Properties

Label 324.3.f.o.271.1
Level $324$
Weight $3$
Character 324.271
Analytic conductor $8.828$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [324,3,Mod(55,324)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(324, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 4]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("324.55");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 324 = 2^{2} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 324.f (of order \(6\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(8.82836056527\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.207360000.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + 6x^{6} + 32x^{4} + 24x^{2} + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{4}\cdot 3^{2} \)
Twist minimal: no (minimal twist has level 108)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 271.1
Root \(0.437016 + 0.756934i\) of defining polynomial
Character \(\chi\) \(=\) 324.271
Dual form 324.3.f.o.55.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.85123 + 0.756934i) q^{2} +(2.85410 - 2.80252i) q^{4} +(-3.70246 + 6.41285i) q^{5} +(-8.20820 + 4.73901i) q^{7} +(-3.16228 + 7.34847i) q^{8} +O(q^{10})\) \(q+(-1.85123 + 0.756934i) q^{2} +(2.85410 - 2.80252i) q^{4} +(-3.70246 + 6.41285i) q^{5} +(-8.20820 + 4.73901i) q^{7} +(-3.16228 + 7.34847i) q^{8} +(2.00000 - 14.6742i) q^{10} +(-5.86319 + 3.38511i) q^{11} +(7.20820 - 12.4850i) q^{13} +(11.6082 - 14.9861i) q^{14} +(0.291796 - 15.9973i) q^{16} +17.8933 q^{17} +5.19615i q^{19} +(7.40492 + 28.6791i) q^{20} +(8.29180 - 10.7047i) q^{22} +(-21.5958 - 12.4683i) q^{23} +(-14.9164 - 25.8360i) q^{25} +(-3.89374 + 28.5687i) q^{26} +(-10.1459 + 36.5292i) q^{28} +(-14.8098 - 25.6514i) q^{29} +(-14.8328 - 8.56373i) q^{31} +(11.5687 + 29.8356i) q^{32} +(-33.1246 + 13.5440i) q^{34} -70.1839i q^{35} +6.41641 q^{37} +(-3.93314 - 9.61927i) q^{38} +(-35.4164 - 47.4866i) q^{40} +(-4.32145 + 7.48497i) q^{41} +(43.4164 - 25.0665i) q^{43} +(-7.24730 + 26.0931i) q^{44} +(49.4164 + 6.73516i) q^{46} +(45.0485 - 26.0088i) q^{47} +(20.4164 - 35.3623i) q^{49} +(47.1698 + 36.5376i) q^{50} +(-14.4164 - 55.8345i) q^{52} -82.6921 q^{53} -50.1329i q^{55} +(-8.86784 - 75.3038i) q^{56} +(46.8328 + 36.2765i) q^{58} +(-72.5075 - 41.8622i) q^{59} +(4.20820 + 7.28882i) q^{61} +(33.9411 + 4.62597i) q^{62} +(-44.0000 - 46.4758i) q^{64} +(53.3762 + 92.4502i) q^{65} +(25.1656 + 14.5294i) q^{67} +(51.0693 - 50.1463i) q^{68} +(53.1246 + 129.927i) q^{70} -113.287i q^{71} +2.16718 q^{73} +(-11.8782 + 4.85680i) q^{74} +(14.5623 + 14.8303i) q^{76} +(32.0841 - 55.5714i) q^{77} +(-129.457 + 74.7423i) q^{79} +(101.508 + 61.1007i) q^{80} +(2.33437 - 17.1275i) q^{82} +(11.7264 - 6.77022i) q^{83} +(-66.2492 + 114.747i) q^{85} +(-61.4001 + 79.2672i) q^{86} +(-6.33437 - 53.7901i) q^{88} +17.8933 q^{89} +136.639i q^{91} +(-96.5792 + 24.9366i) q^{92} +(-63.7082 + 82.2469i) q^{94} +(-33.3221 - 19.2385i) q^{95} +(69.1656 + 119.798i) q^{97} +(-11.0286 + 80.9175i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 4 q^{4} - 12 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 4 q^{4} - 12 q^{7} + 16 q^{10} + 4 q^{13} + 56 q^{16} + 120 q^{22} - 12 q^{25} - 108 q^{28} + 96 q^{31} - 104 q^{34} - 56 q^{37} - 176 q^{40} + 240 q^{43} + 288 q^{46} + 56 q^{49} - 8 q^{52} + 160 q^{58} - 20 q^{61} - 352 q^{64} - 228 q^{67} + 264 q^{70} + 232 q^{73} + 36 q^{76} - 660 q^{79} + 448 q^{82} - 208 q^{85} - 480 q^{88} - 456 q^{94} + 124 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).

\(n\) \(163\) \(245\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.85123 + 0.756934i −0.925615 + 0.378467i
\(3\) 0 0
\(4\) 2.85410 2.80252i 0.713525 0.700629i
\(5\) −3.70246 + 6.41285i −0.740492 + 1.28257i 0.211780 + 0.977317i \(0.432074\pi\)
−0.952272 + 0.305252i \(0.901259\pi\)
\(6\) 0 0
\(7\) −8.20820 + 4.73901i −1.17260 + 0.677001i −0.954291 0.298878i \(-0.903388\pi\)
−0.218309 + 0.975880i \(0.570054\pi\)
\(8\) −3.16228 + 7.34847i −0.395285 + 0.918559i
\(9\) 0 0
\(10\) 2.00000 14.6742i 0.200000 1.46742i
\(11\) −5.86319 + 3.38511i −0.533017 + 0.307737i −0.742244 0.670130i \(-0.766238\pi\)
0.209227 + 0.977867i \(0.432905\pi\)
\(12\) 0 0
\(13\) 7.20820 12.4850i 0.554477 0.960383i −0.443467 0.896291i \(-0.646252\pi\)
0.997944 0.0640919i \(-0.0204151\pi\)
\(14\) 11.6082 14.9861i 0.829154 1.07043i
\(15\) 0 0
\(16\) 0.291796 15.9973i 0.0182373 0.999834i
\(17\) 17.8933 1.05255 0.526274 0.850315i \(-0.323589\pi\)
0.526274 + 0.850315i \(0.323589\pi\)
\(18\) 0 0
\(19\) 5.19615i 0.273482i 0.990607 + 0.136741i \(0.0436628\pi\)
−0.990607 + 0.136741i \(0.956337\pi\)
\(20\) 7.40492 + 28.6791i 0.370246 + 1.43396i
\(21\) 0 0
\(22\) 8.29180 10.7047i 0.376900 0.486576i
\(23\) −21.5958 12.4683i −0.938946 0.542101i −0.0493164 0.998783i \(-0.515704\pi\)
−0.889630 + 0.456682i \(0.849038\pi\)
\(24\) 0 0
\(25\) −14.9164 25.8360i −0.596656 1.03344i
\(26\) −3.89374 + 28.5687i −0.149759 + 1.09880i
\(27\) 0 0
\(28\) −10.1459 + 36.5292i −0.362354 + 1.30462i
\(29\) −14.8098 25.6514i −0.510684 0.884531i −0.999923 0.0123811i \(-0.996059\pi\)
0.489239 0.872150i \(-0.337274\pi\)
\(30\) 0 0
\(31\) −14.8328 8.56373i −0.478478 0.276249i 0.241304 0.970450i \(-0.422425\pi\)
−0.719782 + 0.694200i \(0.755758\pi\)
\(32\) 11.5687 + 29.8356i 0.361523 + 0.932363i
\(33\) 0 0
\(34\) −33.1246 + 13.5440i −0.974253 + 0.398354i
\(35\) 70.1839i 2.00526i
\(36\) 0 0
\(37\) 6.41641 0.173416 0.0867082 0.996234i \(-0.472365\pi\)
0.0867082 + 0.996234i \(0.472365\pi\)
\(38\) −3.93314 9.61927i −0.103504 0.253139i
\(39\) 0 0
\(40\) −35.4164 47.4866i −0.885410 1.18717i
\(41\) −4.32145 + 7.48497i −0.105401 + 0.182560i −0.913902 0.405935i \(-0.866946\pi\)
0.808501 + 0.588495i \(0.200279\pi\)
\(42\) 0 0
\(43\) 43.4164 25.0665i 1.00968 0.582941i 0.0985848 0.995129i \(-0.468568\pi\)
0.911099 + 0.412187i \(0.135235\pi\)
\(44\) −7.24730 + 26.0931i −0.164711 + 0.593026i
\(45\) 0 0
\(46\) 49.4164 + 6.73516i 1.07427 + 0.146416i
\(47\) 45.0485 26.0088i 0.958479 0.553378i 0.0627743 0.998028i \(-0.480005\pi\)
0.895705 + 0.444650i \(0.146672\pi\)
\(48\) 0 0
\(49\) 20.4164 35.3623i 0.416661 0.721679i
\(50\) 47.1698 + 36.5376i 0.943396 + 0.730752i
\(51\) 0 0
\(52\) −14.4164 55.8345i −0.277239 1.07374i
\(53\) −82.6921 −1.56023 −0.780114 0.625637i \(-0.784839\pi\)
