Properties

Label 432.2.y.e.37.13
Level $432$
Weight $2$
Character 432.37
Analytic conductor $3.450$
Analytic rank $0$
Dimension $72$
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] = [432,2,Mod(37,432)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(432, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 3, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("432.37");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 432.y (of order \(12\), degree \(4\), 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: \(3.44953736732\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(18\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 144)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 37.13
Character \(\chi\) \(=\) 432.37
Dual form 432.2.y.e.397.13

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.812713 + 1.15737i) q^{2} +(-0.678997 + 1.88121i) q^{4} +(2.69708 - 0.722679i) q^{5} +(-2.89314 + 1.67035i) q^{7} +(-2.72908 + 0.743037i) q^{8} +O(q^{10})\) \(q+(0.812713 + 1.15737i) q^{2} +(-0.678997 + 1.88121i) q^{4} +(2.69708 - 0.722679i) q^{5} +(-2.89314 + 1.67035i) q^{7} +(-2.72908 + 0.743037i) q^{8} +(3.02835 + 2.53418i) q^{10} +(-1.23365 + 4.60405i) q^{11} +(0.398486 + 1.48717i) q^{13} +(-4.28450 - 1.99090i) q^{14} +(-3.07793 - 2.55468i) q^{16} +6.47719 q^{17} +(0.957336 - 0.957336i) q^{19} +(-0.471792 + 5.56447i) q^{20} +(-6.33117 + 2.31398i) q^{22} +(3.70277 + 2.13780i) q^{23} +(2.42183 - 1.39824i) q^{25} +(-1.39735 + 1.66984i) q^{26} +(-1.17786 - 6.57677i) q^{28} +(1.07893 + 0.289099i) q^{29} +(1.89670 - 3.28518i) q^{31} +(0.455227 - 5.63851i) q^{32} +(5.26409 + 7.49649i) q^{34} +(-6.59588 + 6.59588i) q^{35} +(-6.14639 - 6.14639i) q^{37} +(1.88603 + 0.329950i) q^{38} +(-6.82357 + 3.97628i) q^{40} +(-5.04156 - 2.91075i) q^{41} +(1.69287 - 6.31788i) q^{43} +(-7.82355 - 5.44689i) q^{44} +(0.535074 + 6.02288i) q^{46} +(-1.81739 - 3.14781i) q^{47} +(2.08016 - 3.60295i) q^{49} +(3.58653 + 1.66657i) q^{50} +(-3.06826 - 0.260146i) q^{52} +(-0.762460 - 0.762460i) q^{53} +13.3090i q^{55} +(6.65448 - 6.70824i) q^{56} +(0.542268 + 1.48367i) q^{58} +(8.11476 - 2.17434i) q^{59} +(6.74711 + 1.80788i) q^{61} +(5.34363 - 0.474729i) q^{62} +(6.89579 - 4.05562i) q^{64} +(2.14950 + 3.72304i) q^{65} +(-0.487339 - 1.81878i) q^{67} +(-4.39799 + 12.1850i) q^{68} +(-12.9944 - 2.27330i) q^{70} -3.98472i q^{71} +5.45461i q^{73} +(2.11838 - 12.1089i) q^{74} +(1.15092 + 2.45098i) q^{76} +(-4.12126 - 15.3808i) q^{77} +(-2.95225 - 5.11344i) q^{79} +(-10.1476 - 4.66580i) q^{80} +(-0.728538 - 8.20053i) q^{82} +(10.3428 + 2.77135i) q^{83} +(17.4695 - 4.68093i) q^{85} +(8.68792 - 3.17535i) q^{86} +(-0.0542436 - 13.4815i) q^{88} -2.24307i q^{89} +(-3.63698 - 3.63698i) q^{91} +(-6.53582 + 5.51415i) q^{92} +(2.16615 - 4.66165i) q^{94} +(1.89016 - 3.27385i) q^{95} +(6.50191 + 11.2616i) q^{97} +(5.86050 - 0.520649i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q - 4 q^{2} - 2 q^{4} - 4 q^{5} + 8 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 72 q - 4 q^{2} - 2 q^{4} - 4 q^{5} + 8 q^{8} - 20 q^{10} + 2 q^{11} - 16 q^{13} + 4 q^{14} - 10 q^{16} + 16 q^{17} + 28 q^{19} - 12 q^{20} - 8 q^{22} + 4 q^{26} - 16 q^{28} - 4 q^{29} + 28 q^{31} + 46 q^{32} - 14 q^{34} + 16 q^{35} + 16 q^{37} - 2 q^{38} - 10 q^{40} - 10 q^{43} - 60 q^{44} + 20 q^{46} + 56 q^{47} + 4 q^{49} + 36 q^{50} + 6 q^{52} + 8 q^{53} - 52 q^{56} - 14 q^{58} + 14 q^{59} - 32 q^{61} - 16 q^{62} - 44 q^{64} + 64 q^{65} - 18 q^{67} - 16 q^{68} + 14 q^{70} - 38 q^{74} + 10 q^{76} + 36 q^{77} + 44 q^{79} - 144 q^{80} - 88 q^{82} - 20 q^{83} - 8 q^{85} - 76 q^{86} - 42 q^{88} - 80 q^{91} + 68 q^{92} + 20 q^{94} - 48 q^{95} + 40 q^{97} - 88 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).

\(n\) \(271\) \(325\) \(353\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.812713 + 1.15737i 0.574675 + 0.818382i
\(3\) 0 0
\(4\) −0.678997 + 1.88121i −0.339498 + 0.940607i
\(5\) 2.69708 0.722679i 1.20617 0.323192i 0.400911 0.916117i \(-0.368694\pi\)
0.805258 + 0.592925i \(0.202027\pi\)
\(6\) 0 0
\(7\) −2.89314 + 1.67035i −1.09350 + 0.631334i −0.934507 0.355945i \(-0.884159\pi\)
−0.158996 + 0.987279i \(0.550826\pi\)
\(8\) −2.72908 + 0.743037i −0.964877 + 0.262703i
\(9\) 0 0
\(10\) 3.02835 + 2.53418i 0.957649 + 0.801377i
\(11\) −1.23365 + 4.60405i −0.371960 + 1.38817i 0.485777 + 0.874083i \(0.338537\pi\)
−0.857737 + 0.514089i \(0.828130\pi\)
\(12\) 0 0
\(13\) 0.398486 + 1.48717i 0.110520 + 0.412467i 0.998913 0.0466175i \(-0.0148442\pi\)
−0.888393 + 0.459084i \(0.848178\pi\)
\(14\) −4.28450 1.99090i −1.14508 0.532092i
\(15\) 0 0
\(16\) −3.07793 2.55468i −0.769482 0.638669i
\(17\) 6.47719 1.57095 0.785475 0.618894i \(-0.212419\pi\)
0.785475 + 0.618894i \(0.212419\pi\)
\(18\) 0 0
\(19\) 0.957336 0.957336i 0.219628 0.219628i −0.588714 0.808342i \(-0.700365\pi\)
0.808342 + 0.588714i \(0.200365\pi\)
\(20\) −0.471792 + 5.56447i −0.105496 + 1.24425i
\(21\) 0 0
\(22\) −6.33117 + 2.31398i −1.34981 + 0.493342i
\(23\) 3.70277 + 2.13780i 0.772081 + 0.445761i 0.833617 0.552343i \(-0.186266\pi\)
−0.0615352 + 0.998105i \(0.519600\pi\)
\(24\) 0 0
\(25\) 2.42183 1.39824i 0.484365 0.279648i
\(26\) −1.39735 + 1.66984i −0.274042 + 0.327482i
\(27\) 0 0
\(28\) −1.17786 6.57677i −0.222595 1.24289i
\(29\) 1.07893 + 0.289099i 0.200353 + 0.0536843i 0.357600 0.933875i \(-0.383595\pi\)
−0.157247 + 0.987559i \(0.550262\pi\)
\(30\) 0 0
\(31\) 1.89670 3.28518i 0.340657 0.590036i −0.643898 0.765112i \(-0.722684\pi\)
0.984555 + 0.175076i \(0.0560171\pi\)
\(32\) 0.455227 5.63851i 0.0804734 0.996757i
\(33\) 0 0
\(34\) 5.26409 + 7.49649i 0.902785 + 1.28564i
\(35\) −6.59588 + 6.59588i −1.11491 + 1.11491i
\(36\) 0 0
\(37\) −6.14639 6.14639i −1.01046 1.01046i −0.999945 0.0105160i \(-0.996653\pi\)
−0.0105160 0.999945i \(-0.503347\pi\)
\(38\) 1.88603 + 0.329950i 0.305954 + 0.0535249i
\(39\) 0 0
\(40\) −6.82357 + 3.97628i −1.07890 + 0.628705i
\(41\) −5.04156 2.91075i −0.787359 0.454582i 0.0516729 0.998664i \(-0.483545\pi\)
−0.839032 + 0.544082i \(0.816878\pi\)
\(42\) 0 0
\(43\) 1.69287 6.31788i 0.258160 0.963468i −0.708144 0.706068i \(-0.750467\pi\)
0.966305 0.257400i \(-0.0828659\pi\)
\(44\) −7.82355 5.44689i −1.17944 0.821150i
\(45\) 0 0
\(46\) 0.535074 + 6.02288i 0.0788924 + 0.888025i
\(47\) −1.81739 3.14781i −0.265093 0.459155i 0.702495 0.711689i \(-0.252069\pi\)
−0.967588 + 0.252534i \(0.918736\pi\)
\(48\) 0 0
\(49\) 2.08016 3.60295i 0.297166 0.514707i
\(50\) 3.58653 + 1.66657i 0.507212 + 0.235689i
