Properties

Label 432.2.bg.a.205.25
Level $432$
Weight $2$
Character 432.205
Analytic conductor $3.450$
Analytic rank $0$
Dimension $840$
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] = [432,2,Mod(13,432)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(432, base_ring=CyclotomicField(36))
 
chi = DirichletCharacter(H, H._module([0, 27, 16]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("432.13");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 432.bg (of order \(36\), degree \(12\), 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: \(3.44953736732\)
Analytic rank: \(0\)
Dimension: \(840\)
Relative dimension: \(70\) over \(\Q(\zeta_{36})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label 205.25
Character \(\chi\) \(=\) 432.205
Dual form 432.2.bg.a.373.25

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.708823 + 1.22375i) q^{2} +(-1.03448 + 1.38919i) q^{3} +(-0.995139 - 1.73485i) q^{4} +(0.369435 - 0.172270i) q^{5} +(-0.966761 - 2.25064i) q^{6} +(-0.192057 - 0.0338649i) q^{7} +(2.82840 + 0.0118979i) q^{8} +(-0.859701 - 2.87418i) q^{9} +O(q^{10})\) \(q+(-0.708823 + 1.22375i) q^{2} +(-1.03448 + 1.38919i) q^{3} +(-0.995139 - 1.73485i) q^{4} +(0.369435 - 0.172270i) q^{5} +(-0.966761 - 2.25064i) q^{6} +(-0.192057 - 0.0338649i) q^{7} +(2.82840 + 0.0118979i) q^{8} +(-0.859701 - 2.87418i) q^{9} +(-0.0510479 + 0.574205i) q^{10} +(2.20949 - 4.73827i) q^{11} +(3.43949 + 0.412229i) q^{12} +(-3.16428 - 0.276839i) q^{13} +(0.177577 - 0.211026i) q^{14} +(-0.142857 + 0.691425i) q^{15} +(-2.01940 + 3.45283i) q^{16} +(-2.82437 - 4.89195i) q^{17} +(4.12666 + 0.985226i) q^{18} +(6.31308 - 1.69158i) q^{19} +(-0.666501 - 0.469480i) q^{20} +(0.245724 - 0.231772i) q^{21} +(4.23233 + 6.06246i) q^{22} +(6.29539 - 1.11005i) q^{23} +(-2.94245 + 3.91688i) q^{24} +(-3.10713 + 3.70294i) q^{25} +(2.58170 - 3.67607i) q^{26} +(4.88213 + 1.77900i) q^{27} +(0.132373 + 0.366891i) q^{28} +(0.0432539 + 0.494394i) q^{29} +(-0.744873 - 0.664920i) q^{30} +(-0.0834595 - 0.473322i) q^{31} +(-2.79401 - 4.91869i) q^{32} +(4.29668 + 7.97105i) q^{33} +(7.98852 + 0.0112014i) q^{34} +(-0.0767866 + 0.0205749i) q^{35} +(-4.13075 + 4.35166i) q^{36} +(5.20800 + 1.39548i) q^{37} +(-2.40478 + 8.92468i) q^{38} +(3.65797 - 4.10941i) q^{39} +(1.04696 - 0.482854i) q^{40} +(-4.59889 - 5.48075i) q^{41} +(0.109456 + 0.464991i) q^{42} +(-2.26439 + 4.85599i) q^{43} +(-10.4189 + 0.882103i) q^{44} +(-0.812739 - 0.913721i) q^{45} +(-3.10390 + 8.49083i) q^{46} +(-0.983159 + 5.57577i) q^{47} +(-2.70761 - 6.37721i) q^{48} +(-6.54211 - 2.38113i) q^{49} +(-2.32907 - 6.42709i) q^{50} +(9.71761 + 1.13704i) q^{51} +(2.66863 + 5.76505i) q^{52} +(7.79778 - 7.79778i) q^{53} +(-5.63762 + 4.71352i) q^{54} -2.13111i q^{55} +(-0.542813 - 0.0980686i) q^{56} +(-4.18082 + 10.5200i) q^{57} +(-0.635675 - 0.297506i) q^{58} +(0.187215 - 0.0872996i) q^{59} +(1.34168 - 0.440229i) q^{60} +(11.1903 - 7.83552i) q^{61} +(0.638387 + 0.233368i) q^{62} +(0.0677781 + 0.581121i) q^{63} +(7.99972 + 0.0673039i) q^{64} +(-1.21669 + 0.442838i) q^{65} +(-12.8002 - 0.391991i) q^{66} +(-0.690597 - 0.0604194i) q^{67} +(-5.67616 + 9.76803i) q^{68} +(-4.97039 + 9.89382i) q^{69} +(0.0292495 - 0.108552i) q^{70} +(10.2594 - 5.92327i) q^{71} +(-2.39738 - 8.13957i) q^{72} +(-3.72854 - 2.15267i) q^{73} +(-5.39928 + 5.38416i) q^{74} +(-1.92982 - 8.14702i) q^{75} +(-9.21703 - 9.26888i) q^{76} +(-0.584810 + 0.835195i) q^{77} +(2.43604 + 7.38930i) q^{78} +(-9.69633 - 8.13619i) q^{79} +(-0.151216 + 1.62348i) q^{80} +(-7.52183 + 4.94187i) q^{81} +(9.96688 - 1.74302i) q^{82} +(-0.654837 - 7.48482i) q^{83} +(-0.646619 - 0.195650i) q^{84} +(-1.88616 - 1.32070i) q^{85} +(-4.33748 - 6.21309i) q^{86} +(-0.731553 - 0.451353i) q^{87} +(6.30570 - 13.3754i) q^{88} +(-6.13508 - 3.54209i) q^{89} +(1.69426 - 0.346924i) q^{90} +(0.598349 + 0.160327i) q^{91} +(-8.19055 - 9.81690i) q^{92} +(0.743872 + 0.373702i) q^{93} +(-6.12648 - 5.15538i) q^{94} +(2.04086 - 1.71249i) q^{95} +(9.72335 + 1.20687i) q^{96} +(1.98469 - 0.722370i) q^{97} +(7.55112 - 6.31812i) q^{98} +(-15.5181 - 2.27698i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 840 q - 12 q^{2} - 12 q^{3} - 12 q^{4} - 12 q^{5} - 12 q^{6} - 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 840 q - 12 q^{2} - 12 q^{3} - 12 q^{4} - 12 q^{5} - 12 q^{6} - 6 q^{8} - 6 q^{10} - 12 q^{11} - 30 q^{12} - 12 q^{13} - 12 q^{14} - 24 q^{15} - 12 q^{16} - 12 q^{17} - 12 q^{18} - 6 q^{19} - 54 q^{20} - 12 q^{21} - 12 q^{22} + 18 q^{24} - 24 q^{26} - 12 q^{27} - 24 q^{28} - 12 q^{29} - 12 q^{30} - 24 q^{31} - 12 q^{32} - 24 q^{33} - 6 q^{35} - 12 q^{36} - 6 q^{37} - 12 q^{38} - 12 q^{40} - 72 q^{42} - 12 q^{43} - 6 q^{44} - 12 q^{45} - 6 q^{46} - 24 q^{47} - 12 q^{48} - 24 q^{49} - 168 q^{50} + 6 q^{51} - 12 q^{52} - 24 q^{53} + 156 q^{54} - 54 q^{56} + 42 q^{58} - 48 q^{59} - 72 q^{60} - 12 q^{61} + 60 q^{62} - 24 q^{63} - 6 q^{64} - 24 q^{65} - 198 q^{66} - 12 q^{67} - 66 q^{68} - 12 q^{69} - 54 q^{70} - 144 q^{72} - 96 q^{74} - 96 q^{75} - 12 q^{76} - 12 q^{77} - 90 q^{78} - 24 q^{79} - 204 q^{80} - 24 q^{81} - 24 q^{82} + 48 q^{83} + 36 q^{84} + 18 q^{85} - 72 q^{86} - 12 q^{88} - 66 q^{90} - 6 q^{91} + 102 q^{92} - 12 q^{93} - 12 q^{94} - 24 q^{95} - 120 q^{96} - 24 q^{97} - 6 q^{98} - 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).

\(n\) \(271\) \(325\) \(353\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{2}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.708823 + 1.22375i −0.501214 + 0.865323i
\(3\) −1.03448 + 1.38919i −0.597258 + 0.802050i
\(4\) −0.995139 1.73485i −0.497569 0.867424i
\(5\) 0.369435 0.172270i 0.165216 0.0770416i −0.338251 0.941056i \(-0.609835\pi\)
0.503467 + 0.864014i \(0.332057\pi\)
\(6\) −0.966761 2.25064i −0.394679 0.918819i
\(7\) −0.192057 0.0338649i −0.0725909 0.0127997i 0.137235 0.990539i \(-0.456179\pi\)
−0.209826 + 0.977739i \(0.567290\pi\)
\(8\) 2.82840 + 0.0118979i 0.999991 + 0.00420653i
\(9\) −0.859701 2.87418i −0.286567 0.958060i
\(10\) −0.0510479 + 0.574205i −0.0161428 + 0.181580i
\(11\) 2.20949 4.73827i 0.666186 1.42864i −0.224706 0.974427i \(-0.572142\pi\)
0.890892 0.454215i \(-0.150080\pi\)
\(12\) 3.43949 + 0.412229i 0.992894 + 0.119000i
\(13\) −3.16428 0.276839i −0.877614 0.0767813i −0.360562 0.932735i \(-0.617415\pi\)
−0.517052 + 0.855954i \(0.672971\pi\)
\(14\) 0.177577 0.211026i 0.0474595 0.0563992i
\(15\) −0.142857 + 0.691425i −0.0368854 + 0.178525i
\(16\) −2.01940 + 3.45283i −0.504849 + 0.863207i
\(17\) −2.82437 4.89195i −0.685011 1.18647i −0.973433 0.228970i \(-0.926464\pi\)
0.288423 0.957503i \(-0.406869\pi\)
\(18\) 4.12666 + 0.985226i 0.972663 + 0.232220i
\(19\) 6.31308 1.69158i 1.44832 0.388076i 0.552881 0.833260i \(-0.313528\pi\)
0.895439 + 0.445184i \(0.146862\pi\)
\(20\) −0.666501 0.469480i −0.149034 0.104979i
\(21\) 0.245724 0.231772i 0.0536215 0.0505767i
\(22\) 4.23233 + 6.06246i 0.902335 + 1.29252i
\(23\) 6.29539 1.11005i 1.31268 0.231461i 0.526879 0.849940i \(-0.323362\pi\)
0.785801 + 0.618479i \(0.212251\pi\)
\(24\) −2.94245 + 3.91688i −0.600626 + 0.799530i
\(25\) −3.10713 + 3.70294i −0.621427 + 0.740587i
\(26\) 2.58170 3.67607i 0.506313 0.720937i
\(27\) 4.88213 + 1.77900i 0.939566 + 0.342368i
\(28\) 0.132373 + 0.366891i 0.0250162 + 0.0693358i
\(29\) 0.0432539 + 0.494394i 0.00803204 + 0.0918067i 0.999153 0.0411598i \(-0.0131053\pi\)
−0.991121 + 0.132967i \(0.957550\pi\)
\(30\) −0.744873 0.664920i −0.135995 0.121397i
\(31\) −0.0834595 0.473322i −0.0149898 0.0850112i 0.976395 0.215992i \(-0.0692985\pi\)
−0.991385 + 0.130981i \(0.958187\pi\)
\(32\) −2.79401 4.91869i −0.493916 0.869510i
\(33\) 4.29668 + 7.97105i 0.747956 + 1.38758i
\(34\) 7.98852 + 0.0112014i 1.37002 + 0.00192102i
\(35\) −0.0767866 + 0.0205749i −0.0129793 + 0.00347779i
\(36\) −4.13075 + 4.35166i −0.688458 + 0.725277i
\(37\) 5.20800 + 1.39548i 0.856190 + 0.229415i 0.660107 0.751172i \(-0.270511\pi\)
0.196083 + 0.980587i \(0.437178\pi\)
\(38\) −2.40478 + 8.92468i −0.390107 + 1.44777i
\(39\) 3.65797 4.10941i 0.585744 0.658032i
\(40\) 1.04696 0.482854i 0.165539 0.0763459i
\(41\) −4.59889 5.48075i −0.718226 0.855949i 0.276231 0.961091i \(-0.410915\pi\)
−0.994457 + 0.105143i \(0.966470\pi\)
\(42\) 0.109456 + 0.464991i 0.0168894 + 0.0717497i