−0.780114 + 0.625637i \(0.784839\pi\)
\(54\) 0 0
\(55\) 50.1329i 0.911508i
\(56\) −8.86784 75.3038i −0.158354 1.34471i
\(57\) 0 0
\(58\) 46.8328 + 36.2765i 0.807462 + 0.625458i
\(59\) −72.5075 41.8622i −1.22894 0.709529i −0.262132 0.965032i \(-0.584425\pi\)
−0.966808 + 0.255503i \(0.917759\pi\)
\(60\) 0 0
\(61\) 4.20820 + 7.28882i 0.0689869 + 0.119489i 0.898456 0.439064i \(-0.144690\pi\)
−0.829469 + 0.558553i \(0.811357\pi\)
\(62\) 33.9411 + 4.62597i 0.547438 + 0.0746124i
\(63\) 0 0
\(64\) −44.0000 46.4758i −0.687500 0.726184i
\(65\) 53.3762 + 92.4502i 0.821172 + 1.42231i
\(66\) 0 0
\(67\) 25.1656 + 14.5294i 0.375606 + 0.216856i 0.675905 0.736989i \(-0.263753\pi\)
−0.300299 + 0.953845i \(0.597086\pi\)
\(68\) 51.0693 50.1463i 0.751019 0.737445i
\(69\) 0 0
\(70\) 53.1246 + 129.927i 0.758923 + 1.85609i
\(71\) 113.287i 1.59559i −0.602928 0.797796i \(-0.705999\pi\)
0.602928 0.797796i \(-0.294001\pi\)
\(72\) 0 0
\(73\) 2.16718 0.0296875 0.0148437 0.999890i \(-0.495275\pi\)
0.0148437 + 0.999890i \(0.495275\pi\)
\(74\) −11.8782 + 4.85680i −0.160517 + 0.0656324i
\(75\) 0 0
\(76\) 14.5623 + 14.8303i 0.191609 + 0.195136i
\(77\) 32.0841 55.5714i 0.416677 0.721706i
\(78\) 0 0
\(79\) −129.457 + 74.7423i −1.63870 + 0.946105i −0.657421 + 0.753524i \(0.728352\pi\)
−0.981281 + 0.192581i \(0.938314\pi\)
\(80\) 101.508 + 61.1007i 1.26885 + 0.763759i
\(81\) 0 0
\(82\) 2.33437 17.1275i 0.0284679 0.208871i
\(83\) 11.7264 6.77022i 0.141282 0.0815690i −0.427693 0.903924i \(-0.640674\pi\)
0.568975 + 0.822355i \(0.307340\pi\)
\(84\) 0 0
\(85\) −66.2492 + 114.747i −0.779403 + 1.34996i
\(86\) −61.4001 + 79.2672i −0.713954 + 0.921711i
\(87\) 0 0
\(88\) −6.33437 53.7901i −0.0719815 0.611251i
\(89\) 17.8933 0.201048 0.100524 0.994935i \(-0.467948\pi\)
0.100524 + 0.994935i \(0.467948\pi\)
\(90\) 0 0
\(91\) 136.639i 1.50153i
\(92\) −96.5792 + 24.9366i −1.04977 + 0.271050i
\(93\) 0 0
\(94\) −63.7082 + 82.2469i −0.677747 + 0.874967i
\(95\) −33.3221 19.2385i −0.350759 0.202511i
\(96\) 0 0
\(97\) 69.1656 + 119.798i 0.713048 + 1.23503i 0.963708 + 0.266960i \(0.0860191\pi\)
−0.250660 + 0.968075i \(0.580648\pi\)
\(98\) −11.0286 + 80.9175i −0.112536 + 0.825689i
\(99\) 0 0
\(100\) −114.979 31.9350i −1.14979 0.319350i
\(101\) −48.7510 84.4391i −0.482683 0.836031i 0.517120 0.855913i \(-0.327004\pi\)
−0.999802 + 0.0198821i \(0.993671\pi\)
\(102\) 0 0
\(103\) 36.7918 + 21.2418i 0.357202 + 0.206231i 0.667853 0.744294i \(-0.267214\pi\)
−0.310651 + 0.950524i \(0.600547\pi\)
\(104\) 68.9511 + 92.4502i 0.662991 + 0.888944i
\(105\) 0 0
\(106\) 153.082 62.5924i 1.44417 0.590495i
\(107\) 97.2648i 0.909017i 0.890742 + 0.454509i \(0.150185\pi\)
−0.890742 + 0.454509i \(0.849815\pi\)
\(108\) 0 0
\(109\) −96.8328 −0.888374 −0.444187 0.895934i \(-0.646507\pi\)
−0.444187 + 0.895934i \(0.646507\pi\)
\(110\) 37.9473 + 92.8076i 0.344976 + 0.843705i
\(111\) 0 0
\(112\) 73.4164 + 132.692i 0.655504 + 1.18475i
\(113\) −19.4350 + 33.6625i −0.171991 + 0.297898i −0.939116 0.343600i \(-0.888353\pi\)
0.767125 + 0.641498i \(0.221687\pi\)
\(114\) 0 0
\(115\) 159.915 92.3269i 1.39056 0.802842i
\(116\) −114.157 31.7069i −0.984114 0.273335i
\(117\) 0 0
\(118\) 165.915 + 22.6132i 1.40606 + 0.191637i
\(119\) −146.872 + 84.7965i −1.23422 + 0.712576i
\(120\) 0 0
\(121\) −37.5820 + 65.0940i −0.310595 + 0.537967i
\(122\) −13.3075 10.3080i −0.109078 0.0844914i
\(123\) 0 0
\(124\) −66.3344 + 17.1275i −0.534955 + 0.138125i
\(125\) 35.7866 0.286293
\(126\) 0 0
\(127\) 99.0165i 0.779657i −0.920887 0.389829i \(-0.872534\pi\)
0.920887 0.389829i \(-0.127466\pi\)
\(128\) 116.633 + 52.7323i 0.911197 + 0.411971i
\(129\) 0 0
\(130\) −168.790 130.744i −1.29839 1.00573i
\(131\) 46.9055 + 27.0809i 0.358057 + 0.206724i 0.668228 0.743956i \(-0.267053\pi\)
−0.310171 + 0.950681i \(0.600386\pi\)
\(132\) 0 0
\(133\) −24.6246 42.6511i −0.185147 0.320685i
\(134\) −57.5851 7.84850i −0.429740 0.0585709i
\(135\) 0 0
\(136\) −56.5836 + 131.488i −0.416056 + 0.966826i
\(137\) 2.77972 + 4.81461i 0.0202899 + 0.0351432i 0.875992 0.482325i \(-0.160208\pi\)
−0.855702 + 0.517469i \(0.826874\pi\)
\(138\) 0 0
\(139\) −132.084 76.2585i −0.950242 0.548622i −0.0570857 0.998369i \(-0.518181\pi\)
−0.893156 + 0.449747i \(0.851514\pi\)
\(140\) −196.692 200.312i −1.40494 1.43080i
\(141\) 0 0
\(142\) 85.7508 + 209.720i 0.603879 + 1.47690i
\(143\) 97.6023i 0.682534i
\(144\) 0 0
\(145\) 219.331 1.51263
\(146\) −4.01196 + 1.64042i −0.0274791 + 0.0112357i
\(147\) 0 0
\(148\) 18.3131 17.9821i 0.123737 0.121501i
\(149\) −68.4897 + 118.628i −0.459663 + 0.796159i −0.998943 0.0459672i \(-0.985363\pi\)
0.539280 + 0.842126i \(0.318696\pi\)
\(150\) 0 0
\(151\) 67.5395 38.9939i 0.447281 0.258238i −0.259400 0.965770i \(-0.583525\pi\)
0.706681 + 0.707532i \(0.250191\pi\)
\(152\) −38.1838 16.4317i −0.251209 0.108103i
\(153\) 0 0
\(154\) −17.3313 + 127.161i −0.112541 + 0.825720i
\(155\) 109.836 63.4137i 0.708618 0.409121i
\(156\) 0 0
\(157\) 36.0820 62.4959i 0.229822 0.398063i −0.727933 0.685648i \(-0.759519\pi\)
0.957755 + 0.287585i \(0.0928523\pi\)
\(158\) 183.080 236.356i 1.15874 1.49592i
\(159\) 0 0
\(160\) −234.164 36.2765i −1.46353 0.226728i
\(161\) 236.350 1.46801
\(162\) 0 0
\(163\) 56.5785i 0.347108i −0.984824 0.173554i \(-0.944475\pi\)
0.984824 0.173554i \(-0.0555250\pi\)
\(164\) 8.64290 + 33.4738i 0.0527006 + 0.204109i
\(165\) 0 0
\(166\) −16.5836 + 21.4093i −0.0999012 + 0.128972i
\(167\) 174.623 + 100.819i 1.04565 + 0.603705i 0.921428 0.388550i \(-0.127024\pi\)
0.124220 + 0.992255i \(0.460357\pi\)
\(168\) 0 0
\(169\) −19.4164 33.6302i −0.114890 0.198995i
\(170\) 35.7866 262.569i 0.210509 1.54453i
\(171\) 0 0
\(172\) 53.6656 193.217i 0.312009 1.12336i
\(173\) −46.2750 80.1506i −0.267485 0.463298i 0.700726 0.713430i \(-0.252859\pi\)
−0.968212 + 0.250132i \(0.919526\pi\)
\(174\) 0 0
\(175\) 244.874 + 141.378i 1.39928 + 0.807874i
\(176\) 52.4419 + 94.7831i 0.297965 + 0.538540i
\(177\) 0 0
\(178\) −33.1246 + 13.5440i −0.186093 + 0.0760902i
\(179\) 4.28851i 0.0239581i −0.999928 0.0119791i \(-0.996187\pi\)
0.999928 0.0119791i \(-0.00381315\pi\)
\(180\) 0 0
\(181\) −289.748 −1.60082 −0.800408 0.599456i \(-0.795384\pi\)
−0.800408 + 0.599456i \(0.795384\pi\)
\(182\) −103.427 252.950i −0.568278 1.38984i
\(183\) 0 0
