Properties

Label 81.2.g.a.7.1
Level $81$
Weight $2$
Character 81.7
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 7.1
Character \(\chi\) \(=\) 81.7
Dual form 81.2.g.a.58.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.45464 - 1.95391i) q^{2} +(-0.684440 + 1.59108i) q^{3} +(-1.12821 + 3.76849i) q^{4} +(-2.46571 + 1.62172i) q^{5} +(4.10445 - 0.977107i) q^{6} +(-1.57141 + 1.66559i) q^{7} +(4.42639 - 1.61107i) q^{8} +(-2.06308 - 2.17800i) q^{9} +O(q^{10})\) \(q+(-1.45464 - 1.95391i) q^{2} +(-0.684440 + 1.59108i) q^{3} +(-1.12821 + 3.76849i) q^{4} +(-2.46571 + 1.62172i) q^{5} +(4.10445 - 0.977107i) q^{6} +(-1.57141 + 1.66559i) q^{7} +(4.42639 - 1.61107i) q^{8} +(-2.06308 - 2.17800i) q^{9} +(6.75541 + 2.45877i) q^{10} +(2.11643 - 1.06291i) q^{11} +(-5.22378 - 4.37438i) q^{12} +(0.243103 + 0.563577i) q^{13} +(5.54025 + 0.647562i) q^{14} +(-0.892662 - 5.03311i) q^{15} +(-3.01348 - 1.98200i) q^{16} +(-5.54151 + 4.64988i) q^{17} +(-1.25459 + 7.19928i) q^{18} +(-3.45309 - 2.89749i) q^{19} +(-3.32960 - 11.1216i) q^{20} +(-1.57456 - 3.64024i) q^{21} +(-5.15546 - 2.58917i) q^{22} +(5.13927 + 5.44731i) q^{23} +(-0.466247 + 8.14542i) q^{24} +(1.46933 - 3.40630i) q^{25} +(0.747554 - 1.29480i) q^{26} +(4.87743 - 1.79182i) q^{27} +(-4.50389 - 7.80096i) q^{28} +(2.15715 - 0.252135i) q^{29} +(-8.53577 + 9.06553i) q^{30} +(3.02111 - 0.716016i) q^{31} +(-0.0369153 - 0.633812i) q^{32} +(0.242609 + 4.09491i) q^{33} +(17.1464 + 4.06376i) q^{34} +(1.17350 - 6.65525i) q^{35} +(10.5354 - 5.31746i) q^{36} +(0.740274 + 4.19830i) q^{37} +(-0.638454 + 10.9618i) q^{38} +(-1.06309 + 0.00106272i) q^{39} +(-8.30146 + 11.1508i) q^{40} +(-3.84487 + 5.16456i) q^{41} +(-4.82229 + 8.37177i) q^{42} +(0.236494 - 4.06045i) q^{43} +(1.61778 + 9.17491i) q^{44} +(8.61907 + 2.02457i) q^{45} +(3.16781 - 17.9655i) q^{46} +(-0.841921 - 0.199539i) q^{47} +(5.21607 - 3.43814i) q^{48} +(0.102130 + 1.75351i) q^{49} +(-8.79296 + 2.08397i) q^{50} +(-3.60551 - 11.9996i) q^{51} +(-2.39810 + 0.280298i) q^{52} +(-1.55323 - 2.69028i) q^{53} +(-10.5960 - 6.92364i) q^{54} +(-3.49475 + 6.05308i) q^{55} +(-4.27226 + 9.90421i) q^{56} +(6.97357 - 3.51099i) q^{57} +(-3.63052 - 3.84812i) q^{58} +(0.548384 + 0.275409i) q^{59} +(19.9743 + 2.31443i) q^{60} +(1.56794 + 5.23730i) q^{61} +(-5.79364 - 4.86144i) q^{62} +(6.86961 - 0.0137345i) q^{63} +(-6.71074 + 5.63098i) q^{64} +(-1.51339 - 0.995369i) q^{65} +(7.64819 - 6.43063i) q^{66} +(-0.280399 - 0.0327739i) q^{67} +(-11.2710 - 26.1292i) q^{68} +(-12.1846 + 4.44865i) q^{69} +(-14.7108 + 7.38804i) q^{70} +(7.71930 + 2.80960i) q^{71} +(-12.6409 - 6.31689i) q^{72} +(-14.3245 + 5.21369i) q^{73} +(7.12630 - 7.55343i) q^{74} +(4.41403 + 4.66924i) q^{75} +(14.8149 - 9.74394i) q^{76} +(-1.55539 + 5.19537i) q^{77} +(1.54848 + 2.07563i) q^{78} +(4.45162 + 5.97957i) q^{79} +10.6446 q^{80} +(-0.487373 + 8.98679i) q^{81} +15.6840 q^{82} +(-3.27078 - 4.39342i) q^{83} +(15.4946 - 1.82676i) q^{84} +(6.12294 - 20.4520i) q^{85} +(-8.27778 + 5.44438i) q^{86} +(-1.07527 + 3.60478i) q^{87} +(7.65569 - 8.11456i) q^{88} +(8.64084 - 3.14501i) q^{89} +(-8.58177 - 19.7859i) q^{90} +(-1.32070 - 0.480697i) q^{91} +(-26.3263 + 13.2216i) q^{92} +(-0.928528 + 5.29690i) q^{93} +(0.834806 + 1.93530i) q^{94} +(13.2132 + 1.54440i) q^{95} +(1.03371 + 0.375071i) q^{96} +(1.43000 + 0.940523i) q^{97} +(3.27764 - 2.75027i) q^{98} +(-6.68138 - 2.41671i) 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 \(\left(\mathbb{Z}/81\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{8}{27}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.45464 1.95391i −1.02858 1.38163i −0.921942 0.387328i \(-0.873398\pi\)
−0.106641 0.994298i \(-0.534009\pi\)
\(3\) −0.684440 + 1.59108i −0.395162 + 0.918612i
\(4\) −1.12821 + 3.76849i −0.564105 + 1.88424i
\(5\) −2.46571 + 1.62172i −1.10270 + 0.725256i −0.964218 0.265110i \(-0.914592\pi\)
−0.138480 + 0.990365i \(0.544222\pi\)
\(6\) 4.10445 0.977107i 1.67563 0.398902i
\(7\) −1.57141 + 1.66559i −0.593936 + 0.629535i −0.952707 0.303890i \(-0.901714\pi\)
0.358771 + 0.933426i \(0.383196\pi\)
\(8\) 4.42639 1.61107i 1.56496 0.569600i
\(9\) −2.06308 2.17800i −0.687695 0.726000i
\(10\) 6.75541 + 2.45877i 2.13625 + 0.777531i
\(11\) 2.11643 1.06291i 0.638127 0.320479i −0.100155 0.994972i \(-0.531934\pi\)
0.738282 + 0.674493i \(0.235638\pi\)
\(12\) −5.22378 4.37438i −1.50797 1.26277i
\(13\) 0.243103 + 0.563577i 0.0674247 + 0.156308i 0.948596 0.316488i \(-0.102504\pi\)
−0.881172 + 0.472796i \(0.843245\pi\)
\(14\) 5.54025 + 0.647562i 1.48069 + 0.173068i
\(15\) −0.892662 5.03311i −0.230484 1.29954i
\(16\) −3.01348 1.98200i −0.753371 0.495500i
\(17\) −5.54151 + 4.64988i −1.34401 + 1.12776i −0.363439 + 0.931618i \(0.618398\pi\)
−0.980575 + 0.196144i \(0.937158\pi\)
\(18\) −1.25459 + 7.19928i −0.295710 + 1.69689i
\(19\) −3.45309 2.89749i −0.792193 0.664729i 0.154094 0.988056i \(-0.450754\pi\)
−0.946287 + 0.323327i \(0.895199\pi\)
\(20\) −3.32960 11.1216i −0.744520 2.48687i
\(21\) −1.57456 3.64024i −0.343598 0.794365i
\(22\) −5.15546 2.58917i −1.09915 0.552013i
\(23\) 5.13927 + 5.44731i 1.07161 + 1.13584i 0.990270 + 0.139156i \(0.0444390\pi\)
0.0813417 + 0.996686i \(0.474079\pi\)
\(24\) −0.466247 + 8.14542i −0.0951723 + 1.66268i
\(25\) 1.46933 3.40630i 0.293867 0.681260i
\(26\) 0.747554 1.29480i 0.146607 0.253931i
\(27\) 4.87743 1.79182i 0.938663 0.344837i
\(28\) −4.50389 7.80096i −0.851155 1.47424i
\(29\) 2.15715 0.252135i 0.400573 0.0468203i 0.0865783 0.996245i \(-0.472407\pi\)
0.313995 + 0.949425i \(0.398333\pi\)
\(30\) −8.53577 + 9.06553i −1.55841 + 1.65513i
\(31\) 3.02111 0.716016i 0.542607 0.128600i 0.0498330 0.998758i \(-0.484131\pi\)
0.492774 + 0.870157i \(0.335983\pi\)
\(32\) −0.0369153 0.633812i −0.00652577 0.112043i
\(33\) 0.242609 + 4.09491i 0.0422328 + 0.712831i
\(34\) 17.1464 + 4.06376i 2.94057 + 0.696929i
\(35\) 1.17350 6.65525i 0.198358 1.12494i
\(36\) 10.5354 5.31746i 1.75589 0.886243i
\(37\) 0.740274 + 4.19830i 0.121700 + 0.690197i 0.983213 + 0.182461i \(0.0584063\pi\)
−0.861513 + 0.507736i \(0.830483\pi\)
\(38\) −0.638454 + 10.9618i −0.103571 + 1.77824i
\(39\) −1.06309 + 0.00106272i −0.170230 + 0.000170171i
\(40\) −8.30146 + 11.1508i −1.31258 + 1.76310i
\(41\) −3.84487 + 5.16456i −0.600468 + 0.806568i −0.993605 0.112912i \(-0.963982\pi\)
0.393137 + 0.919480i \(0.371390\pi\)
\(42\) −4.82229 + 8.37177i −0.744096 + 1.29179i
\(43\) 0.236494 4.06045i 0.0360650 0.619213i −0.931053 0.364884i \(-0.881109\pi\)
0.967118 0.254328i \(-0.0818544\pi\)
\(44\) 1.61778 + 9.17491i 0.243890 + 1.38317i
\(45\) 8.61907 + 2.02457i 1.28486 + 0.301804i
\(46\) 3.16781 17.9655i 0.467068 2.64887i
\(47\) −0.841921 0.199539i −0.122807 0.0291058i 0.168753 0.985658i \(-0.446026\pi\)
−0.291560 + 0.956553i \(0.594174\pi\)
\(48\) 5.21607 3.43814i 0.752875 0.496252i
\(49\) 0.102130 + 1.75351i 0.0145900 + 0.250501i
\(50\) −8.79296 + 2.08397i −1.24351 + 0.294718i
\(51\) −3.60551 11.9996i −0.504872 1.68028i
\(52\) −2.39810 + 0.280298i −0.332557 + 0.0388703i
\(53\) −1.55323 2.69028i −0.213353 0.369538i 0.739409 0.673257i \(-0.235105\pi\)
−0.952762 + 0.303718i \(0.901772\pi\)
\(54\) −10.5960 6.92364i −1.44193 0.942188i
\(55\) −3.49475 + 6.05308i −0.471231 + 0.816197i
\(56\) −4.27226 + 9.90421i −0.570905 + 1.32351i
\(57\) 6.97357 3.51099i 0.923672 0.465042i
\(58\) −3.63052 3.84812i −0.476710 0.505283i
\(59\) 0.548384 + 0.275409i 0.0713935 + 0.0358552i 0.484138 0.874992i \(-0.339133\pi\)
−0.412744 + 0.910847i \(0.635430\pi\)
\(60\) 19.9743 + 2.31443i 2.57867 + 0.298791i
\(61\) 1.56794 + 5.23730i 0.200755 + 0.670567i 0.997778 + 0.0666193i \(0.0212213\pi\)
−0.797024 + 0.603948i \(0.793594\pi\)
\(62\) −5.79364 4.86144i −0.735793 0.617404i
\(63\) 6.86961 0.0137345i 0.865489 0.00173038i
\(64\) −6.71074 + 5.63098i −0.838842 + 0.703872i
\(65\) −1.51339 0.995369i −0.187712 0.123460i
\(66\) 7.64819 6.43063i 0.941427 0.791556i
\(67\) −0.280399 0.0327739i −0.0342561 0.00400397i 0.0989476 0.995093i \(-0.468452\pi\)
