Properties

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

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [729,2,Mod(82,729)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(729, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("729.82");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 729 = 3^{6} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 729.e (of order \(9\), degree \(6\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.82109430735\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(2\) over \(\Q(\zeta_{9})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} + 18x^{10} + 105x^{8} + 266x^{6} + 306x^{4} + 132x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 82.1
Root \(-1.91182i\) of defining polynomial
Character \(\chi\) \(=\) 729.82
Dual form 729.2.e.k.649.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.426791 - 2.42045i) q^{2} +(-3.79704 + 1.38201i) q^{4} +(-2.35962 - 1.97995i) q^{5} +(2.49833 + 0.909318i) q^{7} +(2.50784 + 4.34371i) q^{8} +O(q^{10})\) \(q+(-0.426791 - 2.42045i) q^{2} +(-3.79704 + 1.38201i) q^{4} +(-2.35962 - 1.97995i) q^{5} +(2.49833 + 0.909318i) q^{7} +(2.50784 + 4.34371i) q^{8} +(-3.78532 + 6.55636i) q^{10} +(-2.63086 + 2.20755i) q^{11} +(-0.580672 + 3.29315i) q^{13} +(1.13469 - 6.43517i) q^{14} +(3.25265 - 2.72930i) q^{16} +(-1.28641 + 2.22813i) q^{17} +(1.04838 + 1.81585i) q^{19} +(11.6959 + 4.25696i) q^{20} +(6.46609 + 5.42570i) q^{22} +(-0.502213 + 0.182791i) q^{23} +(0.779336 + 4.41984i) q^{25} +8.21874 q^{26} -10.7430 q^{28} +(0.439485 + 2.49244i) q^{29} +(-7.24945 + 2.63858i) q^{31} +(-0.309858 - 0.260001i) q^{32} +(5.94209 + 2.16275i) q^{34} +(-4.09470 - 7.09222i) q^{35} +(5.14783 - 8.91631i) q^{37} +(3.94774 - 3.31254i) q^{38} +(2.68280 - 15.2149i) q^{40} +(-0.848272 + 4.81079i) q^{41} +(2.10010 - 1.76220i) q^{43} +(6.93862 - 12.0180i) q^{44} +(0.656775 + 1.13757i) q^{46} +(5.31678 + 1.93515i) q^{47} +(0.0524824 + 0.0440380i) q^{49} +(10.3654 - 3.77269i) q^{50} +(-2.34634 - 13.3067i) q^{52} +6.42657 q^{53} +10.5787 q^{55} +(2.31560 + 13.1324i) q^{56} +(5.84527 - 2.12750i) q^{58} +(1.26777 + 1.06378i) q^{59} +(-13.5055 - 4.91558i) q^{61} +(9.48056 + 16.4208i) q^{62} +(3.74896 - 6.49338i) q^{64} +(7.89046 - 6.62088i) q^{65} +(-1.02087 + 5.78967i) q^{67} +(1.80526 - 10.2381i) q^{68} +(-15.4188 + 12.9379i) q^{70} +(-7.40813 + 12.8313i) q^{71} +(-0.940699 - 1.62934i) q^{73} +(-23.7785 - 8.65467i) q^{74} +(-6.49027 - 5.44599i) q^{76} +(-8.58012 + 3.12291i) q^{77} +(2.98562 + 16.9323i) q^{79} -13.0789 q^{80} +12.0063 q^{82} +(0.689172 + 3.90849i) q^{83} +(7.44702 - 2.71049i) q^{85} +(-5.16161 - 4.33111i) q^{86} +(-16.1867 - 5.89149i) q^{88} +(-2.54940 - 4.41569i) q^{89} +(-4.44523 + 7.69937i) q^{91} +(1.65431 - 1.38813i) q^{92} +(2.41478 - 13.6949i) q^{94} +(1.12152 - 6.36046i) q^{95} +(-8.14449 + 6.83404i) q^{97} +(0.0841927 - 0.145826i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 3 q^{2} - 3 q^{4} - 6 q^{5} + 6 q^{7} - 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 3 q^{2} - 3 q^{4} - 6 q^{5} + 6 q^{7} - 6 q^{8} - 6 q^{10} + 15 q^{11} - 3 q^{13} + 21 q^{14} + 9 q^{16} + 9 q^{17} - 12 q^{19} + 3 q^{20} + 33 q^{22} - 15 q^{23} - 12 q^{25} + 48 q^{26} + 6 q^{28} + 6 q^{29} - 12 q^{31} + 27 q^{32} + 27 q^{34} - 30 q^{35} - 3 q^{37} + 39 q^{38} + 24 q^{40} + 39 q^{41} + 24 q^{43} + 33 q^{44} + 3 q^{46} + 42 q^{47} - 30 q^{49} + 15 q^{50} - 45 q^{52} - 18 q^{53} + 30 q^{55} - 12 q^{56} - 30 q^{58} - 15 q^{59} - 3 q^{61} + 30 q^{62} - 6 q^{64} + 6 q^{65} - 3 q^{67} - 36 q^{68} - 75 q^{70} - 12 q^{73} - 60 q^{74} + 30 q^{76} - 33 q^{77} + 33 q^{79} - 42 q^{80} - 42 q^{82} + 33 q^{83} - 18 q^{85} + 30 q^{86} - 42 q^{88} + 9 q^{89} - 18 q^{91} - 33 q^{92} - 66 q^{94} - 12 q^{95} + 15 q^{97} - 18 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.426791 2.42045i −0.301787 1.71152i −0.638258 0.769823i \(-0.720345\pi\)
0.336471 0.941694i \(-0.390767\pi\)
\(3\) 0 0
\(4\) −3.79704 + 1.38201i −1.89852 + 0.691005i
\(5\) −2.35962 1.97995i −1.05525 0.885463i −0.0616172 0.998100i \(-0.519626\pi\)
−0.993636 + 0.112637i \(0.964070\pi\)
\(6\) 0 0
\(7\) 2.49833 + 0.909318i 0.944280 + 0.343690i 0.767855 0.640624i \(-0.221324\pi\)
0.176425 + 0.984314i \(0.443547\pi\)
\(8\) 2.50784 + 4.34371i 0.886656 + 1.53573i
\(9\) 0 0
\(10\) −3.78532 + 6.55636i −1.19702 + 2.07330i
\(11\) −2.63086 + 2.20755i −0.793233 + 0.665602i −0.946543 0.322576i \(-0.895451\pi\)
0.153310 + 0.988178i \(0.451007\pi\)
\(12\) 0 0
\(13\) −0.580672 + 3.29315i −0.161049 + 0.913357i 0.791995 + 0.610527i \(0.209042\pi\)
−0.953045 + 0.302829i \(0.902069\pi\)
\(14\) 1.13469 6.43517i 0.303260 1.71987i
\(15\) 0 0
\(16\) 3.25265 2.72930i 0.813162 0.682324i
\(17\) −1.28641 + 2.22813i −0.312000 + 0.540400i −0.978795 0.204841i \(-0.934332\pi\)
0.666795 + 0.745241i \(0.267666\pi\)
\(18\) 0 0
\(19\) 1.04838 + 1.81585i 0.240515 + 0.416585i 0.960861 0.277030i \(-0.0893503\pi\)
−0.720346 + 0.693615i \(0.756017\pi\)
\(20\) 11.6959 + 4.25696i 2.61528 + 0.951884i
\(21\) 0 0
\(22\) 6.46609 + 5.42570i 1.37858 + 1.15676i