\(43\) −2.26439 + 4.85599i −0.345316 + 0.740532i −0.999880 0.0154742i \(-0.995074\pi\)
0.654565 + 0.756006i \(0.272852\pi\)
\(44\) −10.4189 + 0.882103i −1.57071 + 0.132982i
\(45\) −0.812739 0.913721i −0.121156 0.136209i
\(46\) −3.10390 + 8.49083i −0.457645 + 1.25190i
\(47\) −0.983159 + 5.57577i −0.143408 + 0.813310i 0.825223 + 0.564807i \(0.191050\pi\)
−0.968631 + 0.248502i \(0.920062\pi\)
\(48\) −2.70761 6.37721i −0.390810 0.920471i
\(49\) −6.54211 2.38113i −0.934587 0.340162i
\(50\) −2.32907 6.42709i −0.329380 0.908928i
\(51\) 9.71761 + 1.13704i 1.36074 + 0.159218i
\(52\) 2.66863 + 5.76505i 0.370072 + 0.799468i
\(53\) 7.79778 7.79778i 1.07111 1.07111i 0.0738371 0.997270i \(-0.476476\pi\)
0.997270 0.0738371i \(-0.0235245\pi\)
\(54\) −5.63762 + 4.71352i −0.767182 + 0.641429i
\(55\) 2.13111i 0.287359i
\(56\) −0.542813 0.0980686i −0.0725364 0.0131050i
\(57\) −4.18082 + 10.5200i −0.553764 + 1.39341i
\(58\) −0.635675 0.297506i −0.0834683 0.0390645i
\(59\) 0.187215 0.0872996i 0.0243733 0.0113654i −0.410393 0.911909i \(-0.634609\pi\)
0.434767 + 0.900543i \(0.356831\pi\)
\(60\) 1.34168 0.440229i 0.173210 0.0568333i
\(61\) 11.1903 7.83552i 1.43277 1.00324i 0.438231 0.898862i \(-0.355605\pi\)
0.994538 0.104374i \(-0.0332838\pi\)
\(62\) 0.638387 + 0.233368i 0.0810753 + 0.0296378i
\(63\) 0.0677781 + 0.581121i 0.00853923 + 0.0732144i
\(64\) 7.99972 + 0.0673039i 0.999965 + 0.00841299i
\(65\) −1.21669 + 0.442838i −0.150911 + 0.0549273i
\(66\) −12.8002 0.391991i −1.57559 0.0482508i
\(67\) −0.690597 0.0604194i −0.0843699 0.00738141i 0.0448926 0.998992i \(-0.485705\pi\)
−0.129262 + 0.991610i \(0.541261\pi\)
\(68\) −5.67616 + 9.76803i −0.688335 + 1.18455i
\(69\) −4.97039 + 9.89382i −0.598365 + 1.19108i
\(70\) 0.0292495 0.108552i 0.00349599 0.0129744i
\(71\) 10.2594 5.92327i 1.21757 0.702963i 0.253170 0.967422i \(-0.418527\pi\)
0.964397 + 0.264459i \(0.0851933\pi\)
\(72\) −2.39738 8.13957i −0.282534 0.959257i
\(73\) −3.72854 2.15267i −0.436393 0.251951i 0.265674 0.964063i \(-0.414406\pi\)
−0.702066 + 0.712112i \(0.747739\pi\)
\(74\) −5.39928 + 5.38416i −0.627653 + 0.625895i
\(75\) −1.92982 8.14702i −0.222836 0.940736i
\(76\) −9.21703 9.26888i −1.05727 1.06321i
\(77\) −0.584810 + 0.835195i −0.0666453 + 0.0951793i
\(78\) 2.43604 + 7.38930i 0.275827 + 0.836673i
\(79\) −9.69633 8.13619i −1.09092 0.915393i −0.0941413 0.995559i \(-0.530011\pi\)
−0.996782 + 0.0801659i \(0.974455\pi\)
\(80\) −0.151216 + 1.62348i −0.0169064 + 0.181510i
\(81\) −7.52183 + 4.94187i −0.835759 + 0.549097i
\(82\) 9.96688 1.74302i 1.10066 0.192485i
\(83\) −0.654837 7.48482i −0.0718777 0.821566i −0.943497 0.331382i \(-0.892485\pi\)
0.871619 0.490184i \(-0.163070\pi\)
\(84\) −0.646619 0.195650i −0.0705519 0.0213471i
\(85\) −1.88616 1.32070i −0.204583 0.143250i
\(86\) −4.33748 6.21309i −0.467723 0.669975i
\(87\) −0.731553 0.451353i −0.0784307 0.0483901i
\(88\) 6.30570 13.3754i 0.672190 1.42583i
\(89\) −6.13508 3.54209i −0.650318 0.375461i 0.138260 0.990396i \(-0.455849\pi\)
−0.788578 + 0.614935i \(0.789182\pi\)
\(90\) 1.69426 0.346924i 0.178590 0.0365690i
\(91\) 0.598349 + 0.160327i 0.0627240 + 0.0168068i
\(92\) −8.19055 9.81690i −0.853924 1.02348i
\(93\) 0.743872 + 0.373702i 0.0771360 + 0.0387510i
\(94\) −6.12648 5.15538i −0.631898 0.531737i
\(95\) 2.04086 1.71249i 0.209388 0.175697i
\(96\) 9.72335 + 1.20687i 0.992385 + 0.123176i
\(97\) 1.98469 0.722370i 0.201515 0.0733455i −0.239291 0.970948i \(-0.576915\pi\)
0.440806 + 0.897602i \(0.354693\pi\)
\(98\) 7.55112 6.31812i 0.762778 0.638226i
\(99\) −15.5181 2.27698i −1.55963 0.228845i
\(100\) 9.51606 + 1.70547i 0.951606 + 0.170547i
\(101\) −8.31518 11.8753i −0.827392 1.18164i −0.981096 0.193521i \(-0.938009\pi\)
0.153704 0.988117i \(-0.450880\pi\)
\(102\) −8.27953 + 11.0860i −0.819795 + 1.09768i
\(103\) −2.02300 + 5.55815i −0.199332 + 0.547660i −0.998576 0.0533463i \(-0.983011\pi\)
0.799244 + 0.601007i \(0.205234\pi\)
\(104\) −8.94657 0.820660i −0.877284 0.0804724i
\(105\) 0.0508517 0.127955i 0.00496262 0.0124872i
\(106\) 4.01530 + 15.0698i 0.390001 + 1.46371i
\(107\) 2.26558 2.26558i 0.219022 0.219022i −0.589064 0.808086i \(-0.700503\pi\)
0.808086 + 0.589064i \(0.200503\pi\)
\(108\) −1.77211 10.2401i −0.170521 0.985354i
\(109\) 11.8467 + 11.8467i 1.13470 + 1.13470i 0.989385 + 0.145318i \(0.0464207\pi\)
0.145318 + 0.989385i \(0.453579\pi\)
\(110\) 2.60795 + 1.51058i 0.248658 + 0.144028i
\(111\) −7.32616 + 5.79131i −0.695369 + 0.549687i
\(112\) 0.504770 0.594755i 0.0476963 0.0561990i
\(113\) 10.1615 + 3.69850i 0.955917 + 0.347925i 0.772432 0.635097i \(-0.219040\pi\)
0.183485 + 0.983023i \(0.441262\pi\)
\(114\) −9.91039 12.5731i −0.928193 1.17758i
\(115\) 2.13451 1.49460i 0.199044 0.139372i
\(116\) 0.814655 0.567030i 0.0756388 0.0526474i
\(117\) 1.92465 + 9.33272i 0.177934 + 0.862810i
\(118\) −0.0258690 + 0.290984i −0.00238144 + 0.0267873i
\(119\) 0.376776 + 1.03518i 0.0345390 + 0.0948951i
\(120\) −0.412283 + 1.95393i −0.0376361 + 0.178368i
\(121\) −10.4987 12.5118i −0.954424 1.13744i
\(122\) 1.65680 + 19.2481i 0.150000 + 1.74264i
\(123\) 12.3713 0.719013i 1.11548 0.0648312i
\(124\) −0.738089 + 0.615811i −0.0662823 + 0.0553015i
\(125\) −1.03748 + 3.87194i −0.0927954 + 0.346317i
\(126\) −0.759191 0.328969i −0.0676341 0.0293069i
\(127\) −5.16934 + 8.95355i −0.458704 + 0.794499i −0.998893 0.0470448i \(-0.985020\pi\)
0.540188 + 0.841544i \(0.318353\pi\)
\(128\) −5.75275 + 9.74196i −0.508476 + 0.861076i
\(129\) −4.40344 8.16909i −0.387701 0.719249i
\(130\) 0.320492 1.80282i 0.0281090 0.158118i
\(131\) 2.41851 3.45399i 0.211306 0.301777i −0.699482 0.714650i \(-0.746586\pi\)
0.910788 + 0.412874i \(0.135475\pi\)
\(132\) 9.55276 15.3864i 0.831461 1.33921i
\(133\) −1.26976 + 0.111090i −0.110102 + 0.00963268i
\(134\) 0.563450 0.802293i 0.0486746 0.0693075i
\(135\) 2.11009 0.183823i 0.181608 0.0158209i
\(136\) −7.93025 13.8700i −0.680014 1.18934i
\(137\) −6.60058 + 7.86626i −0.563925 + 0.672060i −0.970372 0.241614i \(-0.922323\pi\)
0.406447 + 0.913674i \(0.366768\pi\)
\(138\) −8.58446 13.0955i −0.730757 1.11476i
\(139\) −8.69137 6.08576i −0.737192 0.516187i 0.143632 0.989631i \(-0.454122\pi\)
−0.880824 + 0.473444i \(0.843011\pi\)
\(140\) 0.112108 + 0.112738i 0.00947482 + 0.00952811i
\(141\) −6.72875 7.13382i −0.566663 0.600776i
\(142\) −0.0234915 + 16.7535i −0.00197136 + 1.40592i
\(143\) −8.30319 + 14.3815i −0.694348 + 1.20265i
\(144\) 11.6601 + 2.83571i 0.971678 + 0.236309i
\(145\) 0.101149 + 0.175195i 0.00839995 + 0.0145491i
\(146\) 5.27721 3.03694i 0.436745 0.251339i
\(147\) 10.0755 6.62500i 0.831016 0.546421i
\(148\) −2.76174 10.4238i −0.227014 0.856830i
\(149\) −1.55976 + 17.8282i −0.127781 + 1.46054i 0.613685 + 0.789551i \(0.289686\pi\)
−0.741466 + 0.670990i \(0.765869\pi\)
\(150\) 11.3378 + 3.41318i 0.925730 + 0.278685i
\(151\) 0.0207999 + 0.0571473i 0.00169267 + 0.00465058i 0.940536 0.339694i \(-0.110323\pi\)
−0.938843 + 0.344344i \(0.888101\pi\)
\(152\) 17.8761 4.70937i 1.44994 0.381980i
\(153\) −11.6322 + 12.3234i −0.940411 + 0.996285i
\(154\) −0.607545 1.30767i −0.0489574 0.105375i
\(155\) −0.112372 0.160484i −0.00902595 0.0128904i
\(156\) −10.7694 2.25659i −0.862241 0.180672i
\(157\) 2.48487 + 5.32883i 0.198314 + 0.425287i 0.980166 0.198178i \(-0.0635023\pi\)
−0.781852 + 0.623465i \(0.785725\pi\)
\(158\) 16.8297 6.09879i 1.33890 0.485194i
\(159\) 2.76595 + 18.8993i 0.219354 + 1.49881i
\(160\) −1.87955 1.33581i −0.148591 0.105605i
\(161\) −1.24667 −0.0982512
\(162\) −0.715977 12.7078i −0.0562524 0.998417i
\(163\) 3.50392 + 3.50392i 0.274448 + 0.274448i 0.830888 0.556440i \(-0.187833\pi\)
−0.556440 + 0.830888i \(0.687833\pi\)
\(164\) −4.93173 + 13.4325i −0.385103 + 1.04890i
\(165\) 2.96052 + 2.20459i 0.230476 + 0.171627i
\(166\) 9.62373 + 4.50406i 0.746947 + 0.349583i
\(167\) 3.46846 9.52952i 0.268398 0.737417i −0.730137 0.683301i \(-0.760544\pi\)
0.998535 0.0541158i \(-0.0172340\pi\)
\(168\) 0.697765 0.652620i 0.0538337 0.0503507i
\(169\) −2.86645 0.505432i −0.220496 0.0388794i
\(170\) 2.95317 1.37205i 0.226497 0.105231i
\(171\) −10.2893 16.6907i −0.786841 1.27637i
\(172\) 10.6778 0.904019i 0.814174 0.0689308i
\(173\) −0.0760281 0.0354525i −0.00578031 0.00269540i 0.419726 0.907651i \(-0.362126\pi\)
−0.425506 + 0.904955i \(0.639904\pi\)
\(174\) 1.07089 0.575310i 0.0811837 0.0436141i
