Properties

Label 164.2.o.b.11.6
Level $164$
Weight $2$
Character 164.11
Analytic conductor $1.310$
Analytic rank $0$
Dimension $288$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [164,2,Mod(7,164)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(164, base_ring=CyclotomicField(40))
 
chi = DirichletCharacter(H, H._module([20, 39]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("164.7");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 164 = 2^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 164.o (of order \(40\), degree \(16\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.30954659315\)
Analytic rank: \(0\)
Dimension: \(288\)
Relative dimension: \(18\) over \(\Q(\zeta_{40})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{40}]$

Embedding invariants

Embedding label 11.6
Character \(\chi\) \(=\) 164.11
Dual form 164.2.o.b.15.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.855915 + 1.12579i) q^{2} +(-0.107548 + 0.259643i) q^{3} +(-0.534820 - 1.92717i) q^{4} +(0.160579 - 0.315153i) q^{5} +(-0.200253 - 0.343309i) q^{6} +(0.730639 + 3.04333i) q^{7} +(2.62735 + 1.04739i) q^{8} +(2.06547 + 2.06547i) q^{9} +O(q^{10})\) \(q+(-0.855915 + 1.12579i) q^{2} +(-0.107548 + 0.259643i) q^{3} +(-0.534820 - 1.92717i) q^{4} +(0.160579 - 0.315153i) q^{5} +(-0.200253 - 0.343309i) q^{6} +(0.730639 + 3.04333i) q^{7} +(2.62735 + 1.04739i) q^{8} +(2.06547 + 2.06547i) q^{9} +(0.217356 + 0.450522i) q^{10} +(-2.95352 + 3.45813i) q^{11} +(0.557895 + 0.0683999i) q^{12} +(0.756418 + 1.23436i) q^{13} +(-4.05153 - 1.78228i) q^{14} +(0.0645576 + 0.0755872i) q^{15} +(-3.42793 + 2.06137i) q^{16} +(-0.587614 - 7.46634i) q^{17} +(-4.09316 + 0.557427i) q^{18} +(3.57340 + 2.18978i) q^{19} +(-0.693233 - 0.140911i) q^{20} +(-0.868760 - 0.137598i) q^{21} +(-1.36518 - 6.28492i) q^{22} +(-1.40629 - 1.02173i) q^{23} +(-0.554514 + 0.569530i) q^{24} +(2.86539 + 3.94387i) q^{25} +(-2.03706 - 0.204938i) q^{26} +(-1.53735 + 0.636793i) q^{27} +(5.47424 - 3.03570i) q^{28} +(-0.426203 + 5.41542i) q^{29} +(-0.140351 + 0.00798228i) q^{30} +(2.29687 - 7.06903i) q^{31} +(0.613337 - 5.62351i) q^{32} +(-0.580236 - 1.13878i) q^{33} +(8.90850 + 5.72902i) q^{34} +(1.07644 + 0.258430i) q^{35} +(2.87585 - 5.08516i) q^{36} +(-0.0407975 - 0.125562i) q^{37} +(-5.52376 + 2.14864i) q^{38} +(-0.401845 + 0.0636460i) q^{39} +(0.751985 - 0.659829i) q^{40} +(4.51550 - 4.53985i) q^{41} +(0.898491 - 0.860271i) q^{42} +(-1.66707 - 10.5255i) q^{43} +(8.24399 + 3.84245i) q^{44} +(0.982611 - 0.319270i) q^{45} +(2.35393 - 0.708681i) q^{46} +(0.405424 - 1.68871i) q^{47} +(-0.166556 - 1.11174i) q^{48} +(-2.49098 + 1.26922i) q^{49} +(-6.89251 - 0.149780i) q^{50} +(2.00178 + 0.650419i) q^{51} +(1.97427 - 2.11790i) q^{52} +(-12.0624 - 0.949332i) q^{53} +(0.598947 - 2.27578i) q^{54} +(0.615568 + 1.48611i) q^{55} +(-1.26792 + 8.76116i) q^{56} +(-0.952874 + 0.692303i) q^{57} +(-5.73185 - 5.11495i) q^{58} +(1.86793 - 2.57098i) q^{59} +(0.111142 - 0.164839i) q^{60} +(-0.239761 + 1.51379i) q^{61} +(5.99235 + 8.63629i) q^{62} +(-4.77680 + 7.79503i) q^{63} +(5.80594 + 5.50373i) q^{64} +(0.510477 - 0.0401754i) q^{65} +(1.77866 + 0.321470i) q^{66} +(4.08936 - 3.49264i) q^{67} +(-14.0746 + 5.12558i) q^{68} +(0.416530 - 0.255250i) q^{69} +(-1.21228 + 0.990655i) q^{70} +(-5.17653 - 4.42117i) q^{71} +(3.26336 + 7.59008i) q^{72} +(2.80206 - 2.80206i) q^{73} +(0.176276 + 0.0615407i) q^{74} +(-1.33217 + 0.319825i) q^{75} +(2.30895 - 8.05767i) q^{76} +(-12.6822 - 6.46190i) q^{77} +(0.272293 - 0.506870i) q^{78} +(5.16660 + 2.14007i) q^{79} +(0.0991961 + 1.41134i) q^{80} +8.29541i q^{81} +(1.24605 + 8.96925i) q^{82} +1.59911i q^{83} +(0.199456 + 1.74783i) q^{84} +(-2.44740 - 1.01375i) q^{85} +(13.2764 + 7.13212i) q^{86} +(-1.36024 - 0.693077i) q^{87} +(-11.3820 + 5.99222i) q^{88} +(0.293320 - 0.0704200i) q^{89} +(-0.481599 + 1.37948i) q^{90} +(-3.20390 + 3.20390i) q^{91} +(-1.21693 + 3.25661i) q^{92} +(1.58840 + 1.35663i) q^{93} +(1.55413 + 1.90182i) q^{94} +(1.26393 - 0.774536i) q^{95} +(1.39414 + 0.764045i) q^{96} +(2.46358 - 2.10410i) q^{97} +(0.703190 - 3.89068i) q^{98} +(-13.2431 + 1.04225i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 288 q - 12 q^{2} - 20 q^{4} - 32 q^{5} - 28 q^{6} - 24 q^{8} - 40 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 288 q - 12 q^{2} - 20 q^{4} - 32 q^{5} - 28 q^{6} - 24 q^{8} - 40 q^{9} - 12 q^{10} - 8 q^{12} - 24 q^{13} - 4 q^{14} - 28 q^{16} - 12 q^{18} - 44 q^{20} - 32 q^{21} - 40 q^{22} + 8 q^{24} - 40 q^{25} + 4 q^{26} - 48 q^{29} - 44 q^{30} + 108 q^{32} - 72 q^{33} + 12 q^{34} - 20 q^{36} - 24 q^{37} + 56 q^{38} + 8 q^{41} - 112 q^{42} - 40 q^{45} - 48 q^{46} - 68 q^{48} - 16 q^{49} - 60 q^{50} - 124 q^{52} - 64 q^{53} + 64 q^{54} - 84 q^{56} - 24 q^{57} + 40 q^{60} - 8 q^{61} - 44 q^{62} - 20 q^{64} + 64 q^{65} + 60 q^{66} - 28 q^{68} - 8 q^{69} + 128 q^{70} + 160 q^{72} - 32 q^{73} + 80 q^{74} + 288 q^{76} - 32 q^{77} + 116 q^{78} + 176 q^{80} + 212 q^{82} + 152 q^{84} - 56 q^{85} + 180 q^{86} + 144 q^{88} - 72 q^{89} + 224 q^{90} + 36 q^{92} - 8 q^{93} + 52 q^{94} + 136 q^{96} - 88 q^{97} + 104 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/164\mathbb{Z}\right)^\times\).

\(n\) \(83\) \(129\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{40}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.855915 + 1.12579i −0.605223 + 0.796056i
\(3\) −0.107548 + 0.259643i −0.0620928 + 0.149905i −0.951881 0.306469i \(-0.900852\pi\)
0.889788 + 0.456375i \(0.150852\pi\)
\(4\) −0.534820 1.92717i −0.267410 0.963583i
\(5\) 0.160579 0.315153i 0.0718129 0.140941i −0.852309 0.523039i \(-0.824798\pi\)
0.924122 + 0.382098i \(0.124798\pi\)
\(6\) −0.200253 0.343309i −0.0817530 0.140155i
\(7\) 0.730639 + 3.04333i 0.276156 + 1.15027i 0.922120 + 0.386904i \(0.126455\pi\)
−0.645965 + 0.763367i \(0.723545\pi\)
\(8\) 2.62735 + 1.04739i 0.928909 + 0.370309i
\(9\) 2.06547 + 2.06547i 0.688491 + 0.688491i
\(10\) 0.217356 + 0.450522i 0.0687339 + 0.142468i
\(11\) −2.95352 + 3.45813i −0.890521 + 1.04267i 0.108300 + 0.994118i \(0.465459\pi\)
−0.998821 + 0.0485474i \(0.984541\pi\)
\(12\) 0.557895 + 0.0683999i 0.161050 + 0.0197453i
\(13\) 0.756418 + 1.23436i 0.209793 + 0.342350i 0.940177 0.340686i \(-0.110659\pi\)
−0.730385 + 0.683036i \(0.760659\pi\)
\(14\) −4.05153 1.78228i −1.08282 0.476335i
\(15\) 0.0645576 + 0.0755872i 0.0166687 + 0.0195165i
\(16\) −3.42793 + 2.06137i −0.856984 + 0.515344i
\(17\) −0.587614 7.46634i −0.142517 1.81085i −0.488447 0.872593i \(-0.662436\pi\)
0.345930 0.938260i \(-0.387564\pi\)
\(18\) −4.09316 + 0.557427i −0.964768 + 0.131387i
\(19\) 3.57340 + 2.18978i 0.819794 + 0.502370i 0.868057 0.496464i \(-0.165369\pi\)
−0.0482633 + 0.998835i \(0.515369\pi\)
\(20\) −0.693233 0.140911i −0.155012 0.0315087i
\(21\) −0.868760 0.137598i −0.189579 0.0300263i
\(22\) −1.36518 6.28492i −0.291057 1.33995i
\(23\) −1.40629 1.02173i −0.293233 0.213046i 0.431436 0.902144i \(-0.358007\pi\)
−0.724669 + 0.689098i \(0.758007\pi\)
\(24\) −0.554514 + 0.569530i −0.113190 + 0.116255i
\(25\) 2.86539 + 3.94387i 0.573078 + 0.788774i
\(26\) −2.03706 0.204938i −0.399501 0.0401917i
\(27\) −1.53735 + 0.636793i −0.295864 + 0.122551i
\(28\) 5.47424 3.03570i 1.03453 0.573693i
\(29\) −0.426203 + 5.41542i −0.0791439 + 1.00562i 0.821257 + 0.570558i \(0.193273\pi\)
−0.900401 + 0.435060i \(0.856727\pi\)
\(30\) −0.140351 + 0.00798228i −0.0256245 + 0.00145736i
\(31\) 2.29687 7.06903i 0.412530 1.26964i −0.501912 0.864919i \(-0.667370\pi\)
0.914442 0.404717i \(-0.132630\pi\)
\(32\) 0.613337 5.62351i 0.108424 0.994105i
\(33\) −0.580236 1.13878i −0.101006 0.198236i
\(34\) 8.90850 + 5.72902i 1.52780 + 0.982519i
\(35\) 1.07644 + 0.258430i 0.181952 + 0.0436827i
\(36\) 2.87585 5.08516i 0.479308 0.847527i
\(37\) −0.0407975 0.125562i −0.00670707 0.0206423i 0.947647 0.319320i \(-0.103454\pi\)
−0.954354 + 0.298678i \(0.903454\pi\)
\(38\) −5.52376 + 2.14864i −0.896073 + 0.348556i
\(39\) −0.401845 + 0.0636460i −0.0643467 + 0.0101915i
\(40\) 0.751985 0.659829i 0.118899 0.104328i
\(41\) 4.51550 4.53985i 0.705203 0.709005i
\(42\) 0.898491 0.860271i 0.138640 0.132743i
\(43\) −1.66707 10.5255i −0.254226 1.60512i −0.702811 0.711377i \(-0.748072\pi\)
0.448585 0.893740i \(-0.351928\pi\)
