Properties

Label 169.2.e.b.147.1
Level $169$
Weight $2$
Character 169.147
Analytic conductor $1.349$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [169,2,Mod(23,169)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(169, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("169.23");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 169 = 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 169.e (of order \(6\), degree \(2\), 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: \(1.34947179416\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: 12.0.17213603549184.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 5x^{10} + 19x^{8} - 28x^{6} + 31x^{4} - 6x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 147.1
Root \(1.07992 - 0.623490i\) of defining polynomial
Character \(\chi\) \(=\) 169.147
Dual form 169.2.e.b.23.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.94594 - 1.12349i) q^{2} +(0.277479 - 0.480608i) q^{3} +(1.52446 + 2.64044i) q^{4} +1.44504i q^{5} +(-1.07992 + 0.623490i) q^{6} +(1.77441 - 1.02446i) q^{7} -2.35690i q^{8} +(1.34601 + 2.33136i) q^{9} +O(q^{10})\) \(q+(-1.94594 - 1.12349i) q^{2} +(0.277479 - 0.480608i) q^{3} +(1.52446 + 2.64044i) q^{4} +1.44504i q^{5} +(-1.07992 + 0.623490i) q^{6} +(1.77441 - 1.02446i) q^{7} -2.35690i q^{8} +(1.34601 + 2.33136i) q^{9} +(1.62349 - 2.81197i) q^{10} +(2.21266 + 1.27748i) q^{11} +1.69202 q^{12} -4.60388 q^{14} +(0.694498 + 0.400969i) q^{15} +(0.400969 - 0.694498i) q^{16} +(-2.64795 - 4.58638i) q^{17} -6.04892i q^{18} +(5.06699 - 2.92543i) q^{19} +(-3.81555 + 2.20291i) q^{20} -1.13706i q^{21} +(-2.87047 - 4.97180i) q^{22} +(-0.945042 + 1.63686i) q^{23} +(-1.13274 - 0.653989i) q^{24} +2.91185 q^{25} +3.15883 q^{27} +(5.41004 + 3.12349i) q^{28} +(-1.13437 + 1.96480i) q^{29} +(-0.900969 - 1.56052i) q^{30} +4.26875i q^{31} +(-5.64279 + 3.25786i) q^{32} +(1.22793 - 0.708947i) q^{33} +11.8998i q^{34} +(1.48039 + 2.56410i) q^{35} +(-4.10388 + 7.10812i) q^{36} +(-4.63921 - 2.67845i) q^{37} -13.1468 q^{38} +3.40581 q^{40} +(1.10343 + 0.637063i) q^{41} +(-1.27748 + 2.21266i) q^{42} +(3.06853 + 5.31485i) q^{43} +7.78986i q^{44} +(-3.36891 + 1.94504i) q^{45} +(3.67799 - 2.12349i) q^{46} -2.95108i q^{47} +(-0.222521 - 0.385418i) q^{48} +(-1.40097 + 2.42655i) q^{49} +(-5.66630 - 3.27144i) q^{50} -2.93900 q^{51} +5.52111 q^{53} +(-6.14691 - 3.54892i) q^{54} +(-1.84601 + 3.19738i) q^{55} +(-2.41454 - 4.18211i) q^{56} -3.24698i q^{57} +(4.41485 - 2.54892i) q^{58} +(-10.5722 + 6.10388i) q^{59} +2.44504i q^{60} +(-4.28232 - 7.41720i) q^{61} +(4.79590 - 8.30674i) q^{62} +(4.77676 + 2.75786i) q^{63} +13.0368 q^{64} -3.18598 q^{66} +(0.499461 + 0.288364i) q^{67} +(8.07338 - 13.9835i) q^{68} +(0.524459 + 0.908389i) q^{69} -6.65279i q^{70} +(3.97868 - 2.29709i) q^{71} +(5.49477 - 3.17241i) q^{72} -10.5526i q^{73} +(6.01842 + 10.4242i) q^{74} +(0.807979 - 1.39946i) q^{75} +(15.4488 + 8.91939i) q^{76} +5.23490 q^{77} -15.7778 q^{79} +(1.00358 + 0.579417i) q^{80} +(-3.16152 + 5.47592i) q^{81} +(-1.43147 - 2.47938i) q^{82} -7.72348i q^{83} +(3.00235 - 1.73341i) q^{84} +(6.62751 - 3.82640i) q^{85} -13.7899i q^{86} +(0.629531 + 1.09038i) q^{87} +(3.01089 - 5.21501i) q^{88} +(-5.72751 - 3.30678i) q^{89} +8.74094 q^{90} -5.76271 q^{92} +(2.05159 + 1.18449i) q^{93} +(-3.31551 + 5.74263i) q^{94} +(4.22737 + 7.32201i) q^{95} +3.61596i q^{96} +(-10.3290 + 5.96346i) q^{97} +(5.45241 - 3.14795i) q^{98} +6.87800i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 4 q^{3} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 4 q^{3} + 6 q^{9} + 10 q^{10} - 20 q^{14} - 4 q^{16} - 4 q^{17} - 6 q^{22} - 10 q^{23} + 20 q^{25} + 4 q^{27} + 2 q^{29} - 2 q^{30} - 8 q^{35} - 14 q^{36} - 48 q^{38} - 12 q^{40} - 16 q^{42} + 26 q^{43} - 2 q^{48} - 8 q^{49} + 4 q^{51} + 4 q^{53} - 12 q^{55} - 8 q^{56} - 8 q^{61} + 2 q^{62} + 44 q^{64} + 20 q^{66} + 42 q^{68} - 12 q^{69} + 16 q^{74} + 30 q^{75} - 32 q^{77} - 20 q^{79} + 2 q^{81} - 28 q^{82} + 36 q^{87} + 30 q^{88} + 48 q^{90} - 10 q^{94} + 6 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/169\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.94594 1.12349i −1.37599 0.794427i −0.384315 0.923202i \(-0.625562\pi\)
−0.991674 + 0.128775i \(0.958896\pi\)
\(3\) 0.277479 0.480608i 0.160203 0.277479i −0.774739 0.632282i \(-0.782119\pi\)
0.934941 + 0.354803i \(0.115452\pi\)
\(4\) 1.52446 + 2.64044i 0.762229 + 1.32022i
\(5\) 1.44504i 0.646242i 0.946358 + 0.323121i \(0.104732\pi\)
−0.946358 + 0.323121i \(0.895268\pi\)
\(6\) −1.07992 + 0.623490i −0.440874 + 0.254539i
\(7\) 1.77441 1.02446i 0.670666 0.387209i −0.125663 0.992073i \(-0.540106\pi\)
0.796329 + 0.604864i \(0.206773\pi\)
\(8\) 2.35690i 0.833289i
\(9\) 1.34601 + 2.33136i 0.448670 + 0.777120i
\(10\) 1.62349 2.81197i 0.513393 0.889222i
\(11\) 2.21266 + 1.27748i 0.667142 + 0.385174i 0.794993 0.606619i \(-0.207475\pi\)
−0.127851 + 0.991793i \(0.540808\pi\)
\(12\) 1.69202 0.488445
\(13\) 0 0
\(14\) −4.60388 −1.23044
\(15\) 0.694498 + 0.400969i 0.179319 + 0.103530i
\(16\) 0.400969 0.694498i 0.100242 0.173625i
\(17\) −2.64795 4.58638i −0.642222 1.11236i −0.984936 0.172921i \(-0.944679\pi\)
0.342714 0.939440i \(-0.388654\pi\)
\(18\) 6.04892i 1.42574i
\(19\) 5.06699 2.92543i 1.16245 0.671139i 0.210558 0.977581i \(-0.432472\pi\)
0.951889 + 0.306442i \(0.0991387\pi\)
\(20\) −3.81555 + 2.20291i −0.853182 + 0.492585i
\(21\) 1.13706i 0.248128i
\(22\) −2.87047 4.97180i −0.611986 1.05999i
