Properties

Label 288.2.bc.a.13.12
Level $288$
Weight $2$
Character 288.13
Analytic conductor $2.300$
Analytic rank $0$
Dimension $368$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [288,2,Mod(13,288)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(288, base_ring=CyclotomicField(24))
 
chi = DirichletCharacter(H, H._module([0, 21, 8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("288.13");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 288 = 2^{5} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 288.bc (of order \(24\), degree \(8\), 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: \(2.29969157821\)
Analytic rank: \(0\)
Dimension: \(368\)
Relative dimension: \(46\) over \(\Q(\zeta_{24})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label 13.12
Character \(\chi\) \(=\) 288.13
Dual form 288.2.bc.a.133.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.06040 + 0.935708i) q^{2} +(1.12868 - 1.31380i) q^{3} +(0.248901 - 1.98445i) q^{4} +(0.226472 - 1.72022i) q^{5} +(0.0324819 + 2.44927i) q^{6} +(-3.91012 - 1.04771i) q^{7} +(1.59293 + 2.33721i) q^{8} +(-0.452160 - 2.96573i) q^{9} +O(q^{10})\) \(q+(-1.06040 + 0.935708i) q^{2} +(1.12868 - 1.31380i) q^{3} +(0.248901 - 1.98445i) q^{4} +(0.226472 - 1.72022i) q^{5} +(0.0324819 + 2.44927i) q^{6} +(-3.91012 - 1.04771i) q^{7} +(1.59293 + 2.33721i) q^{8} +(-0.452160 - 2.96573i) q^{9} +(1.36948 + 2.03604i) q^{10} +(1.87311 - 2.44108i) q^{11} +(-2.32625 - 2.56682i) q^{12} +(-5.28160 + 4.05272i) q^{13} +(5.12665 - 2.54774i) q^{14} +(-2.00442 - 2.23912i) q^{15} +(-3.87610 - 0.987866i) q^{16} -1.43138i q^{17} +(3.25453 + 2.72177i) q^{18} +(-1.19094 - 0.493302i) q^{19} +(-3.35733 - 0.877589i) q^{20} +(-5.78977 + 3.95460i) q^{21} +(0.297893 + 4.34120i) q^{22} +(-3.11401 + 0.834395i) q^{23} +(4.86855 + 0.545169i) q^{24} +(1.92175 + 0.514931i) q^{25} +(1.80846 - 9.23954i) q^{26} +(-4.40673 - 2.75331i) q^{27} +(-3.05237 + 7.49867i) q^{28} +(9.16431 - 1.20650i) q^{29} +(4.22066 + 0.498815i) q^{30} +(5.09391 - 8.82292i) q^{31} +(5.03457 - 2.57936i) q^{32} +(-1.09296 - 5.21609i) q^{33} +(1.33936 + 1.51784i) q^{34} +(-2.68784 + 6.48901i) q^{35} +(-5.99789 + 0.159114i) q^{36} +(2.44916 - 1.01448i) q^{37} +(1.72446 - 0.591270i) q^{38} +(-0.636770 + 11.5132i) q^{39} +(4.38129 - 2.21089i) q^{40} +(1.80265 - 0.483019i) q^{41} +(2.43913 - 9.61100i) q^{42} +(1.77472 - 2.31285i) q^{43} +(-4.37798 - 4.32468i) q^{44} +(-5.20412 + 0.106162i) q^{45} +(2.52135 - 3.79859i) q^{46} +(8.10225 - 4.67784i) q^{47} +(-5.67274 + 3.97744i) q^{48} +(8.12918 + 4.69338i) q^{49} +(-2.51965 + 1.25216i) q^{50} +(-1.88055 - 1.61557i) q^{51} +(6.72782 + 11.4898i) q^{52} +(1.74212 + 4.20586i) q^{53} +(7.24920 - 1.20380i) q^{54} +(-3.77500 - 3.77500i) q^{55} +(-3.77983 - 10.8077i) q^{56} +(-1.99229 + 1.00788i) q^{57} +(-8.58891 + 9.85450i) q^{58} +(0.306361 - 2.32704i) q^{59} +(-4.94234 + 3.42036i) q^{60} +(-11.3916 + 1.49973i) q^{61} +(2.85408 + 14.1223i) q^{62} +(-1.33924 + 12.0701i) q^{63} +(-2.92514 + 7.44604i) q^{64} +(5.77545 + 10.0034i) q^{65} +(6.03971 + 4.50846i) q^{66} +(-5.43059 - 7.07728i) q^{67} +(-2.84051 - 0.356273i) q^{68} +(-2.41849 + 5.03296i) q^{69} +(-3.22163 - 9.39598i) q^{70} +(-3.43628 + 3.43628i) q^{71} +(6.21129 - 5.78100i) q^{72} +(8.89183 + 8.89183i) q^{73} +(-1.64784 + 3.36745i) q^{74} +(2.84556 - 1.94361i) q^{75} +(-1.27536 + 2.24057i) q^{76} +(-9.88163 + 7.58244i) q^{77} +(-10.0978 - 12.8045i) q^{78} +(-0.823181 + 0.475264i) q^{79} +(-2.57718 + 6.44403i) q^{80} +(-8.59110 + 2.68197i) q^{81} +(-1.45957 + 2.19895i) q^{82} +(-0.727691 - 5.52736i) q^{83} +(6.40663 + 12.4738i) q^{84} +(-2.46230 - 0.324168i) q^{85} +(0.282246 + 4.11317i) q^{86} +(8.75847 - 13.4019i) q^{87} +(8.68905 + 0.489377i) q^{88} +(-1.60670 + 1.60670i) q^{89} +(5.41912 - 4.98211i) q^{90} +(24.8978 - 10.3130i) q^{91} +(0.880737 + 6.38728i) q^{92} +(-5.84218 - 16.6507i) q^{93} +(-4.21455 + 12.5417i) q^{94} +(-1.11830 + 1.93696i) q^{95} +(2.29365 - 9.52571i) q^{96} +(0.147017 + 0.254642i) q^{97} +(-13.0118 + 2.62967i) q^{98} +(-8.08652 - 4.45137i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 368 q - 4 q^{2} - 8 q^{3} - 4 q^{4} - 4 q^{5} - 8 q^{6} - 4 q^{7} - 16 q^{8} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 368 q - 4 q^{2} - 8 q^{3} - 4 q^{4} - 4 q^{5} - 8 q^{6} - 4 q^{7} - 16 q^{8} - 8 q^{9} - 16 q^{10} - 4 q^{11} - 8 q^{12} - 4 q^{13} - 4 q^{14} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 4 q^{20} - 8 q^{21} - 4 q^{22} - 4 q^{23} - 48 q^{24} - 4 q^{25} - 16 q^{26} - 32 q^{27} - 16 q^{28} - 4 q^{29} + 24 q^{30} - 8 q^{31} - 4 q^{32} - 16 q^{33} + 4 q^{34} - 16 q^{35} + 20 q^{36} - 16 q^{37} - 60 q^{38} - 32 q^{39} - 4 q^{40} - 4 q^{41} - 88 q^{42} - 4 q^{43} - 104 q^{44} - 8 q^{45} - 16 q^{46} - 60 q^{48} + 48 q^{50} + 16 q^{51} - 4 q^{52} - 16 q^{53} - 52 q^{54} - 16 q^{55} - 84 q^{56} - 8 q^{57} - 40 q^{58} - 4 q^{59} - 52 q^{60} - 4 q^{61} - 24 q^{62} - 16 q^{63} - 16 q^{64} - 8 q^{65} + 64 q^{66} - 4 q^{67} + 12 q^{68} - 8 q^{69} - 4 q^{70} - 16 q^{71} - 68 q^{72} - 16 q^{73} - 4 q^{74} - 28 q^{75} + 20 q^{76} - 4 q^{77} - 72 q^{78} + 48 q^{80} - 16 q^{82} + 36 q^{83} + 200 q^{84} + 16 q^{85} + 100 q^{86} - 64 q^{87} - 4 q^{88} - 16 q^{89} + 4 q^{90} - 16 q^{91} - 80 q^{92} + 4 q^{93} - 20 q^{94} - 136 q^{95} + 28 q^{96} - 8 q^{97} + 104 q^{98} - 72 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/288\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.06040 + 0.935708i −0.749817 + 0.661645i
\(3\) 1.12868 1.31380i 0.651644 0.758525i
\(4\) 0.248901 1.98445i 0.124451 0.992226i
\(5\) 0.226472 1.72022i 0.101281 0.769308i −0.863145 0.504956i \(-0.831509\pi\)
0.964426 0.264352i \(-0.0851579\pi\)
\(6\) 0.0324819 + 2.44927i 0.0132607 + 0.999912i
\(7\) −3.91012 1.04771i −1.47789 0.395999i −0.572260 0.820072i \(-0.693933\pi\)
−0.905628 + 0.424074i \(0.860600\pi\)
\(8\) 1.59293 + 2.33721i 0.563186 + 0.826330i
\(9\) −0.452160 2.96573i −0.150720 0.988577i
\(10\) 1.36948 + 2.03604i 0.433066 + 0.643852i
\(11\) 1.87311 2.44108i 0.564763 0.736013i −0.420456 0.907313i \(-0.638130\pi\)
0.985219 + 0.171300i \(0.0547967\pi\)
\(12\) −2.32625 2.56682i −0.671530 0.740977i
\(13\) −5.28160 + 4.05272i −1.46485 + 1.12402i −0.498472 + 0.866906i \(0.666106\pi\)
−0.966381 + 0.257116i \(0.917228\pi\)
\(14\) 5.12665 2.54774i 1.37016 0.680911i
\(15\) −2.00442 2.23912i −0.517540 0.578139i
\(16\) −3.87610 0.987866i −0.969024 0.246966i
\(17\) 1.43138i 0.347161i −0.984820 0.173581i \(-0.944466\pi\)
0.984820 0.173581i \(-0.0555337\pi\)
\(18\) 3.25453 + 2.72177i 0.767099 + 0.641528i
\(19\) −1.19094 0.493302i −0.273219 0.113171i 0.241867 0.970309i \(-0.422240\pi\)
−0.515087 + 0.857138i \(0.672240\pi\)
\(20\) −3.35733 0.877589i −0.750722 0.196235i
\(21\) −5.78977 + 3.95460i −1.26343 + 0.862964i
\(22\) 0.297893 + 4.34120i 0.0635110 + 0.925548i
\(23\) −3.11401 + 0.834395i −0.649315 + 0.173983i −0.568419 0.822739i \(-0.692445\pi\)
−0.0808959 + 0.996723i \(0.525778\pi\)
\(24\) 4.86855 + 0.545169i 0.993789 + 0.111282i
\(25\) 1.92175 + 0.514931i 0.384350 + 0.102986i
\(26\) 1.80846 9.23954i 0.354668 1.81202i
\(27\) −4.40673 2.75331i −0.848076 0.529875i
\(28\) −3.05237 + 7.49867i −0.576844 + 1.41712i
\(29\) 9.16431 1.20650i 1.70177 0.224042i 0.783890 0.620900i \(-0.213233\pi\)
0.917880 + 0.396857i \(0.129899\pi\)
\(30\) 4.22066 + 0.498815i 0.770583 + 0.0910708i
\(31\) 5.09391 8.82292i 0.914894 1.58464i 0.107838 0.994168i \(-0.465607\pi\)
0.807056 0.590475i \(-0.201059\pi\)
\(32\) 5.03457 2.57936i 0.889995 0.455971i
\(33\) −1.09296 5.21609i −0.190260 0.908005i
\(34\) 1.33936 + 1.51784i 0.229698 + 0.260307i
\(35\) −2.68784 + 6.48901i −0.454327 + 1.09684i
\(36\) −5.99789 + 0.159114i −0.999648 + 0.0265191i
\(37\) 2.44916 1.01448i 0.402640 0.166779i −0.172167 0.985068i \(-0.555077\pi\)
0.574807 + 0.818289i \(0.305077\pi\)
\(38\) 1.72446 0.591270i 0.279744 0.0959167i
\(39\) −0.636770 + 11.5132i −0.101965 + 1.84359i
\(40\) 4.38129 2.21089i 0.692742 0.349572i
\(41\) 1.80265 0.483019i 0.281527 0.0754349i −0.115293 0.993332i \(-0.536781\pi\)
0.396820 + 0.917897i \(0.370114\pi\)
\(42\) 2.43913 9.61100i 0.376366 1.48301i
