Properties

Label 720.2.u.a.539.5
Level $720$
Weight $2$
Character 720.539
Analytic conductor $5.749$
Analytic rank $0$
Dimension $96$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [720,2,Mod(179,720)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(720, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 3, 2, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("720.179");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 720.u (of order \(4\), degree \(2\), 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: \(5.74922894553\)
Analytic rank: \(0\)
Dimension: \(96\)
Relative dimension: \(48\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 539.5
Character \(\chi\) \(=\) 720.539
Dual form 720.2.u.a.179.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.31018 + 0.532382i) q^{2} +(1.43314 - 1.39503i) q^{4} +(-1.50698 + 1.65197i) q^{5} +4.30751i q^{7} +(-1.13498 + 2.59072i) q^{8} +O(q^{10})\) \(q+(-1.31018 + 0.532382i) q^{2} +(1.43314 - 1.39503i) q^{4} +(-1.50698 + 1.65197i) q^{5} +4.30751i q^{7} +(-1.13498 + 2.59072i) q^{8} +(1.09494 - 2.96667i) q^{10} +(-4.26649 - 4.26649i) q^{11} +(-2.10930 - 2.10930i) q^{13} +(-2.29324 - 5.64362i) q^{14} +(0.107775 - 3.99855i) q^{16} -3.59142 q^{17} +(0.954870 + 0.954870i) q^{19} +(0.144830 + 4.46979i) q^{20} +(7.86127 + 3.31847i) q^{22} +6.53188 q^{23} +(-0.457999 - 4.97898i) q^{25} +(3.88652 + 1.64061i) q^{26} +(6.00912 + 6.17327i) q^{28} +(1.84857 + 1.84857i) q^{29} -7.64329i q^{31} +(1.98755 + 5.29619i) q^{32} +(4.70541 - 1.91201i) q^{34} +(-7.11588 - 6.49135i) q^{35} +(-1.90965 + 1.90965i) q^{37} +(-1.75941 - 0.742695i) q^{38} +(-2.56939 - 5.77912i) q^{40} +7.67058 q^{41} +(-5.43308 - 5.43308i) q^{43} +(-12.0664 - 0.162586i) q^{44} +(-8.55794 + 3.47746i) q^{46} -3.24864i q^{47} -11.5547 q^{49} +(3.25078 + 6.27953i) q^{50} +(-5.96546 - 0.0803806i) q^{52} +(-6.08323 - 6.08323i) q^{53} +(13.4776 - 0.618574i) q^{55} +(-11.1596 - 4.88894i) q^{56} +(-3.40610 - 1.43781i) q^{58} +(-2.97848 - 2.97848i) q^{59} +(-0.157020 + 0.157020i) q^{61} +(4.06915 + 10.0141i) q^{62} +(-5.42364 - 5.88082i) q^{64} +(6.66318 - 0.305816i) q^{65} +(-0.305394 + 0.305394i) q^{67} +(-5.14701 + 5.01014i) q^{68} +(12.7790 + 4.71647i) q^{70} +1.61808i q^{71} -6.90696 q^{73} +(1.48532 - 3.51865i) q^{74} +(2.70053 + 0.0363879i) q^{76} +(18.3780 - 18.3780i) q^{77} +5.39306i q^{79} +(6.44306 + 6.20379i) q^{80} +(-10.0498 + 4.08368i) q^{82} +(-5.82210 - 5.82210i) q^{83} +(5.41221 - 5.93291i) q^{85} +(10.0108 + 4.22584i) q^{86} +(15.8957 - 6.21090i) q^{88} -7.74878 q^{89} +(9.08585 - 9.08585i) q^{91} +(9.36110 - 9.11218i) q^{92} +(1.72952 + 4.25630i) q^{94} +(-3.01639 + 0.138441i) q^{95} +9.34141i q^{97} +(15.1387 - 6.15150i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 96 q+O(q^{10}) \) Copy content Toggle raw display \( 96 q - 8 q^{16} - 16 q^{19} + 72 q^{34} + 8 q^{40} + 8 q^{46} - 96 q^{49} + 64 q^{55} - 32 q^{61} + 48 q^{64} + 24 q^{70} + 40 q^{76} - 88 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/720\mathbb{Z}\right)^\times\).

\(n\) \(181\) \(271\) \(577\) \(641\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.31018 + 0.532382i −0.926437 + 0.376451i
\(3\) 0 0
\(4\) 1.43314 1.39503i 0.716570 0.697516i
\(5\) −1.50698 + 1.65197i −0.673944 + 0.738783i
\(6\) 0 0
\(7\) 4.30751i 1.62809i 0.580804 + 0.814044i \(0.302738\pi\)
−0.580804 + 0.814044i \(0.697262\pi\)
\(8\) −1.13498 + 2.59072i −0.401276 + 0.915957i
\(9\) 0 0
\(10\) 1.09494 2.96667i 0.346251 0.938142i
\(11\) −4.26649 4.26649i −1.28640 1.28640i −0.936961 0.349435i \(-0.886374\pi\)
−0.349435 0.936961i \(-0.613626\pi\)
\(12\) 0 0
\(13\) −2.10930 2.10930i −0.585015 0.585015i 0.351262 0.936277i \(-0.385753\pi\)
−0.936277 + 0.351262i \(0.885753\pi\)
\(14\) −2.29324 5.64362i −0.612895 1.50832i
\(15\) 0 0
\(16\) 0.107775 3.99855i 0.0269438 0.999637i
\(17\) −3.59142 −0.871048 −0.435524 0.900177i \(-0.643437\pi\)
−0.435524 + 0.900177i \(0.643437\pi\)
\(18\) 0 0
\(19\) 0.954870 + 0.954870i 0.219062 + 0.219062i 0.808103 0.589041i \(-0.200494\pi\)
−0.589041 + 0.808103i \(0.700494\pi\)
\(20\) 0.144830 + 4.46979i 0.0323850 + 0.999475i
\(21\) 0 0
\(22\) 7.86127 + 3.31847i 1.67603 + 0.707499i
\(23\) 6.53188 1.36199 0.680996 0.732287i \(-0.261547\pi\)
0.680996 + 0.732287i \(0.261547\pi\)
\(24\) 0 0
\(25\) −0.457999 4.97898i −0.0915997 0.995796i
\(26\) 3.88652 + 1.64061i 0.762209 + 0.321750i
\(27\) 0 0
\(28\) 6.00912 + 6.17327i 1.13562 + 1.16664i
\(29\) 1.84857 + 1.84857i 0.343270 + 0.343270i 0.857595 0.514325i \(-0.171958\pi\)
−0.514325 + 0.857595i \(0.671958\pi\)
\(30\) 0 0
\(31\) 7.64329i 1.37278i −0.727236 0.686388i \(-0.759195\pi\)
0.727236 0.686388i \(-0.240805\pi\)
\(32\) 1.98755 + 5.29619i 0.351352 + 0.936243i
\(33\) 0 0
\(34\) 4.70541 1.91201i 0.806970 0.327907i
\(35\) −7.11588 6.49135i −1.20280 1.09724i
\(36\) 0 0
\(37\) −1.90965 + 1.90965i −0.313945 + 0.313945i −0.846436 0.532491i \(-0.821256\pi\)
0.532491 + 0.846436i \(0.321256\pi\)
\(38\) −1.75941 0.742695i −0.285413 0.120481i
\(39\) 0 0
\(40\) −2.56939 5.77912i −0.406256 0.913759i
\(41\) 7.67058 1.19794 0.598972 0.800770i \(-0.295576\pi\)
0.598972 + 0.800770i \(0.295576\pi\)
\(42\) 0 0
\(43\) −5.43308 5.43308i −0.828537 0.828537i 0.158777 0.987314i \(-0.449245\pi\)
−0.987314 + 0.158777i \(0.949245\pi\)
\(44\) −12.0664 0.162586i −1.81907 0.0245108i
\(45\) 0 0
\(46\) −8.55794 + 3.47746i −1.26180 + 0.512723i
\(47\) 3.24864i 0.473863i −0.971526 0.236932i \(-0.923858\pi\)
0.971526 0.236932i \(-0.0761417\pi\)
\(48\) 0 0
\(49\) −11.5547 −1.65067
\(50\) 3.25078 + 6.27953i 0.459730 + 0.888059i
\(51\) 0 0
\(52\) −5.96546 0.0803806i −0.827261 0.0111468i
\(53\) −6.08323 6.08323i −0.835596 0.835596i 0.152680 0.988276i \(-0.451210\pi\)
−0.988276 + 0.152680i \(0.951210\pi\)
\(54\) 0 0
\(55\) 13.4776 0.618574i 1.81732 0.0834085i
\(56\) −11.1596 4.88894i −1.49126 0.653312i
\(57\) 0 0
\(58\) −3.40610 1.43781i −0.447243 0.188794i
\(59\) −2.97848 2.97848i −0.387765 0.387765i 0.486125 0.873889i \(-0.338410\pi\)
−0.873889 + 0.486125i \(0.838410\pi\)
\(60\) 0 0
\(61\) −0.157020 + 0.157020i −0.0201044 + 0.0201044i −0.717088 0.696983i \(-0.754525\pi\)
0.696983 + 0.717088i \(0.254525\pi\)
