Properties

Label 648.2.bb.b.155.57
Level $648$
Weight $2$
Character 648.155
Analytic conductor $5.174$
Analytic rank $0$
Dimension $1872$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [648,2,Mod(11,648)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(648, base_ring=CyclotomicField(54))
 
chi = DirichletCharacter(H, H._module([27, 27, 13]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("648.11");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 648 = 2^{3} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 648.bb (of order \(54\), degree \(18\), 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: \(5.17430605098\)
Analytic rank: \(0\)
Dimension: \(1872\)
Relative dimension: \(104\) over \(\Q(\zeta_{54})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{54}]$

Embedding invariants

Embedding label 155.57
Character \(\chi\) \(=\) 648.155
Dual form 648.2.bb.b.347.57

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.212993 - 1.39808i) q^{2} +(-0.739739 + 1.56614i) q^{3} +(-1.90927 - 0.595563i) q^{4} +(0.405895 - 0.266961i) q^{5} +(2.03203 + 1.36779i) q^{6} +(-0.678333 - 0.639974i) q^{7} +(-1.23931 + 2.54246i) q^{8} +(-1.90557 - 2.31707i) q^{9} +O(q^{10})\) \(q+(0.212993 - 1.39808i) q^{2} +(-0.739739 + 1.56614i) q^{3} +(-1.90927 - 0.595563i) q^{4} +(0.405895 - 0.266961i) q^{5} +(2.03203 + 1.36779i) q^{6} +(-0.678333 - 0.639974i) q^{7} +(-1.23931 + 2.54246i) q^{8} +(-1.90557 - 2.31707i) q^{9} +(-0.286781 - 0.624335i) q^{10} +(1.65746 + 3.30027i) q^{11} +(2.34509 - 2.54961i) q^{12} +(1.97624 - 0.852466i) q^{13} +(-1.03922 + 0.812055i) q^{14} +(0.117842 + 0.833168i) q^{15} +(3.29061 + 2.27418i) q^{16} +(-0.154421 - 0.184032i) q^{17} +(-3.64532 + 2.17063i) q^{18} +(2.97832 + 2.49911i) q^{19} +(-0.933954 + 0.267965i) q^{20} +(1.50408 - 0.588948i) q^{21} +(4.96708 - 1.61433i) q^{22} +(0.582884 + 0.617821i) q^{23} +(-3.06508 - 3.82168i) q^{24} +(-1.88692 + 4.37436i) q^{25} +(-0.770893 - 2.94451i) q^{26} +(5.03847 - 1.27036i) q^{27} +(0.913975 + 1.62587i) q^{28} +(7.65039 - 0.894202i) q^{29} +(1.18994 + 0.0127067i) q^{30} +(2.31766 + 9.77897i) q^{31} +(3.88036 - 4.11616i) q^{32} +(-6.39477 + 0.154467i) q^{33} +(-0.290183 + 0.176696i) q^{34} +(-0.446180 - 0.0786735i) q^{35} +(2.25829 + 5.55879i) q^{36} +(-6.33859 + 1.11766i) q^{37} +(4.12832 - 3.63165i) q^{38} +(-0.126822 + 3.72566i) q^{39} +(0.175711 + 1.36282i) q^{40} +(6.78971 + 5.05475i) q^{41} +(-0.503041 - 2.22826i) q^{42} +(0.111122 - 1.90789i) q^{43} +(-1.19902 - 7.28823i) q^{44} +(-1.39203 - 0.431771i) q^{45} +(0.987915 - 0.683329i) q^{46} +(6.25000 + 1.48128i) q^{47} +(-5.99587 + 3.47125i) q^{48} +(-0.356445 - 6.11993i) q^{49} +(5.71382 + 3.56977i) q^{50} +(0.402451 - 0.105709i) q^{51} +(-4.28086 + 0.450612i) q^{52} +(-0.422453 - 0.731710i) q^{53} +(-0.702912 - 7.31477i) q^{54} +(1.55380 + 0.897086i) q^{55} +(2.46777 - 0.931513i) q^{56} +(-6.11714 + 2.81577i) q^{57} +(0.379309 - 10.8863i) q^{58} +(1.02372 - 2.03839i) q^{59} +(0.271213 - 1.66092i) q^{60} +(-3.82294 + 1.14451i) q^{61} +(14.1655 - 1.15743i) q^{62} +(-0.190251 + 2.79126i) q^{63} +(-4.92824 - 6.30178i) q^{64} +(0.574569 - 0.873590i) q^{65} +(-1.14608 + 8.97332i) q^{66} +(13.3990 + 1.56612i) q^{67} +(0.185229 + 0.443334i) q^{68} +(-1.39878 + 0.455850i) q^{69} +(-0.205025 + 0.607039i) q^{70} +(-4.03859 - 1.46993i) q^{71} +(8.25264 - 1.97329i) q^{72} +(-1.45888 + 0.530988i) q^{73} +(0.212513 + 9.09992i) q^{74} +(-5.45503 - 6.19106i) q^{75} +(-4.19804 - 6.54525i) q^{76} +(0.987780 - 3.29942i) q^{77} +(5.18177 + 0.970847i) q^{78} +(-12.3816 + 9.21773i) q^{79} +(1.94276 + 0.0446119i) q^{80} +(-1.73759 + 8.83067i) q^{81} +(8.51312 - 8.41595i) q^{82} +(3.38952 - 2.52340i) q^{83} +(-3.22244 + 0.228688i) q^{84} +(-0.111808 - 0.0334732i) q^{85} +(-2.64373 - 0.561726i) q^{86} +(-4.25885 + 12.6430i) q^{87} +(-10.4449 + 0.123982i) q^{88} +(-3.16548 - 8.69708i) q^{89} +(-0.900144 + 1.85421i) q^{90} +(-1.88610 - 0.686485i) q^{91} +(-0.744931 - 1.52673i) q^{92} +(-17.0297 - 3.60412i) q^{93} +(3.40215 - 8.42251i) q^{94} +(1.87605 + 0.219279i) q^{95} +(3.57601 + 9.12207i) q^{96} +(-13.0559 - 8.58702i) q^{97} +(-8.63208 - 0.805160i) q^{98} +(4.48855 - 10.1294i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 1872 q - 18 q^{2} - 36 q^{3} - 18 q^{4} - 18 q^{6} - 18 q^{8} - 36 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 1872 q - 18 q^{2} - 36 q^{3} - 18 q^{4} - 18 q^{6} - 18 q^{8} - 36 q^{9} - 18 q^{10} - 36 q^{11} - 18 q^{12} - 18 q^{14} - 18 q^{16} - 36 q^{17} - 90 q^{18} - 36 q^{19} - 18 q^{20} - 18 q^{22} - 18 q^{24} - 36 q^{25} - 27 q^{26} - 36 q^{27} - 9 q^{28} - 18 q^{30} - 18 q^{32} - 36 q^{33} - 18 q^{34} - 36 q^{35} - 18 q^{36} + 90 q^{38} - 18 q^{40} - 36 q^{41} - 63 q^{42} - 36 q^{43} + 54 q^{44} - 18 q^{46} + 81 q^{48} - 36 q^{49} - 135 q^{50} - 54 q^{51} - 18 q^{52} - 144 q^{54} + 108 q^{56} - 36 q^{57} - 18 q^{58} + 18 q^{59} + 99 q^{60} - 117 q^{62} - 18 q^{64} - 36 q^{65} - 90 q^{66} - 36 q^{67} + 243 q^{68} - 18 q^{70} - 18 q^{72} - 36 q^{73} - 18 q^{74} - 36 q^{75} - 54 q^{76} - 45 q^{78} - 36 q^{81} - 36 q^{82} - 36 q^{83} + 9 q^{84} - 18 q^{86} + 54 q^{88} - 198 q^{89} - 81 q^{90} - 36 q^{91} - 108 q^{92} - 18 q^{94} - 423 q^{96} - 36 q^{97} - 189 q^{98} - 36 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/648\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(487\) \(569\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{43}{54}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.212993 1.39808i 0.150609 0.988593i
\(3\) −0.739739 + 1.56614i −0.427089 + 0.904210i
\(4\) −1.90927 0.595563i −0.954634 0.297781i
\(5\) 0.405895 0.266961i 0.181522 0.119389i −0.455496 0.890238i \(-0.650538\pi\)
0.637018 + 0.770849i \(0.280168\pi\)
\(6\) 2.03203 + 1.36779i 0.829573 + 0.558399i
\(7\) −0.678333 0.639974i −0.256386 0.241887i 0.547307 0.836932i \(-0.315653\pi\)
−0.803693 + 0.595044i \(0.797134\pi\)
\(8\) −1.23931 + 2.54246i −0.438161 + 0.898897i
\(9\) −1.90557 2.31707i −0.635190 0.772356i
\(10\) −0.286781 0.624335i −0.0906881 0.197432i
\(11\) 1.65746 + 3.30027i 0.499743 + 0.995070i 0.992191 + 0.124728i \(0.0398059\pi\)
−0.492448 + 0.870342i \(0.663898\pi\)
\(12\) 2.34509 2.54961i 0.676970 0.736010i
\(13\) 1.97624 0.852466i 0.548110 0.236431i −0.103972 0.994580i \(-0.533155\pi\)
0.652082 + 0.758149i \(0.273896\pi\)
\(14\) −1.03922 + 0.812055i −0.277742 + 0.217031i
\(15\) 0.117842 + 0.833168i 0.0304265 + 0.215123i
\(16\) 3.29061 + 2.27418i 0.822652 + 0.568545i
\(17\) −0.154421 0.184032i −0.0374527 0.0446344i 0.746993 0.664832i \(-0.231497\pi\)
−0.784446 + 0.620198i \(0.787052\pi\)
\(18\) −3.64532 + 2.17063i −0.859211 + 0.511622i
\(19\) 2.97832 + 2.49911i 0.683275 + 0.573335i 0.916961 0.398977i \(-0.130635\pi\)
−0.233687 + 0.972312i \(0.575079\pi\)
\(20\) −0.933954 + 0.267965i −0.208838 + 0.0599187i
\(21\) 1.50408 0.588948i 0.328216 0.128519i
\(22\) 4.96708 1.61433i 1.05899 0.344177i
\(23\) 0.582884 + 0.617821i 0.121540 + 0.128825i 0.785286 0.619133i \(-0.212516\pi\)
−0.663746 + 0.747958i \(0.731034\pi\)
\(24\) −3.06508 3.82168i −0.625657 0.780098i
\(25\) −1.88692 + 4.37436i −0.377383 + 0.874873i
\(26\) −0.770893 2.94451i −0.151185 0.577466i
\(27\) 5.03847 1.27036i 0.969654 0.244481i
\(28\) 0.913975 + 1.62587i 0.172725 + 0.307261i
\(29\) 7.65039 0.894202i 1.42064 0.166049i 0.629176 0.777263i \(-0.283393\pi\)
0.791465 + 0.611214i \(0.209319\pi\)
\(30\) 1.18994 + 0.0127067i 0.217252 + 0.00231992i
\(31\) 2.31766 + 9.77897i 0.416264 + 1.75636i 0.627203 + 0.778856i \(0.284200\pi\)
−0.210939 + 0.977499i \(0.567652\pi\)
\(32\) 3.88036 4.11616i 0.685958 0.727641i
\(33\) −6.39477 + 0.154467i −1.11319 + 0.0268893i
\(34\) −0.290183 + 0.176696i −0.0497659 + 0.0303031i
\(35\) −0.446180 0.0786735i −0.0754182 0.0132983i
\(36\) 2.25829 + 5.55879i 0.376381 + 0.926465i
\(37\) −6.33859 + 1.11766i −1.04206 + 0.183743i −0.668383 0.743817i \(-0.733013\pi\)
−0.373674 + 0.927560i \(0.621902\pi\)
\(38\) 4.12832 3.63165i 0.669703 0.589132i
\(39\) −0.126822 + 3.72566i −0.0203078 + 0.596583i
\(40\) 0.175711 + 1.36282i 0.0277824 + 0.215481i
\(41\) 6.78971 + 5.05475i 1.06037 + 0.789420i 0.978297 0.207206i \(-0.0664371\pi\)
0.0820776 + 0.996626i \(0.473844\pi\)
\(42\) −0.503041 2.22826i −0.0776209 0.343829i