\(23\) −0.945042 + 1.63686i −0.197055 + 0.341309i −0.947572 0.319542i \(-0.896471\pi\)
0.750517 + 0.660851i \(0.229804\pi\)
\(24\) −1.13274 0.653989i −0.231220 0.133495i
\(25\) 2.91185 0.582371
\(26\) 0 0
\(27\) 3.15883 0.607918
\(28\) 5.41004 + 3.12349i 1.02240 + 0.590284i
\(29\) −1.13437 + 1.96480i −0.210648 + 0.364853i −0.951918 0.306354i \(-0.900891\pi\)
0.741269 + 0.671208i \(0.234224\pi\)
\(30\) −0.900969 1.56052i −0.164494 0.284911i
\(31\) 4.26875i 0.766690i 0.923605 + 0.383345i \(0.125228\pi\)
−0.923605 + 0.383345i \(0.874772\pi\)
\(32\) −5.64279 + 3.25786i −0.997513 + 0.575915i
\(33\) 1.22793 0.708947i 0.213756 0.123412i
\(34\) 11.8998i 2.04079i
\(35\) 1.48039 + 2.56410i 0.250231 + 0.433413i
\(36\) −4.10388 + 7.10812i −0.683979 + 1.18469i
\(37\) −4.63921 2.67845i −0.762681 0.440334i 0.0675764 0.997714i \(-0.478473\pi\)
−0.830258 + 0.557380i \(0.811807\pi\)
\(38\) −13.1468 −2.13268
\(39\) 0 0
\(40\) 3.40581 0.538506
\(41\) 1.10343 + 0.637063i 0.172326 + 0.0994926i 0.583682 0.811982i \(-0.301611\pi\)
−0.411356 + 0.911475i \(0.634945\pi\)
\(42\) −1.27748 + 2.21266i −0.197119 + 0.341421i
\(43\) 3.06853 + 5.31485i 0.467947 + 0.810507i 0.999329 0.0366246i \(-0.0116606\pi\)
−0.531382 + 0.847132i \(0.678327\pi\)
\(44\) 7.78986i 1.17437i
\(45\) −3.36891 + 1.94504i −0.502208 + 0.289950i
\(46\) 3.67799 2.12349i 0.542290 0.313091i
\(47\) 2.95108i 0.430460i −0.976563 0.215230i \(-0.930950\pi\)
0.976563 0.215230i \(-0.0690501\pi\)
\(48\) −0.222521 0.385418i −0.0321181 0.0556302i
\(49\) −1.40097 + 2.42655i −0.200138 + 0.346650i
\(50\) −5.66630 3.27144i −0.801335 0.462651i
\(51\) −2.93900 −0.411542
\(52\) 0 0
\(53\) 5.52111 0.758382 0.379191 0.925318i \(-0.376202\pi\)
0.379191 + 0.925318i \(0.376202\pi\)
\(54\) −6.14691 3.54892i −0.836488 0.482946i
\(55\) −1.84601 + 3.19738i −0.248916 + 0.431135i
\(56\) −2.41454 4.18211i −0.322657 0.558858i
\(57\) 3.24698i 0.430073i
\(58\) 4.41485 2.54892i 0.579699 0.334689i
\(59\) −10.5722 + 6.10388i −1.37639 + 0.794657i −0.991722 0.128400i \(-0.959016\pi\)
−0.384664 + 0.923057i \(0.625683\pi\)
\(60\) 2.44504i 0.315654i
\(61\) −4.28232 7.41720i −0.548295 0.949675i −0.998392 0.0566953i \(-0.981944\pi\)
0.450096 0.892980i \(-0.351390\pi\)
\(62\) 4.79590 8.30674i 0.609080 1.05496i
\(63\) 4.77676 + 2.75786i 0.601815 + 0.347458i
\(64\) 13.0368 1.62960
\(65\) 0 0
\(66\) −3.18598 −0.392167
\(67\) 0.499461 + 0.288364i 0.0610189 + 0.0352293i 0.530199 0.847873i \(-0.322117\pi\)
−0.469180 + 0.883102i \(0.655451\pi\)
\(68\) 8.07338 13.9835i 0.979041 1.69575i
\(69\) 0.524459 + 0.908389i 0.0631374 + 0.109357i
\(70\) 6.65279i 0.795161i
\(71\) 3.97868 2.29709i 0.472183 0.272615i −0.244970 0.969531i \(-0.578778\pi\)
0.717153 + 0.696916i \(0.245445\pi\)
\(72\) 5.49477 3.17241i 0.647565 0.373872i
\(73\) 10.5526i 1.23508i −0.786538 0.617542i \(-0.788128\pi\)
0.786538 0.617542i \(-0.211872\pi\)
\(74\) 6.01842 + 10.4242i 0.699627 + 1.21179i
\(75\) 0.807979 1.39946i 0.0932973 0.161596i
\(76\) 15.4488 + 8.91939i 1.77210 + 1.02312i
\(77\) 5.23490 0.596572
\(78\) 0 0
\(79\) −15.7778 −1.77514 −0.887569 0.460674i \(-0.847608\pi\)
−0.887569 + 0.460674i \(0.847608\pi\)
\(80\) 1.00358 + 0.579417i 0.112204 + 0.0647808i
\(81\) −3.16152 + 5.47592i −0.351280 + 0.608435i
\(82\) −1.43147 2.47938i −0.158079 0.273801i
\(83\) 7.72348i 0.847762i −0.905718 0.423881i \(-0.860667\pi\)
0.905718 0.423881i \(-0.139333\pi\)
\(84\) 3.00235 1.73341i 0.327583 0.189130i
\(85\) 6.62751 3.82640i 0.718855 0.415031i
\(86\) 13.7899i 1.48700i
\(87\) 0.629531 + 1.09038i 0.0674928 + 0.116901i
\(88\) 3.01089 5.21501i 0.320961 0.555922i
\(89\) −5.72751 3.30678i −0.607115 0.350518i 0.164720 0.986340i \(-0.447328\pi\)
−0.771836 + 0.635822i \(0.780661\pi\)
\(90\) 8.74094 0.921376
\(91\) 0 0
\(92\) −5.76271 −0.600804
\(93\) 2.05159 + 1.18449i 0.212740 + 0.122826i
\(94\) −3.31551 + 5.74263i −0.341969 + 0.592307i
\(95\) 4.22737 + 7.32201i 0.433719 + 0.751223i
\(96\) 3.61596i 0.369052i
\(97\) −10.3290 + 5.96346i −1.04875 + 0.605498i −0.922300 0.386475i \(-0.873693\pi\)
−0.126453 + 0.991973i \(0.540359\pi\)
\(98\) 5.45241 3.14795i 0.550776 0.317991i
\(99\) 6.87800i 0.691265i
\(100\) 4.43900 + 7.68858i 0.443900 + 0.768858i
\(101\) 6.53199 11.3137i 0.649957 1.12576i −0.333175 0.942865i \(-0.608120\pi\)
0.983133 0.182894i \(-0.0585466\pi\)
\(102\) 5.71912 + 3.30194i 0.566278 + 0.326941i
\(103\) −9.16852 −0.903401 −0.451701 0.892170i \(-0.649182\pi\)
−0.451701 + 0.892170i \(0.649182\pi\)
\(104\) 0 0
\(105\) 1.64310 0.160351
\(106\) −10.7437 6.20291i −1.04353 0.602480i
\(107\) 3.44989 5.97538i 0.333513 0.577662i −0.649685 0.760204i \(-0.725099\pi\)
0.983198 + 0.182542i \(0.0584325\pi\)
\(108\) 4.81551 + 8.34071i 0.463373 + 0.802585i
\(109\) 0.121998i 0.0116853i −0.999983 0.00584264i \(-0.998140\pi\)
0.999983 0.00584264i \(-0.00185978\pi\)
\(110\) 7.18446 4.14795i 0.685011 0.395491i
\(111\) −2.57457 + 1.48643i −0.244367 + 0.141085i
\(112\) 1.64310i 0.155259i
\(113\) −3.65399 6.32890i −0.343738 0.595372i 0.641385 0.767219i \(-0.278360\pi\)
−0.985124 + 0.171847i \(0.945027\pi\)
\(114\) −3.64795 + 6.31843i −0.341662 + 0.591775i
\(115\) −2.36533 1.36563i −0.220568 0.127345i
\(116\) −6.91723 −0.642249
\(117\) 0 0
\(118\) 27.4306 2.52519
\(119\) −9.39712 5.42543i −0.861432 0.497348i
\(120\) 0.945042 1.63686i 0.0862701 0.149424i
\(121\) −2.23609 3.87303i −0.203281 0.352094i
\(122\) 19.2446i 1.74232i
\(123\) 0.612355 0.353543i 0.0552142 0.0318779i
\(124\) −11.2714 + 6.50753i −1.01220 + 0.584394i
\(125\) 11.4330i 1.02260i
