Properties

Label 169.2.c.b.146.1
Level $169$
Weight $2$
Character 169.146
Analytic conductor $1.349$
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] = [169,2,Mod(22,169)]
 
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([4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("169.22");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 169 = 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 169.c (of order \(3\), 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: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.64827.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{5} + 3x^{4} + 5x^{2} - 2x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 146.1
Root \(0.222521 + 0.385418i\) of defining polynomial
Character \(\chi\) \(=\) 169.146
Dual form 169.2.c.b.22.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.12349 - 1.94594i) q^{2} +(0.277479 + 0.480608i) q^{3} +(-1.52446 + 2.64044i) q^{4} +1.44504 q^{5} +(0.623490 - 1.07992i) q^{6} +(1.02446 - 1.77441i) q^{7} +2.35690 q^{8} +(1.34601 - 2.33136i) q^{9} +O(q^{10})\) \(q+(-1.12349 - 1.94594i) q^{2} +(0.277479 + 0.480608i) q^{3} +(-1.52446 + 2.64044i) q^{4} +1.44504 q^{5} +(0.623490 - 1.07992i) q^{6} +(1.02446 - 1.77441i) q^{7} +2.35690 q^{8} +(1.34601 - 2.33136i) q^{9} +(-1.62349 - 2.81197i) q^{10} +(-1.27748 - 2.21266i) q^{11} -1.69202 q^{12} -4.60388 q^{14} +(0.400969 + 0.694498i) q^{15} +(0.400969 + 0.694498i) q^{16} +(2.64795 - 4.58638i) q^{17} -6.04892 q^{18} +(-2.92543 + 5.06699i) q^{19} +(-2.20291 + 3.81555i) q^{20} +1.13706 q^{21} +(-2.87047 + 4.97180i) q^{22} +(0.945042 + 1.63686i) q^{23} +(0.653989 + 1.13274i) q^{24} -2.91185 q^{25} +3.15883 q^{27} +(3.12349 + 5.41004i) q^{28} +(-1.13437 - 1.96480i) q^{29} +(0.900969 - 1.56052i) q^{30} +4.26875 q^{31} +(3.25786 - 5.64279i) q^{32} +(0.708947 - 1.22793i) q^{33} -11.8998 q^{34} +(1.48039 - 2.56410i) q^{35} +(4.10388 + 7.10812i) q^{36} +(2.67845 + 4.63921i) q^{37} +13.1468 q^{38} +3.40581 q^{40} +(0.637063 + 1.10343i) q^{41} +(-1.27748 - 2.21266i) q^{42} +(-3.06853 + 5.31485i) q^{43} +7.78986 q^{44} +(1.94504 - 3.36891i) q^{45} +(2.12349 - 3.67799i) q^{46} +2.95108 q^{47} +(-0.222521 + 0.385418i) q^{48} +(1.40097 + 2.42655i) q^{49} +(3.27144 + 5.66630i) q^{50} +2.93900 q^{51} +5.52111 q^{53} +(-3.54892 - 6.14691i) q^{54} +(-1.84601 - 3.19738i) q^{55} +(2.41454 - 4.18211i) q^{56} -3.24698 q^{57} +(-2.54892 + 4.41485i) q^{58} +(-6.10388 + 10.5722i) q^{59} -2.44504 q^{60} +(-4.28232 + 7.41720i) q^{61} +(-4.79590 - 8.30674i) q^{62} +(-2.75786 - 4.77676i) q^{63} -13.0368 q^{64} -3.18598 q^{66} +(0.288364 + 0.499461i) q^{67} +(8.07338 + 13.9835i) q^{68} +(-0.524459 + 0.908389i) q^{69} -6.65279 q^{70} +(-2.29709 + 3.97868i) q^{71} +(3.17241 - 5.49477i) q^{72} +10.5526 q^{73} +(6.01842 - 10.4242i) q^{74} +(-0.807979 - 1.39946i) q^{75} +(-8.91939 - 15.4488i) q^{76} -5.23490 q^{77} -15.7778 q^{79} +(0.579417 + 1.00358i) q^{80} +(-3.16152 - 5.47592i) q^{81} +(1.43147 - 2.47938i) q^{82} -7.72348 q^{83} +(-1.73341 + 3.00235i) q^{84} +(3.82640 - 6.62751i) q^{85} +13.7899 q^{86} +(0.629531 - 1.09038i) q^{87} +(-3.01089 - 5.21501i) q^{88} +(3.30678 + 5.72751i) q^{89} -8.74094 q^{90} -5.76271 q^{92} +(1.18449 + 2.05159i) q^{93} +(-3.31551 - 5.74263i) q^{94} +(-4.22737 + 7.32201i) q^{95} +3.61596 q^{96} +(5.96346 - 10.3290i) q^{97} +(3.14795 - 5.45241i) q^{98} -6.87800 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 2 q^{2} + 2 q^{3} + 8 q^{5} - q^{6} - 3 q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 2 q^{2} + 2 q^{3} + 8 q^{5} - q^{6} - 3 q^{7} + 6 q^{8} + 3 q^{9} - 5 q^{10} - 8 q^{11} - 10 q^{14} - 2 q^{15} - 2 q^{16} + 2 q^{17} - 18 q^{18} - 4 q^{19} - 4 q^{21} - 3 q^{22} + 5 q^{23} + 9 q^{24} - 10 q^{25} + 2 q^{27} + 14 q^{28} + q^{29} + q^{30} + 10 q^{31} + 7 