Properties

Label 729.2.e.t.163.2
Level $729$
Weight $2$
Character 729.163
Analytic conductor $5.821$
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] = [729,2,Mod(82,729)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(729, 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("729.82");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 729 = 3^{6} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 729.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: \(5.82109430735\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(2\) over \(\Q(\zeta_{9})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} + 18x^{10} + 105x^{8} + 266x^{6} + 306x^{4} + 132x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 163.2
Root \(-1.37340i\) of defining polynomial
Character \(\chi\) \(=\) 729.163
Dual form 729.2.e.t.568.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.54193 - 0.925187i) q^{2} +(4.07335 - 3.41794i) q^{4} +(0.290407 + 1.64698i) q^{5} +(0.383475 + 0.321774i) q^{7} +(4.48686 - 7.77147i) q^{8} +O(q^{10})\) \(q+(2.54193 - 0.925187i) q^{2} +(4.07335 - 3.41794i) q^{4} +(0.290407 + 1.64698i) q^{5} +(0.383475 + 0.321774i) q^{7} +(4.48686 - 7.77147i) q^{8} +(2.26195 + 3.91782i) q^{10} +(0.333008 - 1.88858i) q^{11} +(-2.92473 - 1.06452i) q^{13} +(1.27247 + 0.463140i) q^{14} +(2.36851 - 13.4325i) q^{16} +(1.33234 + 2.30767i) q^{17} +(-2.89832 + 5.02003i) q^{19} +(6.81220 + 5.71612i) q^{20} +(-0.900809 - 5.10874i) q^{22} +(3.55894 - 2.98631i) q^{23} +(2.07026 - 0.753515i) q^{25} -8.41934 q^{26} +2.66183 q^{28} +(-2.45736 + 0.894407i) q^{29} +(-3.53499 + 2.96621i) q^{31} +(-3.29045 - 18.6611i) q^{32} +(5.52173 + 4.63328i) q^{34} +(-0.418591 + 0.725020i) q^{35} +(2.42934 + 4.20773i) q^{37} +(-2.72285 + 15.4421i) q^{38} +(14.1024 + 5.13287i) q^{40} +(-10.8517 - 3.94970i) q^{41} +(-1.56359 + 8.86754i) q^{43} +(-5.09861 - 8.83106i) q^{44} +(6.28369 - 10.8837i) q^{46} +(-5.23380 - 4.39168i) q^{47} +(-1.17202 - 6.64687i) q^{49} +(4.56532 - 3.83076i) q^{50} +(-15.5519 + 5.66043i) q^{52} +5.43322 q^{53} +3.20716 q^{55} +(4.22125 - 1.53641i) q^{56} +(-5.41895 + 4.54704i) q^{58} +(0.380517 + 2.15802i) q^{59} +(5.24000 + 4.39688i) q^{61} +(-6.24140 + 10.8104i) q^{62} +(-11.9893 - 20.7661i) q^{64} +(0.903872 - 5.12611i) q^{65} +(-11.7307 - 4.26964i) q^{67} +(13.3146 + 4.84610i) q^{68} +(-0.393249 + 2.23022i) q^{70} +(-1.41784 - 2.45578i) q^{71} +(-4.96749 + 8.60394i) q^{73} +(10.0681 + 8.44817i) q^{74} +(5.35234 + 30.3546i) q^{76} +(0.735397 - 0.617071i) q^{77} +(-4.99091 + 1.81654i) q^{79} +22.8109 q^{80} -31.2385 q^{82} +(-2.56362 + 0.933082i) q^{83} +(-3.41377 + 2.86449i) q^{85} +(4.22960 + 23.9873i) q^{86} +(-13.1829 - 11.0618i) q^{88} +(5.60945 - 9.71585i) q^{89} +(-0.779029 - 1.34932i) q^{91} +(4.28977 - 24.3285i) q^{92} +(-17.3671 - 6.32110i) q^{94} +(-9.10957 - 3.31561i) q^{95} +(-1.19629 + 6.78448i) q^{97} +(-9.12879 - 15.8115i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 3 q^{2} - 3 q^{4} + 6 q^{5} + 6 q^{7} + 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 3 q^{2} - 3 q^{4} + 6 q^{5} + 6 q^{7} + 6 q^{8} - 6 q^{10} - 15 q^{11} - 3 q^{13} - 21 q^{14} + 9 q^{16} - 9 q^{17} - 12 q^{19} - 3 q^{20} + 33 q^{22} + 15 q^{23} - 12 q^{25} - 48 q^{26} + 6 q^{28} - 6 q^{29} - 12 q^{31} - 27 q^{32} + 27 q^{34} + 30 q^{35} - 3 q^{37} - 39 q^{38} + 24 q^{40} - 39 q^{41} + 24 q^{43} - 33 q^{44} + 3 q^{46} - 42 q^{47} - 30 q^{49} - 15 q^{50} - 45 q^{52} + 18 q^{53} + 30 q^{55} + 12 q^{56} - 30 q^{58} + 15 q^{59} - 3 q^{61} - 30 q^{62} - 6 q^{64} - 6 q^{65} - 3 q^{67} + 36 q^{68} - 75 q^{70} - 12 q^{73} + 60 q^{74} + 30 q^{76} + 33 q^{77} + 33 q^{79} + 42 q^{80} - 42 q^{82} - 33 q^{83} - 18 q^{85} - 30 q^{86} - 42 q^{88} - 9 q^{89} - 18 q^{91} + 33 q^{92} - 66 q^{94} + 12 q^{95} + 15 q^{97} + 18 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/729\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.54193 0.925187i 1.79742 0.654206i 0.798800 0.601596i \(-0.205468\pi\)
0.998615 0.0526096i \(-0.0167539\pi\)
\(3\) 0 0
\(4\) 4.07335 3.41794i 2.03667 1.70897i
\(5\) 0.290407 + 1.64698i 0.129874 + 0.736551i 0.978293 + 0.207226i \(0.0664436\pi\)
−0.848419 + 0.529325i \(0.822445\pi\)
\(6\) 0 0
\(7\) 0.383475 + 0.321774i 0.144940 + 0.121619i 0.712375 0.701799i \(-0.247620\pi\)
−0.567435 + 0.823418i \(0.692064\pi\)
\(8\) 4.48686 7.77147i 1.58634 2.74763i
\(9\) 0 0
\(10\) 2.26195 + 3.91782i 0.715293 + 1.23892i
\(11\) 0.333008 1.88858i 0.100406 0.569429i −0.892550 0.450948i \(-0.851086\pi\)
0.992956 0.118482i \(-0.0378027\pi\)
\(12\) 0 0
\(13\) −2.92473 1.06452i −0.811175 0.295243i −0.0970658 0.995278i \(-0.530946\pi\)
−0.714109 + 0.700034i \(0.753168\pi\)
\(14\) 1.27247 + 0.463140i 0.340081 + 0.123779i
\(15\) 0 0
\(16\) 2.36851 13.4325i 0.592129 3.35813i
\(17\) 1.33234 + 2.30767i 0.323139 + 0.559693i 0.981134 0.193329i \(-0.0619285\pi\)
−0.657995 + 0.753022i \(0.728595\pi\)
\(18\) 0 0
\(19\) −2.89832 + 5.02003i −0.664920 + 1.15167i 0.314387 + 0.949295i \(0.398201\pi\)
−0.979307 + 0.202380i \(0.935132\pi\)
\(20\) 6.81220 + 5.71612i 1.52325 + 1.27816i
\(21\) 0 0
\(22\) −0.900809 5.10874i −0.192053 1.08919i
\(23\) 3.55894 2.98631i 0.742091 0.622688i −0.191308 0.981530i \(-0.561273\pi\)
0.933398 + 0.358842i \(0.116828\pi\)
\(24\) 0 0
\(25\) 2.07026 0.753515i 0.414053 0.150703i
\(26\) −8.41934 −1.65117
\(27\) 0 0
\(28\) 2.66183 0.503039
\(29\) −2.45736 + 0.894407i −0.456321 + 0.166087i −0.559946 0.828529i \(-0.689178\pi\)
0.103625 + 0.994616i \(0.466956\pi\)
\(30\) 0 0
\(31\) −3.53499 + 2.96621i −0.634903 + 0.532747i −0.902448 0.430798i \(-0.858232\pi\)
0.267545 + 0.963545i \(0.413788\pi\)
\(32\) −3.29045 18.6611i −0.581674 3.29884i
\(33\) 0 0
\(34\) 5.52173 + 4.63328i 0.946969 + 0.794602i
\(35\) −0.418591 + 0.725020i −0.0707547 + 0.122551i
\(36\) 0 0
\(37\) 2.42934 + 4.20773i 0.399381 + 0.691747i 0.993650 0.112519i \(-0.0358919\pi\)
−0.594269 + 0.804266i \(0.702559\pi\)
\(38\) −2.72285 + 15.4421i −0.441705 + 2.50503i
\(39\) 0 0
\(40\) 14.1024 + 5.13287i 2.22979 + 0.811578i
\(41\) −10.8517 3.94970i −1.69475 0.616840i −0.699543 0.714590i \(-0.746613\pi\)
−0.995211 + 0.0977502i \(0.968835\pi\)
\(42\) 0 0
\(43\) −1.56359 + 8.86754i −0.238445 + 1.35229i 0.596792 + 0.802396i \(0.296442\pi\)
−0.835236 + 0.549891i \(0.814669\pi\)
\(44\) −5.09861 8.83106i −0.768645 1.33133i
\(45\) 0 0
\(46\) 6.28369 10.8837i 0.926479 1.60471i
