Properties

Label 162.2.g.b.31.3
Level $162$
Weight $2$
Character 162.31
Analytic conductor $1.294$
Analytic rank $0$
Dimension $90$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [162,2,Mod(7,162)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(162, base_ring=CyclotomicField(54))
 
chi = DirichletCharacter(H, H._module([16]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("162.7");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 162 = 2 \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 162.g (of order \(27\), 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: \(1.29357651274\)
Analytic rank: \(0\)
Dimension: \(90\)
Relative dimension: \(5\) over \(\Q(\zeta_{27})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label 31.3
Character \(\chi\) \(=\) 162.31
Dual form 162.2.g.b.115.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.396080 + 0.918216i) q^{2} +(0.178274 - 1.72285i) q^{3} +(-0.686242 + 0.727374i) q^{4} +(-0.253242 + 4.34800i) q^{5} +(1.65256 - 0.518693i) q^{6} +(3.96081 - 0.938728i) q^{7} +(-0.939693 - 0.342020i) q^{8} +(-2.93644 - 0.614278i) q^{9} +O(q^{10})\) \(q+(0.396080 + 0.918216i) q^{2} +(0.178274 - 1.72285i) q^{3} +(-0.686242 + 0.727374i) q^{4} +(-0.253242 + 4.34800i) q^{5} +(1.65256 - 0.518693i) q^{6} +(3.96081 - 0.938728i) q^{7} +(-0.939693 - 0.342020i) q^{8} +(-2.93644 - 0.614278i) q^{9} +(-4.09271 + 1.48962i) q^{10} +(1.14679 - 0.754256i) q^{11} +(1.13082 + 1.31196i) q^{12} +(0.410136 - 0.0479380i) q^{13} +(2.43075 + 3.26506i) q^{14} +(7.44581 + 1.21143i) q^{15} +(-0.0581448 - 0.998308i) q^{16} +(0.360116 + 0.302173i) q^{17} +(-0.599023 - 2.93959i) q^{18} +(0.227520 - 0.190912i) q^{19} +(-2.98883 - 3.16798i) q^{20} +(-0.911183 - 6.99123i) q^{21} +(1.14679 + 0.754256i) q^{22} +(-6.34530 - 1.50386i) q^{23} +(-0.756772 + 1.55798i) q^{24} +(-13.8748 - 1.62173i) q^{25} +(0.206464 + 0.357606i) q^{26} +(-1.58180 + 4.94954i) q^{27} +(-2.03526 + 3.52518i) q^{28} +(4.14206 - 5.56376i) q^{29} +(1.83678 + 7.31669i) q^{30} +(-2.61346 - 8.72957i) q^{31} +(0.893633 - 0.448799i) q^{32} +(-1.09503 - 2.11021i) q^{33} +(-0.134826 + 0.450349i) q^{34} +(3.07855 + 17.4593i) q^{35} +(2.46191 - 1.71434i) q^{36} +(-0.254225 + 1.44178i) q^{37} +(0.265415 + 0.133296i) q^{38} +(-0.00947370 - 0.715149i) q^{39} +(1.72507 - 3.99917i) q^{40} +(-1.98418 + 4.59985i) q^{41} +(6.05856 - 3.60575i) q^{42} +(-2.26969 - 1.13988i) q^{43} +(-0.238349 + 1.35175i) q^{44} +(3.41451 - 12.6121i) q^{45} +(-1.13237 - 6.42200i) q^{46} +(0.597351 - 1.99529i) q^{47} +(-1.73030 - 0.0777970i) q^{48} +(8.55134 - 4.29464i) q^{49} +(-4.00642 - 13.3824i) q^{50} +(0.584798 - 0.566557i) q^{51} +(-0.246583 + 0.331219i) q^{52} +(1.77553 - 3.07530i) q^{53} +(-5.17126 + 0.507978i) q^{54} +(2.98909 + 5.17725i) q^{55} +(-4.04300 - 0.472559i) q^{56} +(-0.288352 - 0.426018i) q^{57} +(6.74932 + 1.59962i) q^{58} +(4.66336 + 3.06714i) q^{59} +(-5.99079 + 4.58455i) q^{60} +(4.11569 + 4.36238i) q^{61} +(6.98049 - 5.85733i) q^{62} +(-12.2073 + 0.323481i) q^{63} +(0.766044 + 0.642788i) q^{64} +(0.104571 + 1.79541i) q^{65} +(1.50391 - 1.84129i) q^{66} +(2.81104 + 3.77588i) q^{67} +(-0.466919 + 0.0545750i) q^{68} +(-3.72213 + 10.6639i) q^{69} +(-14.8121 + 9.74204i) q^{70} +(-1.16819 + 0.425188i) q^{71} +(2.54925 + 1.58155i) q^{72} +(4.83702 + 1.76053i) q^{73} +(-1.42456 + 0.337627i) q^{74} +(-5.26750 + 23.6150i) q^{75} +(-0.0172694 + 0.296504i) q^{76} +(3.83417 - 4.06399i) q^{77} +(0.652909 - 0.291955i) q^{78} +(3.39340 + 7.86678i) q^{79} +4.35537 q^{80} +(8.24533 + 3.60758i) q^{81} -5.00955 q^{82} +(-3.65159 - 8.46534i) q^{83} +(5.71053 + 4.13490i) q^{84} +(-1.40504 + 1.48926i) q^{85} +(0.147679 - 2.53555i) q^{86} +(-8.84711 - 8.12803i) q^{87} +(-1.33560 + 0.316543i) q^{88} +(-10.4279 - 3.79543i) q^{89} +(12.9330 - 1.86013i) q^{90} +(1.57947 - 0.574879i) q^{91} +(5.44828 - 3.58339i) q^{92} +(-15.5057 + 2.94636i) q^{93} +(2.06871 - 0.241797i) q^{94} +(0.772467 + 1.03760i) q^{95} +(-0.613903 - 1.61961i) q^{96} +(-0.337750 - 5.79894i) q^{97} +(7.33042 + 6.15096i) q^{98} +(-3.83080 + 1.51038i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 90 q - 9 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 90 q - 9 q^{6} - 18 q^{13} - 9 q^{18} - 9 q^{20} - 54 q^{21} + 27 q^{23} - 18 q^{25} - 27 q^{26} - 27 q^{27} - 18 q^{28} - 27 q^{29} + 9 q^{30} + 54 q^{31} - 63 q^{33} - 27 q^{35} - 9 q^{36} - 18 q^{38} - 9 q^{41} - 9 q^{42} - 36 q^{43} + 63 q^{45} + 18 q^{46} - 27 q^{47} - 9 q^{48} - 36 q^{51} + 36 q^{52} - 27 q^{53} - 54 q^{55} - 81 q^{57} - 9 q^{58} - 45 q^{59} - 63 q^{63} + 9 q^{65} + 36 q^{66} + 81 q^{67} + 36 q^{68} + 18 q^{69} - 72 q^{70} + 72 q^{71} + 18 q^{72} - 36 q^{73} + 45 q^{74} + 216 q^{75} - 18 q^{76} + 144 q^{77} + 54 q^{78} - 99 q^{79} + 18 q^{80} + 144 q^{81} + 72 q^{82} + 45 q^{83} + 18 q^{84} - 117 q^{85} + 72 q^{86} + 81 q^{87} - 18 q^{88} + 45 q^{89} + 162 q^{90} - 63 q^{91} + 36 q^{92} + 45 q^{93} - 72 q^{94} + 45 q^{95} + 18 q^{96} + 117 q^{97} + 36 q^{98} - 81 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/162\mathbb{Z}\right)^\times\).

\(n\) \(83\)
\(\chi(n)\) \(e\left(\frac{10}{27}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.396080 + 0.918216i 0.280071 + 0.649277i
\(3\) 0.178274 1.72285i 0.102926 0.994689i
\(4\) −0.686242 + 0.727374i −0.343121 + 0.363687i
\(5\) −0.253242 + 4.34800i −0.113253 + 1.94448i 0.170012 + 0.985442i \(0.445619\pi\)
−0.283265 + 0.959042i \(0.591418\pi\)
\(6\) 1.65256 0.518693i 0.674655 0.211756i
\(7\) 3.96081 0.938728i 1.49704 0.354806i 0.601172 0.799119i \(-0.294701\pi\)
0.895871 + 0.444314i \(0.146552\pi\)
\(8\) −0.939693 0.342020i −0.332232 0.120922i
\(9\) −2.93644 0.614278i −0.978812 0.204759i
\(10\) −4.09271 + 1.48962i −1.29423 + 0.471060i
\(11\) 1.14679 0.754256i 0.345770 0.227417i −0.364730 0.931113i \(-0.618839\pi\)
0.710501 + 0.703696i \(0.248468\pi\)
\(12\) 1.13082 + 1.31196i 0.326439 + 0.378731i
\(13\) 0.410136 0.0479380i 0.113751 0.0132956i −0.0590268 0.998256i \(-0.518800\pi\)
0.172778 + 0.984961i \(0.444726\pi\)
\(14\) 2.43075 + 3.26506i 0.649645 + 0.872625i
\(15\) 7.44581 + 1.21143i 1.92250 + 0.312790i
\(16\) −0.0581448 0.998308i −0.0145362 0.249577i
\(17\) 0.360116 + 0.302173i 0.0873409 + 0.0732877i 0.685413 0.728155i \(-0.259622\pi\)
−0.598072 + 0.801443i \(0.704066\pi\)
\(18\) −0.599023 2.93959i −0.141191 0.692867i
\(19\) 0.227520 0.190912i 0.0521967 0.0437982i −0.616316 0.787499i \(-0.711376\pi\)
0.668513 + 0.743701i \(0.266931\pi\)
\(20\) −2.98883 3.16798i −0.668324 0.708382i
\(21\) −0.911183 6.99123i −0.198836 1.52561i
\(22\) 1.14679 + 0.754256i 0.244497 + 0.160808i
\(23\) −6.34530 1.50386i −1.32309 0.313577i −0.492425 0.870355i \(-0.663889\pi\)
−0.830661 + 0.556778i \(0.812037\pi\)
\(24\) −0.756772 + 1.55798i −0.154476 + 0.318021i
\(25\) −13.8748 1.62173i −2.77495 0.324345i
\(26\) 0.206464 + 0.357606i 0.0404909 + 0.0701323i
\(27\) −1.58180 + 4.94954i −0.304417 + 0.952539i
\(28\) −2.03526 + 3.52518i −0.384629 + 0.666196i
\(29\) 4.14206 5.56376i 0.769162 1.03316i −0.229051 0.973414i \(-0.573562\pi\)
0.998213 0.0597496i \(-0.0190302\pi\)
\(30\) 1.83678 + 7.31669i 0.335348 + 1.33584i
\(31\) −2.61346 8.72957i −0.469392 1.56788i −0.785317 0.619094i \(-0.787500\pi\)
0.315926 0.948784i \(-0.397685\pi\)
\(32\) 0.893633 0.448799i 0.157973 0.0793372i
\(33\) −1.09503 2.11021i −0.190620 0.367341i
\(34\) −0.134826 + 0.450349i −0.0231224 + 0.0772342i
\(35\) 3.07855 + 17.4593i 0.520369 + 2.95116i
\(36\) 2.46191 1.71434i 0.410319 0.285724i
\(37\) −0.254225 + 1.44178i −0.0417943 + 0.237027i −0.998548 0.0538725i \(-0.982844\pi\)
0.956754 + 0.290900i \(0.0939547\pi\)
\(38\) 0.265415 + 0.133296i 0.0430559 + 0.0216235i
\(39\) −0.00947370 0.715149i −0.00151701 0.114516i
\(40\) 1.72507 3.99917i 0.272758 0.632324i
\(41\) −1.98418 + 4.59985i −0.309877 + 0.718376i −0.999986 0.00532951i \(-0.998304\pi\)
0.690108 + 0.723706i \(0.257563\pi\)
\(42\) 6.05856 3.60575i 0.934856 0.556379i
\(43\) −2.26969 1.13988i −0.346124 0.173830i 0.267241 0.963630i \(-0.413888\pi\)
−0.613365 + 0.789800i \(0.710184\pi\)
\(44\) −0.238349 + 1.35175i −0.0359325 + 0.203784i
\(45\) 3.41451 12.6121i 0.509005 1.88010i
\(46\) −1.13237 6.42200i −0.166959 0.946873i
