Properties

Label 288.2.v.d.181.1
Level $288$
Weight $2$
Character 288.181
Analytic conductor $2.300$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [288,2,Mod(37,288)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(288, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([0, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("288.37");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 288 = 2^{5} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 288.v (of order \(8\), degree \(4\), 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: \(2.29969157821\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 96)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 181.1
Character \(\chi\) \(=\) 288.181
Dual form 288.2.v.d.253.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.34416 - 0.439595i) q^{2} +(1.61351 + 1.18177i) q^{4} +(-0.184062 + 0.444366i) q^{5} +(-0.134531 - 0.134531i) q^{7} +(-1.64931 - 2.29777i) q^{8} +O(q^{10})\) \(q+(-1.34416 - 0.439595i) q^{2} +(1.61351 + 1.18177i) q^{4} +(-0.184062 + 0.444366i) q^{5} +(-0.134531 - 0.134531i) q^{7} +(-1.64931 - 2.29777i) q^{8} +(0.442749 - 0.516384i) q^{10} +(4.83050 + 2.00086i) q^{11} +(-0.237510 - 0.573400i) q^{13} +(0.121692 + 0.239970i) q^{14} +(1.20685 + 3.81360i) q^{16} +5.70425i q^{17} +(-0.459376 - 1.10903i) q^{19} +(-0.822124 + 0.499471i) q^{20} +(-5.61338 - 4.81293i) q^{22} +(4.07921 - 4.07921i) q^{23} +(3.37195 + 3.37195i) q^{25} +(0.0671870 + 0.875148i) q^{26} +(-0.0580831 - 0.376053i) q^{28} +(2.33405 - 0.966793i) q^{29} +10.2033 q^{31} +(0.0542480 - 5.65659i) q^{32} +(2.50756 - 7.66741i) q^{34} +(0.0845432 - 0.0350189i) q^{35} +(-3.05654 + 7.37913i) q^{37} +(0.129949 + 1.69265i) q^{38} +(1.32463 - 0.309965i) q^{40} +(0.877147 - 0.877147i) q^{41} +(-2.15605 - 0.893063i) q^{43} +(5.42952 + 8.93695i) q^{44} +(-7.27630 + 3.68990i) q^{46} -4.94536i q^{47} -6.96380i q^{49} +(-3.05014 - 6.01472i) q^{50} +(0.294401 - 1.20587i) q^{52} +(-9.74330 - 4.03581i) q^{53} +(-1.77823 + 1.77823i) q^{55} +(-0.0872381 + 0.531007i) q^{56} +(-3.56232 + 0.273487i) q^{58} +(-4.73462 + 11.4304i) q^{59} +(-9.46851 + 3.92198i) q^{61} +(-13.7148 - 4.48530i) q^{62} +(-2.55953 + 7.57950i) q^{64} +0.298516 q^{65} +(4.79416 - 1.98581i) q^{67} +(-6.74111 + 9.20388i) q^{68} +(-0.129033 + 0.00990617i) q^{70} +(-4.32992 - 4.32992i) q^{71} +(-6.12055 + 6.12055i) q^{73} +(7.35229 - 8.57507i) q^{74} +(0.569410 - 2.33231i) q^{76} +(-0.380675 - 0.919031i) q^{77} -11.9773i q^{79} +(-1.91677 - 0.165658i) q^{80} +(-1.56461 + 0.793434i) q^{82} +(-1.59989 - 3.86247i) q^{83} +(-2.53477 - 1.04994i) q^{85} +(2.50548 + 2.14820i) q^{86} +(-3.36949 - 14.3994i) q^{88} +(8.43934 + 8.43934i) q^{89} +(-0.0451877 + 0.109093i) q^{91} +(11.4025 - 1.76118i) q^{92} +(-2.17395 + 6.64733i) q^{94} +0.577370 q^{95} -9.21817 q^{97} +(-3.06125 + 9.36044i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 8 q^{10} + 32 q^{14} - 8 q^{16} + 32 q^{20} - 8 q^{22} + 16 q^{23} - 40 q^{26} + 40 q^{28} - 48 q^{31} - 40 q^{32} + 40 q^{34} + 48 q^{35} - 40 q^{38} + 8 q^{40} - 16 q^{43} - 8 q^{44} - 32 q^{46} - 24 q^{50} - 8 q^{52} + 32 q^{53} + 32 q^{55} - 56 q^{56} - 32 q^{58} - 64 q^{59} - 32 q^{61} - 48 q^{62} + 24 q^{64} + 16 q^{67} + 8 q^{68} - 24 q^{70} - 64 q^{71} + 32 q^{74} - 56 q^{76} + 32 q^{77} + 56 q^{80} - 40 q^{82} + 64 q^{86} - 48 q^{88} - 48 q^{91} + 80 q^{92} - 32 q^{94} + 80 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/288\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{8}\right)\) \(1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.34416 0.439595i −0.950462 0.310841i
\(3\) 0 0
\(4\) 1.61351 + 1.18177i 0.806756 + 0.590884i
\(5\) −0.184062 + 0.444366i −0.0823152 + 0.198726i −0.959678 0.281101i \(-0.909301\pi\)
0.877363 + 0.479827i \(0.159301\pi\)
\(6\) 0 0
\(7\) −0.134531 0.134531i −0.0508480 0.0508480i 0.681226 0.732074i \(-0.261447\pi\)
−0.732074 + 0.681226i \(0.761447\pi\)
\(8\) −1.64931 2.29777i −0.583120 0.812386i
\(9\) 0 0
\(10\) 0.442749 0.516384i 0.140010 0.163295i
\(11\) 4.83050 + 2.00086i 1.45645 + 0.603282i 0.963724 0.266902i \(-0.0860001\pi\)
0.492727 + 0.870184i \(0.336000\pi\)
\(12\) 0 0
\(13\) −0.237510 0.573400i −0.0658735 0.159033i 0.887515 0.460780i \(-0.152430\pi\)
−0.953388 + 0.301747i \(0.902430\pi\)
\(14\) 0.121692 + 0.239970i 0.0325235 + 0.0641347i
\(15\) 0 0
\(16\) 1.20685 + 3.81360i 0.301712 + 0.953399i
\(17\) 5.70425i 1.38348i 0.722145 + 0.691742i \(0.243157\pi\)
−0.722145 + 0.691742i \(0.756843\pi\)
\(18\) 0 0
\(19\) −0.459376 1.10903i −0.105388 0.254430i 0.862385 0.506253i \(-0.168970\pi\)
−0.967773 + 0.251823i \(0.918970\pi\)
\(20\) −0.822124 + 0.499471i −0.183833 + 0.111685i
\(21\) 0 0
\(22\) −5.61338 4.81293i −1.19678 1.02612i
\(23\) 4.07921 4.07921i 0.850575 0.850575i −0.139629 0.990204i \(-0.544591\pi\)
0.990204 + 0.139629i \(0.0445910\pi\)
\(24\) 0 0
\(25\) 3.37195 + 3.37195i 0.674390 + 0.674390i
\(26\) 0.0671870 + 0.875148i 0.0131765 + 0.171631i
\(27\) 0 0
\(28\) −0.0580831 0.376053i −0.0109767 0.0710673i
\(29\) 2.33405 0.966793i 0.433421 0.179529i −0.155296 0.987868i \(-0.549633\pi\)
0.588717 + 0.808339i \(0.299633\pi\)
\(30\) 0 0
\(31\) 10.2033 1.83256 0.916280 0.400539i \(-0.131177\pi\)
0.916280 + 0.400539i \(0.131177\pi\)
\(32\) 0.0542480 5.65659i 0.00958978 0.999954i
\(33\) 0 0
\(34\) 2.50756 7.66741i 0.430043 1.31495i
\(35\) 0.0845432 0.0350189i 0.0142904 0.00591928i
\(36\) 0 0
\(37\) −3.05654 + 7.37913i −0.502491 + 1.21312i 0.445631 + 0.895217i \(0.352979\pi\)
−0.948123 + 0.317905i \(0.897021\pi\)
\(38\) 0.129949 + 1.69265i 0.0210804 + 0.274585i
\(39\) 0 0
\(40\) 1.32463 0.309965i 0.209442 0.0490098i
\(41\) 0.877147 0.877147i 0.136987 0.136987i −0.635288 0.772275i \(-0.719119\pi\)
0.772275 + 0.635288i \(0.219119\pi\)
\(42\) 0 0
\(43\) −2.15605 0.893063i −0.328794 0.136191i 0.212179 0.977231i \(-0.431944\pi\)
−0.540973 + 0.841040i \(0.681944\pi\)
\(44\) 5.42952 + 8.93695i 0.818531 + 1.34730i
\(45\) 0 0
\(46\) −7.27630 + 3.68990i −1.07283 + 0.544046i
\(47\) 4.94536i 0.721355i −0.932691 0.360677i \(-0.882546\pi\)
0.932691 0.360677i \(-0.117454\pi\)
\(48\) 0 0
\(49\) 6.96380i 0.994829i
\(50\) −3.05014 6.01472i −0.431355 0.850610i
\(51\) 0 0
\(52\) 0.294401 1.20587i 0.0408261 0.167224i
\(53\) −9.74330 4.03581i −1.33834 0.554361i −0.405321 0.914175i \(-0.632840\pi\)
−0.933024 + 0.359814i \(0.882840\pi\)
\(54\) 0 0