\(23\) −0.502213 + 0.182791i −0.104719 + 0.0381145i −0.393848 0.919176i \(-0.628856\pi\)
0.289129 + 0.957290i \(0.406634\pi\)
\(24\) 0 0
\(25\) 0.779336 + 4.41984i 0.155867 + 0.883967i
\(26\) 8.21874 1.61183
\(27\) 0 0
\(28\) −10.7430 −2.03023
\(29\) 0.439485 + 2.49244i 0.0816103 + 0.462835i 0.998037 + 0.0626319i \(0.0199494\pi\)
−0.916426 + 0.400203i \(0.868939\pi\)
\(30\) 0 0
\(31\) −7.24945 + 2.63858i −1.30204 + 0.473904i −0.897660 0.440688i \(-0.854735\pi\)
−0.404379 + 0.914592i \(0.632512\pi\)
\(32\) −0.309858 0.260001i −0.0547756 0.0459622i
\(33\) 0 0
\(34\) 5.94209 + 2.16275i 1.01906 + 0.370908i
\(35\) −4.09470 7.09222i −0.692130 1.19880i
\(36\) 0 0
\(37\) 5.14783 8.91631i 0.846298 1.46583i −0.0381907 0.999270i \(-0.512159\pi\)
0.884489 0.466561i \(-0.154507\pi\)
\(38\) 3.94774 3.31254i 0.640407 0.537365i
\(39\) 0 0
\(40\) 2.68280 15.2149i 0.424188 2.40569i
\(41\) −0.848272 + 4.81079i −0.132478 + 0.751320i 0.844105 + 0.536178i \(0.180132\pi\)
−0.976583 + 0.215142i \(0.930979\pi\)
\(42\) 0 0
\(43\) 2.10010 1.76220i 0.320263 0.268732i −0.468456 0.883487i \(-0.655189\pi\)
0.788718 + 0.614755i \(0.210745\pi\)
\(44\) 6.93862 12.0180i 1.04604 1.81179i
\(45\) 0 0
\(46\) 0.656775 + 1.13757i 0.0968363 + 0.167725i
\(47\) 5.31678 + 1.93515i 0.775532 + 0.282270i 0.699308 0.714820i \(-0.253492\pi\)
0.0762235 + 0.997091i \(0.475714\pi\)
\(48\) 0 0
\(49\) 0.0524824 + 0.0440380i 0.00749749 + 0.00629114i
\(50\) 10.3654 3.77269i 1.46589 0.533539i
\(51\) 0 0
\(52\) −2.34634 13.3067i −0.325379 1.84531i
\(53\) 6.42657 0.882758 0.441379 0.897321i \(-0.354489\pi\)
0.441379 + 0.897321i \(0.354489\pi\)
\(54\) 0 0
\(55\) 10.5787 1.42643
\(56\) 2.31560 + 13.1324i 0.309436 + 1.75490i
\(57\) 0 0
\(58\) 5.84527 2.12750i 0.767521 0.279355i
\(59\) 1.26777 + 1.06378i 0.165049 + 0.138493i 0.721571 0.692340i \(-0.243420\pi\)
−0.556522 + 0.830833i \(0.687865\pi\)
\(60\) 0 0
\(61\) −13.5055 4.91558i −1.72920 0.629376i −0.730624 0.682780i \(-0.760771\pi\)
−0.998573 + 0.0534042i \(0.982993\pi\)
\(62\) 9.48056 + 16.4208i 1.20403 + 2.08544i
\(63\) 0 0
\(64\) 3.74896 6.49338i 0.468620 0.811673i
\(65\) 7.89046 6.62088i 0.978691 0.821219i
\(66\) 0 0
\(67\) −1.02087 + 5.78967i −0.124720 + 0.707320i 0.856754 + 0.515725i \(0.172477\pi\)
−0.981474 + 0.191596i \(0.938634\pi\)
\(68\) 1.80526 10.2381i 0.218920 1.24155i
\(69\) 0 0
\(70\) −15.4188 + 12.9379i −1.84290 + 1.54638i
\(71\) −7.40813 + 12.8313i −0.879184 + 1.52279i −0.0269456 + 0.999637i \(0.508578\pi\)
−0.852238 + 0.523154i \(0.824755\pi\)
\(72\) 0 0
\(73\) −0.940699 1.62934i −0.110101 0.190700i 0.805710 0.592310i \(-0.201784\pi\)
−0.915811 + 0.401610i \(0.868451\pi\)
\(74\) −23.7785 8.65467i −2.76420 1.00609i
\(75\) 0 0
\(76\) −6.49027 5.44599i −0.744486 0.624698i
\(77\) −8.58012 + 3.12291i −0.977795 + 0.355888i
\(78\) 0 0
\(79\) 2.98562 + 16.9323i 0.335908 + 1.90503i 0.418076 + 0.908412i \(0.362704\pi\)
−0.0821680 + 0.996618i \(0.526184\pi\)
\(80\) −13.0789 −1.46227
\(81\) 0 0
\(82\) 12.0063 1.32588
\(83\) 0.689172 + 3.90849i 0.0756465 + 0.429013i 0.998986 + 0.0450274i \(0.0143375\pi\)
−0.923339 + 0.383985i \(0.874551\pi\)
\(84\) 0 0
\(85\) 7.44702 2.71049i 0.807743 0.293994i
\(86\) −5.16161 4.33111i −0.556591 0.467035i
\(87\) 0 0
\(88\) −16.1867 5.89149i −1.72551 0.628035i
\(89\) −2.54940 4.41569i −0.270236 0.468062i 0.698686 0.715428i \(-0.253768\pi\)
−0.968922 + 0.247366i \(0.920435\pi\)
\(90\) 0 0
\(91\) −4.44523 + 7.69937i −0.465987 + 0.807113i
\(92\) 1.65431 1.38813i 0.172473 0.144722i
\(93\) 0 0
\(94\) 2.41478 13.6949i 0.249066 1.41252i
\(95\) 1.12152 6.36046i 0.115066 0.652570i
\(96\) 0 0
\(97\) −8.14449 + 6.83404i −0.826948 + 0.693892i −0.954588 0.297929i \(-0.903704\pi\)
0.127640 + 0.991821i \(0.459260\pi\)
\(98\) 0.0841927 0.145826i 0.00850475 0.0147307i
\(99\) 0 0
\(100\) −9.06744 15.7053i −0.906744 1.57053i
\(101\) −5.31686 1.93518i −0.529048 0.192558i 0.0636653 0.997971i \(-0.479721\pi\)
−0.592713 + 0.805414i \(0.701943\pi\)
\(102\) 0 0
\(103\) 7.94429 + 6.66605i 0.782775 + 0.656826i 0.943946 0.330101i \(-0.107083\pi\)
−0.161171 + 0.986926i \(0.551527\pi\)
\(104\) −15.7607 + 5.73644i −1.54547 + 0.562504i
\(105\) 0 0
\(106\) −2.74280 15.5552i −0.266404 1.51085i
\(107\) −14.2457 −1.37719 −0.688594 0.725147i \(-0.741772\pi\)
−0.688594 + 0.725147i \(0.741772\pi\)
\(108\) 0 0
\(109\) 5.76064 0.551769 0.275884 0.961191i \(-0.411029\pi\)
0.275884 + 0.961191i \(0.411029\pi\)
\(110\) −4.51488 25.6051i −0.430477 2.44136i
\(111\) 0 0
\(112\) 10.6080 3.86099i 1.00236 0.364830i
\(113\) −8.74569 7.33851i −0.822726 0.690349i 0.130883 0.991398i \(-0.458219\pi\)
−0.953609 + 0.301049i \(0.902663\pi\)
\(114\) 0 0
\(115\) 1.54695 + 0.563043i 0.144254 + 0.0525040i
\(116\) −5.11333 8.85654i −0.474761 0.822309i
\(117\) 0 0
\(118\) 2.03376 3.52257i 0.187223 0.324279i
\(119\) −5.23995 + 4.39684i −0.480345 + 0.403058i
\(120\) 0 0
\(121\) 0.137998 0.782623i 0.0125452 0.0711475i
\(122\) −6.13392 + 34.7872i −0.555339 + 3.14949i
\(123\) 0 0
\(124\) 23.8799 20.0376i 2.14448 1.79943i
