Properties

Label 243.2.e.a.55.2
Level $243$
Weight $2$
Character 243.55
Analytic conductor $1.940$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [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 55.2
Root \(0.500000 - 1.68614i\) of defining polynomial
Character \(\chi\) \(=\) 243.55
Dual form 243.2.e.a.190.2

$q$-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 \(\left(\mathbb{Z}/243\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{8}{9}\right)\)

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 0.0329100 0.999458i \(-0.489523\pi\)
0.667650 + 0.744475i \(0.267300\pi\)
\(3\) 0 0
\(4\) −0.680553 + 0.571052i −0.340277 + 0.285526i
\(5\) 0.303153 + 1.71926i 0.135574 + 0.768879i 0.974458 + 0.224569i \(0.0720973\pi\)
−0.838884 + 0.544310i \(0.816792\pi\)
\(6\) 0 0
\(7\) 1.88389 + 1.58077i 0.712044 + 0.597476i 0.925172 0.379548i \(-0.123921\pi\)
−0.213128 + 0.977024i \(0.568365\pi\)
\(8\) −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 −0.934210 0.356723i \(-0.883894\pi\)
0.999877 0.0156913i \(-0.00499490\pi\)
\(12\) 0 0
\(13\) 4.27469 + 1.55586i 1.18559 + 0.431518i 0.858171 0.513363i \(-0.171601\pi\)
0.327414 + 0.944881i \(0.393823\pi\)
\(14\) 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 −0.915554 0.402194i \(-0.868248\pi\)
0.109467 0.993990i \(-0.465086\pi\)
\(18\) 0 0
\(19\) −0.124578 + 0.215776i −0.0285802 + 0.0495023i −0.879962 0.475045i \(-0.842432\pi\)
0.851382 + 0.524547i \(0.175765\pi\)
\(20\) −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 −0.707553 0.706660i \(-0.750201\pi\)
0.573059 + 0.819514i \(0.305757\pi\)
\(24\) 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 −0.386337 0.922358i \(-0.626260\pi\)
0.296928 + 0.954900i \(0.404038\pi\)
\(30\) 0 0
\(31\) −0.628159 + 0.527088i −0.112821 + 0.0946678i −0.697453 0.716631i \(-0.745683\pi\)
0.584632 + 0.811299i \(0.301239\pi\)
\(32\) −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 0.738700 0.674035i \(-0.235440\pi\)
−0.953081 + 0.302715i \(0.902107\pi\)
\(38\) −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 −0.334478 0.942403i \(-0.608560\pi\)
−0.861991 + 0.506924i \(0.830782\pi\)
\(42\) 0 0
\(43\) 0.751401 4.26141i 0.114588 0.649858i −0.872366 0.488853i \(-0.837415\pi\)
0.986954 0.161005i \(-0.0514735\pi\)
\(44\) 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 0.889018 0.457872i \(-0.151388\pi\)
−0.296540 + 0.955020i \(0.595833\pi\)
\(48\) 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 0.999749 + 0.0224233i \(0.00713815\pi\)
−0.931787 + 0.363005i \(0.881751\pi\)
\(60\) 0 0
\(61\) 2.20864 + 1.85327i 0.282787 + 0.237287i 0.773137 0.634239i \(-0.218687\pi\)
−0.490350 + 0.871526i \(0.663131\pi\)
\(62\) −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 −0.309566 0.950878i \(-0.600184\pi\)
−0.848354 + 0.529429i \(0.822406\pi\)
\(68\) 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 0.868668 0.495395i \(-0.164977\pi\)
−0.863358 + 0.504591i \(0.831643\pi\)
\(72\) 0 0
\(73\) 2.66057 4.60824i 0.311396 0.539354i −0.667269 0.744817i \(-0.732537\pi\)
0.978665 + 0.205463i \(0.0658701\pi\)
\(74\) −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 −0.581957 0.813220i \(-0.697713\pi\)
0.0769231 + 0.997037i \(0.475490\pi\)
\(80\) −2.50337 −0.279885
\(81\) 0 0
\(82\) −8.59571 −0.949238
\(83\) 7.55575 2.75007i 0.829351 0.301859i 0.107759 0.994177i \(-0.465633\pi\)
0.721593 + 0.692318i \(0.243410\pi\)
\(84\) 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 −0.631870 0.775074i \(-0.717712\pi\)
0.987169 + 0.159678i \(0.0510457\pi\)
\(90\) 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 −0.897373 0.441273i \(-0.854527\pi\)