\(43\) 0.111122 1.90789i 0.0169460 0.290951i −0.979179 0.203000i \(-0.934931\pi\)
0.996125 0.0879515i \(-0.0280320\pi\)
\(44\) −1.19902 7.28823i −0.180758 1.09874i
\(45\) −1.39203 0.431771i −0.207511 0.0643647i
\(46\) 0.987915 0.683329i 0.145660 0.100751i
\(47\) 6.25000 + 1.48128i 0.911656 + 0.216066i 0.659574 0.751639i \(-0.270737\pi\)
0.252082 + 0.967706i \(0.418885\pi\)
\(48\) −5.99587 + 3.47125i −0.865429 + 0.501031i
\(49\) −0.356445 6.11993i −0.0509207 0.874275i
\(50\) 5.71382 + 3.56977i 0.808056 + 0.504842i
\(51\) 0.402451 0.105709i 0.0563544 0.0148022i
\(52\) −4.28086 + 0.450612i −0.593649 + 0.0624886i
\(53\) −0.422453 0.731710i −0.0580284 0.100508i 0.835552 0.549412i \(-0.185148\pi\)
−0.893580 + 0.448903i \(0.851815\pi\)
\(54\) −0.702912 7.31477i −0.0956542 0.995415i
\(55\) 1.55380 + 0.897086i 0.209514 + 0.120963i
\(56\) 2.46777 0.931513i 0.329770 0.124479i
\(57\) −6.11714 + 2.81577i −0.810234 + 0.372958i
\(58\) 0.379309 10.8863i 0.0498057 1.42944i
\(59\) 1.02372 2.03839i 0.133277 0.265376i −0.817088 0.576512i \(-0.804413\pi\)
0.950365 + 0.311136i \(0.100710\pi\)
\(60\) 0.271213 1.66092i 0.0350135 0.214424i
\(61\) −3.82294 + 1.14451i −0.489477 + 0.146540i −0.522025 0.852930i \(-0.674823\pi\)
0.0325475 + 0.999470i \(0.489638\pi\)
\(62\) 14.1655 1.15743i 1.79901 0.146993i
\(63\) −0.190251 + 2.79126i −0.0239693 + 0.351666i
\(64\) −4.92824 6.30178i −0.616030 0.787723i
\(65\) 0.574569 0.873590i 0.0712665 0.108355i
\(66\) −1.14608 + 8.97332i −0.141073 + 1.10454i
\(67\) 13.3990 + 1.56612i 1.63695 + 0.191332i 0.884245 0.467022i \(-0.154673\pi\)
0.752708 + 0.658355i \(0.228747\pi\)
\(68\) 0.185229 + 0.443334i 0.0224623 + 0.0537622i
\(69\) −1.39878 + 0.455850i −0.168393 + 0.0548779i
\(70\) −0.205025 + 0.607039i −0.0245052 + 0.0725551i
\(71\) −4.03859 1.46993i −0.479292 0.174448i 0.0910650 0.995845i \(-0.470973\pi\)
−0.570357 + 0.821397i \(0.693195\pi\)
\(72\) 8.25264 1.97329i 0.972583 0.232555i
\(73\) −1.45888 + 0.530988i −0.170749 + 0.0621474i −0.425980 0.904733i \(-0.640071\pi\)
0.255231 + 0.966880i \(0.417848\pi\)
\(74\) 0.212513 + 9.09992i 0.0247041 + 1.05784i
\(75\) −5.45503 6.19106i −0.629892 0.714882i
\(76\) −4.19804 6.54525i −0.481549 0.750792i
\(77\) 0.987780 3.29942i 0.112568 0.376003i
\(78\) 5.18177 + 0.970847i 0.586720 + 0.109927i
\(79\) −12.3816 + 9.21773i −1.39303 + 1.03708i −0.400347 + 0.916364i \(0.631110\pi\)
−0.992688 + 0.120712i \(0.961482\pi\)
\(80\) 1.94276 + 0.0446119i 0.217207 + 0.00498776i
\(81\) −1.73759 + 8.83067i −0.193066 + 0.981186i
\(82\) 8.51312 8.41595i 0.940117 0.929386i
\(83\) 3.38952 2.52340i 0.372048 0.276979i −0.394854 0.918744i \(-0.629205\pi\)
0.766902 + 0.641765i \(0.221797\pi\)
\(84\) −3.22244 + 0.228688i −0.351597 + 0.0249519i
\(85\) −0.111808 0.0334732i −0.0121273 0.00363068i
\(86\) −2.64373 0.561726i −0.285080 0.0605725i
\(87\) −4.25885 + 12.6430i −0.456596 + 1.35548i
\(88\) −10.4449 + 0.123982i −1.11343 + 0.0132165i
\(89\) −3.16548 8.69708i −0.335540 0.921889i −0.986643 0.162899i \(-0.947915\pi\)
0.651103 0.758990i \(-0.274307\pi\)
\(90\) −0.900144 + 1.85421i −0.0948835 + 0.195450i
\(91\) −1.88610 0.686485i −0.197717 0.0719632i
\(92\) −0.744931 1.52673i −0.0776645 0.159173i
\(93\) −17.0297 3.60412i −1.76589 0.373730i
\(94\) 3.40215 8.42251i 0.350905 0.868716i
\(95\) 1.87605 + 0.219279i 0.192479 + 0.0224976i
\(96\) 3.57601 + 9.12207i 0.364975 + 0.931017i
\(97\) −13.0559 8.58702i −1.32563 0.871880i −0.328275 0.944582i \(-0.606467\pi\)
−0.997354 + 0.0727024i \(0.976838\pi\)
\(98\) −8.63208 0.805160i −0.871972 0.0813335i
\(99\) 4.48855 10.1294i 0.451116 1.01804i
\(100\) 6.20784 7.22806i 0.620784 0.722806i
\(101\) −0.830535 2.77418i −0.0826413 0.276041i 0.906674 0.421832i \(-0.138613\pi\)
−0.989315 + 0.145790i \(0.953427\pi\)
\(102\) −0.0620709 0.585175i −0.00614594 0.0579410i
\(103\) −3.31799 + 6.60666i −0.326931 + 0.650973i −0.995714 0.0924844i \(-0.970519\pi\)
0.668783 + 0.743458i \(0.266815\pi\)
\(104\) −0.281800 + 6.08098i −0.0276328 + 0.596289i
\(105\) 0.453270 0.640581i 0.0442347 0.0625143i
\(106\) −1.11297 + 0.434775i −0.108101 + 0.0422291i
\(107\) −1.51259 0.873295i −0.146228 0.0844246i 0.425101 0.905146i \(-0.360239\pi\)
−0.571329 + 0.820721i \(0.693572\pi\)
\(108\) −10.3764 0.575265i −0.998467 0.0553549i
\(109\) 2.00876 1.15976i 0.192405 0.111085i −0.400703 0.916208i \(-0.631234\pi\)
0.593108 + 0.805123i \(0.297901\pi\)
\(110\) 1.58515 1.98127i 0.151138 0.188906i
\(111\) 2.93849 10.7539i 0.278909 1.02071i
\(112\) −0.776714 3.64855i −0.0733925 0.344756i
\(113\) 2.27675 0.132606i 0.214179 0.0124745i 0.0492799 0.998785i \(-0.484307\pi\)
0.164899 + 0.986311i \(0.447270\pi\)
\(114\) 2.63378 + 9.15200i 0.246676 + 0.857163i
\(115\) 0.401524 + 0.0951629i 0.0374423 + 0.00887399i
\(116\) −15.1392 2.84901i −1.40564 0.264524i
\(117\) −5.74108 2.95464i −0.530763 0.273157i
\(118\) −2.63180 1.86541i −0.242277 0.171725i
\(119\) −0.0130267 + 0.223661i −0.00119416 + 0.0205029i
\(120\) −2.26434 0.732943i −0.206705 0.0669082i
\(121\) −1.57589 + 2.11679i −0.143263 + 0.192435i
\(122\) 0.785865 + 5.58856i 0.0711489 + 0.505964i
\(123\) −12.9391 + 6.89442i −1.16668 + 0.621649i
\(124\) 1.39896 20.0510i 0.125630 1.80063i
\(125\) 0.823703 + 4.67145i 0.0736742 + 0.417827i
\(126\) 3.86189 + 0.860504i 0.344044 + 0.0766598i
\(127\) −20.5189 3.61803i −1.82075 0.321048i −0.844152 0.536104i \(-0.819896\pi\)
−0.976602 + 0.215056i \(0.931007\pi\)
\(128\) −9.86009 + 5.54785i −0.871517 + 0.490366i
\(129\) 2.90582 + 1.58538i 0.255844 + 0.139585i
\(130\) −1.09897 0.989363i −0.0963862 0.0867729i
\(131\) 2.63919 + 11.1356i 0.230587 + 0.972922i 0.958010 + 0.286733i \(0.0925694\pi\)
−0.727424 + 0.686189i \(0.759282\pi\)
\(132\) 12.3013 + 3.51357i 1.07069 + 0.305817i
\(133\) −0.420929 3.60128i −0.0364992 0.312271i
\(134\) 5.04347 18.3994i 0.435689 1.58946i
\(135\) 1.70595 1.86071i 0.146825 0.160144i
\(136\) 0.659270 0.164538i 0.0565320 0.0141090i
\(137\) 1.64802 + 0.710887i 0.140800 + 0.0607352i 0.465314 0.885146i \(-0.345941\pi\)
−0.324514 + 0.945881i \(0.605201\pi\)
\(138\) 0.339387 + 2.05270i 0.0288905 + 0.174737i
\(139\) −10.6595 11.2984i −0.904126 0.958318i 0.0951840 0.995460i \(-0.469656\pi\)
−0.999310 + 0.0371421i \(0.988175\pi\)
\(140\) 0.805022 + 0.415937i 0.0680368 + 0.0351531i
\(141\) −6.94325 + 8.69260i −0.584727 + 0.732049i
\(142\) −2.91527 + 5.33319i −0.244644 + 0.447552i
\(143\) 6.08890 + 5.10920i 0.509180 + 0.427253i
\(144\) −1.00107 11.9582i −0.0834225 0.996514i
\(145\) 2.86653 2.40531i 0.238053 0.199750i
\(146\) 0.431635 + 2.15273i 0.0357223 + 0.178161i
\(147\) 9.84832 + 3.96891i 0.812276 + 0.327350i
\(148\) 12.7677 + 1.64111i 1.04950 + 0.134898i
\(149\) 3.38982 + 7.85849i 0.277705 + 0.643793i 0.998796 0.0490472i \(-0.0156185\pi\)
−0.721091 + 0.692840i \(0.756359\pi\)
\(150\) −9.81749 + 6.30793i −0.801595 + 0.515040i
\(151\) 8.24400 + 16.4151i 0.670887 + 1.33585i 0.929125 + 0.369765i \(0.120562\pi\)
−0.258239 + 0.966081i \(0.583142\pi\)
\(152\) −10.0450 + 4.47512i −0.814753 + 0.362980i
\(153\) −0.132154 + 0.708491i −0.0106840 + 0.0572781i
\(154\) −4.40246 2.08375i −0.354761 0.167913i
\(155\) 3.55133 + 3.35051i 0.285250 + 0.269119i
\(156\) 2.46100 7.03776i 0.197038 0.563471i
\(157\) 2.17823 + 3.31184i 0.173842 + 0.264313i 0.911890 0.410434i \(-0.134623\pi\)
−0.738049 + 0.674748i \(0.764252\pi\)
\(158\) 10.2500 + 19.2737i 0.815443 + 1.53334i
\(159\) 1.45846 0.120345i 0.115664 0.00954396i
\(160\) 0.476165 2.70663i 0.0376441 0.213978i
\(161\) 0.792119i 0.0624278i
\(162\) 11.9759 + 4.31017i 0.940916 + 0.338639i
\(163\) 16.7882 1.31495 0.657475 0.753476i \(-0.271625\pi\)
0.657475 + 0.753476i \(0.271625\pi\)
\(164\) −9.95296 13.6946i −0.777195 1.06937i
\(165\) −2.55437 + 1.76985i −0.198857 + 0.137783i
\(166\) −2.80598 5.27629i −0.217786 0.409520i
\(167\) 17.3272 11.3963i 1.34082 0.881870i 0.342481 0.939525i \(-0.388733\pi\)
0.998337 + 0.0576551i \(0.0183624\pi\)
\(168\) −0.366632 + 4.55395i −0.0282862 + 0.351345i
\(169\) −5.74232 + 6.08651i −0.441717 + 0.468193i
\(170\) −0.0706126 + 0.149188i −0.00541574 + 0.0114422i
\(171\) 0.115196 11.6632i 0.00880928 0.891908i
\(172\) −1.34843 + 3.57650i −0.102817 + 0.272706i
\(173\) 15.4431 7.75583i 1.17412 0.589664i 0.248689 0.968583i \(-0.420000\pi\)
0.925430 + 0.378919i \(0.123704\pi\)
