Properties

Label 450.2.w.a.23.14
Level $450$
Weight $2$
Character 450.23
Analytic conductor $3.593$
Analytic rank $0$
Dimension $480$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [450,2,Mod(23,450)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(450, base_ring=CyclotomicField(60))
 
chi = DirichletCharacter(H, H._module([50, 33]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("450.23");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 450.w (of order \(60\), degree \(16\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.59326809096\)
Analytic rank: \(0\)
Dimension: \(480\)
Relative dimension: \(30\) over \(\Q(\zeta_{60})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label 23.14
Character \(\chi\) \(=\) 450.23
Dual form 450.2.w.a.137.14

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.358368 - 0.933580i) q^{2} +(1.56679 + 0.738354i) q^{3} +(-0.743145 + 0.669131i) q^{4} +(1.74716 - 1.39550i) q^{5} +(0.127826 - 1.72733i) q^{6} +(-0.469048 - 0.125681i) q^{7} +(0.891007 + 0.453990i) q^{8} +(1.90967 + 2.31369i) q^{9} +O(q^{10})\) \(q+(-0.358368 - 0.933580i) q^{2} +(1.56679 + 0.738354i) q^{3} +(-0.743145 + 0.669131i) q^{4} +(1.74716 - 1.39550i) q^{5} +(0.127826 - 1.72733i) q^{6} +(-0.469048 - 0.125681i) q^{7} +(0.891007 + 0.453990i) q^{8} +(1.90967 + 2.31369i) q^{9} +(-1.92894 - 1.13101i) q^{10} +(1.23109 - 2.76508i) q^{11} +(-1.65841 + 0.499683i) q^{12} +(0.754169 + 0.289498i) q^{13} +(0.0507584 + 0.482934i) q^{14} +(3.76781 - 0.896434i) q^{15} +(0.104528 - 0.994522i) q^{16} +(0.0248660 - 0.0488022i) q^{17} +(1.47566 - 2.61198i) q^{18} +(-1.73522 + 0.563806i) q^{19} +(-0.364621 + 2.20614i) q^{20} +(-0.642103 - 0.543240i) q^{21} +(-3.02261 - 0.158408i) q^{22} +(2.49745 + 2.02239i) q^{23} +(1.06081 + 1.36919i) q^{24} +(1.10515 - 4.87634i) q^{25} -0.807824i q^{26} +(1.28372 + 5.03508i) q^{27} +(0.432668 - 0.220455i) q^{28} +(2.11678 - 0.449935i) q^{29} +(-2.18716 - 3.19630i) q^{30} +(-3.61449 - 0.768283i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(3.97048 - 3.42332i) q^{33} +(-0.0544720 - 0.00572523i) q^{34} +(-0.994891 + 0.434972i) q^{35} +(-2.96732 - 0.441594i) q^{36} +(-0.0503530 + 0.00797513i) q^{37} +(1.14821 + 1.41792i) q^{38} +(0.967872 + 1.01043i) q^{39} +(2.19028 - 0.450206i) q^{40} +(3.49062 + 7.84007i) q^{41} +(-0.277049 + 0.794135i) q^{42} +(1.22798 - 4.58287i) q^{43} +(0.935320 + 2.87862i) q^{44} +(6.56526 + 1.37746i) q^{45} +(0.993061 - 3.05633i) q^{46} +(-2.23689 - 1.45266i) q^{47} +(0.898084 - 1.48103i) q^{48} +(-5.85797 - 3.38210i) q^{49} +(-4.94850 + 0.715776i) q^{50} +(0.0749931 - 0.0581030i) q^{51} +(-0.754169 + 0.289498i) q^{52} +(2.76573 + 5.42805i) q^{53} +(4.24061 - 3.00287i) q^{54} +(-1.70776 - 6.54904i) q^{55} +(-0.360867 - 0.324926i) q^{56} +(-3.13501 - 0.397839i) q^{57} +(-1.17864 - 1.81494i) q^{58} +(2.73215 - 1.21643i) q^{59} +(-2.20020 + 3.18734i) q^{60} +(-4.80099 - 2.13754i) q^{61} +(0.578063 + 3.64974i) q^{62} +(-0.604937 - 1.32524i) q^{63} +(0.587785 + 0.809017i) q^{64} +(1.72165 - 0.546644i) q^{65} +(-4.61884 - 2.47995i) q^{66} +(-13.6587 + 8.87006i) q^{67} +(0.0141760 + 0.0529057i) q^{68} +(2.41973 + 5.01266i) q^{69} +(0.762619 + 0.772931i) q^{70} +(-15.6202 - 5.07532i) q^{71} +(0.651129 + 2.92849i) q^{72} +(6.79278 + 1.07587i) q^{73} +(0.0254903 + 0.0441505i) q^{74} +(5.33200 - 6.82420i) q^{75} +(0.912258 - 1.58008i) q^{76} +(-0.924960 + 1.14223i) q^{77} +(0.596461 - 1.26569i) q^{78} +(-3.38388 - 15.9199i) q^{79} +(-1.20523 - 1.88346i) q^{80} +(-1.70636 + 8.83676i) q^{81} +(6.06841 - 6.06841i) q^{82} +(0.242423 + 4.62570i) q^{83} +(0.840674 - 0.0259450i) q^{84} +(-0.0246587 - 0.119966i) q^{85} +(-4.71855 + 0.495939i) q^{86} +(3.64876 + 0.857979i) q^{87} +(2.35223 - 1.90480i) q^{88} +(-5.00866 + 3.63900i) q^{89} +(-1.06681 - 6.62283i) q^{90} +(-0.317357 - 0.230573i) q^{91} +(-3.20921 + 0.168187i) q^{92} +(-5.09588 - 3.87251i) q^{93} +(-0.554540 + 2.60891i) q^{94} +(-2.24491 + 3.40656i) q^{95} +(-1.70450 - 0.307680i) q^{96} +(-7.58964 + 11.6870i) q^{97} +(-1.05815 + 6.68092i) q^{98} +(8.74853 - 2.43201i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 480 q - 4 q^{3}+O(q^{10}) \) Copy content Toggle raw display \( 480 q - 4 q^{3} + 4 q^{12} + 8 q^{15} - 60 q^{16} + 8 q^{18} + 12 q^{20} + 24 q^{23} - 48 q^{25} + 8 q^{27} + 24 q^{30} - 16 q^{33} + 24 q^{37} - 36 q^{38} + 40 q^{39} - 44 q^{42} + 12 q^{45} - 48 q^{47} - 8 q^{48} - 48 q^{50} + 24 q^{55} + 28 q^{57} - 12 q^{58} - 60 q^{59} - 24 q^{60} + 20 q^{63} + 24 q^{65} + 12 q^{67} - 144 q^{68} - 140 q^{69} + 16 q^{72} - 168 q^{75} - 432 q^{77} - 76 q^{78} + 40 q^{81} + 48 q^{82} - 60 q^{83} - 60 q^{84} + 24 q^{85} - 44 q^{87} - 52 q^{90} + 24 q^{92} - 72 q^{93} - 60 q^{95} + 36 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{20}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.358368 0.933580i −0.253404 0.660141i
\(3\) 1.56679 + 0.738354i 0.904587 + 0.426289i
\(4\) −0.743145 + 0.669131i −0.371572 + 0.334565i
\(5\) 1.74716 1.39550i 0.781355 0.624087i
\(6\) 0.127826 1.72733i 0.0521847 0.705179i
\(7\) −0.469048 0.125681i −0.177284 0.0475030i 0.169085 0.985601i \(-0.445919\pi\)
−0.346369 + 0.938098i \(0.612585\pi\)
\(8\) 0.891007 + 0.453990i 0.315018 + 0.160510i
\(9\) 1.90967 + 2.31369i 0.636555 + 0.771231i
\(10\) −1.92894 1.13101i −0.609984 0.357658i
\(11\) 1.23109 2.76508i 0.371189 0.833703i −0.627302 0.778776i \(-0.715841\pi\)
0.998490 0.0549270i \(-0.0174926\pi\)
\(12\) −1.65841 + 0.499683i −0.478741 + 0.144246i
\(13\) 0.754169 + 0.289498i 0.209169 + 0.0802924i 0.460697 0.887558i \(-0.347600\pi\)
−0.251528 + 0.967850i \(0.580933\pi\)
\(14\) 0.0507584 + 0.482934i 0.0135658 + 0.129070i
\(15\) 3.76781 0.896434i 0.972845 0.231458i
\(16\) 0.104528 0.994522i 0.0261321 0.248630i
\(17\) 0.0248660 0.0488022i 0.00603088 0.0118363i −0.887971 0.459899i \(-0.847886\pi\)
0.894002 + 0.448062i \(0.147886\pi\)
\(18\) 1.47566 2.61198i 0.347816 0.615650i
\(19\) −1.73522 + 0.563806i −0.398086 + 0.129346i −0.501217 0.865322i \(-0.667114\pi\)
0.103131 + 0.994668i \(0.467114\pi\)
\(20\) −0.364621 + 2.20614i −0.0815318 + 0.493308i
\(21\) −0.642103 0.543240i −0.140118 0.118545i
\(22\) −3.02261 0.158408i −0.644423 0.0337728i
\(23\) 2.49745 + 2.02239i 0.520753 + 0.421698i 0.853324 0.521380i \(-0.174583\pi\)
−0.332571 + 0.943078i \(0.607916\pi\)
\(24\) 1.06081 + 1.36919i 0.216538 + 0.279484i
\(25\) 1.10515 4.87634i 0.221030 0.975267i
\(26\) 0.807824i 0.158427i
\(27\) 1.28372 + 5.03508i 0.247052 + 0.969002i
\(28\) 0.432668 0.220455i 0.0817665 0.0416621i
\(29\) 2.11678 0.449935i 0.393076 0.0835509i −0.00713356 0.999975i \(-0.502271\pi\)
0.400209 + 0.916424i \(0.368937\pi\)
\(30\) −2.18716 3.19630i −0.399318 0.583562i
\(31\) −3.61449 0.768283i −0.649181 0.137988i −0.128460 0.991715i \(-0.541004\pi\)
−0.520721 + 0.853727i \(0.674337\pi\)
\(32\) −0.965926 + 0.258819i −0.170753 + 0.0457532i
\(33\) 3.97048 3.42332i 0.691171 0.595923i
\(34\) −0.0544720 0.00572523i −0.00934186 0.000981870i
\(35\) −0.994891 + 0.434972i −0.168167 + 0.0735237i
\(36\) −2.96732 0.441594i −0.494554 0.0735990i
\(37\) −0.0503530 + 0.00797513i −0.00827798 + 0.00131110i −0.160572 0.987024i \(-0.551334\pi\)
0.152294 + 0.988335i \(0.451334\pi\)
\(38\) 1.14821 + 1.41792i 0.186263 + 0.230016i
\(39\) 0.967872 + 1.01043i 0.154984 + 0.161798i
\(40\) 2.19028 0.450206i 0.346313 0.0711839i
\(41\) 3.49062 + 7.84007i 0.545144 + 1.22441i 0.950634 + 0.310314i \(0.100434\pi\)
−0.405490 + 0.914099i \(0.632899\pi\)
\(42\) −0.277049 + 0.794135i −0.0427496 + 0.122538i
\(43\) 1.22798 4.58287i 0.187265 0.698881i −0.806870 0.590730i \(-0.798840\pi\)
0.994134 0.108152i \(-0.0344933\pi\)
\(44\) 0.935320 + 2.87862i 0.141005 + 0.433968i
\(45\) 6.56526 + 1.37746i 0.978691 + 0.205339i
\(46\) 0.993061 3.05633i 0.146419 0.450631i
\(47\) −2.23689 1.45266i −0.326285 0.211892i 0.371093 0.928596i \(-0.378983\pi\)
−0.697377 + 0.716704i \(0.745650\pi\)
\(48\) 0.898084 1.48103i 0.129627 0.213768i
\(49\) −5.85797 3.38210i −0.836852 0.483157i
\(50\) −4.94850 + 0.715776i −0.699824 + 0.101226i
\(51\) 0.0749931 0.0581030i 0.0105011 0.00813604i
\(52\) −0.754169 + 0.289498i −0.104584 + 0.0401462i
\(53\) 2.76573 + 5.42805i 0.379902 + 0.745600i 0.999218 0.0395418i \(-0.0125898\pi\)
