Properties

Label 81.3.h.a.2.6
Level $81$
Weight $3$
Character 81.2
Analytic conductor $2.207$
Analytic rank $0$
Dimension $306$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [81,3,Mod(2,81)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(81, base_ring=CyclotomicField(54))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("81.2");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 81 = 3^{4} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 81.h (of order \(54\), degree \(18\), 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: \(2.20709014132\)
Analytic rank: \(0\)
Dimension: \(306\)
Relative dimension: \(17\) over \(\Q(\zeta_{54})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{54}]$

Embedding invariants

Embedding label 2.6
Character \(\chi\) \(=\) 81.2
Dual form 81.3.h.a.41.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.71539 - 0.0999103i) q^{2} +(-0.611041 + 2.93711i) q^{3} +(-1.04036 - 0.121601i) q^{4} +(0.258193 + 1.08940i) q^{5} +(1.34162 - 4.97725i) q^{6} +(-6.70340 - 9.00422i) q^{7} +(8.54126 + 1.50605i) q^{8} +(-8.25326 - 3.58939i) q^{9} +O(q^{10})\) \(q+(-1.71539 - 0.0999103i) q^{2} +(-0.611041 + 2.93711i) q^{3} +(-1.04036 - 0.121601i) q^{4} +(0.258193 + 1.08940i) q^{5} +(1.34162 - 4.97725i) q^{6} +(-6.70340 - 9.00422i) q^{7} +(8.54126 + 1.50605i) q^{8} +(-8.25326 - 3.58939i) q^{9} +(-0.334060 - 1.89455i) q^{10} +(-4.32578 - 4.08116i) q^{11} +(0.992858 - 2.98135i) q^{12} +(-12.3822 - 6.21860i) q^{13} +(10.5993 + 16.1155i) q^{14} +(-3.35746 + 0.0926729i) q^{15} +(-10.4243 - 2.47061i) q^{16} +(-4.42763 + 12.1648i) q^{17} +(13.7990 + 6.98180i) q^{18} +(-11.5385 + 4.19968i) q^{19} +(-0.136142 - 1.16477i) q^{20} +(30.5425 - 14.1867i) q^{21} +(7.01266 + 7.43299i) q^{22} +(-0.0559966 - 0.0416879i) q^{23} +(-9.64251 + 24.1664i) q^{24} +(21.2207 - 10.6574i) q^{25} +(20.6191 + 11.9045i) q^{26} +(15.5855 - 22.0475i) q^{27} +(5.87903 + 10.1828i) q^{28} +(-21.4124 + 32.5560i) q^{29} +(5.76862 + 0.176474i) q^{30} +(5.86369 + 13.5936i) q^{31} +(-15.5997 - 4.67024i) q^{32} +(14.6301 - 10.2115i) q^{33} +(8.81051 - 20.4251i) q^{34} +(8.07844 - 9.62750i) q^{35} +(8.14989 + 4.73786i) q^{36} +(-43.6214 + 36.6027i) q^{37} +(20.2127 - 6.05129i) q^{38} +(25.8308 - 32.5682i) q^{39} +(0.564594 + 9.69371i) q^{40} +(40.2037 - 2.34160i) q^{41} +(-53.8097 + 21.2842i) q^{42} +(-15.8634 - 52.9875i) q^{43} +(4.00410 + 4.77190i) q^{44} +(1.77935 - 9.91786i) q^{45} +(0.0918911 + 0.0771058i) q^{46} +(-74.4170 - 32.1004i) q^{47} +(13.6261 - 29.1078i) q^{48} +(-22.0872 + 73.7762i) q^{49} +(-37.4666 + 16.1615i) q^{50} +(-33.0239 - 20.4376i) q^{51} +(12.1258 + 7.97527i) q^{52} +(-22.8397 + 13.1865i) q^{53} +(-28.9381 + 36.2630i) q^{54} +(3.32913 - 5.76623i) q^{55} +(-43.6946 - 87.0031i) q^{56} +(-5.28443 - 36.4562i) q^{57} +(39.9834 - 53.7071i) q^{58} +(-8.34391 + 7.87207i) q^{59} +(3.50424 + 0.311856i) q^{60} +(-38.0337 + 4.44550i) q^{61} +(-8.70040 - 23.9041i) q^{62} +(23.0052 + 98.3753i) q^{63} +(66.5611 + 24.2262i) q^{64} +(3.57754 - 15.0948i) q^{65} +(-26.1165 + 16.0551i) q^{66} +(80.0672 - 52.6610i) q^{67} +(6.08558 - 12.1174i) q^{68} +(0.156658 - 0.138995i) q^{69} +(-14.8196 + 15.7078i) q^{70} +(118.033 - 20.8124i) q^{71} +(-65.0874 - 43.0878i) q^{72} +(4.87242 - 27.6329i) q^{73} +(78.4848 - 58.4298i) q^{74} +(18.3354 + 68.8397i) q^{75} +(12.5149 - 2.96609i) q^{76} +(-7.75028 + 66.3079i) q^{77} +(-47.5638 + 53.2866i) q^{78} +(1.46602 - 25.1706i) q^{79} -11.9941i q^{80} +(55.2326 + 59.2483i) q^{81} -69.1991 q^{82} +(-57.8010 - 3.36653i) q^{83} +(-33.5003 + 11.0453i) q^{84} +(-14.3955 - 1.68260i) q^{85} +(21.9180 + 92.4794i) q^{86} +(-82.5368 - 82.7838i) q^{87} +(-30.8012 - 41.3731i) q^{88} +(100.343 + 17.6931i) q^{89} +(-4.04318 + 16.8353i) q^{90} +(27.0094 + 153.178i) q^{91} +(0.0531873 + 0.0501797i) q^{92} +(-43.5088 + 8.91610i) q^{93} +(124.447 + 62.4998i) q^{94} +(-7.55430 - 11.4858i) q^{95} +(23.2491 - 42.9644i) q^{96} +(122.813 + 29.1072i) q^{97} +(45.2592 - 124.349i) q^{98} +(21.0529 + 49.2098i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 306 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 306 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} - 18 q^{10} - 18 q^{11} - 18 q^{12} - 18 q^{13} - 18 q^{14} - 18 q^{15} - 18 q^{16} - 18 q^{17} - 90 q^{18} - 18 q^{19} - 234 q^{20} - 153 q^{21} - 18 q^{22} - 99 q^{23} - 126 q^{24} - 18 q^{25} - 27 q^{26} + 9 q^{27} - 9 q^{28} + 63 q^{29} + 198 q^{30} - 18 q^{31} + 306 q^{32} + 171 q^{33} - 18 q^{34} + 225 q^{35} + 342 q^{36} - 18 q^{37} + 90 q^{38} - 18 q^{39} - 18 q^{40} - 234 q^{41} - 513 q^{42} - 18 q^{43} - 666 q^{44} - 450 q^{45} - 18 q^{46} - 342 q^{47} - 513 q^{48} - 18 q^{49} - 369 q^{50} - 144 q^{51} - 54 q^{52} - 27 q^{53} + 108 q^{54} - 9 q^{55} + 396 q^{56} + 198 q^{57} - 18 q^{58} + 360 q^{59} + 801 q^{60} - 18 q^{61} + 873 q^{62} + 522 q^{63} - 18 q^{64} + 1170 q^{65} + 1926 q^{66} - 369 q^{67} + 2169 q^{68} + 1062 q^{69} - 558 q^{70} + 630 q^{71} + 1710 q^{72} - 18 q^{73} + 846 q^{74} + 432 q^{75} - 342 q^{76} + 414 q^{77} + 189 q^{78} - 72 q^{79} - 90 q^{81} - 36 q^{82} - 234 q^{83} - 945 q^{84} + 252 q^{85} - 882 q^{86} - 1026 q^{87} + 630 q^{88} - 1314 q^{89} - 2529 q^{90} - 18 q^{91} - 3960 q^{92} - 2214 q^{93} + 738 q^{94} - 2394 q^{95} - 3321 q^{96} + 441 q^{97} - 2853 q^{98} - 1566 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/81\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{54}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.71539 0.0999103i −0.857697 0.0499551i −0.376342 0.926481i \(-0.622818\pi\)
−0.481355 + 0.876526i \(0.659855\pi\)
\(3\) −0.611041 + 2.93711i −0.203680 + 0.979037i
\(4\) −1.04036 0.121601i −0.260090 0.0304002i
\(5\) 0.258193 + 1.08940i 0.0516385 + 0.217880i 0.992747 0.120226i \(-0.0383619\pi\)
−0.941108 + 0.338106i \(0.890214\pi\)
\(6\) 1.34162 4.97725i 0.223604 0.829542i
\(7\) −6.70340 9.00422i −0.957628 1.28632i −0.958135 0.286318i \(-0.907569\pi\)
0.000506869 1.00000i \(-0.499839\pi\)
\(8\) 8.54126 + 1.50605i 1.06766 + 0.188257i
\(9\) −8.25326 3.58939i −0.917029 0.398821i
\(10\) −0.334060 1.89455i −0.0334060 0.189455i
\(11\) −4.32578 4.08116i −0.393253 0.371015i 0.464066 0.885801i \(-0.346390\pi\)
−0.857319 + 0.514786i \(0.827871\pi\)
\(12\) 0.992858 2.98135i 0.0827381 0.248446i
\(13\) −12.3822 6.21860i −0.952480 0.478354i −0.0964834 0.995335i \(-0.530759\pi\)
−0.855997 + 0.516981i \(0.827056\pi\)
\(14\) 10.5993 + 16.1155i 0.757096 + 1.15111i
\(15\) −3.35746 + 0.0926729i −0.223830 + 0.00617820i
\(16\) −10.4243 2.47061i −0.651520 0.154413i
\(17\) −4.42763 + 12.1648i −0.260449 + 0.715577i 0.738689 + 0.674047i \(0.235445\pi\)
−0.999137 + 0.0415300i \(0.986777\pi\)
\(18\) 13.7990 + 6.98180i 0.766609 + 0.387878i
\(19\) −11.5385 + 4.19968i −0.607292 + 0.221036i −0.627318 0.778763i \(-0.715847\pi\)
0.0200262 + 0.999799i \(0.493625\pi\)
\(20\) −0.136142 1.16477i −0.00680708 0.0582383i
\(21\) 30.5425 14.1867i 1.45440 0.675556i
\(22\) 7.01266 + 7.43299i 0.318757 + 0.337863i
\(23\) −0.0559966 0.0416879i −0.00243463 0.00181252i 0.595941 0.803029i \(-0.296779\pi\)
−0.598375 + 0.801216i \(0.704187\pi\)
\(24\) −9.64251 + 24.1664i −0.401771 + 1.00693i
\(25\) 21.2207 10.6574i 0.848827 0.426297i
\(26\) 20.6191 + 11.9045i 0.793043 + 0.457864i
\(27\) 15.5855 22.0475i 0.577241 0.816574i
\(28\) 5.87903 + 10.1828i 0.209965 + 0.363671i
\(29\) −21.4124 + 32.5560i −0.738360 + 1.12262i 0.249666 + 0.968332i \(0.419679\pi\)
−0.988026 + 0.154289i \(0.950691\pi\)
\(30\) 5.76862 + 0.176474i 0.192287 + 0.00588247i
\(31\) 5.86369 + 13.5936i 0.189151 + 0.438502i 0.986231 0.165372i \(-0.0528824\pi\)
−0.797080 + 0.603874i \(0.793623\pi\)
\(32\) −15.5997 4.67024i −0.487491 0.145945i
\(33\) 14.6301 10.2115i 0.443335 0.309441i
\(34\) 8.81051 20.4251i 0.259133 0.600737i
\(35\) 8.07844 9.62750i 0.230812 0.275072i
\(36\) 8.14989 + 4.73786i 0.226386 + 0.131607i
\(37\) −43.6214 + 36.6027i −1.17896 + 0.989262i −0.178971 + 0.983854i \(0.557277\pi\)
−0.999985 + 0.00540719i \(0.998279\pi\)
\(38\) 20.2127 6.05129i 0.531914 0.159245i
\(39\) 25.8308 32.5682i 0.662327 0.835083i
\(40\) 0.564594 + 9.69371i 0.0141149 + 0.242343i
\(41\) 40.2037 2.34160i 0.980578 0.0571122i 0.439640 0.898174i \(-0.355106\pi\)
