Properties

Label 729.2.e.l.82.1
Level $729$
Weight $2$
Character 729.82
Analytic conductor $5.821$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

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 82.1
Root \(-0.0878222i\) of defining polynomial
Character \(\chi\) \(=\) 729.82
Dual form 729.2.e.l.649.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.0300370 - 0.170348i) q^{2} +(1.85127 - 0.673807i) q^{4} +(2.86237 + 2.40182i) q^{5} +(-2.84868 - 1.03683i) q^{7} +(-0.343364 - 0.594724i) q^{8} +O(q^{10})\) \(q+(-0.0300370 - 0.170348i) q^{2} +(1.85127 - 0.673807i) q^{4} +(2.86237 + 2.40182i) q^{5} +(-2.84868 - 1.03683i) q^{7} +(-0.343364 - 0.594724i) q^{8} +(0.323168 - 0.559743i) q^{10} +(1.90875 - 1.60163i) q^{11} +(-0.132865 + 0.753515i) q^{13} +(-0.0910570 + 0.516410i) q^{14} +(2.92734 - 2.45633i) q^{16} +(2.31139 - 4.00345i) q^{17} +(0.305922 + 0.529872i) q^{19} +(6.91738 + 2.51772i) q^{20} +(-0.330168 - 0.277044i) q^{22} +(6.13091 - 2.23147i) q^{23} +(1.55622 + 8.82575i) q^{25} +0.132351 q^{26} -5.97229 q^{28} +(1.13755 + 6.45137i) q^{29} +(-6.15539 + 2.24038i) q^{31} +(-1.55849 - 1.30773i) q^{32} +(-0.751407 - 0.273490i) q^{34} +(-5.66369 - 9.80980i) q^{35} +(-2.47984 + 4.29522i) q^{37} +(0.0810738 - 0.0680290i) q^{38} +(0.445582 - 2.52702i) q^{40} +(-0.913431 + 5.18032i) q^{41} +(4.26731 - 3.58070i) q^{43} +(2.45442 - 4.25118i) q^{44} +(-0.564280 - 0.977362i) q^{46} +(1.04082 + 0.378827i) q^{47} +(1.67762 + 1.40769i) q^{49} +(1.45670 - 0.530197i) q^{50} +(0.261754 + 1.48448i) q^{52} -8.84310 q^{53} +9.31038 q^{55} +(0.361503 + 2.05019i) q^{56} +(1.06481 - 0.387559i) q^{58} +(9.07897 + 7.61816i) q^{59} +(-7.69327 - 2.80012i) q^{61} +(0.566533 + 0.981264i) q^{62} +(3.64541 - 6.31404i) q^{64} +(-2.19011 + 1.83772i) q^{65} +(-0.210520 + 1.19392i) q^{67} +(1.58146 - 8.96889i) q^{68} +(-1.50096 + 1.25946i) q^{70} +(-2.45973 + 4.26038i) q^{71} +(-2.14972 - 3.72343i) q^{73} +(0.806169 + 0.293421i) q^{74} +(0.923375 + 0.774804i) q^{76} +(-7.09803 + 2.58347i) q^{77} +(-2.04811 - 11.6154i) q^{79} +14.2788 q^{80} +0.909895 q^{82} +(-1.56562 - 8.87910i) q^{83} +(16.2316 - 5.90782i) q^{85} +(-0.738141 - 0.619374i) q^{86} +(-1.60792 - 0.585237i) q^{88} +(3.76943 + 6.52884i) q^{89} +(1.15976 - 2.00876i) q^{91} +(9.84638 - 8.26210i) q^{92} +(0.0332694 - 0.188680i) q^{94} +(-0.396993 + 2.25146i) q^{95} +(-0.726481 + 0.609590i) q^{97} +(0.189407 - 0.328062i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 3 q^{2} - 3 q^{4} + 12 q^{5} - 3 q^{7} - 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 3 q^{2} - 3 q^{4} + 12 q^{5} - 3 q^{7} - 6 q^{8} - 6 q^{10} - 3 q^{11} + 6 q^{13} - 6 q^{14} + 27 q^{16} + 9 q^{17} - 12 q^{19} + 39 q^{20} - 39 q^{22} + 21 q^{23} + 6 q^{25} + 48 q^{26} + 6 q^{28} + 6 q^{29} + 6 q^{31} + 27 q^{32} - 18 q^{34} - 30 q^{35} - 3 q^{37} + 3 q^{38} + 33 q^{40} - 15 q^{41} - 30 q^{43} + 33 q^{44} + 3 q^{46} - 21 q^{47} - 3 q^{49} + 6 q^{50} - 18 q^{53} + 30 q^{55} + 15 q^{56} - 3 q^{58} + 30 q^{59} - 30 q^{61} + 30 q^{62} - 6 q^{64} - 12 q^{65} - 39 q^{67} + 18 q^{68} + 51 q^{70} - 12 q^{73} + 57 q^{74} + 57 q^{76} - 24 q^{77} + 15 q^{79} - 42 q^{80} - 42 q^{82} - 21 q^{83} + 54 q^{85} - 60 q^{86} + 12 q^{88} + 9 q^{89} - 18 q^{91} - 15 q^{92} + 33 q^{94} + 42 q^{95} - 12 q^{97} - 18 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{4}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.0300370 0.170348i −0.0212393 0.120454i 0.972345 0.233550i \(-0.0750343\pi\)
−0.993584 + 0.113096i \(0.963923\pi\)
\(3\) 0 0
\(4\) 1.85127 0.673807i 0.925635 0.336903i
\(5\) 2.86237 + 2.40182i 1.28009 + 1.07412i 0.993231 + 0.116153i \(0.0370561\pi\)
0.286861 + 0.957972i \(0.407388\pi\)
\(6\) 0 0
\(7\) −2.84868 1.03683i −1.07670 0.391886i −0.258021 0.966139i \(-0.583070\pi\)
−0.818678 + 0.574253i \(0.805292\pi\)
\(8\) −0.343364 0.594724i −0.121398 0.210267i
\(9\) 0 0
\(10\) 0.323168 0.559743i 0.102195 0.177006i
\(11\) 1.90875 1.60163i 0.575510 0.482910i −0.307959 0.951400i \(-0.599646\pi\)
0.883469 + 0.468490i \(0.155202\pi\)
\(12\) 0 0
\(13\) −0.132865 + 0.753515i −0.0368501 + 0.208987i −0.997673 0.0681742i \(-0.978283\pi\)
0.960823 + 0.277162i \(0.0893937\pi\)
\(14\) −0.0910570 + 0.516410i −0.0243360 + 0.138016i
\(15\) 0 0
\(16\) 2.92734 2.45633i 0.731835 0.614083i
\(17\) 2.31139 4.00345i 0.560595 0.970979i −0.436850 0.899534i \(-0.643906\pi\)
0.997445 0.0714442i \(-0.0227608\pi\)
\(18\) 0 0
\(19\) 0.305922 + 0.529872i 0.0701833 + 0.121561i 0.898982 0.437987i \(-0.144308\pi\)
−0.828798 + 0.559548i \(0.810975\pi\)
\(20\) 6.91738 + 2.51772i 1.54677 + 0.562980i
\(21\) 0 0
\(22\) −0.330168 0.277044i −0.0703920 0.0590659i
\(23\) 6.13091 2.23147i 1.27838 0.465293i 0.388486 0.921455i \(-0.372998\pi\)
0.889897 + 0.456161i \(0.150776\pi\)
\(24\) 0 0
\(25\) 1.55622 + 8.82575i 0.311244 + 1.76515i
\(26\) 0.132351 0.0259561
\(27\) 0 0
\(28\) −5.97229 −1.12866
\(29\) 1.13755 + 6.45137i 0.211238 + 1.19799i 0.887317 + 0.461160i \(0.152567\pi\)
−0.676079 + 0.736829i \(0.736322\pi\)
\(30\) 0 0
\(31\) −6.15539 + 2.24038i −1.10554 + 0.402384i −0.829356 0.558721i \(-0.811292\pi\)
−0.276184 + 0.961105i \(0.589070\pi\)
\(32\) −1.55849 1.30773i −0.275504 0.231176i
\(33\) 0 0
\(34\) −0.751407 0.273490i −0.128865 0.0469031i
\(35\) −5.66369 9.80980i −0.957338 1.65816i
\(36\) 0 0
\(37\) −2.47984 + 4.29522i −0.407684 + 0.706129i −0.994630 0.103497i \(-0.966997\pi\)
0.586946 + 0.809626i \(0.300330\pi\)
\(38\) 0.0810738 0.0680290i 0.0131519 0.0110358i
\(39\) 0 0
\(40\) 0.445582 2.52702i 0.0704527 0.399557i
\(41\) −0.913431 + 5.18032i −0.142654 + 0.809031i 0.826567 + 0.562838i \(0.190291\pi\)
−0.969221 + 0.246192i \(0.920820\pi\)
\(42\) 0 0
\(43\) 4.26731 3.58070i 0.650758 0.546051i −0.256543 0.966533i \(-0.582583\pi\)
0.907301 + 0.420482i \(0.138139\pi\)
\(44\) 2.45442 4.25118i 0.370018 0.640889i
\(45\) 0 0
\(46\) −0.564280 0.977362i −0.0831986 0.144104i
\(47\) 1.04082 + 0.378827i 0.151819 + 0.0552576i 0.416812 0.908993i \(-0.363147\pi\)
−0.264993 + 0.964250i \(0.585370\pi\)
\(48\) 0 0
\(49\) 1.67762 + 1.40769i 0.239660 + 0.201099i
\(50\) 1.45670 0.530197i 0.206009 0.0749812i
\(51\) 0 0
\(52\) 0.261754 + 1.48448i 0.0362988 + 0.205861i
\(53\) −8.84310 −1.21469 −0.607346 0.794437i \(-0.707766\pi\)
−0.607346 + 0.794437i \(0.707766\pi\)
\(54\) 0 0
\(55\) 9.31038 1.25541
\(56\) 0.361503 + 2.05019i 0.0483079 + 0.273968i
\(57\) 0 0
\(58\) 1.06481 0.387559i 0.139816 0.0508890i
