76275i) q^{83} +(0.671827 + 2.80921i) q^{85} +(6.24894 - 1.27321i) q^{86} +(1.27471 + 16.0219i) q^{88} -9.16815i q^{89} -2.63841i q^{91} +(-1.64942 - 3.87966i) q^{92} +(-2.63956 - 12.9550i) q^{94} +(-6.05366 + 1.44774i) q^{95} +(-11.1257 - 6.42344i) q^{97} +(2.59507 - 7.76320i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q - 2 q^{4} + 18 q^{5} - 16 q^{10} + 42 q^{14} + 30 q^{16} - 26 q^{25} - 4 q^{34} + 10 q^{40} - 96 q^{41} + 4 q^{46} + 32 q^{49} + 90 q^{50} - 6 q^{56} + 8 q^{61} - 20 q^{64} + 6 q^{65} + 4 q^{70} - 72 q^{74}+ \cdots - 62 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/540\mathbb{Z}\right)^\times\).

\(n\) \(217\) \(271\) \(461\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.937387 1.05892i −0.662833 0.748767i
\(3\) 0 0
\(4\) −0.242609 + 1.98523i −0.121305 + 0.992615i
\(5\) −0.520093 2.17474i −0.232593 0.972574i
\(6\) 0 0
\(7\) −0.550457 + 0.953419i −0.208053 + 0.360358i −0.951101 0.308880i \(-0.900046\pi\)
0.743048 + 0.669238i \(0.233379\pi\)
\(8\) 2.32961 1.60403i 0.823643 0.567109i
\(9\) 0 0
\(10\) −1.81534 + 2.58931i −0.574062 + 0.818812i
\(11\) −2.84126 + 4.92120i −0.856671 + 1.48380i 0.0184153 + 0.999830i \(0.494138\pi\)
−0.875086 + 0.483967i \(0.839195\pi\)
\(12\) 0 0
\(13\) −2.07548 + 1.19828i −0.575636 + 0.332343i −0.759397 0.650627i \(-0.774506\pi\)
0.183761 + 0.982971i \(0.441173\pi\)
\(14\) 1.52558 0.310835i 0.407729 0.0830742i
\(15\) 0 0
\(16\) −3.88228 0.963271i −0.970570 0.240818i
\(17\) −1.29175 −0.313294 −0.156647 0.987655i \(-0.550069\pi\)
−0.156647 + 0.987655i \(0.550069\pi\)
\(18\) 0 0
\(19\) 2.78362i 0.638607i −0.947652 0.319304i \(-0.896551\pi\)
0.947652 0.319304i \(-0.103449\pi\)
\(20\) 4.44354 0.504891i 0.993607 0.112897i
\(21\) 0 0
\(22\) 7.87450 1.60442i 1.67885 0.342063i
\(23\) −1.82546 + 1.05393i −0.380635 + 0.219760i −0.678095 0.734975i \(-0.737194\pi\)
0.297459 + 0.954735i \(0.403861\pi\)
\(24\) 0 0
\(25\) −4.45901 + 2.26214i −0.891801 + 0.452427i
\(26\) 3.21441 + 1.07451i 0.630398 + 0.210729i
\(27\) 0 0
\(28\) −1.75921 1.32409i −0.332459 0.250230i
\(29\) 5.51723 + 3.18537i 1.02452 + 0.591509i 0.915411 0.402521i \(-0.131866\pi\)
0.109112 + 0.994029i \(0.465199\pi\)
\(30\) 0 0
\(31\) −2.78385 + 1.60725i −0.499994 + 0.288671i −0.728711 0.684821i \(-0.759880\pi\)
0.228717 + 0.973493i \(0.426547\pi\)
\(32\) 2.61918 + 5.01397i 0.463010 + 0.886353i
\(33\) 0 0
\(34\) 1.21087 + 1.36785i 0.207662 + 0.234584i
\(35\) 2.35973 + 0.701235i 0.398867 + 0.118530i
\(36\) 0 0
\(37\) 6.51687i 1.07137i 0.844419 + 0.535683i \(0.179946\pi\)
−0.844419 + 0.535683i \(0.820054\pi\)
\(38\) −2.94763 + 2.60933i −0.478168 + 0.423290i
\(39\) 0 0
\(40\) −4.69996 4.23206i −0.743129 0.669148i
\(41\) −6.35642 + 3.66988i −0.992706 + 0.573139i −0.906082 0.423102i \(-0.860941\pi\)
−0.0866240 + 0.996241i \(0.527608\pi\)
\(42\) 0 0
\(43\) −2.25473 + 3.90530i −0.343843 + 0.595553i −0.985143 0.171737i \(-0.945062\pi\)
0.641300 + 0.767290i \(0.278395\pi\)
\(44\) −9.08040 6.83448i −1.36892 1.03034i
\(45\) 0 0
\(46\) 2.82719 + 0.945071i 0.416847 + 0.139343i
\(47\) 8.09628 + 4.67439i 1.18096 + 0.681830i 0.956237 0.292592i \(-0.0945179\pi\)
0.224726 + 0.974422i \(0.427851\pi\)
\(48\) 0 0
\(49\) 2.89400 + 5.01255i 0.413428 + 0.716078i
\(50\) 6.57523 + 2.60122i 0.929878 + 0.367868i
\(51\) 0 0
\(52\) −1.87533 4.41103i −0.260062 0.611700i
\(53\) −11.5954 −1.59275 −0.796377 0.604800i \(-0.793253\pi\)
−0.796377 + 0.604800i \(0.793253\pi\)
\(54\) 0 0
\(55\) 12.1801 + 3.61952i 1.64236 + 0.488056i
\(56\) 0.246959 + 3.10404i 0.0330013 + 0.414795i
\(57\) 0 0
\(58\) −1.79874 8.82821i −0.236186 1.15920i
\(59\) −3.66237 6.34341i −0.476800 0.825842i 0.522846 0.852427i \(-0.324870\pi\)
−0.999647 + 0.0265849i \(0.991537\pi\)
\(60\) 0 0
\(61\) 2.48990 4.31263i 0.318799 0.552175i −0.661439 0.749999i \(-0.730054\pi\)
0.980238 + 0.197823i \(0.0633873\pi\)
\(62\) 4.31149 + 1.44124i 0.547560 + 0.183038i
\(63\) 0 0
\(64\) 2.85419 7.47353i 0.356774 0.934191i
\(65\) 3.68540 + 3.89043i 0.457117 + 0.482548i
\(66\) 0 0
\(67\) −1.85016 3.20457i −0.226033 0.391500i 0.730596 0.682810i \(-0.239242\pi\)
−0.956629 + 0.291310i \(0.905909\pi\)
\(68\) 0.313389 2.56441i 0.0380041 0.310981i
\(69\) 0 0
\(70\) −1.46943 3.15608i −0.175631 0.377224i
\(71\) 12.6950 1.50662 0.753311 0.657664i \(-0.228455\pi\)
0.753311 + 0.657664i \(0.228455\pi\)
\(72\) 0 0
\(73\) 9.86891i 1.15507i 0.816366 + 0.577534i \(0.195985\pi\)
−0.816366 + 0.577534i \(0.804015\pi\)
\(74\) 6.90082 6.10883i 0.802204 0.710137i
\(75\) 0 0
\(76\) 5.52614 + 0.675333i 0.633891 + 0.0774660i
\(77\) −3.12798 5.41781i −0.356466 0.617417i
\(78\) 0 0
\(79\) 0.975531 + 0.563223i 0.109756 + 0.0633676i 0.553873 0.832601i \(-0.313149\pi\)
−0.444117 + 0.895969i \(0.646483\pi\)
\(80\) −0.0757197 + 8.94395i −0.00846572 + 0.999964i
\(81\) 0 0
\(82\) 9.84453 + 3.29082i 1.08715 + 0.363410i
\(83\) −9.98138 5.76275i −1.09560 0.632544i −0.160537 0.987030i \(-0.551323\pi\)
−0.935062 + 0.354485i \(0.884656\pi\)
\(84\) 0 0
\(85\) 0.671827 + 2.80921i 0.0728699 + 0.304702i
\(86\) 6.24894 1.27321i 0.673841 0.137294i
\(87\) 0 0
\(88\) 1.27471 + 16.0219i 0.135885 + 1.70794i
\(89\) 9.16815i 0.971822i −0.874008 0.485911i \(-0.838488\pi\)
0.874008 0.485911i \(-0.161512\pi\)
\(90\) 0 0
\(91\) 2.63841i 0.276580i
\(92\) −1.64942 3.87966i −0.171964 0.404482i
\(93\) 0 0
\(94\) −2.63956 12.9550i −0.272250 1.33621i
\(95\) −6.05366 + 1.44774i −0.621093 + 0.148535i
\(96\) 0 0
\(97\) −11.1257 6.42344i −1.12965 0.652202i −0.185801 0.982587i \(-0.559488\pi\)
−0.943846 + 0.330386i \(0.892821\pi\)
\(98\) 2.59507 7.76320i 0.262142 0.784201i
\(99\) 0 0
\(100\) −3.40906 9.40097i −0.340906 0.940097i
\(101\) −14.4999 8.37150i −1.44279 0.832995i −0.444755 0.895652i \(-0.646709\pi\)
−0.998035 + 0.0626572i \(0.980043\pi\)
\(102\) 0 0
\(103\) 0.679292 + 1.17657i 0.0669327 + 0.115931i 0.897550 0.440913i \(-0.145345\pi\)
−0.830617 + 0.556844i \(0.812012\pi\)
\(104\) −2.91300 + 6.12066i −0.285643 + 0.600181i
\(105\) 0 0
\(106\) 10.8694 + 12.2786i 1.05573 + 1.19260i
\(107\) 2.97211i 0.287324i 0.989627 + 0.143662i \(0.0458879\pi\)
