Properties

Label 243.2.e.d.55.1
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: \( x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} - 258 x^{3} + 108 x^{2} - 27 x + 3 \) 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 55.1
Root \(0.500000 - 1.68614i\) of defining polynomial
Character \(\chi\) \(=\) 243.55
Dual form 243.2.e.d.190.1

$q$-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 −0.667650 0.744475i \(-0.732700\pi\)
−0.0329100 + 0.999458i \(0.510477\pi\)
\(3\) 0 0
\(4\) −0.680553 + 0.571052i −0.340277 + 0.285526i
\(5\) −0.303153 1.71926i −0.135574 0.768879i −0.974458 0.224569i \(-0.927903\pi\)
0.838884 0.544310i \(-0.183208\pi\)
\(6\) 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 \(0.116106\pi\)
−0.999877 + 0.0156913i \(0.995005\pi\)
\(12\) 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 \(0.131752\pi\)
−0.109467 + 0.993990i \(0.534914\pi\)
\(18\) 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 −0.573059 0.819514i \(-0.694243\pi\)
0.707553 + 0.706660i \(0.249799\pi\)
\(24\) 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 \(-0.595962\pi\)
0.386337 + 0.922358i \(0.373740\pi\)
\(30\) 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 0.861991 0.506924i \(-0.169218\pi\)
0.334478 + 0.942403i \(0.391440\pi\)
\(42\) 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 0.296540 0.955020i \(-0.404167\pi\)
−0.889018 + 0.457872i \(0.848612\pi\)
\(48\) 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 \(-0.755882\pi\)
−0.720052 + 0.693920i \(0.755882\pi\)
\(54\) 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 \(-0.992862\pi\)
0.931787 0.363005i \(-0.118249\pi\)
\(60\) 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 0.863358 0.504591i \(-0.168357\pi\)
−0.868668 + 0.495395i \(0.835023\pi\)
\(72\) 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 −0.721593 0.692318i \(-0.756590\pi\)
−0.107759 + 0.994177i \(0.534367\pi\)
\(84\) 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 \(-0.948954\pi\)
0.631870 + 0.775074i \(0.282288\pi\)
\(90\) 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 0.813306 0.581836i \(-0.197666\pi\)
−0.431768 + 0.901985i \(0.642110\pi\)
\(102\) 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 \(-0.110316\pi\)
0.940544 + 0.339673i \(0.110316\pi\)
\(108\) 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 \(-0.950094\pi\)
0.874763 0.484551i \(-0.161017\pi\)
\(114\) 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 −0.978051 0.208364i \(-0.933186\pi\)
0.0353614 + 0.999375i \(0.488742\pi\)
\(132\) 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 \(-0.641864\pi\)
0.249780 + 0.968303i \(0.419642\pi\)
\(138\) 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 0.346133 0.938185i \(-0.387495\pi\)
−0.337901 + 0.941182i \(0.609717\pi\)
\(150\) 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 \(-0.776555\pi\)
0.496671 0.867939i \(-0.334556\pi\)
\(168\) 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 \(-0.688850\pi\)
0.808945 0.587884i \(-0.200039\pi\)
\(174\) 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 \(-0.300392\pi\)
−0.994650 + 0.103302i \(0.967059\pi\)
\(180\) 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 \(-0.181575\pi\)
0.991858 0.127350i \(-0.0406471\pi\)
\(192\) 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 −0.907298 0.420489i \(-0.861859\pi\)
0.817803 + 0.575499i \(0.195192\pi\)
\(198\) 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 \(0.213430\pi\)
−0.948780 + 0.315937i \(0.897681\pi\)
\(228\) 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 0.759626 0.650361i \(-0.225382\pi\)
−0.943042 + 0.332675i \(0.892049\pi\)
\(234\) 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 \(-0.776787\pi\)
0.502693 + 0.864465i \(0.332343\pi\)
\(240\) 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 −0.716742 0.697338i \(-0.754368\pi\)
0.962284 + 0.272048i \(0.0877010\pi\)
\(252\) 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 \(-0.168899\pi\)
0.335420 + 0.942069i \(0.391122\pi\)
\(258\) 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 \(-0.164716\pi\)
−0.336256 + 0.941771i \(0.609161\pi\)
\(264\) 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 \(-0.502987\pi\)
−0.00938226 + 0.999956i \(0.502987\pi\)
\(270\) 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 \(-0.875301\pi\)