q^{32} + 10 q^{33} - 26 q^{34} - 4 q^{35} + 7 q^{36} + 12 q^{37} + 24 q^{38} - 6 q^{40} - 7 q^{41} - 8 q^{42} - 13 q^{43} + 11 q^{45} + 8 q^{46} + 36 q^{47} - q^{48} + 4 q^{49} + q^{50} - 2 q^{51} + 2 q^{53} - 3 q^{54} - 6 q^{55} + 4 q^{56} - 10 q^{57} + 3 q^{58} - 19 q^{59} - 14 q^{60} - 4 q^{61} - q^{62} - 4 q^{63} - 22 q^{64} + 10 q^{66} - q^{67} + 21 q^{68} + 6 q^{69} - 4 q^{70} - 27 q^{71} - 4 q^{72} - 18 q^{73} + 8 q^{74} - 15 q^{75} - 21 q^{76} + 16 q^{77} - 10 q^{79} - 5 q^{80} + q^{81} + 14 q^{82} + 14 q^{83} - 7 q^{84} + 5 q^{85} + 36 q^{86} + 18 q^{87} - 15 q^{88} - 11 q^{89} - 24 q^{90} + 22 q^{93} - 5 q^{94} - 3 q^{95} + 42 q^{96} + 7 q^{97} + 5 q^{98} - 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.12349 1.94594i −0.794427 1.37599i −0.923202 0.384315i \(-0.874438\pi\)
0.128775 0.991674i \(-0.458896\pi\)
\(3\) 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
\(5\) 1.44504 0.646242 0.323121 0.946358i \(-0.395268\pi\)
0.323121 + 0.946358i \(0.395268\pi\)
\(6\) 0.623490 1.07992i 0.254539 0.440874i
\(7\) 1.02446 1.77441i 0.387209 0.670666i −0.604864 0.796329i \(-0.706773\pi\)
0.992073 + 0.125663i \(0.0401059\pi\)
\(8\) 2.35690 0.833289
\(9\) 1.34601 2.33136i 0.448670 0.777120i
\(10\) −1.62349 2.81197i −0.513393 0.889222i
\(11\) −1.27748 2.21266i −0.385174 0.667142i 0.606619 0.794993i \(-0.292525\pi\)
−0.991793 + 0.127851i \(0.959192\pi\)
\(12\) −1.69202 −0.488445
\(13\) 0 0
\(14\) −4.60388 −1.23044
\(15\) 0.400969 + 0.694498i 0.103530 + 0.179319i
\(16\) 0.400969 + 0.694498i 0.100242 + 0.173625i
\(17\) 2.64795 4.58638i 0.642222 1.11236i −0.342714 0.939440i \(-0.611346\pi\)
0.984936 0.172921i \(-0.0553205\pi\)
\(18\) −6.04892 −1.42574
\(19\) −2.92543 + 5.06699i −0.671139 + 1.16245i 0.306442 + 0.951889i \(0.400861\pi\)
−0.977581 + 0.210558i \(0.932472\pi\)
\(20\) −2.20291 + 3.81555i −0.492585 + 0.853182i
\(21\) 1.13706 0.248128
\(22\) −2.87047 + 4.97180i −0.611986 + 1.05999i
\(23\) 0.945042 + 1.63686i 0.197055 + 0.341309i 0.947572 0.319542i \(-0.103529\pi\)
−0.750517 + 0.660851i \(0.770196\pi\)
\(24\) 0.653989 + 1.13274i 0.133495 + 0.231220i
\(25\) −2.91185 −0.582371
\(26\) 0 0
\(27\) 3.15883 0.607918
\(28\) 3.12349 + 5.41004i 0.590284 + 1.02240i
\(29\) −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
\(31\) 4.26875 0.766690 0.383345 0.923605i \(-0.374772\pi\)
0.383345 + 0.923605i \(0.374772\pi\)
\(32\) 3.25786 5.64279i 0.575915 0.997513i
\(33\) 0.708947 1.22793i 0.123412 0.213756i
\(34\) −11.8998 −2.04079
\(35\) 1.48039 2.56410i 0.250231 0.433413i
\(36\) 4.10388 + 7.10812i 0.683979 + 1.18469i
\(37\) 2.67845 + 4.63921i 0.440334 + 0.762681i 0.997714 0.0675764i \(-0.0215267\pi\)
−0.557380 + 0.830258i \(0.688193\pi\)
\(38\) 13.1468 2.13268
\(39\) 0 0
\(40\) 3.40581 0.538506
\(41\) 0.637063 + 1.10343i 0.0994926 + 0.172326i 0.911475 0.411356i \(-0.134945\pi\)
−0.811982 + 0.583682i \(0.801611\pi\)
\(42\) −1.27748 2.21266i −0.197119 0.341421i
\(43\) −3.06853 + 5.31485i −0.467947 + 0.810507i −0.999329 0.0366246i \(-0.988339\pi\)
0.531382 + 0.847132i \(0.321673\pi\)
\(44\) 7.78986 1.17437
\(45\) 1.94504 3.36891i 0.289950 0.502208i
\(46\) 2.12349 3.67799i 0.313091 0.542290i
\(47\) 2.95108 0.430460 0.215230 0.976563i \(-0.430950\pi\)
0.215230 + 0.976563i \(0.430950\pi\)
\(48\) −0.222521 + 0.385418i −0.0321181 + 0.0556302i
\(49\) 1.40097 + 2.42655i 0.200138 + 0.346650i
\(50\) 3.27144 + 5.66630i 0.462651 + 0.801335i
\(51\) 2.93900 0.411542
\(52\) 0 0
\(53\) 5.52111 0.758382 0.379191 0.925318i \(-0.376202\pi\)
0.379191 + 0.925318i \(0.376202\pi\)
\(54\) −3.54892 6.14691i −0.482946 0.836488i
\(55\) −1.84601 3.19738i −0.248916 0.431135i
\(56\) 2.41454 4.18211i 0.322657 0.558858i
\(57\) −3.24698 −0.430073
\(58\) −2.54892 + 4.41485i −0.334689 + 0.579699i