\(62\) 4.06915 + 10.0141i 0.516782 + 1.27179i
\(63\) 0 0
\(64\) −5.42364 5.88082i −0.677955 0.735103i
\(65\) 6.66318 0.305816i 0.826466 0.0379318i
\(66\) 0 0
\(67\) −0.305394 + 0.305394i −0.0373098 + 0.0373098i −0.725516 0.688206i \(-0.758399\pi\)
0.688206 + 0.725516i \(0.258399\pi\)
\(68\) −5.14701 + 5.01014i −0.624166 + 0.607569i
\(69\) 0 0
\(70\) 12.7790 + 4.71647i 1.52738 + 0.563726i
\(71\) 1.61808i 0.192030i 0.995380 + 0.0960152i \(0.0306097\pi\)
−0.995380 + 0.0960152i \(0.969390\pi\)
\(72\) 0 0
\(73\) −6.90696 −0.808399 −0.404199 0.914671i \(-0.632450\pi\)
−0.404199 + 0.914671i \(0.632450\pi\)
\(74\) 1.48532 3.51865i 0.172665 0.409035i
\(75\) 0 0
\(76\) 2.70053 + 0.0363879i 0.309773 + 0.00417398i
\(77\) 18.3780 18.3780i 2.09436 2.09436i
\(78\) 0 0
\(79\) 5.39306i 0.606767i 0.952869 + 0.303383i \(0.0981163\pi\)
−0.952869 + 0.303383i \(0.901884\pi\)
\(80\) 6.44306 + 6.20379i 0.720356 + 0.693605i
\(81\) 0 0
\(82\) −10.0498 + 4.08368i −1.10982 + 0.450967i
\(83\) −5.82210 5.82210i −0.639059 0.639059i 0.311265 0.950323i \(-0.399247\pi\)
−0.950323 + 0.311265i \(0.899247\pi\)
\(84\) 0 0
\(85\) 5.41221 5.93291i 0.587037 0.643515i
\(86\) 10.0108 + 4.22584i 1.07949 + 0.455684i
\(87\) 0 0
\(88\) 15.8957 6.21090i 1.69448 0.662084i
\(89\) −7.74878 −0.821369 −0.410684 0.911778i \(-0.634710\pi\)
−0.410684 + 0.911778i \(0.634710\pi\)
\(90\) 0 0
\(91\) 9.08585 9.08585i 0.952455 0.952455i
\(92\) 9.36110 9.11218i 0.975962 0.950011i
\(93\) 0 0
\(94\) 1.72952 + 4.25630i 0.178386 + 0.439004i
\(95\) −3.01639 + 0.138441i −0.309475 + 0.0142038i
\(96\) 0 0
\(97\) 9.34141i 0.948476i 0.880397 + 0.474238i \(0.157276\pi\)
−0.880397 + 0.474238i \(0.842724\pi\)
\(98\) 15.1387 6.15150i 1.52924 0.621396i
\(99\) 0 0
\(100\) −7.60221 6.49665i −0.760221 0.649665i
\(101\) −7.91178 + 7.91178i −0.787251 + 0.787251i −0.981043 0.193792i \(-0.937921\pi\)
0.193792 + 0.981043i \(0.437921\pi\)
\(102\) 0 0
\(103\) 16.1744i 1.59371i −0.604172 0.796854i \(-0.706496\pi\)
0.604172 0.796854i \(-0.293504\pi\)
\(104\) 7.85862 3.07059i 0.770601 0.301096i
\(105\) 0 0
\(106\) 11.2087 + 4.73152i 1.08869 + 0.459566i
\(107\) 5.26603 5.26603i 0.509086 0.509086i −0.405160 0.914246i \(-0.632784\pi\)
0.914246 + 0.405160i \(0.132784\pi\)
\(108\) 0 0
\(109\) −11.9434 + 11.9434i −1.14397 + 1.14397i −0.156248 + 0.987718i \(0.549940\pi\)
−0.987718 + 0.156248i \(0.950060\pi\)
\(110\) −17.3288 + 7.98570i −1.65224 + 0.761406i
\(111\) 0 0
\(112\) 17.2238 + 0.464243i 1.62750 + 0.0438668i
\(113\) −18.0886 −1.70163 −0.850815 0.525466i \(-0.823891\pi\)
−0.850815 + 0.525466i \(0.823891\pi\)
\(114\) 0 0
\(115\) −9.84344 + 10.7905i −0.917906 + 1.00622i
\(116\) 5.22806 + 0.0704446i 0.485413 + 0.00654062i
\(117\) 0 0
\(118\) 5.48802 + 2.31665i 0.505214 + 0.213265i
\(119\) 15.4701i 1.41814i
\(120\) 0 0
\(121\) 25.4059i 2.30963i
\(122\) 0.122130 0.289319i 0.0110571 0.0261937i
\(123\) 0 0
\(124\) −10.6626 10.9539i −0.957532 0.983689i
\(125\) 8.91531 + 6.74664i 0.797410 + 0.603438i
\(126\) 0 0
\(127\) −7.28333 −0.646291 −0.323145 0.946349i \(-0.604740\pi\)
−0.323145 + 0.946349i \(0.604740\pi\)
\(128\) 10.2368 + 4.81748i 0.904813 + 0.425810i
\(129\) 0 0
\(130\) −8.56715 + 3.94803i −0.751389 + 0.346265i
\(131\) 9.89718 9.89718i 0.864721 0.864721i −0.127161 0.991882i \(-0.540587\pi\)
0.991882 + 0.127161i \(0.0405865\pi\)
\(132\) 0 0
\(133\) −4.11312 + 4.11312i −0.356652 + 0.356652i
\(134\) 0.237535 0.562707i 0.0205199 0.0486105i
\(135\) 0 0
\(136\) 4.07619 9.30436i 0.349530 0.797842i
\(137\) 17.7974i 1.52054i 0.649608 + 0.760269i \(0.274933\pi\)
−0.649608 + 0.760269i \(0.725067\pi\)
\(138\) 0 0
\(139\) 4.98268 4.98268i 0.422625 0.422625i −0.463481 0.886107i \(-0.653400\pi\)
0.886107 + 0.463481i \(0.153400\pi\)
\(140\) −19.2537 + 0.623857i −1.62723 + 0.0527256i
\(141\) 0 0
\(142\) −0.861435 2.11997i −0.0722900 0.177904i
\(143\) 17.9986i 1.50512i
\(144\) 0 0
\(145\) −5.83953 + 0.268013i −0.484947 + 0.0222573i
\(146\) 9.04936 3.67714i 0.748930 0.304322i
\(147\) 0 0
\(148\) −0.0727725 + 5.40082i −0.00598186 + 0.443945i
\(149\) 9.78188 9.78188i 0.801363 0.801363i −0.181946 0.983309i \(-0.558240\pi\)
0.983309 + 0.181946i \(0.0582395\pi\)
\(150\) 0 0
\(151\) −12.0108 −0.977422 −0.488711 0.872446i \(-0.662533\pi\)
−0.488711 + 0.872446i \(0.662533\pi\)
\(152\) −3.55756 + 1.39004i −0.288556 + 0.112747i
\(153\) 0 0
\(154\) −14.2943 + 33.8625i −1.15187 + 2.72872i
\(155\) 12.6265 + 11.5183i 1.01418 + 0.925173i
\(156\) 0 0
\(157\) −8.81467 8.81467i −0.703488 0.703488i 0.261670 0.965157i \(-0.415727\pi\)
−0.965157 + 0.261670i \(0.915727\pi\)
\(158\) −2.87117 7.06588i −0.228418 0.562131i
\(159\) 0 0
\(160\) −11.7443 4.69791i −0.928472 0.371402i
\(161\) 28.1362i 2.21744i
\(162\) 0 0
\(163\) −8.90000 + 8.90000i −0.697102 + 0.697102i −0.963784 0.266682i \(-0.914073\pi\)
0.266682 + 0.963784i \(0.414073\pi\)
\(164\) 10.9930 10.7007i 0.858410 0.835584i
\(165\) 0 0
\(166\) 10.7276 + 4.52841i 0.832621 + 0.351473i
\(167\) 4.24306 0.328338 0.164169 0.986432i \(-0.447506\pi\)
0.164169 + 0.986432i \(0.447506\pi\)
\(168\) 0 0
\(169\) 4.10170i 0.315515i
\(170\) −3.93239 + 10.6545i −0.301601 + 0.817166i
\(171\) 0 0
\(172\) −15.3657 0.207042i −1.17162 0.0157868i
\(173\) −4.03165 + 4.03165i −0.306521 + 0.306521i −0.843558 0.537037i \(-0.819543\pi\)
0.537037 + 0.843558i \(0.319543\pi\)
\(174\) 0 0
\(175\) 21.4470 1.97284i 1.62124 0.149132i
\(176\) −17.5196 + 16.5999i −1.32059 + 1.25127i
\(177\) 0 0
\(178\) 10.1523 4.12531i 0.760946 0.309205i
\(179\) 0.833880 0.833880i 0.0623272 0.0623272i −0.675256 0.737583i \(-0.735967\pi\)
0.737583 + 0.675256i \(0.235967\pi\)
\(180\) 0 0
\(181\) −10.5947 10.5947i −0.787501 0.787501i 0.193583 0.981084i \(-0.437989\pi\)
−0.981084 + 0.193583i \(0.937989\pi\)
\(182\) −7.06695 + 16.7412i −0.523837 + 1.24094i
\(183\) 0 0
\(184\) −7.41355 + 16.9223i −0.546534 + 1.24753i
\(185\) −0.276870 6.03250i −0.0203559 0.443518i
\(186\) 0 0
\(187\) 15.3228 + 15.3228i 1.12051 + 1.12051i
\(188\) −4.53196 4.65575i −0.330527 0.339556i
\(189\) 0 0
\(190\) 3.87831 1.78725i 0.281362 0.129661i
\(191\) 3.83158 0.277244 0.138622 0.990345i \(-0.455733\pi\)
0.138622 + 0.990345i \(0.455733\pi\)
\(192\) 0 0
\(193\) 5.03272i 0.362263i 0.983459 + 0.181132i \(0.0579760\pi\)