−0.133204 + 0.991089i \(0.542526\pi\)
\(68\) −11.2710 26.1292i −1.36681 3.16863i
\(69\) −12.1846 + 4.44865i −1.46686 + 0.535554i
\(70\) −14.7108 + 7.38804i −1.75828 + 0.883040i
\(71\) 7.71930 + 2.80960i 0.916113 + 0.333438i 0.756691 0.653773i \(-0.226815\pi\)
0.159422 + 0.987211i \(0.449037\pi\)
\(72\) −12.6409 6.31689i −1.48975 0.744453i
\(73\) −14.3245 + 5.21369i −1.67656 + 0.610216i −0.992831 0.119525i \(-0.961863\pi\)
−0.683724 + 0.729741i \(0.739641\pi\)
\(74\) 7.12630 7.55343i 0.828415 0.878069i
\(75\) 4.41403 + 4.66924i 0.509688 + 0.539157i
\(76\) 14.8149 9.74394i 1.69939 1.11771i
\(77\) −1.55539 + 5.19537i −0.177253 + 0.592067i
\(78\) 1.54848 + 2.07563i 0.175331 + 0.235019i
\(79\) 4.45162 + 5.97957i 0.500847 + 0.672754i 0.978608 0.205736i \(-0.0659588\pi\)
−0.477761 + 0.878490i \(0.658551\pi\)
\(80\) 10.6446 1.19010
\(81\) −0.487373 + 8.98679i −0.0541525 + 0.998533i
\(82\) 15.6840 1.73201
\(83\) −3.27078 4.39342i −0.359015 0.482241i 0.585517 0.810660i \(-0.300891\pi\)
−0.944532 + 0.328419i \(0.893484\pi\)
\(84\) 15.4946 1.82676i 1.69060 0.199316i
\(85\) 6.12294 20.4520i 0.664126 2.21833i
\(86\) −8.27778 + 5.44438i −0.892616 + 0.587083i
\(87\) −1.07527 + 3.60478i −0.115281 + 0.386472i
\(88\) 7.65569 8.11456i 0.816100 0.865015i
\(89\) 8.64084 3.14501i 0.915927 0.333370i 0.159310 0.987229i \(-0.449073\pi\)
0.756617 + 0.653858i \(0.226851\pi\)
\(90\) −8.58177 19.7859i −0.904599 2.08562i
\(91\) −1.32070 0.480697i −0.138447 0.0503907i
\(92\) −26.3263 + 13.2216i −2.74471 + 1.37844i
\(93\) −0.928528 + 5.29690i −0.0962838 + 0.549263i
\(94\) 0.834806 + 1.93530i 0.0861037 + 0.199611i
\(95\) 13.2132 + 1.54440i 1.35565 + 0.158453i
\(96\) 1.03371 + 0.375071i 0.105503 + 0.0382805i
\(97\) 1.43000 + 0.940523i 0.145194 + 0.0954957i 0.620028 0.784580i \(-0.287121\pi\)
−0.474834 + 0.880076i \(0.657492\pi\)
\(98\) 3.27764 2.75027i 0.331092 0.277819i
\(99\) −6.68138 2.41671i −0.671504 0.242888i
\(100\) 11.1789 + 9.38019i 1.11789 + 0.938019i
\(101\) 2.43084 + 8.11958i 0.241878 + 0.807928i 0.989591 + 0.143907i \(0.0459665\pi\)
−0.747713 + 0.664022i \(0.768848\pi\)
\(102\) −18.2014 + 24.4998i −1.80221 + 2.42585i
\(103\) −1.62114 0.814165i −0.159735 0.0802221i 0.367135 0.930167i \(-0.380339\pi\)
−0.526871 + 0.849945i \(0.676635\pi\)
\(104\) 1.98403 + 2.10295i 0.194550 + 0.206211i
\(105\) 9.78586 + 6.42225i 0.955002 + 0.626748i
\(106\) −2.99719 + 6.94826i −0.291113 + 0.674875i
\(107\) 2.26668 3.92601i 0.219129 0.379542i −0.735413 0.677619i \(-0.763012\pi\)
0.954542 + 0.298077i \(0.0963452\pi\)
\(108\) 1.24969 + 20.4021i 0.120252 + 1.96319i
\(109\) −6.62630 11.4771i −0.634684 1.09931i −0.986582 0.163267i \(-0.947797\pi\)
0.351898 0.936039i \(-0.385537\pi\)
\(110\) 16.9108 1.97659i 1.61238 0.188460i
\(111\) −7.18652 1.69565i −0.682114 0.160944i
\(112\) 8.03661 1.90471i 0.759388 0.179978i
\(113\) 0.249581 + 4.28515i 0.0234786 + 0.403113i 0.989489 + 0.144609i \(0.0461924\pi\)
−0.966010 + 0.258504i \(0.916771\pi\)
\(114\) −17.0042 8.51854i −1.59259 0.797835i
\(115\) −21.5060 5.09701i −2.00544 0.475298i
\(116\) −1.48355 + 8.41365i −0.137745 + 0.781188i
\(117\) 0.725928 1.69218i 0.0671121 0.156442i
\(118\) −0.259574 1.47211i −0.0238957 0.135519i
\(119\) 0.963157 16.5368i 0.0882924 1.51592i
\(120\) −12.0600 20.8404i −1.10092 1.90246i
\(121\) −3.21926 + 4.32422i −0.292660 + 0.393111i
\(122\) 7.95244 10.6820i 0.719980 0.967101i
\(123\) −5.58565 9.65233i −0.503641 0.870322i
\(124\) −0.710151 + 12.1928i −0.0637734 + 1.09495i
\(125\) −0.661249 3.75013i −0.0591439 0.335422i
\(126\) −10.0196 13.4026i −0.892618 1.19400i
\(127\) −1.02230 + 5.79777i −0.0907147 + 0.514469i 0.905262 + 0.424854i \(0.139675\pi\)
−0.995977 + 0.0896144i \(0.971437\pi\)
\(128\) 19.5286 + 4.62836i 1.72610 + 0.409093i
\(129\) 6.29864 + 3.15542i 0.554564 + 0.277819i
\(130\) 0.256558 + 4.40492i 0.0225016 + 0.386337i
\(131\) −12.7074 + 3.01172i −1.11025 + 0.263135i −0.744530 0.667589i \(-0.767326\pi\)
−0.365723 + 0.930724i \(0.619178\pi\)
\(132\) −15.7053 3.70565i −1.36697 0.322535i
\(133\) 10.2522 1.19832i 0.888982 0.103907i
\(134\) 0.343840 + 0.595549i 0.0297033 + 0.0514476i
\(135\) −9.12049 + 12.3280i −0.784967 + 1.06102i
\(136\) −17.0376 + 29.5099i −1.46096 + 2.53046i
\(137\) 1.79314 4.15695i 0.153198 0.355153i −0.824283 0.566179i \(-0.808421\pi\)
0.977480 + 0.211026i \(0.0676805\pi\)
\(138\) 26.4165 + 17.3366i 2.24872 + 1.47579i
\(139\) 3.28896 + 3.48609i 0.278966 + 0.295686i 0.851673 0.524074i \(-0.175588\pi\)
−0.572707 + 0.819760i \(0.694107\pi\)
\(140\) 23.7563 + 11.9308i 2.00777 + 1.00834i
\(141\) 0.893728 1.20299i 0.0752654 0.101310i
\(142\) −5.73906 19.1698i −0.481611 1.60869i
\(143\) 1.11354 + 0.934372i 0.0931189 + 0.0781361i
\(144\) 1.90027 + 10.6524i 0.158356 + 0.887700i
\(145\) −4.91001 + 4.11999i −0.407754 + 0.342146i
\(146\) 31.0240 + 20.4048i 2.56757 + 1.68871i
\(147\) −2.85988 1.03767i −0.235879 0.0855859i
\(148\) −16.6564 1.94686i −1.36915 0.160031i
\(149\) −3.88776 9.01284i −0.318498 0.738360i −0.999979 0.00652473i \(-0.997923\pi\)
0.681481 0.731836i \(-0.261336\pi\)
\(150\) 2.70249 15.4167i 0.220657 1.25877i
\(151\) 11.9329 5.99293i 0.971087 0.487698i 0.108770 0.994067i \(-0.465309\pi\)
0.862317 + 0.506369i \(0.169013\pi\)
\(152\) −19.9528 7.26221i −1.61838 0.589043i
\(153\) 21.5601 + 2.47632i 1.74303 + 0.200199i
\(154\) 12.4138 4.51826i 1.00033 0.364092i
\(155\) −6.28799 + 6.66488i −0.505064 + 0.535336i
\(156\) 1.19538 4.00742i 0.0957070 0.320851i
\(157\) 2.50572 1.64804i 0.199978 0.131528i −0.445571 0.895247i \(-0.646999\pi\)
0.645549 + 0.763719i \(0.276629\pi\)
\(158\) 5.20808 17.3962i 0.414332 1.38397i
\(159\) 5.34355 0.629987i 0.423771 0.0499612i
\(160\) 1.11889 + 1.50293i 0.0884559 + 0.118817i
\(161\) −17.1489 −1.35152
\(162\) 18.2684 12.1202i 1.43530 0.952255i
\(163\) 17.7302 1.38874 0.694370 0.719618i \(-0.255683\pi\)
0.694370 + 0.719618i \(0.255683\pi\)
\(164\) −15.1247 20.3160i −1.18104 1.58642i
\(165\) −7.23900 9.70339i −0.563555 0.755408i
\(166\) −3.82657 + 12.7816i −0.297000 + 0.992048i
\(167\) 18.3735 12.0845i 1.42179 0.935123i 0.422196 0.906505i \(-0.361260\pi\)
0.999590 0.0286186i \(-0.00911083\pi\)
\(168\) −12.8343 13.5764i −0.990188 1.04744i
\(169\) 8.66262 9.18184i 0.666356 0.706296i
\(170\) −48.8682 + 17.7866i −3.74802 + 1.36417i
\(171\) 0.813286 + 13.4986i 0.0621935 + 1.03226i
\(172\) 15.0349 + 5.47227i 1.14640 + 0.417256i
\(173\) 9.67356 4.85824i 0.735467 0.369366i −0.0413055 0.999147i \(-0.513152\pi\)
0.776773 + 0.629781i \(0.216855\pi\)
\(174\) 8.60755 3.14264i 0.652537 0.238243i
\(175\) 3.36459 + 7.79999i 0.254339 + 0.589624i
\(176\) −8.48450 0.991696i −0.639543 0.0747519i
\(177\) −0.813534 + 0.684023i −0.0611490 + 0.0514143i
\(178\) −18.7143 12.3086i −1.40270 0.922570i
\(179\) −6.84973 + 5.74761i −0.511973 + 0.429596i −0.861823 0.507210i \(-0.830677\pi\)
0.349850 + 0.936806i \(0.386233\pi\)
\(180\) −17.3537 + 30.1967i −1.29347 + 2.25073i
\(181\) 3.31310 + 2.78002i 0.246261 + 0.206637i 0.757560 0.652765i \(-0.226391\pi\)
−0.511299 + 0.859403i \(0.670836\pi\)
\(182\) 0.981902 + 3.27978i 0.0727834 + 0.243113i
\(183\) −9.40613 1.08989i −0.695321 0.0805669i
\(184\) 31.5244 + 15.8322i 2.32401 + 1.16716i
\(185\) −8.63378 9.15127i −0.634768 0.672815i
\(186\) 11.7004 5.89079i 0.857912 0.431934i
\(187\) −6.78580 + 15.7313i −0.496227 + 1.15038i
\(188\) 1.70182 2.94765i 0.124118 0.214979i
\(189\) −4.67998 + 10.9395i −0.340419 + 0.795732i
\(190\) −16.2028 28.0640i −1.17547 2.03598i
\(191\) −21.0691 + 2.46263i −1.52451 + 0.178189i −0.836683 0.547688i \(-0.815508\pi\)
−0.687824 + 0.725877i \(0.741434\pi\)
\(192\) −4.36625 14.5314i −0.315107 1.04871i
\(193\) −17.6655 + 4.18680i −1.27159 + 0.301373i −0.810373 0.585914i \(-0.800736\pi\)
−0.461218 + 0.887287i \(0.652587\pi\)
\(194\) −0.242421 4.16221i −0.0174048 0.298829i
\(195\) 2.61954 1.72665i 0.187589 0.123648i
\(196\) −6.72329 1.59345i −0.480235 0.113818i
\(197\) 1.23957 7.02994i 0.0883155 0.500862i −0.908276 0.418371i \(-0.862601\pi\)