\(184\) 159.915 119.268i 0.869102 0.648193i
\(185\) −23.7565 + 41.1474i −0.128413 + 0.222419i
\(186\) 0 0
\(187\) −104.912 + 60.5708i −0.561025 + 0.323908i
\(188\) 55.6830 200.481i 0.296186 1.06639i
\(189\) 0 0
\(190\) 76.2492 + 10.3923i 0.401312 + 0.0546963i
\(191\) 80.2276 46.3194i 0.420040 0.242510i −0.275055 0.961429i \(-0.588696\pi\)
0.695094 + 0.718919i \(0.255363\pi\)
\(192\) 0 0
\(193\) 121.582 210.586i 0.629959 1.09112i −0.357601 0.933875i \(-0.616405\pi\)
0.987559 0.157246i \(-0.0502616\pi\)
\(194\) −218.721 169.421i −1.12743 0.873302i
\(195\) 0 0
\(196\) −40.8328 158.145i −0.208331 0.806861i
\(197\) −139.432 −0.707779 −0.353890 0.935287i \(-0.615141\pi\)
−0.353890 + 0.935287i \(0.615141\pi\)
\(198\) 0 0
\(199\) 110.993i 0.557756i −0.960327 0.278878i \(-0.910038\pi\)
0.960327 0.278878i \(-0.0899624\pi\)
\(200\) 237.025 27.9122i 1.18512 0.139561i
\(201\) 0 0
\(202\) 154.164 + 119.415i 0.763189 + 0.591163i
\(203\) 243.124 + 140.368i 1.19766 + 0.691467i
\(204\) 0 0
\(205\) −32.0000 55.4256i −0.156098 0.270369i
\(206\) −84.1887 11.4744i −0.408683 0.0557010i
\(207\) 0 0
\(208\) −197.623 118.955i −0.950111 0.571900i
\(209\) −17.5896 30.4660i −0.0841606 0.145770i
\(210\) 0 0
\(211\) −229.579 132.547i −1.08805 0.628187i −0.154995 0.987915i \(-0.549536\pi\)
−0.933057 + 0.359728i \(0.882869\pi\)
\(212\) −236.012 + 231.746i −1.11326 + 1.09314i
\(213\) 0 0
\(214\) −73.6231 180.060i −0.344033 0.841400i
\(215\) 371.230i 1.72665i
\(216\) 0 0
\(217\) 162.334 0.748085
\(218\) 179.260 73.2960i 0.822293 0.336220i
\(219\) 0 0
\(220\) −140.498 143.085i −0.638629 0.650384i
\(221\) 128.979 223.397i 0.583613 1.01085i
\(222\) 0 0
\(223\) −275.331 + 158.963i −1.23467 + 0.712837i −0.968000 0.250951i \(-0.919257\pi\)
−0.266670 + 0.963788i \(0.585923\pi\)
\(224\) −236.350 190.072i −1.05513 0.848538i
\(225\) 0 0
\(226\) 10.4984 77.0280i 0.0464533 0.340832i
\(227\) −215.958 + 124.683i −0.951355 + 0.549265i −0.893502 0.449060i \(-0.851759\pi\)
−0.0578535 + 0.998325i \(0.518426\pi\)
\(228\) 0 0
\(229\) −76.1672 + 131.925i −0.332608 + 0.576094i −0.983022 0.183486i \(-0.941262\pi\)
0.650415 + 0.759579i \(0.274595\pi\)
\(230\) −226.154 + 291.963i −0.983277 + 1.26941i
\(231\) 0 0
\(232\) 235.331 27.7128i 1.01436 0.119452i
\(233\) −346.793 −1.48838 −0.744191 0.667966i \(-0.767165\pi\)
−0.744191 + 0.667966i \(0.767165\pi\)
\(234\) 0 0
\(235\) 385.186i 1.63909i
\(236\) −324.263 + 83.7244i −1.37400 + 0.354764i
\(237\) 0 0
\(238\) 207.708 268.150i 0.872724 1.12668i
\(239\) −90.0970 52.0175i −0.376975 0.217647i 0.299526 0.954088i \(-0.403171\pi\)
−0.676501 + 0.736441i \(0.736505\pi\)
\(240\) 0 0
\(241\) −140.913 244.069i −0.584702 1.01273i −0.994912 0.100743i \(-0.967878\pi\)
0.410210 0.911991i \(-0.365455\pi\)
\(242\) 20.3011 148.951i 0.0838889 0.615500i
\(243\) 0 0
\(244\) 32.4377 + 9.00948i 0.132941 + 0.0369241i
\(245\) 151.182 + 261.855i 0.617069 + 1.06879i
\(246\) 0 0
\(247\) 64.8738 + 37.4549i 0.262647 + 0.151639i
\(248\) 109.836 81.9176i 0.442886 0.330313i
\(249\) 0 0
\(250\) −66.2492 + 27.0881i −0.264997 + 0.108352i
\(251\) 271.484i 1.08161i 0.841148 + 0.540804i \(0.181880\pi\)
−0.841148 + 0.540804i \(0.818120\pi\)
\(252\) 0 0
\(253\) 168.827 0.667299
\(254\) 74.9489 + 183.302i 0.295075 + 0.721662i
\(255\) 0 0
\(256\) −255.830 9.33592i −0.999335 0.0364684i
\(257\) 229.552 397.597i 0.893200 1.54707i 0.0571840 0.998364i \(-0.481788\pi\)
0.836016 0.548705i \(-0.184879\pi\)
\(258\) 0 0
\(259\) −52.6672 + 30.4074i −0.203348 + 0.117403i
\(260\) 411.434 + 114.275i 1.58244 + 0.439518i
\(261\) 0 0
\(262\) −107.331 14.6286i −0.409661 0.0558343i
\(263\) 176.480 101.891i 0.671027 0.387418i −0.125439 0.992101i \(-0.540034\pi\)
0.796466 + 0.604684i \(0.206701\pi\)
\(264\) 0 0
\(265\) 306.164 530.292i 1.15534 2.00110i
\(266\) 77.8699 + 60.3177i 0.292744 + 0.226758i
\(267\) 0 0
\(268\) 112.544 29.0588i 0.419941 0.108428i
\(269\) 323.363 1.20209 0.601047 0.799213i \(-0.294750\pi\)
0.601047 + 0.799213i \(0.294750\pi\)
\(270\) 0 0
\(271\) 104.928i 0.387190i 0.981082 + 0.193595i \(0.0620148\pi\)
−0.981082 + 0.193595i \(0.937985\pi\)
\(272\) 5.22120 286.245i 0.0191956 1.05237i
\(273\) 0 0
\(274\) −8.79024 6.80889i −0.0320812 0.0248500i
\(275\) 174.915 + 100.987i 0.636056 + 0.367227i
\(276\) 0 0
\(277\) 24.4164 + 42.2905i 0.0881459 + 0.152673i 0.906727 0.421717i \(-0.138573\pi\)
−0.818582 + 0.574390i \(0.805239\pi\)
\(278\) 302.240 + 41.1934i 1.08719 + 0.148178i
\(279\) 0 0
\(280\) 515.745 + 221.941i 1.84194 + 0.792647i
\(281\) −14.8098 25.6514i −0.0527040 0.0912861i 0.838470 0.544948i \(-0.183451\pi\)
−0.891174 + 0.453662i \(0.850117\pi\)
\(282\) 0 0
\(283\) −333.580 192.593i −1.17873 0.680540i −0.223009 0.974816i \(-0.571588\pi\)
−0.955720 + 0.294276i \(0.904921\pi\)
\(284\) −317.489 323.333i −1.11792 1.13850i
\(285\) 0 0
\(286\) −73.8785 180.684i −0.258316 0.631763i
\(287\) 81.9176i 0.285427i
\(288\) 0 0
\(289\) 31.1703 0.107856
\(290\) −406.033 + 166.019i −1.40011 + 0.572480i
\(291\) 0 0
\(292\) 6.18536 6.07357i 0.0211828 0.0207999i
\(293\) −140.705 + 243.708i −0.480222 + 0.831768i −0.999743 0.0226894i \(-0.992777\pi\)
0.519521 + 0.854458i \(0.326110\pi\)
\(294\) 0 0
\(295\) 536.912 309.986i 1.82004 1.05080i
\(296\) −20.2905 + 47.1508i −0.0685489 + 0.159293i
\(297\) 0 0
\(298\) 36.9969 271.449i 0.124151 0.910904i
\(299\) −311.333 + 179.748i −1.04125 + 0.601165i
\(300\) 0 0
\(301\) −237.580 + 411.501i −0.789304 + 1.36711i
\(302\) −95.5152 + 123.310i −0.316276 + 0.408310i
\(303\) 0 0
\(304\) 83.1246 + 1.51622i 0.273436 + 0.00498756i
\(305\) −62.3228 −0.204337
\(306\) 0 0
\(307\) 553.961i 1.80443i −0.431282 0.902217i \(-0.641939\pi\)
0.431282 0.902217i \(-0.358061\pi\)
\(308\) −64.1683 248.523i −0.208339 0.806892i
\(309\) 0 0
\(310\) −155.331 + 200.532i −0.501069 + 0.646877i
\(311\) 13.5833 + 7.84235i 0.0436764 + 0.0252166i 0.521679 0.853142i \(-0.325306\pi\)
−0.478003 + 0.878358i \(0.658639\pi\)
\(312\) 0 0
\(313\) 154.080 + 266.875i 0.492270 + 0.852637i 0.999960 0.00890304i \(-0.00283396\pi\)
−0.507690 + 0.861540i \(0.669501\pi\)
\(314\) −19.4909 + 143.006i −0.0620728 + 0.455433i
\(315\) 0 0
\(316\) −160.018 + 576.129i −0.506387 + 1.82319i
\(317\) 248.053 + 429.641i 0.782502 + 1.35533i 0.930480 + 0.366343i \(0.119390\pi\)
−0.147977 + 0.988991i \(0.547276\pi\)
\(318\) 0 0
