Properties

Label 648.2.v.b.35.12
Level $648$
Weight $2$
Character 648.35
Analytic conductor $5.174$
Analytic rank $0$
Dimension $192$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [648,2,Mod(35,648)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(648, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([9, 9, 13]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("648.35");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 648 = 2^{3} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 648.v (of order \(18\), degree \(6\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.17430605098\)
Analytic rank: \(0\)
Dimension: \(192\)
Relative dimension: \(32\) over \(\Q(\zeta_{18})\)
Twist minimal: no (minimal twist has level 216)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 35.12
Character \(\chi\) \(=\) 648.35
Dual form 648.2.v.b.611.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.580483 + 1.28959i) q^{2} +(-1.32608 - 1.49717i) q^{4} +(-3.21529 - 1.17027i) q^{5} +(2.85909 + 0.504135i) q^{7} +(2.70050 - 0.841014i) q^{8} +O(q^{10})\) \(q+(-0.580483 + 1.28959i) q^{2} +(-1.32608 - 1.49717i) q^{4} +(-3.21529 - 1.17027i) q^{5} +(2.85909 + 0.504135i) q^{7} +(2.70050 - 0.841014i) q^{8} +(3.37559 - 3.46708i) q^{10} +(0.927560 + 2.54845i) q^{11} +(-1.60411 - 1.91170i) q^{13} +(-2.30978 + 3.39441i) q^{14} +(-0.483033 + 3.97073i) q^{16} +(-4.30856 + 2.48755i) q^{17} +(-1.31569 + 2.27884i) q^{19} +(2.51163 + 6.36570i) q^{20} +(-3.82488 - 0.283162i) q^{22} +(0.157970 + 0.895893i) q^{23} +(5.13833 + 4.31157i) q^{25} +(3.39646 - 0.958928i) q^{26} +(-3.03660 - 4.94907i) q^{28} +(-7.00248 - 5.87578i) q^{29} +(-2.90502 + 0.512234i) q^{31} +(-4.84021 - 2.92786i) q^{32} +(-0.706867 - 7.00026i) q^{34} +(-8.60284 - 4.96685i) q^{35} +(-9.78021 + 5.64661i) q^{37} +(-2.17503 - 3.01952i) q^{38} +(-9.66710 - 0.456210i) q^{40} +(3.04161 + 3.62485i) q^{41} +(-6.12779 + 2.23033i) q^{43} +(2.58544 - 4.76816i) q^{44} +(-1.24703 - 0.316335i) q^{46} +(-0.225833 + 1.28076i) q^{47} +(1.34241 + 0.488598i) q^{49} +(-8.54287 + 4.12354i) q^{50} +(-0.734968 + 4.93668i) q^{52} +10.3399 q^{53} -9.27950i q^{55} +(8.14496 - 1.04312i) q^{56} +(11.6422 - 5.61953i) q^{58} +(-2.96267 + 8.13988i) q^{59} +(-0.720351 - 0.127017i) q^{61} +(1.02575 - 4.04363i) q^{62} +(6.58539 - 4.54231i) q^{64} +(2.92046 + 8.02391i) q^{65} +(5.00144 - 4.19671i) q^{67} +(9.43778 + 3.15196i) q^{68} +(11.3990 - 8.21095i) q^{70} +(-5.18176 - 8.97507i) q^{71} +(-7.34034 + 12.7138i) q^{73} +(-1.60455 - 15.8902i) q^{74} +(5.15651 - 1.05211i) q^{76} +(1.36722 + 7.75387i) q^{77} +(-5.64811 + 6.73115i) q^{79} +(6.19991 - 12.2018i) q^{80} +(-6.44017 + 1.81826i) q^{82} +(-3.15228 + 3.75674i) q^{83} +(16.7644 - 2.95601i) q^{85} +(0.680867 - 9.19700i) q^{86} +(4.64815 + 6.10199i) q^{88} +(4.90094 + 2.82956i) q^{89} +(-3.62253 - 6.27441i) q^{91} +(1.13182 - 1.42453i) q^{92} +(-1.52056 - 1.03469i) q^{94} +(6.89717 - 5.78741i) q^{95} +(-0.126739 + 0.0461291i) q^{97} +(-1.40934 + 1.44754i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 192 q + 6 q^{2} - 6 q^{4} + 9 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 192 q + 6 q^{2} - 6 q^{4} + 9 q^{8} - 3 q^{10} + 30 q^{11} - 9 q^{14} - 6 q^{16} + 18 q^{17} - 6 q^{19} + 27 q^{20} - 18 q^{22} - 12 q^{25} - 12 q^{28} + 36 q^{32} + 12 q^{34} + 18 q^{35} + 102 q^{38} + 9 q^{40} - 18 q^{41} - 42 q^{43} + 81 q^{44} - 3 q^{46} - 12 q^{49} - 57 q^{50} + 21 q^{52} + 69 q^{56} - 33 q^{58} + 84 q^{59} - 90 q^{62} - 51 q^{64} + 12 q^{65} + 30 q^{67} - 63 q^{68} - 33 q^{70} - 6 q^{73} - 51 q^{74} + 30 q^{76} - 12 q^{82} + 72 q^{83} - 42 q^{86} - 78 q^{88} - 144 q^{89} - 6 q^{91} + 3 q^{92} - 33 q^{94} - 42 q^{97} - 162 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/648\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(487\) \(569\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{13}{18}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.580483 + 1.28959i −0.410464 + 0.911877i
\(3\) 0 0
\(4\) −1.32608 1.49717i −0.663039 0.748585i
\(5\) −3.21529 1.17027i −1.43792 0.523361i −0.498731 0.866757i \(-0.666200\pi\)
−0.939191 + 0.343396i \(0.888423\pi\)
\(6\) 0 0
\(7\) 2.85909 + 0.504135i 1.08064 + 0.190545i 0.685496 0.728076i \(-0.259585\pi\)
0.395139 + 0.918621i \(0.370696\pi\)
\(8\) 2.70050 0.841014i 0.954771 0.297343i
\(9\) 0 0
\(10\) 3.37559 3.46708i 1.06745 1.09639i
\(11\) 0.927560 + 2.54845i 0.279670 + 0.768386i 0.997400 + 0.0720650i \(0.0229589\pi\)
−0.717730 + 0.696321i \(0.754819\pi\)
\(12\) 0 0
\(13\) −1.60411 1.91170i −0.444899 0.530210i 0.496260 0.868174i \(-0.334706\pi\)
−0.941159 + 0.337964i \(0.890262\pi\)
\(14\) −2.30978 + 3.39441i −0.617315 + 0.907195i
\(15\) 0 0
\(16\) −0.483033 + 3.97073i −0.120758 + 0.992682i
\(17\) −4.30856 + 2.48755i −1.04498 + 0.603319i −0.921240 0.388995i \(-0.872822\pi\)
−0.123740 + 0.992315i \(0.539489\pi\)
\(18\) 0 0
\(19\) −1.31569 + 2.27884i −0.301839 + 0.522801i −0.976553 0.215279i \(-0.930934\pi\)
0.674713 + 0.738080i \(0.264267\pi\)
\(20\) 2.51163 + 6.36570i 0.561618 + 1.42341i
\(21\) 0 0
\(22\) −3.82488 0.283162i −0.815468 0.0603703i
\(23\) 0.157970 + 0.895893i 0.0329391 + 0.186807i 0.996838 0.0794621i \(-0.0253203\pi\)
−0.963899 + 0.266269i \(0.914209\pi\)
\(24\) 0 0
\(25\) 5.13833 + 4.31157i 1.02767 + 0.862315i
\(26\) 3.39646 0.958928i 0.666101 0.188061i
\(27\) 0 0
\(28\) −3.03660 4.94907i −0.573864 0.935286i
\(29\) −7.00248 5.87578i −1.30033 1.09111i −0.990088 0.140447i \(-0.955146\pi\)
−0.310241 0.950658i \(-0.600410\pi\)
\(30\) 0 0
\(31\) −2.90502 + 0.512234i −0.521758 + 0.0920000i −0.428324 0.903625i \(-0.640896\pi\)
−0.0934343 + 0.995625i \(0.529785\pi\)
\(32\) −4.84021 2.92786i −0.855637 0.517577i
\(33\) 0 0
\(34\) −0.706867 7.00026i −0.121227 1.20053i
\(35\) −8.60284 4.96685i −1.45414 0.839551i
\(36\) 0 0
\(37\) −9.78021 + 5.64661i −1.60786 + 0.928296i −0.618008 + 0.786172i \(0.712060\pi\)
−0.989849 + 0.142124i \(0.954607\pi\)
\(38\) −2.17503 3.01952i −0.352836 0.489831i
\(39\) 0 0
\(40\) −9.66710 0.456210i −1.52850 0.0721332i
\(41\) 3.04161 + 3.62485i 0.475020 + 0.566106i 0.949342 0.314245i \(-0.101751\pi\)
−0.474322 + 0.880351i \(0.657307\pi\)
\(42\) 0 0
\(43\) −6.12779 + 2.23033i −0.934479 + 0.340123i −0.763983 0.645236i \(-0.776759\pi\)
−0.170496 + 0.985358i \(0.554537\pi\)
\(44\) 2.58544 4.76816i 0.389770 0.718827i
\(45\) 0 0
\(46\) −1.24703 0.316335i −0.183865 0.0466410i
\(47\) −0.225833 + 1.28076i −0.0329411 + 0.186818i −0.996838 0.0794561i \(-0.974682\pi\)
0.963897 + 0.266275i \(0.0857928\pi\)