0.996592 0.0824914i \(-0.0262877\pi\)
\(198\) 4.99693 + 16.5703i 0.355117 + 1.17760i
\(199\) −0.634860 3.60047i −0.0450040 0.255231i 0.954002 0.299799i \(-0.0969197\pi\)
−0.999006 + 0.0445688i \(0.985809\pi\)
\(200\) 1.01604 17.4448i 0.0718451 1.23353i
\(201\) 0.244062 0.423705i 0.0172148 0.0298859i
\(202\) 12.3290 16.5607i 0.867463 1.16521i
\(203\) −2.96981 + 3.98914i −0.208440 + 0.279983i
\(204\) 49.2880 0.0492710i 3.45085 0.00344966i
\(205\) 1.10485 18.9696i 0.0771663 1.32489i
\(206\) 0.767353 + 4.35187i 0.0534640 + 0.303209i
\(207\) 1.26150 22.4316i 0.0876801 1.55910i
\(208\) 0.384421 2.18016i 0.0266548 0.151167i
\(209\) −10.3880 2.46199i −0.718551 0.170300i
\(210\) −1.68632 28.4628i −0.116367 1.96412i
\(211\) 1.03801 + 17.8219i 0.0714594 + 1.22691i 0.823316 + 0.567584i \(0.192122\pi\)
−0.751856 + 0.659327i \(0.770841\pi\)
\(212\) 11.8907 2.81814i 0.816654 0.193550i
\(213\) −9.75370 + 10.3590i −0.668312 + 0.709790i
\(214\) −10.9683 + 1.28201i −0.749777 + 0.0876364i
\(215\) 6.00179 + 10.3954i 0.409319 + 0.708961i
\(216\) 18.7026 15.7892i 1.27255 1.07432i
\(217\) −3.55480 + 6.15709i −0.241315 + 0.417970i
\(218\) −12.7864 + 29.6422i −0.866004 + 2.00762i
\(219\) 1.50885 26.3599i 0.101959 1.78124i
\(220\) −18.8681 19.9990i −1.27209 1.34834i
\(221\) −3.96772 1.99267i −0.266898 0.134041i
\(222\) 7.14061 + 16.5084i 0.479246 + 1.10797i
\(223\) 4.04573 + 13.5137i 0.270922 + 0.904942i 0.979862 + 0.199674i \(0.0639883\pi\)
−0.708940 + 0.705268i \(0.750827\pi\)
\(224\) 1.11368 + 0.934490i 0.0744110 + 0.0624383i
\(225\) −10.4503 + 3.82727i −0.696685 + 0.255151i
\(226\) 8.00976 6.72099i 0.532801 0.447073i
\(227\) 4.80660 + 3.16135i 0.319026 + 0.209826i 0.698914 0.715206i \(-0.253667\pi\)
−0.379888 + 0.925032i \(0.624038\pi\)
\(228\) 5.36347 + 30.2409i 0.355204 + 2.00275i
\(229\) 24.4091 + 2.85301i 1.61300 + 0.188532i 0.874258 0.485461i \(-0.161348\pi\)
0.738738 + 0.673993i \(0.235422\pi\)
\(230\) 21.3242 + 49.4351i 1.40608 + 3.25965i
\(231\) −7.20168 6.03067i −0.473836 0.396789i
\(232\) 9.14217 4.59137i 0.600213 0.301438i
\(233\) 11.9802 + 4.36045i 0.784852 + 0.285663i 0.703194 0.710998i \(-0.251756\pi\)
0.0816576 + 0.996660i \(0.473979\pi\)
\(234\) −4.36234 + 1.04311i −0.285175 + 0.0681903i
\(235\) 2.39953 0.873357i 0.156528 0.0569715i
\(236\) −1.65657 + 1.75586i −0.107833 + 0.114297i
\(237\) −12.5609 + 2.99024i −0.815915 + 0.194237i
\(238\) −33.7125 + 22.1730i −2.18525 + 1.43726i
\(239\) −6.98430 + 23.3292i −0.451777 + 1.50904i 0.364403 + 0.931241i \(0.381273\pi\)
−0.816180 + 0.577798i \(0.803912\pi\)
\(240\) −7.28560 + 16.9365i −0.470284 + 1.09324i
\(241\) −17.3603 23.3190i −1.11828 1.50211i −0.840776 0.541384i \(-0.817901\pi\)
−0.277503 0.960725i \(-0.589507\pi\)
\(242\) 13.1320 0.844157
\(243\) −13.9651 6.92637i −0.895865 0.444327i
\(244\) −21.5057 −1.37676
\(245\) −3.09552 4.15801i −0.197766 0.265646i
\(246\) −10.7347 + 24.9545i −0.684423 + 1.59104i
\(247\) 0.793498 2.65047i 0.0504891 0.168645i
\(248\) 12.2190 8.03658i 0.775909 0.510324i
\(249\) 9.22895 2.19705i 0.584861 0.139232i
\(250\) −6.36555 + 6.74709i −0.402593 + 0.426724i
\(251\) 22.4049 8.15471i 1.41418 0.514721i 0.481828 0.876266i \(-0.339973\pi\)
0.932355 + 0.361545i \(0.117751\pi\)
\(252\) −7.69860 + 25.9035i −0.484966 + 1.63177i
\(253\) 16.6669 + 6.06625i 1.04784 + 0.381382i
\(254\) 12.8154 6.43614i 0.804111 0.403839i
\(255\) 28.3501 + 23.7403i 1.77535 + 1.48667i
\(256\) −12.4240 28.8021i −0.776502 1.80013i
\(257\) −12.0552 1.40905i −0.751985 0.0878944i −0.268539 0.963269i \(-0.586541\pi\)
−0.483446 + 0.875374i \(0.660615\pi\)
\(258\) −2.99681 16.8970i −0.186573 1.05196i
\(259\) −8.15594 5.36425i −0.506786 0.333318i
\(260\) 5.45845 4.58018i 0.338519 0.284051i
\(261\) −4.99953 4.17810i −0.309463 0.258618i
\(262\) 24.3693 + 20.4483i 1.50554 + 1.26330i
\(263\) −2.29491 7.66554i −0.141510 0.472677i 0.857624 0.514277i \(-0.171940\pi\)
−0.999134 + 0.0415999i \(0.986755\pi\)
\(264\) 7.67107 + 17.7348i 0.472122 + 1.09150i
\(265\) 8.19270 + 4.11453i 0.503274 + 0.252754i
\(266\) −17.2547 18.2889i −1.05795 1.12136i
\(267\) −0.910171 + 15.9009i −0.0557015 + 0.973116i
\(268\) 0.439856 1.01970i 0.0268685 0.0622882i
\(269\) −11.2578 + 19.4990i −0.686397 + 1.18887i 0.286598 + 0.958051i \(0.407476\pi\)
−0.972995 + 0.230824i \(0.925858\pi\)
\(270\) 37.3547 0.112026i 2.27334 0.00681768i
\(271\) 15.1514 + 26.2430i 0.920381 + 1.59415i 0.798826 + 0.601562i \(0.205455\pi\)
0.121555 + 0.992585i \(0.461212\pi\)
\(272\) 25.9153 3.02907i 1.57135 0.183664i
\(273\) 1.66877 1.77234i 0.100999 0.107267i
\(274\) −10.7307 + 2.54322i −0.648265 + 0.153642i
\(275\) −0.510850 8.77095i −0.0308054 0.528908i
\(276\) −3.01782 50.9366i −0.181651 3.06603i
\(277\) −4.30449 1.02018i −0.258632 0.0612968i 0.0992544 0.995062i \(-0.468354\pi\)
−0.357886 + 0.933765i \(0.616502\pi\)
\(278\) 2.02729 11.4973i 0.121589 0.689564i
\(279\) −7.79228 5.10277i −0.466512 0.305495i
\(280\) −5.52773 31.3493i −0.330345 1.87348i
\(281\) −0.329570 + 5.65850i −0.0196605 + 0.337558i 0.974107 + 0.226087i \(0.0725933\pi\)
−0.993768 + 0.111471i \(0.964444\pi\)
\(282\) −3.65059 + 0.00364933i −0.217390 + 0.000217315i
\(283\) 17.2121 23.1199i 1.02315 1.37433i 0.0978106 0.995205i \(-0.468816\pi\)
0.925344 0.379130i \(-0.123777\pi\)
\(284\) −19.2969 + 25.9203i −1.14506 + 1.53808i
\(285\) −11.5009 + 19.9663i −0.681256 + 1.18270i
\(286\) 0.205886 3.53493i 0.0121743 0.209025i
\(287\) −2.56020 14.5196i −0.151124 0.857065i
\(288\) −1.30428 + 1.38801i −0.0768556 + 0.0817892i
\(289\) 6.13495 34.7930i 0.360879 2.04665i
\(290\) 15.1924 + 3.60066i 0.892127 + 0.211438i
\(291\) −2.47520 + 1.63151i −0.145099 + 0.0956408i
\(292\) −3.48667 59.8638i −0.204042 3.50326i
\(293\) 2.10652 0.499253i 0.123064 0.0291667i −0.168622 0.985681i \(-0.553932\pi\)
0.291686 + 0.956514i \(0.405784\pi\)
\(294\) 2.13255 + 7.09739i 0.124373 + 0.413928i
\(295\) −1.79879 + 0.210249i −0.104730 + 0.0122411i
\(296\) 10.0405 + 17.3907i 0.583593 + 1.01081i
\(297\) 8.41818 8.97653i 0.488473 0.520871i
\(298\) −11.9550 + 20.7067i −0.692537 + 1.19951i
\(299\) −1.82060 + 4.22063i −0.105288 + 0.244085i
\(300\) −22.5759 + 11.3663i −1.30342 + 0.656235i
\(301\) 6.39143 + 6.77452i 0.368396 + 0.390477i
\(302\) −29.0677 14.5984i −1.67266 0.840041i
\(303\) −14.5827 1.68970i −0.837753 0.0970705i
\(304\) 4.66301 + 15.5755i 0.267442 + 0.893318i
\(305\) −12.3595 10.3709i −0.707704 0.593835i
\(306\) −26.5235 45.7286i −1.51625 2.61413i
\(307\) 3.63465 3.04984i 0.207441 0.174063i −0.533148 0.846022i \(-0.678991\pi\)
0.740589 + 0.671959i \(0.234547\pi\)
\(308\) −17.8239 11.7229i −1.01561 0.667976i
\(309\) 2.40497 2.02211i 0.136814 0.115034i
\(310\) 22.1693 + 2.59122i 1.25913 + 0.147172i
\(311\) 9.34927 + 21.6740i 0.530149 + 1.22902i 0.947348 + 0.320207i \(0.103753\pi\)
−0.417199 + 0.908815i \(0.636988\pi\)
\(312\) −4.70392 + 1.71741i −0.266307 + 0.0972293i
\(313\) 21.1167 10.6052i 1.19359 0.599442i 0.262745 0.964865i \(-0.415372\pi\)
0.930841 + 0.365424i \(0.119076\pi\)
\(314\) −6.86503 2.49867i −0.387416 0.141008i
\(315\) −16.9162 + 11.1745i −0.953118 + 0.629609i
\(316\) −27.5563 + 10.0297i −1.55016 + 0.564213i
\(317\) −23.3831 + 24.7847i −1.31333 + 1.39205i −0.445418 + 0.895323i \(0.646945\pi\)
−0.867909 + 0.496723i \(0.834536\pi\)
\(318\) −9.00386 9.52444i −0.504911 0.534104i
\(319\) 4.29745 2.82648i 0.240611 0.158253i
\(320\) 7.41484 24.7673i 0.414502 1.38453i
\(321\) 4.69520 + 6.29360i 0.262060 + 0.351275i
\(322\) 24.9454 + 33.5075i 1.39015 + 1.86730i
\(323\) 32.6083 1.81437
\(324\) −33.3167 11.9757i −1.85093 0.665314i
\(325\) 2.27691 0.126300
\(326\) −25.7910 34.6434i −1.42843 1.91872i
\(327\) 22.7963 2.68761i 1.26064 0.148625i
\(328\) −8.69840 + 29.0547i −0.480289 + 1.60428i
\(329\) 1.65535 1.08874i 0.0912625 0.0600243i
\(330\) −8.42950 + 28.2593i −0.464029 + 1.55562i
\(331\) −17.7922 + 18.8586i −0.977947 + 1.03656i 0.0213759 + 0.999772i \(0.493195\pi\)
−0.999323 + 0.0367918i \(0.988286\pi\)
\(332\) 20.2467 7.36919i 1.11118 0.404437i