\(175\) 0.722147 0.605954i 0.0545892 0.0458058i
\(176\) 11.8986 + 17.1974i 0.896890 + 1.29631i
\(177\) −0.0723941 + 0.350387i −0.00544147 + 0.0263367i
\(178\) 8.68333 4.99710i 0.650843 0.374549i
\(179\) −1.25496 + 4.68356i −0.0937999 + 0.350066i −0.996835 0.0795012i \(-0.974667\pi\)
0.903035 + 0.429567i \(0.141334\pi\)
\(180\) −0.776379 + 2.31926i −0.0578679 + 0.172867i
\(181\) −4.84103 18.0670i −0.359831 1.34291i −0.874295 0.485395i \(-0.838676\pi\)
0.514465 0.857512i \(-0.327991\pi\)
\(182\) −0.620324 + 0.618587i −0.0459815 + 0.0458527i
\(183\) −0.691097 + 23.6511i −0.0510874 + 1.74834i
\(184\) 17.8191 3.06476i 1.31364 0.225937i
\(185\) 2.16442 0.381645i 0.159131 0.0280591i
\(186\) −0.984592 + 0.645427i −0.0721938 + 0.0473250i
\(187\) −29.4198 + 2.57390i −2.15139 + 0.188222i
\(188\) 10.6515 3.84303i 0.776840 0.280282i
\(189\) −0.877403 0.507002i −0.0638217 0.0368790i
\(190\) 0.649048 + 3.71136i 0.0470869 + 0.269250i
\(191\) 14.0263 + 11.7695i 1.01491 + 0.851609i 0.988979 0.148055i \(-0.0473013\pi\)
0.0259285 + 0.999664i \(0.491746\pi\)
\(192\) −8.36905 + 11.0435i −0.603984 + 0.796996i
\(193\) 4.10355 + 23.2724i 0.295380 + 1.67519i 0.665653 + 0.746262i \(0.268153\pi\)
−0.370272 + 0.928923i \(0.620736\pi\)
\(194\) −0.522796 + 2.94081i −0.0375346 + 0.211138i
\(195\) 0.643453 2.14832i 0.0460786 0.153844i
\(196\) 2.37940 + 13.7191i 0.169957 + 0.979938i
\(197\) −0.291406 1.08754i −0.0207618 0.0774842i 0.954768 0.297353i \(-0.0961038\pi\)
−0.975529 + 0.219869i \(0.929437\pi\)
\(198\) 13.7861 17.3764i 0.979734 1.23489i
\(199\) −6.21627 + 3.58897i −0.440660 + 0.254415i −0.703877 0.710321i \(-0.748550\pi\)
0.263218 + 0.964736i \(0.415216\pi\)
\(200\) −8.83228 + 10.4364i −0.624536 + 0.737967i
\(201\) 0.798343 0.896868i 0.0563108 0.0632602i
\(202\) 20.4264 1.75822i 1.43720 0.123708i
\(203\) 0.00843538 0.0964168i 0.000592048 0.00676714i
\(204\) −7.69778 17.9901i −0.538952 1.25956i
\(205\) −2.64316 1.23253i −0.184606 0.0860833i
\(206\) −5.36784 6.41539i −0.373995 0.446982i
\(207\) −8.60263 17.1398i −0.597924 1.19130i
\(208\) 7.34583 10.3667i 0.509341 0.718800i
\(209\) 5.93351 33.6506i 0.410429 2.32766i
\(210\) 0.120541 + 0.152928i 0.00831811 + 0.0105530i
\(211\) −3.73651 8.01297i −0.257232 0.551635i 0.734702 0.678390i \(-0.237322\pi\)
−0.991934 + 0.126754i \(0.959544\pi\)
\(212\) −21.2878 5.76809i −1.46205 0.396154i
\(213\) −2.38460 + 20.3798i −0.163390 + 1.39640i
\(214\) 1.16661 + 4.37841i 0.0797481 + 0.299302i
\(215\) 2.18406i 0.148952i
\(216\) 13.7875 + 5.08980i 0.938118 + 0.346317i
\(217\) 0.0937314i 0.00636290i
\(218\) −22.8945 + 6.10018i −1.55061 + 0.413156i
\(219\) 6.84757 2.95275i 0.462716 0.199529i
\(220\) −3.69715 + 2.12075i −0.249262 + 0.142981i
\(221\) 7.58283 + 16.2614i 0.510076 + 1.09386i
\(222\) −1.89417 13.0704i −0.127129 0.877229i
\(223\) 2.71621 15.4044i 0.181891 1.03155i −0.747995 0.663705i \(-0.768983\pi\)
0.929885 0.367849i \(-0.119906\pi\)
\(224\) 0.370040 + 1.03929i 0.0247243 + 0.0694404i
\(225\) 13.3141 + 5.74704i 0.887608 + 0.383136i
\(226\) −11.7288 + 9.81362i −0.780187 + 0.652792i
\(227\) 25.8923 + 12.0738i 1.71853 + 0.801366i 0.993652 + 0.112493i \(0.0358837\pi\)
0.724882 + 0.688873i \(0.241894\pi\)
\(228\) 22.4111 3.21575i 1.48421 0.212968i
\(229\) −1.81315 + 20.7244i −0.119816 + 1.36951i 0.663636 + 0.748056i \(0.269012\pi\)
−0.783452 + 0.621452i \(0.786543\pi\)
\(230\) 0.316029 + 3.67151i 0.0208383 + 0.242092i
\(231\) −0.555271 1.67641i −0.0365341 0.110299i
\(232\) 0.116457 + 1.39886i 0.00764579 + 0.0918397i
\(233\) 2.42900 1.40238i 0.159129 0.0918733i −0.418321 0.908299i \(-0.637381\pi\)
0.577450 + 0.816426i \(0.304048\pi\)
\(234\) −12.7852 4.25995i −0.835793 0.278482i
\(235\) 0.597326 + 2.22925i 0.0389653 + 0.145420i
\(236\) −0.337756 0.237914i −0.0219861 0.0154869i
\(237\) 21.3334 5.05333i 1.38575 0.328249i
\(238\) −1.53388 0.272682i −0.0994264 0.0176753i
\(239\) 2.98553 + 16.9318i 0.193118 + 1.09522i 0.915074 + 0.403286i \(0.132132\pi\)
−0.721956 + 0.691939i \(0.756757\pi\)
\(240\) −2.09889 1.88952i −0.135483 0.121968i
\(241\) 4.47696 + 3.75662i 0.288387 + 0.241985i 0.775491 0.631359i \(-0.217502\pi\)
−0.487104 + 0.873344i \(0.661947\pi\)
\(242\) 22.7531 3.97909i 1.46262 0.255786i
\(243\) 0.915984 15.5615i 0.0587604 0.998272i
\(244\) −24.7293 11.6160i −1.58313 0.743639i
\(245\) −2.82708 + 0.247337i −0.180615 + 0.0158018i
\(246\) −7.88915 + 15.6490i −0.502994 + 0.997745i
\(247\) −20.4447 + 3.60495i −1.30086 + 0.229377i
\(248\) −0.230426 1.33974i −0.0146320 0.0850735i
\(249\) 11.0753 + 6.83321i 0.701866 + 0.433037i
\(250\) −4.00290 4.01415i −0.253166 0.253877i
\(251\) 0.903677 + 3.37257i 0.0570396 + 0.212875i 0.988563 0.150806i \(-0.0481868\pi\)
−0.931524 + 0.363680i \(0.881520\pi\)
\(252\) 0.940709 0.695881i 0.0592591 0.0438364i
\(253\) 8.64991 32.2819i 0.543815 2.02954i
\(254\) −7.29278 12.6725i −0.457590 0.795142i
\(255\) 3.78590 1.25399i 0.237082 0.0785281i
\(256\) −7.84407 13.9453i −0.490254 0.871580i
\(257\) −1.69336 + 1.42090i −0.105629 + 0.0886332i −0.694073 0.719905i \(-0.744185\pi\)
0.588444 + 0.808538i \(0.299741\pi\)
\(258\) 13.1182 + 0.401731i 0.816704 + 0.0250107i
\(259\) −0.952978 0.444381i −0.0592151 0.0276125i
\(260\) 1.97903 + 1.67008i 0.122734 + 0.103574i
\(261\) 1.38379 0.549351i 0.0856546 0.0340039i
\(262\) 2.51253 + 5.40793i 0.155225 + 0.334103i
\(263\) −10.7948 1.90341i −0.665636 0.117370i −0.169387 0.985550i \(-0.554179\pi\)
−0.496249 + 0.868180i \(0.665290\pi\)
\(264\) 12.0579 + 22.5964i 0.742113 + 1.39072i
\(265\) 1.53744 4.22409i 0.0944445 0.259484i
\(266\) 0.764089 1.63261i 0.0468493 0.100102i
\(267\) 11.2673 4.85858i 0.689545 0.297340i
\(268\) 0.582421 + 1.25821i 0.0355770 + 0.0768572i
\(269\) 1.09526 + 1.09526i 0.0667790 + 0.0667790i 0.739708 0.672929i \(-0.234964\pi\)
−0.672929 + 0.739708i \(0.734964\pi\)
\(270\) −1.27073 + 2.71253i −0.0773342 + 0.165079i
\(271\) 21.3879 1.29922 0.649611 0.760266i \(-0.274932\pi\)
0.649611 + 0.760266i \(0.274932\pi\)
\(272\) 22.5946 + 0.126728i 1.37000 + 0.00768404i
\(273\) −0.841705 + 0.665366i −0.0509423 + 0.0402698i
\(274\) −4.94771 13.6533i −0.298902 0.824824i
\(275\) 10.6803 + 22.9040i 0.644048 + 1.38116i
\(276\) 22.1105 1.22285i 1.33090 0.0736069i
\(277\) 4.09023 + 5.84145i 0.245758 + 0.350979i 0.923012 0.384770i \(-0.125719\pi\)
−0.677254 + 0.735749i \(0.736830\pi\)
\(278\) 13.6081 6.32235i 0.816160 0.379189i
\(279\) −1.28866 + 0.646793i −0.0771503 + 0.0387225i
\(280\) −0.217428 + 0.0572805i −0.0129938 + 0.00342316i
\(281\) −8.46146 23.2477i −0.504768 1.38684i −0.886570 0.462595i \(-0.846918\pi\)
0.381801 0.924244i \(-0.375304\pi\)
\(282\) 13.4995 3.17770i 0.803885 0.189229i
\(283\) −1.16210 + 13.2829i −0.0690796 + 0.789584i 0.880088 + 0.474811i \(0.157484\pi\)
−0.949167 + 0.314772i \(0.898072\pi\)
\(284\) −20.4855 11.9040i −1.21559 0.706375i
\(285\) 0.267738 + 4.60668i 0.0158594 + 0.272876i
\(286\) −11.7140 20.3550i −0.692661 1.20362i
\(287\) 0.697646 + 1.20836i 0.0411808 + 0.0713272i
\(288\) −11.7352 + 12.2591i −0.691502 + 0.722374i
\(289\) −7.45415 + 12.9110i −0.438479 + 0.759468i
\(290\) −0.286092 0.000401153i −0.0167999 2.35565e-5i
\(291\) −1.04962 + 3.50440i −0.0615297 + 0.205431i
\(292\) −0.0241475 + 8.61066i −0.00141312 + 0.503901i
\(293\) −13.8126 9.67168i −0.806940 0.565026i 0.0957058 0.995410i \(-0.469489\pi\)
−0.902646 + 0.430384i \(0.858378\pi\)
\(294\) 0.965587 + 17.0259i 0.0563142 + 0.992971i
\(295\) 0.0541244 0.0645030i 0.00315125 0.00375551i
\(296\) 14.7137 + 4.00894i 0.855218 + 0.233015i
\(297\) 19.2164 19.2022i 1.11505 1.11422i
\(298\) −20.7117 14.5458i −1.19980 0.842615i
\(299\) −20.2277 + 1.76970i −1.16980 + 0.102344i
\(300\) −12.2134 + 11.4554i −0.705141 + 0.661375i
\(301\) 0.599340 0.855946i 0.0345454 0.0493359i
\(302\) −0.0846775 0.0150534i −0.00487265 0.000866225i
\(303\) 25.0990 + 0.733403i 1.44190 + 0.0421329i
\(304\) −6.90787 + 25.2140i −0.396193 + 1.44612i
\(305\) 2.78425 4.82247i 0.159426 0.276134i
\(306\) −6.83554 22.9701i −0.390762 1.31311i
\(307\) −2.18251 + 8.14523i −0.124562 + 0.464873i −0.999824 0.0187775i \(-0.994023\pi\)
0.875261 + 0.483650i \(0.160689\pi\)
\(308\) 2.03090 + 0.183421i 0.115721 + 0.0104514i
\(309\) −5.62857 8.56013i −0.320198 0.486969i
\(310\) 0.276045 0.0237608i 0.0156783 0.00134952i