−0.983459 + 0.181132i \(0.942024\pi\)
\(194\) −4.97320 12.2389i −0.357055 0.878703i
\(195\) 0 0
\(196\) −16.5595 + 16.1191i −1.18282 + 1.15137i
\(197\) 7.01759 + 7.01759i 0.499982 + 0.499982i 0.911432 0.411450i \(-0.134978\pi\)
−0.411450 + 0.911432i \(0.634978\pi\)
\(198\) 0 0
\(199\) 13.7542 0.975009 0.487504 0.873121i \(-0.337907\pi\)
0.487504 + 0.873121i \(0.337907\pi\)
\(200\) 13.4190 + 4.46449i 0.948863 + 0.315687i
\(201\) 0 0
\(202\) 6.15376 14.5779i 0.432977 1.02570i
\(203\) −7.96273 + 7.96273i −0.558874 + 0.558874i
\(204\) 0 0
\(205\) −11.5594 + 12.6716i −0.807346 + 0.885020i
\(206\) 8.61094 + 21.1913i 0.599953 + 1.47647i
\(207\) 0 0
\(208\) −8.66147 + 8.20681i −0.600565 + 0.569040i
\(209\) 8.14789i 0.563601i
\(210\) 0 0
\(211\) 12.8000 + 12.8000i 0.881190 + 0.881190i 0.993656 0.112466i \(-0.0358748\pi\)
−0.112466 + 0.993656i \(0.535875\pi\)
\(212\) −17.2044 0.231818i −1.18160 0.0159213i
\(213\) 0 0
\(214\) −4.09590 + 9.70298i −0.279990 + 0.663282i
\(215\) 17.1628 0.787712i 1.17050 0.0537215i
\(216\) 0 0
\(217\) 32.9236 2.23500
\(218\) 9.28951 22.0064i 0.629165 1.49046i
\(219\) 0 0
\(220\) 18.4524 19.6882i 1.24406 1.32738i
\(221\) 7.57539 + 7.57539i 0.509576 + 0.509576i
\(222\) 0 0
\(223\) 12.7040 0.850723 0.425362 0.905023i \(-0.360147\pi\)
0.425362 + 0.905023i \(0.360147\pi\)
\(224\) −22.8134 + 8.56140i −1.52429 + 0.572033i
\(225\) 0 0
\(226\) 23.6993 9.63002i 1.57645 0.640580i
\(227\) −13.3440 13.3440i −0.885675 0.885675i 0.108429 0.994104i \(-0.465418\pi\)
−0.994104 + 0.108429i \(0.965418\pi\)
\(228\) 0 0
\(229\) −1.09552 1.09552i −0.0723941 0.0723941i 0.669983 0.742377i \(-0.266302\pi\)
−0.742377 + 0.669983i \(0.766302\pi\)
\(230\) 7.15203 19.3779i 0.471591 1.27774i
\(231\) 0 0
\(232\) −6.88720 + 2.69103i −0.452167 + 0.176675i
\(233\) 17.1156i 1.12128i 0.828060 + 0.560640i \(0.189445\pi\)
−0.828060 + 0.560640i \(0.810555\pi\)
\(234\) 0 0
\(235\) 5.36665 + 4.89565i 0.350082 + 0.319357i
\(236\) −8.42364 0.113503i −0.548332 0.00738841i
\(237\) 0 0
\(238\) 8.23600 + 20.2686i 0.533861 + 1.31382i
\(239\) −17.8555 −1.15498 −0.577488 0.816399i \(-0.695967\pi\)
−0.577488 + 0.816399i \(0.695967\pi\)
\(240\) 0 0
\(241\) 5.11525 0.329502 0.164751 0.986335i \(-0.447318\pi\)
0.164751 + 0.986335i \(0.447318\pi\)
\(242\) −13.5256 33.2863i −0.869461 2.13972i
\(243\) 0 0
\(244\) −0.00598368 + 0.444080i −0.000383066 + 0.0284293i
\(245\) 17.4127 19.0880i 1.11246 1.21949i
\(246\) 0 0
\(247\) 4.02822i 0.256309i
\(248\) 19.8016 + 8.67498i 1.25740 + 0.550862i
\(249\) 0 0
\(250\) −15.2724 4.09296i −0.965914 0.258862i
\(251\) −4.02622 4.02622i −0.254133 0.254133i 0.568530 0.822663i \(-0.307512\pi\)
−0.822663 + 0.568530i \(0.807512\pi\)
\(252\) 0 0
\(253\) −27.8682 27.8682i −1.75206 1.75206i
\(254\) 9.54246 3.87751i 0.598747 0.243297i
\(255\) 0 0
\(256\) −15.9768 0.861887i −0.998548 0.0538680i
\(257\) −29.1773 −1.82003 −0.910016 0.414573i \(-0.863931\pi\)
−0.910016 + 0.414573i \(0.863931\pi\)
\(258\) 0 0
\(259\) −8.22585 8.22585i −0.511130 0.511130i
\(260\) 9.12264 9.73362i 0.565762 0.603654i
\(261\) 0 0
\(262\) −7.69800 + 18.2362i −0.475584 + 1.12663i
\(263\) 1.92706 0.118828 0.0594139 0.998233i \(-0.481077\pi\)
0.0594139 + 0.998233i \(0.481077\pi\)
\(264\) 0 0
\(265\) 19.2166 0.881973i 1.18047 0.0541792i
\(266\) 3.19917 7.57867i 0.196154 0.464678i
\(267\) 0 0
\(268\) −0.0116379 + 0.863706i −0.000710895 + 0.0527592i
\(269\) −9.93701 9.93701i −0.605870 0.605870i 0.335994 0.941864i \(-0.390928\pi\)
−0.941864 + 0.335994i \(0.890928\pi\)
\(270\) 0 0
\(271\) 15.0777i 0.915907i 0.888976 + 0.457954i \(0.151417\pi\)
−0.888976 + 0.457954i \(0.848583\pi\)
\(272\) −0.387066 + 14.3605i −0.0234693 + 0.870731i
\(273\) 0 0
\(274\) −9.47504 23.3178i −0.572408 1.40868i
\(275\) −19.2887 + 23.1968i −1.16315 + 1.39882i
\(276\) 0 0
\(277\) −4.33837 + 4.33837i −0.260667 + 0.260667i −0.825325 0.564658i \(-0.809008\pi\)
0.564658 + 0.825325i \(0.309008\pi\)
\(278\) −3.87551 + 9.18089i −0.232438 + 0.550633i
\(279\) 0 0
\(280\) 24.8936 11.0677i 1.48768 0.661420i
\(281\) −2.93138 −0.174871 −0.0874357 0.996170i \(-0.527867\pi\)
−0.0874357 + 0.996170i \(0.527867\pi\)
\(282\) 0 0
\(283\) −12.3064 12.3064i −0.731542 0.731542i 0.239383 0.970925i \(-0.423055\pi\)
−0.970925 + 0.239383i \(0.923055\pi\)
\(284\) 2.25727 + 2.31893i 0.133944 + 0.137603i
\(285\) 0 0
\(286\) −9.58215 23.5814i −0.566604 1.39440i
\(287\) 33.0411i 1.95036i
\(288\) 0 0
\(289\) −4.10170 −0.241276
\(290\) 7.50815 3.46001i 0.440894 0.203179i
\(291\) 0 0
\(292\) −9.89863 + 9.63543i −0.579274 + 0.563871i
\(293\) 15.2191 + 15.2191i 0.889109 + 0.889109i 0.994437 0.105328i \(-0.0335894\pi\)
−0.105328 + 0.994437i \(0.533589\pi\)
\(294\) 0 0
\(295\) 9.40886 0.431832i 0.547805 0.0251422i
\(296\) −2.77996 7.11479i −0.161582 0.413539i
\(297\) 0 0
\(298\) −7.60832 + 18.0237i −0.440738 + 1.04409i
\(299\) −13.7777 13.7777i −0.796786 0.796786i
\(300\) 0 0
\(301\) 23.4031 23.4031i 1.34893 1.34893i
\(302\) 15.7363 6.39432i 0.905520 0.367952i
\(303\) 0 0
\(304\) 3.92100 3.71518i 0.224885 0.213080i
\(305\) −0.0227655 0.496019i −0.00130355 0.0284020i
\(306\) 0 0
\(307\) 3.79402 3.79402i 0.216536 0.216536i −0.590501 0.807037i \(-0.701070\pi\)
0.807037 + 0.590501i \(0.201070\pi\)
\(308\) 0.700342 51.9760i 0.0399057 2.96161i
\(309\) 0 0
\(310\) −22.6751 8.36895i −1.28786 0.475325i
\(311\) 18.1916i 1.03155i −0.856724 0.515775i \(-0.827504\pi\)
0.856724 0.515775i \(-0.172496\pi\)
\(312\) 0 0
\(313\) 16.7785 0.948377 0.474188 0.880423i \(-0.342742\pi\)
0.474188 + 0.880423i \(0.342742\pi\)
\(314\) 16.2416 + 6.85603i 0.916565 + 0.386908i
\(315\) 0 0
\(316\) 7.52349 + 7.72901i 0.423229 + 0.434791i
\(317\) −0.103425 + 0.103425i −0.00580894 + 0.00580894i −0.710005 0.704196i \(-0.751307\pi\)
0.704196 + 0.710005i \(0.251307\pi\)
\(318\) 0 0
\(319\) 15.7738i 0.883163i
\(320\) 17.8883 0.0973777i 0.999985 0.00544358i
\(321\) 0 0
\(322\) −14.9792 36.8634i −0.834758 2.05432i
\(323\) −3.42934 3.42934i −0.190814 0.190814i
\(324\) 0 0
\(325\) −9.53611 + 11.4682i −0.528968 + 0.636143i
\(326\) 6.92240 16.3988i 0.383396 0.908246i
\(327\) 0 0
\(328\) −8.70595 + 19.8723i −0.480706 + 1.09726i
\(329\) 13.9936 0.771490
