Properties

Label 360.2.x.a.53.2
Level $360$
Weight $2$
Character 360.53
Analytic conductor $2.875$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $8$

Related objects

Downloads

Learn more

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 53.2
Character \(\chi\) \(=\) 360.53
Dual form 360.2.x.a.197.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.37774 - 0.319115i) q^{2} +(1.79633 + 0.879316i) q^{4} +(1.42597 - 1.72238i) q^{5} +(3.11972 - 3.11972i) q^{7} +(-2.19427 - 1.78470i) q^{8} +O(q^{10})\) \(q+(-1.37774 - 0.319115i) q^{2} +(1.79633 + 0.879316i) q^{4} +(1.42597 - 1.72238i) q^{5} +(3.11972 - 3.11972i) q^{7} +(-2.19427 - 1.78470i) q^{8} +(-2.51426 + 1.91795i) q^{10} -1.17794 q^{11} +(-2.15100 + 2.15100i) q^{13} +(-5.29371 + 3.30261i) q^{14} +(2.45361 + 3.15908i) q^{16} +(-1.33507 - 1.33507i) q^{17} -0.322444 q^{19} +(4.07604 - 1.84009i) q^{20} +(1.62290 + 0.375899i) q^{22} +(4.71347 - 4.71347i) q^{23} +(-0.933209 - 4.91214i) q^{25} +(3.64993 - 2.27710i) q^{26} +(8.34726 - 2.86083i) q^{28} +6.63043i q^{29} -0.0675826 q^{31} +(-2.37232 - 5.13538i) q^{32} +(1.41334 + 2.26543i) q^{34} +(-0.924721 - 9.82198i) q^{35} +(-7.60938 - 7.60938i) q^{37} +(0.444244 + 0.102897i) q^{38} +(-6.20292 + 1.23444i) q^{40} +3.19684i q^{41} +(6.70505 - 6.70505i) q^{43} +(-2.11597 - 1.03578i) q^{44} +(-7.99807 + 4.98979i) q^{46} +(7.34279 + 7.34279i) q^{47} -12.4653i q^{49} +(-0.281821 + 7.06545i) q^{50} +(-5.75531 + 1.97250i) q^{52} +(5.73432 + 5.73432i) q^{53} +(-1.67971 + 2.02887i) q^{55} +(-12.4133 + 1.27774i) q^{56} +(2.11587 - 9.13501i) q^{58} -8.68448i q^{59} +12.5620i q^{61} +(0.0931112 + 0.0215666i) q^{62} +(1.62966 + 7.83225i) q^{64} +(0.637580 + 6.77210i) q^{65} +(-1.87740 - 1.87740i) q^{67} +(-1.22428 - 3.57219i) q^{68} +(-1.86032 + 13.8272i) q^{70} -4.18221i q^{71} +(3.97893 + 3.97893i) q^{73} +(8.05547 + 12.9120i) q^{74} +(-0.579216 - 0.283530i) q^{76} +(-3.67485 + 3.67485i) q^{77} +9.66644i q^{79} +(8.93993 + 0.278710i) q^{80} +(1.02016 - 4.40441i) q^{82} +(-0.585119 - 0.585119i) q^{83} +(-4.20329 + 0.395732i) q^{85} +(-11.3775 + 7.09813i) q^{86} +(2.58473 + 2.10228i) q^{88} +0.557322 q^{89} +13.4210i q^{91} +(12.6116 - 4.32232i) q^{92} +(-7.77325 - 12.4596i) q^{94} +(-0.459796 + 0.555372i) q^{95} +(-10.5772 + 10.5772i) q^{97} +(-3.97786 + 17.1739i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.37774 0.319115i −0.974209 0.225649i
\(3\) 0 0
\(4\) 1.79633 + 0.879316i 0.898165 + 0.439658i
\(5\) 1.42597 1.72238i 0.637714 0.770273i
\(6\) 0 0
\(7\) 3.11972 3.11972i 1.17914 1.17914i 0.199179 0.979963i \(-0.436172\pi\)
0.979963 0.199179i \(-0.0638277\pi\)
\(8\) −2.19427 1.78470i −0.775792 0.630988i
\(9\) 0 0
\(10\) −2.51426 + 1.91795i −0.795078 + 0.606508i
\(11\) −1.17794 −0.355163 −0.177581 0.984106i \(-0.556827\pi\)
−0.177581 + 0.984106i \(0.556827\pi\)
\(12\) 0 0
\(13\) −2.15100 + 2.15100i −0.596579 + 0.596579i −0.939401 0.342822i \(-0.888617\pi\)
0.342822 + 0.939401i \(0.388617\pi\)
\(14\) −5.29371 + 3.30261i −1.41480 + 0.882659i
\(15\) 0 0
\(16\) 2.45361 + 3.15908i 0.613402 + 0.789771i
\(17\) −1.33507 1.33507i −0.323803 0.323803i 0.526421 0.850224i \(-0.323534\pi\)
−0.850224 + 0.526421i \(0.823534\pi\)
\(18\) 0 0
\(19\) −0.322444 −0.0739738 −0.0369869 0.999316i \(-0.511776\pi\)
−0.0369869 + 0.999316i \(0.511776\pi\)
\(20\) 4.07604 1.84009i 0.911429 0.411457i
\(21\) 0 0
\(22\) 1.62290 + 0.375899i 0.346003 + 0.0801420i
\(23\) 4.71347 4.71347i 0.982826 0.982826i −0.0170294 0.999855i \(-0.505421\pi\)
0.999855 + 0.0170294i \(0.00542088\pi\)
\(24\) 0 0
\(25\) −0.933209 4.91214i −0.186642 0.982428i
\(26\) 3.64993 2.27710i 0.715810 0.446575i
\(27\) 0 0
\(28\) 8.34726 2.86083i 1.57748 0.540646i
\(29\) 6.63043i 1.23124i 0.788043 + 0.615620i \(0.211094\pi\)
−0.788043 + 0.615620i \(0.788906\pi\)
\(30\) 0 0
\(31\) −0.0675826 −0.0121382 −0.00606909 0.999982i \(-0.501932\pi\)
−0.00606909 + 0.999982i \(0.501932\pi\)
\(32\) −2.37232 5.13538i −0.419371 0.907815i
\(33\) 0 0
\(34\) 1.41334 + 2.26543i 0.242386 + 0.388518i
\(35\) −0.924721 9.82198i −0.156306 1.66022i
\(36\) 0 0
\(37\) −7.60938 7.60938i −1.25097 1.25097i −0.955284 0.295690i \(-0.904450\pi\)
−0.295690 0.955284i \(-0.595550\pi\)
\(38\) 0.444244 + 0.102897i 0.0720659 + 0.0166921i
\(39\) 0 0
\(40\) −6.20292 + 1.23444i −0.980767 + 0.195182i
\(41\) 3.19684i 0.499262i 0.968341 + 0.249631i \(0.0803093\pi\)
−0.968341 + 0.249631i \(0.919691\pi\)
\(42\) 0 0
\(43\) 6.70505 6.70505i 1.02251 1.02251i 0.0227703 0.999741i \(-0.492751\pi\)
0.999741 0.0227703i \(-0.00724865\pi\)
\(44\) −2.11597 1.03578i −0.318995 0.156150i
\(45\) 0 0
\(46\) −7.99807 + 4.98979i −1.17925 + 0.735704i
\(47\) 7.34279 + 7.34279i 1.07106 + 1.07106i 0.997274 + 0.0737817i \(0.0235068\pi\)
0.0737817 + 0.997274i \(0.476493\pi\)
\(48\) 0 0
\(49\) 12.4653i 1.78075i
\(50\) −0.281821 + 7.06545i −0.0398555 + 0.999205i
\(51\) 0 0
\(52\) −5.75531 + 1.97250i −0.798117 + 0.273536i
\(53\) 5.73432 + 5.73432i 0.787669 + 0.787669i 0.981112 0.193442i \(-0.0619653\pi\)
−0.193442 + 0.981112i \(0.561965\pi\)
\(54\) 0 0
\(55\) −1.67971 + 2.02887i −0.226492 + 0.273572i
\(56\) −12.4133 + 1.27774i −1.65879 + 0.170745i
\(57\) 0 0
\(58\) 2.11587 9.13501i 0.277828 1.19949i
\(59\) 8.68448i 1.13062i −0.824877 0.565312i \(-0.808756\pi\)
0.824877 0.565312i \(-0.191244\pi\)
\(60\) 0 0
\(61\) 12.5620i 1.60840i 0.594359 + 0.804199i \(0.297406\pi\)
−0.594359 + 0.804199i \(0.702594\pi\)
\(62\) 0.0931112 + 0.0215666i 0.0118251 + 0.00273897i
\(63\) 0 0
\(64\) 1.62966 + 7.83225i 0.203708 + 0.979032i
\(65\) 0.637580 + 6.77210i 0.0790821 + 0.839976i
\(66\) 0 0
\(67\) −1.87740 1.87740i −0.229360 0.229360i 0.583065 0.812425i \(-0.301853\pi\)
−0.812425 + 0.583065i \(0.801853\pi\)
\(68\) −1.22428 3.57219i −0.148466 0.433191i
\(69\) 0 0
\(70\) −1.86032 + 13.8272i −0.222351 + 1.65267i
\(71\) 4.18221i 0.496337i −0.968717 0.248168i \(-0.920171\pi\)
0.968717 0.248168i \(-0.0798286\pi\)
\(72\) 0 0
\(73\) 3.97893 + 3.97893i 0.465699 + 0.465699i 0.900518 0.434819i \(-0.143188\pi\)
−0.434819 + 0.900518i \(0.643188\pi\)
\(74\) 8.05547 + 12.9120i 0.936429 + 1.50099i
\(75\) 0 0