\(59\) −6.10388 + 10.5722i −0.794657 + 1.37639i 0.128400 + 0.991722i \(0.459016\pi\)
−0.923057 + 0.384664i \(0.874317\pi\)
\(60\) −2.44504 −0.315654
\(61\) −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
\(63\) −2.75786 4.77676i −0.347458 0.601815i
\(64\) −13.0368 −1.62960
\(65\) 0 0
\(66\) −3.18598 −0.392167
\(67\) 0.288364 + 0.499461i 0.0352293 + 0.0610189i 0.883102 0.469180i \(-0.155451\pi\)
−0.847873 + 0.530199i \(0.822117\pi\)
\(68\) 8.07338 + 13.9835i 0.979041 + 1.69575i
\(69\) −0.524459 + 0.908389i −0.0631374 + 0.109357i
\(70\) −6.65279 −0.795161
\(71\) −2.29709 + 3.97868i −0.272615 + 0.472183i −0.969531 0.244970i \(-0.921222\pi\)
0.696916 + 0.717153i \(0.254555\pi\)
\(72\) 3.17241 5.49477i 0.373872 0.647565i
\(73\) 10.5526 1.23508 0.617542 0.786538i \(-0.288128\pi\)
0.617542 + 0.786538i \(0.288128\pi\)
\(74\) 6.01842 10.4242i 0.699627 1.21179i
\(75\) −0.807979 1.39946i −0.0932973 0.161596i
\(76\) −8.91939 15.4488i −1.02312 1.77210i
\(77\) −5.23490 −0.596572
\(78\) 0 0
\(79\) −15.7778 −1.77514 −0.887569 0.460674i \(-0.847608\pi\)
−0.887569 + 0.460674i \(0.847608\pi\)
\(80\) 0.579417 + 1.00358i 0.0647808 + 0.112204i
\(81\) −3.16152 5.47592i −0.351280 0.608435i
\(82\) 1.43147 2.47938i 0.158079 0.273801i
\(83\) −7.72348 −0.847762 −0.423881 0.905718i \(-0.639333\pi\)
−0.423881 + 0.905718i \(0.639333\pi\)
\(84\) −1.73341 + 3.00235i −0.189130 + 0.327583i
\(85\) 3.82640 6.62751i 0.415031 0.718855i
\(86\) 13.7899 1.48700
\(87\) 0.629531 1.09038i 0.0674928 0.116901i
\(88\) −3.01089 5.21501i −0.320961 0.555922i
\(89\) 3.30678 + 5.72751i 0.350518 + 0.607115i 0.986340 0.164720i \(-0.0526721\pi\)
−0.635822 + 0.771836i \(0.719339\pi\)
\(90\) −8.74094 −0.921376
\(91\) 0 0
\(92\) −5.76271 −0.600804
\(93\) 1.18449 + 2.05159i 0.122826 + 0.212740i
\(94\) −3.31551 5.74263i −0.341969 0.592307i
\(95\) −4.22737 + 7.32201i −0.433719 + 0.751223i
\(96\) 3.61596 0.369052
\(97\) 5.96346 10.3290i 0.605498 1.04875i −0.386475 0.922300i \(-0.626307\pi\)
0.991973 0.126453i \(-0.0403592\pi\)
\(98\) 3.14795 5.45241i 0.317991 0.550776i
\(99\) −6.87800 −0.691265
\(100\) 4.43900 7.68858i 0.443900 0.768858i
\(101\) −6.53199 11.3137i −0.649957 1.12576i −0.983133 0.182894i \(-0.941453\pi\)
0.333175 0.942865i \(-0.391880\pi\)
\(102\) −3.30194 5.71912i −0.326941 0.566278i
\(103\) 9.16852 0.903401 0.451701 0.892170i \(-0.350818\pi\)
0.451701 + 0.892170i \(0.350818\pi\)
\(104\) 0 0
\(105\) 1.64310 0.160351
\(106\) −6.20291 10.7437i −0.602480 1.04353i
\(107\) 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
\(109\) −0.121998 −0.0116853 −0.00584264 0.999983i \(-0.501860\pi\)
−0.00584264 + 0.999983i \(0.501860\pi\)
\(110\) −4.14795 + 7.18446i −0.395491 + 0.685011i
\(111\) −1.48643 + 2.57457i −0.141085 + 0.244367i
\(112\) 1.64310 0.155259
\(113\) −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
\(115\) 1.36563 + 2.36533i 0.127345 + 0.220568i
\(116\) 6.91723 0.642249
\(117\) 0 0
\(118\) 27.4306 2.52519
\(119\) −5.42543 9.39712i −0.497348 0.861432i
\(120\) 0.945042 + 1.63686i 0.0862701 + 0.149424i
\(121\) 2.23609 3.87303i 0.203281 0.352094i
\(122\) 19.2446 1.74232
\(123\) −0.353543 + 0.612355i −0.0318779 + 0.0552142i
\(124\) −6.50753 + 11.2714i −0.584394 + 1.01220i
\(125\) −11.4330 −1.02260
\(126\) −6.19687 + 10.7333i −0.552061 + 0.956197i
\(127\) 9.48523 + 16.4289i 0.841678 + 1.45783i 0.888475 + 0.458925i \(0.151765\pi\)
−0.0467971 + 0.998904i \(0.514901\pi\)
\(128\) 8.13102 + 14.0833i 0.718688 + 1.24480i
\(129\) −3.40581 −0.299865
\(130\) 0 0
\(131\) 3.25667 0.284536 0.142268 0.989828i \(-0.454560\pi\)
0.142268 + 0.989828i \(0.454560\pi\)
\(132\) 2.16152 + 3.74387i 0.188136 + 0.325862i
\(133\) 5.99396 + 10.3818i 0.519742 + 0.900220i
\(134\) 0.647948 1.12228i 0.0559742 0.0969502i
\(135\) 4.56465 0.392862
\(136\) 6.24094 10.8096i 0.535156 0.926918i