\(333\) 7.61666 10.2738i 0.417390 0.562999i
\(334\) −50.3388 18.3218i −2.75441 1.00252i
\(335\) 0.744531 0.373917i 0.0406781 0.0204293i
\(336\) −2.47003 + 14.0906i −0.134751 + 0.768703i
\(337\) 8.77373 + 20.3398i 0.477936 + 1.10798i 0.971236 + 0.238120i \(0.0765313\pi\)
−0.493300 + 0.869859i \(0.664209\pi\)
\(338\) −30.5415 3.56979i −1.66124 0.194171i
\(339\) −6.98884 2.53582i −0.379582 0.137727i
\(340\) 70.1652 + 46.1484i 3.80524 + 2.50275i
\(341\) 5.63289 4.72656i 0.305038 0.255957i
\(342\) 25.1920 21.2246i 1.36223 1.14770i
\(343\) −15.3601 12.8887i −0.829369 0.695923i
\(344\) −5.49486 18.3541i −0.296263 0.989588i
\(345\) 22.8293 30.7291i 1.22909 1.65440i
\(346\) −23.5641 11.8343i −1.26681 0.636218i
\(347\) −1.23071 1.30447i −0.0660678 0.0700277i 0.693497 0.720460i \(-0.256069\pi\)
−0.759564 + 0.650432i \(0.774588\pi\)
\(348\) −12.3714 8.11910i −0.663177 0.435229i
\(349\) 0.0696613 0.161493i 0.00372889 0.00864453i −0.916341 0.400398i \(-0.868872\pi\)
0.920070 + 0.391753i \(0.128131\pi\)
\(350\) 10.3463 17.9203i 0.553031 0.957878i
\(351\) 2.19555 + 2.31321i 0.117190 + 0.123470i
\(352\) −0.751813 1.30218i −0.0400718 0.0694064i
\(353\) 30.2081 3.53082i 1.60781 0.187927i 0.735727 0.677278i \(-0.236841\pi\)
0.872087 + 0.489351i \(0.162766\pi\)
\(354\) 2.51992 + 0.594572i 0.133932 + 0.0316011i
\(355\) −23.5899 + 5.59091i −1.25202 + 0.296735i
\(356\) 2.10323 + 36.1111i 0.111471 + 1.91388i
\(357\) 25.6521 + 12.8509i 1.35765 + 0.680141i
\(358\) 21.1942 + 5.02311i 1.12015 + 0.265480i
\(359\) −1.11991 + 6.35130i −0.0591064 + 0.335209i −0.999994 0.00351034i \(-0.998883\pi\)
0.940887 + 0.338719i \(0.109994\pi\)
\(360\) 41.4130 4.92444i 2.18266 0.259541i
\(361\) 0.229085 + 1.29920i 0.0120571 + 0.0683792i
\(362\) 0.612570 10.5174i 0.0321960 0.552783i
\(363\) −4.67679 8.08178i −0.245468 0.424183i
\(364\) 3.30153 4.43472i 0.173047 0.232443i
\(365\) 26.8649 36.0858i 1.40617 1.88882i
\(366\) 11.5529 + 19.9642i 0.603882 + 1.04354i
\(367\) −1.07014 + 18.3735i −0.0558607 + 0.959091i 0.847658 + 0.530543i \(0.178012\pi\)
−0.903519 + 0.428548i \(0.859025\pi\)
\(368\) −4.69054 26.6014i −0.244512 1.38669i
\(369\) 19.1807 2.28078i 0.998507 0.118733i
\(370\) −5.32180 + 30.1814i −0.276667 + 1.56906i
\(371\) 6.92167 + 1.64047i 0.359355 + 0.0851688i
\(372\) −18.9137 9.47516i −0.980631 0.491264i
\(373\) 1.87718 + 32.2299i 0.0971967 + 1.66880i 0.596680 + 0.802479i \(0.296486\pi\)
−0.499483 + 0.866324i \(0.666477\pi\)
\(374\) 40.6084 9.62437i 2.09981 0.497664i
\(375\) 6.41935 + 1.51464i 0.331494 + 0.0782155i
\(376\) −4.04814 + 0.473160i −0.208767 + 0.0244013i
\(377\) 0.666508 + 1.15442i 0.0343269 + 0.0594559i
\(378\) 28.1825 6.76871i 1.44955 0.348145i
\(379\) 11.0163 19.0808i 0.565870 0.980116i −0.431098 0.902305i \(-0.641874\pi\)
0.996968 0.0778111i \(-0.0247931\pi\)
\(380\) −20.7274 + 48.0514i −1.06329 + 2.46499i
\(381\) −8.52502 5.59479i −0.436750 0.286630i
\(382\) 35.4596 + 37.5850i 1.81427 + 1.92302i
\(383\) −12.7129 6.38463i −0.649596 0.326240i 0.0933078 0.995637i \(-0.470256\pi\)
−0.742904 + 0.669398i \(0.766552\pi\)
\(384\) −20.7302 + 27.9037i −1.05789 + 1.42396i
\(385\) −4.59030 15.3327i −0.233943 0.781425i
\(386\) 33.8775 + 28.4266i 1.72432 + 1.44688i
\(387\) −9.33157 + 7.86196i −0.474350 + 0.399646i
\(388\) −5.15768 + 4.32781i −0.261842 + 0.219711i
\(389\) −10.2482 6.74032i −0.519603 0.341748i 0.262465 0.964941i \(-0.415465\pi\)
−0.782068 + 0.623194i \(0.785835\pi\)
\(390\) −7.18419 2.60670i −0.363786 0.131996i
\(391\) −53.8087 6.28933i −2.72122 0.318065i
\(392\) 3.27710 + 7.59716i 0.165518 + 0.383715i
\(393\) 3.90559 22.2799i 0.197011 1.12387i
\(394\) −15.5390 + 7.80399i −0.782844 + 0.393159i
\(395\) −20.6736 7.52457i −1.04020 0.378602i
\(396\) 16.6453 22.4521i 0.836459 1.12826i
\(397\) −9.12859 + 3.32254i −0.458151 + 0.166753i −0.560777 0.827967i \(-0.689498\pi\)
0.102626 + 0.994720i \(0.467275\pi\)
\(398\) −6.11152 + 6.47783i −0.306343 + 0.324704i
\(399\) −5.11043 + 17.1323i −0.255841 + 0.857689i
\(400\) −11.1791 + 7.35260i −0.558955 + 0.367630i
\(401\) −0.335348 + 1.12014i −0.0167465 + 0.0559372i −0.965954 0.258712i \(-0.916702\pi\)
0.949208 + 0.314650i \(0.101887\pi\)
\(402\) −1.18290 + 0.139461i −0.0589979 + 0.00695566i
\(403\) 1.13797 + 1.52856i 0.0566864 + 0.0761430i
\(404\) −33.3410 −1.65878
\(405\) −13.3724 22.9492i −0.664478 1.14035i
\(406\) 12.1144 0.601229
\(407\) 6.02915 + 8.09856i 0.298854 + 0.401431i
\(408\) −35.2915 47.3060i −1.74719 2.34199i
\(409\) 7.87588 26.3073i 0.389437 1.30081i −0.508643 0.860978i \(-0.669853\pi\)
0.898080 0.439833i \(-0.144962\pi\)
\(410\) −38.6721 + 25.4351i −1.90988 + 1.25615i
\(411\) 5.38676 + 5.69821i 0.265709 + 0.281072i
\(412\) 4.89715 5.19068i 0.241265 0.255726i
\(413\) −1.32045 + 0.480606i −0.0649753 + 0.0236491i
\(414\) −45.6644 + 30.1649i −2.24428 + 1.48253i
\(415\) 15.1897 + 5.52860i 0.745633 + 0.271388i
\(416\) 0.348227 0.174886i 0.0170732 0.00857451i
\(417\) −7.79775 + 2.84698i −0.381857 + 0.139417i
\(418\) 10.3002 + 23.8785i 0.503798 + 1.16794i
\(419\) −24.4312 2.85560i −1.19354 0.139505i −0.503970 0.863721i \(-0.668128\pi\)
−0.689573 + 0.724216i \(0.742202\pi\)
\(420\) −35.2427 + 29.6322i −1.71967 + 1.44590i
\(421\) 10.2783 + 6.76018i 0.500936 + 0.329471i 0.774703 0.632325i \(-0.217899\pi\)
−0.273767 + 0.961796i \(0.588270\pi\)
\(422\) 33.3126 27.9526i 1.62163 1.36071i
\(423\) 1.30236 + 2.24537i 0.0633228 + 0.109174i
\(424\) −11.2094 9.40584i −0.544379 0.456788i
\(425\) 7.69655 + 25.7083i 0.373338 + 1.24703i
\(426\) 34.4288 + 3.98926i 1.66808 + 0.193280i
\(427\) −11.1871 5.61837i −0.541381 0.271892i
\(428\) 12.2378 + 12.9713i 0.591538 + 0.626993i
\(429\) −2.24881 + 1.13221i −0.108574 + 0.0546638i
\(430\) 11.5813 26.8485i 0.558501 1.29475i
\(431\) 3.97831 6.89064i 0.191628 0.331910i −0.754162 0.656689i \(-0.771956\pi\)
0.945790 + 0.324779i \(0.105290\pi\)
\(432\) −18.2495 4.26744i −0.878027 0.205317i
\(433\) −5.95735 10.3184i −0.286292 0.495872i 0.686630 0.727007i \(-0.259089\pi\)
−0.972922 + 0.231135i \(0.925756\pi\)
\(434\) 17.2014 2.01055i 0.825692 0.0965095i
\(435\) −3.19463 10.6321i −0.153171 0.509771i
\(436\) 50.7271 12.0225i 2.42939 0.575775i
\(437\) −1.96286 33.7010i −0.0938963 1.61214i
\(438\) −53.6998 + 35.3959i −2.56588 + 1.69128i
\(439\) 6.71977 + 1.59261i 0.320717 + 0.0760114i 0.387821 0.921735i \(-0.373228\pi\)
−0.0671041 + 0.997746i \(0.521376\pi\)
\(440\) −5.71714 + 32.4235i −0.272554 + 1.54573i
\(441\) 3.60844 3.84007i 0.171830 0.182861i
\(442\) 1.87809 + 10.6512i 0.0893318 + 0.506626i
\(443\) −0.421264 + 7.23283i −0.0200149 + 0.343642i 0.973403 + 0.229098i \(0.0735777\pi\)
−0.993418 + 0.114544i \(0.963459\pi\)
\(444\) 14.4979 25.1692i 0.688042 1.19448i
\(445\) −16.2055 + 21.7677i −0.768212 + 1.03189i
\(446\) 20.5195 27.5625i 0.971626 1.30512i
\(447\) 17.0011 0.0169952i 0.804124 0.000803847i
\(448\) 1.16638 20.0259i 0.0551061 0.946135i
\(449\) 5.97095 + 33.8630i 0.281787 + 1.59809i 0.716542 + 0.697543i \(0.245724\pi\)
−0.434756 + 0.900548i \(0.643165\pi\)
\(450\) 22.6795 + 14.8517i 1.06912 + 0.700114i
\(451\) −2.64793 + 15.0172i −0.124686 + 0.707130i
\(452\) −16.4301 3.89400i −0.772807 0.183159i
\(453\) 1.36789 + 23.0880i 0.0642689 + 1.08477i
\(454\) −0.814843 13.9903i −0.0382425 0.656598i
\(455\) 4.03602 0.956555i 0.189212 0.0448440i
\(456\) 25.2112 26.7759i 1.18062 1.25390i
\(457\) −16.5411 + 1.93338i −0.773760 + 0.0904396i −0.493804 0.869573i \(-0.664394\pi\)
−0.279956 + 0.960013i \(0.590320\pi\)
\(458\) −29.9317 51.8433i −1.39862 2.42248i
\(459\) −18.6966 + 32.6089i −0.872682 + 1.52205i
\(460\) 43.4712 75.2944i 2.02686 3.51062i
\(461\) 5.45935 12.6562i 0.254267 0.589458i −0.742496 0.669851i \(-0.766358\pi\)
0.996763 + 0.0803927i \(0.0256174\pi\)
\(462\) −1.30759 + 22.8439i −0.0608348 + 1.06279i
\(463\) −8.40156 8.90513i −0.390454 0.413857i 0.502092 0.864814i \(-0.332564\pi\)
−0.892545 + 0.450958i \(0.851082\pi\)
\(464\) −7.00027 3.51567i −0.324979 0.163211i
\(465\) −6.30062 14.5664i −0.292184 0.675501i