\(47\) −5.23380 4.39168i −0.763428 0.640592i 0.175589 0.984464i \(-0.443817\pi\)
−0.939017 + 0.343872i \(0.888262\pi\)
\(48\) 0 0
\(49\) −1.17202 6.64687i −0.167432 0.949553i
\(50\) 4.56532 3.83076i 0.645634 0.541752i
\(51\) 0 0
\(52\) −15.5519 + 5.66043i −2.15666 + 0.784960i
\(53\) 5.43322 0.746309 0.373155 0.927769i \(-0.378276\pi\)
0.373155 + 0.927769i \(0.378276\pi\)
\(54\) 0 0
\(55\) 3.20716 0.432454
\(56\) 4.22125 1.53641i 0.564089 0.205311i
\(57\) 0 0
\(58\) −5.41895 + 4.54704i −0.711543 + 0.597055i
\(59\) 0.380517 + 2.15802i 0.0495392 + 0.280950i 0.999507 0.0313973i \(-0.00999570\pi\)
−0.949968 + 0.312348i \(0.898885\pi\)
\(60\) 0 0
\(61\) 5.24000 + 4.39688i 0.670914 + 0.562963i 0.913336 0.407208i \(-0.133497\pi\)
−0.242422 + 0.970171i \(0.577942\pi\)
\(62\) −6.24140 + 10.8104i −0.792659 + 1.37293i
\(63\) 0 0
\(64\) −11.9893 20.7661i −1.49866 2.59576i
\(65\) 0.903872 5.12611i 0.112111 0.635816i
\(66\) 0 0
\(67\) −11.7307 4.26964i −1.43314 0.521620i −0.495309 0.868717i \(-0.664945\pi\)
−0.937829 + 0.347097i \(0.887167\pi\)
\(68\) 13.3146 + 4.84610i 1.61463 + 0.587677i
\(69\) 0 0
\(70\) −0.393249 + 2.23022i −0.0470022 + 0.266563i
\(71\) −1.41784 2.45578i −0.168267 0.291447i 0.769544 0.638594i \(-0.220484\pi\)
−0.937811 + 0.347147i \(0.887150\pi\)
\(72\) 0 0
\(73\) −4.96749 + 8.60394i −0.581400 + 1.00701i 0.413913 + 0.910316i \(0.364162\pi\)
−0.995314 + 0.0966986i \(0.969172\pi\)
\(74\) 10.0681 + 8.44817i 1.17040 + 0.982080i
\(75\) 0 0
\(76\) 5.35234 + 30.3546i 0.613955 + 3.48191i
\(77\) 0.735397 0.617071i 0.0838063 0.0703218i
\(78\) 0 0
\(79\) −4.99091 + 1.81654i −0.561521 + 0.204377i −0.607158 0.794581i \(-0.707690\pi\)
0.0456370 + 0.998958i \(0.485468\pi\)
\(80\) 22.8109 2.55033
\(81\) 0 0
\(82\) −31.2385 −3.44972
\(83\) −2.56362 + 0.933082i −0.281394 + 0.102419i −0.478862 0.877890i \(-0.658950\pi\)
0.197468 + 0.980309i \(0.436728\pi\)
\(84\) 0 0
\(85\) −3.41377 + 2.86449i −0.370275 + 0.310698i
\(86\) 4.22960 + 23.9873i 0.456090 + 2.58661i
\(87\) 0 0
\(88\) −13.1829 11.0618i −1.40530 1.17919i
\(89\) 5.60945 9.71585i 0.594600 1.02988i −0.399003 0.916950i \(-0.630644\pi\)
0.993603 0.112928i \(-0.0360230\pi\)
\(90\) 0 0
\(91\) −0.779029 1.34932i −0.0816644 0.141447i
\(92\) 4.28977 24.3285i 0.447240 2.53642i
\(93\) 0 0
\(94\) −17.3671 6.32110i −1.79128 0.651971i
\(95\) −9.10957 3.31561i −0.934623 0.340175i
\(96\) 0 0
\(97\) −1.19629 + 6.78448i −0.121465 + 0.688860i 0.861881 + 0.507111i \(0.169287\pi\)
−0.983345 + 0.181748i \(0.941824\pi\)
\(98\) −9.12879 15.8115i −0.922147 1.59721i
\(99\) 0 0
\(100\) 5.85743 10.1454i 0.585743 1.01454i
\(101\) −2.85708 2.39737i −0.284290 0.238547i 0.489480 0.872015i \(-0.337187\pi\)
−0.773769 + 0.633467i \(0.781631\pi\)
\(102\) 0 0
\(103\) 1.33376 + 7.56411i 0.131419 + 0.745314i 0.977287 + 0.211921i \(0.0679720\pi\)
−0.845868 + 0.533393i \(0.820917\pi\)
\(104\) −21.3957 + 17.9531i −2.09802 + 1.76045i
\(105\) 0 0
\(106\) 13.8108 5.02674i 1.34143 0.488240i
\(107\) 10.7658 1.04077 0.520383 0.853933i \(-0.325789\pi\)
0.520383 + 0.853933i \(0.325789\pi\)
\(108\) 0 0
\(109\) 12.2298 1.17141 0.585703 0.810526i \(-0.300819\pi\)
0.585703 + 0.810526i \(0.300819\pi\)
\(110\) 8.15238 2.96722i 0.777299 0.282914i
\(111\) 0 0
\(112\) 5.23050 4.38891i 0.494236 0.414713i
\(113\) 0.337563 + 1.91442i 0.0317553 + 0.180093i 0.996560 0.0828742i \(-0.0264100\pi\)
−0.964805 + 0.262967i \(0.915299\pi\)
\(114\) 0 0
\(115\) 5.95192 + 4.99425i 0.555019 + 0.465717i
\(116\) −6.95266 + 12.0424i −0.645538 + 1.11810i
\(117\) 0 0
\(118\) 2.96382 + 5.13349i 0.272842 + 0.472576i
\(119\) −0.231631 + 1.31365i −0.0212336 + 0.120422i
\(120\) 0 0
\(121\) 6.88076 + 2.50439i 0.625524 + 0.227672i
\(122\) 17.3877 + 6.32859i 1.57420 + 0.572963i
\(123\) 0 0
\(124\) −4.26091 + 24.1648i −0.382641 + 2.17006i
\(125\) 6.02320 + 10.4325i 0.538732 + 0.933110i
\(126\) 0 0
\(127\) −1.17217 + 2.03025i −0.104013 + 0.180156i −0.913335 0.407210i \(-0.866502\pi\)
0.809322 + 0.587366i \(0.199835\pi\)
\(128\) −20.6570 17.3333i −1.82584 1.53206i
\(129\) 0 0
\(130\) −2.44503 13.8665i −0.214443 1.21617i
\(131\) 13.1012 10.9932i 1.14466 0.960480i 0.145075 0.989421i \(-0.453658\pi\)
0.999581 + 0.0289402i \(0.00921323\pi\)
\(132\) 0 0
\(133\) −2.72675 + 0.992455i −0.236439 + 0.0860568i
\(134\) −33.7689 −2.91719
\(135\) 0 0
\(136\) 23.9120 2.05044
\(137\) 13.0872 4.76337i 1.11812 0.406962i 0.284154 0.958779i \(-0.408287\pi\)
0.833965 + 0.551817i \(0.186065\pi\)
\(138\) 0 0
\(139\) 6.06450 5.08872i 0.514384 0.431619i −0.348285 0.937389i \(-0.613236\pi\)
0.862669 + 0.505770i \(0.168791\pi\)
\(140\) 0.773013 + 4.38398i 0.0653315 + 0.370514i
\(141\) 0 0
\(142\) −5.87611 4.93064i −0.493112 0.413770i
\(143\) −2.98439 + 5.16911i −0.249567 + 0.432263i
\(144\) 0 0
\(145\) −2.18670 3.78748i −0.181596 0.314533i
\(146\) −4.66675 + 26.4665i −0.386223 + 2.19038i
\(147\) 0 0
\(148\) 24.2773 + 8.83622i 1.99558 + 0.726333i
\(149\) 0.684223 + 0.249037i 0.0560537 + 0.0204019i 0.369895 0.929074i \(-0.379394\pi\)
−0.313841 + 0.949476i \(0.601616\pi\)
\(150\) 0 0
\(151\) 0.753996 4.27612i 0.0613593 0.347986i −0.938636 0.344910i \(-0.887910\pi\)
0.999995 0.00307656i \(-0.000979301\pi\)
\(152\) 26.0087 + 45.0484i 2.10958 + 3.65390i
\(153\) 0 0
\(154\) 1.29842 2.24893i 0.104630 0.181224i
\(155\) −5.91187 4.96064i −0.474852 0.398449i
\(156\) 0 0
\(157\) −2.69559 15.2874i −0.215131 1.22007i −0.880679 0.473714i \(-0.842913\pi\)
0.665547 0.746356i \(-0.268198\pi\)
\(158\) −11.0059 + 9.23504i −0.875582 + 0.734700i
\(159\) 0 0
\(160\) 29.7788 10.8386i 2.35422 0.856865i
\(161\) 2.32568 0.183289
\(162\) 0 0
\(163\) 8.49738 0.665566 0.332783 0.943003i \(-0.392012\pi\)
0.332783 + 0.943003i \(0.392012\pi\)
\(164\) −57.7027 + 21.0021i −4.50582 + 1.63999i
\(165\) 0 0
\(166\) −5.65327 + 4.74366i −0.438779 + 0.368179i
\(167\) −4.01856 22.7904i −0.310965 1.76357i −0.594003 0.804463i \(-0.702453\pi\)
0.283038 0.959109i \(-0.408658\pi\)
\(168\) 0 0
\(169\) −2.53771 2.12939i −0.195209 0.163799i
\(170\) −6.02737 + 10.4397i −0.462278 + 0.800689i
\(171\) 0 0
\(172\) 23.9397 + 41.4648i 1.82539 + 3.16166i
\(173\) 0.447748 2.53931i 0.0340417 0.193060i −0.963045 0.269342i \(-0.913194\pi\)
0.997086 + 0.0762821i \(0.0243049\pi\)
\(174\) 0 0
\(175\) 1.03636 + 0.377203i 0.0783411 + 0.0285138i
\(176\) −24.5797 8.94628i −1.85276 0.674351i
\(177\) 0 0
\(178\) 5.26985 29.8868i 0.394992 2.24011i
\(179\) −4.44806 7.70427i −0.332464 0.575844i 0.650530 0.759480i \(-0.274547\pi\)
