Properties

Label 81.2.g.a.13.6
Level $81$
Weight $2$
Character 81.13
Analytic conductor $0.647$
Analytic rank $0$
Dimension $144$
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] = [81,2,Mod(4,81)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(81, base_ring=CyclotomicField(54))
 
chi = DirichletCharacter(H, H._module([2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("81.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 81 = 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 81.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: \(0.646788256372\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(8\) over \(\Q(\zeta_{27})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label 13.6
Character \(\chi\) \(=\) 81.13
Dual form 81.2.g.a.25.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.744407 + 0.373855i) q^{2} +(0.703902 + 1.58257i) q^{3} +(-0.779943 - 1.04765i) q^{4} +(0.345929 + 1.15548i) q^{5} +(-0.0676620 + 1.44123i) q^{6} +(-0.520803 - 1.20736i) q^{7} +(-0.478230 - 2.71217i) q^{8} +(-2.00904 + 2.22795i) q^{9} +O(q^{10})\) \(q+(0.744407 + 0.373855i) q^{2} +(0.703902 + 1.58257i) q^{3} +(-0.779943 - 1.04765i) q^{4} +(0.345929 + 1.15548i) q^{5} +(-0.0676620 + 1.44123i) q^{6} +(-0.520803 - 1.20736i) q^{7} +(-0.478230 - 2.71217i) q^{8} +(-2.00904 + 2.22795i) q^{9} +(-0.174471 + 0.989477i) q^{10} +(2.11479 - 0.501215i) q^{11} +(1.10897 - 1.97175i) q^{12} +(-3.80561 - 2.50299i) q^{13} +(0.0636874 - 1.09347i) q^{14} +(-1.58513 + 1.36080i) q^{15} +(-0.0912185 + 0.304691i) q^{16} +(3.54217 - 1.28924i) q^{17} +(-2.32848 + 0.907406i) q^{18} +(-2.50517 - 0.911807i) q^{19} +(0.940731 - 1.26362i) q^{20} +(1.54413 - 1.67407i) q^{21} +(1.76165 + 0.417519i) q^{22} +(-2.38967 + 5.53988i) q^{23} +(3.95557 - 2.66594i) q^{24} +(2.96197 - 1.94812i) q^{25} +(-1.89717 - 3.28599i) q^{26} +(-4.94005 - 1.61120i) q^{27} +(-0.858686 + 1.48729i) q^{28} +(0.241756 + 4.15079i) q^{29} +(-1.68873 + 0.420381i) q^{30} +(-7.40674 + 0.865723i) q^{31} +(-3.96165 + 4.19911i) q^{32} +(2.28181 + 2.99400i) q^{33} +(3.11881 + 0.364536i) q^{34} +(1.21492 - 1.01944i) q^{35} +(3.90104 + 0.367096i) q^{36} +(7.47819 + 6.27494i) q^{37} +(-1.52398 - 1.61533i) q^{38} +(1.28237 - 7.78449i) q^{39} +(2.96844 - 1.49081i) q^{40} +(5.17242 - 2.59769i) q^{41} +(1.77532 - 0.668906i) q^{42} +(3.46904 + 3.67697i) q^{43} +(-2.17451 - 1.82463i) q^{44} +(-3.26934 - 1.55071i) q^{45} +(-3.85000 + 3.23053i) q^{46} +(2.97767 + 0.348040i) q^{47} +(-0.546403 + 0.0701130i) q^{48} +(3.61722 - 3.83402i) q^{49} +(2.93322 - 0.342844i) q^{50} +(4.53365 + 4.69822i) q^{51} +(0.345914 + 5.93911i) q^{52} +(-6.22987 + 10.7905i) q^{53} +(-3.07505 - 3.04625i) q^{54} +(1.31071 + 2.27022i) q^{55} +(-3.02550 + 1.98990i) q^{56} +(-0.320396 - 4.60642i) q^{57} +(-1.37183 + 3.18026i) q^{58} +(-10.6138 - 2.51552i) q^{59} +(2.66195 + 0.599306i) q^{60} +(7.04237 - 9.45955i) q^{61} +(-5.83728 - 2.12460i) q^{62} +(3.73624 + 1.26531i) q^{63} +(-3.92120 + 1.42720i) q^{64} +(1.57569 - 5.26317i) q^{65} +(0.579276 + 3.08182i) q^{66} +(0.0482665 - 0.828703i) q^{67} +(-4.11336 - 2.70540i) q^{68} +(-10.4493 + 0.117714i) q^{69} +(1.28552 - 0.304673i) q^{70} +(1.25916 - 7.14107i) q^{71} +(7.00336 + 4.38341i) q^{72} +(-1.41006 - 7.99685i) q^{73} +(3.22089 + 7.46687i) q^{74} +(5.16796 + 3.31623i) q^{75} +(0.998639 + 3.33569i) q^{76} +(-1.70654 - 2.29228i) q^{77} +(3.86488 - 5.31541i) q^{78} +(-10.2764 - 5.16099i) q^{79} -0.383620 q^{80} +(-0.927480 - 8.95208i) q^{81} +4.82155 q^{82} +(-4.26695 - 2.14294i) q^{83} +(-2.95816 - 0.312025i) q^{84} +(2.71504 + 3.64693i) q^{85} +(1.20772 + 4.03408i) q^{86} +(-6.39873 + 3.30434i) q^{87} +(-2.37074 - 5.49599i) q^{88} +(0.578632 + 3.28158i) q^{89} +(-1.85398 - 2.37662i) q^{90} +(-1.04003 + 5.89829i) q^{91} +(7.66763 - 1.81726i) q^{92} +(-6.58368 - 11.1123i) q^{93} +(2.08648 + 1.37230i) q^{94} +(0.186967 - 3.21010i) q^{95} +(-9.43399 - 3.31383i) q^{96} +(-0.390985 + 1.30598i) q^{97} +(4.12605 - 1.50176i) q^{98} +(-3.13203 + 5.71861i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} - 18 q^{10} - 18 q^{11} - 18 q^{12} - 18 q^{13} - 18 q^{14} - 18 q^{15} - 18 q^{16} - 18 q^{17} - 9 q^{18} - 18 q^{19} + 18 q^{20} + 9 q^{21} - 18 q^{22} + 9 q^{23} + 36 q^{24} - 18 q^{25} + 45 q^{26} + 9 q^{27} - 9 q^{28} + 9 q^{29} + 36 q^{30} - 18 q^{31} + 36 q^{32} + 9 q^{33} - 18 q^{34} + 9 q^{35} + 18 q^{36} - 18 q^{37} - 9 q^{38} - 18 q^{39} - 18 q^{40} + 27 q^{42} - 18 q^{43} + 54 q^{44} + 36 q^{45} - 18 q^{46} + 36 q^{47} + 81 q^{48} - 18 q^{49} + 99 q^{50} + 45 q^{51} + 45 q^{53} + 108 q^{54} - 9 q^{55} + 126 q^{56} + 36 q^{57} - 18 q^{58} + 45 q^{59} + 99 q^{60} - 18 q^{61} + 81 q^{62} + 36 q^{63} - 18 q^{64} - 18 q^{66} + 9 q^{67} - 99 q^{68} - 72 q^{69} + 36 q^{70} - 90 q^{71} - 234 q^{72} - 18 q^{73} - 162 q^{74} - 108 q^{75} + 63 q^{76} - 162 q^{77} - 135 q^{78} + 36 q^{79} - 288 q^{80} - 90 q^{81} - 36 q^{82} - 90 q^{83} - 243 q^{84} + 36 q^{85} - 162 q^{86} - 162 q^{87} + 63 q^{88} - 81 q^{89} - 99 q^{90} - 18 q^{91} - 144 q^{92} + 36 q^{94} + 18 q^{95} - 27 q^{96} + 9 q^{97} + 81 q^{98} + 54 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/81\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{4}{27}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.744407 + 0.373855i 0.526375 + 0.264356i 0.692081 0.721820i \(-0.256694\pi\)
−0.165706 + 0.986175i \(0.552990\pi\)
\(3\) 0.703902 + 1.58257i 0.406398 + 0.913696i
\(4\) −0.779943 1.04765i −0.389972 0.523823i
\(5\) 0.345929 + 1.15548i 0.154704 + 0.516747i 0.999842 0.0178015i \(-0.00566669\pi\)
−0.845137 + 0.534549i \(0.820482\pi\)
\(6\) −0.0676620 + 1.44123i −0.0276229 + 0.588381i
\(7\) −0.520803 1.20736i −0.196845 0.456338i 0.790993 0.611825i \(-0.209565\pi\)
−0.987838 + 0.155487i \(0.950305\pi\)
\(8\) −0.478230 2.71217i −0.169080 0.958899i
\(9\) −2.00904 + 2.22795i −0.669682 + 0.742648i
\(10\) −0.174471 + 0.989477i −0.0551727 + 0.312900i
\(11\) 2.11479 0.501215i 0.637634 0.151122i 0.100931 0.994893i \(-0.467818\pi\)
0.536703 + 0.843771i \(0.319670\pi\)
\(12\) 1.10897 1.97175i 0.320131 0.569196i
\(13\) −3.80561 2.50299i −1.05549 0.694204i −0.101738 0.994811i \(-0.532440\pi\)
−0.953748 + 0.300607i \(0.902811\pi\)
\(14\) 0.0636874 1.09347i 0.0170212 0.292242i
\(15\) −1.58513 + 1.36080i −0.409279 + 0.351358i
\(16\) −0.0912185 + 0.304691i −0.0228046 + 0.0761727i
\(17\) 3.54217 1.28924i 0.859102 0.312688i 0.125356 0.992112i \(-0.459993\pi\)
0.733746 + 0.679424i \(0.237770\pi\)
\(18\) −2.32848 + 0.907406i −0.548827 + 0.213878i
\(19\) −2.50517 0.911807i −0.574725 0.209183i 0.0382728 0.999267i \(-0.487814\pi\)
−0.612998 + 0.790084i \(0.710037\pi\)
\(20\) 0.940731 1.26362i 0.210354 0.282554i
\(21\) 1.54413 1.67407i 0.336957 0.365311i
\(22\) 1.76165 + 0.417519i 0.375585 + 0.0890153i
\(23\) −2.38967 + 5.53988i −0.498281 + 1.15514i 0.464674 + 0.885482i \(0.346171\pi\)
−0.962955 + 0.269663i \(0.913088\pi\)
\(24\) 3.95557 2.66594i 0.807428 0.544182i
\(25\) 2.96197 1.94812i 0.592393 0.389623i
\(26\) −1.89717 3.28599i −0.372065 0.644435i
\(27\) −4.94005 1.61120i −0.950712 0.310075i
\(28\) −0.858686 + 1.48729i −0.162276 + 0.281071i
\(29\) 0.241756 + 4.15079i 0.0448929 + 0.770782i 0.943366 + 0.331753i \(0.107640\pi\)
−0.898473 + 0.439028i \(0.855323\pi\)
\(30\) −1.68873 + 0.420381i −0.308318 + 0.0767508i
\(31\) −7.40674 + 0.865723i −1.33029 + 0.155488i −0.751362 0.659891i \(-0.770603\pi\)
−0.578927 + 0.815379i \(0.696529\pi\)
\(32\) −3.96165 + 4.19911i −0.700328 + 0.742304i
\(33\) 2.28181 + 2.99400i 0.397213 + 0.521188i
\(34\) 3.11881 + 0.364536i 0.534871 + 0.0625174i
\(35\) 1.21492 1.01944i 0.205359 0.172317i
\(36\) 3.90104 + 0.367096i 0.650173 + 0.0611826i
\(37\) 7.47819 + 6.27494i 1.22941 + 1.03159i 0.998277 + 0.0586711i \(0.0186863\pi\)
0.231129 + 0.972923i \(0.425758\pi\)
\(38\) −1.52398 1.61533i −0.247222 0.262040i
\(39\) 1.28237 7.78449i 0.205344 1.24652i
\(40\) 2.96844 1.49081i 0.469351 0.235717i
\(41\) 5.17242 2.59769i 0.807797 0.405691i 0.00355548 0.999994i \(-0.498868\pi\)
0.804241 + 0.594303i \(0.202572\pi\)
\(42\) 1.77532 0.668906i 0.273938 0.103214i
\(43\) 3.46904 + 3.67697i 0.529024 + 0.560732i 0.935680 0.352849i \(-0.114787\pi\)
−0.406657 + 0.913581i \(0.633305\pi\)
\(44\) −2.17451 1.82463i −0.327820 0.275074i