\(125\) −0.788517 + 1.36575i −0.0705271 + 0.122157i
\(126\) 0 0
\(127\) −1.29510 2.24317i −0.114921 0.199049i 0.802827 0.596212i \(-0.203328\pi\)
−0.917748 + 0.397163i \(0.869995\pi\)
\(128\) −18.0771 6.57954i −1.59781 0.581554i
\(129\) 0 0
\(130\) −19.3931 16.2727i −1.70089 1.42721i
\(131\) 4.14497 1.50865i 0.362148 0.131811i −0.154536 0.987987i \(-0.549388\pi\)
0.516684 + 0.856176i \(0.327166\pi\)
\(132\) 0 0
\(133\) 0.968018 + 5.48990i 0.0839378 + 0.476035i
\(134\) 14.4493 1.24823
\(135\) 0 0
\(136\) −12.9044 −1.10655
\(137\) 3.15479 + 17.8917i 0.269531 + 1.52859i 0.755813 + 0.654787i \(0.227242\pi\)
−0.486282 + 0.873802i \(0.661647\pi\)
\(138\) 0 0
\(139\) −1.83987 + 0.669656i −0.156055 + 0.0567995i −0.418867 0.908048i \(-0.637573\pi\)
0.262811 + 0.964847i \(0.415350\pi\)
\(140\) 25.3493 + 21.2706i 2.14240 + 1.79769i
\(141\) 0 0
\(142\) 34.2192 + 12.4548i 2.87161 + 1.04518i
\(143\) −5.74214 9.94568i −0.480182 0.831700i
\(144\) 0 0
\(145\) 3.89791 6.75138i 0.323704 0.560671i
\(146\) −3.54225 + 2.97230i −0.293159 + 0.245989i
\(147\) 0 0
\(148\) −7.22411 + 40.9700i −0.593818 + 3.36771i
\(149\) 1.27027 7.20405i 0.104065 0.590179i −0.887525 0.460759i \(-0.847577\pi\)
0.991590 0.129420i \(-0.0413116\pi\)
\(150\) 0 0
\(151\) 3.71607 3.11815i 0.302410 0.253752i −0.478937 0.877849i \(-0.658978\pi\)
0.781346 + 0.624098i \(0.214533\pi\)
\(152\) −5.25835 + 9.10773i −0.426508 + 0.738734i
\(153\) 0 0
\(154\) 11.2208 + 19.4349i 0.904194 + 1.56611i
\(155\) 22.3302 + 8.12753i 1.79361 + 0.652819i
\(156\) 0 0
\(157\) 1.13122 + 0.949206i 0.0902812 + 0.0757549i 0.686811 0.726836i \(-0.259010\pi\)
−0.596530 + 0.802591i \(0.703454\pi\)
\(158\) 39.7095 14.4531i 3.15912 1.14983i
\(159\) 0 0
\(160\) 0.216355 + 1.22701i 0.0171043 + 0.0970035i
\(161\) −1.42091 −0.111983
\(162\) 0 0
\(163\) −17.2536 −1.35141 −0.675703 0.737174i \(-0.736160\pi\)
−0.675703 + 0.737174i \(0.736160\pi\)
\(164\) −3.42764 19.4391i −0.267654 1.51794i
\(165\) 0 0
\(166\) 9.16617 3.33621i 0.711433 0.258940i
\(167\) 5.24002 + 4.39690i 0.405485 + 0.340242i 0.822609 0.568607i \(-0.192518\pi\)
−0.417124 + 0.908850i \(0.636962\pi\)
\(168\) 0 0
\(169\) 1.70832 + 0.621778i 0.131409 + 0.0478291i
\(170\) −9.73894 16.8683i −0.746942 1.29374i
\(171\) 0 0
\(172\) −5.53881 + 9.59350i −0.422330 + 0.731497i
\(173\) −18.3601 + 15.4059i −1.39589 + 1.17129i −0.433002 + 0.901393i \(0.642546\pi\)
−0.962889 + 0.269899i \(0.913010\pi\)
\(174\) 0 0
\(175\) −2.07200 + 11.7509i −0.156628 + 0.888283i
\(176\) −2.53219 + 14.3608i −0.190871 + 1.08248i
\(177\) 0 0
\(178\) −9.59989 + 8.05527i −0.719542 + 0.603768i
\(179\) 10.2861 17.8161i 0.768820 1.33163i −0.169384 0.985550i \(-0.554178\pi\)
0.938203 0.346084i \(-0.112489\pi\)
\(180\) 0 0
\(181\) 7.73507 + 13.3975i 0.574943 + 0.995830i 0.996048 + 0.0888184i \(0.0283091\pi\)
−0.421105 + 0.907012i \(0.638358\pi\)
\(182\) 20.5331 + 7.47345i 1.52202 + 0.553969i
\(183\) 0 0
\(184\) −2.05346 1.72306i −0.151383 0.127025i
\(185\) −29.8008 + 10.8466i −2.19100 + 0.797458i
\(186\) 0 0
\(187\) −1.53434 8.70170i −0.112202 0.636331i
\(188\) −22.8624 −1.66741
\(189\) 0 0
\(190\) −15.8738 −1.15161
\(191\) −1.90159 10.7845i −0.137595 0.780338i −0.973018 0.230730i \(-0.925888\pi\)
0.835423 0.549607i \(-0.185223\pi\)
\(192\) 0 0
\(193\) −1.07581 + 0.391562i −0.0774384 + 0.0281853i −0.380449 0.924802i \(-0.624230\pi\)
0.303010 + 0.952987i \(0.402008\pi\)
\(194\) 20.0174 + 16.7966i 1.43717 + 1.20593i
\(195\) 0 0
\(196\) −0.260139 0.0946828i −0.0185814 0.00676306i
\(197\) 2.52097 + 4.36645i 0.179612 + 0.311097i 0.941748 0.336320i \(-0.109182\pi\)
−0.762136 + 0.647417i \(0.775849\pi\)
\(198\) 0 0
\(199\) −6.86291 + 11.8869i −0.486499 + 0.842640i −0.999880 0.0155206i \(-0.995059\pi\)
0.513381 + 0.858161i \(0.328393\pi\)
\(200\) −17.2440 + 14.4695i −1.21934 + 1.02315i
\(201\) 0 0
\(202\) −2.41482 + 13.6951i −0.169906 + 0.963585i
\(203\) −1.16844 + 6.62658i −0.0820087 + 0.465095i
\(204\) 0 0
\(205\) 11.5268 9.67209i 0.805063 0.675528i
\(206\) 12.7443 22.0738i 0.887938 1.53795i
\(207\) 0 0
\(208\) 7.09927 + 12.2963i 0.492246 + 0.852595i
\(209\) −6.76673 2.46289i −0.468064 0.170361i
\(210\) 0 0
\(211\) −4.46997 3.75075i −0.307725 0.258212i 0.475826 0.879540i \(-0.342149\pi\)
−0.783551 + 0.621327i \(0.786594\pi\)
\(212\) −24.4020 + 8.88159i −1.67593 + 0.609990i
\(213\) 0 0
\(214\) 6.07995 + 34.4811i 0.415617 + 2.35708i
\(215\) −8.44451 −0.575911
\(216\) 0 0
\(217\) −20.5108 −1.39237
\(218\) −2.45859 13.9433i −0.166516 0.944362i
\(219\) 0 0
\(220\) −40.1677 + 14.6198i −2.70810 + 0.985669i
\(221\) −6.59058 5.53015i −0.443330 0.371998i
\(222\) 0 0
\(223\) −8.20228 2.98538i −0.549265 0.199916i 0.0524549 0.998623i \(-0.483295\pi\)
−0.601720 + 0.798707i \(0.705518\pi\)
\(224\) −0.537703 0.931329i −0.0359268 0.0622270i
\(225\) 0 0
\(226\) −14.0299 + 24.3005i −0.933256 + 1.61645i
\(227\) 18.6015 15.6085i 1.23462 1.03597i 0.236700 0.971583i \(-0.423934\pi\)
0.997925 0.0643900i \(-0.0205101\pi\)
\(228\) 0 0
\(229\) 3.15196 17.8757i 0.208288 1.18126i −0.683894 0.729581i \(-0.739715\pi\)