\(55\) −1.77823 + 1.77823i −0.239776 + 0.239776i
\(56\) −0.0872381 + 0.531007i −0.0116577 + 0.0709587i
\(57\) 0 0
\(58\) −3.56232 + 0.273487i −0.467756 + 0.0359106i
\(59\) −4.73462 + 11.4304i −0.616395 + 1.48811i 0.239466 + 0.970905i \(0.423028\pi\)
−0.855861 + 0.517205i \(0.826972\pi\)
\(60\) 0 0
\(61\) −9.46851 + 3.92198i −1.21232 + 0.502159i −0.894960 0.446147i \(-0.852796\pi\)
−0.317358 + 0.948306i \(0.602796\pi\)
\(62\) −13.7148 4.48530i −1.74178 0.569634i
\(63\) 0 0
\(64\) −2.55953 + 7.57950i −0.319941 + 0.947437i
\(65\) 0.298516 0.0370264
\(66\) 0 0
\(67\) 4.79416 1.98581i 0.585700 0.242605i −0.0700997 0.997540i \(-0.522332\pi\)
0.655799 + 0.754935i \(0.272332\pi\)
\(68\) −6.74111 + 9.20388i −0.817479 + 1.11613i
\(69\) 0 0
\(70\) −0.129033 + 0.00990617i −0.0154224 + 0.00118401i
\(71\) −4.32992 4.32992i −0.513867 0.513867i 0.401842 0.915709i \(-0.368370\pi\)
−0.915709 + 0.401842i \(0.868370\pi\)
\(72\) 0 0
\(73\) −6.12055 + 6.12055i −0.716356 + 0.716356i −0.967857 0.251501i \(-0.919076\pi\)
0.251501 + 0.967857i \(0.419076\pi\)
\(74\) 7.35229 8.57507i 0.854686 0.996831i
\(75\) 0 0
\(76\) 0.569410 2.33231i 0.0653158 0.267535i
\(77\) −0.380675 0.919031i −0.0433820 0.104733i
\(78\) 0 0
\(79\) 11.9773i 1.34756i −0.738934 0.673778i \(-0.764670\pi\)
0.738934 0.673778i \(-0.235330\pi\)
\(80\) −1.91677 0.165658i −0.214301 0.0185212i
\(81\) 0 0
\(82\) −1.56461 + 0.793434i −0.172783 + 0.0876201i
\(83\) −1.59989 3.86247i −0.175610 0.423961i 0.811426 0.584455i \(-0.198691\pi\)
−0.987037 + 0.160493i \(0.948691\pi\)
\(84\) 0 0
\(85\) −2.53477 1.04994i −0.274935 0.113882i
\(86\) 2.50548 + 2.14820i 0.270172 + 0.231647i
\(87\) 0 0
\(88\) −3.36949 14.3994i −0.359189 1.53499i
\(89\) 8.43934 + 8.43934i 0.894569 + 0.894569i 0.994949 0.100381i \(-0.0320060\pi\)
−0.100381 + 0.994949i \(0.532006\pi\)
\(90\) 0 0
\(91\) −0.0451877 + 0.109093i −0.00473696 + 0.0114360i
\(92\) 11.4025 1.76118i 1.18880 0.183615i
\(93\) 0 0
\(94\) −2.17395 + 6.64733i −0.224226 + 0.685620i
\(95\) 0.577370 0.0592369
\(96\) 0 0
\(97\) −9.21817 −0.935964 −0.467982 0.883738i \(-0.655019\pi\)
−0.467982 + 0.883738i \(0.655019\pi\)
\(98\) −3.06125 + 9.36044i −0.309233 + 0.945547i
\(99\) 0 0
\(100\) 1.45582 + 9.42555i 0.145582 + 0.942555i
\(101\) −1.27818 + 3.08581i −0.127184 + 0.307050i −0.974626 0.223838i \(-0.928141\pi\)
0.847442 + 0.530888i \(0.178141\pi\)
\(102\) 0 0
\(103\) −7.17872 7.17872i −0.707340 0.707340i 0.258635 0.965975i \(-0.416727\pi\)
−0.965975 + 0.258635i \(0.916727\pi\)
\(104\) −0.925816 + 1.49146i −0.0907837 + 0.146250i
\(105\) 0 0
\(106\) 11.3224 + 9.70786i 1.09973 + 0.942910i
\(107\) −1.52273 0.630735i −0.147208 0.0609755i 0.307863 0.951431i \(-0.400386\pi\)
−0.455071 + 0.890455i \(0.650386\pi\)
\(108\) 0 0
\(109\) −5.64602 13.6307i −0.540791 1.30558i −0.924166 0.381992i \(-0.875238\pi\)
0.383375 0.923593i \(-0.374762\pi\)
\(110\) 3.17191 1.60851i 0.302430 0.153366i
\(111\) 0 0
\(112\) 0.350689 0.675406i 0.0331370 0.0638199i
\(113\) 4.48349i 0.421771i −0.977511 0.210886i \(-0.932365\pi\)
0.977511 0.210886i \(-0.0676348\pi\)
\(114\) 0 0
\(115\) 1.06183 + 2.56349i 0.0990164 + 0.239047i
\(116\) 4.90854 + 1.19837i 0.455746 + 0.111266i
\(117\) 0 0
\(118\) 11.3888 13.2829i 1.04843 1.22279i
\(119\) 0.767400 0.767400i 0.0703474 0.0703474i
\(120\) 0 0
\(121\) 11.5521 + 11.5521i 1.05019 + 1.05019i
\(122\) 14.4512 1.10945i 1.30835 0.100445i
\(123\) 0 0
\(124\) 16.4631 + 12.0579i 1.47843 + 1.08283i
\(125\) −4.34086 + 1.79804i −0.388258 + 0.160822i
\(126\) 0 0
\(127\) 10.5535 0.936470 0.468235 0.883604i \(-0.344890\pi\)
0.468235 + 0.883604i \(0.344890\pi\)
\(128\) 6.77232 9.06288i 0.598594 0.801053i
\(129\) 0 0
\(130\) −0.401252 0.131226i −0.0351922 0.0115093i
\(131\) −6.23238 + 2.58153i −0.544525 + 0.225550i −0.637952 0.770076i \(-0.720218\pi\)
0.0934264 + 0.995626i \(0.470218\pi\)
\(132\) 0 0
\(133\) −0.0873991 + 0.211000i −0.00757846 + 0.0182960i
\(134\) −7.31705 + 0.561745i −0.632097 + 0.0485274i
\(135\) 0 0
\(136\) 13.1071 9.40810i 1.12392 0.806738i
\(137\) 10.4945 10.4945i 0.896606 0.896606i −0.0985279 0.995134i \(-0.531413\pi\)
0.995134 + 0.0985279i \(0.0314134\pi\)
\(138\) 0 0
\(139\) 9.16542 + 3.79644i 0.777401 + 0.322010i 0.735866 0.677127i \(-0.236775\pi\)
0.0415348 + 0.999137i \(0.486775\pi\)
\(140\) 0.177796 + 0.0434070i 0.0150265 + 0.00366856i
\(141\) 0 0
\(142\) 3.91668 + 7.72350i 0.328681 + 0.648142i
\(143\) 3.24504i 0.271364i
\(144\) 0 0
\(145\) 1.21512i 0.100910i
\(146\) 10.9175 5.53641i 0.903542 0.458197i
\(147\) 0 0
\(148\) −13.6522 + 8.29420i −1.12220 + 0.681779i
\(149\) −9.74535 4.03666i −0.798370 0.330696i −0.0540667 0.998537i \(-0.517218\pi\)
−0.744303 + 0.667842i \(0.767218\pi\)
\(150\) 0 0
\(151\) −8.98745 + 8.98745i −0.731388 + 0.731388i −0.970895 0.239507i \(-0.923014\pi\)
0.239507 + 0.970895i \(0.423014\pi\)
\(152\) −1.79065 + 2.88469i −0.145241 + 0.233979i
\(153\) 0 0
\(154\) 0.107686 + 1.40266i 0.00867755 + 0.113030i
\(155\) −1.87804 + 4.53398i −0.150847 + 0.364178i
\(156\) 0 0
\(157\) 20.8461 8.63473i 1.66370 0.689127i 0.665348 0.746533i \(-0.268283\pi\)
0.998351 + 0.0574062i \(0.0182830\pi\)
\(158\) −5.26518 + 16.0994i −0.418875 + 1.28080i
\(159\) 0 0
\(160\) 2.50361 + 1.06527i 0.197928 + 0.0842171i
\(161\) −1.09756 −0.0865001
\(162\) 0 0
\(163\) −7.04554 + 2.91836i −0.551849 + 0.228584i −0.641142 0.767422i \(-0.721539\pi\)
0.0892930 + 0.996005i \(0.471539\pi\)
\(164\) 2.45187 0.378703i 0.191459 0.0295717i
\(165\) 0 0
\(166\) 0.452577 + 5.89507i 0.0351268 + 0.457546i
\(167\) 0.832153 + 0.832153i 0.0643940 + 0.0643940i 0.738570 0.674176i \(-0.235501\pi\)
−0.674176 + 0.738570i \(0.735501\pi\)
\(168\) 0 0
\(169\) 8.92001 8.92001i 0.686155 0.686155i
\(170\) 2.94559 + 2.52555i 0.225916 + 0.193701i
\(171\) 0 0
\(172\) −2.42341 3.98891i −0.184783 0.304152i
\(173\) −4.67762 11.2928i −0.355633 0.858573i −0.995903 0.0904237i \(-0.971178\pi\)
0.640271 0.768149i \(-0.278822\pi\)
\(174\) 0 0
\(175\) 0.907266i 0.0685828i
\(176\) −1.80080 + 20.8363i −0.135740 + 1.57060i
\(177\) 0 0
\(178\) −7.63390 15.0537i −0.572185 1.12832i
\(179\) −4.58465 11.0683i −0.342673 0.827285i −0.997444 0.0714579i \(-0.977235\pi\)
0.654771 0.755828i \(-0.272765\pi\)
\(180\) 0 0
\(181\) 4.59848 + 1.90475i 0.341802 + 0.141579i 0.546980 0.837146i \(-0.315777\pi\)
−0.205178 + 0.978725i \(0.565777\pi\)
\(182\) 0.108696 0.126774i 0.00805709 0.00939708i
\(183\) 0 0