\(47\) 0.597351 1.99529i 0.0871326 0.291043i −0.903306 0.428997i \(-0.858867\pi\)
0.990439 + 0.137953i \(0.0440524\pi\)
\(48\) −1.73030 0.0777970i −0.249748 0.0112290i
\(49\) 8.55134 4.29464i 1.22162 0.613521i
\(50\) −4.00642 13.3824i −0.566593 1.89255i
\(51\) 0.584798 0.566557i 0.0818882 0.0793338i
\(52\) −0.246583 + 0.331219i −0.0341950 + 0.0459318i
\(53\) 1.77553 3.07530i 0.243887 0.422425i −0.717931 0.696114i \(-0.754911\pi\)
0.961818 + 0.273689i \(0.0882439\pi\)
\(54\) −5.17126 + 0.507978i −0.703720 + 0.0691271i
\(55\) 2.98909 + 5.17725i 0.403049 + 0.698101i
\(56\) −4.04300 0.472559i −0.540269 0.0631484i
\(57\) −0.288352 0.426018i −0.0381932 0.0564275i
\(58\) 6.74932 + 1.59962i 0.886229 + 0.210040i
\(59\) 4.66336 + 3.06714i 0.607118 + 0.399307i 0.815514 0.578737i \(-0.196454\pi\)
−0.208397 + 0.978044i \(0.566825\pi\)
\(60\) −5.99079 + 4.58455i −0.773407 + 0.591863i
\(61\) 4.11569 + 4.36238i 0.526960 + 0.558545i 0.935104 0.354372i \(-0.115305\pi\)
−0.408144 + 0.912917i \(0.633824\pi\)
\(62\) 6.98049 5.85733i 0.886524 0.743882i
\(63\) −12.2073 + 0.323481i −1.53797 + 0.0407548i
\(64\) 0.766044 + 0.642788i 0.0957556 + 0.0803485i
\(65\) 0.104571 + 1.79541i 0.0129704 + 0.222693i
\(66\) 1.50391 1.84129i 0.185119 0.226647i
\(67\) 2.81104 + 3.77588i 0.343423 + 0.461297i 0.939958 0.341290i \(-0.110864\pi\)
−0.596535 + 0.802587i \(0.703456\pi\)
\(68\) −0.466919 + 0.0545750i −0.0566223 + 0.00661819i
\(69\) −3.72213 + 10.6639i −0.448092 + 1.28378i
\(70\) −14.8121 + 9.74204i −1.77038 + 1.16440i
\(71\) −1.16819 + 0.425188i −0.138639 + 0.0504605i −0.410408 0.911902i \(-0.634614\pi\)
0.271769 + 0.962363i \(0.412391\pi\)
\(72\) 2.54925 + 1.58155i 0.300432 + 0.186388i
\(73\) 4.83702 + 1.76053i 0.566131 + 0.206055i 0.609199 0.793017i \(-0.291491\pi\)
−0.0430682 + 0.999072i \(0.513713\pi\)
\(74\) −1.42456 + 0.337627i −0.165602 + 0.0392483i
\(75\) −5.26750 + 23.6150i −0.608238 + 2.72683i
\(76\) −0.0172694 + 0.296504i −0.00198093 + 0.0340113i
\(77\) 3.83417 4.06399i 0.436945 0.463134i
\(78\) 0.652909 0.291955i 0.0739274 0.0330574i
\(79\) 3.39340 + 7.86678i 0.381787 + 0.885081i 0.995430 + 0.0954977i \(0.0304443\pi\)
−0.613643 + 0.789584i \(0.710296\pi\)
\(80\) 4.35537 0.486945
\(81\) 8.24533 + 3.60758i 0.916147 + 0.400842i
\(82\) −5.00955 −0.553213
\(83\) −3.65159 8.46534i −0.400814 0.929192i −0.992412 0.122958i \(-0.960762\pi\)
0.591598 0.806233i \(-0.298497\pi\)
\(84\) 5.71053 + 4.13490i 0.623070 + 0.451155i
\(85\) −1.40504 + 1.48926i −0.152398 + 0.161533i
\(86\) 0.147679 2.53555i 0.0159246 0.273415i
\(87\) −8.84711 8.12803i −0.948510 0.871417i
\(88\) −1.33560 + 0.316543i −0.142376 + 0.0337436i
\(89\) −10.4279 3.79543i −1.10535 0.402315i −0.276065 0.961139i \(-0.589031\pi\)
−0.829286 + 0.558824i \(0.811253\pi\)
\(90\) 12.9330 1.86013i 1.36326 0.196074i
\(91\) 1.57947 0.574879i 0.165573 0.0602637i
\(92\) 5.44828 3.58339i 0.568022 0.373594i
\(93\) −15.5057 + 2.94636i −1.60786 + 0.305523i
\(94\) 2.06871 0.241797i 0.213371 0.0249395i
\(95\) 0.772467 + 1.03760i 0.0792535 + 0.106456i
\(96\) −0.613903 1.61961i −0.0626563 0.165300i
\(97\) −0.337750 5.79894i −0.0342933 0.588793i −0.971060 0.238838i \(-0.923234\pi\)
0.936766 0.349956i \(-0.113803\pi\)
\(98\) 7.33042 + 6.15096i 0.740485 + 0.621340i
\(99\) −3.83080 + 1.51038i −0.385010 + 0.151799i
\(100\) 10.7010 8.97924i 1.07010 0.897924i
\(101\) −0.717214 0.760202i −0.0713655 0.0756430i 0.690707 0.723135i \(-0.257299\pi\)
−0.762072 + 0.647492i \(0.775818\pi\)
\(102\) 0.751848 + 0.312570i 0.0744441 + 0.0309490i
\(103\) 2.76671 + 1.81969i 0.272612 + 0.179300i 0.678453 0.734644i \(-0.262651\pi\)
−0.405841 + 0.913944i \(0.633021\pi\)
\(104\) −0.401797 0.0952277i −0.0393995 0.00933785i
\(105\) 30.6286 2.19135i 2.98905 0.213853i
\(106\) 3.52704 + 0.412252i 0.342577 + 0.0400415i
\(107\) 2.20473 + 3.81871i 0.213140 + 0.369169i 0.952696 0.303926i \(-0.0982977\pi\)
−0.739556 + 0.673095i \(0.764964\pi\)
\(108\) −2.51467 4.54714i −0.241974 0.437548i
\(109\) −6.61618 + 11.4596i −0.633715 + 1.09763i 0.353071 + 0.935597i \(0.385138\pi\)
−0.986786 + 0.162030i \(0.948196\pi\)
\(110\) −3.56992 + 4.79523i −0.340378 + 0.457208i
\(111\) 2.43865 + 0.695023i 0.231467 + 0.0659687i
\(112\) −1.16744 3.89952i −0.110313 0.368470i
\(113\) −9.76552 + 4.90443i −0.918663 + 0.461370i −0.844306 0.535862i \(-0.819987\pi\)
−0.0743573 + 0.997232i \(0.523691\pi\)
\(114\) 0.276966 0.433507i 0.0259402 0.0406016i
\(115\) 8.14569 27.2085i 0.759589 2.53721i
\(116\) 1.20447 + 6.83091i 0.111833 + 0.634234i
\(117\) −1.23379 0.111170i −0.114063 0.0102777i
\(118\) −0.969235 + 5.49680i −0.0892253 + 0.506022i
\(119\) 1.71001 + 0.858798i 0.156756 + 0.0787259i
\(120\) −6.58244 3.68499i −0.600892 0.336392i
\(121\) −3.61065 + 8.37043i −0.328241 + 0.760948i
\(122\) −2.37546 + 5.50694i −0.215064 + 0.498575i
\(123\) 7.57114 + 4.23849i 0.682667 + 0.382171i
\(124\) 8.14313 + 4.08963i 0.731274 + 0.367260i
\(125\) 6.78343 38.4707i 0.606729 3.44093i
\(126\) −5.13209 11.0808i −0.457203 0.987157i
\(127\) 0.618189 + 3.50592i 0.0548554 + 0.311100i 0.999873 0.0159183i \(-0.00506715\pi\)
−0.945018 + 0.327019i \(0.893956\pi\)
\(128\) −0.286803 + 0.957990i −0.0253501 + 0.0846751i
\(129\) −2.36847 + 3.70712i −0.208532 + 0.326394i
\(130\) −1.60716 + 0.807144i −0.140957 + 0.0707912i
\(131\) 2.37243 + 7.92448i 0.207281 + 0.692365i 0.996894 + 0.0787602i \(0.0250961\pi\)
−0.789613 + 0.613605i \(0.789719\pi\)
\(132\) 2.28637 + 0.651622i 0.199003 + 0.0567164i
\(133\) 0.721948 0.969745i 0.0626009 0.0840875i
\(134\) −2.35368 + 4.07669i −0.203327 + 0.352172i
\(135\) −21.1200 8.13109i −1.81772 0.699813i
\(136\) −0.235049 0.407117i −0.0201553 0.0349100i
\(137\) −18.3333 2.14286i −1.56632 0.183077i −0.711758 0.702425i \(-0.752101\pi\)
−0.854563 + 0.519348i \(0.826175\pi\)
\(138\) −11.2660 + 0.806037i −0.959029 + 0.0686144i
\(139\) 12.4118 + 2.94165i 1.05275 + 0.249507i 0.720336 0.693625i \(-0.243987\pi\)
0.332418 + 0.943132i \(0.392136\pi\)
\(140\) −14.8121 9.74204i −1.25185 0.823353i
\(141\) −3.33110 1.38485i −0.280529 0.116626i
\(142\) −0.853113 0.904247i −0.0715916 0.0758827i
\(143\) 0.434182 0.364322i 0.0363081 0.0304662i
\(144\) −0.442500 + 2.96719i −0.0368750 + 0.247266i
\(145\) 23.1423 + 19.4187i 1.92186 + 1.61263i
\(146\) 0.299298 + 5.13874i 0.0247701 + 0.425286i
\(147\) −5.87456 15.4983i −0.484525 1.27828i
\(148\) −0.874254 1.17433i −0.0718632 0.0965291i
\(149\) −6.17878 + 0.722195i −0.506185 + 0.0591645i −0.365353 0.930869i \(-0.619052\pi\)
−0.140832 + 0.990034i \(0.544978\pi\)
\(150\) −23.7701 + 4.51674i −1.94082 + 0.368790i
\(151\) 15.9160 10.4681i 1.29523 0.851884i 0.300434 0.953803i \(-0.402869\pi\)
0.994793 + 0.101919i \(0.0324982\pi\)
\(152\) −0.279095 + 0.101582i −0.0226376 + 0.00823940i
\(153\) −0.871839 1.10852i −0.0704840 0.0896188i
\(154\) 5.25026 + 1.91094i 0.423078 + 0.153988i
\(155\) 38.6180 9.15263i 3.10187 0.735157i
\(156\) 0.526682 + 0.483874i 0.0421683 + 0.0387409i
\(157\) 0.673757 11.5680i 0.0537717 0.923224i −0.858288 0.513168i \(-0.828472\pi\)
0.912060 0.410057i \(-0.134491\pi\)
\(158\) −5.87935 + 6.23174i −0.467736 + 0.495771i
\(159\) −4.98176 3.60722i −0.395079 0.286071i
\(160\) 1.72507 + 3.99917i 0.136379 + 0.316162i
\(161\) −26.5442 −2.09198
\(162\) −0.0467284 + 8.99988i −0.00367133 + 0.707097i
\(163\) −8.76205 −0.686297 −0.343148 0.939281i \(-0.611493\pi\)
−0.343148 + 0.939281i \(0.611493\pi\)
\(164\) −1.98418 4.59985i −0.154939 0.359188i
\(165\) 9.45251 4.22679i 0.735877 0.329055i
\(166\) 6.32669 6.70590i 0.491046 0.520479i
\(167\) −0.583365 + 10.0160i −0.0451421 + 0.775060i 0.897450 + 0.441115i \(0.145417\pi\)
−0.942593 + 0.333945i \(0.891620\pi\)
\(168\) −1.53491 + 6.88125i −0.118421 + 0.530900i
\(169\) −12.4837 + 2.95868i −0.960282 + 0.227591i
\(170\) −1.92397 0.700268i −0.147562 0.0537081i
\(171\) −0.785371 + 0.420841i −0.0600589 + 0.0321825i
\(172\) 2.38667 0.868678i 0.181982 0.0662360i
\(173\) 10.0925 6.63794i 0.767319 0.504674i −0.104486 0.994526i \(-0.533320\pi\)
0.871805 + 0.489853i \(0.162949\pi\)
\(174\) 3.95913 11.3429i 0.300141 0.859904i
\(175\) −56.4776 + 6.60128i −4.26930 + 0.499010i
\(176\) −0.819660 1.10099i −0.0617842 0.0829906i
\(177\) 6.11558 7.48749i 0.459675 0.562794i