−0.989627 + 0.143662i \(0.954112\pi\)
\(108\) 0 0
\(109\) 5.12076 0.490480 0.245240 0.969462i \(-0.421133\pi\)
0.245240 + 0.969462i \(0.421133\pi\)
\(110\) −7.58466 16.2906i −0.723169 1.55324i
\(111\) 0 0
\(112\) 3.05543 3.17120i 0.288711 0.299650i
\(113\) 4.18521 + 7.24900i 0.393711 + 0.681928i 0.992936 0.118653i \(-0.0378576\pi\)
−0.599224 + 0.800581i \(0.704524\pi\)
\(114\) 0 0
\(115\) 3.24144 + 3.42177i 0.302266 + 0.319082i
\(116\) −7.66223 + 10.1802i −0.711420 + 0.945205i
\(117\) 0 0
\(118\) −3.28409 + 9.82438i −0.302325 + 0.904408i
\(119\) 0.711050 1.23157i 0.0651818 0.112898i
\(120\) 0 0
\(121\) −10.6455 18.4385i −0.967770 1.67623i
\(122\) −6.90071 + 1.40601i −0.624761 + 0.127294i
\(123\) 0 0
\(124\) −2.51538 5.91651i −0.225888 0.531318i
\(125\) 7.23866 + 8.52067i 0.647445 + 0.762112i
\(126\) 0 0
\(127\) −5.14729 −0.456748 −0.228374 0.973573i \(-0.573341\pi\)
−0.228374 + 0.973573i \(0.573341\pi\)
\(128\) −10.5893 + 3.98324i −0.935973 + 0.352072i
\(129\) 0 0
\(130\) 0.664991 7.54937i 0.0583236 0.662123i
\(131\) −7.10028 12.2980i −0.620354 1.07449i −0.989420 0.145082i \(-0.953656\pi\)
0.369065 0.929403i \(-0.379678\pi\)
\(132\) 0 0
\(133\) 2.65396 + 1.53226i 0.230127 + 0.132864i
\(134\) −1.65906 + 4.96309i −0.143321 + 0.428746i
\(135\) 0 0
\(136\) −3.00927 + 2.07199i −0.258042 + 0.177672i
\(137\) 3.47139 6.01263i 0.296581 0.513693i −0.678770 0.734351i \(-0.737487\pi\)
0.975351 + 0.220657i \(0.0708202\pi\)
\(138\) 0 0
\(139\) 10.3321 5.96523i 0.876356 0.505964i 0.00690070 0.999976i \(-0.497803\pi\)
0.869455 + 0.494012i \(0.164470\pi\)
\(140\) −1.96461 + 4.51448i −0.166039 + 0.381543i
\(141\) 0 0
\(142\) −11.9002 13.4430i −0.998640 1.12811i
\(143\) 13.6185i 1.13884i
\(144\) 0 0
\(145\) 4.05789 13.6552i 0.336990 1.13401i
\(146\) 10.4504 9.25100i 0.864878 0.765618i
\(147\) 0 0
\(148\) −12.9375 1.58105i −1.06345 0.129962i
\(149\) −4.98019 + 2.87531i −0.407993 + 0.235555i −0.689927 0.723879i \(-0.742357\pi\)
0.281934 + 0.959434i \(0.409024\pi\)
\(150\) 0 0
\(151\) −1.85084 1.06858i −0.150619 0.0869599i 0.422796 0.906225i \(-0.361049\pi\)
−0.573415 + 0.819265i \(0.694382\pi\)
\(152\) −4.46501 6.48477i −0.362160 0.525984i
\(153\) 0 0
\(154\) −2.80489 + 8.39086i −0.226024 + 0.676155i
\(155\) 4.94322 + 5.21823i 0.397049 + 0.419138i
\(156\) 0 0
\(157\) 8.70855 5.02788i 0.695018 0.401269i −0.110471 0.993879i \(-0.535236\pi\)
0.805489 + 0.592611i \(0.201903\pi\)
\(158\) −0.318044 1.56097i −0.0253022 0.124184i
\(159\) 0 0
\(160\) 9.54188 8.30377i 0.754352 0.656470i
\(161\) 2.32057i 0.182887i
\(162\) 0 0
\(163\) −18.2146 −1.42668 −0.713339 0.700819i \(-0.752818\pi\)
−0.713339 + 0.700819i \(0.752818\pi\)
\(164\) −5.74343 13.5093i −0.448487 1.05490i
\(165\) 0 0
\(166\) 3.25415 + 15.9714i 0.252571 + 1.23962i
\(167\) 6.44716 3.72227i 0.498896 0.288038i −0.229362 0.973341i \(-0.573664\pi\)
0.728258 + 0.685304i \(0.240330\pi\)
\(168\) 0 0
\(169\) −3.62824 + 6.28430i −0.279096 + 0.483408i
\(170\) 2.34496 3.34473i 0.179850 0.256529i
\(171\) 0 0
\(172\) −7.20591 5.42361i −0.549445 0.413547i
\(173\) −4.33441 + 7.50742i −0.329539 + 0.570778i −0.982420 0.186682i \(-0.940227\pi\)
0.652881 + 0.757460i \(0.273560\pi\)
\(174\) 0 0
\(175\) 0.297727 5.49651i 0.0225061 0.415497i
\(176\) 15.7710 16.3686i 1.18878 1.23383i
\(177\) 0 0
\(178\) −9.70831 + 8.59411i −0.727668 + 0.644156i
\(179\) −1.10988 −0.0829560 −0.0414780 0.999139i \(-0.513207\pi\)
−0.0414780 + 0.999139i \(0.513207\pi\)
\(180\) 0 0
\(181\) −12.6629 −0.941229 −0.470615 0.882339i \(-0.655968\pi\)
−0.470615 + 0.882339i \(0.655968\pi\)
\(182\) −2.79385 + 2.47321i −0.207094 + 0.183327i
\(183\) 0 0
\(184\) −2.56209 + 5.38335i −0.188880 + 0.396866i
\(185\) 14.1725 3.38938i 1.04198 0.249192i
\(186\) 0 0
\(187\) 3.67018 6.35694i 0.268390 0.464865i
\(188\) −11.2440 + 14.9389i −0.820051 + 1.08953i
\(189\) 0 0
\(190\) 7.20767 + 5.05323i 0.522899 + 0.366600i
\(191\) −11.3827 + 19.7154i −0.823625 + 1.42656i 0.0793411 + 0.996848i \(0.474718\pi\)
−0.902966 + 0.429712i \(0.858615\pi\)
\(192\) 0 0
\(193\) 10.0687 5.81319i 0.724764 0.418443i −0.0917396 0.995783i \(-0.529243\pi\)
0.816504 + 0.577340i \(0.195909\pi\)
\(194\) 3.62723 + 17.8025i 0.260420 + 1.27814i
\(195\) 0 0
\(196\) −10.6532 + 4.52916i −0.760941 + 0.323511i
\(197\) 12.2003 0.869238 0.434619 0.900614i \(-0.356883\pi\)
0.434619 + 0.900614i \(0.356883\pi\)
\(198\) 0 0
\(199\) 7.07921i 0.501832i 0.968009 + 0.250916i \(0.0807318\pi\)
−0.968009 + 0.250916i \(0.919268\pi\)
\(200\) −6.75923 + 12.4223i −0.477950 + 0.878387i
\(201\) 0 0
\(202\) 4.72727 + 23.2015i 0.332609 + 1.63245i
\(203\) −6.07399 + 3.50682i −0.426310 + 0.246130i
\(204\) 0 0
\(205\) 11.2870 + 11.9149i 0.788316 + 0.832172i
\(206\) 0.609128 1.82222i 0.0424400 0.126960i
\(207\) 0 0
\(208\) 9.21188 2.65281i 0.638729 0.183939i
\(209\) 13.6988 + 7.90899i 0.947564 + 0.547076i
\(210\) 0 0
\(211\) −5.61368 + 3.24106i −0.386462 + 0.223124i −0.680626 0.732631i \(-0.738292\pi\)
0.294164 + 0.955755i \(0.404959\pi\)
\(212\) 2.81316 23.0196i 0.193209 1.58099i
\(213\) 0 0
\(214\) 3.14721 2.78601i 0.215139 0.190448i
\(215\) 9.66569 + 2.87233i 0.659195 + 0.195891i
\(216\) 0 0
\(217\) 3.53890i 0.240236i
\(218\) −4.80014 5.42246i −0.325106 0.367255i
\(219\) 0 0
\(220\) −10.1406 + 23.3021i −0.683677 + 1.57103i
\(221\) 2.68100 1.54787i 0.180343 0.104121i
\(222\) 0 0
\(223\) 7.84799 13.5931i 0.525540 0.910263i −0.474017 0.880516i \(-0.657197\pi\)
0.999557 0.0297470i \(-0.00947015\pi\)
\(224\) −6.22216 0.262800i −0.415735 0.0175590i
\(225\) 0 0
\(226\) 3.75292 11.2269i 0.249640 0.746803i
\(227\) 0.169745 + 0.0980022i 0.0112664 + 0.00650463i 0.505623 0.862755i \(-0.331263\pi\)
−0.494356 + 0.869259i \(0.664596\pi\)
\(228\) 0 0
\(229\) 0.825139 + 1.42918i 0.0545267 + 0.0944431i 0.892000 0.452035i \(-0.149302\pi\)
−0.837474 + 0.546478i \(0.815968\pi\)
\(230\) 0.584884 6.63994i 0.0385661 0.437825i
\(231\) 0 0
\(232\) 17.9624 1.42910i 1.17929 0.0938248i
\(233\) 20.2270 1.32512 0.662559 0.749010i \(-0.269470\pi\)
0.662559 + 0.749010i \(0.269470\pi\)
\(234\) 0 0
\(235\) 5.95477 20.0384i 0.388447 1.30716i
