Properties

Label 55.2.l.a.52.1
Level $55$
Weight $2$
Character 55.52
Analytic conductor $0.439$
Analytic rank $0$
Dimension $32$
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] = [55,2,Mod(2,55)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(55, base_ring=CyclotomicField(20))
 
chi = DirichletCharacter(H, H._module([5, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("55.2");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 55 = 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 55.l (of order \(20\), degree \(8\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.439177211117\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(4\) over \(\Q(\zeta_{20})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label 52.1
Character \(\chi\) \(=\) 55.52
Dual form 55.2.l.a.18.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.237790 + 1.50135i) q^{2} +(0.710333 + 0.361933i) q^{3} +(-0.295389 - 0.0959778i) q^{4} +(-1.71486 - 1.43501i) q^{5} +(-0.712297 + 0.980393i) q^{6} +(0.0869260 + 0.170602i) q^{7} +(-1.16585 + 2.28811i) q^{8} +(-1.38978 - 1.91287i) q^{9} +O(q^{10})\) \(q+(-0.237790 + 1.50135i) q^{2} +(0.710333 + 0.361933i) q^{3} +(-0.295389 - 0.0959778i) q^{4} +(-1.71486 - 1.43501i) q^{5} +(-0.712297 + 0.980393i) q^{6} +(0.0869260 + 0.170602i) q^{7} +(-1.16585 + 2.28811i) q^{8} +(-1.38978 - 1.91287i) q^{9} +(2.56223 - 2.23337i) q^{10} +(1.77694 - 2.80044i) q^{11} +(-0.175087 - 0.175087i) q^{12} +(3.05749 + 0.484259i) q^{13} +(-0.276803 + 0.0899388i) q^{14} +(-0.698743 - 1.64000i) q^{15} +(-3.66057 - 2.65956i) q^{16} +(-3.66088 + 0.579827i) q^{17} +(3.20235 - 1.63168i) q^{18} +(0.229844 + 0.707388i) q^{19} +(0.368822 + 0.588475i) q^{20} +0.152646i q^{21} +(3.78190 + 3.33373i) q^{22} +(-1.14886 + 1.14886i) q^{23} +(-1.65629 + 1.20336i) q^{24} +(0.881484 + 4.92169i) q^{25} +(-1.45408 + 4.47521i) q^{26} +(-0.669017 - 4.22401i) q^{27} +(-0.00930302 - 0.0587369i) q^{28} +(-2.95025 + 9.07993i) q^{29} +(2.62836 - 0.659081i) q^{30} +(-0.283900 + 0.206266i) q^{31} +(1.23166 - 1.23166i) q^{32} +(2.27579 - 1.34611i) q^{33} -5.63413i q^{34} +(0.0957498 - 0.417298i) q^{35} +(0.226933 + 0.698428i) q^{36} +(-4.81621 + 2.45398i) q^{37} +(-1.11669 + 0.176866i) q^{38} +(1.99657 + 1.45059i) q^{39} +(5.28274 - 2.25078i) q^{40} +(6.36824 - 2.06917i) q^{41} +(-0.229174 - 0.0362976i) q^{42} +(-3.72708 - 3.72708i) q^{43} +(-0.793670 + 0.656674i) q^{44} +(-0.361710 + 5.27464i) q^{45} +(-1.45165 - 1.99802i) q^{46} +(5.61318 - 11.0165i) q^{47} +(-1.63764 - 3.21405i) q^{48} +(4.09295 - 5.63346i) q^{49} +(-7.59877 + 0.153087i) q^{50} +(-2.81030 - 0.913123i) q^{51} +(-0.856672 - 0.436496i) q^{52} +(-1.41265 + 8.91914i) q^{53} +6.50079 q^{54} +(-7.06587 + 2.25243i) q^{55} -0.491699 q^{56} +(-0.0927608 + 0.585669i) q^{57} +(-12.9306 - 6.58847i) q^{58} +(9.15496 + 2.97463i) q^{59} +(0.0489978 + 0.551502i) q^{60} +(-3.46383 + 4.76756i) q^{61} +(-0.242168 - 0.475281i) q^{62} +(0.205531 - 0.403377i) q^{63} +(-3.76284 - 5.17911i) q^{64} +(-4.54825 - 5.21797i) q^{65} +(1.47982 + 3.73685i) q^{66} +(4.13426 + 4.13426i) q^{67} +(1.13704 + 0.180089i) q^{68} +(-1.23188 + 0.400262i) q^{69} +(0.603742 + 0.242983i) q^{70} +(9.27272 + 6.73702i) q^{71} +(5.99713 - 0.949851i) q^{72} +(2.14008 - 1.09042i) q^{73} +(-2.53903 - 7.81434i) q^{74} +(-1.15517 + 3.81507i) q^{75} -0.231015i q^{76} +(0.632224 + 0.0597184i) q^{77} +(-2.65261 + 2.65261i) q^{78} +(0.542434 - 0.394101i) q^{79} +(2.46086 + 9.81373i) q^{80} +(-1.13837 + 3.50353i) q^{81} +(1.59224 + 10.0530i) q^{82} +(-2.60980 - 16.4776i) q^{83} +(0.0146506 - 0.0450899i) q^{84} +(7.10995 + 4.25908i) q^{85} +(6.48191 - 4.70938i) q^{86} +(-5.38198 + 5.38198i) q^{87} +(4.33608 + 7.33074i) q^{88} -7.92190i q^{89} +(-7.83306 - 1.79731i) q^{90} +(0.183160 + 0.563709i) q^{91} +(0.449625 - 0.229095i) q^{92} +(-0.276318 + 0.0437645i) q^{93} +(15.2048 + 11.0469i) q^{94} +(0.620959 - 1.54290i) q^{95} +(1.32067 - 0.429111i) q^{96} +(-1.36201 - 0.215721i) q^{97} +(7.48452 + 7.48452i) q^{98} +(-7.82643 + 0.492943i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 10 q^{2} - 4 q^{3} - 2 q^{5} - 20 q^{6} - 10 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 10 q^{2} - 4 q^{3} - 2 q^{5} - 20 q^{6} - 10 q^{8} - 24 q^{11} + 12 q^{12} - 10 q^{13} + 14 q^{15} - 8 q^{16} - 10 q^{18} + 16 q^{20} + 10 q^{22} - 24 q^{23} + 16 q^{25} + 20 q^{26} - 16 q^{27} + 50 q^{28} + 30 q^{30} - 28 q^{31} + 66 q^{33} - 10 q^{35} + 24 q^{36} - 8 q^{37} + 10 q^{38} - 50 q^{40} + 40 q^{41} - 10 q^{42} - 28 q^{45} + 60 q^{46} - 28 q^{47} - 54 q^{48} - 50 q^{50} + 20 q^{51} - 50 q^{52} - 24 q^{53} - 64 q^{55} - 80 q^{56} + 30 q^{57} - 50 q^{58} + 34 q^{60} - 60 q^{61} + 100 q^{62} - 30 q^{63} - 100 q^{66} - 8 q^{67} - 30 q^{68} + 30 q^{70} + 24 q^{71} + 80 q^{72} + 50 q^{73} + 34 q^{75} + 70 q^{77} + 60 q^{78} + 98 q^{80} - 12 q^{81} - 10 q^{82} + 90 q^{83} + 30 q^{85} + 100 q^{86} + 170 q^{88} - 20 q^{90} + 20 q^{91} - 68 q^{92} - 8 q^{93} - 40 q^{95} - 8 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/55\mathbb{Z}\right)^\times\).

\(n\) \(12\) \(46\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{3}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.237790 + 1.50135i −0.168143 + 1.06161i 0.748859 + 0.662730i \(0.230602\pi\)
−0.917002 + 0.398884i \(0.869398\pi\)
\(3\) 0.710333 + 0.361933i 0.410111 + 0.208962i 0.646860 0.762609i \(-0.276082\pi\)
−0.236749 + 0.971571i \(0.576082\pi\)
\(4\) −0.295389 0.0959778i −0.147695 0.0479889i
\(5\) −1.71486 1.43501i −0.766908 0.641757i
\(6\) −0.712297 + 0.980393i −0.290794 + 0.400244i
\(7\) 0.0869260 + 0.170602i 0.0328550 + 0.0644815i 0.906851 0.421452i \(-0.138480\pi\)
−0.873996 + 0.485934i \(0.838480\pi\)
\(8\) −1.16585 + 2.28811i −0.412191 + 0.808970i
\(9\) −1.38978 1.91287i −0.463259 0.637622i
\(10\) 2.56223 2.23337i 0.810248 0.706253i
\(11\) 1.77694 2.80044i 0.535768 0.844365i
\(12\) −0.175087 0.175087i −0.0505433 0.0505433i
\(13\) 3.05749 + 0.484259i 0.847995 + 0.134309i 0.565285 0.824896i \(-0.308766\pi\)
0.282711 + 0.959205i \(0.408766\pi\)
\(14\) −0.276803 + 0.0899388i −0.0739787 + 0.0240372i
\(15\) −0.698743 1.64000i −0.180415 0.423446i
\(16\) −3.66057 2.65956i −0.915143 0.664890i
\(17\) −3.66088 + 0.579827i −0.887894 + 0.140629i −0.583688 0.811978i \(-0.698391\pi\)
−0.304206 + 0.952606i \(0.598391\pi\)
\(18\) 3.20235 1.63168i 0.754802 0.384591i
\(19\) 0.229844 + 0.707388i 0.0527299 + 0.162286i 0.973954 0.226747i \(-0.0728091\pi\)
−0.921224 + 0.389033i \(0.872809\pi\)
\(20\) 0.368822 + 0.588475i 0.0824710 + 0.131587i
\(21\) 0.152646i 0.0333100i
\(22\) 3.78190 + 3.33373i 0.806304 + 0.710753i
\(23\) −1.14886 + 1.14886i −0.239553 + 0.239553i −0.816665 0.577112i \(-0.804180\pi\)
0.577112 + 0.816665i \(0.304180\pi\)
\(24\) −1.65629 + 1.20336i −0.338088 + 0.245635i
\(25\) 0.881484 + 4.92169i 0.176297 + 0.984337i
\(26\) −1.45408 + 4.47521i −0.285169 + 0.877660i
\(27\) −0.669017 4.22401i −0.128752 0.812911i
\(28\) −0.00930302 0.0587369i −0.00175811 0.0111002i
\(29\) −2.95025 + 9.07993i −0.547847 + 1.68610i 0.166275 + 0.986079i \(0.446826\pi\)
−0.714122 + 0.700021i \(0.753174\pi\)
\(30\) 2.62836 0.659081i 0.479871 0.120331i
\(31\) −0.283900 + 0.206266i −0.0509900 + 0.0370464i −0.612988 0.790092i \(-0.710033\pi\)
0.561998 + 0.827138i \(0.310033\pi\)
\(32\) 1.23166 1.23166i 0.217729 0.217729i
\(33\) 2.27579 1.34611i 0.396165 0.234328i
\(34\) 5.63413i 0.966246i
\(35\) 0.0957498 0.417298i 0.0161847 0.0705363i
\(36\) 0.226933 + 0.698428i 0.0378222 + 0.116405i
\(37\) −4.81621 + 2.45398i −0.791780 + 0.403432i −0.802606 0.596510i \(-0.796554\pi\)
0.0108264 + 0.999941i \(0.496554\pi\)
\(38\) −1.11669 + 0.176866i −0.181151 + 0.0286915i
\(39\) 1.99657 + 1.45059i 0.319707 + 0.232280i
\(40\) 5.28274 2.25078i 0.835274 0.355880i
\(41\) 6.36824 2.06917i 0.994552 0.323150i 0.233866 0.972269i \(-0.424862\pi\)
0.760687 + 0.649119i \(0.224862\pi\)
\(42\) −0.229174 0.0362976i −0.0353623 0.00560084i
\(43\) −3.72708 3.72708i −0.568374 0.568374i 0.363299 0.931673i \(-0.381650\pi\)
−0.931673 + 0.363299i \(0.881650\pi\)
\(44\) −0.793670 + 0.656674i −0.119650 + 0.0989973i
\(45\) −0.361710 + 5.27464i −0.0539205 + 0.786297i
\(46\) −1.45165 1.99802i −0.214034 0.294592i
\(47\) 5.61318 11.0165i 0.818766 1.60692i 0.0242272 0.999706i \(-0.492287\pi\)
0.794539 0.607213i \(-0.207713\pi\)
