Properties

Label 169.2.e.b.23.1
Level $169$
Weight $2$
Character 169.23
Analytic conductor $1.349$
Analytic rank $0$
Dimension $12$
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 23.1
Root \(1.07992 + 0.623490i\) of defining polynomial
Character \(\chi\) \(=\) 169.23
Dual form 169.2.e.b.147.1

$q$-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 \(\left(\mathbb{Z}/169\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\)

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 −0.991674 0.128775i \(-0.958896\pi\)
−0.384315 + 0.923202i \(0.625562\pi\)
\(3\) 0.277479 + 0.480608i 0.160203 + 0.277479i 0.934941 0.354803i \(-0.115452\pi\)
−0.774739 + 0.632282i \(0.782119\pi\)
\(4\) 1.52446 2.64044i 0.762229 1.32022i
\(5\) 1.44504i 0.646242i −0.946358 0.323121i \(-0.895268\pi\)
0.946358 0.323121i \(-0.104732\pi\)
\(6\) −1.07992 0.623490i −0.440874 0.254539i
\(7\) 1.77441 + 1.02446i 0.670666 + 0.387209i 0.796329 0.604864i \(-0.206773\pi\)
−0.125663 + 0.992073i \(0.540106\pi\)
\(8\) 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 −0.127851 0.991793i \(-0.540808\pi\)
0.794993 + 0.606619i \(0.207475\pi\)
\(12\) 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 0.342714 + 0.939440i \(0.388654\pi\)
−0.984936 + 0.172921i \(0.944679\pi\)
\(18\) 6.04892i 1.42574i
\(19\) 5.06699 + 2.92543i 1.16245 + 0.671139i 0.951889 0.306442i \(-0.0991387\pi\)
0.210558 + 0.977581i \(0.432472\pi\)
\(20\) −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 0.750517 0.660851i \(-0.229804\pi\)
−0.947572 + 0.319542i \(0.896471\pi\)
\(24\) −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 0.741269 0.671208i \(-0.234224\pi\)
−0.951918 + 0.306354i \(0.900891\pi\)
\(30\) −0.900969 + 1.56052i −0.164494 + 0.284911i
\(31\) 4.26875i 0.766690i −0.923605 0.383345i \(-0.874772\pi\)
0.923605 0.383345i \(-0.125228\pi\)
\(32\) −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 −0.830258 0.557380i \(-0.811807\pi\)
0.0675764 + 0.997714i \(0.478473\pi\)
\(38\) −13.1468 −2.13268
\(39\) 0 0
\(40\) 3.40581 0.538506
\(41\) 1.10343 0.637063i 0.172326 0.0994926i −0.411356 0.911475i \(-0.634945\pi\)
0.583682 + 0.811982i \(0.301611\pi\)
\(42\) −1.27748 2.21266i −0.197119 0.341421i
\(43\) 3.06853 5.31485i 0.467947 0.810507i −0.531382 0.847132i \(-0.678327\pi\)
0.999329 + 0.0366246i \(0.0116606\pi\)
\(44\) 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 \(0.0690501\pi\)
−0.976563 + 0.215230i \(0.930950\pi\)
\(48\) −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 −0.384664 0.923057i \(-0.625683\pi\)
−0.991722 + 0.128400i \(0.959016\pi\)
\(60\) 2.44504i 0.315654i
\(61\) −4.28232 + 7.41720i −0.548295 + 0.949675i 0.450096 + 0.892980i \(0.351390\pi\)
−0.998392 + 0.0566953i \(0.981944\pi\)
\(62\) 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 −0.469180 0.883102i \(-0.655451\pi\)
0.530199 + 0.847873i \(0.322117\pi\)
\(68\) 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 0.717153 0.696916i \(-0.245445\pi\)
−0.244970 + 0.969531i \(0.578778\pi\)
\(72\) 5.49477 + 3.17241i 0.647565 + 0.373872i
\(73\) 10.5526i 1.23508i 0.786538 + 0.617542i \(0.211872\pi\)
−0.786538 + 0.617542i \(0.788128\pi\)
\(74\) 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 \(0.139333\pi\)
−0.905718 + 0.423881i \(0.860667\pi\)
\(84\) 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 −0.771836 0.635822i \(-0.780661\pi\)