\(45\) −3.26934 1.55071i −0.487364 0.231166i
\(46\) −3.85000 + 3.23053i −0.567652 + 0.476316i
\(47\) 2.97767 + 0.348040i 0.434338 + 0.0507669i 0.330453 0.943822i \(-0.392798\pi\)
0.103885 + 0.994589i \(0.466873\pi\)
\(48\) −0.546403 + 0.0701130i −0.0788665 + 0.0101199i
\(49\) 3.61722 3.83402i 0.516745 0.547718i
\(50\) 2.93322 0.342844i 0.414820 0.0484855i
\(51\) 4.53365 + 4.69822i 0.634839 + 0.657883i
\(52\) 0.345914 + 5.93911i 0.0479696 + 0.823607i
\(53\) −6.22987 + 10.7905i −0.855739 + 1.48218i 0.0202187 + 0.999796i \(0.493564\pi\)
−0.875958 + 0.482388i \(0.839770\pi\)
\(54\) −3.07505 3.04625i −0.418461 0.414542i
\(55\) 1.31071 + 2.27022i 0.176737 + 0.306117i
\(56\) −3.02550 + 1.98990i −0.404300 + 0.265912i
\(57\) −0.320396 4.60642i −0.0424375 0.610136i
\(58\) −1.37183 + 3.18026i −0.180130 + 0.417588i
\(59\) −10.6138 2.51552i −1.38180 0.327493i −0.528510 0.848927i \(-0.677249\pi\)
−0.853292 + 0.521434i \(0.825397\pi\)
\(60\) 2.66195 + 0.599306i 0.343656 + 0.0773701i
\(61\) 7.04237 9.45955i 0.901684 1.21117i −0.0751502 0.997172i \(-0.523944\pi\)
0.976834 0.213999i \(-0.0686490\pi\)
\(62\) −5.83728 2.12460i −0.741336 0.269824i
\(63\) 3.73624 + 1.26531i 0.470722 + 0.159415i
\(64\) −3.92120 + 1.42720i −0.490150 + 0.178400i
\(65\) 1.57569 5.26317i 0.195440 0.652816i
\(66\) 0.579276 + 3.08182i 0.0713040 + 0.379346i
\(67\) 0.0482665 0.828703i 0.00589669 0.101242i −0.994076 0.108691i \(-0.965334\pi\)
0.999972 + 0.00744893i \(0.00237109\pi\)
\(68\) −4.11336 2.70540i −0.498818 0.328078i
\(69\) −10.4493 + 0.117714i −1.25795 + 0.0141711i
\(70\) 1.28552 0.304673i 0.153649 0.0364154i
\(71\) 1.25916 7.14107i 0.149435 0.847489i −0.814263 0.580496i \(-0.802859\pi\)
0.963698 0.266993i \(-0.0860301\pi\)
\(72\) 7.00336 + 4.38341i 0.825354 + 0.516590i
\(73\) −1.41006 7.99685i −0.165035 0.935960i −0.949028 0.315191i \(-0.897931\pi\)
0.783993 0.620769i \(-0.213180\pi\)
\(74\) 3.22089 + 7.46687i 0.374421 + 0.868006i
\(75\) 5.16796 + 3.31623i 0.596745 + 0.382925i
\(76\) 0.998639 + 3.33569i 0.114552 + 0.382629i
\(77\) −1.70654 2.29228i −0.194478 0.261229i
\(78\) 3.86488 5.31541i 0.437612 0.601851i
\(79\) −10.2764 5.16099i −1.15618 0.580657i −0.235849 0.971790i \(-0.575787\pi\)
−0.920334 + 0.391133i \(0.872083\pi\)
\(80\) −0.383620 −0.0428900
\(81\) −0.927480 8.95208i −0.103053 0.994676i
\(82\) 4.82155 0.532451
\(83\) −4.26695 2.14294i −0.468358 0.235218i 0.198936 0.980012i \(-0.436251\pi\)
−0.667294 + 0.744794i \(0.732548\pi\)
\(84\) −2.95816 0.312025i −0.322762 0.0340447i
\(85\) 2.71504 + 3.64693i 0.294487 + 0.395565i
\(86\) 1.20772 + 4.03408i 0.130232 + 0.435006i
\(87\) −6.39873 + 3.30434i −0.686016 + 0.354262i
\(88\) −2.37074 5.49599i −0.252722 0.585875i
\(89\) 0.578632 + 3.28158i 0.0613348 + 0.347847i 0.999995 + 0.00300484i \(0.000956472\pi\)
−0.938661 + 0.344842i \(0.887932\pi\)
\(90\) −1.85398 2.37662i −0.195427 0.250517i
\(91\) −1.04003 + 5.89829i −0.109025 + 0.618309i
\(92\) 7.66763 1.81726i 0.799406 0.189463i
\(93\) −6.58368 11.1123i −0.682696 1.15229i
\(94\) 2.08648 + 1.37230i 0.215204 + 0.141542i
\(95\) 0.186967 3.21010i 0.0191824 0.329349i
\(96\) −9.43399 3.31383i −0.962852 0.338216i
\(97\) −0.390985 + 1.30598i −0.0396985 + 0.132602i −0.975542 0.219814i \(-0.929455\pi\)
0.935843 + 0.352417i \(0.114640\pi\)
\(98\) 4.12605 1.50176i 0.416794 0.151701i
\(99\) −3.13203 + 5.71861i −0.314781 + 0.574742i
\(100\) −4.35110 1.58367i −0.435110 0.158367i
\(101\) 1.38233 1.85679i 0.137547 0.184757i −0.728013 0.685564i \(-0.759556\pi\)
0.865559 + 0.500807i \(0.166963\pi\)
\(102\) 1.61843 + 5.19232i 0.160248 + 0.514116i
\(103\) 4.42692 + 1.04920i 0.436198 + 0.103381i 0.442847 0.896597i \(-0.353968\pi\)
−0.00664935 + 0.999978i \(0.502117\pi\)
\(104\) −4.96858 + 11.5185i −0.487210 + 1.12948i
\(105\) 2.46852 + 1.20511i 0.240902 + 0.117607i
\(106\) −8.67163 + 5.70342i −0.842263 + 0.553965i
\(107\) 6.14665 + 10.6463i 0.594219 + 1.02922i 0.993657 + 0.112457i \(0.0358721\pi\)
−0.399438 + 0.916760i \(0.630795\pi\)
\(108\) 2.16499 + 6.43206i 0.208327 + 0.618925i
\(109\) 4.45327 7.71330i 0.426546 0.738800i −0.570017 0.821633i \(-0.693063\pi\)
0.996563 + 0.0828329i \(0.0263968\pi\)
\(110\) 0.126970 + 2.17999i 0.0121061 + 0.207854i
\(111\) −4.66662 + 16.2517i −0.442936 + 1.54254i
\(112\) 0.415378 0.0485507i 0.0392495 0.00458761i
\(113\) 11.9342 12.6496i 1.12268 1.18997i 0.142932 0.989733i \(-0.454347\pi\)
0.979747 0.200238i \(-0.0641716\pi\)
\(114\) 1.48363 3.54884i 0.138955 0.332379i
\(115\) −7.22789 0.844819i −0.674004 0.0787798i
\(116\) 4.16000 3.49065i 0.386246 0.324099i
\(117\) 13.2222 3.45007i 1.22239 0.318959i
\(118\) −6.96056 5.84061i −0.640772 0.537671i
\(119\) −3.40135 3.60522i −0.311801 0.330490i
\(120\) 4.44879 + 3.64837i 0.406117 + 0.333049i
\(121\) −5.60882 + 2.81686i −0.509893 + 0.256078i
\(122\) 8.77890 4.40893i 0.794804 0.399166i
\(123\) 7.75190 + 6.35720i 0.698965 + 0.573209i
\(124\) 6.68380 + 7.08442i 0.600223 + 0.636199i
\(125\) 7.89548 + 6.62509i 0.706193 + 0.592566i
\(126\) 2.30824 + 2.33872i 0.205634 + 0.208350i
\(127\) 4.35255 3.65222i 0.386226 0.324082i −0.428915 0.903345i \(-0.641104\pi\)
0.815141 + 0.579263i \(0.196660\pi\)
\(128\) 8.01534 + 0.936859i 0.708462 + 0.0828074i
\(129\) −3.37719 + 8.07822i −0.297345 + 0.711247i
\(130\) 3.14062 3.32886i 0.275450 0.291960i
\(131\) 19.3865 2.26596i 1.69381 0.197978i 0.786250 0.617909i \(-0.212020\pi\)
0.907556 + 0.419931i \(0.137946\pi\)
\(132\) 1.35696 4.72568i 0.118109 0.411318i
\(133\) 0.203823 + 3.49951i 0.0176737 + 0.303446i
\(134\) 0.345745 0.598848i 0.0298678 0.0517326i
\(135\) 0.152805 6.26550i 0.0131513 0.539248i
\(136\) −5.19062 8.99042i −0.445092 0.770922i
\(137\) −13.2460 + 8.71204i −1.13168 + 0.744320i −0.970140 0.242546i \(-0.922018\pi\)
−0.161543 + 0.986866i \(0.551647\pi\)
\(138\) −7.82256 3.81891i −0.665901 0.325087i
\(139\) −4.13477 + 9.58547i −0.350707 + 0.813029i 0.647973 + 0.761663i \(0.275617\pi\)
−0.998680 + 0.0513663i \(0.983642\pi\)
\(140\) −2.01558 0.477701i −0.170347 0.0403731i
\(141\) 1.54519 + 4.95736i 0.130129 + 0.417485i
\(142\) 3.60706 4.84512i 0.302697 0.406593i
\(143\) −9.30261 3.38587i −0.777923 0.283141i
\(144\) −0.495573 0.815367i −0.0412977 0.0679473i
\(145\) −4.71253 + 1.71522i −0.391354 + 0.142441i
\(146\) 1.94001 6.48007i 0.160556 0.536294i
\(147\) 8.61377 + 3.02571i 0.710452 + 0.249557i
\(148\) 0.741356 12.7286i 0.0609391 1.04628i
\(149\) 2.43554 + 1.60188i 0.199527 + 0.131231i 0.645341 0.763895i \(-0.276715\pi\)
−0.445814 + 0.895126i \(0.647086\pi\)
\(150\) 2.60727 + 4.40069i 0.212883 + 0.359315i
\(151\) −12.4159 + 2.94262i −1.01039 + 0.239467i −0.702293 0.711888i \(-0.747840\pi\)
−0.308098 + 0.951355i \(0.599692\pi\)
\(152\) −1.27493 + 7.23051i −0.103411 + 0.586472i
\(153\) −4.24401 + 10.4819i −0.343108 + 0.847412i
\(154\) −0.413378 2.34439i −0.0333110 0.188916i
\(155\) −3.56253 8.25887i −0.286149 0.663369i
\(156\) −9.15556 + 4.72799i −0.733032 + 0.378542i
\(157\) 0.364422 + 1.21726i 0.0290841 + 0.0971476i 0.971299 0.237861i \(-0.0764461\pi\)
−0.942215 + 0.335008i \(0.891261\pi\)
\(158\) −5.72035 7.68376i −0.455086 0.611287i
\(159\) −21.4619 2.26378i −1.70204 0.179529i
\(160\) −6.22244 3.12503i −0.491927 0.247055i
\(161\) 7.93316 0.625221
\(162\) 2.65636 7.01074i 0.208703 0.550816i
\(163\) 12.3636 0.968391 0.484195 0.874960i \(-0.339112\pi\)
0.484195 + 0.874960i \(0.339112\pi\)
\(164\) −6.75565 3.39282i −0.527528 0.264934i
\(165\) −2.67017 + 3.67231i −0.207872 + 0.285889i
\(166\) −2.37520 3.19044i −0.184351 0.247626i
\(167\) −1.09374 3.65334i −0.0846359 0.282704i 0.905186 0.425016i \(-0.139731\pi\)
−0.989822 + 0.142312i \(0.954546\pi\)
\(168\) −5.27881 3.38737i −0.407269 0.261341i
\(169\) 3.06867 + 7.11397i 0.236051 + 0.547228i
\(170\) 0.657669 + 3.72983i 0.0504409 + 0.286065i
\(171\) 7.06445 3.74952i 0.540232 0.286733i
\(172\) 1.14650 6.50215i 0.0874201 0.495784i
\(173\) −23.4213 + 5.55096i −1.78069 + 0.422031i −0.983383 0.181542i \(-0.941891\pi\)
−0.797307 + 0.603574i \(0.793743\pi\)
\(174\) −5.99861 + 0.0675756i −0.454753 + 0.00512289i
\(175\) −3.89467 2.56157i −0.294410 0.193636i
\(176\) −0.0401925 + 0.690078i −0.00302962 + 0.0520166i
\(177\) −3.49010 18.5678i −0.262332 1.39564i
\(178\) −0.796100 + 2.65916i −0.0596702 + 0.199312i
