Properties

Label 162.2.e.a.37.1
Level $162$
Weight $2$
Character 162.37
Analytic conductor $1.294$
Analytic rank $0$
Dimension $6$
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: \(6\)
Coefficient field: \(\Q(\zeta_{18})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{3} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 54)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 37.1
Root \(0.939693 + 0.342020i\) of defining polynomial
Character \(\chi\) \(=\) 162.37
Dual form 162.2.e.a.127.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.766044 - 0.642788i) q^{2} +(0.173648 - 0.984808i) q^{4} +(1.26604 - 0.460802i) q^{5} +(-0.0209445 - 0.118782i) q^{7} +(-0.500000 - 0.866025i) q^{8} +O(q^{10})\) \(q+(0.766044 - 0.642788i) q^{2} +(0.173648 - 0.984808i) q^{4} +(1.26604 - 0.460802i) q^{5} +(-0.0209445 - 0.118782i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(0.673648 - 1.16679i) q^{10} +(3.49273 + 1.27125i) q^{11} +(-4.64543 - 3.89798i) q^{13} +(-0.0923963 - 0.0775297i) q^{14} +(-0.939693 - 0.342020i) q^{16} +(-2.58512 + 4.47756i) q^{17} +(2.96064 + 5.12797i) q^{19} +(-0.233956 - 1.32683i) q^{20} +(3.49273 - 1.27125i) q^{22} +(0.826352 - 4.68647i) q^{23} +(-2.43969 + 2.04715i) q^{25} -6.06418 q^{26} -0.120615 q^{28} +(-4.55303 + 3.82045i) q^{29} +(-0.875515 + 4.96529i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(0.897804 + 5.09170i) q^{34} +(-0.0812519 - 0.140732i) q^{35} +(-0.145430 + 0.251892i) q^{37} +(5.56418 + 2.02520i) q^{38} +(-1.03209 - 0.866025i) q^{40} +(-4.44356 - 3.72859i) q^{41} +(-0.426022 - 0.155059i) q^{43} +(1.85844 - 3.21891i) q^{44} +(-2.37939 - 4.12122i) q^{46} +(0.134285 + 0.761570i) q^{47} +(6.56418 - 2.38917i) q^{49} +(-0.553033 + 3.13641i) q^{50} +(-4.64543 + 3.89798i) q^{52} +7.29086 q^{53} +5.00774 q^{55} +(-0.0923963 + 0.0775297i) q^{56} +(-1.03209 + 5.85327i) q^{58} +(-1.40033 + 0.509678i) q^{59} +(-0.656574 - 3.72362i) q^{61} +(2.52094 + 4.36640i) q^{62} +(-0.500000 + 0.866025i) q^{64} +(-7.67752 - 2.79439i) q^{65} +(-5.08512 - 4.26692i) q^{67} +(3.96064 + 3.32337i) q^{68} +(-0.152704 - 0.0555796i) q^{70} +(2.87211 - 4.97464i) q^{71} +(-5.20961 - 9.02330i) q^{73} +(0.0505072 + 0.286441i) q^{74} +(5.56418 - 2.02520i) q^{76} +(0.0778483 - 0.441500i) q^{77} +(10.7194 - 8.99465i) q^{79} -1.34730 q^{80} -5.80066 q^{82} +(1.81521 - 1.52314i) q^{83} +(-1.20961 + 6.86002i) q^{85} +(-0.426022 + 0.155059i) q^{86} +(-0.645430 - 3.66041i) q^{88} +(-1.08512 - 1.87949i) q^{89} +(-0.365715 + 0.633436i) q^{91} +(-4.47178 - 1.62760i) q^{92} +(0.592396 + 0.497079i) q^{94} +(6.11128 + 5.12797i) q^{95} +(3.21941 + 1.17177i) q^{97} +(3.49273 - 6.04958i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 3 q^{5} + 3 q^{7} - 3 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 3 q^{5} + 3 q^{7} - 3 q^{8} + 3 q^{10} + 3 q^{11} - 12 q^{13} + 3 q^{14} + 6 q^{17} + 9 q^{19} - 6 q^{20} + 3 q^{22} + 6 q^{23} - 9 q^{25} - 18 q^{26} - 12 q^{28} - 15 q^{29} - 18 q^{31} + 6 q^{34} - 3 q^{35} + 15 q^{37} + 15 q^{38} + 3 q^{40} + 3 q^{41} - 18 q^{43} + 3 q^{44} - 3 q^{46} - 9 q^{47} + 21 q^{49} + 9 q^{50} - 12 q^{52} + 12 q^{53} - 18 q^{55} + 3 q^{56} + 3 q^{58} + 6 q^{59} + 18 q^{61} + 12 q^{62} - 3 q^{64} - 21 q^{65} - 9 q^{67} + 15 q^{68} - 3 q^{70} - 12 q^{71} + 3 q^{73} + 3 q^{74} + 15 q^{76} - 39 q^{77} + 33 q^{79} - 6 q^{80} - 6 q^{82} + 18 q^{83} + 27 q^{85} - 18 q^{86} + 12 q^{88} + 15 q^{89} - 12 q^{91} - 12 q^{92} - 21 q^{95} - 12 q^{97} + 3 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(83\)
\(\chi(n)\) \(e\left(\frac{7}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.766044 0.642788i 0.541675 0.454519i
\(3\) 0 0
\(4\) 0.173648 0.984808i 0.0868241 0.492404i
\(5\) 1.26604 0.460802i 0.566192 0.206077i −0.0430339 0.999074i \(-0.513702\pi\)
0.609226 + 0.792996i \(0.291480\pi\)
\(6\) 0 0
\(7\) −0.0209445 0.118782i −0.00791629 0.0448955i 0.980594 0.196051i \(-0.0628118\pi\)
−0.988510 + 0.151155i \(0.951701\pi\)
\(8\) −0.500000 0.866025i −0.176777 0.306186i
\(9\) 0 0
\(10\) 0.673648 1.16679i 0.213026 0.368972i
\(11\) 3.49273 + 1.27125i 1.05310 + 0.383296i 0.809831 0.586664i \(-0.199559\pi\)
0.243266 + 0.969960i \(0.421781\pi\)
\(12\) 0 0
\(13\) −4.64543 3.89798i −1.28841 1.08110i −0.992026 0.126036i \(-0.959775\pi\)
−0.296385 0.955069i \(-0.595781\pi\)
\(14\) −0.0923963 0.0775297i −0.0246939 0.0207207i
\(15\) 0 0
\(16\) −0.939693 0.342020i −0.234923 0.0855050i
\(17\) −2.58512 + 4.47756i −0.626984 + 1.08597i 0.361169 + 0.932500i \(0.382378\pi\)
−0.988154 + 0.153468i \(0.950956\pi\)
\(18\) 0 0
\(19\) 2.96064 + 5.12797i 0.679217 + 1.17644i 0.975217 + 0.221250i \(0.0710137\pi\)
−0.296000 + 0.955188i \(0.595653\pi\)
\(20\) −0.233956 1.32683i −0.0523141 0.296688i
\(21\) 0 0
\(22\) 3.49273 1.27125i 0.744652 0.271031i
\(23\) 0.826352 4.68647i 0.172306 0.977197i −0.768901 0.639368i \(-0.779196\pi\)
0.941207 0.337830i \(-0.109693\pi\)
\(24\) 0 0
\(25\) −2.43969 + 2.04715i −0.487939 + 0.409429i
\(26\) −6.06418 −1.18928
\(27\) 0 0
\(28\) −0.120615 −0.0227940
\(29\) −4.55303 + 3.82045i −0.845477 + 0.709440i −0.958789 0.284120i \(-0.908299\pi\)