\(44\) 8.24399 + 3.84245i 1.24283 + 0.579271i
\(45\) 0.982611 0.319270i 0.146479 0.0475939i
\(46\) 2.35393 0.708681i 0.347068 0.104489i
\(47\) 0.405424 1.68871i 0.0591371 0.246324i −0.934970 0.354727i \(-0.884574\pi\)
0.994107 + 0.108403i \(0.0345738\pi\)
\(48\) −0.166556 1.11174i −0.0240402 0.160465i
\(49\) −2.49098 + 1.26922i −0.355855 + 0.181317i
\(50\) −6.89251 0.149780i −0.974748 0.0211821i
\(51\) 2.00178 + 0.650419i 0.280306 + 0.0910769i
\(52\) 1.97427 2.11790i 0.273782 0.293700i
\(53\) −12.0624 0.949332i −1.65690 0.130401i −0.784807 0.619741i \(-0.787238\pi\)
−0.872093 + 0.489340i \(0.837238\pi\)
\(54\) 0.598947 2.27578i 0.0815063 0.309695i
\(55\) 0.615568 + 1.48611i 0.0830032 + 0.200387i
\(56\) −1.26792 + 8.76116i −0.169432 + 1.17076i
\(57\) −0.952874 + 0.692303i −0.126211 + 0.0916978i
\(58\) −5.73185 5.11495i −0.752629 0.671626i
\(59\) 1.86793 2.57098i 0.243183 0.334713i −0.669926 0.742428i \(-0.733674\pi\)
0.913109 + 0.407715i \(0.133674\pi\)
\(60\) 0.111142 0.164839i 0.0143484 0.0212806i
\(61\) −0.239761 + 1.51379i −0.0306983 + 0.193821i −0.998272 0.0587691i \(-0.981282\pi\)
0.967573 + 0.252590i \(0.0812824\pi\)
\(62\) 5.99235 + 8.63629i 0.761029 + 1.09681i
\(63\) −4.77680 + 7.79503i −0.601820 + 0.982081i
\(64\) 5.80594 + 5.50373i 0.725742 + 0.687966i
\(65\) 0.510477 0.0401754i 0.0633169 0.00498315i
\(66\) 1.77866 + 0.321470i 0.218938 + 0.0395703i
\(67\) 4.08936 3.49264i 0.499595 0.426694i −0.363608 0.931552i \(-0.618455\pi\)
0.863203 + 0.504858i \(0.168455\pi\)
\(68\) −14.0746 + 5.12558i −1.70680 + 0.621568i
\(69\) 0.416530 0.255250i 0.0501443 0.0307285i
\(70\) −1.21228 + 0.990655i −0.144895 + 0.118406i
\(71\) −5.17653 4.42117i −0.614341 0.524696i 0.286931 0.957951i \(-0.407365\pi\)
−0.901271 + 0.433255i \(0.857365\pi\)
\(72\) 3.26336 + 7.59008i 0.384591 + 0.894499i
\(73\) 2.80206 2.80206i 0.327957 0.327957i −0.523852 0.851809i \(-0.675506\pi\)
0.851809 + 0.523852i \(0.175506\pi\)
\(74\) 0.176276 + 0.0615407i 0.0204917 + 0.00715396i
\(75\) −1.33217 + 0.319825i −0.153825 + 0.0369302i
\(76\) 2.30895 8.05767i 0.264854 0.924278i
\(77\) −12.6822 6.46190i −1.44527 0.736402i
\(78\) 0.272293 0.506870i 0.0308311 0.0573917i
\(79\) 5.16660 + 2.14007i 0.581287 + 0.240777i 0.653897 0.756583i \(-0.273133\pi\)
−0.0726100 + 0.997360i \(0.523133\pi\)
\(80\) 0.0991961 + 1.41134i 0.0110905 + 0.157792i
\(81\) 8.29541i 0.921712i
\(82\) 1.24605 + 8.96925i 0.137603 + 0.990487i
\(83\) 1.59911i 0.175525i 0.996141 + 0.0877625i \(0.0279717\pi\)
−0.996141 + 0.0877625i \(0.972028\pi\)
\(84\) 0.199456 + 1.74783i 0.0217625 + 0.190704i
\(85\) −2.44740 1.01375i −0.265458 0.109956i
\(86\) 13.2764 + 7.13212i 1.43163 + 0.769076i
\(87\) −1.36024 0.693077i −0.145833 0.0743057i
\(88\) −11.3820 + 5.99222i −1.21332 + 0.638773i
\(89\) 0.293320 0.0704200i 0.0310919 0.00746451i −0.217870 0.975978i \(-0.569911\pi\)
0.248961 + 0.968513i \(0.419911\pi\)
\(90\) −0.481599 + 1.37948i −0.0507650 + 0.145410i
\(91\) −3.20390 + 3.20390i −0.335860 + 0.335860i
\(92\) −1.21693 + 3.25661i −0.126874 + 0.339525i
\(93\) 1.58840 + 1.35663i 0.164710 + 0.140676i
\(94\) 1.55413 + 1.90182i 0.160296 + 0.196157i
\(95\) 1.26393 0.774536i 0.129676 0.0794657i
\(96\) 1.39414 + 0.764045i 0.142289 + 0.0779800i
\(97\) 2.46358 2.10410i 0.250139 0.213639i −0.515534 0.856869i \(-0.672406\pi\)
0.765672 + 0.643231i \(0.222406\pi\)
\(98\) 0.703190 3.89068i 0.0710330 0.393018i
\(99\) −13.2431 + 1.04225i −1.33098 + 0.104750i
\(100\) 6.06802 7.63134i 0.606802 0.763134i
\(101\) −4.28703 + 6.99580i −0.426575 + 0.696108i −0.991654 0.128929i \(-0.958846\pi\)
0.565078 + 0.825037i \(0.308846\pi\)
\(102\) −2.44559 + 1.69689i −0.242150 + 0.168017i
\(103\) −3.02632 + 19.1074i −0.298192 + 1.88271i 0.149863 + 0.988707i \(0.452117\pi\)
−0.448056 + 0.894006i \(0.647883\pi\)
\(104\) 0.694514 + 4.03537i 0.0681027 + 0.395700i
\(105\) −0.182869 + 0.251697i −0.0178461 + 0.0245631i
\(106\) 11.3931 12.7672i 1.10660 1.24006i
\(107\) 8.55795 6.21771i 0.827328 0.601089i −0.0914742 0.995807i \(-0.529158\pi\)
0.918802 + 0.394719i \(0.129158\pi\)
\(108\) 2.04941 + 2.62217i 0.197205 + 0.252318i
\(109\) −4.08791 9.86909i −0.391551 0.945287i −0.989602 0.143830i \(-0.954058\pi\)
0.598052 0.801458i \(-0.295942\pi\)
\(110\) −2.19993 0.578984i −0.209755 0.0552039i
\(111\) 0.0369890 + 0.00291110i 0.00351084 + 0.000276309i
\(112\) −8.77803 8.92622i −0.829446 0.843448i
\(113\) 10.6026 + 3.44498i 0.997405 + 0.324077i 0.761828 0.647779i \(-0.224302\pi\)
0.235577 + 0.971856i \(0.424302\pi\)
\(114\) 0.0361882 1.66529i 0.00338934 0.155969i
\(115\) −0.547823 + 0.279130i −0.0510848 + 0.0260290i
\(116\) 10.6644 2.07491i 0.990160 0.192651i
\(117\) −0.987180 + 4.11190i −0.0912648 + 0.380145i
\(118\) 1.29561 + 4.30344i 0.119270 + 0.396164i
\(119\) 22.2932 7.24350i 2.04362 0.664011i
\(120\) 0.0904459 + 0.266211i 0.00825655 + 0.0243016i
\(121\) −1.51459 9.56276i −0.137690 0.869342i
\(122\) −1.49900 1.56560i −0.135713 0.141743i
\(123\) 0.693110 + 1.66067i 0.0624956 + 0.149738i
\(124\) −14.8516 0.645782i −1.33371 0.0579929i
\(125\) 3.44979 0.546394i 0.308559 0.0488709i
\(126\) −4.68706 12.0496i −0.417556 1.07346i
\(127\) −4.11659 12.6696i −0.365289 1.12424i −0.949800 0.312857i \(-0.898714\pi\)
0.584512 0.811385i \(-0.301286\pi\)
\(128\) −11.1655 + 1.82556i −0.986896 + 0.161358i
\(129\) 2.91216 + 0.699147i 0.256401 + 0.0615564i
\(130\) −0.391696 + 0.609079i −0.0343540 + 0.0534197i
\(131\) 1.31193 + 2.57480i 0.114623 + 0.224961i 0.941190 0.337878i \(-0.109709\pi\)
−0.826567 + 0.562839i \(0.809709\pi\)
\(132\) −1.88429 + 1.72725i −0.164006 + 0.150338i
\(133\) −4.05336 + 12.4750i −0.351471 + 1.08172i
\(134\) 0.431851 + 7.59318i 0.0373063 + 0.655951i
\(135\) −0.0461788 + 0.586757i −0.00397444 + 0.0505000i
\(136\) 6.27632 20.2322i 0.538190 1.73489i
\(137\) 6.30803 2.61287i 0.538931 0.223233i −0.0965786 0.995325i \(-0.530790\pi\)
0.635510 + 0.772093i \(0.280790\pi\)
\(138\) −0.0691555 + 0.687399i −0.00588691 + 0.0585153i
\(139\) −8.45389 11.6358i −0.717050 0.986934i −0.999617 0.0276866i \(-0.991186\pi\)
0.282567 0.959248i \(-0.408814\pi\)
\(140\) −0.0776639 2.21269i −0.00656380 0.187007i
\(141\) 0.394860 + 0.286883i 0.0332532 + 0.0241599i
\(142\) 9.40799 2.04355i 0.789501 0.171491i
\(143\) −6.50268 1.02992i −0.543781 0.0861265i
\(144\) −11.3380 2.82259i −0.944835 0.235216i
\(145\) 1.63825 + 1.00392i 0.136049 + 0.0833710i
\(146\) 0.756217 + 5.55287i 0.0625850 + 0.459559i
\(147\) −0.0616446 0.783269i −0.00508436 0.0646030i
\(148\) −0.220159 + 0.145777i −0.0180970 + 0.0119828i
\(149\) 5.11371 + 5.98738i 0.418931 + 0.490506i 0.929235 0.369488i \(-0.120467\pi\)
−0.510304 + 0.859994i \(0.670467\pi\)
\(150\) 0.780164 1.77349i 0.0637002 0.144805i
\(151\) 5.30261 + 8.65308i 0.431521 + 0.704178i 0.992310 0.123781i \(-0.0395021\pi\)
−0.560789 + 0.827959i \(0.689502\pi\)
\(152\) 7.09501 + 9.49607i 0.575481 + 0.770233i
\(153\) 14.2078 16.6352i 1.14863 1.34488i
\(154\) 18.1296 8.74669i 1.46093 0.704829i
\(155\) −1.85900 1.85900i −0.149318 0.149318i
\(156\) 0.337571 + 0.740383i 0.0270273 + 0.0592781i
\(157\) 3.83686 + 15.9817i 0.306214 + 1.27547i 0.887133 + 0.461513i \(0.152693\pi\)
−0.580919 + 0.813961i \(0.697307\pi\)
\(158\) −6.83144 + 3.98480i −0.543481 + 0.317013i
\(159\) 1.54377 3.02983i 0.122429 0.240281i
\(160\) −1.67378 1.09631i −0.132324 0.0866709i
\(161\) 2.08198 5.02634i 0.164083 0.396131i
\(162\) −9.33891 7.10016i −0.733734 0.557841i
\(163\) −11.4197 −0.894460 −0.447230 0.894419i \(-0.647589\pi\)
−0.447230 + 0.894419i \(0.647589\pi\)
\(164\) −11.1640 6.27412i −0.871764 0.489926i
\(165\) −0.452063 −0.0351930
\(166\) −1.80027 1.36870i −0.139728 0.106232i
\(167\) 6.16097 14.8739i 0.476750 1.15098i −0.484374 0.874861i \(-0.660953\pi\)
0.961124 0.276116i \(-0.0890473\pi\)
\(168\) −2.13842 1.27145i −0.164982 0.0980945i
\(169\) 4.95040 9.71570i 0.380800 0.747361i
\(170\) 3.23603 1.88759i 0.248192 0.144771i
\(171\) 2.85782 + 11.9037i 0.218543 + 0.910298i
\(172\) −19.3927 + 8.84194i −1.47868 + 0.674192i
\(173\) −7.40958 7.40958i −0.563340 0.563340i 0.366915 0.930255i \(-0.380414\pi\)
−0.930255 + 0.366915i \(0.880414\pi\)
\(174\) 1.94451 0.938135i 0.147413 0.0711198i
\(175\) −9.90894 + 11.6019i −0.749045 + 0.877019i
\(176\) 2.99598 17.9426i 0.225830 1.35247i
