Properties

Label 55.2.l.a.8.4
Level $55$
Weight $2$
Character 55.8
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 8.4
Character \(\chi\) \(=\) 55.8
Dual form 55.2.l.a.7.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.50135 + 0.237790i) q^{2} +(-0.361933 + 0.710333i) q^{3} +(0.295389 + 0.0959778i) q^{4} +(-1.89470 - 1.18749i) q^{5} +(-0.712297 + 0.980393i) q^{6} +(0.170602 - 0.0869260i) q^{7} +(-2.28811 - 1.16585i) q^{8} +(1.38978 + 1.91287i) q^{9} +O(q^{10})\) \(q+(1.50135 + 0.237790i) q^{2} +(-0.361933 + 0.710333i) q^{3} +(0.295389 + 0.0959778i) q^{4} +(-1.89470 - 1.18749i) q^{5} +(-0.712297 + 0.980393i) q^{6} +(0.170602 - 0.0869260i) q^{7} +(-2.28811 - 1.16585i) 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} +(-0.484259 + 3.05749i) q^{13} +(0.276803 - 0.0899388i) q^{14} +(1.52926 - 0.916076i) q^{15} +(-3.66057 - 2.65956i) q^{16} +(0.579827 + 3.66088i) q^{17} +(1.63168 + 3.20235i) q^{18} +(-0.229844 - 0.707388i) q^{19} +(-0.445701 - 0.532619i) q^{20} +0.152646i q^{21} +(3.33373 - 3.78190i) q^{22} +(-1.14886 - 1.14886i) q^{23} +(1.65629 - 1.20336i) q^{24} +(2.17976 + 4.49985i) q^{25} +(-1.45408 + 4.47521i) q^{26} +(-4.22401 + 0.669017i) q^{27} +(0.0587369 - 0.00930302i) q^{28} +(2.95025 - 9.07993i) q^{29} +(2.51379 - 1.01171i) q^{30} +(-0.283900 + 0.206266i) q^{31} +(-1.23166 - 1.23166i) q^{32} +(1.34611 + 2.27579i) q^{33} +5.63413i q^{34} +(-0.426463 - 0.0378887i) q^{35} +(0.226933 + 0.698428i) q^{36} +(2.45398 + 4.81621i) q^{37} +(-0.176866 - 1.11669i) q^{38} +(-1.99657 - 1.45059i) q^{39} +(2.95085 + 4.92603i) q^{40} +(6.36824 - 2.06917i) q^{41} +(-0.0362976 + 0.229174i) 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} +(-11.0165 - 5.61318i) q^{47} +(3.21405 - 1.63764i) q^{48} +(-4.09295 + 5.63346i) q^{49} +(2.20256 + 7.27417i) q^{50} +(-2.81030 - 0.913123i) q^{51} +(-0.436496 + 0.856672i) q^{52} +(-8.91914 - 1.41265i) q^{53} -6.50079 q^{54} +(-6.69225 + 3.19590i) q^{55} -0.491699 q^{56} +(0.585669 + 0.0927608i) q^{57} +(6.58847 - 12.9306i) q^{58} +(-9.15496 - 2.97463i) q^{59} +(0.539651 - 0.123824i) q^{60} +(-3.46383 + 4.76756i) q^{61} +(-0.475281 + 0.242168i) q^{62} +(0.403377 + 0.205531i) 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} +(-0.180089 + 1.13704i) q^{68} +(1.23188 - 0.400262i) q^{69} +(-0.631259 - 0.158293i) q^{70} +(9.27272 + 6.73702i) q^{71} +(-0.949851 - 5.99713i) q^{72} +(1.09042 + 2.14008i) q^{73} +(2.53903 + 7.81434i) q^{74} +(-3.98532 - 0.0802892i) q^{75} -0.231015i q^{76} +(0.0597184 - 0.632224i) q^{77} +(-2.65261 - 2.65261i) q^{78} +(-0.542434 + 0.394101i) q^{79} +(3.77749 + 9.38594i) q^{80} +(-1.13837 + 3.50353i) q^{81} +(10.0530 - 1.59224i) q^{82} +(16.4776 - 2.60980i) q^{83} +(-0.0146506 + 0.0450899i) q^{84} +(3.24865 - 7.62480i) q^{85} +(6.48191 - 4.70938i) q^{86} +(5.38198 + 5.38198i) q^{87} +(-7.33074 + 4.33608i) q^{88} +7.92190i q^{89} +(0.711206 - 8.00509i) q^{90} +(0.183160 + 0.563709i) q^{91} +(-0.229095 - 0.449625i) q^{92} +(-0.0437645 - 0.276318i) q^{93} +(-15.2048 - 11.0469i) q^{94} +(-0.404527 + 1.61322i) q^{95} +(1.32067 - 0.429111i) q^{96} +(-0.215721 + 1.36201i) 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 \(\left(\mathbb{Z}/55\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.50135 + 0.237790i 1.06161 + 0.168143i 0.662730 0.748859i \(-0.269398\pi\)
0.398884 + 0.917002i \(0.369398\pi\)
\(3\) −0.361933 + 0.710333i −0.208962 + 0.410111i −0.971571 0.236749i \(-0.923918\pi\)
0.762609 + 0.646860i \(0.223918\pi\)
\(4\) 0.295389 + 0.0959778i 0.147695 + 0.0479889i
\(5\) −1.89470 1.18749i −0.847335 0.531060i
\(6\) −0.712297 + 0.980393i −0.290794 + 0.400244i
\(7\) 0.170602 0.0869260i 0.0644815 0.0328550i −0.421452 0.906851i \(-0.638480\pi\)
0.485934 + 0.873996i \(0.338480\pi\)
\(8\) −2.28811 1.16585i −0.808970 0.412191i
\(9\) 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
\(13\) −0.484259 + 3.05749i −0.134309 + 0.847995i 0.824896 + 0.565285i \(0.191234\pi\)
−0.959205 + 0.282711i \(0.908766\pi\)
\(14\) 0.276803 0.0899388i 0.0739787 0.0240372i
\(15\) 1.52926 0.916076i 0.394854 0.236530i
\(16\) −3.66057 2.65956i −0.915143 0.664890i
\(17\) 0.579827 + 3.66088i 0.140629 + 0.887894i 0.952606 + 0.304206i \(0.0983910\pi\)
−0.811978 + 0.583688i \(0.801609\pi\)
\(18\) 1.63168 + 3.20235i 0.384591 + 0.754802i
\(19\) −0.229844 0.707388i −0.0527299 0.162286i 0.921224 0.389033i \(-0.127191\pi\)
−0.973954 + 0.226747i \(0.927191\pi\)
\(20\) −0.445701 0.532619i −0.0996618 0.119097i
\(21\) 0.152646i 0.0333100i
\(22\) 3.33373 3.78190i 0.710753 0.806304i
\(23\) −1.14886 1.14886i −0.239553 0.239553i 0.577112 0.816665i \(-0.304180\pi\)
−0.816665 + 0.577112i \(0.804180\pi\)
\(24\) 1.65629 1.20336i 0.338088 0.245635i
\(25\) 2.17976 + 4.49985i 0.435952 + 0.899970i
\(26\) −1.45408 + 4.47521i −0.285169 + 0.877660i
\(27\) −4.22401 + 0.669017i −0.812911 + 0.128752i
\(28\) 0.0587369 0.00930302i 0.0111002 0.00175811i
\(29\) 2.95025 9.07993i 0.547847 1.68610i −0.166275 0.986079i \(-0.553174\pi\)
0.714122 0.700021i \(-0.246826\pi\)
\(30\) 2.51379 1.01171i 0.458953 0.184711i
\(31\) −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
\(33\) 1.34611 + 2.27579i 0.234328 + 0.396165i
\(34\) 5.63413i 0.966246i
\(35\) −0.426463 0.0378887i −0.0720853 0.00640437i
\(36\) 0.226933 + 0.698428i 0.0378222 + 0.116405i
\(37\) 2.45398 + 4.81621i 0.403432 + 0.791780i 0.999941 0.0108264i \(-0.00344622\pi\)
−0.596510 + 0.802606i \(0.703446\pi\)
\(38\) −0.176866 1.11669i −0.0286915 0.181151i
\(39\) −1.99657 1.45059i −0.319707 0.232280i
\(40\) 2.95085 + 4.92603i 0.466570 + 0.778874i
\(41\) 6.36824 2.06917i 0.994552 0.323150i 0.233866 0.972269i \(-0.424862\pi\)
0.760687 + 0.649119i \(0.224862\pi\)
\(42\) −0.0362976 + 0.229174i −0.00560084 + 0.0353623i
\(43\) 3.72708 3.72708i 0.568374 0.568374i −0.363299 0.931673i \(-0.618350\pi\)
0.931673 + 0.363299i \(0.118350\pi\)
\(44\) 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
\(47\) −11.0165 5.61318i −1.60692 0.818766i −0.999706 0.0242272i \(-0.992287\pi\)
−0.607213 0.794539i \(-0.707713\pi\)
\(48\) 3.21405 1.63764i 0.463909 0.236373i
\(49\) −4.09295 + 5.63346i −0.584707 + 0.804780i
\(50\) 2.20256 + 7.27417i 0.311488 + 1.02872i
\(51\) −2.81030 0.913123i −0.393521 0.127863i
\(52\) −0.436496 + 0.856672i −0.0605311 + 0.118799i
\(53\) −8.91914 1.41265i −1.22514 0.194043i −0.489855 0.871804i \(-0.662950\pi\)
−0.735282 + 0.677761i \(0.762950\pi\)
\(54\) −6.50079 −0.884646
\(55\) −6.69225 + 3.19590i −0.902383 + 0.430935i
\(56\) −0.491699 −0.0657061
\(57\) 0.585669 + 0.0927608i 0.0775737 + 0.0122865i
\(58\) 6.58847 12.9306i 0.865108 1.69787i
\(59\) −9.15496 2.97463i −1.19187 0.387263i −0.355108 0.934825i \(-0.615556\pi\)
−0.836765 + 0.547562i \(0.815556\pi\)
\(60\) 0.539651 0.123824i 0.0696686 0.0159856i
\(61\) −3.46383 + 4.76756i −0.443498 + 0.610423i −0.970985 0.239140i \(-0.923134\pi\)
0.527487 + 0.849563i \(0.323134\pi\)
\(62\) −0.475281 + 0.242168i −0.0603608 + 0.0307554i
\(63\) 0.403377 + 0.205531i 0.0508207 + 0.0258944i
\(64\) 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 −0.407932 0.913012i \(-0.633750\pi\)
0.913012 + 0.407932i \(0.133750\pi\)
\(68\) −0.180089 + 1.13704i −0.0218390 + 0.137886i
\(69\) 1.23188 0.400262i 0.148301 0.0481859i
\(70\) −0.631259 0.158293i −0.0754499 0.0189196i
\(71\) 9.27272 + 6.73702i 1.10047 + 0.799538i 0.981136 0.193317i \(-0.0619245\pi\)
0.119333 + 0.992854i \(0.461925\pi\)
\(72\) −0.949851 5.99713i −0.111941 0.706768i
