Properties

Label 164.2.o.b.11.16
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 11.16
Character \(\chi\) \(=\) 164.11
Dual form 164.2.o.b.15.16

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.23500 + 0.689031i) q^{2} +(-0.900558 + 2.17414i) q^{3} +(1.05047 + 1.70191i) q^{4} +(-0.390234 + 0.765878i) q^{5} +(-2.61024 + 2.06456i) q^{6} +(-0.876658 - 3.65154i) q^{7} +(0.124665 + 2.82568i) q^{8} +(-1.79456 - 1.79456i) q^{9} +O(q^{10})\) \(q+(1.23500 + 0.689031i) q^{2} +(-0.900558 + 2.17414i) q^{3} +(1.05047 + 1.70191i) q^{4} +(-0.390234 + 0.765878i) q^{5} +(-2.61024 + 2.06456i) q^{6} +(-0.876658 - 3.65154i) q^{7} +(0.124665 + 2.82568i) q^{8} +(-1.79456 - 1.79456i) q^{9} +(-1.00965 + 0.676979i) q^{10} +(1.26843 - 1.48514i) q^{11} +(-4.64621 + 0.751199i) q^{12} +(1.79670 + 2.93195i) q^{13} +(1.43335 - 5.11372i) q^{14} +(-1.31370 - 1.53814i) q^{15} +(-1.79302 + 3.57562i) q^{16} +(-0.302571 - 3.84453i) q^{17} +(-0.979781 - 3.45280i) q^{18} +(5.10695 + 3.12954i) q^{19} +(-1.71339 + 0.140388i) q^{20} +(8.72845 + 1.38245i) q^{21} +(2.58983 - 0.960167i) q^{22} +(-1.43017 - 1.03908i) q^{23} +(-6.25569 - 2.27365i) q^{24} +(2.50464 + 3.44734i) q^{25} +(0.198728 + 4.85896i) q^{26} +(-1.00469 + 0.416157i) q^{27} +(5.29371 - 5.32784i) q^{28} +(0.535913 - 6.80942i) q^{29} +(-0.562594 - 2.80479i) q^{30} +(0.437955 - 1.34789i) q^{31} +(-4.67810 + 3.18046i) q^{32} +(2.08661 + 4.09520i) q^{33} +(2.27533 - 4.95649i) q^{34} +(3.13874 + 0.753545i) q^{35} +(1.16905 - 4.93932i) q^{36} +(-2.67942 - 8.24640i) q^{37} +(4.15075 + 7.38385i) q^{38} +(-7.99251 + 1.26589i) q^{39} +(-2.21277 - 1.00720i) q^{40} +(-5.03089 + 3.96108i) q^{41} +(9.82712 + 7.72151i) q^{42} +(-1.17766 - 7.43544i) q^{43} +(3.86003 + 0.598661i) q^{44} +(2.07471 - 0.674115i) q^{45} +(-1.05031 - 2.26869i) q^{46} +(1.70845 - 7.11622i) q^{47} +(-6.15919 - 7.11833i) q^{48} +(-6.32820 + 3.22438i) q^{49} +(0.717915 + 5.98326i) q^{50} +(8.63103 + 2.80439i) q^{51} +(-3.10254 + 6.13776i) q^{52} +(-3.84688 - 0.302756i) q^{53} +(-1.52754 - 0.178308i) q^{54} +(0.642452 + 1.55102i) q^{55} +(10.2088 - 2.93237i) q^{56} +(-11.4032 + 8.28489i) q^{57} +(5.35376 - 8.04041i) q^{58} +(-7.28865 + 10.0320i) q^{59} +(1.23778 - 3.85157i) q^{60} +(-1.26968 + 8.01646i) q^{61} +(1.46961 - 1.36288i) q^{62} +(-4.97970 + 8.12613i) q^{63} +(-7.96892 + 0.704525i) q^{64} +(-2.94665 + 0.231906i) q^{65} +(-0.244751 + 6.49533i) q^{66} +(7.01810 - 5.99402i) q^{67} +(6.22522 - 4.55352i) q^{68} +(3.54705 - 2.17363i) q^{69} +(3.35714 + 3.09332i) q^{70} +(-2.24322 - 1.91589i) q^{71} +(4.84713 - 5.29457i) q^{72} +(8.30463 - 8.30463i) q^{73} +(2.37294 - 12.0305i) q^{74} +(-9.75058 + 2.34091i) q^{75} +(0.0384930 + 11.9791i) q^{76} +(-6.53504 - 3.32977i) q^{77} +(-10.7430 - 3.94371i) q^{78} +(1.23669 + 0.512252i) q^{79} +(-2.03879 - 2.76856i) q^{80} -10.1728i q^{81} +(-8.94248 + 1.42551i) q^{82} +13.0912i q^{83} +(6.81618 + 16.3073i) q^{84} +(3.06251 + 1.26853i) q^{85} +(3.66884 - 9.99425i) q^{86} +(14.3220 + 7.29743i) q^{87} +(4.35466 + 3.39903i) q^{88} +(-6.69744 + 1.60791i) q^{89} +(3.02676 + 0.597007i) q^{90} +(9.13106 - 9.13106i) q^{91} +(0.266070 - 3.52554i) q^{92} +(2.53609 + 2.16603i) q^{93} +(7.01325 - 7.61139i) q^{94} +(-4.38975 + 2.69004i) q^{95} +(-2.70187 - 13.0350i) q^{96} +(-8.34501 + 7.12731i) q^{97} +(-10.0371 - 0.378207i) q^{98} +(-4.94145 + 0.388900i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.23500 + 0.689031i 0.873280 + 0.487219i
\(3\) −0.900558 + 2.17414i −0.519938 + 1.25524i 0.418003 + 0.908445i \(0.362730\pi\)
−0.937941 + 0.346795i \(0.887270\pi\)
\(4\) 1.05047 + 1.70191i 0.525236 + 0.850957i
\(5\) −0.390234 + 0.765878i −0.174518 + 0.342511i −0.961653 0.274270i \(-0.911564\pi\)
0.787135 + 0.616781i \(0.211564\pi\)
\(6\) −2.61024 + 2.06456i −1.06563 + 0.842853i
\(7\) −0.876658 3.65154i −0.331346 1.38015i −0.850725 0.525611i \(-0.823837\pi\)
0.519380 0.854544i \(-0.326163\pi\)
\(8\) 0.124665 + 2.82568i 0.0440756 + 0.999028i
\(9\) −1.79456 1.79456i −0.598187 0.598187i
\(10\) −1.00965 + 0.676979i −0.319281 + 0.214079i
\(11\) 1.26843 1.48514i 0.382446 0.447787i −0.535474 0.844552i \(-0.679867\pi\)
0.917920 + 0.396765i \(0.129867\pi\)
\(12\) −4.64621 + 0.751199i −1.34125 + 0.216853i
\(13\) 1.79670 + 2.93195i 0.498316 + 0.813177i 0.998612 0.0526774i \(-0.0167755\pi\)
−0.500296 + 0.865854i \(0.666775\pi\)
\(14\) 1.43335 5.11372i 0.383080 1.36670i
\(15\) −1.31370 1.53814i −0.339195 0.397146i
\(16\) −1.79302 + 3.57562i −0.448255 + 0.893906i
\(17\) −0.302571 3.84453i −0.0733843 0.932435i −0.917876 0.396867i \(-0.870097\pi\)
0.844492 0.535568i \(-0.179903\pi\)
\(18\) −0.979781 3.45280i −0.230937 0.813832i
\(19\) 5.10695 + 3.12954i 1.17161 + 0.717966i 0.965459 0.260553i \(-0.0839050\pi\)
0.206155 + 0.978519i \(0.433905\pi\)
\(20\) −1.71339 + 0.140388i −0.383125 + 0.0313917i
\(21\) 8.72845 + 1.38245i 1.90470 + 0.301676i
\(22\) 2.58983 0.960167i 0.552153 0.204708i
\(23\) −1.43017 1.03908i −0.298210 0.216663i 0.428611 0.903489i \(-0.359003\pi\)
−0.726821 + 0.686827i \(0.759003\pi\)
\(24\) −6.25569 2.27365i −1.27694 0.464107i
\(25\) 2.50464 + 3.44734i 0.500928 + 0.689468i
\(26\) 0.198728 + 4.85896i 0.0389738 + 0.952920i
\(27\) −1.00469 + 0.416157i −0.193353 + 0.0800894i
\(28\) 5.29371 5.32784i 1.00042 1.00687i
\(29\) 0.535913 6.80942i 0.0995166 1.26448i −0.721032 0.692902i \(-0.756332\pi\)
0.820549 0.571577i \(-0.193668\pi\)
\(30\) −0.562594 2.80479i −0.102715 0.512082i
\(31\) 0.437955 1.34789i 0.0786590 0.242088i −0.903993 0.427548i \(-0.859378\pi\)
0.982652 + 0.185460i \(0.0593776\pi\)
\(32\) −4.67810 + 3.18046i −0.826980 + 0.562232i
\(33\) 2.08661 + 4.09520i 0.363232 + 0.712883i
\(34\) 2.27533 4.95649i 0.390215 0.850031i
\(35\) 3.13874 + 0.753545i 0.530544 + 0.127372i
\(36\) 1.16905 4.93932i 0.194842 0.823220i
\(37\) −2.67942 8.24640i −0.440494 1.35570i −0.887351 0.461095i \(-0.847457\pi\)
0.446857 0.894605i \(-0.352543\pi\)
\(38\) 4.15075 + 7.38385i 0.673341 + 1.19782i
\(39\) −7.99251 + 1.26589i −1.27983 + 0.202704i
\(40\) −2.21277 1.00720i −0.349870 0.159252i
\(41\) −5.03089 + 3.96108i −0.785693 + 0.618617i
\(42\) 9.82712 + 7.72151i 1.51636 + 1.19145i
\(43\) −1.17766 7.43544i −0.179591 1.13389i −0.898559 0.438852i \(-0.855385\pi\)
0.718968 0.695043i \(-0.244615\pi\)
\(44\) 3.86003 + 0.598661i 0.581922 + 0.0902515i
\(45\) 2.07471 0.674115i 0.309280 0.100491i
\(46\) −1.05031 2.26869i −0.154859 0.334501i
\(47\) 1.70845 7.11622i 0.249204 1.03801i −0.697674 0.716415i \(-0.745782\pi\)
0.946878 0.321593i \(-0.104218\pi\)
\(48\) −6.15919 7.11833i −0.889002 1.02744i
\(49\) −6.32820 + 3.22438i −0.904029 + 0.460626i
\(50\) 0.717915 + 5.98326i 0.101528 + 0.846160i
\(51\) 8.63103 + 2.80439i 1.20859 + 0.392693i
\(52\) −3.10254 + 6.13776i −0.430245 + 0.851155i
\(53\) −3.84688 0.302756i −0.528410 0.0415868i −0.188551 0.982063i \(-0.560379\pi\)
−0.339858 + 0.940477i \(0.610379\pi\)
\(54\) −1.52754 0.178308i −0.207872 0.0242647i
\(55\) 0.642452 + 1.55102i 0.0866282 + 0.209139i
\(56\) 10.2088 2.93237i 1.36421 0.391855i
\(57\) −11.4032 + 8.28489i −1.51039 + 1.09736i
\(58\) 5.35376 8.04041i 0.702983 1.05576i
\(59\) −7.28865 + 10.0320i −0.948901 + 1.30605i 0.00311249 + 0.999995i \(0.499009\pi\)
−0.952014 + 0.306055i \(0.900991\pi\)
\(60\) 1.23778 3.85157i 0.159797 0.497236i
\(61\) −1.26968 + 8.01646i −0.162566 + 1.02640i 0.762608 + 0.646861i \(0.223918\pi\)
−0.925174 + 0.379542i \(0.876082\pi\)
\(62\) 1.46961 1.36288i 0.186641 0.173086i
\(63\) −4.97970 + 8.12613i −0.627383 + 1.02380i
\(64\) −7.96892 + 0.704525i −0.996115 + 0.0880656i
\(65\) −2.94665 + 0.231906i −0.365487 + 0.0287645i
\(66\) −0.244751 + 6.49533i −0.0301268 + 0.799520i
\(67\) 7.01810 5.99402i 0.857397 0.732286i −0.107699 0.994184i \(-0.534348\pi\)
0.965096 + 0.261897i \(0.0843482\pi\)
\(68\) 6.22522 4.55352i 0.754918 0.552195i
\(69\) 3.54705 2.17363i 0.427014 0.261675i
\(70\) 3.35714 + 3.09332i 0.401255 + 0.369723i