\(184\) −16.1010 2.64521i −1.18698 0.195007i
\(185\) −2.71644 2.71644i −0.199717 0.199717i
\(186\) 0 0
\(187\) −11.4134 + 27.5544i −0.834631 + 2.01498i
\(188\) 5.84427 7.97940i 0.426237 0.581957i
\(189\) 0 0
\(190\) −0.776075 0.253809i −0.0563024 0.0184132i
\(191\) 16.3142 1.18045 0.590227 0.807238i \(-0.299038\pi\)
0.590227 + 0.807238i \(0.299038\pi\)
\(192\) 0 0
\(193\) 3.22234 0.231949 0.115975 0.993252i \(-0.463001\pi\)
0.115975 + 0.993252i \(0.463001\pi\)
\(194\) 12.3907 + 4.05226i 0.889598 + 0.290936i
\(195\) 0 0
\(196\) 8.22960 11.2362i 0.587829 0.802585i
\(197\) −8.79059 + 21.2224i −0.626303 + 1.51203i 0.217880 + 0.975976i \(0.430086\pi\)
−0.844183 + 0.536055i \(0.819914\pi\)
\(198\) 0 0
\(199\) −7.10324 7.10324i −0.503535 0.503535i 0.409000 0.912535i \(-0.365878\pi\)
−0.912535 + 0.409000i \(0.865878\pi\)
\(200\) 2.18658 13.3094i 0.154614 0.941116i
\(201\) 0 0
\(202\) 3.07459 3.58593i 0.216327 0.252305i
\(203\) −0.444066 0.183938i −0.0311673 0.0129099i
\(204\) 0 0
\(205\) 0.228324 + 0.551224i 0.0159469 + 0.0384992i
\(206\) 6.49359 + 12.8051i 0.452430 + 0.892170i
\(207\) 0 0
\(208\) 1.90008 1.59777i 0.131747 0.110786i
\(209\) 6.27633i 0.434143i
\(210\) 0 0
\(211\) −4.72147 11.3986i −0.325040 0.784715i −0.998946 0.0458984i \(-0.985385\pi\)
0.673906 0.738817i \(-0.264615\pi\)
\(212\) −10.9515 18.0261i −0.752155 1.23804i
\(213\) 0 0
\(214\) 1.76952 + 1.51719i 0.120962 + 0.103713i
\(215\) 0.793693 0.793693i 0.0541294 0.0541294i
\(216\) 0 0
\(217\) −1.37266 1.37266i −0.0931820 0.0931820i
\(218\) 1.59715 + 20.8038i 0.108173 + 1.40901i
\(219\) 0 0
\(220\) −4.97064 + 0.767739i −0.335121 + 0.0517609i
\(221\) 3.27082 1.35482i 0.220019 0.0911349i
\(222\) 0 0
\(223\) −13.9899 −0.936832 −0.468416 0.883508i \(-0.655175\pi\)
−0.468416 + 0.883508i \(0.655175\pi\)
\(224\) −0.768287 + 0.753691i −0.0513333 + 0.0503581i
\(225\) 0 0
\(226\) −1.97092 + 6.02651i −0.131104 + 0.400878i
\(227\) −2.11043 + 0.874170i −0.140074 + 0.0580207i −0.451619 0.892211i \(-0.649154\pi\)
0.311545 + 0.950231i \(0.399154\pi\)
\(228\) 0 0
\(229\) −3.24245 + 7.82798i −0.214267 + 0.517287i −0.994070 0.108738i \(-0.965319\pi\)
0.779803 + 0.626025i \(0.215319\pi\)
\(230\) −0.300372 3.91251i −0.0198059 0.257983i
\(231\) 0 0
\(232\) −6.07105 3.76856i −0.398584 0.247418i
\(233\) −7.83849 + 7.83849i −0.513516 + 0.513516i −0.915602 0.402086i \(-0.868285\pi\)
0.402086 + 0.915602i \(0.368285\pi\)
\(234\) 0 0
\(235\) 2.19755 + 0.910254i 0.143352 + 0.0593784i
\(236\) −21.1474 + 12.8478i −1.37658 + 0.836324i
\(237\) 0 0
\(238\) −1.36885 + 0.694160i −0.0887294 + 0.0449957i
\(239\) 8.50653i 0.550242i 0.961410 + 0.275121i \(0.0887179\pi\)
−0.961410 + 0.275121i \(0.911282\pi\)
\(240\) 0 0
\(241\) 10.3310i 0.665475i −0.943019 0.332738i \(-0.892028\pi\)
0.943019 0.332738i \(-0.107972\pi\)
\(242\) −10.4496 20.6061i −0.671726 1.32461i
\(243\) 0 0
\(244\) −19.9124 4.86141i −1.27476 0.311220i
\(245\) 3.09448 + 1.28177i 0.197699 + 0.0818895i
\(246\) 0 0
\(247\) −0.526813 + 0.526813i −0.0335203 + 0.0335203i
\(248\) −16.8284 23.4448i −1.06860 1.48875i
\(249\) 0 0
\(250\) 6.62520 0.508631i 0.419015 0.0321686i
\(251\) 0.371186 0.896122i 0.0234291 0.0565627i −0.911732 0.410785i \(-0.865255\pi\)
0.935161 + 0.354223i \(0.115255\pi\)
\(252\) 0 0
\(253\) 27.8666 11.5427i 1.75196 0.725684i
\(254\) −14.1855 4.63926i −0.890079 0.291093i
\(255\) 0 0
\(256\) −13.0870 + 9.20485i −0.817940 + 0.575303i
\(257\) 11.9183 0.743442 0.371721 0.928345i \(-0.378768\pi\)
0.371721 + 0.928345i \(0.378768\pi\)
\(258\) 0 0
\(259\) 1.40392 0.581524i 0.0872355 0.0361341i
\(260\) 0.481660 + 0.352777i 0.0298713 + 0.0218783i
\(261\) 0 0
\(262\) 9.51212 0.730265i 0.587661 0.0451159i
\(263\) −0.627327 0.627327i −0.0386827 0.0386827i 0.687501 0.726184i \(-0.258708\pi\)
−0.726184 + 0.687501i \(0.758708\pi\)
\(264\) 0 0
\(265\) 3.58675 3.58675i 0.220332 0.220332i
\(266\) 0.210233 0.245197i 0.0128902 0.0150340i
\(267\) 0 0
\(268\) 10.0822 + 2.46146i 0.615868 + 0.150358i
\(269\) 1.22418 + 2.95542i 0.0746393 + 0.180195i 0.956795 0.290762i \(-0.0939087\pi\)
−0.882156 + 0.470957i \(0.843909\pi\)
\(270\) 0 0
\(271\) 26.7281i 1.62362i 0.583925 + 0.811808i \(0.301516\pi\)
−0.583925 + 0.811808i \(0.698484\pi\)
\(272\) −21.7537 + 6.88415i −1.31901 + 0.417413i
\(273\) 0 0
\(274\) −18.7196 + 9.49293i −1.13089 + 0.573489i
\(275\) 9.54142 + 23.0350i 0.575369 + 1.38906i
\(276\) 0 0
\(277\) −26.1483 10.8310i −1.57110 0.650770i −0.584126 0.811663i \(-0.698563\pi\)
−0.986972 + 0.160893i \(0.948563\pi\)
\(278\) −10.6509 9.13208i −0.638796 0.547706i
\(279\) 0 0
\(280\) −0.219904 0.136504i −0.0131418 0.00815767i
\(281\) 13.5386 + 13.5386i 0.807646 + 0.807646i 0.984277 0.176631i \(-0.0565201\pi\)
−0.176631 + 0.984277i \(0.556520\pi\)
\(282\) 0 0
\(283\) −4.00203 + 9.66174i −0.237896 + 0.574331i −0.997065 0.0765624i \(-0.975606\pi\)
0.759169 + 0.650893i \(0.225606\pi\)
\(284\) −1.86942 12.1033i −0.110930 0.718202i
\(285\) 0 0
\(286\) −1.42650 + 4.36184i −0.0843508 + 0.257921i
\(287\) −0.236007 −0.0139311
\(288\) 0 0
\(289\) −15.5385 −0.914029
\(290\) 0.534161 1.63331i 0.0313670 0.0959114i
\(291\) 0 0
\(292\) −17.1087 + 2.64251i −1.00121 + 0.154641i
\(293\) 11.0520 26.6818i 0.645663 1.55877i −0.173268 0.984875i \(-0.555433\pi\)
0.818930 0.573893i \(-0.194567\pi\)
\(294\) 0 0
\(295\) −4.20781 4.20781i −0.244988 0.244988i
\(296\) 21.9968 5.14727i 1.27854 0.299179i
\(297\) 0 0
\(298\) 11.3248 + 9.70990i 0.656027 + 0.562480i
\(299\) −3.30788 1.37017i −0.191300 0.0792389i
\(300\) 0 0
\(301\) 0.169911 + 0.410200i 0.00979348 + 0.0236436i
\(302\) 16.0314 8.12970i 0.922501 0.467811i
\(303\) 0 0
\(304\) 3.67501 3.09031i 0.210776 0.177241i
\(305\) 4.92937i 0.282255i
\(306\) 0 0
\(307\) −9.87747 23.8463i −0.563737 1.36098i −0.906757 0.421653i \(-0.861450\pi\)
0.343020 0.939328i \(-0.388550\pi\)
\(308\) 0.471858 1.93274i 0.0268866 0.110128i
\(309\) 0 0
\(310\) 4.51749 5.26880i 0.256576 0.299248i
\(311\) −18.0382 + 18.0382i −1.02285 + 1.02285i −0.0231182 + 0.999733i \(0.507359\pi\)
−0.999733 + 0.0231182i \(0.992641\pi\)
\(312\) 0 0
\(313\) 13.4949 + 13.4949i 0.762778 + 0.762778i 0.976824 0.214046i \(-0.0686643\pi\)
−0.214046 + 0.976824i \(0.568664\pi\)
\(314\) −31.8162 + 2.44260i −1.79549 + 0.137844i
\(315\) 0 0
\(316\) 14.1544 19.3256i 0.796250 1.08715i
\(317\) 9.96898 4.12929i 0.559914 0.231924i −0.0847339 0.996404i \(-0.527004\pi\)
0.644648 + 0.764480i \(0.277004\pi\)