\(48\) 0 0
\(49\) 1.34241 + 0.488598i 0.191773 + 0.0697997i
\(50\) −8.54287 + 4.12354i −1.20814 + 0.583157i
\(51\) 0 0
\(52\) −0.734968 + 4.93668i −0.101922 + 0.684595i
\(53\) 10.3399 1.42029 0.710146 0.704054i \(-0.248629\pi\)
0.710146 + 0.704054i \(0.248629\pi\)
\(54\) 0 0
\(55\) 9.27950i 1.25125i
\(56\) 8.14496 1.04312i 1.08842 0.139393i
\(57\) 0 0
\(58\) 11.6422 5.61953i 1.52869 0.737881i
\(59\) −2.96267 + 8.13988i −0.385707 + 1.05972i 0.583207 + 0.812324i \(0.301798\pi\)
−0.968914 + 0.247398i \(0.920425\pi\)
\(60\) 0 0
\(61\) −0.720351 0.127017i −0.0922315 0.0162629i 0.127342 0.991859i \(-0.459355\pi\)
−0.219573 + 0.975596i \(0.570467\pi\)
\(62\) 1.02575 4.04363i 0.130270 0.513542i
\(63\) 0 0
\(64\) 6.58539 4.54231i 0.823174 0.567789i
\(65\) 2.92046 + 8.02391i 0.362239 + 0.995243i
\(66\) 0 0
\(67\) 5.00144 4.19671i 0.611023 0.512709i −0.283944 0.958841i \(-0.591643\pi\)
0.894968 + 0.446131i \(0.147199\pi\)
\(68\) 9.43778 + 3.15196i 1.14450 + 0.382232i
\(69\) 0 0
\(70\) 11.3990 8.21095i 1.36244 0.981396i
\(71\) −5.18176 8.97507i −0.614961 1.06514i −0.990391 0.138294i \(-0.955838\pi\)
0.375430 0.926851i \(-0.377495\pi\)
\(72\) 0 0
\(73\) −7.34034 + 12.7138i −0.859122 + 1.48804i 0.0136452 + 0.999907i \(0.495656\pi\)
−0.872767 + 0.488136i \(0.837677\pi\)
\(74\) −1.60455 15.8902i −0.186525 1.84720i
\(75\) 0 0
\(76\) 5.15651 1.05211i 0.591492 0.120685i
\(77\) 1.36722 + 7.75387i 0.155809 + 0.883635i
\(78\) 0 0
\(79\) −5.64811 + 6.73115i −0.635462 + 0.757314i −0.983646 0.180112i \(-0.942354\pi\)
0.348184 + 0.937426i \(0.386798\pi\)
\(80\) 6.19991 12.2018i 0.693171 1.36420i
\(81\) 0 0
\(82\) −6.44017 + 1.81826i −0.711197 + 0.200793i
\(83\) −3.15228 + 3.75674i −0.346007 + 0.412356i −0.910781 0.412891i \(-0.864519\pi\)
0.564773 + 0.825246i \(0.308964\pi\)
\(84\) 0 0
\(85\) 16.7644 2.95601i 1.81835 0.320625i
\(86\) 0.680867 9.19700i 0.0734198 0.991738i
\(87\) 0 0
\(88\) 4.64815 + 6.10199i 0.495495 + 0.650475i
\(89\) 4.90094 + 2.82956i 0.519499 + 0.299933i 0.736730 0.676187i \(-0.236369\pi\)
−0.217231 + 0.976120i \(0.569702\pi\)
\(90\) 0 0
\(91\) −3.62253 6.27441i −0.379745 0.657737i
\(92\) 1.13182 1.42453i 0.118001 0.148518i
\(93\) 0 0
\(94\) −1.52056 1.03469i −0.156834 0.106720i
\(95\) 6.89717 5.78741i 0.707635 0.593776i
\(96\) 0 0
\(97\) −0.126739 + 0.0461291i −0.0128684 + 0.00468370i −0.348446 0.937329i \(-0.613291\pi\)
0.335578 + 0.942012i \(0.391068\pi\)
\(98\) −1.40934 + 1.44754i −0.142365 + 0.146223i
\(99\) 0 0
\(100\) −0.358675 13.4104i −0.0358675 1.34104i
\(101\) −2.26461 + 12.8432i −0.225337 + 1.27795i 0.636704 + 0.771109i \(0.280298\pi\)
−0.862040 + 0.506840i \(0.830814\pi\)
\(102\) 0 0
\(103\) −0.422665 + 1.16126i −0.0416464 + 0.114423i −0.958773 0.284174i \(-0.908281\pi\)
0.917126 + 0.398597i \(0.130503\pi\)
\(104\) −5.93965 3.81347i −0.582431 0.373941i
\(105\) 0 0
\(106\) −6.00213 + 13.3342i −0.582979 + 1.29513i
\(107\) 15.9792i 1.54476i −0.635159 0.772382i \(-0.719065\pi\)
0.635159 0.772382i \(-0.280935\pi\)
\(108\) 0 0
\(109\) 2.38211i 0.228165i −0.993471 0.114082i \(-0.963607\pi\)
0.993471 0.114082i \(-0.0363927\pi\)
\(110\) 11.9667 + 5.38659i 1.14098 + 0.513591i
\(111\) 0 0
\(112\) −3.38282 + 11.1092i −0.319646 + 1.04972i
\(113\) 3.24570 8.91748i 0.305330 0.838886i −0.688221 0.725501i \(-0.741608\pi\)
0.993551 0.113386i \(-0.0361695\pi\)
\(114\) 0 0
\(115\) 0.540517 3.06542i 0.0504035 0.285852i
\(116\) 0.488800 + 18.2757i 0.0453840 + 1.69685i
\(117\) 0 0
\(118\) −8.77731 8.54569i −0.808017 0.786695i
\(119\) −13.5726 + 4.94004i −1.24420 + 0.452853i
\(120\) 0 0
\(121\) 2.79226 2.34299i 0.253842 0.212999i
\(122\) 0.581952 0.855225i 0.0526874 0.0774284i
\(123\) 0 0
\(124\) 4.61919 + 3.67005i 0.414816 + 0.329580i
\(125\) −2.92143 5.06006i −0.261300 0.452586i
\(126\) 0 0
\(127\) 3.94090 + 2.27528i 0.349698 + 0.201898i 0.664552 0.747242i \(-0.268622\pi\)
−0.314854 + 0.949140i \(0.601956\pi\)
\(128\) 2.03501 + 11.1292i 0.179871 + 0.983690i
\(129\) 0 0
\(130\) −12.0428 0.891548i −1.05623 0.0781939i
\(131\) −1.53208 + 0.270147i −0.133858 + 0.0236028i −0.240176 0.970729i \(-0.577205\pi\)
0.106318 + 0.994332i \(0.466094\pi\)
\(132\) 0 0
\(133\) −4.91051 + 5.85212i −0.425796 + 0.507443i
\(134\) 2.50877 + 8.88592i 0.216725 + 0.767627i
\(135\) 0 0
\(136\) −9.54321 + 10.3412i −0.818323 + 0.886749i
\(137\) 0.557261 0.664118i 0.0476101 0.0567394i −0.741714 0.670716i \(-0.765987\pi\)
0.789324 + 0.613977i \(0.210431\pi\)
\(138\) 0 0
\(139\) −2.63752 14.9581i −0.223711 1.26873i −0.865133 0.501542i \(-0.832766\pi\)
0.641422 0.767188i \(-0.278345\pi\)
\(140\) 3.97182 + 19.4663i 0.335680 + 1.64521i
\(141\) 0 0
\(142\) 14.5821 1.47246i 1.22370 0.123566i
\(143\) 3.38397 5.86120i 0.282981 0.490138i
\(144\) 0 0
\(145\) 15.6388 + 27.0871i 1.29873 + 2.24946i
\(146\) −12.1347 16.8462i −1.00427 1.39420i
\(147\) 0 0
\(148\) 21.4232 + 7.15479i 1.76098 + 0.588120i
\(149\) −6.54605 + 5.49279i −0.536273 + 0.449987i −0.870261 0.492591i \(-0.836050\pi\)
0.333988 + 0.942577i \(0.391606\pi\)
\(150\) 0 0
\(151\) −3.59322 9.87229i −0.292412 0.803396i −0.995712 0.0925028i \(-0.970513\pi\)
0.703300 0.710893i \(-0.251709\pi\)
\(152\) −1.63648 + 7.26051i −0.132736 + 0.588905i
\(153\) 0 0
\(154\) −10.7929 2.73784i −0.869720 0.220622i
\(155\) 9.93995 + 1.75268i 0.798396 + 0.140779i
\(156\) 0 0
\(157\) −3.29479 + 9.05237i −0.262953 + 0.722458i 0.736012 + 0.676969i \(0.236707\pi\)
−0.998965 + 0.0454891i \(0.985515\pi\)
\(158\) −5.40179 11.1911i −0.429743 0.890313i
\(159\) 0 0
\(160\) 12.1363 + 15.0783i 0.959459 + 1.19204i
\(161\) 2.64108i 0.208146i
\(162\) 0 0
\(163\) 19.6202 1.53678 0.768388 0.639984i \(-0.221059\pi\)
0.768388 + 0.639984i \(0.221059\pi\)
\(164\) 1.39360 9.36064i 0.108822 0.730943i
\(165\) 0 0
\(166\) −3.01480 6.24587i −0.233994 0.484773i
\(167\) −10.7043 3.89606i −0.828327 0.301486i −0.107155 0.994242i \(-0.534174\pi\)
−0.721172 + 0.692756i \(0.756396\pi\)
\(168\) 0 0
\(169\) 1.17599 6.66936i 0.0904606 0.513028i
\(170\) −5.91940 + 23.3351i −0.453998 + 1.78972i
\(171\) 0 0
\(172\) 11.4651 + 6.21674i 0.874207 + 0.474022i
\(173\) 14.8832 5.41704i 1.13155 0.411850i 0.292694 0.956206i \(-0.405448\pi\)
0.838854 + 0.544356i \(0.183226\pi\)
\(174\) 0 0
\(175\) 12.5174 + 14.9176i 0.946223 + 1.12767i
\(176\) −10.5672 + 2.45210i −0.796536 + 0.184834i
\(177\) 0 0
\(178\) −6.49389 + 4.67769i −0.486737 + 0.350608i
\(179\) −13.6572 + 7.88498i −1.02079 + 0.589351i −0.914331 0.404967i \(-0.867283\pi\)
−0.106454 + 0.994318i \(0.533950\pi\)
\(180\) 0 0
