Properties

Label 99.2.m.b.70.6
Level $99$
Weight $2$
Character 99.70
Analytic conductor $0.791$
Analytic rank $0$
Dimension $72$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [99,2,Mod(4,99)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(99, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([10, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("99.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 99 = 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 99.m (of order \(15\), degree \(8\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.790518980011\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(9\) over \(\Q(\zeta_{15})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label 70.6
Character \(\chi\) \(=\) 99.70
Dual form 99.2.m.b.58.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.527858 - 0.235017i) q^{2} +(-1.46440 + 0.924946i) q^{3} +(-1.11486 + 1.23818i) q^{4} +(2.74468 + 1.22201i) q^{5} +(-0.555618 + 0.832400i) q^{6} +(1.13888 + 0.242076i) q^{7} +(-0.654602 + 2.01466i) q^{8} +(1.28895 - 2.70899i) q^{9} +1.73599 q^{10} +(-2.54741 + 2.12385i) q^{11} +(0.487356 - 2.84438i) q^{12} +(0.412487 - 3.92455i) q^{13} +(0.658057 - 0.139874i) q^{14} +(-5.14961 + 0.749167i) q^{15} +(-0.220374 - 2.09672i) q^{16} +(0.254185 - 0.184677i) q^{17} +(0.0437225 - 1.73288i) q^{18} +(1.96794 - 6.05670i) q^{19} +(-4.57300 + 2.03603i) q^{20} +(-1.89168 + 0.698904i) q^{21} +(-0.845527 + 1.71977i) q^{22} +(0.0427501 + 0.0740453i) q^{23} +(-0.904849 - 3.55574i) q^{24} +(2.69431 + 2.99234i) q^{25} +(-0.704604 - 2.16855i) q^{26} +(0.618128 + 5.15926i) q^{27} +(-1.56942 + 1.14025i) q^{28} +(7.53156 + 1.60088i) q^{29} +(-2.54219 + 1.60570i) q^{30} +(-0.682449 + 6.49307i) q^{31} +(-2.72743 - 4.72404i) q^{32} +(1.76598 - 5.46638i) q^{33} +(0.0907715 - 0.157221i) q^{34} +(2.83004 + 2.05614i) q^{35} +(1.91721 + 4.61609i) q^{36} +(-1.92922 - 5.93753i) q^{37} +(-0.384637 - 3.65957i) q^{38} +(3.02595 + 6.12865i) q^{39} +(-4.25861 + 4.72966i) q^{40} +(-5.68213 + 1.20777i) q^{41} +(-0.834284 + 0.813500i) q^{42} +(3.39229 - 5.87562i) q^{43} +(0.210303 - 5.52194i) q^{44} +(6.84817 - 5.86020i) q^{45} +(0.0399679 + 0.0290384i) q^{46} +(-0.219298 - 0.243555i) q^{47} +(2.26207 + 2.86660i) q^{48} +(-5.15638 - 2.29577i) q^{49} +(2.12546 + 0.946318i) q^{50} +(-0.201414 + 0.505549i) q^{51} +(4.39943 + 4.88606i) q^{52} +(1.96000 + 1.42402i) q^{53} +(1.53880 + 2.57808i) q^{54} +(-9.58718 + 2.71632i) q^{55} +(-1.23321 + 2.13598i) q^{56} +(2.72026 + 10.6897i) q^{57} +(4.35183 - 0.925009i) q^{58} +(-1.53634 + 1.70628i) q^{59} +(4.81350 - 7.21136i) q^{60} +(1.43070 + 13.6122i) q^{61} +(1.16575 + 3.58780i) q^{62} +(2.12373 - 2.77318i) q^{63} +(0.861321 + 0.625787i) q^{64} +(5.92799 - 10.2676i) q^{65} +(-0.352506 - 3.30051i) q^{66} +(-5.83989 - 10.1150i) q^{67} +(-0.0547189 + 0.520616i) q^{68} +(-0.131091 - 0.0688906i) q^{69} +(1.97708 + 0.420242i) q^{70} +(-7.05272 + 5.12410i) q^{71} +(4.61393 + 4.37010i) q^{72} +(0.910538 + 2.80235i) q^{73} +(-2.41378 - 2.68077i) q^{74} +(-6.71331 - 1.88989i) q^{75} +(5.30529 + 9.18904i) q^{76} +(-3.41531 + 1.80213i) q^{77} +(3.03761 + 2.52391i) q^{78} +(-8.11886 + 3.61475i) q^{79} +(1.95735 - 6.02412i) q^{80} +(-5.67722 - 6.98349i) q^{81} +(-2.71551 + 1.97293i) q^{82} +(-0.518229 - 4.93062i) q^{83} +(1.24359 - 3.12142i) q^{84} +(0.923335 - 0.196261i) q^{85} +(0.409774 - 3.89874i) q^{86} +(-12.5100 + 4.62195i) q^{87} +(-2.61129 - 6.52242i) q^{88} +2.12862 q^{89} +(2.23761 - 4.70279i) q^{90} +(1.41981 - 4.36973i) q^{91} +(-0.139342 - 0.0296180i) q^{92} +(-5.00636 - 10.1397i) q^{93} +(-0.172998 - 0.0770236i) q^{94} +(12.8027 - 14.2189i) q^{95} +(8.36354 + 4.39518i) q^{96} +(-0.0811587 + 0.0361342i) q^{97} -3.26138 q^{98} +(2.47000 + 9.63842i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q - q^{2} - 12 q^{3} + 11 q^{4} - 8 q^{5} - 7 q^{6} - 2 q^{7} + 6 q^{8} - 22 q^{9} - 8 q^{10} - 2 q^{11} - 16 q^{12} - 11 q^{13} - 10 q^{14} - 20 q^{15} - 9 q^{16} - 20 q^{17} - 21 q^{18} + 8 q^{19}+ \cdots - 182 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/99\mathbb{Z}\right)^\times\).

\(n\) \(46\) \(56\)
\(\chi(n)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.527858 0.235017i 0.373252 0.166182i −0.211533 0.977371i \(-0.567846\pi\)
0.584785 + 0.811188i \(0.301179\pi\)
\(3\) −1.46440 + 0.924946i −0.845473 + 0.534018i
\(4\) −1.11486 + 1.23818i −0.557430 + 0.619089i
\(5\) 2.74468 + 1.22201i 1.22746 + 0.546500i 0.915009 0.403434i \(-0.132184\pi\)
0.312450 + 0.949934i \(0.398850\pi\)
\(6\) −0.555618 + 0.832400i −0.226830 + 0.339826i
\(7\) 1.13888 + 0.242076i 0.430455 + 0.0914960i 0.418044 0.908427i \(-0.362716\pi\)
0.0124114 + 0.999923i \(0.496049\pi\)
\(8\) −0.654602 + 2.01466i −0.231437 + 0.712289i
\(9\) 1.28895 2.70899i 0.429650 0.902996i
\(10\) 1.73599 0.548970
\(11\) −2.54741 + 2.12385i −0.768072 + 0.640364i
\(12\) 0.487356 2.84438i 0.140688 0.821101i
\(13\) 0.412487 3.92455i 0.114403 1.08848i −0.775192 0.631726i \(-0.782347\pi\)
0.889595 0.456750i \(-0.150986\pi\)
\(14\) 0.658057 0.139874i 0.175873 0.0373830i
\(15\) −5.14961 + 0.749167i −1.32962 + 0.193434i
\(16\) −0.220374 2.09672i −0.0550935 0.524179i
\(17\) 0.254185 0.184677i 0.0616490 0.0447906i −0.556534 0.830825i \(-0.687869\pi\)
0.618183 + 0.786034i \(0.287869\pi\)
\(18\) 0.0437225 1.73288i 0.0103055 0.408445i
\(19\) 1.96794 6.05670i 0.451477 1.38950i −0.423746 0.905781i \(-0.639285\pi\)
0.875222 0.483721i \(-0.160715\pi\)
\(20\) −4.57300 + 2.03603i −1.02255 + 0.455271i
\(21\) −1.89168 + 0.698904i −0.412799 + 0.152513i
\(22\) −0.845527 + 1.71977i −0.180267 + 0.366657i
\(23\) 0.0427501 + 0.0740453i 0.00891401 + 0.0154395i 0.870448 0.492260i \(-0.163829\pi\)
−0.861534 + 0.507700i \(0.830496\pi\)
\(24\) −0.904849 3.55574i −0.184702 0.725813i
\(25\) 2.69431 + 2.99234i 0.538862 + 0.598467i
\(26\) −0.704604 2.16855i −0.138184 0.425287i
\(27\) 0.618128 + 5.15926i 0.118959 + 0.992899i
\(28\) −1.56942 + 1.14025i −0.296593 + 0.215487i
\(29\) 7.53156 + 1.60088i 1.39858 + 0.297276i 0.844663 0.535298i \(-0.179801\pi\)
0.553913 + 0.832575i \(0.313134\pi\)
\(30\) −2.54219 + 1.60570i −0.464139 + 0.293160i
\(31\) −0.682449 + 6.49307i −0.122571 + 1.16619i 0.744366 + 0.667772i \(0.232752\pi\)
−0.866937 + 0.498418i \(0.833915\pi\)
\(32\) −2.72743 4.72404i −0.482146 0.835101i
\(33\) 1.76598 5.46638i 0.307418 0.951574i
\(34\) 0.0907715 0.157221i 0.0155672 0.0269632i
\(35\) 2.83004 + 2.05614i 0.478363 + 0.347551i
\(36\) 1.91721 + 4.61609i 0.319535 + 0.769349i
\(37\) −1.92922 5.93753i −0.317162 0.976124i −0.974855 0.222838i \(-0.928468\pi\)
0.657694 0.753286i \(-0.271532\pi\)
\(38\) −0.384637 3.65957i −0.0623963 0.593661i
\(39\) 3.02595 + 6.12865i 0.484540 + 0.981370i
\(40\) −4.25861 + 4.72966i −0.673345 + 0.747825i
\(41\) −5.68213 + 1.20777i −0.887399 + 0.188623i −0.628990 0.777413i \(-0.716532\pi\)
−0.258409 + 0.966036i \(0.583198\pi\)
\(42\) −0.834284 + 0.813500i −0.128733 + 0.125526i
\(43\) 3.39229 5.87562i 0.517320 0.896024i −0.482478 0.875908i \(-0.660263\pi\)
0.999798 0.0201157i \(-0.00640347\pi\)
\(44\) 0.210303 5.52194i 0.0317043 0.832463i
\(45\) 6.84817 5.86020i 1.02086 0.873587i
\(46\) 0.0399679 + 0.0290384i 0.00589294 + 0.00428147i
\(47\) −0.219298 0.243555i −0.0319879 0.0355262i 0.726939 0.686703i \(-0.240942\pi\)
−0.758926 + 0.651176i \(0.774276\pi\)
\(48\) 2.26207 + 2.86660i 0.326501 + 0.413759i
\(49\) −5.15638 2.29577i −0.736625 0.327967i
\(50\) 2.12546 + 0.946318i 0.300586 + 0.133830i
\(51\) −0.201414 + 0.505549i −0.0282036 + 0.0707910i
\(52\) 4.39943 + 4.88606i 0.610091 + 0.677575i
\(53\) 1.96000 + 1.42402i 0.269227 + 0.195605i 0.714205 0.699937i \(-0.246789\pi\)
−0.444978 + 0.895541i \(0.646789\pi\)
\(54\) 1.53880 + 2.57808i 0.209404 + 0.350832i
\(55\) −9.58718 + 2.71632i −1.29274 + 0.366269i
\(56\) −1.23321 + 2.13598i −0.164795 + 0.285433i
\(57\) 2.72026 + 10.6897i 0.360308 + 1.41588i
\(58\) 4.35183 0.925009i 0.571423 0.121460i
\(59\) −1.53634 + 1.70628i −0.200015 + 0.222139i −0.834805 0.550545i \(-0.814420\pi\)
0.634790 + 0.772685i \(0.281087\pi\)
\(60\) 4.81350 7.21136i 0.621420 0.930982i
\(61\) 1.43070 + 13.6122i 0.183183 + 1.74287i 0.570839 + 0.821062i \(0.306618\pi\)