\(76\) −0.579216 0.283530i −0.0664407 0.0325231i
\(77\) −3.67485 + 3.67485i −0.418788 + 0.418788i
\(78\) 0 0
\(79\) 9.66644i 1.08756i 0.839228 + 0.543780i \(0.183007\pi\)
−0.839228 + 0.543780i \(0.816993\pi\)
\(80\) 8.93993 + 0.278710i 0.999514 + 0.0311607i
\(81\) 0 0
\(82\) 1.02016 4.40441i 0.112658 0.486385i
\(83\) −0.585119 0.585119i −0.0642251 0.0642251i 0.674265 0.738490i \(-0.264461\pi\)
−0.738490 + 0.674265i \(0.764461\pi\)
\(84\) 0 0
\(85\) −4.20329 + 0.395732i −0.455911 + 0.0429231i
\(86\) −11.3775 + 7.09813i −1.22687 + 0.765411i
\(87\) 0 0
\(88\) 2.58473 + 2.10228i 0.275533 + 0.224104i
\(89\) 0.557322 0.0590760 0.0295380 0.999564i \(-0.490596\pi\)
0.0295380 + 0.999564i \(0.490596\pi\)
\(90\) 0 0
\(91\) 13.4210i 1.40690i
\(92\) 12.6116 4.32232i 1.31485 0.450633i
\(93\) 0 0
\(94\) −7.77325 12.4596i −0.801750 1.28511i
\(95\) −0.459796 + 0.555372i −0.0471741 + 0.0569800i
\(96\) 0 0
\(97\) −10.5772 + 10.5772i −1.07395 + 1.07395i −0.0769138 + 0.997038i \(0.524507\pi\)
−0.997038 + 0.0769138i \(0.975493\pi\)
\(98\) −3.97786 + 17.1739i −0.401825 + 1.73483i
\(99\) 0 0
\(100\) 2.64297 9.64441i 0.264297 0.964441i
\(101\) 9.52870 0.948141 0.474071 0.880487i \(-0.342784\pi\)
0.474071 + 0.880487i \(0.342784\pi\)
\(102\) 0 0
\(103\) −0.162450 0.162450i −0.0160066 0.0160066i 0.699058 0.715065i \(-0.253603\pi\)
−0.715065 + 0.699058i \(0.753603\pi\)
\(104\) 8.55876 0.880979i 0.839256 0.0863871i
\(105\) 0 0
\(106\) −6.07049 9.73030i −0.589618 0.945091i
\(107\) −11.7955 + 11.7955i −1.14032 + 1.14032i −0.151925 + 0.988392i \(0.548547\pi\)
−0.988392 + 0.151925i \(0.951453\pi\)
\(108\) 0 0
\(109\) 10.8601 1.04021 0.520105 0.854102i \(-0.325893\pi\)
0.520105 + 0.854102i \(0.325893\pi\)
\(110\) 2.96165 2.25923i 0.282382 0.215409i
\(111\) 0 0
\(112\) 17.5100 + 2.20088i 1.65454 + 0.207964i
\(113\) −8.74476 + 8.74476i −0.822637 + 0.822637i −0.986486 0.163848i \(-0.947609\pi\)
0.163848 + 0.986486i \(0.447609\pi\)
\(114\) 0 0
\(115\) −1.39713 14.8397i −0.130283 1.38381i
\(116\) −5.83024 + 11.9105i −0.541325 + 1.10586i
\(117\) 0 0
\(118\) −2.77135 + 11.9650i −0.255124 + 1.10146i
\(119\) −8.33011 −0.763620
\(120\) 0 0
\(121\) −9.61245 −0.873859
\(122\) 4.00873 17.3072i 0.362933 1.56692i
\(123\) 0 0
\(124\) −0.121401 0.0594264i −0.0109021 0.00533665i
\(125\) −9.79132 5.39723i −0.875762 0.482743i
\(126\) 0 0
\(127\) −3.83755 + 3.83755i −0.340528 + 0.340528i −0.856566 0.516038i \(-0.827406\pi\)
0.516038 + 0.856566i \(0.327406\pi\)
\(128\) 0.254145 11.3109i 0.0224635 0.999748i
\(129\) 0 0
\(130\) 1.28266 9.53365i 0.112497 0.836156i
\(131\) 1.85715 0.162260 0.0811298 0.996704i \(-0.474147\pi\)
0.0811298 + 0.996704i \(0.474147\pi\)
\(132\) 0 0
\(133\) −1.00593 + 1.00593i −0.0872256 + 0.0872256i
\(134\) 1.98746 + 3.18567i 0.171690 + 0.275200i
\(135\) 0 0
\(136\) 0.546804 + 5.31223i 0.0468880 + 0.455520i
\(137\) −1.89240 1.89240i −0.161678 0.161678i 0.621631 0.783310i \(-0.286470\pi\)
−0.783310 + 0.621631i \(0.786470\pi\)
\(138\) 0 0
\(139\) 18.4370 1.56380 0.781902 0.623401i \(-0.214250\pi\)
0.781902 + 0.623401i \(0.214250\pi\)
\(140\) 6.97552 18.4566i 0.589539 1.55987i
\(141\) 0 0
\(142\) −1.33461 + 5.76199i −0.111998 + 0.483536i
\(143\) 2.53375 2.53375i 0.211883 0.211883i
\(144\) 0 0
\(145\) 11.4201 + 9.45481i 0.948392 + 0.785179i
\(146\) −4.21219 6.75167i −0.348603 0.558772i
\(147\) 0 0
\(148\) −6.97791 20.3600i −0.573581 1.67358i
\(149\) 1.24573i 0.102054i 0.998697 + 0.0510272i \(0.0162495\pi\)
−0.998697 + 0.0510272i \(0.983750\pi\)
\(150\) 0 0
\(151\) 16.7587 1.36380 0.681902 0.731444i \(-0.261153\pi\)
0.681902 + 0.731444i \(0.261153\pi\)
\(152\) 0.707530 + 0.575468i 0.0573883 + 0.0466766i
\(153\) 0 0
\(154\) 6.23568 3.89028i 0.502485 0.313488i
\(155\) −0.0963708 + 0.116403i −0.00774069 + 0.00934972i
\(156\) 0 0
\(157\) −6.90784 6.90784i −0.551306 0.551306i 0.375512 0.926818i \(-0.377467\pi\)
−0.926818 + 0.375512i \(0.877467\pi\)
\(158\) 3.08471 13.3178i 0.245406 1.05951i
\(159\) 0 0
\(160\) −12.2279 3.23686i −0.966704 0.255896i
\(161\) 29.4094i 2.31778i
\(162\) 0 0
\(163\) −6.07821 + 6.07821i −0.476082 + 0.476082i −0.903876 0.427794i \(-0.859291\pi\)
0.427794 + 0.903876i \(0.359291\pi\)
\(164\) −2.81103 + 5.74257i −0.219504 + 0.448420i
\(165\) 0 0
\(166\) 0.619421 + 0.992861i 0.0480764 + 0.0770610i
\(167\) −2.82159 2.82159i −0.218341 0.218341i 0.589458 0.807799i \(-0.299341\pi\)
−0.807799 + 0.589458i \(0.799341\pi\)
\(168\) 0 0
\(169\) 3.74643i 0.288187i
\(170\) 5.91732 + 0.796119i 0.453838 + 0.0610596i
\(171\) 0 0
\(172\) 17.9404 6.14864i 1.36794 0.468829i
\(173\) 7.27921 + 7.27921i 0.553428 + 0.553428i 0.927428 0.374001i \(-0.122014\pi\)
−0.374001 + 0.927428i \(0.622014\pi\)
\(174\) 0 0
\(175\) −18.2358 12.4131i −1.37850 0.938345i
\(176\) −2.89021 3.72122i −0.217858 0.280497i
\(177\) 0 0
\(178\) −0.767845 0.177850i −0.0575524 0.0133304i
\(179\) 9.56604i 0.714999i −0.933913 0.357500i \(-0.883629\pi\)
0.933913 0.357500i \(-0.116371\pi\)
\(180\) 0 0
\(181\) 4.44857i 0.330659i −0.986238 0.165330i \(-0.947131\pi\)
0.986238 0.165330i \(-0.0528688\pi\)
\(182\) 4.28285 18.4906i 0.317466 1.37062i
\(183\) 0 0
\(184\) −18.7548 + 1.93048i −1.38262 + 0.142317i
\(185\) −23.9570 + 2.25551i −1.76136 + 0.165828i
\(186\) 0 0
\(187\) 1.57264 + 1.57264i 0.115003 + 0.115003i
\(188\) 6.73345 + 19.6467i 0.491087 + 1.43288i
\(189\) 0 0
\(190\) 0.810707 0.618430i 0.0588149 0.0448657i
\(191\) 3.16704i 0.229159i 0.993414 + 0.114579i \(0.0365521\pi\)
−0.993414 + 0.114579i \(0.963448\pi\)
\(192\) 0 0
\(193\) 1.07726 + 1.07726i 0.0775426 + 0.0775426i 0.744814 0.667272i \(-0.232538\pi\)
−0.667272 + 0.744814i \(0.732538\pi\)
\(194\) 17.9480 11.1973i 1.28859 0.803917i
\(195\) 0 0
\(196\) 10.9609 22.3918i 0.782922 1.59941i
\(197\) −5.59062 + 5.59062i −0.398315 + 0.398315i −0.877638 0.479323i \(-0.840882\pi\)
0.479323 + 0.877638i \(0.340882\pi\)
\(198\) 0 0
\(199\) 15.7707i 1.11796i 0.829182 + 0.558978i \(0.188806\pi\)
−0.829182 + 0.558978i \(0.811194\pi\)
\(200\) −6.71900 + 12.4441i −0.475105 + 0.879929i
\(201\) 0 0
\(202\) −13.1281 3.04076i −0.923688 0.213947i
\(203\) 20.6851 + 20.6851i 1.45181 + 1.45181i
\(204\) 0 0