\(181\) −4.39147 2.53542i −0.326416 0.188456i 0.327833 0.944736i \(-0.393682\pi\)
−0.654249 + 0.756280i \(0.727015\pi\)
\(182\) 10.1942 1.02939i 0.755647 0.0763033i
\(183\) 0 0
\(184\) 1.18006 + 2.28650i 0.0869949 + 0.168563i
\(185\) 38.0543 6.70999i 2.79780 0.493328i
\(186\) 0 0
\(187\) −10.3358 8.67280i −0.755832 0.634218i
\(188\) 2.21699 1.36028i 0.161691 0.0992087i
\(189\) 0 0
\(190\) 3.45969 + 12.2540i 0.250992 + 0.888999i
\(191\) 19.1259 + 16.0486i 1.38390 + 1.16123i 0.967742 + 0.251944i \(0.0810697\pi\)
0.416163 + 0.909290i \(0.363375\pi\)
\(192\) 0 0
\(193\) −1.63585 9.27734i −0.117751 0.667798i −0.985351 0.170536i \(-0.945450\pi\)
0.867601 0.497262i \(-0.165661\pi\)
\(194\) 0.0140821 0.190218i 0.00101104 0.0136569i
\(195\) 0 0
\(196\) −1.04863 2.65774i −0.0749021 0.189838i
\(197\) 0.195281 0.338236i 0.0139132 0.0240983i −0.858985 0.512001i \(-0.828904\pi\)
0.872898 + 0.487902i \(0.162238\pi\)
\(198\) 0 0
\(199\) −6.27422 + 3.62242i −0.444768 + 0.256787i −0.705618 0.708592i \(-0.749330\pi\)
0.260850 + 0.965379i \(0.415997\pi\)
\(200\) 17.5022 + 7.32199i 1.23759 + 0.517743i
\(201\) 0 0
\(202\) −15.2479 10.3757i −1.07284 0.730031i
\(203\) −17.0586 20.3296i −1.19728 1.42686i
\(204\) 0 0
\(205\) −5.53760 15.2144i −0.386763 1.06262i
\(206\) −1.25220 1.21916i −0.0872450 0.0849427i
\(207\) 0 0
\(208\) 8.36568 5.44606i 0.580055 0.377616i
\(209\) −7.02788 1.23920i −0.486128 0.0857176i
\(210\) 0 0
\(211\) 20.9809 + 7.63642i 1.44438 + 0.525713i 0.941017 0.338359i \(-0.109872\pi\)
0.503368 + 0.864072i \(0.332094\pi\)
\(212\) −13.7115 15.4806i −0.941710 1.06321i
\(213\) 0 0
\(214\) 20.6065 + 9.27563i 1.40863 + 0.634069i
\(215\) 22.3127 1.52171
\(216\) 0 0
\(217\) −8.56397 −0.581360
\(218\) 3.07194 + 1.38277i 0.208058 + 0.0936532i
\(219\) 0 0
\(220\) −13.8930 + 12.3053i −0.936664 + 0.829626i
\(221\) 11.6668 + 4.24638i 0.784797 + 0.285643i
\(222\) 0 0
\(223\) 7.83765 + 1.38199i 0.524848 + 0.0925448i 0.429793 0.902927i \(-0.358586\pi\)
0.0950544 + 0.995472i \(0.469697\pi\)
\(224\) −12.3626 10.8111i −0.826010 0.722349i
\(225\) 0 0
\(226\) 9.61581 + 9.36207i 0.639634 + 0.622755i
\(227\) 2.95471 + 8.11801i 0.196111 + 0.538811i 0.998302 0.0582571i \(-0.0185543\pi\)
−0.802190 + 0.597068i \(0.796332\pi\)
\(228\) 0 0
\(229\) 4.90565 + 5.84633i 0.324175 + 0.386336i 0.903377 0.428848i \(-0.141080\pi\)
−0.579202 + 0.815184i \(0.696636\pi\)
\(230\) 3.63938 + 2.47647i 0.239973 + 0.163294i
\(231\) 0 0
\(232\) −23.8518 9.97836i −1.56595 0.655111i
\(233\) 6.15633 3.55436i 0.403315 0.232854i −0.284599 0.958647i \(-0.591860\pi\)
0.687913 + 0.725793i \(0.258527\pi\)
\(234\) 0 0
\(235\) 2.22496 3.85374i 0.145140 0.251390i
\(236\) 16.1155 6.35849i 1.04903 0.413902i
\(237\) 0 0
\(238\) 1.50808 20.3707i 0.0977540 1.32044i
\(239\) 0.386367 + 2.19120i 0.0249920 + 0.141737i 0.994751 0.102330i \(-0.0326297\pi\)
−0.969759 + 0.244066i \(0.921519\pi\)
\(240\) 0 0
\(241\) 0.156407 + 0.131241i 0.0100750 + 0.00845397i 0.647811 0.761801i \(-0.275685\pi\)
−0.637736 + 0.770255i \(0.720129\pi\)
\(242\) 1.40063 + 4.96094i 0.0900358 + 0.318901i
\(243\) 0 0
\(244\) 0.765075 + 1.24692i 0.0489789 + 0.0798260i
\(245\) −3.74445 3.14197i −0.239224 0.200733i
\(246\) 0 0
\(247\) 6.46696 1.14030i 0.411483 0.0725555i
\(248\) −7.41422 + 3.82645i −0.470804 + 0.242980i
\(249\) 0 0
\(250\) 8.22124 0.830159i 0.519957 0.0525039i
\(251\) −11.4836 6.63004i −0.724837 0.418485i 0.0916936 0.995787i \(-0.470772\pi\)
−0.816530 + 0.577303i \(0.804105\pi\)
\(252\) 0 0
\(253\) −2.13661 + 1.23357i −0.134328 + 0.0775541i
\(254\) −5.22180 + 3.76138i −0.327645 + 0.236010i
\(255\) 0 0
\(256\) −15.5334 3.83599i −0.970835 0.239749i
\(257\) −14.5879 17.3851i −0.909966 1.08446i −0.996105 0.0881721i \(-0.971897\pi\)
0.0861393 0.996283i \(-0.472547\pi\)
\(258\) 0 0
\(259\) −30.8092 + 11.2136i −1.91439 + 0.696781i
\(260\) 8.14039 15.0128i 0.504845 0.931052i
\(261\) 0 0
\(262\) 0.540968 2.13257i 0.0334211 0.131750i
\(263\) 3.05022 17.2987i 0.188085 1.06668i −0.733843 0.679319i \(-0.762275\pi\)
0.921927 0.387363i \(-0.126614\pi\)
\(264\) 0 0
\(265\) −33.2457 12.1005i −2.04227 0.743325i
\(266\) −4.69636 9.72960i −0.287952 0.596560i
\(267\) 0 0
\(268\) −12.9155 1.92284i −0.788939 0.117456i
\(269\) −25.2404 −1.53894 −0.769468 0.638686i \(-0.779478\pi\)
−0.769468 + 0.638686i \(0.779478\pi\)
\(270\) 0 0
\(271\) 28.2779i 1.71776i 0.512175 + 0.858881i \(0.328840\pi\)
−0.512175 + 0.858881i \(0.671160\pi\)
\(272\) −7.79621 18.3097i −0.472714 1.11019i
\(273\) 0 0
\(274\) 0.532958 + 1.10415i 0.0321972 + 0.0667040i
\(275\) −6.22172 + 17.0940i −0.375184 + 1.03081i
\(276\) 0 0
\(277\) 10.7115 + 1.88873i 0.643592 + 0.113483i 0.485912 0.874008i \(-0.338488\pi\)
0.157680 + 0.987490i \(0.449599\pi\)
\(278\) 20.8208 + 5.28162i 1.24875 + 0.316770i
\(279\) 0 0
\(280\) −27.4091 6.17787i −1.63801 0.369199i
\(281\) −1.98862 5.46370i −0.118631 0.325937i 0.866137 0.499806i \(-0.166595\pi\)
−0.984769 + 0.173869i \(0.944373\pi\)
\(282\) 0 0
\(283\) 6.97262 5.85072i 0.414479 0.347789i −0.411579 0.911374i \(-0.635023\pi\)
0.826058 + 0.563585i \(0.190578\pi\)
\(284\) −6.56578 + 19.6596i −0.389607 + 1.16658i
\(285\) 0 0
\(286\) 5.59420 + 7.76625i 0.330792 + 0.459228i
\(287\) 6.86883 + 11.8972i 0.405454 + 0.702267i
\(288\) 0 0
\(289\) 3.87581 6.71310i 0.227989 0.394888i
\(290\) −44.0093 + 4.44394i −2.58432 + 0.260957i
\(291\) 0 0
\(292\) 28.7687 5.86982i 1.68356 0.343505i
\(293\) 0.704403 + 3.99487i 0.0411517 + 0.233383i 0.998446 0.0557335i \(-0.0177497\pi\)
−0.957294 + 0.289116i \(0.906639\pi\)
\(294\) 0 0
\(295\) 19.0517 22.7049i 1.10923 1.32193i
\(296\) −21.6626 + 23.4739i −1.25911 + 1.36440i
\(297\) 0 0
\(298\) −3.28357 11.6302i −0.190212 0.673719i
\(299\) 1.45928 1.73910i 0.0843922 0.100575i
\(300\) 0 0
\(301\) −18.6443 + 3.28749i −1.07464 + 0.189488i
\(302\) 14.8170 + 1.09692i 0.852623 + 0.0631209i
\(303\) 0 0
\(304\) −8.41312 6.32499i −0.482526 0.362763i
\(305\) 2.16749 + 1.25140i 0.124110 + 0.0716551i
\(306\) 0 0
\(307\) −16.8379 29.1641i −0.960989 1.66448i −0.720025 0.693948i \(-0.755870\pi\)
−0.240964 0.970534i \(-0.577464\pi\)
\(308\) 9.79582 12.3292i 0.558169 0.702521i
\(309\) 0 0
\(310\) −8.03021 + 11.8010i −0.456085 + 0.670254i
\(311\) −9.39589 + 7.88409i −0.532792 + 0.447066i −0.869064 0.494699i \(-0.835278\pi\)
0.336272 + 0.941765i \(0.390834\pi\)
\(312\) 0 0
\(313\) −5.01611 + 1.82572i −0.283528 + 0.103196i −0.479869 0.877340i \(-0.659316\pi\)
0.196342 + 0.980535i \(0.437094\pi\)
\(314\) −9.76126 9.50368i −0.550860 0.536324i
\(315\) 0 0
\(316\) 17.5675 0.469860i 0.988250 0.0264317i