\(318\) 0 0
\(319\) 13.2090 0.739564
\(320\) −2.89696 2.53247i −0.161945 0.141569i
\(321\) 0 0
\(322\) 1.47530 + 0.482483i 0.0822151 + 0.0268877i
\(323\) 6.32620 2.62040i 0.351999 0.145803i
\(324\) 0 0
\(325\) 1.13261 2.73435i 0.0628257 0.151675i
\(326\) 10.7532 0.825546i 0.595565 0.0457228i
\(327\) 0 0
\(328\) −3.46218 0.568795i −0.191167 0.0314064i
\(329\) −0.665305 + 0.665305i −0.0366795 + 0.0366795i
\(330\) 0 0
\(331\) 11.3038 + 4.68220i 0.621314 + 0.257357i 0.671058 0.741405i \(-0.265840\pi\)
−0.0497433 + 0.998762i \(0.515840\pi\)
\(332\) 1.98311 8.12284i 0.108837 0.445799i
\(333\) 0 0
\(334\) −0.752734 1.48435i −0.0411878 0.0812203i
\(335\) 2.49587i 0.136364i
\(336\) 0 0
\(337\) 1.45068i 0.0790237i 0.999219 + 0.0395118i \(0.0125803\pi\)
−0.999219 + 0.0395118i \(0.987420\pi\)
\(338\) −15.9111 + 8.06870i −0.865449 + 0.438879i
\(339\) 0 0
\(340\) −2.84911 4.68960i −0.154514 0.254329i
\(341\) 49.2869 + 20.4153i 2.66903 + 1.10555i
\(342\) 0 0
\(343\) −1.87857 + 1.87857i −0.101433 + 0.101433i
\(344\) 1.50394 + 6.42704i 0.0810869 + 0.346523i
\(345\) 0 0
\(346\) 1.32321 + 17.2355i 0.0711360 + 0.926586i
\(347\) 4.88124 11.7844i 0.262039 0.632618i −0.737026 0.675865i \(-0.763770\pi\)
0.999064 + 0.0432472i \(0.0137703\pi\)
\(348\) 0 0
\(349\) −7.72369 + 3.19926i −0.413440 + 0.171252i −0.579701 0.814829i \(-0.696831\pi\)
0.166261 + 0.986082i \(0.446831\pi\)
\(350\) −0.398829 + 1.21951i −0.0213183 + 0.0651854i
\(351\) 0 0
\(352\) 11.5801 27.2156i 0.617221 1.45060i
\(353\) −17.4309 −0.927751 −0.463875 0.885900i \(-0.653541\pi\)
−0.463875 + 0.885900i \(0.653541\pi\)
\(354\) 0 0
\(355\) 2.72104 1.12709i 0.144418 0.0598199i
\(356\) 3.64364 + 23.5903i 0.193112 + 1.25029i
\(357\) 0 0
\(358\) 1.29691 + 16.8929i 0.0685437 + 0.892820i
\(359\) −4.53639 4.53639i −0.239422 0.239422i 0.577189 0.816611i \(-0.304150\pi\)
−0.816611 + 0.577189i \(0.804150\pi\)
\(360\) 0 0
\(361\) 12.4161 12.4161i 0.653479 0.653479i
\(362\) −5.34375 4.58175i −0.280861 0.240811i
\(363\) 0 0
\(364\) −0.201833 + 0.122621i −0.0105789 + 0.00642710i
\(365\) −1.59320 3.84632i −0.0833919 0.201326i
\(366\) 0 0
\(367\) 7.18068i 0.374828i −0.982281 0.187414i \(-0.939989\pi\)
0.982281 0.187414i \(-0.0600106\pi\)
\(368\) 20.4795 + 10.6335i 1.06757 + 0.554309i
\(369\) 0 0
\(370\) 2.45719 + 4.84545i 0.127743 + 0.251903i
\(371\) 0.767836 + 1.85372i 0.0398640 + 0.0962403i
\(372\) 0 0
\(373\) 14.3497 + 5.94383i 0.742998 + 0.307760i 0.721881 0.692017i \(-0.243278\pi\)
0.0211168 + 0.999777i \(0.493278\pi\)
\(374\) 27.4542 32.0201i 1.41962 1.65572i
\(375\) 0 0
\(376\) −11.3633 + 8.15645i −0.586018 + 0.420637i
\(377\) −1.10872 1.10872i −0.0571020 0.0571020i
\(378\) 0 0
\(379\) 3.45126 8.33209i 0.177280 0.427991i −0.810115 0.586272i \(-0.800595\pi\)
0.987394 + 0.158281i \(0.0505951\pi\)
\(380\) 0.931594 + 0.682318i 0.0477897 + 0.0350022i
\(381\) 0 0
\(382\) −21.9288 7.17164i −1.12198 0.366933i
\(383\) 4.45958 0.227874 0.113937 0.993488i \(-0.463654\pi\)
0.113937 + 0.993488i \(0.463654\pi\)
\(384\) 0 0
\(385\) 0.478454 0.0243843
\(386\) −4.33133 1.41652i −0.220459 0.0720992i
\(387\) 0 0
\(388\) −14.8736 10.8937i −0.755095 0.553046i
\(389\) −2.19268 + 5.29359i −0.111173 + 0.268396i −0.969668 0.244427i \(-0.921400\pi\)
0.858495 + 0.512823i \(0.171400\pi\)
\(390\) 0 0
\(391\) 23.2689 + 23.2689i 1.17676 + 1.17676i
\(392\) −16.0012 + 11.4855i −0.808185 + 0.580105i
\(393\) 0 0
\(394\) 21.1452 24.6619i 1.06528 1.24245i
\(395\) 5.32232 + 2.20458i 0.267795 + 0.110924i
\(396\) 0 0
\(397\) 5.25839 + 12.6949i 0.263911 + 0.637137i 0.999174 0.0406449i \(-0.0129412\pi\)
−0.735263 + 0.677782i \(0.762941\pi\)
\(398\) 6.42531 + 12.6704i 0.322072 + 0.635110i
\(399\) 0 0
\(400\) −8.78984 + 16.9287i −0.439492 + 0.846435i
\(401\) 22.6945i 1.13331i −0.823955 0.566655i \(-0.808237\pi\)
0.823955 0.566655i \(-0.191763\pi\)
\(402\) 0 0
\(403\) −2.42338 5.85055i −0.120717 0.291437i
\(404\) −5.70908 + 3.46848i −0.284037 + 0.172563i
\(405\) 0 0
\(406\) 0.516036 + 0.442451i 0.0256104 + 0.0219585i
\(407\) −29.5292 + 29.5292i −1.46371 + 1.46371i
\(408\) 0 0
\(409\) −18.9178 18.9178i −0.935424 0.935424i 0.0626139 0.998038i \(-0.480056\pi\)
−0.998038 + 0.0626139i \(0.980056\pi\)
\(410\) −0.0645885 0.841302i −0.00318980 0.0415489i
\(411\) 0 0
\(412\) −3.09937 20.0665i −0.152695 0.988608i
\(413\) 2.17470 0.900790i 0.107010 0.0443250i
\(414\) 0 0
\(415\) 2.01083 0.0987077
\(416\) −3.25638 + 1.31239i −0.159657 + 0.0643454i
\(417\) 0 0
\(418\) −2.75904 + 8.43637i −0.134949 + 0.412636i
\(419\) 20.8524 8.63734i 1.01871 0.421962i 0.190082 0.981768i \(-0.439125\pi\)
0.828623 + 0.559807i \(0.189125\pi\)
\(420\) 0 0
\(421\) −14.3106 + 34.5489i −0.697456 + 1.68381i 0.0317327 + 0.999496i \(0.489897\pi\)
−0.729189 + 0.684312i \(0.760103\pi\)
\(422\) 1.33561 + 17.3971i 0.0650166 + 0.846877i
\(423\) 0 0
\(424\) 6.79639 + 29.0442i 0.330062 + 1.41051i
\(425\) −19.2345 + 19.2345i −0.933008 + 0.933008i
\(426\) 0 0
\(427\) 1.80144 + 0.746181i 0.0871777 + 0.0361102i
\(428\) −1.71156 2.81721i −0.0827314 0.136175i
\(429\) 0 0
\(430\) −1.41575 + 0.717944i −0.0682736 + 0.0346224i
\(431\) 38.4560i 1.85236i −0.377080 0.926181i \(-0.623072\pi\)
0.377080 0.926181i \(-0.376928\pi\)
\(432\) 0 0
\(433\) 8.55433i 0.411095i 0.978647 + 0.205547i \(0.0658975\pi\)
−0.978647 + 0.205547i \(0.934102\pi\)
\(434\) 1.24165 + 2.44848i 0.0596012 + 0.117531i
\(435\) 0 0
\(436\) 6.99841 28.6656i 0.335163 1.37283i
\(437\) −6.39787 2.65009i −0.306052 0.126771i
\(438\) 0 0
\(439\) 5.13653 5.13653i 0.245153 0.245153i −0.573825 0.818978i \(-0.694541\pi\)
0.818978 + 0.573825i \(0.194541\pi\)
\(440\) 7.01881 + 1.15311i 0.334609 + 0.0549723i
\(441\) 0 0
\(442\) −4.99207 + 0.383252i −0.237448 + 0.0182294i
\(443\) −2.45339 + 5.92301i −0.116564 + 0.281411i −0.971384 0.237514i \(-0.923667\pi\)
0.854820 + 0.518925i \(0.173667\pi\)
\(444\) 0 0
\(445\) −5.30352 + 2.19679i −0.251411 + 0.104138i
\(446\) 18.8046 + 6.14988i 0.890423 + 0.291205i
\(447\) 0 0
\(448\) 1.36402 0.675343i 0.0644437 0.0319070i
\(449\) −23.7582 −1.12122 −0.560610 0.828080i \(-0.689433\pi\)
−0.560610 + 0.828080i \(0.689433\pi\)
\(450\) 0 0
\(451\) 5.99211 2.48201i 0.282157 0.116873i
\(452\) 5.29845 7.23417i 0.249218 0.340267i
\(453\) 0 0
\(454\) 3.22103 0.247286i 0.151171 0.0116057i
\(455\) −0.0401598 0.0401598i −0.00188272 0.00188272i
\(456\) 0 0
\(457\) −1.16506 + 1.16506i −0.0544992 + 0.0544992i −0.733831 0.679332i \(-0.762270\pi\)
