Properties

Label 403.2.f.c.94.16
Level $403$
Weight $2$
Character 403.94
Analytic conductor $3.218$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [403,2,Mod(94,403)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(403, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("403.94");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 403 = 13 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 403.f (of order \(3\), 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: \(3.21797120146\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(18\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 94.16
Character \(\chi\) \(=\) 403.94
Dual form 403.2.f.c.373.16

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.06256 + 1.84040i) q^{2} +(0.793339 + 1.37410i) q^{3} +(-1.25806 + 2.17902i) q^{4} -1.24766 q^{5} +(-1.68594 + 2.92013i) q^{6} +(-1.62133 + 2.80822i) q^{7} -1.09681 q^{8} +(0.241228 - 0.417818i) q^{9} +O(q^{10})\) \(q+(1.06256 + 1.84040i) q^{2} +(0.793339 + 1.37410i) q^{3} +(-1.25806 + 2.17902i) q^{4} -1.24766 q^{5} +(-1.68594 + 2.92013i) q^{6} +(-1.62133 + 2.80822i) q^{7} -1.09681 q^{8} +(0.241228 - 0.417818i) q^{9} +(-1.32571 - 2.29620i) q^{10} +(1.35817 + 2.35242i) q^{11} -3.99226 q^{12} +(-0.214302 - 3.59918i) q^{13} -6.89102 q^{14} +(-0.989819 - 1.71442i) q^{15} +(1.35070 + 2.33947i) q^{16} +(-0.450587 + 0.780439i) q^{17} +1.02527 q^{18} +(1.39693 - 2.41956i) q^{19} +(1.56963 - 2.71868i) q^{20} -5.14505 q^{21} +(-2.88627 + 4.99917i) q^{22} +(-3.13581 - 5.43138i) q^{23} +(-0.870138 - 1.50712i) q^{24} -3.44334 q^{25} +(6.39623 - 4.21874i) q^{26} +5.52553 q^{27} +(-4.07945 - 7.06582i) q^{28} +(2.78531 + 4.82431i) q^{29} +(2.10348 - 3.64333i) q^{30} +1.00000 q^{31} +(-3.96719 + 6.87138i) q^{32} +(-2.15498 + 3.73254i) q^{33} -1.91510 q^{34} +(2.02287 - 3.50372i) q^{35} +(0.606956 + 1.05128i) q^{36} +(6.01222 + 10.4135i) q^{37} +5.93729 q^{38} +(4.77562 - 3.14984i) q^{39} +1.36844 q^{40} +(0.0645330 + 0.111775i) q^{41} +(-5.46692 - 9.46898i) q^{42} +(3.65482 - 6.33033i) q^{43} -6.83464 q^{44} +(-0.300970 + 0.521296i) q^{45} +(6.66396 - 11.5423i) q^{46} +12.7885 q^{47} +(-2.14312 + 3.71199i) q^{48} +(-1.75742 - 3.04394i) q^{49} +(-3.65875 - 6.33714i) q^{50} -1.42987 q^{51} +(8.11228 + 4.06100i) q^{52} -6.98426 q^{53} +(5.87120 + 10.1692i) q^{54} +(-1.69454 - 2.93503i) q^{55} +(1.77828 - 3.08008i) q^{56} +4.43296 q^{57} +(-5.91911 + 10.2522i) q^{58} +(1.68337 - 2.91569i) q^{59} +4.98100 q^{60} +(1.96570 - 3.40469i) q^{61} +(1.06256 + 1.84040i) q^{62} +(0.782218 + 1.35484i) q^{63} -11.4587 q^{64} +(0.267377 + 4.49056i) q^{65} -9.15917 q^{66} +(-7.66166 - 13.2704i) q^{67} +(-1.13373 - 1.96367i) q^{68} +(4.97552 - 8.61785i) q^{69} +8.59767 q^{70} +(-2.57790 + 4.46506i) q^{71} +(-0.264580 + 0.458265i) q^{72} +4.79465 q^{73} +(-12.7767 + 22.1298i) q^{74} +(-2.73173 - 4.73150i) q^{75} +(3.51485 + 6.08789i) q^{76} -8.80818 q^{77} +(10.8714 + 5.44219i) q^{78} -8.45202 q^{79} +(-1.68521 - 2.91887i) q^{80} +(3.65994 + 6.33920i) q^{81} +(-0.137140 + 0.237534i) q^{82} +13.8984 q^{83} +(6.47277 - 11.2112i) q^{84} +(0.562180 - 0.973724i) q^{85} +15.5338 q^{86} +(-4.41940 + 7.65462i) q^{87} +(-1.48965 - 2.58015i) q^{88} +(-5.17578 - 8.96472i) q^{89} -1.27919 q^{90} +(10.4548 + 5.23364i) q^{91} +15.7801 q^{92} +(0.793339 + 1.37410i) q^{93} +(13.5886 + 23.5361i) q^{94} +(-1.74290 + 3.01879i) q^{95} -12.5893 q^{96} +(-2.76400 + 4.78739i) q^{97} +(3.73472 - 6.46872i) q^{98} +1.31051 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q - 5 q^{2} - 19 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} + 30 q^{8} - 22 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 36 q - 5 q^{2} - 19 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} + 30 q^{8} - 22 q^{9} - 3 q^{10} - 17 q^{11} + 8 q^{12} + 8 q^{13} + 4 q^{14} - 12 q^{15} - 17 q^{16} + 7 q^{17} - 14 q^{18} - 4 q^{19} - 15 q^{20} + 28 q^{21} - 30 q^{22} + 4 q^{23} - 48 q^{24} + 24 q^{25} + 25 q^{26} - 6 q^{27} - q^{28} + 15 q^{29} + 35 q^{30} + 36 q^{31} - 35 q^{32} - 17 q^{33} - 6 q^{34} - 17 q^{35} - 35 q^{36} - 3 q^{37} + 14 q^{38} + 3 q^{39} - 2 q^{40} - 44 q^{41} + 57 q^{42} + 4 q^{43} + 64 q^{44} + 5 q^{45} - 13 q^{46} + 24 q^{47} - 89 q^{48} - 44 q^{49} - 84 q^{50} - 28 q^{51} + 50 q^{52} - 28 q^{53} - 21 q^{54} + 29 q^{55} + 11 q^{56} + 32 q^{57} + 49 q^{58} - 11 q^{59} + 54 q^{60} - 4 q^{61} - 5 q^{62} - 9 q^{63} + 34 q^{64} - 5 q^{65} + 52 q^{66} - 16 q^{67} + 53 q^{68} + 4 q^{69} - 44 q^{70} - 5 q^{71} - 27 q^{72} + 64 q^{73} + q^{74} - 98 q^{75} - 42 q^{76} - 22 q^{77} + 143 q^{78} - 6 q^{79} - 2 q^{80} + 10 q^{81} + 22 q^{82} + 36 q^{83} + 38 q^{84} + 2 q^{85} + 84 q^{86} - 34 q^{87} - 69 q^{88} - 54 q^{89} - 32 q^{90} - 43 q^{91} - 86 q^{92} + 44 q^{94} - 2 q^{95} + 170 q^{96} - 28 q^{97} - 29 q^{98} + 154 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/403\mathbb{Z}\right)^\times\).

\(n\) \(249\) \(313\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.06256 + 1.84040i 0.751342 + 1.30136i 0.947173 + 0.320724i \(0.103926\pi\)
−0.195831 + 0.980638i \(0.562740\pi\)
\(3\) 0.793339 + 1.37410i 0.458034 + 0.793339i 0.998857 0.0477979i \(-0.0152204\pi\)
−0.540823 + 0.841137i \(0.681887\pi\)
\(4\) −1.25806 + 2.17902i −0.629029 + 1.08951i
\(5\) −1.24766 −0.557971 −0.278986 0.960295i \(-0.589998\pi\)
−0.278986 + 0.960295i \(0.589998\pi\)
\(6\) −1.68594 + 2.92013i −0.688281 + 1.19214i
\(7\) −1.62133 + 2.80822i −0.612805 + 1.06141i 0.377960 + 0.925822i \(0.376626\pi\)
−0.990765 + 0.135587i \(0.956708\pi\)
\(8\) −1.09681 −0.387779
\(9\) 0.241228 0.417818i 0.0804092 0.139273i
\(10\) −1.32571 2.29620i −0.419227 0.726123i
\(11\) 1.35817 + 2.35242i 0.409504 + 0.709282i 0.994834 0.101513i \(-0.0323683\pi\)
−0.585330 + 0.810795i \(0.699035\pi\)
\(12\) −3.99226 −1.15247
\(13\) −0.214302 3.59918i −0.0594368 0.998232i
\(14\) −6.89102 −1.84170
\(15\) −0.989819 1.71442i −0.255570 0.442660i
\(16\) 1.35070 + 2.33947i 0.337674 + 0.584869i
\(17\) −0.450587 + 0.780439i −0.109283 + 0.189284i −0.915480 0.402363i \(-0.868189\pi\)
0.806197 + 0.591647i \(0.201522\pi\)
\(18\) 1.02527 0.241659
\(19\) 1.39693 2.41956i 0.320478 0.555085i −0.660108 0.751170i \(-0.729490\pi\)
0.980587 + 0.196085i \(0.0628230\pi\)
\(20\) 1.56963 2.71868i 0.350980 0.607916i
\(21\) −5.14505 −1.12274
\(22\) −2.88627 + 4.99917i −0.615356 + 1.06583i
\(23\) −3.13581 5.43138i −0.653862 1.13252i −0.982178 0.187954i \(-0.939815\pi\)
0.328316 0.944568i \(-0.393519\pi\)
\(24\) −0.870138 1.50712i −0.177616 0.307640i
\(25\) −3.44334 −0.688668
\(26\) 6.39623 4.21874i 1.25440 0.827362i
\(27\) 5.52553 1.06339
\(28\) −4.07945 7.06582i −0.770944 1.33531i
\(29\) 2.78531 + 4.82431i 0.517220 + 0.895851i 0.999800 + 0.0199993i \(0.00636640\pi\)
−0.482580 + 0.875852i \(0.660300\pi\)
\(30\) 2.10348 3.64333i 0.384041 0.665178i
\(31\) 1.00000 0.179605
\(32\) −3.96719 + 6.87138i −0.701307 + 1.21470i
\(33\) −2.15498 + 3.73254i −0.375134 + 0.649751i
\(34\) −1.91510 −0.328436
\(35\) 2.02287 3.50372i 0.341928 0.592236i
\(36\) 0.606956 + 1.05128i 0.101159 + 0.175213i
\(37\) 6.01222 + 10.4135i 0.988403 + 1.71196i 0.625709 + 0.780057i \(0.284810\pi\)
0.362694 + 0.931908i \(0.381857\pi\)
\(38\) 5.93729 0.963155
\(39\) 4.77562 3.14984i 0.764712 0.504378i
\(40\) 1.36844 0.216370
\(41\) 0.0645330 + 0.111775i 0.0100784 + 0.0174562i 0.871021 0.491246i \(-0.163459\pi\)