\(466\) −8.90694 29.7512i −0.412606 1.37820i
\(467\) −11.7925 9.89507i −0.545691 0.457889i 0.327788 0.944751i \(-0.393697\pi\)
−0.873479 + 0.486862i \(0.838141\pi\)
\(468\) 5.55797 + 4.64479i 0.256917 + 0.214705i
\(469\) 0.495208 0.415529i 0.0228666 0.0191873i
\(470\) −5.19690 3.41806i −0.239715 0.157663i
\(471\) 0.907147 + 5.11478i 0.0417991 + 0.235677i
\(472\) 2.87106 + 0.335579i 0.132151 + 0.0154463i
\(473\) −3.81537 8.84501i −0.175431 0.406694i
\(474\) 24.1141 + 20.1931i 1.10760 + 0.927501i
\(475\) −14.9434 + 7.50488i −0.685652 + 0.344347i
\(476\) 61.2319 + 22.2866i 2.80656 + 1.02150i
\(477\) −2.65498 + 8.93322i −0.121563 + 0.409024i
\(478\) 55.7428 20.2887i 2.54962 0.927985i
\(479\) 10.3968 11.0200i 0.475043 0.503516i −0.444894 0.895583i \(-0.646758\pi\)
0.919937 + 0.392067i \(0.128240\pi\)
\(480\) −3.15709 + 0.751579i −0.144101 + 0.0343047i
\(481\) −2.18610 + 1.43782i −0.0996777 + 0.0655591i
\(482\) −20.3103 + 67.8413i −0.925111 + 3.09008i
\(483\) 11.7374 27.2853i 0.534070 1.24152i
\(484\) −12.6637 17.0104i −0.575625 0.773198i
\(485\) −5.05122 −0.229364
\(486\) 6.78066 + 37.3620i 0.307577 + 1.69478i
\(487\) −9.74343 −0.441517 −0.220758 0.975329i \(-0.570853\pi\)
−0.220758 + 0.975329i \(0.570853\pi\)
\(488\) 15.3780 + 20.6562i 0.696129 + 0.935063i
\(489\) −12.1353 + 28.2103i −0.548777 + 1.27571i
\(490\) −3.62154 + 12.0968i −0.163604 + 0.546477i
\(491\) 15.9865 10.5145i 0.721461 0.474512i −0.134920 0.990856i \(-0.543078\pi\)
0.856381 + 0.516344i \(0.172707\pi\)
\(492\) 42.6765 10.1596i 1.92400 0.458029i
\(493\) −10.7815 + 11.4277i −0.485574 + 0.514678i
\(494\) −6.33304 + 2.30504i −0.284937 + 0.103709i
\(495\) 20.3936 4.87644i 0.916622 0.219180i
\(496\) −10.5232 3.83013i −0.472506 0.171978i
\(497\) −16.8098 + 8.44220i −0.754023 + 0.378685i
\(498\) −17.7176 14.8367i −0.793944 0.664847i
\(499\) −10.3471 23.9872i −0.463198 1.07381i −0.976483 0.215596i \(-0.930831\pi\)
0.513284 0.858219i \(-0.328429\pi\)
\(500\) 14.8783 + 1.73903i 0.665379 + 0.0777717i
\(501\) 6.65178 + 37.5049i 0.297180 + 1.67559i
\(502\) −48.5245 31.9151i −2.16576 1.42444i
\(503\) 0.849443 0.712768i 0.0378748 0.0317807i −0.623654 0.781701i \(-0.714352\pi\)
0.661529 + 0.749920i \(0.269908\pi\)
\(504\) 30.3854 11.1282i 1.35347 0.495691i
\(505\) −19.1614 16.0784i −0.852673 0.715477i
\(506\) −12.3913 41.3898i −0.550861 1.84000i
\(507\) 8.68002 + 20.0674i 0.385493 + 0.891223i
\(508\) −20.6954 10.3936i −0.918211 0.461143i
\(509\) 11.6487 + 12.3469i 0.516321 + 0.547268i 0.932102 0.362197i \(-0.117973\pi\)
−0.415781 + 0.909465i \(0.636492\pi\)
\(510\) 5.14746 89.9271i 0.227933 3.98204i
\(511\) 13.8257 32.0516i 0.611614 1.41788i
\(512\) −18.1349 + 31.4106i −0.801458 + 1.38817i
\(513\) −22.0340 7.94497i −0.972825 0.350779i
\(514\) 14.7828 + 25.6045i 0.652041 + 1.12937i
\(515\) 5.31760 0.621538i 0.234321 0.0273882i
\(516\) −18.9973 + 20.1764i −0.836311 + 0.888215i
\(517\) −1.99396 + 0.472576i −0.0876941 + 0.0207839i
\(518\) 1.38264 + 23.7390i 0.0607498 + 1.04303i
\(519\) 1.10889 + 18.7166i 0.0486750 + 0.821568i
\(520\) −8.30244 1.96771i −0.364086 0.0862900i
\(521\) −5.42618 + 30.7734i −0.237725 + 1.34821i 0.599072 + 0.800695i \(0.295536\pi\)
−0.836798 + 0.547512i \(0.815575\pi\)
\(522\) −0.891155 + 15.8463i −0.0390048 + 0.693572i
\(523\) −2.23807 12.6927i −0.0978638 0.555013i −0.993832 0.110895i \(-0.964628\pi\)
0.895968 0.444118i \(-0.146483\pi\)
\(524\) 2.98705 51.2856i 0.130490 2.24042i
\(525\) −14.7133 + 0.0147082i −0.642141 + 0.000641919i
\(526\) −11.6395 + 15.6346i −0.507508 + 0.681702i
\(527\) −13.4121 + 18.0156i −0.584241 + 0.784772i
\(528\) 7.38500 12.8208i 0.321391 0.557953i
\(529\) −1.92374 + 33.0293i −0.0836408 + 1.43606i
\(530\) −3.87796 21.9930i −0.168448 0.955314i
\(531\) −0.531522 1.76257i −0.0230661 0.0764891i
\(532\) −7.05085 + 39.9874i −0.305693 + 1.73367i
\(533\) −3.84532 0.911358i −0.166559 0.0394753i
\(534\) 32.3929 21.3515i 1.40178 0.923972i
\(535\) 0.777918 + 13.3563i 0.0336323 + 0.577445i
\(536\) −1.29395 + 0.306672i −0.0558903 + 0.0132462i
\(537\) −4.45668 14.8324i −0.192320 0.640064i
\(538\) 54.4753 6.36725i 2.34860 0.274512i
\(539\) 2.07997 + 3.60261i 0.0895907 + 0.155176i
\(540\) −36.1679 48.2789i −1.55642 2.07760i
\(541\) −3.97103 + 6.87802i −0.170728 + 0.295709i −0.938675 0.344804i \(-0.887945\pi\)
0.767947 + 0.640514i \(0.221279\pi\)
\(542\) 29.2368 67.7785i 1.25583 2.91133i
\(543\) −6.69086 + 3.36865i −0.287132 + 0.144563i
\(544\) 3.15172 + 3.34063i 0.135129 + 0.143228i
\(545\) 34.9511 + 17.5531i 1.49714 + 0.751893i
\(546\) −5.89045 0.682527i −0.252088 0.0292094i
\(547\) 3.10681 + 10.3775i 0.132838 + 0.443709i 0.998365 0.0571522i \(-0.0182020\pi\)
−0.865528 + 0.500861i \(0.833017\pi\)
\(548\) 13.6424 + 11.4473i 0.582774 + 0.489005i
\(549\) 8.17204 14.2200i 0.348774 0.606893i
\(550\) −16.3946 + 13.7567i −0.699067 + 0.586587i
\(551\) −8.17939 5.37967i −0.348454 0.229182i
\(552\) −46.7668 + 39.3218i −1.99053 + 1.67364i
\(553\) −16.9548 1.98174i −0.720993 0.0842720i
\(554\) 4.26811 + 9.89459i 0.181335 + 0.420381i
\(555\) 20.4697 7.47355i 0.868892 0.317235i
\(556\) −16.8479 + 8.46134i −0.714511 + 0.358841i
\(557\) 1.66135 + 0.604682i 0.0703937 + 0.0256212i 0.376977 0.926223i \(-0.376964\pi\)
−0.306583 + 0.951844i \(0.599186\pi\)
\(558\) 1.36454 + 22.6481i 0.0577657 + 0.958771i
\(559\) 2.34587 0.853825i 0.0992196 0.0361130i
\(560\) −16.7270 + 17.7296i −0.706845 + 0.749212i
\(561\) −20.3852 21.5639i −0.860666 0.910427i
\(562\) 11.5356 7.58710i 0.486601 0.320042i
\(563\) 2.19425 7.32932i 0.0924768 0.308894i −0.899219 0.437498i \(-0.855865\pi\)
0.991696 + 0.128604i \(0.0410498\pi\)
\(564\) 3.52515 + 4.72523i 0.148436 + 0.198968i
\(565\) −7.56471 10.1612i −0.318250 0.427484i
\(566\) −70.2116 −2.95121
\(567\) −14.2025 14.9337i −0.596448 0.627155i
\(568\) 38.6951 1.62361
\(569\) 11.8825 + 15.9609i 0.498139 + 0.669116i 0.978091 0.208178i \(-0.0667535\pi\)
−0.479952 + 0.877295i \(0.659346\pi\)
\(570\) 55.7420 6.57180i 2.33478 0.275262i
\(571\) 13.2127 44.1334i 0.552933 1.84692i 0.0215917 0.999767i \(-0.493127\pi\)
0.531341 0.847158i \(-0.321688\pi\)
\(572\) −4.77747 + 3.14219i −0.199756 + 0.131382i
\(573\) 10.5023 35.2082i 0.438740 1.47084i
\(574\) −24.6459 + 26.1231i −1.02870 + 1.09036i
\(575\) 26.1065 9.50198i 1.08872 0.396260i
\(576\) 26.1091 + 2.99881i 1.08788 + 0.124951i
\(577\) −24.3829 8.87465i −1.01507 0.369457i −0.219695 0.975569i \(-0.570506\pi\)
−0.795379 + 0.606112i \(0.792728\pi\)
\(578\) −76.9067 + 38.6240i −3.19890 + 1.60655i
\(579\) 5.42944 30.9729i 0.225640 1.28719i
\(580\) −9.98659 23.1515i −0.414671 0.961314i
\(581\) 12.4574 + 1.45606i 0.516819 + 0.0604075i
\(582\) 6.78834 + 2.46307i 0.281386 + 0.102098i
\(583\) −6.14683 4.04283i −0.254576 0.167437i
\(584\) −55.0061 + 46.1556i −2.27617 + 1.90993i
\(585\) 0.954326 + 5.34968i 0.0394565 + 0.221182i
\(586\) −4.03971 3.38972i −0.166879 0.140028i
\(587\) −6.02715 20.1321i −0.248767 0.830939i −0.987592 0.157042i \(-0.949804\pi\)
0.738825 0.673897i \(-0.235381\pi\)
\(588\) 7.13700 9.60669i 0.294325 0.396173i
\(589\) −12.5068 6.28115i −0.515334 0.258810i
\(590\) 3.02739 + 3.20885i 0.124636 + 0.132106i
\(591\) 10.3368 + 6.78383i 0.425199 + 0.279049i
\(592\) 6.09023 14.1187i 0.250307 0.580277i
\(593\) −12.9024 + 22.3476i −0.529837 + 0.917705i 0.469557 + 0.882902i \(0.344414\pi\)
−0.999394 + 0.0348027i \(0.988920\pi\)
\(594\) −29.7848 3.39083i −1.22208 0.139127i
\(595\) 24.4432 + 42.3368i 1.00207 + 1.73564i
\(596\) 38.3510 4.48258i 1.57092 0.183614i
\(597\) 6.16317 + 1.45419i 0.252242 + 0.0595161i
\(598\) 10.8951 2.58218i 0.445532 0.105593i
\(599\) 1.59636 + 27.4085i 0.0652255 + 1.11988i 0.859104 + 0.511802i \(0.171022\pi\)
−0.793878 + 0.608077i \(0.791941\pi\)
\(600\) 27.0607 + 13.5565i 1.10475 + 0.553443i
\(601\) 0.371180 + 0.0879713i 0.0151407 + 0.00358842i 0.238179 0.971221i \(-0.423449\pi\)
−0.223039 + 0.974810i \(0.571598\pi\)
\(602\) 3.93963 22.3428i 0.160567 0.910623i
\(603\) 0.507104 + 0.678323i 0.0206509 + 0.0276235i
