Properties

Label 418.2.n.e.49.5
Level $418$
Weight $2$
Character 418.49
Analytic conductor $3.338$
Analytic rank $0$
Dimension $72$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [418,2,Mod(49,418)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(418, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([12, 20]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("418.49");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 418 = 2 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 418.n (of order \(15\), degree \(8\), 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: \(3.33774680449\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(9\) over \(\Q(\zeta_{15})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label 49.5
Character \(\chi\) \(=\) 418.49
Dual form 418.2.n.e.273.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.978148 - 0.207912i) q^{2} +(-0.604189 + 0.269002i) q^{3} +(0.913545 + 0.406737i) q^{4} +(-1.30272 - 1.44681i) q^{5} +(0.646915 - 0.137506i) q^{6} +(-0.622011 + 0.451917i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-1.71471 + 1.90438i) q^{9} +O(q^{10})\) \(q+(-0.978148 - 0.207912i) q^{2} +(-0.604189 + 0.269002i) q^{3} +(0.913545 + 0.406737i) q^{4} +(-1.30272 - 1.44681i) q^{5} +(0.646915 - 0.137506i) q^{6} +(-0.622011 + 0.451917i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-1.71471 + 1.90438i) q^{9} +(0.973440 + 1.68605i) q^{10} +(3.22884 - 0.758017i) q^{11} -0.661367 q^{12} +(-0.255977 + 0.284291i) q^{13} +(0.702377 - 0.312719i) q^{14} +(1.17628 + 0.523715i) q^{15} +(0.669131 + 0.743145i) q^{16} +(4.99791 + 5.55074i) q^{17} +(2.07318 - 1.50625i) q^{18} +(-4.09781 + 1.48592i) q^{19} +(-0.601619 - 1.85159i) q^{20} +(0.254245 - 0.440366i) q^{21} +(-3.31588 + 0.0701391i) q^{22} +(1.89880 + 3.28881i) q^{23} +(0.646915 + 0.137506i) q^{24} +(0.126444 - 1.20303i) q^{25} +(0.309491 - 0.224858i) q^{26} +(1.13685 - 3.49886i) q^{27} +(-0.752046 + 0.159852i) q^{28} +(3.10896 + 1.38420i) q^{29} +(-1.04169 - 0.756834i) q^{30} +(2.98978 + 9.20158i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.74692 + 1.32655i) q^{33} +(-3.73463 - 6.46857i) q^{34} +(1.46414 + 0.311213i) q^{35} +(-2.34105 + 1.04230i) q^{36} +(-5.58544 + 4.05806i) q^{37} +(4.31720 - 0.601466i) q^{38} +(0.0781834 - 0.240624i) q^{39} +(0.203504 + 1.93621i) q^{40} +(8.84509 - 3.93809i) q^{41} +(-0.340247 + 0.377882i) q^{42} +(-3.27961 + 5.68045i) q^{43} +(3.25801 + 0.620804i) q^{44} +4.98906 q^{45} +(-1.17352 - 3.61173i) q^{46} +(-1.05947 + 10.0802i) q^{47} +(-0.604189 - 0.269002i) q^{48} +(-1.98045 + 6.09520i) q^{49} +(-0.373805 + 1.15045i) q^{50} +(-4.51284 - 2.00925i) q^{51} +(-0.349478 + 0.155598i) q^{52} +(0.935627 - 1.03912i) q^{53} +(-1.83946 + 3.18603i) q^{54} +(-5.30297 - 3.68405i) q^{55} +0.768848 q^{56} +(2.07614 - 2.00010i) q^{57} +(-2.75323 - 2.00034i) q^{58} +(-0.950957 - 9.04775i) q^{59} +(0.861574 + 0.956875i) q^{60} +(7.99986 - 1.70042i) q^{61} +(-1.01133 - 9.62212i) q^{62} +(0.205947 - 1.95945i) q^{63} +(0.309017 + 0.951057i) q^{64} +0.744781 q^{65} +(1.98455 - 0.934357i) q^{66} +(-0.609188 - 1.05514i) q^{67} +(2.30813 + 7.10368i) q^{68} +(-2.03193 - 1.47628i) q^{69} +(-1.36744 - 0.608825i) q^{70} +(5.17764 + 5.75035i) q^{71} +(2.50659 - 0.532793i) q^{72} +(-1.34255 - 12.7735i) q^{73} +(6.30710 - 2.80810i) q^{74} +(0.247222 + 0.760872i) q^{75} +(-4.34791 - 0.309274i) q^{76} +(-1.66581 + 1.93066i) q^{77} +(-0.126503 + 0.219110i) q^{78} +(0.587203 + 0.124814i) q^{79} +(0.203504 - 1.93621i) q^{80} +(-0.549262 - 5.22588i) q^{81} +(-9.47058 + 2.01303i) q^{82} +(-3.05405 + 9.39941i) q^{83} +(0.411377 - 0.298883i) q^{84} +(1.52003 - 14.4621i) q^{85} +(4.38898 - 4.87445i) q^{86} -2.25075 q^{87} +(-3.05774 - 1.28462i) q^{88} +(-8.89886 - 15.4133i) q^{89} +(-4.88004 - 1.03728i) q^{90} +(0.0307443 - 0.292512i) q^{91} +(0.396957 + 3.77679i) q^{92} +(-4.28164 - 4.75524i) q^{93} +(3.13210 - 9.63962i) q^{94} +(7.48813 + 3.99303i) q^{95} +(0.535057 + 0.388742i) q^{96} +(-14.6001 - 3.10335i) q^{97} +(3.20444 - 5.55025i) q^{98} +(-4.09297 + 7.44871i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q + 9 q^{2} - 2 q^{3} + 9 q^{4} + 8 q^{5} + 3 q^{6} - 20 q^{7} - 18 q^{8} + 9 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 72 q + 9 q^{2} - 2 q^{3} + 9 q^{4} + 8 q^{5} + 3 q^{6} - 20 q^{7} - 18 q^{8} + 9 q^{9} - 22 q^{10} + 10 q^{11} + 4 q^{12} + 15 q^{13} + 10 q^{14} + 9 q^{15} + 9 q^{16} + 6 q^{17} - 28 q^{18} + 7 q^{19} - 16 q^{20} + 48 q^{21} - 15 q^{22} - 20 q^{23} + 3 q^{24} + 7 q^{25} + 30 q^{26} - 56 q^{27} - 10 q^{28} + 35 q^{29} - 18 q^{30} + 52 q^{31} - 36 q^{32} - 12 q^{33} - 4 q^{34} - 9 q^{35} + 14 q^{36} - 52 q^{37} - 2 q^{38} - 42 q^{39} + 3 q^{40} + 41 q^{41} - 2 q^{42} + 14 q^{43} + 116 q^{45} - 50 q^{46} + 19 q^{47} - 2 q^{48} + 46 q^{49} - 44 q^{50} + 33 q^{51} - 15 q^{52} - 15 q^{53} - 2 q^{54} - 55 q^{55} - 33 q^{57} - 70 q^{58} - 13 q^{59} - 6 q^{60} + 8 q^{61} + 19 q^{62} + 40 q^{63} - 18 q^{64} + 120 q^{65} + 23 q^{66} + 2 q^{67} - 12 q^{68} - 194 q^{69} + q^{70} + 52 q^{71} + 9 q^{72} - 48 q^{73} + 26 q^{74} - 158 q^{75} + 20 q^{76} + 130 q^{77} + 46 q^{78} - 48 q^{79} + 3 q^{80} + 48 q^{81} - 14 q^{82} - 62 q^{83} + 44 q^{84} - 27 q^{85} - 16 q^{86} - 164 q^{87} + 10 q^{88} + 20 q^{89} + 52 q^{90} + 4 q^{91} - 15 q^{92} - 39 q^{93} - 8 q^{94} + 69 q^{95} + 4 q^{96} + 2 q^{97} - 48 q^{98} + 9 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/418\mathbb{Z}\right)^\times\).

\(n\) \(287\) \(343\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{5}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.978148 0.207912i −0.691655 0.147016i
\(3\) −0.604189 + 0.269002i −0.348829 + 0.155309i −0.573669 0.819087i \(-0.694481\pi\)
0.224841 + 0.974396i \(0.427814\pi\)
\(4\) 0.913545 + 0.406737i 0.456773 + 0.203368i
\(5\) −1.30272 1.44681i −0.582593 0.647035i 0.377733 0.925914i \(-0.376704\pi\)
−0.960326 + 0.278880i \(0.910037\pi\)
\(6\) 0.646915 0.137506i 0.264102 0.0561366i
\(7\) −0.622011 + 0.451917i −0.235098 + 0.170809i −0.699097 0.715027i \(-0.746414\pi\)
0.463999 + 0.885836i \(0.346414\pi\)
\(8\) −0.809017 0.587785i −0.286031 0.207813i
\(9\) −1.71471 + 1.90438i −0.571570 + 0.634793i
\(10\) 0.973440 + 1.68605i 0.307829 + 0.533175i
\(11\) 3.22884 0.758017i 0.973532 0.228551i
\(12\) −0.661367 −0.190920
\(13\) −0.255977 + 0.284291i −0.0709952 + 0.0788481i −0.777596 0.628764i \(-0.783561\pi\)
0.706601 + 0.707612i \(0.250228\pi\)
\(14\) 0.702377 0.312719i 0.187718 0.0835775i
\(15\) 1.17628 + 0.523715i 0.303715 + 0.135223i
\(16\) 0.669131 + 0.743145i 0.167283 + 0.185786i
\(17\) 4.99791 + 5.55074i 1.21217 + 1.34625i 0.920991 + 0.389583i \(0.127381\pi\)
0.291179 + 0.956668i \(0.405952\pi\)
\(18\) 2.07318 1.50625i 0.488654 0.355028i
\(19\) −4.09781 + 1.48592i −0.940102 + 0.340893i
\(20\) −0.601619 1.85159i −0.134526 0.414029i
\(21\) 0.254245 0.440366i 0.0554809 0.0960957i
\(22\) −3.31588 + 0.0701391i −0.706949 + 0.0149537i
\(23\) 1.89880 + 3.28881i 0.395926 + 0.685765i 0.993219 0.116259i \(-0.0370902\pi\)
−0.597292 + 0.802024i \(0.703757\pi\)
\(24\) 0.646915 + 0.137506i 0.132051 + 0.0280683i
\(25\) 0.126444 1.20303i 0.0252888 0.240606i
\(26\) 0.309491 0.224858i 0.0606961 0.0440983i
\(27\) 1.13685 3.49886i 0.218786 0.673355i
\(28\) −0.752046 + 0.159852i −0.142123 + 0.0302093i
\(29\) 3.10896 + 1.38420i 0.577319 + 0.257039i 0.674558 0.738222i \(-0.264334\pi\)
−0.0972386 + 0.995261i \(0.531001\pi\)
\(30\) −1.04169 0.756834i −0.190186 0.138178i
\(31\) 2.98978 + 9.20158i 0.536980 + 1.65265i 0.739333 + 0.673340i \(0.235141\pi\)
−0.202353 + 0.979313i \(0.564859\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) −1.74692 + 1.32655i −0.304100 + 0.230923i
\(34\) −3.73463 6.46857i −0.640483 1.10935i
\(35\) 1.46414 + 0.311213i 0.247486 + 0.0526047i
\(36\) −2.34105 + 1.04230i −0.390174 + 0.173717i
\(37\) −5.58544 + 4.05806i −0.918240 + 0.667141i −0.943085 0.332551i \(-0.892091\pi\)
0.0248451 + 0.999691i \(0.492091\pi\)
\(38\) 4.31720 0.601466i 0.700343 0.0975707i
\(39\) 0.0781834 0.240624i 0.0125194 0.0385306i
\(40\) 0.203504 + 1.93621i 0.0321769 + 0.306142i
\(41\) 8.84509 3.93809i 1.38137 0.615026i 0.424470 0.905442i \(-0.360460\pi\)