\(48\) −1.63764 3.21405i −0.236373 0.463909i
\(49\) 4.09295 5.63346i 0.584707 0.804780i
\(50\) −7.59877 + 0.153087i −1.07463 + 0.0216497i
\(51\) −2.81030 0.913123i −0.393521 0.127863i
\(52\) −0.856672 0.436496i −0.118799 0.0605311i
\(53\) −1.41265 + 8.91914i −0.194043 + 1.22514i 0.677761 + 0.735282i \(0.262950\pi\)
−0.871804 + 0.489855i \(0.837050\pi\)
\(54\) 6.50079 0.884646
\(55\) −7.06587 + 2.25243i −0.952762 + 0.303718i
\(56\) −0.491699 −0.0657061
\(57\) −0.0927608 + 0.585669i −0.0122865 + 0.0775737i
\(58\) −12.9306 6.58847i −1.69787 0.865108i
\(59\) 9.15496 + 2.97463i 1.19187 + 0.387263i 0.836765 0.547562i \(-0.184444\pi\)
0.355108 + 0.934825i \(0.384444\pi\)
\(60\) 0.0489978 + 0.551502i 0.00632558 + 0.0711986i
\(61\) −3.46383 + 4.76756i −0.443498 + 0.610423i −0.970985 0.239140i \(-0.923134\pi\)
0.527487 + 0.849563i \(0.323134\pi\)
\(62\) −0.242168 0.475281i −0.0307554 0.0603608i
\(63\) 0.205531 0.403377i 0.0258944 0.0508207i
\(64\) −3.76284 5.17911i −0.470356 0.647389i
\(65\) −4.54825 5.21797i −0.564141 0.647209i
\(66\) 1.47982 + 3.73685i 0.182154 + 0.459974i
\(67\) 4.13426 + 4.13426i 0.505081 + 0.505081i 0.913012 0.407932i \(-0.133750\pi\)
−0.407932 + 0.913012i \(0.633750\pi\)
\(68\) 1.13704 + 0.180089i 0.137886 + 0.0218390i
\(69\) −1.23188 + 0.400262i −0.148301 + 0.0481859i
\(70\) 0.603742 + 0.242983i 0.0721609 + 0.0290421i
\(71\) 9.27272 + 6.73702i 1.10047 + 0.799538i 0.981136 0.193317i \(-0.0619245\pi\)
0.119333 + 0.992854i \(0.461925\pi\)
\(72\) 5.99713 0.949851i 0.706768 0.111941i
\(73\) 2.14008 1.09042i 0.250477 0.127624i −0.324245 0.945973i \(-0.605110\pi\)
0.574722 + 0.818349i \(0.305110\pi\)
\(74\) −2.53903 7.81434i −0.295156 0.908398i
\(75\) −1.15517 + 3.81507i −0.133388 + 0.440527i
\(76\) 0.231015i 0.0264992i
\(77\) 0.632224 + 0.0597184i 0.0720486 + 0.00680554i
\(78\) −2.65261 + 2.65261i −0.300348 + 0.300348i
\(79\) 0.542434 0.394101i 0.0610286 0.0443399i −0.556853 0.830611i \(-0.687991\pi\)
0.617881 + 0.786271i \(0.287991\pi\)
\(80\) 2.46086 + 9.81373i 0.275133 + 1.09721i
\(81\) −1.13837 + 3.50353i −0.126485 + 0.389282i
\(82\) 1.59224 + 10.0530i 0.175833 + 1.11017i
\(83\) −2.60980 16.4776i −0.286463 1.80865i −0.540372 0.841426i \(-0.681716\pi\)
0.253909 0.967228i \(-0.418284\pi\)
\(84\) 0.0146506 0.0450899i 0.00159851 0.00491971i
\(85\) 7.10995 + 4.25908i 0.771183 + 0.461963i
\(86\) 6.48191 4.70938i 0.698962 0.507826i
\(87\) −5.38198 + 5.38198i −0.577009 + 0.577009i
\(88\) 4.33608 + 7.33074i 0.462227 + 0.781460i
\(89\) 7.92190i 0.839720i −0.907589 0.419860i \(-0.862079\pi\)
0.907589 0.419860i \(-0.137921\pi\)
\(90\) −7.83306 1.79731i −0.825678 0.189453i
\(91\) 0.183160 + 0.563709i 0.0192004 + 0.0590927i
\(92\) 0.449625 0.229095i 0.0468766 0.0238848i
\(93\) −0.276318 + 0.0437645i −0.0286528 + 0.00453817i
\(94\) 15.2048 + 11.0469i 1.56826 + 1.13941i
\(95\) 0.620959 1.54290i 0.0637090 0.158298i
\(96\) 1.32067 0.429111i 0.134790 0.0437960i
\(97\) −1.36201 0.215721i −0.138291 0.0219032i 0.0869051 0.996217i \(-0.472302\pi\)
−0.225196 + 0.974313i \(0.572302\pi\)
\(98\) 7.48452 + 7.48452i 0.756051 + 0.756051i
\(99\) −7.82643 + 0.492943i −0.786585 + 0.0495427i
\(100\) 0.211991 1.53842i 0.0211991 0.153842i
\(101\) −2.83633 3.90387i −0.282225 0.388449i 0.644244 0.764820i \(-0.277172\pi\)
−0.926469 + 0.376370i \(0.877172\pi\)
\(102\) 2.03918 4.00211i 0.201909 0.396268i
\(103\) −1.46972 2.88449i −0.144816 0.284217i 0.807193 0.590287i \(-0.200986\pi\)
−0.952009 + 0.306071i \(0.900986\pi\)
\(104\) −4.67262 + 6.43131i −0.458188 + 0.630641i
\(105\) 0.219048 0.261766i 0.0213769 0.0255457i
\(106\) −13.0548 4.24177i −1.26800 0.411997i
\(107\) −9.85055 5.01911i −0.952289 0.485215i −0.0924142 0.995721i \(-0.529458\pi\)
−0.859875 + 0.510505i \(0.829458\pi\)
\(108\) −0.207790 + 1.31194i −0.0199946 + 0.126241i
\(109\) −9.54212 −0.913969 −0.456985 0.889475i \(-0.651071\pi\)
−0.456985 + 0.889475i \(0.651071\pi\)
\(110\) −1.70149 11.1439i −0.162231 1.06253i
\(111\) −4.30929 −0.409019
\(112\) 0.135527 0.855686i 0.0128061 0.0808547i
\(113\) 3.69562 + 1.88301i 0.347654 + 0.177139i 0.619094 0.785317i \(-0.287500\pi\)
−0.271440 + 0.962455i \(0.587500\pi\)
\(114\) −0.857235 0.278533i −0.0802874 0.0260870i
\(115\) 3.61875 0.321505i 0.337450 0.0299805i
\(116\) 1.74294 2.39895i 0.161828 0.222737i
\(117\) −3.32291 6.52158i −0.307203 0.602920i
\(118\) −6.64291 + 13.0374i −0.611529 + 1.20019i
\(119\) −0.417145 0.574151i −0.0382397 0.0526324i
\(120\) 4.56713 + 0.313192i 0.416920 + 0.0285904i
\(121\) −4.68496 9.95245i −0.425905 0.904768i
\(122\) −6.33410 6.33410i −0.573462 0.573462i
\(123\) 5.27247 + 0.835077i 0.475403 + 0.0752964i
\(124\) 0.103658 0.0336805i 0.00930877 0.00302460i
\(125\) 5.55105 9.70494i 0.496501 0.868036i
\(126\) 0.556736 + 0.404492i 0.0495980 + 0.0360350i
\(127\) 14.3879 2.27881i 1.27672 0.202212i 0.518987 0.854782i \(-0.326309\pi\)
0.757728 + 0.652570i \(0.226309\pi\)
\(128\) 11.7744 5.99935i 1.04072 0.530273i
\(129\) −1.29851 3.99642i −0.114328 0.351865i
\(130\) 8.91552 5.58772i 0.781943 0.490076i
\(131\) 9.76926i 0.853544i 0.904359 + 0.426772i \(0.140349\pi\)
−0.904359 + 0.426772i \(0.859651\pi\)
\(132\) −0.801441 + 0.179202i −0.0697565 + 0.0155975i
\(133\) −0.100702 + 0.100702i −0.00873200 + 0.00873200i
\(134\) −7.19006 + 5.22388i −0.621126 + 0.451275i
\(135\) −4.91423 + 8.20363i −0.422949 + 0.706056i
\(136\) 2.94133 9.05250i 0.252217 0.776245i
\(137\) 0.677380 + 4.27681i 0.0578725 + 0.365392i 0.999581 + 0.0289612i \(0.00921994\pi\)
−0.941708 + 0.336431i \(0.890780\pi\)
\(138\) −0.308004 1.94466i −0.0262190 0.165540i
\(139\) −3.24794 + 9.99613i −0.275487 + 0.847860i 0.713604 + 0.700550i \(0.247062\pi\)
−0.989090 + 0.147311i \(0.952938\pi\)
\(140\) −0.0683348 + 0.114076i −0.00577535 + 0.00964114i
\(141\) 7.97445 5.79378i 0.671570 0.487924i
\(142\) −12.3196 + 12.3196i −1.03384 + 1.03384i
\(143\) 6.78912 7.70183i 0.567735 0.644059i
\(144\) 10.6984i 0.891532i
\(145\) 18.0891 11.3372i 1.50221 0.941500i
\(146\) 1.12822 + 3.47229i 0.0933719 + 0.287369i
\(147\) 4.94629 2.52026i 0.407963 0.207868i
\(148\) 1.65818 0.262630i 0.136302 0.0215881i
\(149\) −4.66189 3.38706i −0.381917 0.277479i 0.380218 0.924897i \(-0.375849\pi\)
−0.762135 + 0.647418i \(0.775849\pi\)
\(150\) −5.45306 2.64150i −0.445241 0.215678i
\(151\) −14.2318 + 4.62419i −1.15817 + 0.376311i −0.824214 0.566278i \(-0.808383\pi\)
−0.333953 + 0.942590i \(0.608383\pi\)
\(152\) −1.88655 0.298800i −0.153019 0.0242358i
\(153\) 6.19694 + 6.19694i 0.500993 + 0.500993i
\(154\) −0.239995 + 0.934987i −0.0193393 + 0.0753434i
\(155\) 0.782843 + 0.0536836i 0.0628795 + 0.00431197i
\(156\) −0.450540 0.620115i −0.0360721 0.0496489i
\(157\) −2.24640 + 4.40881i −0.179282 + 0.351861i −0.963106 0.269122i \(-0.913267\pi\)
0.783824 + 0.620983i \(0.213267\pi\)
\(158\) 0.462698 + 0.908095i 0.0368103 + 0.0722442i
\(159\) −4.23158 + 5.82427i −0.335586 + 0.461895i
\(160\) −3.87958 + 0.344678i −0.306707 + 0.0272492i
\(161\) −0.295863 0.0961317i −0.0233173 0.00757624i
\(162\) −4.98933 2.54219i −0.391999 0.199733i
\(163\) −1.56695 + 9.89335i −0.122733 + 0.774907i 0.847153 + 0.531349i \(0.178315\pi\)
−0.969886 + 0.243558i \(0.921685\pi\)
\(164\) −2.07970 −0.162398
\(165\) −5.83435 0.957393i −0.454204 0.0745329i
\(166\) 25.3592 1.96826
\(167\) −1.88695 + 11.9137i −0.146017 + 0.921913i 0.800517 + 0.599310i \(0.204558\pi\)
−0.946534 + 0.322604i \(0.895442\pi\)
\(168\) −0.349270 0.177962i −0.0269468 0.0137301i
\(169\) −3.24999 1.05599i −0.250000 0.0812298i
\(170\) −8.08505 + 9.66175i −0.620095 + 0.741022i
\(171\) 1.03371 1.42277i 0.0790494 0.108802i
\(172\) 0.743222 + 1.45866i 0.0566702 + 0.111221i
\(173\) −5.65903 + 11.1065i −0.430248 + 0.844410i 0.569501 + 0.821991i \(0.307137\pi\)
−0.999749 + 0.0224186i \(0.992863\pi\)
\(174\) −6.80045 9.36001i −0.515540 0.709581i
\(175\) −0.763025 + 0.578206i −0.0576793 + 0.0437082i
\(176\) −13.9526 + 5.52533i −1.05171 + 0.416488i
\(177\) 5.42645 + 5.42645i 0.407877 + 0.407877i
\(178\) 11.8935 + 1.88375i 0.891458 + 0.141193i
\(179\) 19.1909 6.23551i 1.43440 0.466064i 0.514252 0.857639i \(-0.328070\pi\)
0.920146 + 0.391575i \(0.128070\pi\)
\(180\) 0.613094 1.52336i 0.0456973 0.113544i
\(181\) −3.72935 2.70953i −0.277200 0.201398i 0.440495 0.897755i \(-0.354803\pi\)
−0.717695 + 0.696357i \(0.754803\pi\)
\(182\) −0.889877 + 0.140943i −0.0659620 + 0.0104474i