\(205\) 5.50618 + 4.55860i 0.384568 + 0.318386i
\(206\) 0.171973 + 0.275653i 0.0119819 + 0.0192057i
\(207\) 0 0
\(208\) −12.0729 1.51747i −0.837104 0.105218i
\(209\) 0.379820 0.0262727
\(210\) 0 0
\(211\) 10.9274i 0.752273i 0.926564 + 0.376137i \(0.122748\pi\)
−0.926564 + 0.376137i \(0.877252\pi\)
\(212\) 5.25846 + 15.3430i 0.361152 + 1.05376i
\(213\) 0 0
\(214\) 20.0153 12.4870i 1.36822 0.853596i
\(215\) −1.98746 21.1099i −0.135543 1.43968i
\(216\) 0 0
\(217\) −0.210839 + 0.210839i −0.0143127 + 0.0143127i
\(218\) −14.9624 3.46563i −1.01338 0.234722i
\(219\) 0 0
\(220\) −4.80133 + 2.16752i −0.323706 + 0.146134i
\(221\) 5.74348 0.386348
\(222\) 0 0
\(223\) 0.947865 + 0.947865i 0.0634737 + 0.0634737i 0.738131 0.674657i \(-0.235709\pi\)
−0.674657 + 0.738131i \(0.735709\pi\)
\(224\) −23.4219 8.61996i −1.56494 0.575945i
\(225\) 0 0
\(226\) 14.8386 9.25741i 0.987048 0.615794i
\(227\) 4.87410 4.87410i 0.323506 0.323506i −0.526605 0.850110i \(-0.676535\pi\)
0.850110 + 0.526605i \(0.176535\pi\)
\(228\) 0 0
\(229\) 17.1740 1.13489 0.567444 0.823412i \(-0.307932\pi\)
0.567444 + 0.823412i \(0.307932\pi\)
\(230\) −2.81069 + 20.8910i −0.185331 + 1.37751i
\(231\) 0 0
\(232\) 11.8334 14.5490i 0.776898 0.955187i
\(233\) 17.1696 17.1696i 1.12482 1.12482i 0.133811 0.991007i \(-0.457278\pi\)
0.991007 0.133811i \(-0.0427216\pi\)
\(234\) 0 0
\(235\) 23.1177 2.17649i 1.50803 0.141978i
\(236\) 7.63640 15.6002i 0.497087 1.01549i
\(237\) 0 0
\(238\) 11.4767 + 2.65827i 0.743926 + 0.172310i
\(239\) −19.8347 −1.28300 −0.641501 0.767122i \(-0.721688\pi\)
−0.641501 + 0.767122i \(0.721688\pi\)
\(240\) 0 0
\(241\) −2.89615 −0.186557 −0.0932787 0.995640i \(-0.529735\pi\)
−0.0932787 + 0.995640i \(0.529735\pi\)
\(242\) 13.2435 + 3.06748i 0.851321 + 0.197185i
\(243\) 0 0
\(244\) −11.0460 + 22.5655i −0.707145 + 1.44461i
\(245\) −21.4700 17.7751i −1.37167 1.13561i
\(246\) 0 0
\(247\) 0.693576 0.693576i 0.0441312 0.0441312i
\(248\) 0.148295 + 0.120615i 0.00941671 + 0.00765905i
\(249\) 0 0
\(250\) 11.7675 + 10.5605i 0.744245 + 0.667907i
\(251\) −8.93270 −0.563827 −0.281914 0.959440i \(-0.590969\pi\)
−0.281914 + 0.959440i \(0.590969\pi\)
\(252\) 0 0
\(253\) −5.55219 + 5.55219i −0.349063 + 0.349063i
\(254\) 6.51177 4.06252i 0.408584 0.254905i
\(255\) 0 0
\(256\) −3.95961 + 15.5023i −0.247476 + 0.968894i
\(257\) 12.4301 + 12.4301i 0.775367 + 0.775367i 0.979039 0.203672i \(-0.0652877\pi\)
−0.203672 + 0.979039i \(0.565288\pi\)
\(258\) 0 0
\(259\) −47.4782 −2.95015
\(260\) −4.80951 + 12.7256i −0.298273 + 0.789206i
\(261\) 0 0
\(262\) −2.55866 0.592644i −0.158075 0.0366137i
\(263\) −12.1529 + 12.1529i −0.749383 + 0.749383i −0.974363 0.224981i \(-0.927768\pi\)
0.224981 + 0.974363i \(0.427768\pi\)
\(264\) 0 0
\(265\) 18.0537 1.69972i 1.10903 0.104413i
\(266\) 1.70693 1.06491i 0.104658 0.0652936i
\(267\) 0 0
\(268\) −1.72160 5.02325i −0.105163 0.306844i
\(269\) 19.0912i 1.16401i −0.813185 0.582005i \(-0.802268\pi\)
0.813185 0.582005i \(-0.197732\pi\)
\(270\) 0 0
\(271\) 13.6087 0.826670 0.413335 0.910579i \(-0.364364\pi\)
0.413335 + 0.910579i \(0.364364\pi\)
\(272\) 0.941862 7.49336i 0.0571088 0.454352i
\(273\) 0 0
\(274\) 2.00334 + 3.21112i 0.121026 + 0.193991i
\(275\) 1.09927 + 5.78622i 0.0662882 + 0.348922i
\(276\) 0 0
\(277\) 13.9103 + 13.9103i 0.835788 + 0.835788i 0.988301 0.152514i \(-0.0487368\pi\)
−0.152514 + 0.988301i \(0.548737\pi\)
\(278\) −25.4014 5.88353i −1.52347 0.352870i
\(279\) 0 0
\(280\) −15.5002 + 23.2024i −0.926317 + 1.38661i
\(281\) 13.9435i 0.831799i 0.909411 + 0.415899i \(0.136533\pi\)
−0.909411 + 0.415899i \(0.863467\pi\)
\(282\) 0 0
\(283\) −14.3526 + 14.3526i −0.853174 + 0.853174i −0.990523 0.137349i \(-0.956142\pi\)
0.137349 + 0.990523i \(0.456142\pi\)
\(284\) 3.67748 7.51263i 0.218218 0.445793i
\(285\) 0 0
\(286\) −4.29940 + 2.68229i −0.254229 + 0.158607i
\(287\) 9.97323 + 9.97323i 0.588701 + 0.588701i
\(288\) 0 0
\(289\) 13.4352i 0.790303i
\(290\) −12.7168 16.6706i −0.746757 0.978932i
\(291\) 0 0
\(292\) 3.64874 + 10.6462i 0.213526 + 0.623022i
\(293\) −12.4180 12.4180i −0.725465 0.725465i 0.244248 0.969713i \(-0.421459\pi\)
−0.969713 + 0.244248i \(0.921459\pi\)
\(294\) 0 0
\(295\) −14.9580 12.3838i −0.870889 0.721014i
\(296\) 3.11656 + 30.2775i 0.181146 + 1.75985i
\(297\) 0 0
\(298\) 0.397533 1.71630i 0.0230285 0.0994224i
\(299\) 20.2773i 1.17267i
\(300\) 0 0
\(301\) 41.8357i 2.41137i
\(302\) −23.0891 5.34796i −1.32863 0.307740i
\(303\) 0 0
\(304\) −0.791152 1.01863i −0.0453757 0.0584223i
\(305\) 21.6366 + 17.9131i 1.23891 + 1.02570i
\(306\) 0 0
\(307\) −14.9940 14.9940i −0.855753 0.855753i 0.135082 0.990834i \(-0.456870\pi\)
−0.990834 + 0.135082i \(0.956870\pi\)
\(308\) −9.83259 + 3.36989i −0.560264 + 0.192017i
\(309\) 0 0
\(310\) 0.169920 0.129620i 0.00965080 0.00736190i
\(311\) 32.7316i 1.85604i 0.372534 + 0.928019i \(0.378489\pi\)
−0.372534 + 0.928019i \(0.621511\pi\)
\(312\) 0 0
\(313\) 8.25286 + 8.25286i 0.466479 + 0.466479i 0.900772 0.434293i \(-0.143002\pi\)
−0.434293 + 0.900772i \(0.643002\pi\)
\(314\) 7.31281 + 11.7216i 0.412686 + 0.661488i
\(315\) 0 0
\(316\) −8.49985 + 17.3641i −0.478154 + 0.976808i
\(317\) 8.30940 8.30940i 0.466702 0.466702i −0.434142 0.900844i \(-0.642948\pi\)
0.900844 + 0.434142i \(0.142948\pi\)
\(318\) 0 0
\(319\) 7.81027i 0.437291i
\(320\) 15.8140 + 8.36167i 0.884029 + 0.467432i
\(321\) 0 0
\(322\) −9.38498 + 40.5184i −0.523005 + 2.25800i
\(323\) 0.430487 + 0.430487i 0.0239529 + 0.0239529i
\(324\) 0 0
\(325\) 12.5733 + 8.55867i 0.697443 + 0.474749i
\(326\) 10.3138 6.43454i 0.571231 0.356376i
\(327\) 0 0
\(328\) 5.70541 7.01473i 0.315028 0.387324i
\(329\) 45.8149 2.52586
\(330\) 0 0
\(331\) 7.43429i 0.408626i −0.978906 0.204313i \(-0.934504\pi\)
0.978906 0.204313i \(-0.0654960\pi\)
\(332\) −0.536563 1.56557i −0.0294477 0.0859219i
\(333\) 0 0
\(334\) 2.98700 + 4.78782i 0.163441 + 0.261978i
\(335\) −5.91071 + 0.556482i −0.322936 + 0.0304038i
\(336\) 0 0
\(337\) −3.88868 + 3.88868i −0.211830 + 0.211830i −0.805044 0.593215i \(-0.797859\pi\)
0.593215 + 0.805044i \(0.297859\pi\)
\(338\) 1.19554 5.16160i 0.0650290 0.280754i
\(339\) 0 0