\(126\) −6.19687 10.7333i −0.552061 0.956197i
\(127\) −9.48523 + 16.4289i −0.841678 + 1.45783i 0.0467971 + 0.998904i \(0.485099\pi\)
−0.888475 + 0.458925i \(0.848235\pi\)
\(128\) −14.0833 8.13102i −1.24480 0.718688i
\(129\) 3.40581 0.299865
\(130\) 0 0
\(131\) 3.25667 0.284536 0.142268 0.989828i \(-0.454560\pi\)
0.142268 + 0.989828i \(0.454560\pi\)
\(132\) 3.74387 + 2.16152i 0.325862 + 0.188136i
\(133\) 5.99396 10.3818i 0.519742 0.900220i
\(134\) −0.647948 1.12228i −0.0559742 0.0969502i
\(135\) 4.56465i 0.392862i
\(136\) −10.8096 + 6.24094i −0.926918 + 0.535156i
\(137\) 0.686108 0.396125i 0.0586181 0.0338432i −0.470405 0.882451i \(-0.655892\pi\)
0.529023 + 0.848608i \(0.322559\pi\)
\(138\) 2.35690i 0.200632i
\(139\) 5.66972 + 9.82024i 0.480899 + 0.832942i 0.999760 0.0219169i \(-0.00697694\pi\)
−0.518861 + 0.854859i \(0.673644\pi\)
\(140\) −4.51357 + 7.81774i −0.381467 + 0.660720i
\(141\) −1.41831 0.818864i −0.119444 0.0689608i
\(142\) −10.3230 −0.866291
\(143\) 0 0
\(144\) 2.15883 0.179903
\(145\) −2.83921 1.63922i −0.235784 0.136130i
\(146\) −11.8557 + 20.5347i −0.981185 + 1.69946i
\(147\) 0.777479 + 1.34663i 0.0641254 + 0.111068i
\(148\) 16.3327i 1.34254i
\(149\) −7.27965 + 4.20291i −0.596372 + 0.344316i −0.767613 0.640914i \(-0.778556\pi\)
0.171241 + 0.985229i \(0.445222\pi\)
\(150\) −3.14456 + 1.81551i −0.256752 + 0.148236i
\(151\) 14.1293i 1.14983i 0.818215 + 0.574913i \(0.194964\pi\)
−0.818215 + 0.574913i \(0.805036\pi\)
\(152\) −6.89493 11.9424i −0.559253 0.968654i
\(153\) 7.12833 12.3466i 0.576292 0.998166i
\(154\) −10.1868 5.88135i −0.820876 0.473933i
\(155\) −6.16852 −0.495468
\(156\) 0 0
\(157\) −9.43296 −0.752832 −0.376416 0.926451i \(-0.622844\pi\)
−0.376416 + 0.926451i \(0.622844\pi\)
\(158\) 30.7026 + 17.7262i 2.44257 + 1.41022i
\(159\) 1.53199 2.65349i 0.121495 0.210435i
\(160\) −4.70775 8.15406i −0.372180 0.644635i
\(161\) 3.87263i 0.305206i
\(162\) 12.3043 7.10388i 0.966715 0.558133i
\(163\) 7.53797 4.35205i 0.590420 0.340879i −0.174844 0.984596i \(-0.555942\pi\)
0.765263 + 0.643717i \(0.222609\pi\)
\(164\) 3.88471i 0.303345i
\(165\) 1.02446 + 1.77441i 0.0797540 + 0.138138i
\(166\) −8.67725 + 15.0294i −0.673485 + 1.16651i
\(167\) 20.6580 + 11.9269i 1.59857 + 0.922933i 0.991764 + 0.128080i \(0.0408815\pi\)
0.606803 + 0.794853i \(0.292452\pi\)
\(168\) −2.67994 −0.206762
\(169\) 0 0
\(170\) −17.1957 −1.31885
\(171\) 13.6404 + 7.87531i 1.04311 + 0.602240i
\(172\) −9.35570 + 16.2045i −0.713365 + 1.23559i
\(173\) −9.42758 16.3291i −0.716766 1.24147i −0.962274 0.272081i \(-0.912288\pi\)
0.245509 0.969394i \(-0.421045\pi\)
\(174\) 2.82908i 0.214472i
\(175\) 5.16684 2.98307i 0.390576 0.225499i
\(176\) 1.77441 1.02446i 0.133752 0.0772215i
\(177\) 6.77479i 0.509224i
\(178\) 7.43027 + 12.8696i 0.556922 + 0.964618i
\(179\) 3.01089 5.21501i 0.225044 0.389788i −0.731289 0.682068i \(-0.761081\pi\)
0.956333 + 0.292280i \(0.0944140\pi\)
\(180\) −10.2715 5.93027i −0.765595 0.442016i
\(181\) 4.77777 0.355129 0.177565 0.984109i \(-0.443178\pi\)
0.177565 + 0.984109i \(0.443178\pi\)
\(182\) 0 0
\(183\) −4.75302 −0.351353
\(184\) 3.85791 + 2.22737i 0.284409 + 0.164204i
\(185\) 3.87047 6.70385i 0.284563 0.492877i
\(186\) −2.66152 4.60989i −0.195152 0.338014i
\(187\) 13.5308i 0.989470i
\(188\) 7.79216 4.49880i 0.568301 0.328109i
\(189\) 5.60508 3.23609i 0.407710 0.235391i
\(190\) 18.9976i 1.37823i
\(191\) −9.21528 15.9613i −0.666795 1.15492i −0.978795 0.204840i \(-0.934333\pi\)
0.312001 0.950082i \(-0.399001\pi\)
\(192\) 3.61745 6.26561i 0.261067 0.452181i
\(193\) −5.24317 3.02715i −0.377412 0.217899i 0.299280 0.954165i \(-0.403254\pi\)
−0.676692 + 0.736267i \(0.736587\pi\)
\(194\) 26.7995 1.92410
\(195\) 0 0
\(196\) −8.54288 −0.610205
\(197\) −9.88611 5.70775i −0.704357 0.406660i 0.104611 0.994513i \(-0.466640\pi\)
−0.808968 + 0.587853i \(0.799973\pi\)
\(198\) 7.72737 13.3842i 0.549160 0.951173i
\(199\) −6.95257 12.0422i −0.492855 0.853650i 0.507111 0.861881i \(-0.330713\pi\)
−0.999966 + 0.00823084i \(0.997380\pi\)
\(200\) 6.86294i 0.485283i
\(201\) 0.277180 0.160030i 0.0195508 0.0112876i
\(202\) −25.4217 + 14.6773i −1.78867 + 1.03269i
\(203\) 4.64848i 0.326259i
\(204\) −4.48039 7.76026i −0.313690 0.543327i
\(205\) −0.920583 + 1.59450i −0.0642963 + 0.111364i
\(206\) 17.8414 + 10.3007i 1.24307 + 0.717687i
\(207\) −5.08815 −0.353651
\(208\) 0 0
\(209\) 14.9487 1.03402
\(210\) −3.19738 1.84601i −0.220640 0.127387i
\(211\) 6.62229 11.4701i 0.455897 0.789638i −0.542842 0.839835i \(-0.682652\pi\)
0.998739 + 0.0501974i \(0.0159850\pi\)
\(212\) 8.41670 + 14.5781i 0.578061 + 1.00123i
\(213\) 2.54958i 0.174694i
\(214\) −13.4266 + 7.75182i −0.917820 + 0.529904i
\(215\) −7.68018 + 4.43416i −0.523784 + 0.302407i
\(216\) 7.44504i 0.506571i
\(217\) 4.37316 + 7.57453i 0.296869 + 0.514193i
\(218\) −0.137063 + 0.237401i −0.00928310 + 0.0160788i
\(219\) −5.07165 2.92812i −0.342710 0.197864i
\(220\) −11.2567 −0.758924
\(221\) 0 0
\(222\) 6.67994 0.448328
\(223\) −6.35241 3.66756i −0.425389 0.245598i 0.271992 0.962300i \(-0.412318\pi\)
−0.697380 + 0.716701i \(0.745651\pi\)
\(224\) −6.67510 + 11.5616i −0.445999 + 0.772492i
\(225\) 3.91939 + 6.78858i 0.261292 + 0.452572i
\(226\) 16.4209i 1.09230i
\(227\) 7.51239 4.33728i 0.498615 0.287875i −0.229526 0.973302i \(-0.573718\pi\)
0.728141 + 0.685427i \(0.240384\pi\)
\(228\) 8.57345 4.94989i 0.567791 0.327814i
\(229\) 13.6866i 0.904439i −0.891907 0.452219i \(-0.850632\pi\)
0.891907 0.452219i \(-0.149368\pi\)