\(330\) 0 0
\(331\) 2.18428 2.18428i 0.120059 0.120059i −0.644525 0.764583i \(-0.722945\pi\)
0.764583 + 0.644525i \(0.222945\pi\)
\(332\) −16.4659 0.221867i −0.903683 0.0121765i
\(333\) 0 0
\(334\) −5.55917 + 2.25893i −0.304184 + 0.123603i
\(335\) −0.0442773 0.964725i −0.00241913 0.0527085i
\(336\) 0 0
\(337\) 20.9206i 1.13962i −0.821778 0.569808i \(-0.807018\pi\)
0.821778 0.569808i \(-0.192982\pi\)
\(338\) 2.18367 + 5.37396i 0.118776 + 0.292305i
\(339\) 0 0
\(340\) −0.520145 16.0529i −0.0282088 0.870591i
\(341\) −32.6100 + 32.6100i −1.76593 + 1.76593i
\(342\) 0 0
\(343\) 19.6193i 1.05934i
\(344\) 20.2420 7.90915i 1.09138 0.426433i
\(345\) 0 0
\(346\) 3.13581 7.42857i 0.168582 0.399362i
\(347\) 4.34853 4.34853i 0.233441 0.233441i −0.580686 0.814127i \(-0.697216\pi\)
0.814127 + 0.580686i \(0.197216\pi\)
\(348\) 0 0
\(349\) 3.70979 3.70979i 0.198580 0.198580i −0.600811 0.799391i \(-0.705155\pi\)
0.799391 + 0.600811i \(0.205155\pi\)
\(350\) −27.0491 + 14.0028i −1.44584 + 0.748480i
\(351\) 0 0
\(352\) 14.1163 31.0760i 0.752401 1.65636i
\(353\) 16.3398 0.869681 0.434840 0.900508i \(-0.356805\pi\)
0.434840 + 0.900508i \(0.356805\pi\)
\(354\) 0 0
\(355\) −2.67301 2.43842i −0.141869 0.129418i
\(356\) −11.1051 + 10.8098i −0.588568 + 0.572917i
\(357\) 0 0
\(358\) −0.648590 + 1.53648i −0.0342790 + 0.0812053i
\(359\) 24.6929i 1.30324i 0.758545 + 0.651621i \(0.225911\pi\)
−0.758545 + 0.651621i \(0.774089\pi\)
\(360\) 0 0
\(361\) 17.1764i 0.904024i
\(362\) 19.5215 + 8.24056i 1.02603 + 0.433114i
\(363\) 0 0
\(364\) 0.346241 25.6963i 0.0181479 1.34685i
\(365\) 10.4087 11.4101i 0.544815 0.597231i
\(366\) 0 0
\(367\) 6.68177 0.348786 0.174393 0.984676i \(-0.444204\pi\)
0.174393 + 0.984676i \(0.444204\pi\)
\(368\) 0.703974 26.1180i 0.0366972 1.36150i
\(369\) 0 0
\(370\) 3.57434 + 7.75626i 0.185821 + 0.403229i
\(371\) 26.2036 26.2036i 1.36042 1.36042i
\(372\) 0 0
\(373\) 18.9638 18.9638i 0.981911 0.981911i −0.0179284 0.999839i \(-0.505707\pi\)
0.999839 + 0.0179284i \(0.00570709\pi\)
\(374\) −28.2331 11.9180i −1.45990 0.616265i
\(375\) 0 0
\(376\) 8.41631 + 3.68714i 0.434038 + 0.190150i
\(377\) 7.79837i 0.401636i
\(378\) 0 0
\(379\) −17.4207 + 17.4207i −0.894843 + 0.894843i −0.994974 0.100131i \(-0.968074\pi\)
0.100131 + 0.994974i \(0.468074\pi\)
\(380\) −4.12977 + 4.40636i −0.211853 + 0.226042i
\(381\) 0 0
\(382\) −5.02006 + 2.03986i −0.256849 + 0.104369i
\(383\) 10.4542i 0.534182i 0.963671 + 0.267091i \(0.0860625\pi\)
−0.963671 + 0.267091i \(0.913938\pi\)
\(384\) 0 0
\(385\) 2.66452 + 58.0551i 0.135796 + 2.95876i
\(386\) −2.67933 6.59376i −0.136374 0.335614i
\(387\) 0 0
\(388\) 13.0316 + 13.3875i 0.661577 + 0.679649i
\(389\) −6.71454 + 6.71454i −0.340441 + 0.340441i −0.856533 0.516092i \(-0.827386\pi\)
0.516092 + 0.856533i \(0.327386\pi\)
\(390\) 0 0
\(391\) −23.4587 −1.18636
\(392\) 13.1143 29.9349i 0.662373 1.51194i
\(393\) 0 0
\(394\) −12.9303 5.45826i −0.651421 0.274983i
\(395\) −8.90917 8.12726i −0.448269 0.408927i
\(396\) 0 0
\(397\) 25.8345 + 25.8345i 1.29660 + 1.29660i 0.930628 + 0.365968i \(0.119262\pi\)
0.365968 + 0.930628i \(0.380738\pi\)
\(398\) −18.0205 + 7.32248i −0.903284 + 0.367043i
\(399\) 0 0
\(400\) −19.9580 + 1.29472i −0.997902 + 0.0647360i
\(401\) 18.5375i 0.925717i −0.886432 0.462858i \(-0.846824\pi\)
0.886432 0.462858i \(-0.153176\pi\)
\(402\) 0 0
\(403\) −16.1220 + 16.1220i −0.803094 + 0.803094i
\(404\) −0.301500 + 22.3759i −0.0150002 + 1.11324i
\(405\) 0 0
\(406\) 6.19339 14.6718i 0.307373 0.728150i
\(407\) 16.2950 0.807715
\(408\) 0 0
\(409\) 6.45252i 0.319057i −0.987193 0.159528i \(-0.949003\pi\)
0.987193 0.159528i \(-0.0509973\pi\)
\(410\) 8.39883 22.7560i 0.414789 1.12384i
\(411\) 0 0
\(412\) −22.5638 23.1801i −1.11164 1.14200i
\(413\) 12.8298 12.8298i 0.631315 0.631315i
\(414\) 0 0
\(415\) 18.3917 0.844113i 0.902815 0.0414359i
\(416\) 6.97892 15.3636i 0.342170 0.753263i
\(417\) 0 0
\(418\) 4.33779 + 10.6752i 0.212168 + 0.522141i
\(419\) −12.0000 + 12.0000i −0.586236 + 0.586236i −0.936610 0.350374i \(-0.886055\pi\)
0.350374 + 0.936610i \(0.386055\pi\)
\(420\) 0 0
\(421\) 23.9012 + 23.9012i 1.16487 + 1.16487i 0.983395 + 0.181478i \(0.0580882\pi\)
0.181478 + 0.983395i \(0.441912\pi\)
\(422\) −23.5848 9.95582i −1.14809 0.484642i
\(423\) 0 0
\(424\) 22.6643 8.85560i 1.10067 0.430066i
\(425\) 1.64487 + 17.8816i 0.0797877 + 0.867386i
\(426\) 0 0
\(427\) −0.676366 0.676366i −0.0327317 0.0327317i
\(428\) 0.200676 14.8932i 0.00970005 0.719891i
\(429\) 0 0
\(430\) −22.0670 + 10.1692i −1.06417 + 0.490404i
\(431\) 12.5590 0.604944 0.302472 0.953158i \(-0.402188\pi\)
0.302472 + 0.953158i \(0.402188\pi\)
\(432\) 0 0
\(433\) 4.64837i 0.223386i −0.993743 0.111693i \(-0.964373\pi\)
0.993743 0.111693i \(-0.0356274\pi\)
\(434\) −43.1358 + 17.5279i −2.07058 + 0.841367i
\(435\) 0 0
\(436\) −0.455134 + 33.7778i −0.0217970 + 1.61767i
\(437\) 6.23710 + 6.23710i 0.298361 + 0.298361i
\(438\) 0 0
\(439\) 7.09686 0.338715 0.169357 0.985555i \(-0.445831\pi\)
0.169357 + 0.985555i \(0.445831\pi\)
\(440\) −13.6943 + 35.6188i −0.652850 + 1.69806i
\(441\) 0 0
\(442\) −13.9581 5.89212i −0.663920 0.280259i
\(443\) −16.7044 + 16.7044i −0.793649 + 0.793649i −0.982085 0.188436i \(-0.939658\pi\)
0.188436 + 0.982085i \(0.439658\pi\)
\(444\) 0 0
\(445\) 11.6773 12.8007i 0.553556 0.606813i
\(446\) −16.6445 + 6.76338i −0.788141 + 0.320255i
\(447\) 0 0
\(448\) 25.3317 23.3624i 1.19681 1.10377i
\(449\) 22.3540i 1.05495i −0.849571 0.527475i \(-0.823139\pi\)
0.849571 0.527475i \(-0.176861\pi\)
\(450\) 0 0
\(451\) −32.7265 32.7265i −1.54103 1.54103i
\(452\) −25.9234 + 25.2341i −1.21934 + 1.18691i
\(453\) 0 0
\(454\) 24.5872 + 10.3790i 1.15393 + 0.487109i
\(455\) 1.31731 + 28.7018i 0.0617562 + 1.34556i
\(456\) 0 0
\(457\) −28.9883 −1.35602 −0.678008 0.735055i \(-0.737156\pi\)
−0.678008 + 0.735055i \(0.737156\pi\)
\(458\) 2.01856 + 0.852093i 0.0943213 + 0.0398157i
\(459\) 0 0
\(460\) 0.946013 + 29.1961i 0.0441081 + 1.36128i
\(461\) −3.75610 3.75610i −0.174939 0.174939i 0.614206 0.789146i \(-0.289476\pi\)
−0.789146 + 0.614206i \(0.789476\pi\)
\(462\) 0 0
\(463\) −18.4896 −0.859286 −0.429643 0.902999i \(-0.641361\pi\)
−0.429643 + 0.902999i \(0.641361\pi\)
