Properties

Label 243.2.e.a.190.2
Level $243$
Weight $2$
Character 243.190
Analytic conductor $1.940$
Analytic rank $0$
Dimension $12$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [243,2,Mod(28,243)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(243, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("243.28");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 243 = 3^{5} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 243.e (of order \(9\), degree \(6\), not 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: \(1.94036476912\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(2\) over \(\Q(\zeta_{9})\)
Coefficient field: 12.0.1952986685049.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} + \cdots + 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 27)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 190.2
Root \(0.500000 + 1.68614i\) of defining polynomial
Character \(\chi\) \(=\) 243.190
Dual form 243.2.e.a.55.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.990741 + 0.360600i) q^{2} +(-0.680553 - 0.571052i) q^{4} +(0.303153 - 1.71926i) q^{5} +(1.88389 - 1.58077i) q^{7} +(-1.52266 - 2.63732i) q^{8} +O(q^{10})\) \(q+(0.990741 + 0.360600i) q^{2} +(-0.680553 - 0.571052i) q^{4} +(0.303153 - 1.71926i) q^{5} +(1.88389 - 1.58077i) q^{7} +(-1.52266 - 2.63732i) q^{8} +(0.920313 - 1.59403i) q^{10} +(0.217792 + 1.23516i) q^{11} +(4.27469 - 1.55586i) q^{13} +(2.43648 - 0.886805i) q^{14} +(-0.249003 - 1.41216i) q^{16} +(-3.32358 + 5.75662i) q^{17} +(-0.124578 - 0.215776i) q^{19} +(-1.18810 + 0.996935i) q^{20} +(-0.229623 + 1.30226i) q^{22} +(-0.645010 - 0.541228i) q^{23} +(1.83449 + 0.667701i) q^{25} +4.79615 q^{26} -2.18479 q^{28} +(-0.481483 - 0.175245i) q^{29} +(-0.628159 - 0.527088i) q^{31} +(-0.795096 + 4.50921i) q^{32} +(-5.36865 + 4.50483i) q^{34} +(-2.14666 - 3.71812i) q^{35} +(-1.30403 + 2.25865i) q^{37} +(-0.0456159 - 0.258701i) q^{38} +(-4.99584 + 1.81834i) q^{40} +(-7.66114 + 2.78843i) q^{41} +(0.751401 + 4.26141i) q^{43} +(0.557121 - 0.964962i) q^{44} +(-0.443871 - 0.768808i) q^{46} +(4.06182 - 3.40828i) q^{47} +(-0.165332 + 0.937642i) q^{49} +(1.57674 + 1.32304i) q^{50} +(-3.79763 - 1.38222i) q^{52} +10.4841 q^{53} +2.18959 q^{55} +(-7.03752 - 2.56145i) q^{56} +(-0.413831 - 0.347246i) q^{58} +(0.522022 - 2.96053i) q^{59} +(2.20864 - 1.85327i) q^{61} +(-0.432275 - 0.748722i) q^{62} +(-3.84771 + 6.66442i) q^{64} +(-1.37905 - 7.82099i) q^{65} +(-9.47799 + 3.44971i) q^{67} +(5.54920 - 2.01975i) q^{68} +(-0.786028 - 4.45779i) q^{70} +(0.0447378 - 0.0774882i) q^{71} +(2.66057 + 4.60824i) q^{73} +(-2.10643 + 1.76750i) q^{74} +(-0.0384370 + 0.217987i) q^{76} +(2.36280 + 1.98263i) q^{77} +(-4.48884 - 1.63380i) q^{79} -2.50337 q^{80} -8.59571 q^{82} +(7.55575 + 2.75007i) q^{83} +(8.88960 + 7.45926i) q^{85} +(-0.792220 + 4.49291i) q^{86} +(2.92588 - 2.45511i) q^{88} +(3.35189 + 5.80564i) q^{89} +(5.59359 - 9.68839i) q^{91} +(0.129895 + 0.736669i) q^{92} +(5.25324 - 1.91202i) q^{94} +(-0.408742 + 0.148770i) q^{95} +(0.953429 + 5.40716i) q^{97} +(-0.501915 + 0.869342i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 3 q^{2} + 3 q^{4} - 6 q^{5} + 3 q^{7} - 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 3 q^{2} + 3 q^{4} - 6 q^{5} + 3 q^{7} - 6 q^{8} - 3 q^{10} + 6 q^{11} + 3 q^{13} + 21 q^{14} + 9 q^{16} - 9 q^{17} - 3 q^{19} - 24 q^{20} + 12 q^{22} + 12 q^{23} + 12 q^{25} + 30 q^{26} - 12 q^{28} + 24 q^{29} + 12 q^{31} - 27 q^{32} - 12 q^{35} - 3 q^{37} + 30 q^{38} - 15 q^{40} - 6 q^{41} - 15 q^{43} - 3 q^{44} - 3 q^{46} - 12 q^{47} - 33 q^{49} - 21 q^{50} - 45 q^{52} + 18 q^{53} - 12 q^{55} - 30 q^{56} - 51 q^{58} + 3 q^{59} - 33 q^{61} + 12 q^{62} + 12 q^{64} - 21 q^{65} - 6 q^{67} - 9 q^{68} - 15 q^{70} - 27 q^{71} + 6 q^{73} + 21 q^{74} + 6 q^{76} + 12 q^{77} + 21 q^{79} - 42 q^{80} - 12 q^{82} + 6 q^{83} + 36 q^{85} + 21 q^{86} + 42 q^{88} - 9 q^{89} + 6 q^{91} + 3 q^{92} + 48 q^{94} - 3 q^{95} + 39 q^{97} + 45 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/243\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.990741 + 0.360600i 0.700560 + 0.254983i 0.667650 0.744475i \(-0.267300\pi\)
0.0329100 + 0.999458i \(0.489523\pi\)
\(3\) 0 0
\(4\) −0.680553 0.571052i −0.340277 0.285526i
\(5\) 0.303153 1.71926i 0.135574 0.768879i −0.838884 0.544310i \(-0.816792\pi\)
0.974458 0.224569i \(-0.0720973\pi\)
\(6\) 0 0
\(7\) 1.88389 1.58077i 0.712044 0.597476i −0.213128 0.977024i \(-0.568365\pi\)
0.925172 + 0.379548i \(0.123921\pi\)
\(8\) −1.52266 2.63732i −0.538340 0.932432i
\(9\) 0 0
\(10\) 0.920313 1.59403i 0.291029 0.504076i
\(11\) 0.217792 + 1.23516i 0.0656667 + 0.372414i 0.999877 + 0.0156913i \(0.00499490\pi\)
−0.934210 + 0.356723i \(0.883894\pi\)
\(12\) 0 0
\(13\) 4.27469 1.55586i 1.18559 0.431518i 0.327414 0.944881i \(-0.393823\pi\)
0.858171 + 0.513363i \(0.171601\pi\)
\(14\) 2.43648 0.886805i 0.651176 0.237009i
\(15\) 0 0
\(16\) −0.249003 1.41216i −0.0622506 0.353041i
\(17\) −3.32358 + 5.75662i −0.806088 + 1.39618i 0.109467 + 0.993990i \(0.465086\pi\)
−0.915554 + 0.402194i \(0.868248\pi\)
\(18\) 0 0
\(19\) −0.124578 0.215776i −0.0285802 0.0495023i 0.851382 0.524547i \(-0.175765\pi\)