0.164720 + 0.986340i \(0.447328\pi\)
\(90\) 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 −0.126453 0.991973i \(-0.540359\pi\)
−0.922300 + 0.386475i \(0.873693\pi\)
\(98\) 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 0.983133 + 0.182894i \(0.0585466\pi\)
−0.333175 + 0.942865i \(0.608120\pi\)
\(102\) 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 0.983198 0.182542i \(-0.0584325\pi\)
−0.649685 + 0.760204i \(0.725099\pi\)
\(108\) 4.81551 8.34071i 0.463373 0.802585i
\(109\) 0.121998i 0.0116853i 0.999983 + 0.00584264i \(0.00185978\pi\)
−0.999983 + 0.00584264i \(0.998140\pi\)
\(110\) 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 −0.985124 0.171847i \(-0.945027\pi\)
0.641385 + 0.767219i \(0.278360\pi\)
\(114\) −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 −0.888475 0.458925i \(-0.848235\pi\)
0.0467971 0.998904i \(-0.485099\pi\)
\(128\) −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 0.529023 0.848608i \(-0.322559\pi\)
−0.470405 + 0.882451i \(0.655892\pi\)
\(138\) 2.35690i 0.200632i
\(139\) 5.66972 9.82024i 0.480899 0.832942i −0.518861 0.854859i \(-0.673644\pi\)
0.999760 + 0.0219169i \(0.00697694\pi\)
\(140\) −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 0.171241 0.985229i \(-0.445222\pi\)
−0.767613 + 0.640914i \(0.778556\pi\)
\(150\) −3.14456 1.81551i −0.256752 0.148236i
\(151\) 14.1293i 1.14983i −0.818215 0.574913i \(-0.805036\pi\)
0.818215 0.574913i \(-0.194964\pi\)
\(152\) −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 0.765263 0.643717i \(-0.222609\pi\)
−0.174844 + 0.984596i \(0.555942\pi\)
\(164\) 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 0.606803 0.794853i \(-0.292452\pi\)
0.991764 0.128080i \(-0.0408815\pi\)
\(168\) −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 0.245509 + 0.969394i \(0.421045\pi\)
−0.962274 + 0.272081i \(0.912288\pi\)
\(174\) 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 0.956333 0.292280i \(-0.0944140\pi\)
−0.731289 + 0.682068i \(0.761081\pi\)
\(180\) −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 0.312001 + 0.950082i \(0.399001\pi\)
−0.978795 + 0.204840i \(0.934333\pi\)
\(192\) 3.61745 + 6.26561i 0.261067 + 0.452181i
\(193\) −5.24317 + 3.02715i −0.377412 + 0.217899i −0.676692 0.736267i \(-0.736587\pi\)
0.299280 + 0.954165i \(0.403254\pi\)
\(194\) 26.7995 1.92410
\(195\) 0 0
\(196\) −8.54288 −0.610205
\(197\) −9.88611 + 5.70775i −0.704357 + 0.406660i −0.808968 0.587853i \(-0.799973\pi\)
0.104611 + 0.994513i \(0.466640\pi\)
\(198\) 7.72737 + 13.3842i 0.549160 + 0.951173i
\(199\) −6.95257 + 12.0422i −0.492855 + 0.853650i −0.999966 0.00823084i \(-0.997380\pi\)
0.507111 + 0.861881i \(0.330713\pi\)
\(200\) 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 0.998739 0.0501974i \(-0.0159850\pi\)
−0.542842 + 0.839835i \(0.682652\pi\)
\(212\) 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 −0.697380 0.716701i \(-0.745651\pi\)
0.271992 + 0.962300i \(0.412318\pi\)
\(224\) −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 0.728141 0.685427i \(-0.240384\pi\)
−0.229526 + 0.973302i \(0.573718\pi\)
\(228\) 8.57345 + 4.94989i 0.567791 + 0.327814i
\(229\) 13.6866i 0.904439i 0.891907 + 0.452219i \(0.149368\pi\)
−0.891907 + 0.452219i \(0.850632\pi\)
\(230\) 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 \(-0.885058\pi\)
0.935508 0.353305i \(-0.114942\pi\)