0.113312 + 0.993559i \(0.463854\pi\)
\(30\) 0 0
\(31\) −0.875515 + 4.96529i −0.157247 + 0.891793i 0.799455 + 0.600725i \(0.205121\pi\)
−0.956703 + 0.291067i \(0.905990\pi\)
\(32\) −0.939693 + 0.342020i −0.166116 + 0.0604612i
\(33\) 0 0
\(34\) 0.897804 + 5.09170i 0.153972 + 0.873219i
\(35\) −0.0812519 0.140732i −0.0137341 0.0237881i
\(36\) 0 0
\(37\) −0.145430 + 0.251892i −0.0239085 + 0.0414107i −0.877732 0.479152i \(-0.840944\pi\)
0.853824 + 0.520562i \(0.174278\pi\)
\(38\) 5.56418 + 2.02520i 0.902629 + 0.328530i
\(39\) 0 0
\(40\) −1.03209 0.866025i −0.163188 0.136931i
\(41\) −4.44356 3.72859i −0.693968 0.582308i 0.226082 0.974108i \(-0.427408\pi\)
−0.920050 + 0.391800i \(0.871853\pi\)
\(42\) 0 0
\(43\) −0.426022 0.155059i −0.0649678 0.0236463i 0.309332 0.950954i \(-0.399895\pi\)
−0.374300 + 0.927308i \(0.622117\pi\)
\(44\) 1.85844 3.21891i 0.280170 0.485270i
\(45\) 0 0
\(46\) −2.37939 4.12122i −0.350821 0.607640i
\(47\) 0.134285 + 0.761570i 0.0195875 + 0.111086i 0.993034 0.117829i \(-0.0375933\pi\)
−0.973446 + 0.228915i \(0.926482\pi\)
\(48\) 0 0
\(49\) 6.56418 2.38917i 0.937740 0.341309i
\(50\) −0.553033 + 3.13641i −0.0782107 + 0.443555i
\(51\) 0 0
\(52\) −4.64543 + 3.89798i −0.644205 + 0.540552i
\(53\) 7.29086 1.00148 0.500738 0.865599i \(-0.333062\pi\)
0.500738 + 0.865599i \(0.333062\pi\)
\(54\) 0 0
\(55\) 5.00774 0.675244
\(56\) −0.0923963 + 0.0775297i −0.0123470 + 0.0103603i
\(57\) 0 0
\(58\) −1.03209 + 5.85327i −0.135520 + 0.768572i
\(59\) −1.40033 + 0.509678i −0.182307 + 0.0663545i −0.431561 0.902084i \(-0.642037\pi\)
0.249253 + 0.968438i \(0.419815\pi\)
\(60\) 0 0
\(61\) −0.656574 3.72362i −0.0840657 0.476760i −0.997554 0.0698959i \(-0.977733\pi\)
0.913489 0.406864i \(-0.133378\pi\)
\(62\) 2.52094 + 4.36640i 0.320160 + 0.554534i
\(63\) 0 0
\(64\) −0.500000 + 0.866025i −0.0625000 + 0.108253i
\(65\) −7.67752 2.79439i −0.952279 0.346601i
\(66\) 0 0
\(67\) −5.08512 4.26692i −0.621247 0.521288i 0.276949 0.960885i \(-0.410677\pi\)
−0.898195 + 0.439597i \(0.855121\pi\)
\(68\) 3.96064 + 3.32337i 0.480298 + 0.403018i
\(69\) 0 0
\(70\) −0.152704 0.0555796i −0.0182516 0.00664303i
\(71\) 2.87211 4.97464i 0.340857 0.590381i −0.643735 0.765248i \(-0.722616\pi\)
0.984592 + 0.174867i \(0.0559495\pi\)
\(72\) 0 0
\(73\) −5.20961 9.02330i −0.609738 1.05610i −0.991283 0.131748i \(-0.957941\pi\)
0.381545 0.924350i \(-0.375392\pi\)
\(74\) 0.0505072 + 0.286441i 0.00587134 + 0.0332980i
\(75\) 0 0
\(76\) 5.56418 2.02520i 0.638255 0.232306i
\(77\) 0.0778483 0.441500i 0.00887164 0.0503136i
\(78\) 0 0
\(79\) 10.7194 8.99465i 1.20603 1.01198i 0.206591 0.978427i \(-0.433763\pi\)
0.999437 0.0335498i \(-0.0106812\pi\)
\(80\) −1.34730 −0.150632
\(81\) 0 0
\(82\) −5.80066 −0.640576
\(83\) 1.81521 1.52314i 0.199245 0.167186i −0.537706 0.843132i \(-0.680709\pi\)
0.736951 + 0.675946i \(0.236265\pi\)
\(84\) 0 0
\(85\) −1.20961 + 6.86002i −0.131200 + 0.744074i
\(86\) −0.426022 + 0.155059i −0.0459391 + 0.0167205i
\(87\) 0 0
\(88\) −0.645430 3.66041i −0.0688030 0.390201i
\(89\) −1.08512 1.87949i −0.115023 0.199225i 0.802766 0.596294i \(-0.203361\pi\)
−0.917789 + 0.397069i \(0.870027\pi\)
\(90\) 0 0
\(91\) −0.365715 + 0.633436i −0.0383373 + 0.0664022i
\(92\) −4.47178 1.62760i −0.466215 0.169689i
\(93\) 0 0
\(94\) 0.592396 + 0.497079i 0.0611010 + 0.0512698i
\(95\) 6.11128 + 5.12797i 0.627004 + 0.526119i
\(96\) 0 0
\(97\) 3.21941 + 1.17177i 0.326881 + 0.118975i 0.500248 0.865882i \(-0.333242\pi\)
−0.173366 + 0.984857i \(0.555464\pi\)
\(98\) 3.49273 6.04958i 0.352819 0.611100i
\(99\) 0 0
\(100\) 1.59240 + 2.75811i 0.159240 + 0.275811i
\(101\) −1.49660 8.48762i −0.148917 0.844550i −0.964138 0.265400i \(-0.914496\pi\)
0.815221 0.579149i \(-0.196615\pi\)
\(102\) 0 0
\(103\) 2.05303 0.747243i 0.202291 0.0736280i −0.238887 0.971047i \(-0.576783\pi\)
0.441179 + 0.897419i \(0.354560\pi\)
\(104\) −1.05303 + 5.97205i −0.103258 + 0.585608i
\(105\) 0 0
\(106\) 5.58512 4.68647i 0.542475 0.455191i
\(107\) 10.2909 0.994855 0.497427 0.867506i \(-0.334278\pi\)
0.497427 + 0.867506i \(0.334278\pi\)
\(108\) 0 0
\(109\) −11.0915 −1.06237 −0.531187 0.847254i \(-0.678254\pi\)
−0.531187 + 0.847254i \(0.678254\pi\)
\(110\) 3.83615 3.21891i 0.365763 0.306911i
\(111\) 0 0
\(112\) −0.0209445 + 0.118782i −0.00197907 + 0.0112239i
\(113\) 5.56670 2.02611i 0.523671 0.190601i −0.0666389 0.997777i \(-0.521228\pi\)
0.590310 + 0.807176i \(0.299005\pi\)
\(114\) 0 0
\(115\) −1.11334 6.31407i −0.103820 0.588790i
\(116\) 2.97178 + 5.14728i 0.275923 + 0.477913i
\(117\) 0 0
\(118\) −0.745100 + 1.29055i −0.0685920 + 0.118805i
\(119\) 0.586000 + 0.213286i 0.0537185 + 0.0195519i
\(120\) 0 0
\(121\) 2.15657 + 1.80958i 0.196052 + 0.164507i
\(122\) −2.89646 2.43042i −0.262233 0.220040i
\(123\) 0 0
\(124\) 4.73783 + 1.72443i 0.425469 + 0.154858i
\(125\) −5.51367 + 9.54996i −0.493158 + 0.854174i
\(126\) 0 0
\(127\) 2.86959 + 4.97027i 0.254634 + 0.441040i 0.964796 0.262999i \(-0.0847115\pi\)
−0.710162 + 0.704039i \(0.751378\pi\)
\(128\) 0.173648 + 0.984808i 0.0153485 + 0.0870455i
\(129\) 0 0
\(130\) −7.67752 + 2.79439i −0.673363 + 0.245084i