−0.879962 + 0.475045i \(0.842432\pi\)
\(20\) −1.18810 + 0.996935i −0.265667 + 0.222921i
\(21\) 0 0
\(22\) −0.229623 + 1.30226i −0.0489559 + 0.277642i
\(23\) −0.645010 0.541228i −0.134494 0.112854i 0.573059 0.819514i \(-0.305757\pi\)
−0.707553 + 0.706660i \(0.750201\pi\)
\(24\) 0 0
\(25\) 1.83449 + 0.667701i 0.366899 + 0.133540i
\(26\) 4.79615 0.940603
\(27\) 0 0
\(28\) −2.18479 −0.412887
\(29\) −0.481483 0.175245i −0.0894091 0.0325422i 0.296928 0.954900i \(-0.404038\pi\)
−0.386337 + 0.922358i \(0.626260\pi\)
\(30\) 0 0
\(31\) −0.628159 0.527088i −0.112821 0.0946678i 0.584632 0.811299i \(-0.301239\pi\)
−0.697453 + 0.716631i \(0.745683\pi\)
\(32\) −0.795096 + 4.50921i −0.140554 + 0.797124i
\(33\) 0 0
\(34\) −5.36865 + 4.50483i −0.920716 + 0.772572i
\(35\) −2.14666 3.71812i −0.362852 0.628478i
\(36\) 0 0
\(37\) −1.30403 + 2.25865i −0.214381 + 0.371319i −0.953081 0.302715i \(-0.902107\pi\)
0.738700 + 0.674035i \(0.235440\pi\)
\(38\) −0.0456159 0.258701i −0.00739988 0.0419668i
\(39\) 0 0
\(40\) −4.99584 + 1.81834i −0.789912 + 0.287504i
\(41\) −7.66114 + 2.78843i −1.19647 + 0.435479i −0.861991 0.506924i \(-0.830782\pi\)
−0.334478 + 0.942403i \(0.608560\pi\)
\(42\) 0 0
\(43\) 0.751401 + 4.26141i 0.114588 + 0.649858i 0.986954 + 0.161005i \(0.0514735\pi\)
−0.872366 + 0.488853i \(0.837415\pi\)
\(44\) 0.557121 0.964962i 0.0839891 0.145473i
\(45\) 0 0
\(46\) −0.443871 0.768808i −0.0654452 0.113354i
\(47\) 4.06182 3.40828i 0.592478 0.497148i −0.296540 0.955020i \(-0.595833\pi\)
0.889018 + 0.457872i \(0.151388\pi\)
\(48\) 0 0
\(49\) −0.165332 + 0.937642i −0.0236188 + 0.133949i
\(50\) 1.57674 + 1.32304i 0.222984 + 0.187106i
\(51\) 0 0
\(52\) −3.79763 1.38222i −0.526637 0.191680i
\(53\) 10.4841 1.44010 0.720052 0.693920i \(-0.244118\pi\)
0.720052 + 0.693920i \(0.244118\pi\)
\(54\) 0 0
\(55\) 2.18959 0.295244
\(56\) −7.03752 2.56145i −0.940428 0.342288i
\(57\) 0 0
\(58\) −0.413831 0.347246i −0.0543387 0.0455956i
\(59\) 0.522022 2.96053i 0.0679614 0.385428i −0.931787 0.363005i \(-0.881751\pi\)
0.999749 0.0224233i \(-0.00713815\pi\)
\(60\) 0 0
\(61\) 2.20864 1.85327i 0.282787 0.237287i −0.490350 0.871526i \(-0.663131\pi\)
0.773137 + 0.634239i \(0.218687\pi\)
\(62\) −0.432275 0.748722i −0.0548990 0.0950878i
\(63\) 0 0
\(64\) −3.84771 + 6.66442i −0.480963 + 0.833053i
\(65\) −1.37905 7.82099i −0.171050 0.970074i
\(66\) 0 0
\(67\) −9.47799 + 3.44971i −1.15792 + 0.421449i −0.848354 0.529429i \(-0.822406\pi\)
−0.309566 + 0.950878i \(0.600184\pi\)
\(68\) 5.54920 2.01975i 0.672940 0.244930i
\(69\) 0 0
\(70\) −0.786028 4.45779i −0.0939483 0.532807i
\(71\) 0.0447378 0.0774882i 0.00530940 0.00919615i −0.863358 0.504591i \(-0.831643\pi\)
0.868668 + 0.495395i \(0.164977\pi\)
\(72\) 0 0
\(73\) 2.66057 + 4.60824i 0.311396 + 0.539354i 0.978665 0.205463i \(-0.0658701\pi\)
−0.667269 + 0.744817i \(0.732537\pi\)
\(74\) −2.10643 + 1.76750i −0.244867 + 0.205468i
\(75\) 0 0
\(76\) −0.0384370 + 0.217987i −0.00440903 + 0.0250049i
\(77\) 2.36280 + 1.98263i 0.269266 + 0.225941i
\(78\) 0 0
\(79\) −4.48884 1.63380i −0.505034 0.183817i 0.0769231 0.997037i \(-0.475490\pi\)
−0.581957 + 0.813220i \(0.697713\pi\)
\(80\) −2.50337 −0.279885
\(81\) 0 0
\(82\) −8.59571 −0.949238
\(83\) 7.55575 + 2.75007i 0.829351 + 0.301859i 0.721593 0.692318i \(-0.243410\pi\)
0.107759 + 0.994177i \(0.465633\pi\)
\(84\) 0 0
\(85\) 8.88960 + 7.45926i 0.964212 + 0.809070i
\(86\) −0.792220 + 4.49291i −0.0854273 + 0.484482i
\(87\) 0 0
\(88\) 2.92588 2.45511i 0.311900 0.261715i
\(89\) 3.35189 + 5.80564i 0.355299 + 0.615396i 0.987169 0.159678i \(-0.0510457\pi\)
−0.631870 + 0.775074i \(0.717712\pi\)
\(90\) 0 0
\(91\) 5.59359 9.68839i 0.586368 1.01562i
\(92\) 0.129895 + 0.736669i 0.0135424 + 0.0768030i
\(93\) 0 0
\(94\) 5.25324 1.91202i 0.541831 0.197210i
\(95\) −0.408742 + 0.148770i −0.0419360 + 0.0152635i
\(96\) 0 0
\(97\) 0.953429 + 5.40716i 0.0968060 + 0.549014i 0.994179 + 0.107741i \(0.0343618\pi\)
−0.897373 + 0.441273i \(0.854527\pi\)
\(98\) −0.501915 + 0.869342i −0.0507010 + 0.0878168i
\(99\) 0 0
\(100\) −0.867179 1.50200i −0.0867179 0.150200i
\(101\) −3.83441 + 3.21745i −0.381538 + 0.320148i −0.813306 0.581836i \(-0.802334\pi\)
0.431768 + 0.901985i \(0.357890\pi\)
\(102\) 0 0
\(103\) 2.01765 11.4426i 0.198805 1.12748i −0.708091 0.706121i \(-0.750443\pi\)
0.906896 0.421356i \(-0.138446\pi\)
\(104\) −10.6122 8.90467i −1.04061 0.873175i
\(105\) 0 0
\(106\) 10.3870 + 3.78057i 1.00888 + 0.367202i
\(107\) −19.4581 −1.88109 −0.940544 0.339673i \(-0.889684\pi\)
−0.940544 + 0.339673i \(0.889684\pi\)
\(108\) 0 0
\(109\) 6.31515 0.604881 0.302441 0.953168i \(-0.402199\pi\)
0.302441 + 0.953168i \(0.402199\pi\)
\(110\) 2.16932 + 0.789566i 0.206836 + 0.0752822i
\(111\) 0 0
\(112\) −2.70140 2.26675i −0.255259 0.214188i
\(113\) 1.20090 6.81066i 0.112971 0.640693i −0.874763 0.484551i \(-0.838983\pi\)
0.987735 0.156142i \(-0.0499058\pi\)
\(114\) 0 0
\(115\) −1.12605 + 0.944868i −0.105005 + 0.0881094i
\(116\) 0.227600 + 0.394215i 0.0211322 + 0.0366020i
\(117\) 0 0
\(118\) 1.58476 2.74488i 0.145889 0.252687i
\(119\) 2.83863 + 16.0987i 0.260217 + 1.47576i
