Properties

Label 729.2.e.q.163.2
Level $729$
Weight $2$
Character 729.163
Analytic conductor $5.821$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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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: \(\Q(\zeta_{36})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - x^{6} + 1 \) 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 \(0.342020 - 0.939693i\) of defining polynomial
Character \(\chi\) \(=\) 729.163
Dual form 729.2.e.q.568.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.20805 - 0.439693i) q^{2} +(-0.266044 + 0.223238i) q^{4} +(-0.0775297 - 0.439693i) q^{5} +(-2.70574 - 2.27038i) q^{7} +(-1.50881 + 2.61334i) q^{8} +O(q^{10})\) \(q+(1.20805 - 0.439693i) q^{2} +(-0.266044 + 0.223238i) q^{4} +(-0.0775297 - 0.439693i) q^{5} +(-2.70574 - 2.27038i) q^{7} +(-1.50881 + 2.61334i) q^{8} +(-0.286989 - 0.497079i) q^{10} +(0.482753 - 2.73783i) q^{11} +(-3.09240 - 1.12554i) q^{13} +(-4.26692 - 1.55303i) q^{14} +(-0.553033 + 3.13641i) q^{16} +(-3.51968 - 6.09627i) q^{17} +(2.59240 - 4.49016i) q^{19} +(0.118782 + 0.0996702i) q^{20} +(-0.620615 - 3.51968i) q^{22} +(-5.57445 + 4.67752i) q^{23} +(4.51114 - 1.64192i) q^{25} -4.23065 q^{26} +1.22668 q^{28} +(3.40090 - 1.23783i) q^{29} +(-1.48293 + 1.24432i) q^{31} +(-0.337044 - 1.91147i) q^{32} +(-6.93242 - 5.81699i) q^{34} +(-0.788496 + 1.36571i) q^{35} +(1.61334 + 2.79439i) q^{37} +(1.15744 - 6.56418i) q^{38} +(1.26604 + 0.460802i) q^{40} +(-4.56769 - 1.66250i) q^{41} +(-1.00000 + 5.67128i) q^{43} +(0.482753 + 0.836152i) q^{44} +(-4.67752 + 8.10170i) q^{46} +(-2.31164 - 1.93969i) q^{47} +(0.950837 + 5.39246i) q^{49} +(4.72773 - 3.96703i) q^{50} +(1.07398 - 0.390896i) q^{52} -8.77141 q^{53} -1.24123 q^{55} +(10.0157 - 3.64543i) q^{56} +(3.56418 - 2.99070i) q^{58} +(-0.514654 - 2.91875i) q^{59} +(6.04189 + 5.06975i) q^{61} +(-1.24432 + 2.15523i) q^{62} +(-4.43242 - 7.67717i) q^{64} +(-0.255139 + 1.44697i) q^{65} +(8.86959 + 3.22826i) q^{67} +(2.29731 + 0.836152i) q^{68} +(-0.352044 + 1.99654i) q^{70} +(2.65366 + 4.59627i) q^{71} +(0.777189 - 1.34613i) q^{73} +(3.17766 + 2.66637i) q^{74} +(0.312681 + 1.77330i) q^{76} +(-7.52211 + 6.31180i) q^{77} +(11.1839 - 4.07061i) q^{79} +1.42193 q^{80} -6.24897 q^{82} +(-15.2768 + 5.56031i) q^{83} +(-2.40760 + 2.02022i) q^{85} +(1.28558 + 7.29086i) q^{86} +(6.42649 + 5.39246i) q^{88} +(9.21291 - 15.9572i) q^{89} +(5.81180 + 10.0663i) q^{91} +(0.438852 - 2.48886i) q^{92} +(-3.64543 - 1.32683i) q^{94} +(-2.17528 - 0.791737i) q^{95} +(1.75624 - 9.96016i) q^{97} +(3.51968 + 6.09627i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 6 q^{4} - 12 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 6 q^{4} - 12 q^{7} + 12 q^{10} - 30 q^{13} + 18 q^{16} + 24 q^{19} - 30 q^{22} + 42 q^{25} - 12 q^{28} + 24 q^{31} - 36 q^{34} + 6 q^{37} + 6 q^{40} - 12 q^{43} - 6 q^{46} - 12 q^{49} - 18 q^{52} - 60 q^{55} + 6 q^{58} + 60 q^{61} - 6 q^{64} + 78 q^{67} - 66 q^{70} - 12 q^{73} + 48 q^{76} + 6 q^{79} - 24 q^{82} - 36 q^{85} - 24 q^{88} - 12 q^{94} + 6 q^{97}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.20805 0.439693i 0.854217 0.310910i 0.122459 0.992474i \(-0.460922\pi\)
0.731759 + 0.681564i \(0.238700\pi\)
\(3\) 0 0
\(4\) −0.266044 + 0.223238i −0.133022 + 0.111619i
\(5\) −0.0775297 0.439693i −0.0346723 0.196637i 0.962552 0.271099i \(-0.0873870\pi\)
−0.997224 + 0.0744624i \(0.976276\pi\)
\(6\) 0 0
\(7\) −2.70574 2.27038i −1.02267 0.858124i −0.0327115 0.999465i \(-0.510414\pi\)
−0.989961 + 0.141341i \(0.954859\pi\)
\(8\) −1.50881 + 2.61334i −0.533446 + 0.923956i
\(9\) 0 0
\(10\) −0.286989 0.497079i −0.0907539 0.157190i
\(11\) 0.482753 2.73783i 0.145555 0.825486i −0.821364 0.570404i \(-0.806787\pi\)
0.966920 0.255081i \(-0.0821023\pi\)
\(12\) 0 0
\(13\) −3.09240 1.12554i −0.857676 0.312169i −0.124510 0.992218i \(-0.539736\pi\)
−0.733166 + 0.680050i \(0.761958\pi\)
\(14\) −4.26692 1.55303i −1.14038 0.415066i
\(15\) 0 0
\(16\) −0.553033 + 3.13641i −0.138258 + 0.784102i
\(17\) −3.51968 6.09627i −0.853648 1.47856i −0.877894 0.478856i \(-0.841052\pi\)
0.0242455 0.999706i \(-0.492282\pi\)
\(18\) 0 0
\(19\) 2.59240 4.49016i 0.594736 1.03011i −0.398848 0.917017i \(-0.630590\pi\)
0.993584 0.113097i \(-0.0360769\pi\)
\(20\) 0.118782 + 0.0996702i 0.0265605 + 0.0222869i
\(21\) 0 0
\(22\) −0.620615 3.51968i −0.132316 0.750399i
\(23\) −5.57445 + 4.67752i −1.16235 + 0.975330i −0.999935 0.0113920i \(-0.996374\pi\)
−0.162418 + 0.986722i \(0.551929\pi\)
\(24\) 0 0
\(25\) 4.51114 1.64192i 0.902229 0.328384i
\(26\) −4.23065 −0.829698
\(27\) 0 0
\(28\) 1.22668 0.231821
\(29\) 3.40090 1.23783i 0.631531 0.229859i −0.00636650 0.999980i \(-0.502027\pi\)
0.637898 + 0.770121i \(0.279804\pi\)
\(30\) 0 0
\(31\) −1.48293 + 1.24432i −0.266341 + 0.223487i −0.766171 0.642637i \(-0.777840\pi\)
0.499830 + 0.866124i \(0.333396\pi\)
\(32\) −0.337044 1.91147i −0.0595816 0.337904i
\(33\) 0 0
\(34\) −6.93242 5.81699i −1.18890 0.997606i