\(43\) 1.77472 2.31285i 0.270642 0.352707i −0.638184 0.769884i \(-0.720314\pi\)
0.908825 + 0.417177i \(0.136981\pi\)
\(44\) −4.37798 4.32468i −0.660006 0.651969i
\(45\) −5.20412 + 0.106162i −0.775785 + 0.0158256i
\(46\) 2.52135 3.79859i 0.371752 0.560072i
\(47\) 8.10225 4.67784i 1.18183 0.682332i 0.225396 0.974267i \(-0.427632\pi\)
0.956438 + 0.291935i \(0.0942990\pi\)
\(48\) −5.67274 + 3.97744i −0.818789 + 0.574095i
\(49\) 8.12918 + 4.69338i 1.16131 + 0.670483i
\(50\) −2.51965 + 1.25216i −0.356332 + 0.177082i
\(51\) −1.88055 1.61557i −0.263330 0.226226i
\(52\) 6.72782 + 11.4898i 0.932981 + 1.59335i
\(53\) 1.74212 + 4.20586i 0.239299 + 0.577719i 0.997211 0.0746383i \(-0.0237802\pi\)
−0.757912 + 0.652357i \(0.773780\pi\)
\(54\) 7.24920 1.20380i 0.986491 0.163816i
\(55\) −3.77500 3.77500i −0.509021 0.509021i
\(56\) −3.77983 10.8077i −0.505101 1.44424i
\(57\) −1.99229 + 1.00788i −0.263885 + 0.133496i
\(58\) −8.58891 + 9.85450i −1.12778 + 1.29396i
\(59\) 0.306361 2.32704i 0.0398848 0.302955i −0.959862 0.280471i \(-0.909509\pi\)
0.999747 0.0224837i \(-0.00715738\pi\)
\(60\) −4.94234 + 3.42036i −0.638053 + 0.441566i
\(61\) −11.3916 + 1.49973i −1.45855 + 0.192021i −0.817699 0.575646i \(-0.804750\pi\)
−0.640848 + 0.767668i \(0.721417\pi\)
\(62\) 2.85408 + 14.1223i 0.362469 + 1.79353i
\(63\) −1.33924 + 12.0701i −0.168728 + 1.52069i
\(64\) −2.92514 + 7.44604i −0.365642 + 0.930755i
\(65\) 5.77545 + 10.0034i 0.716356 + 1.24076i
\(66\) 6.03971 + 4.50846i 0.743437 + 0.554953i
\(67\) −5.43059 7.07728i −0.663452 0.864628i 0.333491 0.942753i \(-0.391773\pi\)
−0.996944 + 0.0781253i \(0.975107\pi\)
\(68\) −2.84051 0.356273i −0.344462 0.0432045i
\(69\) −2.41849 + 5.03296i −0.291152 + 0.605897i
\(70\) −3.22163 9.39598i −0.385059 1.12303i
\(71\) −3.43628 + 3.43628i −0.407812 + 0.407812i −0.880975 0.473163i \(-0.843112\pi\)
0.473163 + 0.880975i \(0.343112\pi\)
\(72\) 6.21129 5.78100i 0.732007 0.681297i
\(73\) 8.89183 + 8.89183i 1.04071 + 1.04071i 0.999135 + 0.0415742i \(0.0132373\pi\)
0.0415742 + 0.999135i \(0.486763\pi\)
\(74\) −1.64784 + 3.36745i −0.191558 + 0.391459i
\(75\) 2.84556 1.94361i 0.328577 0.224428i
\(76\) −1.27536 + 2.24057i −0.146294 + 0.257011i
\(77\) −9.88163 + 7.58244i −1.12612 + 0.864099i
\(78\) −10.0978 12.8045i −1.14335 1.44982i
\(79\) −0.823181 + 0.475264i −0.0926151 + 0.0534713i −0.545592 0.838051i \(-0.683695\pi\)
0.452977 + 0.891522i \(0.350362\pi\)
\(80\) −2.57718 + 6.44403i −0.288137 + 0.720464i
\(81\) −8.59110 + 2.68197i −0.954567 + 0.297996i
\(82\) −1.45957 + 2.19895i −0.161183 + 0.242833i
\(83\) −0.727691 5.52736i −0.0798745 0.606707i −0.983833 0.179087i \(-0.942686\pi\)
0.903959 0.427620i \(-0.140648\pi\)
\(84\) 6.40663 + 12.4738i 0.699020 + 1.36101i
\(85\) −2.46230 0.324168i −0.267074 0.0351609i
\(86\) 0.282246 + 4.11317i 0.0304353 + 0.443534i
\(87\) 8.75847 13.4019i 0.939007 1.43683i
\(88\) 8.68905 + 0.489377i 0.926256 + 0.0521678i
\(89\) −1.60670 + 1.60670i −0.170310 + 0.170310i −0.787116 0.616805i \(-0.788427\pi\)
0.616805 + 0.787116i \(0.288427\pi\)
\(90\) 5.41912 4.98211i 0.571225 0.525161i
\(91\) 24.8978 10.3130i 2.61000 1.08110i
\(92\) 0.880737 + 6.38728i 0.0918231 + 0.665920i
\(93\) −5.84218 16.6507i −0.605806 1.72659i
\(94\) −4.21455 + 12.5417i −0.434697 + 1.29358i
\(95\) −1.11830 + 1.93696i −0.114735 + 0.198728i
\(96\) 2.29365 9.52571i 0.234095 0.972214i
\(97\) 0.147017 + 0.254642i 0.0149274 + 0.0258549i 0.873393 0.487017i \(-0.161915\pi\)
−0.858465 + 0.512872i \(0.828582\pi\)
\(98\) −13.0118 + 2.62967i −1.31439 + 0.265637i
\(99\) −8.08652 4.45137i −0.812726 0.447379i
\(100\) 1.50018 3.68545i 0.150018 0.368545i
\(101\) 3.38893 + 2.60042i 0.337211 + 0.258751i 0.763461 0.645855i \(-0.223499\pi\)
−0.426249 + 0.904606i \(0.640165\pi\)
\(102\) 3.50585 0.0464941i 0.347131 0.00460360i
\(103\) 1.34029 + 5.00202i 0.132062 + 0.492864i 0.999993 0.00382235i \(-0.00121669\pi\)
−0.867930 + 0.496686i \(0.834550\pi\)
\(104\) −17.8853 5.88854i −1.75380 0.577418i
\(105\) 5.49158 + 10.8553i 0.535923 + 1.05937i
\(106\) −5.78280 2.82978i −0.561676 0.274852i
\(107\) −0.883900 2.13392i −0.0854498 0.206294i 0.875379 0.483438i \(-0.160612\pi\)
−0.960828 + 0.277144i \(0.910612\pi\)
\(108\) −6.56066 + 8.05964i −0.631300 + 0.775539i
\(109\) −0.147431 0.0610679i −0.0141213 0.00584925i 0.375612 0.926777i \(-0.377433\pi\)
−0.389733 + 0.920928i \(0.627433\pi\)
\(110\) 7.53531 + 0.470717i 0.718463 + 0.0448811i
\(111\) 1.43150 4.36274i 0.135872 0.414093i
\(112\) 14.1210 + 7.92372i 1.33431 + 0.748721i
\(113\) 7.41644 + 4.28189i 0.697680 + 0.402806i 0.806483 0.591257i \(-0.201368\pi\)
−0.108803 + 0.994063i \(0.534702\pi\)
\(114\) 1.16955 2.93295i 0.109538 0.274696i
\(115\) 0.730113 + 5.54576i 0.0680833 + 0.517144i
\(116\) −0.113239 18.4864i −0.0105140 1.71642i
\(117\) 14.4074 + 13.8313i 1.33196 + 1.27871i
\(118\) 1.85256 + 2.75426i 0.170542 + 0.253550i
\(119\) −1.49968 + 5.59688i −0.137475 + 0.513065i
\(120\) 2.04040 8.25153i 0.186262 0.753259i
\(121\) 0.396668 + 1.48039i 0.0360608 + 0.134581i
\(122\) 10.6764 12.2495i 0.966593 1.10902i
\(123\) 1.40003 2.91351i 0.126236 0.262702i
\(124\) −16.2408 12.3047i −1.45846 1.10499i
\(125\) 4.64093 11.2042i 0.415097 1.00213i
\(126\) −9.87396 14.0523i −0.879642 1.25188i
\(127\) 2.92301 0.259375 0.129688 0.991555i \(-0.458603\pi\)
0.129688 + 0.991555i \(0.458603\pi\)
\(128\) −3.86550 10.6329i −0.341665 0.939822i
\(129\) −1.03555 4.94210i −0.0911750 0.435128i
\(130\) −15.4845 5.20345i −1.35808 0.456373i
\(131\) 5.94333 + 7.74549i 0.519271 + 0.676727i 0.977214 0.212254i \(-0.0680805\pi\)
−0.457944 + 0.888981i \(0.651414\pi\)
\(132\) −10.6231 + 0.870633i −0.924624 + 0.0757789i
\(133\) 4.13987 + 3.17663i 0.358972 + 0.275449i
\(134\) 12.3809 + 2.42331i 1.06954 + 0.209342i
\(135\) −5.73432 + 6.95701i −0.493531 + 0.598765i
\(136\) 3.34545 2.28009i 0.286870 0.195516i
\(137\) 0.335167 1.25086i 0.0286352 0.106868i −0.950129 0.311857i \(-0.899049\pi\)
0.978764 + 0.204989i \(0.0657157\pi\)
\(138\) −2.14481 7.59995i −0.182579 0.646951i
\(139\) −4.07562 0.536566i −0.345690 0.0455109i −0.0443176 0.999017i \(-0.514111\pi\)
−0.301372 + 0.953507i \(0.597445\pi\)
\(140\) 12.2081 + 6.94900i 1.03177 + 0.587298i
\(141\) 2.99910 15.9245i 0.252569 1.34109i
\(142\) 0.428482 6.85920i 0.0359574 0.575611i
\(143\) 20.4840i 1.71296i
\(144\) −1.17713 + 11.9421i −0.0980941 + 0.995177i
\(145\) 16.0379i 1.33188i
\(146\) −17.7491 1.10875i −1.46892 0.0917609i
\(147\) 15.3414 5.38281i 1.26534 0.443967i
\(148\) −1.40358 5.11275i −0.115374 0.420266i
\(149\) −13.2374 1.74274i −1.08445 0.142771i −0.432949 0.901418i \(-0.642527\pi\)
−0.651501 + 0.758648i \(0.725860\pi\)
\(150\) −1.19878 + 4.72361i −0.0978804 + 0.385681i
\(151\) 0.692177 2.58324i 0.0563286 0.210221i −0.932026 0.362393i \(-0.881960\pi\)
0.988354 + 0.152172i \(0.0486266\pi\)
\(152\) −0.744128 3.56927i −0.0603567 0.289506i
\(153\) −4.24509 + 0.647213i −0.343195 + 0.0523241i
\(154\) 3.38354 17.2867i 0.272654 1.39301i
\(155\) −14.0238 10.7608i −1.12642 0.864330i
\(156\) 22.6889 + 4.12930i 1.81657 + 0.330608i
\(157\) −7.10174 9.25517i −0.566781 0.738643i 0.418757 0.908098i \(-0.362466\pi\)
−0.985538 + 0.169455i \(0.945799\pi\)
\(158\) 0.428194 1.27423i 0.0340653 0.101372i
\(159\) 7.49197 + 2.45826i 0.594152 + 0.194953i
\(160\) −3.29689 9.24474i −0.260642 0.730861i
\(161\) 13.0504 1.02851
\(162\) 6.60048 10.8827i 0.518583 0.855027i
\(163\) −4.91332 + 11.8618i −0.384841 + 0.929089i 0.606173 + 0.795333i \(0.292704\pi\)
−0.991014 + 0.133756i \(0.957296\pi\)
\(164\) −0.509846 3.69750i −0.0398123 0.288726i
\(165\) −9.22037 + 0.698838i −0.717805 + 0.0544045i
\(166\) 5.94364 + 5.18032i 0.461316 + 0.402071i
\(167\) −1.63143 6.08859i −0.126244 0.471149i 0.873637 0.486578i \(-0.161755\pi\)
−0.999881 + 0.0154292i \(0.995089\pi\)
\(168\) −18.4655 7.23253i −1.42464 0.558002i
\(169\) 8.10617 30.2526i 0.623552 2.32713i
\(170\) 2.91435 1.96024i 0.223520 0.150344i
\(171\) −0.924507 + 3.75505i −0.0706988 + 0.287156i
\(172\) −4.14802 4.09751i −0.316283 0.312432i
\(173\) −1.44430 10.9705i −0.109808 0.834074i −0.954372 0.298620i \(-0.903474\pi\)
0.844564 0.535454i \(-0.179860\pi\)
\(174\) 3.25274 + 22.4067i 0.246589 + 1.69865i
\(175\) −6.97477 4.02689i −0.527243 0.304404i