\(179\) 5.95691 2.16814i 0.445240 0.162054i −0.109664 0.993969i \(-0.534977\pi\)
0.554904 + 0.831915i \(0.312755\pi\)
\(180\) 0.925308 + 4.63457i 0.0689684 + 0.345440i
\(181\) −5.82014 2.11836i −0.432608 0.157456i 0.116532 0.993187i \(-0.462822\pi\)
−0.549140 + 0.835731i \(0.685045\pi\)
\(182\) −2.97931 + 4.00191i −0.220841 + 0.296641i
\(183\) 19.9275 + 4.48644i 1.47309 + 0.331647i
\(184\) 16.1679 + 3.83187i 1.19192 + 0.282489i
\(185\) −4.66367 + 10.8116i −0.342880 + 0.794884i
\(186\) −0.746554 10.7334i −0.0547400 0.787011i
\(187\) 6.84476 4.50187i 0.500539 0.329210i
\(188\) −1.95779 3.39100i −0.142787 0.247314i
\(189\) 0.627502 + 6.80352i 0.0456441 + 0.494883i
\(190\) 1.33929 2.31972i 0.0971625 0.168290i
\(191\) −0.392632 6.74123i −0.0284098 0.487778i −0.982263 0.187506i \(-0.939960\pi\)
0.953854 0.300272i \(-0.0970774\pi\)
\(192\) −5.01878 5.20095i −0.362199 0.375347i
\(193\) 15.8040 1.84722i 1.13759 0.132966i 0.473626 0.880726i \(-0.342945\pi\)
0.663969 + 0.747761i \(0.268871\pi\)
\(194\) −0.779300 + 0.826010i −0.0559505 + 0.0593041i
\(195\) 9.43845 1.21112i 0.675902 0.0867300i
\(196\) −6.83792 0.799238i −0.488423 0.0570884i
\(197\) −8.88023 + 7.45140i −0.632690 + 0.530890i −0.901764 0.432229i \(-0.857727\pi\)
0.269073 + 0.963120i \(0.413283\pi\)
\(198\) −4.46944 + 3.08604i −0.317629 + 0.219316i
\(199\) 3.29385 + 2.76387i 0.233495 + 0.195925i 0.752026 0.659133i \(-0.229077\pi\)
−0.518531 + 0.855059i \(0.673521\pi\)
\(200\) −6.70013 7.10172i −0.473771 0.502168i
\(201\) 1.34545 0.506941i 0.0949010 0.0357568i
\(202\) 1.72318 0.865416i 0.121243 0.0608904i
\(203\) 4.88558 2.45363i 0.342900 0.172211i
\(204\) 1.38608 8.41401i 0.0970448 0.589098i
\(205\) 4.79087 + 5.07803i 0.334609 + 0.354665i
\(206\) 2.90318 + 2.43606i 0.202274 + 0.169728i
\(207\) −7.54159 16.4539i −0.524177 1.14363i
\(208\) 1.10978 0.931215i 0.0769493 0.0645682i
\(209\) −5.75493 0.672654i −0.398077 0.0465285i
\(210\) 1.38704 + 1.81996i 0.0957151 + 0.125589i
\(211\) −9.80038 + 10.3878i −0.674686 + 0.715126i −0.970763 0.240038i \(-0.922840\pi\)
0.296077 + 0.955164i \(0.404321\pi\)
\(212\) 16.1635 1.88924i 1.11012 0.129754i
\(213\) 12.1876 3.03390i 0.835077 0.207879i
\(214\) 0.595430 + 10.2231i 0.0407028 + 0.698840i
\(215\) −3.04863 + 5.28038i −0.207915 + 0.360119i
\(216\) −2.00737 + 14.1688i −0.136584 + 0.964064i
\(217\) 4.90269 + 8.49171i 0.332816 + 0.576455i
\(218\) 6.19871 4.07695i 0.419829 0.276126i
\(219\) 11.6630 7.86051i 0.788113 0.531164i
\(220\) 1.35611 3.14381i 0.0914286 0.211955i
\(221\) −16.7071 3.95965i −1.12384 0.266355i
\(222\) −9.54964 + 10.3532i −0.640930 + 0.694863i
\(223\) −12.0568 + 16.1950i −0.807381 + 1.08450i 0.187382 + 0.982287i \(0.440000\pi\)
−0.994762 + 0.102214i \(0.967408\pi\)
\(224\) 7.13306 + 2.59622i 0.476598 + 0.173467i
\(225\) −1.61043 + 10.5129i −0.107362 + 0.700863i
\(226\) 13.6130 4.95474i 0.905526 0.329585i
\(227\) −0.781091 + 2.60903i −0.0518428 + 0.173167i −0.979990 0.199046i \(-0.936216\pi\)
0.928147 + 0.372213i \(0.121401\pi\)
\(228\) −4.57601 + 3.92841i −0.303053 + 0.260165i
\(229\) −0.0887613 + 1.52397i −0.00586551 + 0.100707i −0.999970 0.00771732i \(-0.997543\pi\)
0.994105 + 0.108424i \(0.0345805\pi\)
\(230\) −5.06465 3.33107i −0.333953 0.219645i
\(231\) 2.42645 4.31425i 0.159649 0.283857i
\(232\) 11.1420 2.64071i 0.731511 0.173371i
\(233\) −1.13347 + 6.42825i −0.0742563 + 0.421128i 0.924906 + 0.380197i \(0.124144\pi\)
−0.999162 + 0.0409317i \(0.986967\pi\)
\(234\) 11.1325 + 2.37491i 0.727754 + 0.155253i
\(235\) 0.627909 + 3.56105i 0.0409602 + 0.232297i
\(236\) 5.64280 + 13.0815i 0.367315 + 0.851532i
\(237\) 0.934060 19.8959i 0.0606737 1.29238i
\(238\) −1.18416 3.95536i −0.0767576 0.256388i
\(239\) −10.0905 13.5539i −0.652702 0.876731i 0.345391 0.938459i \(-0.387746\pi\)
−0.998093 + 0.0617275i \(0.980339\pi\)
\(240\) −0.270031 0.607105i −0.0174304 0.0391885i
\(241\) −11.2588 5.65439i −0.725244 0.364231i 0.0475663 0.998868i \(-0.484853\pi\)
−0.772811 + 0.634637i \(0.781150\pi\)
\(242\) −5.22835 −0.336091
\(243\) 13.5144 7.76919i 0.866951 0.498394i
\(244\) −15.4029 −0.986070
\(245\) 5.68145 + 2.85333i 0.362974 + 0.182293i
\(246\) 3.39390 + 7.63043i 0.216387 + 0.486498i
\(247\) 7.25145 + 9.74038i 0.461399 + 0.619766i
\(248\) 5.89011 + 19.6743i 0.374023 + 1.24932i
\(249\) 0.387839 8.26115i 0.0245783 0.523529i
\(250\) 3.40062 + 7.88353i 0.215074 + 0.498598i
\(251\) −4.48052 25.4103i −0.282808 1.60388i −0.713012 0.701152i \(-0.752669\pi\)
0.430204 0.902732i \(-0.358442\pi\)
\(252\) −1.58846 4.90113i −0.100063 0.308742i
\(253\) −2.27699 + 12.9134i −0.143153 + 0.811861i
\(254\) 4.60547 1.09152i 0.288973 0.0684878i
\(255\) −3.86039 + 6.86381i −0.241747 + 0.429828i
\(256\) 12.5892 + 8.28002i 0.786822 + 0.517501i
\(257\) −0.841489 + 14.4478i −0.0524906 + 0.901229i 0.864578 + 0.502499i \(0.167586\pi\)
−0.917068 + 0.398730i \(0.869451\pi\)
\(258\) −5.53409 + 4.75090i −0.344537 + 0.295778i
\(259\) 3.68144 12.2969i 0.228753 0.764089i
\(260\) −6.74288 + 2.45421i −0.418176 + 0.152204i
\(261\) −9.73342 7.80050i −0.602484 0.482839i
\(262\) 15.2786 + 5.56095i 0.943914 + 0.343557i
\(263\) −6.24306 + 8.38588i −0.384963 + 0.517096i −0.951794 0.306739i \(-0.900762\pi\)
0.566830 + 0.823835i \(0.308170\pi\)
\(264\) 7.02902 7.62050i 0.432606 0.469009i
\(265\) −14.6233 3.46578i −0.898301 0.212901i
\(266\) −1.15658 + 2.68126i −0.0709146 + 0.164398i
\(267\) −4.78603 + 3.22564i −0.292900 + 0.197406i
\(268\) −0.905832 + 0.595775i −0.0553325 + 0.0363928i
\(269\) 0.105374 + 0.182513i 0.00642476 + 0.0111280i 0.869220 0.494426i \(-0.164622\pi\)
−0.862795 + 0.505554i \(0.831288\pi\)
\(270\) 2.45614 4.60695i 0.149476 0.280370i
\(271\) 5.70846 9.88735i 0.346765 0.600614i −0.638908 0.769283i \(-0.720614\pi\)
0.985673 + 0.168669i \(0.0539470\pi\)
\(272\) 0.0697097 + 1.19687i 0.00422677 + 0.0725708i
\(273\) −10.0665 + 2.50590i −0.609254 + 0.151664i
\(274\) −13.1175 + 1.53321i −0.792455 + 0.0926247i
\(275\) 5.28752 5.60444i 0.318850 0.337961i
\(276\) 8.27320 + 10.8554i 0.497988 + 0.653417i
\(277\) 11.0740 + 1.29437i 0.665375 + 0.0777712i 0.442074 0.896978i \(-0.354243\pi\)
0.223301 + 0.974750i \(0.428317\pi\)
\(278\) −6.66153 + 5.58969i −0.399532 + 0.335247i
\(279\) 12.9517 18.2411i 0.775397 1.09206i
\(280\) −3.34591 2.80755i −0.199956 0.167783i
\(281\) 14.8936 + 15.7863i 0.888478 + 0.941732i 0.998638 0.0521821i \(-0.0166176\pi\)
−0.110159 + 0.993914i \(0.535136\pi\)
\(282\) −0.703082 + 4.26797i −0.0418679 + 0.254154i
\(283\) −0.264982 + 0.133079i −0.0157515 + 0.00791072i −0.456658 0.889643i \(-0.650954\pi\)
0.440906 + 0.897553i \(0.354657\pi\)
\(284\) −8.46338 + 4.25047i −0.502209 + 0.252219i
\(285\) 5.21181 1.96371i 0.308721 0.116320i
\(286\) −5.65910 5.99830i −0.334630 0.354687i
\(287\) −5.83015 4.89208i −0.344143 0.288770i
\(288\) −1.39624 17.2625i −0.0822744 1.01720i
\(289\) −2.13795 + 1.79396i −0.125762 + 0.105527i
\(290\) −4.14929 0.484982i −0.243654 0.0284791i
\(291\) −2.34202 + 0.300522i −0.137292 + 0.0176169i
\(292\) −7.27809 + 7.71433i −0.425918 + 0.451447i
\(293\) 14.4085 1.68412i 0.841755 0.0983871i 0.315723 0.948852i \(-0.397753\pi\)
0.526032 + 0.850464i \(0.323679\pi\)
\(294\) 5.28097 + 5.47267i 0.307993 + 0.319172i
\(295\) −0.764985 13.1343i −0.0445391 0.764707i
\(296\) 13.4425 23.2830i 0.781327 1.35330i
\(297\) −11.2547 0.931320i −0.653066 0.0540407i
\(298\) 1.21416 + 2.10299i 0.0703346 + 0.121823i
\(299\) 22.9604 15.1013i 1.32783 0.873330i
\(300\) −0.556480 8.00066i −0.0321284 0.461918i
\(301\) 2.63273 6.10335i 0.151748 0.351791i
\(302\) −10.3426 2.45124i −0.595149 0.141053i
\(303\) 3.91152 + 0.880631i 0.224711 + 0.0505909i
\(304\) 0.506337 0.680128i 0.0290404 0.0390080i
\(305\) 13.3665 + 4.86501i 0.765364 + 0.278570i
\(306\) −7.07799 + 6.21616i −0.404621 + 0.355354i
\(307\) −3.56052 + 1.29592i −0.203210 + 0.0739622i −0.441620 0.897202i \(-0.645596\pi\)
0.238410 + 0.971165i \(0.423374\pi\)
\(308\) −1.07049 + 3.57569i −0.0609969 + 0.203744i
\(309\) 1.45569 + 7.74444i 0.0828112 + 0.440566i
\(310\) 0.435651 7.47984i 0.0247433 0.424826i
\(311\) −10.3012 6.77519i −0.584126 0.384186i 0.222777 0.974869i \(-0.428488\pi\)
−0.806903 + 0.590684i \(0.798858\pi\)
\(312\) −21.7262 + 0.244750i −1.23000 + 0.0138562i
\(313\) 6.62237 1.56953i 0.374319 0.0887151i −0.0391504 0.999233i \(-0.512465\pi\)
