Properties

Label 162.2.e.b.145.2
Level $162$
Weight $2$
Character 162.145
Analytic conductor $1.294$
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] = [162,2,Mod(19,162)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(162, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([16]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("162.19");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 162 = 2 \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 162.e (of order \(9\), degree \(6\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.29357651274\)
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: \( x^{12} - 6 x^{11} + 33 x^{10} - 110 x^{9} + 318 x^{8} - 678 x^{7} + 1225 x^{6} - 1698 x^{5} + 1905 x^{4} - 1584 x^{3} + 936 x^{2} - 342 x + 57 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3^{3} \)
Twist minimal: no (minimal twist has level 54)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 145.2
Root \(0.500000 - 1.96356i\) of defining polynomial
Character \(\chi\) \(=\) 162.145
Dual form 162.2.e.b.19.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.939693 + 0.342020i) q^{2} +(0.766044 + 0.642788i) q^{4} +(0.177398 - 1.00607i) q^{5} +(2.04289 - 1.71418i) q^{7} +(0.500000 + 0.866025i) q^{8} +O(q^{10})\) \(q+(0.939693 + 0.342020i) q^{2} +(0.766044 + 0.642788i) q^{4} +(0.177398 - 1.00607i) q^{5} +(2.04289 - 1.71418i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.510796 - 0.884725i) q^{10} +(0.720058 + 4.08365i) q^{11} +(-3.68356 + 1.34071i) q^{13} +(2.50597 - 0.912098i) q^{14} +(0.173648 + 0.984808i) q^{16} +(-0.925795 + 1.60352i) q^{17} +(-3.21653 - 5.57120i) q^{19} +(0.782585 - 0.656667i) q^{20} +(-0.720058 + 4.08365i) q^{22} +(-6.69746 - 5.61984i) q^{23} +(3.71775 + 1.35315i) q^{25} -3.91997 q^{26} +2.66680 q^{28} +(1.17759 + 0.428609i) q^{29} +(-2.56758 - 2.15445i) q^{31} +(-0.173648 + 0.984808i) q^{32} +(-1.41840 + 1.19018i) q^{34} +(-1.36219 - 2.35938i) q^{35} +(-4.58887 + 7.94816i) q^{37} +(-1.11709 - 6.33533i) q^{38} +(0.959983 - 0.349405i) q^{40} +(3.53914 - 1.28814i) q^{41} +(0.536567 + 3.04303i) q^{43} +(-2.07332 + 3.59110i) q^{44} +(-4.37146 - 7.57159i) q^{46} +(2.11809 - 1.77729i) q^{47} +(0.0194152 - 0.110109i) q^{49} +(3.03074 + 2.54309i) q^{50} +(-3.68356 - 1.34071i) q^{52} +0.231576 q^{53} +4.23618 q^{55} +(2.50597 + 0.912098i) q^{56} +(0.959983 + 0.805521i) q^{58} +(-0.613793 + 3.48099i) q^{59} +(0.405075 - 0.339899i) q^{61} +(-1.67587 - 2.90269i) q^{62} +(-0.500000 + 0.866025i) q^{64} +(0.695393 + 3.94377i) q^{65} +(7.67276 - 2.79266i) q^{67} +(-1.73993 + 0.633281i) q^{68} +(-0.473084 - 2.68299i) q^{70} +(4.03086 - 6.98165i) q^{71} +(1.57397 + 2.72620i) q^{73} +(-7.03056 + 5.89934i) q^{74} +(1.11709 - 6.33533i) q^{76} +(8.47113 + 7.10812i) q^{77} +(2.43473 + 0.886167i) q^{79} +1.02159 q^{80} +3.76627 q^{82} +(-7.55488 - 2.74975i) q^{83} +(1.44903 + 1.21588i) q^{85} +(-0.536567 + 3.04303i) q^{86} +(-3.17652 + 2.66541i) q^{88} +(6.12693 + 10.6122i) q^{89} +(-5.22688 + 9.05322i) q^{91} +(-1.51819 - 8.61009i) q^{92} +(2.59823 - 0.945677i) q^{94} +(-6.17564 + 2.24775i) q^{95} +(-1.51264 - 8.57862i) q^{97} +(0.0559038 - 0.0968282i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 3 q^{5} - 3 q^{7} + 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 3 q^{5} - 3 q^{7} + 6 q^{8} - 3 q^{10} + 12 q^{11} + 12 q^{13} + 3 q^{14} + 6 q^{17} - 9 q^{19} - 6 q^{20} - 12 q^{22} - 30 q^{23} - 9 q^{25} - 18 q^{26} + 12 q^{28} - 15 q^{29} - 15 q^{34} - 3 q^{35} - 15 q^{37} - 3 q^{38} - 3 q^{40} + 12 q^{41} + 9 q^{43} + 3 q^{44} + 3 q^{46} + 9 q^{47} - 39 q^{49} + 27 q^{50} + 12 q^{52} + 12 q^{53} + 18 q^{55} + 3 q^{56} - 3 q^{58} - 12 q^{59} - 36 q^{61} + 12 q^{62} - 6 q^{64} + 15 q^{65} + 36 q^{67} - 3 q^{68} + 39 q^{70} - 12 q^{71} - 21 q^{73} - 33 q^{74} + 3 q^{76} - 3 q^{77} + 39 q^{79} - 6 q^{80} + 6 q^{82} - 18 q^{83} + 45 q^{85} - 9 q^{86} + 6 q^{88} - 12 q^{89} - 6 q^{91} + 6 q^{92} + 36 q^{94} + 15 q^{95} + 39 q^{97} + 12 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/162\mathbb{Z}\right)^\times\).

\(n\) \(83\)
\(\chi(n)\) \(e\left(\frac{1}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.939693 + 0.342020i 0.664463 + 0.241845i
\(3\) 0 0
\(4\) 0.766044 + 0.642788i 0.383022 + 0.321394i
\(5\) 0.177398 1.00607i 0.0793347 0.449929i −0.919101 0.394021i \(-0.871084\pi\)
0.998436 0.0559078i \(-0.0178053\pi\)
\(6\) 0 0
\(7\) 2.04289 1.71418i 0.772138 0.647901i −0.169118 0.985596i \(-0.554092\pi\)
0.941256 + 0.337695i \(0.109647\pi\)
\(8\) 0.500000 + 0.866025i 0.176777 + 0.306186i
\(9\) 0 0
\(10\) 0.510796 0.884725i 0.161528 0.279775i
\(11\) 0.720058 + 4.08365i 0.217106 + 1.23127i 0.877215 + 0.480098i \(0.159399\pi\)
−0.660109 + 0.751169i \(0.729490\pi\)
\(12\) 0 0
\(13\) −3.68356 + 1.34071i −1.02164 + 0.371845i −0.797891 0.602802i \(-0.794051\pi\)
−0.223746 + 0.974647i \(0.571829\pi\)
\(14\) 2.50597 0.912098i 0.669749 0.243769i
\(15\) 0 0
\(16\) 0.173648 + 0.984808i 0.0434120 + 0.246202i
\(17\) −0.925795 + 1.60352i −0.224538 + 0.388912i −0.956181 0.292777i \(-0.905421\pi\)
0.731643 + 0.681688i \(0.238754\pi\)
\(18\) 0 0