\(73\) 1.09042 + 2.14008i 0.127624 + 0.250477i 0.945973 0.324245i \(-0.105110\pi\)
−0.818349 + 0.574722i \(0.805110\pi\)
\(74\) 2.53903 + 7.81434i 0.295156 + 0.908398i
\(75\) −3.98532 0.0802892i −0.460185 0.00927099i
\(76\) 0.231015i 0.0264992i
\(77\) 0.0597184 0.632224i 0.00680554 0.0720486i
\(78\) −2.65261 2.65261i −0.300348 0.300348i
\(79\) −0.542434 + 0.394101i −0.0610286 + 0.0443399i −0.617881 0.786271i \(-0.712009\pi\)
0.556853 + 0.830611i \(0.312009\pi\)
\(80\) 3.77749 + 9.38594i 0.422336 + 1.04938i
\(81\) −1.13837 + 3.50353i −0.126485 + 0.389282i
\(82\) 10.0530 1.59224i 1.11017 0.175833i
\(83\) 16.4776 2.60980i 1.80865 0.286463i 0.841426 0.540372i \(-0.181716\pi\)
0.967228 + 0.253909i \(0.0817163\pi\)
\(84\) −0.0146506 + 0.0450899i −0.00159851 + 0.00491971i
\(85\) 3.24865 7.62480i 0.352365 0.827025i
\(86\) 6.48191 4.70938i 0.698962 0.507826i
\(87\) 5.38198 + 5.38198i 0.577009 + 0.577009i
\(88\) −7.33074 + 4.33608i −0.781460 + 0.462227i
\(89\) 7.92190i 0.839720i 0.907589 + 0.419860i \(0.137921\pi\)
−0.907589 + 0.419860i \(0.862079\pi\)
\(90\) 0.711206 8.00509i 0.0749677 0.843810i
\(91\) 0.183160 + 0.563709i 0.0192004 + 0.0590927i
\(92\) −0.229095 0.449625i −0.0238848 0.0468766i
\(93\) −0.0437645 0.276318i −0.00453817 0.0286528i
\(94\) −15.2048 11.0469i −1.56826 1.13941i
\(95\) −0.404527 + 1.61322i −0.0415036 + 0.165513i
\(96\) 1.32067 0.429111i 0.134790 0.0437960i
\(97\) −0.215721 + 1.36201i −0.0219032 + 0.138291i −0.996217 0.0869051i \(-0.972302\pi\)
0.974313 + 0.225196i \(0.0723023\pi\)
\(98\) −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 \(0.877172\pi\)
\(102\) −4.00211 2.03918i −0.396268 0.201909i
\(103\) 2.88449 1.46972i 0.284217 0.144816i −0.306071 0.952009i \(-0.599014\pi\)
0.590287 + 0.807193i \(0.299014\pi\)
\(104\) 4.67262 6.43131i 0.458188 0.630641i
\(105\) 0.181264 0.289217i 0.0176896 0.0282247i
\(106\) −13.0548 4.24177i −1.26800 0.411997i
\(107\) −5.01911 + 9.85055i −0.485215 + 0.952289i 0.510505 + 0.859875i \(0.329458\pi\)
−0.995721 + 0.0924142i \(0.970542\pi\)
\(108\) −1.31194 0.207790i −0.126241 0.0199946i
\(109\) 9.54212 0.913969 0.456985 0.889475i \(-0.348929\pi\)
0.456985 + 0.889475i \(0.348929\pi\)
\(110\) −10.8074 + 3.20681i −1.03044 + 0.305757i
\(111\) −4.30929 −0.409019
\(112\) −0.855686 0.135527i −0.0808547 0.0128061i
\(113\) −1.88301 + 3.69562i −0.177139 + 0.347654i −0.962455 0.271440i \(-0.912500\pi\)
0.785317 + 0.619094i \(0.212500\pi\)
\(114\) 0.857235 + 0.278533i 0.0802874 + 0.0260870i
\(115\) 0.812486 + 3.54099i 0.0757647 + 0.330199i
\(116\) 1.74294 2.39895i 0.161828 0.222737i
\(117\) −6.52158 + 3.32291i −0.602920 + 0.307203i
\(118\) −13.0374 6.64291i −1.20019 0.611529i
\(119\) 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
\(123\) −0.835077 + 5.27247i −0.0752964 + 0.475403i
\(124\) −0.103658 + 0.0336805i −0.00930877 + 0.00302460i
\(125\) 1.21352 11.1143i 0.108541 0.994092i
\(126\) 0.556736 + 0.404492i 0.0495980 + 0.0360350i
\(127\) −2.27881 14.3879i −0.202212 1.27672i −0.854782 0.518987i \(-0.826309\pi\)
0.652570 0.757728i \(-0.273691\pi\)
\(128\) 5.99935 + 11.7744i 0.530273 + 1.04072i
\(129\) 1.29851 + 3.99642i 0.114328 + 0.351865i
\(130\) 8.06929 6.75246i 0.707723 0.592230i
\(131\) 9.76926i 0.853544i 0.904359 + 0.426772i \(0.140349\pi\)
−0.904359 + 0.426772i \(0.859651\pi\)
\(132\) 0.179202 + 0.801441i 0.0155975 + 0.0697565i
\(133\) −0.100702 0.100702i −0.00873200 0.00873200i
\(134\) 7.19006 5.22388i 0.621126 0.451275i
\(135\) 8.79767 + 3.74836i 0.757182 + 0.322608i
\(136\) 2.94133 9.05250i 0.252217 0.776245i
\(137\) 4.27681 0.677380i 0.365392 0.0578725i 0.0289612 0.999581i \(-0.490780\pi\)
0.336431 + 0.941708i \(0.390780\pi\)
\(138\) 1.94466 0.308004i 0.165540 0.0262190i
\(139\) 3.24794 9.99613i 0.275487 0.847860i −0.713604 0.700550i \(-0.752938\pi\)
0.989090 0.147311i \(-0.0470618\pi\)
\(140\) −0.122336 0.0521228i −0.0103393 0.00440518i
\(141\) 7.97445 5.79378i 0.671570 0.487924i
\(142\) 12.3196 + 12.3196i 1.03384 + 1.03384i
\(143\) 7.70183 + 6.78912i 0.644059 + 0.567735i
\(144\) 10.6984i 0.891532i
\(145\) −16.3721 + 13.7003i −1.35963 + 1.13775i
\(146\) 1.12822 + 3.47229i 0.0933719 + 0.287369i
\(147\) −2.52026 4.94629i −0.207868 0.407963i
\(148\) 0.262630 + 1.65818i 0.0215881 + 0.136302i
\(149\) 4.66189 + 3.38706i 0.381917 + 0.277479i 0.762135 0.647418i \(-0.224151\pi\)
−0.380218 + 0.924897i \(0.624151\pi\)
\(150\) −5.96426 1.06821i −0.486980 0.0872191i
\(151\) −14.2318 + 4.62419i −1.15817 + 0.376311i −0.824214 0.566278i \(-0.808383\pi\)
−0.333953 + 0.942590i \(0.608383\pi\)
\(152\) −0.298800 + 1.88655i −0.0242358 + 0.153019i
\(153\) −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
\(157\) 4.40881 + 2.24640i 0.351861 + 0.179282i 0.620983 0.783824i \(-0.286733\pi\)
−0.269122 + 0.963106i \(0.586733\pi\)
\(158\) −0.908095 + 0.462698i −0.0722442 + 0.0368103i
\(159\) 4.23158 5.82427i 0.335586 0.461895i
\(160\) 0.871047 + 3.79621i 0.0688623 + 0.300117i
\(161\) −0.295863 0.0961317i −0.0233173 0.00757624i
\(162\) −2.54219 + 4.98933i −0.199733 + 0.391999i
\(163\) −9.89335 1.56695i −0.774907 0.122733i −0.243558 0.969886i \(-0.578315\pi\)
−0.531349 + 0.847153i \(0.678315\pi\)
\(164\) 2.07970 0.162398
\(165\) 0.151992 5.91043i 0.0118325 0.460126i
\(166\) 25.3592 1.96826
\(167\) 11.9137 + 1.88695i 0.921913 + 0.146017i 0.599310 0.800517i \(-0.295442\pi\)
0.322604 + 0.946534i \(0.395442\pi\)
\(168\) 0.177962 0.349270i 0.0137301 0.0269468i
\(169\) 3.24999 + 1.05599i 0.250000 + 0.0812298i
\(170\) 6.69045 10.6750i 0.513134 0.818734i
\(171\) 1.03371 1.42277i 0.0790494 0.108802i
\(172\) 1.45866 0.743222i 0.111221 0.0566702i
\(173\) −11.1065 5.65903i −0.844410 0.430248i −0.0224186 0.999749i \(-0.507137\pi\)
−0.821991 + 0.569501i \(0.807137\pi\)
\(174\) 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
\(178\) −1.88375 + 11.8935i −0.141193 + 0.891458i
\(179\) −19.1909 + 6.23551i −1.43440 + 0.466064i −0.920146 0.391575i \(-0.871930\pi\)
−0.514252 + 0.857639i \(0.671930\pi\)
\(180\) 0.399403 1.59279i 0.0297698 0.118719i
\(181\) −3.72935 2.70953i −0.277200 0.201398i 0.440495 0.897755i \(-0.354803\pi\)
−0.717695 + 0.696357i \(0.754803\pi\)
\(182\) 0.140943 + 0.889877i 0.0104474 + 0.0659620i
\(183\) −2.13288 4.18601i −0.157667 0.309439i
\(184\) 1.28932 + 3.96811i 0.0950497 + 0.292533i
\(185\) 1.06962 12.0393i 0.0786403 0.885148i
\(186\) 0.425256i 0.0311813i
\(187\) 11.2824 + 4.88140i 0.825051 + 0.356963i
\(188\) −2.71541 2.71541i −0.198042 0.198042i
\(189\) −0.662469 + 0.481312i −0.0481875 + 0.0350103i
\(190\) −0.990944 + 2.32582i −0.0718907 + 0.168732i
\(191\) 1.95493 6.01667i 0.141454 0.435351i −0.855084 0.518490i \(-0.826495\pi\)
0.996538 + 0.0831389i \(0.0264945\pi\)
\(192\) −5.04079 + 0.798383i −0.363788 + 0.0576183i
\(193\) 5.85885 0.927951i 0.421729 0.0667954i 0.0580368 0.998314i \(-0.481516\pi\)
0.363692 + 0.931519i \(0.381516\pi\)
\(194\) −0.647745 + 1.99355i −0.0465054 + 0.143129i
\(195\) 2.06034 + 5.11932i 0.147544 + 0.366602i
\(196\) −1.74970 + 1.27123i −0.124979 + 0.0908022i
\(197\) −9.90515 9.90515i −0.705713 0.705713i 0.259918 0.965631i \(-0.416304\pi\)
−0.965631 + 0.259918i \(0.916304\pi\)
\(198\) 11.8674 + 1.12097i 0.843380 + 0.0796637i
\(199\) 13.3828i 0.948680i 0.880342 + 0.474340i \(0.157313\pi\)
−0.880342 + 0.474340i \(0.842687\pi\)
\(200\) 0.258626 12.8374i 0.0182876 0.907744i
\(201\) 1.44038 + 4.43303i 0.101596 + 0.312682i
\(202\) −3.33001 6.53551i −0.234299 0.459837i