−0.860942 + 0.508703i \(0.830125\pi\)
\(42\) −5.46692 9.46898i −0.843563 1.46109i
\(43\) 3.65482 6.33033i 0.557355 0.965367i −0.440361 0.897821i \(-0.645150\pi\)
0.997716 0.0675463i \(-0.0215170\pi\)
\(44\) −6.83464 −1.03036
\(45\) −0.300970 + 0.521296i −0.0448660 + 0.0777102i
\(46\) 6.66396 11.5423i 0.982547 1.70182i
\(47\) 12.7885 1.86540 0.932700 0.360654i \(-0.117446\pi\)
0.932700 + 0.360654i \(0.117446\pi\)
\(48\) −2.14312 + 3.71199i −0.309333 + 0.535780i
\(49\) −1.75742 3.04394i −0.251060 0.434848i
\(50\) −3.65875 6.33714i −0.517425 0.896206i
\(51\) −1.42987 −0.200222
\(52\) 8.11228 + 4.06100i 1.12497 + 0.563160i
\(53\) −6.98426 −0.959362 −0.479681 0.877443i \(-0.659248\pi\)
−0.479681 + 0.877443i \(0.659248\pi\)
\(54\) 5.87120 + 10.1692i 0.798969 + 1.38385i
\(55\) −1.69454 2.93503i −0.228492 0.395759i
\(56\) 1.77828 3.08008i 0.237633 0.411593i
\(57\) 4.43296 0.587160
\(58\) −5.91911 + 10.2522i −0.777218 + 1.34618i
\(59\) 1.68337 2.91569i 0.219157 0.379590i −0.735394 0.677640i \(-0.763003\pi\)
0.954550 + 0.298050i \(0.0963361\pi\)
\(60\) 4.98100 0.643044
\(61\) 1.96570 3.40469i 0.251682 0.435926i −0.712307 0.701868i \(-0.752350\pi\)
0.963989 + 0.265942i \(0.0856830\pi\)
\(62\) 1.06256 + 1.84040i 0.134945 + 0.233732i
\(63\) 0.782218 + 1.35484i 0.0985503 + 0.170694i
\(64\) −11.4587 −1.43234
\(65\) 0.267377 + 4.49056i 0.0331640 + 0.556985i
\(66\) −9.15917 −1.12742
\(67\) −7.66166 13.2704i −0.936021 1.62124i −0.772803 0.634646i \(-0.781146\pi\)
−0.163218 0.986590i \(-0.552188\pi\)
\(68\) −1.13373 1.96367i −0.137485 0.238131i
\(69\) 4.97552 8.61785i 0.598982 1.03747i
\(70\) 8.59767 1.02762
\(71\) −2.57790 + 4.46506i −0.305941 + 0.529905i −0.977470 0.211073i \(-0.932304\pi\)
0.671530 + 0.740978i \(0.265638\pi\)
\(72\) −0.264580 + 0.458265i −0.0311810 + 0.0540071i
\(73\) 4.79465 0.561172 0.280586 0.959829i \(-0.409471\pi\)
0.280586 + 0.959829i \(0.409471\pi\)
\(74\) −12.7767 + 22.1298i −1.48526 + 2.57254i
\(75\) −2.73173 4.73150i −0.315433 0.546347i
\(76\) 3.51485 + 6.08789i 0.403180 + 0.698329i
\(77\) −8.80818 −1.00379
\(78\) 10.8714 + 5.44219i 1.23094 + 0.616207i
\(79\) −8.45202 −0.950927 −0.475463 0.879736i \(-0.657720\pi\)
−0.475463 + 0.879736i \(0.657720\pi\)
\(80\) −1.68521 2.91887i −0.188413 0.326340i
\(81\) 3.65994 + 6.33920i 0.406660 + 0.704355i
\(82\) −0.137140 + 0.237534i −0.0151446 + 0.0262312i
\(83\) 13.8984 1.52555 0.762776 0.646663i \(-0.223836\pi\)
0.762776 + 0.646663i \(0.223836\pi\)
\(84\) 6.47277 11.2112i 0.706238 1.22324i
\(85\) 0.562180 0.973724i 0.0609770 0.105615i
\(86\) 15.5338 1.67506
\(87\) −4.41940 + 7.65462i −0.473809 + 0.820661i
\(88\) −1.48965 2.58015i −0.158797 0.275045i
\(89\) −5.17578 8.96472i −0.548632 0.950258i −0.998369 0.0570971i \(-0.981816\pi\)
0.449737 0.893161i \(-0.351518\pi\)
\(90\) −1.27919 −0.134839
\(91\) 10.4548 + 5.23364i 1.09596 + 0.548635i
\(92\) 15.7801 1.64519
\(93\) 0.793339 + 1.37410i 0.0822654 + 0.142488i
\(94\) 13.5886 + 23.5361i 1.40155 + 2.42756i
\(95\) −1.74290 + 3.01879i −0.178818 + 0.309722i
\(96\) −12.5893 −1.28489
\(97\) −2.76400 + 4.78739i −0.280642 + 0.486086i −0.971543 0.236863i \(-0.923881\pi\)
0.690901 + 0.722949i \(0.257214\pi\)
\(98\) 3.73472 6.46872i 0.377263 0.653439i
\(99\) 1.31051 0.131712
\(100\) 4.33192 7.50311i 0.433192 0.750311i
\(101\) 0.278393 + 0.482190i 0.0277011 + 0.0479797i 0.879544 0.475818i \(-0.157848\pi\)
−0.851843 + 0.523798i \(0.824515\pi\)
\(102\) −1.51932 2.63154i −0.150435 0.260561i
\(103\) −4.27121 −0.420855 −0.210428 0.977609i \(-0.567486\pi\)
−0.210428 + 0.977609i \(0.567486\pi\)
\(104\) 0.235048 + 3.94760i 0.0230484 + 0.387094i
\(105\) 6.41929 0.626458
\(106\) −7.42118 12.8539i −0.720809 1.24848i
\(107\) −4.46116 7.72695i −0.431276 0.746992i 0.565707 0.824606i \(-0.308603\pi\)
−0.996984 + 0.0776138i \(0.975270\pi\)
\(108\) −6.95144 + 12.0402i −0.668903 + 1.15857i
\(109\) −13.8573 −1.32729 −0.663645 0.748048i \(-0.730991\pi\)
−0.663645 + 0.748048i \(0.730991\pi\)
\(110\) 3.60109 6.23728i 0.343351 0.594701i
\(111\) −9.53946 + 16.5228i −0.905445 + 1.56828i
\(112\) −8.75970 −0.827713
\(113\) 2.72590 4.72140i 0.256431 0.444152i −0.708852 0.705357i \(-0.750787\pi\)
0.965283 + 0.261205i \(0.0841199\pi\)
\(114\) 4.71028 + 8.15844i 0.441158 + 0.764108i
\(115\) 3.91243 + 6.77653i 0.364836 + 0.631915i
\(116\) −14.0163 −1.30139
\(117\) −1.55550 0.778681i −0.143806 0.0719891i
\(118\) 7.15473 0.658646
\(119\) −1.46110 2.53070i −0.133939 0.231989i
\(120\) 1.08564 + 1.88038i 0.0991048 + 0.171655i
\(121\) 1.81074 3.13629i 0.164612 0.285117i
\(122\) 8.35467 0.756396
\(123\) −0.102393 + 0.177350i −0.00923248 + 0.0159911i
\(124\) −1.25806 + 2.17902i −0.112977 + 0.195682i
\(125\) 10.5344 0.942228
\(126\) −1.66230 + 2.87920i −0.148090 + 0.256499i
\(127\) −5.02437 8.70246i −0.445841 0.772219i 0.552270 0.833666i \(-0.313762\pi\)
−0.998110 + 0.0614468i \(0.980429\pi\)
\(128\) −4.24114 7.34587i −0.374867 0.649290i
\(129\) 11.5980 1.02115
\(130\) −7.98034 + 5.26356i −0.699922 + 0.461645i
\(131\) 2.31730 0.202463 0.101232 0.994863i \(-0.467722\pi\)
0.101232 + 0.994863i \(0.467722\pi\)
\(132\) −5.42218 9.39150i −0.471940 0.817425i
\(133\) 4.52978 + 7.84580i 0.392781 + 0.680317i
\(134\) 16.2819 28.2011i 1.40654 2.43621i
\(135\) −6.89400 −0.593341
\(136\) 0.494206 0.855990i 0.0423778 0.0734005i
\(137\) 7.15132 12.3865i 0.610979 1.05825i −0.380097 0.924947i \(-0.624109\pi\)
0.991076 0.133300i \(-0.0425572\pi\)
\(138\) 21.1471 1.80016
\(139\) −1.39462 + 2.41555i −0.118290 + 0.204884i −0.919090 0.394047i \(-0.871075\pi\)
0.800800 + 0.598932i \(0.204408\pi\)
\(140\) 5.08978 + 8.81575i 0.430165 + 0.745067i
\(141\) 10.1456 + 17.5728i 0.854417 + 1.47989i
\(142\) −10.9567 −0.919464
\(143\) 8.17573 5.39243i 0.683689 0.450938i
\(144\) 1.30330 0.108608
\(145\) −3.47513 6.01910i −0.288594 0.499859i
\(146\) 5.09460 + 8.82410i 0.421632 + 0.730288i
\(147\) 2.78845 4.82975i 0.229988 0.398351i
\(148\) −30.2549 −2.48694
\(149\) −2.92119 + 5.05964i −0.239313 + 0.414502i −0.960517 0.278220i \(-0.910256\pi\)
0.721204 + 0.692722i \(0.243589\pi\)
\(150\) 5.80525 10.0550i 0.473997 0.820986i
\(151\) −19.6799 −1.60153 −0.800763 0.598981i \(-0.795572\pi\)
−0.800763 + 0.598981i \(0.795572\pi\)
\(152\) −1.53216 + 2.65379i −0.124275 + 0.215250i
\(153\) 0.217388 + 0.376527i 0.0175748 + 0.0304404i
\(154\) −9.35920 16.2106i −0.754186 1.30629i
\(155\) −1.24766 −0.100215
\(156\) 0.855552 + 14.3689i 0.0684990 + 1.15043i
\(157\) −11.3121 −0.902803 −0.451402 0.892321i \(-0.649076\pi\)
−0.451402 + 0.892321i \(0.649076\pi\)
\(158\) −8.98076 15.5551i −0.714471 1.23750i
\(159\) −5.54088 9.59709i −0.439421 0.761099i
\(160\) 4.94971 8.57316i 0.391309 0.677768i
\(161\) 20.3367 1.60276
\(162\) −7.77779 + 13.4715i −0.611081 + 1.05842i
\(163\) 4.39296 7.60882i 0.344083 0.595969i −0.641104 0.767454i \(-0.721523\pi\)
0.985187 + 0.171485i \(0.0548566\pi\)
\(164\) −0.324745 −0.0253583
\(165\) 2.68869 4.65695i 0.209314 0.362543i
\(166\) 14.7679 + 25.5787i 1.14621 + 1.98530i
\(167\) 4.14100 + 7.17242i 0.320440 + 0.555019i 0.980579 0.196125i \(-0.0628359\pi\)
−0.660139 + 0.751144i \(0.729503\pi\)
\(168\) 5.64312 0.435376
\(169\) −12.9081 + 1.54262i −0.992935 + 0.118663i
\(170\) 2.38939 0.183258
\(171\) −0.673957 1.16733i −0.0515388 0.0892678i
\(172\) 9.19595 + 15.9279i 0.701185 + 1.21449i
