Properties

Label 360.2.x.a.53.19
Level $360$
Weight $2$
Character 360.53
Analytic conductor $2.875$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [360,2,Mod(53,360)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(360, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 2, 2, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("360.53");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 360.x (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.87461447277\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 53.19
Character \(\chi\) \(=\) 360.53
Dual form 360.2.x.a.197.19

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.16389 + 0.803348i) q^{2} +(0.709264 + 1.87001i) q^{4} +(1.29263 - 1.82458i) q^{5} +(-0.306649 + 0.306649i) q^{7} +(-0.676767 + 2.74627i) q^{8} +O(q^{10})\) \(q+(1.16389 + 0.803348i) q^{2} +(0.709264 + 1.87001i) q^{4} +(1.29263 - 1.82458i) q^{5} +(-0.306649 + 0.306649i) q^{7} +(-0.676767 + 2.74627i) q^{8} +(2.97025 - 1.08518i) q^{10} +4.06731 q^{11} +(0.625224 - 0.625224i) q^{13} +(-0.603251 + 0.110559i) q^{14} +(-2.99389 + 2.65267i) q^{16} +(3.57491 + 3.57491i) q^{17} -6.82524 q^{19} +(4.32881 + 1.12312i) q^{20} +(4.73389 + 3.26747i) q^{22} +(-1.58940 + 1.58940i) q^{23} +(-1.65821 - 4.71703i) q^{25} +(1.22996 - 0.225418i) q^{26} +(-0.790933 - 0.355942i) q^{28} -8.50925i q^{29} -2.56730 q^{31} +(-5.61556 + 0.682268i) q^{32} +(1.28889 + 7.03269i) q^{34} +(0.163123 + 0.955891i) q^{35} +(-1.69023 - 1.69023i) q^{37} +(-7.94381 - 5.48305i) q^{38} +(4.13599 + 4.78473i) q^{40} -5.19315i q^{41} +(-4.18889 + 4.18889i) q^{43} +(2.88480 + 7.60592i) q^{44} +(-3.12673 + 0.573041i) q^{46} +(4.58429 + 4.58429i) q^{47} +6.81193i q^{49} +(1.85944 - 6.82221i) q^{50} +(1.61263 + 0.725727i) q^{52} +(-7.41934 - 7.41934i) q^{53} +(5.25753 - 7.42115i) q^{55} +(-0.634611 - 1.04967i) q^{56} +(6.83589 - 9.90380i) q^{58} +8.79560i q^{59} -6.08412i q^{61} +(-2.98805 - 2.06244i) q^{62} +(-7.08397 - 3.71717i) q^{64} +(-0.332590 - 1.94896i) q^{65} +(-6.18046 - 6.18046i) q^{67} +(-4.14957 + 9.22069i) q^{68} +(-0.578056 + 1.24359i) q^{70} -14.7516i q^{71} +(3.05881 + 3.05881i) q^{73} +(-0.609393 - 3.32507i) q^{74} +(-4.84090 - 12.7633i) q^{76} +(-1.24724 + 1.24724i) q^{77} -8.56106i q^{79} +(0.970019 + 8.89152i) q^{80} +(4.17190 - 6.04424i) q^{82} +(5.13122 + 5.13122i) q^{83} +(11.1438 - 1.90169i) q^{85} +(-8.24053 + 1.51026i) q^{86} +(-2.75262 + 11.1699i) q^{88} -9.88328 q^{89} +0.383449i q^{91} +(-4.09951 - 1.84489i) q^{92} +(1.65282 + 9.01838i) q^{94} +(-8.82252 + 12.4532i) q^{95} +(1.75624 - 1.75624i) q^{97} +(-5.47235 + 7.92832i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q+O(q^{10}) \) Copy content Toggle raw display \( 48 q + 16 q^{10} - 8 q^{16} + 16 q^{22} - 32 q^{28} + 32 q^{31} - 56 q^{40} - 16 q^{46} - 56 q^{52} - 80 q^{58} - 64 q^{70} + 48 q^{76} - 48 q^{82} + 64 q^{88} - 32 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/360\mathbb{Z}\right)^\times\).

\(n\) \(181\) \(217\) \(271\) \(281\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{4}\right)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.16389 + 0.803348i 0.822992 + 0.568053i
\(3\) 0 0
\(4\) 0.709264 + 1.87001i 0.354632 + 0.935006i
\(5\) 1.29263 1.82458i 0.578082 0.815979i
\(6\) 0 0
\(7\) −0.306649 + 0.306649i −0.115902 + 0.115902i −0.762679 0.646777i \(-0.776117\pi\)
0.646777 + 0.762679i \(0.276117\pi\)
\(8\) −0.676767 + 2.74627i −0.239273 + 0.970952i
\(9\) 0 0
\(10\) 2.97025 1.08518i 0.939276 0.343163i
\(11\) 4.06731 1.22634 0.613170 0.789951i \(-0.289894\pi\)
0.613170 + 0.789951i \(0.289894\pi\)
\(12\) 0 0
\(13\) 0.625224 0.625224i 0.173406 0.173406i −0.615068 0.788474i \(-0.710871\pi\)
0.788474 + 0.615068i \(0.210871\pi\)
\(14\) −0.603251 + 0.110559i −0.161226 + 0.0295481i
\(15\) 0 0
\(16\) −2.99389 + 2.65267i −0.748472 + 0.663166i
\(17\) 3.57491 + 3.57491i 0.867044 + 0.867044i 0.992144 0.125100i \(-0.0399253\pi\)
−0.125100 + 0.992144i \(0.539925\pi\)
\(18\) 0 0
\(19\) −6.82524 −1.56582 −0.782909 0.622136i \(-0.786265\pi\)
−0.782909 + 0.622136i \(0.786265\pi\)
\(20\) 4.32881 + 1.12312i 0.967951 + 0.251138i
\(21\) 0 0
\(22\) 4.73389 + 3.26747i 1.00927 + 0.696626i
\(23\) −1.58940 + 1.58940i −0.331413 + 0.331413i −0.853123 0.521710i \(-0.825294\pi\)
0.521710 + 0.853123i \(0.325294\pi\)
\(24\) 0 0
\(25\) −1.65821 4.71703i −0.331643 0.943405i
\(26\) 1.22996 0.225418i 0.241216 0.0442080i
\(27\) 0 0
\(28\) −0.790933 0.355942i −0.149472 0.0672667i
\(29\) 8.50925i 1.58013i −0.613025 0.790064i \(-0.710047\pi\)
0.613025 0.790064i \(-0.289953\pi\)
\(30\) 0 0
\(31\) −2.56730 −0.461101 −0.230551 0.973060i \(-0.574053\pi\)
−0.230551 + 0.973060i \(0.574053\pi\)
\(32\) −5.61556 + 0.682268i −0.992700 + 0.120609i
\(33\) 0 0
\(34\) 1.28889 + 7.03269i 0.221044 + 1.20610i
\(35\) 0.163123 + 0.955891i 0.0275728 + 0.161575i
\(36\) 0 0
\(37\) −1.69023 1.69023i −0.277872 0.277872i 0.554387 0.832259i \(-0.312953\pi\)
−0.832259 + 0.554387i \(0.812953\pi\)
\(38\) −7.94381 5.48305i −1.28866 0.889467i
\(39\) 0 0
\(40\) 4.13599 + 4.78473i 0.653957 + 0.756532i
\(41\) 5.19315i 0.811033i −0.914088 0.405517i \(-0.867092\pi\)
0.914088 0.405517i \(-0.132908\pi\)
\(42\) 0 0
\(43\) −4.18889 + 4.18889i −0.638800 + 0.638800i −0.950259 0.311460i \(-0.899182\pi\)
0.311460 + 0.950259i \(0.399182\pi\)
\(44\) 2.88480 + 7.60592i 0.434900 + 1.14664i
\(45\) 0 0
\(46\) −3.12673 + 0.573041i −0.461011 + 0.0844903i
\(47\) 4.58429 + 4.58429i 0.668688 + 0.668688i 0.957412 0.288724i \(-0.0932311\pi\)
−0.288724 + 0.957412i \(0.593231\pi\)
\(48\) 0 0
\(49\) 6.81193i 0.973133i
\(50\) 1.85944 6.82221i 0.262965 0.964805i
\(51\) 0 0
\(52\) 1.61263 + 0.725727i 0.223631 + 0.100640i
\(53\) −7.41934 7.41934i −1.01912 1.01912i −0.999814 0.0193111i \(-0.993853\pi\)
−0.0193111 0.999814i \(-0.506147\pi\)
\(54\) 0 0
\(55\) 5.25753 7.42115i 0.708925 1.00067i
\(56\) −0.634611 1.04967i −0.0848034 0.140268i
\(57\) 0 0
\(58\) 6.83589 9.90380i 0.897596 1.30043i
\(59\) 8.79560i 1.14509i 0.819874 + 0.572545i \(0.194044\pi\)
−0.819874 + 0.572545i \(0.805956\pi\)
\(60\) 0 0
\(61\) 6.08412i 0.778992i −0.921028 0.389496i \(-0.872649\pi\)
0.921028 0.389496i \(-0.127351\pi\)
\(62\) −2.98805 2.06244i −0.379483 0.261930i