0.994179 0.107741i \(-0.0343618\pi\)
\(98\) −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 0.431768 0.901985i \(-0.357890\pi\)
−0.813306 + 0.581836i \(0.802334\pi\)
\(102\) 0 0
\(103\) 2.01765 + 11.4426i 0.198805 + 1.12748i 0.906896 + 0.421356i \(0.138446\pi\)
−0.708091 + 0.706121i \(0.750443\pi\)
\(104\) −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 0.987735 + 0.156142i \(0.0499058\pi\)
−0.874763 + 0.484551i \(0.838983\pi\)
\(114\) 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 0.465792 + 0.884894i \(0.345770\pi\)
−0.999237 + 0.0390598i \(0.987564\pi\)
\(128\) 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 −0.0353614 0.999375i \(-0.511258\pi\)
0.978051 + 0.208364i \(0.0668138\pi\)
\(132\) 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 −0.249780 0.968303i \(-0.580358\pi\)
0.431071 + 0.902318i \(0.358136\pi\)
\(138\) 0 0
\(139\) −6.10928 + 5.12629i −0.518182 + 0.434806i −0.863997 0.503496i \(-0.832047\pi\)
0.345815 + 0.938303i \(0.387602\pi\)
\(140\) −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 0.337901 0.941182i \(-0.390283\pi\)
−0.346133 + 0.938185i \(0.612505\pi\)
\(150\) 0 0
\(151\) −3.51801 + 19.9516i −0.286292 + 1.62364i 0.414344 + 0.910121i \(0.364011\pi\)
−0.700635 + 0.713520i \(0.747100\pi\)
\(152\) −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 −0.695979 0.718062i \(-0.745029\pi\)
0.408415 0.912797i \(-0.366082\pi\)
\(158\) −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 0.763570 + 0.645724i \(0.223445\pi\)
−0.496671 + 0.867939i \(0.665444\pi\)
\(168\) 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 0.559091 + 0.829106i \(0.311150\pi\)
−0.808945 + 0.587884i \(0.799961\pi\)
\(174\) 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 0.994650 0.103302i \(-0.0329409\pi\)
−0.586787 + 0.809741i \(0.699608\pi\)
\(180\) 0 0
\(181\) 8.97393 15.5433i 0.667027 1.15532i −0.311704 0.950179i \(-0.600900\pi\)
0.978731 0.205146i \(-0.0657668\pi\)
\(182\) 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 −0.841666 + 0.539998i \(0.818425\pi\)
−0.991858 + 0.127350i \(0.959353\pi\)
\(192\) 0 0
\(193\) −13.1413 + 11.0269i −0.945935 + 0.793734i −0.978608 0.205733i \(-0.934042\pi\)
0.0326735 + 0.999466i \(0.489598\pi\)
\(194\) −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 −0.817803 0.575499i \(-0.804808\pi\)
0.907298 + 0.420489i \(0.138141\pi\)
\(198\) 0 0
\(199\) −9.26942 16.0551i −0.657092 1.13812i −0.981365 0.192153i \(-0.938453\pi\)
0.324273 0.945964i \(-0.394880\pi\)
\(200\) −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 0.954763 0.297366i \(-0.0961082\pi\)
−0.998889 + 0.0471155i \(0.984997\pi\)
\(212\) −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 −0.0929417 0.995672i \(-0.529627\pi\)
−0.996684 + 0.0813669i \(0.974071\pi\)
\(224\) 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 −0.783505 0.621386i \(-0.786570\pi\)
0.948780 0.315937i \(-0.102319\pi\)
\(228\) 0 0
\(229\) −15.8675 5.77529i −1.04855 0.381642i −0.240436 0.970665i \(-0.577290\pi\)
−0.808116 + 0.589023i \(0.799513\pi\)
\(230\) −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 0.943042 0.332675i \(-0.107951\pi\)
−0.759626 + 0.650361i \(0.774618\pi\)
\(234\) 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 −0.502693 0.864465i \(-0.667657\pi\)
0.764040 + 0.645169i \(0.223213\pi\)
\(240\) 0 0
\(241\) 8.36559 3.04483i 0.538875 0.196135i −0.0582216 0.998304i \(-0.518543\pi\)
0.597097 + 0.802169i \(0.296321\pi\)
\(242\) 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 −0.962284 0.272048i \(-0.912299\pi\)
0.716742 + 0.697338i \(0.245632\pi\)