−0.619316 + 0.785142i \(0.712590\pi\)
\(54\) 4.24061 3.00287i 0.577074 0.408639i
\(55\) −1.70776 6.54904i −0.230274 0.883072i
\(56\) −0.360867 0.324926i −0.0482229 0.0434201i
\(57\) −3.13501 0.397839i −0.415242 0.0526951i
\(58\) −1.17864 1.81494i −0.154763 0.238313i
\(59\) 2.73215 1.21643i 0.355696 0.158366i −0.221107 0.975250i \(-0.570967\pi\)
0.576802 + 0.816884i \(0.304300\pi\)
\(60\) −2.20020 + 3.18734i −0.284044 + 0.411484i
\(61\) −4.80099 2.13754i −0.614704 0.273684i 0.0756742 0.997133i \(-0.475889\pi\)
−0.690378 + 0.723449i \(0.742556\pi\)
\(62\) 0.578063 + 3.64974i 0.0734140 + 0.463518i
\(63\) −0.604937 1.32524i −0.0762150 0.166965i
\(64\) 0.587785 + 0.809017i 0.0734732 + 0.101127i
\(65\) 1.72165 0.546644i 0.213544 0.0678028i
\(66\) −4.61884 2.47995i −0.568539 0.305261i
\(67\) −13.6587 + 8.87006i −1.66868 + 1.08365i −0.779046 + 0.626967i \(0.784296\pi\)
−0.889629 + 0.456683i \(0.849037\pi\)
\(68\) 0.0141760 + 0.0529057i 0.00171910 + 0.00641576i
\(69\) 2.41973 + 5.01266i 0.291302 + 0.603454i
\(70\) 0.762619 + 0.772931i 0.0911504 + 0.0923829i
\(71\) −15.6202 5.07532i −1.85378 0.602330i −0.996109 0.0881343i \(-0.971910\pi\)
−0.857673 0.514196i \(-0.828090\pi\)
\(72\) 0.651129 + 2.92849i 0.0767363 + 0.345125i
\(73\) 6.79278 + 1.07587i 0.795034 + 0.125921i 0.540722 0.841201i \(-0.318151\pi\)
0.254312 + 0.967122i \(0.418151\pi\)
\(74\) 0.0254903 + 0.0441505i 0.00296319 + 0.00513240i
\(75\) 5.33200 6.82420i 0.615687 0.787991i
\(76\) 0.912258 1.58008i 0.104643 0.181247i
\(77\) −0.924960 + 1.14223i −0.105409 + 0.130169i
\(78\) 0.596461 1.26569i 0.0675359 0.143311i
\(79\) −3.38388 15.9199i −0.380716 1.79113i −0.583724 0.811952i \(-0.698405\pi\)
0.203008 0.979177i \(-0.434928\pi\)
\(80\) −1.20523 1.88346i −0.134749 0.210577i
\(81\) −1.70636 + 8.83676i −0.189595 + 0.981862i
\(82\) 6.06841 6.06841i 0.670144 0.670144i
\(83\) 0.242423 + 4.62570i 0.0266093 + 0.507737i 0.979127 + 0.203252i \(0.0651510\pi\)
−0.952517 + 0.304485i \(0.901516\pi\)
\(84\) 0.840674 0.0259450i 0.0917250 0.00283083i
\(85\) −0.0246587 0.119966i −0.00267461 0.0130121i
\(86\) −4.71855 + 0.495939i −0.508814 + 0.0534785i
\(87\) 3.64876 + 0.857979i 0.391188 + 0.0919850i
\(88\) 2.35223 1.90480i 0.250749 0.203052i
\(89\) −5.00866 + 3.63900i −0.530917 + 0.385733i −0.820701 0.571359i \(-0.806417\pi\)
0.289784 + 0.957092i \(0.406417\pi\)
\(90\) −1.06681 6.62283i −0.112452 0.698108i
\(91\) −0.317357 0.230573i −0.0332681 0.0241707i
\(92\) −3.20921 + 0.168187i −0.334583 + 0.0175348i
\(93\) −5.09588 3.87251i −0.528418 0.401561i
\(94\) −0.554540 + 2.60891i −0.0571965 + 0.269088i
\(95\) −2.24491 + 3.40656i −0.230323 + 0.349506i
\(96\) −1.70450 0.307680i −0.173965 0.0314025i
\(97\) −7.58964 + 11.6870i −0.770611 + 1.18664i 0.207435 + 0.978249i \(0.433488\pi\)
−0.978046 + 0.208388i \(0.933178\pi\)
\(98\) −1.05815 + 6.68092i −0.106890 + 0.674875i
\(99\) 8.74853 2.43201i 0.879260 0.244426i
\(100\) 2.44162 + 4.36331i 0.244162 + 0.436331i
\(101\) 8.96463 5.17573i 0.892014 0.515004i 0.0174130 0.999848i \(-0.494457\pi\)
0.874601 + 0.484844i \(0.161124\pi\)
\(102\) −0.0811189 0.0491899i −0.00803197 0.00487052i
\(103\) −0.970469 + 18.5176i −0.0956231 + 1.82460i 0.358356 + 0.933585i \(0.383338\pi\)
−0.453979 + 0.891013i \(0.649996\pi\)
\(104\) 0.540540 + 0.600330i 0.0530043 + 0.0588672i
\(105\) −1.87995 0.0530718i −0.183464 0.00517928i
\(106\) 4.07637 4.52727i 0.395932 0.439728i
\(107\) 3.81425 + 3.81425i 0.368738 + 0.368738i 0.867017 0.498279i \(-0.166035\pi\)
−0.498279 + 0.867017i \(0.666035\pi\)
\(108\) −4.32312 2.88282i −0.415992 0.277400i
\(109\) −3.63804 + 5.00733i −0.348461 + 0.479615i −0.946889 0.321561i \(-0.895792\pi\)
0.598428 + 0.801177i \(0.295792\pi\)
\(110\) −5.50205 + 3.94129i −0.524600 + 0.375787i
\(111\) −0.0847811 0.0246830i −0.00804706 0.00234281i
\(112\) −0.174021 + 0.453341i −0.0164435 + 0.0428367i
\(113\) −5.28074 + 13.7568i −0.496770 + 1.29413i 0.424577 + 0.905392i \(0.360423\pi\)
−0.921348 + 0.388740i \(0.872911\pi\)
\(114\) 0.752073 + 3.06936i 0.0704381 + 0.287472i
\(115\) 7.18569 + 0.0482557i 0.670069 + 0.00449986i
\(116\) −1.27201 + 1.75077i −0.118103 + 0.162555i
\(117\) 0.770400 + 2.29776i 0.0712235 + 0.212428i
\(118\) −2.11475 2.11475i −0.194679 0.194679i
\(119\) −0.0177969 + 0.0197654i −0.00163143 + 0.00181189i
\(120\) 3.76412 + 0.911822i 0.343615 + 0.0832376i
\(121\) 1.23036 + 1.36645i 0.111850 + 0.124223i
\(122\) −0.275043 + 5.24814i −0.0249012 + 0.475144i
\(123\) −0.319674 + 14.8611i −0.0288240 + 1.33998i
\(124\) 3.20017 1.84762i 0.287384 0.165921i
\(125\) −4.87406 10.0620i −0.435949 0.899971i
\(126\) −1.02043 + 1.03968i −0.0909072 + 0.0926223i
\(127\) −1.53648 + 9.70097i −0.136341 + 0.860822i 0.820803 + 0.571211i \(0.193526\pi\)
−0.957144 + 0.289611i \(0.906474\pi\)
\(128\) 0.544639 0.838671i 0.0481397 0.0741287i
\(129\) 5.30777 6.27372i 0.467323 0.552370i
\(130\) −1.12732 1.41140i −0.0988725 0.123788i
\(131\) −2.38584 + 11.2245i −0.208452 + 0.980690i 0.742139 + 0.670246i \(0.233811\pi\)
−0.950591 + 0.310445i \(0.899522\pi\)
\(132\) −0.659990 + 5.20079i −0.0574448 + 0.452671i
\(133\) 0.884760 0.0463683i 0.0767185 0.00402064i
\(134\) 13.1758 + 9.57274i 1.13821 + 0.826959i
\(135\) 9.26933 + 7.00567i 0.797777 + 0.602952i
\(136\) 0.0443115 0.0321942i 0.00379968 0.00276063i
\(137\) 7.65442 6.19842i 0.653961 0.529567i −0.243926 0.969794i \(-0.578435\pi\)
0.897887 + 0.440227i \(0.145102\pi\)
\(138\) 3.81257 4.05539i 0.324548 0.345218i
\(139\) −8.79140 + 0.924014i −0.745677 + 0.0783738i −0.469744 0.882803i \(-0.655654\pi\)
−0.275933 + 0.961177i \(0.588987\pi\)
\(140\) 0.448295 0.988960i 0.0378878 0.0835823i
\(141\) −2.43217 3.92763i −0.204826 0.330766i
\(142\) 0.859571 + 16.4016i 0.0721336 + 1.37639i
\(143\) 1.72894 1.72894i 0.144581 0.144581i
\(144\) 2.50063 1.65736i 0.208386 0.138113i
\(145\) 3.07047 3.74008i 0.254989 0.310597i
\(146\) −1.42990 6.72716i −0.118340 0.556744i
\(147\) −6.68102 9.62430i −0.551041 0.793799i
\(148\) 0.0320832 0.0396194i 0.00263722 0.00325670i
\(149\) 6.94662 12.0319i 0.569089 0.985691i −0.427567 0.903984i \(-0.640629\pi\)
0.996656 0.0817077i \(-0.0260374\pi\)
\(150\) −8.28176 2.53228i −0.676203 0.206760i
\(151\) −6.66328 11.5411i −0.542250 0.939205i −0.998774 0.0494940i \(-0.984239\pi\)
0.456524 0.889711i \(-0.349094\pi\)
\(152\) −1.80205 0.285417i −0.146166 0.0231504i
\(153\) 0.160399 0.0356637i 0.0129675 0.00288324i
\(154\) 1.39784 + 0.454186i 0.112641 + 0.0365993i
\(155\) −7.38724 + 3.70171i −0.593357 + 0.297329i
\(156\) −1.39538 0.103261i −0.111720 0.00826748i
\(157\) −1.29372 4.82823i −0.103250 0.385335i 0.894891 0.446286i \(-0.147253\pi\)
−0.998141 + 0.0609506i \(0.980587\pi\)
\(158\) −13.6498 + 8.86431i −1.08592 + 0.705206i
\(159\) 0.325494 + 10.5467i 0.0258134 + 0.836409i
\(160\) −1.32645 + 1.80015i −0.104865 + 0.142314i
\(161\) −0.917246 1.26248i −0.0722891 0.0994974i
\(162\) 8.86133 1.57379i 0.696212 0.123649i
\(163\) 1.57213 + 9.92602i 0.123138 + 0.777466i 0.969542 + 0.244924i \(0.0787630\pi\)
−0.846404 + 0.532542i \(0.821237\pi\)
\(164\) −7.84007 3.49062i −0.612207 0.272572i
\(165\) 2.15981 11.5219i 0.168141 0.896979i
\(166\) 4.23159 1.88402i 0.328435 0.146229i
\(167\) −10.5153 16.1921i −0.813696 1.25298i −0.964412 0.264404i \(-0.914825\pi\)
0.150716 0.988577i \(-0.451842\pi\)
\(168\) −0.325492 0.775539i −0.0251123 0.0598341i
\(169\) −9.17592 8.26204i −0.705840 0.635541i
\(170\) −0.103161 + 0.0660128i −0.00791208 + 0.00506295i
\(171\) −4.61816 2.93808i −0.353160 0.224681i
\(172\) 2.15398 + 4.22741i 0.164239 + 0.322337i
\(173\) −0.668509 + 0.256617i −0.0508258 + 0.0195102i −0.383648 0.923479i \(-0.625332\pi\)
0.332822 + 0.942990i \(0.391999\pi\)
\(174\) −0.506607 3.71388i −0.0384057 0.281549i
\(175\) −1.13123 + 2.14834i −0.0855131 + 0.162399i
\(176\) −2.62125 1.51338i −0.197584 0.114075i
\(177\) 5.17886 + 0.111402i 0.389267 + 0.00837347i
\(178\) 5.19224 + 3.37188i 0.389175 + 0.252733i
\(179\) 4.41585 13.5906i 0.330056 1.01581i −0.639051 0.769165i \(-0.720673\pi\)
0.969106 0.246643i \(-0.0793274\pi\)
\(180\) −5.80064 + 3.36937i −0.432354 + 0.251138i
\(181\) 1.22141 + 3.75913i 0.0907870 + 0.279414i 0.986133 0.165958i \(-0.0530716\pi\)
−0.895346 + 0.445372i \(0.853072\pi\)
\(182\) −0.101528 + 0.378908i −0.00752577 + 0.0280866i