0.413469 + 0.910518i \(0.364317\pi\)
\(314\) −0.183799 + 1.04238i −0.0103724 + 0.0588246i
\(315\) −0.169574 + 4.75487i −0.00955443 + 0.267907i
\(316\) 2.60810 + 14.7913i 0.146717 + 0.832074i
\(317\) −5.91605 13.7150i −0.332279 0.770309i −0.999672 0.0256033i \(-0.991849\pi\)
0.667394 0.744705i \(-0.267410\pi\)
\(318\) −15.1300 9.70880i −0.848450 0.544443i
\(319\) 2.59170 + 8.65688i 0.145107 + 0.484692i
\(320\) −3.00556 4.03717i −0.168016 0.225684i
\(321\) −12.5219 + 17.2214i −0.698903 + 0.961207i
\(322\) 5.90550 + 2.96585i 0.329101 + 0.165281i
\(323\) −10.0493 −0.559156
\(324\) −8.65523 + 7.95378i −0.480846 + 0.441877i
\(325\) −16.1482 −0.895740
\(326\) 9.20354 + 4.62219i 0.509737 + 0.256000i
\(327\) 15.3415 + 1.61821i 0.848386 + 0.0894870i
\(328\) −9.51899 12.7862i −0.525598 0.706001i
\(329\) −1.13057 3.77638i −0.0623305 0.208198i
\(330\) −3.36060 + 1.73543i −0.184995 + 0.0955325i
\(331\) −1.46304 3.39172i −0.0804162 0.186426i 0.873265 0.487246i \(-0.161999\pi\)
−0.953681 + 0.300821i \(0.902739\pi\)
\(332\) 1.08293 + 6.14162i 0.0594337 + 0.337065i
\(333\) −29.0042 + 4.05435i −1.58942 + 0.222177i
\(334\) 0.551633 3.12847i 0.0301840 0.171182i
\(335\) 0.974249 0.230901i 0.0532289 0.0126155i
\(336\) 0.369220 + 0.623189i 0.0201426 + 0.0339977i
\(337\) −15.4103 10.1355i −0.839450 0.552115i 0.0554092 0.998464i \(-0.482354\pi\)
−0.894859 + 0.446349i \(0.852724\pi\)
\(338\) −0.375258 + 6.44292i −0.0204113 + 0.350449i
\(339\) 28.4193 + 9.98271i 1.54353 + 0.542186i
\(340\) 1.70311 5.68879i 0.0923642 0.308518i
\(341\) −15.2298 + 5.54319i −0.824740 + 0.300181i
\(342\) 6.66060 0.150085i 0.360164 0.00811568i
\(343\) −15.1621 5.51854i −0.818675 0.297973i
\(344\) 8.31358 11.1671i 0.448238 0.602089i
\(345\) −3.75074 12.0333i −0.201933 0.647851i
\(346\) −19.5103 4.62402i −1.04888 0.248589i
\(347\) −13.3067 + 30.8484i −0.714341 + 1.65603i 0.0397080 + 0.999211i \(0.487357\pi\)
−0.754049 + 0.656818i \(0.771902\pi\)
\(348\) 8.45242 + 4.12640i 0.453097 + 0.221198i
\(349\) 27.5190 18.0995i 1.47306 0.968844i 0.477115 0.878841i \(-0.341683\pi\)
0.995941 0.0900033i \(-0.0286878\pi\)
\(350\) −1.94157 3.36289i −0.103781 0.179754i
\(351\) 14.7671 + 18.4964i 0.788208 + 0.987267i
\(352\) −6.27342 + 10.8659i −0.334374 + 0.579154i
\(353\) −0.775734 13.3188i −0.0412881 0.708890i −0.953911 0.300088i \(-0.902984\pi\)
0.912623 0.408802i \(-0.134053\pi\)
\(354\) 4.34361 15.1268i 0.230860 0.803979i
\(355\) 8.68696 1.01536i 0.461056 0.0538897i
\(356\) 2.98664 3.16565i 0.158291 0.167779i
\(357\) 3.31129 7.92059i 0.175252 0.419202i
\(358\) 5.24493 + 0.613045i 0.277203 + 0.0324004i
\(359\) 6.91454 5.80199i 0.364936 0.306217i −0.441819 0.897104i \(-0.645667\pi\)
0.806754 + 0.590887i \(0.201222\pi\)
\(360\) −2.64229 + 9.60861i −0.139261 + 0.506418i
\(361\) −9.11037 7.64450i −0.479493 0.402342i
\(362\) −3.54060 3.75281i −0.186090 0.197243i
\(363\) −8.40593 6.89356i −0.441197 0.361818i
\(364\) 6.99048 3.51075i 0.366401 0.184013i
\(365\) 8.75244 4.39564i 0.458124 0.230078i
\(366\) 13.1569 + 10.7898i 0.687723 + 0.563989i
\(367\) −17.5705 18.6236i −0.917171 0.972145i 0.0825298 0.996589i \(-0.473700\pi\)
−0.999701 + 0.0244437i \(0.992219\pi\)
\(368\) −1.46997 1.23345i −0.0766274 0.0642980i
\(369\) −4.60412 + 16.7427i −0.239681 + 0.871593i
\(370\) −7.51364 + 6.30469i −0.390616 + 0.327765i
\(371\) 16.2725 + 1.90198i 0.844825 + 0.0987459i
\(372\) −6.50683 + 15.5643i −0.337364 + 0.806972i
\(373\) 15.0065 15.9060i 0.777008 0.823580i −0.211080 0.977469i \(-0.567698\pi\)
0.988088 + 0.153888i \(0.0491796\pi\)
\(374\) 6.77834 0.792274i 0.350500 0.0409675i
\(375\) −4.92702 + 17.1585i −0.254430 + 0.886064i
\(376\) −0.480066 8.24241i −0.0247575 0.425070i
\(377\) 9.46934 16.4014i 0.487696 0.844714i
\(378\) −2.07641 + 5.29918i −0.106799 + 0.272560i
\(379\) −5.26717 9.12300i −0.270556 0.468617i 0.698448 0.715661i \(-0.253874\pi\)
−0.969004 + 0.247043i \(0.920541\pi\)
\(380\) −3.50887 + 2.30782i −0.180001 + 0.118389i
\(381\) 8.84365 + 4.31740i 0.453074 + 0.221187i
\(382\) 2.22797 5.16500i 0.113993 0.264265i
\(383\) 21.2791 + 5.04324i 1.08731 + 0.257698i 0.734919 0.678154i \(-0.237220\pi\)
0.352393 + 0.935852i \(0.385368\pi\)
\(384\) 4.15937 + 13.3443i 0.212257 + 0.680972i
\(385\) 2.05835 2.76484i 0.104903 0.140909i
\(386\) 12.4552 + 4.53331i 0.633952 + 0.230740i
\(387\) −15.1615 + 0.341639i −0.770704 + 0.0173665i
\(388\) 1.67315 0.608977i 0.0849414 0.0309161i
\(389\) −6.99531 + 23.3660i −0.354676 + 1.18470i 0.575566 + 0.817755i \(0.304782\pi\)
−0.930242 + 0.366946i \(0.880403\pi\)
\(390\) 7.47883 + 2.62705i 0.378706 + 0.133026i
\(391\) −1.32236 + 22.7040i −0.0668746 + 1.14819i
\(392\) −12.1284 7.97698i −0.612577 0.402898i
\(393\) 17.2322 + 29.0854i 0.869250 + 1.46717i
\(394\) −9.39625 + 2.22695i −0.473376 + 0.112192i
\(395\) 2.40854 13.6595i 0.121187 0.687285i
\(396\) 8.43388 1.17893i 0.423818 0.0592433i
\(397\) 4.16728 + 23.6338i 0.209150 + 1.18615i 0.890775 + 0.454445i \(0.150163\pi\)
−0.681625 + 0.731702i \(0.738726\pi\)
\(398\) 1.41868 + 3.28887i 0.0711119 + 0.164856i
\(399\) −5.39474 + 2.78587i −0.270075 + 0.139468i
\(400\) 0.323387 + 1.08019i 0.0161694 + 0.0540094i
\(401\) −22.0434 29.6094i −1.10079 1.47862i −0.861558 0.507660i \(-0.830511\pi\)
−0.239235 0.970962i \(-0.576897\pi\)
\(402\) 1.19109 + 0.125635i 0.0594061 + 0.00626610i
\(403\) 30.3540 + 15.2444i 1.51204 + 0.759376i
\(404\) −3.02339 −0.150419
\(405\) 10.0231 4.16847i 0.498053 0.207133i
\(406\) 4.55416 0.226019
\(407\) 18.9599 + 9.52203i 0.939808 + 0.471989i
\(408\) 10.5743 14.5429i 0.523504 0.719980i
\(409\) −1.70501 2.29023i −0.0843075 0.113245i 0.757968 0.652291i \(-0.226192\pi\)
−0.842276 + 0.539047i \(0.818785\pi\)
\(410\) 1.66791 + 5.57121i 0.0823723 + 0.275143i
\(411\) −23.1113 14.8303i −1.14000 0.731525i
\(412\) −2.35356 5.45616i −0.115952 0.268806i
\(413\) 2.49058 + 14.1248i 0.122553 + 0.695035i
\(414\) 0.537370 15.0679i 0.0264103 0.740546i
\(415\) 1.00007 5.67169i 0.0490916 0.278412i
\(416\) 25.5868 6.06418i 1.25450 0.297321i
\(417\) −18.0801 + 0.203677i −0.885388 + 0.00997409i
\(418\) −4.03253 2.65224i −0.197238 0.129725i
\(419\) −1.99872 + 34.3166i −0.0976437 + 1.67648i 0.493372 + 0.869818i \(0.335764\pi\)
−0.591016 + 0.806660i \(0.701273\pi\)
\(420\) −0.662775 3.52604i −0.0323401 0.172053i
\(421\) −1.79299 + 5.98899i −0.0873849 + 0.291886i −0.990500 0.137513i \(-0.956089\pi\)
0.903115 + 0.429398i \(0.141274\pi\)
\(422\) −11.1790 + 4.06883i −0.544186 + 0.198067i
\(423\) −6.75769 + 5.93486i −0.328570 + 0.288563i
\(424\) 32.2449 + 11.7362i 1.56595 + 0.569960i
\(425\) 7.98018 10.7192i 0.387096 0.519960i
\(426\) 10.2067 + 2.29793i 0.494518 + 0.111335i
\(427\) −15.0887 3.57610i −0.730196 0.173060i
\(428\) 6.35952 14.7430i 0.307399 0.712631i
\(429\) −1.18975 17.1053i −0.0574416 0.825853i
\(430\) −4.24352 + 2.79101i −0.204641 + 0.134594i
\(431\) −1.50862 2.61301i −0.0726679 0.125864i 0.827402 0.561610i \(-0.189818\pi\)
−0.900070 + 0.435746i \(0.856485\pi\)
\(432\) 0.941540 1.35822i 0.0452999 0.0653472i
\(433\) −15.3659 + 26.6146i −0.738439 + 1.27901i 0.214759 + 0.976667i \(0.431104\pi\)
−0.953198 + 0.302347i \(0.902230\pi\)
\(434\) 0.474927 + 8.15418i 0.0227972 + 0.391413i
\(435\) −6.03161 6.25055i −0.289194 0.299691i
\(436\) −11.5541 + 1.35048i −0.553341 + 0.0646763i
\(437\) 11.0378 11.6994i 0.528011 0.559659i
\(438\) 11.6207 1.49114i 0.555260 0.0712495i
\(439\) −0.454536 0.0531276i −0.0216938 0.00253564i 0.105239 0.994447i \(-0.466439\pi\)
−0.126933 + 0.991911i \(0.540513\pi\)
\(440\) 5.53042 4.64057i 0.263652 0.221231i
\(441\) 1.27485 + 15.7617i 0.0607071 + 0.750556i
\(442\) −10.9565 9.19361i −0.521148 0.437296i
\(443\) 23.9557 + 25.3916i 1.13817 + 1.20639i 0.975568 + 0.219698i \(0.0705072\pi\)
0.162602 + 0.986692i \(0.448011\pi\)
\(444\) 20.6657 7.78643i 0.980750 0.369527i
\(445\) −3.59165 + 1.80379i −0.170260 + 0.0855080i
\(446\) −15.0297 + 7.54822i −0.711679 + 0.357419i
\(447\) −0.820704 + 4.98198i −0.0388180 + 0.235640i
\(448\) 3.76531 + 3.99100i 0.177894 + 0.188557i
\(449\) −5.48196 4.59991i −0.258710 0.217083i 0.504202 0.863586i \(-0.331787\pi\)
−0.762912 + 0.646502i \(0.776231\pi\)
\(450\) −5.12913 + 7.22385i −0.241790 + 0.340535i
\(451\) 9.63661 8.08607i 0.453770 0.380758i
\(452\) −22.5603 2.63692i −1.06115 0.124030i