\(51\) 0 0
\(52\) −3.06826 0.260146i −0.425491 0.0360758i
\(53\) −0.762460 0.762460i −0.104732 0.104732i 0.652799 0.757531i \(-0.273595\pi\)
−0.757531 + 0.652799i \(0.773595\pi\)
\(54\) 0 0
\(55\) 13.3090i 1.79458i
\(56\) 6.65448 6.70824i 0.889242 0.896427i
\(57\) 0 0
\(58\) 0.542268 + 1.48367i 0.0712033 + 0.194816i
\(59\) 8.11476 2.17434i 1.05645 0.283075i 0.311536 0.950234i \(-0.399156\pi\)
0.744915 + 0.667159i \(0.232490\pi\)
\(60\) 0 0
\(61\) 6.74711 + 1.80788i 0.863879 + 0.231476i 0.663439 0.748230i \(-0.269096\pi\)
0.200440 + 0.979706i \(0.435763\pi\)
\(62\) 5.34363 0.474729i 0.678641 0.0602907i
\(63\) 0 0
\(64\) 6.89579 4.05562i 0.861974 0.506953i
\(65\) 2.14950 + 3.72304i 0.266612 + 0.461786i
\(66\) 0 0
\(67\) −0.487339 1.81878i −0.0595380 0.222199i 0.929746 0.368201i \(-0.120026\pi\)
−0.989284 + 0.146002i \(0.953359\pi\)
\(68\) −4.39799 + 12.1850i −0.533335 + 1.47765i
\(69\) 0 0
\(70\) −12.9944 2.27330i −1.55313 0.271711i
\(71\) 3.98472i 0.472899i −0.971644 0.236450i \(-0.924016\pi\)
0.971644 0.236450i \(-0.0759838\pi\)
\(72\) 0 0
\(73\) 5.45461i 0.638414i 0.947685 + 0.319207i \(0.103417\pi\)
−0.947685 + 0.319207i \(0.896583\pi\)
\(74\) 2.11838 12.1089i 0.246257 1.40763i
\(75\) 0 0
\(76\) 1.15092 + 2.45098i 0.132020 + 0.281147i
\(77\) −4.12126 15.3808i −0.469662 1.75280i
\(78\) 0 0
\(79\) −2.95225 5.11344i −0.332154 0.575307i 0.650780 0.759266i \(-0.274442\pi\)
−0.982934 + 0.183959i \(0.941109\pi\)
\(80\) −10.1476 4.66580i −1.13454 0.521652i
\(81\) 0 0
\(82\) −0.728538 8.20053i −0.0804535 0.905597i
\(83\) 10.3428 + 2.77135i 1.13527 + 0.304195i 0.777048 0.629441i \(-0.216716\pi\)
0.358223 + 0.933636i \(0.383383\pi\)
\(84\) 0 0
\(85\) 17.4695 4.68093i 1.89483 0.507718i
\(86\) 8.68792 3.17535i 0.936843 0.342407i
\(87\) 0 0
\(88\) −0.0542436 13.4815i −0.00578239 1.43713i
\(89\) 2.24307i 0.237765i −0.992908 0.118883i \(-0.962069\pi\)
0.992908 0.118883i \(-0.0379312\pi\)
\(90\) 0 0
\(91\) −3.63698 3.63698i −0.381259 0.381259i
\(92\) −6.53582 + 5.51415i −0.681407 + 0.574890i
\(93\) 0 0
\(94\) 2.16615 4.66165i 0.223422 0.480812i
\(95\) 1.89016 3.27385i 0.193926 0.335890i
\(96\) 0 0
\(97\) 6.50191 + 11.2616i 0.660169 + 1.14345i 0.980571 + 0.196165i \(0.0628488\pi\)
−0.320402 + 0.947282i \(0.603818\pi\)
\(98\) 5.86050 0.520649i 0.592000 0.0525935i
\(99\) 0 0
\(100\) 0.985980 + 5.50537i 0.0985980 + 0.550537i
\(101\) 2.36072 8.81034i 0.234901 0.876662i −0.743293 0.668966i \(-0.766737\pi\)
0.978194 0.207696i \(-0.0665963\pi\)
\(102\) 0 0
\(103\) −3.73262 2.15503i −0.367786 0.212342i 0.304705 0.952447i \(-0.401442\pi\)
−0.672491 + 0.740105i \(0.734776\pi\)
\(104\) −2.19253 3.76252i −0.214995 0.368946i
\(105\) 0 0
\(106\) 0.262785 1.50211i 0.0255239 0.145897i
\(107\) −0.0516852 0.0516852i −0.00499659 0.00499659i 0.704604 0.709601i \(-0.251125\pi\)
−0.709601 + 0.704604i \(0.751125\pi\)
\(108\) 0 0
\(109\) 5.73510 5.73510i 0.549323 0.549323i −0.376922 0.926245i \(-0.623018\pi\)
0.926245 + 0.376922i \(0.123018\pi\)
\(110\) −15.4034 + 10.8164i −1.46866 + 1.03130i
\(111\) 0 0
\(112\) 13.1721 + 2.24980i 1.24464 + 0.212586i
\(113\) −7.13575 + 12.3595i −0.671275 + 1.16268i 0.306268 + 0.951945i \(0.400920\pi\)
−0.977543 + 0.210737i \(0.932414\pi\)
\(114\) 0 0
\(115\) 11.5316 + 3.08988i 1.07533 + 0.288133i
\(116\) −1.27645 + 1.83340i −0.118515 + 0.170227i
\(117\) 0 0
\(118\) 9.11148 + 7.62464i 0.838780 + 0.701905i
\(119\) −18.7394 + 10.8192i −1.71784 + 0.991794i
\(120\) 0 0
\(121\) −10.1491 5.85956i −0.922642 0.532688i
\(122\) 3.39108 + 9.27818i 0.307014 + 0.840007i
\(123\) 0 0
\(124\) 4.89227 + 5.79872i 0.439339 + 0.520740i
\(125\) −4.35061 + 4.35061i −0.389131 + 0.389131i
\(126\) 0 0
\(127\) −16.2634 −1.44315 −0.721573 0.692338i \(-0.756581\pi\)
−0.721573 + 0.692338i \(0.756581\pi\)
\(128\) 10.2981 + 4.68491i 0.910235 + 0.414091i
\(129\) 0 0
\(130\) −2.56200 + 5.51351i −0.224702 + 0.483567i
\(131\) 4.58345 + 17.1057i 0.400458 + 1.49453i 0.812281 + 0.583267i \(0.198226\pi\)
−0.411822 + 0.911264i \(0.635108\pi\)
\(132\) 0 0
\(133\) −1.17061 + 4.36879i −0.101505 + 0.378822i
\(134\) 1.70892 2.04217i 0.147629 0.176417i
\(135\) 0 0
\(136\) −17.6768 + 4.81279i −1.51577 + 0.412694i
\(137\) 9.62551 5.55729i 0.822363 0.474791i −0.0288677 0.999583i \(-0.509190\pi\)
0.851231 + 0.524792i \(0.175857\pi\)
\(138\) 0 0
\(139\) 6.50347 1.74260i 0.551617 0.147805i 0.0277649 0.999614i \(-0.491161\pi\)
0.523852 + 0.851809i \(0.324494\pi\)
\(140\) −7.92968 16.8868i −0.670180 1.42720i
\(141\) 0 0
\(142\) 4.61178 3.23843i 0.387012 0.271763i
\(143\) −7.33859 −0.613684
\(144\) 0 0
\(145\) 3.11889 0.259009
\(146\) −6.31299 + 4.43303i −0.522467 + 0.366880i
\(147\) 0 0
\(148\) 15.7361 7.38930i 1.29350 0.607396i
\(149\) 10.7583 2.88268i 0.881354 0.236158i 0.210363 0.977623i \(-0.432535\pi\)
0.670991 + 0.741465i \(0.265869\pi\)
\(150\) 0 0
\(151\) −18.9045 + 10.9145i −1.53842 + 0.888210i −0.539493 + 0.841990i \(0.681384\pi\)
−0.998931 + 0.0462196i \(0.985283\pi\)
\(152\) −1.90131 + 3.32398i −0.154217 + 0.269611i
\(153\) 0 0
\(154\) 14.4518 17.2700i 1.16456 1.39165i
\(155\) 2.74141 10.2311i 0.220195 0.821780i
\(156\) 0 0
\(157\) −2.18429 8.15189i −0.174326 0.650592i −0.996666 0.0815954i \(-0.973998\pi\)
0.822340 0.568996i \(-0.192668\pi\)
\(158\) 3.51880 7.57259i 0.279941 0.602443i
\(159\) 0 0
\(160\) −2.84705 15.5365i −0.225079 1.22827i
\(161\) −14.2835 −1.12570
\(162\) 0 0
\(163\) −6.93193 + 6.93193i −0.542950 + 0.542950i −0.924393 0.381442i \(-0.875428\pi\)
0.381442 + 0.924393i \(0.375428\pi\)
\(164\) 8.89893 7.50786i 0.694890 0.586265i
\(165\) 0 0
\(166\) 5.19827 + 14.2227i 0.403464 + 1.10390i
\(167\) −7.33544 4.23512i −0.567633 0.327723i 0.188570 0.982060i \(-0.439615\pi\)
−0.756204 + 0.654336i \(0.772948\pi\)
\(168\) 0 0
\(169\) 9.20544 5.31477i 0.708111 0.408828i
\(170\) 19.6152 + 16.4143i 1.50442 + 1.25892i
\(171\) 0 0
\(172\) 10.7358 + 7.47447i 0.818599 + 0.569923i
\(173\) 5.81815 + 1.55897i 0.442346 + 0.118526i 0.473116 0.881000i \(-0.343129\pi\)
−0.0307700 + 0.999526i \(0.509796\pi\)
\(174\) 0 0
\(175\) −4.67112 + 8.09061i −0.353103 + 0.611593i
\(176\) 15.5589 11.0193i 1.17280 0.830614i
\(177\) 0 0
\(178\) 2.59606 1.82297i 0.194583 0.136638i
\(179\) 8.34442 8.34442i 0.623692 0.623692i −0.322782 0.946473i \(-0.604618\pi\)
0.946473 + 0.322782i \(0.104618\pi\)
\(180\) 0 0
\(181\) −13.3444 13.3444i −0.991880 0.991880i 0.00808779 0.999967i \(-0.497426\pi\)
−0.999967 + 0.00808779i \(0.997426\pi\)
\(182\) 1.25350 7.16513i 0.0929156 0.531115i