0.956901 + 0.290416i \(0.0937937\pi\)
\(42\) −0.340247 + 0.377882i −0.0525012 + 0.0583085i
\(43\) −3.27961 + 5.68045i −0.500136 + 0.866261i 0.499864 + 0.866104i \(0.333383\pi\)
−1.00000 0.000157156i \(0.999950\pi\)
\(44\) 3.25801 + 0.620804i 0.491163 + 0.0935898i
\(45\) 4.98906 0.743725
\(46\) −1.17352 3.61173i −0.173026 0.532520i
\(47\) −1.05947 + 10.0802i −0.154539 + 1.47034i 0.592503 + 0.805568i \(0.298140\pi\)
−0.747042 + 0.664776i \(0.768527\pi\)
\(48\) −0.604189 0.269002i −0.0872072 0.0388271i
\(49\) −1.98045 + 6.09520i −0.282922 + 0.870743i
\(50\) −0.373805 + 1.15045i −0.0528640 + 0.162699i
\(51\) −4.51284 2.00925i −0.631924 0.281351i
\(52\) −0.349478 + 0.155598i −0.0484639 + 0.0215775i
\(53\) 0.935627 1.03912i 0.128518 0.142734i −0.675451 0.737405i \(-0.736051\pi\)
0.803969 + 0.594671i \(0.202718\pi\)
\(54\) −1.83946 + 3.18603i −0.250319 + 0.433564i
\(55\) −5.30297 3.68405i −0.715053 0.496757i
\(56\) 0.768848 0.102742
\(57\) 2.07614 2.00010i 0.274991 0.264919i
\(58\) −2.75323 2.00034i −0.361517 0.262657i
\(59\) −0.950957 9.04775i −0.123804 1.17792i −0.863277 0.504731i \(-0.831592\pi\)
0.739473 0.673186i \(-0.235075\pi\)
\(60\) 0.861574 + 0.956875i 0.111229 + 0.123532i
\(61\) 7.99986 1.70042i 1.02428 0.217717i 0.335003 0.942217i \(-0.391263\pi\)
0.689274 + 0.724500i \(0.257929\pi\)
\(62\) −1.01133 9.62212i −0.128438 1.22201i
\(63\) 0.205947 1.95945i 0.0259468 0.246868i
\(64\) 0.309017 + 0.951057i 0.0386271 + 0.118882i
\(65\) 0.744781 0.0923788
\(66\) 1.98455 0.934357i 0.244281 0.115011i
\(67\) −0.609188 1.05514i −0.0744241 0.128906i 0.826412 0.563067i \(-0.190379\pi\)
−0.900836 + 0.434160i \(0.857045\pi\)
\(68\) 2.30813 + 7.10368i 0.279902 + 0.861448i
\(69\) −2.03193 1.47628i −0.244616 0.177724i
\(70\) −1.36744 0.608825i −0.163441 0.0727685i
\(71\) 5.17764 + 5.75035i 0.614473 + 0.682441i 0.967413 0.253205i \(-0.0814846\pi\)
−0.352940 + 0.935646i \(0.614818\pi\)
\(72\) 2.50659 0.532793i 0.295405 0.0627903i
\(73\) −1.34255 12.7735i −0.157134 1.49503i −0.734538 0.678568i \(-0.762601\pi\)
0.577404 0.816459i \(-0.304066\pi\)
\(74\) 6.30710 2.80810i 0.733185 0.326435i
\(75\) 0.247222 + 0.760872i 0.0285468 + 0.0878580i
\(76\) −4.34791 0.309274i −0.498740 0.0354762i
\(77\) −1.66581 + 1.93066i −0.189837 + 0.220020i
\(78\) −0.126503 + 0.219110i −0.0143237 + 0.0248094i
\(79\) 0.587203 + 0.124814i 0.0660655 + 0.0140427i 0.240826 0.970568i \(-0.422582\pi\)
−0.174760 + 0.984611i \(0.555915\pi\)
\(80\) 0.203504 1.93621i 0.0227525 0.216475i
\(81\) −0.549262 5.22588i −0.0610291 0.580653i
\(82\) −9.47058 + 2.01303i −1.04585 + 0.222302i
\(83\) −3.05405 + 9.39941i −0.335226 + 1.03172i 0.631385 + 0.775470i \(0.282487\pi\)
−0.966611 + 0.256250i \(0.917513\pi\)
\(84\) 0.411377 0.298883i 0.0448850 0.0326108i
\(85\) 1.52003 14.4621i 0.164870 1.56863i
\(86\) 4.38898 4.87445i 0.473276 0.525626i
\(87\) −2.25075 −0.241306
\(88\) −3.05774 1.28462i −0.325956 0.136941i
\(89\) −8.89886 15.4133i −0.943277 1.63380i −0.759164 0.650899i \(-0.774392\pi\)
−0.184113 0.982905i \(-0.558941\pi\)
\(90\) −4.88004 1.03728i −0.514401 0.109339i
\(91\) 0.0307443 0.292512i 0.00322288 0.0306636i
\(92\) 0.396957 + 3.77679i 0.0413856 + 0.393758i
\(93\) −4.28164 4.75524i −0.443985 0.493095i
\(94\) 3.13210 9.63962i 0.323052 0.994251i
\(95\) 7.48813 + 3.99303i 0.768266 + 0.409677i
\(96\) 0.535057 + 0.388742i 0.0546090 + 0.0396758i
\(97\) −14.6001 3.10335i −1.48242 0.315097i −0.605541 0.795814i \(-0.707043\pi\)
−0.876876 + 0.480717i \(0.840376\pi\)
\(98\) 3.20444 5.55025i 0.323697 0.560660i
\(99\) −4.09297 + 7.44871i −0.411359 + 0.748624i
\(100\) 0.604830 1.04760i 0.0604830 0.104760i
\(101\) −4.53999 + 5.04217i −0.451746 + 0.501714i −0.925398 0.378998i \(-0.876269\pi\)
0.473652 + 0.880712i \(0.342935\pi\)
\(102\) 3.99648 + 2.90361i 0.395710 + 0.287500i
\(103\) −14.5290 + 10.5559i −1.43158 + 1.04010i −0.441860 + 0.897084i \(0.645681\pi\)
−0.989720 + 0.143020i \(0.954319\pi\)
\(104\) 0.374192 0.0795369i 0.0366925 0.00779923i
\(105\) −0.968337 + 0.205826i −0.0945000 + 0.0200866i
\(106\) −1.13123 + 0.821884i −0.109874 + 0.0798285i
\(107\) −9.98352 7.25345i −0.965144 0.701218i −0.0108040 0.999942i \(-0.503439\pi\)
−0.954340 + 0.298724i \(0.903439\pi\)
\(108\) 2.46168 2.73397i 0.236875 0.263076i
\(109\) 5.67658 9.83212i 0.543717 0.941746i −0.454969 0.890507i \(-0.650350\pi\)
0.998686 0.0512389i \(-0.0163170\pi\)
\(110\) 4.42114 + 4.70609i 0.421539 + 0.448708i
\(111\) 2.28303 3.95433i 0.216696 0.375328i
\(112\) −0.752046 0.159852i −0.0710617 0.0151046i
\(113\) 2.38384 + 1.73196i 0.224253 + 0.162929i 0.694239 0.719745i \(-0.255741\pi\)
−0.469986 + 0.882674i \(0.655741\pi\)
\(114\) −2.44661 + 1.52474i −0.229146 + 0.142805i
\(115\) 2.28470 7.03160i 0.213050 0.655700i
\(116\) 2.27717 + 2.52906i 0.211430 + 0.234817i
\(117\) −0.102472 0.974953i −0.00947351 0.0901345i
\(118\) −0.950957 + 9.04775i −0.0875427 + 0.832913i
\(119\) −5.61723 1.19398i −0.514930 0.109452i
\(120\) −0.643801 1.11510i −0.0587707 0.101794i
\(121\) 9.85082 4.89503i 0.895529 0.445003i
\(122\) −8.17858 −0.740454
\(123\) −4.28475 + 4.75870i −0.386343 + 0.429077i
\(124\) −1.01133 + 9.62212i −0.0908197 + 0.864092i
\(125\) −9.78058 + 7.10601i −0.874802 + 0.635581i
\(126\) −0.608839 + 1.87381i −0.0542397 + 0.166933i
\(127\) 14.1149 3.00021i 1.25249 0.266225i 0.466533 0.884504i \(-0.345503\pi\)
0.785959 + 0.618279i \(0.212170\pi\)
\(128\) −0.104528 0.994522i −0.00923910 0.0879041i
\(129\) 0.453450 4.31429i 0.0399241 0.379852i
\(130\) −0.728506 0.154849i −0.0638942 0.0135811i
\(131\) 4.53434 7.85371i 0.396167 0.686182i −0.597082 0.802180i \(-0.703673\pi\)
0.993249 + 0.115998i \(0.0370068\pi\)
\(132\) −2.13545 + 0.501328i −0.185867 + 0.0436350i
\(133\) 1.87737 2.77613i 0.162789 0.240721i
\(134\) 0.376499 + 1.15874i 0.0325245 + 0.100100i
\(135\) −6.54319 + 2.91321i −0.563148 + 0.250730i
\(136\) −0.780750 7.42834i −0.0669487 0.636975i
\(137\) 10.0442 2.13495i 0.858130 0.182401i 0.242223 0.970221i \(-0.422123\pi\)
0.615906 + 0.787819i \(0.288790\pi\)
\(138\) 1.68059 + 1.86649i 0.143061 + 0.158886i
\(139\) 15.3521 + 6.83520i 1.30215 + 0.579754i 0.936392 0.350957i \(-0.114144\pi\)
0.365757 + 0.930711i \(0.380810\pi\)
\(140\) 1.21098 + 0.879829i 0.102347 + 0.0743591i
\(141\) −2.07147 6.37533i −0.174449 0.536900i
\(142\) −3.86893 6.70118i −0.324673 0.562351i
\(143\) −0.611011 + 1.11197i −0.0510953 + 0.0929872i
\(144\) −2.56259 −0.213549
\(145\) −2.04742 6.30130i −0.170029 0.523295i
\(146\) −1.34255 + 12.7735i −0.111110 + 1.05714i
\(147\) −0.443056 4.21540i −0.0365427 0.347680i
\(148\) −6.75311 + 1.43542i −0.555102 + 0.117991i
\(149\) 4.39861 + 4.88516i 0.360349 + 0.400208i 0.895872 0.444313i \(-0.146552\pi\)
−0.535523 + 0.844521i \(0.679886\pi\)
\(150\) −0.0836258 0.795646i −0.00682802 0.0649642i
\(151\) 3.50154 + 2.54402i 0.284952 + 0.207030i 0.721074 0.692858i \(-0.243649\pi\)
−0.436123 + 0.899887i \(0.643649\pi\)
\(152\) 4.18860 + 1.20650i 0.339740 + 0.0978599i
\(153\) −19.1407 −1.54743
\(154\) 2.03082 1.54213i 0.163648 0.124269i
\(155\) 9.41815 16.3127i 0.756484 1.31027i
\(156\) 0.169295 0.188021i 0.0135544 0.0150537i
\(157\) −21.2336 + 9.45381i −1.69463 + 0.754496i −0.695266 + 0.718753i \(0.744713\pi\)
−0.999361 + 0.0357439i \(0.988620\pi\)
\(158\) −0.548421 0.244173i −0.0436300 0.0194253i
\(159\) −0.285770 + 0.879510i −0.0226631 + 0.0697497i
\(160\) −0.601619 + 1.85159i −0.0475622 + 0.146381i
\(161\) −2.66734 1.18758i −0.210216 0.0935942i
\(162\) −0.549262 + 5.22588i −0.0431541 + 0.410584i
\(163\) 1.18958 + 3.66114i 0.0931749 + 0.286763i 0.986774 0.162104i \(-0.0518279\pi\)
−0.893599 + 0.448867i \(0.851828\pi\)
\(164\) 9.68216 0.756049
\(165\) 4.19502 + 0.799349i 0.326582 + 0.0622292i
\(166\) 4.94156 8.55904i 0.383540 0.664310i
\(167\) −1.26419 + 1.40403i −0.0978260 + 0.108647i −0.790070 0.613017i \(-0.789956\pi\)
0.692244 + 0.721664i \(0.256622\pi\)
\(168\) −0.464529 + 0.206822i −0.0358392 + 0.0159566i
\(169\) 1.34357 + 12.7832i 0.103352 + 0.983326i
\(170\) −4.49365 + 13.8300i −0.344647 + 1.06071i
\(171\) 4.19680 10.3517i 0.320937 0.791614i
\(172\) −5.30652 + 3.85541i −0.404619 + 0.293973i
\(173\) 4.71916 2.10111i 0.358791 0.159744i −0.219421 0.975630i \(-0.570417\pi\)