\(453\) −13.3965 17.5777i −0.629421 0.825871i
\(454\) −1.55685 + 1.65016i −0.0730665 + 0.0774459i
\(455\) −7.17515 + 0.838655i −0.336376 + 0.0393167i
\(456\) −12.3402 + 3.07190i −0.577883 + 0.143855i
\(457\) 0.737417 + 12.6610i 0.0344949 + 0.592255i 0.970625 + 0.240599i \(0.0773440\pi\)
−0.936130 + 0.351655i \(0.885619\pi\)
\(458\) −0.635820 + 1.10127i −0.0297099 + 0.0514591i
\(459\) −19.5757 + 0.661797i −0.913715 + 0.0308900i
\(460\) 4.75227 + 8.23117i 0.221576 + 0.383780i
\(461\) −0.385841 + 0.253772i −0.0179704 + 0.0118193i −0.558462 0.829530i \(-0.688608\pi\)
0.540492 + 0.841349i \(0.318238\pi\)
\(462\) 3.41917 2.30442i 0.159074 0.107211i
\(463\) 14.6949 34.0667i 0.682931 1.58321i −0.123809 0.992306i \(-0.539511\pi\)
0.806740 0.590906i \(-0.201230\pi\)
\(464\) −1.28676 0.304968i −0.0597363 0.0141578i
\(465\) 10.5626 11.4514i 0.489827 0.531045i
\(466\) −3.24700 + 4.36148i −0.150414 + 0.202042i
\(467\) −25.8480 9.40792i −1.19611 0.435347i −0.334242 0.942487i \(-0.608480\pi\)
−0.861863 + 0.507141i \(0.830702\pi\)
\(468\) −13.9270 11.1613i −0.643775 0.515930i
\(469\) −1.02568 + 0.373316i −0.0473614 + 0.0172381i
\(470\) −0.863897 + 2.88562i −0.0398486 + 0.133104i
\(471\) −1.66987 + 1.43355i −0.0769437 + 0.0660546i
\(472\) −1.74669 + 29.9895i −0.0803980 + 1.38038i
\(473\) 9.17926 + 6.03729i 0.422063 + 0.277595i
\(474\) 8.13351 14.4614i 0.373584 0.664236i
\(475\) −9.19653 + 2.17962i −0.421966 + 0.100008i
\(476\) −1.12413 + 6.37527i −0.0515245 + 0.292210i
\(477\) −11.5245 35.5583i −0.527669 1.62810i
\(478\) −2.44425 13.8620i −0.111798 0.634035i
\(479\) −5.64829 13.0942i −0.258077 0.598290i 0.739082 0.673616i \(-0.235260\pi\)
−0.997159 + 0.0753257i \(0.976000\pi\)
\(480\) 0.565582 12.0472i 0.0258152 0.549875i
\(481\) −12.7529 42.5978i −0.581484 1.94229i
\(482\) −6.26722 8.41834i −0.285464 0.383445i
\(483\) 5.58417 + 12.5548i 0.254088 + 0.571262i
\(484\) 7.32563 + 3.67907i 0.332983 + 0.167230i
\(485\) −1.64429 −0.0746634
\(486\) 12.9648 0.730998i 0.588095 0.0331587i
\(487\) 9.07752 0.411342 0.205671 0.978621i \(-0.434062\pi\)
0.205671 + 0.978621i \(0.434062\pi\)
\(488\) −29.0238 14.5763i −1.31385 0.659839i
\(489\) 8.70275 + 19.5662i 0.393552 + 0.884815i
\(490\) 3.16258 + 4.24808i 0.142871 + 0.191909i
\(491\) 7.99691 + 26.7115i 0.360896 + 1.20548i 0.925063 + 0.379815i \(0.124012\pi\)
−0.564167 + 0.825661i \(0.690803\pi\)
\(492\) 0.614047 13.0795i 0.0276834 0.589669i
\(493\) 6.20771 + 14.3911i 0.279581 + 0.648142i
\(494\) 1.75653 + 9.96180i 0.0790302 + 0.448203i
\(495\) −7.69121 1.64078i −0.345694 0.0737476i
\(496\) 0.411853 2.33573i 0.0184927 0.104878i
\(497\) −9.27760 + 2.19883i −0.416157 + 0.0986310i
\(498\) 3.37719 6.00467i 0.151335 0.269075i
\(499\) 19.8773 + 13.0735i 0.889828 + 0.585249i 0.910028 0.414547i \(-0.136060\pi\)
−0.0202000 + 0.999796i \(0.506430\pi\)
\(500\) 0.782724 13.4389i 0.0350045 0.601004i
\(501\) 5.01177 4.30250i 0.223909 0.192222i
\(502\) 6.16444 20.5907i 0.275133 0.919007i
\(503\) 7.57016 2.75531i 0.337537 0.122853i −0.167690 0.985840i \(-0.553631\pi\)
0.505227 + 0.862986i \(0.331409\pi\)
\(504\) 1.64497 10.7385i 0.0732728 0.478329i
\(505\) 2.62367 + 0.954939i 0.116752 + 0.0424942i
\(506\) −6.52276 + 8.76159i −0.289972 + 0.389500i
\(507\) −9.09830 + 9.86390i −0.404070 + 0.438071i
\(508\) −7.22097 1.71140i −0.320379 0.0759311i
\(509\) −7.64624 + 17.7260i −0.338914 + 0.785690i 0.660479 + 0.750844i \(0.270353\pi\)
−0.999393 + 0.0348457i \(0.988906\pi\)
\(510\) −5.43977 + 3.66624i −0.240877 + 0.162344i
\(511\) −8.92069 + 5.86723i −0.394628 + 0.259551i
\(512\) −1.79397 3.10725i −0.0792832 0.137323i
\(513\) 10.9065 + 8.54068i 0.481536 + 0.377080i
\(514\) −6.02780 + 10.4405i −0.265875 + 0.460509i
\(515\) 0.319068 + 5.47818i 0.0140598 + 0.241398i
\(516\) 11.0971 2.76245i 0.488524 0.121610i
\(517\) 6.47161 0.756422i 0.284621 0.0332674i
\(518\) 7.33773 7.77754i 0.322401 0.341725i
\(519\) −25.2711 33.1585i −1.10928 1.45550i
\(520\) −15.0282 1.75654i −0.659029 0.0770294i
\(521\) 2.04454 1.71557i 0.0895727 0.0751604i −0.596902 0.802314i \(-0.703602\pi\)
0.686474 + 0.727154i \(0.259157\pi\)
\(522\) −4.32937 9.44564i −0.189491 0.413424i
\(523\) 11.7693 + 9.87562i 0.514636 + 0.431831i 0.862757 0.505619i \(-0.168736\pi\)
−0.348121 + 0.937450i \(0.613180\pi\)
\(524\) −17.4943 18.5429i −0.764241 0.810048i
\(525\) 1.31239 7.96668i 0.0572773 0.347694i
\(526\) −7.78248 + 3.90851i −0.339332 + 0.170419i
\(527\) −25.1198 + 12.6156i −1.09423 + 0.549545i
\(528\) −1.12039 + 0.422140i −0.0487586 + 0.0183713i
\(529\) −9.19617 9.74738i −0.399834 0.423799i
\(530\) −9.58997 8.04694i −0.416562 0.349537i
\(531\) 26.9281 18.5932i 1.16858 0.806877i
\(532\) 3.50727 2.94295i 0.152059 0.127593i
\(533\) −26.1862 3.06073i −1.13425 0.132575i
\(534\) −4.76867 + 0.611904i −0.206361 + 0.0264797i
\(535\) −10.1753 + 10.7852i −0.439917 + 0.466285i
\(536\) −2.27067 + 0.265403i −0.0980780 + 0.0114637i
\(537\) 7.62430 + 7.90105i 0.329013 + 0.340956i
\(538\) 0.0102077 + 0.175259i 0.000440083 + 0.00755594i
\(539\) 5.72799 9.92117i 0.246722 0.427335i
\(540\) −6.68320 + 4.72664i −0.287599 + 0.203402i
\(541\) 9.39421 + 16.2713i 0.403889 + 0.699556i 0.994191 0.107626i \(-0.0343250\pi\)
−0.590303 + 0.807182i \(0.700992\pi\)
\(542\) 7.94586 5.22607i 0.341304 0.224479i
\(543\) −0.744362 10.7019i −0.0319436 0.459262i
\(544\) −8.61917 + 19.9815i −0.369544 + 0.856699i
\(545\) 10.4531 + 2.47743i 0.447761 + 0.106121i
\(546\) −8.43044 1.89801i −0.360790 0.0812274i
\(547\) −6.84395 + 9.19302i −0.292626 + 0.393065i −0.923987 0.382424i \(-0.875089\pi\)
0.631361 + 0.775489i \(0.282497\pi\)
\(548\) 19.4583 + 7.08223i 0.831216 + 0.302538i
\(549\) 6.92692 + 34.6947i 0.295634 + 1.48073i
\(550\) 6.03132 2.19522i 0.257176 0.0936045i
\(551\) 3.17908 10.6189i 0.135433 0.452378i
\(552\) 5.31644 + 28.2841i 0.226283 + 1.20385i
\(553\) −0.879191 + 15.0951i −0.0373870 + 0.641910i
\(554\) 7.75969 + 5.10363i 0.329678 + 0.216832i
\(555\) −20.3929 + 0.229730i −0.865628 + 0.00975149i
\(556\) 13.2671 3.14435i 0.562649 0.133350i
\(557\) 4.33665 24.5943i 0.183750 1.04210i −0.743802 0.668400i \(-0.766979\pi\)
0.927551 0.373695i \(-0.121909\pi\)
\(558\) 16.4608 8.73673i 0.696843 0.369855i
\(559\) −3.99840 22.6761i −0.169114 0.959095i
\(560\) 0.199791 + 0.463167i 0.00844269 + 0.0195724i
\(561\) 11.9426 + 7.66343i 0.504215 + 0.323550i
\(562\) 5.18511 + 17.3195i 0.218721 + 0.730579i
\(563\) −10.4988 14.1023i −0.442471 0.594341i 0.523809 0.851836i \(-0.324511\pi\)
−0.966280 + 0.257494i \(0.917103\pi\)
\(564\) 3.98839 5.48527i 0.167942 0.230972i
\(565\) 18.7447 + 9.41396i 0.788597 + 0.396048i
\(566\) −0.247007 −0.0103825
\(567\) −10.3253 + 5.78207i −0.433623 + 0.242824i
\(568\) −19.9700 −0.837922
\(569\) 14.2884 + 7.17589i 0.599000 + 0.300829i 0.722343 0.691535i \(-0.243065\pi\)
−0.123343 + 0.992364i \(0.539362\pi\)
\(570\) 4.61385 + 0.486665i 0.193253 + 0.0203841i
\(571\) 6.16873 + 8.28604i 0.258153 + 0.346760i 0.912238 0.409662i \(-0.134353\pi\)
−0.654084 + 0.756422i \(0.726946\pi\)
\(572\) 3.70831 + 12.3866i 0.155052 + 0.517911i
\(573\) 10.3921 5.36653i 0.434135 0.224190i
\(574\) −2.51108 5.82133i −0.104810 0.242978i
\(575\) 3.71420 + 21.0643i 0.154893 + 0.878441i
\(576\) 4.69814 11.6035i 0.195756 0.483480i
\(577\) 6.79785 38.5525i 0.282998 1.60496i −0.429351 0.903138i \(-0.641258\pi\)
0.712349 0.701825i \(-0.247631\pi\)
\(578\) −2.26219 + 0.536148i −0.0940946 + 0.0223008i
\(579\) 14.0478 + 23.7106i 0.583806 + 0.985379i
\(580\) 5.47245 + 3.59929i 0.227231 + 0.149452i
\(581\) −0.365057 + 6.26778i −0.0151451 + 0.260031i
\(582\) −1.85577 0.651866i −0.0769241 0.0270207i
\(583\) −7.76656 + 25.9421i −0.321658 + 1.07441i
\(584\) −21.0145 + 7.64866i −0.869587 + 0.316504i
\(585\) 8.56042 + 14.0845i 0.353930 + 0.582322i
\(586\) 11.3554 + 4.13304i 0.469088 + 0.170734i
\(587\) −10.6305 + 14.2792i −0.438766 + 0.589365i −0.965415 0.260718i \(-0.916041\pi\)
0.526649 + 0.850083i \(0.323448\pi\)
\(588\) −3.54837 11.3841i −0.146333 0.469471i
\(589\) 19.3445 + 4.58473i 0.797076 + 0.188910i
\(590\) 4.34086 10.0632i 0.178710 0.414297i
\(591\) −18.0432 8.80852i −0.742196 0.362334i
\(592\) −2.59407 + 1.70614i −0.106615 + 0.0701221i
\(593\) 6.92687 + 11.9977i 0.284452 + 0.492686i 0.972476 0.233002i \(-0.0748549\pi\)