0.892182 0.451676i \(-0.149174\pi\)
\(230\) 0.702595 3.98461i 0.0463277 0.262738i
\(231\) 0 0
\(232\) −9.72429 + 8.15965i −0.638431 + 0.535707i
\(233\) −5.26900 + 9.12617i −0.345183 + 0.597875i −0.985387 0.170330i \(-0.945517\pi\)
0.640204 + 0.768205i \(0.278850\pi\)
\(234\) 0 0
\(235\) −8.71406 15.0932i −0.568442 0.984571i
\(236\) −6.28392 2.28716i −0.409048 0.148881i
\(237\) 0 0
\(238\) 12.8787 + 10.8065i 0.834801 + 0.700482i
\(239\) 8.96147 3.26171i 0.579670 0.210982i −0.0355102 0.999369i \(-0.511306\pi\)
0.615180 + 0.788387i \(0.289083\pi\)
\(240\) 0 0
\(241\) −1.22201 6.93037i −0.0787166 0.446424i −0.998536 0.0540831i \(-0.982776\pi\)
0.919820 0.392341i \(-0.128335\pi\)
\(242\) −1.95320 −0.125556
\(243\) 0 0
\(244\) 58.0742 3.71782
\(245\) −0.0366453 0.207826i −0.00234118 0.0132775i
\(246\) 0 0
\(247\) −6.58864 + 2.39807i −0.419225 + 0.152585i
\(248\) −29.6417 24.8723i −1.88225 1.57940i
\(249\) 0 0
\(250\) 3.64227 + 1.32568i 0.230357 + 0.0838431i
\(251\) 7.79350 + 13.4987i 0.491921 + 0.852033i 0.999957 0.00930331i \(-0.00296138\pi\)
−0.508035 + 0.861336i \(0.669628\pi\)
\(252\) 0 0
\(253\) 0.917731 1.58956i 0.0576973 0.0999346i
\(254\) −4.87676 + 4.09208i −0.305995 + 0.256760i
\(255\) 0 0
\(256\) −5.60629 + 31.7949i −0.350393 + 1.98718i
\(257\) −2.11673 + 12.0046i −0.132038 + 0.748825i 0.844838 + 0.535021i \(0.179696\pi\)
−0.976877 + 0.213804i \(0.931415\pi\)
\(258\) 0 0
\(259\) 20.9687 17.5949i 1.30293 1.09329i
\(260\) −20.8103 + 36.0445i −1.29060 + 2.23538i
\(261\) 0 0
\(262\) −5.42064 9.38882i −0.334888 0.580043i
\(263\) −6.47414 2.35639i −0.399212 0.145301i 0.134609 0.990899i \(-0.457022\pi\)
−0.533821 + 0.845597i \(0.679244\pi\)
\(264\) 0 0
\(265\) −15.1643 12.7243i −0.931533 0.781649i
\(266\) 12.8749 4.68608i 0.789411 0.287322i
\(267\) 0 0
\(268\) −4.12508 23.3945i −0.251979 1.42905i
\(269\) −7.05875 −0.430380 −0.215190 0.976572i \(-0.569037\pi\)
−0.215190 + 0.976572i \(0.569037\pi\)
\(270\) 0 0
\(271\) 23.7575 1.44316 0.721581 0.692330i \(-0.243416\pi\)
0.721581 + 0.692330i \(0.243416\pi\)
\(272\) 1.89698 + 10.7583i 0.115021 + 0.652318i
\(273\) 0 0
\(274\) 41.9595 15.2720i 2.53486 0.922615i
\(275\) −11.8073 9.90754i −0.712009 0.597447i
\(276\) 0 0
\(277\) 0.0981638 + 0.0357287i 0.00589809 + 0.00214673i 0.344968 0.938615i \(-0.387890\pi\)
−0.339069 + 0.940761i \(0.610112\pi\)
\(278\) 2.40611 + 4.16750i 0.144309 + 0.249950i
\(279\) 0 0
\(280\) 20.5377 35.5723i 1.22736 2.12585i
\(281\) −6.24495 + 5.24013i −0.372542 + 0.312600i −0.809766 0.586753i \(-0.800406\pi\)
0.437224 + 0.899353i \(0.355962\pi\)
\(282\) 0 0
\(283\) 4.10087 23.2572i 0.243772 1.38250i −0.579557 0.814932i \(-0.696774\pi\)
0.823328 0.567565i \(-0.192115\pi\)
\(284\) 10.3961 58.9590i 0.616893 3.49857i
\(285\) 0 0
\(286\) −21.6223 + 18.1433i −1.27856 + 1.07284i
\(287\) −6.49380 + 11.2476i −0.383317 + 0.663925i
\(288\) 0 0
\(289\) 5.19030 + 8.98987i 0.305312 + 0.528816i
\(290\) −18.0050 6.55327i −1.05729 0.384821i
\(291\) 0 0
\(292\) 5.82364 + 4.88661i 0.340803 + 0.285967i
\(293\) 20.3216 7.39644i 1.18720 0.432105i 0.328459 0.944518i \(-0.393471\pi\)
0.858739 + 0.512413i \(0.171248\pi\)
\(294\) 0 0
\(295\) −0.885203 5.02024i −0.0515385 0.292289i
\(296\) 51.6398 3.00150
\(297\) 0 0
\(298\) −17.9792 −1.04151
\(299\) −0.310337 1.76001i −0.0179472 0.101784i
\(300\) 0 0
\(301\) 6.84915 2.49289i 0.394778 0.143688i
\(302\) −9.13332 7.66377i −0.525564 0.441000i
\(303\) 0 0
\(304\) 8.36601 + 3.04498i 0.479824 + 0.174642i
\(305\) 22.1351 + 38.3391i 1.26745 + 2.19529i
\(306\) 0 0
\(307\) −8.17997 + 14.1681i −0.466855 + 0.808617i −0.999283 0.0378581i \(-0.987946\pi\)
0.532428 + 0.846475i \(0.321280\pi\)
\(308\) 28.2632 23.7156i 1.61044 1.35132i
\(309\) 0 0
\(310\) 10.1420 57.5179i 0.576025 3.26680i
\(311\) −1.34662 + 7.63705i −0.0763597 + 0.433057i 0.922529 + 0.385928i \(0.126119\pi\)
−0.998889 + 0.0471298i \(0.984993\pi\)
\(312\) 0 0
\(313\) 11.8109 9.91053i 0.667592 0.560177i −0.244759 0.969584i \(-0.578709\pi\)
0.912352 + 0.409407i \(0.134264\pi\)
\(314\) 1.81471 3.14317i 0.102410 0.177380i
\(315\) 0 0
\(316\) −34.7371 60.1664i −1.95412 3.38463i
\(317\) −8.11538 2.95376i −0.455805 0.165899i 0.103906 0.994587i \(-0.466866\pi\)
−0.559711 + 0.828688i \(0.689088\pi\)
\(318\) 0 0
\(319\) −6.65842 5.58708i −0.372800 0.312816i
\(320\) −21.7027 + 7.89914i −1.21322 + 0.441575i
\(321\) 0 0
\(322\) 0.606431 + 3.43924i 0.0337951 + 0.191661i
\(323\) −5.39459 −0.300163
\(324\) 0 0
\(325\) −15.0077 −0.832480
\(326\) 7.36368 + 41.7615i 0.407836 + 2.31295i
\(327\) 0 0
\(328\) −23.0240 + 8.38005i −1.27129 + 0.462711i
\(329\) 11.5234 + 9.66928i 0.635306 + 0.533085i
\(330\) 0 0
\(331\) −19.3055 7.02664i −1.06113 0.386219i −0.248276 0.968689i \(-0.579864\pi\)
−0.812852 + 0.582470i \(0.802086\pi\)
\(332\) −8.01839 13.8883i −0.440066 0.762217i
\(333\) 0 0
\(334\) 8.40609 14.5598i 0.459961 0.796675i
\(335\) 13.8722 11.6401i 0.757917 0.635968i
\(336\) 0 0
\(337\) 2.77459 15.7355i 0.151141 0.857165i −0.811088 0.584924i \(-0.801124\pi\)
0.962229 0.272241i \(-0.0877647\pi\)