\(63\) 0 0
\(64\) −7.08397 3.71717i −0.885497 0.464646i
\(65\) −0.332590 1.94896i −0.0412527 0.241738i
\(66\) 0 0
\(67\) −6.18046 6.18046i −0.755063 0.755063i 0.220356 0.975419i \(-0.429278\pi\)
−0.975419 + 0.220356i \(0.929278\pi\)
\(68\) −4.14957 + 9.22069i −0.503209 + 1.11817i
\(69\) 0 0
\(70\) −0.578056 + 1.24359i −0.0690909 + 0.148638i
\(71\) 14.7516i 1.75069i −0.483500 0.875344i \(-0.660635\pi\)
0.483500 0.875344i \(-0.339365\pi\)
\(72\) 0 0
\(73\) 3.05881 + 3.05881i 0.358007 + 0.358007i 0.863078 0.505071i \(-0.168534\pi\)
−0.505071 + 0.863078i \(0.668534\pi\)
\(74\) −0.609393 3.32507i −0.0708405 0.386532i
\(75\) 0 0
\(76\) −4.84090 12.7633i −0.555290 1.46405i
\(77\) −1.24724 + 1.24724i −0.142136 + 0.142136i
\(78\) 0 0
\(79\) 8.56106i 0.963194i −0.876393 0.481597i \(-0.840057\pi\)
0.876393 0.481597i \(-0.159943\pi\)
\(80\) 0.970019 + 8.89152i 0.108451 + 0.994102i
\(81\) 0 0
\(82\) 4.17190 6.04424i 0.460710 0.667474i
\(83\) 5.13122 + 5.13122i 0.563224 + 0.563224i 0.930222 0.366998i \(-0.119614\pi\)
−0.366998 + 0.930222i \(0.619614\pi\)
\(84\) 0 0
\(85\) 11.1438 1.90169i 1.20871 0.206267i
\(86\) −8.24053 + 1.51026i −0.888599 + 0.162855i
\(87\) 0 0
\(88\) −2.75262 + 11.1699i −0.293430 + 1.19072i
\(89\) −9.88328 −1.04763 −0.523813 0.851833i \(-0.675491\pi\)
−0.523813 + 0.851833i \(0.675491\pi\)
\(90\) 0 0
\(91\) 0.383449i 0.0401964i
\(92\) −4.09951 1.84489i −0.427403 0.192343i
\(93\) 0 0
\(94\) 1.65282 + 9.01838i 0.170475 + 0.930175i
\(95\) −8.82252 + 12.4532i −0.905171 + 1.27767i
\(96\) 0 0
\(97\) 1.75624 1.75624i 0.178319 0.178319i −0.612303 0.790623i \(-0.709757\pi\)
0.790623 + 0.612303i \(0.209757\pi\)
\(98\) −5.47235 + 7.92832i −0.552791 + 0.800881i
\(99\) 0 0
\(100\) 7.64478 6.44650i 0.764478 0.644650i
\(101\) 1.88077 0.187143 0.0935716 0.995613i \(-0.470172\pi\)
0.0935716 + 0.995613i \(0.470172\pi\)
\(102\) 0 0
\(103\) 10.7376 + 10.7376i 1.05800 + 1.05800i 0.998211 + 0.0597943i \(0.0190445\pi\)
0.0597943 + 0.998211i \(0.480956\pi\)
\(104\) 1.29390 + 2.14016i 0.126878 + 0.209860i
\(105\) 0 0
\(106\) −2.67496 14.5956i −0.259815 1.41765i
\(107\) −9.59725 + 9.59725i −0.927801 + 0.927801i −0.997564 0.0697628i \(-0.977776\pi\)
0.0697628 + 0.997564i \(0.477776\pi\)
\(108\) 0 0
\(109\) 3.12119 0.298956 0.149478 0.988765i \(-0.452241\pi\)
0.149478 + 0.988765i \(0.452241\pi\)
\(110\) 12.0809 4.41375i 1.15187 0.420835i
\(111\) 0 0
\(112\) 0.104636 1.73151i 0.00988715 0.163612i
\(113\) 5.85646 5.85646i 0.550929 0.550929i −0.375780 0.926709i \(-0.622625\pi\)
0.926709 + 0.375780i \(0.122625\pi\)
\(114\) 0 0
\(115\) 0.845488 + 4.95451i 0.0788421 + 0.462010i
\(116\) 15.9124 6.03531i 1.47743 0.560364i
\(117\) 0 0
\(118\) −7.06592 + 10.2371i −0.650471 + 0.942399i
\(119\) −2.19249 −0.200985
\(120\) 0 0
\(121\) 5.54302 0.503911
\(122\) 4.88767 7.08123i 0.442509 0.641104i
\(123\) 0 0
\(124\) −1.82090 4.80088i −0.163521 0.431132i
\(125\) −10.7501 3.07182i −0.961515 0.274752i
\(126\) 0 0
\(127\) −14.7376 + 14.7376i −1.30775 + 1.30775i −0.384712 + 0.923037i \(0.625699\pi\)
−0.923037 + 0.384712i \(0.874301\pi\)
\(128\) −5.25876 10.0173i −0.464813 0.885409i
\(129\) 0 0
\(130\) 1.17859 2.53555i 0.103370 0.222383i
\(131\) 5.86888 0.512766 0.256383 0.966575i \(-0.417469\pi\)
0.256383 + 0.966575i \(0.417469\pi\)
\(132\) 0 0
\(133\) 2.09295 2.09295i 0.181482 0.181482i
\(134\) −2.22830 12.1584i −0.192495 1.05033i
\(135\) 0 0
\(136\) −12.2370 + 7.39829i −1.04932 + 0.634398i
\(137\) 13.4582 + 13.4582i 1.14981 + 1.14981i 0.986589 + 0.163222i \(0.0521887\pi\)
0.163222 + 0.986589i \(0.447811\pi\)
\(138\) 0 0
\(139\) 16.0990 1.36550 0.682752 0.730650i \(-0.260783\pi\)
0.682752 + 0.730650i \(0.260783\pi\)
\(140\) −1.67183 + 0.983021i −0.141295 + 0.0830805i
\(141\) 0 0
\(142\) 11.8506 17.1691i 0.994483 1.44080i
\(143\) 2.54298 2.54298i 0.212655 0.212655i
\(144\) 0 0
\(145\) −15.5258 10.9993i −1.28935 0.913443i
\(146\) 1.10282 + 6.01740i 0.0912701 + 0.498004i
\(147\) 0 0
\(148\) 1.96193 4.35956i 0.161269 0.358354i
\(149\) 4.56103i 0.373654i 0.982393 + 0.186827i \(0.0598204\pi\)
−0.982393 + 0.186827i \(0.940180\pi\)
\(150\) 0 0
\(151\) −12.4433 −1.01262 −0.506309 0.862352i \(-0.668991\pi\)
−0.506309 + 0.862352i \(0.668991\pi\)
\(152\) 4.61910 18.7439i 0.374658 1.52033i
\(153\) 0 0
\(154\) −2.45361 + 0.449677i −0.197717 + 0.0362360i
\(155\) −3.31857 + 4.68426i −0.266554 + 0.376249i
\(156\) 0 0
\(157\) 13.4700 + 13.4700i 1.07502 + 1.07502i 0.996948 + 0.0780736i \(0.0248769\pi\)
0.0780736 + 0.996948i \(0.475123\pi\)
\(158\) 6.87751 9.96410i 0.547145 0.792701i
\(159\) 0 0
\(160\) −6.01399 + 11.1280i −0.475448 + 0.879744i
\(161\) 0.974777i 0.0768232i
\(162\) 0 0
\(163\) −6.23902 + 6.23902i −0.488678 + 0.488678i −0.907889 0.419211i \(-0.862307\pi\)
0.419211 + 0.907889i \(0.362307\pi\)
\(164\) 9.71125 3.68331i 0.758321 0.287619i
\(165\) 0 0
\(166\) 1.85000 + 10.0943i 0.143588 + 0.783470i
\(167\) −4.26961 4.26961i −0.330392 0.330392i 0.522343 0.852735i \(-0.325058\pi\)
−0.852735 + 0.522343i \(0.825058\pi\)
\(168\) 0 0
\(169\) 12.2182i 0.939861i
\(170\) 14.4978 + 6.73898i 1.11193 + 0.516856i
\(171\) 0 0
\(172\) −10.8043 4.86224i −0.823821 0.370743i
\(173\) 14.0168 + 14.0168i 1.06568 + 1.06568i 0.997686 + 0.0679921i \(0.0216593\pi\)
0.0679921 + 0.997686i \(0.478341\pi\)
\(174\) 0 0
\(175\) 1.95496 + 0.937982i 0.147781 + 0.0709048i
\(176\) −12.1771 + 10.7892i −0.917882 + 0.813268i
\(177\) 0 0
\(178\) −11.5030 7.93972i −0.862188 0.595107i
\(179\) 16.8624i 1.26036i −0.776451 0.630178i \(-0.782982\pi\)
0.776451 0.630178i \(-0.217018\pi\)
\(180\) 0 0
\(181\) 18.7043i 1.39028i 0.718874 + 0.695140i \(0.244658\pi\)
−0.718874 + 0.695140i \(0.755342\pi\)
\(182\) −0.308043 + 0.446291i −0.0228337 + 0.0330813i
\(183\) 0 0
\(184\) −3.28927 5.44058i −0.242488 0.401085i
\(185\) −5.26880 + 0.899123i −0.387370 + 0.0661048i
\(186\) 0 0
\(187\) 14.5403 + 14.5403i 1.06329 + 1.06329i
\(188\) −5.32121 + 11.8242i −0.388089 + 0.862365i
\(189\) 0 0
\(190\) −20.2727 + 7.40660i −1.47074 + 0.537331i
\(191\) 6.52419i 0.472074i −0.971744 0.236037i \(-0.924151\pi\)
0.971744 0.236037i \(-0.0758486\pi\)
\(192\) 0 0
\(193\) 1.52917 + 1.52917i 0.110072 + 0.110072i 0.759998 0.649926i \(-0.225200\pi\)