\(183\) −4.18601 + 2.13288i −0.309439 + 0.157667i
\(184\) −1.28932 3.96811i −0.0950497 0.292533i
\(185\) 11.7806 + 2.70308i 0.866127 + 0.198735i
\(186\) 0.425256i 0.0311813i
\(187\) −4.88140 + 11.2824i −0.356963 + 0.825051i
\(188\) −2.71541 + 2.71541i −0.198042 + 0.198042i
\(189\) 0.662469 0.481312i 0.0481875 0.0350103i
\(190\) 2.16877 + 1.29916i 0.157339 + 0.0942511i
\(191\) 1.95493 6.01667i 0.141454 0.435351i −0.855084 0.518490i \(-0.826495\pi\)
0.996538 + 0.0831389i \(0.0264945\pi\)
\(192\) −0.798383 5.04079i −0.0576183 0.363788i
\(193\) −0.927951 5.85885i −0.0667954 0.421729i −0.998314 0.0580368i \(-0.981516\pi\)
0.931519 0.363692i \(-0.118484\pi\)
\(194\) 0.647745 1.99355i 0.0465054 0.143129i
\(195\) −1.34222 5.35265i −0.0961181 0.383312i
\(196\) −1.74970 + 1.27123i −0.124979 + 0.0908022i
\(197\) 9.90515 9.90515i 0.705713 0.705713i −0.259918 0.965631i \(-0.583696\pi\)
0.965631 + 0.259918i \(0.0836955\pi\)
\(198\) 1.12097 11.8674i 0.0796637 0.843380i
\(199\) 13.3828i 0.948680i −0.880342 0.474340i \(-0.842687\pi\)
0.880342 0.474340i \(-0.157313\pi\)
\(200\) −12.2890 3.72102i −0.868967 0.263116i
\(201\) 1.44038 + 4.43303i 0.101596 + 0.312682i
\(202\) 6.53551 3.33001i 0.459837 0.234299i
\(203\) −1.80551 + 0.285964i −0.126722 + 0.0200708i
\(204\) 0.742493 + 0.539453i 0.0519849 + 0.0377693i
\(205\) −13.8899 5.59017i −0.970114 0.390434i
\(206\) 4.68010 1.52066i 0.326078 0.105949i
\(207\) 3.79427 + 0.600953i 0.263720 + 0.0417691i
\(208\) −9.90424 9.90424i −0.686736 0.686736i
\(209\) 2.38942 + 0.613321i 0.165280 + 0.0424243i
\(210\) 0.340914 + 0.391113i 0.0235253 + 0.0269893i
\(211\) 3.48696 + 4.79939i 0.240052 + 0.330404i 0.911996 0.410198i \(-0.134540\pi\)
−0.671944 + 0.740602i \(0.734540\pi\)
\(212\) 1.27332 2.49903i 0.0874521 0.171634i
\(213\) 4.14837 + 8.14163i 0.284241 + 0.557855i
\(214\) 9.87779 13.5956i 0.675232 0.929377i
\(215\) 1.04301 + 11.7398i 0.0711330 + 0.800649i
\(216\) 10.4450 + 3.39378i 0.710691 + 0.230917i
\(217\) −0.0598677 0.0305041i −0.00406408 0.00207075i
\(218\) 2.26902 14.3260i 0.153678 0.970282i
\(219\) 1.91483 0.129392
\(220\) 2.30337 + 0.0128223i 0.155293 + 0.000864476i
\(221\) −11.4739 −0.771818
\(222\) 1.02471 6.46974i 0.0687738 0.434220i
\(223\) −18.9389 9.64984i −1.26824 0.646201i −0.315195 0.949027i \(-0.602070\pi\)
−0.953046 + 0.302826i \(0.902070\pi\)
\(224\) 0.317188 + 0.103060i 0.0211930 + 0.00688602i
\(225\) 8.18945 8.52621i 0.545964 0.568414i
\(226\) −3.70584 + 5.10065i −0.246509 + 0.339290i
\(227\) 5.93372 + 11.6456i 0.393835 + 0.772944i 0.999745 0.0225888i \(-0.00719083\pi\)
−0.605910 + 0.795533i \(0.707191\pi\)
\(228\) 0.0836117 0.164097i 0.00553732 0.0108676i
\(229\) 9.65796 + 13.2930i 0.638216 + 0.878429i 0.998519 0.0544066i \(-0.0173267\pi\)
−0.360303 + 0.932835i \(0.617327\pi\)
\(230\) −0.377812 + 5.50946i −0.0249122 + 0.363283i
\(231\) 0.427475 + 0.271242i 0.0281258 + 0.0178464i
\(232\) −17.3363 17.3363i −1.13819 1.13819i
\(233\) −15.4510 2.44720i −1.01223 0.160321i −0.371779 0.928321i \(-0.621252\pi\)
−0.640450 + 0.768000i \(0.721252\pi\)
\(234\) 10.5813 3.43808i 0.691722 0.224754i
\(235\) −25.4346 + 10.8367i −1.65917 + 0.706911i
\(236\) −2.41878 1.75734i −0.157449 0.114393i
\(237\) 0.527947 0.0836185i 0.0342938 0.00543161i
\(238\) 0.961194 0.489753i 0.0623050 0.0317460i
\(239\) −1.63214 5.02322i −0.105575 0.324925i 0.884290 0.466938i \(-0.154643\pi\)
−0.989865 + 0.142012i \(0.954643\pi\)
\(240\) −1.80388 + 7.86168i −0.116440 + 0.507470i
\(241\) 16.1676i 1.04144i −0.853726 0.520722i \(-0.825663\pi\)
0.853726 0.520722i \(-0.174337\pi\)
\(242\) 16.0561 4.66716i 1.03213 0.300016i
\(243\) −11.1488 + 11.1488i −0.715198 + 0.715198i
\(244\) 1.48076 1.07583i 0.0947959 0.0688732i
\(245\) −15.1029 + 3.78716i −0.964889 + 0.241953i
\(246\) −2.50748 + 7.71724i −0.159871 + 0.492033i
\(247\) 0.360188 + 2.27413i 0.0229182 + 0.144700i
\(248\) −0.140973 0.890071i −0.00895182 0.0565196i
\(249\) 4.10997 12.6492i 0.260458 0.801609i
\(250\) 13.2505 + 10.6418i 0.838036 + 0.673047i
\(251\) −15.6486 + 11.3694i −0.987729 + 0.717627i −0.959423 0.281972i \(-0.909011\pi\)
−0.0283063 + 0.999599i \(0.509011\pi\)
\(252\) −0.0994268 + 0.0994268i −0.00626330 + 0.00626330i
\(253\) 1.17586 + 5.25876i 0.0739254 + 0.330615i
\(254\) 22.1431i 1.38938i
\(255\) 3.50893 + 5.59869i 0.219738 + 0.350604i
\(256\) 2.25079 + 6.92722i 0.140674 + 0.432951i
\(257\) −4.19318 + 2.13653i −0.261563 + 0.133273i −0.579855 0.814720i \(-0.696891\pi\)
0.318292 + 0.947993i \(0.396891\pi\)
\(258\) 6.30879 0.999214i 0.392768 0.0622083i
\(259\) −0.837308 0.608340i −0.0520278 0.0378004i
\(260\) 0.842694 + 1.97786i 0.0522617 + 0.122662i
\(261\) 21.4689 6.97566i 1.32889 0.431783i
\(262\) −14.6671 2.32303i −0.906134 0.143517i
\(263\) 11.2218 + 11.2218i 0.691964 + 0.691964i 0.962664 0.270700i \(-0.0872550\pi\)
−0.270700 + 0.962664i \(0.587255\pi\)
\(264\) 0.426823 + 6.77663i 0.0262691 + 0.417073i
\(265\) 15.2216 13.2679i 0.935053 0.815040i
\(266\) −0.127243 0.175135i −0.00780178 0.0107382i
\(267\) 2.86720 5.62719i 0.175470 0.344378i
\(268\) −0.824419 1.61801i −0.0503594 0.0988359i
\(269\) −6.64926 + 9.15192i −0.405412 + 0.558002i −0.962092 0.272725i \(-0.912075\pi\)
0.556680 + 0.830727i \(0.312075\pi\)
\(270\) −11.1479 9.32871i −0.678442 0.567727i
\(271\) 16.9556 + 5.50921i 1.02998 + 0.334661i 0.774782 0.632228i \(-0.217859\pi\)
0.255198 + 0.966889i \(0.417859\pi\)
\(272\) 14.9430 + 7.61384i 0.906052 + 0.461657i
\(273\) −0.0739200 + 0.466712i −0.00447384 + 0.0282467i
\(274\) −6.58205 −0.397636
\(275\) 15.3492 + 6.27700i 0.925594 + 0.378517i
\(276\) 0.402300 0.0242156
\(277\) 0.732361 4.62395i 0.0440033 0.277826i −0.955869 0.293793i \(-0.905083\pi\)
0.999873 + 0.0159666i \(0.00508253\pi\)
\(278\) −14.2353 7.25327i −0.853779 0.435022i
\(279\) 0.789117 + 0.256400i 0.0472432 + 0.0153502i
\(280\) 0.843195 + 0.705594i 0.0503905 + 0.0421673i
\(281\) −7.75247 + 10.6704i −0.462474 + 0.636541i −0.975019 0.222119i \(-0.928703\pi\)
0.512546 + 0.858660i \(0.328703\pi\)
\(282\) 6.80223 + 13.3501i 0.405067 + 0.794989i
\(283\) 10.3449 20.3029i 0.614938 1.20688i −0.348084 0.937463i \(-0.613168\pi\)
0.963022 0.269421i \(-0.0868324\pi\)
\(284\) −2.09246 2.88002i −0.124164 0.170898i
\(285\) 0.999513 0.871227i 0.0592061 0.0516070i
\(286\) 9.94874 + 12.0243i 0.588281 + 0.711009i
\(287\) 0.906570 + 0.906570i 0.0535131 + 0.0535131i
\(288\) −4.06774 0.644267i −0.239694 0.0379638i
\(289\) −3.10211 + 1.00794i −0.182477 + 0.0592904i
\(290\) 12.7196 + 29.8538i 0.746922 + 1.75308i
\(291\) −0.889404 0.646190i −0.0521378 0.0378803i
\(292\) −0.736812 + 0.116700i −0.0431187 + 0.00682933i
\(293\) −6.43996 + 3.28132i −0.376226 + 0.191697i −0.631870 0.775074i \(-0.717713\pi\)
0.255644 + 0.966771i \(0.417713\pi\)
\(294\) 2.60761 + 8.02539i 0.152079 + 0.468051i
\(295\) −11.4308 18.2385i −0.665529 1.06189i
\(296\) 13.8810i 0.806817i
\(297\) −13.0179 5.63227i −0.755375 0.326818i
\(298\) 6.19371 6.19371i 0.358792 0.358792i
\(299\) −4.06896 + 2.95628i −0.235314 + 0.170966i
\(300\) 0.707387 1.01606i 0.0408410 0.0586623i
\(301\) 0.311867 0.959827i 0.0179757 0.0553235i
\(302\) −3.55834 22.4665i −0.204759 1.29280i
\(303\) −0.601798 3.79960i −0.0345724 0.218282i
\(304\) 1.03998 3.20073i 0.0596469 0.183574i
\(305\) 12.7815 3.20505i 0.731866 0.183521i
\(306\) −10.7773 + 7.83020i −0.616100 + 0.447623i
\(307\) 20.1272 20.1272i 1.14872 1.14872i 0.161918 0.986804i \(-0.448232\pi\)
0.986804 0.161918i \(-0.0517681\pi\)
\(308\) −0.181020 0.0783196i −0.0103146 0.00446267i
\(309\) 2.58088i 0.146821i
\(310\) −0.266750 + 1.16255i −0.0151504 + 0.0660286i
\(311\) −2.32254 7.14803i −0.131699 0.405328i 0.863363 0.504583i \(-0.168354\pi\)
−0.995062 + 0.0992557i \(0.968354\pi\)
\(312\) −5.64681 + 2.87720i −0.319688 + 0.162889i
\(313\) −1.32951 + 0.210574i −0.0751483 + 0.0119023i −0.193895 0.981022i \(-0.562112\pi\)
0.118747 + 0.992925i \(0.462112\pi\)
\(314\) −6.08499 4.42100i −0.343396 0.249492i
\(315\) −0.931306 + 0.396795i −0.0524732 + 0.0223569i
\(316\) −0.198054 + 0.0643517i −0.0111414 + 0.00362006i
\(317\) −11.1924 1.77271i −0.628630 0.0995652i −0.166013 0.986124i \(-0.553089\pi\)
−0.462617 + 0.886558i \(0.653089\pi\)
\(318\) −7.73803 7.73803i −0.433927 0.433927i
\(319\) 20.1854 + 24.3965i 1.13017 + 1.36594i
\(320\) −0.979335 + 14.2812i −0.0547465 + 0.798342i
\(321\) −5.18059 7.13047i −0.289152 0.397984i
