Properties

Label 675.2.l.c.76.1
Level $675$
Weight $2$
Character 675.76
Analytic conductor $5.390$
Analytic rank $0$
Dimension $12$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [675,2,Mod(76,675)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(675, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([14, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("675.76");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 675 = 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 675.l (of order \(9\), degree \(6\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.38990213644\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(2\) over \(\Q(\zeta_{9})\)
Coefficient field: 12.0.1952986685049.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} + \cdots + 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 27)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 76.1
Root \(0.500000 + 2.22827i\) of defining polynomial
Character \(\chi\) \(=\) 675.76
Dual form 675.2.l.c.151.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.318266 - 0.267057i) q^{2} +(-0.159815 + 1.72466i) q^{3} +(-0.317323 + 1.79963i) q^{4} +(0.409719 + 0.591580i) q^{6} +(0.229151 + 1.29958i) q^{7} +(0.795075 + 1.37711i) q^{8} +(-2.94892 - 0.551252i) q^{9} +O(q^{10})\) \(q+(0.318266 - 0.267057i) q^{2} +(-0.159815 + 1.72466i) q^{3} +(-0.317323 + 1.79963i) q^{4} +(0.409719 + 0.591580i) q^{6} +(0.229151 + 1.29958i) q^{7} +(0.795075 + 1.37711i) q^{8} +(-2.94892 - 0.551252i) q^{9} +(4.90067 + 1.78370i) q^{11} +(-3.05303 - 0.834881i) q^{12} +(0.0138336 + 0.0116078i) q^{13} +(0.419993 + 0.352416i) q^{14} +(-2.81355 - 1.02405i) q^{16} +(-1.56640 + 2.71308i) q^{17} +(-1.08575 + 0.612083i) q^{18} +(-0.208676 - 0.361438i) q^{19} +(-2.27796 + 0.187516i) q^{21} +(2.03606 - 0.741067i) q^{22} +(0.179619 - 1.01867i) q^{23} +(-2.50212 + 1.15115i) q^{24} +0.00750270 q^{26} +(1.42200 - 4.99779i) q^{27} -2.41147 q^{28} +(-5.98068 + 5.01839i) q^{29} +(0.647649 - 3.67300i) q^{31} +(-4.15744 + 1.51319i) q^{32} +(-3.85948 + 8.16694i) q^{33} +(0.226015 + 1.28180i) q^{34} +(1.92781 - 5.13202i) q^{36} +(2.21238 - 3.83195i) q^{37} +(-0.162939 - 0.0593049i) q^{38} +(-0.0222303 + 0.0220032i) q^{39} +(-2.81517 - 2.36221i) q^{41} +(-0.674919 + 0.668024i) q^{42} +(-7.80685 - 2.84146i) q^{43} +(-4.76508 + 8.25337i) q^{44} +(-0.214876 - 0.372177i) q^{46} +(1.23254 + 6.99008i) q^{47} +(2.21579 - 4.68877i) q^{48} +(4.94145 - 1.79854i) q^{49} +(-4.42881 - 3.13510i) q^{51} +(-0.0252794 + 0.0212119i) q^{52} +1.30057 q^{53} +(-0.882118 - 1.97038i) q^{54} +(-1.60747 + 1.34883i) q^{56} +(0.656707 - 0.302133i) q^{57} +(-0.563252 + 3.19436i) q^{58} +(3.47856 - 1.26609i) q^{59} +(1.20064 + 6.80919i) q^{61} +(-0.774775 - 1.34195i) q^{62} +(0.0406486 - 3.95868i) q^{63} +(2.07506 - 3.59410i) q^{64} +(0.952697 + 3.62996i) q^{66} +(8.44702 + 7.08789i) q^{67} +(-4.38548 - 3.67985i) q^{68} +(1.72816 + 0.472581i) q^{69} +(3.04214 - 5.26914i) q^{71} +(-1.58548 - 4.49927i) q^{72} +(-0.273486 - 0.473692i) q^{73} +(-0.319224 - 1.81041i) q^{74} +(0.716670 - 0.260847i) q^{76} +(-1.19507 + 6.77756i) q^{77} +(-0.00119904 + 0.0129396i) q^{78} +(0.374706 - 0.314416i) q^{79} +(8.39224 + 3.25120i) q^{81} -1.52681 q^{82} +(-3.53428 + 2.96561i) q^{83} +(0.385389 - 4.15898i) q^{84} +(-3.24348 + 1.18053i) q^{86} +(-7.69922 - 11.1167i) q^{87} +(1.44005 + 8.16694i) q^{88} +(1.68653 + 2.92116i) q^{89} +(-0.0119153 + 0.0206379i) q^{91} +(1.77623 + 0.646495i) q^{92} +(6.23118 + 1.70398i) q^{93} +(2.25902 + 1.89554i) q^{94} +(-1.94531 - 7.41201i) q^{96} +(9.34182 + 3.40014i) q^{97} +(1.09238 - 1.89206i) q^{98} +(-13.4684 - 7.96149i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 6 q^{2} + 6 q^{3} - 6 q^{4} + 6 q^{7} - 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 6 q^{2} + 6 q^{3} - 6 q^{4} + 6 q^{7} - 6 q^{8} + 3 q^{11} - 12 q^{12} + 6 q^{13} + 15 q^{14} - 9 q^{17} - 9 q^{18} - 3 q^{19} - 12 q^{21} - 3 q^{22} + 12 q^{23} - 18 q^{24} - 30 q^{26} + 9 q^{27} + 12 q^{28} - 6 q^{29} + 3 q^{31} + 9 q^{34} + 18 q^{36} + 3 q^{37} - 42 q^{38} + 33 q^{39} + 15 q^{41} - 18 q^{42} - 3 q^{43} + 3 q^{44} - 3 q^{46} + 15 q^{47} + 15 q^{48} + 12 q^{49} - 18 q^{51} - 9 q^{52} + 18 q^{53} - 54 q^{54} - 33 q^{56} + 3 q^{57} - 21 q^{58} - 12 q^{59} + 12 q^{61} + 12 q^{62} - 9 q^{63} + 12 q^{64} - 9 q^{66} + 15 q^{67} - 9 q^{68} + 9 q^{69} + 27 q^{71} - 18 q^{72} - 6 q^{73} + 33 q^{74} - 48 q^{76} - 15 q^{77} - 18 q^{78} - 42 q^{79} + 36 q^{81} + 12 q^{82} - 39 q^{83} + 6 q^{84} + 51 q^{86} - 9 q^{87} + 30 q^{88} + 9 q^{89} + 6 q^{91} + 39 q^{92} + 39 q^{93} - 15 q^{94} - 3 q^{97} + 45 q^{98} - 27 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/675\mathbb{Z}\right)^\times\).