\(174\) 16.7689 + 8.64709i 1.27125 + 0.655535i
\(175\) 4.07944 1.75970i 0.308376 0.133021i
\(176\) −2.05136 + 14.6293i −0.154627 + 1.10272i
\(177\) 2.43512 + 3.11117i 0.183035 + 0.233850i
\(178\) −12.8335 + 2.57319i −0.961909 + 0.192868i
\(179\) −6.52494 7.77612i −0.487697 0.581215i 0.464933 0.885346i \(-0.346078\pi\)
−0.952630 + 0.304131i \(0.901634\pi\)
\(180\) 2.40061 + 1.65341i 0.178931 + 0.123238i
\(181\) −0.335615 + 0.399970i −0.0249461 + 0.0297295i −0.778373 0.627802i \(-0.783955\pi\)
0.753427 + 0.657531i \(0.228399\pi\)
\(182\) −1.36149 + 2.49071i −0.100920 + 0.184624i
\(183\) 1.03551 6.83389i 0.0765474 0.505176i
\(184\) −2.29316 + 0.716293i −0.169054 + 0.0528058i
\(185\) −2.27443 + 2.14581i −0.167219 + 0.157763i
\(186\) −8.66605 + 23.0412i −0.635426 + 1.68947i
\(187\) 0.351409 0.814659i 0.0256976 0.0595737i
\(188\) −11.0507 6.55042i −0.805957 0.477739i
\(189\) −4.23076 2.36276i −0.307742 0.171866i
\(190\) 0.706156 2.57617i 0.0512299 0.186895i
\(191\) 3.91819 0.457971i 0.283510 0.0331376i 0.0268507 0.999639i \(-0.491452\pi\)
0.256660 + 0.966502i \(0.417378\pi\)
\(192\) 13.5151 3.05663i 0.975366 0.220593i
\(193\) −1.48159 + 0.351142i −0.106647 + 0.0252758i −0.283593 0.958945i \(-0.591526\pi\)
0.176946 + 0.984221i \(0.443378\pi\)
\(194\) −14.7862 + 16.4243i −1.06159 + 1.17920i
\(195\) 0.943130 + 1.54608i 0.0675390 + 0.110717i
\(196\) −2.96425 + 11.8969i −0.211732 + 0.849776i
\(197\) 0.494678 2.80546i 0.0352444 0.199881i −0.962101 0.272692i \(-0.912086\pi\)
0.997346 + 0.0728113i \(0.0231971\pi\)
\(198\) −13.2056 8.43284i −0.938484 0.599296i
\(199\) −12.3977 + 2.18605i −0.878852 + 0.154965i −0.594829 0.803852i \(-0.702780\pi\)
−0.284023 + 0.958818i \(0.591669\pi\)
\(200\) −8.78319 10.2186i −0.621066 0.722564i
\(201\) −12.3646 + 19.8262i −0.872129 + 1.39843i
\(202\) −4.05543 + 0.570276i −0.285339 + 0.0401245i
\(203\) −5.76177 4.28948i −0.404397 0.301063i
\(204\) −0.831343 0.0378578i −0.0582057 0.00265058i
\(205\) 4.10533 + 0.239108i 0.286729 + 0.0167000i
\(206\) 8.52994 + 6.04599i 0.594309 + 0.421244i
\(207\) 0.320805 2.52789i 0.0222975 0.175700i
\(208\) 8.44168 + 1.68918i 0.585326 + 0.117124i
\(209\) −3.31130 + 13.9715i −0.229047 + 0.966427i
\(210\) −0.799042 0.770148i −0.0551391 0.0531453i
\(211\) 0.569526 + 9.77839i 0.0392078 + 0.673172i 0.959460 + 0.281846i \(0.0909466\pi\)
−0.920252 + 0.391326i \(0.872016\pi\)
\(212\) 0.370797 + 1.64863i 0.0254664 + 0.113228i
\(213\) 5.28961 5.23762i 0.362438 0.358876i
\(214\) −1.54311 + 1.92872i −0.105485 + 0.131845i
\(215\) −0.464230 0.804070i −0.0316602 0.0548371i
\(216\) −3.01436 + 14.3845i −0.205101 + 0.978741i
\(217\) 4.68614 8.11664i 0.318116 0.550993i
\(218\) −1.19359 3.05544i −0.0808399 0.206940i
\(219\) 0.247589 2.67760i 0.0167305 0.180935i
\(220\) −2.43235 2.63816i −0.163989 0.177865i
\(221\) −0.462054 0.232052i −0.0310811 0.0156095i
\(222\) −14.4089 6.39874i −0.967064 0.429456i
\(223\) 21.5637 6.45575i 1.44401 0.432309i 0.533504 0.845798i \(-0.320875\pi\)
0.910509 + 0.413488i \(0.135690\pi\)
\(224\) −5.26641 + 0.308794i −0.351877 + 0.0206322i
\(225\) 13.7313 3.96355i 0.915423 0.264237i
\(226\) 0.299538 3.21133i 0.0199249 0.213614i
\(227\) −7.54329 + 11.4690i −0.500666 + 0.761225i −0.994089 0.108564i \(-0.965375\pi\)
0.493424 + 0.869789i \(0.335745\pi\)
\(228\) 13.3562 1.73293i 0.884537 0.114766i
\(229\) −0.374671 + 3.20551i −0.0247589 + 0.211826i −0.999955 0.00951790i \(-0.996970\pi\)
0.975196 + 0.221344i \(0.0710444\pi\)
\(230\) 0.218567 0.541095i 0.0144119 0.0356787i
\(231\) 4.43664 + 3.98771i 0.291909 + 0.262372i
\(232\) −7.20769 + 20.5590i −0.473208 + 1.34977i
\(233\) −3.65202 + 10.0338i −0.239252 + 0.657338i 0.760714 + 0.649087i \(0.224849\pi\)
−0.999966 + 0.00825163i \(0.997373\pi\)
\(234\) −5.35364 + 7.39719i −0.349978 + 0.483569i
\(235\) 2.93229 1.06726i 0.191281 0.0696207i
\(236\) −3.16855 + 3.28215i −0.206255 + 0.213650i
\(237\) −5.27710 26.2099i −0.342785 1.70252i
\(238\) 0.309921 + 0.0658506i 0.0200892 + 0.00426846i
\(239\) 5.36658 17.9256i 0.347135 1.15951i −0.589077 0.808077i \(-0.700509\pi\)
0.936212 0.351435i \(-0.114306\pi\)
\(240\) −1.50700 + 3.00962i −0.0972766 + 0.194270i
\(241\) −10.5179 14.1280i −0.677520 0.910067i 0.321805 0.946806i \(-0.395710\pi\)
−0.999325 + 0.0367387i \(0.988303\pi\)
\(242\) 2.62379 + 2.65409i 0.168664 + 0.170611i
\(243\) −12.5447 9.25371i −0.804741 0.593626i
\(244\) 7.98065 + 0.0916184i 0.510909 + 0.00586527i
\(245\) −1.77846 2.38889i −0.113622 0.152620i
\(246\) 6.88304 + 19.5583i 0.438847 + 1.24699i
\(247\) 8.01628 + 2.39992i 0.510064 + 0.152703i
\(248\) −27.7350 6.22658i −1.76117 0.395388i
\(249\) 1.44464 + 7.17511i 0.0915500 + 0.454704i
\(250\) 6.70651 0.156619i 0.424157 0.00990546i
\(251\) −3.22211 8.85267i −0.203378 0.558776i 0.795509 0.605941i \(-0.207203\pi\)
−0.998887 + 0.0471656i \(0.984981\pi\)
\(252\) 2.02561 5.21595i 0.127601 0.328574i
\(253\) −1.07287 + 2.94769i −0.0674509 + 0.185320i
\(254\) −9.42867 + 27.9164i −0.591607 + 1.75163i
\(255\) 0.135133 0.150346i 0.00846233 0.00941501i
\(256\) 5.65623 + 14.9669i 0.353514 + 0.935429i
\(257\) 1.02413 8.76197i 0.0638833 0.546557i −0.922962 0.384891i \(-0.874239\pi\)
0.986846 0.161666i \(-0.0516867\pi\)
\(258\) 2.83541 3.72491i 0.176525 0.231903i
\(259\) 5.01495 + 3.29838i 0.311614 + 0.204952i
\(260\) −1.61728 + 1.32573i −0.100300 + 0.0822180i
\(261\) −16.6503 16.0225i −1.03063 0.991767i
\(262\) 16.1306 1.31800i 0.996553 0.0814261i
\(263\) −2.65265 8.86047i −0.163569 0.546360i 0.836429 0.548075i \(-0.184639\pi\)
−0.999999 + 0.00171513i \(0.999454\pi\)
\(264\) 7.53235 16.4499i 0.463584 1.01242i
\(265\) −0.366810 0.184219i −0.0225329 0.0113165i
\(266\) −5.12454 0.178553i −0.314206 0.0109478i
\(267\) 15.9625 + 1.47600i 0.976886 + 0.0903297i
\(268\) −24.6496 10.9701i −1.50572 0.670107i
\(269\) −7.50663 + 13.0019i −0.457687 + 0.792738i −0.998838 0.0481878i \(-0.984655\pi\)
0.541151 + 0.840925i \(0.317989\pi\)
\(270\) −2.23807 2.78138i −0.136205 0.169269i
\(271\) −3.93492 + 2.27183i −0.239029 + 0.138004i −0.614731 0.788737i \(-0.710735\pi\)
0.375701 + 0.926741i \(0.377402\pi\)
\(272\) −0.0896184 0.956760i −0.00543391 0.0580121i
\(273\) 2.47035 2.44608i 0.149513 0.148043i
\(274\) 1.34490 2.15266i 0.0812481 0.130047i
\(275\) −17.5641 + 1.02299i −1.05915 + 0.0616887i
\(276\) 2.94213 0.0372816i 0.177095 0.00224409i
\(277\) 5.71858 24.1286i 0.343596 1.44975i −0.477336 0.878721i \(-0.658398\pi\)
0.820932 0.571025i \(-0.193454\pi\)
\(278\) −18.0665 + 12.4964i −1.08356 + 0.749482i
\(279\) 18.2421 24.0047i 1.09212 1.43712i
\(280\) 0.752978 1.03690i 0.0449990 0.0619664i
\(281\) 11.1226 + 0.647818i 0.663519 + 0.0386456i 0.386600 0.922248i \(-0.373649\pi\)
0.276919 + 0.960893i \(0.410686\pi\)
\(282\) 10.6741 + 11.5587i 0.635634 + 0.688311i
\(283\) −2.54316 + 3.41606i −0.151175 + 0.203064i −0.871259 0.490823i \(-0.836696\pi\)
0.720084 + 0.693887i \(0.244103\pi\)
\(284\) 6.83531 + 5.21171i 0.405601 + 0.309258i
\(285\) −1.73121 + 2.77595i −0.102548 + 0.164433i
\(286\) 8.43997 7.42457i 0.499066 0.439024i
\(287\) −1.37077 7.77404i −0.0809142 0.458887i
\(288\) −16.9317 1.14743i −0.997712 0.0676127i
\(289\) 2.94200 16.6849i 0.173059 0.981464i
\(290\) −2.75227 4.51996i −0.161619 0.265421i
\(291\) 23.1064 14.0952i 1.35452 0.826276i
\(292\) 3.10163 0.144945i 0.181509 0.00848228i
\(293\) 23.2839 5.51839i 1.36026 0.322388i 0.515205 0.857067i \(-0.327716\pi\)
0.845055 + 0.534679i \(0.179567\pi\)
\(294\) 7.64648 12.9234i 0.445952 0.753709i
\(295\) −0.128650 1.10067i −0.00749027 0.0640833i
\(296\) 5.01383 17.5008i 0.291423 1.01721i
\(297\) 12.5436 + 14.5228i 0.727854 + 0.842696i
\(298\) 11.7088 3.06545i 0.678274 0.177577i
\(299\) 1.67859 + 0.724073i 0.0970753 + 0.0418742i
\(300\) 6.72795 + 15.0692i 0.388438 + 0.870021i
\(301\) −1.29638 + 1.22307i −0.0747222 + 0.0704967i
\(302\) 24.7056 8.02948i 1.42165 0.462045i
\(303\) 4.95912 + 0.751438i 0.284894 + 0.0431690i
\(304\) 4.11708 + 14.9968i 0.236131 + 0.860128i
\(305\) −1.24617 + 1.48513i −0.0713555 + 0.0850382i
\(306\) 0.962381 + 0.335665i 0.0550156 + 0.0191887i
\(307\) −0.525391 + 0.440856i −0.0299857 + 0.0251610i −0.657657 0.753317i \(-0.728453\pi\)
0.627672 + 0.778478i \(0.284008\pi\)
\(308\) −3.85095 + 5.71118i −0.219428 + 0.325425i
\(309\) −7.89248 10.0836i −0.448988 0.573637i