0.679332 + 0.733831i \(0.262270\pi\)
\(458\) 7.79950 9.09666i 0.364447 0.425059i
\(459\) 0 0
\(460\) −1.31617 + 5.39107i −0.0613669 + 0.251360i
\(461\) −1.61683 3.90337i −0.0753032 0.181798i 0.881745 0.471726i \(-0.156369\pi\)
−0.957049 + 0.289928i \(0.906369\pi\)
\(462\) 0 0
\(463\) 3.11687i 0.144853i 0.997374 + 0.0724267i \(0.0230743\pi\)
−0.997374 + 0.0724267i \(0.976926\pi\)
\(464\) 6.50380 + 7.73434i 0.301931 + 0.359058i
\(465\) 0 0
\(466\) 13.9819 7.09039i 0.647699 0.328456i
\(467\) −7.59921 18.3461i −0.351649 0.848957i −0.996417 0.0845781i \(-0.973046\pi\)
0.644767 0.764379i \(-0.276954\pi\)
\(468\) 0 0
\(469\) −0.912117 0.377811i −0.0421176 0.0174457i
\(470\) −2.55370 2.18955i −0.117794 0.100997i
\(471\) 0 0
\(472\) 34.0733 7.97321i 1.56835 0.366997i
\(473\) −8.62788 8.62788i −0.396711 0.396711i
\(474\) 0 0
\(475\) 2.19061 5.28860i 0.100512 0.242658i
\(476\) 2.14510 0.331320i 0.0983204 0.0151860i
\(477\) 0 0
\(478\) 3.73943 11.4341i 0.171037 0.522984i
\(479\) −14.5634 −0.665418 −0.332709 0.943030i \(-0.607963\pi\)
−0.332709 + 0.943030i \(0.607963\pi\)
\(480\) 0 0
\(481\) 4.95716 0.226027
\(482\) −4.54144 + 13.8864i −0.206857 + 0.632509i
\(483\) 0 0
\(484\) 4.98756 + 32.2914i 0.226707 + 1.46779i
\(485\) 1.69672 4.09624i 0.0770440 0.186001i
\(486\) 0 0
\(487\) 12.0901 + 12.0901i 0.547856 + 0.547856i 0.925820 0.377964i \(-0.123376\pi\)
−0.377964 + 0.925820i \(0.623376\pi\)
\(488\) 24.6284 + 15.2879i 1.11487 + 0.692051i
\(489\) 0 0
\(490\) −3.59600 3.08322i −0.162451 0.139286i
\(491\) −20.2368 8.38236i −0.913274 0.378290i −0.123965 0.992287i \(-0.539561\pi\)
−0.789309 + 0.613996i \(0.789561\pi\)
\(492\) 0 0
\(493\) 5.51483 + 13.3140i 0.248376 + 0.599632i
\(494\) 0.939704 0.476535i 0.0422793 0.0214403i
\(495\) 0 0
\(496\) 12.3138 + 38.9111i 0.552904 + 1.74716i
\(497\) 1.16502i 0.0522583i
\(498\) 0 0
\(499\) −3.26197 7.87508i −0.146026 0.352537i 0.833896 0.551922i \(-0.186106\pi\)
−0.979921 + 0.199385i \(0.936106\pi\)
\(500\) −9.12890 2.22873i −0.408257 0.0996716i
\(501\) 0 0
\(502\) −0.892863 + 1.04136i −0.0398504 + 0.0464780i
\(503\) 12.2760 12.2760i 0.547362 0.547362i −0.378315 0.925677i \(-0.623496\pi\)
0.925677 + 0.378315i \(0.123496\pi\)
\(504\) 0 0
\(505\) −1.13596 1.13596i −0.0505497 0.0505497i
\(506\) −42.5311 + 3.26521i −1.89074 + 0.145156i
\(507\) 0 0
\(508\) 17.0282 + 12.4718i 0.755503 + 0.553345i
\(509\) 0.842977 0.349172i 0.0373643 0.0154768i −0.363923 0.931429i \(-0.618563\pi\)
0.401287 + 0.915952i \(0.368563\pi\)
\(510\) 0 0
\(511\) 1.64681 0.0728506
\(512\) 21.6374 6.61976i 0.956249 0.292555i
\(513\) 0 0
\(514\) −16.0200 5.23922i −0.706613 0.231092i
\(515\) 4.51131 1.86865i 0.198792 0.0823424i
\(516\) 0 0
\(517\) 9.89496 23.8886i 0.435180 1.05062i
\(518\) −2.14273 + 0.164502i −0.0941460 + 0.00722779i
\(519\) 0 0
\(520\) −0.492347 0.685923i −0.0215908 0.0300797i
\(521\) −4.87761 + 4.87761i −0.213692 + 0.213692i −0.805834 0.592142i \(-0.798283\pi\)
0.592142 + 0.805834i \(0.298283\pi\)
\(522\) 0 0
\(523\) −20.5648 8.51821i −0.899235 0.372475i −0.115309 0.993330i \(-0.536786\pi\)
−0.783926 + 0.620854i \(0.786786\pi\)
\(524\) −13.1068 3.19989i −0.572573 0.139788i
\(525\) 0 0
\(526\) 0.567456 + 1.11900i 0.0247423 + 0.0487905i
\(527\) 58.2020i 2.53532i
\(528\) 0 0
\(529\) 10.2800i 0.446955i
\(530\) −6.39787 + 3.24443i −0.277906 + 0.140929i
\(531\) 0 0
\(532\) −0.390373 + 0.237166i −0.0169248 + 0.0102824i
\(533\) −0.711288 0.294625i −0.0308093 0.0127616i
\(534\) 0 0
\(535\) 0.560554 0.560554i 0.0242349 0.0242349i
\(536\) −12.4700 7.74067i −0.538622 0.334346i
\(537\) 0 0
\(538\) −0.346295 4.51069i −0.0149298 0.194470i
\(539\) 13.9336 33.6387i 0.600162 1.44892i
\(540\) 0 0
\(541\) −8.72081 + 3.61228i −0.374937 + 0.155304i −0.562191 0.827008i \(-0.690041\pi\)
0.187254 + 0.982312i \(0.440041\pi\)
\(542\) 11.7495 35.9267i 0.504686 1.54319i
\(543\) 0 0
\(544\) 32.2666 + 0.309444i 1.38342 + 0.0132673i
\(545\) 7.09624 0.303969
\(546\) 0 0
\(547\) 3.50970 1.45377i 0.150064 0.0621586i −0.306387 0.951907i \(-0.599120\pi\)
0.456451 + 0.889748i \(0.349120\pi\)
\(548\) 29.3351 4.53094i 1.25313 0.193552i
\(549\) 0 0
\(550\) −2.69908 35.1570i −0.115089 1.49910i
\(551\) −2.14441 2.14441i −0.0913550 0.0913550i
\(552\) 0 0
\(553\) −1.61133 + 1.61133i −0.0685206 + 0.0685206i
\(554\) 30.3861 + 26.0532i 1.29098 + 1.10689i
\(555\) 0 0
\(556\) 10.3020 + 16.9570i 0.436902 + 0.719138i
\(557\) 11.0388 + 26.6499i 0.467727 + 1.12919i 0.965153 + 0.261687i \(0.0842788\pi\)
−0.497425 + 0.867507i \(0.665721\pi\)
\(558\) 0 0
\(559\) 1.44839i 0.0612603i
\(560\) 0.235579 + 0.280151i 0.00995502 + 0.0118386i
\(561\) 0 0
\(562\) −12.2465 24.1495i −0.516588 1.01869i
\(563\) 0.499373 + 1.20559i 0.0210461 + 0.0508097i 0.934053 0.357134i \(-0.116246\pi\)
−0.913007 + 0.407944i \(0.866246\pi\)
\(564\) 0 0
\(565\) 1.99231 + 0.825242i 0.0838171 + 0.0347182i
\(566\) 9.62660 11.2276i 0.404636 0.471932i
\(567\) 0 0
\(568\) −2.80778 + 17.0906i −0.117812 + 0.717105i
\(569\) −24.7043 24.7043i −1.03566 1.03566i −0.999340 0.0363184i \(-0.988437\pi\)
−0.0363184 0.999340i \(-0.511563\pi\)
\(570\) 0 0
\(571\) 12.4201 29.9848i 0.519765 1.25482i −0.418282 0.908317i \(-0.637368\pi\)
0.938047 0.346507i \(-0.112632\pi\)
\(572\) 3.83488 5.23591i 0.160344 0.218924i
\(573\) 0 0
\(574\) 0.317231 + 0.103748i 0.0132410 + 0.00433034i
\(575\) 27.5098 1.14724
\(576\) 0 0
\(577\) −38.7977 −1.61517 −0.807585 0.589752i \(-0.799226\pi\)
−0.807585 + 0.589752i \(0.799226\pi\)
\(578\) 20.8862 + 6.83064i 0.868750 + 0.284117i
\(579\) 0 0
\(580\) −1.43599 + 1.96061i −0.0596263 + 0.0814100i
\(581\) −0.304388 + 0.734858i −0.0126281 + 0.0304870i
\(582\) 0 0
\(583\) −38.9899 38.9899i −1.61480 1.61480i
\(584\) 24.1583 + 3.96893i 0.999679 + 0.164236i
\(585\) 0 0
\(586\) −26.5848 + 31.0061i −1.09821 + 1.28085i
\(587\) 32.3256 + 13.3897i 1.33422 + 0.552652i 0.931856 0.362828i \(-0.118189\pi\)
0.402363 + 0.915480i \(0.368189\pi\)
\(588\) 0 0
\(589\) −4.68714 11.3157i −0.193130 0.466257i
\(590\) 3.80622 + 7.50568i 0.156700 + 0.309004i
\(591\) 0 0
\(592\) −31.8298 2.75092i −1.30820 0.113062i
\(593\) 25.8554i 1.06176i 0.847448 + 0.530878i \(0.178138\pi\)
−0.847448 + 0.530878i \(0.821862\pi\)
\(594\) 0 0
\(595\) 0.199757 + 0.482256i 0.00818923 + 0.0197706i
\(596\) −10.9539 18.0299i −0.448687 0.738535i
\(597\) 0 0
\(598\) 3.84399 + 3.29585i 0.157192 + 0.134777i