\(59\) 9.07897 + 7.61816i 1.18198 + 0.991800i 0.999964 + 0.00850504i \(0.00270727\pi\)
0.182018 + 0.983295i \(0.441737\pi\)
\(60\) 0 0
\(61\) −7.69327 2.80012i −0.985022 0.358519i −0.201231 0.979544i \(-0.564494\pi\)
−0.783791 + 0.621025i \(0.786716\pi\)
\(62\) 0.566533 + 0.981264i 0.0719498 + 0.124621i
\(63\) 0 0
\(64\) 3.64541 6.31404i 0.455677 0.789255i
\(65\) −2.19011 + 1.83772i −0.271650 + 0.227941i
\(66\) 0 0
\(67\) −0.210520 + 1.19392i −0.0257192 + 0.145861i −0.994963 0.100241i \(-0.968039\pi\)
0.969244 + 0.246102i \(0.0791497\pi\)
\(68\) 1.58146 8.96889i 0.191780 1.08764i
\(69\) 0 0
\(70\) −1.50096 + 1.25946i −0.179399 + 0.150534i
\(71\) −2.45973 + 4.26038i −0.291916 + 0.505614i −0.974263 0.225415i \(-0.927626\pi\)
0.682346 + 0.731029i \(0.260960\pi\)
\(72\) 0 0
\(73\) −2.14972 3.72343i −0.251606 0.435795i 0.712362 0.701812i \(-0.247625\pi\)
−0.963968 + 0.266017i \(0.914292\pi\)
\(74\) 0.806169 + 0.293421i 0.0937152 + 0.0341095i
\(75\) 0 0
\(76\) 0.923375 + 0.774804i 0.105918 + 0.0888761i
\(77\) −7.09803 + 2.58347i −0.808896 + 0.294414i
\(78\) 0 0
\(79\) −2.04811 11.6154i −0.230431 1.30684i −0.852027 0.523499i \(-0.824627\pi\)
0.621596 0.783338i \(-0.286485\pi\)
\(80\) 14.2788 1.59642
\(81\) 0 0
\(82\) 0.909895 0.100481
\(83\) −1.56562 8.87910i −0.171850 0.974608i −0.941718 0.336404i \(-0.890789\pi\)
0.769868 0.638203i \(-0.220322\pi\)
\(84\) 0 0
\(85\) 16.2316 5.90782i 1.76057 0.640793i
\(86\) −0.738141 0.619374i −0.0795958 0.0667888i
\(87\) 0 0
\(88\) −1.60792 0.585237i −0.171405 0.0623865i
\(89\) 3.76943 + 6.52884i 0.399558 + 0.692055i 0.993671 0.112326i \(-0.0358302\pi\)
−0.594113 + 0.804382i \(0.702497\pi\)
\(90\) 0 0
\(91\) 1.15976 2.00876i 0.121576 0.210575i
\(92\) 9.84638 8.26210i 1.02656 0.861383i
\(93\) 0 0
\(94\) 0.0332694 0.188680i 0.00343148 0.0194609i
\(95\) −0.396993 + 2.25146i −0.0407306 + 0.230995i
\(96\) 0 0
\(97\) −0.726481 + 0.609590i −0.0737630 + 0.0618945i −0.678924 0.734209i \(-0.737553\pi\)
0.605161 + 0.796103i \(0.293109\pi\)
\(98\) 0.189407 0.328062i 0.0191330 0.0331393i
\(99\) 0 0
\(100\) 8.82783 + 15.2902i 0.882783 + 1.52902i
\(101\) −5.26994 1.91810i −0.524379 0.190858i 0.0662479 0.997803i \(-0.478897\pi\)
−0.590627 + 0.806945i \(0.701119\pi\)
\(102\) 0 0
\(103\) −7.21998 6.05829i −0.711406 0.596941i 0.213587 0.976924i \(-0.431485\pi\)
−0.924993 + 0.379983i \(0.875930\pi\)
\(104\) 0.493754 0.179712i 0.0484166 0.0176222i
\(105\) 0 0
\(106\) 0.265620 + 1.50640i 0.0257993 + 0.146315i
\(107\) 1.27825 0.123573 0.0617864 0.998089i \(-0.480320\pi\)
0.0617864 + 0.998089i \(0.480320\pi\)
\(108\) 0 0
\(109\) −7.40689 −0.709451 −0.354726 0.934970i \(-0.615426\pi\)
−0.354726 + 0.934970i \(0.615426\pi\)
\(110\) −0.279655 1.58600i −0.0266641 0.151220i
\(111\) 0 0
\(112\) −10.8858 + 3.96212i −1.02862 + 0.374386i
\(113\) −7.16402 6.01133i −0.673934 0.565498i 0.240293 0.970700i \(-0.422757\pi\)
−0.914227 + 0.405203i \(0.867201\pi\)
\(114\) 0 0
\(115\) 22.9085 + 8.33802i 2.13623 + 0.777524i
\(116\) 6.45289 + 11.1767i 0.599136 + 1.03773i
\(117\) 0 0
\(118\) 1.02503 1.77541i 0.0943621 0.163440i
\(119\) −10.7353 + 9.00800i −0.984105 + 0.825762i
\(120\) 0 0
\(121\) −0.832027 + 4.71866i −0.0756388 + 0.428969i
\(122\) −0.245913 + 1.39464i −0.0222639 + 0.126265i
\(123\) 0 0
\(124\) −9.88569 + 8.29508i −0.887762 + 0.744920i
\(125\) −7.40194 + 12.8205i −0.662050 + 1.14670i
\(126\) 0 0
\(127\) −10.3984 18.0106i −0.922710 1.59818i −0.795204 0.606342i \(-0.792636\pi\)
−0.127505 0.991838i \(-0.540697\pi\)
\(128\) −5.00862 1.82299i −0.442704 0.161131i
\(129\) 0 0
\(130\) 0.378837 + 0.317882i 0.0332262 + 0.0278801i
\(131\) −0.616278 + 0.224307i −0.0538445 + 0.0195978i −0.368802 0.929508i \(-0.620232\pi\)
0.314958 + 0.949106i \(0.398010\pi\)
\(132\) 0 0
\(133\) −0.322083 1.82662i −0.0279282 0.158388i
\(134\) 0.209705 0.0181158
\(135\) 0 0
\(136\) −3.17460 −0.272219
\(137\) −1.49122 8.45714i −0.127404 0.722542i −0.979851 0.199729i \(-0.935994\pi\)
0.852447 0.522813i \(-0.175117\pi\)
\(138\) 0 0
\(139\) −12.6352 + 4.59885i −1.07171 + 0.390069i −0.816815 0.576900i \(-0.804262\pi\)
−0.254892 + 0.966969i \(0.582040\pi\)
\(140\) −17.0949 14.3443i −1.44478 1.21232i
\(141\) 0 0
\(142\) 0.799630 + 0.291042i 0.0671035 + 0.0244237i
\(143\) 0.953247 + 1.65107i 0.0797145 + 0.138070i
\(144\) 0 0
\(145\) −12.2389 + 21.1984i −1.01639 + 1.76043i
\(146\) −0.569708 + 0.478042i −0.0471494 + 0.0395630i
\(147\) 0 0
\(148\) −1.69671 + 9.62254i −0.139469 + 0.790968i
\(149\) −1.67085 + 9.47589i −0.136882 + 0.776295i 0.836649 + 0.547739i \(0.184511\pi\)
−0.973531 + 0.228556i \(0.926600\pi\)
\(150\) 0 0
\(151\) −5.46052 + 4.58192i −0.444371 + 0.372871i −0.837342 0.546679i \(-0.815892\pi\)
0.392971 + 0.919551i \(0.371447\pi\)
\(152\) 0.210085 0.363878i 0.0170402 0.0295144i
\(153\) 0 0
\(154\) 0.653293 + 1.13154i 0.0526439 + 0.0911818i
\(155\) −23.0000 8.37131i −1.84740 0.672400i
\(156\) 0 0
\(157\) 5.88764 + 4.94032i 0.469885 + 0.394280i 0.846753 0.531987i \(-0.178554\pi\)
−0.376868 + 0.926267i \(0.622999\pi\)
\(158\) −1.91714 + 0.697784i −0.152520 + 0.0555127i
\(159\) 0 0
\(160\) −1.32005 7.48640i −0.104360 0.591852i
\(161\) −19.7786 −1.55877
\(162\) 0 0
\(163\) 1.04750 0.0820465 0.0410232 0.999158i \(-0.486938\pi\)
0.0410232 + 0.999158i \(0.486938\pi\)
\(164\) 1.79953 + 10.2056i 0.140520 + 0.796927i
\(165\) 0 0
\(166\) −1.46551 + 0.533402i −0.113746 + 0.0414000i
\(167\) −6.39959 5.36990i −0.495215 0.415535i 0.360676 0.932691i \(-0.382546\pi\)
−0.855891 + 0.517156i \(0.826991\pi\)
\(168\) 0 0
\(169\) 11.6659 + 4.24603i 0.897375 + 0.326618i
\(170\) −1.49393 2.58757i −0.114580 0.198458i
\(171\) 0 0
\(172\) 5.48724 9.50417i 0.418398 0.724686i
\(173\) −16.7348 + 14.0422i −1.27233 + 1.06761i −0.278073 + 0.960560i \(0.589696\pi\)
−0.994254 + 0.107049i \(0.965860\pi\)
\(174\) 0 0
\(175\) 4.71767 26.7552i 0.356622 2.02251i
\(176\) 1.65343 9.37704i 0.124632 0.706821i
\(177\) 0 0
\(178\) 0.998953 0.838221i 0.0748747 0.0628273i
\(179\) −4.54433 + 7.87101i −0.339659 + 0.588307i −0.984369 0.176121i \(-0.943645\pi\)
0.644709 + 0.764428i \(0.276978\pi\)
\(180\) 0 0
\(181\) 3.56539 + 6.17543i 0.265013 + 0.459016i 0.967567 0.252614i \(-0.0812904\pi\)
−0.702554 + 0.711630i \(0.747957\pi\)
\(182\) −0.377024 0.137225i −0.0279469 0.0101718i
\(183\) 0 0
\(184\) −3.43224 2.87999i −0.253028 0.212316i
\(185\) −17.4146 + 6.33838i −1.28034 + 0.466007i
\(186\) 0 0
\(187\) −2.00018 11.3436i −0.146268 0.829525i
\(188\) 2.18209 0.159145
\(189\) 0 0