0.578213 + 0.815886i \(0.303750\pi\)
\(174\) 2.20157 + 0.467957i 0.166900 + 0.0354758i
\(175\) 0.465022 + 0.805441i 0.0351523 + 0.0608856i
\(176\) 2.72383 + 1.89228i 0.205317 + 0.142636i
\(177\) 3.00842 + 5.21074i 0.226127 + 0.391663i
\(178\) 5.49980 + 16.9266i 0.412227 + 1.26870i
\(179\) 1.92699 + 1.40004i 0.144030 + 0.104644i 0.657467 0.753483i \(-0.271628\pi\)
−0.513437 + 0.858127i \(0.671628\pi\)
\(180\) 4.55773 + 2.02923i 0.339713 + 0.151250i
\(181\) 14.7655 3.13850i 1.09751 0.233283i 0.376645 0.926358i \(-0.377078\pi\)
0.720866 + 0.693074i \(0.243744\pi\)
\(182\) −0.0908892 + 0.279728i −0.00673716 + 0.0207348i
\(183\) −4.37601 + 3.17936i −0.323484 + 0.235025i
\(184\) 0.396957 3.77679i 0.0292640 0.278429i
\(185\) 13.1475 + 2.79459i 0.966623 + 0.205462i
\(186\) 3.19940 + 5.54153i 0.234592 + 0.406324i
\(187\) 20.3450 + 14.1339i 1.48777 + 1.03358i
\(188\) −5.06785 + 8.77777i −0.369611 + 0.640185i
\(189\) 0.874063 + 2.69009i 0.0635787 + 0.195675i
\(190\) −6.49430 5.46265i −0.471146 0.396302i
\(191\) 1.42444 1.03491i 0.103069 0.0748838i −0.535057 0.844816i \(-0.679710\pi\)
0.638126 + 0.769932i \(0.279710\pi\)
\(192\) −0.442541 0.491492i −0.0319376 0.0354703i
\(193\) 3.16145 + 3.51115i 0.227566 + 0.252738i 0.846105 0.533017i \(-0.178942\pi\)
−0.618539 + 0.785754i \(0.712275\pi\)
\(194\) 13.6358 + 6.07107i 0.978996 + 0.435877i
\(195\) −0.449989 + 0.200348i −0.0322244 + 0.0143472i
\(196\) −4.28837 + 4.76272i −0.306312 + 0.340194i
\(197\) 25.0078 1.78173 0.890865 0.454269i \(-0.150100\pi\)
0.890865 + 0.454269i \(0.150100\pi\)
\(198\) 5.55221 6.43496i 0.394578 0.457313i
\(199\) 9.68257 + 16.7707i 0.686379 + 1.18884i 0.973001 + 0.230800i \(0.0741342\pi\)
−0.286622 + 0.958044i \(0.592532\pi\)
\(200\) −0.809420 + 0.898952i −0.0572346 + 0.0635655i
\(201\) 0.651900 + 0.473633i 0.0459815 + 0.0334075i
\(202\) 5.48910 3.98807i 0.386212 0.280599i
\(203\) −2.55935 + 0.544006i −0.179631 + 0.0381818i
\(204\) −3.30545 3.67108i −0.231428 0.257027i
\(205\) −17.2203 7.66698i −1.20272 0.535485i
\(206\) 16.4062 7.30449i 1.14307 0.508928i
\(207\) −9.51903 2.02333i −0.661618 0.140631i
\(208\) −0.382551 −0.0265252
\(209\) −12.1048 + 7.90401i −0.837308 + 0.546732i
\(210\) 0.989970 0.0683144
\(211\) −19.3632 4.11577i −1.33302 0.283341i −0.514334 0.857590i \(-0.671961\pi\)
−0.818681 + 0.574249i \(0.805294\pi\)
\(212\) 1.27739 0.568729i 0.0877312 0.0390605i
\(213\) −4.67513 2.08150i −0.320335 0.142622i
\(214\) 8.25728 + 9.17064i 0.564456 + 0.626892i
\(215\) 12.4910 2.65504i 0.851877 0.181072i
\(216\) −2.97631 + 2.16241i −0.202512 + 0.147134i
\(217\) −6.01803 4.37235i −0.408530 0.296815i
\(218\) −7.59674 + 8.43704i −0.514516 + 0.571428i
\(219\) 4.24726 + 7.35647i 0.287003 + 0.497104i
\(220\) −3.34607 5.52246i −0.225592 0.372324i
\(221\) −2.85737 −0.192208
\(222\) −3.05529 + 3.39325i −0.205058 + 0.227740i
\(223\) −19.7099 + 8.77541i −1.31987 + 0.587645i −0.941189 0.337882i \(-0.890290\pi\)
−0.378683 + 0.925526i \(0.623623\pi\)
\(224\) 0.702377 + 0.312719i 0.0469296 + 0.0208944i
\(225\) 2.07421 + 2.30365i 0.138281 + 0.153577i
\(226\) −1.97165 2.18974i −0.131152 0.145660i
\(227\) −10.1469 + 7.37212i −0.673470 + 0.489305i −0.871185 0.490955i \(-0.836648\pi\)
0.197715 + 0.980260i \(0.436648\pi\)
\(228\) 2.71016 0.982738i 0.179484 0.0650834i
\(229\) −4.28291 13.1814i −0.283023 0.871054i −0.986984 0.160816i \(-0.948587\pi\)
0.703962 0.710238i \(-0.251413\pi\)
\(230\) −3.69673 + 6.40292i −0.243755 + 0.422196i
\(231\) 0.487113 1.61459i 0.0320497 0.106232i
\(232\) −1.70159 2.94724i −0.111715 0.193496i
\(233\) 20.1385 + 4.28058i 1.31932 + 0.280430i 0.813175 0.582019i \(-0.197737\pi\)
0.506144 + 0.862449i \(0.331070\pi\)
\(234\) −0.102472 + 0.974953i −0.00669879 + 0.0637347i
\(235\) 15.9643 11.5988i 1.04140 0.756620i
\(236\) 2.81131 8.65232i 0.183001 0.563218i
\(237\) −0.388357 + 0.0825478i −0.0252265 + 0.00536205i
\(238\) 5.24624 + 2.33577i 0.340063 + 0.151406i
\(239\) −16.0975 11.6955i −1.04126 0.756522i −0.0707314 0.997495i \(-0.522533\pi\)
−0.970532 + 0.240973i \(0.922533\pi\)
\(240\) 0.397891 + 1.22458i 0.0256838 + 0.0790465i
\(241\) −4.14738 7.18347i −0.267156 0.462728i 0.700970 0.713191i \(-0.252751\pi\)
−0.968126 + 0.250463i \(0.919417\pi\)
\(242\) −10.6533 + 2.73996i −0.684819 + 0.176132i
\(243\) 7.25601 + 12.5678i 0.465473 + 0.806223i
\(244\) 7.99986 + 1.70042i 0.512139 + 0.108858i
\(245\) 11.3986 5.07498i 0.728229 0.324228i
\(246\) 5.18051 3.76386i 0.330297 0.239975i
\(247\) 0.626511 1.54533i 0.0398639 0.0983271i
\(248\) 2.98978 9.20158i 0.189851 0.584301i
\(249\) −0.683237 6.50057i −0.0432984 0.411957i
\(250\) 11.0443 4.91723i 0.698501 0.310993i
\(251\) −9.65135 + 10.7189i −0.609188 + 0.676571i −0.966279 0.257498i \(-0.917102\pi\)
0.357091 + 0.934070i \(0.383769\pi\)
\(252\) 0.985122 1.70628i 0.0620569 0.107486i
\(253\) 8.62389 + 9.17973i 0.542179 + 0.577125i
\(254\) −14.4302 −0.905431
\(255\) 2.97195 + 9.14672i 0.186111 + 0.572790i
\(256\) −0.104528 + 0.994522i −0.00653303 + 0.0621576i
\(257\) −9.79911 4.36285i −0.611252 0.272147i 0.0776738 0.996979i \(-0.475251\pi\)
−0.688926 + 0.724832i \(0.741917\pi\)
\(258\) −1.34053 + 4.12573i −0.0834579 + 0.256857i
\(259\) 1.64030 5.04831i 0.101923 0.313687i
\(260\) 0.680392 + 0.302930i 0.0421961 + 0.0187869i
\(261\) −7.96700 + 3.54714i −0.493145 + 0.219562i
\(262\) −6.06813 + 6.73934i −0.374890 + 0.416358i
\(263\) −3.32995 + 5.76764i −0.205334 + 0.355648i −0.950239 0.311522i \(-0.899161\pi\)
0.744905 + 0.667170i \(0.232495\pi\)
\(264\) 2.19302 0.0463877i 0.134971 0.00285497i
\(265\) −2.72227 −0.167228
\(266\) −2.41353 + 2.32514i −0.147983 + 0.142563i
\(267\) 9.52280 + 6.91872i 0.582786 + 0.423419i
\(268\) −0.127355 1.21170i −0.00777944 0.0740164i
\(269\) −3.66159 4.06661i −0.223251 0.247946i 0.621105 0.783727i \(-0.286684\pi\)
−0.844357 + 0.535781i \(0.820017\pi\)
\(270\) 7.00589 1.48915i 0.426365 0.0906267i
\(271\) 1.17604 + 11.1893i 0.0714394 + 0.679700i 0.970372 + 0.241614i \(0.0776768\pi\)
−0.898933 + 0.438086i \(0.855656\pi\)
\(272\) −0.780750 + 7.42834i −0.0473399 + 0.450409i
\(273\) 0.0601111 + 0.185003i 0.00363809 + 0.0111969i
\(274\) −10.2685 −0.620345
\(275\) −0.503653 3.98025i −0.0303714 0.240018i
\(276\) −1.25580 2.17511i −0.0755904 0.130926i
\(277\) −3.07375 9.46004i −0.184684 0.568399i 0.815259 0.579097i \(-0.196595\pi\)
−0.999943 + 0.0106981i \(0.996595\pi\)
\(278\) −13.5955 9.87771i −0.815404 0.592426i
\(279\) −22.6499 10.0844i −1.35601 0.603736i
\(280\) −1.00159 1.11238i −0.0598565 0.0664774i
\(281\) 0.612065 0.130098i 0.0365127 0.00776102i −0.189619 0.981858i \(-0.560725\pi\)
0.226132 + 0.974097i \(0.427392\pi\)
\(282\) 0.700698 + 6.66670i 0.0417260 + 0.396996i
\(283\) 19.0002 8.45942i 1.12944 0.502860i 0.245006 0.969521i \(-0.421210\pi\)
0.884436 + 0.466661i \(0.154543\pi\)
\(284\) 2.39113 + 7.35914i 0.141888 + 0.436685i
\(285\) −5.59838 0.398222i −0.331620 0.0235887i
\(286\) 0.828849 0.960630i 0.0490109 0.0568032i
\(287\) −3.72205 + 6.44678i −0.219706 + 0.380541i
\(288\) 2.50659 + 0.532793i 0.147703 + 0.0313951i
\(289\) −4.05464 + 38.5773i −0.238508 + 2.26925i
\(290\) 0.692562 + 6.58929i 0.0406686 + 0.386936i
\(291\) 9.65603 2.05245i 0.566047 0.120317i
\(292\) 3.96898 12.2152i 0.232267 0.714843i
\(293\) 3.40647 2.47494i 0.199008 0.144588i −0.483818 0.875168i \(-0.660751\pi\)
0.682826 + 0.730581i \(0.260751\pi\)
\(294\) −0.443056 + 4.21540i −0.0258396 + 0.245847i
\(295\) −11.8516 + 13.1625i −0.690026 + 0.766351i
\(296\) 6.90398 0.401286
\(297\) 1.01851 12.1590i 0.0590997 0.705537i
\(298\) −3.28681 5.69293i −0.190400 0.329782i
\(299\) −1.42103 0.302049i −0.0821802 0.0174679i
\(300\) −0.0836258 + 0.795646i −0.00482814 + 0.0459366i
\(301\) −0.527142 5.01542i −0.0303839 0.289084i
\(302\) −2.89610 3.21644i −0.166652 0.185085i
\(303\) 1.38666 4.26769i 0.0796613 0.245172i
\(304\) −3.84622 2.05099i −0.220596 0.117632i
\(305\) −12.8817 9.35914i −0.737607 0.535903i
\(306\) 18.7224 + 3.97957i 1.07029 + 0.227497i
\(307\) 7.11058 12.3159i 0.405822 0.702905i −0.588594 0.808429i \(-0.700318\pi\)
0.994417 + 0.105523i \(0.0336518\pi\)
\(308\) −2.30707 + 1.08620i −0.131457 + 0.0618921i