\(71\) −2.24322 1.91589i −0.266221 0.227375i 0.506309 0.862352i \(-0.331009\pi\)
−0.772531 + 0.634977i \(0.781009\pi\)
\(72\) 4.84713 5.29457i 0.571240 0.623971i
\(73\) 8.30463 8.30463i 0.971984 0.971984i −0.0276344 0.999618i \(-0.508797\pi\)
0.999618 + 0.0276344i \(0.00879741\pi\)
\(74\) 2.37294 12.0305i 0.275848 1.39852i
\(75\) −9.75058 + 2.34091i −1.12590 + 0.270305i
\(76\) 0.0384930 + 11.9791i 0.00441545 + 1.37409i
\(77\) −6.53504 3.32977i −0.744737 0.379462i
\(78\) −10.7430 3.94371i −1.21641 0.446537i
\(79\) 1.23669 + 0.512252i 0.139138 + 0.0576329i 0.451166 0.892440i \(-0.351008\pi\)
−0.312028 + 0.950073i \(0.601008\pi\)
\(80\) −2.03879 2.76856i −0.227944 0.309535i
\(81\) 10.1728i 1.13031i
\(82\) −8.94248 + 1.42551i −0.987531 + 0.157422i
\(83\) 13.0912i 1.43695i 0.695554 + 0.718474i \(0.255159\pi\)
−0.695554 + 0.718474i \(0.744841\pi\)
\(84\) 6.81618 + 16.3073i 0.743706 + 1.77927i
\(85\) 3.06251 + 1.26853i 0.332176 + 0.137592i
\(86\) 3.66884 9.99425i 0.395621 1.07771i
\(87\) 14.3220 + 7.29743i 1.53548 + 0.782367i
\(88\) 4.35466 + 3.39903i 0.464208 + 0.362338i
\(89\) −6.69744 + 1.60791i −0.709927 + 0.170438i −0.572298 0.820045i \(-0.693948\pi\)
−0.137629 + 0.990484i \(0.543948\pi\)
\(90\) 3.02676 + 0.597007i 0.319049 + 0.0629301i
\(91\) 9.13106 9.13106i 0.957195 0.957195i
\(92\) 0.266070 3.52554i 0.0277397 0.367563i
\(93\) 2.53609 + 2.16603i 0.262980 + 0.224606i
\(94\) 7.01325 7.61139i 0.723361 0.785055i
\(95\) −4.38975 + 2.69004i −0.450379 + 0.275993i
\(96\) −2.70187 13.0350i −0.275758 1.33038i
\(97\) −8.34501 + 7.12731i −0.847307 + 0.723669i −0.962967 0.269620i \(-0.913102\pi\)
0.115659 + 0.993289i \(0.463102\pi\)
\(98\) −10.0371 0.378207i −1.01390 0.0382047i
\(99\) −4.94145 + 0.388900i −0.496634 + 0.0390860i
\(100\) −3.23602 + 7.88401i −0.323602 + 0.788401i
\(101\) 7.52760 12.2839i 0.749024 1.22230i −0.220041 0.975491i \(-0.570619\pi\)
0.969065 0.246806i \(-0.0793809\pi\)
\(102\) 8.72704 + 9.41049i 0.864106 + 0.931777i
\(103\) −1.80384 + 11.3890i −0.177737 + 1.12219i 0.723967 + 0.689835i \(0.242317\pi\)
−0.901704 + 0.432354i \(0.857683\pi\)
\(104\) −8.06077 + 5.44241i −0.790423 + 0.533673i
\(105\) −4.46493 + 6.14545i −0.435732 + 0.599734i
\(106\) −4.54231 3.02453i −0.441188 0.293768i
\(107\) −8.44274 + 6.13401i −0.816191 + 0.592997i −0.915619 0.402047i \(-0.868299\pi\)
0.0994279 + 0.995045i \(0.468299\pi\)
\(108\) −1.76366 1.27274i −0.169708 0.122469i
\(109\) 4.39210 + 10.6035i 0.420687 + 1.01563i 0.982145 + 0.188124i \(0.0602406\pi\)
−0.561458 + 0.827505i \(0.689759\pi\)
\(110\) −0.275268 + 2.35818i −0.0262458 + 0.224844i
\(111\) 20.3418 + 1.60093i 1.93076 + 0.151954i
\(112\) 14.6284 + 3.41269i 1.38226 + 0.322469i
\(113\) −10.8124 3.51316i −1.01715 0.330491i −0.247449 0.968901i \(-0.579592\pi\)
−0.769696 + 0.638410i \(0.779592\pi\)
\(114\) −19.7915 + 2.37473i −1.85364 + 0.222414i
\(115\) 1.35391 0.689850i 0.126252 0.0643288i
\(116\) 12.1520 6.24103i 1.12829 0.579465i
\(117\) 2.03727 8.48585i 0.188346 0.784517i
\(118\) −15.9139 + 7.36741i −1.46499 + 0.678225i
\(119\) −13.7732 + 4.47519i −1.26259 + 0.410240i
\(120\) 4.18252 3.90384i 0.381810 0.356370i
\(121\) 1.12405 + 7.09697i 0.102186 + 0.645179i
\(122\) −7.09166 + 9.02552i −0.642049 + 0.817132i
\(123\) −4.08134 14.5050i −0.368002 1.30788i
\(124\) 2.75405 0.670555i 0.247321 0.0602176i
\(125\) −7.86255 + 1.24531i −0.703248 + 0.111384i
\(126\) −11.7491 + 6.60464i −1.04669 + 0.588388i
\(127\) −0.606893 1.86782i −0.0538530 0.165743i 0.920513 0.390713i \(-0.127771\pi\)
−0.974366 + 0.224970i \(0.927771\pi\)
\(128\) −10.3271 4.62074i −0.912794 0.408420i
\(129\) 17.2262 + 4.13566i 1.51669 + 0.364124i
\(130\) −3.79892 1.74393i −0.333187 0.152953i
\(131\) 1.19791 + 2.35102i 0.104661 + 0.205410i 0.937398 0.348260i \(-0.113227\pi\)
−0.832737 + 0.553669i \(0.813227\pi\)
\(132\) −4.77776 + 7.85312i −0.415850 + 0.683527i
\(133\) 6.95061 21.3918i 0.602695 1.85490i
\(134\) 12.7975 2.56695i 1.10553 0.221751i
\(135\) 0.0733397 0.931869i 0.00631208 0.0802025i
\(136\) 10.8257 1.33425i 0.928295 0.114411i
\(137\) 8.66519 3.58924i 0.740317 0.306649i 0.0195331 0.999809i \(-0.493782\pi\)
0.720784 + 0.693160i \(0.243782\pi\)
\(138\) 5.87832 0.240420i 0.500396 0.0204659i
\(139\) −3.19387 4.39598i −0.270900 0.372862i 0.651793 0.758397i \(-0.274017\pi\)
−0.922693 + 0.385535i \(0.874017\pi\)
\(140\) 2.01469 + 6.13344i 0.170272 + 0.518370i
\(141\) 13.9331 + 10.1230i 1.17338 + 0.852510i
\(142\) −1.45028 3.91179i −0.121705 0.328270i
\(143\) 6.63335 + 1.05062i 0.554709 + 0.0878573i
\(144\) 9.63435 3.19899i 0.802862 0.266582i
\(145\) 5.00605 + 3.06771i 0.415730 + 0.254760i
\(146\) 15.9784 4.53410i 1.32238 0.375245i
\(147\) −1.31134 16.6621i −0.108157 1.37427i
\(148\) 11.2200 13.2227i 0.922279 1.08690i
\(149\) 12.4828 + 14.6155i 1.02263 + 1.19735i 0.980151 + 0.198254i \(0.0635272\pi\)
0.0424841 + 0.999097i \(0.486473\pi\)
\(150\) −13.6550 3.82742i −1.11492 0.312508i
\(151\) −9.59656 15.6602i −0.780957 1.27441i −0.957019 0.290027i \(-0.906336\pi\)
0.176062 0.984379i \(-0.443664\pi\)
\(152\) −8.20642 + 14.8207i −0.665629 + 1.20212i
\(153\) −6.35626 + 7.44222i −0.513873 + 0.601668i
\(154\) −5.77649 8.61513i −0.465483 0.694227i
\(155\) 0.861411 + 0.861411i 0.0691902 + 0.0691902i
\(156\) −10.5503 12.2728i −0.844703 0.982609i
\(157\) −2.46579 10.2707i −0.196791 0.819694i −0.980171 0.198152i \(-0.936506\pi\)
0.783380 0.621543i \(-0.213494\pi\)
\(158\) 1.17435 + 1.48475i 0.0934266 + 0.118120i
\(159\) 4.12258 8.09101i 0.326941 0.641659i
\(160\) −0.610290 4.82398i −0.0482476 0.381369i
\(161\) −2.54047 + 6.13323i −0.200217 + 0.483367i
\(162\) 7.00937 12.5634i 0.550708 0.987076i
\(163\) 7.88850 0.617875 0.308938 0.951082i \(-0.400027\pi\)
0.308938 + 0.951082i \(0.400027\pi\)
\(164\) −12.0262 4.40113i −0.939090 0.343671i
\(165\) −3.95069 −0.307561
\(166\) −9.02026 + 16.1677i −0.700108 + 1.25486i
\(167\) 1.53595 3.70810i 0.118855 0.286941i −0.853244 0.521512i \(-0.825368\pi\)
0.972099 + 0.234570i \(0.0753683\pi\)
\(168\) −2.81823 + 24.8361i −0.217431 + 1.91615i
\(169\) 0.533676 1.04740i 0.0410520 0.0805691i
\(170\) 2.90816 + 3.67681i 0.223045 + 0.281999i
\(171\) −3.54857 14.7809i −0.271366 1.13032i
\(172\) 11.4174 9.81500i 0.870568 0.748386i
\(173\) −11.8822 11.8822i −0.903389 0.903389i 0.0923389 0.995728i \(-0.470566\pi\)
−0.995728 + 0.0923389i \(0.970566\pi\)
\(174\) 12.6596 + 18.8807i 0.959721 + 1.43134i
\(175\) 10.3924 12.1679i 0.785592 0.919810i
\(176\) 3.03598 + 7.19832i 0.228846 + 0.542594i
\(177\) −15.2470 24.8809i −1.14604 1.87016i
\(178\) −9.37927 2.62897i −0.703006 0.197049i
\(179\) −5.27846 6.18029i −0.394531 0.461936i 0.527214 0.849732i \(-0.323237\pi\)
−0.921745 + 0.387796i \(0.873237\pi\)
\(180\) 3.32671 + 2.82284i 0.247958 + 0.210402i
\(181\) 0.757125 + 9.62019i 0.0562767 + 0.715063i 0.958738 + 0.284292i \(0.0917584\pi\)
−0.902461 + 0.430771i \(0.858242\pi\)
\(182\) 17.5685 4.98531i 1.30226 0.369536i
\(183\) −16.2855 9.97976i −1.20386 0.737725i
\(184\) 2.75781 4.17073i 0.203308 0.307470i
\(185\) 7.36134 + 1.16592i 0.541216 + 0.0857202i
\(186\) 1.63962 + 4.42250i 0.120223 + 0.324273i
\(187\) −6.09346 4.42716i −0.445598 0.323746i
\(188\) 13.9059 4.56775i 1.01419 0.333137i
\(189\) 2.40039 + 3.30385i 0.174602 + 0.240320i
\(190\) −7.27489 + 0.297538i −0.527776 + 0.0215857i
\(191\) 8.03911 3.32991i 0.581689 0.240944i −0.0723813 0.997377i \(-0.523060\pi\)
0.654071 + 0.756433i \(0.273060\pi\)
\(192\) 5.64474 17.9600i 0.407374 1.29615i
\(193\) 0.140797 1.78899i 0.0101348 0.128775i −0.989768 0.142683i \(-0.954427\pi\)
0.999903 + 0.0139080i \(0.00442718\pi\)
\(194\) −15.2171 + 3.05229i −1.09252 + 0.219141i
\(195\) 2.14943 6.61528i 0.153924 0.473730i
\(196\) −12.1352 7.38294i −0.866801 0.527353i
\(197\) 5.40538 + 10.6087i 0.385117 + 0.755835i 0.999448 0.0332132i \(-0.0105740\pi\)
−0.614331 + 0.789048i \(0.710574\pi\)
\(198\) −6.37068 2.92452i −0.452744 0.207837i