−0.982994 + 0.183636i \(0.941213\pi\)
\(180\) 0 0
\(181\) −3.95592 + 6.85185i −0.294041 + 0.509294i −0.974761 0.223250i \(-0.928334\pi\)
0.680720 + 0.732543i \(0.261667\pi\)
\(182\) −3.22861 2.70912i −0.239320 0.200814i
\(183\) 0 0
\(184\) −7.23952 41.0573i −0.533704 3.02679i
\(185\) −6.22455 + 5.22302i −0.457638 + 0.384004i
\(186\) 0 0
\(187\) 4.80191 1.74775i 0.351151 0.127808i
\(188\) −36.3296 −2.64961
\(189\) 0 0
\(190\) −26.2235 −1.90245
\(191\) −14.9386 + 5.43721i −1.08092 + 0.393423i −0.820250 0.572005i \(-0.806166\pi\)
−0.260671 + 0.965428i \(0.583944\pi\)
\(192\) 0 0
\(193\) −3.51215 + 2.94704i −0.252810 + 0.212133i −0.760381 0.649477i \(-0.774988\pi\)
0.507571 + 0.861610i \(0.330543\pi\)
\(194\) 3.23603 + 18.3525i 0.232334 + 1.31763i
\(195\) 0 0
\(196\) −27.4927 23.0691i −1.96376 1.64779i
\(197\) 1.49708 2.59303i 0.106663 0.184745i −0.807754 0.589520i \(-0.799317\pi\)
0.914416 + 0.404775i \(0.132650\pi\)
\(198\) 0 0
\(199\) −7.44425 12.8938i −0.527709 0.914018i −0.999478 0.0322965i \(-0.989718\pi\)
0.471770 0.881722i \(-0.343615\pi\)
\(200\) 3.43307 19.4699i 0.242755 1.37673i
\(201\) 0 0
\(202\) −9.48050 3.45062i −0.667046 0.242785i
\(203\) −1.23013 0.447732i −0.0863385 0.0314246i
\(204\) 0 0
\(205\) 3.35366 19.0196i 0.234230 1.32838i
\(206\) 10.3885 + 17.9935i 0.723803 + 1.25366i
\(207\) 0 0
\(208\) −21.2264 + 36.7652i −1.47179 + 2.54921i
\(209\) 8.51559 + 7.14543i 0.589036 + 0.494260i
\(210\) 0 0
\(211\) 2.41006 + 13.6681i 0.165915 + 0.940951i 0.948116 + 0.317925i \(0.102986\pi\)
−0.782201 + 0.623026i \(0.785903\pi\)
\(212\) 22.1314 18.5704i 1.51999 1.27542i
\(213\) 0 0
\(214\) 27.3658 9.96034i 1.87069 0.680874i
\(215\) −15.0587 −1.02700
\(216\) 0 0
\(217\) −2.31003 −0.156815
\(218\) 31.0874 11.3149i 2.10550 0.766340i
\(219\) 0 0
\(220\) 13.0639 10.9619i 0.880767 0.739051i
\(221\) −1.44017 8.16762i −0.0968764 0.549414i
\(222\) 0 0
\(223\) −5.21828 4.37866i −0.349442 0.293216i 0.451124 0.892461i \(-0.351023\pi\)
−0.800566 + 0.599245i \(0.795468\pi\)
\(224\) 4.74283 8.21483i 0.316894 0.548876i
\(225\) 0 0
\(226\) 2.62925 + 4.55400i 0.174895 + 0.302928i
\(227\) 1.69148 9.59286i 0.112267 0.636700i −0.875799 0.482675i \(-0.839665\pi\)
0.988067 0.154025i \(-0.0492237\pi\)
\(228\) 0 0
\(229\) 13.1978 + 4.80362i 0.872138 + 0.317432i 0.739032 0.673670i \(-0.235283\pi\)
0.133105 + 0.991102i \(0.457505\pi\)
\(230\) 19.7500 + 7.18840i 1.30227 + 0.473989i
\(231\) 0 0
\(232\) −4.07498 + 23.1104i −0.267536 + 1.51727i
\(233\) 2.66167 + 4.61014i 0.174372 + 0.302020i 0.939944 0.341330i \(-0.110877\pi\)
−0.765572 + 0.643350i \(0.777544\pi\)
\(234\) 0 0
\(235\) 5.71307 9.89532i 0.372679 0.645499i
\(236\) 8.92597 + 7.48978i 0.581031 + 0.487543i
\(237\) 0 0
\(238\) 0.626578 + 3.55350i 0.0406150 + 0.230339i
\(239\) −13.6153 + 11.4246i −0.880700 + 0.738995i −0.966323 0.257332i \(-0.917156\pi\)
0.0856227 + 0.996328i \(0.472712\pi\)
\(240\) 0 0
\(241\) 1.88577 0.686364i 0.121473 0.0442126i −0.280568 0.959834i \(-0.590523\pi\)
0.402041 + 0.915621i \(0.368301\pi\)
\(242\) 19.8075 1.27327
\(243\) 0 0
\(244\) 36.3726 2.32852
\(245\) 10.6069 3.86059i 0.677649 0.246644i
\(246\) 0 0
\(247\) 13.8207 11.5970i 0.879391 0.737896i
\(248\) 7.19080 + 40.7810i 0.456616 + 2.58960i
\(249\) 0 0
\(250\) 24.9626 + 20.9461i 1.57877 + 1.32475i
\(251\) 11.7822 20.4073i 0.743683 1.28810i −0.207125 0.978314i \(-0.566411\pi\)
0.950808 0.309782i \(-0.100256\pi\)
\(252\) 0 0
\(253\) −4.45473 7.71582i −0.280067 0.485090i
\(254\) −1.10120 + 6.24523i −0.0690956 + 0.391860i
\(255\) 0 0
\(256\) −23.4802 8.54611i −1.46751 0.534132i
\(257\) 5.52029 + 2.00922i 0.344346 + 0.125332i 0.508403 0.861119i \(-0.330236\pi\)
−0.164057 + 0.986451i \(0.552458\pi\)
\(258\) 0 0
\(259\) −0.422349 + 2.39526i −0.0262435 + 0.148834i
\(260\) −13.8390 23.9698i −0.858257 1.48654i
\(261\) 0 0
\(262\) 23.1315 40.0650i 1.42907 2.47522i
\(263\) −16.8362 14.1273i −1.03817 0.871125i −0.0463663 0.998925i \(-0.514764\pi\)
−0.991800 + 0.127800i \(0.959209\pi\)
\(264\) 0 0
\(265\) 1.57784 + 8.94838i 0.0969260 + 0.549695i
\(266\) −6.01300 + 5.04550i −0.368680 + 0.309360i
\(267\) 0 0
\(268\) −62.3768 + 22.7033i −3.81027 + 1.38682i
\(269\) 30.6026 1.86587 0.932937 0.360041i \(-0.117237\pi\)
0.932937 + 0.360041i \(0.117237\pi\)
\(270\) 0 0
\(271\) −16.0823 −0.976928 −0.488464 0.872584i \(-0.662443\pi\)
−0.488464 + 0.872584i \(0.662443\pi\)
\(272\) 34.1535 12.4309i 2.07086 0.753732i
\(273\) 0 0
\(274\) 28.8599 24.2163i 1.74349 1.46296i
\(275\) −0.733660 4.16079i −0.0442414 0.250905i
\(276\) 0 0
\(277\) −15.9441 13.3787i −0.957990 0.803849i 0.0226353 0.999744i \(-0.492794\pi\)
−0.980625 + 0.195895i \(0.937239\pi\)
\(278\) 10.7075 18.5459i 0.642194 1.11231i
\(279\) 0 0
\(280\) 3.75631 + 6.50612i 0.224483 + 0.388815i
\(281\) −2.12897 + 12.0740i −0.127004 + 0.720275i 0.853093 + 0.521758i \(0.174724\pi\)
−0.980097 + 0.198517i \(0.936387\pi\)
\(282\) 0 0
\(283\) −4.29682 1.56391i −0.255419 0.0929650i 0.211137 0.977456i \(-0.432283\pi\)
−0.466556 + 0.884491i \(0.654506\pi\)
\(284\) −14.1691 5.15712i −0.840779 0.306019i
\(285\) 0 0
\(286\) −2.80371 + 15.9006i −0.165787 + 0.940224i
\(287\) −2.89045 5.00641i −0.170618 0.295519i
\(288\) 0 0
\(289\) 4.94976 8.57324i 0.291162 0.504308i
\(290\) −9.06257 7.60440i −0.532172 0.446546i
\(291\) 0 0
\(292\) 9.17348 + 52.0254i 0.536837 + 3.04456i
\(293\) −20.0117 + 16.7918i −1.16910 + 0.980988i −0.999989 0.00460992i \(-0.998533\pi\)
−0.169106 + 0.985598i \(0.554088\pi\)
\(294\) 0 0
\(295\) −3.44371 + 1.25341i −0.200500 + 0.0729762i
\(296\) 43.6004 2.53422
\(297\) 0 0
\(298\) 1.96965 0.114099
\(299\) −13.5879 + 4.94560i −0.785810 + 0.286011i
\(300\) 0 0
\(301\) −3.45294 + 2.89736i −0.199024 + 0.167001i
\(302\) −2.03961 11.5672i −0.117366 0.665617i
\(303\) 0 0
\(304\) 60.5670 + 50.8217i 3.47375 + 2.91483i
\(305\) −5.71984 + 9.90705i −0.327517 + 0.567276i
\(306\) 0 0
\(307\) −1.64638 2.85162i −0.0939641 0.162751i 0.815212 0.579163i \(-0.196621\pi\)
−0.909176 + 0.416412i \(0.863287\pi\)
\(308\) 0.886412 5.02709i 0.0505080 0.286445i
\(309\) 0 0
\(310\) −19.6171 7.14003i −1.11417 0.405526i
\(311\) 32.6944 + 11.8998i 1.85393 + 0.674775i 0.983067 + 0.183246i \(0.0586606\pi\)
0.870861 + 0.491529i \(0.163562\pi\)
\(312\) 0 0
\(313\) 1.84550 10.4664i 0.104314 0.591594i −0.887178 0.461427i \(-0.847337\pi\)
0.991492 0.130167i \(-0.0415514\pi\)
\(314\) −20.9957 36.3657i −1.18486 2.05223i
\(315\) 0 0
\(316\) −14.1209 + 24.4580i −0.794360 + 1.37587i