\(322\) 0.214680 0.421334i 0.0119637 0.0234800i
\(323\) −1.25159 2.45639i −0.0696406 0.136677i
\(324\) 0.672523 0.925648i 0.0373624 0.0514249i
\(325\) 0.311760 + 15.4749i 0.0172934 + 0.858391i
\(326\) −14.4808 4.70509i −0.802015 0.260591i
\(327\) −6.77808 3.45360i −0.374829 0.190985i
\(328\) −2.68994 + 16.9836i −0.148527 + 0.937762i
\(329\) 2.36737 0.130517
\(330\) 2.82473 8.53173i 0.155496 0.469656i
\(331\) −17.7048 −0.973145 −0.486572 0.873640i \(-0.661753\pi\)
−0.486572 + 0.873640i \(0.661753\pi\)
\(332\) −0.810579 + 5.11780i −0.0444863 + 0.280876i
\(333\) 11.3876 + 5.80227i 0.624036 + 0.317962i
\(334\) −17.4380 5.66594i −0.954164 0.310027i
\(335\) −1.15696 13.0224i −0.0632117 0.711489i
\(336\) 0.405970 0.558770i 0.0221475 0.0304834i
\(337\) 3.45945 + 6.78954i 0.188448 + 0.369850i 0.965829 0.259180i \(-0.0834523\pi\)
−0.777381 + 0.629030i \(0.783452\pi\)
\(338\) 2.35822 4.62827i 0.128270 0.251745i
\(339\) 1.94359 + 2.67513i 0.105562 + 0.145293i
\(340\) −1.69143 1.94049i −0.0917305 0.105238i
\(341\) 0.0731608 + 1.16157i 0.00396188 + 0.0629025i
\(342\) 1.89027 + 1.89027i 0.102214 + 0.102214i
\(343\) 2.64066 + 0.418239i 0.142582 + 0.0225828i
\(344\) 12.8732 4.18275i 0.694076 0.225519i
\(345\) 2.68688 + 1.08137i 0.144657 + 0.0582189i
\(346\) −15.3290 11.1372i −0.824093 0.598739i
\(347\) −9.21879 + 1.46011i −0.494891 + 0.0783830i −0.398891 0.916998i \(-0.630605\pi\)
−0.0959998 + 0.995381i \(0.530605\pi\)
\(348\) 2.10633 1.07323i 0.112911 0.0575311i
\(349\) 0.464073 + 1.42827i 0.0248413 + 0.0764536i 0.962709 0.270540i \(-0.0872024\pi\)
−0.937867 + 0.346994i \(0.887202\pi\)
\(350\) −0.686648 1.28306i −0.0367029 0.0685823i
\(351\) 13.2388i 0.706637i
\(352\) −1.26061 5.63779i −0.0671906 0.300495i
\(353\) 4.40229 4.40229i 0.234310 0.234310i −0.580179 0.814489i \(-0.697017\pi\)
0.814489 + 0.580179i \(0.197017\pi\)
\(354\) −9.43735 + 6.85664i −0.501589 + 0.364426i
\(355\) −6.23370 24.8595i −0.330850 1.31941i
\(356\) −0.760327 + 2.34004i −0.0402972 + 0.124022i
\(357\) −0.0885080 0.558817i −0.00468434 0.0295757i
\(358\) 4.79826 + 30.2950i 0.253596 + 1.60114i
\(359\) 8.12845 25.0168i 0.429003 1.32034i −0.470105 0.882611i \(-0.655784\pi\)
0.899108 0.437726i \(-0.144216\pi\)
\(360\) −11.6473 6.97708i −0.613865 0.367725i
\(361\) 14.9238 10.8427i 0.785461 0.570671i
\(362\) 4.95475 4.95475i 0.260416 0.260416i
\(363\) 0.274237 8.76519i 0.0143937 0.460053i
\(364\) 0.184093i 0.00964908i
\(365\) −5.23470 1.20111i −0.273997 0.0628691i
\(366\) −2.20680 6.79184i −0.115351 0.355015i
\(367\) 7.27872 3.70869i 0.379946 0.193592i −0.253579 0.967315i \(-0.581608\pi\)
0.633524 + 0.773723i \(0.281608\pi\)
\(368\) 7.26093 1.15002i 0.378502 0.0599488i
\(369\) −12.8085 9.30591i −0.666783 0.484446i
\(370\) −6.85958 + 17.0440i −0.356613 + 0.886077i
\(371\) −1.64442 + 0.534304i −0.0853740 + 0.0277397i
\(372\) 0.0858218 + 0.0135928i 0.00444965 + 0.000704756i
\(373\) 6.12473 + 6.12473i 0.317126 + 0.317126i 0.847662 0.530536i \(-0.178009\pi\)
−0.530536 + 0.847662i \(0.678009\pi\)
\(374\) −15.7781 10.0115i −0.815864 0.517684i
\(375\) 7.45563 4.88463i 0.385007 0.252241i
\(376\) 18.6628 + 25.6872i 0.962461 + 1.32471i
\(377\) −13.4174 + 26.3331i −0.691031 + 1.35622i
\(378\) 0.565088 + 1.10905i 0.0290650 + 0.0570433i
\(379\) −0.363481 + 0.500288i −0.0186708 + 0.0256981i −0.818250 0.574862i \(-0.805056\pi\)
0.799580 + 0.600560i \(0.205056\pi\)
\(380\) −0.331509 + 0.396158i −0.0170060 + 0.0203225i
\(381\) 11.0449 + 3.58872i 0.565849 + 0.183856i
\(382\) 8.56825 + 4.36574i 0.438390 + 0.223371i
\(383\) 1.62362 10.2511i 0.0829629 0.523807i −0.910850 0.412738i \(-0.864572\pi\)
0.993813 0.111069i \(-0.0354275\pi\)
\(384\) 10.5351 0.537617
\(385\) −0.998478 1.00966i −0.0508871 0.0514569i
\(386\) 9.01683 0.458945
\(387\) −1.94959 + 12.3092i −0.0991031 + 0.625712i
\(388\) 0.381619 + 0.194444i 0.0193737 + 0.00987142i
\(389\) −21.0630 6.84378i −1.06794 0.346993i −0.278252 0.960508i \(-0.589755\pi\)
−0.789683 + 0.613515i \(0.789755\pi\)
\(390\) 8.35536 0.742326i 0.423090 0.0375891i
\(391\) 3.53969 4.87197i 0.179010 0.246386i
\(392\) 8.11822 + 15.9329i 0.410032 + 0.804733i
\(393\) −3.53581 + 6.93942i −0.178358 + 0.350048i
\(394\) 12.5157 + 17.2264i 0.630534 + 0.867855i
\(395\) −1.49574 0.102571i −0.0752587 0.00516089i
\(396\) 2.35915 + 0.605553i 0.118552 + 0.0304302i
\(397\) 10.7769 + 10.7769i 0.540876 + 0.540876i 0.923786 0.382910i \(-0.125078\pi\)
−0.382910 + 0.923786i \(0.625078\pi\)
\(398\) 20.0922 + 3.18229i 1.00713 + 0.159514i
\(399\) −0.107980 + 0.0350847i −0.00540574 + 0.00175643i
\(400\) 9.86278 20.3605i 0.493139 1.01803i
\(401\) 3.46399 + 2.51673i 0.172983 + 0.125680i 0.670908 0.741540i \(-0.265904\pi\)
−0.497925 + 0.867220i \(0.665904\pi\)
\(402\) −6.99803 + 1.10838i −0.349030 + 0.0552809i
\(403\) −0.967909 + 0.493174i −0.0482150 + 0.0245668i
\(404\) 0.463135 + 1.42538i 0.0230418 + 0.0709155i
\(405\) 6.97975 4.37450i 0.346827 0.217371i
\(406\) 2.77869i 0.137904i
\(407\) −1.68589 + 17.8481i −0.0835664 + 0.884697i
\(408\) 5.36572 5.36572i 0.265643 0.265643i
\(409\) 3.47523 2.52490i 0.171839 0.124848i −0.498541 0.866866i \(-0.666131\pi\)
0.670381 + 0.742017i \(0.266131\pi\)
\(410\) 11.6957 19.5243i 0.577608 0.964237i
\(411\) −1.06675 + 3.28312i −0.0526190 + 0.161945i
\(412\) 0.157293 + 0.993106i 0.00774925 + 0.0489268i
\(413\) 0.288327 + 1.82043i 0.0141877 + 0.0895773i
\(414\) −1.80448 + 5.55361i −0.0886853 + 0.272945i
\(415\) −19.1701 + 32.0019i −0.941025 + 1.57091i
\(416\) 4.36224 3.16935i 0.213876 0.155390i
\(417\) −5.92504 + 5.92504i −0.290151 + 0.290151i
\(418\) −1.48899 + 3.44151i −0.0728288 + 0.168330i
\(419\) 1.20241i 0.0587414i 0.999569 + 0.0293707i \(0.00935032\pi\)
−0.999569 + 0.0293707i \(0.990650\pi\)
\(420\) −0.0898281 + 0.0562990i −0.00438316 + 0.00274711i
\(421\) 9.67493 + 29.7764i 0.471527 + 1.45121i 0.850584 + 0.525839i \(0.176248\pi\)
−0.379057 + 0.925373i \(0.623752\pi\)
\(422\) −8.03473 + 4.09390i −0.391124 + 0.199288i
\(423\) −28.8741 + 4.57321i −1.40391 + 0.222357i
\(424\) −18.7610 13.6307i −0.911117 0.661965i
\(425\) −6.08073 17.5066i −0.294959 0.849195i
\(426\) −13.2099 + 4.29214i −0.640020 + 0.207955i
\(427\) −1.11445 0.176512i −0.0539321 0.00854201i
\(428\) 2.42802 + 2.42802i 0.117363 + 0.117363i
\(429\) 7.61008 3.01366i 0.367418 0.145501i
\(430\) −17.8736 1.22568i −0.861940 0.0591078i
\(431\) −5.81395 8.00222i −0.280048 0.385453i 0.645702 0.763590i \(-0.276565\pi\)
−0.925750 + 0.378137i \(0.876565\pi\)
\(432\) −8.78502 + 17.2416i −0.422669 + 0.829536i
\(433\) 12.2497 + 24.0414i 0.588683 + 1.15536i 0.972708 + 0.232033i \(0.0745378\pi\)
−0.384025 + 0.923323i \(0.625462\pi\)
\(434\) 0.0600332 0.0826286i 0.00288169 0.00396630i
\(435\) 16.9525 1.50614i 0.812812 0.0722137i
\(436\) 2.81864 + 0.915831i 0.134988 + 0.0438604i
\(437\) −1.07675 0.548629i −0.0515077 0.0262445i
\(438\) −0.455327 + 2.87482i −0.0217564 + 0.137364i
\(439\) −24.5862 −1.17344 −0.586718 0.809791i \(-0.699580\pi\)
−0.586718 + 0.809791i \(0.699580\pi\)
\(440\) 3.08394 18.7935i 0.147021 0.895945i
\(441\) −16.4643 −0.784016
\(442\) 2.72838 17.2263i 0.129776 0.819372i
\(443\) 27.4404 + 13.9816i 1.30373 + 0.664286i 0.961364 0.275279i \(-0.0887704\pi\)
0.342370 + 0.939565i \(0.388770\pi\)
\(444\) 1.27292 + 0.413596i 0.0604099 + 0.0196284i
\(445\) −11.3680 + 13.5849i −0.538896 + 0.643988i
\(446\) 18.9912 26.1392i 0.899262 1.23773i
\(447\) −2.08561 4.09323i −0.0986458 0.193603i
\(448\) 0.556477 1.09215i 0.0262911 0.0515992i
\(449\) −4.30536 5.92582i −0.203182 0.279657i 0.695250 0.718768i \(-0.255293\pi\)
−0.898433 + 0.439111i \(0.855293\pi\)
\(450\) 10.8534 + 14.3227i 0.511636 + 0.675177i
\(451\) 5.52141 21.5107i 0.259993 1.01290i
\(452\) −0.910918 0.910918i −0.0428460 0.0428460i
\(453\) −11.7830 1.86624i −0.553612 0.0876835i
\(454\) −18.8951 + 6.13938i −0.886789 + 0.288135i
\(455\) 0.494835 1.22952i 0.0231982 0.0576407i
\(456\) −1.23193 0.895050i −0.0576904 0.0419146i
\(457\) −6.65265 + 1.05368i −0.311198 + 0.0492889i −0.310080 0.950710i \(-0.600356\pi\)
−0.00111791 + 0.999999i \(0.500356\pi\)
\(458\) −22.2540 + 11.3390i −1.03986 + 0.529837i
\(459\) 4.89838 + 15.0757i 0.228637 + 0.703672i
\(460\) −1.09980 0.252351i −0.0512783 0.0117659i
\(461\) 29.0801i 1.35440i 0.735801 + 0.677198i \(0.236806\pi\)
−0.735801 + 0.677198i \(0.763194\pi\)