\(199\) 19.4822 + 4.67726i 1.38106 + 0.331562i 0.854885 0.518817i \(-0.173627\pi\)
0.526171 + 0.850379i \(0.323627\pi\)
\(200\) −9.42884 + 7.50707i −0.666720 + 0.530830i
\(201\) 6.71164 + 20.6563i 0.473402 + 1.45698i
\(202\) 17.7606 9.98395i 1.24963 0.702468i
\(203\) −25.3347 + 4.01263i −1.77815 + 0.281631i
\(204\) 4.29382 + 17.6352i 0.300627 + 1.23471i
\(205\) −1.07048 5.39879i −0.0747656 0.377068i
\(206\) −10.0751 + 12.8225i −0.701966 + 0.893388i
\(207\) 0.701834 + 4.43121i 0.0487808 + 0.307990i
\(208\) −13.7051 + 1.16728i −0.950276 + 0.0809365i
\(209\) 11.1256 3.61493i 0.769575 0.250050i
\(210\) −9.74861 + 4.51318i −0.672718 + 0.311439i
\(211\) −4.16042 + 17.3294i −0.286415 + 1.19300i 0.624704 + 0.780862i \(0.285220\pi\)
−0.911119 + 0.412143i \(0.864780\pi\)
\(212\) −3.52577 6.86510i −0.242151 0.471497i
\(213\) 6.18557 3.15171i 0.423828 0.215951i
\(214\) −14.6534 + 1.75822i −1.00168 + 0.120189i
\(215\) 6.15420 + 1.99962i 0.419713 + 0.136373i
\(216\) −1.30117 2.78705i −0.0885337 0.189635i
\(217\) −5.30580 0.417576i −0.360181 0.0283469i
\(218\) −1.88186 + 16.1216i −0.127456 + 1.09190i
\(219\) 10.5766 + 25.5342i 0.714702 + 1.72544i
\(220\) −1.96482 + 2.72270i −0.132468 + 0.183564i
\(221\) 10.7283 7.79460i 0.721667 0.524321i
\(222\) 24.0191 + 15.9933i 1.61206 + 1.07340i
\(223\) −15.9256 + 21.9197i −1.06646 + 1.46785i −0.192846 + 0.981229i \(0.561772\pi\)
−0.873612 + 0.486624i \(0.838228\pi\)
\(224\) 15.7147 + 14.2941i 1.04998 + 0.955066i
\(225\) 1.69173 10.6812i 0.112782 0.712079i
\(226\) −10.9327 11.7889i −0.727232 0.784183i
\(227\) −3.22726 + 5.26641i −0.214201 + 0.349544i −0.941636 0.336632i \(-0.890712\pi\)
0.727435 + 0.686176i \(0.240712\pi\)
\(228\) −26.0789 10.7042i −1.72711 0.708901i
\(229\) 7.65708 0.602625i 0.505994 0.0398226i 0.177106 0.984192i \(-0.443326\pi\)
0.328887 + 0.944369i \(0.393326\pi\)
\(230\) 2.14741 + 0.0809166i 0.141596 + 0.00533548i
\(231\) 13.1246 11.2094i 0.863533 0.737527i
\(232\) 19.3080 + 0.665424i 1.26764 + 0.0436872i
\(233\) −13.8065 + 8.46062i −0.904493 + 0.554274i −0.895191 0.445683i \(-0.852961\pi\)
−0.00930179 + 0.999957i \(0.502961\pi\)
\(234\) 8.36306 9.07632i 0.546710 0.593337i
\(235\) 4.78346 + 4.08546i 0.312039 + 0.266506i
\(236\) −24.7301 1.86636i −1.60979 0.121490i
\(237\) −2.22742 + 2.22742i −0.144686 + 0.144686i
\(238\) −20.0935 3.96330i −1.30247 0.256903i
\(239\) −9.01902 + 2.16527i −0.583392 + 0.140060i −0.514390 0.857557i \(-0.671982\pi\)
−0.0690021 + 0.997617i \(0.521982\pi\)
\(240\) 7.85530 1.93937i 0.507057 0.125186i
\(241\) 13.2071 + 6.72934i 0.850742 + 0.433475i 0.824285 0.566175i \(-0.191577\pi\)
0.0264570 + 0.999650i \(0.491577\pi\)
\(242\) −3.50183 + 9.53930i −0.225106 + 0.613209i
\(243\) 19.1030 + 7.91271i 1.22546 + 0.507601i
\(244\) −14.9771 + 6.26017i −0.958810 + 0.400767i
\(245\) 6.10489i 0.390027i
\(246\) 4.95396 20.7260i 0.315853 1.32144i
\(247\) 20.5962i 1.31050i
\(248\) 3.86329 + 1.06949i 0.245319 + 0.0679124i
\(249\) −28.4621 11.7894i −1.80371 0.747123i
\(250\) −10.5683 3.87959i −0.668400 0.245367i
\(251\) 19.7529 + 10.0646i 1.24679 + 0.635271i 0.947764 0.318973i \(-0.103338\pi\)
0.299027 + 0.954245i \(0.403338\pi\)
\(252\) −19.0610 + 0.0612497i −1.20073 + 0.00385837i
\(253\) −3.35724 + 0.806003i −0.211068 + 0.0506730i
\(254\) 0.537474 2.72494i 0.0337241 0.170978i
\(255\) −5.51594 + 5.51594i −0.345422 + 0.345422i
\(256\) −9.57016 12.8223i −0.598135 0.801395i
\(257\) −11.4843 9.80849i −0.716369 0.611837i 0.214700 0.976680i \(-0.431123\pi\)
−0.931069 + 0.364843i \(0.881123\pi\)
\(258\) 18.4249 + 16.9770i 1.14708 + 1.05694i
\(259\) −27.7632 + 17.0133i −1.72512 + 1.05715i
\(260\) −3.49006 4.77133i −0.216444 0.295906i
\(261\) −13.1816 + 11.2582i −0.815923 + 0.696864i
\(262\) −0.140510 + 3.72892i −0.00868071 + 0.230373i
\(263\) −6.93876 + 0.546092i −0.427862 + 0.0336735i −0.290562 0.956856i \(-0.593842\pi\)
−0.137300 + 0.990530i \(0.543842\pi\)
\(264\) −11.3116 + 6.40662i −0.696181 + 0.394300i
\(265\) 1.73306 2.82810i 0.106461 0.173729i
\(266\) 23.3237 21.6298i 1.43006 1.32621i
\(267\) 2.53561 16.0092i 0.155177 0.979747i
\(268\) 17.5736 + 5.64765i 1.07348 + 0.344985i
\(269\) 12.5669 17.2969i 0.766219 1.05461i −0.230452 0.973084i \(-0.574020\pi\)
0.996671 0.0815268i \(-0.0259796\pi\)
\(270\) 0.732662 1.10033i 0.0445884 0.0669639i
\(271\) 1.35766 0.986396i 0.0824718 0.0599193i −0.545785 0.837925i \(-0.683769\pi\)
0.628257 + 0.778006i \(0.283769\pi\)
\(272\) 14.2891 + 5.81144i 0.866404 + 0.352370i
\(273\) 11.6291 + 28.0752i 0.703828 + 1.69919i
\(274\) 13.1746 + 1.53786i 0.795909 + 0.0929056i
\(275\) 8.29675 + 0.652969i 0.500313 + 0.0393755i
\(276\) 7.42541 + 3.75343i 0.446957 + 0.225930i
\(277\) 22.4999 + 7.31066i 1.35189 + 0.439255i 0.893327 0.449407i \(-0.148365\pi\)
0.458562 + 0.888663i \(0.348365\pi\)
\(278\) −0.915471 7.62973i −0.0549063 0.457601i
\(279\) −3.20480 + 1.63293i −0.191866 + 0.0977607i
\(280\) −1.73798 + 8.96301i −0.103864 + 0.535642i
\(281\) −2.31355 + 9.63663i −0.138015 + 0.574873i 0.859908 + 0.510449i \(0.170521\pi\)
−0.997923 + 0.0644236i \(0.979479\pi\)
\(282\) 10.2324 + 22.1023i 0.609330 + 1.31617i
\(283\) 0.463373 0.150559i 0.0275447 0.00894981i −0.295212 0.955432i \(-0.595390\pi\)
0.322757 + 0.946482i \(0.395390\pi\)
\(284\) 0.904243 5.83036i 0.0536570 0.345968i
\(285\) −1.89530 11.9665i −0.112268 0.708833i
\(286\) 7.46831 + 5.86811i 0.441610 + 0.346989i
\(287\) 18.8744 + 14.8980i 1.11412 + 0.879401i
\(288\) 14.1027 + 2.68761i 0.831008 + 0.158369i
\(289\) 2.10184 0.332899i 0.123638 0.0195823i
\(290\) 4.06875 + 7.23797i 0.238925 + 0.425028i
\(291\) −7.98061 24.5618i −0.467831 1.43984i
\(292\) 22.8575 + 5.40999i 1.33764 + 0.316596i
\(293\) 1.02145 + 0.245227i 0.0596735 + 0.0143263i 0.263172 0.964749i \(-0.415231\pi\)
−0.203499 + 0.979075i \(0.565231\pi\)
\(294\) 9.86123 21.4814i 0.575119 1.25282i
\(295\) −4.83898 9.49703i −0.281736 0.552938i
\(296\) 22.9676 8.59921i 1.33497 0.499819i
\(297\) −0.656329 + 2.01997i −0.0380841 + 0.117211i
\(298\) 5.34581 + 26.6513i 0.309674 + 1.54387i
\(299\) 0.476940 6.06009i 0.0275821 0.350464i
\(300\) −14.2267 14.1356i −0.821380 0.816118i
\(301\) −26.1185 + 10.8186i −1.50544 + 0.623575i
\(302\) −1.06145 25.9527i −0.0610795 1.49341i
\(303\) 19.9279 + 27.4284i 1.14483 + 1.57572i
\(304\) −20.3469 + 12.6492i −1.16698 + 0.725481i
\(305\) −5.64416 4.10072i −0.323184 0.234807i
\(306\) −12.9779 + 4.81151i −0.741899 + 0.275056i
\(307\) −17.8371 2.82512i −1.01802 0.161238i −0.374948 0.927046i \(-0.622340\pi\)
−0.643070 + 0.765808i \(0.722340\pi\)
\(308\) −1.19789 14.6199i −0.0682563 0.833046i
\(309\) −23.1368 14.1782i −1.31620 0.806571i
\(310\) 0.470307 + 1.65739i 0.0267117 + 0.0941332i
\(311\) −1.34899 17.1405i −0.0764942 0.971951i −0.908691 0.417470i \(-0.862917\pi\)
0.832197 0.554481i \(-0.187083\pi\)
\(312\) −4.57338 22.4264i −0.258917 1.26965i
\(313\) −13.2941 15.5654i −0.751429 0.879811i 0.244527 0.969642i \(-0.421367\pi\)
−0.995957 + 0.0898315i \(0.971367\pi\)
\(314\) 4.03161 14.3834i 0.227517 0.811703i
\(315\) −4.28037 6.98493i −0.241172 0.393556i
\(316\) 0.427294 + 2.64284i 0.0240372 + 0.148671i
\(317\) −13.3147 + 15.5895i −0.747829 + 0.875595i −0.995646 0.0932119i \(-0.970287\pi\)
0.247818 + 0.968807i \(0.420287\pi\)
\(318\) 10.6664 7.15185i 0.598140 0.401056i
\(319\) −9.43319 9.43319i −0.528157 0.528157i
\(320\) 2.57016 6.37815i 0.143677 0.356549i
\(321\) −5.73302 23.8797i −0.319986 1.33284i
\(322\) −7.36348 + 5.82411i −0.410351 + 0.324565i
\(323\) 10.4864 20.5807i 0.583479 1.14514i
\(324\) 17.3132 10.6862i 0.961844 0.593679i
\(325\) −5.60735 + 13.5373i −0.311040 + 0.750916i
\(326\) 9.74234 + 5.43543i 0.539578 + 0.301040i
\(327\) −27.0088 −1.49359
\(328\) −11.8199 13.7219i −0.652646 0.757663i
\(329\) −27.4829 −1.51518
\(330\) −4.87912 2.72215i −0.268587 0.149849i
\(331\) −4.86776 + 11.7518i −0.267556 + 0.645937i −0.999367 0.0355701i \(-0.988675\pi\)