−0.387656 + 0.921804i \(0.626715\pi\)
\(62\) 1.16575 + 3.58780i 0.148050 + 0.455652i
\(63\) 2.12373 2.77318i 0.267565 0.349388i
\(64\) 0.861321 + 0.625787i 0.107665 + 0.0782233i
\(65\) 5.92799 10.2676i 0.735277 1.27354i
\(66\) −0.352506 3.30051i −0.0433905 0.406264i
\(67\) −5.83989 10.1150i −0.713456 1.23574i −0.963552 0.267521i \(-0.913795\pi\)
0.250096 0.968221i \(-0.419538\pi\)
\(68\) −0.0547189 + 0.520616i −0.00663564 + 0.0631339i
\(69\) −0.131091 0.0688906i −0.0157815 0.00829345i
\(70\) 1.97708 + 0.420242i 0.236307 + 0.0502286i
\(71\) −7.05272 + 5.12410i −0.837004 + 0.608119i −0.921532 0.388302i \(-0.873062\pi\)
0.0845279 + 0.996421i \(0.473062\pi\)
\(72\) 4.61393 + 4.37010i 0.543757 + 0.515021i
\(73\) 0.910538 + 2.80235i 0.106570 + 0.327990i 0.990096 0.140393i \(-0.0448367\pi\)
−0.883525 + 0.468383i \(0.844837\pi\)
\(74\) −2.41378 2.68077i −0.280596 0.311633i
\(75\) −6.71331 1.88989i −0.775186 0.218226i
\(76\) 5.30529 + 9.18904i 0.608559 + 1.05405i
\(77\) −3.41531 + 1.80213i −0.389211 + 0.205372i
\(78\) 3.03761 + 2.52391i 0.343942 + 0.285776i
\(79\) −8.11886 + 3.61475i −0.913443 + 0.406691i −0.808979 0.587838i \(-0.799979\pi\)
−0.104464 + 0.994529i \(0.533313\pi\)
\(80\) 1.95735 6.02412i 0.218839 0.673517i
\(81\) −5.67722 6.98349i −0.630802 0.775944i
\(82\) −2.71551 + 1.97293i −0.299878 + 0.217874i
\(83\) −0.518229 4.93062i −0.0568831 0.541206i −0.985441 0.170018i \(-0.945617\pi\)
0.928558 0.371188i \(-0.121049\pi\)
\(84\) 1.24359 3.12142i 0.135687 0.340575i
\(85\) 0.923335 0.196261i 0.100150 0.0212875i
\(86\) 0.409774 3.89874i 0.0441871 0.420412i
\(87\) −12.5100 + 4.62195i −1.34121 + 0.495525i
\(88\) −2.61129 6.52242i −0.278364 0.695293i
\(89\) 2.12862 0.225634 0.112817 0.993616i \(-0.464013\pi\)
0.112817 + 0.993616i \(0.464013\pi\)
\(90\) 2.23761 4.70279i 0.235865 0.495717i
\(91\) 1.41981 4.36973i 0.148837 0.458072i
\(92\) −0.139342 0.0296180i −0.0145274 0.00308789i
\(93\) −5.00636 10.1397i −0.519135 1.05144i
\(94\) −0.172998 0.0770236i −0.0178434 0.00794437i
\(95\) 12.8027 14.2189i 1.31353 1.45882i
\(96\) 8.36354 + 4.39518i 0.853600 + 0.448581i
\(97\) −0.0811587 + 0.0361342i −0.00824041 + 0.00366887i −0.410853 0.911702i \(-0.634769\pi\)
0.402612 + 0.915371i \(0.368102\pi\)
\(98\) −3.26138 −0.329449
\(99\) 2.47000 + 9.63842i 0.248244 + 0.968698i
\(100\) −6.70883 −0.670883
\(101\) −1.87869 + 0.836447i −0.186937 + 0.0832296i −0.498071 0.867137i \(-0.665958\pi\)
0.311134 + 0.950366i \(0.399291\pi\)
\(102\) 0.0124948 + 0.314194i 0.00123717 + 0.0311098i
\(103\) −2.01858 + 2.24186i −0.198896 + 0.220897i −0.834340 0.551251i \(-0.814151\pi\)
0.635443 + 0.772148i \(0.280817\pi\)
\(104\) 7.63662 + 3.40004i 0.748832 + 0.333401i
\(105\) −6.04613 0.393387i −0.590042 0.0383907i
\(106\) 1.36927 + 0.291048i 0.132995 + 0.0282690i
\(107\) 3.70600 11.4059i 0.358272 1.10265i −0.595815 0.803121i \(-0.703171\pi\)
0.954088 0.299527i \(-0.0968290\pi\)
\(108\) −7.07720 4.98650i −0.681004 0.479826i
\(109\) 5.20013 0.498082 0.249041 0.968493i \(-0.419885\pi\)
0.249041 + 0.968493i \(0.419885\pi\)
\(110\) −4.42228 + 3.68699i −0.421648 + 0.351540i
\(111\) 8.31705 + 6.91051i 0.789420 + 0.655916i
\(112\) 0.256586 2.44125i 0.0242451 0.230676i
\(113\) −18.8074 + 3.99763i −1.76925 + 0.376066i −0.973343 0.229354i \(-0.926339\pi\)
−0.795907 + 0.605419i \(0.793005\pi\)
\(114\) 3.94817 + 5.00332i 0.369780 + 0.468604i
\(115\) 0.0268512 + 0.255472i 0.00250389 + 0.0238229i
\(116\) −10.3788 + 7.54065i −0.963649 + 0.700132i
\(117\) −10.0999 6.17597i −0.933735 0.570969i
\(118\) −0.409965 + 1.26174i −0.0377403 + 0.116153i
\(119\) 0.334192 0.148792i 0.0306353 0.0136397i
\(120\) 1.86163 10.8651i 0.169943 0.991844i
\(121\) 1.97856 10.8206i 0.179869 0.983691i
\(122\) 3.95432 + 6.84907i 0.358007 + 0.620086i
\(123\) 7.20380 7.02433i 0.649544 0.633362i
\(124\) −7.27874 8.08386i −0.653650 0.725952i
\(125\) −0.903736 2.78141i −0.0808326 0.248777i
\(126\) 0.469284 1.96296i 0.0418071 0.174874i
\(127\) 10.6652 7.74873i 0.946384 0.687588i −0.00356461 0.999994i \(-0.501135\pi\)
0.949949 + 0.312405i \(0.101135\pi\)
\(128\) 11.2730 + 2.39616i 0.996405 + 0.211792i
\(129\) 0.466954 + 11.7420i 0.0411130 + 1.03382i
\(130\) 0.716076 6.81300i 0.0628040 0.597540i
\(131\) 8.98588 + 15.5640i 0.785100 + 1.35983i 0.928939 + 0.370233i \(0.120722\pi\)
−0.143839 + 0.989601i \(0.545945\pi\)
\(132\) 4.79953 + 8.28085i 0.417745 + 0.720756i
\(133\) 3.70742 6.42144i 0.321474 0.556810i
\(134\) −5.45983 3.96680i −0.471657 0.342679i
\(135\) −4.60810 + 14.9159i −0.396602 + 1.28375i
\(136\) 0.205670 + 0.632986i 0.0176360 + 0.0542781i
\(137\) 1.71445 + 16.3119i 0.146475 + 1.39362i 0.782836 + 0.622228i \(0.213772\pi\)
−0.636361 + 0.771391i \(0.719561\pi\)
\(138\) −0.0853880 0.00555571i −0.00726871 0.000472934i
\(139\) −7.96373 + 8.84461i −0.675475 + 0.750190i −0.979273 0.202546i \(-0.935078\pi\)
0.303798 + 0.952736i \(0.401745\pi\)
\(140\) −5.70096 + 1.21178i −0.481819 + 0.102414i
\(141\) 0.546416 + 0.153824i 0.0460165 + 0.0129543i
\(142\) −2.51858 + 4.36231i −0.211355 + 0.366077i
\(143\) 7.28438 + 10.8735i 0.609150 + 0.909287i
\(144\) −5.96403 2.10557i −0.497002 0.175464i
\(145\) 18.7154 + 13.5976i 1.55423 + 1.12922i
\(146\) 1.13923 + 1.26525i 0.0942837 + 0.104713i
\(147\) 9.67447 1.40745i 0.797937 0.116084i
\(148\) 9.50253 + 4.23080i 0.781103 + 0.347770i
\(149\) −4.13993 1.84321i −0.339156 0.151002i 0.230090 0.973169i \(-0.426098\pi\)
−0.569246 + 0.822167i \(0.692765\pi\)
\(150\) −3.98783 + 0.580150i −0.325605 + 0.0473691i
\(151\) −1.96113 2.17806i −0.159595 0.177248i 0.658044 0.752979i \(-0.271384\pi\)
−0.817639 + 0.575732i \(0.804717\pi\)
\(152\) 10.9140 + 7.92945i 0.885239 + 0.643164i
\(153\) −0.172654 0.926624i −0.0139583 0.0749131i
\(154\) −1.37927 + 1.75393i −0.111144 + 0.141336i
\(155\) −9.80771 + 16.9874i −0.787774 + 1.36446i
\(156\) −10.9619 3.08593i −0.877653 0.247072i
\(157\) 17.6591 3.75356i 1.40935 0.299567i 0.560481 0.828167i \(-0.310616\pi\)
0.848871 + 0.528600i \(0.177283\pi\)
\(158\) −3.43607 + 3.81614i −0.273359 + 0.303596i
\(159\) −4.18737 0.272449i −0.332080 0.0216066i
\(160\) −1.71309 16.2989i −0.135431 1.28854i
\(161\) 0.0307625 + 0.0946773i 0.00242443 + 0.00746161i
\(162\) −4.63801 2.35204i −0.364396 0.184794i
\(163\) 4.71129 + 3.42295i 0.369017 + 0.268106i 0.756803 0.653643i \(-0.226760\pi\)
−0.387786 + 0.921749i \(0.626760\pi\)
\(164\) 4.83934 8.38199i 0.377889 0.654523i
\(165\) 11.5270 12.8454i 0.897379 1.00001i
\(166\) −1.43233 2.48087i −0.111171 0.192553i
\(167\) 0.524913 4.99422i 0.0406190 0.386464i −0.955260 0.295769i \(-0.904424\pi\)
0.995879 0.0906956i \(-0.0289090\pi\)
\(168\) −0.169753 4.26859i −0.0130968 0.329329i
\(169\) −2.51606 0.534805i −0.193543 0.0411388i
\(170\) 0.441265 0.320598i 0.0338435 0.0245887i
\(171\) −13.8709 13.1379i −1.06074 1.00468i
\(172\) 3.49313 + 10.7508i 0.266349 + 0.819738i
\(173\) −10.4317 11.5855i −0.793104 0.880831i 0.202028 0.979380i \(-0.435247\pi\)
−0.995132 + 0.0985486i \(0.968580\pi\)
\(174\) −5.51724 + 5.37979i −0.418261 + 0.407841i
\(175\) 2.34412 + 4.06013i 0.177199 + 0.306917i
\(176\) 5.01449 + 4.87315i 0.377981 + 0.367327i
\(177\) 0.671606 3.91972i 0.0504810 0.294624i
\(178\) 1.12361 0.500263i 0.0842181 0.0374963i
\(179\) 2.17822 6.70387i 0.162808 0.501071i −0.836060 0.548638i \(-0.815147\pi\)
0.998868 + 0.0475668i \(0.0151467\pi\)
\(180\) −0.378783 + 15.0126i −0.0282328 + 1.11897i
\(181\) −2.02068 + 1.46811i −0.150196 + 0.109124i −0.660345 0.750962i \(-0.729590\pi\)
0.510149 + 0.860086i \(0.329590\pi\)
\(182\) −0.277504 2.64028i −0.0205700 0.195710i
\(183\) −14.6857 18.6104i −1.08560 1.37572i
\(184\) −0.177160 + 0.0376566i −0.0130604 + 0.00277608i
\(185\) 1.96063 18.6542i 0.144148 1.37148i
\(186\) −5.02565 4.17573i −0.368499 0.306180i
\(187\) −0.255289 + 1.01030i −0.0186686 + 0.0738802i
\(188\) 0.546051 0.0398249
\(189\) −0.544960 + 6.02539i −0.0396400 + 0.438283i
\(190\) 3.41633 10.5144i 0.247847 0.762795i
\(191\) 11.5646 + 2.45814i 0.836786 + 0.177864i 0.606325 0.795217i \(-0.292643\pi\)
0.230461 + 0.973081i \(0.425976\pi\)
\(192\) −1.84014 0.119727i −0.132801 0.00864058i
\(193\) 6.16338 + 2.74411i 0.443650 + 0.197526i 0.616389 0.787442i \(-0.288595\pi\)