−0.649926 + 0.759998i \(0.725200\pi\)
\(194\) 3.45494 0.633194i 0.248050 0.0454606i
\(195\) 0 0
\(196\) −12.7384 + 4.83146i −0.909885 + 0.345104i
\(197\) −3.85488 + 3.85488i −0.274648 + 0.274648i −0.830968 0.556320i \(-0.812213\pi\)
0.556320 + 0.830968i \(0.312213\pi\)
\(198\) 0 0
\(199\) 14.3090i 1.01434i −0.861847 0.507168i \(-0.830693\pi\)
0.861847 0.507168i \(-0.169307\pi\)
\(200\) 14.0764 1.36157i 0.995355 0.0962776i
\(201\) 0 0
\(202\) 2.18900 + 1.51091i 0.154017 + 0.106307i
\(203\) 2.60935 + 2.60935i 0.183141 + 0.183141i
\(204\) 0 0
\(205\) −9.47533 6.71282i −0.661786 0.468844i
\(206\) 3.87131 + 21.1233i 0.269727 + 1.47173i
\(207\) 0 0
\(208\) −0.213341 + 3.53036i −0.0147925 + 0.244787i
\(209\) −27.7604 −1.92023
\(210\) 0 0
\(211\) 8.62279i 0.593618i −0.954937 0.296809i \(-0.904078\pi\)
0.954937 0.296809i \(-0.0959224\pi\)
\(212\) 8.61198 19.1365i 0.591473 1.31430i
\(213\) 0 0
\(214\) −18.8800 + 3.46018i −1.29061 + 0.236533i
\(215\) 2.22830 + 13.0577i 0.151968 + 0.890526i
\(216\) 0 0
\(217\) 0.787261 0.787261i 0.0534427 0.0534427i
\(218\) 3.63271 + 2.50740i 0.246038 + 0.169823i
\(219\) 0 0
\(220\) 17.6066 + 4.56809i 1.18704 + 0.307980i
\(221\) 4.47024 0.300701
\(222\) 0 0
\(223\) 6.87395 + 6.87395i 0.460314 + 0.460314i 0.898758 0.438444i \(-0.144470\pi\)
−0.438444 + 0.898758i \(0.644470\pi\)
\(224\) 1.51279 1.93122i 0.101077 0.129035i
\(225\) 0 0
\(226\) 11.5210 2.11148i 0.766368 0.140454i
\(227\) 9.19431 9.19431i 0.610248 0.610248i −0.332763 0.943011i \(-0.607981\pi\)
0.943011 + 0.332763i \(0.107981\pi\)
\(228\) 0 0
\(229\) −2.31517 −0.152991 −0.0764954 0.997070i \(-0.524373\pi\)
−0.0764954 + 0.997070i \(0.524373\pi\)
\(230\) −2.99614 + 6.44570i −0.197560 + 0.425017i
\(231\) 0 0
\(232\) 23.3687 + 5.75878i 1.53423 + 0.378082i
\(233\) 13.1377 13.1377i 0.860682 0.860682i −0.130735 0.991417i \(-0.541734\pi\)
0.991417 + 0.130735i \(0.0417338\pi\)
\(234\) 0 0
\(235\) 14.2902 2.43863i 0.932191 0.159079i
\(236\) −16.4479 + 6.23840i −1.07067 + 0.406085i
\(237\) 0 0
\(238\) −2.55181 1.76133i −0.165409 0.114170i
\(239\) 12.3925 0.801604 0.400802 0.916165i \(-0.368732\pi\)
0.400802 + 0.916165i \(0.368732\pi\)
\(240\) 0 0
\(241\) 18.0131 1.16033 0.580164 0.814499i \(-0.302988\pi\)
0.580164 + 0.814499i \(0.302988\pi\)
\(242\) 6.45145 + 4.45298i 0.414715 + 0.286248i
\(243\) 0 0
\(244\) 11.3774 4.31525i 0.728362 0.276256i
\(245\) 12.4289 + 8.80531i 0.794056 + 0.562551i
\(246\) 0 0
\(247\) −4.26731 + 4.26731i −0.271522 + 0.271522i
\(248\) 1.73746 7.05050i 0.110329 0.447707i
\(249\) 0 0
\(250\) −10.0441 12.2113i −0.635246 0.772310i
\(251\) −12.9632 −0.818228 −0.409114 0.912483i \(-0.634162\pi\)
−0.409114 + 0.912483i \(0.634162\pi\)
\(252\) 0 0
\(253\) −6.46459 + 6.46459i −0.406425 + 0.406425i
\(254\) −28.9923 + 5.31347i −1.81914 + 0.333397i
\(255\) 0 0
\(256\) 1.92674 15.8836i 0.120421 0.992723i
\(257\) 8.26946 + 8.26946i 0.515835 + 0.515835i 0.916308 0.400473i \(-0.131154\pi\)
−0.400473 + 0.916308i \(0.631154\pi\)
\(258\) 0 0
\(259\) 1.03661 0.0644120
\(260\) 3.40868 2.00427i 0.211397 0.124300i
\(261\) 0 0
\(262\) 6.83071 + 4.71475i 0.422003 + 0.291278i
\(263\) 2.53991 2.53991i 0.156617 0.156617i −0.624448 0.781066i \(-0.714676\pi\)
0.781066 + 0.624448i \(0.214676\pi\)
\(264\) 0 0
\(265\) −23.1277 + 3.94674i −1.42072 + 0.242447i
\(266\) 4.11733 0.754591i 0.252450 0.0462670i
\(267\) 0 0
\(268\) 7.17395 15.9411i 0.438219 0.973758i
\(269\) 1.90816i 0.116342i 0.998307 + 0.0581712i \(0.0185269\pi\)
−0.998307 + 0.0581712i \(0.981473\pi\)
\(270\) 0 0
\(271\) 14.2812 0.867524 0.433762 0.901028i \(-0.357186\pi\)
0.433762 + 0.901028i \(0.357186\pi\)
\(272\) −20.1859 1.21984i −1.22395 0.0739639i
\(273\) 0 0
\(274\) 4.85220 + 26.4754i 0.293132 + 1.59944i
\(275\) −6.74447 19.1856i −0.406707 1.15694i
\(276\) 0 0
\(277\) −20.5605 20.5605i −1.23536 1.23536i −0.961876 0.273488i \(-0.911823\pi\)
−0.273488 0.961876i \(-0.588177\pi\)
\(278\) 18.7375 + 12.9331i 1.12380 + 0.775678i
\(279\) 0 0
\(280\) −2.73553 0.198936i −0.163479 0.0118887i
\(281\) 9.40066i 0.560796i 0.959884 + 0.280398i \(0.0904665\pi\)
−0.959884 + 0.280398i \(0.909533\pi\)
\(282\) 0 0
\(283\) 18.4043 18.4043i 1.09402 1.09402i 0.0989268 0.995095i \(-0.468459\pi\)
0.995095 0.0989268i \(-0.0315410\pi\)
\(284\) 27.5856 10.4628i 1.63690 0.620850i
\(285\) 0 0
\(286\) 5.00264 0.916843i 0.295812 0.0542141i
\(287\) 1.59247 + 1.59247i 0.0940008 + 0.0940008i
\(288\) 0 0
\(289\) 8.56000i 0.503530i
\(290\) −9.23404 25.2746i −0.542241 1.48418i
\(291\) 0 0
\(292\) −3.55051 + 7.88952i −0.207778 + 0.461699i
\(293\) 10.8096 + 10.8096i 0.631504 + 0.631504i 0.948445 0.316941i \(-0.102656\pi\)
−0.316941 + 0.948445i \(0.602656\pi\)
\(294\) 0 0
\(295\) 16.0483 + 11.3695i 0.934369 + 0.661955i
\(296\) 5.78571 3.49793i 0.336287 0.203313i
\(297\) 0 0
\(298\) −3.66409 + 5.30852i −0.212255 + 0.307514i
\(299\) 1.98746i 0.114938i
\(300\) 0 0
\(301\) 2.56904i 0.148077i
\(302\) −14.4826 9.99627i −0.833377 0.575221i
\(303\) 0 0
\(304\) 20.4340 18.1051i 1.17197 1.03840i
\(305\) −11.1010 7.86452i −0.635641 0.450321i
\(306\) 0 0
\(307\) −23.8171 23.8171i −1.35931 1.35931i −0.874766 0.484546i \(-0.838985\pi\)
−0.484546 0.874766i \(-0.661015\pi\)
\(308\) −3.21697 1.44773i −0.183304 0.0824919i
\(309\) 0 0
\(310\) −7.62553 + 2.78598i −0.433101 + 0.158233i
\(311\) 0.743382i 0.0421533i 0.999778 + 0.0210767i \(0.00670941\pi\)
−0.999778 + 0.0210767i \(0.993291\pi\)
\(312\) 0 0
\(313\) −16.4757 16.4757i −0.931262 0.931262i 0.0665231 0.997785i \(-0.478809\pi\)
−0.997785 + 0.0665231i \(0.978809\pi\)
\(314\) 4.85645 + 26.4986i 0.274065 + 1.49540i
\(315\) 0 0
\(316\) 16.0093 6.07205i 0.900592 0.341580i
\(317\) −12.0047 + 12.0047i −0.674252 + 0.674252i −0.958693 0.284442i \(-0.908192\pi\)
0.284442 + 0.958693i \(0.408192\pi\)
\(318\) 0 0
\(319\) 34.6098i 1.93777i
\(320\) −15.9392 + 8.12038i −0.891031 + 0.453943i
\(321\) 0 0
\(322\) 0.783085 1.13453i 0.0436396 0.0632249i
\(323\) −24.3997 24.3997i −1.35763 1.35763i
\(324\) 0 0
\(325\) −3.98595 1.91244i −0.221101 0.106083i
\(326\) −12.2736 + 2.24941i −0.679773 + 0.124583i
\(327\) 0 0
\(328\) 14.2618 + 3.51455i 0.787475 + 0.194059i
\(329\) −2.81154 −0.155005
\(330\) 0 0