\(317\) 11.8739 + 9.96335i 0.666902 + 0.559598i 0.912147 0.409864i \(-0.134424\pi\)
−0.245244 + 0.969461i \(0.578868\pi\)
\(318\) 0 0
\(319\) 0.870840 + 4.93878i 0.0487577 + 0.276519i
\(320\) 30.7195 25.7767i 1.71727 1.44096i
\(321\) 0 0
\(322\) 5.91172 2.15169i 0.329447 0.119909i
\(323\) −15.4461 −0.859446
\(324\) 0 0
\(325\) −6.85710 −0.380363
\(326\) 21.5997 7.86166i 1.19630 0.435417i
\(327\) 0 0
\(328\) −79.3851 + 66.6120i −4.38331 + 3.67803i
\(329\) −0.593904 3.36820i −0.0327430 0.185695i
\(330\) 0 0
\(331\) −11.1615 9.36559i −0.613490 0.514780i 0.282259 0.959338i \(-0.408916\pi\)
−0.895750 + 0.444559i \(0.853361\pi\)
\(332\) −7.25330 + 12.5631i −0.398077 + 0.689489i
\(333\) 0 0
\(334\) −31.3002 54.2136i −1.71267 2.96644i
\(335\) 3.62532 20.5602i 0.198072 1.12332i
\(336\) 0 0
\(337\) 19.3716 + 7.05067i 1.05524 + 0.384074i 0.810636 0.585550i \(-0.199121\pi\)
0.244599 + 0.969624i \(0.421344\pi\)
\(338\) −8.42077 3.06491i −0.458030 0.166709i
\(339\) 0 0
\(340\) −4.11479 + 23.3361i −0.223156 + 1.26558i
\(341\) 4.42475 + 7.66390i 0.239614 + 0.415023i
\(342\) 0 0
\(343\) 3.44142 5.96071i 0.185819 0.321848i
\(344\) 61.8982 + 51.9388i 3.33733 + 2.80035i
\(345\) 0 0
\(346\) −1.21119 6.86899i −0.0651138 0.369279i
\(347\) 16.2275 13.6165i 0.871140 0.730973i −0.0931979 0.995648i \(-0.529709\pi\)
0.964338 + 0.264674i \(0.0852645\pi\)
\(348\) 0 0
\(349\) 4.34699 1.58218i 0.232689 0.0846919i −0.223044 0.974808i \(-0.571599\pi\)
0.455733 + 0.890116i \(0.349377\pi\)
\(350\) 2.98333 0.159466
\(351\) 0 0
\(352\) −36.3387 −1.93686
\(353\) −12.8206 + 4.66632i −0.682372 + 0.248363i −0.659866 0.751383i \(-0.729387\pi\)
−0.0225065 + 0.999747i \(0.507165\pi\)
\(354\) 0 0
\(355\) 3.63286 3.04833i 0.192812 0.161788i
\(356\) −10.3590 58.7488i −0.549026 3.11368i
\(357\) 0 0
\(358\) −18.4346 15.4684i −0.974297 0.817532i
\(359\) −14.1223 + 24.4606i −0.745349 + 1.29098i 0.204683 + 0.978828i \(0.434384\pi\)
−0.950032 + 0.312153i \(0.898950\pi\)
\(360\) 0 0
\(361\) −7.30050 12.6448i −0.384237 0.665517i
\(362\) −3.71642 + 21.0769i −0.195331 + 1.10778i
\(363\) 0 0
\(364\) −7.78514 2.83356i −0.408052 0.148519i
\(365\) −15.6131 5.68270i −0.817226 0.297446i
\(366\) 0 0
\(367\) 6.05688 34.3503i 0.316167 1.79307i −0.249434 0.968392i \(-0.580245\pi\)
0.565601 0.824679i \(-0.308644\pi\)
\(368\) −31.6842 54.8786i −1.65165 2.86075i
\(369\) 0 0
\(370\) −10.9901 + 19.0354i −0.571348 + 0.989604i
\(371\) 2.08350 + 1.74827i 0.108170 + 0.0907655i
\(372\) 0 0
\(373\) 0.531266 + 3.01296i 0.0275079 + 0.156005i 0.995468 0.0951001i \(-0.0303171\pi\)
−0.967960 + 0.251105i \(0.919206\pi\)
\(374\) 10.5891 8.88533i 0.547551 0.459450i
\(375\) 0 0
\(376\) −57.6131 + 20.9694i −2.97117 + 1.08142i
\(377\) 8.13924 0.419192
\(378\) 0 0
\(379\) −7.67705 −0.394344 −0.197172 0.980369i \(-0.563176\pi\)
−0.197172 + 0.980369i \(0.563176\pi\)
\(380\) −48.4390 + 17.6304i −2.48487 + 0.904419i
\(381\) 0 0
\(382\) −32.9425 + 27.6420i −1.68548 + 1.41429i
\(383\) −1.79933 10.2045i −0.0919416 0.521427i −0.995642 0.0932607i \(-0.970271\pi\)
0.903700 0.428166i \(-0.140840\pi\)
\(384\) 0 0
\(385\) 1.22987 + 1.03198i 0.0626798 + 0.0525946i
\(386\) −6.20106 + 10.7406i −0.315626 + 0.546680i
\(387\) 0 0
\(388\) 18.3161 + 31.7244i 0.929858 + 1.61056i
\(389\) 0.0741393 0.420465i 0.00375901 0.0213184i −0.982871 0.184297i \(-0.940999\pi\)
0.986630 + 0.162979i \(0.0521102\pi\)
\(390\) 0 0
\(391\) 11.6331 + 4.23411i 0.588313 + 0.214128i
\(392\) −56.9146 20.7152i −2.87462 1.04628i
\(393\) 0 0
\(394\) 1.40645 7.97637i 0.0708559 0.401844i
\(395\) −4.44119 7.69238i −0.223461 0.387045i
\(396\) 0 0
\(397\) 13.5445 23.4598i 0.679781 1.17741i −0.295266 0.955415i \(-0.595408\pi\)
0.975047 0.221999i \(-0.0712583\pi\)
\(398\) −30.8519 25.8879i −1.54647 1.29764i
\(399\) 0 0
\(400\) −5.21814 29.5936i −0.260907 1.47968i
\(401\) −22.4914 + 18.8725i −1.12317 + 0.942450i −0.998760 0.0497810i \(-0.984148\pi\)
−0.124408 + 0.992231i \(0.539703\pi\)
\(402\) 0 0
\(403\) 13.4965 4.91232i 0.672308 0.244700i
\(404\) −19.8319 −0.986675
\(405\) 0 0
\(406\) −3.54115 −0.175744
\(407\) 8.75565 3.18680i 0.434001 0.157964i
\(408\) 0 0
\(409\) −15.4618 + 12.9740i −0.764536 + 0.641522i −0.939303 0.343088i \(-0.888527\pi\)
0.174767 + 0.984610i \(0.444083\pi\)
\(410\) −9.07187 51.4491i −0.448028 2.54089i
\(411\) 0 0
\(412\) 31.2865 + 26.2525i 1.54138 + 1.29337i
\(413\) −0.548476 + 0.949988i −0.0269887 + 0.0467459i
\(414\) 0 0
\(415\) −2.28126 3.95126i −0.111983 0.193960i
\(416\) −10.2413 + 58.0813i −0.502121 + 2.84767i
\(417\) 0 0
\(418\) 28.2569 + 10.2847i 1.38209 + 0.503039i
\(419\) 22.9006 + 8.33514i 1.11877 + 0.407198i 0.834203 0.551458i \(-0.185928\pi\)
0.284566 + 0.958657i \(0.408151\pi\)
\(420\) 0 0
\(421\) −4.54516 + 25.7769i −0.221518 + 1.25629i 0.647714 + 0.761884i \(0.275725\pi\)
−0.869232 + 0.494405i \(0.835386\pi\)
\(422\) 18.7717 + 32.5136i 0.913794 + 1.58274i
\(423\) 0 0
\(424\) 24.3781 42.2240i 1.18390 2.05058i
\(425\) 4.49715 + 3.77356i 0.218144 + 0.183045i
\(426\) 0 0
\(427\) 0.594608 + 3.37219i 0.0287751 + 0.163192i
\(428\) 43.8527 36.7967i 2.11970 1.77864i
\(429\) 0 0
\(430\) −38.2782 + 13.9321i −1.84594 + 0.671867i
\(431\) −31.9185 −1.53746 −0.768731 0.639572i \(-0.779111\pi\)
−0.768731 + 0.639572i \(0.779111\pi\)
\(432\) 0 0
\(433\) 0.0123080 0.000591484 0.000295742 1.00000i \(-0.499906\pi\)
0.000295742 1.00000i \(0.499906\pi\)
\(434\) −5.87193 + 2.13721i −0.281862 + 0.102589i
\(435\) 0 0
\(436\) 49.8164 41.8009i 2.38577 2.00190i
\(437\) 4.67642 + 26.5213i 0.223703 + 1.26868i
\(438\) 0 0
\(439\) 4.06372 + 3.40986i 0.193951 + 0.162744i 0.734592 0.678510i \(-0.237374\pi\)
−0.540641 + 0.841253i \(0.681818\pi\)
\(440\) 14.3901 24.9244i 0.686020 1.18822i
\(441\) 0 0
\(442\) −11.2174 19.4291i −0.533557 0.924147i
\(443\) −7.06684 + 40.0781i −0.335756 + 1.90417i 0.0838834 + 0.996476i \(0.473268\pi\)
−0.419639 + 0.907691i \(0.637843\pi\)
\(444\) 0 0
\(445\) 17.6308 + 6.41709i 0.835780 + 0.304199i
\(446\) −17.3156 6.30235i −0.819916 0.298425i
\(447\) 0 0
\(448\) 2.08438 11.8211i 0.0984778 0.558496i
\(449\) 7.71401 + 13.3611i 0.364047 + 0.630547i 0.988623 0.150417i \(-0.0480615\pi\)
−0.624576 + 0.780964i \(0.714728\pi\)
\(450\) 0 0
\(451\) −11.0731 + 19.1791i −0.521410 + 0.903109i
\(452\) 7.91838 + 6.64431i 0.372449 + 0.312522i
\(453\) 0 0
\(454\) −4.57556 25.9493i −0.214742 1.21786i
\(455\) 1.99606 1.67489i 0.0935767 0.0785202i
\(456\) 0 0