\(203\) −0.285964 1.80551i −0.0200708 0.126722i
\(204\) −0.742493 0.539453i −0.0519849 0.0377693i
\(205\) −14.5230 3.64175i −1.01433 0.254351i
\(206\) 4.68010 1.52066i 0.326078 0.105949i
\(207\) 0.600953 3.79427i 0.0417691 0.263720i
\(208\) 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 \(0.734540\pi\)
\(212\) −2.49903 1.27332i −0.171634 0.0874521i
\(213\) −8.14163 + 4.14837i −0.557855 + 0.284241i
\(214\) −9.87779 + 13.5956i −0.675232 + 0.929377i
\(215\) −11.4875 + 2.63584i −0.783444 + 0.179763i
\(216\) 10.4450 + 3.39378i 0.710691 + 0.230917i
\(217\) −0.0305041 + 0.0598677i −0.00207075 + 0.00406408i
\(218\) 14.3260 + 2.26902i 0.970282 + 0.153678i
\(219\) −1.91483 −0.129392
\(220\) −2.28355 + 0.301727i −0.153957 + 0.0203424i
\(221\) −11.4739 −0.771818
\(222\) −6.46974 1.02471i −0.434220 0.0687738i
\(223\) 9.64984 18.9389i 0.646201 1.26824i −0.302826 0.953046i \(-0.597930\pi\)
0.949027 0.315195i \(-0.102070\pi\)
\(224\) −0.317188 0.103060i −0.0211930 0.00688602i
\(225\) −5.57823 + 10.4234i −0.371882 + 0.694892i
\(226\) −3.70584 + 5.10065i −0.246509 + 0.339290i
\(227\) 11.6456 5.93372i 0.772944 0.393835i −0.0225888 0.999745i \(-0.507191\pi\)
0.795533 + 0.605910i \(0.207191\pi\)
\(228\) 0.164097 + 0.0836117i 0.0108676 + 0.00553732i
\(229\) −9.65796 13.2930i −0.638216 0.878429i 0.360303 0.932835i \(-0.382673\pi\)
−0.998519 + 0.0544066i \(0.982673\pi\)
\(230\) 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
\(233\) 2.44720 15.4510i 0.160321 1.01223i −0.768000 0.640450i \(-0.778748\pi\)
0.928321 0.371779i \(-0.121252\pi\)
\(234\) −10.5813 + 3.43808i −0.691722 + 0.224754i
\(235\) 14.2073 + 23.7172i 0.926785 + 1.54714i
\(236\) −2.41878 1.75734i −0.157449 0.114393i
\(237\) −0.0836185 0.527947i −0.00543161 0.0342938i
\(238\) 0.489753 + 0.961194i 0.0317460 + 0.0623050i
\(239\) 1.63214 + 5.02322i 0.105575 + 0.324925i 0.989865 0.142012i \(-0.0453572\pi\)
−0.884290 + 0.466938i \(0.845357\pi\)
\(240\) −8.03434 0.713804i −0.518614 0.0460759i
\(241\) 16.1676i 1.04144i −0.853726 0.520722i \(-0.825663\pi\)
0.853726 0.520722i \(-0.174337\pi\)
\(242\) −4.66716 16.0561i −0.300016 1.03213i
\(243\) −11.1488 11.1488i −0.715198 0.715198i
\(244\) −1.48076 + 1.07583i −0.0947959 + 0.0688732i
\(245\) 14.4445 5.81339i 0.922828 0.371404i
\(246\) −2.50748 + 7.71724i −0.159871 + 0.492033i
\(247\) 2.27413 0.360188i 0.144700 0.0229182i
\(248\) 0.890071 0.140973i 0.0565196 0.00895182i
\(249\) −4.10997 + 12.6492i −0.260458 + 0.801609i
\(250\) 4.46479 16.3978i 0.282378 1.03709i
\(251\) −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
\(253\) −5.25876 + 1.17586i −0.330615 + 0.0739254i
\(254\) 22.1431i 1.38938i
\(255\) 4.24035 + 5.06728i 0.265541 + 0.317326i
\(256\) 2.25079 + 6.92722i 0.140674 + 0.432951i
\(257\) 2.13653 + 4.19318i 0.133273 + 0.261563i 0.947993 0.318292i \(-0.103109\pi\)
−0.814720 + 0.579855i \(0.803109\pi\)
\(258\) 0.999214 + 6.30879i 0.0622083 + 0.392768i
\(259\) 0.837308 + 0.608340i 0.0520278 + 0.0378004i
\(260\) 1.84431 1.10480i 0.114379 0.0685169i
\(261\) 21.4689 6.97566i 1.32889 0.431783i
\(262\) −2.32303 + 14.6671i −0.143517 + 0.906134i
\(263\) −11.2218 + 11.2218i −0.691964 + 0.691964i −0.962664 0.270700i \(-0.912745\pi\)
0.270700 + 0.962664i \(0.412745\pi\)
\(264\) −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
\(267\) −5.62719 2.86720i −0.344378 0.175470i
\(268\) 1.61801 0.824419i 0.0988359 0.0503594i
\(269\) 6.64926 9.15192i 0.405412 0.558002i −0.556680 0.830727i \(-0.687925\pi\)
0.962092 + 0.272725i \(0.0879249\pi\)
\(270\) 12.3170 + 7.71959i 0.749591 + 0.469800i
\(271\) 16.9556 + 5.50921i 1.02998 + 0.334661i 0.774782 0.632228i \(-0.217859\pi\)
0.255198 + 0.966889i \(0.417859\pi\)
\(272\) 7.61384 14.9430i 0.461657 0.906052i
\(273\) −0.466712 0.0739200i −0.0282467 0.00447384i
\(274\) 6.58205 0.397636
\(275\) 16.4749 + 1.89169i 0.993472 + 0.114073i
\(276\) 0.402300 0.0242156
\(277\) −4.62395 0.732361i −0.277826 0.0440033i 0.0159666 0.999873i \(-0.494917\pi\)
−0.293793 + 0.955869i \(0.594917\pi\)
\(278\) 7.25327 14.2353i 0.435022 0.853779i
\(279\) −0.789117 0.256400i −0.0472432 0.0153502i
\(280\) 0.931621 + 0.583886i 0.0556750 + 0.0348938i
\(281\) −7.75247 + 10.6704i −0.462474 + 0.636541i −0.975019 0.222119i \(-0.928703\pi\)
0.512546 + 0.858660i \(0.328703\pi\)
\(282\) 13.3501 6.80223i 0.794989 0.405067i
\(283\) 20.3029 + 10.3449i 1.20688 + 0.614938i 0.937463 0.348084i \(-0.113168\pi\)
0.269421 + 0.963022i \(0.413168\pi\)
\(284\) 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
\(288\) 0.644267 4.06774i 0.0379638 0.239694i
\(289\) 3.10211 1.00794i 0.182477 0.0592904i
\(290\) −27.8380 + 16.6759i −1.63471 + 0.979240i
\(291\) −0.889404 0.646190i −0.0521378 0.0378803i
\(292\) 0.116700 + 0.736812i 0.00682933 + 0.0431187i
\(293\) −3.28132 6.43996i −0.191697 0.376226i 0.775074 0.631870i \(-0.217713\pi\)
−0.966771 + 0.255644i \(0.917713\pi\)
\(294\) −2.60761 8.02539i −0.152079 0.468051i
\(295\) 13.8135 + 16.5074i 0.804256 + 0.961097i
\(296\) 13.8810i 0.806817i
\(297\) −5.63227 + 13.0179i −0.326818 + 0.755375i
\(298\) 6.19371 + 6.19371i 0.358792 + 0.358792i
\(299\) 4.06896 2.95628i 0.235314 0.170966i
\(300\) −1.16951 0.406218i −0.0675219 0.0234530i
\(301\) 0.311867 0.959827i 0.0179757 0.0553235i
\(302\) −22.4665 + 3.55834i −1.29280 + 0.204759i
\(303\) 3.79960 0.601798i 0.218282 0.0345724i
\(304\) −1.03998 + 3.20073i −0.0596469 + 0.183574i
\(305\) 12.2243 4.91983i 0.699963 0.281709i
\(306\) −10.7773 + 7.83020i −0.616100 + 0.447623i
\(307\) −20.1272 20.1272i −1.14872 1.14872i −0.986804 0.161918i \(-0.948232\pi\)
−0.161918 0.986804i \(-0.551768\pi\)
\(308\) 0.0783196 0.181020i 0.00446267 0.0103146i
\(309\) 2.58088i 0.146821i
\(310\) 1.18809 + 0.105555i 0.0674787 + 0.00599509i
\(311\) −2.32254 7.14803i −0.131699 0.405328i 0.863363 0.504583i \(-0.168354\pi\)
−0.995062 + 0.0992557i \(0.968354\pi\)
\(312\) 2.87720 + 5.64681i 0.162889 + 0.319688i
\(313\) −0.210574 1.32951i −0.0119023 0.0751483i 0.981022 0.193895i \(-0.0621122\pi\)
−0.992925 + 0.118747i \(0.962112\pi\)
\(314\) 6.08499 + 4.42100i 0.343396 + 0.249492i
\(315\) −0.520212 0.868422i −0.0293106 0.0489301i
\(316\) −0.198054 + 0.0643517i −0.0111414 + 0.00362006i
\(317\) −1.77271 + 11.1924i −0.0995652 + 0.628630i 0.886558 + 0.462617i \(0.153089\pi\)
−0.986124 + 0.166013i \(0.946911\pi\)
\(318\) 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
\(322\) −0.421334 0.214680i −0.0234800 0.0119637i
\(323\) 2.45639 1.25159i 0.136677 0.0696406i
\(324\) −0.672523 + 0.925648i −0.0373624 + 0.0514249i
\(325\) −14.8138 + 4.48550i −0.821723 + 0.248811i
\(326\) −14.4808 4.70509i −0.802015 0.260591i
\(327\) −3.45360 + 6.77808i −0.190985 + 0.374829i
\(328\) −16.9836 2.68994i −0.937762 0.148527i
\(329\) −2.36737 −0.130517
\(330\) 1.63363 8.83747i 0.0899286 0.486486i
\(331\) −17.7048 −0.973145 −0.486572 0.873640i \(-0.661753\pi\)
−0.486572 + 0.873640i \(0.661753\pi\)
\(332\) 5.11780 + 0.810579i 0.280876 + 0.0444863i
\(333\) −5.80227 + 11.3876i −0.317962 + 0.624036i
\(334\) 17.4380 + 5.66594i 0.954164 + 0.310027i
\(335\) −12.7426 + 2.92380i −0.696200 + 0.159744i
\(336\) 0.405970 0.558770i 0.0221475 0.0304834i
\(337\) 6.78954 3.45945i 0.369850 0.188448i −0.259180 0.965829i \(-0.583452\pi\)
0.629030 + 0.777381i \(0.283452\pi\)
\(338\) 4.62827 + 2.35822i 0.251745 + 0.128270i
\(339\) −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
\(343\) −0.418239 + 2.64066i −0.0225828 + 0.142582i
