Properties

Label 819.2.ew.a.470.71
Level $819$
Weight $2$
Character 819.470
Analytic conductor $6.540$
Analytic rank $0$
Dimension $336$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [819,2,Mod(176,819)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(819, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([10, 0, 11]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("819.176");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.ew (of order \(12\), degree \(4\), 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: \(6.53974792554\)
Analytic rank: \(0\)
Dimension: \(336\)
Relative dimension: \(84\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 470.71
Character \(\chi\) \(=\) 819.470
Dual form 819.2.ew.a.176.71

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.48617 + 1.48617i) q^{2} +(-1.58281 + 0.703362i) q^{3} +2.41742i q^{4} +(0.520566 - 1.94278i) q^{5} +(-3.39764 - 1.30701i) q^{6} +(0.258819 - 0.965926i) q^{7} +(-0.620354 + 0.620354i) q^{8} +(2.01056 - 2.22658i) q^{9} +O(q^{10})\) \(q+(1.48617 + 1.48617i) q^{2} +(-1.58281 + 0.703362i) q^{3} +2.41742i q^{4} +(0.520566 - 1.94278i) q^{5} +(-3.39764 - 1.30701i) q^{6} +(0.258819 - 0.965926i) q^{7} +(-0.620354 + 0.620354i) q^{8} +(2.01056 - 2.22658i) q^{9} +(3.66095 - 2.11365i) q^{10} +(0.127021 - 0.127021i) q^{11} +(-1.70032 - 3.82631i) q^{12} +(-1.73307 - 3.16172i) q^{13} +(1.82018 - 1.05088i) q^{14} +(0.542521 + 3.44119i) q^{15} +2.99093 q^{16} +(2.23081 - 3.86388i) q^{17} +(6.29712 - 0.321031i) q^{18} +(-0.736005 - 2.74681i) q^{19} +(4.69651 + 1.25843i) q^{20} +(0.269735 + 1.71092i) q^{21} +0.377551 q^{22} +(-0.646752 + 1.12021i) q^{23} +(0.545568 - 1.41824i) q^{24} +(0.826728 + 0.477312i) q^{25} +(2.12321 - 7.27450i) q^{26} +(-1.61625 + 4.93840i) q^{27} +(2.33505 + 0.625674i) q^{28} -2.31274i q^{29} +(-4.30792 + 5.92048i) q^{30} +(4.94144 + 1.32405i) q^{31} +(5.68574 + 5.68574i) q^{32} +(-0.111708 + 0.290392i) q^{33} +(9.05777 - 2.42702i) q^{34} +(-1.74185 - 1.00566i) q^{35} +(5.38256 + 4.86037i) q^{36} +(-0.359658 + 1.34226i) q^{37} +(2.98840 - 5.17606i) q^{38} +(4.96696 + 3.78541i) q^{39} +(0.882276 + 1.52815i) q^{40} +(-7.09357 + 1.90072i) q^{41} +(-2.14185 + 2.94359i) q^{42} +(-0.901082 + 0.520240i) q^{43} +(0.307063 + 0.307063i) q^{44} +(-3.27911 - 5.06516i) q^{45} +(-2.62601 + 0.703636i) q^{46} +(1.79649 + 6.70458i) q^{47} +(-4.73406 + 2.10371i) q^{48} +(-0.866025 - 0.500000i) q^{49} +(0.519293 + 1.93803i) q^{50} +(-0.813241 + 7.68486i) q^{51} +(7.64319 - 4.18956i) q^{52} -0.127341i q^{53} +(-9.74133 + 4.93729i) q^{54} +(-0.180651 - 0.312897i) q^{55} +(0.438657 + 0.759776i) q^{56} +(3.09696 + 3.82999i) q^{57} +(3.43712 - 3.43712i) q^{58} +(7.30409 - 7.30409i) q^{59} +(-8.31880 + 1.31150i) q^{60} +(-2.87568 - 4.98082i) q^{61} +(5.37605 + 9.31160i) q^{62} +(-1.63033 - 2.51833i) q^{63} +10.9181i q^{64} +(-7.04470 + 1.72109i) q^{65} +(-0.597591 + 0.265555i) q^{66} +(0.487651 + 1.81994i) q^{67} +(9.34062 + 5.39281i) q^{68} +(0.235773 - 2.22797i) q^{69} +(-1.09411 - 4.08326i) q^{70} +(3.89691 - 1.04417i) q^{71} +(0.134004 + 2.62853i) q^{72} +(-2.28964 - 2.28964i) q^{73} +(-2.52934 + 1.46032i) q^{74} +(-1.64428 - 0.174003i) q^{75} +(6.64018 - 1.77923i) q^{76} +(-0.0898176 - 0.155569i) q^{77} +(1.75597 + 13.0075i) q^{78} +(-5.97837 + 10.3548i) q^{79} +(1.55698 - 5.81071i) q^{80} +(-0.915273 - 8.95334i) q^{81} +(-13.3671 - 7.71748i) q^{82} +(3.17172 - 0.849859i) q^{83} +(-4.13600 + 0.652062i) q^{84} +(-6.34539 - 6.34539i) q^{85} +(-2.11233 - 0.565997i) q^{86} +(1.62669 + 3.66062i) q^{87} +0.157596i q^{88} +(-8.94508 - 2.39683i) q^{89} +(2.65437 - 12.4010i) q^{90} +(-3.50254 + 0.855707i) q^{91} +(-2.70801 - 1.56347i) q^{92} +(-8.75263 + 1.37990i) q^{93} +(-7.29427 + 12.6340i) q^{94} -5.71958 q^{95} +(-12.9986 - 5.00030i) q^{96} +(3.34484 + 0.896248i) q^{97} +(-0.543977 - 2.03015i) q^{98} +(-0.0274381 - 0.538206i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 336 q + 24 q^{6} - 36 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 336 q + 24 q^{6} - 36 q^{8} + 16 q^{15} - 336 q^{16} + 20 q^{18} + 8 q^{21} + 8 q^{24} + 96 q^{26} + 24 q^{27} - 96 q^{30} - 72 q^{32} - 36 q^{33} - 12 q^{36} - 72 q^{38} - 16 q^{39} - 48 q^{41} - 28 q^{45} + 60 q^{47} - 48 q^{48} + 132 q^{50} - 36 q^{52} - 108 q^{54} + 68 q^{57} - 72 q^{58} - 44 q^{60} - 36 q^{62} - 8 q^{63} - 72 q^{65} - 20 q^{66} - 72 q^{69} + 48 q^{71} - 104 q^{72} + 12 q^{74} + 104 q^{78} - 12 q^{79} + 96 q^{80} - 68 q^{81} - 120 q^{83} - 12 q^{84} + 36 q^{85} + 48 q^{86} - 24 q^{87} - 60 q^{89} - 72 q^{92} - 172 q^{93} - 48 q^{94} - 152 q^{96} + 48 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.48617 + 1.48617i 1.05088 + 1.05088i 0.998634 + 0.0522485i \(0.0166388\pi\)
0.0522485 + 0.998634i \(0.483361\pi\)
\(3\) −1.58281 + 0.703362i −0.913835 + 0.406086i
\(4\) 2.41742i 1.20871i
\(5\) 0.520566 1.94278i 0.232804 0.868837i −0.746322 0.665585i \(-0.768182\pi\)
0.979126 0.203252i \(-0.0651511\pi\)
\(6\) −3.39764 1.30701i −1.38708 0.533584i
\(7\) 0.258819 0.965926i 0.0978244 0.365086i
\(8\) −0.620354 + 0.620354i −0.219328 + 0.219328i
\(9\) 2.01056 2.22658i 0.670188 0.742192i
\(10\) 3.66095 2.11365i 1.15770 0.668396i
\(11\) 0.127021 0.127021i 0.0382983 0.0382983i −0.687698 0.725997i \(-0.741379\pi\)
0.725997 + 0.687698i \(0.241379\pi\)
\(12\) −1.70032 3.82631i −0.490840 1.10456i
\(13\) −1.73307 3.16172i −0.480668 0.876903i
\(14\) 1.82018 1.05088i 0.486464 0.280860i
\(15\) 0.542521 + 3.44119i 0.140078 + 0.888512i
\(16\) 2.99093 0.747732
\(17\) 2.23081 3.86388i 0.541052 0.937130i −0.457792 0.889059i \(-0.651360\pi\)
0.998844 0.0480703i \(-0.0153071\pi\)
\(18\) 6.29712 0.321031i 1.48424 0.0756678i
\(19\) −0.736005 2.74681i −0.168851 0.630161i −0.997518 0.0704184i \(-0.977567\pi\)
0.828666 0.559743i \(-0.189100\pi\)
\(20\) 4.69651 + 1.25843i 1.05017 + 0.281392i
\(21\) 0.269735 + 1.71092i 0.0588610 + 0.373353i
\(22\) 0.377551 0.0804941
\(23\) −0.646752 + 1.12021i −0.134857 + 0.233579i −0.925543 0.378643i \(-0.876391\pi\)
0.790686 + 0.612222i \(0.209724\pi\)
\(24\) 0.545568 1.41824i 0.111364 0.289496i
\(25\) 0.826728 + 0.477312i 0.165346 + 0.0954623i
\(26\) 2.12321 7.27450i 0.416396 1.42665i
\(27\) −1.61625 + 4.93840i −0.311047 + 0.950395i
\(28\) 2.33505 + 0.625674i 0.441282 + 0.118241i
\(29\) 2.31274i 0.429464i −0.976673 0.214732i \(-0.931112\pi\)
0.976673 0.214732i \(-0.0688879\pi\)
\(30\) −4.30792 + 5.92048i −0.786516 + 1.08093i
\(31\) 4.94144 + 1.32405i 0.887508 + 0.237807i 0.673644 0.739056i \(-0.264728\pi\)
0.213864 + 0.976863i \(0.431395\pi\)
\(32\) 5.68574 + 5.68574i 1.00511 + 1.00511i
\(33\) −0.111708 + 0.290392i −0.0194459 + 0.0505508i
\(34\) 9.05777 2.42702i 1.55340 0.416231i
\(35\) −1.74185 1.00566i −0.294426 0.169987i
\(36\) 5.38256 + 4.86037i 0.897094 + 0.810062i
\(37\) −0.359658 + 1.34226i −0.0591273 + 0.220666i −0.989167 0.146792i \(-0.953105\pi\)
0.930040 + 0.367458i \(0.119772\pi\)
\(38\) 2.98840 5.17606i 0.484783 0.839668i
\(39\) 4.96696 + 3.78541i 0.795349 + 0.606151i
\(40\) 0.882276 + 1.52815i 0.139500 + 0.241621i
\(41\) −7.09357 + 1.90072i −1.10783 + 0.296842i −0.765949 0.642901i \(-0.777731\pi\)
−0.341881 + 0.939743i \(0.611064\pi\)
\(42\) −2.14185 + 2.94359i −0.330494 + 0.454206i
\(43\) −0.901082 + 0.520240i −0.137414 + 0.0793359i −0.567131 0.823628i \(-0.691947\pi\)
0.429717 + 0.902964i \(0.358613\pi\)
\(44\) 0.307063 + 0.307063i 0.0462915 + 0.0462915i
\(45\) −3.27911 5.06516i −0.488821 0.755069i
\(46\) −2.62601 + 0.703636i −0.387184 + 0.103746i
\(47\) 1.79649 + 6.70458i 0.262044 + 0.977963i 0.964035 + 0.265776i \(0.0856283\pi\)
−0.701990 + 0.712187i \(0.747705\pi\)
\(48\) −4.73406 + 2.10371i −0.683303 + 0.303644i
\(49\) −0.866025 0.500000i −0.123718 0.0714286i
\(50\) 0.519293 + 1.93803i 0.0734391 + 0.274079i
\(51\) −0.813241 + 7.68486i −0.113877 + 1.07610i
\(52\) 7.64319 4.18956i 1.05992 0.580988i