\(177\) 0.466647 + 0.761499i 0.0350753 + 0.0572378i
\(178\) −0.171779 + 0.390492i −0.0128754 + 0.0292686i
\(179\) 15.8219 + 18.5251i 1.18259 + 1.38463i 0.905804 + 0.423697i \(0.139268\pi\)
0.276782 + 0.960933i \(0.410732\pi\)
\(180\) −1.14081 1.72290i −0.0850306 0.128417i
\(181\) 1.47147 + 18.6968i 0.109374 + 1.38972i 0.769538 + 0.638601i \(0.220487\pi\)
−0.660164 + 0.751121i \(0.729513\pi\)
\(182\) −0.864665 6.34920i −0.0640932 0.470634i
\(183\) −0.367260 0.225057i −0.0271487 0.0166367i
\(184\) −2.62467 4.15739i −0.193493 0.306487i
\(185\) −0.0461224 0.00730508i −0.00339099 0.000537080i
\(186\) −2.88682 + 0.627059i −0.211672 + 0.0459782i
\(187\) 27.5551 + 20.0200i 2.01503 + 1.46400i
\(188\) −3.47126 + 0.121839i −0.253167 + 0.00888599i
\(189\) −3.06122 4.21341i −0.222671 0.306481i
\(190\) −0.209847 + 2.08586i −0.0152239 + 0.151324i
\(191\) −11.2697 + 4.66805i −0.815444 + 0.337768i −0.751124 0.660161i \(-0.770488\pi\)
−0.0643205 + 0.997929i \(0.520488\pi\)
\(192\) −2.05342 + 0.915560i −0.148193 + 0.0660748i
\(193\) −0.227250 + 2.88749i −0.0163578 + 0.207846i 0.983307 + 0.181955i \(0.0582424\pi\)
−0.999665 + 0.0258913i \(0.991758\pi\)
\(194\) 0.260163 + 4.57441i 0.0186786 + 0.328423i
\(195\) −0.0444695 + 0.136863i −0.00318452 + 0.00980096i
\(196\) 3.77822 + 4.12173i 0.269873 + 0.294409i
\(197\) −8.37864 16.4440i −0.596953 1.17159i −0.969847 0.243713i \(-0.921635\pi\)
0.372894 0.927874i \(-0.378365\pi\)
\(198\) 10.1616 15.8011i 0.722153 1.12293i
\(199\) −16.6918 4.00735i −1.18325 0.284074i −0.406363 0.913712i \(-0.633203\pi\)
−0.776889 + 0.629638i \(0.783203\pi\)
\(200\) 3.39760 + 13.3631i 0.240247 + 0.944915i
\(201\) 0.467040 + 1.43740i 0.0329425 + 0.101387i
\(202\) −4.20649 10.8141i −0.295968 0.760878i
\(203\) −16.7923 + 2.65964i −1.17859 + 0.186670i
\(204\) 0.182870 4.20563i 0.0128035 0.294453i
\(205\) −0.705655 2.15208i −0.0492851 0.150308i
\(206\) −18.9208 19.7614i −1.31827 1.37684i
\(207\) −0.794301 5.01502i −0.0552078 0.348568i
\(208\) −5.13743 2.67205i −0.356217 0.185273i
\(209\) −18.1267 + 5.88971i −1.25385 + 0.407400i
\(210\) −0.126839 0.421303i −0.00875271 0.0290727i
\(211\) 2.32449 9.68219i 0.160024 0.666549i −0.833460 0.552580i \(-0.813643\pi\)
0.993484 0.113969i \(-0.0363566\pi\)
\(212\) 4.62170 + 23.7540i 0.317420 + 1.63143i
\(213\) 1.70465 0.868564i 0.116801 0.0595130i
\(214\) −0.325014 + 14.9563i −0.0222175 + 1.02239i
\(215\) −3.58483 1.16478i −0.244483 0.0794374i
\(216\) −4.70614 + 0.0628656i −0.320212 + 0.00427747i
\(217\) 23.1916 + 1.82522i 1.57435 + 0.123904i
\(218\) 14.6095 + 3.84496i 0.989477 + 0.260413i
\(219\) 0.426182 + 1.02889i 0.0287987 + 0.0695262i
\(220\) 2.53477 1.98111i 0.170894 0.133566i
\(221\) 8.77168 6.37300i 0.590047 0.428695i
\(222\) −0.0349367 + 0.0391503i −0.00234480 + 0.00262760i
\(223\) −3.04159 + 4.18639i −0.203680 + 0.280342i −0.898621 0.438725i \(-0.855430\pi\)
0.694941 + 0.719066i \(0.255430\pi\)
\(224\) 17.5623 2.24216i 1.17343 0.149811i
\(225\) −2.22757 + 14.0643i −0.148505 + 0.937623i
\(226\) −12.9532 + 8.98768i −0.861636 + 0.597852i
\(227\) 3.57928 5.84085i 0.237565 0.387671i −0.711533 0.702653i \(-0.751999\pi\)
0.949098 + 0.314982i \(0.101999\pi\)
\(228\) 1.84380 + 1.46609i 0.122109 + 0.0970940i
\(229\) 1.68617 0.132705i 0.111425 0.00876936i −0.0226238 0.999744i \(-0.507202\pi\)
0.134049 + 0.990975i \(0.457202\pi\)
\(230\) 0.154647 0.855647i 0.0101971 0.0564197i
\(231\) 3.04173 2.59789i 0.200131 0.170928i
\(232\) −6.79185 + 13.7818i −0.445907 + 0.904820i
\(233\) 0.0471366 0.0288853i 0.00308802 0.00189234i −0.520954 0.853585i \(-0.674424\pi\)
0.524042 + 0.851693i \(0.324424\pi\)
\(234\) −3.78421 4.63080i −0.247381 0.302725i
\(235\) −0.467100 0.398941i −0.0304703 0.0260241i
\(236\) −5.95371 2.22479i −0.387554 0.144822i
\(237\) −1.11131 + 1.11131i −0.0721875 + 0.0721875i
\(238\) −10.9264 + 31.2974i −0.708253 + 2.02871i
\(239\) 20.1990 4.84936i 1.30657 0.313679i 0.480373 0.877064i \(-0.340501\pi\)
0.826194 + 0.563385i \(0.190501\pi\)
\(240\) −0.377113 0.126031i −0.0243425 0.00813524i
\(241\) 10.8081 + 5.50701i 0.696212 + 0.354738i 0.766015 0.642823i \(-0.222237\pi\)
−0.0698029 + 0.997561i \(0.522237\pi\)
\(242\) 12.0621 + 6.47979i 0.775378 + 0.416537i
\(243\) −6.76591 2.80253i −0.434033 0.179782i
\(244\) 3.04556 0.347547i 0.194972 0.0222494i
\(245\) 0.988851i 0.0631753i
\(246\) −2.46282 0.641095i −0.157023 0.0408748i
\(247\) 6.06726i 0.386050i
\(248\) 13.4387 16.1671i 0.853360 1.02661i
\(249\) −0.415198 0.171981i −0.0263121 0.0108988i
\(250\) −2.33760 + 4.35142i −0.147843 + 0.275208i
\(251\) 18.6812 + 9.51857i 1.17915 + 0.600807i 0.929965 0.367649i \(-0.119837\pi\)
0.249185 + 0.968456i \(0.419837\pi\)
\(252\) 17.5770 + 5.03674i 1.10725 + 0.317285i
\(253\) 7.68681 1.84544i 0.483265 0.116022i
\(254\) 17.7868 + 6.20964i 1.11604 + 0.389627i
\(255\) 0.526425 0.526425i 0.0329660 0.0329660i
\(256\) 7.50147 14.1325i 0.468842 0.883282i
\(257\) −4.28979 3.66382i −0.267590 0.228543i 0.505521 0.862814i \(-0.331300\pi\)
−0.773111 + 0.634271i \(0.781300\pi\)
\(258\) −3.27965 + 2.68007i −0.204182 + 0.166854i
\(259\) 0.352318 0.215901i 0.0218920 0.0134154i
\(260\) −0.350438 0.962288i −0.0217333 0.0596786i
\(261\) −12.0657 + 10.3051i −0.746849 + 0.637869i
\(262\) −4.02159 0.726851i −0.248454 0.0449050i
\(263\) −20.1491 + 1.58577i −1.24245 + 0.0977826i −0.682586 0.730805i \(-0.739145\pi\)
−0.559859 + 0.828588i \(0.689145\pi\)
\(264\) −0.331737 3.59970i −0.0204170 0.221546i
\(265\) −2.23615 + 3.64906i −0.137366 + 0.224160i
\(266\) −10.5749 15.2408i −0.648389 0.934471i
\(267\) −0.0132619 + 0.0837323i −0.000811614 + 0.00512433i
\(268\) −8.91798 6.01294i −0.544752 0.367299i
\(269\) 14.1395 19.4613i 0.862099 1.18658i −0.118965 0.992898i \(-0.537958\pi\)
0.981065 0.193680i \(-0.0620422\pi\)
\(270\) −0.621042 0.554202i −0.0377954 0.0337276i
\(271\) −8.21433 + 5.96806i −0.498985 + 0.362534i −0.808629 0.588319i \(-0.799790\pi\)
0.309644 + 0.950853i \(0.399790\pi\)
\(272\) 17.4052 + 24.3828i 1.05535 + 1.47843i
\(273\) −0.487300 1.17645i −0.0294927 0.0712017i
\(274\) −2.45758 + 9.33793i −0.148468 + 0.564125i
\(275\) −22.1014 1.73942i −1.33277 0.104891i
\(276\) −0.714678 0.666210i −0.0430185 0.0401011i
\(277\) −18.3903 5.97536i −1.10496 0.359024i −0.300953 0.953639i \(-0.597305\pi\)
−0.804011 + 0.594615i \(0.797305\pi\)
\(278\) 20.3353 + 0.441904i 1.21963 + 0.0265036i
\(279\) 19.3450 9.85677i 1.15816 0.590110i
\(280\) 2.55751 + 1.80644i 0.152840 + 0.107956i
\(281\) −3.76429 + 15.6794i −0.224559 + 0.935355i 0.740235 + 0.672348i \(0.234714\pi\)
−0.964794 + 0.263007i \(0.915286\pi\)
\(282\) −0.660938 + 0.198984i −0.0393583 + 0.0118493i
\(283\) 3.06364 0.995436i 0.182114 0.0591725i −0.216540 0.976274i \(-0.569477\pi\)
0.398655 + 0.917101i \(0.369477\pi\)
\(284\) −5.75182 + 12.3406i −0.341307 + 0.732277i
\(285\) 0.0651705 + 0.411470i 0.00386037 + 0.0243734i
\(286\) 6.72522 6.43915i 0.397671 0.380755i
\(287\) 17.1155 + 10.4252i 1.01029 + 0.615379i
\(288\) 12.8820 10.3484i 0.759081 0.609783i
\(289\) −38.6103 + 6.11527i −2.27119 + 0.359722i
\(290\) −2.53241 + 0.985058i −0.148708 + 0.0578446i
\(291\) 0.281362 + 0.865944i 0.0164937 + 0.0507625i
\(292\) −6.89864 3.90144i −0.403713 0.228315i
\(293\) −23.0821 5.54151i −1.34847 0.323739i −0.506023 0.862520i \(-0.668885\pi\)
−0.842446 + 0.538781i \(0.818885\pi\)
\(294\) 0.934562 + 0.601013i 0.0545047 + 0.0350518i
\(295\) −0.510304 1.00153i −0.0297110 0.0583112i
\(296\) 0.0243231 0.372626i 0.00141375 0.0216585i
\(297\) 2.33850 7.19715i 0.135693 0.417621i
\(298\) −11.1175 + 0.632289i −0.644017 + 0.0366275i
\(299\) 0.197442 2.50873i 0.0114183 0.145084i
\(300\) 1.32883 + 2.39626i 0.0767198 + 0.138348i
\(301\) 30.8144 12.7637i 1.77611 0.735690i
\(302\) −14.2802 1.43665i −0.821731 0.0826700i
\(303\) −1.35535 1.86548i −0.0778629 0.107169i
\(304\) −16.7633 0.140313i −0.961443 0.00804750i
\(305\) 0.438576 + 0.318644i 0.0251128 + 0.0182455i
\(306\) 6.56714 + 30.2334i 0.375418 + 1.72833i
\(307\) −17.8889 2.83332i −1.02097 0.161706i −0.376567 0.926390i \(-0.622895\pi\)
−0.644406 + 0.764683i \(0.722895\pi\)
\(308\) −5.67046 + 27.8966i −0.323104 + 1.58956i
\(309\) −4.63565 2.84073i −0.263713 0.161603i
\(310\) 3.68399 0.501704i 0.209237 0.0284949i