\(309\) 5.93867 10.2861i 0.337839 0.585155i
\(310\) −12.6039 + 13.9981i −0.715856 + 0.795038i
\(311\) 18.0115 + 13.0861i 1.02134 + 0.742044i 0.966556 0.256454i \(-0.0825543\pi\)
0.0547799 + 0.998498i \(0.482554\pi\)
\(312\) −0.204687 + 0.148714i −0.0115881 + 0.00841926i
\(313\) −2.98635 + 0.634768i −0.168798 + 0.0358792i −0.291535 0.956560i \(-0.594166\pi\)
0.122737 + 0.992439i \(0.460833\pi\)
\(314\) 22.7352 4.83251i 1.28302 0.272714i
\(315\) −3.10325 + 2.25464i −0.174848 + 0.127035i
\(316\) 0.485670 + 0.352860i 0.0273211 + 0.0198499i
\(317\) 16.3247 18.1304i 0.916888 1.01831i −0.0828760 0.996560i \(-0.526411\pi\)
0.999764 0.0217469i \(-0.00692279\pi\)
\(318\) 0.462386 0.800876i 0.0259293 0.0449109i
\(319\) 11.0876 + 2.11271i 0.620785 + 0.118289i
\(320\) 0.973440 1.68605i 0.0544169 0.0942529i
\(321\) 7.98313 + 1.69687i 0.445575 + 0.0947098i
\(322\) 2.36214 + 1.71620i 0.131637 + 0.0956400i
\(323\) −28.7284 15.3194i −1.59849 0.852393i
\(324\) 1.62378 4.99748i 0.0902101 0.277638i
\(325\) 0.309645 + 0.343895i 0.0171760 + 0.0190759i
\(326\) −0.402388 3.82847i −0.0222862 0.212039i
\(327\) −0.784863 + 7.46747i −0.0434030 + 0.412952i
\(328\) −9.47058 2.01303i −0.522925 0.111151i
\(329\) −3.89640 6.74877i −0.214816 0.372072i
\(330\) −3.93715 1.65407i −0.216733 0.0910538i
\(331\) 0.278238 0.0152934 0.00764668 0.999971i \(-0.497566\pi\)
0.00764668 + 0.999971i \(0.497566\pi\)
\(332\) −6.61310 + 7.34460i −0.362941 + 0.403087i
\(333\) 1.84933 17.5952i 0.101343 0.964210i
\(334\) 1.52848 1.11050i 0.0836346 0.0607641i
\(335\) −0.732998 + 2.25593i −0.0400479 + 0.123255i
\(336\) 0.497379 0.105721i 0.0271342 0.00576756i
\(337\) 1.56399 + 14.8803i 0.0851958 + 0.810584i 0.950790 + 0.309837i \(0.100275\pi\)
−0.865594 + 0.500747i \(0.833059\pi\)
\(338\) 1.34357 12.7832i 0.0730807 0.695317i
\(339\) −1.90619 0.405174i −0.103530 0.0220060i
\(340\) 7.27087 12.5935i 0.394318 0.682979i
\(341\) 16.6285 + 27.4441i 0.900482 + 1.48618i
\(342\) −6.25733 + 9.25293i −0.338358 + 0.500341i
\(343\) −3.18577 9.80480i −0.172016 0.529410i
\(344\) 5.99215 2.66788i 0.323075 0.143842i
\(345\) 0.511122 + 4.86300i 0.0275179 + 0.261815i
\(346\) −5.05288 + 1.07402i −0.271645 + 0.0577399i
\(347\) −3.35209 3.72287i −0.179950 0.199854i 0.646421 0.762981i \(-0.276265\pi\)
−0.826371 + 0.563127i \(0.809598\pi\)
\(348\) −2.05616 0.915463i −0.110222 0.0490740i
\(349\) −13.2678 9.63961i −0.710208 0.515997i 0.173032 0.984916i \(-0.444643\pi\)
−0.883241 + 0.468919i \(0.844643\pi\)
\(350\) −0.287399 0.884524i −0.0153621 0.0472798i
\(351\) 0.703687 + 1.21882i 0.0375600 + 0.0650559i
\(352\) −2.27088 2.41725i −0.121038 0.128840i
\(353\) 12.1725 0.647878 0.323939 0.946078i \(-0.394993\pi\)
0.323939 + 0.946078i \(0.394993\pi\)
\(354\) −1.85931 5.72236i −0.0988211 0.304140i
\(355\) 1.57469 14.9822i 0.0835758 0.795171i
\(356\) −1.86037 17.7002i −0.0985993 0.938110i
\(357\) 3.71505 0.789658i 0.196621 0.0417931i
\(358\) −1.59380 1.77009i −0.0842347 0.0935521i
\(359\) −0.189969 1.80744i −0.0100262 0.0953929i 0.988364 0.152105i \(-0.0486051\pi\)
−0.998391 + 0.0567117i \(0.981938\pi\)
\(360\) −4.03624 2.93250i −0.212728 0.154556i
\(361\) 14.5841 12.1780i 0.767584 0.640949i
\(362\) −15.0954 −0.793395
\(363\) −4.63498 + 5.60742i −0.243273 + 0.294313i
\(364\) 0.147062 0.254719i 0.00770813 0.0133509i
\(365\) −16.7319 + 18.5827i −0.875789 + 0.972662i
\(366\) 4.94141 2.20006i 0.258292 0.114999i
\(367\) −12.1231 5.39754i −0.632819 0.281749i 0.0651519 0.997875i \(-0.479247\pi\)
−0.697971 + 0.716126i \(0.745913\pi\)
\(368\) −1.17352 + 3.61173i −0.0611740 + 0.188274i
\(369\) −7.66715 + 23.5971i −0.399136 + 1.22841i
\(370\) −12.2792 5.46704i −0.638363 0.284218i
\(371\) −0.112374 + 1.06917i −0.00583418 + 0.0555085i
\(372\) −1.97734 6.08562i −0.102520 0.315525i
\(373\) 10.5103 0.544202 0.272101 0.962269i \(-0.412282\pi\)
0.272101 + 0.962269i \(0.412282\pi\)
\(374\) −16.9618 18.0551i −0.877074 0.933604i
\(375\) 3.99779 6.92437i 0.206445 0.357573i
\(376\) 6.78211 7.53229i 0.349760 0.388448i
\(377\) −1.18934 + 0.529527i −0.0612539 + 0.0272720i
\(378\) −0.295661 2.81303i −0.0152072 0.144687i
\(379\) 7.64301 23.5228i 0.392595 1.20828i −0.538224 0.842802i \(-0.680904\pi\)
0.930819 0.365481i \(-0.119096\pi\)
\(380\) 5.21664 + 6.69352i 0.267608 + 0.343370i
\(381\) −7.72098 + 5.60962i −0.395558 + 0.287390i
\(382\) −1.60848 + 0.716142i −0.0822970 + 0.0366410i
\(383\) −0.855604 0.181864i −0.0437193 0.00929283i 0.186000 0.982550i \(-0.440448\pi\)
−0.229719 + 0.973257i \(0.573781\pi\)
\(384\) 0.330684 + 0.572761i 0.0168751 + 0.0292286i
\(385\) 4.96339 0.104988i 0.252958 0.00535069i
\(386\) −2.36236 4.09172i −0.120241 0.208263i
\(387\) −5.19415 15.9860i −0.264034 0.812612i
\(388\) −12.0756 8.77345i −0.613047 0.445404i
\(389\) 10.8325 + 4.82293i 0.549228 + 0.244532i 0.662539 0.749028i \(-0.269479\pi\)
−0.113311 + 0.993560i \(0.536146\pi\)
\(390\) 0.481810 0.102412i 0.0243974 0.00518583i
\(391\) −8.76533 + 26.9769i −0.443282 + 1.36428i
\(392\) 5.18489 3.76704i 0.261876 0.190264i
\(393\) −0.626933 + 5.96487i −0.0316246 + 0.300888i
\(394\) −24.4613 5.19941i −1.23234 0.261942i
\(395\) −0.584377 1.01217i −0.0294032 0.0509278i
\(396\) −6.76878 + 5.13998i −0.340144 + 0.258293i
\(397\) 5.25841 9.10784i 0.263912 0.457109i −0.703366 0.710828i \(-0.748320\pi\)
0.967278 + 0.253719i \(0.0816538\pi\)
\(398\) −5.98416 18.4173i −0.299959 0.923178i
\(399\) −0.387501 + 2.18232i −0.0193993 + 0.109253i
\(400\) 0.978635 0.711020i 0.0489317 0.0355510i
\(401\) −17.9232 19.9058i −0.895043 0.994046i 0.104957 0.994477i \(-0.466530\pi\)
−1.00000 0.000430820i \(0.999863\pi\)
\(402\) −0.539181 0.598821i −0.0268919 0.0298665i
\(403\) −3.38124 1.50543i −0.168432 0.0749906i
\(404\) −6.19832 + 2.75967i −0.308378 + 0.137299i
\(405\) −6.84534 + 7.60252i −0.340148 + 0.377772i
\(406\) 2.61653 0.129856
\(407\) −14.9584 + 17.3367i −0.741461 + 0.859347i
\(408\) 2.46996 + 4.27810i 0.122281 + 0.211797i
\(409\) −16.9356 + 18.8088i −0.837410 + 0.930038i −0.998379 0.0569218i \(-0.981871\pi\)
0.160969 + 0.986959i \(0.448538\pi\)
\(410\) 15.2500 + 11.0797i 0.753142 + 0.547190i
\(411\) −5.49426 + 3.99181i −0.271012 + 0.196902i
\(412\) −17.5663 + 3.73384i −0.865431 + 0.183953i
\(413\) 4.68034 + 5.19805i 0.230305 + 0.255779i
\(414\) 8.89034 + 3.95823i 0.436936 + 0.194537i
\(415\) 17.5778 7.82613i 0.862859 0.384169i
\(416\) 0.374192 + 0.0795369i 0.0183463 + 0.00389962i
\(417\) −11.1143 −0.544267
\(418\) 13.4836 5.21455i 0.659506 0.255052i
\(419\) −15.4290 −0.753756 −0.376878 0.926263i \(-0.623002\pi\)
−0.376878 + 0.926263i \(0.623002\pi\)
\(420\) −0.968337 0.205826i −0.0472500 0.0100433i
\(421\) 29.5223 13.1442i 1.43883 0.640607i 0.468734 0.883339i \(-0.344710\pi\)
0.970093 + 0.242732i \(0.0780437\pi\)
\(422\) 18.0843 + 8.05166i 0.880331 + 0.391949i
\(423\) −17.3798 19.3022i −0.845034 0.938505i
\(424\) −1.36772 + 0.290717i −0.0664222 + 0.0141185i
\(425\) 7.30967 5.31079i 0.354571 0.257611i
\(426\) 4.14020 + 3.00803i 0.200593 + 0.145740i
\(427\) −4.20755 + 4.67296i −0.203618 + 0.226140i
\(428\) −6.17016 10.6870i −0.298246 0.516577i
\(429\) 0.0700448 0.836200i 0.00338179 0.0403721i
\(430\) −12.7700 −0.615825
\(431\) 22.0954 24.5395i 1.06430 1.18202i 0.0816293 0.996663i \(-0.473988\pi\)
0.982670 0.185362i \(-0.0593457\pi\)
\(432\) 3.36086 1.49635i 0.161699 0.0719932i
\(433\) −0.501354 0.223217i −0.0240935 0.0107271i 0.394655 0.918830i \(-0.370864\pi\)
−0.418748 + 0.908102i \(0.637531\pi\)
\(434\) 4.97746 + 5.52802i 0.238926 + 0.265354i
\(435\) 2.93209 + 3.25642i 0.140583 + 0.156133i
\(436\) 9.18489 6.67322i 0.439877 0.319589i
\(437\) −12.6678 10.6555i −0.605984 0.509720i
\(438\) −2.62495 8.07876i −0.125425 0.386018i
\(439\) −11.1388 + 19.2929i −0.531625 + 0.920802i 0.467693 + 0.883891i \(0.345085\pi\)
−0.999319 + 0.0369113i \(0.988248\pi\)
\(440\) 2.12477 + 6.09747i 0.101294 + 0.290685i
\(441\) −8.21167 14.2230i −0.391032 0.677287i
\(442\) 2.79493 + 0.594081i 0.132941 + 0.0282576i
\(443\) 0.975209 9.27849i 0.0463336 0.440834i −0.946622 0.322346i \(-0.895529\pi\)
0.992955 0.118488i \(-0.0378048\pi\)
\(444\) 3.69402 2.68387i 0.175311 0.127371i
\(445\) −10.7074 + 32.9541i −0.507582 + 1.56218i