\(137\) 0.396125 0.686108i 0.0338432 0.0586181i −0.848608 0.529023i \(-0.822559\pi\)
0.882451 + 0.470405i \(0.155892\pi\)
\(138\) 2.35690 0.200632
\(139\) 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
\(141\) 0.818864 + 1.41831i 0.0689608 + 0.119444i
\(142\) 10.3230 0.866291
\(143\) 0 0
\(144\) 2.15883 0.179903
\(145\) −1.63922 2.83921i −0.136130 0.235784i
\(146\) −11.8557 20.5347i −0.981185 1.69946i
\(147\) −0.777479 + 1.34663i −0.0641254 + 0.111068i
\(148\) −16.3327 −1.34254
\(149\) 4.20291 7.27965i 0.344316 0.596372i −0.640914 0.767613i \(-0.721444\pi\)
0.985229 + 0.171241i \(0.0547777\pi\)
\(150\) −1.81551 + 3.14456i −0.148236 + 0.256752i
\(151\) −14.1293 −1.14983 −0.574913 0.818215i \(-0.694964\pi\)
−0.574913 + 0.818215i \(0.694964\pi\)
\(152\) −6.89493 + 11.9424i −0.559253 + 0.968654i
\(153\) −7.12833 12.3466i −0.576292 0.998166i
\(154\) 5.88135 + 10.1868i 0.473933 + 0.820876i
\(155\) 6.16852 0.495468
\(156\) 0 0
\(157\) −9.43296 −0.752832 −0.376416 0.926451i \(-0.622844\pi\)
−0.376416 + 0.926451i \(0.622844\pi\)
\(158\) 17.7262 + 30.7026i 1.41022 + 2.44257i
\(159\) 1.53199 + 2.65349i 0.121495 + 0.210435i
\(160\) 4.70775 8.15406i 0.372180 0.644635i
\(161\) 3.87263 0.305206
\(162\) −7.10388 + 12.3043i −0.558133 + 0.966715i
\(163\) 4.35205 7.53797i 0.340879 0.590420i −0.643717 0.765263i \(-0.722609\pi\)
0.984596 + 0.174844i \(0.0559420\pi\)
\(164\) −3.88471 −0.303345
\(165\) 1.02446 1.77441i 0.0797540 0.138138i
\(166\) 8.67725 + 15.0294i 0.673485 + 1.16651i
\(167\) −11.9269 20.6580i −0.922933 1.59857i −0.794853 0.606803i \(-0.792452\pi\)
−0.128080 0.991764i \(-0.540881\pi\)
\(168\) 2.67994 0.206762
\(169\) 0 0
\(170\) −17.1957 −1.31885
\(171\) 7.87531 + 13.6404i 0.602240 + 1.04311i
\(172\) −9.35570 16.2045i −0.713365 1.23559i
\(173\) 9.42758 16.3291i 0.716766 1.24147i −0.245509 0.969394i \(-0.578955\pi\)
0.962274 0.272081i \(-0.0877117\pi\)
\(174\) −2.82908 −0.214472
\(175\) −2.98307 + 5.16684i −0.225499 + 0.390576i
\(176\) 1.02446 1.77441i 0.0772215 0.133752i
\(177\) −6.77479 −0.509224
\(178\) 7.43027 12.8696i 0.556922 0.964618i
\(179\) −3.01089 5.21501i −0.225044 0.389788i 0.731289 0.682068i \(-0.238919\pi\)
−0.956333 + 0.292280i \(0.905586\pi\)
\(180\) 5.93027 + 10.2715i 0.442016 + 0.765595i
\(181\) −4.77777 −0.355129 −0.177565 0.984109i \(-0.556822\pi\)
−0.177565 + 0.984109i \(0.556822\pi\)
\(182\) 0 0
\(183\) −4.75302 −0.351353
\(184\) 2.22737 + 3.85791i 0.164204 + 0.284409i
\(185\) 3.87047 + 6.70385i 0.284563 + 0.492877i
\(186\) 2.66152 4.60989i 0.195152 0.338014i
\(187\) −13.5308 −0.989470
\(188\) −4.49880 + 7.79216i −0.328109 + 0.568301i
\(189\) 3.23609 5.60508i 0.235391 0.407710i
\(190\) 18.9976 1.37823
\(191\) −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
\(193\) 3.02715 + 5.24317i 0.217899 + 0.377412i 0.954165 0.299280i \(-0.0967464\pi\)
−0.736267 + 0.676692i \(0.763413\pi\)
\(194\) −26.7995 −1.92410
\(195\) 0 0
\(196\) −8.54288 −0.610205
\(197\) −5.70775 9.88611i −0.406660 0.704357i 0.587853 0.808968i \(-0.299973\pi\)
−0.994513 + 0.104611i \(0.966640\pi\)
\(198\) 7.72737 + 13.3842i 0.549160 + 0.951173i
\(199\) 6.95257 12.0422i 0.492855 0.853650i −0.507111 0.861881i \(-0.669287\pi\)
0.999966 + 0.00823084i \(0.00261999\pi\)
\(200\) −6.86294 −0.485283
\(201\) −0.160030 + 0.277180i −0.0112876 + 0.0195508i
\(202\) −14.6773 + 25.4217i −1.03269 + 1.78867i
\(203\) −4.64848 −0.326259
\(204\) −4.48039 + 7.76026i −0.313690 + 0.543327i
\(205\) 0.920583 + 1.59450i 0.0642963 + 0.111364i
\(206\) −10.3007 17.8414i −0.717687 1.24307i
\(207\) 5.08815 0.353651
\(208\) 0 0
\(209\) 14.9487 1.03402
\(210\) −1.84601 3.19738i −0.127387 0.220640i
\(211\) 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
\(213\) −2.54958 −0.174694
\(214\) 7.75182 13.4266i 0.529904 0.917820i
\(215\) −4.43416 + 7.68018i −0.302407 + 0.523784i