\(604\) 9.12145 + 51.7303i 0.371146 + 2.10488i
\(605\) 0.925079 15.8830i 0.0376098 0.645736i
\(606\) 17.9110 + 30.9512i 0.727583 + 1.25731i
\(607\) 3.67880 4.94148i 0.149318 0.200569i −0.721171 0.692757i \(-0.756396\pi\)
0.870488 + 0.492189i \(0.163803\pi\)
\(608\) −1.70899 + 2.29557i −0.0693087 + 0.0930977i
\(609\) −4.31440 7.45554i −0.174828 0.302114i
\(610\) −2.28520 + 39.2353i −0.0925249 + 1.58859i
\(611\) −0.0922182 0.522996i −0.00373075 0.0211581i
\(612\) −33.6563 + 78.4549i −1.36047 + 3.17135i
\(613\) −4.86771 + 27.6062i −0.196605 + 1.11500i 0.713509 + 0.700646i \(0.247105\pi\)
−0.910114 + 0.414357i \(0.864006\pi\)
\(614\) −11.2462 2.66540i −0.453860 0.107567i
\(615\) 29.4260 + 14.7415i 1.18657 + 0.594433i
\(616\) 1.48535 + 25.5025i 0.0598466 + 1.02753i
\(617\) −14.5202 + 3.44136i −0.584563 + 0.138544i −0.512247 0.858838i \(-0.671187\pi\)
−0.0723152 + 0.997382i \(0.523039\pi\)
\(618\) −7.44940 1.75768i −0.299659 0.0707041i
\(619\) 4.14630 0.484633i 0.166654 0.0194790i −0.0323567 0.999476i \(-0.510301\pi\)
0.199011 + 0.979997i \(0.436227\pi\)
\(620\) −18.0223 31.2156i −0.723794 1.25365i
\(621\) 34.8271 + 17.3602i 1.39756 + 0.696642i
\(622\) 28.7494 49.7955i 1.15275 1.99662i
\(623\) −8.33996 + 19.3342i −0.334134 + 0.774609i
\(624\) 3.20570 + 2.10383i 0.128331 + 0.0842207i
\(625\) 20.4408 + 21.6660i 0.817633 + 0.866641i
\(626\) −51.4388 25.8335i −2.05591 1.03251i
\(627\) 11.0272 14.8430i 0.440383 0.592773i
\(628\) 3.38362 + 11.3021i 0.135021 + 0.451003i
\(629\) −23.6239 19.8228i −0.941945 0.790386i
\(630\) 46.4408 + 16.7980i 1.85024 + 0.669248i
\(631\) 24.5789 20.6241i 0.978470 0.821034i −0.00538805 0.999985i \(-0.501715\pi\)
0.983858 + 0.178952i \(0.0572706\pi\)
\(632\) 29.3381 + 19.2960i 1.16701 + 0.767553i
\(633\) −29.0666 10.5465i −1.15529 0.419185i
\(634\) 82.4410 + 9.63597i 3.27415 + 0.382693i
\(635\) −6.88166 15.9535i −0.273090 0.633095i
\(636\) −3.65455 + 20.8479i −0.144912 + 0.826671i
\(637\) −0.963408 + 0.483841i −0.0381716 + 0.0191705i
\(638\) −11.7739 4.28536i −0.466134 0.169659i
\(639\) −9.80626 22.6091i −0.387930 0.894401i
\(640\) −55.6576 + 20.2577i −2.20006 + 0.800757i
\(641\) 27.0420 28.6629i 1.06810 1.13212i 0.0772655 0.997011i \(-0.475381\pi\)
0.990831 0.135106i \(-0.0431374\pi\)
\(642\) 5.46736 18.3289i 0.215779 0.723384i
\(643\) 23.8482 15.6852i 0.940483 0.618565i 0.0160342 0.999871i \(-0.494896\pi\)
0.924449 + 0.381306i \(0.124526\pi\)
\(644\) 19.3476 64.6253i 0.762401 2.54660i
\(645\) −20.6478 + 2.43431i −0.813007 + 0.0958508i
\(646\) −47.4332 63.7138i −1.86623 2.50679i
\(647\) 3.61582 0.142153 0.0710764 0.997471i \(-0.477357\pi\)
0.0710764 + 0.997471i \(0.477357\pi\)
\(648\) 12.3211 + 40.5642i 0.484018 + 1.59351i
\(649\) 1.45335 0.0570489
\(650\) −3.31207 4.44889i −0.129910 0.174500i
\(651\) −7.36339 9.87013i −0.288594 0.386841i
\(652\) −20.0035 + 66.8162i −0.783396 + 2.61672i
\(653\) −9.91451 + 6.52088i −0.387985 + 0.255182i −0.728483 0.685063i \(-0.759774\pi\)
0.340499 + 0.940245i \(0.389404\pi\)
\(654\) −38.4116 40.6325i −1.50201 1.58886i
\(655\) 26.4486 28.0339i 1.03343 1.09538i
\(656\) 21.8226 7.94277i 0.852029 0.310113i
\(657\) 40.9080 + 20.4425i 1.59597 + 0.797537i
\(658\) −4.53524 1.65069i −0.176802 0.0643507i
\(659\) −2.35237 + 1.18141i −0.0916354 + 0.0460210i −0.494027 0.869447i \(-0.664475\pi\)
0.402391 + 0.915468i \(0.368179\pi\)
\(660\) 44.7342 16.3326i 1.74128 0.635745i
\(661\) 10.2372 + 23.7324i 0.398179 + 0.923083i 0.992878 + 0.119135i \(0.0380120\pi\)
−0.594699 + 0.803948i \(0.702729\pi\)
\(662\) 62.7293 + 7.33200i 2.43804 + 0.284966i
\(663\) 5.88616 4.94911i 0.228600 0.192208i
\(664\) −21.5559 14.1775i −0.836529 0.550194i
\(665\) −23.3357 + 19.5810i −0.904919 + 0.759317i
\(666\) −31.1535 + 0.0622856i −1.20717 + 0.00241352i
\(667\) 12.4596 + 10.4549i 0.482439 + 0.404815i
\(668\) 24.8109 + 82.8742i 0.959962 + 3.20650i
\(669\) −24.2704 2.81221i −0.938348 0.108726i
\(670\) −1.81362 0.910836i −0.0700664 0.0351887i
\(671\) 8.88521 + 9.41777i 0.343010 + 0.363569i
\(672\) −2.24910 + 1.13236i −0.0867609 + 0.0436816i
\(673\) 0.476679 1.10507i 0.0183746 0.0425972i −0.908782 0.417272i \(-0.862986\pi\)
0.927156 + 0.374675i \(0.122246\pi\)
\(674\) 26.9796 46.7301i 1.03922 1.79998i
\(675\) 1.06309 19.2468i 0.0409184 0.740809i
\(676\) 24.8284 + 43.0040i 0.954938 + 1.65400i
\(677\) 38.9380 4.55120i 1.49651 0.174917i 0.671910 0.740633i \(-0.265474\pi\)
0.824600 + 0.565716i \(0.191400\pi\)
\(678\) 5.21144 + 17.3443i 0.200144 + 0.666104i
\(679\) −3.81363 + 0.903848i −0.146354 + 0.0346865i
\(680\) −5.84723 100.393i −0.224231 3.84990i
\(681\) −8.31981 + 5.48394i −0.318816 + 0.210145i
\(682\) −17.4291 4.13077i −0.667394 0.158175i
\(683\) 1.15437 6.54674i 0.0441706 0.250504i −0.954725 0.297490i \(-0.903851\pi\)
0.998896 + 0.0469860i \(0.0149616\pi\)
\(684\) −51.7868 12.1644i −1.98012 0.465117i
\(685\) 2.32008 + 13.1578i 0.0886455 + 0.502734i
\(686\) −2.83999 + 48.7607i −0.108431 + 1.86169i
\(687\) −21.2459 + 36.8841i −0.810582 + 1.40722i
\(688\) −8.76047 + 11.7674i −0.333990 + 0.448626i
\(689\) 1.13858 1.52938i 0.0433765 0.0582648i
\(690\) −93.2504 + 0.0932183i −3.54998 + 0.00354876i
\(691\) 0.661006 11.3490i 0.0251458 0.431738i −0.962117 0.272638i \(-0.912104\pi\)
0.987263 0.159100i \(-0.0508591\pi\)
\(692\) 7.39441 + 41.9358i 0.281093 + 1.59416i
\(693\) 14.5244 7.33084i 0.551737 0.278475i
\(694\) −0.758598 + 4.30222i −0.0287960 + 0.163310i
\(695\) −13.7631 3.26191i −0.522063 0.123731i
\(696\) 1.04798 + 17.6885i 0.0397235 + 0.670480i
\(697\) −2.70818 46.4977i −0.102580 1.76122i
\(698\) −0.416876 + 0.0988013i −0.0157790 + 0.00373969i
\(699\) −15.1376 + 16.0771i −0.572557 + 0.608091i
\(700\) −33.1901 + 3.87937i −1.25447 + 0.146626i
\(701\) −14.2748 24.7247i −0.539152 0.933838i −0.998950 0.0458147i \(-0.985412\pi\)
0.459798 0.888023i \(-0.347922\pi\)
\(702\) 1.32609 7.65479i 0.0500500 0.288911i
\(703\) 9.60829 16.6421i 0.362384 0.627667i
\(704\) −8.21756 + 19.0504i −0.309711 + 0.717991i
\(705\) −0.252751 + 4.41561i −0.00951915 + 0.166301i
\(706\) −50.8407 53.8879i −1.91341 2.02810i
\(707\) −17.3438 8.71036i −0.652279 0.327587i
\(708\) −1.65989 3.83751i −0.0623826 0.144223i
\(709\) 12.5196 + 41.8183i 0.470183 + 1.57052i 0.783827 + 0.620979i \(0.213265\pi\)
−0.313645 + 0.949540i \(0.601550\pi\)
\(710\) 45.2389 + 37.9599i 1.69779 + 1.42461i
\(711\) 3.83943 22.0320i 0.143990 0.826264i
\(712\) 33.1808 27.8420i 1.24350 1.04342i
\(713\) 19.4267 + 12.7771i 0.727534 + 0.478507i
\(714\) −12.2050 68.8154i −0.456759 2.57535i
\(715\) −4.26096 0.498034i −0.159351 0.0186254i
\(716\) −13.9318 32.2976i −0.520657 1.20702i
\(717\) −32.3383 27.0800i −1.20770 1.01132i
\(718\) 14.0390 7.05063i 0.523929 0.263127i
\(719\) −28.1797 10.2566i −1.05093 0.382506i −0.241914 0.970298i \(-0.577775\pi\)
−0.809012 + 0.587792i \(0.799998\pi\)
\(720\) −21.9607 23.1840i −0.818428 0.864016i
\(721\) 3.90353 1.42077i 0.145375 0.0529122i
\(722\) 2.20530 2.33748i 0.0820728 0.0869920i
\(723\) 48.9845 11.6613i 1.82176 0.433688i
\(724\) −14.2143 + 9.34891i −0.528272 + 0.347450i
\(725\) 2.31073 7.71837i 0.0858183 0.286653i
\(726\) −8.98807 + 20.8941i −0.333578 + 0.775452i
\(727\) 23.9355 + 32.1509i 0.887717 + 1.19241i 0.980460 + 0.196721i \(0.0630293\pi\)
−0.0927425 + 0.995690i \(0.529563\pi\)
\(728\) −6.62038 −0.245368
\(729\) 20.5787 17.4790i 0.762175 0.647371i
\(730\) −109.587 −4.05600
\(731\) 17.5701 + 23.6007i 0.649853 + 0.872903i
\(732\) 14.7193 34.2173i 0.544042 1.26471i
\(733\) −7.87673 + 26.3101i −0.290934 + 0.971787i 0.680155 + 0.733068i \(0.261912\pi\)
−0.971089 + 0.238718i \(0.923273\pi\)
\(734\) 37.4570 24.6358i 1.38256 0.909325i
\(735\) 8.73444 2.07932i 0.322174 0.0766970i
\(736\) 3.26285 3.45842i 0.120270 0.127479i
\(737\) −0.628278 + 0.228675i −0.0231429 + 0.00842334i
\(738\) −32.3574 34.1597i −1.19109 1.25744i
\(739\) −29.1919 10.6250i −1.07384 0.390846i −0.256229 0.966616i \(-0.582480\pi\)
−0.817612 + 0.575770i \(0.804702\pi\)
\(740\) 44.2272 22.2117i 1.62582 0.816519i