0.540939 + 0.841062i \(0.318069\pi\)
\(42\) −53.8097 + 21.2842i −1.28118 + 0.506767i
\(43\) −15.8634 52.9875i −0.368917 1.23227i −0.918027 0.396518i \(-0.870218\pi\)
0.549110 0.835750i \(-0.314967\pi\)
\(44\) 4.00410 + 4.77190i 0.0910022 + 0.108452i
\(45\) 1.77935 9.91786i 0.0395412 0.220397i
\(46\) 0.0918911 + 0.0771058i 0.00199763 + 0.00167621i
\(47\) −74.4170 32.1004i −1.58334 0.682986i −0.591017 0.806659i \(-0.701274\pi\)
−0.992323 + 0.123672i \(0.960533\pi\)
\(48\) 13.6261 29.1078i 0.283878 0.606411i
\(49\) −22.0872 + 73.7762i −0.450758 + 1.50564i
\(50\) −37.4666 + 16.1615i −0.749332 + 0.323230i
\(51\) −33.0239 20.4376i −0.647528 0.400738i
\(52\) 12.1258 + 7.97527i 0.233189 + 0.153371i
\(53\) −22.8397 + 13.1865i −0.430938 + 0.248802i −0.699746 0.714391i \(-0.746704\pi\)
0.268808 + 0.963194i \(0.413370\pi\)
\(54\) −28.9381 + 36.2630i −0.535890 + 0.671536i
\(55\) 3.32913 5.76623i 0.0605297 0.104841i
\(56\) −43.6946 87.0031i −0.780261 1.55363i
\(57\) −5.28443 36.4562i −0.0927093 0.639582i
\(58\) 39.9834 53.7071i 0.689370 0.925984i
\(59\) −8.34391 + 7.87207i −0.141422 + 0.133425i −0.753702 0.657216i \(-0.771734\pi\)
0.612280 + 0.790641i \(0.290252\pi\)
\(60\) 3.50424 + 0.311856i 0.0584039 + 0.00519760i
\(61\) −38.0337 + 4.44550i −0.623503 + 0.0728770i −0.421978 0.906606i \(-0.638664\pi\)
−0.201525 + 0.979483i \(0.564590\pi\)
\(62\) −8.70040 23.9041i −0.140329 0.385551i
\(63\) 23.0052 + 98.3753i 0.365162 + 1.56151i
\(64\) 66.5611 + 24.2262i 1.04002 + 0.378535i
\(65\) 3.57754 15.0948i 0.0550390 0.232228i
\(66\) −26.1165 + 16.0551i −0.395705 + 0.243259i
\(67\) 80.0672 52.6610i 1.19503 0.785985i 0.213437 0.976957i \(-0.431534\pi\)
0.981596 + 0.190971i \(0.0611638\pi\)
\(68\) 6.08558 12.1174i 0.0894938 0.178197i
\(69\) 0.156658 0.138995i 0.00227041 0.00201442i
\(70\) −14.8196 + 15.7078i −0.211708 + 0.224398i
\(71\) 118.033 20.8124i 1.66244 0.293133i 0.738096 0.674696i \(-0.235725\pi\)
0.924343 + 0.381563i \(0.124614\pi\)
\(72\) −65.0874 43.0878i −0.903992 0.598441i
\(73\) 4.87242 27.6329i 0.0667455 0.378533i −0.933077 0.359678i \(-0.882887\pi\)
0.999822 0.0188553i \(-0.00600218\pi\)
\(74\) 78.4848 58.4298i 1.06061 0.789592i
\(75\) 18.3354 + 68.8397i 0.244472 + 0.917862i
\(76\) 12.5149 2.96609i 0.164670 0.0390275i
\(77\) −7.75028 + 66.3079i −0.100653 + 0.861142i
\(78\) −47.5638 + 53.2866i −0.609793 + 0.683161i
\(79\) 1.46602 25.1706i 0.0185572 0.318615i −0.976237 0.216707i \(-0.930468\pi\)
0.994794 0.101908i \(-0.0324946\pi\)
\(80\) 11.9941i 0.149927i
\(81\) 55.2326 + 59.2483i 0.681883 + 0.731461i
\(82\) −69.1991 −0.843892
\(83\) −57.8010 3.36653i −0.696398 0.0405606i −0.293706 0.955896i \(-0.594889\pi\)
−0.402692 + 0.915335i \(0.631926\pi\)
\(84\) −33.5003 + 11.0453i −0.398813 + 0.131491i
\(85\) −14.3955 1.68260i −0.169359 0.0197952i
\(86\) 21.9180 + 92.4794i 0.254861 + 1.07534i
\(87\) −82.5368 82.7838i −0.948699 0.951538i
\(88\) −30.8012 41.3731i −0.350013 0.470149i
\(89\) 100.343 + 17.6931i 1.12744 + 0.198799i 0.706107 0.708105i \(-0.250450\pi\)
0.421338 + 0.906904i \(0.361561\pi\)
\(90\) −4.04318 + 16.8353i −0.0449243 + 0.187058i
\(91\) 27.0094 + 153.178i 0.296807 + 1.68328i
\(92\) 0.0531873 + 0.0501797i 0.000578123 + 0.000545431i
\(93\) −43.5088 + 8.91610i −0.467836 + 0.0958720i
\(94\) 124.447 + 62.4998i 1.32391 + 0.664891i
\(95\) −7.55430 11.4858i −0.0795190 0.120903i
\(96\) 23.2491 42.9644i 0.242178 0.447545i
\(97\) 122.813 + 29.1072i 1.26611 + 0.300074i 0.808192 0.588919i \(-0.200446\pi\)
0.457920 + 0.888993i \(0.348594\pi\)
\(98\) 45.2592 124.349i 0.461828 1.26886i
\(99\) 21.0529 + 49.2098i 0.212655 + 0.497069i
\(100\) −23.3731 + 8.50712i −0.233731 + 0.0850712i
\(101\) 17.0744 + 146.080i 0.169053 + 1.44634i 0.765369 + 0.643591i \(0.222556\pi\)
−0.596316 + 0.802750i \(0.703370\pi\)
\(102\) 54.6071 + 38.3580i 0.535364 + 0.376059i
\(103\) −20.9861 22.2439i −0.203748 0.215961i 0.617440 0.786618i \(-0.288170\pi\)
−0.821188 + 0.570658i \(0.806688\pi\)
\(104\) −96.3944 71.7630i −0.926870 0.690029i
\(105\) 23.3408 + 29.6101i 0.222293 + 0.282001i
\(106\) 40.4966 20.3382i 0.382043 0.191869i
\(107\) −175.591 101.377i −1.64104 0.947453i −0.980466 0.196690i \(-0.936981\pi\)
−0.660571 0.750763i \(-0.729686\pi\)
\(108\) −18.8955 + 21.0421i −0.174959 + 0.194835i
\(109\) −90.5634 156.860i −0.830857 1.43909i −0.897360 0.441300i \(-0.854517\pi\)
0.0665026 0.997786i \(-0.478816\pi\)
\(110\) −6.28688 + 9.55874i −0.0571535 + 0.0868976i
\(111\) −80.8518 150.487i −0.728394 1.35574i
\(112\) 47.6324 + 110.424i 0.425289 + 0.985932i
\(113\) −25.6711 7.68542i −0.227178 0.0680125i 0.171191 0.985238i \(-0.445238\pi\)
−0.398369 + 0.917225i \(0.630424\pi\)
\(114\) 5.42253 + 63.0646i 0.0475661 + 0.553199i
\(115\) 0.0309569 0.0717662i 0.000269190 0.000624054i
\(116\) 26.2355 31.2662i 0.226168 0.269537i
\(117\) 79.8729 + 95.7684i 0.682674 + 0.818533i
\(118\) 15.0996 12.6701i 0.127963 0.107373i
\(119\) 139.215 41.6782i 1.16987 0.350237i
\(120\) −28.8165 4.26497i −0.240137 0.0355414i
\(121\) −4.97904 85.4869i −0.0411491 0.706503i
\(122\) 65.6869 3.82582i 0.538417 0.0313592i
\(123\) −17.6886 + 119.514i −0.143809 + 0.971655i
\(124\) −4.44736 14.8552i −0.0358658 0.119800i
\(125\) 35.0805 + 41.8073i 0.280644 + 0.334459i
\(126\) −29.6343 171.051i −0.235192 1.35755i
\(127\) −92.7360 77.8147i −0.730205 0.612714i 0.199983 0.979799i \(-0.435911\pi\)
−0.930187 + 0.367085i \(0.880356\pi\)
\(128\) −51.9498 22.4090i −0.405858 0.175070i
\(129\) 165.323 14.2151i 1.28158 0.110195i
\(130\) −7.64501 + 25.5361i −0.0588078 + 0.196432i
\(131\) −51.8509 + 22.3663i −0.395808 + 0.170735i −0.584675 0.811268i \(-0.698778\pi\)
0.188867 + 0.982003i \(0.439519\pi\)
\(132\) −16.4623 + 8.84466i −0.124714 + 0.0670050i
\(133\) 115.162 + 75.7434i 0.865882 + 0.569499i
\(134\) −142.608 + 82.3348i −1.06424 + 0.614439i
\(135\) 28.0426 + 11.2864i 0.207723 + 0.0836027i
\(136\) −56.1384 + 97.2345i −0.412782 + 0.714960i
\(137\) 13.6835 + 27.2461i 0.0998794 + 0.198876i 0.938023 0.346574i \(-0.112655\pi\)
−0.838143 + 0.545450i \(0.816359\pi\)
\(138\) −0.282617 + 0.222780i −0.00204795 + 0.00161435i
\(139\) −0.559660 + 0.751753i −0.00402633 + 0.00540830i −0.804132 0.594451i \(-0.797369\pi\)
0.800105 + 0.599859i \(0.204777\pi\)
\(140\) −9.57520 + 9.03373i −0.0683943 + 0.0645267i
\(141\) 139.754 198.956i 0.991164 1.41104i
\(142\) −204.553 + 23.9088i −1.44051 + 0.168372i
\(143\) 28.1837 + 77.4342i 0.197089 + 0.541498i
\(144\) 77.1666 + 57.8075i 0.535879 + 0.401441i
\(145\) −40.9951 14.9210i −0.282725 0.102903i
\(146\) −11.1189 + 46.9145i −0.0761571 + 0.321332i
\(147\) −203.193 109.953i −1.38227 0.747978i
\(148\) 49.8329 32.7756i 0.336709 0.221457i
\(149\) 10.5461 20.9990i 0.0707792 0.140933i −0.855460 0.517868i \(-0.826726\pi\)
0.926240 + 0.376935i \(0.123022\pi\)
\(150\) −24.5746 119.919i −0.163831 0.799460i
\(151\) −124.071 + 131.507i −0.821661 + 0.870910i −0.993455 0.114223i \(-0.963562\pi\)
0.171794 + 0.985133i \(0.445044\pi\)
\(152\) −104.879 + 18.4929i −0.689991 + 0.121664i
\(153\) 80.2066 84.5068i 0.524226 0.552332i
\(154\) 19.9196 112.970i 0.129348 0.733570i
\(155\) −13.2949 + 9.89766i −0.0857733 + 0.0638559i
\(156\) −30.8336 + 30.7417i −0.197652 + 0.197062i
\(157\) −210.810 + 49.9628i −1.34274 + 0.318234i −0.838297 0.545213i \(-0.816449\pi\)
−0.504439 + 0.863448i \(0.668300\pi\)
\(158\) −5.02960 + 43.0310i −0.0318329 + 0.272348i
\(159\) −24.7743 75.1404i −0.155813 0.472581i
\(160\) 1.06004 18.2001i 0.00662523 0.113751i
\(161\) 0.783656i 0.00486743i
\(162\) −88.8261 107.152i −0.548309 0.661435i
\(163\) 35.2293 0.216131 0.108065 0.994144i \(-0.465534\pi\)
0.108065 + 0.994144i \(0.465534\pi\)
\(164\) −42.1111 2.45269i −0.256775 0.0149554i
\(165\) 14.9018 + 13.3014i 0.0903141 + 0.0806148i
\(166\) 98.8152 + 11.5498i 0.595272 + 0.0695773i
\(167\) 23.3986 + 98.7263i 0.140111 + 0.591176i 0.997118 + 0.0758701i \(0.0241734\pi\)
−0.857006 + 0.515306i \(0.827678\pi\)
\(168\) 282.237 75.1735i 1.67998 0.447461i
\(169\) 13.7292 + 18.4415i 0.0812379 + 0.109121i
\(170\) 24.5259 + 4.32457i 0.144270 + 0.0254387i
\(171\) 110.305 + 6.75523i 0.645058 + 0.0395043i
\(172\) 10.0604 + 57.0551i 0.0584905 + 0.331716i
\(173\) 118.318 + 111.627i 0.683916 + 0.645242i 0.947634 0.319358i \(-0.103467\pi\)