\(236\) 13.4817 5.73168i 0.877581 0.373101i
\(237\) 0 0
\(238\) −1.97066 + 0.401520i −0.127739 + 0.0260267i
\(239\) 10.1646 + 17.6056i 0.657494 + 1.13881i 0.981262 + 0.192676i \(0.0617168\pi\)
−0.323769 + 0.946136i \(0.604950\pi\)
\(240\) 0 0
\(241\) 8.62268 14.9349i 0.555436 0.962043i −0.442434 0.896801i \(-0.645885\pi\)
0.997869 0.0652417i \(-0.0207818\pi\)
\(242\) −9.54590 + 28.5567i −0.613634 + 1.83569i
\(243\) 0 0
\(244\) 7.95749 + 5.98930i 0.509426 + 0.383426i
\(245\) 9.39585 8.90068i 0.600279 0.568644i
\(246\) 0 0
\(247\) 3.33556 + 5.77737i 0.212237 + 0.367605i
\(248\) −3.90720 + 8.20965i −0.248108 + 0.521313i
\(249\) 0 0
\(250\) 2.23725 15.6523i 0.141496 0.989939i
\(251\) −9.92020 −0.626157 −0.313079 0.949727i \(-0.601360\pi\)
−0.313079 + 0.949727i \(0.601360\pi\)
\(252\) 0 0
\(253\) 11.9780i 0.753048i
\(254\) 4.82501 + 5.45055i 0.302748 + 0.341998i
\(255\) 0 0
\(256\) 14.1442 + 7.47938i 0.884014 + 0.467461i
\(257\) 8.67485 + 15.0253i 0.541122 + 0.937252i 0.998840 + 0.0481539i \(0.0153338\pi\)
−0.457717 + 0.889098i \(0.651333\pi\)
\(258\) 0 0
\(259\) −6.21330 3.58725i −0.386076 0.222901i
\(260\) −8.61750 + 6.37251i −0.534435 + 0.395206i
\(261\) 0 0
\(262\) −6.36689 + 19.0466i −0.393348 + 1.17671i
\(263\) 8.32487 + 4.80637i 0.513334 + 0.296373i 0.734203 0.678930i \(-0.237556\pi\)
−0.220869 + 0.975303i \(0.570889\pi\)
\(264\) 0 0
\(265\) 6.03070 + 25.2171i 0.370463 + 1.54907i
\(266\) −0.865248 4.24665i −0.0530518 0.260379i
\(267\) 0 0
\(268\) 6.81068 2.89553i 0.416028 0.176873i
\(269\) 1.34482i 0.0819953i 0.999159 + 0.0409977i \(0.0130536\pi\)
−0.999159 + 0.0409977i \(0.986946\pi\)
\(270\) 0 0
\(271\) 21.7288i 1.31993i 0.751297 + 0.659964i \(0.229429\pi\)
−0.751297 + 0.659964i \(0.770571\pi\)
\(272\) 5.01492 + 1.24430i 0.304074 + 0.0754468i
\(273\) 0 0
\(274\) −9.62091 + 1.96025i −0.581221 + 0.118423i
\(275\) 1.53676 28.3710i 0.0926701 1.71083i
\(276\) 0 0
\(277\) 12.0501 + 6.95713i 0.724021 + 0.418014i 0.816231 0.577726i \(-0.196060\pi\)
−0.0922100 + 0.995740i \(0.529393\pi\)
\(278\) −16.0018 5.34908i −0.959727 0.320817i
\(279\) 0 0
\(280\) 6.62205 2.15146i 0.395743 0.128575i
\(281\) −10.0948 5.82824i −0.602206 0.347684i 0.167703 0.985838i \(-0.446365\pi\)
−0.769909 + 0.638154i \(0.779698\pi\)
\(282\) 0 0
\(283\) 6.21367 + 10.7624i 0.369365 + 0.639758i 0.989466 0.144763i \(-0.0462420\pi\)
−0.620102 + 0.784521i \(0.712909\pi\)
\(284\) −3.07993 + 25.2026i −0.182760 + 1.49550i
\(285\) 0 0
\(286\) −14.4209 + 12.7658i −0.852723 + 0.754858i
\(287\) 8.08044i 0.476973i
\(288\) 0 0
\(289\) −15.3314 −0.901847
\(290\) −18.2636 + 8.50328i −1.07247 + 0.499330i
\(291\) 0 0
\(292\) −19.5921 2.39429i −1.14654 0.140115i
\(293\) −4.77472 8.27006i −0.278942 0.483142i 0.692180 0.721725i \(-0.256650\pi\)
−0.971122 + 0.238583i \(0.923317\pi\)
\(294\) 0 0
\(295\) −11.8905 + 11.2639i −0.692292 + 0.655808i
\(296\) 10.4532 + 15.1818i 0.607582 + 0.882423i
\(297\) 0 0
\(298\) 7.71308 + 2.57832i 0.446807 + 0.149358i
\(299\) 2.52581 4.37484i 0.146072 0.253003i
\(300\) 0 0
\(301\) −2.48226 4.29940i −0.143075 0.247813i
\(302\) 0.603413 + 2.96156i 0.0347225 + 0.170418i
\(303\) 0 0
\(304\) −2.68138 + 10.8068i −0.153788 + 0.619813i
\(305\) −10.6738 3.17192i −0.611182 0.181623i
\(306\) 0 0
\(307\) 13.4685 0.768689 0.384345 0.923190i \(-0.374427\pi\)
0.384345 + 0.923190i \(0.374427\pi\)
\(308\) 11.5145 4.89534i 0.656099 0.278938i
\(309\) 0 0
\(310\) 0.891953 10.1260i 0.0506595 0.575116i
\(311\) 5.13110 + 8.88732i 0.290958 + 0.503954i 0.974037 0.226391i \(-0.0726927\pi\)
−0.683079 + 0.730345i \(0.739359\pi\)
\(312\) 0 0
\(313\) 1.39067 + 0.802903i 0.0786052 + 0.0453827i 0.538787 0.842442i \(-0.318883\pi\)
−0.460182 + 0.887824i \(0.652216\pi\)
\(314\) −13.4874 4.50855i −0.761138 0.254432i
\(315\) 0 0
\(316\) −1.35480 + 1.80001i −0.0762135 + 0.101259i
\(317\) −2.23127 + 3.86467i −0.125320 + 0.217061i −0.921858 0.387528i \(-0.873329\pi\)
0.796538 + 0.604589i \(0.206663\pi\)
\(318\) 0 0
\(319\) −31.3517 + 18.1009i −1.75536 + 1.01346i
\(320\) −17.7374 2.32021i −0.991553 0.129704i
\(321\) 0 0
\(322\) −2.45730 + 2.17528i −0.136940 + 0.121223i
\(323\) 3.59573i 0.200072i
\(324\) 0 0
\(325\) 6.54392 10.0382i 0.362992 0.556818i
\(326\) 17.0741 + 19.2878i 0.945649 + 1.06825i
\(327\) 0 0
\(328\) −8.92141 + 18.7453i −0.492602 + 1.03503i
\(329\) −8.91330 + 5.14610i −0.491406 + 0.283713i
\(330\) 0 0
\(331\) −10.2107 5.89512i −0.561228 0.324025i 0.192410 0.981315i \(-0.438370\pi\)
−0.753638 + 0.657289i \(0.771703\pi\)
\(332\) 13.8620 18.4172i 0.760775 1.01078i
\(333\) 0 0
\(334\) −9.98506 3.33780i −0.546358 0.182636i
\(335\) −6.00686 + 5.69029i −0.328190 + 0.310894i
\(336\) 0 0
\(337\) 9.14715 5.28111i 0.498277 0.287680i −0.229725 0.973256i \(-0.573783\pi\)
0.728002 + 0.685575i \(0.240449\pi\)
\(338\) 10.0556 2.04882i 0.546954 0.111441i
\(339\) 0 0
\(340\) −5.73993 + 0.652191i −0.311291 + 0.0353700i
\(341\) 18.2665i 0.989186i
\(342\) 0 0
\(343\) −14.0785 −0.760166
\(344\) 1.01157 + 12.7145i 0.0545401 + 0.685519i
\(345\) 0 0
\(346\) 12.0127 2.44758i 0.645809 0.131583i
\(347\) −20.1864 + 11.6546i −1.08366 + 0.625652i −0.931882 0.362763i \(-0.881834\pi\)
−0.151779 + 0.988414i \(0.548500\pi\)
\(348\) 0 0
\(349\) 2.84689 4.93095i 0.152390 0.263948i −0.779715 0.626134i \(-0.784636\pi\)
0.932106 + 0.362186i \(0.117970\pi\)
\(350\) −6.09943 + 4.83709i −0.326028 + 0.258553i
\(351\) 0 0
\(352\) −32.1165 1.35648i −1.71182 0.0723004i
\(353\) 0.761369 1.31873i 0.0405236 0.0701889i −0.845052 0.534684i \(-0.820431\pi\)
0.885576 + 0.464495i \(0.153764\pi\)
\(354\) 0 0
\(355\) −6.60259 27.6084i −0.350429 1.46530i
\(356\) 18.2009 + 2.22428i 0.964645 + 0.117887i
\(357\) 0 0
\(358\) 1.04038 + 1.17527i 0.0549860 + 0.0621148i
\(359\) 9.46115 0.499341 0.249670 0.968331i \(-0.419678\pi\)
0.249670 + 0.968331i \(0.419678\pi\)
\(360\) 0 0
\(361\) 11.2514 0.592181
\(362\) 11.8701 + 13.4090i 0.623878 + 0.704762i
\(363\) 0 0
\(364\) 5.23785 + 0.640102i 0.274538 + 0.0335505i
\(365\) 21.4623 5.13275i 1.12339 0.268660i
\(366\) 0 0