\(317\) 0.00253246 0.0143623i 0.000142237 0.000806666i −0.984737 0.174051i \(-0.944314\pi\)
0.984879 + 0.173245i \(0.0554252\pi\)
\(318\) 0 0
\(319\) 8.47891 23.2956i 0.474728 1.30430i
\(320\) −26.4897 + 6.89817i −1.48082 + 0.385619i
\(321\) 0 0
\(322\) −3.40591 1.53310i −0.189804 0.0854365i
\(323\) 13.0914i 0.728422i
\(324\) 0 0
\(325\) 16.7392i 0.928523i
\(326\) −11.3892 + 25.3021i −0.630791 + 1.40135i
\(327\) 0 0
\(328\) 11.2624 + 7.23087i 0.621863 + 0.399258i
\(329\) −1.29136 + 3.54797i −0.0711947 + 0.195606i
\(330\) 0 0
\(331\) 0.663118 3.76073i 0.0364482 0.206708i −0.961145 0.276043i \(-0.910977\pi\)
0.997593 + 0.0693351i \(0.0220878\pi\)
\(332\) 9.80464 0.262235i 0.538100 0.0143920i
\(333\) 0 0
\(334\) 11.2380 11.5426i 0.614917 0.631583i
\(335\) −20.9924 + 7.64060i −1.14694 + 0.417450i
\(336\) 0 0
\(337\) 6.62429 5.55844i 0.360848 0.302787i −0.444281 0.895888i \(-0.646541\pi\)
0.805129 + 0.593100i \(0.202096\pi\)
\(338\) 7.91809 + 5.38799i 0.430687 + 0.293068i
\(339\) 0 0
\(340\) −26.6565 21.1792i −1.44565 1.14860i
\(341\) −3.99999 6.92818i −0.216611 0.375182i
\(342\) 0 0
\(343\) −14.0079 8.08749i −0.756358 0.436684i
\(344\) −14.6723 + 11.1766i −0.791080 + 0.602600i
\(345\) 0 0
\(346\) −1.65369 + 22.3377i −0.0889031 + 1.20088i
\(347\) 24.1858 4.26461i 1.29836 0.228936i 0.518602 0.855016i \(-0.326453\pi\)
0.779759 + 0.626079i \(0.215341\pi\)
\(348\) 0 0
\(349\) 4.36508 5.20210i 0.233658 0.278462i −0.636457 0.771313i \(-0.719601\pi\)
0.870114 + 0.492850i \(0.164045\pi\)
\(350\) −26.5037 + 7.48282i −1.41668 + 0.399974i
\(351\) 0 0
\(352\) 2.97190 15.0508i 0.158403 0.802210i
\(353\) −9.32471 + 11.1128i −0.496304 + 0.591472i −0.954809 0.297220i \(-0.903941\pi\)
0.458505 + 0.888692i \(0.348385\pi\)
\(354\) 0 0
\(355\) 6.15760 + 34.9215i 0.326812 + 1.85344i
\(356\) −2.26270 11.0898i −0.119923 0.587756i
\(357\) 0 0
\(358\) −2.24061 22.1893i −0.118420 1.17274i
\(359\) −1.61294 + 2.79370i −0.0851279 + 0.147446i −0.905446 0.424462i \(-0.860463\pi\)
0.820318 + 0.571908i \(0.193797\pi\)
\(360\) 0 0
\(361\) 6.03793 + 10.4580i 0.317786 + 0.550422i
\(362\) 5.81882 4.19142i 0.305830 0.220296i
\(363\) 0 0
\(364\) −4.59010 + 13.7439i −0.240586 + 0.720377i
\(365\) 38.4800 32.2885i 2.01413 1.69006i
\(366\) 0 0
\(367\) −10.2734 28.2260i −0.536268 1.47338i −0.851492 0.524367i \(-0.824302\pi\)
0.315224 0.949017i \(-0.397920\pi\)
\(368\) −3.63365 + 0.194510i −0.189417 + 0.0101396i
\(369\) 0 0
\(370\) −13.4367 + 52.9694i −0.698542 + 2.75375i
\(371\) 29.5627 + 5.21270i 1.53482 + 0.270630i
\(372\) 0 0
\(373\) 5.31103 14.5919i 0.274995 0.755542i −0.722916 0.690936i \(-0.757199\pi\)
0.997911 0.0646062i \(-0.0205791\pi\)
\(374\) 17.1841 8.29457i 0.888570 0.428902i
\(375\) 0 0
\(376\) 0.467277 + 3.64863i 0.0240980 + 0.188164i
\(377\) 22.8120i 1.17488i
\(378\) 0 0
\(379\) −6.68763 −0.343521 −0.171760 0.985139i \(-0.554945\pi\)
−0.171760 + 0.985139i \(0.554945\pi\)
\(380\) −17.8109 2.65167i −0.913681 0.136028i
\(381\) 0 0
\(382\) −31.7983 + 15.3487i −1.62694 + 0.785306i
\(383\) 6.52420 + 2.37461i 0.333371 + 0.121337i 0.503282 0.864122i \(-0.332126\pi\)
−0.169911 + 0.985459i \(0.554348\pi\)
\(384\) 0 0
\(385\) 4.67812 26.5309i 0.238419 1.35214i
\(386\) 12.9135 + 3.27577i 0.657282 + 0.166732i
\(387\) 0 0
\(388\) 0.237129 + 0.128579i 0.0120384 + 0.00652759i
\(389\) −1.33770 + 0.486883i −0.0678241 + 0.0246860i −0.375709 0.926738i \(-0.622601\pi\)
0.307885 + 0.951423i \(0.400379\pi\)
\(390\) 0 0
\(391\) −2.90920 3.46705i −0.147125 0.175336i
\(392\) 4.03610 + 0.190472i 0.203854 + 0.00962028i
\(393\) 0 0
\(394\) 0.322828 + 0.448172i 0.0162639 + 0.0225786i
\(395\) 26.0376 15.0328i 1.31009 0.756382i
\(396\) 0 0
\(397\) 16.5544 + 9.55769i 0.830842 + 0.479687i 0.854141 0.520042i \(-0.174084\pi\)
−0.0232990 + 0.999729i \(0.507417\pi\)
\(398\) −1.02936 10.1939i −0.0515969 0.510975i
\(399\) 0 0
\(400\) −19.6021 + 18.3203i −0.980104 + 0.916015i
\(401\) 18.4212 3.24815i 0.919909 0.162205i 0.306409 0.951900i \(-0.400872\pi\)
0.613500 + 0.789695i \(0.289761\pi\)
\(402\) 0 0
\(403\) 5.63921 + 4.73186i 0.280909 + 0.235711i
\(404\) 22.2315 13.6406i 1.10606 0.678646i
\(405\) 0 0
\(406\) 36.1190 10.1975i 1.79256 0.506095i
\(407\) −23.4618 19.6868i −1.16296 0.975838i
\(408\) 0 0
\(409\) −3.21877 18.2546i −0.159158 0.902630i −0.954885 0.296975i \(-0.904022\pi\)
0.795727 0.605655i \(-0.207089\pi\)
\(410\) 22.8349 + 1.69050i 1.12773 + 0.0834877i
\(411\) 0 0
\(412\) 2.29909 0.907124i 0.113268 0.0446908i
\(413\) −12.5742 + 21.7791i −0.618734 + 1.07168i
\(414\) 0 0
\(415\) 14.5319 8.38999i 0.713342 0.411848i
\(416\) 2.16704 + 13.9496i 0.106248 + 0.683937i
\(417\) 0 0
\(418\) 5.67763 8.34373i 0.277702 0.408105i
\(419\) 14.4375 + 17.2059i 0.705317 + 0.840564i 0.993117 0.117126i \(-0.0373682\pi\)
−0.287800 + 0.957691i \(0.592924\pi\)
\(420\) 0 0
\(421\) 5.98056 + 16.4314i 0.291475 + 0.800820i 0.995851 + 0.0909935i \(0.0290043\pi\)
−0.704377 + 0.709826i \(0.748774\pi\)
\(422\) −22.0269 + 22.6239i −1.07225 + 1.10131i
\(423\) 0 0
\(424\) 27.9229 8.69599i 1.35605 0.422314i
\(425\) −32.8641 5.79483i −1.59414 0.281090i
\(426\) 0 0
\(427\) −1.99552 0.726309i −0.0965698 0.0351485i
\(428\) −23.9235 + 21.1896i −1.15639 + 1.02424i
\(429\) 0 0
\(430\) −12.9522 + 28.7742i −0.624608 + 1.38762i
\(431\) −13.1374 −0.632807 −0.316403 0.948625i \(-0.602475\pi\)
−0.316403 + 0.948625i \(0.602475\pi\)
\(432\) 0 0
\(433\) −22.6607 −1.08900 −0.544502 0.838759i \(-0.683281\pi\)
−0.544502 + 0.838759i \(0.683281\pi\)
\(434\) 4.97124 11.0440i 0.238627 0.530129i
\(435\) 0 0
\(436\) −3.56642 + 3.15886i −0.170800 + 0.151282i
\(437\) −2.24943 0.818727i −0.107605 0.0391650i
\(438\) 0 0
\(439\) −14.8982 2.62696i −0.711053 0.125378i −0.193589 0.981083i \(-0.562013\pi\)
−0.517464 + 0.855705i \(0.673124\pi\)
\(440\) −7.80418 25.0593i −0.372050 1.19465i
\(441\) 0 0
\(442\) −12.2485 + 12.5805i −0.582602 + 0.598392i
\(443\) −1.36146 3.74057i −0.0646848 0.177720i 0.903139 0.429347i \(-0.141256\pi\)
−0.967824 + 0.251628i \(0.919034\pi\)
\(444\) 0 0
\(445\) −12.4466 14.8333i −0.590026 0.703165i
\(446\) −6.33182 + 9.30512i −0.299821 + 0.440610i
\(447\) 0 0
\(448\) 21.1182 9.66697i 0.997741 0.456721i
\(449\) −22.3682 + 12.9143i −1.05562 + 0.609464i −0.924218 0.381865i \(-0.875282\pi\)
−0.131404 + 0.991329i \(0.541948\pi\)
\(450\) 0 0
\(451\) −6.41647 + 11.1136i −0.302140 + 0.523321i
\(452\) −17.6550 + 6.96592i −0.830423 + 0.327649i
\(453\) 0 0
\(454\) −12.1841 0.902004i −0.571826 0.0423331i
\(455\) 4.30474 + 24.4134i 0.201809 + 1.14452i