\(311\) −1.16383 14.7878i −0.0659947 0.838542i −0.937462 0.348088i \(-0.886831\pi\)
0.871467 0.490454i \(-0.163169\pi\)
\(312\) −1.12245 0.253669i −0.0635462 0.0143612i
\(313\) −18.4097 21.5550i −1.04058 1.21836i −0.975390 0.220485i \(-0.929236\pi\)
−0.0651857 0.997873i \(-0.520764\pi\)
\(314\) −21.2761 9.35942i −1.20068 0.528183i
\(315\) 1.68958 + 2.75714i 0.0951968 + 0.155347i
\(316\) 1.36108 11.1014i 0.0765665 0.624505i
\(317\) −12.9212 + 15.1288i −0.725727 + 0.849717i −0.993508 0.113763i \(-0.963710\pi\)
0.267781 + 0.963480i \(0.413710\pi\)
\(318\) 2.08962 + 4.33124i 0.117180 + 0.242884i
\(319\) −17.4684 17.4684i −0.978044 0.978044i
\(320\) 2.66683 0.945979i 0.149080 0.0528818i
\(321\) 0.694000 + 2.89072i 0.0387353 + 0.161344i
\(322\) 3.87662 + 6.64599i 0.216036 + 0.370367i
\(323\) 14.2499 27.9670i 0.792884 1.55612i
\(324\) 15.9866 4.43655i 0.888146 0.246475i
\(325\) −2.70073 + 6.52014i −0.149810 + 0.361672i
\(326\) 9.77429 12.8562i 0.541348 0.712040i
\(327\) 3.00209 0.166016
\(328\) 16.6188 7.19827i 0.917620 0.397458i
\(329\) 5.43553 0.299670
\(330\) 0.386927 0.508929i 0.0212996 0.0280156i
\(331\) 2.97659 7.18612i 0.163608 0.394985i −0.820720 0.571330i \(-0.806428\pi\)
0.984328 + 0.176345i \(0.0564275\pi\)
\(332\) 3.08175 0.855236i 0.169133 0.0469372i
\(333\) 0.175078 0.343611i 0.00959424 0.0188298i
\(334\) 11.4717 + 19.6668i 0.627702 + 1.07612i
\(335\) −0.444054 1.84962i −0.0242613 0.101055i
\(336\) 3.26169 1.31916i 0.177940 0.0719662i
\(337\) −9.70401 9.70401i −0.528611 0.528611i 0.391547 0.920158i \(-0.371940\pi\)
−0.920158 + 0.391547i \(0.871940\pi\)
\(338\) 6.70075 + 13.8889i 0.364473 + 0.755458i
\(339\) −2.03475 + 2.38239i −0.110512 + 0.129393i
\(340\) −0.644737 + 5.25872i −0.0349658 + 0.285194i
\(341\) 17.6618 + 28.8214i 0.956439 + 1.56077i
\(342\) −15.8471 6.97122i −0.856915 0.376961i
\(343\) 8.54587 + 10.0059i 0.461434 + 0.540269i
\(344\) 6.64431 29.4001i 0.358237 1.58515i
\(345\) −0.0135570 0.172258i −0.000729886 0.00927408i
\(346\) 14.6836 1.99969i 0.789396 0.107504i
\(347\) −11.3025 6.92618i −0.606750 0.371817i 0.184931 0.982752i \(-0.440794\pi\)
−0.791681 + 0.610934i \(0.790794\pi\)
\(348\) −0.608190 + 2.99208i −0.0326024 + 0.160392i
\(349\) −2.96558 0.469702i −0.158744 0.0251426i 0.0765566 0.997065i \(-0.475607\pi\)
−0.235300 + 0.971923i \(0.575607\pi\)
\(350\) −4.58011 21.0856i −0.244817 1.12707i
\(351\) −1.94891 1.41597i −0.104025 0.0755788i
\(352\) 17.6353 + 18.7302i 0.939965 + 0.998320i
\(353\) −3.21600 4.42644i −0.171170 0.235596i 0.714810 0.699319i \(-0.246513\pi\)
−0.885980 + 0.463723i \(0.846513\pi\)
\(354\) −1.25670 0.126430i −0.0667929 0.00671967i
\(355\) −2.22458 + 0.921453i −0.118069 + 0.0489057i
\(356\) −0.292585 0.527615i −0.0155070 0.0279635i
\(357\) −0.516859 + 6.56731i −0.0273551 + 0.347579i
\(358\) −34.3976 + 1.95632i −1.81797 + 0.103394i
\(359\) 0.0982596 0.302412i 0.00518594 0.0159607i −0.948430 0.316986i \(-0.897329\pi\)
0.953616 + 0.301026i \(0.0973290\pi\)
\(360\) 2.91606 + 0.190346i 0.153690 + 0.0100321i
\(361\) −0.651785 1.27920i −0.0343045 0.0673263i
\(362\) −22.3082 14.3463i −1.17249 0.754025i
\(363\) 2.64580 + 0.635200i 0.138868 + 0.0333394i
\(364\) 7.88796 + 4.46094i 0.413442 + 0.233817i
\(365\) −0.433128 1.33303i −0.0226710 0.0697740i
\(366\) 0.567712 0.220829i 0.0296748 0.0115429i
\(367\) 29.5898 4.68656i 1.54457 0.244636i 0.674767 0.738031i \(-0.264244\pi\)
0.869806 + 0.493395i \(0.164244\pi\)
\(368\) 6.92686 + 0.603533i 0.361087 + 0.0314613i
\(369\) 18.7036 0.0502856i 0.973669 0.00261776i
\(370\) 0.0477009 0.0456718i 0.00247985 0.00237436i
\(371\) −5.92414 37.4035i −0.307566 1.94189i
\(372\) 1.76493 3.78667i 0.0915074 0.196330i
\(373\) −1.51928 + 0.493645i −0.0786655 + 0.0255600i −0.348085 0.937463i \(-0.613168\pi\)
0.269420 + 0.963023i \(0.413168\pi\)
\(374\) −46.1232 + 13.8860i −2.38497 + 0.718027i
\(375\) −0.229150 + 0.954480i −0.0118333 + 0.0492891i
\(376\) 2.83393 4.01220i 0.146149 0.206913i
\(377\) −7.00697 + 3.57023i −0.360877 + 0.183876i
\(378\) 7.36357 + 0.160017i 0.378741 + 0.00823038i
\(379\) −13.1978 4.28822i −0.677925 0.220271i −0.0502381 0.998737i \(-0.515998\pi\)
−0.627686 + 0.778466i \(0.715998\pi\)
\(380\) −2.16863 2.02156i −0.111249 0.103704i
\(381\) 3.73230 + 0.293739i 0.191212 + 0.0150487i
\(382\) 4.39062 16.6828i 0.224643 0.853565i
\(383\) 12.9701 + 31.3126i 0.662740 + 1.60000i 0.793491 + 0.608582i \(0.208261\pi\)
−0.130751 + 0.991415i \(0.541739\pi\)
\(384\) 0.726825 3.09537i 0.0370906 0.157960i
\(385\) −4.07298 + 2.95919i −0.207578 + 0.150814i
\(386\) −3.05621 2.72728i −0.155557 0.138815i
\(387\) 18.2968 25.1833i 0.930076 1.28014i
\(388\) −5.37252 3.62241i −0.272748 0.183900i
\(389\) 3.79455 23.9578i 0.192391 1.21471i −0.682680 0.730717i \(-0.739186\pi\)
0.875072 0.483994i \(-0.160814\pi\)
\(390\) −0.116017 0.167206i −0.00587476 0.00846682i
\(391\) −6.80225 + 11.1003i −0.344004 + 0.561364i
\(392\) −7.87406 + 0.725648i −0.397700 + 0.0366508i
\(393\) −0.809624 + 0.0637188i −0.0408401 + 0.00321419i
\(394\) 25.6839 + 4.64205i 1.29394 + 0.233863i
\(395\) 1.50410 1.28462i 0.0756792 0.0646362i
\(396\) 9.09127 + 24.9642i 0.456854 + 1.25450i
\(397\) 19.7829 12.1230i 0.992876 0.608435i 0.0716361 0.997431i \(-0.477178\pi\)
0.921239 + 0.388996i \(0.127178\pi\)
\(398\) 18.7982 15.3616i 0.942270 0.770007i
\(399\) −2.80311 2.39409i −0.140331 0.119854i
\(400\) −17.9522 7.61269i −0.897608 0.380634i
\(401\) −17.8985 + 17.8985i −0.893808 + 0.893808i −0.994879 0.101071i \(-0.967773\pi\)
0.101071 + 0.994879i \(0.467773\pi\)
\(402\) −2.01796 0.704503i −0.100647 0.0351374i
\(403\) 10.4631 2.51198i 0.521206 0.125130i
\(404\) 15.7749 + 4.52032i 0.784828 + 0.224894i
\(405\) 2.61432 + 1.33206i 0.129907 + 0.0661908i
\(406\) 11.3786 21.1811i 0.564709 1.05120i
\(407\) 0.554706 + 0.229767i 0.0274958 + 0.0113891i
\(408\) 4.57814 + 3.80553i 0.226652 + 0.188402i
\(409\) 6.87390i 0.339892i −0.985453 0.169946i \(-0.945641\pi\)
0.985453 0.169946i \(-0.0543594\pi\)
\(410\) 3.02677 + 1.04757i 0.149482 + 0.0517360i
\(411\) 1.91885i 0.0946498i
\(412\) 38.4417 4.38683i 1.89389 0.216123i
\(413\) 9.18913 + 3.80626i 0.452168 + 0.187294i
\(414\) 6.32573 + 3.39821i 0.310893 + 0.167013i
\(415\) 0.503964 + 0.256783i 0.0247386 + 0.0126050i
\(416\) 7.40538 3.49664i 0.363079 0.171437i
\(417\) 3.93035 0.943594i 0.192470 0.0462080i
\(418\) 8.88428 25.4480i 0.434544 1.24470i
\(419\) −25.0424 + 25.0424i −1.22340 + 1.22340i −0.256987 + 0.966415i \(0.582730\pi\)
−0.966415 + 0.256987i \(0.917270\pi\)
\(420\) 0.582864 + 0.217805i 0.0284408 + 0.0106278i
\(421\) 4.65409 + 3.97497i 0.226826 + 0.193728i 0.755597 0.655037i \(-0.227347\pi\)
−0.528771 + 0.848765i \(0.677347\pi\)
\(422\) 8.91058 + 10.9040i 0.433760 + 0.530799i
\(423\) 4.32538 2.65059i 0.210307 0.128876i
\(424\) −30.6979 15.1283i −1.49082 0.734695i
\(425\) 27.7625 23.7115i 1.34668 1.15017i
\(426\) −0.481214 + 2.66250i −0.0233149 + 0.128999i
\(427\) −4.78215 + 0.376363i −0.231424 + 0.0182135i
\(428\) −16.5595 13.1672i −0.800435 0.636462i
\(429\) 0.966762 1.57761i 0.0466757 0.0761679i
\(430\) 4.37961 3.03882i 0.211203 0.146545i
\(431\) −2.16300 + 13.6566i −0.104188 + 0.657817i 0.879221 + 0.476414i \(0.158064\pi\)
−0.983409 + 0.181403i \(0.941936\pi\)
\(432\) 3.95728 5.35195i 0.190395 0.257496i
\(433\) −22.4510 + 30.9011i −1.07892 + 1.48501i −0.218226 + 0.975898i \(0.570027\pi\)
−0.860699 + 0.509114i \(0.829973\pi\)
\(434\) −21.9048 + 24.5467i −1.05147 + 1.17828i
\(435\) −0.436851 + 0.317391i −0.0209454 + 0.0152177i
\(436\) −16.8331 + 13.1563i −0.806158 + 0.630071i
\(437\) −2.78788 6.73054i −0.133362 0.321965i
\(438\) −1.52310 0.400853i −0.0727764 0.0191535i
\(439\) −31.2708 2.46107i −1.49248 0.117460i −0.694213 0.719770i \(-0.744247\pi\)
−0.798263 + 0.602309i \(0.794247\pi\)
\(440\) 0.0607703 + 4.54928i 0.00289711 + 0.216879i
\(441\) −7.76659 2.52352i −0.369838 0.120168i
\(442\) −0.333131 + 15.3298i −0.0158454 + 0.729167i
\(443\) 8.33307 4.24591i 0.395916 0.201729i −0.244686 0.969602i \(-0.578685\pi\)
0.640602 + 0.767873i \(0.278685\pi\)
\(444\) −0.0141723 0.0728409i −0.000672588 0.00345687i
\(445\) 0.0249079 0.103749i 0.00118075 0.00491816i
\(446\) −2.10967 7.00740i −0.0998957 0.331810i
\(447\) −2.10455 + 0.683811i −0.0995420 + 0.0323431i
\(448\) −12.5076 + 21.6906i −0.590930 + 1.02479i