\(173\) 4.31285 7.47008i 0.327900 0.567940i −0.654195 0.756326i \(-0.726992\pi\)
0.982095 + 0.188386i \(0.0603257\pi\)
\(174\) −18.7835 −1.42397
\(175\) 5.58279 9.66967i 0.422019 0.730958i
\(176\) −3.66896 + 6.35482i −0.276558 + 0.479013i
\(177\) 5.34194 0.401525
\(178\) 10.9991 19.0511i 0.824420 1.42794i
\(179\) 9.54222 + 16.5276i 0.713219 + 1.23533i 0.963643 + 0.267195i \(0.0860968\pi\)
−0.250424 + 0.968136i \(0.580570\pi\)
\(180\) −0.757276 1.31164i −0.0564441 0.0977640i
\(181\) −21.7233 −1.61468 −0.807339 0.590088i \(-0.799093\pi\)
−0.807339 + 0.590088i \(0.799093\pi\)
\(182\) 1.47676 + 24.8020i 0.109465 + 1.83845i
\(183\) 6.23786 0.461116
\(184\) 3.43937 + 5.95717i 0.253554 + 0.439168i
\(185\) −7.50122 12.9925i −0.551501 0.955227i
\(186\) −1.68594 + 2.92013i −0.123619 + 0.214114i
\(187\) −2.44790 −0.179008
\(188\) −16.0887 + 27.8665i −1.17339 + 2.03237i
\(189\) −8.95871 + 15.5169i −0.651650 + 1.12869i
\(190\) −7.40773 −0.537413
\(191\) 7.18551 12.4457i 0.519925 0.900537i −0.479807 0.877374i \(-0.659293\pi\)
0.999732 0.0231625i \(-0.00737352\pi\)
\(192\) −9.09063 15.7454i −0.656059 1.13633i
\(193\) −3.44353 5.96436i −0.247870 0.429324i 0.715064 0.699059i \(-0.246397\pi\)
−0.962935 + 0.269734i \(0.913064\pi\)
\(194\) −11.7476 −0.843431
\(195\) −5.95837 + 3.92994i −0.426687 + 0.281429i
\(196\) 8.84373 0.631695
\(197\) 1.61598 + 2.79896i 0.115134 + 0.199418i 0.917833 0.396966i \(-0.129937\pi\)
−0.802699 + 0.596384i \(0.796604\pi\)
\(198\) 1.39250 + 2.41188i 0.0989605 + 0.171405i
\(199\) 0.470684 0.815248i 0.0333659 0.0577914i −0.848860 0.528617i \(-0.822711\pi\)
0.882226 + 0.470826i \(0.156044\pi\)
\(200\) 3.77667 0.267051
\(201\) 12.1566 21.0558i 0.857460 1.48516i
\(202\) −0.591616 + 1.02471i −0.0416260 + 0.0720983i
\(203\) −18.0636 −1.26782
\(204\) 1.79886 3.11572i 0.125945 0.218144i
\(205\) −0.0805154 0.139457i −0.00562344 0.00974009i
\(206\) −4.53841 7.86076i −0.316206 0.547685i
\(207\) −3.02577 −0.210306
\(208\) 8.13073 5.36275i 0.563764 0.371840i
\(209\) 7.58910 0.524949
\(210\) 6.82086 + 11.8141i 0.470684 + 0.815249i
\(211\) −5.70230 9.87666i −0.392562 0.679938i 0.600225 0.799832i \(-0.295078\pi\)
−0.992787 + 0.119894i \(0.961745\pi\)
\(212\) 8.78660 15.2188i 0.603466 1.04523i
\(213\) −8.18059 −0.560525
\(214\) 9.48047 16.4207i 0.648072 1.12249i
\(215\) −4.55998 + 7.89812i −0.310988 + 0.538647i
\(216\) −6.06044 −0.412360
\(217\) −1.62133 + 2.80822i −0.110063 + 0.190635i
\(218\) −14.7242 25.5031i −0.997248 1.72729i
\(219\) 3.80379 + 6.58835i 0.257036 + 0.445199i
\(220\) 8.52732 0.574912
\(221\) 2.90550 + 1.45449i 0.195445 + 0.0978397i
\(222\) −40.5449 −2.72120
\(223\) 3.47656 + 6.02158i 0.232808 + 0.403235i 0.958633 0.284644i \(-0.0918754\pi\)
−0.725826 + 0.687879i \(0.758542\pi\)
\(224\) −12.8642 22.2815i −0.859529 1.48875i
\(225\) −0.830628 + 1.43869i −0.0553752 + 0.0959127i
\(226\) 11.5857 0.770671
\(227\) 9.73492 16.8614i 0.646129 1.11913i −0.337910 0.941178i \(-0.609720\pi\)
0.984039 0.177950i \(-0.0569466\pi\)
\(228\) −5.57693 + 9.65952i −0.369341 + 0.639717i
\(229\) −6.77938 −0.447994 −0.223997 0.974590i \(-0.571911\pi\)
−0.223997 + 0.974590i \(0.571911\pi\)
\(230\) −8.31437 + 14.4009i −0.548233 + 0.949568i
\(231\) −6.98787 12.1033i −0.459768 0.796342i
\(232\) −3.05495 5.29133i −0.200567 0.347393i
\(233\) 14.6813 0.961802 0.480901 0.876775i \(-0.340310\pi\)
0.480901 + 0.876775i \(0.340310\pi\)
\(234\) −0.219718 3.69014i −0.0143634 0.241232i
\(235\) −15.9558 −1.04084
\(236\) 4.23556 + 7.33621i 0.275712 + 0.477547i
\(237\) −6.70532 11.6139i −0.435557 0.754407i
\(238\) 3.10500 5.37802i 0.201267 0.348606i
\(239\) 2.84201 0.183834 0.0919171 0.995767i \(-0.470701\pi\)
0.0919171 + 0.995767i \(0.470701\pi\)
\(240\) 2.67389 4.63131i 0.172599 0.298950i
\(241\) −14.4586 + 25.0431i −0.931361 + 1.61316i −0.150364 + 0.988631i \(0.548044\pi\)
−0.780998 + 0.624534i \(0.785289\pi\)
\(242\) 7.69604 0.494720
\(243\) 2.48116 4.29750i 0.159167 0.275685i
\(244\) 4.94592 + 8.56659i 0.316630 + 0.548420i
\(245\) 2.19266 + 3.79780i 0.140084 + 0.242633i
\(246\) −0.435194 −0.0277470
\(247\) −9.00779 4.50929i −0.573152 0.286919i
\(248\) −1.09681 −0.0696472
\(249\) 11.0262 + 19.0979i 0.698755 + 1.21028i
\(250\) 11.1934 + 19.3876i 0.707936 + 1.22618i
\(251\) −11.1975 + 19.3946i −0.706780 + 1.22418i 0.259266 + 0.965806i \(0.416519\pi\)
−0.966045 + 0.258372i \(0.916814\pi\)
\(252\) −3.93630 −0.247964
\(253\) 8.51794 14.7535i 0.535518 0.927545i
\(254\) 10.6774 18.4937i 0.669957 1.16040i
\(255\) 1.78400 0.111718
\(256\) −2.44578 + 4.23621i −0.152861 + 0.264763i
\(257\) −10.3777 17.9748i −0.647346 1.12124i −0.983754 0.179520i \(-0.942546\pi\)
0.336408 0.941716i \(-0.390788\pi\)
\(258\) 12.3236 + 21.3451i 0.767233 + 1.32889i
\(259\) −38.9912 −2.42279
\(260\) −10.1214 5.06676i −0.627702 0.314227i
\(261\) 2.68758 0.166357
\(262\) 2.46226 + 4.26476i 0.152119 + 0.263478i
\(263\) −1.88224 3.26014i −0.116064 0.201029i 0.802141 0.597135i \(-0.203694\pi\)
−0.918205 + 0.396107i \(0.870361\pi\)
\(264\) 2.36360 4.09387i 0.145469 0.251960i
\(265\) 8.71400 0.535296
\(266\) −9.62630 + 16.6732i −0.590226 + 1.02230i
\(267\) 8.21230 14.2241i 0.502584 0.870502i
\(268\) 38.5553 2.35514
\(269\) −5.32415 + 9.22171i −0.324619 + 0.562257i −0.981435 0.191794i \(-0.938570\pi\)
0.656816 + 0.754051i \(0.271903\pi\)
\(270\) −7.32527 12.6877i −0.445802 0.772151i
\(271\) −3.58480 6.20905i −0.217761 0.377173i 0.736362 0.676588i \(-0.236542\pi\)
−0.954123 + 0.299415i \(0.903209\pi\)
\(272\) −2.43442 −0.147609
\(273\) 1.10260 + 18.5180i 0.0667322 + 1.12076i
\(274\) 30.3948 1.83622
\(275\) −4.67665 8.10019i −0.282013 0.488460i
\(276\) 12.5190 + 21.6835i 0.753554 + 1.30519i
\(277\) −1.97993 + 3.42934i −0.118963 + 0.206049i −0.919357 0.393425i \(-0.871290\pi\)
0.800394 + 0.599474i \(0.204624\pi\)
\(278\) −5.92745 −0.355505
\(279\) 0.241228 0.417818i 0.0144419 0.0250141i
\(280\) −2.21870 + 3.84290i −0.132592 + 0.229657i
\(281\) −11.7185 −0.699069 −0.349534 0.936924i \(-0.613660\pi\)
−0.349534 + 0.936924i \(0.613660\pi\)
\(282\) −21.5607 + 37.3441i −1.28392 + 2.22381i
\(283\) −3.74115 6.47986i −0.222388 0.385188i 0.733144 0.680073i \(-0.238052\pi\)
−0.955533 + 0.294885i \(0.904719\pi\)
\(284\) −6.48630 11.2346i −0.384891 0.666651i
\(285\) −5.53084 −0.327619
\(286\) 18.6114 + 9.31687i 1.10052 + 0.550918i
\(287\) −0.418517 −0.0247043
\(288\) 1.91399 + 3.31513i 0.112783 + 0.195346i
\(289\) 8.09394 + 14.0191i 0.476114 + 0.824654i
\(290\) 7.38506 12.7913i 0.433665 0.751130i
\(291\) −8.77115 −0.514174
\(292\) −6.03195 + 10.4476i −0.352993 + 0.611402i
\(293\) −4.36890 + 7.56716i −0.255234 + 0.442078i −0.964959 0.262400i \(-0.915486\pi\)
0.709725 + 0.704479i \(0.248819\pi\)
\(294\) 11.8516 0.691198
\(295\) −2.10028 + 3.63779i −0.122283 + 0.211801i
\(296\) −6.59424 11.4216i −0.383282 0.663865i
\(297\) 7.50463 + 12.9984i 0.435463 + 0.754243i
\(298\) −12.4157 −0.719223
\(299\) −18.8765 + 12.4503i −1.09166 + 0.720019i
\(300\) 13.7467 0.793667
\(301\) 11.8513 + 20.5271i 0.683100 + 1.18316i
\(302\) −20.9110 36.2189i −1.20329 2.08417i
\(303\) −0.441719 + 0.765080i −0.0253761 + 0.0439527i
\(304\) 7.54733 0.432869
\(305\) −2.45253 + 4.24790i −0.140431 + 0.243234i
\(306\) −0.461974 + 0.800163i −0.0264093 + 0.0457423i
\(307\) 23.4380 1.33768 0.668839 0.743408i \(-0.266792\pi\)