−0.688024 + 0.725688i \(0.741522\pi\)
\(594\) −8.02992 4.90092i −0.329472 0.201087i
\(595\) 2.98914 5.17735i 0.122543 0.212251i
\(596\) −0.221381 3.80096i −0.00906811 0.155693i
\(597\) −2.05546 + 7.15823i −0.0841245 + 0.292967i
\(598\) 22.7376 2.65764i 0.929809 0.108679i
\(599\) −2.48356 + 2.63242i −0.101475 + 0.107558i −0.776121 0.630585i \(-0.782815\pi\)
0.674645 + 0.738142i \(0.264297\pi\)
\(600\) 6.52273 15.6023i 0.266289 0.636962i
\(601\) 10.3128 + 1.20539i 0.420667 + 0.0491689i 0.323794 0.946128i \(-0.395042\pi\)
0.0968736 + 0.995297i \(0.469116\pi\)
\(602\) 4.24159 3.55912i 0.172874 0.145059i
\(603\) 1.74934 + 1.77244i 0.0712385 + 0.0721792i
\(604\) 12.7665 + 10.7124i 0.519462 + 0.435880i
\(605\) −5.19508 5.50647i −0.211210 0.223870i
\(606\) 2.58253 + 2.11789i 0.104908 + 0.0860334i
\(607\) 12.0040 6.02866i 0.487229 0.244696i −0.188186 0.982133i \(-0.560261\pi\)
0.675415 + 0.737438i \(0.263964\pi\)
\(608\) 13.7534 6.90721i 0.557773 0.280124i
\(609\) 7.32200 + 6.00464i 0.296702 + 0.243320i
\(610\) 8.13131 + 8.61869i 0.329227 + 0.348960i
\(611\) −10.4607 8.77758i −0.423195 0.355103i
\(612\) 14.2914 3.72907i 0.577696 0.150739i
\(613\) 22.2652 18.6827i 0.899281 0.754587i −0.0707686 0.997493i \(-0.522545\pi\)
0.970050 + 0.242906i \(0.0781007\pi\)
\(614\) −3.13496 0.366425i −0.126517 0.0147877i
\(615\) −4.66402 + 11.1563i −0.188072 + 0.449866i
\(616\) −5.40094 + 5.72466i −0.217610 + 0.230653i
\(617\) −12.3463 + 1.44308i −0.497044 + 0.0580961i −0.360922 0.932596i \(-0.617538\pi\)
−0.136122 + 0.990692i \(0.543464\pi\)
\(618\) −1.81168 + 6.30924i −0.0728763 + 0.253795i
\(619\) −2.00980 34.5070i −0.0807807 1.38695i −0.758520 0.651650i \(-0.774077\pi\)
0.677739 0.735302i \(-0.262960\pi\)
\(620\) −5.87380 + 10.1737i −0.235898 + 0.408586i
\(621\) 20.7309 23.5170i 0.831903 0.943706i
\(622\) −5.13533 8.89464i −0.205908 0.356643i
\(623\) 3.66069 2.40767i 0.146662 0.0964614i
\(624\) 2.25489 + 1.10082i 0.0902677 + 0.0440679i
\(625\) 2.09699 4.86137i 0.0838796 0.194455i
\(626\) 5.51652 + 1.30744i 0.220484 + 0.0522558i
\(627\) −2.98638 9.58105i −0.119265 0.382630i
\(628\) 0.991023 1.33118i 0.0395461 0.0531197i
\(629\) 34.5789 + 12.5857i 1.37875 + 0.501825i
\(630\) −1.90387 + 3.47616i −0.0758519 + 0.138494i
\(631\) 12.4258 4.52262i 0.494663 0.180042i −0.0826292 0.996580i \(-0.526332\pi\)
0.577292 + 0.816538i \(0.304109\pi\)
\(632\) −9.08304 + 30.3395i −0.361304 + 1.20684i
\(633\) −23.3379 8.19779i −0.927599 0.325833i
\(634\) 0.723456 12.4213i 0.0287321 0.493311i
\(635\) 5.72575 + 3.76588i 0.227219 + 0.149445i
\(636\) 14.3674 + 24.2500i 0.569704 + 0.961576i
\(637\) −23.3622 + 5.53695i −0.925645 + 0.219382i
\(638\) −1.30714 + 7.41317i −0.0517502 + 0.293490i
\(639\) 13.3802 + 17.1521i 0.529312 + 0.678525i
\(640\) 1.69021 + 9.58567i 0.0668115 + 0.378907i
\(641\) −2.08848 4.84165i −0.0824901 0.191234i 0.871979 0.489543i \(-0.162836\pi\)
−0.954469 + 0.298310i \(0.903577\pi\)
\(642\) −15.7597 + 8.13840i −0.621986 + 0.321197i
\(643\) −1.25523 4.19275i −0.0495013 0.165346i 0.929665 0.368406i \(-0.120096\pi\)
−0.979166 + 0.203060i \(0.934911\pi\)
\(644\) −6.18741 8.31114i −0.243818 0.327505i
\(645\) −10.5025 1.10780i −0.413536 0.0436194i
\(646\) −7.48075 3.75697i −0.294326 0.147816i
\(647\) 5.42624 0.213327 0.106664 0.994295i \(-0.465983\pi\)
0.106664 + 0.994295i \(0.465983\pi\)
\(648\) −23.8361 + 6.79664i −0.936369 + 0.266997i
\(649\) −23.7069 −0.930576
\(650\) −12.0208 6.03709i −0.471496 0.236794i
\(651\) −9.98769 + 13.7362i −0.391449 + 0.538363i
\(652\) −9.64289 12.9527i −0.377645 0.507265i
\(653\) −3.18380 10.6346i −0.124592 0.416166i 0.872822 0.488039i \(-0.162288\pi\)
−0.997414 + 0.0718731i \(0.977102\pi\)
\(654\) 10.8153 + 6.94010i 0.422913 + 0.271379i
\(655\) 9.32462 + 21.6169i 0.364343 + 0.844642i
\(656\) 0.319672 + 1.81295i 0.0124811 + 0.0707837i
\(657\) 20.6494 + 12.9245i 0.805610 + 0.504232i
\(658\) 0.570212 3.23383i 0.0222292 0.126068i
\(659\) −7.23488 + 1.71470i −0.281831 + 0.0667951i −0.369100 0.929390i \(-0.620334\pi\)
0.0872694 + 0.996185i \(0.472186\pi\)
\(660\) 5.92985 0.0668011i 0.230819 0.00260023i
\(661\) 3.20127 + 2.10551i 0.124515 + 0.0818948i 0.610239 0.792218i \(-0.291074\pi\)
−0.485724 + 0.874112i \(0.661444\pi\)
\(662\) 0.178911 3.07178i 0.00695358 0.119388i
\(663\) −5.49372 29.2273i −0.213358 1.13509i
\(664\) −3.77145 + 12.5975i −0.146361 + 0.488879i
\(665\) −3.97311 + 1.44609i −0.154071 + 0.0560771i
\(666\) −23.1067 7.82530i −0.895366 0.303224i
\(667\) −23.5726 8.57971i −0.912733 0.332208i
\(668\) −2.97435 + 3.99524i −0.115081 + 0.154581i
\(669\) −34.1166 7.68093i −1.31902 0.296962i
\(670\) 0.811561 + 0.192344i 0.0313533 + 0.00743088i
\(671\) 10.1519 23.5347i 0.391910 0.908549i
\(672\) 0.912276 + 13.1160i 0.0351918 + 0.505962i
\(673\) −35.1668 + 23.1295i −1.35558 + 0.891578i −0.999087 0.0427202i \(-0.986398\pi\)
−0.356492 + 0.934298i \(0.616027\pi\)
\(674\) −7.68230 13.3061i −0.295911 0.512533i
\(675\) −17.7710 + 4.85147i −0.684008 + 0.186733i
\(676\) 5.05953 8.76336i 0.194597 0.337052i
\(677\) 0.144919 + 2.48817i 0.00556970 + 0.0956281i 0.999947 0.0102640i \(-0.00326720\pi\)
−0.994378 + 0.105892i \(0.966230\pi\)
\(678\) 17.4235 + 18.0559i 0.669144 + 0.693433i
\(679\) 1.78041 0.208100i 0.0683260 0.00798616i
\(680\) 8.59269 9.10772i 0.329515 0.349265i
\(681\) −4.67877 + 0.600368i −0.179291 + 0.0230061i
\(682\) −13.4095 1.56735i −0.513477 0.0600169i
\(683\) −11.7411 + 9.85194i −0.449260 + 0.376974i −0.839161 0.543883i \(-0.816954\pi\)
0.389901 + 0.920857i \(0.372509\pi\)
\(684\) −9.43803 4.47663i −0.360872 0.171168i
\(685\) −14.6488 12.2918i −0.559701 0.469645i
\(686\) −9.22362 9.77646i −0.352159 0.373267i
\(687\) −2.47427 + 0.932257i −0.0943993 + 0.0355678i
\(688\) −1.43678 + 0.721578i −0.0547767 + 0.0275099i
\(689\) 50.7168 25.4710i 1.93216 0.970366i
\(690\) 1.70663 10.3599i 0.0649705 0.394395i
\(691\) −25.4658 26.9922i −0.968765 1.02683i −0.999627 0.0273073i \(-0.991307\pi\)
0.0308620 0.999524i \(-0.490175\pi\)
\(692\) 24.0827 + 20.2078i 0.915488 + 0.768186i
\(693\) 8.53558 + 0.803216i 0.324240 + 0.0305116i
\(694\) −21.4384 + 17.9890i −0.813792 + 0.682853i
\(695\) −12.5062 1.46176i −0.474387 0.0554478i
\(696\) 12.0220 + 15.7742i 0.455693 + 0.597921i
\(697\) 14.9725 15.8700i 0.567125 0.601118i
\(698\) 27.2519 3.18529i 1.03150 0.120565i
\(699\) −10.9710 + 2.73105i −0.414961 + 0.103298i
\(700\) 0.354010 + 6.07811i 0.0133803 + 0.229731i
\(701\) −3.35489 + 5.81083i −0.126712 + 0.219472i −0.922401 0.386234i \(-0.873776\pi\)
0.795689 + 0.605706i \(0.207109\pi\)
\(702\) 4.07772 + 19.2896i 0.153904 + 0.728040i
\(703\) −13.0126 22.5385i −0.490779 0.850054i
\(704\) −7.57719 + 4.98360i −0.285576 + 0.187826i
\(705\) −5.19361 + 3.50034i −0.195603 + 0.131830i
\(706\) 4.40186 10.2046i 0.165666 0.384057i
\(707\) −2.96173 0.701942i −0.111387 0.0263993i
\(708\) −16.7304 + 18.1382i −0.628766 + 0.681675i
\(709\) −14.2011 + 19.0753i −0.533332 + 0.716389i −0.984369 0.176116i \(-0.943647\pi\)
0.451037 + 0.892505i \(0.351054\pi\)
\(710\) 6.84623 + 2.49182i 0.256934 + 0.0935165i
\(711\) 32.1441 12.5265i 1.20550 0.469782i
\(712\) 8.62351 3.13870i 0.323180 0.117628i
\(713\) 12.9037 43.1012i 0.483246 1.61415i
\(714\) 5.42610 4.65820i 0.203067 0.174329i
\(715\) 0.694277 11.9203i 0.0259645 0.445793i
\(716\) −6.91748 4.54970i −0.258519 0.170030i
\(717\) 14.3473 25.5096i 0.535809 0.952674i
\(718\) 7.31634 1.73400i 0.273043 0.0647125i
\(719\) −7.41202 + 42.0356i −0.276422 + 1.56766i 0.457988 + 0.888958i \(0.348570\pi\)
−0.734410 + 0.678706i \(0.762541\pi\)
\(720\) 0.770710 0.854684i 0.0287227 0.0318522i
\(721\) −1.03880 5.89131i −0.0386868 0.219404i
\(722\) −3.92388 9.09658i −0.146032 0.338540i
\(723\) 1.02336 21.7980i 0.0380591 0.810676i
\(724\) 2.32009 + 7.74965i 0.0862255 + 0.288013i
\(725\) 8.80228 + 11.8235i 0.326909 + 0.439114i
\(726\) −3.68024 8.27421i −0.136587 0.307085i
\(727\) 17.0289 + 8.55222i 0.631565 + 0.317184i 0.735627 0.677387i \(-0.236888\pi\)
−0.104062 + 0.994571i \(0.533184\pi\)
\(728\) 16.4946 0.611329
\(729\) 21.8081 + 15.9188i 0.807707 + 0.589584i
\(730\) 8.15871 0.301967
\(731\) 17.0284 + 8.55200i 0.629819 + 0.316307i
\(732\) −10.8421 24.3761i −0.400737 0.900968i
\(733\) −10.7269 14.4087i −0.396207 0.532199i 0.558595 0.829441i \(-0.311341\pi\)