\(190\) 0.395456 0.0286894
\(191\) −2.07607 11.7740i −0.150219 0.851936i −0.963027 0.269404i \(-0.913173\pi\)
0.812808 0.582532i \(-0.197938\pi\)
\(192\) 0 0
\(193\) 8.33849 3.03496i 0.600218 0.218461i −0.0239999 0.999712i \(-0.507640\pi\)
0.624218 + 0.781251i \(0.285418\pi\)
\(194\) 0.125664 + 0.105444i 0.00902214 + 0.00757047i
\(195\) 0 0
\(196\) 4.05424 + 1.47562i 0.289589 + 0.105402i
\(197\) 3.69895 + 6.40677i 0.263539 + 0.456464i 0.967180 0.254093i \(-0.0817768\pi\)
−0.703641 + 0.710556i \(0.748443\pi\)
\(198\) 0 0
\(199\) 5.19187 8.99259i 0.368042 0.637468i −0.621217 0.783638i \(-0.713362\pi\)
0.989259 + 0.146171i \(0.0466948\pi\)
\(200\) 4.71454 3.95597i 0.333368 0.279729i
\(201\) 0 0
\(202\) −0.168452 + 0.955338i −0.0118522 + 0.0672174i
\(203\) 3.44848 19.5573i 0.242036 1.37265i
\(204\) 0 0
\(205\) −15.0568 + 12.6341i −1.05161 + 0.882406i
\(206\) −0.815151 + 1.41188i −0.0567942 + 0.0983705i
\(207\) 0 0
\(208\) 1.46194 + 2.53215i 0.101367 + 0.175573i
\(209\) 1.43259 + 0.521420i 0.0990942 + 0.0360674i
\(210\) 0 0
\(211\) 15.9806 + 13.4093i 1.10015 + 0.923133i 0.997435 0.0715777i \(-0.0228034\pi\)
0.102712 + 0.994711i \(0.467248\pi\)
\(212\) −16.3710 + 5.95854i −1.12436 + 0.409234i
\(213\) 0 0
\(214\) −0.0383946 0.217747i −0.00262460 0.0148849i
\(215\) 20.8148 1.41956
\(216\) 0 0
\(217\) 19.8576 1.34802
\(218\) 0.222480 + 1.26175i 0.0150683 + 0.0854564i
\(219\) 0 0
\(220\) 17.2360 6.27340i 1.16205 0.422952i
\(221\) 2.70955 + 2.27358i 0.182264 + 0.152938i
\(222\) 0 0
\(223\) −22.1565 8.06432i −1.48371 0.540027i −0.531926 0.846791i \(-0.678531\pi\)
−0.951786 + 0.306764i \(0.900754\pi\)
\(224\) 3.08373 + 5.34118i 0.206041 + 0.356873i
\(225\) 0 0
\(226\) −0.808832 + 1.40094i −0.0538027 + 0.0931890i
\(227\) 8.03131 6.73907i 0.533057 0.447288i −0.336099 0.941827i \(-0.609108\pi\)
0.869155 + 0.494539i \(0.164663\pi\)
\(228\) 0 0
\(229\) −2.41066 + 13.6715i −0.159301 + 0.903439i 0.795447 + 0.606023i \(0.207236\pi\)
−0.954748 + 0.297416i \(0.903875\pi\)
\(230\) 0.732263 4.15287i 0.0482840 0.273832i
\(231\) 0 0
\(232\) 3.44619 2.89170i 0.226254 0.189849i
\(233\) 3.79982 6.58149i 0.248935 0.431167i −0.714296 0.699844i \(-0.753253\pi\)
0.963230 + 0.268676i \(0.0865862\pi\)
\(234\) 0 0
\(235\) 2.06934 + 3.58420i 0.134989 + 0.233807i
\(236\) 21.9408 + 7.98579i 1.42822 + 0.519831i
\(237\) 0 0
\(238\) 1.85695 + 1.55817i 0.120368 + 0.101001i
\(239\) 15.5601 5.66340i 1.00650 0.366335i 0.214411 0.976744i \(-0.431217\pi\)
0.792087 + 0.610408i \(0.208995\pi\)
\(240\) 0 0
\(241\) −2.52111 14.2979i −0.162399 0.921010i −0.951706 0.307011i \(-0.900671\pi\)
0.789307 0.613999i \(-0.210440\pi\)
\(242\) 0.828806 0.0532776
\(243\) 0 0
\(244\) −16.1290 −1.03256
\(245\) 1.42096 + 8.05867i 0.0907819 + 0.514850i
\(246\) 0 0
\(247\) −0.439913 + 0.160115i −0.0279910 + 0.0101879i
\(248\) 3.44595 + 2.89149i 0.218818 + 0.183610i
\(249\) 0 0
\(250\) 2.40629 + 0.875816i 0.152187 + 0.0553915i
\(251\) 4.52591 + 7.83910i 0.285673 + 0.494800i 0.972772 0.231764i \(-0.0744497\pi\)
−0.687099 + 0.726563i \(0.741116\pi\)
\(252\) 0 0
\(253\) 8.12838 14.0788i 0.511027 0.885125i
\(254\) −2.75573 + 2.31233i −0.172910 + 0.145089i
\(255\) 0 0
\(256\) 2.37198 13.4522i 0.148249 0.840760i
\(257\) −1.68437 + 9.55251i −0.105068 + 0.595870i 0.886125 + 0.463446i \(0.153387\pi\)
−0.991193 + 0.132424i \(0.957724\pi\)
\(258\) 0 0
\(259\) 11.5177 9.66449i 0.715675 0.600522i
\(260\) −2.81622 + 4.87783i −0.174654 + 0.302510i
\(261\) 0 0
\(262\) 0.0567214 + 0.0982443i 0.00350426 + 0.00606955i
\(263\) −25.2357 9.18503i −1.55610 0.566373i −0.586260 0.810123i \(-0.699400\pi\)
−0.969838 + 0.243749i \(0.921623\pi\)
\(264\) 0 0
\(265\) −25.3122 21.2395i −1.55492 1.30473i
\(266\) −0.301488 + 0.109732i −0.0184854 + 0.00672813i
\(267\) 0 0
\(268\) 0.414742 + 2.35212i 0.0253344 + 0.143678i
\(269\) −11.7388 −0.715729 −0.357865 0.933774i \(-0.616495\pi\)
−0.357865 + 0.933774i \(0.616495\pi\)
\(270\) 0 0
\(271\) 0.144576 0.00878238 0.00439119 0.999990i \(-0.498602\pi\)
0.00439119 + 0.999990i \(0.498602\pi\)
\(272\) −3.06756 17.3970i −0.185998 1.05485i
\(273\) 0 0
\(274\) −1.39587 + 0.508053i −0.0843273 + 0.0306926i
\(275\) 17.1060 + 14.3537i 1.03153 + 0.865558i
\(276\) 0 0
\(277\) 0.953248 + 0.346954i 0.0572751 + 0.0208464i 0.370499 0.928833i \(-0.379187\pi\)
−0.313224 + 0.949679i \(0.601409\pi\)
\(278\) 1.16293 + 2.01425i 0.0697479 + 0.120807i
\(279\) 0 0
\(280\) −3.88942 + 6.73667i −0.232437 + 0.402593i
\(281\) 21.0888 17.6956i 1.25805 1.05563i 0.262165 0.965023i \(-0.415564\pi\)
0.995887 0.0906075i \(-0.0288809\pi\)
\(282\) 0 0
\(283\) −4.65427 + 26.3957i −0.276668 + 1.56906i 0.456946 + 0.889494i \(0.348943\pi\)
−0.733614 + 0.679566i \(0.762168\pi\)
\(284\) −1.68295 + 9.54449i −0.0998648 + 0.566361i
\(285\) 0 0
\(286\) 0.252624 0.211977i 0.0149380 0.0125345i
\(287\) 7.97320 13.8100i 0.470643 0.815178i
\(288\) 0 0
\(289\) −2.18506 3.78464i −0.128533 0.222626i
\(290\) 3.97873 + 1.44814i 0.233639 + 0.0850376i
\(291\) 0 0
\(292\) −6.48859 5.44458i −0.379716 0.318620i
\(293\) 17.5321 6.38116i 1.02424 0.372791i 0.225352 0.974277i \(-0.427647\pi\)
0.798883 + 0.601486i \(0.205424\pi\)
\(294\) 0 0
\(295\) 7.68998 + 43.6120i 0.447728 + 2.53919i
\(296\) 3.40596 0.197967
\(297\) 0 0
\(298\) 1.66439 0.0964153
\(299\) 0.866861 + 4.91621i 0.0501319 + 0.284312i
\(300\) 0 0
\(301\) −15.8688 + 5.77576i −0.914660 + 0.332909i
\(302\) 0.944539 + 0.792562i 0.0543521 + 0.0456068i
\(303\) 0 0
\(304\) 2.19708 + 0.799671i 0.126011 + 0.0458643i
\(305\) −15.2956 26.4928i −0.875825 1.51697i
\(306\) 0 0
\(307\) −16.8946 + 29.2624i −0.964227 + 1.67009i −0.252551 + 0.967584i \(0.581269\pi\)
−0.711677 + 0.702507i \(0.752064\pi\)
\(308\) −11.3996 + 9.56541i −0.649553 + 0.545040i
\(309\) 0 0
\(310\) −0.735187 + 4.16945i −0.0417558 + 0.236809i
\(311\) −6.02326 + 34.1596i −0.341548 + 1.93701i 0.00766664 + 0.999971i \(0.497560\pi\)
−0.349214 + 0.937043i \(0.613552\pi\)
\(312\) 0 0
\(313\) 2.55888 2.14716i 0.144636 0.121364i −0.567599 0.823305i \(-0.692127\pi\)
0.712235 + 0.701941i \(0.247683\pi\)
\(314\) 0.664726 1.15134i 0.0375127 0.0649739i
\(315\) 0 0
\(316\) −11.6182 20.1232i −0.653572 1.13202i
\(317\) 29.1613 + 10.6138i 1.63786 + 0.596133i 0.986663 0.162775i \(-0.0520445\pi\)
0.651198 + 0.758908i \(0.274267\pi\)
\(318\) 0 0
\(319\) 12.5040 + 10.4921i 0.700090 + 0.587446i
\(320\) 25.5997 9.31753i 1.43107 0.520866i
\(321\) 0 0
\(322\) 0.594090 + 3.36925i 0.0331073 + 0.187761i