\(19\) −3.21653 5.57120i −0.737923 1.27812i −0.953429 0.301618i \(-0.902473\pi\)
0.215505 0.976503i \(-0.430860\pi\)
\(20\) 0.782585 0.656667i 0.174991 0.146835i
\(21\) 0 0
\(22\) −0.720058 + 4.08365i −0.153517 + 0.870637i
\(23\) −6.69746 5.61984i −1.39652 1.17182i −0.962620 0.270854i \(-0.912694\pi\)
−0.433897 0.900963i \(-0.642862\pi\)
\(24\) 0 0
\(25\) 3.71775 + 1.35315i 0.743550 + 0.270630i
\(26\) −3.91997 −0.768769
\(27\) 0 0
\(28\) 2.66680 0.503977
\(29\) 1.17759 + 0.428609i 0.218674 + 0.0795907i 0.449034 0.893515i \(-0.351768\pi\)
−0.230360 + 0.973105i \(0.573990\pi\)
\(30\) 0 0
\(31\) −2.56758 2.15445i −0.461151 0.386952i 0.382403 0.923995i \(-0.375096\pi\)
−0.843554 + 0.537044i \(0.819541\pi\)
\(32\) −0.173648 + 0.984808i −0.0306970 + 0.174091i
\(33\) 0 0
\(34\) −1.41840 + 1.19018i −0.243254 + 0.204114i
\(35\) −1.36219 2.35938i −0.230252 0.398808i
\(36\) 0 0
\(37\) −4.58887 + 7.94816i −0.754406 + 1.30667i 0.191263 + 0.981539i \(0.438742\pi\)
−0.945669 + 0.325131i \(0.894592\pi\)
\(38\) −1.11709 6.33533i −0.181216 1.02773i
\(39\) 0 0
\(40\) 0.959983 0.349405i 0.151787 0.0552458i
\(41\) 3.53914 1.28814i 0.552720 0.201174i −0.0505345 0.998722i \(-0.516092\pi\)
0.603255 + 0.797549i \(0.293870\pi\)
\(42\) 0 0
\(43\) 0.536567 + 3.04303i 0.0818258 + 0.464057i 0.997997 + 0.0632688i \(0.0201526\pi\)
−0.916171 + 0.400788i \(0.868736\pi\)
\(44\) −2.07332 + 3.59110i −0.312565 + 0.541379i
\(45\) 0 0
\(46\) −4.37146 7.57159i −0.644536 1.11637i
\(47\) 2.11809 1.77729i 0.308956 0.259244i −0.475105 0.879929i \(-0.657590\pi\)
0.784060 + 0.620685i \(0.213145\pi\)
\(48\) 0 0
\(49\) 0.0194152 0.110109i 0.00277360 0.0157298i
\(50\) 3.03074 + 2.54309i 0.428611 + 0.359647i
\(51\) 0 0
\(52\) −3.68356 1.34071i −0.510818 0.185923i
\(53\) 0.231576 0.0318094 0.0159047 0.999874i \(-0.494937\pi\)
0.0159047 + 0.999874i \(0.494937\pi\)
\(54\) 0 0
\(55\) 4.23618 0.571207
\(56\) 2.50597 + 0.912098i 0.334874 + 0.121884i
\(57\) 0 0
\(58\) 0.959983 + 0.805521i 0.126052 + 0.105770i
\(59\) −0.613793 + 3.48099i −0.0799090 + 0.453187i 0.918430 + 0.395582i \(0.129457\pi\)
−0.998339 + 0.0576042i \(0.981654\pi\)
\(60\) 0 0
\(61\) 0.405075 0.339899i 0.0518646 0.0435196i −0.616487 0.787365i \(-0.711445\pi\)
0.668351 + 0.743846i \(0.267000\pi\)
\(62\) −1.67587 2.90269i −0.212835 0.368642i
\(63\) 0 0
\(64\) −0.500000 + 0.866025i −0.0625000 + 0.108253i
\(65\) 0.695393 + 3.94377i 0.0862529 + 0.489164i
\(66\) 0 0
\(67\) 7.67276 2.79266i 0.937377 0.341177i 0.172247 0.985054i \(-0.444897\pi\)
0.765130 + 0.643876i \(0.222675\pi\)
\(68\) −1.73993 + 0.633281i −0.210997 + 0.0767966i
\(69\) 0 0
\(70\) −0.473084 2.68299i −0.0565443 0.320679i
\(71\) 4.03086 6.98165i 0.478375 0.828570i −0.521318 0.853363i \(-0.674559\pi\)
0.999693 + 0.0247929i \(0.00789263\pi\)
\(72\) 0 0
\(73\) 1.57397 + 2.72620i 0.184219 + 0.319078i 0.943313 0.331904i \(-0.107691\pi\)
−0.759094 + 0.650981i \(0.774358\pi\)
\(74\) −7.03056 + 5.89934i −0.817286 + 0.685784i
\(75\) 0 0
\(76\) 1.11709 6.33533i 0.128139 0.726713i
\(77\) 8.47113 + 7.10812i 0.965374 + 0.810045i
\(78\) 0 0
\(79\) 2.43473 + 0.886167i 0.273928 + 0.0997016i 0.475332 0.879807i \(-0.342328\pi\)
−0.201404 + 0.979508i \(0.564550\pi\)
\(80\) 1.02159 0.114218
\(81\) 0 0
\(82\) 3.76627 0.415915
\(83\) −7.55488 2.74975i −0.829256 0.301824i −0.107702 0.994183i \(-0.534349\pi\)
−0.721553 + 0.692359i \(0.756572\pi\)
\(84\) 0 0
\(85\) 1.44903 + 1.21588i 0.157169 + 0.131880i
\(86\) −0.536567 + 3.04303i −0.0578596 + 0.328138i
\(87\) 0 0
\(88\) −3.17652 + 2.66541i −0.338618 + 0.284134i
\(89\) 6.12693 + 10.6122i 0.649453 + 1.12489i 0.983254 + 0.182242i \(0.0583355\pi\)
−0.333800 + 0.942644i \(0.608331\pi\)
\(90\) 0 0
\(91\) −5.22688 + 9.05322i −0.547926 + 0.949035i
\(92\) −1.51819 8.61009i −0.158282 0.897664i
\(93\) 0 0
\(94\) 2.59823 0.945677i 0.267986 0.0975391i
\(95\) −6.17564 + 2.24775i −0.633607 + 0.230614i
\(96\) 0 0
\(97\) −1.51264 8.57862i −0.153586 0.871027i −0.960068 0.279768i \(-0.909742\pi\)
0.806482 0.591259i \(-0.201369\pi\)
\(98\) 0.0559038 0.0968282i 0.00564713 0.00978112i
\(99\) 0 0
\(100\) 1.97817 + 3.42630i 0.197817 + 0.342630i
\(101\) 4.14121 3.47489i 0.412066 0.345764i −0.413069 0.910700i \(-0.635543\pi\)
0.825135 + 0.564935i \(0.191099\pi\)
\(102\) 0 0
\(103\) 1.87292 10.6218i 0.184544 1.04660i −0.741996 0.670405i \(-0.766120\pi\)
0.926540 0.376197i \(-0.122768\pi\)
\(104\) −3.00287 2.51971i −0.294455 0.247077i
\(105\) 0 0
\(106\) 0.217610 + 0.0792037i 0.0211362 + 0.00769295i
\(107\) 14.8511 1.43571 0.717856 0.696191i \(-0.245124\pi\)
0.717856 + 0.696191i \(0.245124\pi\)
\(108\) 0 0
\(109\) 17.6598 1.69150 0.845752 0.533576i \(-0.179152\pi\)
0.845752 + 0.533576i \(0.179152\pi\)
\(110\) 3.98071 + 1.44886i 0.379546 + 0.138143i
\(111\) 0 0
\(112\) 2.04289 + 1.71418i 0.193035 + 0.161975i
\(113\) −0.339716 + 1.92663i −0.0319578 + 0.181242i −0.996608 0.0822905i \(-0.973776\pi\)
0.964651 + 0.263532i \(0.0848876\pi\)
\(114\) 0 0
\(115\) −6.84208 + 5.74118i −0.638027 + 0.535368i
\(116\) 0.626584 + 1.08528i 0.0581769 + 0.100765i
\(117\) 0 0
\(118\) −1.76735 + 3.06113i −0.162697 + 0.281800i
\(119\) 0.857442 + 4.86280i 0.0786016 + 0.445772i