\(183\) 0 0
\(184\) −11.6936 3.08293i −0.862066 0.227276i
\(185\) −21.0192 12.1354i −1.54536 0.892214i
\(186\) 0 0
\(187\) −7.99059 + 29.8213i −0.584330 + 2.18075i
\(188\) 7.15570 1.28154i 0.521883 0.0934661i
\(189\) 0 0
\(190\) 5.32521 0.473093i 0.386331 0.0343218i
\(191\) 0.892527 + 1.54590i 0.0645810 + 0.111858i 0.896508 0.443027i \(-0.146096\pi\)
−0.831927 + 0.554885i \(0.812762\pi\)
\(192\) 0 0
\(193\) −8.20588 + 14.2130i −0.590672 + 1.02307i 0.403470 + 0.914993i \(0.367804\pi\)
−0.994142 + 0.108081i \(0.965529\pi\)
\(194\) −7.74967 + 16.6776i −0.556394 + 1.19738i
\(195\) 0 0
\(196\) 5.36549 + 6.35962i 0.383249 + 0.454258i
\(197\) 3.44937 + 3.44937i 0.245758 + 0.245758i 0.819227 0.573469i \(-0.194403\pi\)
−0.573469 + 0.819227i \(0.694403\pi\)
\(198\) 0 0
\(199\) 15.0093i 1.06398i −0.846751 0.531990i \(-0.821444\pi\)
0.846751 0.531990i \(-0.178556\pi\)
\(200\) −5.57042 + 5.61543i −0.393888 + 0.397071i
\(201\) 0 0
\(202\) 12.1154 4.42805i 0.852436 0.311557i
\(203\) −3.60439 + 0.965795i −0.252979 + 0.0677855i
\(204\) 0 0
\(205\) −15.7010 4.20707i −1.09661 0.293835i
\(206\) −0.539388 6.07144i −0.0375809 0.423017i
\(207\) 0 0
\(208\) 2.57273 5.59541i 0.178386 0.387972i
\(209\) 3.22660 + 5.58863i 0.223189 + 0.386574i
\(210\) 0 0
\(211\) −3.18415 11.8834i −0.219206 0.818089i −0.984643 0.174578i \(-0.944144\pi\)
0.765437 0.643511i \(-0.222523\pi\)
\(212\) 1.95206 0.916642i 0.134068 0.0629552i
\(213\) 0 0
\(214\) 0.0178135 0.101824i 0.00121771 0.00696054i
\(215\) 18.2632i 1.24554i
\(216\) 0 0
\(217\) 12.6726i 0.860274i
\(218\) 11.2986 + 1.97663i 0.765238 + 0.133874i
\(219\) 0 0
\(220\) −25.0371 9.03676i −1.68800 0.609258i
\(221\) 2.58107 + 9.63269i 0.173622 + 0.647965i
\(222\) 0 0
\(223\) 0.258294 + 0.447379i 0.0172967 + 0.0299587i 0.874544 0.484946i \(-0.161161\pi\)
−0.857248 + 0.514905i \(0.827827\pi\)
\(224\) 8.10127 + 17.0734i 0.541289 + 1.14076i
\(225\) 0 0
\(226\) −20.1038 + 1.78602i −1.33728 + 0.118805i
\(227\) −9.84745 2.63862i −0.653598 0.175131i −0.0832432 0.996529i \(-0.526528\pi\)
−0.570355 + 0.821398i \(0.693194\pi\)
\(228\) 0 0
\(229\) −20.6838 + 5.54222i −1.36683 + 0.366240i −0.866319 0.499491i \(-0.833520\pi\)
−0.500508 + 0.865732i \(0.666854\pi\)
\(230\) 5.79575 + 15.8575i 0.382160 + 1.04561i
\(231\) 0 0
\(232\) −3.15931 + 0.0127117i −0.207419 + 0.000834563i
\(233\) 23.2468i 1.52295i 0.648194 + 0.761476i \(0.275525\pi\)
−0.648194 + 0.761476i \(0.724475\pi\)
\(234\) 0 0
\(235\) −7.17649 7.17649i −0.468142 0.468142i
\(236\) −1.41949 + 16.7420i −0.0924010 + 1.08981i
\(237\) 0 0
\(238\) −27.7515 12.8955i −1.79886 0.835889i
\(239\) −0.219358 + 0.379939i −0.0141891 + 0.0245762i −0.873033 0.487662i \(-0.837850\pi\)
0.858844 + 0.512238i \(0.171183\pi\)
\(240\) 0 0
\(241\) 7.67406 + 13.2919i 0.494330 + 0.856204i 0.999979 0.00653501i \(-0.00208017\pi\)
−0.505649 + 0.862739i \(0.668747\pi\)
\(242\) −1.46660 16.5083i −0.0942769 1.06120i
\(243\) 0 0
\(244\) −7.98228 + 11.4652i −0.511013 + 0.733985i
\(245\) 3.00658 11.2207i 0.192083 0.716865i
\(246\) 0 0
\(247\) 1.80521 + 1.04224i 0.114863 + 0.0663159i
\(248\) −2.73524 + 10.3748i −0.173688 + 0.658803i
\(249\) 0 0
\(250\) −8.57105 1.49946i −0.542081 0.0948341i
\(251\) −8.02147 8.02147i −0.506310 0.506310i 0.407081 0.913392i \(-0.366547\pi\)
−0.913392 + 0.407081i \(0.866547\pi\)
\(252\) 0 0
\(253\) −14.4104 + 14.4104i −0.905977 + 0.905977i
\(254\) −13.2175 18.8228i −0.829339 1.18104i
\(255\) 0 0
\(256\) 2.94727 + 15.7262i 0.184204 + 0.982888i
\(257\) −4.72936 + 8.19149i −0.295009 + 0.510971i −0.974987 0.222262i \(-0.928656\pi\)
0.679978 + 0.733233i \(0.261989\pi\)
\(258\) 0 0
\(259\) 28.0490 + 7.51571i 1.74288 + 0.467003i
\(260\) −8.46332 + 1.51573i −0.524873 + 0.0940016i
\(261\) 0 0
\(262\) −16.0725 + 19.2067i −0.992964 + 1.18660i
\(263\) −16.2413 + 9.37694i −1.00148 + 0.578207i −0.908687 0.417478i \(-0.862914\pi\)
−0.0927966 + 0.995685i \(0.529581\pi\)
\(264\) 0 0
\(265\) −2.60743 1.50540i −0.160173 0.0924759i
\(266\) −6.00767 + 2.19574i −0.368354 + 0.134630i
\(267\) 0 0
\(268\) 3.75241 + 0.318153i 0.229215 + 0.0194343i
\(269\) 13.5606 13.5606i 0.826805 0.826805i −0.160269 0.987073i \(-0.551236\pi\)
0.987073 + 0.160269i \(0.0512361\pi\)
\(270\) 0 0
\(271\) 30.6233 1.86023 0.930115 0.367268i \(-0.119707\pi\)
0.930115 + 0.367268i \(0.119707\pi\)
\(272\) −19.9363 16.5471i −1.20882 1.00332i
\(273\) 0 0
\(274\) 14.2546 + 6.62377i 0.861152 + 0.400156i
\(275\) 3.44988 + 12.8751i 0.208036 + 0.776400i
\(276\) 0 0
\(277\) 5.40521 20.1725i 0.324767 1.21205i −0.589778 0.807565i \(-0.700785\pi\)
0.914545 0.404483i \(-0.132549\pi\)
\(278\) 7.30228 + 6.11067i 0.437962 + 0.366494i
\(279\) 0 0
\(280\) 13.0997 22.9017i 0.782858 1.36864i
\(281\) −10.6538 + 6.15097i −0.635552 + 0.366936i −0.782899 0.622149i \(-0.786260\pi\)
0.147347 + 0.989085i \(0.452927\pi\)
\(282\) 0 0
\(283\) 12.8013 3.43009i 0.760957 0.203898i 0.142584 0.989783i \(-0.454459\pi\)
0.618373 + 0.785885i \(0.287792\pi\)
\(284\) 7.49611 + 2.70561i 0.444812 + 0.160548i
\(285\) 0 0
\(286\) −5.96417 8.49345i −0.352669 0.502228i
\(287\) 19.4479 1.14797
\(288\) 0 0
\(289\) 24.9540 1.46788
\(290\) 2.53476 + 3.60970i 0.148846 + 0.211969i
\(291\) 0 0
\(292\) −10.2613 3.70366i −0.600497 0.216741i
\(293\) −21.3351 + 5.71672i −1.24641 + 0.333974i −0.820948 0.571003i \(-0.806554\pi\)
−0.425460 + 0.904977i \(0.639888\pi\)
\(294\) 0 0
\(295\) 20.3148 11.7287i 1.18277 0.682874i
\(296\) 21.3410 + 12.2070i 1.24042 + 0.709518i
\(297\) 0 0
\(298\) 12.0797 + 10.1085i 0.699759 + 0.585570i
\(299\) −1.70377 + 6.35854i −0.0985313 + 0.367724i
\(300\) 0 0
\(301\) 5.65539 + 21.1062i 0.325971 + 1.21654i
\(302\) −27.9960 13.0091i −1.61099 0.748587i
\(303\) 0 0
\(304\) −5.39229 + 0.500928i −0.309269 + 0.0287302i
\(305\) 19.5040 1.11680
\(306\) 0 0
\(307\) −3.59225 + 3.59225i −0.205021 + 0.205021i −0.802147 0.597126i \(-0.796309\pi\)
0.597126 + 0.802147i \(0.296309\pi\)
\(308\) 31.7328 + 2.69051i 1.80815 + 0.153306i
\(309\) 0 0
\(310\) 14.0691 5.14211i 0.799071 0.292052i
\(311\) 8.62665 + 4.98060i 0.489173 + 0.282424i 0.724231 0.689557i \(-0.242195\pi\)
−0.235058 + 0.971981i \(0.575528\pi\)
\(312\) 0 0
\(313\) −22.1588 + 12.7934i −1.25249 + 0.723124i −0.971603 0.236617i \(-0.923961\pi\)
−0.280885 + 0.959741i \(0.590628\pi\)
\(314\) 7.65953 9.15317i 0.432252 0.516543i
\(315\) 0 0
\(316\) 11.6240 2.08180i 0.653903 0.117110i
\(317\) −17.8781 4.79041i −1.00413 0.269056i −0.280957 0.959720i \(-0.590652\pi\)
−0.723176 + 0.690664i \(0.757318\pi\)