\(319\) 173.666 + 100.266i 0.544406 + 0.314313i
\(320\) 460.950 110.091i 1.44047 0.344033i
\(321\) 0 0
\(322\) −437.538 + 178.901i −1.35881 + 0.555594i
\(323\) 92.9763i 0.287852i
\(324\) 0 0
\(325\) −430.082 −1.32333
\(326\) 42.8262 + 104.740i 0.131369 + 0.321288i
\(327\) 0 0
\(328\) −41.3375 55.4256i −0.126029 0.168981i
\(329\) −246.512 + 426.970i −0.749275 + 1.29778i
\(330\) 0 0
\(331\) 74.9164 43.2530i 0.226334 0.130674i −0.382546 0.923936i \(-0.624953\pi\)
0.608879 + 0.793263i \(0.291619\pi\)
\(332\) 14.4946 52.1863i 0.0436584 0.157188i
\(333\) 0 0
\(334\) −399.580 54.4604i −1.19635 0.163055i
\(335\) −186.349 + 107.589i −0.556267 + 0.321161i
\(336\) 0 0
\(337\) −160.330 + 277.699i −0.475756 + 0.824033i −0.999614 0.0277721i \(-0.991159\pi\)
0.523858 + 0.851805i \(0.324492\pi\)
\(338\) 61.4001 + 47.5603i 0.181657 + 0.140711i
\(339\) 0 0
\(340\) 132.498 + 513.164i 0.389701 + 1.50931i
\(341\) 115.957 0.340049
\(342\) 0 0
\(343\) 77.4087i 0.225681i
\(344\) 46.9055 + 398.311i 0.136353 + 1.15788i
\(345\) 0 0
\(346\) 146.334 + 113.350i 0.422932 + 0.327601i
\(347\) −584.358 337.379i −1.68403 0.972275i −0.958936 0.283624i \(-0.908463\pi\)
−0.725093 0.688650i \(-0.758203\pi\)
\(348\) 0 0
\(349\) −76.9590 133.297i −0.220513 0.381939i 0.734451 0.678662i \(-0.237440\pi\)
−0.954964 + 0.296722i \(0.904106\pi\)
\(350\) −560.331 76.3698i −1.60095 0.218199i
\(351\) 0 0
\(352\) −168.827 135.770i −0.479621 0.385711i
\(353\) −311.614 539.731i −0.882759 1.52898i −0.848260 0.529579i \(-0.822350\pi\)
−0.0344990 0.999405i \(-0.510984\pi\)
\(354\) 0 0
\(355\) 726.492 + 419.440i 2.04646 + 1.18152i
\(356\) 51.0693 50.1463i 0.143453 0.140860i
\(357\) 0 0
\(358\) 3.24612 + 7.93901i 0.00906737 + 0.0221760i
\(359\) 160.341i 0.446633i −0.974746 0.223316i \(-0.928312\pi\)
0.974746 0.223316i \(-0.0716883\pi\)
\(360\) 0 0
\(361\) 334.000 0.925208
\(362\) 536.389 219.320i 1.48174 0.605856i
\(363\) 0 0
\(364\) 382.933 + 389.982i 1.05201 + 1.07138i
\(365\) −8.02391 + 13.8978i −0.0219833 + 0.0380762i
\(366\) 0 0
\(367\) −246.457 + 142.292i −0.671546 + 0.387717i −0.796662 0.604425i \(-0.793403\pi\)
0.125116 + 0.992142i \(0.460070\pi\)
\(368\) −205.761 + 341.837i −0.559134 + 0.928904i
\(369\) 0 0
\(370\) 12.8328 94.1555i 0.0346833 0.254474i
\(371\) 678.754 391.879i 1.82952 1.05628i
\(372\) 0 0
\(373\) −150.710 + 261.037i −0.404048 + 0.699831i −0.994210 0.107453i \(-0.965730\pi\)
0.590163 + 0.807284i \(0.299064\pi\)
\(374\) 148.368 191.542i 0.396705 0.512144i
\(375\) 0 0
\(376\) 48.6687 + 413.284i 0.129438 + 1.09916i
\(377\) −427.009 −1.13265
\(378\) 0 0
\(379\) 248.547i 0.655796i 0.944713 + 0.327898i \(0.106340\pi\)
−0.944713 + 0.327898i \(0.893660\pi\)
\(380\) −149.021 + 38.4771i −0.392161 + 0.101255i
\(381\) 0 0
\(382\) −113.459 + 146.475i −0.297013 + 0.383442i
\(383\) 422.734 + 244.065i 1.10374 + 0.637247i 0.937202 0.348788i \(-0.113407\pi\)
0.166542 + 0.986034i \(0.446740\pi\)
\(384\) 0 0
\(385\) 237.580 + 411.501i 0.617092 + 1.06883i
\(386\) −65.6764 + 481.873i −0.170146 + 1.24838i
\(387\) 0 0
\(388\) 533.143 + 148.079i 1.37408 + 0.381647i
\(389\) −207.934 360.152i −0.534534 0.925840i −0.999186 0.0403465i \(-0.987154\pi\)
0.464652 0.885493i \(-0.346180\pi\)
\(390\) 0 0
\(391\) −386.420 223.099i −0.988285 0.570587i
\(392\) 195.296 + 261.855i 0.498204 + 0.667996i
\(393\) 0 0
\(394\) 258.122 105.541i 0.655131 0.267871i
\(395\) 1106.92i 2.80233i
\(396\) 0 0
\(397\) −670.827 −1.68974 −0.844870 0.534972i \(-0.820322\pi\)
−0.844870 + 0.534972i \(0.820322\pi\)
\(398\) 84.0146 + 205.474i 0.211092 + 0.516267i
\(399\) 0 0
\(400\) −417.659 + 231.084i −1.04415 + 0.577710i
\(401\) 57.3709 99.3693i 0.143070 0.247804i −0.785582 0.618758i \(-0.787636\pi\)
0.928651 + 0.370955i \(0.120969\pi\)
\(402\) 0 0
\(403\) −213.836 + 123.458i −0.530610 + 0.306348i
\(404\) −375.782 104.373i −0.930154 0.258348i
\(405\) 0 0
\(406\) −556.328 75.8241i −1.37027 0.186759i
\(407\) −37.6206 + 21.7203i −0.0924339 + 0.0533667i
\(408\) 0 0
\(409\) 73.3359 127.022i 0.179305 0.310566i −0.762337 0.647180i \(-0.775948\pi\)
0.941643 + 0.336614i \(0.109282\pi\)
\(410\) 101.193 + 78.3837i 0.246812 + 0.191180i
\(411\) 0 0
\(412\) 164.538 42.4835i 0.399364 0.103115i
\(413\) 793.541 1.92141
\(414\) 0 0
\(415\) 100.266i 0.241605i
\(416\) 455.887 + 70.6257i 1.09588 + 0.169773i
\(417\) 0 0
\(418\) 55.6231 + 43.0854i 0.133070 + 0.103075i
\(419\) −464.945 268.436i −1.10965 0.640659i −0.170914 0.985286i \(-0.554672\pi\)
−0.938740 + 0.344627i \(0.888005\pi\)
\(420\) 0 0
\(421\) 183.707 + 318.189i 0.436358 + 0.755794i 0.997405 0.0719896i \(-0.0229349\pi\)
−0.561048 + 0.827784i \(0.689602\pi\)
\(422\) 525.333 + 71.5997i 1.24486 + 0.169668i
\(423\) 0 0
\(424\) 261.495 607.660i 0.616734 1.43316i
\(425\) −266.904 462.291i −0.628009 1.08774i
\(426\) 0 0
\(427\) −69.0836 39.8854i −0.161788 0.0934085i
\(428\) 272.586 + 277.604i 0.636884 + 0.648607i
\(429\) 0 0
\(430\) −280.997 687.233i −0.653481 1.59822i
\(431\) 735.353i 1.70616i −0.521784 0.853078i \(-0.674733\pi\)
0.521784 0.853078i \(-0.325267\pi\)
\(432\) 0 0
\(433\) 765.161 1.76712 0.883558 0.468322i \(-0.155141\pi\)
0.883558 + 0.468322i \(0.155141\pi\)
\(434\) −300.518 + 122.876i −0.692438 + 0.283125i
\(435\) 0 0
\(436\) −276.371 + 271.376i −0.633878 + 0.622421i
\(437\) 64.7873 112.215i 0.148255 0.256785i
\(438\) 0 0
\(439\) 40.1703 23.1923i 0.0915041 0.0528299i −0.453550 0.891231i \(-0.649843\pi\)
0.545054 + 0.838401i \(0.316509\pi\)
\(440\) 368.400 + 158.534i 0.837274 + 0.360305i
\(441\) 0 0
\(442\) −69.6718 + 511.188i −0.157629 + 1.15653i
\(443\) 120.978 69.8465i 0.273087 0.157667i −0.357203 0.934027i \(-0.616269\pi\)
0.630290 + 0.776360i \(0.282936\pi\)
\(444\) 0 0
\(445\) −66.2492 + 114.747i −0.148875 + 0.257858i
\(446\) 389.377 502.684i 0.873043 1.12709i
\(447\) 0 0
\(448\) 581.410 + 172.966i 1.29779 + 0.386086i
\(449\) 267.139 0.594963 0.297482 0.954728i \(-0.403853\pi\)
0.297482 + 0.954728i \(0.403853\pi\)
\(450\) 0 0
\(451\) 58.5144i 0.129744i
\(452\) 38.8701 + 150.543i 0.0859957 + 0.333060i
\(453\) 0 0
\(454\) 305.410 394.283i 0.672710 0.868464i
\(455\) −876.245 505.900i −1.92581 1.11187i
\(456\) 0 0
\(457\) −118.915 205.967i −0.260208 0.450693i 0.706089 0.708123i \(-0.250458\pi\)
−0.966297 + 0.257430i \(0.917124\pi\)