\(310\) 5.44069 4.25142i 0.309011 0.241464i
\(311\) −5.84253 13.5445i −0.331300 0.768039i −0.999706 0.0242426i \(-0.992283\pi\)
0.668406 0.743796i \(-0.266977\pi\)
\(312\) −9.31519 4.93968i −0.527369 0.279654i
\(313\) −5.62291 + 2.82393i −0.317826 + 0.159618i −0.600559 0.799581i \(-0.705055\pi\)
0.282733 + 0.959199i \(0.408759\pi\)
\(314\) 5.09417 2.33995i 0.287481 0.132051i
\(315\) 0.667936 + 1.18375i 0.0376339 + 0.0666966i
\(316\) 29.1295 10.2251i 1.63866 0.575208i
\(317\) 12.1820 12.9122i 0.684210 0.725220i −0.288439 0.957498i \(-0.593136\pi\)
0.972649 + 0.232278i \(0.0746179\pi\)
\(318\) 0.142390 2.06469i 0.00798486 0.115782i
\(319\) 15.6313 + 23.7663i 0.875186 + 1.33066i
\(320\) −3.68268 1.24221i −0.205868 0.0694417i
\(321\) 2.48662 1.72291i 0.138790 0.0961637i
\(322\) −1.10745 0.168716i −0.0617157 0.00940216i
\(323\) 0.934024i 0.0519705i
\(324\) 8.57675 15.8253i 0.476486 0.879182i
\(325\) 10.2533i 0.568752i
\(326\) 3.57576 23.4712i 0.198043 1.29995i
\(327\) 0.330382 + 4.00392i 0.0182702 + 0.221417i
\(328\) −21.2661 + 10.9982i −1.17422 + 0.607274i
\(329\) −3.29160 5.00464i −0.181472 0.275915i
\(330\) 1.93034 + 3.94818i 0.106262 + 0.217340i
\(331\) 9.93529 10.5308i 0.546093 0.578825i −0.394271 0.918994i \(-0.629003\pi\)
0.940364 + 0.340169i \(0.110484\pi\)
\(332\) −7.97435 + 2.79918i −0.437649 + 0.153625i
\(333\) 14.6683 + 12.5571i 0.803820 + 0.688127i
\(334\) −12.2424 26.6521i −0.669872 1.45834i
\(335\) 5.85669 2.94134i 0.319985 0.160703i
\(336\) 6.28870 + 1.48254i 0.343077 + 0.0808791i
\(337\) 10.4988 + 24.3390i 0.571908 + 1.32583i 0.921299 + 0.388855i \(0.127129\pi\)
−0.349391 + 0.936977i \(0.613611\pi\)
\(338\) 7.28637 + 9.32462i 0.396326 + 0.507193i
\(339\) −1.47652 + 3.66379i −0.0801937 + 0.198990i
\(340\) 0.193536 + 0.130498i 0.0104960 + 0.00707725i
\(341\) −28.4319 + 23.8572i −1.53967 + 1.29194i
\(342\) −16.2816 2.64523i −0.880408 0.143038i
\(343\) −7.87095 + 9.38024i −0.424992 + 0.506485i
\(344\) 4.71304 + 2.64699i 0.254110 + 0.142716i
\(345\) −0.446061 + 0.558446i −0.0240151 + 0.0300657i
\(346\) −7.55401 23.2427i −0.406106 1.24953i
\(347\) −5.07629 + 4.78923i −0.272510 + 0.257099i −0.810349 0.585948i \(-0.800722\pi\)
0.537839 + 0.843047i \(0.319241\pi\)
\(348\) 15.6610 21.6025i 0.839518 1.15802i
\(349\) 14.1486 + 6.10311i 0.757357 + 0.326692i 0.739507 0.673149i \(-0.235059\pi\)
0.0178500 + 0.999841i \(0.494318\pi\)
\(350\) −1.59131 6.07819i −0.0850592 0.324893i
\(351\) 8.87427 6.80566i 0.473674 0.363259i
\(352\) 20.0160 + 5.98390i 1.06686 + 0.318943i
\(353\) −4.25916 36.4394i −0.226692 1.93947i −0.328130 0.944632i \(-0.606418\pi\)
0.101438 0.994842i \(-0.467656\pi\)
\(354\) 4.86833 2.74184i 0.258749 0.145727i
\(355\) −2.03165 + 0.481511i −0.107829 + 0.0255559i
\(356\) 0.864090 + 18.4903i 0.0457967 + 0.979984i
\(357\) −0.340647 0.185852i −0.0180289 0.00983634i
\(358\) −12.2614 + 7.46615i −0.648036 + 0.394598i
\(359\) −2.08749 + 11.8387i −0.110174 + 0.624825i 0.878854 + 0.477092i \(0.158309\pi\)
−0.989027 + 0.147734i \(0.952802\pi\)
\(360\) 2.82291 3.00408i 0.148781 0.158329i
\(361\) −0.674454 3.82502i −0.0354976 0.201317i
\(362\) 0.487708 + 0.554408i 0.0256333 + 0.0291390i
\(363\) −2.14943 4.03393i −0.112816 0.211727i
\(364\) 3.19223 + 2.43398i 0.167318 + 0.127575i
\(365\) −0.450397 + 0.604989i −0.0235749 + 0.0316666i
\(366\) −9.33378 2.90330i −0.487885 0.151758i
\(367\) −33.4571 1.94865i −1.74645 0.101719i −0.845043 0.534699i \(-0.820425\pi\)
−0.901404 + 0.432980i \(0.857462\pi\)
\(368\) 0.513009 + 3.35859i 0.0267425 + 0.175079i
\(369\) −1.22608 25.3644i −0.0638273 1.32042i
\(370\) 2.51558 + 3.63688i 0.130779 + 0.189072i
\(371\) −0.181712 + 0.766702i −0.00943401 + 0.0398052i
\(372\) 30.3677 + 17.0235i 1.57449 + 0.882626i
\(373\) 23.8028 1.38635i 1.23246 0.0717827i 0.570485 0.821308i \(-0.306755\pi\)
0.661976 + 0.749525i \(0.269718\pi\)
\(374\) −1.06411 0.664816i −0.0550239 0.0343768i
\(375\) −7.92546 2.16562i −0.409269 0.111832i
\(376\) −11.5118 + 14.0546i −0.593673 + 0.724813i
\(377\) 14.3567 8.28885i 0.739408 0.426897i
\(378\) −4.20446 + 5.41170i −0.216254 + 0.278348i
\(379\) −8.02095 + 13.8927i −0.412009 + 0.713620i −0.995109 0.0987801i \(-0.968506\pi\)
0.583101 + 0.812400i \(0.301839\pi\)
\(380\) −3.45129 1.53597i −0.177048 0.0787936i
\(381\) 20.8449 29.4589i 1.06792 1.50923i
\(382\) 0.194265 5.57550i 0.00993948 0.285267i
\(383\) −32.9073 16.5267i −1.68149 0.844474i −0.992850 0.119365i \(-0.961914\pi\)
−0.688635 0.725108i \(-0.741790\pi\)
\(384\) −1.39480 19.5462i −0.0711783 0.997464i
\(385\) −0.479881 1.60291i −0.0244570 0.0816921i
\(386\) 0.175359 + 2.14617i 0.00892553 + 0.109237i
\(387\) −4.63247 + 3.37815i −0.235482 + 0.171721i
\(388\) 19.8132 + 24.1705i 1.00586 + 1.22707i
\(389\) 30.5819 + 20.1140i 1.55056 + 1.01982i 0.980101 + 0.198500i \(0.0636069\pi\)
0.570464 + 0.821323i \(0.306763\pi\)
\(390\) 2.36243 0.989269i 0.119626 0.0500936i
\(391\) 0.0236892 0.202674i 0.00119802 0.0102497i
\(392\) 16.0014 + 6.67821i 0.808194 + 0.337301i
\(393\) −19.3922 4.10411i −0.978206 0.207025i
\(394\) −3.81690 1.28914i −0.192293 0.0649461i
\(395\) −2.56483 + 7.04682i −0.129051 + 0.354564i
\(396\) −14.6025 + 16.6664i −0.733803 + 0.837520i
\(397\) −9.13556 25.0998i −0.458501 1.25972i −0.926601 0.376045i \(-0.877284\pi\)
0.468101 0.883675i \(-0.344939\pi\)
\(398\) 0.415657 + 17.7987i 0.0208350 + 0.892166i
\(399\) 5.95148 + 2.00478i 0.297946 + 0.100364i
\(400\) −16.1572 + 10.1031i −0.807860 + 0.505157i
\(401\) 25.0358 + 7.49523i 1.25023 + 0.374294i 0.842444 0.538784i \(-0.181116\pi\)
0.407785 + 0.913078i \(0.366301\pi\)
\(402\) 25.0851 + 21.5095i 1.25113 + 1.07280i
\(403\) 12.9165 + 17.3498i 0.643416 + 0.864257i
\(404\) −0.0664844 + 5.79129i −0.00330772 + 0.288127i
\(405\) 1.65217 + 4.04819i 0.0820968 + 0.201156i
\(406\) −7.22426 + 7.14181i −0.358534 + 0.354442i
\(407\) −14.1946 19.0666i −0.703598 0.945096i
\(408\) −0.229998 + 1.15422i −0.0113866 + 0.0571426i
\(409\) −5.02767 + 16.7936i −0.248602 + 0.830390i 0.739039 + 0.673662i \(0.235280\pi\)
−0.987642 + 0.156728i \(0.949905\pi\)
\(410\) 1.20870 5.68866i 0.0596934 0.280943i
\(411\) −2.33245 + 2.05516i −0.115051 + 0.101373i
\(412\) 10.2696 10.6378i 0.505947 0.524087i
\(413\) −1.99894 + 0.727556i −0.0983615 + 0.0358007i
\(414\) −3.46586 0.986934i −0.170338 0.0485051i
\(415\) 0.702137 1.92911i 0.0344666 0.0946961i
\(416\) 4.15964 11.4424i 0.203943 0.561009i
\(417\) 25.5801 8.33635i 1.25266 0.408233i
\(418\) 18.8280 + 7.60529i 0.920906 + 0.371987i
\(419\) −4.17341 + 35.7058i −0.203884 + 1.74434i 0.373284 + 0.927717i \(0.378232\pi\)
−0.577169 + 0.816625i \(0.695842\pi\)
\(420\) −1.24692 + 0.953090i −0.0608435 + 0.0465060i
\(421\) 10.7050 16.2762i 0.521731 0.793253i −0.474476 0.880268i \(-0.657363\pi\)
0.996207 + 0.0870155i \(0.0277330\pi\)
\(422\) 13.7923 + 1.28648i 0.671398 + 0.0626249i
\(423\) −8.47760 17.3043i −0.412195 0.841366i
\(424\) 2.38390 0.167259i 0.115772 0.00812280i
\(425\) 1.09640 0.328242i 0.0531834 0.0159221i
\(426\) −6.19597 8.51088i −0.300196 0.412353i
\(427\) 3.32568 + 1.67022i 0.160941 + 0.0808277i
\(428\) 2.36784 + 2.56820i 0.114454 + 0.124139i
\(429\) −12.5059 + 5.75659i −0.603791 + 0.277931i
\(430\) −1.22303 + 0.477771i −0.0589799 + 0.0230401i
\(431\) −3.51375 + 6.08600i −0.169252 + 0.293152i −0.938157 0.346210i \(-0.887468\pi\)
0.768905 + 0.639363i \(0.220802\pi\)
\(432\) 19.4687 + 7.27812i 0.936687 + 0.350169i
\(433\) 3.30268 + 5.72042i 0.158717 + 0.274906i 0.934406 0.356209i \(-0.115931\pi\)
−0.775689 + 0.631115i \(0.782598\pi\)
\(434\) −10.3496 8.28040i −0.496797 0.397472i
\(435\) 1.64655 + 6.26869i 0.0789462 + 0.300560i
\(436\) −4.52598 + 1.01795i −0.216755 + 0.0487508i
\(437\) 0.192015 + 3.29677i 0.00918531 + 0.157706i
\(438\) −3.69076 0.916458i −0.176352 0.0437901i
\(439\) 0.210074 0.886372i 0.0100263 0.0423042i −0.967802 0.251713i \(-0.919006\pi\)
0.977828 + 0.209409i \(0.0671541\pi\)
\(440\) −4.20644 + 2.83871i −0.200534 + 0.135330i
\(441\) −13.5010 + 12.4879i −0.642907 + 0.594660i
\(442\) −0.422842 + 0.596564i −0.0201126 + 0.0283757i
\(443\) −12.6494 0.736746i −0.600993 0.0350038i −0.245048 0.969511i \(-0.578804\pi\)
−0.355945 + 0.934507i \(0.615841\pi\)
\(444\) −12.0150 + 18.7820i −0.570205 + 0.891353i
\(445\) −3.60663 2.68504i −0.170971 0.127283i
\(446\) −4.43276 31.5229i −0.209897 1.49265i