\(252\) 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 −0.335420 0.942069i \(-0.608878\pi\)
−0.862497 + 0.506062i \(0.831101\pi\)
\(258\) 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 0.336256 0.941771i \(-0.390839\pi\)
−0.869073 + 0.494684i \(0.835284\pi\)
\(264\) 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 −0.0784094 0.996921i \(-0.524984\pi\)
−0.995391 + 0.0958953i \(0.969429\pi\)
\(278\) −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 0.924241 + 0.381811i \(0.124699\pi\)
−0.999089 + 0.0426756i \(0.986412\pi\)
\(282\) 0 0
\(283\) −6.69088 2.43528i −0.397732 0.144763i 0.135408 0.990790i \(-0.456766\pi\)
−0.533139 + 0.846027i \(0.678988\pi\)
\(284\) −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 −0.655067 0.755571i \(-0.727359\pi\)
0.630341 + 0.776318i \(0.282915\pi\)
\(294\) 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 0.753903 0.656986i \(-0.228169\pi\)
−0.945918 + 0.324406i \(0.894836\pi\)
\(308\) −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 0.718505 0.695521i \(-0.244827\pi\)
0.103335 + 0.994647i \(0.467049\pi\)
\(312\) 0 0
\(313\) −4.09130 + 23.2029i −0.231254 + 1.31151i 0.619107 + 0.785307i \(0.287495\pi\)
−0.850361 + 0.526200i \(0.823616\pi\)
\(314\) −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 0.473305 0.880898i \(-0.343061\pi\)
−0.785327 + 0.619081i \(0.787505\pi\)
\(318\) 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 0.998689 + 0.0511815i \(0.0162987\pi\)
0.223825 + 0.974629i \(0.428146\pi\)
\(332\) −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 0.371516 0.928427i \(-0.378838\pi\)
−0.312184 + 0.950022i \(0.601060\pi\)
\(338\) 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 −0.755807 0.654794i \(-0.772755\pi\)
0.513602 + 0.858029i \(0.328311\pi\)
\(348\) 0 0
\(349\) 28.7477 10.4633i 1.53883 0.560089i 0.573066 0.819509i \(-0.305754\pi\)
0.965764 + 0.259421i \(0.0835316\pi\)
\(350\) 5.06182 0.270566
\(351\) 0 0
\(352\) −5.74276 −0.306090
\(353\) 34.7322 12.6415i 1.84861 0.672839i 0.862664 0.505778i \(-0.168794\pi\)
0.985947 0.167061i \(-0.0534278\pi\)
\(354\) 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 0.273792 + 0.961789i \(0.411722\pi\)
−0.969830 + 0.243783i \(0.921611\pi\)
\(360\) 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 0.889626 + 0.456690i \(0.150965\pi\)
−0.992172 + 0.124879i \(0.960146\pi\)
\(368\) −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 0.999743 0.0226503i \(-0.00721043\pi\)
−0.947198 + 0.320648i \(0.896099\pi\)
\(374\) −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 0.997046 0.0768065i \(-0.0244724\pi\)
−0.963186 + 0.268835i \(0.913361\pi\)
\(384\) 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 0.899152 + 0.437637i \(0.144184\pi\)
−0.994607 + 0.103716i \(0.966927\pi\)
\(390\) 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 −0.703507 0.710689i \(-0.748383\pi\)
0.967228 + 0.253910i \(0.0817168\pi\)
\(398\) −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 −0.874788 0.484507i \(-0.838999\pi\)
0.325241 + 0.945631i \(0.394555\pi\)
\(402\) 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 −0.243223 0.969971i \(-0.578205\pi\)
0.912999 + 0.407961i \(0.133760\pi\)
\(410\) −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 0.543051 0.839700i \(-0.317269\pi\)
−0.123747 + 0.992314i \(0.539491\pi\)
\(420\) 0 0
\(421\) 4.20140 23.8273i 0.204764 1.16127i −0.693047 0.720892i \(-0.743732\pi\)
0.897811 0.440381i \(-0.145157\pi\)
\(422\) −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 0.519306 0.854588i \(-0.326191\pi\)
−0.751429 + 0.659814i \(0.770635\pi\)