\(35\) −0.788496 + 1.36571i −0.133280 + 0.230848i
\(36\) 0 0
\(37\) 1.61334 + 2.79439i 0.265232 + 0.459395i 0.967624 0.252395i \(-0.0812183\pi\)
−0.702393 + 0.711790i \(0.747885\pi\)
\(38\) 1.15744 6.56418i 0.187762 1.06485i
\(39\) 0 0
\(40\) 1.26604 + 0.460802i 0.200179 + 0.0728593i
\(41\) −4.56769 1.66250i −0.713354 0.259639i −0.0402521 0.999190i \(-0.512816\pi\)
−0.673102 + 0.739550i \(0.735038\pi\)
\(42\) 0 0
\(43\) −1.00000 + 5.67128i −0.152499 + 0.864862i 0.808539 + 0.588443i \(0.200259\pi\)
−0.961037 + 0.276419i \(0.910852\pi\)
\(44\) 0.482753 + 0.836152i 0.0727777 + 0.126055i
\(45\) 0 0
\(46\) −4.67752 + 8.10170i −0.689662 + 1.19453i
\(47\) −2.31164 1.93969i −0.337187 0.282933i 0.458434 0.888729i \(-0.348411\pi\)
−0.795621 + 0.605795i \(0.792855\pi\)
\(48\) 0 0
\(49\) 0.950837 + 5.39246i 0.135834 + 0.770352i
\(50\) 4.72773 3.96703i 0.668602 0.561023i
\(51\) 0 0
\(52\) 1.07398 0.390896i 0.148934 0.0542075i
\(53\) −8.77141 −1.20485 −0.602423 0.798177i \(-0.705798\pi\)
−0.602423 + 0.798177i \(0.705798\pi\)
\(54\) 0 0
\(55\) −1.24123 −0.167367
\(56\) 10.0157 3.64543i 1.33841 0.487141i
\(57\) 0 0
\(58\) 3.56418 2.99070i 0.467999 0.392698i
\(59\) −0.514654 2.91875i −0.0670022 0.379989i −0.999808 0.0196084i \(-0.993758\pi\)
0.932805 0.360380i \(-0.117353\pi\)
\(60\) 0 0
\(61\) 6.04189 + 5.06975i 0.773585 + 0.649115i 0.941624 0.336666i \(-0.109299\pi\)
−0.168040 + 0.985780i \(0.553744\pi\)
\(62\) −1.24432 + 2.15523i −0.158029 + 0.273714i
\(63\) 0 0
\(64\) −4.43242 7.67717i −0.554052 0.959647i
\(65\) −0.255139 + 1.44697i −0.0316461 + 0.179474i
\(66\) 0 0
\(67\) 8.86959 + 3.22826i 1.08359 + 0.394395i 0.821244 0.570578i \(-0.193281\pi\)
0.262349 + 0.964973i \(0.415503\pi\)
\(68\) 2.29731 + 0.836152i 0.278590 + 0.101398i
\(69\) 0 0
\(70\) −0.352044 + 1.99654i −0.0420773 + 0.238632i
\(71\) 2.65366 + 4.59627i 0.314931 + 0.545476i 0.979423 0.201819i \(-0.0646853\pi\)
−0.664492 + 0.747296i \(0.731352\pi\)
\(72\) 0 0
\(73\) 0.777189 1.34613i 0.0909631 0.157553i −0.816954 0.576703i \(-0.804339\pi\)
0.907917 + 0.419151i \(0.137672\pi\)
\(74\) 3.17766 + 2.66637i 0.369396 + 0.309960i
\(75\) 0 0
\(76\) 0.312681 + 1.77330i 0.0358670 + 0.203412i
\(77\) −7.52211 + 6.31180i −0.857225 + 0.719297i
\(78\) 0 0
\(79\) 11.1839 4.07061i 1.25829 0.457980i 0.375094 0.926987i \(-0.377610\pi\)
0.883194 + 0.469007i \(0.155388\pi\)
\(80\) 1.42193 0.158977
\(81\) 0 0
\(82\) −6.24897 −0.690083
\(83\) −15.2768 + 5.56031i −1.67685 + 0.610323i −0.992873 0.119181i \(-0.961973\pi\)
−0.683976 + 0.729504i \(0.739751\pi\)
\(84\) 0 0
\(85\) −2.40760 + 2.02022i −0.261141 + 0.219124i
\(86\) 1.28558 + 7.29086i 0.138627 + 0.786194i
\(87\) 0 0
\(88\) 6.42649 + 5.39246i 0.685066 + 0.574839i
\(89\) 9.21291 15.9572i 0.976567 1.69146i 0.301902 0.953339i \(-0.402378\pi\)
0.674665 0.738125i \(-0.264288\pi\)
\(90\) 0 0
\(91\) 5.81180 + 10.0663i 0.609243 + 1.05524i
\(92\) 0.438852 2.48886i 0.0457535 0.259481i
\(93\) 0 0
\(94\) −3.64543 1.32683i −0.375997 0.136852i
\(95\) −2.17528 0.791737i −0.223179 0.0812305i
\(96\) 0 0
\(97\) 1.75624 9.96016i 0.178320 1.01130i −0.755922 0.654661i \(-0.772811\pi\)
0.934242 0.356640i \(-0.116078\pi\)
\(98\) 3.51968 + 6.09627i 0.355541 + 0.615816i
\(99\) 0 0
\(100\) −0.833626 + 1.44388i −0.0833626 + 0.144388i
\(101\) 1.59397 + 1.33750i 0.158606 + 0.133086i 0.718637 0.695386i \(-0.244766\pi\)
−0.560031 + 0.828472i \(0.689211\pi\)
\(102\) 0 0
\(103\) −0.251497 1.42631i −0.0247807 0.140538i 0.969907 0.243475i \(-0.0782873\pi\)
−0.994688 + 0.102936i \(0.967176\pi\)
\(104\) 7.60727 6.38326i 0.745954 0.625930i
\(105\) 0 0
\(106\) −10.5963 + 3.85673i −1.02920 + 0.374598i
\(107\) 2.23583 0.216146 0.108073 0.994143i \(-0.465532\pi\)
0.108073 + 0.994143i \(0.465532\pi\)
\(108\) 0 0
\(109\) −11.5030 −1.10179 −0.550893 0.834576i \(-0.685713\pi\)
−0.550893 + 0.834576i \(0.685713\pi\)
\(110\) −1.49946 + 0.545759i −0.142968 + 0.0520361i
\(111\) 0 0
\(112\) 8.61721 7.23070i 0.814250 0.683237i
\(113\) −0.293144 1.66250i −0.0275767 0.156395i 0.967910 0.251297i \(-0.0808572\pi\)
−0.995487 + 0.0949023i \(0.969746\pi\)
\(114\) 0 0
\(115\) 2.48886 + 2.08840i 0.232087 + 0.194744i
\(116\) −0.628461 + 1.08853i −0.0583511 + 0.101067i
\(117\) 0 0
\(118\) −1.90508 3.29969i −0.175377 0.303761i
\(119\) −4.31753 + 24.4859i −0.395787 + 2.24462i
\(120\) 0 0
\(121\) 3.07398 + 1.11884i 0.279453 + 0.101712i
\(122\) 9.52801 + 3.46791i 0.862625 + 0.313970i
\(123\) 0 0
\(124\) 0.116744 0.662090i 0.0104840 0.0594575i
\(125\) −2.18788 3.78952i −0.195690 0.338945i
\(126\) 0 0
\(127\) 1.33615 2.31428i 0.118564 0.205359i −0.800635 0.599153i \(-0.795504\pi\)
0.919199 + 0.393793i \(0.128837\pi\)
\(128\) −5.75643 4.83022i −0.508802 0.426935i
\(129\) 0 0
\(130\) 0.328001 + 1.86018i 0.0287676 + 0.163149i
\(131\) 2.23675 1.87686i 0.195426 0.163982i −0.539824 0.841778i \(-0.681509\pi\)
0.735250 + 0.677796i \(0.237065\pi\)
\(132\) 0 0
\(133\) −17.2087 + 6.26347i −1.49219 + 0.543111i
\(134\) 12.1343 1.04824
\(135\) 0 0
\(136\) 21.2422 1.82150