\(176\) −9.67180 + 7.61148i −0.729039 + 0.573737i
\(177\) −2.71149 3.02898i −0.203808 0.227672i
\(178\) 0.200345 3.20716i 0.0150165 0.240386i
\(179\) 9.18365 + 3.80399i 0.686419 + 0.284324i 0.698507 0.715603i \(-0.253848\pi\)
−0.0120886 + 0.999927i \(0.503848\pi\)
\(180\) −1.08464 + 10.3537i −0.0808443 + 0.771723i
\(181\) 2.48949 + 6.01017i 0.185043 + 0.446732i 0.988993 0.147964i \(-0.0472721\pi\)
−0.803950 + 0.594697i \(0.797272\pi\)
\(182\) −16.7517 + 34.2330i −1.24172 + 2.53752i
\(183\) −10.8871 + 16.6591i −0.804800 + 1.23147i
\(184\) −6.91056 5.94896i −0.509453 0.438563i
\(185\) −1.19046 4.44286i −0.0875244 0.326646i
\(186\) 21.7752 + 12.1898i 1.59664 + 0.893800i
\(187\) −3.49412 2.68113i −0.255515 0.196064i
\(188\) −7.26628 17.2428i −0.529948 1.25756i
\(189\) 14.3462 + 15.3828i 1.04353 + 1.11893i
\(190\) −0.626577 3.10036i −0.0454567 0.224924i
\(191\) 11.7096 + 20.2816i 0.847275 + 1.46752i 0.883631 + 0.468185i \(0.155092\pi\)
−0.0363552 + 0.999339i \(0.511575\pi\)
\(192\) 6.48109 + 12.2473i 0.467733 + 0.883870i
\(193\) −5.64624 + 9.77958i −0.406426 + 0.703950i −0.994486 0.104867i \(-0.966558\pi\)
0.588061 + 0.808817i \(0.299892\pi\)
\(194\) −0.394168 0.132457i −0.0282996 0.00950985i
\(195\) 19.6611 + 3.70281i 1.40796 + 0.265163i
\(196\) 11.3372 14.9638i 0.809797 1.06884i
\(197\) 22.3777 9.26913i 1.59434 0.660398i 0.603741 0.797180i \(-0.293676\pi\)
0.990601 + 0.136782i \(0.0436759\pi\)
\(198\) 12.7401 2.84639i 0.905402 0.202284i
\(199\) 5.82964 5.82964i 0.413253 0.413253i −0.469617 0.882870i \(-0.655608\pi\)
0.882870 + 0.469617i \(0.155608\pi\)
\(200\) 1.85771 + 5.31179i 0.131360 + 0.375600i
\(201\) −15.4276 0.853264i −1.08818 0.0601846i
\(202\) −6.02686 + 0.413563i −0.424048 + 0.0290982i
\(203\) −37.0977 4.88400i −2.60375 0.342790i
\(204\) −3.67410 + 3.32975i −0.257238 + 0.233129i
\(205\) −0.422652 3.21036i −0.0295193 0.224221i
\(206\) −6.10167 4.05003i −0.425124 0.282179i
\(207\) 3.88262 + 8.85802i 0.269861 + 0.615675i
\(208\) 24.4755 10.4912i 1.69707 0.727434i
\(209\) −3.43494 + 1.98316i −0.237600 + 0.137178i
\(210\) −15.9807 6.37247i −1.10277 0.439742i
\(211\) −0.0767573 + 0.0588979i −0.00528419 + 0.00405470i −0.611400 0.791322i \(-0.709393\pi\)
0.606116 + 0.795376i \(0.292727\pi\)
\(212\) 8.77994 2.41031i 0.603009 0.165541i
\(213\) 0.636134 + 8.39307i 0.0435872 + 0.575083i
\(214\) 2.93402 + 1.43574i 0.200565 + 0.0981454i
\(215\) −3.57670 3.57670i −0.243929 0.243929i
\(216\) −0.584538 14.6853i −0.0397727 0.999209i
\(217\) −29.1617 + 29.1617i −1.97963 + 1.97963i
\(218\) 0.213478 0.0731959i 0.0144585 0.00495745i
\(219\) 21.7181 1.64608i 1.46758 0.111232i
\(220\) −8.43090 + 6.55170i −0.568411 + 0.441715i
\(221\) 5.80099 + 7.55999i 0.390217 + 0.508540i
\(222\) 2.56429 + 5.96572i 0.172104 + 0.400393i
\(223\) −0.990320 1.71529i −0.0663168 0.114864i 0.830961 0.556331i \(-0.187791\pi\)
−0.897277 + 0.441467i \(0.854458\pi\)
\(224\) −22.3882 + 4.81082i −1.49588 + 0.321437i
\(225\) 0.658209 5.93221i 0.0438806 0.395481i
\(226\) −11.8710 + 2.39911i −0.789647 + 0.159586i
\(227\) −25.5873 + 3.36863i −1.69829 + 0.223584i −0.916520 0.399988i \(-0.869014\pi\)
−0.781766 + 0.623572i \(0.785681\pi\)
\(228\) 1.50420 + 4.20446i 0.0996179 + 0.278447i
\(229\) −2.06747 + 15.7040i −0.136622 + 1.03775i 0.776516 + 0.630098i \(0.216985\pi\)
−0.913138 + 0.407651i \(0.866348\pi\)
\(230\) −5.96342 5.19755i −0.393216 0.342717i
\(231\) −1.19137 + 21.5407i −0.0783862 + 1.41727i
\(232\) 17.4180 + 19.4971i 1.14355 + 1.28005i
\(233\) 9.54703 + 9.54703i 0.625446 + 0.625446i 0.946919 0.321472i \(-0.104178\pi\)
−0.321472 + 0.946919i \(0.604178\pi\)
\(234\) −28.2197 1.18565i −1.84478 0.0775086i
\(235\) −6.21199 14.9971i −0.405226 0.978302i
\(236\) −4.54165 1.18716i −0.295636 0.0772777i
\(237\) −0.304705 + 1.61792i −0.0197927 + 0.105095i
\(238\) −3.64678 7.33820i −0.236386 0.475665i
\(239\) 3.00582 + 1.73541i 0.194430 + 0.112254i 0.594055 0.804425i \(-0.297526\pi\)
−0.399625 + 0.916679i \(0.630860\pi\)
\(240\) 5.55738 + 10.6592i 0.358727 + 0.688046i
\(241\) 12.3195 7.11267i 0.793569 0.458167i −0.0476485 0.998864i \(-0.515173\pi\)
0.841217 + 0.540697i \(0.181839\pi\)
\(242\) −1.80584 1.19864i −0.116084 0.0770514i
\(243\) −6.17304 + 14.3141i −0.396000 + 0.918250i
\(244\) 0.140761 + 22.9794i 0.00901129 + 1.47110i
\(245\) 9.91470 12.9211i 0.633427 0.825498i
\(246\) 1.24160 + 4.39950i 0.0791616 + 0.280502i
\(247\) 8.28926 2.22110i 0.527433 0.141325i
\(248\) 28.7353 2.14874i 1.82469 0.136445i
\(249\) −8.08320 5.28259i −0.512252 0.334770i
\(250\) 5.56260 + 16.2235i 0.351810 + 1.02606i
\(251\) −16.7760 + 6.94886i −1.05889 + 0.438608i −0.843059 0.537822i \(-0.819247\pi\)
−0.215835 + 0.976430i \(0.569247\pi\)
\(252\) 23.6192 + 5.66192i 1.48787 + 0.356667i
\(253\) −3.79604 + 9.16445i −0.238655 + 0.576164i
\(254\) −3.09957 + 2.73509i −0.194484 + 0.171615i
\(255\) −3.20504 + 2.86909i −0.200707 + 0.179670i
\(256\) 14.0482 + 7.65813i 0.878015 + 0.478633i
\(257\) 11.2836 19.5438i 0.703854 1.21911i −0.263249 0.964728i \(-0.584794\pi\)
0.967104 0.254383i \(-0.0818724\pi\)
\(258\) 5.72246 + 4.27164i 0.356265 + 0.265941i
\(259\) −10.6394 + 1.40071i −0.661101 + 0.0870356i
\(260\) 21.2887 8.97124i 1.32027 0.556373i
\(261\) −7.72190 26.6333i −0.477974 1.64856i
\(262\) −13.5498 2.65211i −0.837111 0.163848i
\(263\) 7.92004 + 2.12217i 0.488371 + 0.130859i 0.494598 0.869122i \(-0.335315\pi\)
−0.00622698 + 0.999981i \(0.501982\pi\)
\(264\) 10.4501 10.8634i 0.643160 0.668593i
\(265\) 7.62956 2.04433i 0.468680 0.125582i
\(266\) −7.36232 + 0.505202i −0.451413 + 0.0309759i
\(267\) 0.297437 + 3.92435i 0.0182029 + 0.240166i
\(268\) −15.3962 + 9.01520i −0.940473 + 0.550691i
\(269\) −25.4457 10.5399i −1.55145 0.642631i −0.567871 0.823117i \(-0.692233\pi\)
−0.983577 + 0.180486i \(0.942233\pi\)
\(270\) −0.429059 12.7429i −0.0261117 0.775506i
\(271\) 17.5837i 1.06813i −0.845442 0.534067i \(-0.820663\pi\)
0.845442 0.534067i \(-0.179337\pi\)
\(272\) −1.41401 + 5.54817i −0.0857372 + 0.336408i
\(273\) 14.5524 44.3509i 0.880752 2.68424i
\(274\) 0.815028 + 1.64003i 0.0492376 + 0.0990779i
\(275\) 4.85662 3.72662i 0.292865 0.224724i
\(276\) 9.38570 + 6.05208i 0.564953 + 0.364292i
\(277\) 1.38278 1.80207i 0.0830830 0.108276i −0.749963 0.661480i \(-0.769929\pi\)
0.833045 + 0.553204i \(0.186595\pi\)
\(278\) 4.82386 3.24462i 0.289316 0.194599i
\(279\) −28.4697 11.1178i −1.70443 0.665606i
\(280\) −19.4477 + 4.05450i −1.16223 + 0.242303i
\(281\) 9.49178 + 2.54332i 0.566232 + 0.151722i 0.530568 0.847642i \(-0.321979\pi\)
0.0356643 + 0.999364i \(0.488645\pi\)
\(282\) 11.7205 + 19.6927i 0.697944 + 1.17268i
\(283\) −3.84409 + 29.1987i −0.228507 + 1.73568i 0.365135 + 0.930955i \(0.381023\pi\)
−0.593642 + 0.804729i \(0.702310\pi\)
\(284\) 5.96384 + 7.67443i 0.353889 + 0.455394i
\(285\) 1.28258 + 3.65544i 0.0759732 + 0.216529i
\(286\) −19.1670 21.7212i −1.13337 1.28440i
\(287\) −7.55466 −0.445938
\(288\) −9.92611 13.7649i −0.584902 0.811104i
\(289\) 14.9511 0.879479
\(290\) 15.0068 + 17.0066i 0.881230 + 0.998663i
\(291\) 0.500485 + 0.0942571i 0.0293389 + 0.00552545i
\(292\) 19.8586 15.4322i 1.16214 0.903102i
\(293\) 1.87236 14.2220i 0.109385 0.830859i −0.845519 0.533945i \(-0.820709\pi\)
0.954904 0.296914i \(-0.0959576\pi\)
\(294\) −11.2313 + 20.0630i −0.655025 + 1.17010i
\(295\) −3.93365 1.05402i −0.229026 0.0613673i
\(296\) 6.27240 + 4.10823i 0.364576 + 0.238786i
\(297\) −14.9753 + 5.59993i −0.868956 + 0.324941i
\(298\) 15.6676 10.5383i 0.907602 0.610469i
\(299\) 13.0654 17.0271i 0.755590 0.984704i
\(300\) −3.14873 6.13064i −0.181792 0.353953i
\(301\) −9.36257 + 7.18415i −0.539649 + 0.414088i
\(302\) 1.68317 + 3.38695i 0.0968557 + 0.194897i
\(303\) 7.24146 1.51735i 0.416011 0.0871693i
\(304\) 4.12887 + 3.08857i 0.236807 + 0.177142i
\(305\) 19.9358i 1.14152i
\(306\) 3.89590 4.65847i 0.222714 0.266307i
\(307\) −4.88742 2.02444i −0.278940 0.115541i 0.238828 0.971062i \(-0.423237\pi\)
−0.517768 + 0.855521i \(0.673237\pi\)
\(308\) 12.5874 + 21.4969i 0.717236 + 1.22490i
\(309\) 8.08443 + 3.88481i 0.459907 + 0.220999i
\(310\) 24.9398 1.71137i 1.41649 0.0971992i
\(311\) 12.0325 3.22410i 0.682300 0.182822i 0.0990110 0.995086i \(-0.468432\pi\)
0.583289 + 0.812265i \(0.301765\pi\)