\(456\) 0 0
\(457\) 2.14884 + 1.80309i 0.100518 + 0.0843449i 0.691662 0.722221i \(-0.256879\pi\)
−0.591143 + 0.806566i \(0.701323\pi\)
\(458\) −10.3870 + 2.93258i −0.485353 + 0.137030i
\(459\) 0 0
\(460\) −5.30623 + 3.25575i −0.247404 + 0.151800i
\(461\) −11.5119 9.65964i −0.536163 0.449894i 0.334060 0.942552i \(-0.391581\pi\)
−0.870223 + 0.492657i \(0.836026\pi\)
\(462\) 0 0
\(463\) −21.5380 + 3.79772i −1.00095 + 0.176495i −0.650030 0.759909i \(-0.725244\pi\)
−0.350924 + 0.936404i \(0.614132\pi\)
\(464\) 26.7136 24.9668i 1.24015 1.15905i
\(465\) 0 0
\(466\) 1.01001 + 10.0024i 0.0467880 + 0.463351i
\(467\) 16.2109 + 9.35938i 0.750152 + 0.433100i 0.825749 0.564038i \(-0.190753\pi\)
−0.0755968 + 0.997138i \(0.524086\pi\)
\(468\) 0 0
\(469\) 16.4153 9.47738i 0.757988 0.437625i
\(470\) 3.67819 + 5.10631i 0.169662 + 0.235536i
\(471\) 0 0
\(472\) −1.15495 + 24.4734i −0.0531608 + 1.12648i
\(473\) −11.3678 13.5476i −0.522691 0.622919i
\(474\) 0 0
\(475\) −16.5858 + 6.03674i −0.761009 + 0.276985i
\(476\) 25.3945 + 13.7697i 1.16395 + 0.631132i
\(477\) 0 0
\(478\) −3.05002 0.773698i −0.139505 0.0353881i
\(479\) 3.48398 19.7587i 0.159187 0.902796i −0.795670 0.605731i \(-0.792881\pi\)
0.954857 0.297065i \(-0.0960080\pi\)
\(480\) 0 0
\(481\) 26.4831 + 9.63907i 1.20753 + 0.439504i
\(482\) −0.260038 + 0.125517i −0.0118444 + 0.00571716i
\(483\) 0 0
\(484\) −7.21061 1.07351i −0.327755 0.0487958i
\(485\) 0.461485 0.0209550
\(486\) 0 0
\(487\) 14.0996i 0.638916i 0.947600 + 0.319458i \(0.103501\pi\)
−0.947600 + 0.319458i \(0.896499\pi\)
\(488\) −2.05213 + 0.262815i −0.0928956 + 0.0118971i
\(489\) 0 0
\(490\) 6.22544 3.00494i 0.281237 0.135749i
\(491\) −0.766879 + 2.10698i −0.0346088 + 0.0950868i −0.955794 0.294039i \(-0.905001\pi\)
0.921185 + 0.389125i \(0.127223\pi\)
\(492\) 0 0
\(493\) 44.7869 + 7.89715i 2.01710 + 0.355670i
\(494\) −2.28344 + 9.00164i −0.102737 + 0.405003i
\(495\) 0 0
\(496\) −0.630720 11.7825i −0.0283201 0.529049i
\(497\) −10.2905 28.2729i −0.461591 1.26821i
\(498\) 0 0
\(499\) −7.09602 + 5.95427i −0.317661 + 0.266550i −0.787650 0.616123i \(-0.788702\pi\)
0.469989 + 0.882672i \(0.344258\pi\)
\(500\) −3.70173 + 11.0839i −0.165546 + 0.495688i
\(501\) 0 0
\(502\) 15.2161 10.9605i 0.679126 0.489189i
\(503\) 7.08381 + 12.2695i 0.315852 + 0.547071i 0.979618 0.200869i \(-0.0643765\pi\)
−0.663767 + 0.747940i \(0.731043\pi\)
\(504\) 0 0
\(505\) 22.3114 38.6445i 0.992844 1.71966i
\(506\) −0.350535 3.47142i −0.0155832 0.154323i
\(507\) 0 0
\(508\) −1.81946 8.91739i −0.0807255 0.395645i
\(509\) 7.28735 + 41.3286i 0.323006 + 1.83186i 0.523333 + 0.852129i \(0.324689\pi\)
−0.200327 + 0.979729i \(0.564200\pi\)
\(510\) 0 0
\(511\) −27.3962 + 32.6495i −1.21194 + 1.44433i
\(512\) 13.9637 17.8049i 0.617114 0.786874i
\(513\) 0 0
\(514\) 30.8877 8.72056i 1.36240 0.384647i
\(515\) 2.71798 3.23916i 0.119769 0.142735i
\(516\) 0 0
\(517\) −3.47343 + 0.612460i −0.152761 + 0.0269359i
\(518\) 3.42325 46.2405i 0.150409 2.03169i
\(519\) 0 0
\(520\) 14.6349 + 19.2124i 0.641784 + 0.842520i
\(521\) −4.99532 2.88405i −0.218849 0.126353i 0.386568 0.922261i \(-0.373660\pi\)
−0.605417 + 0.795908i \(0.706994\pi\)
\(522\) 0 0
\(523\) −3.83688 6.64566i −0.167775 0.290595i 0.769862 0.638210i \(-0.220325\pi\)
−0.937637 + 0.347615i \(0.886991\pi\)
\(524\) 2.43611 + 1.93555i 0.106422 + 0.0845547i
\(525\) 0 0
\(526\) 20.5376 + 13.9751i 0.895481 + 0.609344i
\(527\) 11.2423 9.43339i 0.489721 0.410925i
\(528\) 0 0
\(529\) 20.8353 7.58341i 0.905881 0.329714i
\(530\) 34.9032 35.8492i 1.51610 1.55719i
\(531\) 0 0
\(532\) 15.2733 0.408501i 0.662183 0.0177107i
\(533\) 2.05056 11.6293i 0.0888195 0.503720i
\(534\) 0 0
\(535\) −18.6999 + 51.3776i −0.808468 + 2.22125i
\(536\) 9.97690 15.5395i 0.430937 0.671204i
\(537\) 0 0
\(538\) 14.6516 32.5498i 0.631677 1.40332i
\(539\) 3.87427i 0.166877i
\(540\) 0 0
\(541\) 34.8844i 1.49980i 0.661552 + 0.749899i \(0.269898\pi\)
−0.661552 + 0.749899i \(0.730102\pi\)
\(542\) −36.4669 16.4149i −1.56639 0.705079i
\(543\) 0 0
\(544\) 28.1375 + 0.574577i 1.20639 + 0.0246348i
\(545\) −2.78771 + 7.65917i −0.119412 + 0.328083i
\(546\) 0 0
\(547\) −5.15974 + 29.2623i −0.220614 + 1.25117i 0.650279 + 0.759695i \(0.274652\pi\)
−0.870894 + 0.491471i \(0.836459\pi\)
\(548\) −1.73327 + 0.0463580i −0.0740416 + 0.00198032i
\(549\) 0 0
\(550\) −18.4327 17.9463i −0.785971 0.765231i
\(551\) 22.6030 8.22683i 0.962921 0.350475i
\(552\) 0 0
\(553\) −19.5419 + 16.3976i −0.831005 + 0.697296i
\(554\) −8.65353 + 12.7171i −0.367653 + 0.540296i
\(555\) 0 0
\(556\) −18.8973 + 23.7844i −0.801422 + 1.00868i
\(557\) 8.65814 + 14.9963i 0.366857 + 0.635415i 0.989072 0.147431i \(-0.0471004\pi\)
−0.622215 + 0.782846i \(0.713767\pi\)
\(558\) 0 0
\(559\) 14.0934 + 8.13680i 0.596085 + 0.344150i
\(560\) 23.8775 31.7604i 1.00901 1.34212i
\(561\) 0 0
\(562\) 8.20029 + 0.607080i 0.345908 + 0.0256081i
\(563\) −19.0265 + 3.35488i −0.801870 + 0.141391i −0.559541 0.828803i \(-0.689022\pi\)
−0.242329 + 0.970194i \(0.577911\pi\)
\(564\) 0 0
\(565\) −20.8717 + 24.8739i −0.878080 + 1.04645i
\(566\) 3.49753 + 12.3881i 0.147012 + 0.520709i
\(567\) 0 0
\(568\) −21.5415 19.8792i −0.903861 0.834114i
\(569\) −14.3568 + 17.1097i −0.601867 + 0.717277i −0.977840 0.209353i \(-0.932864\pi\)
0.375973 + 0.926631i \(0.377309\pi\)
\(570\) 0 0
\(571\) 6.51955 + 36.9742i 0.272835 + 1.54732i 0.745757 + 0.666218i \(0.232088\pi\)
−0.472922 + 0.881104i \(0.656801\pi\)
\(572\) −13.2626 + 2.70604i −0.554538 + 0.113145i
\(573\) 0 0
\(574\) −19.3297 + 1.95186i −0.806805 + 0.0814691i
\(575\) −3.05101 + 5.28450i −0.127236 + 0.220379i
\(576\) 0 0
\(577\) 11.0922 + 19.2123i 0.461775 + 0.799817i 0.999050 0.0435901i \(-0.0138796\pi\)
−0.537275 + 0.843407i \(0.680546\pi\)
\(578\) 6.40729 + 8.89504i 0.266508 + 0.369985i
\(579\) 0 0
\(580\) 19.8158 59.3335i 0.822807 2.46369i
\(581\) −10.9066 + 9.15169i −0.452480 + 0.379676i
\(582\) 0 0
\(583\) 9.59086 + 26.3507i 0.397213 + 1.09133i
\(584\) −9.13007 + 40.5071i −0.377805 + 1.67619i
\(585\) 0 0
\(586\) −5.56063 1.41056i −0.229708 0.0582699i
\(587\) 8.52654 + 1.50346i 0.351928 + 0.0620544i 0.346818 0.937933i \(-0.387262\pi\)
0.00511024 + 0.999987i \(0.498373\pi\)
\(588\) 0 0
\(589\) 2.65481 7.29402i 0.109389 0.300545i
\(590\) 18.2208 + 37.7487i 0.750140 + 1.55409i
\(591\) 0 0
\(592\) −17.6970 41.5620i −0.727341 1.70819i
\(593\) 19.4361i 0.798144i 0.916920 + 0.399072i \(0.130668\pi\)
−0.916920 + 0.399072i \(0.869332\pi\)
\(594\) 0 0
\(595\) 49.4212 2.02607
\(596\) 16.9042 + 2.51668i 0.692424 + 0.103087i