\(131\) −2.99020 + 16.9583i −0.261255 + 1.48165i 0.518236 + 0.855237i \(0.326589\pi\)
−0.779491 + 0.626413i \(0.784522\pi\)
\(132\) 0 0
\(133\) 0.547104 0.459074i 0.0474399 0.0398068i
\(134\) −6.63816 −0.573449
\(135\) 0 0
\(136\) 5.17024 0.443345
\(137\) −0.0662372 + 0.0555796i −0.00565902 + 0.00474848i −0.645613 0.763665i \(-0.723398\pi\)
0.639954 + 0.768413i \(0.278954\pi\)
\(138\) 0 0
\(139\) −3.18866 + 18.0838i −0.270459 + 1.53385i 0.482568 + 0.875859i \(0.339704\pi\)
−0.753027 + 0.657990i \(0.771407\pi\)
\(140\) −0.152704 + 0.0555796i −0.0129058 + 0.00469733i
\(141\) 0 0
\(142\) −0.997474 5.65695i −0.0837061 0.474721i
\(143\) −11.2699 19.5201i −0.942438 1.63235i
\(144\) 0 0
\(145\) −4.00387 + 6.93491i −0.332503 + 0.575913i
\(146\) −9.79086 3.56358i −0.810297 0.294924i
\(147\) 0 0
\(148\) 0.222811 + 0.186961i 0.0183150 + 0.0153681i
\(149\) 3.75490 + 3.15074i 0.307613 + 0.258118i 0.783505 0.621386i \(-0.213430\pi\)
−0.475891 + 0.879504i \(0.657874\pi\)
\(150\) 0 0
\(151\) −1.62701 0.592184i −0.132404 0.0481912i 0.274968 0.961453i \(-0.411333\pi\)
−0.407372 + 0.913262i \(0.633555\pi\)
\(152\) 2.96064 5.12797i 0.240139 0.415934i
\(153\) 0 0
\(154\) −0.224155 0.388249i −0.0180630 0.0312860i
\(155\) 1.17958 + 6.68972i 0.0947460 + 0.537331i
\(156\) 0 0
\(157\) 5.46451 1.98892i 0.436115 0.158733i −0.114627 0.993409i \(-0.536567\pi\)
0.550742 + 0.834676i \(0.314345\pi\)
\(158\) 2.42989 13.7806i 0.193312 1.09633i
\(159\) 0 0
\(160\) −1.03209 + 0.866025i −0.0815938 + 0.0684653i
\(161\) −0.573978 −0.0452358
\(162\) 0 0
\(163\) −2.70914 −0.212196 −0.106098 0.994356i \(-0.533836\pi\)
−0.106098 + 0.994356i \(0.533836\pi\)
\(164\) −4.44356 + 3.72859i −0.346984 + 0.291154i
\(165\) 0 0
\(166\) 0.411474 2.33359i 0.0319366 0.181121i
\(167\) −23.1202 + 8.41507i −1.78910 + 0.651177i −0.789811 + 0.613351i \(0.789821\pi\)
−0.999284 + 0.0378268i \(0.987956\pi\)
\(168\) 0 0
\(169\) 4.12836 + 23.4131i 0.317566 + 1.80101i
\(170\) 3.48293 + 6.03260i 0.267128 + 0.462680i
\(171\) 0 0
\(172\) −0.226682 + 0.392624i −0.0172843 + 0.0299373i
\(173\) −10.0753 3.66712i −0.766013 0.278806i −0.0706849 0.997499i \(-0.522518\pi\)
−0.695328 + 0.718693i \(0.744741\pi\)
\(174\) 0 0
\(175\) 0.294263 + 0.246916i 0.0222442 + 0.0186651i
\(176\) −2.84730 2.38917i −0.214623 0.180090i
\(177\) 0 0
\(178\) −2.03936 0.742267i −0.152857 0.0556353i
\(179\) −6.92262 + 11.9903i −0.517421 + 0.896199i 0.482374 + 0.875965i \(0.339774\pi\)
−0.999795 + 0.0202340i \(0.993559\pi\)
\(180\) 0 0
\(181\) −1.75490 3.03958i −0.130441 0.225930i 0.793406 0.608693i \(-0.208306\pi\)
−0.923847 + 0.382763i \(0.874973\pi\)
\(182\) 0.127011 + 0.720317i 0.00941471 + 0.0533935i
\(183\) 0 0
\(184\) −4.47178 + 1.62760i −0.329664 + 0.119988i
\(185\) −0.0680482 + 0.385920i −0.00500300 + 0.0283734i
\(186\) 0 0
\(187\) −14.7212 + 12.3526i −1.07652 + 0.903309i
\(188\) 0.773318 0.0564000
\(189\) 0 0
\(190\) 7.97771 0.578764
\(191\) 16.7704 14.0720i 1.21346 1.01822i 0.214322 0.976763i \(-0.431246\pi\)
0.999140 0.0414526i \(-0.0131986\pi\)
\(192\) 0 0
\(193\) 4.44743 25.2226i 0.320133 1.81557i −0.221740 0.975106i \(-0.571174\pi\)
0.541873 0.840460i \(-0.317715\pi\)
\(194\) 3.21941 1.17177i 0.231140 0.0841281i
\(195\) 0 0
\(196\) −1.21301 6.87933i −0.0866436 0.491381i
\(197\) 6.84255 + 11.8516i 0.487511 + 0.844395i 0.999897 0.0143611i \(-0.00457142\pi\)
−0.512385 + 0.858756i \(0.671238\pi\)
\(198\) 0 0
\(199\) 6.19981 10.7384i 0.439493 0.761224i −0.558158 0.829735i \(-0.688492\pi\)
0.997650 + 0.0685113i \(0.0218249\pi\)
\(200\) 2.99273 + 1.08926i 0.211618 + 0.0770225i
\(201\) 0 0
\(202\) −6.60220 5.53990i −0.464529 0.389786i
\(203\) 0.549163 + 0.460802i 0.0385437 + 0.0323420i
\(204\) 0 0
\(205\) −7.34389 2.67296i −0.512920 0.186688i
\(206\) 1.09240 1.89209i 0.0761109 0.131828i
\(207\) 0 0
\(208\) 3.03209 + 5.25173i 0.210238 + 0.364142i
\(209\) 3.82177 + 21.6743i 0.264357 + 1.49924i
\(210\) 0 0
\(211\) −13.9474 + 5.07645i −0.960181 + 0.349477i −0.774104 0.633058i \(-0.781799\pi\)
−0.186077 + 0.982535i \(0.559577\pi\)
\(212\) 1.26604 7.18009i 0.0869523 0.493131i
\(213\) 0 0
\(214\) 7.88326 6.61484i 0.538888 0.452181i
\(215\) −0.610815 −0.0416572
\(216\) 0 0
\(217\) 0.608126 0.0412823
\(218\) −8.49660 + 7.12949i −0.575462 + 0.482870i
\(219\) 0 0
\(220\) 0.869585 4.93166i 0.0586274 0.332493i
\(221\) 29.4624 10.7235i 1.98186 0.721338i
\(222\) 0 0
\(223\) −1.16890 6.62916i −0.0782754 0.443922i −0.998606 0.0527806i \(-0.983192\pi\)
0.920331 0.391141i \(-0.127920\pi\)
\(224\) 0.0603074 + 0.104455i 0.00402946 + 0.00697922i
\(225\) 0 0
\(226\) 2.96198 5.13030i 0.197028 0.341263i
\(227\) 13.6211 + 4.95767i 0.904063 + 0.329052i 0.751880 0.659300i \(-0.229147\pi\)
0.152183 + 0.988352i \(0.451370\pi\)
\(228\) 0 0
\(229\) 19.7540 + 16.5756i 1.30538 + 1.09535i 0.989188 + 0.146652i \(0.0468496\pi\)
0.316194 + 0.948694i \(0.397595\pi\)
\(230\) −4.91147 4.12122i −0.323853 0.271745i
\(231\) 0 0
\(232\) 5.58512 + 2.03282i 0.366681 + 0.133461i
\(233\) 5.19846 9.00400i 0.340563 0.589872i −0.643975 0.765047i \(-0.722716\pi\)
0.984537 + 0.175175i \(0.0560491\pi\)
\(234\) 0 0