\(53\) 0.127341i 0.0174916i −0.999962 0.00874579i \(-0.997216\pi\)
0.999962 0.00874579i \(-0.00278391\pi\)
\(54\) −9.74133 + 4.93729i −1.32563 + 0.671880i
\(55\) −0.180651 0.312897i −0.0243590 0.0421910i
\(56\) 0.438657 + 0.759776i 0.0586180 + 0.101529i
\(57\) 3.09696 + 3.82999i 0.410202 + 0.507295i
\(58\) 3.43712 3.43712i 0.451317 0.451317i
\(59\) 7.30409 7.30409i 0.950912 0.950912i −0.0479382 0.998850i \(-0.515265\pi\)
0.998850 + 0.0479382i \(0.0152650\pi\)
\(60\) −8.31880 + 1.31150i −1.07395 + 0.169314i
\(61\) −2.87568 4.98082i −0.368193 0.637729i 0.621090 0.783739i \(-0.286690\pi\)
−0.989283 + 0.146010i \(0.953357\pi\)
\(62\) 5.37605 + 9.31160i 0.682760 + 1.18257i
\(63\) −1.63033 2.51833i −0.205403 0.317280i
\(64\) 10.9181i 1.36477i
\(65\) −7.04470 + 1.72109i −0.873787 + 0.213476i
\(66\) −0.597591 + 0.265555i −0.0735583 + 0.0326876i
\(67\) 0.487651 + 1.81994i 0.0595761 + 0.222341i 0.989295 0.145929i \(-0.0466170\pi\)
−0.929719 + 0.368270i \(0.879950\pi\)
\(68\) 9.34062 + 5.39281i 1.13272 + 0.653974i
\(69\) 0.235773 2.22797i 0.0283837 0.268217i
\(70\) −1.09411 4.08326i −0.130771 0.488043i
\(71\) 3.89691 1.04417i 0.462478 0.123921i −0.0200541 0.999799i \(-0.506384\pi\)
0.482532 + 0.875878i \(0.339717\pi\)
\(72\) 0.134004 + 2.62853i 0.0157925 + 0.309775i
\(73\) −2.28964 2.28964i −0.267982 0.267982i 0.560305 0.828286i \(-0.310684\pi\)
−0.828286 + 0.560305i \(0.810684\pi\)
\(74\) −2.52934 + 1.46032i −0.294030 + 0.169758i
\(75\) −1.64428 0.174003i −0.189865 0.0200922i
\(76\) 6.64018 1.77923i 0.761681 0.204092i
\(77\) −0.0898176 0.155569i −0.0102357 0.0177287i
\(78\) 1.75597 + 13.0075i 0.198825 + 1.47281i
\(79\) −5.97837 + 10.3548i −0.672619 + 1.16501i 0.304539 + 0.952500i \(0.401497\pi\)
−0.977159 + 0.212511i \(0.931836\pi\)
\(80\) 1.55698 5.81071i 0.174075 0.649657i
\(81\) −0.915273 8.95334i −0.101697 0.994815i
\(82\) −13.3671 7.71748i −1.47615 0.852253i
\(83\) 3.17172 0.849859i 0.348141 0.0932841i −0.0805111 0.996754i \(-0.525655\pi\)
0.428652 + 0.903470i \(0.358989\pi\)
\(84\) −4.13600 + 0.652062i −0.451275 + 0.0711458i
\(85\) −6.34539 6.34539i −0.688254 0.688254i
\(86\) −2.11233 0.565997i −0.227778 0.0610331i
\(87\) 1.62669 + 3.66062i 0.174400 + 0.392459i
\(88\) 0.157596i 0.0167998i
\(89\) −8.94508 2.39683i −0.948176 0.254063i −0.248588 0.968609i \(-0.579966\pi\)
−0.699588 + 0.714546i \(0.746633\pi\)
\(90\) 2.65437 12.4010i 0.279795 1.30718i
\(91\) −3.50254 + 0.855707i −0.367166 + 0.0897025i
\(92\) −2.70801 1.56347i −0.282330 0.163003i
\(93\) −8.75263 + 1.37990i −0.907606 + 0.143089i
\(94\) −7.29427 + 12.6340i −0.752346 + 1.30310i
\(95\) −5.71958 −0.586817
\(96\) −12.9986 5.00030i −1.32666 0.510341i
\(97\) 3.34484 + 0.896248i 0.339617 + 0.0910002i 0.424597 0.905383i \(-0.360416\pi\)
−0.0849796 + 0.996383i \(0.527083\pi\)
\(98\) −0.543977 2.03015i −0.0549500 0.205076i
\(99\) −0.0274381 0.538206i −0.00275763 0.0540918i
\(100\) −1.15386 + 1.99855i −0.115386 + 0.199855i
\(101\) 10.1450 1.00946 0.504732 0.863276i \(-0.331591\pi\)
0.504732 + 0.863276i \(0.331591\pi\)
\(102\) −12.6296 + 10.2124i −1.25052 + 1.01118i
\(103\) −14.8616 + 8.58036i −1.46436 + 0.845448i −0.999208 0.0397832i \(-0.987333\pi\)
−0.465151 + 0.885231i \(0.654000\pi\)
\(104\) 3.03650 + 0.886266i 0.297754 + 0.0869055i
\(105\) 3.46435 + 0.366611i 0.338086 + 0.0357775i
\(106\) 0.189250 0.189250i 0.0183816 0.0183816i
\(107\) 15.9421 9.20420i 1.54118 0.889803i 0.542420 0.840108i \(-0.317508\pi\)
0.998764 0.0496955i \(-0.0158251\pi\)
\(108\) −11.9382 3.90714i −1.14875 0.375965i
\(109\) 5.64858 5.64858i 0.541036 0.541036i −0.382797 0.923833i \(-0.625039\pi\)
0.923833 + 0.382797i \(0.125039\pi\)
\(110\) 0.196540 0.733498i 0.0187394 0.0699363i
\(111\) −0.374826 2.37751i −0.0355769 0.225663i
\(112\) 0.774109 2.88901i 0.0731464 0.272986i
\(113\) 0.482065i 0.0453488i −0.999743 0.0226744i \(-0.992782\pi\)
0.999743 0.0226744i \(-0.00721811\pi\)
\(114\) −1.08942 + 10.2946i −0.102033 + 0.964182i
\(115\) 1.83964 + 1.83964i 0.171547 + 0.171547i
\(116\) 5.59085 0.519097
\(117\) −10.5243 2.49801i −0.972968 0.230942i
\(118\) 21.7103 1.99859
\(119\) −3.15485 3.15485i −0.289204 0.289204i
\(120\) −2.47131 1.79820i −0.225599 0.164153i
\(121\) 10.9677i 0.997066i
\(122\) 3.12860 11.6761i 0.283250 1.05711i
\(123\) 9.89087 7.99782i 0.891830 0.721139i
\(124\) −3.20079 + 11.9455i −0.287439 + 1.07274i
\(125\) 8.46874 8.46874i 0.757467 0.757467i
\(126\) 1.31972 6.16564i 0.117570 0.549279i
\(127\) 1.67462 0.966841i 0.148598 0.0857933i −0.423857 0.905729i \(-0.639324\pi\)
0.572456 + 0.819936i \(0.305991\pi\)
\(128\) −4.85475 + 4.85475i −0.429103 + 0.429103i
\(129\) 1.06032 1.45723i 0.0933563 0.128302i
\(130\) −13.0275 7.91179i −1.14259 0.693910i
\(131\) 12.3381 7.12338i 1.07798 0.622373i 0.147630 0.989043i \(-0.452836\pi\)
0.930351 + 0.366670i \(0.119502\pi\)
\(132\) −0.701999 0.270046i −0.0611012 0.0235044i
\(133\) −2.84371 −0.246581
\(134\) −1.98001 + 3.42948i −0.171047 + 0.296262i
\(135\) 8.75284 + 5.71077i 0.753325 + 0.491505i
\(136\) 1.01308 + 3.78087i 0.0868711 + 0.324207i
\(137\) −3.70490 0.992725i −0.316531 0.0848142i 0.0970557 0.995279i \(-0.469057\pi\)
−0.413587 + 0.910465i \(0.635724\pi\)
\(138\) 3.66155 2.96076i 0.311692 0.252036i
\(139\) −15.7587 −1.33664 −0.668318 0.743876i \(-0.732985\pi\)
−0.668318 + 0.743876i \(0.732985\pi\)
\(140\) 2.43109 4.21077i 0.205465 0.355875i
\(141\) −7.55924 9.34848i −0.636603 0.787284i
\(142\) 7.34330 + 4.23966i 0.616236 + 0.355784i
\(143\) −0.621742 0.181468i −0.0519927 0.0151751i
\(144\) 6.01345 6.65953i 0.501121 0.554960i
\(145\) −4.49313 1.20393i −0.373134 0.0999811i
\(146\) 6.80559i 0.563235i
\(147\) 1.72243 + 0.182274i 0.142064 + 0.0150337i
\(148\) −3.24480 0.869442i −0.266721 0.0714677i
\(149\) 5.55091 + 5.55091i 0.454748 + 0.454748i 0.896927 0.442179i \(-0.145794\pi\)
−0.442179 + 0.896927i \(0.645794\pi\)
\(150\) −2.18508 2.70228i −0.178411 0.220640i
\(151\) 2.26297 0.606361i 0.184158 0.0493450i −0.165561 0.986199i \(-0.552944\pi\)
0.349719 + 0.936855i \(0.386277\pi\)
\(152\) 2.16058 + 1.24741i 0.175246 + 0.101178i
\(153\) −4.11804 12.7357i −0.332923 1.02962i
\(154\) 0.0977173 0.364686i 0.00787429 0.0293872i
\(155\) 5.14469 8.91086i 0.413231 0.715737i
\(156\) −9.15092 + 12.0072i −0.732660 + 0.961346i
\(157\) 7.31351 + 12.6674i 0.583682 + 1.01097i 0.995038 + 0.0994917i \(0.0317217\pi\)
−0.411357 + 0.911474i \(0.634945\pi\)
\(158\) −24.2740 + 6.50419i −1.93113 + 0.517446i
\(159\) 0.0895666 + 0.201556i 0.00710309 + 0.0159844i
\(160\) 14.0059 8.08633i 1.10727 0.639281i
\(161\) 0.914646 + 0.914646i 0.0720842 + 0.0720842i
\(162\) 11.9460 14.6665i 0.938563 1.15231i
\(163\) −21.6745 + 5.80766i −1.69768 + 0.454891i −0.972353 0.233517i \(-0.924976\pi\)
−0.725323 + 0.688408i \(0.758310\pi\)
\(164\) −4.59483 17.1481i −0.358796 1.33904i
\(165\) 0.506016 + 0.368193i 0.0393933 + 0.0286638i
\(166\) 5.97675 + 3.45068i 0.463886 + 0.267825i
\(167\) 2.66372 + 9.94113i 0.206125 + 0.769267i 0.989104 + 0.147220i \(0.0470324\pi\)
−0.782979 + 0.622048i \(0.786301\pi\)
\(168\) −1.22871 0.894045i −0.0947968 0.0689770i
\(169\) −6.99291 + 10.9590i −0.537917 + 0.842998i
\(170\) 18.8607i 1.44655i
\(171\) −7.59576 3.88386i −0.580862 0.297006i
\(172\) −1.25764 2.17829i −0.0958940 0.166093i
\(173\) −3.99360 6.91712i −0.303628 0.525899i 0.673327 0.739345i \(-0.264865\pi\)
−0.976955 + 0.213446i \(0.931531\pi\)
\(174\) −3.02276 + 7.85785i −0.229155 + 0.595702i
\(175\) 0.675021 0.675021i 0.0510268 0.0510268i
\(176\) 0.379911 0.379911i 0.0286369 0.0286369i
\(177\) −6.42356 + 16.6984i −0.482824 + 1.25513i
\(178\) −9.73183 16.8560i −0.729431 1.26341i
\(179\) 5.17436 + 8.96226i 0.386750 + 0.669870i 0.992010 0.126157i \(-0.0402643\pi\)
−0.605260 + 0.796028i \(0.706931\pi\)
\(180\) 12.2446 7.92698i 0.912659 0.590842i
\(181\) 14.7605i 1.09714i −0.836106 0.548568i \(-0.815173\pi\)
0.836106 0.548568i \(-0.184827\pi\)
\(182\) −6.47710 3.93365i −0.480115 0.291581i