\(457\) −2.24469 + 0.816999i −0.105002 + 0.0382176i −0.393987 0.919116i \(-0.628904\pi\)
0.288985 + 0.957334i \(0.406682\pi\)
\(458\) 37.9922 1.77526
\(459\) 0 0
\(460\) 41.3143 1.92629
\(461\) 30.5248 11.1101i 1.42168 0.517451i 0.487148 0.873319i \(-0.338037\pi\)
0.934536 + 0.355869i \(0.115815\pi\)
\(462\) 0 0
\(463\) 25.9525 21.7767i 1.20611 1.01205i 0.206679 0.978409i \(-0.433734\pi\)
0.999434 0.0336404i \(-0.0107101\pi\)
\(464\) 6.19383 + 35.1270i 0.287541 + 1.63073i
\(465\) 0 0
\(466\) 11.0310 + 9.25612i 0.511002 + 0.428781i
\(467\) −6.90133 + 11.9535i −0.319356 + 0.553140i −0.980354 0.197247i \(-0.936800\pi\)
0.660998 + 0.750388i \(0.270133\pi\)
\(468\) 0 0
\(469\) −3.12459 5.41195i −0.144280 0.249901i
\(470\) 5.36719 30.4389i 0.247570 1.40404i
\(471\) 0 0
\(472\) 18.4783 + 6.72556i 0.850534 + 0.309569i
\(473\) 16.2264 + 5.90593i 0.746091 + 0.271555i
\(474\) 0 0
\(475\) −2.21762 + 12.5767i −0.101751 + 0.577060i
\(476\) 3.54645 + 6.14264i 0.162551 + 0.281547i
\(477\) 0 0
\(478\) −24.0392 + 41.6372i −1.09953 + 1.90444i
\(479\) −4.51286 3.78674i −0.206198 0.173020i 0.533841 0.845585i \(-0.320748\pi\)
−0.740038 + 0.672565i \(0.765193\pi\)
\(480\) 0 0
\(481\) −2.62596 14.8926i −0.119734 0.679042i
\(482\) 4.15848 3.48938i 0.189413 0.158937i
\(483\) 0 0
\(484\) 36.5876 13.3168i 1.66307 0.605309i
\(485\) −11.5213 −0.523155
\(486\) 0 0
\(487\) 29.0299 1.31547 0.657736 0.753249i \(-0.271514\pi\)
0.657736 + 0.753249i \(0.271514\pi\)
\(488\) 57.6814 20.9943i 2.61111 0.950368i
\(489\) 0 0
\(490\) 23.3902 19.6267i 1.05666 0.886644i
\(491\) −0.761188 4.31691i −0.0343519 0.194820i 0.962802 0.270206i \(-0.0870919\pi\)
−0.997154 + 0.0753869i \(0.975981\pi\)
\(492\) 0 0
\(493\) −5.33803 4.47914i −0.240413 0.201730i
\(494\) 24.4019 42.2654i 1.09789 1.90161i
\(495\) 0 0
\(496\) 31.4710 + 54.5093i 1.41309 + 2.44754i
\(497\) 0.246497 1.39795i 0.0110569 0.0627068i
\(498\) 0 0
\(499\) −33.2120 12.0882i −1.48677 0.541142i −0.534177 0.845373i \(-0.679378\pi\)
−0.952598 + 0.304231i \(0.901600\pi\)
\(500\) 60.1922 + 21.9082i 2.69188 + 0.979764i
\(501\) 0 0
\(502\) 11.0688 62.7746i 0.494027 2.80177i
\(503\) −4.18829 7.25434i −0.186747 0.323455i 0.757417 0.652932i \(-0.226461\pi\)
−0.944164 + 0.329477i \(0.893128\pi\)
\(504\) 0 0
\(505\) 3.11870 5.40175i 0.138780 0.240375i
\(506\) −18.4622 15.4916i −0.820745 0.688687i
\(507\) 0 0
\(508\) 2.16465 + 12.2763i 0.0960406 + 0.544673i
\(509\) 2.94389 2.47021i 0.130485 0.109490i −0.575209 0.818006i \(-0.695079\pi\)
0.705695 + 0.708516i \(0.250635\pi\)
\(510\) 0 0
\(511\) −4.67343 + 1.70099i −0.206740 + 0.0752473i
\(512\) −13.6601 −0.603699
\(513\) 0 0
\(514\) 15.8911 0.700925
\(515\) −12.0706 + 4.39333i −0.531894 + 0.193593i
\(516\) 0 0
\(517\) −10.0369 + 8.42200i −0.441425 + 0.370399i
\(518\) 1.14248 + 6.47933i 0.0501977 + 0.284685i
\(519\) 0 0
\(520\) −35.7819 30.0245i −1.56914 1.31666i
\(521\) 9.82615 17.0194i 0.430491 0.745633i −0.566424 0.824114i \(-0.691674\pi\)
0.996916 + 0.0784810i \(0.0250070\pi\)
\(522\) 0 0
\(523\) 19.8051 + 34.3035i 0.866018 + 1.49999i 0.866032 + 0.499988i \(0.166662\pi\)
−1.41543e−5 1.00000i \(0.500005\pi\)
\(524\) 15.7915 89.5582i 0.689856 3.91237i
\(525\) 0 0
\(526\) −55.8669 20.3339i −2.43591 0.886599i
\(527\) −11.5548 4.20562i −0.503337 0.183200i
\(528\) 0 0
\(529\) −0.245870 + 1.39440i −0.0106900 + 0.0606259i
\(530\) 12.2897 + 21.2864i 0.533830 + 0.924620i
\(531\) 0 0
\(532\) −7.71483 + 13.3625i −0.334480 + 0.579337i
\(533\) 27.5339 + 23.1037i 1.19262 + 1.00073i
\(534\) 0 0
\(535\) 3.12645 + 17.7310i 0.135168 + 0.766576i
\(536\) −85.8156 + 72.0078i −3.70667 + 3.11026i
\(537\) 0 0
\(538\) 77.7896 28.3131i 3.35375 1.22066i
\(539\) −12.9435 −0.557514
\(540\) 0 0
\(541\) −41.8257 −1.79823 −0.899115 0.437713i \(-0.855788\pi\)
−0.899115 + 0.437713i \(0.855788\pi\)
\(542\) −40.8800 + 14.8791i −1.75595 + 0.639112i
\(543\) 0 0
\(544\) 38.6796 32.4561i 1.65838 1.39154i
\(545\) 3.55162 + 20.1423i 0.152135 + 0.862800i
\(546\) 0 0
\(547\) −13.0490 10.9495i −0.557937 0.468165i 0.319681 0.947525i \(-0.396424\pi\)
−0.877618 + 0.479360i \(0.840869\pi\)
\(548\) 37.0280 64.1343i 1.58176 2.73968i
\(549\) 0 0
\(550\) −5.71442 9.89767i −0.243664 0.422038i
\(551\) 2.63227 14.9283i 0.112138 0.635968i
\(552\) 0 0
\(553\) −2.49840 0.909345i −0.106243 0.0386693i
\(554\) −52.9066 19.2564i −2.24779 0.818128i
\(555\) 0 0
\(556\) 7.30985 41.4562i 0.310007 1.75813i
\(557\) −16.8840 29.2439i −0.715398 1.23911i −0.962806 0.270194i \(-0.912912\pi\)
0.247408 0.968911i \(-0.420421\pi\)
\(558\) 0 0
\(559\) 14.0127 24.2707i 0.592674 1.02654i
\(560\) 8.74740 + 7.33994i 0.369645 + 0.310169i
\(561\) 0 0
\(562\) 5.75902 + 32.6610i 0.242929 + 1.37772i
\(563\) 17.3978 14.5985i 0.733232 0.615254i −0.197779 0.980247i \(-0.563373\pi\)
0.931011 + 0.364992i \(0.118928\pi\)
\(564\) 0 0
\(565\) −3.05497 + 1.11192i −0.128524 + 0.0467787i
\(566\) −12.3691 −0.519913
\(567\) 0 0
\(568\) −25.4466 −1.06772
\(569\) 10.2158 3.71825i 0.428269 0.155877i −0.118887 0.992908i \(-0.537933\pi\)
0.547156 + 0.837031i \(0.315710\pi\)
\(570\) 0 0
\(571\) 11.4016 9.56706i 0.477141 0.400369i −0.372250 0.928132i \(-0.621414\pi\)
0.849391 + 0.527763i \(0.176969\pi\)
\(572\) 5.51128 + 31.2560i 0.230438 + 1.30688i
\(573\) 0 0
\(574\) −11.9792 10.0517i −0.500002 0.419551i
\(575\) 5.11772 8.86416i 0.213424 0.369661i
\(576\) 0 0
\(577\) 18.5582 + 32.1437i 0.772586 + 1.33816i 0.936141 + 0.351624i \(0.114371\pi\)
−0.163555 + 0.986534i \(0.552296\pi\)
\(578\) 4.65010 26.3720i 0.193419 1.09693i
\(579\) 0 0
\(580\) −21.8526 7.95369i −0.907379 0.330259i
\(581\) −1.28333 0.467093i −0.0532414 0.0193783i
\(582\) 0 0
\(583\) 1.80931 10.2611i 0.0749338 0.424971i
\(584\) 44.5768 + 77.2093i 1.84460 + 3.19494i
\(585\) 0 0
\(586\) −35.3328 + 61.1981i −1.45958 + 2.52807i
\(587\) −11.2174 9.41248i −0.462990 0.388495i 0.381240 0.924476i \(-0.375497\pi\)
−0.844230 + 0.535982i \(0.819942\pi\)
\(588\) 0 0
\(589\) −4.64495 26.3428i −0.191392 1.08544i
\(590\) −7.59403 + 6.37215i −0.312641 + 0.262337i
\(591\) 0 0
\(592\) 62.2744 22.6660i 2.55946 0.931568i
\(593\) 36.4392 1.49638 0.748189 0.663485i \(-0.230924\pi\)
0.748189 + 0.663485i \(0.230924\pi\)
\(594\) 0 0
\(595\) −2.23081 −0.0914544
\(596\) 3.63827 1.32422i 0.149029 0.0542422i
\(597\) 0 0
\(598\) −29.9639 + 25.1427i −1.22532 + 1.02816i
\(599\) 4.77444 + 27.0772i 0.195078 + 1.10634i 0.912307 + 0.409506i \(0.134299\pi\)
−0.717229 + 0.696838i \(0.754590\pi\)
