Properties

Label 432.3.x.a.125.1
Level $432$
Weight $3$
Character 432.125
Analytic conductor $11.771$
Analytic rank $0$
Dimension $184$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [432,3,Mod(125,432)]
 
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, 9, 10]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("432.125");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 432.x (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: \(11.7711474204\)
Analytic rank: \(0\)
Dimension: \(184\)
Relative dimension: \(46\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 144)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 125.1
Character \(\chi\) \(=\) 432.125
Dual form 432.3.x.a.197.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.99910 - 0.0600540i) q^{2} +(3.99279 + 0.240108i) q^{4} +(-7.92852 + 2.12444i) q^{5} +(-8.42400 + 4.86360i) q^{7} +(-7.96755 - 0.719782i) q^{8} +O(q^{10})\) \(q+(-1.99910 - 0.0600540i) q^{2} +(3.99279 + 0.240108i) q^{4} +(-7.92852 + 2.12444i) q^{5} +(-8.42400 + 4.86360i) q^{7} +(-7.96755 - 0.719782i) q^{8} +(15.9775 - 3.77083i) q^{10} +(-4.48604 + 16.7421i) q^{11} +(-2.61707 + 0.701241i) q^{13} +(17.1325 - 9.21691i) q^{14} +(15.8847 + 1.91740i) q^{16} -11.6490i q^{17} +(-1.19978 - 1.19978i) q^{19} +(-32.1670 + 6.57874i) q^{20} +(9.97346 - 33.1997i) q^{22} +(16.5761 - 28.7106i) q^{23} +(36.6976 - 21.1874i) q^{25} +(5.27388 - 1.24468i) q^{26} +(-34.8030 + 17.3966i) q^{28} +(7.75438 + 2.07778i) q^{29} +(-12.2003 + 21.1316i) q^{31} +(-31.6399 - 4.78701i) q^{32} +(-0.699566 + 23.2874i) q^{34} +(56.4574 - 56.4574i) q^{35} +(-18.8900 + 18.8900i) q^{37} +(2.32643 + 2.47054i) q^{38} +(64.7001 - 11.2198i) q^{40} +(2.81364 - 4.87337i) q^{41} +(-24.9252 - 6.67869i) q^{43} +(-21.9317 + 65.7706i) q^{44} +(-34.8614 + 56.3999i) q^{46} +(-8.51428 + 4.91572i) q^{47} +(22.8092 - 39.5066i) q^{49} +(-74.6345 + 40.1518i) q^{50} +(-10.6178 + 2.17153i) q^{52} +(-26.1790 - 26.1790i) q^{53} -142.271i q^{55} +(70.6194 - 32.6875i) q^{56} +(-15.3770 - 4.61937i) q^{58} +(80.0226 - 21.4420i) q^{59} +(6.70562 - 25.0257i) q^{61} +(25.6587 - 41.5114i) q^{62} +(62.9638 + 11.4698i) q^{64} +(19.2597 - 11.1196i) q^{65} +(100.615 - 26.9596i) q^{67} +(2.79700 - 46.5118i) q^{68} +(-116.254 + 109.473i) q^{70} -113.848 q^{71} -17.1016i q^{73} +(38.8973 - 36.6285i) q^{74} +(-4.50240 - 5.07856i) q^{76} +(-43.6366 - 162.854i) q^{77} +(-9.83045 - 17.0268i) q^{79} +(-130.016 + 18.5440i) q^{80} +(-5.91742 + 9.57338i) q^{82} +(80.8500 + 21.6637i) q^{83} +(24.7475 + 92.3590i) q^{85} +(49.4269 + 14.8482i) q^{86} +(47.7934 - 130.165i) q^{88} +99.5952 q^{89} +(18.6356 - 18.6356i) q^{91} +(73.0785 - 110.655i) q^{92} +(17.3161 - 9.31570i) q^{94} +(12.0614 + 6.96365i) q^{95} +(-70.2440 - 121.666i) q^{97} +(-47.9703 + 77.6079i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 184 q + 6 q^{2} - 2 q^{4} + 6 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 184 q + 6 q^{2} - 2 q^{4} + 6 q^{5} - 8 q^{10} + 6 q^{11} - 2 q^{13} + 6 q^{14} - 2 q^{16} - 8 q^{19} - 120 q^{20} - 2 q^{22} - 72 q^{28} + 6 q^{29} - 4 q^{31} + 6 q^{32} + 6 q^{34} - 8 q^{37} + 6 q^{38} - 2 q^{40} - 2 q^{43} - 160 q^{46} + 12 q^{47} + 472 q^{49} - 228 q^{50} - 2 q^{52} + 300 q^{56} - 92 q^{58} + 438 q^{59} - 2 q^{61} + 244 q^{64} + 12 q^{65} - 2 q^{67} + 144 q^{68} + 96 q^{70} - 246 q^{74} - 158 q^{76} + 6 q^{77} - 4 q^{79} - 388 q^{82} + 726 q^{83} + 48 q^{85} - 894 q^{86} + 22 q^{88} - 204 q^{91} + 348 q^{92} - 18 q^{94} + 12 q^{95} - 4 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(271\) \(325\) \(353\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.99910 0.0600540i −0.999549 0.0300270i
\(3\) 0 0
\(4\) 3.99279 + 0.240108i 0.998197 + 0.0600269i
\(5\) −7.92852 + 2.12444i −1.58570 + 0.424888i −0.940686 0.339278i \(-0.889817\pi\)
−0.645019 + 0.764167i \(0.723151\pi\)
\(6\) 0 0
\(7\) −8.42400 + 4.86360i −1.20343 + 0.694800i −0.961316 0.275449i \(-0.911174\pi\)
−0.242113 + 0.970248i \(0.577840\pi\)
\(8\) −7.96755 0.719782i −0.995944 0.0899727i
\(9\) 0 0
\(10\) 15.9775 3.77083i 1.59775 0.377083i
\(11\) −4.48604 + 16.7421i −0.407822 + 1.52201i 0.390970 + 0.920403i \(0.372140\pi\)
−0.798792 + 0.601607i \(0.794527\pi\)
\(12\) 0 0
\(13\) −2.61707 + 0.701241i −0.201313 + 0.0539416i −0.358066 0.933696i \(-0.616564\pi\)
0.156754 + 0.987638i \(0.449897\pi\)
\(14\) 17.1325 9.21691i 1.22375 0.658351i
\(15\) 0 0
\(16\) 15.8847 + 1.91740i 0.992794 + 0.119837i
\(17\) 11.6490i 0.685233i −0.939475 0.342616i \(-0.888687\pi\)
0.939475 0.342616i \(-0.111313\pi\)
\(18\) 0 0
\(19\) −1.19978 1.19978i −0.0631465 0.0631465i 0.674828 0.737975i \(-0.264218\pi\)
−0.737975 + 0.674828i \(0.764218\pi\)
\(20\) −32.1670 + 6.57874i −1.60835 + 0.328937i
\(21\) 0 0
\(22\) 9.97346 33.1997i 0.453339 1.50908i
\(23\) 16.5761 28.7106i 0.720700 1.24829i −0.240020 0.970768i \(-0.577154\pi\)
0.960720 0.277521i \(-0.0895128\pi\)
\(24\) 0 0
\(25\) 36.6976 21.1874i 1.46790 0.847495i
\(26\) 5.27388 1.24468i 0.202842 0.0478725i
\(27\) 0 0
\(28\) −34.8030 + 17.3966i −1.24296 + 0.621309i
\(29\) 7.75438 + 2.07778i 0.267392 + 0.0716476i 0.390024 0.920805i \(-0.372467\pi\)
−0.122632 + 0.992452i \(0.539133\pi\)
\(30\) 0 0
\(31\) −12.2003 + 21.1316i −0.393559 + 0.681664i −0.992916 0.118818i \(-0.962090\pi\)
0.599357 + 0.800482i \(0.295423\pi\)
\(32\) −31.6399 4.78701i −0.988748 0.149594i
\(33\) 0 0
\(34\) −0.699566 + 23.2874i −0.0205755 + 0.684924i
\(35\) 56.4574 56.4574i 1.61307 1.61307i
\(36\) 0 0
\(37\) −18.8900 + 18.8900i −0.510540 + 0.510540i −0.914692 0.404152i \(-0.867567\pi\)
0.404152 + 0.914692i \(0.367567\pi\)
\(38\) 2.32643 + 2.47054i 0.0612219 + 0.0650142i
\(39\) 0 0
\(40\) 64.7001 11.2198i 1.61750 0.280495i
\(41\) 2.81364 4.87337i 0.0686255 0.118863i −0.829671 0.558253i \(-0.811472\pi\)
0.898296 + 0.439390i \(0.144805\pi\)
\(42\) 0 0
\(43\) −24.9252 6.67869i −0.579656 0.155318i −0.0429346 0.999078i \(-0.513671\pi\)
−0.536721 + 0.843760i \(0.680337\pi\)
\(44\) −21.9317 + 65.7706i −0.498448 + 1.49479i
\(45\) 0 0
\(46\) −34.8614 + 56.3999i −0.757857 + 1.22609i
\(47\) −8.51428 + 4.91572i −0.181155 + 0.104590i −0.587835 0.808981i \(-0.700020\pi\)
0.406680 + 0.913571i \(0.366686\pi\)
\(48\) 0 0
\(49\) 22.8092 39.5066i 0.465493 0.806258i
\(50\) −74.6345 + 40.1518i −1.49269 + 0.803036i
\(51\) 0 0
\(52\) −10.6178 + 2.17153i −0.204188 + 0.0417601i