\(311\) 21.4698 + 25.5867i 1.21744 + 1.45089i 0.854797 + 0.518962i \(0.173681\pi\)
0.362644 + 0.931928i \(0.381874\pi\)
\(312\) 10.3951 11.5795i 0.588507 0.655562i
\(313\) −6.37345 17.5109i −0.360249 0.989775i −0.978941 0.204142i \(-0.934560\pi\)
0.618693 0.785633i \(-0.287663\pi\)
\(314\) −8.28250 0.736329i −0.467409 0.0415534i
\(315\) 0.125149 + 0.203010i 0.00705137 + 0.0114383i
\(316\) −4.46586 + 24.9183i −0.251224 + 1.40176i
\(317\) −9.25318 + 6.47915i −0.519711 + 0.363905i −0.803807 0.594890i \(-0.797195\pi\)
0.284096 + 0.958796i \(0.408307\pi\)
\(318\) −25.0886 10.0114i −1.40690 0.561411i
\(319\) 2.43814 + 0.887411i 0.136510 + 0.0496855i
\(320\) 2.96697 1.35325i 0.165858 0.0756489i
\(321\) 0.803626 + 5.49103i 0.0448540 + 0.306479i
\(322\) 0.883668 1.52561i 0.0492449 0.0850191i
\(323\) −26.1056 26.1056i −1.45256 1.45256i
\(324\) 16.0587 + 8.13139i 0.892148 + 0.451744i
\(325\) 10.8570 10.8570i 0.602236 0.602236i
\(326\) −6.77159 + 1.80427i −0.375044 + 0.0999293i
\(327\) −28.7124 + 4.20213i −1.58780 + 0.232378i
\(328\) −12.9423 15.5565i −0.714619 0.858962i
\(329\) 0.377646 1.03757i 0.0208203 0.0572033i
\(330\) −4.79636 + 2.06027i −0.264031 + 0.113414i
\(331\) 4.92230 + 7.02977i 0.270554 + 0.386391i 0.931321 0.364200i \(-0.118658\pi\)
−0.660767 + 0.750591i \(0.729769\pi\)
\(332\) −12.3334 + 8.58448i −0.676882 + 0.471135i
\(333\) −0.466462 16.1684i −0.0255620 0.886025i
\(334\) 9.20325 + 10.9993i 0.503579 + 0.601854i
\(335\) −0.265539 + 0.0966482i −0.0145079 + 0.00528046i
\(336\) 0.304053 + 1.31648i 0.0165875 + 0.0718201i
\(337\) −9.90181 + 8.30861i −0.539386 + 0.452599i −0.871328 0.490701i \(-0.836741\pi\)
0.331942 + 0.943300i \(0.392296\pi\)
\(338\) 2.65033 3.14956i 0.144159 0.171313i
\(339\) −15.6498 + 10.2903i −0.849982 + 0.558892i
\(340\) −0.414229 + 4.58648i −0.0224647 + 0.248737i
\(341\) −2.42713 0.650348i −0.131436 0.0352183i
\(342\) 27.7185 0.760787i 1.49885 0.0411387i
\(343\) 2.35807 + 1.36143i 0.127324 + 0.0735105i
\(344\) −6.46237 + 13.7078i −0.348428 + 0.739073i
\(345\) −0.131824 + 4.51137i −0.00709718 + 0.242884i
\(346\) 0.0972756 0.0679100i 0.00522957 0.00365086i
\(347\) −23.5909 16.5185i −1.26643 0.886760i −0.269339 0.963045i \(-0.586805\pi\)
−0.997086 + 0.0762849i \(0.975694\pi\)
\(348\) −0.0550325 + 1.71829i −0.00295005 + 0.0921102i
\(349\) 1.25599 + 14.3561i 0.0672319 + 0.768464i 0.952730 + 0.303820i \(0.0982621\pi\)
−0.885498 + 0.464644i \(0.846182\pi\)
\(350\) 0.229662 + 1.31324i 0.0122760 + 0.0701958i
\(351\) −14.9559 6.98081i −0.798289 0.372608i
\(352\) −29.4794 + 2.37098i −1.57126 + 0.126374i
\(353\) −24.4363 20.5045i −1.30061 1.09134i −0.990039 0.140792i \(-0.955035\pi\)
−0.310572 0.950550i \(-0.600520\pi\)
\(354\) −0.377472 0.336955i −0.0200624 0.0179089i
\(355\) 2.76978 3.95565i 0.147004 0.209944i
\(356\) −0.0397332 + 14.1683i −0.00210586 + 0.750919i
\(357\) −1.82783 0.547463i −0.0967392 0.0289748i
\(358\) −4.84198 4.85558i −0.255907 0.256625i
\(359\) 16.2182 + 9.36358i 0.855964 + 0.494191i 0.862659 0.505787i \(-0.168798\pi\)
−0.00669474 + 0.999978i \(0.502131\pi\)
\(360\) −2.28788 2.59404i −0.120582 0.136718i
\(361\) 20.5390 11.8582i 1.08100 0.624117i
\(362\) 25.5409 + 6.88206i 1.34240 + 0.361713i
\(363\) 28.2420 1.64141i 1.48232 0.0861518i
\(364\) −0.317297 1.19759i −0.0166309 0.0627709i
\(365\) −1.74829 0.152956i −0.0915098 0.00800607i
\(366\) −28.4533 17.6102i −1.48728 0.920500i
\(367\) −28.5316 + 10.3847i −1.48934 + 0.542074i −0.953275 0.302104i \(-0.902311\pi\)
−0.536062 + 0.844178i \(0.680089\pi\)
\(368\) −8.88010 + 23.9785i −0.462907 + 1.24997i
\(369\) −11.7990 + 17.9298i −0.614230 + 0.933391i
\(370\) −1.06715 + 2.91923i −0.0554785 + 0.151763i
\(371\) −1.76169 + 1.23355i −0.0914625 + 0.0640427i
\(372\) −0.0919406 1.66239i −0.00476690 0.0861909i
\(373\) 26.5815 12.3951i 1.37634 0.641796i 0.413158 0.910659i \(-0.364426\pi\)
0.963178 + 0.268863i \(0.0866478\pi\)
\(374\) 17.7036 37.8270i 0.915433 1.95599i
\(375\) −4.30561 5.44671i −0.222341 0.281267i
\(376\) −2.84711 + 15.7588i −0.146828 + 0.812699i
\(377\) 1.57638i 0.0811876i
\(378\) 1.24237 0.714349i 0.0639006 0.0367422i
\(379\) 3.34000 3.34000i 0.171564 0.171564i −0.616102 0.787666i \(-0.711289\pi\)
0.787666 + 0.616102i \(0.211289\pi\)
\(380\) −5.00184 1.83642i −0.256589 0.0942065i
\(381\) −7.09061 16.4435i −0.363263 0.842424i
\(382\) −24.3451 + 8.82225i −1.24560 + 0.451385i
\(383\) 13.3359 + 4.85388i 0.681433 + 0.248021i 0.659463 0.751737i \(-0.270784\pi\)
0.0219705 + 0.999759i \(0.493006\pi\)
\(384\) −7.58234 18.0695i −0.386935 0.922107i
\(385\) −0.0721698 + 0.409295i −0.00367811 + 0.0208596i
\(386\) −31.3884 11.4743i −1.59763 0.584026i
\(387\) 15.9037 + 2.33356i 0.808430 + 0.118621i
\(388\) −3.22825 2.72429i −0.163889 0.138305i
\(389\) −9.71534 + 20.8346i −0.492587 + 1.05636i 0.490199 + 0.871611i \(0.336924\pi\)
−0.982786 + 0.184747i \(0.940854\pi\)
\(390\) 2.17291 + 2.31020i 0.110030 + 0.116982i
\(391\) −23.2108 27.6616i −1.17382 1.39891i
\(392\) −18.4754 6.81264i −0.933148 0.344090i
\(393\) 2.29635 + 6.93286i 0.115836 + 0.349716i
\(394\) 1.53744 + 0.414266i 0.0774550 + 0.0208704i
\(395\) −4.98378 1.33540i −0.250761 0.0671913i
\(396\) 11.4925 + 29.1875i 0.577519 + 1.46673i
\(397\) 13.7204 3.67636i 0.688605 0.184511i 0.102484 0.994735i \(-0.467321\pi\)
0.586121 + 0.810223i \(0.300654\pi\)
\(398\) 0.0142337 10.1511i 0.000713472 0.508829i
\(399\) 1.15922 1.87886i 0.0580334 0.0940605i
\(400\) −6.51107 18.2061i −0.325554 0.910305i
\(401\) 1.77760 + 10.0813i 0.0887693 + 0.503436i 0.996479 + 0.0838379i \(0.0267178\pi\)
−0.907710 + 0.419598i \(0.862171\pi\)
\(402\) 0.531660 + 1.61270i 0.0265168 + 0.0804339i
\(403\) 0.133055 + 1.52083i 0.00662797 + 0.0757580i
\(404\) −12.3271 + 26.2432i −0.613296 + 1.30565i
\(405\) −1.92749 + 3.12148i −0.0957776 + 0.155108i
\(406\) 0.112011 + 0.0786653i 0.00555902 + 0.00390409i
\(407\) 18.1192 21.5936i 0.898135 1.07036i
\(408\) 27.4718 + 3.33163i 1.36006 + 0.164940i
\(409\) −2.96149 + 0.522191i −0.146436 + 0.0258207i −0.246386 0.969172i \(-0.579243\pi\)
0.0999494 + 0.994993i \(0.468132\pi\)
\(410\) 3.38184 2.36093i 0.167017 0.116598i
\(411\) −4.09957 17.3070i −0.202217 0.853689i
\(412\) 11.6557 2.02153i 0.574235 0.0995936i
\(413\) −0.0389124 + 0.0104265i −0.00191475 + 0.000513056i
\(414\) 27.0726 + 1.62159i 1.33055 + 0.0796970i
\(415\) −1.53133 2.65234i −0.0751701 0.130198i
\(416\) 7.47936 + 16.3376i 0.366706 + 0.801018i
\(417\) 17.4453 5.77836i 0.854301 0.282968i
\(418\) 36.9742 + 31.1135i 1.80847 + 1.52181i
\(419\) −9.29082 0.812842i −0.453886 0.0397099i −0.142079 0.989855i \(-0.545379\pi\)
−0.311807 + 0.950145i \(0.600934\pi\)
\(420\) −0.272588 + 0.0391134i −0.0133009 + 0.00190854i
\(421\) 0.791849 1.69813i 0.0385924 0.0827616i −0.886066 0.463558i \(-0.846572\pi\)
0.924659 + 0.380797i \(0.124350\pi\)
\(422\) 12.4544 + 1.10722i 0.606271 + 0.0538986i
\(423\) 16.8710 1.96772i 0.820296 0.0956738i
\(424\) 22.1480 21.9625i 1.07560 1.06659i
\(425\) 26.8903 + 4.74149i 1.30437 + 0.229996i
\(426\) −23.2495 17.3638i −1.12644 0.841280i
\(427\) −2.41453 + 1.12591i −0.116847 + 0.0544867i
\(428\) −6.18501 1.67587i −0.298964 0.0810064i
\(429\) −11.3892 26.4121i −0.549877 1.27519i
\(430\) −2.67275 1.54811i −0.128891 0.0746566i
\(431\) −21.6750 −1.04405 −0.522024 0.852931i \(-0.674823\pi\)
−0.522024 + 0.852931i \(0.674823\pi\)
\(432\) −16.0015 + 13.2647i −0.769874 + 0.638196i
\(433\) −6.67791 −0.320920 −0.160460 0.987042i \(-0.551298\pi\)
−0.160460 + 0.987042i \(0.551298\pi\)
\(434\) −0.114704 0.0664390i −0.00550597 0.00318917i
\(435\) −0.348016 0.0407207i −0.0166861 0.00195241i
\(436\) 8.76308 32.3412i 0.419675 1.54886i
\(437\) 37.8656 17.6570i 1.81136 0.844649i
\(438\) −1.24028 + 10.4727i −0.0592630 + 0.500406i
\(439\) −5.84980 1.03148i −0.279196 0.0492297i 0.0322969 0.999478i \(-0.489718\pi\)
−0.311493 + 0.950249i \(0.600829\pi\)
\(440\) 0.0253557 6.02763i 0.00120878 0.287356i
\(441\) −1.21955 + 20.8503i −0.0580738 + 0.992870i
\(442\) −25.2748 2.24698i −1.20220 0.106878i
\(443\) 2.46581 5.28794i 0.117154 0.251237i −0.838983 0.544158i \(-0.816849\pi\)
0.956137 + 0.292920i \(0.0946271\pi\)
\(444\) 17.3376 + 6.94662i 0.822806 + 0.329672i
\(445\) −2.87671 0.251679i −0.136369 0.0119307i
\(446\) 16.9258 + 14.2430i 0.801462 + 0.674423i
\(447\) −23.1532 20.6097i −1.09511 0.974806i