\(137\) −4.37636 + 1.59286i −0.373897 + 0.136087i −0.522132 0.852865i \(-0.674863\pi\)
0.148235 + 0.988952i \(0.452641\pi\)
\(138\) 0 0
\(139\) −6.13041 + 5.14403i −0.519975 + 0.436311i −0.864623 0.502421i \(-0.832443\pi\)
0.344648 + 0.938732i \(0.387998\pi\)
\(140\) −0.0951042 0.539363i −0.00803777 0.0455845i
\(141\) 0 0
\(142\) 5.22668 + 4.38571i 0.438613 + 0.368040i
\(143\) −4.57440 + 7.92309i −0.382530 + 0.662562i
\(144\) 0 0
\(145\) −0.807934 1.39938i −0.0670952 0.116212i
\(146\) 0.346996 1.96791i 0.0287176 0.162865i
\(147\) 0 0
\(148\) −1.05303 0.383273i −0.0865588 0.0315048i
\(149\) 18.9928 + 6.91282i 1.55595 + 0.566320i 0.969804 0.243884i \(-0.0784217\pi\)
0.586147 + 0.810204i \(0.300644\pi\)
\(150\) 0 0
\(151\) 1.16385 6.60051i 0.0947126 0.537142i −0.900122 0.435637i \(-0.856523\pi\)
0.994835 0.101505i \(-0.0323657\pi\)
\(152\) 7.82288 + 13.5496i 0.634520 + 1.09902i
\(153\) 0 0
\(154\) −6.31180 + 10.9324i −0.508620 + 0.880955i
\(155\) 0.662090 + 0.555560i 0.0531804 + 0.0446236i
\(156\) 0 0
\(157\) 0.924678 + 5.24411i 0.0737973 + 0.418525i 0.999216 + 0.0395801i \(0.0126020\pi\)
−0.925419 + 0.378945i \(0.876287\pi\)
\(158\) 11.7209 9.83497i 0.932462 0.782428i
\(159\) 0 0
\(160\) −0.814330 + 0.296392i −0.0643784 + 0.0234318i
\(161\) 25.7028 2.02566
\(162\) 0 0
\(163\) 3.81521 0.298830 0.149415 0.988775i \(-0.452261\pi\)
0.149415 + 0.988775i \(0.452261\pi\)
\(164\) 1.58634 0.577382i 0.123873 0.0450859i
\(165\) 0 0
\(166\) −16.0103 + 13.4342i −1.24264 + 1.04270i
\(167\) 1.58634 + 8.99660i 0.122755 + 0.696178i 0.982616 + 0.185650i \(0.0594389\pi\)
−0.859861 + 0.510528i \(0.829450\pi\)
\(168\) 0 0
\(169\) −1.66250 1.39501i −0.127885 0.107308i
\(170\) −2.02022 + 3.49912i −0.154944 + 0.268370i
\(171\) 0 0
\(172\) −1.00000 1.73205i −0.0762493 0.132068i
\(173\) 1.05471 5.98158i 0.0801884 0.454771i −0.918103 0.396342i \(-0.870280\pi\)
0.998292 0.0584296i \(-0.0186093\pi\)
\(174\) 0 0
\(175\) −15.9338 5.79942i −1.20448 0.438395i
\(176\) 8.31996 + 3.02822i 0.627141 + 0.228261i
\(177\) 0 0
\(178\) 4.11334 23.3279i 0.308308 1.74850i
\(179\) −5.14057 8.90373i −0.384224 0.665496i 0.607437 0.794368i \(-0.292198\pi\)
−0.991661 + 0.128872i \(0.958864\pi\)
\(180\) 0 0
\(181\) 11.5706 20.0408i 0.860034 1.48962i −0.0118609 0.999930i \(-0.503776\pi\)
0.871895 0.489693i \(-0.162891\pi\)
\(182\) 11.4470 + 9.60519i 0.848510 + 0.711984i
\(183\) 0 0
\(184\) −3.81315 21.6254i −0.281109 1.59425i
\(185\) 1.10359 0.926022i 0.0811376 0.0680825i
\(186\) 0 0
\(187\) −18.3897 + 6.69329i −1.34478 + 0.489462i
\(188\) 1.04801 0.0764340
\(189\) 0 0
\(190\) −2.97596 −0.215899
\(191\) −13.7856 + 5.01754i −0.997490 + 0.363057i −0.788616 0.614886i \(-0.789202\pi\)
−0.208874 + 0.977943i \(0.566980\pi\)
\(192\) 0 0
\(193\) 17.9572 15.0679i 1.29259 1.08461i 0.301215 0.953556i \(-0.402608\pi\)
0.991375 0.131055i \(-0.0418366\pi\)
\(194\) −2.25778 12.8045i −0.162099 0.919312i
\(195\) 0 0
\(196\) −1.45677 1.22237i −0.104055 0.0873123i
\(197\) 4.51384 7.81820i 0.321598 0.557024i −0.659220 0.751950i \(-0.729113\pi\)
0.980818 + 0.194926i \(0.0624468\pi\)
\(198\) 0 0
\(199\) −1.30200 2.25514i −0.0922966 0.159862i 0.816181 0.577797i \(-0.196087\pi\)
−0.908477 + 0.417935i \(0.862754\pi\)
\(200\) −2.51557 + 14.2665i −0.177878 + 1.00879i
\(201\) 0 0
\(202\) 2.51367 + 0.914901i 0.176861 + 0.0643722i
\(203\) −12.0123 4.37211i −0.843097 0.306862i
\(204\) 0 0
\(205\) −0.376859 + 2.13727i −0.0263210 + 0.149274i
\(206\) −0.930956 1.61246i −0.0648628 0.112346i
\(207\) 0 0
\(208\) 5.24035 9.07656i 0.363353 0.629346i
\(209\) −11.0418 9.26517i −0.763777 0.640885i
\(210\) 0 0
\(211\) −2.84002 16.1066i −0.195515 1.10882i −0.911683 0.410894i \(-0.865217\pi\)
0.716168 0.697928i \(-0.245894\pi\)
\(212\) 2.33359 1.95811i 0.160271 0.134484i
\(213\) 0 0
\(214\) 2.70099 0.983080i 0.184636 0.0672019i
\(215\) 2.57115 0.175351
\(216\) 0 0
\(217\) 6.83750 0.464159
\(218\) −13.8961 + 5.05778i −0.941165 + 0.342556i
\(219\) 0 0
\(220\) 0.330222 0.277089i 0.0222636 0.0186814i
\(221\) 4.02266 + 22.8136i 0.270593 + 1.53461i
\(222\) 0 0
\(223\) 2.83615 + 2.37981i 0.189923 + 0.159364i 0.732791 0.680454i \(-0.238217\pi\)
−0.542868 + 0.839818i \(0.682662\pi\)
\(224\) −3.42782 + 5.93717i −0.229031 + 0.396694i
\(225\) 0 0
\(226\) −1.08512 1.87949i −0.0721813 0.125022i
\(227\) −1.83386 + 10.4003i −0.121717 + 0.690294i 0.861486 + 0.507781i \(0.169534\pi\)
−0.983203 + 0.182513i \(0.941577\pi\)
\(228\) 0 0
\(229\) −12.7096 4.62592i −0.839875 0.305689i −0.113969 0.993484i \(-0.536357\pi\)
−0.725905 + 0.687795i \(0.758579\pi\)
\(230\) 3.92490 + 1.42855i 0.258801 + 0.0941957i
\(231\) 0 0
\(232\) −1.89646 + 10.7554i −0.124509 + 0.706124i
\(233\) −6.35035 10.9991i −0.416025 0.720576i 0.579510 0.814965i \(-0.303244\pi\)
−0.995535 + 0.0943883i \(0.969910\pi\)
\(234\) 0 0
\(235\) −0.673648 + 1.16679i −0.0439440 + 0.0761132i
\(236\) 0.788496 + 0.661626i 0.0513267 + 0.0430682i
\(237\) 0 0
\(238\) 5.55051 + 31.4785i 0.359786 + 2.04045i
\(239\) −4.48254 + 3.76130i −0.289951 + 0.243298i −0.776147 0.630552i \(-0.782829\pi\)