\(312\) −27.9232 + 16.8515i −1.58084 + 0.954028i
\(313\) 13.7087 + 3.67323i 0.774860 + 0.207623i 0.624518 0.781011i \(-0.285296\pi\)
0.150343 + 0.988634i \(0.451962\pi\)
\(314\) 16.1908 + 3.16904i 0.913702 + 0.178839i
\(315\) 20.4600 + 5.03733i 1.15279 + 0.283821i
\(316\) 0.738247 + 1.75186i 0.0415296 + 0.0985496i
\(317\) −10.1840 + 1.34075i −0.571989 + 0.0753038i −0.410972 0.911648i \(-0.634811\pi\)
−0.161017 + 0.986952i \(0.551477\pi\)
\(318\) −10.2447 + 4.40355i −0.574495 + 0.246939i
\(319\) 14.2206 24.6307i 0.796198 1.37906i
\(320\) 12.1464 + 6.71821i 0.679005 + 0.375559i
\(321\) −3.80120 1.24725i −0.212162 0.0696146i
\(322\) −13.8386 + 12.2113i −0.771196 + 0.680510i
\(323\) −0.706104 + 1.70468i −0.0392887 + 0.0948512i
\(324\) 3.18389 + 17.7162i 0.176883 + 0.984232i
\(325\) −12.2368 + 5.06864i −0.678774 + 0.281158i
\(326\) −5.88910 17.1757i −0.326167 0.951275i
\(327\) −0.246634 + 0.124769i −0.0136389 + 0.00689975i
\(328\) 4.00042 + 3.44377i 0.220886 + 0.190150i
\(329\) −36.5818 + 9.80207i −2.01682 + 0.540406i
\(330\) 9.12338 9.36862i 0.502226 0.515726i
\(331\) 6.78704 8.84505i 0.373050 0.486168i −0.568670 0.822566i \(-0.692542\pi\)
0.941720 + 0.336398i \(0.109209\pi\)
\(332\) −11.1499 + 0.0682990i −0.611931 + 0.00374840i
\(333\) −4.11608 6.80485i −0.225560 0.372904i
\(334\) 7.42711 + 4.92980i 0.406394 + 0.269747i
\(335\) −13.4044 + 7.73903i −0.732360 + 0.422828i
\(336\) 26.3483 9.60889i 1.43742 0.524208i
\(337\) −9.38070 5.41595i −0.510999 0.295026i 0.222245 0.974991i \(-0.428661\pi\)
−0.733244 + 0.679965i \(0.761995\pi\)
\(338\) 19.7118 + 39.6649i 1.07218 + 2.15749i
\(339\) 13.9964 4.91087i 0.760178 0.266722i
\(340\) −1.25616 + 4.80563i −0.0681251 + 0.260622i
\(341\) −11.9960 28.9609i −0.649620 1.56832i
\(342\) −2.53328 4.84692i −0.136984 0.262092i
\(343\) −6.83191 6.83191i −0.368888 0.368888i
\(344\) 8.23264 + 0.463671i 0.443874 + 0.0249995i
\(345\) 8.11010 + 5.30016i 0.436633 + 0.285351i
\(346\) 11.7967 + 10.2817i 0.634197 + 0.552749i
\(347\) −3.20940 + 24.3778i −0.172290 + 1.30867i 0.658710 + 0.752397i \(0.271103\pi\)
−0.830999 + 0.556273i \(0.812231\pi\)
\(348\) −24.4154 20.7165i −1.30880 1.11052i
\(349\) −3.87824 + 0.510580i −0.207598 + 0.0273307i −0.233608 0.972331i \(-0.575053\pi\)
0.0260101 + 0.999662i \(0.491720\pi\)
\(350\) 11.1640 2.25623i 0.596743 0.120601i
\(351\) 34.4330 3.31732i 1.83790 0.177065i
\(352\) 3.13386 17.1212i 0.167035 0.912563i
\(353\) −13.3392 23.1041i −0.709973 1.22971i −0.964867 0.262740i \(-0.915374\pi\)
0.254893 0.966969i \(-0.417960\pi\)
\(354\) 5.70951 + 0.674775i 0.303457 + 0.0358639i
\(355\) 5.13296 + 6.68940i 0.272429 + 0.355036i
\(356\) 2.78851 + 3.58834i 0.147791 + 0.190181i
\(357\) 5.66054 + 8.28738i 0.299588 + 0.438614i
\(358\) −13.2978 + 4.55946i −0.702810 + 0.240975i
\(359\) 14.1337 14.1337i 0.745946 0.745946i −0.227770 0.973715i \(-0.573143\pi\)
0.973715 + 0.227770i \(0.0731433\pi\)
\(360\) −8.53793 11.9940i −0.449988 0.632141i
\(361\) −12.2600 12.2600i −0.645266 0.645266i
\(362\) −8.26362 4.04375i −0.434326 0.212535i
\(363\) 2.39265 + 1.14974i 0.125581 + 0.0603457i
\(364\) −14.2686 51.9754i −0.747876 2.72425i
\(365\) 17.3097 13.2822i 0.906030 0.695221i
\(366\) −4.04328 27.8525i −0.211346 1.45587i
\(367\) −26.5535 + 15.3307i −1.38608 + 0.800256i −0.992871 0.119192i \(-0.961970\pi\)
−0.393212 + 0.919448i \(0.628636\pi\)
\(368\) 12.8945 0.157977i 0.672170 0.00823510i
\(369\) −2.24759 5.12778i −0.117005 0.266941i
\(370\) 5.41959 + 3.59729i 0.281751 + 0.187014i
\(371\) −2.40538 18.2707i −0.124881 0.948566i
\(372\) −34.4966 + 7.44915i −1.78856 + 0.386220i
\(373\) −8.57693 1.12917i −0.444097 0.0584665i −0.0948379 0.995493i \(-0.530233\pi\)
−0.349259 + 0.937026i \(0.613567\pi\)
\(374\) 6.21392 0.426399i 0.321314 0.0220486i
\(375\) −9.48198 18.7432i −0.489647 0.967896i
\(376\) 23.8394 + 11.4852i 1.22942 + 0.592305i
\(377\) −43.5126 + 43.5126i −2.24102 + 2.24102i
\(378\) −29.6065 2.88810i −1.52279 0.148548i
\(379\) −13.6939 + 5.67222i −0.703411 + 0.291362i −0.705575 0.708635i \(-0.749311\pi\)
0.00216403 + 0.999998i \(0.499311\pi\)
\(380\) 3.56545 + 2.70133i 0.182904 + 0.138575i
\(381\) 3.29915 3.84026i 0.169020 0.196743i
\(382\) −31.3945 10.5499i −1.60628 0.539778i
\(383\) 10.4039 18.0200i 0.531612 0.920780i −0.467707 0.883884i \(-0.654920\pi\)
0.999319 0.0368960i \(-0.0117470\pi\)
\(384\) −18.3324 6.92260i −0.935522 0.353268i
\(385\) 10.8056 + 18.7158i 0.550704 + 0.953847i
\(386\) −3.16355 15.6535i −0.161020 0.796743i
\(387\) −7.66176 4.21755i −0.389469 0.214390i
\(388\) 0.541917 0.228368i 0.0275117 0.0115936i
\(389\) −3.48406 2.67341i −0.176649 0.135547i 0.516653 0.856195i \(-0.327178\pi\)
−0.693301 + 0.720648i \(0.743845\pi\)
\(390\) −24.3134 + 14.4706i −1.23116 + 0.732746i
\(391\) 1.19434 + 4.45733i 0.0604003 + 0.225417i
\(392\) 1.97978 + 26.4759i 0.0999942 + 1.33723i
\(393\) 16.8842 + 0.933826i 0.851694 + 0.0471053i
\(394\) −15.0561 + 30.7680i −0.758516 + 1.55007i
\(395\) 0.631133 + 1.52369i 0.0317557 + 0.0766651i
\(396\) −10.8463 + 14.9394i −0.545046 + 0.750731i
\(397\) 6.92854 + 2.86989i 0.347733 + 0.144036i 0.549712 0.835354i \(-0.314737\pi\)
−0.201979 + 0.979390i \(0.564737\pi\)
\(398\) −0.726918 + 11.6366i −0.0364371 + 0.583290i
\(399\) 8.84606 1.85357i 0.442857 0.0927945i
\(400\) −6.94020 3.89435i −0.347010 0.194718i
\(401\) −12.9177 7.45804i −0.645079 0.372437i 0.141489 0.989940i \(-0.454811\pi\)
−0.786568 + 0.617503i \(0.788144\pi\)
\(402\) 17.1578 13.5309i 0.855754 0.674860i
\(403\) 8.85276 + 67.2434i 0.440987 + 3.34963i
\(404\) 6.00391 6.07792i 0.298706 0.302388i
\(405\) 2.66794 + 15.3860i 0.132571 + 0.764537i
\(406\) 43.9084 29.5336i 2.17914 1.46573i
\(407\) 2.11112 7.87882i 0.104645 0.390539i
\(408\) 0.780345 6.96876i 0.0386329 0.345005i
\(409\) −6.38440 23.8269i −0.315688 1.17816i −0.923347 0.383967i \(-0.874558\pi\)
0.607659 0.794198i \(-0.292109\pi\)
\(410\) 3.45214 + 3.00879i 0.170489 + 0.148593i
\(411\) −1.26509 1.85216i −0.0624022 0.0913605i
\(412\) 10.2599 1.41473i 0.505467 0.0696985i
\(413\) −3.63598 + 8.77804i −0.178915 + 0.431939i
\(414\) −12.4057 5.76006i −0.609705 0.283091i
\(415\) −9.67311 −0.474834
\(416\) −16.1372 + 34.0268i −0.791191 + 1.66830i
\(417\) −5.30502 + 4.74896i −0.259788 + 0.232557i
\(418\) 1.78675 5.31705i 0.0873929 0.260065i
\(419\) 16.8186 + 21.9184i 0.821641 + 1.07078i 0.996282 + 0.0861516i \(0.0274569\pi\)
−0.174641 + 0.984632i \(0.555876\pi\)
\(420\) 22.9087 8.19586i 1.11783 0.399917i
\(421\) 10.2225 + 7.84400i 0.498214 + 0.382293i 0.827081 0.562083i \(-0.190000\pi\)
−0.328866 + 0.944376i \(0.606667\pi\)
\(422\) 0.0262822 0.134278i 0.00127940 0.00653654i
\(423\) −17.5367 21.9140i −0.852664 1.06549i
\(424\) −7.05491 + 10.7714i −0.342616 + 0.523103i
\(425\) 0.737063 2.75076i 0.0357528 0.133431i
\(426\) −8.52802 8.30478i −0.413184 0.402368i
\(427\) 46.1139 + 6.07101i 2.23161 + 0.293797i
\(428\) −4.45467 + 1.22292i −0.215325 + 0.0591121i
\(429\) 26.9119 + 23.1199i 1.29932 + 1.11624i
\(430\) 7.13949 + 0.445991i 0.344297 + 0.0215076i
\(431\) 24.3828i 1.17448i −0.809414 0.587238i \(-0.800215\pi\)
0.809414 0.587238i \(-0.199785\pi\)
\(432\) 14.3610 + 15.0254i 0.690944 + 0.722908i
\(433\) 37.8913i 1.82094i 0.413573 + 0.910471i \(0.364281\pi\)
−0.413573 + 0.910471i \(0.635719\pi\)
\(434\) 3.63627 58.2100i 0.174547 2.79417i
\(435\) −21.0707 18.1017i −1.01026 0.867909i
\(436\) −0.157882 + 0.277370i −0.00756118 + 0.0132836i
\(437\) 4.12019 + 0.542433i 0.197095 + 0.0259481i
\(438\) −21.4897 + 22.0673i −1.02682 + 1.05442i
\(439\) −7.53141 + 28.1076i −0.359455 + 1.34150i 0.515331 + 0.856992i \(0.327669\pi\)
−0.874785 + 0.484511i \(0.838998\pi\)
\(440\) 2.80966 14.8363i 0.133945 0.707292i
\(441\) 10.2436 26.2311i 0.487792 1.24910i
\(442\) −13.2253 2.58860i −0.629064 0.123127i
\(443\) 4.39086 + 3.36923i 0.208616 + 0.160077i 0.707785 0.706428i \(-0.249695\pi\)
−0.499169 + 0.866505i \(0.666361\pi\)
\(444\) −8.30134 3.92664i −0.393964 0.186350i
\(445\) 2.40002 + 3.12776i 0.113772 + 0.148270i
\(446\) 2.65514 + 0.892240i 0.125725 + 0.0422488i
\(447\) −17.2304 + 15.4243i −0.814970 + 0.729546i
\(448\) 19.2390 26.0502i 0.908956 1.23076i
\(449\) 28.3704 1.33888 0.669440 0.742866i \(-0.266534\pi\)