\(367\) −4.06621 + 7.04288i −0.212254 + 0.367635i −0.952420 0.304790i \(-0.901414\pi\)
0.740165 + 0.672425i \(0.234747\pi\)
\(368\) 8.10218 2.33324i 0.422356 0.121629i
\(369\) 0 0
\(370\) −16.8742 11.8303i −0.877248 0.615031i
\(371\) 6.38278 11.0553i 0.331377 0.573963i
\(372\) 0 0
\(373\) −10.0593 + 5.80775i −0.520851 + 0.300714i −0.737283 0.675584i \(-0.763892\pi\)
0.216432 + 0.976298i \(0.430558\pi\)
\(374\) −10.1718 + 2.07250i −0.525974 + 0.107166i
\(375\) 0 0
\(376\) 26.3590 2.09713i 1.35936 0.108151i
\(377\) −15.2679 −0.786336
\(378\) 0 0
\(379\) 0.194316i 0.00998136i 0.999988 + 0.00499068i \(0.00158859\pi\)
−0.999988 + 0.00499068i \(0.998411\pi\)
\(380\) −1.40543 12.3692i −0.0720969 0.634524i
\(381\) 0 0
\(382\) 31.5470 6.42766i 1.61409 0.328868i
\(383\) 16.0220 9.25031i 0.818686 0.472669i −0.0312769 0.999511i \(-0.509957\pi\)
0.849963 + 0.526842i \(0.176624\pi\)
\(384\) 0 0
\(385\) −10.1555 + 9.62031i −0.517573 + 0.490296i
\(386\) −15.5940 5.21275i −0.793714 0.265322i
\(387\) 0 0
\(388\) 15.4512 20.5288i 0.784417 1.04219i
\(389\) 20.3869 + 11.7704i 1.03366 + 0.596783i 0.918031 0.396509i \(-0.129779\pi\)
0.115628 + 0.993293i \(0.463112\pi\)
\(390\) 0 0
\(391\) 2.35803 1.36141i 0.119251 0.0688495i
\(392\) 14.7821 + 7.03525i 0.746611 + 0.355334i
\(393\) 0 0
\(394\) −11.4364 12.9191i −0.576160 0.650857i
\(395\) 0.717499 2.41446i 0.0361013 0.121485i
\(396\) 0 0
\(397\) 23.4091i 1.17487i −0.809272 0.587435i \(-0.800138\pi\)
0.809272 0.587435i \(-0.199862\pi\)
\(398\) 7.49629 6.63596i 0.375755 0.332631i
\(399\) 0 0
\(400\) 19.4902 4.48701i 0.974508 0.224351i
\(401\) −25.9256 + 14.9681i −1.29466 + 0.747474i −0.979477 0.201557i \(-0.935400\pi\)
−0.315185 + 0.949030i \(0.602067\pi\)
\(402\) 0 0
\(403\) 3.85189 6.67166i 0.191876 0.332339i
\(404\) 20.1372 26.7546i 1.00186 1.33109i
\(405\) 0 0
\(406\) 9.40711 + 3.14460i 0.466867 + 0.156064i
\(407\) −32.0708 18.5161i −1.58969 0.917809i
\(408\) 0 0
\(409\) 1.04012 + 1.80153i 0.0514304 + 0.0890800i 0.890594 0.454798i \(-0.150289\pi\)
−0.839164 + 0.543878i \(0.816955\pi\)
\(410\) 2.03662 23.1208i 0.100581 1.14186i
\(411\) 0 0
\(412\) −2.50056 + 1.06311i −0.123194 + 0.0523754i
\(413\) 8.06390 0.396799
\(414\) 0 0
\(415\) −7.34126 + 24.7041i −0.360368 + 1.21268i
\(416\) −11.4442 7.26791i −0.561099 0.356338i
\(417\) 0 0
\(418\) −4.46610 21.9196i −0.218444 1.07212i
\(419\) −4.89021 8.47010i −0.238903 0.413791i 0.721497 0.692417i \(-0.243454\pi\)
−0.960400 + 0.278626i \(0.910121\pi\)
\(420\) 0 0
\(421\) 1.05097 1.82034i 0.0512212 0.0887177i −0.839278 0.543703i \(-0.817022\pi\)
0.890499 + 0.454985i \(0.150355\pi\)
\(422\) 8.69420 + 2.90629i 0.423227 + 0.141476i
\(423\) 0 0
\(424\) −27.0129 + 18.5994i −1.31186 + 0.903266i
\(425\) 5.75990 2.92210i 0.279396 0.141743i
\(426\) 0 0
\(427\) 2.74116 + 4.74783i 0.132654 + 0.229764i
\(428\) −5.90031 0.721061i −0.285202 0.0348538i
\(429\) 0 0
\(430\) −6.01894 12.9276i −0.290259 0.623426i
\(431\) 3.84204 0.185064 0.0925322 0.995710i \(-0.470504\pi\)
0.0925322 + 0.995710i \(0.470504\pi\)
\(432\) 0 0
\(433\) 6.66853i 0.320469i 0.987079 + 0.160235i \(0.0512251\pi\)
−0.987079 + 0.160235i \(0.948775\pi\)
\(434\) −3.74740 + 3.31732i −0.179881 + 0.159236i
\(435\) 0 0
\(436\) −1.24234 + 10.1659i −0.0594975 + 0.486858i
\(437\) 2.93375 + 5.08140i 0.140340 + 0.243077i
\(438\) 0 0
\(439\) 33.5536 + 19.3722i 1.60143 + 0.924585i 0.991202 + 0.132357i \(0.0422544\pi\)
0.610225 + 0.792228i \(0.291079\pi\)
\(440\) 34.1806 11.1051i 1.62950 0.529413i
\(441\) 0 0
\(442\) −4.15220 1.38799i −0.197500 0.0660202i
\(443\) 20.2821 + 11.7099i 0.963633 + 0.556354i 0.897289 0.441443i \(-0.145533\pi\)
0.0663436 + 0.997797i \(0.478867\pi\)
\(444\) 0 0
\(445\) −19.9384 + 4.76829i −0.945169 + 0.226039i
\(446\) −21.7506 + 4.43165i −1.02992 + 0.209845i
\(447\) 0 0
\(448\) 5.55429 + 6.83509i 0.262416 + 0.322928i
\(449\) 15.7865i 0.745011i −0.928030 0.372506i \(-0.878499\pi\)
0.928030 0.372506i \(-0.121501\pi\)
\(450\) 0 0
\(451\) 41.7083i 1.96397i
\(452\) −15.4063 + 6.54993i −0.724651 + 0.308083i
\(453\) 0 0
\(454\) −0.0553404 0.271612i −0.00259726 0.0127474i
\(455\) −5.73786 + 1.37222i −0.268995 + 0.0643305i
\(456\) 0 0
\(457\) 7.28867 + 4.20812i 0.340950 + 0.196847i 0.660692 0.750657i \(-0.270263\pi\)
−0.319742 + 0.947505i \(0.603596\pi\)
\(458\) 0.739911 2.21345i 0.0345738 0.103428i
\(459\) 0 0
\(460\) −7.57941 + 5.60485i −0.353392 + 0.261328i
\(461\) −21.4798 12.4014i −1.00042 0.577590i −0.0920445 0.995755i \(-0.529340\pi\)
−0.908371 + 0.418165i \(0.862674\pi\)
\(462\) 0 0
\(463\) 10.3598 + 17.9437i 0.481460 + 0.833913i 0.999774 0.0212774i \(-0.00677331\pi\)
−0.518314 + 0.855191i \(0.673440\pi\)
\(464\) −18.3511 17.6811i −0.851926 0.820824i
\(465\) 0 0
\(466\) −18.9606 21.4188i −0.878332 0.992205i
\(467\) 1.59588i 0.0738487i −0.999318 0.0369243i \(-0.988244\pi\)
0.999318 0.0369243i \(-0.0117561\pi\)
\(468\) 0 0
\(469\) 4.07373 0.188107
\(470\) −26.8010 + 12.4782i −1.23624 + 0.575575i
\(471\) 0 0
\(472\) −18.7069 8.90315i −0.861055 0.409801i
\(473\) −12.8125 22.1919i −0.589120 1.02039i
\(474\) 0 0
\(475\) 6.29693 + 12.4122i 0.288923 + 0.569511i
\(476\) 2.27245 + 1.71039i 0.104158 + 0.0783955i
\(477\) 0 0
\(478\) 9.11471 27.2668i 0.416897 1.24715i
\(479\) 2.98947 5.17791i 0.136592 0.236585i −0.789612 0.613606i \(-0.789718\pi\)
0.926205 + 0.377021i \(0.123052\pi\)
\(480\) 0 0
\(481\) −7.80904 13.5257i −0.356062 0.616717i
\(482\) −23.8976 + 4.86911i −1.08851 + 0.221782i
\(483\) 0 0
\(484\) 39.1874 16.6604i 1.78124 0.757289i
\(485\) −8.18292 + 27.5364i −0.371567 + 1.25036i
\(486\) 0 0
\(487\) 16.5971 0.752086 0.376043 0.926602i \(-0.377284\pi\)
0.376043 + 0.926602i \(0.377284\pi\)
\(488\) −1.11708 14.0406i −0.0505677 0.635589i
\(489\) 0 0
\(490\) −18.2326 1.60603i −0.823666 0.0725533i
\(491\) 6.66941 + 11.5518i 0.300986 + 0.521323i 0.976360 0.216153i \(-0.0693509\pi\)
−0.675373 + 0.737476i \(0.736018\pi\)
\(492\) 0 0
\(493\) −7.12685 4.11469i −0.320977 0.185316i
\(494\) 2.99103 8.94772i 0.134573 0.402577i
\(495\) 0 0
\(496\) 12.3559 3.55822i 0.554796 0.159769i
\(497\) −6.98806 + 12.1037i −0.313457 + 0.542924i