\(331\) 20.3586i 1.11901i 0.828827 + 0.559505i \(0.189009\pi\)
−0.828827 + 0.559505i \(0.810991\pi\)
\(332\) −5.95605 + 13.2348i −0.326881 + 0.726356i
\(333\) 0 0
\(334\) −1.53936 8.39932i −0.0842300 0.459590i
\(335\) −19.2658 + 3.28772i −1.05260 + 0.179627i
\(336\) 0 0
\(337\) 12.3690 12.3690i 0.673782 0.673782i −0.284804 0.958586i \(-0.591928\pi\)
0.958586 + 0.284804i \(0.0919284\pi\)
\(338\) −9.81546 + 14.2206i −0.533890 + 0.773498i
\(339\) 0 0
\(340\) 11.4601 + 19.4902i 0.621509 + 1.05700i
\(341\) −10.4420 −0.565467
\(342\) 0 0
\(343\) −4.23542 4.23542i −0.228691 0.228691i
\(344\) −8.66891 14.3387i −0.467396 0.773092i
\(345\) 0 0
\(346\) 5.05360 + 27.5743i 0.271683 + 1.48241i
\(347\) 8.65625 8.65625i 0.464692 0.464692i −0.435498 0.900190i \(-0.643428\pi\)
0.900190 + 0.435498i \(0.143428\pi\)
\(348\) 0 0
\(349\) −26.6201 −1.42494 −0.712469 0.701703i \(-0.752423\pi\)
−0.712469 + 0.701703i \(0.752423\pi\)
\(350\) 1.52183 + 2.66222i 0.0813451 + 0.142302i
\(351\) 0 0
\(352\) −22.8402 + 2.77499i −1.21739 + 0.147908i
\(353\) 2.06573 2.06573i 0.109948 0.109948i −0.649993 0.759940i \(-0.725228\pi\)
0.759940 + 0.649993i \(0.225228\pi\)
\(354\) 0 0
\(355\) −26.9155 19.0683i −1.42852 1.01204i
\(356\) −7.00986 18.4819i −0.371522 0.979536i
\(357\) 0 0
\(358\) 13.5464 19.6259i 0.715949 1.03726i
\(359\) 25.0314 1.32110 0.660552 0.750780i \(-0.270322\pi\)
0.660552 + 0.750780i \(0.270322\pi\)
\(360\) 0 0
\(361\) 27.5840 1.45179
\(362\) −15.0261 + 21.7697i −0.789753 + 1.14419i
\(363\) 0 0
\(364\) −0.717054 + 0.271967i −0.0375838 + 0.0142549i
\(365\) 9.53497 1.62715i 0.499083 0.0851687i
\(366\) 0 0
\(367\) −17.6828 + 17.6828i −0.923033 + 0.923033i −0.997243 0.0742100i \(-0.976356\pi\)
0.0742100 + 0.997243i \(0.476356\pi\)
\(368\) 0.542341 8.97464i 0.0282715 0.467835i
\(369\) 0 0
\(370\) −6.85460 3.18620i −0.356354 0.165643i
\(371\) 4.55027 0.236238
\(372\) 0 0
\(373\) −17.6344 + 17.6344i −0.913073 + 0.913073i −0.996513 0.0834395i \(-0.973409\pi\)
0.0834395 + 0.996513i \(0.473409\pi\)
\(374\) 5.24234 + 28.6041i 0.271075 + 1.47909i
\(375\) 0 0
\(376\) −15.6922 + 9.48720i −0.809263 + 0.489265i
\(377\) −5.32019 5.32019i −0.274004 0.274004i
\(378\) 0 0
\(379\) 17.1117 0.878971 0.439486 0.898250i \(-0.355161\pi\)
0.439486 + 0.898250i \(0.355161\pi\)
\(380\) −29.5452 7.66558i −1.51564 0.393236i
\(381\) 0 0
\(382\) 5.24119 7.59342i 0.268163 0.388513i
\(383\) 7.26450 7.26450i 0.371199 0.371199i −0.496715 0.867914i \(-0.665461\pi\)
0.867914 + 0.496715i \(0.165461\pi\)
\(384\) 0 0
\(385\) 0.663472 + 3.88791i 0.0338137 + 0.198146i
\(386\) 0.551324 + 3.00823i 0.0280616 + 0.153115i
\(387\) 0 0
\(388\) 4.52983 + 2.03855i 0.229968 + 0.103492i
\(389\) 4.30166i 0.218103i 0.994036 + 0.109051i \(0.0347813\pi\)
−0.994036 + 0.109051i \(0.965219\pi\)
\(390\) 0 0
\(391\) −11.3639 −0.574699
\(392\) −18.7074 4.61009i −0.944866 0.232845i
\(393\) 0 0
\(394\) −7.58344 + 1.38983i −0.382048 + 0.0700187i
\(395\) −15.6204 11.0663i −0.785946 0.556805i
\(396\) 0 0
\(397\) −9.05589 9.05589i −0.454502 0.454502i 0.442344 0.896846i \(-0.354147\pi\)
−0.896846 + 0.442344i \(0.854147\pi\)
\(398\) 11.4951 16.6540i 0.576196 0.834790i
\(399\) 0 0
\(400\) 17.4772 + 9.72356i 0.873860 + 0.486178i
\(401\) 16.9061i 0.844249i 0.906538 + 0.422124i \(0.138715\pi\)
−0.906538 + 0.422124i \(0.861285\pi\)
\(402\) 0 0
\(403\) −1.60514 + 1.60514i −0.0799577 + 0.0799577i
\(404\) 1.33396 + 3.51706i 0.0663670 + 0.174980i
\(405\) 0 0
\(406\) 0.940773 + 5.13321i 0.0466898 + 0.254757i
\(407\) −6.87468 6.87468i −0.340765 0.340765i
\(408\) 0 0
\(409\) 1.92157i 0.0950153i −0.998871 0.0475077i \(-0.984872\pi\)
0.998871 0.0475077i \(-0.0151278\pi\)
\(410\) −5.63548 15.4250i −0.278317 0.761784i
\(411\) 0 0
\(412\) −12.4636 + 27.6952i −0.614038 + 1.36444i
\(413\) −2.69716 2.69716i −0.132719 0.132719i
\(414\) 0 0
\(415\) 15.9951 2.72957i 0.785169 0.133989i
\(416\) −3.08441 + 3.93755i −0.151226 + 0.193054i
\(417\) 0 0
\(418\) −32.3100 22.3013i −1.58033 1.09079i
\(419\) 8.33374i 0.407130i −0.979061 0.203565i \(-0.934747\pi\)
0.979061 0.203565i \(-0.0652528\pi\)
\(420\) 0 0
\(421\) 11.0584i 0.538956i −0.963007 0.269478i \(-0.913149\pi\)
0.963007 0.269478i \(-0.0868511\pi\)
\(422\) 6.92710 10.0360i 0.337206 0.488543i
\(423\) 0 0
\(424\) 25.3967 15.3543i 1.23337 0.745672i
\(425\) 10.9350 22.7909i 0.530425 1.10552i
\(426\) 0 0
\(427\) 1.86569 + 1.86569i 0.0902871 + 0.0902871i
\(428\) −24.7539 11.1400i −1.19653 0.538471i
\(429\) 0 0
\(430\) −7.89637 + 16.9877i −0.380797 + 0.819222i
\(431\) 26.6362i 1.28302i −0.767115 0.641509i \(-0.778309\pi\)
0.767115 0.641509i \(-0.221691\pi\)
\(432\) 0 0
\(433\) −16.5454 16.5454i −0.795123 0.795123i 0.187199 0.982322i \(-0.440059\pi\)
−0.982322 + 0.187199i \(0.940059\pi\)
\(434\) 1.54873 0.283838i 0.0743412 0.0136247i
\(435\) 0 0
\(436\) 2.21375 + 5.83666i 0.106019 + 0.279525i
\(437\) 10.8481 10.8481i 0.518933 0.518933i
\(438\) 0 0
\(439\) 5.35402i 0.255533i −0.991804 0.127767i \(-0.959219\pi\)
0.991804 0.127767i \(-0.0407808\pi\)
\(440\) 16.8223 + 19.4610i 0.801974 + 0.927766i
\(441\) 0 0
\(442\) 5.20286 + 3.59116i 0.247475 + 0.170814i
\(443\) 2.73227 + 2.73227i 0.129814 + 0.129814i 0.769028 0.639215i \(-0.220740\pi\)
−0.639215 + 0.769028i \(0.720740\pi\)
\(444\) 0 0
\(445\) −12.7754 + 18.0329i −0.605614 + 0.854841i
\(446\) 2.47833 + 13.5227i 0.117352 + 0.640317i
\(447\) 0 0
\(448\) 3.31216 1.03243i 0.156485 0.0487777i
\(449\) 28.9286 1.36522 0.682612 0.730781i \(-0.260844\pi\)
0.682612 + 0.730781i \(0.260844\pi\)
\(450\) 0 0
\(451\) 21.1222i 0.994603i
\(452\) 15.1054 + 6.79787i 0.710500 + 0.319745i
\(453\) 0 0
\(454\) 18.0874 3.31491i 0.848882 0.155576i
\(455\) 0.699635 + 0.495658i 0.0327994 + 0.0232368i
\(456\) 0 0
\(457\) 10.5512 10.5512i 0.493564 0.493564i −0.415863 0.909427i \(-0.636520\pi\)
0.909427 + 0.415863i \(0.136520\pi\)
\(458\) −2.69460 1.85989i −0.125910 0.0869068i
\(459\) 0 0
\(460\) −8.66531 + 5.09513i −0.404022 + 0.237561i
\(461\) 11.9624 0.557146 0.278573 0.960415i \(-0.410139\pi\)
0.278573 + 0.960415i \(0.410139\pi\)
\(462\) 0 0
\(463\) 8.05265 + 8.05265i 0.374238 + 0.374238i 0.869018 0.494780i \(-0.164751\pi\)
−0.494780 + 0.869018i \(0.664751\pi\)