\(178\) −0.645239 11.0783i −0.0483627 0.830356i
\(179\) 10.0604 + 8.44166i 0.751948 + 0.630960i 0.936017 0.351954i \(-0.114483\pi\)
−0.184069 + 0.982913i \(0.558927\pi\)
\(180\) 6.83050 + 11.1385i 0.509116 + 0.830218i
\(181\) −0.397081 + 0.333191i −0.0295148 + 0.0247659i −0.657426 0.753519i \(-0.728355\pi\)
0.627911 + 0.778285i \(0.283910\pi\)
\(182\) 1.15346 + 1.22259i 0.0855000 + 0.0906247i
\(183\) 8.24945 6.31303i 0.609817 0.466673i
\(184\) 5.44828 + 3.58339i 0.401652 + 0.264171i
\(185\) −6.20448 1.47049i −0.456163 0.108112i
\(186\) −8.84688 13.0706i −0.648684 0.958380i
\(187\) 0.640893 + 0.0749097i 0.0468668 + 0.00547794i
\(188\) 1.04139 + 1.80375i 0.0759515 + 0.131552i
\(189\) −1.61893 + 21.0890i −0.117760 + 1.53400i
\(190\) −0.646786 + 1.12027i −0.0469228 + 0.0812726i
\(191\) −14.1730 + 19.0377i −1.02552 + 1.37752i −0.101648 + 0.994820i \(0.532412\pi\)
−0.923874 + 0.382696i \(0.874996\pi\)
\(192\) 1.24399 1.20519i 0.0897775 0.0869770i
\(193\) 0.705059 + 2.35506i 0.0507513 + 0.169521i 0.979608 0.200918i \(-0.0643925\pi\)
−0.928857 + 0.370439i \(0.879207\pi\)
\(194\) 5.19091 2.60697i 0.372685 0.187170i
\(195\) 3.11187 + 0.139914i 0.222845 + 0.0100195i
\(196\) −2.74447 + 9.16718i −0.196034 + 0.654799i
\(197\) 0.961541 + 5.45317i 0.0685070 + 0.388522i 0.999711 + 0.0240249i \(0.00764811\pi\)
−0.931204 + 0.364497i \(0.881241\pi\)
\(198\) −2.90416 2.91927i −0.206389 0.207464i
\(199\) 0.939417 5.32770i 0.0665935 0.377670i −0.933237 0.359261i \(-0.883029\pi\)
0.999831 0.0184092i \(-0.00586016\pi\)
\(200\) 12.4833 + 6.26937i 0.882706 + 0.443312i
\(201\) 7.00641 4.16986i 0.494194 0.294119i
\(202\) 0.413956 0.959658i 0.0291259 0.0675213i
\(203\) 11.1831 25.9252i 0.784897 1.81959i
\(204\) 0.0107853 + 0.814162i 0.000755125 + 0.0570027i
\(205\) −19.4977 9.79210i −1.36178 0.683910i
\(206\) −0.575034 + 3.26118i −0.0400645 + 0.227217i
\(207\) 17.7088 + 8.31378i 1.23085 + 0.577847i
\(208\) −0.0717042 0.406655i −0.00497179 0.0281964i
\(209\) 0.116921 0.390544i 0.00808762 0.0270145i
\(210\) 14.1435 + 27.2557i 0.975994 + 1.88082i
\(211\) −9.52718 + 4.78473i −0.655878 + 0.329394i −0.745426 0.666588i \(-0.767754\pi\)
0.0895483 + 0.995982i \(0.471458\pi\)
\(212\) 1.01845 + 3.40187i 0.0699477 + 0.233642i
\(213\) 0.524278 + 2.08843i 0.0359229 + 0.143097i
\(214\) −2.63315 + 3.53694i −0.179999 + 0.241780i
\(215\) 5.53097 9.57993i 0.377209 0.653346i
\(216\) 3.17925 4.11004i 0.216320 0.279653i
\(217\) −18.5461 32.1228i −1.25899 2.18064i
\(218\) −13.1429 1.53618i −0.890149 0.104043i
\(219\) 3.89545 8.01962i 0.263230 0.541916i
\(220\) −5.81703 1.37866i −0.392184 0.0929494i
\(221\) 0.162182 + 0.106669i 0.0109095 + 0.00717532i
\(222\) 0.327720 + 2.51450i 0.0219951 + 0.168762i
\(223\) −6.68089 7.08133i −0.447386 0.474201i 0.463952 0.885860i \(-0.346431\pi\)
−0.911338 + 0.411659i \(0.864949\pi\)
\(224\) 3.11820 2.61648i 0.208344 0.174821i
\(225\) 39.7462 + 13.2851i 2.64974 + 0.885671i
\(226\) −8.37125 7.02431i −0.556847 0.467250i
\(227\) 0.417303 + 7.16481i 0.0276973 + 0.475545i 0.983428 + 0.181301i \(0.0580308\pi\)
−0.955730 + 0.294244i \(0.904932\pi\)
\(228\) 0.507754 + 0.0826114i 0.0336268 + 0.00547107i
\(229\) 11.0280 + 14.8131i 0.728748 + 0.978879i 0.999867 + 0.0163328i \(0.00519912\pi\)
−0.271118 + 0.962546i \(0.587393\pi\)
\(230\) 28.2096 3.29723i 1.86009 0.217413i
\(231\) −6.31811 7.33021i −0.415701 0.482293i
\(232\) −5.79518 + 3.81155i −0.380473 + 0.250241i
\(233\) 20.2463 7.36906i 1.32638 0.482763i 0.420883 0.907115i \(-0.361720\pi\)
0.905497 + 0.424352i \(0.139498\pi\)
\(234\) −0.386599 1.17691i −0.0252728 0.0769373i
\(235\) 8.52425 + 3.10257i 0.556061 + 0.202389i
\(236\) −5.43115 + 1.28721i −0.353538 + 0.0837899i
\(237\) 14.1582 4.44388i 0.919677 0.288661i
\(238\) −0.111263 + 1.91031i −0.00721209 + 0.123827i
\(239\) 7.63560 8.09326i 0.493906 0.523510i −0.431690 0.902022i \(-0.642083\pi\)
0.925596 + 0.378512i \(0.123564\pi\)
\(240\) 0.776447 7.50365i 0.0501194 0.484359i
\(241\) 10.3566 + 24.0094i 0.667129 + 1.54658i 0.828685 + 0.559715i \(0.189089\pi\)
−0.161556 + 0.986863i \(0.551651\pi\)
\(242\) −9.11597 −0.585997
\(243\) 7.68524 13.5623i 0.493009 0.870024i
\(244\) −5.99744 −0.383947
\(245\) 16.5075 + 38.2688i 1.05463 + 2.44490i
\(246\) −0.893071 + 8.63072i −0.0569401 + 0.550275i
\(247\) 0.0841622 0.0892067i 0.00535511 0.00567609i
\(248\) −0.529838 + 9.09697i −0.0336448 + 0.577658i
\(249\) −15.2355 + 4.78200i −0.965511 + 0.303047i
\(250\) 38.0112 9.00883i 2.40404 0.569768i
\(251\) −15.2966 5.56752i −0.965515 0.351419i −0.189323 0.981915i \(-0.560629\pi\)
−0.776192 + 0.630496i \(0.782851\pi\)
\(252\) 8.14186 9.10125i 0.512889 0.573325i
\(253\) −8.41103 + 3.06136i −0.528797 + 0.192466i
\(254\) −2.97434 + 1.95626i −0.186627 + 0.122746i
\(255\) 2.31529 + 2.68618i 0.144989 + 0.168215i
\(256\) −0.993238 + 0.116093i −0.0620774 + 0.00725581i
\(257\) 11.9707 + 16.0794i 0.746710 + 1.00301i 0.999371 + 0.0354509i \(0.0112867\pi\)
−0.252661 + 0.967555i \(0.581306\pi\)
\(258\) −4.34204 0.706449i −0.270324 0.0439816i
\(259\) 0.346505 + 5.94926i 0.0215308 + 0.369669i
\(260\) −1.37769 1.15602i −0.0854410 0.0716935i
\(261\) −15.5806 + 13.7932i −0.964415 + 0.853781i
\(262\) −6.33671 + 5.31714i −0.391484 + 0.328494i
\(263\) −22.1950 23.5253i −1.36860 1.45063i −0.738971 0.673738i \(-0.764688\pi\)
−0.629630 0.776895i \(-0.716794\pi\)
\(264\) 0.307255 + 2.35747i 0.0189102 + 0.145093i
\(265\) 12.9218 + 8.49878i 0.793778 + 0.522076i
\(266\) 1.17638 + 0.278808i 0.0721288 + 0.0170948i
\(267\) −8.39798 + 17.2890i −0.513948 + 1.05807i
\(268\) −4.67552 0.546490i −0.285603 0.0333822i
\(269\) 6.50632 + 11.2693i 0.396697 + 0.687100i 0.993316 0.115425i \(-0.0368229\pi\)
−0.596619 + 0.802525i \(0.703490\pi\)
\(270\) −0.899107 22.6133i −0.0547179 1.37620i
\(271\) 6.52939 11.3092i 0.396632 0.686987i −0.596676 0.802482i \(-0.703512\pi\)
0.993308 + 0.115495i \(0.0368455\pi\)
\(272\) 0.280723 0.377076i 0.0170213 0.0228636i
\(273\) −0.708854 2.82367i −0.0429018 0.170896i
\(274\) −5.29385 17.6827i −0.319813 1.06825i
\(275\) −17.1346 + 8.60534i −1.03326 + 0.518922i
\(276\) −5.20236 10.0254i −0.313146 0.603458i
\(277\) −6.54671 + 21.8675i −0.393354 + 1.31389i 0.500578 + 0.865691i \(0.333121\pi\)
−0.893932 + 0.448202i \(0.852064\pi\)
\(278\) 2.21499 + 12.5618i 0.132846 + 0.753409i
\(279\) 2.31188 + 27.2392i 0.138409 + 1.63077i
\(280\) 3.07855 17.4593i 0.183978 1.04339i
\(281\) −2.36917 1.18984i −0.141333 0.0709799i 0.376727 0.926324i \(-0.377049\pi\)
−0.518060 + 0.855344i \(0.673346\pi\)
\(282\) −0.0477849 3.60718i −0.00284555 0.214805i
\(283\) 4.81566 11.1640i 0.286262 0.663629i −0.713035 0.701128i \(-0.752680\pi\)
0.999297 + 0.0374995i \(0.0119393\pi\)
\(284\) 0.492393 1.14150i 0.0292182 0.0677353i
\(285\) 1.92535 1.14587i 0.114048 0.0678755i
\(286\) 0.506497 + 0.254373i 0.0299498 + 0.0150414i
\(287\) −3.54095 + 20.0817i −0.209016 + 1.18539i
\(288\) −2.89978 + 0.768932i −0.170871 + 0.0453097i
\(289\) −2.91364 16.5241i −0.171391 0.972006i
\(290\) −8.66435 + 28.9409i −0.508788 + 1.69947i
\(291\) −10.0509 0.451905i −0.589196 0.0264911i
\(292\) −4.59993 + 2.31017i −0.269191 + 0.135193i
\(293\) −7.17957 23.9814i −0.419435 1.40101i −0.863198 0.504866i \(-0.831542\pi\)
0.443763 0.896144i \(-0.353643\pi\)
\(294\) 11.9040 11.5327i 0.694256 0.672600i
\(295\) −14.5169 + 19.4995i −0.845205 + 1.13531i
\(296\) 0.732011 1.26788i 0.0425473 0.0736941i
\(297\) 1.91923 + 6.86916i 0.111365 + 0.398589i
\(298\) −3.11042 5.38740i −0.180182 0.312084i
\(299\) −2.67453 0.312607i −0.154672 0.0180785i
\(300\) −13.5622 20.0371i −0.783013 1.15684i
\(301\) −10.0598 2.38422i −0.579839 0.137424i
\(302\) 15.9160 + 10.4681i 0.915863 + 0.602373i
\(303\) −1.43758 + 1.10013i −0.0825866 + 0.0632008i
\(304\) −0.203818 0.216035i −0.0116898 0.0123904i
\(305\) −20.0099 + 16.7903i −1.14576 + 0.961409i
\(306\) 0.672546 1.23960i 0.0384469 0.0708632i
\(307\) −12.9945 10.9037i −0.741638 0.622308i 0.191639 0.981465i \(-0.438620\pi\)
−0.933277 + 0.359158i \(0.883064\pi\)
\(308\) 0.324867 + 5.57775i 0.0185110 + 0.317822i
\(309\) 3.62829 4.44223i 0.206406 0.252709i
\(310\) 23.6999 + 31.8345i 1.34606 + 1.80808i
\(311\) 21.9206 2.56215i 1.24300 0.145286i 0.530946 0.847406i \(-0.321837\pi\)