\(318\) 0 0
\(319\) −2.66205 + 4.61080i −0.149046 + 0.258155i
\(320\) 15.6676 15.9218i 0.875843 0.890054i
\(321\) 0 0
\(322\) −11.6084 16.5313i −0.646910 0.921251i
\(323\) 6.20084 6.20084i 0.345024 0.345024i
\(324\) 0 0
\(325\) 3.04449 + 3.04449i 0.168878 + 0.168878i
\(326\) −13.6564 2.38912i −0.756361 0.132321i
\(327\) 0 0
\(328\) 15.9216 + 4.19760i 0.879125 + 0.231774i
\(329\) 10.5159 + 6.07136i 0.579760 + 0.334725i
\(330\) 0 0
\(331\) 5.10146 19.0389i 0.280402 1.04647i −0.671733 0.740794i \(-0.734450\pi\)
0.952134 0.305680i \(-0.0988836\pi\)
\(332\) −12.2362 + 17.5753i −0.671550 + 0.964570i
\(333\) 0 0
\(334\) −1.06002 11.9317i −0.0580016 0.652875i
\(335\) −2.62878 4.55319i −0.143626 0.248767i
\(336\) 0 0
\(337\) 3.29609 5.70899i 0.179549 0.310988i −0.762177 0.647369i \(-0.775869\pi\)
0.941726 + 0.336380i \(0.109203\pi\)
\(338\) 13.6325 + 6.33470i 0.741511 + 0.344562i
\(339\) 0 0
\(340\) −3.05588 + 36.0421i −0.165729 + 1.95466i
\(341\) 12.7852 + 12.7852i 0.692360 + 0.692360i
\(342\) 0 0
\(343\) 9.48653i 0.512224i
\(344\) 0.0744356 + 18.4999i 0.00401330 + 0.997447i
\(345\) 0 0
\(346\) 2.92418 + 8.00073i 0.157205 + 0.430122i
\(347\) 3.20074 0.857635i 0.171825 0.0460403i −0.171881 0.985118i \(-0.554984\pi\)
0.343706 + 0.939077i \(0.388318\pi\)
\(348\) 0 0
\(349\) −22.0000 5.89488i −1.17763 0.315546i −0.383645 0.923480i \(-0.625331\pi\)
−0.793987 + 0.607935i \(0.791998\pi\)
\(350\) −13.1601 + 1.16915i −0.703436 + 0.0624935i
\(351\) 0 0
\(352\) 25.3984 + 9.05183i 1.35374 + 0.482464i
\(353\) −14.2071 24.6074i −0.756167 1.30972i −0.944792 0.327670i \(-0.893737\pi\)
0.188626 0.982049i \(-0.439597\pi\)
\(354\) 0 0
\(355\) −2.87967 10.7471i −0.152837 0.570396i
\(356\) 4.21970 + 1.52304i 0.223644 + 0.0807209i
\(357\) 0 0
\(358\) 16.4392 + 2.87594i 0.868838 + 0.151998i
\(359\) 7.35521i 0.388193i 0.980982 + 0.194097i \(0.0621775\pi\)
−0.980982 + 0.194097i \(0.937823\pi\)
\(360\) 0 0
\(361\) 17.1670i 0.903527i
\(362\) 4.59920 26.2895i 0.241728 1.38174i
\(363\) 0 0
\(364\) 9.31142 4.37243i 0.488051 0.229178i
\(365\) 3.94194 + 14.7115i 0.206330 + 0.770035i
\(366\) 0 0
\(367\) −17.0496 29.5308i −0.889984 1.54150i −0.839893 0.542752i \(-0.817382\pi\)
−0.0500906 0.998745i \(-0.515951\pi\)
\(368\) −5.93549 16.0394i −0.309409 0.836110i
\(369\) 0 0
\(370\) −3.03740 34.1895i −0.157907 1.77743i
\(371\) 3.47948 + 0.932323i 0.180646 + 0.0484038i
\(372\) 0 0
\(373\) 23.8179 6.38198i 1.23324 0.330447i 0.417402 0.908722i \(-0.362941\pi\)
0.815842 + 0.578275i \(0.196274\pi\)
\(374\) −41.0082 + 14.9881i −2.12048 + 0.775015i
\(375\) 0 0
\(376\) 7.29874 + 7.24024i 0.376404 + 0.373387i
\(377\) 1.71976i 0.0885720i
\(378\) 0 0
\(379\) −2.66916 2.66916i −0.137106 0.137106i 0.635223 0.772329i \(-0.280908\pi\)
−0.772329 + 0.635223i \(0.780908\pi\)
\(380\) 4.87540 + 5.77873i 0.250103 + 0.296443i
\(381\) 0 0
\(382\) −1.06381 + 2.28936i −0.0544292 + 0.117134i
\(383\) 3.14570 5.44851i 0.160738 0.278406i −0.774396 0.632701i \(-0.781946\pi\)
0.935133 + 0.354296i \(0.115279\pi\)
\(384\) 0 0
\(385\) −22.2307 38.5047i −1.13298 1.96238i
\(386\) −23.1187 + 2.05387i −1.17671 + 0.104539i
\(387\) 0 0
\(388\) −25.6003 + 4.58487i −1.29966 + 0.232761i
\(389\) 0.724164 2.70262i 0.0367166 0.137028i −0.945135 0.326681i \(-0.894070\pi\)
0.981851 + 0.189653i \(0.0607363\pi\)
\(390\) 0 0
\(391\) 23.9836 + 13.8469i 1.21290 + 0.700269i
\(392\) −2.99981 + 11.3784i −0.151513 + 0.574695i
\(393\) 0 0
\(394\) −1.18884 + 6.79554i −0.0598930 + 0.342354i
\(395\) −11.6578 11.6578i −0.586568 0.586568i
\(396\) 0 0
\(397\) −4.29700 + 4.29700i −0.215660 + 0.215660i −0.806667 0.591007i \(-0.798731\pi\)
0.591007 + 0.806667i \(0.298731\pi\)
\(398\) 17.3712 12.1982i 0.870742 0.611442i
\(399\) 0 0
\(400\) −11.0263 1.88329i −0.551313 0.0941646i
\(401\) 6.63116 11.4855i 0.331145 0.573559i −0.651592 0.758570i \(-0.725899\pi\)
0.982737 + 0.185010i \(0.0592319\pi\)
\(402\) 0 0
\(403\) 5.64143 + 1.51162i 0.281020 + 0.0752990i
\(404\) 14.9712 + 10.4232i 0.744846 + 0.518575i
\(405\) 0 0
\(406\) −4.04712 3.38669i −0.200855 0.168079i
\(407\) 35.8808 20.7158i 1.77854 1.02684i
\(408\) 0 0
\(409\) −10.6538 6.15100i −0.526799 0.304147i 0.212913 0.977071i \(-0.431705\pi\)
−0.739712 + 0.672924i \(0.765038\pi\)
\(410\) −7.89128 21.5910i −0.389722 1.06630i
\(411\) 0 0
\(412\) 6.58851 5.55860i 0.324593 0.273853i
\(413\) −19.8452 + 19.8452i −0.976518 + 0.976518i
\(414\) 0 0
\(415\) 29.8981 1.46764
\(416\) 8.56683 1.56987i 0.420023 0.0769691i
\(417\) 0 0
\(418\) −3.84580 + 8.27631i −0.188104 + 0.404808i
\(419\) −7.82317 29.1965i −0.382187 1.42634i −0.842554 0.538612i \(-0.818949\pi\)
0.460367 0.887729i \(-0.347718\pi\)
\(420\) 0 0
\(421\) −5.75964 + 21.4953i −0.280708 + 1.04762i 0.671211 + 0.741266i \(0.265774\pi\)
−0.951919 + 0.306350i \(0.900892\pi\)
\(422\) 11.1657 13.3430i 0.543537 0.649529i
\(423\) 0 0
\(424\) 2.64735 + 1.51428i 0.128567 + 0.0735399i
\(425\) 15.6866 9.05668i 0.760913 0.439314i
\(426\) 0 0
\(427\) −22.5401 + 6.03961i −1.09079 + 0.292277i
\(428\) 0.132325 0.0621368i 0.00639616 0.00300349i
\(429\) 0 0
\(430\) 21.1372 14.8427i 1.01933 0.715780i
\(431\) −15.3940 −0.741505 −0.370752 0.928732i \(-0.620900\pi\)
−0.370752 + 0.928732i \(0.620900\pi\)
\(432\) 0 0
\(433\) −17.2454 −0.828763 −0.414382 0.910103i \(-0.636002\pi\)
−0.414382 + 0.910103i \(0.636002\pi\)
\(434\) −14.6669 + 10.2992i −0.704033 + 0.494378i
\(435\) 0 0
\(436\) 6.89483 + 14.6831i 0.330203 + 0.703191i
\(437\) 5.59138 1.49821i 0.267472 0.0716690i
\(438\) 0 0
\(439\) −4.55070 + 2.62735i −0.217193 + 0.125397i −0.604650 0.796491i \(-0.706687\pi\)
0.387457 + 0.921888i \(0.373354\pi\)
\(440\) −9.88908 36.3214i −0.471443 1.73155i
\(441\) 0 0
\(442\) −9.05089 + 10.8159i −0.430507 + 0.514458i
\(443\) −3.35032 + 12.5036i −0.159179 + 0.594062i 0.839533 + 0.543309i \(0.182829\pi\)
−0.998711 + 0.0507532i \(0.983838\pi\)
\(444\) 0 0
\(445\) −1.62102 6.04974i −0.0768438 0.286785i
\(446\) −0.307863 + 0.662532i −0.0145777 + 0.0313718i
\(447\) 0 0
\(448\) −13.1761 + 23.2519i −0.622514 + 1.09855i
\(449\) −27.9740 −1.32018 −0.660088 0.751189i \(-0.729481\pi\)
−0.660088 + 0.751189i \(0.729481\pi\)
\(450\) 0 0
\(451\) 19.6207 19.6207i 0.923904 0.923904i
\(452\) −18.4057 21.8159i −0.865730 1.02613i
\(453\) 0 0
\(454\) −4.94930 13.5416i −0.232282 0.635537i
\(455\) −12.4376 7.18083i −0.583082 0.336643i
\(456\) 0 0
\(457\) 35.2732 20.3650i 1.65001 0.952635i 0.672947 0.739690i \(-0.265028\pi\)
0.977064 0.212944i \(-0.0683053\pi\)