0.668839 + 0.743408i \(0.266792\pi\)
\(308\) 11.0812 19.1932i 0.631410 1.09363i
\(309\) −3.38852 5.86909i −0.192766 0.333881i
\(310\) −1.32571 2.29620i −0.0752954 0.130416i
\(311\) 11.0569 0.626980 0.313490 0.949592i \(-0.398502\pi\)
0.313490 + 0.949592i \(0.398502\pi\)
\(312\) −5.23793 + 3.45476i −0.296540 + 0.195587i
\(313\) 33.9646 1.91979 0.959896 0.280355i \(-0.0904521\pi\)
0.959896 + 0.280355i \(0.0904521\pi\)
\(314\) −12.0198 20.8188i −0.678314 1.17487i
\(315\) −0.975944 1.69039i −0.0549882 0.0952424i
\(316\) 10.6331 18.4171i 0.598160 1.03604i
\(317\) 17.4288 0.978899 0.489449 0.872032i \(-0.337198\pi\)
0.489449 + 0.872032i \(0.337198\pi\)
\(318\) 11.7750 20.3949i 0.660310 1.14369i
\(319\) −7.56587 + 13.1045i −0.423608 + 0.733710i
\(320\) 14.2966 0.799203
\(321\) 7.07842 12.2602i 0.395079 0.684296i
\(322\) 21.6089 + 37.4278i 1.20422 + 2.08577i
\(323\) 1.25888 + 2.18044i 0.0700459 + 0.121323i
\(324\) −18.4176 −1.02320
\(325\) 0.737916 + 12.3932i 0.0409322 + 0.687450i
\(326\) 18.6711 1.03410
\(327\) −10.9935 19.0414i −0.607944 1.05299i
\(328\) −0.0707802 0.122595i −0.00390818 0.00676917i
\(329\) −20.7344 + 35.9131i −1.14313 + 1.97995i
\(330\) 11.4275 0.629066
\(331\) −6.43945 + 11.1535i −0.353944 + 0.613049i −0.986937 0.161109i \(-0.948493\pi\)
0.632993 + 0.774158i \(0.281826\pi\)
\(332\) −17.4850 + 30.2850i −0.959616 + 1.66210i
\(333\) 5.80125 0.317907
\(334\) −8.80010 + 15.2422i −0.481520 + 0.834017i
\(335\) 9.55917 + 16.5570i 0.522273 + 0.904604i
\(336\) −6.94940 12.0367i −0.379121 0.656657i
\(337\) −10.6352 −0.579339 −0.289669 0.957127i \(-0.593545\pi\)
−0.289669 + 0.957127i \(0.593545\pi\)
\(338\) −16.5547 22.1171i −0.900457 1.20301i
\(339\) 8.65026 0.469818
\(340\) 1.41451 + 2.45000i 0.0767126 + 0.132870i
\(341\) 1.35817 + 2.35242i 0.0735492 + 0.127391i
\(342\) 1.43224 2.48071i 0.0774465 0.134141i
\(343\) −11.3012 −0.610207
\(344\) −4.00863 + 6.94315i −0.216131 + 0.374349i
\(345\) −6.20777 + 10.7522i −0.334215 + 0.578877i
\(346\) 18.3306 0.985461
\(347\) −3.91697 + 6.78440i −0.210274 + 0.364205i −0.951800 0.306718i \(-0.900769\pi\)
0.741526 + 0.670924i \(0.234102\pi\)
\(348\) −11.1197 19.2599i −0.596079 1.03244i
\(349\) −10.1905 17.6505i −0.545485 0.944808i −0.998576 0.0533440i \(-0.983012\pi\)
0.453091 0.891464i \(-0.350321\pi\)
\(350\) 23.7281 1.26832
\(351\) −1.18413 19.8874i −0.0632044 1.06151i
\(352\) −21.5525 −1.14875
\(353\) 10.3888 + 17.9939i 0.552938 + 0.957717i 0.998061 + 0.0622472i \(0.0198267\pi\)
−0.445123 + 0.895470i \(0.646840\pi\)
\(354\) 5.67612 + 9.83133i 0.301682 + 0.522529i
\(355\) 3.21635 5.57088i 0.170706 0.295672i
\(356\) 26.0457 1.38042
\(357\) 2.31829 4.01540i 0.122697 0.212517i
\(358\) −20.2783 + 35.1231i −1.07174 + 1.85631i
\(359\) 36.7030 1.93711 0.968554 0.248803i \(-0.0800372\pi\)
0.968554 + 0.248803i \(0.0800372\pi\)
\(360\) 0.330106 0.571760i 0.0173981 0.0301344i
\(361\) 5.59716 + 9.69456i 0.294587 + 0.510240i
\(362\) −23.0822 39.9796i −1.21318 2.10128i
\(363\) 5.74610 0.301592
\(364\) −24.5569 + 16.1969i −1.28713 + 0.848948i
\(365\) −5.98211 −0.313118
\(366\) 6.62808 + 11.4802i 0.346455 + 0.600079i
\(367\) 0.539964 + 0.935245i 0.0281859 + 0.0488194i 0.879774 0.475392i \(-0.157694\pi\)
−0.851588 + 0.524211i \(0.824360\pi\)
\(368\) 8.47105 14.6723i 0.441584 0.764846i
\(369\) 0.0622686 0.00324157
\(370\) 15.9410 27.6106i 0.828731 1.43540i
\(371\) 11.3238 19.6134i 0.587902 1.01828i
\(372\) −3.99226 −0.206989
\(373\) −4.67714 + 8.10104i −0.242173 + 0.419456i −0.961333 0.275389i \(-0.911193\pi\)
0.719160 + 0.694844i \(0.244527\pi\)
\(374\) −2.60103 4.50512i −0.134496 0.232954i
\(375\) 8.35737 + 14.4754i 0.431573 + 0.747506i
\(376\) −14.0265 −0.723363
\(377\) 16.7666 11.0587i 0.863525 0.569552i
\(378\) −38.0766 −1.95845
\(379\) 4.22434 + 7.31676i 0.216990 + 0.375837i 0.953886 0.300169i \(-0.0970429\pi\)
−0.736897 + 0.676005i \(0.763710\pi\)
\(380\) −4.38534 7.59563i −0.224963 0.389648i
\(381\) 7.97205 13.8080i 0.408421 0.707405i
\(382\) 30.5401 1.56257
\(383\) 6.03164 10.4471i 0.308202 0.533822i −0.669767 0.742571i \(-0.733606\pi\)
0.977969 + 0.208750i \(0.0669393\pi\)
\(384\) 6.72932 11.6555i 0.343404 0.594794i
\(385\) 10.9896 0.560084
\(386\) 7.31789 12.6750i 0.372471 0.645139i
\(387\) −1.76329 3.05410i −0.0896329 0.155249i
\(388\) −6.95455 12.0456i −0.353064 0.611524i
\(389\) −33.5547 −1.70129 −0.850646 0.525738i \(-0.823789\pi\)
−0.850646 + 0.525738i \(0.823789\pi\)
\(390\) −13.5638 6.79002i −0.686829 0.343826i
\(391\) 5.65182 0.285825
\(392\) 1.92755 + 3.33861i 0.0973558 + 0.168625i
\(393\) 1.83840 + 3.18420i 0.0927351 + 0.160622i
\(394\) −3.43414 + 5.94811i −0.173010 + 0.299662i
\(395\) 10.5453 0.530590
\(396\) −1.64870 + 2.85564i −0.0828504 + 0.143501i
\(397\) 8.76960 15.1894i 0.440134 0.762334i −0.557565 0.830133i \(-0.688264\pi\)
0.997699 + 0.0677993i \(0.0215978\pi\)
\(398\) 2.00051 0.100277
\(399\) −7.18729 + 12.4488i −0.359815 + 0.623217i
\(400\) −4.65091 8.05561i −0.232545 0.402780i
\(401\) −0.632250 1.09509i −0.0315730 0.0546861i 0.849807 0.527094i \(-0.176718\pi\)
−0.881380 + 0.472408i \(0.843385\pi\)
\(402\) 51.6683 2.57698
\(403\) −0.214302 3.59918i −0.0106752 0.179288i
\(404\) −1.40094 −0.0696992
\(405\) −4.56636 7.90917i −0.226904 0.393010i
\(406\) −19.1937 33.2444i −0.952566 1.64989i
\(407\) −16.3313 + 28.2866i −0.809511 + 1.40211i
\(408\) 1.56829 0.0776420
\(409\) −7.14096 + 12.3685i −0.353098 + 0.611583i −0.986790 0.162002i \(-0.948205\pi\)
0.633693 + 0.773585i \(0.281538\pi\)
\(410\) 0.171105 0.296362i 0.00845025 0.0146363i
\(411\) 22.6937 1.11940
\(412\) 5.37344 9.30706i 0.264730 0.458526i
\(413\) 5.45861 + 9.45458i 0.268600 + 0.465230i
\(414\) −3.21506 5.56865i −0.158012 0.273684i
\(415\) −17.3406 −0.851214
\(416\) 25.5815 + 12.8061i 1.25424 + 0.627869i
\(417\) −4.42562 −0.216723
\(418\) 8.06386 + 13.9670i 0.394416 + 0.683149i
\(419\) −15.1205 26.1895i −0.738685 1.27944i −0.953088 0.302695i \(-0.902114\pi\)
0.214403 0.976745i \(-0.431220\pi\)
\(420\) −8.07584 + 13.9878i −0.394060 + 0.682533i
\(421\) 29.7190 1.44842 0.724209 0.689581i \(-0.242205\pi\)
0.724209 + 0.689581i \(0.242205\pi\)
\(422\) 12.1180 20.9891i 0.589897 1.02173i
\(423\) 3.08495 5.34328i 0.149995 0.259799i
\(424\) 7.66037 0.372021
\(425\) 1.55152 2.68732i 0.0752599 0.130354i
\(426\) −8.69235 15.0556i −0.421146 0.729446i
\(427\) 6.37409 + 11.0402i 0.308464 + 0.534275i
\(428\) 22.4496 1.08514
\(429\) 13.8959 + 6.95627i 0.670899 + 0.335852i
\(430\) −19.3810 −0.934633
\(431\) 2.64047 + 4.57343i 0.127187 + 0.220294i 0.922586 0.385792i \(-0.126072\pi\)
−0.795399 + 0.606087i \(0.792738\pi\)
\(432\) 7.46332 + 12.9268i 0.359079 + 0.621943i
\(433\) 9.09156 15.7470i 0.436912 0.756754i −0.560537 0.828129i \(-0.689405\pi\)
0.997450 + 0.0713749i \(0.0227387\pi\)
\(434\) −6.89102 −0.330780
\(435\) 5.51391 9.55038i 0.264372 0.457905i
\(436\) 17.4333 30.1954i 0.834904 1.44610i
\(437\) −17.5221 −0.838194
\(438\) −8.08348 + 14.0010i −0.386244 + 0.668994i
\(439\) −16.9313 29.3258i −0.808085 1.39964i −0.914188 0.405289i \(-0.867171\pi\)
0.106103 0.994355i \(-0.466163\pi\)
\(440\) 1.85858 + 3.21916i 0.0886044 + 0.153467i
\(441\) −1.69575 −0.0807500
\(442\) 0.410410 + 6.89277i 0.0195212 + 0.327856i
\(443\) −21.8544 −1.03834 −0.519168 0.854673i \(-0.673758\pi\)
−0.519168 + 0.854673i \(0.673758\pi\)
\(444\) −24.0024 41.5733i −1.13910 1.97298i