−0.954802 + 0.297242i \(0.903933\pi\)
\(734\) −6.11705 20.4324i −0.225784 0.754173i
\(735\) −0.516409 + 10.9997i −0.0190480 + 0.405732i
\(736\) −13.7955 31.9816i −0.508509 1.17886i
\(737\) −0.313285 1.77673i −0.0115400 0.0654466i
\(738\) −9.68671 + 10.7421i −0.356573 + 0.395424i
\(739\) 2.16602 12.2841i 0.0796782 0.451878i −0.918700 0.394955i \(-0.870760\pi\)
0.998379 0.0569224i \(-0.0181288\pi\)
\(740\) 14.9641 3.54656i 0.550092 0.130374i
\(741\) −10.3105 + 18.3322i −0.378766 + 0.673450i
\(742\) 11.4023 + 7.49940i 0.418591 + 0.275312i
\(743\) 1.50694 25.8731i 0.0552842 0.949193i −0.850639 0.525751i \(-0.823784\pi\)
0.905923 0.423443i \(-0.139179\pi\)
\(744\) −26.9899 + 23.1703i −0.989499 + 0.849465i
\(745\) −1.00842 + 3.36836i −0.0369457 + 0.123407i
\(746\) 17.1175 6.23026i 0.626716 0.228106i
\(747\) 13.3468 5.20126i 0.488335 0.190304i
\(748\) −10.0549 3.65968i −0.367643 0.133811i
\(749\) 9.65270 12.9658i 0.352702 0.473761i
\(750\) −10.0825 + 10.9310i −0.368162 + 0.399142i
\(751\) 10.2130 + 2.42053i 0.372679 + 0.0883265i 0.412687 0.910873i \(-0.364590\pi\)
−0.0400083 + 0.999199i \(0.512738\pi\)
\(752\) −0.377663 + 0.875522i −0.0137720 + 0.0319270i
\(753\) 37.0597 24.9771i 1.35053 0.910216i
\(754\) 13.1808 8.66914i 0.480016 0.315711i
\(755\) −7.69516 13.3284i −0.280056 0.485070i
\(756\) 6.63826 5.96375i 0.241431 0.216900i
\(757\) −0.0864170 + 0.149679i −0.00314088 + 0.00544016i −0.867592 0.497277i \(-0.834333\pi\)
0.864451 + 0.502718i \(0.167666\pi\)
\(758\) −0.510234 8.76039i −0.0185326 0.318192i
\(759\) −22.0392 + 5.48630i −0.799971 + 0.199140i
\(760\) −8.79576 + 1.02808i −0.319056 + 0.0372923i
\(761\) −1.28543 + 1.36248i −0.0465968 + 0.0493897i −0.750253 0.661151i \(-0.770068\pi\)
0.703656 + 0.710541i \(0.251550\pi\)
\(762\) 4.96920 + 6.52015i 0.180015 + 0.236200i
\(763\) −11.6320 1.35958i −0.421106 0.0492203i
\(764\) −6.75618 + 5.66911i −0.244430 + 0.205101i
\(765\) −13.5798 1.27789i −0.490978 0.0462021i
\(766\) 13.9549 + 11.7095i 0.504211 + 0.423083i
\(767\) 34.0957 + 36.1394i 1.23113 + 1.30492i
\(768\) −4.24217 + 25.7515i −0.153076 + 0.929228i
\(769\) −24.9413 + 12.5260i −0.899405 + 0.451698i −0.837534 0.546386i \(-0.816003\pi\)
−0.0618716 + 0.998084i \(0.519707\pi\)
\(770\) 2.56590 1.28864i 0.0924685 0.0464394i
\(771\) −23.4570 + 8.83812i −0.844782 + 0.318297i
\(772\) −14.2614 15.1162i −0.513280 0.544045i
\(773\) 0.0418155 + 0.0350873i 0.00150400 + 0.00126200i 0.643539 0.765413i \(-0.277465\pi\)
−0.642035 + 0.766675i \(0.721910\pi\)
\(774\) −11.4141 5.41390i −0.410271 0.194599i
\(775\) −20.2520 + 16.9934i −0.727472 + 0.610422i
\(776\) 3.72903 + 0.435861i 0.133864 + 0.0156465i
\(777\) 22.0520 2.82965i 0.791110 0.101513i
\(778\) −13.9429 + 14.7786i −0.499875 + 0.529837i
\(779\) −15.3264 + 1.79140i −0.549125 + 0.0641835i
\(780\) −8.63028 8.94355i −0.309014 0.320230i
\(781\) −0.916342 15.7330i −0.0327893 0.562971i
\(782\) −9.47240 + 16.4067i −0.338732 + 0.586702i
\(783\) 5.49344 20.8946i 0.196320 0.746712i
\(784\) 0.838235 + 1.45187i 0.0299370 + 0.0518524i
\(785\) −1.28045 + 0.842167i −0.0457013 + 0.0300582i
\(786\) 1.95404 + 28.0938i 0.0696983 + 1.00207i
\(787\) −13.4349 + 31.1455i −0.478901 + 1.11022i 0.491970 + 0.870612i \(0.336277\pi\)
−0.970871 + 0.239604i \(0.922982\pi\)
\(788\) 14.7325 + 3.49167i 0.524824 + 0.124385i
\(789\) −17.6657 3.97723i −0.628917 0.141593i
\(790\) 6.89962 9.26779i 0.245477 0.329733i
\(791\) −21.4879 7.82097i −0.764023 0.278082i
\(792\) 17.0077 + 5.75982i 0.604342 + 0.204666i
\(793\) −50.4776 + 18.3724i −1.79251 + 0.652422i
\(794\) −5.73347 + 19.1511i −0.203473 + 0.679648i
\(795\) −4.80852 25.5819i −0.170541 0.907297i
\(796\) 0.326538 5.60645i 0.0115738 0.198715i
\(797\) −12.1670 8.00239i −0.430979 0.283459i 0.315428 0.948950i \(-0.397852\pi\)
−0.746406 + 0.665491i \(0.768222\pi\)
\(798\) −5.05739 + 0.0569726i −0.179030 + 0.00201681i
\(799\) 10.9961 2.60613i 0.389015 0.0921982i
\(800\) −3.55394 + 20.1554i −0.125651 + 0.712600i
\(801\) −8.47368 5.30369i −0.299403 0.187397i
\(802\) −5.33961 30.2825i −0.188548 1.06931i
\(803\) −6.99013 16.2049i −0.246676 0.571860i
\(804\) −1.58047 1.01417i −0.0557389 0.0357672i
\(805\) 2.74431 + 9.16663i 0.0967242 + 0.323081i
\(806\) 16.8966 + 22.6960i 0.595156 + 0.799433i
\(807\) −0.214666 + 0.295233i −0.00755662 + 0.0103927i
\(808\) −5.69700 2.86114i −0.200420 0.100655i
\(809\) 28.0189 0.985092 0.492546 0.870286i \(-0.336066\pi\)
0.492546 + 0.870286i \(0.336066\pi\)
\(810\) 9.01970 + 0.644163i 0.316920 + 0.0226336i
\(811\) 29.1924 1.02508 0.512542 0.858662i \(-0.328704\pi\)
0.512542 + 0.858662i \(0.328704\pi\)
\(812\) −6.38100 3.20466i −0.223929 0.112462i
\(813\) 19.6656 + 2.07431i 0.689703 + 0.0727493i
\(814\) 10.5540 + 14.1765i 0.369919 + 0.496887i
\(815\) 4.27692 + 14.2859i 0.149814 + 0.500413i
\(816\) −1.84506 + 0.952798i −0.0645900 + 0.0333546i
\(817\) −5.33785 12.3745i −0.186748 0.432930i
\(818\) −0.413009 2.34229i −0.0144405 0.0818964i
\(819\) −11.0516 14.1671i −0.386174 0.495037i
\(820\) 1.58337 8.97971i 0.0552935 0.313585i
\(821\) −29.0511 + 6.88525i −1.01389 + 0.240297i −0.703791 0.710407i \(-0.748511\pi\)
−0.310101 + 0.950704i \(0.600363\pi\)
\(822\) −11.6598 19.6801i −0.406683 0.686421i
\(823\) 33.5799 + 22.0858i 1.17052 + 0.769864i 0.977418 0.211315i \(-0.0677745\pi\)
0.193103 + 0.981178i \(0.438145\pi\)
\(824\) 0.728528 12.5084i 0.0253795 0.435749i
\(825\) 12.5913 + 4.42288i 0.438373 + 0.153985i
\(826\) −3.42662 + 11.4457i −0.119227 + 0.398247i
\(827\) 39.9498 14.5405i 1.38919 0.505623i 0.464238 0.885710i \(-0.346328\pi\)
0.924951 + 0.380087i \(0.124106\pi\)
\(828\) −11.3559 + 20.7340i −0.394643 + 0.720557i
\(829\) 5.90599 + 2.14960i 0.205124 + 0.0746589i 0.442539 0.896749i \(-0.354078\pi\)
−0.237415 + 0.971408i \(0.576300\pi\)
\(830\) 2.86485 3.84816i 0.0994404 0.133572i
\(831\) 5.74661 + 18.4365i 0.199348 + 0.639557i
\(832\) 18.4948 + 4.38335i 0.641192 + 0.151965i
\(833\) 7.86979 18.2442i 0.272672 0.632125i
\(834\) −13.5351 6.60774i −0.468683 0.228807i
\(835\) 3.84301 2.52759i 0.132993 0.0874708i
\(836\) 3.78381 + 6.55375i 0.130866 + 0.226666i
\(837\) 37.9845 + 7.65699i 1.31293 + 0.264664i
\(838\) −14.3173 + 24.7983i −0.494584 + 0.856644i
\(839\) −0.963006 16.5342i −0.0332466 0.570823i −0.973263 0.229694i \(-0.926228\pi\)
0.940016 0.341129i \(-0.110809\pi\)
\(840\) 2.08795 7.27136i 0.0720410 0.250886i
\(841\) 11.6333 1.35974i 0.401149 0.0468876i
\(842\) −3.57373 + 3.78793i −0.123159 + 0.130541i
\(843\) −14.4993 + 34.6822i −0.499381 + 1.19452i
\(844\) 18.5265 + 2.16543i 0.637707 + 0.0745373i
\(845\) −7.15852 + 6.00671i −0.246261 + 0.206637i
\(846\) −7.24926 + 1.89156i −0.249235 + 0.0650330i
\(847\) 6.32205 + 5.30483i 0.217228 + 0.182276i
\(848\) −2.71947 2.88247i −0.0933871 0.0989846i
\(849\) −0.397128 0.325677i −0.0136294 0.0111772i
\(850\) 9.94795 4.99605i 0.341212 0.171363i
\(851\) −52.6328 + 26.4332i −1.80423 + 0.906118i
\(852\) −12.6840 10.4020i −0.434548 0.356365i
\(853\) 35.7674 + 37.9112i 1.22465 + 1.29806i 0.940709 + 0.339214i \(0.110161\pi\)
0.283943 + 0.958841i \(0.408357\pi\)
\(854\) −9.89523 8.30308i −0.338608 0.284126i
\(855\) 6.77630 + 6.86578i 0.231745 + 0.234805i
\(856\) 25.9351 21.7622i 0.886445 0.743815i
\(857\) 38.6194 + 4.51396i 1.31921 + 0.154194i 0.746404 0.665493i \(-0.231779\pi\)
0.572811 + 0.819687i \(0.305853\pi\)
\(858\) 5.50926 13.1781i 0.188083 0.449894i
\(859\) 14.8940 15.7867i 0.508177 0.538637i −0.421589 0.906787i \(-0.638527\pi\)
0.929766 + 0.368151i \(0.120009\pi\)
\(860\) 7.90973 0.924515i 0.269720 0.0315257i
\(861\) 3.63819 12.6702i 0.123989 0.431798i
\(862\) −0.146142 2.50915i −0.00497760 0.0854621i
\(863\) −21.9404 + 38.0020i −0.746861 + 1.29360i 0.202459 + 0.979291i \(0.435107\pi\)
−0.949320 + 0.314311i \(0.898227\pi\)
\(864\) 26.3363 14.3608i 0.895980 0.488564i
\(865\) −14.5161 25.1427i −0.493564 0.854877i
\(866\) −21.3885 + 14.0674i −0.726811 + 0.478031i
\(867\) −4.34397 2.12069i −0.147529 0.0720223i
\(868\) 5.07248 11.7593i 0.172171 0.399138i
\(869\) −24.3192 5.76375i −0.824972 0.195522i
\(870\) −2.15317 6.90791i −0.0729994 0.234200i
\(871\) −2.25792 + 3.03291i −0.0765066 + 0.102766i
\(872\) −23.0495 8.38933i −0.780554 0.284099i
\(873\) −2.12415 3.49487i −0.0718915 0.118283i
\(874\) 12.5905 4.58258i 0.425881 0.155008i