−0.172739 + 0.984968i \(0.555262\pi\)
\(194\) −0.0343481 + 0.0381474i −0.00246605 + 0.00273882i
\(195\) 0.815997 + 20.5190i 0.0584348 + 1.46939i
\(196\) 8.59121 3.82505i 0.613658 0.273218i
\(197\) −20.6474 −1.47107 −0.735534 0.677488i \(-0.763069\pi\)
−0.735534 + 0.677488i \(0.763069\pi\)
\(198\) 3.56900 + 4.50722i 0.253638 + 0.320314i
\(199\) −13.2862 −0.941832 −0.470916 0.882178i \(-0.656077\pi\)
−0.470916 + 0.882178i \(0.656077\pi\)
\(200\) −7.79224 + 3.46933i −0.550994 + 0.245318i
\(201\) 17.9078 + 9.41083i 1.26312 + 0.663789i
\(202\) −0.795102 + 0.883050i −0.0559432 + 0.0621312i
\(203\) 8.18999 + 3.64642i 0.574824 + 0.255928i
\(204\) −0.401411 0.813003i −0.0281044 0.0569216i
\(205\) −17.0715 3.62867i −1.19233 0.253437i
\(206\) −0.538646 + 1.65778i −0.0375292 + 0.115503i
\(207\) 0.255690 0.0203688i 0.0177717 0.00141573i
\(208\) −8.31958 −0.576859
\(209\) 7.85035 + 19.6085i 0.543020 + 1.35635i
\(210\) −3.28395 + 1.21329i −0.226614 + 0.0837252i
\(211\) 0.872292 8.29930i 0.0600510 0.571348i −0.922584 0.385797i \(-0.873926\pi\)
0.982635 0.185551i \(-0.0594068\pi\)
\(212\) −3.94832 + 0.839242i −0.271172 + 0.0576394i
\(213\) 5.58851 14.0271i 0.382918 0.961124i
\(214\) −0.724343 6.89166i −0.0495150 0.471104i
\(215\) 16.4908 11.9813i 1.12467 0.817117i
\(216\) −10.7988 2.13194i −0.734763 0.145060i
\(217\) −2.34904 + 7.22960i −0.159463 + 0.490778i
\(218\) 2.74493 1.22212i 0.185910 0.0827724i
\(219\) −3.92541 3.26156i −0.265255 0.220396i
\(220\) 7.32508 14.8990i 0.493857 1.00449i
\(221\) −0.619925 1.07374i −0.0417007 0.0722277i
\(222\) 6.01431 + 1.69311i 0.403654 + 0.113634i
\(223\) −0.256716 0.285112i −0.0171910 0.0190925i 0.734488 0.678622i \(-0.237422\pi\)
−0.751679 + 0.659529i \(0.770756\pi\)
\(224\) −1.96263 6.04035i −0.131134 0.403588i
\(225\) 11.5790 3.44189i 0.771936 0.229459i
\(226\) −8.98811 + 6.53024i −0.597880 + 0.434385i
\(227\) −17.6204 3.74533i −1.16951 0.248586i −0.418084 0.908408i \(-0.637298\pi\)
−0.751422 + 0.659822i \(0.770632\pi\)
\(228\) −16.2684 8.54934i −1.07740 0.566194i
\(229\) −1.40359 + 13.3543i −0.0927521 + 0.882478i 0.844905 + 0.534916i \(0.179657\pi\)
−0.937657 + 0.347561i \(0.887010\pi\)
\(230\) 0.0742139 + 0.128542i 0.00489352 + 0.00847583i
\(231\) 3.33452 5.79803i 0.219395 0.381482i
\(232\) −8.15540 + 14.1256i −0.535428 + 0.927389i
\(233\) 2.72611 + 1.98063i 0.178593 + 0.129756i 0.673490 0.739196i \(-0.264794\pi\)
−0.494897 + 0.868952i \(0.664794\pi\)
\(234\) −6.78276 0.886384i −0.443403 0.0579447i
\(235\) −0.304276 0.936466i −0.0198488 0.0610883i
\(236\) −0.399873 3.80454i −0.0260295 0.247654i
\(237\) 8.54582 12.8029i 0.555111 0.831641i
\(238\) 0.141437 0.157082i 0.00916800 0.0101821i
\(239\) 22.6899 4.82289i 1.46769 0.311967i 0.596379 0.802703i \(-0.296606\pi\)
0.871308 + 0.490736i \(0.163272\pi\)
\(240\) 2.70563 + 10.6322i 0.174648 + 0.686304i
\(241\) −7.58206 + 13.1325i −0.488404 + 0.845940i −0.999911 0.0133389i \(-0.995754\pi\)
0.511507 + 0.859279i \(0.329087\pi\)
\(242\) −1.49863 6.17673i −0.0963358 0.397055i
\(243\) 14.7731 + 4.97552i 0.947694 + 0.319180i
\(244\) −18.4494 13.4043i −1.18110 0.858120i
\(245\) −11.3472 12.6023i −0.724944 0.805131i
\(246\) 2.15174 5.40086i 0.137190 0.344346i
\(247\) −22.9581 10.2216i −1.46079 0.650385i
\(248\) −12.6346 5.62528i −0.802297 0.357205i
\(249\) 5.31946 + 6.74108i 0.337107 + 0.427199i
\(250\) −1.13072 1.25580i −0.0715133 0.0794235i
\(251\) 0.471095 + 0.342271i 0.0297353 + 0.0216039i 0.602554 0.798078i \(-0.294150\pi\)
−0.572818 + 0.819682i \(0.694150\pi\)
\(252\) 1.06602 + 5.72127i 0.0671531 + 0.360406i
\(253\) −0.266163 0.0978289i −0.0167335 0.00615045i
\(254\) 3.80863 6.59673i 0.238974 0.413916i
\(255\) −1.17060 + 1.14144i −0.0733060 + 0.0714798i
\(256\) 4.43092 0.941821i 0.276933 0.0588638i
\(257\) −7.34131 + 8.15335i −0.457939 + 0.508592i −0.927251 0.374440i \(-0.877835\pi\)
0.469313 + 0.883032i \(0.344502\pi\)
\(258\) 3.00605 + 6.08834i 0.187148 + 0.379044i
\(259\) −0.759813 7.22913i −0.0472125 0.449197i
\(260\) 6.10421 + 18.7868i 0.378567 + 1.16511i
\(261\) 14.0446 18.3394i 0.869337 1.13518i
\(262\) 8.40108 + 6.10374i 0.519020 + 0.377090i
\(263\) 7.19768 12.4668i 0.443828 0.768733i −0.554142 0.832422i \(-0.686953\pi\)
0.997970 + 0.0636896i \(0.0202868\pi\)
\(264\) 9.85686 + 7.13615i 0.606648 + 0.439200i
\(265\) 3.63940 + 6.30363i 0.223567 + 0.387229i
\(266\) 0.447840 4.26092i 0.0274589 0.261254i
\(267\) −3.11716 + 1.96886i −0.190767 + 0.120492i
\(268\) 19.0348 + 4.04598i 1.16274 + 0.247147i
\(269\) −0.395590 + 0.287413i −0.0241195 + 0.0175239i −0.599780 0.800165i \(-0.704745\pi\)
0.575660 + 0.817689i \(0.304745\pi\)
\(270\) 1.07307 + 8.95644i 0.0653047 + 0.545072i
\(271\) 6.77950 + 20.8652i 0.411825 + 1.26747i 0.915060 + 0.403318i \(0.132143\pi\)
−0.503234 + 0.864150i \(0.667857\pi\)
\(272\) −0.443230 0.492257i −0.0268748 0.0298475i
\(273\) 1.96259 + 7.71229i 0.118781 + 0.466769i
\(274\) 4.73856 + 8.20743i 0.286267 + 0.495829i
\(275\) −13.2188 1.90039i −0.797122 0.114598i
\(276\) 0.231447 0.0855109i 0.0139315 0.00514715i
\(277\) 2.62144 1.16714i 0.157507 0.0701267i −0.326469 0.945208i \(-0.605859\pi\)
0.483976 + 0.875081i \(0.339192\pi\)
\(278\) −2.12508 + 6.54031i −0.127454 + 0.392262i
\(279\) 16.7100 + 10.2180i 1.00040 + 0.611735i
\(280\) −5.99497 + 4.35560i −0.358268 + 0.260297i
\(281\) −1.90013 18.0785i −0.113352 1.07847i −0.892318 0.451406i \(-0.850922\pi\)
0.778967 0.627066i \(-0.215744\pi\)
\(282\) 0.324581 0.0472201i 0.0193285 0.00281192i
\(283\) 20.0883 4.26991i 1.19413 0.253820i 0.432378 0.901692i \(-0.357674\pi\)
0.761749 + 0.647873i \(0.224341\pi\)
\(284\) 1.51825 14.4452i 0.0900916 0.857164i
\(285\) −5.59665 + 32.6640i −0.331517 + 1.93485i
\(286\) 6.40057 + 4.02770i 0.378474 + 0.238163i
\(287\) −6.76362 −0.399244
\(288\) −16.3129 + 1.29952i −0.961246 + 0.0765747i
\(289\) −5.22278 + 16.0741i −0.307223 + 0.945534i
\(290\) 13.0747 + 2.77912i 0.767776 + 0.163196i
\(291\) 0.0854268 0.127982i 0.00500781 0.00750246i
\(292\) −4.48493 1.99682i −0.262461 0.116855i
\(293\) 0.575497 0.639154i 0.0336209 0.0373398i −0.726100 0.687589i \(-0.758669\pi\)
0.759721 + 0.650250i \(0.225336\pi\)
\(294\) 4.77597 3.01660i 0.278540 0.175932i
\(295\) −6.30187 + 2.80578i −0.366909 + 0.163359i
\(296\) 13.2250 0.768685
\(297\) −12.5321 11.8299i −0.727185 0.686441i
\(298\) −2.61848 −0.151684
\(299\) 0.308229 0.137232i 0.0178253 0.00793635i
\(300\) 9.82443 6.20531i 0.567214 0.358264i
\(301\) 5.28575 5.87042i 0.304665 0.338365i
\(302\) −1.54708 0.688804i −0.0890244 0.0396362i
\(303\) 1.97749 2.96258i 0.113604 0.170196i
\(304\) −13.1329 2.79148i −0.753221 0.160102i
\(305\) −12.7075 + 39.1095i −0.727627 + 2.23941i
\(306\) −0.308910 0.448549i −0.0176592 0.0256418i
\(307\) 3.48920 0.199139 0.0995696 0.995031i \(-0.468253\pi\)
0.0995696 + 0.995031i \(0.468253\pi\)
\(308\) 1.57624 6.23790i 0.0898144 0.355437i
\(309\) 0.882412 5.15005i 0.0501986 0.292976i
\(310\) −1.18473 + 11.2719i −0.0672880 + 0.640203i
\(311\) −10.6083 + 2.25486i −0.601542 + 0.127862i −0.498610 0.866827i \(-0.666156\pi\)
−0.102932 + 0.994688i \(0.532822\pi\)
\(312\) −14.3279 + 2.08443i −0.811160 + 0.118008i
\(313\) 2.95618 + 28.1261i 0.167093 + 1.58978i 0.681226 + 0.732073i \(0.261447\pi\)
−0.514133 + 0.857710i \(0.671886\pi\)
\(314\) 8.43935 6.13155i 0.476260 0.346023i
\(315\) 9.21783 5.01627i 0.519366 0.282635i
\(316\) 4.57569 14.0825i 0.257403 0.792204i
\(317\) −1.01634 + 0.452505i −0.0570836 + 0.0254152i −0.435080 0.900392i \(-0.643280\pi\)
0.377996 + 0.925807i \(0.376613\pi\)
\(318\) −2.27437 + 0.840291i −0.127540 + 0.0471212i
\(319\) −22.5860 + 11.9178i −1.26457 + 0.667267i
\(320\) 1.59933 + 2.77013i 0.0894055 + 0.154855i
\(321\) 5.12276 + 20.1307i 0.285925 + 1.12358i
\(322\) 0.0384890 + 0.0427464i 0.00214491 + 0.00238216i
\(323\) −0.618308 1.90296i −0.0344036 0.105883i
\(324\) 14.9761 + 0.756208i 0.832007 + 0.0420116i
\(325\) 12.8550 9.33967i 0.713065 0.518072i
\(326\) 3.29134 + 0.699597i 0.182291 + 0.0387471i
\(327\) −7.61508 + 4.80984i −0.421115 + 0.265985i
\(328\) 1.28628 12.2382i 0.0710230 0.675739i
\(329\) −0.190795 0.330466i −0.0105188 0.0182192i
\(330\) 3.06574 9.48961i 0.168763 0.522386i