\(n\) \(326\) \(352\)
\(\chi(n)\) \(e\left(\frac{7}{9}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.318266 0.267057i 0.225048 0.188837i −0.523291 0.852154i \(-0.675296\pi\)
0.748339 + 0.663316i \(0.230852\pi\)
\(3\) −0.159815 + 1.72466i −0.0922690 + 0.995734i
\(4\) −0.317323 + 1.79963i −0.158661 + 0.899813i
\(5\) 0 0
\(6\) 0.409719 + 0.591580i 0.167267 + 0.241512i
\(7\) 0.229151 + 1.29958i 0.0866110 + 0.491195i 0.996997 + 0.0774361i \(0.0246734\pi\)
−0.910386 + 0.413759i \(0.864216\pi\)
\(8\) 0.795075 + 1.37711i 0.281102 + 0.486882i
\(9\) −2.94892 0.551252i −0.982973 0.183751i
\(10\) 0 0
\(11\) 4.90067 + 1.78370i 1.47761 + 0.537805i 0.950155 0.311778i \(-0.100925\pi\)
0.527454 + 0.849584i \(0.323147\pi\)
\(12\) −3.05303 0.834881i −0.881335 0.241009i
\(13\) 0.0138336 + 0.0116078i 0.00383676 + 0.00321942i 0.644704 0.764432i \(-0.276981\pi\)
−0.640867 + 0.767652i \(0.721425\pi\)
\(14\) 0.419993 + 0.352416i 0.112248 + 0.0941870i
\(15\) 0 0
\(16\) −2.81355 1.02405i −0.703389 0.256012i
\(17\) −1.56640 + 2.71308i −0.379907 + 0.658019i −0.991048 0.133503i \(-0.957377\pi\)
0.611141 + 0.791522i \(0.290711\pi\)
\(18\) −1.08575 + 0.612083i −0.255915 + 0.144269i
\(19\) −0.208676 0.361438i −0.0478736 0.0829195i 0.841096 0.540886i \(-0.181911\pi\)
−0.888969 + 0.457967i \(0.848578\pi\)
\(20\) 0 0
\(21\) −2.27796 + 0.187516i −0.497092 + 0.0409194i
\(22\) 2.03606 0.741067i 0.434090 0.157996i
\(23\) 0.179619 1.01867i 0.0374532 0.212408i −0.960338 0.278839i \(-0.910050\pi\)
0.997791 + 0.0664316i \(0.0211614\pi\)
\(24\) −2.50212 + 1.15115i −0.510742 + 0.234978i
\(25\) 0 0
\(26\) 0.00750270 0.00147140
\(27\) 1.42200 4.99779i 0.273665 0.961825i
\(28\) −2.41147 −0.455726
\(29\) −5.98068 + 5.01839i −1.11058 + 0.931891i −0.998091 0.0617615i \(-0.980328\pi\)
−0.112493 + 0.993652i \(0.535884\pi\)
\(30\) 0 0
\(31\) 0.647649 3.67300i 0.116321 0.659691i −0.869766 0.493464i \(-0.835730\pi\)
0.986088 0.166227i \(-0.0531584\pi\)
\(32\) −4.15744 + 1.51319i −0.734939 + 0.267496i
\(33\) −3.85948 + 8.16694i −0.671849 + 1.42168i
\(34\) 0.226015 + 1.28180i 0.0387613 + 0.219826i
\(35\) 0 0
\(36\) 1.92781 5.13202i 0.321301 0.855337i
\(37\) 2.21238 3.83195i 0.363713 0.629969i −0.624856 0.780740i \(-0.714842\pi\)
0.988569 + 0.150771i \(0.0481756\pi\)
\(38\) −0.162939 0.0593049i −0.0264322 0.00962052i
\(39\) −0.0222303 + 0.0220032i −0.00355970 + 0.00352334i
\(40\) 0 0
\(41\) −2.81517 2.36221i −0.439655 0.368915i 0.395925 0.918283i \(-0.370424\pi\)
−0.835580 + 0.549368i \(0.814868\pi\)
\(42\) −0.674919 + 0.668024i −0.104142 + 0.103078i
\(43\) −7.80685 2.84146i −1.19053 0.433319i −0.330622 0.943763i \(-0.607259\pi\)
−0.859911 + 0.510445i \(0.829481\pi\)
\(44\) −4.76508 + 8.25337i −0.718363 + 1.24424i
\(45\) 0 0
\(46\) −0.214876 0.372177i −0.0316818 0.0548745i
\(47\) 1.23254 + 6.99008i 0.179784 + 1.01961i 0.932475 + 0.361234i \(0.117644\pi\)
−0.752691 + 0.658374i \(0.771245\pi\)
\(48\) 2.21579 4.68877i 0.319821 0.676766i
\(49\) 4.94145 1.79854i 0.705921 0.256934i
\(50\) 0 0
\(51\) −4.42881 3.13510i −0.620158 0.439001i
\(52\) −0.0252794 + 0.0212119i −0.00350562 + 0.00294157i
\(53\) 1.30057 0.178648 0.0893238 0.996003i \(-0.471529\pi\)
0.0893238 + 0.996003i \(0.471529\pi\)
\(54\) −0.882118 1.97038i −0.120041 0.268135i
\(55\) 0 0
\(56\) −1.60747 + 1.34883i −0.214808 + 0.180245i
\(57\) 0.656707 0.302133i 0.0869830 0.0400185i
\(58\) −0.563252 + 3.19436i −0.0739586 + 0.419440i
\(59\) 3.47856 1.26609i 0.452871 0.164831i −0.105507 0.994419i \(-0.533646\pi\)
0.558377 + 0.829587i \(0.311424\pi\)
\(60\) 0 0
\(61\) 1.20064 + 6.80919i 0.153727 + 0.871828i 0.959941 + 0.280204i \(0.0904020\pi\)
−0.806214 + 0.591624i \(0.798487\pi\)
\(62\) −0.774775 1.34195i −0.0983965 0.170428i
\(63\) 0.0406486 3.95868i 0.00512125 0.498747i
\(64\) 2.07506 3.59410i 0.259382 0.449263i
\(65\) 0 0
\(66\) 0.952697 + 3.62996i 0.117269 + 0.446817i
\(67\) 8.44702 + 7.08789i 1.03197 + 0.865923i 0.991084 0.133241i \(-0.0425383\pi\)
0.0408835 + 0.999164i \(0.486983\pi\)
\(68\) −4.38548 3.67985i −0.531817 0.446247i
\(69\) 1.72816 + 0.472581i 0.208046 + 0.0568921i
\(70\) 0 0
\(71\) 3.04214 5.26914i 0.361035 0.625332i −0.627096 0.778942i \(-0.715757\pi\)
0.988132 + 0.153610i \(0.0490900\pi\)
\(72\) −1.58548 4.49927i −0.186850 0.530245i
\(73\) −0.273486 0.473692i −0.0320092 0.0554415i 0.849577 0.527465i \(-0.176857\pi\)
−0.881586 + 0.472023i \(0.843524\pi\)
\(74\) −0.319224 1.81041i −0.0371090 0.210456i
\(75\) 0 0
\(76\) 0.716670 0.260847i 0.0822077 0.0299212i
\(77\) −1.19507 + 6.77756i −0.136190 + 0.772374i
\(78\) −0.00119904 + 0.0129396i −0.000135765 + 0.00146512i
\(79\) 0.374706 0.314416i 0.0421577 0.0353745i −0.621465 0.783442i \(-0.713462\pi\)
0.663623 + 0.748067i \(0.269018\pi\)
\(80\) 0 0
\(81\) 8.39224 + 3.25120i 0.932471 + 0.361244i
\(82\) −1.52681 −0.168608
\(83\) −3.53428 + 2.96561i −0.387937 + 0.325518i −0.815809 0.578321i \(-0.803708\pi\)
0.427872 + 0.903839i \(0.359263\pi\)
\(84\) 0.385389 4.15898i 0.0420493 0.453782i
\(85\) 0 0
\(86\) −3.24348 + 1.18053i −0.349754 + 0.127300i
\(87\) −7.69922 11.1167i −0.825443 1.19183i
\(88\) 1.44005 + 8.16694i 0.153510 + 0.870599i
\(89\) 1.68653 + 2.92116i 0.178772 + 0.309642i 0.941460 0.337124i \(-0.109454\pi\)
−0.762688 + 0.646766i \(0.776121\pi\)
\(90\) 0 0
\(91\) −0.0119153 + 0.0206379i −0.00124906 + 0.00216344i
\(92\) 1.77623 + 0.646495i 0.185185 + 0.0674018i
\(93\) 6.23118 + 1.70398i 0.646144 + 0.176694i
\(94\) 2.25902 + 1.89554i 0.233000 + 0.195510i
\(95\) 0 0
\(96\) −1.94531 7.41201i −0.198543 0.756485i
\(97\) 9.34182 + 3.40014i 0.948518 + 0.345232i 0.769524 0.638618i \(-0.220493\pi\)
0.178994 + 0.983850i \(0.442716\pi\)
\(98\) 1.09238 1.89206i 0.110347 0.191127i
\(99\) −13.4684 7.96149i −1.35363 0.800160i
\(100\) 0 0
\(101\) 2.39626 + 13.5898i 0.238436 + 1.35224i 0.835255 + 0.549863i \(0.185320\pi\)
−0.596818 + 0.802377i \(0.703569\pi\)