\(449\) 3.22566 + 20.3660i 0.152228 + 0.961132i 0.939007 + 0.343897i \(0.111747\pi\)
−0.786779 + 0.617235i \(0.788253\pi\)
\(450\) −13.9269 14.5457i −0.656522 0.685689i
\(451\) 2.36275 + 29.0237i 0.111258 + 1.36667i
\(452\) 0.968583 22.2753i 0.0455583 1.04774i
\(453\) −2.81700 + 0.446169i −0.132354 + 0.0209629i
\(454\) 3.51203 + 9.02879i 0.164828 + 0.423742i
\(455\) 0.495242 + 1.52420i 0.0232173 + 0.0714555i
\(456\) −3.22865 + 0.820891i −0.151195 + 0.0384417i
\(457\) −16.8202 4.03818i −0.786818 0.188898i −0.179923 0.983681i \(-0.557585\pi\)
−0.606894 + 0.794782i \(0.707585\pi\)
\(458\) −1.29382 + 2.01186i −0.0604563 + 0.0940082i
\(459\) 5.65788 + 11.1042i 0.264087 + 0.518301i
\(460\) 0.830916 + 0.906461i 0.0387417 + 0.0422640i
\(461\) 3.05328 9.39702i 0.142205 0.437663i −0.854436 0.519557i \(-0.826097\pi\)
0.996641 + 0.0818943i \(0.0260970\pi\)
\(462\) 0.321218 + 5.64793i 0.0149444 + 0.262765i
\(463\) 1.16227 14.7680i 0.0540151 0.686326i −0.908986 0.416828i \(-0.863142\pi\)
0.963001 0.269499i \(-0.0868581\pi\)
\(464\) −9.70221 19.4423i −0.450414 0.902584i
\(465\) 0.682609 0.282746i 0.0316552 0.0131120i
\(466\) −0.00782598 + 0.0777895i −0.000362532 + 0.00360353i
\(467\) 14.4531 + 19.8929i 0.668808 + 0.920536i 0.999733 0.0231217i \(-0.00736051\pi\)
−0.330924 + 0.943657i \(0.607361\pi\)
\(468\) 8.45228 0.296669i 0.390707 0.0137135i
\(469\) 13.6171 + 9.89342i 0.628780 + 0.456836i
\(470\) 0.848923 0.184399i 0.0391579 0.00850567i
\(471\) −4.56218 0.722578i −0.210214 0.0332946i
\(472\) 7.60053 4.79842i 0.349843 0.220865i
\(473\) 41.3221 + 25.3222i 1.89999 + 1.16432i
\(474\) −0.299919 2.20230i −0.0137758 0.101155i
\(475\) 1.60297 + 20.3676i 0.0735491 + 0.934530i
\(476\) −25.8823 39.0887i −1.18631 1.79163i
\(477\) −22.9538 26.8754i −1.05098 1.23054i
\(478\) −11.8293 + 26.8906i −0.541058 + 1.22995i
\(479\) 20.0821 + 32.7710i 0.917574 + 1.49734i 0.866813 + 0.498634i \(0.166165\pi\)
0.0507617 + 0.998711i \(0.483835\pi\)
\(480\) 0.464661 0.316679i 0.0212088 0.0144544i
\(481\) 0.124129 0.145336i 0.00565979 0.00662676i
\(482\) −15.4506 + 7.45417i −0.703754 + 0.339528i
\(483\) 1.08114 + 1.08114i 0.0491937 + 0.0491937i
\(484\) −17.6190 + 8.03323i −0.800863 + 0.365147i
\(485\) −0.267514 1.11428i −0.0121472 0.0505967i
\(486\) 8.94611 5.21829i 0.405804 0.236706i
\(487\) 4.69827 9.22087i 0.212899 0.417838i −0.759718 0.650253i \(-0.774663\pi\)
0.972617 + 0.232415i \(0.0746629\pi\)
\(488\) −2.21547 + 3.72614i −0.100290 + 0.168674i
\(489\) 1.22816 2.96505i 0.0555395 0.134084i
\(490\) −1.11324 0.846372i −0.0502911 0.0382352i
\(491\) −34.1778 −1.54242 −0.771210 0.636580i \(-0.780348\pi\)
−0.771210 + 0.636580i \(0.780348\pi\)
\(492\) 2.82970 2.22390i 0.127573 0.100261i
\(493\) 40.6838 1.83231
\(494\) −6.83048 5.19305i −0.307318 0.233647i
\(495\) −1.79809 + 4.34097i −0.0808180 + 0.195112i
\(496\) 6.69841 + 28.9669i 0.300768 + 1.30065i
\(497\) 9.67291 18.9842i 0.433889 0.851556i
\(498\) 0.548989 0.320226i 0.0246008 0.0143497i
\(499\) 8.43677 + 35.1417i 0.377682 + 1.57316i 0.760503 + 0.649334i \(0.224952\pi\)
−0.382821 + 0.923822i \(0.625048\pi\)
\(500\) −2.89801 6.35610i −0.129603 0.284253i
\(501\) 3.19931 + 3.19931i 0.142935 + 0.142935i
\(502\) −26.7055 + 12.8841i −1.19192 + 0.575047i
\(503\) −4.13656 + 4.84329i −0.184440 + 0.215951i −0.844921 0.534891i \(-0.820352\pi\)
0.660481 + 0.750843i \(0.270352\pi\)
\(504\) −20.7148 + 15.4771i −0.922710 + 0.689404i
\(505\) 1.51634 + 2.47445i 0.0674764 + 0.110111i
\(506\) −4.50167 + 10.2333i −0.200124 + 0.454925i
\(507\) 1.99021 + 2.33024i 0.0883885 + 0.103490i
\(508\) −22.2147 + 14.7093i −0.985619 + 0.652620i
\(509\) 1.16746 + 14.8340i 0.0517469 + 0.657506i 0.967025 + 0.254683i \(0.0819711\pi\)
−0.915278 + 0.402823i \(0.868029\pi\)
\(510\) 0.142071 + 1.04322i 0.00629100 + 0.0461946i
\(511\) 10.5749 + 6.48031i 0.467806 + 0.286672i
\(512\) 9.48967 + 20.5413i 0.419388 + 0.907807i
\(513\) −6.88801 1.09095i −0.304113 0.0481668i
\(514\) 7.79640 1.69349i 0.343884 0.0746967i
\(515\) 5.53581 + 4.02200i 0.243937 + 0.177231i
\(516\) −0.210109 5.98612i −0.00924952 0.263524i
\(517\) 4.64236 + 6.38965i 0.204171 + 0.281017i
\(518\) −0.0584946 + 0.581430i −0.00257010 + 0.0255466i
\(519\) 2.72073 1.12696i 0.119427 0.0494682i
\(520\) 1.38328 + 0.429115i 0.0606609 + 0.0188179i
\(521\) −0.436680 + 5.54855i −0.0191313 + 0.243086i 0.979915 + 0.199417i \(0.0639048\pi\)
−0.999046 + 0.0436694i \(0.986095\pi\)
\(522\) −1.27418 22.4038i −0.0557694 0.980586i
\(523\) 0.613353 1.88771i 0.0268200 0.0825436i −0.936751 0.349998i \(-0.886182\pi\)
0.963571 + 0.267454i \(0.0861824\pi\)
\(524\) 4.26042 3.90535i 0.186117 0.170606i
\(525\) −1.94667 3.82055i −0.0849595 0.166742i
\(526\) 15.4606 24.0410i 0.674116 1.04824i
\(527\) −54.1295 12.9953i −2.35792 0.566086i
\(528\) 4.33646 + 2.70757i 0.188720 + 0.117832i
\(529\) −6.17366 19.0006i −0.268420 0.826112i
\(530\) −2.19414 5.64073i −0.0953073 0.245018i
\(531\) 9.16844 1.45214i 0.397877 0.0630175i
\(532\) 26.2092 + 1.13963i 1.13631 + 0.0494094i
\(533\) 9.01942 + 2.13974i 0.390675 + 0.0926825i
\(534\) −0.0829142 0.0865978i −0.00358805 0.00374745i
\(535\) −0.585309 3.69549i −0.0253051 0.159770i
\(536\) 14.4024 4.89324i 0.622087 0.211356i
\(537\) −6.51153 + 2.11572i −0.280993 + 0.0913003i
\(538\) 9.80724 + 32.5754i 0.422820 + 1.40442i
\(539\) 2.96805 12.3628i 0.127843 0.532504i
\(540\) 1.15548 0.224816i 0.0497237 0.00967452i
\(541\) 13.7629 7.01255i 0.591714 0.301493i −0.132375 0.991200i \(-0.542260\pi\)
0.724089 + 0.689706i \(0.242260\pi\)
\(542\) 0.311964 14.3558i 0.0134000 0.616634i
\(543\) −5.01276 1.62874i −0.215118 0.0698961i
\(544\) −42.3474 1.27494i −1.81563 0.0546624i
\(545\) −3.76671 0.296446i −0.161348 0.0126984i
\(546\) 1.74152 + 0.458338i 0.0745302 + 0.0196151i
\(547\) 5.95274 + 14.3712i 0.254521 + 0.614467i 0.998559 0.0536699i \(-0.0170919\pi\)
−0.744038 + 0.668137i \(0.767092\pi\)
\(548\) −8.40910 10.7592i −0.359219 0.459610i
\(549\) −3.62191 + 2.63147i −0.154580 + 0.112309i
\(550\) 20.8752 23.3928i 0.890119 0.997474i
\(551\) −13.3816 + 18.4182i −0.570074 + 0.784640i
\(552\) 1.36172 0.234361i 0.0579585 0.00997506i
\(553\) −2.73804 + 17.2873i −0.116433 + 0.735130i
\(554\) 22.4675 15.5892i 0.954553 0.662323i
\(555\) 0.00685708 0.0111897i 0.000291067 0.000474978i
\(556\) −17.9028 + 22.5151i −0.759246 + 0.954853i
\(557\) 20.0485 1.57785i 0.849482 0.0668557i 0.353759 0.935336i \(-0.384903\pi\)
0.495723 + 0.868481i \(0.334903\pi\)
\(558\) −5.46099 + 30.2150i −0.231182 + 1.27910i
\(559\) 11.7312 10.0194i 0.496178 0.423776i
\(560\) −4.22269 + 1.33306i −0.178441 + 0.0563322i
\(561\) −8.16155 + 5.00140i −0.344581 + 0.211159i
\(562\) −14.4299 17.6581i −0.608687 0.744860i
\(563\) 21.3070 + 18.1979i 0.897982 + 0.766949i 0.973138 0.230222i \(-0.0739454\pi\)
−0.0751557 + 0.997172i \(0.523945\pi\)
\(564\) 0.341691 0.914392i 0.0143878 0.0385029i
\(565\) 2.78824 2.78824i 0.117302 0.117302i
\(566\) −1.50156 + 4.30103i −0.0631152 + 0.180786i
\(567\) −25.2457 + 6.06095i −1.06022 + 0.254536i
\(568\) −8.96985 17.0378i −0.376366 0.714891i
\(569\) −26.5809 13.5437i −1.11433 0.567780i −0.202886 0.979202i \(-0.565032\pi\)
−0.911445 + 0.411422i \(0.865032\pi\)
\(570\) −0.519011 0.278815i −0.0217390 0.0116783i
\(571\) −9.45143 3.91491i −0.395530 0.163834i 0.176048 0.984382i \(-0.443669\pi\)
−0.571578 + 0.820548i \(0.693669\pi\)
\(572\) 1.49293 + 13.0826i 0.0624227 + 0.547010i
\(573\) 3.42813i 0.143212i
\(574\) −26.3860 + 10.3454i −1.10133 + 0.431809i
\(575\) 8.47391i 0.353386i
\(576\) 0.624203 + 23.3598i 0.0260084 + 0.973325i
\(577\) −27.5368 11.4061i −1.14637 0.474843i −0.273056 0.961998i \(-0.588035\pi\)
−0.873315 + 0.487155i \(0.838035\pi\)
\(578\) 26.1626 48.7013i 1.08822 2.02571i
\(579\) −0.725277 0.369547i −0.0301415 0.0153579i
\(580\) 1.05855 3.69409i 0.0439539 0.153389i
\(581\) −4.86662 + 1.16837i −0.201901 + 0.0484722i
\(582\) −1.21570 0.424418i −0.0503922 0.0175927i
\(583\) 38.9095 38.9095i 1.61147 1.61147i
\(584\) 10.2969 4.42715i 0.426087 0.183197i
\(585\) 1.13736 + 0.971396i 0.0470240 + 0.0401623i
\(586\) 25.9949 21.2426i 1.07384 0.877522i
\(587\) −12.6491 + 7.75138i −0.522084 + 0.319934i −0.758451 0.651730i \(-0.774043\pi\)
0.236366 + 0.971664i \(0.424043\pi\)
\(588\) −1.47652 + 0.537708i −0.0608907 + 0.0221747i