\(120\) 0 0
\(121\) 8.85844 3.22421i 0.805312 0.293110i
\(122\) 2.85648 1.03967i 0.258613 0.0941276i
\(123\) 0 0
\(124\) 0.126501 + 0.717423i 0.0113601 + 0.0644265i
\(125\) 6.06855 10.5110i 0.542788 0.940136i
\(126\) 0 0
\(127\) −6.01162 10.4124i −0.533445 0.923954i −0.999237 0.0390598i \(-0.987564\pi\)
0.465792 0.884894i \(-0.345770\pi\)
\(128\) 0.799814 0.671124i 0.0706943 0.0593195i
\(129\) 0 0
\(130\) 1.45397 8.24586i 0.127521 0.723210i
\(131\) 10.7896 + 9.05353i 0.942690 + 0.791011i 0.978051 0.208364i \(-0.0668138\pi\)
−0.0353614 + 0.999375i \(0.511258\pi\)
\(132\) 0 0
\(133\) −0.575784 0.209568i −0.0499268 0.0181719i
\(134\) −10.6342 −0.918655
\(135\) 0 0
\(136\) 20.2427 1.73580
\(137\) 2.12196 + 0.772329i 0.181291 + 0.0659846i 0.431071 0.902318i \(-0.358136\pi\)
−0.249780 + 0.968303i \(0.580358\pi\)
\(138\) 0 0
\(139\) −6.10928 5.12629i −0.518182 0.434806i 0.345815 0.938303i \(-0.387602\pi\)
−0.863997 + 0.503496i \(0.832047\pi\)
\(140\) −0.662326 + 3.75624i −0.0559768 + 0.317460i
\(141\) 0 0
\(142\) 0.0722659 0.0606383i 0.00606442 0.00508865i
\(143\) 2.85273 + 4.94107i 0.238557 + 0.413193i
\(144\) 0 0
\(145\) −0.447256 + 0.774670i −0.0371426 + 0.0643328i
\(146\) 0.974203 + 5.52498i 0.0806256 + 0.457250i
\(147\) 0 0
\(148\) 2.17727 0.792461i 0.178970 0.0651399i
\(149\) −0.100489 + 0.0365751i −0.00823240 + 0.00299635i −0.346133 0.938185i \(-0.612505\pi\)
0.337901 + 0.941182i \(0.390283\pi\)
\(150\) 0 0
\(151\) −3.51801 19.9516i −0.286292 1.62364i −0.700635 0.713520i \(-0.747100\pi\)
0.414344 0.910121i \(-0.364011\pi\)
\(152\) −0.379379 + 0.657104i −0.0307717 + 0.0532982i
\(153\) 0 0
\(154\) 1.62599 + 2.81630i 0.131026 + 0.226944i
\(155\) −1.09663 + 0.920184i −0.0880836 + 0.0739109i
\(156\) 0 0
\(157\) −3.60317 + 20.4346i −0.287564 + 1.63086i 0.408415 + 0.912797i \(0.366082\pi\)
−0.695979 + 0.718062i \(0.745029\pi\)
\(158\) −3.85813 3.23735i −0.306936 0.257550i
\(159\) 0 0
\(160\) 7.51149 + 2.73396i 0.593836 + 0.216139i
\(161\) −2.07069 −0.163193
\(162\) 0 0
\(163\) −20.1346 −1.57706 −0.788531 0.614995i \(-0.789158\pi\)
−0.788531 + 0.614995i \(0.789158\pi\)
\(164\) 6.80615 + 2.47724i 0.531471 + 0.193440i
\(165\) 0 0
\(166\) 6.49412 + 5.44921i 0.504041 + 0.422941i
\(167\) 3.44910 19.5608i 0.266900 1.51366i −0.496671 0.867939i \(-0.665444\pi\)
0.763570 0.645724i \(-0.223445\pi\)
\(168\) 0 0
\(169\) 5.89369 4.94540i 0.453361 0.380415i
\(170\) 6.11748 + 10.5958i 0.469189 + 0.812660i
\(171\) 0 0
\(172\) 1.92212 3.32920i 0.146560 0.253849i
\(173\) −3.28631 18.6376i −0.249854 1.41699i −0.808945 0.587884i \(-0.799961\pi\)
0.559091 0.829106i \(-0.311150\pi\)
\(174\) 0 0
\(175\) 4.51147 1.64204i 0.341035 0.124127i
\(176\) 1.69002 0.615115i 0.127390 0.0463661i
\(177\) 0 0
\(178\) 1.22734 + 6.96057i 0.0919928 + 0.521717i
\(179\) 5.45683 9.45151i 0.407863 0.706439i −0.586787 0.809741i \(-0.699608\pi\)
0.994650 + 0.103302i \(0.0329409\pi\)
\(180\) 0 0
\(181\) 8.97393 + 15.5433i 0.667027 + 1.15532i 0.978731 + 0.205146i \(0.0657668\pi\)
−0.311704 + 0.950179i \(0.600900\pi\)
\(182\) 9.03544 7.58163i 0.669751 0.561988i
\(183\) 0 0
\(184\) −0.445261 + 2.52520i −0.0328251 + 0.186160i
\(185\) 3.48789 + 2.92669i 0.256435 + 0.215174i
\(186\) 0 0
\(187\) −7.83419 2.85141i −0.572892 0.208516i
\(188\) −4.71059 −0.343555
\(189\) 0 0
\(190\) −0.458604 −0.0332706
\(191\) −25.3398 9.22293i −1.83352 0.667348i −0.991858 0.127350i \(-0.959353\pi\)
−0.841666 0.539998i \(-0.818425\pi\)
\(192\) 0 0
\(193\) −13.1413 11.0269i −0.945935 0.793734i 0.0326735 0.999466i \(-0.489598\pi\)
−0.978608 + 0.205733i \(0.934042\pi\)
\(194\) −1.00522 + 5.70091i −0.0721709 + 0.409301i
\(195\) 0 0
\(196\) 0.647959 0.543702i 0.0462828 0.0388359i
\(197\) 1.25612 + 2.17567i 0.0894951 + 0.155010i 0.907298 0.420489i \(-0.138141\pi\)
−0.817803 + 0.575499i \(0.804808\pi\)
\(198\) 0 0
\(199\) −9.26942 + 16.0551i −0.657092 + 1.13812i 0.324273 + 0.945964i \(0.394880\pi\)
−0.981365 + 0.192153i \(0.938453\pi\)
\(200\) −1.03236 5.85482i −0.0729991 0.413998i
\(201\) 0 0
\(202\) −4.95912 + 1.80497i −0.348922 + 0.126997i
\(203\) −1.18408 + 0.430971i −0.0831064 + 0.0302483i
\(204\) 0 0
\(205\) 2.47155 + 14.0168i 0.172620 + 0.978979i
\(206\) 6.12519 10.6091i 0.426762 0.739173i
\(207\) 0 0
\(208\) −3.26154 5.64915i −0.226147 0.391698i
\(209\) 0.239385 0.200868i 0.0165586 0.0138943i
\(210\) 0 0
\(211\) −0.640967 + 3.63510i −0.0441260 + 0.250251i −0.998889 0.0471155i \(-0.984997\pi\)
0.954763 + 0.297366i \(0.0961082\pi\)
\(212\) −7.13500 5.98697i −0.490034 0.411187i
\(213\) 0 0
\(214\) −19.2780 7.01660i −1.31781 0.479645i
\(215\) 7.55427 0.515197
\(216\) 0 0
\(217\) −2.01659 −0.136895
\(218\) 6.25668 + 2.27724i 0.423756 + 0.154234i
\(219\) 0 0
\(220\) −1.49013 1.25037i −0.100465 0.0842999i
\(221\) −5.25080 + 29.7788i −0.353207 + 2.00314i
\(222\) 0 0
\(223\) −16.2716 + 13.6535i −1.08963 + 0.914305i −0.996684 0.0813669i \(-0.974071\pi\)
−0.0929417 + 0.995672i \(0.529627\pi\)
\(224\) 5.63017 + 9.75174i 0.376181 + 0.651565i
\(225\) 0 0
\(226\) 3.64571 6.31456i 0.242509 0.420038i
\(227\) 2.49012 + 14.1222i 0.165275 + 0.937323i 0.948780 + 0.315937i \(0.102319\pi\)