\(498\) 0 0
\(499\) 35.7135 20.6192i 1.59875 0.923041i 0.607026 0.794682i \(-0.292362\pi\)
0.991728 0.128359i \(-0.0409711\pi\)
\(500\) −18.6717 + 12.3032i −0.835022 + 0.550216i
\(501\) 0 0
\(502\) 9.29907 + 10.5047i 0.415038 + 0.468846i
\(503\) 24.1634i 1.07739i 0.842500 + 0.538696i \(0.181083\pi\)
−0.842500 + 0.538696i \(0.818917\pi\)
\(504\) 0 0
\(505\) −10.6646 + 35.8874i −0.474567 + 1.59697i
\(506\) −12.6837 + 11.2280i −0.563858 + 0.499145i
\(507\) 0 0
\(508\) 1.24878 10.2186i 0.0554057 0.453375i
\(509\) −10.2084 + 5.89380i −0.452478 + 0.261238i −0.708876 0.705333i \(-0.750797\pi\)
0.256398 + 0.966571i \(0.417464\pi\)
\(510\) 0 0
\(511\) −9.40921 5.43241i −0.416239 0.240316i
\(512\) −5.33857 21.9886i −0.235934 0.971769i
\(513\) 0 0
\(514\) 7.77883 23.2705i 0.343109 1.02642i
\(515\) 2.20544 2.08921i 0.0971833 0.0920616i
\(516\) 0 0
\(517\) −46.0072 + 26.5623i −2.02339 + 1.16821i
\(518\) 2.02567 + 9.94202i 0.0890029 + 0.436827i
\(519\) 0 0
\(520\) 14.8259 + 3.15171i 0.650159 + 0.138212i
\(521\) 32.5010i 1.42389i 0.702234 + 0.711947i \(0.252186\pi\)
−0.702234 + 0.711947i \(0.747814\pi\)
\(522\) 0 0
\(523\) −11.2435 −0.491645 −0.245822 0.969315i \(-0.579058\pi\)
−0.245822 + 0.969315i \(0.579058\pi\)
\(524\) 26.1370 11.1121i 1.14180 0.485433i
\(525\) 0 0
\(526\) −2.71409 13.3208i −0.118340 0.580813i
\(527\) 3.59602 2.07616i 0.156645 0.0904391i
\(528\) 0 0
\(529\) −9.27846 + 16.0708i −0.403411 + 0.698729i
\(530\) 21.0497 30.0242i 0.914339 1.30417i
\(531\) 0 0
\(532\) −3.68577 + 4.89698i −0.159799 + 0.212311i
\(533\) 8.79510 15.2336i 0.380958 0.659839i
\(534\) 0 0
\(535\) 6.46356 1.54577i 0.279444 0.0668295i
\(536\) −9.45037 4.49770i −0.408194 0.194271i
\(537\) 0 0
\(538\) 1.42406 1.26062i 0.0613954 0.0543492i
\(539\) −32.8903 −1.41669
\(540\) 0 0
\(541\) −8.40855 −0.361512 −0.180756 0.983528i \(-0.557854\pi\)
−0.180756 + 0.983528i \(0.557854\pi\)
\(542\) 23.0090 20.3683i 0.988319 0.874892i
\(543\) 0 0
\(544\) −3.38331 6.47677i −0.145058 0.277689i
\(545\) −2.66327 11.1363i −0.114082 0.477028i
\(546\) 0 0
\(547\) 2.12301 3.67716i 0.0907734 0.157224i −0.817063 0.576548i \(-0.804399\pi\)
0.907837 + 0.419324i \(0.137733\pi\)
\(548\) 11.0943 + 8.35023i 0.473923 + 0.356704i
\(549\) 0 0
\(550\) −31.4830 + 24.9673i −1.34244 + 1.06461i
\(551\) 8.86688 15.3579i 0.377742 0.654268i
\(552\) 0 0
\(553\) −1.07398 + 0.620060i −0.0456701 + 0.0263676i
\(554\) −3.92860 19.2816i −0.166910 0.819196i
\(555\) 0 0
\(556\) 9.33570 + 21.9588i 0.395922 + 0.931260i
\(557\) −21.0221 −0.890734 −0.445367 0.895348i \(-0.646927\pi\)
−0.445367 + 0.895348i \(0.646927\pi\)
\(558\) 0 0
\(559\) 10.8072i 0.457095i
\(560\) −8.48565 4.99545i −0.358584 0.211096i
\(561\) 0 0
\(562\) 3.29113 + 16.1529i 0.138828 + 0.681369i
\(563\) −18.9272 + 10.9277i −0.797688 + 0.460546i −0.842662 0.538443i \(-0.819013\pi\)
0.0449739 + 0.998988i \(0.485680\pi\)
\(564\) 0 0
\(565\) 13.5880 12.8719i 0.571651 0.541525i
\(566\) 5.57187 16.6683i 0.234203 0.700621i
\(567\) 0 0
\(568\) 29.5745 20.3632i 1.24092 0.854420i
\(569\) −12.7253 7.34697i −0.533473 0.308001i 0.208956 0.977925i \(-0.432993\pi\)
−0.742430 + 0.669924i \(0.766327\pi\)
\(570\) 0 0
\(571\) 15.5333 8.96816i 0.650049 0.375306i −0.138426 0.990373i \(-0.544204\pi\)
0.788475 + 0.615067i \(0.210871\pi\)
\(572\) 27.0359 + 3.30397i 1.13043 + 0.138146i
\(573\) 0 0
\(574\) −8.55651 + 7.57450i −0.357142 + 0.316154i
\(575\) 5.75562 8.82893i 0.240026 0.368192i
\(576\) 0 0
\(577\) 38.2696i 1.59318i 0.604517 + 0.796592i \(0.293366\pi\)
−0.604517 + 0.796592i \(0.706634\pi\)
\(578\) 14.3715 + 16.2347i 0.597774 + 0.675273i
\(579\) 0 0
\(580\) 26.1243 + 11.3687i 1.08475 + 0.472061i
\(581\) 10.9886 6.34429i 0.455885 0.263206i
\(582\) 0 0
\(583\) 32.9456 57.0634i 1.36447 2.36333i
\(584\) 15.8300 + 22.9907i 0.655050 + 0.951364i
\(585\) 0 0
\(586\) −4.28154 + 12.8083i −0.176869 + 0.529105i
\(587\) 7.27939 + 4.20276i 0.300453 + 0.173466i 0.642646 0.766163i \(-0.277837\pi\)
−0.342194 + 0.939629i \(0.611170\pi\)
\(588\) 0 0
\(589\) 4.47399 + 7.74918i 0.184348 + 0.319299i
\(590\) 23.0735 + 2.03245i 0.949922 + 0.0836746i
\(591\) 0 0
\(592\) 6.27751 25.3003i 0.258004 1.03984i
\(593\) −35.1831 −1.44480 −0.722398 0.691477i \(-0.756960\pi\)
−0.722398 + 0.691477i \(0.756960\pi\)
\(594\) 0 0
\(595\) −3.04817 0.905817i −0.124963 0.0371349i
\(596\) −4.49992 10.5844i −0.184324 0.433554i
\(597\) 0 0
\(598\) −7.00025 + 1.42629i −0.286262 + 0.0583254i
\(599\) 7.34116 + 12.7153i 0.299952 + 0.519532i 0.976125 0.217211i \(-0.0696961\pi\)
−0.676173 + 0.736743i \(0.736363\pi\)
\(600\) 0 0
\(601\) 13.6252 23.5995i 0.555783 0.962644i −0.442059 0.896986i \(-0.645752\pi\)
0.997842 0.0656584i \(-0.0209148\pi\)
\(602\) −2.22587 + 6.65871i −0.0907195 + 0.271389i
\(603\) 0 0
\(604\) 2.57041 3.41509i 0.104589 0.138958i
\(605\) −34.5623 + 32.7409i −1.40516 + 1.33111i
\(606\) 0 0
\(607\) −3.91627 6.78317i −0.158956 0.275320i 0.775536 0.631303i \(-0.217480\pi\)
−0.934493 + 0.355983i \(0.884146\pi\)
\(608\) 13.9570 7.29081i 0.566032 0.295681i
\(609\) 0 0
\(610\) 6.64672 + 14.2760i 0.269118 + 0.578019i
\(611\) −22.4049 −0.906406
\(612\) 0 0
\(613\) 1.17677i 0.0475293i −0.999718 0.0237646i \(-0.992435\pi\)
0.999718 0.0237646i \(-0.00756523\pi\)
\(614\) −12.6252 14.2620i −0.509513 0.575569i
\(615\) 0 0
\(616\) −15.9773 7.60405i −0.643744 0.306376i
\(617\) −20.4261 35.3790i −0.822322 1.42430i −0.903949 0.427641i \(-0.859345\pi\)
0.0816263 0.996663i \(-0.473989\pi\)
\(618\) 0 0
\(619\) −42.7230 24.6661i −1.71718 0.991416i −0.923965 0.382478i \(-0.875071\pi\)
−0.793218 0.608938i \(-0.791596\pi\)
\(620\) −11.5587 + 8.54745i −0.464207 + 0.343274i
\(621\) 0 0
\(622\) 4.60111 13.7643i 0.184488 0.551897i
\(623\) 8.74109 + 5.04667i 0.350204 + 0.202190i
\(624\) 0 0
\(625\) 14.7655 20.1738i 0.590619 0.806950i
\(626\) −0.453388 2.22523i −0.0181210 0.0889382i
\(627\) 0 0
\(628\) 7.86873 + 18.5083i 0.313997 + 0.738561i
\(629\) 8.41813i 0.335653i
\(630\) 0 0
\(631\) 27.6752i 1.10173i 0.834594 + 0.550866i \(0.185703\pi\)
−0.834594 + 0.550866i \(0.814297\pi\)