\(183\) −5.94389 6.89391i −0.439385 0.509612i
\(184\) 1.30709 + 2.93578i 0.0963602 + 0.216429i
\(185\) −0.0768455 + 0.0842016i −0.00564980 + 0.00619062i
\(186\) −1.78910 + 6.14520i −0.131183 + 0.450588i
\(187\) −0.104330 0.128837i −0.00762935 0.00942146i
\(188\) 2.63435 0.417241i 0.192130 0.0304304i
\(189\) 0.0306884 2.52304i 0.00223226 0.183524i
\(190\) 3.98480 + 0.875005i 0.289088 + 0.0634795i
\(191\) −6.78034 0.712643i −0.490608 0.0515650i −0.144005 0.989577i \(-0.545998\pi\)
−0.346603 + 0.938012i \(0.612665\pi\)
\(192\) 0.323595 + 1.70155i 0.0233535 + 0.122799i
\(193\) 2.00642 0.537619i 0.144425 0.0386987i −0.185882 0.982572i \(-0.559514\pi\)
0.330307 + 0.943873i \(0.392848\pi\)
\(194\) 13.6307 + 2.89729i 0.978624 + 0.208013i
\(195\) 3.10108 + 0.414712i 0.222073 + 0.0296982i
\(196\) 6.61638 1.40636i 0.472599 0.100454i
\(197\) 22.5573 11.4935i 1.60714 0.818878i 0.607439 0.794366i \(-0.292197\pi\)
0.999700 0.0245115i \(-0.00780304\pi\)
\(198\) −5.40566 7.29590i −0.384164 0.518497i
\(199\) 0.696232i 0.0493546i −0.999695 0.0246773i \(-0.992144\pi\)
0.999695 0.0246773i \(-0.00785582\pi\)
\(200\) 3.19851 3.84312i 0.226168 0.271750i
\(201\) −27.9496 + 3.81257i −1.97141 + 0.268918i
\(202\) −8.04459 6.51438i −0.566016 0.458350i
\(203\) −1.04942 0.0549977i −0.0736548 0.00386008i
\(204\) −0.0168523 + 0.0933591i −0.00117990 + 0.00653644i
\(205\) 17.0395 + 8.82670i 1.19009 + 0.616483i
\(206\) 17.6355 5.73012i 1.22872 0.399236i
\(207\) 0.0900906 + 9.64042i 0.00626173 + 0.670055i
\(208\) 0.366745 0.719777i 0.0254292 0.0499075i
\(209\) −0.577245 + 5.49212i −0.0399288 + 0.379898i
\(210\) 0.624167 + 1.77410i 0.0430716 + 0.122425i
\(211\) 0.720547 + 6.85555i 0.0496045 + 0.471955i 0.990923 + 0.134434i \(0.0429217\pi\)
−0.941318 + 0.337521i \(0.890412\pi\)
\(212\) −5.68741 2.18319i −0.390613 0.149942i
\(213\) −20.7263 19.4852i −1.42014 1.33511i
\(214\) 2.19401 4.92782i 0.149979 0.336859i
\(215\) −4.24993 9.72066i −0.289843 0.662944i
\(216\) −1.14208 + 5.06909i −0.0777085 + 0.344908i
\(217\) 1.59881 + 0.814635i 0.108534 + 0.0553010i
\(218\) 5.97850 + 1.60194i 0.404915 + 0.108497i
\(219\) 9.84848 + 6.70114i 0.665499 + 0.452821i
\(220\) 5.65127 + 3.72417i 0.381009 + 0.251084i
\(221\) 0.0328813 0.0296065i 0.00221184 0.00199155i
\(222\) 0.00733925 + 0.0879956i 0.000492578 + 0.00590588i
\(223\) 0.898584 + 2.34089i 0.0601737 + 0.156758i 0.960371 0.278724i \(-0.0899114\pi\)
−0.900198 + 0.435482i \(0.856578\pi\)
\(224\) 0.485594 0.0324451
\(225\) 13.3928 6.75519i 0.892854 0.450346i
\(226\) 14.7355 0.980193
\(227\) −8.31951 21.6731i −0.552185 1.43849i −0.871288 0.490772i \(-0.836715\pi\)
0.319103 0.947720i \(-0.396619\pi\)
\(228\) 2.59597 1.80208i 0.171923 0.119346i
\(229\) 17.7504 15.9826i 1.17298 1.05616i 0.175555 0.984470i \(-0.443828\pi\)
0.997427 0.0716879i \(-0.0228385\pi\)
\(230\) −2.53007 6.72572i −0.166828 0.443481i
\(231\) −2.29259 + 1.10669i −0.150841 + 0.0728147i
\(232\) 2.09033 + 0.560102i 0.137237 + 0.0367725i
\(233\) 11.3486 + 5.78238i 0.743468 + 0.378816i 0.784326 0.620349i \(-0.213009\pi\)
−0.0408575 + 0.999165i \(0.513009\pi\)
\(234\) 1.86906 1.54267i 0.122184 0.100848i
\(235\) −5.93540 + 0.583565i −0.387183 + 0.0380676i
\(236\) −1.21643 + 2.73215i −0.0791829 + 0.177848i
\(237\) 6.45270 27.4417i 0.419148 1.78253i
\(238\) 0.0248304 + 0.00953151i 0.00160952 + 0.000617836i
\(239\) −1.18336 11.2589i −0.0765451 0.728278i −0.963733 0.266869i \(-0.914011\pi\)
0.887188 0.461409i \(-0.152656\pi\)
\(240\) −0.497680 3.84087i −0.0321251 0.247927i
\(241\) 2.55544 24.3134i 0.164610 1.56616i −0.530767 0.847518i \(-0.678096\pi\)
0.695377 0.718645i \(-0.255237\pi\)
\(242\) 0.834769 1.63833i 0.0536610 0.105316i
\(243\) −9.19817 + 12.5855i −0.590063 + 0.807357i
\(244\) 4.99812 1.62399i 0.319972 0.103965i
\(245\) −14.9545 + 2.26573i −0.955411 + 0.144752i
\(246\) 13.9886 5.02729i 0.891878 0.320528i
\(247\) −1.47187 0.0771373i −0.0936527 0.00490813i
\(248\) −2.87174 2.32549i −0.182356 0.147669i
\(249\) −3.03558 + 7.42650i −0.192372 + 0.470635i
\(250\) −7.64697 + 8.15622i −0.483637 + 0.515845i
\(251\) 3.94946i 0.249288i 0.992202 + 0.124644i \(0.0397788\pi\)
−0.992202 + 0.124644i \(0.960221\pi\)
\(252\) 1.33632 + 0.580065i 0.0841800 + 0.0365407i
\(253\) 8.66666 4.41589i 0.544869 0.277624i
\(254\) 9.60726 2.04209i 0.602813 0.128132i
\(255\) 0.0499423 0.206168i 0.00312751 0.0129108i
\(256\) −0.978148 0.207912i −0.0611342 0.0129945i
\(257\) 14.4536 3.87284i 0.901593 0.241581i 0.221893 0.975071i \(-0.428777\pi\)
0.679700 + 0.733490i \(0.262110\pi\)
\(258\) −7.75915 2.70693i −0.483064 0.168526i
\(259\) 0.0246203 + 0.00258770i 0.00152983 + 0.000160792i
\(260\) −0.913660 + 1.55824i −0.0566628 + 0.0966382i
\(261\) 5.08335 + 4.03835i 0.314652 + 0.249968i
\(262\) 11.3340 1.79513i 0.700217 0.110903i
\(263\) 6.14452 + 7.58785i 0.378887 + 0.467887i 0.930542 0.366186i \(-0.119337\pi\)
−0.551654 + 0.834073i \(0.686003\pi\)
\(264\) 5.09187 1.24764i 0.313383 0.0767870i
\(265\) 12.4070 + 5.62410i 0.762158 + 0.345486i
\(266\) −0.360358 0.809378i −0.0220950 0.0496262i
\(267\) −10.5344 + 2.00339i −0.644694 + 0.122605i
\(268\) 4.21516 15.7312i 0.257482 0.960935i
\(269\) 2.28607 + 7.03581i 0.139384 + 0.428981i 0.996246 0.0865653i \(-0.0275891\pi\)
−0.856862 + 0.515546i \(0.827589\pi\)
\(270\) 3.21853 11.1643i 0.195873 0.679436i
\(271\) 2.04584 6.29645i 0.124276 0.382482i −0.869492 0.493946i \(-0.835554\pi\)
0.993768 + 0.111464i \(0.0355540\pi\)
\(272\) −0.0459357 0.0298310i −0.00278526 0.00180877i
\(273\) −0.326987 0.595582i −0.0197902 0.0360463i
\(274\) −8.52982 4.92470i −0.515305 0.297512i
\(275\) −12.1229 9.05905i −0.731040 0.546281i
\(276\) −5.15234 2.10602i −0.310134 0.126767i
\(277\) 3.89530 1.49526i 0.234046 0.0898418i −0.238519 0.971138i \(-0.576662\pi\)
0.472564 + 0.881296i \(0.343328\pi\)
\(278\) 4.01320 + 7.87634i 0.240696 + 0.472392i
\(279\) −5.12489 9.82998i −0.306819 0.588506i
\(280\) −1.08393 0.0641080i −0.0647771 0.00383118i
\(281\) 13.1936 + 11.8796i 0.787065 + 0.708676i 0.961142 0.276056i \(-0.0890275\pi\)
−0.174077 + 0.984732i \(0.555694\pi\)
\(282\) −2.79515 + 3.67816i −0.166449 + 0.219031i
\(283\) 7.29425 + 11.2322i 0.433598 + 0.667683i 0.986161 0.165788i \(-0.0530168\pi\)
−0.552563 + 0.833471i \(0.686350\pi\)
\(284\) 15.0042 6.68028i 0.890333 0.396402i
\(285\) −6.03256 + 3.67982i −0.357338 + 0.217974i
\(286\) −2.23370 0.994507i −0.132081 0.0588064i
\(287\) −0.651922 4.11608i −0.0384818 0.242964i
\(288\) −2.44342 1.74060i −0.143980 0.102566i
\(289\) 9.99059 + 13.7509i 0.587682 + 0.808874i
\(290\) −4.59202 1.52621i −0.269653 0.0896219i
\(291\) −20.5205 + 12.7073i −1.20294 + 0.744913i
\(292\) −5.76791 + 3.74573i −0.337542 + 0.219202i
\(293\) −5.82689 21.7462i −0.340410 1.27043i −0.897883 0.440234i \(-0.854896\pi\)
0.557473 0.830195i \(-0.311771\pi\)
\(294\) −6.59079 + 9.68631i −0.384383 + 0.564917i
\(295\) 3.07598 5.93802i 0.179090 0.345725i
\(296\) −0.0484855 0.0157539i −0.00281816 0.000915676i
\(297\) 15.5028 + 2.64907i 0.899563 + 0.153715i
\(298\) −13.7222 2.17338i −0.794905 0.125901i
\(299\) 1.29802 + 2.24823i 0.0750663 + 0.130019i
\(300\) 0.603834 + 8.63918i 0.0348624 + 0.498783i
\(301\) −1.15196 + 1.99525i −0.0663979 + 0.115005i
\(302\) −8.38668 + 10.3567i −0.482599 + 0.595960i
\(303\) 17.8672 1.49021i 1.02644 0.0856104i
\(304\) 0.379338 + 1.78465i 0.0217565 + 0.102356i
\(305\) −11.3710 + 2.96516i −0.651104 + 0.169785i
\(306\) −0.0907768 0.136965i −0.00518936 0.00782975i
\(307\) −10.4379 + 10.4379i −0.595722 + 0.595722i −0.939171 0.343449i \(-0.888405\pi\)
0.343449 + 0.939171i \(0.388405\pi\)
\(308\) −0.0769222 1.46776i −0.00438305 0.0836335i
\(309\) −15.1931 + 28.2967i −0.864306 + 1.60974i
\(310\) 6.10319 + 5.57001i 0.346638 + 0.316355i
\(311\) 29.7961 3.13170i 1.68958 0.177582i 0.789634 0.613579i \(-0.210271\pi\)
0.899948 + 0.435996i \(0.143604\pi\)
\(312\) 0.403656 + 1.33970i 0.0228525 + 0.0758457i
\(313\) −5.38300 + 4.35907i −0.304265 + 0.246389i −0.769277 0.638915i \(-0.779383\pi\)
0.465012 + 0.885304i \(0.346050\pi\)
\(314\) −4.04392 + 2.93808i −0.228211 + 0.165805i
\(315\) −2.90630 1.47122i −0.163752 0.0828940i
\(316\) 13.1672 + 9.56654i 0.740713 + 0.538160i
\(317\) −9.26828 + 0.485730i −0.520559 + 0.0272813i −0.310806 0.950473i \(-0.600599\pi\)