\(183\) 8.05497 + 5.86104i 0.595440 + 0.433260i
\(184\) −0.293710 1.09614i −0.0216526 0.0808086i
\(185\) 2.42049 + 1.39747i 0.177958 + 0.102744i
\(186\) −15.0587 10.9572i −1.10416 0.803418i
\(187\) −0.207434 0.774156i −0.0151691 0.0566119i
\(188\) −16.2078 + 4.34286i −1.18207 + 0.316735i
\(189\) 4.35181 + 2.83932i 0.316547 + 0.206530i
\(190\) −8.50028 8.50028i −0.616675 0.616675i
\(191\) −9.73853 + 5.62254i −0.704655 + 0.406833i −0.809079 0.587700i \(-0.800034\pi\)
0.104424 + 0.994533i \(0.466700\pi\)
\(192\) −7.67940 17.2813i −0.554213 1.24717i
\(193\) −22.0925 + 5.91966i −1.59025 + 0.426106i −0.942080 0.335389i \(-0.891132\pi\)
−0.648171 + 0.761495i \(0.724466\pi\)
\(194\) 3.63903 + 6.30299i 0.261267 + 0.452528i
\(195\) 9.93985 7.67914i 0.711807 0.549914i
\(196\) 1.20871 2.09354i 0.0863363 0.149539i
\(197\) 0.336559 1.25606i 0.0239789 0.0894903i −0.952899 0.303286i \(-0.901916\pi\)
0.976878 + 0.213796i \(0.0685828\pi\)
\(198\) 0.759090 0.840645i 0.0539462 0.0597421i
\(199\) 21.6559 + 12.5030i 1.53515 + 0.886317i 0.999113 + 0.0421212i \(0.0134116\pi\)
0.536034 + 0.844196i \(0.319922\pi\)
\(200\) −0.808967 + 0.216762i −0.0572026 + 0.0153274i
\(201\) −2.05194 2.53762i −0.144732 0.178990i
\(202\) 15.0772 + 15.0772i 1.06083 + 1.06083i
\(203\) −2.23393 0.598580i −0.156791 0.0420121i
\(204\) −18.5775 1.96594i −1.30069 0.137644i
\(205\) 14.7707i 1.03163i
\(206\) −34.8388 9.33504i −2.42734 0.650403i
\(207\) 1.19389 + 3.69229i 0.0829811 + 0.256632i
\(208\) −5.18350 9.45647i −0.359411 0.655688i
\(209\) −0.442391 0.255415i −0.0306008 0.0176674i
\(210\) 4.60378 + 5.69347i 0.317691 + 0.392887i
\(211\) −7.64311 + 13.2383i −0.526173 + 0.911359i 0.473362 + 0.880868i \(0.343040\pi\)
−0.999535 + 0.0304908i \(0.990293\pi\)
\(212\) 0.307835 0.0211422
\(213\) −5.43363 + 4.39366i −0.372306 + 0.301049i
\(214\) 37.3718 + 10.0137i 2.55468 + 0.684525i
\(215\) 0.541639 + 2.02142i 0.0369394 + 0.137860i
\(216\) −2.06091 4.06620i −0.140227 0.276670i
\(217\) 2.55788 4.43037i 0.173640 0.300753i
\(218\) 16.7895 1.13713
\(219\) 5.23450 + 2.01361i 0.353715 + 0.136067i
\(220\) 0.756403 0.436709i 0.0509966 0.0294429i
\(221\) −16.0827 0.356811i −1.08184 0.0240017i
\(222\) 2.97633 4.09045i 0.199758 0.274533i
\(223\) −4.35587 + 4.35587i −0.291691 + 0.291691i −0.837748 0.546057i \(-0.816128\pi\)
0.546057 + 0.837748i \(0.316128\pi\)
\(224\) 6.96358 4.02043i 0.465274 0.268626i
\(225\) 2.72496 0.881107i 0.181664 0.0587405i
\(226\) 0.716431 0.716431i 0.0476563 0.0476563i
\(227\) −1.99060 + 7.42903i −0.132121 + 0.493082i −0.999993 0.00370553i \(-0.998820\pi\)
0.867872 + 0.496787i \(0.165487\pi\)
\(228\) −9.25869 + 7.48664i −0.613172 + 0.495815i
\(229\) −5.03220 + 18.7804i −0.332537 + 1.24104i 0.573978 + 0.818871i \(0.305400\pi\)
−0.906515 + 0.422174i \(0.861267\pi\)
\(230\) 5.46804i 0.360552i
\(231\) 0.251585 + 0.183061i 0.0165531 + 0.0120445i
\(232\) 1.43472 + 1.43472i 0.0941937 + 0.0941937i
\(233\) 25.4894 1.66987 0.834933 0.550352i \(-0.185506\pi\)
0.834933 + 0.550352i \(0.185506\pi\)
\(234\) −11.9284 19.3533i −0.779782 1.26517i
\(235\) 13.9607 0.910695
\(236\) 17.6570 + 17.6570i 1.14938 + 1.14938i
\(237\) 2.17941 20.5947i 0.141568 1.33777i
\(238\) 9.37730i 0.607840i
\(239\) 1.81812 6.78532i 0.117604 0.438906i −0.881864 0.471504i \(-0.843711\pi\)
0.999469 + 0.0325980i \(0.0103781\pi\)
\(240\) 1.62264 + 10.2924i 0.104741 + 0.664369i
\(241\) −1.44575 + 5.39562i −0.0931291 + 0.347562i −0.996729 0.0808147i \(-0.974248\pi\)
0.903600 + 0.428377i \(0.140914\pi\)
\(242\) −16.2999 + 16.2999i −1.04780 + 1.04780i
\(243\) 7.74614 + 13.5276i 0.496915 + 0.867799i
\(244\) 12.0407 6.95171i 0.770828 0.445038i
\(245\) −1.42221 + 1.42221i −0.0908618 + 0.0908618i
\(246\) 26.5857 + 2.81340i 1.69504 + 0.179376i
\(247\) −7.40908 + 7.08746i −0.471429 + 0.450964i
\(248\) −3.88682 + 2.24406i −0.246814 + 0.142498i
\(249\) −4.42246 + 3.57603i −0.280262 + 0.226622i
\(250\) 25.1720 1.59202
\(251\) −12.5426 + 21.7245i −0.791683 + 1.37124i 0.133240 + 0.991084i \(0.457462\pi\)
−0.924924 + 0.380152i \(0.875872\pi\)
\(252\) 6.08787 3.94120i 0.383500 0.248272i
\(253\) 0.0601389 + 0.224441i 0.00378090 + 0.0141105i
\(254\) 3.92566 + 1.05188i 0.246318 + 0.0660007i
\(255\) 14.5066 + 5.58042i 0.908441 + 0.349460i
\(256\) 7.40629 0.462893
\(257\) −12.6325 + 21.8802i −0.787995 + 1.36485i 0.139199 + 0.990264i \(0.455547\pi\)
−0.927194 + 0.374583i \(0.877786\pi\)
\(258\) 3.74152 0.589869i 0.232937 0.0367236i
\(259\) 1.20344 + 0.694805i 0.0747780 + 0.0431731i
\(260\) −4.16060 17.0300i −0.258030 1.05615i
\(261\) −5.14948 4.64990i −0.318745 0.287822i
\(262\) 28.9230 + 7.74991i 1.78687 + 0.478791i
\(263\) 22.3243i 1.37658i −0.725437 0.688289i \(-0.758362\pi\)
0.725437 0.688289i \(-0.241638\pi\)
\(264\) −0.110847 0.249445i −0.00682218 0.0153523i
\(265\) −0.247395 0.0662892i −0.0151973 0.00407211i
\(266\) −4.22624 4.22624i −0.259127 0.259127i
\(267\) 15.8442 2.49791i 0.969648 0.152870i
\(268\) −4.39955 + 1.17886i −0.268746 + 0.0720102i
\(269\) −8.35236 4.82223i −0.509252 0.294017i 0.223274 0.974756i \(-0.428326\pi\)
−0.732526 + 0.680739i \(0.761659\pi\)
\(270\) 4.52105 + 21.4954i 0.275142 + 1.30817i
\(271\) 5.79430 21.6246i 0.351978 1.31360i −0.532266 0.846577i \(-0.678659\pi\)
0.884244 0.467024i \(-0.154674\pi\)
\(272\) 6.67221 11.5566i 0.404562 0.700722i
\(273\) 4.94197 3.81797i 0.299102 0.231074i
\(274\) −4.03076 6.98148i −0.243507 0.421767i
\(275\) 0.165641 0.0443833i 0.00998851 0.00267641i
\(276\) 5.38595 + 0.569961i 0.324196 + 0.0343076i
\(277\) 5.15145 2.97419i 0.309521 0.178702i −0.337191 0.941436i \(-0.609477\pi\)
0.646712 + 0.762734i \(0.276144\pi\)
\(278\) −23.4201 23.4201i −1.40465 1.40465i
\(279\) 12.8832 8.34038i 0.771295 0.499326i
\(280\) 1.70443 0.456699i 0.101859 0.0272930i
\(281\) −4.46763 16.6734i −0.266516 0.994653i −0.961316 0.275449i \(-0.911173\pi\)
0.694799 0.719204i \(-0.255493\pi\)
\(282\) 2.65912 25.1278i 0.158348 1.49634i
\(283\) 8.39886 + 4.84908i 0.499260 + 0.288248i 0.728408 0.685144i \(-0.240261\pi\)
−0.229148 + 0.973392i \(0.573594\pi\)
\(284\) 2.52420 + 9.42045i 0.149784 + 0.559001i
\(285\) 9.05300 4.02294i 0.536253 0.238298i
\(286\) −0.654323 1.19371i −0.0386909 0.0705855i
\(287\) 7.34381i 0.433491i
\(288\) 24.0913 1.22819i 1.41959 0.0723718i
\(289\) −1.45307 2.51679i −0.0854746 0.148046i
\(290\) −4.88832 8.46682i −0.287052 0.497189i
\(291\) −5.92463 + 0.934048i −0.347308 + 0.0547548i
\(292\) 5.53501 5.53501i 0.323912 0.323912i
\(293\) −22.8428 + 22.8428i −1.33449 + 1.33449i −0.433181 + 0.901307i \(0.642609\pi\)
−0.901307 + 0.433181i \(0.857391\pi\)
\(294\) 2.28894 + 2.83072i 0.133494 + 0.165091i
\(295\) −10.3880 17.9925i −0.604811 1.04756i
\(296\) −0.609562 1.05579i −0.0354301 0.0613667i
\(297\) 0.421983 + 0.832578i 0.0244860 + 0.0483111i
\(298\) 16.4992i 0.955774i
\(299\) 4.66265 + 0.103446i 0.269648 + 0.00598243i
\(300\) 0.420639 3.97490i 0.0242856 0.229491i
\(301\) 0.269296 + 1.00503i 0.0155220 + 0.0579288i
\(302\) 4.26432 + 2.46201i 0.245384 + 0.141673i
\(303\) −16.0576 + 7.13560i −0.922482 + 0.409929i
\(304\) −2.20134 8.21551i −0.126255 0.471192i
\(305\) −11.1736 + 2.99396i −0.639799 + 0.171434i
\(306\) 12.8073 25.0475i 0.732143 1.43187i
\(307\) 18.1855 + 18.1855i 1.03790 + 1.03790i 0.999253 + 0.0386487i \(0.0123053\pi\)
0.0386487 + 0.999253i \(0.487695\pi\)
\(308\) 0.376074 0.217127i 0.0214288 0.0123719i
\(309\) 17.4880 24.0342i 0.994857 1.36726i
\(310\) 20.8890 5.59718i 1.18641 0.317898i
\(311\) 3.89896 + 6.75320i 0.221090 + 0.382939i 0.955139 0.296157i \(-0.0957053\pi\)
−0.734049 + 0.679096i \(0.762372\pi\)
\(312\) −5.42957 + 0.732974i −0.307389 + 0.0414965i
\(313\) −14.5254 + 25.1587i −0.821024 + 1.42206i 0.0838962 + 0.996475i \(0.473264\pi\)
−0.904920 + 0.425581i \(0.860070\pi\)
\(314\) −7.95676 + 29.6950i −0.449026 + 1.67579i
\(315\) −5.74126 + 1.85642i −0.323484 + 0.104597i
\(316\) −25.0320 14.4522i −1.40816 0.813001i