\(120\) 0 0
\(121\) −5.82110 + 2.11871i −0.529191 + 0.192610i
\(122\) 0.496899 0.180856i 0.0449871 0.0163740i
\(123\) 0 0
\(124\) −0.582023 3.30082i −0.0522672 0.296422i
\(125\) 4.57487 7.92391i 0.409189 0.708736i
\(126\) 0 0
\(127\) −2.78998 4.83239i −0.247571 0.428805i 0.715281 0.698837i \(-0.246299\pi\)
−0.962851 + 0.270032i \(0.912966\pi\)
\(128\) −0.766044 + 0.642788i −0.0677094 + 0.0568149i
\(129\) 0 0
\(130\) −0.695393 + 3.94377i −0.0609900 + 0.345891i
\(131\) −1.18532 0.994600i −0.103562 0.0868986i 0.589537 0.807742i \(-0.299310\pi\)
−0.693098 + 0.720843i \(0.743755\pi\)
\(132\) 0 0
\(133\) −16.1211 5.86759i −1.39787 0.508785i
\(134\) 8.16518 0.705364
\(135\) 0 0
\(136\) −1.85159 −0.158773
\(137\) −18.8496 6.86070i −1.61043 0.586149i −0.628906 0.777481i \(-0.716497\pi\)
−0.981525 + 0.191332i \(0.938719\pi\)
\(138\) 0 0
\(139\) 2.98779 + 2.50705i 0.253421 + 0.212645i 0.760644 0.649170i \(-0.224883\pi\)
−0.507223 + 0.861815i \(0.669328\pi\)
\(140\) 0.473084 2.68299i 0.0399829 0.226754i
\(141\) 0 0
\(142\) 6.17564 5.18197i 0.518248 0.434862i
\(143\) −8.12736 14.0770i −0.679644 1.17718i
\(144\) 0 0
\(145\) 0.640114 1.10871i 0.0531586 0.0920734i
\(146\) 0.546635 + 3.10012i 0.0452398 + 0.256568i
\(147\) 0 0
\(148\) −8.62426 + 3.13897i −0.708910 + 0.258022i
\(149\) −9.24128 + 3.36355i −0.757075 + 0.275553i −0.691580 0.722300i \(-0.743085\pi\)
−0.0654951 + 0.997853i \(0.520863\pi\)
\(150\) 0 0
\(151\) 0.697011 + 3.95294i 0.0567219 + 0.321686i 0.999945 0.0104735i \(-0.00333387\pi\)
−0.943223 + 0.332160i \(0.892223\pi\)
\(152\) 3.21653 5.57120i 0.260895 0.451884i
\(153\) 0 0
\(154\) 5.52913 + 9.57674i 0.445550 + 0.771716i
\(155\) −2.62302 + 2.20098i −0.210686 + 0.176787i
\(156\) 0 0
\(157\) −2.48817 + 14.1111i −0.198578 + 1.12619i 0.708653 + 0.705557i \(0.249303\pi\)
−0.907231 + 0.420634i \(0.861808\pi\)
\(158\) 1.98481 + 1.66545i 0.157903 + 0.132496i
\(159\) 0 0
\(160\) 0.959983 + 0.349405i 0.0758933 + 0.0276229i
\(161\) −23.3156 −1.83753
\(162\) 0 0
\(163\) −14.2911 −1.11937 −0.559683 0.828707i \(-0.689077\pi\)
−0.559683 + 0.828707i \(0.689077\pi\)
\(164\) 3.53914 + 1.28814i 0.276360 + 0.100587i
\(165\) 0 0
\(166\) −6.15879 5.16784i −0.478015 0.401102i
\(167\) 1.65921 9.40983i 0.128393 0.728154i −0.850841 0.525423i \(-0.823907\pi\)
0.979234 0.202731i \(-0.0649818\pi\)
\(168\) 0 0
\(169\) 1.81256 1.52092i 0.139428 0.116994i
\(170\) 0.945785 + 1.63815i 0.0725384 + 0.125640i
\(171\) 0 0
\(172\) −1.54498 + 2.67599i −0.117804 + 0.204042i
\(173\) −1.73345 9.83089i −0.131792 0.747429i −0.977040 0.213055i \(-0.931659\pi\)
0.845248 0.534374i \(-0.179453\pi\)
\(174\) 0 0
\(175\) 9.91449 3.60858i 0.749465 0.272783i
\(176\) −3.89657 + 1.41824i −0.293715 + 0.106904i
\(177\) 0 0
\(178\) 2.12786 + 12.0677i 0.159490 + 0.904512i
\(179\) −11.2541 + 19.4927i −0.841174 + 1.45696i 0.0477290 + 0.998860i \(0.484802\pi\)
−0.888903 + 0.458096i \(0.848532\pi\)
\(180\) 0 0
\(181\) −0.248078 0.429684i −0.0184395 0.0319382i 0.856658 0.515884i \(-0.172536\pi\)
−0.875098 + 0.483946i \(0.839203\pi\)
\(182\) −8.00804 + 6.71954i −0.593595 + 0.498086i
\(183\) 0 0
\(184\) 1.51819 8.61009i 0.111923 0.634744i
\(185\) 7.18237 + 6.02672i 0.528058 + 0.443093i
\(186\) 0 0
\(187\) −7.21486 2.62599i −0.527603 0.192032i
\(188\) 2.76497 0.201656
\(189\) 0 0
\(190\) −6.57197 −0.476781
\(191\) 6.75481 + 2.45855i 0.488761 + 0.177894i 0.574632 0.818412i \(-0.305145\pi\)
−0.0858713 + 0.996306i \(0.527367\pi\)
\(192\) 0 0
\(193\) −10.3185 8.65825i −0.742742 0.623234i 0.190831 0.981623i \(-0.438882\pi\)
−0.933572 + 0.358389i \(0.883326\pi\)
\(194\) 1.51264 8.57862i 0.108601 0.615909i
\(195\) 0 0
\(196\) 0.0856496 0.0718685i 0.00611783 0.00513346i
\(197\) 2.53340 + 4.38797i 0.180497 + 0.312630i 0.942050 0.335473i \(-0.108896\pi\)
−0.761553 + 0.648103i \(0.775563\pi\)
\(198\) 0 0
\(199\) 8.97242 15.5407i 0.636038 1.10165i −0.350256 0.936654i \(-0.613906\pi\)
0.986294 0.164996i \(-0.0527611\pi\)
\(200\) 0.687013 + 3.89624i 0.0485791 + 0.275506i
\(201\) 0 0
\(202\) 5.07995 1.84895i 0.357424 0.130092i
\(203\) 3.14040 1.14301i 0.220413 0.0802238i
\(204\) 0 0
\(205\) −0.668128 3.78914i −0.0466641 0.264645i
\(206\) 5.39285 9.34070i 0.375738 0.650797i
\(207\) 0 0
\(208\) −1.95998 3.39479i −0.135900 0.235386i
\(209\) 20.4347 17.1468i 1.41350 1.18607i
\(210\) 0 0
\(211\) −0.884489 + 5.01618i −0.0608907 + 0.345328i 0.939108 + 0.343623i \(0.111654\pi\)
−0.999999 + 0.00170581i \(0.999457\pi\)
\(212\) 0.177398 + 0.148854i 0.0121837 + 0.0102234i
\(213\) 0 0
\(214\) 13.9555 + 5.07938i 0.953978 + 0.347220i
\(215\) 3.15669 0.215284
\(216\) 0 0
\(217\) −8.93840 −0.606778
\(218\) 16.5948 + 6.04001i 1.12394 + 0.409081i
\(219\) 0 0
\(220\) 3.24511 + 2.72297i 0.218785 + 0.183582i
\(221\) 1.26037 7.14790i 0.0847815 0.480820i
\(222\) 0 0
\(223\) 2.92334 2.45297i 0.195761 0.164263i −0.539638 0.841897i \(-0.681439\pi\)
0.735399 + 0.677634i \(0.236995\pi\)
\(224\) 1.33340 + 2.30951i 0.0890914 + 0.154311i
\(225\) 0 0
\(226\) −0.978174 + 1.69425i −0.0650672 + 0.112700i
\(227\) 3.53875 + 20.0693i 0.234875 + 1.33204i 0.842876 + 0.538108i \(0.180861\pi\)