\(599\) 27.4466 27.4466i 1.12144 1.12144i 0.129914 0.991525i \(-0.458530\pi\)
0.991525 0.129914i \(-0.0414701\pi\)
\(600\) 0 0
\(601\) −17.2120 17.2120i −0.702091 0.702091i 0.262768 0.964859i \(-0.415365\pi\)
−0.964859 + 0.262768i \(0.915365\pi\)
\(602\) −0.0480644 0.626065i −0.00195896 0.0255165i
\(603\) 0 0
\(604\) −25.1224 + 3.88028i −1.02222 + 0.157886i
\(605\) −7.25968 + 3.00706i −0.295148 + 0.122254i
\(606\) 0 0
\(607\) −35.6136 −1.44551 −0.722756 0.691103i \(-0.757125\pi\)
−0.722756 + 0.691103i \(0.757125\pi\)
\(608\) −6.29827 + 2.53834i −0.255428 + 0.102943i
\(609\) 0 0
\(610\) −2.16693 + 6.62584i −0.0877362 + 0.268273i
\(611\) −2.83567 + 1.17457i −0.114719 + 0.0475181i
\(612\) 0 0
\(613\) 7.20887 17.4038i 0.291164 0.702931i −0.708833 0.705376i \(-0.750778\pi\)
0.999997 + 0.00244484i \(0.000778219\pi\)
\(614\) 2.79414 + 36.3953i 0.112762 + 1.46879i
\(615\) 0 0
\(616\) −1.48387 + 2.39048i −0.0597869 + 0.0963150i
\(617\) −12.8299 + 12.8299i −0.516511 + 0.516511i −0.916514 0.400003i \(-0.869009\pi\)
0.400003 + 0.916514i \(0.369009\pi\)
\(618\) 0 0
\(619\) 12.1156 + 5.01844i 0.486966 + 0.201708i 0.612638 0.790364i \(-0.290108\pi\)
−0.125671 + 0.992072i \(0.540108\pi\)
\(620\) −8.38835 + 5.09623i −0.336884 + 0.204669i
\(621\) 0 0
\(622\) 32.1756 16.3166i 1.29012 0.654237i
\(623\) 2.27071i 0.0909741i
\(624\) 0 0
\(625\) 21.5834i 0.863337i
\(626\) −12.2070 24.0716i −0.487889 0.962093i
\(627\) 0 0
\(628\) 43.8397 + 10.7030i 1.74939 + 0.427096i
\(629\) −42.0924 17.4352i −1.67833 0.695189i
\(630\) 0 0
\(631\) −9.99914 + 9.99914i −0.398059 + 0.398059i −0.877548 0.479489i \(-0.840822\pi\)
0.479489 + 0.877548i \(0.340822\pi\)
\(632\) −27.5212 + 19.7544i −1.09474 + 0.785788i
\(633\) 0 0
\(634\) −15.2151 + 1.16809i −0.604268 + 0.0463910i
\(635\) −1.94250 + 4.68960i −0.0770857 + 0.186101i
\(636\) 0 0
\(637\) −3.99305 + 1.65397i −0.158210 + 0.0655329i
\(638\) −17.7550 5.80662i −0.702927 0.229886i
\(639\) 0 0
\(640\) 2.78070 + 4.67752i 0.109917 + 0.184895i
\(641\) −28.5513 −1.12771 −0.563854 0.825875i \(-0.690682\pi\)
−0.563854 + 0.825875i \(0.690682\pi\)
\(642\) 0 0
\(643\) −5.76614 + 2.38841i −0.227394 + 0.0941898i −0.493472 0.869762i \(-0.664272\pi\)
0.266077 + 0.963952i \(0.414272\pi\)
\(644\) −1.77093 1.29707i −0.0697845 0.0511115i
\(645\) 0 0
\(646\) −9.65532 + 0.741259i −0.379883 + 0.0291645i
\(647\) 0.783090 + 0.783090i 0.0307864 + 0.0307864i 0.722332 0.691546i \(-0.243070\pi\)
−0.691546 + 0.722332i \(0.743070\pi\)
\(648\) 0 0
\(649\) −45.7412 + 45.7412i −1.79550 + 1.79550i
\(650\) −2.72441 + 3.17751i −0.106860 + 0.124632i
\(651\) 0 0
\(652\) −14.8169 3.61739i −0.580274 0.141668i
\(653\) 3.54194 + 8.55101i 0.138607 + 0.334627i 0.977907 0.209042i \(-0.0670346\pi\)
−0.839300 + 0.543669i \(0.817035\pi\)
\(654\) 0 0
\(655\) 3.24462i 0.126778i
\(656\) 4.40367 + 2.28650i 0.171934 + 0.0892730i
\(657\) 0 0
\(658\) 1.18674 0.601809i 0.0462639 0.0234610i
\(659\) −17.7016 42.7355i −0.689557 1.66474i −0.745673 0.666313i \(-0.767872\pi\)
0.0561160 0.998424i \(-0.482128\pi\)
\(660\) 0 0
\(661\) −0.187232 0.0775542i −0.00728249 0.00301651i 0.379039 0.925381i \(-0.376255\pi\)
−0.386322 + 0.922364i \(0.626255\pi\)
\(662\) −13.1358 11.2627i −0.510539 0.437738i
\(663\) 0 0
\(664\) −6.23636 + 10.0466i −0.242018 + 0.389884i
\(665\) −0.0776743 0.0776743i −0.00301208 0.00301208i
\(666\) 0 0
\(667\) 5.57731 13.4648i 0.215954 0.521360i
\(668\) 0.359277 + 2.32610i 0.0139009 + 0.0899996i
\(669\) 0 0
\(670\) 1.09717 3.35484i 0.0423875 0.129609i
\(671\) −53.5850 −2.06862
\(672\) 0 0
\(673\) 48.7073 1.87753 0.938765 0.344558i \(-0.111971\pi\)
0.938765 + 0.344558i \(0.111971\pi\)
\(674\) 0.637712 1.94994i 0.0245638 0.0751090i
\(675\) 0 0
\(676\) 24.9339 3.85116i 0.958998 0.148122i
\(677\) −10.9016 + 26.3188i −0.418982 + 1.01151i 0.563661 + 0.826006i \(0.309393\pi\)
−0.982643 + 0.185506i \(0.940607\pi\)
\(678\) 0 0
\(679\) 1.24013 + 1.24013i 0.0475919 + 0.0475919i
\(680\) 1.76812 + 7.55601i 0.0678042 + 0.289760i
\(681\) 0 0
\(682\) −57.2748 49.1076i −2.19316 1.88043i
\(683\) −16.7740 6.94800i −0.641838 0.265858i 0.0379356 0.999280i \(-0.487922\pi\)
−0.679773 + 0.733422i \(0.737922\pi\)
\(684\) 0 0
\(685\) 2.73176 + 6.59504i 0.104375 + 0.251984i
\(686\) 3.35090 1.69928i 0.127938 0.0648788i
\(687\) 0 0
\(688\) 0.803768 9.30008i 0.0306434 0.354562i
\(689\) 6.54536i 0.249358i
\(690\) 0 0
\(691\) 17.5044 + 42.2593i 0.665898 + 1.60762i 0.788407 + 0.615154i \(0.210906\pi\)
−0.122509 + 0.992467i \(0.539094\pi\)
\(692\) 5.79804 23.7489i 0.220408 0.902797i
\(693\) 0 0
\(694\) −11.7415 + 13.6943i −0.445701 + 0.519827i
\(695\) −3.37402 + 3.37402i −0.127984 + 0.127984i
\(696\) 0 0
\(697\) 5.00347 + 5.00347i 0.189520 + 0.189520i
\(698\) 11.7882 0.905007i 0.446191 0.0342550i
\(699\) 0 0
\(700\) 1.07218 1.46388i 0.0405245 0.0553296i
\(701\) 9.76630 4.04533i 0.368868 0.152790i −0.190547 0.981678i \(-0.561026\pi\)
0.559414 + 0.828888i \(0.311026\pi\)
\(702\) 0 0
\(703\) 9.58780 0.361611
\(704\) −27.5293 + 31.4915i −1.03755 + 1.18688i
\(705\) 0 0
\(706\) 23.4298 + 7.66251i 0.881792 + 0.288383i
\(707\) 0.587094 0.243182i 0.0220799 0.00914581i
\(708\) 0 0
\(709\) −2.23164 + 5.38765i −0.0838109 + 0.202337i −0.960229 0.279213i \(-0.909926\pi\)
0.876418 + 0.481551i \(0.159926\pi\)
\(710\) −4.15297 + 0.318833i −0.155858 + 0.0119656i
\(711\) 0 0
\(712\) 5.47258 33.3108i 0.205093 1.24838i
\(713\) 41.6213 41.6213i 1.55873 1.55873i
\(714\) 0 0
\(715\) 1.44198 + 0.597289i 0.0539271 + 0.0223373i
\(716\) 5.68281 23.2769i 0.212376 0.869898i
\(717\) 0 0
\(718\) 4.10344 + 8.09179i 0.153139 + 0.301983i
\(719\) 12.8188i 0.478059i 0.971012 + 0.239030i \(0.0768293\pi\)
−0.971012 + 0.239030i \(0.923171\pi\)
\(720\) 0 0
\(721\) 1.93152i 0.0719337i
\(722\) −22.1472 + 11.2311i −0.824235 + 0.417979i
\(723\) 0 0
\(724\) 5.16872 + 8.50767i 0.192094 + 0.316185i
\(725\) 11.1303 + 4.61031i 0.413368 + 0.171223i
\(726\) 0 0
\(727\) 22.1336 22.1336i 0.820889 0.820889i −0.165347 0.986235i \(-0.552874\pi\)
0.986235 + 0.165347i \(0.0528743\pi\)
\(728\) 0.325199 0.0760971i 0.0120527 0.00282035i
\(729\) 0 0
\(730\) 0.450685 + 5.87042i 0.0166806 + 0.217274i
\(731\) 5.09426 12.2986i 0.188418 0.454881i
\(732\) 0 0
\(733\) −17.7464 + 7.35081i −0.655479 + 0.271508i −0.685535 0.728040i \(-0.740432\pi\)
0.0300555 + 0.999548i \(0.490432\pi\)
\(734\) −3.15659 + 9.65195i −0.116512 + 0.356260i
\(735\) 0 0