\(317\) 5.98943 1.60486i 0.336400 0.0901381i −0.0866648 0.996238i \(-0.527621\pi\)
0.423065 + 0.906099i \(0.360954\pi\)
\(318\) −0.166435 + 0.432658i −0.00933322 + 0.0242623i
\(319\) −0.293767 0.293767i −0.0164478 0.0164478i
\(320\) 21.2115 + 5.68361i 1.18576 + 0.317723i
\(321\) −18.7595 + 25.7816i −1.04705 + 1.43899i
\(322\) 2.71864i 0.151504i
\(323\) −12.2552 3.28378i −0.681900 0.182715i
\(324\) 21.6440 2.21260i 1.20244 0.122922i
\(325\) 0.0763444 3.44110i 0.00423483 0.190878i
\(326\) −40.8432 23.5808i −2.26210 1.30602i
\(327\) −4.96762 + 12.9136i −0.274710 + 0.714125i
\(328\) 3.22141 5.57965i 0.177873 0.308084i
\(329\) 6.94109 0.382675
\(330\) 0.204829 + 1.29922i 0.0112755 + 0.0715200i
\(331\) 6.47091 + 1.73388i 0.355674 + 0.0953025i 0.432231 0.901763i \(-0.357726\pi\)
−0.0765579 + 0.997065i \(0.524393\pi\)
\(332\) 2.05446 + 7.66736i 0.112753 + 0.420801i
\(333\) 2.26553 + 3.49950i 0.124150 + 0.191772i
\(334\) −10.8155 + 18.7330i −0.591797 + 1.02502i
\(335\) 3.78959 0.207048
\(336\) 0.806758 + 5.11723i 0.0440122 + 0.279168i
\(337\) −15.7734 + 9.10680i −0.859234 + 0.496079i −0.863756 0.503911i \(-0.831894\pi\)
0.00452190 + 0.999990i \(0.498561\pi\)
\(338\) −26.6796 + 5.89425i −1.45118 + 0.320605i
\(339\) 0.339066 + 0.763016i 0.0184155 + 0.0414413i
\(340\) 15.3394 15.3394i 0.831898 0.831898i
\(341\) 0.795850 0.459484i 0.0430977 0.0248825i
\(342\) −5.51652 17.0607i −0.298299 0.922537i
\(343\) −0.707107 + 0.707107i −0.0381802 + 0.0381802i
\(344\) 0.236257 0.881724i 0.0127381 0.0475394i
\(345\) −4.20573 1.61786i −0.226429 0.0871028i
\(346\) 4.34485 16.2152i 0.233581 0.871735i
\(347\) 16.1015i 0.864376i 0.901784 + 0.432188i \(0.142258\pi\)
−0.901784 + 0.432188i \(0.857742\pi\)
\(348\) −8.84924 + 3.93239i −0.474369 + 0.210798i
\(349\) −2.55102 2.55102i −0.136553 0.136553i 0.635526 0.772079i \(-0.280783\pi\)
−0.772079 + 0.635526i \(0.780783\pi\)
\(350\) 2.00639 0.107246
\(351\) 18.4149 3.44849i 0.982914 0.184067i
\(352\) 1.44442 0.0769878
\(353\) −1.25311 1.25311i −0.0666961 0.0666961i 0.672972 0.739668i \(-0.265017\pi\)
−0.739668 + 0.672972i \(0.765017\pi\)
\(354\) −34.3632 + 15.2702i −1.82638 + 0.811602i
\(355\) 8.11439i 0.430667i
\(356\) 5.79413 21.6240i 0.307088 1.14607i
\(357\) 7.21252 + 2.77452i 0.381727 + 0.146843i
\(358\) −5.62947 + 21.0095i −0.297527 + 1.11038i
\(359\) 23.2719 23.2719i 1.22824 1.22824i 0.263614 0.964628i \(-0.415086\pi\)
0.964628 0.263614i \(-0.0849144\pi\)
\(360\) 5.17640 + 1.10798i 0.272820 + 0.0583957i
\(361\) 9.45123 5.45667i 0.497433 0.287193i
\(362\) 21.9366 21.9366i 1.15296 1.15296i
\(363\) −7.71429 17.3598i −0.404895 0.911154i
\(364\) −2.06860 8.46709i −0.108424 0.443796i
\(365\) −5.64016 + 3.25635i −0.295220 + 0.170445i
\(366\) 3.26055 + 20.6816i 0.170432 + 1.08104i
\(367\) −29.4807 −1.53888 −0.769440 0.638719i \(-0.779465\pi\)
−0.769440 + 0.638719i \(0.779465\pi\)
\(368\) −1.93439 + 3.35046i −0.100837 + 0.174655i
\(369\) −10.0300 + 19.6159i −0.522140 + 1.02116i
\(370\) 1.52038 + 5.67415i 0.0790409 + 0.294985i
\(371\) −0.123002 0.0329582i −0.00638592 0.00171110i
\(372\) −3.33579 21.1588i −0.172952 1.09703i
\(373\) −10.8374 −0.561140 −0.280570 0.959834i \(-0.590523\pi\)
−0.280570 + 0.959834i \(0.590523\pi\)
\(374\) 0.842246 1.45881i 0.0435515 0.0754334i
\(375\) −7.44780 + 19.3610i −0.384603 + 0.999797i
\(376\) −5.27367 3.04476i −0.271969 0.157021i
\(377\) −7.31222 + 4.00814i −0.376598 + 0.206430i
\(378\) 2.24781 + 10.6873i 0.115615 + 0.549694i
\(379\) 21.5306 + 5.76912i 1.10595 + 0.296340i 0.765187 0.643808i \(-0.222646\pi\)
0.340768 + 0.940148i \(0.389313\pi\)
\(380\) 13.8266i 0.709290i
\(381\) −1.97056 + 2.70819i −0.100955 + 0.138745i
\(382\) −22.8292 6.11707i −1.16804 0.312976i
\(383\) 15.1077 + 15.1077i 0.771968 + 0.771968i 0.978450 0.206482i \(-0.0662016\pi\)
−0.206482 + 0.978450i \(0.566202\pi\)
\(384\) 4.26949 11.0988i 0.217876 0.566382i
\(385\) −0.348991 + 0.0935119i −0.0177862 + 0.00476581i
\(386\) −41.6308 24.0356i −2.11895 1.22338i
\(387\) −0.653329 + 3.05230i −0.0332106 + 0.155157i
\(388\) −2.16660 + 8.08588i −0.109993 + 0.410498i
\(389\) 16.5885 28.7321i 0.841070 1.45678i −0.0479207 0.998851i \(-0.515259\pi\)
0.888991 0.457925i \(-0.151407\pi\)
\(390\) 26.1848 + 3.35981i 1.32592 + 0.170130i
\(391\) 2.88557 + 4.99795i 0.145929 + 0.252757i
\(392\) 0.847420 0.227065i 0.0428012 0.0114685i
\(393\) −14.5185 + 19.9531i −0.732359 + 1.00650i
\(394\) 2.36690 1.36653i 0.119243 0.0688448i
\(395\) 17.0050 + 17.0050i 0.855616 + 0.855616i
\(396\) 1.30107 0.0663294i 0.0653812 0.00333318i
\(397\) −21.1877 + 5.67722i −1.06338 + 0.284932i −0.747770 0.663958i \(-0.768876\pi\)
−0.315609 + 0.948889i \(0.602209\pi\)
\(398\) 13.6027 + 50.7661i 0.681844 + 2.54467i
\(399\) 4.50104 2.00016i 0.225334 0.100133i
\(400\) 2.47268 + 1.42760i 0.123634 + 0.0713802i
\(401\) −6.92418 25.8414i −0.345777 1.29046i −0.891702 0.452623i \(-0.850488\pi\)
0.545925 0.837834i \(-0.316178\pi\)
\(402\) 0.721811 6.82087i 0.0360006 0.340194i
\(403\) −4.37759 17.9181i −0.218063 0.892564i
\(404\) 24.5246i 1.22015i
\(405\) −17.8708 2.88263i −0.888008 0.143239i
\(406\) −2.43041 4.20960i −0.120619 0.208919i
\(407\) 0.124811 + 0.216180i 0.00618667 + 0.0107156i
\(408\) −4.26284 5.27183i −0.211042 0.260995i
\(409\) 21.4988 21.4988i 1.06305 1.06305i 0.0651713 0.997874i \(-0.479241\pi\)
0.997874 0.0651713i \(-0.0207594\pi\)
\(410\) −21.9518 + 21.9518i −1.08412 + 1.08412i
\(411\) 6.56239 1.03459i 0.323699 0.0510328i
\(412\) −20.7423 35.9267i −1.02190 1.76998i
\(413\) −5.16478 8.94565i −0.254142 0.440187i
\(414\) −3.71305 + 7.26171i −0.182487 + 0.356893i
\(415\) 6.60435i 0.324195i
\(416\) 8.12290 27.8305i 0.398258 1.36450i
\(417\) 24.9430 11.0841i 1.22146 0.542789i
\(418\) −0.277879 1.03706i −0.0135915 0.0507243i
\(419\) 0.0679725 + 0.0392440i 0.00332068 + 0.00191719i 0.501659 0.865065i \(-0.332723\pi\)
−0.498339 + 0.866982i \(0.666056\pi\)
\(420\) −0.886251 + 8.37478i −0.0432446 + 0.408648i
\(421\) 2.17516 + 8.11782i 0.106011 + 0.395638i 0.998458 0.0555141i \(-0.0176798\pi\)
−0.892447 + 0.451152i \(0.851013\pi\)
\(422\) −31.0333 + 8.31535i −1.51068 + 0.404785i
\(423\) 18.5402 + 9.47996i 0.901455 + 0.460932i
\(424\) 0.0789963 + 0.0789963i 0.00383640 + 0.00383640i
\(425\) 3.68855 2.12959i 0.178921 0.103300i
\(426\) −14.6050 1.54556i −0.707617 0.0748827i
\(427\) −5.55538 + 1.48856i −0.268844 + 0.0720365i
\(428\) 22.2504 + 38.5388i 1.07551 + 1.86284i
\(429\) 1.11174 0.150081i 0.0536751 0.00724597i
\(430\) −2.19921 + 3.80915i −0.106056 + 0.183694i
\(431\) −7.19743 + 26.8612i −0.346688 + 1.29386i 0.543940 + 0.839124i \(0.316932\pi\)
−0.890628 + 0.454733i \(0.849735\pi\)
\(432\) −4.83408 + 14.7704i −0.232580 + 0.710640i
\(433\) 11.2278 + 6.48236i 0.539573 + 0.311522i 0.744906 0.667170i \(-0.232494\pi\)
−0.205333 + 0.978692i \(0.565828\pi\)
\(434\) 10.3857 2.78285i 0.498531 0.133581i
\(435\) 7.95857 1.25471i 0.381584 0.0601586i
\(436\) 13.6550 + 13.6550i 0.653955 + 0.653955i
\(437\) 3.55301 + 0.952026i 0.169964 + 0.0455416i
\(438\) 4.78679 + 10.7719i 0.228722 + 0.514703i
\(439\) 37.7111i 1.79985i 0.436042 + 0.899926i \(0.356380\pi\)
−0.436042 + 0.899926i \(0.643620\pi\)
\(440\) 0.306175 + 0.0820393i 0.0145963 + 0.00391107i
\(441\) −2.85449 + 0.922989i −0.135928 + 0.0439519i
\(442\) −23.3713 24.4319i −1.11166 1.16211i
\(443\) −14.7627 8.52326i −0.701398 0.404952i 0.106470 0.994316i \(-0.466045\pi\)
−0.807868 + 0.589364i \(0.799379\pi\)
\(444\) 5.74743 0.906112i 0.272761 0.0430022i
\(445\) −9.31300 + 16.1306i −0.441479 + 0.764663i
\(446\) −12.9471 −0.613065
\(447\) −12.6903 4.88172i −0.600232 0.230898i
\(448\) 10.5461 + 2.82582i 0.498257 + 0.133508i
\(449\) −1.35255 5.04777i −0.0638306 0.238219i 0.926639 0.375953i \(-0.122685\pi\)
−0.990469 + 0.137734i \(0.956018\pi\)
\(450\) 5.35924 + 2.74028i 0.252637 + 0.129178i
\(451\) −0.659603 + 1.14247i −0.0310595 + 0.0537966i
\(452\) 1.16535 0.0548135