\(338\) 0.775887 4.40028i 0.0422027 0.239343i
\(339\) 0 0
\(340\) −24.5307 + 20.5837i −1.33037 + 1.11631i
\(341\) 13.2475 22.9453i 0.717390 1.24256i
\(342\) 0 0
\(343\) −9.21426 15.9596i −0.497523 0.861736i
\(344\) 12.9212 + 4.70293i 0.696664 + 0.253565i
\(345\) 0 0
\(346\) 45.1252 + 37.8645i 2.42595 + 2.03561i
\(347\) 9.21300 3.35326i 0.494580 0.180012i −0.0826746 0.996577i \(-0.526346\pi\)
0.577255 + 0.816564i \(0.304124\pi\)
\(348\) 0 0
\(349\) −1.63837 9.29164i −0.0876997 0.497370i −0.996741 0.0806644i \(-0.974296\pi\)
0.909042 0.416705i \(-0.136815\pi\)
\(350\) 29.3267 1.56758
\(351\) 0 0
\(352\) 1.38916 0.0740424
\(353\) −0.587827 3.33374i −0.0312869 0.177437i 0.965160 0.261661i \(-0.0842701\pi\)
−0.996447 + 0.0842237i \(0.973159\pi\)
\(354\) 0 0
\(355\) 42.8857 15.6091i 2.27614 0.828446i
\(356\) 15.7827 + 13.2433i 0.836482 + 0.701891i
\(357\) 0 0
\(358\) −47.5129 17.2933i −2.51113 0.913978i
\(359\) −17.6137 30.5078i −0.929614 1.61014i −0.783968 0.620801i \(-0.786807\pi\)
−0.145646 0.989337i \(-0.546526\pi\)
\(360\) 0 0
\(361\) 7.30179 12.6471i 0.384305 0.665636i
\(362\) 29.1268 24.4403i 1.53087 1.28455i
\(363\) 0 0
\(364\) 6.23813 35.3782i 0.326967 1.85432i
\(365\) −1.00633 + 5.70716i −0.0526735 + 0.298726i
\(366\) 0 0
\(367\) −24.1652 + 20.2770i −1.26141 + 1.05845i −0.265883 + 0.964005i \(0.585664\pi\)
−0.995530 + 0.0944462i \(0.969892\pi\)
\(368\) −1.13463 + 1.96524i −0.0591469 + 0.102445i
\(369\) 0 0
\(370\) 38.9724 + 67.5021i 2.02608 + 3.50927i
\(371\) 16.0557 + 5.84380i 0.833571 + 0.303395i
\(372\) 0 0
\(373\) 11.0635 + 9.28334i 0.572844 + 0.480673i 0.882588 0.470147i \(-0.155799\pi\)
−0.309744 + 0.950820i \(0.600243\pi\)
\(374\) −20.4072 + 7.42760i −1.05523 + 0.384072i
\(375\) 0 0
\(376\) 4.92791 + 27.9476i 0.254138 + 1.44129i
\(377\) −8.46320 −0.435877
\(378\) 0 0
\(379\) 1.00099 0.0514176 0.0257088 0.999669i \(-0.491816\pi\)
0.0257088 + 0.999669i \(0.491816\pi\)
\(380\) 4.53176 + 25.7009i 0.232474 + 1.31843i
\(381\) 0 0
\(382\) −25.2917 + 9.20543i −1.29404 + 0.470991i
\(383\) 3.15407 + 2.64658i 0.161165 + 0.135234i 0.719804 0.694177i \(-0.244232\pi\)
−0.558639 + 0.829411i \(0.688676\pi\)
\(384\) 0 0
\(385\) 26.4290 + 9.61937i 1.34695 + 0.490249i
\(386\) 1.40690 + 2.43683i 0.0716094 + 0.124031i
\(387\) 0 0
\(388\) 21.4803 37.2049i 1.09050 1.88879i
\(389\) −11.8889 + 9.97601i −0.602793 + 0.505804i −0.892342 0.451359i \(-0.850939\pi\)
0.289549 + 0.957163i \(0.406495\pi\)
\(390\) 0 0
\(391\) 0.238771 1.35414i 0.0120752 0.0684817i
\(392\) −0.0596706 + 0.338409i −0.00301382 + 0.0170922i
\(393\) 0 0
\(394\) 9.49286 7.96545i 0.478243 0.401294i
\(395\) 26.4802 45.8651i 1.33237 2.30772i
\(396\) 0 0
\(397\) 0.774463 + 1.34141i 0.0388692 + 0.0673234i 0.884806 0.465960i \(-0.154291\pi\)
−0.845936 + 0.533284i \(0.820958\pi\)
\(398\) 31.7007 + 11.5381i 1.58901 + 0.578353i
\(399\) 0 0
\(400\) 14.5980 + 12.2491i 0.729898 + 0.612457i
\(401\) −7.46809 + 2.71816i −0.372939 + 0.135739i −0.521688 0.853136i \(-0.674697\pi\)
0.148749 + 0.988875i \(0.452475\pi\)
\(402\) 0 0
\(403\) −4.47971 25.4057i −0.223150 1.26555i
\(404\) 22.8628 1.13747
\(405\) 0 0
\(406\) 16.5380 0.820766
\(407\) 6.13999 + 34.8216i 0.304348 + 1.72604i
\(408\) 0 0
\(409\) −24.8599 + 9.04828i −1.22925 + 0.447409i −0.873339 0.487113i \(-0.838050\pi\)
−0.355906 + 0.934522i \(0.615828\pi\)
\(410\) −28.3303 23.7720i −1.39914 1.17401i
\(411\) 0 0
\(412\) −39.3774 14.3322i −1.93998 0.706097i
\(413\) 2.19998 + 3.81048i 0.108254 + 0.187501i
\(414\) 0 0
\(415\) 6.11245 10.5871i 0.300048 0.519699i
\(416\) 1.03615 0.869434i 0.0508015 0.0426275i
\(417\) 0 0
\(418\) −3.07332 + 17.4297i −0.150321 + 0.852512i
\(419\) 6.65767 37.7575i 0.325248 1.84458i −0.182675 0.983173i \(-0.558476\pi\)
0.507923 0.861402i \(-0.330413\pi\)
\(420\) 0 0
\(421\) 5.62621 4.72095i 0.274205 0.230085i −0.495307 0.868718i \(-0.664944\pi\)
0.769511 + 0.638633i \(0.220500\pi\)
\(422\) −7.17076 + 12.4201i −0.349067 + 0.604602i
\(423\) 0 0
\(424\) 16.1168 + 27.9152i 0.782702 + 1.35568i
\(425\) −10.8505 3.94926i −0.526326 0.191567i
\(426\) 0 0
\(427\) −29.2713 24.5615i −1.41654 1.18861i
\(428\) 54.0917 19.6878i 2.61462 0.951644i
\(429\) 0 0
\(430\) 3.60404 + 20.4395i 0.173802 + 0.985681i
\(431\) −15.8463 −0.763289 −0.381644 0.924309i \(-0.624642\pi\)
−0.381644 + 0.924309i \(0.624642\pi\)
\(432\) 0 0
\(433\) −23.8507 −1.14619 −0.573097 0.819488i \(-0.694258\pi\)
−0.573097 + 0.819488i \(0.694258\pi\)
\(434\) 8.75383 + 49.6454i 0.420197 + 2.38306i
\(435\) 0 0
\(436\) −21.8734 + 7.96126i −1.04755 + 0.381275i
\(437\) −0.858431 0.720309i −0.0410643 0.0344571i
\(438\) 0 0
\(439\) 20.1751 + 7.34315i 0.962907 + 0.350469i 0.775172 0.631750i \(-0.217663\pi\)
0.187735 + 0.982220i \(0.439885\pi\)
\(440\) 26.5296 + 45.9507i 1.26475 + 2.19061i
\(441\) 0 0
\(442\) −10.5727 + 18.3124i −0.502890 + 0.871031i
\(443\) 24.1671 20.2786i 1.14821 0.963466i 0.148538 0.988907i \(-0.452543\pi\)
0.999676 + 0.0254409i \(0.00809897\pi\)
\(444\) 0 0
\(445\) −2.72725 + 15.4670i −0.129284 + 0.733208i
\(446\) −3.72532 + 21.1273i −0.176399 + 1.00041i
\(447\) 0 0