\(632\) 3.17604 0.252687i 0.126336 0.0100513i
\(633\) 0 0
\(634\) 6.18392 1.25996i 0.245595 0.0500396i
\(635\) 2.67707 + 11.1940i 0.106236 + 0.444222i
\(636\) 0 0
\(637\) −12.0129 6.93564i −0.475968 0.274800i
\(638\) 48.5561 + 16.2313i 1.92235 + 0.642602i
\(639\) 0 0
\(640\) 14.1699 + 20.9574i 0.560116 + 0.828414i
\(641\) 13.0424 + 7.53005i 0.515145 + 0.297419i 0.734946 0.678126i \(-0.237207\pi\)
−0.219801 + 0.975545i \(0.570541\pi\)
\(642\) 0 0
\(643\) 23.7098 + 41.0665i 0.935022 + 1.61951i 0.774595 + 0.632458i \(0.217954\pi\)
0.160427 + 0.987048i \(0.448713\pi\)
\(644\) 4.60688 + 0.562993i 0.181536 + 0.0221850i
\(645\) 0 0
\(646\) 3.80758 3.37060i 0.149807 0.132614i
\(647\) 19.7634i 0.776977i 0.921453 + 0.388489i \(0.127003\pi\)
−0.921453 + 0.388489i \(0.872997\pi\)
\(648\) 0 0
\(649\) 41.6229 1.63384
\(650\) −16.7638 + 2.48019i −0.657530 + 0.0972809i
\(651\) 0 0
\(652\) 4.41903 36.1602i 0.173063 1.41614i
\(653\) 17.4740 + 30.2658i 0.683809 + 1.18439i 0.973809 + 0.227366i \(0.0730112\pi\)
−0.290000 + 0.957027i \(0.593655\pi\)
\(654\) 0 0
\(655\) −23.0523 + 21.8374i −0.900727 + 0.853258i
\(656\) 28.2125 8.12455i 1.10151 0.317211i
\(657\) 0 0
\(658\) 13.8045 + 4.61456i 0.538155 + 0.179894i
\(659\) 17.4893 30.2924i 0.681288 1.18003i −0.293300 0.956021i \(-0.594753\pi\)
0.974588 0.224005i \(-0.0719133\pi\)
\(660\) 0 0
\(661\) 17.7487 + 30.7417i 0.690346 + 1.19571i 0.971725 + 0.236117i \(0.0758749\pi\)
−0.281379 + 0.959597i \(0.590792\pi\)
\(662\) 3.32889 + 16.3382i 0.129381 + 0.635004i
\(663\) 0 0
\(664\) −32.4964 + 2.58542i −1.26110 + 0.100334i
\(665\) 1.95197 6.56860i 0.0756943 0.254719i
\(666\) 0 0
\(667\) −13.4287 −0.519960
\(668\) 5.82542 + 13.7022i 0.225392 + 0.530152i
\(669\) 0 0
\(670\) 11.6563 + 1.02675i 0.450322 + 0.0396670i
\(671\) 14.1489 + 24.5066i 0.546211 + 0.946065i
\(672\) 0 0
\(673\) −41.4746 23.9454i −1.59873 0.923027i −0.991733 0.128322i \(-0.959041\pi\)
−0.606997 0.794704i \(-0.707626\pi\)
\(674\) −14.1667 4.73563i −0.545680 0.182409i
\(675\) 0 0
\(676\) −11.5955 8.72753i −0.445982 0.335674i
\(677\) −0.0431856 + 0.0747996i −0.00165976 + 0.00287478i −0.866854 0.498562i \(-0.833862\pi\)
0.865194 + 0.501437i \(0.167195\pi\)
\(678\) 0 0
\(679\) 12.2485 7.07165i 0.470053 0.271385i
\(680\) 6.07115 + 5.46675i 0.232818 + 0.209640i
\(681\) 0 0
\(682\) −19.3427 + 17.1228i −0.740670 + 0.655665i
\(683\) 24.0380i 0.919788i 0.887974 + 0.459894i \(0.152113\pi\)
−0.887974 + 0.459894i \(0.847887\pi\)
\(684\) 0 0
\(685\) −14.8814 4.42226i −0.568588 0.168966i
\(686\) 13.1970 + 14.9079i 0.503863 + 0.569187i
\(687\) 0 0
\(688\) 12.5153 12.9896i 0.477143 0.495222i
\(689\) 24.0661 13.8946i 0.916846 0.529342i
\(690\) 0 0
\(691\) 36.1685 + 20.8819i 1.37591 + 0.794384i 0.991665 0.128845i \(-0.0411271\pi\)
0.384249 + 0.923229i \(0.374460\pi\)
\(692\) −13.8524 10.4262i −0.526589 0.396344i
\(693\) 0 0
\(694\) 31.2637 + 10.4508i 1.18675 + 0.396707i
\(695\) −18.3465 19.3671i −0.695922 0.734638i
\(696\) 0 0
\(697\) 8.21087 4.74055i 0.311009 0.179561i
\(698\) −7.89010 + 1.60760i −0.298645 + 0.0608484i
\(699\) 0 0
\(700\) 10.8396 + 1.92456i 0.409699 + 0.0727416i
\(701\) 2.12514i 0.0802654i 0.999194 + 0.0401327i \(0.0127781\pi\)
−0.999194 + 0.0401327i \(0.987222\pi\)
\(702\) 0 0
\(703\) 18.1405 0.684182
\(704\) 28.6692 + 35.2803i 1.08051 + 1.32967i
\(705\) 0 0
\(706\) −2.11012 + 0.429934i −0.0794155 + 0.0161808i
\(707\) 15.9631 9.21629i 0.600354 0.346614i
\(708\) 0 0
\(709\) 2.08824 3.61694i 0.0784256 0.135837i −0.824145 0.566379i \(-0.808344\pi\)
0.902571 + 0.430541i \(0.141677\pi\)
\(710\) −23.0458 + 32.8714i −0.864895 + 1.23364i
\(711\) 0 0
\(712\) −14.7060 21.3582i −0.551129 0.800434i
\(713\) 3.38787 5.86797i 0.126877 0.219757i
\(714\) 0 0
\(715\) −29.6167 + 7.08288i −1.10760 + 0.264885i
\(716\) 0.269266 2.20336i 0.0100630 0.0823434i
\(717\) 0 0
\(718\) −8.86877 10.0186i −0.330979 0.373890i
\(719\) −24.0884 −0.898346 −0.449173 0.893445i \(-0.648281\pi\)
−0.449173 + 0.893445i \(0.648281\pi\)
\(720\) 0 0
\(721\) −1.49568 −0.0557022
\(722\) −10.5470 11.9143i −0.392517 0.443406i
\(723\) 0 0
\(724\) 3.07215 25.1389i 0.114176 0.934279i
\(725\) −31.8071 1.72288i −1.18129 0.0639863i
\(726\) 0 0
\(727\) −23.4466 + 40.6108i −0.869587 + 1.50617i −0.00716831 + 0.999974i \(0.502282\pi\)
−0.862419 + 0.506195i \(0.831052\pi\)
\(728\) −4.23208 6.14647i −0.156851 0.227803i
\(729\) 0 0
\(730\) −25.5537 17.9155i −0.945784 0.663081i
\(731\) 2.91253 5.04465i 0.107724 0.186583i
\(732\) 0 0
\(733\) 15.3758 8.87721i 0.567917 0.327887i −0.188400 0.982092i \(-0.560330\pi\)
0.756317 + 0.654205i \(0.226997\pi\)
\(734\) 11.2694 2.29613i 0.415962 0.0847517i
\(735\) 0 0
\(736\) −10.0656 6.39239i −0.371023 0.235626i
\(737\) 21.0271 0.774543
\(738\) 0 0
\(739\) 8.50437i 0.312838i 0.987691 + 0.156419i \(0.0499951\pi\)
−0.987691 + 0.156419i \(0.950005\pi\)
\(740\) 3.29031 + 28.9580i 0.120954 + 1.06452i
\(741\) 0 0
\(742\) −17.6898 + 3.60427i −0.649412 + 0.132317i
\(743\) 43.6052 25.1755i 1.59972 0.923598i 0.608179 0.793800i \(-0.291900\pi\)
0.991540 0.129798i \(-0.0414330\pi\)
\(744\) 0 0
\(745\) 8.84322 + 9.33519i 0.323991 + 0.342015i
\(746\) 15.5794 + 5.20786i 0.570402 + 0.190673i
\(747\) 0 0
\(748\) 11.7296 + 8.82840i 0.428875 + 0.322798i
\(749\) −2.83366 1.63601i −0.103540 0.0597787i
\(750\) 0 0
\(751\) −44.8169 + 25.8750i −1.63539 + 0.944193i −0.652999 + 0.757359i \(0.726489\pi\)
−0.982391 + 0.186834i \(0.940177\pi\)
\(752\) −26.9293 25.9462i −0.982011 0.946160i
\(753\) 0 0
\(754\) 14.3119 + 16.1674i 0.521210 + 0.588783i
\(755\) −1.36128 + 4.58085i −0.0495421 + 0.166714i
\(756\) 0 0
\(757\) 16.5374i 0.601064i −0.953772 0.300532i \(-0.902836\pi\)
0.953772 0.300532i \(-0.0971642\pi\)
\(758\) 0.205765 0.182150i 0.00747372 0.00661598i
\(759\) 0 0
\(760\) −11.7805 + 13.0829i −0.427323 + 0.474568i
\(761\) 30.1188 17.3891i 1.09180 0.630354i 0.157748 0.987479i \(-0.449577\pi\)
0.934056 + 0.357126i \(0.116243\pi\)
\(762\) 0 0
\(763\) −2.81876 + 4.88223i −0.102046 + 0.176749i
\(764\) −36.3782 27.3805i −1.31612 0.990591i
\(765\) 0 0
\(766\) −24.8141 8.29485i −0.896571 0.299705i