−0.263718 + 0.964600i \(0.584949\pi\)
\(174\) 133.312 + 150.253i 0.766162 + 0.863523i
\(175\) −238.213 119.635i −1.36121 0.683628i
\(176\) 35.0103 + 53.2306i 0.198922 + 0.302447i
\(177\) −18.0227 29.3171i −0.101823 0.165634i
\(178\) −170.359 40.3759i −0.957075 0.226831i
\(179\) 27.7178 76.1541i 0.154848 0.425442i −0.837875 0.545862i \(-0.816202\pi\)
0.992723 + 0.120421i \(0.0384244\pi\)
\(180\) −3.05719 + 10.1018i −0.0169844 + 0.0561210i
\(181\) 191.681 69.7661i 1.05901 0.385448i 0.246954 0.969027i \(-0.420570\pi\)
0.812056 + 0.583579i \(0.198348\pi\)
\(182\) −31.0278 265.459i −0.170482 1.45857i
\(183\) 10.1832 114.426i 0.0556458 0.625276i
\(184\) −0.415497 0.440401i −0.00225814 0.00239348i
\(185\) −51.1377 38.0706i −0.276420 0.205787i
\(186\) 75.5254 10.9476i 0.406051 0.0588583i
\(187\) 68.7995 34.5524i 0.367912 0.184772i
\(188\) 73.5171 + 42.4451i 0.391048 + 0.225772i
\(189\) −302.996 + 7.45755i −1.60316 + 0.0394579i
\(190\) 11.8111 + 20.4574i 0.0621635 + 0.107670i
\(191\) −181.645 + 276.178i −0.951023 + 1.44596i −0.0567758 + 0.998387i \(0.518082\pi\)
−0.894247 + 0.447573i \(0.852288\pi\)
\(192\) −111.827 + 180.694i −0.582431 + 0.941115i
\(193\) −40.2177 93.2351i −0.208382 0.483084i 0.781686 0.623672i \(-0.214360\pi\)
−0.990068 + 0.140588i \(0.955101\pi\)
\(194\) −207.764 62.2006i −1.07095 0.320621i
\(195\) 42.1491 + 19.7312i 0.216149 + 0.101186i
\(196\) 31.9499 74.0681i 0.163009 0.377898i
\(197\) −136.481 + 162.652i −0.692798 + 0.825645i −0.991691 0.128642i \(-0.958938\pi\)
0.298893 + 0.954287i \(0.403383\pi\)
\(198\) −31.1974 86.5176i −0.157563 0.436957i
\(199\) 6.68377 5.60834i 0.0335868 0.0281826i −0.625840 0.779952i \(-0.715244\pi\)
0.659427 + 0.751769i \(0.270799\pi\)
\(200\) 197.302 59.0684i 0.986511 0.295342i
\(201\) 105.747 + 267.344i 0.526105 + 1.33007i
\(202\) −14.6943 252.291i −0.0727440 1.24897i
\(203\) 436.678 25.4336i 2.15112 0.125289i
\(204\) 31.8716 + 25.2782i 0.156233 + 0.123913i
\(205\) 12.9312 + 43.1933i 0.0630792 + 0.210699i
\(206\) 33.7770 + 40.2538i 0.163966 + 0.195407i
\(207\) 0.312520 + 0.545054i 0.00150976 + 0.00263311i
\(208\) 113.713 + 95.4163i 0.546696 + 0.458732i
\(209\) 67.0528 + 28.9237i 0.320827 + 0.138391i
\(210\) −37.0803 53.1249i −0.176573 0.252976i
\(211\) −25.0701 + 83.7399i −0.118815 + 0.396871i −0.996620 0.0821473i \(-0.973822\pi\)
0.877805 + 0.479019i \(0.159007\pi\)
\(212\) 25.3651 10.9414i 0.119646 0.0516104i
\(213\) −10.9946 + 359.394i −0.0516178 + 1.68729i
\(214\) 291.079 + 191.446i 1.36018 + 0.894606i
\(215\) 53.6288 30.9626i 0.249436 0.144012i
\(216\) 166.325 164.841i 0.770022 0.763151i
\(217\) 83.0928 143.921i 0.382916 0.663230i
\(218\) 139.680 + 278.126i 0.640734 + 1.27581i
\(219\) 78.1837 + 31.1957i 0.357003 + 0.142446i
\(220\) −4.16468 + 5.59413i −0.0189304 + 0.0254279i
\(221\) 130.472 123.094i 0.590371 0.556986i
\(222\) 123.657 + 266.222i 0.557015 + 1.19920i
\(223\) −111.248 + 13.0030i −0.498870 + 0.0583095i −0.361807 0.932253i \(-0.617840\pi\)
−0.137062 + 0.990562i \(0.543766\pi\)
\(224\) 62.5190 + 171.770i 0.279103 + 0.766829i
\(225\) −213.393 + 11.7892i −0.948415 + 0.0523965i
\(226\) 43.2682 + 15.7483i 0.191452 + 0.0696828i
\(227\) 14.4334 60.8994i 0.0635834 0.268279i −0.931963 0.362554i \(-0.881905\pi\)
0.995546 + 0.0942744i \(0.0300531\pi\)
\(228\) 1.06462 + 38.5701i 0.00466938 + 0.169167i
\(229\) −132.666 + 87.2560i −0.579329 + 0.381031i −0.805090 0.593152i \(-0.797883\pi\)
0.225762 + 0.974183i \(0.427513\pi\)
\(230\) −0.0602734 + 0.120014i −0.000262058 + 0.000521801i
\(231\) −190.018 63.2803i −0.822589 0.273941i
\(232\) −231.920 + 245.821i −0.999657 + 1.05957i
\(233\) −130.655 + 23.0379i −0.560749 + 0.0988752i −0.446837 0.894616i \(-0.647449\pi\)
−0.113912 + 0.993491i \(0.536338\pi\)
\(234\) −127.445 172.261i −0.544638 0.736156i
\(235\) 15.7562 89.3580i 0.0670478 0.380247i
\(236\) 9.63792 7.17517i 0.0408386 0.0304032i
\(237\) 73.0330 + 19.6861i 0.308156 + 0.0830637i
\(238\) −242.972 + 57.5855i −1.02089 + 0.241956i
\(239\) 52.7232 451.076i 0.220599 1.88735i −0.199542 0.979889i \(-0.563945\pi\)
0.420141 0.907459i \(-0.361980\pi\)
\(240\) 35.2282 + 7.32891i 0.146784 + 0.0305371i
\(241\) 8.10649 139.183i 0.0336369 0.577523i −0.938815 0.344421i \(-0.888075\pi\)
0.972452 0.233102i \(-0.0748877\pi\)
\(242\) 147.141i 0.608021i
\(243\) −207.768 + 126.021i −0.855014 + 0.518605i
\(244\) 40.1093 0.164382
\(245\) −86.0746 5.01327i −0.351325 0.0204623i
\(246\) 42.2835 203.246i 0.171884 0.826202i
\(247\) 168.989 + 19.7520i 0.684167 + 0.0799676i
\(248\) 29.6107 + 124.937i 0.119398 + 0.503779i
\(249\) 45.2066 167.711i 0.181553 0.673538i
\(250\) −55.9999 75.2209i −0.224000 0.300884i
\(251\) −34.5998 6.10087i −0.137848 0.0243063i 0.104299 0.994546i \(-0.466740\pi\)
−0.242146 + 0.970240i \(0.577851\pi\)
\(252\) −11.9712 105.143i −0.0475047 0.417235i
\(253\) 0.0720937 + 0.408864i 0.000284955 + 0.00161606i
\(254\) 151.304 + 142.748i 0.595686 + 0.562001i
\(255\) 13.7382 41.2531i 0.0538754 0.161777i
\(256\) −166.319 83.5283i −0.649682 0.326282i
\(257\) −220.085 334.623i −0.856361 1.30203i −0.951838 0.306602i \(-0.900808\pi\)
0.0954770 0.995432i \(-0.469562\pi\)
\(258\) −285.015 + 7.86702i −1.10471 + 0.0304923i
\(259\) 621.990 + 147.414i 2.40151 + 0.569167i
\(260\) −5.55747 + 15.2690i −0.0213749 + 0.0587270i
\(261\) 293.579 191.836i 1.12482 0.735003i
\(262\) 91.1793 33.1865i 0.348012 0.126666i
\(263\) −32.0737 274.408i −0.121953 1.04338i −0.906177 0.422899i \(-0.861013\pi\)
0.784224 0.620478i \(-0.213062\pi\)
\(264\) 140.338 65.1858i 0.531584 0.246916i
\(265\) −20.2625 21.4769i −0.0764621 0.0810451i
\(266\) −189.981 141.436i −0.714215 0.531713i
\(267\) −113.280 + 283.906i −0.424270 + 1.06332i
\(268\) −89.7024 + 45.0502i −0.334710 + 0.168098i
\(269\) −268.421 154.973i −0.997848 0.576108i −0.0902374 0.995920i \(-0.528763\pi\)
−0.907611 + 0.419812i \(0.862096\pi\)
\(270\) −46.9765 22.1623i −0.173987 0.0820826i
\(271\) 20.6211 + 35.7168i 0.0760927 + 0.131796i 0.901561 0.432652i \(-0.142422\pi\)
−0.825468 + 0.564449i \(0.809089\pi\)
\(272\) 76.2095 115.871i 0.280182 0.425996i
\(273\) −466.405 14.2683i −1.70844 0.0522649i
\(274\) −20.7504 48.1048i −0.0757314 0.175565i
\(275\) −135.291 40.5034i −0.491966 0.147285i
\(276\) −0.179883 + 0.125555i −0.000651750 + 0.000454911i
\(277\) 178.088 412.855i 0.642917 1.49045i −0.214975 0.976620i \(-0.568967\pi\)
0.857892 0.513830i \(-0.171774\pi\)
\(278\) 1.03514 1.23364i 0.00372354 0.00443754i
\(279\) 0.398040 133.238i 0.00142667 0.477556i
\(280\) 83.4996 70.0645i 0.298213 0.250230i
\(281\) −283.016 + 84.7295i −1.00717 + 0.301528i −0.747567 0.664186i \(-0.768778\pi\)
−0.259607 + 0.965714i \(0.583593\pi\)
\(282\) −259.611 + 327.326i −0.920607 + 1.16073i
\(283\) 5.25979 + 90.3072i 0.0185858 + 0.319107i 0.994768 + 0.102156i \(0.0325741\pi\)
−0.976183 + 0.216951i \(0.930389\pi\)
\(284\) −125.328 + 7.29951i −0.441295 + 0.0257025i
\(285\) 38.3510 15.1696i 0.134565 0.0532266i
\(286\) −40.6097 135.646i −0.141992 0.474287i
\(287\) −290.586 346.306i −1.01249 1.20664i
\(288\) 111.985 + 94.5381i 0.388837 + 0.328257i
\(289\) 93.0082 + 78.0432i 0.321828 + 0.270046i
\(290\) 68.8319 + 29.6912i 0.237351 + 0.102383i
\(291\) −160.535 + 342.930i −0.551666 + 1.17845i
\(292\) −8.42926 + 28.1557i −0.0288673 + 0.0964236i
\(293\) 381.849 164.713i 1.30324 0.562162i 0.372562 0.928007i \(-0.378479\pi\)
0.930676 + 0.365845i \(0.119220\pi\)
\(294\) 337.570 + 208.913i 1.14820 + 0.710589i
\(295\) −10.7302 7.05734i −0.0363735 0.0239232i
\(296\) −427.707 + 246.937i −1.44496 + 0.834246i
\(297\) −157.399 + 31.7655i −0.529962 + 0.106955i
\(298\) −20.1887 + 34.9679i −0.0677474 + 0.117342i
\(299\) 0.434123 + 0.864410i 0.00145192 + 0.00289100i
\(300\) −10.7044 73.8477i −0.0356815 0.246159i
\(301\) −370.773 + 498.034i −1.23180 + 1.65460i
\(302\) 225.969 213.191i 0.748242 0.705930i
\(303\) −439.488 39.1118i −1.45045 0.129082i
\(304\) 130.657 15.2716i 0.429793 0.0502356i
\(305\) −14.6629 40.2861i −0.0480752 0.132086i
\(306\) −146.029 + 136.949i −0.477219 + 0.447546i
\(307\) 444.083 + 161.633i 1.44652 + 0.526492i 0.941618 0.336683i \(-0.109305\pi\)
0.504906 + 0.863175i \(0.331527\pi\)
\(308\) 16.1262 68.0417i 0.0523577 0.220915i