\(216\) 7.44504 0.506571
\(217\) 4.37316 7.57453i 0.296869 0.514193i
\(218\) 0.137063 + 0.237401i 0.00928310 + 0.0160788i
\(219\) 2.92812 + 5.07165i 0.197864 + 0.342710i
\(220\) 11.2567 0.758924
\(221\) 0 0
\(222\) 6.67994 0.448328
\(223\) −3.66756 6.35241i −0.245598 0.425389i 0.716701 0.697380i \(-0.245651\pi\)
−0.962300 + 0.271992i \(0.912318\pi\)
\(224\) −6.67510 11.5616i −0.445999 0.772492i
\(225\) −3.91939 + 6.78858i −0.261292 + 0.452572i
\(226\) 16.4209 1.09230
\(227\) −4.33728 + 7.51239i −0.287875 + 0.498615i −0.973302 0.229526i \(-0.926282\pi\)
0.685427 + 0.728141i \(0.259616\pi\)
\(228\) 4.94989 8.57345i 0.327814 0.567791i
\(229\) 13.6866 0.904439 0.452219 0.891907i \(-0.350632\pi\)
0.452219 + 0.891907i \(0.350632\pi\)
\(230\) 3.06853 5.31485i 0.202333 0.350451i
\(231\) −1.45257 2.51593i −0.0955724 0.165536i
\(232\) −2.67360 4.63082i −0.175531 0.304028i
\(233\) −5.08815 −0.333336 −0.166668 0.986013i \(-0.553301\pi\)
−0.166668 + 0.986013i \(0.553301\pi\)
\(234\) 0 0
\(235\) 4.26444 0.278181
\(236\) −18.6102 32.2338i −1.21142 2.09824i
\(237\) −4.37800 7.58292i −0.284382 0.492564i
\(238\) −12.1908 + 21.1151i −0.790214 + 1.36869i
\(239\) 10.9239 0.706611 0.353305 0.935508i \(-0.385058\pi\)
0.353305 + 0.935508i \(0.385058\pi\)
\(240\) −0.321552 + 0.556945i −0.0207561 + 0.0359506i
\(241\) 5.95742 10.3186i 0.383751 0.664676i −0.607844 0.794056i \(-0.707965\pi\)
0.991595 + 0.129380i \(0.0412987\pi\)
\(242\) −10.0489 −0.645969
\(243\) 6.49276 11.2458i 0.416511 0.721418i
\(244\) −13.0565 22.6144i −0.835854 1.44774i
\(245\) 2.02446 + 3.50647i 0.129338 + 0.224020i
\(246\) 1.58881 0.101299
\(247\) 0 0
\(248\) 10.0610 0.638874
\(249\) −2.14310 3.71197i −0.135814 0.235236i
\(250\) 12.8448 + 22.2479i 0.812377 + 1.40708i
\(251\) −11.1739 + 19.3538i −0.705290 + 1.22160i 0.261296 + 0.965259i \(0.415850\pi\)
−0.966587 + 0.256340i \(0.917483\pi\)
\(252\) 16.8170 1.05937
\(253\) 2.41454 4.18211i 0.151801 0.262927i
\(254\) 21.3131 36.9154i 1.33730 2.31628i
\(255\) 4.24698 0.265956
\(256\) 5.23341 9.06453i 0.327088 0.566533i
\(257\) 9.33004 + 16.1601i 0.581992 + 1.00804i 0.995243 + 0.0974228i \(0.0310599\pi\)
−0.413251 + 0.910617i \(0.635607\pi\)
\(258\) 3.82640 + 6.62751i 0.238221 + 0.412611i
\(259\) 10.9758 0.682005
\(260\) 0 0
\(261\) −6.10752 −0.378046
\(262\) −3.65883 6.33729i −0.226043 0.391519i
\(263\) −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
\(265\) 7.97823 0.490099
\(266\) 13.4683 23.3278i 0.825795 1.43032i
\(267\) −1.83513 + 3.17853i −0.112308 + 0.194523i
\(268\) −1.75840 −0.107411
\(269\) −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
\(271\) −0.997844 1.72832i −0.0606147 0.104988i 0.834126 0.551574i \(-0.185973\pi\)
−0.894740 + 0.446587i \(0.852639\pi\)
\(272\) 4.24698 0.257511
\(273\) 0 0
\(274\) −1.78017 −0.107544
\(275\) 3.71983 + 6.44294i 0.224314 + 0.388524i
\(276\) −1.59903 2.76960i −0.0962504 0.166711i
\(277\) −5.89224 + 10.2057i −0.354030 + 0.613199i −0.986952 0.161018i \(-0.948522\pi\)
0.632921 + 0.774216i \(0.281856\pi\)
\(278\) −25.4795 −1.52816
\(279\) 5.74578 9.95199i 0.343991 0.595810i
\(280\) 3.48911 6.04332i 0.208514 0.361158i
\(281\) 6.47219 0.386098 0.193049 0.981189i \(-0.438162\pi\)
0.193049 + 0.981189i \(0.438162\pi\)
\(282\) 1.83997 3.18692i 0.109569 0.189778i
\(283\) −3.29052 5.69935i −0.195601 0.338791i 0.751496 0.659737i \(-0.229332\pi\)
−0.947097 + 0.320946i \(0.895999\pi\)
\(284\) −7.00365 12.1307i −0.415590 0.719823i
\(285\) −4.69202 −0.277931
\(286\) 0 0
\(287\) 2.61058 0.154098
\(288\) −8.77024 15.1905i −0.516791 0.895109i
\(289\) −5.52326 9.56657i −0.324898 0.562739i
\(290\) −3.68329 + 6.37965i −0.216290 + 0.374626i
\(291\) 6.61894 0.388009
\(292\) −16.0869 + 27.8634i −0.941418 + 1.63058i