\(323\) 2.82842 0.157378
\(324\) 0 0
\(325\) −6.85710 −0.380363
\(326\) −0.0314637 0.178440i −0.00174261 0.00988285i
\(327\) 0 0
\(328\) 3.39450 1.23550i 0.187430 0.0682190i
\(329\) −2.57217 2.15831i −0.141809 0.118992i
\(330\) 0 0
\(331\) −3.07437 1.11898i −0.168983 0.0615047i 0.256143 0.966639i \(-0.417548\pi\)
−0.425126 + 0.905134i \(0.639770\pi\)
\(332\) −8.88119 15.3827i −0.487419 0.844234i
\(333\) 0 0
\(334\) −0.722527 + 1.25145i −0.0395349 + 0.0684765i
\(335\) −3.47016 + 2.91181i −0.189595 + 0.159089i
\(336\) 0 0
\(337\) 1.10541 6.26910i 0.0602156 0.341500i −0.939784 0.341768i \(-0.888974\pi\)
1.00000 0.000268386i \(8.54299e-5\pi\)
\(338\) 0.372896 2.11480i 0.0202829 0.115030i
\(339\) 0 0
\(340\) 26.0683 21.8739i 1.41375 1.18628i
\(341\) −8.16083 + 14.1350i −0.441934 + 0.765452i
\(342\) 0 0
\(343\) 7.29078 + 12.6280i 0.393665 + 0.681848i
\(344\) −3.59477 1.30839i −0.193817 0.0705435i
\(345\) 0 0
\(346\) 2.89473 + 2.42896i 0.155621 + 0.130582i
\(347\) 8.26216 3.00718i 0.443536 0.161434i −0.110591 0.993866i \(-0.535274\pi\)
0.554127 + 0.832432i \(0.313052\pi\)
\(348\) 0 0
\(349\) 2.50057 + 14.1815i 0.133853 + 0.759116i 0.975652 + 0.219325i \(0.0703855\pi\)
−0.841799 + 0.539791i \(0.818503\pi\)
\(350\) −4.69941 −0.251194
\(351\) 0 0
\(352\) −5.06926 −0.270192
\(353\) 5.76520 + 32.6961i 0.306851 + 1.74024i 0.614663 + 0.788790i \(0.289292\pi\)
−0.307812 + 0.951447i \(0.599597\pi\)
\(354\) 0 0
\(355\) −17.2733 + 6.28697i −0.916773 + 0.333678i
\(356\) 11.3774 + 9.54677i 0.603001 + 0.505978i
\(357\) 0 0
\(358\) 1.47731 + 0.537697i 0.0780782 + 0.0284182i
\(359\) −2.47257 4.28262i −0.130497 0.226028i 0.793371 0.608738i \(-0.208324\pi\)
−0.923868 + 0.382710i \(0.874991\pi\)
\(360\) 0 0
\(361\) 9.31282 16.1303i 0.490149 0.848962i
\(362\) 0.944879 0.792848i 0.0496617 0.0416711i
\(363\) 0 0
\(364\) 0.793508 4.50021i 0.0415911 0.235875i
\(365\) 2.78969 15.8211i 0.146019 0.828114i
\(366\) 0 0
\(367\) −1.90933 + 1.60212i −0.0996662 + 0.0836299i −0.691259 0.722607i \(-0.742944\pi\)
0.591593 + 0.806237i \(0.298499\pi\)
\(368\) 12.4660 21.5918i 0.649837 1.12555i
\(369\) 0 0
\(370\) 1.60281 + 2.77615i 0.0833262 + 0.144325i
\(371\) 25.1911 + 9.16882i 1.30786 + 0.476021i
\(372\) 0 0
\(373\) −21.4857 18.0286i −1.11249 0.933487i −0.114286 0.993448i \(-0.536458\pi\)
−0.998201 + 0.0599605i \(0.980903\pi\)
\(374\) −1.87228 + 0.681453i −0.0968131 + 0.0352371i
\(375\) 0 0
\(376\) −0.132082 0.749075i −0.00681162 0.0386306i
\(377\) −5.01234 −0.258149
\(378\) 0 0
\(379\) 5.13991 0.264019 0.132010 0.991248i \(-0.457857\pi\)
0.132010 + 0.991248i \(0.457857\pi\)
\(380\) 0.782108 + 4.43556i 0.0401213 + 0.227539i
\(381\) 0 0
\(382\) −1.94332 + 0.707310i −0.0994288 + 0.0361891i
\(383\) −0.0342214 0.0287152i −0.00174863 0.00146728i 0.641913 0.766778i \(-0.278141\pi\)
−0.643662 + 0.765310i \(0.722586\pi\)
\(384\) 0 0
\(385\) −26.5223 9.65331i −1.35170 0.491978i
\(386\) −0.767463 1.32928i −0.0390628 0.0676588i
\(387\) 0 0
\(388\) −0.934167 + 1.61802i −0.0474251 + 0.0821427i
\(389\) 16.0733 13.4871i 0.814951 0.683825i −0.136833 0.990594i \(-0.543692\pi\)
0.951784 + 0.306769i \(0.0992479\pi\)
\(390\) 0 0
\(391\) 5.23736 29.7026i 0.264865 1.50212i
\(392\) 0.261153 1.48107i 0.0131902 0.0748054i
\(393\) 0 0
\(394\) 0.980276 0.822549i 0.0493856 0.0414394i
\(395\) 22.0356 38.1668i 1.10873 1.92038i
\(396\) 0 0
\(397\) 0.00122821 + 0.00212731i 6.16419e−5 + 0.000106767i 0.866056 0.499947i \(-0.166647\pi\)
−0.865995 + 0.500053i \(0.833314\pi\)
\(398\) −1.68782 0.614316i −0.0846027 0.0307929i
\(399\) 0 0
\(400\) 26.2345 + 22.0134i 1.31173 + 1.10067i
\(401\) −23.7332 + 8.63817i −1.18518 + 0.431370i −0.858028 0.513603i \(-0.828311\pi\)
−0.327150 + 0.944972i \(0.606088\pi\)
\(402\) 0 0
\(403\) −0.870322 4.93584i −0.0433538 0.245872i
\(404\) −11.0485 −0.549684
\(405\) 0 0
\(406\) −3.43513 −0.170483
\(407\) 2.14595 + 12.1703i 0.106371 + 0.603259i
\(408\) 0 0
\(409\) 21.8841 7.96515i 1.08210 0.393851i 0.261410 0.965228i \(-0.415813\pi\)
0.820688 + 0.571377i \(0.193590\pi\)
\(410\) 2.60446 + 2.18540i 0.128625 + 0.107929i
\(411\) 0 0
\(412\) −17.4482 6.35064i −0.859613 0.312874i
\(413\) −17.9643 31.1151i −0.883965 1.53107i
\(414\) 0 0
\(415\) 16.8446 29.1756i 0.826867 1.43218i
\(416\) 1.19246 1.00059i 0.0584651 0.0490581i
\(417\) 0 0
\(418\) 0.0457922 0.259701i 0.00223977 0.0127024i
\(419\) 5.43317 30.8130i 0.265428 1.50531i −0.502387 0.864643i \(-0.667545\pi\)
0.767815 0.640672i \(-0.221344\pi\)
\(420\) 0 0
\(421\) 23.3870 19.6240i 1.13981 0.956417i 0.140381 0.990098i \(-0.455167\pi\)
0.999433 + 0.0336807i \(0.0107229\pi\)
\(422\) 1.80424 3.12503i 0.0878289 0.152124i
\(423\) 0 0
\(424\) 3.03640 + 5.25920i 0.147461 + 0.255409i
\(425\) 38.9304 + 14.1695i 1.88840 + 0.687323i
\(426\) 0 0
\(427\) 19.0124 + 15.9533i 0.920073 + 0.772033i
\(428\) 2.36638 0.861291i 0.114383 0.0416321i
\(429\) 0 0
\(430\) −0.625213 3.54576i −0.0301505 0.170992i
\(431\) 12.4246 0.598474 0.299237 0.954179i \(-0.403268\pi\)
0.299237 + 0.954179i \(0.403268\pi\)
\(432\) 0 0
\(433\) −0.760649 −0.0365545 −0.0182772 0.999833i \(-0.505818\pi\)
−0.0182772 + 0.999833i \(0.505818\pi\)
\(434\) −0.596462 3.38270i −0.0286311 0.162375i
\(435\) 0 0
\(436\) −13.7121 + 4.99081i −0.656692 + 0.239017i
\(437\) 3.05797 + 2.56594i 0.146283 + 0.122746i
\(438\) 0 0
\(439\) −28.2935 10.2980i −1.35038 0.491497i −0.437312 0.899310i \(-0.644069\pi\)
−0.913065 + 0.407813i \(0.866292\pi\)
\(440\) −3.19685 5.53711i −0.152404 0.263971i
\(441\) 0 0
\(442\) 0.305914 0.529859i 0.0145508 0.0252028i
\(443\) −10.4654 + 8.78149i −0.497225 + 0.417221i −0.856607 0.515969i \(-0.827432\pi\)
0.359382 + 0.933191i \(0.382987\pi\)
\(444\) 0 0
\(445\) −4.89156 + 27.7414i −0.231882 + 1.31507i
\(446\) −0.708226 + 4.01655i −0.0335355 + 0.190189i
\(447\) 0 0
\(448\) −16.9312 + 14.2070i −0.799925 + 0.671217i
\(449\) −10.9995 + 19.0516i −0.519097 + 0.899102i 0.480657 + 0.876909i \(0.340398\pi\)
−0.999754 + 0.0221934i \(0.992935\pi\)
\(450\) 0 0
\(451\) 6.55346 + 11.3509i 0.308590 + 0.534494i
\(452\) −17.3130 6.30142i −0.814335 0.296394i
\(453\) 0 0
\(454\) −1.38922 1.16570i −0.0651995 0.0547089i
\(455\) 8.14433 2.96429i 0.381812 0.138968i
\(456\) 0 0
\(457\) −0.258532 1.46621i −0.0120936 0.0685863i 0.978164 0.207836i \(-0.0666420\pi\)
−0.990257 + 0.139250i \(0.955531\pi\)
\(458\) 2.40132 0.112206
\(459\) 0 0
\(460\) 48.0281 2.23932
\(461\) 1.23522 + 7.00527i 0.0575298 + 0.326268i 0.999967 0.00811518i \(-0.00258317\pi\)