\(600\) 0 0
\(601\) 34.6076 + 29.0392i 1.41167 + 1.18453i 0.955628 + 0.294578i \(0.0951789\pi\)
0.456045 + 0.889957i \(0.349266\pi\)
\(602\) −6.09653 + 10.5595i −0.248476 + 0.430373i
\(603\) 0 0
\(604\) −11.5443 19.9953i −0.469729 0.813595i
\(605\) −2.12646 + 12.0598i −0.0864529 + 0.490299i
\(606\) 0 0
\(607\) −16.1037 5.86126i −0.653628 0.237901i −0.00614504 0.999981i \(-0.501956\pi\)
−0.647483 + 0.762080i \(0.724178\pi\)
\(608\) 103.216 + 37.5675i 4.18596 + 1.52356i
\(609\) 0 0
\(610\) −5.37355 + 30.4749i −0.217569 + 1.23389i
\(611\) 10.6324 + 18.4159i 0.430143 + 0.745029i
\(612\) 0 0
\(613\) 0.234380 0.405959i 0.00946653 0.0163965i −0.861253 0.508176i \(-0.830320\pi\)
0.870720 + 0.491779i \(0.163653\pi\)
\(614\) −6.82327 5.72541i −0.275365 0.231059i
\(615\) 0 0
\(616\) −1.49593 8.48383i −0.0602726 0.341823i
\(617\) −1.63539 + 1.37225i −0.0658383 + 0.0552449i −0.675113 0.737714i \(-0.735905\pi\)
0.609275 + 0.792959i \(0.291461\pi\)
\(618\) 0 0
\(619\) −8.02272 + 2.92003i −0.322460 + 0.117366i −0.498178 0.867075i \(-0.665998\pi\)
0.175718 + 0.984441i \(0.443775\pi\)
\(620\) −41.0363 −1.64806
\(621\) 0 0
\(622\) 94.1163 3.77372
\(623\) 5.27739 1.92081i 0.211434 0.0769557i
\(624\) 0 0
\(625\) −6.99443 + 5.86902i −0.279777 + 0.234761i
\(626\) −4.99221 28.3122i −0.199529 1.13158i
\(627\) 0 0
\(628\) −63.2316 53.0576i −2.52322 2.11723i
\(629\) −6.47339 + 11.2122i −0.258111 + 0.447061i
\(630\) 0 0
\(631\) 5.93539 + 10.2804i 0.236284 + 0.409256i 0.959645 0.281214i \(-0.0907370\pi\)
−0.723361 + 0.690470i \(0.757404\pi\)
\(632\) −8.27630 + 46.9372i −0.329214 + 1.86706i
\(633\) 0 0
\(634\) 39.4005 + 14.3406i 1.56479 + 0.569538i
\(635\) −3.68418 1.34093i −0.146202 0.0532133i
\(636\) 0 0
\(637\) −3.64784 + 20.6880i −0.144533 + 0.819686i
\(638\) 6.78291 + 11.7483i 0.268538 + 0.465121i
\(639\) 0 0
\(640\) 22.5486 39.0554i 0.891313 1.54380i
\(641\) 4.06284 + 3.40913i 0.160472 + 0.134652i 0.719488 0.694505i \(-0.244376\pi\)
−0.559016 + 0.829157i \(0.688821\pi\)
\(642\) 0 0
\(643\) −0.143063 0.811352i −0.00564187 0.0319966i 0.981857 0.189624i \(-0.0607268\pi\)
−0.987499 + 0.157627i \(0.949616\pi\)
\(644\) 9.47330 7.94904i 0.373300 0.313236i
\(645\) 0 0
\(646\) −39.2630 + 14.2906i −1.54478 + 0.562254i
\(647\) −40.8373 −1.60548 −0.802740 0.596329i \(-0.796626\pi\)
−0.802740 + 0.596329i \(0.796626\pi\)
\(648\) 0 0
\(649\) 4.20232 0.164955
\(650\) −17.4303 + 6.34409i −0.683671 + 0.248836i
\(651\) 0 0
\(652\) 34.6128 29.0436i 1.35554 1.13743i
\(653\) 0.185692 + 1.05311i 0.00726668 + 0.0412114i 0.988225 0.153004i \(-0.0488949\pi\)
−0.980959 + 0.194216i \(0.937784\pi\)
\(654\) 0 0
\(655\) 21.9102 + 18.3849i 0.856103 + 0.718356i
\(656\) −78.7569 + 136.411i −3.07494 + 5.32595i
\(657\) 0 0
\(658\) −4.62587 8.01225i −0.180335 0.312350i
\(659\) −4.97750 + 28.2288i −0.193896 + 1.09964i 0.720086 + 0.693884i \(0.244102\pi\)
−0.913982 + 0.405754i \(0.867009\pi\)
\(660\) 0 0
\(661\) 4.22459 + 1.53763i 0.164318 + 0.0598067i 0.422869 0.906191i \(-0.361023\pi\)
−0.258552 + 0.965997i \(0.583245\pi\)
\(662\) −37.0366 13.4802i −1.43947 0.523924i
\(663\) 0 0
\(664\) −4.25119 + 24.1097i −0.164978 + 0.935638i
\(665\) −2.42642 4.20268i −0.0940924 0.162973i
\(666\) 0 0
\(667\) −6.07464 + 10.5216i −0.235211 + 0.407397i
\(668\) −94.2651 79.0978i −3.64723 3.06039i
\(669\) 0 0
\(670\) −9.80672 55.6167i −0.378867 2.14866i
\(671\) 10.0488 8.43198i 0.387931 0.325513i
\(672\) 0 0
\(673\) −16.9695 + 6.17640i −0.654127 + 0.238083i −0.647699 0.761897i \(-0.724268\pi\)
−0.00642810 + 0.999979i \(0.502046\pi\)
\(674\) 55.7643 2.14796
\(675\) 0 0
\(676\) −17.6151 −0.677505
\(677\) −14.7900 + 5.38311i −0.568425 + 0.206890i −0.610214 0.792237i \(-0.708917\pi\)
0.0417888 + 0.999126i \(0.486694\pi\)
\(678\) 0 0
\(679\) −2.64181 + 2.21675i −0.101384 + 0.0850709i
\(680\) 6.94420 + 39.3825i 0.266298 + 1.51025i
\(681\) 0 0
\(682\) 18.3380 + 15.3874i 0.702196 + 0.589213i
\(683\) 1.38059 2.39125i 0.0528268 0.0914987i −0.838403 0.545051i \(-0.816510\pi\)
0.891230 + 0.453552i \(0.149844\pi\)
\(684\) 0 0
\(685\) 11.6458 + 20.1711i 0.444963 + 0.770698i
\(686\) 3.23307 18.3357i 0.123439 0.700058i
\(687\) 0 0
\(688\) 115.410 + 42.0058i 4.39996 + 1.60146i
\(689\) −15.8907 5.78374i −0.605387 0.220343i
\(690\) 0 0
\(691\) −5.99530 + 34.0010i −0.228072 + 1.29346i 0.628653 + 0.777686i \(0.283607\pi\)
−0.856725 + 0.515774i \(0.827504\pi\)
\(692\) −6.85537 11.8738i −0.260602 0.451376i
\(693\) 0 0
\(694\) 28.6514 49.6257i 1.08759 1.88377i
\(695\) 10.1422 + 8.51029i 0.384714 + 0.322814i
\(696\) 0 0
\(697\) −5.34351 30.3046i −0.202400 1.14787i
\(698\) 9.58594 8.04356i 0.362833 0.304453i
\(699\) 0 0
\(700\) 5.51069 2.00573i 0.208285 0.0758094i
\(701\) −20.7410 −0.783378 −0.391689 0.920098i \(-0.628109\pi\)
−0.391689 + 0.920098i \(0.628109\pi\)
\(702\) 0 0
\(703\) −28.1640 −1.06222
\(704\) −43.2110 + 15.7275i −1.62858 + 0.592754i
\(705\) 0 0
\(706\) −28.2719 + 23.7229i −1.06403 + 0.892824i
\(707\) −0.324206 1.83866i −0.0121930 0.0691501i
\(708\) 0 0
\(709\) 21.2249 + 17.8098i 0.797117 + 0.668861i 0.947496 0.319768i \(-0.103605\pi\)
−0.150379 + 0.988628i \(0.548049\pi\)
\(710\) 6.41419 11.1097i 0.240720 0.416940i
\(711\) 0 0
\(712\) −50.3376 87.1873i −1.88648 3.26748i
\(713\) −3.72282 + 21.1131i −0.139421 + 0.790693i
\(714\) 0 0
\(715\) −9.38009 3.41407i −0.350796 0.127679i
\(716\) −44.4513 16.1789i −1.66122 0.604635i
\(717\) 0 0
\(718\) −13.2674 + 75.2429i −0.495133 + 2.80804i
\(719\) −16.5657 28.6927i −0.617797 1.07006i −0.989887 0.141859i \(-0.954692\pi\)
0.372090 0.928197i \(-0.378641\pi\)
\(720\) 0 0
\(721\) −1.92247 + 3.32981i −0.0715965 + 0.124009i
\(722\) −30.2562 25.3879i −1.12602 0.944842i
\(723\) 0 0
\(724\) 7.30541 + 41.4310i 0.271503 + 1.53977i
\(725\) −4.41344 + 3.70332i −0.163911 + 0.137538i
\(726\) 0 0
\(727\) 0.0776238 0.0282527i 0.00287891 0.00104784i −0.340580 0.940215i \(-0.610624\pi\)
0.343459 + 0.939168i \(0.388401\pi\)
\(728\) −13.9816 −0.518191
\(729\) 0 0
\(730\) −44.9449 −1.66349
\(731\) −22.5466 + 8.20630i −0.833917 + 0.303521i
\(732\) 0 0
\(733\) −24.4502 + 20.5162i −0.903089 + 0.757782i −0.970792 0.239924i \(-0.922878\pi\)
0.0677025 + 0.997706i \(0.478433\pi\)
\(734\) −16.3843 92.9198i −0.604754 3.42973i
\(735\) 0 0
\(736\) −67.4381 56.5873i −2.48580 2.08584i
\(737\) −11.9700 + 20.7327i −0.440921 + 0.763698i
\(738\) 0 0
\(739\) 17.8960 + 30.9967i 0.658314 + 1.14023i 0.981052 + 0.193745i \(0.0620634\pi\)