0.712059 + 0.702119i \(0.247763\pi\)
\(312\) −0.235693 + 0.675261i −0.0133435 + 0.0382291i
\(313\) 14.3553 9.44161i 0.811408 0.533671i −0.0746699 0.997208i \(-0.523790\pi\)
0.886078 + 0.463537i \(0.153420\pi\)
\(314\) 10.8888 3.96318i 0.614488 0.223655i
\(315\) 1.68491 53.1592i 0.0949337 2.99518i
\(316\) −8.05078 2.93024i −0.452892 0.164839i
\(317\) −7.84023 + 1.85817i −0.440351 + 0.104365i −0.444810 0.895625i \(-0.646729\pi\)
0.00445880 + 0.999990i \(0.498581\pi\)
\(318\) 1.33903 6.00308i 0.0750890 0.336636i
\(319\) 0.553582 9.50464i 0.0309947 0.532158i
\(320\) −2.98883 + 3.16798i −0.167081 + 0.177095i
\(321\) 6.97212 3.11766i 0.389146 0.174011i
\(322\) −10.5136 24.3733i −0.585901 1.35827i
\(323\) 0.139622 0.00776878
\(324\) −8.28234 + 3.52176i −0.460130 + 0.195654i
\(325\) −5.76828 −0.319967
\(326\) −3.47047 8.04546i −0.192212 0.445597i
\(327\) 18.5636 + 13.4416i 1.02657 + 0.743324i
\(328\) 3.43777 3.64382i 0.189819 0.201196i
\(329\) 0.492955 8.46371i 0.0271775 0.466619i
\(330\) 7.62505 + 7.00531i 0.419745 + 0.385629i
\(331\) 9.75325 2.31156i 0.536087 0.127055i 0.0463502 0.998925i \(-0.485241\pi\)
0.489737 + 0.871870i \(0.337093\pi\)
\(332\) 8.66334 + 3.15320i 0.475462 + 0.173054i
\(333\) 1.63217 4.07753i 0.0894424 0.223448i
\(334\) −9.42790 + 3.43147i −0.515872 + 0.187762i
\(335\) −17.1294 + 11.2662i −0.935878 + 0.615537i
\(336\) −6.92642 + 1.31614i −0.377867 + 0.0718016i
\(337\) −20.6739 + 2.41643i −1.12618 + 0.131631i −0.658723 0.752386i \(-0.728903\pi\)
−0.467455 + 0.884017i \(0.654829\pi\)
\(338\) −7.66124 10.2908i −0.416717 0.559747i
\(339\) 6.70867 + 17.6989i 0.364365 + 0.961271i
\(340\) −0.119049 2.04398i −0.00645631 0.110851i
\(341\) −9.58143 8.03977i −0.518863 0.435378i
\(342\) −0.697492 0.554454i −0.0377161 0.0299815i
\(343\) 8.01125 6.72224i 0.432567 0.362967i
\(344\) 1.74295 + 1.84742i 0.0939734 + 0.0996059i
\(345\) −45.4241 18.8844i −2.44555 1.01670i
\(346\) 10.0925 + 6.63794i 0.542576 + 0.356858i
\(347\) 13.8597 + 3.28480i 0.744026 + 0.176337i 0.585109 0.810955i \(-0.301052\pi\)
0.158917 + 0.987292i \(0.449200\pi\)
\(348\) 11.9834 0.857359i 0.642376 0.0459593i
\(349\) 34.8459 + 4.07290i 1.86526 + 0.218018i 0.972563 0.232641i \(-0.0747366\pi\)
0.892697 + 0.450658i \(0.148811\pi\)
\(350\) −28.4310 49.2440i −1.51970 2.63220i
\(351\) −0.411481 + 2.10581i −0.0219633 + 0.112400i
\(352\) 0.686300 1.18871i 0.0365799 0.0633583i
\(353\) 9.32601 12.5270i 0.496374 0.666746i −0.481378 0.876513i \(-0.659863\pi\)
0.977751 + 0.209768i \(0.0672708\pi\)
\(354\) 9.29739 + 2.64978i 0.494151 + 0.140834i
\(355\) −1.55288 5.18698i −0.0824183 0.275296i
\(356\) 9.91673 4.98037i 0.525586 0.263959i
\(357\) 1.78443 2.79299i 0.0944421 0.147821i
\(358\) −3.76656 + 12.5812i −0.199069 + 0.664936i
\(359\) −5.25256 29.7888i −0.277220 1.57219i −0.731822 0.681496i \(-0.761330\pi\)
0.454602 0.890695i \(-0.349781\pi\)
\(360\) −7.52217 + 10.6836i −0.396453 + 0.563077i
\(361\) −3.28400 + 18.6245i −0.172842 + 0.980236i
\(362\) −0.463217 0.232636i −0.0243461 0.0122271i
\(363\) 13.7773 + 7.71284i 0.723122 + 0.404819i
\(364\) −0.665744 + 1.54337i −0.0348945 + 0.0808945i
\(365\) −8.87973 + 20.5855i −0.464786 + 1.07750i
\(366\) 9.06417 + 5.07431i 0.473791 + 0.265239i
\(367\) −12.6294 6.34275i −0.659252 0.331089i 0.0875260 0.996162i \(-0.472104\pi\)
−0.746778 + 0.665073i \(0.768400\pi\)
\(368\) −1.13237 + 6.42200i −0.0590290 + 0.334770i
\(369\) 8.65202 12.2883i 0.450406 0.639705i
\(370\) −1.10724 6.27949i −0.0575628 0.326455i
\(371\) 4.14564 13.8474i 0.215231 0.718922i
\(372\) 8.49754 13.3003i 0.440577 0.689590i
\(373\) 1.85728 0.932761i 0.0961663 0.0482965i −0.400066 0.916486i \(-0.631013\pi\)
0.496232 + 0.868190i \(0.334716\pi\)
\(374\) 0.185062 + 0.618149i 0.00956931 + 0.0319637i
\(375\) −65.0701 18.5452i −3.36021 0.957668i
\(376\) −1.24376 + 1.67065i −0.0641418 + 0.0861574i
\(377\) 1.43209 2.48046i 0.0737566 0.127750i
\(378\) −20.0055 + 6.86641i −1.02897 + 0.353170i
\(379\) 11.2910 + 19.5565i 0.579978 + 1.00455i 0.995481 + 0.0949594i \(0.0302721\pi\)
−0.415503 + 0.909592i \(0.636395\pi\)
\(380\) −1.28482 0.150174i −0.0659101 0.00770379i
\(381\) 6.15039 0.440034i 0.315094 0.0225436i
\(382\) −23.0943 5.47345i −1.18161 0.280046i
\(383\) 22.3115 + 14.6745i 1.14006 + 0.749831i 0.971776 0.235907i \(-0.0758061\pi\)
0.168287 + 0.985738i \(0.446176\pi\)
\(384\) 1.59934 + 0.664904i 0.0816162 + 0.0339307i
\(385\) 16.6992 + 17.7001i 0.851071 + 0.902083i
\(386\) −1.88320 + 1.58019i −0.0958521 + 0.0804295i
\(387\) 5.96459 + 4.74140i 0.303197 + 0.241019i
\(388\) 4.44978 + 3.73381i 0.225903 + 0.189555i
\(389\) 0.607370 + 10.4281i 0.0307949 + 0.528728i 0.978066 + 0.208295i \(0.0667914\pi\)
−0.947271 + 0.320433i \(0.896172\pi\)
\(390\) 1.10408 + 2.91278i 0.0559071 + 0.147495i
\(391\) −1.83061 2.45894i −0.0925782 0.124354i
\(392\) −9.50448 + 1.11091i −0.480049 + 0.0561097i
\(393\) 14.0757 2.67463i 0.710023 0.134917i
\(394\) −4.62634 + 3.04279i −0.233072 + 0.153294i
\(395\) −35.0641 + 12.7623i −1.76427 + 0.642140i
\(396\) 1.53025 3.82291i 0.0768978 0.192108i
\(397\) −31.9768 11.6386i −1.60487 0.584124i −0.624453 0.781063i \(-0.714678\pi\)
−0.980416 + 0.196938i \(0.936900\pi\)
\(398\) 5.26406 1.24761i 0.263863 0.0625368i
\(399\) −1.54202 1.41669i −0.0771977 0.0709232i
\(400\) −0.812238 + 13.9456i −0.0406119 + 0.697279i
\(401\) 16.6682 17.6673i 0.832370 0.882261i −0.162154 0.986765i \(-0.551844\pi\)
0.994524 + 0.104504i \(0.0333256\pi\)
\(402\) 6.60393 + 4.78180i 0.329374 + 0.238495i
\(403\) −1.49035 3.45503i −0.0742398 0.172107i
\(404\) 1.04513 0.0519973
\(405\) −17.7738 + 34.9371i −0.883187 + 1.73604i
\(406\) 28.2343 1.40125
\(407\) 0.795929 + 1.84517i 0.0394528 + 0.0914618i
\(408\) −0.743305 + 0.332376i −0.0367991 + 0.0164551i
\(409\) −17.7750 + 18.8404i −0.878917 + 0.931598i −0.998121 0.0612717i \(-0.980484\pi\)
0.119204 + 0.992870i \(0.461966\pi\)
\(410\) 1.26863 21.7815i 0.0626532 1.07571i
\(411\) −6.96017 + 31.2036i −0.343320 + 1.53916i
\(412\) −3.22223 + 0.763682i −0.158748 + 0.0376239i
\(413\) 21.3499 + 7.77071i 1.05056 + 0.382372i
\(414\) −0.619754 + 19.5534i −0.0304593 + 0.960997i
\(415\) 37.7320 13.7333i 1.85219 0.674143i
\(416\) 0.344996 0.226908i 0.0169148 0.0111251i
\(417\) 7.28072 20.8593i 0.356538 1.02148i
\(418\) 0.404914 0.0473277i 0.0198050 0.00231487i
\(419\) −9.26854 12.4498i −0.452798 0.608213i 0.515841 0.856684i \(-0.327479\pi\)
−0.968639 + 0.248471i \(0.920072\pi\)
\(420\) −19.4247 + 23.7822i −0.947828 + 1.16045i
\(421\) 1.84735 + 31.7178i 0.0900345 + 1.54583i 0.676856 + 0.736116i \(0.263342\pi\)
−0.586821 + 0.809716i \(0.699621\pi\)
\(422\) −8.16694 6.85287i −0.397560 0.333593i
\(423\) −2.97975 + 5.49211i −0.144880 + 0.267035i
\(424\) −2.72027 + 2.28257i −0.132108 + 0.110852i
\(425\) −4.50648 4.77659i −0.218596 0.231699i
\(426\) −1.70997 + 1.30858i −0.0828483 + 0.0634011i
\(427\) 20.3965 + 13.4150i 0.987058 + 0.649198i
\(428\) −4.29061 1.01689i −0.207395 0.0491534i
\(429\) −0.550270 0.812981i −0.0265673 0.0392511i
\(430\) 10.9872 + 1.28421i 0.529847 + 0.0619303i
\(431\) −7.53078 13.0437i −0.362745 0.628293i 0.625667 0.780091i \(-0.284827\pi\)
−0.988412 + 0.151798i \(0.951494\pi\)
\(432\) 5.03314 + 1.29133i 0.242157 + 0.0621293i
\(433\) 11.3852 19.7198i 0.547138 0.947672i −0.451331 0.892357i \(-0.649050\pi\)
0.998469 0.0553147i \(-0.0176162\pi\)
\(434\) 22.1499 29.7525i 1.06323 1.42817i
\(435\) 37.5811 36.4089i 1.80188 1.74567i
\(436\) −3.79508 12.6765i −0.181752 0.607092i
\(437\) −1.73079 + 0.869234i −0.0827948 + 0.0415811i
\(438\) 8.90665 + 0.400457i 0.425576 + 0.0191346i
\(439\) 9.77250 32.6424i 0.466416 1.55794i −0.324422 0.945913i \(-0.605170\pi\)
0.790838 0.612026i \(-0.209645\pi\)
\(440\) −1.03810 5.88735i −0.0494894 0.280669i
\(441\) −27.7486 + 7.35805i −1.32136 + 0.350383i
\(442\) −0.0337080 + 0.191167i −0.00160332 + 0.00909291i
\(443\) 3.85187 + 1.93448i 0.183008 + 0.0919101i 0.537944 0.842980i \(-0.319201\pi\)
−0.354936 + 0.934891i \(0.615497\pi\)
\(444\) −2.17905 + 1.29686i −0.103413 + 0.0615462i
\(445\) 19.1433 44.3792i 0.907480 2.10377i
\(446\) 3.85603 8.93927i 0.182588 0.423287i
\(447\) 0.142723 + 10.7739i 0.00675057 + 0.509586i
\(448\) 3.63756 + 1.82685i 0.171858 + 0.0863105i