−0.942437 + 0.334383i \(0.891472\pi\)
\(462\) 0 0
\(463\) 24.9401 9.07746i 1.15907 0.421866i 0.310302 0.950638i \(-0.399570\pi\)
0.848764 + 0.528772i \(0.177347\pi\)
\(464\) 19.1767 + 16.0912i 0.890256 + 0.747013i
\(465\) 0 0
\(466\) −1.23528 0.449605i −0.0572232 0.0208275i
\(467\) 13.0760 + 22.6482i 0.605084 + 1.04804i 0.992038 + 0.125937i \(0.0401937\pi\)
−0.386955 + 0.922099i \(0.626473\pi\)
\(468\) 0 0
\(469\) 1.83760 3.18282i 0.0848525 0.146969i
\(470\) 0.548405 0.460166i 0.0252960 0.0212259i
\(471\) 0 0
\(472\) 1.41331 8.01529i 0.0650529 0.368933i
\(473\) 2.41027 13.6693i 0.110824 0.628515i
\(474\) 0 0
\(475\) −4.20044 + 3.52459i −0.192729 + 0.161719i
\(476\) −13.8043 + 23.9098i −0.632719 + 1.09590i
\(477\) 0 0
\(478\) −1.43213 2.48052i −0.0655040 0.113456i
\(479\) −9.77896 3.55925i −0.446812 0.162626i 0.108808 0.994063i \(-0.465297\pi\)
−0.555620 + 0.831437i \(0.687519\pi\)
\(480\) 0 0
\(481\) −2.90702 2.43928i −0.132549 0.111222i
\(482\) −2.35990 + 0.858932i −0.107490 + 0.0391233i
\(483\) 0 0
\(484\) 1.63916 + 9.29613i 0.0745072 + 0.422551i
\(485\) −3.54358 −0.160906
\(486\) 0 0
\(487\) −18.4664 −0.836791 −0.418396 0.908265i \(-0.637407\pi\)
−0.418396 + 0.908265i \(0.637407\pi\)
\(488\) 0.976293 + 5.53683i 0.0441947 + 0.250641i
\(489\) 0 0
\(490\) 1.33010 0.484116i 0.0600877 0.0218701i
\(491\) 13.0028 + 10.9106i 0.586806 + 0.492389i 0.887174 0.461435i \(-0.152665\pi\)
−0.300368 + 0.953823i \(0.597110\pi\)
\(492\) 0 0
\(493\) 28.4570 + 10.3575i 1.28164 + 0.466479i
\(494\) 0.0404890 + 0.0701289i 0.00182168 + 0.00315525i
\(495\) 0 0
\(496\) −12.5158 + 21.6780i −0.561976 + 0.973371i
\(497\) 11.4243 9.58611i 0.512449 0.429996i
\(498\) 0 0
\(499\) 4.27976 24.2717i 0.191589 1.08655i −0.725605 0.688111i \(-0.758440\pi\)
0.917194 0.398441i \(-0.130449\pi\)
\(500\) −5.06442 + 28.7218i −0.226488 + 1.28448i
\(501\) 0 0
\(502\) 1.19943 1.00644i 0.0535332 0.0449197i
\(503\) 20.0569 34.7395i 0.894291 1.54896i 0.0596120 0.998222i \(-0.481014\pi\)
0.834679 0.550736i \(-0.185653\pi\)
\(504\) 0 0
\(505\) −10.4776 18.1478i −0.466248 0.807564i
\(506\) −2.64244 0.961770i −0.117471 0.0427559i
\(507\) 0 0
\(508\) −31.3859 26.3359i −1.39252 1.16847i
\(509\) 4.65009 1.69249i 0.206111 0.0750184i −0.236901 0.971534i \(-0.576132\pi\)
0.443013 + 0.896515i \(0.353910\pi\)
\(510\) 0 0
\(511\) 2.26329 + 12.8358i 0.100122 + 0.567821i
\(512\) −13.0229 −0.575537
\(513\) 0 0
\(514\) 1.67785 0.0740066
\(515\) −6.11540 34.6821i −0.269477 1.52828i
\(516\) 0 0
\(517\) 2.59340 0.943922i 0.114058 0.0415136i
\(518\) −1.99228 1.67172i −0.0875359 0.0734514i
\(519\) 0 0
\(520\) 1.84494 + 0.671505i 0.0809061 + 0.0294474i
\(521\) 3.86979 + 6.70267i 0.169539 + 0.293649i 0.938258 0.345937i \(-0.112439\pi\)
−0.768719 + 0.639586i \(0.779106\pi\)
\(522\) 0 0
\(523\) −18.0070 + 31.1891i −0.787391 + 1.36380i 0.140169 + 0.990128i \(0.455236\pi\)
−0.927560 + 0.373674i \(0.878098\pi\)
\(524\) −0.989757 + 0.830505i −0.0432378 + 0.0362808i
\(525\) 0 0
\(526\) −0.806650 + 4.57474i −0.0351716 + 0.199468i
\(527\) −5.25827 + 29.8212i −0.229054 + 1.29903i
\(528\) 0 0
\(529\) 14.9896 12.5777i 0.651720 0.546858i
\(530\) −2.85780 + 4.94986i −0.124135 + 0.215008i
\(531\) 0 0
\(532\) −1.82705 3.16455i −0.0792129 0.137201i
\(533\) −3.78209 1.37657i −0.163820 0.0596257i
\(534\) 0 0
\(535\) 3.65882 + 3.07011i 0.158184 + 0.132733i
\(536\) 0.782338 0.284748i 0.0337919 0.0122992i
\(537\) 0 0
\(538\) 0.352599 + 1.99969i 0.0152016 + 0.0862126i
\(539\) 5.45676 0.235039
\(540\) 0 0
\(541\) −24.4147 −1.04967 −0.524834 0.851204i \(-0.675873\pi\)
−0.524834 + 0.851204i \(0.675873\pi\)
\(542\) −0.00434263 0.0246283i −0.000186532 0.00105787i
\(543\) 0 0
\(544\) −8.83769 + 3.21666i −0.378913 + 0.137913i
\(545\) −21.2013 17.7900i −0.908163 0.762039i
\(546\) 0 0
\(547\) 26.6514 + 9.70030i 1.13953 + 0.414755i 0.841743 0.539878i \(-0.181530\pi\)
0.297786 + 0.954633i \(0.403752\pi\)
\(548\) −8.45913 14.6516i −0.361356 0.625887i
\(549\) 0 0
\(550\) 1.93130 3.34512i 0.0823511 0.142636i
\(551\) −3.07040 + 2.57637i −0.130803 + 0.109757i
\(552\) 0 0
\(553\) −6.20885 + 35.2121i −0.264027 + 1.49737i
\(554\) 0.0304702 0.172805i 0.00129456 0.00734179i
\(555\) 0 0
\(556\) −20.2925 + 17.0274i −0.860593 + 0.722124i
\(557\) −18.4687 + 31.9887i −0.782542 + 1.35540i 0.147914 + 0.989000i \(0.452744\pi\)
−0.930456 + 0.366403i \(0.880589\pi\)
\(558\) 0 0
\(559\) 2.13113 + 3.69123i 0.0901372 + 0.156122i
\(560\) −40.6757 14.8047i −1.71886 0.625614i
\(561\) 0 0
\(562\) −3.64785 3.06091i −0.153875 0.129117i
\(563\) 21.4019 7.78965i 0.901982 0.328295i 0.150935 0.988544i \(-0.451771\pi\)
0.751047 + 0.660249i \(0.229549\pi\)
\(564\) 0 0
\(565\) −6.06800 34.4133i −0.255282 1.44778i
\(566\) 4.63625 0.194876
\(567\) 0 0
\(568\) 3.37833 0.141752
\(569\) −5.36030 30.3998i −0.224716 1.27443i −0.863228 0.504814i \(-0.831561\pi\)
0.638512 0.769611i \(-0.279550\pi\)
\(570\) 0 0
\(571\) −12.0473 + 4.38487i −0.504165 + 0.183501i −0.581566 0.813499i \(-0.697560\pi\)
0.0774015 + 0.997000i \(0.475338\pi\)
\(572\) 2.87722 + 2.41427i 0.120303 + 0.100946i
\(573\) 0 0
\(574\) −2.59200 0.943409i −0.108188 0.0393771i
\(575\) 29.2354 + 50.6372i 1.21920 + 2.11172i
\(576\) 0 0
\(577\) 11.7632 20.3745i 0.489708 0.848200i −0.510222 0.860043i \(-0.670437\pi\)
0.999930 + 0.0118433i \(0.00376992\pi\)
\(578\) −0.579073 + 0.485900i −0.0240863 + 0.0202108i
\(579\) 0 0
\(580\) −8.37388 + 47.4906i −0.347706 + 1.97194i
\(581\) −4.74619 + 26.9170i −0.196905 + 1.11670i
\(582\) 0 0
\(583\) −16.8793 + 14.1634i −0.699068 + 0.586587i
\(584\) −1.47628 + 2.55699i −0.0610888 + 0.105809i
\(585\) 0 0
\(586\) −1.61363 2.79489i −0.0666584 0.115456i
\(587\) 10.7007 + 3.89473i 0.441665 + 0.160753i 0.553274 0.832999i \(-0.313378\pi\)
−0.111609 + 0.993752i \(0.535600\pi\)
\(588\) 0 0
\(589\) −3.07018 2.57619i −0.126505 0.106150i
\(590\) 7.19824 2.61995i 0.296347 0.107861i
\(591\) 0 0
\(592\) 3.29112 + 18.6649i 0.135264 + 0.767122i
\(593\) 37.7324 1.54948 0.774742 0.632277i \(-0.217880\pi\)
0.774742 + 0.632277i \(0.217880\pi\)
\(594\) 0 0
\(595\) −52.3640 −2.14672
\(596\) 3.29172 + 18.6682i 0.134834 + 0.764681i
\(597\) 0 0
\(598\) 0.811429 0.295336i 0.0331818 0.0120772i
\(599\) −36.2785 30.4413i −1.48230 1.24380i −0.903687 0.428193i \(-0.859150\pi\)
−0.578611 0.815604i \(-0.696405\pi\)
\(600\) 0 0
\(601\) 29.2314 + 10.6394i 1.19237 + 0.433989i 0.860557 0.509354i \(-0.170116\pi\)
0.331818 + 0.943343i \(0.392338\pi\)