\(344\) −12.8732 + 4.18275i −0.694076 + 0.225519i
\(345\) −2.80935 0.704464i −0.151250 0.0379270i
\(346\) −15.3290 11.1372i −0.824093 0.598739i
\(347\) 1.46011 + 9.21879i 0.0783830 + 0.494891i 0.995381 + 0.0959998i \(0.0306048\pi\)
−0.916998 + 0.398891i \(0.869395\pi\)
\(348\) 1.07323 + 2.10633i 0.0575311 + 0.112911i
\(349\) −0.464073 1.42827i −0.0248413 0.0764536i 0.937867 0.346994i \(-0.112798\pi\)
−0.962709 + 0.270540i \(0.912798\pi\)
\(350\) 1.00807 + 1.04953i 0.0538839 + 0.0560996i
\(351\) 13.2388i 0.706637i
\(352\) −5.63779 + 1.26061i −0.300495 + 0.0671906i
\(353\) 4.40229 + 4.40229i 0.234310 + 0.234310i 0.814489 0.580179i \(-0.197017\pi\)
−0.580179 + 0.814489i \(0.697017\pi\)
\(354\) 9.43735 6.85664i 0.501589 0.364426i
\(355\) −9.56888 23.7758i −0.507863 1.26189i
\(356\) −0.760327 + 2.34004i −0.0402972 + 0.124022i
\(357\) −0.558817 + 0.0885080i −0.0295757 + 0.00468434i
\(358\) −30.2950 + 4.79826i −1.60114 + 0.253596i
\(359\) −8.12845 + 25.0168i −0.429003 + 1.32034i 0.470105 + 0.882611i \(0.344216\pi\)
−0.899108 + 0.437726i \(0.855784\pi\)
\(360\) −5.32182 + 12.4907i −0.280484 + 0.658316i
\(361\) 14.9238 10.8427i 0.785461 0.570671i
\(362\) −4.95475 4.95475i −0.260416 0.260416i
\(363\) 8.76519 + 0.274237i 0.460053 + 0.0143937i
\(364\) 0.184093i 0.00964908i
\(365\) 0.475287 5.34966i 0.0248776 0.280014i
\(366\) −2.20680 6.79184i −0.115351 0.355015i
\(367\) −3.70869 7.27872i −0.193592 0.379946i 0.773723 0.633524i \(-0.218392\pi\)
−0.967315 + 0.253579i \(0.918392\pi\)
\(368\) 1.15002 + 7.26093i 0.0599488 + 0.378502i
\(369\) 12.8085 + 9.30591i 0.666783 + 0.484446i
\(370\) 4.46871 17.8209i 0.232317 0.926463i
\(371\) −1.64442 + 0.534304i −0.0853740 + 0.0277397i
\(372\) 0.0135928 0.0858218i 0.000704756 0.00444965i
\(373\) −6.12473 + 6.12473i −0.317126 + 0.317126i −0.847662 0.530536i \(-0.821991\pi\)
0.530536 + 0.847662i \(0.321991\pi\)
\(374\) 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
\(377\) 26.3331 + 13.4174i 1.35622 + 0.691031i
\(378\) −1.10905 + 0.565088i −0.0570433 + 0.0290650i
\(379\) 0.363481 0.500288i 0.0186708 0.0256981i −0.799580 0.600560i \(-0.794944\pi\)
0.818250 + 0.574862i \(0.194944\pi\)
\(380\) −0.274326 + 0.437703i −0.0140726 + 0.0224537i
\(381\) 11.0449 + 3.58872i 0.565849 + 0.183856i
\(382\) 4.36574 8.56825i 0.223371 0.438390i
\(383\) 10.2511 + 1.62362i 0.523807 + 0.0829629i 0.412738 0.910850i \(-0.364572\pi\)
0.111069 + 0.993813i \(0.464572\pi\)
\(384\) −10.5351 −0.537617
\(385\) −0.863904 + 1.12696i −0.0440286 + 0.0574351i
\(386\) 9.01683 0.458945
\(387\) 12.3092 + 1.94959i 0.625712 + 0.0991031i
\(388\) −0.194444 + 0.381619i −0.00987142 + 0.0193737i
\(389\) 21.0630 + 6.84378i 1.06794 + 0.346993i 0.789683 0.613515i \(-0.210245\pi\)
0.278252 + 0.960508i \(0.410245\pi\)
\(390\) 1.87596 + 8.17582i 0.0949927 + 0.413999i
\(391\) 3.53969 4.87197i 0.179010 0.246386i
\(392\) 15.9329 8.11822i 0.804733 0.410032i
\(393\) −6.93942 3.53581i −0.350048 0.178358i
\(394\) −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 −0.382910 0.923786i \(-0.625078\pi\)
0.923786 + 0.382910i \(0.125078\pi\)
\(398\) −3.18229 + 20.0922i −0.159514 + 1.00713i
\(399\) 0.107980 0.0350847i 0.00540574 0.00175643i
\(400\) 3.98847 22.2692i 0.199423 1.11346i
\(401\) 3.46399 + 2.51673i 0.172983 + 0.125680i 0.670908 0.741540i \(-0.265904\pi\)
−0.497925 + 0.867220i \(0.665904\pi\)
\(402\) 1.10838 + 6.99803i 0.0552809 + 0.349030i
\(403\) −0.493174 0.967909i −0.0245668 0.0482150i
\(404\) −0.463135 1.42538i −0.0230418 0.0709155i
\(405\) 6.31726 5.28634i 0.313907 0.262681i
\(406\) 2.77869i 0.137904i
\(407\) 17.8481 + 1.68589i 0.884697 + 0.0835664i
\(408\) 5.36572 + 5.36572i 0.265643 + 0.265643i
\(409\) −3.47523 + 2.52490i −0.171839 + 0.124848i −0.670381 0.742017i \(-0.733869\pi\)
0.498541 + 0.866866i \(0.333869\pi\)
\(410\) −20.9381 8.92096i −1.03406 0.440575i
\(411\) −1.06675 + 3.28312i −0.0526190 + 0.161945i
\(412\) 0.993106 0.157293i 0.0489268 0.00774925i
\(413\) −1.82043 + 0.288327i −0.0895773 + 0.0141877i
\(414\) 1.80448 5.55361i 0.0886853 0.272945i
\(415\) −34.3192 14.6222i −1.68466 0.717773i
\(416\) 4.36224 3.16935i 0.213876 0.155390i
\(417\) 5.92504 + 5.92504i 0.290151 + 0.290151i
\(418\) −3.44151 1.48899i −0.168330 0.0728288i
\(419\) 1.20241i 0.0587414i −0.999569 0.0293707i \(-0.990650\pi\)
0.999569 0.0293707i \(-0.00935032\pi\)
\(420\) 0.0813020 0.0680343i 0.00396713 0.00331973i
\(421\) 9.67493 + 29.7764i 0.471527 + 1.45121i 0.850584 + 0.525839i \(0.176248\pi\)
−0.379057 + 0.925373i \(0.623752\pi\)
\(422\) 4.09390 + 8.03473i 0.199288 + 0.391124i
\(423\) −4.57321 28.8741i −0.222357 1.40391i
\(424\) 18.7610 + 13.6307i 0.911117 + 0.661965i
\(425\) −15.2095 + 10.5890i −0.737771 + 0.513640i
\(426\) −13.2099 + 4.29214i −0.640020 + 0.207955i
\(427\) −0.176512 + 1.11445i −0.00854201 + 0.0539321i
\(428\) −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 \(0.876565\pi\)
\(432\) 17.2416 + 8.78502i 0.829536 + 0.422669i
\(433\) −24.0414 + 12.2497i −1.15536 + 0.588683i −0.923323 0.384025i \(-0.874538\pi\)
−0.232033 + 0.972708i \(0.574538\pi\)
\(434\) −0.0600332 + 0.0826286i −0.00288169 + 0.00396630i
\(435\) −3.80620 16.5882i −0.182494 0.795346i
\(436\) 2.81864 + 0.915831i 0.134988 + 0.0438604i
\(437\) −0.548629 + 1.07675i −0.0262445 + 0.0515077i
\(438\) −2.87482 0.455327i −0.137364 0.0217564i
\(439\) 24.5862 1.17344 0.586718 0.809791i \(-0.300420\pi\)
0.586718 + 0.809791i \(0.300420\pi\)
\(440\) 19.0386 + 0.489593i 0.907628 + 0.0233404i
\(441\) −16.4643 −0.784016
\(442\) −17.2263 2.72838i −0.819372 0.129776i
\(443\) −13.9816 + 27.4404i −0.664286 + 1.30373i 0.275279 + 0.961364i \(0.411230\pi\)
−0.939565 + 0.342370i \(0.888770\pi\)
\(444\) −1.27292 0.413596i −0.0604099 0.0196284i
\(445\) 9.40714 15.0096i 0.445941 0.711524i
\(446\) 18.9912 26.1392i 0.899262 1.23773i
\(447\) −4.09323 + 2.08561i −0.193603 + 0.0986458i
\(448\) 1.09215 + 0.556477i 0.0515992 + 0.0262911i
\(449\) 4.30536 + 5.92582i 0.203182 + 0.279657i 0.898433 0.439111i \(-0.144707\pi\)
−0.695250 + 0.718768i \(0.744707\pi\)
\(450\) −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
\(453\) 1.86624 11.7830i 0.0876835 0.553612i
\(454\) 18.8951 6.13938i 0.886789 0.288135i
\(455\) 0.322363 1.28556i 0.0151126 0.0602678i
\(456\) −1.23193 0.895050i −0.0576904 0.0419146i
\(457\) 1.05368 + 6.65265i 0.0492889 + 0.311198i 0.999999 + 0.00111791i \(0.000355842\pi\)
−0.950710 + 0.310080i \(0.899644\pi\)
\(458\) −11.3390 22.2540i −0.529837 1.03986i
\(459\) −4.89838 15.0757i −0.228637 0.703672i
\(460\) −0.0998565 + 1.12395i −0.00465583 + 0.0524044i
\(461\) 29.0801i 1.35440i 0.735801 + 0.677198i \(0.236806\pi\)
−0.735801 + 0.677198i \(0.763194\pi\)
\(462\) 0.577290 + 0.508879i 0.0268580 + 0.0236752i
\(463\) 17.5146 + 17.5146i 0.813970 + 0.813970i 0.985227 0.171256i \(-0.0547826\pi\)
−0.171256 + 0.985227i \(0.554783\pi\)
\(464\) −34.9482 + 25.3914i −1.62243 + 1.17876i
\(465\) −0.245203 + 0.575509i −0.0113710 + 0.0266886i
\(466\) 7.34819 22.6154i 0.340398 1.04764i
\(467\) −26.1320 + 4.13890i −1.20924 + 0.191525i −0.728320 0.685237i \(-0.759698\pi\)
−0.480923 + 0.876763i \(0.659698\pi\)
\(468\) −2.24533 + 0.355625i −0.103790 + 0.0164388i
\(469\) 0.345938 1.06469i 0.0159739 0.0491627i
\(470\) 15.6904 + 38.9861i 0.723746 + 1.79830i
\(471\) −3.19138 + 2.31868i −0.147051 + 0.106839i
\(472\) 17.4796 + 17.4796i 0.804563 + 0.804563i
\(473\) −3.81467 17.0603i −0.175399 0.784432i