0.999089 0.0426756i \(-0.0135882\pi\)
\(282\) 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 −0.630341 0.776318i \(-0.717085\pi\)
0.655067 + 0.755571i \(0.272641\pi\)
\(294\) 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 −0.103335 0.994647i \(-0.532951\pi\)
−0.718505 + 0.695521i \(0.755173\pi\)
\(312\) 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 0.785327 0.619081i \(-0.212495\pi\)
−0.473305 + 0.880898i \(0.656939\pi\)
\(318\) 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 −0.513602 0.858029i \(-0.671689\pi\)
0.755807 + 0.654794i \(0.227245\pi\)
\(348\) 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 \(0.831206\pi\)
−0.985947 + 0.167061i \(0.946572\pi\)
\(354\) 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 \(-0.588278\pi\)
0.969830 0.243783i \(-0.0783886\pi\)
\(360\) 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 0.963186 0.268835i \(-0.0866387\pi\)
−0.997046 + 0.0768065i \(0.975528\pi\)
\(384\) 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 \(-0.855816\pi\)
0.994607 0.103716i \(-0.0330732\pi\)
\(390\) 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 −0.325241 0.945631i \(-0.605445\pi\)
0.874788 + 0.484507i \(0.161001\pi\)
\(402\) 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 0.123747 0.992314i \(-0.460509\pi\)
−0.543051 + 0.839700i \(0.682731\pi\)
\(420\) 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 \(-0.751885\pi\)
−0.711282 + 0.702907i \(0.751885\pi\)
\(432\) 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 \(-0.825601\pi\)
0.980299 0.197517i \(-0.0632878\pi\)
\(444\) 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 \(0.106195\pi\)
−0.188836 + 0.982009i \(0.560471\pi\)
\(450\) 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 −0.225248 0.974301i \(-0.572319\pi\)
0.453719 + 0.891145i \(0.350097\pi\)
\(462\) 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 −0.998711 0.0507511i \(-0.983838\pi\)
0.543307 + 0.839534i \(0.317172\pi\)
\(468\) 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 \(-0.510760\pi\)
−0.990114 + 0.140264i \(0.955205\pi\)
\(480\) 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 \(0.0738700\pi\)
−0.835840 + 0.548973i \(0.815019\pi\)
\(492\) 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 0.961994 0.273070i \(-0.0880392\pi\)
−0.717483 + 0.696576i \(0.754706\pi\)
\(504\) 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 \(-0.867603\pi\)
0.239068 + 0.971003i \(0.423158\pi\)
\(510\) 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 \(0.446034\pi\)
−0.937973 + 0.346708i \(0.887300\pi\)
\(522\) 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 \(-0.939513\pi\)
0.327422 0.944878i \(-0.393820\pi\)
\(558\) 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 \(-0.531393\pi\)
0.962924 + 0.269773i \(0.0869486\pi\)
\(564\) 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 \(-0.741938\pi\)
−0.0619006 + 0.998082i \(0.519716\pi\)
\(570\) 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 −0.0453217 0.998972i \(-0.514431\pi\)
−0.991666 + 0.128837i \(0.958876\pi\)
\(588\) 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 \(-0.384096\pi\)
0.356129 + 0.934437i \(0.384096\pi\)
\(594\) 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 \(0.110612\pi\)
−0.767052 + 0.641584i \(0.778277\pi\)
\(600\) 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 0.0549420 0.998490i \(-0.482503\pi\)
0.992861 + 0.119279i \(0.0380582\pi\)
\(618\) 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 0.0185622 0.999828i \(-0.494091\pi\)
−0.981415 + 0.191898i \(0.938536\pi\)
\(642\) 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 \(-0.312642\pi\)
0.555200 + 0.831717i \(0.312642\pi\)
\(648\) 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 \(0.114260\pi\)
−0.759648 + 0.650335i \(0.774629\pi\)
\(654\) 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 \(0.433571\pi\)
−0.529286 + 0.848443i \(0.677540\pi\)
\(660\) 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 −0.0821842 0.996617i \(-0.526190\pi\)
0.577656 + 0.816280i \(0.303967\pi\)
\(678\) 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 \(0.572306\pi\)
−0.731175 + 0.682190i \(0.761028\pi\)
\(684\) 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 \(-0.274532\pi\)
0.650565 + 0.759450i \(0.274532\pi\)