\(767\) 15.2024 + 8.77710i 0.548926 + 0.316923i
\(768\) 0 0
\(769\) −7.71708 13.3664i −0.278285 0.482003i 0.692674 0.721251i \(-0.256433\pi\)
−0.970959 + 0.239248i \(0.923099\pi\)
\(770\) 19.7068 + 1.73588i 0.710182 + 0.0625569i
\(771\) 0 0
\(772\) 9.09776 + 21.3991i 0.327435 + 0.770171i
\(773\) 29.3290 1.05489 0.527446 0.849589i \(-0.323150\pi\)
0.527446 + 0.849589i \(0.323150\pi\)
\(774\) 0 0
\(775\) 8.77736 13.4642i 0.315292 0.483648i
\(776\) −36.2220 + 2.88184i −1.30029 + 0.103452i
\(777\) 0 0
\(778\) −6.64658 32.6215i −0.238292 1.16954i
\(779\) 10.2156 + 17.6939i 0.366011 + 0.633949i
\(780\) 0 0
\(781\) −36.0698 + 62.4748i −1.29068 + 2.23552i
\(782\) −3.65201 1.22079i −0.130596 0.0436554i
\(783\) 0 0
\(784\) −6.40686 22.2478i −0.228817 0.794565i
\(785\) −15.4636 16.3239i −0.551920 0.582624i
\(786\) 0 0
\(787\) −26.3106 45.5713i −0.937872 1.62444i −0.769431 0.638730i \(-0.779460\pi\)
−0.168442 0.985712i \(-0.553873\pi\)
\(788\) −2.95992 + 24.2205i −0.105443 + 0.862819i
\(789\) 0 0
\(790\) −3.22928 + 1.50351i −0.114893 + 0.0534925i
\(791\) −9.21510 −0.327651
\(792\) 0 0
\(793\) 11.9344i 0.423803i
\(794\) −24.7883 + 21.9434i −0.879704 + 0.778742i
\(795\) 0 0
\(796\) −14.0539 1.71748i −0.498126 0.0608746i
\(797\) 1.24198 + 2.15117i 0.0439931 + 0.0761983i 0.887183 0.461417i \(-0.152659\pi\)
−0.843190 + 0.537615i \(0.819325\pi\)
\(798\) 0 0
\(799\) −10.4583 6.03812i −0.369989 0.213613i
\(800\) −23.0212 16.4324i −0.813923 0.580973i
\(801\) 0 0
\(802\) 40.1523 + 13.4221i 1.41783 + 0.473950i
\(803\) −48.5669 28.0401i −1.71389 0.989514i
\(804\) 0 0
\(805\) −5.04665 + 1.20691i −0.177871 + 0.0425381i
\(806\) −10.6754 + 2.17511i −0.376027 + 0.0766148i
\(807\) 0 0
\(808\) −47.2072 + 3.75582i −1.66074 + 0.132129i
\(809\) 25.6629i 0.902261i 0.892458 + 0.451131i \(0.148979\pi\)
−0.892458 + 0.451131i \(0.851021\pi\)
\(810\) 0 0
\(811\) 26.5970i 0.933948i 0.884271 + 0.466974i \(0.154656\pi\)
−0.884271 + 0.466974i \(0.845344\pi\)
\(812\) −5.48824 12.9091i −0.192599 0.453019i
\(813\) 0 0
\(814\) 10.4558 + 51.3171i 0.366475 + 1.79866i
\(815\) 9.47329 + 39.6121i 0.331835 + 1.38755i
\(816\) 0 0
\(817\) 10.8709 + 6.27631i 0.380324 + 0.219580i
\(818\) 0.932682 2.79013i 0.0326105 0.0975546i
\(819\) 0 0
\(820\) −26.3921 + 19.5166i −0.921654 + 0.681548i
\(821\) 26.3429 + 15.2091i 0.919373 + 0.530800i 0.883435 0.468554i \(-0.155225\pi\)
0.0359383 + 0.999354i \(0.488558\pi\)
\(822\) 0 0
\(823\) −4.23623 7.33737i −0.147666 0.255764i 0.782699 0.622401i \(-0.213843\pi\)
−0.930364 + 0.366636i \(0.880509\pi\)
\(824\) 3.46974 + 1.65135i 0.120874 + 0.0575274i
\(825\) 0 0
\(826\) −7.55900 8.53900i −0.263011 0.297110i
\(827\) 37.2624i 1.29574i −0.761750 0.647871i \(-0.775660\pi\)
0.761750 0.647871i \(-0.224340\pi\)
\(828\) 0 0
\(829\) −18.4167 −0.639639 −0.319820 0.947478i \(-0.603622\pi\)
−0.319820 + 0.947478i \(0.603622\pi\)
\(830\) 33.0412 15.3835i 1.14688 0.533970i
\(831\) 0 0
\(832\) 3.03155 + 18.9313i 0.105100 + 0.656325i
\(833\) −3.73830 6.47493i −0.129525 0.224343i
\(834\) 0 0
\(835\) −11.4481 12.0850i −0.396178 0.418218i
\(836\) −19.0246 + 25.2764i −0.657980 + 0.874203i
\(837\) 0 0
\(838\) −4.38510 + 13.1181i −0.151481 + 0.453157i
\(839\) 7.35228 12.7345i 0.253829 0.439645i −0.710748 0.703447i \(-0.751643\pi\)
0.964577 + 0.263802i \(0.0849766\pi\)
\(840\) 0 0
\(841\) 5.79320 + 10.0341i 0.199765 + 0.346004i
\(842\) −2.91275 + 0.593469i −0.100380 + 0.0204523i
\(843\) 0 0
\(844\) −5.07232 11.9308i −0.174596 0.410674i
\(845\) 15.5538 + 4.62207i 0.535066 + 0.159004i
\(846\) 0 0
\(847\) 23.4395 0.805390
\(848\) 45.0167 + 11.1695i 1.54588 + 0.383564i
\(849\) 0 0
\(850\) −8.49352 3.36011i −0.291325 0.115251i
\(851\) −6.86833 11.8963i −0.235443 0.407800i
\(852\) 0 0
\(853\) 11.2327 + 6.48519i 0.384600 + 0.222049i 0.679818 0.733381i \(-0.262059\pi\)
−0.295218 + 0.955430i \(0.595392\pi\)
\(854\) 2.45803 7.35322i 0.0841119 0.251622i
\(855\) 0 0
\(856\) 4.76734 + 6.92385i 0.162944 + 0.236652i
\(857\) 3.36521 5.82871i 0.114953 0.199105i −0.802808 0.596238i \(-0.796661\pi\)
0.917761 + 0.397133i \(0.129995\pi\)
\(858\) 0 0
\(859\) −33.3860 + 19.2754i −1.13912 + 0.657669i −0.946212 0.323549i \(-0.895124\pi\)
−0.192904 + 0.981218i \(0.561791\pi\)
\(860\) −8.04722 + 18.4918i −0.274408 + 0.630564i
\(861\) 0 0
\(862\) −3.60148 4.06840i −0.122667 0.138570i
\(863\) 13.4795i 0.458847i −0.973327 0.229424i \(-0.926316\pi\)
0.973327 0.229424i \(-0.0736841\pi\)
\(864\) 0 0
\(865\) 18.5810 + 5.52167i 0.631773 + 0.187742i
\(866\) 7.06142 6.25100i 0.239957 0.212418i
\(867\) 0 0
\(868\) 7.02552 + 0.858569i 0.238462 + 0.0291417i
\(869\) −5.54347 + 3.20052i −0.188049 + 0.108570i
\(870\) 0 0
\(871\) 7.67995 + 4.43402i 0.260225 + 0.150241i
\(872\) 11.9294 8.21384i 0.403980 0.278156i
\(873\) 0 0
\(874\) 2.63072 7.86984i 0.0889855 0.266201i
\(875\) −12.1083 + 2.21121i −0.409336 + 0.0747527i
\(876\) 0 0
\(877\) 13.5129 7.80171i 0.456300 0.263445i −0.254187 0.967155i \(-0.581808\pi\)
0.710487 + 0.703710i \(0.248475\pi\)
\(878\) −10.9392 53.6898i −0.369180 1.81194i
\(879\) 0 0
\(880\) −43.7998 25.7847i −1.47649 0.869202i
\(881\) 25.0226i 0.843032i 0.906821 + 0.421516i \(0.138502\pi\)
−0.906821 + 0.421516i \(0.861498\pi\)
\(882\) 0 0
\(883\) −13.8202 −0.465085 −0.232543 0.972586i \(-0.574705\pi\)
−0.232543 + 0.972586i \(0.574705\pi\)
\(884\) 2.42245 + 5.69793i 0.0814759 + 0.191642i
\(885\) 0 0
\(886\) −6.61241 32.4538i −0.222148 1.09031i
\(887\) −16.1656 + 9.33323i −0.542789 + 0.313379i −0.746208 0.665712i \(-0.768128\pi\)
0.203420 + 0.979092i \(0.434794\pi\)
\(888\) 0 0
\(889\) 2.83336 4.90753i 0.0950279 0.164593i
\(890\) 23.7392 + 16.6433i 0.795739 + 0.557886i
\(891\) 0 0
\(892\) 25.0815 + 18.8779i 0.839790 + 0.632079i
\(893\) 13.0117 22.5370i 0.435421 0.754172i
\(894\) 0 0
\(895\) 0.577239 + 2.41369i 0.0192950 + 0.0806809i
\(896\) 2.03127 12.2887i 0.0678600 0.410535i
\(897\) 0 0
\(898\) −16.7166 + 14.7981i −0.557840 + 0.493818i
\(899\) −20.4788 −0.683007
\(900\) 0 0
\(901\) 14.9783 0.499001
\(902\) −44.1656 + 39.0968i −1.47055 + 1.30178i
\(903\) 0 0