\(293\) −12.1691 + 21.0774i −0.710924 + 1.23136i 0.253587 + 0.967313i \(0.418390\pi\)
−0.964511 + 0.264044i \(0.914944\pi\)
\(294\) 3.49396 0.203772
\(295\) −8.82036 + 15.2773i −0.513541 + 0.889479i
\(296\) 6.31282 + 10.9341i 0.366925 + 0.635533i
\(297\) −4.03534 6.98942i −0.234154 0.405567i
\(298\) −18.8877 −1.09413
\(299\) 0 0
\(300\) 4.92692 0.284456
\(301\) 6.28717 + 10.8897i 0.362386 + 0.627672i
\(302\) 15.8741 + 27.4948i 0.913453 + 1.58215i
\(303\) 3.62498 6.27865i 0.208250 0.360699i
\(304\) −4.69202 −0.269106
\(305\) −6.18814 + 10.7182i −0.354332 + 0.613720i
\(306\) −16.0172 + 27.7426i −0.915644 + 1.58594i
\(307\) 14.0737 0.803227 0.401613 0.915809i \(-0.368450\pi\)
0.401613 + 0.915809i \(0.368450\pi\)
\(308\) 7.98039 13.8224i 0.454725 0.787606i
\(309\) 2.54407 + 4.40646i 0.144727 + 0.250675i
\(310\) −6.93027 12.0036i −0.393613 0.681758i
\(311\) −29.7700 −1.68810 −0.844051 0.536263i \(-0.819836\pi\)
−0.844051 + 0.536263i \(0.819836\pi\)
\(312\) 0 0
\(313\) −7.47889 −0.422732 −0.211366 0.977407i \(-0.567791\pi\)
−0.211366 + 0.977407i \(0.567791\pi\)
\(314\) 10.5978 + 18.3560i 0.598070 + 1.03589i
\(315\) −3.98523 6.90262i −0.224542 0.388919i
\(316\) 24.0526 41.6603i 1.35306 2.34357i
\(317\) −30.0301 −1.68666 −0.843330 0.537396i \(-0.819408\pi\)
−0.843330 + 0.537396i \(0.819408\pi\)
\(318\) 3.44235 5.96233i 0.193038 0.334351i
\(319\) −2.89828 + 5.01997i −0.162273 + 0.281064i
\(320\) −18.8388 −1.05312
\(321\) −1.91454 + 3.31608i −0.106859 + 0.185086i
\(322\) −4.35086 7.53590i −0.242464 0.419959i
\(323\) 15.4928 + 26.8343i 0.862040 + 1.49310i
\(324\) 19.2784 1.07102
\(325\) 0 0
\(326\) −19.5579 −1.08321
\(327\) −0.0338518 0.0586331i −0.00187201 0.00324242i
\(328\) 1.50149 + 2.60066i 0.0829060 + 0.143597i
\(329\) 3.02326 5.23644i 0.166678 0.288694i
\(330\) −4.60388 −0.253435
\(331\) −7.85839 + 13.6111i −0.431936 + 0.748135i −0.997040 0.0768845i \(-0.975503\pi\)
0.565104 + 0.825020i \(0.308836\pi\)
\(332\) 11.7741 20.3934i 0.646189 1.11923i
\(333\) 14.4209 0.790259
\(334\) −26.7995 + 46.4182i −1.46641 + 2.53989i
\(335\) 0.416698 + 0.721743i 0.0227667 + 0.0394330i
\(336\) 0.455927 + 0.789689i 0.0248729 + 0.0430811i
\(337\) 1.95407 0.106445 0.0532224 0.998583i \(-0.483051\pi\)
0.0532224 + 0.998583i \(0.483051\pi\)
\(338\) 0 0
\(339\) −4.05562 −0.220271
\(340\) 11.6664 + 20.2067i 0.632698 + 1.09586i
\(341\) −5.45324 9.44529i −0.295309 0.511491i
\(342\) 17.6957 30.6498i 0.956872 1.65735i
\(343\) 20.0834 1.08440
\(344\) −7.23221 + 12.5266i −0.389935 + 0.675387i
\(345\) −0.757865 + 1.31266i −0.0408021 + 0.0706713i
\(346\) −42.3672 −2.27767
\(347\) 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
\(349\) −5.23341 9.06453i −0.280138 0.485213i 0.691281 0.722586i \(-0.257047\pi\)
−0.971418 + 0.237373i \(0.923713\pi\)
\(350\) 13.4058 0.716571
\(351\) 0 0
\(352\) −16.6474 −0.887310
\(353\) 7.76540 + 13.4501i 0.413310 + 0.715875i 0.995249 0.0973578i \(-0.0310391\pi\)
−0.581939 + 0.813232i \(0.697706\pi\)
\(354\) 7.61141 + 13.1833i 0.404542 + 0.700687i
\(355\) −3.31940 + 5.74936i −0.176175 + 0.305144i
\(356\) −20.1642 −1.06870
\(357\) 3.01089 5.21501i 0.159353 0.276007i
\(358\) −6.76540 + 11.7180i −0.357562 + 0.619316i
\(359\) 21.4263 1.13083 0.565417 0.824805i \(-0.308715\pi\)
0.565417 + 0.824805i \(0.308715\pi\)
\(360\) 4.58426 7.94017i 0.241612 0.418484i
\(361\) −7.61625 13.1917i −0.400855 0.694302i
\(362\) 5.36778 + 9.29727i 0.282124 + 0.488654i
\(363\) 2.48188 0.130265
\(364\) 0 0
\(365\) 15.2489 0.798164
\(366\) 5.33997 + 9.24910i 0.279125 + 0.483458i
\(367\) −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
\(369\) 3.42998 0.178557
\(370\) 8.69687 15.0634i 0.452129 0.783110i
\(371\) 5.65615 9.79673i 0.293652 0.508621i
\(372\) −7.22282 −0.374486
\(373\) 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
\(375\) −3.17241 5.49477i −0.163822 0.283749i