\(447\) −14.8151 0.504308i −0.700728 0.0238530i
\(448\) −0.689988 + 7.42865i −0.0325989 + 0.350971i
\(449\) 20.8258 3.67216i 0.982832 0.173300i 0.340932 0.940088i \(-0.389257\pi\)
0.641900 + 0.766788i \(0.278146\pi\)
\(450\) −2.61670 20.0418i −0.123352 0.944778i
\(451\) −5.42840 + 30.7860i −0.255613 + 1.44965i
\(452\) −4.42590 1.10277i −0.208177 0.0518698i
\(453\) −31.8068 + 0.768300i −1.49441 + 0.0360979i
\(454\) 14.4280 + 12.9890i 0.677138 + 0.609602i
\(455\) −0.948824 + 0.224875i −0.0444815 + 0.0105423i
\(456\) 0.421999 19.0422i 0.0197619 0.891733i
\(457\) −24.9580 + 2.91718i −1.16749 + 0.136460i −0.677671 0.735366i \(-0.737010\pi\)
−0.489817 + 0.871825i \(0.662936\pi\)
\(458\) 4.40177 + 1.20657i 0.205681 + 0.0563794i
\(459\) −1.01183 0.731070i −0.0472284 0.0341234i
\(460\) −0.709942 0.420824i −0.0331012 0.0196210i
\(461\) −7.68437 + 17.8144i −0.357897 + 0.829699i 0.640210 + 0.768200i \(0.278847\pi\)
−0.998107 + 0.0614987i \(0.980412\pi\)
\(462\) 6.52011 5.35343i 0.303343 0.249064i
\(463\) 20.8137 19.6367i 0.967293 0.912594i −0.0289166 0.999582i \(-0.509206\pi\)
0.996209 + 0.0869882i \(0.0277242\pi\)
\(464\) 27.2080 + 14.4559i 1.26310 + 0.671097i
\(465\) −7.87441 + 3.08337i −0.365167 + 0.142988i
\(466\) 13.2503 + 7.24296i 0.613807 + 0.335523i
\(467\) 6.75207 8.04680i 0.312448 0.372362i −0.586851 0.809695i \(-0.699633\pi\)
0.899299 + 0.437333i \(0.144077\pi\)
\(468\) 9.20159 + 9.06037i 0.425344 + 0.418816i
\(469\) −8.08673 9.63739i −0.373410 0.445013i
\(470\) −0.867568 4.32690i −0.0400179 0.199585i
\(471\) −6.79812 + 0.961510i −0.313241 + 0.0443041i
\(472\) 3.91384 + 5.12897i 0.180149 + 0.236080i
\(473\) 6.48076 2.79553i 0.297986 0.128538i
\(474\) −37.7676 + 1.79530i −1.73472 + 0.0824607i
\(475\) −16.5519 + 8.31266i −0.759452 + 0.381411i
\(476\) 0.158076 0.419270i 0.00724538 0.0192172i
\(477\) −0.890407 + 2.37318i −0.0407689 + 0.108660i
\(478\) −23.9185 11.3209i −1.09400 0.517808i
\(479\) −9.93770 + 10.5333i −0.454065 + 0.481281i −0.913447 0.406958i \(-0.866589\pi\)
0.459382 + 0.888239i \(0.348071\pi\)
\(480\) 3.88672 + 2.74794i 0.177404 + 0.125426i
\(481\) −11.5738 + 7.61220i −0.527719 + 0.347086i
\(482\) −21.9924 + 11.6958i −1.00173 + 0.532728i
\(483\) 1.24057 + 0.585962i 0.0564478 + 0.0266622i
\(484\) 4.26948 3.10298i 0.194067 0.141044i
\(485\) −7.59173 −0.344723
\(486\) −15.6094 + 15.5675i −0.708055 + 0.706157i
\(487\) 1.58837i 0.0719761i 0.999352 + 0.0359880i \(0.0114578\pi\)
−0.999352 + 0.0359880i \(0.988542\pi\)
\(488\) 1.82791 11.1381i 0.0827456 0.504198i
\(489\) −12.4189 + 26.2926i −0.561600 + 1.18899i
\(490\) −3.71866 + 1.97762i −0.167992 + 0.0893398i
\(491\) −20.5423 31.2330i −0.927060 1.40953i −0.912249 0.409636i \(-0.865656\pi\)
−0.0148111 0.999890i \(-0.504715\pi\)
\(492\) 28.8102 5.45728i 1.29886 0.246033i
\(493\) −1.34594 1.26983i −0.0606183 0.0571904i
\(494\) 5.06269 10.6963i 0.227781 0.481247i
\(495\) −0.882267 5.30972i −0.0396549 0.238654i
\(496\) −14.6126 + 37.4495i −0.656126 + 1.68153i
\(497\) 1.79879 + 3.58169i 0.0806868 + 0.160661i
\(498\) 10.3391 0.491472i 0.463306 0.0220234i
\(499\) 2.91910 + 6.76723i 0.130677 + 0.302943i 0.970975 0.239182i \(-0.0768792\pi\)
−0.840298 + 0.542125i \(0.817620\pi\)
\(500\) 1.20947 9.40962i 0.0540892 0.420811i
\(501\) 5.03052 + 35.5670i 0.224747 + 1.58902i
\(502\) −13.0630 + 2.61922i −0.583032 + 0.116901i
\(503\) −17.6442 + 14.8053i −0.786717 + 0.660134i −0.944931 0.327271i \(-0.893871\pi\)
0.158213 + 0.987405i \(0.449427\pi\)
\(504\) −6.86089 3.94293i −0.305608 0.175632i
\(505\) −1.07771 0.904304i −0.0479574 0.0402410i
\(506\) 3.89260 + 2.12780i 0.173047 + 0.0945923i
\(507\) −5.28448 13.4957i −0.234692 0.599365i
\(508\) 37.0212 + 19.1280i 1.64255 + 0.848670i
\(509\) 17.3059 + 18.3432i 0.767072 + 0.813049i 0.986703 0.162534i \(-0.0519668\pi\)
−0.219631 + 0.975583i \(0.570485\pi\)
\(510\) −0.181413 0.220949i −0.00803311 0.00978378i
\(511\) 1.32942 + 0.573457i 0.0588102 + 0.0253682i
\(512\) 22.1296 4.72004i 0.978001 0.208598i
\(513\) 18.1810 + 8.80815i 0.802710 + 0.388889i
\(514\) −12.0318 3.29805i −0.530701 0.145471i
\(515\) 0.416967 + 3.56738i 0.0183738 + 0.157198i
\(516\) −4.60380 4.75751i −0.202671 0.209438i
\(517\) 5.47050 + 23.0819i 0.240592 + 1.01514i
\(518\) 5.67956 6.30878i 0.249545 0.277192i
\(519\) 0.722805 + 29.9233i 0.0317276 + 1.31349i
\(520\) 1.50900 + 2.54347i 0.0661742 + 0.111538i
\(521\) −42.3795 7.47265i −1.85668 0.327383i −0.870385 0.492372i \(-0.836130\pi\)
−0.986295 + 0.164989i \(0.947241\pi\)
\(522\) −25.9471 + 19.8658i −1.13568 + 0.869502i
\(523\) −3.37084 19.1170i −0.147397 0.835929i −0.965411 0.260731i \(-0.916036\pi\)
0.818015 0.575197i \(-0.195075\pi\)
\(524\) 1.59304 22.8326i 0.0695921 0.997449i
\(525\) −0.261792 + 7.69067i −0.0114256 + 0.335649i
\(526\) −12.9527 + 1.82141i −0.564763 + 0.0794172i
\(527\) 1.44175 1.93661i 0.0628036 0.0843598i
\(528\) −21.3940 14.0346i −0.931054 0.610776i
\(529\) 1.29538 22.2409i 0.0563210 0.966994i
\(530\) −0.335681 + 0.473593i −0.0145810 + 0.0205716i
\(531\) −6.67387 + 1.51228i −0.289621 + 0.0656273i
\(532\) −1.34112 + 7.12650i −0.0581450 + 0.308973i
\(533\) 17.7271 + 4.20140i 0.767845 + 0.181983i
\(534\) 5.46346 22.0024i 0.236427 0.952139i
\(535\) −0.847089 + 0.0493373i −0.0366228 + 0.00213304i
\(536\) −20.5873 + 32.1257i −0.889237 + 1.38762i
\(537\) 17.0052 4.46665i 0.733830 0.192750i
\(538\) 16.5788 + 13.2642i 0.714764 + 0.571860i
\(539\) 19.6066 11.3199i 0.844518 0.487583i
\(540\) −4.36529 + 2.53659i −0.187852 + 0.109157i
\(541\) 24.6046 + 14.2055i 1.05783 + 0.610741i 0.924832 0.380375i \(-0.124205\pi\)
0.133002 + 0.991116i \(0.457538\pi\)
\(542\) 2.33809 + 5.98522i 0.100430 + 0.257087i
\(543\) −0.378141 0.821492i −0.0162276 0.0352536i
\(544\) −1.35672 0.0784890i −0.0581687 0.00336519i
\(545\) 0.505735 1.00700i 0.0216633 0.0431352i
\(546\) −2.89365 3.97475i −0.123837 0.170104i
\(547\) 10.9569 + 36.5986i 0.468483 + 1.56484i 0.787017 + 0.616931i \(0.211624\pi\)
−0.318534 + 0.947911i \(0.603191\pi\)
\(548\) −2.72314 2.33878i −0.116327 0.0999075i
\(549\) 9.93680 + 6.67705i 0.424092 + 0.284970i
\(550\) −2.31080 + 24.7739i −0.0985327 + 1.05636i
\(551\) 25.0200 + 16.4559i 1.06589 + 0.701047i
\(552\) 0.574529 4.12127i 0.0244536 0.175413i
\(553\) 14.2979 + 1.67119i 0.608010 + 0.0710661i
\(554\) −32.5157 13.1343i −1.38146 0.558021i
\(555\) −1.67815 5.14940i −0.0712335 0.218580i
\(556\) 13.6229 + 27.9201i 0.577740 + 1.18407i
\(557\) −36.1233 13.1478i −1.53059 0.557090i −0.566825 0.823838i \(-0.691829\pi\)
−0.963766 + 0.266748i \(0.914051\pi\)
\(558\) −29.6751 30.6167i −1.25625 1.29611i
\(559\) −1.40681 3.86518i −0.0595018 0.163480i
\(560\) −1.28929 1.27358i −0.0544823 0.0538184i
\(561\) 1.01592 + 1.15299i 0.0428920 + 0.0486793i
\(562\) 3.27474 15.4123i 0.138137 0.650130i
\(563\) −22.0327 6.59614i −0.928566 0.277994i −0.213413 0.976962i \(-0.568458\pi\)
−0.715153 + 0.698968i \(0.753643\pi\)
\(564\) 18.4335 12.4614i 0.776191 0.524718i
\(565\) 0.888720 0.661627i 0.0373887 0.0278349i
\(566\) 4.23426 + 4.28315i 0.177979 + 0.180034i
\(567\) 6.83007 4.87812i 0.286836 0.204862i
\(568\) 8.74228 8.44627i 0.366818 0.354398i
\(569\) 32.5316 24.2189i 1.36380 1.01531i 0.367437 0.930048i \(-0.380235\pi\)
0.996359 0.0852604i \(-0.0271722\pi\)
\(570\) 3.51226 + 3.01163i 0.147113 + 0.126143i
\(571\) 1.52970 5.10956i 0.0640161 0.213829i −0.919997 0.391926i \(-0.871809\pi\)
0.984013 + 0.178097i \(0.0569942\pi\)
\(572\) −8.58250 13.3812i −0.358853 0.559494i
\(573\) −2.18120 + 6.47521i −0.0911207 + 0.270506i
\(574\) −11.1607 + 0.260639i −0.465839 + 0.0108789i
\(575\) −3.80243 + 1.38397i −0.158572 + 0.0577156i
\(576\) −5.21053 + 23.4276i −0.217105 + 0.976148i
\(577\) −14.9827 5.45327i −0.623739 0.227023i 0.0107647 0.999942i \(-0.496573\pi\)
−0.634504 + 0.772919i \(0.718796\pi\)
\(578\) −22.7002 7.66692i −0.944205 0.318902i
\(579\) 0.546050 2.58012i 0.0226931 0.107226i
\(580\) −6.90549 + 2.88518i −0.286735 + 0.119800i
\(581\) −3.91413 0.457497i −0.162386 0.0189802i
\(582\) −14.7848 35.3069i −0.612849 1.46352i
\(583\) 1.71465 2.60699i 0.0710134 0.107971i
\(584\) 0.457978 4.36720i 0.0189513 0.180716i
\(585\) −3.11905 + 0.333373i −0.128957 + 0.0137833i
\(586\) −2.75586 33.7282i −0.113843 1.39330i
\(587\) 15.5646 4.65973i 0.642420 0.192328i 0.0510088 0.998698i \(-0.483756\pi\)