\(462\) −0.508879 + 0.577290i −0.0236752 + 0.0268580i
\(463\) 17.5146 17.5146i 0.813970 0.813970i −0.171256 0.985227i \(-0.554783\pi\)
0.985227 + 0.171256i \(0.0547826\pi\)
\(464\) 34.9482 25.3914i 1.62243 1.17876i
\(465\) 0.536649 + 0.321470i 0.0248865 + 0.0149078i
\(466\) 7.34819 22.6154i 0.340398 1.04764i
\(467\) −4.13890 26.1320i −0.191525 1.20924i −0.876763 0.480923i \(-0.840302\pi\)
0.685237 0.728320i \(-0.259698\pi\)
\(468\) 0.355625 + 2.24533i 0.0164388 + 0.103790i
\(469\) −0.345938 + 1.06469i −0.0159739 + 0.0491627i
\(470\) −10.2216 40.7631i −0.471489 1.88026i
\(471\) −3.19138 + 2.31868i −0.147051 + 0.106839i
\(472\) −17.4796 + 17.4796i −0.804563 + 0.804563i
\(473\) −17.0603 + 3.81467i −0.784432 + 0.175399i
\(474\) 0.812515i 0.0373201i
\(475\) −3.27894 + 1.75477i −0.150448 + 0.0805145i
\(476\) 0.0681145 + 0.209635i 0.00312202 + 0.00960860i
\(477\) 19.0244 9.69341i 0.871067 0.443831i
\(478\) 7.92972 1.25594i 0.362697 0.0574455i
\(479\) 21.2408 + 15.4324i 0.970519 + 0.705123i 0.955570 0.294765i \(-0.0952413\pi\)
0.0149492 + 0.999888i \(0.495241\pi\)
\(480\) −2.88054 1.15931i −0.131478 0.0529150i
\(481\) −15.9139 + 5.17073i −0.725610 + 0.235765i
\(482\) 24.2731 + 3.84449i 1.10561 + 0.175112i
\(483\) −0.175368 0.175368i −0.00797952 0.00797952i
\(484\) 0.428672 + 3.38950i 0.0194851 + 0.154068i
\(485\) 2.02609 + 2.32443i 0.0920001 + 0.105547i
\(486\) −14.0872 19.3894i −0.639008 0.879519i
\(487\) 10.5939 20.7917i 0.480056 0.942163i −0.516262 0.856431i \(-0.672677\pi\)
0.996318 0.0857326i \(-0.0273231\pi\)
\(488\) −6.87039 13.4839i −0.311008 0.610388i
\(489\) −4.69379 + 6.46044i −0.212260 + 0.292151i
\(490\) −2.09453 23.5753i −0.0946211 1.06502i
\(491\) 17.4497 + 5.66974i 0.787493 + 0.255872i 0.675036 0.737785i \(-0.264128\pi\)
0.112457 + 0.993657i \(0.464128\pi\)
\(492\) −1.47728 0.752713i −0.0666010 0.0339349i
\(493\) 5.53572 34.9512i 0.249316 1.57412i
\(494\) −3.49992 −0.157469
\(495\) 14.1286 + 10.3857i 0.635033 + 0.466802i
\(496\) 1.58781 0.0712949
\(497\) −0.343309 + 2.16757i −0.0153995 + 0.0972286i
\(498\) 18.0135 + 9.17834i 0.807204 + 0.411291i
\(499\) 11.1824 + 3.63339i 0.500595 + 0.162653i 0.548421 0.836203i \(-0.315229\pi\)
−0.0478260 + 0.998856i \(0.515229\pi\)
\(500\) −2.57118 + 2.33396i −0.114987 + 0.104378i
\(501\) −5.65234 + 7.77978i −0.252528 + 0.347575i
\(502\) −13.3483 26.1975i −0.595763 1.16925i
\(503\) −2.42460 + 4.75855i −0.108108 + 0.212173i −0.938722 0.344674i \(-0.887989\pi\)
0.830615 + 0.556848i \(0.187989\pi\)
\(504\) 0.683353 + 0.940555i 0.0304390 + 0.0418956i
\(505\) −0.738195 + 10.7647i −0.0328492 + 0.479025i
\(506\) −8.17484 + 0.514888i −0.363416 + 0.0228896i
\(507\) −1.92638 1.92638i −0.0855536 0.0855536i
\(508\) −4.46873 0.707777i −0.198268 0.0314025i
\(509\) −18.6283 + 6.05272i −0.825687 + 0.268282i −0.691228 0.722637i \(-0.742930\pi\)
−0.134459 + 0.990919i \(0.542930\pi\)
\(510\) −9.23998 + 3.93681i −0.409153 + 0.174325i
\(511\) 0.372057 + 0.270315i 0.0164588 + 0.0119580i
\(512\) 15.1686 2.40248i 0.670365 0.106175i
\(513\) 2.83424 1.44412i 0.125135 0.0637594i
\(514\) −2.21058 6.80347i −0.0975046 0.300088i
\(515\) −1.61891 + 7.05555i −0.0713376 + 0.310905i
\(516\) 1.30513i 0.0574550i
\(517\) −20.8767 35.2950i −0.918158 1.55227i
\(518\) 1.11243 1.11243i 0.0488775 0.0488775i
\(519\) −8.03959 + 5.84110i −0.352899 + 0.256396i
\(520\) 17.2419 4.32353i 0.756106 0.189599i
\(521\) 5.78913 17.8171i 0.253626 0.780582i −0.740471 0.672089i \(-0.765397\pi\)
0.994097 0.108493i \(-0.0346026\pi\)
\(522\) 5.36781 + 33.8910i 0.234943 + 1.48337i
\(523\) 0.403961 + 2.55051i 0.0176640 + 0.111526i 0.994945 0.100422i \(-0.0320193\pi\)
−0.977281 + 0.211948i \(0.932019\pi\)
\(524\) 0.937631 2.88573i 0.0409606 0.126064i
\(525\) −0.751273 + 0.134555i −0.0327883 + 0.00587245i
\(526\) −19.5162 + 14.1794i −0.850948 + 0.618250i
\(527\) 0.919727 0.919727i 0.0400639 0.0400639i
\(528\) −11.9108 1.12506i −0.518350 0.0489621i
\(529\) 20.3603i 0.885228i
\(530\) 16.3002 + 26.0078i 0.708035 + 1.12971i
\(531\) −7.03330 21.6463i −0.305219 0.939368i
\(532\) 0.0394115 0.0200812i 0.00170871 0.000870630i
\(533\) 20.4729 3.24258i 0.886778 0.140452i
\(534\) 7.76658 + 5.64275i 0.336093 + 0.244186i
\(535\) 9.68984 + 22.7427i 0.418928 + 0.983253i
\(536\) −14.2796 + 4.63972i −0.616784 + 0.200405i
\(537\) 15.8888 + 2.51654i 0.685652 + 0.108597i
\(538\) −12.1591 12.1591i −0.524216 0.524216i
\(539\) −8.50325 21.4724i −0.366261 0.924881i
\(540\) 2.23898 1.95161i 0.0963502 0.0839837i
\(541\) 5.42829 + 7.47139i 0.233380 + 0.321220i 0.909604 0.415476i \(-0.136385\pi\)
−0.676224 + 0.736696i \(0.736385\pi\)
\(542\) −12.3031 + 24.1462i −0.528464 + 1.03717i
\(543\) −1.66841 3.27444i −0.0715983 0.140520i
\(544\) −3.79482 + 5.22312i −0.162701 + 0.223939i
\(545\) 16.3634 + 13.6931i 0.700931 + 0.586546i
\(546\) −0.683120 0.221959i −0.0292348 0.00949898i
\(547\) 0.954295 + 0.486237i 0.0408027 + 0.0207900i 0.474273 0.880378i \(-0.342711\pi\)
−0.433470 + 0.901168i \(0.642711\pi\)
\(548\) 0.210388 1.32834i 0.00898732 0.0567437i
\(549\) 13.9337 0.594674
\(550\) −13.0739 + 21.5519i −0.557471 + 0.918978i
\(551\) −7.10113 −0.302518
\(552\) 0.520344 3.28533i 0.0221473 0.139833i
\(553\) 0.114386 + 0.0582826i 0.00486419 + 0.00247843i
\(554\) 6.76800 + 2.19906i 0.287545 + 0.0934290i
\(555\) 7.38982 + 6.18387i 0.313680 + 0.262491i
\(556\) 1.91881 2.64102i 0.0813758 0.112004i
\(557\) −19.5384 38.3462i −0.827868 1.62478i −0.779876 0.625934i \(-0.784718\pi\)
−0.0479915 0.998848i \(-0.515282\pi\)
\(558\) −0.572590 + 1.12377i −0.0242396 + 0.0475730i
\(559\) −9.59064 13.2004i −0.405641 0.558316i
\(560\) −1.46033 + 1.27290i −0.0617102 + 0.0537897i
\(561\) −7.55089 + 6.24752i −0.318799 + 0.263771i
\(562\) −14.1765 14.1765i −0.597998 0.597998i
\(563\) −25.5439 4.04575i −1.07655 0.170508i −0.407111 0.913379i \(-0.633464\pi\)
−0.669435 + 0.742871i \(0.733464\pi\)
\(564\) −2.91164 + 0.946049i −0.122602 + 0.0398359i
\(565\) −3.63532 8.53235i −0.152939 0.358959i
\(566\) 28.0219 + 20.3591i 1.17785 + 0.855756i
\(567\) −0.696664 + 0.110341i −0.0292571 + 0.00463387i
\(568\) −26.2257 + 13.3626i −1.10040 + 0.560684i
\(569\) 8.39651 + 25.8418i 0.352000 + 1.08334i 0.957729 + 0.287673i \(0.0928816\pi\)
−0.605729 + 0.795671i \(0.707118\pi\)
\(570\) 1.07034 + 1.70779i 0.0448316 + 0.0715313i
\(571\) 40.5475i 1.69686i 0.529308 + 0.848430i \(0.322451\pi\)
−0.529308 + 0.848430i \(0.677549\pi\)
\(572\) −2.74464 + 1.62343i −0.114759 + 0.0678791i
\(573\) 3.56628 3.56628i 0.148984 0.148984i
\(574\) −1.57665 + 1.14550i −0.0658081 + 0.0478124i
\(575\) −6.66701 4.64161i −0.278034 0.193569i
\(576\) −4.67742 + 14.3956i −0.194893 + 0.599818i
\(577\) 5.28872 + 33.3917i 0.220172 + 1.39011i 0.811815 + 0.583914i \(0.198479\pi\)
−0.591643 + 0.806200i \(0.701521\pi\)
\(578\) −0.775613 4.89703i −0.0322612 0.203689i
\(579\) 1.46136 4.49759i 0.0607319 0.186913i
\(580\) −6.43143 + 1.61273i −0.267051 + 0.0669649i
\(581\) 2.58426 1.87757i 0.107213 0.0778948i
\(582\) 1.18165 1.18165i 0.0489808 0.0489808i
\(583\) 22.4673 + 19.8048i 0.930502 + 0.820233i
\(584\) 6.16801i 0.255234i
\(585\) −3.66022 + 15.9520i −0.151331 + 0.659534i
\(586\) −3.39505 10.4489i −0.140248 0.431640i
\(587\) 8.62859 4.39649i 0.356140 0.181462i −0.266762 0.963763i \(-0.585954\pi\)
0.622902 + 0.782300i \(0.285954\pi\)
\(588\) −1.70297 + 0.269724i −0.0702293 + 0.0111232i
\(589\) −0.211163 0.153419i −0.00870081 0.00632151i
\(590\) 30.1005 12.8247i 1.23922 0.527986i
\(591\) 10.6210 3.45096i 0.436888 0.141953i
\(592\) 24.1566 + 3.82603i 0.992829 + 0.157249i
\(593\) −14.0452 14.0452i −0.576769 0.576769i 0.357243 0.934012i \(-0.383717\pi\)
−0.934012 + 0.357243i \(0.883717\pi\)
\(594\) 11.5515 18.2051i 0.473965 0.746964i
\(595\) −0.108568 + 1.58320i −0.00445086 + 0.0649048i
\(596\) 1.05199 + 1.44794i 0.0430912 + 0.0593099i
\(597\) 4.84367 9.50623i 0.198238 0.389064i
\(598\) −3.47084 6.81191i −0.141933 0.278560i
\(599\) 2.65433 3.65338i 0.108453 0.149273i −0.751340 0.659915i \(-0.770592\pi\)
0.859793 + 0.510642i \(0.170592\pi\)
\(600\) −7.38256 7.09097i −0.301392 0.289488i
\(601\) −7.96746 2.58878i −0.324999 0.105599i 0.141973 0.989871i \(-0.454655\pi\)
−0.466973 + 0.884272i \(0.654655\pi\)
\(602\) 1.36688 + 0.696458i 0.0557097 + 0.0283855i
\(603\) 2.16258 13.6540i 0.0880671 0.556034i
\(604\) 4.64774 0.189114
\(605\) −6.24783 + 23.7900i −0.254011 + 0.967201i