0.486196 + 0.873850i \(0.338384\pi\)
\(240\) 0 0
\(241\) 8.02481 2.92079i 0.516924 0.188145i −0.0703666 0.997521i \(-0.522417\pi\)
0.587290 + 0.809376i \(0.300195\pi\)
\(242\) 4.20545 0.270337
\(243\) 0 0
\(244\) −2.73917 −0.175357
\(245\) 2.29731 0.836152i 0.146770 0.0534198i
\(246\) 0 0
\(247\) −13.0706 + 10.9675i −0.831661 + 0.697846i
\(248\) −1.01438 5.75284i −0.0644133 0.365306i
\(249\) 0 0
\(250\) −4.30928 3.61591i −0.272543 0.228690i
\(251\) 3.37895 5.85251i 0.213277 0.369407i −0.739461 0.673199i \(-0.764920\pi\)
0.952738 + 0.303792i \(0.0982529\pi\)
\(252\) 0 0
\(253\) 10.1152 + 17.5200i 0.635934 + 1.10147i
\(254\) 0.596559 3.38326i 0.0374315 0.212284i
\(255\) 0 0
\(256\) 7.58260 + 2.75984i 0.473912 + 0.172490i
\(257\) −3.46085 1.25965i −0.215882 0.0785747i 0.231815 0.972760i \(-0.425534\pi\)
−0.447697 + 0.894185i \(0.647756\pi\)
\(258\) 0 0
\(259\) 1.97906 11.2238i 0.122973 0.697412i
\(260\) −0.255139 0.441914i −0.0158231 0.0274064i
\(261\) 0 0
\(262\) 1.87686 3.25082i 0.115953 0.200836i
\(263\) 2.78677 + 2.33837i 0.171839 + 0.144190i 0.724651 0.689116i \(-0.242001\pi\)
−0.552812 + 0.833306i \(0.686445\pi\)
\(264\) 0 0
\(265\) 0.680045 + 3.85673i 0.0417748 + 0.236917i
\(266\) −18.0349 + 15.1331i −1.10579 + 0.927870i
\(267\) 0 0
\(268\) −3.08037 + 1.12116i −0.188164 + 0.0684860i
\(269\) −7.08672 −0.432085 −0.216042 0.976384i \(-0.569315\pi\)
−0.216042 + 0.976384i \(0.569315\pi\)
\(270\) 0 0
\(271\) −19.0000 −1.15417 −0.577084 0.816685i \(-0.695809\pi\)
−0.577084 + 0.816685i \(0.695809\pi\)
\(272\) 21.0669 7.66772i 1.27737 0.464924i
\(273\) 0 0
\(274\) −4.58647 + 3.84850i −0.277079 + 0.232497i
\(275\) −2.31753 13.1434i −0.139752 0.792575i
\(276\) 0 0
\(277\) −10.6420 8.92972i −0.639417 0.536535i 0.264422 0.964407i \(-0.414819\pi\)
−0.903839 + 0.427872i \(0.859263\pi\)
\(278\) −5.14403 + 8.90972i −0.308518 + 0.534369i
\(279\) 0 0
\(280\) −2.37939 4.12122i −0.142195 0.246290i
\(281\) 3.84240 21.7913i 0.229218 1.29996i −0.625236 0.780435i \(-0.714997\pi\)
0.854455 0.519526i \(-0.173891\pi\)
\(282\) 0 0
\(283\) 22.3011 + 8.11695i 1.32566 + 0.482502i 0.905269 0.424839i \(-0.139669\pi\)
0.420395 + 0.907341i \(0.361891\pi\)
\(284\) −1.73205 0.630415i −0.102778 0.0374082i
\(285\) 0 0
\(286\) −2.04236 + 11.5828i −0.120767 + 0.684904i
\(287\) 8.58445 + 14.8687i 0.506724 + 0.877672i
\(288\) 0 0
\(289\) −16.2763 + 28.1914i −0.957430 + 1.65832i
\(290\) −1.59132 1.33527i −0.0934454 0.0784100i
\(291\) 0 0
\(292\) 0.0937404 + 0.531628i 0.00548574 + 0.0311112i
\(293\) 14.2531 11.9598i 0.832674 0.698697i −0.123229 0.992378i \(-0.539325\pi\)
0.955903 + 0.293682i \(0.0948805\pi\)
\(294\) 0 0
\(295\) −1.24345 + 0.452579i −0.0723965 + 0.0263502i
\(296\) −9.73692 −0.565947
\(297\) 0 0
\(298\) 25.9837 1.50520
\(299\) 22.5031 8.19047i 1.30139 0.473667i
\(300\) 0 0
\(301\) 15.5817 13.0746i 0.898115 0.753608i
\(302\) −1.49621 8.48545i −0.0860974 0.488283i
\(303\) 0 0
\(304\) 12.6493 + 10.6140i 0.725487 + 0.608756i
\(305\) 1.76070 3.04963i 0.100818 0.174621i
\(306\) 0 0
\(307\) −10.3735 17.9674i −0.592044 1.02545i −0.993957 0.109773i \(-0.964988\pi\)
0.401912 0.915678i \(-0.368346\pi\)
\(308\) 0.592184 3.35844i 0.0337428 0.191365i
\(309\) 0 0
\(310\) 1.04411 + 0.380025i 0.0593015 + 0.0215840i
\(311\) −19.1561 6.97225i −1.08624 0.395360i −0.264015 0.964519i \(-0.585047\pi\)
−0.822228 + 0.569159i \(0.807269\pi\)
\(312\) 0 0
\(313\) −5.18180 + 29.3874i −0.292893 + 1.66108i 0.382753 + 0.923851i \(0.374976\pi\)
−0.675646 + 0.737226i \(0.736135\pi\)
\(314\) 3.42285 + 5.92855i 0.193163 + 0.334567i
\(315\) 0 0
\(316\) −2.06670 + 3.57964i −0.116261 + 0.201370i
\(317\) 3.30671 + 2.77466i 0.185724 + 0.155841i 0.730909 0.682475i \(-0.239096\pi\)
−0.545186 + 0.838315i \(0.683541\pi\)
\(318\) 0 0
\(319\) −1.74716 9.90863i −0.0978221 0.554777i
\(320\) −3.03195 + 2.54411i −0.169491 + 0.142220i
\(321\) 0 0
\(322\) 31.0501 11.3013i 1.73035 0.629797i
\(323\) −36.4976 −2.03078
\(324\) 0 0
\(325\) −15.7983 −0.876332
\(326\) 4.60894 1.67752i 0.255266 0.0929092i
\(327\) 0 0
\(328\) 11.2365 9.42853i 0.620431 0.520603i
\(329\) 1.85083 + 10.4966i 0.102040 + 0.578696i
\(330\) 0 0
\(331\) −2.23601 1.87624i −0.122902 0.103127i 0.579265 0.815139i \(-0.303340\pi\)
−0.702167 + 0.712012i \(0.747784\pi\)
\(332\) 2.82304 4.88965i 0.154935 0.268355i
\(333\) 0 0
\(334\) 5.87211 + 10.1708i 0.321308 + 0.556521i
\(335\) 0.731788 4.15018i 0.0399819 0.226748i
\(336\) 0 0
\(337\) −13.5706 4.93929i −0.739236 0.269060i −0.0551671 0.998477i \(-0.517569\pi\)
−0.684069 + 0.729417i \(0.739791\pi\)
\(338\) −2.62175 0.954241i −0.142605 0.0519038i
\(339\) 0 0
\(340\) 0.189540 1.07494i 0.0102793 0.0582966i
\(341\) 2.69085 + 4.66069i 0.145718 + 0.252391i
\(342\) 0 0
\(343\) −2.69207 + 4.66280i −0.145358 + 0.251767i
\(344\) −13.3122 11.1702i −0.717745 0.602259i
\(345\) 0 0
\(346\) −1.35591 7.68977i −0.0728944 0.413405i
\(347\) −1.11386 + 0.934640i −0.0597952 + 0.0501741i −0.672195 0.740374i \(-0.734649\pi\)