−0.322738 + 0.946488i \(0.604603\pi\)
\(740\) −7.50277 + 42.5503i −0.275807 + 1.56418i
\(741\) 0 0
\(742\) 6.91359 + 2.51634i 0.253806 + 0.0923778i
\(743\) −18.5861 6.76477i −0.681856 0.248175i −0.0222120 0.999753i \(-0.507071\pi\)
−0.659644 + 0.751578i \(0.729293\pi\)
\(744\) 0 0
\(745\) −0.211455 + 1.19922i −0.00774711 + 0.0439361i
\(746\) 4.13799 + 7.16721i 0.151503 + 0.262410i
\(747\) 0 0
\(748\) 13.5861 23.5319i 0.496758 0.860411i
\(749\) 4.12840 + 3.46414i 0.150848 + 0.126577i
\(750\) 0 0
\(751\) 5.31026 + 30.1160i 0.193774 + 1.09895i 0.914154 + 0.405367i \(0.132856\pi\)
−0.720380 + 0.693580i \(0.756032\pi\)
\(752\) −71.3876 + 59.9013i −2.60324 + 2.18438i
\(753\) 0 0
\(754\) 20.6894 7.53031i 0.753462 0.274238i
\(755\) 7.26165 0.264278
\(756\) 0 0
\(757\) 25.4129 0.923647 0.461824 0.886972i \(-0.347195\pi\)
0.461824 + 0.886972i \(0.347195\pi\)
\(758\) −19.5145 + 7.10271i −0.708799 + 0.257982i
\(759\) 0 0
\(760\) −66.6405 + 55.9181i −2.41731 + 2.02836i
\(761\) 8.12986 + 46.1067i 0.294707 + 1.67137i 0.668391 + 0.743810i \(0.266983\pi\)
−0.373684 + 0.927556i \(0.621905\pi\)
\(762\) 0 0
\(763\) 4.68984 + 3.93524i 0.169784 + 0.142465i
\(764\) −42.2661 + 73.2070i −1.52913 + 2.64854i
\(765\) 0 0
\(766\) −14.0149 24.2744i −0.506377 0.877071i
\(767\) 1.18434 6.71670i 0.0427639 0.242526i
\(768\) 0 0
\(769\) −13.6870 4.98167i −0.493567 0.179644i 0.0832316 0.996530i \(-0.473476\pi\)
−0.576798 + 0.816887i \(0.695698\pi\)
\(770\) 4.08101 + 1.48537i 0.147069 + 0.0535289i
\(771\) 0 0
\(772\) −4.23337 + 24.0086i −0.152362 + 0.864089i
\(773\) 12.1767 + 21.0906i 0.437964 + 0.758576i 0.997532 0.0702080i \(-0.0223663\pi\)
−0.559568 + 0.828784i \(0.689033\pi\)
\(774\) 0 0
\(775\) −5.08328 + 8.80451i −0.182597 + 0.316267i
\(776\) 47.3578 + 39.7379i 1.70005 + 1.42651i
\(777\) 0 0
\(778\) −0.200552 1.13738i −0.00719012 0.0407772i
\(779\) 51.2794 43.0285i 1.83727 1.54166i
\(780\) 0 0
\(781\) −5.11009 + 1.85992i −0.182853 + 0.0665532i
\(782\) 33.4879 1.19753
\(783\) 0 0
\(784\) −92.0601 −3.28786
\(785\) 24.3952 8.87914i 0.870703 0.316910i
\(786\) 0 0
\(787\) −21.1177 + 17.7198i −0.752764 + 0.631644i −0.936232 0.351381i \(-0.885712\pi\)
0.183468 + 0.983026i \(0.441268\pi\)
\(788\) −2.76467 15.6792i −0.0984874 0.558550i
\(789\) 0 0
\(790\) −18.4061 15.4445i −0.654859 0.549492i
\(791\) −0.486562 + 0.842750i −0.0173001 + 0.0299647i
\(792\) 0 0
\(793\) −10.6451 18.4378i −0.378017 0.654744i
\(794\) 12.7245 72.1644i 0.451577 2.56102i
\(795\) 0 0
\(796\) −74.3933 27.0770i −2.63680 0.959717i
\(797\) −6.21787 2.26312i −0.220248 0.0801638i 0.229539 0.973299i \(-0.426278\pi\)
−0.449787 + 0.893136i \(0.648500\pi\)
\(798\) 0 0
\(799\) 3.16138 17.9291i 0.111842 0.634286i
\(800\) −20.8735 36.1539i −0.737989 1.27823i
\(801\) 0 0
\(802\) −39.7110 + 68.7815i −1.40224 + 2.42876i
\(803\) 14.5950 + 12.2467i 0.515048 + 0.432177i
\(804\) 0 0
\(805\) 0.675393 + 3.83034i 0.0238045 + 0.135002i
\(806\) 29.7623 24.9735i 1.04833 0.879655i
\(807\) 0 0
\(808\) −31.4504 + 11.4470i −1.10642 + 0.402704i
\(809\) 8.61362 0.302839 0.151419 0.988470i \(-0.451616\pi\)
0.151419 + 0.988470i \(0.451616\pi\)
\(810\) 0 0
\(811\) −9.58716 −0.336651 −0.168325 0.985732i \(-0.553836\pi\)
−0.168325 + 0.985732i \(0.553836\pi\)
\(812\) −6.54108 + 2.38076i −0.229547 + 0.0835483i
\(813\) 0 0
\(814\) 19.3079 16.2012i 0.676740 0.567852i
\(815\) 2.46770 + 13.9950i 0.0864396 + 0.490223i
\(816\) 0 0
\(817\) −39.9836 33.5502i −1.39885 1.17377i
\(818\) −27.2994 + 47.2840i −0.954502 + 1.65325i
\(819\) 0 0
\(820\) −51.3472 88.9359i −1.79312 3.10578i
\(821\) 2.40737 13.6529i 0.0840177 0.476488i −0.913547 0.406734i \(-0.866668\pi\)
0.997564 0.0697537i \(-0.0222213\pi\)
\(822\) 0 0
\(823\) −44.9415 16.3574i −1.56656 0.570182i −0.594334 0.804218i \(-0.702584\pi\)
−0.972228 + 0.234037i \(0.924806\pi\)
\(824\) 64.7686 + 23.5738i 2.25632 + 0.821234i
\(825\) 0 0
\(826\) −0.515271 + 2.92225i −0.0179286 + 0.101678i
\(827\) −21.2209 36.7556i −0.737921 1.27812i −0.953430 0.301615i \(-0.902474\pi\)
0.215508 0.976502i \(-0.430859\pi\)
\(828\) 0 0
\(829\) −13.0018 + 22.5199i −0.451573 + 0.782147i −0.998484 0.0550437i \(-0.982470\pi\)
0.546911 + 0.837191i \(0.315804\pi\)
\(830\) −9.45445 7.93322i −0.328169 0.275366i
\(831\) 0 0
\(832\) 12.9597 + 73.4981i 0.449296 + 2.54809i
\(833\) 13.7773 11.5605i 0.477354 0.400548i
\(834\) 0 0
\(835\) 36.3682 13.2369i 1.25857 0.458083i
\(836\) 59.1096 2.04435
\(837\) 0 0
\(838\) 65.9233 2.27728
\(839\) 1.18051 0.429672i 0.0407558 0.0148339i −0.321562 0.946889i \(-0.604208\pi\)
0.362318 + 0.932055i \(0.381986\pi\)
\(840\) 0 0
\(841\) −16.9766 + 14.2451i −0.585401 + 0.491210i
\(842\) 12.2950 + 69.7282i 0.423712 + 2.40299i
\(843\) 0 0
\(844\) 56.5338 + 47.4375i 1.94597 + 1.63287i
\(845\) 2.77009 4.79794i 0.0952941 0.165054i
\(846\) 0 0
\(847\) 1.83275 + 3.17442i 0.0629742 + 0.109074i
\(848\) 12.8687 72.9817i 0.441911 2.50620i
\(849\) 0 0
\(850\) 14.9227 + 5.43142i 0.511844 + 0.186296i
\(851\) 21.2115 + 7.72034i 0.727119 + 0.264650i
\(852\) 0 0
\(853\) 0.252545 1.43225i 0.00864696 0.0490394i −0.980179 0.198114i \(-0.936518\pi\)
0.988826 + 0.149075i \(0.0476295\pi\)
\(854\) 4.63136 + 8.02175i 0.158482 + 0.274499i
\(855\) 0 0
\(856\) 48.3044 83.6657i 1.65101 2.85964i
\(857\) 40.0715 + 33.6240i 1.36882 + 1.14857i 0.973148 + 0.230182i \(0.0739322\pi\)
0.395670 + 0.918393i \(0.370512\pi\)
\(858\) 0 0
\(859\) −3.64736 20.6852i −0.124446 0.705771i −0.981635 0.190768i \(-0.938902\pi\)
0.857189 0.515003i \(-0.172209\pi\)
\(860\) −61.3394 + 51.4698i −2.09165 + 1.75511i
\(861\) 0 0
\(862\) −81.1347 + 29.5306i −2.76346 + 1.00582i
\(863\) −12.9813 −0.441890 −0.220945 0.975286i \(-0.570914\pi\)
−0.220945 + 0.975286i \(0.570914\pi\)
\(864\) 0 0
\(865\) 4.31221 0.146619
\(866\) 0.0312860 0.0113872i 0.00106314 0.000386952i
\(867\) 0 0
\(868\) −9.40955 + 7.89555i −0.319381 + 0.267992i
\(869\) 1.76868 + 10.0307i 0.0599983 + 0.340267i
\(870\) 0 0
\(871\) 29.7642 + 24.9751i 1.00852 + 0.846250i
\(872\) 54.8735 95.0438i 1.85825 3.21859i
\(873\) 0 0
\(874\) 36.4243 + 63.0887i 1.23207 + 2.13401i
\(875\) −1.04715 + 5.93871i −0.0354003 + 0.200765i
\(876\) 0 0
\(877\) −29.1734 10.6182i −0.985115 0.358553i −0.201288 0.979532i \(-0.564513\pi\)
−0.783827 + 0.620979i \(0.786735\pi\)
\(878\) 13.4844 + 4.90793i 0.455078 + 0.165635i
\(879\) 0 0
\(880\) 7.59621 43.0803i 0.256068 1.45224i
\(881\) 9.64783 + 16.7105i 0.325044 + 0.562992i 0.981521 0.191353i \(-0.0612877\pi\)