\(606\) 5.84763 0.237544
\(607\) 1.20123 7.58425i 0.0487563 0.307835i −0.951244 0.308441i \(-0.900193\pi\)
1.00000 0.000605683i \(0.000192795\pi\)
\(608\) 1.15435 + 0.588172i 0.0468152 + 0.0238535i
\(609\) −1.38601 0.450342i −0.0561640 0.0182488i
\(610\) 1.77258 + 19.9516i 0.0717698 + 0.807816i
\(611\) 22.4971 30.9646i 0.910134 1.25269i
\(612\) −1.23574 2.42528i −0.0499519 0.0980361i
\(613\) 19.4882 38.2477i 0.787120 1.54481i −0.0506058 0.998719i \(-0.516115\pi\)
0.837726 0.546091i \(-0.183885\pi\)
\(614\) 25.4319 + 35.0041i 1.02635 + 1.41265i
\(615\) −7.84320 8.99810i −0.316268 0.362838i
\(616\) −0.873721 + 1.37698i −0.0352032 + 0.0554799i
\(617\) 33.4407 + 33.4407i 1.34627 + 1.34627i 0.889671 + 0.456601i \(0.150933\pi\)
0.456601 + 0.889671i \(0.349067\pi\)
\(618\) 3.87481 + 0.613709i 0.155868 + 0.0246870i
\(619\) −20.0674 + 6.52029i −0.806576 + 0.262073i −0.683147 0.730281i \(-0.739389\pi\)
−0.123429 + 0.992353i \(0.539389\pi\)
\(620\) −0.226091 0.0909931i −0.00908003 0.00365437i
\(621\) 5.62139 + 4.08418i 0.225578 + 0.163892i
\(622\) 11.2840 1.78720i 0.452445 0.0716603i
\(623\) 1.35149 0.688620i 0.0541464 0.0275890i
\(624\) −3.45064 10.6200i −0.138136 0.425139i
\(625\) −23.4460 + 8.67678i −0.937839 + 0.347071i
\(626\) 2.04613i 0.0817798i
\(627\) 1.47530 + 1.30047i 0.0589179 + 0.0519358i
\(628\) 1.08671 1.08671i 0.0433645 0.0433645i
\(629\) 16.2087 11.7763i 0.646282 0.469552i
\(630\) −0.374273 1.49257i −0.0149114 0.0594654i
\(631\) −8.72043 + 26.8387i −0.347155 + 1.06843i 0.613265 + 0.789877i \(0.289856\pi\)
−0.960420 + 0.278555i \(0.910144\pi\)
\(632\) 0.269351 + 1.70061i 0.0107142 + 0.0676467i
\(633\) 0.739847 + 4.67121i 0.0294063 + 0.185664i
\(634\) 5.32290 16.3822i 0.211399 0.650621i
\(635\) −27.9433 16.7389i −1.10889 0.664263i
\(636\) 1.80896 1.31429i 0.0717301 0.0521150i
\(637\) 15.2422 15.2422i 0.603918 0.603918i
\(638\) −41.4275 + 24.5041i −1.64013 + 0.970125i
\(639\) 27.1004i 1.07208i
\(640\) −28.8006 6.60834i −1.13844 0.261218i
\(641\) −5.23436 16.1097i −0.206745 0.636295i −0.999637 0.0269333i \(-0.991426\pi\)
0.792893 0.609362i \(-0.208574\pi\)
\(642\) 11.9372 6.08232i 0.471124 0.240050i
\(643\) 6.19838 0.981726i 0.244440 0.0387155i −0.0330121 0.999455i \(-0.510510\pi\)
0.277452 + 0.960739i \(0.410510\pi\)
\(644\) 0.0781682 + 0.0567925i 0.00308026 + 0.00223794i
\(645\) −3.50814 + 8.71668i −0.138133 + 0.343219i
\(646\) 3.98552 1.29497i 0.156808 0.0509500i
\(647\) −42.9518 6.80289i −1.68861 0.267449i −0.763128 0.646247i \(-0.776338\pi\)
−0.925479 + 0.378798i \(0.876338\pi\)
\(648\) −6.68931 6.68931i −0.262781 0.262781i
\(649\) 24.5981 20.3522i 0.965559 0.798893i
\(650\) −23.3073 3.21171i −0.914188 0.125974i
\(651\) −0.0314855 0.0433361i −0.00123402 0.00169848i
\(652\) 1.41240 2.77200i 0.0553140 0.108560i
\(653\) −4.41780 8.67042i −0.172882 0.339300i 0.788266 0.615335i \(-0.210979\pi\)
−0.961147 + 0.276035i \(0.910979\pi\)
\(654\) 6.79682 9.35503i 0.265777 0.365810i
\(655\) 14.0190 16.7529i 0.547767 0.654590i
\(656\) −28.8145 9.36239i −1.12502 0.365540i
\(657\) −5.06007 2.57823i −0.197412 0.100586i
\(658\) −0.562936 + 3.55424i −0.0219455 + 0.138559i
\(659\) −3.37375 −0.131423 −0.0657113 0.997839i \(-0.520932\pi\)
−0.0657113 + 0.997839i \(0.520932\pi\)
\(660\) 1.63152 + 0.842771i 0.0635067 + 0.0328048i
\(661\) 9.93056 0.386254 0.193127 0.981174i \(-0.438137\pi\)
0.193127 + 0.981174i \(0.438137\pi\)
\(662\) 4.21003 26.5811i 0.163628 1.03310i
\(663\) −8.15028 4.15278i −0.316531 0.161280i
\(664\) 40.7453 + 13.2389i 1.58122 + 0.513771i
\(665\) 0.317199 0.0281813i 0.0123005 0.00109282i
\(666\) −11.4191 + 15.7170i −0.442481 + 0.609022i
\(667\) −7.04213 13.8210i −0.272672 0.535150i
\(668\) 1.70084 3.33809i 0.0658075 0.129154i
\(669\) −9.96031 13.7092i −0.385088 0.530028i
\(670\) 19.8263 + 1.35959i 0.765955 + 0.0525256i
\(671\) 7.19624 + 18.1719i 0.277808 + 0.701520i
\(672\) 0.188008 + 0.188008i 0.00725256 + 0.00725256i
\(673\) −37.7823 5.98412i −1.45640 0.230671i −0.622514 0.782609i \(-0.713889\pi\)
−0.833885 + 0.551938i \(0.813889\pi\)
\(674\) −11.0161 + 3.57935i −0.424324 + 0.137871i
\(675\) 20.1995 7.01609i 0.777479 0.270049i
\(676\) 0.858662 + 0.623855i 0.0330255 + 0.0239944i
\(677\) −31.7956 + 5.03592i −1.22200 + 0.193546i −0.733911 0.679246i \(-0.762307\pi\)
−0.488092 + 0.872792i \(0.662307\pi\)
\(678\) −4.47847 + 2.28189i −0.171994 + 0.0876356i
\(679\) −0.0815917 0.251113i −0.00313120 0.00963684i
\(680\) −18.0344 + 11.3029i −0.691588 + 0.433447i
\(681\) 10.4198i 0.399289i
\(682\) −1.76132 0.166370i −0.0674443 0.00637063i
\(683\) −28.7223 + 28.7223i −1.09903 + 1.09903i −0.104505 + 0.994524i \(0.533326\pi\)
−0.994524 + 0.104505i \(0.966674\pi\)
\(684\) −0.441900 + 0.321059i −0.0168965 + 0.0122760i
\(685\) 4.97566 8.30617i 0.190110 0.317363i
\(686\) −1.25585 + 3.86510i −0.0479484 + 0.147570i
\(687\) 2.04918 + 12.9380i 0.0781811 + 0.493616i
\(688\) 3.73084 + 23.5556i 0.142237 + 0.898050i
\(689\) −8.63834 + 26.5861i −0.329095 + 1.01285i
\(690\) −2.26243 + 3.77681i −0.0861291 + 0.143781i
\(691\) 20.4397 14.8503i 0.777564 0.564933i −0.126683 0.991943i \(-0.540433\pi\)
0.904247 + 0.427010i \(0.140433\pi\)
\(692\) 2.73759 2.73759i 0.104068 0.104068i
\(693\) −0.764417 1.29235i −0.0290378 0.0490925i
\(694\) 14.1878i 0.538562i
\(695\) 19.9143 12.4811i 0.755393 0.473436i
\(696\) −6.03999 18.5892i −0.228945 0.704621i
\(697\) −22.1136 + 11.2675i −0.837613 + 0.426785i
\(698\) −2.25468 + 0.357107i −0.0853410 + 0.0135167i
\(699\) −10.0896 7.33055i −0.381625 0.277267i
\(700\) 0.280884 0.0975622i 0.0106164 0.00368751i
\(701\) 26.8458 8.72273i 1.01395 0.329453i 0.245525 0.969390i \(-0.421040\pi\)
0.768427 + 0.639937i \(0.221040\pi\)
\(702\) 19.8761 + 3.14807i 0.750175 + 0.118816i
\(703\) −2.84289 2.84289i −0.107222 0.107222i
\(704\) −21.1902 + 1.33465i −0.798634 + 0.0503015i
\(705\) −21.9892 1.50791i −0.828161 0.0567914i
\(706\) 5.56255 + 7.65620i 0.209349 + 0.288145i
\(707\) 0.419457 0.823230i 0.0157753 0.0309608i
\(708\) −1.08210 2.12373i −0.0406677 0.0798148i
\(709\) 4.79615 6.60134i 0.180123 0.247918i −0.709402 0.704804i \(-0.751035\pi\)
0.889526 + 0.456885i \(0.151035\pi\)
\(710\) 38.8051 3.44761i 1.45633 0.129386i
\(711\) −1.50773 0.489890i −0.0565441 0.0183723i
\(712\) 18.1262 + 9.23576i 0.679308 + 0.346125i
\(713\) 0.0891912 0.563131i 0.00334024 0.0210894i
\(714\) 0.860026 0.0321856
\(715\) −22.6946 + 3.46508i −0.848730 + 0.129587i
\(716\) −6.26727 −0.234219
\(717\) 0.658703 4.15889i 0.0245997 0.155317i
\(718\) 35.6261 + 18.1524i 1.32955 + 0.677441i
\(719\) 0.986856 + 0.320649i 0.0368035 + 0.0119582i 0.327361 0.944899i \(-0.393841\pi\)
−0.290557 + 0.956858i \(0.593841\pi\)
\(720\) 15.3523 18.3462i 0.572146 0.683723i
\(721\) 0.364342 0.501474i 0.0135688 0.0186759i
\(722\) 12.7300 + 24.9840i 0.473762 + 0.929810i
\(723\) 5.85157 11.4843i 0.217622 0.427107i
\(724\) 0.841554 + 1.15830i 0.0312761 + 0.0430479i
\(725\) −47.2892 6.51637i −1.75627 0.242012i
\(726\) 13.0944 + 2.49600i 0.485978 + 0.0926353i
\(727\) −3.27903 3.27903i −0.121612 0.121612i 0.643681 0.765294i \(-0.277406\pi\)
−0.765294 + 0.643681i \(0.777406\pi\)
\(728\) −1.50337 0.238110i −0.0557184 0.00882493i
\(729\) −1.44390 + 0.469153i −0.0534779 + 0.0173760i
\(730\) 3.04805 7.57350i 0.112813 0.280308i
\(731\) 15.8055 + 11.4833i 0.584586 + 0.424726i
\(732\) 1.44121 0.228265i 0.0532687 0.00843693i
\(733\) 40.6968 20.7361i 1.50317 0.765904i 0.507751 0.861504i \(-0.330477\pi\)
0.995420 + 0.0956003i \(0.0304771\pi\)
\(734\) 3.83723 + 11.8098i 0.141635 + 0.435907i
\(735\) −12.0988 2.77609i −0.446271 0.102398i
\(736\) 2.83001i 0.104315i
\(737\) 18.9241 4.23142i 0.697079 0.155866i
\(738\) 17.0171 17.0171i 0.626410 0.626410i
\(739\) −3.07164 + 2.23167i −0.112992 + 0.0820934i −0.642846 0.765995i \(-0.722247\pi\)
0.529854 + 0.848089i \(0.322247\pi\)
\(740\) −3.22043 1.92914i −0.118385 0.0709165i
\(741\) −0.567231 + 1.74576i −0.0208377 + 0.0641320i
\(742\) −0.411150 2.59590i −0.0150938 0.0952984i
\(743\) 6.63736 + 41.9067i 0.243501 + 1.53741i 0.741931 + 0.670476i \(0.233910\pi\)
−0.498430 + 0.866930i \(0.666090\pi\)
\(744\) 0.222008 0.683270i 0.00813920 0.0250499i
\(745\) 3.13401 + 12.4982i 0.114821 + 0.457899i
\(746\) −10.6517 + 7.73895i −0.389988 + 0.283343i
\(747\) −27.8924 + 27.8924i −1.02053 + 1.02053i
\(748\) 2.52477 2.86419i 0.0923149 0.104725i