\(230\) 3.06853 + 5.31485i 0.202333 + 0.350451i
\(231\) 1.45257 2.51593i 0.0955724 0.165536i
\(232\) 4.63082 + 2.67360i 0.304028 + 0.175531i
\(233\) 5.08815 0.333336 0.166668 0.986013i \(-0.446699\pi\)
0.166668 + 0.986013i \(0.446699\pi\)
\(234\) 0 0
\(235\) 4.26444 0.278181
\(236\) −32.2338 18.6102i −2.09824 1.21142i
\(237\) −4.37800 + 7.58292i −0.284382 + 0.492564i
\(238\) 12.1908 + 21.1151i 0.790214 + 1.36869i
\(239\) 10.9239i 0.706611i 0.935508 + 0.353305i \(0.114942\pi\)
−0.935508 + 0.353305i \(0.885058\pi\)
\(240\) 0.556945 0.321552i 0.0359506 0.0207561i
\(241\) 10.3186 5.95742i 0.664676 0.383751i −0.129380 0.991595i \(-0.541299\pi\)
0.794056 + 0.607844i \(0.207965\pi\)
\(242\) 10.0489i 0.645969i
\(243\) 6.49276 + 11.2458i 0.416511 + 0.721418i
\(244\) 13.0565 22.6144i 0.835854 1.44774i
\(245\) −3.50647 2.02446i −0.224020 0.129338i
\(246\) −1.58881 −0.101299
\(247\) 0 0
\(248\) 10.0610 0.638874
\(249\) −3.71197 2.14310i −0.235236 0.135814i
\(250\) 12.8448 22.2479i 0.812377 1.40708i
\(251\) 11.1739 + 19.3538i 0.705290 + 1.22160i 0.966587 + 0.256340i \(0.0825167\pi\)
−0.261296 + 0.965259i \(0.584150\pi\)
\(252\) 16.8170i 1.05937i
\(253\) −4.18211 + 2.41454i −0.262927 + 0.151801i
\(254\) 36.9154 21.3131i 2.31628 1.33730i
\(255\) 4.24698i 0.265956i
\(256\) 5.23341 + 9.06453i 0.327088 + 0.566533i
\(257\) −9.33004 + 16.1601i −0.581992 + 1.00804i 0.413251 + 0.910617i \(0.364393\pi\)
−0.995243 + 0.0974228i \(0.968940\pi\)
\(258\) −6.62751 3.82640i −0.412611 0.238221i
\(259\) −10.9758 −0.682005
\(260\) 0 0
\(261\) −6.10752 −0.378046
\(262\) −6.33729 3.65883i −0.391519 0.226043i
\(263\) −7.19955 + 12.4700i −0.443944 + 0.768933i −0.997978 0.0635610i \(-0.979754\pi\)
0.554034 + 0.832494i \(0.313088\pi\)
\(264\) −1.67092 2.89411i −0.102838 0.178120i
\(265\) 7.97823i 0.490099i
\(266\) −23.3278 + 13.4683i −1.43032 + 0.825795i
\(267\) −3.17853 + 1.83513i −0.194523 + 0.112308i
\(268\) 1.75840i 0.107411i
\(269\) −0.326396 0.565335i −0.0199007 0.0344691i 0.855904 0.517136i \(-0.173002\pi\)
−0.875804 + 0.482666i \(0.839668\pi\)
\(270\) 5.12833 8.88254i 0.312100 0.540574i
\(271\) 1.72832 + 0.997844i 0.104988 + 0.0606147i 0.551574 0.834126i \(-0.314027\pi\)
−0.446587 + 0.894740i \(0.647361\pi\)
\(272\) −4.24698 −0.257511
\(273\) 0 0
\(274\) −1.78017 −0.107544
\(275\) 6.44294 + 3.71983i 0.388524 + 0.224314i
\(276\) −1.59903 + 2.76960i −0.0962504 + 0.166711i
\(277\) 5.89224 + 10.2057i 0.354030 + 0.613199i 0.986952 0.161018i \(-0.0514776\pi\)
−0.632921 + 0.774216i \(0.718144\pi\)
\(278\) 25.4795i 1.52816i
\(279\) −9.95199 + 5.74578i −0.595810 + 0.343991i
\(280\) 6.04332 3.48911i 0.361158 0.208514i
\(281\) 6.47219i 0.386098i −0.981189 0.193049i \(-0.938162\pi\)
0.981189 0.193049i \(-0.0618377\pi\)
\(282\) 1.83997 + 3.18692i 0.109569 + 0.189778i
\(283\) 3.29052 5.69935i 0.195601 0.338791i −0.751496 0.659737i \(-0.770668\pi\)
0.947097 + 0.320946i \(0.104001\pi\)
\(284\) 12.1307 + 7.00365i 0.719823 + 0.415590i
\(285\) 4.69202 0.277931
\(286\) 0 0
\(287\) 2.61058 0.154098
\(288\) −15.1905 8.77024i −0.895109 0.516791i
\(289\) −5.52326 + 9.56657i −0.324898 + 0.562739i
\(290\) 3.68329 + 6.37965i 0.216290 + 0.374626i
\(291\) 6.61894i 0.388009i
\(292\) 27.8634 16.0869i 1.63058 0.941418i
\(293\) −21.0774 + 12.1691i −1.23136 + 0.710924i −0.967313 0.253587i \(-0.918390\pi\)
−0.264044 + 0.964511i \(0.585056\pi\)
\(294\) 3.49396i 0.203772i
\(295\) −8.82036 15.2773i −0.513541 0.889479i
\(296\) −6.31282 + 10.9341i −0.366925 + 0.635533i
\(297\) 6.98942 + 4.03534i 0.405567 + 0.234154i
\(298\) 18.8877 1.09413
\(299\) 0 0
\(300\) 4.92692 0.284456
\(301\) 10.8897 + 6.28717i 0.627672 + 0.362386i
\(302\) 15.8741 27.4948i 0.913453 1.58215i
\(303\) −3.62498 6.27865i −0.208250 0.360699i
\(304\) 4.69202i 0.269106i
\(305\) 10.7182 6.18814i 0.613720 0.354332i
\(306\) −27.7426 + 16.0172i −1.58594 + 0.915644i
\(307\) 14.0737i 0.803227i −0.915809 0.401613i \(-0.868450\pi\)
0.915809 0.401613i \(-0.131550\pi\)
\(308\) 7.98039 + 13.8224i 0.454725 + 0.787606i
\(309\) −2.54407 + 4.40646i −0.144727 + 0.250675i
\(310\) 12.0036 + 6.93027i 0.681758 + 0.393613i
\(311\) 29.7700 1.68810 0.844051 0.536263i \(-0.180164\pi\)
0.844051 + 0.536263i \(0.180164\pi\)
\(312\) 0 0
\(313\) −7.47889 −0.422732 −0.211366 0.977407i \(-0.567791\pi\)
−0.211366 + 0.977407i \(0.567791\pi\)
\(314\) 18.3560 + 10.5978i 1.03589 + 0.598070i
\(315\) −3.98523 + 6.90262i −0.224542 + 0.388919i
\(316\) −24.0526 41.6603i −1.35306 2.34357i
\(317\) 30.0301i 1.68666i −0.537396 0.843330i \(-0.680592\pi\)
0.537396 0.843330i \(-0.319408\pi\)
\(318\) −5.96233 + 3.44235i −0.334351 + 0.193038i
\(319\) −5.01997 + 2.89828i −0.281064 + 0.162273i
\(320\) 18.8388i 1.05312i
\(321\) −1.91454 3.31608i −0.106859 0.185086i
\(322\) 4.35086 7.53590i 0.242464 0.419959i
\(323\) −26.8343 15.4928i −1.49310 0.862040i
\(324\) −19.2784 −1.07102
\(325\) 0 0
\(326\) −19.5579 −1.08321
\(327\) −0.0586331 0.0338518i −0.00324242 0.00187201i
\(328\) 1.50149 2.60066i 0.0829060 0.143597i
\(329\) −3.02326 5.23644i −0.166678 0.288694i
\(330\) 4.60388i 0.253435i
\(331\) 13.6111 7.85839i 0.748135 0.431936i −0.0768845 0.997040i \(-0.524497\pi\)
0.825020 + 0.565104i \(0.191164\pi\)
\(332\) 20.3934 11.7741i 1.11923 0.646189i
\(333\) 14.4209i 0.790259i
\(334\) −26.7995 46.4182i −1.46641 2.53989i
\(335\) −0.416698 + 0.721743i −0.0227667 + 0.0394330i
\(336\) −0.789689 0.455927i −0.0430811 0.0248729i
\(337\) −1.95407 −0.106445 −0.0532224 0.998583i \(-0.516949\pi\)