\(240\) 0.556945 + 0.321552i 0.0359506 + 0.0207561i
\(241\) 10.3186 + 5.95742i 0.664676 + 0.383751i 0.794056 0.607844i \(-0.207965\pi\)
−0.129380 + 0.991595i \(0.541299\pi\)
\(242\) 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 −0.261296 0.965259i \(-0.584150\pi\)
0.966587 0.256340i \(-0.0825167\pi\)
\(252\) 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 −0.995243 0.0974228i \(-0.968940\pi\)
0.413251 0.910617i \(-0.364393\pi\)
\(258\) −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 0.554034 0.832494i \(-0.313088\pi\)
−0.997978 + 0.0635610i \(0.979754\pi\)
\(264\) −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 −0.875804 0.482666i \(-0.839668\pi\)
0.855904 + 0.517136i \(0.173002\pi\)
\(270\) 5.12833 + 8.88254i 0.312100 + 0.540574i
\(271\) 1.72832 0.997844i 0.104988 0.0606147i −0.446587 0.894740i \(-0.647361\pi\)
0.551574 + 0.834126i \(0.314027\pi\)
\(272\) −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 −0.632921 0.774216i \(-0.718144\pi\)
0.986952 + 0.161018i \(0.0514776\pi\)
\(278\) 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 \(0.0618377\pi\)
−0.981189 + 0.193049i \(0.938162\pi\)
\(282\) 1.83997 3.18692i 0.109569 0.189778i
\(283\) 3.29052 + 5.69935i 0.195601 + 0.338791i 0.947097 0.320946i \(-0.104001\pi\)
−0.751496 + 0.659737i \(0.770668\pi\)
\(284\) 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 −0.264044 0.964511i \(-0.585056\pi\)
−0.967313 + 0.253587i \(0.918390\pi\)
\(294\) 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 \(0.131550\pi\)
−0.915809 + 0.401613i \(0.868450\pi\)
\(308\) 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 \(0.319408\pi\)
−0.537396 + 0.843330i \(0.680592\pi\)
\(318\) −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 0.825020 0.565104i \(-0.191164\pi\)
−0.0768845 + 0.997040i \(0.524497\pi\)
\(332\) 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 −0.539284 0.842124i \(-0.681305\pi\)
0.998943 + 0.0459718i \(0.0146384\pi\)
\(348\) −1.91939 3.32448i −0.102890 0.178211i
\(349\) 9.06453 5.23341i 0.485213 0.280138i −0.237373 0.971418i \(-0.576287\pi\)
0.722586 + 0.691281i \(0.242953\pi\)
\(350\) −13.4058 −0.716571
\(351\) 0 0
\(352\) −16.6474 −0.887310
\(353\) 13.4501 7.76540i 0.715875 0.413310i −0.0973578 0.995249i \(-0.531039\pi\)
0.813232 + 0.581939i \(0.197706\pi\)
\(354\) 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 \(0.191285\pi\)
−0.824805 + 0.565417i \(0.808715\pi\)
\(360\) 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 −0.833425 0.552632i \(-0.813624\pi\)
−0.0618807 0.998084i \(-0.519710\pi\)
\(368\) 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 −0.655634 0.755079i \(-0.727598\pi\)
0.981735 + 0.190256i \(0.0609318\pi\)
\(374\) −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 −0.0847951 0.996398i \(-0.527024\pi\)
0.820509 + 0.571634i \(0.193690\pi\)
\(380\) −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 0.323900 0.946091i \(-0.395006\pi\)
−0.657389 + 0.753551i \(0.728339\pi\)
\(384\) −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 0.529084 0.848569i \(-0.322536\pi\)
−0.470341 + 0.882485i \(0.655869\pi\)
\(398\) 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 −0.512470 0.858705i \(-0.671270\pi\)
0.487425 + 0.873165i \(0.337936\pi\)
\(402\) −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 0.788103 0.615544i \(-0.211064\pi\)