\(440\) −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 0.853625 + 0.520887i \(0.174399\pi\)
−0.980299 + 0.197517i \(0.936712\pi\)
\(444\) 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 −0.944862 0.327468i \(-0.893805\pi\)
0.188836 0.982009i \(-0.439529\pi\)
\(450\) 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 −0.727007 0.686630i \(-0.759089\pi\)
−0.115562 + 0.993300i \(0.536867\pi\)
\(458\) −17.8031 −0.831886
\(459\) 0 0
\(460\) 1.30591 0.0608882
\(461\) −4.90547 + 1.78545i −0.228471 + 0.0831565i −0.453719 0.891145i \(-0.649903\pi\)
0.225248 + 0.974301i \(0.427681\pi\)
\(462\) 0 0
\(463\) 1.30028 1.09106i 0.0604289 0.0507059i −0.612073 0.790801i \(-0.709664\pi\)
0.672502 + 0.740095i \(0.265220\pi\)
\(464\) −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 −0.543307 0.839534i \(-0.682828\pi\)
0.998711 + 0.0507511i \(0.0161615\pi\)
\(468\) 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 0.990114 0.140264i \(-0.0447951\pi\)
0.0337985 + 0.999429i \(0.489240\pi\)
\(480\) 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 −0.973193 0.229992i \(-0.926130\pi\)
0.835840 0.548973i \(-0.184981\pi\)
\(492\) 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 0.711027 0.703164i \(-0.248230\pi\)
0.0926931 + 0.995695i \(0.470452\pi\)
\(500\) −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 0.717483 0.696576i \(-0.245294\pi\)
−0.961994 + 0.273070i \(0.911961\pi\)
\(504\) 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 −0.239068 0.971003i \(-0.576842\pi\)
0.914737 + 0.404049i \(0.132397\pi\)
\(510\) 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 −0.168729 0.985662i \(-0.553966\pi\)
0.937973 0.346708i \(-0.112700\pi\)
\(522\) 0 0
\(523\) 7.12269 + 12.3369i 0.311453 + 0.539453i 0.978677 0.205404i \(-0.0658509\pi\)
−0.667224 + 0.744857i \(0.732518\pi\)
\(524\) −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 0.335450 0.942058i \(-0.391112\pi\)
−0.869496 + 0.493940i \(0.835556\pi\)
\(548\) −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 0.982000 + 0.188883i \(0.0604867\pi\)
−0.327422 + 0.944878i \(0.606180\pi\)
\(558\) 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 −0.962924 0.269773i \(-0.913051\pi\)
0.0984645 + 0.995141i \(0.468607\pi\)
\(564\) 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 0.0619006 0.998082i \(-0.480284\pi\)
0.688974 + 0.724786i \(0.258062\pi\)
\(570\) 0 0
\(571\) −14.3819 + 12.0678i −0.601863 + 0.505023i −0.892044 0.451949i \(-0.850729\pi\)
0.290181 + 0.956972i \(0.406284\pi\)
\(572\) 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 0.912161 0.409833i \(-0.134413\pi\)
−0.811006 + 0.585038i \(0.801080\pi\)
\(578\) −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 0.991666 0.128837i \(-0.0411243\pi\)
0.0453217 + 0.998972i \(0.485569\pi\)
\(588\) 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 −0.940228 0.340545i \(-0.889388\pi\)
0.767052 0.641584i \(-0.221723\pi\)
\(600\) 0 0
\(601\) 6.02897 + 5.05891i 0.245927 + 0.206357i 0.757416 0.652933i \(-0.226461\pi\)
−0.511489 + 0.859290i \(0.670906\pi\)
\(602\) 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 0.529790 0.848129i \(-0.322271\pi\)
−0.139324 + 0.990247i \(0.544493\pi\)
\(608\) 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 −0.887711 0.460401i \(-0.847706\pi\)
0.842574 + 0.538580i \(0.181039\pi\)
\(614\) −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 −0.992861 0.119279i \(-0.961942\pi\)
−0.0549420 + 0.998490i \(0.517497\pi\)
\(618\) 0 0
\(619\) 27.1157 9.86932i 1.08987 0.396682i 0.266300 0.963890i \(-0.414199\pi\)
0.823574 + 0.567209i \(0.191977\pi\)