\(448\) 15.2707 12.8136i 0.721472 0.605387i
\(449\) −10.3949 + 18.0045i −0.490565 + 0.849684i −0.999941 0.0108605i \(-0.996543\pi\)
0.509376 + 0.860544i \(0.329876\pi\)
\(450\) 0 0
\(451\) −8.38839 14.5291i −0.394994 0.684149i
\(452\) 43.3497 + 15.7780i 2.03900 + 0.742134i
\(453\) 0 0
\(454\) −45.7186 38.3624i −2.14568 1.80044i
\(455\) 25.7335 9.36621i 1.20640 0.439095i
\(456\) 0 0
\(457\) −3.02629 17.1630i −0.141564 0.802850i −0.970062 0.242858i \(-0.921915\pi\)
0.828498 0.559992i \(-0.189196\pi\)
\(458\) −44.6124 −2.08460
\(459\) 0 0
\(460\) −6.65196 −0.310149
\(461\) −5.38387 30.5334i −0.250752 1.42208i −0.806746 0.590898i \(-0.798774\pi\)
0.555994 0.831186i \(-0.312338\pi\)
\(462\) 0 0
\(463\) −6.09668 + 2.21901i −0.283337 + 0.103126i −0.479779 0.877389i \(-0.659283\pi\)
0.196443 + 0.980515i \(0.437061\pi\)
\(464\) 8.23211 + 6.90756i 0.382166 + 0.320676i
\(465\) 0 0
\(466\) 24.3382 + 8.85838i 1.12745 + 0.410357i
\(467\) −0.971950 1.68347i −0.0449765 0.0779016i 0.842661 0.538445i \(-0.180988\pi\)
−0.887637 + 0.460543i \(0.847655\pi\)
\(468\) 0 0
\(469\) −7.81513 + 13.5362i −0.360869 + 0.625044i
\(470\) −32.8132 + 27.5336i −1.51356 + 1.27003i
\(471\) 0 0
\(472\) −1.44140 + 8.17460i −0.0663459 + 0.376266i
\(473\) −1.63493 + 9.27217i −0.0751744 + 0.426335i
\(474\) 0 0
\(475\) −7.20872 + 6.04883i −0.330759 + 0.277540i
\(476\) 13.8198 23.9367i 0.633431 1.09713i
\(477\) 0 0
\(478\) −11.7195 20.2987i −0.536036 0.928442i
\(479\) −1.24922 0.454678i −0.0570783 0.0207748i 0.313323 0.949647i \(-0.398558\pi\)
−0.370402 + 0.928872i \(0.620780\pi\)
\(480\) 0 0
\(481\) 26.3736 + 22.1300i 1.20253 + 1.00904i
\(482\) −16.2531 + 5.91563i −0.740307 + 0.269450i
\(483\) 0 0
\(484\) 0.557611 + 3.16237i 0.0253459 + 0.143744i
\(485\) 32.7490 1.48705
\(486\) 0 0
\(487\) 21.2040 0.960844 0.480422 0.877037i \(-0.340484\pi\)
0.480422 + 0.877037i \(0.340484\pi\)
\(488\) −12.5177 70.9913i −0.566649 3.21362i
\(489\) 0 0
\(490\) −0.487392 + 0.177396i −0.0220181 + 0.00801394i
\(491\) 20.6910 + 17.3618i 0.933770 + 0.783526i 0.976490 0.215561i \(-0.0691579\pi\)
−0.0427200 + 0.999087i \(0.513602\pi\)
\(492\) 0 0
\(493\) −6.11884 2.22707i −0.275578 0.100302i
\(494\) 8.61638 + 14.9240i 0.387669 + 0.671463i
\(495\) 0 0
\(496\) −16.3784 + 28.3683i −0.735414 + 1.27377i
\(497\) −30.1757 + 25.3204i −1.35356 + 1.13577i
\(498\) 0 0
\(499\) 2.61148 14.8104i 0.116906 0.663006i −0.868883 0.495018i \(-0.835162\pi\)
0.985789 0.167989i \(-0.0537273\pi\)
\(500\) 1.10655 6.27556i 0.0494864 0.280651i
\(501\) 0 0
\(502\) 29.3468 24.6249i 1.30981 1.09906i
\(503\) −2.30325 + 3.98934i −0.102697 + 0.177876i −0.912795 0.408418i \(-0.866080\pi\)
0.810098 + 0.586294i \(0.199414\pi\)
\(504\) 0 0
\(505\) 8.71420 + 15.0934i 0.387777 + 0.671649i
\(506\) −4.23912 1.54291i −0.188452 0.0685909i
\(507\) 0 0
\(508\) 8.01763 + 6.72759i 0.355725 + 0.298489i
\(509\) −27.9997 + 10.1911i −1.24106 + 0.451711i −0.877373 0.479809i \(-0.840706\pi\)
−0.363692 + 0.931519i \(0.618484\pi\)
\(510\) 0 0
\(511\) −0.868590 4.92602i −0.0384242 0.217914i
\(512\) 40.8760 1.80648
\(513\) 0 0
\(514\) 29.9599 1.32147
\(515\) −5.54702 31.4587i −0.244431 1.38624i
\(516\) 0 0
\(517\) −18.2596 + 6.64596i −0.803057 + 0.292289i
\(518\) −51.5367 43.2445i −2.26439 1.90005i
\(519\) 0 0
\(520\) 48.5472 + 17.6697i 2.12894 + 0.774869i
\(521\) 5.88104 + 10.1863i 0.257653 + 0.446268i 0.965613 0.259985i \(-0.0837175\pi\)
−0.707960 + 0.706253i \(0.750384\pi\)
\(522\) 0 0
\(523\) −14.6926 + 25.4484i −0.642464 + 1.11278i 0.342417 + 0.939548i \(0.388754\pi\)
−0.984881 + 0.173232i \(0.944579\pi\)
\(524\) −13.6537 + 11.4568i −0.596463 + 0.500492i
\(525\) 0 0
\(526\) −2.94043 + 16.6760i −0.128209 + 0.727109i
\(527\) 3.44666 19.5470i 0.150139 0.851480i
\(528\) 0 0
\(529\) −17.4002 + 14.6005i −0.756531 + 0.634805i
\(530\) −24.3266 + 42.1350i −1.05668 + 1.83023i
\(531\) 0 0
\(532\) −11.2627 19.5076i −0.488301 0.845761i
\(533\) −15.3501 5.58698i −0.664887 0.241999i
\(534\) 0 0
\(535\) 33.6145 + 28.2059i 1.45328 + 1.21945i
\(536\) −27.7088 + 10.0852i −1.19684 + 0.435614i
\(537\) 0 0
\(538\) 3.01261 + 17.0854i 0.129883 + 0.736602i
\(539\) −0.235290 −0.0101347
\(540\) 0 0
\(541\) −22.9116 −0.985046 −0.492523 0.870300i \(-0.663925\pi\)
−0.492523 + 0.870300i \(0.663925\pi\)
\(542\) −10.1395 57.5037i −0.435527 2.47000i
\(543\) 0 0
\(544\) 0.977920 0.355934i 0.0419280 0.0152605i
\(545\) −13.5929 11.4058i −0.582256 0.488571i
\(546\) 0 0
\(547\) 12.9280 + 4.70541i 0.552762 + 0.201189i 0.603273 0.797535i \(-0.293863\pi\)
−0.0505115 + 0.998723i \(0.516085\pi\)
\(548\) −36.7053 63.5755i −1.56797 2.71581i
\(549\) 0 0
\(550\) −18.9414 + 32.8075i −0.807665 + 1.39892i
\(551\) −4.06516 + 3.41107i −0.173181 + 0.145317i
\(552\) 0 0
\(553\) −7.93776 + 45.0173i −0.337548 + 1.91433i
\(554\) 0.0445841 0.252849i 0.00189420 0.0107425i
\(555\) 0 0
\(556\) 6.06058 5.08543i 0.257026 0.215670i
\(557\) −10.9520 + 18.9695i −0.464053 + 0.803763i −0.999158 0.0410224i \(-0.986938\pi\)
0.535106 + 0.844785i \(0.320272\pi\)
\(558\) 0 0
\(559\) 4.58371 + 7.93922i 0.193870 + 0.335793i