−0.608001 + 0.793936i \(0.708028\pi\)
\(228\) 0 0
\(229\) 1.41711 0.515787i 0.0936455 0.0340842i −0.294773 0.955567i \(-0.595244\pi\)
0.388418 + 0.921483i \(0.373022\pi\)
\(230\) −8.39305 + 3.05482i −0.553421 + 0.201429i
\(231\) 0 0
\(232\) 0.217610 + 1.23413i 0.0142868 + 0.0810246i
\(233\) −10.0838 + 17.4656i −0.660610 + 1.14421i 0.319845 + 0.947470i \(0.396369\pi\)
−0.980456 + 0.196741i \(0.936964\pi\)
\(234\) 0 0
\(235\) −1.41234 2.44624i −0.0921308 0.159575i
\(236\) −2.70773 + 2.27206i −0.176258 + 0.147898i
\(237\) 0 0
\(238\) −0.857442 + 4.86280i −0.0555797 + 0.315208i
\(239\) 9.68541 + 8.12702i 0.626497 + 0.525693i 0.899838 0.436224i \(-0.143684\pi\)
−0.273341 + 0.961917i \(0.588129\pi\)
\(240\) 0 0
\(241\) 26.1605 + 9.52166i 1.68515 + 0.613344i 0.994001 0.109369i \(-0.0348831\pi\)
0.691148 + 0.722713i \(0.257105\pi\)
\(242\) −6.19469 −0.398210
\(243\) 0 0
\(244\) 0.528788 0.0338522
\(245\) −0.107333 0.0390661i −0.00685728 0.00249584i
\(246\) 0 0
\(247\) 19.3177 + 16.2094i 1.22915 + 1.03138i
\(248\) 0.582023 3.30082i 0.0369585 0.209602i
\(249\) 0 0
\(250\) 7.00911 5.88134i 0.443295 0.371969i
\(251\) −0.336641 0.583079i −0.0212486 0.0368036i 0.855206 0.518289i \(-0.173431\pi\)
−0.876454 + 0.481485i \(0.840097\pi\)
\(252\) 0 0
\(253\) 18.1269 31.3967i 1.13963 1.97389i
\(254\) −0.968950 5.49519i −0.0607973 0.344799i
\(255\) 0 0
\(256\) −0.939693 + 0.342020i −0.0587308 + 0.0213763i
\(257\) 28.7904 10.4789i 1.79590 0.653653i 0.797141 0.603793i \(-0.206345\pi\)
0.998756 0.0498599i \(-0.0158775\pi\)
\(258\) 0 0
\(259\) 4.25007 + 24.1033i 0.264087 + 1.49771i
\(260\) −2.00230 + 3.46809i −0.124178 + 0.215082i
\(261\) 0 0
\(262\) −0.773661 1.34002i −0.0477969 0.0827867i
\(263\) 4.54929 3.81731i 0.280521 0.235385i −0.491661 0.870787i \(-0.663610\pi\)
0.772182 + 0.635402i \(0.219165\pi\)
\(264\) 0 0
\(265\) 0.0410811 0.232982i 0.00252359 0.0143120i
\(266\) −13.1420 11.0275i −0.805789 0.676137i
\(267\) 0 0
\(268\) 7.67276 + 2.79266i 0.468688 + 0.170589i
\(269\) −15.3624 −0.936661 −0.468330 0.883553i \(-0.655144\pi\)
−0.468330 + 0.883553i \(0.655144\pi\)
\(270\) 0 0
\(271\) −14.5939 −0.886516 −0.443258 0.896394i \(-0.646177\pi\)
−0.443258 + 0.896394i \(0.646177\pi\)
\(272\) −1.73993 0.633281i −0.105498 0.0383983i
\(273\) 0 0
\(274\) −15.3663 12.8939i −0.928315 0.778949i
\(275\) −2.84880 + 16.1563i −0.171789 + 0.974264i
\(276\) 0 0
\(277\) 4.35786 3.65668i 0.261838 0.219709i −0.502412 0.864629i \(-0.667554\pi\)
0.764250 + 0.644920i \(0.223109\pi\)
\(278\) 1.95014 + 3.37774i 0.116962 + 0.202584i
\(279\) 0 0
\(280\) 1.36219 2.35938i 0.0814064 0.141000i
\(281\) −2.37136 13.4487i −0.141464 0.802281i −0.970139 0.242551i \(-0.922016\pi\)
0.828675 0.559730i \(-0.189095\pi\)
\(282\) 0 0
\(283\) −24.3720 + 8.87068i −1.44876 + 0.527307i −0.942246 0.334922i \(-0.891290\pi\)
−0.506519 + 0.862229i \(0.669068\pi\)
\(284\) 7.57554 2.75727i 0.449525 0.163614i
\(285\) 0 0
\(286\) −2.82260 16.0078i −0.166904 0.946559i
\(287\) 5.02194 8.69825i 0.296436 0.513442i
\(288\) 0 0
\(289\) 6.78581 + 11.7534i 0.399165 + 0.691374i
\(290\) 0.980712 0.822915i 0.0575894 0.0483232i
\(291\) 0 0
\(292\) −0.546635 + 3.10012i −0.0319894 + 0.181421i
\(293\) −15.2378 12.7860i −0.890199 0.746966i 0.0780511 0.996949i \(-0.475130\pi\)
−0.968250 + 0.249984i \(0.919575\pi\)
\(294\) 0 0
\(295\) 3.39325 + 1.23504i 0.197562 + 0.0719068i
\(296\) −9.17774 −0.533446
\(297\) 0 0
\(298\) −9.83436 −0.569689
\(299\) 32.2051 + 11.7217i 1.86247 + 0.677883i
\(300\) 0 0
\(301\) 6.31245 + 5.29678i 0.363844 + 0.305301i
\(302\) −0.697011 + 3.95294i −0.0401085 + 0.227466i
\(303\) 0 0
\(304\) 4.92802 4.13510i 0.282641 0.237164i
\(305\) −0.270103 0.467832i −0.0154661 0.0267880i
\(306\) 0 0
\(307\) 4.75733 8.23993i 0.271515 0.470278i −0.697735 0.716356i \(-0.745809\pi\)
0.969250 + 0.246078i \(0.0791420\pi\)
\(308\) 1.92025 + 10.8903i 0.109416 + 0.620531i
\(309\) 0 0
\(310\) −3.21761 + 1.17111i −0.182748 + 0.0665148i
\(311\) −13.5916 + 4.94693i −0.770707 + 0.280514i −0.697292 0.716787i \(-0.745612\pi\)
−0.0734150 + 0.997301i \(0.523390\pi\)
\(312\) 0 0
\(313\) −2.32518 13.1867i −0.131427 0.745359i −0.977281 0.211946i \(-0.932020\pi\)
0.845855 0.533414i \(-0.179091\pi\)
\(314\) −7.16441 + 12.4091i −0.404311 + 0.700287i
\(315\) 0 0
\(316\) 1.29549 + 2.24385i 0.0728770 + 0.126227i
\(317\) −19.2768 + 16.1751i −1.08269 + 0.908487i −0.996142 0.0877609i \(-0.972029\pi\)
−0.0865506 + 0.996247i \(0.527584\pi\)
\(318\) 0 0
\(319\) −0.902354 + 5.11750i −0.0505221 + 0.286525i
\(320\) 0.782585 + 0.656667i 0.0437479 + 0.0367088i
\(321\) 0 0
\(322\) −21.9095 7.97440i −1.22097 0.444396i
\(323\) 11.9114 0.662768
\(324\) 0 0
\(325\) −15.5088 −0.860271
\(326\) −13.4292 4.88784i −0.743777 0.270713i
\(327\) 0 0
\(328\) 2.88513 + 2.42091i 0.159305 + 0.133672i
\(329\) 1.28042 7.26160i 0.0705916 0.400345i
\(330\) 0 0
\(331\) −16.1905 + 13.5855i −0.889912 + 0.746725i −0.968193 0.250206i \(-0.919502\pi\)
0.0782802 + 0.996931i \(0.475057\pi\)
\(332\) −4.01987 6.96261i −0.220619 0.382123i
\(333\) 0 0
\(334\) 4.77749 8.27486i 0.261413 0.452780i
\(335\) −1.44848 8.21476i −0.0791392 0.448820i