−0.0532224 + 0.998583i \(0.516949\pi\)
\(338\) 0 0
\(339\) −4.05562 −0.220271
\(340\) 20.2067 + 11.6664i 1.09586 + 0.632698i
\(341\) −5.45324 + 9.44529i −0.295309 + 0.511491i
\(342\) −17.6957 30.6498i −0.956872 1.65735i
\(343\) 20.0834i 1.08440i
\(344\) 12.5266 7.23221i 0.675387 0.389935i
\(345\) −1.31266 + 0.757865i −0.0706713 + 0.0408021i
\(346\) 42.3672i 2.27767i
\(347\) 8.56249 + 14.8307i 0.459659 + 0.796152i 0.998943 0.0459718i \(-0.0146384\pi\)
−0.539284 + 0.842124i \(0.681305\pi\)
\(348\) −1.91939 + 3.32448i −0.102890 + 0.178211i
\(349\) 9.06453 + 5.23341i 0.485213 + 0.280138i 0.722586 0.691281i \(-0.242953\pi\)
−0.237373 + 0.971418i \(0.576287\pi\)
\(350\) −13.4058 −0.716571
\(351\) 0 0
\(352\) −16.6474 −0.887310
\(353\) 13.4501 + 7.76540i 0.715875 + 0.413310i 0.813232 0.581939i \(-0.197706\pi\)
−0.0973578 + 0.995249i \(0.531039\pi\)
\(354\) 7.61141 13.1833i 0.404542 0.700687i
\(355\) 3.31940 + 5.74936i 0.176175 + 0.305144i
\(356\) 20.1642i 1.06870i
\(357\) −5.21501 + 3.01089i −0.276007 + 0.159353i
\(358\) −11.7180 + 6.76540i −0.619316 + 0.357562i
\(359\) 21.4263i 1.13083i −0.824805 0.565417i \(-0.808715\pi\)
0.824805 0.565417i \(-0.191285\pi\)
\(360\) 4.58426 + 7.94017i 0.241612 + 0.418484i
\(361\) 7.61625 13.1917i 0.400855 0.694302i
\(362\) −9.29727 5.36778i −0.488654 0.282124i
\(363\) −2.48188 −0.130265
\(364\) 0 0
\(365\) 15.2489 0.798164
\(366\) 9.24910 + 5.33997i 0.483458 + 0.279125i
\(367\) −17.1516 + 29.7074i −0.895306 + 1.55072i −0.0618807 + 0.998084i \(0.519710\pi\)
−0.833425 + 0.552632i \(0.813624\pi\)
\(368\) 0.757865 + 1.31266i 0.0395064 + 0.0684271i
\(369\) 3.42998i 0.178557i
\(370\) −15.0634 + 8.69687i −0.783110 + 0.452129i
\(371\) 9.79673 5.65615i 0.508621 0.293652i
\(372\) 7.22282i 0.374486i
\(373\) 6.29805 + 10.9085i 0.326101 + 0.564823i 0.981735 0.190256i \(-0.0609318\pi\)
−0.655634 + 0.755079i \(0.727598\pi\)
\(374\) −15.2017 + 26.3301i −0.786062 + 1.36150i
\(375\) 5.49477 + 3.17241i 0.283749 + 0.163822i
\(376\) −6.95539 −0.358697
\(377\) 0 0
\(378\) −14.5429 −0.748005
\(379\) 14.3228 + 8.26928i 0.735714 + 0.424765i 0.820509 0.571634i \(-0.193690\pi\)
−0.0847951 + 0.996398i \(0.527024\pi\)
\(380\) −12.8889 + 22.3242i −0.661186 + 1.14521i
\(381\) 5.26391 + 9.11735i 0.269678 + 0.467096i
\(382\) 41.4131i 2.11888i
\(383\) −6.52652 + 3.76809i −0.333489 + 0.192540i −0.657389 0.753551i \(-0.728339\pi\)
0.323900 + 0.946091i \(0.395006\pi\)
\(384\) −7.81567 + 4.51238i −0.398842 + 0.230271i
\(385\) 7.56465i 0.385530i
\(386\) 6.80194 + 11.7813i 0.346210 + 0.599652i
\(387\) −8.26055 + 14.3077i −0.419908 + 0.727301i
\(388\) −31.4923 18.1821i −1.59878 0.923056i
\(389\) −35.5555 −1.80274 −0.901369 0.433052i \(-0.857437\pi\)
−0.901369 + 0.433052i \(0.857437\pi\)
\(390\) 0 0
\(391\) 10.0097 0.506212
\(392\) 5.71912 + 3.30194i 0.288859 + 0.166773i
\(393\) 0.903657 1.56518i 0.0455835 0.0789529i
\(394\) 12.8252 + 22.2139i 0.646124 + 1.11912i
\(395\) 22.7995i 1.14717i
\(396\) −18.1610 + 10.4852i −0.912622 + 0.526903i
\(397\) 1.17045 0.675760i 0.0587432 0.0339154i −0.470341 0.882485i \(-0.655869\pi\)
0.529084 + 0.848569i \(0.322536\pi\)
\(398\) 31.2446i 1.56615i
\(399\) −3.32640 5.76149i −0.166528 0.288435i
\(400\) 1.16756 2.02228i 0.0583781 0.101114i
\(401\) −0.501534 0.289561i −0.0250454 0.0144600i 0.487425 0.873165i \(-0.337936\pi\)
−0.512470 + 0.858705i \(0.671270\pi\)
\(402\) −0.719169 −0.0358689
\(403\) 0 0
\(404\) 39.8310 1.98167
\(405\) −7.91293 4.56853i −0.393197 0.227012i
\(406\) 5.22252 9.04567i 0.259189 0.448929i
\(407\) −6.84332 11.8530i −0.339211 0.587531i
\(408\) 6.92692i 0.342934i
\(409\) 13.1268 7.57875i 0.649078 0.374745i −0.139025 0.990289i \(-0.544397\pi\)
0.788103 + 0.615544i \(0.211064\pi\)
\(410\) 3.58280 2.06853i 0.176942 0.102157i
\(411\) 0.439665i 0.0216871i
\(412\) −13.9770 24.2089i −0.688599 1.19269i
\(413\) −12.5063 + 21.6616i −0.615397 + 1.06590i
\(414\) 9.90123 + 5.71648i 0.486619 + 0.280950i
\(415\) 11.1608 0.547860
\(416\) 0 0
\(417\) 6.29291 0.308165
\(418\) −29.0893 16.7947i −1.42280 0.821456i
\(419\) 17.8617 30.9374i 0.872603 1.51139i 0.0133088 0.999911i \(-0.495764\pi\)
0.859294 0.511481i \(-0.170903\pi\)
\(420\) 2.50484 + 4.33852i 0.122224 + 0.211698i
\(421\) 35.0465i 1.70806i 0.520221 + 0.854032i \(0.325849\pi\)
−0.520221 + 0.854032i \(0.674151\pi\)
\(422\) −25.7732 + 14.8802i −1.25462 + 0.724355i
\(423\) 6.88003 3.97219i 0.334519 0.193134i
\(424\) 13.0127i 0.631951i
\(425\) −7.71044 13.3549i −0.374011 0.647806i
\(426\) −2.86443 + 4.96134i −0.138782 + 0.240378i
\(427\) −15.1972 8.77413i −0.735446 0.424610i
\(428\) 21.0368 1.01685
\(429\) 0 0
\(430\) 19.9269 0.960961
\(431\) −29.6886 17.1407i −1.43005 0.825639i −0.432925 0.901430i \(-0.642519\pi\)
−0.997124 + 0.0757909i \(0.975852\pi\)
\(432\) 1.26659 2.19381i 0.0609390 0.105549i
\(433\) 6.86927 + 11.8979i 0.330116 + 0.571778i 0.982534 0.186081i \(-0.0595787\pi\)
−0.652418 + 0.757859i \(0.726245\pi\)
\(434\) 19.6528i 0.943364i
\(435\) −1.57564 + 0.909698i −0.0755463 + 0.0436167i
\(436\) 0.322128 0.185981i 0.0154271 0.00890686i
\(437\) 11.0586i 0.529005i
\(438\) 6.57942 + 11.3959i 0.314377 + 0.544516i
\(439\) 5.12014 8.86834i 0.244371 0.423263i −0.717584 0.696472i \(-0.754752\pi\)
0.961955 + 0.273210i \(0.0880853\pi\)
\(440\) 7.53590 + 4.35086i 0.359260 + 0.207419i
\(441\) −7.54288 −0.359185
\(442\) 0 0
\(443\) 12.1763 0.578513 0.289257 0.957252i \(-0.406592\pi\)
0.289257 + 0.957252i \(0.406592\pi\)
\(444\) −7.84964 4.53199i −0.372527 0.215079i