\(331\) 6.18915 10.7199i 0.340187 0.589221i −0.644281 0.764789i \(-0.722843\pi\)
0.984467 + 0.175569i \(0.0561764\pi\)
\(332\) 6.68275 + 4.85530i 0.366763 + 0.266469i
\(333\) −18.5714 2.42694i −1.01770 0.132995i
\(334\) −0.896648 2.75960i −0.0490624 0.150999i
\(335\) −3.66801 34.8988i −0.200405 1.90673i
\(336\) 1.88228 + 3.81230i 0.102687 + 0.207978i
\(337\) 9.01561 10.0128i 0.491112 0.545435i −0.445740 0.895163i \(-0.647059\pi\)
0.936851 + 0.349728i \(0.113726\pi\)
\(338\) −1.45381 + 0.309017i −0.0790768 + 0.0168083i
\(339\) 23.8440 23.2500i 1.29503 1.26276i
\(340\) −0.786384 + 1.36206i −0.0426477 + 0.0738679i
\(341\) −12.0518 17.9899i −0.652642 0.974208i
\(342\) −10.4095 3.67503i −0.562882 0.198723i
\(343\) −11.9104 8.65342i −0.643102 0.467241i
\(344\) 9.61676 + 10.6805i 0.518501 + 0.575854i
\(345\) −0.275619 0.349278i −0.0148388 0.0188045i
\(346\) −8.22923 3.66389i −0.442406 0.196972i
\(347\) 8.89717 + 3.96128i 0.477625 + 0.212652i 0.631406 0.775453i \(-0.282478\pi\)
−0.153781 + 0.988105i \(0.549145\pi\)
\(348\) 8.22407 20.6424i 0.440856 1.10655i
\(349\) −2.97107 3.29971i −0.159038 0.176629i 0.658360 0.752703i \(-0.271251\pi\)
−0.817397 + 0.576074i \(0.804584\pi\)
\(350\) 2.19156 + 1.59226i 0.117144 + 0.0851100i
\(351\) 20.5027 0.297748i 1.09436 0.0158926i
\(352\) 16.9810 + 6.24142i 0.905090 + 0.332669i
\(353\) −16.2618 + 28.1662i −0.865527 + 1.49914i 0.000996749 1.00000i \(0.499683\pi\)
−0.866523 + 0.499137i \(0.833651\pi\)
\(354\) −0.566690 2.22689i −0.0301193 0.118358i
\(355\) −25.6192 + 5.44553i −1.35973 + 0.289019i
\(356\) −2.37312 + 2.63561i −0.125775 + 0.139687i
\(357\) −0.351767 + 0.527000i −0.0186175 + 0.0278918i
\(358\) −0.425736 4.05061i −0.0225008 0.214081i
\(359\) −8.58143 26.4109i −0.452911 1.39392i −0.873571 0.486697i \(-0.838201\pi\)
0.420660 0.907218i \(-0.361799\pi\)
\(360\) 7.32347 + 17.6328i 0.385981 + 0.929330i
\(361\) −17.4395 12.6705i −0.917868 0.666870i
\(362\) −0.721600 + 1.24985i −0.0379264 + 0.0656905i
\(363\) 7.11107 + 17.6758i 0.373234 + 0.927737i
\(364\) 3.82761 + 6.62962i 0.200621 + 0.347487i
\(365\) −0.925362 + 8.80424i −0.0484357 + 0.460835i
\(366\) −12.1257 6.37227i −0.633822 0.333084i
\(367\) −1.14658 0.243713i −0.0598511 0.0127217i 0.177889 0.984051i \(-0.443073\pi\)
−0.237740 + 0.971329i \(0.576407\pi\)
\(368\) 0.145831 0.105952i 0.00760197 0.00552315i
\(369\) −4.05213 + 16.9496i −0.210945 + 0.882359i
\(370\) −3.34912 10.3075i −0.174112 0.535862i
\(371\) 1.88748 + 2.09626i 0.0979929 + 0.108832i
\(372\) 18.1361 + 5.10558i 0.940315 + 0.264712i
\(373\) −10.8834 18.8506i −0.563520 0.976046i −0.997186 0.0749719i \(-0.976113\pi\)
0.433665 0.901074i \(-0.357220\pi\)
\(374\) 0.102681 + 0.593290i 0.00530951 + 0.0306783i
\(375\) 3.89609 + 3.23720i 0.201193 + 0.167168i
\(376\) 0.634233 0.282379i 0.0327081 0.0145626i
\(377\) 9.38942 28.8977i 0.483580 1.48831i
\(378\) 1.12841 + 3.30862i 0.0580392 + 0.170177i
\(379\) 13.1440 9.54967i 0.675161 0.490533i −0.196588 0.980486i \(-0.562986\pi\)
0.871749 + 0.489953i \(0.162986\pi\)
\(380\) 3.33224 + 31.7041i 0.170940 + 1.62639i
\(381\) −8.45100 + 21.2120i −0.432958 + 1.08672i
\(382\) 6.68218 1.42034i 0.341890 0.0726709i
\(383\) −0.647381 + 6.15942i −0.0330796 + 0.314732i 0.965453 + 0.260577i \(0.0839129\pi\)
−0.998533 + 0.0541542i \(0.982754\pi\)
\(384\) −18.7246 + 6.91801i −0.955534 + 0.353033i
\(385\) −11.5762 + 0.772734i −0.589977 + 0.0393821i
\(386\) 3.89830 0.198418
\(387\) −11.5445 16.7630i −0.586839 0.852114i
\(388\) 0.0457401 0.140773i 0.00232210 0.00714669i
\(389\) 0.707409 + 0.150365i 0.0358671 + 0.00762378i 0.225810 0.974171i \(-0.427497\pi\)
−0.189943 + 0.981795i \(0.560830\pi\)
\(390\) 5.25304 + 10.6393i 0.265998 + 0.538743i
\(391\) 0.0245409 + 0.0109263i 0.00124109 + 0.000552567i
\(392\) 8.00056 8.88552i 0.404089 0.448787i
\(393\) −27.5548 14.4805i −1.38996 0.730445i
\(394\) −10.8989 + 4.85250i −0.549079 + 0.244466i
\(395\) −26.7009 −1.34347
\(396\) −14.6878 7.68720i −0.738089 0.386296i
\(397\) 4.08994 0.205268 0.102634 0.994719i \(-0.467273\pi\)
0.102634 + 0.994719i \(0.467273\pi\)
\(398\) −7.01321 + 3.12248i −0.351540 + 0.156516i
\(399\) 0.510332 + 12.8327i 0.0255486 + 0.642441i
\(400\) 5.68033 6.30864i 0.284016 0.315432i
\(401\) −5.15812 2.29654i −0.257584 0.114684i 0.273882 0.961763i \(-0.411692\pi\)
−0.531466 + 0.847079i \(0.678359\pi\)
\(402\) 11.6645 + 0.758940i 0.581770 + 0.0378525i
\(403\) 25.2009 + 5.35662i 1.25535 + 0.266832i
\(404\) 1.05881 3.25868i 0.0526777 0.162125i
\(405\) −7.04826 26.1051i −0.350231 1.29717i
\(406\) 5.18012 0.257085
\(407\) 17.5249 + 11.0279i 0.868677 + 0.546634i
\(408\) −0.886662 0.736713i −0.0438963 0.0364727i
\(409\) −0.987666 + 9.39701i −0.0488369 + 0.464652i 0.942586 + 0.333962i \(0.108386\pi\)
−0.991423 + 0.130690i \(0.958281\pi\)
\(410\) −9.86414 + 2.09669i −0.487155 + 0.103548i
\(411\) −17.5983 22.3014i −0.868058 1.10005i
\(412\) −0.525386 4.99871i −0.0258839 0.246269i
\(413\) −2.16276 + 1.57134i −0.106422 + 0.0773204i
\(414\) 0.130181 0.0708435i 0.00639805 0.00348177i
\(415\) 4.60290 14.1663i 0.225948 0.695395i
\(416\) −19.6648 + 8.75533i −0.964145 + 0.429265i
\(417\) 3.48131 20.3181i 0.170480 0.994981i
\(418\) 8.75220 + 8.50551i 0.428084 + 0.416018i
\(419\) −0.0757820 0.131258i −0.00370219 0.00641238i 0.864168 0.503203i \(-0.167845\pi\)
−0.867871 + 0.496790i \(0.834512\pi\)
\(420\) 7.22768 7.04762i 0.352675 0.343888i
\(421\) 11.3595 + 12.6160i 0.553630 + 0.614868i 0.953386 0.301753i \(-0.0975719\pi\)
−0.399756 + 0.916622i \(0.630905\pi\)
\(422\) −1.49003 4.58585i −0.0725337 0.223236i
\(423\) −0.942451 + 0.280145i −0.0458236 + 0.0136211i
\(424\) −4.15194 + 3.01656i −0.201636 + 0.146497i
\(425\) 1.23747 + 0.263032i 0.0600261 + 0.0127589i
\(426\) −0.346686 8.71773i −0.0167970 0.422375i
\(427\) −1.66580 + 15.8490i −0.0806135 + 0.766986i
\(428\) 9.99085 + 17.3047i 0.482926 + 0.836453i
\(429\) −20.7247 9.18551i −1.00060 0.443481i
\(430\) 5.88900 10.2000i 0.283993 0.491890i
\(431\) 20.5242 + 14.9117i 0.988618 + 0.718273i 0.959618 0.281307i \(-0.0907678\pi\)
0.0289998 + 0.999579i \(0.490768\pi\)
\(432\) 10.6813 2.43300i 0.513903 0.117058i
\(433\) 5.10950 + 15.7254i 0.245547 + 0.755716i 0.995546 + 0.0942769i \(0.0300539\pi\)
−0.749999 + 0.661439i \(0.769946\pi\)
\(434\) 0.459123 + 4.36827i 0.0220386 + 0.209684i
\(435\) −39.9839 2.60153i −1.91708 0.124734i
\(436\) −5.79742 + 6.43868i −0.277646 + 0.308357i
\(437\) 0.532600 0.113208i 0.0254777 0.00541545i
\(438\) −2.83858 0.799102i −0.135633 0.0381825i
\(439\) 19.6207 33.9840i 0.936443 1.62197i 0.164403 0.986393i \(-0.447430\pi\)
0.772040 0.635574i \(-0.219237\pi\)
\(440\) 0.803326 21.0930i 0.0382971 1.00557i
\(441\) −12.8655 + 11.0094i −0.612643 + 0.524259i
\(442\) −0.579580 0.421089i −0.0275678 0.0200292i
\(443\) 21.5389 + 23.9214i 1.02334 + 1.13654i 0.990561 + 0.137075i \(0.0437703\pi\)
0.0327827 + 0.999463i \(0.489563\pi\)
\(444\) −17.8288 + 2.59374i −0.846117 + 0.123093i
\(445\) 5.84239 + 2.60120i 0.276956 + 0.123309i
\(446\) −0.202515 0.0901657i −0.00958939 0.00426947i
\(447\) 7.76739 1.13000i 0.367385 0.0534473i
\(448\) 0.829451 + 0.921199i 0.0391879 + 0.0435226i
\(449\) 20.9085 + 15.1909i 0.986731 + 0.716902i 0.959203 0.282719i \(-0.0912364\pi\)
0.0275281 + 0.999621i \(0.491236\pi\)
\(450\) 5.30318 4.53810i 0.249994 0.213928i
\(451\) 11.9096 15.1447i 0.560799 0.713134i
\(452\) 16.0178 27.7437i 0.753415 1.30495i
\(453\) 4.88647 + 1.37561i 0.229586 + 0.0646318i
\(454\) −10.1813 + 2.16410i −0.477831 + 0.101566i
\(455\) 9.23679 10.2585i 0.433027 0.480926i
\(456\) −23.3167 1.51709i −1.09191 0.0710441i
\(457\) 1.32921 + 12.6466i 0.0621780 + 0.591584i 0.980605 + 0.195994i \(0.0627932\pi\)
−0.918427 + 0.395590i \(0.870540\pi\)
\(458\) 2.39760 + 7.37904i 0.112032 + 0.344800i
\(459\) 1.10991 + 1.19725i 0.0518063 + 0.0558830i
\(460\) −0.346255 0.251569i −0.0161442 0.0117295i
\(461\) 9.51087 16.4733i 0.442965 0.767238i −0.554943 0.831889i \(-0.687260\pi\)
0.997908 + 0.0646502i \(0.0205932\pi\)
\(462\) 0.397512 3.84420i 0.0184939 0.178849i
\(463\) 11.4334 + 19.8032i 0.531353 + 0.920331i 0.999330 + 0.0365903i \(0.0116497\pi\)
−0.467977 + 0.883741i \(0.655017\pi\)