\(445\) 6.45763 + 11.1849i 0.306121 + 0.530217i
\(446\) −7.38809 + 12.7965i −0.349836 + 0.605934i
\(447\) −9.26996 −0.438454
\(448\) 18.5783 32.1786i 0.877743 1.52030i
\(449\) −19.6062 + 33.9589i −0.925272 + 1.60262i −0.134149 + 0.990961i \(0.542830\pi\)
−0.791123 + 0.611657i \(0.790503\pi\)
\(450\) −3.53036 −0.166423
\(451\) −0.175294 + 0.303618i −0.00825427 + 0.0142968i
\(452\) 6.85869 + 11.8796i 0.322606 + 0.558769i
\(453\) −15.6128 27.0422i −0.733554 1.27055i
\(454\) 41.3756 1.94186
\(455\) −13.0440 6.52982i −0.611512 0.306123i
\(456\) −4.86210 −0.227689
\(457\) 10.7905 + 18.6897i 0.504759 + 0.874269i 0.999985 + 0.00550432i \(0.00175209\pi\)
−0.495226 + 0.868764i \(0.664915\pi\)
\(458\) −7.20349 12.4768i −0.336597 0.583003i
\(459\) −2.48973 + 4.31234i −0.116211 + 0.201283i
\(460\) −19.6883 −0.917970
\(461\) −8.33564 + 14.4378i −0.388230 + 0.672433i −0.992211 0.124565i \(-0.960247\pi\)
0.603982 + 0.796998i \(0.293580\pi\)
\(462\) 14.8500 25.7210i 0.690886 1.19665i
\(463\) −7.89838 −0.367069 −0.183534 0.983013i \(-0.558754\pi\)
−0.183534 + 0.983013i \(0.558754\pi\)
\(464\) −7.52423 + 13.0323i −0.349304 + 0.605011i
\(465\) −0.989819 1.71442i −0.0459017 0.0795041i
\(466\) 15.5997 + 27.0195i 0.722642 + 1.25165i
\(467\) 8.15177 0.377219 0.188609 0.982052i \(-0.439602\pi\)
0.188609 + 0.982052i \(0.439602\pi\)
\(468\) 3.65367 2.40983i 0.168891 0.111395i
\(469\) 49.6883 2.29439
\(470\) −16.9539 29.3651i −0.782026 1.35451i
\(471\) −8.97432 15.5440i −0.413515 0.716229i
\(472\) −1.84633 + 3.19794i −0.0849844 + 0.147197i
\(473\) 19.8555 0.912957
\(474\) 14.2496 24.6810i 0.654504 1.13363i
\(475\) −4.81011 + 8.33136i −0.220703 + 0.382269i
\(476\) 7.35259 0.337005
\(477\) −1.68480 + 2.91815i −0.0771415 + 0.133613i
\(478\) 3.01980 + 5.23044i 0.138122 + 0.239235i
\(479\) 19.3336 + 33.4869i 0.883377 + 1.53005i 0.847563 + 0.530695i \(0.178069\pi\)
0.0358141 + 0.999358i \(0.488598\pi\)
\(480\) 15.7072 0.716932
\(481\) 36.1915 23.8707i 1.65019 1.08841i
\(482\) −61.4524 −2.79908
\(483\) 16.1339 + 27.9447i 0.734118 + 1.27153i
\(484\) 4.55602 + 7.89126i 0.207092 + 0.358693i
\(485\) 3.44854 5.97304i 0.156590 0.271222i
\(486\) 10.5455 0.478354
\(487\) −18.9104 + 32.7538i −0.856912 + 1.48422i 0.0179474 + 0.999839i \(0.494287\pi\)
−0.874860 + 0.484377i \(0.839046\pi\)
\(488\) −2.15599 + 3.73428i −0.0975970 + 0.169043i
\(489\) 13.9404 0.630407
\(490\) −4.65966 + 8.07077i −0.210502 + 0.364600i
\(491\) −7.13604 12.3600i −0.322045 0.557798i 0.658865 0.752261i \(-0.271037\pi\)
−0.980910 + 0.194463i \(0.937704\pi\)
\(492\) −0.257633 0.446233i −0.0116150 0.0201178i
\(493\) −5.02010 −0.226094
\(494\) −1.27238 21.3693i −0.0572469 0.961452i
\(495\) −1.63508 −0.0734913
\(496\) 1.35070 + 2.33947i 0.0606481 + 0.105046i
\(497\) −8.35925 14.4786i −0.374964 0.649456i
\(498\) −23.4319 + 40.5852i −1.05001 + 1.81867i
\(499\) 17.4787 0.782455 0.391228 0.920294i \(-0.372051\pi\)
0.391228 + 0.920294i \(0.372051\pi\)
\(500\) −13.2529 + 22.9547i −0.592689 + 1.02657i
\(501\) −6.57043 + 11.3803i −0.293545 + 0.508435i
\(502\) −47.5919 −2.12413
\(503\) −5.88149 + 10.1870i −0.262243 + 0.454218i −0.966838 0.255392i \(-0.917795\pi\)
0.704595 + 0.709610i \(0.251129\pi\)
\(504\) −0.857942 1.48600i −0.0382158 0.0661916i
\(505\) −0.347340 0.601610i −0.0154564 0.0267713i
\(506\) 36.2032 1.60943
\(507\) −12.3603 16.5133i −0.548938 0.733381i
\(508\) 25.2838 1.12179
\(509\) 13.1640 + 22.8008i 0.583485 + 1.01063i 0.995062 + 0.0992508i \(0.0316446\pi\)
−0.411577 + 0.911375i \(0.635022\pi\)
\(510\) 1.89560 + 3.28327i 0.0839385 + 0.145386i
\(511\) −7.77371 + 13.4645i −0.343889 + 0.595633i
\(512\) −27.3597 −1.20914
\(513\) 7.71880 13.3694i 0.340793 0.590271i
\(514\) 22.0539 38.1985i 0.972756 1.68486i
\(515\) 5.32903 0.234825
\(516\) −14.5910 + 25.2724i −0.642333 + 1.11255i
\(517\) 17.3690 + 30.0841i 0.763889 + 1.32310i
\(518\) −41.4304 71.7595i −1.82035 3.15293i
\(519\) 13.6862 0.600758
\(520\) −0.293261 4.92527i −0.0128603 0.215987i
\(521\) 19.1419 0.838624 0.419312 0.907842i \(-0.362271\pi\)
0.419312 + 0.907842i \(0.362271\pi\)
\(522\) 2.85571 + 4.94623i 0.124991 + 0.216491i
\(523\) 9.40829 + 16.2956i 0.411396 + 0.712558i 0.995043 0.0994494i \(-0.0317081\pi\)
−0.583647 + 0.812007i \(0.698375\pi\)
\(524\) −2.91529 + 5.04944i −0.127355 + 0.220586i
\(525\) 17.7162 0.773197
\(526\) 3.99998 6.92817i 0.174407 0.302083i
\(527\) −0.450587 + 0.780439i −0.0196279 + 0.0339965i
\(528\) −11.6429 −0.506692
\(529\) −8.16661 + 14.1450i −0.355070 + 0.614999i
\(530\) 9.25912 + 16.0373i 0.402191 + 0.696615i
\(531\) −0.812152 1.40669i −0.0352444 0.0610451i
\(532\) −22.7949 −0.988284
\(533\) 0.388467 0.256219i 0.0168264 0.0110981i
\(534\) 34.9042 1.51045
\(535\) 5.56602 + 9.64062i 0.240640 + 0.416800i
\(536\) 8.40336 + 14.5550i 0.362970 + 0.628682i
\(537\) −15.1404 + 26.2240i −0.653357 + 1.13165i
\(538\) −22.6289 −0.975601
\(539\) 4.77375 8.26838i 0.205620 0.356144i
\(540\) 8.67305 15.0222i 0.373229 0.646451i
\(541\) −31.4255 −1.35109 −0.675544 0.737320i \(-0.736091\pi\)
−0.675544 + 0.737320i \(0.736091\pi\)
\(542\) 7.61811 13.1949i 0.327226 0.566771i
\(543\) −17.2339 29.8500i −0.739578 1.28099i
\(544\) −3.57513 6.19230i −0.153282 0.265493i
\(545\) 17.2892 0.740590
\(546\) −32.9089 + 21.7056i −1.40837 + 0.928915i
\(547\) −29.4560 −1.25945 −0.629724 0.776819i \(-0.716832\pi\)
−0.629724 + 0.776819i \(0.716832\pi\)
\(548\) 17.9936 + 31.1658i 0.768647 + 1.33133i
\(549\) −0.948361 1.64261i −0.0404751 0.0701049i
\(550\) 9.93842 17.2138i 0.423776 0.734001i
\(551\) 15.5636 0.663031
\(552\) −5.45718 + 9.45211i −0.232273 + 0.402308i
\(553\) 13.7035 23.7352i 0.582733 1.00932i
\(554\) −8.41516 −0.357526
\(555\) 11.9020 20.6149i 0.505213 0.875054i
\(556\) −3.50902 6.07780i −0.148816 0.257756i
\(557\) −13.3624 23.1443i −0.566182 0.980656i −0.996939 0.0781876i \(-0.975087\pi\)
0.430757 0.902468i \(-0.358247\pi\)
\(558\) 1.02527 0.0434033
\(559\) −23.5672 11.7977i −0.996788 0.498991i
\(560\) 10.9291 0.461840
\(561\) −1.94201 3.36366i −0.0819918 0.142014i
\(562\) −12.4516 21.5668i −0.525240 0.909742i
\(563\) −16.9699 + 29.3926i −0.715194 + 1.23875i 0.247691 + 0.968839i \(0.420328\pi\)
−0.962885 + 0.269913i \(0.913005\pi\)
\(564\) −51.0552 −2.14981
\(565\) −3.40101 + 5.89072i −0.143081 + 0.247824i
\(566\) 7.95038 13.7705i 0.334179 0.578816i
\(567\) −23.7358 −0.996812
\(568\) 2.82746 4.89730i 0.118637 0.205486i
\(569\) 2.03218 + 3.51984i 0.0851933 + 0.147559i 0.905474 0.424403i \(-0.139516\pi\)
−0.820280 + 0.571962i \(0.806183\pi\)
\(570\) −5.87684 10.1790i −0.246154 0.426351i
\(571\) 15.9467 0.667348 0.333674 0.942688i \(-0.391711\pi\)
0.333674 + 0.942688i \(0.391711\pi\)
\(572\) 1.46468 + 24.5991i 0.0612413 + 1.02854i
\(573\) 22.8022 0.952574
\(574\) −0.444699 0.770241i −0.0185614 0.0321492i
\(575\) 10.7977 + 18.7021i 0.450293 + 0.779931i
\(576\) −2.76415 + 4.78765i −0.115173 + 0.199486i
\(577\) 14.4117 0.599965 0.299983 0.953945i \(-0.403019\pi\)
0.299983 + 0.953945i \(0.403019\pi\)
\(578\) −17.2006 + 29.7923i −0.715449 + 1.23919i
\(579\) 5.46377 9.46352i 0.227066 0.393290i
\(580\) 17.4877 0.726136
\(581\) −22.5339 + 39.0299i −0.934866 + 1.61923i
\(582\) −9.31986 16.1425i −0.386321 0.669127i
\(583\) −9.48583 16.4299i −0.392863 0.680458i
\(584\) −5.25880 −0.217611
\(585\) 1.94074 + 0.971531i 0.0802395 + 0.0401679i