−0.783505 + 0.621386i \(0.786570\pi\)
\(228\) 0 0
\(229\) −15.8675 + 5.77529i −1.04855 + 0.381642i −0.808116 0.589023i \(-0.799513\pi\)
−0.240436 + 0.970665i \(0.577290\pi\)
\(230\) −1.45634 + 0.530066i −0.0960285 + 0.0349515i
\(231\) 0 0
\(232\) 0.270955 + 1.53666i 0.0177890 + 0.100887i
\(233\) 2.79972 4.84926i 0.183416 0.317686i −0.759626 0.650361i \(-0.774618\pi\)
0.943042 + 0.332675i \(0.107951\pi\)
\(234\) 0 0
\(235\) −4.62837 8.01658i −0.301922 0.522944i
\(236\) −2.04588 + 1.71670i −0.133176 + 0.111748i
\(237\) 0 0
\(238\) −2.99284 + 16.9732i −0.193997 + 1.10021i
\(239\) 4.04033 + 3.39024i 0.261347 + 0.219296i 0.764040 0.645169i \(-0.223213\pi\)
−0.502693 + 0.864465i \(0.667657\pi\)
\(240\) 0 0
\(241\) 8.36559 + 3.04483i 0.538875 + 0.196135i 0.597097 0.802169i \(-0.296321\pi\)
−0.0582216 + 0.998304i \(0.518543\pi\)
\(242\) 9.93907 0.638907
\(243\) 0 0
\(244\) −2.56141 −0.163977
\(245\) 1.56193 + 0.568497i 0.0997883 + 0.0363200i
\(246\) 0 0
\(247\) −0.868249 0.728548i −0.0552454 0.0463564i
\(248\) −0.433628 + 2.45923i −0.0275354 + 0.156161i
\(249\) 0 0
\(250\) 9.80265 8.22540i 0.619974 0.520220i
\(251\) −3.89010 6.73786i −0.245541 0.425290i 0.716742 0.697338i \(-0.245632\pi\)
−0.962284 + 0.272048i \(0.912299\pi\)
\(252\) 0 0
\(253\) 0.528024 0.914565i 0.0331966 0.0574982i
\(254\) −2.20123 12.4838i −0.138118 0.783305i
\(255\) 0 0
\(256\) 15.4971 5.64047i 0.968566 0.352529i
\(257\) −19.2041 + 6.98971i −1.19792 + 0.436006i −0.862497 0.506062i \(-0.831101\pi\)
−0.335420 + 0.942069i \(0.608878\pi\)
\(258\) 0 0
\(259\) 1.11376 + 6.31643i 0.0692054 + 0.392484i
\(260\) −3.52767 + 6.11011i −0.218777 + 0.378933i
\(261\) 0 0
\(262\) 7.42498 + 12.8604i 0.458717 + 0.794520i
\(263\) −8.64084 + 7.25052i −0.532817 + 0.447086i −0.869073 0.494684i \(-0.835284\pi\)
0.336256 + 0.941771i \(0.390839\pi\)
\(264\) 0 0
\(265\) 3.17829 18.0250i 0.195241 1.10726i
\(266\) −0.494883 0.415256i −0.0303432 0.0254610i
\(267\) 0 0
\(268\) 8.42024 + 3.06472i 0.514348 + 0.187207i
\(269\) 0.307761 0.0187645 0.00938226 0.999956i \(-0.497013\pi\)
0.00938226 + 0.999956i \(0.497013\pi\)
\(270\) 0 0
\(271\) −2.22251 −0.135008 −0.0675040 0.997719i \(-0.521504\pi\)
−0.0675040 + 0.997719i \(0.521504\pi\)
\(272\) 8.95687 + 3.26003i 0.543090 + 0.197669i
\(273\) 0 0
\(274\) 1.82381 + 1.53036i 0.110180 + 0.0924523i
\(275\) −0.425179 + 2.41131i −0.0256393 + 0.145408i
\(276\) 0 0
\(277\) −17.8716 + 14.9961i −1.07380 + 0.901026i −0.995391 0.0958953i \(-0.969429\pi\)
−0.0784094 + 0.996921i \(0.524984\pi\)
\(278\) −4.20417 7.28184i −0.252149 0.436735i
\(279\) 0 0
\(280\) −6.53725 + 11.3228i −0.390675 + 0.676670i
\(281\) −1.25469 7.11568i −0.0748484 0.424486i −0.999089 0.0426756i \(-0.986412\pi\)
0.924241 0.381811i \(-0.124699\pi\)
\(282\) 0 0
\(283\) −6.69088 + 2.43528i −0.397732 + 0.144763i −0.533139 0.846027i \(-0.678988\pi\)
0.135408 + 0.990790i \(0.456766\pi\)
\(284\) −0.0746962 + 0.0271872i −0.00443241 + 0.00161326i
\(285\) 0 0
\(286\) 1.04456 + 5.92401i 0.0617663 + 0.350294i
\(287\) −10.0249 + 17.3636i −0.591751 + 1.02494i
\(288\) 0 0
\(289\) −13.5924 23.5428i −0.799555 1.38487i
\(290\) −0.722461 + 0.606217i −0.0424244 + 0.0355983i
\(291\) 0 0
\(292\) 0.820886 4.65548i 0.0480387 0.272441i
\(293\) −0.423228 0.355131i −0.0247253 0.0207469i 0.630341 0.776318i \(-0.282915\pi\)
−0.655067 + 0.755571i \(0.727359\pi\)
\(294\) 0 0
\(295\) −4.93169 1.79499i −0.287134 0.104508i
\(296\) 7.94236 0.461640
\(297\) 0 0
\(298\) −0.112748 −0.00653131
\(299\) −3.59929 1.31004i −0.208152 0.0757613i
\(300\) 0 0
\(301\) 8.15187 + 6.84023i 0.469866 + 0.394265i
\(302\) 3.70913 21.0355i 0.213436 1.21046i
\(303\) 0 0
\(304\) −0.273690 + 0.229653i −0.0156972 + 0.0131715i
\(305\) −2.51670 4.35906i −0.144106 0.249599i
\(306\) 0 0
\(307\) −3.36438 + 5.82728i −0.192015 + 0.332580i −0.945918 0.324406i \(-0.894836\pi\)
0.753903 + 0.656986i \(0.228169\pi\)
\(308\) −0.475830 2.69857i −0.0271129 0.153765i
\(309\) 0 0
\(310\) −1.41830 + 0.516218i −0.0805539 + 0.0293192i
\(311\) 14.4933 5.27513i 0.821840 0.299125i 0.103335 0.994647i \(-0.467049\pi\)
0.718505 + 0.695521i \(0.244827\pi\)
\(312\) 0 0
\(313\) −4.09130 23.2029i −0.231254 1.31151i −0.850361 0.526200i \(-0.823616\pi\)
0.619107 0.785307i \(-0.287495\pi\)
\(314\) −10.9385 + 18.9461i −0.617297 + 1.06919i
\(315\) 0 0
\(316\) 2.12191 + 3.67525i 0.119367 + 0.206749i
\(317\) −5.55539 + 4.66152i −0.312022 + 0.261817i −0.785327 0.619081i \(-0.787505\pi\)
0.473305 + 0.880898i \(0.343061\pi\)
\(318\) 0 0
\(319\) 0.111593 0.632874i 0.00624800 0.0354342i
\(320\) 10.2915 + 8.63556i 0.575310 + 0.482743i
\(321\) 0 0
\(322\) −2.05152 0.746691i −0.114327 0.0416115i
\(323\) 1.65618 0.0921525
\(324\) 0 0
\(325\) 8.88074 0.492615
\(326\) −19.9482 7.26054i −1.10483 0.402124i
\(327\) 0 0
\(328\) 19.0192 + 15.9590i 1.05016 + 0.881190i
\(329\) 2.26433 12.8416i 0.124836 0.707983i
\(330\) 0 0
\(331\) 22.2417 18.6630i 1.22251 1.02581i 0.223825 0.974629i \(-0.428146\pi\)
0.998689 0.0511815i \(-0.0162987\pi\)
\(332\) −3.57166 6.18629i −0.196020 0.339517i
\(333\) 0 0
\(334\) 10.4708 18.1360i 0.572938 0.992357i
\(335\) 3.05768 + 17.3410i 0.167059 + 0.947438i