−0.209752 + 0.977755i \(0.567266\pi\)
\(318\) 9.72956 4.08348i 0.545606 0.228990i
\(319\) 1.36184 6.40698i 0.0762487 0.358722i
\(320\) 2.15594 + 0.593228i 0.120521 + 0.0331625i
\(321\) 3.15986 + 8.79240i 0.176366 + 0.490744i
\(322\) −0.849916 + 1.30876i −0.0473640 + 0.0729341i
\(323\) −0.0156329 + 0.0987021i −0.000869836 + 0.00549193i
\(324\) −4.64488 7.70877i −0.258049 0.428265i
\(325\) 2.24516 3.35764i 0.124539 0.186248i
\(326\) 8.70333 5.02487i 0.482033 0.278302i
\(327\) −9.39723 + 5.15928i −0.519668 + 0.285309i
\(328\) −0.449149 + 8.57026i −0.0248001 + 0.473214i
\(329\) 0.866640 + 0.962501i 0.0477794 + 0.0530644i
\(330\) −11.5306 + 2.11272i −0.634740 + 0.116301i
\(331\) −7.25351 + 8.05584i −0.398689 + 0.442789i −0.908745 0.417352i \(-0.862958\pi\)
0.510056 + 0.860141i \(0.329625\pi\)
\(332\) −3.27535 3.27535i −0.179758 0.179758i
\(333\) −0.114609 0.101272i −0.00628056 0.00554965i
\(334\) −11.3483 + 15.6196i −0.620950 + 0.854665i
\(335\) −11.4858 + 34.5582i −0.627534 + 1.88811i
\(336\) −0.607382 + 0.581802i −0.0331354 + 0.0317399i
\(337\) 9.48909 24.7199i 0.516904 1.34658i −0.388273 0.921544i \(-0.626928\pi\)
0.905177 0.425036i \(-0.139738\pi\)
\(338\) −4.42492 + 11.5273i −0.240684 + 0.627003i
\(339\) −18.4312 + 17.6550i −1.00105 + 0.958886i
\(340\) 0.0985978 + 0.0726521i 0.00534722 + 0.00394012i
\(341\) −6.57414 + 9.04853i −0.356010 + 0.490005i
\(342\) −1.08793 + 5.36434i −0.0588287 + 0.290070i
\(343\) 4.72617 + 4.72617i 0.255189 + 0.255189i
\(344\) 3.17472 3.52588i 0.171169 0.190103i
\(345\) 11.2228 + 5.38120i 0.604218 + 0.289714i
\(346\) 0.479144 + 0.532144i 0.0257590 + 0.0286082i
\(347\) 1.58639 30.2700i 0.0851617 1.62498i −0.538040 0.842920i \(-0.680835\pi\)
0.623201 0.782062i \(-0.285832\pi\)
\(348\) −3.28566 + 1.80389i −0.176130 + 0.0966989i
\(349\) −19.8208 + 11.4436i −1.06099 + 0.612560i −0.925705 0.378247i \(-0.876527\pi\)
−0.135281 + 0.990807i \(0.543194\pi\)
\(350\) 2.41104 + 0.286199i 0.128876 + 0.0152980i
\(351\) −0.489507 + 4.16894i −0.0261279 + 0.222521i
\(352\) −0.473489 + 2.98949i −0.0252371 + 0.159341i
\(353\) 5.32534 8.20031i 0.283439 0.436459i −0.668061 0.744107i \(-0.732875\pi\)
0.951500 + 0.307648i \(0.0995420\pi\)
\(354\) −1.75194 4.87481i −0.0931144 0.259093i
\(355\) −34.3737 + 12.9307i −1.82437 + 0.686288i
\(356\) 1.28719 6.05575i 0.0682209 0.320954i
\(357\) −0.0424778 + 0.0178279i −0.00224816 + 0.000943551i
\(358\) −14.2704 + 0.747880i −0.754214 + 0.0395267i
\(359\) −10.5785 7.68570i −0.558310 0.405636i 0.272530 0.962147i \(-0.412140\pi\)
−0.830840 + 0.556511i \(0.812140\pi\)
\(360\) 5.22434 + 4.20789i 0.275347 + 0.221775i
\(361\) −12.6782 + 9.21127i −0.667275 + 0.484803i
\(362\) 3.07173 2.48744i 0.161447 0.130737i
\(363\) 0.918786 + 3.04938i 0.0482238 + 0.160051i
\(364\) 0.390126 0.0410039i 0.0204482 0.00214919i
\(365\) 13.3695 7.59961i 0.699789 0.397782i
\(366\) −4.30592 + 8.01965i −0.225074 + 0.419194i
\(367\) 0.360553 + 6.87976i 0.0188207 + 0.359121i 0.991764 + 0.128077i \(0.0408806\pi\)
−0.972943 + 0.231043i \(0.925786\pi\)
\(368\) 2.27237 2.27237i 0.118455 0.118455i
\(369\) −11.4736 + 23.0481i −0.597292 + 1.19984i
\(370\) 0.106148 + 0.0415664i 0.00551837 + 0.00216093i
\(371\) −0.615058 2.89362i −0.0319322 0.150229i
\(372\) 6.37820 0.531972i 0.330694 0.0275815i
\(373\) 14.6764 18.1239i 0.759916 0.938417i −0.239557 0.970882i \(-0.577002\pi\)
0.999473 + 0.0324647i \(0.0103357\pi\)
\(374\) −0.0828908 + 0.143571i −0.00428618 + 0.00742388i
\(375\) −0.207319 19.3638i −0.0107059 0.999943i
\(376\) −1.33360 2.30986i −0.0687749 0.119122i
\(377\) 1.72666 + 0.273477i 0.0889277 + 0.0140848i
\(378\) −2.36645 + 0.875525i −0.121717 + 0.0450321i
\(379\) 10.8136 + 3.51356i 0.555458 + 0.180479i 0.573277 0.819362i \(-0.305672\pi\)
−0.0178182 + 0.999841i \(0.505672\pi\)
\(380\) −0.611138 4.03371i −0.0313507 0.206925i
\(381\) −9.57010 + 14.0649i −0.490291 + 0.720568i
\(382\) 1.76455 + 6.58538i 0.0902821 + 0.336938i
\(383\) −0.903655 + 0.586840i −0.0461746 + 0.0299861i −0.567520 0.823360i \(-0.692097\pi\)
0.521345 + 0.853346i \(0.325430\pi\)
\(384\) 1.47257 0.911884i 0.0751468 0.0465344i
\(385\) −0.0220702 + 3.28645i −0.00112480 + 0.167493i
\(386\) −1.22095 1.68049i −0.0621446 0.0855348i
\(387\) 12.9484 5.91059i 0.658203 0.300452i
\(388\) −2.17994 13.7636i −0.110670 0.698741i
\(389\) −6.19272 2.75718i −0.313983 0.139794i 0.243694 0.969852i \(-0.421641\pi\)
−0.557677 + 0.830058i \(0.688307\pi\)
\(390\) −0.724161 3.04373i −0.0366693 0.154125i
\(391\) 0.160799 0.0715922i 0.00813194 0.00362057i
\(392\) −3.68405 5.67293i −0.186072 0.286526i
\(393\) −12.0258 + 15.8249i −0.606621 + 0.798259i
\(394\) −18.8139 16.9401i −0.947831 0.853431i
\(395\) −28.1284 23.0924i −1.41530 1.16191i
\(396\) −4.87409 + 7.66124i −0.244932 + 0.384992i
\(397\) 12.7865 + 25.0950i 0.641737 + 1.25948i 0.951202 + 0.308569i \(0.0998500\pi\)
−0.309465 + 0.950911i \(0.600150\pi\)
\(398\) −0.649988 + 0.249507i −0.0325810 + 0.0125067i
\(399\) 1.42047 + 0.580617i 0.0711125 + 0.0290672i
\(400\) −4.73410 1.60881i −0.236705 0.0804406i
\(401\) 33.3668 + 19.2643i 1.66626 + 0.962015i 0.969628 + 0.244584i \(0.0786515\pi\)
0.696630 + 0.717430i \(0.254682\pi\)
\(402\) 13.5756 + 24.7269i 0.677088 + 1.23326i
\(403\) −2.50352 1.62580i −0.124709 0.0809871i
\(404\) −3.19878 + 9.84482i −0.159145 + 0.489798i
\(405\) 9.35043 + 17.8205i 0.464627 + 0.885507i
\(406\) 0.324733 + 0.999427i 0.0161163 + 0.0496007i
\(407\) −0.0399374 + 0.149048i −0.00197962 + 0.00738805i
\(408\) 0.0931975 0.0177240i 0.00461397 0.000877466i
\(409\) −7.58211 17.0297i −0.374911 0.842064i −0.998194 0.0600680i \(-0.980868\pi\)
0.623283 0.781996i \(-0.285798\pi\)
\(410\) 2.13402 19.0710i 0.105392 0.941848i
\(411\) 16.5695 4.05996i 0.817313 0.200263i
\(412\) −11.6695 14.4107i −0.574916 0.709962i
\(413\) −1.43439 + 0.227185i −0.0705818 + 0.0111791i
\(414\) 8.96782 3.53892i 0.440744 0.173929i
\(415\) 6.87872 + 7.74355i 0.337663 + 0.380116i
\(416\) −0.803399 0.0844406i −0.0393899 0.00414004i
\(417\) −14.4565 5.04344i −0.707940 0.246978i
\(418\) 5.33420 1.42929i 0.260904 0.0699091i
\(419\) 7.26032 + 1.54323i 0.354690 + 0.0753917i 0.381811 0.924240i \(-0.375301\pi\)
−0.0271209 + 0.999632i \(0.508634\pi\)
\(420\) 1.43259 1.21849i 0.0699031 0.0594563i
\(421\) 10.6820 2.27053i 0.520610 0.110659i 0.0598905 0.998205i \(-0.480925\pi\)
0.460719 + 0.887546i \(0.347592\pi\)
\(422\) 6.14198 3.12950i 0.298987 0.152342i
\(423\) −0.910718 7.94958i −0.0442806 0.386522i
\(424\) 6.09205i 0.295856i
\(425\) −0.210495 0.175189i −0.0102105 0.00849789i
\(426\) −10.7634 + 26.3325i −0.521489 + 1.27581i
\(427\) 1.98325 + 1.60600i 0.0959761 + 0.0777199i
\(428\) −5.38677 0.282309i −0.260380 0.0136459i
\(429\) 3.98545 1.43232i 0.192420 0.0691528i
\(430\) −7.55198 + 7.45123i −0.364189 + 0.359330i
\(431\) 23.5815 7.66209i 1.13588 0.369070i 0.320073 0.947393i \(-0.396293\pi\)
0.815808 + 0.578323i \(0.196293\pi\)
\(432\) 5.14169 0.750378i 0.247379 0.0361026i
\(433\) 12.3717 24.2808i 0.594544 1.16686i −0.376154 0.926557i \(-0.622754\pi\)
0.970698 0.240302i \(-0.0772465\pi\)
\(434\) 0.187565 1.78456i 0.00900339 0.0856615i
\(435\) 7.57229 3.59282i 0.363063 0.172263i
\(436\) −0.646969 6.15550i −0.0309842 0.294795i
\(437\) −5.47385 2.10121i −0.261850 0.100515i
\(438\) 2.72667 11.5958i 0.130285 0.554070i
\(439\) −8.69073 + 19.5197i −0.414786 + 0.931624i 0.578472 + 0.815702i \(0.303649\pi\)
−0.993258 + 0.115922i \(0.963018\pi\)
\(440\) 1.45158 6.61054i 0.0692013 0.315145i
\(441\) −3.36162 20.0122i −0.160077 0.952963i
\(442\) −0.0394236 0.0200873i −0.00187519 0.000955457i
\(443\) 18.8225 + 5.04348i 0.894286 + 0.239623i 0.676561 0.736387i \(-0.263470\pi\)
0.217725 + 0.976010i \(0.430136\pi\)
\(444\) 0.0795208 0.0383866i 0.00377389 0.00182175i
\(445\) −3.67270 + 13.3475i −0.174103 + 0.632733i
\(446\) 1.86339 1.67780i 0.0882339 0.0794462i
\(447\) 19.7677 13.7224i 0.934980 0.649047i
\(448\) −0.174021 0.453341i −0.00822174 0.0214184i
\(449\) −33.7785 −1.59411 −0.797053 0.603909i \(-0.793609\pi\)
−0.797053 + 0.603909i \(0.793609\pi\)
\(450\) −11.1061 10.0824i −0.523545 0.475290i
\(451\) 25.9757 1.22315
\(452\) −5.28074 13.7568i −0.248385 0.647066i
\(453\) −1.91851 23.0024i −0.0901396 1.08075i
\(454\) −17.2521 + 15.5339i −0.809681 + 0.729040i