\(736\) −22.8532 23.2957i −0.842379 0.858692i
\(737\) 27.1315 0.999402
\(738\) 0 0
\(739\) 20.4272 8.46123i 0.751428 0.311251i 0.0261037 0.999659i \(-0.491690\pi\)
0.725324 + 0.688408i \(0.241690\pi\)
\(740\) −1.17281 7.59321i −0.0431132 0.279132i
\(741\) 0 0
\(742\) −0.217206 2.82923i −0.00797387 0.103864i
\(743\) 26.6427 + 26.6427i 0.977427 + 0.977427i 0.999751 0.0223237i \(-0.00710644\pi\)
−0.0223237 + 0.999751i \(0.507106\pi\)
\(744\) 0 0
\(745\) 3.58750 3.58750i 0.131436 0.131436i
\(746\) −16.6753 14.2975i −0.610527 0.523468i
\(747\) 0 0
\(748\) −50.9786 + 30.9714i −1.86396 + 1.13243i
\(749\) 0.120001 + 0.289708i 0.00438474 + 0.0105857i
\(750\) 0 0
\(751\) 23.4989i 0.857486i −0.903427 0.428743i \(-0.858957\pi\)
0.903427 0.428743i \(-0.141043\pi\)
\(752\) 18.8596 5.96829i 0.687739 0.217641i
\(753\) 0 0
\(754\) 1.00291 + 1.97768i 0.0365237 + 0.0720229i
\(755\) −2.33946 5.64796i −0.0851418 0.205550i
\(756\) 0 0
\(757\) 39.9311 + 16.5400i 1.45132 + 0.601157i 0.962513 0.271234i \(-0.0874317\pi\)
0.488809 + 0.872391i \(0.337432\pi\)
\(758\) −8.30178 + 9.68247i −0.301534 + 0.351683i
\(759\) 0 0
\(760\) −0.952264 1.32667i −0.0345423 0.0481232i
\(761\) −33.7925 33.7925i −1.22498 1.22498i −0.965841 0.259134i \(-0.916563\pi\)
−0.259134 0.965841i \(-0.583437\pi\)
\(762\) 0 0
\(763\) −1.07419 + 2.59332i −0.0388883 + 0.0938845i
\(764\) 26.3232 + 19.2796i 0.952338 + 0.697511i
\(765\) 0 0
\(766\) −5.99437 1.96041i −0.216585 0.0708324i
\(767\) 7.67871 0.277262
\(768\) 0 0
\(769\) −22.1545 −0.798913 −0.399457 0.916752i \(-0.630801\pi\)
−0.399457 + 0.916752i \(0.630801\pi\)
\(770\) −0.643117 0.210326i −0.0231763 0.00757962i
\(771\) 0 0
\(772\) 5.19929 + 3.80806i 0.187126 + 0.137055i
\(773\) −4.56113 + 11.0116i −0.164053 + 0.396058i −0.984433 0.175760i \(-0.943762\pi\)
0.820380 + 0.571818i \(0.193762\pi\)
\(774\) 0 0
\(775\) 34.4049 + 34.4049i 1.23586 + 1.23586i
\(776\) 15.2037 + 21.1813i 0.545780 + 0.760364i
\(777\) 0 0
\(778\) 5.27434 6.15152i 0.189094 0.220543i
\(779\) −1.37573 0.569844i −0.0492905 0.0204168i
\(780\) 0 0
\(781\) −12.2521 29.5793i −0.438416 1.05843i
\(782\) −21.0481 41.5059i −0.752679 1.48425i
\(783\) 0 0
\(784\) 26.5571 8.40424i 0.948469 0.300151i
\(785\) 10.8526i 0.387347i
\(786\) 0 0
\(787\) 14.4233 + 34.8210i 0.514137 + 1.24124i 0.941456 + 0.337135i \(0.109458\pi\)
−0.427320 + 0.904101i \(0.640542\pi\)
\(788\) −39.2636 + 23.8541i −1.39871 + 0.849767i
\(789\) 0 0
\(790\) −6.18491 5.30296i −0.220049 0.188671i
\(791\) −0.603170 + 0.603170i −0.0214462 + 0.0214462i
\(792\) 0 0
\(793\) 4.49773 + 4.49773i 0.159719 + 0.159719i
\(794\) −1.48749 19.3755i −0.0527892 0.687609i
\(795\) 0 0
\(796\) −3.06678 19.8555i −0.108699 0.703761i
\(797\) −5.47061 + 2.26600i −0.193779 + 0.0802659i −0.477463 0.878652i \(-0.658443\pi\)
0.283684 + 0.958918i \(0.408443\pi\)
\(798\) 0 0
\(799\) 28.2096 0.997983
\(800\) 19.2567 18.8908i 0.680827 0.667892i
\(801\) 0 0
\(802\) −9.97639 + 30.5050i −0.352279 + 1.07717i
\(803\) −41.8117 + 17.3190i −1.47550 + 0.611173i
\(804\) 0 0
\(805\) 0.202020 0.487719i 0.00712027 0.0171899i
\(806\) 0.685526 + 8.92936i 0.0241466 + 0.314523i
\(807\) 0 0
\(808\) 9.19862 2.15249i 0.323606 0.0757244i
\(809\) 20.7326 20.7326i 0.728920 0.728920i −0.241485 0.970405i \(-0.577634\pi\)
0.970405 + 0.241485i \(0.0776344\pi\)
\(810\) 0 0
\(811\) −37.2071 15.4117i −1.30652 0.541177i −0.382651 0.923893i \(-0.624989\pi\)
−0.923866 + 0.382716i \(0.874989\pi\)
\(812\) −0.499134 0.821570i −0.0175162 0.0288314i
\(813\) 0 0
\(814\) 52.6727 26.7110i 1.84618 0.936219i
\(815\) 3.66796i 0.128483i
\(816\) 0 0
\(817\) 2.80138i 0.0980077i
\(818\) 17.1123 + 33.7446i 0.598317 + 1.17985i
\(819\) 0 0
\(820\) −0.283015 + 1.15923i −0.00988331 + 0.0404822i
\(821\) 29.1884 + 12.0902i 1.01868 + 0.421952i 0.828615 0.559820i \(-0.189130\pi\)
0.190067 + 0.981771i \(0.439130\pi\)
\(822\) 0 0
\(823\) −3.31937 + 3.31937i −0.115706 + 0.115706i −0.762589 0.646883i \(-0.776072\pi\)
0.646883 + 0.762589i \(0.276072\pi\)
\(824\) −4.65511 + 28.3350i −0.162169 + 0.987098i
\(825\) 0 0
\(826\) −3.31912 + 0.254816i −0.115487 + 0.00886617i
\(827\) −2.47114 + 5.96586i −0.0859300 + 0.207453i −0.961003 0.276537i \(-0.910813\pi\)
0.875073 + 0.483991i \(0.160813\pi\)
\(828\) 0 0
\(829\) −0.339967 + 0.140819i −0.0118075 + 0.00489085i −0.388579 0.921415i \(-0.627034\pi\)
0.376772 + 0.926306i \(0.377034\pi\)
\(830\) −2.70287 0.883950i −0.0938179 0.0306823i
\(831\) 0 0
\(832\) 4.95400 0.332575i 0.171749 0.0115299i
\(833\) 39.7233 1.37633
\(834\) 0 0
\(835\) −0.522948 + 0.216612i −0.0180974 + 0.00749618i
\(836\) 7.41717 10.1269i 0.256528 0.350247i
\(837\) 0 0
\(838\) −31.8258 + 2.44333i −1.09940 + 0.0844036i
\(839\) 32.9364 + 32.9364i 1.13709 + 1.13709i 0.988969 + 0.148122i \(0.0473227\pi\)
0.148122 + 0.988969i \(0.452677\pi\)
\(840\) 0 0
\(841\) −15.9930 + 15.9930i −0.551483 + 0.551483i
\(842\) 34.4232 40.1482i 1.18630 1.38360i
\(843\) 0 0
\(844\) 5.85240 23.9715i 0.201448 0.825135i
\(845\) 2.32191 + 5.60559i 0.0798761 + 0.192838i
\(846\) 0 0
\(847\) 3.10824i 0.106801i
\(848\) 3.63228 42.0276i 0.124733 1.44323i
\(849\) 0 0
\(850\) 34.3095 17.3988i 1.17681 0.596772i
\(851\) 17.6328 + 42.5693i 0.604444 + 1.45926i
\(852\) 0 0
\(853\) 2.43815 + 1.00992i 0.0834808 + 0.0345789i 0.424033 0.905647i \(-0.360614\pi\)
−0.340552 + 0.940226i \(0.610614\pi\)
\(854\) −2.09340 1.79489i −0.0716346 0.0614198i
\(855\) 0 0
\(856\) 1.06217 + 4.53917i 0.0363043 + 0.155146i
\(857\) 31.8225 + 31.8225i 1.08704 + 1.08704i 0.995832 + 0.0912053i \(0.0290720\pi\)
0.0912053 + 0.995832i \(0.470928\pi\)
\(858\) 0 0
\(859\) 11.6288 28.0745i 0.396771 0.957890i −0.591656 0.806191i \(-0.701526\pi\)
0.988427 0.151699i \(-0.0484744\pi\)
\(860\) 2.21860 0.342672i 0.0756535 0.0116850i
\(861\) 0 0
\(862\) −16.9051 + 51.6909i −0.575789 + 1.76060i
\(863\) −18.9524 −0.645148 −0.322574 0.946544i \(-0.604548\pi\)
−0.322574 + 0.946544i \(0.604548\pi\)
\(864\) 0 0
\(865\) 5.87909 0.199895
\(866\) 3.76044 11.4984i 0.127785 0.390730i
\(867\) 0 0
\(868\) −0.592637 3.83696i −0.0201154 0.130235i
\(869\) 23.9650 57.8566i 0.812956 1.96265i
\(870\) 0 0
\(871\) −2.27732 2.27732i −0.0771642 0.0771642i
\(872\) −22.0082 + 35.4546i −0.745292 + 1.20064i
\(873\) 0 0
\(874\) 7.43478 + 6.37460i 0.251485 + 0.215624i
\(875\) 0.825874 + 0.342088i 0.0279196 + 0.0115647i
\(876\) 0 0
\(877\) 16.0645 + 38.7831i 0.542459 + 1.30961i 0.922983 + 0.384842i \(0.125744\pi\)