\(445\) 4.77844 8.27650i 0.226520 0.392344i
\(446\) 8.24094 + 14.2737i 0.390220 + 0.675880i
\(447\) 4.66487i 0.220641i
\(448\) 23.1327 13.3557i 1.09292 0.630997i
\(449\) −11.1762 + 6.45257i −0.527437 + 0.304516i −0.739972 0.672638i \(-0.765161\pi\)
0.212535 + 0.977153i \(0.431828\pi\)
\(450\) 17.6136i 0.830311i
\(451\) 1.62767 + 2.81921i 0.0766440 + 0.132751i
\(452\) 11.1407 19.2963i 0.524015 0.907621i
\(453\) 6.79065 + 3.92058i 0.319053 + 0.184205i
\(454\) −19.4916 −0.914785
\(455\) 0 0
\(456\) −7.65279 −0.358375
\(457\) 4.03317 + 2.32855i 0.188664 + 0.108925i 0.591357 0.806410i \(-0.298592\pi\)
−0.402693 + 0.915335i \(0.631926\pi\)
\(458\) −15.3768 + 26.6334i −0.718511 + 1.24450i
\(459\) −8.36443 14.4876i −0.390418 0.676224i
\(460\) 8.32736i 0.388265i
\(461\) 27.3149 15.7702i 1.27218 0.734493i 0.296782 0.954945i \(-0.404087\pi\)
0.975398 + 0.220452i \(0.0707532\pi\)
\(462\) −5.65325 + 3.26391i −0.263013 + 0.151851i
\(463\) 17.6504i 0.820284i 0.912022 + 0.410142i \(0.134521\pi\)
−0.912022 + 0.410142i \(0.865479\pi\)
\(464\) 0.909698 + 1.57564i 0.0422317 + 0.0731474i
\(465\) −1.71164 + 2.96464i −0.0793752 + 0.137482i
\(466\) −9.90123 5.71648i −0.458666 0.264811i
\(467\) 32.1726 1.48877 0.744385 0.667751i \(-0.232743\pi\)
0.744385 + 0.667751i \(0.232743\pi\)
\(468\) 0 0
\(469\) 1.18167 0.0545644
\(470\) −8.29835 4.79105i −0.382774 0.220995i
\(471\) −2.61745 + 4.53355i −0.120606 + 0.208895i
\(472\) 14.3862 + 24.9176i 0.662178 + 1.14693i
\(473\) 15.6799i 0.720964i
\(474\) 17.0387 9.83728i 0.782612 0.451841i
\(475\) 14.7543 8.51842i 0.676975 0.390852i
\(476\) 33.0834i 1.51637i
\(477\) 7.43147 + 12.8717i 0.340264 + 0.589354i
\(478\) 12.2729 21.2573i 0.561351 0.972288i
\(479\) 30.2241 + 17.4499i 1.38097 + 0.797306i 0.992275 0.124059i \(-0.0395912\pi\)
0.388699 + 0.921365i \(0.372925\pi\)
\(480\) −5.22521 −0.238497
\(481\) 0 0
\(482\) −26.7724 −1.21945
\(483\) 1.86121 + 1.07457i 0.0846882 + 0.0488947i
\(484\) 6.81767 11.8085i 0.309894 0.536752i
\(485\) −8.61745 14.9259i −0.391298 0.677748i
\(486\) 29.1782i 1.32355i
\(487\) −36.2302 + 20.9175i −1.64175 + 0.947864i −0.661536 + 0.749914i \(0.730095\pi\)
−0.980212 + 0.197950i \(0.936572\pi\)
\(488\) −17.4816 + 10.0930i −0.791354 + 0.456888i
\(489\) 4.83041i 0.218439i
\(490\) 4.54892 + 7.87896i 0.205499 + 0.355935i
\(491\) 10.9227 18.9187i 0.492936 0.853791i −0.507031 0.861928i \(-0.669257\pi\)
0.999967 + 0.00813732i \(0.00259022\pi\)
\(492\) 1.86702 + 1.07792i 0.0841718 + 0.0485966i
\(493\) 12.0151 0.541131
\(494\) 0 0
\(495\) −9.93900 −0.446725
\(496\) 2.96464 + 1.71164i 0.133116 + 0.0768547i
\(497\) 4.70655 8.15199i 0.211118 0.365667i
\(498\) 4.81551 + 8.34071i 0.215788 + 0.373756i
\(499\) 23.5472i 1.05412i −0.849829 0.527058i \(-0.823295\pi\)
0.849829 0.527058i \(-0.176705\pi\)
\(500\) −30.1880 + 17.4291i −1.35005 + 0.779452i
\(501\) 11.4643 6.61894i 0.512189 0.295712i
\(502\) 50.2150i 2.24121i
\(503\) 3.54341 + 6.13736i 0.157993 + 0.273652i 0.934145 0.356894i \(-0.116164\pi\)
−0.776152 + 0.630546i \(0.782831\pi\)
\(504\) 6.50000 11.2583i 0.289533 0.501486i
\(505\) 16.3488 + 9.43900i 0.727513 + 0.420030i
\(506\) 10.8509 0.482379
\(507\) 0 0
\(508\) −57.8394 −2.56621
\(509\) 6.59820 + 3.80947i 0.292460 + 0.168852i 0.639051 0.769165i \(-0.279327\pi\)
−0.346591 + 0.938016i \(0.612661\pi\)
\(510\) −4.77144 + 8.26437i −0.211283 + 0.365953i
\(511\) −10.8107 18.7246i −0.478236 0.828329i
\(512\) 9.00538i 0.397985i
\(513\) 16.0058 9.24094i 0.706672 0.407997i
\(514\) 36.3114 20.9644i 1.60163 0.924701i
\(515\) 13.2489i 0.583816i
\(516\) 5.19202 + 8.99284i 0.228566 + 0.395888i
\(517\) 3.76995 6.52974i 0.165802 0.287178i
\(518\) 21.3583 + 12.3312i 0.938431 + 0.541804i
\(519\) −10.4638 −0.459311
\(520\) 0 0
\(521\) −39.5133 −1.73111 −0.865555 0.500813i \(-0.833034\pi\)
−0.865555 + 0.500813i \(0.833034\pi\)
\(522\) 11.8849 + 6.86174i 0.520187 + 0.300330i
\(523\) 7.90970 13.7000i 0.345867 0.599059i −0.639644 0.768671i \(-0.720918\pi\)
0.985511 + 0.169612i \(0.0542515\pi\)
\(524\) 4.96466 + 8.59904i 0.216882 + 0.375651i
\(525\) 3.31096i 0.144502i
\(526\) 28.0198 16.1773i 1.22172 0.705362i
\(527\) 19.5781 11.3034i 0.852836 0.492385i
\(528\) 1.13706i 0.0494843i
\(529\) 9.71379 + 16.8248i 0.422339 + 0.731512i
\(530\) 8.96346 15.5252i 0.389348 0.674370i
\(531\) −28.4606 16.4318i −1.23509 0.713078i
\(532\) 36.5502 1.58465
\(533\) 0 0
\(534\) 8.24698 0.356882
\(535\) 8.63467 + 4.98523i 0.373309 + 0.215530i
\(536\) 0.679644 1.17718i 0.0293562 0.0508464i
\(537\) −1.67092 2.89411i −0.0721053 0.124890i
\(538\) 1.46681i 0.0632388i
\(539\) −6.19973 + 3.57942i −0.267041 + 0.154176i
\(540\) −12.0527 + 6.95862i −0.518665 + 0.299451i
\(541\) 34.4819i 1.48249i 0.671234 + 0.741246i \(0.265765\pi\)
−0.671234 + 0.741246i \(0.734235\pi\)
\(542\) −2.24214 3.88349i −0.0963080 0.166810i
\(543\) 1.32573 2.29624i 0.0568926 0.0985409i
\(544\) 29.8836 + 17.2533i 1.28125 + 0.739730i
\(545\) 0.176292 0.00755152
\(546\) 0 0
\(547\) 36.8582 1.57594 0.787970 0.615713i \(-0.211132\pi\)
0.787970 + 0.615713i \(0.211132\pi\)
\(548\) 2.09189 + 1.20775i 0.0893609 + 0.0515926i
\(549\) 11.5281 19.9673i 0.492008 0.852182i
\(550\) −8.35839 14.4772i −0.356403 0.617308i
\(551\) 13.2741i 0.565497i
\(552\) 2.14098 1.23609i 0.0911261 0.0526117i
\(553\) −27.9963 + 16.1637i −1.19052 + 0.687350i
\(554\) 26.4795i 1.12501i
\(555\) −2.14795 3.72036i −0.0911753 0.157920i
\(556\) −17.2865 + 29.9411i −0.733111 + 1.26979i
\(557\) −1.10550 0.638260i −0.0468415 0.0270439i 0.476396 0.879231i \(-0.341943\pi\)