\(455\) −0.876240 + 0.0400233i −0.0410788 + 0.00187632i
\(456\) −2.61270 1.77774i −0.122351 0.0832504i
\(457\) 18.6182 + 4.98873i 0.870923 + 0.233363i 0.666487 0.745517i \(-0.267797\pi\)
0.204436 + 0.978880i \(0.434464\pi\)
\(458\) −21.2822 10.8438i −0.994452 0.506698i
\(459\) 0.277644 + 0.0625539i 0.0129593 + 0.00291977i
\(460\) −5.37230 + 4.77231i −0.250485 + 0.222510i
\(461\) −9.87221 + 22.1733i −0.459795 + 1.03272i 0.523721 + 0.851890i \(0.324544\pi\)
−0.983515 + 0.180826i \(0.942123\pi\)
\(462\) 1.85477 + 1.74372i 0.0862919 + 0.0811250i
\(463\) 23.0479 + 8.84725i 1.07112 + 0.411166i 0.829098 0.559103i \(-0.188854\pi\)
0.242027 + 0.970270i \(0.422188\pi\)
\(464\) −0.226207 2.15221i −0.0105014 0.0999140i
\(465\) −14.3074 + 0.345405i −0.663491 + 0.0160178i
\(466\) 1.33136 12.6670i 0.0616739 0.586788i
\(467\) −4.78341 + 9.38796i −0.221350 + 0.434423i −0.974800 0.223082i \(-0.928388\pi\)
0.753450 + 0.657505i \(0.228388\pi\)
\(468\) −2.11002 1.19207i −0.0975357 0.0551035i
\(469\) 7.52138 2.44385i 0.347305 0.112846i
\(470\) 2.67186 + 5.33204i 0.123244 + 0.245949i
\(471\) 1.53796 8.52006i 0.0708654 0.392584i
\(472\) 2.98661 + 0.156522i 0.137470 + 0.00720449i
\(473\) −11.1603 9.03740i −0.513149 0.415540i
\(474\) −27.9314 + 3.81009i −1.28293 + 0.175003i
\(475\) 0.831634 + 9.08459i 0.0381580 + 0.416830i
\(476\) 0.0265970i 0.00121907i
\(477\) −7.27723 + 16.7648i −0.333202 + 0.767608i
\(478\) −10.0870 + 5.13959i −0.461369 + 0.235079i
\(479\) 34.6936 7.37435i 1.58519 0.336943i 0.670757 0.741677i \(-0.265969\pi\)
0.914434 + 0.404734i \(0.132636\pi\)
\(480\) −3.40741 + 1.84107i −0.155526 + 0.0840330i
\(481\) −0.0402835 0.00856251i −0.00183677 0.000390417i
\(482\) −23.6143 + 6.32743i −1.07560 + 0.288207i
\(483\) −0.504974 2.65530i −0.0229771 0.120820i
\(484\) −1.82866 0.192200i −0.0831211 0.00873638i
\(485\) 3.04893 + 31.0105i 0.138445 + 1.40811i
\(486\) 15.0459 + 4.07700i 0.682494 + 0.184937i
\(487\) −40.8589 + 6.47142i −1.85149 + 0.293248i −0.980274 0.197645i \(-0.936671\pi\)
−0.871220 + 0.490893i \(0.836671\pi\)
\(488\) −3.30729 4.08417i −0.149714 0.184881i
\(489\) −4.86573 + 16.7128i −0.220036 + 0.755778i
\(490\) 7.47447 + 13.1493i 0.337662 + 0.594025i
\(491\) 10.9436 + 24.5798i 0.493879 + 1.10927i 0.972849 + 0.231439i \(0.0743433\pi\)
−0.478971 + 0.877831i \(0.658990\pi\)
\(492\) −9.70643 11.2578i −0.437600 0.507542i
\(493\) 0.0306779 0.114492i 0.00138166 0.00515644i
\(494\) 0.455456 + 1.40175i 0.0204920 + 0.0630678i
\(495\) 11.8912 16.4577i 0.534471 0.739718i
\(496\) −1.14189 + 3.51438i −0.0512724 + 0.157800i
\(497\) 6.68877 + 4.34374i 0.300032 + 0.194843i
\(498\) 8.02109 + 0.172540i 0.359434 + 0.00773172i
\(499\) −34.7764 20.0782i −1.55681 0.898823i −0.997559 0.0698231i \(-0.977757\pi\)
−0.559248 0.829000i \(-0.688910\pi\)
\(500\) 10.3549 + 4.21613i 0.463086 + 0.188551i
\(501\) −4.51972 33.1336i −0.201926 1.48030i
\(502\) 3.68714 1.41536i 0.164565 0.0631706i
\(503\) −18.3586 36.0307i −0.818568 1.60653i −0.794845 0.606812i \(-0.792448\pi\)
−0.0237233 0.999719i \(-0.507552\pi\)
\(504\) 0.0626443 1.45544i 0.00279040 0.0648303i
\(505\) 8.43991 21.5530i 0.375571 0.959095i
\(506\) −7.22844 6.50852i −0.321343 0.289339i
\(507\) −8.27643 19.7200i −0.367569 0.875794i
\(508\) −5.34939 8.23734i −0.237341 0.365473i
\(509\) −0.649197 + 0.289041i −0.0287751 + 0.0128115i −0.421074 0.907026i \(-0.638347\pi\)
0.392299 + 0.919838i \(0.371680\pi\)
\(510\) −0.210372 + 0.0272589i −0.00931545 + 0.00120705i
\(511\) −3.05092 1.35836i −0.134965 0.0600902i
\(512\) 0.156434 + 0.987688i 0.00691349 + 0.0436501i
\(513\) −5.06634 8.01320i −0.223685 0.353791i
\(514\) −8.79532 12.1057i −0.387945 0.533961i
\(515\) 24.1458 + 33.7076i 1.06399 + 1.48533i
\(516\) 0.253498 + 8.21387i 0.0111596 + 0.361595i
\(517\) −6.77054 + 4.39684i −0.297768 + 0.193373i
\(518\) −0.00640730 0.0239124i −0.000281521 0.00105065i
\(519\) −1.23689 0.0915322i −0.0542933 0.00401782i
\(520\) 1.78217 + 0.294550i 0.0781535 + 0.0129169i
\(521\) 6.05567 + 1.96761i 0.265304 + 0.0862024i 0.438648 0.898659i \(-0.355457\pi\)
−0.173345 + 0.984861i \(0.555457\pi\)
\(522\) 1.94842 6.19293i 0.0852799 0.271057i
\(523\) 12.7356 + 2.01712i 0.556888 + 0.0882023i 0.428533 0.903526i \(-0.359030\pi\)
0.128354 + 0.991728i \(0.459030\pi\)
\(524\) −5.73764 9.93788i −0.250650 0.434138i
\(525\) −3.35864 + 2.53075i −0.146583 + 0.110451i
\(526\) 4.88187 8.45565i 0.212860 0.368684i
\(527\) −0.127372 + 0.157291i −0.00554840 + 0.00685170i
\(528\) −2.98954 4.30656i −0.130103 0.187419i
\(529\) −2.63480 12.3958i −0.114557 0.538946i
\(530\) 0.804269 13.5985i 0.0349352 0.590680i
\(531\) 8.03194 + 3.99838i 0.348557 + 0.173515i
\(532\) −0.626479 + 0.626479i −0.0271613 + 0.0271613i
\(533\) 0.362833 + 6.92327i 0.0157160 + 0.299880i
\(534\) 5.64551 + 9.11675i 0.244305 + 0.394520i
\(535\) 11.9869 + 1.34132i 0.518239 + 0.0579903i
\(536\) −16.1969 + 1.70236i −0.699600 + 0.0735309i
\(537\) 16.9534 18.0331i 0.731592 0.778187i
\(538\) 5.74924 4.65564i 0.247867 0.200719i
\(539\) −16.5635 + 12.0341i −0.713440 + 0.518344i
\(540\) −11.5762 + 0.996165i −0.498159 + 0.0428681i
\(541\) −19.9464 14.4919i −0.857562 0.623055i 0.0696586 0.997571i \(-0.477809\pi\)
−0.927221 + 0.374516i \(0.877809\pi\)
\(542\) −6.61141 + 0.346489i −0.283984 + 0.0148830i
\(543\) −0.861868 + 6.79160i −0.0369863 + 0.291455i
\(544\) −0.0113877 + 0.0535751i −0.000488245 + 0.00229701i
\(545\) 0.631497 + 13.8255i 0.0270503 + 0.592220i
\(546\) −0.438842 + 0.518706i −0.0187807 + 0.0221986i
\(547\) −4.02034 + 6.19077i −0.171897 + 0.264698i −0.914110 0.405465i \(-0.867109\pi\)
0.742213 + 0.670164i \(0.233776\pi\)
\(548\) −1.54078 + 9.72813i −0.0658190 + 0.415565i
\(549\) −4.22268 15.1900i −0.180219 0.648294i
\(550\) −4.11289 + 14.5642i −0.175374 + 0.621019i
\(551\) −3.41940 + 1.97419i −0.145671 + 0.0841033i
\(552\) −0.119705 + 5.56485i −0.00509497 + 0.236856i
\(553\) −0.413628 + 7.89249i −0.0175892 + 0.335623i
\(554\) −2.79190 3.10072i −0.118616 0.131737i
\(555\) −0.182571 + 0.0751870i −0.00774973 + 0.00319151i
\(556\) 5.91500 6.56927i 0.250852 0.278599i
\(557\) 15.7462 + 15.7462i 0.667189 + 0.667189i 0.957064 0.289876i \(-0.0936140\pi\)
−0.289876 + 0.957064i \(0.593614\pi\)
\(558\) −7.34048 + 8.30725i −0.310747 + 0.351674i
\(559\) 2.25284 3.10076i 0.0952848 0.131148i
\(560\) 0.328595 + 1.03491i 0.0138857 + 0.0437328i
\(561\) −0.0683359 0.278892i −0.00288514 0.0117748i
\(562\) 6.36237 16.5746i 0.268381 0.699155i
\(563\) −4.49302 + 11.7047i −0.189358 + 0.493295i −0.995089 0.0989873i \(-0.968440\pi\)
0.805730 + 0.592282i \(0.201773\pi\)
\(564\) 4.43555 + 1.29136i 0.186770 + 0.0543760i
\(565\) 9.97133 + 31.4047i 0.419497 + 1.32120i
\(566\) 7.87210 10.8350i 0.330889 0.455430i
\(567\) 1.91098 3.93041i 0.0802535 0.165062i
\(568\) −11.6136 11.6136i −0.487295 0.487295i
\(569\) −21.8734 + 24.2929i −0.916982 + 1.01841i 0.0827795 + 0.996568i \(0.473620\pi\)
−0.999761 + 0.0218437i \(0.993046\pi\)
\(570\) 5.59729 + 4.31315i 0.234445 + 0.180658i
\(571\) 10.6183 + 11.7928i 0.444362 + 0.493514i 0.923163 0.384410i \(-0.125595\pi\)
−0.478801 + 0.877924i \(0.658928\pi\)
\(572\) −0.127966 + 2.44174i −0.00535053 + 0.102094i
\(573\) −10.0972 6.12286i −0.421816 0.255786i
\(574\) −3.60906 + 2.08369i −0.150639 + 0.0869716i
\(575\) 12.6219 9.94334i 0.526370 0.414666i
\(576\) −0.749344 + 2.90491i −0.0312227 + 0.121038i
\(577\) 3.12270 19.7160i 0.130000 0.820787i −0.833391 0.552685i \(-0.813603\pi\)
0.963390 0.268102i \(-0.0863966\pi\)
\(578\) 9.25723 14.2549i 0.385050 0.592925i
\(579\) 3.54060 + 0.639114i 0.147142 + 0.0265607i
\(580\) 0.220797 + 4.83396i 0.00916810 + 0.200719i
\(581\) 0.467655 2.20014i 0.0194016 0.0912774i
\(582\) 19.2172 + 14.6037i 0.796577 + 0.605343i
\(583\) 18.4139 0.965030i 0.762625 0.0399675i
\(584\) 5.56397 + 4.04246i 0.230239 + 0.167278i
\(585\) 4.55254 + 2.93947i 0.188224 + 0.121532i
\(586\) −18.2137 + 13.2330i −0.752401 + 0.546651i
\(587\) −29.6522 + 24.0119i −1.22388 + 0.991078i −0.224015 + 0.974586i \(0.571916\pi\)
−0.999864 + 0.0164919i \(0.994750\pi\)
\(588\) 11.4049 + 2.68177i 0.470329 + 0.110594i
\(589\) 6.70509 0.704733i 0.276278 0.0290380i
\(590\) −6.64595 0.743674i −0.273610 0.0306166i
\(591\) 43.8288 1.35265i 1.80288 0.0556406i