0.591411 + 0.806370i \(0.298571\pi\)
\(588\) −16.4394 13.4430i −0.677947 0.554380i
\(589\) −17.5360 + 34.9170i −0.722558 + 1.43873i
\(590\) −1.56622 0.0545715i −0.0644804 0.00224667i
\(591\) 4.02780 + 2.85004i 0.165682 + 0.117235i
\(592\) −23.3996 10.7373i −0.961717 0.441299i
\(593\) 14.6921 + 8.48250i 0.603333 + 0.348334i 0.770352 0.637619i \(-0.220081\pi\)
−0.167019 + 0.985954i \(0.553414\pi\)
\(594\) 22.9757 14.4437i 0.942705 0.592634i
\(595\) 0.0544212 + 0.0942603i 0.00223105 + 0.00386430i
\(596\) −1.79185 17.0228i −0.0733972 0.697282i
\(597\) 5.74743 21.0337i 0.235227 0.860850i
\(598\) 1.36984 2.19258i 0.0560170 0.0896614i
\(599\) 0.230851 + 3.96356i 0.00943232 + 0.161947i 0.999735 + 0.0230201i \(0.00732818\pi\)
−0.990303 + 0.138927i \(0.955635\pi\)
\(600\) 22.5010 6.19659i 0.918599 0.252975i
\(601\) 26.1918 + 6.20758i 1.06839 + 0.253212i 0.726949 0.686692i \(-0.240938\pi\)
0.341438 + 0.939904i \(0.389086\pi\)
\(602\) 1.43384 + 2.07295i 0.0584388 + 0.0844872i
\(603\) −21.9040 34.0308i −0.892000 1.38584i
\(604\) −5.96375 36.2507i −0.242662 1.47502i
\(605\) −0.0745454 + 1.27990i −0.00303070 + 0.0520352i
\(606\) 2.10683 6.77321i 0.0855841 0.275143i
\(607\) 0.340477 + 0.253476i 0.0138195 + 0.0102883i 0.604046 0.796949i \(-0.293554\pi\)
−0.590227 + 0.807238i \(0.700962\pi\)
\(608\) 21.8437 2.56180i 0.885880 0.103895i
\(609\) 10.9801 5.85063i 0.444937 0.237079i
\(610\) 1.81091 + 2.05857i 0.0733214 + 0.0833491i
\(611\) 13.6142 2.40055i 0.550772 0.0971160i
\(612\) 0.674268 1.27399i 0.0272557 0.0514981i
\(613\) 3.71605 + 0.655240i 0.150090 + 0.0264649i 0.248188 0.968712i \(-0.420165\pi\)
−0.0980984 + 0.995177i \(0.531276\pi\)
\(614\) 0.504448 + 0.828439i 0.0203579 + 0.0334331i
\(615\) −3.41135 + 6.25263i −0.137559 + 0.252131i
\(616\) 7.16448 + 6.60038i 0.288665 + 0.265937i
\(617\) −4.16491 17.5732i −0.167673 0.707469i −0.990307 0.138897i \(-0.955644\pi\)
0.822634 0.568572i \(-0.192504\pi\)
\(618\) −15.7788 + 8.88660i −0.634716 + 0.357472i
\(619\) 10.5875 1.23751i 0.425549 0.0497396i 0.0993769 0.995050i \(-0.468315\pi\)
0.326172 + 0.945310i \(0.394241\pi\)
\(620\) −4.78501 8.51206i −0.192170 0.341852i
\(621\) 3.72170 + 2.37240i 0.149347 + 0.0952012i
\(622\) −20.1808 + 5.28346i −0.809175 + 0.211847i
\(623\) −3.41866 + 7.92534i −0.136966 + 0.317522i
\(624\) −8.89014 + 11.9713i −0.355890 + 0.479235i
\(625\) −14.7648 15.6498i −0.590591 0.625990i
\(626\) 2.75045 + 8.46277i 0.109930 + 0.338240i
\(627\) −19.4317 15.5212i −0.776029 0.619857i
\(628\) −2.18642 7.62046i −0.0872476 0.304089i
\(629\) 1.18450 + 0.993913i 0.0472291 + 0.0396299i
\(630\) 1.79724 0.681700i 0.0716038 0.0271596i
\(631\) −18.3098 21.8208i −0.728901 0.868670i 0.266562 0.963818i \(-0.414112\pi\)
−0.995463 + 0.0951474i \(0.969668\pi\)
\(632\) −8.09120 42.9032i −0.321851 1.70660i
\(633\) −15.7356 6.34150i −0.625434 0.252052i
\(634\) −15.4576 19.7817i −0.613900 0.785630i
\(635\) −9.29437 + 4.00920i −0.368836 + 0.159100i
\(636\) −2.85627 0.638837i −0.113259 0.0253315i
\(637\) −5.92145 11.7906i −0.234616 0.467159i
\(638\) 36.5566 16.7918i 1.44729 0.664795i
\(639\) 4.28990 + 12.1587i 0.169706 + 0.480992i
\(640\) −2.52110 + 4.88410i −0.0996551 + 0.193061i
\(641\) −10.4617 9.87015i −0.413214 0.389848i 0.451369 0.892337i \(-0.350936\pi\)
−0.864583 + 0.502490i \(0.832417\pi\)
\(642\) −1.87914 3.84347i −0.0741639 0.151690i
\(643\) −7.96715 + 5.24008i −0.314194 + 0.206648i −0.696804 0.717261i \(-0.745395\pi\)
0.382611 + 0.923910i \(0.375025\pi\)
\(644\) −0.471757 + 1.51237i −0.0185898 + 0.0595957i
\(645\) 1.60269 0.132246i 0.0631060 0.00520717i
\(646\) −1.30584 0.198940i −0.0513777 0.00782720i
\(647\) 24.1747 0.950406 0.475203 0.879876i \(-0.342375\pi\)
0.475203 + 0.879876i \(0.342375\pi\)
\(648\) −20.2982 15.3617i −0.797391 0.603464i
\(649\) 8.42404 0.330672
\(650\) 14.3350 + 2.18388i 0.562264 + 0.0856589i
\(651\) 9.24524 + 13.3433i 0.362350 + 0.522967i
\(652\) −32.0531 9.99840i −1.25530 0.391568i
\(653\) −33.6444 + 22.1282i −1.31661 + 0.865945i −0.996674 0.0814957i \(-0.974030\pi\)
−0.319932 + 0.947441i \(0.603660\pi\)
\(654\) 5.66817 + 0.390904i 0.221643 + 0.0152856i
\(655\) 4.04400 + 3.81532i 0.158012 + 0.149077i
\(656\) 10.8469 + 32.0742i 0.423500 + 1.25229i
\(657\) 4.01033 + 2.36848i 0.156458 + 0.0924032i
\(658\) −7.69798 + 3.53598i −0.300099 + 0.137847i
\(659\) 3.90072 + 7.76696i 0.151950 + 0.302558i 0.956710 0.291043i \(-0.0940022\pi\)
−0.804760 + 0.593601i \(0.797706\pi\)
\(660\) 5.93103 1.85784i 0.230865 0.0723162i
\(661\) −2.44818 + 1.05604i −0.0952232 + 0.0410753i −0.443159 0.896443i \(-0.646142\pi\)
0.347935 + 0.937519i \(0.386883\pi\)
\(662\) −12.6068 16.1333i −0.489976 0.627040i
\(663\) 0.705225 0.551982i 0.0273887 0.0214372i
\(664\) 2.21501 + 11.7450i 0.0859590 + 0.455794i
\(665\) −1.13225 1.34937i −0.0439070 0.0523263i
\(666\) 20.6802 17.8330i 0.801340 0.691013i
\(667\) 5.01175 + 4.20536i 0.194056 + 0.162832i
\(668\) −39.8694 + 11.4391i −1.54259 + 0.442592i
\(669\) −5.84093 + 38.5473i −0.225824 + 1.49033i
\(670\) −2.86480 8.81462i −0.110677 0.340539i
\(671\) −10.1136 10.7198i −0.390430 0.413832i
\(672\) 3.41216 8.47635i 0.131627 0.326982i
\(673\) 14.8793 34.4942i 0.573557 1.32965i −0.346567 0.938025i \(-0.612653\pi\)
0.920124 0.391628i \(-0.128088\pi\)
\(674\) 36.2642 9.49420i 1.39684 0.365703i
\(675\) −3.95015 + 24.4372i −0.152041 + 0.940587i
\(676\) 14.5885 8.20086i 0.561098 0.315418i
\(677\) −17.2652 + 2.01801i −0.663556 + 0.0775585i −0.441202 0.897408i \(-0.645448\pi\)
−0.222353 + 0.974966i \(0.571374\pi\)
\(678\) 4.80780 + 2.84466i 0.184642 + 0.109249i
\(679\) 3.36080 + 14.1803i 0.128976 + 0.544190i
\(680\) 0.223669 0.242785i 0.00857731 0.00931037i
\(681\) −12.3820 20.2979i −0.474479 0.777818i
\(682\) 27.2985 + 44.8315i 1.04531 + 1.71669i
\(683\) −46.5839 8.21401i −1.78249 0.314300i −0.817367 0.576117i \(-0.804567\pi\)
−0.965118 + 0.261817i \(0.915678\pi\)
\(684\) −7.16612 + 22.1996i −0.274003 + 0.848823i
\(685\) 0.858703 0.151412i 0.0328093 0.00578517i
\(686\) 11.4379 + 13.0022i 0.436701 + 0.496425i
\(687\) −4.74311 2.95803i −0.180961 0.112856i
\(688\) 4.70455 6.02543i 0.179359 0.229717i
\(689\) −1.45863 1.08591i −0.0555692 0.0413698i
\(690\) 0.685746 + 0.742575i 0.0261059 + 0.0282694i
\(691\) 1.39165 23.8938i 0.0529410 0.908962i −0.862386 0.506251i \(-0.831031\pi\)
0.915327 0.402711i \(-0.131932\pi\)
\(692\) −34.1041 + 5.61060i −1.29644 + 0.213283i
\(693\) −9.52725 + 3.99852i −0.361910 + 0.151891i
\(694\) 5.61453 + 8.11714i 0.213125 + 0.308123i
\(695\) −7.34286 1.74029i −0.278531 0.0660130i
\(696\) −26.8664 26.4966i −1.01837 1.00435i
\(697\) −0.118239 2.03009i −0.00447863 0.0768950i
\(698\) 11.5462 18.4810i 0.437030 0.699516i
\(699\) −13.0128 13.1420i −0.492190 0.497075i
\(700\) −8.83675 + 0.930173i −0.333998 + 0.0351572i
\(701\) 3.02596 + 5.24112i 0.114289 + 0.197954i 0.917495 0.397747i \(-0.130208\pi\)
−0.803206 + 0.595701i \(0.796874\pi\)
\(702\) −7.62471 13.8565i −0.287776 0.522981i
\(703\) −21.6715 12.5121i −0.817357 0.471902i
\(704\) 12.6292 26.7095i 0.475982 1.00665i
\(705\) −0.497644 + 5.38186i −0.0187424 + 0.202693i
\(706\) −51.8525 1.80668i −1.95149 0.0679953i
\(707\) −1.21202 + 2.41334i −0.0455828 + 0.0907629i
\(708\) −2.79640 7.39032i −0.105095 0.277745i
\(709\) 43.3968 12.9921i 1.62980 0.487930i 0.664112 0.747633i \(-0.268810\pi\)
0.965689 + 0.259703i \(0.0836246\pi\)
\(710\) 0.240464 + 2.94298i 0.00902446 + 0.110448i
\(711\) 44.9520 + 11.1239i 1.68583 + 0.417177i
\(712\) 26.0350 + 2.73023i 0.975703 + 0.102320i
\(713\) −4.69073 + 7.13191i −0.175669 + 0.267092i
\(714\) −0.332392 + 0.436667i −0.0124395 + 0.0163419i
\(715\) 3.83541 + 0.448295i 0.143436 + 0.0167653i
\(716\) 7.82669 + 18.7327i 0.292497 + 0.700074i
\(717\) 24.1041 + 21.6651i 0.900185 + 0.809098i
\(718\) 16.1069 + 5.44005i 0.601105 + 0.203021i
\(719\) −37.2340 13.5521i −1.38859 0.505407i −0.463822 0.885929i \(-0.653522\pi\)
−0.924772 + 0.380522i \(0.875744\pi\)
\(720\) −3.59870 4.58651i −0.134115 0.170929i
\(721\) 6.47879 2.35809i 0.241283 0.0878197i
\(722\) −5.49134 + 0.128241i −0.204367 + 0.00477263i
\(723\) 29.9070 6.02147i 1.11225 0.223941i
\(724\) 0.878986 0.563771i 0.0326673 0.0209524i
\(725\) −10.5241 + 35.1529i −0.390854 + 1.30554i