\(458\) 41.1441 301.878i 0.0898343 0.659122i
\(459\) 0 0
\(460\) 197.666 711.674i 0.429708 1.54712i
\(461\) 149.325 + 258.638i 0.323915 + 0.561037i 0.981292 0.192524i \(-0.0616675\pi\)
−0.657377 + 0.753562i \(0.728334\pi\)
\(462\) 0 0
\(463\) −423.950 244.767i −0.915658 0.528655i −0.0334107 0.999442i \(-0.510637\pi\)
−0.882247 + 0.470786i \(0.843970\pi\)
\(464\) −414.675 + 229.433i −0.893697 + 0.494468i
\(465\) 0 0
\(466\) 641.994 262.500i 1.37767 0.563304i
\(467\) 454.280i 0.972762i 0.873747 + 0.486381i \(0.161683\pi\)
−0.873747 + 0.486381i \(0.838317\pi\)
\(468\) 0 0
\(469\) −275.420 −0.587248
\(470\) −291.560 713.067i −0.620341 1.51716i
\(471\) 0 0
\(472\) 536.912 400.439i 1.13752 0.848387i
\(473\) −169.706 + 293.939i −0.358786 + 0.621435i
\(474\) 0 0
\(475\) 134.248 77.5079i 0.282627 0.163175i
\(476\) −181.544 + 653.629i −0.381394 + 1.37317i
\(477\) 0 0
\(478\) 206.164 + 28.0989i 0.431306 + 0.0587843i
\(479\) −3.12946 + 1.80679i −0.00653332 + 0.00377201i −0.503263 0.864133i \(-0.667867\pi\)
0.496730 + 0.867905i \(0.334534\pi\)
\(480\) 0 0
\(481\) 46.2508 80.1087i 0.0961555 0.166546i
\(482\) 445.607 + 345.166i 0.924496 + 0.716111i
\(483\) 0 0
\(484\) 75.1641 + 291.109i 0.155298 + 0.601465i
\(485\) −1024.33 −2.11202
\(486\) 0 0
\(487\) 874.538i 1.79577i 0.440234 + 0.897883i \(0.354896\pi\)
−0.440234 + 0.897883i \(0.645104\pi\)
\(488\) −66.8692 + 7.87457i −0.137027 + 0.0161364i
\(489\) 0 0
\(490\) −478.079 370.318i −0.975671 0.755752i
\(491\) 558.756 + 322.598i 1.13800 + 0.657022i 0.945934 0.324360i \(-0.105149\pi\)
0.192063 + 0.981383i \(0.438482\pi\)
\(492\) 0 0
\(493\) −264.997 458.988i −0.537519 0.931010i
\(494\) −148.447 20.2325i −0.300501 0.0409564i
\(495\) 0 0
\(496\) −141.325 + 234.787i −0.284930 + 0.473360i
\(497\) 536.868 + 929.883i 1.08022 + 1.87099i
\(498\) 0 0
\(499\) 489.167 + 282.421i 0.980295 + 0.565974i 0.902359 0.430985i \(-0.141834\pi\)
0.0779358 + 0.996958i \(0.475167\pi\)
\(500\) 102.139 100.293i 0.204277 0.200585i
\(501\) 0 0
\(502\) −205.495 502.579i −0.409353 1.00115i
\(503\) 483.048i 0.960334i −0.877177 0.480167i \(-0.840576\pi\)
0.877177 0.480167i \(-0.159424\pi\)
\(504\) 0 0
\(505\) 721.994 1.42969
\(506\) −312.537 + 127.791i −0.617662 + 0.252551i
\(507\) 0 0
\(508\) −277.495 282.603i −0.546251 0.556305i
\(509\) −108.002 + 187.065i −0.212184 + 0.367514i −0.952398 0.304858i \(-0.901391\pi\)
0.740214 + 0.672372i \(0.234724\pi\)
\(510\) 0 0
\(511\) −17.7887 + 10.2703i −0.0348115 + 0.0200984i
\(512\) 480.666 176.363i 0.938801 0.344459i
\(513\) 0 0
\(514\) −124.000 + 909.799i −0.241245 + 1.77004i
\(515\) −272.440 + 157.293i −0.529010 + 0.305424i
\(516\) 0 0
\(517\) −176.085 + 304.988i −0.340590 + 0.589920i
\(518\) 74.4826 96.1567i 0.143789 0.185631i
\(519\) 0 0
\(520\) −848.158 + 99.8798i −1.63107 + 0.192077i
\(521\) −454.806 −0.872949 −0.436475 0.899717i \(-0.643773\pi\)
−0.436475 + 0.899717i \(0.643773\pi\)
\(522\) 0 0
\(523\) 325.041i 0.621493i −0.950493 0.310747i \(-0.899421\pi\)
0.950493 0.310747i \(-0.100579\pi\)
\(524\) 209.768 54.1618i 0.400320 0.103362i
\(525\) 0 0
\(526\) −249.580 + 322.207i −0.474488 + 0.612561i
\(527\) −265.408 153.233i −0.503621 0.290765i
\(528\) 0 0
\(529\) 46.4180 + 80.3983i 0.0877466 + 0.151982i
\(530\) −165.384 + 1213.44i −0.312046 + 2.28951i
\(531\) 0 0
\(532\) −189.812 52.7196i −0.356789 0.0990971i
\(533\) 62.2998 + 107.906i 0.116885 + 0.202451i
\(534\) 0 0
\(535\) −623.745 360.119i −1.16588 0.673120i
\(536\) −186.349 + 138.983i −0.347667 + 0.259296i
\(537\) 0 0
\(538\) −598.620 + 244.765i −1.11268 + 0.454953i
\(539\) 276.447i 0.512889i
\(540\) 0 0
\(541\) −962.574 −1.77925 −0.889625 0.456692i \(-0.849034\pi\)
−0.889625 + 0.456692i \(0.849034\pi\)
\(542\) −79.4239 194.247i −0.146539 0.358389i
\(543\) 0 0
\(544\) 207.003 + 533.858i 0.380520 + 0.981356i
\(545\) 358.520 620.974i 0.657834 1.13940i
\(546\) 0 0
\(547\) −115.588 + 66.7349i −0.211313 + 0.122002i −0.601921 0.798555i \(-0.705598\pi\)
0.390608 + 0.920557i \(0.372265\pi\)
\(548\) 21.4266 + 5.95119i 0.0390997 + 0.0108598i
\(549\) 0 0
\(550\) −400.249 54.5515i −0.727726 0.0991846i
\(551\) 133.289 76.9542i 0.241903 0.139663i
\(552\) 0 0
\(553\) 708.409 1227.00i 1.28103 2.21881i
\(554\) −77.2115 59.8077i −0.139371 0.107956i
\(555\) 0 0
\(556\) −590.696 + 152.517i −1.06240 + 0.274311i
\(557\) −413.437 −0.742258 −0.371129 0.928581i \(-0.621029\pi\)
−0.371129 + 0.928581i \(0.621029\pi\)
\(558\) 0 0
\(559\) 722.737i 1.29291i
\(560\) −1122.76 20.4794i −2.00492 0.0365704i
\(561\) 0 0
\(562\) 46.8328 + 36.2765i 0.0833324 + 0.0645490i
\(563\) −447.356 258.281i −0.794592 0.458758i 0.0469843 0.998896i \(-0.485039\pi\)
−0.841577 + 0.540137i \(0.818372\pi\)
\(564\) 0 0
\(565\) −143.915 249.268i −0.254717 0.441182i
\(566\) 763.314 + 104.035i 1.34861 + 0.183808i
\(567\) 0 0
\(568\) 832.486 + 358.245i 1.46564 + 0.630713i
\(569\) 234.178 + 405.608i 0.411560 + 0.712843i 0.995061 0.0992699i \(-0.0316507\pi\)
−0.583500 + 0.812113i \(0.698317\pi\)
\(570\) 0 0
\(571\) 585.409 + 337.986i 1.02523 + 0.591919i 0.915616 0.402055i \(-0.131704\pi\)
0.109618 + 0.993974i \(0.465037\pi\)
\(572\) 273.532 + 278.567i 0.478203 + 0.487005i
\(573\) 0 0
\(574\) 62.0062 + 151.648i 0.108025 + 0.264196i
\(575\) 743.930i 1.29379i
\(576\) 0 0
\(577\) −354.823 −0.614945 −0.307473 0.951557i \(-0.599483\pi\)
−0.307473 + 0.951557i \(0.599483\pi\)
\(578\) −57.7034 + 23.5939i −0.0998328 + 0.0408198i
\(579\) 0 0
\(580\) 625.994 614.680i 1.07930 1.05979i
\(581\) −64.1683 + 111.143i −0.110445 + 0.191296i
\(582\) 0 0
\(583\) 484.839 279.922i 0.831628 0.480141i
\(584\) −6.85324 + 15.9255i −0.0117350 + 0.0272697i
\(585\) 0 0
\(586\) 76.0062 557.664i 0.129703 0.951645i
\(587\) −190.940 + 110.239i −0.325281 + 0.187801i −0.653744 0.756716i \(-0.726803\pi\)
0.328463 + 0.944517i \(0.393469\pi\)
\(588\) 0 0
\(589\) 44.4984 77.0736i 0.0755491 0.130855i
\(590\) −759.308 + 980.262i −1.28696 + 1.66146i
\(591\) 0 0
\(592\) 1.87228 102.645i 0.00316264 0.173388i
\(593\) 993.520 1.67541 0.837707 0.546121i \(-0.183896\pi\)
0.837707 + 0.546121i \(0.183896\pi\)
\(594\) 0 0
\(595\) 1255.82i 2.11063i
\(596\) 136.979 + 530.519i 0.229831 + 0.890133i
\(597\) 0 0
\(598\) 440.292 568.414i 0.736274 0.950526i
\(599\) 243.124 + 140.368i 0.405884 + 0.234337i 0.689020 0.724743i \(-0.258041\pi\)