\(309\) 78.1563 48.0465i 0.252933 0.155490i
\(310\) 23.7948 15.6501i 0.0767574 0.0504842i
\(311\) 95.2565 189.671i 0.306291 0.609875i −0.686850 0.726799i \(-0.741007\pi\)
0.993141 + 0.116924i \(0.0373034\pi\)
\(312\) 269.677 239.271i 0.864349 0.766895i
\(313\) −391.304 + 414.758i −1.25017 + 1.32511i −0.324925 + 0.945740i \(0.605339\pi\)
−0.925247 + 0.379366i \(0.876142\pi\)
\(314\) 366.613 64.6438i 1.16756 0.205872i
\(315\) −101.230 + 50.4616i −0.321366 + 0.160196i
\(316\) −4.58595 + 26.0082i −0.0145125 + 0.0823044i
\(317\) −281.186 + 209.335i −0.887023 + 0.660364i −0.941084 0.338174i \(-0.890191\pi\)
0.0540610 + 0.998538i \(0.482783\pi\)
\(318\) 34.9904 + 131.371i 0.110033 + 0.413115i
\(319\) 225.492 53.4426i 0.706871 0.167532i
\(320\) −9.20650 + 78.7667i −0.0287703 + 0.246146i
\(321\) 405.050 453.785i 1.26184 1.41366i
\(322\) 0.0782953 1.34428i 0.000243153 0.00417478i
\(323\) 158.959i 0.492132i
\(324\) −50.2571 68.3559i −0.155115 0.210975i
\(325\) −329.034 −1.01241
\(326\) −60.4321 3.51977i −0.185375 0.0107968i
\(327\) 516.055 170.147i 1.57815 0.520327i
\(328\) 346.917 + 40.5488i 1.05767 + 0.123624i
\(329\) 209.808 + 885.249i 0.637714 + 2.69073i
\(330\) −24.2336 24.3061i −0.0734350 0.0736547i
\(331\) 233.882 + 314.158i 0.706592 + 0.949118i 0.999976 0.00687657i \(-0.00218890\pi\)
−0.293384 + 0.955995i \(0.594781\pi\)
\(332\) 59.7245 + 10.5310i 0.179893 + 0.0317200i
\(333\) 491.400 145.517i 1.47568 0.436989i
\(334\) −30.2740 171.692i −0.0906407 0.514049i
\(335\) 78.0417 + 73.6285i 0.232960 + 0.219787i
\(336\) −353.434 + 72.4280i −1.05189 + 0.215560i
\(337\) 242.002 + 121.538i 0.718107 + 0.360647i 0.770033 0.638004i \(-0.220240\pi\)
−0.0519260 + 0.998651i \(0.516536\pi\)
\(338\) −21.7085 33.0062i −0.0642263 0.0976514i
\(339\) 38.2590 70.7027i 0.112858 0.208563i
\(340\) 14.7719 + 3.50101i 0.0434469 + 0.0102971i
\(341\) 30.1125 82.7334i 0.0883064 0.242620i
\(342\) −188.541 22.6085i −0.551290 0.0661066i
\(343\) 295.480 107.546i 0.861457 0.313545i
\(344\) −55.6915 476.471i −0.161894 1.38509i
\(345\) 0.191869 + 0.134776i 0.000556143 + 0.000390655i
\(346\) −191.808 203.305i −0.554360 0.587587i
\(347\) −245.207 182.550i −0.706648 0.526080i 0.182781 0.983154i \(-0.441490\pi\)
−0.889429 + 0.457074i \(0.848897\pi\)
\(348\) 75.8015 + 96.1615i 0.217820 + 0.276326i
\(349\) −52.0027 + 26.1167i −0.149005 + 0.0748330i −0.521739 0.853105i \(-0.674717\pi\)
0.372734 + 0.927938i \(0.378420\pi\)
\(350\) 396.675 + 229.021i 1.13336 + 0.654345i
\(351\) −330.088 + 176.077i −0.940422 + 0.501645i
\(352\) 48.4208 + 83.8673i 0.137559 + 0.238259i
\(353\) 257.225 391.092i 0.728683 1.10791i −0.261098 0.965312i \(-0.584084\pi\)
0.989781 0.142597i \(-0.0455452\pi\)
\(354\) 27.9869 + 52.0911i 0.0790591 + 0.147150i
\(355\) 53.1483 + 123.212i 0.149714 + 0.347075i
\(356\) −102.241 30.6089i −0.287194 0.0859802i
\(357\) 37.3476 + 434.356i 0.104615 + 1.21668i
\(358\) −55.1555 + 127.865i −0.154066 + 0.357164i
\(359\) −202.060 + 240.805i −0.562841 + 0.670767i −0.970145 0.242525i \(-0.922024\pi\)
0.407304 + 0.913292i \(0.366469\pi\)
\(360\) 30.1347 82.0312i 0.0837076 0.227864i
\(361\) −161.042 + 135.130i −0.446098 + 0.374321i
\(362\) −335.779 + 100.525i −0.927565 + 0.277695i
\(363\) 254.127 + 37.6119i 0.700074 + 0.103614i
\(364\) −9.47299 162.645i −0.0260247 0.446827i
\(365\) 31.3613 1.82659i 0.0859214 0.00500435i
\(366\) −28.9005 + 195.267i −0.0789630 + 0.533518i
\(367\) 97.1134 + 324.381i 0.264614 + 0.883873i 0.982270 + 0.187474i \(0.0600301\pi\)
−0.717655 + 0.696398i \(0.754785\pi\)
\(368\) 0.480731 + 0.572913i 0.00130634 + 0.00155683i
\(369\) −340.216 124.981i −0.921996 0.338702i
\(370\) 83.9176 + 70.4152i 0.226804 + 0.190311i
\(371\) 271.838 + 117.260i 0.732717 + 0.316063i
\(372\) 46.3490 3.98526i 0.124594 0.0107131i
\(373\) 133.455 445.770i 0.357788 1.19509i −0.569893 0.821719i \(-0.693015\pi\)
0.927680 0.373375i \(-0.121800\pi\)
\(374\) −121.470 + 52.3972i −0.324787 + 0.140099i
\(375\) −144.228 + 77.4894i −0.384609 + 0.206639i
\(376\) −587.270 386.254i −1.56189 1.02727i
\(377\) 467.587 269.961i 1.24028 0.716078i
\(378\) 520.503 + 17.4798i 1.37699 + 0.0462429i
\(379\) −154.431 + 267.483i −0.407471 + 0.705760i −0.994606 0.103729i \(-0.966922\pi\)
0.587135 + 0.809489i \(0.300256\pi\)
\(380\) 6.46252 + 12.8679i 0.0170066 + 0.0338630i
\(381\) 285.216 224.828i 0.748599 0.590100i
\(382\) 339.186 455.606i 0.887923 1.19269i
\(383\) 26.4911 24.9931i 0.0691674 0.0652561i −0.650882 0.759179i \(-0.725601\pi\)
0.720049 + 0.693923i \(0.244119\pi\)
\(384\) 97.5611 138.890i 0.254065 0.361692i
\(385\) −74.2369 + 8.67705i −0.192823 + 0.0225378i
\(386\) 59.6741 + 163.953i 0.154596 + 0.424749i
\(387\) −59.2679 + 494.260i −0.153147 + 1.27716i
\(388\) −124.230 45.2161i −0.320181 0.116536i
\(389\) −68.0805 + 287.254i −0.175014 + 0.738443i 0.812766 + 0.582590i \(0.197961\pi\)
−0.987780 + 0.155853i \(0.950187\pi\)
\(390\) −70.3310 38.0579i −0.180336 0.0975843i
\(391\) 0.755057 0.496609i 0.00193109 0.00127010i
\(392\) −299.763 + 596.878i −0.764702 + 1.52265i
\(393\) −34.0093 165.959i −0.0865376 0.422286i
\(394\) 250.370 265.376i 0.635456 0.673544i
\(395\) 27.7993 4.90177i 0.0703781 0.0124096i
\(396\) −15.9187 53.7560i −0.0401986 0.135747i
\(397\) 89.9844 510.327i 0.226661 1.28546i −0.632824 0.774296i \(-0.718104\pi\)
0.859485 0.511162i \(-0.170785\pi\)
\(398\) −12.0256 + 8.95274i −0.0302151 + 0.0224943i
\(399\) −292.836 + 291.962i −0.733924 + 0.731735i
\(400\) −247.542 + 58.6684i −0.618854 + 0.146671i
\(401\) −76.3929 + 653.583i −0.190506 + 1.62988i 0.472544 + 0.881307i \(0.343336\pi\)
−0.663050 + 0.748575i \(0.730738\pi\)
\(402\) −154.687 469.166i −0.384794 1.16708i
\(403\) 11.9272 204.783i 0.0295961 0.508146i
\(404\) 154.053i 0.381318i
\(405\) −50.2845 + 75.4678i −0.124159 + 0.186340i
\(406\) −751.615 −1.85127
\(407\) 338.078 + 19.6908i 0.830658 + 0.0483803i
\(408\) −251.286 224.299i −0.615897 0.549752i
\(409\) −343.428 40.1409i −0.839676 0.0981441i −0.314626 0.949216i \(-0.601879\pi\)
−0.525050 + 0.851071i \(0.675953\pi\)
\(410\) −17.8667 75.3855i −0.0435773 0.183867i
\(411\) −88.3859 + 23.5415i −0.215051 + 0.0572785i
\(412\) 19.1282 + 25.6936i 0.0464277 + 0.0623632i
\(413\) 126.814 + 22.3608i 0.307057 + 0.0541424i
\(414\) −0.481638 0.966207i −0.00116338 0.00233383i
\(415\) −11.2563 63.8377i −0.0271236 0.153826i
\(416\) 164.117 + 154.836i 0.394512 + 0.372203i
\(417\) −1.86601 2.10314i −0.00447484 0.00504349i
\(418\) −112.132 56.3149i −0.268259 0.134725i
\(419\) −235.305 357.764i −0.561588 0.853853i 0.437380 0.899277i \(-0.355907\pi\)
−0.998968 + 0.0454239i \(0.985536\pi\)
\(420\) −20.6823 33.6434i −0.0492435 0.0801034i
\(421\) 10.2135 + 2.42065i 0.0242602 + 0.00574977i 0.242728 0.970094i \(-0.421958\pi\)
−0.218468 + 0.975844i \(0.570106\pi\)
\(422\) 51.3715 141.142i 0.121733 0.334460i
\(423\) 498.962 + 532.044i 1.17958 + 1.25779i
\(424\) −214.940 + 78.2317i −0.506933 + 0.184509i
\(425\) 35.6883 + 305.333i 0.0839724 + 0.718430i
\(426\) 54.7672 615.403i 0.128561 1.44461i
\(427\) 294.983 + 312.664i 0.690827 + 0.732234i
\(428\) 170.350 + 126.821i 0.398015 + 0.296311i
\(429\) −244.654 + 35.4634i −0.570290 + 0.0826652i
\(430\) −95.0880 + 47.7550i −0.221135 + 0.111058i
\(431\) −249.380 143.979i −0.578607 0.334059i 0.181972 0.983304i \(-0.441752\pi\)
−0.760580 + 0.649245i \(0.775085\pi\)
\(432\) −216.939 + 191.324i −0.502174 + 0.442880i
\(433\) −198.794 344.321i −0.459108 0.795199i 0.539806 0.841790i \(-0.318498\pi\)
−0.998914 + 0.0465905i \(0.985164\pi\)
\(434\) −156.916 + 238.579i −0.361558 + 0.549722i
\(435\) 68.8743 111.290i 0.158332 0.255839i
\(436\) 75.1443 + 174.204i 0.172349 + 0.399550i
\(437\) 0.821194 + 0.245849i 0.00187916 + 0.000562585i
\(438\) −130.999 61.3242i −0.299084 0.140010i
\(439\) −13.6088 + 31.5488i −0.0309996 + 0.0718651i −0.933013 0.359844i \(-0.882830\pi\)
0.902013 + 0.431709i \(0.142089\pi\)
\(440\) 37.1193 44.2370i 0.0843620 0.100539i
\(441\) 447.103 529.615i 1.01384 1.20094i
\(442\) −236.109 + 198.119i −0.534184 + 0.448233i
\(443\) 174.895 52.3601i 0.394796 0.118194i −0.0832504 0.996529i \(-0.526530\pi\)
0.478047 + 0.878334i \(0.341345\pi\)
\(444\) 65.8157 + 166.392i 0.148234 + 0.374757i
\(445\) 6.63284 + 113.881i 0.0149053 + 0.255913i