\(602\) 1.46054 + 2.52973i 0.0595271 + 0.103104i
\(603\) 0 0
\(604\) −7.02156 + 12.1617i −0.285703 + 0.494853i
\(605\) −13.7149 + 11.5082i −0.557591 + 0.467874i
\(606\) 0 0
\(607\) 5.12027 29.0385i 0.207825 1.17864i −0.685106 0.728443i \(-0.740244\pi\)
0.892932 0.450192i \(-0.148645\pi\)
\(608\) 0.216153 1.22586i 0.00876614 0.0497153i
\(609\) 0 0
\(610\) −4.05356 + 3.40134i −0.164124 + 0.137716i
\(611\) −0.423740 + 0.733939i −0.0171427 + 0.0296920i
\(612\) 0 0
\(613\) 3.05214 + 5.28646i 0.123275 + 0.213518i 0.921057 0.389427i \(-0.127327\pi\)
−0.797782 + 0.602945i \(0.793994\pi\)
\(614\) 5.49225 + 1.99901i 0.221649 + 0.0806737i
\(615\) 0 0
\(616\) 3.97366 + 3.33430i 0.160103 + 0.134343i
\(617\) −17.9670 + 6.53946i −0.723325 + 0.263269i −0.677337 0.735673i \(-0.736866\pi\)
−0.0459884 + 0.998942i \(0.514644\pi\)
\(618\) 0 0
\(619\) −1.17279 6.65125i −0.0471386 0.267336i 0.952125 0.305709i \(-0.0988936\pi\)
−0.999263 + 0.0383731i \(0.987782\pi\)
\(620\) −48.2198 −1.93655
\(621\) 0 0
\(622\) 5.99994 0.240576
\(623\) −3.96856 22.5068i −0.158997 0.901716i
\(624\) 0 0
\(625\) −9.87255 + 3.59331i −0.394902 + 0.143733i
\(626\) −0.442625 0.371406i −0.0176908 0.0148444i
\(627\) 0 0
\(628\) 14.2284 + 5.17872i 0.567776 + 0.206654i
\(629\) 11.4638 + 19.8559i 0.457091 + 0.791705i
\(630\) 0 0
\(631\) 0.228453 0.395693i 0.00909458 0.0157523i −0.861442 0.507855i \(-0.830438\pi\)
0.870537 + 0.492103i \(0.163772\pi\)
\(632\) −6.20472 + 5.20638i −0.246811 + 0.207099i
\(633\) 0 0
\(634\) 0.932131 5.28638i 0.0370196 0.209949i
\(635\) 13.4940 76.5280i 0.535491 3.03692i
\(636\) 0 0
\(637\) −1.28361 + 1.07708i −0.0508586 + 0.0426754i
\(638\) 1.41173 2.44519i 0.0558909 0.0968058i
\(639\) 0 0
\(640\) −9.95805 17.2479i −0.393627 0.681781i
\(641\) 2.69789 + 0.981950i 0.106560 + 0.0387847i 0.394750 0.918789i \(-0.370831\pi\)
−0.288190 + 0.957573i \(0.593053\pi\)
\(642\) 0 0
\(643\) −1.30445 1.09457i −0.0514426 0.0431655i 0.616704 0.787195i \(-0.288468\pi\)
−0.668146 + 0.744030i \(0.732912\pi\)
\(644\) −36.6156 + 13.3270i −1.44286 + 0.525156i
\(645\) 0 0
\(646\) −0.0849572 0.481816i −0.00334260 0.0189568i
\(647\) 36.1004 1.41925 0.709626 0.704579i \(-0.248864\pi\)
0.709626 + 0.704579i \(0.248864\pi\)
\(648\) 0 0
\(649\) 29.5310 1.15919
\(650\) 0.205966 + 1.16809i 0.00807866 + 0.0458164i
\(651\) 0 0
\(652\) 1.93920 0.705812i 0.0759451 0.0276417i
\(653\) −33.3750 28.0050i −1.30606 1.09592i −0.989063 0.147494i \(-0.952879\pi\)
−0.317002 0.948425i \(-0.602676\pi\)
\(654\) 0 0
\(655\) −2.30276 0.838137i −0.0899764 0.0327487i
\(656\) 10.0507 + 17.4083i 0.392412 + 0.679678i
\(657\) 0 0
\(658\) −0.290404 + 0.502994i −0.0113211 + 0.0196087i
\(659\) 19.5196 16.3789i 0.760374 0.638030i −0.177850 0.984058i \(-0.556914\pi\)
0.938224 + 0.346028i \(0.112470\pi\)
\(660\) 0 0
\(661\) 5.93307 33.6481i 0.230770 1.30876i −0.620572 0.784149i \(-0.713100\pi\)
0.851342 0.524611i \(-0.175789\pi\)
\(662\) −0.0982712 + 0.557324i −0.00381942 + 0.0216610i
\(663\) 0 0
\(664\) −4.74303 + 3.97988i −0.184065 + 0.154449i
\(665\) 3.46529 6.00207i 0.134378 0.232750i
\(666\) 0 0
\(667\) 21.3702 + 37.0143i 0.827459 + 1.43320i
\(668\) −15.4656 5.62903i −0.598384 0.217794i
\(669\) 0 0
\(670\) 0.600255 + 0.503674i 0.0231899 + 0.0194586i
\(671\) −19.1693 + 6.97705i −0.740022 + 0.269346i
\(672\) 0 0
\(673\) −5.13021 29.0949i −0.197755 1.12153i −0.908440 0.418015i \(-0.862726\pi\)
0.710685 0.703511i \(-0.248385\pi\)
\(674\) −1.10113 −0.0424140
\(675\) 0 0
\(676\) 24.4577 0.940680
\(677\) 7.08141 + 40.1607i 0.272161 + 1.54350i 0.747838 + 0.663881i \(0.231092\pi\)
−0.475677 + 0.879620i \(0.657797\pi\)
\(678\) 0 0
\(679\) 2.70155 0.983285i 0.103676 0.0377350i
\(680\) −9.08688 7.62479i −0.348466 0.292398i
\(681\) 0 0
\(682\) 2.65299 + 0.965610i 0.101588 + 0.0369751i
\(683\) −15.8213 27.4033i −0.605384 1.04856i −0.991991 0.126312i \(-0.959686\pi\)
0.386606 0.922245i \(-0.373647\pi\)
\(684\) 0 0
\(685\) 16.0441 27.7891i 0.613012 1.06177i
\(686\) 1.93216 1.62128i 0.0737704 0.0619007i
\(687\) 0 0
\(688\) 3.69649 20.9638i 0.140927 0.799238i
\(689\) 1.17494 6.66340i 0.0447616 0.253855i
\(690\) 0 0
\(691\) −21.8972 + 18.3739i −0.833008 + 0.698977i −0.955980 0.293433i \(-0.905202\pi\)
0.122971 + 0.992410i \(0.460758\pi\)
\(692\) −21.5190 + 37.2719i −0.818028 + 1.41687i
\(693\) 0 0
\(694\) −0.760438 1.31712i −0.0288658 0.0499971i
\(695\) −47.2124 17.1839i −1.79087 0.651822i
\(696\) 0 0
\(697\) 18.6279 + 15.6306i 0.705581 + 0.592052i
\(698\) 2.34067 0.851935i 0.0885958 0.0322462i
\(699\) 0 0
\(700\) −9.29418 52.7099i −0.351287 1.99225i
\(701\) −7.52982 −0.284397 −0.142199 0.989838i \(-0.545417\pi\)
−0.142199 + 0.989838i \(0.545417\pi\)
\(702\) 0 0
\(703\) −3.03455 −0.114450
\(704\) −3.15459 17.8905i −0.118893 0.674275i
\(705\) 0 0
\(706\) 5.39655 1.96418i 0.203102 0.0739230i
\(707\) 13.0236 + 10.9281i 0.489803 + 0.410994i
\(708\) 0 0
\(709\) −7.53069 2.74095i −0.282821 0.102938i 0.196715 0.980461i \(-0.436973\pi\)
−0.479536 + 0.877522i \(0.659195\pi\)
\(710\) 1.58981 + 2.75363i 0.0596646 + 0.103342i
\(711\) 0 0
\(712\) 2.58857 4.48354i 0.0970108 0.168028i
\(713\) −32.7388 + 27.4711i −1.22608 + 1.02880i
\(714\) 0 0
\(715\) −1.23702 + 7.01551i −0.0462620 + 0.262365i
\(716\) −3.10924 + 17.6334i −0.116198 + 0.658990i
\(717\) 0 0
\(718\) −0.655267 + 0.549835i −0.0244544 + 0.0205196i
\(719\) −13.4913 + 23.3676i −0.503140 + 0.871464i 0.496854 + 0.867834i \(0.334489\pi\)
−0.999993 + 0.00362928i \(0.998845\pi\)
\(720\) 0 0
\(721\) 14.2860 + 24.7440i 0.532037 + 0.921515i
\(722\) −3.02749 1.10192i −0.112672 0.0410091i
\(723\) 0 0
\(724\) 10.7615 + 9.03000i 0.399949 + 0.335597i
\(725\) −55.1679 + 20.0795i −2.04888 + 0.745733i
\(726\) 0 0
\(727\) −2.55164 14.4711i −0.0946353 0.536703i −0.994859 0.101275i \(-0.967708\pi\)
0.900223 0.435429i \(-0.143403\pi\)
\(728\) −1.59288 −0.0590360
\(729\) 0 0
\(730\) −2.77889 −0.102851
\(731\) −4.47171 25.3603i −0.165392 0.937986i
\(732\) 0 0
\(733\) 29.4535 10.7202i 1.08789 0.395960i 0.265051 0.964234i \(-0.414611\pi\)
0.822839 + 0.568275i \(0.192389\pi\)
\(734\) 0.330268 + 0.277128i 0.0121904 + 0.0102290i
\(735\) 0 0
\(736\) −12.4731 4.53984i −0.459764 0.167341i
\(737\) 1.51039 + 2.61607i 0.0556359 + 0.0963642i
\(738\) 0 0
\(739\) −0.241454 + 0.418211i −0.00888205 + 0.0153842i −0.870432 0.492288i \(-0.836161\pi\)
0.861550 + 0.507672i \(0.169494\pi\)
\(740\) −27.9682 + 23.4681i −1.02813 + 0.862704i
\(741\) 0 0
\(742\) 0.805225 4.56666i 0.0295608 0.167647i