\(336\) 0 0
\(337\) −4.48414 + 1.63209i −0.244267 + 0.0889058i −0.461252 0.887269i \(-0.652600\pi\)
0.216986 + 0.976175i \(0.430378\pi\)
\(338\) 2.22344 0.809266i 0.120939 0.0440183i
\(339\) 0 0
\(340\) 0.328468 + 1.86283i 0.0178137 + 0.101026i
\(341\) 6.94924 12.0364i 0.376322 0.651809i
\(342\) 0 0
\(343\) 9.18471 + 15.9084i 0.495928 + 0.858972i
\(344\) −2.36705 + 1.98619i −0.127623 + 0.107088i
\(345\) 0 0
\(346\) 1.73345 9.83089i 0.0931909 0.528512i
\(347\) −12.0020 10.0708i −0.644299 0.540631i 0.261036 0.965329i \(-0.415936\pi\)
−0.905335 + 0.424698i \(0.860380\pi\)
\(348\) 0 0
\(349\) −18.6170 6.77604i −0.996547 0.362713i −0.208295 0.978066i \(-0.566791\pi\)
−0.788252 + 0.615353i \(0.789014\pi\)
\(350\) 10.5508 0.563963
\(351\) 0 0
\(352\) −4.14665 −0.221017
\(353\) −14.8445 5.40296i −0.790093 0.287570i −0.0847183 0.996405i \(-0.526999\pi\)
−0.705375 + 0.708835i \(0.749221\pi\)
\(354\) 0 0
\(355\) −6.30898 5.29387i −0.334846 0.280969i
\(356\) −2.12786 + 12.0677i −0.112776 + 0.639587i
\(357\) 0 0
\(358\) −17.2423 + 14.4680i −0.911286 + 0.764660i
\(359\) 2.43474 + 4.21710i 0.128501 + 0.222570i 0.923096 0.384570i \(-0.125650\pi\)
−0.794595 + 0.607140i \(0.792317\pi\)
\(360\) 0 0
\(361\) −11.1922 + 19.3854i −0.589062 + 1.02028i
\(362\) −0.0861567 0.488619i −0.00452830 0.0256812i
\(363\) 0 0
\(364\) −9.82332 + 3.57539i −0.514882 + 0.187402i
\(365\) 3.02197 1.09991i 0.158177 0.0575718i
\(366\) 0 0
\(367\) −1.47394 8.35914i −0.0769392 0.436344i −0.998807 0.0488385i \(-0.984448\pi\)
0.921868 0.387505i \(-0.126663\pi\)
\(368\) 4.37146 7.57159i 0.227878 0.394696i
\(369\) 0 0
\(370\) 4.68796 + 8.11978i 0.243715 + 0.422127i
\(371\) 0.473084 0.396964i 0.0245613 0.0206094i
\(372\) 0 0
\(373\) 0.783900 4.44572i 0.0405888 0.230190i −0.957765 0.287553i \(-0.907158\pi\)
0.998353 + 0.0573629i \(0.0182692\pi\)
\(374\) −5.88161 4.93525i −0.304131 0.255196i
\(375\) 0 0
\(376\) 2.59823 + 0.945677i 0.133993 + 0.0487695i
\(377\) −4.91238 −0.253000
\(378\) 0 0
\(379\) 11.1018 0.570262 0.285131 0.958489i \(-0.407963\pi\)
0.285131 + 0.958489i \(0.407963\pi\)
\(380\) −6.17564 2.24775i −0.316803 0.115307i
\(381\) 0 0
\(382\) 5.50657 + 4.62056i 0.281741 + 0.236408i
\(383\) 3.82767 21.7078i 0.195585 1.10922i −0.715999 0.698101i \(-0.754029\pi\)
0.911584 0.411114i \(-0.134860\pi\)
\(384\) 0 0
\(385\) 8.65404 7.26160i 0.441051 0.370085i
\(386\) −6.73492 11.6652i −0.342798 0.593744i
\(387\) 0 0
\(388\) 4.35548 7.54391i 0.221116 0.382984i
\(389\) 2.95836 + 16.7777i 0.149995 + 0.850663i 0.963220 + 0.268714i \(0.0865985\pi\)
−0.813225 + 0.581949i \(0.802290\pi\)
\(390\) 0 0
\(391\) 15.2120 5.53672i 0.769305 0.280004i
\(392\) 0.105065 0.0382404i 0.00530657 0.00193143i
\(393\) 0 0
\(394\) 0.879840 + 4.98982i 0.0443257 + 0.251383i
\(395\) 1.32346 2.29231i 0.0665907 0.115338i
\(396\) 0 0
\(397\) 7.80452 + 13.5178i 0.391698 + 0.678441i 0.992674 0.120827i \(-0.0385545\pi\)
−0.600976 + 0.799267i \(0.705221\pi\)
\(398\) 13.7465 11.5347i 0.689052 0.578183i
\(399\) 0 0
\(400\) −0.687013 + 3.89624i −0.0343506 + 0.194812i
\(401\) 2.82242 + 2.36829i 0.140945 + 0.118267i 0.710534 0.703663i \(-0.248453\pi\)
−0.569589 + 0.821929i \(0.692898\pi\)
\(402\) 0 0
\(403\) 12.3463 + 4.49370i 0.615015 + 0.223847i
\(404\) 5.40597 0.268957
\(405\) 0 0
\(406\) 3.34195 0.165858
\(407\) −35.7618 13.0162i −1.77264 0.645190i
\(408\) 0 0
\(409\) −10.3077 8.64918i −0.509682 0.427674i 0.351335 0.936250i \(-0.385728\pi\)
−0.861017 + 0.508576i \(0.830172\pi\)
\(410\) 0.668128 3.78914i 0.0329965 0.187132i
\(411\) 0 0
\(412\) 8.26233 6.93292i 0.407056 0.341560i
\(413\) 4.71316 + 8.16342i 0.231919 + 0.401696i
\(414\) 0 0
\(415\) −4.10667 + 7.11296i −0.201588 + 0.349161i
\(416\) −0.680695 3.86041i −0.0333738 0.189272i
\(417\) 0 0
\(418\) 25.0669 9.12361i 1.22606 0.446251i
\(419\) 1.29440 0.471124i 0.0632357 0.0230159i −0.310209 0.950668i \(-0.600399\pi\)
0.373444 + 0.927653i \(0.378177\pi\)
\(420\) 0 0
\(421\) −1.39368 7.90398i −0.0679240 0.385216i −0.999751 0.0223134i \(-0.992897\pi\)
0.931827 0.362903i \(-0.118214\pi\)
\(422\) −2.54678 + 4.41116i −0.123975 + 0.214732i
\(423\) 0 0
\(424\) 0.115788 + 0.200551i 0.00562317 + 0.00973961i
\(425\) −5.61168 + 4.70876i −0.272207 + 0.228409i
\(426\) 0 0
\(427\) 0.244874 1.38875i 0.0118503 0.0672062i
\(428\) 11.3766 + 9.54612i 0.549910 + 0.461429i
\(429\) 0 0
\(430\) 2.96632 + 1.07965i 0.143049 + 0.0520654i
\(431\) 34.6923 1.67107 0.835534 0.549438i \(-0.185158\pi\)
0.835534 + 0.549438i \(0.185158\pi\)
\(432\) 0 0
\(433\) 0.605990 0.0291220 0.0145610 0.999894i \(-0.495365\pi\)
0.0145610 + 0.999894i \(0.495365\pi\)
\(434\) −8.39935 3.05711i −0.403182 0.146746i
\(435\) 0 0
\(436\) 13.5282 + 11.3515i 0.647884 + 0.543639i
\(437\) −9.76663 + 55.3893i −0.467201 + 2.64963i
\(438\) 0 0
\(439\) −0.853735 + 0.716369i −0.0407466 + 0.0341904i −0.662934 0.748678i \(-0.730689\pi\)
0.622187 + 0.782869i \(0.286244\pi\)
\(440\) 2.11809 + 3.66864i 0.100976 + 0.174896i
\(441\) 0 0
\(442\) 3.62908 6.28576i 0.172618 0.298983i
\(443\) −1.06252 6.02583i −0.0504817 0.286296i 0.949108 0.314952i \(-0.101988\pi\)
−0.999589 + 0.0286559i \(0.990877\pi\)