\(449\) −1.78444 + 10.1201i −0.0842131 + 0.477596i 0.913310 + 0.407264i \(0.133517\pi\)
−0.997524 + 0.0703324i \(0.977594\pi\)
\(450\) 3.54410 + 41.7575i 0.167070 + 1.96847i
\(451\) 1.19402 + 6.77165i 0.0562244 + 0.318865i
\(452\) 3.13415 10.4688i 0.147418 0.492411i
\(453\) −15.1976 29.2871i −0.714047 1.37603i
\(454\) −6.41356 + 3.22101i −0.301003 + 0.151169i
\(455\) 2.09959 + 7.01310i 0.0984301 + 0.328779i
\(456\) 0.125256 + 0.498948i 0.00586564 + 0.0233654i
\(457\) 0.725223 0.974143i 0.0339245 0.0455685i −0.784837 0.619702i \(-0.787254\pi\)
0.818762 + 0.574133i \(0.194661\pi\)
\(458\) −9.23370 + 15.9932i −0.431462 + 0.747315i
\(459\) −2.06525 + 1.30443i −0.0963975 + 0.0608855i
\(460\) 14.2008 + 24.5966i 0.662117 + 1.14682i
\(461\) 37.2341 + 4.35204i 1.73416 + 0.202695i 0.923706 0.383102i \(-0.125144\pi\)
0.810458 + 0.585796i \(0.199218\pi\)
\(462\) 4.22824 8.70474i 0.196716 0.404981i
\(463\) 3.82971 + 0.907657i 0.177982 + 0.0421824i 0.318640 0.947876i \(-0.396774\pi\)
−0.140659 + 0.990058i \(0.544922\pi\)
\(464\) −5.79518 3.81155i −0.269035 0.176947i
\(465\) −8.88406 68.1648i −0.411989 3.16107i
\(466\) 14.7855 + 15.6718i 0.684927 + 0.725981i
\(467\) −13.9066 + 11.6690i −0.643521 + 0.539978i −0.905097 0.425204i \(-0.860202\pi\)
0.261576 + 0.965183i \(0.415758\pi\)
\(468\) 0.927537 0.821133i 0.0428754 0.0379569i
\(469\) 14.6785 + 12.3167i 0.677790 + 0.568733i
\(470\) 0.527450 + 9.05597i 0.0243295 + 0.417721i
\(471\) −19.8098 3.22305i −0.912786 0.148510i
\(472\) −3.33310 4.47713i −0.153418 0.206077i
\(473\) −3.46262 + 0.404722i −0.159211 + 0.0186091i
\(474\) 9.68824 + 11.2402i 0.444995 + 0.516279i
\(475\) −3.46639 + 2.27988i −0.159049 + 0.104608i
\(476\) −1.79814 + 0.654471i −0.0824178 + 0.0299976i
\(477\) −7.10281 + 7.93977i −0.325216 + 0.363537i
\(478\) 10.4557 + 3.80555i 0.478231 + 0.174062i
\(479\) −9.66806 + 2.29137i −0.441745 + 0.104696i −0.445469 0.895298i \(-0.646963\pi\)
0.00372352 + 0.999993i \(0.498815\pi\)
\(480\) 7.19751 2.25910i 0.328520 0.103113i
\(481\) −0.0351506 + 0.603513i −0.00160273 + 0.0275178i
\(482\) −17.9437 + 19.0192i −0.817314 + 0.866303i
\(483\) −4.73213 + 45.7317i −0.215319 + 2.08087i
\(484\) −3.61065 8.37043i −0.164120 0.380474i
\(485\) 25.2993 1.14878
\(486\) 15.4971 + 1.68495i 0.702964 + 0.0764307i
\(487\) −14.1362 −0.640573 −0.320287 0.947321i \(-0.603779\pi\)
−0.320287 + 0.947321i \(0.603779\pi\)
\(488\) −2.37546 5.50694i −0.107532 0.249288i
\(489\) −1.56204 + 15.0957i −0.0706380 + 0.682652i
\(490\) −28.6007 + 30.3150i −1.29205 + 1.36949i
\(491\) −1.23323 + 21.1738i −0.0556550 + 0.955560i 0.848726 + 0.528833i \(0.177370\pi\)
−0.904381 + 0.426726i \(0.859667\pi\)
\(492\) −8.27859 + 2.59842i −0.373228 + 0.117146i
\(493\) 3.17284 0.751977i 0.142898 0.0338673i
\(494\) 0.115246 + 0.0419461i 0.00518516 + 0.00188724i
\(495\) −5.59700 17.0388i −0.251566 0.765837i
\(496\) −8.56284 + 3.11662i −0.384483 + 0.139940i
\(497\) −4.22785 + 2.78070i −0.189645 + 0.124732i
\(498\) −10.4254 12.0954i −0.467173 0.542009i
\(499\) 37.8455 4.42351i 1.69420 0.198023i 0.786483 0.617612i \(-0.211900\pi\)
0.907715 + 0.419588i \(0.137825\pi\)
\(500\) 23.3275 + 31.3343i 1.04324 + 1.40131i
\(501\) 17.1521 + 2.79064i 0.766298 + 0.124676i
\(502\) −0.946501 16.2508i −0.0422444 0.725309i
\(503\) −19.7261 16.5522i −0.879545 0.738026i 0.0865408 0.996248i \(-0.472419\pi\)
−0.966085 + 0.258223i \(0.916863\pi\)
\(504\) 11.5817 + 3.87117i 0.515892 + 0.172436i
\(505\) 3.48699 2.92593i 0.155169 0.130202i
\(506\) −6.14243 6.51060i −0.273064 0.289431i
\(507\) 2.87187 + 22.0350i 0.127544 + 0.978607i
\(508\) −2.97434 1.95626i −0.131965 0.0867948i
\(509\) 17.8731 + 4.23601i 0.792212 + 0.187758i 0.606749 0.794894i \(-0.292473\pi\)
0.185463 + 0.982651i \(0.440622\pi\)
\(510\) −1.54945 + 3.18988i −0.0686109 + 0.141250i
\(511\) 20.8112 + 2.43248i 0.920632 + 0.107606i
\(512\) −0.500000 0.866025i −0.0220971 0.0382733i
\(513\) 0.585035 + 1.42810i 0.0258299 + 0.0630523i
\(514\) −10.0230 + 17.3604i −0.442097 + 0.765734i
\(515\) −8.61267 + 11.5688i −0.379520 + 0.509783i
\(516\) −1.07112 4.26674i −0.0471535 0.187833i
\(517\) −0.819924 2.73874i −0.0360602 0.120449i
\(518\) −5.32546 + 2.67455i −0.233987 + 0.117513i
\(519\) −9.63697 18.5713i −0.423016 0.815188i
\(520\) 0.515802 1.72290i 0.0226194 0.0755541i
\(521\) −3.28343 18.6212i −0.143850 0.815811i −0.968284 0.249853i \(-0.919618\pi\)
0.824434 0.565958i \(-0.191494\pi\)
\(522\) −18.8363 8.84314i −0.824444 0.387054i
\(523\) −6.18344 + 35.0680i −0.270383 + 1.53342i 0.482872 + 0.875691i \(0.339593\pi\)
−0.753256 + 0.657728i \(0.771518\pi\)
\(524\) −7.39212 3.71246i −0.322926 0.162180i
\(525\) 1.30457 + 98.4793i 0.0569362 + 4.29799i
\(526\) 12.8103 29.6977i 0.558557 1.29488i
\(527\) 1.69669 3.93337i 0.0739091 0.171340i
\(528\) −2.04297 + 1.21587i −0.0889090 + 0.0529141i
\(529\) 17.4476 + 8.76254i 0.758593 + 0.380980i
\(530\) −2.68567 + 15.2312i −0.116658 + 0.661600i
\(531\) −11.8096 11.8711i −0.512492 0.515160i
\(532\) 0.209936 + 1.19061i 0.00910187 + 0.0516193i
\(533\) −0.593277 + 1.98168i −0.0256977 + 0.0858362i
\(534\) −19.2013 0.863321i −0.830923 0.0373596i
\(535\) −17.1621 + 8.61912i −0.741982 + 0.372637i
\(536\) −1.35008 4.50960i −0.0583148 0.194785i
\(537\) 16.3372 15.8276i 0.705004 0.683012i
\(538\) −7.77061 + 10.4377i −0.335015 + 0.450003i
\(539\) 6.56733 11.3750i 0.282875 0.489954i
\(540\) 20.4078 9.78224i 0.878210 0.420960i
\(541\) −17.9602 31.1080i −0.772169 1.33744i −0.936372 0.351010i \(-0.885838\pi\)
0.164203 0.986427i \(-0.447495\pi\)
\(542\) 12.9705 + 1.51603i 0.557130 + 0.0651192i
\(543\) 0.503249 + 0.743511i 0.0215965 + 0.0319071i
\(544\) 0.457426 + 0.108412i 0.0196120 + 0.00464813i
\(545\) −48.1506 31.6692i −2.06255 1.35656i
\(546\) 2.31198 1.76928i 0.0989436 0.0757182i
\(547\) −17.9951 19.0737i −0.769415 0.815532i 0.217621 0.976033i \(-0.430170\pi\)
−0.987036 + 0.160501i \(0.948689\pi\)
\(548\) 14.1397 11.8646i 0.604020 0.506833i
\(549\) −9.40576 15.3380i −0.401428 0.654611i
\(550\) −14.6882 12.3249i −0.626309 0.525536i
\(551\) −0.119785 2.05664i −0.00510303 0.0876157i
\(552\) 7.14493 8.74775i 0.304108 0.372329i
\(553\) 20.8253 + 27.9733i 0.885584 + 1.18955i
\(554\) −22.6722 + 2.65000i −0.963248 + 0.112588i
\(555\) −3.63953 + 10.4273i −0.154489 + 0.442612i
\(556\) −10.6572 + 7.00933i −0.451964 + 0.297262i
\(557\) 18.3756 6.68818i 0.778600 0.283387i 0.0780115 0.996952i \(-0.475143\pi\)
0.700589 + 0.713565i \(0.252921\pi\)
\(558\) −24.0958 + 12.9117i −1.02006 + 0.546597i
\(559\) −0.985523 0.358701i −0.0416832 0.0151714i
\(560\) 17.2508 4.08850i 0.728978 0.172771i
\(561\) 0.243313 1.09081i 0.0102727 0.0460540i
\(562\) 0.154152 2.64668i 0.00650249 0.111643i
\(563\) 13.6682 14.4875i 0.576047 0.610574i −0.372183 0.928159i \(-0.621391\pi\)
0.948230 + 0.317585i \(0.102872\pi\)
\(564\) 3.29325 1.47261i 0.138671 0.0620080i
\(565\) −18.8514 43.7025i −0.793085 1.83858i
\(566\) 12.1583 0.511052
\(567\) 36.0447 + 6.54879i 1.51373 + 0.275023i
\(568\) 1.24317 0.0521621
\(569\) −0.603019 1.39796i −0.0252799 0.0586054i 0.905108 0.425181i \(-0.139789\pi\)
−0.930388 + 0.366575i \(0.880530\pi\)
\(570\) 1.81475 + 1.31403i 0.0760114 + 0.0550387i
\(571\) 1.02010 1.08124i 0.0426897 0.0452484i −0.705677 0.708534i \(-0.749357\pi\)
0.748367 + 0.663285i \(0.230838\pi\)
\(572\) −0.0329556 + 0.565826i −0.00137794 + 0.0236584i
\(573\) 30.2724 + 27.8119i 1.26465 + 1.16186i
\(574\) −19.8419 + 4.70261i −0.828184 + 0.196283i
\(575\) 85.6006 + 31.1561i 3.56979 + 1.29930i
\(576\) −1.85459 2.35807i −0.0772746 0.0982529i
\(577\) −31.2779 + 11.3842i −1.30211 + 0.473931i −0.897685 0.440638i \(-0.854752\pi\)
−0.404430 + 0.914569i \(0.632530\pi\)
\(578\) 14.0187 9.22022i 0.583099 0.383510i
\(579\) 4.18311 0.794867i 0.173844 0.0330335i
\(580\) −30.0058 + 3.50718i −1.24592 + 0.145628i
\(581\) −22.4099 30.1017i −0.929719 1.24883i
\(582\) −3.56602 9.40792i −0.147816 0.389971i
\(583\) −0.283408 4.86593i −0.0117376 0.201526i
\(584\) −3.94318 3.30872i −0.163170 0.136916i
\(585\) 0.795815 5.33634i 0.0329029 0.220631i
\(586\) 19.1765 16.0910i 0.792172 0.664711i
\(587\) −6.04447 6.40676i −0.249482 0.264435i 0.590515 0.807027i \(-0.298925\pi\)
−0.839997 + 0.542591i \(0.817443\pi\)