\(102\) −2.24679 + 0.184950i −0.222465 + 0.0183128i
\(103\) 4.28981 1.56136i 0.422687 0.153846i −0.121914 0.992541i \(-0.538903\pi\)
0.544601 + 0.838695i \(0.316681\pi\)
\(104\) −0.00498644 + 0.0282795i −0.000488961 + 0.00277303i
\(105\) 0 0
\(106\) 0.413928 0.347327i 0.0402042 0.0337354i
\(107\) 11.2965 1.09207 0.546035 0.837762i \(-0.316136\pi\)
0.546035 + 0.837762i \(0.316136\pi\)
\(108\) 8.54292 + 4.14499i 0.822043 + 0.398851i
\(109\) 14.5032 1.38915 0.694577 0.719419i \(-0.255592\pi\)
0.694577 + 0.719419i \(0.255592\pi\)
\(110\) 0 0
\(111\) 6.25525 + 4.42801i 0.593722 + 0.420288i
\(112\) 0.686107 3.89110i 0.0648310 0.367675i
\(113\) 11.8011 4.29523i 1.11015 0.404062i 0.279102 0.960262i \(-0.409963\pi\)
0.831049 + 0.556200i \(0.187741\pi\)
\(114\) 0.128321 0.271536i 0.0120183 0.0254317i
\(115\) 0 0
\(116\) −7.13341 12.3554i −0.662321 1.14717i
\(117\) −0.0343954 0.0418563i −0.00317986 0.00386961i
\(118\) 0.768989 1.33193i 0.0707912 0.122614i
\(119\) −3.88481 1.41395i −0.356120 0.129617i
\(120\) 0 0
\(121\) 12.4085 + 10.4120i 1.12805 + 0.946544i
\(122\) 2.20056 + 1.84649i 0.199230 + 0.167174i
\(123\) 4.52391 4.47770i 0.407907 0.403740i
\(124\) 6.40452 + 2.33105i 0.575143 + 0.209335i
\(125\) 0 0
\(126\) −1.04425 1.27077i −0.0930295 0.113209i
\(127\) −4.19749 7.27027i −0.372467 0.645132i 0.617477 0.786589i \(-0.288155\pi\)
−0.989944 + 0.141456i \(0.954821\pi\)
\(128\) −1.83594 10.4121i −0.162276 0.920310i
\(129\) 6.14821 13.0101i 0.541319 1.14547i
\(130\) 0 0
\(131\) −2.69761 + 15.2989i −0.235691 + 1.33667i 0.605463 + 0.795874i \(0.292988\pi\)
−0.841154 + 0.540796i \(0.818123\pi\)
\(132\) −13.4727 9.53717i −1.17265 0.830104i
\(133\) 0.421899 0.354015i 0.0365833 0.0306970i
\(134\) 4.58126 0.395761
\(135\) 0 0
\(136\) −4.98162 −0.427170
\(137\) −9.19820 + 7.71820i −0.785855 + 0.659411i −0.944716 0.327890i \(-0.893662\pi\)
0.158861 + 0.987301i \(0.449218\pi\)
\(138\) 0.676219 0.311110i 0.0575636 0.0264834i
\(139\) 1.06709 6.05176i 0.0905093 0.513304i −0.905522 0.424299i \(-0.860520\pi\)
0.996031 0.0890042i \(-0.0283685\pi\)
\(140\) 0 0
\(141\) −12.2525 + 1.00860i −1.03185 + 0.0849392i
\(142\) −0.438950 2.48941i −0.0368359 0.208907i
\(143\) 0.0470893 + 0.0815610i 0.00393780 + 0.00682047i
\(144\) 7.73243 + 4.57082i 0.644369 + 0.380901i
\(145\) 0 0
\(146\) −0.213544 0.0777237i −0.0176730 0.00643246i
\(147\) 2.31216 + 8.80976i 0.190704 + 0.726617i
\(148\) 6.19404 + 5.19742i 0.509147 + 0.427225i
\(149\) 0.676280 + 0.567466i 0.0554030 + 0.0464886i 0.670069 0.742299i \(-0.266265\pi\)
−0.614666 + 0.788788i \(0.710709\pi\)
\(150\) 0 0
\(151\) −7.72942 2.81328i −0.629011 0.228941i 0.00778980 0.999970i \(-0.497520\pi\)
−0.636801 + 0.771028i \(0.719743\pi\)
\(152\) 0.331826 0.574740i 0.0269147 0.0466176i
\(153\) 6.11477 7.13717i 0.494350 0.577006i
\(154\) 1.42964 + 2.47621i 0.115204 + 0.199539i
\(155\) 0 0
\(156\) −0.0325434 0.0469884i −0.00260556 0.00376208i
\(157\) 11.8024 4.29571i 0.941932 0.342835i 0.175003 0.984568i \(-0.444006\pi\)
0.766928 + 0.641733i \(0.221784\pi\)
\(158\) 0.0352893 0.200135i 0.00280746 0.0159219i
\(159\) −0.207851 + 2.24305i −0.0164836 + 0.177886i
\(160\) 0 0
\(161\) 1.36501 0.107578
\(162\) 3.53922 1.20646i 0.278067 0.0947884i
\(163\) −3.31466 −0.259624 −0.129812 0.991539i \(-0.541437\pi\)
−0.129812 + 0.991539i \(0.541437\pi\)
\(164\) 5.14440 4.31667i 0.401710 0.337075i
\(165\) 0 0
\(166\) −0.332853 + 1.88770i −0.0258344 + 0.146514i
\(167\) −19.3229 + 7.03295i −1.49525 + 0.544226i −0.954826 0.297167i \(-0.903958\pi\)
−0.540424 + 0.841393i \(0.681736\pi\)
\(168\) −2.06938 2.98791i −0.159656 0.230522i
\(169\) −2.25737 12.8022i −0.173644 0.984783i
\(170\) 0 0
\(171\) 0.416126 + 1.18088i 0.0318219 + 0.0903044i
\(172\) 7.59085 13.1477i 0.578797 1.00251i
\(173\) 13.1870 + 4.79966i 1.00259 + 0.364911i 0.790581 0.612357i \(-0.209779\pi\)
0.212005 + 0.977269i \(0.432001\pi\)
\(174\) −5.41917 1.48192i −0.410827 0.112344i
\(175\) 0 0
\(176\) −11.9617 10.0371i −0.901648 0.756572i
\(177\) 1.62766 + 6.20169i 0.122342 + 0.466148i
\(178\) 1.31688 + 0.479305i 0.0987043 + 0.0359254i
\(179\) −5.09500 + 8.82479i −0.380818 + 0.659596i −0.991179 0.132527i \(-0.957691\pi\)
0.610361 + 0.792123i \(0.291024\pi\)
\(180\) 0 0
\(181\) −12.0274 20.8320i −0.893987 1.54843i −0.835054 0.550169i \(-0.814563\pi\)
−0.0589331 0.998262i \(-0.518770\pi\)
\(182\) 0.00171925 + 0.00975037i 0.000127440 + 0.000722746i
\(183\) −11.9354 + 0.982498i −0.882293 + 0.0726283i
\(184\) 1.54563 0.562565i 0.113946 0.0414728i
\(185\) 0 0
\(186\) 2.43823 1.12176i 0.178780 0.0822516i
\(187\) −12.5157 + 10.5019i −0.915240 + 0.767978i
\(188\) −12.9706 −0.945981
\(189\) 6.82089 + 0.702760i 0.496146 + 0.0511182i
\(190\) 0 0
\(191\) 8.38541 7.03619i 0.606747 0.509121i −0.286860 0.957973i \(-0.592611\pi\)
0.893606 + 0.448852i \(0.148167\pi\)
\(192\) 5.86699 + 4.15316i 0.423414 + 0.299729i
\(193\) 1.87644 10.6418i 0.135069 0.766013i −0.839743 0.542984i \(-0.817294\pi\)
0.974812 0.223029i \(-0.0715945\pi\)
\(194\) 3.88121 1.41265i 0.278655 0.101422i
\(195\) 0 0
\(196\) 1.66867 + 9.46347i 0.119190 + 0.675962i
\(197\) −11.0367 19.1161i −0.786331 1.36196i −0.928201 0.372080i \(-0.878645\pi\)
0.141870 0.989885i \(-0.454689\pi\)
\(198\) −6.41270 + 1.06296i −0.455731 + 0.0755413i
\(199\) −6.44338 + 11.1603i −0.456759 + 0.791130i −0.998787 0.0492301i \(-0.984323\pi\)
0.542028 + 0.840360i \(0.317657\pi\)
\(200\) 0 0
\(201\) −13.5742 + 13.4355i −0.957448 + 0.947667i
\(202\) 4.39190 + 3.68524i 0.309013 + 0.259293i
\(203\) −7.89228 6.62241i −0.553929 0.464802i
\(204\) 7.04736 6.97537i 0.493414 0.488374i
\(205\) 0 0
\(206\) 0.948326 1.64255i 0.0660730 0.114442i
\(207\) −1.09123 + 2.90496i −0.0758456 + 0.201909i
\(208\) −0.0270347 0.0468255i −0.00187452 0.00324676i
\(209\) −0.377957 2.14350i −0.0261439 0.148269i
\(210\) 0 0