\(453\) −3.15536 + 2.55144i −0.148252 + 0.119877i
\(454\) −13.9992 + 8.08244i −0.657015 + 0.379328i
\(455\) −0.160851 + 7.25010i −0.00754083 + 0.339890i
\(456\) −4.29716 0.454742i −0.201233 0.0212953i
\(457\) 16.3502 16.3502i 0.764829 0.764829i −0.212362 0.977191i \(-0.568116\pi\)
0.977191 + 0.212362i \(0.0681155\pi\)
\(458\) −35.3897 + 20.4322i −1.65365 + 0.954735i
\(459\) 15.4758 + 17.2616i 0.722350 + 0.805704i
\(460\) −4.44717 + 4.44717i −0.207351 + 0.207351i
\(461\) −0.992217 + 3.70301i −0.0462122 + 0.172466i −0.985175 0.171552i \(-0.945122\pi\)
0.938963 + 0.344019i \(0.111788\pi\)
\(462\) 0.101839 + 0.645959i 0.00473796 + 0.0300527i
\(463\) −2.40570 + 8.97818i −0.111802 + 0.417251i −0.999028 0.0440843i \(-0.985963\pi\)
0.887226 + 0.461336i \(0.152630\pi\)
\(464\) 6.91723i 0.321124i
\(465\) −1.87549 + 17.7228i −0.0869737 + 0.821873i
\(466\) 37.8816 + 37.8816i 1.75483 + 1.75483i
\(467\) 14.9370 0.691201 0.345601 0.938382i \(-0.387675\pi\)
0.345601 + 0.938382i \(0.387675\pi\)
\(468\) 6.03874 25.4415i 0.279141 1.17603i
\(469\) 1.88414 0.0870015
\(470\) 20.7480 + 20.7480i 0.957034 + 0.957034i
\(471\) −20.4856 14.9060i −0.943928 0.686831i
\(472\) 9.06225i 0.417124i
\(473\) −0.0483750 + 0.180538i −0.00222429 + 0.00830115i
\(474\) 33.8462 27.3683i 1.55461 1.25707i
\(475\) 0.702608 2.62217i 0.0322379 0.120313i
\(476\) 7.62659 7.62659i 0.349564 0.349564i
\(477\) −0.283533 0.256026i −0.0129821 0.0117226i
\(478\) 12.7862 7.38211i 0.584827 0.337650i
\(479\) −14.1199 + 14.1199i −0.645156 + 0.645156i −0.951818 0.306663i \(-0.900788\pi\)
0.306663 + 0.951818i \(0.400788\pi\)
\(480\) −16.4811 + 22.6504i −0.752256 + 1.03384i
\(481\) 4.86716 1.18910i 0.221923 0.0542183i
\(482\) −10.1675 + 5.87018i −0.463115 + 0.267380i
\(483\) −2.09104 0.804381i −0.0951454 0.0366006i
\(484\) −26.5136 −1.20516
\(485\) 3.48242 6.03173i 0.158129 0.273887i
\(486\) −8.59232 + 31.6165i −0.389755 + 1.43415i
\(487\) −7.12407 26.5874i −0.322822 1.20479i −0.916483 0.400074i \(-0.868984\pi\)
0.593661 0.804716i \(-0.297682\pi\)
\(488\) 4.87381 + 1.30593i 0.220627 + 0.0591168i
\(489\) 30.2216 24.4374i 1.36667 1.10510i
\(490\) −4.22731 −0.190970
\(491\) 15.5521 26.9370i 0.701855 1.21565i −0.265960 0.963984i \(-0.585689\pi\)
0.967815 0.251664i \(-0.0809778\pi\)
\(492\) 19.3341 + 23.9104i 0.871647 + 1.07796i
\(493\) −8.93614 5.15929i −0.402464 0.232363i
\(494\) −21.5444 0.477985i −0.969327 0.0215056i
\(495\) −1.05990 0.226866i −0.0476389 0.0101969i
\(496\) 14.7795 + 3.96015i 0.663618 + 0.177816i
\(497\) 4.03438i 0.180967i
\(498\) −11.8871 1.25794i −0.532675 0.0563697i
\(499\) −22.5308 6.03711i −1.00862 0.270258i −0.283565 0.958953i \(-0.591517\pi\)
−0.725051 + 0.688695i \(0.758184\pi\)
\(500\) 20.4725 + 20.4725i 0.915557 + 0.915557i
\(501\) −11.2084 13.8613i −0.500753 0.619279i
\(502\) −50.9268 + 13.6458i −2.27297 + 0.609042i
\(503\) −23.1717 13.3782i −1.03317 0.596503i −0.115281 0.993333i \(-0.536777\pi\)
−0.917892 + 0.396830i \(0.870110\pi\)
\(504\) 2.57364 + 0.550875i 0.114639 + 0.0245379i
\(505\) 5.28113 19.7094i 0.235007 0.877059i
\(506\) −0.244182 + 0.422935i −0.0108552 + 0.0188018i
\(507\) 3.36031 22.2645i 0.149237 0.988802i
\(508\) 2.33726 + 4.04825i 0.103699 + 0.179612i
\(509\) 30.7480 8.23889i 1.36288 0.365182i 0.498006 0.867173i \(-0.334066\pi\)
0.864873 + 0.501991i \(0.167399\pi\)
\(510\) 13.2659 + 29.8528i 0.587423 + 1.32191i
\(511\) −2.80422 + 1.61902i −0.124051 + 0.0716211i
\(512\) 20.7165 + 20.7165i 0.915549 + 0.915549i
\(513\) 14.7544 + 0.804835i 0.651422 + 0.0355344i
\(514\) −51.2918 + 13.7436i −2.26238 + 0.606204i
\(515\) 8.93329 + 33.3395i 0.393648 + 1.46911i
\(516\) 3.52273 + 2.56324i 0.155079 + 0.112841i
\(517\) 1.07982 + 0.623432i 0.0474902 + 0.0274185i
\(518\) 0.755916 + 2.82112i 0.0332130 + 0.123953i
\(519\) 11.1863 + 8.13952i 0.491026 + 0.357285i
\(520\) 3.30252 5.43790i 0.144825 0.238467i
\(521\) 11.9181i 0.522142i 0.965320 + 0.261071i \(0.0840757\pi\)
−0.965320 + 0.261071i \(0.915924\pi\)
\(522\) −0.742460 14.5636i −0.0324966 0.637430i
\(523\) −13.8980 24.0720i −0.607715 1.05259i −0.991616 0.129219i \(-0.958753\pi\)
0.383901 0.923374i \(-0.374580\pi\)
\(524\) 17.2202 + 29.8262i 0.752267 + 1.30296i
\(525\) −0.593644 + 1.54321i −0.0259088 + 0.0673513i
\(526\) 33.1778 33.1778i 1.44662 1.44662i
\(527\) 16.1394 16.1394i 0.703044 0.703044i
\(528\) −0.334111 + 0.868542i −0.0145403 + 0.0377984i
\(529\) 10.6634 + 18.4696i 0.463627 + 0.803026i
\(530\) −0.269154 0.466188i −0.0116913 0.0202499i
\(531\) −1.57777 30.9485i −0.0684695 1.34305i
\(532\) 6.87442i 0.298044i
\(533\) 18.3032 + 19.1338i 0.792800 + 0.828776i
\(534\) 27.2595 + 19.8348i 1.17963 + 0.858338i
\(535\) −9.58278 35.7634i −0.414300 1.54619i
\(536\) −1.43152 0.826491i −0.0618324 0.0356990i
\(537\) −14.4937 10.5461i −0.625451 0.455097i
\(538\) −5.24637 19.5797i −0.226187 0.844141i
\(539\) −0.173514 + 0.0464930i −0.00747379 + 0.00200259i
\(540\) −13.8053 + 21.1593i −0.594086 + 0.910550i
\(541\) −27.7569 27.7569i −1.19336 1.19336i −0.976117 0.217248i \(-0.930292\pi\)
−0.217248 0.976117i \(-0.569708\pi\)
\(542\) 40.7492 23.5266i 1.75033 1.01055i
\(543\) 10.3819 + 23.3630i 0.445532 + 1.00260i
\(544\) 34.6529 9.28522i 1.48573 0.398100i
\(545\) −8.03348 13.9144i −0.344117 0.596027i
\(546\) 13.0188 + 1.67046i 0.557153 + 0.0714889i
\(547\) −6.05457 + 10.4868i −0.258875 + 0.448384i −0.965941 0.258763i \(-0.916685\pi\)
0.707066 + 0.707147i \(0.250018\pi\)
\(548\) 2.39983 8.95629i 0.102516 0.382594i
\(549\) −16.8719 3.61134i −0.720075 0.154128i
\(550\) 0.312132 + 0.180209i 0.0133093 + 0.00768416i
\(551\) −6.35264 + 1.70219i −0.270632 + 0.0725156i
\(552\) 1.23587 + 1.52840i 0.0526022 + 0.0650529i
\(553\) 8.45469 + 8.45469i 0.359530 + 0.359530i
\(554\) 12.0761 + 3.23578i 0.513064 + 0.137475i
\(555\) −4.81410 0.509446i −0.204347 0.0216248i
\(556\) 38.0953i 1.61560i
\(557\) 11.8448 + 3.17381i 0.501881 + 0.134479i 0.500873 0.865521i \(-0.333012\pi\)
0.00100818 + 0.999999i \(0.499679\pi\)
\(558\) 31.5419 + 6.75137i 1.33527 + 0.285808i
\(559\) 3.20649 + 1.94735i 0.135620 + 0.0823643i
\(560\) −5.20974 3.00784i −0.220152 0.127105i
\(561\) 0.872841 + 1.07944i 0.0368514 + 0.0455739i
\(562\) 18.1399 31.4193i 0.765186 1.32534i
\(563\) 42.9396 1.80969 0.904844 0.425743i \(-0.139987\pi\)
0.904844 + 0.425743i \(0.139987\pi\)
\(564\) 22.5992 18.2738i 0.951597 0.769467i
\(565\) −0.936545 0.250946i −0.0394007 0.0105574i
\(566\) 5.27558 + 19.6887i 0.221749 + 0.827579i
\(567\) −8.88515 1.43321i −0.373141 0.0601891i
\(568\) −1.76971 + 3.06522i −0.0742552 + 0.128614i
\(569\) 8.01701 0.336090 0.168045 0.985779i \(-0.446255\pi\)
0.168045 + 0.985779i \(0.446255\pi\)
\(570\) 19.4331 + 7.47554i 0.813963 + 0.313116i
\(571\) 11.1676 6.44763i 0.467350 0.269825i −0.247780 0.968816i \(-0.579701\pi\)
0.715130 + 0.698992i \(0.246368\pi\)
\(572\) 0.438684 1.50301i 0.0183423 0.0628440i
\(573\) 11.4595 15.7491i 0.478729 0.657929i
\(574\) −10.9142 + 10.9142i −0.455548 + 0.455548i
\(575\) −1.06938 + 0.617405i −0.0445961 + 0.0257476i
\(576\) 24.3100 + 21.9516i 1.01292 + 0.914650i
\(577\) 14.9564 14.9564i 0.622645 0.622645i −0.323562 0.946207i \(-0.604880\pi\)
0.946207 + 0.323562i \(0.104880\pi\)
\(578\) 1.58087 5.89989i 0.0657556 0.245403i
\(579\) 30.8045 24.9087i 1.28019 1.03517i
\(580\) 2.91040 10.8618i 0.120848 0.451011i
\(581\) 3.28360i 0.136227i
\(582\) −10.1932 7.41687i −0.422521 0.307439i
\(583\) −0.0161750 0.0161750i −0.000669898 0.000669898i
\(584\) 2.84077 0.117552
\(585\) −10.3317 + 19.1459i −0.427161 + 0.791586i
\(586\) −67.8965 −2.80478
\(587\) 19.7722 + 19.7722i 0.816087 + 0.816087i 0.985539 0.169452i \(-0.0541996\pi\)
−0.169452 + 0.985539i \(0.554200\pi\)
\(588\) −0.440633 + 4.16384i −0.0181714 + 0.171714i
\(589\) 14.5477i 0.599427i
\(590\) 11.3016 42.1783i 0.465281 1.73645i
\(591\) 0.350754 + 2.22482i 0.0144281 + 0.0915168i
\(592\) −1.07571 + 4.01460i −0.0442114 + 0.164999i