\(336\) 0 0
\(337\) 1.08919 0.396434i 0.0593321 0.0215951i −0.312184 0.950022i \(-0.601060\pi\)
0.371516 + 0.928427i \(0.378838\pi\)
\(338\) 7.62244 2.77434i 0.414606 0.150904i
\(339\) 0 0
\(340\) −1.79022 10.1528i −0.0970883 0.550615i
\(341\) 0.514230 0.890672i 0.0278471 0.0482326i
\(342\) 0 0
\(343\) 9.77810 + 16.9362i 0.527968 + 0.914467i
\(344\) 10.0946 8.47033i 0.544262 0.456690i
\(345\) 0 0
\(346\) 3.46484 19.6501i 0.186271 1.05640i
\(347\) −4.51178 3.78583i −0.242205 0.203234i 0.513602 0.858029i \(-0.328311\pi\)
−0.755807 + 0.654794i \(0.772755\pi\)
\(348\) 0 0
\(349\) 28.7477 + 10.4633i 1.53883 + 0.560089i 0.965764 0.259421i \(-0.0835316\pi\)
0.573066 + 0.819509i \(0.305754\pi\)
\(350\) 5.06182 0.270566
\(351\) 0 0
\(352\) −5.74276 −0.306090
\(353\) 34.7322 + 12.6415i 1.84861 + 0.672839i 0.985947 + 0.167061i \(0.0534278\pi\)
0.862664 + 0.505778i \(0.168794\pi\)
\(354\) 0 0
\(355\) −0.119660 0.100407i −0.00635091 0.00532904i
\(356\) 1.03418 5.86514i 0.0548116 0.310852i
\(357\) 0 0
\(358\) 8.81452 7.39626i 0.465862 0.390905i
\(359\) −13.1880 22.8423i −0.696037 1.20557i −0.969830 0.243783i \(-0.921611\pi\)
0.273792 0.961789i \(-0.411722\pi\)
\(360\) 0 0
\(361\) 9.46896 16.4007i 0.498366 0.863196i
\(362\) 3.28592 + 18.6354i 0.172704 + 0.979455i
\(363\) 0 0
\(364\) −9.33931 + 3.39923i −0.489513 + 0.178168i
\(365\) 8.72935 3.17722i 0.456915 0.166303i
\(366\) 0 0
\(367\) −1.96450 11.1413i −0.102546 0.581569i −0.992172 0.124879i \(-0.960146\pi\)
0.889626 0.456690i \(-0.150965\pi\)
\(368\) −0.603693 + 1.04563i −0.0314697 + 0.0545071i
\(369\) 0 0
\(370\) 2.40023 + 4.15733i 0.124782 + 0.216129i
\(371\) 19.7509 16.5730i 1.02542 0.860428i
\(372\) 0 0
\(373\) 1.01481 5.75529i 0.0525451 0.297998i −0.947198 0.320648i \(-0.896099\pi\)
0.999743 + 0.0226503i \(0.00721043\pi\)
\(374\) −6.73343 5.65002i −0.348177 0.292156i
\(375\) 0 0
\(376\) −15.1735 5.52269i −0.782511 0.284811i
\(377\) −2.33085 −0.120045
\(378\) 0 0
\(379\) 24.3265 1.24957 0.624783 0.780798i \(-0.285187\pi\)
0.624783 + 0.780798i \(0.285187\pi\)
\(380\) 0.363126 + 0.132167i 0.0186280 + 0.00678002i
\(381\) 0 0
\(382\) −21.7794 18.2751i −1.11433 0.935035i
\(383\) 0.662650 3.75808i 0.0338598 0.192029i −0.963186 0.268835i \(-0.913361\pi\)
0.997046 + 0.0768065i \(0.0244724\pi\)
\(384\) 0 0
\(385\) 4.12495 3.46124i 0.210227 0.176401i
\(386\) −9.04337 15.6636i −0.460295 0.797255i
\(387\) 0 0
\(388\) 2.43891 4.22432i 0.123817 0.214457i
\(389\) −1.88267 10.6771i −0.0954550 0.541352i −0.994607 0.103716i \(-0.966927\pi\)
0.899152 0.437637i \(-0.144184\pi\)
\(390\) 0 0
\(391\) 5.25939 1.91426i 0.265979 0.0968083i
\(392\) 2.72460 0.991674i 0.137613 0.0500871i
\(393\) 0 0
\(394\) 0.459946 + 2.60848i 0.0231718 + 0.131414i
\(395\) −4.16974 + 7.22221i −0.209802 + 0.363389i
\(396\) 0 0
\(397\) 5.25461 + 9.10124i 0.263721 + 0.456778i 0.967228 0.253910i \(-0.0817168\pi\)
−0.703507 + 0.710689i \(0.748383\pi\)
\(398\) −14.9731 + 12.5639i −0.750533 + 0.629772i
\(399\) 0 0
\(400\) 0.486110 2.75687i 0.0243055 0.137843i
\(401\) −11.0047 9.23401i −0.549547 0.461125i 0.325241 0.945631i \(-0.394555\pi\)
−0.874788 + 0.484507i \(0.838999\pi\)
\(402\) 0 0
\(403\) −3.50526 1.27581i −0.174609 0.0635527i
\(404\) 4.44685 0.221239
\(405\) 0 0
\(406\) −1.32853 −0.0659338
\(407\) −3.07380 1.11877i −0.152362 0.0554554i
\(408\) 0 0
\(409\) 13.5454 + 11.3659i 0.669777 + 0.562009i 0.912999 0.407961i \(-0.133760\pi\)
−0.243223 + 0.969971i \(0.578205\pi\)
\(410\) −2.60581 + 14.7783i −0.128692 + 0.729849i
\(411\) 0 0
\(412\) −7.90746 + 6.63514i −0.389572 + 0.326890i
\(413\) −3.69650 6.40252i −0.181893 0.315047i
\(414\) 0 0
\(415\) 7.01864 12.1566i 0.344532 0.596746i
\(416\) 3.61691 + 20.5125i 0.177334 + 1.00571i
\(417\) 0 0
\(418\) 0.309602 0.112686i 0.0151431 0.00551164i
\(419\) 8.58293 3.12393i 0.419304 0.152614i −0.123747 0.992314i \(-0.539491\pi\)
0.543051 + 0.839700i \(0.317269\pi\)
\(420\) 0 0
\(421\) 4.20140 + 23.8273i 0.204764 + 1.16127i 0.897811 + 0.440381i \(0.145157\pi\)
−0.693047 + 0.720892i \(0.743732\pi\)
\(422\) −1.94585 + 3.37031i −0.0947226 + 0.164064i
\(423\) 0 0
\(424\) −15.9637 27.6499i −0.775265 1.34280i
\(425\) −9.94080 + 8.34132i −0.482199 + 0.404613i
\(426\) 0 0
\(427\) 1.23124 6.98271i 0.0595839 0.337917i
\(428\) 13.2423 + 11.1116i 0.640090 + 0.537099i
\(429\) 0 0
\(430\) 7.48433 + 2.72407i 0.360926 + 0.131366i
\(431\) 29.5332 1.42256 0.711282 0.702907i \(-0.248115\pi\)
0.711282 + 0.702907i \(0.248115\pi\)
\(432\) 0 0
\(433\) 0.669754 0.0321863 0.0160932 0.999870i \(-0.494877\pi\)
0.0160932 + 0.999870i \(0.494877\pi\)
\(434\) −1.99792 0.727183i −0.0959032 0.0349059i
\(435\) 0 0
\(436\) −4.29779 3.60628i −0.205827 0.172709i
\(437\) −0.0364296 + 0.206603i −0.00174266 + 0.00988314i
\(438\) 0 0
\(439\) −4.86352 + 4.08097i −0.232123 + 0.194774i −0.751429 0.659814i \(-0.770635\pi\)
0.519306 + 0.854588i \(0.326191\pi\)
\(440\) −3.33399 5.77464i −0.158942 0.275295i
\(441\) 0 0
\(442\) −15.9404 + 27.6096i −0.758209 + 1.31326i
\(443\) −2.66618 15.1207i −0.126674 0.718404i −0.980299 0.197517i \(-0.936712\pi\)
0.853625 0.520887i \(-0.174399\pi\)
\(444\) 0 0