−0.283136 + 0.959080i \(0.591375\pi\)
\(600\) 0 0
\(601\) −280.915 486.559i −0.467412 0.809582i 0.531894 0.846811i \(-0.321480\pi\)
−0.999307 + 0.0372287i \(0.988147\pi\)
\(602\) 128.337 941.616i 0.213184 1.56415i
\(603\) 0 0
\(604\) 83.4834 300.573i 0.138218 0.497638i
\(605\) −278.292 482.016i −0.459987 0.796720i
\(606\) 0 0
\(607\) 72.7918 + 42.0264i 0.119921 + 0.0692362i 0.558760 0.829329i \(-0.311277\pi\)
−0.438840 + 0.898565i \(0.644610\pi\)
\(608\) −155.030 + 60.1130i −0.254984 + 0.0988700i
\(609\) 0 0
\(610\) 115.374 47.1743i 0.189137 0.0773348i
\(611\) 749.906i 1.22734i
\(612\) 0 0
\(613\) 730.234 1.19125 0.595623 0.803264i \(-0.296905\pi\)
0.595623 + 0.803264i \(0.296905\pi\)
\(614\) 419.312 + 1025.51i 0.682919 + 1.67021i
\(615\) 0 0
\(616\) 306.906 + 411.501i 0.498223 + 0.668022i
\(617\) 274.893 476.129i 0.445532 0.771684i −0.552557 0.833475i \(-0.686348\pi\)
0.998089 + 0.0617910i \(0.0196812\pi\)
\(618\) 0 0
\(619\) −63.3297 + 36.5634i −0.102310 + 0.0590685i −0.550282 0.834979i \(-0.685480\pi\)
0.447972 + 0.894048i \(0.352146\pi\)
\(620\) 135.765 488.806i 0.218975 0.788397i
\(621\) 0 0
\(622\) −31.0820 4.23629i −0.0499711 0.00681076i
\(623\) −146.872 + 84.7965i −0.235749 + 0.136110i
\(624\) 0 0
\(625\) 240.412 416.405i 0.384659 0.666249i
\(626\) −487.245 377.419i −0.778347 0.602905i
\(627\) 0 0
\(628\) −72.1641 279.490i −0.114911 0.445048i
\(629\) 114.811 0.182529
\(630\) 0 0
\(631\) 779.849i 1.23589i 0.786220 + 0.617947i \(0.212035\pi\)
−0.786220 + 0.617947i \(0.787965\pi\)
\(632\) −139.861 1187.67i −0.221299 1.87922i
\(633\) 0 0
\(634\) −784.413 607.604i −1.23724 0.958366i
\(635\) 634.977 + 366.604i 0.999965 + 0.577330i
\(636\) 0 0
\(637\) −294.331 509.797i −0.462058 0.800309i
\(638\) −397.390 54.1618i −0.622868 0.0848931i
\(639\) 0 0
\(640\) −769.994 + 552.712i −1.20312 + 0.863612i
\(641\) −222.171 384.811i −0.346600 0.600329i 0.639043 0.769171i \(-0.279331\pi\)
−0.985643 + 0.168842i \(0.945997\pi\)
\(642\) 0 0
\(643\) 386.420 + 223.099i 0.600963 + 0.346966i 0.769421 0.638743i \(-0.220545\pi\)
−0.168457 + 0.985709i \(0.553878\pi\)
\(644\) 674.567 662.375i 1.04746 1.02853i
\(645\) 0 0
\(646\) −70.3769 172.121i −0.108943 0.266440i
\(647\) 861.386i 1.33135i 0.746240 + 0.665677i \(0.231857\pi\)
−0.746240 + 0.665677i \(0.768143\pi\)
\(648\) 0 0
\(649\) 566.833 0.873394
\(650\) 796.181 325.544i 1.22489 0.500836i
\(651\) 0 0
\(652\) −158.562 161.481i −0.243194 0.247670i
\(653\) 438.151 758.900i 0.670982 1.16217i −0.306644 0.951824i \(-0.599206\pi\)
0.977626 0.210350i \(-0.0674605\pi\)
\(654\) 0 0
\(655\) −347.331 + 200.532i −0.530277 + 0.306155i
\(656\) 118.479 + 71.3158i 0.180608 + 0.108713i
\(657\) 0 0
\(658\) 133.161 977.013i 0.202372 1.48482i
\(659\) −489.963 + 282.880i −0.743494 + 0.429257i −0.823338 0.567551i \(-0.807891\pi\)
0.0798443 + 0.996807i \(0.474558\pi\)
\(660\) 0 0
\(661\) −316.290 + 547.831i −0.478503 + 0.828791i −0.999696 0.0246476i \(-0.992154\pi\)
0.521194 + 0.853438i \(0.325487\pi\)
\(662\) −105.948 + 136.778i −0.160042 + 0.206613i
\(663\) 0 0
\(664\) 12.6687 + 107.580i 0.0190794 + 0.162018i
\(665\) 364.686 0.548401
\(666\) 0 0
\(667\) 738.615i 1.10737i
\(668\) 780.938 201.637i 1.16907 0.301852i
\(669\) 0 0
\(670\) 263.538 340.226i 0.393340 0.507800i
\(671\) −49.3470 28.4905i −0.0735424 0.0424597i
\(672\) 0 0
\(673\) 536.330 + 928.950i 0.796924 + 1.38031i 0.921610 + 0.388116i \(0.126874\pi\)
−0.124687 + 0.992196i \(0.539793\pi\)
\(674\) 86.6071 635.444i 0.128497 0.942795i
\(675\) 0 0
\(676\) −149.666 41.5692i −0.221399 0.0614929i
\(677\) −239.399 414.651i −0.353617 0.612483i 0.633263 0.773937i \(-0.281715\pi\)
−0.986880 + 0.161454i \(0.948382\pi\)
\(678\) 0 0
\(679\) −1135.45 655.553i −1.67224 0.965468i
\(680\) −633.717 849.692i −0.931936 1.24955i
\(681\) 0 0
\(682\) −214.663 + 87.7716i −0.314754 + 0.128697i
\(683\) 318.418i 0.466206i 0.972452 + 0.233103i \(0.0748879\pi\)
−0.972452 + 0.233103i \(0.925112\pi\)
\(684\) 0 0
\(685\) −41.1672 −0.0600981
\(686\) 58.5933 + 143.301i 0.0854130 + 0.208894i
\(687\) 0 0
\(688\) −388.328 701.861i −0.564430 1.02015i
\(689\) −596.061 + 1032.41i −0.865111 + 1.49842i
\(690\) 0 0
\(691\) −971.076 + 560.651i −1.40532 + 0.811362i −0.994932 0.100550i \(-0.967940\pi\)
−0.410388 + 0.911911i \(0.634607\pi\)
\(692\) −356.697 99.0716i −0.515458 0.143167i
\(693\) 0 0
\(694\) 1337.15 + 182.246i 1.92674 + 0.262602i
\(695\) 978.068 564.688i 1.40729 0.812501i
\(696\) 0 0
\(697\) −77.3251 + 133.931i −0.110940 + 0.192153i
\(698\) 243.366 + 188.510i 0.348661 + 0.270072i
\(699\) 0 0
\(700\) 1095.11 282.756i 1.56444 0.403937i
\(701\) −413.437 −0.589782 −0.294891 0.955531i \(-0.595283\pi\)
−0.294891 + 0.955531i \(0.595283\pi\)
\(702\) 0 0
\(703\) 33.3406i 0.0474262i
\(704\) 415.306 + 123.551i 0.589923 + 0.175499i
\(705\) 0 0
\(706\) 985.410 + 763.295i 1.39577 + 1.08116i
\(707\) 800.316 + 462.062i 1.13199 + 0.653554i
\(708\) 0 0
\(709\) 341.457 + 591.422i 0.481604 + 0.834163i 0.999777 0.0211129i \(-0.00672093\pi\)
−0.518173 + 0.855276i \(0.673388\pi\)
\(710\) −1662.39 226.574i −2.34140 0.319118i
\(711\) 0 0
\(712\) −56.5836 + 131.488i −0.0794713 + 0.184675i
\(713\) 213.551 + 369.881i 0.299510 + 0.518767i
\(714\) 0 0
\(715\) −625.909 361.369i −0.875397 0.505411i
\(716\) −12.0186 12.2398i −0.0167858 0.0170948i
\(717\) 0 0
\(718\) 121.368 + 296.828i 0.169036 + 0.413410i
\(719\) 286.374i 0.398295i 0.979970 + 0.199148i \(0.0638173\pi\)
−0.979970 + 0.199148i \(0.936183\pi\)
\(720\) 0 0
\(721\) −402.659 −0.558474
\(722\) −618.311 + 252.816i −0.856386 + 0.350161i
\(723\) 0 0
\(724\) −826.969 + 812.023i −1.14222 + 1.12158i
\(725\) −441.819 + 765.253i −0.609406 + 1.05552i
\(726\) 0 0
\(727\) 279.659 161.461i 0.384676 0.222093i −0.295175 0.955443i \(-0.595378\pi\)
0.679851 + 0.733351i \(0.262045\pi\)
\(728\) −1004.09 432.090i −1.37924 0.593531i
\(729\) 0 0
\(730\) 4.33437 31.8016i 0.00593749 0.0435639i
\(731\) 776.863 448.522i 1.06274 0.613573i
\(732\) 0 0
\(733\) 260.915 451.918i 0.355955 0.616532i −0.631326 0.775517i \(-0.717489\pi\)
0.987281 + 0.158986i \(0.0508224\pi\)
\(734\) 348.543 449.968i 0.474855 0.613035i
\(735\) 0 0
\(736\) 122.164 788.566i 0.165984 1.07142i
\(737\) −196.734 −0.266939
\(738\) 0 0
\(739\) 965.020i 1.30585i 0.757424 + 0.652923i \(0.226458\pi\)