\(444\) 0 0
\(445\) 11.7635 4.28156i 0.557643 0.202966i
\(446\) 3.58600 1.30520i 0.169802 0.0618029i
\(447\) 0 0
\(448\) 0.463084 + 2.62628i 0.0218787 + 0.124080i
\(449\) 18.1443 31.4269i 0.856283 1.48313i −0.0191664 0.999816i \(-0.506101\pi\)
0.875450 0.483310i \(-0.160565\pi\)
\(450\) 0 0
\(451\) 7.80870 + 13.5251i 0.367697 + 0.636870i
\(452\) −1.49865 + 1.25752i −0.0704906 + 0.0591486i
\(453\) 0 0
\(454\) −3.53875 + 20.0693i −0.166082 + 0.941897i
\(455\) 8.18096 + 6.86464i 0.383529 + 0.321819i
\(456\) 0 0
\(457\) −19.4942 7.09531i −0.911900 0.331905i −0.156889 0.987616i \(-0.550146\pi\)
−0.755011 + 0.655712i \(0.772369\pi\)
\(458\) 1.50806 0.0704670
\(459\) 0 0
\(460\) −8.93170 −0.416443
\(461\) 38.8668 + 14.1464i 1.81021 + 0.658861i 0.997045 + 0.0768243i \(0.0244780\pi\)
0.813162 + 0.582037i \(0.197744\pi\)
\(462\) 0 0
\(463\) −18.1032 15.1904i −0.841328 0.705958i 0.116534 0.993187i \(-0.462822\pi\)
−0.957862 + 0.287229i \(0.907266\pi\)
\(464\) −0.217610 + 1.23413i −0.0101023 + 0.0572931i
\(465\) 0 0
\(466\) −15.4492 + 12.9635i −0.715672 + 0.600520i
\(467\) −10.5877 18.3384i −0.489939 0.848599i 0.509994 0.860178i \(-0.329648\pi\)
−0.999933 + 0.0115789i \(0.996314\pi\)
\(468\) 0 0
\(469\) 10.8874 18.8576i 0.502735 0.870763i
\(470\) −0.490500 2.78176i −0.0226251 0.128313i
\(471\) 0 0
\(472\) −3.32153 + 1.20894i −0.152886 + 0.0556458i
\(473\) −12.0403 + 4.38231i −0.553613 + 0.201499i
\(474\) 0 0
\(475\) −4.41960 25.0648i −0.202785 1.15005i
\(476\) −2.46891 + 4.27627i −0.113162 + 0.196003i
\(477\) 0 0
\(478\) 6.32170 + 10.9495i 0.289148 + 0.500819i
\(479\) −10.2101 + 8.56728i −0.466511 + 0.391449i −0.845520 0.533944i \(-0.820709\pi\)
0.379009 + 0.925393i \(0.376265\pi\)
\(480\) 0 0
\(481\) 6.24724 35.4299i 0.284850 1.61546i
\(482\) 21.3263 + 17.8949i 0.971385 + 0.815089i
\(483\) 0 0
\(484\) −5.82110 2.11871i −0.264596 0.0963049i
\(485\) −8.89905 −0.404085
\(486\) 0 0
\(487\) −18.3872 −0.833202 −0.416601 0.909090i \(-0.636779\pi\)
−0.416601 + 0.909090i \(0.636779\pi\)
\(488\) 0.496899 + 0.180856i 0.0224935 + 0.00818698i
\(489\) 0 0
\(490\) −0.0874990 0.0734203i −0.00395280 0.00331679i
\(491\) −3.35081 + 19.0034i −0.151220 + 0.857610i 0.810941 + 0.585128i \(0.198956\pi\)
−0.962161 + 0.272482i \(0.912155\pi\)
\(492\) 0 0
\(493\) −1.77749 + 1.49150i −0.0800543 + 0.0671736i
\(494\) 12.6087 + 21.8389i 0.567292 + 0.982579i
\(495\) 0 0
\(496\) 1.67587 2.90269i 0.0752487 0.130335i
\(497\) −3.73326 21.1724i −0.167459 0.949710i
\(498\) 0 0
\(499\) 15.3641 5.59206i 0.687790 0.250335i 0.0256013 0.999672i \(-0.491850\pi\)
0.662189 + 0.749337i \(0.269628\pi\)
\(500\) 8.59794 3.12940i 0.384512 0.139951i
\(501\) 0 0
\(502\) −0.116914 0.663053i −0.00521814 0.0295935i
\(503\) −19.9756 + 34.5988i −0.890670 + 1.54269i −0.0515962 + 0.998668i \(0.516431\pi\)
−0.839074 + 0.544018i \(0.816902\pi\)
\(504\) 0 0
\(505\) −2.76135 4.78280i −0.122878 0.212832i
\(506\) 27.7720 23.3035i 1.23462 1.03597i
\(507\) 0 0
\(508\) 0.968950 5.49519i 0.0429902 0.243810i
\(509\) −24.7041 20.7292i −1.09499 0.918805i −0.0979108 0.995195i \(-0.531216\pi\)
−0.997078 + 0.0763905i \(0.975660\pi\)
\(510\) 0 0
\(511\) 7.88865 + 2.87123i 0.348973 + 0.127016i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 30.6381 1.35139
\(515\) −10.3541 3.76858i −0.456256 0.166064i
\(516\) 0 0
\(517\) 8.78298 + 7.36980i 0.386275 + 0.324123i
\(518\) −4.25007 + 24.1033i −0.186737 + 1.05904i
\(519\) 0 0
\(520\) −3.06771 + 2.57411i −0.134528 + 0.112882i
\(521\) 18.6915 + 32.3746i 0.818890 + 1.41836i 0.906501 + 0.422204i \(0.138743\pi\)
−0.0876112 + 0.996155i \(0.527923\pi\)
\(522\) 0 0
\(523\) −14.5920 + 25.2740i −0.638062 + 1.10516i 0.347795 + 0.937570i \(0.386930\pi\)
−0.985858 + 0.167586i \(0.946403\pi\)
\(524\) −0.268690 1.52382i −0.0117378 0.0665682i
\(525\) 0 0
\(526\) 5.58053 2.03115i 0.243323 0.0885622i
\(527\) 5.83177 2.12259i 0.254036 0.0924615i
\(528\) 0 0
\(529\) 9.27951 + 52.6267i 0.403457 + 2.28812i
\(530\) 0.118288 0.204881i 0.00513812 0.00889948i
\(531\) 0 0
\(532\) −8.57784 14.8573i −0.371897 0.644144i
\(533\) −11.3096 + 9.48989i −0.489874 + 0.411053i
\(534\) 0 0
\(535\) 2.63456 14.9413i 0.113902 0.645969i
\(536\) 6.25489 + 5.24848i 0.270170 + 0.226700i
\(537\) 0 0
\(538\) −14.4359 5.25424i −0.622377 0.226527i
\(539\) 0.463627 0.0199698
\(540\) 0 0
\(541\) 12.6132 0.542283 0.271142 0.962539i \(-0.412599\pi\)
0.271142 + 0.962539i \(0.412599\pi\)
\(542\) −13.7138 4.99141i −0.589057 0.214399i
\(543\) 0 0
\(544\) −1.41840 1.19018i −0.0608134 0.0510285i
\(545\) 3.13281 17.7671i 0.134195 0.761057i
\(546\) 0 0
\(547\) 22.3688 18.7696i 0.956419 0.802531i −0.0239476 0.999713i \(-0.507623\pi\)
0.980367 + 0.197182i \(0.0631790\pi\)
\(548\) −10.0297 17.3719i −0.428446 0.742091i
\(549\) 0 0
\(550\) −8.20279 + 14.2077i −0.349768 + 0.605816i
\(551\) −1.39990 7.93924i −0.0596379 0.338223i
\(552\) 0 0
\(553\) 6.49292 2.36323i 0.276107 0.100495i
\(554\) 5.34571 1.94568i 0.227117 0.0826639i
\(555\) 0 0
\(556\) 0.677277 + 3.84103i 0.0287229 + 0.162896i
\(557\) 21.6137 37.4361i 0.915804 1.58622i 0.110083 0.993922i \(-0.464888\pi\)
0.805720 0.592296i \(-0.201778\pi\)