\(211\) 22.5485 8.20699i 1.55230 0.564992i 0.583347 0.812223i \(-0.301743\pi\)
0.968957 + 0.247230i \(0.0795204\pi\)
\(212\) −0.412702 + 2.34055i −0.0283445 + 0.160749i
\(213\) 8.60131 + 6.08875i 0.589352 + 0.417194i
\(214\) 3.59528 3.01680i 0.245768 0.206224i
\(215\) 0 0
\(216\) 8.01311 2.01536i 0.545223 0.137128i
\(217\) 4.92177 0.334112
\(218\) 4.61587 3.87317i 0.312626 0.262324i
\(219\) 0.860667 0.395969i 0.0581585 0.0267571i
\(220\) 0 0
\(221\) −0.0531618 + 0.0193493i −0.00357605 + 0.00130158i
\(222\) 3.17336 0.261224i 0.212982 0.0175322i
\(223\) −3.76160 21.3331i −0.251895 1.42857i −0.803918 0.594740i \(-0.797255\pi\)
0.552023 0.833829i \(-0.313856\pi\)
\(224\) −2.91919 5.05618i −0.195047 0.337831i
\(225\) 0 0
\(226\) 2.60880 4.51858i 0.173535 0.300571i
\(227\) 20.3367 + 7.40196i 1.34979 + 0.491285i 0.912884 0.408220i \(-0.133850\pi\)
0.436911 + 0.899505i \(0.356072\pi\)
\(228\) 0.335338 + 1.27770i 0.0222083 + 0.0846178i
\(229\) −8.27739 6.94555i −0.546985 0.458975i 0.326934 0.945047i \(-0.393985\pi\)
−0.873919 + 0.486072i \(0.838429\pi\)
\(230\) 0 0
\(231\) −11.4980 3.14424i −0.756513 0.206876i
\(232\) −11.6660 4.24606i −0.765908 0.278768i
\(233\) 3.81950 6.61557i 0.250224 0.433400i −0.713364 0.700794i \(-0.752829\pi\)
0.963587 + 0.267394i \(0.0861625\pi\)
\(234\) −0.0221249 0.00413588i −0.00144635 0.000270371i
\(235\) 0 0
\(236\) 1.17467 + 6.66187i 0.0764644 + 0.433651i
\(237\) 0.482377 + 0.696490i 0.0313338 + 0.0452419i
\(238\) −1.61401 + 0.587451i −0.104621 + 0.0380788i
\(239\) −0.561143 + 3.18240i −0.0362973 + 0.205852i −0.997563 0.0697711i \(-0.977773\pi\)
0.961266 + 0.275623i \(0.0888842\pi\)
\(240\) 0 0
\(241\) −20.3346 + 17.0628i −1.30987 + 1.09911i −0.321518 + 0.946903i \(0.604193\pi\)
−0.988349 + 0.152206i \(0.951362\pi\)
\(242\) 6.72979 0.432608
\(243\) −6.94842 + 13.9542i −0.445741 + 0.895162i
\(244\) −12.6350 −0.808873
\(245\) 0 0
\(246\) 0.244007 2.63324i 0.0155573 0.167889i
\(247\) 0.00130875 0.00742226i 8.32735e−5 0.000472267i
\(248\) 5.57306 2.02843i 0.353890 0.128805i
\(249\) −4.54985 6.56938i −0.288335 0.416318i
\(250\) 0 0
\(251\) 2.24965 + 3.89651i 0.141997 + 0.245945i 0.928248 0.371961i \(-0.121314\pi\)
−0.786252 + 0.617906i \(0.787981\pi\)
\(252\) 7.11124 + 1.32933i 0.447966 + 0.0837399i
\(253\) 2.69726 4.67179i 0.169575 0.293713i
\(254\) −3.27749 1.19291i −0.205648 0.0748498i
\(255\) 0 0
\(256\) 2.99340 + 2.51176i 0.187088 + 0.156985i
\(257\) −10.5219 8.82895i −0.656340 0.550735i 0.252647 0.967559i \(-0.418699\pi\)
−0.908987 + 0.416824i \(0.863143\pi\)
\(258\) −1.51766 5.78258i −0.0944854 0.360007i
\(259\) 5.48690 + 1.99707i 0.340939 + 0.124092i
\(260\) 0 0
\(261\) 20.4029 11.5020i 1.26291 0.711953i
\(262\) 3.22711 + 5.58952i 0.199372 + 0.345322i
\(263\) 4.20273 + 23.8349i 0.259151 + 1.46972i 0.785187 + 0.619258i \(0.212567\pi\)
−0.526036 + 0.850462i \(0.676322\pi\)
\(264\) −14.3154 + 1.17841i −0.881049 + 0.0725260i
\(265\) 0 0
\(266\) 0.0397339 0.225342i 0.00243624 0.0138166i
\(267\) −5.30755 + 2.44185i −0.324817 + 0.149439i
\(268\) −15.4360 + 12.9523i −0.942902 + 0.791189i
\(269\) 12.0062 0.732032 0.366016 0.930609i \(-0.380722\pi\)
0.366016 + 0.930609i \(0.380722\pi\)
\(270\) 0 0
\(271\) 3.71777 0.225839 0.112919 0.993604i \(-0.463980\pi\)
0.112919 + 0.993604i \(0.463980\pi\)
\(272\) 7.18547 6.02933i 0.435683 0.365582i
\(273\) −0.0336891 0.0238481i −0.00203896 0.00144335i
\(274\) −0.866273 + 4.91288i −0.0523335 + 0.296798i
\(275\) 0 0
\(276\) −1.39885 + 2.96008i −0.0842011 + 0.178176i
\(277\) 4.07780 + 23.1264i 0.245011 + 1.38953i 0.820466 + 0.571695i \(0.193714\pi\)
−0.575455 + 0.817833i \(0.695175\pi\)
\(278\) −1.27654 2.21104i −0.0765621 0.132609i
\(279\) −3.93462 + 10.4744i −0.235559 + 0.627084i
\(280\) 0 0
\(281\) 19.1432 + 6.96754i 1.14199 + 0.415649i 0.842630 0.538493i \(-0.181006\pi\)
0.299356 + 0.954142i \(0.403228\pi\)
\(282\) −3.63020 + 3.59311i −0.216175 + 0.213967i
\(283\) −8.88607 7.45630i −0.528222 0.443231i 0.339265 0.940691i \(-0.389822\pi\)
−0.867487 + 0.497460i \(0.834266\pi\)
\(284\) 8.51714 + 7.14673i 0.505399 + 0.424080i
\(285\) 0 0
\(286\) 0.0367683 + 0.0133826i 0.00217416 + 0.000791328i
\(287\) 2.42478 4.19984i 0.143130 0.247909i
\(288\) 13.0941 2.17046i 0.771578 0.127896i
\(289\) 3.59280 + 6.22291i 0.211341 + 0.366053i
\(290\) 0 0
\(291\) −7.35706 + 15.5681i −0.431279 + 0.912618i
\(292\) 0.939253 0.341860i 0.0549656 0.0200058i
\(293\) −5.48280 + 31.0945i −0.320308 + 1.81656i 0.220470 + 0.975394i \(0.429241\pi\)
−0.540779 + 0.841165i \(0.681870\pi\)
\(294\) 3.08858 + 2.18637i 0.180130 + 0.127511i
\(295\) 0 0
\(296\) 7.03603 0.408961
\(297\) 15.8833 21.9561i 0.921644 1.27402i
\(298\) 0.366782 0.0212471
\(299\) 0.0143093 0.0120069i 0.000827529 0.000694379i
\(300\) 0 0
\(301\) 1.90376 10.7968i 0.109731 0.622315i
\(302\) −3.21131 + 1.16882i −0.184790 + 0.0672581i
\(303\) −23.8208 + 1.96088i −1.36847 + 0.112649i
\(304\) 0.216991 + 1.23062i 0.0124453 + 0.0705809i
\(305\) 0 0
\(306\) 0.0400924 3.90451i 0.00229193 0.223206i
\(307\) −4.06027 + 7.03259i −0.231732 + 0.401371i −0.958318 0.285704i \(-0.907773\pi\)
0.726586 + 0.687075i \(0.241106\pi\)
\(308\) −11.8178 4.30134i −0.673384 0.245092i
\(309\) 2.00725 + 7.64800i 0.114188 + 0.435079i
\(310\) 0 0
\(311\) −18.2691 15.3296i −1.03594 0.869259i −0.0443970 0.999014i \(-0.514137\pi\)
−0.991546 + 0.129754i \(0.958581\pi\)
\(312\) −0.0479757 0.0131194i −0.00271609 0.000742740i
\(313\) 25.2876 + 9.20392i 1.42934 + 0.520236i 0.936742 0.350022i \(-0.113826\pi\)
0.492596 + 0.870258i \(0.336048\pi\)
\(314\) 2.60909 4.51908i 0.147240 0.255026i
\(315\) 0 0
\(316\) 0.446928 + 0.774102i 0.0251417 + 0.0435466i
\(317\) 1.44689 + 8.20574i 0.0812657 + 0.460881i 0.998100 + 0.0616130i \(0.0196244\pi\)
−0.916834 + 0.399268i \(0.869264\pi\)
\(318\) 0.532870 + 0.769394i 0.0298819 + 0.0431455i
\(319\) −38.2606 + 13.9257i −2.14218 + 0.779692i