\(464\) 22.5722 + 25.4757i 1.04789 + 1.18268i
\(465\) 0 0
\(466\) 25.8450 4.73666i 1.19725 0.219422i
\(467\) 13.8717 13.8717i 0.641906 0.641906i −0.309118 0.951024i \(-0.600034\pi\)
0.951024 + 0.309118i \(0.100034\pi\)
\(468\) 0 0
\(469\) 3.79046 0.175027
\(470\) 18.5913 + 8.64173i 0.857551 + 0.398613i
\(471\) 0 0
\(472\) −24.1551 5.95257i −1.11183 0.273989i
\(473\) −17.0375 + 17.0375i −0.783386 + 0.783386i
\(474\) 0 0
\(475\) 11.3177 + 32.1949i 0.519292 + 1.47720i
\(476\) −1.55505 4.09998i −0.0712757 0.187922i
\(477\) 0 0
\(478\) 14.4235 + 9.95548i 0.659713 + 0.455353i
\(479\) 5.00618 0.228738 0.114369 0.993438i \(-0.463515\pi\)
0.114369 + 0.993438i \(0.463515\pi\)
\(480\) 0 0
\(481\) −2.11354 −0.0963693
\(482\) 20.9653 + 14.4708i 0.954941 + 0.659128i
\(483\) 0 0
\(484\) 3.93147 + 10.3655i 0.178703 + 0.471160i
\(485\) −0.934240 5.47458i −0.0424216 0.248588i
\(486\) 0 0
\(487\) −7.84638 + 7.84638i −0.355554 + 0.355554i −0.862171 0.506617i \(-0.830896\pi\)
0.506617 + 0.862171i \(0.330896\pi\)
\(488\) 16.7086 + 4.11753i 0.756364 + 0.186392i
\(489\) 0 0
\(490\) 7.39215 + 20.2331i 0.333943 + 0.914041i
\(491\) 1.65566 0.0747189 0.0373594 0.999302i \(-0.488105\pi\)
0.0373594 + 0.999302i \(0.488105\pi\)
\(492\) 0 0
\(493\) 30.4198 30.4198i 1.37004 1.37004i
\(494\) −8.39480 + 1.53853i −0.377700 + 0.0692217i
\(495\) 0 0
\(496\) 7.68621 6.81019i 0.345121 0.305787i
\(497\) 4.52355 + 4.52355i 0.202909 + 0.202909i
\(498\) 0 0
\(499\) −28.0466 −1.25554 −0.627768 0.778400i \(-0.716031\pi\)
−0.627768 + 0.778400i \(0.716031\pi\)
\(500\) −1.88030 22.2815i −0.0840894 0.996458i
\(501\) 0 0
\(502\) −15.0877 10.4139i −0.673395 0.464797i
\(503\) −26.8464 + 26.8464i −1.19702 + 1.19702i −0.221965 + 0.975055i \(0.571247\pi\)
−0.975055 + 0.221965i \(0.928753\pi\)
\(504\) 0 0
\(505\) 2.43114 3.43162i 0.108184 0.152705i
\(506\) −12.7174 + 2.33074i −0.565356 + 0.103614i
\(507\) 0 0
\(508\) −38.0123 17.1066i −1.68652 0.758983i
\(509\) 12.0740i 0.535170i 0.963534 + 0.267585i \(0.0862256\pi\)
−0.963534 + 0.267585i \(0.913774\pi\)
\(510\) 0 0
\(511\) −1.87596 −0.0829878
\(512\) 15.0025 16.9388i 0.663024 0.748598i
\(513\) 0 0
\(514\) 2.98146 + 16.2680i 0.131507 + 0.717550i
\(515\) 33.4713 5.71189i 1.47492 0.251696i
\(516\) 0 0
\(517\) 18.6457 + 18.6457i 0.820039 + 0.820039i
\(518\) 1.20650 + 0.832761i 0.0530106 + 0.0365894i
\(519\) 0 0
\(520\) 5.57745 + 0.405608i 0.244587 + 0.0177871i
\(521\) 20.1076i 0.880928i 0.897770 + 0.440464i \(0.145186\pi\)
−0.897770 + 0.440464i \(0.854814\pi\)
\(522\) 0 0
\(523\) 5.72970 5.72970i 0.250542 0.250542i −0.570651 0.821193i \(-0.693309\pi\)
0.821193 + 0.570651i \(0.193309\pi\)
\(524\) 4.16259 + 10.9749i 0.181843 + 0.479440i
\(525\) 0 0
\(526\) 4.99660 0.915736i 0.217862 0.0399280i
\(527\) −9.17788 9.17788i −0.399795 0.399795i
\(528\) 0 0
\(529\) 17.9476i 0.780331i
\(530\) −30.0886 13.9860i −1.30697 0.607513i
\(531\) 0 0
\(532\) 5.39831 + 2.42939i 0.234046 + 0.105328i
\(533\) −3.24688 3.24688i −0.140638 0.140638i
\(534\) 0 0
\(535\) 5.10529 + 29.9167i 0.220721 + 1.29341i
\(536\) 21.1559 12.7905i 0.913797 0.552464i
\(537\) 0 0
\(538\) −1.53291 + 2.22088i −0.0660887 + 0.0957489i
\(539\) 27.7063i 1.19339i
\(540\) 0 0
\(541\) 33.4356i 1.43751i 0.695263 + 0.718755i \(0.255288\pi\)
−0.695263 + 0.718755i \(0.744712\pi\)
\(542\) 16.6218 + 11.4728i 0.713965 + 0.492799i
\(543\) 0 0
\(544\) −22.5142 17.6361i −0.965288 0.756141i
\(545\) 4.03454 5.69487i 0.172821 0.243941i
\(546\) 0 0
\(547\) 9.08411 + 9.08411i 0.388409 + 0.388409i 0.874119 0.485711i \(-0.161439\pi\)
−0.485711 + 0.874119i \(0.661439\pi\)
\(548\) −15.6216 + 34.7124i −0.667320 + 1.48284i
\(549\) 0 0
\(550\) 7.56292 27.7480i 0.322484 1.18318i
\(551\) 58.0777i 2.47419i
\(552\) 0 0
\(553\) 2.62524 + 2.62524i 0.111637 + 0.111637i
\(554\) −7.41287 40.4474i −0.314943 1.71845i
\(555\) 0 0
\(556\) 11.4185 + 30.1054i 0.484251 + 1.27675i
\(557\) 5.55956 5.55956i 0.235566 0.235566i −0.579445 0.815011i \(-0.696731\pi\)
0.815011 + 0.579445i \(0.196731\pi\)
\(558\) 0 0
\(559\) 5.23799i 0.221543i
\(560\) −3.02403 2.42912i −0.127789 0.102649i
\(561\) 0 0
\(562\) −7.55200 + 10.9413i −0.318562 + 0.461531i
\(563\) 6.38203 + 6.38203i 0.268970 + 0.268970i 0.828685 0.559715i \(-0.189089\pi\)
−0.559715 + 0.828685i \(0.689089\pi\)
\(564\) 0 0
\(565\) −3.11537 18.2558i −0.131064 0.768029i
\(566\) 36.2056 6.63546i 1.52183 0.278909i
\(567\) 0 0
\(568\) 40.5117 + 9.98337i 1.69983 + 0.418893i
\(569\) −24.2945 −1.01848 −0.509240 0.860625i \(-0.670073\pi\)
−0.509240 + 0.860625i \(0.670073\pi\)
\(570\) 0 0
\(571\) 3.35468i 0.140389i −0.997533 0.0701945i \(-0.977638\pi\)
0.997533 0.0701945i \(-0.0223620\pi\)
\(572\) 6.55905 + 2.95176i 0.274248 + 0.123419i
\(573\) 0 0
\(574\) 0.574149 + 3.13277i 0.0239645 + 0.130759i
\(575\) 10.1328 + 4.86168i 0.422568 + 0.202746i
\(576\) 0 0
\(577\) −16.6998 + 16.6998i −0.695223 + 0.695223i −0.963376 0.268153i \(-0.913587\pi\)
0.268153 + 0.963376i \(0.413587\pi\)
\(578\) −6.87666 + 9.96287i −0.286031 + 0.414401i
\(579\) 0 0
\(580\) 9.55692 36.8349i 0.396830 1.52949i
\(581\) −3.14697 −0.130558
\(582\) 0 0
\(583\) −30.1768 30.1768i −1.24979 1.24979i
\(584\) −10.4704 + 6.33021i −0.433269 + 0.261946i
\(585\) 0 0
\(586\) 3.89728 + 21.2650i 0.160995 + 0.878450i
\(587\) −31.8287 + 31.8287i −1.31371 + 1.31371i −0.395050 + 0.918659i \(0.629273\pi\)
−0.918659 + 0.395050i \(0.870727\pi\)
\(588\) 0 0
\(589\) 17.5225 0.722000
\(590\) 9.54478 + 26.1251i 0.392952 + 1.07555i
\(591\) 0 0
\(592\) 9.54396 + 0.576745i 0.392254 + 0.0237041i
\(593\) 8.80387 8.80387i 0.361532 0.361532i −0.502845 0.864377i \(-0.667713\pi\)
0.864377 + 0.502845i \(0.167713\pi\)
\(594\) 0 0
\(595\) −2.83408 + 4.00038i −0.116186 + 0.163999i
\(596\) −8.52918 + 3.23498i −0.349369 + 0.132510i
\(597\) 0 0
\(598\) −1.59663 + 2.31318i −0.0652909 + 0.0945931i
\(599\) 36.2251 1.48012 0.740060 0.672541i \(-0.234797\pi\)
0.740060 + 0.672541i \(0.234797\pi\)
\(600\) 0 0
\(601\) −5.92157 −0.241546 −0.120773 0.992680i \(-0.538537\pi\)
−0.120773 + 0.992680i \(0.538537\pi\)
\(602\) 2.06383 2.99007i 0.0841155 0.121866i
\(603\) 0 0
\(604\) −8.82556 23.2691i −0.359107 0.946804i
\(605\) 7.16508 10.1137i 0.291302 0.411181i
\(606\) 0 0