−0.523238 + 0.852187i \(0.675276\pi\)
\(558\) 25.8213 1.09310
\(559\) 0 0
\(560\) 2.37435 0.100335
\(561\) −6.50301 3.75451i −0.274557 0.158516i
\(562\) −7.27144 + 12.5945i −0.306727 + 0.531267i
\(563\) −4.56369 7.90454i −0.192336 0.333137i 0.753688 0.657233i \(-0.228273\pi\)
−0.946024 + 0.324096i \(0.894940\pi\)
\(564\) 4.99330i 0.210256i
\(565\) 9.14552 5.28017i 0.384755 0.222138i
\(566\) −12.8063 + 7.39373i −0.538290 + 0.310782i
\(567\) 12.9554i 0.544075i
\(568\) −5.41401 9.37734i −0.227167 0.393464i
\(569\) −2.86078 + 4.95502i −0.119930 + 0.207725i −0.919740 0.392529i \(-0.871600\pi\)
0.799810 + 0.600254i \(0.204934\pi\)
\(570\) −9.13040 5.27144i −0.382430 0.220796i
\(571\) −7.60148 −0.318112 −0.159056 0.987270i \(-0.550845\pi\)
−0.159056 + 0.987270i \(0.550845\pi\)
\(572\) 0 0
\(573\) −10.2282 −0.427289
\(574\) −5.08004 2.93296i −0.212037 0.122419i
\(575\) −2.75182 + 4.76630i −0.114759 + 0.198768i
\(576\) 17.5477 + 30.3935i 0.731155 + 1.26640i
\(577\) 45.1564i 1.87989i −0.341330 0.939944i \(-0.610877\pi\)
0.341330 0.939944i \(-0.389123\pi\)
\(578\) 21.4959 12.4107i 0.894111 0.516215i
\(579\) −2.90974 + 1.67994i −0.120925 + 0.0698159i
\(580\) 9.99569i 0.415048i
\(581\) −7.91239 13.7047i −0.328261 0.568565i
\(582\) 7.43631 12.8801i 0.308245 0.533896i
\(583\) 12.2163 + 7.05310i 0.505948 + 0.292109i
\(584\) −24.8713 −1.02918
\(585\) 0 0
\(586\) 54.6872 2.25911
\(587\) −28.0627 16.2020i −1.15827 0.668728i −0.207382 0.978260i \(-0.566494\pi\)
−0.950889 + 0.309532i \(0.899828\pi\)
\(588\) −2.37047 + 4.10577i −0.0977565 + 0.169319i
\(589\) 12.4879 + 21.6297i 0.514556 + 0.891237i
\(590\) 39.6383i 1.63188i
\(591\) −5.48638 + 3.16756i −0.225680 + 0.130296i
\(592\) −3.72036 + 2.14795i −0.152906 + 0.0882801i
\(593\) 36.6848i 1.50647i 0.657754 + 0.753233i \(0.271507\pi\)
−0.657754 + 0.753233i \(0.728493\pi\)
\(594\) −9.06734 15.7051i −0.372037 0.644387i
\(595\) 7.83997 13.5792i 0.321407 0.556694i
\(596\) −22.1950 12.8143i −0.909144 0.524895i
\(597\) −7.71678 −0.315827
\(598\) 0 0
\(599\) −9.99223 −0.408271 −0.204136 0.978943i \(-0.565438\pi\)
−0.204136 + 0.978943i \(0.565438\pi\)
\(600\) −3.29838 1.90432i −0.134656 0.0777436i
\(601\) 0.905813 1.56891i 0.0369489 0.0639974i −0.846960 0.531657i \(-0.821569\pi\)
0.883908 + 0.467660i \(0.154903\pi\)
\(602\) −14.1271 24.4689i −0.575779 0.997279i
\(603\) 1.55257i 0.0632253i
\(604\) −37.3076 + 21.5395i −1.51802 + 0.876431i
\(605\) 5.59669 3.23125i 0.227538 0.131369i
\(606\) 16.2905i 0.661757i
\(607\) −5.60806 9.71344i −0.227624 0.394256i 0.729479 0.684003i \(-0.239762\pi\)
−0.957103 + 0.289746i \(0.906429\pi\)
\(608\) −19.0613 + 33.0151i −0.773038 + 1.33894i
\(609\) 2.23410 + 1.28986i 0.0905302 + 0.0522676i
\(610\) −27.8092 −1.12596
\(611\) 0 0
\(612\) 43.4674 1.75707
\(613\) −18.0951 10.4472i −0.730853 0.421958i 0.0878810 0.996131i \(-0.471990\pi\)
−0.818734 + 0.574173i \(0.805324\pi\)
\(614\) −15.8116 + 27.3865i −0.638105 + 1.10523i
\(615\) 0.510885 + 0.884879i 0.0206009 + 0.0356818i
\(616\) 12.3381i 0.497117i
\(617\) −10.4782 + 6.04958i −0.421836 + 0.243547i −0.695862 0.718175i \(-0.744978\pi\)
0.274027 + 0.961722i \(0.411644\pi\)
\(618\) 9.90123 5.71648i 0.398286 0.229951i
\(619\) 10.5526i 0.424143i −0.977254 0.212072i \(-0.931979\pi\)
0.977254 0.212072i \(-0.0680210\pi\)
\(620\) −9.40366 16.2876i −0.377660 0.654126i
\(621\) −2.98523 + 5.17057i −0.119793 + 0.207488i
\(622\) −57.9307 33.4463i −2.32281 1.34107i
\(623\) −13.5506 −0.542895
\(624\) 0 0
\(625\) −1.96184 −0.0784735
\(626\) 14.5535 + 8.40246i 0.581674 + 0.335830i
\(627\) 4.14795 7.18446i 0.165653 0.286920i
\(628\) −14.3802 24.9072i −0.573831 0.993904i
\(629\) 28.3696i 1.13117i
\(630\) 15.5100 8.95473i 0.617935 0.356765i
\(631\) −11.9957 + 6.92572i −0.477541 + 0.275709i −0.719391 0.694605i \(-0.755579\pi\)
0.241850 + 0.970314i \(0.422246\pi\)
\(632\) 37.1866i 1.47920i
\(633\) −3.67510 6.36545i −0.146072 0.253004i
\(634\) −33.7385 + 58.4369i −1.33993 + 2.32082i
\(635\) −23.7404 13.7066i −0.942111 0.543928i
\(636\) 9.34183 0.370428
\(637\) 0 0
\(638\) 13.0248 0.515655
\(639\) 10.7107 + 6.18382i 0.423709 + 0.244628i
\(640\) 11.7497 20.3510i 0.464446 0.804445i
\(641\) 17.4804 + 30.2769i 0.690434 + 1.19587i 0.971696 + 0.236235i \(0.0759136\pi\)
−0.281262 + 0.959631i \(0.590753\pi\)
\(642\) 8.60388i 0.339568i
\(643\) −28.9236 + 16.6990i −1.14063 + 0.658545i −0.946587 0.322447i \(-0.895495\pi\)
−0.194046 + 0.980992i \(0.562161\pi\)
\(644\) −10.2254 + 5.90366i −0.402939 + 0.232637i
\(645\) 4.92154i 0.193786i
\(646\) 34.8119 + 60.2960i 1.36966 + 2.37232i
\(647\) 1.16421 2.01647i 0.0457698 0.0792757i −0.842233 0.539114i \(-0.818759\pi\)
0.888003 + 0.459838i \(0.152093\pi\)
\(648\) 12.9062 + 7.45138i 0.507002 + 0.292718i
\(649\) −31.1903 −1.22433
\(650\) 0 0
\(651\) 4.85384 0.190237
\(652\) 22.9827 + 13.2690i 0.900070 + 0.519656i
\(653\) −7.28568 + 12.6192i −0.285111 + 0.493826i −0.972636 0.232334i \(-0.925364\pi\)
0.687525 + 0.726160i \(0.258697\pi\)
\(654\) 0.0760644 + 0.131747i 0.00297435 + 0.00515173i
\(655\) 4.70602i 0.183879i
\(656\) 0.884879 0.510885i 0.0345487 0.0199467i
\(657\) 24.6018 14.2039i 0.959808 0.554146i
\(658\) 13.5864i 0.529654i
\(659\) −5.56973 9.64705i −0.216966 0.375796i 0.736913 0.675988i \(-0.236283\pi\)
−0.953879 + 0.300192i \(0.902949\pi\)
\(660\) −3.12349 + 5.41004i −0.121582 + 0.210586i
\(661\) 11.9943 + 6.92490i 0.466523 + 0.269347i 0.714783 0.699346i \(-0.246525\pi\)
−0.248260 + 0.968693i \(0.579859\pi\)