\(464\) 7.59081 7.19235i 0.352395 0.333897i
\(465\) 0 0
\(466\) −9.11203 22.4245i −0.422107 1.03879i
\(467\) −17.8623 17.8623i −0.826570 0.826570i 0.160471 0.987041i \(-0.448699\pi\)
−0.987041 + 0.160471i \(0.948699\pi\)
\(468\) 0 0
\(469\) −1.31549 1.31549i −0.0607436 0.0607436i
\(470\) −9.63763 3.55707i −0.444551 0.164075i
\(471\) 0 0
\(472\) 11.0969 4.33588i 0.510776 0.199575i
\(473\) 46.3604i 2.13165i
\(474\) 0 0
\(475\) 4.31695 5.19161i 0.198075 0.238207i
\(476\) −21.5813 22.1708i −0.989176 1.01620i
\(477\) 0 0
\(478\) 23.3939 9.50594i 1.07001 0.434792i
\(479\) 21.2617 0.971474 0.485737 0.874105i \(-0.338551\pi\)
0.485737 + 0.874105i \(0.338551\pi\)
\(480\) 0 0
\(481\) 8.05606 0.367325
\(482\) −6.70190 + 2.72327i −0.305263 + 0.124041i
\(483\) 0 0
\(484\) 35.4420 + 36.4102i 1.61100 + 1.65501i
\(485\) −15.4317 14.0773i −0.700718 0.639219i
\(486\) 0 0
\(487\) 38.2041i 1.73119i −0.500744 0.865595i \(-0.666940\pi\)
0.500744 0.865595i \(-0.333060\pi\)
\(488\) −0.228580 0.585010i −0.0103473 0.0264821i
\(489\) 0 0
\(490\) −12.6517 + 34.2789i −0.571545 + 1.54856i
\(491\) −11.2555 11.2555i −0.507953 0.507953i 0.405945 0.913898i \(-0.366943\pi\)
−0.913898 + 0.405945i \(0.866943\pi\)
\(492\) 0 0
\(493\) −6.63898 6.63898i −0.299005 0.299005i
\(494\) 2.14455 + 5.27769i 0.0964879 + 0.237454i
\(495\) 0 0
\(496\) −30.5621 0.823756i −1.37228 0.0369877i
\(497\) −6.96989 −0.312642
\(498\) 0 0
\(499\) 19.2924 + 19.2924i 0.863646 + 0.863646i 0.991759 0.128114i \(-0.0408923\pi\)
−0.128114 + 0.991759i \(0.540892\pi\)
\(500\) 22.1887 2.76826i 0.992307 0.123800i
\(501\) 0 0
\(502\) 7.41856 + 3.13159i 0.331107 + 0.139770i
\(503\) −27.8587 −1.24216 −0.621078 0.783748i \(-0.713305\pi\)
−0.621078 + 0.783748i \(0.713305\pi\)
\(504\) 0 0
\(505\) −1.14708 24.9929i −0.0510445 1.11217i
\(506\) 51.3489 + 21.6758i 2.28274 + 0.963608i
\(507\) 0 0
\(508\) −10.4380 + 10.1605i −0.463112 + 0.450798i
\(509\) 0.475925 + 0.475925i 0.0210950 + 0.0210950i 0.717576 0.696481i \(-0.245252\pi\)
−0.696481 + 0.717576i \(0.745252\pi\)
\(510\) 0 0
\(511\) 29.7518i 1.31614i
\(512\) 21.3913 7.37652i 0.945370 0.325999i
\(513\) 0 0
\(514\) 38.2275 15.5335i 1.68614 0.685153i
\(515\) 26.7196 + 24.3745i 1.17740 + 1.07407i
\(516\) 0 0
\(517\) −13.8603 + 13.8603i −0.609575 + 0.609575i
\(518\) 15.1566 + 6.39805i 0.665945 + 0.281114i
\(519\) 0 0
\(520\) −6.77029 + 17.6095i −0.296897 + 0.772229i
\(521\) −28.2023 −1.23557 −0.617783 0.786348i \(-0.711969\pi\)
−0.617783 + 0.786348i \(0.711969\pi\)
\(522\) 0 0
\(523\) 10.5066 + 10.5066i 0.459420 + 0.459420i 0.898465 0.439045i \(-0.144683\pi\)
−0.439045 + 0.898465i \(0.644683\pi\)
\(524\) 0.377159 27.9909i 0.0164763 1.22279i
\(525\) 0 0
\(526\) −2.52480 + 1.02593i −0.110086 + 0.0447328i
\(527\) 27.4503i 1.19575i
\(528\) 0 0
\(529\) 19.6655 0.855022
\(530\) −24.7077 + 11.3861i −1.07323 + 0.494582i
\(531\) 0 0
\(532\) −0.156741 + 11.6326i −0.00679560 + 0.504337i
\(533\) −16.1796 16.1796i −0.700815 0.700815i
\(534\) 0 0
\(535\) 0.763491 + 16.6351i 0.0330086 + 0.719199i
\(536\) −0.444574 1.13781i −0.0192027 0.0491457i
\(537\) 0 0
\(538\) 18.3095 + 7.72898i 0.789380 + 0.333220i
\(539\) 49.2979 + 49.2979i 2.12341 + 2.12341i
\(540\) 0 0
\(541\) −12.4368 + 12.4368i −0.534698 + 0.534698i −0.921967 0.387269i \(-0.873419\pi\)
0.387269 + 0.921967i \(0.373419\pi\)
\(542\) −8.02711 19.7545i −0.344794 0.848530i
\(543\) 0 0
\(544\) −7.13813 19.0209i −0.306045 0.815512i
\(545\) −1.73160 37.7285i −0.0741736 1.61611i
\(546\) 0 0
\(547\) 5.78283 5.78283i 0.247256 0.247256i −0.572588 0.819844i \(-0.694060\pi\)
0.819844 + 0.572588i \(0.194060\pi\)
\(548\) 24.8280 + 25.5062i 1.06060 + 1.08957i
\(549\) 0 0
\(550\) 12.9221 40.6610i 0.551001 1.73379i
\(551\) 3.53028i 0.150395i
\(552\) 0 0
\(553\) −23.2307 −0.987870
\(554\) 3.37437 7.99371i 0.143363 0.339620i
\(555\) 0 0
\(556\) 0.189878 14.0919i 0.00805264 0.597628i
\(557\) 12.9551 12.9551i 0.548924 0.548924i −0.377205 0.926130i \(-0.623115\pi\)
0.926130 + 0.377205i \(0.123115\pi\)
\(558\) 0 0
\(559\) 22.9200i 0.969413i
\(560\) −26.7229 + 27.7536i −1.12925 + 1.17280i
\(561\) 0 0
\(562\) 3.84063 1.56061i 0.162007 0.0658305i
\(563\) −14.1388 14.1388i −0.595881 0.595881i 0.343333 0.939214i \(-0.388444\pi\)
−0.939214 + 0.343333i \(0.888444\pi\)
\(564\) 0 0
\(565\) 27.2592 29.8817i 1.14680 1.25713i
\(566\) 22.6754 + 9.57192i 0.953117 + 0.402338i
\(567\) 0 0
\(568\) −4.19198 1.83648i −0.175892 0.0770572i
\(569\) 1.34936 0.0565679 0.0282840 0.999600i \(-0.490996\pi\)
0.0282840 + 0.999600i \(0.490996\pi\)
\(570\) 0 0
\(571\) −32.6417 + 32.6417i −1.36601 + 1.36601i −0.499967 + 0.866045i \(0.666654\pi\)
−0.866045 + 0.499967i \(0.833346\pi\)
\(572\) 25.1087 + 25.7945i 1.04985 + 1.07852i
\(573\) 0 0
\(574\) −17.5905 43.2898i −0.734213 1.80688i
\(575\) −2.99159 32.5221i −0.124758 1.35627i
\(576\) 0 0
\(577\) 40.3389i 1.67933i −0.543104 0.839665i \(-0.682751\pi\)
0.543104 0.839665i \(-0.317249\pi\)
\(578\) 5.37396 2.18367i 0.223527 0.0908286i
\(579\) 0 0
\(580\) −7.99498 + 8.53043i −0.331973 + 0.354207i
\(581\) 25.0788 25.0788i 1.04044 1.04044i
\(582\) 0 0
\(583\) 51.9081i 2.14981i
\(584\) 7.83926 17.8940i 0.324391 0.740459i
\(585\) 0 0
\(586\) −28.0421 11.8374i −1.15841 0.488997i
\(587\) 9.96452 9.96452i 0.411280 0.411280i −0.470905 0.882184i \(-0.656072\pi\)
0.882184 + 0.470905i \(0.156072\pi\)
\(588\) 0 0
\(589\) 7.29835 7.29835i 0.300723 0.300723i
\(590\) −12.0974 + 5.57489i −0.498042 + 0.229514i
\(591\) 0 0
\(592\) 7.43002 + 7.84165i 0.305372 + 0.322290i
\(593\) −19.4892 −0.800324 −0.400162 0.916444i \(-0.631046\pi\)
−0.400162 + 0.916444i \(0.631046\pi\)
\(594\) 0 0
\(595\) 25.5561 + 23.3132i 1.04770 + 0.955748i
\(596\) 0.372765 27.6648i 0.0152690 1.13320i
\(597\) 0 0
\(598\) 25.3863 + 10.7163i 1.03812 + 0.438221i
\(599\) 16.4963i 0.674020i 0.941501 + 0.337010i \(0.109416\pi\)
−0.941501 + 0.337010i \(0.890584\pi\)
\(600\) 0 0
\(601\) 8.09948i 0.330385i 0.986261 + 0.165192i \(0.0528245\pi\)
−0.986261 + 0.165192i \(0.947176\pi\)
\(602\) −18.2029 + 43.1216i −0.741893 + 1.75751i
\(603\) 0 0
\(604\) −17.2131 + 16.7554i −0.700391 + 0.681768i
\(605\) −41.9697 38.2863i −1.70631 1.55656i
\(606\) 0 0