0.731811 + 0.681507i \(0.238675\pi\)
\(332\) −22.2801 + 13.7519i −1.22278 + 0.754736i
\(333\) −9.99028 + 19.6070i −0.547464 + 1.07446i
\(334\) 4.45190 3.52121i 0.243597 0.192672i
\(335\) 1.85199 + 7.71408i 0.101185 + 0.421465i
\(336\) −20.5934 + 28.7309i −1.12346 + 1.56740i
\(337\) 18.1659 + 18.1659i 0.989558 + 0.989558i 0.999946 0.0103877i \(-0.00330657\pi\)
−0.0103877 + 0.999946i \(0.503307\pi\)
\(338\) 1.38078 0.925822i 0.0751047 0.0503581i
\(339\) 17.3753 20.3439i 0.943698 1.10493i
\(340\) 1.05815 + 6.54469i 0.0573860 + 0.354936i
\(341\) −1.44629 2.36013i −0.0783208 0.127808i
\(342\) 5.80198 20.6995i 0.313735 1.11930i
\(343\) 0.249519 + 0.292149i 0.0134728 + 0.0157746i
\(344\) 20.8634 4.25462i 1.12488 0.229394i
\(345\) 0.280558 + 3.56483i 0.0151048 + 0.191924i
\(346\) −6.48737 22.8618i −0.348763 1.22906i
\(347\) 4.56067 + 2.79478i 0.244829 + 0.150032i 0.639500 0.768791i \(-0.279141\pi\)
−0.394671 + 0.918823i \(0.629141\pi\)
\(348\) 2.62527 + 32.0406i 0.140729 + 1.71756i
\(349\) −8.33592 1.32028i −0.446212 0.0706730i −0.0707146 0.997497i \(-0.522528\pi\)
−0.375497 + 0.926824i \(0.622528\pi\)
\(350\) 21.2188 7.86677i 1.13419 0.420497i
\(351\) −3.02528 2.19800i −0.161478 0.117320i
\(352\) −1.21041 + 10.9818i −0.0645152 + 0.585334i
\(353\) −0.963109 1.32561i −0.0512611 0.0705549i 0.782617 0.622504i \(-0.213884\pi\)
−0.833878 + 0.551949i \(0.813884\pi\)
\(354\) −1.68643 41.2337i −0.0896329 2.19155i
\(355\) 2.34272 0.970387i 0.124339 0.0515028i
\(356\) −9.77200 9.70940i −0.517915 0.514597i
\(357\) 2.67390 33.9751i 0.141518 1.79815i
\(358\) −2.26051 11.2697i −0.119472 0.595623i
\(359\) 4.02462 12.3865i 0.212411 0.653735i −0.786916 0.617060i \(-0.788323\pi\)
0.999327 0.0366749i \(-0.0116766\pi\)
\(360\) 2.16347 + 5.77843i 0.114025 + 0.304550i
\(361\) 7.66107 + 15.0357i 0.403214 + 0.791352i
\(362\) −5.69356 + 12.4027i −0.299247 + 0.651869i
\(363\) −16.4421 3.94740i −0.862986 0.207185i
\(364\) 25.1322 + 5.94836i 1.31728 + 0.311779i
\(365\) 3.11958 + 9.60109i 0.163286 + 0.502544i
\(366\) −13.2363 23.5463i −0.691872 1.23078i
\(367\) 9.90526 1.56884i 0.517050 0.0818927i 0.107545 0.994200i \(-0.465701\pi\)
0.409506 + 0.912308i \(0.365701\pi\)
\(368\) 6.27967 3.25065i 0.327350 0.169452i
\(369\) 16.1366 + 1.91983i 0.840039 + 0.0999424i
\(370\) 8.28793 + 6.51211i 0.430869 + 0.338548i
\(371\) 2.26687 + 14.3125i 0.117690 + 0.743067i
\(372\) −1.02230 + 6.59155i −0.0530037 + 0.341756i
\(373\) 7.26310 2.35992i 0.376069 0.122192i −0.114883 0.993379i \(-0.536649\pi\)
0.490952 + 0.871187i \(0.336649\pi\)
\(374\) −4.47500 9.66615i −0.231397 0.499824i
\(375\) 4.37322 18.2158i 0.225832 0.940657i
\(376\) 20.3211 + 3.94040i 1.04798 + 0.203211i
\(377\) 20.9278 10.6632i 1.07784 0.549184i
\(378\) 0.688032 + 5.73421i 0.0353885 + 0.294936i
\(379\) 1.79221 + 0.582324i 0.0920595 + 0.0299120i 0.354685 0.934986i \(-0.384588\pi\)
−0.262625 + 0.964898i \(0.584588\pi\)
\(380\) −9.18953 4.64517i −0.471413 0.238292i
\(381\) 4.60745 + 0.362614i 0.236047 + 0.0185773i
\(382\) 12.2227 + 1.42675i 0.625370 + 0.0729988i
\(383\) −2.96764 7.16452i −0.151639 0.366090i 0.829745 0.558142i \(-0.188486\pi\)
−0.981385 + 0.192052i \(0.938486\pi\)
\(384\) 19.3463 18.2913i 0.987261 0.933423i
\(385\) 5.10039 3.70565i 0.259940 0.188858i
\(386\) 1.40656 2.11240i 0.0715919 0.107518i
\(387\) −11.2300 + 15.4567i −0.570851 + 0.785710i
\(388\) −20.8963 6.71545i −1.06085 0.340925i
\(389\) −2.42233 + 15.2940i −0.122817 + 0.775438i 0.846998 + 0.531596i \(0.178408\pi\)
−0.969815 + 0.243841i \(0.921592\pi\)
\(390\) 7.21269 6.68887i 0.365229 0.338704i
\(391\) −3.56204 + 5.81271i −0.180140 + 0.293962i
\(392\) −9.89997 17.4795i −0.500024 0.882848i
\(393\) −6.19023 + 0.487182i −0.312256 + 0.0245751i
\(394\) −0.634029 + 16.8262i −0.0319419 + 0.847692i
\(395\) −0.874920 + 0.747252i −0.0440220 + 0.0375983i
\(396\) −5.85273 8.00139i −0.294111 0.402085i
\(397\) −27.7429 + 17.0009i −1.39238 + 0.853250i −0.997844 0.0656314i \(-0.979094\pi\)
−0.394534 + 0.918881i \(0.629094\pi\)
\(398\) 20.8378 + 19.2003i 1.04451 + 0.962423i
\(399\) 40.2493 + 34.3762i 2.01499 + 1.72096i
\(400\) −16.8173 + 2.77450i −0.840863 + 0.138725i
\(401\) 16.7738 16.7738i 0.837642 0.837642i −0.150906 0.988548i \(-0.548219\pi\)
0.988548 + 0.150906i \(0.0482191\pi\)
\(402\) −5.94394 + 30.1351i −0.296457 + 1.50300i
\(403\) 4.73881 1.13769i 0.236057 0.0566723i
\(404\) 28.8137 0.0925886i 1.43354 0.00460645i
\(405\) 7.79111 + 3.96977i 0.387143 + 0.197259i
\(406\) −34.0533 12.5008i −1.69004 0.620405i
\(407\) −15.6457 6.48067i −0.775530 0.321235i
\(408\) −6.84832 + 24.7381i −0.339043 + 1.22472i
\(409\) 19.5737i 0.967858i −0.875107 0.483929i \(-0.839209\pi\)
0.875107 0.483929i \(-0.160791\pi\)
\(410\) 2.39789 7.40513i 0.118423 0.365713i
\(411\) 22.0717i 1.08871i
\(412\) −21.2779 + 8.89382i −1.04829 + 0.438167i
\(413\) 43.0218 + 17.8202i 2.11697 + 0.876876i
\(414\) −2.18647 + 5.95614i −0.107459 + 0.292728i
\(415\) −10.0263 5.10864i −0.492170 0.250773i
\(416\) −17.7301 8.00163i −0.869291 0.392312i
\(417\) 12.4337 2.98508i 0.608883 0.146180i
\(418\) 16.2310 + 3.20144i 0.793884 + 0.156588i
\(419\) 10.2583 10.2583i 0.501149 0.501149i −0.410646 0.911795i \(-0.634697\pi\)
0.911795 + 0.410646i \(0.134697\pi\)
\(420\) −15.1493 1.14331i −0.739210 0.0557877i
\(421\) −23.9391 20.4459i −1.16672 0.996473i −0.999945 0.0104784i \(-0.996665\pi\)
−0.166775 0.985995i \(-0.553335\pi\)
\(422\) −17.0786 + 18.5352i −0.831375 + 0.902280i
\(423\) −15.8364 + 9.70456i −0.769993 + 0.471852i
\(424\) 0.375921 10.9078i 0.0182563 0.529729i
\(425\) 12.4956 10.6722i 0.606124 0.517679i
\(426\) 9.81083 + 0.369682i 0.475336 + 0.0179112i
\(427\) 30.3856 2.39139i 1.47046 0.115728i
\(428\) −19.3084 7.92522i −0.933308 0.383080i
\(429\) −8.25792 + 13.4757i −0.398696 + 0.650613i
\(430\) 6.22267 + 6.70998i 0.300084 + 0.323584i
\(431\) 2.96333 18.7097i 0.142738 0.901215i −0.807540 0.589813i \(-0.799201\pi\)
0.950278 0.311402i \(-0.100799\pi\)
\(432\) 0.313412 4.33857i 0.0150790 0.208740i
\(433\) 12.6067 17.3517i 0.605841 0.833868i −0.390387 0.920651i \(-0.627659\pi\)
0.996227 + 0.0867830i \(0.0276587\pi\)
\(434\) −6.26497 4.17157i −0.300728 0.200242i
\(435\) −11.1779 + 8.12121i −0.535938 + 0.389382i
\(436\) −13.4324 + 18.6136i −0.643296 + 0.891431i
\(437\) −4.05195 9.78228i −0.193831 0.467950i
\(438\) −4.53171 + 38.8225i −0.216534 + 1.85501i
\(439\) −7.86784 0.619212i −0.375511 0.0295534i −0.110701 0.993854i \(-0.535309\pi\)
−0.264811 + 0.964300i \(0.585309\pi\)
\(440\) −4.30258 + 2.00872i −0.205117 + 0.0957619i
\(441\) 17.1427 + 5.56999i 0.816318 + 0.265238i
\(442\) 18.6203 2.23420i 0.885676 0.106270i
\(443\) 25.2828 12.8822i 1.20122 0.612053i 0.265268 0.964175i \(-0.414540\pi\)
0.935954 + 0.352121i \(0.114540\pi\)
\(444\) 18.6438 + 36.3017i 0.884797 + 1.72280i
\(445\) 1.38211 5.75688i 0.0655181 0.272902i
\(446\) −34.7716 + 16.0977i −1.64648 + 0.762248i
\(447\) −43.0178 + 13.9773i −2.03467 + 0.661104i
\(448\) 9.55862 + 28.4812i 0.451602 + 1.34561i
\(449\) 3.87442 + 24.4621i 0.182845 + 1.15444i 0.892887 + 0.450280i \(0.148676\pi\)
−0.710042 + 0.704159i \(0.751324\pi\)
\(450\) 9.44897 12.0257i 0.445429 0.566895i
\(451\) −0.498565 + 12.4959i −0.0234765 + 0.588411i
\(452\) −5.37902 22.0923i −0.253008 1.03913i
\(453\) 42.6896 6.76138i 2.00573 0.317677i
\(454\) −7.61440 + 4.28036i −0.357362 + 0.200887i
\(455\) 3.43002 + 10.5565i 0.160802 + 0.494898i
\(456\) −24.8320 31.1888i −1.16286 1.46055i
\(457\) 0.585547 + 0.140577i 0.0273907 + 0.00657593i 0.247118 0.968986i \(-0.420517\pi\)
−0.219727 + 0.975561i \(0.570517\pi\)
\(458\) 9.87175 + 4.53172i 0.461277 + 0.211753i
\(459\) 1.90392 + 3.73665i 0.0888672 + 0.174412i
\(460\) 2.59630 + 1.57956i 0.121053 + 0.0736476i
\(461\) −8.91464 + 27.4364i −0.415196 + 1.27784i 0.496879 + 0.867820i \(0.334479\pi\)
−0.912075 + 0.410023i \(0.865521\pi\)
\(462\) 23.9326 4.80047i 1.11344 0.223338i