\(875\) 3.88687 12.9830i 0.131400 0.438907i
\(876\) −17.3315 6.08795i −0.585578 0.205693i
\(877\) 1.46065 25.0784i 0.0493226 0.846837i −0.879405 0.476074i \(-0.842059\pi\)
0.928728 0.370763i \(-0.120904\pi\)
\(878\) −0.318498 0.209479i −0.0107488 0.00706958i
\(879\) 12.8074 + 21.6170i 0.431983 + 0.729124i
\(880\) −0.811277 + 0.192276i −0.0273481 + 0.00648163i
\(881\) 0.463850 2.63063i 0.0156275 0.0886281i −0.975996 0.217786i \(-0.930116\pi\)
0.991624 + 0.129158i \(0.0412275\pi\)
\(882\) −4.94358 + 12.2097i −0.166459 + 0.411123i
\(883\) 6.82642 + 38.7145i 0.229727 + 1.30285i 0.853439 + 0.521193i \(0.174513\pi\)
−0.623711 + 0.781655i \(0.714376\pi\)
\(884\) 8.88225 + 20.5914i 0.298742 + 0.692563i
\(885\) 20.2474 10.4559i 0.680610 0.351471i
\(886\) 8.34003 + 27.8576i 0.280189 + 0.935895i
\(887\) 19.9569 + 26.8067i 0.670086 + 0.900081i 0.999020 0.0442716i \(-0.0140967\pi\)
−0.328934 + 0.944353i \(0.606689\pi\)
\(888\) 46.3091 + 4.88465i 1.55403 + 0.163918i
\(889\) −6.67635 3.35299i −0.223918 0.112456i
\(890\) −3.34800 −0.112225
\(891\) −6.44835 18.4669i −0.216028 0.618666i
\(892\) 26.3703 0.882942
\(893\) −7.14223 3.58696i −0.239006 0.120033i
\(894\) −2.47348 + 3.40180i −0.0827254 + 0.113773i
\(895\) 4.56591 + 6.13308i 0.152621 + 0.205006i
\(896\) −3.04329 10.1653i −0.101669 0.339599i
\(897\) 40.0607 + 25.7066i 1.33759 + 0.858317i
\(898\) −2.36111 5.47367i −0.0787912 0.182659i
\(899\) −5.38405 30.5345i −0.179568 1.01838i
\(900\) 12.2699 6.51235i 0.408996 0.217078i
\(901\) −8.15573 + 46.2534i −0.271707 + 1.54093i
\(902\) 10.1966 2.41663i 0.339509 0.0804651i
\(903\) 11.5121 0.129687i 0.383100 0.00431571i
\(904\) −40.0151 26.3184i −1.33088 0.875336i
\(905\) 0.434372 7.45788i 0.0144390 0.247908i
\(906\) −3.40092 18.0933i −0.112988 0.601109i
\(907\) 3.52864 11.7865i 0.117167 0.391364i −0.879208 0.476438i \(-0.841928\pi\)
0.996375 + 0.0850742i \(0.0271127\pi\)
\(908\) 3.34254 1.21658i 0.110926 0.0403738i
\(909\) 1.35966 + 6.81012i 0.0450972 + 0.225877i
\(910\) −5.65477 2.05817i −0.187454 0.0682276i
\(911\) −13.0498 + 17.5289i −0.432359 + 0.580759i −0.963897 0.266276i \(-0.914207\pi\)
0.531538 + 0.847034i \(0.321614\pi\)
\(912\) 1.43276 + 0.322569i 0.0474435 + 0.0106813i
\(913\) −10.0978 2.39322i −0.334188 0.0792040i
\(914\) −4.18443 + 9.70059i −0.138409 + 0.320867i
\(915\) 1.70950 + 24.5779i 0.0565142 + 0.812520i
\(916\) 1.66581 1.09562i 0.0550400 0.0362004i
\(917\) −12.8324 22.2263i −0.423762 0.733977i
\(918\) −14.8197 6.82583i −0.489123 0.225286i
\(919\) 27.9349 48.3846i 0.921487 1.59606i 0.124370 0.992236i \(-0.460309\pi\)
0.797116 0.603826i \(-0.206358\pi\)
\(920\) 1.16529 + 20.0073i 0.0384186 + 0.659622i
\(921\) −4.55714 4.72256i −0.150163 0.155614i
\(922\) −0.382097 + 0.0446607i −0.0125837 + 0.00147082i
\(923\) −22.6659 + 24.0244i −0.746056 + 0.790774i
\(924\) −6.41230 + 0.822809i −0.210949 + 0.0270684i
\(925\) 34.3744 + 4.01780i 1.13022 + 0.132104i
\(926\) 23.6750 19.8657i 0.778009 0.652827i
\(927\) −11.2314 + 7.75505i −0.368889 + 0.254709i
\(928\) −18.3873 15.4288i −0.603594 0.506476i
\(929\) −29.4428 31.2075i −0.965986 1.02389i −0.999701 0.0244537i \(-0.992215\pi\)
0.0337151 0.999431i \(-0.489266\pi\)
\(930\) 12.1440 4.57562i 0.398218 0.150041i
\(931\) −12.5576 + 6.30668i −0.411560 + 0.206693i
\(932\) 7.61857 3.82619i 0.249554 0.125331i
\(933\) 3.47118 21.0714i 0.113641 0.689846i
\(934\) −15.7243 16.6668i −0.514514 0.545353i
\(935\) 7.56964 + 6.35168i 0.247554 + 0.207722i
\(936\) −15.6804 34.2109i −0.512531 1.11822i
\(937\) −10.4519 + 8.77015i −0.341447 + 0.286508i −0.797345 0.603524i \(-0.793763\pi\)
0.455898 + 0.890032i \(0.349318\pi\)
\(938\) −0.903088 0.105556i −0.0294869 0.00344652i
\(939\) 7.14539 + 9.37556i 0.233181 + 0.305960i
\(940\) 3.24098 3.43524i 0.105709 0.112045i
\(941\) −44.1544 + 5.16091i −1.43939 + 0.168241i −0.799704 0.600395i \(-0.795010\pi\)
−0.639687 + 0.768635i \(0.720936\pi\)
\(942\) −1.77901 + 0.442855i −0.0579631 + 0.0144290i
\(943\) 2.03049 + 34.8622i 0.0661219 + 1.13527i
\(944\) 1.73463 3.00447i 0.0564575 0.0977873i
\(945\) −7.64427 + 3.07860i −0.248668 + 0.100147i
\(946\) 4.57603 + 7.92592i 0.148780 + 0.257694i
\(947\) 3.62204 2.38225i 0.117700 0.0774128i −0.489294 0.872119i \(-0.662745\pi\)
0.606994 + 0.794706i \(0.292375\pi\)
\(948\) −21.5724 + 14.5391i −0.700638 + 0.472208i
\(949\) −14.6499 + 33.9622i −0.475555 + 1.10246i
\(950\) −7.66082 1.81565i −0.248550 0.0589074i
\(951\) 17.5405 19.0165i 0.568791 0.616653i
\(952\) −8.15136 + 10.9492i −0.264187 + 0.354865i
\(953\) −34.6339 12.6057i −1.12190 0.408339i −0.286556 0.958063i \(-0.592511\pi\)
−0.835346 + 0.549724i \(0.814733\pi\)
\(954\) 4.71478 30.7784i 0.152647 0.996486i
\(955\) 7.65355 2.78566i 0.247663 0.0901419i
\(956\) −6.32968 + 21.1426i −0.204716 + 0.683801i
\(957\) −11.8758 + 10.1951i −0.383890 + 0.329562i
\(958\) 0.690712 11.8591i 0.0223159 0.383149i
\(959\) 17.4171 + 11.4554i 0.562428 + 0.369915i
\(960\) 4.27347 7.59827i 0.137926 0.245233i
\(961\) 23.9459 5.67527i 0.772447 0.183073i
\(962\) 6.43203 36.4778i 0.207377 1.17609i
\(963\) −36.0683 7.69451i −1.16228 0.247952i
\(964\) 2.85744 + 16.2054i 0.0920320 + 0.521939i
\(965\) 7.60147 + 17.6222i 0.244700 + 0.567279i
\(966\) −0.536774 + 11.4335i −0.0172704 + 0.367868i
\(967\) 2.93507 + 9.80383i 0.0943856 + 0.315270i 0.992124 0.125259i \(-0.0399761\pi\)
−0.897738 + 0.440529i \(0.854791\pi\)
\(968\) 10.3221 + 13.8650i 0.331765 + 0.445638i
\(969\) −7.07370 15.9037i −0.227240 0.510899i
\(970\) −1.22402 0.614727i −0.0393010 0.0197377i
\(971\) −43.9486 −1.41038 −0.705188 0.709020i \(-0.749138\pi\)
−0.705188 + 0.709020i \(0.749138\pi\)
\(972\) −18.6798 8.09880i −0.599156 0.259769i
\(973\) 13.7265 0.440051
\(974\) 6.75737 + 3.39368i 0.216520 + 0.108740i
\(975\) −11.3667 25.5556i −0.364027 0.818435i
\(976\) 2.23984 + 3.00863i 0.0716957 + 0.0963040i
\(977\) −16.9236 56.5287i −0.541433 1.80851i −0.587045 0.809554i \(-0.699709\pi\)
0.0456115 0.998959i \(-0.485476\pi\)
\(978\) −0.836545 + 17.8188i −0.0267498 + 0.569782i
\(979\) 2.86847 + 6.64985i 0.0916766 + 0.212530i
\(980\) −1.44193 8.17758i −0.0460607 0.261223i
\(981\) 8.23798 + 25.4180i 0.263018 + 0.811535i
\(982\) −4.03329 + 22.8740i −0.128708 + 0.729937i
\(983\) −26.0666 + 6.17791i −0.831397 + 0.197045i −0.624210 0.781257i \(-0.714579\pi\)
−0.207187 + 0.978301i \(0.566431\pi\)
\(984\) 13.5346 24.0647i 0.431468 0.767155i
\(985\) −11.6819 7.68330i −0.372216 0.244810i
\(986\) −0.759122 + 13.0336i −0.0241754 + 0.415075i
\(987\) 5.18056 4.44741i 0.164899 0.141563i
\(988\) 4.54875 15.1939i 0.144715 0.483382i
\(989\) −28.6598 + 10.4313i −0.911329 + 0.331697i
\(990\) −5.11198 4.09681i −0.162469 0.130205i
\(991\) 8.60252 + 3.13106i 0.273268 + 0.0994614i 0.475019 0.879975i \(-0.342441\pi\)
−0.201751 + 0.979437i \(0.564663\pi\)
\(992\) 25.7076 34.5314i 0.816219 1.09637i
\(993\) 4.33778 4.70280i 0.137655 0.149239i
\(994\) −7.72835 1.83165i −0.245128 0.0580965i
\(995\) −2.05416 + 4.76209i −0.0651214 + 0.150968i
\(996\) −8.95725 + 6.03691i −0.283821 + 0.191287i
\(997\) −35.3642 + 23.2594i −1.12000 + 0.736633i −0.967801 0.251718i \(-0.919005\pi\)
−0.152195 + 0.988350i \(0.548634\pi\)
\(998\) 9.90918 + 17.1632i 0.313670 + 0.543292i
\(999\) −26.8324 43.0473i −0.848940 1.36196i
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 81.2.g.a.13.6 144
3.2 odd 2 243.2.g.a.10.3 144
9.2 odd 6 729.2.g.a.514.6 144
9.4 even 3 729.2.g.c.28.3 144
9.5 odd 6 729.2.g.b.28.6 144
9.7 even 3 729.2.g.d.514.3 144
81.2 odd 54 729.2.g.b.703.6 144
81.5 odd 54 6561.2.a.d.1.24 72
81.25 even 27 inner 81.2.g.a.25.6 yes 144
81.29 odd 54 729.2.g.a.217.6 144
81.52 even 27 729.2.g.d.217.3 144
81.56 odd 54 243.2.g.a.73.3 144
81.76 even 27 6561.2.a.c.1.49 72
81.79 even 27 729.2.g.c.703.3 144
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
81.2.g.a.13.6 144 1.1 even 1 trivial
81.2.g.a.25.6 yes 144 81.25 even 27 inner
243.2.g.a.10.3 144 3.2 odd 2
243.2.g.a.73.3 144 81.56 odd 54
729.2.g.a.217.6 144 81.29 odd 54
729.2.g.a.514.6 144 9.2 odd 6
729.2.g.b.28.6 144 9.5 odd 6
729.2.g.b.703.6 144 81.2 odd 54
729.2.g.c.28.3 144 9.4 even 3
729.2.g.c.703.3 144 81.79 even 27
729.2.g.d.217.3 144 81.52 even 27
729.2.g.d.514.3 144 9.7 even 3
6561.2.a.c.1.49 72 81.76 even 27
6561.2.a.d.1.24 72 81.5 odd 54