\(592\) 0.00266812 + 0.0509108i 0.000109659 + 0.00209242i
\(593\) −29.0596 + 29.0596i −1.19334 + 1.19334i −0.217210 + 0.976125i \(0.569696\pi\)
−0.976125 + 0.217210i \(0.930304\pi\)
\(594\) −3.08258 15.4224i −0.126480 0.632791i
\(595\) −0.00351132 + 0.0593689i −0.000143950 + 0.00243389i
\(596\) 2.88857 + 13.5896i 0.118320 + 0.556653i
\(597\) 0.514066 1.09085i 0.0210393 0.0446455i
\(598\) 1.63374 2.01750i 0.0668085 0.0825016i
\(599\) 11.2299 19.4508i 0.458842 0.794738i −0.540058 0.841628i \(-0.681598\pi\)
0.998900 + 0.0468899i \(0.0149310\pi\)
\(600\) 7.84897 3.65973i 0.320433 0.149408i
\(601\) −1.87674 3.25060i −0.0765537 0.132595i 0.825207 0.564830i \(-0.191058\pi\)
−0.901761 + 0.432235i \(0.857725\pi\)
\(602\) 2.27556 + 0.360413i 0.0927447 + 0.0146893i
\(603\) −46.6061 14.6632i −1.89795 0.597131i
\(604\) 12.6743 + 4.11814i 0.515711 + 0.167565i
\(605\) 4.05651 + 0.670443i 0.164921 + 0.0272574i
\(606\) −7.79427 16.1464i −0.316621 0.655904i
\(607\) 3.32089 + 12.3937i 0.134791 + 0.503045i 0.999999 + 0.00163237i \(0.000519599\pi\)
−0.865208 + 0.501413i \(0.832814\pi\)
\(608\) 1.53017 0.993703i 0.0620565 0.0403000i
\(609\) −1.60361 0.861013i −0.0649817 0.0348900i
\(610\) 6.84324 + 9.55317i 0.277075 + 0.386796i
\(611\) −1.26645 1.74313i −0.0512353 0.0705193i
\(612\) −0.0953361 + 0.133831i −0.00385373 + 0.00540981i
\(613\) −1.96542 12.4091i −0.0793824 0.501201i −0.995059 0.0992849i \(-0.968344\pi\)
0.915677 0.401916i \(-0.131656\pi\)
\(614\) 13.4852 + 6.00401i 0.544220 + 0.242302i
\(615\) 20.1801 + 26.4108i 0.813741 + 1.06499i
\(616\) −1.34271 + 0.597812i −0.0540992 + 0.0240865i
\(617\) 12.0864 + 18.6114i 0.486579 + 0.749266i 0.993635 0.112647i \(-0.0359329\pi\)
−0.507056 + 0.861913i \(0.669266\pi\)
\(618\) 31.8620 + 4.04335i 1.28168 + 0.162647i
\(619\) 26.7747 + 24.1081i 1.07617 + 0.968986i 0.999606 0.0280789i \(-0.00893897\pi\)
0.0765622 + 0.997065i \(0.475606\pi\)
\(620\) 3.01286 7.69393i 0.120999 0.308996i
\(621\) −6.97689 + 15.1710i −0.279973 + 0.608792i
\(622\) −13.6017 26.6948i −0.545377 1.07036i
\(623\) 2.80666 1.07737i 0.112446 0.0431641i
\(624\) 1.10606 0.856952i 0.0442779 0.0343055i
\(625\) −22.5573 10.7782i −0.902292 0.431126i
\(626\) 5.99864 + 3.46331i 0.239754 + 0.138422i
\(627\) −4.95955 + 8.17878i −0.198065 + 0.326629i
\(628\) 4.19214 + 2.72241i 0.167285 + 0.108636i
\(629\) −0.000862872 0.00265565i −3.44050e−5 0.000105888i
\(630\) −0.331978 + 3.24051i −0.0132263 + 0.129105i
\(631\) −13.8176 42.5263i −0.550071 1.69294i −0.708617 0.705593i \(-0.750681\pi\)
0.158546 0.987352i \(-0.449319\pi\)
\(632\) 4.21243 15.7210i 0.167561 0.625347i
\(633\) −3.93288 + 11.2732i −0.156318 + 0.448070i
\(634\) 3.77492 + 8.47862i 0.149921 + 0.336729i
\(635\) 10.8532 + 19.0933i 0.430698 + 0.757696i
\(636\) −7.29902 7.61994i −0.289425 0.302150i
\(637\) −3.43878 4.24655i −0.136250 0.168254i
\(638\) −6.46947 + 1.02466i −0.256129 + 0.0405668i
\(639\) −18.0867 45.8326i −0.715498 1.81311i
\(640\) −0.218794 2.22534i −0.00864858 0.0879642i
\(641\) −26.2758 2.76170i −1.03783 0.109081i −0.429745 0.902950i \(-0.641397\pi\)
−0.608088 + 0.793869i \(0.708063\pi\)
\(642\) 7.07602 6.10090i 0.279268 0.240783i
\(643\) −0.423651 + 0.113517i −0.0167071 + 0.00447667i −0.267163 0.963651i \(-0.586086\pi\)
0.250456 + 0.968128i \(0.419420\pi\)
\(644\) 1.52641 + 0.324449i 0.0601490 + 0.0127851i
\(645\) 0.518542 18.3682i 0.0204176 0.723247i
\(646\) 0.0977486 0.0207771i 0.00384587 0.000817465i
\(647\) 38.4660 19.5994i 1.51225 0.770532i 0.515965 0.856609i \(-0.327433\pi\)
0.996288 + 0.0860776i \(0.0274333\pi\)
\(648\) −5.53218 + 7.09894i −0.217325 + 0.278873i
\(649\) 9.05215i 0.355328i
\(650\) −3.93922 0.892767i −0.154509 0.0350172i
\(651\) 1.90351 + 2.45685i 0.0746045 + 0.0962916i
\(652\) −7.81012 6.32451i −0.305868 0.247687i
\(653\) −46.8004 2.45271i −1.83144 0.0959818i −0.894842 0.446382i \(-0.852712\pi\)
−0.936600 + 0.350400i \(0.886046\pi\)
\(654\) 8.18427 + 6.92415i 0.320030 + 0.270756i
\(655\) 11.4954 + 22.9405i 0.449161 + 0.896359i
\(656\) 8.16199 2.65199i 0.318672 0.103543i
\(657\) 10.4827 + 17.7710i 0.408969 + 0.693311i
\(658\) 0.587996 1.15401i 0.0229225 0.0449879i
\(659\) −0.00347215 + 0.0330353i −0.000135256 + 0.00128687i −0.994589 0.103885i \(-0.966873\pi\)
0.994454 + 0.105172i \(0.0335393\pi\)
\(660\) 6.10460 + 10.0076i 0.237621 + 0.389547i
\(661\) 2.12981 + 20.2638i 0.0828401 + 0.788171i 0.954530 + 0.298114i \(0.0963575\pi\)
−0.871690 + 0.490057i \(0.836976\pi\)
\(662\) 10.1202 + 3.88478i 0.393333 + 0.150986i
\(663\) 0.0733782 0.0221091i 0.00284977 0.000858645i
\(664\) −1.88402 + 4.23159i −0.0731143 + 0.164217i
\(665\) 1.48111 1.31570i 0.0574351 0.0510206i
\(666\) −0.0534728 + 0.143290i −0.00207203 + 0.00555236i
\(667\) 6.19648 + 3.15727i 0.239929 + 0.122250i
\(668\) 18.6490 + 4.99698i 0.721551 + 0.193339i
\(669\) −0.320515 + 4.33116i −0.0123918 + 0.167452i
\(670\) 36.3790 1.66165i 1.40544 0.0641952i
\(671\) −11.8209 + 10.6436i −0.456342 + 0.410892i
\(672\) 0.760825 + 0.358541i 0.0293494 + 0.0138310i
\(673\) −10.2739 26.7644i −0.396030 1.03169i −0.976137 0.217154i \(-0.930323\pi\)
0.580107 0.814540i \(-0.303011\pi\)
\(674\) −26.4786 −1.01992
\(675\) 25.9715 0.695327i 0.999642 0.0267631i
\(676\) 12.3474 0.474901
\(677\) −9.26473 24.1354i −0.356072 0.927600i −0.988260 0.152785i \(-0.951176\pi\)
0.632187 0.774816i \(-0.282157\pi\)
\(678\) 23.0875 + 10.8800i 0.886670 + 0.417846i
\(679\) 5.02874 4.52790i 0.192985 0.173765i
\(680\) 0.0324923 0.118085i 0.00124602 0.00452836i
\(681\) 2.96748 40.0999i 0.113714 1.53663i
\(682\) 10.8035 + 2.89479i 0.413687 + 0.110847i
\(683\) 23.9462 + 12.2012i 0.916277 + 0.466866i 0.847518 0.530767i \(-0.178096\pi\)
0.0687591 + 0.997633i \(0.478096\pi\)
\(684\) 5.39792 0.906733i 0.206395 0.0346698i
\(685\) 4.72359 21.5114i 0.180479 0.821908i
\(686\) 2.71855 6.10597i 0.103795 0.233127i
\(687\) 39.6120 11.9352i 1.51129 0.455357i
\(688\) −4.42941 1.70029i −0.168870 0.0648230i
\(689\) 0.514416 + 4.89434i 0.0195977 + 0.186460i
\(690\) 1.00187 12.4059i 0.0381405 0.472284i
\(691\) 3.20966 30.5379i 0.122101 1.16172i −0.746215 0.665705i \(-0.768131\pi\)
0.868316 0.496011i \(-0.165202\pi\)
\(692\) 0.325089 0.638023i 0.0123580 0.0242540i
\(693\) −4.40914 + 0.0412038i −0.167489 + 0.00156520i
\(694\) −28.8280 + 9.36680i −1.09430 + 0.355559i
\(695\) −14.0705 + 13.8828i −0.533726 + 0.526605i
\(696\) 2.86155 + 2.42097i 0.108467 + 0.0917665i
\(697\) 0.469411 + 0.0246008i 0.0177802 + 0.000931821i
\(698\) 17.7866 + 14.4033i 0.673235 + 0.545175i
\(699\) 13.5114 + 17.4390i 0.511047 + 0.659605i
\(700\) −0.596851 2.35347i −0.0225589 0.0889528i
\(701\) 25.9358i 0.979583i 0.871840 + 0.489792i \(0.162927\pi\)
−0.871840 + 0.489792i \(0.837073\pi\)
\(702\) 4.06746 1.03702i 0.153516 0.0391398i
\(703\) 0.0828770 0.0422279i 0.00312576 0.00159266i
\(704\) 2.96062 0.629298i 0.111582 0.0237176i
\(705\) −9.73041 3.46811i −0.366468 0.130616i
\(706\) −9.56408 2.03291i −0.359949 0.0765095i
\(707\) −4.85533 + 1.30098i −0.182604 + 0.0489285i
\(708\) −3.92319 + 3.38255i −0.147442 + 0.127124i
\(709\) 42.8648 + 4.50527i 1.60982 + 0.169199i 0.866303 0.499518i \(-0.166490\pi\)
0.743517 + 0.668717i \(0.233156\pi\)
\(710\) 24.3902 + 27.4567i 0.915350 + 1.03043i
\(711\) 30.3717 38.2309i 1.13903 1.43377i
\(712\) −6.11482 + 0.968492i −0.229163 + 0.0362958i
\(713\) −7.47322 9.22866i −0.279874 0.345616i
\(714\) 0.0318664 + 0.0332675i 0.00119257 + 0.00124501i
\(715\) 0.607999 5.43347i 0.0227379 0.203200i
\(716\) 5.81226 + 13.0545i 0.217214 + 0.487871i
\(717\) 6.45898 18.5141i 0.241215 0.691421i
\(718\) −3.38424 + 12.6302i −0.126299 + 0.471353i
\(719\) −8.39639 25.8414i −0.313133 0.963723i −0.976516 0.215444i \(-0.930880\pi\)
0.663384 0.748279i \(-0.269120\pi\)
\(720\) 2.05617 6.38531i 0.0766288 0.237966i
\(721\) 2.78251 8.56370i 0.103626 0.318929i
\(722\) 13.1429 + 8.53512i 0.489129 + 0.317644i
\(723\) 21.9557 36.2072i 0.816543 1.34656i
\(724\) −3.42303 1.97629i −0.127216 0.0734482i
\(725\) 0.145322 10.8194i 0.00539712 0.401821i
\(726\) 2.51757 1.95056i 0.0934359 0.0723920i
\(727\) 42.7183 16.3980i 1.58433 0.608169i 0.602535 0.798093i \(-0.294157\pi\)
0.981799 + 0.189924i \(0.0608241\pi\)
\(728\) −0.178089 0.349520i −0.00660042 0.0129541i
\(729\) −23.7041 + 12.9273i −0.877931 + 0.478788i