\(589\) 23.6873 20.2308i 0.976017 0.833597i
\(590\) 1.56429 + 0.282726i 0.0644008 + 0.0116396i
\(591\) 5.17068 0.406942i 0.212693 0.0167393i
\(592\) 0.398681 + 0.346319i 0.0163857 + 0.0142336i
\(593\) −10.9508 + 17.8700i −0.449694 + 0.733835i −0.994501 0.104727i \(-0.966603\pi\)
0.544807 + 0.838562i \(0.316603\pi\)
\(594\) 6.10095 + 8.79281i 0.250325 + 0.360773i
\(595\) 1.29700 8.18893i 0.0531718 0.335713i
\(596\) 8.80377 13.0571i 0.360616 0.534841i
\(597\) 2.83565 3.90294i 0.116055 0.159737i
\(598\) 2.65532 + 2.36954i 0.108584 + 0.0968977i
\(599\) −0.581795 + 0.422699i −0.0237715 + 0.0172710i −0.599608 0.800294i \(-0.704677\pi\)
0.575836 + 0.817565i \(0.304677\pi\)
\(600\) −3.83505 0.555009i −0.156565 0.0226581i
\(601\) −1.82675 4.41017i −0.0745147 0.179894i 0.882233 0.470813i \(-0.156039\pi\)
−0.956748 + 0.290918i \(0.906039\pi\)
\(602\) −12.0052 + 45.6153i −0.489294 + 1.85914i
\(603\) 15.6604 + 1.23250i 0.637742 + 0.0501914i
\(604\) 13.8400 14.8469i 0.563140 0.604110i
\(605\) −3.25695 1.05825i −0.132414 0.0430238i
\(606\) 3.26021 + 0.0708473i 0.132437 + 0.00287797i
\(607\) 30.4206 15.5001i 1.23473 0.629128i 0.290018 0.957021i \(-0.406339\pi\)
0.944715 + 0.327893i \(0.106339\pi\)
\(608\) 14.5059 18.7520i 0.588294 0.760492i
\(609\) 1.11542 4.64605i 0.0451990 0.188268i
\(610\) −0.734110 + 0.221014i −0.0297233 + 0.00894858i
\(611\) 2.39115 0.776932i 0.0967356 0.0314313i
\(612\) −39.6575 18.4840i −1.60306 0.747170i
\(613\) 2.95344 + 18.6473i 0.119288 + 0.753157i 0.972725 + 0.231960i \(0.0745140\pi\)
−0.853437 + 0.521196i \(0.825486\pi\)
\(614\) 18.5011 17.7141i 0.746644 0.714883i
\(615\) 0.634664 + 0.0482326i 0.0255921 + 0.00194493i
\(616\) −26.5524 30.2609i −1.06983 1.21925i
\(617\) −15.7183 + 2.48953i −0.632794 + 0.100225i −0.464588 0.885527i \(-0.653798\pi\)
−0.168207 + 0.985752i \(0.553798\pi\)
\(618\) 7.16579 2.78736i 0.288250 0.112124i
\(619\) −12.4248 38.2395i −0.499394 1.53698i −0.809995 0.586437i \(-0.800530\pi\)
0.310601 0.950540i \(-0.399470\pi\)
\(620\) −2.58837 + 4.57683i −0.103951 + 0.183810i
\(621\) 2.81260 + 0.675246i 0.112866 + 0.0270967i
\(622\) 17.6442 + 11.3469i 0.707468 + 0.454969i
\(623\) 0.428623 + 0.841220i 0.0171724 + 0.0337027i
\(624\) 1.24630 1.04653i 0.0498919 0.0418946i
\(625\) −7.15036 + 22.0065i −0.286014 + 0.880262i
\(626\) 40.0235 2.27628i 1.59966 0.0909785i
\(627\) 0.420259 5.33990i 0.0167835 0.213255i
\(628\) 28.7473 15.9416i 1.14714 0.636138i
\(629\) −0.913515 + 0.378390i −0.0364242 + 0.0150874i
\(630\) −4.55010 0.457761i −0.181280 0.0182376i
\(631\) −17.5499 24.1554i −0.698650 0.961610i −0.999967 0.00808555i \(-0.997426\pi\)
0.301317 0.953524i \(-0.402574\pi\)
\(632\) 11.3330 + 11.0342i 0.450801 + 0.438916i
\(633\) 2.26392 + 1.64484i 0.0899829 + 0.0653764i
\(634\) −5.97244 27.4955i −0.237196 1.09199i
\(635\) −4.65389 0.737104i −0.184684 0.0292511i
\(636\) −6.66462 1.35470i −0.264269 0.0537172i
\(637\) −3.45090 2.11471i −0.136730 0.0837880i
\(638\) 34.6173 4.71435i 1.37051 0.186643i
\(639\) −1.56016 19.8238i −0.0617192 0.784216i
\(640\) −1.21760 + 3.81197i −0.0481299 + 0.150681i
\(641\) 20.7531 + 24.2987i 0.819696 + 0.959741i 0.999714 0.0239222i \(-0.00761540\pi\)
−0.180017 + 0.983663i \(0.557615\pi\)
\(642\) −3.84835 1.69291i −0.151882 0.0668137i
\(643\) −20.2170 32.9911i −0.797279 1.30104i −0.949837 0.312746i \(-0.898751\pi\)
0.152558 0.988295i \(-0.451249\pi\)
\(644\) −10.8001 1.32413i −0.425582 0.0521779i
\(645\) 0.687968 0.805507i 0.0270887 0.0317168i
\(646\) 19.2883 + 39.9797i 0.758889 + 1.57298i
\(647\) 8.71002 + 8.71002i 0.342426 + 0.342426i 0.857279 0.514853i \(-0.172153\pi\)
−0.514853 + 0.857279i \(0.672153\pi\)
\(648\) −8.68854 + 21.7949i −0.341318 + 0.856186i
\(649\) 3.37382 + 14.0530i 0.132434 + 0.551628i
\(650\) −5.02874 8.62115i −0.197243 0.338149i
\(651\) −2.96811 + 5.82525i −0.116329 + 0.228309i
\(652\) 6.10749 + 22.0077i 0.239188 + 0.861886i
\(653\) 3.61708 8.73240i 0.141547 0.341725i −0.837169 0.546945i \(-0.815791\pi\)
0.978716 + 0.205219i \(0.0657908\pi\)
\(654\) −2.56953 + 3.37973i −0.100477 + 0.132158i
\(655\) 1.02212 0.0399376
\(656\) −6.12052 + 24.8704i −0.238966 + 0.971028i
\(657\) 11.5752 0.451591
\(658\) −4.65235 + 6.11928i −0.181367 + 0.238554i
\(659\) 7.11469 17.1764i 0.277149 0.669097i −0.722605 0.691261i \(-0.757056\pi\)
0.999754 + 0.0221637i \(0.00705551\pi\)
\(660\) 0.241772 + 0.871200i 0.00941098 + 0.0339114i
\(661\) 13.5053 26.5056i 0.525294 1.03095i −0.464113 0.885776i \(-0.653627\pi\)
0.989407 0.145171i \(-0.0463732\pi\)
\(662\) 5.54238 + 9.50173i 0.215411 + 0.369295i
\(663\) 0.711333 + 2.96291i 0.0276259 + 0.115070i
\(664\) −1.67489 + 4.20142i −0.0649985 + 0.163047i
\(665\) 3.28064 + 3.28064i 0.127218 + 0.127218i
\(666\) 0.236982 + 0.491204i 0.00918288 + 0.0190338i
\(667\) 6.13248 7.18021i 0.237450 0.278019i
\(668\) −31.9595 3.91835i −1.23655 0.151605i
\(669\) −0.759853 1.23997i −0.0293776 0.0479399i
\(670\) 2.46236 + 1.08320i 0.0951293 + 0.0418478i
\(671\) −4.52675 5.30014i −0.174753 0.204610i
\(672\) −1.30663 + 4.80108i −0.0504042 + 0.185206i
\(673\) 0.745089 + 9.46725i 0.0287211 + 0.364936i 0.994437 + 0.105334i \(0.0335912\pi\)
−0.965716 + 0.259602i \(0.916409\pi\)
\(674\) 19.2305 2.61890i 0.740731 0.100876i
\(675\) −6.91655 4.23847i −0.266218 0.163139i
\(676\) −21.3713 4.34408i −0.821974 0.167080i
\(677\) 29.1383 + 4.61506i 1.11988 + 0.177371i 0.688805 0.724947i \(-0.258136\pi\)
0.431072 + 0.902318i \(0.358136\pi\)
\(678\) −0.940501 4.32983i −0.0361197 0.166286i
\(679\) 8.20345 + 5.96015i 0.314819 + 0.228730i
\(680\) −5.36839 5.22685i −0.205868 0.200441i
\(681\) 1.13159 + 1.55751i 0.0433628 + 0.0596838i
\(682\) −47.5639 4.78515i −1.82132 0.183233i
\(683\) 37.1415 15.3845i 1.42118 0.588672i 0.466023 0.884772i \(-0.345686\pi\)
0.955157 + 0.296100i \(0.0956863\pi\)
\(684\) 21.4120 11.8738i 0.818707 0.454007i
\(685\) 0.189480 2.40757i 0.00723964 0.0919884i
\(686\) −18.5791 + 1.05666i −0.709355 + 0.0403435i
\(687\) −0.146888 + 0.452075i −0.00560413 + 0.0172477i
\(688\) 27.4115 + 32.6441i 1.04505 + 1.24455i
\(689\) −7.95240 15.6075i −0.302962 0.594597i
\(690\) 0.205531 + 0.132176i 0.00782443 + 0.00503186i
\(691\) 17.5311 + 4.20885i 0.666915 + 0.160112i 0.552747 0.833349i \(-0.313580\pi\)
0.114168 + 0.993461i \(0.463580\pi\)
\(692\) −10.3167 + 18.2423i −0.392182 + 0.693467i
\(693\) −12.8478 39.5416i −0.488049 1.50206i
\(694\) 17.4714 6.79606i 0.663206 0.257975i
\(695\) −5.02457 + 0.795813i −0.190593 + 0.0301869i
\(696\) −2.84791 3.24566i −0.107950 0.123027i
\(697\) −36.5494 31.0466i −1.38441 1.17597i
\(698\) 3.06707 2.93660i 0.116090 0.111152i
\(699\) 0.00243045 + 0.0153453i 9.19281e−5 + 0.000580411i
\(700\) 27.6582 + 12.8912i 1.04538 + 0.487243i
\(701\) −34.9218 + 11.3468i −1.31898 + 0.428562i −0.882144 0.470979i \(-0.843901\pi\)
−0.436835 + 0.899542i \(0.643901\pi\)
\(702\) 3.26219 0.982126i 0.123124 0.0370679i
\(703\) 0.129167 0.538020i 0.00487164 0.0202918i
\(704\) −36.1806 + 3.82230i −1.36361 + 0.144058i
\(705\) 0.153818 0.0783743i 0.00579313 0.00295175i
\(706\) 7.73588 + 0.168108i 0.291144 + 0.00632681i
\(707\) −24.4228 7.93545i −0.918514 0.298443i
\(708\) 1.21796 1.30657i 0.0457738 0.0491040i
\(709\) −29.7048 2.33782i −1.11559 0.0877985i −0.492765 0.870163i \(-0.664014\pi\)
−0.622821 + 0.782364i \(0.714014\pi\)
\(710\) 0.866689 3.29311i 0.0325263 0.123588i
\(711\) 6.25120 + 15.0917i 0.234438 + 0.565984i
\(712\) 0.844413 + 0.122203i 0.0316457 + 0.00457977i
\(713\) −10.4527 + 7.59436i −0.391458 + 0.284411i
\(714\) −6.95105 6.20293i −0.260136 0.232139i
\(715\) −1.36877 + 1.88396i −0.0511893 + 0.0704560i
\(716\) 27.2390 40.3991i 1.01797 1.50978i
\(717\) −0.913258 + 5.76609i −0.0341063 + 0.215338i
\(718\) 0.256351 + 0.369459i 0.00956695 + 0.0137881i
\(719\) 4.67765 7.63323i 0.174447 0.284671i −0.753452 0.657502i \(-0.771613\pi\)
0.927899 + 0.372831i \(0.121613\pi\)
\(720\) −2.71019 + 3.11996i −0.101003 + 0.116274i
\(721\) −60.3614 + 4.75055i −2.24798 + 0.176920i
\(722\) 1.99799 + 0.361111i 0.0743574 + 0.0134392i
\(723\) −2.59225 + 2.21399i −0.0964067 + 0.0823391i
\(724\) 35.2449 12.8352i 1.30987 0.477017i
\(725\) −22.5790 + 13.8364i −0.838561 + 0.513871i
\(726\) −2.97968 + 2.43495i −0.110586 + 0.0903693i