\(586\) −18.5688 −0.767072
\(587\) −10.9440 18.9555i −0.451707 0.782379i 0.546786 0.837273i \(-0.315851\pi\)
−0.998492 + 0.0548938i \(0.982518\pi\)
\(588\) 7.01608 + 12.1522i 0.289338 + 0.501148i
\(589\) 1.39693 2.41956i 0.0575596 0.0996962i
\(590\) −8.92668 −0.367506
\(591\) −2.56404 + 4.44105i −0.105470 + 0.182680i
\(592\) −16.2414 + 28.1309i −0.667516 + 1.15617i
\(593\) −12.1341 −0.498288 −0.249144 0.968466i \(-0.580149\pi\)
−0.249144 + 0.968466i \(0.580149\pi\)
\(594\) −15.9482 + 27.6231i −0.654362 + 1.13339i
\(595\) 1.82296 + 3.15746i 0.0747340 + 0.129443i
\(596\) −7.35004 12.7306i −0.301069 0.521468i
\(597\) 1.49365 0.0611309
\(598\) −42.9709 21.5112i −1.75721 0.879659i
\(599\) 10.5415 0.430713 0.215357 0.976535i \(-0.430909\pi\)
0.215357 + 0.976535i \(0.430909\pi\)
\(600\) 2.99618 + 5.18954i 0.122319 + 0.211862i
\(601\) −6.81000 11.7953i −0.277786 0.481139i 0.693048 0.720891i \(-0.256267\pi\)
−0.970834 + 0.239752i \(0.922934\pi\)
\(602\) −25.1855 + 43.6225i −1.02648 + 1.77792i
\(603\) −7.39282 −0.301059
\(604\) 24.7584 42.8829i 1.00741 1.74488i
\(605\) −2.25919 + 3.91302i −0.0918490 + 0.159087i
\(606\) −1.87741 −0.0762645
\(607\) −9.70688 + 16.8128i −0.393990 + 0.682411i −0.992972 0.118352i \(-0.962239\pi\)
0.598982 + 0.800763i \(0.295572\pi\)
\(608\) 11.0838 + 19.1977i 0.449508 + 0.778570i
\(609\) −14.3306 24.8213i −0.580705 1.00581i
\(610\) −10.4238 −0.422048
\(611\) −2.74061 46.0282i −0.110873 1.86210i
\(612\) −1.09395 −0.0442201
\(613\) −18.6190 32.2490i −0.752013 1.30252i −0.946846 0.321688i \(-0.895750\pi\)
0.194833 0.980836i \(-0.437584\pi\)
\(614\) 24.9042 + 43.1354i 1.00505 + 1.74080i
\(615\) 0.127752 0.221273i 0.00515146 0.00892259i
\(616\) 9.66086 0.389247
\(617\) −16.9177 + 29.3023i −0.681081 + 1.17967i 0.293570 + 0.955938i \(0.405157\pi\)
−0.974651 + 0.223730i \(0.928177\pi\)
\(618\) 7.20100 12.4725i 0.289667 0.501717i
\(619\) −23.9463 −0.962482 −0.481241 0.876588i \(-0.659814\pi\)
−0.481241 + 0.876588i \(0.659814\pi\)
\(620\) 1.56963 2.71868i 0.0630379 0.109185i
\(621\) −17.3270 30.0113i −0.695309 1.20431i
\(622\) 11.7486 + 20.3492i 0.471076 + 0.815928i
\(623\) 33.5666 1.34482
\(624\) 13.8194 + 6.91798i 0.553218 + 0.276941i
\(625\) 4.07328 0.162931
\(626\) 36.0894 + 62.5086i 1.44242 + 2.49835i
\(627\) 6.02073 + 10.4282i 0.240445 + 0.416463i
\(628\) 14.2313 24.6493i 0.567889 0.983613i
\(629\) −10.8361 −0.432064
\(630\) 2.07399 3.59226i 0.0826299 0.143119i
\(631\) −13.3635 + 23.1462i −0.531992 + 0.921437i 0.467311 + 0.884093i \(0.345223\pi\)
−0.999302 + 0.0373439i \(0.988110\pi\)
\(632\) 9.27022 0.368750
\(633\) 9.04770 15.6711i 0.359614 0.622870i
\(634\) 18.5191 + 32.0760i 0.735487 + 1.27390i
\(635\) 6.26871 + 10.8577i 0.248766 + 0.430876i
\(636\) 27.8830 1.10563
\(637\) −10.5790 + 6.97758i −0.419157 + 0.276462i
\(638\) −32.1567 −1.27310
\(639\) 1.24372 + 2.15419i 0.0492009 + 0.0852184i
\(640\) 5.29151 + 9.16517i 0.209165 + 0.362285i
\(641\) 6.71183 11.6252i 0.265101 0.459169i −0.702489 0.711695i \(-0.747928\pi\)
0.967590 + 0.252526i \(0.0812612\pi\)
\(642\) 30.0849 1.18736
\(643\) −20.4950 + 35.4985i −0.808246 + 1.39992i 0.105832 + 0.994384i \(0.466249\pi\)
−0.914078 + 0.405538i \(0.867084\pi\)
\(644\) −25.5848 + 44.3141i −1.00818 + 1.74622i
\(645\) −14.4704 −0.569773
\(646\) −2.67526 + 4.63369i −0.105257 + 0.182310i
\(647\) −1.69947 2.94356i −0.0668129 0.115723i 0.830684 0.556744i \(-0.187950\pi\)
−0.897497 + 0.441021i \(0.854616\pi\)
\(648\) −4.01424 6.95286i −0.157694 0.273134i
\(649\) 9.14525 0.358982
\(650\) −22.0244 + 14.5265i −0.863868 + 0.569778i
\(651\) −5.14505 −0.201651
\(652\) 11.0532 + 19.1447i 0.432876 + 0.749763i
\(653\) 4.61156 + 7.98745i 0.180464 + 0.312573i 0.942039 0.335504i \(-0.108907\pi\)
−0.761575 + 0.648077i \(0.775573\pi\)
\(654\) 23.3626 40.4651i 0.913548 1.58231i
\(655\) −2.89120 −0.112969
\(656\) −0.174329 + 0.301947i −0.00680641 + 0.0117890i
\(657\) 1.15660 2.00329i 0.0451234 0.0781560i
\(658\) −88.1261 −3.43551
\(659\) −1.73692 + 3.00844i −0.0676609 + 0.117192i −0.897871 0.440258i \(-0.854887\pi\)
0.830210 + 0.557450i \(0.188220\pi\)
\(660\) 6.76505 + 11.7174i 0.263329 + 0.456100i
\(661\) 0.655426 + 1.13523i 0.0254931 + 0.0441554i 0.878491 0.477760i \(-0.158551\pi\)
−0.852997 + 0.521915i \(0.825218\pi\)
\(662\) −27.3691 −1.06373
\(663\) 0.306425 + 5.14636i 0.0119006 + 0.199868i
\(664\) −15.2439 −0.591578
\(665\) −5.65163 9.78891i −0.219161 0.379598i
\(666\) 6.16417 + 10.6767i 0.238857 + 0.413712i
\(667\) 17.4684 30.2562i 0.676380 1.17153i
\(668\) −20.8385 −0.806265
\(669\) −5.51618 + 9.55430i −0.213268 + 0.369391i
\(670\) −20.3143 + 35.1855i −0.784811 + 1.35933i
\(671\) 10.6790 0.412259
\(672\) 20.4114 35.3536i 0.787387 1.36379i
\(673\) 9.93987 + 17.2164i 0.383154 + 0.663642i 0.991511 0.130021i \(-0.0415045\pi\)
−0.608357 + 0.793663i \(0.708171\pi\)
\(674\) −11.3006 19.5732i −0.435281 0.753930i
\(675\) −19.0263 −0.732322
\(676\) 12.8778 30.0678i 0.495300 1.15645i
\(677\) −34.0960 −1.31041 −0.655207 0.755449i \(-0.727419\pi\)
−0.655207 + 0.755449i \(0.727419\pi\)
\(678\) 9.19140 + 15.9200i 0.352994 + 0.611403i
\(679\) −8.96271 15.5239i −0.343957 0.595751i
\(680\) −0.616602 + 1.06799i −0.0236456 + 0.0409554i
\(681\) 30.8923 1.18380
\(682\) −2.88627 + 4.99917i −0.110521 + 0.191428i
\(683\) 6.84605 11.8577i 0.261957 0.453723i −0.704805 0.709401i \(-0.748965\pi\)
0.966762 + 0.255678i \(0.0822988\pi\)
\(684\) 3.39151 0.129678
\(685\) −8.92243 + 15.4541i −0.340909 + 0.590471i
\(686\) −12.0082 20.7988i −0.458474 0.794101i
\(687\) −5.37835 9.31557i −0.205197 0.355411i
\(688\) 19.7462 0.752817
\(689\) 1.49674 + 25.1376i 0.0570214 + 0.957666i
\(690\) −26.3844 −1.00444
\(691\) −25.7464 44.5941i −0.979440 1.69644i −0.664427 0.747353i \(-0.731324\pi\)
−0.315013 0.949087i \(-0.602009\pi\)
\(692\) 10.8516 + 18.7956i 0.412518 + 0.714501i
\(693\) −2.12478 + 3.68022i −0.0807135 + 0.139800i
\(694\) −16.6480 −0.631951
\(695\) 1.74001 3.01379i 0.0660024 0.114320i
\(696\) 4.84722 8.39563i 0.183733 0.318235i
\(697\) −0.116311 −0.00440559
\(698\) 21.6560 37.5093i 0.819692 1.41975i
\(699\) 11.6472 + 20.1736i 0.440538 + 0.763035i
\(700\) 14.0469 + 24.3300i 0.530924 + 0.919588i
\(701\) −40.7595 −1.53947 −0.769733 0.638366i \(-0.779611\pi\)
−0.769733 + 0.638366i \(0.779611\pi\)
\(702\) 35.3426 23.3108i 1.33392 0.879808i
\(703\) 33.5947 1.26705
\(704\) −15.5629 26.9557i −0.586548 1.01593i
\(705\) −12.6583 21.9249i −0.476740 0.825738i
\(706\) −22.0773 + 38.2390i −0.830891 + 1.43915i
\(707\) −1.80546 −0.0679015
\(708\) −6.72047 + 11.6402i −0.252571 + 0.437465i
\(709\) −8.58295 + 14.8661i −0.322340 + 0.558309i −0.980970 0.194158i \(-0.937803\pi\)
0.658631 + 0.752466i \(0.271136\pi\)
\(710\) 13.6702 0.513034
\(711\) −2.03886 + 3.53141i −0.0764632 + 0.132438i
\(712\) 5.67683 + 9.83255i 0.212748 + 0.368491i
\(713\) −3.13581 5.43138i −0.117437 0.203407i
\(714\) 9.85328 0.368750
\(715\) −10.2005 + 6.72793i −0.381479 + 0.251610i
\(716\) −48.0186 −1.79454
\(717\) 2.25467 + 3.90521i 0.0842024 + 0.145843i
\(718\) 38.9990 + 67.5483i 1.45543 + 2.52088i
\(719\) 4.49459 7.78485i 0.167620 0.290326i −0.769963 0.638089i \(-0.779725\pi\)
0.937583 + 0.347763i \(0.113059\pi\)
\(720\) −1.62608 −0.0606004
\(721\) 6.92505 11.9945i 0.257902 0.446700i
\(722\) −11.8946 + 20.6021i −0.442671 + 0.766729i
\(723\) −45.8823 −1.70638