\(53\) −26.1790 26.1790i −0.493944 0.493944i 0.415603 0.909546i \(-0.363571\pi\)
−0.909546 + 0.415603i \(0.863571\pi\)
\(54\) 0 0
\(55\) 142.271i 2.58674i
\(56\) 70.6194 32.6875i 1.26106 0.583706i
\(57\) 0 0
\(58\) −15.3770 4.61937i −0.265121 0.0796443i
\(59\) 80.0226 21.4420i 1.35632 0.363424i 0.493853 0.869545i \(-0.335588\pi\)
0.862462 + 0.506122i \(0.168921\pi\)
\(60\) 0 0
\(61\) 6.70562 25.0257i 0.109928 0.410257i −0.888929 0.458044i \(-0.848550\pi\)
0.998858 + 0.0477868i \(0.0152168\pi\)
\(62\) 25.6587 41.5114i 0.413850 0.669539i
\(63\) 0 0
\(64\) 62.9638 + 11.4698i 0.983810 + 0.179216i
\(65\) 19.2597 11.1196i 0.296304 0.171071i
\(66\) 0 0
\(67\) 100.615 26.9596i 1.50171 0.402383i 0.588039 0.808833i \(-0.299900\pi\)
0.913673 + 0.406450i \(0.133233\pi\)
\(68\) 2.79700 46.5118i 0.0411324 0.683997i
\(69\) 0 0
\(70\) −116.254 + 109.473i −1.66078 + 1.56391i
\(71\) −113.848 −1.60349 −0.801746 0.597665i \(-0.796095\pi\)
−0.801746 + 0.597665i \(0.796095\pi\)
\(72\) 0 0
\(73\) 17.1016i 0.234268i −0.993116 0.117134i \(-0.962629\pi\)
0.993116 0.117134i \(-0.0373707\pi\)
\(74\) 38.8973 36.6285i 0.525639 0.494979i
\(75\) 0 0
\(76\) −4.50240 5.07856i −0.0592422 0.0668231i
\(77\) −43.6366 162.854i −0.566709 2.11499i
\(78\) 0 0
\(79\) −9.83045 17.0268i −0.124436 0.215530i 0.797076 0.603879i \(-0.206379\pi\)
−0.921512 + 0.388349i \(0.873046\pi\)
\(80\) −130.016 + 18.5440i −1.62520 + 0.231800i
\(81\) 0 0
\(82\) −5.91742 + 9.57338i −0.0721636 + 0.116749i
\(83\) 80.8500 + 21.6637i 0.974097 + 0.261008i 0.710557 0.703640i \(-0.248443\pi\)
0.263540 + 0.964648i \(0.415110\pi\)
\(84\) 0 0
\(85\) 24.7475 + 92.3590i 0.291147 + 1.08658i
\(86\) 49.4269 + 14.8482i 0.574731 + 0.172654i
\(87\) 0 0
\(88\) 47.7934 130.165i 0.543107 1.47914i
\(89\) 99.5952 1.11905 0.559524 0.828814i \(-0.310984\pi\)
0.559524 + 0.828814i \(0.310984\pi\)
\(90\) 0 0
\(91\) 18.6356 18.6356i 0.204787 0.204787i
\(92\) 73.0785 110.655i 0.794331 1.20278i
\(93\) 0 0
\(94\) 17.3161 9.31570i 0.184214 0.0991031i
\(95\) 12.0614 + 6.96365i 0.126962 + 0.0733015i
\(96\) 0 0
\(97\) −70.2440 121.666i −0.724165 1.25429i −0.959317 0.282332i \(-0.908892\pi\)
0.235152 0.971959i \(-0.424441\pi\)
\(98\) −47.9703 + 77.6079i −0.489493 + 0.791917i
\(99\) 0 0
\(100\) 151.613 75.7853i 1.51613 0.757853i
\(101\) −49.5515 + 184.929i −0.490609 + 1.83098i 0.0627431 + 0.998030i \(0.480015\pi\)
−0.553352 + 0.832948i \(0.686652\pi\)
\(102\) 0 0
\(103\) 52.9787 + 30.5873i 0.514356 + 0.296964i 0.734622 0.678476i \(-0.237359\pi\)
−0.220266 + 0.975440i \(0.570693\pi\)
\(104\) 21.3564 3.70346i 0.205350 0.0356102i
\(105\) 0 0
\(106\) 50.7623 + 53.9066i 0.478889 + 0.508553i
\(107\) 63.7744 + 63.7744i 0.596023 + 0.596023i 0.939252 0.343229i \(-0.111521\pi\)
−0.343229 + 0.939252i \(0.611521\pi\)
\(108\) 0 0
\(109\) −120.966 120.966i −1.10978 1.10978i −0.993179 0.116600i \(-0.962800\pi\)
−0.116600 0.993179i \(-0.537200\pi\)
\(110\) −8.54392 + 284.413i −0.0776720 + 2.58557i
\(111\) 0 0
\(112\) −143.138 + 61.1046i −1.27802 + 0.545577i
\(113\) −54.5148 31.4741i −0.482432 0.278532i 0.238998 0.971020i \(-0.423181\pi\)
−0.721429 + 0.692488i \(0.756515\pi\)
\(114\) 0 0
\(115\) −70.4299 + 262.848i −0.612434 + 2.28564i
\(116\) 30.4627 + 10.1580i 0.262610 + 0.0875691i
\(117\) 0 0
\(118\) −161.261 + 38.0590i −1.36662 + 0.322534i
\(119\) 56.6558 + 98.1308i 0.476099 + 0.824628i
\(120\) 0 0
\(121\) −155.385 89.7115i −1.28417 0.741418i
\(122\) −14.9081 + 49.6261i −0.122197 + 0.406772i
\(123\) 0 0
\(124\) −53.7872 + 81.4445i −0.433768 + 0.656811i
\(125\) −100.845 + 100.845i −0.806756 + 0.806756i
\(126\) 0 0
\(127\) 86.2129 0.678842 0.339421 0.940635i \(-0.389769\pi\)
0.339421 + 0.940635i \(0.389769\pi\)
\(128\) −125.182 26.7105i −0.977985 0.208676i
\(129\) 0 0
\(130\) −39.1699 + 21.0726i −0.301307 + 0.162097i
\(131\) 52.7912 + 197.019i 0.402986 + 1.50397i 0.807740 + 0.589539i \(0.200691\pi\)
−0.404753 + 0.914426i \(0.632643\pi\)
\(132\) 0 0
\(133\) 15.9422 + 4.27171i 0.119866 + 0.0321181i
\(134\) −202.758 + 47.8526i −1.51312 + 0.357109i
\(135\) 0 0
\(136\) −8.38470 + 92.8137i −0.0616522 + 0.682453i
\(137\) −82.3443 142.624i −0.601053 1.04105i −0.992662 0.120923i \(-0.961415\pi\)
0.391609 0.920132i \(-0.371919\pi\)
\(138\) 0 0
\(139\) 7.79178 + 29.0793i 0.0560560 + 0.209204i 0.988273 0.152695i \(-0.0487952\pi\)
−0.932217 + 0.361899i \(0.882129\pi\)
\(140\) 238.978 211.867i 1.70699 1.51333i
\(141\) 0 0
\(142\) 227.593 + 6.83703i 1.60277 + 0.0481481i
\(143\) 46.9610i 0.328399i
\(144\) 0 0
\(145\) −65.8949 −0.454448
\(146\) −1.02702 + 34.1877i −0.00703437 + 0.234162i
\(147\) 0 0
\(148\) −79.9592 + 70.8880i −0.540265 + 0.478973i
\(149\) −129.656 + 34.7413i −0.870177 + 0.233163i −0.666164 0.745805i \(-0.732065\pi\)
−0.204013 + 0.978968i \(0.565398\pi\)
\(150\) 0 0
\(151\) 46.8407 27.0435i 0.310203 0.179096i −0.336814 0.941571i \(-0.609349\pi\)
0.647017 + 0.762475i \(0.276016\pi\)
\(152\) 8.69576 + 10.4229i 0.0572090 + 0.0685719i
\(153\) 0 0
\(154\) 77.4537 + 328.181i 0.502946 + 2.13105i
\(155\) 51.8378 193.461i 0.334437 1.24814i
\(156\) 0 0
\(157\) 69.8242 18.7093i 0.444740 0.119168i −0.0294971 0.999565i \(-0.509391\pi\)
0.474237 + 0.880397i \(0.342724\pi\)
\(158\) 18.6295 + 34.6287i 0.117908 + 0.219169i
\(159\) 0 0
\(160\) 261.028 29.2633i 1.63142 0.182895i
\(161\) 322.478i 2.00297i
\(162\) 0 0
\(163\) 38.2729 + 38.2729i 0.234803 + 0.234803i 0.814694 0.579891i \(-0.196905\pi\)
−0.579891 + 0.814694i \(0.696905\pi\)
\(164\) 12.4044 18.7828i 0.0756367 0.114529i
\(165\) 0 0
\(166\) −160.326 48.1632i −0.965820 0.290140i
\(167\) 23.8430 41.2972i 0.142772 0.247289i −0.785767 0.618522i \(-0.787732\pi\)
0.928540 + 0.371233i \(0.121065\pi\)
\(168\) 0 0
\(169\) −140.001 + 80.8296i −0.828408 + 0.478282i
\(170\) −43.9262 186.121i −0.258389 1.09483i
\(171\) 0 0
\(172\) −97.9174 32.6513i −0.569287 0.189833i
\(173\) 147.635 + 39.5586i 0.853381 + 0.228663i 0.658888 0.752241i \(-0.271027\pi\)
0.194493 + 0.980904i \(0.437694\pi\)
\(174\) 0 0
\(175\) −206.094 + 356.965i −1.17768 + 2.03980i
\(176\) −103.361 + 257.342i −0.587276 + 1.46217i
\(177\) 0 0
\(178\) −199.101 5.98109i −1.11854 0.0336017i
\(179\) 8.85078 8.85078i 0.0494457 0.0494457i −0.681952 0.731397i \(-0.738869\pi\)
0.731397 + 0.681952i \(0.238869\pi\)
\(180\) 0 0
\(181\) −19.6456 + 19.6456i −0.108539 + 0.108539i −0.759291 0.650752i \(-0.774454\pi\)
0.650752 + 0.759291i \(0.274454\pi\)
\(182\) −38.3736 + 36.1353i −0.210844 + 0.198545i