\(607\) 22.5127 22.5127i 0.913763 0.913763i −0.0828026 0.996566i \(-0.526387\pi\)
0.996566 + 0.0828026i \(0.0263871\pi\)
\(608\) 38.3276 4.65664i 1.55439 0.188852i
\(609\) 0 0
\(610\) −6.60235 18.0714i −0.267321 0.731689i
\(611\) 5.73242 0.231909
\(612\) 0 0
\(613\) 17.8351 17.8351i 0.720352 0.720352i −0.248325 0.968677i \(-0.579880\pi\)
0.968677 + 0.248325i \(0.0798800\pi\)
\(614\) −8.58698 46.8538i −0.346542 1.89086i
\(615\) 0 0
\(616\) −2.58116 4.26934i −0.103998 0.172016i
\(617\) −4.87456 4.87456i −0.196242 0.196242i 0.602145 0.798387i \(-0.294313\pi\)
−0.798387 + 0.602145i \(0.794313\pi\)
\(618\) 0 0
\(619\) 33.3372 1.33994 0.669968 0.742390i \(-0.266308\pi\)
0.669968 + 0.742390i \(0.266308\pi\)
\(620\) −11.1134 2.88339i −0.446323 0.115800i
\(621\) 0 0
\(622\) −0.597195 + 0.865213i −0.0239453 + 0.0346919i
\(623\) 3.03070 3.03070i 0.121422 0.121422i
\(624\) 0 0
\(625\) −19.5007 + 15.6437i −0.780026 + 0.625747i
\(626\) −5.94013 32.4116i −0.237415 1.29543i
\(627\) 0 0
\(628\) −15.6352 + 34.7428i −0.623914 + 1.38639i
\(629\) 12.0848i 0.481854i
\(630\) 0 0
\(631\) −11.3469 −0.451715 −0.225857 0.974160i \(-0.572518\pi\)
−0.225857 + 0.974160i \(0.572518\pi\)
\(632\) 23.5110 + 5.79384i 0.935216 + 0.230467i
\(633\) 0 0
\(634\) −23.6161 + 4.32816i −0.937914 + 0.171893i
\(635\) 7.83971 + 45.9402i 0.311109 + 1.82308i
\(636\) 0 0
\(637\) 4.25899 + 4.25899i 0.168747 + 0.168747i
\(638\) 27.8037 40.2818i 1.10076 1.59477i
\(639\) 0 0
\(640\) −25.0750 3.35355i −0.991175 0.132561i
\(641\) 0.578269i 0.0228403i 0.999935 + 0.0114201i \(0.00363522\pi\)
−0.999935 + 0.0114201i \(0.996365\pi\)
\(642\) 0 0
\(643\) −23.4952 + 23.4952i −0.926559 + 0.926559i −0.997482 0.0709229i \(-0.977406\pi\)
0.0709229 + 0.997482i \(0.477406\pi\)
\(644\) 1.82284 0.691374i 0.0718301 0.0272440i
\(645\) 0 0
\(646\) −8.79702 47.9998i −0.346114 1.88853i
\(647\) −25.6996 25.6996i −1.01036 1.01036i −0.999946 0.0104099i \(-0.996686\pi\)
−0.0104099 0.999946i \(-0.503314\pi\)
\(648\) 0 0
\(649\) 35.7744i 1.40427i
\(650\) −3.10284 5.42797i −0.121703 0.212903i
\(651\) 0 0
\(652\) −16.0922 7.24193i −0.630218 0.283616i
\(653\) −24.0153 24.0153i −0.939791 0.939791i 0.0584965 0.998288i \(-0.481369\pi\)
−0.998288 + 0.0584965i \(0.981369\pi\)
\(654\) 0 0
\(655\) 7.58629 10.7083i 0.296421 0.418406i
\(656\) 13.7757 + 15.5477i 0.537850 + 0.607036i
\(657\) 0 0
\(658\) −3.27231 2.25864i −0.127568 0.0880511i
\(659\) 6.25348i 0.243601i −0.992555 0.121800i \(-0.961133\pi\)
0.992555 0.121800i \(-0.0388668\pi\)
\(660\) 0 0
\(661\) 11.0800i 0.430960i 0.976508 + 0.215480i \(0.0691317\pi\)
−0.976508 + 0.215480i \(0.930868\pi\)
\(662\) −16.3550 + 23.6951i −0.635657 + 0.920937i
\(663\) 0 0
\(664\) −17.5643 + 10.6191i −0.681629 + 0.412100i
\(665\) −1.11335 6.52419i −0.0431740 0.252997i
\(666\) 0 0
\(667\) 13.5246 + 13.5246i 0.523675 + 0.523675i
\(668\) 4.95594 11.0125i 0.191751 0.426086i
\(669\) 0 0
\(670\) −25.0644 11.6506i −0.968323 0.450103i
\(671\) 24.7460i 0.955310i
\(672\) 0 0
\(673\) 5.39727 + 5.39727i 0.208049 + 0.208049i 0.803438 0.595389i \(-0.203002\pi\)
−0.595389 + 0.803438i \(0.703002\pi\)
\(674\) 24.3327 4.45950i 0.937261 0.171774i
\(675\) 0 0
\(676\) −22.8482 + 8.66593i −0.878775 + 0.333305i
\(677\) 7.81449 7.81449i 0.300335 0.300335i −0.540810 0.841145i \(-0.681882\pi\)
0.841145 + 0.540810i \(0.181882\pi\)
\(678\) 0 0
\(679\) 1.07710i 0.0413353i
\(680\) −2.31919 + 31.8908i −0.0889369 + 1.22296i
\(681\) 0 0
\(682\) −12.1533 8.38857i −0.465375 0.321215i
\(683\) 19.2280 + 19.2280i 0.735740 + 0.735740i 0.971750 0.236011i \(-0.0758400\pi\)
−0.236011 + 0.971750i \(0.575840\pi\)
\(684\) 0 0
\(685\) 41.9521 7.15914i 1.60291 0.273536i
\(686\) −1.52703 8.33206i −0.0583023 0.318119i
\(687\) 0 0
\(688\) 1.42935 23.6528i 0.0544933 0.901754i
\(689\) −9.27750 −0.353445
\(690\) 0 0
\(691\) 23.0256i 0.875936i 0.898991 + 0.437968i \(0.144302\pi\)
−0.898991 + 0.437968i \(0.855698\pi\)
\(692\) −16.2700 + 36.1532i −0.618492 + 1.37434i
\(693\) 0 0
\(694\) 17.0289 3.12091i 0.646407 0.118468i
\(695\) 20.8101 29.3741i 0.789373 1.11422i
\(696\) 0 0
\(697\) 18.5651 18.5651i 0.703201 0.703201i
\(698\) −30.9827 21.3852i −1.17271 0.809440i
\(699\) 0 0
\(700\) −0.367453 + 4.32108i −0.0138884 + 0.163321i
\(701\) −36.0487 −1.36154 −0.680771 0.732496i \(-0.738355\pi\)
−0.680771 + 0.732496i \(0.738355\pi\)
\(702\) 0 0
\(703\) 11.5362 + 11.5362i 0.435097 + 0.435097i
\(704\) −28.8127 15.1189i −1.08592 0.569814i
\(705\) 0 0
\(706\) 4.06378 0.744776i 0.152942 0.0280300i
\(707\) −0.576735 + 0.576735i −0.0216904 + 0.0216904i
\(708\) 0 0
\(709\) 10.2426 0.384667 0.192334 0.981330i \(-0.438394\pi\)
0.192334 + 0.981330i \(0.438394\pi\)
\(710\) −16.0081 43.8158i −0.600772 1.64438i
\(711\) 0 0
\(712\) 6.68868 27.1421i 0.250669 1.01719i
\(713\) 4.08047 4.08047i 0.152815 0.152815i
\(714\) 0 0
\(715\) −1.35275 7.92702i −0.0505899 0.296454i
\(716\) 31.5329 11.9599i 1.17844 0.446963i
\(717\) 0 0
\(718\) 29.1337 + 20.1089i 1.08726 + 0.750457i
\(719\) −39.2886 −1.46522 −0.732609 0.680650i \(-0.761698\pi\)
−0.732609 + 0.680650i \(0.761698\pi\)
\(720\) 0 0
\(721\) −6.58534 −0.245251
\(722\) 32.1046 + 22.1595i 1.19481 + 0.824692i
\(723\) 0 0
\(724\) −34.9773 + 13.2663i −1.29992 + 0.493038i
\(725\) −40.1383 + 14.1101i −1.49070 + 0.524038i
\(726\) 0 0
\(727\) 15.2333 15.2333i 0.564970 0.564970i −0.365745 0.930715i \(-0.619186\pi\)
0.930715 + 0.365745i \(0.119186\pi\)
\(728\) −1.05305 0.259505i −0.0390287 0.00961791i
\(729\) 0 0
\(730\) 12.4048 + 5.76609i 0.459122 + 0.213412i
\(731\) −29.9498 −1.10773
\(732\) 0 0
\(733\) −12.3754 + 12.3754i −0.457097 + 0.457097i −0.897701 0.440604i \(-0.854764\pi\)
0.440604 + 0.897701i \(0.354764\pi\)
\(734\) −34.7861 + 6.37532i −1.28398 + 0.235317i
\(735\) 0 0
\(736\) 7.84098 10.0098i 0.289022 0.368965i
\(737\) −25.1379 25.1379i −0.925965 0.925965i
\(738\) 0 0
\(739\) −25.8730 −0.951753 −0.475876 0.879512i \(-0.657869\pi\)
−0.475876 + 0.879512i \(0.657869\pi\)
\(740\) −5.41834 9.21501i −0.199182 0.338750i
\(741\) 0 0
\(742\) 5.29599 + 3.65545i 0.194422 + 0.134196i
\(743\) −15.9812 + 15.9812i −0.586292 + 0.586292i −0.936625 0.350333i \(-0.886068\pi\)
0.350333 + 0.936625i \(0.386068\pi\)
\(744\) 0 0