\(340\) −7.89847 2.98515i −0.428355 0.161893i
\(341\) 0.0796083 0.00431103
\(342\) 0 0
\(343\) −17.0501 17.0501i −0.920620 0.920620i
\(344\) −26.6793 + 2.74617i −1.43845 + 0.148064i
\(345\) 0 0
\(346\) −7.70594 12.3518i −0.414274 0.664034i
\(347\) −20.7432 + 20.7432i −1.11355 + 1.11355i −0.120889 + 0.992666i \(0.538574\pi\)
−0.992666 + 0.120889i \(0.961426\pi\)
\(348\) 0 0
\(349\) 3.04055 0.162757 0.0813783 0.996683i \(-0.474068\pi\)
0.0813783 + 0.996683i \(0.474068\pi\)
\(350\) 21.1630 + 22.9214i 1.13121 + 1.22520i
\(351\) 0 0
\(352\) 2.79446 + 6.04918i 0.148945 + 0.322422i
\(353\) −3.46489 + 3.46489i −0.184417 + 0.184417i −0.793278 0.608860i \(-0.791627\pi\)
0.608860 + 0.793278i \(0.291627\pi\)
\(354\) 0 0
\(355\) −7.20337 5.96371i −0.382315 0.316521i
\(356\) 1.00113 + 0.490062i 0.0530600 + 0.0259732i
\(357\) 0 0
\(358\) −3.05267 + 13.1795i −0.161339 + 0.696558i
\(359\) 8.63299 0.455632 0.227816 0.973704i \(-0.426842\pi\)
0.227816 + 0.973704i \(0.426842\pi\)
\(360\) 0 0
\(361\) −18.8960 −0.994528
\(362\) −1.41961 + 6.12897i −0.0746129 + 0.322131i
\(363\) 0 0
\(364\) −11.8013 + 24.1086i −0.618556 + 1.26363i
\(365\) 12.5271 1.17940i 0.655698 0.0617327i
\(366\) 0 0
\(367\) 15.3844 15.3844i 0.803060 0.803060i −0.180512 0.983573i \(-0.557776\pi\)
0.983573 + 0.180512i \(0.0577756\pi\)
\(368\) 26.4552 + 3.32523i 1.37907 + 0.173340i
\(369\) 0 0
\(370\) 33.7263 + 4.53755i 1.75335 + 0.235896i
\(371\) 35.7789 1.85755
\(372\) 0 0
\(373\) −7.40616 + 7.40616i −0.383476 + 0.383476i −0.872353 0.488877i \(-0.837407\pi\)
0.488877 + 0.872353i \(0.337407\pi\)
\(374\) −1.66483 2.66854i −0.0860866 0.137987i
\(375\) 0 0
\(376\) −3.00737 29.2168i −0.155093 1.50674i
\(377\) −14.2620 14.2620i −0.734532 0.734532i
\(378\) 0 0
\(379\) −6.54952 −0.336426 −0.168213 0.985751i \(-0.553800\pi\)
−0.168213 + 0.985751i \(0.553800\pi\)
\(380\) −1.31429 + 0.593327i −0.0674219 + 0.0304370i
\(381\) 0 0
\(382\) 1.01065 4.36336i 0.0517094 0.223249i
\(383\) 14.8778 14.8778i 0.760222 0.760222i −0.216140 0.976362i \(-0.569347\pi\)
0.976362 + 0.216140i \(0.0693468\pi\)
\(384\) 0 0
\(385\) 1.08927 + 11.5697i 0.0555142 + 0.589648i
\(386\) −1.14041 1.82795i −0.0580453 0.0930401i
\(387\) 0 0
\(388\) −28.3008 + 9.69945i −1.43676 + 0.492415i
\(389\) 0.254115i 0.0128842i −0.999979 0.00644208i \(-0.997949\pi\)
0.999979 0.00644208i \(-0.00205059\pi\)
\(390\) 0 0
\(391\) −12.5857 −0.636484
\(392\) −22.2468 + 27.3522i −1.12363 + 1.38150i
\(393\) 0 0
\(394\) 9.48647 5.91836i 0.477921 0.298163i
\(395\) 16.6493 + 13.7841i 0.837718 + 0.693552i
\(396\) 0 0
\(397\) −20.6584 20.6584i −1.03682 1.03682i −0.999296 0.0375215i \(-0.988054\pi\)
−0.0375215 0.999296i \(-0.511946\pi\)
\(398\) 5.03268 21.7279i 0.252265 1.08912i
\(399\) 0 0
\(400\) 13.2281 15.0006i 0.661407 0.750028i
\(401\) 20.6863i 1.03303i −0.856279 0.516513i \(-0.827230\pi\)
0.856279 0.516513i \(-0.172770\pi\)
\(402\) 0 0
\(403\) 0.145370 0.145370i 0.00724139 0.00724139i
\(404\) 17.1167 + 8.37874i 0.851588 + 0.416858i
\(405\) 0 0
\(406\) −21.8977 35.0996i −1.08677 1.74196i
\(407\) 8.96340 + 8.96340i 0.444299 + 0.444299i
\(408\) 0 0
\(409\) 26.9787i 1.33401i −0.745053 0.667005i \(-0.767576\pi\)
0.745053 0.667005i \(-0.232424\pi\)
\(410\) −6.13136 8.03766i −0.302806 0.396952i
\(411\) 0 0
\(412\) −0.148969 0.434658i −0.00733916 0.0214140i
\(413\) −27.0931 27.0931i −1.33317 1.33317i
\(414\) 0 0
\(415\) −1.84216 + 0.173436i −0.0904282 + 0.00851364i
\(416\) 16.1490 + 5.94333i 0.791771 + 0.291395i
\(417\) 0 0
\(418\) −0.523294 0.121207i −0.0255951 0.00592841i
\(419\) 34.3778i 1.67946i −0.543001 0.839732i \(-0.682712\pi\)
0.543001 0.839732i \(-0.317288\pi\)
\(420\) 0 0
\(421\) 4.05773i 0.197762i 0.995099 + 0.0988809i \(0.0315263\pi\)
−0.995099 + 0.0988809i \(0.968474\pi\)
\(422\) 3.48710 15.0551i 0.169749 0.732871i
\(423\) 0 0
\(424\) −2.34859 22.8167i −0.114058 1.10808i
\(425\) −5.31217 + 7.80398i −0.257678 + 0.378549i
\(426\) 0 0
\(427\) 39.1899 + 39.1899i 1.89653 + 1.89653i
\(428\) −31.5607 + 10.8167i −1.52554 + 0.522844i
\(429\) 0 0
\(430\) −3.99830 + 29.7182i −0.192815 + 1.43314i
\(431\) 16.0853i 0.774800i −0.921912 0.387400i \(-0.873373\pi\)
0.921912 0.387400i \(-0.126627\pi\)
\(432\) 0 0
\(433\) −3.04812 3.04812i −0.146483 0.146483i 0.630062 0.776545i \(-0.283030\pi\)
−0.776545 + 0.630062i \(0.783030\pi\)
\(434\) 0.357762 0.223199i 0.0171731 0.0107139i
\(435\) 0 0
\(436\) 19.5084 + 9.54947i 0.934281 + 0.457337i
\(437\) −1.51983 + 1.51983i −0.0727033 + 0.0727033i
\(438\) 0 0
\(439\) 4.78470i 0.228361i −0.993460 0.114181i \(-0.963576\pi\)
0.993460 0.114181i \(-0.0364243\pi\)
\(440\) 7.30667 1.45410i 0.348332 0.0693214i
\(441\) 0 0
\(442\) −7.91302 1.83283i −0.376384 0.0871790i
\(443\) −11.2608 11.2608i −0.535019 0.535019i 0.387043 0.922062i \(-0.373497\pi\)
−0.922062 + 0.387043i \(0.873497\pi\)
\(444\) 0 0
\(445\) 0.794726 0.959922i 0.0376736 0.0455047i
\(446\) −1.00343 1.60839i −0.0475139 0.0761594i
\(447\) 0 0
\(448\) 29.5185 + 19.3503i 1.39462 + 0.914218i
\(449\) −7.49133 −0.353538 −0.176769 0.984252i \(-0.556565\pi\)
−0.176769 + 0.984252i \(0.556565\pi\)
\(450\) 0 0
\(451\) 3.76569i 0.177319i
\(452\) −23.3979 + 8.01907i −1.10054 + 0.377185i
\(453\) 0 0
\(454\) −8.27065 + 5.15984i −0.388161 + 0.242163i
\(455\) 23.1161 + 19.1380i 1.08370 + 0.897202i
\(456\) 0 0
\(457\) −14.2198 + 14.2198i −0.665173 + 0.665173i −0.956595 0.291422i \(-0.905872\pi\)
0.291422 + 0.956595i \(0.405872\pi\)
\(458\) −23.6613 5.48048i −1.10562 0.256086i
\(459\) 0 0
\(460\) 10.5390 27.8855i 0.491386 1.30017i
\(461\) 19.4366 0.905254 0.452627 0.891700i \(-0.350487\pi\)
0.452627 + 0.891700i \(0.350487\pi\)
\(462\) 0 0
\(463\) −2.18789 2.18789i −0.101680 0.101680i 0.654437 0.756117i \(-0.272906\pi\)
−0.756117 + 0.654437i \(0.772906\pi\)
\(464\) −20.9461 + 16.2685i −0.972398 + 0.755246i
\(465\) 0 0
\(466\) −29.1343 + 18.1762i −1.34962 + 0.841994i
\(467\) 2.06992 2.06992i 0.0957845 0.0957845i −0.657591 0.753375i \(-0.728424\pi\)
0.753375 + 0.657591i \(0.228424\pi\)
\(468\) 0 0
\(469\) −11.7139 −0.540897
\(470\) −32.5447 4.37858i −1.50118 0.201969i
\(471\) 0 0
\(472\) −15.4992 + 19.0561i −0.713410 + 0.877129i