\(597\) 0 0
\(598\) 1.39564 + 2.89139i 0.0570719 + 0.118238i
\(599\) −6.17877 2.24889i −0.252458 0.0918871i 0.212691 0.977119i \(-0.431777\pi\)
−0.465149 + 0.885232i \(0.653999\pi\)
\(600\) 0 0
\(601\) −0.821185 + 4.65717i −0.0334968 + 0.189970i −0.996965 0.0778536i \(-0.975193\pi\)
0.963468 + 0.267824i \(0.0863044\pi\)
\(602\) 6.58319 25.9518i 0.268311 1.05772i
\(603\) 0 0
\(604\) −10.0156 + 18.4711i −0.407529 + 0.751578i
\(605\) −11.7199 + 4.26568i −0.476480 + 0.173425i
\(606\) 0 0
\(607\) −22.8132 27.1877i −0.925960 1.10352i −0.994381 0.105859i \(-0.966241\pi\)
0.0684212 0.997657i \(-0.478204\pi\)
\(608\) 13.0403 7.17791i 0.528854 0.291103i
\(609\) 0 0
\(610\) −2.87199 + 2.06876i −0.116283 + 0.0837615i
\(611\) 2.81069 1.62275i 0.113709 0.0656496i
\(612\) 0 0
\(613\) −35.0635 20.2439i −1.41620 0.817644i −0.420238 0.907414i \(-0.638053\pi\)
−0.995963 + 0.0897701i \(0.971387\pi\)
\(614\) 47.3838 4.78469i 1.91225 0.193094i
\(615\) 0 0
\(616\) 10.2133 + 19.7895i 0.411505 + 0.797340i
\(617\) −10.1725 + 1.79368i −0.409528 + 0.0722109i −0.374617 0.927179i \(-0.622226\pi\)
−0.0349111 + 0.999390i \(0.511115\pi\)
\(618\) 0 0
\(619\) 10.0980 + 8.47326i 0.405874 + 0.340569i 0.822759 0.568390i \(-0.192434\pi\)
−0.416885 + 0.908959i \(0.636878\pi\)
\(620\) −10.5571 17.2060i −0.423983 0.691009i
\(621\) 0 0
\(622\) −4.71307 16.6934i −0.188977 0.669345i
\(623\) 12.5858 + 10.5607i 0.504238 + 0.423106i
\(624\) 0 0
\(625\) −2.35223 13.3402i −0.0940891 0.533606i
\(626\) 0.557347 7.52852i 0.0222761 0.300900i
\(627\) 0 0
\(628\) 17.9221 7.07129i 0.715169 0.282175i
\(629\) 28.0924 48.6575i 1.12012 1.94010i
\(630\) 0 0
\(631\) 30.9490 17.8684i 1.23206 0.711329i 0.264600 0.964358i \(-0.414760\pi\)
0.967459 + 0.253029i \(0.0814267\pi\)
\(632\) −9.59172 + 22.9276i −0.381538 + 0.912012i
\(633\) 0 0
\(634\) 0.0170514 + 0.0116029i 0.000677197 + 0.000460810i
\(635\) −10.0084 11.9276i −0.397173 0.473332i
\(636\) 0 0
\(637\) −1.21932 3.35005i −0.0483112 0.132734i
\(638\) 25.1199 + 24.4570i 0.994506 + 0.968263i
\(639\) 0 0
\(640\) 6.48102 38.1651i 0.256185 1.50861i
\(641\) −23.8743 4.20968i −0.942977 0.166272i −0.319035 0.947743i \(-0.603359\pi\)
−0.623942 + 0.781471i \(0.714470\pi\)
\(642\) 0 0
\(643\) 24.2825 + 8.83811i 0.957609 + 0.348541i 0.773096 0.634289i \(-0.218707\pi\)
0.184513 + 0.982830i \(0.440929\pi\)
\(644\) 3.95415 3.50228i 0.155815 0.138009i
\(645\) 0 0
\(646\) 16.8825 + 7.59931i 0.664231 + 0.298991i
\(647\) −19.0593 −0.749298 −0.374649 0.927167i \(-0.622237\pi\)
−0.374649 + 0.927167i \(0.622237\pi\)
\(648\) 0 0
\(649\) −23.4921 −0.922146
\(650\) 21.5867 + 9.71681i 0.846698 + 0.381125i
\(651\) 0 0
\(652\) −26.0180 29.3748i −1.01894 1.15041i
\(653\) −37.3455 13.5927i −1.46144 0.531922i −0.515680 0.856781i \(-0.672461\pi\)
−0.945762 + 0.324860i \(0.894683\pi\)
\(654\) 0 0
\(655\) 5.24222 + 0.924345i 0.204831 + 0.0361172i
\(656\) −15.8625 + 10.3265i −0.619326 + 0.403181i
\(657\) 0 0
\(658\) −3.82581 3.72485i −0.149146 0.145210i
\(659\) 8.73494 + 23.9990i 0.340265 + 0.934870i 0.985318 + 0.170732i \(0.0546132\pi\)
−0.645053 + 0.764138i \(0.723165\pi\)
\(660\) 0 0
\(661\) 4.94246 + 5.89019i 0.192239 + 0.229102i 0.853551 0.521009i \(-0.174444\pi\)
−0.661312 + 0.750111i \(0.730000\pi\)
\(662\) 4.46486 + 3.03819i 0.173532 + 0.118083i
\(663\) 0 0
\(664\) −5.35326 + 12.7962i −0.207747 + 0.496588i
\(665\) 22.6373 13.0696i 0.877836 0.506819i
\(666\) 0 0
\(667\) 4.15789 7.20168i 0.160994 0.278850i
\(668\) 8.36173 + 21.1927i 0.323525 + 0.819970i
\(669\) 0 0
\(670\) 2.33249 31.5068i 0.0901120 1.21721i
\(671\) −0.344471 1.95359i −0.0132982 0.0754176i
\(672\) 0 0
\(673\) 8.06476 + 6.76714i 0.310874 + 0.260854i 0.784853 0.619682i \(-0.212738\pi\)
−0.473979 + 0.880536i \(0.657183\pi\)
\(674\) 3.32281 + 11.7692i 0.127990 + 0.453332i
\(675\) 0 0
\(676\) −11.5446 + 7.08344i −0.444024 + 0.272440i
\(677\) 27.3660 + 22.9628i 1.05176 + 0.882533i 0.993278 0.115756i \(-0.0369290\pi\)
0.0584838 + 0.998288i \(0.481373\pi\)
\(678\) 0 0
\(679\) −0.385613 + 0.0679940i −0.0147985 + 0.00260937i
\(680\) 42.7862 22.0818i 1.64077 0.846798i
\(681\) 0 0
\(682\) 11.2564 1.13664i 0.431031 0.0435244i
\(683\) −11.6024 6.69864i −0.443953 0.256316i 0.261320 0.965252i \(-0.415842\pi\)
−0.705273 + 0.708936i \(0.749176\pi\)
\(684\) 0 0
\(685\) −2.56895 + 1.48319i −0.0981547 + 0.0566696i
\(686\) 18.5609 13.3698i 0.708659 0.510463i
\(687\) 0 0
\(688\) −5.89612 25.4091i −0.224787 0.968713i
\(689\) −16.5863 19.7668i −0.631887 0.753054i
\(690\) 0 0
\(691\) 32.2794 11.7487i 1.22797 0.446943i 0.355066 0.934841i \(-0.384458\pi\)
0.872901 + 0.487898i \(0.162236\pi\)
\(692\) −27.8465 15.0992i −1.05857 0.573987i
\(693\) 0 0
\(694\) −8.53986 + 33.6653i −0.324169 + 1.27792i
\(695\) −9.02463 + 51.1812i −0.342324 + 1.94142i
\(696\) 0 0
\(697\) −22.1220 8.05173i −0.837929 0.304981i
\(698\) 4.17472 + 8.64890i 0.158015 + 0.327366i
\(699\) 0 0
\(700\) 5.73519 38.5225i 0.216770 1.45601i
\(701\) 5.81942 0.219796 0.109898 0.993943i \(-0.464948\pi\)
0.109898 + 0.993943i \(0.464948\pi\)
\(702\) 0 0
\(703\) 29.7167i 1.12079i
\(704\) 17.6842 + 12.5693i 0.666498 + 0.473722i
\(705\) 0 0
\(706\) −8.91804 18.4758i −0.335635 0.695346i
\(707\) −12.9494 + 35.5783i −0.487014 + 1.33806i
\(708\) 0 0
\(709\) −43.2874 7.63273i −1.62569 0.286653i −0.714809 0.699320i \(-0.753486\pi\)
−0.910882 + 0.412666i \(0.864598\pi\)
\(710\) −48.6087 12.3306i −1.82425 0.462758i
\(711\) 0 0
\(712\) 15.6147 + 3.51947i 0.585185 + 0.131898i
\(713\) −0.917815 2.52167i −0.0343724 0.0944375i
\(714\) 0 0
\(715\) −17.7396 + 14.8853i −0.663424 + 0.556679i
\(716\) 29.9156 + 9.99102i 1.11800 + 0.373382i
\(717\) 0 0
\(718\) −2.66644 3.70173i −0.0995106 0.138147i
\(719\) −13.4590 23.3117i −0.501938 0.869381i −0.999997 0.00223877i \(-0.999287\pi\)
0.498060 0.867143i \(-0.334046\pi\)
\(720\) 0 0
\(721\) −1.79387 + 3.10708i −0.0668073 + 0.115714i
\(722\) −16.9915 + 1.71575i −0.632356 + 0.0638537i
\(723\) 0 0
\(724\) 2.02749 + 9.93694i 0.0753509 + 0.369303i
\(725\) −10.6472 60.3835i −0.395428 2.24259i
\(726\) 0 0
\(727\) 7.10391 8.46611i 0.263470 0.313991i −0.618050 0.786139i \(-0.712077\pi\)
0.881519 + 0.472148i \(0.156521\pi\)
\(728\) −15.0595 13.8975i −0.558143 0.515074i
\(729\) 0 0
\(730\) 19.3019 + 68.3663i 0.714397 + 2.53035i
\(731\) 20.8539 24.8527i 0.771309 0.919211i
\(732\) 0 0
\(733\) −5.25607 + 0.926787i −0.194137 + 0.0342316i −0.269871 0.962896i \(-0.586981\pi\)
0.0757339 + 0.997128i \(0.475870\pi\)
\(734\) 42.3635 + 3.13623i 1.56366 + 0.115760i
\(735\) 0 0