\(448\) −1.53413 0.283836i −0.0724806 0.0134100i
\(449\) −0.115986 0.200894i −0.00547372 0.00948076i 0.863276 0.504733i \(-0.168409\pi\)
−0.868749 + 0.495252i \(0.835076\pi\)
\(450\) −16.4703 + 12.2195i −0.776418 + 0.576035i
\(451\) −36.1304 + 9.68112i −1.70132 + 0.455866i
\(452\) −3.69581 21.3092i −0.173836 1.00230i
\(453\) −0.100906 0.0302227i −0.00474096 0.00141999i
\(454\) −33.1284 + 23.1276i −1.55479 + 1.08543i
\(455\) 0.248670 0.0438473i 0.0116578 0.00205559i
\(456\) −11.9502 + 29.7050i −0.559620 + 1.39106i
\(457\) 11.3680 13.5479i 0.531775 0.633744i −0.431548 0.902090i \(-0.642032\pi\)
0.963323 + 0.268346i \(0.0864769\pi\)
\(458\) −24.0763 16.9088i −1.12501 0.790096i
\(459\) −5.08618 28.9077i −0.237403 1.34930i
\(460\) −4.71703 2.21571i −0.219933 0.103308i
\(461\) −1.34367 15.3582i −0.0625811 0.715305i −0.961069 0.276307i \(-0.910889\pi\)
0.898488 0.438998i \(-0.144666\pi\)
\(462\) 2.44509 + 0.508761i 0.113756 + 0.0236697i
\(463\) 1.51242 + 8.57737i 0.0702882 + 0.398624i 0.999572 + 0.0292575i \(0.00931427\pi\)
−0.929284 + 0.369367i \(0.879575\pi\)
\(464\) −1.79441 0.849030i −0.0833032 0.0394152i
\(465\) 0.339190 + 0.00991128i 0.0157295 + 0.000459625i
\(466\) −0.00556181 + 3.96654i −0.000257646 + 0.183746i
\(467\) −31.0124 + 8.30975i −1.43508 + 0.384530i −0.890809 0.454378i \(-0.849862\pi\)
−0.544275 + 0.838907i \(0.683195\pi\)
\(468\) 14.2756 12.6263i 0.659888 0.583652i
\(469\) 0.130588 + 0.0349910i 0.00603000 + 0.00161573i
\(470\) −3.15145 0.849167i −0.145366 0.0391691i
\(471\) −9.97331 2.06061i −0.459546 0.0949477i
\(472\) 0.530557 0.244691i 0.0244209 0.0112628i
\(473\) 18.0059 + 21.4585i 0.827910 + 0.986665i
\(474\) −8.93758 + 29.6887i −0.410517 + 1.36365i
\(475\) −13.3517 + 28.6329i −0.612620 + 1.31377i
\(476\) 1.42094 1.68380i 0.0651287 0.0771768i
\(477\) −29.1160 15.7085i −1.33313 0.719241i
\(478\) −22.8365 8.34808i −1.04452 0.381832i
\(479\) 4.10355 23.2724i 0.187496 1.06334i −0.735210 0.677839i \(-0.762916\pi\)
0.922706 0.385504i \(-0.125972\pi\)
\(480\) 3.80005 1.22918i 0.173448 0.0561042i
\(481\) −16.0933 5.85747i −0.733790 0.267078i
\(482\) −7.77055 + 2.81591i −0.353939 + 0.128261i
\(483\) 1.28965 1.73186i 0.0586813 0.0788023i
\(484\) −11.2585 + 30.6646i −0.511749 + 1.39384i
\(485\) 0.608772 0.608772i 0.0276429 0.0276429i
\(486\) 18.3942 + 12.1513i 0.834377 + 0.551195i
\(487\) 20.6439i 0.935466i 0.883870 + 0.467733i \(0.154929\pi\)
−0.883870 + 0.467733i \(0.845071\pi\)
\(488\) 31.7439 22.0289i 1.43698 0.997200i
\(489\) −8.49235 + 1.24288i −0.384037 + 0.0562048i
\(490\) 1.70122 3.63496i 0.0768533 0.164211i
\(491\) 11.1155 5.18326i 0.501637 0.233917i −0.155293 0.987868i \(-0.549632\pi\)
0.656931 + 0.753951i \(0.271854\pi\)
\(492\) −13.5585 20.7467i −0.611264 0.935336i
\(493\) 2.29639 1.60795i 0.103424 0.0724184i
\(494\) 10.0801 27.5745i 0.453525 1.24063i
\(495\) −6.12519 + 1.83212i −0.275307 + 0.0823475i
\(496\) 1.80284 + 0.667655i 0.0809499 + 0.0299786i
\(497\) −2.17099 + 0.790174i −0.0973820 + 0.0354442i
\(498\) −16.2126 + 8.70984i −0.726502 + 0.390297i
\(499\) 27.2615 + 2.38507i 1.22039 + 0.106770i 0.679088 0.734057i \(-0.262376\pi\)
0.541303 + 0.840828i \(0.317931\pi\)
\(500\) 7.74967 2.05324i 0.346576 0.0918238i
\(501\) 9.65027 + 14.6765i 0.431142 + 0.655696i
\(502\) −4.76774 1.28468i −0.212794 0.0573380i
\(503\) −7.83788 + 4.52520i −0.349474 + 0.201769i −0.664453 0.747330i \(-0.731336\pi\)
0.314980 + 0.949098i \(0.398002\pi\)
\(504\) 0.184789 + 1.64445i 0.00823118 + 0.0732497i
\(505\) −5.11768 2.95469i −0.227734 0.131482i
\(506\) 33.3738 + 33.4675i 1.48365 + 1.48781i
\(507\) 3.66743 3.45918i 0.162876 0.153628i
\(508\) 20.6773 + 0.0579867i 0.917405 + 0.00257275i
\(509\) −19.0540 + 27.2120i −0.844555 + 1.20615i 0.132078 + 0.991239i \(0.457835\pi\)
−0.976634 + 0.214911i \(0.931054\pi\)
\(510\) −1.14896 + 5.52186i −0.0508767 + 0.244512i
\(511\) 0.643193 + 0.539703i 0.0284532 + 0.0238751i
\(512\) 22.6256 + 0.285542i 0.999920 + 0.0126193i
\(513\) 33.8306 + 2.97241i 1.49366 + 0.131235i
\(514\) −0.538533 3.07942i −0.0237537 0.135827i
\(515\) 0.210137 + 2.40187i 0.00925973 + 0.105839i
\(516\) −9.79011 + 15.7687i −0.430986 + 0.694177i
\(517\) 24.2472 + 16.9781i 1.06639 + 0.746695i
\(518\) 1.21930 0.851221i 0.0535732 0.0374005i
\(519\) 0.127900 0.0689426i 0.00561418 0.00302625i
\(520\) −3.44655 + 1.23805i −0.151141 + 0.0542920i
\(521\) 10.1362 + 5.85211i 0.444073 + 0.256386i 0.705324 0.708885i \(-0.250802\pi\)
−0.261251 + 0.965271i \(0.584135\pi\)
\(522\) −0.308596 + 2.08281i −0.0135069 + 0.0911622i
\(523\) 31.8194 + 8.52599i 1.39137 + 0.372816i 0.875237 0.483695i \(-0.160706\pi\)
0.516130 + 0.856510i \(0.327372\pi\)
\(524\) −8.39890 0.758548i −0.366908 0.0331373i
\(525\) 0.0947378 + 1.63005i 0.00413469 + 0.0711411i
\(526\) 9.98091 11.8610i 0.435188 0.517163i
\(527\) −2.07975 + 1.74512i −0.0905954 + 0.0760185i
\(528\) −36.1994 1.26100i −1.57538 0.0548781i
\(529\) 16.7868 6.10991i 0.729862 0.265648i
\(530\) 4.07947 + 4.87559i 0.177201 + 0.211782i
\(531\) −0.411863 0.463037i −0.0178734 0.0200941i
\(532\) 1.45631 + 2.09229i 0.0631390 + 0.0907123i
\(533\) 13.0349 + 18.6158i 0.564605 + 0.806339i
\(534\) −2.04081 + 17.2322i −0.0883144 + 0.745711i
\(535\) 0.446692 1.22728i 0.0193122 0.0530598i
\(536\) −1.95257 0.179107i −0.0843381 0.00773624i
\(537\) −5.20813 6.58843i −0.224748 0.284312i
\(538\) −2.11667 + 0.563980i −0.0912560 + 0.0243149i
\(539\) −25.7372 + 25.7372i −1.10858 + 1.10858i
\(540\) −2.41874 3.47777i −0.104086 0.149659i
\(541\) 24.4675 + 24.4675i 1.05194 + 1.05194i 0.998575 + 0.0533651i \(0.0169947\pi\)
0.0533651 + 0.998575i \(0.483005\pi\)
\(542\) −15.1602 + 26.1735i −0.651188 + 1.12425i
\(543\) 30.1064 + 11.9648i 1.29199 + 0.513459i
\(544\) −16.1707 + 27.5604i −0.693312 + 1.18164i
\(545\) 6.41739 + 2.33574i 0.274891 + 0.100052i
\(546\) −0.217622 1.50167i −0.00931337 0.0642653i
\(547\) 22.1224 15.4902i 0.945884 0.662315i 0.00462080 0.999989i \(-0.498529\pi\)
0.941263 + 0.337674i \(0.109640\pi\)
\(548\) 20.2153 + 3.62298i 0.863553 + 0.154766i
\(549\) −32.1410 25.4267i −1.37174 1.08519i
\(550\) −35.5993 3.16484i −1.51796 0.134949i
\(551\) 1.10937 + 3.04798i 0.0472610 + 0.129848i
\(552\) −14.1760 + 27.9246i −0.603370 + 1.18855i
\(553\) 1.58672 + 1.89098i 0.0674743 + 0.0804127i
\(554\) −10.0477 + 0.864868i −0.426887 + 0.0367447i
\(555\) −1.70887 + 3.40159i −0.0725374 + 0.144389i
\(556\) −1.90876 + 21.1344i −0.0809493 + 0.896297i
\(557\) −3.28205 + 12.2488i −0.139065 + 0.518998i 0.860883 + 0.508803i \(0.169912\pi\)
−0.999948 + 0.0101947i \(0.996755\pi\)
\(558\) 0.121920 2.03547i 0.00516130 0.0861682i
\(559\) 8.50949 14.7389i 0.359913 0.623388i
\(560\) 0.0840210 0.306680i 0.00355053 0.0129596i
\(561\) 26.8586 43.5324i 1.13397 1.83794i
\(562\) 34.4471 + 6.12376i 1.45306 + 0.258315i
\(563\) −7.50186 + 10.7138i −0.316166 + 0.451531i −0.945509 0.325596i \(-0.894435\pi\)
0.629343 + 0.777127i \(0.283324\pi\)
\(564\) −5.68006 + 18.7725i −0.239174 + 0.790465i
\(565\) 4.39116 0.384177i 0.184738 0.0161624i
\(566\) −15.4312 10.8373i −0.648622 0.455527i
\(567\) 1.61198 0.694397i 0.0676967 0.0291619i
\(568\) 29.0882 16.6313i 1.22051 0.697835i
\(569\) −9.41788 + 11.2238i −0.394818 + 0.470526i −0.926433 0.376461i \(-0.877141\pi\)
0.531615 + 0.846986i \(0.321586\pi\)
\(570\) −5.82721 2.93767i −0.244075 0.123046i
\(571\) 31.3866 + 21.9771i 1.31349 + 0.919714i 0.999558 0.0297323i \(-0.00946548\pi\)
0.313930 + 0.949446i \(0.398354\pi\)
\(572\) 33.2126 + 0.0931406i 1.38869 + 0.00389440i
\(573\) −30.8600 + 7.30993i −1.28919 + 0.305377i
\(574\) −1.97324 0.00276684i −0.0823614 0.000115486i
\(575\) −15.4502 + 26.7605i −0.644317 + 1.11599i
\(576\) −6.68392 23.0505i −0.278497 0.960437i
\(577\) −4.10333 7.10718i −0.170824 0.295876i 0.767884 0.640589i \(-0.221310\pi\)
−0.938708 + 0.344713i \(0.887976\pi\)
\(578\) −10.5161 18.2736i −0.437414 0.760082i
\(579\) −36.5749 18.3742i −1.52000 0.763607i
\(580\) 0.203280 0.349821i 0.00844072 0.0145255i
\(581\) −0.127706 + 1.45969i −0.00529816 + 0.0605582i
\(582\) −3.54452 3.76847i −0.146925 0.156208i
\(583\) −19.7188 54.1771i −0.816671 2.24379i
\(584\) −10.5202 6.13299i −0.435329 0.253785i
\(585\) 2.31878 + 3.11627i 0.0958699 + 0.128842i
\(586\) 21.6264 10.0477i 0.893379 0.415066i