\(726\) −6.09759 + 2.14589i −0.226303 + 0.0796413i
\(727\) 2.21428 1.64847i 0.0821231 0.0611384i −0.555314 0.831641i \(-0.687402\pi\)
0.637437 + 0.770502i \(0.279995\pi\)
\(728\) 4.08282 3.94458i 0.151319 0.146196i
\(729\) 23.7724 12.8014i 0.880458 0.474124i
\(730\) 0.749893 + 0.758551i 0.0277548 + 0.0280752i
\(731\) −0.368274 + 0.274170i −0.0136211 + 0.0101405i
\(732\) −6.04709 + 12.4310i −0.223507 + 0.459464i
\(733\) 4.90567 + 1.46866i 0.181195 + 0.0542463i 0.376115 0.926573i \(-0.377260\pi\)
−0.194920 + 0.980819i \(0.562445\pi\)
\(734\) −9.85050 + 46.3607i −0.363589 + 1.71121i
\(735\) 5.05693 1.01816i 0.186528 0.0375554i
\(736\) 4.80486 0.00187341i 0.177109 6.90549e-5i
\(737\) 17.0397 + 46.8163i 0.627667 + 1.72450i
\(738\) −35.7227 3.68827i −1.31497 0.135767i
\(739\) −30.6968 11.1727i −1.12920 0.410996i −0.291199 0.956662i \(-0.594054\pi\)
−0.838002 + 0.545667i \(0.816277\pi\)
\(740\) 5.62045 2.74236i 0.206612 0.100811i
\(741\) −9.68856 + 10.7793i −0.355918 + 0.395987i
\(742\) 1.03321 + 0.417350i 0.0379303 + 0.0153214i
\(743\) −24.1540 2.82320i −0.886126 0.103573i −0.339160 0.940729i \(-0.610143\pi\)
−0.546965 + 0.837155i \(0.684217\pi\)
\(744\) 30.2683 38.8307i 1.10969 1.42360i
\(745\) 3.47382 + 2.28477i 0.127271 + 0.0837075i
\(746\) 3.13158 33.5735i 0.114655 1.22921i
\(747\) −12.3059 3.04522i −0.450248 0.111419i
\(748\) −1.15612 + 1.34612i −0.0422718 + 0.0492188i
\(749\) 0.467154 + 1.56040i 0.0170694 + 0.0570159i
\(750\) −4.71578 + 10.6192i −0.172196 + 0.387758i
\(751\) −8.68790 + 17.2990i −0.317026 + 0.631251i −0.994551 0.104249i \(-0.966756\pi\)
0.677525 + 0.735499i \(0.263052\pi\)
\(752\) 17.1976 + 19.0879i 0.627133 + 0.696065i
\(753\) 16.2480 + 1.50240i 0.592111 + 0.0547507i
\(754\) −8.53062 21.8373i −0.310667 0.795268i
\(755\) 7.72840 + 4.46199i 0.281265 + 0.162389i
\(756\) 6.67048 + 7.03083i 0.242603 + 0.255709i
\(757\) 0.414901 0.239543i 0.0150798 0.00870635i −0.492441 0.870346i \(-0.663895\pi\)
0.507521 + 0.861639i \(0.330562\pi\)
\(758\) 17.7147 + 14.1730i 0.643428 + 0.514786i
\(759\) −3.82285 3.86079i −0.138761 0.140138i
\(760\) −2.88251 + 4.49804i −0.104560 + 0.163161i
\(761\) 5.57790 0.324876i 0.202199 0.0117767i 0.0432535 0.999064i \(-0.486228\pi\)
0.158945 + 0.987287i \(0.449191\pi\)
\(762\) −36.7462 35.4175i −1.33117 1.28304i
\(763\) −2.10483 0.498853i −0.0761998 0.0180597i
\(764\) −7.75363 1.45914i −0.280516 0.0527898i
\(765\) 0.135499 + 0.322853i 0.00489898 + 0.0116728i
\(766\) −30.1147 + 42.4871i −1.08809 + 1.53512i
\(767\) 0.285453 4.90104i 0.0103071 0.176966i
\(768\) −27.6243 2.21315i −0.996806 0.0798602i
\(769\) −13.0141 + 17.4809i −0.469300 + 0.630379i −0.972252 0.233935i \(-0.924840\pi\)
0.502953 + 0.864314i \(0.332247\pi\)
\(770\) −2.34322 + 0.329504i −0.0844437 + 0.0118745i
\(771\) 12.9649 + 8.08550i 0.466918 + 0.291192i
\(772\) 3.03787 + 0.211953i 0.109335 + 0.00762834i
\(773\) 2.34743 + 13.3129i 0.0844312 + 0.478833i 0.997478 + 0.0709781i \(0.0226121\pi\)
−0.913047 + 0.407855i \(0.866277\pi\)
\(774\) 3.73625 + 7.19610i 0.134297 + 0.258658i
\(775\) −47.1500 8.31382i −1.69368 0.298641i
\(776\) 38.0125 22.5523i 1.36457 0.809580i
\(777\) −8.87547 + 5.41415i −0.318406 + 0.194232i
\(778\) 34.6348 38.4719i 1.24172 1.37928i
\(779\) 7.58958 + 32.0229i 0.271925 + 1.14734i
\(780\) −0.879899 3.51358i −0.0315054 0.125806i
\(781\) −1.84264 15.7648i −0.0659348 0.564108i
\(782\) −0.278310 0.0762876i −0.00995233 0.00272804i
\(783\) 37.4103 14.2242i 1.33693 0.508330i
\(784\) 12.7449 20.9489i 0.455174 0.748175i
\(785\) 1.76826 + 0.762755i 0.0631121 + 0.0272239i
\(786\) −9.86828 + 26.2377i −0.351990 + 0.935869i
\(787\) −20.1068 21.3119i −0.716729 0.759688i 0.261951 0.965081i \(-0.415634\pi\)
−0.978680 + 0.205393i \(0.934153\pi\)
\(788\) −2.61530 + 5.06176i −0.0931662 + 0.180318i
\(789\) 15.8390 + 2.40002i 0.563883 + 0.0854431i
\(790\) 9.30575 + 5.08677i 0.331084 + 0.180979i
\(791\) −1.62926 1.36711i −0.0579297 0.0486088i
\(792\) 20.1908 + 23.9653i 0.717450 + 0.851571i
\(793\) −6.57938 + 5.52075i −0.233641 + 0.196048i
\(794\) −37.0373 + 7.42620i −1.31441 + 0.263546i
\(795\) 0.559856 0.438201i 0.0198560 0.0155414i
\(796\) 24.9725 + 3.20986i 0.885128 + 0.113771i
\(797\) −17.6223 40.8532i −0.624215 1.44709i −0.877440 0.479686i \(-0.840750\pi\)
0.253225 0.967408i \(-0.418509\pi\)
\(798\) 4.07046 7.89365i 0.144093 0.279432i
\(799\) −0.692530 1.37894i −0.0245000 0.0487834i
\(800\) 10.6837 + 24.7410i 0.377724 + 0.874726i
\(801\) −14.1197 + 23.9075i −0.498894 + 0.844731i
\(802\) 15.8114 33.4057i 0.558320 1.17960i
\(803\) −4.17044 3.93460i −0.147172 0.138849i
\(804\) 35.4150 30.4897i 1.24899 1.07529i
\(805\) −0.211465 0.321517i −0.00745317 0.0113320i
\(806\) 27.0076 14.3629i 0.951303 0.505912i
\(807\) −14.8098 21.3744i −0.521328 0.752415i
\(808\) 8.08254 + 1.32645i 0.284343 + 0.0466645i
\(809\) 33.5965i 1.18119i 0.806968 + 0.590595i \(0.201107\pi\)
−0.806968 + 0.590595i \(0.798893\pi\)
\(810\) 6.01161 1.44763i 0.211226 0.0508645i
\(811\) −23.3802 −0.820991 −0.410495 0.911863i \(-0.634644\pi\)
−0.410495 + 0.911863i \(0.634644\pi\)
\(812\) 8.44612 + 11.6213i 0.296401 + 0.407827i
\(813\) −0.647178 7.84318i −0.0226975 0.275072i
\(814\) −29.6800 + 15.7841i −1.04028 + 0.553233i
\(815\) 6.81422 4.48179i 0.238692 0.156990i
\(816\) 1.56471 + 0.567398i 0.0547758 + 0.0198629i
\(817\) 5.09900 5.40462i 0.178391 0.189084i
\(818\) 22.4080 + 10.6060i 0.783477 + 0.370831i
\(819\) 2.00347 + 5.67837i 0.0700070 + 0.198418i
\(820\) −7.69577 2.90150i −0.268748 0.101325i
\(821\) 10.5927 5.31984i 0.369687 0.185664i −0.254250 0.967139i \(-0.581829\pi\)
0.623937 + 0.781475i \(0.285532\pi\)
\(822\) 2.37648 + 3.69870i 0.0828894 + 0.129007i
\(823\) 36.4463 15.7214i 1.27044 0.548013i 0.349212 0.937044i \(-0.386449\pi\)
0.921225 + 0.389031i \(0.127190\pi\)
\(824\) −12.6852 16.6235i −0.441909 0.579108i
\(825\) 11.3907 28.2645i 0.396573 0.984044i
\(826\) 0.591422 + 2.94965i 0.0205782 + 0.102631i
\(827\) −26.8136 31.9552i −0.932401 1.11119i −0.993587 0.113066i \(-0.963933\pi\)
0.0611865 0.998126i \(-0.480512\pi\)
\(828\) −2.11802 + 4.63535i −0.0736062 + 0.161090i
\(829\) −15.0920 + 17.9860i −0.524167 + 0.624678i −0.961561 0.274592i \(-0.911457\pi\)
0.437394 + 0.899270i \(0.355902\pi\)
\(830\) −2.54750 1.39253i −0.0884250 0.0483355i
\(831\) 33.5584 + 26.8049i 1.16413 + 0.929853i
\(832\) −15.1114 8.25266i −0.523894 0.286109i
\(833\) −1.07122 + 1.01064i −0.0371156 + 0.0350168i
\(834\) −6.20653 37.5386i −0.214915 1.29986i
\(835\) 3.99065 9.25137i 0.138102 0.320157i
\(836\) 14.6430 24.7032i 0.506440 0.854378i
\(837\) 24.1003 + 46.3268i 0.833028 + 1.60129i
\(838\) 49.0307 + 13.4398i 1.69374 + 0.464272i
\(839\) −45.4084 + 5.30749i −1.56767 + 0.183235i −0.855138 0.518401i \(-0.826528\pi\)
−0.712536 + 0.701636i \(0.752453\pi\)
\(840\) 1.06691 + 1.94630i 0.0368120 + 0.0671537i
\(841\) 29.5105 6.99412i 1.01760 0.241177i
\(842\) −20.4754 18.4332i −0.705627 0.635250i
\(843\) −9.24240 + 16.9403i −0.318325 + 0.583455i
\(844\) 4.73626 19.0087i 0.163029 0.654308i
\(845\) −0.705918 + 4.00346i −0.0242843 + 0.137723i
\(846\) −25.9986 + 8.16669i −0.893849 + 0.280776i
\(847\) 2.42367 0.427358i 0.0832783 0.0146842i
\(848\) 0.273911 3.36851i 0.00940615 0.115675i
\(849\) −3.46874 6.50994i −0.119047 0.223420i
\(850\) −0.225383 1.60278i −0.00773057 0.0549748i
\(851\) −4.38518 3.26465i −0.150322 0.111911i
\(852\) −13.2186 + 6.84973i −0.452862 + 0.234668i
\(853\) −51.5390 3.00181i −1.76466 0.102780i −0.855130 0.518413i \(-0.826523\pi\)
−0.909532 + 0.415633i \(0.863560\pi\)
\(854\) 3.04345 4.29384i 0.104145 0.146932i
\(855\) −3.06687 4.76479i −0.104885 0.162952i
\(856\) 4.09488 2.76343i 0.139960 0.0944520i
\(857\) 5.71031 24.0937i 0.195061 0.823025i −0.784214 0.620490i \(-0.786934\pi\)
0.979275 0.202535i \(-0.0649181\pi\)
\(858\) 5.38451 + 18.7104i 0.183824 + 0.638762i
\(859\) −1.26520 21.7227i −0.0431682 0.741170i −0.948561 0.316595i \(-0.897461\pi\)
0.905393 0.424575i \(-0.139577\pi\)
\(860\) 0.407465 + 1.81166i 0.0138945 + 0.0617772i
\(861\) 13.1892 + 3.60395i 0.449488 + 0.122822i
\(862\) 7.76033 + 6.20879i 0.264318 + 0.211472i
\(863\) 22.5587 + 39.0728i 0.767906 + 1.33005i 0.938696 + 0.344745i \(0.112035\pi\)
−0.170790 + 0.985307i \(0.554632\pi\)
\(864\) 14.3221 25.6686i 0.487247 0.873264i
\(865\) 4.19778 7.27076i 0.142729 0.247213i