\(464\) 1.69684 16.1443i 0.0787738 0.749482i
\(465\) −1.35005 33.9481i −0.0626069 1.57430i
\(466\) 1.90448 + 0.404810i 0.0882233 + 0.0187524i
\(467\) −12.8819 + 9.35921i −0.596101 + 0.433093i −0.844493 0.535567i \(-0.820098\pi\)
0.248392 + 0.968660i \(0.420098\pi\)
\(468\) 18.9069 5.62012i 0.873973 0.259790i
\(469\) −4.20232 12.9334i −0.194045 0.597210i
\(470\) −0.380700 0.422810i −0.0175604 0.0195028i
\(471\) −22.3882 + 21.8305i −1.03159 + 1.00589i
\(472\) −2.43188 4.21215i −0.111936 0.193880i
\(473\) 3.83737 + 22.1723i 0.176443 + 1.01948i
\(474\) 1.50206 8.76655i 0.0689920 0.402661i
\(475\) 23.4259 10.4299i 1.07486 0.478556i
\(476\) −0.188347 + 0.579671i −0.00863285 + 0.0265692i
\(477\) 6.38400 3.47412i 0.292303 0.159069i
\(478\) 10.8436 7.87832i 0.495973 0.360346i
\(479\) 1.71322 + 16.3002i 0.0782789 + 0.744774i 0.961312 + 0.275463i \(0.0888311\pi\)
−0.883033 + 0.469311i \(0.844502\pi\)
\(480\) 17.5843 + 22.2837i 0.802609 + 1.01711i
\(481\) −24.0979 + 5.12217i −1.09877 + 0.233551i
\(482\) −0.915880 + 8.71402i −0.0417172 + 0.396913i
\(483\) −0.132620 0.110192i −0.00603442 0.00501391i
\(484\) 11.1920 + 14.5133i 0.508728 + 0.659694i
\(485\) −0.266911 −0.0121198
\(486\) 8.96742 0.845568i 0.406771 0.0383558i
\(487\) 7.04142 21.6713i 0.319077 0.982019i −0.654966 0.755658i \(-0.727317\pi\)
0.974044 0.226361i \(-0.0726828\pi\)
\(488\) −28.3605 6.02821i −1.28382 0.272884i
\(489\) −10.0653 0.654890i −0.455167 0.0296151i
\(490\) −8.95145 3.98544i −0.404385 0.180044i
\(491\) −29.2029 + 32.4331i −1.31791 + 1.46368i −0.529836 + 0.848100i \(0.677747\pi\)
−0.788071 + 0.615584i \(0.788920\pi\)
\(492\) 0.666143 + 16.7507i 0.0300320 + 0.755181i
\(493\) 2.21006 0.983982i 0.0995360 0.0443163i
\(494\) −14.5209 −0.653324
\(495\) −4.99890 + 29.4728i −0.224684 + 1.32470i
\(496\) 13.7645 0.618045
\(497\) −9.27261 + 4.12843i −0.415933 + 0.185185i
\(498\) 4.39219 + 2.30817i 0.196819 + 0.103431i
\(499\) −13.4519 + 14.9398i −0.602189 + 0.668798i −0.964752 0.263161i \(-0.915235\pi\)
0.362563 + 0.931959i \(0.381902\pi\)
\(500\) 4.45142 + 1.98190i 0.199074 + 0.0886333i
\(501\) 3.85070 + 7.79906i 0.172037 + 0.348436i
\(502\) 0.329111 + 0.0699546i 0.0146889 + 0.00312223i
\(503\) −3.27815 + 10.0891i −0.146165 + 0.449850i −0.997159 0.0753254i \(-0.976000\pi\)
0.850994 + 0.525176i \(0.176000\pi\)
\(504\) 4.19681 + 6.09393i 0.186941 + 0.271445i
\(505\) −6.17856 −0.274942
\(506\) −0.163487 + 0.0109131i −0.00726791 + 0.000485148i
\(507\) 4.17919 1.54405i 0.185604 0.0685736i
\(508\) −2.29592 + 21.8442i −0.101865 + 0.969179i
\(509\) 43.4966 9.24549i 1.92795 0.409799i 0.928715 0.370794i \(-0.120914\pi\)
0.999239 0.0390051i \(-0.0124189\pi\)
\(510\) −0.349654 + 0.877630i −0.0154829 + 0.0388621i
\(511\) 0.358610 + 3.41195i 0.0158640 + 0.150936i
\(512\) −16.5301 + 12.0098i −0.730534 + 0.530764i
\(513\) 32.4645 + 6.40930i 1.43334 + 0.282977i
\(514\) −1.95899 + 6.02915i −0.0864073 + 0.265934i
\(515\) −8.27992 + 3.68646i −0.364857 + 0.162445i
\(516\) −15.0592 12.5125i −0.662946 0.550831i
\(517\) 1.07591 + 0.154679i 0.0473187 + 0.00680275i
\(518\) −2.10004 3.63738i −0.0922707 0.159817i
\(519\) 25.9921 + 7.31715i 1.14093 + 0.321187i
\(520\) 16.8052 + 18.6641i 0.736956 + 0.818473i
\(521\) 5.23819 + 16.1215i 0.229489 + 0.706296i 0.997805 + 0.0662243i \(0.0210953\pi\)
−0.768315 + 0.640071i \(0.778905\pi\)
\(522\) 3.10344 12.9813i 0.135834 0.568177i
\(523\) −24.4438 + 17.7595i −1.06885 + 0.776567i −0.975706 0.219085i \(-0.929693\pi\)
−0.0931472 + 0.995652i \(0.529693\pi\)
\(524\) −29.2890 6.22557i −1.27950 0.271965i
\(525\) −7.18814 3.77748i −0.313716 0.164863i
\(526\) 0.869448 8.27225i 0.0379098 0.360687i
\(527\) 1.02565 + 1.77648i 0.0446780 + 0.0773845i
\(528\) −11.8506 2.49812i −0.515732 0.108717i
\(529\) 11.4963 19.9123i 0.499841 0.865750i
\(530\) 3.40255 + 2.47210i 0.147797 + 0.107381i
\(531\) 2.64203 + 6.36125i 0.114654 + 0.276055i
\(532\) 3.81763 + 11.7495i 0.165515 + 0.509404i
\(533\) 2.39617 + 22.7980i 0.103790 + 0.987491i
\(534\) −1.18270 + 1.77187i −0.0511805 + 0.0766761i
\(535\) 24.1099 26.7768i 1.04236 1.15766i
\(536\) 24.2010 5.14409i 1.04533 0.222191i
\(537\) 3.01093 + 11.8319i 0.129931 + 0.510584i
\(538\) −0.141268 + 0.244683i −0.00609050 + 0.0105491i
\(539\) 18.0112 5.10310i 0.775799 0.219806i
\(540\) −13.3311 22.3348i −0.573680 0.961136i
\(541\) −9.57164 6.95421i −0.411517 0.298985i 0.362699 0.931906i \(-0.381855\pi\)
−0.774216 + 0.632922i \(0.781855\pi\)
\(542\) 8.48229 + 9.42053i 0.364345 + 0.404647i
\(543\) 1.60117 4.01892i 0.0687126 0.172469i
\(544\) −1.56569 0.697091i −0.0671285 0.0298875i
\(545\) 14.2727 + 6.35461i 0.611375 + 0.272202i
\(546\) 2.84849 + 3.60975i 0.121904 + 0.154483i
\(547\) 1.70348 + 1.89190i 0.0728355 + 0.0808920i 0.778461 0.627693i \(-0.216001\pi\)
−0.705626 + 0.708585i \(0.749334\pi\)
\(548\) −22.1084 16.0627i −0.944424 0.686164i
\(549\) 38.7194 + 13.6697i 1.65251 + 0.583409i
\(550\) −7.42425 + 2.10350i −0.316571 + 0.0896937i
\(551\) 24.5177 42.4659i 1.04449 1.80911i
\(552\) 0.224604 0.219008i 0.00955976 0.00932160i
\(553\) −10.1214 + 2.15137i −0.430407 + 0.0914857i
\(554\) 1.10945 1.23217i 0.0471360 0.0523498i
\(555\) 14.3829 + 29.1307i 0.610522 + 1.23653i
\(556\) −2.07276 19.7210i −0.0879048 0.836358i
\(557\) 2.98987 + 9.20189i 0.126685 + 0.389896i 0.994204 0.107507i \(-0.0342868\pi\)
−0.867519 + 0.497404i \(0.834287\pi\)
\(558\) 11.2219 + 1.46650i 0.475061 + 0.0620819i
\(559\) −21.6599 15.7368i −0.916117 0.665598i
\(560\) 3.68748 6.38690i 0.155824 0.269896i
\(561\) −0.560625 1.71561i −0.0236696 0.0724331i
\(562\) −5.25175 9.09630i −0.221532 0.383704i
\(563\) 2.50735 23.8558i 0.105672 1.00540i −0.805281 0.592893i \(-0.797986\pi\)
0.910953 0.412510i \(-0.135348\pi\)
\(564\) −0.799639 + 0.505068i −0.0336709 + 0.0212672i
\(565\) −56.5054 12.0106i −2.37720 0.505290i
\(566\) 9.60027 6.97501i 0.403530 0.293181i
\(567\) −4.77512 9.32766i −0.200536 0.391725i
\(568\) −5.70659 17.5631i −0.239443 0.736930i
\(569\) −25.1721 27.9565i −1.05527 1.17200i −0.984659 0.174492i \(-0.944172\pi\)
−0.0706111 0.997504i \(-0.522495\pi\)
\(570\) 4.72236 + 18.5572i 0.197798 + 0.777277i
\(571\) 7.37740 + 12.7780i 0.308735 + 0.534744i 0.978086 0.208202i \(-0.0667612\pi\)
−0.669351 + 0.742946i \(0.733428\pi\)
\(572\) −21.5844 3.10307i −0.902488 0.129746i
\(573\) −19.2089 + 7.09695i −0.802463 + 0.296479i
\(574\) −3.57023 + 1.58957i −0.149018 + 0.0663473i
\(575\) −0.106386 + 0.327424i −0.00443662 + 0.0136545i
\(576\) 2.80545 1.52670i 0.116894 0.0636126i
\(577\) 18.0466 13.1116i 0.751289 0.545843i −0.144937 0.989441i \(-0.546298\pi\)
0.896226 + 0.443598i \(0.146298\pi\)
\(578\) 1.02080 + 9.71227i 0.0424597 + 0.403977i
\(579\) −11.5638 + 1.68231i −0.480576 + 0.0699143i
\(580\) −37.7013 + 8.01366i −1.56546 + 0.332749i
\(581\) 0.603385 5.74083i 0.0250326 0.238170i
\(582\) 0.0150151 0.0876332i 0.000622396 0.00363251i
\(583\) −8.01732 + 0.535173i −0.332044 + 0.0221646i
\(584\) −6.24181 −0.258288
\(585\) −20.1739 29.2933i −0.834087 1.21113i
\(586\) 0.153568 0.472634i 0.00634384 0.0195243i
\(587\) 2.44553 + 0.519814i 0.100938 + 0.0214550i 0.258104 0.966117i \(-0.416902\pi\)
−0.157166 + 0.987572i \(0.550236\pi\)
\(588\) −9.04302 + 13.5478i −0.372928 + 0.558703i
\(589\) 37.9836 + 16.9114i 1.56508 + 0.696821i
\(590\) −2.66709 + 2.96210i −0.109802 + 0.121948i
\(591\) 30.2361 19.0978i 1.24375 0.785577i
\(592\) −12.0242 + 5.35351i −0.494190 + 0.220028i
\(593\) −10.8953 −0.447417 −0.223708 0.974656i \(-0.571816\pi\)
−0.223708 + 0.974656i \(0.571816\pi\)
\(594\) −9.39539 3.29925i −0.385498 0.135370i
\(595\) 1.09907 0.0450577
\(596\) 6.89767 3.07104i 0.282540 0.125795i
\(597\) 19.4563 12.2890i 0.796294 0.502955i
\(598\) 0.130449 0.144878i 0.00533445 0.00592451i
\(599\) −33.6533 14.9834i −1.37504 0.612205i −0.419682 0.907671i \(-0.637858\pi\)
−0.955353 + 0.295466i \(0.904525\pi\)
\(600\) 8.20203 12.2879i 0.334846 0.501651i
\(601\) 15.1166 + 3.21313i 0.616618 + 0.131066i 0.505623 0.862755i \(-0.331263\pi\)
0.110995 + 0.993821i \(0.464596\pi\)
\(602\) 1.41047 4.34099i 0.0574866 0.176925i
\(603\) −34.9287 + 2.78249i −1.42241 + 0.113312i
\(604\) 4.88321 0.198695
\(605\) 18.6534 27.2813i 0.758368 1.10914i