−0.380523 + 0.924771i \(0.624256\pi\)
\(878\) −9.16230 + 4.64631i −0.309213 + 0.156805i
\(879\) 0 0
\(880\) −8.92748 4.63539i −0.300945 0.156259i
\(881\) 21.4254i 0.721841i 0.932597 + 0.360921i \(0.117537\pi\)
−0.932597 + 0.360921i \(0.882463\pi\)
\(882\) 0 0
\(883\) 2.94264 + 7.10415i 0.0990276 + 0.239074i 0.965627 0.259930i \(-0.0836995\pi\)
−0.866600 + 0.499004i \(0.833699\pi\)
\(884\) 6.87859 + 1.67934i 0.231352 + 0.0564822i
\(885\) 0 0
\(886\) 5.90147 6.88295i 0.198264 0.231237i
\(887\) 30.7269 30.7269i 1.03171 1.03171i 0.0322295 0.999480i \(-0.489739\pi\)
0.999480 0.0322295i \(-0.0102607\pi\)
\(888\) 0 0
\(889\) −1.41977 1.41977i −0.0476176 0.0476176i
\(890\) 8.09446 0.621429i 0.271327 0.0208303i
\(891\) 0 0
\(892\) −22.5728 16.5328i −0.755795 0.553559i
\(893\) −5.48456 + 2.27178i −0.183534 + 0.0760222i
\(894\) 0 0
\(895\) 5.76225 0.192611
\(896\) −2.13033 + 0.308152i −0.0711693 + 0.0102946i
\(897\) 0 0
\(898\) 31.9348 + 10.4440i 1.06568 + 0.348521i
\(899\) 23.8149 9.86444i 0.794271 0.328998i
\(900\) 0 0
\(901\) 23.0213 55.5782i 0.766949 1.85158i
\(902\) −9.14541 + 0.702113i −0.304509 + 0.0233778i
\(903\) 0 0
\(904\) −10.3021 + 7.39469i −0.342641 + 0.245944i
\(905\) −1.69281 + 1.69281i −0.0562710 + 0.0562710i
\(906\) 0 0
\(907\) 32.8338 + 13.6002i 1.09023 + 0.451588i 0.854087 0.520131i \(-0.174117\pi\)
0.236142 + 0.971718i \(0.424117\pi\)
\(908\) −4.43828 1.08356i −0.147289 0.0359592i
\(909\) 0 0
\(910\) 0.0363270 + 0.0716350i 0.00120423 + 0.00237468i
\(911\) 15.3896i 0.509879i −0.966957 0.254940i \(-0.917944\pi\)
0.966957 0.254940i \(-0.0820556\pi\)
\(912\) 0 0
\(913\) 21.8588i 0.723421i
\(914\) 2.07818 1.05387i 0.0687399 0.0348588i
\(915\) 0 0
\(916\) −14.4826 + 8.79871i −0.478518 + 0.290718i
\(917\) 1.18575 + 0.491152i 0.0391568 + 0.0162193i
\(918\) 0 0
\(919\) 1.60663 1.60663i 0.0529979 0.0529979i −0.680111 0.733109i \(-0.738068\pi\)
0.733109 + 0.680111i \(0.238068\pi\)
\(920\) 4.13903 6.66785i 0.136460 0.219833i
\(921\) 0 0
\(922\) 0.457369 + 5.95749i 0.0150626 + 0.196199i
\(923\) −1.45438 + 3.51118i −0.0478715 + 0.115572i
\(924\) 0 0
\(925\) −35.1886 + 14.5756i −1.15699 + 0.479242i
\(926\) 1.37016 4.18956i 0.0450263 0.137678i
\(927\) 0 0
\(928\) −5.34214 13.2552i −0.175364 0.435123i
\(929\) −8.22205 −0.269757 −0.134878 0.990862i \(-0.543064\pi\)
−0.134878 + 0.990862i \(0.543064\pi\)
\(930\) 0 0
\(931\) −7.72308 + 3.19901i −0.253114 + 0.104843i
\(932\) −21.9108 + 3.38422i −0.717711 + 0.110854i
\(933\) 0 0
\(934\) 2.14967 + 28.0006i 0.0703393 + 0.916208i
\(935\) −10.1435 10.1435i −0.331726 0.331726i
\(936\) 0 0
\(937\) 10.3496 10.3496i 0.338105 0.338105i −0.517549 0.855654i \(-0.673155\pi\)
0.855654 + 0.517549i \(0.173155\pi\)
\(938\) 1.05994 + 0.908799i 0.0346084 + 0.0296733i
\(939\) 0 0
\(940\) 2.47006 + 4.06570i 0.0805645 + 0.132608i
\(941\) 19.5970 + 47.3114i 0.638844 + 1.54231i 0.828221 + 0.560402i \(0.189353\pi\)
−0.189376 + 0.981905i \(0.560647\pi\)
\(942\) 0 0
\(943\) 7.15614i 0.233036i
\(944\) −49.3049 4.26122i −1.60474 0.138691i
\(945\) 0 0
\(946\) 7.80445 + 15.3900i 0.253745 + 0.500372i
\(947\) 9.51949 + 22.9821i 0.309342 + 0.746817i 0.999727 + 0.0233749i \(0.00744115\pi\)
−0.690385 + 0.723442i \(0.742559\pi\)
\(948\) 0 0
\(949\) 4.96322 + 2.05583i 0.161113 + 0.0667352i
\(950\) −5.26936 + 6.14572i −0.170961 + 0.199394i
\(951\) 0 0
\(952\) −3.02900 0.497628i −0.0981703 0.0161282i
\(953\) 26.5521 + 26.5521i 0.860106 + 0.860106i 0.991350 0.131244i \(-0.0418972\pi\)
−0.131244 + 0.991350i \(0.541897\pi\)
\(954\) 0 0
\(955\) −3.00283 + 7.24947i −0.0971692 + 0.234587i
\(956\) −10.0528 + 13.7254i −0.325129 + 0.443911i
\(957\) 0 0
\(958\) 19.5755 + 6.40199i 0.632454 + 0.206839i
\(959\) −2.82368 −0.0911813
\(960\) 0 0
\(961\) 73.1065 2.35827
\(962\) −6.66319 2.17914i −0.214830 0.0702583i
\(963\) 0 0
\(964\) 12.2088 16.6691i 0.393219 0.536876i
\(965\) −0.593112 + 1.43190i −0.0190929 + 0.0460944i
\(966\) 0 0
\(967\) −17.5385 17.5385i −0.564001 0.564001i 0.366440 0.930442i \(-0.380576\pi\)
−0.930442 + 0.366440i \(0.880576\pi\)
\(968\) 7.49109 45.5973i 0.240773 1.46555i
\(969\) 0 0
\(970\) −4.08134 + 4.76012i −0.131044 + 0.152838i
\(971\) 26.0783 + 10.8020i 0.836894 + 0.346653i 0.759628 0.650358i \(-0.225381\pi\)
0.0772656 + 0.997011i \(0.475381\pi\)
\(972\) 0 0
\(973\) −0.722295 1.74378i −0.0231557 0.0559029i
\(974\) −10.9363 21.5658i −0.350420 0.691012i
\(975\) 0 0
\(976\) −26.3839 31.3758i −0.844528 1.00432i
\(977\) 18.6808i 0.597651i −0.954308 0.298825i \(-0.903405\pi\)
0.954308 0.298825i \(-0.0965948\pi\)
\(978\) 0 0
\(979\) 23.8803 + 57.6522i 0.763218 + 1.84257i
\(980\) 3.47822 + 5.72511i 0.111108 + 0.182882i
\(981\) 0 0
\(982\) 23.5166 + 20.1632i 0.750444 + 0.643433i
\(983\) 2.93163 2.93163i 0.0935046 0.0935046i −0.658807 0.752312i \(-0.728939\pi\)
0.752312 + 0.658807i \(0.228939\pi\)
\(984\) 0 0
\(985\) −7.81247 7.81247i −0.248926 0.248926i
\(986\) −1.56004 20.3204i −0.0496817 0.647132i
\(987\) 0 0
\(988\) −1.47259 + 0.227448i −0.0468494 + 0.00723610i
\(989\) −12.4380 + 5.15197i −0.395504 + 0.163823i
\(990\) 0 0
\(991\) −56.5710 −1.79704 −0.898519 0.438935i \(-0.855356\pi\)
−0.898519 + 0.438935i \(0.855356\pi\)
\(992\) 0.553506 57.7157i 0.0175738 1.83248i
\(993\) 0 0
\(994\) 0.512137 1.56597i 0.0162440 0.0496695i
\(995\) 4.46387 1.84900i 0.141514 0.0586171i
\(996\) 0 0
\(997\) 3.90402 9.42514i 0.123642 0.298497i −0.849924 0.526906i \(-0.823352\pi\)
0.973565 + 0.228408i \(0.0733522\pi\)
\(998\) 0.922746 + 12.0193i 0.0292090 + 0.380464i
\(999\) 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 288.2.v.d.181.1 32
3.2 odd 2 96.2.n.a.85.8 yes 32
4.3 odd 2 1152.2.v.c.433.4 32
12.11 even 2 384.2.n.a.49.6 32
24.5 odd 2 768.2.n.a.97.7 32
24.11 even 2 768.2.n.b.97.3 32
32.3 odd 8 1152.2.v.c.721.4 32
32.29 even 8 inner 288.2.v.d.253.1 32
96.29 odd 8 96.2.n.a.61.8 32
96.35 even 8 384.2.n.a.337.6 32
96.77 odd 8 768.2.n.a.673.7 32
96.83 even 8 768.2.n.b.673.3 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
96.2.n.a.61.8 32 96.29 odd 8
96.2.n.a.85.8 yes 32 3.2 odd 2
288.2.v.d.181.1 32 1.1 even 1 trivial
288.2.v.d.253.1 32 32.29 even 8 inner
384.2.n.a.49.6 32 12.11 even 2
384.2.n.a.337.6 32 96.35 even 8
768.2.n.a.97.7 32 24.5 odd 2
768.2.n.a.673.7 32 96.77 odd 8
768.2.n.b.97.3 32 24.11 even 2
768.2.n.b.673.3 32 96.83 even 8
1152.2.v.c.433.4 32 4.3 odd 2
1152.2.v.c.721.4 32 32.3 odd 8