\(183\) 0 0
\(184\) −152.736 + 216.822i −0.830089 + 1.17838i
\(185\) 109.639 189.900i 0.592643 1.02649i
\(186\) 0 0
\(187\) 195.028 + 52.2576i 1.04293 + 0.279453i
\(188\) −35.1760 + 17.5831i −0.187106 + 0.0935271i
\(189\) 0 0
\(190\) −23.6937 14.6453i −0.124704 0.0770808i
\(191\) 291.669 168.395i 1.52706 0.881651i 0.527582 0.849504i \(-0.323099\pi\)
0.999483 0.0321469i \(-0.0102344\pi\)
\(192\) 0 0
\(193\) 46.6824 80.8563i 0.241878 0.418945i −0.719371 0.694626i \(-0.755570\pi\)
0.961249 + 0.275681i \(0.0889034\pi\)
\(194\) 133.118 + 247.441i 0.686176 + 1.27547i
\(195\) 0 0
\(196\) 100.558 152.265i 0.513051 0.776862i
\(197\) −160.979 160.979i −0.817150 0.817150i 0.168544 0.985694i \(-0.446093\pi\)
−0.985694 + 0.168544i \(0.946093\pi\)
\(198\) 0 0
\(199\) 42.0675i 0.211394i 0.994398 + 0.105697i \(0.0337074\pi\)
−0.994398 + 0.105697i \(0.966293\pi\)
\(200\) −307.641 + 142.397i −1.53820 + 0.711987i
\(201\) 0 0
\(202\) 110.164 366.715i 0.545366 1.81542i
\(203\) −75.4284 + 20.2110i −0.371568 + 0.0995614i
\(204\) 0 0
\(205\) −11.9548 + 44.6161i −0.0583163 + 0.217639i
\(206\) −104.073 64.3285i −0.505207 0.312274i
\(207\) 0 0
\(208\) −42.9159 + 6.12104i −0.206326 + 0.0294281i
\(209\) 25.4692 14.7046i 0.121862 0.0703572i
\(210\) 0 0
\(211\) −20.4176 + 5.47088i −0.0967659 + 0.0259284i −0.306877 0.951749i \(-0.599284\pi\)
0.210111 + 0.977677i \(0.432617\pi\)
\(212\) −98.2414 110.813i −0.463403 0.522703i
\(213\) 0 0
\(214\) −123.661 131.321i −0.577857 0.613651i
\(215\) 211.809 0.985156
\(216\) 0 0
\(217\) 237.350i 1.09378i
\(218\) 234.558 + 249.087i 1.07596 + 1.14260i
\(219\) 0 0
\(220\) 34.1603 568.056i 0.155274 2.58207i
\(221\) 8.16872 + 30.4861i 0.0369625 + 0.137946i
\(222\) 0 0
\(223\) 36.6216 + 63.4305i 0.164223 + 0.284442i 0.936379 0.350991i \(-0.114155\pi\)
−0.772156 + 0.635433i \(0.780822\pi\)
\(224\) 289.817 113.558i 1.29382 0.506956i
\(225\) 0 0
\(226\) 107.090 + 66.1937i 0.473851 + 0.292892i
\(227\) −289.360 77.5337i −1.27471 0.341558i −0.442878 0.896582i \(-0.646043\pi\)
−0.831835 + 0.555024i \(0.812709\pi\)
\(228\) 0 0
\(229\) 48.1927 + 179.858i 0.210449 + 0.785405i 0.987719 + 0.156239i \(0.0499369\pi\)
−0.777271 + 0.629166i \(0.783396\pi\)
\(230\) 156.581 521.229i 0.680789 2.26621i
\(231\) 0 0
\(232\) −60.2879 22.1363i −0.259862 0.0954150i
\(233\) −156.231 −0.670520 −0.335260 0.942126i \(-0.608824\pi\)
−0.335260 + 0.942126i \(0.608824\pi\)
\(234\) 0 0
\(235\) 57.0625 57.0625i 0.242819 0.242819i
\(236\) 324.662 66.3992i 1.37568 0.281353i
\(237\) 0 0
\(238\) −107.367 199.575i −0.451124 0.838552i
\(239\) −270.739 156.311i −1.13280 0.654021i −0.188160 0.982138i \(-0.560252\pi\)
−0.944637 + 0.328118i \(0.893586\pi\)
\(240\) 0 0
\(241\) −189.723 328.609i −0.787231 1.36352i −0.927657 0.373433i \(-0.878180\pi\)
0.140426 0.990091i \(-0.455153\pi\)
\(242\) 305.242 + 188.674i 1.26133 + 0.779643i
\(243\) 0 0
\(244\) 32.7830 98.3122i 0.134356 0.402919i
\(245\) −96.9135 + 361.686i −0.395565 + 1.47627i
\(246\) 0 0
\(247\) 3.98125 + 2.29858i 0.0161184 + 0.00930598i
\(248\) 112.417 159.586i 0.453294 0.643490i
\(249\) 0 0
\(250\) 207.654 195.542i 0.830617 0.782168i
\(251\) −261.495 261.495i −1.04181 1.04181i −0.999087 0.0427244i \(-0.986396\pi\)
−0.0427244 0.999087i \(-0.513604\pi\)
\(252\) 0 0
\(253\) 406.316 + 406.316i 1.60599 + 1.60599i
\(254\) −172.348 5.17743i −0.678536 0.0203836i
\(255\) 0 0
\(256\) 248.647 + 60.9146i 0.971278 + 0.237948i
\(257\) 93.3244 + 53.8809i 0.363130 + 0.209653i 0.670453 0.741952i \(-0.266100\pi\)
−0.307323 + 0.951605i \(0.599433\pi\)
\(258\) 0 0
\(259\) 67.2558 251.002i 0.259675 0.969121i
\(260\) 79.5699 39.7738i 0.306038 0.152976i
\(261\) 0 0
\(262\) −93.7030 397.032i −0.357645 1.51539i
\(263\) −188.786 326.987i −0.717817 1.24330i −0.961863 0.273532i \(-0.911808\pi\)
0.244046 0.969764i \(-0.421525\pi\)
\(264\) 0 0
\(265\) 263.177 + 151.945i 0.993120 + 0.573378i
\(266\) −31.6136 9.49697i −0.118848 0.0357029i
\(267\) 0 0
\(268\) 408.206 83.4857i 1.52316 0.311514i
\(269\) 92.7359 92.7359i 0.344743 0.344743i −0.513404 0.858147i \(-0.671616\pi\)
0.858147 + 0.513404i \(0.171616\pi\)
\(270\) 0 0
\(271\) 212.088 0.782613 0.391307 0.920260i \(-0.372023\pi\)
0.391307 + 0.920260i \(0.372023\pi\)
\(272\) 22.3357 185.040i 0.0821165 0.680294i
\(273\) 0 0
\(274\) 156.049 + 290.065i 0.569522 + 1.05863i
\(275\) 190.095 + 709.443i 0.691254 + 2.57979i
\(276\) 0 0
\(277\) −438.552 117.510i −1.58322 0.424223i −0.643300 0.765614i \(-0.722435\pi\)
−0.939921 + 0.341391i \(0.889102\pi\)
\(278\) −13.8302 58.6004i −0.0497489 0.210793i
\(279\) 0 0
\(280\) −490.465 + 409.191i −1.75166 + 1.46140i
\(281\) 120.649 + 208.971i 0.429357 + 0.743669i 0.996816 0.0797330i \(-0.0254068\pi\)
−0.567459 + 0.823402i \(0.692073\pi\)
\(282\) 0 0
\(283\) −63.5940 237.336i −0.224714 0.838643i −0.982519 0.186163i \(-0.940395\pi\)
0.757805 0.652481i \(-0.226272\pi\)
\(284\) −454.571 27.3358i −1.60060 0.0962527i
\(285\) 0 0
\(286\) −2.82020 + 93.8797i −0.00986083 + 0.328251i
\(287\) 54.7377i 0.190724i
\(288\) 0 0
\(289\) 153.302 0.530456
\(290\) 131.730 + 3.95725i 0.454243 + 0.0136457i
\(291\) 0 0
\(292\) 4.10622 68.2829i 0.0140624 0.233846i
\(293\) 2.31983 0.621597i 0.00791751 0.00212149i −0.254858 0.966978i \(-0.582029\pi\)
0.262776 + 0.964857i \(0.415362\pi\)
\(294\) 0 0
\(295\) −588.909 + 340.007i −1.99630 + 1.15256i
\(296\) 164.103 136.910i 0.554404 0.462534i
\(297\) 0 0
\(298\) 261.282 61.6649i 0.876786 0.206929i
\(299\) −23.2477 + 86.7615i −0.0777514 + 0.290172i
\(300\) 0 0
\(301\) 242.452 64.9649i 0.805490 0.215830i
\(302\) −95.2632 + 51.2496i −0.315441 + 0.169701i
\(303\) 0 0
\(304\) −16.7577 21.3587i −0.0551241 0.0702588i
\(305\) 212.663i 0.697254i
\(306\) 0 0
\(307\) 178.526 + 178.526i 0.581517 + 0.581517i 0.935320 0.353803i \(-0.115112\pi\)
−0.353803 + 0.935320i \(0.615112\pi\)
\(308\) −135.129 660.718i −0.438731 2.14519i
\(309\) 0 0
\(310\) −115.247 + 383.635i −0.371764 + 1.23753i
\(311\) 42.8211 74.1683i 0.137688 0.238483i −0.788933 0.614479i \(-0.789366\pi\)
0.926621 + 0.375996i \(0.122699\pi\)
\(312\) 0 0
\(313\) −230.617 + 133.147i −0.736797 + 0.425390i −0.820904 0.571067i \(-0.806530\pi\)
0.0841066 + 0.996457i \(0.473196\pi\)
\(314\) −140.709 + 33.2086i −0.448118 + 0.105760i
\(315\) 0 0
\(316\) −35.1626 70.3449i −0.111274 0.222611i
\(317\) −245.123 65.6804i −0.773257 0.207194i −0.149447 0.988770i \(-0.547749\pi\)