\(730\) −11.8860 9.75801i −0.439922 0.361160i
\(731\) −0.193119 0.173886i −0.00714278 0.00643139i
\(732\) 9.03009 + 1.14594i 0.333762 + 0.0423550i
\(733\) 4.99056 + 7.68478i 0.184330 + 0.283844i 0.918740 0.394862i \(-0.129208\pi\)
−0.734410 + 0.678706i \(0.762541\pi\)
\(734\) 6.29360 2.80209i 0.232301 0.103427i
\(735\) −25.1035 7.49183i −0.925958 0.276340i
\(736\) −2.93578 1.30709i −0.108214 0.0481801i
\(737\) 7.71131 + 48.6873i 0.284050 + 1.79342i
\(738\) 25.6291 + 2.45181i 0.943419 + 0.0902523i
\(739\) −30.6535 42.1909i −1.12761 1.55202i −0.792535 0.609826i \(-0.791239\pi\)
−0.335072 0.942193i \(-0.608761\pi\)
\(740\) 0.000765527 0.113994i 2.81413e−5 0.00419049i
\(741\) −2.24915 1.20762i −0.0826248 0.0443630i
\(742\) −2.48101 + 1.61119i −0.0910807 + 0.0591485i
\(743\) −4.90855 18.3190i −0.180077 0.672058i −0.995631 0.0933760i \(-0.970234\pi\)
0.815554 0.578681i \(-0.196433\pi\)
\(744\) −2.78238 5.76392i −0.102007 0.211315i
\(745\) −4.65367 30.7157i −0.170497 1.12534i
\(746\) −22.1796 7.20660i −0.812054 0.263852i
\(747\) −10.2395 + 9.39443i −0.374644 + 0.343724i
\(748\) 0.163741 + 0.0259340i 0.00598695 + 0.000948239i
\(749\) −1.30969 2.26845i −0.0478550 0.0828872i
\(750\) −18.0034 + 7.13292i −0.657390 + 0.260457i
\(751\) 13.0100 22.5340i 0.474743 0.822279i −0.524839 0.851202i \(-0.675874\pi\)
0.999582 + 0.0289227i \(0.00920765\pi\)
\(752\) −1.67852 + 2.07280i −0.0612092 + 0.0755871i
\(753\) −2.91610 + 6.18798i −0.106269 + 0.225502i
\(754\) −0.363469 1.70999i −0.0132367 0.0622740i
\(755\) −27.7475 10.8656i −1.00984 0.395441i
\(756\) 1.66543 + 1.89552i 0.0605713 + 0.0689392i
\(757\) −16.4627 + 16.4627i −0.598347 + 0.598347i −0.939872 0.341526i \(-0.889056\pi\)
0.341526 + 0.939872i \(0.389056\pi\)
\(758\) −0.595066 11.3545i −0.0216138 0.412415i
\(759\) 16.8393 0.519698i 0.611229 0.0188638i
\(760\) −3.54678 + 2.01610i −0.128655 + 0.0731316i
\(761\) −8.79913 + 0.924826i −0.318968 + 0.0335249i −0.262660 0.964888i \(-0.584600\pi\)
−0.0563085 + 0.998413i \(0.517933\pi\)
\(762\) 16.5604 + 3.89404i 0.599918 + 0.141066i
\(763\) 2.33574 1.89145i 0.0845596 0.0684750i
\(764\) 5.51563 4.00734i 0.199548 0.144980i
\(765\) 0.230474 0.286147i 0.00833282 0.0103457i
\(766\) 0.871703 + 0.633329i 0.0314959 + 0.0228831i
\(767\) 2.41266 0.126442i 0.0871160 0.00456556i
\(768\) −1.37904 1.04797i −0.0497618 0.0378155i
\(769\) 0.605366 2.84802i 0.0218300 0.102702i −0.965884 0.258976i \(-0.916615\pi\)
0.987714 + 0.156274i \(0.0499482\pi\)
\(770\) 3.07607 1.15715i 0.110854 0.0417009i
\(771\) 25.5053 + 4.60398i 0.918552 + 0.165808i
\(772\) −1.13133 + 1.74209i −0.0407173 + 0.0626991i
\(773\) 0.944704 5.96463i 0.0339786 0.214533i −0.964857 0.262776i \(-0.915362\pi\)
0.998836 + 0.0482428i \(0.0153621\pi\)
\(774\) −10.1583 9.97019i −0.365132 0.358371i
\(775\) −7.74096 + 16.7764i −0.278063 + 0.602626i
\(776\) −12.0682 + 6.96759i −0.433224 + 0.250122i
\(777\) 0.0366642 + 0.0222329i 0.00131532 + 0.000797601i
\(778\) −0.354774 + 6.76949i −0.0127193 + 0.242698i
\(779\) −10.4773 11.6362i −0.375387 0.416910i
\(780\) −2.58205 + 1.76684i −0.0924522 + 0.0632629i
\(781\) −33.2637 + 36.9430i −1.19027 + 1.32193i
\(782\) −0.124462 0.124462i −0.00445076 0.00445076i
\(783\) 4.98281 + 10.0806i 0.178071 + 0.360250i
\(784\) −3.97590 + 5.47235i −0.141996 + 0.195441i
\(785\) −8.99815 6.63032i −0.321158 0.236646i
\(786\) 19.0834 + 5.55592i 0.680684 + 0.198173i
\(787\) 4.09227 10.6607i 0.145874 0.380014i −0.841104 0.540874i \(-0.818094\pi\)
0.986977 + 0.160860i \(0.0514269\pi\)
\(788\) −9.07266 + 23.6351i −0.323200 + 0.841965i
\(789\) 4.02465 + 16.4254i 0.143281 + 0.584760i
\(790\) −11.4783 + 34.5357i −0.408380 + 1.22873i
\(791\) 4.20589 5.78891i 0.149544 0.205830i
\(792\) 8.89910 + 1.80481i 0.316216 + 0.0641313i
\(793\) −3.00194 3.00194i −0.106602 0.106602i
\(794\) 18.8459 20.9305i 0.668815 0.742795i
\(795\) 15.2866 + 17.9726i 0.542161 + 0.637422i
\(796\) 0.465870 + 0.517401i 0.0165123 + 0.0183388i
\(797\) −2.35842 + 45.0013i −0.0835395 + 1.59403i 0.559918 + 0.828548i \(0.310832\pi\)
−0.643458 + 0.765482i \(0.722501\pi\)
\(798\) 0.0330019 1.53420i 0.00116825 0.0543100i
\(799\) −0.126515 + 0.0730437i −0.00447579 + 0.00258410i
\(800\) 0.194596 + 4.99621i 0.00688001 + 0.176643i
\(801\) −17.9844 4.63922i −0.635447 0.163919i
\(802\) 6.02721 38.0543i 0.212828 1.34374i
\(803\) 11.3374 17.4581i 0.400088 0.616082i
\(804\) 18.2195 21.5352i 0.642551 0.759488i
\(805\) −3.36437 0.925740i −0.118579 0.0326280i
\(806\) −0.620638 + 2.91987i −0.0218610 + 0.102848i
\(807\) −1.61312 + 12.7116i −0.0567846 + 0.447468i
\(808\) 10.3373 0.541753i 0.363664 0.0190588i
\(809\) 14.2655 + 10.3645i 0.501547 + 0.364395i 0.809607 0.586972i \(-0.199680\pi\)
−0.308061 + 0.951367i \(0.599680\pi\)
\(810\) 13.2860 15.1157i 0.466821 0.531111i
\(811\) −31.0478 + 22.5576i −1.09024 + 0.792104i −0.979439 0.201739i \(-0.935341\pi\)
−0.110798 + 0.993843i \(0.535341\pi\)
\(812\) 0.816671 0.661327i 0.0286595 0.0232080i
\(813\) 7.85442 8.35466i 0.275466 0.293011i
\(814\) 0.153461 0.0161294i 0.00537880 0.000565335i
\(815\) 16.5985 + 15.1485i 0.581421 + 0.530627i
\(816\) −0.0499457 0.0806557i −0.00174845 0.00282351i
\(817\) 0.453045 + 8.64462i 0.0158501 + 0.302437i
\(818\) −13.1814 + 13.1814i −0.460877 + 0.460877i
\(819\) −0.0725695 1.17459i −0.00253579 0.0410433i
\(820\) −18.5690 + 4.84215i −0.648459 + 0.169095i
\(821\) −4.42058 20.7972i −0.154279 0.725827i −0.985471 0.169842i \(-0.945674\pi\)
0.831192 0.555985i \(-0.187659\pi\)
\(822\) −9.72828 14.0140i −0.339313 0.488794i
\(823\) 4.84604 5.98436i 0.168922 0.208602i −0.685654 0.727928i \(-0.740484\pi\)
0.854576 + 0.519326i \(0.173817\pi\)
\(824\) −9.27153 + 16.0588i −0.322989 + 0.559433i
\(825\) −12.3053 23.1446i −0.428415 0.805793i
\(826\) 0.726136 + 1.25770i 0.0252655 + 0.0437611i
\(827\) −26.5586 4.20647i −0.923534 0.146273i −0.323482 0.946234i \(-0.604853\pi\)
−0.600052 + 0.799961i \(0.704853\pi\)
\(828\) −6.51765 7.10394i −0.226504 0.246879i
\(829\) 12.7880 + 4.15507i 0.444145 + 0.144311i 0.522547 0.852610i \(-0.324982\pi\)
−0.0784023 + 0.996922i \(0.524982\pi\)
\(830\) 4.76411 9.19688i 0.165365 0.319228i
\(831\) 7.20715 + 0.533344i 0.250013 + 0.0185015i
\(832\) 0.209080 + 0.780298i 0.00724856 + 0.0270520i
\(833\) −0.310718 + 0.201783i −0.0107657 + 0.00699135i
\(834\) 0.472306 + 15.3037i 0.0163546 + 0.529925i
\(835\) −40.9680 13.6161i −1.41775 0.471206i
\(836\) −3.24597 4.46769i −0.112264 0.154518i
\(837\) −0.771619 19.1855i −0.0266711 0.663148i
\(838\) −1.16114 7.33114i −0.0401109 0.253250i
\(839\) 5.65728 + 2.51878i 0.195311 + 0.0869580i 0.502062 0.864832i \(-0.332575\pi\)
−0.306751 + 0.951790i \(0.599242\pi\)
\(840\) −1.65095 0.900767i −0.0569633 0.0310794i
\(841\) −22.2145 + 9.89054i −0.766018 + 0.341053i
\(842\) −5.94782 9.15884i −0.204975 0.315634i
\(843\) 11.9003 + 28.3544i 0.409867 + 0.976576i
\(844\) −5.12273 4.61252i −0.176332 0.158770i
\(845\) −27.5615 1.63010i −0.948145 0.0560772i
\(846\) −7.09520 + 3.69910i −0.243938 + 0.127178i
\(847\) −0.405359 0.795562i −0.0139283 0.0273358i
\(848\) 5.68741 2.18319i 0.195307 0.0749712i
\(849\) 3.13525 + 22.9842i 0.107601 + 0.788815i
\(850\) −0.0881178 + 0.259296i −0.00302242 + 0.00889379i
\(851\) −0.141883 0.0819160i −0.00486368 0.00280805i
\(852\) 28.4408 + 0.611785i 0.974365 + 0.0209594i
\(853\) −28.0483 18.2147i −0.960354 0.623661i −0.0336421 0.999434i \(-0.510711\pi\)
−0.926712 + 0.375773i \(0.877377\pi\)
\(854\) 0.788600 2.42706i 0.0269853 0.0830523i
\(855\) −12.1688 + 1.31135i −0.416163 + 0.0448472i
\(856\) 1.66689 + 5.13016i 0.0569731 + 0.175345i
\(857\) 3.80251 14.1912i 0.129891 0.484761i −0.870075 0.492919i \(-0.835930\pi\)
0.999967 + 0.00815755i \(0.00259666\pi\)
\(858\) −2.76544 3.20745i −0.0944106 0.109500i
\(859\) 15.1257 + 33.9730i 0.516084 + 1.15914i 0.964202 + 0.265168i \(0.0854276\pi\)
−0.448119 + 0.893974i \(0.647906\pi\)
\(860\) 9.66271 + 4.38010i 0.329496 + 0.149360i
\(861\) 2.01770 6.93038i 0.0687629 0.236187i
\(862\) −15.6040 19.2694i −0.531476 0.656318i
\(863\) −15.1595 + 2.40103i −0.516037 + 0.0817322i −0.409021 0.912525i \(-0.634130\pi\)
−0.107016 + 0.994257i \(0.534130\pi\)
\(864\) −2.54315 4.53127i −0.0865198 0.154157i
\(865\) −0.809885 + 1.38126i −0.0275369 + 0.0469641i
\(866\) −27.1017 2.84850i −0.920952 0.0967959i