\(558\) 0 0
\(559\) −6.05629 10.4898i −0.256154 0.443671i
\(560\) 2.08700 1.75120i 0.0881917 0.0740016i
\(561\) 0 0
\(562\) 2.37136 13.4487i 0.100030 0.567298i
\(563\) 5.18375 + 4.34968i 0.218469 + 0.183317i 0.745454 0.666558i \(-0.232233\pi\)
−0.526984 + 0.849875i \(0.676677\pi\)
\(564\) 0 0
\(565\) 1.87806 + 0.683558i 0.0790106 + 0.0287575i
\(566\) −25.9361 −1.09018
\(567\) 0 0
\(568\) 8.06172 0.338262
\(569\) −1.78951 0.651329i −0.0750203 0.0273051i 0.304237 0.952596i \(-0.401598\pi\)
−0.379258 + 0.925291i \(0.623821\pi\)
\(570\) 0 0
\(571\) −8.59231 7.20980i −0.359577 0.301721i 0.445045 0.895508i \(-0.353188\pi\)
−0.804622 + 0.593787i \(0.797632\pi\)
\(572\) 2.82260 16.0078i 0.118019 0.669319i
\(573\) 0 0
\(574\) 7.69406 6.45608i 0.321144 0.269472i
\(575\) −17.2950 29.9558i −0.721252 1.24924i
\(576\) 0 0
\(577\) −19.6634 + 34.0581i −0.818600 + 1.41786i 0.0881143 + 0.996110i \(0.471916\pi\)
−0.906714 + 0.421746i \(0.861417\pi\)
\(578\) 2.35669 + 13.3654i 0.0980252 + 0.555929i
\(579\) 0 0
\(580\) 1.20302 0.437864i 0.0499527 0.0181813i
\(581\) −20.1473 + 7.33303i −0.835852 + 0.304225i
\(582\) 0 0
\(583\) 0.166748 + 0.945677i 0.00690601 + 0.0391659i
\(584\) −1.57397 + 2.72620i −0.0651314 + 0.112811i
\(585\) 0 0
\(586\) −9.94574 17.2265i −0.410855 0.711621i
\(587\) −5.98030 + 5.01807i −0.246834 + 0.207118i −0.757807 0.652478i \(-0.773729\pi\)
0.510974 + 0.859596i \(0.329285\pi\)
\(588\) 0 0
\(589\) −3.74419 + 21.2344i −0.154277 + 0.874947i
\(590\) 2.76620 + 2.32112i 0.113883 + 0.0955589i
\(591\) 0 0
\(592\) −8.62426 3.13897i −0.354455 0.129011i
\(593\) 12.2602 0.503465 0.251733 0.967797i \(-0.419000\pi\)
0.251733 + 0.967797i \(0.419000\pi\)
\(594\) 0 0
\(595\) 5.04444 0.206802
\(596\) −9.24128 3.36355i −0.378537 0.137776i
\(597\) 0 0
\(598\) 26.2538 + 22.0296i 1.07360 + 0.900856i
\(599\) 3.40179 19.2925i 0.138993 0.788271i −0.833002 0.553270i \(-0.813380\pi\)
0.971995 0.235001i \(-0.0755093\pi\)
\(600\) 0 0
\(601\) −3.14380 + 2.63796i −0.128238 + 0.107605i −0.704651 0.709554i \(-0.748896\pi\)
0.576413 + 0.817159i \(0.304452\pi\)
\(602\) 4.12016 + 7.13633i 0.167925 + 0.290855i
\(603\) 0 0
\(604\) −2.00696 + 3.47616i −0.0816622 + 0.141443i
\(605\) 1.09892 + 6.23230i 0.0446776 + 0.253379i
\(606\) 0 0
\(607\) −15.2753 + 5.55976i −0.620006 + 0.225664i −0.632876 0.774253i \(-0.718126\pi\)
0.0128694 + 0.999917i \(0.495903\pi\)
\(608\) 6.04511 2.20024i 0.245161 0.0892315i
\(609\) 0 0
\(610\) −0.0938059 0.531999i −0.00379809 0.0215400i
\(611\) −5.41930 + 9.38650i −0.219241 + 0.379737i
\(612\) 0 0
\(613\) −8.52562 14.7668i −0.344347 0.596426i 0.640888 0.767634i \(-0.278566\pi\)
−0.985235 + 0.171208i \(0.945233\pi\)
\(614\) 7.28865 6.11590i 0.294146 0.246818i
\(615\) 0 0
\(616\) −1.92025 + 10.8903i −0.0773690 + 0.438781i
\(617\) 21.2848 + 17.8601i 0.856895 + 0.719020i 0.961297 0.275515i \(-0.0888484\pi\)
−0.104402 + 0.994535i \(0.533293\pi\)
\(618\) 0 0
\(619\) −7.09199 2.58127i −0.285051 0.103750i 0.195538 0.980696i \(-0.437355\pi\)
−0.480589 + 0.876946i \(0.659577\pi\)
\(620\) −3.42411 −0.137516
\(621\) 0 0
\(622\) −14.4638 −0.579947
\(623\) 30.7078 + 11.1767i 1.23028 + 0.447786i
\(624\) 0 0
\(625\) 7.99324 + 6.70713i 0.319730 + 0.268285i
\(626\) 2.32518 13.1867i 0.0929329 0.527048i
\(627\) 0 0
\(628\) −10.9765 + 9.21039i −0.438011 + 0.367534i
\(629\) −8.49671 14.7167i −0.338786 0.586794i
\(630\) 0 0
\(631\) 12.3054 21.3136i 0.489872 0.848483i −0.510060 0.860139i \(-0.670377\pi\)
0.999932 + 0.0116559i \(0.00371028\pi\)
\(632\) 0.449919 + 2.55162i 0.0178968 + 0.101498i
\(633\) 0 0
\(634\) −23.6465 + 8.60661i −0.939122 + 0.341812i
\(635\) −5.35667 + 1.94967i −0.212573 + 0.0773702i
\(636\) 0 0
\(637\) 0.0761068 + 0.431623i 0.00301546 + 0.0171015i
\(638\) −2.59823 + 4.50026i −0.102865 + 0.178167i
\(639\) 0 0
\(640\) 0.510796 + 0.884725i 0.0201910 + 0.0349718i
\(641\) −23.1248 + 19.4040i −0.913373 + 0.766411i −0.972758 0.231824i \(-0.925531\pi\)
0.0593849 + 0.998235i \(0.481086\pi\)
\(642\) 0 0
\(643\) −2.06856 + 11.7314i −0.0815762 + 0.462641i 0.916467 + 0.400111i \(0.131028\pi\)
−0.998043 + 0.0625308i \(0.980083\pi\)
\(644\) −17.8608 14.9870i −0.703813 0.590569i
\(645\) 0 0
\(646\) 11.1931 + 4.07394i 0.440385 + 0.160287i
\(647\) −20.4896 −0.805528 −0.402764 0.915304i \(-0.631951\pi\)
−0.402764 + 0.915304i \(0.631951\pi\)
\(648\) 0 0
\(649\) −14.6571 −0.575343
\(650\) −14.5735 5.30431i −0.571618 0.208052i
\(651\) 0 0
\(652\) −10.9476 9.18614i −0.428742 0.359757i
\(653\) 8.53662 48.4136i 0.334064 1.89457i −0.102222 0.994762i \(-0.532595\pi\)
0.436286 0.899808i \(-0.356294\pi\)
\(654\) 0 0
\(655\) −1.21091 + 1.01608i −0.0473142 + 0.0397014i
\(656\) 1.88313 + 3.26169i 0.0735241 + 0.127347i
\(657\) 0 0
\(658\) 3.68681 6.38574i 0.143727 0.248942i
\(659\) −4.93483 27.9868i −0.192234 1.09021i −0.916303 0.400485i \(-0.868842\pi\)
0.724070 0.689727i \(-0.242269\pi\)
\(660\) 0 0
\(661\) −40.5404 + 14.7555i −1.57684 + 0.573923i −0.974514 0.224328i \(-0.927981\pi\)
−0.602326 + 0.798251i \(0.705759\pi\)
\(662\) −19.8606 + 7.22868i −0.771905 + 0.280951i
\(663\) 0 0
\(664\) −1.39609 7.91759i −0.0541786 0.307262i