\(458\) −23.2244 19.4346i −1.08521 0.908118i
\(459\) 0 0
\(460\) −13.6426 + 19.5954i −0.636092 + 0.913639i
\(461\) 36.8721 + 9.87984i 1.71730 + 0.460150i 0.977196 0.212339i \(-0.0681082\pi\)
0.740107 + 0.672489i \(0.234775\pi\)
\(462\) 0 0
\(463\) −17.7637 + 30.7676i −0.825549 + 1.42989i 0.0759497 + 0.997112i \(0.475801\pi\)
−0.901499 + 0.432781i \(0.857532\pi\)
\(464\) −2.58232 3.64614i −0.119881 0.169268i
\(465\) 0 0
\(466\) −26.9051 + 18.8930i −1.24636 + 0.875201i
\(467\) 17.1010 17.1010i 0.791341 0.791341i −0.190371 0.981712i \(-0.560969\pi\)
0.981712 + 0.190371i \(0.0609692\pi\)
\(468\) 0 0
\(469\) 4.44794 + 4.44794i 0.205387 + 0.205387i
\(470\) 2.47341 14.1383i 0.114090 0.652149i
\(471\) 0 0
\(472\) −20.5302 + 11.9635i −0.944981 + 0.550666i
\(473\) 26.9994 + 15.5881i 1.24143 + 0.716742i
\(474\) 0 0
\(475\) 0.979914 3.65709i 0.0449615 0.167799i
\(476\) −7.62923 42.5990i −0.349685 1.95252i
\(477\) 0 0
\(478\) −0.618004 + 0.0549036i −0.0282668 + 0.00251123i
\(479\) 6.76619 + 11.7194i 0.309155 + 0.535473i 0.978178 0.207769i \(-0.0666204\pi\)
−0.669023 + 0.743242i \(0.733287\pi\)
\(480\) 0 0
\(481\) 6.69148 11.5900i 0.305105 0.528458i
\(482\) −9.14676 + 19.6842i −0.416624 + 0.896590i
\(483\) 0 0
\(484\) 17.9143 15.1139i 0.814285 0.686997i
\(485\) 25.6747 + 25.6747i 1.16583 + 1.16583i
\(486\) 0 0
\(487\) 16.1436i 0.731536i 0.930706 + 0.365768i \(0.119194\pi\)
−0.930706 + 0.365768i \(0.880806\pi\)
\(488\) −19.7568 + 0.0794927i −0.894347 + 0.00359847i
\(489\) 0 0
\(490\) 15.4300 5.63950i 0.697055 0.254766i
\(491\) 34.9555 9.36630i 1.57752 0.422695i 0.639363 0.768905i \(-0.279198\pi\)
0.938157 + 0.346209i \(0.112531\pi\)
\(492\) 0 0
\(493\) 6.98844 + 1.87255i 0.314744 + 0.0843353i
\(494\) 0.260864 + 2.93633i 0.0117368 + 0.132112i
\(495\) 0 0
\(496\) −14.2305 + 5.26609i −0.638967 + 0.236454i
\(497\) 6.65589 + 11.5283i 0.298557 + 0.517117i
\(498\) 0 0
\(499\) −1.70347 6.35742i −0.0762576 0.284597i 0.917258 0.398294i \(-0.130398\pi\)
−0.993516 + 0.113696i \(0.963731\pi\)
\(500\) −5.23038 11.1385i −0.233910 0.498128i
\(501\) 0 0
\(502\) 2.76463 15.8029i 0.123392 0.705319i
\(503\) 8.67964i 0.387006i 0.981100 + 0.193503i \(0.0619849\pi\)
−0.981100 + 0.193503i \(0.938015\pi\)
\(504\) 0 0
\(505\) 25.4682i 1.13332i
\(506\) −28.3897 4.96662i −1.26208 0.220793i
\(507\) 0 0
\(508\) 11.0428 30.5950i 0.489946 1.35743i
\(509\) −0.894794 3.33942i −0.0396611 0.148017i 0.943256 0.332067i \(-0.107746\pi\)
−0.982917 + 0.184050i \(0.941079\pi\)
\(510\) 0 0
\(511\) −9.11113 15.7809i −0.403053 0.698108i
\(512\) −15.8057 + 16.1920i −0.698520 + 0.715590i
\(513\) 0 0
\(514\) −13.3242 + 1.18372i −0.587704 + 0.0522118i
\(515\) −11.6246 3.11479i −0.512240 0.137254i
\(516\) 0 0
\(517\) 16.7347 4.48404i 0.735990 0.197208i
\(518\) 14.0973 + 38.5711i 0.619402 + 1.69472i
\(519\) 0 0
\(520\) −8.63251 8.56332i −0.378560 0.375526i
\(521\) 15.7843i 0.691524i −0.938322 0.345762i \(-0.887620\pi\)
0.938322 0.345762i \(-0.112380\pi\)
\(522\) 0 0
\(523\) 6.62449 + 6.62449i 0.289669 + 0.289669i 0.836949 0.547280i \(-0.184337\pi\)
−0.547280 + 0.836949i \(0.684337\pi\)
\(524\) −35.2916 2.99225i −1.54172 0.130717i
\(525\) 0 0
\(526\) −24.0521 11.1764i −1.04872 0.487315i
\(527\) 12.2853 21.2787i 0.535155 0.926916i
\(528\) 0 0
\(529\) −2.35965 4.08703i −0.102593 0.177697i
\(530\) −0.376790 4.24120i −0.0163667 0.184226i
\(531\) 0 0
\(532\) −7.42379 5.16857i −0.321862 0.224086i
\(533\) 2.31978 8.65755i 0.100481 0.375000i
\(534\) 0 0
\(535\) −0.176751 0.102047i −0.00764160 0.00441188i
\(536\) 2.68141 + 4.60148i 0.115819 + 0.198754i
\(537\) 0 0
\(538\) 26.7155 + 4.67372i 1.15179 + 0.201498i
\(539\) 14.0219 + 14.0219i 0.603967 + 0.603967i
\(540\) 0 0
\(541\) 32.2832 32.2832i 1.38796 1.38796i 0.558377 0.829587i \(-0.311424\pi\)
0.829587 0.558377i \(-0.188576\pi\)
\(542\) 24.8879 + 35.4423i 1.06903 + 1.52238i
\(543\) 0 0
\(544\) 2.94859 36.5217i 0.126420 1.56585i
\(545\) 11.3234 19.6126i 0.485040 0.840113i
\(546\) 0 0
\(547\) −7.43060 1.99102i −0.317710 0.0851300i 0.0964402 0.995339i \(-0.469254\pi\)
−0.414150 + 0.910209i \(0.635921\pi\)
\(548\) 3.91876 + 21.8810i 0.167401 + 0.934711i
\(549\) 0 0
\(550\) −12.0975 + 14.4566i −0.515839 + 0.616430i
\(551\) 1.30966 0.756135i 0.0557936 0.0322124i
\(552\) 0 0
\(553\) 17.0825 + 9.86259i 0.726422 + 0.419400i
\(554\) 27.7399 10.1386i 1.17855 0.430750i
\(555\) 0 0
\(556\) −1.13763 + 13.4176i −0.0482464 + 0.569035i
\(557\) −24.4143 + 24.4143i −1.03447 + 1.03447i −0.0350828 + 0.999384i \(0.511170\pi\)
−0.999384 + 0.0350828i \(0.988830\pi\)
\(558\) 0 0
\(559\) 10.0704 0.425931
\(560\) 37.1520 3.45131i 1.56996 0.145844i
\(561\) 0 0
\(562\) −15.7774 7.33138i −0.665530 0.309256i
\(563\) −3.30278 12.3261i −0.139196 0.519485i −0.999945 0.0104567i \(-0.996671\pi\)
0.860750 0.509028i \(-0.169995\pi\)
\(564\) 0 0
\(565\) −10.3137 + 38.4913i −0.433901 + 1.61934i
\(566\) 14.3736 + 12.0281i 0.604169 + 0.505578i
\(567\) 0 0
\(568\) 2.96079 + 10.8746i 0.124232 + 0.456289i
\(569\) −22.2747 + 12.8603i −0.933803 + 0.539132i −0.888012 0.459819i \(-0.847914\pi\)
−0.0457910 + 0.998951i \(0.514581\pi\)
\(570\) 0 0
\(571\) 33.6207 9.00865i 1.40698 0.377000i 0.526136 0.850400i \(-0.323640\pi\)
0.880848 + 0.473400i \(0.156973\pi\)
\(572\) 4.98288 13.8055i 0.208345 0.577235i
\(573\) 0 0
\(574\) 15.8055 + 22.5084i 0.659711 + 0.939480i
\(575\) 11.9566 0.498626
\(576\) 0 0
\(577\) −26.7695 −1.11443 −0.557215 0.830369i \(-0.688130\pi\)
−0.557215 + 0.830369i \(0.688130\pi\)
\(578\) 20.2804 + 28.8809i 0.843554 + 1.20129i
\(579\) 0 0
\(580\) −2.11771 + 5.86729i −0.0879333 + 0.243626i
\(581\) −34.5523 + 9.25826i −1.43347 + 0.384097i
\(582\) 0 0
\(583\) 4.45101 2.56979i 0.184342 0.106430i
\(584\) −4.05298 14.8861i −0.167714 0.615991i
\(585\) 0 0
\(586\) −23.9556 20.0465i −0.989598 0.828112i
\(587\) −9.79668 + 36.5617i −0.404352 + 1.50906i 0.400895 + 0.916124i \(0.368699\pi\)
−0.805247 + 0.592939i \(0.797967\pi\)
\(588\) 0 0
\(589\) −1.32924 4.96080i −0.0547704 0.204406i
\(590\) 30.0845 + 13.9796i 1.23856 + 0.575529i
\(591\) 0 0
\(592\) 3.21611 + 34.6202i 0.132181 + 1.42288i
\(593\) 7.98596 0.327944 0.163972 0.986465i \(-0.447569\pi\)
0.163972 + 0.986465i \(0.447569\pi\)
\(594\) 0 0
\(595\) −42.7228 + 42.7228i −1.75146 + 1.75146i
\(596\) −1.88192 + 22.1960i −0.0770863 + 0.909183i
\(597\) 0 0
\(598\) −8.74383 + 3.19578i −0.357562 + 0.130685i
\(599\) −1.64879 0.951932i −0.0673679 0.0388949i 0.465938 0.884818i \(-0.345717\pi\)
−0.533306 + 0.845923i \(0.679050\pi\)