\(445\) 10.9976 4.00278i 0.521334 0.189750i
\(446\) −21.0444 + 7.65953i −0.996480 + 0.362689i
\(447\) 0 0
\(448\) 3.28628 + 18.6374i 0.155262 + 0.880535i
\(449\) −16.0199 + 27.7473i −0.756027 + 1.30948i 0.188836 + 0.982009i \(0.439529\pi\)
−0.944862 + 0.327468i \(0.893805\pi\)
\(450\) 0 0
\(451\) −5.11268 8.85543i −0.240747 0.416986i
\(452\) −4.70652 + 3.94924i −0.221376 + 0.185757i
\(453\) 0 0
\(454\) −2.62540 + 14.8894i −0.123216 + 0.698793i
\(455\) −14.9612 12.5539i −0.701391 0.588537i
\(456\) 0 0
\(457\) −18.0121 6.55586i −0.842569 0.306670i −0.115562 0.993300i \(-0.536867\pi\)
−0.727007 + 0.686630i \(0.759089\pi\)
\(458\) −17.8031 −0.831886
\(459\) 0 0
\(460\) 1.30591 0.0608882
\(461\) −4.90547 1.78545i −0.228471 0.0831565i 0.225248 0.974301i \(-0.427681\pi\)
−0.453719 + 0.891145i \(0.649903\pi\)
\(462\) 0 0
\(463\) 1.30028 + 1.09106i 0.0604289 + 0.0507059i 0.672502 0.740095i \(-0.265220\pi\)
−0.612073 + 0.790801i \(0.709664\pi\)
\(464\) −0.127585 + 0.723569i −0.00592297 + 0.0335908i
\(465\) 0 0
\(466\) 4.52245 3.79478i 0.209498 0.175790i
\(467\) 9.84136 + 17.0457i 0.455404 + 0.788783i 0.998711 0.0507511i \(-0.0161615\pi\)
−0.543307 + 0.839534i \(0.682828\pi\)
\(468\) 0 0
\(469\) −12.4023 + 21.4814i −0.572685 + 0.991920i
\(470\) −1.69474 9.61135i −0.0781725 0.443338i
\(471\) 0 0
\(472\) −8.60272 + 3.13113i −0.395972 + 0.144122i
\(473\) −5.09986 + 1.85620i −0.234492 + 0.0853481i
\(474\) 0 0
\(475\) −0.0844641 0.479020i −0.00387548 0.0219789i
\(476\) 7.26134 12.5770i 0.332823 0.576467i
\(477\) 0 0
\(478\) 2.78040 + 4.81579i 0.127173 + 0.220269i
\(479\) 22.4094 18.8037i 1.02391 0.859165i 0.0337985 0.999429i \(-0.489240\pi\)
0.990114 + 0.140264i \(0.0447951\pi\)
\(480\) 0 0
\(481\) −2.06019 + 11.6839i −0.0939365 + 0.532740i
\(482\) 7.19017 + 6.03327i 0.327503 + 0.274808i
\(483\) 0 0
\(484\) −7.86983 2.86438i −0.357719 0.130199i
\(485\) 9.58538 0.435250
\(486\) 0 0
\(487\) −20.5056 −0.929199 −0.464600 0.885521i \(-0.653802\pi\)
−0.464600 + 0.885521i \(0.653802\pi\)
\(488\) −8.25065 3.00299i −0.373489 0.135939i
\(489\) 0 0
\(490\) 1.34247 + 1.12647i 0.0606467 + 0.0508886i
\(491\) −3.04353 + 17.2607i −0.137353 + 0.778965i 0.835840 + 0.548973i \(0.184981\pi\)
−0.973193 + 0.229992i \(0.926130\pi\)
\(492\) 0 0
\(493\) 2.60907 2.18927i 0.117507 0.0985997i
\(494\) −0.597496 1.03489i −0.0268826 0.0465620i
\(495\) 0 0
\(496\) −0.587922 + 1.01831i −0.0263985 + 0.0457235i
\(497\) −0.0382100 0.216700i −0.00171395 0.00972031i
\(498\) 0 0
\(499\) 17.9538 6.53463i 0.803720 0.292530i 0.0926931 0.995695i \(-0.470452\pi\)
0.711027 + 0.703164i \(0.248230\pi\)
\(500\) −10.1323 + 3.68787i −0.453131 + 0.164926i
\(501\) 0 0
\(502\) −1.42441 8.07825i −0.0635747 0.360550i
\(503\) −5.48381 + 9.49824i −0.244511 + 0.423506i −0.961994 0.273070i \(-0.911961\pi\)
0.717483 + 0.696576i \(0.245294\pi\)
\(504\) 0 0
\(505\) 4.36924 + 7.56774i 0.194429 + 0.336760i
\(506\) 0.852928 0.715691i 0.0379173 0.0318164i
\(507\) 0 0
\(508\) −1.85481 + 10.5192i −0.0822940 + 0.466712i
\(509\) 15.2438 + 12.7911i 0.675669 + 0.566954i 0.914737 0.404049i \(-0.132397\pi\)
−0.239068 + 0.971003i \(0.576842\pi\)
\(510\) 0 0
\(511\) 12.2968 + 4.47567i 0.543979 + 0.197992i
\(512\) 15.2994 0.676143
\(513\) 0 0
\(514\) −21.5468 −0.950387
\(515\) −19.0613 6.93774i −0.839940 0.305713i
\(516\) 0 0
\(517\) 5.09439 + 4.27470i 0.224051 + 0.188001i
\(518\) −1.17426 + 6.65956i −0.0515941 + 0.292604i
\(519\) 0 0
\(520\) −18.5266 + 15.5457i −0.812445 + 0.681722i
\(521\) 17.5583 + 30.4119i 0.769244 + 1.33237i 0.937973 + 0.346708i \(0.112700\pi\)
−0.168729 + 0.985662i \(0.553966\pi\)
\(522\) 0 0
\(523\) 7.12269 12.3369i 0.311453 0.539453i −0.667224 0.744857i \(-0.732518\pi\)
0.978677 + 0.205404i \(0.0658509\pi\)
\(524\) −2.17285 12.3228i −0.0949212 0.538325i
\(525\) 0 0
\(526\) −11.1754 + 4.06750i −0.487269 + 0.177352i
\(527\) 5.12199 1.86425i 0.223117 0.0812080i
\(528\) 0 0
\(529\) −3.87080 21.9524i −0.168296 0.954451i
\(530\) 9.64867 16.7120i 0.419111 0.725922i
\(531\) 0 0
\(532\) 0.272177 + 0.471425i 0.0118004 + 0.0204389i
\(533\) −28.4106 + 23.8393i −1.23060 + 1.03260i
\(534\) 0 0
\(535\) −5.89878 + 33.4537i −0.255027 + 1.44633i
\(536\) 23.5297 + 19.7437i 1.01633 + 0.852800i
\(537\) 0 0
\(538\) 0.304911 + 0.110979i 0.0131457 + 0.00478463i
\(539\) −1.19414 −0.0514354
\(540\) 0 0
\(541\) −13.2368 −0.569094 −0.284547 0.958662i \(-0.591843\pi\)
−0.284547 + 0.958662i \(0.591843\pi\)
\(542\) −2.20194 0.801439i −0.0945813 0.0344248i
\(543\) 0 0
\(544\) −23.3152 19.5638i −0.999633 0.838792i
\(545\) 1.91445 10.8574i 0.0820062 0.465080i
\(546\) 0 0
\(547\) −12.4903 + 10.4806i −0.534046 + 0.448118i −0.869496 0.493940i \(-0.835556\pi\)
0.335450 + 0.942058i \(0.391112\pi\)
\(548\) −1.00306 1.73736i −0.0428488 0.0742163i
\(549\) 0 0
\(550\) −1.29076 + 2.23567i −0.0550383 + 0.0953291i
\(551\) 0.0221685 + 0.125724i 0.000944411 + 0.00535602i
\(552\) 0 0
\(553\) −11.0392 + 4.01792i −0.469433 + 0.170859i
\(554\) −23.1137 + 8.41271i −0.982008 + 0.357422i
\(555\) 0 0
\(556\) 1.23031 + 6.97743i 0.0521767 + 0.295909i
\(557\) 15.4486 26.7577i 0.654577 1.13376i −0.327422 0.944878i \(-0.606180\pi\)