−0.623810 + 0.781576i \(0.714416\pi\)
\(318\) 0 0
\(319\) −69.5729 + 120.504i −0.218097 + 0.377755i
\(320\) −523.577 + 42.8244i −1.63618 + 0.133826i
\(321\) 0 0
\(322\) 19.3661 644.665i 0.0601431 2.00207i
\(323\) −13.9762 + 13.9762i −0.0432701 + 0.0432701i
\(324\) 0 0
\(325\) −81.1826 + 81.1826i −0.249793 + 0.249793i
\(326\) −74.2129 78.8098i −0.227647 0.241748i
\(327\) 0 0
\(328\) −25.9256 + 36.8037i −0.0790415 + 0.112206i
\(329\) 47.8162 82.8201i 0.145338 0.251733i
\(330\) 0 0
\(331\) −66.3184 17.7700i −0.200358 0.0536857i 0.157244 0.987560i \(-0.449739\pi\)
−0.357602 + 0.933874i \(0.616406\pi\)
\(332\) 317.615 + 105.911i 0.956672 + 0.319010i
\(333\) 0 0
\(334\) −50.1445 + 81.1253i −0.150133 + 0.242890i
\(335\) −740.452 + 427.500i −2.21030 + 1.27612i
\(336\) 0 0
\(337\) 18.4530 31.9616i 0.0547568 0.0948416i −0.837348 0.546671i \(-0.815895\pi\)
0.892105 + 0.451829i \(0.149228\pi\)
\(338\) 284.730 153.179i 0.842396 0.453191i
\(339\) 0 0
\(340\) 76.6355 + 374.712i 0.225398 + 1.10209i
\(341\) −299.056 299.056i −0.876998 0.876998i
\(342\) 0 0
\(343\) 32.8942i 0.0959013i
\(344\) 193.786 + 71.1535i 0.563331 + 0.206842i
\(345\) 0 0
\(346\) −292.761 87.9477i −0.846130 0.254184i
\(347\) 272.511 73.0192i 0.785335 0.210430i 0.156200 0.987726i \(-0.450076\pi\)
0.629136 + 0.777296i \(0.283409\pi\)
\(348\) 0 0
\(349\) 67.5509 252.104i 0.193556 0.722360i −0.799080 0.601224i \(-0.794680\pi\)
0.992636 0.121135i \(-0.0386535\pi\)
\(350\) 433.439 701.231i 1.23840 2.00352i
\(351\) 0 0
\(352\) 222.082 508.245i 0.630916 1.44388i
\(353\) 184.388 106.456i 0.522345 0.301576i −0.215549 0.976493i \(-0.569154\pi\)
0.737893 + 0.674917i \(0.235821\pi\)
\(354\) 0 0
\(355\) 902.646 241.863i 2.54267 0.681305i
\(356\) 397.663 + 23.9136i 1.11703 + 0.0671730i
\(357\) 0 0
\(358\) −18.2251 + 17.1621i −0.0509081 + 0.0479387i
\(359\) 453.564 1.26341 0.631705 0.775209i \(-0.282355\pi\)
0.631705 + 0.775209i \(0.282355\pi\)
\(360\) 0 0
\(361\) 358.121i 0.992025i
\(362\) 40.4533 38.0937i 0.111749 0.105231i
\(363\) 0 0
\(364\) 78.8826 69.9335i 0.216710 0.192125i
\(365\) 36.3313 + 135.590i 0.0995378 + 0.371480i
\(366\) 0 0
\(367\) −123.584 214.053i −0.336740 0.583251i 0.647078 0.762424i \(-0.275991\pi\)
−0.983817 + 0.179173i \(0.942658\pi\)
\(368\) 318.356 424.277i 0.865098 1.15293i
\(369\) 0 0
\(370\) −230.583 + 373.045i −0.623198 + 1.00823i
\(371\) 347.856 + 93.2078i 0.937618 + 0.251234i
\(372\) 0 0
\(373\) 66.7846 + 249.244i 0.179047 + 0.668213i 0.995827 + 0.0912634i \(0.0290905\pi\)
−0.816780 + 0.576950i \(0.804243\pi\)
\(374\) −386.742 116.180i −1.03407 0.310643i
\(375\) 0 0
\(376\) 71.3762 33.0379i 0.189830 0.0878666i
\(377\) −21.7508 −0.0576943
\(378\) 0 0
\(379\) 13.5829 13.5829i 0.0358388 0.0358388i −0.688960 0.724799i \(-0.741933\pi\)
0.724799 + 0.688960i \(0.241933\pi\)
\(380\) 46.4865 + 30.7004i 0.122333 + 0.0807905i
\(381\) 0 0
\(382\) −593.189 + 319.123i −1.55285 + 0.835401i
\(383\) −80.5661 46.5149i −0.210355 0.121449i 0.391121 0.920339i \(-0.372087\pi\)
−0.601477 + 0.798890i \(0.705421\pi\)
\(384\) 0 0
\(385\) 691.947 + 1198.49i 1.79727 + 3.11295i
\(386\) −98.1785 + 158.836i −0.254348 + 0.411493i
\(387\) 0 0
\(388\) −251.256 502.653i −0.647568 1.29550i
\(389\) 79.3503 296.139i 0.203985 0.761284i −0.785771 0.618517i \(-0.787734\pi\)
0.989756 0.142766i \(-0.0455997\pi\)
\(390\) 0 0
\(391\) −334.449 193.094i −0.855368 0.493847i
\(392\) −210.169 + 298.354i −0.536146 + 0.761106i
\(393\) 0 0
\(394\) 312.145 + 331.479i 0.792245 + 0.841318i
\(395\) 114.114 + 114.114i 0.288895 + 0.288895i
\(396\) 0 0
\(397\) −455.184 455.184i −1.14656 1.14656i −0.987225 0.159333i \(-0.949066\pi\)
−0.159333 0.987225i \(-0.550934\pi\)
\(398\) 2.52632 84.0970i 0.00634754 0.211299i
\(399\) 0 0
\(400\) 623.555 266.191i 1.55889 0.665478i
\(401\) −647.690 373.944i −1.61519 0.932529i −0.988141 0.153546i \(-0.950931\pi\)
−0.627046 0.778982i \(-0.715736\pi\)
\(402\) 0 0
\(403\) 17.1107 63.8581i 0.0424584 0.158457i
\(404\) −242.251 + 726.483i −0.599632 + 1.79823i
\(405\) 0 0
\(406\) 152.002 35.8739i 0.374390 0.0883595i
\(407\) −231.517 400.999i −0.568838 0.985256i
\(408\) 0 0
\(409\) 164.913 + 95.2128i 0.403211 + 0.232794i 0.687869 0.725835i \(-0.258546\pi\)
−0.284657 + 0.958629i \(0.591880\pi\)
\(410\) 26.5783 88.4740i 0.0648251 0.215790i
\(411\) 0 0
\(412\) 204.188 + 134.849i 0.495603 + 0.327303i
\(413\) −569.825 + 569.825i −1.37972 + 1.37972i
\(414\) 0 0
\(415\) −687.045 −1.65553
\(416\) 86.1606 9.65929i 0.207117 0.0232194i
\(417\) 0 0
\(418\) −51.7985 + 27.8665i −0.123920 + 0.0666663i
\(419\) 137.696 + 513.889i 0.328630 + 1.22646i 0.910612 + 0.413263i \(0.135611\pi\)
−0.581982 + 0.813202i \(0.697722\pi\)
\(420\) 0 0
\(421\) 627.309 + 168.087i 1.49004 + 0.399256i 0.909752 0.415152i \(-0.136272\pi\)
0.580292 + 0.814408i \(0.302938\pi\)
\(422\) 41.1454 9.71067i 0.0975009 0.0230111i
\(423\) 0 0
\(424\) 189.740 + 227.426i 0.447499 + 0.536382i
\(425\) −246.811 427.489i −0.580731 1.00586i
\(426\) 0 0
\(427\) 65.2268 + 243.430i 0.152756 + 0.570093i
\(428\) 239.325 + 269.950i 0.559170 + 0.630725i
\(429\) 0 0
\(430\) −423.426 12.7200i −0.984712 0.0295813i
\(431\) 16.9333i 0.0392884i −0.999807 0.0196442i \(-0.993747\pi\)
0.999807 0.0196442i \(-0.00625334\pi\)
\(432\) 0 0
\(433\) 594.294 1.37250 0.686252 0.727364i \(-0.259255\pi\)
0.686252 + 0.727364i \(0.259255\pi\)
\(434\) −14.2538 + 474.486i −0.0328429 + 1.09329i
\(435\) 0 0
\(436\) −453.946 512.036i −1.04116 1.17439i
\(437\) −54.3343 + 14.5588i −0.124335 + 0.0333154i
\(438\) 0 0
\(439\) 317.692 183.420i 0.723672 0.417812i −0.0924309 0.995719i \(-0.529464\pi\)
0.816103 + 0.577907i \(0.196130\pi\)
\(440\) −102.404 + 1133.55i −0.232736 + 2.57625i
\(441\) 0 0
\(442\) −14.4993 61.4352i −0.0328038 0.138994i
\(443\) −129.561 + 483.527i −0.292462 + 1.09148i 0.650751 + 0.759292i \(0.274454\pi\)
−0.943212 + 0.332190i \(0.892212\pi\)
\(444\) 0 0
\(445\) −789.643 + 211.584i −1.77448 + 0.475470i
\(446\) −69.4010 129.003i −0.155608 0.289245i
\(447\) 0 0
\(448\) −586.192 + 209.609i −1.30846 + 0.467878i
\(449\) 684.125i 1.52366i −0.647774 0.761832i \(-0.724300\pi\)
0.647774 0.761832i \(-0.275700\pi\)
\(450\) 0 0
\(451\) 68.9685 + 68.9685i 0.152923 + 0.152923i
\(452\) −210.109 138.759i −0.464842 0.306989i
\(453\) 0 0
\(454\) 573.802 + 172.375i 1.26388 + 0.379680i
\(455\) −108.163 + 187.343i −0.237720 + 0.411743i
\(456\) 0 0