\(235\) 0.520945 + 0.902302i 0.0339827 + 0.0588597i
\(236\) 0.258770 + 1.46756i 0.0168445 + 0.0955300i
\(237\) 0 0
\(238\) 0.586000 0.213286i 0.0379847 0.0138253i
\(239\) 3.97906 22.5663i 0.257384 1.45970i −0.532495 0.846433i \(-0.678746\pi\)
0.789879 0.613263i \(-0.210143\pi\)
\(240\) 0 0
\(241\) −9.25150 + 7.76293i −0.595941 + 0.500054i −0.890138 0.455691i \(-0.849392\pi\)
0.294197 + 0.955745i \(0.404948\pi\)
\(242\) 2.81521 0.180968
\(243\) 0 0
\(244\) −3.78106 −0.242058
\(245\) 7.20961 6.04958i 0.460605 0.386493i
\(246\) 0 0
\(247\) 6.23530 35.3621i 0.396743 2.25004i
\(248\) 4.73783 1.72443i 0.300852 0.109501i
\(249\) 0 0
\(250\) 1.91488 + 10.8598i 0.121107 + 0.686835i
\(251\) −7.02347 12.1650i −0.443318 0.767849i 0.554616 0.832107i \(-0.312865\pi\)
−0.997933 + 0.0642581i \(0.979532\pi\)
\(252\) 0 0
\(253\) 8.84389 15.3181i 0.556011 0.963039i
\(254\) 5.39306 + 1.96291i 0.338390 + 0.123164i
\(255\) 0 0
\(256\) 0.766044 + 0.642788i 0.0478778 + 0.0401742i
\(257\) −13.8983 11.6620i −0.866950 0.727458i 0.0965034 0.995333i \(-0.469234\pi\)
−0.963454 + 0.267875i \(0.913679\pi\)
\(258\) 0 0
\(259\) 0.0329662 + 0.0119987i 0.00204842 + 0.000745565i
\(260\) −4.08512 + 7.07564i −0.253349 + 0.438813i
\(261\) 0 0
\(262\) 8.60994 + 14.9128i 0.531924 + 0.921319i
\(263\) −0.742107 4.20870i −0.0457603 0.259519i 0.953342 0.301894i \(-0.0976188\pi\)
−0.999102 + 0.0423745i \(0.986508\pi\)
\(264\) 0 0
\(265\) 9.23055 3.35965i 0.567028 0.206381i
\(266\) 0.124018 0.703343i 0.00760405 0.0431247i
\(267\) 0 0
\(268\) −5.08512 + 4.26692i −0.310623 + 0.260644i
\(269\) −13.0615 −0.796373 −0.398187 0.917304i \(-0.630360\pi\)
−0.398187 + 0.917304i \(0.630360\pi\)
\(270\) 0 0
\(271\) 8.48751 0.515580 0.257790 0.966201i \(-0.417006\pi\)
0.257790 + 0.966201i \(0.417006\pi\)
\(272\) 3.96064 3.32337i 0.240149 0.201509i
\(273\) 0 0
\(274\) −0.0150147 + 0.0851529i −0.000907074 + 0.00514427i
\(275\) −11.1236 + 4.04866i −0.670779 + 0.244144i
\(276\) 0 0
\(277\) 1.14842 + 6.51303i 0.0690020 + 0.391330i 0.999675 + 0.0254787i \(0.00811100\pi\)
−0.930673 + 0.365851i \(0.880778\pi\)
\(278\) 9.18139 + 15.9026i 0.550663 + 0.953776i
\(279\) 0 0
\(280\) −0.0812519 + 0.140732i −0.00485573 + 0.00841037i
\(281\) 27.9320 + 10.1664i 1.66628 + 0.606478i 0.991332 0.131384i \(-0.0419420\pi\)
0.674952 + 0.737861i \(0.264164\pi\)
\(282\) 0 0
\(283\) −2.15657 1.80958i −0.128195 0.107568i 0.576436 0.817142i \(-0.304443\pi\)
−0.704631 + 0.709574i \(0.748887\pi\)
\(284\) −4.40033 3.69232i −0.261112 0.219099i
\(285\) 0 0
\(286\) −21.1805 7.70908i −1.25243 0.455847i
\(287\) −0.349823 + 0.605910i −0.0206494 + 0.0357658i
\(288\) 0 0
\(289\) −4.86571 8.42767i −0.286219 0.495745i
\(290\) 1.39053 + 7.88609i 0.0816547 + 0.463087i
\(291\) 0 0
\(292\) −9.79086 + 3.56358i −0.572967 + 0.208543i
\(293\) −1.70796 + 9.68631i −0.0997800 + 0.565881i 0.893397 + 0.449267i \(0.148315\pi\)
−0.993177 + 0.116613i \(0.962796\pi\)
\(294\) 0 0
\(295\) −1.53802 + 1.29055i −0.0895469 + 0.0751388i
\(296\) 0.290859 0.0169059
\(297\) 0 0
\(298\) 4.90167 0.283946
\(299\) −22.1065 + 18.5496i −1.27845 + 1.07275i
\(300\) 0 0
\(301\) −0.00949548 + 0.0538515i −0.000547310 + 0.00310395i
\(302\) −1.62701 + 0.592184i −0.0936240 + 0.0340763i
\(303\) 0 0
\(304\) −1.02822 5.83132i −0.0589724 0.334449i
\(305\) −2.54710 4.41171i −0.145847 0.252614i
\(306\) 0 0
\(307\) −6.78106 + 11.7451i −0.387015 + 0.670330i −0.992047 0.125871i \(-0.959827\pi\)
0.605031 + 0.796202i \(0.293161\pi\)
\(308\) −0.421274 0.153331i −0.0240043 0.00873686i
\(309\) 0 0
\(310\) 5.20368 + 4.36640i 0.295549 + 0.247995i
\(311\) 8.10220 + 6.79855i 0.459433 + 0.385510i 0.842922 0.538035i \(-0.180833\pi\)
−0.383489 + 0.923545i \(0.625278\pi\)
\(312\) 0 0
\(313\) 10.0544 + 3.65949i 0.568307 + 0.206847i 0.610162 0.792277i \(-0.291104\pi\)
−0.0418547 + 0.999124i \(0.513327\pi\)
\(314\) 2.90760 5.03612i 0.164086 0.284205i
\(315\) 0 0
\(316\) −6.99660 12.1185i −0.393589 0.681717i
\(317\) −5.06717 28.7374i −0.284601 1.61405i −0.706708 0.707505i \(-0.749821\pi\)
0.422108 0.906546i \(-0.361290\pi\)
\(318\) 0 0
\(319\) −20.7592 + 7.55574i −1.16229 + 0.423040i
\(320\) −0.233956 + 1.32683i −0.0130785 + 0.0741719i
\(321\) 0 0
\(322\) −0.439693 + 0.368946i −0.0245031 + 0.0205606i
\(323\) −30.6144 −1.70343
\(324\) 0 0
\(325\) 19.3131 1.07130
\(326\) −2.07532 + 1.74140i −0.114941 + 0.0964473i
\(327\) 0 0
\(328\) −1.00727 + 5.71253i −0.0556174 + 0.315422i
\(329\) 0.0876485 0.0319015i 0.00483222 0.00175878i
\(330\) 0 0
\(331\) −1.26739 7.18772i −0.0696620 0.395073i −0.999624 0.0274173i \(-0.991272\pi\)
0.929962 0.367655i \(-0.119839\pi\)
\(332\) −1.18479 2.05212i −0.0650239 0.112625i
\(333\) 0 0
\(334\) −12.3020 + 21.3077i −0.673136 + 1.16591i
\(335\) −8.40420 3.05888i −0.459171 0.167124i
\(336\) 0 0
\(337\) −1.24376 1.04363i −0.0677517 0.0568504i 0.608283 0.793720i \(-0.291859\pi\)
−0.676035 + 0.736870i \(0.736303\pi\)
\(338\) 18.2121 + 15.2818i 0.990609 + 0.831220i
\(339\) 0 0
\(340\) 6.54576 + 2.38246i 0.354994 + 0.129207i
\(341\) −9.37005 + 16.2294i −0.507417 + 0.878872i
\(342\) 0 0
\(343\) −0.843426 1.46086i −0.0455407 0.0788788i