0.669440 + 0.742866i \(0.266534\pi\)
\(450\) 4.85285 + 6.90642i 0.228766 + 0.325572i
\(451\) 2.19747 5.30516i 0.103475 0.249810i
\(452\) 10.3432 13.6518i 0.486501 0.642127i
\(453\) −2.61262 3.82504i −0.122752 0.179716i
\(454\) 23.9807 27.5143i 1.12547 1.29131i
\(455\) −12.1020 45.1654i −0.567352 2.11739i
\(456\) −5.52920 3.05093i −0.258929 0.142873i
\(457\) 4.10907 15.3353i 0.192214 0.717353i −0.800756 0.598990i \(-0.795569\pi\)
0.992970 0.118363i \(-0.0377645\pi\)
\(458\) −12.5020 18.5871i −0.584180 0.868517i
\(459\) −3.94104 + 6.30771i −0.183952 + 0.294419i
\(460\) 11.1870 0.0685263i 0.521597 0.00319505i
\(461\) 1.67162 + 12.6972i 0.0778553 + 0.591369i 0.985254 + 0.171098i \(0.0547316\pi\)
−0.907399 + 0.420271i \(0.861935\pi\)
\(462\) −18.8924 23.9565i −0.878956 1.11456i
\(463\) 22.0780 + 12.7467i 1.02605 + 0.592391i 0.915851 0.401519i \(-0.131518\pi\)
0.110200 + 0.993909i \(0.464851\pi\)
\(464\) −36.7136 4.37658i −1.70439 0.203178i
\(465\) −29.9660 + 6.27895i −1.38964 + 0.291179i
\(466\) −19.0569 1.19045i −0.882794 0.0551465i
\(467\) −0.208936 0.0865443i −0.00966842 0.00400479i 0.377844 0.925869i \(-0.376666\pi\)
−0.387512 + 0.921864i \(0.626666\pi\)
\(468\) 31.0336 25.1481i 1.43453 1.16247i
\(469\) 13.8193 + 33.3628i 0.638116 + 1.54055i
\(470\) 20.6201 + 10.0903i 0.951134 + 0.465431i
\(471\) −20.1751 1.11584i −0.929619 0.0514151i
\(472\) 5.92680 2.99079i 0.272803 0.137662i
\(473\) −2.32163 8.66444i −0.106749 0.398391i
\(474\) −1.19079 2.00076i −0.0546948 0.0918979i
\(475\) −2.03466 1.56125i −0.0933567 0.0716351i
\(476\) 10.7335 + 4.36911i 0.491968 + 0.200258i
\(477\) 11.6857 7.06838i 0.535052 0.323639i
\(478\) −4.81121 + 0.972336i −0.220059 + 0.0444736i
\(479\) 4.03595 + 6.99047i 0.184407 + 0.319403i 0.943377 0.331724i \(-0.107630\pi\)
−0.758969 + 0.651126i \(0.774297\pi\)
\(480\) −15.8669 6.10290i −0.724222 0.278558i
\(481\) −8.82412 + 15.2838i −0.402345 + 0.696883i
\(482\) −6.40824 + 19.0697i −0.291887 + 0.868603i
\(483\) 14.7297 17.1456i 0.670224 0.780152i
\(484\) 3.03649 0.418699i 0.138022 0.0190318i
\(485\) 0.471336 0.195234i 0.0214023 0.00886511i
\(486\) −6.84793 20.9549i −0.310628 0.950531i
\(487\) −14.4163 + 14.4163i −0.653266 + 0.653266i −0.953778 0.300512i \(-0.902843\pi\)
0.300512 + 0.953778i \(0.402843\pi\)
\(488\) −21.6513 24.2357i −0.980107 1.09710i
\(489\) 10.0385 + 19.8433i 0.453957 + 0.897347i
\(490\) 1.57681 + 22.9788i 0.0712328 + 1.03808i
\(491\) −4.82843 0.635675i −0.217904 0.0286876i 0.0207837 0.999784i \(-0.493384\pi\)
−0.238688 + 0.971096i \(0.576717\pi\)
\(492\) −5.43324 3.50346i −0.244950 0.157948i
\(493\) −1.72697 13.1176i −0.0777788 0.590789i
\(494\) −6.71164 + 10.1116i −0.301971 + 0.454942i
\(495\) −9.48872 + 12.9025i −0.426486 + 0.579925i
\(496\) −28.4604 + 29.1664i −1.27791 + 1.30961i
\(497\) 17.0365 9.83605i 0.764193 0.441207i
\(498\) 13.5144 1.96186i 0.605594 0.0879128i
\(499\) −2.66382 + 2.04402i −0.119249 + 0.0915029i −0.666664 0.745358i \(-0.732278\pi\)
0.547415 + 0.836861i \(0.315612\pi\)
\(500\) −21.0790 11.9984i −0.942683 0.536586i
\(501\) −9.84058 4.72869i −0.439645 0.211262i
\(502\) 11.2872 23.0661i 0.503773 1.02949i
\(503\) 21.1740 + 21.1740i 0.944101 + 0.944101i 0.998518 0.0544176i \(-0.0173302\pi\)
−0.0544176 + 0.998518i \(0.517330\pi\)
\(504\) −30.3437 + 16.0968i −1.35162 + 0.717007i
\(505\) 5.24080 5.24080i 0.233212 0.233212i
\(506\) −4.54992 13.2700i −0.202269 0.589922i
\(507\) −30.5968 44.7955i −1.35885 1.98944i
\(508\) 0.727542 5.80058i 0.0322795 0.257359i
\(509\) 15.4154 + 20.0897i 0.683275 + 0.890461i 0.998280 0.0586289i \(-0.0186729\pi\)
−0.315005 + 0.949090i \(0.602006\pi\)
\(510\) 0.713995 6.04137i 0.0316162 0.267516i
\(511\) −25.4520 44.0842i −1.12593 1.95017i
\(512\) −22.0625 + 5.02436i −0.975036 + 0.222048i
\(513\) 3.88992 + 5.45287i 0.171744 + 0.240750i
\(514\) 6.32214 + 31.2825i 0.278857 + 1.37981i
\(515\) 8.90813 1.17278i 0.392539 0.0516788i
\(516\) −10.0651 + 0.824900i −0.443092 + 0.0363142i
\(517\) 3.75740 28.5403i 0.165250 1.25520i
\(518\) 9.97140 11.4407i 0.438118 0.502675i
\(519\) −16.0433 10.4847i −0.704221 0.460227i
\(520\) −14.1801 + 29.4331i −0.621839 + 1.29073i
\(521\) −6.17342 6.17342i −0.270462 0.270462i 0.558824 0.829286i \(-0.311253\pi\)
−0.829286 + 0.558824i \(0.811253\pi\)
\(522\) 33.1093 + 21.0166i 1.44916 + 0.919871i
\(523\) −10.3823 25.0650i −0.453984 1.09602i −0.970794 0.239915i \(-0.922880\pi\)
0.516810 0.856100i \(-0.327120\pi\)
\(524\) 16.8499 9.86638i 0.736090 0.431015i
\(525\) −13.1628 + 4.61841i −0.574473 + 0.201564i
\(526\) −10.3841 + 5.16049i −0.452770 + 0.225008i
\(527\) −12.6290 7.29134i −0.550127 0.317616i
\(528\) −0.916382 + 21.2978i −0.0398804 + 0.926866i
\(529\) −10.9178 + 6.30338i −0.474685 + 0.274060i
\(530\) −6.17749 + 9.30685i −0.268333 + 0.404264i
\(531\) −7.03990 + 0.143611i −0.305506 + 0.00623217i
\(532\) 7.33429 7.42470i 0.317982 0.321901i
\(533\) −7.56336 + 9.85676i −0.327605 + 0.426944i
\(534\) −3.98745 3.88307i −0.172554 0.168037i
\(535\) −3.87100 + 1.03723i −0.167358 + 0.0448435i
\(536\) 7.89057 23.9661i 0.340821 1.03518i
\(537\) 15.3631 7.77202i 0.662967 0.335388i
\(538\) 36.8449 12.6331i 1.58850 0.544653i
\(539\) 26.6837 11.0528i 1.14935 0.476076i
\(540\) 12.3786 + 13.1111i 0.532689 + 0.564211i
\(541\) 12.7923 30.8833i 0.549984 1.32778i −0.367507 0.930021i \(-0.619789\pi\)
0.917491 0.397757i \(-0.130211\pi\)
\(542\) 16.4532 + 18.6458i 0.706725 + 0.800904i
\(543\) 10.7060 + 3.51286i 0.459439 + 0.150751i
\(544\) −3.69205 7.20639i −0.158295 0.308972i
\(545\) −0.138439 + 0.239784i −0.00593010 + 0.0102712i
\(546\) 26.0681 + 60.6466i 1.11561 + 2.59543i
\(547\) 34.4731 4.53847i 1.47396 0.194051i 0.649672 0.760215i \(-0.274906\pi\)
0.824293 + 0.566164i \(0.191573\pi\)
\(548\) −2.39885 0.976463i −0.102474 0.0417124i
\(549\) 9.59863 + 33.1063i 0.409660 + 1.41294i
\(550\) −1.66294 + 8.49609i −0.0709081 + 0.362275i
\(551\) −11.5093 3.08390i −0.490312 0.131379i
\(552\) −15.6156 + 2.36464i −0.664643 + 0.100646i
\(553\) 3.71668 0.995881i 0.158049 0.0423492i
\(554\) 0.219913 + 3.20479i 0.00934319 + 0.136158i
\(555\) −7.18070 3.45054i −0.304804 0.146467i
\(556\) −2.07922 + 7.95432i −0.0881785 + 0.337338i
\(557\) 33.0017 + 13.6698i 1.39833 + 0.579206i 0.949317 0.314320i \(-0.101777\pi\)
0.449010 + 0.893526i \(0.351777\pi\)
\(558\) 40.5923 14.8499i 1.71841 0.628648i
\(559\) 19.4080i 0.820871i
\(560\) 16.8286 22.4968i 0.711137 0.950664i
\(561\) −7.46622 + 1.56444i −0.315224 + 0.0660508i
\(562\) −12.4449 + 6.18460i −0.524956 + 0.260882i
\(563\) 1.77889 1.36499i 0.0749715 0.0575276i −0.570596 0.821231i \(-0.693288\pi\)
0.645567 + 0.763703i \(0.276621\pi\)
\(564\) −30.8550 9.91520i −1.29923 0.417505i
\(565\) 9.04542 11.7882i 0.380544 0.495934i
\(566\) −23.2452 34.5593i −0.977069 1.45264i
\(567\) 36.4022 1.48579i 1.52875 0.0623975i
\(568\) −13.5051 2.55756i −0.566661 0.107313i
\(569\) 18.1139 + 4.85362i 0.759376 + 0.203474i 0.617673 0.786435i \(-0.288075\pi\)
0.141703 + 0.989909i \(0.454742\pi\)
\(570\) −4.78047 2.67612i −0.200232 0.112090i
\(571\) −2.50913 + 19.0588i −0.105004 + 0.797585i 0.855203 + 0.518294i \(0.173433\pi\)
−0.960207 + 0.279291i \(0.909901\pi\)
\(572\) 40.6495 + 5.09849i 1.69964 + 0.213179i
\(573\) 39.8624 + 7.50735i 1.66528 + 0.313624i
\(574\) 8.01097 7.06896i 0.334371 0.295052i
\(575\) −6.41399 −0.267482
\(576\) 23.4056 + 5.30837i 0.975233 + 0.221182i
\(577\) 17.3231 0.721169 0.360584 0.932727i \(-0.382577\pi\)
0.360584 + 0.932727i \(0.382577\pi\)
\(578\) −15.8542 + 13.9899i −0.659448 + 0.581903i
\(579\) 6.47564 + 18.4561i 0.269119 + 0.767009i
\(580\) −31.8265 3.99186i −1.32152 0.165753i
\(581\) −2.94574 + 22.3751i −0.122210 + 0.928275i
\(582\) −0.618912 + 0.368357i −0.0256547 + 0.0152689i
\(583\) 13.5300 + 3.62536i 0.560356 + 0.150147i
\(584\) −6.61803 + 34.9462i −0.273856 + 1.44608i
\(585\) 27.0559 21.6515i 1.11862 0.895181i
\(586\) 11.3222 + 16.8330i 0.467715 + 0.695366i
\(587\) 3.43856 4.48122i 0.141925 0.184960i −0.716983 0.697091i \(-0.754477\pi\)
0.858907 + 0.512131i \(0.171144\pi\)
\(588\) −6.86343 31.7841i −0.283043 1.31076i
\(589\) −10.4189 + 7.99470i −0.429303 + 0.329416i
\(590\) 5.15750 2.56306i 0.212331 0.105520i