\(457\) −599.509 + 346.127i −1.31184 + 0.757389i −0.982400 0.186789i \(-0.940192\pi\)
−0.329436 + 0.944178i \(0.606859\pi\)
\(458\) −85.5408 362.447i −0.186770 0.791370i
\(459\) 0 0
\(460\) −344.324 + 1032.59i −0.748529 + 2.24475i
\(461\) 370.466 + 99.2660i 0.803614 + 0.215328i 0.637170 0.770723i \(-0.280105\pi\)
0.166444 + 0.986051i \(0.446772\pi\)
\(462\) 0 0
\(463\) 91.5118 158.503i 0.197650 0.342339i −0.750116 0.661306i \(-0.770002\pi\)
0.947766 + 0.318967i \(0.103336\pi\)
\(464\) 119.192 + 47.8731i 0.256879 + 0.103175i
\(465\) 0 0
\(466\) 312.321 + 9.38231i 0.670218 + 0.0201337i
\(467\) 250.843 250.843i 0.537137 0.537137i −0.385550 0.922687i \(-0.625988\pi\)
0.922687 + 0.385550i \(0.125988\pi\)
\(468\) 0 0
\(469\) −716.457 + 716.457i −1.52763 + 1.52763i
\(470\) −117.500 + 110.647i −0.250001 + 0.235419i
\(471\) 0 0
\(472\) −653.018 + 113.241i −1.38351 + 0.239918i
\(473\) 223.631 387.340i 0.472792 0.818900i
\(474\) 0 0
\(475\) −69.4495 18.6089i −0.146209 0.0391767i
\(476\) 202.653 + 405.419i 0.425741 + 0.851720i
\(477\) 0 0
\(478\) 531.846 + 328.740i 1.11265 + 0.687740i
\(479\) −116.611 + 67.3256i −0.243448 + 0.140555i −0.616760 0.787151i \(-0.711555\pi\)
0.373313 + 0.927706i \(0.378222\pi\)
\(480\) 0 0
\(481\) 36.1899 62.6827i 0.0752388 0.130317i
\(482\) 359.540 + 668.316i 0.745934 + 1.38655i
\(483\) 0 0
\(484\) −598.878 395.508i −1.23735 0.817166i
\(485\) 815.404 + 815.404i 1.68125 + 1.68125i
\(486\) 0 0
\(487\) 190.468i 0.391105i −0.980693 0.195552i \(-0.937350\pi\)
0.980693 0.195552i \(-0.0626500\pi\)
\(488\) −71.4404 + 194.567i −0.146394 + 0.398703i
\(489\) 0 0
\(490\) 215.460 717.226i 0.439715 1.46373i
\(491\) −283.349 + 75.9231i −0.577085 + 0.154629i −0.535544 0.844507i \(-0.679893\pi\)
−0.0415410 + 0.999137i \(0.513227\pi\)
\(492\) 0 0
\(493\) 24.2040 90.3304i 0.0490953 0.183226i
\(494\) −7.82087 4.83417i −0.0158317 0.00978577i
\(495\) 0 0
\(496\) −234.316 + 312.276i −0.472412 + 0.629589i
\(497\) 959.055 553.711i 1.92969 1.11411i
\(498\) 0 0
\(499\) 134.030 35.9133i 0.268598 0.0719706i −0.122006 0.992529i \(-0.538933\pi\)
0.390604 + 0.920559i \(0.372266\pi\)
\(500\) −426.864 + 378.437i −0.853729 + 0.756874i
\(501\) 0 0
\(502\) 507.050 + 538.457i 1.01006 + 1.07262i
\(503\) −67.2546 −0.133707 −0.0668535 0.997763i \(-0.521296\pi\)
−0.0668535 + 0.997763i \(0.521296\pi\)
\(504\) 0 0
\(505\) 1571.48i 3.11184i
\(506\) −787.865 836.667i −1.55704 1.65349i
\(507\) 0 0
\(508\) 344.230 + 20.7004i 0.677618 + 0.0407488i
\(509\) 45.8166 + 170.990i 0.0900129 + 0.335933i 0.996216 0.0869096i \(-0.0276991\pi\)
−0.906203 + 0.422842i \(0.861032\pi\)
\(510\) 0 0
\(511\) 83.1752 + 144.064i 0.162769 + 0.281925i
\(512\) −493.412 136.706i −0.963695 0.267005i
\(513\) 0 0
\(514\) −183.329 113.318i −0.356671 0.220462i
\(515\) −485.024 129.962i −0.941794 0.252353i
\(516\) 0 0
\(517\) −44.1042 164.599i −0.0853080 0.318374i
\(518\) −149.525 + 497.739i −0.288658 + 0.960886i
\(519\) 0 0
\(520\) −161.457 + 74.7333i −0.310494 + 0.143718i
\(521\) 31.1461 0.0597815 0.0298907 0.999553i \(-0.490484\pi\)
0.0298907 + 0.999553i \(0.490484\pi\)
\(522\) 0 0
\(523\) −596.838 + 596.838i −1.14118 + 1.14118i −0.152948 + 0.988234i \(0.548877\pi\)
−0.988234 + 0.152948i \(0.951123\pi\)
\(524\) 163.478 + 799.332i 0.311981 + 1.52544i
\(525\) 0 0
\(526\) 357.765 + 665.016i 0.680161 + 1.26429i
\(527\) 246.161 + 142.121i 0.467098 + 0.269679i
\(528\) 0 0
\(529\) −285.034 493.694i −0.538817 0.933258i
\(530\) −516.991 319.558i −0.975455 0.602940i
\(531\) 0 0
\(532\) 62.6283 + 20.8839i 0.117722 + 0.0392554i
\(533\) −3.94608 + 14.7270i −0.00740353 + 0.0276304i
\(534\) 0 0
\(535\) −641.122 370.152i −1.19836 0.691873i
\(536\) −821.058 + 142.382i −1.53182 + 0.265637i
\(537\) 0 0
\(538\) −190.957 + 179.819i −0.354939 + 0.334236i
\(539\) 559.102 + 559.102i 1.03729 + 1.03729i
\(540\) 0 0
\(541\) 423.104 + 423.104i 0.782078 + 0.782078i 0.980181 0.198103i \(-0.0634781\pi\)
−0.198103 + 0.980181i \(0.563478\pi\)
\(542\) −423.985 12.7367i −0.782260 0.0234995i
\(543\) 0 0
\(544\) −55.7636 + 368.572i −0.102507 + 0.677522i
\(545\) 1216.07 + 702.096i 2.23131 + 1.28825i
\(546\) 0 0
\(547\) 20.9826 78.3083i 0.0383595 0.143160i −0.944090 0.329687i \(-0.893057\pi\)
0.982450 + 0.186528i \(0.0597234\pi\)
\(548\) −294.538 589.241i −0.537478 1.07526i
\(549\) 0 0
\(550\) −337.413 1429.66i −0.613478 2.59939i
\(551\) −6.81069 11.7965i −0.0123606 0.0214092i
\(552\) 0 0
\(553\) 165.623 + 95.6227i 0.299500 + 0.172916i
\(554\) 869.652 + 261.250i 1.56977 + 0.471571i
\(555\) 0 0
\(556\) 24.1288 + 117.978i 0.0433970 + 0.212191i
\(557\) 415.890 415.890i 0.746661 0.746661i −0.227189 0.973851i \(-0.572954\pi\)
0.973851 + 0.227189i \(0.0729536\pi\)
\(558\) 0 0
\(559\) 69.9143 0.125070
\(560\) 1005.06 788.558i 1.79475 1.40814i
\(561\) 0 0
\(562\) −228.640 424.999i −0.406834 0.756226i
\(563\) −145.642 543.542i −0.258688 0.965438i −0.966001 0.258537i \(-0.916759\pi\)
0.707313 0.706901i \(-0.249907\pi\)
\(564\) 0 0
\(565\) 499.087 + 133.730i 0.883339 + 0.236690i
\(566\) 112.878 + 478.277i 0.199431 + 0.845013i
\(567\) 0 0
\(568\) 907.089 + 81.9457i 1.59699 + 0.144271i
\(569\) 151.528 + 262.455i 0.266306 + 0.461256i 0.967905 0.251316i \(-0.0808634\pi\)
−0.701599 + 0.712572i \(0.747530\pi\)
\(570\) 0 0
\(571\) −175.962 656.698i −0.308164 1.15008i −0.930187 0.367086i \(-0.880356\pi\)
0.622023 0.782999i \(-0.286311\pi\)
\(572\) 11.2757 187.505i 0.0197128 0.327807i
\(573\) 0 0
\(574\) 3.28722 109.426i 0.00572686 0.190638i
\(575\) 1404.82i 2.44316i
\(576\) 0 0
\(577\) −48.7518 −0.0844918 −0.0422459 0.999107i \(-0.513451\pi\)
−0.0422459 + 0.999107i \(0.513451\pi\)
\(578\) −306.466 9.20639i −0.530217 0.0159280i
\(579\) 0 0
\(580\) −263.104 15.8219i −0.453628 0.0272791i
\(581\) −786.444 + 210.727i −1.35360 + 0.362697i
\(582\) 0 0
\(583\) 555.732 320.852i 0.953228 0.550347i
\(584\) −12.3094 + 136.258i −0.0210777 + 0.233318i
\(585\) 0 0
\(586\) −4.67490 + 1.10332i −0.00797765 + 0.00188280i
\(587\) 148.170 552.978i 0.252419 0.942040i −0.717089 0.696981i \(-0.754526\pi\)
0.969508 0.245059i \(-0.0788073\pi\)
\(588\) 0 0
\(589\) 39.9911 10.7156i 0.0678966 0.0181928i
\(590\) 1197.71 644.340i 2.03001 1.09210i
\(591\) 0 0
\(592\) −336.281 + 263.842i −0.568042 + 0.445679i
\(593\) 303.689i 0.512123i −0.966660 0.256062i \(-0.917575\pi\)
0.966660 0.256062i \(-0.0824250\pi\)
\(594\) 0 0
\(595\) −657.670 657.670i −1.10533 1.10533i