0.982000 0.188883i \(-0.0604867\pi\)
\(558\) 0 0
\(559\) 9.84215 + 17.0471i 0.416279 + 0.721016i
\(560\) −4.71608 + 3.95726i −0.199291 + 0.167225i
\(561\) 0 0
\(562\) 1.32285 7.50224i 0.0558010 0.316463i
\(563\) −20.5116 17.2112i −0.864459 0.725368i 0.0984645 0.995141i \(-0.468607\pi\)
−0.962924 + 0.269773i \(0.913051\pi\)
\(564\) 0 0
\(565\) −11.3453 4.12934i −0.477299 0.173723i
\(566\) −7.50710 −0.315547
\(567\) 0 0
\(568\) −0.272481 −0.0114331
\(569\) 17.9111 + 6.51912i 0.750874 + 0.273296i 0.688974 0.724786i \(-0.258062\pi\)
0.0619006 + 0.998082i \(0.480284\pi\)
\(570\) 0 0
\(571\) −14.3819 12.0678i −0.601863 0.505023i 0.290181 0.956972i \(-0.406284\pi\)
−0.892044 + 0.451949i \(0.850729\pi\)
\(572\) 0.880174 4.99171i 0.0368019 0.208714i
\(573\) 0 0
\(574\) −16.1934 + 13.5879i −0.675899 + 0.567147i
\(575\) −0.821889 1.42355i −0.0342751 0.0593663i
\(576\) 0 0
\(577\) 2.42981 4.20856i 0.101154 0.175204i −0.811006 0.585038i \(-0.801080\pi\)
0.912161 + 0.409833i \(0.134413\pi\)
\(578\) −4.97705 28.2262i −0.207018 1.17406i
\(579\) 0 0
\(580\) 0.746758 0.271798i 0.0310074 0.0112858i
\(581\) 18.5815 6.76310i 0.770889 0.280580i
\(582\) 0 0
\(583\) 2.28335 + 12.9495i 0.0945669 + 0.536315i
\(584\) 8.10226 14.0335i 0.335274 0.580712i
\(585\) 0 0
\(586\) −0.291249 0.504459i −0.0120314 0.0208390i
\(587\) 25.1242 21.0817i 1.03699 0.870136i 0.0453217 0.998972i \(-0.485569\pi\)
0.991666 + 0.128837i \(0.0411243\pi\)
\(588\) 0 0
\(589\) −0.0354779 + 0.201205i −0.00146184 + 0.00829051i
\(590\) −4.23875 3.55674i −0.174507 0.146428i
\(591\) 0 0
\(592\) 3.51429 + 1.27910i 0.144436 + 0.0525705i
\(593\) −17.3446 −0.712258 −0.356129 0.934437i \(-0.615904\pi\)
−0.356129 + 0.934437i \(0.615904\pi\)
\(594\) 0 0
\(595\) 28.5384 1.16996
\(596\) 0.0892745 + 0.0324933i 0.00365683 + 0.00133098i
\(597\) 0 0
\(598\) −3.09357 2.59581i −0.126505 0.106151i
\(599\) −4.23839 + 24.0371i −0.173176 + 0.982129i 0.767052 + 0.641584i \(0.221723\pi\)
−0.940228 + 0.340545i \(0.889388\pi\)
\(600\) 0 0
\(601\) 6.02897 5.05891i 0.245927 0.206357i −0.511489 0.859290i \(-0.670906\pi\)
0.757416 + 0.652933i \(0.226461\pi\)
\(602\) 5.60981 + 9.71647i 0.228639 + 0.396014i
\(603\) 0 0
\(604\) −8.99922 + 15.5871i −0.366173 + 0.634230i
\(605\) −2.85781 16.2074i −0.116186 0.658925i
\(606\) 0 0
\(607\) 9.62007 3.50142i 0.390467 0.142118i −0.139324 0.990247i \(-0.544493\pi\)
0.529790 + 0.848129i \(0.322271\pi\)
\(608\) 1.07203 0.390187i 0.0434765 0.0158242i
\(609\) 0 0
\(610\) −0.921524 5.22622i −0.0373114 0.211604i
\(611\) 12.0602 20.8889i 0.487905 0.845076i
\(612\) 0 0
\(613\) −1.11753 1.93563i −0.0451368 0.0781792i 0.842574 0.538580i \(-0.181039\pi\)
−0.887711 + 0.460401i \(0.847706\pi\)
\(614\) −5.43455 + 4.56013i −0.219321 + 0.184032i
\(615\) 0 0
\(616\) 1.63108 9.25031i 0.0657181 0.372706i
\(617\) −26.0269 21.8391i −1.04780 0.879211i −0.0549420 0.998490i \(-0.517497\pi\)
−0.992861 + 0.119279i \(0.961942\pi\)
\(618\) 0 0
\(619\) 27.1157 + 9.86932i 1.08987 + 0.396682i 0.823574 0.567209i \(-0.191977\pi\)
0.266300 + 0.963890i \(0.414199\pi\)
\(620\) 1.27179 0.0510763
\(621\) 0 0
\(622\) 16.2613 0.652020
\(623\) 15.4920 + 5.63862i 0.620673 + 0.225907i
\(624\) 0 0
\(625\) −8.75410 7.34556i −0.350164 0.293823i
\(626\) 4.31356 24.4634i 0.172405 0.977755i
\(627\) 0 0
\(628\) 14.1214 11.8492i 0.563504 0.472836i
\(629\) −8.66811 15.0136i −0.345620 0.598632i
\(630\) 0 0
\(631\) 1.57039 2.71999i 0.0625162 0.108281i −0.833073 0.553163i \(-0.813421\pi\)
0.895590 + 0.444881i \(0.146754\pi\)
\(632\) 2.52610 + 14.3262i 0.100483 + 0.569866i
\(633\) 0 0
\(634\) −7.18490 + 2.61509i −0.285349 + 0.103858i
\(635\) −19.7242 + 7.17901i −0.782730 + 0.284890i
\(636\) 0 0
\(637\) 0.752098 + 4.26536i 0.0297992 + 0.169000i
\(638\) 0.338774 0.586774i 0.0134122 0.0232306i
\(639\) 0 0
\(640\) −0.911374 1.57855i −0.0360252 0.0623975i
\(641\) 24.3775 20.4551i 0.962853 0.807929i −0.0185622 0.999828i \(-0.505909\pi\)
0.981415 + 0.191898i \(0.0614644\pi\)
\(642\) 0 0
\(643\) −2.23087 + 12.6519i −0.0879769 + 0.498942i 0.908698 + 0.417455i \(0.137078\pi\)
−0.996674 + 0.0814867i \(0.974033\pi\)
\(644\) 1.40921 + 1.18247i 0.0555308 + 0.0465959i
\(645\) 0 0
\(646\) 1.64085 + 0.597220i 0.0645584 + 0.0234973i
\(647\) −28.2444 −1.11040 −0.555200 0.831717i \(-0.687358\pi\)
−0.555200 + 0.831717i \(0.687358\pi\)
\(648\) 0 0
\(649\) 3.77042 0.148002
\(650\) 8.79852 + 3.20240i 0.345106 + 0.125608i
\(651\) 0 0
\(652\) 13.7027 + 11.4979i 0.536637 + 0.450292i
\(653\) −4.51320 + 25.5956i −0.176615 + 1.00163i 0.759648 + 0.650335i \(0.225371\pi\)
−0.936263 + 0.351300i \(0.885740\pi\)
\(654\) 0 0
\(655\) 18.8363 15.8055i 0.735996 0.617574i
\(656\) 5.84536 + 10.1245i 0.228223 + 0.395294i
\(657\) 0 0
\(658\) 6.87407 11.9062i 0.267979 0.464153i
\(659\) 8.26875 + 46.8944i 0.322105 + 1.82675i 0.529286 + 0.848443i \(0.322460\pi\)
−0.207181 + 0.978303i \(0.566429\pi\)
\(660\) 0 0
\(661\) 0.823648 0.299783i 0.0320362 0.0116602i −0.325952 0.945386i \(-0.605685\pi\)
0.357989 + 0.933726i \(0.383463\pi\)
\(662\) 28.7656 10.4698i 1.11801 0.406922i
\(663\) 0 0
\(664\) −4.25200 24.1143i −0.165010 0.935817i