\(749\) 2.11681i 0.0773467i
\(750\) 5.56065 + 12.3550i 0.203046 + 0.451141i
\(751\) −3.08775 9.50312i −0.112674 0.346774i 0.878781 0.477225i \(-0.158357\pi\)
−0.991455 + 0.130451i \(0.958357\pi\)
\(752\) −49.8464 + 25.3980i −1.81771 + 0.926171i
\(753\) −15.2306 + 2.41230i −0.555035 + 0.0879089i
\(754\) −36.3446 26.4059i −1.32359 0.961647i
\(755\) 31.0413 + 12.4930i 1.12971 + 0.454665i
\(756\) −0.241881 + 0.0785920i −0.00879714 + 0.00285837i
\(757\) 29.0217 + 4.59658i 1.05481 + 0.167065i 0.659670 0.751555i \(-0.270696\pi\)
0.395140 + 0.918621i \(0.370696\pi\)
\(758\) −0.664675 0.664675i −0.0241421 0.0241421i
\(759\) −1.06807 + 4.16105i −0.0387684 + 0.151037i
\(760\) 2.80638 + 3.21961i 0.101798 + 0.116788i
\(761\) −17.8404 24.5552i −0.646713 0.890124i 0.352238 0.935910i \(-0.385421\pi\)
−0.998951 + 0.0457864i \(0.985421\pi\)
\(762\) −8.01429 + 15.7289i −0.290327 + 0.569799i
\(763\) −0.829459 1.62790i −0.0300284 0.0589341i
\(764\) −1.15493 + 1.58963i −0.0417840 + 0.0575107i
\(765\) −1.73420 19.5196i −0.0627002 0.705731i
\(766\) 15.0044 + 4.87523i 0.542131 + 0.176149i
\(767\) 26.5507 + 13.5283i 0.958690 + 0.488477i
\(768\) −0.908377 + 5.73527i −0.0327782 + 0.206954i
\(769\) 37.6421 1.35741 0.678705 0.734411i \(-0.262542\pi\)
0.678705 + 0.734411i \(0.262542\pi\)
\(770\) 1.75327 1.25898i 0.0631836 0.0453704i
\(771\) −3.75184 −0.135119
\(772\) −0.288213 + 1.81970i −0.0103730 + 0.0654926i
\(773\) 22.9995 + 11.7188i 0.827234 + 0.421497i 0.815727 0.578437i \(-0.196337\pi\)
0.0115072 + 0.999934i \(0.496337\pi\)
\(774\) −18.0168 5.85402i −0.647601 0.210418i
\(775\) −1.26543 1.21545i −0.0454555 0.0436602i
\(776\) 2.08149 2.86493i 0.0747213 0.102845i
\(777\) −0.374589 0.735173i −0.0134383 0.0263742i
\(778\) 15.2835 29.9955i 0.547939 1.07539i
\(779\) 2.92741 + 4.02923i 0.104885 + 0.144362i
\(780\) −0.117260 + 1.70994i −0.00419856 + 0.0612257i
\(781\) 35.3437 13.9964i 1.26470 0.500831i
\(782\) 6.47282 + 6.47282i 0.231467 + 0.231467i
\(783\) 40.3275 + 6.38724i 1.44119 + 0.228261i
\(784\) −29.9651 + 9.73624i −1.07018 + 0.347723i
\(785\) 10.1790 4.33688i 0.363302 0.154790i
\(786\) −9.57771 6.95861i −0.341626 0.248206i
\(787\) −17.0625 + 2.70244i −0.608213 + 0.0963315i −0.452942 0.891540i \(-0.649625\pi\)
−0.155272 + 0.987872i \(0.549625\pi\)
\(788\) −3.87655 + 1.97520i −0.138096 + 0.0703636i
\(789\) 3.90967 + 12.0327i 0.139188 + 0.428376i
\(790\) 0.509666 2.22123i 0.0181331 0.0790279i
\(791\) 0.794162i 0.0282372i
\(792\) 7.99654 18.4824i 0.284145 0.656745i
\(793\) −12.8994 + 12.8994i −0.458070 + 0.458070i
\(794\) −18.7425 + 13.6172i −0.665145 + 0.483256i
\(795\) 15.6145 3.91544i 0.553788 0.138866i
\(796\) −1.28445 + 3.95313i −0.0455261 + 0.140115i
\(797\) −6.97213 44.0203i −0.246965 1.55928i −0.729858 0.683599i \(-0.760414\pi\)
0.482892 0.875680i \(-0.339586\pi\)
\(798\) −0.0269979 0.170458i −0.000955714 0.00603414i
\(799\) −14.1615 + 43.5847i −0.500999 + 1.54192i
\(800\) 7.14755 + 4.97616i 0.252704 + 0.175934i
\(801\) −15.1535 + 11.0097i −0.535424 + 0.389008i
\(802\) −4.60219 + 4.60219i −0.162509 + 0.162509i
\(803\) 0.749124 7.93078i 0.0264360 0.279871i
\(804\) 1.44771i 0.0510569i
\(805\) 0.369413 + 0.589419i 0.0130201 + 0.0207743i
\(806\) −0.510267 1.57044i −0.0179734 0.0553164i
\(807\) −8.03556 + 4.09432i −0.282865 + 0.144127i
\(808\) 12.2392 1.93850i 0.430574 0.0681962i
\(809\) 12.3255 + 8.95497i 0.433340 + 0.314840i 0.782983 0.622043i \(-0.213697\pi\)
−0.349643 + 0.936883i \(0.613697\pi\)
\(810\) 4.90793 + 11.5193i 0.172447 + 0.404745i
\(811\) −43.3276 + 14.0780i −1.52144 + 0.494345i −0.946183 0.323631i \(-0.895096\pi\)
−0.575253 + 0.817976i \(0.695096\pi\)
\(812\) 0.560774 + 0.0888178i 0.0196793 + 0.00311689i
\(813\) 10.0502 + 10.0502i 0.352475 + 0.352475i
\(814\) −26.3953 6.77521i −0.925155 0.237471i
\(815\) 16.8842 14.7171i 0.591427 0.515518i
\(816\) 7.85881 + 10.8167i 0.275113 + 0.378661i
\(817\) 1.77984 3.49314i 0.0622688 0.122209i
\(818\) 2.96438 + 5.81793i 0.103647 + 0.203419i
\(819\) 0.823747 1.13379i 0.0287840 0.0396178i
\(820\) 3.56640 + 2.98440i 0.124544 + 0.104220i
\(821\) −27.3071 8.87260i −0.953023 0.309656i −0.209079 0.977899i \(-0.567047\pi\)
−0.743943 + 0.668243i \(0.767047\pi\)
\(822\) −4.67545 2.38226i −0.163075 0.0830909i
\(823\) −4.21701 + 26.6252i −0.146996 + 0.928095i 0.798390 + 0.602141i \(0.205686\pi\)
−0.945386 + 0.325954i \(0.894314\pi\)
\(824\) 8.31350 0.289614
\(825\) 8.63122 + 10.0142i 0.300501 + 0.348648i
\(826\) −2.80165 −0.0974820
\(827\) −6.20779 + 39.1944i −0.215866 + 1.36292i 0.607006 + 0.794697i \(0.292370\pi\)
−0.822872 + 0.568227i \(0.807630\pi\)
\(828\) −1.06311 0.541680i −0.0369455 0.0188247i
\(829\) 10.3353 + 3.35814i 0.358959 + 0.116633i 0.482944 0.875651i \(-0.339567\pi\)
−0.123985 + 0.992284i \(0.539567\pi\)
\(830\) −43.4875 36.3908i −1.50947 1.26314i
\(831\) 2.19378 3.01948i 0.0761013 0.104744i
\(832\) −8.99683 17.6573i −0.311909 0.612156i
\(833\) −11.7174 + 22.9966i −0.405983 + 0.796786i
\(834\) −7.48663 10.3045i −0.259241 0.356815i
\(835\) 20.3322 17.7226i 0.703625 0.613316i
\(836\) −0.646943 0.410500i −0.0223750 0.0141974i
\(837\) 1.06120 + 1.06120i 0.0366805 + 0.0366805i
\(838\) −1.80523 0.285920i −0.0623606 0.00987695i
\(839\) −38.3426 + 12.4583i −1.32373 + 0.430107i −0.883775 0.467912i \(-0.845007\pi\)
−0.439958 + 0.898019i \(0.645007\pi\)
\(840\) 0.343572 + 0.806387i 0.0118543 + 0.0278230i
\(841\) −50.2797 36.5303i −1.73378 1.25967i
\(842\) −47.0053 + 7.44491i −1.61991 + 0.256569i
\(843\) −9.36879 + 4.77364i −0.322678 + 0.164413i
\(844\) −0.569376 1.75236i −0.0195987 0.0603187i
\(845\) 4.05793 + 6.47465i 0.139597 + 0.222735i
\(846\) 44.4376i 1.52780i
\(847\) 1.29066 1.66439i 0.0443477 0.0571891i
\(848\) 28.8921 28.8921i 0.992159 0.992159i
\(849\) 14.6966 10.6777i 0.504386 0.366458i
\(850\) 27.7294 4.96640i 0.951112 0.170346i
\(851\) 2.71386 8.35241i 0.0930300 0.286317i
\(852\) −0.443967 2.80310i −0.0152101 0.0960326i
\(853\) −2.18326 13.7845i −0.0747533 0.471974i −0.996459 0.0840831i \(-0.973204\pi\)
0.921705 0.387890i \(-0.126796\pi\)
\(854\) 0.530012 1.63121i 0.0181366 0.0558188i
\(855\) −3.81435 + 0.956477i −0.130448 + 0.0327108i
\(856\) 22.9686 16.6876i 0.785049 0.570372i
\(857\) 26.9229 26.9229i 0.919668 0.919668i −0.0773373 0.997005i \(-0.524642\pi\)
0.997005 + 0.0773373i \(0.0246418\pi\)
\(858\) 2.71494 + 12.1420i 0.0926867 + 0.414521i
\(859\) 18.3200i 0.625071i 0.949906 + 0.312535i \(0.101178\pi\)
−0.949906 + 0.312535i \(0.898822\pi\)
\(860\) 0.818666 3.56792i 0.0279163 0.121665i
\(861\) 0.315849 + 0.972084i 0.0107641 + 0.0331285i
\(862\) 13.3966 6.82592i 0.456291 0.232492i
\(863\) −12.0033 + 1.90114i −0.408597 + 0.0647154i −0.357350 0.933971i \(-0.616320\pi\)
−0.0512472 + 0.998686i \(0.516320\pi\)
\(864\) −6.02655 4.37855i −0.205028 0.148961i
\(865\) 25.6424 10.9253i 0.871866 0.371470i
\(866\) −39.0074 + 12.6743i −1.32552 + 0.430689i
\(867\) −2.56834 0.406785i −0.0872253 0.0138151i
\(868\) 0.0147565 + 0.0147565i 0.000500870 + 0.000500870i
\(869\) −0.139785 2.21935i −0.00474187 0.0752863i
\(870\) −1.76991 + 25.8098i −0.0600057 + 0.875035i
\(871\) 10.6384 + 14.6425i 0.360469 + 0.496143i
\(872\) 11.1247 21.8334i 0.376730 0.739374i
\(873\) 1.48025 + 2.90515i 0.0500987 + 0.0983243i
\(874\) 1.07972 1.48611i 0.0365222 0.0502685i
\(875\) 2.13821 + 0.103409i 0.0722848 + 0.00349585i
\(876\) −0.565619 0.183781i −0.0191105 0.00620938i
\(877\) −11.4361 5.82698i −0.386169 0.196763i 0.250118 0.968215i \(-0.419531\pi\)
−0.636287 + 0.771452i \(0.719531\pi\)
\(878\) 5.84636 36.9125i 0.197305 1.24574i
\(879\) −5.76213 −0.194352
\(880\) 31.8556 + 10.5469i 1.07385 + 0.355537i
\(881\) 13.8380 0.466216 0.233108 0.972451i \(-0.425110\pi\)
0.233108 + 0.972451i \(0.425110\pi\)
\(882\) 3.91506 24.7187i 0.131827 0.832322i
\(883\) 38.8377 + 19.7888i 1.30699 + 0.665947i 0.962100 0.272695i \(-0.0879150\pi\)
0.344893 + 0.938642i \(0.387915\pi\)
\(884\) 3.38926 + 1.10124i 0.113993 + 0.0370387i
\(885\) −1.51858 17.0926i −0.0510465 0.574562i
\(886\) −27.5163 + 37.8730i −0.924429 + 1.27237i
\(887\) −4.72114 9.26576i −0.158520 0.311114i 0.798062 0.602575i \(-0.205859\pi\)
−0.956583 + 0.291461i \(0.905859\pi\)
\(888\) 5.02399 9.86013i 0.168594 0.330884i
\(889\) 1.63945 + 2.25651i 0.0549853 + 0.0756808i
\(890\) −17.6925 20.2977i −0.593055 0.680381i
\(891\) 7.78863 + 9.41351i 0.260929 + 0.315364i