\(745\) 8.32198 + 5.89573i 0.304894 + 0.216003i
\(746\) −34.6910 + 6.35788i −1.27013 + 0.232778i
\(747\) 0 0
\(748\) −16.8776 + 37.5034i −0.617106 + 1.37126i
\(749\) 5.88597i 0.215069i
\(750\) 0 0
\(751\) −33.3102 −1.21551 −0.607754 0.794125i \(-0.707929\pi\)
−0.607754 + 0.794125i \(0.707929\pi\)
\(752\) −25.8855 1.56427i −0.943945 0.0570430i
\(753\) 0 0
\(754\) −1.91813 10.4661i −0.0698543 0.381151i
\(755\) −16.0845 + 22.7038i −0.585376 + 0.826275i
\(756\) 0 0
\(757\) 35.1121 + 35.1121i 1.27617 + 1.27617i 0.942793 + 0.333378i \(0.108188\pi\)
0.333378 + 0.942793i \(0.391812\pi\)
\(758\) 19.9161 + 13.7467i 0.723386 + 0.499302i
\(759\) 0 0
\(760\) −28.2291 32.6569i −1.02398 1.18459i
\(761\) 22.5518i 0.817502i −0.912646 0.408751i \(-0.865964\pi\)
0.912646 0.408751i \(-0.134036\pi\)
\(762\) 0 0
\(763\) −0.957109 + 0.957109i −0.0346497 + 0.0346497i
\(764\) 12.2003 4.62737i 0.441392 0.167413i
\(765\) 0 0
\(766\) 14.2910 2.61913i 0.516354 0.0946331i
\(767\) 5.49922 + 5.49922i 0.198565 + 0.198565i
\(768\) 0 0
\(769\) 16.8578i 0.607907i −0.952687 0.303953i \(-0.901693\pi\)
0.952687 0.303953i \(-0.0983067\pi\)
\(770\) −2.35113 + 5.05808i −0.0847290 + 0.182281i
\(771\) 0 0
\(772\) −1.77498 + 3.94414i −0.0638828 + 0.141953i
\(773\) 2.59499 + 2.59499i 0.0933354 + 0.0933354i 0.752233 0.658897i \(-0.228977\pi\)
−0.658897 + 0.752233i \(0.728977\pi\)
\(774\) 0 0
\(775\) 4.25713 + 12.1100i 0.152921 + 0.435005i
\(776\) 3.63455 + 6.01168i 0.130473 + 0.215807i
\(777\) 0 0
\(778\) −3.45573 + 5.00664i −0.123894 + 0.179497i
\(779\) 35.4445i 1.26993i
\(780\) 0 0
\(781\) 59.9992i 2.14694i
\(782\) −13.2263 9.12920i −0.472973 0.326460i
\(783\) 0 0
\(784\) −18.0698 20.3942i −0.645349 0.728363i
\(785\) 41.9888 7.16540i 1.49864 0.255744i
\(786\) 0 0
\(787\) −25.1710 25.1710i −0.897248 0.897248i 0.0979438 0.995192i \(-0.468773\pi\)
−0.995192 + 0.0979438i \(0.968773\pi\)
\(788\) −9.94279 4.47454i −0.354197 0.159399i
\(789\) 0 0
\(790\) −9.29026 25.4285i −0.330533 0.904705i
\(791\) 3.59176i 0.127708i
\(792\) 0 0
\(793\) −3.80394 3.80394i −0.135082 0.135082i
\(794\) −3.26500 17.8151i −0.115870 0.632233i
\(795\) 0 0
\(796\) 26.7579 10.1488i 0.948409 0.359716i
\(797\) −0.184398 + 0.184398i −0.00653173 + 0.00653173i −0.710365 0.703833i \(-0.751470\pi\)
0.703833 + 0.710365i \(0.251470\pi\)
\(798\) 0 0
\(799\) 32.7769i 1.15956i
\(800\) 12.5301 + 25.3574i 0.443005 + 0.896519i
\(801\) 0 0
\(802\) −13.5815 + 19.6767i −0.479578 + 0.694810i
\(803\) 12.4411 + 12.4411i 0.439038 + 0.439038i
\(804\) 0 0
\(805\) −1.77856 1.26003i −0.0626861 0.0444101i
\(806\) −3.15769 + 0.578715i −0.111225 + 0.0203844i
\(807\) 0 0
\(808\) −1.27284 + 5.16509i −0.0447784 + 0.181707i
\(809\) 23.3352 0.820422 0.410211 0.911991i \(-0.365455\pi\)
0.410211 + 0.911991i \(0.365455\pi\)
\(810\) 0 0
\(811\) 4.50503i 0.158193i 0.996867 + 0.0790964i \(0.0252035\pi\)
−0.996867 + 0.0790964i \(0.974797\pi\)
\(812\) −3.02880 + 6.73024i −0.106290 + 0.236185i
\(813\) 0 0
\(814\) −2.47859 13.5241i −0.0868745 0.474020i
\(815\) 3.31887 + 19.4484i 0.116255 + 0.681247i
\(816\) 0 0
\(817\) 28.5902 28.5902i 1.00024 1.00024i
\(818\) 1.54369 2.23648i 0.0539737 0.0781968i
\(819\) 0 0
\(820\) 5.83254 22.4802i 0.203681 0.785041i
\(821\) −13.4411 −0.469097 −0.234549 0.972104i \(-0.575361\pi\)
−0.234549 + 0.972104i \(0.575361\pi\)
\(822\) 0 0
\(823\) 12.1118 + 12.1118i 0.422190 + 0.422190i 0.885957 0.463767i \(-0.153503\pi\)
−0.463767 + 0.885957i \(0.653503\pi\)
\(824\) −36.7551 + 22.2214i −1.28042 + 0.774120i
\(825\) 0 0
\(826\) −0.972431 5.30595i −0.0338352 0.184618i
\(827\) 3.92415 3.92415i 0.136456 0.136456i −0.635579 0.772035i \(-0.719239\pi\)
0.772035 + 0.635579i \(0.219239\pi\)
\(828\) 0 0
\(829\) 7.47321 0.259555 0.129778 0.991543i \(-0.458574\pi\)
0.129778 + 0.991543i \(0.458574\pi\)
\(830\) 20.8093 + 9.67273i 0.722301 + 0.335745i
\(831\) 0 0
\(832\) −6.75313 + 2.10501i −0.234123 + 0.0729781i
\(833\) −24.3521 + 24.3521i −0.843749 + 0.843749i
\(834\) 0 0
\(835\) −13.3093 + 2.27123i −0.460587 + 0.0785992i
\(836\) −19.6895 51.9123i −0.680974 1.79542i
\(837\) 0 0
\(838\) 6.69489 9.69953i 0.231271 0.335065i
\(839\) −19.0880 −0.658991 −0.329495 0.944157i \(-0.606879\pi\)
−0.329495 + 0.944157i \(0.606879\pi\)
\(840\) 0 0
\(841\) −43.4073 −1.49680
\(842\) 8.88378 12.8708i 0.306155 0.443556i
\(843\) 0 0
\(844\) 16.1247 6.11584i 0.555036 0.210516i
\(845\) 22.2931 + 15.7936i 0.766906 + 0.543316i
\(846\) 0 0
\(847\) −1.69976 + 1.69976i −0.0584045 + 0.0584045i
\(848\) 41.8937 + 2.53165i 1.43864 + 0.0869372i
\(849\) 0 0
\(850\) 31.0361 17.7415i 1.06453 0.608527i
\(851\) 5.37290 0.184181
\(852\) 0 0
\(853\) 0.0201924 0.0201924i 0.000691373 0.000691373i −0.706761 0.707452i \(-0.749844\pi\)
0.707452 + 0.706761i \(0.249844\pi\)
\(854\) 0.672654 + 3.67025i 0.0230177 + 0.125593i
\(855\) 0 0
\(856\) −19.8615 32.8517i −0.678852 1.12285i
\(857\) −1.32849 1.32849i −0.0453805 0.0453805i 0.684052 0.729433i \(-0.260216\pi\)
−0.729433 + 0.684052i \(0.760216\pi\)
\(858\) 0 0
\(859\) −10.8364 −0.369735 −0.184867 0.982764i \(-0.559186\pi\)
−0.184867 + 0.982764i \(0.559186\pi\)
\(860\) −22.8375 + 13.4283i −0.778754 + 0.457900i
\(861\) 0 0
\(862\) 21.3981 31.0015i 0.728822 1.05591i
\(863\) −8.57479 + 8.57479i −0.291889 + 0.291889i −0.837826 0.545937i \(-0.816174\pi\)
0.545937 + 0.837826i \(0.316174\pi\)
\(864\) 0 0
\(865\) 43.6934 7.45629i 1.48562 0.253521i
\(866\) −5.96527 32.5487i −0.202708 1.10605i
\(867\) 0 0
\(868\) 2.03056 + 0.913811i 0.0689218 + 0.0310168i
\(869\) 34.8205i 1.18120i
\(870\) 0 0
\(871\) −7.72835 −0.261865
\(872\) −2.11232 + 8.57162i −0.0715321 + 0.290272i
\(873\) 0 0
\(874\) 21.3407 3.91114i 0.721859 0.132296i
\(875\) 4.23847 2.35453i 0.143286 0.0795975i
\(876\) 0 0
\(877\) −6.82619 6.82619i −0.230504 0.230504i 0.582399 0.812903i \(-0.302114\pi\)
−0.812903 + 0.582399i \(0.802114\pi\)
\(878\) 4.30114 6.23147i 0.145156 0.210302i
\(879\) 0 0
\(880\) 3.94537 + 36.1646i 0.132998 + 1.21911i
\(881\) 33.3297i 1.12290i 0.827509 + 0.561452i \(0.189757\pi\)
−0.827509 + 0.561452i \(0.810243\pi\)
\(882\) 0 0
\(883\) 15.0182 15.0182i 0.505403 0.505403i −0.407709 0.913112i \(-0.633672\pi\)
0.913112 + 0.407709i \(0.133672\pi\)
\(884\) 3.17058 + 8.35941i 0.106638 + 0.281157i