\(600\) 0 0
\(601\) −11.7530 + 6.78561i −0.479416 + 0.276791i −0.720173 0.693794i \(-0.755938\pi\)
0.240757 + 0.970585i \(0.422604\pi\)
\(602\) −19.8314 + 23.6986i −0.808268 + 0.965884i
\(603\) 0 0
\(604\) −7.69643 42.9743i −0.313163 1.74860i
\(605\) −31.6074 8.46917i −1.28502 0.344321i
\(606\) 0 0
\(607\) −3.16527 + 5.48241i −0.128474 + 0.222524i −0.923086 0.384594i \(-0.874341\pi\)
0.794611 + 0.607119i \(0.207675\pi\)
\(608\) −4.96214 5.83375i −0.201241 0.236590i
\(609\) 0 0
\(610\) 15.8511 + 22.5733i 0.641794 + 0.913966i
\(611\) 3.95712 3.95712i 0.160088 0.160088i
\(612\) 0 0
\(613\) −1.83081 1.83081i −0.0739458 0.0739458i 0.669167 0.743112i \(-0.266651\pi\)
−0.743112 + 0.669167i \(0.766651\pi\)
\(614\) −7.07703 1.23809i −0.285606 0.0499651i
\(615\) 0 0
\(616\) 22.6758 + 38.9131i 0.913632 + 1.56786i
\(617\) −3.82758 2.20985i −0.154092 0.0889653i 0.420971 0.907074i \(-0.361689\pi\)
−0.575064 + 0.818109i \(0.695023\pi\)
\(618\) 0 0
\(619\) 3.75899 14.0287i 0.151087 0.563863i −0.848322 0.529480i \(-0.822387\pi\)
0.999409 0.0343824i \(-0.0109464\pi\)
\(620\) 17.3854 + 12.1040i 0.698216 + 0.486110i
\(621\) 0 0
\(622\) 1.24661 + 14.0320i 0.0499844 + 0.562632i
\(623\) 3.74672 + 6.48952i 0.150109 + 0.259997i
\(624\) 0 0
\(625\) −15.5810 + 26.9872i −0.623242 + 1.07949i
\(626\) −32.8154 15.2485i −1.31157 0.609453i
\(627\) 0 0
\(628\) 16.8186 + 1.42599i 0.671134 + 0.0569031i
\(629\) −39.8114 39.8114i −1.58738 1.58738i
\(630\) 0 0
\(631\) 33.6255i 1.33861i −0.742987 0.669305i \(-0.766592\pi\)
0.742987 0.669305i \(-0.233408\pi\)
\(632\) 11.8564 + 11.7614i 0.471622 + 0.467842i
\(633\) 0 0
\(634\) −8.98546 24.5847i −0.356858 0.976384i
\(635\) −43.8637 + 11.7532i −1.74068 + 0.466413i
\(636\) 0 0
\(637\) 6.18711 + 1.65783i 0.245142 + 0.0656857i
\(638\) −7.49987 + 0.666291i −0.296923 + 0.0263787i
\(639\) 0 0
\(640\) 31.1605 + 5.19330i 1.23173 + 0.205283i
\(641\) 22.9601 + 39.7681i 0.906871 + 1.57075i 0.818386 + 0.574668i \(0.194869\pi\)
0.0884843 + 0.996078i \(0.471798\pi\)
\(642\) 0 0
\(643\) 6.92565 + 25.8469i 0.273121 + 1.01930i 0.957090 + 0.289790i \(0.0935855\pi\)
−0.683969 + 0.729511i \(0.739748\pi\)
\(644\) 9.69845 26.8703i 0.382173 1.05884i
\(645\) 0 0
\(646\) 12.2162 + 2.13715i 0.480638 + 0.0840850i
\(647\) 11.4351i 0.449559i 0.974410 + 0.224780i \(0.0721662\pi\)
−0.974410 + 0.224780i \(0.927834\pi\)
\(648\) 0 0
\(649\) 40.0431i 1.57183i
\(650\) −1.04930 + 5.99789i −0.0411568 + 0.235256i
\(651\) 0 0
\(652\) −8.33368 17.7472i −0.326372 0.695034i
\(653\) −5.73613 21.4075i −0.224472 0.837741i −0.982615 0.185653i \(-0.940560\pi\)
0.758143 0.652088i \(-0.226107\pi\)
\(654\) 0 0
\(655\) 24.7239 + 42.8230i 0.966041 + 1.67323i
\(656\) 8.08154 + 21.8386i 0.315531 + 0.852654i
\(657\) 0 0
\(658\) 1.51962 + 17.1050i 0.0592408 + 0.666823i
\(659\) −26.7345 7.16348i −1.04143 0.279050i −0.302723 0.953079i \(-0.597896\pi\)
−0.738705 + 0.674029i \(0.764562\pi\)
\(660\) 0 0
\(661\) 9.68293 2.59453i 0.376622 0.100916i −0.0655417 0.997850i \(-0.520878\pi\)
0.442164 + 0.896934i \(0.354211\pi\)
\(662\) 26.1810 9.56890i 1.01755 0.371906i
\(663\) 0 0
\(664\) −30.2856 + 0.121856i −1.17531 + 0.00472894i
\(665\) 12.6289i 0.489729i
\(666\) 0 0
\(667\) 3.37700 + 3.37700i 0.130758 + 0.130758i
\(668\) 12.9479 10.9239i 0.500969 0.422658i
\(669\) 0 0
\(670\) 3.13326 6.74290i 0.121048 0.260501i
\(671\) −16.6472 + 28.8337i −0.642656 + 1.11311i
\(672\) 0 0
\(673\) −16.7789 29.0620i −0.646781 1.12026i −0.983887 0.178791i \(-0.942782\pi\)
0.337106 0.941467i \(-0.390552\pi\)
\(674\) 9.28616 0.824985i 0.357690 0.0317773i
\(675\) 0 0
\(676\) 3.74774 + 20.9261i 0.144144 + 0.804850i
\(677\) −6.92612 + 25.8486i −0.266192 + 0.993443i 0.695324 + 0.718696i \(0.255261\pi\)
−0.961517 + 0.274747i \(0.911406\pi\)
\(678\) 0 0
\(679\) −37.6218 21.7210i −1.44379 0.833575i
\(680\) −44.1975 + 25.7551i −1.69490 + 0.987664i
\(681\) 0 0
\(682\) −4.40649 + 25.1880i −0.168733 + 0.964497i
\(683\) 9.62993 + 9.62993i 0.368479 + 0.368479i 0.866922 0.498443i \(-0.166095\pi\)
−0.498443 + 0.866922i \(0.666095\pi\)
\(684\) 0 0
\(685\) 21.9446 21.9446i 0.838460 0.838460i
\(686\) 10.9794 7.70982i 0.419195 0.294362i
\(687\) 0 0
\(688\) −21.3507 + 15.1212i −0.813987 + 0.576492i
\(689\) 0.830078 1.43774i 0.0316235 0.0547734i
\(690\) 0 0
\(691\) −36.8896 9.88454i −1.40335 0.376025i −0.523801 0.851841i \(-0.675486\pi\)
−0.879545 + 0.475815i \(0.842153\pi\)
\(692\) −6.88325 + 9.88664i −0.261662 + 0.375834i
\(693\) 0 0
\(694\) 3.59388 + 3.00742i 0.136422 + 0.114160i
\(695\) 16.2810 9.39985i 0.617574 0.356557i
\(696\) 0 0
\(697\) −32.6551 18.8534i −1.23690 0.714125i
\(698\) −11.0571 30.2529i −0.418518 1.14509i
\(699\) 0 0
\(700\) −12.0485 14.2809i −0.455390 0.539766i
\(701\) 24.7308 24.7308i 0.934070 0.934070i −0.0638873 0.997957i \(-0.520350\pi\)
0.997957 + 0.0638873i \(0.0203498\pi\)
\(702\) 0 0
\(703\) −11.7683 −0.443851
\(704\) 10.1653 + 36.7518i 0.383118 + 1.38513i
\(705\) 0 0
\(706\) 16.9335 36.4415i 0.637301 1.37150i
\(707\) 7.88649 + 29.4328i 0.296602 + 1.10693i
\(708\) 0 0
\(709\) −7.27509 + 27.1510i −0.273222 + 1.01968i 0.683802 + 0.729668i \(0.260325\pi\)
−0.957024 + 0.290010i \(0.906341\pi\)
\(710\) 10.0980 12.0671i 0.378970 0.452871i
\(711\) 0 0
\(712\) 1.66669 + 6.12153i 0.0624617 + 0.229414i
\(713\) 14.0461 8.10951i 0.526030 0.303704i
\(714\) 0 0
\(715\) −19.7927 + 5.30345i −0.740207 + 0.198338i
\(716\) 10.0318 + 21.3635i 0.374906 + 0.798391i
\(717\) 0 0
\(718\) −8.51267 + 5.97767i −0.317690 + 0.223085i
\(719\) −12.7928 −0.477091 −0.238546 0.971131i \(-0.576671\pi\)
−0.238546 + 0.971131i \(0.576671\pi\)
\(720\) 0 0
\(721\) 14.3987 0.536234
\(722\) −19.8685 + 13.9519i −0.739430 + 0.519234i
\(723\) 0 0
\(724\) 34.1644 16.0428i 1.26971 0.596227i
\(725\) 3.01722 0.808460i 0.112057 0.0300255i
\(726\) 0 0
\(727\) 3.44828 1.99086i 0.127890 0.0738371i −0.434690 0.900580i \(-0.643142\pi\)
0.562580 + 0.826743i \(0.309809\pi\)
\(728\) 12.6280 + 7.22320i 0.468026 + 0.267710i
\(729\) 0 0
\(730\) −13.8230 + 16.5185i −0.511610 + 0.611377i
\(731\) 10.9650 40.9221i 0.405557 1.51356i
\(732\) 0 0
\(733\) 9.71206 + 36.2459i 0.358723 + 1.33877i 0.875734 + 0.482794i \(0.160378\pi\)
−0.517011 + 0.855979i \(0.672955\pi\)
\(734\) 20.3216 43.7328i 0.750082 1.61421i
\(735\) 0 0
\(736\) 13.7396 19.9049i 0.506448 0.733705i
\(737\) 8.97493 0.330596
\(738\) 0 0
\(739\) 3.06425 3.06425i 0.112720 0.112720i −0.648497 0.761217i \(-0.724602\pi\)
0.761217 + 0.648497i \(0.224602\pi\)