\(607\) 0.975144 0.0395799 0.0197899 0.999804i \(-0.493700\pi\)
0.0197899 + 0.999804i \(0.493700\pi\)
\(608\) −3.15932 + 6.95503i −0.128127 + 0.282064i
\(609\) 0 0
\(610\) 0.293898 + 0.637754i 0.0118996 + 0.0258219i
\(611\) −6.85236 + 6.85236i −0.277217 + 0.277217i
\(612\) 0 0
\(613\) 7.41162 7.41162i 0.299353 0.299353i −0.541408 0.840760i \(-0.682108\pi\)
0.840760 + 0.541408i \(0.182108\pi\)
\(614\) −2.95098 + 6.99072i −0.119092 + 0.282122i
\(615\) 0 0
\(616\) 26.7535 + 68.4708i 1.07793 + 2.75877i
\(617\) 15.5875i 0.627531i −0.949501 0.313765i \(-0.898409\pi\)
0.949501 0.313765i \(-0.101591\pi\)
\(618\) 0 0
\(619\) −3.34655 + 3.34655i −0.134509 + 0.134509i −0.771156 0.636647i \(-0.780321\pi\)
0.636647 + 0.771156i \(0.280321\pi\)
\(620\) 34.1639 1.10698i 1.37206 0.0444573i
\(621\) 0 0
\(622\) 9.68486 + 23.8342i 0.388328 + 0.955665i
\(623\) 33.3780i 1.33726i
\(624\) 0 0
\(625\) −24.5805 + 4.56073i −0.983219 + 0.182429i
\(626\) −21.9828 + 8.93257i −0.878611 + 0.357017i
\(627\) 0 0
\(628\) −24.9294 0.335907i −0.994791 0.0134041i
\(629\) 6.85837 6.85837i 0.273461 0.273461i
\(630\) 0 0
\(631\) −17.5464 −0.698510 −0.349255 0.937028i \(-0.613565\pi\)
−0.349255 + 0.937028i \(0.613565\pi\)
\(632\) −13.9719 6.12102i −0.555773 0.243481i
\(633\) 0 0
\(634\) 0.0804439 0.190567i 0.00319483 0.00756840i
\(635\) 10.9759 12.0318i 0.435564 0.477468i
\(636\) 0 0
\(637\) 24.3723 + 24.3723i 0.965666 + 0.965666i
\(638\) 8.39768 + 20.6665i 0.332467 + 0.818194i
\(639\) 0 0
\(640\) −23.3850 + 9.65098i −0.924374 + 0.381488i
\(641\) 30.7369i 1.21403i 0.794689 + 0.607016i \(0.207634\pi\)
−0.794689 + 0.607016i \(0.792366\pi\)
\(642\) 0 0
\(643\) 2.00487 2.00487i 0.0790643 0.0790643i −0.666469 0.745533i \(-0.732195\pi\)
0.745533 + 0.666469i \(0.232195\pi\)
\(644\) 39.2509 + 40.3231i 1.54670 + 1.58895i
\(645\) 0 0
\(646\) 6.31877 + 2.66733i 0.248609 + 0.104945i
\(647\) 41.0262 1.61291 0.806453 0.591298i \(-0.201384\pi\)
0.806453 + 0.591298i \(0.201384\pi\)
\(648\) 0 0
\(649\) 25.4153i 0.997637i
\(650\) 6.38854 20.1023i 0.250579 0.788476i
\(651\) 0 0
\(652\) −0.339159 + 25.1707i −0.0132825 + 0.985762i
\(653\) −10.2034 + 10.2034i −0.399291 + 0.399291i −0.877983 0.478692i \(-0.841111\pi\)
0.478692 + 0.877983i \(0.341111\pi\)
\(654\) 0 0
\(655\) 1.43494 + 31.2647i 0.0560676 + 1.22161i
\(656\) 0.826697 30.6712i 0.0322771 1.19751i
\(657\) 0 0
\(658\) −18.3341 + 7.44992i −0.714737 + 0.290428i
\(659\) −14.6544 + 14.6544i −0.570853 + 0.570853i −0.932367 0.361514i \(-0.882260\pi\)
0.361514 + 0.932367i \(0.382260\pi\)
\(660\) 0 0
\(661\) 31.9191 + 31.9191i 1.24151 + 1.24151i 0.959376 + 0.282131i \(0.0910414\pi\)
0.282131 + 0.959376i \(0.408959\pi\)
\(662\) −1.69892 + 4.02466i −0.0660306 + 0.156423i
\(663\) 0 0
\(664\) 21.6914 8.47546i 0.841789 0.328912i
\(665\) −0.596337 12.9931i −0.0231250 0.503852i
\(666\) 0 0
\(667\) 12.0746 + 12.0746i 0.467531 + 0.467531i
\(668\) 6.08089 5.91920i 0.235277 0.229021i
\(669\) 0 0
\(670\) 0.571613 + 1.24039i 0.0220833 + 0.0479204i
\(671\) 1.33985 0.0517243
\(672\) 0 0
\(673\) 3.74068i 0.144193i 0.997398 + 0.0720963i \(0.0229689\pi\)
−0.997398 + 0.0720963i \(0.977031\pi\)
\(674\) 11.1377 + 27.4097i 0.429009 + 1.05578i
\(675\) 0 0
\(676\) −5.72199 5.87830i −0.220077 0.226088i
\(677\) −14.8520 14.8520i −0.570808 0.570808i 0.361546 0.932354i \(-0.382249\pi\)
−0.932354 + 0.361546i \(0.882249\pi\)
\(678\) 0 0
\(679\) −40.2382 −1.54420
\(680\) 9.22776 + 20.7553i 0.353868 + 0.795928i
\(681\) 0 0
\(682\) 25.3640 60.0860i 0.971237 2.30081i
\(683\) 0.704118 0.704118i 0.0269423 0.0269423i −0.693507 0.720450i \(-0.743935\pi\)
0.720450 + 0.693507i \(0.243935\pi\)
\(684\) 0 0
\(685\) −29.4008 26.8205i −1.12335 1.02476i
\(686\) 10.4450 + 25.7049i 0.398791 + 0.981416i
\(687\) 0 0
\(688\) −22.3100 + 21.1389i −0.850560 + 0.805913i
\(689\) 25.6627i 0.977672i
\(690\) 0 0
\(691\) −27.9600 27.9600i −1.06365 1.06365i −0.997832 0.0658160i \(-0.979035\pi\)
−0.0658160 0.997832i \(-0.520965\pi\)
\(692\) −0.153637 + 11.4022i −0.00584040 + 0.433447i
\(693\) 0 0
\(694\) −3.38227 + 8.01243i −0.128389 + 0.304148i
\(695\) 0.722410 + 15.7400i 0.0274026 + 0.597054i
\(696\) 0 0
\(697\) −27.5483 −1.04347
\(698\) −2.88546 + 6.83551i −0.109216 + 0.258728i
\(699\) 0 0
\(700\) 27.9844 32.7466i 1.05771 1.23771i
\(701\) 3.89364 + 3.89364i 0.147061 + 0.147061i 0.776804 0.629743i \(-0.216840\pi\)
−0.629743 + 0.776804i \(0.716840\pi\)
\(702\) 0 0
\(703\) −3.64694 −0.137547
\(704\) −1.95056 + 48.2304i −0.0735146 + 1.81775i
\(705\) 0 0
\(706\) −21.4081 + 8.69902i −0.805704 + 0.327392i
\(707\) −34.0801 34.0801i −1.28171 1.28171i
\(708\) 0 0
\(709\) −24.4875 24.4875i −0.919648 0.919648i 0.0773555 0.997004i \(-0.475352\pi\)
−0.997004 + 0.0773555i \(0.975352\pi\)
\(710\) 4.80029 + 1.77170i 0.180152 + 0.0664907i
\(711\) 0 0
\(712\) 8.79470 20.0749i 0.329595 0.752338i
\(713\) 49.9251i 1.86971i
\(714\) 0 0
\(715\) −29.7332 27.1236i −1.11196 1.01437i
\(716\) 0.0317773 2.35836i 0.00118757 0.0881359i
\(717\) 0 0
\(718\) −13.1461 32.3521i −0.490606 1.20737i
\(719\) 16.1711 0.603079 0.301540 0.953454i \(-0.402499\pi\)
0.301540 + 0.953454i \(0.402499\pi\)
\(720\) 0 0
\(721\) 69.6714 2.59470
\(722\) 9.14443 + 22.5042i 0.340320 + 0.837520i
\(723\) 0 0
\(724\) −29.9637 0.403741i −1.11359 0.0150049i
\(725\) 8.35734 10.0506i 0.310384 0.373271i
\(726\) 0 0
\(727\) 37.5868i 1.39402i 0.717063 + 0.697008i \(0.245486\pi\)
−0.717063 + 0.697008i \(0.754514\pi\)
\(728\) 13.2266 + 33.8511i 0.490211 + 1.25461i
\(729\) 0 0
\(730\) −7.56271 + 20.4906i −0.279909 + 0.758393i
\(731\) 19.5125 + 19.5125i 0.721695 + 0.721695i
\(732\) 0 0
\(733\) −10.5565 10.5565i −0.389913 0.389913i 0.484744 0.874656i \(-0.338913\pi\)
−0.874656 + 0.484744i \(0.838913\pi\)
\(734\) −8.75432 + 3.55726i −0.323128 + 0.131301i
\(735\) 0 0
\(736\) 12.9824 + 34.5941i 0.478539 + 1.27516i
\(737\) 2.60592 0.0959903
\(738\) 0 0
\(739\) −5.50334 5.50334i −0.202444 0.202444i 0.598603 0.801046i \(-0.295723\pi\)
−0.801046 + 0.598603i \(0.795723\pi\)
\(740\) −8.81232 8.25917i −0.323947 0.303613i
\(741\) 0 0
\(742\) −20.3811 + 48.2817i −0.748214 + 1.77248i
\(743\) 5.53668 0.203121 0.101561 0.994829i \(-0.467616\pi\)
0.101561 + 0.994829i \(0.467616\pi\)
\(744\) 0 0