\(736\) 1.85844 4.79883i 0.0685029 0.176887i
\(737\) 15.3342 + 8.85322i 0.564844 + 0.326113i
\(738\) 0 0
\(739\) 7.72474 + 13.3796i 0.284159 + 0.492178i 0.972405 0.233299i \(-0.0749522\pi\)
−0.688246 + 0.725478i \(0.741619\pi\)
\(740\) −60.5089 48.0757i −2.22435 1.76730i
\(741\) 0 0
\(742\) −23.8829 + 35.0978i −0.876769 + 1.28848i
\(743\) 21.9616 18.4280i 0.805692 0.676056i −0.143883 0.989595i \(-0.545959\pi\)
0.949575 + 0.313539i \(0.101515\pi\)
\(744\) 0 0
\(745\) 27.4755 10.0003i 1.00662 0.366381i
\(746\) 15.7346 + 15.3194i 0.576086 + 0.560884i
\(747\) 0 0
\(748\) 0.721481 + 26.9753i 0.0263800 + 0.986315i
\(749\) 8.05566 45.6859i 0.294347 1.66933i
\(750\) 0 0
\(751\) −8.91474 + 24.4930i −0.325303 + 0.893764i 0.663979 + 0.747751i \(0.268866\pi\)
−0.989283 + 0.146013i \(0.953356\pi\)
\(752\) −4.97647 1.51537i −0.181473 0.0552599i
\(753\) 0 0
\(754\) −29.4181 13.2420i −1.07135 0.482245i
\(755\) 35.9473i 1.30826i
\(756\) 0 0
\(757\) 6.07158i 0.220675i −0.993894 0.110338i \(-0.964807\pi\)
0.993894 0.110338i \(-0.0351932\pi\)
\(758\) 3.88206 8.62430i 0.141003 0.313249i
\(759\) 0 0
\(760\) 13.7585 21.4295i 0.499074 0.777330i
\(761\) −7.74422 + 21.2771i −0.280728 + 0.771293i 0.716549 + 0.697537i \(0.245721\pi\)
−0.997276 + 0.0737560i \(0.976501\pi\)
\(762\) 0 0
\(763\) 1.20090 6.81067i 0.0434757 0.246563i
\(764\) −1.33506 49.9164i −0.0483009 1.80591i
\(765\) 0 0
\(766\) −6.84946 + 7.03511i −0.247481 + 0.254189i
\(767\) 20.3134 7.39349i 0.733476 0.266963i
\(768\) 0 0
\(769\) −11.2565 + 9.44536i −0.405921 + 0.340608i −0.822777 0.568364i \(-0.807576\pi\)
0.416856 + 0.908973i \(0.363132\pi\)
\(770\) 31.4984 + 21.4336i 1.13512 + 0.772414i
\(771\) 0 0
\(772\) −11.7205 + 14.7516i −0.421830 + 0.530922i
\(773\) 9.84699 + 17.0555i 0.354172 + 0.613443i 0.986976 0.160869i \(-0.0514296\pi\)
−0.632804 + 0.774312i \(0.718096\pi\)
\(774\) 0 0
\(775\) −17.1355 9.89320i −0.615526 0.355374i
\(776\) −0.303463 + 0.231161i −0.0108937 + 0.00829818i
\(777\) 0 0
\(778\) 0.148634 2.00771i 0.00532878 0.0719799i
\(779\) −12.2622 + 2.16216i −0.439341 + 0.0774676i
\(780\) 0 0
\(781\) 18.0661 21.5304i 0.646456 0.770417i
\(782\) 6.15982 1.73911i 0.220275 0.0621904i
\(783\) 0 0
\(784\) −2.58852 + 5.09434i −0.0924471 + 0.181941i
\(785\) 21.1874 25.2502i 0.756212 0.901218i
\(786\) 0 0
\(787\) −2.49296 14.1383i −0.0888646 0.503976i −0.996456 0.0841207i \(-0.973192\pi\)
0.907591 0.419855i \(-0.137919\pi\)
\(788\) −0.765354 + 0.156159i −0.0272646 + 0.00556294i
\(789\) 0 0
\(790\) 4.27175 + 42.3041i 0.151982 + 1.50511i
\(791\) 13.7754 23.8596i 0.489796 0.848351i
\(792\) 0 0
\(793\) 0.912701 + 1.58084i 0.0324110 + 0.0561374i
\(794\) −21.9350 + 15.8003i −0.778446 + 0.560732i
\(795\) 0 0
\(796\) 13.7435 + 4.58996i 0.487125 + 0.162687i
\(797\) −16.5677 + 13.9019i −0.586857 + 0.492431i −0.887191 0.461403i \(-0.847346\pi\)
0.300334 + 0.953834i \(0.402902\pi\)
\(798\) 0 0
\(799\) −2.21295 6.08002i −0.0782884 0.215096i
\(800\) −12.2470 35.9132i −0.432996 1.26972i
\(801\) 0 0
\(802\) −6.50440 + 25.6412i −0.229678 + 0.905423i
\(803\) −39.2092 6.91364i −1.38366 0.243977i
\(804\) 0 0
\(805\) 3.09078 8.49184i 0.108936 0.299298i
\(806\) −9.37562 + 4.52550i −0.330242 + 0.159404i
\(807\) 0 0
\(808\) 4.68576 + 36.5877i 0.164844 + 1.28715i
\(809\) 27.7706i 0.976363i −0.872742 0.488182i \(-0.837660\pi\)
0.872742 0.488182i \(-0.162340\pi\)
\(810\) 0 0
\(811\) −6.91746 −0.242905 −0.121452 0.992597i \(-0.538755\pi\)
−0.121452 + 0.992597i \(0.538755\pi\)
\(812\) −7.81587 + 52.4982i −0.274283 + 1.84233i
\(813\) 0 0
\(814\) 39.0071 18.8282i 1.36720 0.659929i
\(815\) −63.0848 22.9610i −2.20976 0.804288i
\(816\) 0 0
\(817\) 2.97969 16.8987i 0.104246 0.591209i
\(818\) 25.4093 + 6.44558i 0.888416 + 0.225364i
\(819\) 0 0
\(820\) −15.4353 + 28.4663i −0.539024 + 0.994085i
\(821\) 6.71754 2.44498i 0.234444 0.0853305i −0.222127 0.975018i \(-0.571300\pi\)
0.456570 + 0.889687i \(0.349078\pi\)
\(822\) 0 0
\(823\) −1.29022 1.53762i −0.0449742 0.0535981i 0.743088 0.669193i \(-0.233360\pi\)
−0.788063 + 0.615595i \(0.788916\pi\)
\(824\) −0.164769 + 3.49146i −0.00574000 + 0.121631i
\(825\) 0 0
\(826\) −20.7870 28.8579i −0.723271 1.00409i
\(827\) 22.7464 13.1326i 0.790969 0.456666i −0.0493347 0.998782i \(-0.515710\pi\)
0.840303 + 0.542116i \(0.182377\pi\)
\(828\) 0 0
\(829\) 36.0689 + 20.8244i 1.25272 + 0.723260i 0.971649 0.236426i \(-0.0759761\pi\)
0.281074 + 0.959686i \(0.409309\pi\)
\(830\) 2.38412 + 23.6104i 0.0827539 + 0.819529i
\(831\) 0 0
\(832\) −19.2472 5.30294i −0.667277 0.183846i
\(833\) −6.99928 + 1.23416i −0.242511 + 0.0427611i
\(834\) 0 0
\(835\) 29.8581 + 25.0539i 1.03328 + 0.867027i
\(836\) 7.46422 + 12.1652i 0.258155 + 0.420742i
\(837\) 0 0
\(838\) −30.5693 + 8.63066i −1.05600 + 0.298141i
\(839\) 17.8040 + 14.9393i 0.614662 + 0.515762i 0.896120 0.443811i \(-0.146374\pi\)
−0.281459 + 0.959573i \(0.590818\pi\)
\(840\) 0 0
\(841\) 9.47417 + 53.7307i 0.326696 + 1.85278i
\(842\) −24.6614 1.82572i −0.849889 0.0629185i
\(843\) 0 0
\(844\) −16.3893 41.5385i −0.564143 1.42981i
\(845\) −11.5861 + 20.0677i −0.398574 + 0.690350i
\(846\) 0 0
\(847\) 9.16452 5.29114i 0.314897 0.181806i
\(848\) −4.99451 + 41.0569i −0.171512 + 1.40990i
\(849\) 0 0
\(850\) 26.5500 39.0174i 0.910658 1.33828i
\(851\) −6.60374 7.87003i −0.226373 0.269781i
\(852\) 0 0
\(853\) −0.546744 1.50217i −0.0187202 0.0514332i 0.929981 0.367609i \(-0.119823\pi\)
−0.948701 + 0.316175i \(0.897601\pi\)
\(854\) 2.09500 2.15179i 0.0716895 0.0736326i
\(855\) 0 0
\(856\) −13.4387 43.1517i −0.459325 1.47489i
\(857\) 21.3303 + 3.76110i 0.728629 + 0.128477i 0.525644 0.850705i \(-0.323825\pi\)
0.202985 + 0.979182i \(0.434936\pi\)
\(858\) 0 0
\(859\) −13.9293 5.06987i −0.475263 0.172982i 0.0932719 0.995641i \(-0.470267\pi\)
−0.568535 + 0.822659i \(0.692490\pi\)
\(860\) −29.5884 33.4059i −1.00896 1.13913i
\(861\) 0 0
\(862\) 7.62605 16.9419i 0.259744 0.577042i
\(863\) −37.5749 −1.27907 −0.639533 0.768764i \(-0.720872\pi\)
−0.639533 + 0.768764i \(0.720872\pi\)
\(864\) 0 0
\(865\) −54.1932 −1.84262
\(866\) 13.1542 29.2230i 0.446997 0.993038i
\(867\) 0 0
\(868\) 11.3565 + 12.8217i 0.385465 + 0.435197i
\(869\) −22.3930 8.15037i −0.759629 0.276482i
\(870\) 0 0
\(871\) −16.0457 2.82929i −0.543688 0.0958668i
\(872\) −2.00338 6.43288i −0.0678432 0.217845i
\(873\) 0 0
\(874\) 2.36158 2.42559i 0.0798816 0.0820467i
\(875\) −5.80168 15.9400i −0.196133 0.538870i
\(876\) 0 0
\(877\) 25.3049 + 30.1572i 0.854484 + 1.01833i 0.999582 + 0.0289176i \(0.00920603\pi\)
−0.145097 + 0.989417i \(0.546350\pi\)