\(587\) 19.6953 + 28.1277i 0.812910 + 1.16096i 0.984430 + 0.175775i \(0.0562432\pi\)
−0.171520 + 0.985181i \(0.554868\pi\)
\(588\) −21.5199 10.8867i −0.887467 0.448961i
\(589\) −1.32755 2.84694i −0.0547008 0.117306i
\(590\) 0.0405710 + 0.111956i 0.00167028 + 0.00460916i
\(591\) 1.81226 + 0.720222i 0.0745463 + 0.0296260i
\(592\) −15.3354 + 15.1643i −0.630280 + 0.623250i
\(593\) −29.7816 −1.22298 −0.611491 0.791251i \(-0.709430\pi\)
−0.611491 + 0.791251i \(0.709430\pi\)
\(594\) 9.87767 + 37.1270i 0.405286 + 1.52334i
\(595\) 0.317525 + 0.317525i 0.0130173 + 0.0130173i
\(596\) 32.4814 15.0356i 1.33049 0.615880i
\(597\) 1.44485 12.3483i 0.0591339 0.505382i
\(598\) 12.1722 26.0081i 0.497759 1.06355i
\(599\) 10.4979 28.8427i 0.428932 1.17848i −0.517529 0.855666i \(-0.673148\pi\)
0.946462 0.322816i \(-0.104630\pi\)
\(600\) −5.36137 23.0660i −0.218877 0.941665i
\(601\) 24.2976 + 4.28432i 0.991120 + 0.174761i 0.645621 0.763658i \(-0.276599\pi\)
0.345499 + 0.938419i \(0.387710\pi\)
\(602\) 0.622640 + 1.34016i 0.0253769 + 0.0546208i
\(603\) 0.420051 + 2.03684i 0.0171058 + 0.0829467i
\(604\) 0.0784430 0.0929541i 0.00319180 0.00378225i
\(605\) −6.03398 2.81369i −0.245316 0.114393i
\(606\) −18.6882 + 30.1951i −0.759158 + 1.22659i
\(607\) 31.2066 26.1854i 1.26664 1.06283i 0.271695 0.962383i \(-0.412416\pi\)
0.994942 0.100451i \(-0.0320286\pi\)
\(608\) −25.9592 26.3258i −1.05278 1.06765i
\(609\) 0.125215 + 0.111460i 0.00507397 + 0.00451657i
\(610\) 3.92796 + 6.82551i 0.159038 + 0.276357i
\(611\) 4.65458 17.3711i 0.188304 0.702761i
\(612\) 32.9549 + 7.91672i 1.33212 + 0.320014i
\(613\) −5.88716 21.9712i −0.237780 0.887408i −0.976876 0.213807i \(-0.931414\pi\)
0.739096 0.673600i \(-0.235253\pi\)
\(614\) −8.42073 8.44437i −0.339833 0.340787i
\(615\) 4.44651 2.39683i 0.179300 0.0966494i
\(616\) −1.66401 + 2.35531i −0.0670451 + 0.0948981i
\(617\) 11.7771 2.07662i 0.474128 0.0836015i 0.0685218 0.997650i \(-0.478172\pi\)
0.405606 + 0.914048i \(0.367061\pi\)
\(618\) 14.4651 0.820359i 0.581873 0.0329997i
\(619\) 2.35671 0.206185i 0.0947241 0.00828729i −0.0396951 0.999212i \(-0.512639\pi\)
0.134419 + 0.990925i \(0.457083\pi\)
\(620\) −0.166590 + 0.354653i −0.00669040 + 0.0142432i
\(621\) 32.7097 + 5.78008i 1.31259 + 0.231947i
\(622\) −46.5301 + 8.13726i −1.86569 + 0.326274i
\(623\) 1.05834 + 0.888049i 0.0424013 + 0.0355789i
\(624\) 6.80219 + 20.9289i 0.272306 + 0.837826i
\(625\) −3.91320 22.1929i −0.156528 0.887715i
\(626\) 25.9467 + 4.61262i 1.03704 + 0.184357i
\(627\) 40.6090 + 43.0537i 1.62177 + 1.71940i
\(628\) 6.77191 9.61380i 0.270229 0.383632i
\(629\) −7.88271 29.4187i −0.314304 1.17300i
\(630\) −0.337143 + 0.00925352i −0.0134321 + 0.000368669i
\(631\) 27.3047 15.7644i 1.08698 0.627570i 0.154211 0.988038i \(-0.450716\pi\)
0.932772 + 0.360468i \(0.117383\pi\)
\(632\) −27.3283 23.1278i −1.08706 0.919974i
\(633\) 14.9969 + 3.09854i 0.596073 + 0.123156i
\(634\) −1.37000 15.9162i −0.0544096 0.632112i
\(635\) −0.367301 + 4.19827i −0.0145759 + 0.166603i
\(636\) 30.0348 23.6059i 1.19096 0.936034i
\(637\) 20.0419 + 9.34569i 0.794089 + 0.370290i
\(638\) −2.81418 + 2.35466i −0.111415 + 0.0932220i
\(639\) −25.8446 24.3951i −1.02240 0.965057i
\(640\) −0.447015 + 4.59005i −0.0176698 + 0.181437i
\(641\) 8.47626 48.0712i 0.334792 1.89870i −0.0944833 0.995526i \(-0.530120\pi\)
0.429275 0.903174i \(-0.358769\pi\)
\(642\) −7.28929 2.90873i −0.287685 0.114798i
\(643\) 16.4430 + 35.2622i 0.648450 + 1.39061i 0.905558 + 0.424223i \(0.139453\pi\)
−0.257107 + 0.966383i \(0.582769\pi\)
\(644\) 1.24061 + 2.16278i 0.0488868 + 0.0852255i
\(645\) −3.03407 2.25936i −0.119466 0.0889624i
\(646\) 50.4511 13.4425i 1.98497 0.528890i
\(647\) 28.0842i 1.10410i 0.833810 + 0.552051i \(0.186155\pi\)
−0.833810 + 0.552051i \(0.813845\pi\)
\(648\) −21.3336 + 13.8881i −0.838061 + 0.545576i
\(649\) 1.07996i 0.0423922i
\(650\) 5.59057 + 20.9819i 0.219280 + 0.822978i
\(651\) −0.130211 0.0969633i −0.00510336 0.00380029i
\(652\) 2.59188 9.56566i 0.101506 0.374620i
\(653\) −6.87415 14.7417i −0.269006 0.576886i 0.724679 0.689086i \(-0.241988\pi\)
−0.993686 + 0.112200i \(0.964210\pi\)
\(654\) 15.2096 38.1154i 0.594744 1.49043i
\(655\) 0.298462 1.69266i 0.0116619 0.0661377i
\(656\) 28.2111 4.81138i 1.10146 0.187853i
\(657\) −2.98174 + 12.5672i −0.116329 + 0.490291i
\(658\) 1.00205 + 1.19760i 0.0390639 + 0.0466874i
\(659\) 13.0700 + 6.09466i 0.509137 + 0.237414i 0.660173 0.751114i \(-0.270483\pi\)
−0.151036 + 0.988528i \(0.548261\pi\)
\(660\) 0.878505 7.32992i 0.0341958 0.285317i
\(661\) −1.54673 + 17.6792i −0.0601610 + 0.687643i 0.904901 + 0.425622i \(0.139945\pi\)
−0.965062 + 0.262021i \(0.915611\pi\)
\(662\) −12.0917 + 1.04081i −0.469958 + 0.0404521i
\(663\) −30.4345 6.28813i −1.18198 0.244211i
\(664\) −1.76309 21.1779i −0.0684211 0.821861i
\(665\) −0.449956 + 0.259782i −0.0174485 + 0.0100739i
\(666\) 20.1168 + 10.8897i 0.779510 + 0.421968i
\(667\) 0.821101 + 3.06439i 0.0317932 + 0.118654i
\(668\) −19.9839 + 3.46594i −0.773200 + 0.134101i
\(669\) 18.5898 + 19.7089i 0.718722 + 0.761989i
\(670\) 0.0699467 0.393460i 0.00270228 0.0152007i
\(671\) −12.4020 70.3351i −0.478773 2.71526i
\(672\) −1.82657 0.561069i −0.0704615 0.0216437i
\(673\) 35.8732 + 30.1012i 1.38281 + 1.16032i 0.968159 + 0.250336i \(0.0805410\pi\)
0.414652 + 0.909980i \(0.363903\pi\)
\(674\) −3.14904 18.0067i −0.121296 0.693592i
\(675\) −21.7569 + 12.5506i −0.837425 + 0.483074i
\(676\) 1.97567 + 5.47583i 0.0759871 + 0.210609i
\(677\) −13.1364 + 1.14929i −0.504872 + 0.0441706i −0.336747 0.941595i \(-0.609327\pi\)
−0.168125 + 0.985766i \(0.553771\pi\)
\(678\) −1.49980 26.4455i −0.0575994 1.01563i
\(679\) −0.405638 + 0.0715250i −0.0155670 + 0.00274488i
\(680\) −5.31910 3.75792i −0.203978 0.144110i
\(681\) −43.5579 + 23.4793i −1.66914 + 0.899728i
\(682\) 2.51627 2.50922i 0.0963530 0.0960832i
\(683\) 0.232612 + 0.868119i 0.00890064 + 0.0332176i 0.970233 0.242172i \(-0.0778598\pi\)
−0.961333 + 0.275390i \(0.911193\pi\)
\(684\) −18.7165 + 34.4599i −0.715644 + 1.31761i
\(685\) −1.08336 + 4.04315i −0.0413930 + 0.154481i
\(686\) −3.33751 + 1.92068i −0.127427 + 0.0733319i
\(687\) −26.9145 23.9578i −1.02685 0.914048i
\(688\) −12.1942 17.6247i −0.464900 0.671936i
\(689\) −26.8331 + 22.5157i −1.02226 + 0.857778i
\(690\) −5.42736 3.35908i −0.206616 0.127878i
\(691\) −2.37431 1.10716i −0.0903231 0.0421183i 0.376932 0.926241i \(-0.376979\pi\)
−0.467255 + 0.884123i \(0.654757\pi\)
\(692\) 0.0141538 + 0.167177i 0.000538048 + 0.00635513i
\(693\) 2.90326 + 0.962831i 0.110286 + 0.0365749i
\(694\) 36.9363 17.1607i 1.40208 0.651411i
\(695\) −4.25929 0.751027i −0.161564 0.0284881i
\(696\) −2.06376 1.28531i −0.0782265 0.0487196i
\(697\) −13.8226 + 37.9772i −0.523568 + 1.43849i
\(698\) −18.4586 8.63890i −0.698667 0.326987i
\(699\) −0.564575 + 4.82508i −0.0213542 + 0.182501i
\(700\) −1.76987 0.649808i −0.0668950 0.0245604i
\(701\) 19.7056 + 19.7056i 0.744270 + 0.744270i 0.973397 0.229126i \(-0.0735869\pi\)
−0.229126 + 0.973397i \(0.573587\pi\)
\(702\) 19.1439 13.3542i 0.722540 0.504022i
\(703\) 35.2391 1.32907
\(704\) 17.9942 37.7561i 0.678182 1.42299i
\(705\) −3.71478 1.47632i −0.139907 0.0556013i
\(706\) 42.4134 15.3699i 1.59625 0.578453i
\(707\) 1.19484 + 2.56233i 0.0449364 + 0.0963665i
\(708\) 0.679910 0.223091i 0.0255526 0.00838426i
\(709\) −19.3863 27.6865i −0.728068 1.03979i −0.997058 0.0766465i \(-0.975579\pi\)
0.268990 0.963143i \(-0.413310\pi\)
\(710\) 2.87745 + 6.19338i 0.107989 + 0.232433i
\(711\) −15.0489 + 34.8637i −0.564379 + 1.30749i
\(712\) −17.3103 10.0915i −0.648733 0.378193i
\(713\) −1.05082 2.88711i −0.0393535 0.108123i
\(714\) 1.96557 1.84876i 0.0735596 0.0691881i
\(715\) −0.589974 + 6.74343i −0.0220638 + 0.252190i
\(716\) 9.37413 2.48364i 0.350328 0.0928178i
\(717\) −26.6099 13.3681i −0.993765 0.499241i
\(718\) −22.9545 + 13.2099i −0.856656 + 0.492990i
\(719\) 14.2567 + 24.6932i 0.531683 + 0.920903i 0.999316 + 0.0369798i \(0.0117737\pi\)
−0.467633 + 0.883923i \(0.654893\pi\)
\(720\) 4.79617 0.961083i 0.178743 0.0358174i
\(721\) 0.576758 0.998974i 0.0214796 0.0372038i
\(722\) −0.0470293 + 33.5401i −0.00175025 + 1.24823i
\(723\) −9.84999 + 2.33321i −0.366325 + 0.0867729i
\(724\) −26.5259 + 26.3776i −0.985829 + 0.980315i
\(725\) −1.96511 1.37598i −0.0729822 0.0511027i