\(446\) 192.133 11.1905i 0.430792 0.0250908i
\(447\) 55.2323 + 43.8063i 0.123562 + 0.0980007i
\(448\) −228.047 761.729i −0.509033 1.70029i
\(449\) −82.2467 98.0178i −0.183178 0.218302i 0.666640 0.745380i \(-0.267732\pi\)
−0.849817 + 0.527078i \(0.823288\pi\)
\(450\) 367.232 + 1.09708i 0.816070 + 0.00243795i
\(451\) −183.469 153.949i −0.406804 0.341349i
\(452\) 25.7726 + 11.1172i 0.0570191 + 0.0245956i
\(453\) −310.440 444.766i −0.685297 0.981824i
\(454\) −30.8435 + 103.024i −0.0679372 + 0.226926i
\(455\) −159.899 + 68.9736i −0.351426 + 0.151590i
\(456\) 9.76928 319.340i 0.0214239 0.700308i
\(457\) 121.542 + 79.9392i 0.265955 + 0.174922i 0.675482 0.737377i \(-0.263936\pi\)
−0.409526 + 0.912298i \(0.634306\pi\)
\(458\) 236.293 136.424i 0.515923 0.297868i
\(459\) 199.197 + 287.213i 0.433979 + 0.625736i
\(460\) −0.0409332 + 0.0708983i −8.89851e−5 + 0.000154127i
\(461\) 87.1199 + 173.470i 0.188980 + 0.376291i 0.968092 0.250594i \(-0.0806260\pi\)
−0.779112 + 0.626885i \(0.784330\pi\)
\(462\) 319.633 + 127.535i 0.691847 + 0.276051i
\(463\) 45.4966 61.1125i 0.0982647 0.131992i −0.750271 0.661130i \(-0.770077\pi\)
0.848536 + 0.529138i \(0.177485\pi\)
\(464\) 303.643 286.473i 0.654403 0.617398i
\(465\) −20.9468 45.0964i −0.0450470 0.0969815i
\(466\) 226.426 26.4654i 0.485892 0.0567926i
\(467\) 10.4408 + 28.6858i 0.0223571 + 0.0614256i 0.950369 0.311125i \(-0.100706\pi\)
−0.928012 + 0.372550i \(0.878483\pi\)
\(468\) −71.4511 109.346i −0.152673 0.233646i
\(469\) −1010.89 367.935i −2.15542 0.784510i
\(470\) −35.9559 + 151.710i −0.0765019 + 0.322787i
\(471\) −17.9331 649.701i −0.0380745 1.37941i
\(472\) −83.1233 + 54.6710i −0.176109 + 0.115828i
\(473\) −147.629 + 293.953i −0.312112 + 0.621466i
\(474\) −123.313 41.0662i −0.260155 0.0866375i
\(475\) −200.098 + 212.091i −0.421259 + 0.446508i
\(476\) −149.902 + 26.4317i −0.314919 + 0.0555288i
\(477\) 235.834 26.8511i 0.494411 0.0562916i
\(478\) −135.508 + 768.506i −0.283490 + 1.60775i
\(479\) 514.560 383.076i 1.07424 0.799741i 0.0936085 0.995609i \(-0.470160\pi\)
0.980630 + 0.195868i \(0.0627524\pi\)
\(480\) 52.8081 + 14.2345i 0.110017 + 0.0296551i
\(481\) 767.748 181.960i 1.59615 0.378294i
\(482\) −27.8117 + 237.944i −0.0577005 + 0.493660i
\(483\) −2.30169 0.478846i −0.00476539 0.000991399i
\(484\) −5.21526 + 89.5426i −0.0107753 + 0.185005i
\(485\) 141.308i 0.291356i
\(486\) 368.995 195.418i 0.759249 0.402094i
\(487\) 546.864 1.12292 0.561462 0.827502i \(-0.310239\pi\)
0.561462 + 0.827502i \(0.310239\pi\)
\(488\) −331.551 19.3106i −0.679407 0.0395710i
\(489\) −21.5265 + 103.472i −0.0440216 + 0.211600i
\(490\) 147.151 + 17.1995i 0.300308 + 0.0351010i
\(491\) 208.581 + 880.074i 0.424809 + 1.79241i 0.591393 + 0.806384i \(0.298578\pi\)
−0.166583 + 0.986027i \(0.553273\pi\)
\(492\) 32.9354 122.186i 0.0669419 0.248346i
\(493\) −301.231 404.624i −0.611017 0.820738i
\(494\) −287.909 50.7662i −0.582813 0.102766i
\(495\) −48.1735 + 35.6406i −0.0973201 + 0.0720013i
\(496\) −27.5406 156.190i −0.0555254 0.314900i
\(497\) −978.622 923.282i −1.96906 1.85771i
\(498\) −94.3032 + 283.174i −0.189364 + 0.568622i
\(499\) 45.9931 + 23.0986i 0.0921706 + 0.0462898i 0.494287 0.869299i \(-0.335429\pi\)
−0.402117 + 0.915588i \(0.631725\pi\)
\(500\) −31.4126 47.7605i −0.0628252 0.0955210i
\(501\) −304.268 + 8.39844i −0.607321 + 0.0167633i
\(502\) 58.7427 + 13.9223i 0.117017 + 0.0277336i
\(503\) −190.011 + 522.051i −0.377756 + 1.03788i 0.594529 + 0.804074i \(0.297339\pi\)
−0.972284 + 0.233801i \(0.924884\pi\)
\(504\) 48.3348 + 874.896i 0.0959024 + 1.73590i
\(505\) −154.732 + 56.3177i −0.306399 + 0.111520i
\(506\) −0.0828194 0.708565i −0.000163675 0.00140033i
\(507\) −62.5539 + 29.0557i −0.123381 + 0.0573091i
\(508\) 87.0165 + 92.2321i 0.171292 + 0.181559i
\(509\) 9.29558 + 6.92030i 0.0182624 + 0.0135959i 0.606251 0.795273i \(-0.292673\pi\)
−0.587989 + 0.808869i \(0.700080\pi\)
\(510\) −27.6881 + 69.3928i −0.0542903 + 0.136064i
\(511\) −281.475 + 141.362i −0.550831 + 0.276638i
\(512\) 472.945 + 273.055i 0.923720 + 0.533310i
\(513\) −87.2416 + 319.850i −0.170062 + 0.623489i
\(514\) 344.100 + 595.998i 0.669455 + 1.15953i
\(515\) 18.8141 28.6055i 0.0365322 0.0555446i
\(516\) −173.725 5.31460i −0.336676 0.0102996i
\(517\) 190.905 + 442.567i 0.369255 + 0.856029i
\(518\) −1052.23 315.017i −2.03133 0.608141i
\(519\) −400.157 + 279.303i −0.771016 + 0.538157i
\(520\) 53.2903 123.541i 0.102481 0.237578i
\(521\) 438.469 522.547i 0.841591 1.00297i −0.158288 0.987393i \(-0.550597\pi\)
0.999879 0.0155758i \(-0.00495813\pi\)
\(522\) −522.769 + 299.742i −1.00147 + 0.574219i
\(523\) 495.539 415.807i 0.947494 0.795042i −0.0313801 0.999508i \(-0.509990\pi\)
0.978874 + 0.204466i \(0.0655458\pi\)
\(524\) 56.6634 16.9639i 0.108136 0.0323738i
\(525\) 496.938 626.555i 0.946549 1.19344i
\(526\) 27.6028 + 473.923i 0.0524769 + 0.900993i
\(527\) −191.325 + 11.1434i −0.363046 + 0.0211450i
\(528\) −177.737 + 70.3032i −0.336623 + 0.133150i
\(529\) −151.718 506.772i −0.286801 0.957981i
\(530\) 32.6123 + 38.8658i 0.0615327 + 0.0733318i
\(531\) 97.1203 35.0207i 0.182901 0.0659523i
\(532\) −110.600 92.8043i −0.207894 0.174444i
\(533\) −512.374 221.016i −0.961301 0.414665i
\(534\) 222.685 475.693i 0.417013 0.890811i
\(535\) 65.1044 217.464i 0.121690 0.406474i
\(536\) 763.185 329.206i 1.42385 0.614190i
\(537\) 206.736 + 127.944i 0.384984 + 0.238256i
\(538\) 444.965 + 292.658i 0.827072 + 0.543974i
\(539\) 396.637 228.998i 0.735876 0.424858i
\(540\) −27.8020 15.1519i −0.0514852 0.0280591i
\(541\) 105.291 182.370i 0.194623 0.337097i −0.752154 0.658988i \(-0.770985\pi\)
0.946777 + 0.321890i \(0.104318\pi\)
\(542\) −31.8048 63.3286i −0.0586805 0.116843i
\(543\) 87.7862 + 605.618i 0.161669 + 1.11532i
\(544\) 125.882 169.089i 0.231401 0.310826i
\(545\) 147.501 139.160i 0.270644 0.255339i
\(546\) 798.643 + 71.0745i 1.46272 + 0.130173i
\(547\) −496.284 + 58.0072i −0.907282 + 0.106046i −0.556918 0.830567i \(-0.688016\pi\)
−0.350364 + 0.936613i \(0.613942\pi\)
\(548\) −10.9226 30.0096i −0.0199318 0.0547621i
\(549\) 329.858 + 99.8278i 0.600835 + 0.181836i
\(550\) 228.030 + 82.9962i 0.414600 + 0.150902i
\(551\) 110.343 465.574i 0.200260 0.844963i
\(552\) 1.54739 0.951258i 0.00280325 0.00172329i
\(553\) −236.469 + 155.528i −0.427611 + 0.281244i
\(554\) −346.740 + 690.415i −0.625884 + 1.24624i
\(555\) 143.065 126.934i 0.257774 0.228711i
\(556\) 0.673662 0.714040i 0.00121162 0.00128424i
\(557\) −265.011 + 46.7287i −0.475784 + 0.0838935i −0.406397 0.913696i \(-0.633215\pi\)
−0.0693862 + 0.997590i \(0.522104\pi\)
\(558\) −13.9947 + 228.516i −0.0250800 + 0.409527i
\(559\) −133.083 + 754.753i −0.238074 + 1.35018i
\(560\) −107.998 + 80.4015i −0.192854 + 0.143574i
\(561\) 59.4450 + 223.185i 0.105963 + 0.397834i
\(562\) 493.949 117.068i 0.878913 0.208306i
\(563\) 6.31752 54.0498i 0.0112212 0.0960032i −0.986467 0.163959i \(-0.947574\pi\)
0.997688 + 0.0679556i \(0.0216476\pi\)
\(564\) −169.588 + 189.992i −0.300688 + 0.336866i
\(565\) 1.74441 29.9504i 0.00308746 0.0530096i
\(566\) 155.438i 0.274625i
\(567\) 163.239 894.491i 0.287900 1.57759i
\(568\) 1039.50 1.83010
\(569\) 11.9714 + 0.697252i 0.0210393 + 0.00122540i 0.0686612 0.997640i \(-0.478127\pi\)
−0.0476220 + 0.998865i \(0.515164\pi\)
\(570\) −67.3026 + 22.1901i −0.118075 + 0.0389301i
\(571\) −583.319 68.1802i −1.02157 0.119405i −0.411222 0.911535i \(-0.634898\pi\)
−0.610352 + 0.792130i \(0.708972\pi\)
\(572\) −19.9052 83.9867i −0.0347993 0.146830i
\(573\) −700.174 702.269i −1.22194 1.22560i
\(574\) 463.869 + 623.084i 0.808134 + 1.08551i
\(575\) −1.63257 0.287866i −0.00283925 0.000500637i
\(576\) −462.388 438.859i −0.802757 0.761908i
\(577\) 165.093 + 936.287i 0.286123 + 1.62268i 0.701248 + 0.712917i \(0.252627\pi\)
−0.415125 + 0.909764i \(0.636262\pi\)
\(578\) −151.748 143.167i −0.262540 0.247694i
\(579\) 298.417 61.1535i 0.515400 0.105619i
\(580\) 40.8353 + 20.5082i 0.0704056 + 0.0353590i
\(581\) 357.150 + 543.020i 0.614716 + 0.934631i
\(582\) 309.643 572.220i 0.532032 0.983196i
\(583\) 152.616 + 36.1707i 0.261777 + 0.0620423i
\(584\) 83.2333 228.682i 0.142523 0.391578i
\(585\) −83.7075 + 111.740i −0.143090 + 0.191009i
\(586\) −671.477 + 244.398i −1.14587 + 0.417061i