\(446\) 21.1037 4.48573i 0.999289 0.212405i
\(447\) −3.97171 1.76832i −0.187856 0.0836387i
\(448\) −0.622011 0.451917i −0.0293872 0.0213511i
\(449\) 0.159611 + 0.491231i 0.00753249 + 0.0231826i 0.954752 0.297403i \(-0.0961204\pi\)
−0.947220 + 0.320585i \(0.896120\pi\)
\(450\) −1.54993 2.68456i −0.0730645 0.126551i
\(451\) 25.5742 19.4202i 1.20424 0.914461i
\(452\) 1.47329 + 2.55182i 0.0692980 + 0.120028i
\(453\) −2.79994 0.595146i −0.131553 0.0279624i
\(454\) 11.4579 5.10137i 0.537744 0.239419i
\(455\) −0.463262 + 0.336580i −0.0217181 + 0.0157791i
\(456\) −2.85526 + 0.397790i −0.133710 + 0.0186282i
\(457\) −1.31877 + 4.05874i −0.0616893 + 0.189860i −0.977152 0.212544i \(-0.931825\pi\)
0.915462 + 0.402404i \(0.131825\pi\)
\(458\) 1.44874 + 13.7839i 0.0676953 + 0.644078i
\(459\) 25.1031 11.1766i 1.17171 0.521680i
\(460\) 4.94719 5.49441i 0.230664 0.256178i
\(461\) 8.01902 13.8893i 0.373483 0.646891i −0.616616 0.787264i \(-0.711497\pi\)
0.990099 + 0.140373i \(0.0448301\pi\)
\(462\) −0.812161 + 1.47803i −0.0377851 + 0.0687644i
\(463\) −3.82341 −0.177689 −0.0888445 0.996046i \(-0.528317\pi\)
−0.0888445 + 0.996046i \(0.528317\pi\)
\(464\) 1.05164 + 3.23662i 0.0488212 + 0.150256i
\(465\) −1.30218 + 12.3895i −0.0603874 + 0.574547i
\(466\) −18.8085 8.37408i −0.871286 0.387922i
\(467\) 8.03956 24.7432i 0.372027 1.14498i −0.573436 0.819250i \(-0.694390\pi\)
0.945463 0.325730i \(-0.105610\pi\)
\(468\) 0.302937 0.932343i 0.0140033 0.0430976i
\(469\) 0.855759 + 0.381008i 0.0395153 + 0.0175933i
\(470\) −18.0270 + 8.02613i −0.831523 + 0.370218i
\(471\) 10.2860 11.4238i 0.473955 0.526380i
\(472\) −4.54879 + 7.87874i −0.209375 + 0.362649i
\(473\) −6.28346 + 20.8273i −0.288914 + 0.957639i
\(474\) 0.397033 0.0182363
\(475\) 1.26947 + 5.11768i 0.0582471 + 0.234815i
\(476\) −4.64596 3.37549i −0.212947 0.154715i
\(477\) 0.374547 + 3.56358i 0.0171493 + 0.163165i
\(478\) 13.3141 + 14.7868i 0.608974 + 0.676334i
\(479\) −25.6942 + 5.46148i −1.17400 + 0.249541i −0.753312 0.657664i \(-0.771545\pi\)
−0.420688 + 0.907205i \(0.638211\pi\)
\(480\) −0.134591 1.28055i −0.00614321 0.0584488i
\(481\) 0.276073 2.62666i 0.0125878 0.119765i
\(482\) 2.56322 + 7.88879i 0.116752 + 0.359324i
\(483\) 1.93104 0.0878654
\(484\) 10.9902 0.465146i 0.499553 0.0211430i
\(485\) 14.5298 + 25.1664i 0.659766 + 1.14275i
\(486\) −4.48446 13.8017i −0.203419 0.626060i
\(487\) −2.43876 1.77186i −0.110511 0.0802907i 0.531157 0.847273i \(-0.321757\pi\)
−0.641668 + 0.766982i \(0.721757\pi\)
\(488\) −7.47151 3.32653i −0.338219 0.150585i
\(489\) −1.70359 1.89202i −0.0770388 0.0855603i
\(490\) −12.2046 + 2.59418i −0.551350 + 0.117193i
\(491\) −3.71223 35.3195i −0.167531 1.59395i −0.678665 0.734448i \(-0.737441\pi\)
0.511134 0.859501i \(-0.329226\pi\)
\(492\) −5.84985 + 2.60452i −0.263732 + 0.117421i
\(493\) 7.85497 + 24.1751i 0.353770 + 1.08879i
\(494\) −0.934112 + 1.38130i −0.0420277 + 0.0621478i
\(495\) 16.1089 3.78179i 0.724040 0.169979i
\(496\) −4.83756 + 8.37890i −0.217213 + 0.376224i
\(497\) −5.81923 1.23692i −0.261028 0.0554833i
\(498\) −0.683237 + 6.50057i −0.0306166 + 0.291297i
\(499\) 0.498933 + 4.74703i 0.0223353 + 0.212506i 0.999997 + 0.00232290i \(0.000739404\pi\)
−0.977662 + 0.210183i \(0.932594\pi\)
\(500\) −11.8253 + 2.51354i −0.528842 + 0.112409i
\(501\) 0.386124 1.18837i 0.0172507 0.0530923i
\(502\) 11.6690 8.47804i 0.520814 0.378394i
\(503\) 0.562773 5.35442i 0.0250928 0.238742i −0.974786 0.223144i \(-0.928368\pi\)
0.999878 0.0155982i \(-0.00496526\pi\)
\(504\) −1.31835 + 1.46418i −0.0587240 + 0.0652196i
\(505\) 13.2094 0.587810
\(506\) −6.52686 10.7721i −0.290154 0.478880i
\(507\) −4.25049 7.36207i −0.188771 0.326961i
\(508\) 14.1149 + 3.00021i 0.626246 + 0.133113i
\(509\) 0.575430 5.47485i 0.0255055 0.242668i −0.974340 0.225082i \(-0.927735\pi\)
0.999845 0.0175866i \(-0.00559828\pi\)
\(510\) −1.00530 9.56474i −0.0445152 0.423534i
\(511\) 6.60765 + 7.33854i 0.292305 + 0.324638i
\(512\) 0.309017 0.951057i 0.0136568 0.0420312i
\(513\) 0.540435 + 16.0269i 0.0238608 + 0.707606i
\(514\) 8.67789 + 6.30486i 0.382765 + 0.278095i
\(515\) 34.1995 + 7.26934i 1.50701 + 0.320325i
\(516\) 2.16903 3.75687i 0.0954861 0.165387i
\(517\) 4.22009 + 33.3504i 0.185599 + 1.46675i
\(518\) −2.65405 + 4.59696i −0.116612 + 0.201979i
\(519\) −2.28606 + 2.53893i −0.100347 + 0.111447i
\(520\) −0.602541 0.437772i −0.0264232 0.0191976i
\(521\) 17.3963 12.6391i 0.762145 0.553731i −0.137422 0.990513i \(-0.543882\pi\)
0.899568 + 0.436782i \(0.143882\pi\)
\(522\) 8.53039 1.81319i 0.373365 0.0793612i
\(523\) 13.3950 2.84719i 0.585721 0.124499i 0.0944862 0.995526i \(-0.469879\pi\)
0.491234 + 0.871027i \(0.336546\pi\)
\(524\) 7.33672 5.33044i 0.320506 0.232861i
\(525\) −0.497626 0.361547i −0.0217182 0.0157792i
\(526\) 4.45634 4.94927i 0.194306 0.215798i
\(527\) −36.1330 + 62.5841i −1.57398 + 2.72621i
\(528\) −2.15474 0.410580i −0.0937729 0.0178682i
\(529\) 4.28914 7.42901i 0.186484 0.323000i
\(530\) 2.66278 + 0.565992i 0.115664 + 0.0245851i
\(531\) 18.8610 + 13.7033i 0.818496 + 0.594672i
\(532\) 2.84422 1.77253i 0.123312 0.0768487i
\(533\) −1.14457 + 3.52264i −0.0495770 + 0.152582i
\(534\) −7.87622 8.74743i −0.340837 0.378538i
\(535\) 2.51131 + 23.8935i 0.108573 + 1.03301i
\(536\) −0.127355 + 1.21170i −0.00550089 + 0.0523375i
\(537\) −1.54088 0.327524i −0.0664939 0.0141337i
\(538\) 2.73608 + 4.73904i 0.117961 + 0.204314i
\(539\) −1.77429 + 21.1816i −0.0764242 + 0.912358i
\(540\) −7.16241 −0.308221
\(541\) 7.68500 8.53506i 0.330404 0.366951i −0.554938 0.831892i \(-0.687258\pi\)
0.885342 + 0.464941i \(0.153925\pi\)
\(542\) 1.17604 11.1893i 0.0505153 0.480621i
\(543\) −8.07689 + 5.86820i −0.346612 + 0.251829i
\(544\) 2.30813 7.10368i 0.0989601 0.304568i
\(545\) −21.6202 + 4.59552i −0.926108 + 0.196850i
\(546\) −0.0203333 0.193458i −0.000870183 0.00827924i
\(547\) −2.59898 + 24.7276i −0.111124 + 1.05728i 0.786825 + 0.617177i \(0.211724\pi\)
−0.897949 + 0.440100i \(0.854943\pi\)
\(548\) 10.0442 + 2.13495i 0.429065 + 0.0912005i
\(549\) −10.4792 + 18.1505i −0.447241 + 0.774644i
\(550\) −0.334893 + 3.99798i −0.0142799 + 0.170475i
\(551\) −14.7967 1.05252i −0.630362 0.0448387i
\(552\) 0.776128 + 2.38868i 0.0330342 + 0.101669i
\(553\) −0.421652 + 0.187732i −0.0179305 + 0.00798316i
\(554\) 1.03973 + 9.89238i 0.0441739 + 0.420287i
\(555\) −8.69532 + 1.84825i −0.369096 + 0.0784537i
\(556\) 11.2447 + 12.4885i 0.476882 + 0.529631i
\(557\) 16.6489 + 7.41256i 0.705436 + 0.314080i 0.727915 0.685667i \(-0.240489\pi\)
−0.0224797 + 0.999747i \(0.507156\pi\)
\(558\) 20.0583 + 14.5732i 0.849135 + 0.616932i
\(559\) −0.775398 2.38643i −0.0327958 0.100935i
\(560\) 0.748427 + 1.29631i 0.0316268 + 0.0547792i
\(561\) −16.0943 3.06672i −0.679501 0.129477i
\(562\) −0.625739 −0.0263952
\(563\) 8.11479 + 24.9748i 0.341998 + 1.05256i 0.963172 + 0.268888i \(0.0866560\pi\)
−0.621174 + 0.783673i \(0.713344\pi\)
\(564\) 0.700698 6.66670i 0.0295047 0.280719i
\(565\) −0.599644 5.70523i −0.0252272 0.240021i
\(566\) −20.3438 + 4.32420i −0.855113 + 0.181760i
\(567\) 2.70331 + 3.00233i 0.113528 + 0.126086i
\(568\) −0.808827 7.69547i −0.0339376 0.322895i
\(569\) 5.64026 + 4.09789i 0.236452 + 0.171792i 0.699701 0.714436i \(-0.253316\pi\)
−0.463249 + 0.886228i \(0.653316\pi\)
\(570\) 5.39325 + 1.55349i 0.225898 + 0.0650685i
\(571\) 13.7941 0.577264 0.288632 0.957440i \(-0.406800\pi\)
0.288632 + 0.957440i \(0.406800\pi\)
\(572\) −1.01046 + 0.767310i −0.0422496 + 0.0320829i
\(573\) −0.582235 + 1.00846i −0.0243232 + 0.0421290i
\(574\) 4.98108 5.53205i 0.207906 0.230903i
\(575\) 4.19664 1.86846i 0.175012 0.0779203i
\(576\) −2.34105 1.04230i −0.0975436 0.0434292i
\(577\) 6.80872 20.9551i 0.283451 0.872371i −0.703408 0.710786i \(-0.748339\pi\)
0.986859 0.161585i \(-0.0516607\pi\)
\(578\) 11.9867 36.8913i 0.498581 1.53447i
\(579\) −2.85462 1.27096i −0.118634 0.0528192i
\(580\) 0.692562 6.58929i 0.0287571 0.273605i
\(581\) −2.34810 7.22672i −0.0974157 0.299815i
\(582\) −9.87175 −0.409197
\(583\) 2.23332 4.06437i 0.0924947 0.168329i
\(584\) −6.42194 + 11.1231i −0.265742 + 0.460278i
\(585\) −1.27708 + 1.41835i −0.0528009 + 0.0586414i
\(586\) −3.84660 + 1.71262i −0.158902 + 0.0707475i