\(320\) 0 0
\(321\) −1.80534 + 19.4826i −0.100764 + 1.08741i
\(322\) 0.434435 0.364534i 0.0242101 0.0203147i
\(323\) 1.30748 0.0727501
\(324\) −8.51398 + 14.0712i −0.472999 + 0.781734i
\(325\) 0 0
\(326\) −1.05494 + 0.885201i −0.0584278 + 0.0490268i
\(327\) −2.31782 + 25.0131i −0.128176 + 1.38323i
\(328\) 1.01475 5.75493i 0.0560301 0.317763i
\(329\) −8.80173 + 3.20357i −0.485255 + 0.176618i
\(330\) 0 0
\(331\) −1.11487 6.32272i −0.0612786 0.347528i −0.999996 0.00284030i \(-0.999096\pi\)
0.938717 0.344688i \(-0.112015\pi\)
\(332\) −4.21548 7.30143i −0.231355 0.400718i
\(333\) −8.63650 + 10.0805i −0.473277 + 0.552410i
\(334\) −4.27161 + 7.39865i −0.233732 + 0.404836i
\(335\) 0 0
\(336\) 6.60119 + 1.80516i 0.360124 + 0.0984794i
\(337\) −5.72610 4.80477i −0.311921 0.261732i 0.473365 0.880867i \(-0.343039\pi\)
−0.785285 + 0.619134i \(0.787484\pi\)
\(338\) −4.13735 3.47165i −0.225042 0.188833i
\(339\) 5.52185 + 21.0393i 0.299906 + 1.14270i
\(340\) 0 0
\(341\) 9.72545 16.8450i 0.526663 0.912206i
\(342\) 0.447801 + 0.264706i 0.0242143 + 0.0143136i
\(343\) 8.08839 + 14.0095i 0.436732 + 0.756442i
\(344\) −2.29403 13.0101i −0.123686 0.701456i
\(345\) 0 0
\(346\) 5.47874 1.99410i 0.294539 0.107203i
\(347\) 5.46202 30.9766i 0.293216 1.66291i −0.381148 0.924514i \(-0.624471\pi\)
0.674364 0.738399i \(-0.264418\pi\)
\(348\) 22.4490 10.3281i 1.20339 0.553647i
\(349\) 9.07988 7.61893i 0.486035 0.407832i −0.366568 0.930391i \(-0.619467\pi\)
0.852603 + 0.522560i \(0.175023\pi\)
\(350\) 0 0
\(351\) 0.0776848 0.0526312i 0.00414651 0.00280925i
\(352\) −23.0733 −1.22981
\(353\) 6.28699 5.27541i 0.334623 0.280782i −0.459958 0.887941i \(-0.652135\pi\)
0.794580 + 0.607159i \(0.207691\pi\)
\(354\) 2.17423 + 1.53911i 0.115559 + 0.0818026i
\(355\) 0 0
\(356\) −5.79217 + 2.10818i −0.306984 + 0.111733i
\(357\) 3.05944 6.47401i 0.161923 0.342641i
\(358\) 0.735157 + 4.16928i 0.0388542 + 0.220353i
\(359\) −8.86365 15.3523i −0.467806 0.810263i 0.531517 0.847047i \(-0.321622\pi\)
−0.999323 + 0.0367840i \(0.988289\pi\)
\(360\) 0 0
\(361\) 9.41291 16.3036i 0.495416 0.858086i
\(362\) −9.39122 3.41812i −0.493591 0.179653i
\(363\) −19.9402 + 19.7365i −1.04659 + 1.03590i
\(364\) −0.0333594 0.0279919i −0.00174851 0.00146717i
\(365\) 0 0
\(366\) −3.53626 + 3.50013i −0.184843 + 0.182955i
\(367\) −19.0941 6.94969i −0.996704 0.362771i −0.208392 0.978045i \(-0.566823\pi\)
−0.788313 + 0.615275i \(0.789045\pi\)
\(368\) −1.54854 + 2.68215i −0.0807232 + 0.139817i
\(369\) 6.99953 + 8.51782i 0.364381 + 0.443420i
\(370\) 0 0
\(371\) 0.298028 + 1.69020i 0.0154728 + 0.0877509i
\(372\) −5.04381 + 10.6731i −0.261510 + 0.553374i
\(373\) −9.09758 + 3.31125i −0.471055 + 0.171450i −0.566630 0.823972i \(-0.691753\pi\)
0.0955754 + 0.995422i \(0.469531\pi\)
\(374\) −1.17871 + 6.68481i −0.0609498 + 0.345663i
\(375\) 0 0
\(376\) −8.64615 + 7.25498i −0.445891 + 0.374147i
\(377\) −0.140987 −0.00726119
\(378\) 2.35853 1.59790i 0.121310 0.0821870i
\(379\) −4.12905 −0.212095 −0.106048 0.994361i \(-0.533820\pi\)
−0.106048 + 0.994361i \(0.533820\pi\)
\(380\) 0 0
\(381\) 13.2096 6.07736i 0.676748 0.311353i
\(382\) 0.789725 4.47876i 0.0404059 0.229153i
\(383\) 4.46371 1.62466i 0.228085 0.0830162i −0.225450 0.974255i \(-0.572385\pi\)
0.453535 + 0.891239i \(0.350163\pi\)
\(384\) 18.2508 1.50236i 0.931357 0.0766672i
\(385\) 0 0
\(386\) −2.24476 3.88803i −0.114255 0.197896i
\(387\) 21.4554 + 12.6828i 1.09064 + 0.644702i
\(388\) −9.08336 + 15.7328i −0.461138 + 0.798714i
\(389\) 20.4978 + 7.46059i 1.03928 + 0.378267i 0.804607 0.593807i \(-0.202376\pi\)
0.234673 + 0.972074i \(0.424598\pi\)
\(390\) 0 0
\(391\) 2.48238 + 2.08297i 0.125539 + 0.105340i
\(392\) 6.40561 + 5.37495i 0.323532 + 0.271476i
\(393\) −25.9543 7.09745i −1.30922 0.358019i
\(394\) −8.61767 3.13658i −0.434152 0.158018i
\(395\) 0 0
\(396\) 18.6015 21.7117i 0.934762 1.09106i
\(397\) −17.4245 30.1802i −0.874512 1.51470i −0.857282 0.514847i \(-0.827849\pi\)
−0.0172294 0.999852i \(-0.505485\pi\)
\(398\) 0.929715 + 5.27268i 0.0466024 + 0.264295i
\(399\) 0.543131 + 0.784210i 0.0271906 + 0.0392596i
\(400\) 0 0
\(401\) −3.26911 + 18.5401i −0.163252 + 0.925847i 0.787597 + 0.616191i \(0.211325\pi\)
−0.950849 + 0.309656i \(0.899786\pi\)
\(402\) −0.732152 + 7.90113i −0.0365164 + 0.394072i
\(403\) 0.0515948 0.0432932i 0.00257012 0.00215659i
\(404\) −25.2170 −1.25459
\(405\) 0 0
\(406\) −4.28040 −0.212433
\(407\) 17.6772 14.8329i 0.876226 0.735241i
\(408\) 0.796135 8.59160i 0.0394145 0.425348i
\(409\) −1.10439 + 6.26334i −0.0546088 + 0.309702i −0.999862 0.0166371i \(-0.994704\pi\)
0.945253 + 0.326339i \(0.105815\pi\)
\(410\) 0 0
\(411\) −11.8413 17.0973i −0.584088 0.843346i
\(412\) 1.44862 + 8.21551i 0.0713682 + 0.404749i
\(413\) 2.44251 + 4.23055i 0.120188 + 0.208172i
\(414\) 0.428490 + 1.21597i 0.0210591 + 0.0597617i
\(415\) 0 0
\(416\) −0.0750772 0.0273259i −0.00368096 0.00133976i
\(417\) 10.2667 + 2.80753i 0.502763 + 0.137485i
\(418\) −0.692727 0.581267i −0.0338824 0.0284307i
\(419\) −18.6286 15.6313i −0.910069 0.763638i 0.0620632 0.998072i \(-0.480232\pi\)
−0.972132 + 0.234434i \(0.924676\pi\)
\(420\) 0 0
\(421\) 7.50818 + 2.73275i 0.365926 + 0.133186i 0.518438 0.855115i \(-0.326514\pi\)
−0.152511 + 0.988302i \(0.548736\pi\)
\(422\) 4.98469 8.63373i 0.242651 0.420283i
\(423\) 0.218637 21.2926i 0.0106305 1.03528i
\(424\) 1.03405 + 1.79103i 0.0502181 + 0.0869803i
\(425\) 0 0
\(426\) 4.36354 0.359197i 0.211414 0.0174031i
\(427\) −8.57397 + 3.12067i −0.414924 + 0.151020i
\(428\) −3.58462 + 20.3294i −0.173269 + 0.982659i
\(429\) −0.148191 + 0.0681784i −0.00715472 + 0.00329169i
\(430\) 0 0
\(431\) 9.87124 0.475481 0.237740 0.971329i \(-0.423593\pi\)
0.237740 + 0.971329i \(0.423593\pi\)
\(432\) −9.11887 + 12.6053i −0.438732 + 0.606475i
\(433\) 6.10369 0.293325 0.146662 0.989187i \(-0.453147\pi\)
0.146662 + 0.989187i \(0.453147\pi\)