\(866\) 8.70106 3.39902i 0.295674 0.115503i
\(867\) 23.9545 + 16.9500i 0.813538 + 0.575654i
\(868\) −13.7811 + 12.7059i −0.467760 + 0.431268i
\(869\) −50.9430 25.5845i −1.72812 0.867895i
\(870\) 9.11484 0.966833i 0.309022 0.0327787i
\(871\) 27.8147 8.32719i 0.942467 0.282156i
\(872\) 0.459175 + 6.54450i 0.0155496 + 0.221625i
\(873\) 4.98231 + 46.6146i 0.168626 + 1.57767i
\(874\) 4.65005 + 0.433735i 0.157290 + 0.0146713i
\(875\) 2.43086 3.69595i 0.0821781 0.124946i
\(876\) −2.06739 + 4.96479i −0.0698506 + 0.167745i
\(877\) 3.33721 28.5517i 0.112690 0.964121i −0.812068 0.583563i \(-0.801658\pi\)
0.924757 0.380558i \(-0.124268\pi\)
\(878\) −1.19448 0.482491i −0.0403116 0.0162833i
\(879\) −8.58147 + 40.5480i −0.289446 + 1.36765i
\(880\) 3.07281 + 6.48558i 0.103584 + 0.218629i
\(881\) −8.83721 + 24.2800i −0.297733 + 0.818015i 0.697145 + 0.716930i \(0.254453\pi\)
−0.994878 + 0.101084i \(0.967769\pi\)
\(882\) 14.5834 + 21.5354i 0.491050 + 0.725135i
\(883\) −1.26542 + 0.460575i −0.0425847 + 0.0154996i −0.363225 0.931702i \(-0.618324\pi\)
0.320640 + 0.947201i \(0.396102\pi\)
\(884\) 0.743984 + 0.718232i 0.0250229 + 0.0241568i
\(885\) 1.81896 + 0.612724i 0.0611438 + 0.0205965i
\(886\) −3.72427 + 17.5280i −0.125119 + 0.588866i
\(887\) 11.8329 39.5246i 0.397310 1.32711i −0.492316 0.870416i \(-0.663850\pi\)
0.889626 0.456690i \(-0.150965\pi\)
\(888\) 23.6997 + 20.7983i 0.795308 + 0.697947i
\(889\) 11.6032 + 15.5858i 0.389158 + 0.522730i
\(890\) −4.52209 + 4.47048i −0.151581 + 0.149851i
\(891\) −32.0236 + 8.90195i −1.07283 + 0.298226i
\(892\) −45.0157 0.516784i −1.50724 0.0173032i
\(893\) 14.9127 + 20.0312i 0.499033 + 0.670318i
\(894\) −3.86057 + 20.6053i −0.129117 + 0.689143i
\(895\) −4.72436 1.41438i −0.157918 0.0472775i
\(896\) 10.2389 + 2.54691i 0.342058 + 0.0850863i
\(897\) −2.37572 + 2.09328i −0.0793229 + 0.0698925i
\(898\) −0.698225 29.8984i −0.0233001 0.997722i
\(899\) 26.4754 + 72.7405i 0.883003 + 2.42603i
\(900\) −28.5774 0.610395i −0.952579 0.0203465i
\(901\) −0.0694225 + 0.190737i −0.00231280 + 0.00635436i
\(902\) 41.8851 + 14.1465i 1.39462 + 0.471028i
\(903\) −0.956515 2.93507i −0.0318308 0.0976729i
\(904\) −2.48444 + 5.95289i −0.0826314 + 0.197990i
\(905\) −0.0294478 + 0.251942i −0.000978877 + 0.00837483i
\(906\) −5.70047 + 44.6321i −0.189385 + 1.48280i
\(907\) 38.6007 + 25.3881i 1.28171 + 0.842996i 0.993418 0.114545i \(-0.0365410\pi\)
0.288296 + 0.957541i \(0.406911\pi\)
\(908\) 21.2327 17.4049i 0.704631 0.577603i
\(909\) −4.84531 + 7.21080i −0.160709 + 0.239167i
\(910\) 0.112302 + 1.37443i 0.00372276 + 0.0455619i
\(911\) 14.1885 + 47.3927i 0.470084 + 1.57019i 0.784013 + 0.620745i \(0.213170\pi\)
−0.313928 + 0.949447i \(0.601645\pi\)
\(912\) −26.5327 4.64584i −0.878585 0.153839i
\(913\) 13.9459 + 7.00390i 0.461542 + 0.231795i
\(914\) −1.23743 + 35.5147i −0.0409305 + 1.17472i
\(915\) −1.40407 3.05028i −0.0464172 0.100839i
\(916\) 2.62443 5.89704i 0.0867136 0.194844i
\(917\) 5.33625 9.24265i 0.176218 0.305219i
\(918\) −1.23761 + 1.25892i −0.0408472 + 0.0415504i
\(919\) 21.9774 12.6887i 0.724967 0.418560i −0.0916110 0.995795i \(-0.529202\pi\)
0.816578 + 0.577235i \(0.195868\pi\)
\(920\) −0.739559 + 0.902924i −0.0243826 + 0.0297685i
\(921\) −0.301788 1.14895i −0.00994425 0.0378593i
\(922\) 23.2693 + 14.5377i 0.766332 + 0.478774i
\(923\) −9.23427 + 0.537835i −0.303950 + 0.0177030i
\(924\) −6.09580 10.2559i −0.200537 0.337394i
\(925\) 7.07131 29.8362i 0.232503 0.981009i
\(926\) −23.0205 33.2817i −0.756502 1.09370i
\(927\) 21.6307 4.90146i 0.710446 0.160985i
\(928\) 26.0056 34.9600i 0.853676 1.14762i
\(929\) −21.6792 1.26267i −0.711272 0.0414269i −0.301306 0.953528i \(-0.597422\pi\)
−0.409966 + 0.912101i \(0.634459\pi\)
\(930\) 2.63361 + 11.6658i 0.0863595 + 0.382537i
\(931\) 14.2328 19.1179i 0.466460 0.626565i
\(932\) 12.9485 16.9823i 0.424141 0.556273i
\(933\) 25.5345 + 0.869201i 0.835962 + 0.0284564i
\(934\) −9.81195 11.1539i −0.321057 0.364965i
\(935\) −0.0748470 0.424478i −0.00244776 0.0138819i
\(936\) 14.6270 10.9348i 0.478099 0.357415i
\(937\) 4.17692 23.6885i 0.136454 0.773870i −0.837382 0.546618i \(-0.815915\pi\)
0.973836 0.227252i \(-0.0729740\pi\)
\(938\) −15.1963 + 9.25322i −0.496176 + 0.302128i
\(939\) −0.263177 10.8952i −0.00858845 0.355552i
\(940\) −6.23414 + 0.291334i −0.203335 + 0.00950227i
\(941\) 50.8820 12.0593i 1.65871 0.393121i 0.708740 0.705470i \(-0.249264\pi\)
0.949967 + 0.312349i \(0.101116\pi\)
\(942\) −0.103679 + 9.70912i −0.00337803 + 0.316340i
\(943\) 0.834683 + 7.14117i 0.0271810 + 0.232548i
\(944\) 8.00434 4.37944i 0.260519 0.142539i
\(945\) −2.34801 + 0.170415i −0.0763807 + 0.00554361i
\(946\) −2.52802 9.65606i −0.0821930 0.313946i
\(947\) 29.7256 + 12.8224i 0.965952 + 0.416671i 0.819837 0.572597i \(-0.194064\pi\)
0.146115 + 0.989268i \(0.453323\pi\)
\(948\) −5.53426 + 53.1846i −0.179744 + 1.72736i
\(949\) −2.43044 + 2.29300i −0.0788954 + 0.0744340i
\(950\) 8.09636 + 24.9114i 0.262681 + 0.808233i
\(951\) 11.2107 + 28.6303i 0.363533 + 0.928403i
\(952\) −0.552505 0.310304i −0.0179068 0.0100570i
\(953\) 22.5492 26.8731i 0.730440 0.870505i −0.265160 0.964204i \(-0.585425\pi\)
0.995601 + 0.0936997i \(0.0298693\pi\)
\(954\) 3.12825 + 1.75033i 0.101281 + 0.0566691i
\(955\) 1.46811 1.23189i 0.0475070 0.0398631i
\(956\) −20.9221 + 31.0287i −0.676668 + 1.00354i
\(957\) −48.7843 + 6.89995i −1.57697 + 0.223044i
\(958\) 12.6098 + 16.1372i 0.407405 + 0.521371i
\(959\) −0.662958 1.53691i −0.0214080 0.0496294i
\(960\) 4.66969 4.84867i 0.150714 0.156490i
\(961\) −62.5541 + 31.4159i −2.01788 + 1.01342i
\(962\) 8.17734 + 17.8024i 0.263648 + 0.573974i
\(963\) 0.858868 + 5.16890i 0.0276766 + 0.166565i
\(964\) 11.6674 + 33.2383i 0.375783 + 1.07053i
\(965\) −0.507626 + 0.538053i −0.0163411 + 0.0173205i
\(966\) 1.08345 1.60961i 0.0348596 0.0517884i
\(967\) −5.14602 7.82415i −0.165485 0.251608i 0.743220 0.669048i \(-0.233298\pi\)
−0.908705 + 0.417440i \(0.862927\pi\)
\(968\) −3.42885 6.63000i −0.110207 0.213096i
\(969\) 1.46281 + 0.690934i 0.0469922 + 0.0221960i
\(970\) −1.61698 + 10.6139i −0.0519182 + 0.340791i
\(971\) 14.6164i 0.469062i −0.972109 0.234531i \(-0.924645\pi\)
0.972109 0.234531i \(-0.0753554\pi\)
\(972\) 18.4400 + 25.1390i 0.591463 + 0.806332i
\(973\) 14.4859i 0.464396i
\(974\) 2.22068 + 0.338312i 0.0711551 + 0.0108402i
\(975\) −16.0581 7.58478i −0.514271 0.242907i
\(976\) −15.1826 4.92790i −0.485984 0.157738i
\(977\) 16.8051 + 25.5510i 0.537644 + 0.817447i 0.997509 0.0705413i \(-0.0224727\pi\)
−0.459865 + 0.887989i \(0.652102\pi\)
\(978\) 34.1140 + 22.9627i 1.09085 + 0.734266i
\(979\) 23.4561 24.8620i 0.749660 0.794594i
\(980\) 1.97283 + 5.62021i 0.0630197 + 0.179531i
\(981\) −6.51508 2.44443i −0.208010 0.0780447i
\(982\) −48.0417 + 22.0674i −1.53307 + 0.704199i
\(983\) 27.5033 13.8127i 0.877218 0.440556i 0.0475868 0.998867i \(-0.484847\pi\)
0.829631 + 0.558312i \(0.188551\pi\)
\(984\) −1.49336 41.4414i −0.0476067 1.32110i
\(985\) −0.548161 1.27078i −0.0174659 0.0404905i
\(986\) −2.06201 + 1.61128i −0.0656677 + 0.0513135i
\(987\) 10.2729 1.45297i 0.326989 0.0462486i
\(988\) −13.8759 9.35629i −0.441452 0.297663i
\(989\) 1.24351 1.04343i 0.0395413 0.0331791i
\(990\) −7.61134 + 0.102550i −0.241904 + 0.00325924i
\(991\) −8.25841 + 9.84199i −0.262337 + 0.312641i −0.881094 0.472942i \(-0.843192\pi\)
0.618757 + 0.785583i \(0.287637\pi\)
\(992\) 49.2452 + 28.4061i 1.56354 + 0.901895i
\(993\) 9.14314 + 23.3501i 0.290149 + 0.740992i
\(994\) 5.39062 1.75198i 0.170980 0.0555696i
\(995\) −4.44858 + 4.19702i −0.141030 + 0.133054i
\(996\) 1.51503 14.5596i 0.0480057 0.461338i
\(997\) −8.15096 3.51598i −0.258143 0.111352i 0.263075 0.964775i \(-0.415263\pi\)
−0.521219 + 0.853423i \(0.674522\pi\)
\(998\) 10.0829 2.63977i 0.319168 0.0835604i
\(999\) −30.5169 + 13.6836i −0.965513 + 0.432930i
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 648.2.bb.b.155.57 1872
8.3 odd 2 inner 648.2.bb.b.155.101 yes 1872
81.23 odd 54 inner 648.2.bb.b.347.101 yes 1872
648.347 even 54 inner 648.2.bb.b.347.57 yes 1872
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
648.2.bb.b.155.57 1872 1.1 even 1 trivial
648.2.bb.b.155.101 yes 1872 8.3 odd 2 inner
648.2.bb.b.347.57 yes 1872 648.347 even 54 inner
648.2.bb.b.347.101 yes 1872 81.23 odd 54 inner