\(593\) 3.60170 3.60170i 0.147904 0.147904i −0.629277 0.777181i \(-0.716649\pi\)
0.777181 + 0.629277i \(0.216649\pi\)
\(594\) −0.610215 + 1.86450i −0.0250374 + 0.0765012i
\(595\) −7.77148 + 4.48686i −0.318600 + 0.183944i
\(596\) −13.4189 + 13.4189i −0.549658 + 0.549658i
\(597\) −43.0713 4.55797i −1.76279 0.186545i
\(598\) 6.77576 + 7.08324i 0.277082 + 0.289655i
\(599\) 24.2256 13.9866i 0.989829 0.571478i 0.0846059 0.996414i \(-0.473037\pi\)
0.905223 + 0.424936i \(0.139704\pi\)
\(600\) 1.12798 0.912089i 0.0460495 0.0372359i
\(601\) −12.3336 −0.503098 −0.251549 0.967845i \(-0.580940\pi\)
−0.251549 + 0.967845i \(0.580940\pi\)
\(602\) −1.09342 + 1.89386i −0.0445646 + 0.0771881i
\(603\) 5.03269 + 2.57331i 0.204947 + 0.104793i
\(604\) 1.46583 + 5.47054i 0.0596437 + 0.222593i
\(605\) 21.3079 + 5.70943i 0.866288 + 0.232121i
\(606\) −34.4690 13.2596i −1.40021 0.538633i
\(607\) −7.98497 −0.324100 −0.162050 0.986783i \(-0.551811\pi\)
−0.162050 + 0.986783i \(0.551811\pi\)
\(608\) 11.4329 19.8024i 0.463666 0.803093i
\(609\) 3.95690 0.623826i 0.160342 0.0252787i
\(610\) −21.0554 12.1564i −0.852510 0.492197i
\(611\) 18.0845 17.2995i 0.731622 0.699863i
\(612\) 30.7874 9.95501i 1.24451 0.402407i
\(613\) 14.6591 + 3.92788i 0.592074 + 0.158646i 0.542401 0.840120i \(-0.317515\pi\)
0.0496731 + 0.998766i \(0.484182\pi\)
\(614\) 54.0536i 2.18143i
\(615\) −10.3891 23.3792i −0.418931 0.942739i
\(616\) 0.152226 + 0.0407889i 0.00613337 + 0.00164343i
\(617\) 31.5843 + 31.5843i 1.27154 + 1.27154i 0.945281 + 0.326257i \(0.105787\pi\)
0.326257 + 0.945281i \(0.394213\pi\)
\(618\) 61.7091 9.72875i 2.48230 0.391348i
\(619\) 38.1473 10.2215i 1.53327 0.410838i 0.609185 0.793028i \(-0.291497\pi\)
0.924084 + 0.382190i \(0.124830\pi\)
\(620\) 21.5413 + 12.4369i 0.865118 + 0.499476i
\(621\) −4.48672 5.00445i −0.180046 0.200822i
\(622\) −4.24189 + 15.8309i −0.170084 + 0.634763i
\(623\) −4.63031 + 8.01993i −0.185510 + 0.321312i
\(624\) 14.8558 + 11.3219i 0.594708 + 0.453239i
\(625\) −9.65779 16.7278i −0.386312 0.669111i
\(626\) −58.9775 + 15.8030i −2.35721 + 0.631613i
\(627\) 0.879870 + 0.0931112i 0.0351386 + 0.00371850i
\(628\) −30.6223 + 17.6798i −1.22196 + 0.705501i
\(629\) 4.38401 + 4.38401i 0.174802 + 0.174802i
\(630\) −11.2915 5.77355i −0.449863 0.230024i
\(631\) 13.8750 3.71779i 0.552354 0.148003i 0.0281626 0.999603i \(-0.491034\pi\)
0.524191 + 0.851601i \(0.324368\pi\)
\(632\) −2.71496 10.1324i −0.107995 0.403044i
\(633\) 2.78629 26.3295i 0.110745 1.04650i
\(634\) 11.2864 + 6.51622i 0.448241 + 0.258792i
\(635\) −1.00661 3.75672i −0.0399461 0.149081i
\(636\) −0.487244 + 0.216520i −0.0193205 + 0.00858557i
\(637\) −0.0799733 + 3.60466i −0.00316866 + 0.142822i
\(638\) 0.873175i 0.0345693i
\(639\) 5.51005 10.7761i 0.217974 0.426297i
\(640\) 6.90448 + 11.9589i 0.272924 + 0.472717i
\(641\) 10.3712 + 17.9635i 0.409640 + 0.709517i 0.994849 0.101365i \(-0.0323211\pi\)
−0.585210 + 0.810882i \(0.698988\pi\)
\(642\) −66.1956 + 10.4361i −2.61253 + 0.411879i
\(643\) 11.4333 11.4333i 0.450884 0.450884i −0.444764 0.895648i \(-0.646712\pi\)
0.895648 + 0.444764i \(0.146712\pi\)
\(644\) −2.21108 + 2.21108i −0.0871288 + 0.0871288i
\(645\) −2.27910 2.81856i −0.0897396 0.110981i
\(646\) −13.3331 23.0937i −0.524585 0.908609i
\(647\) 13.9659 + 24.1896i 0.549054 + 0.950990i 0.998340 + 0.0576017i \(0.0183454\pi\)
−0.449285 + 0.893388i \(0.648321\pi\)
\(648\) 6.12204 + 4.98645i 0.240496 + 0.195886i
\(649\) 1.85555i 0.0728367i
\(650\) 5.22752 5.00060i 0.205040 0.196140i
\(651\) −0.932471 + 8.81154i −0.0365464 + 0.345351i
\(652\) −14.0395 52.3963i −0.549831 2.05200i
\(653\) −12.4343 7.17895i −0.486592 0.280934i 0.236568 0.971615i \(-0.423978\pi\)
−0.723160 + 0.690681i \(0.757311\pi\)
\(654\) −26.5746 + 11.8091i −1.03915 + 0.461773i
\(655\) −7.41638 27.6783i −0.289782 1.08148i
\(656\) −21.2164 + 5.68491i −0.828360 + 0.221958i
\(657\) −9.70151 + 0.494589i −0.378492 + 0.0192958i
\(658\) 10.3157 + 10.3157i 0.402146 + 0.402146i
\(659\) −3.28092 + 1.89424i −0.127807 + 0.0737892i −0.562540 0.826770i \(-0.690176\pi\)
0.434734 + 0.900559i \(0.356843\pi\)
\(660\) −0.890075 + 1.22325i −0.0346461 + 0.0476150i
\(661\) 40.1706 10.7637i 1.56245 0.418658i 0.629014 0.777394i \(-0.283459\pi\)
0.933439 + 0.358736i \(0.116792\pi\)
\(662\) 7.04006 + 12.1937i 0.273620 + 0.473923i
\(663\) 25.7068 10.7472i 0.998368 0.417386i
\(664\) −1.44037 + 2.49480i −0.0558974 + 0.0968171i
\(665\) −1.48034 + 5.52469i −0.0574050 + 0.214238i
\(666\) −1.83390 + 8.56783i −0.0710621 + 0.331997i
\(667\) 2.59074 + 1.49577i 0.100314 + 0.0579163i
\(668\) −24.0318 + 6.43931i −0.929820 + 0.249145i
\(669\) 3.83075 9.95826i 0.148105 0.385008i
\(670\) 5.63199 + 5.63199i 0.217583 + 0.217583i
\(671\) −0.997942 0.267398i −0.0385251 0.0103228i
\(672\) −8.19420 + 11.2615i −0.316098 + 0.434421i
\(673\) 30.6280i 1.18062i 0.807176 + 0.590311i \(0.200995\pi\)
−0.807176 + 0.590311i \(0.799005\pi\)
\(674\) −36.9763 9.90777i −1.42427 0.381633i
\(675\) −3.69335 + 3.31126i −0.142157 + 0.127450i
\(676\) −26.4924 16.9048i −1.01894 0.650184i
\(677\) −38.4387 22.1926i −1.47732 0.852931i −0.477648 0.878551i \(-0.658511\pi\)
−0.999672 + 0.0256201i \(0.991844\pi\)
\(678\) −0.630062 + 1.63788i −0.0241974 + 0.0629025i
\(679\) 1.73142 2.99890i 0.0664457 0.115087i
\(680\) 7.87277 0.301907
\(681\) −2.07456 13.1588i −0.0794972 0.504248i
\(682\) 1.86564 + 0.499898i 0.0714392 + 0.0191421i
\(683\) −4.95172 18.4801i −0.189472 0.707120i −0.993629 0.112703i \(-0.964049\pi\)
0.804156 0.594418i \(-0.202617\pi\)
\(684\) 9.38892 18.3621i 0.358994 0.702093i
\(685\) −3.85729 + 6.68102i −0.147379 + 0.255269i
\(686\) −2.10177 −0.0802458
\(687\) −5.24443 33.2653i −0.200088 1.26915i
\(688\) −2.69507 + 1.55600i −0.102749 + 0.0593220i
\(689\) −0.402615 + 0.220691i −0.0153384 + 0.00840764i
\(690\) −3.84601 8.65486i −0.146415 0.329485i
\(691\) 6.09902 6.09902i 0.232018 0.232018i −0.581517 0.813534i \(-0.697541\pi\)
0.813534 + 0.581517i \(0.197541\pi\)
\(692\) 16.7216 9.65419i 0.635658 0.366997i
\(693\) −0.526969 0.112795i −0.0200179 0.00428472i
\(694\) −23.9297 + 23.9297i −0.908358 + 0.908358i
\(695\) −8.20344 + 30.6157i −0.311174 + 1.16132i
\(696\) −3.28000 1.26175i −0.124328 0.0478267i
\(697\) −8.48029 + 31.6489i −0.321214 + 1.19879i
\(698\) 7.58252i 0.287003i
\(699\) −40.3448 + 17.9283i −1.52598 + 0.678110i
\(700\) 1.63181 + 1.63181i 0.0616765 + 0.0616765i
\(701\) 11.7749 0.444732 0.222366 0.974963i \(-0.428622\pi\)
0.222366 + 0.974963i \(0.428622\pi\)
\(702\) 32.4927 + 22.2426i 1.22636 + 0.839495i
\(703\) 3.95164 0.149039
\(704\) 1.38683 + 1.38683i 0.0522683 + 0.0522683i
\(705\) −22.0971 + 9.81943i −0.832225 + 0.369821i
\(706\) 3.72467i 0.140180i
\(707\) 2.62571 9.79930i 0.0987501 0.368540i
\(708\) −40.3670 15.5284i −1.51709 0.583594i
\(709\) 6.49962 24.2569i 0.244098 0.910988i −0.729736 0.683729i \(-0.760357\pi\)
0.973834 0.227259i \(-0.0729763\pi\)
\(710\) 12.0594 12.0594i 0.452581 0.452581i
\(711\) 11.0359 + 34.1304i 0.413880 + 1.27999i
\(712\) 7.03600 4.06223i 0.263685 0.152239i
\(713\) −4.67910 + 4.67910i −0.175234 + 0.175234i
\(714\) 6.59564 + 14.8425i 0.246836 + 0.555465i
\(715\) −0.676210 + 1.11344i −0.0252888 + 0.0416403i
\(716\) −21.6655 + 12.5086i −0.809678 + 0.467468i
\(717\) 1.89480 + 12.0186i 0.0707626 + 0.448845i
\(718\) 69.1720 2.58148
\(719\) −5.85138 + 10.1349i −0.218219 + 0.377967i −0.954264 0.298966i \(-0.903358\pi\)
0.736044 + 0.676933i \(0.236692\pi\)
\(720\) −9.80759 15.1495i −0.365507 0.564589i
\(721\) 4.44152 + 16.5760i 0.165411 + 0.617322i
\(722\) 22.1557 + 5.93660i 0.824550 + 0.220937i
\(723\) −1.50673 9.55712i −0.0560358 0.355433i
\(724\) 35.6822 1.32612
\(725\) 1.10390 1.91200i 0.0409977 0.0710100i
\(726\) 14.3349 37.2644i 0.532019 1.38301i
\(727\) −36.7618 21.2244i −1.36342 0.787171i −0.373343 0.927693i \(-0.621788\pi\)
−0.990078 + 0.140522i \(0.955122\pi\)
\(728\) 1.64197 2.70366i 0.0608555 0.100204i
\(729\) −21.7755 15.9633i −0.806500 0.591234i