−0.757424 + 0.652923i \(0.773542\pi\)
\(740\) 47.5130 + 184.017i 0.0642067 + 0.248672i
\(741\) 0 0
\(742\) −959.902 + 1239.23i −1.29367 + 1.67012i
\(743\) 950.317 + 548.666i 1.27903 + 0.738447i 0.976669 0.214748i \(-0.0688930\pi\)
0.302357 + 0.953195i \(0.402226\pi\)
\(744\) 0 0
\(745\) −507.161 878.429i −0.680753 1.17910i
\(746\) 81.4106 597.317i 0.109130 0.800693i
\(747\) 0 0
\(748\) −129.678 + 466.892i −0.173366 + 0.624188i
\(749\) −460.939 798.370i −0.615406 1.06591i
\(750\) 0 0
\(751\) 1196.02 + 690.524i 1.59257 + 0.919472i 0.992864 + 0.119255i \(0.0380505\pi\)
0.599709 + 0.800218i \(0.295283\pi\)
\(752\) −402.926 728.245i −0.535806 0.968411i
\(753\) 0 0
\(754\) 790.492 323.218i 1.04840 0.428671i
\(755\) 577.494i 0.764892i
\(756\) 0 0
\(757\) −516.252 −0.681971 −0.340986 0.940068i \(-0.610761\pi\)
−0.340986 + 0.940068i \(0.610761\pi\)
\(758\) −188.133 460.117i −0.248197 0.607014i
\(759\) 0 0
\(760\) 246.748 184.029i 0.324668 0.242143i
\(761\) −608.092 + 1053.25i −0.799069 + 1.38403i 0.121154 + 0.992634i \(0.461341\pi\)
−0.920223 + 0.391394i \(0.871993\pi\)
\(762\) 0 0
\(763\) 794.823 458.892i 1.04171 0.601431i
\(764\) 99.1668 357.040i 0.129799 0.467329i
\(765\) 0 0
\(766\) −967.319 131.840i −1.26282 0.172114i
\(767\) −1045.30 + 603.502i −1.36284 + 0.786835i
\(768\) 0 0
\(769\) −502.163 + 869.771i −0.653007 + 1.13104i 0.329382 + 0.944197i \(0.393160\pi\)
−0.982389 + 0.186845i \(0.940174\pi\)
\(770\) −751.295 581.951i −0.975708 0.755780i
\(771\) 0 0
\(772\) −243.164 941.770i −0.314979 1.21991i
\(773\) 382.580 0.494929 0.247464 0.968897i \(-0.420403\pi\)
0.247464 + 0.968897i \(0.420403\pi\)
\(774\) 0 0
\(775\) 510.960i 0.659304i
\(776\) −1099.06 + 129.426i −1.41631 + 0.166786i
\(777\) 0 0
\(778\) 657.544 + 509.331i 0.845172 + 0.654668i
\(779\) −38.8931 22.4549i −0.0499269 0.0288253i
\(780\) 0 0
\(781\) 383.489 + 664.223i 0.491023 + 0.850477i
\(782\) 884.223 + 120.514i 1.13072 + 0.154110i
\(783\) 0 0
\(784\) −559.745 336.927i −0.713960 0.429754i
\(785\) 267.185 + 462.777i 0.340362 + 0.589525i
\(786\) 0 0
\(787\) −413.327 238.634i −0.525193 0.303220i 0.213864 0.976863i \(-0.431395\pi\)
−0.739057 + 0.673643i \(0.764728\pi\)
\(788\) −397.954 + 390.762i −0.505018 + 0.495891i
\(789\) 0 0
\(790\) 837.866 + 2049.16i 1.06059 + 2.59388i
\(791\) 368.411i 0.465754i
\(792\) 0 0
\(793\) 121.334 0.153007
\(794\) 1241.85 507.771i 1.56405 0.639511i
\(795\) 0 0
\(796\) −311.061 316.786i −0.390780 0.397973i
\(797\) 257.304 445.663i 0.322840 0.559176i −0.658233 0.752815i \(-0.728696\pi\)
0.981073 + 0.193639i \(0.0620290\pi\)
\(798\) 0 0
\(799\) 806.067 465.383i 1.00884 0.582456i
\(800\) 598.268 743.930i 0.747835 0.929913i
\(801\) 0 0
\(802\) −30.9907 + 227.381i −0.0386417 + 0.283518i
\(803\) −12.7066 + 7.33616i −0.0158239 + 0.00913594i
\(804\) 0 0
\(805\) −875.076 + 1515.68i −1.08705 + 1.88283i
\(806\) 302.410 390.409i 0.375198 0.484379i
\(807\) 0 0
\(808\) 774.663 91.2249i 0.958741 0.112902i
\(809\) 1463.74 1.80932 0.904662 0.426129i \(-0.140123\pi\)
0.904662 + 0.426129i \(0.140123\pi\)
\(810\) 0 0
\(811\) 1163.05i 1.43410i −0.697023 0.717049i \(-0.745492\pi\)
0.697023 0.717049i \(-0.254508\pi\)
\(812\) 1087.29 280.736i 1.33902 0.345734i
\(813\) 0 0
\(814\) 53.2035 68.6855i 0.0653606 0.0843802i
\(815\) 362.830 + 209.480i 0.445190 + 0.257030i
\(816\) 0 0
\(817\) 130.249 + 225.598i 0.159424 + 0.276130i
\(818\) −39.6147 + 290.656i −0.0484287 + 0.355326i
\(819\) 0 0
\(820\) −246.663 68.5098i −0.300808 0.0835486i
\(821\) −196.276 339.961i −0.239070 0.414081i 0.721378 0.692542i \(-0.243509\pi\)
−0.960448 + 0.278461i \(0.910176\pi\)
\(822\) 0 0
\(823\) 1081.53 + 624.422i 1.31413 + 0.758714i 0.982778 0.184792i \(-0.0591613\pi\)
0.331354 + 0.943507i \(0.392495\pi\)
\(824\) −272.440 + 203.191i −0.330631 + 0.246591i
\(825\) 0 0
\(826\) −1469.03 + 600.658i −1.77848 + 0.727189i
\(827\) 1369.15i 1.65557i 0.561049 + 0.827783i \(0.310398\pi\)
−0.561049 + 0.827783i \(0.689602\pi\)
\(828\) 0 0
\(829\) −73.7477 −0.0889598 −0.0444799 0.999010i \(-0.514163\pi\)
−0.0444799 + 0.999010i \(0.514163\pi\)
\(830\) −75.8947 185.615i −0.0914394 0.223633i
\(831\) 0 0
\(832\) −897.410 + 214.332i −1.07862 + 0.257610i
\(833\) 365.317 632.748i 0.438556 0.759601i
\(834\) 0 0
\(835\) −1293.07 + 746.554i −1.54859 + 0.894077i
\(836\) −135.584 37.6581i −0.162182 0.0450455i
\(837\) 0 0
\(838\) 1063.91 + 145.004i 1.26958 + 0.173036i
\(839\) −1039.73 + 600.286i −1.23924 + 0.715478i −0.968940 0.247297i \(-0.920458\pi\)
−0.270305 + 0.962775i \(0.587124\pi\)
\(840\) 0 0
\(841\) −18.1625 + 31.4584i −0.0215963 + 0.0374060i
\(842\) −580.931 449.988i −0.689942 0.534427i
\(843\) 0 0
\(844\) −1026.71 + 265.095i −1.21648 + 0.314094i
\(845\) 287.554 0.340300
\(846\) 0 0
\(847\) 712.406i 0.841094i
\(848\) −24.1292 + 1322.85i −0.0284543 + 1.55997i
\(849\) 0 0
\(850\) 844.024 + 653.778i 0.992969 + 0.769151i
\(851\) −138.567 80.0018i −0.162829 0.0940092i
\(852\) 0 0
\(853\) 219.539 + 380.254i 0.257373 + 0.445784i 0.965537 0.260264i \(-0.0838097\pi\)
−0.708164 + 0.706048i \(0.750476\pi\)
\(854\) 158.080 + 21.5454i 0.185106 + 0.0252288i
\(855\) 0 0
\(856\) −714.748 307.578i −0.834986 0.359321i
\(857\) 255.481 + 442.506i 0.298111 + 0.516344i 0.975704 0.219094i \(-0.0703101\pi\)
−0.677593 + 0.735437i \(0.736977\pi\)
\(858\) 0 0
\(859\) −153.093 88.3882i −0.178222 0.102897i 0.408235 0.912877i \(-0.366144\pi\)
−0.586457 + 0.809980i \(0.699478\pi\)
\(860\) 1040.38 + 1059.53i 1.20974 + 1.23201i
\(861\) 0 0
\(862\) 556.614 + 1361.31i 0.645724 + 1.57924i
\(863\) 1028.28i 1.19152i 0.803163 + 0.595759i \(0.203149\pi\)
−0.803163 + 0.595759i \(0.796851\pi\)
\(864\) 0 0
\(865\) 685.325 0.792283
\(866\) −1416.49 + 579.176i −1.63567 + 0.668795i
\(867\) 0 0
\(868\) 463.319 454.945i 0.533777 0.524130i
\(869\) 506.022 876.456i 0.582304 1.00858i
\(870\) 0 0
\(871\) 362.798 209.462i 0.416530 0.240484i
\(872\) 306.212 711.573i 0.351161 0.816024i
\(873\) 0 0
\(874\) −34.9969 + 256.775i −0.0400422 + 0.293793i
\(875\) −293.744 + 169.593i −0.335707 + 0.193821i
\(876\) 0 0
\(877\) 470.457 814.856i 0.536439 0.929140i −0.462653 0.886540i \(-0.653102\pi\)
0.999092 0.0426008i \(-0.0135644\pi\)
\(878\) −56.8094 + 73.3406i −0.0647032 + 0.0835314i
\(879\) 0 0
\(880\) −801.994 14.6286i −0.911357 0.0166234i