\(596\) −526.032 + 107.583i −0.882604 + 0.180509i
\(597\) 0 0
\(598\) 51.6848 172.049i 0.0864294 0.287707i
\(599\) 18.6944 32.3796i 0.0312093 0.0540561i −0.849999 0.526784i \(-0.823397\pi\)
0.881208 + 0.472728i \(0.156731\pi\)
\(600\) 0 0
\(601\) −99.3340 + 57.3505i −0.165281 + 0.0954251i −0.580359 0.814361i \(-0.697088\pi\)
0.415078 + 0.909786i \(0.363754\pi\)
\(602\) −488.587 + 115.311i −0.811607 + 0.191547i
\(603\) 0 0
\(604\) 193.518 96.7321i 0.320394 0.160152i
\(605\) 1422.56 + 381.174i 2.35134 + 0.630039i
\(606\) 0 0
\(607\) −448.633 + 777.056i −0.739099 + 1.28016i 0.213802 + 0.976877i \(0.431415\pi\)
−0.952901 + 0.303281i \(0.901918\pi\)
\(608\) 32.2177 + 43.7044i 0.0529896 + 0.0718823i
\(609\) 0 0
\(610\) 12.7712 425.133i 0.0209365 0.696940i
\(611\) 18.8353 18.8353i 0.0308271 0.0308271i
\(612\) 0 0
\(613\) 262.772 262.772i 0.428666 0.428666i −0.459508 0.888174i \(-0.651974\pi\)
0.888174 + 0.459508i \(0.151974\pi\)
\(614\) −346.169 367.612i −0.563794 0.598716i
\(615\) 0 0
\(616\) 230.457 + 1328.96i 0.374119 + 2.15740i
\(617\) −56.2999 + 97.5142i −0.0912478 + 0.158046i −0.908036 0.418891i \(-0.862419\pi\)
0.816789 + 0.576937i \(0.195752\pi\)
\(618\) 0 0
\(619\) −260.515 69.8049i −0.420865 0.112770i 0.0421700 0.999110i \(-0.486573\pi\)
−0.463035 + 0.886340i \(0.653240\pi\)
\(620\) 253.429 760.003i 0.408756 1.22581i
\(621\) 0 0
\(622\) −90.0577 + 145.698i −0.144787 + 0.234241i
\(623\) −838.990 + 484.391i −1.34669 + 0.777514i
\(624\) 0 0
\(625\) 55.6256 96.3463i 0.0890009 0.154154i
\(626\) 469.023 252.324i 0.749238 0.403074i
\(627\) 0 0
\(628\) 283.285 57.9371i 0.451091 0.0922565i
\(629\) 220.048 + 220.048i 0.349838 + 0.349838i
\(630\) 0 0
\(631\) 950.245i 1.50593i −0.658058 0.752967i \(-0.728622\pi\)
0.658058 0.752967i \(-0.271378\pi\)
\(632\) 66.0690 + 142.738i 0.104540 + 0.225851i
\(633\) 0 0
\(634\) 486.080 + 146.022i 0.766687 + 0.230319i
\(635\) −683.541 + 183.154i −1.07644 + 0.288432i
\(636\) 0 0
\(637\) −31.9894 + 119.386i −0.0502189 + 0.187419i
\(638\) 146.320 236.721i 0.229341 0.371036i
\(639\) 0 0
\(640\) 1049.25 54.1672i 1.63946 0.0846363i
\(641\) −394.622 + 227.835i −0.615635 + 0.355437i −0.775168 0.631755i \(-0.782335\pi\)
0.159532 + 0.987193i \(0.449001\pi\)
\(642\) 0 0
\(643\) −1079.45 + 289.237i −1.67877 + 0.449824i −0.967453 0.253051i \(-0.918566\pi\)
−0.711314 + 0.702875i \(0.751899\pi\)
\(644\) −77.4294 + 1287.59i −0.120232 + 1.99936i
\(645\) 0 0
\(646\) 28.7792 27.1005i 0.0445498 0.0419513i
\(647\) 278.716 0.430783 0.215391 0.976528i \(-0.430897\pi\)
0.215391 + 0.976528i \(0.430897\pi\)
\(648\) 0 0
\(649\) 1435.94i 2.21254i
\(650\) 167.167 157.417i 0.257181 0.242180i
\(651\) 0 0
\(652\) 143.626 + 162.005i 0.220285 + 0.248474i
\(653\) −185.375 691.828i −0.283882 1.05946i −0.949653 0.313304i \(-0.898564\pi\)
0.665771 0.746156i \(-0.268103\pi\)
\(654\) 0 0
\(655\) −837.113 1449.92i −1.27803 2.21362i
\(656\) 54.0381 72.0172i 0.0823751 0.109782i
\(657\) 0 0
\(658\) −100.563 + 162.694i −0.152831 + 0.247255i
\(659\) −251.743 67.4543i −0.382007 0.102359i 0.0627047 0.998032i \(-0.480027\pi\)
−0.444712 + 0.895674i \(0.646694\pi\)
\(660\) 0 0
\(661\) 13.0220 + 48.5988i 0.0197005 + 0.0735232i 0.975076 0.221870i \(-0.0712160\pi\)
−0.955376 + 0.295393i \(0.904549\pi\)
\(662\) 131.510 + 39.5066i 0.198655 + 0.0596776i
\(663\) 0 0
\(664\) −628.584 230.801i −0.946662 0.347592i
\(665\) −135.473 −0.203720
\(666\) 0 0
\(667\) 188.192 188.192i 0.282147 0.282147i
\(668\) 105.116 159.166i 0.157359 0.238273i
\(669\) 0 0
\(670\) 1505.91 810.148i 2.24763 1.20918i
\(671\) 388.902 + 224.532i 0.579585 + 0.334624i
\(672\) 0 0
\(673\) −100.586 174.220i −0.149459 0.258871i 0.781568 0.623820i \(-0.214420\pi\)
−0.931028 + 0.364948i \(0.881087\pi\)
\(674\) −38.8089 + 62.7862i −0.0575799 + 0.0931546i
\(675\) 0 0
\(676\) −578.402 + 289.120i −0.855624 + 0.427692i
\(677\) 116.729 435.638i 0.172421 0.643483i −0.824556 0.565781i \(-0.808575\pi\)
0.996977 0.0777025i \(-0.0247584\pi\)
\(678\) 0 0
\(679\) 1183.47 + 683.277i 1.74296 + 1.00630i
\(680\) −130.699 753.688i −0.192204 1.10837i
\(681\) 0 0
\(682\) 579.884 + 615.803i 0.850269 + 0.902937i
\(683\) −412.234 412.234i −0.603564 0.603564i 0.337692 0.941257i \(-0.390354\pi\)
−0.941257 + 0.337692i \(0.890354\pi\)
\(684\) 0 0
\(685\) 955.866 + 955.866i 1.39542 + 1.39542i
\(686\) −1.97543 + 65.7586i −0.00287963 + 0.0958581i
\(687\) 0 0
\(688\) −383.124 153.880i −0.556866 0.223663i
\(689\) 86.8700 + 50.1544i 0.126081 + 0.0727931i
\(690\) 0 0
\(691\) 20.8188 77.6969i 0.0301285 0.112441i −0.949224 0.314601i \(-0.898129\pi\)
0.979353 + 0.202160i \(0.0647960\pi\)
\(692\) 579.976 + 193.398i 0.838116 + 0.279476i
\(693\) 0 0
\(694\) −549.162 + 129.607i −0.791299 + 0.186754i
\(695\) −123.555 214.003i −0.177776 0.307918i
\(696\) 0 0
\(697\) −56.7697 32.7760i −0.0814486 0.0470244i
\(698\) −150.181 + 499.923i −0.215159 + 0.716222i
\(699\) 0 0
\(700\) −908.599 + 1375.80i −1.29800 + 1.96543i
\(701\) −462.921 + 462.921i −0.660372 + 0.660372i −0.955468 0.295095i \(-0.904649\pi\)
0.295095 + 0.955468i \(0.404649\pi\)
\(702\) 0 0
\(703\) 45.3278 0.0644776
\(704\) −474.487 + 1002.69i −0.673987 + 1.42428i
\(705\) 0 0
\(706\) −375.002 + 201.743i −0.531165 + 0.285755i
\(707\) −481.997 1798.84i −0.681750 2.54432i
\(708\) 0 0
\(709\) 708.278 + 189.782i 0.998982 + 0.267676i 0.721019 0.692916i \(-0.243674\pi\)
0.277963 + 0.960592i \(0.410341\pi\)
\(710\) −1819.00 + 429.301i −2.56198 + 0.604649i
\(711\) 0 0
\(712\) −793.530 71.6869i −1.11451 0.100684i
\(713\) 404.468 + 700.559i 0.567276 + 0.982551i
\(714\) 0 0
\(715\) 99.7660 + 372.332i 0.139533 + 0.520744i
\(716\) 37.4644 33.2142i 0.0523246 0.0463885i
\(717\) 0 0
\(718\) −906.720 27.2384i −1.26284 0.0379364i
\(719\) 18.9955i 0.0264193i 0.999913 + 0.0132096i \(0.00420488\pi\)
−0.999913 + 0.0132096i \(0.995795\pi\)
\(720\) 0 0
\(721\) −595.056 −0.825321
\(722\) −21.5066 + 715.919i −0.0297875 + 0.991578i
\(723\) 0 0
\(724\) −83.1577 + 73.7236i −0.114859 + 0.101828i
\(725\) 328.590 88.0454i 0.453228 0.121442i
\(726\) 0 0
\(727\) −241.043 + 139.166i −0.331558 + 0.191425i −0.656533 0.754298i \(-0.727978\pi\)
0.324975 + 0.945723i \(0.394644\pi\)
\(728\) −161.894 + 135.067i −0.222382 + 0.185531i
\(729\) 0 0
\(730\) −64.4871 273.240i −0.0883385 0.374301i
\(731\) −77.7997 + 290.353i −0.106429 + 0.397199i
\(732\) 0 0
\(733\) −984.880 + 263.898i −1.34363 + 0.360024i −0.857779 0.514018i \(-0.828156\pi\)