\(587\) −2.19829 20.9154i −0.0907333 0.863270i −0.941338 0.337465i \(-0.890431\pi\)
0.850605 0.525805i \(-0.176236\pi\)
\(588\) 1.30980 4.03117i 0.0540154 0.166242i
\(589\) −25.9243 33.2638i −1.06819 1.37061i
\(590\) 14.3292 10.4108i 0.589925 0.428606i
\(591\) −15.1094 + 6.72714i −0.621518 + 0.276718i
\(592\) −6.75311 1.43542i −0.277551 0.0589953i
\(593\) −2.28129 3.95131i −0.0936814 0.162261i 0.815376 0.578932i \(-0.196530\pi\)
−0.909058 + 0.416671i \(0.863197\pi\)
\(594\) −3.52425 + 11.6815i −0.144602 + 0.479299i
\(595\) 5.59019 + 9.68250i 0.229176 + 0.396944i
\(596\) 2.03136 + 6.25189i 0.0832078 + 0.256087i
\(597\) −10.3615 7.52804i −0.424066 0.308102i
\(598\) 1.32718 + 0.590897i 0.0542722 + 0.0241636i
\(599\) 26.6698 5.66883i 1.08970 0.231622i 0.372178 0.928161i \(-0.378611\pi\)
0.717519 + 0.696539i \(0.245278\pi\)
\(600\) 0.247222 0.760872i 0.0100928 0.0310625i
\(601\) 6.22058 4.51952i 0.253743 0.184355i −0.453641 0.891184i \(-0.649875\pi\)
0.707384 + 0.706829i \(0.249875\pi\)
\(602\) −0.527142 + 5.01542i −0.0214847 + 0.204413i
\(603\) 3.05397 + 0.649142i 0.124367 + 0.0264351i
\(604\) 2.16407 + 3.74829i 0.0880549 + 0.152516i
\(605\) −19.9150 7.87546i −0.809661 0.320183i
\(606\) −2.24366 + 3.88613i −0.0911423 + 0.157863i
\(607\) −7.78942 23.9734i −0.316163 0.973049i −0.975273 0.221003i \(-0.929067\pi\)
0.659110 0.752046i \(-0.270933\pi\)
\(608\) 3.33575 + 2.80585i 0.135282 + 0.113792i
\(609\) 1.39999 1.01715i 0.0567305 0.0412171i
\(610\) 10.6544 + 11.8329i 0.431383 + 0.479100i
\(611\) −2.59450 2.88149i −0.104962 0.116573i
\(612\) −17.4859 7.78521i −0.706824 0.314698i
\(613\) −29.2146 + 13.0072i −1.17997 + 0.525355i −0.900523 0.434807i \(-0.856816\pi\)
−0.279443 + 0.960162i \(0.590150\pi\)
\(614\) −9.51582 + 10.5684i −0.384027 + 0.426505i
\(615\) 12.4668 0.502708
\(616\) 2.48249 0.582800i 0.100022 0.0234817i
\(617\) 5.65616 + 9.79676i 0.227709 + 0.394403i 0.957129 0.289663i \(-0.0935433\pi\)
−0.729420 + 0.684066i \(0.760210\pi\)
\(618\) −7.94749 + 8.82658i −0.319695 + 0.355057i
\(619\) 0.515342 + 0.374418i 0.0207133 + 0.0150491i 0.598094 0.801426i \(-0.295925\pi\)
−0.577380 + 0.816475i \(0.695925\pi\)
\(620\) 15.2389 11.0717i 0.612008 0.444650i
\(621\) 13.6657 2.90474i 0.548387 0.116563i
\(622\) −14.8971 16.5449i −0.597320 0.663391i
\(623\) 12.5007 + 5.56568i 0.500830 + 0.222984i
\(624\) 0.231133 0.102907i 0.00925274 0.00411958i
\(625\) 17.1063 + 3.63605i 0.684251 + 0.145442i
\(626\) 3.05306 0.122025
\(627\) 5.18740 8.03174i 0.207165 0.320757i
\(628\) −23.2431 −0.927500
\(629\) −50.4407 10.7215i −2.01120 0.427494i
\(630\) 3.50420 1.56017i 0.139611 0.0621587i
\(631\) 29.9329 + 13.3270i 1.19161 + 0.530539i 0.904134 0.427249i \(-0.140517\pi\)
0.287476 + 0.957788i \(0.407184\pi\)
\(632\) −0.401693 0.446126i −0.0159785 0.0177459i
\(633\) 12.8062 2.72203i 0.508999 0.108191i
\(634\) −19.7375 + 14.3401i −0.783877 + 0.569520i
\(635\) −22.7284 16.5132i −0.901950 0.655305i
\(636\) −0.618793 + 0.687240i −0.0245367 + 0.0272508i
\(637\) −1.22586 2.12325i −0.0485704 0.0841264i
\(638\) −10.4060 4.37178i −0.411979 0.173080i
\(639\) −19.8290 −0.784423
\(640\) −1.30272 + 1.44681i −0.0514944 + 0.0571903i
\(641\) 5.87699 2.61660i 0.232127 0.103350i −0.287377 0.957817i \(-0.592783\pi\)
0.519504 + 0.854468i \(0.326117\pi\)
\(642\) −7.45588 3.31957i −0.294260 0.131013i
\(643\) 5.78611 + 6.42612i 0.228182 + 0.253422i 0.846354 0.532621i \(-0.178793\pi\)
−0.618172 + 0.786043i \(0.712126\pi\)
\(644\) −1.95371 2.16981i −0.0769869 0.0855026i
\(645\) −6.83269 + 4.96424i −0.269037 + 0.195467i
\(646\) 24.9156 + 20.9576i 0.980290 + 0.824565i
\(647\) −13.9150 42.8260i −0.547055 1.68366i −0.716053 0.698046i \(-0.754053\pi\)
0.168998 0.985616i \(-0.445947\pi\)
\(648\) −2.62733 + 4.55067i −0.103211 + 0.178767i
\(649\) −9.92884 28.4929i −0.389741 1.11844i
\(650\) −0.231378 0.400759i −0.00907540 0.0157191i
\(651\) 4.81220 + 1.02286i 0.188605 + 0.0400892i
\(652\) −0.402388 + 3.82847i −0.0157587 + 0.149934i
\(653\) −14.1371 + 10.2712i −0.553228 + 0.401944i −0.828974 0.559287i \(-0.811075\pi\)
0.275746 + 0.961231i \(0.411075\pi\)
\(654\) 2.32029 7.14110i 0.0907303 0.279239i
\(655\) −17.2698 + 3.67081i −0.674787 + 0.143430i
\(656\) 8.84509 + 3.93809i 0.345343 + 0.153756i
\(657\) 26.6277 + 19.3461i 1.03884 + 0.754765i
\(658\) 2.40811 + 7.41140i 0.0938779 + 0.288926i
\(659\) 7.15874 + 12.3993i 0.278865 + 0.483009i 0.971103 0.238661i \(-0.0767084\pi\)
−0.692238 + 0.721669i \(0.743375\pi\)
\(660\) 3.50721 + 2.43651i 0.136518 + 0.0948410i
\(661\) 23.6626 + 40.9848i 0.920368 + 1.59412i 0.798847 + 0.601535i \(0.205444\pi\)
0.121521 + 0.992589i \(0.461223\pi\)
\(662\) −0.272158 0.0578490i −0.0105777 0.00224837i
\(663\) 1.72639 0.768640i 0.0670476 0.0298515i
\(664\) 7.99562 5.80916i 0.310290 0.225439i
\(665\) −6.46222 + 0.900307i −0.250594 + 0.0349124i
\(666\) −5.46716 + 16.8262i −0.211848 + 0.652001i
\(667\) 1.35091 + 12.8531i 0.0523076 + 0.497674i
\(668\) −1.72596 + 0.768449i −0.0667796 + 0.0297322i
\(669\) 9.54789 10.6040i 0.369143 0.409975i
\(670\) 1.18601 2.05424i 0.0458198 0.0793621i
\(671\) 24.5413 11.5544i 0.947407 0.446054i
\(672\) −0.508491 −0.0196154
\(673\) −4.70148 14.4697i −0.181229 0.557764i 0.818634 0.574315i \(-0.194732\pi\)
−0.999863 + 0.0165506i \(0.994732\pi\)
\(674\) 1.56399 14.8803i 0.0602425 0.573170i
\(675\) −4.06549 1.81007i −0.156481 0.0696698i
\(676\) −3.97200 + 12.2246i −0.152769 + 0.470175i
\(677\) −12.4066 + 38.1837i −0.476826 + 1.46752i 0.366653 + 0.930358i \(0.380503\pi\)
−0.843479 + 0.537162i \(0.819497\pi\)
\(678\) 1.78030 + 0.792639i 0.0683719 + 0.0304411i
\(679\) 10.4839 4.66772i 0.402334 0.179131i
\(680\) −9.73033 + 10.8066i −0.373141 + 0.414415i
\(681\) 4.14750 7.18368i 0.158933 0.275279i
\(682\) −10.5591 30.3017i −0.404330 1.16031i
\(683\) 18.3648 0.702710 0.351355 0.936242i \(-0.385721\pi\)
0.351355 + 0.936242i \(0.385721\pi\)
\(684\) 8.04438 7.74976i 0.307585 0.296319i
\(685\) −16.1736 11.7508i −0.617960 0.448974i
\(686\) 1.07762 + 10.2529i 0.0411439 + 0.391458i
\(687\) 6.13352 + 6.81197i 0.234009 + 0.259893i
\(688\) −6.41589 + 1.36374i −0.244603 + 0.0519921i
\(689\) 0.0559135 + 0.531981i 0.00213013 + 0.0202669i
\(690\) 0.511122 4.86300i 0.0194581 0.185131i
\(691\) 1.51888 + 4.67462i 0.0577808 + 0.177831i 0.975781 0.218748i \(-0.0701973\pi\)
−0.918001 + 0.396579i \(0.870197\pi\)
\(692\) 5.16577 0.196373
\(693\) −0.820329 6.48287i −0.0311617 0.246264i
\(694\) 2.50481 + 4.33846i 0.0950813 + 0.164686i
\(695\) −10.1102 31.1160i −0.383501 1.18030i
\(696\) 1.82090 + 1.32296i 0.0690209 + 0.0501466i
\(697\) 66.0662 + 29.4146i 2.50244 + 1.11416i
\(698\) 10.9737 + 12.1875i 0.415359 + 0.461303i
\(699\) −13.3190 + 2.83103i −0.503770 + 0.107080i
\(700\) 0.0972160 + 0.924949i 0.00367442 + 0.0349598i
\(701\) −3.22840 + 1.43737i −0.121935 + 0.0542889i −0.466797 0.884364i \(-0.654592\pi\)
0.344862 + 0.938653i \(0.387926\pi\)
\(702\) −0.434903 1.33849i −0.0164143 0.0505181i
\(703\) 16.8581 24.9287i 0.635816 0.940202i
\(704\) 1.71868 + 2.83657i 0.0647753 + 0.106907i
\(705\) −6.52537 + 11.3023i −0.245760 + 0.425668i
\(706\) −11.9065 2.53081i −0.448108 0.0952483i
\(707\) 0.545279 5.18798i 0.0205073 0.195114i
\(708\) 0.628932 + 5.98388i 0.0236367 + 0.224888i
\(709\) −11.2390 + 2.38892i −0.422089 + 0.0897178i −0.414059 0.910250i \(-0.635889\pi\)
−0.00802980 + 0.999968i \(0.502556\pi\)
\(710\) −4.65524 + 14.3274i −0.174708 + 0.537697i
\(711\) −1.24458 + 0.904237i −0.0466752 + 0.0339115i
\(712\) −1.86037 + 17.7002i −0.0697202 + 0.663344i
\(713\) −24.5853 + 27.3047i −0.920727 + 1.02257i
\(714\) −3.79805 −0.142138
\(715\) 2.40478 0.564557i 0.0899337 0.0211132i
\(716\) 1.19095 + 2.06278i 0.0445077 + 0.0770896i
\(717\) 12.8721 + 2.73605i 0.480717 + 0.102179i
\(718\) −0.189969 + 1.80744i −0.00708960 + 0.0674530i
\(719\) −0.241425 2.29700i −0.00900362 0.0856638i 0.989097 0.147263i \(-0.0470465\pi\)
−0.998101 + 0.0615996i \(0.980380\pi\)
\(720\) 3.33833 + 3.70760i 0.124412 + 0.138174i
\(721\) 4.26677 13.1318i 0.158903 0.489053i
\(722\) −16.7973 + 8.87971i −0.625132 + 0.330469i
\(723\) 4.43817 + 3.22452i 0.165057 + 0.119921i
\(724\) 14.7655 + 3.13850i 0.548756 + 0.116642i
\(725\) 2.05834 3.56516i 0.0764450 0.132407i