\(473\) −7.89816 + 7.89816i −0.363158 + 0.363158i
\(474\) 0 0
\(475\) 0.300908 + 1.58389i 0.0138066 + 0.0726739i
\(476\) −14.9636 7.32480i −0.685857 0.335732i
\(477\) 0 0
\(478\) 27.3271 + 6.32957i 1.24991 + 0.289508i
\(479\) −27.5481 −1.25871 −0.629353 0.777120i \(-0.716680\pi\)
−0.629353 + 0.777120i \(0.716680\pi\)
\(480\) 0 0
\(481\) 32.7355 1.49261
\(482\) 3.99014 + 0.924206i 0.181746 + 0.0420964i
\(483\) 0 0
\(484\) −17.2671 8.45238i −0.784870 0.384199i
\(485\) 3.13520 + 33.3008i 0.142362 + 1.51211i
\(486\) 0 0
\(487\) 27.7336 27.7336i 1.25673 1.25673i 0.304083 0.952646i \(-0.401650\pi\)
0.952646 0.304083i \(-0.0983500\pi\)
\(488\) 22.4195 27.5644i 1.01488 1.24778i
\(489\) 0 0
\(490\) 23.9077 + 31.3409i 1.08004 + 1.41584i
\(491\) −2.58679 −0.116740 −0.0583700 0.998295i \(-0.518590\pi\)
−0.0583700 + 0.998295i \(0.518590\pi\)
\(492\) 0 0
\(493\) 8.85213 8.85213i 0.398680 0.398680i
\(494\) −1.17690 + 0.734236i −0.0529511 + 0.0330349i
\(495\) 0 0
\(496\) −0.165821 0.213499i −0.00744559 0.00958639i
\(497\) −13.0473 13.0473i −0.585252 0.585252i
\(498\) 0 0
\(499\) −25.5951 −1.14579 −0.572897 0.819627i \(-0.694181\pi\)
−0.572897 + 0.819627i \(0.694181\pi\)
\(500\) −12.8426 18.3049i −0.574338 0.818619i
\(501\) 0 0
\(502\) 12.3069 + 2.85056i 0.549285 + 0.127227i
\(503\) 9.39909 9.39909i 0.419085 0.419085i −0.465804 0.884888i \(-0.654235\pi\)
0.884888 + 0.465804i \(0.154235\pi\)
\(504\) 0 0
\(505\) 13.5877 16.4121i 0.604643 0.730328i
\(506\) 9.42126 5.87768i 0.418826 0.261295i
\(507\) 0 0
\(508\) −10.2679 + 3.51909i −0.455566 + 0.156134i
\(509\) 11.5075i 0.510059i 0.966933 + 0.255030i \(0.0820852\pi\)
−0.966933 + 0.255030i \(0.917915\pi\)
\(510\) 0 0
\(511\) 24.8263 1.09825
\(512\) 10.4023 20.0946i 0.459723 0.888062i
\(513\) 0 0
\(514\) −13.1588 21.0920i −0.580409 0.930329i
\(515\) −0.511449 + 0.0481519i −0.0225371 + 0.00212183i
\(516\) 0 0
\(517\) −8.64938 8.64938i −0.380399 0.380399i
\(518\) 65.4126 + 15.1510i 2.87406 + 0.665698i
\(519\) 0 0
\(520\) 10.6872 15.9977i 0.468664 0.701547i
\(521\) 8.12668i 0.356036i 0.984027 + 0.178018i \(0.0569686\pi\)
−0.984027 + 0.178018i \(0.943031\pi\)
\(522\) 0 0
\(523\) 23.2646 23.2646i 1.01729 1.01729i 0.0174440 0.999848i \(-0.494447\pi\)
0.999848 0.0174440i \(-0.00555287\pi\)
\(524\) 3.33605 + 1.63302i 0.145736 + 0.0713387i
\(525\) 0 0
\(526\) 20.6218 12.8654i 0.899152 0.560958i
\(527\) 0.0902278 + 0.0902278i 0.00393038 + 0.00393038i
\(528\) 0 0
\(529\) 21.4335i 0.931892i
\(530\) −25.4157 3.41944i −1.10399 0.148531i
\(531\) 0 0
\(532\) −2.69153 + 0.922457i −0.116692 + 0.0399936i
\(533\) −6.87638 6.87638i −0.297849 0.297849i
\(534\) 0 0
\(535\) 3.49633 + 37.1365i 0.151160 + 1.60555i
\(536\) 0.768921 + 7.47011i 0.0332123 + 0.322660i
\(537\) 0 0
\(538\) −6.09229 + 26.3027i −0.262657 + 1.13399i
\(539\) 14.6834i 0.632458i
\(540\) 0 0
\(541\) 21.6496i 0.930787i 0.885104 + 0.465393i \(0.154087\pi\)
−0.885104 + 0.465393i \(0.845913\pi\)
\(542\) −18.7492 4.34275i −0.805349 0.186537i
\(543\) 0 0
\(544\) −3.68889 + 10.0233i −0.158160 + 0.429747i
\(545\) 15.4862 18.7053i 0.663357 0.801246i
\(546\) 0 0
\(547\) −15.4574 15.4574i −0.660912 0.660912i 0.294683 0.955595i \(-0.404786\pi\)
−0.955595 + 0.294683i \(0.904786\pi\)
\(548\) −1.73536 5.06339i −0.0741308 0.216297i
\(549\) 0 0
\(550\) 0.331969 8.32269i 0.0141552 0.354881i
\(551\) 2.13794i 0.0910795i
\(552\) 0 0
\(553\) 30.1566 + 30.1566i 1.28239 + 1.28239i
\(554\) −14.7258 23.6037i −0.625637 1.00283i
\(555\) 0 0
\(556\) 33.1189 + 16.2119i 1.40456 + 0.687539i
\(557\) 10.9318 10.9318i 0.463194 0.463194i −0.436507 0.899701i \(-0.643785\pi\)
0.899701 + 0.436507i \(0.143785\pi\)
\(558\) 0 0
\(559\) 28.8451i 1.22002i
\(560\) 28.7595 27.0206i 1.21531 1.14183i
\(561\) 0 0
\(562\) 4.44958 19.2105i 0.187694 0.810346i
\(563\) −13.9005 13.9005i −0.585835 0.585835i 0.350666 0.936501i \(-0.385955\pi\)
−0.936501 + 0.350666i \(0.885955\pi\)
\(564\) 0 0
\(565\) 2.59205 + 27.5316i 0.109048 + 1.15826i
\(566\) 24.3543 15.1940i 1.02369 0.638652i
\(567\) 0 0
\(568\) −7.46401 + 9.17690i −0.313183 + 0.385054i
\(569\) 3.03632 0.127289 0.0636446 0.997973i \(-0.479728\pi\)
0.0636446 + 0.997973i \(0.479728\pi\)
\(570\) 0 0
\(571\) 1.26119i 0.0527792i −0.999652 0.0263896i \(-0.991599\pi\)
0.999652 0.0263896i \(-0.00840105\pi\)
\(572\) 6.77942 2.32349i 0.283462 0.0971498i
\(573\) 0 0
\(574\) −10.5579 16.9231i −0.440678 0.706357i
\(575\) −27.5519 18.7546i −1.14899 0.782119i
\(576\) 0 0
\(577\) −5.10444 + 5.10444i −0.212501 + 0.212501i −0.805329 0.592828i \(-0.798011\pi\)
0.592828 + 0.805329i \(0.298011\pi\)
\(578\) −4.28736 + 18.5101i −0.178331 + 0.769920i
\(579\) 0 0
\(580\) 12.2006 + 27.0259i 0.506602 + 1.12219i
\(581\) −3.65081 −0.151461
\(582\) 0 0
\(583\) −6.75469 6.75469i −0.279751 0.279751i
\(584\) −1.62964 15.8321i −0.0674351 0.655136i
\(585\) 0 0
\(586\) 13.1459 + 21.0715i 0.543054 + 0.870454i
\(587\) −2.16591 + 2.16591i −0.0893966 + 0.0893966i −0.750391 0.660994i \(-0.770135\pi\)
0.660994 + 0.750391i \(0.270135\pi\)
\(588\) 0 0
\(589\) 0.0217916 0.000897908
\(590\) 16.6564 + 21.8350i 0.685732 + 0.898934i
\(591\) 0 0
\(592\) 5.36823 42.7091i 0.220633 1.75533i
\(593\) −14.8495 + 14.8495i −0.609795 + 0.609795i −0.942892 0.333097i \(-0.891906\pi\)
0.333097 + 0.942892i \(0.391906\pi\)
\(594\) 0 0
\(595\) −11.8785 + 14.3476i −0.486971 + 0.588196i
\(596\) −1.09539 + 2.23775i −0.0448690 + 0.0916618i
\(597\) 0 0
\(598\) 6.47080 27.9368i 0.264611 1.14242i
\(599\) −20.1979 −0.825262 −0.412631 0.910898i \(-0.635390\pi\)
−0.412631 + 0.910898i \(0.635390\pi\)
\(600\) 0 0
\(601\) −30.9787 −1.26365 −0.631823 0.775113i \(-0.717693\pi\)
−0.631823 + 0.775113i \(0.717693\pi\)
\(602\) −13.3504 + 57.6388i −0.544123 + 2.34918i
\(603\) 0 0
\(604\) 30.1042 + 14.7362i 1.22492 + 0.599607i
\(605\) −13.7071 + 16.5563i −0.557272 + 0.673110i
\(606\) 0 0
\(607\) −7.72619 + 7.72619i −0.313596 + 0.313596i −0.846301 0.532705i \(-0.821176\pi\)
0.532705 + 0.846301i \(0.321176\pi\)
\(608\) 0.764941 + 1.65587i 0.0310224 + 0.0671545i
\(609\) 0 0
\(610\) −24.0932 31.5841i −0.975506 1.27880i
\(611\) −31.5886 −1.27794
\(612\) 0 0