\(474\) 0.812515i 0.0373201i
\(475\) 2.68213 2.57620i 0.123065 0.118204i
\(476\) 0.0681145 + 0.209635i 0.00312202 + 0.00960860i
\(477\) −9.69341 19.0244i −0.443831 0.871067i
\(478\) 1.25594 + 7.92972i 0.0574455 + 0.362697i
\(479\) −21.2408 15.4324i −0.970519 0.705123i −0.0149492 0.999888i \(-0.504759\pi\)
−0.955570 + 0.294765i \(0.904759\pi\)
\(480\) −3.01183 0.755239i −0.137471 0.0344718i
\(481\) −15.9139 + 5.17073i −0.725610 + 0.235765i
\(482\) 3.84449 24.2731i 0.175112 1.10561i
\(483\) 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
\(487\) −20.7917 10.5939i −0.942163 0.480056i −0.0857326 0.996318i \(-0.527323\pi\)
−0.856431 + 0.516262i \(0.827323\pi\)
\(488\) 13.4839 6.87039i 0.610388 0.311008i
\(489\) 4.69379 6.46044i 0.212260 0.292151i
\(490\) 23.0687 5.29315i 1.04214 0.239120i
\(491\) 17.4497 + 5.66974i 0.787493 + 0.255872i 0.675036 0.737785i \(-0.264128\pi\)
0.112457 + 0.993657i \(0.464128\pi\)
\(492\) −0.752713 + 1.47728i −0.0339349 + 0.0666010i
\(493\) 34.9512 + 5.53572i 1.57412 + 0.249316i
\(494\) 3.49992 0.157469
\(495\) −15.4141 8.35979i −0.692811 0.375744i
\(496\) 1.58781 0.0712949
\(497\) 2.16757 + 0.343309i 0.0972286 + 0.0153995i
\(498\) −9.17834 + 18.0135i −0.411291 + 0.807204i
\(499\) −11.1824 3.63339i −0.500595 0.162653i 0.0478260 0.998856i \(-0.484771\pi\)
−0.548421 + 0.836203i \(0.684771\pi\)
\(500\) 1.42519 3.16657i 0.0637363 0.141613i
\(501\) −5.65234 + 7.77978i −0.252528 + 0.347575i
\(502\) −26.1975 + 13.3483i −1.16925 + 0.595763i
\(503\) −4.75855 2.42460i −0.212173 0.108108i 0.344674 0.938722i \(-0.387989\pi\)
−0.556848 + 0.830615i \(0.687989\pi\)
\(504\) −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
\(508\) 0.707777 4.46873i 0.0314025 0.198268i
\(509\) 18.6283 6.05272i 0.825687 0.268282i 0.134459 0.990919i \(-0.457070\pi\)
0.691228 + 0.722637i \(0.257070\pi\)
\(510\) 5.16130 + 8.61607i 0.228546 + 0.381526i
\(511\) 0.372057 + 0.270315i 0.0164588 + 0.0119580i
\(512\) −2.40248 15.1686i −0.106175 0.670365i
\(513\) 1.44412 + 2.83424i 0.0637594 + 0.125135i
\(514\) 2.21058 + 6.80347i 0.0975046 + 0.300088i
\(515\) −7.21050 0.640611i −0.317732 0.0282287i
\(516\) 1.30513i 0.0574550i
\(517\) −35.2950 + 20.8767i −1.55227 + 0.918158i
\(518\) 1.11243 + 1.11243i 0.0488775 + 0.0488775i
\(519\) 8.03959 5.84110i 0.352899 0.256396i
\(520\) −16.4903 + 6.63672i −0.723147 + 0.291039i
\(521\) 5.78913 17.8171i 0.253626 0.780582i −0.740471 0.672089i \(-0.765397\pi\)
0.994097 0.108493i \(-0.0346026\pi\)
\(522\) 33.8910 5.36781i 1.48337 0.234943i
\(523\) −2.55051 + 0.403961i −0.111526 + 0.0176640i −0.211948 0.977281i \(-0.567981\pi\)
0.100422 + 0.994945i \(0.467981\pi\)
\(524\) −0.937631 + 2.88573i −0.0409606 + 0.126064i
\(525\) −0.686882 + 0.332730i −0.0299780 + 0.0145215i
\(526\) −19.5162 + 14.1794i −0.850948 + 0.618250i
\(527\) −0.919727 0.919727i −0.0400639 0.0400639i
\(528\) 1.12506 11.9108i 0.0489621 0.518350i
\(529\) 20.3603i 0.885228i
\(530\) 19.6979 + 23.5393i 0.855622 + 1.02248i
\(531\) −7.03330 21.6463i −0.305219 0.939368i
\(532\) −0.0200812 0.0394115i −0.000870630 0.00170871i
\(533\) 3.24258 + 20.4729i 0.140452 + 0.886778i
\(534\) −7.76658 5.64275i −0.336093 0.244186i
\(535\) 21.2071 12.7037i 0.916862 0.549229i
\(536\) −14.2796 + 4.63972i −0.616784 + 0.200405i
\(537\) 2.51654 15.8888i 0.108597 0.685652i
\(538\) 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 \(0.736385\pi\)
\(542\) 24.1462 + 12.3031i 1.03717 + 0.528464i
\(543\) 3.27444 1.66841i 0.140520 0.0715983i
\(544\) 3.79482 5.22312i 0.162701 0.223939i
\(545\) −18.0794 11.3311i −0.774438 0.485372i
\(546\) −0.683120 0.221959i −0.0292348 0.00949898i
\(547\) 0.486237 0.954295i 0.0207900 0.0408027i −0.880378 0.474273i \(-0.842711\pi\)
0.901168 + 0.433470i \(0.142711\pi\)
\(548\) 1.32834 + 0.210388i 0.0567437 + 0.00898732i
\(549\) −13.9337 −0.594674
\(550\) 24.2847 + 6.75764i 1.03550 + 0.288147i
\(551\) −7.10113 −0.302518
\(552\) −3.28533 0.520344i −0.139833 0.0221473i
\(553\) −0.0582826 + 0.114386i −0.00247843 + 0.00486419i
\(554\) −6.76800 2.19906i −0.287545 0.0934290i
\(555\) 8.16479 + 5.11721i 0.346576 + 0.217214i
\(556\) 1.91881 2.64102i 0.0813758 0.112004i
\(557\) −38.3462 + 19.5384i −1.62478 + 0.827868i −0.625934 + 0.779876i \(0.715282\pi\)
−0.998848 + 0.0479915i \(0.984718\pi\)
\(558\) −1.12377 0.572590i −0.0475730 0.0242396i
\(559\) 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
\(563\) 4.04575 25.5439i 0.170508 1.07655i −0.742871 0.669435i \(-0.766536\pi\)
0.913379 0.407111i \(-0.133464\pi\)
\(564\) 2.91164 0.946049i 0.122602 0.0398359i
\(565\) 7.95622 4.76603i 0.334721 0.200508i
\(566\) 28.0219 + 20.3591i 1.17785 + 0.855756i
\(567\) 0.110341 + 0.696664i 0.00463387 + 0.0292571i
\(568\) −13.3626 26.2257i −0.560684 1.10040i
\(569\) −8.39651 25.8418i −0.352000 1.08334i −0.957729 0.287673i \(-0.907118\pi\)
0.605729 0.795671i \(-0.292882\pi\)
\(570\) −1.29345 1.54569i −0.0541766 0.0647418i
\(571\) 40.5475i 1.69686i 0.529308 + 0.848430i \(0.322451\pi\)
−0.529308 + 0.848430i \(0.677549\pi\)
\(572\) 1.62343 + 2.74464i 0.0678791 + 0.114759i
\(573\) 3.56628 + 3.56628i 0.148984 + 0.148984i
\(574\) 1.57665 1.14550i 0.0658081 0.0478124i
\(575\) 2.66546 7.67392i 0.111157 0.320024i
\(576\) −4.67742 + 14.3956i −0.194893 + 0.599818i
\(577\) 33.3917 5.28872i 1.39011 0.220172i 0.583914 0.811815i \(-0.301521\pi\)
0.806200 + 0.591643i \(0.201521\pi\)
\(578\) 4.89703 0.775613i 0.203689 0.0322612i
\(579\) −1.46136 + 4.49759i −0.0607319 + 0.186913i
\(580\) −6.15107 + 2.47558i −0.255409 + 0.102793i
\(581\) 2.58426 1.87757i 0.107213 0.0778948i
\(582\) −1.18165 1.18165i −0.0489808 0.0489808i
\(583\) −19.8048 + 22.4673i −0.820233 + 0.930502i
\(584\) 6.16801i 0.255234i
\(585\) 16.3023 + 1.44837i 0.674018 + 0.0598826i
\(586\) −3.39505 10.4489i −0.140248 0.431640i
\(587\) −4.39649 8.62859i −0.181462 0.356140i 0.782300 0.622902i \(-0.214046\pi\)
−0.963763 + 0.266762i \(0.914046\pi\)
\(588\) −0.269724 1.70297i −0.0111232 0.0702293i
\(589\) 0.211163 + 0.153419i 0.00870081 + 0.00632151i
\(590\) 16.8137 + 28.0681i 0.692207 + 1.15554i
\(591\) 10.6210 3.45096i 0.436888 0.141953i
\(592\) 3.82603 24.1566i 0.157249 0.992829i
\(593\) 14.0452 14.0452i 0.576769 0.576769i −0.357243 0.934012i \(-0.616283\pi\)
0.934012 + 0.357243i \(0.116283\pi\)
\(594\) −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
\(597\) −9.50623 4.84367i −0.389064 0.198238i
\(598\) 6.81191 3.47084i 0.278560 0.141933i
\(599\) −2.65433 + 3.65338i −0.108453 + 0.149273i −0.859793 0.510642i \(-0.829408\pi\)
0.751340 + 0.659915i \(0.229408\pi\)
\(600\) 9.02525 + 4.83000i 0.368454 + 0.197184i
\(601\) −7.96746 2.58878i −0.324999 0.105599i 0.141973 0.989871i \(-0.454655\pi\)
−0.466973 + 0.884272i \(0.654655\pi\)
\(602\) 0.696458 1.36688i 0.0283855 0.0557097i
\(603\) 13.6540 + 2.16258i 0.556034 + 0.0880671i
\(604\) −4.64774 −0.189114
\(605\) −2.94181 + 24.4202i −0.119601 + 0.992822i
\(606\) 5.84763 0.237544
\(607\) −7.58425 1.20123i −0.307835 0.0487563i 0.000605683 1.00000i \(-0.499807\pi\)
−0.308441 + 0.951244i \(0.599807\pi\)
\(608\) −0.588172 + 1.15435i −0.0238535 + 0.0468152i
\(609\) 1.38601 + 0.450342i 0.0561640 + 0.0182488i
\(610\) 19.5229 4.47955i 0.790457 0.181372i
\(611\) 22.4971 30.9646i 0.910134 1.25269i
\(612\) −2.42528 + 1.23574i −0.0980361 + 0.0499519i
\(613\) 38.2477 + 19.4882i 1.54481 + 0.787120i 0.998719 0.0506058i \(-0.0161152\pi\)
0.546091 + 0.837726i \(0.316115\pi\)