\(591\) 13.0794 39.8617i 0.538015 1.63969i
\(592\) −10.4954 + 1.51276i −0.431357 + 0.0621742i
\(593\) 12.5351i 0.514755i 0.966311 + 0.257378i \(0.0828584\pi\)
−0.966311 + 0.257378i \(0.917142\pi\)
\(594\) 10.6400 19.9507i 0.436563 0.818587i
\(595\) 9.28825 + 3.84732i 0.380781 + 0.157725i
\(596\) −6.75318 + 25.8352i −0.276621 + 1.05825i
\(597\) −1.07920 14.2388i −0.0441687 0.582756i
\(598\) 2.07788 + 30.2810i 0.0849708 + 1.23828i
\(599\) 32.5828 8.73052i 1.33130 0.356719i 0.478097 0.878307i \(-0.341327\pi\)
0.853198 + 0.521587i \(0.174660\pi\)
\(600\) 9.07540 + 3.55464i 0.370502 + 0.145118i
\(601\) 8.46909 + 2.26929i 0.345461 + 0.0925661i 0.427378 0.904073i \(-0.359437\pi\)
−0.0819165 + 0.996639i \(0.526104\pi\)
\(602\) 3.20581 16.3787i 0.130659 0.667546i
\(603\) −18.5338 + 19.3057i −0.754755 + 0.786190i
\(604\) −4.95403 2.01656i −0.201577 0.0820528i
\(605\) 2.63643 0.347093i 0.107186 0.0141113i
\(606\) −6.25906 + 8.38488i −0.254257 + 0.340613i
\(607\) −2.69541 + 4.66859i −0.109403 + 0.189492i −0.915529 0.402253i \(-0.868227\pi\)
0.806125 + 0.591745i \(0.201561\pi\)
\(608\) −7.26826 + 0.588289i −0.294767 + 0.0238583i
\(609\) −48.2880 + 43.2266i −1.95673 + 1.75163i
\(610\) −18.6541 21.1399i −0.755281 0.855930i
\(611\) −23.8349 + 57.5426i −0.964258 + 2.32792i
\(612\) 0.227753 + 8.58527i 0.00920638 + 0.347039i
\(613\) −7.39650 + 3.06373i −0.298742 + 0.123743i −0.527020 0.849853i \(-0.676691\pi\)
0.228278 + 0.973596i \(0.426691\pi\)
\(614\) 7.07691 2.42648i 0.285601 0.0979249i
\(615\) −4.69482 3.06819i −0.189313 0.123721i
\(616\) −33.4625 11.0172i −1.34824 0.443894i
\(617\) −31.0735 + 8.32612i −1.25097 + 0.335197i −0.822712 0.568459i \(-0.807540\pi\)
−0.428260 + 0.903656i \(0.640873\pi\)
\(618\) −12.2078 + 3.44521i −0.491069 + 0.138587i
\(619\) −17.3564 + 22.6194i −0.697614 + 0.909149i −0.999016 0.0443485i \(-0.985879\pi\)
0.301402 + 0.953497i \(0.402545\pi\)
\(620\) −24.8449 + 25.1511i −0.997794 + 1.01009i
\(621\) 16.0199 + 4.89688i 0.642858 + 0.196505i
\(622\) −9.74246 + 14.6777i −0.390637 + 0.588524i
\(623\) 7.96577 4.59904i 0.319142 0.184257i
\(624\) 13.8417 43.9973i 0.554111 1.76130i
\(625\) −9.60772 5.54702i −0.384309 0.221881i
\(626\) −17.9738 + 8.93222i −0.718376 + 0.357003i
\(627\) −1.27146 + 6.75119i −0.0507773 + 0.269617i
\(628\) −20.1341 + 11.7894i −0.803437 + 0.470450i
\(629\) −1.45210 3.50569i −0.0578992 0.139781i
\(630\) −26.4093 + 13.8030i −1.05217 + 0.549924i
\(631\) 1.40904 + 1.40904i 0.0560931 + 0.0560931i 0.734597 0.678504i \(-0.237371\pi\)
−0.678504 + 0.734597i \(0.737371\pi\)
\(632\) −2.42206 1.16689i −0.0963445 0.0464163i
\(633\) −0.00925415 + 0.167321i −0.000367819 + 0.00665041i
\(634\) 9.54455 10.9510i 0.379063 0.434918i
\(635\) 0.661980 5.02824i 0.0262699 0.199540i
\(636\) 6.74307 14.2556i 0.267380 0.565271i
\(637\) −61.9561 + 8.15667i −2.45479 + 0.323179i
\(638\) 7.96767 + 39.4247i 0.315443 + 1.56084i
\(639\) 11.7448 + 8.63734i 0.464618 + 0.341688i
\(640\) −19.1663 + 4.24148i −0.757616 + 0.167659i
\(641\) 6.11925 + 10.5988i 0.241696 + 0.418629i 0.961197 0.275861i \(-0.0889631\pi\)
−0.719502 + 0.694491i \(0.755630\pi\)
\(642\) 5.19785 2.23423i 0.205143 0.0881779i
\(643\) −17.4259 22.7098i −0.687209 0.895589i 0.311292 0.950314i \(-0.399238\pi\)
−0.998501 + 0.0547256i \(0.982572\pi\)
\(644\) 3.24825 25.8978i 0.127999 1.02052i
\(645\) −8.73605 + 0.662130i −0.343981 + 0.0260713i
\(646\) −0.846334 2.46836i −0.0332986 0.0971162i
\(647\) 30.3749 30.3749i 1.19416 1.19416i 0.218274 0.975888i \(-0.429957\pi\)
0.975888 0.218274i \(-0.0700426\pi\)
\(648\) −19.9534 15.8071i −0.783842 0.620960i
\(649\) −5.10664 5.10664i −0.200453 0.200453i
\(650\) 8.23313 16.8248i 0.322930 0.659925i
\(651\) 5.39850 + 71.2271i 0.211584 + 2.79161i
\(652\) 22.3163 + 12.7027i 0.873972 + 0.497475i
\(653\) 25.0900 19.2522i 0.981846 0.753397i 0.0127091 0.999919i \(-0.495954\pi\)
0.969137 + 0.246522i \(0.0792878\pi\)
\(654\) 0.144783 0.363083i 0.00566147 0.0141977i
\(655\) 14.6700 8.46972i 0.573204 0.330939i
\(656\) −7.46441 + 0.0914503i −0.291436 + 0.00357054i
\(657\) 22.3502 30.3913i 0.871965 1.18568i
\(658\) 29.6195 44.6240i 1.15469 1.73963i
\(659\) −2.11544 16.0684i −0.0824058 0.625934i −0.981955 0.189115i \(-0.939438\pi\)
0.899549 0.436819i \(-0.143895\pi\)
\(660\) −0.908154 + 18.4713i −0.0353498 + 0.718995i
\(661\) 19.5894 + 2.57900i 0.761940 + 0.100311i 0.501475 0.865172i \(-0.332791\pi\)
0.260465 + 0.965483i \(0.416124\pi\)
\(662\) 1.07939 + 15.7300i 0.0419517 + 0.611363i
\(663\) 16.4798 + 0.911461i 0.640023 + 0.0353982i
\(664\) 11.7595 10.5055i 0.456356 0.407692i
\(665\) 6.40208 6.40208i 0.248262 0.248262i
\(666\) 10.7320 + 3.36443i 0.415858 + 0.130369i
\(667\) −27.5310 + 11.4037i −1.06601 + 0.441554i
\(668\) −12.4886 + 1.72204i −0.483198 + 0.0666277i
\(669\) −3.37130 0.634923i −0.130342 0.0245475i
\(670\) 6.97256 20.7491i 0.269374 0.801607i
\(671\) −17.6767 + 30.6170i −0.682402 + 1.18196i
\(672\) −18.9487 + 34.8436i −0.730961 + 1.34412i
\(673\) −3.05440 5.29038i −0.117739 0.203929i 0.801133 0.598487i \(-0.204231\pi\)
−0.918871 + 0.394558i \(0.870898\pi\)
\(674\) 15.0150 3.03451i 0.578358 0.116885i
\(675\) −7.05086 7.56033i −0.271388 0.290997i
\(676\) −58.0173 23.6162i −2.23143 0.908317i
\(677\) −34.3163 26.3318i −1.31888 1.01201i −0.997890 0.0649328i \(-0.979317\pi\)
−0.320993 0.947082i \(-0.604017\pi\)
\(678\) −10.2466 + 18.3040i −0.393519 + 0.702960i
\(679\) −0.308065 1.14971i −0.0118224 0.0441219i
\(680\) −3.16462 6.27129i −0.121358 0.240493i
\(681\) −24.4541 + 37.4188i −0.937085 + 1.43389i
\(682\) 39.8195 + 19.4854i 1.52477 + 0.746136i
\(683\) −14.4312 34.8400i −0.552195 1.33312i −0.915827 0.401574i \(-0.868463\pi\)
0.363631 0.931543i \(-0.381537\pi\)
\(684\) 7.22160 + 2.76928i 0.276125 + 0.105886i
\(685\) −2.07585 0.859846i −0.0793143 0.0328530i
\(686\) 13.6372 + 0.851893i 0.520672 + 0.0325254i
\(687\) 18.2984 + 20.4410i 0.698129 + 0.779874i
\(688\) −9.16376 + 7.21167i −0.349365 + 0.274942i
\(689\) −26.2463 15.1533i −0.999906 0.577296i
\(690\) −13.5594 + 1.96838i −0.516196 + 0.0749350i
\(691\) −3.90988 29.6985i −0.148739 1.12978i −0.889145 0.457625i \(-0.848700\pi\)
0.740406 0.672159i \(-0.234633\pi\)
\(692\) −22.1300 + 0.135558i −0.841255 + 0.00515313i
\(693\) 26.9555 + 25.8778i 1.02396 + 0.983015i
\(694\) −19.4073 28.8533i −0.736690 1.09526i
\(695\) −1.84603 + 6.88947i −0.0700238 + 0.261332i
\(696\) 45.2747 0.877829i 1.71613 0.0332740i
\(697\) −0.691385 2.58028i −0.0261881 0.0977353i
\(698\) 3.63474 4.17032i 0.137577 0.157849i
\(699\) 23.3185 1.76737i 0.881985 0.0668482i
\(700\) −9.72719 + 12.8388i −0.367653 + 0.485261i
\(701\) −7.47474 + 18.0456i −0.282317 + 0.681573i −0.999889 0.0149111i \(-0.995253\pi\)
0.717572 + 0.696484i \(0.245253\pi\)
\(702\) −33.4087 + 35.7369i −1.26093 + 1.34880i
\(703\) −3.41724 −0.128884
\(704\) 12.6973 + 21.0877i 0.478547 + 0.794773i
\(705\) −26.7146 8.76558i −1.00613 0.330131i
\(706\) 35.7636 + 12.0181i 1.34598 + 0.452307i
\(707\) −10.5266 13.7186i −0.395895 0.515940i
\(708\) −6.68577 + 4.62690i −0.251266 + 0.173890i
\(709\) 34.3796 + 26.3804i 1.29115 + 0.990737i 0.999414 + 0.0342399i \(0.0109010\pi\)
0.291741 + 0.956498i \(0.405766\pi\)
\(710\) −11.7023 2.29050i −0.439180 0.0859609i
\(711\) 1.78171 + 2.22644i 0.0668195 + 0.0834979i
\(712\) −6.31458 1.19584i −0.236649 0.0448160i
\(713\) −8.50068 + 31.7250i −0.318353 + 1.18811i
\(714\) −13.7570 3.49133i −0.514843 0.130660i
\(715\) 35.2370 + 4.63904i 1.31779 + 0.173490i
\(716\) 9.83467 17.2777i 0.367539 0.645698i
\(717\) 5.67259 1.99033i 0.211847 0.0743302i
\(718\) −1.76237 + 28.2123i −0.0657711 + 1.05287i
\(719\) 5.50552i 0.205321i −0.994716 0.102661i \(-0.967264\pi\)
0.994716 0.102661i \(-0.0327356\pi\)
\(720\) 20.2765 + 4.72948i 0.755662 + 0.176257i
\(721\) 20.9628i 0.780694i
\(722\) 24.4724 + 1.52875i 0.910768 + 0.0568940i
\(723\) 4.56014 24.2133i 0.169593 0.900504i
\(724\) 12.5465 3.44434i 0.466288 0.128008i
\(725\) 18.2328 + 2.40039i 0.677148 + 0.0891482i
\(726\) −3.61299 + 1.01964i −0.134091 + 0.0378422i
\(727\) 5.09838 19.0274i 0.189088 0.705687i −0.804630 0.593777i \(-0.797636\pi\)
0.993718 0.111911i \(-0.0356970\pi\)
\(728\) 63.7642 + 41.7636i 2.36326 + 1.54786i
\(729\) 11.8385 + 24.2662i 0.438464 + 0.898749i