\(885\) 0 0
\(886\) 0.985087 + 5.37501i 0.0330947 + 0.180577i
\(887\) −37.6074 37.6074i −1.26273 1.26273i −0.949763 0.312971i \(-0.898676\pi\)
−0.312971 0.949763i \(-0.601324\pi\)
\(888\) 0 0
\(889\) 9.03853i 0.303143i
\(890\) −29.3558 + 10.7251i −0.984010 + 0.359507i
\(891\) 0 0
\(892\) −7.97892 + 17.7298i −0.267154 + 0.593638i
\(893\) −31.2889 31.2889i −1.04704 1.04704i
\(894\) 0 0
\(895\) −30.7669 21.7969i −1.02842 0.728589i
\(896\) 4.68438 + 1.45919i 0.156494 + 0.0487480i
\(897\) 0 0
\(898\) 33.6696 + 23.2397i 1.12357 + 0.775520i
\(899\) 21.8458i 0.728598i
\(900\) 0 0
\(901\) 53.0470i 1.76725i
\(902\) 16.9684 24.5838i 0.564987 0.818551i
\(903\) 0 0
\(904\) 12.1200 + 20.0469i 0.403104 + 0.666749i
\(905\) 34.1276 + 24.1778i 1.13444 + 0.803696i
\(906\) 0 0
\(907\) 29.6844 + 29.6844i 0.985654 + 0.985654i 0.999899 0.0142450i \(-0.00453448\pi\)
−0.0142450 + 0.999899i \(0.504534\pi\)
\(908\) 23.7147 + 10.6723i 0.786999 + 0.354172i
\(909\) 0 0
\(910\) 0.416110 + 1.13894i 0.0137939 + 0.0377555i
\(911\) 9.37413i 0.310579i 0.987869 + 0.155289i \(0.0496310\pi\)
−0.987869 + 0.155289i \(0.950369\pi\)
\(912\) 0 0
\(913\) 20.8703 + 20.8703i 0.690705 + 0.690705i
\(914\) 20.7567 3.80412i 0.686570 0.125829i
\(915\) 0 0
\(916\) −1.64207 4.32940i −0.0542554 0.143047i
\(917\) −1.79969 + 1.79969i −0.0594309 + 0.0594309i
\(918\) 0 0
\(919\) 12.2408i 0.403788i 0.979407 + 0.201894i \(0.0647097\pi\)
−0.979407 + 0.201894i \(0.935290\pi\)
\(920\) −14.1786 1.03111i −0.467454 0.0339947i
\(921\) 0 0
\(922\) 13.9229 + 9.61000i 0.458527 + 0.316489i
\(923\) −9.22303 9.22303i −0.303580 0.303580i
\(924\) 0 0
\(925\) −5.17009 + 10.7756i −0.169991 + 0.354300i
\(926\) 2.90329 + 15.8415i 0.0954081 + 0.520583i
\(927\) 0 0
\(928\) 5.80558 + 47.7842i 0.190578 + 1.56859i
\(929\) 3.79903 0.124642 0.0623210 0.998056i \(-0.480150\pi\)
0.0623210 + 0.998056i \(0.480150\pi\)
\(930\) 0 0
\(931\) 46.4931i 1.52375i
\(932\) 33.8859 + 15.2496i 1.10997 + 0.499517i
\(933\) 0 0
\(934\) 27.2889 5.00129i 0.892920 0.163647i
\(935\) 45.3252 7.73476i 1.48229 0.252954i
\(936\) 0 0
\(937\) −6.03853 + 6.03853i −0.197270 + 0.197270i −0.798829 0.601559i \(-0.794547\pi\)
0.601559 + 0.798829i \(0.294547\pi\)
\(938\) 4.41167 + 3.04506i 0.144046 + 0.0994248i
\(939\) 0 0
\(940\) 14.6958 + 24.9933i 0.479325 + 0.815190i
\(941\) 29.9232 0.975469 0.487735 0.872992i \(-0.337823\pi\)
0.487735 + 0.872992i \(0.337823\pi\)
\(942\) 0 0
\(943\) 8.25400 + 8.25400i 0.268787 + 0.268787i
\(944\) −23.3318 26.3330i −0.759385 0.857067i
\(945\) 0 0
\(946\) −33.5168 + 6.14269i −1.08973 + 0.199716i
\(947\) 24.1129 24.1129i 0.783564 0.783564i −0.196867 0.980430i \(-0.563077\pi\)
0.980430 + 0.196867i \(0.0630766\pi\)
\(948\) 0 0
\(949\) 3.82489 0.124161
\(950\) −12.6911 + 46.5632i −0.411755 + 1.51071i
\(951\) 0 0
\(952\) 1.48380 6.02116i 0.0480903 0.195147i
\(953\) −2.14110 + 2.14110i −0.0693571 + 0.0693571i −0.740934 0.671577i \(-0.765617\pi\)
0.671577 + 0.740934i \(0.265617\pi\)
\(954\) 0 0
\(955\) −11.9039 8.43336i −0.385202 0.272897i
\(956\) 8.78955 + 23.1741i 0.284274 + 0.749504i
\(957\) 0 0
\(958\) 5.82662 + 4.02170i 0.188250 + 0.129935i
\(959\) −8.25389 −0.266532
\(960\) 0 0
\(961\) −24.4090 −0.787386
\(962\) −2.45992 1.69791i −0.0793111 0.0547428i
\(963\) 0 0
\(964\) 12.7761 + 33.6848i 0.411490 + 1.08491i
\(965\) 4.76674 0.813445i 0.153447 0.0261857i
\(966\) 0 0
\(967\) 32.0860 32.0860i 1.03182 1.03182i 0.0323385 0.999477i \(-0.489705\pi\)
0.999477 0.0323385i \(-0.0102954\pi\)
\(968\) −3.75133 + 15.2226i −0.120572 + 0.489274i
\(969\) 0 0
\(970\) 3.31065 7.12232i 0.106298 0.228684i
\(971\) 43.3908 1.39248 0.696239 0.717810i \(-0.254856\pi\)
0.696239 + 0.717810i \(0.254856\pi\)
\(972\) 0 0
\(973\) −4.93676 + 4.93676i −0.158265 + 0.158265i
\(974\) −15.4357 + 2.82892i −0.494591 + 0.0906446i
\(975\) 0 0
\(976\) 16.1391 + 18.2152i 0.516601 + 0.583054i
\(977\) −24.5104 24.5104i −0.784156 0.784156i 0.196374 0.980529i \(-0.437083\pi\)
−0.980529 + 0.196374i \(0.937083\pi\)
\(978\) 0 0
\(979\) −40.1984 −1.28475
\(980\) −7.65063 + 29.4876i −0.244390 + 0.941946i
\(981\) 0 0
\(982\) 1.92700 + 1.33007i 0.0614930 + 0.0424443i
\(983\) 20.3315 20.3315i 0.648473 0.648473i −0.304151 0.952624i \(-0.598373\pi\)
0.952624 + 0.304151i \(0.0983727\pi\)
\(984\) 0 0
\(985\) 2.05061 + 12.0165i 0.0653380 + 0.382877i
\(986\) 59.8429 10.9675i 1.90579 0.349277i
\(987\) 0 0
\(988\) −11.0066 4.95327i −0.350165 0.157584i
\(989\) 13.3157i 0.423413i
\(990\) 0 0
\(991\) 3.08590 0.0980269 0.0490135 0.998798i \(-0.484392\pi\)
0.0490135 + 0.998798i \(0.484392\pi\)
\(992\) 14.4168 1.75159i 0.457735 0.0556129i
\(993\) 0 0
\(994\) 1.63092 + 8.89889i 0.0517295 + 0.282256i
\(995\) −26.1079 18.4962i −0.827676 0.586369i
\(996\) 0 0
\(997\) −18.0364 18.0364i −0.571217 0.571217i 0.361251 0.932468i \(-0.382350\pi\)
−0.932468 + 0.361251i \(0.882350\pi\)
\(998\) −32.6430 22.5311i −1.03330 0.713211i
\(999\) 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 360.2.x.a.53.19 yes 48
3.2 odd 2 inner 360.2.x.a.53.6 48
4.3 odd 2 1440.2.bj.a.593.15 48
5.2 odd 4 inner 360.2.x.a.197.7 yes 48
8.3 odd 2 1440.2.bj.a.593.9 48
8.5 even 2 inner 360.2.x.a.53.18 yes 48
12.11 even 2 1440.2.bj.a.593.10 48
15.2 even 4 inner 360.2.x.a.197.18 yes 48
20.7 even 4 1440.2.bj.a.17.16 48
24.5 odd 2 inner 360.2.x.a.53.7 yes 48
24.11 even 2 1440.2.bj.a.593.16 48
40.27 even 4 1440.2.bj.a.17.10 48
40.37 odd 4 inner 360.2.x.a.197.6 yes 48
60.47 odd 4 1440.2.bj.a.17.9 48
120.77 even 4 inner 360.2.x.a.197.19 yes 48
120.107 odd 4 1440.2.bj.a.17.15 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
360.2.x.a.53.6 48 3.2 odd 2 inner
360.2.x.a.53.7 yes 48 24.5 odd 2 inner
360.2.x.a.53.18 yes 48 8.5 even 2 inner
360.2.x.a.53.19 yes 48 1.1 even 1 trivial
360.2.x.a.197.6 yes 48 40.37 odd 4 inner
360.2.x.a.197.7 yes 48 5.2 odd 4 inner
360.2.x.a.197.18 yes 48 15.2 even 4 inner
360.2.x.a.197.19 yes 48 120.77 even 4 inner
1440.2.bj.a.17.9 48 60.47 odd 4
1440.2.bj.a.17.10 48 40.27 even 4
1440.2.bj.a.17.15 48 120.107 odd 4
1440.2.bj.a.17.16 48 20.7 even 4
1440.2.bj.a.593.9 48 8.3 odd 2
1440.2.bj.a.593.10 48 12.11 even 2
1440.2.bj.a.593.15 48 4.3 odd 2
1440.2.bj.a.593.16 48 24.11 even 2