−0.656478 + 0.754346i \(0.727954\pi\)
\(882\) 0 0
\(883\) 4.91194 8.50773i 0.165300 0.286308i −0.771462 0.636276i \(-0.780474\pi\)
0.936762 + 0.349968i \(0.113807\pi\)
\(884\) −33.7828 28.3471i −1.13624 0.953417i
\(885\) 0 0
\(886\) 19.1163 + 108.414i 0.642224 + 3.64223i
\(887\) −33.7927 + 28.3555i −1.13465 + 0.952084i −0.999251 0.0387076i \(-0.987676\pi\)
−0.135399 + 0.990791i \(0.543231\pi\)
\(888\) 0 0
\(889\) −1.10278 + 0.401378i −0.0369860 + 0.0134618i
\(890\) 50.7533 1.70125
\(891\) 0 0
\(892\) −36.2219 −1.21280
\(893\) 37.2156 13.5454i 1.24537 0.453278i
\(894\) 0 0
\(895\) 11.3970 9.56323i 0.380960 0.319664i
\(896\) −2.34405 13.2938i −0.0783093 0.444114i
\(897\) 0 0
\(898\) 31.9699 + 26.8260i 1.06685 + 0.895194i
\(899\) 6.03376 10.4508i 0.201237 0.348553i
\(900\) 0 0
\(901\) 7.23887 + 12.5381i 0.241162 + 0.417704i
\(902\) −10.4027 + 58.9966i −0.346372 + 1.96437i
\(903\) 0 0
\(904\) 16.3924 + 5.96635i 0.545204 + 0.198438i
\(905\) −12.4337 4.52548i −0.413309 0.150432i
\(906\) 0 0
\(907\) −7.36483 + 41.7680i −0.244545 + 1.38689i 0.577001 + 0.816743i \(0.304223\pi\)
−0.821546 + 0.570142i \(0.806888\pi\)
\(908\) −25.8979 44.8564i −0.859451 1.48861i
\(909\) 0 0
\(910\) 3.52426 6.10419i 0.116828 0.202352i
\(911\) −28.1218 23.5970i −0.931716 0.781802i 0.0444090 0.999013i \(-0.485860\pi\)
−0.976125 + 0.217211i \(0.930304\pi\)
\(912\) 0 0
\(913\) 0.908497 + 5.15234i 0.0300668 + 0.170518i
\(914\) −4.94996 + 4.15351i −0.163730 + 0.137386i
\(915\) 0 0
\(916\) 70.1779 25.5427i 2.31874 0.843953i
\(917\) 8.56130 0.282719
\(918\) 0 0
\(919\) −14.0589 −0.463761 −0.231881 0.972744i \(-0.574488\pi\)
−0.231881 + 0.972744i \(0.574488\pi\)
\(920\) 65.5181 23.8466i 2.16007 0.786200i
\(921\) 0 0
\(922\) 67.3131 56.4824i 2.21684 1.86015i
\(923\) 1.53260 + 8.69180i 0.0504461 + 0.286094i
\(924\) 0 0
\(925\) 8.19996 + 6.88058i 0.269613 + 0.226232i
\(926\) 45.8218 79.3657i 1.50580 2.60812i
\(927\) 0 0
\(928\) 24.7764 + 42.9140i 0.813325 + 1.40872i
\(929\) 3.21553 18.2362i 0.105498 0.598309i −0.885522 0.464597i \(-0.846199\pi\)
0.991020 0.133712i \(-0.0426898\pi\)
\(930\) 0 0
\(931\) 36.7644 + 13.3812i 1.20490 + 0.438550i
\(932\) 26.5991 + 9.68128i 0.871282 + 0.317121i
\(933\) 0 0
\(934\) −6.48352 + 36.7699i −0.212147 + 1.20315i
\(935\) 4.27302 + 7.40108i 0.139743 + 0.242041i
\(936\) 0 0
\(937\) −2.23409 + 3.86955i −0.0729845 + 0.126413i −0.900208 0.435460i \(-0.856586\pi\)
0.827224 + 0.561873i \(0.189919\pi\)
\(938\) −12.9495 10.8660i −0.422818 0.354786i
\(939\) 0 0
\(940\) −10.5503 59.8340i −0.344114 1.95157i
\(941\) 1.53505 1.28806i 0.0500410 0.0419894i −0.617424 0.786630i \(-0.711824\pi\)
0.667465 + 0.744641i \(0.267379\pi\)
\(942\) 0 0
\(943\) −50.4157 + 18.3498i −1.64176 + 0.597552i
\(944\) 29.8889 0.972801
\(945\) 0 0
\(946\) 46.7105 1.51869
\(947\) −11.8249 + 4.30392i −0.384258 + 0.139859i −0.526924 0.849912i \(-0.676655\pi\)
0.142666 + 0.989771i \(0.454433\pi\)
\(948\) 0 0
\(949\) 23.6876 19.8763i 0.768932 0.645210i
\(950\) 5.99879 + 34.0209i 0.194627 + 1.10378i
\(951\) 0 0
\(952\) 9.16966 + 7.69426i 0.297190 + 0.249372i
\(953\) −9.98205 + 17.2894i −0.323350 + 0.560059i −0.981177 0.193110i \(-0.938143\pi\)
0.657827 + 0.753169i \(0.271476\pi\)
\(954\) 0 0
\(955\) −13.2932 23.0246i −0.430159 0.745058i
\(956\) −16.4112 + 93.0726i −0.530777 + 3.01018i
\(957\) 0 0
\(958\) −14.9748 5.45038i −0.483814 0.176094i
\(959\) 6.55136 + 2.38450i 0.211554 + 0.0769995i
\(960\) 0 0
\(961\) −1.68533 + 9.55799i −0.0543655 + 0.308322i
\(962\) −20.4534 35.4263i −0.659444 1.14219i
\(963\) 0 0
\(964\) 5.33544 9.24125i 0.171843 0.297640i
\(965\) −5.87366 4.92858i −0.189080 0.158657i
\(966\) 0 0
\(967\) −5.59296 31.7193i −0.179858 1.02002i −0.932386 0.361463i \(-0.882277\pi\)
0.752529 0.658559i \(-0.228834\pi\)
\(968\) 50.3358 42.2368i 1.61785 1.35754i
\(969\) 0 0
\(970\) −29.2863 + 10.6593i −0.940327 + 0.342251i
\(971\) 6.62934 0.212746 0.106373 0.994326i \(-0.466076\pi\)
0.106373 + 0.994326i \(0.466076\pi\)
\(972\) 0 0
\(973\) 3.96300 0.127048
\(974\) 73.7920 26.8581i 2.36445 0.860589i
\(975\) 0 0
\(976\) 71.4722 59.9723i 2.28777 1.91967i
\(977\) −2.05888 11.6765i −0.0658696 0.373565i −0.999867 0.0162861i \(-0.994816\pi\)
0.933998 0.357279i \(-0.116295\pi\)
\(978\) 0 0
\(979\) −16.4812 13.8294i −0.526742 0.441989i
\(980\) 30.0102 51.9792i 0.958642 1.66042i
\(981\) 0 0
\(982\) −5.92884 10.2690i −0.189197 0.327698i
\(983\) 9.04099 51.2740i 0.288363 1.63539i −0.404657 0.914469i \(-0.632609\pi\)
0.693020 0.720918i \(-0.256280\pi\)
\(984\) 0 0
\(985\) 4.70542 + 1.71263i 0.149927 + 0.0545690i
\(986\) −17.7129 6.44698i −0.564095 0.205314i
\(987\) 0 0
\(988\) 16.6588 94.4768i 0.529987 3.00571i
\(989\) 20.9165 + 36.2284i 0.665105 + 1.15200i
\(990\) 0 0
\(991\) −0.735575 + 1.27405i −0.0233663 + 0.0404716i −0.877472 0.479628i \(-0.840772\pi\)
0.854106 + 0.520099i \(0.174105\pi\)
\(992\) 66.9843 + 56.2065i 2.12675 + 1.78456i
\(993\) 0 0
\(994\) −0.666790 3.78155i −0.0211493 0.119944i
\(995\) 19.0740 16.0050i 0.604685 0.507391i
\(996\) 0 0
\(997\) 24.8279 9.03661i 0.786307 0.286192i 0.0825071 0.996590i \(-0.473707\pi\)
0.703800 + 0.710398i \(0.251485\pi\)
\(998\) −95.6065 −3.02637
\(999\) 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 729.2.e.t.163.2 12
3.2 odd 2 729.2.e.k.163.1 12
9.2 odd 6 729.2.e.u.406.2 12
9.4 even 3 729.2.e.s.649.1 12
9.5 odd 6 729.2.e.l.649.2 12
9.7 even 3 729.2.e.j.406.1 12
27.2 odd 18 729.2.a.e.1.6 yes 6
27.4 even 9 inner 729.2.e.t.568.2 12
27.5 odd 18 729.2.e.l.82.2 12
27.7 even 9 729.2.c.d.487.6 12
27.11 odd 18 729.2.c.a.244.1 12
27.13 even 9 729.2.e.j.325.1 12
27.14 odd 18 729.2.e.u.325.2 12
27.16 even 9 729.2.c.d.244.6 12
27.20 odd 18 729.2.c.a.487.1 12
27.22 even 9 729.2.e.s.82.1 12
27.23 odd 18 729.2.e.k.568.1 12
27.25 even 9 729.2.a.b.1.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
729.2.a.b.1.1 6 27.25 even 9
729.2.a.e.1.6 yes 6 27.2 odd 18
729.2.c.a.244.1 12 27.11 odd 18
729.2.c.a.487.1 12 27.20 odd 18
729.2.c.d.244.6 12 27.16 even 9
729.2.c.d.487.6 12 27.7 even 9
729.2.e.j.325.1 12 27.13 even 9
729.2.e.j.406.1 12 9.7 even 3
729.2.e.k.163.1 12 3.2 odd 2
729.2.e.k.568.1 12 27.23 odd 18
729.2.e.l.82.2 12 27.5 odd 18
729.2.e.l.649.2 12 9.5 odd 6
729.2.e.s.82.1 12 27.22 even 9
729.2.e.s.649.1 12 9.4 even 3
729.2.e.t.163.2 12 1.1 even 1 trivial
729.2.e.t.568.2 12 27.4 even 9 inner
729.2.e.u.325.2 12 27.14 odd 18
729.2.e.u.406.2 12 9.2 odd 6