−0.485849 + 0.874043i \(0.661490\pi\)
\(734\) 234.201 + 435.335i 0.319075 + 0.593099i
\(735\) 0 0
\(736\) −661.905 + 829.053i −0.899327 + 1.12643i
\(737\) 1805.45i 2.44972i
\(738\) 0 0
\(739\) 129.050 + 129.050i 0.174628 + 0.174628i 0.789009 0.614381i \(-0.210594\pi\)
−0.614381 + 0.789009i \(0.710594\pi\)
\(740\) 483.361 731.906i 0.653191 0.989062i
\(741\) 0 0
\(742\) −689.801 207.222i −0.929651 0.279274i
\(743\) −85.7487 + 148.521i −0.115409 + 0.199894i −0.917943 0.396712i \(-0.870151\pi\)
0.802534 + 0.596606i \(0.203484\pi\)
\(744\) 0 0
\(745\) 954.178 550.895i 1.28078 0.739456i
\(746\) −118.541 502.273i −0.158902 0.673288i
\(747\) 0 0
\(748\) 766.158 + 255.481i 1.02428 + 0.341553i
\(749\) −847.409 227.063i −1.13139 0.303154i
\(750\) 0 0
\(751\) 355.011 614.897i 0.472717 0.818771i −0.526795 0.849992i \(-0.676606\pi\)
0.999512 + 0.0312217i \(0.00993978\pi\)
\(752\) −144.672 + 61.7595i −0.192383 + 0.0821270i
\(753\) 0 0
\(754\) 43.4819 + 1.30622i 0.0576683 + 0.00173239i
\(755\) −313.925 + 313.925i −0.415795 + 0.415795i
\(756\) 0 0
\(757\) 342.380 342.380i 0.452286 0.452286i −0.443827 0.896113i \(-0.646379\pi\)
0.896113 + 0.443827i \(0.146379\pi\)
\(758\) −27.9693 + 26.3378i −0.0368988 + 0.0347465i
\(759\) 0 0
\(760\) −91.0875 64.1648i −0.119852 0.0844274i
\(761\) 436.757 756.485i 0.573925 0.994067i −0.422233 0.906487i \(-0.638754\pi\)
0.996158 0.0875792i \(-0.0279131\pi\)
\(762\) 0 0
\(763\) 1607.35 + 430.687i 2.10661 + 0.564465i
\(764\) 1205.01 602.335i 1.57723 0.788396i
\(765\) 0 0
\(766\) 158.266 + 97.8261i 0.206614 + 0.127710i
\(767\) −194.388 + 112.230i −0.253440 + 0.146324i
\(768\) 0 0
\(769\) 308.567 534.454i 0.401258 0.694999i −0.592620 0.805482i \(-0.701906\pi\)
0.993878 + 0.110483i \(0.0352398\pi\)
\(770\) −1311.30 2437.45i −1.70298 3.16552i
\(771\) 0 0
\(772\) 205.807 311.633i 0.266590 0.403670i
\(773\) −187.872 187.872i −0.243043 0.243043i 0.575065 0.818108i \(-0.304977\pi\)
−0.818108 + 0.575065i \(0.804977\pi\)
\(774\) 0 0
\(775\) 1033.97i 1.33416i
\(776\) 472.100 + 1019.94i 0.608376 + 1.31436i
\(777\) 0 0
\(778\) −176.413 + 587.246i −0.226752 + 0.754815i
\(779\) −9.22276 + 2.47123i −0.0118392 + 0.00317231i
\(780\) 0 0
\(781\) 510.726 1906.06i 0.653939 2.44053i
\(782\) 657.000 + 406.099i 0.840154 + 0.519309i
\(783\) 0 0
\(784\) 438.067 583.817i 0.558758 0.744664i
\(785\) −513.856 + 296.675i −0.654593 + 0.377930i
\(786\) 0 0
\(787\) 978.732 262.250i 1.24362 0.333228i 0.423754 0.905777i \(-0.360712\pi\)
0.819870 + 0.572549i \(0.194046\pi\)
\(788\) −604.101 681.405i −0.766626 0.864728i
\(789\) 0 0
\(790\) −221.271 234.977i −0.280090 0.297439i
\(791\) 612.310 0.774096
\(792\) 0 0
\(793\) 70.1962i 0.0885198i
\(794\) 882.621 + 937.292i 1.11161 + 1.18047i
\(795\) 0 0
\(796\) −10.1007 + 167.967i −0.0126894 + 0.211013i
\(797\) −233.907 872.954i −0.293485 1.09530i −0.942413 0.334451i \(-0.891449\pi\)
0.648929 0.760849i \(-0.275217\pi\)
\(798\) 0 0
\(799\) 57.2630 + 99.1825i 0.0716684 + 0.124133i
\(800\) −1262.53 + 494.695i −1.57817 + 0.618369i
\(801\) 0 0
\(802\) 1272.34 + 786.447i 1.58646 + 0.980608i
\(803\) 286.316 + 76.7183i 0.356559 + 0.0955396i
\(804\) 0 0
\(805\) −685.086 2556.77i −0.851038 3.17612i
\(806\) −38.0410 + 126.631i −0.0471972 + 0.157111i
\(807\) 0 0
\(808\) 527.913 1437.76i 0.653357 1.77941i
\(809\) −328.581 −0.406157 −0.203079 0.979162i \(-0.565095\pi\)
−0.203079 + 0.979162i \(0.565095\pi\)
\(810\) 0 0
\(811\) 195.562 195.562i 0.241137 0.241137i −0.576183 0.817321i \(-0.695459\pi\)
0.817321 + 0.576183i \(0.195459\pi\)
\(812\) −306.022 + 62.5872i −0.376875 + 0.0770778i
\(813\) 0 0
\(814\) 438.744 + 815.540i 0.538997 + 1.00189i
\(815\) −384.757 222.139i −0.472094 0.272564i
\(816\) 0 0
\(817\) 21.8919 + 37.9178i 0.0267954 + 0.0464111i
\(818\) −323.960 200.243i −0.396039 0.244796i
\(819\) 0 0
\(820\) −58.4458 + 175.272i −0.0712754 + 0.213746i
\(821\) 404.751 1510.55i 0.492997 1.83989i −0.0479719 0.998849i \(-0.515276\pi\)
0.540969 0.841042i \(-0.318058\pi\)
\(822\) 0 0
\(823\) 744.966 + 430.106i 0.905183 + 0.522608i 0.878878 0.477046i \(-0.158293\pi\)
0.0263048 + 0.999654i \(0.491626\pi\)
\(824\) −400.094 281.839i −0.485551 0.342037i
\(825\) 0 0
\(826\) 1173.36 1104.92i 1.42053 1.33767i
\(827\) 355.212 + 355.212i 0.429519 + 0.429519i 0.888465 0.458945i \(-0.151773\pi\)
−0.458945 + 0.888465i \(0.651773\pi\)
\(828\) 0 0
\(829\) 421.761 + 421.761i 0.508759 + 0.508759i 0.914145 0.405387i \(-0.132863\pi\)
−0.405387 + 0.914145i \(0.632863\pi\)
\(830\) 1373.47 + 41.2598i 1.65478 + 0.0497106i
\(831\) 0 0
\(832\) −172.824 + 14.1356i −0.207721 + 0.0169899i
\(833\) −460.211 265.703i −0.552474 0.318971i
\(834\) 0 0
\(835\) −101.306 + 378.079i −0.121325 + 0.452789i
\(836\) 105.224 52.5972i 0.125866 0.0629153i
\(837\) 0 0
\(838\) −244.407 1035.58i −0.291655 1.23578i
\(839\) 223.741 + 387.530i 0.266676 + 0.461896i 0.968001 0.250945i \(-0.0807414\pi\)
−0.701326 + 0.712841i \(0.747408\pi\)
\(840\) 0 0
\(841\) −672.514 388.276i −0.799660 0.461684i
\(842\) −1243.96 373.695i −1.47738 0.443818i
\(843\) 0 0
\(844\) −82.8368 + 16.9416i −0.0981479 + 0.0200730i
\(845\) 938.284 938.284i 1.11039 1.11039i
\(846\) 0 0
\(847\) 1745.28 2.06055
\(848\) −365.650 466.041i −0.431191 0.549577i
\(849\) 0 0
\(850\) 467.727 + 869.414i 0.550267 + 1.02284i
\(851\) 229.221 + 855.465i 0.269355 + 1.00525i
\(852\) 0 0
\(853\) 933.333 + 250.086i 1.09418 + 0.293184i 0.760391 0.649465i \(-0.225007\pi\)
0.333786 + 0.942649i \(0.391674\pi\)
\(854\) −115.776 490.557i −0.135569 0.574423i
\(855\) 0 0
\(856\) −462.223 554.030i −0.539980 0.647231i
\(857\) 639.394 + 1107.46i 0.746084 + 1.29226i 0.949686 + 0.313202i \(0.101402\pi\)
−0.203602 + 0.979054i \(0.565265\pi\)
\(858\) 0 0
\(859\) −393.723 1469.39i −0.458350 1.71059i −0.678048 0.735018i \(-0.737174\pi\)
0.219698 0.975568i \(-0.429493\pi\)
\(860\) 845.707 + 50.8569i 0.983380 + 0.0591359i
\(861\) 0 0
\(862\) −1.01691 + 33.8513i −0.00117971 + 0.0392707i
\(863\) 1121.29i 1.29930i 0.760235 + 0.649648i \(0.225084\pi\)
−0.760235 + 0.649648i \(0.774916\pi\)
\(864\) 0 0
\(865\) −1254.57 −1.45037
\(866\) −1188.05 35.6898i −1.37189 0.0412122i
\(867\) 0 0
\(868\) 56.9896 947.688i 0.0656562 1.09181i
\(869\) 329.165 88.1996i 0.378786 0.101495i
\(870\) 0 0
\(871\) −244.410 + 141.110i −0.280609 + 0.162009i
\(872\) 876.733 + 1050.87i 1.00543 + 1.20513i
\(873\) 0 0
\(874\) 109.494 25.8415i 0.125279 0.0295670i