−0.139025 + 0.990289i \(0.544397\pi\)
\(410\) 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 0.859294 + 0.511481i \(0.170903\pi\)
0.0133088 + 0.999911i \(0.495764\pi\)
\(420\) 2.50484 4.33852i 0.122224 0.211698i
\(421\) 35.0465i 1.70806i −0.520221 0.854032i \(-0.674151\pi\)
0.520221 0.854032i \(-0.325849\pi\)
\(422\) −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 −0.997124 0.0757909i \(-0.975852\pi\)
−0.432925 + 0.901430i \(0.642519\pi\)
\(432\) 1.26659 + 2.19381i 0.0609390 + 0.105549i
\(433\) 6.86927 11.8979i 0.330116 0.571778i −0.652418 0.757859i \(-0.726245\pi\)
0.982534 + 0.186081i \(0.0595787\pi\)
\(434\) 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 0.961955 0.273210i \(-0.0880853\pi\)
−0.717584 + 0.696472i \(0.754752\pi\)
\(440\) 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 0.212535 0.977153i \(-0.431828\pi\)
−0.739972 + 0.672638i \(0.765161\pi\)
\(450\) 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 −0.402693 0.915335i \(-0.631926\pi\)
0.591357 + 0.806410i \(0.298592\pi\)
\(458\) −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 0.975398 0.220452i \(-0.0707532\pi\)
0.296782 + 0.954945i \(0.404087\pi\)
\(462\) −5.65325 3.26391i −0.263013 0.151851i
\(463\) 17.6504i 0.820284i −0.912022 0.410142i \(-0.865479\pi\)
0.912022 0.410142i \(-0.134521\pi\)
\(464\) 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 0.388699 0.921365i \(-0.372925\pi\)
0.992275 + 0.124059i \(0.0395912\pi\)
\(480\) −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 −0.980212 0.197950i \(-0.936572\pi\)
−0.661536 0.749914i \(-0.730095\pi\)
\(488\) −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 0.999967 0.00813732i \(-0.00259022\pi\)
−0.507031 + 0.861928i \(0.669257\pi\)
\(492\) 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 \(0.176705\pi\)
−0.849829 + 0.527058i \(0.823295\pi\)
\(500\) −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 −0.776152 0.630546i \(-0.782831\pi\)
0.934145 + 0.356894i \(0.116164\pi\)
\(504\) 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 −0.346591 0.938016i \(-0.612661\pi\)
0.639051 + 0.769165i \(0.279327\pi\)
\(510\) −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 0.985511 0.169612i \(-0.0542515\pi\)
−0.639644 + 0.768671i \(0.720918\pi\)
\(524\) 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 \(-0.734235\pi\)
0.671234 0.741246i \(-0.265765\pi\)
\(542\) −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 −0.523238 0.852187i \(-0.675276\pi\)
0.476396 + 0.879231i \(0.341943\pi\)
\(558\) 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 −0.946024 0.324096i \(-0.894940\pi\)
0.753688 + 0.657233i \(0.228273\pi\)
\(564\) 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 0.799810 0.600254i \(-0.204934\pi\)
−0.919740 + 0.392529i \(0.871600\pi\)
\(570\) −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 \(0.389123\pi\)
−0.341330 + 0.939944i \(0.610877\pi\)
\(578\) 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 −0.950889 0.309532i \(-0.899828\pi\)
−0.207382 + 0.978260i \(0.566494\pi\)
\(588\) −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 \(-0.728493\pi\)
0.657754 0.753233i \(-0.271507\pi\)
\(594\) −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 0.883908 0.467660i \(-0.154903\pi\)
−0.846960 + 0.531657i \(0.821569\pi\)
\(602\) −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 −0.957103 0.289746i \(-0.906429\pi\)