\(745\) 1.41822 + 30.9005i 0.0519595 + 1.13211i
\(746\) −14.7500 + 34.9421i −0.540037 + 1.27932i
\(747\) 0 0
\(748\) 43.3354 + 0.583915i 1.58450 + 0.0213501i
\(749\) 22.6835 + 22.6835i 0.828837 + 0.828837i
\(750\) 0 0
\(751\) 30.2295i 1.10309i 0.834145 + 0.551546i \(0.185962\pi\)
−0.834145 + 0.551546i \(0.814038\pi\)
\(752\) −12.9898 0.350123i −0.473691 0.0127677i
\(753\) 0 0
\(754\) 4.15171 + 10.2173i 0.151196 + 0.372091i
\(755\) 18.1000 19.8414i 0.658728 0.722103i
\(756\) 0 0
\(757\) −25.8317 + 25.8317i −0.938870 + 0.938870i −0.998236 0.0593667i \(-0.981092\pi\)
0.0593667 + 0.998236i \(0.481092\pi\)
\(758\) 13.5498 32.0988i 0.492151 1.16588i
\(759\) 0 0
\(760\) 3.06488 7.97174i 0.111175 0.289165i
\(761\) 6.93351 0.251340 0.125670 0.992072i \(-0.459892\pi\)
0.125670 + 0.992072i \(0.459892\pi\)
\(762\) 0 0
\(763\) −51.4462 51.4462i −1.86248 1.86248i
\(764\) 5.49119 5.34518i 0.198664 0.193382i
\(765\) 0 0
\(766\) −5.56560 13.6968i −0.201093 0.494886i
\(767\) 12.5650i 0.453696i
\(768\) 0 0
\(769\) 18.4481 0.665257 0.332629 0.943058i \(-0.392064\pi\)
0.332629 + 0.943058i \(0.392064\pi\)
\(770\) −34.3985 74.6441i −1.23964 2.68999i
\(771\) 0 0
\(772\) 7.02080 + 7.21259i 0.252684 + 0.259587i
\(773\) 8.74138 + 8.74138i 0.314405 + 0.314405i 0.846614 0.532208i \(-0.178638\pi\)
−0.532208 + 0.846614i \(0.678638\pi\)
\(774\) 0 0
\(775\) −38.0558 + 3.50062i −1.36700 + 0.125746i
\(776\) −24.2010 10.6023i −0.868763 0.380601i
\(777\) 0 0
\(778\) 5.22255 12.3719i 0.187237 0.443556i
\(779\) 7.32440 + 7.32440i 0.262424 + 0.262424i
\(780\) 0 0
\(781\) 6.90351 6.90351i 0.247027 0.247027i
\(782\) 30.7352 12.4890i 1.09909 0.446606i
\(783\) 0 0
\(784\) −1.24531 + 46.2019i −0.0444752 + 1.65007i
\(785\) 27.8451 1.27799i 0.993836 0.0456134i
\(786\) 0 0
\(787\) 16.3355 16.3355i 0.582299 0.582299i −0.353235 0.935534i \(-0.614919\pi\)
0.935534 + 0.353235i \(0.114919\pi\)
\(788\) 19.8469 + 0.267424i 0.707018 + 0.00952659i
\(789\) 0 0
\(790\) 15.9994 + 5.90509i 0.569234 + 0.210094i
\(791\) 77.9168i 2.77040i
\(792\) 0 0
\(793\) 0.662406 0.0235227
\(794\) −47.6016 20.0940i −1.68932 0.713109i
\(795\) 0 0
\(796\) 19.7117 19.1875i 0.698662 0.680084i
\(797\) −11.3444 + 11.3444i −0.401841 + 0.401841i −0.878881 0.477040i \(-0.841710\pi\)
0.477040 + 0.878881i \(0.341710\pi\)
\(798\) 0 0
\(799\) 11.6672i 0.412757i
\(800\) 25.4593 12.3216i 0.900123 0.435635i
\(801\) 0 0
\(802\) 9.86901 + 24.2874i 0.348487 + 0.857618i
\(803\) 29.4685 + 29.4685i 1.03992 + 1.03992i
\(804\) 0 0
\(805\) −46.4801 42.4008i −1.63821 1.49443i
\(806\) 12.5396 29.7058i 0.441690 1.04634i
\(807\) 0 0
\(808\) −11.5175 29.4769i −0.405184 1.03699i
\(809\) −14.8157 −0.520893 −0.260446 0.965488i \(-0.583870\pi\)
−0.260446 + 0.965488i \(0.583870\pi\)
\(810\) 0 0
\(811\) −9.73571 + 9.73571i −0.341867 + 0.341867i −0.857069 0.515202i \(-0.827717\pi\)
0.515202 + 0.857069i \(0.327717\pi\)
\(812\) −0.303441 + 22.5200i −0.0106487 + 0.790295i
\(813\) 0 0
\(814\) −21.3494 + 8.67518i −0.748296 + 0.304065i
\(815\) −1.29036 28.1147i −0.0451994 0.984815i
\(816\) 0 0
\(817\) 10.3758i 0.363002i
\(818\) 3.43520 + 8.45396i 0.120109 + 0.295586i
\(819\) 0 0
\(820\) 1.11093 + 34.2859i 0.0387953 + 1.19731i
\(821\) −0.499371 + 0.499371i −0.0174282 + 0.0174282i −0.715767 0.698339i \(-0.753923\pi\)
0.698339 + 0.715767i \(0.253923\pi\)
\(822\) 0 0
\(823\) 33.6494i 1.17295i −0.809969 0.586473i \(-0.800516\pi\)
0.809969 0.586473i \(-0.199484\pi\)
\(824\) 41.9033 + 18.3576i 1.45977 + 0.639517i
\(825\) 0 0
\(826\) −9.97900 + 23.6397i −0.347214 + 0.822532i
\(827\) 11.7750 11.7750i 0.409456 0.409456i −0.472093 0.881549i \(-0.656501\pi\)
0.881549 + 0.472093i \(0.156501\pi\)
\(828\) 0 0
\(829\) 35.3882 35.3882i 1.22908 1.22908i 0.264772 0.964311i \(-0.414703\pi\)
0.964311 0.264772i \(-0.0852968\pi\)
\(830\) −23.6471 + 10.8974i −0.820802 + 0.378253i
\(831\) 0 0
\(832\) −0.964334 + 23.8445i −0.0334323 + 0.826660i
\(833\) 41.4977 1.43781
\(834\) 0 0
\(835\) −6.39422 + 7.00940i −0.221281 + 0.242570i
\(836\) −11.3666 11.6771i −0.393121 0.403859i
\(837\) 0 0
\(838\) 9.33354 22.1107i 0.322422 0.763800i
\(839\) 20.9084i 0.721838i 0.932597 + 0.360919i \(0.117537\pi\)
−0.932597 + 0.360919i \(0.882463\pi\)
\(840\) 0 0
\(841\) 22.1656i 0.764331i
\(842\) −44.0394 18.5903i −1.51770 0.640664i
\(843\) 0 0
\(844\) 36.2007 + 0.487779i 1.24608 + 0.0167901i
\(845\) 6.77587 + 6.18119i 0.233097 + 0.212639i
\(846\) 0 0
\(847\) −109.436 −3.76027
\(848\) −24.9797 + 23.6685i −0.857807 + 0.812779i
\(849\) 0 0
\(850\) −11.6749 22.5524i −0.400446 0.773542i
\(851\) −12.4736 + 12.4736i −0.427590 + 0.427590i
\(852\) 0 0
\(853\) −33.7697 + 33.7697i −1.15625 + 1.15625i −0.170976 + 0.985275i \(0.554692\pi\)
−0.985275 + 0.170976i \(0.945308\pi\)
\(854\) 1.24625 + 0.526076i 0.0426457 + 0.0180020i
\(855\) 0 0
\(856\) 7.66596 + 19.6196i 0.262017 + 0.670585i
\(857\) 44.3305i 1.51430i −0.653241 0.757150i \(-0.726591\pi\)
0.653241 0.757150i \(-0.273409\pi\)
\(858\) 0 0
\(859\) 31.2008 31.2008i 1.06456 1.06456i 0.0667892 0.997767i \(-0.478724\pi\)
0.997767 0.0667892i \(-0.0212755\pi\)
\(860\) 23.4979 25.0716i 0.801270 0.854935i
\(861\) 0 0
\(862\) −16.4545 + 6.68616i −0.560442 + 0.227732i
\(863\) 47.7067i 1.62396i −0.583689 0.811978i \(-0.698391\pi\)
0.583689 0.811978i \(-0.301609\pi\)
\(864\) 0 0
\(865\) −0.584527 12.7358i −0.0198745 0.433030i
\(866\) 2.47471 + 6.09019i 0.0840940 + 0.206953i
\(867\) 0 0
\(868\) 47.1841 45.9294i 1.60153 1.55895i
\(869\) 23.0095 23.0095i 0.780542 0.780542i
\(870\) 0 0
\(871\) 1.28834 0.0436536
\(872\) −17.3864 44.4973i −0.588778 1.50687i
\(873\) 0 0
\(874\) −11.4922 4.85120i −0.388731 0.164094i
\(875\) −29.0613 + 38.4028i −0.982450 + 1.29825i
\(876\) 0 0
\(877\) 11.6792 + 11.6792i 0.394379 + 0.394379i 0.876245 0.481866i \(-0.160041\pi\)
−0.481866 + 0.876245i \(0.660041\pi\)
\(878\) −9.29816 + 3.77824i −0.313798 + 0.127509i
\(879\) 0 0
\(880\) −1.02085 53.9577i −0.0344127 1.81891i
\(881\) 26.5637i 0.894953i 0.894296 + 0.447477i \(0.147677\pi\)
−0.894296 + 0.447477i \(0.852323\pi\)
\(882\) 0 0
\(883\) 23.1556 23.1556i 0.779249 0.779249i −0.200454 0.979703i \(-0.564242\pi\)
0.979703 + 0.200454i \(0.0642419\pi\)
\(884\) 21.4245 + 0.288681i 0.720584 + 0.00970938i