\(463\) 2.32275 29.5133i 0.107947 1.37160i −0.669575 0.742745i \(-0.733524\pi\)
0.777522 0.628856i \(-0.216476\pi\)
\(464\) 23.3870 + 14.1257i 1.08572 + 0.655767i
\(465\) −2.64858 + 1.09708i −0.122825 + 0.0508758i
\(466\) −22.8807 + 0.935806i −1.05993 + 0.0433504i
\(467\) 8.07107 + 11.1089i 0.373485 + 0.514058i 0.953844 0.300303i \(-0.0970878\pi\)
−0.580359 + 0.814361i \(0.697088\pi\)
\(468\) 16.5823 5.44688i 0.766516 0.251782i
\(469\) −28.0399 20.3722i −1.29476 0.940700i
\(470\) 3.09258 + 8.34152i 0.142650 + 0.384765i
\(471\) 24.5506 + 3.88844i 1.13123 + 0.179170i
\(472\) −29.2557 19.3447i −1.34660 0.890414i
\(473\) −12.5365 7.68236i −0.576427 0.353235i
\(474\) −4.28563 + 1.21611i −0.196845 + 0.0558577i
\(475\) 2.00247 + 25.4438i 0.0918795 + 1.16744i
\(476\) −22.0848 18.7398i −1.01225 0.858936i
\(477\) 6.36014 + 7.44677i 0.291211 + 0.340964i
\(478\) −12.6305 3.54026i −0.577704 0.161928i
\(479\) −17.4401 28.4596i −0.796858 1.30035i −0.950031 0.312155i \(-0.898949\pi\)
0.153173 0.988199i \(-0.451051\pi\)
\(480\) 11.0376 + 3.01742i 0.503796 + 0.137726i
\(481\) 19.3639 22.6722i 0.882919 1.03377i
\(482\) 11.6741 + 17.4108i 0.531739 + 0.793042i
\(483\) −11.0467 11.0467i −0.502641 0.502641i
\(484\) −10.8977 + 9.36820i −0.495348 + 0.425827i
\(485\) −2.20214 9.17258i −0.0999941 0.416505i
\(486\) 18.1402 + 22.9348i 0.822854 + 1.04034i
\(487\) −9.07698 + 17.8146i −0.411317 + 0.807255i −0.999999 0.00110933i \(-0.999647\pi\)
0.588682 + 0.808364i \(0.299647\pi\)
\(488\) −22.8102 2.58835i −1.03257 0.117169i
\(489\) −7.10406 + 17.1507i −0.321257 + 0.775582i
\(490\) 4.20646 7.53957i 0.190029 0.340603i
\(491\) 5.56524 0.251156 0.125578 0.992084i \(-0.459921\pi\)
0.125578 + 0.992084i \(0.459921\pi\)
\(492\) 20.3990 22.1832i 0.919658 1.00010i
\(493\) −26.3412 −1.18635
\(494\) −14.1914 + 25.4364i −0.638502 + 1.14444i
\(495\) 1.63047 3.93631i 0.0732843 0.176924i
\(496\) 4.03427 + 3.98275i 0.181144 + 0.178831i
\(497\) −5.02943 + 9.87081i −0.225601 + 0.442766i
\(498\) −27.0276 34.1713i −1.21114 1.53125i
\(499\) −5.31042 22.1195i −0.237727 0.990205i −0.955749 0.294184i \(-0.904952\pi\)
0.718022 0.696021i \(-0.245048\pi\)
\(500\) −10.3788 12.0732i −0.464153 0.539931i
\(501\) 6.67872 + 6.67872i 0.298383 + 0.298383i
\(502\) 17.4601 + 26.0402i 0.779281 + 1.16223i
\(503\) −5.14437 + 6.02328i −0.229376 + 0.268565i −0.863143 0.504959i \(-0.831508\pi\)
0.633767 + 0.773524i \(0.281508\pi\)
\(504\) −23.5826 13.0580i −1.05045 0.581649i
\(505\) 6.47046 + 10.5588i 0.287932 + 0.469862i
\(506\) −4.70157 1.31783i −0.209010 0.0585847i
\(507\) 1.79658 + 2.10353i 0.0797891 + 0.0934210i
\(508\) 2.54135 2.99497i 0.112754 0.132880i
\(509\) −1.00352 12.7510i −0.0444803 0.565176i −0.978267 0.207347i \(-0.933517\pi\)
0.933787 0.357829i \(-0.116483\pi\)
\(510\) −10.6129 + 3.01156i −0.469946 + 0.133354i
\(511\) −37.6051 23.0444i −1.66355 1.01942i
\(512\) −2.98420 22.4298i −0.131884 0.991265i
\(513\) −6.43328 1.01893i −0.284036 0.0449870i
\(514\) −7.42476 20.0265i −0.327492 0.883333i
\(515\) −8.01864 5.82588i −0.353344 0.256719i
\(516\) 11.0572 + 33.6620i 0.486764 + 1.48189i
\(517\) −8.40154 11.5637i −0.369499 0.508572i
\(518\) −46.0103 + 1.88179i −2.02158 + 0.0826812i
\(519\) 36.5343 15.1330i 1.60368 0.664264i
\(520\) −1.02264 8.29738i −0.0448456 0.363864i
\(521\) −1.24882 + 15.8678i −0.0547119 + 0.695181i 0.907002 + 0.421126i \(0.138365\pi\)
−0.961714 + 0.274055i \(0.911635\pi\)
\(522\) −24.0366 + 4.82134i −1.05205 + 0.211024i
\(523\) −2.56010 + 7.87919i −0.111946 + 0.344533i −0.991298 0.131639i \(-0.957976\pi\)
0.879352 + 0.476172i \(0.157976\pi\)
\(524\) −2.74287 + 4.50841i −0.119823 + 0.196951i
\(525\) 17.0959 + 33.5525i 0.746124 + 1.46435i
\(526\) −8.94567 4.10660i −0.390050 0.179056i
\(527\) −5.31450 1.27590i −0.231503 0.0555790i
\(528\) −18.3842 + 0.118151i −0.800071 + 0.00514187i
\(529\) −6.14169 18.9022i −0.267030 0.821834i
\(530\) 4.08898 2.29858i 0.177614 0.0998438i
\(531\) 31.0829 4.92304i 1.34888 0.213642i
\(532\) 43.7084 10.6421i 1.89500 0.461394i
\(533\) −20.6527 7.63343i −0.894568 0.330641i
\(534\) 14.1623 18.0243i 0.612864 0.779988i
\(535\) −1.40326 8.85981i −0.0606681 0.383043i
\(536\) 17.8121 + 19.0836i 0.769365 + 0.824288i
\(537\) 18.1904 5.91041i 0.784973 0.255053i
\(538\) 27.4383 12.7027i 1.18295 0.547654i
\(539\) −3.23823 + 13.4882i −0.139480 + 0.580977i
\(540\) 1.66300 0.854084i 0.0715642 0.0367539i
\(541\) −21.0699 + 10.7356i −0.905864 + 0.461561i −0.843889 0.536517i \(-0.819740\pi\)
−0.0619744 + 0.998078i \(0.519740\pi\)
\(542\) 2.35637 0.282735i 0.101215 0.0121445i
\(543\) −21.5975 7.01744i −0.926836 0.301147i
\(544\) 13.6428 + 17.0228i 0.584932 + 0.729846i
\(545\) −9.83492 0.774025i −0.421282 0.0331556i
\(546\) −4.98268 + 42.6859i −0.213239 + 1.82679i
\(547\) 5.66280 + 13.6712i 0.242124 + 0.584539i 0.997493 0.0707604i \(-0.0225426\pi\)
−0.755369 + 0.655299i \(0.772543\pi\)
\(548\) 15.2111 + 10.9770i 0.649786 + 0.468915i
\(549\) 16.6645 12.1075i 0.711225 0.516735i
\(550\) 9.79661 + 6.52314i 0.417729 + 0.278148i
\(551\) 24.0473 33.0982i 1.02445 1.41003i
\(552\) 6.58418 + 9.75184i 0.280241 + 0.415066i
\(553\) 0.786360 4.96488i 0.0334394 0.211128i
\(554\) 22.7502 + 24.5318i 0.966564 + 1.04226i
\(555\) −9.16419 + 14.9546i −0.388998 + 0.634787i
\(556\) 4.12651 10.0535i 0.175003 0.426365i
\(557\) −26.0149 + 2.04742i −1.10229 + 0.0867518i −0.616522 0.787338i \(-0.711459\pi\)
−0.485764 + 0.874090i \(0.661459\pi\)
\(558\) −5.08308 0.191536i −0.215184 0.00810835i
\(559\) 19.6845 16.8121i 0.832564 0.711077i
\(560\) −8.32221 + 9.87183i −0.351678 + 0.417161i
\(561\) 15.1128 9.26112i 0.638062 0.391005i
\(562\) −9.49718 + 10.3072i −0.400614 + 0.434782i
\(563\) −21.9549 18.7513i −0.925289 0.790271i 0.0527686 0.998607i \(-0.483195\pi\)
−0.978057 + 0.208335i \(0.933195\pi\)
\(564\) −2.59213 + 34.3469i −0.109148 + 1.44626i
\(565\) 6.91003 6.91003i 0.290707 0.290707i
\(566\) 0.676008 + 0.133338i 0.0284147 + 0.00560460i
\(567\) −37.1464 + 8.91806i −1.56000 + 0.374523i
\(568\) 5.13405 6.57747i 0.215420 0.275984i
\(569\) 5.25561 + 2.67787i 0.220327 + 0.112262i 0.560670 0.828039i \(-0.310543\pi\)
−0.340344 + 0.940301i \(0.610543\pi\)
\(570\) 5.90457 16.0846i 0.247315 0.673709i
\(571\) 22.1776 + 9.18625i 0.928102 + 0.384432i 0.794958 0.606664i \(-0.207493\pi\)
0.133144 + 0.991097i \(0.457493\pi\)
\(572\) 5.18008 + 12.3930i 0.216590 + 0.518179i
\(573\) 20.4769i 0.855436i
\(574\) 13.0448 + 31.4042i 0.544480 + 1.31078i
\(575\) 7.53279i 0.314139i
\(576\) 15.5650 + 13.0364i 0.648542 + 0.543183i
\(577\) 22.8118 + 9.44896i 0.949668 + 0.393365i 0.803106 0.595836i \(-0.203179\pi\)
0.146562 + 0.989201i \(0.453179\pi\)
\(578\) 2.82516 + 1.03710i 0.117511 + 0.0431378i
\(579\) 3.76273 + 1.91721i 0.156374 + 0.0796764i
\(580\) 0.0377325 + 11.7424i 0.00156676 + 0.487577i
\(581\) 47.8032 11.4765i 1.98321 0.476126i
\(582\) 7.06776 35.8328i 0.292968 1.48532i
\(583\) −5.32914 + 5.32914i −0.220710 + 0.220710i
\(584\) 24.5015 + 22.4309i 1.01388 + 0.928198i
\(585\) 5.70411 + 4.87177i 0.235836 + 0.201423i
\(586\) 1.09252 + 1.00666i 0.0451316 + 0.0415849i
\(587\) 6.84398 4.19399i 0.282481 0.173105i −0.374039 0.927413i \(-0.622028\pi\)
0.656521 + 0.754308i \(0.272028\pi\)
\(588\) 26.9800 19.7349i 1.11264 0.813853i
\(589\) 6.45488 5.51299i 0.265969 0.227159i
\(590\) 0.567593 15.0631i 0.0233674 0.620137i
\(591\) −27.9326 + 2.19834i −1.14899 + 0.0904276i
\(592\) 34.2903 + 5.20537i 1.40932 + 0.213939i
\(593\) 10.0974 16.4774i 0.414649 0.676646i −0.575320 0.817928i \(-0.695122\pi\)
0.989969 + 0.141282i \(0.0451224\pi\)
\(594\) −2.20240 + 2.04245i −0.0903654 + 0.0838025i
\(595\) 1.94733 12.2950i 0.0798329 0.504045i
\(596\) −11.7615 + 36.5979i −0.481770 + 1.49911i
\(597\) −27.7139 + 38.1449i −1.13425 + 1.56117i
\(598\) 4.76462 7.15561i 0.194840 0.292615i
\(599\) −3.75901 + 2.73108i −0.153589 + 0.111589i −0.661926 0.749570i \(-0.730261\pi\)
0.508337 + 0.861158i \(0.330261\pi\)