\(587\) 112.517 + 962.642i 0.191681 + 1.63994i 0.656354 + 0.754453i \(0.272098\pi\)
−0.464673 + 0.885483i \(0.653828\pi\)
\(588\) 198.024 + 139.099i 0.336775 + 0.236563i
\(589\) −124.747 132.224i −0.211795 0.224489i
\(590\) 17.7014 + 13.1782i 0.0300023 + 0.0223359i
\(591\) −394.332 500.248i −0.667228 0.846443i
\(592\) 545.154 273.787i 0.920868 0.462477i
\(593\) 274.719 + 158.609i 0.463271 + 0.267469i 0.713418 0.700738i \(-0.247146\pi\)
−0.250148 + 0.968208i \(0.580479\pi\)
\(594\) 273.175 38.7646i 0.459890 0.0652603i
\(595\) 81.3484 + 140.900i 0.136720 + 0.236806i
\(596\) −13.5252 + 20.5641i −0.0226933 + 0.0345036i
\(597\) 12.3883 + 23.0579i 0.0207509 + 0.0386229i
\(598\) −0.658328 1.52618i −0.00110088 0.00255213i
\(599\) −867.029 259.572i −1.44746 0.433341i −0.535821 0.844331i \(-0.679998\pi\)
−0.911640 + 0.410990i \(0.865183\pi\)
\(600\) 52.9309 + 615.592i 0.0882181 + 1.02599i
\(601\) 176.778 409.818i 0.294140 0.681894i −0.705500 0.708710i \(-0.749278\pi\)
0.999640 + 0.0268162i \(0.00853688\pi\)
\(602\) 685.780 817.280i 1.13917 1.35761i
\(603\) −849.836 + 147.233i −1.40935 + 0.244167i
\(604\) 145.070 121.728i 0.240182 0.201536i
\(605\) 91.8439 27.4963i 0.151808 0.0454484i
\(606\) 749.987 + 111.001i 1.23760 + 0.183171i
\(607\) 7.56658 + 129.913i 0.0124655 + 0.214025i 0.998789 + 0.0492027i \(0.0156680\pi\)
−0.986323 + 0.164822i \(0.947295\pi\)
\(608\) 199.611 11.6260i 0.328308 0.0191218i
\(609\) −192.127 + 1298.11i −0.315479 + 2.13155i
\(610\) 21.1277 + 70.5715i 0.0346356 + 0.115691i
\(611\) 721.830 + 860.244i 1.18139 + 1.40793i
\(612\) −93.7199 + 78.1644i −0.153137 + 0.127720i
\(613\) −153.693 128.964i −0.250723 0.210381i 0.508761 0.860908i \(-0.330104\pi\)
−0.759483 + 0.650527i \(0.774548\pi\)
\(614\) −745.628 321.633i −1.21438 0.523831i
\(615\) −134.765 + 11.5876i −0.219130 + 0.0188416i
\(616\) −166.061 + 554.681i −0.269579 + 0.900456i
\(617\) 201.025 86.7139i 0.325811 0.140541i −0.226891 0.973920i \(-0.572856\pi\)
0.552702 + 0.833379i \(0.313597\pi\)
\(618\) −138.869 + 74.6100i −0.224707 + 0.120728i
\(619\) −559.970 368.298i −0.904636 0.594989i 0.00969605 0.999953i \(-0.496914\pi\)
−0.914333 + 0.404964i \(0.867284\pi\)
\(620\) 15.0350 8.68047i 0.0242500 0.0140008i
\(621\) −1.79185 + 0.584856i −0.00288542 + 0.000941797i
\(622\) −182.352 + 315.844i −0.293171 + 0.507787i
\(623\) −513.323 1022.11i −0.823954 1.64063i
\(624\) −349.732 + 275.684i −0.560467 + 0.441801i
\(625\) 318.024 427.180i 0.508838 0.683488i
\(626\) 712.679 672.378i 1.13846 1.07409i
\(627\) −125.924 + 179.268i −0.200836 + 0.285914i
\(628\) 225.393 26.3447i 0.358907 0.0419502i
\(629\) −252.125 692.709i −0.400835 1.10129i
\(630\) 178.691 76.4476i 0.283637 0.121345i
\(631\) −520.918 189.599i −0.825544 0.300474i −0.105515 0.994418i \(-0.533649\pi\)
−0.720029 + 0.693944i \(0.755871\pi\)
\(632\) 50.4299 212.781i 0.0797942 0.336678i
\(633\) −230.635 124.802i −0.364352 0.197160i
\(634\) 503.260 330.999i 0.793785 0.522081i
\(635\) 60.8276 121.118i 0.0957916 0.190737i
\(636\) 16.6371 + 81.1857i 0.0261589 + 0.127650i
\(637\) 732.273 776.164i 1.14957 1.21847i
\(638\) −392.147 + 69.1460i −0.614650 + 0.108379i
\(639\) −1048.86 251.897i −1.64141 0.394204i
\(640\) 10.9993 62.3800i 0.0171864 0.0974687i
\(641\) −237.150 + 176.552i −0.369969 + 0.275432i −0.766046 0.642785i \(-0.777779\pi\)
0.396077 + 0.918217i \(0.370371\pi\)
\(642\) −740.158 + 737.951i −1.15289 + 1.14946i
\(643\) −138.650 + 32.8606i −0.215629 + 0.0511051i −0.337011 0.941501i \(-0.609416\pi\)
0.121381 + 0.992606i \(0.461268\pi\)
\(644\) 0.0952931 0.815285i 0.000147971 0.00126597i
\(645\) 58.1713 + 176.433i 0.0901880 + 0.273540i
\(646\) −15.8816 + 272.677i −0.0245845 + 0.422100i
\(647\) 20.2309i 0.0312688i 0.999878 + 0.0156344i \(0.00497679\pi\)
−0.999878 + 0.0156344i \(0.995023\pi\)
\(648\) 382.525 + 589.239i 0.590316 + 0.909319i
\(649\) 68.2211 0.105117
\(650\) 564.423 + 32.8739i 0.868343 + 0.0505752i
\(651\) 371.939 + 331.994i 0.571335 + 0.509976i
\(652\) −36.6512 4.28391i −0.0562135 0.00657041i
\(653\) −6.75689 28.5096i −0.0103475 0.0436594i 0.967626 0.252388i \(-0.0812158\pi\)
−0.977974 + 0.208728i \(0.933068\pi\)
\(654\) −902.236 + 240.310i −1.37957 + 0.367446i
\(655\) −37.7533 50.7115i −0.0576387 0.0774222i
\(656\) −424.881 74.9181i −0.647685 0.114204i
\(657\) −139.399 + 210.572i −0.212174 + 0.320506i
\(658\) −271.457 1539.51i −0.412549 2.33968i
\(659\) 343.848 + 324.404i 0.521772 + 0.492267i 0.901469 0.432844i \(-0.142490\pi\)
−0.379696 + 0.925111i \(0.623972\pi\)
\(660\) −13.8858 15.6504i −0.0210391 0.0237127i
\(661\) 645.004 + 323.933i 0.975800 + 0.490065i 0.863905 0.503655i \(-0.168012\pi\)
0.111895 + 0.993720i \(0.464308\pi\)
\(662\) −369.812 562.272i −0.558629 0.849353i
\(663\) 281.817 + 458.426i 0.425064 + 0.691442i
\(664\) −488.624 115.806i −0.735879 0.174406i
\(665\) −52.7809 + 145.014i −0.0793697 + 0.218066i
\(666\) −857.483 + 200.523i −1.28751 + 0.301086i
\(667\) 2.55621 0.930386i 0.00383241 0.00139488i
\(668\) −12.3378 105.556i −0.0184697 0.158018i
\(669\) 29.7857 334.693i 0.0445227 0.500289i
\(670\) −126.516 134.099i −0.188830 0.200148i
\(671\) 182.668 + 135.991i 0.272233 + 0.202670i
\(672\) −542.708 + 78.6672i −0.807602 + 0.117064i
\(673\) −436.732 + 219.335i −0.648933 + 0.325906i −0.742637 0.669694i \(-0.766425\pi\)
0.0937047 + 0.995600i \(0.470129\pi\)
\(674\) −402.986 232.664i −0.597902 0.345199i
\(675\) 95.7659 633.964i 0.141875 0.939206i
\(676\) −12.0408 20.8553i −0.0178119 0.0308511i
\(677\) 61.9674 94.2169i 0.0915324 0.139168i −0.786819 0.617184i \(-0.788273\pi\)
0.878351 + 0.478016i \(0.158644\pi\)
\(678\) −72.6932 + 117.461i −0.107217 + 0.173246i
\(679\) −561.176 1300.95i −0.826474 1.91598i
\(680\) −120.422 36.0519i −0.177091 0.0530176i
\(681\) 170.049 + 79.6046i 0.249705 + 0.116894i
\(682\) −59.9207 + 138.912i −0.0878602 + 0.203683i
\(683\) −813.573 + 969.579i −1.19118 + 1.41959i −0.307463 + 0.951560i \(0.599480\pi\)
−0.883713 + 0.468029i \(0.844964\pi\)
\(684\) −113.935 20.4410i −0.166572 0.0298845i
\(685\) −26.1489 + 21.9415i −0.0381735 + 0.0320314i
\(686\) −517.609 + 154.962i −0.754532 + 0.225892i
\(687\) −175.216 442.973i −0.255045 0.644793i
\(688\) 34.4539 + 591.551i 0.0500784 + 0.859813i
\(689\) 364.809 21.2477i 0.529476 0.0308385i
\(690\) −0.315666 0.250364i −0.000457487 0.000362846i
\(691\) 27.9940 + 93.5065i 0.0405123 + 0.135321i 0.975853 0.218427i \(-0.0700925\pi\)
−0.935341 + 0.353747i \(0.884907\pi\)
\(692\) −109.519 130.520i −0.158264 0.188612i
\(693\) 301.970 519.438i 0.435743 0.749549i
\(694\) 402.387 + 337.643i 0.579809 + 0.486518i
\(695\) −0.963460 0.415596i −0.00138627 0.000597980i
\(696\) −580.292 831.383i −0.833753 1.19452i
\(697\) −149.522 + 499.438i −0.214522 + 0.716554i
\(698\) 91.8143 39.6048i 0.131539 0.0567405i
\(699\) 12.1703 397.824i 0.0174110 0.569133i
\(700\) 233.279 + 153.430i 0.333256 + 0.219186i
\(701\) −62.2295 + 35.9282i −0.0887724 + 0.0512528i −0.543729 0.839261i \(-0.682988\pi\)
0.454957 + 0.890514i \(0.349655\pi\)
\(702\) 583.823 269.063i 0.831657 0.383280i
\(703\) 349.607 605.537i 0.497308 0.861362i
\(704\) −189.057 376.444i −0.268547 0.534721i
\(705\) 252.827 + 100.879i 0.358620 + 0.143091i
\(706\) −480.317 + 645.177i −0.680335 + 0.913849i
\(707\) 1200.88 1132.98i 1.69856 1.60251i
\(708\) 15.1851 + 32.6920i 0.0214479 + 0.0461751i
\(709\) 803.813 93.9523i 1.13373 0.132514i 0.471535 0.881847i \(-0.343700\pi\)
0.662193 + 0.749334i \(0.269626\pi\)
\(710\) −78.8602 216.667i −0.111071 0.305164i
\(711\) −102.446 + 202.477i −0.144088 + 0.284778i
\(712\) 830.406 + 302.243i 1.16630 + 0.424499i
\(713\) 0.238340 1.00564i 0.000334278 0.00141043i
\(714\) −20.6691 748.824i −0.0289483 1.04877i
\(715\) −77.0800 + 50.6963i −0.107804 + 0.0709039i
\(716\) −38.0969 + 75.8572i −0.0532080 + 0.105946i
\(717\) 1292.65 + 430.480i 1.80285 + 0.600390i
\(718\) 370.671 392.888i 0.516255 0.547198i
\(719\) 701.905 123.765i 0.976224 0.172135i 0.337294 0.941399i \(-0.390488\pi\)
0.638930 + 0.769265i \(0.279377\pi\)
\(720\) −43.0517 + 98.9908i −0.0597940 + 0.137487i
\(721\) −59.6114 + 338.073i −0.0826788 + 0.468895i
\(722\) 289.750 215.711i 0.401316 0.298769i
\(723\) 403.843 + 108.856i 0.558566 + 0.150562i
\(724\) −207.901 + 49.2734i −0.287156 + 0.0680572i