\(613\) 7.56398 7.56398i 0.305506 0.305506i −0.537657 0.843164i \(-0.680691\pi\)
0.843164 + 0.537657i \(0.180691\pi\)
\(614\) 15.8730 + 25.4426i 0.640582 + 1.02678i
\(615\) 0 0
\(616\) 14.6221 1.50510i 0.589142 0.0606422i
\(617\) −20.1379 20.1379i −0.810722 0.810722i 0.174020 0.984742i \(-0.444324\pi\)
−0.984742 + 0.174020i \(0.944324\pi\)
\(618\) 0 0
\(619\) 26.5448 1.06692 0.533462 0.845824i \(-0.320891\pi\)
0.533462 + 0.845824i \(0.320891\pi\)
\(620\) −0.275469 + 0.124358i −0.0110631 + 0.00499434i
\(621\) 0 0
\(622\) 10.4451 45.0956i 0.418812 1.80817i
\(623\) 1.73869 1.73869i 0.0696591 0.0696591i
\(624\) 0 0
\(625\) −23.2582 + 9.16811i −0.930330 + 0.366724i
\(626\) −8.73667 14.0039i −0.349188 0.559708i
\(627\) 0 0
\(628\) −6.33460 18.4829i −0.252778 0.737550i
\(629\) 20.3182i 0.810139i
\(630\) 0 0
\(631\) −38.2805 −1.52392 −0.761961 0.647623i \(-0.775763\pi\)
−0.761961 + 0.647623i \(0.775763\pi\)
\(632\) 17.2517 21.2108i 0.686237 0.843720i
\(633\) 0 0
\(634\) −14.0998 + 8.79653i −0.559976 + 0.349355i
\(635\) 1.13749 + 12.0820i 0.0451401 + 0.479458i
\(636\) 0 0
\(637\) 26.8128 + 26.8128i 1.06236 + 1.06236i
\(638\) −2.49238 + 10.7605i −0.0986741 + 0.426013i
\(639\) 0 0
\(640\) −19.1192 16.5667i −0.755754 0.654856i
\(641\) 24.4013i 0.963792i 0.876228 + 0.481896i \(0.160052\pi\)
−0.876228 + 0.481896i \(0.839948\pi\)
\(642\) 0 0
\(643\) −1.08062 + 1.08062i −0.0426157 + 0.0426157i −0.728094 0.685478i \(-0.759593\pi\)
0.685478 + 0.728094i \(0.259593\pi\)
\(644\) 25.8601 52.8289i 1.01903 2.08175i
\(645\) 0 0
\(646\) −0.455724 0.730474i −0.0179302 0.0287401i
\(647\) −22.0445 22.0445i −0.866659 0.866659i 0.125442 0.992101i \(-0.459965\pi\)
−0.992101 + 0.125442i \(0.959965\pi\)
\(648\) 0 0
\(649\) 10.2298i 0.401556i
\(650\) −14.5916 15.8040i −0.572328 0.619882i
\(651\) 0 0
\(652\) −16.2631 + 5.57381i −0.636914 + 0.218287i
\(653\) 20.9241 + 20.9241i 0.818823 + 0.818823i 0.985937 0.167115i \(-0.0534450\pi\)
−0.167115 + 0.985937i \(0.553445\pi\)
\(654\) 0 0
\(655\) 2.64824 3.19872i 0.103475 0.124984i
\(656\) −10.0991 + 7.84378i −0.394302 + 0.306248i
\(657\) 0 0
\(658\) −63.1209 14.6202i −2.46071 0.569956i
\(659\) 7.22520i 0.281454i −0.990048 0.140727i \(-0.955056\pi\)
0.990048 0.140727i \(-0.0449440\pi\)
\(660\) 0 0
\(661\) 20.3836i 0.792830i −0.918071 0.396415i \(-0.870254\pi\)
0.918071 0.396415i \(-0.129746\pi\)
\(662\) −2.37240 + 10.2425i −0.0922059 + 0.398087i
\(663\) 0 0
\(664\) 0.239646 + 2.32817i 0.00930006 + 0.0903507i
\(665\) 0.298171 + 3.16704i 0.0115626 + 0.122813i
\(666\) 0 0
\(667\) 31.2523 + 31.2523i 1.21009 + 1.21009i
\(668\) −2.58744 7.54957i −0.100111 0.292102i
\(669\) 0 0
\(670\) 8.32100 + 1.11951i 0.321468 + 0.0432505i
\(671\) 14.7973i 0.571244i
\(672\) 0 0
\(673\) −19.4517 19.4517i −0.749807 0.749807i 0.224636 0.974443i \(-0.427881\pi\)
−0.974443 + 0.224636i \(0.927881\pi\)
\(674\) 6.59852 4.11664i 0.254165 0.158567i
\(675\) 0 0
\(676\) −3.29429 + 6.72983i −0.126704 + 0.258839i
\(677\) 24.8145 24.8145i 0.953698 0.953698i −0.0452768 0.998974i \(-0.514417\pi\)
0.998974 + 0.0452768i \(0.0144170\pi\)
\(678\) 0 0
\(679\) 65.9957i 2.53268i
\(680\) 9.92943 + 6.63329i 0.380776 + 0.254375i
\(681\) 0 0
\(682\) −0.109680 0.0254042i −0.00419985 0.000972779i
\(683\) −7.85886 7.85886i −0.300711 0.300711i 0.540581 0.841292i \(-0.318204\pi\)
−0.841292 + 0.540581i \(0.818204\pi\)
\(684\) 0 0
\(685\) −5.95794 + 0.560928i −0.227641 + 0.0214320i
\(686\) 18.0497 + 28.9316i 0.689139 + 1.10461i
\(687\) 0 0
\(688\) 37.6334 + 4.73025i 1.43476 + 0.180339i
\(689\) −24.6690 −0.939814
\(690\) 0 0
\(691\) 49.6748i 1.88972i −0.327479 0.944858i \(-0.606199\pi\)
0.327479 0.944858i \(-0.393801\pi\)
\(692\) 6.67514 + 19.4766i 0.253751 + 0.740389i
\(693\) 0 0
\(694\) 35.1982 21.9593i 1.33611 0.833563i
\(695\) 26.2906 31.7556i 0.997260 1.20456i
\(696\) 0 0
\(697\) 4.26802 4.26802i 0.161663 0.161663i
\(698\) −4.18908 0.970285i −0.158559 0.0367258i
\(699\) 0 0
\(700\) −21.8425 38.3332i −0.825570 1.44886i
\(701\) −30.5703 −1.15462 −0.577312 0.816524i \(-0.695898\pi\)
−0.577312 + 0.816524i \(0.695898\pi\)
\(702\) 0 0
\(703\) 2.45360 + 2.45360i 0.0925393 + 0.0925393i
\(704\) −1.91965 9.22594i −0.0723494 0.347716i
\(705\) 0 0
\(706\) 5.87941 3.66801i 0.221275 0.138047i
\(707\) 29.7269 29.7269i 1.11799 1.11799i
\(708\) 0 0
\(709\) 11.1384 0.418310 0.209155 0.977882i \(-0.432929\pi\)
0.209155 + 0.977882i \(0.432929\pi\)
\(710\) 8.02125 + 10.5151i 0.301032 + 0.394626i
\(711\) 0 0
\(712\) −1.22292 0.994655i −0.0458307 0.0372763i
\(713\) −0.318548 + 0.318548i −0.0119297 + 0.0119297i
\(714\) 0 0
\(715\) −0.751033 7.97714i −0.0280870 0.298328i
\(716\) 8.41157 17.1838i 0.314355 0.642188i
\(717\) 0 0
\(718\) −11.8940 2.75492i −0.443880 0.102813i
\(719\) 41.0316 1.53022 0.765111 0.643899i \(-0.222684\pi\)
0.765111 + 0.643899i \(0.222684\pi\)
\(720\) 0 0
\(721\) −1.01359 −0.0377482
\(722\) 26.0338 + 6.03001i 0.968878 + 0.224414i
\(723\) 0 0
\(724\) 3.91169 7.99110i 0.145377 0.296987i
\(725\) 32.5696 6.18758i 1.20961 0.229801i
\(726\) 0 0
\(727\) −4.35975 + 4.35975i −0.161694 + 0.161694i −0.783317 0.621623i \(-0.786474\pi\)
0.621623 + 0.783317i \(0.286474\pi\)
\(728\) 23.9525 29.4493i 0.887740 1.09146i
\(729\) 0 0
\(730\) −17.6354 2.37268i −0.652716 0.0878168i
\(731\) −17.9035 −0.662185
\(732\) 0 0
\(733\) −28.3786 + 28.3786i −1.04819 + 1.04819i −0.0494094 + 0.998779i \(0.515734\pi\)
−0.998779 + 0.0494094i \(0.984266\pi\)
\(734\) −26.1051 + 16.2863i −0.963558 + 0.601139i
\(735\) 0 0
\(736\) −35.3873 13.0236i −1.30439 0.480055i
\(737\) 2.21146 + 2.21146i 0.0814603 + 0.0814603i
\(738\) 0 0
\(739\) 6.53862 0.240527 0.120264 0.992742i \(-0.461626\pi\)
0.120264 + 0.992742i \(0.461626\pi\)
\(740\) −45.0180 17.0141i −1.65490 0.625452i
\(741\) 0 0
\(742\) −49.2940 11.4176i −1.80964 0.419153i
\(743\) −20.0409 + 20.0409i −0.735230 + 0.735230i −0.971651 0.236421i \(-0.924026\pi\)
0.236421 + 0.971651i \(0.424026\pi\)
\(744\) 0 0
\(745\) 2.14563 + 1.77638i 0.0786098 + 0.0650816i
\(746\) 12.5672 7.84033i 0.460117 0.287055i
\(747\) 0 0
\(748\) 1.44214 + 4.20783i 0.0527297 + 0.153854i
\(749\) 73.5974i 2.68919i
\(750\) 0 0