\(620\) 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 0.895590 0.444881i \(-0.146754\pi\)
−0.833073 + 0.553163i \(0.813421\pi\)
\(632\) 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 0.981415 0.191898i \(-0.0614644\pi\)
−0.0185622 + 0.999828i \(0.505909\pi\)
\(642\) 0 0
\(643\) −2.23087 12.6519i −0.0879769 0.498942i −0.996674 0.0814867i \(-0.974033\pi\)
0.908698 0.417455i \(-0.137078\pi\)
\(644\) 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 −0.936263 0.351300i \(-0.885740\pi\)
0.759648 0.650335i \(-0.225371\pi\)
\(654\) 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 −0.207181 0.978303i \(-0.566429\pi\)
0.529286 0.848443i \(-0.322460\pi\)
\(660\) 0 0
\(661\) 0.823648 + 0.299783i 0.0320362 + 0.0116602i 0.357989 0.933726i \(-0.383463\pi\)
−0.325952 + 0.945386i \(0.605685\pi\)
\(662\) 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 −0.913736 0.406309i \(-0.866816\pi\)
−0.438792 + 0.898589i \(0.644593\pi\)
\(674\) 1.22206 0.0470721
\(675\) 0 0
\(676\) −6.83505 −0.262886
\(677\) −12.8918 + 4.69223i −0.495472 + 0.180337i −0.577656 0.816280i \(-0.696033\pi\)
0.0821842 + 0.996617i \(0.473810\pi\)
\(678\) 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 0.225206 0.974311i \(-0.427694\pi\)
0.731175 0.682190i \(-0.238972\pi\)
\(684\) 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 −0.799315 0.600913i \(-0.794804\pi\)
0.956634 0.291291i \(-0.0940849\pi\)
\(692\) −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 0.838171 0.545408i \(-0.183625\pi\)
−0.391575 + 0.920146i \(0.628070\pi\)
\(710\) −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 0.956249 0.292555i \(-0.0945056\pi\)
−0.731485 + 0.681858i \(0.761172\pi\)
\(720\) 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 0.274171 0.961681i \(-0.411597\pi\)
0.828184 + 0.560457i \(0.189374\pi\)
\(728\) −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 −0.871013 0.491260i \(-0.836537\pi\)
0.332547 + 0.943087i \(0.392092\pi\)
\(734\) 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 0.672002 0.740550i \(-0.265435\pi\)
−0.977336 + 0.211696i \(0.932101\pi\)
\(740\) −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 −0.303271 0.952904i \(-0.598079\pi\)
−0.844834 + 0.535028i \(0.820301\pi\)
\(744\) 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 0.936938 + 0.349494i \(0.113647\pi\)
−0.760900 + 0.648869i \(0.775242\pi\)
\(752\) −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 0.733471 + 0.679720i \(0.237899\pi\)
−0.456760 + 0.889590i \(0.650990\pi\)
\(762\) 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 0.278346 0.960481i \(-0.410214\pi\)
−0.404160 + 0.914688i \(0.632436\pi\)
\(770\) 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 0.774037 0.633140i \(-0.218234\pi\)
−0.935334 + 0.353766i \(0.884901\pi\)
\(774\) 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 0.0467819i
\(780\) 0 0
\(781\) 0.105454 0.0383820i 0.00377343 0.00137342i
\(782\) 5.90098 0.211018
\(783\) 0 0
\(784\) 1.36527 0.0487597
\(785\) 34.0402 12.3896i 1.21495 0.442204i
\(786\) 0 0
\(787\) 33.5921 28.1872i 1.19743 1.00476i 0.197731 0.980256i \(-0.436643\pi\)
0.999700 0.0245073i \(-0.00780170\pi\)
\(788\) 0.387562 + 2.19797i 0.0138063 + 0.0782995i
\(789\) 0 0
\(790\) −6.73547 5.65173i −0.239637 0.201079i
\(791\) −8.50374 + 14.7289i −0.302358 + 0.523699i
\(792\) 0 0
\(793\) 6.55782 + 11.3585i 0.232875 + 0.403351i
\(794\) 1.92404 10.9118i 0.0682817 0.387245i
\(795\) 0 0
\(796\) 15.4766 + 5.63304i 0.548555 + 0.199658i
\(797\) 11.2914 + 4.10972i 0.399961 + 0.145574i 0.534166 0.845380i \(-0.320626\pi\)
−0.134205 + 0.990954i \(0.542848\pi\)
\(798\) 0 0