\(724\) 27.3291 47.3355i 1.01568 1.75921i
\(725\) −9.59078 16.6117i −0.356193 0.616944i
\(726\) 6.10557 + 10.5752i 0.226599 + 0.392481i
\(727\) 46.1691 1.71232 0.856159 0.516713i \(-0.172845\pi\)
0.856159 + 0.516713i \(0.172845\pi\)
\(728\) −11.4668 5.74029i −0.424989 0.212749i
\(729\) 29.8332 1.10493
\(730\) −6.35634 11.0095i −0.235259 0.407480i
\(731\) 3.29363 + 5.70473i 0.121819 + 0.210997i
\(732\) −7.84759 + 13.5924i −0.290055 + 0.502390i
\(733\) 17.5457 0.648066 0.324033 0.946046i \(-0.394961\pi\)
0.324033 + 0.946046i \(0.394961\pi\)
\(734\) −1.14749 + 1.98750i −0.0423545 + 0.0733601i
\(735\) −3.47905 + 6.02589i −0.128327 + 0.222268i
\(736\) 49.7614 1.83423
\(737\) 20.8117 36.0470i 0.766610 1.32781i
\(738\) 0.0661640 + 0.114599i 0.00243553 + 0.00421846i
\(739\) 4.53787 + 7.85982i 0.166928 + 0.289128i 0.937338 0.348420i \(-0.113282\pi\)
−0.770410 + 0.637549i \(0.779949\pi\)
\(740\) 37.7479 1.38764
\(741\) −0.949995 15.9550i −0.0348989 0.586122i
\(742\) 48.1287 1.76686
\(743\) 4.42124 + 7.65782i 0.162200 + 0.280938i 0.935657 0.352910i \(-0.114808\pi\)
−0.773458 + 0.633848i \(0.781474\pi\)
\(744\) −0.870138 1.50712i −0.0319008 0.0552538i
\(745\) 3.64465 6.31273i 0.133530 0.231280i
\(746\) −19.8789 −0.727819
\(747\) 3.35269 5.80702i 0.122668 0.212468i
\(748\) 3.07960 5.33402i 0.112601 0.195031i
\(749\) 28.9320 1.05715
\(750\) −17.7604 + 30.7619i −0.648518 + 1.12327i
\(751\) −11.1515 19.3150i −0.406925 0.704815i 0.587618 0.809138i \(-0.300066\pi\)
−0.994543 + 0.104323i \(0.966732\pi\)
\(752\) 17.2734 + 29.9185i 0.629897 + 1.09101i
\(753\) −35.5336 −1.29492
\(754\) 38.1680 + 19.1069i 1.39000 + 0.695831i
\(755\) 24.5538 0.893606
\(756\) −22.5411 39.0424i −0.819814 1.41996i
\(757\) −12.7630 22.1062i −0.463880 0.803464i 0.535270 0.844681i \(-0.320210\pi\)
−0.999150 + 0.0412171i \(0.986876\pi\)
\(758\) −8.97720 + 15.5490i −0.326067 + 0.564764i
\(759\) 27.0304 0.981143
\(760\) 1.91162 3.31103i 0.0693419 0.120104i
\(761\) 14.0503 24.3358i 0.509323 0.882173i −0.490619 0.871374i \(-0.663229\pi\)
0.999942 0.0107990i \(-0.00343750\pi\)
\(762\) 33.8831 1.22745
\(763\) 22.4673 38.9145i 0.813370 1.40880i
\(764\) 18.0796 + 31.3147i 0.654096 + 1.13293i
\(765\) −0.271227 0.469778i −0.00980622 0.0169849i
\(766\) 25.6358 0.926261
\(767\) −10.8548 5.43392i −0.391945 0.196208i
\(768\) −7.76133 −0.280063
\(769\) −21.8669 37.8745i −0.788540 1.36579i −0.926861 0.375404i \(-0.877504\pi\)
0.138322 0.990387i \(-0.455829\pi\)
\(770\) 11.6771 + 20.2254i 0.420814 + 0.728871i
\(771\) 16.4661 28.5202i 0.593013 1.02713i
\(772\) 17.3286 0.623671
\(773\) −12.2113 + 21.1506i −0.439211 + 0.760735i −0.997629 0.0688245i \(-0.978075\pi\)
0.558418 + 0.829560i \(0.311408\pi\)
\(774\) 3.74719 6.49032i 0.134690 0.233290i
\(775\) −3.44334 −0.123688
\(776\) 3.03157 5.25084i 0.108827 0.188494i
\(777\) −30.9332 53.5779i −1.10972 1.92210i
\(778\) −35.6538 61.7543i −1.27825 2.21400i
\(779\) 0.360593 0.0129196
\(780\) −1.06744 17.9275i −0.0382205 0.641907i
\(781\) −14.0049 −0.501136
\(782\) 6.00538 + 10.4016i 0.214752 + 0.371961i
\(783\) 15.3903 + 26.6569i 0.550006 + 0.952638i
\(784\) 4.74748 8.22287i 0.169553 0.293674i
\(785\) 14.1137 0.503738
\(786\) −3.90682 + 6.76680i −0.139351 + 0.241364i
\(787\) 14.9041 25.8146i 0.531273 0.920191i −0.468061 0.883696i \(-0.655047\pi\)
0.999334 0.0364951i \(-0.0116193\pi\)
\(788\) −8.13199 −0.289690
\(789\) 2.98651 5.17279i 0.106323 0.184156i
\(790\) 11.2050 + 19.4076i 0.398654 + 0.690490i
\(791\) 8.83918 + 15.3099i 0.314285 + 0.544357i
\(792\) −1.43738 −0.0510751
\(793\) −12.6753 6.34526i −0.450114 0.225327i
\(794\) 37.2728 1.32276
\(795\) 6.91315 + 11.9739i 0.245184 + 0.424671i
\(796\) 1.18429 + 2.05126i 0.0419762 + 0.0727049i
\(797\) 1.08540 1.87997i 0.0384468 0.0665918i −0.846162 0.532926i \(-0.821092\pi\)
0.884609 + 0.466334i \(0.154426\pi\)
\(798\) −30.5477 −1.08138
\(799\) −5.76234 + 9.98067i −0.203857 + 0.353091i
\(800\) 13.6604 23.6605i 0.482968 0.836524i
\(801\) −4.99416 −0.176460
\(802\) 1.34360 2.32719i 0.0474443 0.0821759i
\(803\) 6.51197 + 11.2791i 0.229802 + 0.398029i
\(804\) 30.5874 + 52.9789i 1.07873 + 1.86842i
\(805\) −25.3734 −0.894293
\(806\) 6.39623 4.21874i 0.225298 0.148599i
\(807\) −16.8954 −0.594747
\(808\) −0.305343 0.528869i −0.0107419 0.0186055i
\(809\) 12.6935 + 21.9859i 0.446281 + 0.772981i 0.998140 0.0609558i \(-0.0194149\pi\)
−0.551859 + 0.833937i \(0.686082\pi\)
\(810\) 9.70405 16.8079i 0.340966 0.590570i
\(811\) −9.66994 −0.339557 −0.169779 0.985482i \(-0.554305\pi\)
−0.169779 + 0.985482i \(0.554305\pi\)
\(812\) 22.7251 39.3611i 0.797495 1.38130i
\(813\) 5.68791 9.85176i 0.199484 0.345516i
\(814\) −69.4117 −2.43288
\(815\) −5.48092 + 9.49324i −0.191988 + 0.332534i
\(816\) −1.93132 3.34515i −0.0676098 0.117104i
\(817\) −10.2111 17.6861i −0.357240 0.618759i
\(818\) −30.3507 −1.06119
\(819\) 4.70869 3.10569i 0.164535 0.108522i
\(820\) 0.405172 0.0141492
\(821\) −5.64426 9.77615i −0.196986 0.341190i 0.750564 0.660798i \(-0.229782\pi\)
−0.947550 + 0.319608i \(0.896449\pi\)
\(822\) 24.1133 + 41.7655i 0.841050 + 1.45674i
\(823\) 13.4783 23.3450i 0.469823 0.813757i −0.529582 0.848259i \(-0.677651\pi\)
0.999405 + 0.0345021i \(0.0109845\pi\)
\(824\) 4.68469 0.163199
\(825\) 7.42033 12.8524i 0.258343 0.447463i
\(826\) −11.6002 + 20.0921i −0.403622 + 0.699093i
\(827\) −52.0112 −1.80861 −0.904303 0.426891i \(-0.859609\pi\)
−0.904303 + 0.426891i \(0.859609\pi\)
\(828\) 3.80660 6.59322i 0.132288 0.229130i
\(829\) −2.44236 4.23029i −0.0848267 0.146924i 0.820491 0.571660i \(-0.193700\pi\)
−0.905317 + 0.424736i \(0.860367\pi\)
\(830\) −18.4253 31.9136i −0.639553 1.10774i
\(831\) −6.28302 −0.217956
\(832\) 2.45563 + 41.2419i 0.0851335 + 1.42980i
\(833\) 3.16748 0.109747
\(834\) −4.70247 8.14492i −0.162833 0.282036i
\(835\) −5.16657 8.94876i −0.178796 0.309685i
\(836\) −9.54753 + 16.5368i −0.330208 + 0.571938i
\(837\) 5.52553 0.190990
\(838\) 32.1328 55.6557i 1.11001 1.92259i
\(839\) 20.8862 36.1760i 0.721072 1.24893i −0.239499 0.970897i \(-0.576983\pi\)
0.960571 0.278036i \(-0.0896836\pi\)
\(840\) −7.04071 −0.242928
\(841\) −1.01595 + 1.75968i −0.0350328 + 0.0606786i
\(842\) 31.5782 + 54.6950i 1.08826 + 1.88492i
\(843\) −9.29676 16.1025i −0.320198 0.554598i
\(844\) 28.6953 0.987732
\(845\) 16.1050 1.92467i 0.554029 0.0662108i
\(846\) 13.1117 0.450791
\(847\) 5.87160 + 10.1699i 0.201750 + 0.349442i
\(848\) −9.43361 16.3395i −0.323952 0.561101i
\(849\) 5.93600 10.2815i 0.203723 0.352859i
\(850\) 6.59433 0.226184
\(851\) 37.7064 65.3094i 1.29256 2.23878i
\(852\) 10.2917 17.8257i 0.352586 0.610698i
\(853\) −5.74115 −0.196573 −0.0982867 0.995158i \(-0.531336\pi\)
−0.0982867 + 0.995158i \(0.531336\pi\)
\(854\) −13.5457 + 23.4618i −0.463523 + 0.802846i
\(855\) 0.840871 + 1.45643i 0.0287572 + 0.0498089i
\(856\) 4.89302 + 8.47496i 0.167240 + 0.289668i
\(857\) 41.4949 1.41744 0.708719 0.705491i \(-0.249274\pi\)
0.708719 + 0.705491i \(0.249274\pi\)
\(858\) 1.96283 + 32.9655i 0.0670100 + 1.12542i
\(859\) 39.9628 1.36351 0.681757 0.731579i \(-0.261216\pi\)
0.681757 + 0.731579i \(0.261216\pi\)
\(860\) −11.4734 19.8726i −0.391241 0.677649i
\(861\) −0.332026 0.575086i −0.0113154 0.0195989i
\(862\) −5.61131 + 9.71907i −0.191122 + 0.331033i
\(863\) 27.6874 0.942491 0.471246 0.882002i \(-0.343805\pi\)
0.471246 + 0.882002i \(0.343805\pi\)