\(751\) 7.89337 0.288033 0.144017 0.989575i \(-0.453998\pi\)
0.144017 + 0.989575i \(0.453998\pi\)
\(752\) −5.18016 + 41.2128i −0.188901 + 1.50288i
\(753\) 0 0
\(754\) 15.0981 + 24.2006i 0.549842 + 0.881334i
\(755\) 23.8974 28.8649i 0.869717 1.05050i
\(756\) 0 0
\(757\) −5.76852 5.76852i −0.209660 0.209660i 0.594463 0.804123i \(-0.297365\pi\)
−0.804123 + 0.594463i \(0.797365\pi\)
\(758\) 9.02352 + 2.09005i 0.327749 + 0.0759141i
\(759\) 0 0
\(760\) 2.00009 0.398038i 0.0725510 0.0144384i
\(761\) 11.7806i 0.427045i 0.976938 + 0.213522i \(0.0684936\pi\)
−0.976938 + 0.213522i \(0.931506\pi\)
\(762\) 0 0
\(763\) 33.8805 33.8805i 1.22656 1.22656i
\(764\) −2.78483 + 5.68905i −0.100752 + 0.205823i
\(765\) 0 0
\(766\) −25.2455 + 15.7500i −0.912158 + 0.569072i
\(767\) 18.6803 + 18.6803i 0.674506 + 0.674506i
\(768\) 0 0
\(769\) 34.7788i 1.25416i 0.778956 + 0.627078i \(0.215749\pi\)
−0.778956 + 0.627078i \(0.784251\pi\)
\(770\) 2.19135 16.2877i 0.0789708 0.586967i
\(771\) 0 0
\(772\) 0.987861 + 2.88236i 0.0355539 + 0.103738i
\(773\) 27.6201 + 27.6201i 0.993426 + 0.993426i 0.999979 0.00655287i \(-0.00208586\pi\)
−0.00655287 + 0.999979i \(0.502086\pi\)
\(774\) 0 0
\(775\) 0.0630687 + 0.331975i 0.00226549 + 0.0119249i
\(776\) 42.0864 4.33208i 1.51081 0.155513i
\(777\) 0 0
\(778\) −0.0810921 + 0.350105i −0.00290729 + 0.0125519i
\(779\) 1.03080i 0.0369323i
\(780\) 0 0
\(781\) 4.92640i 0.176280i
\(782\) 17.3398 + 4.01628i 0.620068 + 0.143622i
\(783\) 0 0
\(784\) 39.3788 30.5849i 1.40639 1.09232i
\(785\) −21.7483 + 2.04756i −0.776232 + 0.0730807i
\(786\) 0 0
\(787\) 18.2310 + 18.2310i 0.649864 + 0.649864i 0.952960 0.303096i \(-0.0980203\pi\)
−0.303096 + 0.952960i \(0.598020\pi\)
\(788\) −14.9585 + 5.12668i −0.532875 + 0.182631i
\(789\) 0 0
\(790\) −18.5397 24.3039i −0.659613 0.864694i
\(791\) 54.5623i 1.94001i
\(792\) 0 0
\(793\) −27.0208 27.0208i −0.959537 0.959537i
\(794\) 21.8695 + 35.0544i 0.776120 + 1.24403i
\(795\) 0 0
\(796\) −13.8674 + 28.3294i −0.491518 + 1.00411i
\(797\) −11.4983 + 11.4983i −0.407290 + 0.407290i −0.880793 0.473502i \(-0.842990\pi\)
0.473502 + 0.880793i \(0.342990\pi\)
\(798\) 0 0
\(799\) 19.6064i 0.693623i
\(800\) −23.0118 + 16.4455i −0.813591 + 0.581438i
\(801\) 0 0
\(802\) −6.60133 + 28.5004i −0.233101 + 1.00638i
\(803\) −4.68695 4.68695i −0.165399 0.165399i
\(804\) 0 0
\(805\) −50.6542 41.9369i −1.78533 1.47808i
\(806\) −0.246672 + 0.153892i −0.00868863 + 0.00542061i
\(807\) 0 0
\(808\) −20.9086 17.0059i −0.735561 0.598266i
\(809\) −17.8481 −0.627506 −0.313753 0.949505i \(-0.601586\pi\)
−0.313753 + 0.949505i \(0.601586\pi\)
\(810\) 0 0
\(811\) 41.5242i 1.45811i 0.684454 + 0.729056i \(0.260041\pi\)
−0.684454 + 0.729056i \(0.739959\pi\)
\(812\) 18.9685 + 55.3460i 0.665665 + 1.94226i
\(813\) 0 0
\(814\) −9.48887 15.2096i −0.332585 0.533096i
\(815\) 1.80165 + 19.1364i 0.0631091 + 0.670317i
\(816\) 0 0
\(817\) −2.16201 + 2.16201i −0.0756390 + 0.0756390i
\(818\) −8.60931 + 37.1696i −0.301017 + 1.29960i
\(819\) 0 0
\(820\) 5.88247 + 13.0304i 0.205425 + 0.455042i
\(821\) −28.9849 −1.01158 −0.505790 0.862657i \(-0.668799\pi\)
−0.505790 + 0.862657i \(0.668799\pi\)
\(822\) 0 0
\(823\) 20.6586 + 20.6586i 0.720112 + 0.720112i 0.968628 0.248516i \(-0.0799428\pi\)
−0.248516 + 0.968628i \(0.579943\pi\)
\(824\) 0.0665341 + 0.646383i 0.00231783 + 0.0225178i
\(825\) 0 0
\(826\) 28.6814 + 45.9731i 0.997955 + 1.59961i
\(827\) 25.4075 25.4075i 0.883504 0.883504i −0.110385 0.993889i \(-0.535208\pi\)
0.993889 + 0.110385i \(0.0352082\pi\)
\(828\) 0 0
\(829\) −24.7882 −0.860931 −0.430465 0.902607i \(-0.641651\pi\)
−0.430465 + 0.902607i \(0.641651\pi\)
\(830\) 2.59336 + 0.348913i 0.0900170 + 0.0121109i
\(831\) 0 0
\(832\) −20.3525 13.3418i −0.705598 0.462542i
\(833\) −16.6421 + 16.6421i −0.576614 + 0.576614i
\(834\) 0 0
\(835\) −8.88336 + 0.836351i −0.307421 + 0.0289431i
\(836\) 0.682283 + 0.333982i 0.0235973 + 0.0115510i
\(837\) 0 0
\(838\) −10.9705 + 47.3636i −0.378969 + 1.63615i
\(839\) 52.8553 1.82477 0.912383 0.409338i \(-0.134240\pi\)
0.912383 + 0.409338i \(0.134240\pi\)
\(840\) 0 0
\(841\) −14.9627 −0.515954
\(842\) 1.29488 5.59050i 0.0446247 0.192661i
\(843\) 0 0
\(844\) −9.60864 + 19.6292i −0.330743 + 0.675666i
\(845\) 6.45279 + 5.34230i 0.221983 + 0.183781i
\(846\) 0 0
\(847\) −29.9881 + 29.9881i −1.03040 + 1.03040i
\(848\) −4.04542 + 32.1850i −0.138920 + 1.10524i
\(849\) 0 0
\(850\) 9.80916 9.05665i 0.336451 0.310641i
\(851\) −71.7331 −2.45898
\(852\) 0 0
\(853\) −7.39491 + 7.39491i −0.253197 + 0.253197i −0.822280 0.569083i \(-0.807298\pi\)
0.569083 + 0.822280i \(0.307298\pi\)
\(854\) −41.4873 66.4995i −1.41967 2.27557i
\(855\) 0 0
\(856\) 46.9341 4.83107i 1.60418 0.165123i
\(857\) 6.82308 + 6.82308i 0.233072 + 0.233072i 0.813974 0.580902i \(-0.197300\pi\)
−0.580902 + 0.813974i \(0.697300\pi\)
\(858\) 0 0
\(859\) 43.6736 1.49012 0.745061 0.666996i \(-0.232420\pi\)
0.745061 + 0.666996i \(0.232420\pi\)
\(860\) 14.9921 39.6679i 0.511227 1.35267i
\(861\) 0 0
\(862\) −5.13306 + 22.1613i −0.174833 + 0.754817i
\(863\) 13.1338 13.1338i 0.447080 0.447080i −0.447303 0.894383i \(-0.647615\pi\)
0.894383 + 0.447303i \(0.147615\pi\)
\(864\) 0 0
\(865\) 22.9175 2.15764i 0.779219 0.0733620i
\(866\) 3.22681 + 5.17221i 0.109651 + 0.175759i
\(867\) 0 0
\(868\) −0.564129 + 0.193342i −0.0191478 + 0.00656246i
\(869\) 11.3865i 0.386261i
\(870\) 0 0
\(871\) 8.07654 0.273663
\(872\) −23.8301 19.3821i −0.806987 0.656361i
\(873\) 0 0
\(874\) 2.57893 1.60893i 0.0872336 0.0544228i
\(875\) −47.3840 + 13.7083i −1.60187 + 0.463426i
\(876\) 0 0
\(877\) 28.9437 + 28.9437i 0.977360 + 0.977360i 0.999749 0.0223891i \(-0.00712727\pi\)
−0.0223891 + 0.999749i \(0.507127\pi\)
\(878\) −1.52687 + 6.59207i −0.0515294 + 0.222472i
\(879\) 0 0
\(880\) −10.5307 0.328304i −0.354990 0.0110671i
\(881\) 7.23302i 0.243687i −0.992549 0.121843i \(-0.961119\pi\)
0.992549 0.121843i \(-0.0388805\pi\)
\(882\) 0 0
\(883\) −7.01625 + 7.01625i −0.236116 + 0.236116i −0.815239 0.579124i \(-0.803395\pi\)
0.579124 + 0.815239i \(0.303395\pi\)
\(884\) 10.3172 + 5.05033i 0.347005 + 0.169861i
\(885\) 0 0