\(799\) 6.12032 34.7101i 0.216521 1.22795i
\(800\) −4.46940 7.74124i −0.158017 0.273694i
\(801\) 0 0
\(802\) −7.57299 + 13.1168i −0.267412 + 0.463171i
\(803\) −5.11246 4.28986i −0.180415 0.151386i
\(804\) 0 0
\(805\) −0.627735 3.56006i −0.0221247 0.125476i
\(806\) −3.01275 + 2.52800i −0.106120 + 0.0890449i
\(807\) 0 0
\(808\) 14.3239 5.21348i 0.503914 0.183410i
\(809\) 8.02937 0.282298 0.141149 0.989988i \(-0.454920\pi\)
0.141149 + 0.989988i \(0.454920\pi\)
\(810\) 0 0
\(811\) −12.8345 −0.450681 −0.225341 0.974280i \(-0.572349\pi\)
−0.225341 + 0.974280i \(0.572349\pi\)
\(812\) 1.05194 0.382875i 0.0369158 0.0134363i
\(813\) 0 0
\(814\) −2.64191 + 2.21682i −0.0925988 + 0.0776996i
\(815\) −6.10385 34.6167i −0.213809 1.21257i
\(816\) 0 0
\(817\) 0.825899 + 0.693012i 0.0288946 + 0.0242454i
\(818\) 9.32142 16.1452i 0.325916 0.564503i
\(819\) 0 0
\(820\) 6.32233 + 10.9506i 0.220785 + 0.382411i
\(821\) 5.15134 29.2147i 0.179783 1.01960i −0.752694 0.658371i \(-0.771246\pi\)
0.932477 0.361230i \(-0.117643\pi\)
\(822\) 0 0
\(823\) −46.5531 16.9439i −1.62274 0.590628i −0.638836 0.769343i \(-0.720584\pi\)
−0.983901 + 0.178715i \(0.942806\pi\)
\(824\) −33.2500 12.1020i −1.15832 0.421594i
\(825\) 0 0
\(826\) −1.35352 + 7.67620i −0.0470950 + 0.267089i
\(827\) 20.4215 + 35.3711i 0.710126 + 1.22997i 0.964809 + 0.262950i \(0.0846955\pi\)
−0.254683 + 0.967025i \(0.581971\pi\)
\(828\) 0 0
\(829\) 4.72638 8.18633i 0.164154 0.284323i −0.772201 0.635379i \(-0.780844\pi\)
0.936355 + 0.351056i \(0.114177\pi\)
\(830\) 11.3373 + 9.51316i 0.393525 + 0.330207i
\(831\) 0 0
\(832\) −6.07884 34.4748i −0.210746 1.19520i
\(833\) −4.84815 + 4.06808i −0.167978 + 0.140951i
\(834\) 0 0
\(835\) −32.5847 + 11.8598i −1.12764 + 0.410427i
\(836\) −0.277620 −0.00960170
\(837\) 0 0
\(838\) 9.62995 0.332661
\(839\) −11.5459 + 4.20236i −0.398609 + 0.145082i −0.533543 0.845773i \(-0.679140\pi\)
0.134934 + 0.990855i \(0.456918\pi\)
\(840\) 0 0
\(841\) −22.0142 + 18.4721i −0.759109 + 0.636968i
\(842\) −4.42964 25.1218i −0.152656 0.865753i
\(843\) 0 0
\(844\) 2.51204 + 2.10786i 0.0864681 + 0.0725554i
\(845\) −6.71575 + 11.6320i −0.231029 + 0.400154i
\(846\) 0 0
\(847\) 11.5916 + 20.0772i 0.398292 + 0.689862i
\(848\) −2.61057 + 14.8053i −0.0896474 + 0.508416i
\(849\) 0 0
\(850\) −12.8566 4.67943i −0.440979 0.160503i
\(851\) 2.06356 + 0.751073i 0.0707378 + 0.0257464i
\(852\) 0 0
\(853\) −5.35980 + 30.3969i −0.183516 + 1.04077i 0.744331 + 0.667811i \(0.232768\pi\)
−0.927847 + 0.372960i \(0.878343\pi\)
\(854\) 3.73781 + 6.47408i 0.127905 + 0.221538i
\(855\) 0 0
\(856\) 29.6280 51.3172i 1.01266 1.75399i
\(857\) −8.53835 7.16453i −0.291665 0.244736i 0.485200 0.874403i \(-0.338747\pi\)
−0.776865 + 0.629667i \(0.783191\pi\)
\(858\) 0 0
\(859\) 0.720410 + 4.08565i 0.0245801 + 0.139401i 0.994628 0.103512i \(-0.0330082\pi\)
−0.970048 + 0.242913i \(0.921897\pi\)
\(860\) −5.14108 + 4.31388i −0.175310 + 0.147102i
\(861\) 0 0
\(862\) 29.2598 10.6497i 0.996591 0.362730i
\(863\) 47.2534 1.60852 0.804262 0.594275i \(-0.202561\pi\)
0.804262 + 0.594275i \(0.202561\pi\)
\(864\) 0 0
\(865\) −33.0392 −1.12337
\(866\) 0.663553 0.241514i 0.0225484 0.00820696i
\(867\) 0 0
\(868\) 1.37240 1.15158i 0.0465822 0.0390871i
\(869\) 1.04037 + 5.90025i 0.0352923 + 0.200152i
\(870\) 0 0
\(871\) −35.1482 29.4928i −1.19095 0.999327i
\(872\) −9.61579 + 16.6550i −0.325632 + 0.564011i
\(873\) 0 0
\(874\) −0.110593 0.191553i −0.00374087 0.00647938i
\(875\) −5.18308 + 29.3947i −0.175220 + 0.993722i
\(876\) 0 0
\(877\) −33.0306 12.0222i −1.11536 0.405959i −0.282406 0.959295i \(-0.591132\pi\)
−0.832958 + 0.553336i \(0.813355\pi\)