\(730\) −5.92696 + 30.2813i −0.219367 + 1.12076i
\(731\) −3.31058 2.54030i −0.122446 0.0939563i
\(732\) 30.3493 + 25.7515i 1.12174 + 0.951802i
\(733\) −25.4325 33.1442i −0.939369 1.22421i −0.974399 0.224824i \(-0.927819\pi\)
0.0350300 0.999386i \(-0.488847\pi\)
\(734\) 13.8124 41.1030i 0.509823 1.51714i
\(735\) −5.78524 27.6098i −0.213392 1.01840i
\(736\) −13.5255 + 12.2330i −0.498556 + 0.450913i
\(737\) −27.4483 −1.01107
\(738\) 7.18145 + 3.33441i 0.264353 + 0.122741i
\(739\) −10.0958 + 24.3735i −0.371381 + 0.896592i 0.622137 + 0.782909i \(0.286265\pi\)
−0.993517 + 0.113683i \(0.963735\pi\)
\(740\) −9.11295 + 1.25658i −0.334999 + 0.0461927i
\(741\) 6.43784 13.3974i 0.236500 0.492165i
\(742\) 19.6467 + 17.1235i 0.721252 + 0.628624i
\(743\) 13.5034 + 50.3952i 0.495390 + 1.84882i 0.527833 + 0.849348i \(0.323005\pi\)
−0.0324428 + 0.999474i \(0.510329\pi\)
\(744\) 29.6100 40.1778i 1.08555 1.47299i
\(745\) −5.99579 + 22.3766i −0.219669 + 0.819815i
\(746\) 10.1516 6.82813i 0.371675 0.249995i
\(747\) −16.0636 + 4.65739i −0.587738 + 0.170405i
\(748\) −6.19026 + 6.26657i −0.226338 + 0.229128i
\(749\) 1.22042 + 9.26998i 0.0445930 + 0.338718i
\(750\) 27.5929 + 11.0030i 1.00755 + 0.401772i
\(751\) −25.5665 14.7608i −0.932936 0.538631i −0.0451973 0.998978i \(-0.514392\pi\)
−0.887739 + 0.460347i \(0.847725\pi\)
\(752\) −36.0262 + 10.1278i −1.31374 + 0.369323i
\(753\) −9.80535 + 29.8835i −0.357327 + 1.08901i
\(754\) 5.42574 86.8560i 0.197594 3.16311i
\(755\) −4.28699 1.77573i −0.156020 0.0646255i
\(756\) 34.0972 24.6405i 1.24010 0.896166i
\(757\) −5.39119 13.0155i −0.195946 0.473056i 0.795116 0.606458i \(-0.207410\pi\)
−0.991062 + 0.133402i \(0.957410\pi\)
\(758\) 9.21354 18.8284i 0.334651 0.683877i
\(759\) 7.75577 + 15.3310i 0.281516 + 0.556479i
\(760\) −6.30847 + 0.471728i −0.228832 + 0.0171114i
\(761\) 0.846534 + 3.15931i 0.0306868 + 0.114525i 0.979570 0.201101i \(-0.0644521\pi\)
−0.948884 + 0.315626i \(0.897785\pi\)
\(762\) 0.0949451 + 7.15926i 0.00343950 + 0.259353i
\(763\) 0.512492 + 0.393249i 0.0185534 + 0.0142366i
\(764\) 43.1623 18.1890i 1.56156 0.658054i
\(765\) 0.151958 + 7.44909i 0.00549405 + 0.269322i
\(766\) 5.82920 + 28.8434i 0.210618 + 1.04216i
\(767\) 7.81276 + 13.5321i 0.282102 + 0.488616i
\(768\) 25.9173 9.81305i 0.935208 0.354098i
\(769\) −17.1349 + 29.6785i −0.617899 + 1.07023i 0.371969 + 0.928245i \(0.378683\pi\)
−0.989868 + 0.141988i \(0.954651\pi\)
\(770\) −28.9708 9.73541i −1.04404 0.350840i
\(771\) −12.9411 36.8832i −0.466064 1.32832i
\(772\) 18.0017 + 13.6389i 0.647897 + 0.490873i
\(773\) 16.2733 6.74060i 0.585308 0.242443i −0.0703225 0.997524i \(-0.522403\pi\)
0.655631 + 0.755082i \(0.272403\pi\)
\(774\) 12.0709 2.69687i 0.433881 0.0969371i
\(775\) 14.3324 14.3324i 0.514835 0.514835i
\(776\) −0.360963 + 0.749238i −0.0129578 + 0.0268961i
\(777\) −10.1682 + 15.5590i −0.364784 + 0.558178i
\(778\) 6.19603 0.425172i 0.222139 0.0152431i
\(779\) −2.38512 0.314007i −0.0854557 0.0112505i
\(780\) 12.2417 38.0949i 0.438324 1.36401i
\(781\) 1.95172 + 14.8248i 0.0698379 + 0.530472i
\(782\) −5.43724 3.60901i −0.194435 0.129058i
\(783\) −43.7065 19.9155i −1.56194 0.711721i
\(784\) −26.8730 26.2225i −0.959752 0.936520i
\(785\) −17.5293 + 10.1206i −0.625648 + 0.361218i
\(786\) −18.7778 + 14.8084i −0.669782 + 0.528199i
\(787\) −26.7747 + 20.5449i −0.954415 + 0.732348i −0.963527 0.267610i \(-0.913766\pi\)
0.00911235 + 0.999958i \(0.497099\pi\)
\(788\) −12.8243 46.7145i −0.456847 1.66413i
\(789\) 11.7273 8.01013i 0.417503 0.285168i
\(790\) −2.09498 1.02517i −0.0745361 0.0364738i
\(791\) −24.5130 24.5130i −0.871582 0.871582i
\(792\) −2.47748 25.9907i −0.0880334 0.923538i
\(793\) 54.0880 54.0880i 1.92072 1.92072i
\(794\) −10.0324 + 3.43985i −0.356037 + 0.122076i
\(795\) 5.92548 12.3311i 0.210155 0.437341i
\(796\) −10.1176 13.0197i −0.358610 0.461469i
\(797\) 14.0534 + 18.3147i 0.497796 + 0.648741i 0.972910 0.231184i \(-0.0742598\pi\)
−0.475114 + 0.879924i \(0.657593\pi\)
\(798\) −7.64597 + 10.2429i −0.270665 + 0.362593i
\(799\) −6.69577 11.5974i −0.236879 0.410287i
\(800\) 11.0034 2.36442i 0.389028 0.0835950i
\(801\) 5.49153 + 4.03856i 0.194034 + 0.142696i
\(802\) 20.6765 4.17868i 0.730112 0.147554i
\(803\) 38.3610 5.05032i 1.35373 0.178222i
\(804\) −5.53321 + 30.4029i −0.195141 + 1.07223i
\(805\) 2.95554 22.4495i 0.104169 0.791242i
\(806\) −72.3076 63.0213i −2.54693 2.21983i
\(807\) −42.5674 + 21.5344i −1.49844 + 0.758046i
\(808\) −0.679398 + 12.0629i −0.0239011 + 0.424373i
\(809\) −2.00937 2.00937i −0.0706458 0.0706458i 0.670901 0.741547i \(-0.265908\pi\)
−0.741547 + 0.670901i \(0.765908\pi\)
\(810\) −17.2259 13.8189i −0.605256 0.485548i
\(811\) 1.66716 + 4.02487i 0.0585418 + 0.141332i 0.950444 0.310896i \(-0.100629\pi\)
−0.891902 + 0.452229i \(0.850629\pi\)
\(812\) −18.9257 + 72.4029i −0.664163 + 2.54084i
\(813\) −23.1015 19.8464i −0.810205 0.696043i
\(814\) 5.13364 + 10.3301i 0.179934 + 0.362070i
\(815\) 19.2922 + 11.1384i 0.675778 + 0.390160i
\(816\) 5.69324 + 8.11985i 0.199303 + 0.284252i
\(817\) −3.25451 + 1.87899i −0.113861 + 0.0657376i
\(818\) 29.0651 + 19.2921i 1.01624 + 0.674534i
\(819\) −41.8434 69.1770i −1.46213 2.41724i
\(820\) −6.47600 + 0.0396689i −0.226152 + 0.00138530i
\(821\) −16.5684 + 21.5924i −0.578243 + 0.753581i −0.987289 0.158933i \(-0.949195\pi\)
0.409047 + 0.912514i \(0.365861\pi\)
\(822\) 3.07459 + 0.780285i 0.107238 + 0.0272156i
\(823\) 27.8599 7.46503i 0.971133 0.260214i 0.261827 0.965115i \(-0.415675\pi\)
0.709306 + 0.704900i \(0.249008\pi\)
\(824\) −9.55581 + 11.1004i −0.332892 + 0.386701i
\(825\) 0.585533 10.5868i 0.0203856 0.368585i
\(826\) −4.35808 12.7105i −0.151637 0.442253i
\(827\) 15.2814 6.32977i 0.531387 0.220108i −0.100824 0.994904i \(-0.532148\pi\)
0.632210 + 0.774797i \(0.282148\pi\)
\(828\) 18.5447 5.50009i 0.644473 0.191142i
\(829\) 2.99278 7.22520i 0.103943 0.250942i −0.863348 0.504609i \(-0.831637\pi\)
0.967292 + 0.253667i \(0.0816368\pi\)
\(830\) 10.2574 9.05120i 0.356039 0.314172i
\(831\) −0.806852 3.85066i −0.0279894 0.133578i
\(832\) −14.7273 51.1818i −0.510577 1.77441i
\(833\) 6.71803 11.6360i 0.232766 0.403162i
\(834\) 1.18181 9.99975i 0.0409228 0.346263i
\(835\) −10.8432 + 1.42754i −0.375245 + 0.0494019i
\(836\) 3.08053 + 7.31008i 0.106542 + 0.252824i
\(837\) −46.7398 + 24.8551i −1.61556 + 0.859117i
\(838\) −38.3437 7.50502i −1.32456 0.259257i
\(839\) 27.7332 + 7.43108i 0.957455 + 0.256549i 0.703523 0.710673i \(-0.251609\pi\)
0.253932 + 0.967222i \(0.418276\pi\)
\(840\) −16.6235 + 30.1268i −0.573564 + 1.03947i
\(841\) 54.5171 14.6078i 1.87990 0.503718i
\(842\) −18.1797 + 1.24749i −0.626512 + 0.0429912i
\(843\) 14.0546 9.59975i 0.484067 0.330633i
\(844\) 0.0977751 + 0.166981i 0.00336556 + 0.00574772i
\(845\) −50.2055 20.7958i −1.72712 0.715397i
\(846\) 39.1010 + 6.82835i 1.34432 + 0.234763i
\(847\) 6.20409i 0.213175i
\(848\) −2.59781 18.0233i −0.0892093 0.618922i
\(849\) 34.0226 + 38.0064i 1.16765 + 1.30438i
\(850\) 1.79232 + 3.60658i 0.0614761 + 0.123705i
\(851\) −6.78024 + 5.20266i −0.232423 + 0.178345i
\(852\) 16.8140 + 0.826669i 0.576037 + 0.0283212i
\(853\) 31.6660 41.2679i 1.08422 1.41299i 0.181173 0.983451i \(-0.442011\pi\)
0.903050 0.429535i \(-0.141323\pi\)
\(854\) −54.5799 + 36.7114i −1.86769 + 1.25624i
\(855\) 6.25015 + 2.44077i 0.213750 + 0.0834726i
\(856\) 3.57944 5.46506i 0.122343 0.186792i
\(857\) −29.3308 7.85917i −1.00192 0.268464i −0.279671 0.960096i \(-0.590225\pi\)
−0.722250 + 0.691632i \(0.756892\pi\)
\(858\) −50.1709 + 0.665359i −1.71281 + 0.0227150i
\(859\) 3.02910 23.0083i 0.103351 0.785032i −0.858761 0.512377i \(-0.828765\pi\)
0.962112 0.272655i \(-0.0879017\pi\)
\(860\) −7.98805 + 6.20755i −0.272390 + 0.211676i
\(861\) −8.52680 + 9.92534i −0.290593 + 0.338255i
\(862\) 22.8151 + 25.8555i 0.777087 + 0.880642i
\(863\) −49.1751 −1.67394 −0.836970 0.547248i \(-0.815675\pi\)
−0.836970 + 0.547248i \(0.815675\pi\)
\(864\) −29.2878 2.49521i −0.996390 0.0848887i
\(865\) −19.1989 −0.652781
\(866\) −35.4552 40.1800i −1.20482 1.36537i
\(867\) 16.8751 19.6429i 0.573107 0.667107i
\(868\) 50.6117 + 65.1284i 1.71787 + 2.21060i
\(869\) −0.381749 + 2.89967i −0.0129499 + 0.0983645i