\(702\) 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 0.731485 0.681858i \(-0.238828\pi\)
−0.956249 + 0.292555i \(0.905494\pi\)
\(720\) 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 0.844834 0.535028i \(-0.179699\pi\)
0.303271 + 0.952904i \(0.401921\pi\)
\(744\) 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 \(-0.762101\pi\)
0.456760 0.889590i \(-0.349010\pi\)
\(762\) 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 0.935334 0.353766i \(-0.115099\pi\)
−0.774037 + 0.633140i \(0.781766\pi\)
\(774\) 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 0.134205 0.990954i \(-0.457152\pi\)
−0.534166 + 0.845380i \(0.679374\pi\)
\(798\) 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 \(-0.545080\pi\)
−0.141149 + 0.989988i \(0.545080\pi\)
\(810\) 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 \(0.228754\pi\)
−0.932477 + 0.361230i \(0.882357\pi\)
\(822\) 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 \(-0.915305\pi\)
0.254683 0.967025i \(-0.418029\pi\)
\(828\) 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 −0.134934 0.990855i \(-0.543082\pi\)
0.533543 + 0.845773i \(0.320860\pi\)
\(840\) 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 0.776865 0.629667i \(-0.216809\pi\)
−0.485200 + 0.874403i \(0.661253\pi\)
\(858\) 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 \(-0.797439\pi\)
−0.804262 + 0.594275i \(0.797439\pi\)
\(864\) 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 0.981739 0.190235i \(-0.0609250\pi\)
−0.655618 + 0.755093i \(0.727592\pi\)
\(882\) 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 −0.939924 0.341384i \(-0.889104\pi\)
0.172981 + 0.984925i \(0.444660\pi\)
\(888\) 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 0.145914 0.989297i \(-0.453388\pi\)
−0.948930 + 0.315487i \(0.897832\pi\)
\(912\) 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 \(-0.807366\pi\)
0.967382 0.253321i \(-0.0815228\pi\)
\(930\) 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 −0.533320 0.845913i \(-0.679056\pi\)
0.740452 + 0.672109i \(0.234612\pi\)
\(942\) 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 0.442109 0.896961i \(-0.354230\pi\)
0.915231 + 0.402930i \(0.132008\pi\)
\(948\) 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 −0.777012 0.629486i \(-0.783265\pi\)
0.933657 + 0.358169i \(0.116599\pi\)
\(954\) 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 \(-0.645074\pi\)
−0.440149 + 0.897925i \(0.645074\pi\)
\(972\) 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 \(0.142139\pi\)
−0.699850 + 0.714290i \(0.746750\pi\)
\(978\) 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 \(-0.709887\pi\)
0.846003 0.533177i \(-0.179002\pi\)
\(984\) 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.d.55.1 12
3.2 odd 2 243.2.e.a.55.2 12
9.2 odd 6 243.2.e.b.136.1 12
9.4 even 3 27.2.e.a.25.2 yes 12
9.5 odd 6 81.2.e.a.73.1 12
9.7 even 3 243.2.e.c.136.2 12
27.2 odd 18 729.2.a.d.1.2 6
27.4 even 9 inner 243.2.e.d.190.1 12
27.5 odd 18 81.2.e.a.10.1 12
27.7 even 9 729.2.c.e.487.2 12
27.11 odd 18 729.2.c.b.244.5 12
27.13 even 9 243.2.e.c.109.2 12
27.14 odd 18 243.2.e.b.109.1 12
27.16 even 9 729.2.c.e.244.2 12
27.20 odd 18 729.2.c.b.487.5 12
27.22 even 9 27.2.e.a.13.2 12
27.23 odd 18 243.2.e.a.190.2 12
27.25 even 9 729.2.a.a.1.5 6
36.31 odd 6 432.2.u.c.241.2 12
45.4 even 6 675.2.l.c.376.1 12
45.13 odd 12 675.2.u.b.349.2 24
45.22 odd 12 675.2.u.b.349.3 24
108.103 odd 18 432.2.u.c.337.2 12
135.22 odd 36 675.2.u.b.499.2 24
135.49 even 18 675.2.l.c.526.1 12
135.103 odd 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 27.22 even 9
27.2.e.a.25.2 yes 12 9.4 even 3
81.2.e.a.10.1 12 27.5 odd 18
81.2.e.a.73.1 12 9.5 odd 6
243.2.e.a.55.2 12 3.2 odd 2
243.2.e.a.190.2 12 27.23 odd 18
243.2.e.b.109.1 12 27.14 odd 18
243.2.e.b.136.1 12 9.2 odd 6
243.2.e.c.109.2 12 27.13 even 9
243.2.e.c.136.2 12 9.7 even 3
243.2.e.d.55.1 12 1.1 even 1 trivial
243.2.e.d.190.1 12 27.4 even 9 inner
432.2.u.c.241.2 12 36.31 odd 6
432.2.u.c.337.2 12 108.103 odd 18
675.2.l.c.376.1 12 45.4 even 6
675.2.l.c.526.1 12 135.49 even 18
675.2.u.b.349.2 24 45.13 odd 12
675.2.u.b.349.3 24 45.22 odd 12
675.2.u.b.499.2 24 135.22 odd 36
675.2.u.b.499.3 24 135.103 odd 36
729.2.a.a.1.5 6 27.25 even 9
729.2.a.d.1.2 6 27.2 odd 18
729.2.c.b.244.5 12 27.11 odd 18
729.2.c.b.487.5 12 27.20 odd 18
729.2.c.e.244.2 12 27.16 even 9
729.2.c.e.487.2 12 27.7 even 9