\(881\) −1065.75 −1.20970 −0.604851 0.796339i \(-0.706767\pi\)
−0.604851 + 0.796339i \(0.706767\pi\)
\(882\) 0 0
\(883\) 1001.97i 1.13474i −0.823464 0.567368i \(-0.807962\pi\)
0.823464 0.567368i \(-0.192038\pi\)
\(884\) −257.957 999.064i −0.291807 1.13016i
\(885\) 0 0
\(886\) −171.088 + 220.874i −0.193102 + 0.249293i
\(887\) 583.774 + 337.042i 0.658144 + 0.379980i 0.791569 0.611079i \(-0.209264\pi\)
−0.133426 + 0.991059i \(0.542598\pi\)
\(888\) 0 0
\(889\) 469.240 + 812.747i 0.527829 + 0.914227i
\(890\) 35.7866 262.569i 0.0402097 0.295022i
\(891\) 0 0
\(892\) −340.328 + 1225.32i −0.381534 + 1.37367i
\(893\) 135.146 + 234.079i 0.151339 + 0.262126i
\(894\) 0 0
\(895\) 27.5016 + 15.8780i 0.0307280 + 0.0177408i
\(896\) −1207.25 + 119.888i −1.34737 + 0.133804i
\(897\) 0 0
\(898\) −494.535 + 202.206i −0.550707 + 0.225174i
\(899\) 507.310i 0.564305i
\(900\) 0 0
\(901\) −1479.63 −1.64221
\(902\) 44.2915 + 108.324i 0.0491037 + 0.120093i
\(903\) 0 0
\(904\) −185.909 249.268i −0.205651 0.275739i
\(905\) 1072.78 1858.11i 1.18539 2.05316i
\(906\) 0 0
\(907\) 1023.16 590.723i 1.12807 0.651293i 0.184624 0.982809i \(-0.440893\pi\)
0.943450 + 0.331516i \(0.107560\pi\)
\(908\) −266.938 + 961.083i −0.293985 + 1.05846i
\(909\) 0 0
\(910\) 2005.06 + 273.278i 2.20337 + 0.300305i
\(911\) 1207.61 697.213i 1.32559 0.765328i 0.340973 0.940073i \(-0.389244\pi\)
0.984614 + 0.174746i \(0.0559103\pi\)
\(912\) 0 0
\(913\) −45.8359 + 79.3901i −0.0502036 + 0.0869553i
\(914\) 376.042 + 291.281i 0.411424 + 0.318688i
\(915\) 0 0
\(916\) 152.334 + 589.988i 0.166304 + 0.644092i
\(917\) −513.346 −0.559811
\(918\) 0 0
\(919\) 210.163i 0.228686i −0.993441 0.114343i \(-0.963524\pi\)
0.993441 0.114343i \(-0.0364763\pi\)
\(920\) 172.766 + 1467.09i 0.187789 + 1.59467i
\(921\) 0 0
\(922\) −472.207 365.770i −0.512155 0.396713i
\(923\) −1414.39 816.596i −1.53238 0.884719i
\(924\) 0 0
\(925\) −95.7098 165.774i −0.103470 0.179215i
\(926\) 970.101 + 132.219i 1.04763 + 0.142785i
\(927\) 0 0
\(928\) 593.994 738.615i 0.640080 0.795921i
\(929\) 83.2996 + 144.279i 0.0896659 + 0.155306i 0.907370 0.420333i \(-0.138087\pi\)
−0.817704 + 0.575639i \(0.804753\pi\)
\(930\) 0 0
\(931\) 183.748 + 106.087i 0.197366 + 0.113949i
\(932\) −989.783 + 971.894i −1.06200 + 1.04280i
\(933\) 0 0
\(934\) −343.860 840.976i −0.368158 0.900403i
\(935\) 897.044i 0.959405i
\(936\) 0 0
\(937\) 251.158 0.268045 0.134022 0.990978i \(-0.457211\pi\)
0.134022 + 0.990978i \(0.457211\pi\)
\(938\) 509.865 208.474i 0.543566 0.222254i
\(939\) 0 0
\(940\) 1079.49 + 1099.36i 1.14839 + 1.16953i
\(941\) −407.282 + 705.433i −0.432818 + 0.749663i −0.997115 0.0759090i \(-0.975814\pi\)
0.564296 + 0.825572i \(0.309147\pi\)
\(942\) 0 0
\(943\) 186.650 107.762i 0.197932 0.114276i
\(944\) −690.841 + 1147.71i −0.731823 + 1.21580i
\(945\) 0 0
\(946\) 91.6718 672.604i 0.0969047 0.710998i
\(947\) −513.020 + 296.192i −0.541731 + 0.312769i −0.745780 0.666192i \(-0.767923\pi\)
0.204049 + 0.978961i \(0.434590\pi\)
\(948\) 0 0
\(949\) 15.6215 27.0572i 0.0164610 0.0285113i
\(950\) −189.855 + 245.102i −0.199847 + 0.258002i
\(951\) 0 0
\(952\) −158.675 1347.43i −0.166675 1.41537i
\(953\) −844.768 −0.886430 −0.443215 0.896415i \(-0.646162\pi\)
−0.443215 + 0.896415i \(0.646162\pi\)
\(954\) 0 0
\(955\) 685.983i 0.718307i
\(956\) −402.926 + 104.035i −0.421471 + 0.108823i
\(957\) 0 0
\(958\) 4.42572 5.71359i 0.00461975 0.00596408i
\(959\) −45.6330 26.3462i −0.0475839 0.0274726i
\(960\) 0 0
\(961\) −333.825 578.202i −0.347373 0.601667i
\(962\) −24.9838 + 183.308i −0.0259707 + 0.190549i
\(963\) 0 0
\(964\) −1086.19 301.686i −1.12675 0.312952i
\(965\) 900.305 + 1559.37i 0.932959 + 1.61593i
\(966\) 0 0
\(967\) 156.035 + 90.0867i 0.161360 + 0.0931611i 0.578505 0.815679i \(-0.303636\pi\)
−0.417146 + 0.908840i \(0.636970\pi\)
\(968\) −359.496 482.016i −0.371381 0.497950i
\(969\) 0 0
\(970\) 1896.27 775.351i 1.95492 0.799331i
\(971\) 411.395i 0.423682i −0.977304 0.211841i \(-0.932054\pi\)
0.977304 0.211841i \(-0.0679458\pi\)
\(972\) 0 0
\(973\) 1445.56 1.48567
\(974\) −661.968 1618.97i −0.679638 1.66219i
\(975\) 0 0
\(976\) 117.830 65.1932i 0.120727 0.0667963i
\(977\) −878.125 + 1520.96i −0.898797 + 1.55676i −0.0697635 + 0.997564i \(0.522224\pi\)
−0.829034 + 0.559199i \(0.811109\pi\)
\(978\) 0 0
\(979\) −104.912 + 60.5708i −0.107162 + 0.0618701i
\(980\) 1165.34 + 323.670i 1.18912 + 0.330276i
\(981\) 0 0
\(982\) −1278.57 174.261i −1.30201 0.177456i
\(983\) −695.466 + 401.528i −0.707494 + 0.408472i −0.810132 0.586247i \(-0.800605\pi\)
0.102639 + 0.994719i \(0.467271\pi\)
\(984\) 0 0
\(985\) 516.243 894.159i 0.524105 0.907776i
\(986\) 837.994 + 649.107i 0.849892 + 0.658324i
\(987\) 0 0
\(988\) 290.125 74.9099i 0.293648 0.0758197i
\(989\) −1250.15 −1.26405
\(990\) 0 0
\(991\) 338.466i 0.341540i −0.985311 0.170770i \(-0.945375\pi\)
0.985311 0.170770i \(-0.0546254\pi\)
\(992\) 83.9071 541.618i 0.0845837 0.545986i
\(993\) 0 0
\(994\) −1697.73 1315.05i −1.70797 1.32299i
\(995\) 711.783 + 410.948i 0.715360 + 0.413013i
\(996\) 0 0
\(997\) −295.906 512.523i −0.296796 0.514066i 0.678605 0.734503i \(-0.262585\pi\)
−0.975401 + 0.220438i \(0.929251\pi\)
\(998\) −1119.33 152.558i −1.12158 0.152864i
\(999\) 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 324.3.f.o.271.1 8
3.2 odd 2 inner 324.3.f.o.271.4 8
4.3 odd 2 324.3.f.p.271.3 8
9.2 odd 6 324.3.f.p.55.1 8
9.4 even 3 108.3.d.d.55.5 yes 8
9.5 odd 6 108.3.d.d.55.4 yes 8
9.7 even 3 324.3.f.p.55.4 8
12.11 even 2 324.3.f.p.271.2 8
36.7 odd 6 inner 324.3.f.o.55.1 8
36.11 even 6 inner 324.3.f.o.55.4 8
36.23 even 6 108.3.d.d.55.3 8
36.31 odd 6 108.3.d.d.55.6 yes 8
72.5 odd 6 1728.3.g.l.703.7 8
72.13 even 6 1728.3.g.l.703.1 8
72.59 even 6 1728.3.g.l.703.8 8
72.67 odd 6 1728.3.g.l.703.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
108.3.d.d.55.3 8 36.23 even 6
108.3.d.d.55.4 yes 8 9.5 odd 6
108.3.d.d.55.5 yes 8 9.4 even 3
108.3.d.d.55.6 yes 8 36.31 odd 6
324.3.f.o.55.1 8 36.7 odd 6 inner
324.3.f.o.55.4 8 36.11 even 6 inner
324.3.f.o.271.1 8 1.1 even 1 trivial
324.3.f.o.271.4 8 3.2 odd 2 inner
324.3.f.p.55.1 8 9.2 odd 6
324.3.f.p.55.4 8 9.7 even 3
324.3.f.p.271.2 8 12.11 even 2
324.3.f.p.271.3 8 4.3 odd 2
1728.3.g.l.703.1 8 72.13 even 6
1728.3.g.l.703.2 8 72.67 odd 6
1728.3.g.l.703.7 8 72.5 odd 6
1728.3.g.l.703.8 8 72.59 even 6