0.612400 + 0.790548i \(0.290204\pi\)
\(348\) 0 0
\(349\) 25.9183 9.43350i 1.38738 0.504964i 0.462971 0.886374i \(-0.346784\pi\)
0.924406 + 0.381410i \(0.124561\pi\)
\(350\) −21.7987 −1.16519
\(351\) 0 0
\(352\) −5.39599 −0.287607
\(353\) −9.89695 + 3.60220i −0.526762 + 0.191726i −0.591692 0.806164i \(-0.701540\pi\)
0.0649301 + 0.997890i \(0.479318\pi\)
\(354\) 0 0
\(355\) 1.81521 1.52314i 0.0963412 0.0808399i
\(356\) 1.11121 + 6.30200i 0.0588942 + 0.334006i
\(357\) 0 0
\(358\) −10.1250 8.49584i −0.535120 0.449019i
\(359\) −7.35273 + 12.7353i −0.388062 + 0.672143i −0.992189 0.124745i \(-0.960189\pi\)
0.604127 + 0.796888i \(0.293522\pi\)
\(360\) 0 0
\(361\) −3.94104 6.82608i −0.207423 0.359267i
\(362\) 5.16598 29.2977i 0.271518 1.53985i
\(363\) 0 0
\(364\) −3.79339 1.38068i −0.198827 0.0723673i
\(365\) −0.652139 0.237359i −0.0341345 0.0124239i
\(366\) 0 0
\(367\) −3.70961 + 21.0382i −0.193640 + 1.09819i 0.720702 + 0.693245i \(0.243819\pi\)
−0.914342 + 0.404942i \(0.867292\pi\)
\(368\) −11.5878 20.0706i −0.604053 1.04625i
\(369\) 0 0
\(370\) 0.926022 1.60392i 0.0481416 0.0833837i
\(371\) 23.7331 + 19.9145i 1.23216 + 1.03391i
\(372\) 0 0
\(373\) 3.92871 + 22.2808i 0.203421 + 1.15366i 0.899905 + 0.436085i \(0.143635\pi\)
−0.696484 + 0.717572i \(0.745253\pi\)
\(374\) −19.2725 + 16.1716i −0.996560 + 0.836213i
\(375\) 0 0
\(376\) 8.55690 3.11446i 0.441289 0.160616i
\(377\) −11.9101 −0.613404
\(378\) 0 0
\(379\) −17.0743 −0.877047 −0.438523 0.898720i \(-0.644498\pi\)
−0.438523 + 0.898720i \(0.644498\pi\)
\(380\) 0.755466 0.274967i 0.0387546 0.0141055i
\(381\) 0 0
\(382\) −14.4474 + 12.1228i −0.739195 + 0.620258i
\(383\) −6.77082 38.3992i −0.345973 1.96211i −0.258891 0.965906i \(-0.583357\pi\)
−0.0870812 0.996201i \(-0.527754\pi\)
\(384\) 0 0
\(385\) 3.35844 + 2.81807i 0.171162 + 0.143622i
\(386\) 15.0679 26.0984i 0.766936 1.32837i
\(387\) 0 0
\(388\) 1.75624 + 3.04190i 0.0891598 + 0.154429i
\(389\) 1.77330 10.0569i 0.0899101 0.509905i −0.906279 0.422681i \(-0.861089\pi\)
0.996189 0.0872245i \(-0.0277997\pi\)
\(390\) 0 0
\(391\) 48.1357 + 17.5200i 2.43433 + 0.886022i
\(392\) −15.5270 5.65136i −0.784231 0.285437i
\(393\) 0 0
\(394\) 2.01532 11.4294i 0.101530 0.575807i
\(395\) −2.65690 4.60189i −0.133683 0.231546i
\(396\) 0 0
\(397\) 0.571452 0.989783i 0.0286803 0.0496758i −0.851329 0.524632i \(-0.824203\pi\)
0.880009 + 0.474956i \(0.157536\pi\)
\(398\) −2.56445 2.15183i −0.128544 0.107861i
\(399\) 0 0
\(400\) 2.65493 + 15.0568i 0.132746 + 0.752841i
\(401\) −15.7452 + 13.2118i −0.786280 + 0.659767i −0.944822 0.327585i \(-0.893765\pi\)
0.158542 + 0.987352i \(0.449321\pi\)
\(402\) 0 0
\(403\) 5.98633 2.17885i 0.298200 0.108536i
\(404\) −0.722645 −0.0359530
\(405\) 0 0
\(406\) −16.4338 −0.815594
\(407\) 8.42939 3.06805i 0.417830 0.152078i
\(408\) 0 0
\(409\) −6.22668 + 5.22481i −0.307890 + 0.258350i −0.783619 0.621242i \(-0.786629\pi\)
0.475730 + 0.879592i \(0.342184\pi\)
\(410\) 0.484481 + 2.74763i 0.0239268 + 0.135696i
\(411\) 0 0
\(412\) 0.385315 + 0.323318i 0.0189831 + 0.0159287i
\(413\) −5.23416 + 9.06583i −0.257556 + 0.446100i
\(414\) 0 0
\(415\) 3.62923 + 6.28602i 0.178152 + 0.308568i
\(416\) −1.10917 + 6.29039i −0.0543813 + 0.308412i
\(417\) 0 0
\(418\) −17.4128 6.33775i −0.851689 0.309989i
\(419\) −33.6207 12.2369i −1.64248 0.597814i −0.655010 0.755620i \(-0.727336\pi\)
−0.987470 + 0.157806i \(0.949558\pi\)
\(420\) 0 0
\(421\) −2.27807 + 12.9196i −0.111026 + 0.629661i 0.877615 + 0.479366i \(0.159133\pi\)
−0.988641 + 0.150295i \(0.951978\pi\)
\(422\) −10.5128 18.2087i −0.511756 0.886387i
\(423\) 0 0
\(424\) 13.2344 22.9227i 0.642720 1.11322i
\(425\) −25.8874 21.7221i −1.25572 1.05368i
\(426\) 0 0
\(427\) −4.83750 27.4348i −0.234103 1.32766i
\(428\) −0.594831 + 0.499123i −0.0287523 + 0.0241260i
\(429\) 0 0
\(430\) 3.10607 1.13052i 0.149788 0.0545183i
\(431\) 9.48411 0.456833 0.228417 0.973563i \(-0.426645\pi\)
0.228417 + 0.973563i \(0.426645\pi\)
\(432\) 0 0
\(433\) 17.6628 0.848820 0.424410 0.905470i \(-0.360481\pi\)
0.424410 + 0.905470i \(0.360481\pi\)
\(434\) 8.26001 3.00640i 0.396493 0.144312i
\(435\) 0 0
\(436\) 3.06031 2.56790i 0.146562 0.122980i
\(437\) 6.55163 + 37.1562i 0.313407 + 1.77742i
\(438\) 0 0
\(439\) −13.5326 11.3552i −0.645874 0.541952i 0.259942 0.965624i \(-0.416297\pi\)
−0.905816 + 0.423672i \(0.860741\pi\)
\(440\) 1.87278 3.24376i 0.0892814 0.154640i
\(441\) 0 0
\(442\) 14.8905 + 25.7912i 0.708270 + 1.22676i
\(443\) −2.25606 + 12.7947i −0.107188 + 0.607896i 0.883135 + 0.469119i \(0.155428\pi\)
−0.990324 + 0.138777i \(0.955683\pi\)
\(444\) 0 0
\(445\) −7.73055 2.81369i −0.366463 0.133382i
\(446\) 4.47259 + 1.62789i 0.211783 + 0.0770828i
\(447\) 0 0
\(448\) −5.43717 + 30.8357i −0.256882 + 1.45685i
\(449\) 2.31428 + 4.00846i 0.109218 + 0.189171i 0.915454 0.402424i \(-0.131832\pi\)
−0.806236 + 0.591594i \(0.798499\pi\)
\(450\) 0 0
\(451\) −6.75671 + 11.7030i −0.318161 + 0.551071i
\(452\) 0.449123 + 0.376859i 0.0211250 + 0.0177260i
\(453\) 0 0