\(867\) 5.50015 + 28.9213i 0.186795 + 0.982219i
\(868\) −1.73325 + 0.464422i −0.0588302 + 0.0157635i
\(869\) −48.1857 10.2422i −1.63459 0.347442i
\(870\) −6.06785 5.78178i −0.205720 0.196021i
\(871\) −12.8688 + 2.73535i −0.436044 + 0.0926839i
\(872\) −5.51480 + 2.80993i −0.186755 + 0.0951562i
\(873\) −41.5339 + 4.75820i −1.40571 + 0.161041i
\(874\) 5.86329i 0.198329i
\(875\) 1.02157 + 5.33213i 0.0345353 + 0.180259i
\(876\) −11.8028 + 1.61000i −0.398779 + 0.0543970i
\(877\) −24.3134 19.6886i −0.821007 0.664838i 0.123858 0.992300i \(-0.460473\pi\)
−0.944864 + 0.327462i \(0.893807\pi\)
\(878\) 21.3377 + 1.11826i 0.720112 + 0.0377395i
\(879\) 6.92692 38.3741i 0.233639 1.29433i
\(880\) −6.69167 + 1.01384i −0.225576 + 0.0341765i
\(881\) 37.2659 12.1084i 1.25552 0.407943i 0.395625 0.918412i \(-0.370528\pi\)
0.859896 + 0.510469i \(0.170528\pi\)
\(882\) −17.4783 + 10.3101i −0.588526 + 0.347158i
\(883\) −3.84098 + 7.53836i −0.129259 + 0.253686i −0.946561 0.322524i \(-0.895469\pi\)
0.817302 + 0.576210i \(0.195469\pi\)
\(884\) −0.00462498 + 0.0440038i −0.000155555 + 0.00148001i
\(885\) 9.20377 7.03248i 0.309381 0.236394i
\(886\) −2.03690 19.3798i −0.0684309 0.651076i
\(887\) 10.1565 + 3.89871i 0.341021 + 0.130906i 0.522851 0.852424i \(-0.324869\pi\)
−0.181829 + 0.983330i \(0.558202\pi\)
\(888\) −0.0643347 0.0604825i −0.00215893 0.00202966i
\(889\) 1.93991 4.35712i 0.0650626 0.146133i
\(890\) 13.7772 1.35456i 0.461811 0.0454050i
\(891\) 22.3337 + 15.5971i 0.748206 + 0.522522i
\(892\) −2.23414 1.13835i −0.0748046 0.0381148i
\(893\) 4.70052 + 1.25950i 0.157297 + 0.0421475i
\(894\) −19.8951 13.5371i −0.665391 0.452747i
\(895\) −11.2505 29.9073i −0.376062 0.999689i
\(896\) −0.360867 + 0.324926i −0.0120557 + 0.0108550i
\(897\) 0.373729 + 4.48090i 0.0124784 + 0.149613i
\(898\) 12.1051 + 31.5350i 0.403954 + 1.05233i
\(899\) −7.99675 −0.266707
\(900\) −5.43269 + 13.9816i −0.181090 + 0.466054i
\(901\) 0.333674 0.0111163
\(902\) −9.30886 24.2504i −0.309951 0.807451i
\(903\) −3.27809 + 2.27559i −0.109088 + 0.0757269i
\(904\) −10.9506 + 9.86000i −0.364213 + 0.327939i
\(905\) 7.37988 + 4.86332i 0.245315 + 0.161662i
\(906\) −20.7871 + 10.0344i −0.690604 + 0.333371i
\(907\) −4.94939 1.32619i −0.164342 0.0440353i 0.175710 0.984442i \(-0.443778\pi\)
−0.340052 + 0.940407i \(0.610445\pi\)
\(908\) 20.6847 + 10.5394i 0.686446 + 0.349762i
\(909\) 29.0945 + 10.8575i 0.965003 + 0.360120i
\(910\) 0.351381 + 0.803697i 0.0116482 + 0.0266423i
\(911\) −9.99522 + 22.4496i −0.331156 + 0.743789i 0.668844 + 0.743403i \(0.266790\pi\)
−1.00000 0.000386179i \(0.999877\pi\)
\(912\) −0.723358 + 3.07625i −0.0239528 + 0.101865i
\(913\) 13.0889 + 5.02435i 0.433179 + 0.166282i
\(914\) −2.01479 19.1694i −0.0666432 0.634067i
\(915\) −20.0054 3.75007i −0.661358 0.123974i
\(916\) −2.49672 + 23.7547i −0.0824940 + 0.784878i
\(917\) 2.52979 4.96498i 0.0835409 0.163958i
\(918\) −0.0410997 0.281620i −0.00135649 0.00929486i
\(919\) 21.8273 7.09211i 0.720015 0.233947i 0.0739855 0.997259i \(-0.476428\pi\)
0.646030 + 0.763312i \(0.276428\pi\)
\(920\) 6.38059 + 3.30523i 0.210362 + 0.108970i
\(921\) −24.0609 + 8.64713i −0.792833 + 0.284933i
\(922\) 24.2385 + 1.27029i 0.798252 + 0.0418346i
\(923\) −10.3110 8.34968i −0.339391 0.274833i
\(924\) 0.963208 2.35647i 0.0316872 0.0775222i
\(925\) −0.0167582 + 0.254352i −0.000551005 + 0.00836304i
\(926\) 24.6876i 0.811285i
\(927\) −44.6974 + 33.1171i −1.46806 + 1.08771i
\(928\) −1.92820 + 0.982467i −0.0632962 + 0.0322510i
\(929\) 47.2478 10.0428i 1.55015 0.329495i 0.648247 0.761430i \(-0.275502\pi\)
0.901905 + 0.431935i \(0.142169\pi\)
\(930\) 5.44979 + 13.2334i 0.178706 + 0.433939i
\(931\) 12.0717 + 2.56592i 0.395634 + 0.0840946i
\(932\) −12.3028 + 3.29652i −0.402991 + 0.107981i
\(933\) 48.9966 + 17.0934i 1.60408 + 0.559612i
\(934\) 10.4786 + 1.10135i 0.342871 + 0.0360372i
\(935\) −0.362073 0.0795059i −0.0118410 0.00260012i
\(936\) −0.356730 + 2.39707i −0.0116601 + 0.0783508i
\(937\) −35.2519 + 5.58336i −1.15163 + 0.182400i −0.702914 0.711274i \(-0.748118\pi\)
−0.448715 + 0.893675i \(0.648118\pi\)
\(938\) −4.97695 6.14602i −0.162503 0.200675i
\(939\) −11.6526 + 2.85518i −0.380267 + 0.0931754i
\(940\) 4.02038 4.40523i 0.131130 0.143683i
\(941\) 10.9708 + 24.6408i 0.357637 + 0.803266i 0.999340 + 0.0363133i \(0.0115614\pi\)
−0.641703 + 0.766953i \(0.721772\pi\)
\(942\) −8.50531 + 1.61751i −0.277118 + 0.0527013i
\(943\) −7.13805 + 26.6396i −0.232447 + 0.867503i
\(944\) −0.924180 2.84433i −0.0300795 0.0925752i
\(945\) −3.46728 4.45098i −0.112791 0.144790i
\(946\) −4.43766 + 13.6577i −0.144281 + 0.444051i
\(947\) −18.7962 12.2064i −0.610795 0.396655i 0.201848 0.979417i \(-0.435305\pi\)
−0.812643 + 0.582762i \(0.801972\pi\)
\(948\) 13.5668 + 24.7108i 0.440628 + 0.802570i
\(949\) 4.81144 + 2.77788i 0.156186 + 0.0901740i
\(950\) 8.18317 4.03202i 0.265497 0.130816i
\(951\) −14.8801 6.08224i −0.482520 0.197230i
\(952\) −0.0248304 + 0.00953151i −0.000804759 + 0.000308918i
\(953\) 10.7589 + 21.1155i 0.348514 + 0.683998i 0.997014 0.0772167i \(-0.0246033\pi\)
−0.648500 + 0.761215i \(0.724603\pi\)
\(954\) 18.2592 + 0.785907i 0.591164 + 0.0254447i
\(955\) −12.8408 + 8.21688i −0.415520 + 0.265892i
\(956\) 8.41308 + 7.57517i 0.272098 + 0.244999i
\(957\) 6.86435 9.03287i 0.221893 0.291991i
\(958\) −19.3176 29.7465i −0.624124 0.961067i
\(959\) −4.36931 + 1.94534i −0.141093 + 0.0628184i
\(960\) 2.93989 + 2.52131i 0.0948847 + 0.0813750i
\(961\) −15.8456 7.05493i −0.511150 0.227578i
\(962\) 0.00644251 + 0.0406764i 0.000207715 + 0.00131146i
\(963\) −1.54107 + 16.1090i −0.0496602 + 0.519104i
\(964\) 14.3698 + 19.7783i 0.462819 + 0.637016i
\(965\) 2.75530 3.73927i 0.0886961 0.120371i
\(966\) −2.29797 + 1.42301i −0.0739358 + 0.0457845i
\(967\) 25.2796 16.4168i 0.812937 0.527928i −0.0699290 0.997552i \(-0.522277\pi\)
0.882866 + 0.469624i \(0.155611\pi\)
\(968\) 0.475900 + 1.77608i 0.0152960 + 0.0570855i
\(969\) −0.0973706 + 0.143103i −0.00312799 + 0.00459713i
\(970\) 27.8581 13.9596i 0.894471 0.448215i
\(971\) −2.86887 0.932152i −0.0920663 0.0299142i 0.262622 0.964899i \(-0.415413\pi\)
−0.354688 + 0.934985i \(0.615413\pi\)
\(972\) −1.58575 15.5076i −0.0508628 0.497406i
\(973\) 4.23972 + 0.671506i 0.135919 + 0.0215275i
\(974\) 20.6841 + 35.8259i 0.662762 + 1.14794i
\(975\) 5.99683 3.60300i 0.192052 0.115388i
\(976\) −2.62767 + 4.55126i −0.0841096 + 0.145682i
\(977\) −20.0927 + 24.8124i −0.642821 + 0.793818i −0.989557 0.144145i \(-0.953957\pi\)
0.346736 + 0.937963i \(0.387290\pi\)
\(978\) 17.3464 1.44678i 0.554678 0.0462628i
\(979\) 3.89601 + 18.3293i 0.124517 + 0.585807i
\(980\) 9.59732 11.6903i 0.306575 0.373433i
\(981\) −18.5329 + 1.14502i −0.591709 + 0.0365576i
\(982\) 19.0254 19.0254i 0.607124 0.607124i
\(983\) −1.10450 21.0751i −0.0352280 0.672191i −0.957987 0.286812i \(-0.907404\pi\)
0.922759 0.385378i \(-0.125929\pi\)
\(984\) −7.03161 + 13.0962i −0.224160 + 0.417491i
\(985\) 23.3720 51.5597i 0.744694 1.64283i
\(986\) −0.117881 + 0.0123898i −0.00375410 + 0.000394572i
\(987\) 0.647176 + 2.14792i 0.0205998 + 0.0683692i
\(988\) 1.14543 0.927548i 0.0364409 0.0295092i
\(989\) 12.3352 8.96202i 0.392235 0.284976i
\(990\) −19.6260 5.20350i −0.623756 0.165378i
\(991\) 5.25476 + 3.81781i 0.166923 + 0.121277i 0.668111 0.744062i \(-0.267103\pi\)
−0.501187 + 0.865339i \(0.667103\pi\)
\(992\) 3.69017 0.193394i 0.117163 0.00614026i
\(993\) −17.3128 + 7.26615i −0.549405 + 0.230584i
\(994\) 1.65819 7.80116i 0.0525946 0.247438i
\(995\) −0.971593 1.21643i −0.0308016 0.0385634i
\(996\) −2.71342 7.55016i −0.0859780 0.239236i
\(997\) −31.2535 + 48.1261i −0.989807 + 1.52417i −0.144767 + 0.989466i \(0.546243\pi\)
−0.845040 + 0.534704i \(0.820423\pi\)
\(998\) −6.28184 + 39.6620i −0.198848 + 1.25548i
\(999\) −0.104795 0.243294i −0.00331555 0.00769747i
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 450.2.w.a.23.14 480
9.2 odd 6 inner 450.2.w.a.173.24 yes 480
25.12 odd 20 inner 450.2.w.a.437.24 yes 480
225.137 even 60 inner 450.2.w.a.137.14 yes 480
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
450.2.w.a.23.14 480 1.1 even 1 trivial
450.2.w.a.137.14 yes 480 225.137 even 60 inner
450.2.w.a.173.24 yes 480 9.2 odd 6 inner
450.2.w.a.437.24 yes 480 25.12 odd 20 inner