0.729479 + 0.684003i \(0.239762\pi\)
\(608\) −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 −0.818734 0.574173i \(-0.805324\pi\)
0.0878810 + 0.996131i \(0.471990\pi\)
\(614\) −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 0.274027 0.961722i \(-0.411644\pi\)
−0.695862 + 0.718175i \(0.744978\pi\)
\(618\) 9.90123 + 5.71648i 0.398286 + 0.229951i
\(619\) 10.5526i 0.424143i 0.977254 + 0.212072i \(0.0680210\pi\)
−0.977254 + 0.212072i \(0.931979\pi\)
\(620\) −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 0.241850 0.970314i \(-0.422246\pi\)
−0.719391 + 0.694605i \(0.755579\pi\)
\(632\) 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 −0.281262 0.959631i \(-0.590753\pi\)
0.971696 0.236235i \(-0.0759136\pi\)
\(642\) 8.60388i 0.339568i
\(643\) −28.9236 16.6990i −1.14063 0.658545i −0.194046 0.980992i \(-0.562161\pi\)
−0.946587 + 0.322447i \(0.895495\pi\)
\(644\) −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 0.888003 0.459838i \(-0.152093\pi\)
−0.842233 + 0.539114i \(0.818759\pi\)
\(648\) 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 0.687525 0.726160i \(-0.258697\pi\)
−0.972636 + 0.232334i \(0.925364\pi\)
\(654\) 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 −0.953879 0.300192i \(-0.902949\pi\)
0.736913 + 0.675988i \(0.236283\pi\)
\(660\) −3.12349 5.41004i −0.121582 0.210586i
\(661\) 11.9943 6.92490i 0.466523 0.269347i −0.248260 0.968693i \(-0.579859\pi\)
0.714783 + 0.699346i \(0.246525\pi\)
\(662\) −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 0.796214 0.605015i \(-0.206833\pi\)
−0.922065 + 0.387034i \(0.873500\pi\)
\(674\) 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 0.716184 0.697912i \(-0.245887\pi\)
−0.246317 + 0.969189i \(0.579221\pi\)
\(684\) 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 0.102032 0.994781i \(-0.467466\pi\)
0.912522 + 0.409028i \(0.134132\pi\)
\(692\) 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 −0.998220 0.0596324i \(-0.981007\pi\)
−0.550753 0.834668i \(-0.685660\pi\)
\(710\) 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 −0.916478 0.400084i \(-0.868981\pi\)
0.804722 + 0.593651i \(0.202314\pi\)
\(720\) 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 \(0.232011\pi\)
−0.745918 + 0.666038i \(0.767989\pi\)
\(734\) 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 −0.869630 0.493704i \(-0.835643\pi\)
−0.00725452 + 0.999974i \(0.502309\pi\)
\(740\) 23.6015 0.867608
\(741\) 0 0
\(742\) −25.4185 −0.933142
\(743\) −9.06660 + 5.23460i −0.332621 + 0.192039i −0.657004 0.753887i \(-0.728177\pi\)
0.324383 + 0.945926i \(0.394843\pi\)
\(744\) 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 0.900745 0.434348i \(-0.143021\pi\)
−0.826529 + 0.562894i \(0.809688\pi\)
\(752\) −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 0.618436 0.785835i \(-0.287767\pi\)
−0.989771 + 0.142664i \(0.954433\pi\)
\(758\) −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 0.0117336 0.999931i \(-0.496265\pi\)
−0.860099 + 0.510127i \(0.829598\pi\)
\(762\) 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 −0.957137 0.289635i \(-0.906466\pi\)
−0.227737 + 0.973723i \(0.573133\pi\)
\(770\) 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 0.732379 0.680897i \(-0.238410\pi\)
−0.223485 + 0.974707i \(0.571743\pi\)
\(774\) 32.1491 + 18.5613i 1.15558