\(878\) 12.0359 17.6877i 0.406191 0.596930i
\(879\) 0 0
\(880\) 36.8464 + 4.48230i 1.24209 + 0.151098i
\(881\) −22.6325 + 13.0669i −0.762509 + 0.440235i −0.830196 0.557472i \(-0.811772\pi\)
0.0676867 + 0.997707i \(0.478438\pi\)
\(882\) 0 0
\(883\) −24.4508 + 42.3501i −0.822837 + 1.42519i 0.0807251 + 0.996736i \(0.474276\pi\)
−0.903562 + 0.428458i \(0.859057\pi\)
\(884\) −9.11359 23.0983i −0.306523 0.776879i
\(885\) 0 0
\(886\) 5.61410 + 0.415620i 0.188609 + 0.0139630i
\(887\) −2.89846 16.4380i −0.0973207 0.551933i −0.994011 0.109276i \(-0.965147\pi\)
0.896691 0.442658i \(-0.145964\pi\)
\(888\) 0 0
\(889\) 10.1203 + 8.49198i 0.339425 + 0.284812i
\(890\) 26.3539 7.44052i 0.883384 0.249407i
\(891\) 0 0
\(892\) −8.32427 13.5669i −0.278717 0.454254i
\(893\) −2.62152 2.19972i −0.0877259 0.0736108i
\(894\) 0 0
\(895\) 53.1394 9.36990i 1.77625 0.313201i
\(896\) 0.207655 + 32.8453i 0.00693728 + 1.09728i
\(897\) 0 0
\(898\) −3.66976 36.3423i −0.122461 1.21276i
\(899\) 23.3522 + 13.4824i 0.778838 + 0.449663i
\(900\) 0 0
\(901\) −44.5501 + 25.7210i −1.48418 + 0.856890i
\(902\) −10.6074 14.7259i −0.353187 0.490319i
\(903\) 0 0
\(904\) 1.26528 26.8113i 0.0420826 0.891732i
\(905\) 11.1527 + 13.2913i 0.370729 + 0.441818i
\(906\) 0 0
\(907\) 9.94085 3.61817i 0.330081 0.120140i −0.171663 0.985156i \(-0.554914\pi\)
0.501744 + 0.865016i \(0.332692\pi\)
\(908\) 8.23586 15.1888i 0.273316 0.504059i
\(909\) 0 0
\(910\) −33.9821 8.62023i −1.12649 0.285758i
\(911\) −10.2298 + 58.0158i −0.338927 + 1.92215i 0.0454332 + 0.998967i \(0.485533\pi\)
−0.384360 + 0.923183i \(0.625578\pi\)
\(912\) 0 0
\(913\) −12.4978 4.54882i −0.413616 0.150544i
\(914\) −3.57261 + 1.72445i −0.118171 + 0.0570399i
\(915\) 0 0
\(916\) 2.24767 15.0973i 0.0742650 0.498828i
\(917\) −4.51655 −0.149150
\(918\) 0 0
\(919\) 25.4259i 0.838724i 0.907819 + 0.419362i \(0.137746\pi\)
−0.907819 + 0.419362i \(0.862254\pi\)
\(920\) −1.11840 8.73276i −0.0368725 0.287911i
\(921\) 0 0
\(922\) 19.1394 9.23837i 0.630324 0.304250i
\(923\) −8.84554 + 24.3029i −0.291155 + 0.799941i
\(924\) 0 0
\(925\) −74.5997 13.1539i −2.45282 0.432499i
\(926\) 7.60492 29.9796i 0.249913 0.985191i
\(927\) 0 0
\(928\) 16.6901 + 48.9423i 0.547879 + 1.60661i
\(929\) 1.65289 + 4.54128i 0.0542296 + 0.148995i 0.963850 0.266446i \(-0.0858495\pi\)
−0.909620 + 0.415441i \(0.863627\pi\)
\(930\) 0 0
\(931\) −2.87963 + 2.41630i −0.0943760 + 0.0791909i
\(932\) −13.4853 4.50371i −0.441724 0.147524i
\(933\) 0 0
\(934\) −21.4799 + 15.4725i −0.702845 + 0.506274i
\(935\) 23.0832 + 39.9813i 0.754902 + 1.30753i
\(936\) 0 0
\(937\) 25.7048 44.5220i 0.839738 1.45447i −0.0503753 0.998730i \(-0.516042\pi\)
0.890114 0.455739i \(-0.150625\pi\)
\(938\) 2.69311 + 26.6704i 0.0879332 + 0.870821i
\(939\) 0 0
\(940\) −8.72016 + 1.77922i −0.284420 + 0.0580318i
\(941\) 6.83831 + 38.7820i 0.222922 + 1.26426i 0.866617 + 0.498973i \(0.166289\pi\)
−0.643695 + 0.765282i \(0.722599\pi\)
\(942\) 0 0
\(943\) −2.76699 + 3.29758i −0.0901057 + 0.107384i
\(944\) −30.8902 15.6958i −1.00539 0.510855i
\(945\) 0 0
\(946\) 24.0696 6.79561i 0.782571 0.220944i
\(947\) −18.2848 + 21.7910i −0.594178 + 0.708113i −0.976403 0.215956i \(-0.930713\pi\)
0.382226 + 0.924069i \(0.375158\pi\)
\(948\) 0 0
\(949\) 36.0798 6.36183i 1.17120 0.206514i
\(950\) 1.84287 24.8931i 0.0597907 0.807639i
\(951\) 0 0
\(952\) −32.4983 + 24.7553i −1.05328 + 0.802325i
\(953\) 24.5811 + 14.1919i 0.796261 + 0.459722i 0.842162 0.539224i \(-0.181282\pi\)
−0.0459008 + 0.998946i \(0.514616\pi\)
\(954\) 0 0
\(955\) −42.7143 73.9833i −1.38220 2.39404i
\(956\) 2.76824 3.48415i 0.0895312 0.112686i
\(957\) 0 0
\(958\) 23.4581 + 15.9625i 0.757898 + 0.515724i
\(959\) 1.92807 1.61784i 0.0622605 0.0522428i
\(960\) 0 0
\(961\) −20.9537 + 7.62652i −0.675925 + 0.246017i
\(962\) −27.8034 + 28.5570i −0.896419 + 0.920715i
\(963\) 0 0
\(964\) −0.0109178 0.408203i −0.000351638 0.0131473i
\(965\) −5.59727 + 31.7437i −0.180183 + 1.02187i
\(966\) 0 0
\(967\) 14.1101 38.7671i 0.453749 1.24667i −0.476317 0.879274i \(-0.658028\pi\)
0.930066 0.367392i \(-0.119749\pi\)
\(968\) 5.57002 8.67557i 0.179027 0.278843i
\(969\) 0 0
\(970\) −0.267884 + 0.595126i −0.00860125 + 0.0191083i
\(971\) 5.59715i 0.179621i −0.995959 0.0898105i \(-0.971374\pi\)
0.995959 0.0898105i \(-0.0286261\pi\)
\(972\) 0 0
\(973\) 44.0963i 1.41366i
\(974\) −18.1827 8.18461i −0.582613 0.262252i
\(975\) 0 0
\(976\) 0.852305 2.79896i 0.0272816 0.0895927i
\(977\) −7.61083 + 20.9106i −0.243492 + 0.668989i 0.756397 + 0.654112i \(0.226958\pi\)
−0.999889 + 0.0148763i \(0.995265\pi\)
\(978\) 0 0
\(979\) −2.66507 + 15.1144i −0.0851762 + 0.483058i
\(980\) 0.261377 + 9.77257i 0.00834938 + 0.312173i
\(981\) 0 0
\(982\) −2.27198 2.21203i −0.0725018 0.0705886i
\(983\) 43.7402 15.9201i 1.39510 0.507774i 0.468378 0.883528i \(-0.344839\pi\)
0.926719 + 0.375755i \(0.122617\pi\)
\(984\) 0 0
\(985\) −1.02371 + 0.858996i −0.0326182 + 0.0273699i
\(986\) −36.1821 + 53.1726i −1.15227 + 1.69336i
\(987\) 0 0
\(988\) −10.2829 8.17000i −0.327143 0.259922i
\(989\) −2.96615 5.13752i −0.0943180 0.163364i
\(990\) 0 0
\(991\) −38.1847 22.0460i −1.21298 0.700313i −0.249571 0.968357i \(-0.580289\pi\)
−0.963407 + 0.268044i \(0.913623\pi\)
\(992\) 15.5607 + 6.02617i 0.494052 + 0.191331i
\(993\) 0 0
\(994\) 42.4338 + 3.14144i 1.34592 + 0.0996403i
\(995\) 24.4127 4.30461i 0.773933 0.136465i
\(996\) 0 0
\(997\) 13.4946 16.0822i 0.427378 0.509330i −0.508786 0.860893i \(-0.669905\pi\)
0.936164 + 0.351563i \(0.114350\pi\)
\(998\) −3.55943 12.6073i −0.112672 0.399077i
\(999\) 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 648.2.v.b.35.12 192
3.2 odd 2 216.2.v.b.11.21 192
8.3 odd 2 inner 648.2.v.b.35.6 192
12.11 even 2 864.2.bh.b.335.28 192
24.5 odd 2 864.2.bh.b.335.27 192
24.11 even 2 216.2.v.b.11.27 yes 192
27.5 odd 18 inner 648.2.v.b.611.6 192
27.22 even 9 216.2.v.b.59.27 yes 192
108.103 odd 18 864.2.bh.b.815.27 192
216.59 even 18 inner 648.2.v.b.611.12 192
216.157 even 18 864.2.bh.b.815.28 192
216.211 odd 18 216.2.v.b.59.21 yes 192
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
216.2.v.b.11.21 192 3.2 odd 2
216.2.v.b.11.27 yes 192 24.11 even 2
216.2.v.b.59.21 yes 192 216.211 odd 18
216.2.v.b.59.27 yes 192 27.22 even 9
648.2.v.b.35.6 192 8.3 odd 2 inner
648.2.v.b.35.12 192 1.1 even 1 trivial
648.2.v.b.611.6 192 27.5 odd 18 inner
648.2.v.b.611.12 192 216.59 even 18 inner
864.2.bh.b.335.27 192 24.5 odd 2
864.2.bh.b.335.28 192 12.11 even 2
864.2.bh.b.815.27 192 108.103 odd 18
864.2.bh.b.815.28 192 216.157 even 18