\(560\) −32.6754 11.8929i −1.38079 0.502566i
\(561\) 0 0
\(562\) 15.3488 + 12.8791i 0.647448 + 0.543274i
\(563\) −13.6898 + 4.98270i −0.576958 + 0.209996i −0.613984 0.789319i \(-0.710434\pi\)
0.0370255 + 0.999314i \(0.488212\pi\)
\(564\) 0 0
\(565\) 6.10658 + 34.6322i 0.256906 + 1.45699i
\(566\) −58.0431 −2.43973
\(567\) 0 0
\(568\) −74.3137 −3.11813
\(569\) −3.88226 22.0174i −0.162753 0.923016i −0.951351 0.308108i \(-0.900304\pi\)
0.788599 0.614908i \(-0.210807\pi\)
\(570\) 0 0
\(571\) 14.4958 5.27605i 0.606632 0.220796i −0.0203971 0.999792i \(-0.506493\pi\)
0.627029 + 0.778996i \(0.284271\pi\)
\(572\) 35.5482 + 29.8285i 1.48635 + 1.24719i
\(573\) 0 0
\(574\) 29.9957 + 10.9176i 1.25200 + 0.455690i
\(575\) −1.19930 2.07724i −0.0500142 0.0866271i
\(576\) 0 0
\(577\) −16.4040 + 28.4126i −0.682909 + 1.18283i 0.291180 + 0.956668i \(0.405952\pi\)
−0.974089 + 0.226165i \(0.927381\pi\)
\(578\) 19.5444 16.3997i 0.812938 0.682136i
\(579\) 0 0
\(580\) −5.47005 + 31.0222i −0.227132 + 1.28813i
\(581\) −1.83228 + 10.3914i −0.0760158 + 0.431107i
\(582\) 0 0
\(583\) −16.9074 + 14.1870i −0.700233 + 0.587565i
\(584\) 4.71825 8.17225i 0.195242 0.338170i
\(585\) 0 0
\(586\) −26.5758 46.0306i −1.09784 1.90151i
\(587\) −28.4109 10.3407i −1.17264 0.426807i −0.319046 0.947739i \(-0.603362\pi\)
−0.853598 + 0.520932i \(0.825585\pi\)
\(588\) 0 0
\(589\) −12.3915 10.3977i −0.510581 0.428428i
\(590\) −11.7734 + 4.28518i −0.484705 + 0.176418i
\(591\) 0 0
\(592\) −7.59116 43.0516i −0.311995 1.76941i
\(593\) 41.1023 1.68787 0.843935 0.536446i \(-0.180234\pi\)
0.843935 + 0.536446i \(0.180234\pi\)
\(594\) 0 0
\(595\) 21.0698 0.863778
\(596\) 5.13281 + 29.1096i 0.210248 + 1.19238i
\(597\) 0 0
\(598\) −4.12756 + 1.50231i −0.168788 + 0.0614340i
\(599\) 27.9993 + 23.4942i 1.14402 + 0.959948i 0.999563 0.0295630i \(-0.00941155\pi\)
0.144458 + 0.989511i \(0.453856\pi\)
\(600\) 0 0
\(601\) −3.70784 1.34954i −0.151246 0.0550491i 0.265288 0.964169i \(-0.414533\pi\)
−0.416534 + 0.909120i \(0.636755\pi\)
\(602\) −8.95706 15.5141i −0.365062 0.632307i
\(603\) 0 0
\(604\) −9.80076 + 16.9754i −0.398787 + 0.690720i
\(605\) −1.87518 + 1.57346i −0.0762369 + 0.0639703i
\(606\) 0 0
\(607\) 1.73848 9.85942i 0.0705628 0.400182i −0.928985 0.370117i \(-0.879318\pi\)
0.999548 0.0300646i \(-0.00957131\pi\)
\(608\) 0.147275 0.835236i 0.00597277 0.0338733i
\(609\) 0 0
\(610\) 83.3508 69.9397i 3.37478 2.83177i
\(611\) −9.46005 + 16.3853i −0.382712 + 0.662877i
\(612\) 0 0
\(613\) 9.37838 + 16.2438i 0.378789 + 0.656082i 0.990886 0.134700i \(-0.0430072\pi\)
−0.612097 + 0.790783i \(0.709674\pi\)
\(614\) 37.7844 + 13.7524i 1.52485 + 0.555001i
\(615\) 0 0
\(616\) −35.0826 29.4378i −1.41352 1.18608i
\(617\) 21.6224 7.86991i 0.870485 0.316830i 0.132121 0.991234i \(-0.457821\pi\)
0.738363 + 0.674403i \(0.235599\pi\)
\(618\) 0 0
\(619\) 1.28743 + 7.30138i 0.0517462 + 0.293467i 0.999688 0.0249762i \(-0.00795098\pi\)
−0.947942 + 0.318444i \(0.896840\pi\)
\(620\) −96.0211 −3.85630
\(621\) 0 0
\(622\) 19.0598 0.764229
\(623\) −2.35398 13.3501i −0.0943100 0.534859i
\(624\) 0 0
\(625\) 25.6515 9.33639i 1.02606 0.373456i
\(626\) −29.0287 24.3580i −1.16022 0.973542i
\(627\) 0 0
\(628\) −5.60710 2.04082i −0.223748 0.0814376i
\(629\) 13.2444 + 22.9400i 0.528090 + 0.914679i
\(630\) 0 0
\(631\) 15.4962 26.8402i 0.616894 1.06849i −0.373155 0.927769i \(-0.621724\pi\)
0.990049 0.140723i \(-0.0449426\pi\)
\(632\) −66.0614 + 55.4321i −2.62778 + 2.20497i
\(633\) 0 0
\(634\) −3.68585 + 20.9035i −0.146384 + 0.830184i
\(635\) −1.38545 + 7.85727i −0.0549798 + 0.311806i
\(636\) 0 0
\(637\) −0.175499 + 0.147261i −0.00695352 + 0.00583470i
\(638\) −10.6815 + 18.5009i −0.422884 + 0.732457i
\(639\) 0 0
\(640\) 29.6279 + 51.3171i 1.17115 + 2.02849i
\(641\) 33.2145 + 12.0891i 1.31189 + 0.477490i 0.900852 0.434126i \(-0.142943\pi\)
0.411042 + 0.911617i \(0.365165\pi\)
\(642\) 0 0
\(643\) −15.0918 12.6635i −0.595162 0.499400i 0.294724 0.955582i \(-0.404772\pi\)
−0.889887 + 0.456182i \(0.849217\pi\)
\(644\) 5.39525 1.96371i 0.212603 0.0773811i
\(645\) 0 0
\(646\) 2.30236 + 13.0573i 0.0905852 + 0.513734i
\(647\) 46.8317 1.84114 0.920572 0.390572i \(-0.127723\pi\)
0.920572 + 0.390572i \(0.127723\pi\)
\(648\) 0 0
\(649\) −5.68366 −0.223103
\(650\) 6.40516 + 36.3255i 0.251231 + 1.42480i
\(651\) 0 0
\(652\) 65.5127 23.8447i 2.56567 0.933829i
\(653\) 13.2730 + 11.1374i 0.519414 + 0.435840i 0.864427 0.502758i \(-0.167681\pi\)
−0.345013 + 0.938598i \(0.612126\pi\)
\(654\) 0 0
\(655\) −12.7676 4.64703i −0.498871 0.181574i
\(656\) 10.3709 + 17.9630i 0.404918 + 0.701338i
\(657\) 0 0
\(658\) 18.4859 32.0186i 0.720657 1.24821i
\(659\) 33.5023 28.1118i 1.30507 1.09508i 0.315820 0.948819i \(-0.397721\pi\)
0.989246 0.146261i \(-0.0467239\pi\)
\(660\) 0 0
\(661\) −1.57792 + 8.94881i −0.0613738 + 0.348068i 0.938621 + 0.344949i \(0.112104\pi\)
−0.999995 + 0.00311890i \(0.999007\pi\)
\(662\) −8.76821 + 49.7270i −0.340786 + 1.93269i
\(663\) 0 0
\(664\) −15.2490 + 12.7954i −0.591776 + 0.496559i
\(665\) 8.58561 14.8707i 0.332936 0.576661i