\(600\) −7.83020 27.2602i −0.319667 1.11289i
\(601\) 10.5326 + 25.4279i 0.429632 + 1.03722i 0.979404 + 0.201910i \(0.0647147\pi\)
−0.549772 + 0.835315i \(0.685285\pi\)
\(602\) −39.7108 4.63540i −1.61849 0.188925i
\(603\) −23.3510 1.83777i −0.950927 0.0748396i
\(604\) 16.5713 32.7831i 0.674278 1.33392i
\(605\) −5.87406 1.90860i −0.238814 0.0775955i
\(606\) 5.71202 + 47.6052i 0.232035 + 1.93383i
\(607\) 10.2705 5.23309i 0.416868 0.212405i −0.232960 0.972486i \(-0.574841\pi\)
0.649828 + 0.760082i \(0.274841\pi\)
\(608\) −33.8442 + 1.60214i −1.37256 + 0.0649752i
\(609\) 14.0914 58.6948i 0.571012 2.37844i
\(610\) −4.14503 8.95341i −0.167828 0.362513i
\(611\) 23.9340 7.77663i 0.968266 0.314609i
\(612\) −19.3431 2.99996i −0.781898 0.121266i
\(613\) 0.680693 + 4.29773i 0.0274929 + 0.173584i 0.997614 0.0690375i \(-0.0219928\pi\)
−0.970121 + 0.242621i \(0.921993\pi\)
\(614\) −20.0823 15.7794i −0.810456 0.636804i
\(615\) 12.7018 + 2.53456i 0.512185 + 0.102203i
\(616\) 8.59417 18.8810i 0.346269 0.760738i
\(617\) 22.1472 3.50777i 0.891613 0.141218i 0.306214 0.951963i \(-0.400938\pi\)
0.585399 + 0.810745i \(0.300938\pi\)
\(618\) −18.8048 33.4521i −0.756438 1.34564i
\(619\) −5.67146 17.4549i −0.227955 0.701573i −0.997978 0.0635575i \(-0.979755\pi\)
0.770023 0.638016i \(-0.220245\pi\)
\(620\) −0.561160 + 2.37094i −0.0225367 + 0.0952191i
\(621\) 1.86929 + 0.448778i 0.0750122 + 0.0180088i
\(622\) 10.1444 22.0981i 0.406752 0.886054i
\(623\) 11.7427 + 23.0464i 0.470463 + 0.923335i
\(624\) 9.80438 30.8480i 0.392489 1.23491i
\(625\) −4.46935 + 13.7553i −0.178774 + 0.550210i
\(626\) −5.69325 28.3835i −0.227548 1.13443i
\(627\) −2.15990 + 27.4441i −0.0862580 + 1.09601i
\(628\) 14.8897 14.9857i 0.594163 0.597994i
\(629\) −30.8928 + 12.7962i −1.23178 + 0.510219i
\(630\) −0.473440 11.5757i −0.0188623 0.461188i
\(631\) −12.0632 16.6035i −0.480227 0.660975i 0.498322 0.866992i \(-0.333950\pi\)
−0.978548 + 0.206017i \(0.933950\pi\)
\(632\) −1.29329 + 3.55834i −0.0514442 + 0.141543i
\(633\) −33.9298 24.6515i −1.34859 0.979808i
\(634\) −27.1854 + 10.0789i −1.07967 + 0.400283i
\(635\) 1.66735 + 0.264083i 0.0661670 + 0.0104798i
\(636\) 18.1008 1.48311i 0.717745 0.0588090i
\(637\) −20.8236 12.7607i −0.825062 0.505599i
\(638\) −5.15026 18.1498i −0.203901 0.718557i
\(639\) 0.587412 + 7.46378i 0.0232377 + 0.295263i
\(640\) 7.56891 6.10611i 0.299187 0.241365i
\(641\) 15.7814 + 18.4776i 0.623326 + 0.729821i 0.978789 0.204869i \(-0.0656769\pi\)
−0.355463 + 0.934690i \(0.615677\pi\)
\(642\) 9.37359 33.4418i 0.369946 1.31984i
\(643\) 19.7947 + 32.3021i 0.780629 + 1.27387i 0.957156 + 0.289574i \(0.0935137\pi\)
−0.176527 + 0.984296i \(0.556486\pi\)
\(644\) −13.1069 + 2.11913i −0.516485 + 0.0835054i
\(645\) −9.88968 + 11.5793i −0.389406 + 0.455936i
\(646\) 27.1315 18.1918i 1.06748 0.715748i
\(647\) 13.7618 + 13.7618i 0.541031 + 0.541031i 0.923831 0.382800i \(-0.125040\pi\)
−0.382800 + 0.923831i \(0.625040\pi\)
\(648\) 28.7450 1.26819i 1.12921 0.0498191i
\(649\) 5.65374 + 23.5495i 0.221929 + 0.924400i
\(650\) −16.2527 + 12.8550i −0.637485 + 0.504215i
\(651\) 5.68605 11.1595i 0.222854 0.437376i
\(652\) 8.28665 + 13.4256i 0.324530 + 0.525785i
\(653\) −7.57706 + 18.2926i −0.296513 + 0.715847i 0.703473 + 0.710722i \(0.251631\pi\)
−0.999987 + 0.00512517i \(0.998369\pi\)
\(654\) −33.3560 18.6099i −1.30432 0.727705i
\(655\) −2.26806 −0.0886204
\(656\) −5.14285 25.0909i −0.200795 0.979633i
\(657\) −29.8063 −1.16286
\(658\) −33.9415 18.9366i −1.32318 0.738226i
\(659\) −6.90254 + 16.6642i −0.268885 + 0.649146i −0.999431 0.0337173i \(-0.989265\pi\)
0.730546 + 0.682863i \(0.239265\pi\)
\(660\) −4.15009 6.72373i −0.161542 0.261721i
\(661\) −4.44872 + 8.73110i −0.173035 + 0.339601i −0.961195 0.275870i \(-0.911034\pi\)
0.788160 + 0.615471i \(0.211034\pi\)
\(662\) −14.1091 + 11.1595i −0.548364 + 0.433726i
\(663\) 7.28505 + 30.3444i 0.282928 + 1.17848i
\(664\) −36.9916 + 1.63201i −1.43555 + 0.0633344i
\(665\) 13.6711 + 13.6711i 0.530144 + 0.530144i
\(666\) −25.8479 + 17.3312i −1.00159 + 0.671568i
\(667\) −7.84196 + 9.18176i −0.303642 + 0.355519i
\(668\) 7.92433 1.28121i 0.306602 0.0495714i
\(669\) −33.3146 54.3645i −1.28802 2.10185i
\(670\) −3.02803 + 10.8030i −0.116983 + 0.417356i
\(671\) 10.2951 + 12.0540i 0.397437 + 0.465339i
\(672\) −45.2294 + 21.2933i −1.74476 + 0.821406i
\(673\) −3.20254 40.6921i −0.123449 1.56857i −0.677146 0.735849i \(-0.736784\pi\)
0.553697 0.832718i \(-0.313216\pi\)
\(674\) 9.91808 + 34.9518i 0.382030 + 1.34629i
\(675\) −3.95102 2.42119i −0.152075 0.0931917i
\(676\) 2.34319 0.191991i 0.0901228 0.00738428i
\(677\) 7.58826 + 1.20186i 0.291641 + 0.0461913i 0.300541 0.953769i \(-0.402833\pi\)
−0.00889983 + 0.999960i \(0.502833\pi\)
\(678\) 35.4762 13.1526i 1.36245 0.505124i
\(679\) 33.3414 + 24.2240i 1.27953 + 0.929630i
\(680\) −3.20268 + 8.81182i −0.122817 + 0.337918i
\(681\) −8.54358 11.7592i −0.327391 0.450614i
\(682\) −0.159970 3.91130i −0.00612556 0.149771i
\(683\) 30.8408 12.7747i 1.18009 0.488810i 0.295575 0.955320i \(-0.404489\pi\)
0.884516 + 0.466510i \(0.154489\pi\)
\(684\) 21.4281 21.5662i 0.819324 0.824606i
\(685\) −0.632535 + 8.03712i −0.0241679 + 0.307083i
\(686\) 0.106857 + 0.532732i 0.00407982 + 0.0203398i
\(687\) −5.58545 + 17.1903i −0.213098 + 0.655849i
\(688\) 28.6979 + 9.12104i 1.09410 + 0.347736i
\(689\) −6.02403 11.8228i −0.229497 0.450414i
\(690\) −2.10979 + 4.59590i −0.0803183 + 0.174963i
\(691\) −48.0284 11.5306i −1.82709 0.438645i −0.833578 0.552401i \(-0.813712\pi\)
−0.993509 + 0.113757i \(0.963712\pi\)
\(692\) 7.74058 32.7045i 0.294253 1.24324i
\(693\) 5.75205 + 17.7030i 0.218502 + 0.672481i
\(694\) 3.70675 + 6.59401i 0.140706 + 0.250305i
\(695\) 4.61314 0.730650i 0.174986 0.0277151i
\(696\) −18.8347 + 41.3792i −0.713929 + 1.56847i
\(697\) 16.7507 + 18.1429i 0.634478 + 0.687211i
\(698\) −9.38518 7.37426i −0.355234 0.279120i
\(699\) −5.96104 37.6365i −0.225467 1.42354i
\(700\) 31.6257 + 4.90490i 1.19534 + 0.185388i
\(701\) 9.70184 3.15232i 0.366433 0.119061i −0.120012 0.992772i \(-0.538293\pi\)
0.486445 + 0.873711i \(0.338293\pi\)
\(702\) −2.22175 4.79905i −0.0838545 0.181128i
\(703\) 12.1238 50.4993i 0.457258 1.90462i
\(704\) −9.06170 + 12.7286i −0.341526 + 0.479728i
\(705\) −13.1901 + 6.72072i −0.496770 + 0.253117i
\(706\) −0.276060 2.30074i −0.0103896 0.0865896i
\(707\) −51.4544 16.7186i −1.93514 0.628766i
\(708\) 26.3286 52.0858i 0.989489 1.95751i
\(709\) −9.65728 0.760045i −0.362687 0.0285441i −0.104193 0.994557i \(-0.533226\pi\)
−0.258494 + 0.966013i \(0.583226\pi\)
\(710\) 3.56190 + 0.415777i 0.133676 + 0.0156038i
\(711\) −1.30004 3.13857i −0.0487553 0.117706i
\(712\) −5.37838 18.7244i −0.201563 0.701725i
\(713\) −2.02691 + 1.47263i −0.0759082 + 0.0551506i
\(714\) 26.7122 40.1170i 0.999678 1.50134i
\(715\) −3.39321 + 4.67035i −0.126899 + 0.174661i
\(716\) 4.97344 15.4757i 0.185866 0.578354i
\(717\) 3.41454 21.5586i 0.127518 0.805119i
\(718\) 13.5051 12.5243i 0.504007 0.467403i
\(719\) 3.61393 5.89740i 0.134777 0.219936i −0.778131 0.628103i \(-0.783832\pi\)
0.912907 + 0.408167i \(0.133832\pi\)
\(720\) −1.30962 + 8.62709i −0.0488066 + 0.321513i
\(721\) 43.1687 3.39745i 1.60769 0.126528i
\(722\) −0.898612 + 23.8479i −0.0334429 + 0.887525i
\(723\) −26.5242 + 22.6538i −0.986447 + 0.842506i
\(724\) −15.5774 + 11.3943i −0.578929 + 0.423466i
\(725\) 24.8167 15.2077i 0.921668 0.564799i
\(726\) −17.5862 16.2042i −0.652684 0.601393i
\(727\) 28.1823 + 24.0700i 1.04523 + 0.892707i 0.994366 0.105999i \(-0.0338041\pi\)
0.0508591 + 0.998706i \(0.483804\pi\)
\(728\) 26.9398 + 24.6631i 0.998454 + 0.914076i
\(729\) −12.8270 + 12.8270i −0.475073 + 0.475073i
\(730\) −2.76275 + 14.0069i −0.102254 + 0.518418i
\(731\) −28.2295 + 6.77729i −1.04410 + 0.250667i
\(732\) −0.122750 38.2000i −0.00453697 1.41191i
\(733\) 10.1521 + 5.17277i 0.374977 + 0.191060i 0.631314 0.775527i \(-0.282516\pi\)
−0.256337 + 0.966587i \(0.582516\pi\)