\(454\) 2.35756 + 13.3704i 0.110646 + 0.627504i
\(455\) 3.97551 3.33585i 0.186375 0.156387i
\(456\) 0 0
\(457\) −19.3268 + 7.03439i −0.904070 + 0.329055i −0.751883 0.659297i \(-0.770854\pi\)
−0.152188 + 0.988352i \(0.548632\pi\)
\(458\) −17.3878 −0.812477
\(459\) 0 0
\(460\) −1.12836 −0.0526098
\(461\) 31.5478 11.4825i 1.46933 0.534791i 0.521410 0.853307i \(-0.325406\pi\)
0.947918 + 0.318515i \(0.103184\pi\)
\(462\) 0 0
\(463\) 10.0590 8.44047i 0.467480 0.392262i −0.378395 0.925644i \(-0.623524\pi\)
0.845874 + 0.533382i \(0.179079\pi\)
\(464\) 2.00152 + 11.3512i 0.0929181 + 0.526965i
\(465\) 0 0
\(466\) −12.5077 10.4952i −0.579410 0.486183i
\(467\) −11.8154 + 20.4648i −0.546750 + 0.946999i 0.451745 + 0.892147i \(0.350802\pi\)
−0.998495 + 0.0548513i \(0.982532\pi\)
\(468\) 0 0
\(469\) −16.6694 28.8722i −0.769720 1.33319i
\(470\) −0.300767 + 1.70574i −0.0138734 + 0.0786798i
\(471\) 0 0
\(472\) 8.40420 + 3.05888i 0.386835 + 0.140796i
\(473\) 15.0442 + 5.47565i 0.691734 + 0.251771i
\(474\) 0 0
\(475\) 4.32218 24.5123i 0.198315 1.12470i
\(476\) −4.31753 7.47818i −0.197894 0.342762i
\(477\) 0 0
\(478\) −3.76130 + 6.51476i −0.172038 + 0.297978i
\(479\) −4.50449 3.77972i −0.205815 0.172700i 0.534054 0.845451i \(-0.320668\pi\)
−0.739869 + 0.672751i \(0.765113\pi\)
\(480\) 0 0
\(481\) −1.84389 10.4572i −0.0840743 0.476809i
\(482\) 8.41009 7.05690i 0.383069 0.321433i
\(483\) 0 0
\(484\) −1.06758 + 0.388568i −0.0485264 + 0.0176622i
\(485\) −4.51557 −0.205041
\(486\) 0 0
\(487\) 38.7965 1.75804 0.879020 0.476786i \(-0.158198\pi\)
0.879020 + 0.476786i \(0.158198\pi\)
\(488\) −22.3651 + 8.14022i −1.01242 + 0.368490i
\(489\) 0 0
\(490\) 2.40760 2.02022i 0.108764 0.0912642i
\(491\) −6.52644 37.0133i −0.294534 1.67039i −0.669090 0.743181i \(-0.733316\pi\)
0.374557 0.927204i \(-0.377795\pi\)
\(492\) 0 0
\(493\) −19.5162 16.3760i −0.878965 0.737539i
\(494\) −10.9675 + 18.9963i −0.493452 + 0.854684i
\(495\) 0 0
\(496\) −3.08260 5.33921i −0.138413 0.239738i
\(497\) 3.25519 18.4611i 0.146015 0.828094i
\(498\) 0 0
\(499\) −31.7165 11.5439i −1.41982 0.516774i −0.485827 0.874055i \(-0.661482\pi\)
−0.933997 + 0.357281i \(0.883704\pi\)
\(500\) 1.42804 + 0.519762i 0.0638637 + 0.0232445i
\(501\) 0 0
\(502\) 1.50862 8.55580i 0.0673329 0.381864i
\(503\) 9.35597 + 16.2050i 0.417162 + 0.722546i 0.995653 0.0931429i \(-0.0296913\pi\)
−0.578491 + 0.815689i \(0.696358\pi\)
\(504\) 0 0
\(505\) 0.464508 0.804551i 0.0206703 0.0358020i
\(506\) 19.9230 + 16.7173i 0.885684 + 0.743177i
\(507\) 0 0
\(508\) 0.161160 + 0.913982i 0.00715030 + 0.0405514i
\(509\) 16.6754 13.9923i 0.739124 0.620198i −0.193478 0.981105i \(-0.561977\pi\)
0.932602 + 0.360906i \(0.117533\pi\)
\(510\) 0 0
\(511\) −5.15910 + 1.87776i −0.228225 + 0.0830672i
\(512\) 25.4026 1.12265
\(513\) 0 0
\(514\) −4.73473 −0.208840
\(515\) −0.607639 + 0.221162i −0.0267758 + 0.00974558i
\(516\) 0 0
\(517\) −6.42649 + 5.39246i −0.282637 + 0.237160i
\(518\) −2.54422 14.4290i −0.111787 0.633975i
\(519\) 0 0
\(520\) −3.39646 2.84997i −0.148945 0.124979i
\(521\) 3.23822 5.60876i 0.141869 0.245724i −0.786332 0.617805i \(-0.788022\pi\)
0.928200 + 0.372081i \(0.121356\pi\)
\(522\) 0 0
\(523\) 5.43629 + 9.41593i 0.237712 + 0.411730i 0.960057 0.279803i \(-0.0902691\pi\)
−0.722345 + 0.691533i \(0.756936\pi\)
\(524\) −0.176090 + 0.998656i −0.00769253 + 0.0436265i
\(525\) 0 0
\(526\) 4.39470 + 1.59954i 0.191618 + 0.0697433i
\(527\) 12.8051 + 4.66069i 0.557801 + 0.203023i
\(528\) 0 0
\(529\) 5.20140 29.4986i 0.226148 1.28255i
\(530\) 2.51730 + 4.36009i 0.109344 + 0.189390i
\(531\) 0 0
\(532\) 3.18004 5.50800i 0.137872 0.238802i
\(533\) 12.2539 + 10.2822i 0.530775 + 0.445373i
\(534\) 0 0
\(535\) −0.173343 0.983080i −0.00749429 0.0425022i
\(536\) −21.8191 + 18.3084i −0.942442 + 0.790802i
\(537\) 0 0
\(538\) −8.56108 + 3.11598i −0.369094 + 0.134339i
\(539\) 15.2226 0.655686
\(540\) 0 0
\(541\) 24.6459 1.05961 0.529805 0.848120i \(-0.322265\pi\)
0.529805 + 0.848120i \(0.322265\pi\)
\(542\) −22.9529 + 8.35416i −0.985910 + 0.358842i
\(543\) 0 0
\(544\) −10.4666 + 8.78249i −0.448750 + 0.376546i
\(545\) 0.891823 + 5.05778i 0.0382015 + 0.216652i
\(546\) 0 0
\(547\) 23.6917 + 19.8797i 1.01298 + 0.849993i 0.988729 0.149713i \(-0.0478350\pi\)
0.0242526 + 0.999706i \(0.492279\pi\)
\(548\) 0.808718 1.40074i 0.0345467 0.0598367i
\(549\) 0 0
\(550\) −8.57873 14.8588i −0.365798 0.633581i
\(551\) 3.25844 18.4795i 0.138814 0.787254i
\(552\) 0 0
\(553\) −39.5026 14.3778i −1.67982 0.611405i
\(554\) −16.7824 6.10829i −0.713015 0.259516i
\(555\) 0 0
\(556\) 0.482621 2.73708i 0.0204677 0.116078i
\(557\) −11.6813 20.2327i −0.494954 0.857286i 0.505029 0.863102i \(-0.331482\pi\)
−0.999983 + 0.00581674i \(0.998148\pi\)
\(558\) 0 0
\(559\) 9.47565 16.4123i 0.400777 0.694167i
\(560\) −3.84737 3.22833i −0.162581 0.136422i
\(561\) 0 0
\(562\) −4.93969 28.0144i −0.208368 1.18172i
\(563\) 25.8063 21.6540i 1.08761 0.912609i 0.0910754 0.995844i \(-0.470970\pi\)
0.996530 + 0.0832347i \(0.0265251\pi\)
\(564\) 0 0