\(743\) 7.47568 42.3967i 0.274256 1.55538i −0.467058 0.884226i \(-0.654686\pi\)
0.741315 0.671158i \(-0.234203\pi\)
\(744\) 0 0
\(745\) −27.5419 + 23.1104i −1.00906 + 0.846701i
\(746\) −2.42578 + 4.20157i −0.0888140 + 0.153830i
\(747\) 0 0
\(748\) −11.3462 19.6523i −0.414860 0.718558i
\(749\) −3.64131 1.32533i −0.133051 0.0484264i
\(750\) 0 0
\(751\) 33.6459 + 28.2323i 1.22776 + 1.03021i 0.998381 + 0.0568722i \(0.0181127\pi\)
0.229375 + 0.973338i \(0.426332\pi\)
\(752\) 3.97735 1.44764i 0.145039 0.0527899i
\(753\) 0 0
\(754\) 0.150555 + 0.853843i 0.00548291 + 0.0310951i
\(755\) −26.6350 −0.969346
\(756\) 0 0
\(757\) 22.4143 0.814661 0.407331 0.913281i \(-0.366460\pi\)
0.407331 + 0.913281i \(0.366460\pi\)
\(758\) −0.154387 0.875574i −0.00560760 0.0318023i
\(759\) 0 0
\(760\) 1.47531 0.536969i 0.0535152 0.0194779i
\(761\) −7.65795 6.42578i −0.277600 0.232934i 0.493348 0.869832i \(-0.335773\pi\)
−0.770948 + 0.636898i \(0.780217\pi\)
\(762\) 0 0
\(763\) 21.0998 + 7.67971i 0.763865 + 0.278024i
\(764\) −11.7768 20.3980i −0.426069 0.737972i
\(765\) 0 0
\(766\) −0.00386367 + 0.00669207i −0.000139600 + 0.000241794i
\(767\) −6.94667 + 5.82895i −0.250830 + 0.210471i
\(768\) 0 0
\(769\) −1.30170 + 7.38231i −0.0469405 + 0.266213i −0.999241 0.0389483i \(-0.987599\pi\)
0.952301 + 0.305161i \(0.0987103\pi\)
\(770\) −0.847775 + 4.80797i −0.0305517 + 0.173267i
\(771\) 0 0
\(772\) 13.3918 11.2371i 0.481982 0.404431i
\(773\) 9.91954 17.1812i 0.356781 0.617963i −0.630640 0.776076i \(-0.717207\pi\)
0.987421 + 0.158112i \(0.0505408\pi\)
\(774\) 0 0
\(775\) −29.3521 50.8394i −1.05436 1.82620i
\(776\) 0.611986 + 0.222745i 0.0219690 + 0.00799606i
\(777\) 0 0
\(778\) −2.78030 2.33295i −0.0996787 0.0836403i
\(779\) −3.02435 + 1.10077i −0.108359 + 0.0394393i
\(780\) 0 0
\(781\) 2.12855 + 12.0716i 0.0761654 + 0.431955i
\(782\) −5.21709 −0.186563
\(783\) 0 0
\(784\) 8.36872 0.298883
\(785\) 4.98689 + 28.2821i 0.177990 + 1.00943i
\(786\) 0 0
\(787\) −37.3323 + 13.5879i −1.33075 + 0.484355i −0.906889 0.421370i \(-0.861549\pi\)
−0.423866 + 0.905725i \(0.639327\pi\)
\(788\) 11.1647 + 9.36828i 0.397725 + 0.333731i
\(789\) 0 0
\(790\) −7.16353 2.60731i −0.254867 0.0927640i
\(791\) 14.1752 + 24.5522i 0.504013 + 0.872976i
\(792\) 0 0
\(793\) 3.13210 5.42495i 0.111224 0.192646i
\(794\) 0.000325492 0 0.000273120i 1.15513e−5 0 9.69268e-6i
\(795\) 0 0
\(796\) 3.55229 20.1460i 0.125908 0.714057i
\(797\) −1.58123 + 8.96761i −0.0560101 + 0.317649i −0.999921 0.0125505i \(-0.996005\pi\)
0.943911 + 0.330200i \(0.107116\pi\)
\(798\) 0 0
\(799\) 3.92235 3.29124i 0.138763 0.116436i
\(800\) 9.11632 15.7899i 0.322311 0.558258i
\(801\) 0 0
\(802\) 2.18437 + 3.78344i 0.0771327 + 0.133598i
\(803\) −10.0669 3.66404i −0.355252 0.129301i
\(804\) 0 0
\(805\) −56.6138 47.5046i −1.99537 1.67432i
\(806\) −0.814669 + 0.296515i −0.0286955 + 0.0104443i
\(807\) 0 0
\(808\) 0.668767 + 3.79277i 0.0235272 + 0.133429i
\(809\) 3.01910 0.106146 0.0530730 0.998591i \(-0.483098\pi\)
0.0530730 + 0.998591i \(0.483098\pi\)
\(810\) 0 0
\(811\) 33.1722 1.16483 0.582416 0.812891i \(-0.302107\pi\)
0.582416 + 0.812891i \(0.302107\pi\)
\(812\) −6.79378 38.5295i −0.238415 1.35212i
\(813\) 0 0
\(814\) 2.00873 0.731117i 0.0704058 0.0256256i
\(815\) 2.99833 + 2.51590i 0.105027 + 0.0881282i
\(816\) 0 0
\(817\) 3.20277 + 1.16571i 0.112051 + 0.0407832i
\(818\) −2.01418 3.48866i −0.0704241 0.121978i
\(819\) 0 0
\(820\) −19.3612 + 33.5345i −0.676121 + 1.17108i
\(821\) 32.7576 27.4869i 1.14325 0.959298i 0.143707 0.989620i \(-0.454098\pi\)
0.999540 + 0.0303224i \(0.00965340\pi\)
\(822\) 0 0
\(823\) −6.11743 + 34.6936i −0.213240 + 1.20934i 0.670694 + 0.741734i \(0.265996\pi\)
−0.883934 + 0.467611i \(0.845115\pi\)
\(824\) −1.12393 + 6.37410i −0.0391538 + 0.222052i
\(825\) 0 0
\(826\) −4.76080 + 3.99478i −0.165649 + 0.138996i
\(827\) −13.0190 + 22.5495i −0.452714 + 0.784125i −0.998554 0.0537655i \(-0.982878\pi\)
0.545839 + 0.837890i \(0.316211\pi\)
\(828\) 0 0
\(829\) 3.95134 + 6.84392i 0.137236 + 0.237699i 0.926449 0.376420i \(-0.122845\pi\)
−0.789214 + 0.614119i \(0.789512\pi\)
\(830\) −5.47597 1.99309i −0.190074 0.0691812i
\(831\) 0 0
\(832\) 4.27338 + 3.58579i 0.148153 + 0.124315i
\(833\) 9.51326 3.46254i 0.329615 0.119970i
\(834\) 0 0
\(835\) −5.42052 30.7413i −0.187585 1.06385i
\(836\) 3.00344 0.103876
\(837\) 0 0
\(838\) −5.41213 −0.186959
\(839\) 0.894009 + 5.07018i 0.0308646 + 0.175042i 0.996343 0.0854401i \(-0.0272296\pi\)
−0.965479 + 0.260482i \(0.916119\pi\)
\(840\) 0 0
\(841\) −13.0751 + 4.75893i −0.450864 + 0.164101i
\(842\) −4.04539 3.39449i −0.139413 0.116982i
\(843\) 0 0
\(844\) 38.6196 + 14.0564i 1.32934 + 0.483841i
\(845\) 23.1939 + 40.1730i 0.797894 + 1.38199i
\(846\) 0 0
\(847\) 7.26264 12.5793i 0.249547 0.432228i
\(848\) −25.8868 + 21.7216i −0.888955 + 0.745922i
\(849\) 0 0
\(850\) 1.24440 7.05733i 0.0426825 0.242065i
\(851\) −5.61906 + 31.8673i −0.192619 + 1.09240i
\(852\) 0 0
\(853\) 19.9098 16.7063i 0.681700 0.572014i −0.234802 0.972043i \(-0.575444\pi\)
0.916503 + 0.400029i \(0.131000\pi\)
\(854\) 2.14653 3.71791i 0.0734529 0.127224i
\(855\) 0 0
\(856\) −0.438904 0.760204i −0.0150014 0.0259832i
\(857\) 3.87072 + 1.40883i 0.132221 + 0.0481246i 0.407283 0.913302i \(-0.366476\pi\)
−0.275062 + 0.961426i \(0.588698\pi\)
\(858\) 0 0
\(859\) −4.92523 4.13276i −0.168047 0.141008i 0.554886 0.831926i \(-0.312762\pi\)
−0.722933 + 0.690919i \(0.757206\pi\)
\(860\) 38.5338 14.0252i 1.31399 0.478254i
\(861\) 0 0
\(862\) −0.373199 2.11651i −0.0127112 0.0720888i
\(863\) 29.6195 1.00826 0.504129 0.863628i \(-0.331813\pi\)
0.504129 + 0.863628i \(0.331813\pi\)
\(864\) 0 0
\(865\) −81.6282 −2.77544
\(866\) 0.0228476 + 0.129575i 0.000776393 + 0.00440314i
\(867\) 0 0
\(868\) 36.7618 13.3802i 1.24778 0.454153i
\(869\) −22.5130 18.8906i −0.763700 0.640820i
\(870\) 0 0
\(871\) −0.871665 0.317260i −0.0295353 0.0107500i
\(872\) 2.54326 + 4.40505i 0.0861256 + 0.149174i
\(873\) 0 0
\(874\) 0.345251 0.597993i 0.0116783 0.0202274i
\(875\) 34.3785 28.8470i 1.16221 0.975206i
\(876\) 0 0
\(877\) −5.53377 + 31.3835i −0.186862 + 1.05975i 0.736678 + 0.676244i \(0.236393\pi\)
−0.923540 + 0.383503i \(0.874718\pi\)
\(878\) −0.904393 + 5.12907i −0.0305218 + 0.173098i
\(879\) 0 0
\(880\) 27.2546 22.8694i 0.918754 0.770926i
\(881\) −17.3932 + 30.1259i −0.585991 + 1.01497i 0.408760 + 0.912642i \(0.365961\pi\)
−0.994751 + 0.102325i \(0.967372\pi\)
\(882\) 0 0