\(434\) 1.56643 1.31439i 0.0751911 0.0630928i
\(435\) 0 0
\(436\) −4.60219 + 26.1003i −0.220405 + 1.24998i
\(437\) −0.405669 + 0.147651i −0.0194058 + 0.00706312i
\(438\) 0.168174 0.355870i 0.00803569 0.0170041i
\(439\) −2.62800 14.9041i −0.125427 0.711334i −0.981053 0.193739i \(-0.937938\pi\)
0.855626 0.517595i \(-0.173173\pi\)
\(440\) 0 0
\(441\) −15.5634 + 2.57976i −0.741113 + 0.122846i
\(442\) −0.0117522 + 0.0203554i −0.000558996 + 0.000968210i
\(443\) −0.679204 0.247210i −0.0322699 0.0117453i 0.325835 0.945427i \(-0.394355\pi\)
−0.358105 + 0.933681i \(0.616577\pi\)
\(444\) −9.95369 + 9.85201i −0.472381 + 0.467555i
\(445\) 0 0
\(446\) −6.89432 5.78502i −0.326456 0.273929i
\(447\) −1.08677 + 1.07566i −0.0514023 + 0.0508772i
\(448\) 5.14633 + 1.87311i 0.243141 + 0.0884962i
\(449\) −0.834224 + 1.44492i −0.0393695 + 0.0681899i −0.885039 0.465517i \(-0.845868\pi\)
0.845669 + 0.533707i \(0.179202\pi\)
\(450\) 0 0
\(451\) −9.58275 16.5978i −0.451234 0.781560i
\(452\) 3.98507 + 22.6005i 0.187442 + 1.06304i
\(453\) 6.08723 12.8810i 0.286003 0.605204i
\(454\) 8.44922 3.07526i 0.396541 0.144329i
\(455\) 0 0
\(456\) 0.938202 + 0.664140i 0.0439353 + 0.0311012i
\(457\) −8.49041 + 7.12430i −0.397165 + 0.333261i −0.819397 0.573227i \(-0.805691\pi\)
0.422232 + 0.906488i \(0.361247\pi\)
\(458\) −4.48926 −0.209769
\(459\) 11.3320 + 11.6865i 0.528932 + 0.545481i
\(460\) 0 0
\(461\) −16.7644 + 14.0670i −0.780797 + 0.655166i −0.943449 0.331517i \(-0.892439\pi\)
0.162653 + 0.986683i \(0.447995\pi\)
\(462\) −4.49911 + 2.06992i −0.209318 + 0.0963012i
\(463\) −4.31546 + 24.4742i −0.200556 + 1.13741i 0.703724 + 0.710473i \(0.251519\pi\)
−0.904281 + 0.426938i \(0.859592\pi\)
\(464\) 21.9660 7.99499i 1.01975 0.371158i
\(465\) 0 0
\(466\) −0.551115 3.12553i −0.0255299 0.144787i
\(467\) −5.91777 10.2499i −0.273842 0.474308i 0.696001 0.718041i \(-0.254961\pi\)
−0.969842 + 0.243734i \(0.921628\pi\)
\(468\) 0.0862400 0.0486170i 0.00398645 0.00224732i
\(469\) −7.27564 + 12.6018i −0.335958 + 0.581896i
\(470\) 0 0
\(471\) 5.52246 + 21.0416i 0.254462 + 0.969547i
\(472\) 4.50927 + 3.78373i 0.207556 + 0.174160i
\(473\) −33.1905 27.8501i −1.52610 1.28055i
\(474\) 0.339526 + 0.0928466i 0.0155950 + 0.00426459i
\(475\) 0 0
\(476\) 3.77733 6.54252i 0.173134 0.299876i
\(477\) −3.83529 0.716944i −0.175606 0.0328266i
\(478\) 0.671288 + 1.16270i 0.0307040 + 0.0531809i
\(479\) 0.501383 + 2.84349i 0.0229088 + 0.129922i 0.994117 0.108309i \(-0.0345436\pi\)
−0.971209 + 0.238231i \(0.923432\pi\)
\(480\) 0 0
\(481\) 0.0750857 0.0273290i 0.00342361 0.00124609i
\(482\) −1.91508 + 10.8610i −0.0872297 + 0.494704i
\(483\) −0.218148 + 2.35417i −0.00992607 + 0.107119i
\(484\) −22.6752 + 19.0267i −1.03069 + 0.864852i
\(485\) 0 0
\(486\) 1.51512 + 6.29676i 0.0687271 + 0.285627i
\(487\) −8.75903 −0.396910 −0.198455 0.980110i \(-0.563592\pi\)
−0.198455 + 0.980110i \(0.563592\pi\)
\(488\) −8.42241 + 7.06724i −0.381265 + 0.319919i
\(489\) 0.529731 5.71667i 0.0239553 0.258517i
\(490\) 0 0
\(491\) 21.2117 7.72044i 0.957272 0.348418i 0.184308 0.982869i \(-0.440996\pi\)
0.772964 + 0.634450i \(0.218773\pi\)
\(492\) 6.62264 + 9.56222i 0.298572 + 0.431098i
\(493\) −4.24716 24.0869i −0.191283 1.08482i
\(494\) −0.00156564 0.00271176i −7.04413e−5 0.000122008i
\(495\) 0 0
\(496\) −5.58354 + 9.67097i −0.250708 + 0.434239i
\(497\) 7.54478 + 2.74608i 0.338430 + 0.123178i
\(498\) −3.20246 0.875741i −0.143505 0.0392429i
\(499\) −19.4061 16.2836i −0.868734 0.728955i 0.0950968 0.995468i \(-0.469684\pi\)
−0.963831 + 0.266513i \(0.914128\pi\)
\(500\) 0 0
\(501\) −9.04139 34.4494i −0.403940 1.53909i
\(502\) 1.75657 + 0.639340i 0.0783997 + 0.0285352i
\(503\) 1.87207 3.24252i 0.0834714 0.144577i −0.821267 0.570543i \(-0.806733\pi\)
0.904739 + 0.425967i \(0.140066\pi\)
\(504\) 5.48386 3.09147i 0.244270 0.137705i
\(505\) 0 0
\(506\) −0.389187 2.20719i −0.0173015 0.0981216i
\(507\) 22.4402 1.84723i 0.996604 0.0820382i
\(508\) 14.4157 5.24690i 0.639595 0.232793i
\(509\) 4.22831 23.9800i 0.187417 1.06289i −0.735394 0.677640i \(-0.763003\pi\)
0.922811 0.385253i \(-0.125886\pi\)
\(510\) 0 0
\(511\) 0.552932 0.463965i 0.0244603 0.0205246i
\(512\) 22.7690 1.00626
\(513\) −2.10313 + 0.528954i −0.0928554 + 0.0233539i
\(514\) −5.70660 −0.251707
\(515\) 0 0
\(516\) 21.4623 + 15.1929i 0.944824 + 0.668828i
\(517\) −6.42792 + 36.4546i −0.282700 + 1.60327i
\(518\) 2.27962 0.829715i 0.100161 0.0364556i
\(519\) −10.3853 + 21.9760i −0.455862 + 0.964639i
\(520\) 0 0
\(521\) −9.81046 16.9922i −0.429804 0.744443i 0.567051 0.823682i \(-0.308084\pi\)
−0.996856 + 0.0792397i \(0.974751\pi\)
\(522\) 3.42188 9.10941i 0.149772 0.398708i
\(523\) 10.4077 18.0267i 0.455097 0.788251i −0.543597 0.839346i \(-0.682938\pi\)
0.998694 + 0.0510956i \(0.0162713\pi\)
\(524\) −26.6763 9.70937i −1.16536 0.424156i
\(525\) 0 0
\(526\) 7.70284 + 6.46345i 0.335860 + 0.281820i
\(527\) 8.95067 + 7.51051i 0.389897 + 0.327163i
\(528\) 19.2222 19.0258i 0.836539 0.827993i
\(529\) 20.6075 + 7.50052i 0.895978 + 0.326109i
\(530\) 0 0
\(531\) −10.9559 + 1.81604i −0.475447 + 0.0788095i
\(532\) 0.503217 + 0.871598i 0.0218172 + 0.0377886i
\(533\) −0.0115240 0.0653558i −0.000499159 0.00283087i
\(534\) −1.03710 + 2.19457i −0.0448795 + 0.0949685i
\(535\) 0 0
\(536\) −3.04479 + 17.2679i −0.131515 + 0.745859i
\(537\) −14.4055 10.1975i −0.621645 0.440054i
\(538\) 3.82117 3.20634i 0.164742 0.138235i
\(539\) 27.4245 1.18126
\(540\) 0 0
\(541\) −30.6272 −1.31676 −0.658382 0.752684i \(-0.728759\pi\)
−0.658382 + 0.752684i \(0.728759\pi\)
\(542\) 1.18324 0.992856i 0.0508245 0.0426468i
\(543\) 37.8503 17.4139i 1.62431 0.747301i
\(544\) 2.40681 13.6497i 0.103191 0.585227i
\(545\) 0 0
\(546\) −0.0170909 + 0.00140688i −0.000731421 + 6.02089e-5i
\(547\) −3.93273 22.3036i −0.168151 0.953633i −0.945756 0.324879i \(-0.894676\pi\)
0.777604 0.628754i \(-0.216435\pi\)