\(565\) −0.708263 + 0.257787i −0.0297969 + 0.0108452i
\(566\) 30.5097 1.28242
\(567\) 0 0
\(568\) −16.0155 −0.671995
\(569\) 28.9386 10.5328i 1.21317 0.441558i 0.345368 0.938467i \(-0.387754\pi\)
0.867803 + 0.496909i \(0.165532\pi\)
\(570\) 0 0
\(571\) −22.8858 + 19.2035i −0.957740 + 0.803639i −0.980584 0.196100i \(-0.937172\pi\)
0.0228438 + 0.999739i \(0.492728\pi\)
\(572\) −0.551740 3.12907i −0.0230694 0.130833i
\(573\) 0 0
\(574\) 16.9081 + 14.1876i 0.705729 + 0.592177i
\(575\) −17.4670 + 30.2538i −0.728425 + 1.26167i
\(576\) 0 0
\(577\) −2.40373 4.16339i −0.100069 0.173324i 0.811644 0.584152i \(-0.198573\pi\)
−0.911713 + 0.410828i \(0.865240\pi\)
\(578\) −7.26698 + 41.2131i −0.302266 + 1.71424i
\(579\) 0 0
\(580\) 0.527341 + 0.191936i 0.0218966 + 0.00796973i
\(581\) 53.9591 + 19.6395i 2.23860 + 0.814784i
\(582\) 0 0
\(583\) −4.23442 + 24.0146i −0.175372 + 0.994583i
\(584\) 2.34527 + 4.06212i 0.0970478 + 0.168092i
\(585\) 0 0
\(586\) 11.9598 20.7149i 0.494053 0.855725i
\(587\) 6.08056 + 5.10220i 0.250972 + 0.210590i 0.759591 0.650402i \(-0.225399\pi\)
−0.508619 + 0.860992i \(0.669844\pi\)
\(588\) 0 0
\(589\) 1.74288 + 9.88435i 0.0718141 + 0.407278i
\(590\) −1.30315 + 1.09347i −0.0536498 + 0.0450176i
\(591\) 0 0
\(592\) −9.65657 + 3.51471i −0.396883 + 0.144454i
\(593\) 36.2753 1.48965 0.744824 0.667261i \(-0.232533\pi\)
0.744824 + 0.667261i \(0.232533\pi\)
\(594\) 0 0
\(595\) 11.1010 0.455097
\(596\) −6.59613 + 2.40080i −0.270188 + 0.0983405i
\(597\) 0 0
\(598\) 23.5835 19.7889i 0.964402 0.809230i
\(599\) 5.84240 + 33.1339i 0.238714 + 1.35381i 0.834650 + 0.550781i \(0.185670\pi\)
−0.595936 + 0.803032i \(0.703219\pi\)
\(600\) 0 0
\(601\) −2.28106 1.91404i −0.0930463 0.0780752i 0.595078 0.803668i \(-0.297121\pi\)
−0.688124 + 0.725593i \(0.741566\pi\)
\(602\) 13.0746 22.6459i 0.532882 0.922978i
\(603\) 0 0
\(604\) 1.16385 + 2.01584i 0.0473563 + 0.0820235i
\(605\) 0.253620 1.43835i 0.0103111 0.0584772i
\(606\) 0 0
\(607\) 14.7049 + 5.35213i 0.596852 + 0.217236i 0.622740 0.782429i \(-0.286019\pi\)
−0.0258885 + 0.999665i \(0.508242\pi\)
\(608\) −9.45658 3.44191i −0.383515 0.139588i
\(609\) 0 0
\(610\) 0.786112 4.45826i 0.0318287 0.180510i
\(611\) 4.96529 + 8.60014i 0.200874 + 0.347924i
\(612\) 0 0
\(613\) 0.533433 0.923933i 0.0215452 0.0373173i −0.855052 0.518543i \(-0.826475\pi\)
0.876597 + 0.481225i \(0.159808\pi\)
\(614\) −20.4317 17.1442i −0.824557 0.691886i
\(615\) 0 0
\(616\) −5.14543 29.1812i −0.207315 1.17574i
\(617\) −10.0122 + 8.40121i −0.403075 + 0.338220i −0.821681 0.569948i \(-0.806963\pi\)
0.418606 + 0.908168i \(0.362519\pi\)
\(618\) 0 0
\(619\) −19.2802 + 7.01741i −0.774936 + 0.282054i −0.699059 0.715064i \(-0.746398\pi\)
−0.0758765 + 0.997117i \(0.524175\pi\)
\(620\) −0.300167 −0.0120550
\(621\) 0 0
\(622\) −26.2071 −1.05081
\(623\) −61.1568 + 22.2592i −2.45019 + 0.891798i
\(624\) 0 0
\(625\) 16.8910 14.1732i 0.675640 0.566929i
\(626\) 6.66159 + 37.7798i 0.266251 + 1.50998i
\(627\) 0 0
\(628\) −1.41669 1.18874i −0.0565320 0.0474360i
\(629\) 11.3569 19.6707i 0.452829 0.784323i
\(630\) 0 0
\(631\) 5.15611 + 8.93064i 0.205261 + 0.355523i 0.950216 0.311592i \(-0.100862\pi\)
−0.744955 + 0.667115i \(0.767529\pi\)
\(632\) −6.23654 + 35.3692i −0.248076 + 1.40691i
\(633\) 0 0
\(634\) 5.21466 + 1.89798i 0.207101 + 0.0753785i
\(635\) −1.12116 0.408071i −0.0444921 0.0161938i
\(636\) 0 0
\(637\) 3.12907 17.7458i 0.123978 0.703116i
\(638\) −6.46740 11.2019i −0.256047 0.443486i
\(639\) 0 0
\(640\) −1.67752 + 2.90555i −0.0663097 + 0.114852i
\(641\) 2.68588 + 2.25372i 0.106086 + 0.0890165i 0.694288 0.719698i \(-0.255720\pi\)
−0.588202 + 0.808714i \(0.700164\pi\)
\(642\) 0 0
\(643\) 5.47889 + 31.0723i 0.216066 + 1.22537i 0.879046 + 0.476736i \(0.158180\pi\)
−0.662980 + 0.748637i \(0.730708\pi\)
\(644\) −6.83807 + 5.73783i −0.269458 + 0.226102i
\(645\) 0 0
\(646\) −44.0908 + 16.0477i −1.73473 + 0.631390i
\(647\) −3.04628 −0.119762 −0.0598808 0.998206i \(-0.519072\pi\)
−0.0598808 + 0.998206i \(0.519072\pi\)
\(648\) 0 0
\(649\) −8.23947 −0.323428
\(650\) −19.0851 + 6.94639i −0.748578 + 0.272460i
\(651\) 0 0
\(652\) −1.01501 + 0.851698i −0.0397510 + 0.0333551i
\(653\) −5.33749 30.2704i −0.208872 1.18457i −0.891229 0.453553i \(-0.850156\pi\)
0.682357 0.731019i \(-0.260955\pi\)
\(654\) 0 0
\(655\) −0.998656 0.837972i −0.0390207 0.0327423i
\(656\) 7.74038 13.4067i 0.302211 0.523445i
\(657\) 0 0
\(658\) 6.85117 + 11.8666i 0.267086 + 0.462607i
\(659\) −5.76233 + 32.6798i −0.224469 + 1.27302i 0.639230 + 0.769016i \(0.279253\pi\)
−0.863699 + 0.504009i \(0.831858\pi\)
\(660\) 0 0
\(661\) 14.0086 + 5.09872i 0.544872 + 0.198317i 0.599767 0.800175i \(-0.295260\pi\)
−0.0548946 + 0.998492i \(0.517482\pi\)
\(662\) −3.52618 1.28342i −0.137049 0.0498817i
\(663\) 0 0
\(664\) 8.51889 48.3130i 0.330597 1.87491i
\(665\) 4.08819 + 7.08095i 0.158533 + 0.274587i
\(666\) 0 0
\(667\) −13.1682 + 22.8080i −0.509874 + 0.883128i
\(668\) −2.43042 2.03936i −0.0940357 0.0789053i
\(669\) 0 0