\(864\) −21.9208 + 37.9680i −0.745762 + 1.29170i
\(865\) −5.38099 + 9.32014i −0.182959 + 0.316894i
\(866\) 38.6412 1.31308
\(867\) −12.8425 + 22.2438i −0.436153 + 0.755440i
\(868\) −4.07945 7.06582i −0.138466 0.239830i
\(869\) −11.4793 19.8827i −0.389409 0.674476i
\(870\) 23.4354 0.794534
\(871\) −46.1206 + 30.4196i −1.56274 + 1.03073i
\(872\) 15.1988 0.514696
\(873\) 1.33351 + 2.30970i 0.0451323 + 0.0781715i
\(874\) −18.6182 32.2477i −0.629770 1.09079i
\(875\) −17.0798 + 29.5831i −0.577402 + 1.00009i
\(876\) −19.1415 −0.646732
\(877\) 18.7013 32.3917i 0.631500 1.09379i −0.355746 0.934583i \(-0.615773\pi\)
0.987245 0.159206i \(-0.0508936\pi\)
\(878\) 35.9809 62.3207i 1.21430 2.10322i
\(879\) −13.8641 −0.467624
\(880\) 4.57762 7.92867i 0.154312 0.267275i
\(881\) −15.4397 26.7423i −0.520176 0.900970i −0.999725 0.0234555i \(-0.992533\pi\)
0.479549 0.877515i \(-0.340800\pi\)
\(882\) −1.80183 3.12087i −0.0606708 0.105085i
\(883\) 29.3210 0.986730 0.493365 0.869822i \(-0.335767\pi\)
0.493365 + 0.869822i \(0.335767\pi\)
\(884\) −6.82465 + 4.50131i −0.229538 + 0.151395i
\(885\) −6.66494 −0.224039
\(886\) −23.2216 40.2210i −0.780144 1.35125i
\(887\) −27.6258 47.8493i −0.927584 1.60662i −0.787352 0.616504i \(-0.788548\pi\)
−0.140232 0.990119i \(-0.544785\pi\)
\(888\) 10.4629 18.1223i 0.351113 0.608145i
\(889\) 32.5846 1.09285
\(890\) −13.7232 + 23.7693i −0.460003 + 0.796748i
\(891\) −9.94165 + 17.2194i −0.333058 + 0.576873i
\(892\) −17.4949 −0.585771
\(893\) 17.8647 30.9426i 0.597820 1.03545i
\(894\) −9.84987 17.0605i −0.329429 0.570588i
\(895\) −11.9055 20.6209i −0.397956 0.689280i
\(896\) 27.5051 0.918883
\(897\) −32.0834 16.0609i −1.07123 0.536259i
\(898\) −83.3307 −2.78078
\(899\) 2.78531 + 4.82431i 0.0928954 + 0.160900i
\(900\) −2.08996 3.61991i −0.0696652 0.120664i
\(901\) 3.14701 5.45079i 0.104842 0.181592i
\(902\) −0.745040 −0.0248071
\(903\) −18.8042 + 32.5699i −0.625766 + 1.08386i
\(904\) −2.98979 + 5.17846i −0.0994388 + 0.172233i
\(905\) 27.1033 0.900944
\(906\) 33.1790 57.4678i 1.10230 1.90924i
\(907\) −14.7965 25.6283i −0.491311 0.850975i 0.508639 0.860980i \(-0.330149\pi\)
−0.999950 + 0.0100045i \(0.996815\pi\)
\(908\) 24.4942 + 42.4252i 0.812868 + 1.40793i
\(909\) 0.268624 0.00890969
\(910\) −1.84250 30.9445i −0.0610783 1.02580i
\(911\) 50.8154 1.68359 0.841795 0.539797i \(-0.181499\pi\)
0.841795 + 0.539797i \(0.181499\pi\)
\(912\) 5.98759 + 10.3708i 0.198269 + 0.343412i
\(913\) 18.8765 + 32.6950i 0.624720 + 1.08205i
\(914\) −22.9311 + 39.7178i −0.758494 + 1.31375i
\(915\) −7.78274 −0.257289
\(916\) 8.52886 14.7724i 0.281801 0.488094i
\(917\) −3.75710 + 6.50749i −0.124070 + 0.214896i
\(918\) −10.5819 −0.349256
\(919\) 10.2516 17.7564i 0.338170 0.585728i −0.645918 0.763407i \(-0.723525\pi\)
0.984089 + 0.177678i \(0.0568587\pi\)
\(920\) −4.29118 7.43254i −0.141476 0.245043i
\(921\) 18.5943 + 32.2062i 0.612702 + 1.06123i
\(922\) −35.4284 −1.16677
\(923\) 16.6230 + 8.32145i 0.547152 + 0.273904i
\(924\) 35.1646 1.15683
\(925\) −20.7021 35.8571i −0.680682 1.17898i
\(926\) −8.39248 14.5362i −0.275794 0.477689i
\(927\) −1.03033 + 1.78459i −0.0338406 + 0.0586137i
\(928\) −44.1995 −1.45092
\(929\) −16.4580 + 28.5061i −0.539970 + 0.935256i 0.458935 + 0.888470i \(0.348231\pi\)
−0.998905 + 0.0467859i \(0.985102\pi\)
\(930\) 2.10348 3.64333i 0.0689758 0.119470i
\(931\) −9.81998 −0.321837
\(932\) −18.4699 + 31.9908i −0.605001 + 1.04789i
\(933\) 8.77188 + 15.1933i 0.287178 + 0.497407i
\(934\) 8.66172 + 15.0025i 0.283420 + 0.490898i
\(935\) 3.05415 0.0998814
\(936\) 1.70608 + 0.854062i 0.0557649 + 0.0279159i
\(937\) −13.5194 −0.441659 −0.220829 0.975312i \(-0.570876\pi\)
−0.220829 + 0.975312i \(0.570876\pi\)
\(938\) 52.7967 + 91.4466i 1.72387 + 2.98584i
\(939\) 26.9454 + 46.6709i 0.879331 + 1.52305i
\(940\) 20.0733 34.7679i 0.654718 1.13401i
\(941\) 14.1855 0.462434 0.231217 0.972902i \(-0.425729\pi\)
0.231217 + 0.972902i \(0.425729\pi\)
\(942\) 19.0715 33.0328i 0.621382 1.07627i
\(943\) 0.404727 0.701007i 0.0131797 0.0228279i
\(944\) 9.09491 0.296014
\(945\) 11.1774 19.3599i 0.363602 0.629777i
\(946\) 21.0976 + 36.5422i 0.685943 + 1.18809i
\(947\) 22.4378 + 38.8634i 0.729130 + 1.26289i 0.957251 + 0.289257i \(0.0934083\pi\)
−0.228122 + 0.973633i \(0.573258\pi\)
\(948\) 33.7427 1.09591
\(949\) −1.02751 17.2568i −0.0333543 0.560180i
\(950\) −20.4441 −0.663294
\(951\) 13.8269 + 23.9490i 0.448369 + 0.776598i
\(952\) 1.60254 + 2.77568i 0.0519387 + 0.0899604i
\(953\) −13.8506 + 23.9899i −0.448665 + 0.777111i −0.998299 0.0582947i \(-0.981434\pi\)
0.549634 + 0.835405i \(0.314767\pi\)
\(954\) −7.16077 −0.231838
\(955\) −8.96509 + 15.5280i −0.290103 + 0.502474i
\(956\) −3.57541 + 6.19279i −0.115637 + 0.200289i
\(957\) −24.0092 −0.776107
\(958\) −41.0862 + 71.1634i −1.32744 + 2.29919i
\(959\) 23.1893 + 40.1650i 0.748821 + 1.29700i
\(960\) 11.3420 + 19.6450i 0.366062 + 0.634039i
\(961\) 1.00000 0.0322581
\(962\) 82.3873 + 41.2430i 2.65627 + 1.32973i
\(963\) −4.30461 −0.138714
\(964\) −36.3795 63.0112i −1.17171 2.02945i
\(965\) 4.29636 + 7.44151i 0.138305 + 0.239551i
\(966\) −34.2864 + 59.3858i −1.10315 + 1.91071i
\(967\) 57.2301 1.84040 0.920198 0.391454i \(-0.128028\pi\)
0.920198 + 0.391454i \(0.128028\pi\)
\(968\) −1.98602 + 3.43990i −0.0638332 + 0.110562i
\(969\) −1.99743 + 3.45966i −0.0641668 + 0.111140i
\(970\) 14.6571 0.470611
\(971\) 6.76148 11.7112i 0.216986 0.375831i −0.736899 0.676003i \(-0.763711\pi\)
0.953885 + 0.300172i \(0.0970440\pi\)
\(972\) 6.24289 + 10.8130i 0.200241 + 0.346827i
\(973\) −4.52227 7.83280i −0.144977 0.251108i
\(974\) −80.3736 −2.57534
\(975\) −16.4441 + 10.8460i −0.526633 + 0.347349i
\(976\) 10.6202 0.339946
\(977\) −4.83532 8.37503i −0.154696 0.267941i 0.778252 0.627952i \(-0.216106\pi\)
−0.932948 + 0.360011i \(0.882773\pi\)
\(978\) 14.8125 + 25.6560i 0.473651 + 0.820388i
\(979\) 14.0592 24.3513i 0.449334 0.778270i
\(980\) −11.0340 −0.352468
\(981\) −3.34277 + 5.78984i −0.106726 + 0.184855i
\(982\) 15.1649 26.2664i 0.483931 0.838194i
\(983\) 32.5285 1.03750 0.518750 0.854926i \(-0.326398\pi\)
0.518750 + 0.854926i \(0.326398\pi\)
\(984\) 0.112305 0.194519i 0.00358016 0.00620103i
\(985\) −2.01620 3.49216i −0.0642414 0.111269i
\(986\) −5.33415 9.23902i −0.169874 0.294230i
\(987\) −65.7977 −2.09436
\(988\) 21.1582 13.9552i 0.673131 0.443974i
\(989\) −45.8433 −1.45773
\(990\) −1.73737 3.00921i −0.0552171 0.0956388i
\(991\) −13.0365 22.5798i −0.414117 0.717271i 0.581218 0.813748i \(-0.302576\pi\)
−0.995335 + 0.0964762i \(0.969243\pi\)
\(992\) −3.96719 + 6.87138i −0.125958 + 0.218166i
\(993\) −20.4347 −0.648474
\(994\) 17.7644 30.7688i 0.563452 0.975927i
\(995\) −0.587254 + 1.01715i −0.0186172 + 0.0322460i
\(996\) −55.4862 −1.75815
\(997\) −22.6944 + 39.3079i −0.718740 + 1.24489i 0.242759 + 0.970087i \(0.421947\pi\)
−0.961499 + 0.274807i \(0.911386\pi\)
\(998\) 18.5722 + 32.1679i 0.587891 + 1.01826i
\(999\) 33.2207 + 57.5400i 1.05106 + 1.82048i
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 403.2.f.c.94.16 36
13.3 even 3 5239.2.a.p.1.3 18
13.9 even 3 inner 403.2.f.c.373.16 yes 36
13.10 even 6 5239.2.a.o.1.16 18
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
403.2.f.c.94.16 36 1.1 even 1 trivial
403.2.f.c.373.16 yes 36 13.9 even 3 inner
5239.2.a.o.1.16 18 13.10 even 6
5239.2.a.p.1.3 18 13.3 even 3