\(741\) 3.67401 + 3.07661i 0.134968 + 0.113022i
\(742\) −6.86318 15.9106i −0.251955 0.584098i
\(743\) 6.43298 + 0.751908i 0.236003 + 0.0275848i 0.233272 0.972411i \(-0.425057\pi\)
0.00273096 + 0.999996i \(0.499131\pi\)
\(744\) 4.42367 + 24.9420i 0.162180 + 0.914420i
\(745\) 24.2024 + 15.9182i 0.886707 + 0.583196i
\(746\) 60.2439 50.5507i 2.20569 1.85079i
\(747\) −2.82098 + 16.1878i −0.103214 + 0.592279i
\(748\) −51.6272 43.3204i −1.88768 1.58395i
\(749\) 2.97726 + 9.94474i 0.108787 + 0.363373i
\(750\) −6.37834 14.7461i −0.232904 0.538451i
\(751\) −6.62351 3.32645i −0.241695 0.121384i 0.323829 0.946116i \(-0.395030\pi\)
−0.565524 + 0.824732i \(0.691326\pi\)
\(752\) 2.14163 + 2.26999i 0.0780972 + 0.0827782i
\(753\) −2.35999 + 41.2294i −0.0860027 + 1.50248i
\(754\) 1.28612 2.98157i 0.0468378 0.108582i
\(755\) −19.7042 + 34.1287i −0.717109 + 1.24207i
\(756\) −35.9454 29.9785i −1.30732 1.09031i
\(757\) −22.2841 38.5972i −0.809930 1.40284i −0.912912 0.408157i \(-0.866172\pi\)
0.102981 0.994683i \(-0.467162\pi\)
\(758\) −53.3070 + 6.23070i −1.93620 + 0.226309i
\(759\) −21.0594 + 22.3664i −0.764407 + 0.811849i
\(760\) 60.9750 14.4513i 2.21179 0.524205i
\(761\) 1.16403 + 19.9857i 0.0421961 + 0.724480i 0.951368 + 0.308058i \(0.0996790\pi\)
−0.909171 + 0.416422i \(0.863284\pi\)
\(762\) 1.46905 + 24.7955i 0.0532180 + 0.898247i
\(763\) 29.5288 + 6.99845i 1.06901 + 0.253361i
\(764\) 14.4900 82.1770i 0.524231 2.97306i
\(765\) −57.1767 + 28.8585i −2.06723 + 1.04338i
\(766\) 6.01753 + 34.1271i 0.217422 + 1.23306i
\(767\) −0.0219000 + 0.376009i −0.000790765 + 0.0135769i
\(768\) 54.3300 0.0543113i 1.96047 0.00195979i
\(769\) −2.97889 + 4.00134i −0.107421 + 0.144292i −0.852583 0.522592i \(-0.824965\pi\)
0.745161 + 0.666884i \(0.232372\pi\)
\(770\) −23.2815 + 31.2725i −0.839007 + 1.12698i
\(771\) 10.4930 18.2164i 0.377896 0.656049i
\(772\) 4.15251 71.2958i 0.149452 2.56599i
\(773\) −4.06522 23.0550i −0.146216 0.829232i −0.966383 0.257108i \(-0.917231\pi\)
0.820167 0.572124i \(-0.193881\pi\)
\(774\) 28.9356 + 6.79680i 1.04007 + 0.244306i
\(775\) 2.00005 11.3429i 0.0718440 0.407448i
\(776\) 7.84496 + 1.85929i 0.281618 + 0.0667446i
\(777\) 14.1172 9.30527i 0.506452 0.333825i
\(778\) 1.73733 + 29.8287i 0.0622862 + 1.06941i
\(779\) 28.2409 6.69322i 1.01184 0.239809i
\(780\) 3.55147 + 11.8197i 0.127163 + 0.423213i
\(781\) 19.3237 2.25861i 0.691456 0.0808196i
\(782\) 65.9832 + 114.286i 2.35955 + 4.08687i
\(783\) 10.0696 5.09501i 0.359857 0.182081i
\(784\) 3.16768 5.48659i 0.113132 0.195950i
\(785\) −3.50571 + 8.12715i −0.125124 + 0.290070i
\(786\) −49.2142 + 24.7779i −1.75541 + 0.883800i
\(787\) 34.2546 + 36.3078i 1.22105 + 1.29423i 0.942657 + 0.333764i \(0.108319\pi\)
0.278388 + 0.960469i \(0.410200\pi\)
\(788\) 25.0937 + 12.6025i 0.893927 + 0.448947i
\(789\) 13.7672 + 1.59521i 0.490126 + 0.0567909i
\(790\) 15.3702 + 51.3399i 0.546846 + 1.82659i
\(791\) −7.52951 6.31801i −0.267719 0.224642i
\(792\) −33.4679 + 0.0669127i −1.18923 + 0.00237764i
\(793\) −2.57045 + 2.15686i −0.0912792 + 0.0765923i
\(794\) 19.7707 + 13.0034i 0.701636 + 0.461474i
\(795\) −12.1540 + 10.2191i −0.431057 + 0.362435i
\(796\) 14.2846 + 1.66963i 0.506303 + 0.0591784i
\(797\) −15.9248 36.9179i −0.564087 1.30770i −0.926715 0.375766i \(-0.877380\pi\)
0.362628 0.931934i \(-0.381880\pi\)
\(798\) 40.9089 14.9360i 1.44816 0.528727i
\(799\) 5.59335 2.80909i 0.197879 0.0993783i
\(800\) −2.21319 0.805537i −0.0782482 0.0284800i
\(801\) −24.6766 12.3313i −0.871905 0.435706i
\(802\) 2.67647 0.974155i 0.0945094 0.0343986i
\(803\) −24.7751 + 26.2600i −0.874293 + 0.926696i
\(804\) 1.32137 + 1.39777i 0.0466013 + 0.0492956i
\(805\) 42.2841 27.8107i 1.49032 0.980199i
\(806\) 1.33134 4.44699i 0.0468945 0.156639i
\(807\) −23.3192 31.2579i −0.820876 1.10033i
\(808\) 23.8411 + 32.0241i 0.838726 + 1.12660i
\(809\) 44.4490 1.56274 0.781371 0.624066i \(-0.214521\pi\)
0.781371 + 0.624066i \(0.214521\pi\)
\(810\) −25.3888 + 59.5111i −0.892073 + 2.09101i
\(811\) −38.6494 −1.35716 −0.678582 0.734524i \(-0.737405\pi\)
−0.678582 + 0.734524i \(0.737405\pi\)
\(812\) −11.6825 15.6923i −0.409974 0.550691i
\(813\) −52.1249 + 6.14536i −1.82810 + 0.215527i
\(814\) 7.05367 23.5609i 0.247231 0.825809i
\(815\) −43.7176 + 28.7535i −1.53136 + 1.00719i
\(816\) −12.9180 + 43.3066i −0.452220 + 1.51603i
\(817\) −12.5817 + 13.3359i −0.440179 + 0.466562i
\(818\) −62.8587 + 22.8787i −2.19780 + 0.799934i
\(819\) 1.67776 + 3.86821i 0.0586258 + 0.135166i
\(820\) 70.2401 + 25.5653i 2.45289 + 0.892780i
\(821\) 38.6944 19.4330i 1.35044 0.678218i 0.381238 0.924477i \(-0.375498\pi\)
0.969204 + 0.246259i \(0.0792015\pi\)
\(822\) 3.29804 18.8141i 0.115032 0.656217i
\(823\) −11.9237 27.6422i −0.415633 0.963545i −0.989492 0.144591i \(-0.953813\pi\)
0.573859 0.818954i \(-0.305446\pi\)
\(824\) −8.48745 0.992041i −0.295674 0.0345594i
\(825\) 14.3049 + 5.19039i 0.498034 + 0.180706i
\(826\) 2.85984 + 1.88095i 0.0995066 + 0.0654465i
\(827\) −12.5660 + 10.5441i −0.436963 + 0.366655i −0.834571 0.550900i \(-0.814285\pi\)
0.397609 + 0.917555i \(0.369840\pi\)
\(828\) 83.1099 + 30.0615i 2.88827 + 1.04471i
\(829\) 22.2396 + 18.6612i 0.772413 + 0.648132i 0.941326 0.337500i \(-0.109581\pi\)
−0.168913 + 0.985631i \(0.554026\pi\)
\(830\) −11.2931 37.7214i −0.391988 1.30933i
\(831\) 4.56936 6.15054i 0.158509 0.213360i
\(832\) −4.80489 2.41311i −0.166580 0.0836594i
\(833\) −8.71956 9.24219i −0.302115 0.320223i
\(834\) 16.9056 + 11.0948i 0.585394 + 0.384182i
\(835\) −25.7061 + 59.5935i −0.889597 + 2.06232i
\(836\) 20.9978 36.3693i 0.726224 1.25786i
\(837\) 13.4523 8.90561i 0.464979 0.307823i
\(838\) 29.9589 + 51.8904i 1.03491 + 1.79252i
\(839\) −35.2631 + 4.12166i −1.21742 + 0.142296i −0.700445 0.713707i \(-0.747015\pi\)
−0.516972 + 0.856002i \(0.672941\pi\)
\(840\) 53.6627 + 12.6616i 1.85154 + 0.436868i
\(841\) −23.6286 + 5.60007i −0.814778 + 0.193106i
\(842\) −1.74244 29.9166i −0.0600486 1.03099i
\(843\) −8.77756 4.39728i −0.302315 0.151450i
\(844\) −68.3327 16.1951i −2.35211 0.557460i
\(845\) −6.46910 + 36.6881i −0.222544 + 1.26211i
\(846\) 2.49281 5.81089i 0.0857044 0.199783i
\(847\) −2.14362 12.1571i −0.0736557 0.417722i
\(848\) −0.651488 + 11.1856i −0.0223722 + 0.384116i
\(849\) 25.0050 + 43.2101i 0.858168 + 1.48297i
\(850\) 39.0361 52.4346i 1.33893 1.79849i
\(851\) −19.0650 + 25.6087i −0.653540 + 0.877856i
\(852\) −28.0337 48.4439i −0.960418 1.65966i
\(853\) 0.0559581 0.960764i 0.00191597 0.0328959i −0.997215 0.0745849i \(-0.976237\pi\)
0.999131 + 0.0416890i \(0.0132739\pi\)
\(854\) 5.29532 + 30.0313i 0.181202 + 1.02765i
\(855\) −23.8963 31.9646i −0.817235 1.09317i
\(856\) 3.70813 21.0298i 0.126741 0.718785i
\(857\) 0.552270 + 0.130890i 0.0188652 + 0.00447113i 0.240038 0.970764i \(-0.422840\pi\)
−0.221172 + 0.975235i \(0.570988\pi\)
\(858\) 5.48345 + 2.74703i 0.187202 + 0.0937821i
\(859\) −1.16923 20.0749i −0.0398936 0.684947i −0.957673 0.287857i \(-0.907057\pi\)
0.917780 0.397090i \(-0.129980\pi\)
\(860\) −45.9462 + 10.8895i −1.56675 + 0.371327i
\(861\) 24.8542 + 5.86432i 0.847029 + 0.199855i
\(862\) −19.2507 + 2.25008i −0.655682 + 0.0766382i
\(863\) −18.8153 32.5891i −0.640481 1.10935i −0.985326 0.170686i \(-0.945402\pi\)
0.344845 0.938660i \(-0.387932\pi\)
\(864\) −1.31573 3.02523i −0.0447621 0.102920i
\(865\) −15.9735 + 27.6668i −0.543114 + 0.940700i
\(866\) −11.4956 + 26.6497i −0.390635 + 0.905594i
\(867\) 51.1596 + 33.5750i 1.73747 + 1.14027i
\(868\) −19.1923 20.3427i −0.651431 0.690476i
\(869\) 15.7773 + 7.92365i 0.535207 + 0.268791i
\(870\) −16.1272 + 21.7079i −0.546764 + 0.735966i
\(871\) −0.0496952 0.165993i −0.00168386 0.00562447i
\(872\) −47.8210 40.1266i −1.61942 1.35886i
\(873\) −0.901741 5.05491i −0.0305193 0.171083i
\(874\) −62.9936 + 52.8579i −2.13079 + 1.78795i
\(875\) 7.28528 + 4.79160i 0.246287 + 0.161986i
\(876\) 97.6346 + 35.4256i 3.29877 + 1.19692i
\(877\) −27.2207 3.18164i −0.919178 0.107437i −0.356672 0.934230i \(-0.616089\pi\)