\(875\) 359.047 1339.98i 0.410339 1.53141i
\(876\) 0 0
\(877\) −892.541 + 239.156i −1.01772 + 0.272697i −0.728852 0.684672i \(-0.759946\pi\)
−0.288868 + 0.957369i \(0.593279\pi\)
\(878\) −646.112 + 347.595i −0.735891 + 0.395894i
\(879\) 0 0
\(880\) 272.789 2259.93i 0.309988 2.56810i
\(881\) 1111.35i 1.26146i −0.776002 0.630730i \(-0.782756\pi\)
0.776002 0.630730i \(-0.217244\pi\)
\(882\) 0 0
\(883\) −779.205 779.205i −0.882452 0.882452i 0.111331 0.993783i \(-0.464489\pi\)
−0.993783 + 0.111331i \(0.964489\pi\)
\(884\) 25.2960 + 123.686i 0.0286154 + 0.139916i
\(885\) 0 0
\(886\) 288.042 958.836i 0.325104 1.08221i
\(887\) −836.843 + 1449.46i −0.943454 + 1.63411i −0.184635 + 0.982807i \(0.559110\pi\)
−0.758818 + 0.651302i \(0.774223\pi\)
\(888\) 0 0
\(889\) −726.258 + 419.305i −0.816938 + 0.471659i
\(890\) 1591.28 375.557i 1.78796 0.421974i
\(891\) 0 0
\(892\) 130.992 + 262.058i 0.146852 + 0.293787i
\(893\) 16.1131 + 4.31749i 0.0180438 + 0.00483482i
\(894\) 0 0
\(895\) −51.3707 + 88.9766i −0.0573974 + 0.0994152i
\(896\) 1184.44 383.826i 1.32192 0.428377i
\(897\) 0 0
\(898\) −41.0845 + 1367.63i −0.0457511 + 1.52298i
\(899\) −138.513 + 138.513i −0.154074 + 0.154074i
\(900\) 0 0
\(901\) −304.958 + 304.958i −0.338466 + 0.338466i
\(902\) −133.733 142.017i −0.148263 0.157446i
\(903\) 0 0
\(904\) 411.695 + 290.011i 0.455415 + 0.320808i
\(905\) 114.025 197.496i 0.125994 0.218228i
\(906\) 0 0
\(907\) −928.848 248.884i −1.02409 0.274403i −0.292583 0.956240i \(-0.594515\pi\)
−0.731505 + 0.681837i \(0.761182\pi\)
\(908\) −1136.74 379.053i −1.25191 0.417459i
\(909\) 0 0
\(910\) 227.478 368.022i 0.249976 0.404420i
\(911\) 1192.73 688.620i 1.30925 0.755895i 0.327278 0.944928i \(-0.393869\pi\)
0.981971 + 0.189033i \(0.0605354\pi\)
\(912\) 0 0
\(913\) −725.392 + 1256.42i −0.794515 + 1.37614i
\(914\) 1219.26 655.939i 1.33399 0.717657i
\(915\) 0 0
\(916\) 149.238 + 729.705i 0.162924 + 0.796621i
\(917\) −1402.94 1402.94i −1.52992 1.52992i
\(918\) 0 0
\(919\) 1721.85i 1.87361i 0.349851 + 0.936805i \(0.386232\pi\)
−0.349851 + 0.936805i \(0.613768\pi\)
\(920\) 750.347 2043.56i 0.815595 2.22126i
\(921\) 0 0
\(922\) −734.636 220.691i −0.796786 0.239361i
\(923\) 297.948 79.8348i 0.322803 0.0864949i
\(924\) 0 0
\(925\) −292.988 + 1093.45i −0.316744 + 1.18210i
\(926\) −192.460 + 311.368i −0.207840 + 0.336250i
\(927\) 0 0
\(928\) −235.402 102.861i −0.253666 0.110842i
\(929\) −1270.78 + 733.688i −1.36791 + 0.789761i −0.990660 0.136353i \(-0.956462\pi\)
−0.377245 + 0.926113i \(0.623129\pi\)
\(930\) 0 0
\(931\) −74.7655 + 20.0334i −0.0803067 + 0.0215181i
\(932\) −623.798 37.5123i −0.669311 0.0402493i
\(933\) 0 0
\(934\) −516.524 + 486.395i −0.553023 + 0.520766i
\(935\) −1657.30 −1.77252
\(936\) 0 0
\(937\) 801.474i 0.855361i 0.903930 + 0.427681i \(0.140669\pi\)
−0.903930 + 0.427681i \(0.859331\pi\)
\(938\) 1475.29 1389.24i 1.57281 1.48107i
\(939\) 0 0
\(940\) 241.540 214.137i 0.256957 0.227806i
\(941\) 20.6877 + 77.2074i 0.0219848 + 0.0820482i 0.976047 0.217561i \(-0.0698102\pi\)
−0.954062 + 0.299610i \(0.903144\pi\)
\(942\) 0 0
\(943\) −93.2785 161.563i −0.0989167 0.171329i
\(944\) 1312.25 187.164i 1.39009 0.198267i
\(945\) 0 0
\(946\) −470.321 + 760.901i −0.497168 + 0.804335i
\(947\) 844.141 + 226.187i 0.891384 + 0.238846i 0.675312 0.737532i \(-0.264009\pi\)
0.216072 + 0.976377i \(0.430675\pi\)
\(948\) 0 0
\(949\) 11.9923 + 44.7559i 0.0126368 + 0.0471612i
\(950\) 137.719 + 41.3718i 0.144967 + 0.0435493i
\(951\) 0 0
\(952\) −380.776 822.642i −0.399974 0.864120i
\(953\) −1763.84 −1.85083 −0.925415 0.378956i \(-0.876283\pi\)
−0.925415 + 0.378956i \(0.876283\pi\)
\(954\) 0 0
\(955\) −1954.76 + 1954.76i −2.04687 + 2.04687i
\(956\) −1043.47 689.123i −1.09150 0.720840i
\(957\) 0 0
\(958\) 237.161 127.588i 0.247558 0.133181i
\(959\) 1387.34 + 800.979i 1.44665 + 0.835223i
\(960\) 0 0
\(961\) 182.804 + 316.626i 0.190223 + 0.329475i
\(962\) −76.1115 + 123.136i −0.0791179 + 0.128000i
\(963\) 0 0
\(964\) −678.621 1357.62i −0.703964 1.40832i
\(965\) −198.348 + 740.245i −0.205542 + 0.767094i
\(966\) 0 0
\(967\) 242.348 + 139.920i 0.250618 + 0.144695i 0.620047 0.784564i \(-0.287113\pi\)
−0.369429 + 0.929259i \(0.620447\pi\)
\(968\) 1173.46 + 826.625i 1.21226 + 0.853951i
\(969\) 0 0
\(970\) −1581.10 1679.04i −1.63000 1.73097i
\(971\) −416.563 416.563i −0.429004 0.429004i 0.459285 0.888289i \(-0.348106\pi\)
−0.888289 + 0.459285i \(0.848106\pi\)
\(972\) 0 0
\(973\) −207.068 207.068i −0.212814 0.212814i
\(974\) −11.4384 + 380.764i −0.0117437 + 0.390928i
\(975\) 0 0
\(976\) 154.501 384.668i 0.158300 0.394127i
\(977\) 6.88893 + 3.97733i 0.00705111 + 0.00407096i 0.503521 0.863983i \(-0.332038\pi\)
−0.496470 + 0.868054i \(0.665371\pi\)
\(978\) 0 0
\(979\) −446.788 + 1667.44i −0.456372 + 1.70320i
\(980\) −473.799 + 1420.87i −0.483468 + 1.44986i
\(981\) 0 0
\(982\) 571.001 134.761i 0.581468 0.137232i
\(983\) 677.851 + 1174.07i 0.689574 + 1.19438i 0.971976 + 0.235081i \(0.0755355\pi\)
−0.282402 + 0.959296i \(0.591131\pi\)
\(984\) 0 0
\(985\) 1618.31 + 934.333i 1.64296 + 0.948562i
\(986\) −53.8108 + 179.126i −0.0545749 + 0.181669i
\(987\) 0 0
\(988\) 15.3444 + 10.1337i 0.0155308 + 0.0102567i
\(989\) −604.912 + 604.912i −0.611640 + 0.611640i
\(990\) 0 0
\(991\) 991.305 1.00031 0.500154 0.865937i \(-0.333277\pi\)
0.500154 + 0.865937i \(0.333277\pi\)
\(992\) 487.175 610.199i 0.491103 0.615120i
\(993\) 0 0
\(994\) −1950.50 + 1049.33i −1.96227 + 1.05566i
\(995\) −89.3699 333.533i −0.0898190 0.335209i
\(996\) 0 0
\(997\) −1027.66 275.362i −1.03076 0.276190i −0.296478 0.955040i \(-0.595812\pi\)
−0.734278 + 0.678849i \(0.762479\pi\)
\(998\) −270.097 + 63.7452i −0.270638 + 0.0638730i
\(999\) 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 432.3.x.a.125.1 184
3.2 odd 2 144.3.w.a.77.46 yes 184
9.2 odd 6 inner 432.3.x.a.413.16 184
9.7 even 3 144.3.w.a.29.31 yes 184
16.5 even 4 inner 432.3.x.a.341.16 184
48.5 odd 4 144.3.w.a.5.31 184
144.101 odd 12 inner 432.3.x.a.197.1 184
144.133 even 12 144.3.w.a.101.46 yes 184
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
144.3.w.a.5.31 184 48.5 odd 4
144.3.w.a.29.31 yes 184 9.7 even 3
144.3.w.a.77.46 yes 184 3.2 odd 2
144.3.w.a.101.46 yes 184 144.133 even 12
432.3.x.a.125.1 184 1.1 even 1 trivial
432.3.x.a.197.1 184 144.101 odd 12 inner
432.3.x.a.341.16 184 16.5 even 4 inner
432.3.x.a.413.16 184 9.2 odd 6 inner