\(904\) 21.3775 + 10.1742i 0.711005 + 0.338388i
\(905\) 6.58591 + 27.5386i 0.218923 + 0.915415i
\(906\) 0 0
\(907\) −20.7283 + 35.9025i −0.688273 + 1.19212i 0.284123 + 0.958788i \(0.408297\pi\)
−0.972396 + 0.233336i \(0.925036\pi\)
\(908\) −0.235739 + 0.313206i −0.00782326 + 0.0103941i
\(909\) 0 0
\(910\) 6.83166 + 4.78961i 0.226467 + 0.158774i
\(911\) 2.80277 4.85454i 0.0928600 0.160838i −0.815853 0.578259i \(-0.803732\pi\)
0.908713 + 0.417420i \(0.137066\pi\)
\(912\) 0 0
\(913\) 56.7193 32.7469i 1.87714 1.08376i
\(914\) −2.37626 11.6627i −0.0785998 0.385769i
\(915\) 0 0
\(916\) −3.03744 + 1.29136i −0.100360 + 0.0426677i
\(917\) 15.6336 0.516266
\(918\) 0 0
\(919\) 30.8044i 1.01614i −0.861315 0.508072i \(-0.830358\pi\)
0.861315 0.508072i \(-0.169642\pi\)
\(920\) 13.0399 + 2.77204i 0.429913 + 0.0913915i
\(921\) 0 0
\(922\) 7.00289 + 34.3703i 0.230628 + 1.13192i
\(923\) −26.3483 + 15.2122i −0.867266 + 0.500716i
\(924\) 0 0
\(925\) −14.7420 29.0588i −0.484715 0.955446i
\(926\) 9.28972 27.7903i 0.305279 0.913247i
\(927\) 0 0
\(928\) −1.52077 + 36.0063i −0.0499216 + 1.18196i
\(929\) −23.8104 13.7469i −0.781194 0.451023i 0.0556590 0.998450i \(-0.482274\pi\)
−0.836853 + 0.547427i \(0.815607\pi\)
\(930\) 0 0
\(931\) 13.9530 8.05579i 0.457293 0.264018i
\(932\) −4.90727 + 40.1554i −0.160743 + 1.31533i
\(933\) 0 0
\(934\) −1.68991 + 1.49596i −0.0552955 + 0.0489494i
\(935\) −15.7335 4.67550i −0.514541 0.152905i
\(936\) 0 0
\(937\) 13.6341i 0.445407i −0.974886 0.222704i \(-0.928512\pi\)
0.974886 0.222704i \(-0.0714882\pi\)
\(938\) −3.81866 4.31374i −0.124684 0.140849i
\(939\) 0 0
\(940\) 38.3362 + 16.6831i 1.25039 + 0.544143i
\(941\) 49.7730 28.7364i 1.62255 0.936781i 0.636319 0.771426i \(-0.280456\pi\)
0.986234 0.165355i \(-0.0528771\pi\)
\(942\) 0 0
\(943\) 7.73561 13.3985i 0.251906 0.436314i
\(944\) 8.10793 + 28.1548i 0.263891 + 0.916360i
\(945\) 0 0
\(946\) −11.4891 + 34.3698i −0.373543 + 1.11746i
\(947\) 16.7732 + 9.68402i 0.545056 + 0.314688i 0.747126 0.664683i \(-0.231433\pi\)
−0.202069 + 0.979371i \(0.564767\pi\)
\(948\) 0 0
\(949\) −11.8257 20.4828i −0.383880 0.664899i
\(950\) 7.24082 18.3030i 0.234923 0.593827i
\(951\) 0 0
\(952\) −0.319008 4.00963i −0.0103391 0.129953i
\(953\) −4.34158 −0.140638 −0.0703188 0.997525i \(-0.522402\pi\)
−0.0703188 + 0.997525i \(0.522402\pi\)
\(954\) 0 0
\(955\) 48.7961 + 14.5006i 1.57900 + 0.469229i
\(956\) −37.4172 + 15.9078i −1.21016 + 0.514495i
\(957\) 0 0
\(958\) −8.28526 + 1.68811i −0.267685 + 0.0545404i
\(959\) 3.82170 + 6.61938i 0.123409 + 0.213751i
\(960\) 0 0
\(961\) −10.3335 + 17.8981i −0.333338 + 0.577358i
\(962\) −7.00245 + 20.9479i −0.225768 + 0.675388i
\(963\) 0 0
\(964\) 27.5573 + 20.7414i 0.887561 + 0.668034i
\(965\) −17.8789 18.8735i −0.575541 0.607560i
\(966\) 0 0
\(967\) −16.5665 28.6939i −0.532741 0.922735i −0.999269 0.0382285i \(-0.987829\pi\)
0.466528 0.884507i \(-0.345505\pi\)
\(968\) −54.3757 25.8789i −1.74770 0.831780i
\(969\) 0 0
\(970\) 36.8293 17.1472i 1.18252 0.550564i
\(971\) 22.0082 0.706277 0.353138 0.935571i \(-0.385114\pi\)
0.353138 + 0.935571i \(0.385114\pi\)
\(972\) 0 0
\(973\) 13.1344i 0.421070i
\(974\) −15.5579 17.5749i −0.498508 0.563137i
\(975\) 0 0
\(976\) −13.8207 + 14.3444i −0.442390 + 0.459153i
\(977\) 14.7558 + 25.5578i 0.472080 + 0.817667i 0.999490 0.0319442i \(-0.0101699\pi\)
−0.527409 + 0.849611i \(0.676837\pi\)
\(978\) 0 0
\(979\) 45.1183 + 26.0491i 1.44199 + 0.832532i
\(980\) 15.3904 + 20.8123i 0.491628 + 0.664825i
\(981\) 0 0
\(982\) 5.98052 17.8908i 0.190846 0.570919i
\(983\) 39.8190 + 22.9895i 1.27003 + 0.733251i 0.974993 0.222235i \(-0.0713354\pi\)
0.295035 + 0.955486i \(0.404669\pi\)
\(984\) 0 0
\(985\) −6.34531 26.5326i −0.202178 0.845399i
\(986\) 2.32351 + 11.4038i 0.0739956 + 0.363171i
\(987\) 0 0
\(988\) −12.2786 + 5.22022i −0.390636 + 0.166077i
\(989\) 9.50531i 0.302251i
\(990\) 0 0
\(991\) 52.8232i 1.67798i −0.544144 0.838992i \(-0.683146\pi\)
0.544144 0.838992i \(-0.316854\pi\)
\(992\) −15.3501 9.74844i −0.487367 0.309513i
\(993\) 0 0
\(994\) 19.3673 3.94606i 0.614294 0.125161i
\(995\) 15.3955 3.68185i 0.488069 0.116722i
\(996\) 0 0
\(997\) 43.4452 + 25.0831i 1.37592 + 0.794389i 0.991666 0.128837i \(-0.0411244\pi\)
0.384257 + 0.923226i \(0.374458\pi\)
\(998\) −55.3113 18.4894i −1.75085 0.585272i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 540.2.n.d.359.7 48
3.2 odd 2 180.2.n.d.119.18 yes 48
4.3 odd 2 inner 540.2.n.d.359.23 48
5.4 even 2 inner 540.2.n.d.359.18 48
9.4 even 3 180.2.n.d.59.23 yes 48
9.5 odd 6 inner 540.2.n.d.179.2 48
12.11 even 2 180.2.n.d.119.2 yes 48
15.2 even 4 900.2.r.g.551.6 48
15.8 even 4 900.2.r.g.551.19 48
15.14 odd 2 180.2.n.d.119.7 yes 48
20.19 odd 2 inner 540.2.n.d.359.2 48
36.23 even 6 inner 540.2.n.d.179.18 48
36.31 odd 6 180.2.n.d.59.7 yes 48
45.4 even 6 180.2.n.d.59.2 48
45.13 odd 12 900.2.r.g.851.11 48
45.14 odd 6 inner 540.2.n.d.179.23 48
45.22 odd 12 900.2.r.g.851.14 48
60.23 odd 4 900.2.r.g.551.11 48
60.47 odd 4 900.2.r.g.551.14 48
60.59 even 2 180.2.n.d.119.23 yes 48
180.59 even 6 inner 540.2.n.d.179.7 48
180.67 even 12 900.2.r.g.851.6 48
180.103 even 12 900.2.r.g.851.19 48
180.139 odd 6 180.2.n.d.59.18 yes 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
180.2.n.d.59.2 48 45.4 even 6
180.2.n.d.59.7 yes 48 36.31 odd 6
180.2.n.d.59.18 yes 48 180.139 odd 6
180.2.n.d.59.23 yes 48 9.4 even 3
180.2.n.d.119.2 yes 48 12.11 even 2
180.2.n.d.119.7 yes 48 15.14 odd 2
180.2.n.d.119.18 yes 48 3.2 odd 2
180.2.n.d.119.23 yes 48 60.59 even 2
540.2.n.d.179.2 48 9.5 odd 6 inner
540.2.n.d.179.7 48 180.59 even 6 inner
540.2.n.d.179.18 48 36.23 even 6 inner
540.2.n.d.179.23 48 45.14 odd 6 inner
540.2.n.d.359.2 48 20.19 odd 2 inner
540.2.n.d.359.7 48 1.1 even 1 trivial
540.2.n.d.359.18 48 5.4 even 2 inner
540.2.n.d.359.23 48 4.3 odd 2 inner
900.2.r.g.551.6 48 15.2 even 4
900.2.r.g.551.11 48 60.23 odd 4
900.2.r.g.551.14 48 60.47 odd 4
900.2.r.g.551.19 48 15.8 even 4
900.2.r.g.851.6 48 180.67 even 12
900.2.r.g.851.11 48 45.13 odd 12
900.2.r.g.851.14 48 45.22 odd 12
900.2.r.g.851.19 48 180.103 even 12