\(878\) −6.29009 2.28940i −0.212280 0.0772637i
\(879\) 0 0
\(880\) −0.545213 + 3.09206i −0.0183791 + 0.104233i
\(881\) −9.67981 16.7659i −0.326121 0.564858i 0.655618 0.755093i \(-0.272408\pi\)
−0.981739 + 0.190235i \(0.939075\pi\)
\(882\) 0 0
\(883\) 6.89302 11.9391i 0.231969 0.401781i −0.726419 0.687252i \(-0.758817\pi\)
0.958387 + 0.285471i \(0.0921500\pi\)
\(884\) 20.5787 + 17.2676i 0.692136 + 0.580771i
\(885\) 0 0
\(886\) 2.81102 + 15.9421i 0.0944381 + 0.535585i
\(887\) 22.8415 19.1663i 0.766942 0.643541i −0.172981 0.984925i \(-0.555340\pi\)
0.939924 + 0.341384i \(0.110896\pi\)
\(888\) 0 0
\(889\) −27.7849 + 10.1129i −0.931877 + 0.339176i
\(890\) 12.3391 0.413609
\(891\) 0 0
\(892\) 18.8705 0.631832
\(893\) −1.24144 + 0.451846i −0.0415431 + 0.0151205i
\(894\) 0 0
\(895\) −14.5954 + 12.2470i −0.487870 + 0.409372i
\(896\) 0.445869 + 2.52865i 0.0148954 + 0.0844763i
\(897\) 0 0
\(898\) −25.8773 21.7136i −0.863536 0.724593i
\(899\) 0.210078 0.363866i 0.00700649 0.0121356i
\(900\) 0 0
\(901\) −34.8448 60.3530i −1.16085 2.01065i
\(902\) −1.87208 + 10.6171i −0.0623333 + 0.353510i
\(903\) 0 0
\(904\) −19.7904 7.20313i −0.658220 0.239572i
\(905\) 29.4435 + 10.7166i 0.978736 + 0.356231i
\(906\) 0 0
\(907\) −1.08210 + 6.13690i −0.0359306 + 0.203772i −0.997488 0.0708301i \(-0.977435\pi\)
0.961558 + 0.274603i \(0.0885463\pi\)
\(908\) 6.36984 + 11.0329i 0.211391 + 0.366139i
\(909\) 0 0
\(910\) −10.2957 + 17.8327i −0.341300 + 0.591148i
\(911\) 24.2372 + 20.3375i 0.803016 + 0.673810i 0.948930 0.315487i \(-0.102168\pi\)
−0.145914 + 0.989297i \(0.546612\pi\)
\(912\) 0 0
\(913\) −1.75119 9.93149i −0.0579559 0.328684i
\(914\) −15.4813 + 12.9903i −0.512074 + 0.429681i
\(915\) 0 0
\(916\) 14.0966 5.13076i 0.465766 0.169525i
\(917\) 34.6380 1.14385
\(918\) 0 0
\(919\) 36.0031 1.18763 0.593816 0.804601i \(-0.297621\pi\)
0.593816 + 0.804601i \(0.297621\pi\)
\(920\) 4.20650 1.53104i 0.138684 0.0504770i
\(921\) 0 0
\(922\) −4.21622 + 3.53783i −0.138854 + 0.116512i
\(923\) 0.0706795 + 0.400844i 0.00232645 + 0.0131939i
\(924\) 0 0
\(925\) −3.90034 3.27277i −0.128242 0.107608i
\(926\) 0.894800 1.54984i 0.0294049 0.0509309i
\(927\) 0 0
\(928\) 1.17304 + 2.03177i 0.0385070 + 0.0666961i
\(929\) −4.41895 + 25.0611i −0.144981 + 0.822228i 0.822401 + 0.568908i \(0.192634\pi\)
−0.967382 + 0.253321i \(0.918477\pi\)
\(930\) 0 0
\(931\) 0.222917 + 0.0811351i 0.00730580 + 0.00265910i
\(932\) −4.67454 1.70139i −0.153120 0.0557310i
\(933\) 0 0
\(934\) 3.60354 20.4367i 0.117912 0.668710i
\(935\) −7.27728 12.6046i −0.237993 0.412215i
\(936\) 0 0
\(937\) −14.1524 + 24.5127i −0.462338 + 0.800794i −0.999077 0.0429549i \(-0.986323\pi\)
0.536739 + 0.843749i \(0.319656\pi\)
\(938\) −20.0337 16.8103i −0.654123 0.548874i
\(939\) 0 0
\(940\) −1.42803 8.09875i −0.0465771 0.264152i
\(941\) −6.35391 + 5.33156i −0.207132 + 0.173804i −0.740452 0.672109i \(-0.765388\pi\)
0.533320 + 0.845913i \(0.320944\pi\)
\(942\) 0 0
\(943\) 6.45069 2.34786i 0.210063 0.0764568i
\(944\) −4.31074 −0.140303
\(945\) 0 0
\(946\) −5.72199 −0.186038
\(947\) −41.7699 + 15.2030i −1.35734 + 0.494031i −0.915231 0.402930i \(-0.867992\pi\)
−0.442109 + 0.896961i \(0.645770\pi\)
\(948\) 0 0
\(949\) 18.5429 15.5593i 0.601928 0.505077i
\(950\) 0.0890526 + 0.505043i 0.00288925 + 0.0163857i
\(951\) 0 0
\(952\) 38.1351 + 31.9991i 1.23596 + 1.03710i
\(953\) −4.83574 + 8.37576i −0.156645 + 0.271317i −0.933657 0.358169i \(-0.883401\pi\)
0.777012 + 0.629486i \(0.216735\pi\)
\(954\) 0 0
\(955\) −23.5385 40.7699i −0.761688 1.31928i
\(956\) −0.813657 + 4.61448i −0.0263155 + 0.149243i
\(957\) 0 0
\(958\) 28.9826 + 10.5488i 0.936384 + 0.340816i