\(870\) 39.2812 0.520942i 1.33176 0.0176616i
\(871\) 57.3645 + 15.3708i 1.94372 + 0.520818i
\(872\) −0.0921187 0.441855i −0.00311953 0.0149631i
\(873\) 0.688723 0.551153i 0.0233097 0.0186537i
\(874\) −4.87662 + 3.28010i −0.164954 + 0.110951i
\(875\) −29.8854 + 38.9474i −1.01031 + 1.31666i
\(876\) 2.13911 43.5083i 0.0722739 1.47001i
\(877\) 40.3935 30.9950i 1.36399 1.04663i 0.370977 0.928642i \(-0.379023\pi\)
0.993015 0.117986i \(-0.0376438\pi\)
\(878\) −18.3142 36.8525i −0.618074 1.24371i
\(879\) −16.5716 18.5120i −0.558947 0.624395i
\(880\) 10.9031 + 18.3614i 0.367542 + 0.618964i
\(881\) 38.1465i 1.28519i 0.766206 + 0.642594i \(0.222142\pi\)
−0.766206 + 0.642594i \(0.777858\pi\)
\(882\) 13.6823 + 37.4005i 0.460707 + 1.25934i
\(883\) −34.2926 14.2045i −1.15404 0.478018i −0.278153 0.960537i \(-0.589722\pi\)
−0.875886 + 0.482519i \(0.839722\pi\)
\(884\) 16.4463 9.63008i 0.553149 0.323895i
\(885\) −5.82461 + 3.97839i −0.195792 + 0.133732i
\(886\) −7.80869 + 0.535832i −0.262338 + 0.0180016i
\(887\) −20.1254 + 5.39259i −0.675745 + 0.181065i −0.580342 0.814373i \(-0.697081\pi\)
−0.0954039 + 0.995439i \(0.530414\pi\)
\(888\) 12.4769 3.60382i 0.418699 0.120936i
\(889\) −11.4293 3.06248i −0.383328 0.102712i
\(890\) −5.47165 1.07097i −0.183410 0.0358990i
\(891\) −9.54515 + 25.9952i −0.319775 + 0.870871i
\(892\) −3.65039 + 1.53831i −0.122224 + 0.0515063i
\(893\) −11.9568 + 1.57415i −0.400121 + 0.0526769i
\(894\) 3.83846 32.4786i 0.128377 1.08625i
\(895\) 8.62356 14.9364i 0.288254 0.499270i
\(896\) 3.97438 + 45.6258i 0.132775 + 1.52425i
\(897\) −7.62366 36.3835i −0.254547 1.21481i
\(898\) −30.0840 + 26.5464i −1.00392 + 0.885864i
\(899\) 36.0373 87.0018i 1.20191 2.90167i
\(900\) −11.6084 2.78272i −0.386945 0.0927573i
\(901\) 6.02019 2.49364i 0.200562 0.0830753i
\(902\) 2.63388 + 7.68179i 0.0876987 + 0.255776i
\(903\) −1.12879 + 20.4092i −0.0375637 + 0.679175i
\(904\) 1.80620 + 24.1546i 0.0600735 + 0.803369i
\(905\) 10.9026 2.92135i 0.362416 0.0971090i
\(906\) 6.34955 + 1.61142i 0.210950 + 0.0535359i
\(907\) 11.5092 14.9990i 0.382156 0.498035i −0.562182 0.827014i \(-0.690038\pi\)
0.944337 + 0.328979i \(0.106705\pi\)
\(908\) 0.316170 + 51.6152i 0.0104925 + 1.71291i
\(909\) 6.17980 11.2265i 0.204971 0.372358i
\(910\) 55.0946 + 36.5695i 1.82637 + 1.21227i
\(911\) 2.06405 1.19168i 0.0683852 0.0394822i −0.465418 0.885091i \(-0.654096\pi\)
0.533803 + 0.845609i \(0.320762\pi\)
\(912\) 8.71795 1.93851i 0.288680 0.0641905i
\(913\) −14.8558 8.57699i −0.491654 0.283857i
\(914\) 9.99205 + 20.1064i 0.330508 + 0.665061i
\(915\) 26.1917 + 22.5011i 0.865871 + 0.743864i
\(916\) 30.6492 + 8.01154i 1.01268 + 0.264709i
\(917\) −15.1241 36.5127i −0.499441 1.20576i
\(918\) −1.72309 10.3764i −0.0568705 0.342471i
\(919\) −24.2916 24.2916i −0.801305 0.801305i 0.181995 0.983300i \(-0.441745\pi\)
−0.983300 + 0.181995i \(0.941745\pi\)
\(920\) −11.7986 + 10.5404i −0.388988 + 0.347508i
\(921\) −8.17605 + 4.13617i −0.269410 + 0.136291i
\(922\) −13.6535 11.9000i −0.449654 0.391906i
\(923\) 4.22280 32.0754i 0.138995 1.05577i
\(924\) 42.4499 + 7.72571i 1.39650 + 0.254157i
\(925\) 5.22906 0.688419i 0.171930 0.0226351i
\(926\) −35.3387 + 7.14189i −1.16130 + 0.234697i
\(927\) 14.2286 6.23664i 0.467329 0.204838i
\(928\) 43.0264 29.7123i 1.41241 0.975354i
\(929\) 1.94395 + 3.36703i 0.0637791 + 0.110469i 0.896152 0.443748i \(-0.146351\pi\)
−0.832373 + 0.554216i \(0.813018\pi\)
\(930\) 25.9007 34.6976i 0.849317 1.13778i
\(931\) −7.36608 9.59966i −0.241413 0.314616i
\(932\) 21.3219 16.5693i 0.698421 0.542747i
\(933\) 9.34502 19.4473i 0.305942 0.636676i
\(934\) 0.302537 0.103732i 0.00989930 0.00339421i
\(935\) −5.40346 + 5.40346i −0.176712 + 0.176712i
\(936\) −9.37680 + 55.7055i −0.306490 + 1.82079i
\(937\) −16.9736 16.9736i −0.554504 0.554504i 0.373233 0.927738i \(-0.378249\pi\)
−0.927738 + 0.373233i \(0.878249\pi\)
\(938\) −45.8718 22.4471i −1.49777 0.732923i
\(939\) 20.2986 13.8646i 0.662420 0.452454i
\(940\) −31.3072 + 8.59461i −1.02113 + 0.280325i
\(941\) −31.4750 + 24.1516i −1.02606 + 0.787321i −0.977379 0.211493i \(-0.932167\pi\)
−0.0486775 + 0.998815i \(0.515501\pi\)
\(942\) 22.4378 17.6947i 0.731062 0.576526i
\(943\) −5.21044 + 3.00825i −0.169675 + 0.0979621i
\(944\) −3.48629 + 8.71719i −0.113469 + 0.283720i
\(945\) 29.7108 21.1949i 0.966494 0.689469i
\(946\) 10.5692 + 7.01542i 0.343636 + 0.228091i
\(947\) 6.00271 + 45.5951i 0.195062 + 1.48164i 0.756429 + 0.654076i \(0.226942\pi\)
−0.561367 + 0.827567i \(0.689724\pi\)
\(948\) 3.13484 + 1.00738i 0.101815 + 0.0327180i
\(949\) −82.9992 10.9270i −2.69427 0.354707i
\(950\) 3.61843 0.248297i 0.117398 0.00805581i
\(951\) −9.73298 + 14.8930i −0.315614 + 0.482939i
\(952\) −15.4700 + 5.41038i −0.501385 + 0.175351i
\(953\) 25.5953 25.5953i 0.829112 0.829112i −0.158282 0.987394i \(-0.550595\pi\)
0.987394 + 0.158282i \(0.0505954\pi\)
\(954\) −5.77761 + 18.4297i −0.187057 + 0.596685i
\(955\) 37.5408 15.5499i 1.21479 0.503183i
\(956\) 4.19199 5.53295i 0.135579 0.178948i
\(957\) −16.3095 46.4832i −0.527210 1.50259i
\(958\) −10.8208 3.63623i −0.349603 0.117481i
\(959\) −2.62109 + 4.53986i −0.0846393 + 0.146600i
\(960\) 22.5358 8.37527i 0.727340 0.270311i
\(961\) −36.3959 63.0396i −1.17406 2.03354i
\(962\) −4.94409 24.4638i −0.159404 0.788744i
\(963\) −5.92898 + 3.58628i −0.191059 + 0.115566i
\(964\) −11.0484 26.2178i −0.355845 0.844419i
\(965\) 15.5444 + 11.9276i 0.500391 + 0.383963i
\(966\) 0.423901 + 31.9639i 0.0136388 + 1.02842i
\(967\) 6.85716 + 25.5913i 0.220511 + 0.822960i 0.984153 + 0.177320i \(0.0567427\pi\)
−0.763642 + 0.645640i \(0.776591\pi\)
\(968\) −2.82811 + 3.28525i −0.0908990 + 0.105592i
\(969\) 1.44266 + 2.85173i 0.0463448 + 0.0916106i
\(970\) −0.317123 + 0.648059i −0.0101822 + 0.0208079i
\(971\) 21.7155 + 52.4259i 0.696885 + 1.68243i 0.730427 + 0.682991i \(0.239321\pi\)
−0.0335425 + 0.999437i \(0.510679\pi\)
\(972\) 26.8692 + 15.8129i 0.861829 + 0.507199i
\(973\) 15.3740 + 6.36813i 0.492868 + 0.204153i
\(974\) 1.79762 28.7766i 0.0575995 0.922061i
\(975\) −7.15222 + 21.7976i −0.229054 + 0.698082i
\(976\) 45.6365 + 5.44027i 1.46079 + 0.174139i
\(977\) 44.0802 + 25.4497i 1.41025 + 0.814209i 0.995412 0.0956860i \(-0.0305045\pi\)
0.414839 + 0.909895i \(0.363838\pi\)
\(978\) −29.2124 11.6488i −0.934110 0.372487i
\(979\) 0.912564 + 6.93162i 0.0291657 + 0.221535i
\(980\) −23.1735 22.8913i −0.740250 0.731237i
\(981\) −0.114449 + 0.464853i −0.00365406 + 0.0148416i
\(982\) 5.71488 3.84393i 0.182369 0.122665i
\(983\) −12.4024 + 46.2862i −0.395574 + 1.47630i 0.425227 + 0.905087i \(0.360194\pi\)
−0.820801 + 0.571214i \(0.806473\pi\)
\(984\) 9.03963 1.36885i 0.288173 0.0436375i
\(985\) −10.8771 40.5938i −0.346572 1.29343i
\(986\) 14.1056 + 12.2940i 0.449212 + 0.391521i
\(987\) −28.4112 + 59.1247i −0.904339 + 1.88196i
\(988\) −2.34446 17.0025i −0.0745872 0.540921i
\(989\) −3.59664 + 8.68306i −0.114367 + 0.276105i
\(990\) −2.01114 22.5605i −0.0639183 0.717020i
\(991\) 13.1381 0.417346 0.208673 0.977985i \(-0.433086\pi\)
0.208673 + 0.977985i \(0.433086\pi\)
\(992\) 2.88819 57.5587i 0.0917003 1.82749i
\(993\) −3.96025 18.9001i −0.125675 0.599776i
\(994\) −8.86189 + 26.3714i −0.281082 + 0.836449i
\(995\) −8.70805 11.3485i −0.276064 0.359773i
\(996\) −12.4950 + 14.7259i −0.395918 + 0.466607i
\(997\) 4.51776 + 3.46660i 0.143079 + 0.109788i 0.677821 0.735227i \(-0.262925\pi\)
−0.534742 + 0.845015i \(0.679591\pi\)
\(998\) 0.912111 4.66004i 0.0288724 0.147511i
\(999\) −13.5860 2.27279i −0.429841 0.0719079i
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 288.2.bc.a.13.12 368
3.2 odd 2 864.2.bk.a.685.35 368
9.2 odd 6 864.2.bk.a.397.4 368
9.7 even 3 inner 288.2.bc.a.205.43 yes 368
32.5 even 8 inner 288.2.bc.a.229.43 yes 368
96.5 odd 8 864.2.bk.a.37.4 368
288.101 odd 24 864.2.bk.a.613.35 368
288.133 even 24 inner 288.2.bc.a.133.12 yes 368
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
288.2.bc.a.13.12 368 1.1 even 1 trivial
288.2.bc.a.133.12 yes 368 288.133 even 24 inner
288.2.bc.a.205.43 yes 368 9.7 even 3 inner
288.2.bc.a.229.43 yes 368 32.5 even 8 inner
864.2.bk.a.37.4 368 96.5 odd 8
864.2.bk.a.397.4 368 9.2 odd 6
864.2.bk.a.613.35 368 288.101 odd 24
864.2.bk.a.685.35 368 3.2 odd 2