\(665\) −0.534854 + 0.926394i −0.0207407 + 0.0359240i
\(666\) 0 0
\(667\) 0.215714 + 0.373627i 0.00835246 + 0.0144669i
\(668\) −13.5176 + 11.3426i −0.523010 + 0.438857i
\(669\) 0 0
\(670\) −3.22379 + 18.2830i −0.124546 + 0.706334i
\(671\) 2.77010 + 2.32439i 0.106939 + 0.0897322i
\(672\) 0 0
\(673\) −35.0876 12.7708i −1.35253 0.492280i −0.438792 0.898589i \(-0.644593\pi\)
−0.913736 + 0.406309i \(0.866816\pi\)
\(674\) 1.22206 0.0470721
\(675\) 0 0
\(676\) −6.83505 −0.262886
\(677\) −12.8918 4.69223i −0.495472 0.180337i 0.0821842 0.996617i \(-0.473810\pi\)
−0.577656 + 0.816280i \(0.696033\pi\)
\(678\) 0 0
\(679\) 10.3437 + 8.67936i 0.396953 + 0.333083i
\(680\) 6.13663 34.8026i 0.235329 1.33462i
\(681\) 0 0
\(682\) 0.830645 0.696994i 0.0318070 0.0266893i
\(683\) 24.9943 + 43.2914i 0.956381 + 1.65650i 0.731175 + 0.682190i \(0.238972\pi\)
0.225206 + 0.974311i \(0.427694\pi\)
\(684\) 0 0
\(685\) 1.97112 3.41407i 0.0753125 0.130445i
\(686\) 3.58038 + 20.3053i 0.136699 + 0.775261i
\(687\) 0 0
\(688\) 5.83070 2.12220i 0.222293 0.0809082i
\(689\) 44.8163 16.3118i 1.70737 0.621430i
\(690\) 0 0
\(691\) 4.13544 + 23.4533i 0.157320 + 0.892204i 0.956634 + 0.291291i \(0.0940849\pi\)
−0.799315 + 0.600913i \(0.794804\pi\)
\(692\) −8.40653 + 14.5605i −0.319568 + 0.553508i
\(693\) 0 0
\(694\) −3.10483 5.37773i −0.117858 0.204136i
\(695\) −10.6655 + 8.94941i −0.404565 + 0.339471i
\(696\) 0 0
\(697\) 9.41054 53.3698i 0.356450 2.02153i
\(698\) 24.7085 + 20.7329i 0.935230 + 0.784751i
\(699\) 0 0
\(700\) −4.00799 1.45879i −0.151488 0.0551370i
\(701\) −34.4493 −1.30113 −0.650565 0.759450i \(-0.725468\pi\)
−0.650565 + 0.759450i \(0.725468\pi\)
\(702\) 0 0
\(703\) 0.649815 0.0245082
\(704\) −9.06962 3.30107i −0.341824 0.124414i
\(705\) 0 0
\(706\) 29.8521 + 25.0489i 1.12350 + 0.942728i
\(707\) −2.13755 + 12.1227i −0.0803909 + 0.455920i
\(708\) 0 0
\(709\) 11.8915 9.97817i 0.446595 0.374738i −0.391575 0.920146i \(-0.628070\pi\)
0.838171 + 0.545408i \(0.183625\pi\)
\(710\) −0.0823456 0.142627i −0.00309038 0.00535269i
\(711\) 0 0
\(712\) 10.2075 17.6800i 0.382543 0.662585i
\(713\) 0.119894 + 0.679954i 0.00449008 + 0.0254645i
\(714\) 0 0
\(715\) 9.35981 3.40669i 0.350037 0.127403i
\(716\) −9.11097 + 3.31612i −0.340493 + 0.123929i
\(717\) 0 0
\(718\) −4.82897 27.3864i −0.180216 1.02205i
\(719\) 6.02686 10.4388i 0.224764 0.389303i −0.731485 0.681858i \(-0.761172\pi\)
0.956249 + 0.292555i \(0.0945056\pi\)
\(720\) 0 0
\(721\) −14.2872 24.7461i −0.532083 0.921594i
\(722\) 15.2954 12.8344i 0.569236 0.477645i
\(723\) 0 0
\(724\) 2.76880 15.7026i 0.102902 0.583584i
\(725\) −0.766265 0.642973i −0.0284584 0.0238794i
\(726\) 0 0
\(727\) 29.7227 + 10.8182i 1.10235 + 0.401224i 0.828184 0.560457i \(-0.189374\pi\)
0.274171 + 0.961681i \(0.411597\pi\)
\(728\) −34.0685 −1.26266
\(729\) 0 0
\(730\) 9.79423 0.362501
\(731\) −27.0286 9.83761i −0.999690 0.363857i
\(732\) 0 0
\(733\) −14.5784 12.2328i −0.538466 0.451827i 0.332547 0.943087i \(-0.392092\pi\)
−0.871013 + 0.491260i \(0.836537\pi\)
\(734\) 2.07123 11.7465i 0.0764503 0.433571i
\(735\) 0 0
\(736\) 2.95336 2.47816i 0.108862 0.0913462i
\(737\) −6.32516 10.9555i −0.232990 0.403551i
\(738\) 0 0
\(739\) −8.30036 + 14.3767i −0.305334 + 0.528854i −0.977336 0.211696i \(-0.932101\pi\)
0.672002 + 0.740550i \(0.265435\pi\)
\(740\) −0.702405 3.98354i −0.0258209 0.146438i
\(741\) 0 0
\(742\) 25.5443 9.29737i 0.937761 0.341317i
\(743\) −31.2951 + 11.3905i −1.14811 + 0.417876i −0.844834 0.535028i \(-0.820301\pi\)
−0.303271 + 0.952904i \(0.598079\pi\)
\(744\) 0 0
\(745\) 0.0324187 + 0.183855i 0.00118773 + 0.00673594i
\(746\) 3.08078 5.33606i 0.112795 0.195367i
\(747\) 0 0
\(748\) 3.70328 + 6.41426i 0.135405 + 0.234529i
\(749\) −36.6570 + 30.7589i −1.33942 + 1.12390i
\(750\) 0 0
\(751\) 4.82422 27.3595i 0.176038 0.998364i −0.760900 0.648869i \(-0.775242\pi\)
0.936938 0.349494i \(-0.113647\pi\)
\(752\) −5.82445 4.88729i −0.212396 0.178221i
\(753\) 0 0
\(754\) −2.30926 0.840504i −0.0840985 0.0306093i
\(755\) −35.3686 −1.28720
\(756\) 0 0
\(757\) −3.12036 −0.113411 −0.0567057 0.998391i \(-0.518060\pi\)
−0.0567057 + 0.998391i \(0.518060\pi\)
\(758\) 24.1012 + 8.77213i 0.875396 + 0.318618i
\(759\) 0 0
\(760\) 1.01473 + 0.851456i 0.0368080 + 0.0308855i
\(761\) 7.63343 43.2914i 0.276712 1.56931i −0.456760 0.889590i \(-0.650990\pi\)
0.733471 0.679720i \(-0.237899\pi\)
\(762\) 0 0
\(763\) 11.8971 9.98282i 0.430702 0.361402i
\(764\) 11.9783 + 20.7470i 0.433360 + 0.750602i
\(765\) 0 0
\(766\) 2.01168 3.48433i 0.0726849 0.125894i
\(767\) −2.37469 13.4675i −0.0857452 0.486285i
\(768\) 0 0
\(769\) −3.48894 + 1.26987i −0.125815 + 0.0457927i −0.404160 0.914688i \(-0.632436\pi\)
0.278346 + 0.960481i \(0.410214\pi\)
\(770\) 5.33488 1.94174i 0.192256 0.0699754i
\(771\) 0 0
\(772\) 2.64645 + 15.0088i 0.0952479 + 0.540178i
\(773\) −4.48452 + 7.76741i −0.161297 + 0.279374i −0.935334 0.353766i \(-0.884901\pi\)
0.774037 + 0.633140i \(0.218234\pi\)
\(774\) 0 0
\(775\) −0.800417 1.38636i −0.0287518 0.0497996i
\(776\) 12.8087 10.7477i 0.459804 0.385821i
\(777\) 0 0
\(778\) 1.98494 11.2572i 0.0711636 0.403589i
\(779\) 1.55608 + 1.30571i 0.0557525