\(665\) −8.76306 + 15.1781i −0.339817 + 0.588580i
\(666\) 0 0
\(667\) −5.47817 9.48848i −0.212116 0.367395i
\(668\) 7.31955 6.14183i 0.283202 0.237634i
\(669\) 0 0
\(670\) 1.44848 8.21476i 0.0559598 0.317364i
\(671\) 1.67971 + 1.40944i 0.0648443 + 0.0544108i
\(672\) 0 0
\(673\) 33.9219 + 12.3466i 1.30759 + 0.475926i 0.899463 0.436997i \(-0.143958\pi\)
0.408132 + 0.912923i \(0.366180\pi\)
\(674\) −4.77192 −0.183808
\(675\) 0 0
\(676\) 2.36613 0.0910052
\(677\) 40.5216 + 14.7487i 1.55737 + 0.566837i 0.970132 0.242576i \(-0.0779925\pi\)
0.587239 + 0.809413i \(0.300215\pi\)
\(678\) 0 0
\(679\) −17.7955 14.9322i −0.682928 0.573045i
\(680\) −0.328468 + 1.86283i −0.0125962 + 0.0714364i
\(681\) 0 0
\(682\) 10.6468 8.93377i 0.407689 0.342092i
\(683\) 0.0895535 + 0.155111i 0.00342667 + 0.00593517i 0.867734 0.497029i \(-0.165576\pi\)
−0.864307 + 0.502965i \(0.832243\pi\)
\(684\) 0 0
\(685\) −10.2462 + 17.7470i −0.391489 + 0.678078i
\(686\) 3.18982 + 18.0903i 0.121788 + 0.690692i
\(687\) 0 0
\(688\) −2.90362 + 1.05683i −0.110700 + 0.0402913i
\(689\) −0.853026 + 0.310476i −0.0324977 + 0.0118282i
\(690\) 0 0
\(691\) −5.97830 33.9046i −0.227425 1.28979i −0.857994 0.513660i \(-0.828289\pi\)
0.630568 0.776134i \(-0.282822\pi\)
\(692\) 4.99127 8.64514i 0.189740 0.328639i
\(693\) 0 0
\(694\) −7.83372 13.5684i −0.297364 0.515050i
\(695\) 3.05230 2.56119i 0.115780 0.0971514i
\(696\) 0 0
\(697\) −1.21095 + 6.86764i −0.0458680 + 0.260130i
\(698\) −15.1767 12.7348i −0.574448 0.482019i
\(699\) 0 0
\(700\) 9.91449 + 3.60858i 0.374732 + 0.136391i
\(701\) 17.3215 0.654224 0.327112 0.944985i \(-0.393924\pi\)
0.327112 + 0.944985i \(0.393924\pi\)
\(702\) 0 0
\(703\) 59.0410 2.22677
\(704\) −3.89657 1.41824i −0.146858 0.0534518i
\(705\) 0 0
\(706\) −12.1013 10.1542i −0.455440 0.382160i
\(707\) 2.50342 14.1976i 0.0941508 0.533956i
\(708\) 0 0
\(709\) −28.0038 + 23.4980i −1.05171 + 0.882485i −0.993272 0.115806i \(-0.963055\pi\)
−0.0584333 + 0.998291i \(0.518611\pi\)
\(710\) −4.11790 7.13241i −0.154542 0.267674i
\(711\) 0 0
\(712\) −6.12693 + 10.6122i −0.229616 + 0.397707i
\(713\) 5.08858 + 28.8588i 0.190569 + 1.08077i
\(714\) 0 0
\(715\) −15.6043 + 5.67948i −0.583566 + 0.212401i
\(716\) −21.1509 + 7.69828i −0.790445 + 0.287698i
\(717\) 0 0
\(718\) 0.845577 + 4.79551i 0.0315567 + 0.178967i
\(719\) −22.8804 + 39.6301i −0.853296 + 1.47795i 0.0249200 + 0.999689i \(0.492067\pi\)
−0.878216 + 0.478263i \(0.841266\pi\)
\(720\) 0 0
\(721\) −14.3816 24.9097i −0.535601 0.927687i
\(722\) −17.1474 + 14.3884i −0.638160 + 0.535480i
\(723\) 0 0
\(724\) 0.0861567 0.488619i 0.00320199 0.0181594i
\(725\) 3.79803 + 3.18692i 0.141055 + 0.118359i
\(726\) 0 0
\(727\) −8.24873 3.00229i −0.305928 0.111349i 0.184494 0.982834i \(-0.440935\pi\)
−0.490423 + 0.871485i \(0.663158\pi\)
\(728\) −10.4538 −0.387442
\(729\) 0 0
\(730\) 3.21592 0.119026
\(731\) −5.37632 1.95682i −0.198850 0.0723756i
\(732\) 0 0
\(733\) 25.4717 + 21.3733i 0.940820 + 0.789441i 0.977728 0.209877i \(-0.0673065\pi\)
−0.0369082 + 0.999319i \(0.511751\pi\)
\(734\) 1.47394 8.35914i 0.0544042 0.308542i
\(735\) 0 0
\(736\) 6.69746 5.61984i 0.246872 0.207150i
\(737\) 16.9291 + 29.3220i 0.623590 + 1.08009i
\(738\) 0 0
\(739\) 1.03598 1.79437i 0.0381091 0.0660069i −0.846342 0.532640i \(-0.821200\pi\)
0.884451 + 0.466633i \(0.154533\pi\)
\(740\) 1.62811 + 9.23347i 0.0598505 + 0.339429i
\(741\) 0 0
\(742\) 0.580323 0.211220i 0.0213043 0.00775414i
\(743\) 3.31599 1.20692i 0.121652 0.0442777i −0.280477 0.959861i \(-0.590493\pi\)
0.402129 + 0.915583i \(0.368270\pi\)
\(744\) 0 0
\(745\) 1.74459 + 9.89408i 0.0639169 + 0.362491i
\(746\) 2.25715 3.90950i 0.0826401 0.143137i
\(747\) 0 0
\(748\) −3.83895 6.64925i −0.140366 0.243121i
\(749\) 30.3391 25.4576i 1.10857 0.930199i
\(750\) 0 0
\(751\) −6.65211 + 37.7260i −0.242739 + 1.37664i 0.582946 + 0.812511i \(0.301900\pi\)
−0.825685 + 0.564131i \(0.809211\pi\)
\(752\) 2.11809 + 1.77729i 0.0772389 + 0.0648111i
\(753\) 0 0
\(754\) −4.61613 1.68013i −0.168109 0.0611868i
\(755\) 4.10060 0.149236
\(756\) 0 0
\(757\) 12.3900 0.450322 0.225161 0.974322i \(-0.427709\pi\)
0.225161 + 0.974322i \(0.427709\pi\)
\(758\) 10.4323 + 3.79705i 0.378918 + 0.137915i
\(759\) 0 0
\(760\) −5.03442 4.22438i −0.182618 0.153234i
\(761\) 1.41032 7.99834i 0.0511241 0.289939i −0.948517 0.316726i \(-0.897416\pi\)
0.999641 + 0.0267867i \(0.00852750\pi\)
\(762\) 0 0
\(763\) 36.0770 30.2722i 1.30607 1.09593i
\(764\) 3.59416 + 6.22526i 0.130032 + 0.225222i
\(765\) 0 0
\(766\) 11.0213 19.0895i 0.398217 0.689732i
\(767\) −2.40605 13.6454i −0.0868774 0.492706i
\(768\) 0 0
\(769\) 24.7906 9.02303i 0.893971 0.325379i 0.146137 0.989264i \(-0.453316\pi\)
0.747834 + 0.663885i \(0.231094\pi\)
\(770\) 10.6158 3.86382i 0.382565 0.139242i
\(771\) 0 0
\(772\) −2.33901 13.2652i −0.0841829 0.477425i
\(773\) 5.39129 9.33798i 0.193911 0.335864i −0.752632 0.658442i \(-0.771216\pi\)
0.946543 + 0.322578i \(0.104549\pi\)
\(774\) 0 0
\(775\) −6.63032 11.4840i −0.238168 0.412519i
\(776\) 6.67298 5.59930i 0.239546 0.201003i
\(777\) 0 0
\(778\) −2.95836 + 16.7777i −0.106062 + 0.601509i
\(779\) −18.5602 15.5739i