\(666\) 0 0
\(667\) −0.676311 1.17140i −0.0261868 0.0453570i
\(668\) −25.9732 9.45346i −1.00493 0.365765i
\(669\) 0 0
\(670\) −34.0948 28.6090i −1.31720 1.10526i
\(671\) 46.3823 16.8818i 1.79057 0.651714i
\(672\) 0 0
\(673\) 1.30179 + 7.38279i 0.0501801 + 0.284586i 0.999564 0.0295331i \(-0.00940205\pi\)
−0.949384 + 0.314119i \(0.898291\pi\)
\(674\) −39.2711 −1.51266
\(675\) 0 0
\(676\) −7.34587 −0.282534
\(677\) 2.66768 + 15.1292i 0.102527 + 0.581461i 0.992179 + 0.124822i \(0.0398359\pi\)
−0.889652 + 0.456639i \(0.849053\pi\)
\(678\) 0 0
\(679\) −26.5619 + 9.66776i −1.01935 + 0.371014i
\(680\) 30.4495 + 25.5502i 1.16769 + 0.979806i
\(681\) 0 0
\(682\) −61.1918 22.2720i −2.34315 0.852838i
\(683\) −3.31079 5.73445i −0.126684 0.219423i 0.795706 0.605683i \(-0.207100\pi\)
−0.922390 + 0.386260i \(0.873767\pi\)
\(684\) 0 0
\(685\) 27.9806 48.4639i 1.06908 1.85171i
\(686\) −34.6968 + 29.1141i −1.32473 + 1.11158i
\(687\) 0 0
\(688\) 2.02134 11.4636i 0.0770630 0.437046i
\(689\) −3.73173 + 21.1637i −0.142168 + 0.806273i
\(690\) 0 0
\(691\) −14.2920 + 11.9924i −0.543693 + 0.456212i −0.872798 0.488081i \(-0.837697\pi\)
0.329106 + 0.944293i \(0.393253\pi\)
\(692\) 48.4228 83.8708i 1.84076 3.18829i
\(693\) 0 0
\(694\) −12.0484 20.8685i −0.457352 0.792157i
\(695\) 5.66727 + 2.06272i 0.214972 + 0.0782433i
\(696\) 0 0
\(697\) −9.62782 8.07870i −0.364680 0.306003i
\(698\) −21.7907 + 7.93117i −0.824790 + 0.300199i
\(699\) 0 0
\(700\) −8.37238 47.4821i −0.316446 1.79465i
\(701\) 24.8903 0.940092 0.470046 0.882642i \(-0.344237\pi\)
0.470046 + 0.882642i \(0.344237\pi\)
\(702\) 0 0
\(703\) 21.5876 0.814190
\(704\) 4.47151 + 25.3592i 0.168526 + 0.955760i
\(705\) 0 0
\(706\) −7.81826 + 2.84561i −0.294244 + 0.107096i
\(707\) −11.5236 9.66944i −0.433389 0.363657i
\(708\) 0 0
\(709\) 24.6000 + 8.95366i 0.923871 + 0.336262i 0.759778 0.650183i \(-0.225308\pi\)
0.164094 + 0.986445i \(0.447530\pi\)
\(710\) −56.0843 97.1409i −2.10481 3.64563i
\(711\) 0 0
\(712\) 12.7870 22.1477i 0.479212 0.830020i
\(713\) 3.15846 2.65026i 0.118285 0.0992531i
\(714\) 0 0
\(715\) −6.14274 + 34.8372i −0.229725 + 1.30284i
\(716\) −14.4348 + 81.8638i −0.539454 + 3.05940i
\(717\) 0 0
\(718\) −66.3252 + 55.6534i −2.47523 + 2.07697i
\(719\) −10.5145 + 18.2117i −0.392125 + 0.679181i −0.992730 0.120365i \(-0.961593\pi\)
0.600604 + 0.799546i \(0.294927\pi\)
\(720\) 0 0
\(721\) 13.7859 + 23.8779i 0.513414 + 0.889259i
\(722\) −33.7280 12.2760i −1.25522 0.456864i
\(723\) 0 0
\(724\) −47.8859 40.1810i −1.77967 1.49332i
\(725\) −10.6737 + 3.88490i −0.396411 + 0.144282i
\(726\) 0 0
\(727\) 7.18828 + 40.7668i 0.266599 + 1.51196i 0.764444 + 0.644690i \(0.223014\pi\)
−0.497845 + 0.867266i \(0.665875\pi\)
\(728\) −44.5918 −1.65268
\(729\) 0 0
\(730\) 14.2434 0.527171
\(731\) 1.22480 + 6.94620i 0.0453009 + 0.256914i
\(732\) 0 0
\(733\) −31.5988 + 11.5010i −1.16713 + 0.424800i −0.851638 0.524130i \(-0.824391\pi\)
−0.315489 + 0.948929i \(0.602169\pi\)
\(734\) 59.3930 + 49.8366i 2.19223 + 1.83950i
\(735\) 0 0
\(736\) 0.203140 + 0.0739371i 0.00748786 + 0.00272536i
\(737\) −10.0952 17.4854i −0.371862 0.644084i
\(738\) 0 0
\(739\) 6.47268 11.2110i 0.238101 0.412403i −0.722068 0.691822i \(-0.756808\pi\)
0.960169 + 0.279418i \(0.0901417\pi\)
\(740\) 98.1648 82.3700i 3.60861 3.02798i
\(741\) 0 0
\(742\) 7.29220 41.3561i 0.267705 1.51823i
\(743\) −0.0152687 + 0.0865933i −0.000560156 + 0.00317680i −0.985087 0.172060i \(-0.944958\pi\)
0.984526 + 0.175236i \(0.0560690\pi\)
\(744\) 0 0
\(745\) −17.2611 + 14.4837i −0.632396 + 0.530643i
\(746\) 17.7481 30.7406i 0.649803 1.12549i
\(747\) 0 0
\(748\) 17.8518 + 30.9202i 0.652727 + 1.13056i
\(749\) −35.5906 12.9539i −1.30045 0.473325i
\(750\) 0 0
\(751\) 38.2226 + 32.0725i 1.39476 + 1.17034i 0.963369 + 0.268179i \(0.0864220\pi\)
0.431392 + 0.902164i \(0.358022\pi\)
\(752\) 22.5752 8.21670i 0.823233 0.299632i
\(753\) 0 0
\(754\) 3.61201 + 20.4847i 0.131542 + 0.746011i
\(755\) −14.9423 −0.543806
\(756\) 0 0
\(757\) −11.8679 −0.431348 −0.215674 0.976465i \(-0.569195\pi\)
−0.215674 + 0.976465i \(0.569195\pi\)
\(758\) −0.427214 2.42285i −0.0155171 0.0880020i
\(759\) 0 0
\(760\) 30.4406 11.0795i 1.10420 0.401894i
\(761\) 2.90354 + 2.43636i 0.105253 + 0.0883180i 0.693896 0.720076i \(-0.255893\pi\)
−0.588642 + 0.808394i \(0.700337\pi\)
\(762\) 0 0
\(763\) 14.3920 + 5.23825i 0.521024 + 0.189637i
\(764\) 22.1247 + 38.3211i 0.800444 + 1.38641i
\(765\) 0 0
\(766\) 5.05978 8.76379i 0.182817 0.316649i
\(767\) −4.23935 + 3.55724i −0.153074 + 0.128444i
\(768\) 0 0
\(769\) 1.08869 6.17425i 0.0392591 0.222649i −0.958866 0.283860i \(-0.908385\pi\)
0.998125 + 0.0612105i \(0.0194961\pi\)
\(770\) 12.0036 68.0756i 0.432578 2.45327i
\(771\) 0 0
\(772\) 3.54375 2.97356i 0.127542 0.107021i
\(773\) 0.647678 1.12181i 0.0232954 0.0403487i −0.854143 0.520039i \(-0.825918\pi\)
0.877438 + 0.479690i \(0.159251\pi\)
\(774\) 0 0
\(775\) −17.3119 29.9850i −0.621861 1.07709i
\(776\) −50.1102 18.2386i −1.79885 0.654728i
\(777\) 0 0
\(778\) 29.2205 + 24.5189i 1.04761 + 0.879046i
\(779\)