\(734\) 13.3140 + 4.88751i 0.491429 + 0.180401i
\(735\) 13.2729 + 5.49781i 0.489578 + 0.202790i
\(736\) 9.99522 + 0.312318i 0.368429 + 0.0115122i
\(737\) 18.0259i 0.663991i
\(738\) 18.6060 + 13.4896i 0.684896 + 0.496561i
\(739\) 40.0675i 1.47391i 0.675943 + 0.736954i \(0.263736\pi\)
−0.675943 + 0.736954i \(0.736264\pi\)
\(740\) 5.74858 + 13.7531i 0.211322 + 0.505575i
\(741\) −44.7790 18.5481i −1.64500 0.681380i
\(742\) −7.06215 + 19.2379i −0.259260 + 0.706246i
\(743\) 33.5346 + 17.0867i 1.23027 + 0.626852i 0.943571 0.331170i \(-0.107443\pi\)
0.286695 + 0.958022i \(0.407443\pi\)
\(744\) −5.80433 + 7.43620i −0.212797 + 0.272624i
\(745\) −16.0649 + 3.85685i −0.588574 + 0.141304i
\(746\) 10.5960 + 2.08999i 0.387948 + 0.0765199i
\(747\) 23.4930 23.4930i 0.859563 0.859563i
\(748\) 1.13363 15.0211i 0.0414498 0.549227i
\(749\) 29.8000 + 25.4516i 1.08887 + 0.929982i
\(750\) 17.9522 19.4833i 0.655520 0.711428i
\(751\) −2.95929 + 1.81346i −0.107986 + 0.0661740i −0.575443 0.817842i \(-0.695170\pi\)
0.467457 + 0.884016i \(0.345170\pi\)
\(752\) 22.3816 + 18.8683i 0.816174 + 0.688057i
\(753\) −39.6705 + 33.8818i −1.44567 + 1.23472i
\(754\) 33.1932 + 1.25075i 1.20882 + 0.0455498i
\(755\) 15.7387 1.23866i 0.572789 0.0450795i
\(756\) −3.10133 + 7.55585i −0.112794 + 0.274803i
\(757\) −2.22690 + 3.63398i −0.0809382 + 0.132079i −0.890548 0.454889i \(-0.849679\pi\)
0.809610 + 0.586969i \(0.199679\pi\)
\(758\) 1.81215 + 1.95406i 0.0658201 + 0.0709746i
\(759\) 1.27103 8.02497i 0.0461355 0.291288i
\(760\) −8.14845 12.0687i −0.295575 0.437777i
\(761\) −28.3675 + 39.0446i −1.02832 + 1.41536i −0.122122 + 0.992515i \(0.538970\pi\)
−0.906200 + 0.422849i \(0.861030\pi\)
\(762\) 5.44037 + 3.62251i 0.197084 + 0.131230i
\(763\) 34.8687 25.3336i 1.26233 0.917138i
\(764\) 14.1121 + 10.1839i 0.510557 + 0.368440i
\(765\) −3.21940 7.77232i −0.116398 0.281009i
\(766\) 1.27153 10.8930i 0.0459422 0.393580i
\(767\) −42.5088 3.34551i −1.53490 0.120799i
\(768\) 36.4960 9.25962i 1.31694 0.334128i
\(769\) −11.5199 3.74304i −0.415418 0.134977i 0.0938483 0.995587i \(-0.470083\pi\)
−0.509266 + 0.860609i \(0.670083\pi\)
\(770\) 8.85232 1.06217i 0.319015 0.0382778i
\(771\) 31.6673 16.1353i 1.14047 0.581098i
\(772\) 3.19262 1.63966i 0.114905 0.0590128i
\(773\) −6.22565 + 25.9317i −0.223921 + 0.932699i 0.741281 + 0.671195i \(0.234218\pi\)
−0.965202 + 0.261504i \(0.915782\pi\)
\(774\) −24.5192 + 11.3513i −0.881326 + 0.408015i
\(775\) 5.74354 1.86619i 0.206314 0.0670355i
\(776\) −21.1798 22.6918i −0.760311 0.814588i
\(777\) −11.9869 75.6825i −0.430029 2.71509i
\(778\) −13.5297 + 17.2191i −0.485062 + 0.617335i
\(779\) −38.0889 + 4.48467i −1.36467 + 0.160680i
\(780\) 13.5165 3.29101i 0.483970 0.117837i
\(781\) −5.69074 + 0.901325i −0.203631 + 0.0322519i
\(782\) −8.40427 + 4.72437i −0.300536 + 0.168943i
\(783\) 2.29536 + 7.06439i 0.0820295 + 0.252461i
\(784\) −0.182576 28.4086i −0.00652056 1.01459i
\(785\) 8.82837 + 2.11950i 0.315098 + 0.0756483i
\(786\) −7.98065 3.66359i −0.284660 0.130676i
\(787\) −7.06784 13.8714i −0.251941 0.494463i 0.730049 0.683395i \(-0.239497\pi\)
−0.981990 + 0.188932i \(0.939497\pi\)
\(788\) −12.3768 + 20.3436i −0.440906 + 0.724710i
\(789\) 5.06148 15.5776i 0.180193 0.554578i
\(790\) −1.59541 + 0.320012i −0.0567621 + 0.0113855i
\(791\) −3.34969 + 42.5618i −0.119101 + 1.51332i
\(792\) −1.71493 13.9145i −0.0609375 0.494429i
\(793\) −25.7851 + 10.6805i −0.915657 + 0.379277i
\(794\) −45.9768 + 1.88042i −1.63165 + 0.0667336i
\(795\) 4.58795 + 6.31478i 0.162718 + 0.223962i
\(796\) 12.5052 + 38.0703i 0.443235 + 1.34937i
\(797\) 10.3571 + 7.52489i 0.366868 + 0.266545i 0.755911 0.654674i \(-0.227194\pi\)
−0.389043 + 0.921220i \(0.627194\pi\)
\(798\) 26.0218 + 70.1877i 0.921162 + 2.48462i
\(799\) −27.8755 4.41504i −0.986163 0.156193i
\(800\) −22.6811 8.16111i −0.801898 0.288539i
\(801\) 14.9045 + 9.13346i 0.526623 + 0.322715i
\(802\) 32.2733 9.15802i 1.13961 0.323381i
\(803\) −1.79970 22.8674i −0.0635102 0.806973i
\(804\) −28.1048 + 33.1215i −0.991182 + 1.16810i
\(805\) −3.70593 4.33909i −0.130617 0.152933i
\(806\) 6.63636 + 1.86014i 0.233756 + 0.0655207i
\(807\) 26.2886 + 42.8991i 0.925403 + 1.51012i
\(808\) 35.6489 + 19.7392i 1.25412 + 0.694423i
\(809\) −11.3490 + 13.2879i −0.399008 + 0.467179i −0.923143 0.384457i \(-0.874389\pi\)
0.524135 + 0.851635i \(0.324389\pi\)
\(810\) 6.88676 + 10.2710i 0.241976 + 0.360886i
\(811\) 2.51167 + 2.51167i 0.0881967 + 0.0881967i 0.749829 0.661632i \(-0.230136\pi\)
−0.661632 + 0.749829i \(0.730136\pi\)
\(812\) −33.4425 38.9024i −1.17360 1.36521i
\(813\) 0.921913 + 3.84005i 0.0323329 + 0.134676i
\(814\) −14.8572 18.7841i −0.520743 0.658381i
\(815\) −3.07836 + 6.04163i −0.107830 + 0.211629i
\(816\) −25.5031 + 25.8330i −0.892785 + 0.904335i
\(817\) 17.2553 41.6580i 0.603686 1.45743i
\(818\) 13.4869 24.1736i 0.471559 0.845211i
\(819\) −32.7725 −1.14516
\(820\) 8.06377 7.49314i 0.281599 0.261672i
\(821\) 2.25389 0.0786613 0.0393307 0.999226i \(-0.487477\pi\)
0.0393307 + 0.999226i \(0.487477\pi\)
\(822\) −15.2081 + 27.2586i −0.530442 + 0.950752i
\(823\) −3.29783 + 7.96166i −0.114955 + 0.277526i −0.970877 0.239579i \(-0.922990\pi\)
0.855922 + 0.517105i \(0.172990\pi\)
\(824\) −32.4064 3.67726i −1.12893 0.128103i
\(825\) −8.89135 + 17.4503i −0.309557 + 0.607540i
\(826\) 40.8534 + 51.6514i 1.42147 + 1.79718i
\(827\) −4.63203 19.2938i −0.161071 0.670910i −0.993209 0.116342i \(-0.962883\pi\)
0.832138 0.554569i \(-0.187117\pi\)
\(828\) −6.80427 + 5.84932i −0.236465 + 0.203278i
\(829\) 14.1675 + 14.1675i 0.492059 + 0.492059i 0.908955 0.416895i \(-0.136882\pi\)
−0.416895 + 0.908955i \(0.636882\pi\)
\(830\) −8.86247 13.2176i −0.307621 0.458790i
\(831\) −36.1569 + 42.3343i −1.25427 + 1.46856i
\(832\) −16.3834 22.0987i −0.567992 0.766133i
\(833\) 14.3110 + 23.3534i 0.495845 + 0.809146i
\(834\) 17.4125 + 4.88066i 0.602947 + 0.169003i
\(835\) 2.24057 + 2.62337i 0.0775382 + 0.0907856i
\(836\) 17.8395 + 15.1375i 0.616990 + 0.523540i
\(837\) 0.120923 + 1.53647i 0.00417970 + 0.0531081i
\(838\) 19.7373 5.60073i 0.681813 0.193474i
\(839\) −4.40614 2.70009i −0.152117 0.0932174i 0.444357 0.895850i \(-0.353432\pi\)
−0.596474 + 0.802632i \(0.703432\pi\)
\(840\) −17.9217 11.8503i −0.618357 0.408875i
\(841\) −17.4381 2.76192i −0.601313 0.0952386i
\(842\) −15.4770 41.7456i −0.533373 1.43865i
\(843\) −18.8679 13.7083i −0.649845 0.472140i
\(844\) −33.8635 + 11.1234i −1.16563 + 0.382882i
\(845\) 0.593920 + 0.817461i 0.0204315 + 0.0281215i
\(846\) −26.2448 + 1.07339i −0.902314 + 0.0369041i
\(847\) 24.9295 10.3261i 0.856588 0.354810i
\(848\) 7.98008 13.2122i 0.274037 0.453707i
\(849\) −0.0899580 + 1.14303i −0.00308735 + 0.0392285i
\(850\) 22.7856 4.57041i 0.781539 0.156764i
\(851\) −4.73663 + 14.5779i −0.162370 + 0.499722i
\(852\) 11.8617 + 7.21653i 0.406375 + 0.247234i
\(853\) −4.62122 9.06966i −0.158228 0.310539i 0.798259 0.602314i \(-0.205754\pi\)
−0.956487 + 0.291774i \(0.905754\pi\)
\(854\) 39.1740 + 17.9832i 1.34051 + 0.615373i
\(855\) 12.7051 + 3.05023i 0.434506 + 0.104316i
\(856\) −18.3853 23.0918i −0.628395 0.789261i
\(857\) 4.00723 + 12.3330i 0.136884 + 0.421286i 0.995878 0.0906991i \(-0.0289102\pi\)
−0.858994 + 0.511985i \(0.828910\pi\)
\(858\) −19.4837 + 10.9526i −0.665164 + 0.373915i
\(859\) −7.78586 + 1.23316i −0.265650 + 0.0420749i −0.287839 0.957679i \(-0.592937\pi\)
0.0221883 + 0.999754i \(0.492937\pi\)
\(860\) 3.06163 + 12.5745i 0.104401 + 0.428786i
\(861\) −49.3879 + 27.6192i −1.68313 + 0.941258i
\(862\) 16.5513 21.0647i 0.563739 0.717468i
\(863\) 3.80346 + 24.0141i 0.129471 + 0.817450i 0.963887 + 0.266313i \(0.0858056\pi\)
−0.834415 + 0.551136i \(0.814194\pi\)
\(864\) 3.37648 5.14221i 0.114870 0.174941i
\(865\) 13.7372 4.46348i 0.467078 0.151763i
\(866\) 27.5252 12.7430i 0.935345 0.433023i
\(867\) −1.16906 + 4.86950i −0.0397034 + 0.165377i
\(868\) −4.86292 9.46867i −0.165058 0.321388i