\(344\) 0.0787257 + 0.446476i 0.00424460 + 0.0240724i
\(345\) 0 0
\(346\) −10.0753 + 3.66712i −0.541653 + 0.197145i
\(347\) 0.949655 5.38576i 0.0509801 0.289123i −0.948650 0.316329i \(-0.897550\pi\)
0.999630 + 0.0272057i \(0.00866092\pi\)
\(348\) 0 0
\(349\) 2.37346 1.99157i 0.127048 0.106606i −0.577050 0.816709i \(-0.695796\pi\)
0.704098 + 0.710103i \(0.251352\pi\)
\(350\) 0.384133 0.0205328
\(351\) 0 0
\(352\) −3.71688 −0.198110
\(353\) −0.233956 + 0.196312i −0.0124522 + 0.0104486i −0.648992 0.760795i \(-0.724809\pi\)
0.636540 + 0.771243i \(0.280365\pi\)
\(354\) 0 0
\(355\) 1.34389 7.62159i 0.0713264 0.404512i
\(356\) −2.03936 + 0.742267i −0.108086 + 0.0393401i
\(357\) 0 0
\(358\) 2.40420 + 13.6349i 0.127066 + 0.720627i
\(359\) 5.28493 + 9.15377i 0.278928 + 0.483117i 0.971119 0.238597i \(-0.0766876\pi\)
−0.692191 + 0.721715i \(0.743354\pi\)
\(360\) 0 0
\(361\) −8.03074 + 13.9097i −0.422671 + 0.732087i
\(362\) −3.29813 1.20042i −0.173346 0.0630928i
\(363\) 0 0
\(364\) 0.560307 + 0.470154i 0.0293681 + 0.0246428i
\(365\) −10.7536 9.02330i −0.562867 0.472301i
\(366\) 0 0
\(367\) −2.51842 0.916629i −0.131460 0.0478477i 0.275452 0.961315i \(-0.411172\pi\)
−0.406913 + 0.913467i \(0.633395\pi\)
\(368\) −2.37939 + 4.12122i −0.124034 + 0.214833i
\(369\) 0 0
\(370\) 0.195937 + 0.339373i 0.0101863 + 0.0176431i
\(371\) −0.152704 0.866025i −0.00792798 0.0449618i
\(372\) 0 0
\(373\) −22.9008 + 8.33521i −1.18576 + 0.431581i −0.858232 0.513261i \(-0.828437\pi\)
−0.327526 + 0.944842i \(0.606215\pi\)
\(374\) −3.33703 + 18.9252i −0.172554 + 0.978601i
\(375\) 0 0
\(376\) 0.592396 0.497079i 0.0305505 0.0256349i
\(377\) 36.0428 1.85630
\(378\) 0 0
\(379\) −4.08647 −0.209908 −0.104954 0.994477i \(-0.533469\pi\)
−0.104954 + 0.994477i \(0.533469\pi\)
\(380\) 6.11128 5.12797i 0.313502 0.263060i
\(381\) 0 0
\(382\) 3.80154 21.5596i 0.194504 1.10308i
\(383\) −15.4017 + 5.60575i −0.786989 + 0.286440i −0.704084 0.710117i \(-0.748642\pi\)
−0.0829050 + 0.996557i \(0.526420\pi\)
\(384\) 0 0
\(385\) −0.104885 0.594831i −0.00534542 0.0303154i
\(386\) −12.8059 22.1804i −0.651802 1.12895i
\(387\) 0 0
\(388\) 1.71301 2.96702i 0.0869650 0.150628i
\(389\) −26.2263 9.54558i −1.32972 0.483980i −0.423163 0.906054i \(-0.639080\pi\)
−0.906562 + 0.422073i \(0.861302\pi\)
\(390\) 0 0
\(391\) 18.8478 + 15.8152i 0.953172 + 0.799807i
\(392\) −5.35117 4.49016i −0.270275 0.226787i
\(393\) 0 0
\(394\) 12.8598 + 4.68058i 0.647867 + 0.235804i
\(395\) 9.42649 16.3272i 0.474298 0.821508i
\(396\) 0 0
\(397\) 16.2469 + 28.1405i 0.815409 + 1.41233i 0.909034 + 0.416722i \(0.136821\pi\)
−0.0936247 + 0.995608i \(0.529845\pi\)
\(398\) −2.15317 12.2112i −0.107929 0.612094i
\(399\) 0 0
\(400\) 2.99273 1.08926i 0.149636 0.0544632i
\(401\) −2.67096 + 15.1478i −0.133381 + 0.756443i 0.842592 + 0.538553i \(0.181029\pi\)
−0.975973 + 0.217891i \(0.930082\pi\)
\(402\) 0 0
\(403\) 23.4217 19.6532i 1.16672 0.978994i
\(404\) −8.61856 −0.428789
\(405\) 0 0
\(406\) 0.716881 0.0355782
\(407\) −0.828163 + 0.694911i −0.0410505 + 0.0344455i
\(408\) 0 0
\(409\) −1.65822 + 9.40425i −0.0819938 + 0.465010i 0.915971 + 0.401244i \(0.131422\pi\)
−0.997965 + 0.0637658i \(0.979689\pi\)
\(410\) −7.34389 + 2.67296i −0.362689 + 0.132008i
\(411\) 0 0
\(412\) −0.379385 2.15160i −0.0186910 0.106002i
\(413\) 0.0898700 + 0.155659i 0.00442222 + 0.00765950i
\(414\) 0 0
\(415\) 1.59627 2.76481i 0.0783576 0.135719i
\(416\) 5.69846 + 2.07407i 0.279390 + 0.101690i
\(417\) 0 0
\(418\) 16.8596 + 14.1469i 0.824631 + 0.691948i
\(419\) 26.0239 + 21.8367i 1.27135 + 1.06679i 0.994375 + 0.105915i \(0.0337771\pi\)
0.276977 + 0.960876i \(0.410667\pi\)
\(420\) 0 0
\(421\) 11.8229 + 4.30320i 0.576215 + 0.209725i 0.613656 0.789574i \(-0.289698\pi\)
−0.0374406 + 0.999299i \(0.511920\pi\)
\(422\) −7.42127 + 12.8540i −0.361262 + 0.625724i
\(423\) 0 0
\(424\) −3.64543 6.31407i −0.177038 0.306638i
\(425\) −2.85932 16.2160i −0.138697 0.786591i
\(426\) 0 0
\(427\) −0.428548 + 0.155979i −0.0207389 + 0.00754834i
\(428\) 1.78699 10.1345i 0.0863774 0.489870i
\(429\) 0 0
\(430\) −0.467911 + 0.392624i −0.0225647 + 0.0189340i
\(431\) 7.77601 0.374557 0.187279 0.982307i \(-0.440033\pi\)
0.187279 + 0.982307i \(0.440033\pi\)
\(432\) 0 0
\(433\) −40.6536 −1.95369 −0.976845 0.213950i \(-0.931367\pi\)
−0.976845 + 0.213950i \(0.931367\pi\)
\(434\) 0.465852 0.390896i 0.0223616 0.0187636i
\(435\) 0 0
\(436\) −1.92602 + 10.9230i −0.0922397 + 0.523117i
\(437\) 26.4786 9.63744i 1.26665 0.461021i
\(438\) 0 0
\(439\) −3.07280 17.4267i −0.146657 0.831731i −0.966022 0.258459i \(-0.916785\pi\)
0.819366 0.573271i \(-0.194326\pi\)
\(440\) −2.50387 4.33683i −0.119367 0.206750i
\(441\) 0 0
\(442\) 15.6766 27.1527i 0.745662 1.29152i
\(443\) 13.5086 + 4.91673i 0.641814 + 0.233601i 0.642365 0.766399i \(-0.277953\pi\)
−0.000551343 1.00000i \(0.500175\pi\)
\(444\) 0 0
\(445\) −2.23989 1.87949i −0.106181 0.0890962i
\(446\) −5.15657 4.32688i −0.244171 0.204884i
\(447\) 0 0
\(448\) 0.113341 + 0.0412527i 0.00535485 + 0.00194901i
\(449\) 13.9859 24.2243i 0.660036 1.14322i −0.320569 0.947225i \(-0.603874\pi\)