\(548\) −10.9711 19.0025i −0.468661 0.811745i
\(549\) 0.212980 20.7416i 0.00908976 0.885231i
\(550\) 0 0
\(551\) 3.06186 + 1.11443i 0.130440 + 0.0474761i
\(552\) 0.723220 + 2.75560i 0.0307823 + 0.117286i
\(553\) 0.494473 + 0.414912i 0.0210271 + 0.0176439i
\(554\) 7.47387 + 6.27132i 0.317534 + 0.266443i
\(555\) 0 0
\(556\) 10.5523 + 3.84072i 0.447517 + 0.162883i
\(557\) 18.2259 31.5682i 0.772256 1.33759i −0.164067 0.986449i \(-0.552461\pi\)
0.936324 0.351138i \(-0.114205\pi\)
\(558\) 1.54500 + 4.38440i 0.0654049 + 0.185606i
\(559\) −0.0750139 0.129928i −0.00317275 0.00549537i
\(560\) 0 0
\(561\) −16.1121 23.2637i −0.680253 0.982196i
\(562\) 7.95334 2.89478i 0.335491 0.122109i
\(563\) −4.60450 + 26.1134i −0.194056 + 1.10055i 0.719700 + 0.694285i \(0.244279\pi\)
−0.913756 + 0.406263i \(0.866832\pi\)
\(564\) 2.07290 22.3700i 0.0872847 0.941945i
\(565\) 0 0
\(566\) −4.81938 −0.202574
\(567\) −2.30210 + 11.6514i −0.0966791 + 0.489313i
\(568\) 9.67492 0.405950
\(569\) 17.5941 14.7632i 0.737581 0.618904i −0.194606 0.980882i \(-0.562343\pi\)
0.932187 + 0.361978i \(0.117898\pi\)
\(570\) 0 0
\(571\) −0.833165 + 4.72511i −0.0348669 + 0.197740i −0.997266 0.0739009i \(-0.976455\pi\)
0.962399 + 0.271641i \(0.0875662\pi\)
\(572\) −0.161722 + 0.0588619i −0.00676193 + 0.00246114i
\(573\) 10.7949 + 15.5865i 0.450965 + 0.651134i
\(574\) −0.349871 1.98422i −0.0146033 0.0828197i
\(575\) 0 0
\(576\) −8.10043 + 9.45484i −0.337518 + 0.393952i
\(577\) −2.15666 + 3.73545i −0.0897831 + 0.155509i −0.907419 0.420226i \(-0.861951\pi\)
0.817636 + 0.575735i \(0.195284\pi\)
\(578\) 2.80533 + 1.02106i 0.116686 + 0.0424704i
\(579\) 18.0536 + 4.93693i 0.750283 + 0.205172i
\(580\) 0 0
\(581\) −4.66393 3.91351i −0.193493 0.162360i
\(582\) 1.81606 + 6.91954i 0.0752782 + 0.286824i
\(583\) 6.37369 + 2.31983i 0.263971 + 0.0960777i
\(584\) 0.434885 0.753242i 0.0179957 0.0311694i
\(585\) 0 0
\(586\) 6.55900 + 11.3605i 0.270950 + 0.469299i
\(587\) −7.26235 41.1868i −0.299749 1.69996i −0.647246 0.762281i \(-0.724079\pi\)
0.347497 0.937681i \(-0.387032\pi\)
\(588\) −16.5880 + 1.36548i −0.684076 + 0.0563116i
\(589\) −1.46271 + 0.532383i −0.0602699 + 0.0219365i
\(590\) 0 0
\(591\) 34.7326 15.9795i 1.42871 0.657309i
\(592\) −10.1488 + 8.51582i −0.417111 + 0.349998i
\(593\) 31.5370 1.29507 0.647536 0.762035i \(-0.275800\pi\)
0.647536 + 0.762035i \(0.275800\pi\)
\(594\) −0.808405 11.2296i −0.0331693 0.460757i
\(595\) 0 0
\(596\) −1.23583 + 1.03698i −0.0506214 + 0.0424764i
\(597\) −18.2179 12.8962i −0.745611 0.527807i
\(598\) 0.00134763 0.00764279i 5.51087e−5 0.000312537i
\(599\) 11.8686 4.31982i 0.484938 0.176503i −0.0879695 0.996123i \(-0.528038\pi\)
0.572907 + 0.819620i \(0.305816\pi\)
\(600\) 0 0
\(601\) 3.56725 + 20.2309i 0.145511 + 0.825235i 0.966955 + 0.254946i \(0.0820577\pi\)
−0.821444 + 0.570289i \(0.806831\pi\)
\(602\) −2.27744 3.94465i −0.0928216 0.160772i
\(603\) −21.0023 25.5580i −0.855282 1.04080i
\(604\) 7.51556 13.0173i 0.305804 0.529668i
\(605\) 0 0
\(606\) −7.05769 + 6.98559i −0.286699 + 0.283770i
\(607\) −9.89160 8.30003i −0.401487 0.336888i 0.419581 0.907718i \(-0.362177\pi\)
−0.821068 + 0.570830i \(0.806622\pi\)
\(608\) 1.41448 + 1.18689i 0.0573648 + 0.0481348i
\(609\) 12.6827 12.5532i 0.513930 0.508680i
\(610\) 0 0
\(611\) −0.0640889 + 0.111005i −0.00259276 + 0.00449079i
\(612\) 10.9039 + 13.2691i 0.440763 + 0.536371i
\(613\) −15.5799 26.9851i −0.629265 1.08992i −0.987699 0.156364i \(-0.950023\pi\)
0.358434 0.933555i \(-0.383311\pi\)
\(614\) 0.585856 + 3.32255i 0.0236432 + 0.134087i
\(615\) 0 0
\(616\) −10.2836 + 3.74293i −0.414339 + 0.150807i
\(617\) 1.23998 7.03230i 0.0499199 0.283110i −0.949621 0.313400i \(-0.898532\pi\)
0.999541 + 0.0302901i \(0.00964312\pi\)
\(618\) 2.68129 + 1.89805i 0.107857 + 0.0763506i
\(619\) −7.68412 + 6.44774i −0.308851 + 0.259157i −0.784017 0.620740i \(-0.786832\pi\)
0.475166 + 0.879896i \(0.342388\pi\)
\(620\) 0 0
\(621\) −4.83569 2.34625i −0.194049 0.0941520i
\(622\) −9.90827 −0.397285
\(623\) −3.40981 + 2.86117i −0.136611 + 0.114630i
\(624\) 0.0850787 0.0391423i 0.00340587 0.00156695i
\(625\) 0 0
\(626\) 10.5061 3.82392i 0.419909 0.152835i
\(627\) 3.75722 0.309286i 0.150049 0.0123517i
\(628\) 3.98552 + 22.6030i 0.159039 + 0.901957i
\(629\) 6.93093 + 12.0047i 0.276354 + 0.478660i
\(630\) 0 0
\(631\) 3.53780 6.12765i 0.140838 0.243938i −0.786975 0.616985i \(-0.788354\pi\)
0.927812 + 0.373047i \(0.121687\pi\)
\(632\) 0.730905 + 0.266028i 0.0290738 + 0.0105820i
\(633\) 10.5507 + 40.2002i 0.419353 + 1.59781i
\(634\) 2.65189 + 2.22520i 0.105320 + 0.0883741i
\(635\) 0 0
\(636\) −3.97070 1.08582i −0.157448 0.0430557i
\(637\) 0.0892352 + 0.0324790i 0.00353563 + 0.00128686i
\(638\) −8.45809 + 14.6498i −0.334859 + 0.579993i
\(639\) −11.8756 + 13.8613i −0.469793 + 0.548344i
\(640\) 0 0
\(641\) −0.870188 4.93508i −0.0343704 0.194924i 0.962788 0.270258i \(-0.0871089\pi\)
−0.997158 + 0.0753337i \(0.975998\pi\)
\(642\) 4.62838 + 6.68277i 0.182667 + 0.263748i
\(643\) 1.53960 0.560367i 0.0607157 0.0220987i −0.311484 0.950251i \(-0.600826\pi\)
0.372199 + 0.928153i \(0.378604\pi\)
\(644\) −0.433147 + 2.45650i −0.0170684 + 0.0967997i
\(645\) 0 0
\(646\) 0.416126 0.349171i 0.0163722 0.0137379i
\(647\) −34.4927 −1.35605 −0.678024 0.735040i \(-0.737164\pi\)
−0.678024 + 0.735040i \(0.737164\pi\)
\(648\) 2.19521 + 14.1420i 0.0862359 + 0.555550i
\(649\) 19.3056 0.757813
\(650\) 0 0
\(651\) −0.786571 + 8.48840i −0.0308282 + 0.332687i
\(652\) 1.05182 5.96515i 0.0411923 0.233613i
\(653\) 36.4230 13.2569i 1.42534 0.518783i 0.489751 0.871862i \(-0.337088\pi\)
0.935593 + 0.353080i \(0.114866\pi\)
\(654\) 5.94223 + 8.57980i 0.232360 + 0.335497i
\(655\) 0 0
\(656\) 5.50161 + 9.52907i 0.214802 + 0.372048i
\(657\) 0.545365 + 1.54764i 0.0212767 + 0.0603792i
\(658\) −1.94575 + 3.37015i −0.0758534 + 0.131382i