\(727\) 24.1149 + 20.5961i 0.894373 + 0.763867i 0.972458 0.233080i \(-0.0748803\pi\)
−0.0780842 + 0.996947i \(0.524880\pi\)
\(728\) −11.7735 + 5.06203i −0.436356 + 0.187611i
\(729\) −16.1419 + 16.1419i −0.597848 + 0.597848i
\(730\) 1.87144 + 0.653348i 0.0692650 + 0.0241815i
\(731\) −77.6071 + 18.6318i −2.87040 + 0.689122i
\(732\) −0.237305 + 0.828137i −0.00877103 + 0.0306088i
\(733\) −29.0869 14.8205i −1.07435 0.547408i −0.174968 0.984574i \(-0.555982\pi\)
−0.899381 + 0.437166i \(0.855982\pi\)
\(734\) −20.0502 + 37.3232i −0.740067 + 1.37763i
\(735\) −0.256749 0.106349i −0.00947031 0.00392273i
\(736\) −6.60825 + 7.28164i −0.243583 + 0.268405i
\(737\) 24.4572i 0.900891i
\(738\) −15.9521 + 21.0994i −0.587203 + 0.776680i
\(739\) 8.87711i 0.326550i 0.986581 + 0.163275i \(0.0522057\pi\)
−0.986581 + 0.163275i \(0.947794\pi\)
\(740\) 0.0105891 + 0.0927925i 0.000389264 + 0.00341112i
\(741\) −1.57532 0.652520i −0.0578710 0.0239709i
\(742\) 47.1792 + 25.3449i 1.73200 + 0.930440i
\(743\) −9.12438 4.64910i −0.334741 0.170559i 0.278538 0.960425i \(-0.410150\pi\)
−0.613279 + 0.789866i \(0.710150\pi\)
\(744\) 2.75238 + 5.22801i 0.100907 + 0.191668i
\(745\) 2.70810 0.650156i 0.0992169 0.0238199i
\(746\) 0.744635 2.13292i 0.0272630 0.0780916i
\(747\) −3.30292 + 3.30292i −0.120847 + 0.120847i
\(748\) 23.8447 63.8104i 0.871850 2.33314i
\(749\) 25.1753 + 21.5018i 0.919886 + 0.785657i
\(750\) −0.878414 1.07493i −0.0320751 0.0392509i
\(751\) −39.5990 + 24.2663i −1.44499 + 0.885490i −0.999950 0.0100212i \(-0.996810\pi\)
−0.445039 + 0.895511i \(0.646810\pi\)
\(752\) 2.09130 + 6.62452i 0.0762619 + 0.241571i
\(753\) −4.48056 + 3.82676i −0.163281 + 0.139455i
\(754\) 1.97803 10.9442i 0.0720356 0.398565i
\(755\) 3.57853 0.281637i 0.130236 0.0102498i
\(756\) −6.48274 + 8.15290i −0.235775 + 0.296518i
\(757\) 2.16121 3.52677i 0.0785505 0.128183i −0.810953 0.585112i \(-0.801051\pi\)
0.889503 + 0.456929i \(0.151051\pi\)
\(758\) 16.1238 11.1876i 0.585644 0.406353i
\(759\) −0.347543 + 2.19430i −0.0126150 + 0.0796481i
\(760\) 4.13202 0.711149i 0.149884 0.0257961i
\(761\) 25.6287 35.2749i 0.929040 1.27871i −0.0311925 0.999513i \(-0.509930\pi\)
0.960233 0.279201i \(-0.0900695\pi\)
\(762\) −3.52522 + 3.95039i −0.127705 + 0.143107i
\(763\) 27.0481 19.6516i 0.979208 0.711436i
\(764\) 15.0234 + 19.2219i 0.543526 + 0.695426i
\(765\) −2.96117 7.14890i −0.107061 0.258469i
\(766\) −46.3527 12.1992i −1.67479 0.440776i
\(767\) 4.58646 + 0.360962i 0.165607 + 0.0130336i
\(768\) 2.86265 + 3.46763i 0.103297 + 0.125127i
\(769\) −5.82396 1.89232i −0.210018 0.0682388i 0.202119 0.979361i \(-0.435217\pi\)
−0.412136 + 0.911122i \(0.635217\pi\)
\(770\) 0.154684 7.11814i 0.00557441 0.256520i
\(771\) 1.41265 0.719779i 0.0508752 0.0259222i
\(772\) 5.68621 1.10634i 0.204651 0.0398180i
\(773\) −1.89206 + 7.88100i −0.0680527 + 0.283460i −0.996012 0.0892224i \(-0.971562\pi\)
0.927959 + 0.372682i \(0.121562\pi\)
\(774\) 12.6907 + 42.1531i 0.456160 + 1.51516i
\(775\) 34.4608 11.1970i 1.23787 0.402208i
\(776\) 8.67650 2.94786i 0.311468 0.105822i
\(777\) 0.0181662 + 0.114697i 0.000651708 + 0.00411472i
\(778\) 23.7238 + 24.7777i 0.850538 + 0.888325i
\(779\) 26.0770 6.33472i 0.934304 0.226965i
\(780\) 0.287541 + 0.0125029i 0.0102956 + 0.000447677i
\(781\) 30.5780 4.84307i 1.09417 0.173299i
\(782\) −6.67445 17.1588i −0.238678 0.613597i
\(783\) −2.79328 8.59682i −0.0998235 0.307225i
\(784\) 5.92259 9.48565i 0.211521 0.338773i
\(785\) 5.65278 + 1.35711i 0.201757 + 0.0484375i
\(786\) 0.621235 0.966007i 0.0221587 0.0344563i
\(787\) −13.8300 27.1429i −0.492986 0.967540i −0.994731 0.102524i \(-0.967308\pi\)
0.501744 0.865016i \(-0.332692\pi\)
\(788\) −27.2093 + 24.9416i −0.969290 + 0.888508i
\(789\) 1.75526 5.40212i 0.0624888 0.192321i
\(790\) 0.158838 + 2.79282i 0.00565120 + 0.0993642i
\(791\) −2.73757 + 34.7841i −0.0973368 + 1.23678i
\(792\) −35.8859 11.1323i −1.27515 0.395571i
\(793\) −2.04993 + 0.849107i −0.0727950 + 0.0301527i
\(794\) −3.28451 + 32.6477i −0.116563 + 1.15862i
\(795\) −0.706963 0.973051i −0.0250734 0.0345106i
\(796\) 1.20430 + 34.3111i 0.0426851 + 1.21613i
\(797\) 17.7010 + 12.8605i 0.627002 + 0.455544i 0.855360 0.518034i \(-0.173336\pi\)
−0.228358 + 0.973577i \(0.573336\pi\)
\(798\) 5.09447 1.10659i 0.180342 0.0391730i
\(799\) −12.8467 2.03472i −0.454485 0.0719833i
\(800\) 23.9358 13.6946i 0.846260 0.484178i
\(801\) 0.751296 + 0.460395i 0.0265457 + 0.0162672i
\(802\) −4.83042 35.4696i −0.170568 1.25247i
\(803\) 1.41394 + 17.9659i 0.0498970 + 0.634002i
\(804\) 2.52033 1.66882i 0.0888852 0.0588546i
\(805\) −1.24974 1.46326i −0.0440477 0.0515733i
\(806\) −6.12758 + 13.9294i −0.215835 + 0.490641i
\(807\) 3.53234 + 5.76425i 0.124344 + 0.202911i
\(808\) −18.5909 + 13.8902i −0.654025 + 0.488656i
\(809\) 5.29284 6.19713i 0.186087 0.217879i −0.659519 0.751688i \(-0.729240\pi\)
0.845605 + 0.533809i \(0.179240\pi\)
\(810\) −3.73727 + 1.80305i −0.131314 + 0.0633529i
\(811\) 24.1486 + 24.1486i 0.847972 + 0.847972i 0.989880 0.141908i \(-0.0453238\pi\)
−0.141908 + 0.989880i \(0.545324\pi\)
\(812\) 14.1064 + 30.9391i 0.495039 + 1.08575i
\(813\) −0.666134 2.77465i −0.0233624 0.0973112i
\(814\) −0.733451 + 0.427823i −0.0257074 + 0.0149952i
\(815\) −1.83376 + 3.59895i −0.0642338 + 0.126066i
\(816\) −8.20274 + 1.89683i −0.287153 + 0.0664024i
\(817\) 17.0913 41.2622i 0.597951 1.44358i
\(818\) 7.73859 + 5.88347i 0.270573 + 0.205711i
\(819\) −13.2351 −0.462473
\(820\) −3.77001 + 2.51089i −0.131654 + 0.0876840i
\(821\) 21.7380 0.758663 0.379331 0.925261i \(-0.376154\pi\)
0.379331 + 0.925261i \(0.376154\pi\)
\(822\) −2.16023 1.64237i −0.0753465 0.0572842i
\(823\) −5.88546 + 14.2087i −0.205154 + 0.495286i −0.992648 0.121037i \(-0.961378\pi\)
0.787494 + 0.616322i \(0.211378\pi\)
\(824\) −27.9642 + 47.0322i −0.974179 + 1.63844i
\(825\) 2.82859 5.55142i 0.0984788 0.193276i
\(826\) −12.1502 + 7.08722i −0.422759 + 0.246596i
\(827\) −0.927387 3.86284i −0.0322484 0.134324i 0.953923 0.300050i \(-0.0970034\pi\)
−0.986172 + 0.165726i \(0.947003\pi\)
\(828\) −9.23997 + 4.21289i −0.321111 + 0.146408i
\(829\) 29.8144 + 29.8144i 1.03550 + 1.03550i 0.999346 + 0.0361510i \(0.0115097\pi\)
0.0361510 + 0.999346i \(0.488490\pi\)
\(830\) −0.720434 + 0.347575i −0.0250066 + 0.0120645i
\(831\) 3.52929 4.13227i 0.122430 0.143347i
\(832\) −2.40188 + 11.3298i −0.0832702 + 0.392788i
\(833\) 10.9402 + 17.8527i 0.379054 + 0.618560i
\(834\) −2.30175 + 5.23240i −0.0797032 + 0.181183i
\(835\) −3.69824 4.33008i −0.127983 0.149848i
\(836\) 21.0450 + 31.7831i 0.727855 + 1.09924i
\(837\) 0.970410 + 12.3302i 0.0335423 + 0.426195i
\(838\) −6.75841 49.6267i −0.233465 1.71433i
\(839\) −23.4891 14.3942i −0.810935 0.496942i 0.0541701 0.998532i \(-0.482749\pi\)
−0.865106 + 0.501590i \(0.832749\pi\)
\(840\) −0.744085 + 0.469761i −0.0256734 + 0.0162083i
\(841\) −0.502154 0.0795333i −0.0173156 0.00274253i
\(842\) −8.45849 + 1.83731i −0.291499 + 0.0633178i
\(843\) −3.66621 2.66366i −0.126271 0.0917414i
\(844\) −19.9024 + 0.698559i −0.685068 + 0.0240454i
\(845\) −2.26701 3.12027i −0.0779874 0.107340i
\(846\) −0.718132 + 7.13816i −0.0246899 + 0.245415i
\(847\) 27.9960 11.5963i 0.961955 0.398455i
\(848\) 43.3061 21.6109i 1.48714 0.742122i
\(849\) −0.0710291 + 0.902511i −0.00243771 + 0.0309741i
\(850\) 2.93182 + 51.5499i 0.100561 + 1.76815i
\(851\) −0.0709174 + 0.218261i −0.00243102 + 0.00748190i
\(852\) −2.58555 2.82062i −0.0885794 0.0966329i
\(853\) −21.5186 42.2326i −0.736782 1.44602i −0.889113 0.457687i \(-0.848678\pi\)
0.152331 0.988329i \(-0.451322\pi\)
\(854\) 3.66940 5.70584i 0.125564 0.195250i
\(855\) 4.21039 + 1.01083i 0.143992 + 0.0345695i
\(856\) 28.9971 7.37258i 0.991101 0.251990i
\(857\) 10.2692 + 31.6054i 0.350790 + 1.07962i 0.958411 + 0.285393i \(0.0921241\pi\)
−0.607621 + 0.794227i \(0.707876\pi\)
\(858\) 0.948599 + 2.43868i 0.0323847 + 0.0832550i
\(859\) 8.54367 1.35319i 0.291506 0.0461701i −0.00896856 0.999960i \(-0.502855\pi\)
0.300475 + 0.953790i \(0.402855\pi\)
\(860\) −0.327487 + 7.53150i −0.0111672 + 0.256822i
\(861\) −4.54756 + 3.32271i −0.154980 + 0.113238i
\(862\) −13.5232 14.1240i −0.460602 0.481065i
\(863\) −2.58666 16.3315i −0.0880509 0.555931i −0.991793 0.127854i \(-0.959191\pi\)
0.903742 0.428077i \(-0.140809\pi\)
\(864\) 2.63809 + 9.03589i 0.0897497 + 0.307407i