\(883\) 15.1882 + 26.3067i 0.511124 + 0.885292i 0.999917 + 0.0128924i \(0.00410388\pi\)
−0.488793 + 0.872400i \(0.662563\pi\)
\(884\) 6.54807 + 2.38330i 0.220235 + 0.0801591i
\(885\) 0 0
\(886\) 1.81026 + 1.51899i 0.0608168 + 0.0510314i
\(887\) 47.0106 17.1105i 1.57846 0.574513i 0.603593 0.797293i \(-0.293735\pi\)
0.974869 + 0.222780i \(0.0715131\pi\)
\(888\) 0 0
\(889\) 10.9477 + 62.0877i 0.367175 + 2.08235i
\(890\) 4.87263 0.163331
\(891\) 0 0
\(892\) −46.4515 −1.55531
\(893\) 0.117679 + 0.667392i 0.00393799 + 0.0223334i
\(894\) 0 0
\(895\) −31.9123 + 11.6151i −1.06671 + 0.388251i
\(896\) 12.3778 + 10.3862i 0.413513 + 0.346979i
\(897\) 0 0
\(898\) 3.57580 + 1.30148i 0.119326 + 0.0434311i
\(899\) −21.4556 37.1621i −0.715583 1.23943i
\(900\) 0 0
\(901\) −20.4399 + 35.4029i −0.680950 + 1.17944i
\(902\) 1.73676 1.45732i 0.0578278 0.0485233i
\(903\) 0 0
\(904\) −1.11521 + 6.32469i −0.0370914 + 0.210356i
\(905\) −4.62678 + 26.2398i −0.153799 + 0.872240i
\(906\) 0 0
\(907\) −33.7552 + 28.3240i −1.12082 + 0.940483i −0.998646 0.0520254i \(-0.983432\pi\)
−0.122178 + 0.992508i \(0.538988\pi\)
\(908\) 10.3273 17.8874i 0.342723 0.593614i
\(909\) 0 0
\(910\) −0.749593 1.29833i −0.0248488 0.0430393i
\(911\) 34.9361 + 12.7157i 1.15749 + 0.421290i 0.848199 0.529678i \(-0.177687\pi\)
0.309287 + 0.950969i \(0.399910\pi\)
\(912\) 0 0
\(913\) −17.2094 14.4404i −0.569549 0.477908i
\(914\) −0.242000 + 0.0880809i −0.00800466 + 0.00291346i
\(915\) 0 0
\(916\) 4.74918 + 26.9340i 0.156917 + 0.889923i
\(917\) 1.98815 0.0656544
\(918\) 0 0
\(919\) 12.3976 0.408958 0.204479 0.978871i \(-0.434450\pi\)
0.204479 + 0.978871i \(0.434450\pi\)
\(920\) −2.90714 16.4872i −0.0958457 0.543568i
\(921\) 0 0
\(922\) 1.15623 0.420834i 0.0380785 0.0138594i
\(923\) −2.88345 2.41950i −0.0949098 0.0796388i
\(924\) 0 0
\(925\) −41.7677 15.2022i −1.37331 0.499845i
\(926\) −2.29545 3.97584i −0.0754333 0.130654i
\(927\) 0 0
\(928\) 6.66377 11.5420i 0.218749 0.378884i
\(929\) 25.5768 21.4615i 0.839149 0.704130i −0.118223 0.992987i \(-0.537720\pi\)
0.957372 + 0.288857i \(0.0932753\pi\)
\(930\) 0 0
\(931\) −0.232676 + 1.31957i −0.00762563 + 0.0432471i
\(932\) 2.59984 14.7444i 0.0851607 0.482970i
\(933\) 0 0
\(934\) 3.46532 2.90775i 0.113389 0.0951445i
\(935\) 21.5199 37.2736i 0.703777 1.21898i
\(936\) 0 0
\(937\) 12.4220 + 21.5156i 0.405810 + 0.702884i 0.994415 0.105537i \(-0.0336561\pi\)
−0.588605 + 0.808421i \(0.700323\pi\)
\(938\) −0.597383 0.217429i −0.0195052 0.00709932i
\(939\) 0 0
\(940\) 6.24596 + 5.24098i 0.203721 + 0.170942i
\(941\) −23.8963 + 8.69753i −0.778996 + 0.283531i −0.700754 0.713403i \(-0.747153\pi\)
−0.0782422 + 0.996934i \(0.524931\pi\)
\(942\) 0 0
\(943\) 5.95957 + 33.7984i 0.194070 + 1.10063i
\(944\) 45.2900 1.47406
\(945\) 0 0
\(946\) −2.40094 −0.0780612
\(947\) 2.88780 + 16.3775i 0.0938407 + 0.532197i 0.995096 + 0.0989096i \(0.0315355\pi\)
−0.901256 + 0.433288i \(0.857353\pi\)
\(948\) 0 0
\(949\) 3.09128 1.12514i 0.100347 0.0365234i
\(950\) 0.726575 + 0.609669i 0.0235732 + 0.0197803i
\(951\) 0 0
\(952\) 9.04339 + 3.29153i 0.293098 + 0.106679i
\(953\) −7.13357 12.3557i −0.231079 0.400240i 0.727047 0.686588i \(-0.240892\pi\)
−0.958126 + 0.286347i \(0.907559\pi\)
\(954\) 0 0
\(955\) 22.3365 38.6879i 0.722791 1.25191i
\(956\) 24.9898 20.9690i 0.808229 0.678185i
\(957\) 0 0
\(958\) −0.312581 + 1.77274i −0.0100990 + 0.0572745i
\(959\) −4.52064 + 25.6378i −0.145979 + 0.827888i
\(960\) 0 0
\(961\) 9.12211 7.65436i 0.294262 0.246915i
\(962\) −0.328209 + 0.568474i −0.0105819 + 0.0183283i
\(963\) 0 0
\(964\) −14.3013 24.7706i −0.460613 0.797806i
\(965\) 31.1573 + 11.3403i 1.00299 + 0.365058i
\(966\) 0 0
\(967\) −29.9407 25.1232i −0.962827 0.807908i 0.0185839 0.999827i \(-0.494084\pi\)
−0.981411 + 0.191920i \(0.938529\pi\)
\(968\) 3.09199 1.12539i 0.0993802 0.0361714i
\(969\) 0 0
\(970\) 0.106439 + 0.603643i 0.00341753 + 0.0193818i
\(971\) −4.40370 −0.141321 −0.0706607 0.997500i \(-0.522511\pi\)
−0.0706607 + 0.997500i \(0.522511\pi\)
\(972\) 0 0
\(973\) 40.7619 1.30677
\(974\) 0.554674 + 3.14571i 0.0177729 + 0.100795i
\(975\) 0 0
\(976\) −29.3988 + 10.7003i −0.941034 + 0.342508i
\(977\) 32.2708 + 27.0784i 1.03243 + 0.866316i 0.991139 0.132831i \(-0.0424068\pi\)
0.0412962 + 0.999147i \(0.486851\pi\)
\(978\) 0 0
\(979\) 17.6517 + 6.42469i 0.564150 + 0.205334i
\(980\) 8.06057 + 13.9613i 0.257486 + 0.445978i
\(981\) 0 0
\(982\) 1.46804 2.54272i 0.0468470 0.0811413i
\(983\) −15.6473 + 13.1297i −0.499072 + 0.418771i −0.857264 0.514877i \(-0.827838\pi\)
0.358192 + 0.933648i \(0.383393\pi\)
\(984\) 0 0
\(985\) −4.80011 + 27.2228i −0.152944 + 0.867390i
\(986\) 0.909620 5.15871i 0.0289682 0.164287i
\(987\) 0 0
\(988\) −0.706510 + 0.592833i −0.0224771 + 0.0188605i
\(989\) 18.1723 31.4753i 0.577844 1.00086i
\(990\) 0 0
\(991\) −0.0340356 0.0589514i −0.00108118 0.00187265i 0.865484 0.500936i \(-0.167011\pi\)
−0.866565 + 0.499063i \(0.833677\pi\)
\(992\) 12.5229 + 4.55796i 0.397602 + 0.144715i
\(993\) 0 0
\(994\) −1.97613 1.65817i −0.0626789 0.0525938i
\(995\) 36.4596 13.2702i 1.15585 0.420694i
\(996\) 0 0
\(997\) 1.84868 + 10.4844i 0.0585482 + 0.332043i 0.999987 0.00514123i \(-0.00163651\pi\)
−0.941439 + 0.337184i \(0.890525\pi\)
\(998\) −4.26319 −0.134949
\(999\) 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.l.82.1 12
3.2 odd 2 729.2.e.s.82.2 12
9.2 odd 6 729.2.e.j.325.2 12
9.4 even 3 729.2.e.k.568.2 12
9.5 odd 6 729.2.e.t.568.1 12
9.7 even 3 729.2.e.u.325.1 12
27.2 odd 18 729.2.e.s.649.2 12
27.4 even 9 729.2.c.a.487.4 12
27.5 odd 18 729.2.a.b.1.4 6
27.7 even 9 729.2.e.u.406.1 12
27.11 odd 18 729.2.e.t.163.1 12
27.13 even 9 729.2.c.a.244.4 12
27.14 odd 18 729.2.c.d.244.3 12
27.16 even 9 729.2.e.k.163.2 12
27.20 odd 18 729.2.e.j.406.2 12
27.22 even 9 729.2.a.e.1.3 yes 6
27.23 odd 18 729.2.c.d.487.3 12
27.25 even 9 inner 729.2.e.l.649.1 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
729.2.a.b.1.4 6 27.5 odd 18
729.2.a.e.1.3 yes 6 27.22 even 9
729.2.c.a.244.4 12 27.13 even 9
729.2.c.a.487.4 12 27.4 even 9
729.2.c.d.244.3 12 27.14 odd 18
729.2.c.d.487.3 12 27.23 odd 18
729.2.e.j.325.2 12 9.2 odd 6
729.2.e.j.406.2 12 27.20 odd 18
729.2.e.k.163.2 12 27.16 even 9
729.2.e.k.568.2 12 9.4 even 3
729.2.e.l.82.1 12 1.1 even 1 trivial
729.2.e.l.649.1 12 27.25 even 9 inner
729.2.e.s.82.2 12 3.2 odd 2
729.2.e.s.649.2 12 27.2 odd 18
729.2.e.t.163.1 12 27.11 odd 18
729.2.e.t.568.1 12 9.5 odd 6
729.2.e.u.325.1 12 9.7 even 3
729.2.e.u.406.1 12 27.7 even 9