\(588\) 15.3044 + 6.36259i 0.631144 + 0.262389i
\(589\) −2.26120 1.48721i −0.0931709 0.0612795i
\(590\) −23.6546 5.60625i −0.973846 0.230806i
\(591\) 9.56642 0.684437i 0.393510 0.0281540i
\(592\) 1.45412 + 0.169963i 0.0597641 + 0.00698542i
\(593\) 3.72036 + 6.44385i 0.152777 + 0.264617i 0.932247 0.361822i \(-0.117845\pi\)
−0.779470 + 0.626439i \(0.784512\pi\)
\(594\) −5.54721 + 4.48300i −0.227605 + 0.183940i
\(595\) −4.16710 + 7.21762i −0.170834 + 0.295894i
\(596\) 3.71483 4.98988i 0.152165 0.204393i
\(597\) −9.01136 2.56826i −0.368810 0.105112i
\(598\) −0.772285 2.57961i −0.0315811 0.105488i
\(599\) 21.6157 10.8558i 0.883192 0.443556i 0.0514226 0.998677i \(-0.483624\pi\)
0.831769 + 0.555121i \(0.187328\pi\)
\(600\) 13.0267 20.3893i 0.531811 0.832389i
\(601\) −8.96408 + 29.9421i −0.365652 + 1.22136i 0.555287 + 0.831659i \(0.312608\pi\)
−0.920940 + 0.389705i \(0.872577\pi\)
\(602\) −1.79526 10.1814i −0.0731694 0.414964i
\(603\) −5.93499 12.8144i −0.241692 0.521842i
\(604\) −3.30799 + 18.7605i −0.134600 + 0.763356i
\(605\) −35.4802 17.8188i −1.44248 0.724439i
\(606\) −1.57955 0.884267i −0.0641649 0.0359209i
\(607\) 11.5142 26.6928i 0.467345 1.08343i −0.507723 0.861521i \(-0.669512\pi\)
0.975068 0.221907i \(-0.0712283\pi\)
\(608\) 0.117638 0.272716i 0.00477086 0.0110601i
\(609\) −42.6717 23.8885i −1.72914 0.968012i
\(610\) −23.3426 11.7231i −0.945115 0.474654i
\(611\) 0.149345 0.846976i 0.00604184 0.0342650i
\(612\) 1.40460 + 0.126562i 0.0567777 + 0.00511596i
\(613\) −6.78846 38.4993i −0.274183 1.55497i −0.741544 0.670904i \(-0.765906\pi\)
0.467361 0.884067i \(-0.345205\pi\)
\(614\) 4.86509 16.2505i 0.196339 0.655818i
\(615\) −20.3463 + 31.8459i −0.820440 + 1.28415i
\(616\) −4.99291 + 2.50753i −0.201170 + 0.101031i
\(617\) 3.50668 + 11.7131i 0.141173 + 0.471552i 0.999109 0.0422053i \(-0.0134383\pi\)
−0.857936 + 0.513757i \(0.828253\pi\)
\(618\) 5.51602 + 1.57208i 0.221887 + 0.0632384i
\(619\) −0.521047 + 0.699887i −0.0209426 + 0.0281308i −0.812471 0.583001i \(-0.801878\pi\)
0.791529 + 0.611132i \(0.209286\pi\)
\(620\) −19.8439 + 34.3706i −0.796950 + 1.38036i
\(621\) 17.4804 29.0275i 0.701465 1.16483i
\(622\) 11.0349 + 19.1131i 0.442460 + 0.766364i
\(623\) −44.8656 5.24404i −1.79750 0.210098i
\(624\) −0.713388 + 0.0510399i −0.0285584 + 0.00204323i
\(625\) 97.5895 + 23.1291i 3.90358 + 0.925166i
\(626\) 14.3553 + 9.44161i 0.573752 + 0.377363i
\(627\) −0.652006 0.271062i −0.0260386 0.0108252i
\(628\) 7.95187 + 8.42849i 0.317314 + 0.336334i
\(629\) −0.527218 + 0.442388i −0.0210215 + 0.0176392i
\(630\) 49.4790 19.5082i 1.97129 0.777224i
\(631\) 1.85524 + 1.55673i 0.0738560 + 0.0619725i 0.678968 0.734168i \(-0.262427\pi\)
−0.605112 + 0.796140i \(0.706872\pi\)
\(632\) −0.498153 8.55296i −0.0198155 0.340219i
\(633\) 6.54493 + 17.2669i 0.260138 + 0.686298i
\(634\) −4.81156 6.46305i −0.191091 0.256680i
\(635\) −15.4003 + 1.80004i −0.611142 + 0.0714323i
\(636\) 6.04249 1.14818i 0.239600 0.0455283i
\(637\) 3.30133 2.17132i 0.130804 0.0860309i
\(638\) 8.94658 3.25629i 0.354198 0.128918i
\(639\) 3.69151 0.530942i 0.146034 0.0210037i
\(640\) −4.09271 1.48962i −0.161778 0.0588825i
\(641\) 8.99703 2.13234i 0.355361 0.0842222i −0.0490577 0.998796i \(-0.515622\pi\)
0.404419 + 0.914574i \(0.367474\pi\)
\(642\) 5.62420 + 5.16707i 0.221969 + 0.203928i
\(643\) −1.98692 + 34.1141i −0.0783565 + 1.34533i 0.698481 + 0.715629i \(0.253860\pi\)
−0.776837 + 0.629701i \(0.783177\pi\)
\(644\) 18.2157 19.3076i 0.717801 0.760824i
\(645\) −15.5188 11.2369i −0.611051 0.442452i
\(646\) 0.0553015 + 0.128203i 0.00217581 + 0.00504409i
\(647\) 10.2649 0.403555 0.201777 0.979431i \(-0.435328\pi\)
0.201777 + 0.979431i \(0.435328\pi\)
\(648\) −6.51421 6.21008i −0.255902 0.243955i
\(649\) 7.66130 0.300732
\(650\) −2.28470 5.29653i −0.0896132 0.207747i
\(651\) −58.6491 + 26.2256i −2.29864 + 1.02786i
\(652\) 6.01288 6.37329i 0.235483 0.249597i
\(653\) −0.630450 + 10.8244i −0.0246714 + 0.423592i 0.963247 + 0.268617i \(0.0865666\pi\)
−0.987918 + 0.154975i \(0.950470\pi\)
\(654\) −4.98965 + 22.3694i −0.195111 + 0.874712i
\(655\) −35.0564 + 8.30853i −1.36977 + 0.324641i
\(656\) 4.70744 + 1.71337i 0.183795 + 0.0668958i
\(657\) −13.1222 8.14097i −0.511944 0.317609i
\(658\) 7.96676 2.89966i 0.310577 0.113041i
\(659\) −17.8744 + 11.7562i −0.696287 + 0.457955i −0.847673 0.530520i \(-0.821997\pi\)
0.151386 + 0.988475i \(0.451626\pi\)
\(660\) −3.41225 + 9.77611i −0.132822 + 0.380534i
\(661\) −30.8790 + 3.60924i −1.20105 + 0.140383i −0.692997 0.720940i \(-0.743710\pi\)
−0.508057 + 0.861324i \(0.669636\pi\)
\(662\) 5.98558 + 8.04003i 0.232636 + 0.312485i
\(663\) 0.212687 0.260399i 0.00826009 0.0101131i
\(664\) 0.536056 + 9.20373i 0.0208030 + 0.357174i
\(665\) 4.03362 + 3.38461i 0.156417 + 0.131250i
\(666\) 4.39053 0.116345i 0.170129 0.00450826i
\(667\) −34.6498 + 29.0746i −1.34164 + 1.12577i
\(668\) −6.88504 7.29771i −0.266390 0.282357i
\(669\) −13.3911 + 10.2478i −0.517730 + 0.396202i
\(670\) −17.1294 11.2662i −0.661766 0.435250i
\(671\) 8.01019 + 1.89845i 0.309230 + 0.0732888i
\(672\) −3.95192 5.83865i −0.152449 0.225231i
\(673\) −46.5296 5.43853i −1.79358 0.209640i −0.846889 0.531770i \(-0.821527\pi\)
−0.946695 + 0.322130i \(0.895601\pi\)
\(674\) −10.4073 18.0260i −0.400875 0.694335i
\(675\) 29.9739 66.1084i 1.15370 2.54451i
\(676\) 6.41475 11.1107i 0.246721 0.427333i
\(677\) 1.76303 2.36817i 0.0677589 0.0910160i −0.766952 0.641705i \(-0.778227\pi\)
0.834711 + 0.550689i \(0.185635\pi\)
\(678\) −13.5942 + 13.1702i −0.522083 + 0.505798i
\(679\) −6.78139 22.6514i −0.260246 0.869282i
\(680\) 1.82967 0.918893i 0.0701645 0.0352379i
\(681\) 12.4183 + 0.558345i 0.475870 + 0.0213958i
\(682\) 3.58724 11.9822i 0.137362 0.458823i
\(683\) −0.0468507 0.265704i −0.00179269 0.0101669i 0.983898 0.178729i \(-0.0571986\pi\)
−0.985691 + 0.168562i \(0.946088\pi\)
\(684\) 0.232846 0.860057i 0.00890310 0.0328851i
\(685\) 13.9599 79.1705i 0.533380 3.02495i
\(686\) 9.34556 + 4.69352i 0.356815 + 0.179199i
\(687\) 27.4868 16.3588i 1.04869 0.624126i
\(688\) −1.00598 + 2.33213i −0.0383526 + 0.0889114i
\(689\) 0.580783 1.34641i 0.0221261 0.0512940i
\(690\) −0.651612 49.1888i −0.0248065 1.87259i
\(691\) 8.18392 + 4.11012i 0.311331 + 0.156356i 0.597603 0.801792i \(-0.296120\pi\)
−0.286272 + 0.958148i \(0.592416\pi\)
\(692\) −2.09763 + 11.8963i −0.0797399 + 0.452228i
\(693\) −13.7552 + 9.57839i −0.522518 + 0.363853i
\(694\) 2.47337 + 14.0272i 0.0938880 + 0.532465i
\(695\) −15.9335 + 53.2215i −0.604391 + 2.01881i
\(696\) 5.53361 + 10.6637i 0.209751 + 0.404208i
\(697\) −2.10449 + 1.05691i −0.0797131 + 0.0400334i
\(698\) 10.0620 + 33.6093i 0.380851 + 1.27213i
\(699\) −9.08641 36.1951i −0.343680 1.36903i
\(700\) 33.9557 45.6104i 1.28340 1.72391i
\(701\) −14.3073 + 24.7809i −0.540379 + 0.935964i 0.458503 + 0.888693i \(0.348386\pi\)
−0.998882 + 0.0472708i \(0.984948\pi\)
\(702\) −2.09657 + 0.456240i −0.0791299 + 0.0172197i
\(703\) 0.217412 + 0.376569i 0.00819985 + 0.0142026i
\(704\) 1.36332 + 0.159349i 0.0513820 + 0.00600570i
\(705\) 6.86492 14.1329i 0.258548 0.532276i
\(706\) 15.1963 + 3.60160i 0.571922 + 0.135548i
\(707\) −3.55437 2.33774i −0.133676 0.0879199i
\(708\) 1.24943 + 9.58654i 0.0469566 + 0.360284i
\(709\) −29.7909 31.5765i −1.11882 1.18588i −0.980711 0.195462i \(-0.937379\pi\)
−0.138108 0.990417i \(-0.544102\pi\)
\(710\) 4.14771 3.48034i 0.155661 0.130615i
\(711\) −5.13211 25.1848i −0.192469 0.944503i
\(712\) 8.50087 + 7.13308i 0.318584 + 0.267323i
\(713\) 3.45511 + 59.3220i 0.129395 + 2.22163i
\(714\) 3.27134 + 0.532247i 0.122427 + 0.0199188i
\(715\) 1.47412 + 1.98009i 0.0551289 + 0.0740510i
\(716\) −13.0441 + 1.52464i −0.487481 + 0.0569783i
\(717\) −12.5823 14.5978i −0.469893 0.545166i
\(718\) 25.2721 16.6217i 0.943146 0.620317i
\(719\) 13.3534 4.86023i 0.497997 0.181256i −0.0807961 0.996731i \(-0.525746\pi\)
0.578793 + 0.815475i \(0.303524\pi\)
\(720\) −12.7893 2.67541i −0.476628 0.0997065i
\(721\) 12.6666 + 4.61026i 0.471729 + 0.171695i
\(722\) −18.4020 + 4.36136i −0.684852 + 0.162313i
\(723\) 43.2109 13.5627i 1.60703 0.504402i
\(724\) 0.0301395 0.517476i 0.00112013 0.0192318i
\(725\) −66.4931 + 70.4785i −2.46949 + 2.61751i
\(726\) −1.62514 + 15.7055i −0.0603145 + 0.582884i