\(726\) 5.69954 4.52122i 0.211530 0.167798i
\(727\) 4.05612 7.02541i 0.150433 0.260558i −0.780954 0.624589i \(-0.785266\pi\)
0.931387 + 0.364031i \(0.118600\pi\)
\(728\) −0.196807 + 0.218576i −0.00729416 + 0.00810098i
\(729\) 4.98859 + 3.62442i 0.184762 + 0.134238i
\(730\) 20.2299 14.6979i 0.748741 0.543992i
\(731\) −47.9219 + 10.1861i −1.77246 + 0.376747i
\(732\) −5.29084 + 1.12460i −0.195555 + 0.0415666i
\(733\) 9.51795 6.91519i 0.351553 0.255419i −0.397967 0.917400i \(-0.630284\pi\)
0.749520 + 0.661981i \(0.230284\pi\)
\(734\) 10.7359 + 7.80011i 0.396271 + 0.287907i
\(735\) −5.52172 + 6.13249i −0.203672 + 0.226200i
\(736\) 1.89880 3.28881i 0.0699906 0.121227i
\(737\) −2.76679 2.94512i −0.101916 0.108485i
\(738\) 12.4057 21.4873i 0.456661 0.790959i
\(739\) 14.7689 + 3.13923i 0.543284 + 0.115479i 0.471375 0.881933i \(-0.343758\pi\)
0.0719085 + 0.997411i \(0.477091\pi\)
\(740\) 10.8742 + 7.90055i 0.399743 + 0.290430i
\(741\) 0.0371668 + 1.10220i 0.00136536 + 0.0404905i
\(742\) 0.332212 1.02244i 0.0121959 0.0375350i
\(743\) −8.60434 9.55609i −0.315663 0.350579i 0.564344 0.825539i \(-0.309129\pi\)
−0.880007 + 0.474961i \(0.842462\pi\)
\(744\) 0.668857 + 6.36375i 0.0245215 + 0.233306i
\(745\) 1.33776 12.7280i 0.0490118 0.466316i
\(746\) −10.2806 2.18521i −0.376400 0.0800063i
\(747\) −12.6632 21.9333i −0.463323 0.802499i
\(748\) 12.8373 + 21.1871i 0.469378 + 0.774676i
\(749\) 9.48782 0.346677
\(750\) −5.35008 + 5.94187i −0.195357 + 0.216966i
\(751\) 3.98505 37.9152i 0.145416 1.38354i −0.641802 0.766870i \(-0.721813\pi\)
0.787218 0.616674i \(-0.211520\pi\)
\(752\) −8.19995 + 5.95761i −0.299022 + 0.217252i
\(753\) 2.94783 9.07248i 0.107425 0.330619i
\(754\) 1.27344 0.270678i 0.0463760 0.00985752i
\(755\) −0.880797 8.38022i −0.0320555 0.304987i
\(756\) −0.295661 + 2.81303i −0.0107531 + 0.102309i
\(757\) −22.1981 4.71835i −0.806803 0.171491i −0.213994 0.976835i \(-0.568647\pi\)
−0.592808 + 0.805344i \(0.701981\pi\)
\(758\) −12.3666 + 21.4197i −0.449177 + 0.777997i
\(759\) −7.67983 3.22645i −0.278760 0.117113i
\(760\) −3.71098 7.63185i −0.134611 0.276836i
\(761\) 4.22762 + 13.0113i 0.153251 + 0.471659i 0.997980 0.0635366i \(-0.0202380\pi\)
−0.844728 + 0.535195i \(0.820238\pi\)
\(762\) 8.71857 3.88176i 0.315840 0.140621i
\(763\) 0.912413 + 8.68103i 0.0330316 + 0.314274i
\(764\) 1.72223 0.366070i 0.0623079 0.0132440i
\(765\) 24.9349 + 27.6930i 0.901522 + 1.00124i
\(766\) 0.799095 + 0.355780i 0.0288725 + 0.0128549i
\(767\) 2.81562 + 2.04567i 0.101666 + 0.0738647i
\(768\) −0.204374 0.628997i −0.00737470 0.0226970i
\(769\) −18.3312 31.7506i −0.661041 1.14496i −0.980342 0.197303i \(-0.936782\pi\)
0.319301 0.947653i \(-0.396552\pi\)
\(770\) −4.87676 0.929254i −0.175746 0.0334880i
\(771\) 7.09413 0.255489
\(772\) 1.46002 + 4.49347i 0.0525472 + 0.161724i
\(773\) 0.683818 6.50609i 0.0245952 0.234008i −0.975318 0.220806i \(-0.929131\pi\)
0.999913 0.0132013i \(-0.00420224\pi\)
\(774\) 1.75698 + 16.7165i 0.0631533 + 0.600864i
\(775\) 11.4478 2.43331i 0.411219 0.0874072i
\(776\) 9.98763 + 11.0924i 0.358535 + 0.398194i
\(777\) 0.366959 + 3.49138i 0.0131646 + 0.125252i
\(778\) −9.59301 6.96973i −0.343926 0.249877i
\(779\) −30.3938 + 29.2806i −1.08897 + 1.04909i
\(780\) −0.492574 −0.0176370
\(781\) 21.0766 + 14.6422i 0.754181 + 0.523940i
\(782\) 14.1826 24.5650i 0.507169 0.878442i
\(783\) 8.37752 9.30418i 0.299388 0.332504i
\(784\) −5.85480 + 2.60672i −0.209100 + 0.0930973i
\(785\) 41.3393 + 18.4054i 1.47546 + 0.656918i
\(786\) 1.85340 5.70418i 0.0661086 0.203461i
\(787\) −5.31655 + 16.3626i −0.189514 + 0.583265i −0.999997 0.00249751i \(-0.999205\pi\)
0.810482 + 0.585763i \(0.199205\pi\)
\(788\) 22.8457 + 10.1716i 0.813845 + 0.362347i
\(789\) 0.460410 4.38051i 0.0163910 0.155950i
\(790\) 0.361165 + 1.11155i 0.0128497 + 0.0395472i
\(791\) −2.26548 −0.0805512
\(792\) 7.68953 3.62035i 0.273235 0.128643i
\(793\) −1.56436 + 2.70956i −0.0555522 + 0.0962192i
\(794\) −7.03713 + 7.81552i −0.249738 + 0.277363i
\(795\) 1.64477 0.732297i 0.0583338 0.0259719i
\(796\) 2.02421 + 19.2591i 0.0717462 + 0.682619i
\(797\) −8.63909 + 26.5884i −0.306012 + 0.941809i 0.673285 + 0.739383i \(0.264883\pi\)
−0.979298 + 0.202426i \(0.935117\pi\)
\(798\) 0.832763 2.05407i 0.0294795 0.0727132i
\(799\) −61.2475 + 44.4989i −2.16678 + 1.57426i
\(800\) −1.10508 + 0.492013i −0.0390704 + 0.0173953i
\(801\) 44.6117 + 9.48250i 1.57628 + 0.335048i
\(802\) 13.3929 + 23.1972i 0.472920 + 0.819122i
\(803\) −14.0174 40.2260i −0.494664 1.41954i
\(804\) 0.402897 + 0.697837i 0.0142091 + 0.0246108i
\(805\) 1.75659 + 5.40623i 0.0619116 + 0.190544i
\(806\) 2.99436 + 2.17553i 0.105472 + 0.0766297i
\(807\) 3.30622 + 1.47202i 0.116385 + 0.0518177i
\(808\) 6.63664 1.41066i 0.233476 0.0496269i
\(809\) 8.89199 27.3667i 0.312626 0.962163i −0.664095 0.747648i \(-0.731183\pi\)
0.976721 0.214515i \(-0.0688171\pi\)
\(810\) 8.27641 6.01316i 0.290803 0.211281i
\(811\) 3.28227 31.2287i 0.115256 1.09659i −0.772099 0.635502i \(-0.780793\pi\)
0.887355 0.461087i \(-0.152540\pi\)
\(812\) −2.55935 0.544006i −0.0898155 0.0190909i
\(813\) −3.72049 6.44408i −0.130483 0.226004i
\(814\) 18.2360 13.8478i 0.639172 0.485365i
\(815\) 3.74731 6.49053i 0.131263 0.227353i
\(816\) −1.52652 4.69814i −0.0534389 0.164468i
\(817\) 4.99853 28.1507i 0.174876 0.984867i
\(818\) 20.4761 14.8767i 0.715929 0.520153i
\(819\) 0.504337 + 0.560123i 0.0176230 + 0.0195723i
\(820\) −12.6131 14.0083i −0.440469 0.489190i
\(821\) −11.1853 4.98004i −0.390371 0.173805i 0.202159 0.979353i \(-0.435204\pi\)
−0.592530 + 0.805548i \(0.701871\pi\)
\(822\) 6.20414 2.76226i 0.216394 0.0963449i
\(823\) 24.5061 27.2168i 0.854229 0.948717i −0.144942 0.989440i \(-0.546299\pi\)
0.999170 + 0.0407230i \(0.0129661\pi\)
\(824\) 17.9588 0.625623
\(825\) 1.37500 + 2.26934i 0.0478712 + 0.0790082i
\(826\) −3.49733 6.05755i −0.121688 0.210769i
\(827\) 22.1174 24.5639i 0.769099 0.854171i −0.223614 0.974678i \(-0.571785\pi\)
0.992712 + 0.120507i \(0.0384521\pi\)
\(828\) −7.87310 5.72014i −0.273609 0.198789i
\(829\) −30.9812 + 22.5091i −1.07602 + 0.781774i −0.976985 0.213309i \(-0.931576\pi\)
−0.0990355 + 0.995084i \(0.531576\pi\)
\(830\) −18.8208 + 4.00048i −0.653279 + 0.138859i
\(831\) 4.40190 + 4.88880i 0.152700 + 0.169591i
\(832\) −0.349478 0.155598i −0.0121160 0.00539438i
\(833\) −43.7310 + 19.4703i −1.51519 + 0.674605i
\(834\) 10.8714 + 2.31078i 0.376445 + 0.0800159i
\(835\) 3.67825 0.127291
\(836\) −14.2732 + 2.29720i −0.493647 + 0.0794502i
\(837\) 35.5939 1.23031
\(838\) 15.0918 + 3.20787i 0.521339 + 0.110814i
\(839\) −33.6399 + 14.9775i −1.16138 + 0.517079i −0.894683 0.446702i \(-0.852599\pi\)
−0.266696 + 0.963781i \(0.585932\pi\)
\(840\) 0.904383 + 0.402657i 0.0312042 + 0.0138930i
\(841\) −11.6552 12.9444i −0.401902 0.446358i
\(842\) −31.6100 + 6.71890i −1.08935 + 0.231549i
\(843\) −0.334806 + 0.243251i −0.0115313 + 0.00837800i
\(844\) −16.0151 11.6356i −0.551262 0.400516i
\(845\) 16.7447 18.5968i 0.576034 0.639751i
\(846\) 12.9868 + 22.4939i 0.446497 + 0.773355i
\(847\) −3.91517 + 7.49652i −0.134527 + 0.257583i
\(848\) 1.39827 0.0480169
\(849\) −9.20409 + 10.2222i −0.315883 + 0.350824i
\(850\) −8.25411 + 3.67497i −0.283114 + 0.126050i
\(851\) −23.9518 10.6640i −0.821057 0.365558i
\(852\) −3.42432 3.80309i −0.117315 0.130292i
\(853\) −29.8040 33.1007i −1.02047 1.13334i −0.991011 0.133779i \(-0.957289\pi\)
−0.0294572 0.999566i \(-0.509378\pi\)
\(854\) 5.08717 3.69604i 0.174079 0.126476i
\(855\) −20.4442 + 7.41334i −0.699178 + 0.253531i
\(856\) 3.81337 + 11.7363i 0.130338 + 0.401140i
\(857\) −4.07424 + 7.05679i −0.139173 + 0.241055i −0.927184 0.374606i \(-0.877778\pi\)
0.788011 + 0.615662i \(0.211111\pi\)
\(858\) −0.242370 + 0.803364i −0.00827437 + 0.0274264i
\(859\) −6.47397 11.2132i −0.220889 0.382591i 0.734189 0.678945i \(-0.237562\pi\)
−0.955078 + 0.296354i \(0.904229\pi\)
\(860\) 12.4910 + 2.65504i 0.425938 + 0.0905360i
\(861\) 0.514623 4.89631i 0.0175383 0.166866i
\(862\) −26.7146 + 19.4093i −0.909904 + 0.661084i
\(863\) 1.76507 5.43232i 0.0600836 0.184918i −0.916510 0.400012i \(-0.869006\pi\)
0.976593 + 0.215094i \(0.0690058\pi\)
\(864\) −3.59852 + 0.764890i −0.122424 + 0.0260221i