\(376\) 6.95539 0.358697
\(377\) 0 0
\(378\) −14.5429 −0.748005
\(379\) 8.26928 + 14.3228i 0.424765 + 0.735714i 0.996398 0.0847951i \(-0.0270236\pi\)
−0.571634 + 0.820509i \(0.693690\pi\)
\(380\) −12.8889 22.3242i −0.661186 1.14521i
\(381\) −5.26391 + 9.11735i −0.269678 + 0.467096i
\(382\) 41.4131 2.11888
\(383\) 3.76809 6.52652i 0.192540 0.333489i −0.753551 0.657389i \(-0.771661\pi\)
0.946091 + 0.323900i \(0.104994\pi\)
\(384\) −4.51238 + 7.81567i −0.230271 + 0.398842i
\(385\) −7.56465 −0.385530
\(386\) 6.80194 11.7813i 0.346210 0.599652i
\(387\) 8.26055 + 14.3077i 0.419908 + 0.727301i
\(388\) 18.1821 + 31.4923i 0.923056 + 1.59878i
\(389\) 35.5555 1.80274 0.901369 0.433052i \(-0.142563\pi\)
0.901369 + 0.433052i \(0.142563\pi\)
\(390\) 0 0
\(391\) 10.0097 0.506212
\(392\) 3.30194 + 5.71912i 0.166773 + 0.288859i
\(393\) 0.903657 + 1.56518i 0.0455835 + 0.0789529i
\(394\) −12.8252 + 22.2139i −0.646124 + 1.11912i
\(395\) −22.7995 −1.14717
\(396\) 10.4852 18.1610i 0.526903 0.912622i
\(397\) 0.675760 1.17045i 0.0339154 0.0587432i −0.848569 0.529084i \(-0.822536\pi\)
0.882485 + 0.470341i \(0.155869\pi\)
\(398\) −31.2446 −1.56615
\(399\) −3.32640 + 5.76149i −0.166528 + 0.288435i
\(400\) −1.16756 2.02228i −0.0583781 0.101114i
\(401\) 0.289561 + 0.501534i 0.0144600 + 0.0250454i 0.873165 0.487425i \(-0.162064\pi\)
−0.858705 + 0.512470i \(0.828730\pi\)
\(402\) 0.719169 0.0358689
\(403\) 0 0
\(404\) 39.8310 1.98167
\(405\) −4.56853 7.91293i −0.227012 0.393197i
\(406\) 5.22252 + 9.04567i 0.259189 + 0.448929i
\(407\) 6.84332 11.8530i 0.339211 0.587531i
\(408\) 6.92692 0.342934
\(409\) −7.57875 + 13.1268i −0.374745 + 0.649078i −0.990289 0.139025i \(-0.955603\pi\)
0.615544 + 0.788103i \(0.288936\pi\)
\(410\) 2.06853 3.58280i 0.102157 0.176942i
\(411\) 0.439665 0.0216871
\(412\) −13.9770 + 24.2089i −0.688599 + 1.19269i
\(413\) 12.5063 + 21.6616i 0.615397 + 1.06590i
\(414\) −5.71648 9.90123i −0.280950 0.486619i
\(415\) −11.1608 −0.547860
\(416\) 0 0
\(417\) 6.29291 0.308165
\(418\) −16.7947 29.0893i −0.821456 1.42280i
\(419\) 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
\(421\) 35.0465 1.70806 0.854032 0.520221i \(-0.174151\pi\)
0.854032 + 0.520221i \(0.174151\pi\)
\(422\) 14.8802 25.7732i 0.724355 1.25462i
\(423\) 3.97219 6.88003i 0.193134 0.334519i
\(424\) 13.0127 0.631951
\(425\) −7.71044 + 13.3549i −0.374011 + 0.647806i
\(426\) 2.86443 + 4.96134i 0.138782 + 0.240378i
\(427\) 8.77413 + 15.1972i 0.424610 + 0.735446i
\(428\) −21.0368 −1.01685
\(429\) 0 0
\(430\) 19.9269 0.960961
\(431\) −17.1407 29.6886i −0.825639 1.43005i −0.901430 0.432925i \(-0.857481\pi\)
0.0757909 0.997124i \(-0.475852\pi\)
\(432\) 1.26659 + 2.19381i 0.0609390 + 0.105549i
\(433\) −6.86927 + 11.8979i −0.330116 + 0.571778i −0.982534 0.186081i \(-0.940421\pi\)
0.652418 + 0.757859i \(0.273755\pi\)
\(434\) −19.6528 −0.943364
\(435\) 0.909698 1.57564i 0.0436167 0.0755463i
\(436\) 0.185981 0.322128i 0.00890686 0.0154271i
\(437\) −11.0586 −0.529005
\(438\) 6.57942 11.3959i 0.314377 0.544516i
\(439\) −5.12014 8.86834i −0.244371 0.423263i 0.717584 0.696472i \(-0.245248\pi\)
−0.961955 + 0.273210i \(0.911915\pi\)
\(440\) −4.35086 7.53590i −0.207419 0.359260i
\(441\) 7.54288 0.359185
\(442\) 0 0
\(443\) 12.1763 0.578513 0.289257 0.957252i \(-0.406592\pi\)
0.289257 + 0.957252i \(0.406592\pi\)
\(444\) −4.53199 7.84964i −0.215079 0.372527i
\(445\) 4.77844 + 8.27650i 0.226520 + 0.392344i
\(446\) −8.24094 + 14.2737i −0.390220 + 0.675880i
\(447\) 4.66487 0.220641
\(448\) −13.3557 + 23.1327i −0.630997 + 1.09292i
\(449\) −6.45257 + 11.1762i −0.304516 + 0.527437i −0.977153 0.212535i \(-0.931828\pi\)
0.672638 + 0.739972i \(0.265161\pi\)
\(450\) 17.6136 0.830311
\(451\) 1.62767 2.81921i 0.0766440 0.132751i
\(452\) −11.1407 19.2963i −0.524015 0.907621i