\(670\) −0.940769 5.33537i −0.0363451 0.206123i
\(671\) 16.7968 14.0942i 0.648434 0.544101i
\(672\) 0 0
\(673\) −6.47343 + 2.35614i −0.249532 + 0.0908224i −0.463758 0.885962i \(-0.653499\pi\)
0.214226 + 0.976784i \(0.431277\pi\)
\(674\) −18.5656 −0.715122
\(675\) 0 0
\(676\) 0.753718 0.0289892
\(677\) 12.3938 4.51098i 0.476333 0.173371i −0.0926859 0.995695i \(-0.529545\pi\)
0.569019 + 0.822324i \(0.307323\pi\)
\(678\) 0 0
\(679\) −27.3653 + 22.9622i −1.05018 + 0.881209i
\(680\) −1.64690 9.34002i −0.0631557 0.358174i
\(681\) 0 0
\(682\) 5.29994 + 4.44718i 0.202945 + 0.170291i
\(683\) 1.68907 2.92556i 0.0646305 0.111943i −0.831900 0.554926i \(-0.812746\pi\)
0.896530 + 0.442983i \(0.146080\pi\)
\(684\) 0 0
\(685\) 1.03967 + 1.80076i 0.0397237 + 0.0688034i
\(686\) −1.20194 + 6.81655i −0.0458904 + 0.260257i
\(687\) 0 0
\(688\) −17.2344 6.27282i −0.657056 0.239149i
\(689\) 27.1247 + 9.87258i 1.03337 + 0.376115i
\(690\) 0 0
\(691\) 4.06599 23.0594i 0.154678 0.877220i −0.804403 0.594085i \(-0.797514\pi\)
0.959080 0.283135i \(-0.0913745\pi\)
\(692\) 1.05471 + 1.82682i 0.0400942 + 0.0694452i
\(693\) 0 0
\(694\) −0.934640 + 1.61884i −0.0354785 + 0.0614505i
\(695\) 2.73708 + 2.29668i 0.103823 + 0.0871182i
\(696\) 0 0
\(697\) 5.94175 + 33.6974i 0.225060 + 1.27638i
\(698\) 27.1627 22.7922i 1.02812 0.862698i
\(699\) 0 0
\(700\) 5.53374 2.01412i 0.209156 0.0761264i
\(701\) 45.5001 1.71852 0.859258 0.511543i \(-0.170926\pi\)
0.859258 + 0.511543i \(0.170926\pi\)
\(702\) 0 0
\(703\) 16.7297 0.630972
\(704\) −23.1585 + 8.42902i −0.872820 + 0.317680i
\(705\) 0 0
\(706\) −10.3721 + 8.70323i −0.390360 + 0.327551i
\(707\) −1.27622 7.23783i −0.0479973 0.272206i
\(708\) 0 0
\(709\) 29.5822 + 24.8224i 1.11098 + 0.932225i 0.998114 0.0613851i \(-0.0195518\pi\)
0.112868 + 0.993610i \(0.463996\pi\)
\(710\) 1.52314 2.63816i 0.0571624 0.0990082i
\(711\) 0 0
\(712\) 27.8011 + 48.1530i 1.04189 + 1.80461i
\(713\) 2.44615 13.8728i 0.0916092 0.519541i
\(714\) 0 0
\(715\) 3.83837 + 1.39705i 0.143547 + 0.0522468i
\(716\) 3.35527 + 1.22122i 0.125392 + 0.0456391i
\(717\) 0 0
\(718\) −3.28281 + 18.6178i −0.122514 + 0.694809i
\(719\) 24.6591 + 42.7108i 0.919630 + 1.59285i 0.799978 + 0.600030i \(0.204845\pi\)
0.119652 + 0.992816i \(0.461822\pi\)
\(720\) 0 0
\(721\) −2.55778 + 4.43021i −0.0952567 + 0.164990i
\(722\) −7.76233 6.51337i −0.288884 0.242402i
\(723\) 0 0
\(724\) 1.39558 + 7.91474i 0.0518664 + 0.294149i
\(725\) 13.3095 11.1680i 0.494304 0.414770i
\(726\) 0 0
\(727\) 30.3469 11.0454i 1.12550 0.409650i 0.288846 0.957376i \(-0.406729\pi\)
0.836658 + 0.547726i \(0.184506\pi\)
\(728\) −35.0757 −1.29999
\(729\) 0 0
\(730\) −0.892178 −0.0330210
\(731\) 38.0933 13.8648i 1.40893 0.512810i
\(732\) 0 0
\(733\) 30.2328 25.3684i 1.11668 0.937002i 0.118243 0.992985i \(-0.462274\pi\)
0.998432 + 0.0559830i \(0.0178293\pi\)
\(734\) 4.76898 + 27.0462i 0.176026 + 0.998294i
\(735\) 0 0
\(736\) 10.8198 + 9.07888i 0.398823 + 0.334652i
\(737\) 13.1202 22.7249i 0.483290 0.837083i
\(738\) 0 0
\(739\) −17.6545 30.5785i −0.649432 1.12485i −0.983259 0.182215i \(-0.941673\pi\)
0.333827 0.942634i \(-0.391660\pi\)
\(740\) −0.0868809 + 0.492726i −0.00319381 + 0.0181130i
\(741\) 0 0
\(742\) 37.4270 + 13.6223i 1.37399 + 0.500090i
\(743\) 44.5514 + 16.2154i 1.63443 + 0.594884i 0.986053 0.166433i \(-0.0532251\pi\)
0.648379 + 0.761318i \(0.275447\pi\)
\(744\) 0 0
\(745\) 1.56701 8.88695i 0.0574108 0.325593i
\(746\) 14.5428 + 25.1888i 0.532449 + 0.922228i
\(747\) 0 0
\(748\) 3.39827 5.88598i 0.124253 0.215213i
\(749\) −6.04958 5.07620i −0.221047 0.185480i
\(750\) 0 0
\(751\) −1.55035 8.79244i −0.0565729 0.320841i 0.943368 0.331749i \(-0.107639\pi\)
−0.999941 + 0.0109084i \(0.996528\pi\)
\(752\) 7.36208 6.17752i 0.268467 0.225271i
\(753\) 0 0
\(754\) −14.3880 + 5.23680i −0.523980 + 0.190713i
\(755\) −2.99243 −0.108906
\(756\) 0 0
\(757\) −3.63816 −0.132231 −0.0661155 0.997812i \(-0.521061\pi\)
−0.0661155 + 0.997812i \(0.521061\pi\)
\(758\) −20.6265 + 7.50744i −0.749189 + 0.272682i
\(759\) 0 0
\(760\) 5.35117 4.49016i 0.194107 0.162875i
\(761\) −1.16150 6.58718i −0.0421043 0.238785i 0.956492 0.291760i \(-0.0942408\pi\)
−0.998596 + 0.0529748i \(0.983130\pi\)
\(762\) 0 0
\(763\) 31.1241 + 26.1162i 1.12677 + 0.945470i
\(764\) 2.54747 4.41235i 0.0921643 0.159633i
\(765\) 0 0
\(766\) −25.0633 43.4109i −0.905574 1.56850i
\(767\) −1.69365 + 9.60519i −0.0611543 + 0.346823i
\(768\) 0 0
\(769\) 20.1763 + 7.34359i 0.727577 + 0.264816i 0.679139 0.734010i \(-0.262353\pi\)
0.0484383 + 0.998826i \(0.484576\pi\)
\(770\) 5.29623 + 1.92767i 0.190863 + 0.0694684i
\(771\) 0 0
\(772\) −1.41370 + 8.01747i −0.0508800 + 0.288555i
\(773\) 5.12208 + 8.87170i 0.184228 + 0.319093i 0.943316 0.331895i \(-0.107688\pi\)
−0.759088 + 0.650988i \(0.774355\pi\)
\(774\) 0 0
\(775\) −4.64661 + 8.04817i −0.166911 + 0.289099i
\(776\) 23.3794 + 19.6177i 0.839273 + 0.704234i
\(777\) 0 0
\(778\) −2.27972 12.9289i −0.0817317 0.463524i
\(779\) −19.3062 + 16.1998i −0.691716 + 0.580418i
\(780\) 0