\(892\) 4.66817 + 4.66817i 0.156302 + 0.156302i
\(893\) 9.08308 + 1.43862i 0.303954 + 0.0481415i
\(894\) 6.64130 2.15789i 0.222118 0.0721706i
\(895\) −41.8578 16.8462i −1.39915 0.563106i
\(896\) 2.04700 + 1.48723i 0.0683855 + 0.0496850i
\(897\) −3.96029 + 0.627249i −0.132230 + 0.0209432i
\(898\) 9.92048 5.05474i 0.331051 0.168679i
\(899\) −1.03530 3.18633i −0.0345292 0.106270i
\(900\) −3.23740 + 1.73255i −0.107913 + 0.0577515i
\(901\) 33.4710i 1.11508i
\(902\) 30.9821 + 13.4046i 1.03159 + 0.446324i
\(903\) 0.568922 0.568922i 0.0189325 0.0189325i
\(904\) −8.61708 + 6.26067i −0.286600 + 0.208227i
\(905\) 2.50710 + 9.99811i 0.0833388 + 0.332349i
\(906\) 5.60375 17.2466i 0.186172 0.572979i
\(907\) 2.55097 + 16.1062i 0.0847036 + 0.534798i 0.993155 + 0.116806i \(0.0372657\pi\)
−0.908451 + 0.417991i \(0.862734\pi\)
\(908\) −0.635040 4.00948i −0.0210745 0.133059i
\(909\) −3.52571 + 10.8510i −0.116940 + 0.359906i
\(910\) 1.72827 + 1.03529i 0.0572915 + 0.0343194i
\(911\) 14.3281 10.4099i 0.474710 0.344897i −0.324564 0.945864i \(-0.605218\pi\)
0.799274 + 0.600967i \(0.205218\pi\)
\(912\) 1.89718 1.89718i 0.0628219 0.0628219i
\(913\) −50.7821 21.9712i −1.68064 0.727140i
\(914\) 10.2385i 0.338659i
\(915\) 10.2391 + 2.34939i 0.338495 + 0.0776683i
\(916\) −1.57702 4.85357i −0.0521062 0.160366i
\(917\) −1.66665 + 0.849203i −0.0550378 + 0.0280431i
\(918\) −23.7986 + 3.76933i −0.785472 + 0.124406i
\(919\) −7.38632 5.36648i −0.243652 0.177024i 0.459257 0.888304i \(-0.348116\pi\)
−0.702909 + 0.711280i \(0.748116\pi\)
\(920\) −3.48329 + 8.65494i −0.114841 + 0.285345i
\(921\) 21.5818 7.01234i 0.711143 0.231064i
\(922\) −43.6594 6.91497i −1.43785 0.227732i
\(923\) 25.0888 + 25.0888i 0.825807 + 0.825807i
\(924\) −0.100238 0.121150i −0.00329760 0.00398555i
\(925\) −16.3231 21.5407i −0.536701 0.708254i
\(926\) 22.1307 + 30.4602i 0.727259 + 1.00099i
\(927\) −3.47505 + 6.82017i −0.114136 + 0.224004i
\(928\) 7.54970 + 14.8171i 0.247831 + 0.486396i
\(929\) 1.06529 1.46625i 0.0349511 0.0481061i −0.791184 0.611578i \(-0.790535\pi\)
0.826135 + 0.563472i \(0.190535\pi\)
\(930\) −0.610248 + 0.729255i −0.0200108 + 0.0239132i
\(931\) 4.92578 + 1.60048i 0.161436 + 0.0524537i
\(932\) 4.32918 + 2.20583i 0.141807 + 0.0722543i
\(933\) 0.937332 5.91808i 0.0306869 0.193749i
\(934\) 40.2174 1.31595
\(935\) 24.5613 12.3429i 0.803240 0.403655i
\(936\) 18.7961 0.614371
\(937\) −2.37143 + 14.9726i −0.0774711 + 0.489133i 0.918195 + 0.396130i \(0.129647\pi\)
−0.995666 + 0.0930039i \(0.970353\pi\)
\(938\) −1.51621 0.772546i −0.0495059 0.0252245i
\(939\) −1.02061 0.331616i −0.0333063 0.0108219i
\(940\) 8.55319 0.759902i 0.278974 0.0247853i
\(941\) −12.8308 + 17.6600i −0.418271 + 0.575701i −0.965211 0.261471i \(-0.915792\pi\)
0.546940 + 0.837172i \(0.315792\pi\)
\(942\) −2.72226 5.34274i −0.0886961 0.174076i
\(943\) −4.93902 + 9.69338i −0.160837 + 0.315660i
\(944\) −25.6012 35.2370i −0.833247 1.14687i
\(945\) −1.82673 0.125268i −0.0594235 0.00407498i
\(946\) −1.67038 26.5205i −0.0543087 0.862256i
\(947\) 6.90662 + 6.90662i 0.224435 + 0.224435i 0.810363 0.585928i \(-0.199270\pi\)
−0.585928 + 0.810363i \(0.699270\pi\)
\(948\) −0.163975 0.0259711i −0.00532567 0.000843503i
\(949\) 7.07131 2.29761i 0.229545 0.0745835i
\(950\) −1.85483 5.34009i −0.0601785 0.173255i
\(951\) −7.30875 5.31012i −0.237003 0.172192i
\(952\) 1.80005 0.285100i 0.0583400 0.00924015i
\(953\) −11.6216 + 5.92153i −0.376462 + 0.191817i −0.631975 0.774989i \(-0.717756\pi\)
0.255513 + 0.966806i \(0.417756\pi\)
\(954\) 10.0294 + 30.8672i 0.324713 + 0.999363i
\(955\) −11.9864 + 7.51238i −0.387871 + 0.243095i
\(956\) 1.64046i 0.0530561i
\(957\) 5.50846 + 24.6354i 0.178063 + 0.796349i
\(958\) −28.2202 + 28.2202i −0.911755 + 0.911755i
\(959\) −0.670750 + 0.487328i −0.0216596 + 0.0157367i
\(960\) −5.86448 + 9.78993i −0.189275 + 0.315969i
\(961\) −9.54147 + 29.3656i −0.307789 + 0.947279i
\(962\) −3.97890 25.1218i −0.128285 0.809960i
\(963\) 4.08921 + 25.8182i 0.131773 + 0.831981i
\(964\) −1.55173 + 4.77572i −0.0499777 + 0.153816i
\(965\) −6.81621 + 11.3787i −0.219422 + 0.366294i
\(966\) 0.304989 0.221588i 0.00981287 0.00712946i
\(967\) −13.6319 + 13.6319i −0.438372 + 0.438372i −0.891464 0.453092i \(-0.850321\pi\)
0.453092 + 0.891464i \(0.350321\pi\)
\(968\) 28.2343 + 0.883368i 0.907484 + 0.0283925i
\(969\) 2.19785i 0.0706051i
\(970\) −3.97156 + 2.48914i −0.127519 + 0.0799216i
\(971\) 1.26967 + 3.90765i 0.0407457 + 0.125403i 0.969360 0.245643i \(-0.0789992\pi\)
−0.928615 + 0.371046i \(0.878999\pi\)
\(972\) 4.36328 2.22320i 0.139952 0.0713093i
\(973\) −1.98769 + 0.314819i −0.0637224 + 0.0100926i
\(974\) 28.6965 + 20.8492i 0.919495 + 0.668052i
\(975\) −5.37941 + 11.1051i −0.172279 + 0.355649i
\(976\) 25.3592 8.23971i 0.811729 0.263747i
\(977\) 30.3314 + 4.80402i 0.970386 + 0.153694i 0.621451 0.783453i \(-0.286543\pi\)
0.348935 + 0.937147i \(0.386543\pi\)
\(978\) −8.58324 8.58324i −0.274462 0.274462i
\(979\) −22.1848 14.0768i −0.709030 0.449895i
\(980\) 4.82472 + 0.330856i 0.154120 + 0.0105688i
\(981\) 13.2614 + 18.2528i 0.423405 + 0.582767i
\(982\) −12.6616 + 24.8498i −0.404048 + 0.792990i
\(983\) −12.5871 24.7035i −0.401465 0.787919i 0.598447 0.801162i \(-0.295785\pi\)
−0.999912 + 0.0132429i \(0.995785\pi\)
\(984\) −8.05767 + 11.0904i −0.256869 + 0.353550i
\(985\) −31.1999 + 2.77194i −0.994113 + 0.0883212i
\(986\) 51.1575 + 16.6221i 1.62919 + 0.529355i
\(987\) 1.68162 + 0.856827i 0.0535265 + 0.0272731i
\(988\) 0.111871 0.706325i 0.00355909 0.0224712i
\(989\) 8.56376 0.272312
\(990\) −18.9522 + 18.7423i −0.602339 + 0.595670i
\(991\) 9.10087 0.289099 0.144549 0.989498i \(-0.453827\pi\)
0.144549 + 0.989498i \(0.453827\pi\)
\(992\) −0.0956197 + 0.603719i −0.00303593 + 0.0191681i
\(993\) −12.5763 6.40795i −0.399097 0.203350i
\(994\) −3.17264 1.03085i −0.100630 0.0326966i
\(995\) −19.2044 + 22.9496i −0.608822 + 0.727551i
\(996\) −2.42808 + 3.34196i −0.0769366 + 0.105894i
\(997\) 13.1070 + 25.7239i 0.415103 + 0.814685i 0.999994 + 0.00357282i \(0.00113727\pi\)
−0.584891 + 0.811112i \(0.698863\pi\)
\(998\) −8.11406 + 15.9247i −0.256846 + 0.504089i
\(999\) 13.5878 + 18.7019i 0.429898 + 0.591703i
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 55.2.l.a.52.1 yes 32
3.2 odd 2 495.2.bj.a.217.4 32
4.3 odd 2 880.2.cm.a.657.1 32
5.2 odd 4 275.2.bm.b.118.1 32
5.3 odd 4 inner 55.2.l.a.8.4 yes 32
5.4 even 2 275.2.bm.b.107.4 32
11.2 odd 10 605.2.e.b.362.3 32
11.3 even 5 605.2.m.c.457.4 32
11.4 even 5 605.2.m.e.282.1 32
11.5 even 5 605.2.m.d.112.1 32
11.6 odd 10 605.2.m.c.112.4 32
11.7 odd 10 inner 55.2.l.a.7.4 32
11.8 odd 10 605.2.m.d.457.1 32
11.9 even 5 605.2.e.b.362.14 32
11.10 odd 2 605.2.m.e.602.4 32
15.8 even 4 495.2.bj.a.118.1 32
20.3 even 4 880.2.cm.a.833.4 32
33.29 even 10 495.2.bj.a.172.1 32
44.7 even 10 880.2.cm.a.337.4 32
55.3 odd 20 605.2.m.c.578.4 32
55.7 even 20 275.2.bm.b.18.4 32
55.8 even 20 605.2.m.d.578.1 32
55.13 even 20 605.2.e.b.483.14 32
55.18 even 20 inner 55.2.l.a.18.1 yes 32
55.28 even 20 605.2.m.c.233.4 32
55.29 odd 10 275.2.bm.b.7.1 32
55.38 odd 20 605.2.m.d.233.1 32
55.43 even 4 605.2.m.e.118.1 32
55.48 odd 20 605.2.m.e.403.4 32
55.53 odd 20 605.2.e.b.483.3 32
165.128 odd 20 495.2.bj.a.73.4 32
220.183 odd 20 880.2.cm.a.513.1 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
55.2.l.a.7.4 32 11.7 odd 10 inner
55.2.l.a.8.4 yes 32 5.3 odd 4 inner
55.2.l.a.18.1 yes 32 55.18 even 20 inner
55.2.l.a.52.1 yes 32 1.1 even 1 trivial
275.2.bm.b.7.1 32 55.29 odd 10
275.2.bm.b.18.4 32 55.7 even 20
275.2.bm.b.107.4 32 5.4 even 2
275.2.bm.b.118.1 32 5.2 odd 4
495.2.bj.a.73.4 32 165.128 odd 20
495.2.bj.a.118.1 32 15.8 even 4
495.2.bj.a.172.1 32 33.29 even 10
495.2.bj.a.217.4 32 3.2 odd 2
605.2.e.b.362.3 32 11.2 odd 10
605.2.e.b.362.14 32 11.9 even 5
605.2.e.b.483.3 32 55.53 odd 20
605.2.e.b.483.14 32 55.13 even 20
605.2.m.c.112.4 32 11.6 odd 10
605.2.m.c.233.4 32 55.28 even 20
605.2.m.c.457.4 32 11.3 even 5
605.2.m.c.578.4 32 55.3 odd 20
605.2.m.d.112.1 32 11.5 even 5
605.2.m.d.233.1 32 55.38 odd 20
605.2.m.d.457.1 32 11.8 odd 10
605.2.m.d.578.1 32 55.8 even 20
605.2.m.e.118.1 32 55.43 even 4
605.2.m.e.282.1 32 11.4 even 5
605.2.m.e.403.4 32 55.48 odd 20
605.2.m.e.602.4 32 11.10 odd 2
880.2.cm.a.337.4 32 44.7 even 10
880.2.cm.a.513.1 32 220.183 odd 20
880.2.cm.a.657.1 32 4.3 odd 2
880.2.cm.a.833.4 32 20.3 even 4