\(730\) −13.2218 3.54276i −0.489359 0.131123i
\(731\) 4.64224i 0.171699i
\(732\) −14.1686 + 19.4722i −0.523686 + 0.719714i
\(733\) −26.1516 7.00729i −0.965930 0.258820i −0.258821 0.965925i \(-0.583334\pi\)
−0.707108 + 0.707105i \(0.750001\pi\)
\(734\) −43.8134 43.8134i −1.61718 1.61718i
\(735\) 1.25076 3.25142i 0.0461349 0.119930i
\(736\) −10.0465 + 2.69195i −0.370318 + 0.0992265i
\(737\) 0.293113 + 0.169229i 0.0107970 + 0.00623363i
\(738\) −44.0589 + 14.2463i −1.62183 + 0.524413i
\(739\) −7.35287 + 27.4413i −0.270480 + 1.00944i 0.688331 + 0.725397i \(0.258344\pi\)
−0.958810 + 0.284047i \(0.908323\pi\)
\(740\) −3.37827 + 5.85133i −0.124188 + 0.215099i
\(741\) 6.74210 16.4294i 0.247677 0.603548i
\(742\) −0.133820 0.231783i −0.00491269 0.00850903i
\(743\) 1.32992 0.356350i 0.0487899 0.0130732i −0.234342 0.972154i \(-0.575293\pi\)
0.283131 + 0.959081i \(0.408627\pi\)
\(744\) 4.57371 6.28576i 0.167680 0.230447i
\(745\) 13.6738 7.89457i 0.500969 0.289235i
\(746\) −16.1063 16.1063i −0.589692 0.589692i
\(747\) 4.48466 8.77076i 0.164085 0.320905i
\(748\) 1.87146 0.501456i 0.0684273 0.0183350i
\(749\) −4.76444 17.7811i −0.174089 0.649709i
\(750\) −39.8425 + 17.7050i −1.45484 + 0.646497i
\(751\) −32.2161 18.6000i −1.17558 0.678723i −0.220595 0.975366i \(-0.570800\pi\)
−0.954989 + 0.296642i \(0.904133\pi\)
\(752\) 5.37316 + 20.0529i 0.195939 + 0.731254i
\(753\) 4.57240 43.2077i 0.166628 1.57457i
\(754\) −16.8240 4.91043i −0.612694 0.178827i
\(755\) 4.71210i 0.171491i
\(756\) −6.86383 + 10.5201i −0.249635 + 0.382614i
\(757\) 1.43134 + 2.47916i 0.0520230 + 0.0901065i 0.890864 0.454270i \(-0.150100\pi\)
−0.838841 + 0.544376i \(0.816766\pi\)
\(758\) 23.4243 + 40.5722i 0.850811 + 1.47365i
\(759\) −0.253052 0.312948i −0.00918520 0.0113593i
\(760\) 3.54817 3.54817i 0.128706 0.128706i
\(761\) 27.2539 27.2539i 0.987953 0.987953i −0.0119749 0.999928i \(-0.503812\pi\)
0.999928 + 0.0119749i \(0.00381183\pi\)
\(762\) −6.95342 + 1.09624i −0.251896 + 0.0397127i
\(763\) −3.99415 6.91807i −0.144598 0.250451i
\(764\) −13.5920 23.5421i −0.491742 0.851723i
\(765\) −26.8863 + 1.37068i −0.972075 + 0.0495570i
\(766\) 44.9053i 1.62250i
\(767\) −35.7520 10.4350i −1.29093 0.376784i
\(768\) −11.7227 + 5.20931i −0.423008 + 0.187975i
\(769\) −9.46163 35.3113i −0.341195 1.27336i −0.896995 0.442041i \(-0.854254\pi\)
0.555799 0.831316i \(-0.312412\pi\)
\(770\) −0.657636 0.379686i −0.0236996 0.0136829i
\(771\) 4.60517 43.5173i 0.165851 1.56724i
\(772\) −14.3103 53.4067i −0.515038 1.92215i
\(773\) −28.9964 + 7.76957i −1.04293 + 0.279452i −0.739327 0.673347i \(-0.764856\pi\)
−0.303603 + 0.952799i \(0.598189\pi\)
\(774\) −5.50721 + 3.56529i −0.197953 + 0.128152i
\(775\) 3.45324 + 3.45324i 0.124044 + 0.124044i
\(776\) −2.63098 + 1.51900i −0.0944466 + 0.0545288i
\(777\) −2.39351 0.253290i −0.0858667 0.00908674i
\(778\) 67.3543 18.0475i 2.41477 0.647035i
\(779\) 10.4418 + 18.0857i 0.374117 + 0.647989i
\(780\) 18.5637 + 24.0288i 0.664686 + 0.860368i
\(781\) 0.362358 0.627622i 0.0129662 0.0224581i
\(782\) −3.13937 + 11.7163i −0.112263 + 0.418973i
\(783\) 11.4212 + 3.73795i 0.408161 + 0.133583i
\(784\) −2.59022 1.49546i −0.0925078 0.0534094i
\(785\) 28.4171 7.61433i 1.01425 0.271767i
\(786\) −51.2306 + 8.07676i −1.82734 + 0.288089i
\(787\) −23.3979 23.3979i −0.834044 0.834044i 0.154023 0.988067i \(-0.450777\pi\)
−0.988067 + 0.154023i \(0.950777\pi\)
\(788\) 3.03641 + 0.813604i 0.108168 + 0.0289834i
\(789\) 15.7021 + 35.3351i 0.559009 + 1.25796i
\(790\) 50.5448i 1.79830i
\(791\) −0.465639 0.124767i −0.0165562 0.00443622i
\(792\) 0.350900 + 0.316857i 0.0124687 + 0.0112590i
\(793\) −10.7642 + 17.7242i −0.382247 + 0.629405i
\(794\) −39.9259 23.0512i −1.41692 0.818057i
\(795\) 0.438204 0.0690850i 0.0155415 0.00245019i
\(796\) −30.2251 + 52.3514i −1.07130 + 1.85555i
\(797\) −38.9375 −1.37924 −0.689619 0.724173i \(-0.742222\pi\)
−0.689619 + 0.724173i \(0.742222\pi\)
\(798\) 9.66190 + 3.71675i 0.342028 + 0.131571i
\(799\) 29.9133 + 8.01525i 1.05826 + 0.283559i
\(800\) 1.98669 + 7.41444i 0.0702402 + 0.262140i
\(801\) −23.3213 + 15.0979i −0.824019 + 0.533459i
\(802\) 28.1142 48.6953i 0.992748 1.71949i
\(803\) −0.581665 −0.0205265
\(804\) 6.13449 4.96039i 0.216347 0.174939i
\(805\) 2.25309 1.30082i 0.0794109 0.0458479i
\(806\) 20.1235 33.1352i 0.708822 1.16714i
\(807\) 16.6120 + 1.75794i 0.584768 + 0.0618824i
\(808\) −6.29348 + 6.29348i −0.221404 + 0.221404i
\(809\) 2.89373 1.67070i 0.101738 0.0587386i −0.448268 0.893899i \(-0.647959\pi\)
0.550006 + 0.835161i \(0.314625\pi\)
\(810\) −22.2750 30.8432i −0.782665 1.08372i
\(811\) −14.7750 + 14.7750i −0.518820 + 0.518820i −0.917214 0.398394i \(-0.869568\pi\)
0.398394 + 0.917214i \(0.369568\pi\)
\(812\) 1.44702 5.40034i 0.0507804 0.189515i
\(813\) 6.03868 + 38.3031i 0.211786 + 1.34335i
\(814\) −0.135789 + 0.506772i −0.00475940 + 0.0177623i
\(815\) 45.1320i 1.58090i
\(816\) −2.43235 + 22.9849i −0.0851491 + 0.804631i
\(817\) 2.09220 + 2.09220i 0.0731969 + 0.0731969i
\(818\) 63.9017 2.23427
\(819\) −5.13677 + 9.51912i −0.179493 + 0.332625i
\(820\) −35.7069 −1.24694
\(821\) −39.6039 39.6039i −1.38218 1.38218i −0.840730 0.541455i \(-0.817874\pi\)
−0.541455 0.840730i \(-0.682126\pi\)
\(822\) 11.2904 + 8.21526i 0.393799 + 0.286540i
\(823\) 32.1048i 1.11910i 0.828795 + 0.559552i \(0.189027\pi\)
−0.828795 + 0.559552i \(0.810973\pi\)
\(824\) 3.89661 14.5423i 0.135745 0.506606i
\(825\) −0.230960 + 0.186756i −0.00804099 + 0.00650200i
\(826\) 5.61904 20.9705i 0.195511 0.729658i
\(827\) 14.4078 14.4078i 0.501008 0.501008i −0.410743 0.911751i \(-0.634731\pi\)
0.911751 + 0.410743i \(0.134731\pi\)
\(828\) −8.92581 + 2.88613i −0.310193 + 0.100300i
\(829\) −47.6629 + 27.5182i −1.65540 + 0.955747i −0.680606 + 0.732650i \(0.738283\pi\)
−0.974796 + 0.223097i \(0.928383\pi\)
\(830\) 9.81520 9.81520i 0.340691 0.340691i
\(831\) −6.06182 + 8.33091i −0.210282 + 0.288996i
\(832\) 34.5201 18.9219i 1.19677 0.656000i
\(833\) −3.86388 + 2.23081i −0.133876 + 0.0772931i
\(834\) 53.5424 + 20.5967i 1.85402 + 0.713207i
\(835\) 20.7000 0.716355
\(836\) 0.617444 1.06944i 0.0213547 0.0369875i
\(837\) −14.5253 + 22.2628i −0.502067 + 0.769514i
\(838\) 0.0426956 + 0.159342i 0.00147490 + 0.00550439i
\(839\) −49.8312 13.3522i −1.72036 0.460970i −0.742437 0.669916i \(-0.766330\pi\)
−0.977927 + 0.208946i \(0.932997\pi\)
\(840\) −2.37655 + 1.92170i −0.0819989 + 0.0663048i
\(841\) 23.6513 0.815560
\(842\) −8.83181 + 15.2971i −0.304364 + 0.527174i
\(843\) 18.7989 + 23.2485i 0.647467 + 0.800720i
\(844\) −32.0024 18.4766i −1.10157 0.635990i
\(845\) 17.6506 + 19.2906i 0.607199 + 0.663615i
\(846\) 13.4651 + 41.6428i 0.462938 + 1.43171i
\(847\) 10.5940 + 2.83866i 0.364015 + 0.0975374i
\(848\) 0.380867i 0.0130790i
\(849\) −16.7044 1.76773i −0.573295 0.0606683i
\(850\) 8.64676 + 2.31689i 0.296582 + 0.0794688i
\(851\) −1.27100 1.27100i −0.0435694 0.0435694i
\(852\) −10.6213 13.1353i −0.363880 0.450009i
\(853\) 38.2431 10.2472i 1.30942 0.350858i 0.464416 0.885617i \(-0.346264\pi\)
0.845004 + 0.534759i \(0.179598\pi\)
\(854\) −10.4685 6.04400i −0.358225 0.206821i
\(855\) −11.4996 + 12.7351i −0.393277 + 0.435530i
\(856\) −4.17991 + 15.5996i −0.142866 + 0.533184i
\(857\) −14.2508 + 24.6832i −0.486799 + 0.843161i −0.999885 0.0151764i \(-0.995169\pi\)
0.513086 + 0.858337i \(0.328502\pi\)
\(858\) 1.87528 + 1.42919i 0.0640209 + 0.0487916i
\(859\) −10.4691 18.1331i −0.357202 0.618692i 0.630290 0.776360i \(-0.282936\pi\)
−0.987492 + 0.157667i \(0.949603\pi\)
\(860\) −4.88662 + 1.30937i −0.166632 + 0.0446490i
\(861\) −5.16536 11.6238i −0.176035 0.396139i
\(862\) −50.6169 + 29.2237i −1.72402 + 0.995363i
\(863\) −10.4269 10.4269i −0.354937 0.354937i 0.507006 0.861943i \(-0.330752\pi\)
−0.861943 + 0.507006i \(0.830752\pi\)
\(864\) −37.2680 + 18.8889i −1.26788 + 0.642613i
\(865\) −15.5174 + 4.15786i −0.527606 + 0.141372i
\(866\) 7.05251 + 26.3203i 0.239654 + 0.894401i