\(959\) 5.21842 + 1.89935i 0.168511 + 0.0613332i
\(960\) 0 0
\(961\) −5.26633 + 29.8668i −0.169882 + 0.963447i
\(962\) −6.25433 10.8328i −0.201648 0.349264i
\(963\) 0 0
\(964\) −3.95448 + 6.84936i −0.127365 + 0.220603i
\(965\) −22.9420 19.2506i −0.738529 0.619699i
\(966\) 0 0
\(967\) −5.75037 32.6120i −0.184920 1.04873i −0.926059 0.377379i \(-0.876825\pi\)
0.741139 0.671351i \(-0.234286\pi\)
\(968\) −21.9916 + 18.4531i −0.706837 + 0.593106i
\(969\) 0 0
\(970\) 9.49663 3.45649i 0.304918 0.110981i
\(971\) 27.4309 0.880298 0.440149 0.897925i \(-0.354926\pi\)
0.440149 + 0.897925i \(0.354926\pi\)
\(972\) 0 0
\(973\) −19.6127 −0.628755
\(974\) −20.3158 + 7.39434i −0.650960 + 0.236930i
\(975\) 0 0
\(976\) −3.16707 + 2.65749i −0.101376 + 0.0850642i
\(977\) −6.31690 35.8249i −0.202096 1.14614i −0.901945 0.431850i \(-0.857861\pi\)
0.699850 0.714290i \(-0.253250\pi\)
\(978\) 0 0
\(979\) −6.44087 5.40453i −0.205851 0.172730i
\(980\) −0.738337 + 1.27884i −0.0235853 + 0.0408510i
\(981\) 0 0
\(982\) −9.23957 16.0034i −0.294847 0.510689i
\(983\) −7.31705 + 41.4971i −0.233378 + 1.32355i 0.612626 + 0.790373i \(0.290113\pi\)
−0.846003 + 0.533177i \(0.820998\pi\)
\(984\) 0 0
\(985\) 4.12135 + 1.50005i 0.131317 + 0.0477955i
\(986\) 3.37436 + 1.22817i 0.107462 + 0.0391128i
\(987\) 0 0
\(988\) 0.174851 0.991631i 0.00556276 0.0315480i
\(989\) 1.82173 + 3.15533i 0.0579276 + 0.100334i
\(990\) 0 0
\(991\) −12.7705 + 22.1191i −0.405667 + 0.702635i −0.994399 0.105693i \(-0.966294\pi\)
0.588732 + 0.808328i \(0.299627\pi\)
\(992\) 2.87620 + 2.41342i 0.0913194 + 0.0766261i
\(993\) 0 0
\(994\) 0.0402858 + 0.228472i 0.00127779 + 0.00724669i
\(995\) 24.7929 20.8037i 0.785989 0.659523i
\(996\) 0 0
\(997\) −22.1137 + 8.04872i −0.700347 + 0.254905i −0.667559 0.744557i \(-0.732661\pi\)
−0.0327879 + 0.999462i \(0.510439\pi\)
\(998\) 20.1439 0.637644
\(999\) 0 0
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 243.2.e.a.55.2 12
3.2 odd 2 243.2.e.d.55.1 12
9.2 odd 6 243.2.e.c.136.2 12
9.4 even 3 81.2.e.a.73.1 12
9.5 odd 6 27.2.e.a.25.2 yes 12
9.7 even 3 243.2.e.b.136.1 12
27.2 odd 18 729.2.a.a.1.5 6
27.4 even 9 inner 243.2.e.a.190.2 12
27.5 odd 18 27.2.e.a.13.2 12
27.7 even 9 729.2.c.b.487.5 12
27.11 odd 18 729.2.c.e.244.2 12
27.13 even 9 243.2.e.b.109.1 12
27.14 odd 18 243.2.e.c.109.2 12
27.16 even 9 729.2.c.b.244.5 12
27.20 odd 18 729.2.c.e.487.2 12
27.22 even 9 81.2.e.a.10.1 12
27.23 odd 18 243.2.e.d.190.1 12
27.25 even 9 729.2.a.d.1.2 6
36.23 even 6 432.2.u.c.241.2 12
45.14 odd 6 675.2.l.c.376.1 12
45.23 even 12 675.2.u.b.349.2 24
45.32 even 12 675.2.u.b.349.3 24
108.59 even 18 432.2.u.c.337.2 12
135.32 even 36 675.2.u.b.499.2 24
135.59 odd 18 675.2.l.c.526.1 12
135.113 even 36 675.2.u.b.499.3 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
27.2.e.a.13.2 12 27.5 odd 18
27.2.e.a.25.2 yes 12 9.5 odd 6
81.2.e.a.10.1 12 27.22 even 9
81.2.e.a.73.1 12 9.4 even 3
243.2.e.a.55.2 12 1.1 even 1 trivial
243.2.e.a.190.2 12 27.4 even 9 inner
243.2.e.b.109.1 12 27.13 even 9
243.2.e.b.136.1 12 9.7 even 3
243.2.e.c.109.2 12 27.14 odd 18
243.2.e.c.136.2 12 9.2 odd 6
243.2.e.d.55.1 12 3.2 odd 2
243.2.e.d.190.1 12 27.23 odd 18
432.2.u.c.241.2 12 36.23 even 6
432.2.u.c.337.2 12 108.59 even 18
675.2.l.c.376.1 12 45.14 odd 6
675.2.l.c.526.1 12 135.59 odd 18
675.2.u.b.349.2 24 45.23 even 12
675.2.u.b.349.3 24 45.32 even 12
675.2.u.b.499.2 24 135.32 even 36
675.2.u.b.499.3 24 135.113 even 36
729.2.a.a.1.5 6 27.2 odd 18
729.2.a.d.1.2 6 27.25 even 9
729.2.c.b.244.5 12 27.16 even 9
729.2.c.b.487.5 12 27.7 even 9
729.2.c.e.244.2 12 27.11 odd 18
729.2.c.e.487.2 12 27.20 odd 18