\(662\) −35.3153 −1.37257
\(663\) 0 0
\(664\) −18.2034 −0.706430
\(665\) 15.0022 + 8.66152i 0.581760 + 0.335879i
\(666\) −16.2017 + 28.0622i −0.627804 + 1.08739i
\(667\) −2.14406 3.71363i −0.0830185 0.143792i
\(668\) 72.7284i 2.81395i
\(669\) −3.52532 + 2.03534i −0.136297 + 0.0786909i
\(670\) 1.62174 0.936313i 0.0626533 0.0361729i
\(671\) 21.8823i 0.844757i
\(672\) 3.70440 + 6.41621i 0.142900 + 0.247511i
\(673\) −3.26487 + 5.65491i −0.125851 + 0.217981i −0.922065 0.387034i \(-0.873500\pi\)
0.796214 + 0.605015i \(0.206833\pi\)
\(674\) 3.80250 + 2.19537i 0.146467 + 0.0845626i
\(675\) 9.19806 0.354034
\(676\) 0 0
\(677\) −11.3104 −0.434693 −0.217346 0.976095i \(-0.569740\pi\)
−0.217346 + 0.976095i \(0.569740\pi\)
\(678\) 7.89200 + 4.55645i 0.303091 + 0.174989i
\(679\) −12.2186 + 21.1633i −0.468908 + 0.812173i
\(680\) −9.01842 15.6204i −0.345841 0.599013i
\(681\) 4.81402i 0.184474i
\(682\) 21.2234 12.2533i 0.812685 0.469204i
\(683\) 12.2796 7.08964i 0.469866 0.271277i −0.246317 0.969189i \(-0.579221\pi\)
0.716184 + 0.697912i \(0.245887\pi\)
\(684\) 48.0224i 1.83618i
\(685\) 0.572417 + 0.991455i 0.0218709 + 0.0378815i
\(686\) 22.5635 39.0810i 0.861477 1.49212i
\(687\) −6.57791 3.79776i −0.250963 0.144893i
\(688\) 4.92154 0.187632
\(689\) 0 0
\(690\) 3.40581 0.129657
\(691\) 26.6695 + 15.3976i 1.01455 + 0.585753i 0.912522 0.409028i \(-0.134132\pi\)
0.102032 + 0.994781i \(0.467466\pi\)
\(692\) 28.7439 49.7859i 1.09268 1.89258i
\(693\) 7.04623 + 12.2044i 0.267664 + 0.463608i
\(694\) 38.4795i 1.46066i
\(695\) −14.1907 + 8.19298i −0.538282 + 0.310777i
\(696\) 2.56991 1.48374i 0.0974122 0.0562409i
\(697\) 6.74764i 0.255585i
\(698\) −11.7594 20.3678i −0.445098 0.770933i
\(699\) 1.41185 2.44540i 0.0534012 0.0924936i
\(700\) 15.7533 + 9.09515i 0.595417 + 0.343764i
\(701\) −6.73184 −0.254258 −0.127129 0.991886i \(-0.540576\pi\)
−0.127129 + 0.991886i \(0.540576\pi\)
\(702\) 0 0
\(703\) −31.3424 −1.18210
\(704\) 28.8461 + 16.6543i 1.08718 + 0.627682i
\(705\) 1.18329 2.04952i 0.0445654 0.0771895i
\(706\) −17.4487 30.2220i −0.656690 1.13742i
\(707\) 26.7670i 1.00668i
\(708\) −17.8884 + 10.3279i −0.672288 + 0.388146i
\(709\) −41.2446 + 23.8126i −1.54897 + 0.894300i −0.550753 + 0.834668i \(0.685660\pi\)
−0.998220 + 0.0596324i \(0.981007\pi\)
\(710\) 14.9172i 0.559834i
\(711\) −21.2371 36.7837i −0.796452 1.37949i
\(712\) −7.79374 + 13.4992i −0.292083 + 0.505902i
\(713\) −6.98735 4.03415i −0.261678 0.151080i
\(714\) 13.5308 0.506377
\(715\) 0 0
\(716\) 18.3599 0.686141
\(717\) 5.25013 + 3.03116i 0.196070 + 0.113201i
\(718\) −24.0722 + 41.6942i −0.898366 + 1.55602i
\(719\) −2.99665 5.19035i −0.111756 0.193567i 0.804722 0.593651i \(-0.202314\pi\)
−0.916478 + 0.400084i \(0.868981\pi\)
\(720\) 3.11960i 0.116261i
\(721\) −16.2688 + 9.39277i −0.605880 + 0.349805i
\(722\) −29.6416 + 17.1136i −1.10314 + 0.636901i
\(723\) 6.61224i 0.245912i
\(724\) 7.28352 + 12.6154i 0.270690 + 0.468849i
\(725\) −3.30313 + 5.72120i −0.122675 + 0.212480i
\(726\) 4.82959 + 2.78836i 0.179243 + 0.103486i
\(727\) 24.1226 0.894657 0.447329 0.894370i \(-0.352375\pi\)
0.447329 + 0.894370i \(0.352375\pi\)
\(728\) 0 0
\(729\) −11.7627 −0.435656
\(730\) −29.6735 17.1320i −1.09826 0.634083i
\(731\) 16.2506 28.1469i 0.601051 1.04105i
\(732\) −7.24578 12.5501i −0.267812 0.463864i
\(733\) 36.0646i 1.33208i −0.745918 0.666038i \(-0.767989\pi\)
0.745918 0.666038i \(-0.232011\pi\)
\(734\) 66.7520 38.5393i 2.46386 1.42251i
\(735\) −1.94594 + 1.12349i −0.0717771 + 0.0414405i
\(736\) 12.3153i 0.453947i
\(737\) 0.736758 + 1.27610i 0.0271388 + 0.0470059i
\(738\) 3.85354 6.67453i 0.141851 0.245693i
\(739\) −23.8377 13.7627i −0.876884 0.506269i −0.00725452 0.999974i \(-0.502309\pi\)
−0.869630 + 0.493704i \(0.835643\pi\)
\(740\) 23.6015 0.867608
\(741\) 0 0
\(742\) −25.4185 −0.933142
\(743\) −9.06660 5.23460i −0.332621 0.192039i 0.324383 0.945926i \(-0.394843\pi\)
−0.657004 + 0.753887i \(0.728177\pi\)
\(744\) 2.79172 4.83539i 0.102349 0.177274i
\(745\) −6.07338 10.5194i −0.222511 0.385401i
\(746\) 28.3032i 1.03625i
\(747\) 18.0062 10.3959i 0.658813 0.380366i
\(748\) 35.7273 20.6271i 1.30632 0.754203i
\(749\) 14.1371i 0.516557i
\(750\) −7.12833 12.3466i −0.260290 0.450835i
\(751\) 2.03385 3.52273i 0.0742163 0.128546i −0.826529 0.562894i \(-0.809688\pi\)
0.900745 + 0.434348i \(0.143021\pi\)
\(752\) −2.04952 1.18329i −0.0747384 0.0431502i
\(753\) 12.4021 0.451957
\(754\) 0 0
\(755\) −20.4174 −0.743066
\(756\) 17.0894 + 9.86658i 0.621536 + 0.358844i
\(757\) −10.2168 + 17.6960i −0.371335 + 0.643171i −0.989771 0.142664i \(-0.954433\pi\)
0.618436 + 0.785835i \(0.287767\pi\)
\(758\) −18.5809 32.1831i −0.674889 1.16894i
\(759\) 2.67994i 0.0972757i
\(760\) 17.2572 9.96346i 0.625985 0.361413i
\(761\) −23.4032 + 13.5118i −0.848365 + 0.489804i −0.860099 0.510127i \(-0.829598\pi\)
0.0117336 + 0.999931i \(0.496265\pi\)
\(762\) 23.6558i 0.856958i
\(763\) −0.124982 0.216475i −0.00452464 0.00783691i
\(764\) 28.0966 48.6648i 1.01650 1.76063i
\(765\) 17.8414 + 10.3007i 0.645057 + 0.372424i
\(766\) 16.9336 0.611837
\(767\) 0 0
\(768\) 5.80864 0.209601
\(769\) −32.8576 18.9703i −1.18487 0.684088i −0.227737 0.973723i \(-0.573133\pi\)
−0.957137 + 0.289635i \(0.906466\pi\)
\(770\) 8.49880 14.7204i 0.306276 0.530485i
\(771\) 5.17778 + 8.96818i 0.186473 + 0.322981i
\(772\) 18.4590i 0.664355i
\(773\) 14.1487 8.16876i 0.508894 0.293810i −0.223485 0.974707i \(-0.571743\pi\)
0.732379 + 0.680897i \(0.238410\pi\)
\(774\) 32.1491