\(727\) 17.7226 + 41.0856i 0.657294 + 1.52378i 0.841136 + 0.540824i \(0.181887\pi\)
−0.183842 + 0.982956i \(0.558853\pi\)
\(728\) −1.68083 −0.0622958
\(729\) −21.9958 15.6583i −0.814660 0.579939i
\(730\) −22.4190 −0.829766
\(731\) −0.472909 1.09633i −0.0174912 0.0405491i
\(732\) −1.06918 + 10.3327i −0.0395182 + 0.381907i
\(733\) −15.6207 + 16.5569i −0.576962 + 0.611544i −0.948463 0.316889i \(-0.897362\pi\)
0.371501 + 0.928433i \(0.378843\pi\)
\(734\) 0.821744 14.1088i 0.0303311 0.520765i
\(735\) 68.8743 21.6177i 2.54047 0.797382i
\(736\) −6.34530 + 1.50386i −0.233891 + 0.0554331i
\(737\) 6.07165 + 2.20990i 0.223652 + 0.0814027i
\(738\) 14.7102 + 3.07726i 0.541491 + 0.113275i
\(739\) 36.4063 13.2508i 1.33923 0.487439i 0.429658 0.902992i \(-0.358634\pi\)
0.909569 + 0.415553i \(0.136412\pi\)
\(740\) 5.32737 3.50387i 0.195838 0.128805i
\(741\) −0.138686 0.160902i −0.00509476 0.00591089i
\(742\) 14.3569 1.67808i 0.527059 0.0616044i
\(743\) −16.2315 21.8027i −0.595477 0.799865i 0.397571 0.917571i \(-0.369853\pi\)
−0.993048 + 0.117707i \(0.962446\pi\)
\(744\) 15.5783 + 2.53458i 0.571127 + 0.0929223i
\(745\) −1.57538 27.0482i −0.0577174 0.990969i
\(746\) 1.59211 + 1.33594i 0.0582912 + 0.0489121i
\(747\) 5.52260 + 27.1010i 0.202061 + 0.991575i
\(748\) −0.494295 + 0.414763i −0.0180732 + 0.0151652i
\(749\) 12.3173 + 13.0555i 0.450063 + 0.477039i
\(750\) −8.74448 67.0938i −0.319303 2.44992i
\(751\) −29.9114 19.6731i −1.09148 0.717880i −0.129662 0.991558i \(-0.541389\pi\)
−0.961821 + 0.273678i \(0.911760\pi\)
\(752\) −2.02665 0.480324i −0.0739043 0.0175156i
\(753\) −12.3190 + 25.3613i −0.448929 + 0.924217i
\(754\) 2.84482 + 0.332512i 0.103602 + 0.0121094i
\(755\) 41.4848 + 71.8537i 1.50979 + 2.61503i
\(756\) −14.2286 15.6497i −0.517490 0.569175i
\(757\) 0.960884 1.66430i 0.0349239 0.0604900i −0.848035 0.529940i \(-0.822214\pi\)
0.882959 + 0.469450i \(0.155548\pi\)
\(758\) −13.4850 + 18.1135i −0.489797 + 0.657911i
\(759\) 3.77481 + 15.0367i 0.137017 + 0.545798i
\(760\) −0.371000 1.23923i −0.0134576 0.0449515i
\(761\) −23.9331 + 12.0197i −0.867575 + 0.435713i −0.826164 0.563430i \(-0.809482\pi\)
−0.0414109 + 0.999142i \(0.513185\pi\)
\(762\) 2.84009 + 5.47310i 0.102886 + 0.198269i
\(763\) −15.4480 + 51.5999i −0.559255 + 1.86804i
\(764\) −4.12138 23.3735i −0.149106 0.845624i
\(765\) 5.04064 3.51003i 0.182245 0.126905i
\(766\) −4.63723 + 26.2990i −0.167550 + 0.950222i
\(767\) 2.05964 + 1.03439i 0.0743694 + 0.0373497i
\(768\) 0.0229428 + 1.73190i 0.000827875 + 0.0624945i
\(769\) 5.21507 12.0899i 0.188060 0.435972i −0.797936 0.602743i \(-0.794075\pi\)
0.985996 + 0.166770i \(0.0533338\pi\)
\(770\) −9.63833 + 22.3442i −0.347341 + 0.805228i
\(771\) 29.8365 17.7572i 1.07453 0.639509i
\(772\) −2.19685 1.10330i −0.0790664 0.0397086i
\(773\) −0.743084 + 4.21424i −0.0267269 + 0.151576i −0.995251 0.0973454i \(-0.968965\pi\)
0.968524 + 0.248921i \(0.0800760\pi\)
\(774\) −1.99118 + 7.35476i −0.0715715 + 0.264361i
\(775\) 22.1042 + 125.359i 0.794006 + 4.50303i
\(776\) −1.66597 + 5.56474i −0.0598050 + 0.199763i
\(777\) 10.3115 + 0.463619i 0.369922 + 0.0166322i
\(778\) −9.33472 + 4.68807i −0.334666 + 0.168076i
\(779\) 0.426726 + 1.42536i 0.0152890 + 0.0510689i
\(780\) −2.23726 + 2.16747i −0.0801068 + 0.0776080i
\(781\) −1.01897 + 1.36872i −0.0364617 + 0.0489766i
\(782\) 1.53277 2.65484i 0.0548118 0.0949368i
\(783\) 20.9861 + 29.3020i 0.749982 + 1.04717i
\(784\) −4.78459 8.28716i −0.170878 0.295970i
\(785\) 50.1269 + 5.85899i 1.78910 + 0.209116i
\(786\) 8.03097 + 11.8651i 0.286455 + 0.423215i
\(787\) −26.4068 6.25853i −0.941301 0.223092i −0.268806 0.963194i \(-0.586629\pi\)
−0.672495 + 0.740102i \(0.734777\pi\)
\(788\) −4.62634 3.04279i −0.164807 0.108395i
\(789\) −44.4874 + 34.0447i −1.58379 + 1.21202i
\(790\) −25.6067 27.1415i −0.911046 0.965652i
\(791\) −34.0754 + 28.5927i −1.21158 + 1.01664i
\(792\) 4.11635 0.109079i 0.146268 0.00387596i
\(793\) 1.89712 + 1.59187i 0.0673686 + 0.0565289i
\(794\) −1.97861 33.9714i −0.0702182 1.20560i
\(795\) 16.9458 20.7472i 0.601004 0.735827i
\(796\) 3.23056 + 4.33939i 0.114504 + 0.153806i
\(797\) 9.63557 1.12624i 0.341309 0.0398934i 0.0562882 0.998415i \(-0.482073\pi\)
0.285021 + 0.958521i \(0.407999\pi\)
\(798\) 0.690063 1.97703i 0.0244280 0.0699862i
\(799\) 0.818039 0.538032i 0.0289401 0.0190342i
\(800\) −13.1268 + 4.77775i −0.464101 + 0.168919i
\(801\) 28.2893 + 17.5507i 0.999554 + 0.620122i
\(802\) 22.8243 + 8.30737i 0.805954 + 0.293343i
\(803\) 6.87495 1.62939i 0.242612 0.0575000i
\(804\) −1.77504 + 7.95781i −0.0626010 + 0.280650i
\(805\) 6.72211 115.414i 0.236923 4.06781i
\(806\) 2.58216 2.73693i 0.0909528 0.0964043i
\(807\) 20.5752 9.20041i 0.724281 0.323870i
\(808\) 0.413956 + 0.959658i 0.0145629 + 0.0337607i
\(809\) −4.47713 −0.157407 −0.0787037 0.996898i \(-0.525078\pi\)
−0.0787037 + 0.996898i \(0.525078\pi\)
\(810\) −39.1196 2.48232i −1.37452 0.0872199i
\(811\) 10.7641 0.377977 0.188989 0.981979i \(-0.439479\pi\)
0.188989 + 0.981979i \(0.439479\pi\)
\(812\) 11.1831 + 25.9252i 0.392448 + 0.909797i
\(813\) −18.3201 13.2653i −0.642515 0.465235i
\(814\) −1.37901 + 1.46167i −0.0483344 + 0.0512315i
\(815\) 2.21892 38.0974i 0.0777254 1.33449i
\(816\) −0.599601 0.550867i −0.0209902 0.0192842i
\(817\) −0.734016 + 0.173965i −0.0256800 + 0.00608626i
\(818\) −24.3399 8.85899i −0.851024 0.309747i
\(819\) −4.99114 + 0.717864i −0.174405 + 0.0250842i
\(820\) 20.5026 7.46235i 0.715983 0.260596i
\(821\) 42.2005 27.7557i 1.47281 0.968682i 0.476839 0.878991i \(-0.341782\pi\)
0.995970 0.0896910i \(-0.0285880\pi\)
\(822\) −31.4084 + 5.96816i −1.09549 + 0.208163i
\(823\) −12.6456 + 1.47806i −0.440799 + 0.0515220i −0.333598 0.942715i \(-0.608263\pi\)
−0.107201 + 0.994237i \(0.534189\pi\)
\(824\) −1.97748 2.65622i −0.0688889 0.0925339i
\(825\) 11.7711 + 31.0546i 0.409816 + 1.08118i
\(826\) 1.32105 + 22.6816i 0.0459653 + 0.789194i
\(827\) 20.3942 + 17.1128i 0.709176 + 0.595070i 0.924368 0.381502i \(-0.124593\pi\)
−0.215192 + 0.976572i \(0.569038\pi\)
\(828\) −18.1997 + 7.17564i −0.632484 + 0.249371i
\(829\) −29.8261 + 25.0271i −1.03590 + 0.869227i −0.991542 0.129789i \(-0.958570\pi\)
−0.0443624 + 0.999016i \(0.514126\pi\)
\(830\) 27.5550 + 29.2066i 0.956450 + 1.01378i
\(831\) 36.5074 + 15.1774i 1.26643 + 0.526499i
\(832\) 0.344996 + 0.226908i 0.0119606 + 0.00786660i
\(833\) 4.37720 + 1.03741i 0.151661 + 0.0359443i
\(834\) 22.0371 1.57666i 0.763081 0.0545952i
\(835\) −43.4018 5.07294i −1.50198 0.175556i
\(836\) 0.203835 + 0.353053i 0.00704980 + 0.0122106i
\(837\) 47.3413 + 0.873000i 1.63636 + 0.0301753i
\(838\) 7.76054 13.4416i 0.268083 0.464334i
\(839\) 25.7303 34.5617i 0.888307 1.19320i −0.0920069 0.995758i \(-0.529328\pi\)
0.980314 0.197445i \(-0.0632644\pi\)
\(840\) −29.5310 8.41641i −1.01891 0.290394i
\(841\) −5.48141 18.3092i −0.189014 0.631352i
\(842\) −28.3921 + 14.2591i −0.978457 + 0.491400i
\(843\) −2.47228 + 3.86961i −0.0851498 + 0.133276i
\(844\) 3.05766 10.2133i 0.105249 0.351556i
\(845\) −9.70296 55.0282i −0.333792 1.89303i
\(846\) −6.22316 0.560739i −0.213957 0.0192786i
\(847\) −6.44353 + 36.5431i −0.221402 + 1.25563i
\(848\) −3.17334 1.59371i −0.108973 0.0547282i
\(849\) −18.3754 10.2869i −0.630640 0.353046i
\(850\) 2.60102 6.02983i 0.0892141 0.206821i
\(851\) 3.78137 8.76621i 0.129624 0.300502i
\(852\) −1.87885 1.05182i −0.0643682 0.0360347i
\(853\) 1.16228 + 0.583719i 0.0397957 + 0.0199862i 0.468586 0.883418i \(-0.344764\pi\)
−0.428790 + 0.903404i \(0.641060\pi\)
\(854\) −4.23923 + 24.0418i −0.145063 + 0.822695i
\(855\) −1.63092 3.52137i −0.0557765 0.120428i
\(856\) −0.765696 4.34248i −0.0261710 0.148423i
\(857\) 10.9839 36.6889i 0.375204 1.25327i −0.537018 0.843571i \(-0.680449\pi\)
0.912222 0.409697i \(-0.134365\pi\)
\(858\) 0.528541 0.827272i 0.0180441 0.0282426i
\(859\) 17.7121 8.89535i 0.604329 0.303505i −0.120200 0.992750i \(-0.538354\pi\)
0.724529 + 0.689244i \(0.242057\pi\)
\(860\) 3.17260 + 10.5972i 0.108185 + 0.361363i
\(861\) 33.9666 + 9.68058i 1.15758 + 0.329913i
\(862\) 8.99414 12.0812i 0.306342 0.411488i
\(863\) 20.1970 34.9822i 0.687513 1.19081i −0.285127 0.958490i \(-0.592036\pi\)
0.972640 0.232317i \(-0.0746307\pi\)