\(886\) 11.9210 + 19.1080i 0.400494 + 0.641946i
\(887\) −15.2597 15.2597i −0.512371 0.512371i 0.402881 0.915252i \(-0.368009\pi\)
−0.915252 + 0.402881i \(0.868009\pi\)
\(888\) 0 0
\(889\) 23.9441i 0.803061i
\(890\) −1.40125 + 1.06891i −0.0469700 + 0.0358301i
\(891\) 0 0
\(892\) 0.869206 + 2.53615i 0.0291032 + 0.0849166i
\(893\) −2.36764 2.36764i −0.0792301 0.0792301i
\(894\) 0 0
\(895\) −16.4764 13.6409i −0.550745 0.455965i
\(896\) −34.4938 36.0795i −1.15236 1.20533i
\(897\) 0 0
\(898\) 10.3211 + 2.39060i 0.344420 + 0.0797753i
\(899\) 0.448102i 0.0149450i
\(900\) 0 0
\(901\) 15.3115i 0.510100i
\(902\) −1.20169 + 5.18813i −0.0400119 + 0.172746i
\(903\) 0 0
\(904\) 34.7952 3.58157i 1.15727 0.119121i
\(905\) −7.66214 6.34353i −0.254698 0.210866i
\(906\) 0 0
\(907\) −36.0510 36.0510i −1.19706 1.19706i −0.975044 0.222011i \(-0.928738\pi\)
−0.222011 0.975044i \(-0.571262\pi\)
\(908\) 13.0414 4.46963i 0.432793 0.148330i
\(909\) 0 0
\(910\) −25.7408 33.7438i −0.853298 1.11860i
\(911\) 24.0944i 0.798282i −0.916890 0.399141i \(-0.869308\pi\)
0.916890 0.399141i \(-0.130692\pi\)
\(912\) 0 0
\(913\) 0.689236 + 0.689236i 0.0228104 + 0.0228104i
\(914\) 24.1289 15.0534i 0.798113 0.497922i
\(915\) 0 0
\(916\) 30.8501 + 15.1013i 1.01932 + 0.498963i
\(917\) 5.79377 5.79377i 0.191327 0.191327i
\(918\) 0 0
\(919\) 47.1031i 1.55379i −0.629632 0.776893i \(-0.716794\pi\)
0.629632 0.776893i \(-0.283206\pi\)
\(920\) −23.4187 + 35.0557i −0.772093 + 1.15575i
\(921\) 0 0
\(922\) −26.7786 6.20253i −0.881906 0.204269i
\(923\) 8.99592 + 8.99592i 0.296104 + 0.296104i
\(924\) 0 0
\(925\) −30.2772 + 44.4795i −0.995508 + 1.46248i
\(926\) 2.31616 + 3.71254i 0.0761137 + 0.122002i
\(927\) 0 0
\(928\) 34.0498 15.7295i 1.11774 0.516347i
\(929\) 34.0301 1.11649 0.558246 0.829675i \(-0.311474\pi\)
0.558246 + 0.829675i \(0.311474\pi\)
\(930\) 0 0
\(931\) 4.01936i 0.131729i
\(932\) 45.9398 15.7448i 1.50481 0.515738i
\(933\) 0 0
\(934\) −3.51235 + 2.19127i −0.114928 + 0.0717004i
\(935\) 4.95123 0.466149i 0.161923 0.0152447i
\(936\) 0 0
\(937\) 26.9441 26.9441i 0.880227 0.880227i −0.113330 0.993557i \(-0.536152\pi\)
0.993557 + 0.113330i \(0.0361519\pi\)
\(938\) 16.1387 + 3.73808i 0.526947 + 0.122053i
\(939\) 0 0
\(940\) 43.4409 + 16.4181i 1.41689 + 0.535498i
\(941\) −19.1115 −0.623018 −0.311509 0.950243i \(-0.600834\pi\)
−0.311509 + 0.950243i \(0.600834\pi\)
\(942\) 0 0
\(943\) 15.0682 + 15.0682i 0.490687 + 0.490687i
\(944\) 27.4350 21.3083i 0.892934 0.693527i
\(945\) 0 0
\(946\) 13.4020 8.36118i 0.435738 0.271846i
\(947\) 26.6896 26.6896i 0.867294 0.867294i −0.124878 0.992172i \(-0.539854\pi\)
0.992172 + 0.124878i \(0.0398540\pi\)
\(948\) 0 0
\(949\) −17.1173 −0.555652
\(950\) 0.0908715 2.27821i 0.00294826 0.0739150i
\(951\) 0 0
\(952\) 18.2785 + 14.8668i 0.592411 + 0.481835i
\(953\) −18.0251 + 18.0251i −0.583890 + 0.583890i −0.935970 0.352080i \(-0.885475\pi\)
0.352080 + 0.935970i \(0.385475\pi\)
\(954\) 0 0
\(955\) 5.45486 + 4.51611i 0.176515 + 0.146138i
\(956\) −35.6297 17.4410i −1.15235 0.564082i
\(957\) 0 0
\(958\) 37.9541 + 8.79103i 1.22624 + 0.284025i
\(959\) −11.8075 −0.381284
\(960\) 0 0
\(961\) −30.9954 −0.999853
\(962\) −45.1010 10.4464i −1.45411 0.336805i
\(963\) 0 0
\(964\) −5.20244 2.54663i −0.167559 0.0820214i
\(965\) 3.39159 0.319311i 0.109179 0.0102790i
\(966\) 0 0
\(967\) 20.9523 20.9523i 0.673779 0.673779i −0.284806 0.958585i \(-0.591929\pi\)
0.958585 + 0.284806i \(0.0919291\pi\)
\(968\) 21.0923 + 17.1554i 0.677933 + 0.551395i
\(969\) 0 0
\(970\) 6.30730 46.8803i 0.202515 1.50523i
\(971\) −6.93592 −0.222584 −0.111292 0.993788i \(-0.535499\pi\)
−0.111292 + 0.993788i \(0.535499\pi\)
\(972\) 0 0
\(973\) 57.5182 57.5182i 1.84395 1.84395i
\(974\) −47.0599 + 29.3594i −1.50789 + 0.940737i
\(975\) 0 0
\(976\) −39.6844 + 30.8222i −1.27027 + 0.986595i
\(977\) 6.98111 + 6.98111i 0.223346 + 0.223346i 0.809906 0.586560i \(-0.199518\pi\)
−0.586560 + 0.809906i \(0.699518\pi\)
\(978\) 0 0
\(979\) −0.656493 −0.0209816
\(980\) −22.9372 50.8089i −0.732703 1.62303i
\(981\) 0 0
\(982\) 3.56392 + 0.825484i 0.113729 + 0.0263422i
\(983\) −21.0079 + 21.0079i −0.670047 + 0.670047i −0.957727 0.287680i \(-0.907116\pi\)
0.287680 + 0.957727i \(0.407116\pi\)
\(984\) 0 0
\(985\) 1.65712 + 17.6013i 0.0528004 + 0.560823i
\(986\) −15.0208 + 9.37107i −0.478359 + 0.298436i
\(987\) 0 0
\(988\) 1.85576 0.636020i 0.0590397 0.0202345i
\(989\) 63.2081i 2.00990i
\(990\) 0 0
\(991\) 6.65846 0.211513 0.105756 0.994392i \(-0.466274\pi\)
0.105756 + 0.994392i \(0.466274\pi\)
\(992\) 0.160328 + 0.347062i 0.00509040 + 0.0110192i
\(993\) 0 0
\(994\) 13.8122 + 22.1394i 0.438096 + 0.702219i
\(995\) 27.1632 + 22.4886i 0.861132 + 0.712936i
\(996\) 0 0
\(997\) −9.19447 9.19447i −0.291192 0.291192i 0.546359 0.837551i \(-0.316013\pi\)
−0.837551 + 0.546359i \(0.816013\pi\)
\(998\) 35.2634 + 8.16779i 1.11624 + 0.258547i
\(999\) 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.53.2 48
3.2 odd 2 inner 360.2.x.a.53.23 yes 48
4.3 odd 2 1440.2.bj.a.593.17 48
5.2 odd 4 inner 360.2.x.a.197.14 yes 48
8.3 odd 2 1440.2.bj.a.593.7 48
8.5 even 2 inner 360.2.x.a.53.11 yes 48
12.11 even 2 1440.2.bj.a.593.8 48
15.2 even 4 inner 360.2.x.a.197.11 yes 48
20.7 even 4 1440.2.bj.a.17.18 48
24.5 odd 2 inner 360.2.x.a.53.14 yes 48
24.11 even 2 1440.2.bj.a.593.18 48
40.27 even 4 1440.2.bj.a.17.8 48
40.37 odd 4 inner 360.2.x.a.197.23 yes 48
60.47 odd 4 1440.2.bj.a.17.7 48
120.77 even 4 inner 360.2.x.a.197.2 yes 48
120.107 odd 4 1440.2.bj.a.17.17 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
360.2.x.a.53.2 48 1.1 even 1 trivial
360.2.x.a.53.11 yes 48 8.5 even 2 inner
360.2.x.a.53.14 yes 48 24.5 odd 2 inner
360.2.x.a.53.23 yes 48 3.2 odd 2 inner
360.2.x.a.197.2 yes 48 120.77 even 4 inner
360.2.x.a.197.11 yes 48 15.2 even 4 inner
360.2.x.a.197.14 yes 48 5.2 odd 4 inner
360.2.x.a.197.23 yes 48 40.37 odd 4 inner
1440.2.bj.a.17.7 48 60.47 odd 4
1440.2.bj.a.17.8 48 40.27 even 4
1440.2.bj.a.17.17 48 120.107 odd 4
1440.2.bj.a.17.18 48 20.7 even 4
1440.2.bj.a.593.7 48 8.3 odd 2
1440.2.bj.a.593.8 48 12.11 even 2
1440.2.bj.a.593.17 48 4.3 odd 2
1440.2.bj.a.593.18 48 24.11 even 2