\(865\) −3.52497 + 1.14533i −0.119853 + 0.0389425i
\(866\) −15.5721 51.7239i −0.529163 1.75765i
\(867\) 2.56466 10.6826i 0.0871005 0.362800i
\(868\) −8.88584 45.6702i −0.301605 1.55015i
\(869\) −22.6603 + 11.5460i −0.768698 + 0.391671i
\(870\) 0.0165907 0.763463i 0.000562478 0.0258838i
\(871\) 7.40445 + 2.40585i 0.250890 + 0.0815192i
\(872\) −0.403568 30.2112i −0.0136665 1.02308i
\(873\) 9.43441 + 0.742504i 0.319306 + 0.0251300i
\(874\) 9.96338 + 2.62219i 0.337016 + 0.0886968i
\(875\) 4.18341 + 10.0996i 0.141425 + 0.341430i
\(876\) 1.75492 1.37160i 0.0592932 0.0463419i
\(877\) 4.18121 3.03783i 0.141189 0.102580i −0.514948 0.857221i \(-0.672189\pi\)
0.656138 + 0.754641i \(0.272189\pi\)
\(878\) 29.5358 33.0980i 0.996786 1.11700i
\(879\) 3.92124 5.39713i 0.132260 0.182041i
\(880\) −5.17356 3.82538i −0.174401 0.128954i
\(881\) 1.18396 7.47526i 0.0398888 0.251848i −0.959684 0.281082i \(-0.909307\pi\)
0.999573 + 0.0292339i \(0.00930677\pi\)
\(882\) 9.48850 6.58366i 0.319494 0.221683i
\(883\) −23.9799 + 39.1316i −0.806988 + 1.31688i 0.138216 + 0.990402i \(0.455863\pi\)
−0.945203 + 0.326482i \(0.894137\pi\)
\(884\) −16.9731 13.4961i −0.570867 0.453922i
\(885\) 0.314922 0.0247849i 0.0105860 0.000833136i
\(886\) −2.35238 + 13.0155i −0.0790297 + 0.437263i
\(887\) −12.8348 + 10.9620i −0.430951 + 0.368067i −0.838303 0.545204i \(-0.816452\pi\)
0.407352 + 0.913271i \(0.366452\pi\)
\(888\) 0.0941340 + 0.0463905i 0.00315893 + 0.00155676i
\(889\) 35.5500 21.7850i 1.19231 0.730647i
\(890\) 0.0954807 + 0.116841i 0.00320052 + 0.00391653i
\(891\) −28.6866 24.5007i −0.961037 0.820803i
\(892\) 9.69458 + 3.62268i 0.324598 + 0.121296i
\(893\) 5.14665 5.14665i 0.172226 0.172226i
\(894\) 1.03149 2.95458i 0.0344981 0.0988158i
\(895\) 8.37890 2.01160i 0.280076 0.0672402i
\(896\) −13.7137 32.6463i −0.458143 1.09064i
\(897\) 0.630142 + 0.321073i 0.0210398 + 0.0107203i
\(898\) −25.6888 13.8002i −0.857247 0.460517i
\(899\) 37.3028 + 15.4513i 1.24412 + 0.515331i
\(900\) 28.2957 3.22899i 0.943189 0.107633i
\(901\) 90.6199i 3.01899i
\(902\) −34.6970 22.1819i −1.15529 0.738576i
\(903\) 9.37348i 0.311930i
\(904\) 24.2484 + 20.1562i 0.806490 + 0.670386i
\(905\) 6.12864 + 2.53857i 0.203723 + 0.0843848i
\(906\) 1.90882 3.55324i 0.0634162 0.118049i
\(907\) 15.1092 + 7.69851i 0.501692 + 0.255625i 0.686473 0.727155i \(-0.259158\pi\)
−0.184782 + 0.982780i \(0.559158\pi\)
\(908\) −13.1706 3.77405i −0.437080 0.125246i
\(909\) −23.3044 + 5.59488i −0.772957 + 0.185571i
\(910\) −2.13982 0.747043i −0.0709342 0.0247642i
\(911\) −7.31085 + 7.31085i −0.242219 + 0.242219i −0.817768 0.575548i \(-0.804789\pi\)
0.575548 + 0.817768i \(0.304789\pi\)
\(912\) 1.83929 4.33740i 0.0609050 0.143626i
\(913\) −5.52993 4.72300i −0.183014 0.156309i
\(914\) 18.9429 15.4798i 0.626574 0.512025i
\(915\) −0.129902 + 0.0796038i −0.00429442 + 0.00263162i
\(916\) −1.15754 3.17856i −0.0382463 0.105022i
\(917\) −6.87742 + 5.87387i −0.227112 + 0.193972i
\(918\) −17.3437 3.13466i −0.572428 0.103459i
\(919\) −12.3966 + 0.975637i −0.408927 + 0.0321833i −0.281255 0.959633i \(-0.590751\pi\)
−0.127673 + 0.991816i \(0.540751\pi\)
\(920\) −1.73168 + 0.159586i −0.0570918 + 0.00526140i
\(921\) 2.65957 4.34002i 0.0876357 0.143008i
\(922\) 7.96575 + 11.4804i 0.262338 + 0.378087i
\(923\) 1.54171 9.73396i 0.0507459 0.320397i
\(924\) −6.63334 4.47252i −0.218221 0.147135i
\(925\) 0.378299 0.520684i 0.0124384 0.0171200i
\(926\) 15.6309 + 13.9486i 0.513663 + 0.458380i
\(927\) −45.7167 + 33.2151i −1.50153 + 1.09093i
\(928\) 30.1922 + 5.71823i 0.991109 + 0.187710i
\(929\) −7.69082 18.5673i −0.252328 0.609173i 0.746063 0.665875i \(-0.231942\pi\)
−0.998391 + 0.0567018i \(0.981942\pi\)
\(930\) −0.265941 + 1.01048i −0.00872056 + 0.0331350i
\(931\) −11.6806 0.919282i −0.382816 0.0301283i
\(932\) −0.0808765 0.0753916i −0.00264920 0.00246953i
\(933\) 3.96474 + 1.28822i 0.129800 + 0.0421745i
\(934\) −34.7659 0.755494i −1.13758 0.0247205i
\(935\) 10.7341 5.46930i 0.351043 0.178865i
\(936\) −6.90044 + 9.76944i −0.225548 + 0.319324i
\(937\) 0.914826 3.81052i 0.0298861 0.124484i −0.955433 0.295209i \(-0.904611\pi\)
0.985319 + 0.170724i \(0.0546108\pi\)
\(938\) −22.7930 + 6.86214i −0.744219 + 0.224057i
\(939\) 7.57652 2.46176i 0.247250 0.0803366i
\(940\) −0.519011 + 1.11354i −0.0169283 + 0.0363197i
\(941\) −5.58282 35.2486i −0.181995 1.14907i −0.894389 0.447291i \(-0.852389\pi\)
0.712394 0.701780i \(-0.247611\pi\)
\(942\) 4.71831 4.51760i 0.153731 0.147191i
\(943\) −10.9886 + 1.77073i −0.357839 + 0.0576628i
\(944\) −1.10338 + 12.6637i −0.0359118 + 0.412167i
\(945\) −1.81944 + 0.288170i −0.0591863 + 0.00937418i
\(946\) −63.8758 + 24.8465i −2.07678 + 0.807829i
\(947\) 4.22656 + 13.0080i 0.137345 + 0.422703i 0.995947 0.0899383i \(-0.0286670\pi\)
−0.858603 + 0.512642i \(0.828667\pi\)
\(948\) 2.73604 + 1.54733i 0.0888623 + 0.0502550i
\(949\) 5.57829 + 1.33923i 0.181079 + 0.0434732i
\(950\) −24.3017 15.6283i −0.788452 0.507050i
\(951\) −2.53844 4.98197i −0.0823146 0.161552i
\(952\) 66.1589 + 4.31851i 2.14422 + 0.139964i
\(953\) 4.24992 13.0799i 0.137668 0.423699i −0.858327 0.513103i \(-0.828496\pi\)
0.995996 + 0.0894033i \(0.0284960\pi\)
\(954\) 49.9026 2.83814i 1.61566 0.0918881i
\(955\) −0.338516 + 4.30126i −0.0109541 + 0.139185i
\(956\) −20.1484 36.3334i −0.651645 1.17510i
\(957\) 6.41425 2.65687i 0.207343 0.0858844i
\(958\) −54.0819 5.44089i −1.74731 0.175787i
\(959\) 12.5607 + 17.2884i 0.405607 + 0.558270i
\(960\) −0.0411943 + 0.794162i −0.00132954 + 0.0256315i
\(961\) −19.6161 14.2519i −0.632777 0.459740i
\(962\) 0.0573748 + 0.264139i 0.00184984 + 0.00851617i
\(963\) 30.5187 + 4.83369i 0.983452 + 0.155763i
\(964\) 4.83252 23.7743i 0.155645 0.765718i
\(965\) 0.873509 + 0.535287i 0.0281193 + 0.0172315i
\(966\) −2.14251 + 0.291777i −0.0689341 + 0.00938778i
\(967\) 2.07558 + 26.3728i 0.0667463 + 0.848092i 0.935609 + 0.353038i \(0.114851\pi\)
−0.868863 + 0.495053i \(0.835149\pi\)
\(968\) 6.03659 26.7111i 0.194023 0.858527i
\(969\) 5.72889 + 6.70767i 0.184039 + 0.215482i
\(970\) 1.48342 + 0.652561i 0.0476296 + 0.0209525i
\(971\) 10.3138 + 16.8307i 0.330987 + 0.540122i 0.974235 0.225536i \(-0.0724134\pi\)
−0.643248 + 0.765658i \(0.722413\pi\)
\(972\) −1.78240 + 14.5379i −0.0571704 + 0.466303i
\(973\) 29.2348 34.2295i 0.937224 1.09735i
\(974\) 6.35948 + 13.1816i 0.203771 + 0.422364i
\(975\) −1.40245 1.40245i −0.0449145 0.0449145i
\(976\) −2.29861 5.68342i −0.0735766 0.181922i
\(977\) 5.26770 + 21.9415i 0.168529 + 0.701972i 0.991079 + 0.133279i \(0.0425507\pi\)
−0.822550 + 0.568693i \(0.807449\pi\)
\(978\) 2.28683 + 3.92049i 0.0731248 + 0.125363i
\(979\) −0.622807 + 1.22233i −0.0199050 + 0.0390658i
\(980\) 1.90568 0.528857i 0.0608747 0.0168937i
\(981\) 11.9409 28.8278i 0.381243 0.920401i
\(982\) 29.2532 38.4771i 0.933509 1.22785i
\(983\) 37.1487 1.18486 0.592430 0.805622i \(-0.298169\pi\)
0.592430 + 0.805622i \(0.298169\pi\)
\(984\) 0.0816670 + 5.08912i 0.00260345 + 0.162235i
\(985\) −6.52781 −0.207993
\(986\) −34.8219 + 45.8016i −1.10895 + 1.45862i
\(987\) −0.584579 + 1.41130i −0.0186074 + 0.0449221i
\(988\) 11.6926 3.24489i 0.371991 0.103234i
\(989\) −8.40981 + 16.5052i −0.267416 + 0.524834i
\(990\) −3.34802 5.73977i −0.106407 0.182422i
\(991\) −8.58710 35.7678i −0.272778 1.13620i −0.925543 0.378642i \(-0.876391\pi\)
0.652765 0.757561i \(-0.273609\pi\)
\(992\) −38.3440 17.2522i −1.21742 0.547756i
\(993\) 1.54570 + 1.54570i 0.0490514 + 0.0490514i
\(994\) 13.0930 + 27.1385i 0.415286 + 0.860781i
\(995\) −3.94328 + 4.61698i −0.125010 + 0.146368i
\(996\) −0.109379 + 0.892134i −0.00346580 + 0.0282684i
\(997\) −4.42188 7.21585i −0.140042 0.228528i 0.774928 0.632050i \(-0.217786\pi\)
−0.914970 + 0.403521i \(0.867786\pi\)
\(998\) −46.7834 20.5802i −1.48090 0.651455i
\(999\) 0.142677 + 0.167053i 0.00451411 + 0.00528534i
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 164.2.o.b.11.6 yes 288
4.3 odd 2 inner 164.2.o.b.11.4 288
41.15 odd 40 inner 164.2.o.b.15.4 yes 288
164.15 even 40 inner 164.2.o.b.15.6 yes 288
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
164.2.o.b.11.4 288 4.3 odd 2 inner
164.2.o.b.11.6 yes 288 1.1 even 1 trivial
164.2.o.b.15.4 yes 288 41.15 odd 40 inner
164.2.o.b.15.6 yes 288 164.15 even 40 inner