\(606\) 0.347575 2.02857i 0.0141193 0.0824049i
\(607\) 2.66306 25.3373i 0.108090 1.02841i −0.797228 0.603678i \(-0.793701\pi\)
0.905319 0.424733i \(-0.139632\pi\)
\(608\) −33.9795 + 7.22257i −1.37805 + 0.292914i
\(609\) −15.3662 + 2.23548i −0.622669 + 0.0905860i
\(610\) 2.48369 + 23.6307i 0.100562 + 0.956781i
\(611\) −1.04630 + 0.760183i −0.0423289 + 0.0307537i
\(612\) 1.33981 + 0.819280i 0.0541587 + 0.0331174i
\(613\) −11.6728 + 35.9252i −0.471461 + 1.45101i 0.379211 + 0.925310i \(0.376195\pi\)
−0.850672 + 0.525697i \(0.823805\pi\)
\(614\) 1.84180 0.820023i 0.0743290 0.0330934i
\(615\) 28.3559 10.4764i 1.14342 0.422450i
\(616\) −1.39501 8.06037i −0.0562066 0.324761i
\(617\) −20.9464 36.2802i −0.843271 1.46059i −0.887115 0.461549i \(-0.847294\pi\)
0.0438437 0.999038i \(-0.486040\pi\)
\(618\) −0.744564 2.92588i −0.0299508 0.117696i
\(619\) −4.00783 4.45115i −0.161088 0.178907i 0.657197 0.753719i \(-0.271742\pi\)
−0.818286 + 0.574812i \(0.805075\pi\)
\(620\) −10.0993 31.0823i −0.405596 1.24830i
\(621\) −0.355594 + 0.266328i −0.0142695 + 0.0106874i
\(622\) −5.06974 + 3.68338i −0.203278 + 0.147690i
\(623\) 2.42424 + 0.515288i 0.0971251 + 0.0206446i
\(624\) 12.1832 7.69516i 0.487719 0.308053i
\(625\) 3.02291 28.7611i 0.120917 1.15044i
\(626\) 8.17057 + 14.1518i 0.326562 + 0.565621i
\(627\) −29.6329 21.4535i −1.18342 0.856772i
\(628\) −15.0399 + 26.0498i −0.600157 + 1.03950i
\(629\) −1.58690 1.15295i −0.0632739 0.0459712i
\(630\) 3.68679 4.81423i 0.146885 0.191803i
\(631\) −6.64368 20.4471i −0.264481 0.813988i −0.991813 0.127702i \(-0.959240\pi\)
0.727332 0.686286i \(-0.240760\pi\)
\(632\) −1.96786 18.7229i −0.0782772 0.744758i
\(633\) 6.39902 + 12.9603i 0.254338 + 0.515127i
\(634\) −0.430138 + 0.477717i −0.0170830 + 0.0189726i
\(635\) 38.7416 8.23479i 1.53741 0.326788i
\(636\) 5.00568 4.88097i 0.198488 0.193543i
\(637\) −11.1368 + 19.2895i −0.441256 + 0.764278i
\(638\) −9.12129 + 11.5990i −0.361115 + 0.459208i
\(639\) 4.79053 + 25.7104i 0.189510 + 1.01709i
\(640\) 28.0127 + 20.3525i 1.10730 + 0.804501i
\(641\) 8.58963 + 9.53975i 0.339270 + 0.376798i 0.888502 0.458872i \(-0.151746\pi\)
−0.549232 + 0.835670i \(0.685080\pi\)
\(642\) 7.43514 + 9.42218i 0.293442 + 0.371864i
\(643\) 25.9041 + 11.5332i 1.02156 + 0.454827i 0.848000 0.529997i \(-0.177807\pi\)
0.173558 + 0.984824i \(0.444473\pi\)
\(644\) −0.151523 0.0674625i −0.00597085 0.00265839i
\(645\) −13.0672 + 32.7986i −0.514519 + 1.29144i
\(646\) −0.773607 0.859177i −0.0304372 0.0338039i
\(647\) 14.1536 + 10.2832i 0.556436 + 0.404274i 0.830153 0.557536i \(-0.188253\pi\)
−0.273717 + 0.961810i \(0.588253\pi\)
\(648\) 17.7857 6.86625i 0.698687 0.269732i
\(649\) 0.289810 7.60956i 0.0113760 0.298701i
\(650\) 4.59060 7.95116i 0.180058 0.311870i
\(651\) −3.24705 12.7598i −0.127262 0.500095i
\(652\) −9.49066 + 2.01730i −0.371683 + 0.0790036i
\(653\) −19.6070 + 21.7758i −0.767282 + 0.852152i −0.992511 0.122153i \(-0.961020\pi\)
0.225230 + 0.974306i \(0.427687\pi\)
\(654\) −2.88928 + 4.32858i −0.112980 + 0.169261i
\(655\) 5.64400 + 53.6991i 0.220529 + 2.09820i
\(656\) 3.78455 + 11.6477i 0.147762 + 0.454764i
\(657\) 8.76516 + 1.14545i 0.341961 + 0.0446881i
\(658\) −0.178378 0.129599i −0.00695388 0.00505229i
\(659\) −13.7935 + 23.8911i −0.537319 + 0.930664i 0.461728 + 0.887021i \(0.347229\pi\)
−0.999047 + 0.0436422i \(0.986104\pi\)
\(660\) 3.05387 + 28.5934i 0.118872 + 1.11300i
\(661\) −14.8776 25.7688i −0.578672 1.00229i −0.995632 0.0933649i \(-0.970238\pi\)
0.416960 0.908925i \(-0.363096\pi\)
\(662\) 0.747623 7.11315i 0.0290572 0.276461i
\(663\) 1.90097 + 0.998992i 0.0738277 + 0.0387976i
\(664\) 10.2728 + 2.18354i 0.398660 + 0.0847378i
\(665\) 18.0228 13.0943i 0.698893 0.507775i
\(666\) −10.3734 + 3.08351i −0.401961 + 0.119484i
\(667\) 0.203437 + 0.626115i 0.00787711 + 0.0242433i
\(668\) 5.59853 + 6.21779i 0.216613 + 0.240574i
\(669\) 0.639648 + 0.180070i 0.0247302 + 0.00696191i
\(670\) −10.1380 17.5596i −0.391666 0.678385i
\(671\) −32.5548 31.6373i −1.25677 1.22134i
\(672\) 8.46107 + 7.03017i 0.326393 + 0.271195i
\(673\) 8.81907 3.92650i 0.339950 0.151356i −0.229659 0.973271i \(-0.573761\pi\)
0.569609 + 0.821916i \(0.307094\pi\)
\(674\) 2.40577 7.40418i 0.0926666 0.285198i
\(675\) −13.7728 + 15.7503i −0.530115 + 0.606229i
\(676\) 3.46724 2.51910i 0.133355 0.0968883i
\(677\) 0.0102558 + 0.0975777i 0.000394163 + 0.00375021i 0.994717 0.102653i \(-0.0327332\pi\)
−0.994323 + 0.106403i \(0.966067\pi\)
\(678\) 7.12208 17.8764i 0.273522 0.686540i
\(679\) −0.101177 + 0.0215058i −0.00388281 + 0.000825318i
\(680\) −0.209018 + 1.98868i −0.00801549 + 0.0762623i
\(681\) 29.2676 10.8132i 1.12153 0.414364i
\(682\) −10.5896 6.66372i −0.405496 0.255167i
\(683\) 30.5246 1.16799 0.583996 0.811756i \(-0.301488\pi\)
0.583996 + 0.811756i \(0.301488\pi\)
\(684\) 31.7312 2.52777i 1.21327 0.0966517i
\(685\) −15.2277 + 46.8660i −0.581820 + 1.79066i
\(686\) −8.32071 1.76862i −0.317686 0.0675263i
\(687\) −10.2966 20.8543i −0.392839 0.795642i
\(688\) −13.0671 5.81784i −0.498178 0.221803i
\(689\) 6.39713 7.10473i 0.243711 0.270669i
\(690\) −0.227574 0.119594i −0.00866358 0.00455286i
\(691\) 29.9658 13.3416i 1.13995 0.507540i 0.252116 0.967697i \(-0.418873\pi\)
0.887838 + 0.460157i \(0.152207\pi\)
\(692\) 25.9748 0.987413
\(693\) 0.479793 + 11.5749i 0.0182258 + 0.439694i
\(694\) 5.62741 0.213614
\(695\) −32.6661 + 14.5439i −1.23910 + 0.551681i
\(696\) −1.12260 28.2288i −0.0425522 1.07001i
\(697\) −1.22127 + 1.35635i −0.0462588 + 0.0513756i
\(698\) −2.34379 1.04352i −0.0887138 0.0394979i
\(699\) −5.82410 0.378941i −0.220288 0.0143329i
\(700\) −7.64053 1.62405i −0.288785 0.0613831i
\(701\) −2.70365 + 8.32098i −0.102115 + 0.314279i −0.989043 0.147630i \(-0.952835\pi\)
0.886927 + 0.461909i \(0.152835\pi\)
\(702\) 10.7526 4.97567i 0.405829 0.187795i
\(703\) −39.7584 −1.49952
\(704\) −3.52321 + 0.235181i −0.132786 + 0.00886373i
\(705\) 1.31176 + 1.08992i 0.0494039 + 0.0410489i
\(706\) −1.96435 + 18.6895i −0.0739293 + 0.703390i
\(707\) −2.34208 + 0.497825i −0.0880831 + 0.0187226i
\(708\) 4.10457 + 5.20151i 0.154259 + 0.195485i
\(709\) −2.79884 26.6292i −0.105113 1.00008i −0.912227 0.409685i \(-0.865639\pi\)
0.807114 0.590395i \(-0.201028\pi\)
\(710\) −12.2435 + 8.89542i −0.459490 + 0.333839i
\(711\) −0.672486 + 26.6531i −0.0252202 + 0.999569i
\(712\) −1.39340 + 4.28845i −0.0522199 + 0.160716i
\(713\) −0.509956 + 0.227047i −0.0190980 + 0.00850298i
\(714\) −0.0618286 + 0.360852i −0.00231388 + 0.0135046i
\(715\) 6.70577 + 38.7459i 0.250781 + 1.44901i
\(716\) 5.87217 + 10.1709i 0.219453 + 0.380105i
\(717\) −28.7662 + 28.0496i −1.07429 + 1.04753i
\(718\) −10.7368 11.9244i −0.400694 0.445016i
\(719\) −4.63672 14.2703i −0.172920 0.532194i 0.826612 0.562772i \(-0.190265\pi\)
−0.999532 + 0.0305782i \(0.990265\pi\)
\(720\) −13.7963 13.0672i −0.514159 0.486987i
\(721\) −2.84161 + 2.06455i −0.105827 + 0.0768879i
\(722\) −12.1834 2.58965i −0.453418 0.0963769i
\(723\) −1.04368 26.2443i −0.0388150 0.976036i
\(724\) 0.434995 4.13870i 0.0161665 0.153814i
\(725\) 15.5020 + 26.8502i 0.575730 + 0.997193i
\(726\) 7.90774 + 7.65906i 0.293484 + 0.284254i
\(727\) −13.7663 + 23.8438i −0.510562 + 0.884319i 0.489363 + 0.872080i \(0.337229\pi\)
−0.999925 + 0.0122391i \(0.996104\pi\)
\(728\) 7.87410 + 5.72087i 0.291834 + 0.212029i
\(729\) −26.2358 + 6.37816i −0.971698 + 0.236228i
\(730\) 1.58069 + 4.86486i 0.0585039 + 0.180057i
\(731\) −0.222818 2.11997i −0.00824123 0.0784101i
\(732\) 39.4156 + 2.56455i 1.45684 + 0.0947883i
\(733\) 31.9441 35.4775i 1.17988 1.31039i 0.239251 0.970958i \(-0.423098\pi\)
0.940630 0.339433i \(-0.110235\pi\)
\(734\) −0.662509 + 0.140821i −0.0244536 + 0.00519778i
\(735\) 28.2733 + 7.95932i 1.04287 + 0.293584i
\(736\) 0.233195 0.403906i 0.00859570 0.0148882i
\(737\) 36.3593 + 13.3640i 1.33931 + 0.492267i
\(738\) 1.84450 + 9.89928i 0.0678968 + 0.364398i
\(739\) −1.20421 0.874910i −0.0442976 0.0321841i 0.565416 0.824806i \(-0.308716\pi\)
−0.609714 + 0.792622i \(0.708716\pi\)
\(740\) 20.9113 + 23.2244i 0.768716 + 0.853746i
\(741\) 43.0743 6.26646i 1.58237 0.230204i
\(742\) 1.48898 + 0.662935i 0.0546620 + 0.0243371i