0.980606 0.195991i \(-0.0627925\pi\)
\(450\) 0 0
\(451\) −10.7802 18.6718i −0.507619 0.879222i
\(452\) −1.02869 5.83396i −0.0483853 0.274407i
\(453\) 0 0
\(454\) 13.6211 4.95767i 0.639269 0.232675i
\(455\) −0.171122 + 0.970481i −0.00802232 + 0.0454968i
\(456\) 0 0
\(457\) 6.53280 5.48167i 0.305592 0.256422i −0.477075 0.878862i \(-0.658303\pi\)
0.782667 + 0.622440i \(0.213859\pi\)
\(458\) 25.7870 1.20495
\(459\) 0 0
\(460\) −6.41147 −0.298937
\(461\) −16.6361 + 13.9593i −0.774820 + 0.650151i −0.941938 0.335785i \(-0.890998\pi\)
0.167118 + 0.985937i \(0.446554\pi\)
\(462\) 0 0
\(463\) −3.43882 + 19.5025i −0.159815 + 0.906358i 0.794435 + 0.607349i \(0.207767\pi\)
−0.954250 + 0.299009i \(0.903344\pi\)
\(464\) 5.58512 2.03282i 0.259283 0.0943712i
\(465\) 0 0
\(466\) −1.80541 10.2390i −0.0836339 0.474311i
\(467\) 18.4927 + 32.0303i 0.855741 + 1.48219i 0.875956 + 0.482392i \(0.160232\pi\)
−0.0202143 + 0.999796i \(0.506435\pi\)
\(468\) 0 0
\(469\) −0.400330 + 0.693392i −0.0184855 + 0.0320178i
\(470\) 0.979055 + 0.356347i 0.0451605 + 0.0164371i
\(471\) 0 0
\(472\) 1.14156 + 0.957882i 0.0525445 + 0.0440901i
\(473\) −1.29086 1.08316i −0.0593538 0.0498037i
\(474\) 0 0
\(475\) −17.7208 6.44983i −0.813084 0.295938i
\(476\) 0.311804 0.540060i 0.0142915 0.0247536i
\(477\) 0 0
\(478\) −11.4572 19.8445i −0.524042 0.907667i
\(479\) 1.97131 + 11.1799i 0.0900717 + 0.510822i 0.996147 + 0.0877044i \(0.0279531\pi\)
−0.906075 + 0.423117i \(0.860936\pi\)
\(480\) 0 0
\(481\) 1.65745 0.603263i 0.0755733 0.0275064i
\(482\) −2.09714 + 11.8935i −0.0955223 + 0.541734i
\(483\) 0 0
\(484\) 2.15657 1.80958i 0.0980261 0.0822537i
\(485\) 4.61587 0.209596
\(486\) 0 0
\(487\) 1.13785 0.0515610 0.0257805 0.999668i \(-0.491793\pi\)
0.0257805 + 0.999668i \(0.491793\pi\)
\(488\) −2.89646 + 2.43042i −0.131117 + 0.110020i
\(489\) 0 0
\(490\) 1.63429 9.26849i 0.0738295 0.418708i
\(491\) −14.3880 + 5.23680i −0.649322 + 0.236334i −0.645619 0.763659i \(-0.723401\pi\)
−0.00370223 + 0.999993i \(0.501178\pi\)
\(492\) 0 0
\(493\) −5.33615 30.2628i −0.240328 1.36297i
\(494\) −17.9538 31.0969i −0.807781 1.39912i
\(495\) 0 0
\(496\) 2.52094 4.36640i 0.113194 0.196057i
\(497\) −0.651055 0.236965i −0.0292038 0.0106293i
\(498\) 0 0
\(499\) 1.77584 + 1.49011i 0.0794977 + 0.0667065i 0.681671 0.731659i \(-0.261254\pi\)
−0.602173 + 0.798366i \(0.705698\pi\)
\(500\) 8.44743 + 7.08824i 0.377781 + 0.316996i
\(501\) 0 0
\(502\) −13.1998 4.80434i −0.589136 0.214428i
\(503\) 4.02869 6.97789i 0.179630 0.311129i −0.762124 0.647431i \(-0.775843\pi\)
0.941754 + 0.336303i \(0.109177\pi\)
\(504\) 0 0
\(505\) −5.80587 10.0561i −0.258358 0.447489i
\(506\) −3.07145 17.4191i −0.136543 0.774372i
\(507\) 0 0
\(508\) 5.39306 1.96291i 0.239278 0.0870901i
\(509\) −1.24944 + 7.08591i −0.0553803 + 0.314077i −0.999896 0.0143875i \(-0.995420\pi\)
0.944516 + 0.328465i \(0.106531\pi\)
\(510\) 0 0
\(511\) −0.962697 + 0.807798i −0.0425872 + 0.0357349i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −18.1429 −0.800249
\(515\) 2.25490 1.89209i 0.0993628 0.0833753i
\(516\) 0 0
\(517\) −0.499123 + 2.83067i −0.0219514 + 0.124493i
\(518\) 0.0329662 0.0119987i 0.00144845 0.000527194i
\(519\) 0 0
\(520\) 1.41875 + 8.04612i 0.0622162 + 0.352846i
\(521\) 4.84343 + 8.38906i 0.212194 + 0.367531i 0.952401 0.304848i \(-0.0986057\pi\)
−0.740207 + 0.672379i \(0.765272\pi\)
\(522\) 0 0
\(523\) −7.29339 + 12.6325i −0.318917 + 0.552381i −0.980262 0.197701i \(-0.936653\pi\)
0.661345 + 0.750082i \(0.269986\pi\)
\(524\) 16.1814 + 5.88954i 0.706887 + 0.257286i
\(525\) 0 0
\(526\) −3.27379 2.74703i −0.142744 0.119776i
\(527\) −19.9691 16.7561i −0.869867 0.729905i
\(528\) 0 0
\(529\) 0.332748 + 0.121111i 0.0144673 + 0.00526568i
\(530\) 4.91147 8.50692i 0.213341 0.369517i
\(531\) 0 0
\(532\) −0.357097 0.618509i −0.0154821 0.0268158i
\(533\) 6.10829 + 34.6418i 0.264579 + 1.50050i
\(534\) 0 0
\(535\) 13.0287 4.74205i 0.563279 0.205017i
\(536\) −1.15270 + 6.53731i −0.0497892 + 0.282369i
\(537\) 0 0
\(538\) −10.0057 + 8.39576i −0.431376 + 0.361967i
\(539\) 25.9641 1.11835
\(540\) 0 0
\(541\) 23.9786 1.03092 0.515461 0.856913i \(-0.327621\pi\)
0.515461 + 0.856913i \(0.327621\pi\)
\(542\) 6.50181 5.45567i 0.279277 0.234341i
\(543\) 0 0
\(544\) 0.897804 5.09170i 0.0384930 0.218305i
\(545\) −14.0424 + 5.11100i −0.601508 + 0.218931i
\(546\) 0 0
\(547\) 6.94269 + 39.3739i 0.296848 + 1.68351i 0.659596 + 0.751620i \(0.270727\pi\)
−0.362748 + 0.931887i \(0.618161\pi\)
\(548\) 0.0432332 + 0.0748822i 0.00184683 + 0.00319881i
\(549\) 0 0
\(550\) −5.91875 + 10.2516i −0.252376 + 0.437129i
\(551\) −33.0710 12.0369i −1.40887 0.512788i
\(552\) 0 0
\(553\) −1.29292 1.08489i −0.0549805 0.0461341i
\(554\) 5.06624 + 4.25108i 0.215244 + 0.180611i
\(555\) 0 0
\(556\) 17.2554 + 6.28044i 0.731791 + 0.266350i
\(557\) 1.17958 2.04309i 0.0499803 0.0865685i −0.839953 0.542659i \(-0.817417\pi\)
0.889933 + 0.456091i \(0.150751\pi\)
\(558\) 0 0
\(559\) 1.37464 + 2.38094i 0.0581410 + 0.100703i
\(560\) 0.0282185 + 0.160035i 0.00119245 + 0.00676271i
\(561\) 0 0
\(562\) 27.9320 10.1664i 1.17824 0.428845i