−0.562506 + 0.826793i \(0.690163\pi\)
\(878\) −6.66298 15.4465i −0.224865 0.521295i
\(879\) −0.647431 + 3.69335i −0.0218373 + 0.124574i
\(880\) 22.5285 11.3143i 0.759437 0.381404i
\(881\) −31.5862 11.4964i −1.06417 0.387324i −0.250174 0.968201i \(-0.580488\pi\)
−0.813992 + 0.580877i \(0.802710\pi\)
\(882\) −12.7521 1.46467i −0.429387 0.0493181i
\(883\) 40.4061 14.7066i 1.35977 0.494917i 0.443789 0.896131i \(-0.353634\pi\)
0.915984 + 0.401214i \(0.131412\pi\)
\(884\) 11.9858 12.7042i 0.403125 0.427287i
\(885\) 0.896642 3.00593i 0.0301403 0.101043i
\(886\) 14.7451 9.69802i 0.495372 0.325811i
\(887\) 8.89124 29.6988i 0.298539 0.997189i −0.668745 0.743492i \(-0.733168\pi\)
0.967284 0.253697i \(-0.0816466\pi\)
\(888\) −34.5421 + 4.07240i −1.15916 + 0.136661i
\(889\) −8.05027 10.8134i −0.269997 0.362669i
\(890\) 66.1052 2.21585
\(891\) 8.52066 + 19.5379i 0.285453 + 0.654545i
\(892\) −55.4905 −1.85796
\(893\) 2.32907 + 3.12848i 0.0779393 + 0.104691i
\(894\) −24.7636 33.1940i −0.828219 1.11017i
\(895\) 7.56841 25.2803i 0.252984 0.845026i
\(896\) −38.3963 + 25.2536i −1.28273 + 0.843665i
\(897\) −5.46928 5.78550i −0.182614 0.193172i
\(898\) 57.4798 60.9250i 1.91812 2.03309i
\(899\) 6.33645 2.30628i 0.211333 0.0769188i
\(900\) −2.63289 43.6997i −0.0877631 1.45666i
\(901\) 21.1167 + 7.68587i 0.703501 + 0.256053i
\(902\) 33.1940 16.6707i 1.10524 0.555072i
\(903\) −15.1534 + 5.53253i −0.504272 + 0.184111i
\(904\) 8.00843 + 18.5656i 0.266356 + 0.617483i
\(905\) −12.6775 1.48179i −0.421416 0.0492565i
\(906\) 43.1223 36.2574i 1.43264 1.20457i
\(907\) 3.26950 + 2.15039i 0.108562 + 0.0714024i 0.602629 0.798021i \(-0.294120\pi\)
−0.494067 + 0.869424i \(0.664490\pi\)
\(908\) −17.3364 + 14.5469i −0.575328 + 0.482757i
\(909\) 12.6694 22.0457i 0.420218 0.731211i
\(910\) −7.73997 6.49461i −0.256577 0.215294i
\(911\) −11.1761 37.3309i −0.370282 1.23683i −0.916789 0.399373i \(-0.869228\pi\)
0.546507 0.837455i \(-0.315957\pi\)
\(912\) −27.9735 3.24129i −0.926296 0.107330i
\(913\) −11.5922 5.82181i −0.383645 0.192674i
\(914\) 27.8389 + 29.5075i 0.920830 + 0.976022i
\(915\) 24.9603 12.5668i 0.825161 0.415445i
\(916\) −38.2901 + 88.7664i −1.26514 + 2.93292i
\(917\) 14.9522 25.8980i 0.493766 0.855228i
\(918\) 90.9117 10.9025i 3.00053 0.359837i
\(919\) 10.6253 + 18.4036i 0.350497 + 0.607078i 0.986337 0.164743i \(-0.0526794\pi\)
−0.635840 + 0.771821i \(0.719346\pi\)
\(920\) −103.405 + 12.0863i −3.40917 + 0.398475i
\(921\) 2.36484 + 7.87046i 0.0779240 + 0.259341i
\(922\) −32.6705 + 7.74305i −1.07595 + 0.255004i
\(923\) 0.293164 + 5.03344i 0.00964963 + 0.165678i
\(924\) 30.8515 20.3356i 1.01494 0.668991i
\(925\) 15.3884 + 3.64712i 0.505967 + 0.119916i
\(926\) −5.17866 + 29.3696i −0.170181 + 0.965146i
\(927\) 1.57129 + 5.21053i 0.0516078 + 0.171136i
\(928\) −0.239438 1.35792i −0.00785994 0.0445759i
\(929\) −0.950318 + 16.3163i −0.0311789 + 0.535321i 0.946168 + 0.323677i \(0.104919\pi\)
−0.977347 + 0.211645i \(0.932118\pi\)
\(930\) −19.2964 + 33.4997i −0.632755 + 1.09850i
\(931\) 4.72810 6.35094i 0.154957 0.208144i
\(932\) −29.9485 + 40.2279i −0.980997 + 1.31771i
\(933\) −40.8842 + 0.0408701i −1.33849 + 0.00133803i
\(934\) −2.18035 + 37.4352i −0.0713434 + 1.22492i
\(935\) −8.77991 49.7934i −0.287134 1.62842i
\(936\) 0.487005 8.65978i 0.0159182 0.283054i
\(937\) −3.94626 + 22.3803i −0.128919 + 0.731134i 0.849984 + 0.526808i \(0.176611\pi\)
−0.978903 + 0.204326i \(0.934500\pi\)
\(938\) −1.53225 0.363151i −0.0500299 0.0118573i
\(939\) 2.42063 + 40.8570i 0.0789944 + 1.33332i
\(940\) 0.584060 + 10.0279i 0.0190499 + 0.327075i
\(941\) −12.7527 + 3.02245i −0.415727 + 0.0985292i −0.433156 0.901319i \(-0.642600\pi\)
0.0174287 + 0.999848i \(0.494452\pi\)
\(942\) 8.67428 9.21263i 0.282623 0.300164i
\(943\) −47.8928 + 5.59786i −1.55960 + 0.182291i
\(944\) −1.10669 1.91684i −0.0360196 0.0623877i
\(945\) −6.20137 34.5632i −0.201730 1.12434i
\(946\) −11.7324 + 20.3212i −0.381454 + 0.660698i
\(947\) 8.56599 19.8582i 0.278357 0.645305i −0.720482 0.693474i \(-0.756079\pi\)
0.998839 + 0.0481689i \(0.0153386\pi\)
\(948\) 2.90260 50.7090i 0.0942722 1.64695i
\(949\) −6.42064 6.80548i −0.208423 0.220915i
\(950\) 36.4012 + 18.2813i 1.18101 + 0.593125i
\(951\) −23.4301 54.1681i −0.759773 1.75652i
\(952\) −22.3786 74.7498i −0.725295 2.42266i
\(953\) 16.8450 + 14.1347i 0.545665 + 0.457867i 0.873470 0.486878i \(-0.161865\pi\)
−0.327805 + 0.944745i \(0.606309\pi\)
\(954\) 21.3168 7.80697i 0.690156 0.252760i
\(955\) 47.9566 40.2403i 1.55184 1.30215i
\(956\) −80.0359 52.6404i −2.58855 1.70251i
\(957\) 1.55581 + 8.77216i 0.0502922 + 0.283564i
\(958\) −36.6557 4.28444i −1.18429 0.138424i
\(959\) 4.10605 + 9.51890i 0.132591 + 0.307381i
\(960\) 34.3318 + 28.7493i 1.10805 + 0.927881i
\(961\) −19.0882 + 9.58645i −0.615748 + 0.309240i
\(962\) 5.98936 + 2.17995i 0.193105 + 0.0702844i
\(963\) −13.2272 + 3.16285i −0.426241 + 0.101921i
\(964\) 107.463 39.1135i 3.46116 1.25976i
\(965\) 36.7682 38.9720i 1.18361 1.25455i
\(966\) −70.3867 + 16.7563i −2.26466 + 0.539125i
\(967\) −19.8618 + 13.0633i −0.638713 + 0.420088i −0.827137 0.562000i \(-0.810032\pi\)
0.188425 + 0.982088i \(0.439662\pi\)
\(968\) −7.28306 + 24.3271i −0.234086 + 0.781903i
\(969\) −22.3184 + 51.8825i −0.716971 + 1.66671i
\(970\) 7.34768 + 9.86965i 0.235920 + 0.316895i
\(971\) −16.4980 −0.529445 −0.264723 0.964325i \(-0.585280\pi\)
−0.264723 + 0.964325i \(0.585280\pi\)
\(972\) 41.8576 44.8131i 1.34258 1.43738i
\(973\) −10.9747 −0.351833
\(974\) 14.1731 + 19.0378i 0.454136 + 0.610011i
\(975\) −1.55841 + 3.62275i −0.0499090 + 0.116021i
\(976\) 5.65534 18.8902i 0.181023 0.604659i
\(977\) 5.13809 3.37937i 0.164382 0.108116i −0.464653 0.885493i \(-0.653821\pi\)
0.629035 + 0.777377i \(0.283450\pi\)
\(978\) 72.7729 17.3243i 2.32702 0.553971i
\(979\) 14.9448 15.8406i 0.477639 0.506268i
\(980\) 19.1618 6.97433i 0.612101 0.222787i
\(981\) −11.3265 + 38.1103i −0.361627 + 1.21677i
\(982\) −43.7990 15.9415i −1.39768 0.508714i
\(983\) 10.4161 5.23114i 0.332221 0.166847i −0.274867 0.961482i \(-0.588634\pi\)
0.607088 + 0.794635i \(0.292338\pi\)
\(984\) −40.2748 33.7261i −1.28392 1.07515i
\(985\) 8.34419 + 19.3440i 0.265868 + 0.616351i
\(986\) 38.0119 + 4.44295i 1.21054 + 0.141492i
\(987\) 0.599288 + 3.37898i 0.0190756 + 0.107554i
\(988\) 9.09302 + 5.98057i 0.289287 + 0.190267i
\(989\) 23.3339 19.5795i 0.741976 0.622592i
\(990\) −39.1933 32.7538i −1.24565 1.04098i
\(991\) −20.9608 17.5882i −0.665840 0.558706i 0.245991 0.969272i \(-0.420887\pi\)
−0.911831 + 0.410566i \(0.865331\pi\)
\(992\) −0.565345 1.88838i −0.0179497 0.0599562i
\(993\) −17.8279 41.2164i −0.565752 1.30796i
\(994\) 40.9475 + 20.5646i 1.29878 + 0.652269i
\(995\) 7.40434 + 7.84814i 0.234733 + 0.248803i
\(996\) −2.13266 + 37.2579i −0.0675758 + 1.18056i
\(997\) 21.6349 50.1553i 0.685184 1.58843i −0.118211 0.992988i \(-0.537716\pi\)
0.803395 0.595446i \(-0.203025\pi\)
\(998\) −31.8177 + 55.1099i −1.00717 + 1.74447i
\(999\) 11.1333 + 19.1505i 0.352241 + 0.605895i
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.7.1 144
3.2 odd 2 243.2.g.a.100.8 144
9.2 odd 6 729.2.g.b.55.8 144
9.4 even 3 729.2.g.d.298.8 144
9.5 odd 6 729.2.g.a.298.1 144
9.7 even 3 729.2.g.c.55.1 144
81.4 even 27 729.2.g.c.676.1 144
81.23 odd 54 243.2.g.a.226.8 144
81.25 even 27 6561.2.a.c.1.8 72
81.31 even 27 729.2.g.d.433.8 144
81.50 odd 54 729.2.g.a.433.1 144
81.56 odd 54 6561.2.a.d.1.65 72
81.58 even 27 inner 81.2.g.a.58.1 yes 144
81.77 odd 54 729.2.g.b.676.8 144
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
81.2.g.a.7.1 144 1.1 even 1 trivial
81.2.g.a.58.1 yes 144 81.58 even 27 inner
243.2.g.a.100.8 144 3.2 odd 2
243.2.g.a.226.8 144 81.23 odd 54
729.2.g.a.298.1 144 9.5 odd 6
729.2.g.a.433.1 144 81.50 odd 54
729.2.g.b.55.8 144 9.2 odd 6
729.2.g.b.676.8 144 81.77 odd 54
729.2.g.c.55.1 144 9.7 even 3
729.2.g.c.676.1 144 81.4 even 27
729.2.g.d.298.8 144 9.4 even 3
729.2.g.d.433.8 144 81.31 even 27
6561.2.a.c.1.8 72 81.25 even 27
6561.2.a.d.1.65 72 81.56 odd 54