\(726\) −18.0099 + 35.7246i −0.668409 + 1.32587i
\(727\) 4.76778 5.68202i 0.176827 0.210735i −0.670350 0.742045i \(-0.733856\pi\)
0.847177 + 0.531311i \(0.178300\pi\)
\(728\) 1.69046 + 0.460589i 0.0626528 + 0.0170706i
\(729\) 20.6704 + 17.3706i 0.765569 + 0.643354i
\(730\) 1.42641 2.03106i 0.0527938 0.0751728i
\(731\) 30.1508 2.63785i 1.11517 0.0975644i
\(732\) 41.7189 22.3372i 1.54197 0.825607i
\(733\) −24.2281 + 34.6014i −0.894886 + 1.27803i 0.0650699 + 0.997881i \(0.479273\pi\)
−0.959956 + 0.280150i \(0.909616\pi\)
\(734\) 7.51562 42.2765i 0.277407 1.56045i
\(735\) 2.58096 4.18322i 0.0952001 0.154300i
\(736\) −23.0494 27.8636i −0.849611 1.02707i
\(737\) −1.81215 + 3.13874i −0.0667514 + 0.115617i
\(738\) −13.5783 27.1481i −0.499824 0.999336i
\(739\) −0.795613 + 2.96927i −0.0292671 + 0.109226i −0.979014 0.203792i \(-0.934673\pi\)
0.949747 + 0.313018i \(0.101340\pi\)
\(740\) −2.81599 3.37514i −0.103518 0.124073i
\(741\) 16.1417 32.1308i 0.592979 1.18035i
\(742\) −0.260831 3.03024i −0.00957541 0.111244i
\(743\) −23.3975 27.8840i −0.858370 1.02297i −0.999456 0.0329680i \(-0.989504\pi\)
0.141087 0.989997i \(-0.454940\pi\)
\(744\) 2.09952 + 1.06583i 0.0769723 + 0.0390752i
\(745\) 2.49503 + 6.85505i 0.0914109 + 0.251149i
\(746\) −3.67299 + 41.3151i −0.134478 + 1.51265i
\(747\) −20.9498 + 8.31683i −0.766512 + 0.304297i
\(748\) 33.7421 + 48.4775i 1.23373 + 1.77251i
\(749\) −0.511846 + 0.358398i −0.0187024 + 0.0130956i
\(750\) 9.71734 1.40824i 0.354827 0.0514217i
\(751\) −7.69815 2.80190i −0.280909 0.102243i 0.197723 0.980258i \(-0.436645\pi\)
−0.478633 + 0.878015i \(0.658867\pi\)
\(752\) −17.2668 14.6544i −0.629655 0.534390i
\(753\) −5.61998 2.23348i −0.204803 0.0813924i
\(754\) 1.92910 + 1.11737i 0.0702535 + 0.0406923i
\(755\) 0.0175290 + 0.0175290i 0.000637945 + 0.000637945i
\(756\) −0.00643345 + 2.02670i −0.000233982 + 0.0737103i
\(757\) −5.83393 + 5.83393i −0.212038 + 0.212038i −0.805133 0.593095i \(-0.797906\pi\)
0.593095 + 0.805133i \(0.297906\pi\)
\(758\) 1.71986 + 6.45480i 0.0624682 + 0.234449i
\(759\) 35.8975 + 45.4113i 1.30300 + 1.64833i
\(760\) 5.79275 4.81932i 0.210125 0.174815i
\(761\) 3.23541 8.88921i 0.117283 0.322234i −0.867136 0.498072i \(-0.834041\pi\)
0.984419 + 0.175838i \(0.0562636\pi\)
\(762\) 25.1487 + 2.97836i 0.911042 + 0.107895i
\(763\) −1.87405 2.67642i −0.0678452 0.0968930i
\(764\) 6.46012 36.0458i 0.233719 1.30409i
\(765\) −2.17441 + 6.55657i −0.0786158 + 0.237053i
\(766\) −15.3927 + 12.8793i −0.556163 + 0.465348i
\(767\) −0.616568 + 0.224412i −0.0222630 + 0.00810307i
\(768\) 27.4872 + 3.52921i 0.991858 + 0.127349i
\(769\) −28.3247 + 23.7673i −1.02142 + 0.857070i −0.989805 0.142431i \(-0.954508\pi\)
−0.0316111 + 0.999500i \(0.510064\pi\)
\(770\) −0.449720 0.378436i −0.0162068 0.0136379i
\(771\) −0.222150 3.82229i −0.00800054 0.137656i
\(772\) 36.2905 30.2783i 1.30612 1.08974i
\(773\) 30.5392 + 8.18296i 1.09842 + 0.294321i 0.762121 0.647435i \(-0.224158\pi\)
0.336299 + 0.941755i \(0.390825\pi\)
\(774\) −14.1286 + 17.8081i −0.507842 + 0.640099i
\(775\) 2.01200 + 1.16163i 0.0722733 + 0.0417270i
\(776\) 5.62211 2.01954i 0.201822 0.0724972i
\(777\) 1.60317 0.864164i 0.0575133 0.0310017i
\(778\) −18.6100 26.6572i −0.667199 0.955708i
\(779\) −38.3043 26.8210i −1.37239 0.960961i
\(780\) −4.36733 + 1.02158i −0.156375 + 0.0365785i
\(781\) −5.39798 61.6992i −0.193155 2.20777i
\(782\) 50.3033 8.79712i 1.79884 0.314584i
\(783\) −0.668354 + 2.49064i −0.0238850 + 0.0890084i
\(784\) 21.4328 17.7803i 0.765456 0.635012i
\(785\) 1.83600 + 1.54058i 0.0655295 + 0.0549858i
\(786\) −10.1118 2.10401i −0.360676 0.0750475i
\(787\) 29.9388 42.7570i 1.06720 1.52412i 0.233146 0.972442i \(-0.425098\pi\)
0.834056 0.551680i \(-0.186013\pi\)
\(788\) −1.59673 + 1.58780i −0.0568812 + 0.0565630i
\(789\) 13.8112 13.0270i 0.491692 0.463773i
\(790\) 5.16682 5.15235i 0.183827 0.183313i
\(791\) −1.82635 1.05444i −0.0649375 0.0374917i
\(792\) −43.8644 6.62485i −1.55865 0.235404i
\(793\) −37.5784 + 21.6959i −1.33445 + 0.770444i
\(794\) −5.22636 + 19.3962i −0.185477 + 0.688346i
\(795\) 4.27762 + 6.50555i 0.151711 + 0.230728i
\(796\) 12.4124 + 7.21277i 0.439944 + 0.255650i
\(797\) −45.9297 4.01833i −1.62691 0.142336i −0.763145 0.646227i \(-0.776346\pi\)
−0.863767 + 0.503891i \(0.831901\pi\)
\(798\) 1.47758 + 2.75037i 0.0523056 + 0.0973621i
\(799\) 30.0532 10.9385i 1.06321 0.386976i
\(800\) 26.8950 + 4.93697i 0.950880 + 0.174548i
\(801\) −4.90628 + 20.6785i −0.173355 + 0.730638i
\(802\) −13.5970 4.97051i −0.480127 0.175515i
\(803\) −18.4381 + 12.9105i −0.650667 + 0.455602i
\(804\) −2.35039 0.492496i −0.0828919 0.0173690i
\(805\) −0.460562 + 0.214764i −0.0162327 + 0.00756943i
\(806\) −1.95543 0.915174i −0.0688772 0.0322356i
\(807\) −2.65454 + 0.388499i −0.0934444 + 0.0136758i
\(808\) −23.3774 33.6871i −0.822414 1.18511i
\(809\) 2.90330i 0.102074i −0.998697 0.0510372i \(-0.983747\pi\)
0.998697 0.0510372i \(-0.0162527\pi\)
\(810\) −2.45368 4.57135i −0.0862134 0.160621i
\(811\) −20.7760 + 20.7760i −0.729544 + 0.729544i −0.970529 0.240985i \(-0.922530\pi\)
0.240985 + 0.970529i \(0.422530\pi\)
\(812\) −0.175663 + 0.0813140i −0.00616456 + 0.00285356i
\(813\) −22.1254 + 29.7119i −0.775971 + 1.04204i
\(814\) 13.5819 + 37.4794i 0.476046 + 1.31365i
\(815\) 1.89809 + 0.690848i 0.0664872 + 0.0241994i
\(816\) −23.5497 + 31.2571i −0.824406 + 1.09422i
\(817\) −6.08093 + 34.4867i −0.212745 + 1.20654i
\(818\) 1.46014 3.99427i 0.0510527 0.139656i
\(819\) −0.0535920 1.85760i −0.00187266 0.0649097i
\(820\) 0.492065 + 5.81201i 0.0171837 + 0.202964i
\(821\) −8.83220 + 18.9407i −0.308246 + 0.661036i −0.998014 0.0629950i \(-0.979935\pi\)
0.689768 + 0.724031i \(0.257713\pi\)
\(822\) 24.0853 + 7.25072i 0.840071 + 0.252898i
\(823\) 32.3741 + 38.5819i 1.12849 + 1.34488i 0.931188 + 0.364539i \(0.118773\pi\)
0.197302 + 0.980343i \(0.436782\pi\)
\(824\) −5.78799 + 15.6966i −0.201634 + 0.546817i
\(825\) −42.8666 8.85676i −1.49243 0.308353i
\(826\) 0.0148225 0.0550096i 0.000515740 0.00191403i
\(827\) −21.5223 5.76689i −0.748405 0.200534i −0.135594 0.990764i \(-0.543294\pi\)
−0.612810 + 0.790230i \(0.709961\pi\)
\(828\) −21.1741 + 31.9807i −0.735851 + 1.11141i
\(829\) 5.62203 1.50642i 0.195261 0.0523201i −0.159863 0.987139i \(-0.551105\pi\)
0.355124 + 0.934819i \(0.384439\pi\)
\(830\) 4.33125 + 0.00607321i 0.150340 + 0.000210804i
\(831\) −12.3461 0.360760i −0.428283 0.0125146i
\(832\) −25.2947 2.42760i −0.876937 0.0841620i
\(833\) 6.82895 + 38.7289i 0.236609 + 1.34188i
\(834\) −5.29437 + 25.4446i −0.183329 + 0.881074i
\(835\) −0.360283 4.11805i −0.0124681 0.142511i
\(836\) −64.2834 + 23.1933i −2.22329 + 0.802156i
\(837\) 0.434578 2.45929i 0.0150212 0.0850057i
\(838\) 7.58027 10.7935i 0.261856 0.372855i
\(839\) −1.72641 + 2.05745i −0.0596022 + 0.0710312i −0.795022 0.606581i \(-0.792541\pi\)
0.735420 + 0.677612i \(0.236985\pi\)
\(840\) 0.145352 0.361305i 0.00501510 0.0124662i
\(841\) 28.3169 4.99303i 0.976444 0.172173i
\(842\) 1.51680 + 2.17270i 0.0522725 + 0.0748761i
\(843\) 41.0487 + 12.2947i 1.41379 + 0.423451i
\(844\) −10.1829 + 14.4563i −0.350511 + 0.497606i
\(845\) −1.14604 + 0.307079i −0.0394248 + 0.0105639i
\(846\) −9.55056 + 22.0407i −0.328355 + 0.757774i
\(847\) 1.59263 + 2.75852i 0.0547236 + 0.0947840i
\(848\) 11.1776 + 42.6712i 0.383840 + 1.46534i
\(849\) −17.2502 15.3552i −0.592027 0.526990i
\(850\) −24.8629 + 29.5462i −0.852790 + 1.01343i
\(851\) 34.3355 + 3.00396i 1.17700 + 0.102975i
\(852\) 37.7288 16.1438i 1.29257 0.553077i
\(853\) −0.823113 + 1.76517i −0.0281828 + 0.0604383i −0.919895 0.392164i \(-0.871727\pi\)
0.891712 + 0.452602i \(0.149504\pi\)
\(854\) 0.333635 3.75285i 0.0114168 0.128420i
\(855\) −6.67652 4.39358i −0.228332 0.150257i
\(856\) 6.43494 6.38103i 0.219942 0.218099i
\(857\) 15.7460 + 2.77645i 0.537873 + 0.0948416i 0.435984 0.899954i \(-0.356400\pi\)
0.101889 + 0.994796i \(0.467511\pi\)
\(858\) 40.3949 + 4.78396i 1.37906 + 0.163322i
\(859\) 43.8260 20.4364i 1.49532 0.697281i 0.508799 0.860886i \(-0.330090\pi\)
0.986526 + 0.163604i \(0.0523120\pi\)
\(860\) 3.78901 2.17344i 0.129204 0.0741137i
\(861\) −2.40034 0.280860i −0.0818034 0.00957168i
\(862\) 15.3637 26.5248i 0.523291 0.903438i
\(863\) −1.38416 −0.0471173 −0.0235587 0.999722i \(-0.507500\pi\)
−0.0235587 + 0.999722i \(0.507500\pi\)