\(563\) 7.55825 42.8650i 0.318542 1.80654i −0.233090 0.972455i \(-0.574884\pi\)
0.551632 0.834087i \(-0.314005\pi\)
\(564\) 0 0
\(565\) 6.11406 5.13030i 0.257220 0.215833i
\(566\) −2.81521 −0.118332
\(567\) 0 0
\(568\) −5.74422 −0.241022
\(569\) −11.2187 + 9.41360i −0.470312 + 0.394639i −0.846908 0.531739i \(-0.821539\pi\)
0.376596 + 0.926377i \(0.377094\pi\)
\(570\) 0 0
\(571\) −2.57145 + 14.5834i −0.107612 + 0.610297i 0.882533 + 0.470251i \(0.155836\pi\)
−0.990145 + 0.140047i \(0.955275\pi\)
\(572\) −21.1805 + 7.70908i −0.885602 + 0.322333i
\(573\) 0 0
\(574\) 0.121492 + 0.689016i 0.00507098 + 0.0287590i
\(575\) 7.57785 + 13.1252i 0.316018 + 0.547359i
\(576\) 0 0
\(577\) 16.0706 27.8351i 0.669027 1.15879i −0.309150 0.951013i \(-0.600044\pi\)
0.978177 0.207775i \(-0.0666222\pi\)
\(578\) −9.14455 3.32834i −0.380363 0.138441i
\(579\) 0 0
\(580\) 6.13429 + 5.14728i 0.254712 + 0.213729i
\(581\) −0.218941 0.183713i −0.00908320 0.00762171i
\(582\) 0 0
\(583\) 25.4650 + 9.26849i 1.05465 + 0.383862i
\(584\) −5.20961 + 9.02330i −0.215575 + 0.373387i
\(585\) 0 0
\(586\) 4.91787 + 8.51800i 0.203155 + 0.351875i
\(587\) −4.75918 26.9907i −0.196432 1.11402i −0.910364 0.413808i \(-0.864198\pi\)
0.713932 0.700215i \(-0.246913\pi\)
\(588\) 0 0
\(589\) −28.0540 + 10.2108i −1.15594 + 0.420729i
\(590\) −0.348641 + 1.97724i −0.0143533 + 0.0814016i
\(591\) 0 0
\(592\) 0.222811 0.186961i 0.00915748 0.00768404i
\(593\) −36.2377 −1.48810 −0.744052 0.668121i \(-0.767099\pi\)
−0.744052 + 0.668121i \(0.767099\pi\)
\(594\) 0 0
\(595\) 0.840185 0.0344442
\(596\) 3.75490 3.15074i 0.153807 0.129059i
\(597\) 0 0
\(598\) −5.01114 + 28.4196i −0.204921 + 1.16216i
\(599\) 43.2438 15.7395i 1.76689 0.643097i 0.766895 0.641772i \(-0.221801\pi\)
0.999999 0.00132449i \(-0.000421598\pi\)
\(600\) 0 0
\(601\) 0.294673 + 1.67118i 0.0120200 + 0.0681687i 0.990228 0.139460i \(-0.0445366\pi\)
−0.978208 + 0.207628i \(0.933425\pi\)
\(602\) 0.0273411 + 0.0473563i 0.00111434 + 0.00193010i
\(603\) 0 0
\(604\) −0.865715 + 1.49946i −0.0352254 + 0.0610122i
\(605\) 3.56418 + 1.29725i 0.144904 + 0.0527409i
\(606\) 0 0
\(607\) −10.7779 9.04374i −0.437462 0.367074i 0.397297 0.917690i \(-0.369948\pi\)
−0.834758 + 0.550616i \(0.814393\pi\)
\(608\) −4.53596 3.80612i −0.183957 0.154359i
\(609\) 0 0
\(610\) −4.78699 1.74232i −0.193820 0.0705445i
\(611\) 2.34477 4.06126i 0.0948592 0.164301i
\(612\) 0 0
\(613\) 12.8314 + 22.2246i 0.518256 + 0.897645i 0.999775 + 0.0212096i \(0.00675172\pi\)
−0.481520 + 0.876435i \(0.659915\pi\)
\(614\) 2.35504 + 13.3561i 0.0950416 + 0.539007i
\(615\) 0 0
\(616\) −0.421274 + 0.153331i −0.0169736 + 0.00617789i
\(617\) −5.46822 + 31.0118i −0.220142 + 1.24849i 0.651615 + 0.758550i \(0.274092\pi\)
−0.871757 + 0.489938i \(0.837019\pi\)
\(618\) 0 0
\(619\) −2.42674 + 2.03627i −0.0975388 + 0.0818448i −0.690253 0.723568i \(-0.742501\pi\)
0.592714 + 0.805413i \(0.298056\pi\)
\(620\) 6.79292 0.272810
\(621\) 0 0
\(622\) 10.5767 0.424086
\(623\) −0.200522 + 0.168258i −0.00803376 + 0.00674113i
\(624\) 0 0
\(625\) 0.185259 1.05066i 0.00741037 0.0420263i
\(626\) 10.0544 3.65949i 0.401854 0.146263i
\(627\) 0 0
\(628\) −1.00980 5.72686i −0.0402954 0.228527i
\(629\) −0.751907 1.30234i −0.0299805 0.0519277i
\(630\) 0 0
\(631\) −11.2961 + 19.5654i −0.449690 + 0.778885i −0.998366 0.0571498i \(-0.981799\pi\)
0.548676 + 0.836035i \(0.315132\pi\)
\(632\) −13.1493 4.78595i −0.523051 0.190375i
\(633\) 0 0
\(634\) −22.3537 18.7570i −0.887779 0.744935i
\(635\) 5.92333 + 4.97027i 0.235060 + 0.197239i
\(636\) 0 0
\(637\) −39.8063 14.4883i −1.57718 0.574048i
\(638\) −11.0458 + 19.1318i −0.437306 + 0.757436i
\(639\) 0 0
\(640\) 0.673648 + 1.16679i 0.0266283 + 0.0461215i
\(641\) 3.04323 + 17.2590i 0.120200 + 0.681691i 0.984043 + 0.177929i \(0.0569398\pi\)
−0.863843 + 0.503761i \(0.831949\pi\)
\(642\) 0 0
\(643\) 26.4923 9.64241i 1.04475 0.380260i 0.238074 0.971247i \(-0.423484\pi\)
0.806681 + 0.590987i \(0.201262\pi\)
\(644\) −0.0996702 + 0.565258i −0.00392756 + 0.0222743i
\(645\) 0 0
\(646\) −23.4520 + 19.6786i −0.922707 + 0.774243i
\(647\) −32.3492 −1.27178 −0.635888 0.771781i \(-0.719366\pi\)
−0.635888 + 0.771781i \(0.719366\pi\)
\(648\) 0 0
\(649\) −5.53890 −0.217421
\(650\) 14.7947 12.4143i 0.580297 0.486927i
\(651\) 0 0
\(652\) −0.470437 + 2.66798i −0.0184237 + 0.104486i
\(653\) −25.9329 + 9.43880i −1.01483 + 0.369369i −0.795287 0.606234i \(-0.792680\pi\)
−0.219546 + 0.975602i \(0.570457\pi\)
\(654\) 0 0
\(655\) 4.02869 + 22.8478i 0.157414 + 0.892738i
\(656\) 2.90033 + 5.02352i 0.113239 + 0.196135i
\(657\) 0 0
\(658\) 0.0466368 0.0807773i 0.00181809 0.00314903i
\(659\) −4.90508 1.78530i −0.191075 0.0695455i 0.244711 0.969596i \(-0.421307\pi\)
−0.435785 + 0.900051i \(0.643529\pi\)
\(660\) 0 0
\(661\) −36.7294 30.8196i −1.42861 1.19875i −0.946529 0.322618i \(-0.895437\pi\)
−0.482080 0.876127i \(-0.660119\pi\)
\(662\) −5.59105 4.69145i −0.217302 0.182338i
\(663\) 0 0
\(664\) −2.22668 0.810446i −0.0864120 0.0314514i
\(665\) 0.481115 0.833315i 0.0186568 0.0323146i
\(666\) 0 0
\(667\) 14.1420 + 24.4947i 0.547581 + 0.948439i