\(725\) −107.423 + 919.063i −0.148170 + 1.26767i
\(726\) −432.170 89.9092i −0.595275 0.123842i
\(727\) 59.5368 1022.21i 0.0818938 1.40606i −0.667831 0.744313i \(-0.732777\pi\)
0.749725 0.661749i \(-0.230186\pi\)
\(728\) 1349.01i 1.85304i
\(729\) −243.183 687.243i −0.333585 0.942720i
\(730\) −53.9795 −0.0739445
\(731\) 714.820 + 41.6335i 0.977866 + 0.0569542i
\(732\) −24.5084 + 117.806i −0.0334814 + 0.160937i
\(733\) −1126.51 131.671i −1.53685 0.179633i −0.694870 0.719135i \(-0.744538\pi\)
−0.841984 + 0.539502i \(0.818612\pi\)
\(734\) −134.179 566.144i −0.182805 0.771313i
\(735\) 67.3196 249.747i 0.0915913 0.339792i
\(736\) 0.678837 + 0.911836i 0.000922333 + 0.00123891i
\(737\) −561.271 98.9672i −0.761562 0.134284i
\(738\) 571.118 + 248.383i 0.773873 + 0.336562i
\(739\) 93.2322 + 528.746i 0.126160 + 0.715489i 0.980612 + 0.195959i \(0.0627819\pi\)
−0.854452 + 0.519530i \(0.826107\pi\)
\(740\) 48.5722 + 45.8255i 0.0656381 + 0.0619264i
\(741\) −161.273 + 484.271i −0.217642 + 0.653537i
\(742\) −454.594 228.306i −0.612660 0.307690i
\(743\) −610.910 928.844i −0.822221 1.25013i −0.965489 0.260442i \(-0.916132\pi\)
0.143269 0.989684i \(-0.454239\pi\)
\(744\) −385.048 + 10.6281i −0.517537 + 0.0142851i
\(745\) 25.5992 + 6.06713i 0.0343614 + 0.00814380i
\(746\) −273.465 + 751.338i −0.366575 + 1.00716i
\(747\) 464.963 + 235.255i 0.622441 + 0.314933i
\(748\) −75.7779 + 27.5809i −0.101307 + 0.0368728i
\(749\) 264.230 + 2260.63i 0.352777 + 3.01820i
\(750\) 255.151 118.515i 0.340201 0.158020i
\(751\) 322.772 + 342.119i 0.429790 + 0.455551i 0.905685 0.423951i \(-0.139357\pi\)
−0.475895 + 0.879502i \(0.657876\pi\)
\(752\) 696.439 + 518.480i 0.926116 + 0.689468i
\(753\) 39.0608 97.8955i 0.0518736 0.130007i
\(754\) −829.067 + 416.373i −1.09956 + 0.552219i
\(755\) −175.298 101.209i −0.232183 0.134051i
\(756\) 316.132 + 29.0860i 0.418164 + 0.0384736i
\(757\) −199.380 345.336i −0.263381 0.456190i 0.703757 0.710441i \(-0.251504\pi\)
−0.967138 + 0.254251i \(0.918171\pi\)
\(758\) 291.635 443.409i 0.384743 0.584973i
\(759\) −1.24493 0.0380850i −0.00164022 5.01779e-5i
\(760\) −47.2251 109.480i −0.0621383 0.144053i
\(761\) 22.9820 + 6.88036i 0.0301997 + 0.00904121i 0.301867 0.953350i \(-0.402390\pi\)
−0.271668 + 0.962391i \(0.587575\pi\)
\(762\) −511.720 + 357.173i −0.671549 + 0.468730i
\(763\) −805.324 + 1866.95i −1.05547 + 2.44686i
\(764\) 222.560 265.237i 0.291309 0.347169i
\(765\) 112.770 + 65.5580i 0.147412 + 0.0856968i
\(766\) −47.9398 + 40.2262i −0.0625845 + 0.0525147i
\(767\) 152.269 45.5865i 0.198526 0.0594348i
\(768\) 346.959 437.457i 0.451770 0.569605i
\(769\) 32.8130 + 563.378i 0.0426697 + 0.732611i 0.950011 + 0.312216i \(0.101071\pi\)
−0.907341 + 0.420395i \(0.861892\pi\)
\(770\) 128.212 7.46753i 0.166510 0.00969809i
\(771\) 1117.30 441.946i 1.44916 0.573211i
\(772\) 30.5035 + 101.889i 0.0395123 + 0.131980i
\(773\) 374.248 + 446.011i 0.484149 + 0.576987i 0.951719 0.306969i \(-0.0993149\pi\)
−0.467570 + 0.883956i \(0.654870\pi\)
\(774\) 151.049 841.928i 0.195154 1.08776i
\(775\) 269.304 + 225.973i 0.347489 + 0.291578i
\(776\) 1005.14 + 433.575i 1.29528 + 0.558731i
\(777\) −813.034 + 1736.78i −1.04638 + 2.23524i
\(778\) 145.485 485.952i 0.186998 0.624617i
\(779\) −454.058 + 195.862i −0.582873 + 0.251427i
\(780\) −41.4510 25.6529i −0.0531423 0.0328883i
\(781\) −595.524 391.682i −0.762515 0.501514i
\(782\) −1.34484 + 0.776441i −0.00171974 + 0.000992892i
\(783\) 384.055 + 979.493i 0.490491 + 1.25095i
\(784\) 412.516 714.498i 0.526168 0.911350i
\(785\) −108.859 216.756i −0.138674 0.276122i
\(786\) 41.7584 + 288.082i 0.0531277 + 0.366517i
\(787\) −86.6592 + 116.404i −0.110113 + 0.147908i −0.853763 0.520661i \(-0.825686\pi\)
0.743650 + 0.668569i \(0.233093\pi\)
\(788\) 161.768 152.621i 0.205290 0.193681i
\(789\) 825.566 + 73.4704i 1.04634 + 0.0931184i
\(790\) −48.1765 + 5.63103i −0.0609830 + 0.00712789i
\(791\) 102.882 + 282.667i 0.130066 + 0.357353i
\(792\) 105.706 + 452.021i 0.133467 + 0.570733i
\(793\) 498.587 + 181.471i 0.628735 + 0.228841i
\(794\) −205.345 + 866.421i −0.258622 + 1.09121i
\(795\) 75.4614 46.3898i 0.0949200 0.0583520i
\(796\) −7.63550 + 5.02195i −0.00959234 + 0.00630898i
\(797\) −381.155 + 758.942i −0.478237 + 0.952249i 0.517112 + 0.855918i \(0.327007\pi\)
−0.995349 + 0.0963311i \(0.969289\pi\)
\(798\) 531.499 471.573i 0.666038 0.590943i
\(799\) 719.985 763.140i 0.901108 0.955119i
\(800\) −380.809 + 67.1469i −0.476011 + 0.0839336i
\(801\) −764.646 506.195i −0.954614 0.631953i
\(802\) 196.343 1113.52i 0.244817 1.38843i
\(803\) −133.851 + 99.6486i −0.166689 + 0.124095i
\(804\) −77.5058 290.993i −0.0964002 0.361932i
\(805\) −0.853715 + 0.202334i −0.00106052 + 0.000251347i
\(806\) −40.9198 + 350.091i −0.0507690 + 0.434356i
\(807\) 619.190 693.688i 0.767273 0.859589i
\(808\) −74.1686 + 1273.43i −0.0917929 + 1.57602i
\(809\) 1093.65i 1.35186i −0.736966 0.675930i \(-0.763742\pi\)
0.736966 0.675930i \(-0.236258\pi\)
\(810\) 93.7977 124.433i 0.115800 0.153621i
\(811\) 727.194 0.896664 0.448332 0.893867i \(-0.352018\pi\)
0.448332 + 0.893867i \(0.352018\pi\)
\(812\) −457.395 26.6402i −0.563294 0.0328082i
\(813\) −117.505 + 38.7421i −0.144532 + 0.0476533i
\(814\) −577.969 67.5549i −0.710036 0.0829913i
\(815\) 9.09595 + 38.3788i 0.0111607 + 0.0470906i
\(816\) 293.759 + 294.638i 0.359998 + 0.361075i
\(817\) 405.572 + 544.777i 0.496416 + 0.666802i
\(818\) 585.103 + 103.169i 0.715285 + 0.126124i
\(819\) 326.900 1361.17i 0.399146 1.66199i
\(820\) −8.20081 46.5091i −0.0100010 0.0567184i
\(821\) −692.731 653.558i −0.843765 0.796052i 0.137137 0.990552i \(-0.456210\pi\)
−0.980902 + 0.194500i \(0.937691\pi\)
\(822\) 153.969 31.5522i 0.187310 0.0383847i
\(823\) 585.200 + 293.899i 0.711058 + 0.357107i 0.767280 0.641312i \(-0.221609\pi\)
−0.0562228 + 0.998418i \(0.517906\pi\)
\(824\) −145.747 221.597i −0.176877 0.268929i
\(825\) 201.631 372.615i 0.244401 0.451654i
\(826\) −215.302 51.0276i −0.260657 0.0617768i
\(827\) −245.482 + 674.457i −0.296835 + 0.815546i 0.698190 + 0.715913i \(0.253989\pi\)
−0.995024 + 0.0996335i \(0.968233\pi\)
\(828\) −0.258854 0.605056i −0.000312626 0.000730744i
\(829\) −732.857 + 266.738i −0.884026 + 0.321759i −0.743833 0.668365i \(-0.766994\pi\)
−0.140192 + 0.990124i \(0.544772\pi\)
\(830\) 12.9309 + 110.631i 0.0155795 + 0.133291i
\(831\) 1103.78 + 775.336i 1.32826 + 0.933015i
\(832\) −673.522 713.892i −0.809522 0.858043i
\(833\) −799.680 595.340i −0.960000 0.714693i
\(834\) 2.99082 + 3.79414i 0.00358611 + 0.00454933i
\(835\) −101.511 + 50.9808i −0.121570 + 0.0610549i
\(836\) −66.2419 38.2448i −0.0792367 0.0457473i
\(837\) 391.092 + 82.5830i 0.467255 + 0.0986655i
\(838\) 367.897 + 637.216i 0.439018 + 0.760401i
\(839\) −130.018 + 197.683i −0.154968 + 0.235618i −0.904624 0.426210i \(-0.859849\pi\)
0.749656 + 0.661828i \(0.230219\pi\)
\(840\) 154.766 + 288.060i 0.184245 + 0.342928i
\(841\) −268.299 621.988i −0.319024 0.739581i
\(842\) −17.2784 5.17281i −0.0205207 0.00614348i
\(843\) −75.9256 883.023i −0.0900660 1.04748i
\(844\) 36.2647 84.0711i 0.0429677 0.0996103i
\(845\) −16.5454 + 19.7181i −0.0195804 + 0.0233350i
\(846\) −802.760 962.517i −0.948888 1.13773i
\(847\) −736.366 + 617.885i −0.869382 + 0.729498i
\(848\) 270.667 81.0325i 0.319183 0.0955572i
\(849\) −268.456 39.7327i −0.316203 0.0467995i
\(850\) −30.7135 527.331i −0.0361336 0.620390i
\(851\) 3.96854 0.231141i 0.00466338 0.000271611i
\(852\) 55.1409 372.562i 0.0647193 0.437280i
\(853\) 165.560 + 553.010i 0.194092 + 0.648312i 0.998526 + 0.0542705i \(0.0172833\pi\)
−0.804434 + 0.594042i \(0.797531\pi\)
\(854\) −474.774 565.813i −0.555941 0.662545i
\(855\) 21.1207 + 121.910i 0.0247026 + 0.142585i
\(856\) −1347.09 1130.34i −1.57370 1.32049i
\(857\) 418.773 + 180.641i 0.488650 + 0.210783i 0.626126 0.779722i \(-0.284640\pi\)
−0.137476 + 0.990505i \(0.543899\pi\)
\(858\) 423.222 36.3902i 0.493265 0.0424128i
\(859\) 446.091 1490.05i 0.519314 1.73463i −0.147169 0.989111i \(-0.547016\pi\)
0.666484 0.745520i \(-0.267799\pi\)
\(860\) −59.5584 + 25.6910i −0.0692539 + 0.0298732i
\(861\) 1194.70 641.875i 1.38757 0.745500i
\(862\) 413.399 + 271.897i 0.479582 + 0.315426i
\(863\) −1058.74 + 611.265i −1.22682 + 0.708303i −0.966363 0.257183i \(-0.917206\pi\)