\(869\) 2.32942 1.18690i 0.0790200 0.0402627i
\(870\) −19.4005 + 2.32781i −0.657739 + 0.0789203i
\(871\) 30.1836 + 9.80725i 1.02273 + 0.332306i
\(872\) −29.4145 + 13.7326i −0.996100 + 0.465043i
\(873\) 27.7660 + 2.18523i 0.939737 + 0.0739589i
\(874\) 1.73612 14.8731i 0.0587251 0.503089i
\(875\) 11.4401 + 27.6187i 0.386745 + 0.933684i
\(876\) −32.3466 + 44.8235i −1.09289 + 1.51445i
\(877\) −38.9804 + 28.3209i −1.31627 + 0.956330i −0.316304 + 0.948658i \(0.602442\pi\)
−0.999971 + 0.00767174i \(0.997558\pi\)
\(878\) −9.29016 6.18592i −0.313528 0.208765i
\(879\) −1.45303 + 1.99992i −0.0490095 + 0.0674557i
\(880\) −6.69778 0.483837i −0.225782 0.0163101i
\(881\) 6.75208 42.6310i 0.227483 1.43627i −0.564349 0.825536i \(-0.690873\pi\)
0.791833 0.610738i \(-0.209127\pi\)
\(882\) 17.3334 + 18.6908i 0.583645 + 0.629352i
\(883\) 12.1046 19.7528i 0.407351 0.664736i −0.581517 0.813534i \(-0.697541\pi\)
0.988868 + 0.148798i \(0.0475405\pi\)
\(884\) 24.5356 + 10.0707i 0.825220 + 0.338715i
\(885\) 25.0057 1.96799i 0.840556 0.0661532i
\(886\) 40.1006 + 1.51103i 1.34721 + 0.0507642i
\(887\) −2.06129 + 1.76050i −0.0692112 + 0.0591119i −0.683381 0.730062i \(-0.739491\pi\)
0.614170 + 0.789174i \(0.289491\pi\)
\(888\) −1.98782 + 57.6790i −0.0667069 + 1.93558i
\(889\) −6.28840 + 3.85354i −0.210906 + 0.129244i
\(890\) 5.67358 6.15746i 0.190179 0.206399i
\(891\) −15.1080 12.9035i −0.506138 0.432282i
\(892\) −54.0349 4.07797i −1.80922 0.136541i
\(893\) 30.9955 30.9955i 1.03722 1.03722i
\(894\) −62.7579 12.3785i −2.09894 0.414000i
\(895\) 6.79318 1.63090i 0.227071 0.0545149i
\(896\) −7.81952 + 41.7606i −0.261232 + 1.39512i
\(897\) 12.7460 + 6.49440i 0.425576 + 0.216842i
\(898\) −12.0703 + 32.8804i −0.402789 + 1.09723i
\(899\) −8.94362 3.70457i −0.298287 0.123554i
\(900\) 19.9556 8.34110i 0.665186 0.278037i
\(901\) 14.8811i 0.495760i
\(902\) −9.22582 + 15.0890i −0.307186 + 0.502409i
\(903\) 66.5280i 2.21391i
\(904\) 8.57915 30.9904i 0.285338 1.03072i
\(905\) −7.66335 3.17426i −0.254738 0.105516i
\(906\) 57.3807 + 21.0642i 1.90635 + 0.699811i
\(907\) −43.6981 22.2653i −1.45097 0.739307i −0.461926 0.886918i \(-0.652842\pi\)
−0.989045 + 0.147611i \(0.952842\pi\)
\(908\) −12.3531 + 0.0396949i −0.409953 + 0.00131732i
\(909\) −35.5530 + 8.53551i −1.17922 + 0.283105i
\(910\) −3.03768 + 15.4007i −0.100698 + 0.510530i
\(911\) −18.7917 + 18.7917i −0.622596 + 0.622596i −0.946195 0.323598i \(-0.895107\pi\)
0.323598 + 0.946195i \(0.395107\pi\)
\(912\) −9.17752 55.6284i −0.303898 1.84204i
\(913\) 19.4423 + 16.6053i 0.643446 + 0.549555i
\(914\) 0.626291 + 0.577074i 0.0207159 + 0.0190879i
\(915\) 13.9984 8.57825i 0.462774 0.283588i
\(916\) 9.06915 + 12.3986i 0.299653 + 0.409663i
\(917\) 7.53471 6.43525i 0.248818 0.212511i
\(918\) −0.223322 + 5.92663i −0.00737072 + 0.195608i
\(919\) 27.0475 2.12868i 0.892214 0.0702188i 0.375942 0.926643i \(-0.377319\pi\)
0.516272 + 0.856425i \(0.327319\pi\)
\(920\) 2.11808 + 3.73970i 0.0698310 + 0.123294i
\(921\) 22.2056 36.2362i 0.731699 1.19402i
\(922\) −29.9142 + 27.7417i −0.985172 + 0.913623i
\(923\) 1.58690 10.0193i 0.0522335 0.329789i
\(924\) 32.8645 + 10.5617i 1.08116 + 0.347454i
\(925\) 21.7172 29.8911i 0.714057 0.982814i
\(926\) 23.2042 34.8486i 0.762538 1.14520i
\(927\) 23.6753 17.2011i 0.777598 0.564958i
\(928\) 19.1501 + 33.5596i 0.628631 + 1.10165i
\(929\) −8.34103 20.1370i −0.273660 0.660674i 0.725974 0.687722i \(-0.241389\pi\)
−0.999634 + 0.0270481i \(0.991389\pi\)
\(930\) −4.02693 0.470059i −0.132048 0.0154138i
\(931\) −42.4086 3.33763i −1.38989 0.109386i
\(932\) −28.9026 14.6098i −0.946735 0.478560i
\(933\) 38.4808 + 12.5032i 1.25980 + 0.409335i
\(934\) 2.31344 + 19.2807i 0.0756982 + 0.630885i
\(935\) 5.76854 2.93922i 0.188651 0.0961227i
\(936\) 24.2323 + 4.69879i 0.792056 + 0.153585i
\(937\) 0.904276 3.76658i 0.0295414 0.123049i −0.955651 0.294502i \(-0.904846\pi\)
0.985192 + 0.171453i \(0.0548462\pi\)
\(938\) −20.5923 44.4801i −0.672364 1.45233i
\(939\) 45.8136 14.8857i 1.49507 0.485778i
\(940\) −1.92821 + 12.4327i −0.0628914 + 0.405510i
\(941\) 1.29766 + 8.19308i 0.0423024 + 0.267087i 0.999770 0.0214546i \(-0.00682972\pi\)
−0.957467 + 0.288541i \(0.906830\pi\)
\(942\) 27.6409 + 21.7184i 0.900588 + 0.707623i
\(943\) 11.3109 0.437528i 0.368333 0.0142479i
\(944\) −22.8018 44.0490i −0.742136 1.43367i
\(945\) −3.46706 + 0.549128i −0.112783 + 0.0178631i
\(946\) −10.1892 18.1258i −0.331280 0.589319i
\(947\) −8.67838 26.7093i −0.282010 0.867936i −0.987279 0.158997i \(-0.949174\pi\)
0.705269 0.708939i \(-0.250826\pi\)
\(948\) −6.13070 1.45103i −0.199116 0.0471273i
\(949\) 39.2697 + 9.42783i 1.27475 + 0.306040i
\(950\) −15.0585 + 32.8029i −0.488562 + 1.06427i
\(951\) −21.9031 42.9873i −0.710258 1.39396i
\(952\) −14.3625 38.3608i −0.465491 1.24328i
\(953\) 13.3855 41.1964i 0.433600 1.33448i −0.460915 0.887444i \(-0.652479\pi\)
0.894515 0.447039i \(-0.147521\pi\)
\(954\) 2.72375 + 13.5791i 0.0881845 + 0.439641i
\(955\) −0.586833 + 7.45642i −0.0189895 + 0.241284i
\(956\) −13.1593 13.0750i −0.425603 0.422877i
\(957\) 29.0042 12.0139i 0.937573 0.388355i
\(958\) −1.92900 47.1646i −0.0623232 1.52382i
\(959\) −20.7027 28.4948i −0.668524 0.920145i
\(960\) 11.5524 + 11.3318i 0.372852 + 0.365732i
\(961\) 23.4545 + 17.0407i 0.756598 + 0.549701i
\(962\) 39.5364 14.6580i 1.27471 0.472592i
\(963\) 26.1589 + 4.14316i 0.842957 + 0.133511i
\(964\) 2.42090 + 29.5463i 0.0779718 + 0.951621i
\(965\) 1.31521 + 0.805960i 0.0423380 + 0.0259448i
\(966\) −6.03118 21.2542i −0.194050 0.683842i
\(967\) 4.34187 + 55.1686i 0.139625 + 1.77410i 0.524766 + 0.851246i \(0.324153\pi\)
−0.385141 + 0.922858i \(0.625847\pi\)
\(968\) −19.9136 + 4.06095i −0.640049 + 0.130524i
\(969\) 35.3018 + 41.3330i 1.13406 + 1.32781i
\(970\) 3.60054 12.8455i 0.115606 0.412445i
\(971\) 29.5129 + 48.1607i 0.947114 + 1.54555i 0.833854 + 0.551985i \(0.186129\pi\)
0.113260 + 0.993565i \(0.463871\pi\)
\(972\) 6.60038 + 40.8237i 0.211707 + 1.30942i
\(973\) −13.2522 + 15.5163i −0.424846 + 0.497431i
\(974\) −23.4849 + 15.7467i −0.752505 + 0.504558i
\(975\) −24.3823 24.3823i −0.780859 0.780859i
\(976\) −26.3873 18.9136i −0.844636 0.605409i
\(977\) 0.971233 + 4.04547i 0.0310725 + 0.129426i 0.985750 0.168215i \(-0.0538002\pi\)
−0.954678 + 0.297641i \(0.903800\pi\)
\(978\) −20.5909 + 16.2863i −0.658425 + 0.520778i
\(979\) −6.10726 + 11.9862i −0.195189 + 0.383080i
\(980\) 10.3900 6.41302i 0.331896 0.204856i
\(981\) 11.1467 26.9105i 0.355886 0.859185i
\(982\) 6.87310 + 3.83463i 0.219329 + 0.122368i
\(983\) 14.9742 0.477601 0.238801 0.971069i \(-0.423246\pi\)
0.238801 + 0.971069i \(0.423246\pi\)
\(984\) 40.4778 13.3408i 1.29038 0.425290i
\(985\) −10.2343 −0.326092
\(986\) −32.5315 18.1499i −1.03601 0.578011i
\(987\) 24.7500 59.7518i 0.787801 1.90192i
\(988\) −35.0529 + 21.6357i −1.11518 + 0.688323i
\(989\) −6.04175 + 11.8576i −0.192117 + 0.377050i
\(990\) 4.72588 3.73791i 0.150198 0.118799i
\(991\) 2.71449 + 11.3067i 0.0862287 + 0.359168i 0.998757 0.0498454i \(-0.0158729\pi\)
−0.912528 + 0.409014i \(0.865873\pi\)
\(992\) 2.23810 + 7.69845i 0.0710599 + 0.244426i
\(993\) −21.1664 21.1664i −0.671694 0.671694i
\(994\) −13.0127 + 8.72506i −0.412737 + 0.276742i
\(995\) −11.1848 + 13.0958i −0.354583 + 0.415163i
\(996\) −9.83411 60.8245i −0.311606 1.92730i
\(997\) −15.2124 24.8243i −0.481781 0.786195i 0.515727 0.856753i \(-0.327522\pi\)
−0.997508 + 0.0705583i \(0.977522\pi\)
\(998\) 8.68264 30.9767i 0.274844 0.980551i
\(999\) 6.12378 + 7.17003i 0.193748 + 0.226850i
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.11.16 yes 288
4.3 odd 2 inner 164.2.o.b.11.14 288
41.15 odd 40 inner 164.2.o.b.15.14 yes 288
164.15 even 40 inner 164.2.o.b.15.16 yes 288
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
164.2.o.b.11.14 288 4.3 odd 2 inner
164.2.o.b.11.16 yes 288 1.1 even 1 trivial
164.2.o.b.15.14 yes 288 41.15 odd 40 inner
164.2.o.b.15.16 yes 288 164.15 even 40 inner