\(614\) −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 0.456601 0.889671i \(-0.349067\pi\)
0.889671 0.456601i \(-0.150933\pi\)
\(618\) −0.613709 + 3.87481i −0.0246870 + 0.155868i
\(619\) 20.0674 6.52029i 0.806576 0.262073i 0.123429 0.992353i \(-0.460611\pi\)
0.683147 + 0.730281i \(0.260611\pi\)
\(620\) 0.236396 + 0.0592779i 0.00949388 + 0.00238066i
\(621\) 5.62139 + 4.08418i 0.225578 + 0.163892i
\(622\) −1.78720 11.2840i −0.0716603 0.452445i
\(623\) 0.688620 + 1.35149i 0.0275890 + 0.0541464i
\(624\) 3.45064 + 10.6200i 0.138136 + 0.425139i
\(625\) −15.4973 + 19.6172i −0.619892 + 0.784687i
\(626\) 2.04613i 0.0817798i
\(627\) 1.30047 1.47530i 0.0519358 0.0589179i
\(628\) 1.08671 + 1.08671i 0.0433645 + 0.0433645i
\(629\) −16.2087 + 11.7763i −0.646282 + 0.469552i
\(630\) −0.574517 1.42751i −0.0228893 0.0568732i
\(631\) −8.72043 + 26.8387i −0.347155 + 1.06843i 0.613265 + 0.789877i \(0.289856\pi\)
−0.960420 + 0.278555i \(0.910144\pi\)
\(632\) 1.70061 0.269351i 0.0676467 0.0107142i
\(633\) −4.67121 + 0.739847i −0.185664 + 0.0294063i
\(634\) −5.32290 + 16.3822i −0.211399 + 0.650621i
\(635\) −12.7677 + 29.9667i −0.506671 + 1.18919i
\(636\) 1.80896 1.31429i 0.0717301 0.0521150i
\(637\) −15.2422 15.2422i −0.603918 0.603918i
\(638\) −24.5041 41.4275i −0.970125 1.64013i
\(639\) 27.1004i 1.07208i
\(640\) 2.61496 29.4330i 0.103365 1.16344i
\(641\) −5.23436 16.1097i −0.206745 0.636295i −0.999637 0.0269333i \(-0.991426\pi\)
0.792893 0.609362i \(-0.208574\pi\)
\(642\) −6.08232 11.9372i −0.240050 0.471124i
\(643\) 0.981726 + 6.19838i 0.0387155 + 0.244440i 0.999455 0.0330121i \(-0.0105100\pi\)
−0.960739 + 0.277452i \(0.910510\pi\)
\(644\) −0.0781682 0.0567925i −0.00308026 0.00223794i
\(645\) 2.28539 9.11397i 0.0899873 0.358862i
\(646\) 3.98552 1.29497i 0.156808 0.0509500i
\(647\) −6.80289 + 42.9518i −0.267449 + 1.68861i 0.378798 + 0.925479i \(0.376338\pi\)
−0.646247 + 0.763128i \(0.723662\pi\)
\(648\) 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
\(652\) −2.77200 1.41240i −0.108560 0.0553140i
\(653\) 8.67042 4.41780i 0.339300 0.172882i −0.276035 0.961147i \(-0.589021\pi\)
0.615335 + 0.788266i \(0.289021\pi\)
\(654\) −6.79682 + 9.35503i −0.265777 + 0.365810i
\(655\) 11.6008 18.5098i 0.453283 0.723237i
\(656\) −28.8145 9.36239i −1.12502 0.365540i
\(657\) −2.57823 + 5.06007i −0.100586 + 0.197412i
\(658\) −3.55424 0.562936i −0.138559 0.0219455i
\(659\) 3.37375 0.131423 0.0657113 0.997839i \(-0.479068\pi\)
0.0657113 + 0.997839i \(0.479068\pi\)
\(660\) 0.612166 1.73129i 0.0238285 0.0673903i
\(661\) 9.93056 0.386254 0.193127 0.981174i \(-0.438137\pi\)
0.193127 + 0.981174i \(0.438137\pi\)
\(662\) −26.5811 4.21003i −1.03310 0.163628i
\(663\) 4.15278 8.15028i 0.161280 0.316531i
\(664\) −40.7453 13.2389i −1.58122 0.513771i
\(665\) 0.0712179 + 0.310383i 0.00276171 + 0.0120361i
\(666\) −11.4191 + 15.7170i −0.442481 + 0.609022i
\(667\) −13.8210 + 7.04213i −0.535150 + 0.272672i
\(668\) 3.33809 + 1.70084i 0.129154 + 0.0658075i
\(669\) 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
\(673\) 5.98412 37.7823i 0.230671 1.45640i −0.551938 0.833885i \(-0.686111\pi\)
0.782609 0.622514i \(-0.213889\pi\)
\(674\) 11.0161 3.57935i 0.424324 0.137871i
\(675\) −12.2178 17.5491i −0.470263 0.675465i
\(676\) 0.858662 + 0.623855i 0.0330255 + 0.0239944i
\(677\) 5.03592 + 31.7956i 0.193546 + 1.22200i 0.872792 + 0.488092i \(0.162307\pi\)
−0.679246 + 0.733911i \(0.737693\pi\)
\(678\) −2.28189 4.47847i −0.0876356 0.171994i
\(679\) 0.0815917 + 0.251113i 0.00313120 + 0.00963684i
\(680\) −16.3226 + 13.6590i −0.625945 + 0.523797i
\(681\) 10.4198i 0.399289i
\(682\) −0.166370 + 1.76132i −0.00637063 + 0.0674443i
\(683\) −28.7223 28.7223i −1.09903 1.09903i −0.994524 0.104505i \(-0.966674\pi\)
−0.104505 0.994524i \(-0.533326\pi\)
\(684\) 0.441900 0.321059i 0.0168965 0.0122760i
\(685\) −8.90764 3.79522i −0.340343 0.145008i
\(686\) −1.25585 + 3.86510i −0.0479484 + 0.147570i
\(687\) 12.9380 2.04918i 0.493616 0.0781811i
\(688\) −23.5556 + 3.73084i −0.898050 + 0.142237i
\(689\) 8.63834 26.5861i 0.329095 1.01285i
\(690\) −4.05029 1.72568i −0.154192 0.0656955i
\(691\) 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
\(693\) 1.29235 0.764417i 0.0490925 0.0290378i
\(694\) 14.1878i 0.538562i
\(695\) −18.0241 + 15.0828i −0.683694 + 0.572122i
\(696\) −6.03999 18.5892i −0.228945 0.704621i
\(697\) 11.2675 + 22.1136i 0.426785 + 0.837613i
\(698\) −0.357107 2.25468i −0.0135167 0.0853410i
\(699\) 10.0896 + 7.33055i 0.381625 + 0.277267i
\(700\) 0.169895 + 0.244029i 0.00642141 + 0.00922344i
\(701\) 26.8458 8.72273i 1.01395 0.329453i 0.245525 0.969390i \(-0.421040\pi\)
0.768427 + 0.639937i \(0.221040\pi\)
\(702\) 3.14807 19.8761i 0.118816 0.750175i
\(703\) 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
\(707\) −0.823230 0.419457i −0.0309608 0.0157753i
\(708\) 2.12373 1.08210i 0.0798148 0.0406677i
\(709\) −4.79615 + 6.60134i −0.180123 + 0.247918i −0.889526 0.456885i \(-0.848965\pi\)
0.709402 + 0.704804i \(0.248965\pi\)
\(710\) −8.71256 37.9712i −0.326977 1.42503i
\(711\) −1.50773 0.489890i −0.0565441 0.0183723i
\(712\) 9.23576 18.1262i 0.346125 0.679308i
\(713\) 0.563131 + 0.0891912i 0.0210894 + 0.00334024i
\(714\) −0.860026 −0.0321856
\(715\) −6.53065 22.0091i −0.244232 0.823095i
\(716\) −6.26727 −0.234219
\(717\) −4.15889 0.658703i −0.155317 0.0245997i
\(718\) −18.1524 + 35.6261i −0.677441 + 1.32955i
\(719\) −0.986856 0.320649i −0.0368035 0.0119582i 0.290557 0.956858i \(-0.406159\pi\)
−0.327361 + 0.944899i \(0.606159\pi\)
\(720\) −12.7042 + 20.2702i −0.473456 + 0.755426i
\(721\) 0.364342 0.501474i 0.0135688 0.0186759i
\(722\) 24.9840 12.7300i 0.929810 0.473762i
\(723\) 11.4843 + 5.85157i 0.427107 + 0.217622i
\(724\) −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 −0.765294 0.643681i \(-0.777406\pi\)
0.643681 + 0.765294i \(0.277406\pi\)
\(728\) 0.238110 1.50337i 0.00882493 0.0557184i
\(729\) 1.44390 0.469153i 0.0534779 0.0173760i
\(730\) 1.98567 7.91869i 0.0734929 0.293084i
\(731\) 15.8055 + 11.4833i 0.584586 + 0.424726i
\(732\) −0.228265 1.44121i −0.00843693 0.0532687i
\(733\) 20.7361 + 40.6968i 0.765904 + 1.50317i 0.861504 + 0.507751i \(0.169523\pi\)
−0.0956003 + 0.995420i \(0.530477\pi\)
\(734\) −3.83723 11.8098i −0.141635 0.435907i
\(735\) −1.09851 + 12.3645i −0.0405193 + 0.456071i
\(736\) 2.83001i 0.104315i
\(737\) −4.23142 18.9241i −0.155866 0.697079i
\(738\) 17.0171 + 17.0171i 0.626410 + 0.626410i
\(739\) 3.07164 2.23167i 0.112992 0.0820934i −0.529854 0.848089i \(-0.677753\pi\)
0.642846 + 0.765995i \(0.277753\pi\)
\(740\) 1.47146 3.45363i 0.0540920 0.126958i
\(741\) −0.567231 + 1.74576i −0.0208377 + 0.0641320i
\(742\) −2.59590 + 0.411150i −0.0952984 + 0.0150938i
\(743\) −41.9067 + 6.63736i −1.53741 + 0.243501i −0.866930 0.498430i \(-0.833910\pi\)
−0.670476 + 0.741931i \(0.733910\pi\)
\(744\) −0.222008 + 0.683270i −0.00813920 + 0.0250499i
\(745\) −4.81079 11.9534i −0.176254 0.437938i
\(746\) −10.6517 + 7.73895i −0.389988 + 0.283343i
\(747\) 27.8924 + 27.8924i 1.02053 + 1.02053i
\(748\) 2.86419 + 2.52477i 0.104725 + 0.0923149i
\(749\) 2.11681i 0.0773467i
\(750\) 10.0320 + 9.10640i 0.366316 + 0.332519i
\(751\) −3.08775 9.50312i −0.112674 0.346774i 0.878781 0.477225i \(-0.158357\pi\)
−0.991455 + 0.130451i \(0.958357\pi\)
\(752\) 25.3980 + 49.8464i 0.926171 + 1.81771i
\(753\) −2.41230 15.2306i −0.0879089 0.555035i
\(754\) 36.3446 + 26.4059i 1.32359 + 0.961647i
\(755\) 32.4561 + 8.13861i 1.18120 + 0.296194i