\(867\) 4.07014 + 2.96156i 0.138229 + 0.100580i
\(868\) 10.7101 + 6.18345i 0.363523 + 0.209880i
\(869\) 0.555905 + 2.07466i 0.0188578 + 0.0703782i
\(870\) 13.6925 + 9.96309i 0.464220 + 0.337780i
\(871\) 4.90900 4.69591i 0.166335 0.159115i
\(872\) 7.00824i 0.237329i
\(873\) 8.72058 5.64558i 0.295147 0.191074i
\(874\) 3.86551 + 6.69526i 0.130753 + 0.226471i
\(875\) −5.98830 10.3720i −0.202442 0.350639i
\(876\) −4.86774 + 12.6540i −0.164466 + 0.427538i
\(877\) 0.235605 0.235605i 0.00795581 0.00795581i −0.703118 0.711073i \(-0.748209\pi\)
0.711073 + 0.703118i \(0.248209\pi\)
\(878\) −56.0452 + 56.0452i −1.89143 + 1.89143i
\(879\) 20.0890 52.2224i 0.677584 1.76142i
\(880\) −0.540315 0.935852i −0.0182140 0.0315476i
\(881\) −4.87365 8.44141i −0.164197 0.284398i 0.772173 0.635413i \(-0.219170\pi\)
−0.936370 + 0.351015i \(0.885837\pi\)
\(882\) −5.61398 2.87054i −0.189033 0.0966560i
\(883\) 20.3162i 0.683693i 0.939756 + 0.341847i \(0.111052\pi\)
−0.939756 + 0.341847i \(0.888948\pi\)
\(884\) 0.862562 38.8785i 0.0290111 1.30763i
\(885\) 29.0974 + 21.1722i 0.978099 + 0.711695i
\(886\) −9.27292 34.6070i −0.311530 1.16264i
\(887\) 31.6847 + 18.2932i 1.06387 + 0.614225i 0.926500 0.376295i \(-0.122802\pi\)
0.137369 + 0.990520i \(0.456135\pi\)
\(888\) 1.70742 + 1.24237i 0.0572974 + 0.0416913i
\(889\) −0.500474 1.86779i −0.0167854 0.0626438i
\(890\) −37.8136 + 10.1321i −1.26751 + 0.339629i
\(891\) −1.25352 1.02100i −0.0419946 0.0342049i
\(892\) −10.5300 10.5300i −0.352569 0.352569i
\(893\) 17.0940 9.86921i 0.572028 0.330260i
\(894\) −11.6049 26.1151i −0.388127 0.873419i
\(895\) 20.1053 5.38719i 0.672045 0.180074i
\(896\) 3.43282 + 5.94582i 0.114683 + 0.198636i
\(897\) −7.45284 + 3.11580i −0.248843 + 0.104033i
\(898\) 5.49174 9.51198i 0.183262 0.317419i
\(899\) 3.06219 11.4282i 0.102130 0.381153i
\(900\) 2.13000 + 6.58736i 0.0710001 + 0.219579i
\(901\) −0.492029 0.284073i −0.0163919 0.00946386i
\(902\) −2.67818 + 0.717617i −0.0891738 + 0.0238940i
\(903\) −1.13314 1.40135i −0.0377086 0.0466341i
\(904\) 0.299051 + 0.299051i 0.00994628 + 0.00994628i
\(905\) −28.6763 7.68379i −0.953232 0.255418i
\(906\) −8.48129 0.897522i −0.281772 0.0298182i
\(907\) 18.5156i 0.614802i −0.951580 0.307401i \(-0.900541\pi\)
0.951580 0.307401i \(-0.0994593\pi\)
\(908\) −17.9591 4.81212i −0.595992 0.159696i
\(909\) 20.3971 22.5886i 0.676530 0.749215i
\(910\) −11.0140 + 10.5359i −0.365109 + 0.349260i
\(911\) −45.1789 26.0841i −1.49684 0.864203i −0.496851 0.867836i \(-0.665510\pi\)
−0.999993 + 0.00363265i \(0.998844\pi\)
\(912\) 9.26278 + 11.4552i 0.306721 + 0.379321i
\(913\) 0.294925 0.510825i 0.00976060 0.0169059i
\(914\) 48.5984 1.60749
\(915\) 15.5798 12.5980i 0.515054 0.416476i
\(916\) −45.4001 12.1649i −1.50006 0.401940i
\(917\) −3.68733 13.7613i −0.121766 0.454439i
\(918\) −2.65399 + 48.6535i −0.0875949 + 1.60581i
\(919\) −0.166972 + 0.289203i −0.00550788 + 0.00953993i −0.868766 0.495222i \(-0.835087\pi\)
0.863258 + 0.504762i \(0.168420\pi\)
\(920\) −2.28245 −0.0752503
\(921\) −41.5752 15.9932i −1.36995 0.526993i
\(922\) −6.97791 + 4.02870i −0.229805 + 0.132678i
\(923\) −10.0550 10.5113i −0.330965 0.345983i
\(924\) −0.442535 + 0.608186i −0.0145583 + 0.0200079i
\(925\) −0.938016 + 0.938016i −0.0308418 + 0.0308418i
\(926\) −16.9184 + 9.76785i −0.555973 + 0.320991i
\(927\) −10.7754 + 50.3419i −0.353911 + 1.65344i
\(928\) 13.1496 13.1496i 0.431658 0.431658i
\(929\) −9.30753 + 34.7362i −0.305370 + 1.13966i 0.627256 + 0.778813i \(0.284178\pi\)
−0.932626 + 0.360844i \(0.882489\pi\)
\(930\) −29.1264 + 23.5518i −0.955091 + 0.772293i
\(931\) −0.736005 + 2.74681i −0.0241216 + 0.0900230i
\(932\) 61.6185i 2.01838i
\(933\) −10.9213 7.94664i −0.357546 0.260161i
\(934\) 22.1989 + 22.1989i 0.726372 + 0.726372i
\(935\) −1.61200 −0.0527179
\(936\) 8.07842 4.97911i 0.264051 0.162747i
\(937\) 1.76777 0.0577506 0.0288753 0.999583i \(-0.490807\pi\)
0.0288753 + 0.999583i \(0.490807\pi\)
\(938\) 2.80016 + 2.80016i 0.0914284 + 0.0914284i
\(939\) 5.29522 50.0381i 0.172803 1.63293i
\(940\) 33.7488i 1.10077i
\(941\) 2.36900 8.84124i 0.0772273 0.288216i −0.916502 0.400031i \(-0.869000\pi\)
0.993729 + 0.111814i \(0.0356662\pi\)
\(942\) −8.29234 52.5980i −0.270179 1.71374i
\(943\) 2.45859 9.17557i 0.0800626 0.298798i
\(944\) 21.8460 21.8460i 0.711027 0.711027i
\(945\) 7.78158 6.97654i 0.253135 0.226947i
\(946\) −0.340204 + 0.196417i −0.0110610 + 0.00638607i
\(947\) −40.1621 + 40.1621i −1.30509 + 1.30509i −0.380182 + 0.924912i \(0.624139\pi\)
−0.924912 + 0.380182i \(0.875861\pi\)
\(948\) 49.7860 + 5.26854i 1.61697 + 0.171114i
\(949\) −3.27108 + 11.2073i −0.106184 + 0.363804i
\(950\) 4.94119 2.85280i 0.160313 0.0925570i
\(951\) −8.35132 + 6.75293i −0.270810 + 0.218979i
\(952\) 3.91425 0.126861
\(953\) −4.64629 + 8.04761i −0.150508 + 0.260688i −0.931414 0.363960i \(-0.881424\pi\)
0.780906 + 0.624648i \(0.214758\pi\)
\(954\) −0.0408803 0.801879i −0.00132355 0.0259618i
\(955\) 5.85381 + 21.8467i 0.189425 + 0.706943i
\(956\) 16.4029 + 4.39515i 0.530509 + 0.142149i
\(957\) 0.671600 + 0.258352i 0.0217098 + 0.00835133i
\(958\) −41.9693 −1.35597
\(959\) −1.91780 + 3.32172i −0.0619289 + 0.107264i
\(960\) −37.5714 + 5.92332i −1.21261 + 0.191174i
\(961\) −4.18212 2.41455i −0.134907 0.0778886i
\(962\) 9.00065 + 5.46623i 0.290193 + 0.176238i
\(963\) 11.5588 54.0020i 0.372478 1.74019i
\(964\) −13.0435 3.49499i −0.420102 0.112566i
\(965\) 46.0023i 1.48087i
\(966\) −1.91219 4.30309i −0.0615237 0.138450i
\(967\) 3.16113 + 0.847023i 0.101655 + 0.0272384i 0.309288 0.950968i \(-0.399909\pi\)
−0.207633 + 0.978207i \(0.566576\pi\)
\(968\) −6.80388 6.80388i −0.218685 0.218685i
\(969\) 21.7074 3.42228i 0.697342 0.109939i
\(970\) 14.1397 3.78871i 0.453997 0.121648i
\(971\) 25.7777 + 14.8828i 0.827247 + 0.477611i 0.852909 0.522059i \(-0.174836\pi\)
−0.0256620 + 0.999671i \(0.508169\pi\)
\(972\) −32.7020 + 18.7257i −1.04892 + 0.600626i
\(973\) −4.07865 + 15.2217i −0.130756 + 0.487986i
\(974\) 28.9258 50.1010i 0.926844 1.60534i
\(975\) 2.29950 + 5.50029i 0.0736429 + 0.176150i
\(976\) −8.60094 14.8973i −0.275309 0.476850i
\(977\) −23.7162 + 6.35474i −0.758749 + 0.203306i −0.617396 0.786653i \(-0.711812\pi\)
−0.141354 + 0.989959i \(0.545146\pi\)
\(978\) 81.2328 + 8.59636i 2.59754 + 0.274881i
\(979\) −1.44066 + 0.831767i −0.0460438 + 0.0265834i
\(980\) −3.43808 3.43808i −0.109825 0.109825i
\(981\) −1.22016 23.9338i −0.0389568 0.764148i
\(982\) 63.1460 16.9199i 2.01507 0.539937i
\(983\) −3.63293 13.5583i −0.115872 0.432442i 0.883478 0.468472i \(-0.155195\pi\)
−0.999351 + 0.0360303i \(0.988529\pi\)
\(984\) −1.17436 + 11.0973i −0.0374373 + 0.353770i
\(985\) −2.26504 1.30772i −0.0721701 0.0416674i
\(986\) −5.61306 20.9482i −0.178756 0.667128i
\(987\) −10.9864 + 4.88210i −0.349701 + 0.155399i
\(988\) −17.1334 17.9108i −0.545085 0.569820i
\(989\) 1.34587i 0.0427960i
\(990\) −1.23803 1.91235i −0.0393472 0.0607786i
\(991\) −19.4336 33.6600i −0.617328 1.06924i −0.989971 0.141269i \(-0.954882\pi\)
0.372643 0.927975i \(-0.378452\pi\)
\(992\) 20.5675 + 35.6240i 0.653019 + 1.13106i
\(993\) −11.4618 + 1.80700i −0.363728 + 0.0573435i
\(994\) 5.99578 5.99578i 0.190175 0.190175i
\(995\) 35.5640 35.5640i 1.12745 1.12745i
\(996\) −8.64476 10.6909i −0.273920 0.338755i
\(997\) −10.0658 17.4344i −0.318786 0.552154i 0.661449 0.749990i \(-0.269942\pi\)
−0.980235 + 0.197836i \(0.936609\pi\)
\(998\) −24.5125 42.4568i −0.775928 1.34395i
\(999\) −6.04732 3.94555i −0.191329 0.124832i
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 819.2.ew.a.470.71 yes 336
9.5 odd 6 819.2.fy.a.743.71 yes 336
13.7 odd 12 819.2.fy.a.722.71 yes 336
117.59 even 12 inner 819.2.ew.a.176.71 336
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
819.2.ew.a.176.71 336 117.59 even 12 inner
819.2.ew.a.470.71 yes 336 1.1 even 1 trivial
819.2.fy.a.722.71 yes 336 13.7 odd 12
819.2.fy.a.743.71 yes 336 9.5 odd 6