\(864\) 0.807801 + 5.13298i 0.0274819 + 0.174627i
\(865\) 26.3059 + 45.5632i 0.894428 + 1.54919i
\(866\) 22.6165 + 2.64348i 0.768539 + 0.0898293i
\(867\) −28.9880 + 2.07397i −0.984484 + 0.0704356i
\(868\) 36.0924 + 8.55406i 1.22506 + 0.290344i
\(869\) 9.82508 + 6.46206i 0.333293 + 0.219210i
\(870\) 48.3163 + 20.0868i 1.63808 + 0.681006i
\(871\) 1.33391 + 1.41387i 0.0451980 + 0.0479071i
\(872\) 10.1366 8.50560i 0.343268 0.288036i
\(873\) −2.57038 + 17.2357i −0.0869942 + 0.583340i
\(874\) −1.48368 1.24495i −0.0501861 0.0421111i
\(875\) −9.24572 158.743i −0.312562 5.36649i
\(876\) 3.16004 + 8.33684i 0.106768 + 0.281676i
\(877\) 23.5165 + 31.5881i 0.794096 + 1.06666i 0.996183 + 0.0872880i \(0.0278200\pi\)
−0.202088 + 0.979367i \(0.564773\pi\)
\(878\) 33.8435 3.95574i 1.14216 0.133500i
\(879\) −42.5964 + 8.09408i −1.43674 + 0.273007i
\(880\) 4.99469 3.28506i 0.168371 0.110739i
\(881\) 17.9904 6.54798i 0.606113 0.220607i −0.0206888 0.999786i \(-0.506586\pi\)
0.626801 + 0.779179i \(0.284364\pi\)
\(882\) −17.7469 22.5648i −0.597570 0.759797i
\(883\) −17.8413 6.49369i −0.600406 0.218530i 0.0238941 0.999714i \(-0.492394\pi\)
−0.624300 + 0.781185i \(0.714616\pi\)
\(884\) −0.188884 + 0.0447663i −0.00635286 + 0.00150565i
\(885\) 31.0068 + 28.4867i 1.04228 + 0.957569i
\(886\) −0.250625 + 4.30306i −0.00841990 + 0.144564i
\(887\) 10.3544 10.9750i 0.347666 0.368504i −0.529817 0.848112i \(-0.677740\pi\)
0.877483 + 0.479608i \(0.159221\pi\)
\(888\) −2.05387 1.48718i −0.0689235 0.0499064i
\(889\) 5.73963 + 13.3060i 0.192501 + 0.446268i
\(890\) 48.3319 1.62009
\(891\) 12.1767 2.08195i 0.407935 0.0697480i
\(892\) 9.73548 0.325968
\(893\) −0.245016 0.568010i −0.00819914 0.0190077i
\(894\) −9.83621 + 4.39836i −0.328972 + 0.147103i
\(895\) −39.2520 + 41.6047i −1.31205 + 1.39069i
\(896\) −0.236680 + 4.06364i −0.00790693 + 0.135757i
\(897\) −1.01537 + 4.55208i −0.0339023 + 0.151990i
\(898\) −9.99921 + 2.36986i −0.333678 + 0.0790831i
\(899\) −59.3944 21.6178i −1.98091 0.720993i
\(900\) −36.9387 + 19.7936i −1.23129 + 0.659785i
\(901\) 1.56867 0.570949i 0.0522599 0.0190211i
\(902\) −5.74491 + 3.77849i −0.191285 + 0.125810i
\(903\) −5.90106 + 16.9065i −0.196375 + 0.562615i
\(904\) 10.8540 1.26865i 0.360999 0.0421947i
\(905\) −1.34815 1.81089i −0.0448142 0.0601959i
\(906\) 20.8724 25.5547i 0.693440 0.848999i
\(907\) −1.77884 30.5415i −0.0590655 1.01411i −0.889482 0.456971i \(-0.848934\pi\)
0.830416 0.557144i \(-0.188103\pi\)
\(908\) −5.49786 4.61325i −0.182453 0.153096i
\(909\) 1.63908 + 2.67286i 0.0543648 + 0.0886530i
\(910\) −5.60794 + 4.70562i −0.185901 + 0.155990i
\(911\) 39.9071 + 42.2991i 1.32218 + 1.40143i 0.856207 + 0.516634i \(0.172815\pi\)
0.465976 + 0.884798i \(0.345703\pi\)
\(912\) −0.408531 + 0.312635i −0.0135278 + 0.0103524i
\(913\) −10.5726 6.95374i −0.349903 0.230135i
\(914\) 1.18172 + 0.280073i 0.0390878 + 0.00926399i
\(915\) 25.3599 + 37.4673i 0.838373 + 1.23863i
\(916\) −18.3425 2.14393i −0.606054 0.0708376i
\(917\) 16.8357 + 29.1603i 0.555963 + 0.962957i
\(918\) −2.01575 1.37969i −0.0665297 0.0455364i
\(919\) 14.1201 24.4567i 0.465779 0.806753i −0.533457 0.845827i \(-0.679108\pi\)
0.999236 + 0.0390741i \(0.0124409\pi\)
\(920\) −16.9603 + 22.7816i −0.559165 + 0.751088i
\(921\) −21.1021 + 20.4438i −0.695337 + 0.673647i
\(922\) 10.7516 + 35.9127i 0.354084 + 1.18272i
\(923\) −0.458736 + 0.230386i −0.0150995 + 0.00758324i
\(924\) 9.66756 + 0.434668i 0.318039 + 0.0142995i
\(925\) 5.86549 19.5921i 0.192856 0.644184i
\(926\) 0.683444 + 3.87600i 0.0224594 + 0.127373i
\(927\) −7.00647 7.04294i −0.230123 0.231321i
\(928\) 1.20447 6.83091i 0.0395388 0.224236i
\(929\) −42.7172 21.4534i −1.40151 0.703863i −0.422249 0.906480i \(-0.638759\pi\)
−0.979258 + 0.202617i \(0.935055\pi\)
\(930\) 59.0712 35.1562i 1.93702 1.15282i
\(931\) 1.12570 2.60967i 0.0368934 0.0855285i
\(932\) −8.53381 + 19.7836i −0.279534 + 0.648033i
\(933\) −0.506343 38.2228i −0.0165769 1.25136i
\(934\) −16.2228 8.14741i −0.530827 0.266591i
\(935\) −0.488008 + 2.76763i −0.0159596 + 0.0905112i
\(936\) 1.12136 + 0.526445i 0.0366527 + 0.0172074i
\(937\) −0.665387 3.77360i −0.0217372 0.123278i 0.972008 0.234947i \(-0.0754916\pi\)
−0.993745 + 0.111669i \(0.964380\pi\)
\(938\) −5.49555 + 18.3564i −0.179436 + 0.599359i
\(939\) −13.7073 26.4152i −0.447322 0.862027i
\(940\) −8.10642 + 4.07120i −0.264402 + 0.132788i
\(941\) 3.57848 + 11.9529i 0.116655 + 0.389655i 0.996297 0.0859821i \(-0.0274028\pi\)
−0.879642 + 0.475637i \(0.842218\pi\)
\(942\) −4.88680 19.4662i −0.159221 0.634244i
\(943\) 19.5078 26.2035i 0.635261 0.853303i
\(944\) 2.79080 4.83381i 0.0908328 0.157327i
\(945\) −91.2851 12.3797i −2.96950 0.402712i
\(946\) −1.74309 3.01913i −0.0566729 0.0981603i
\(947\) −22.3089 2.60754i −0.724942 0.0847336i −0.254385 0.967103i \(-0.581873\pi\)
−0.470557 + 0.882369i \(0.655947\pi\)
\(948\) −6.48361 + 13.3479i −0.210578 + 0.433520i
\(949\) 2.06823 + 0.490180i 0.0671377 + 0.0159119i
\(950\) −3.46639 2.27988i −0.112465 0.0739692i
\(951\) 1.80364 + 13.8388i 0.0584872 + 0.448755i
\(952\) −1.31315 1.39186i −0.0425596 0.0451105i
\(953\) 0.608669 0.510734i 0.0197167 0.0165443i −0.632876 0.774253i \(-0.718126\pi\)
0.652593 + 0.757709i \(0.273681\pi\)
\(954\) −10.1037 3.37714i −0.327119 0.109339i
\(955\) −79.1865 66.4453i −2.56241 2.15012i
\(956\) 0.646960 + 11.1079i 0.0209242 + 0.359254i
\(957\) −16.2764 2.64817i −0.526141 0.0856031i
\(958\) −5.93330 7.96980i −0.191696 0.257493i
\(959\) −74.6262 + 8.72255i −2.40981 + 0.281666i
\(960\) 4.92513 + 5.71408i 0.158958 + 0.184421i
\(961\) −43.4751 + 28.5940i −1.40242 + 0.922389i
\(962\) −0.568078 + 0.206763i −0.0183156 + 0.00666632i
\(963\) −4.12831 12.5677i −0.133033 0.404989i
\(964\) −24.5709 8.94308i −0.791376 0.288037i
\(965\) −10.4184 + 2.46919i −0.335379 + 0.0794862i
\(966\) −43.8659 + 13.7683i −1.41136 + 0.442988i
\(967\) 0.738478 12.6792i 0.0237479 0.407735i −0.965396 0.260787i \(-0.916018\pi\)
0.989144 0.146948i \(-0.0469450\pi\)
\(968\) 6.25576 6.63072i 0.201068 0.213119i
\(969\) 0.0248909 0.240548i 0.000799611 0.00772752i
\(970\) 10.0205 + 23.2302i 0.321740 + 0.745878i
\(971\) −48.7638 −1.56490 −0.782452 0.622711i \(-0.786031\pi\)
−0.782452 + 0.622711i \(0.786031\pi\)
\(972\) 4.59095 + 14.8971i 0.147255 + 0.477824i
\(973\) 51.9221 1.66455
\(974\) −5.59907 12.9801i −0.179406 0.415909i
\(975\) −1.02833 + 9.93789i −0.0329330 + 0.318267i
\(976\) 4.11569 4.36238i 0.131740 0.139636i
\(977\) −0.381457 + 6.54936i −0.0122039 + 0.209532i 0.986694 + 0.162590i \(0.0519848\pi\)
−0.998898 + 0.0469425i \(0.985052\pi\)
\(978\) −14.4798 + 4.54482i −0.463014 + 0.145327i
\(979\) −14.8213 + 3.51271i −0.473691 + 0.112267i
\(980\) −39.1639 14.2545i −1.25104 0.455343i
\(981\) 26.4673 29.5861i 0.845037 0.944612i
\(982\) −19.9306 + 7.25413i −0.636010 + 0.231489i
\(983\) −7.49132 + 4.92712i −0.238936 + 0.157151i −0.663330 0.748327i \(-0.730857\pi\)
0.424394 + 0.905478i \(0.360487\pi\)
\(984\) −5.66490 6.57236i −0.180590 0.209519i
\(985\) −23.9539 + 2.79981i −0.763234 + 0.0892093i
\(986\) 1.94718 + 2.61551i 0.0620107 + 0.0832948i
\(987\) −14.4938 2.35814i −0.461344 0.0750605i
\(988\) 0.00713101 + 0.122435i 0.000226868 + 0.00389517i
\(989\) 12.6876 + 10.6462i 0.403443 + 0.338529i
\(990\) 13.4284 11.8880i 0.426784 0.377825i
\(991\) −13.2357 + 11.1061i −0.420446 + 0.352796i −0.828333 0.560237i \(-0.810710\pi\)
0.407887 + 0.913032i \(0.366266\pi\)
\(992\) −6.25330 6.62811i −0.198542 0.210443i
\(993\) −2.24373 17.2155i −0.0712027 0.546317i
\(994\) −4.22785 2.78070i −0.134099 0.0881986i
\(995\) 22.9269 + 5.43378i 0.726832 + 0.172262i
\(996\) 6.97694 14.3635i 0.221073 0.455125i
\(997\) 12.5738 + 1.46966i 0.398216 + 0.0465447i 0.312844 0.949804i \(-0.398718\pi\)
0.0853715 + 0.996349i \(0.472792\pi\)
\(998\) 19.0516 + 32.9983i 0.603067 + 1.04454i
\(999\) −6.73402 3.53890i −0.213055 0.111966i
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 162.2.g.b.31.3 90
3.2 odd 2 486.2.g.b.145.5 90
81.34 even 27 inner 162.2.g.b.115.3 yes 90
81.47 odd 54 486.2.g.b.181.5 90
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
162.2.g.b.31.3 90 1.1 even 1 trivial
162.2.g.b.115.3 yes 90 81.34 even 27 inner
486.2.g.b.145.5 90 3.2 odd 2
486.2.g.b.181.5 90 81.47 odd 54