\(659\) −8.82552 3.21223i −0.343794 0.125131i 0.164352 0.986402i \(-0.447447\pi\)
−0.508146 + 0.861271i \(0.669669\pi\)
\(660\) 0 0
\(661\) −18.4980 15.5217i −0.719489 0.603723i 0.207755 0.978181i \(-0.433384\pi\)
−0.927244 + 0.374458i \(0.877829\pi\)
\(662\) −2.04335 1.71457i −0.0794169 0.0666387i
\(663\) −0.0248750 0.0947785i −0.000966065 0.00368089i
\(664\) −6.89399 2.50921i −0.267539 0.0973761i
\(665\) 0 0
\(666\) −0.0566265 + 5.51472i −0.00219423 + 0.213691i
\(667\) 4.03784 + 6.99375i 0.156346 + 0.270799i
\(668\) −6.52510 37.0057i −0.252464 1.43179i
\(669\) 37.3935 3.07815i 1.44572 0.119008i
\(670\) 0 0
\(671\) −6.26159 + 35.5112i −0.241726 + 1.37090i
\(672\) 9.18674 4.22656i 0.354386 0.163043i
\(673\) 20.2742 17.0121i 0.781514 0.655768i −0.162115 0.986772i \(-0.551832\pi\)
0.943630 + 0.331003i \(0.107387\pi\)
\(674\) −3.10557 −0.119622
\(675\) 0 0
\(676\) 23.7554 0.913671
\(677\) −23.7986 + 19.9694i −0.914654 + 0.767486i −0.972999 0.230811i \(-0.925862\pi\)
0.0583448 + 0.998296i \(0.481418\pi\)
\(678\) 7.37609 + 5.22143i 0.283277 + 0.200528i
\(679\) −2.27807 + 12.9196i −0.0874245 + 0.495809i
\(680\) 0 0
\(681\) −16.0160 + 33.8910i −0.613734 + 1.29871i
\(682\) −1.40328 7.95842i −0.0537345 0.304744i
\(683\) 19.0681 + 33.0268i 0.729619 + 1.26374i 0.957044 + 0.289942i \(0.0936359\pi\)
−0.227425 + 0.973796i \(0.573031\pi\)
\(684\) −2.25719 + 0.374149i −0.0863060 + 0.0143060i
\(685\) 0 0
\(686\) 6.31558 + 2.29868i 0.241130 + 0.0877642i
\(687\) 13.3016 13.1657i 0.507487 0.502303i
\(688\) 19.0552 + 15.9892i 0.726472 + 0.609583i
\(689\) 0.0179917 + 0.0150968i 0.000685428 + 0.000575142i
\(690\) 0 0
\(691\) −30.9436 11.2626i −1.17715 0.428448i −0.321957 0.946754i \(-0.604341\pi\)
−0.855195 + 0.518306i \(0.826563\pi\)
\(692\) −12.8221 + 22.2085i −0.487424 + 0.844242i
\(693\) 7.26030 19.3277i 0.275796 0.734198i
\(694\) −6.53414 11.3175i −0.248033 0.429605i
\(695\) 0 0
\(696\) 9.18742 19.4413i 0.348248 0.736919i
\(697\) 10.8185 3.93762i 0.409781 0.149148i
\(698\) 0.855130 4.84968i 0.0323672 0.183563i
\(699\) 10.7992 + 7.64461i 0.408463 + 0.289146i
\(700\) 0 0
\(701\) −2.30710 −0.0871381 −0.0435690 0.999050i \(-0.513873\pi\)
−0.0435690 + 0.999050i \(0.513873\pi\)
\(702\) 0.0106689 0.0374969i 0.000402671 0.00141523i
\(703\) −1.84668 −0.0696490
\(704\) 16.5800 13.9123i 0.624881 0.524338i
\(705\) 0 0
\(706\) 0.592100 3.35796i 0.0222840 0.126379i
\(707\) −17.1120 + 6.22826i −0.643563 + 0.234238i
\(708\) −11.6772 + 0.961241i −0.438857 + 0.0361257i
\(709\) −1.93654 10.9826i −0.0727281 0.412462i −0.999336 0.0364329i \(-0.988400\pi\)
0.926608 0.376029i \(-0.122711\pi\)
\(710\) 0 0
\(711\) −1.27830 + 0.720629i −0.0479400 + 0.0270257i
\(712\) −2.68184 + 4.64508i −0.100506 + 0.174082i
\(713\) −3.62525 1.31948i −0.135767 0.0494151i
\(714\) −0.755212 2.87750i −0.0282631 0.107688i
\(715\) 0 0
\(716\) −14.2646 11.9694i −0.533092 0.447317i
\(717\) −5.39888 1.47637i −0.201625 0.0551362i
\(718\) −6.92093 2.51901i −0.258287 0.0940087i
\(719\) 16.0850 27.8600i 0.599869 1.03900i −0.392971 0.919551i \(-0.628553\pi\)
0.992840 0.119453i \(-0.0381140\pi\)
\(720\) 0 0
\(721\) 3.01213 + 5.21717i 0.112178 + 0.194297i
\(722\) −1.35819 7.70267i −0.0505465 0.286664i
\(723\) −26.1777 37.7972i −0.973560 1.40569i
\(724\) 41.3064 15.0343i 1.53514 0.558745i
\(725\) 0 0
\(726\) −1.07552 + 11.6066i −0.0399163 + 0.430762i
\(727\) 4.11022 3.44888i 0.152440 0.127912i −0.563378 0.826199i \(-0.690499\pi\)
0.715818 + 0.698287i \(0.246054\pi\)
\(728\) −0.0378942 −0.00140445
\(729\) −22.9558 14.2138i −0.850215 0.526435i
\(730\) 0 0
\(731\) 19.9377 16.7297i 0.737424 0.618772i
\(732\) 2.01926 21.7911i 0.0746338 0.805422i
\(733\) 2.53463 14.3746i 0.0936187 0.530938i −0.901543 0.432689i \(-0.857565\pi\)
0.995162 0.0982489i \(-0.0313241\pi\)
\(734\) −7.93296 + 2.88736i −0.292811 + 0.106574i
\(735\) 0 0
\(736\) 0.794682 + 4.50687i 0.0292924 + 0.166125i
\(737\) 28.7534 + 49.8023i 1.05915 + 1.83449i
\(738\) 4.50245 + 0.841659i 0.165737 + 0.0309819i
\(739\) 21.6083 37.4266i 0.794873 1.37676i −0.128047 0.991768i \(-0.540871\pi\)
0.922920 0.384992i \(-0.125796\pi\)
\(740\) 0 0
\(741\) 0.0125917 + 0.00344333i 0.000462569 + 0.000126494i
\(742\) 0.546231 + 0.458343i 0.0200528 + 0.0168263i
\(743\) −6.21431 5.21443i −0.227981 0.191299i 0.521641 0.853165i \(-0.325320\pi\)
−0.749622 + 0.661866i \(0.769765\pi\)
\(744\) 2.60770 + 9.93582i 0.0956028 + 0.364265i
\(745\) 0 0
\(746\) −2.01116 + 3.48342i −0.0736336 + 0.127537i
\(747\) 12.0571 6.79706i 0.441146 0.248692i
\(748\) −14.9280 25.8561i −0.545823 0.945393i
\(749\) 2.58860 + 14.6807i 0.0945854 + 0.536420i
\(750\) 0 0
\(751\) −8.22744 + 2.99454i −0.300223 + 0.109272i −0.487740 0.872989i \(-0.662178\pi\)
0.187516 + 0.982261i \(0.439956\pi\)
\(752\) 3.69037 20.9291i 0.134574 0.763207i
\(753\) −7.07968 + 3.25717i −0.257998 + 0.118698i
\(754\) −0.0448713 + 0.0376515i −0.00163412 + 0.00137119i
\(755\) 0 0
\(756\) −3.42913 + 12.0520i −0.124716 + 0.438329i
\(757\) 32.1511 1.16855 0.584276 0.811555i \(-0.301378\pi\)
0.584276 + 0.811555i \(0.301378\pi\)
\(758\) −1.31414 + 1.10269i −0.0477316 + 0.0400515i
\(759\) 7.62620 + 5.39848i 0.276813 + 0.195952i
\(760\) 0 0
\(761\) 23.0656 8.39520i 0.836128 0.304326i 0.111756 0.993736i \(-0.464352\pi\)
0.724371 + 0.689410i \(0.242130\pi\)
\(762\) 2.58116 5.46192i 0.0935054 0.197865i
\(763\) 3.32342 + 18.8481i 0.120316 + 0.682346i
\(764\) 10.0016 + 17.3233i 0.361846 + 0.626736i
\(765\) 0 0
\(766\) 0.986770 1.70914i 0.0356535 0.0617536i
\(767\) 0.0628177 + 0.0228638i 0.00226822 + 0.000825563i
\(768\) −4.81033 + 4.76119i −0.173578 + 0.171805i
\(769\) 24.0648 + 20.1928i 0.867800 + 0.728170i 0.963634 0.267227i \(-0.0861073\pi\)
−0.0958338 + 0.995397i \(0.530552\pi\)
\(770\) 0 0
\(771\) 16.9085 16.7358i 0.608945 0.602725i
\(772\) 18.5558 + 6.75377i 0.667839 + 0.243073i
\(773\) 14.3573 24.8675i 0.516395 0.894422i