\(743\) −16.5901 7.38641i −0.608633 0.270981i 0.0791896 0.996860i \(-0.474767\pi\)
−0.687823 + 0.725879i \(0.741433\pi\)
\(744\) 23.7052 3.44864i 0.869074 0.126433i
\(745\) −9.11035 10.1181i −0.333778 0.370698i
\(746\) −10.1751 7.39264i −0.372537 0.270664i
\(747\) −14.0250 4.95145i −0.513147 0.181164i
\(748\) −0.966316 1.44243i −0.0353320 0.0527406i
\(749\) 6.98177 12.0928i 0.255108 0.441860i
\(750\) 2.81738 + 0.793132i 0.102876 + 0.0289611i
\(751\) 4.29862 0.913700i 0.156859 0.0333414i −0.128813 0.991669i \(-0.541117\pi\)
0.285672 + 0.958328i \(0.407783\pi\)
\(752\) −0.462338 + 0.513479i −0.0168597 + 0.0187246i
\(753\) −1.00645 0.0654843i −0.0366773 0.00238638i
\(754\) −1.83518 17.4605i −0.0668332 0.635875i
\(755\) −2.72107 8.37459i −0.0990299 0.304783i
\(756\) −6.85295 7.39223i −0.249240 0.268853i
\(757\) 11.1369 + 8.09140i 0.404776 + 0.294087i 0.771483 0.636249i \(-0.219515\pi\)
−0.366708 + 0.930336i \(0.619515\pi\)
\(758\) 4.69382 8.12993i 0.170487 0.295292i
\(759\) 0.480256 0.102925i 0.0174322 0.00373595i
\(760\) 20.2655 + 35.1008i 0.735105 + 1.27324i
\(761\) 3.25147 30.9357i 0.117866 1.12142i −0.762456 0.647041i \(-0.776006\pi\)
0.880321 0.474378i \(-0.157327\pi\)
\(762\) 0.524263 + 13.1830i 0.0189920 + 0.477571i
\(763\) 5.92230 + 1.25882i 0.214402 + 0.0455725i
\(764\) −15.9365 + 11.5786i −0.576564 + 0.418898i
\(765\) 0.658463 2.75427i 0.0238068 0.0995809i
\(766\) 1.10585 + 3.40344i 0.0399558 + 0.122971i
\(767\) 6.06268 + 6.73329i 0.218911 + 0.243125i
\(768\) −5.61752 + 5.47757i −0.202705 + 0.197655i
\(769\) −10.9677 18.9966i −0.395504 0.685034i 0.597661 0.801749i \(-0.296097\pi\)
−0.993165 + 0.116715i \(0.962764\pi\)
\(770\) −5.92897 + 3.12850i −0.213665 + 0.112743i
\(771\) 3.20922 18.7301i 0.115577 0.674549i
\(772\) −10.2690 + 4.57206i −0.369590 + 0.164552i
\(773\) −3.92965 + 12.0942i −0.141340 + 0.434999i −0.996522 0.0833281i \(-0.973445\pi\)
0.855182 + 0.518327i \(0.173445\pi\)
\(774\) −10.0335 6.13535i −0.360645 0.220530i
\(775\) −21.2682 + 15.4522i −0.763976 + 0.555061i
\(776\) −0.0196714 0.187160i −0.000706160 0.00671867i
\(777\) 7.79923 + 9.88358i 0.279796 + 0.354571i
\(778\) 0.408750 0.0868824i 0.0146544 0.00311489i
\(779\) −3.86697 + 36.7918i −0.138549 + 1.31820i
\(780\) −26.3158 21.8654i −0.942258 0.782908i
\(781\) 7.08334 28.0321i 0.253462 1.00307i
\(782\) 0.0155220 0.000555064
\(783\) −3.60390 + 39.8468i −0.128793 + 1.42401i
\(784\) −3.67724 + 11.3174i −0.131330 + 0.404193i
\(785\) 53.0556 + 11.2773i 1.89363 + 0.402504i
\(786\) −17.9482 1.16779i −0.640191 0.0416536i
\(787\) −15.7693 7.02095i −0.562115 0.250270i 0.105951 0.994371i \(-0.466211\pi\)
−0.668067 + 0.744102i \(0.732878\pi\)
\(788\) 23.0190 25.5652i 0.820018 0.910722i
\(789\) 0.990772 + 24.9138i 0.0352724 + 0.886955i
\(790\) −14.0943 + 6.27518i −0.501452 + 0.223261i
\(791\) −22.3870 −0.795991
\(792\) −21.0350 1.33313i −0.747445 0.0473708i
\(793\) 54.0120 1.91802
\(794\) 2.15890 0.961206i 0.0766166 0.0341119i
\(795\) −11.1601 5.86480i −0.395807 0.208003i
\(796\) 14.8122 16.4507i 0.525006 0.583078i
\(797\) 32.1582 + 14.3177i 1.13910 + 0.507161i 0.887563 0.460687i \(-0.152397\pi\)
0.251538 + 0.967847i \(0.419064\pi\)
\(798\) 3.28530 + 6.65393i 0.116298 + 0.235546i
\(799\) −0.100721 0.0214090i −0.00356326 0.000757395i
\(800\) 6.78739 20.8894i 0.239970 0.738553i
\(801\) 2.74369 5.76641i 0.0969434 0.203746i
\(802\) −3.26248 −0.115202
\(803\) −8.27126 5.20487i −0.291887 0.183676i
\(804\) −31.6170 + 11.6812i −1.11504 + 0.411966i
\(805\) −0.0312634 + 0.297451i −0.00110189 + 0.0104838i
\(806\) 14.5614 3.09512i 0.512903 0.109021i
\(807\) 0.313461 0.786787i 0.0110344 0.0276962i
\(808\) −0.455360 4.33246i −0.0160195 0.152415i
\(809\) 15.4367 11.2154i 0.542725 0.394313i −0.282371 0.959305i \(-0.591121\pi\)
0.825096 + 0.564992i \(0.191121\pi\)
\(810\) −9.85563 12.1233i −0.346291 0.425970i
\(811\) −9.59769 + 29.5387i −0.337020 + 1.03724i 0.628698 + 0.777650i \(0.283588\pi\)
−0.965718 + 0.259593i \(0.916412\pi\)
\(812\) −13.6456 + 6.07542i −0.478867 + 0.213205i
\(813\) −29.2271 24.2843i −1.02504 0.851688i
\(814\) 11.8424 + 1.70252i 0.415076 + 0.0596733i
\(815\) 8.74810 + 15.1522i 0.306433 + 0.530757i
\(816\) 1.10438 + 0.310898i 0.0386610 + 0.0108836i
\(817\) −28.9110 32.1090i −1.01147 1.12335i
\(818\) 1.68711 + 5.19240i 0.0589885 + 0.181548i
\(819\) −10.0075 9.47861i −0.349690 0.331209i
\(820\) 23.5253 17.0922i 0.821540 0.596884i
\(821\) −33.2653 7.07077i −1.16097 0.246771i −0.413143 0.910666i \(-0.635569\pi\)
−0.747826 + 0.663895i \(0.768902\pi\)
\(822\) −14.5306 7.63607i −0.506813 0.266338i
\(823\) −1.62605 + 15.4708i −0.0566804 + 0.539278i 0.928931 + 0.370252i \(0.120729\pi\)
−0.985612 + 0.169026i \(0.945938\pi\)
\(824\) −3.19521 5.53426i −0.111310 0.192795i
\(825\) 21.1154 9.44371i 0.735143 0.328788i
\(826\) −0.772337 + 1.33773i −0.0268730 + 0.0465455i
\(827\) −12.9667 9.42084i −0.450895 0.327595i 0.339054 0.940767i \(-0.389893\pi\)
−0.789949 + 0.613172i \(0.789893\pi\)
\(828\) −0.259839 + 0.339299i −0.00903003 + 0.0117914i
\(829\) 5.90205 + 18.1646i 0.204987 + 0.630884i 0.999714 + 0.0239173i \(0.00761382\pi\)
−0.794727 + 0.606967i \(0.792386\pi\)
\(830\) −0.899644 8.55954i −0.0312271 0.297106i
\(831\) −2.75930 + 4.13386i −0.0957191 + 0.143402i
\(832\) 2.81122 3.12217i 0.0974614 0.108242i
\(833\) −1.73465 + 0.368711i −0.0601021 + 0.0127751i
\(834\) −2.93747 11.5432i −0.101716 0.399709i
\(835\) 7.54371 13.0661i 0.261061 0.452171i
\(836\) −33.0308 12.1406i −1.14240 0.419891i
\(837\) −33.9213 + 0.492616i −1.17249 + 0.0170273i
\(838\) −0.0708501 0.0514756i −0.00244747 0.00177819i
\(839\) 0.995613 + 1.10574i 0.0343724 + 0.0381744i 0.760086 0.649823i \(-0.225157\pi\)
−0.725713 + 0.687997i \(0.758490\pi\)
\(840\) 4.75035 11.9234i 0.163903 0.411395i
\(841\) 27.6687 + 12.3189i 0.954095 + 0.424790i
\(842\) 8.96121 + 3.98979i 0.308824 + 0.137497i
\(843\) 19.5042 + 24.7167i 0.671759 + 0.851287i
\(844\) 9.30353 + 10.3326i 0.320241 + 0.355663i
\(845\) −6.25224 4.54252i −0.215084 0.156267i
\(846\) −0.431641 + 0.369369i −0.0148401 + 0.0126992i
\(847\) 4.87274 11.8444i 0.167429 0.406977i
\(848\) 2.55384 4.42338i 0.0876993 0.151900i
\(849\) −25.4680 + 24.8335i −0.874058 + 0.852283i
\(850\) 0.715025 0.151983i 0.0245252 0.00521298i
\(851\) 0.357172 0.396680i 0.0122437 0.0135980i
\(852\) 11.1377 + 22.5579i 0.381571 + 0.772820i
\(853\) −3.95139 37.5950i −0.135293 1.28723i −0.825825 0.563926i \(-0.809290\pi\)
0.690532 0.723302i \(-0.257376\pi\)
\(854\) 2.84548 + 8.75750i 0.0973704 + 0.299675i
\(855\) −22.0167 53.0098i −0.752954 1.81290i
\(856\) 20.5530 + 14.9326i 0.702487 + 0.510387i
\(857\) −9.91348 + 17.1706i −0.338638 + 0.586538i −0.984177 0.177189i \(-0.943300\pi\)
0.645539 + 0.763727i \(0.276633\pi\)
\(858\) −13.0984 + 0.0220111i −0.447173 + 0.000751447i
\(859\) 7.85764 + 13.6098i 0.268099 + 0.464362i 0.968371 0.249515i \(-0.0802711\pi\)
−0.700272 + 0.713876i \(0.746938\pi\)
\(860\) −3.55001 + 33.7761i −0.121054 + 1.15175i
\(861\) 9.90466 6.25598i 0.337550 0.213203i
\(862\) 14.3384 + 3.04772i 0.488368 + 0.103806i
\(863\) −6.57548 + 4.77736i −0.223832 + 0.162623i −0.694050 0.719927i \(-0.744175\pi\)
0.470218 + 0.882550i \(0.344175\pi\)
\(864\) 22.6866 16.9916i 0.771815 0.578064i
\(865\) −14.4739 44.5462i −0.492128 1.51462i
\(866\) 6.39284 + 7.09997i 0.217237 + 0.241267i
\(867\) −7.21940 28.3697i −0.245184 0.963486i
\(868\) −6.33269 10.9685i −0.214945 0.372296i
\(869\) 13.0049 26.4514i 0.441159 0.897303i
\(870\) −21.7172 + 8.02368i −0.736283 + 0.272028i
\(871\) −42.1057 + 18.7467i −1.42670 + 0.635206i
\(872\) −3.40401 + 10.4765i −0.115274 + 0.354778i
\(873\) −0.00672238 + 0.266433i −0.000227518 + 0.00901739i
\(874\) 0.254531 0.184928i 0.00860964 0.00625527i
\(875\) −0.355931 3.38646i −0.0120327 0.114483i
\(876\) 8.41469 1.22417i 0.284306 0.0413609i
\(877\) 2.47817 0.526750i 0.0836817 0.0177871i −0.165881 0.986146i \(-0.553047\pi\)
0.249562 + 0.968359i \(0.419713\pi\)
\(878\) 2.37009 22.5499i 0.0799867 0.761022i
\(879\) −0.251576 + 1.46828i −0.00848544 + 0.0495239i
\(880\) 7.80812 + 19.5030i 0.263212 + 0.657446i
\(881\) −47.4109 −1.59731 −0.798657 0.601786i \(-0.794456\pi\)
−0.798657 + 0.601786i \(0.794456\pi\)