\(756\) −0.241881 + 0.0785920i −0.00879714 + 0.00285837i
\(757\) 4.59658 29.0217i 0.167065 1.05481i −0.751555 0.659670i \(-0.770696\pi\)
0.918621 0.395140i \(-0.129304\pi\)
\(758\) 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 \(0.985421\pi\)
\(762\) 15.7289 + 8.01429i 0.569799 + 0.290327i
\(763\) 1.62790 0.829459i 0.0589341 0.0300284i
\(764\) 1.15493 1.58963i 0.0417840 0.0575107i
\(765\) 19.1001 4.38256i 0.690566 0.158452i
\(766\) 15.0044 + 4.87523i 0.542131 + 0.176149i
\(767\) 13.5283 26.5507i 0.488477 0.958690i
\(768\) −5.73527 0.908377i −0.206954 0.0327782i
\(769\) −37.6421 −1.35741 −0.678705 0.734411i \(-0.737458\pi\)
−0.678705 + 0.734411i \(0.737458\pi\)
\(770\) −1.56500 + 1.48653i −0.0563987 + 0.0535707i
\(771\) −3.75184 −0.135119
\(772\) 1.81970 + 0.288213i 0.0654926 + 0.0103730i
\(773\) −11.7188 + 22.9995i −0.421497 + 0.827234i 0.578437 + 0.815727i \(0.303663\pi\)
−0.999934 + 0.0115072i \(0.996337\pi\)
\(774\) 18.0168 + 5.85402i 0.647601 + 0.210418i
\(775\) −1.54700 0.827900i −0.0555698 0.0297390i
\(776\) 2.08149 2.86493i 0.0747213 0.102845i
\(777\) −0.735173 + 0.374589i −0.0263742 + 0.0134383i
\(778\) 29.9955 + 15.2835i 1.07539 + 0.547939i
\(779\) −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
\(783\) −6.38724 + 40.3275i −0.228261 + 1.44119i
\(784\) 29.9651 9.73624i 1.07018 0.347723i
\(785\) −5.68579 9.49165i −0.202935 0.338771i
\(786\) −9.57771 6.95861i −0.341626 0.248206i
\(787\) 2.70244 + 17.0625i 0.0963315 + 0.608213i 0.987872 + 0.155272i \(0.0496254\pi\)
−0.891540 + 0.452942i \(0.850375\pi\)
\(788\) −1.97520 3.87655i −0.0703636 0.138096i
\(789\) −3.90967 12.0327i −0.139188 0.428376i
\(790\) 2.27001 + 0.201678i 0.0807634 + 0.00717537i
\(791\) 0.794162i 0.0282372i
\(792\) −18.4824 7.99654i −0.656745 0.284145i
\(793\) −12.8994 12.8994i −0.458070 0.458070i
\(794\) 18.7425 13.6172i 0.665145 0.483256i
\(795\) −14.9338 + 6.01029i −0.529647 + 0.213163i
\(796\) −1.28445 + 3.95313i −0.0455261 + 0.140115i
\(797\) −44.0203 + 6.97213i −1.55928 + 0.246965i −0.875680 0.482892i \(-0.839586\pi\)
−0.683599 + 0.729858i \(0.739586\pi\)
\(798\) 0.170458 0.0269979i 0.00603414 0.000955714i
\(799\) 14.1615 43.5847i 0.500999 1.54192i
\(800\) 2.85757 8.22702i 0.101030 0.290869i
\(801\) −15.1535 + 11.0097i −0.535424 + 0.389008i
\(802\) 4.60219 + 4.60219i 0.162509 + 0.162509i
\(803\) 7.93078 + 0.749124i 0.279871 + 0.0264360i
\(804\) 1.44771i 0.0510569i
\(805\) 0.446416 + 0.533473i 0.0157341 + 0.0188025i
\(806\) −0.510267 1.57044i −0.0179734 0.0553164i
\(807\) 4.09432 + 8.03556i 0.144127 + 0.282865i
\(808\) 1.93850 + 12.2392i 0.0681962 + 0.430574i
\(809\) −12.3255 8.95497i −0.433340 0.314840i 0.349643 0.936883i \(-0.386303\pi\)
−0.782983 + 0.622043i \(0.786303\pi\)
\(810\) 10.7414 6.43446i 0.377416 0.226084i
\(811\) −43.3276 + 14.0780i −1.52144 + 0.494345i −0.946183 0.323631i \(-0.895096\pi\)
−0.575253 + 0.817976i \(0.695096\pi\)
\(812\) 0.0888178 0.560774i 0.00311689 0.0196793i
\(813\) −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
\(817\) −3.49314 1.77984i −0.122209 0.0622688i
\(818\) −5.81793 + 2.96438i −0.203419 + 0.103647i
\(819\) −0.823747 + 1.13379i −0.0287840 + 0.0396178i
\(820\) −3.94041 2.46962i −0.137605 0.0862428i
\(821\) −27.3071 8.87260i −0.953023 0.309656i −0.209079 0.977899i \(-0.567047\pi\)
−0.743943 + 0.668243i \(0.767047\pi\)
\(822\) −2.38226 + 4.67545i −0.0830909 + 0.163075i
\(823\) −26.6252 4.21701i −0.928095 0.146996i −0.325954 0.945386i \(-0.605686\pi\)
−0.602141 + 0.798390i \(0.705686\pi\)
\(824\) −8.31350 −0.289614
\(825\) −7.30652 + 11.0180i −0.254380 + 0.383597i
\(826\) −2.80165 −0.0974820
\(827\) 39.1944 + 6.20779i 1.36292 + 0.215866i 0.794697 0.607006i \(-0.207630\pi\)
0.568227 + 0.822872i \(0.307630\pi\)
\(828\) 0.541680 1.06311i 0.0188247 0.0369455i
\(829\) −10.3353 3.35814i −0.358959 0.116633i 0.123985 0.992284i \(-0.460433\pi\)
−0.482944 + 0.875651i \(0.660433\pi\)
\(830\) −48.0481 30.1137i −1.66777 1.04526i
\(831\) 2.19378 3.01948i 0.0761013 0.104744i
\(832\) −17.6573 + 8.99683i −0.612156 + 0.311909i
\(833\) −22.9966 11.7174i −0.796786 0.405983i
\(834\) 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
\(838\) 0.285920 1.80523i 0.00987695 0.0623606i
\(839\) 38.3426 12.4583i 1.32373 0.430107i 0.439958 0.898019i \(-0.354993\pi\)
0.883775 + 0.467912i \(0.154993\pi\)
\(840\) −0.751937 + 0.450434i −0.0259443 + 0.0155415i
\(841\) −50.2797 36.5303i −1.73378 1.25967i
\(842\) 7.44491 + 47.0053i 0.256569 + 1.61991i
\(843\) −4.77364 9.36879i −0.164413 0.322678i
\(844\) 0.569376 + 1.75236i 0.0195987 + 0.0603187i
\(845\) −4.90379 5.86010i −0.168695 0.201593i
\(846\) 44.4376i 1.52780i
\(847\) −1.66439 1.29066i −0.0571891 0.0443477i
\(848\) 28.8921 + 28.8921i 0.992159 + 0.992159i
\(849\) −14.6966 + 10.6777i −0.504386 + 0.366458i
\(850\) −25.3528 + 12.2810i −0.869593 + 0.421237i
\(851\) 2.71386 8.35241i 0.0930300 0.286317i
\(852\) −2.80310 + 0.443967i −0.0960326 + 0.0152101i
\(853\) 13.7845 2.18326i 0.471974 0.0747533i 0.0840831 0.996459i \(-0.473204\pi\)
0.387890 + 0.921705i \(0.373204\pi\)
\(854\) −0.530012 + 1.63121i −0.0181366 + 0.0558188i
\(855\) −3.64808 + 1.46822i −0.124762 + 0.0502119i
\(856\) 22.9686 16.6876i 0.785049 0.570372i
\(857\) −26.9229 26.9229i −0.919668 0.919668i 0.0773373 0.997005i \(-0.475358\pi\)
−0.997005 + 0.0773373i \(0.975358\pi\)
\(858\) −12.1420 + 2.71494i −0.414521 + 0.0926867i
\(859\) 18.3200i 0.625071i −0.949906 0.312535i \(-0.898822\pi\)
0.949906 0.312535i \(-0.101178\pi\)
\(860\) −3.64628 0.323951i −0.124337 0.0110466i
\(861\) 0.315849 + 0.972084i 0.0107641 + 0.0331285i
\(862\) −6.82592 13.3966i −0.232492 0.456291i
\(863\) −1.90114 12.0033i −0.0647154 0.408597i −0.998686 0.0512472i \(-0.983680\pi\)
0.933971 0.357350i \(-0.116320\pi\)
\(864\) 6.02655 + 4.37855i 0.205028 + 0.148961i
\(865\) 14.3234 + 23.9109i 0.487010 + 0.812996i
\(866\) −39.0074 + 12.6743i −1.32552 + 0.430689i
\(867\) −0.406785 + 2.56834i −0.0138151 + 0.0872253i
\(868\) −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
\(872\) −21.8334 11.1247i −0.739374 0.376730i
\(873\) −2.90515 + 1.48025i −0.0983243 + 0.0500987i
\(874\) −1.07972 + 1.48611i −0.0365222 + 0.0502685i
\(875\) −0.759091 2.00161i −0.0256620 0.0676666i
\(876\) −0.565619 0.183781i −0.0191105 0.00620938i
\(877\) −5.82698 + 11.4361i −0.196763 + 0.386169i −0.968215 0.250118i \(-0.919531\pi\)
0.771452 + 0.636287i \(0.219531\pi\)
\(878\) 36.9125 + 5.84636i 1.24574 + 0.197305i
\(879\) 5.76213 0.194352
\(880\) 32.9971 + 6.09963i 1.11233 + 0.205618i
\(881\) 13.8380 0.466216 0.233108 0.972451i \(-0.425110\pi\)
0.233108 + 0.972451i \(0.425110\pi\)
\(882\) −24.7187 3.91506i −0.832322 0.131827i
\(883\) −19.7888 + 38.8377i −0.665947 + 1.30699i 0.272695 + 0.962100i \(0.412085\pi\)
−0.938642 + 0.344893i \(0.887915\pi\)
\(884\) −3.38926 1.10124i −0.113993 0.0370387i
\(885\) −16.7253 + 3.83765i −0.562215 + 0.129001i
\(886\) −27.5163 + 37.8730i −0.924429 + 1.27237i
\(887\) −9.26576 + 4.72114i −0.311114 + 0.158520i −0.602575 0.798062i \(-0.705859\pi\)
0.291461 + 0.956583i \(0.405859\pi\)
\(888\) 9.86013 + 5.02399i 0.330884 + 0.168594i
\(889\) −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
\(893\) −1.43862 + 9.08308i −0.0481415 + 0.303954i
\(894\) −6.64130 + 2.15789i −0.222118 + 0.0721706i
\(895\) 43.7656 + 10.9745i 1.46292 + 0.366838i
\(896\) 2.04700 + 1.48723i 0.0683855 + 0.0496850i
\(897\) 0.627249 + 3.96029i 0.0209432 + 0.132230i