\(885\) 0 0
\(886\) 12.9926 30.7788i 0.436496 1.03404i
\(887\) −44.2415 −1.48549 −0.742743 0.669577i \(-0.766475\pi\)
−0.742743 + 0.669577i \(0.766475\pi\)
\(888\) 0 0
\(889\) 31.3730i 1.05222i
\(890\) −8.48445 + 22.9880i −0.284399 + 0.770560i
\(891\) 0 0
\(892\) 18.2066 17.7225i 0.609602 0.593393i
\(893\) 3.10203 3.10203i 0.103805 0.103805i
\(894\) 0 0
\(895\) 0.120900 + 2.63419i 0.00404123 + 0.0880512i
\(896\) −20.7514 + 44.0951i −0.693255 + 1.47311i
\(897\) 0 0
\(898\) 11.9009 + 29.2877i 0.397137 + 0.977344i
\(899\) 14.1291 14.1291i 0.471233 0.471233i
\(900\) 0 0
\(901\) 21.8474 + 21.8474i 0.727844 + 0.727844i
\(902\) 60.3005 + 25.4545i 2.00779 + 0.847544i
\(903\) 0 0
\(904\) 20.5302 46.8624i 0.682823 1.55862i
\(905\) 33.4683 1.53607i 1.11252 0.0510607i
\(906\) 0 0
\(907\) 36.0867 + 36.0867i 1.19824 + 1.19824i 0.974694 + 0.223545i \(0.0717629\pi\)
0.223545 + 0.974694i \(0.428237\pi\)
\(908\) −37.7392 0.508511i −1.25242 0.0168755i
\(909\) 0 0
\(910\) −17.0062 36.9031i −0.563750 1.22333i
\(911\) −4.93520 −0.163510 −0.0817552 0.996652i \(-0.526053\pi\)
−0.0817552 + 0.996652i \(0.526053\pi\)
\(912\) 0 0
\(913\) 49.6799i 1.64416i
\(914\) 37.9799 15.4328i 1.25626 0.510473i
\(915\) 0 0
\(916\) −3.09832 0.0417478i −0.102371 0.00137939i
\(917\) 42.6323 + 42.6323i 1.40784 + 1.40784i
\(918\) 0 0
\(919\) 28.2846 0.933023 0.466511 0.884515i \(-0.345511\pi\)
0.466511 + 0.884515i \(0.345511\pi\)
\(920\) −16.7829 37.7485i −0.553317 1.24453i
\(921\) 0 0
\(922\) 6.92085 + 2.92149i 0.227926 + 0.0962141i
\(923\) 3.41301 3.41301i 0.112341 0.112341i
\(924\) 0 0
\(925\) 10.3827 + 8.63350i 0.341382 + 0.283868i
\(926\) 24.2247 9.84355i 0.796074 0.323479i
\(927\) 0 0
\(928\) −6.11625 + 13.4645i −0.200776 + 0.441993i
\(929\) 27.7896i 0.911746i −0.890045 0.455873i \(-0.849327\pi\)
0.890045 0.455873i \(-0.150673\pi\)
\(930\) 0 0
\(931\) −11.0332 11.0332i −0.361599 0.361599i
\(932\) 23.8768 + 24.5290i 0.782110 + 0.803475i
\(933\) 0 0
\(934\) 32.9124 + 13.8933i 1.07693 + 0.454602i
\(935\) −48.4039 + 2.22156i −1.58298 + 0.0726528i
\(936\) 0 0
\(937\) 39.5362 1.29159 0.645796 0.763510i \(-0.276526\pi\)
0.645796 + 0.763510i \(0.276526\pi\)
\(938\) 2.42387 + 1.02318i 0.0791421 + 0.0334081i
\(939\) 0 0
\(940\) 14.5207 0.470501i 0.473614 0.0153460i
\(941\) 12.9497 + 12.9497i 0.422149 + 0.422149i 0.885943 0.463794i \(-0.153512\pi\)
−0.463794 + 0.885943i \(0.653512\pi\)
\(942\) 0 0
\(943\) 50.1033 1.63159
\(944\) −12.2306 + 11.5886i −0.398072 + 0.377176i
\(945\) 0 0
\(946\) −24.6814 60.7404i −0.802463 1.97484i
\(947\) 21.0330 + 21.0330i 0.683481 + 0.683481i 0.960783 0.277302i \(-0.0894401\pi\)
−0.277302 + 0.960783i \(0.589440\pi\)
\(948\) 0 0
\(949\) 14.5689 + 14.5689i 0.472925 + 0.472925i
\(950\) −2.89206 + 9.10020i −0.0938308 + 0.295250i
\(951\) 0 0
\(952\) 40.0787 + 17.5582i 1.29896 + 0.569066i
\(953\) 25.8627i 0.837774i −0.908038 0.418887i \(-0.862420\pi\)
0.908038 0.418887i \(-0.137580\pi\)
\(954\) 0 0
\(955\) −5.77413 + 6.32965i −0.186847 + 0.204823i
\(956\) −25.5894 + 24.9090i −0.827621 + 0.805614i
\(957\) 0 0
\(958\) −27.8567 + 11.3194i −0.900009 + 0.365712i
\(959\) −76.6628 −2.47557
\(960\) 0 0
\(961\) −27.4199 −0.884512
\(962\) −10.5549 + 4.28890i −0.340303 + 0.138280i
\(963\) 0 0
\(964\) 7.33087 7.13594i 0.236111 0.229833i
\(965\) −8.31389 7.58423i −0.267634 0.244145i
\(966\) 0 0
\(967\) 29.5467i 0.950157i 0.879943 + 0.475079i \(0.157580\pi\)
−0.879943 + 0.475079i \(0.842420\pi\)
\(968\) −65.8195 28.8352i −2.11552 0.926797i
\(969\) 0 0
\(970\) 27.7128 + 10.2283i 0.889805 + 0.328411i
\(971\) −4.28841 4.28841i −0.137621 0.137621i 0.634940 0.772561i \(-0.281025\pi\)
−0.772561 + 0.634940i \(0.781025\pi\)
\(972\) 0 0
\(973\) 21.4630 + 21.4630i 0.688071 + 0.688071i
\(974\) 20.3391 + 50.0542i 0.651708 + 1.60384i
\(975\) 0 0
\(976\) 0.610930 + 0.644775i 0.0195554 + 0.0206388i
\(977\) 14.9714 0.478976 0.239488 0.970899i \(-0.423020\pi\)
0.239488 + 0.970899i \(0.423020\pi\)
\(978\) 0 0
\(979\) 33.0601 + 33.0601i 1.05660 + 1.05660i
\(980\) −1.67346 51.6470i −0.0534568 1.64980i
\(981\) 0 0
\(982\) 20.7389 + 8.75449i 0.661806 + 0.279367i
\(983\) 9.58755 0.305795 0.152898 0.988242i \(-0.451139\pi\)
0.152898 + 0.988242i \(0.451139\pi\)
\(984\) 0 0
\(985\) −22.1682 + 1.01744i −0.706338 + 0.0324183i
\(986\) 12.2327 + 5.16378i 0.389569 + 0.164448i
\(987\) 0 0
\(988\) −5.61949 5.77299i −0.178780 0.183663i
\(989\) −35.4883 35.4883i −1.12846 1.12846i
\(990\) 0 0
\(991\) 43.4685i 1.38082i −0.723417 0.690412i \(-0.757429\pi\)
0.723417 0.690412i \(-0.242571\pi\)
\(992\) 40.4803 15.1914i 1.28525 0.482328i
\(993\) 0 0
\(994\) 9.13181 3.71064i 0.289643 0.117694i
\(995\) −20.7273 + 22.7215i −0.657101 + 0.720320i
\(996\) 0 0
\(997\) −1.90040 + 1.90040i −0.0601862 + 0.0601862i −0.736559 0.676373i \(-0.763551\pi\)
0.676373 + 0.736559i \(0.263551\pi\)
\(998\) −35.5474 15.0056i −1.12523 0.474993i
\(999\) 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 720.2.u.a.539.5 yes 96
3.2 odd 2 inner 720.2.u.a.539.44 yes 96
4.3 odd 2 2880.2.u.a.719.13 96
5.4 even 2 inner 720.2.u.a.539.43 yes 96
12.11 even 2 2880.2.u.a.719.36 96
15.14 odd 2 inner 720.2.u.a.539.6 yes 96
16.3 odd 4 inner 720.2.u.a.179.6 yes 96
16.13 even 4 2880.2.u.a.2159.37 96
20.19 odd 2 2880.2.u.a.719.12 96
48.29 odd 4 2880.2.u.a.2159.12 96
48.35 even 4 inner 720.2.u.a.179.43 yes 96
60.59 even 2 2880.2.u.a.719.37 96
80.19 odd 4 inner 720.2.u.a.179.44 yes 96
80.29 even 4 2880.2.u.a.2159.36 96
240.29 odd 4 2880.2.u.a.2159.13 96
240.179 even 4 inner 720.2.u.a.179.5 96
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
720.2.u.a.179.5 96 240.179 even 4 inner
720.2.u.a.179.6 yes 96 16.3 odd 4 inner
720.2.u.a.179.43 yes 96 48.35 even 4 inner
720.2.u.a.179.44 yes 96 80.19 odd 4 inner
720.2.u.a.539.5 yes 96 1.1 even 1 trivial
720.2.u.a.539.6 yes 96 15.14 odd 2 inner
720.2.u.a.539.43 yes 96 5.4 even 2 inner
720.2.u.a.539.44 yes 96 3.2 odd 2 inner
2880.2.u.a.719.12 96 20.19 odd 2
2880.2.u.a.719.13 96 4.3 odd 2
2880.2.u.a.719.36 96 12.11 even 2
2880.2.u.a.719.37 96 60.59 even 2
2880.2.u.a.2159.12 96 48.29 odd 4
2880.2.u.a.2159.13 96 240.29 odd 4
2880.2.u.a.2159.36 96 80.29 even 4
2880.2.u.a.2159.37 96 16.13 even 4