\(864\) −4.89040 28.9842i −0.166375 0.986063i
\(865\) −0.0341948 −0.00116266
\(866\) 4.73346 8.17210i 0.160849 0.277699i
\(867\) −10.2246 23.7114i −0.347246 0.805280i
\(868\) 0.162610 0.0932758i 0.00551934 0.00316599i
\(869\) −59.9754 + 27.9670i −2.03453 + 0.948715i
\(870\) 0.296514 0.397021i 0.0100528 0.0134603i
\(871\) 2.16852 + 0.382368i 0.0734774 + 0.0129561i
\(872\) 33.3661 + 33.6480i 1.12992 + 1.13947i
\(873\) −3.78246 5.08335i −0.128017 0.172045i
\(874\) −5.23220 + 58.8538i −0.176982 + 1.99076i
\(875\) 0.330379 0.708501i 0.0111689 0.0239517i
\(876\) −11.9369 8.94110i −0.403309 0.302092i
\(877\) −12.2120 1.06841i −0.412371 0.0360778i −0.120917 0.992663i \(-0.538583\pi\)
−0.291454 + 0.956585i \(0.594139\pi\)
\(878\) 5.40875 6.42757i 0.182536 0.216920i
\(879\) 27.7247 9.18316i 0.935129 0.309740i
\(880\) 7.35836 + 4.30356i 0.248050 + 0.145073i
\(881\) −29.3197 50.7832i −0.987805 1.71093i −0.628739 0.777616i \(-0.716429\pi\)
−0.359066 0.933312i \(-0.616905\pi\)
\(882\) −24.6511 16.2716i −0.830046 0.547893i
\(883\) −57.2289 + 15.3344i −1.92590 + 0.516045i −0.942660 + 0.333755i \(0.891684\pi\)
−0.983245 + 0.182290i \(0.941649\pi\)
\(884\) 20.6651 29.3374i 0.695044 0.986725i
\(885\) 0.0336163 + 0.141916i 0.00113000 + 0.00477046i
\(886\) 4.72330 + 6.76575i 0.158683 + 0.227300i
\(887\) 44.7958 7.89872i 1.50410 0.265213i 0.639936 0.768428i \(-0.278961\pi\)
0.864161 + 0.503215i \(0.167850\pi\)
\(888\) −20.7902 + 16.2930i −0.697675 + 0.546757i
\(889\) 1.29602 1.54454i 0.0434671 0.0518021i
\(890\) 2.34707 3.34198i 0.0786740 0.112024i
\(891\) 6.79650 + 46.5594i 0.227691 + 1.55980i
\(892\) −29.4273 + 10.6173i −0.985298 + 0.355493i
\(893\) 3.22513 + 36.8634i 0.107925 + 1.23359i
\(894\) 41.6327 13.7251i 1.39241 0.459037i
\(895\) 0.343214 + 1.94646i 0.0114724 + 0.0650631i
\(896\) 1.43477 1.67620i 0.0479323 0.0559979i
\(897\) 18.4667 29.9309i 0.616586 0.999362i
\(898\) 0.328058 0.000459997i 0.0109474 1.53503e-5i
\(899\) 0.230398 0.0617349i 0.00768420 0.00205898i
\(900\) −3.27914 28.8171i −0.109305 0.960569i
\(901\) −60.1702 16.1226i −2.00456 0.537120i
\(902\) 13.7628 51.0769i 0.458251 1.70068i
\(903\) 0.569067 + 1.71806i 0.0189374 + 0.0571733i
\(904\) 28.6969 + 10.5817i 0.954445 + 0.351943i
\(905\) −4.90084 5.84059i −0.162909 0.194148i
\(906\) 0.108509 0.102061i 0.00360498 0.00339074i
\(907\) −7.38633 + 15.8400i −0.245259 + 0.525960i −0.989945 0.141456i \(-0.954822\pi\)
0.744686 + 0.667416i \(0.232599\pi\)
\(908\) −4.82027 56.9344i −0.159966 1.88943i
\(909\) −26.9832 + 34.1086i −0.894977 + 1.13131i
\(910\) −0.122605 + 0.335391i −0.00406432 + 0.0111181i
\(911\) −7.74655 + 43.9329i −0.256655 + 1.45556i 0.535135 + 0.844767i \(0.320261\pi\)
−0.791790 + 0.610794i \(0.790850\pi\)
\(912\) −27.8810 35.6797i −0.923231 1.18147i
\(913\) −36.9119 13.4349i −1.22161 0.444629i
\(914\) 8.52134 + 23.5147i 0.281861 + 0.777798i
\(915\) 3.81907 + 8.85660i 0.126255 + 0.292790i
\(916\) 37.7581 17.4781i 1.24756 0.577494i
\(917\) −0.581462 + 0.581462i −0.0192016 + 0.0192016i
\(918\) 38.9811 + 14.2662i 1.28657 + 0.470856i
\(919\) 43.6965i 1.44142i 0.693239 + 0.720708i \(0.256183\pi\)
−0.693239 + 0.720708i \(0.743817\pi\)
\(920\) 6.05503 4.20193i 0.199628 0.138533i
\(921\) −9.05751 11.4580i −0.298455 0.377554i
\(922\) 19.7471 + 9.24196i 0.650337 + 0.304368i
\(923\) −34.1035 + 15.9027i −1.12253 + 0.523444i
\(924\) −2.35574 + 2.63157i −0.0774981 + 0.0865722i
\(925\) −21.3493 + 14.9490i −0.701962 + 0.491519i
\(926\) −11.5686 4.22901i −0.380168 0.138974i
\(927\) 17.7143 + 1.03612i 0.581814 + 0.0340308i
\(928\) 2.31092 1.59410i 0.0758596 0.0523287i
\(929\) 4.21501 1.53414i 0.138290 0.0503335i −0.271948 0.962312i \(-0.587668\pi\)
0.410238 + 0.911978i \(0.365446\pi\)
\(930\) −0.252555 + 0.408059i −0.00828159 + 0.0133808i
\(931\) −45.3288 3.96575i −1.48559 0.129972i
\(932\) −4.85012 2.81838i −0.158871 0.0923192i
\(933\) −57.7549 + 3.35669i −1.89081 + 0.109893i
\(934\) 11.8133 43.8417i 0.386541 1.43454i
\(935\) −10.4253 + 6.01904i −0.340943 + 0.196844i
\(936\) 5.33265 + 26.4196i 0.174303 + 0.863551i
\(937\) −2.90386 1.67655i −0.0948651 0.0547704i 0.451817 0.892111i \(-0.350776\pi\)
−0.546682 + 0.837340i \(0.684109\pi\)
\(938\) −0.135384 + 0.135005i −0.00442045 + 0.00440807i
\(939\) 30.9192 + 9.26076i 1.00901 + 0.302213i
\(940\) 3.27299 3.25469i 0.106753 0.106156i
\(941\) 5.08830 7.26684i 0.165874 0.236892i −0.727607 0.685995i \(-0.759367\pi\)
0.893480 + 0.449102i \(0.148256\pi\)
\(942\) 9.59099 10.7443i 0.312491 0.350067i
\(943\) −35.0357 29.3985i −1.14092 0.957345i
\(944\) −0.0766301 + 0.822713i −0.00249410 + 0.0267770i
\(945\) −0.411484 0.0361536i −0.0133856 0.00117608i
\(946\) −39.0229 + 6.82439i −1.26874 + 0.221880i
\(947\) −3.22220 36.8299i −0.104707 1.19681i −0.848793 0.528726i \(-0.822670\pi\)
0.744086 0.668084i \(-0.232885\pi\)
\(948\) −29.9964 31.9814i −0.974239 1.03871i
\(949\) 11.2022 + 7.84387i 0.363639 + 0.254623i
\(950\) −25.5756 36.6349i −0.829781 1.18859i
\(951\) 0.571464 19.5570i 0.0185310 0.634179i
\(952\) 1.05336 + 2.93240i 0.0341395 + 0.0950395i
\(953\) 32.0848 + 18.5241i 1.03933 + 0.600056i 0.919643 0.392756i \(-0.128478\pi\)
0.119685 + 0.992812i \(0.461812\pi\)
\(954\) 39.8614 24.4962i 1.29056 0.793094i
\(955\) 7.20933 + 1.93173i 0.233288 + 0.0625094i
\(956\) 26.4030 22.0289i 0.853935 0.712465i
\(957\) −3.75499 + 2.46903i −0.121382 + 0.0798125i
\(958\) 25.5710 + 21.5178i 0.826161 + 0.695207i
\(959\) 1.53408 1.28725i 0.0495380 0.0415673i
\(960\) −1.18935 + 5.52159i −0.0383861 + 0.178209i
\(961\) 28.9134 10.5236i 0.932690 0.339472i
\(962\) 18.5754 15.5423i 0.598894 0.501103i
\(963\) −8.45942 4.56397i −0.272601 0.147072i
\(964\) 2.06196 11.5052i 0.0664114 0.370558i
\(965\) 5.52514 + 7.89071i 0.177860 + 0.254011i
\(966\) 1.20523 + 2.80580i 0.0387777 + 0.0902751i
\(967\) 9.63140 26.4620i 0.309725 0.850962i −0.682985 0.730432i \(-0.739319\pi\)
0.992710 0.120530i \(-0.0384592\pi\)
\(968\) −29.5456 35.5134i −0.949631 1.14144i
\(969\) 63.2715 9.25994i 2.03257 0.297472i
\(970\) 0.313474 + 1.17650i 0.0100650 + 0.0377751i
\(971\) 10.2953 10.2953i 0.330392 0.330392i −0.522344 0.852735i \(-0.674942\pi\)
0.852735 + 0.522344i \(0.174942\pi\)
\(972\) −27.9084 + 13.8968i −0.895163 + 0.445739i
\(973\) 1.46315 + 1.46315i 0.0469064 + 0.0469064i
\(974\) −25.2631 14.6329i −0.809481 0.468869i
\(975\) 3.85108 + 26.3137i 0.123333 + 0.842713i
\(976\) 4.45709 + 54.4612i 0.142668 + 1.74326i
\(977\) 48.4004 + 17.6163i 1.54847 + 0.563595i 0.968057 0.250730i \(-0.0806708\pi\)
0.580408 + 0.814326i \(0.302893\pi\)
\(978\) 4.49860 11.2735i 0.143850 0.360487i
\(979\) −30.3388 + 21.2434i −0.969632 + 0.678944i
\(980\) 3.24243 + 4.65842i 0.103576 + 0.148808i
\(981\) 23.8648 44.2340i 0.761946 1.41228i
\(982\) −1.53593 + 17.2767i −0.0490134 + 0.551321i
\(983\) −2.77730 7.63056i −0.0885820 0.243377i 0.887489 0.460829i \(-0.152448\pi\)
−0.976071 + 0.217452i \(0.930226\pi\)
\(984\) 34.9995 1.88647i 1.11574 0.0601384i
\(985\) −0.295006 0.351575i −0.00939969 0.0112021i
\(986\) 0.339997 + 3.94996i 0.0108277 + 0.125792i
\(987\) 1.05072 + 1.59797i 0.0334448 + 0.0508640i
\(988\) 26.5993 + 31.8810i 0.846237 + 1.01427i
\(989\) −8.86482 + 33.0840i −0.281885 + 1.05201i
\(990\) 2.09962 8.79436i 0.0667304 0.279503i
\(991\) −16.1712 + 28.0093i −0.513694 + 0.889744i 0.486180 + 0.873859i \(0.338390\pi\)
−0.999874 + 0.0158854i \(0.994943\pi\)
\(992\) −2.09494 + 1.73298i −0.0665144 + 0.0550222i
\(993\) −14.8577 0.434149i −0.471495 0.0137773i
\(994\) 0.571868 3.21684i 0.0181386 0.102032i
\(995\) −1.67823 + 2.39677i −0.0532036 + 0.0759826i
\(996\) 0.833159 26.0139i 0.0263996 0.824282i
\(997\) −57.5226 + 5.03257i −1.82176 + 0.159383i −0.946169 0.323673i \(-0.895082\pi\)
−0.875589 + 0.483056i \(0.839527\pi\)
\(998\) −22.2423 + 31.6707i −0.704068 + 1.00252i
\(999\) 22.9436 + 16.0779i 0.725903 + 0.508683i
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 432.2.bg.a.205.25 yes 840
16.5 even 4 inner 432.2.bg.a.421.56 yes 840
27.22 even 9 inner 432.2.bg.a.157.56 840
432.373 even 36 inner 432.2.bg.a.373.25 yes 840
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
432.2.bg.a.157.56 840 27.22 even 9 inner
432.2.bg.a.205.25 yes 840 1.1 even 1 trivial
432.2.bg.a.373.25 yes 840 432.373 even 36 inner
432.2.bg.a.421.56 yes 840 16.5 even 4 inner