\(898\) 5.05474 + 9.92048i 0.168679 + 0.331051i
\(899\) 1.03530 + 3.18633i 0.0345292 + 0.106270i
\(900\) −2.64816 + 2.54357i −0.0882720 + 0.0847856i
\(901\) 33.4710i 1.11508i
\(902\) 13.4046 30.9821i 0.446324 1.03159i
\(903\) 0.568922 + 0.568922i 0.0189325 + 0.0189325i
\(904\) 8.61708 6.26067i 0.286600 0.208227i
\(905\) 3.84846 + 9.56228i 0.127927 + 0.317861i
\(906\) 5.60375 17.2466i 0.186172 0.572979i
\(907\) 16.1062 2.55097i 0.534798 0.0847036i 0.116806 0.993155i \(-0.462734\pi\)
0.417991 + 0.908451i \(0.362734\pi\)
\(908\) 4.00948 0.635040i 0.133059 0.0210745i
\(909\) 3.52571 10.8510i 0.116940 0.359906i
\(910\) 0.789672 1.85341i 0.0261774 0.0614401i
\(911\) 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
\(913\) 21.9712 50.7821i 0.727140 1.68064i
\(914\) 10.2385i 0.338659i
\(915\) −0.929665 + 10.4640i −0.0307338 + 0.345929i
\(916\) −1.57702 4.85357i −0.0521062 0.160366i
\(917\) 0.849203 + 1.66665i 0.0280431 + 0.0550378i
\(918\) −3.76933 23.7986i −0.124406 0.785472i
\(919\) 7.38632 + 5.36648i 0.243652 + 0.177024i 0.702909 0.711280i \(-0.251884\pi\)
−0.459257 + 0.888304i \(0.651884\pi\)
\(920\) 2.26921 9.04942i 0.0748135 0.298350i
\(921\) 21.5818 7.01234i 0.711143 0.231064i
\(922\) −6.91497 + 43.6594i −0.227732 + 1.43785i
\(923\) −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
\(927\) 6.82017 + 3.47505i 0.224004 + 0.114136i
\(928\) −14.8171 + 7.54970i −0.486396 + 0.247831i
\(929\) −1.06529 + 1.46625i −0.0349511 + 0.0481061i −0.826135 0.563472i \(-0.809465\pi\)
0.791184 + 0.611578i \(0.209465\pi\)
\(930\) −0.504986 + 0.805732i −0.0165591 + 0.0264210i
\(931\) 4.92578 + 1.60048i 0.161436 + 0.0524537i
\(932\) 2.20583 4.32918i 0.0722543 0.141807i
\(933\) 5.91808 + 0.937332i 0.193749 + 0.0306869i
\(934\) −40.2174 −1.31595
\(935\) −15.5802 22.6465i −0.509525 0.740619i
\(936\) 18.7961 0.614371
\(937\) 14.9726 + 2.37143i 0.489133 + 0.0774711i 0.396130 0.918195i \(-0.370353\pi\)
0.0930039 + 0.995666i \(0.470353\pi\)
\(938\) 0.772546 1.51621i 0.0252245 0.0495059i
\(939\) 1.02061 + 0.331616i 0.0333063 + 0.0108219i
\(940\) 1.92037 + 8.36939i 0.0626356 + 0.272979i
\(941\) −12.8308 + 17.6600i −0.418271 + 0.575701i −0.965211 0.261471i \(-0.915792\pi\)
0.546940 + 0.837172i \(0.315792\pi\)
\(942\) −5.34274 + 2.72226i −0.174076 + 0.0886961i
\(943\) −9.69338 4.93902i −0.315660 0.160837i
\(944\) 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 −0.585928 0.810363i \(-0.699270\pi\)
0.810363 + 0.585928i \(0.199270\pi\)
\(948\) 0.0259711 0.163975i 0.000843503 0.00532567i
\(949\) −7.07131 + 2.29761i −0.229545 + 0.0745835i
\(950\) 4.63941 3.22999i 0.150522 0.104795i
\(951\) −7.30875 5.31012i −0.237003 0.172192i
\(952\) −0.285100 1.80005i −0.00924015 0.0583400i
\(953\) −5.92153 11.6216i −0.191817 0.376462i 0.774989 0.631975i \(-0.217756\pi\)
−0.966806 + 0.255513i \(0.917756\pi\)
\(954\) −10.0294 30.8672i −0.324713 0.999363i
\(955\) −10.8487 + 9.07831i −0.351056 + 0.293767i
\(956\) 1.64046i 0.0530561i
\(957\) 24.6354 5.50846i 0.796349 0.178063i
\(958\) −28.2202 28.2202i −0.911755 0.911755i
\(959\) 0.670750 0.487328i 0.0216596 0.0157367i
\(960\) 10.4988 + 4.47317i 0.338849 + 0.144371i
\(961\) −9.54147 + 29.3656i −0.307789 + 0.947279i
\(962\) −25.1218 + 3.97890i −0.809960 + 0.128285i
\(963\) −25.8182 + 4.08921i −0.831981 + 0.131773i
\(964\) 1.55173 4.77572i 0.0499777 0.153816i
\(965\) −12.2027 5.19911i −0.392818 0.167365i
\(966\) 0.304989 0.221588i 0.00981287 0.00712946i
\(967\) 13.6319 + 13.6319i 0.438372 + 0.438372i 0.891464 0.453092i \(-0.149679\pi\)
−0.453092 + 0.891464i \(0.649679\pi\)
\(968\) −0.883368 + 28.2343i −0.0283925 + 0.907484i
\(969\) 2.19785i 0.0706051i
\(970\) 3.59460 3.00800i 0.115416 0.0965809i
\(971\) 1.26967 + 3.90765i 0.0407457 + 0.125403i 0.969360 0.245643i \(-0.0789992\pi\)
−0.928615 + 0.371046i \(0.878999\pi\)
\(972\) −2.22320 4.36328i −0.0713093 0.139952i
\(973\) −0.314819 1.98769i −0.0100926 0.0637224i
\(974\) −28.6965 20.8492i −0.919495 0.668052i
\(975\) 2.17541 12.1462i 0.0696688 0.388989i
\(976\) 25.3592 8.23971i 0.811729 0.263747i
\(977\) 4.80402 30.3314i 0.153694 0.970386i −0.783453 0.621451i \(-0.786543\pi\)
0.937147 0.348935i \(-0.113457\pi\)
\(978\) 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
\(982\) 24.8498 + 12.6616i 0.792990 + 0.404048i
\(983\) 24.7035 12.5871i 0.787919 0.401465i −0.0132429 0.999912i \(-0.504215\pi\)
0.801162 + 0.598447i \(0.204215\pi\)
\(984\) 8.05767 11.0904i 0.256869 0.353550i
\(985\) 7.00505 + 30.5295i 0.223199 + 0.972750i
\(986\) 51.1575 + 16.6221i 1.62919 + 0.529355i
\(987\) 0.856827 1.68162i 0.0272731 0.0535265i
\(988\) 0.706325 + 0.111871i 0.0224712 + 0.00355909i
\(989\) −8.56376 −0.272312
\(990\) −21.1540 16.2163i −0.672319 0.515387i
\(991\) 9.10087 0.289099 0.144549 0.989498i \(-0.453827\pi\)
0.144549 + 0.989498i \(0.453827\pi\)
\(992\) 0.603719 + 0.0956197i 0.0191681 + 0.00303593i
\(993\) 6.40795 12.5763i 0.203350 0.399097i
\(994\) 3.17264 + 1.03085i 0.100630 + 0.0326966i
\(995\) 15.8919 25.3563i 0.503806 0.803849i
\(996\) −2.42808 + 3.34196i −0.0769366 + 0.105894i
\(997\) 25.7239 13.1070i 0.814685 0.415103i 0.00357282 0.999994i \(-0.498863\pi\)
0.811112 + 0.584891i \(0.198863\pi\)
\(998\) −15.9247 8.11406i −0.504089 0.256846i
\(999\) −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.8.4 yes 32
3.2 odd 2 495.2.bj.a.118.1 32
4.3 odd 2 880.2.cm.a.833.4 32
5.2 odd 4 inner 55.2.l.a.52.1 yes 32
5.3 odd 4 275.2.bm.b.107.4 32
5.4 even 2 275.2.bm.b.118.1 32
11.2 odd 10 605.2.e.b.483.14 32
11.3 even 5 605.2.m.c.578.4 32
11.4 even 5 605.2.m.e.403.4 32
11.5 even 5 605.2.m.d.233.1 32
11.6 odd 10 605.2.m.c.233.4 32
11.7 odd 10 inner 55.2.l.a.18.1 yes 32
11.8 odd 10 605.2.m.d.578.1 32
11.9 even 5 605.2.e.b.483.3 32
11.10 odd 2 605.2.m.e.118.1 32
15.2 even 4 495.2.bj.a.217.4 32
20.7 even 4 880.2.cm.a.657.1 32
33.29 even 10 495.2.bj.a.73.4 32
44.7 even 10 880.2.cm.a.513.1 32
55.2 even 20 605.2.e.b.362.3 32
55.7 even 20 inner 55.2.l.a.7.4 32
55.17 even 20 605.2.m.c.112.4 32
55.18 even 20 275.2.bm.b.7.1 32
55.27 odd 20 605.2.m.d.112.1 32
55.29 odd 10 275.2.bm.b.18.4 32
55.32 even 4 605.2.m.e.602.4 32
55.37 odd 20 605.2.m.e.282.1 32
55.42 odd 20 605.2.e.b.362.14 32
55.47 odd 20 605.2.m.c.457.4 32
55.52 even 20 605.2.m.d.457.1 32
165.62 odd 20 495.2.bj.a.172.1 32
220.7 odd 20 880.2.cm.a.337.4 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
55.2.l.a.7.4 32 55.7 even 20 inner
55.2.l.a.8.4 yes 32 1.1 even 1 trivial
55.2.l.a.18.1 yes 32 11.7 odd 10 inner
55.2.l.a.52.1 yes 32 5.2 odd 4 inner
275.2.bm.b.7.1 32 55.18 even 20
275.2.bm.b.18.4 32 55.29 odd 10
275.2.bm.b.107.4 32 5.3 odd 4
275.2.bm.b.118.1 32 5.4 even 2
495.2.bj.a.73.4 32 33.29 even 10
495.2.bj.a.118.1 32 3.2 odd 2
495.2.bj.a.172.1 32 165.62 odd 20
495.2.bj.a.217.4 32 15.2 even 4
605.2.e.b.362.3 32 55.2 even 20
605.2.e.b.362.14 32 55.42 odd 20
605.2.e.b.483.3 32 11.9 even 5
605.2.e.b.483.14 32 11.2 odd 10
605.2.m.c.112.4 32 55.17 even 20
605.2.m.c.233.4 32 11.6 odd 10
605.2.m.c.457.4 32 55.47 odd 20
605.2.m.c.578.4 32 11.3 even 5
605.2.m.d.112.1 32 55.27 odd 20
605.2.m.d.233.1 32 11.5 even 5
605.2.m.d.457.1 32 55.52 even 20
605.2.m.d.578.1 32 11.8 odd 10
605.2.m.e.118.1 32 11.10 odd 2
605.2.m.e.282.1 32 55.37 odd 20
605.2.m.e.403.4 32 11.4 even 5
605.2.m.e.602.4 32 55.32 even 4
880.2.cm.a.337.4 32 220.7 odd 20
880.2.cm.a.513.1 32 44.7 even 10
880.2.cm.a.657.1 32 20.7 even 4
880.2.cm.a.833.4 32 4.3 odd 2