\(740\) 37.1012 31.3016i 1.36387 1.15067i
\(741\) 0 0
\(742\) 1.74878 + 4.78474i 0.0641996 + 0.175653i
\(743\) 30.1059 + 17.3817i 1.10448 + 0.637671i 0.937394 0.348272i \(-0.113231\pi\)
0.167085 + 0.985943i \(0.446565\pi\)
\(744\) 0 0
\(745\) 26.9327 15.5496i 0.986738 0.569693i
\(746\) 26.7434 + 22.3793i 0.979145 + 0.819365i
\(747\) 0 0
\(748\) −50.6746 35.2805i −1.85285 1.28998i
\(749\) 0.235865 + 0.0631998i 0.00861831 + 0.00230927i
\(750\) 0 0
\(751\) −7.10890 + 12.3130i −0.259407 + 0.449307i −0.966083 0.258231i \(-0.916861\pi\)
0.706676 + 0.707537i \(0.250194\pi\)
\(752\) −2.44784 + 14.3316i −0.0892635 + 0.522618i
\(753\) 0 0
\(754\) −1.99039 + 1.39767i −0.0724858 + 0.0509001i
\(755\) −43.0991 + 43.0991i −1.56854 + 1.56854i
\(756\) 0 0
\(757\) 2.11199 + 2.11199i 0.0767615 + 0.0767615i 0.744445 0.667684i \(-0.232714\pi\)
−0.667684 + 0.744445i \(0.732714\pi\)
\(758\) 0.919938 5.25846i 0.0334137 0.190996i
\(759\) 0 0
\(760\) −2.72581 + 10.3391i −0.0988755 + 0.375038i
\(761\) 16.3519 + 9.44076i 0.592755 + 0.342227i 0.766186 0.642619i \(-0.222152\pi\)
−0.173431 + 0.984846i \(0.555485\pi\)
\(762\) 0 0
\(763\) −7.01279 + 26.1721i −0.253880 + 0.947493i
\(764\) −3.51419 + 0.629371i −0.127139 + 0.0227699i
\(765\) 0 0
\(766\) 8.86247 0.787345i 0.320214 0.0284479i
\(767\) 6.46724 + 11.2016i 0.233519 + 0.404466i
\(768\) 0 0
\(769\) 3.50579 6.07221i 0.126422 0.218970i −0.795866 0.605473i \(-0.792984\pi\)
0.922288 + 0.386503i \(0.126317\pi\)
\(770\) 26.4969 57.0224i 0.954883 2.05494i
\(771\) 0 0
\(772\) −21.1659 25.0876i −0.761778 0.902922i
\(773\) −8.54407 8.54407i −0.307309 0.307309i 0.536556 0.843865i \(-0.319725\pi\)
−0.843865 + 0.536556i \(0.819725\pi\)
\(774\) 0 0
\(775\) 10.6082i 0.381057i
\(776\) −26.1121 25.9028i −0.937369 0.929856i
\(777\) 0 0
\(778\) 3.71646 1.35833i 0.133241 0.0486984i
\(779\) −7.61302 + 2.03990i −0.272765 + 0.0730871i
\(780\) 0 0
\(781\) 18.3458 + 4.91575i 0.656465 + 0.175899i
\(782\) 3.46578 + 39.0113i 0.123936 + 1.39504i
\(783\) 0 0
\(784\) −15.6069 + 5.77547i −0.557391 + 0.206267i
\(785\) −11.7824 20.4077i −0.420532 0.728383i
\(786\) 0 0
\(787\) −6.16205 22.9971i −0.219653 0.819758i −0.984476 0.175517i \(-0.943840\pi\)
0.764823 0.644241i \(-0.222826\pi\)
\(788\) −8.83112 + 4.14689i −0.314596 + 0.147727i
\(789\) 0 0
\(790\) 4.01792 22.9668i 0.142951 0.817122i
\(791\) 47.6769i 1.69519i
\(792\) 0 0
\(793\) 10.7545i 0.381904i
\(794\) −8.46542 1.48098i −0.300427 0.0525580i
\(795\) 0 0
\(796\) 28.2357 + 10.1912i 1.00079 + 0.361219i
\(797\) −1.78931 6.67778i −0.0633804 0.236539i 0.926968 0.375141i \(-0.122406\pi\)
−0.990348 + 0.138602i \(0.955739\pi\)
\(798\) 0 0
\(799\) −11.7716 20.3889i −0.416448 0.721309i
\(800\) −6.78152 14.2920i −0.239763 0.505299i
\(801\) 0 0
\(802\) 18.6822 1.65973i 0.659691 0.0586071i
\(803\) −25.1133 6.72909i −0.886229 0.237464i
\(804\) 0 0
\(805\) −38.5237 + 10.3224i −1.35778 + 0.363817i
\(806\) 2.83537 + 7.75772i 0.0998715 + 0.273254i
\(807\) 0 0
\(808\) 0.103801 + 25.7983i 0.00365171 + 0.907580i
\(809\) 39.0505i 1.37294i −0.727157 0.686471i \(-0.759159\pi\)
0.727157 0.686471i \(-0.240841\pi\)
\(810\) 0 0
\(811\) −2.40853 2.40853i −0.0845748 0.0845748i 0.663554 0.748129i \(-0.269047\pi\)
−0.748129 + 0.663554i \(0.769047\pi\)
\(812\) 0.630506 7.43641i 0.0221264 0.260967i
\(813\) 0 0
\(814\) 53.1365 + 24.6912i 1.86243 + 0.865428i
\(815\) −13.6864 + 23.7055i −0.479413 + 0.830367i
\(816\) 0 0
\(817\) −4.42769 7.66898i −0.154905 0.268304i
\(818\) −1.53955 17.3294i −0.0538291 0.605908i
\(819\) 0 0
\(820\) 18.5753 26.6803i 0.648678 0.931718i
\(821\) −7.66611 + 28.6103i −0.267549 + 0.998506i 0.693123 + 0.720820i \(0.256234\pi\)
−0.960672 + 0.277687i \(0.910432\pi\)
\(822\) 0 0
\(823\) 22.1086 + 12.7644i 0.770659 + 0.444940i 0.833110 0.553108i \(-0.186558\pi\)
−0.0624509 + 0.998048i \(0.519892\pi\)
\(824\) 11.7879 + 3.10778i 0.410651 + 0.108265i
\(825\) 0 0
\(826\) −39.0966 6.83973i −1.36034 0.237985i
\(827\) −5.10050 5.10050i −0.177362 0.177362i 0.612843 0.790205i \(-0.290026\pi\)
−0.790205 + 0.612843i \(0.790026\pi\)
\(828\) 0 0
\(829\) 1.30033 1.30033i 0.0451624 0.0451624i −0.684165 0.729327i \(-0.739833\pi\)
0.729327 + 0.684165i \(0.239833\pi\)
\(830\) 24.2986 + 34.6031i 0.843416 + 1.20109i
\(831\) 0 0
\(832\) 8.77928 + 8.63911i 0.304367 + 0.299507i
\(833\) 13.4736 23.3370i 0.466833 0.808578i
\(834\) 0 0
\(835\) −22.8449 6.12126i −0.790579 0.211835i
\(836\) −12.7043 + 2.27526i −0.439386 + 0.0786914i
\(837\) 0 0
\(838\) 27.4330 32.7826i 0.947658 1.13246i
\(839\) 28.6072 16.5164i 0.987631 0.570209i 0.0830657 0.996544i \(-0.473529\pi\)
0.904565 + 0.426335i \(0.140196\pi\)
\(840\) 0 0
\(841\) −24.0342 13.8762i −0.828766 0.478488i
\(842\) −29.5589 + 10.8035i −1.01867 + 0.372312i
\(843\) 0 0
\(844\) 24.5173 + 2.07873i 0.843920 + 0.0715529i
\(845\) 20.9869 20.9869i 0.721972 0.721972i
\(846\) 0 0
\(847\) 39.1502 1.34522
\(848\) 0.398959 + 4.29463i 0.0137003 + 0.147478i
\(849\) 0 0
\(850\) 23.2306 + 10.7947i 0.796804 + 0.370256i
\(851\) −9.61896 35.8984i −0.329734 1.23058i
\(852\) 0 0
\(853\) −4.12451 + 15.3929i −0.141221 + 0.527043i 0.858674 + 0.512522i \(0.171289\pi\)
−0.999895 + 0.0145204i \(0.995378\pi\)
\(854\) −25.3087 21.1787i −0.866046 0.724721i
\(855\) 0 0
\(856\) 0.179457 + 0.102649i 0.00613372 + 0.00350847i
\(857\) 13.6603 7.88675i 0.466625 0.269406i −0.248201 0.968709i \(-0.579839\pi\)
0.714826 + 0.699302i \(0.246506\pi\)
\(858\) 0 0
\(859\) −31.9956 + 8.57320i −1.09168 + 0.292514i −0.759371 0.650658i \(-0.774493\pi\)
−0.332306 + 0.943172i \(0.607827\pi\)
\(860\) 34.3570 + 12.4007i 1.17156 + 0.422859i
\(861\) 0 0
\(862\) −12.5109 17.8166i −0.426124 0.606834i
\(863\) −37.4407 −1.27449 −0.637247 0.770659i \(-0.719927\pi\)
−0.637247 + 0.770659i \(0.719927\pi\)
\(864\) 0 0
\(865\) 16.8186 0.571850
\(866\) −14.0156 19.9593i −0.476269 0.678245i
\(867\) 0 0
\(868\) −23.8399 8.60467i −0.809180 0.292062i
\(869\) 27.1845 7.28408i 0.922173 0.247095i
\(870\) 0 0
\(871\) 2.51063 1.44951i 0.0850695 0.0491149i
\(872\) −11.3902 + 19.9130i −0.385720 + 0.674338i
\(873\) 0 0
\(874\) 6.27816 + 5.25367i 0.212362 + 0.177708i
\(875\) 5.31986 19.8540i 0.179844 0.671187i
\(876\) 0 0
\(877\) 7.55790 + 28.2065i 0.255212 + 0.952465i 0.967972 + 0.251057i \(0.0807781\pi\)
−0.712760 + 0.701408i \(0.752555\pi\)
\(878\) −6.73922 3.13155i −0.227438 0.105685i
\(879\) 0 0
\(880\) 34.0002 40.9641i 1.14614 1.38090i
\(881\) 11.5567 0.389355 0.194678 0.980867i \(-0.437634\pi\)
0.194678 + 0.980867i \(0.437634\pi\)
\(882\) 0 0