\(882\) −4.20375 + 8.83503i −0.141548 + 0.297491i
\(883\) 8.19295 25.2153i 0.275715 0.848563i −0.713315 0.700844i \(-0.752807\pi\)
0.989029 0.147719i \(-0.0471930\pi\)
\(884\) 2.02061 + 0.429495i 0.0679606 + 0.0144455i
\(885\) 6.63329 9.93768i 0.222976 0.334051i
\(886\) 16.9914 + 7.56506i 0.570837 + 0.254153i
\(887\) −32.0041 + 35.5441i −1.07459 + 1.19345i −0.0943729 + 0.995537i \(0.530085\pi\)
−0.980219 + 0.197918i \(0.936582\pi\)
\(888\) −19.3667 + 12.2324i −0.649903 + 0.410492i
\(889\) 14.0221 6.24306i 0.470288 0.209386i
\(890\) 3.69528 0.123866
\(891\) 29.2941 + 5.73224i 0.981388 + 0.192037i
\(892\) 0.639221 0.0214027
\(893\) −1.90671 + 0.848920i −0.0638055 + 0.0284080i
\(894\) 3.83451 2.42195i 0.128245 0.0810022i
\(895\) 14.1707 15.7382i 0.473675 0.526069i
\(896\) 12.2585 + 5.45786i 0.409529 + 0.182334i
\(897\) −0.324438 + 0.486058i −0.0108327 + 0.0162290i
\(898\) 14.6068 + 3.10477i 0.487435 + 0.103608i
\(899\) −15.5345 + 47.8104i −0.518106 + 1.59457i
\(900\) −8.64734 + 18.1741i −0.288245 + 0.605804i
\(901\) 0.761187 0.0253588
\(902\) 2.72730 10.7932i 0.0908090 0.359373i
\(903\) −2.31064 + 13.4857i −0.0768933 + 0.448776i
\(904\) 4.25749 40.5073i 0.141602 1.34725i
\(905\) −7.34017 + 1.56020i −0.243995 + 0.0518628i
\(906\) 2.90265 0.422279i 0.0964342 0.0140293i
\(907\) −4.96075 47.1984i −0.164719 1.56720i −0.694771 0.719231i \(-0.744494\pi\)
0.530052 0.847965i \(-0.322172\pi\)
\(908\) 24.2817 17.6417i 0.805815 0.585459i
\(909\) −0.155612 + 6.16749i −0.00516133 + 0.204563i
\(910\) 2.46479 7.58583i 0.0817068 0.251468i
\(911\) −25.9741 + 11.5644i −0.860561 + 0.383147i −0.789076 0.614295i \(-0.789440\pi\)
−0.0714850 + 0.997442i \(0.522774\pi\)
\(912\) 21.8138 8.05935i 0.722326 0.266872i
\(913\) 11.7920 + 11.4597i 0.390259 + 0.379259i
\(914\) 3.67381 + 6.36322i 0.121519 + 0.210477i
\(915\) −17.5654 69.0258i −0.580694 2.28192i
\(916\) −14.9702 16.6261i −0.494629 0.549342i
\(917\) 6.46615 + 19.9008i 0.213531 + 0.657181i
\(918\) 0.867251 + 0.371131i 0.0286236 + 0.0122491i
\(919\) −31.0442 + 22.5550i −1.02406 + 0.744020i −0.967110 0.254358i \(-0.918136\pi\)
−0.0569449 + 0.998377i \(0.518136\pi\)
\(920\) −0.532265 0.113136i −0.0175483 0.00373000i
\(921\) −5.10959 + 3.22732i −0.168367 + 0.106344i
\(922\) 1.14887 10.9308i 0.0378361 0.359986i
\(923\) 17.2007 + 29.7924i 0.566167 + 0.980629i
\(924\) 3.46147 + 10.5927i 0.113874 + 0.348475i
\(925\) 12.5692 21.7704i 0.413272 0.715808i
\(926\) 10.6893 + 7.76621i 0.351271 + 0.255214i
\(927\) 3.47132 + 8.35794i 0.114013 + 0.274511i
\(928\) −12.9791 39.9457i −0.426061 1.31128i
\(929\) −1.39939 13.3143i −0.0459126 0.436829i −0.993198 0.116438i \(-0.962852\pi\)
0.947285 0.320391i \(-0.103814\pi\)
\(930\) −8.69102 17.6025i −0.284990 0.577207i
\(931\) −24.0522 + 26.7127i −0.788280 + 0.875473i
\(932\) −5.49160 + 1.16728i −0.179883 + 0.0382354i
\(933\) 13.4492 13.1141i 0.440307 0.429338i
\(934\) −4.60021 + 7.96779i −0.150523 + 0.260714i
\(935\) −1.93528 + 2.46098i −0.0632905 + 0.0804826i
\(936\) 19.0539 16.3050i 0.622795 0.532946i
\(937\) 19.9588 + 14.5010i 0.652027 + 0.473725i 0.863961 0.503559i \(-0.167976\pi\)
−0.211934 + 0.977284i \(0.567976\pi\)
\(938\) −5.25781 5.83939i −0.171674 0.190663i
\(939\) −30.3442 38.4537i −0.990245 1.25489i
\(940\) 1.49874 + 0.667281i 0.0488834 + 0.0217643i
\(941\) 7.58453 + 3.37685i 0.247249 + 0.110082i 0.526620 0.850101i \(-0.323459\pi\)
−0.279371 + 0.960183i \(0.590126\pi\)
\(942\) −6.68725 + 16.7850i −0.217883 + 0.546885i
\(943\) −0.332341 0.369103i −0.0108225 0.0120196i
\(944\) 3.91616 + 2.84526i 0.127460 + 0.0926053i
\(945\) −8.85883 + 15.8718i −0.288178 + 0.516311i
\(946\) 7.23646 + 10.8020i 0.235278 + 0.351202i
\(947\) −18.9748 + 32.8653i −0.616598 + 1.06798i 0.373503 + 0.927629i \(0.378156\pi\)
−0.990102 + 0.140351i \(0.955177\pi\)
\(948\) 6.32493 + 24.8548i 0.205424 + 0.807245i
\(949\) 11.3735 2.41752i 0.369201 0.0784761i
\(950\) 9.91435 11.0110i 0.321664 0.357244i
\(951\) 1.06979 1.60271i 0.0346904 0.0519715i
\(952\) 0.0810019 + 0.770681i 0.00262529 + 0.0249779i
\(953\) −15.0400 46.2884i −0.487194 1.49943i −0.828778 0.559578i \(-0.810963\pi\)
0.341583 0.939852i \(-0.389037\pi\)
\(954\) 2.55336 3.33419i 0.0826682 0.107948i
\(955\) 28.7373 + 20.8789i 0.929918 + 0.675625i
\(956\) −19.3245 + 33.4710i −0.624998 + 1.08253i
\(957\) 22.0516 38.3432i 0.712828 1.23946i
\(958\) 4.73516 + 8.20154i 0.152986 + 0.264980i
\(959\) −1.99617 + 18.9923i −0.0644596 + 0.613292i
\(960\) −4.90429 2.57728i −0.158285 0.0831815i
\(961\) −11.3716 2.41712i −0.366827 0.0779716i
\(962\) −11.5165 + 8.36721i −0.371306 + 0.269770i
\(963\) −26.1216 24.7411i −0.841756 0.797271i
\(964\) −7.80746 24.0289i −0.251461 0.773918i
\(965\) 13.5632 + 15.0634i 0.436614 + 0.484909i
\(966\) −0.0959015 0.0269976i −0.00308558 0.000868635i
\(967\) −5.48901 9.50724i −0.176515 0.305732i 0.764170 0.645015i \(-0.223149\pi\)
−0.940684 + 0.339283i \(0.889816\pi\)
\(968\) 20.5046 + 11.0693i 0.659044 + 0.355781i
\(969\) 2.66559 + 2.21479i 0.0856309 + 0.0711494i
\(970\) −0.140891 + 0.0627287i −0.00452374 + 0.00201410i
\(971\) 4.03687 12.4242i 0.129549 0.398712i −0.865153 0.501508i \(-0.832779\pi\)
0.994702 + 0.102796i \(0.0327789\pi\)
\(972\) −22.6305 + 12.7447i −0.725874 + 0.408787i
\(973\) −11.2108 + 8.14510i −0.359401 + 0.261120i
\(974\) −1.37626 13.0942i −0.0440981 0.419565i
\(975\) −10.1861 + 25.5672i −0.326217 + 0.818805i
\(976\) 28.2257 5.99955i 0.903482 0.192041i
\(977\) 1.15779 11.0156i 0.0370410 0.352421i −0.960266 0.279085i \(-0.909969\pi\)
0.997307 0.0733360i \(-0.0233645\pi\)
\(978\) −5.46694 + 2.01982i −0.174813 + 0.0645869i
\(979\) −5.42247 + 4.52087i −0.173303 + 0.144488i
\(980\) 28.2544 0.902554
\(981\) 6.70270 14.0871i 0.214001 0.449766i
\(982\) −7.79262 + 23.9832i −0.248673 + 0.765336i
\(983\) 25.8539 + 5.49541i 0.824611 + 0.175277i 0.600844 0.799366i \(-0.294831\pi\)
0.223767 + 0.974643i \(0.428165\pi\)
\(984\) 9.43600 + 19.1113i 0.300809 + 0.609247i
\(985\) −56.6706 25.2314i −1.80568 0.803938i
\(986\) 0.935344 1.03880i 0.0297874 0.0330823i
\(987\) 0.585063 + 0.307460i 0.0186228 + 0.00978657i
\(988\) 38.2512 17.0305i 1.21693 0.541814i
\(989\) 0.580083 0.0184456
\(990\) 4.28790 + 16.7322i 0.136278 + 0.531786i
\(991\) −18.9911 −0.603272 −0.301636 0.953423i \(-0.597533\pi\)
−0.301636 + 0.953423i \(0.597533\pi\)
\(992\) 32.5349 14.4855i 1.03298 0.459914i
\(993\) 0.851946 + 21.4229i 0.0270357 + 0.679836i
\(994\) −3.92436 + 4.35845i −0.124473 + 0.138242i
\(995\) −36.4663 16.2359i −1.15606 0.514711i
\(996\) −14.2771 0.928931i −0.452388 0.0294343i
\(997\) −21.6299 4.59758i −0.685027 0.145607i −0.147765 0.989022i \(-0.547208\pi\)
−0.537262 + 0.843416i \(0.680541\pi\)
\(998\) −3.58956 + 11.0475i −0.113625 + 0.349703i
\(999\) 29.4407 13.6235i 0.931463 0.431028i
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 99.2.m.b.70.6 yes 72
3.2 odd 2 297.2.n.b.235.4 72
9.2 odd 6 891.2.f.e.730.6 36
9.4 even 3 inner 99.2.m.b.4.4 72
9.5 odd 6 297.2.n.b.37.6 72
9.7 even 3 891.2.f.f.730.4 36
11.3 even 5 inner 99.2.m.b.25.4 yes 72
11.5 even 5 1089.2.e.p.727.8 36
11.6 odd 10 1089.2.e.o.727.11 36
33.14 odd 10 297.2.n.b.289.6 72
99.14 odd 30 297.2.n.b.91.4 72
99.16 even 15 9801.2.a.cm.1.11 18
99.25 even 15 891.2.f.f.487.4 36
99.38 odd 30 9801.2.a.cp.1.8 18
99.47 odd 30 891.2.f.e.487.6 36
99.49 even 15 1089.2.e.p.364.8 36
99.58 even 15 inner 99.2.m.b.58.6 yes 72
99.61 odd 30 9801.2.a.co.1.8 18
99.83 even 30 9801.2.a.cn.1.11 18
99.94 odd 30 1089.2.e.o.364.11 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
99.2.m.b.4.4 72 9.4 even 3 inner
99.2.m.b.25.4 yes 72 11.3 even 5 inner
99.2.m.b.58.6 yes 72 99.58 even 15 inner
99.2.m.b.70.6 yes 72 1.1 even 1 trivial
297.2.n.b.37.6 72 9.5 odd 6
297.2.n.b.91.4 72 99.14 odd 30
297.2.n.b.235.4 72 3.2 odd 2
297.2.n.b.289.6 72 33.14 odd 10
891.2.f.e.487.6 36 99.47 odd 30
891.2.f.e.730.6 36 9.2 odd 6
891.2.f.f.487.4 36 99.25 even 15
891.2.f.f.730.4 36 9.7 even 3
1089.2.e.o.364.11 36 99.94 odd 30
1089.2.e.o.727.11 36 11.6 odd 10
1089.2.e.p.364.8 36 99.49 even 15
1089.2.e.p.727.8 36 11.5 even 5
9801.2.a.cm.1.11 18 99.16 even 15
9801.2.a.cn.1.11 18 99.83 even 30
9801.2.a.co.1.8 18 99.61 odd 30
9801.2.a.cp.1.8 18 99.38 odd 30