\(668\) 4.27244 + 24.2302i 0.165306 + 0.937495i
\(669\) 0 0
\(670\) −8.40420 + 3.05888i −0.324683 + 0.118175i
\(671\) 2.44041 13.8402i 0.0942109 0.534297i
\(672\) 0 0
\(673\) −8.51960 + 7.14879i −0.328406 + 0.275566i −0.792050 0.610456i \(-0.790986\pi\)
0.463644 + 0.886022i \(0.346542\pi\)
\(674\) −1.62361 −0.0625390
\(675\) 0 0
\(676\) 23.7743 0.914394
\(677\) 36.9550 31.0089i 1.42030 1.19177i 0.469115 0.883137i \(-0.344573\pi\)
0.951181 0.308633i \(-0.0998716\pi\)
\(678\) 0 0
\(679\) 0.0717564 0.406951i 0.00275376 0.0156173i
\(680\) 6.54576 2.38246i 0.251018 0.0913632i
\(681\) 0 0
\(682\) 3.25418 + 18.4554i 0.124609 + 0.706694i
\(683\) 6.60401 + 11.4385i 0.252695 + 0.437681i 0.964267 0.264932i \(-0.0853496\pi\)
−0.711572 + 0.702614i \(0.752016\pi\)
\(684\) 0 0
\(685\) −0.0582480 + 0.100888i −0.00222554 + 0.00385475i
\(686\) −1.58512 0.576937i −0.0605203 0.0220276i
\(687\) 0 0
\(688\) 0.347296 + 0.291416i 0.0132405 + 0.0111101i
\(689\) −33.8692 28.4196i −1.29031 1.08270i
\(690\) 0 0
\(691\) 9.37211 + 3.41117i 0.356532 + 0.129767i 0.514075 0.857745i \(-0.328135\pi\)
−0.157543 + 0.987512i \(0.550357\pi\)
\(692\) −5.36097 + 9.28547i −0.203793 + 0.352980i
\(693\) 0 0
\(694\) −2.73442 4.73616i −0.103797 0.179782i
\(695\) 4.29607 + 24.3642i 0.162959 + 0.924189i
\(696\) 0 0
\(697\) 28.1822 10.2575i 1.06748 0.388529i
\(698\) 0.538019 3.05126i 0.0203643 0.115492i
\(699\) 0 0
\(700\) 0.294263 0.246916i 0.0111221 0.00933254i
\(701\) −46.7588 −1.76605 −0.883027 0.469322i \(-0.844498\pi\)
−0.883027 + 0.469322i \(0.844498\pi\)
\(702\) 0 0
\(703\) −1.72226 −0.0649562
\(704\) −2.84730 + 2.38917i −0.107312 + 0.0900451i
\(705\) 0 0
\(706\) −0.0530334 + 0.300767i −0.00199594 + 0.0113195i
\(707\) −0.976834 + 0.355538i −0.0367376 + 0.0133714i
\(708\) 0 0
\(709\) −6.56907 37.2550i −0.246707 1.39914i −0.816496 0.577351i \(-0.804086\pi\)
0.569789 0.821791i \(-0.307025\pi\)
\(710\) −3.86959 6.70232i −0.145223 0.251534i
\(711\) 0 0
\(712\) −1.08512 + 1.87949i −0.0406667 + 0.0704368i
\(713\) 22.5462 + 8.20616i 0.844363 + 0.307323i
\(714\) 0 0
\(715\) −23.2631 19.5201i −0.869991 0.730009i
\(716\) 10.6061 + 8.89955i 0.396367 + 0.332592i
\(717\) 0 0
\(718\) 9.93242 + 3.61510i 0.370675 + 0.134915i
\(719\) 1.65048 2.85872i 0.0615526 0.106612i −0.833607 0.552358i \(-0.813728\pi\)
0.895160 + 0.445746i \(0.147061\pi\)
\(720\) 0 0
\(721\) −0.131759 0.228213i −0.00490697 0.00849911i
\(722\) 2.78905 + 15.8175i 0.103798 + 0.588666i
\(723\) 0 0
\(724\) −3.29813 + 1.20042i −0.122574 + 0.0446133i
\(725\) 3.28699 18.6414i 0.122076 0.692326i
\(726\) 0 0
\(727\) −16.0548 + 13.4716i −0.595441 + 0.499635i −0.889977 0.456006i \(-0.849280\pi\)
0.294535 + 0.955641i \(0.404835\pi\)
\(728\) 0.731429 0.0271086
\(729\) 0 0
\(730\) −14.0378 −0.519561
\(731\) 1.79561 1.50669i 0.0664129 0.0557271i
\(732\) 0 0
\(733\) −3.11943 + 17.6912i −0.115219 + 0.653439i 0.871423 + 0.490533i \(0.163198\pi\)
−0.986642 + 0.162906i \(0.947913\pi\)
\(734\) −2.51842 + 0.916629i −0.0929565 + 0.0338334i
\(735\) 0 0
\(736\) 0.826352 + 4.68647i 0.0304597 + 0.172746i
\(737\) −12.3366 21.3677i −0.454425 0.787088i
\(738\) 0 0
\(739\) 19.6630 34.0573i 0.723314 1.25282i −0.236350 0.971668i \(-0.575951\pi\)
0.959664 0.281149i \(-0.0907154\pi\)
\(740\) 0.368241 + 0.134029i 0.0135368 + 0.00492699i
\(741\) 0 0
\(742\) −0.673648 0.565258i −0.0247304 0.0207513i
\(743\) 35.7957 + 30.0361i 1.31322 + 1.10192i 0.987696 + 0.156383i \(0.0499835\pi\)
0.325519 + 0.945535i \(0.394461\pi\)
\(744\) 0 0
\(745\) 6.20574 + 2.25870i 0.227361 + 0.0827525i
\(746\) −12.1853 + 21.1055i −0.446134 + 0.772727i
\(747\) 0 0
\(748\) 9.60859 + 16.6426i 0.351325 + 0.608513i
\(749\) −0.215537 1.22237i −0.00787556 0.0446645i
\(750\) 0 0
\(751\) 31.3184 11.3990i 1.14282 0.415954i 0.299891 0.953973i \(-0.403050\pi\)
0.842932 + 0.538020i \(0.180827\pi\)
\(752\) 0.134285 0.761570i 0.00489688 0.0277716i
\(753\) 0 0
\(754\) 27.6104 23.1679i 1.00551 0.843724i
\(755\) −2.33275 −0.0848974
\(756\) 0 0
\(757\) 32.3354 1.17525 0.587626 0.809133i \(-0.300063\pi\)
0.587626 + 0.809133i \(0.300063\pi\)
\(758\) −3.13041 + 2.62673i −0.113702 + 0.0954071i
\(759\) 0 0
\(760\) 1.38532 7.85651i 0.0502507 0.284986i
\(761\) 1.81521 0.660681i 0.0658012 0.0239497i −0.308910 0.951091i \(-0.599964\pi\)
0.374711 + 0.927142i \(0.377742\pi\)
\(762\) 0 0
\(763\) 0.232307 + 1.31748i 0.00841007 + 0.0476959i
\(764\) −10.9461 18.9592i −0.396016 0.685919i
\(765\) 0 0
\(766\) −8.19506 + 14.1943i −0.296100 + 0.512859i
\(767\) 8.49185 + 3.09078i 0.306623 + 0.111602i
\(768\) 0 0
\(769\) −3.66179 3.07261i −0.132047 0.110801i 0.574372 0.818594i \(-0.305246\pi\)
−0.706419 + 0.707793i \(0.749691\pi\)
\(770\) −0.462697 0.388249i −0.0166744 0.0139915i
\(771\) 0 0
\(772\) −24.0672 8.75973i −0.866196 0.315270i
\(773\) −2.95336 + 5.11538i −0.106225 + 0.183987i −0.914238 0.405177i \(-0.867210\pi\)
0.808013 + 0.589165i \(0.200543\pi\)
\(774\) 0 0
\(775\) −8.02869 13.9061i −0.288399 0.499522i
\(776\) −0.594922 3.37397i −0.0213565 0.121119i
\(777\) 0 0
\(778\) −26.2263 + 9.54558i −0.940257 + 0.342226i
\(779\) 5.96435 33.8255i 0.213695 1.21192i