\(883\) −19.2632 + 19.2632i −0.648260 + 0.648260i −0.952572 0.304313i \(-0.901573\pi\)
0.304313 + 0.952572i \(0.401573\pi\)
\(884\) −19.8737 1.68502i −0.668424 0.0566733i
\(885\) 0 0
\(886\) −17.1941 + 6.28426i −0.577646 + 0.211124i
\(887\) 19.8424 + 11.4560i 0.666243 + 0.384656i 0.794652 0.607066i \(-0.207653\pi\)
−0.128408 + 0.991721i \(0.540987\pi\)
\(888\) 0 0
\(889\) 47.0523 27.1657i 1.57808 0.911107i
\(890\) 5.68434 6.79281i 0.190540 0.227696i
\(891\) 0 0
\(892\) −1.01700 + 0.182138i −0.0340515 + 0.00609843i
\(893\) −4.75336 1.27366i −0.159065 0.0426214i
\(894\) 0 0
\(895\) 16.4752 28.5359i 0.550705 0.953850i
\(896\) −37.6194 + 3.64746i −1.25678 + 0.121853i
\(897\) 0 0
\(898\) −22.7348 32.3762i −0.758671 1.08041i
\(899\) 2.99615 2.99615i 0.0999272 0.0999272i
\(900\) 0 0
\(901\) −4.93860 4.93860i −0.164529 0.164529i
\(902\) 38.6544 + 6.76237i 1.28705 + 0.225162i
\(903\) 0 0
\(904\) 10.2905 39.0322i 0.342257 1.29819i
\(905\) −45.6345 26.3471i −1.51694 0.875807i
\(906\) 0 0
\(907\) −12.7169 + 47.4603i −0.422259 + 1.57589i 0.347577 + 0.937651i \(0.387005\pi\)
−0.769836 + 0.638242i \(0.779662\pi\)
\(908\) 11.6502 16.7335i 0.386625 0.555322i
\(909\) 0 0
\(910\) −1.79731 20.2308i −0.0595802 0.670644i
\(911\) −6.47683 11.2182i −0.214587 0.371675i 0.738558 0.674190i \(-0.235507\pi\)
−0.953145 + 0.302515i \(0.902174\pi\)
\(912\) 0 0
\(913\) −25.5188 + 44.1999i −0.844550 + 1.46280i
\(914\) 52.2368 + 24.2732i 1.72784 + 0.802885i
\(915\) 0 0
\(916\) 3.61816 42.6739i 0.119548 1.40998i
\(917\) −41.8331 41.8331i −1.38145 1.38145i
\(918\) 0 0
\(919\) 5.55214i 0.183148i −0.995798 0.0915740i \(-0.970810\pi\)
0.995798 0.0915740i \(-0.0291898\pi\)
\(920\) −33.7666 + 0.135862i −1.11325 + 0.00447925i
\(921\) 0 0
\(922\) 18.5318 + 50.7040i 0.610312 + 1.66985i
\(923\) 5.92596 1.58786i 0.195055 0.0522649i
\(924\) 0 0
\(925\) −23.4796 6.29135i −0.772006 0.206858i
\(926\) −50.0462 + 4.44612i −1.64462 + 0.146109i
\(927\) 0 0
\(928\) 2.12124 5.95196i 0.0696333 0.195383i
\(929\) −28.8356 49.9447i −0.946066 1.63863i −0.753603 0.657330i \(-0.771686\pi\)
−0.192462 0.981304i \(-0.561647\pi\)
\(930\) 0 0
\(931\) −1.45782 5.44064i −0.0477780 0.178310i
\(932\) −43.7323 15.7845i −1.43250 0.517039i
\(933\) 0 0
\(934\) 33.6904 + 5.89394i 1.10238 + 0.192856i
\(935\) 86.2049i 2.81920i
\(936\) 0 0
\(937\) 44.7899i 1.46322i −0.681722 0.731612i \(-0.738768\pi\)
0.681722 0.731612i \(-0.261232\pi\)
\(938\) −1.53300 + 8.76279i −0.0500543 + 0.286115i
\(939\) 0 0
\(940\) 18.3733 8.62769i 0.599271 0.281404i
\(941\) 9.72682 + 36.3010i 0.317085 + 1.18338i 0.922032 + 0.387113i \(0.126528\pi\)
−0.604947 + 0.796266i \(0.706806\pi\)
\(942\) 0 0
\(943\) −12.4452 21.5557i −0.405270 0.701949i
\(944\) −30.5314 14.0381i −0.993712 0.456901i
\(945\) 0 0
\(946\) 3.90159 + 43.9169i 0.126852 + 1.42786i
\(947\) 54.8652 + 14.7011i 1.78288 + 0.477721i 0.991104 0.133093i \(-0.0424908\pi\)
0.791775 + 0.610813i \(0.209157\pi\)
\(948\) 0 0
\(949\) −8.11194 + 2.17359i −0.263325 + 0.0705577i
\(950\) 5.02898 1.83804i 0.163162 0.0596339i
\(951\) 0 0
\(952\) 43.1023 43.4506i 1.39695 1.40824i
\(953\) 7.26359i 0.235291i −0.993056 0.117645i \(-0.962465\pi\)
0.993056 0.117645i \(-0.0375346\pi\)
\(954\) 0 0
\(955\) 3.52440 + 3.52440i 0.114047 + 0.114047i
\(956\) −0.565803 0.670636i −0.0182994 0.0216899i
\(957\) 0 0
\(958\) −8.06467 + 17.3555i −0.260558 + 0.560730i
\(959\) −18.5653 + 32.1560i −0.599504 + 1.03837i
\(960\) 0 0
\(961\) 8.30507 + 14.3848i 0.267905 + 0.464026i
\(962\) 18.8521 1.67483i 0.607817 0.0539986i
\(963\) 0 0
\(964\) −30.2155 + 5.41142i −0.973176 + 0.174290i
\(965\) −11.8604 + 44.2638i −0.381801 + 1.42490i
\(966\) 0 0
\(967\) 4.17378 + 2.40973i 0.134220 + 0.0774917i 0.565606 0.824675i \(-0.308642\pi\)
−0.431387 + 0.902167i \(0.641976\pi\)
\(968\) 32.0515 + 8.45010i 1.03017 + 0.271597i
\(969\) 0 0
\(970\) −8.84890 + 50.5812i −0.284121 + 1.62407i
\(971\) −2.69916 2.69916i −0.0866202 0.0866202i 0.662469 0.749089i \(-0.269509\pi\)
−0.749089 + 0.662469i \(0.769509\pi\)
\(972\) 0 0
\(973\) −15.9047 + 15.9047i −0.509881 + 0.509881i
\(974\) −18.6841 + 13.1201i −0.598676 + 0.420395i
\(975\) 0 0
\(976\) −16.1486 22.8012i −0.516903 0.729849i
\(977\) 6.16168 10.6724i 0.197130 0.341439i −0.750467 0.660908i \(-0.770171\pi\)
0.947597 + 0.319469i \(0.103505\pi\)
\(978\) 0 0
\(979\) 10.3272 + 2.76717i 0.330059 + 0.0884390i
\(980\) 19.0671 + 13.2748i 0.609076 + 0.424049i
\(981\) 0 0
\(982\) 39.2490 + 32.8443i 1.25249 + 1.04810i
\(983\) −42.5445 + 24.5631i −1.35696 + 0.783441i −0.989213 0.146485i \(-0.953204\pi\)
−0.367747 + 0.929926i \(0.619871\pi\)
\(984\) 0 0
\(985\) 11.7960 + 6.81043i 0.375852 + 0.216998i
\(986\) 3.51237 + 9.61004i 0.111857 + 0.306046i
\(987\) 0 0
\(988\) −3.18640 + 2.68830i −0.101373 + 0.0855263i
\(989\) 19.7747 19.7747i 0.628798 0.628798i
\(990\) 0 0
\(991\) −40.4968 −1.28642 −0.643212 0.765688i \(-0.722399\pi\)
−0.643212 + 0.765688i \(0.722399\pi\)
\(992\) −17.6601 12.1901i −0.560708 0.387035i
\(993\) 0 0
\(994\) −7.93319 + 17.0725i −0.251626 + 0.541508i
\(995\) −10.8469 40.4812i −0.343870 1.28334i
\(996\) 0 0
\(997\) 6.26425 23.3785i 0.198391 0.740404i −0.792972 0.609258i \(-0.791467\pi\)
0.991363 0.131147i \(-0.0418659\pi\)
\(998\) 5.97344 7.13829i 0.189086 0.225959i
\(999\) 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 432.2.y.e.37.13 72
3.2 odd 2 144.2.x.e.85.6 yes 72
4.3 odd 2 1728.2.bc.e.1009.17 72
9.2 odd 6 144.2.x.e.133.6 yes 72
9.7 even 3 inner 432.2.y.e.181.13 72
12.11 even 2 576.2.bb.e.49.11 72
16.3 odd 4 1728.2.bc.e.145.2 72
16.13 even 4 inner 432.2.y.e.253.13 72
36.7 odd 6 1728.2.bc.e.1585.2 72
36.11 even 6 576.2.bb.e.241.3 72
48.29 odd 4 144.2.x.e.13.6 72
48.35 even 4 576.2.bb.e.337.3 72
144.29 odd 12 144.2.x.e.61.6 yes 72
144.61 even 12 inner 432.2.y.e.397.13 72
144.83 even 12 576.2.bb.e.529.11 72
144.115 odd 12 1728.2.bc.e.721.17 72
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
144.2.x.e.13.6 72 48.29 odd 4
144.2.x.e.61.6 yes 72 144.29 odd 12
144.2.x.e.85.6 yes 72 3.2 odd 2
144.2.x.e.133.6 yes 72 9.2 odd 6
432.2.y.e.37.13 72 1.1 even 1 trivial
432.2.y.e.181.13 72 9.7 even 3 inner
432.2.y.e.253.13 72 16.13 even 4 inner
432.2.y.e.397.13 72 144.61 even 12 inner
576.2.bb.e.49.11 72 12.11 even 2
576.2.bb.e.241.3 72 36.11 even 6
576.2.bb.e.337.3 72 48.35 even 4
576.2.bb.e.529.11 72 144.83 even 12
1728.2.bc.e.145.2 72 16.3 odd 4
1728.2.bc.e.721.17 72 144.115 odd 12
1728.2.bc.e.1009.17 72 4.3 odd 2
1728.2.bc.e.1585.2 72 36.7 odd 6