\(865\) −9.18764 4.09060i −0.312389 0.139085i
\(866\) 0.443989 + 0.322577i 0.0150874 + 0.0109616i
\(867\) −7.92761 24.3987i −0.269236 0.828622i
\(868\) −3.71935 6.44210i −0.126243 0.218659i
\(869\) 1.99060 0.0421060i 0.0675263 0.00142835i
\(870\) −2.19097 3.79487i −0.0742809 0.128658i
\(871\) 0.455906 + 0.0969058i 0.0154478 + 0.00328353i
\(872\) −10.3716 + 4.61774i −0.351227 + 0.156377i
\(873\) 30.9449 22.4828i 1.04733 0.760927i
\(874\) 10.1756 + 13.0564i 0.344195 + 0.441640i
\(875\) 2.87230 8.84003i 0.0971014 0.298847i
\(876\) 0.887919 + 8.44798i 0.0300000 + 0.285431i
\(877\) −2.41236 + 1.07405i −0.0814596 + 0.0362682i −0.447062 0.894503i \(-0.647530\pi\)
0.365602 + 0.930771i \(0.380863\pi\)
\(878\) 14.9066 16.5555i 0.503074 0.558720i
\(879\) −1.39238 + 2.41168i −0.0469640 + 0.0813440i
\(880\) −0.810601 6.40599i −0.0273254 0.215946i
\(881\) −38.2054 −1.28717 −0.643587 0.765373i \(-0.722554\pi\)
−0.643587 + 0.765373i \(0.722554\pi\)
\(882\) 5.07509 + 15.6195i 0.170887 + 0.525937i
\(883\) 1.18234 11.2492i 0.0397889 0.378566i −0.956449 0.291901i \(-0.905712\pi\)
0.996238 0.0866651i \(-0.0276210\pi\)
\(884\) −2.61034 1.16220i −0.0877953 0.0390890i
\(885\) 3.61985 11.1407i 0.121680 0.374492i
\(886\) −2.88300 + 8.87298i −0.0968564 + 0.298093i
\(887\) 2.90009 + 1.29120i 0.0973756 + 0.0433544i 0.454846 0.890570i \(-0.349694\pi\)
−0.357471 + 0.933924i \(0.616361\pi\)
\(888\) −4.17131 + 1.85719i −0.139980 + 0.0623231i
\(889\) −7.42375 + 8.24491i −0.248985 + 0.276526i
\(890\) 17.3250 30.0078i 0.580736 1.00586i
\(891\) −5.73479 16.4572i −0.192123 0.551336i
\(892\) −21.5752 −0.722390
\(893\) −10.6368 42.8809i −0.355948 1.43496i
\(894\) 3.51727 + 2.55544i 0.117635 + 0.0854668i
\(895\) −0.484725 4.61185i −0.0162026 0.154157i
\(896\) 0.514459 + 0.571365i 0.0171869 + 0.0190880i
\(897\) 0.939821 0.199765i 0.0313797 0.00666996i
\(898\) −0.0539901 0.513681i −0.00180167 0.0171418i
\(899\) −3.44172 + 32.7458i −0.114788 + 1.09213i
\(900\) 0.957911 + 2.94815i 0.0319304 + 0.0982715i
\(901\) 10.4441 0.347942
\(902\) −29.0531 + 13.6786i −0.967361 + 0.455448i
\(903\) 1.66765 + 2.88846i 0.0554960 + 0.0961218i
\(904\) −0.910546 2.80237i −0.0302843 0.0932056i
\(905\) −23.7761 17.2743i −0.790344 0.574219i
\(906\) 2.61502 + 1.16428i 0.0868782 + 0.0386807i
\(907\) 37.8006 + 41.9818i 1.25515 + 1.39398i 0.885387 + 0.464854i \(0.153893\pi\)
0.369760 + 0.929127i \(0.379440\pi\)
\(908\) −12.2681 + 2.60767i −0.407132 + 0.0865386i
\(909\) −1.81743 17.2917i −0.0602804 0.573530i
\(910\) 0.523118 0.232907i 0.0173412 0.00772079i
\(911\) −2.05464 6.32353i −0.0680733 0.209508i 0.911233 0.411891i \(-0.135131\pi\)
−0.979306 + 0.202383i \(0.935131\pi\)
\(912\) 2.87557 + 0.204544i 0.0952195 + 0.00677313i
\(913\) −2.73614 + 32.6642i −0.0905529 + 1.08103i
\(914\) 2.13381 3.69586i 0.0705801 0.122248i
\(915\) 10.3006 + 2.18947i 0.340529 + 0.0723816i
\(916\) 1.44874 13.7839i 0.0478678 0.455432i
\(917\) 0.728818 + 6.93424i 0.0240677 + 0.228989i
\(918\) −26.8783 + 5.71316i −0.887116 + 0.188562i
\(919\) 0.0993105 0.305646i 0.00327595 0.0100823i −0.949405 0.314054i \(-0.898313\pi\)
0.952681 + 0.303971i \(0.0983128\pi\)
\(920\) −5.98143 + 4.34577i −0.197202 + 0.143276i
\(921\) −0.983133 + 9.35389i −0.0323953 + 0.308221i
\(922\) −10.7315 + 11.9186i −0.353424 + 0.392518i
\(923\) −2.96013 −0.0974338
\(924\) 1.10171 1.27688i 0.0362437 0.0420062i
\(925\) 4.17573 + 7.23258i 0.137297 + 0.237806i
\(926\) 3.73986 + 0.794932i 0.122899 + 0.0261231i
\(927\) 4.81051 45.7689i 0.157998 1.50325i
\(928\) −0.355729 3.38454i −0.0116774 0.111103i
\(929\) 15.8415 + 17.5937i 0.519742 + 0.577232i 0.944681 0.327990i \(-0.106371\pi\)
−0.424939 + 0.905222i \(0.639705\pi\)
\(930\) 3.84964 11.8480i 0.126235 0.388511i
\(931\) −0.941467 27.9198i −0.0308553 0.915033i
\(932\) 16.6564 + 12.1016i 0.545599 + 0.396401i
\(933\) −14.4025 3.06135i −0.471517 0.100224i
\(934\) −13.0083 + 22.5310i −0.425644 + 0.737237i
\(935\) −6.05459 47.8480i −0.198006 1.56480i
\(936\) −0.490162 + 0.848985i −0.0160214 + 0.0277499i
\(937\) −14.6137 + 16.2301i −0.477408 + 0.530216i −0.932953 0.359997i \(-0.882778\pi\)
0.455545 + 0.890213i \(0.349444\pi\)
\(938\) −0.757842 0.550605i −0.0247444 0.0179779i
\(939\) 1.63356 1.18685i 0.0533093 0.0387315i
\(940\) 19.3018 4.10272i 0.629554 0.133816i
\(941\) −50.4975 + 10.7336i −1.64617 + 0.349904i −0.935419 0.353540i \(-0.884978\pi\)
−0.710751 + 0.703444i \(0.751645\pi\)
\(942\) −12.4364 + 9.03556i −0.405199 + 0.294394i
\(943\) 29.7467 + 21.6122i 0.968684 + 0.703790i
\(944\) 6.08748 6.76083i 0.198130 0.220046i
\(945\) 2.75340 4.76903i 0.0895681 0.155137i
\(946\) 10.4764 19.0658i 0.340617 0.619881i
\(947\) 10.4730 18.1398i 0.340327 0.589464i −0.644166 0.764886i \(-0.722796\pi\)
0.984493 + 0.175422i \(0.0561288\pi\)
\(948\) −0.388357 0.0825478i −0.0126132 0.00268103i
\(949\) 3.97506 + 2.88805i 0.129036 + 0.0937500i
\(950\) −0.177700 5.26979i −0.00576533 0.170974i
\(951\) −4.98609 + 15.3456i −0.161685 + 0.497615i
\(952\) 3.84263 + 4.26767i 0.124540 + 0.138316i
\(953\) −2.36569 22.5081i −0.0766324 0.729108i −0.963613 0.267302i \(-0.913868\pi\)
0.886981 0.461807i \(-0.152799\pi\)
\(954\) 0.374547 3.56358i 0.0121264 0.115375i
\(955\) −3.35297 0.712695i −0.108499 0.0230623i
\(956\) −9.94883 17.2319i −0.321768 0.557319i
\(957\) −7.26731 + 1.70611i −0.234919 + 0.0551506i
\(958\) 26.2683 0.848689
\(959\) −5.28275 + 5.86709i −0.170589 + 0.189458i
\(960\) −0.134591 + 1.28055i −0.00434391 + 0.0413295i
\(961\) −50.6508 + 36.8000i −1.63390 + 1.18710i
\(962\) −0.816153 + 2.51186i −0.0263138 + 0.0809856i
\(963\) 30.9322 6.57483i 0.996775 0.211871i
\(964\) −0.867039 8.24932i −0.0279254 0.265693i
\(965\) 0.961500 9.14806i 0.0309518 0.294486i
\(966\) −1.88884 0.401486i −0.0607725 0.0129176i
\(967\) 23.3712 40.4801i 0.751566 1.30175i −0.195497 0.980704i \(-0.562632\pi\)
0.947063 0.321047i \(-0.104035\pi\)
\(968\) −10.8467 1.83000i −0.348626 0.0588185i
\(969\) 21.4783 + 1.52779i 0.689984 + 0.0490797i
\(970\) −8.97993 27.6374i −0.288328 0.887383i
\(971\) 12.6510 5.63260i 0.405991 0.180759i −0.193573 0.981086i \(-0.562008\pi\)
0.599563 + 0.800327i \(0.295341\pi\)
\(972\) 1.51692 + 14.4325i 0.0486552 + 0.462923i
\(973\) −12.6381 + 2.68631i −0.405159 + 0.0861193i
\(974\) 2.01707 + 2.24019i 0.0646312 + 0.0717802i
\(975\) −0.279592 0.124483i −0.00895412 0.00398663i
\(976\) 6.61661 + 4.80725i 0.211793 + 0.153876i
\(977\) −5.11197 15.7330i −0.163547 0.503344i 0.835380 0.549673i \(-0.185248\pi\)
−0.998926 + 0.0463289i \(0.985248\pi\)
\(978\) 1.27298 + 2.20487i 0.0407056 + 0.0705041i
\(979\) −40.4165 43.0215i −1.29172 1.37497i
\(980\) 12.4773 0.398573
\(981\) 8.99039 + 27.6696i 0.287041 + 0.883422i
\(982\) −3.71223 + 35.3195i −0.118462 + 1.12709i
\(983\) −0.880072 8.37332i −0.0280699 0.267068i −0.999551 0.0299518i \(-0.990465\pi\)
0.971481 0.237116i \(-0.0762021\pi\)
\(984\) 6.26353 1.33135i 0.199674 0.0424420i
\(985\) −32.5780 36.1816i −1.03802 1.15284i
\(986\) −2.65703 25.2800i −0.0846171 0.805078i
\(987\) 4.16960 + 3.02939i 0.132720 + 0.0964266i
\(988\) 1.20089 1.15691i 0.0382054 0.0368061i
\(989\) −24.9093 −0.792069
\(990\) −16.5431 + 0.349928i −0.525776 + 0.0111215i
\(991\) −13.8941 + 24.0654i −0.441362 + 0.764461i −0.997791 0.0664339i \(-0.978838\pi\)
0.556429 + 0.830895i \(0.312171\pi\)
\(992\) 6.47392 7.19001i 0.205547 0.228283i
\(993\) −0.168109 + 0.0748467i −0.00533476 + 0.00237519i
\(994\) 5.43490 + 2.41977i 0.172385 + 0.0767505i
\(995\) 11.6504 35.8563i 0.369344 1.13672i
\(996\) 2.01985 6.21646i 0.0640014 0.196976i
\(997\) 36.0419 + 16.0469i 1.14146 + 0.508210i 0.888322 0.459221i \(-0.151871\pi\)
0.253136 + 0.967431i \(0.418538\pi\)
\(998\) 0.498933 4.74703i 0.0157934 0.150265i
\(999\) 7.84877 + 24.1560i 0.248324 + 0.764263i
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 418.2.n.e.49.5 72
11.9 even 5 inner 418.2.n.e.163.5 yes 72
19.7 even 3 inner 418.2.n.e.159.5 yes 72
209.64 even 15 inner 418.2.n.e.273.5 yes 72
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
418.2.n.e.49.5 72 1.1 even 1 trivial
418.2.n.e.159.5 yes 72 19.7 even 3 inner
418.2.n.e.163.5 yes 72 11.9 even 5 inner
418.2.n.e.273.5 yes 72 209.64 even 15 inner