−0.260454 + 0.965486i \(0.583872\pi\)
\(864\) −346.096 + 271.146i −0.400575 + 0.313826i
\(865\) −91.0576 + 157.716i −0.105269 + 0.182331i
\(866\) 306.609 + 610.508i 0.354052 + 0.704975i
\(867\) −286.053 + 225.488i −0.329935 + 0.260079i
\(868\) −103.947 + 139.626i −0.119755 + 0.160859i
\(869\) −109.067 + 102.899i −0.125508 + 0.118411i
\(870\) −129.265 + 184.025i −0.148581 + 0.211523i
\(871\) −1318.89 + 154.156i −1.51422 + 0.176987i
\(872\) −537.285 1476.18i −0.616153 1.69287i
\(873\) −909.130 681.053i −1.04139 0.780129i
\(874\) −1.38411 0.503774i −0.00158365 0.000576401i
\(875\) 141.284 596.124i 0.161467 0.681284i
\(876\) −77.5458 41.9619i −0.0885226 0.0479018i
\(877\) 9.10780 5.99030i 0.0103852 0.00683044i −0.544306 0.838887i \(-0.683207\pi\)
0.554691 + 0.832056i \(0.312836\pi\)
\(878\) 26.4965 52.7589i 0.0301783 0.0600898i
\(879\) 250.457 + 1222.18i 0.284934 + 1.39042i
\(880\) −48.9501 + 51.8840i −0.0556251 + 0.0589591i
\(881\) 594.752 104.871i 0.675087 0.119036i 0.174414 0.984672i \(-0.444197\pi\)
0.500673 + 0.865636i \(0.333086\pi\)
\(882\) −819.871 + 863.828i −0.929559 + 0.979397i
\(883\) 6.36087 36.0743i 0.00720370 0.0408542i −0.980994 0.194038i \(-0.937842\pi\)
0.988198 + 0.153184i \(0.0489526\pi\)
\(884\) −150.706 + 112.197i −0.170482 + 0.126919i
\(885\) 27.2848 27.2034i 0.0308303 0.0307383i
\(886\) −305.245 + 72.3443i −0.344520 + 0.0816527i
\(887\) −73.8172 + 631.547i −0.0832212 + 0.712003i 0.885636 + 0.464381i \(0.153723\pi\)
−0.968857 + 0.247622i \(0.920351\pi\)
\(888\) −463.935 1407.11i −0.522449 1.58459i
\(889\) −79.0152 + 1356.64i −0.0888810 + 1.52603i
\(890\) 196.014i 0.220241i
\(891\) 2.87816 481.708i 0.00323026 0.540638i
\(892\) 117.319 0.131524
\(893\) 993.475 + 57.8633i 1.11251 + 0.0647966i
\(894\) −90.3685 80.6633i −0.101083 0.0902274i
\(895\) 90.1188 + 10.5334i 0.100691 + 0.0117691i
\(896\) 146.465 + 617.984i 0.163465 + 0.689714i
\(897\) −2.80413 + 0.746878i −0.00312613 + 0.000832640i
\(898\) 131.292 + 176.356i 0.146205 + 0.196388i
\(899\) −568.108 100.173i −0.631933 0.111427i
\(900\) 223.440 + 13.6838i 0.248266 + 0.0152042i
\(901\) −59.2857 336.226i −0.0657999 0.373170i
\(902\) 299.340 + 282.413i 0.331863 + 0.313096i
\(903\) −1236.22 1393.32i −1.36902 1.54299i
\(904\) −207.689 104.305i −0.229744 0.115382i
\(905\) 125.494 + 190.804i 0.138667 + 0.210833i
\(906\) 488.089 + 793.965i 0.538730 + 0.876341i
\(907\) −685.916 162.565i −0.756246 0.179234i −0.165632 0.986188i \(-0.552966\pi\)
−0.590614 + 0.806954i \(0.701115\pi\)
\(908\) −22.4214 + 61.6022i −0.0246931 + 0.0678439i
\(909\) 383.421 1266.93i 0.421805 1.39376i
\(910\) 281.180 102.341i 0.308989 0.112463i
\(911\) −41.4511 354.637i −0.0455007 0.389283i −0.996730 0.0807997i \(-0.974253\pi\)
0.951230 0.308484i \(-0.0998215\pi\)
\(912\) −34.9823 + 393.086i −0.0383578 + 0.431016i
\(913\) 236.295 + 250.458i 0.258812 + 0.274324i
\(914\) −200.505 149.270i −0.219371 0.163316i
\(915\) 127.284 18.4503i 0.139109 0.0201642i
\(916\) 148.631 74.6454i 0.162261 0.0814906i
\(917\) 548.968 + 316.947i 0.598656 + 0.345634i
\(918\) −313.005 512.585i −0.340964 0.558371i
\(919\) −280.135 485.208i −0.304826 0.527973i 0.672397 0.740191i \(-0.265265\pi\)
−0.977222 + 0.212217i \(0.931932\pi\)
\(920\) 0.372495 0.566351i 0.000404886 0.000615599i
\(921\) −746.087 + 1205.56i −0.810083 + 1.30897i
\(922\) −132.113 306.273i −0.143290 0.332184i
\(923\) −1590.94 476.296i −1.72366 0.516030i
\(924\) 189.992 + 88.9406i 0.205619 + 0.0962561i
\(925\) −535.585 + 1241.63i −0.579011 + 1.34230i
\(926\) −84.1503 + 100.286i −0.0908750 + 0.108301i
\(927\) 93.3613 + 258.912i 0.100713 + 0.279301i
\(928\) 486.072 407.863i 0.523785 0.439507i
\(929\) −166.182 + 49.7517i −0.178883 + 0.0535540i −0.374992 0.927028i \(-0.622355\pi\)
0.196109 + 0.980582i \(0.437169\pi\)
\(930\) 31.4265 + 79.4508i 0.0337919 + 0.0854310i
\(931\) −54.9834 944.029i −0.0590585 1.01399i
\(932\) 138.729 8.08006i 0.148851 0.00866959i
\(933\) 498.880 + 395.676i 0.534705 + 0.424090i
\(934\) −15.0440 50.2505i −0.0161071 0.0538014i
\(935\) 55.4049 + 66.0290i 0.0592566 + 0.0706192i
\(936\) 537.983 + 938.276i 0.574768 + 1.00243i
\(937\) 282.211 + 236.803i 0.301186 + 0.252725i 0.780838 0.624734i \(-0.214793\pi\)
−0.479652 + 0.877459i \(0.659237\pi\)
\(938\) 1697.32 + 732.152i 1.80951 + 0.780546i
\(939\) −979.088 1402.74i −1.04269 1.49386i
\(940\) −27.2581 + 91.0486i −0.0289980 + 0.0968602i
\(941\) 1015.82 438.180i 1.07951 0.465653i 0.219330 0.975651i \(-0.429613\pi\)
0.860176 + 0.509997i \(0.170354\pi\)
\(942\) −34.1494 + 1116.28i −0.0362521 + 1.18501i
\(943\) −2.34889 1.54489i −0.00249086 0.00163827i
\(944\) 106.428 61.4464i 0.112742 0.0650916i
\(945\) −86.3557 328.159i −0.0913817 0.347258i
\(946\) 282.611 489.496i 0.298743 0.517438i
\(947\) 381.077 + 758.787i 0.402404 + 0.801253i 1.00000 0.000544655i \(-0.000173369\pi\)
−0.597595 + 0.801798i \(0.703877\pi\)
\(948\) −73.5868 29.3615i −0.0776232 0.0309721i
\(949\) −232.169 + 311.858i −0.244646 + 0.328617i
\(950\) 364.437 343.828i 0.383618 0.361925i
\(951\) −443.025 953.788i −0.465852 1.00293i
\(952\) 1251.84 146.319i 1.31496 0.153696i
\(953\) 324.618 + 891.882i 0.340628 + 0.935867i 0.985213 + 0.171335i \(0.0548079\pi\)
−0.644585 + 0.764533i \(0.722970\pi\)
\(954\) −407.230 + 22.4980i −0.426866 + 0.0235828i
\(955\) −347.768 126.577i −0.364155 0.132542i
\(956\) −109.702 + 462.871i −0.114751 + 0.484174i
\(957\) 19.1821 + 694.950i 0.0200440 + 0.726176i
\(958\) −920.947 + 605.716i −0.961322 + 0.632272i
\(959\) 153.604 305.850i 0.160171 0.318926i
\(960\) −225.721 75.1702i −0.235126 0.0783023i
\(961\) 509.076 539.589i 0.529736 0.561487i
\(962\) −1335.17 + 235.426i −1.38791 + 0.244726i
\(963\) 1085.31 + 1466.96i 1.12701 + 1.52332i
\(964\) −25.3584 + 143.815i −0.0263054 + 0.149186i
\(965\) 91.1865 67.8858i 0.0944938 0.0703480i
\(966\) 3.90045 + 1.05137i 0.00403774 + 0.00108838i
\(967\) 250.636 59.4019i 0.259190 0.0614290i −0.0989666 0.995091i \(-0.531554\pi\)
0.358156 + 0.933662i \(0.383406\pi\)
\(968\) 86.2206 737.665i 0.0890709 0.762050i
\(969\) 466.880 + 97.1302i 0.481816 + 0.100238i
\(970\) 14.1181 242.398i 0.0145547 0.249895i
\(971\) 485.749i 0.500257i −0.968213 0.250128i \(-0.919527\pi\)
0.968213 0.250128i \(-0.0804728\pi\)
\(972\) 231.478 105.843i 0.238146 0.108892i
\(973\) 10.5206 0.0108125
\(974\) −938.088 54.6374i −0.963129 0.0560959i
\(975\) 201.053 966.410i 0.206208 0.991189i
\(976\) 407.458 + 47.6250i 0.417478 + 0.0487961i
\(977\) −265.268 1119.25i −0.271513 1.14560i −0.922341 0.386377i \(-0.873726\pi\)
0.650828 0.759225i \(-0.274422\pi\)
\(978\) 47.2644 175.345i 0.0483277 0.179290i
\(979\) −361.851 486.051i −0.369613 0.496477i
\(980\) 88.9390 + 15.6823i 0.0907541 + 0.0160024i
\(981\) 184.410 + 1619.68i 0.187982 + 1.65105i
\(982\) −269.871 1530.51i −0.274817 1.55857i
\(983\) 113.527 + 107.107i 0.115490 + 0.108959i 0.741821 0.670598i \(-0.233963\pi\)
−0.626331 + 0.779557i \(0.715444\pi\)
\(984\) −331.077 + 994.157i −0.336460 + 1.01032i
\(985\) −212.432 106.687i −0.215667 0.108312i
\(986\) 476.304 + 724.186i 0.483067 + 0.734468i
\(987\) −2728.28 + 75.3062i −2.76421 + 0.0762981i
\(988\) −173.408 41.0984i −0.175514 0.0415976i
\(989\) −1.32064 + 3.62843i −0.00133533 + 0.00366879i
\(990\) 86.1973 56.3247i 0.0870680 0.0568936i
\(991\) 361.652 131.630i 0.364936 0.132826i −0.153042 0.988220i \(-0.548907\pi\)
0.517978 + 0.855394i \(0.326685\pi\)
\(992\) −27.9865 239.440i −0.0282122 0.241371i
\(993\) −1065.63 + 494.974i −1.07314 + 0.498464i
\(994\) 1586.48 + 1681.57i 1.59605 + 1.69172i
\(995\) 7.83543 + 5.83326i 0.00787481 + 0.00586258i
\(996\) −67.4250 + 168.983i −0.0676958 + 0.169661i
\(997\) 1547.87 777.372i 1.55253 0.779711i 0.553930 0.832563i \(-0.313128\pi\)
0.998602 + 0.0528526i \(0.0168313\pi\)
\(998\) −76.5886 44.2184i −0.0767420 0.0443070i
\(999\) 127.135 + 1532.21i 0.127263 + 1.53375i
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 81.3.h.a.2.6 306
3.2 odd 2 243.3.h.a.8.12 306
81.40 even 27 243.3.h.a.152.12 306
81.41 odd 54 inner 81.3.h.a.41.6 yes 306
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
81.3.h.a.2.6 306 1.1 even 1 trivial
81.3.h.a.41.6 yes 306 81.41 odd 54 inner
243.3.h.a.8.12 306 3.2 odd 2
243.3.h.a.152.12 306 81.40 even 27