\(453\) −3.92058 6.79065i −0.184205 0.319053i
\(454\) 19.4916 0.914785
\(455\) 0 0
\(456\) −7.65279 −0.358375
\(457\) 2.32855 + 4.03317i 0.108925 + 0.188664i 0.915335 0.402693i \(-0.131926\pi\)
−0.806410 + 0.591357i \(0.798592\pi\)
\(458\) −15.3768 26.6334i −0.718511 1.24450i
\(459\) 8.36443 14.4876i 0.390418 0.676224i
\(460\) −8.32736 −0.388265
\(461\) −15.7702 + 27.3149i −0.734493 + 1.27218i 0.220452 + 0.975398i \(0.429247\pi\)
−0.954945 + 0.296782i \(0.904087\pi\)
\(462\) −3.26391 + 5.65325i −0.151851 + 0.263013i
\(463\) −17.6504 −0.820284 −0.410142 0.912022i \(-0.634521\pi\)
−0.410142 + 0.912022i \(0.634521\pi\)
\(464\) 0.909698 1.57564i 0.0422317 0.0731474i
\(465\) 1.71164 + 2.96464i 0.0793752 + 0.137482i
\(466\) 5.71648 + 9.90123i 0.264811 + 0.458666i
\(467\) −32.1726 −1.48877 −0.744385 0.667751i \(-0.767257\pi\)
−0.744385 + 0.667751i \(0.767257\pi\)
\(468\) 0 0
\(469\) 1.18167 0.0545644
\(470\) −4.79105 8.29835i −0.220995 0.382774i
\(471\) −2.61745 4.53355i −0.120606 0.208895i
\(472\) −14.3862 + 24.9176i −0.662178 + 1.14693i
\(473\) 15.6799 0.720964
\(474\) −9.83728 + 17.0387i −0.451841 + 0.782612i
\(475\) 8.51842 14.7543i 0.390852 0.676975i
\(476\) 33.0834 1.51637
\(477\) 7.43147 12.8717i 0.340264 0.589354i
\(478\) −12.2729 21.2573i −0.561351 0.972288i
\(479\) −17.4499 30.2241i −0.797306 1.38097i −0.921365 0.388699i \(-0.872925\pi\)
0.124059 0.992275i \(-0.460409\pi\)
\(480\) 5.22521 0.238497
\(481\) 0 0
\(482\) −26.7724 −1.21945
\(483\) 1.07457 + 1.86121i 0.0488947 + 0.0846882i
\(484\) 6.81767 + 11.8085i 0.309894 + 0.536752i
\(485\) 8.61745 14.9259i 0.391298 0.677748i
\(486\) −29.1782 −1.32355
\(487\) 20.9175 36.2302i 0.947864 1.64175i 0.197950 0.980212i \(-0.436572\pi\)
0.749914 0.661536i \(-0.230095\pi\)
\(488\) −10.0930 + 17.4816i −0.456888 + 0.791354i
\(489\) 4.83041 0.218439
\(490\) 4.54892 7.87896i 0.205499 0.355935i
\(491\) −10.9227 18.9187i −0.492936 0.853791i 0.507031 0.861928i \(-0.330743\pi\)
−0.999967 + 0.00813732i \(0.997410\pi\)
\(492\) −1.07792 1.86702i −0.0485966 0.0841718i
\(493\) −12.0151 −0.541131
\(494\) 0 0
\(495\) −9.93900 −0.446725
\(496\) 1.71164 + 2.96464i 0.0768547 + 0.133116i
\(497\) 4.70655 + 8.15199i 0.211118 + 0.365667i
\(498\) −4.81551 + 8.34071i −0.215788 + 0.373756i
\(499\) −23.5472 −1.05412 −0.527058 0.849829i \(-0.676705\pi\)
−0.527058 + 0.849829i \(0.676705\pi\)
\(500\) 17.4291 30.1880i 0.779452 1.35005i
\(501\) 6.61894 11.4643i 0.295712 0.512189i
\(502\) 50.2150 2.24121
\(503\) 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
\(505\) −9.43900 16.3488i −0.420030 0.727513i
\(506\) −10.8509 −0.482379
\(507\) 0 0
\(508\) −57.8394 −2.56621
\(509\) 3.80947 + 6.59820i 0.168852 + 0.292460i 0.938016 0.346591i \(-0.112661\pi\)
−0.769165 + 0.639051i \(0.779327\pi\)
\(510\) −4.77144 8.26437i −0.211283 0.365953i
\(511\) 10.8107 18.7246i 0.478236 0.828329i
\(512\) 9.00538 0.397985
\(513\) −9.24094 + 16.0058i −0.407997 + 0.706672i
\(514\) 20.9644 36.3114i 0.924701 1.60163i
\(515\) 13.2489 0.583816
\(516\) 5.19202 8.99284i 0.228566 0.395888i
\(517\) −3.76995 6.52974i −0.165802 0.287178i
\(518\) −12.3312 21.3583i −0.541804 0.938431i
\(519\) 10.4638 0.459311
\(520\) 0 0
\(521\) −39.5133 −1.73111 −0.865555 0.500813i \(-0.833034\pi\)
−0.865555 + 0.500813i \(0.833034\pi\)
\(522\) 6.86174 + 11.8849i 0.300330 + 0.520187i
\(523\) 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
\(525\) −3.31096 −0.144502
\(526\) −16.1773 + 28.0198i −0.705362 + 1.22172i
\(527\) 11.3034 19.5781i 0.492385 0.852836i
\(528\) 1.13706 0.0494843
\(529\) 9.71379 16.8248i 0.422339 0.731512i
\(530\) −8.96346 15.5252i −0.389348 0.674370i
\(531\) 16.4318 + 28.4606i 0.713078 + 1.23509i
\(532\) −36.5502 −1.58465
\(533\) 0 0
\(534\) 8.24698 0.356882
\(535\) 4.98523 + 8.63467i 0.215530 + 0.373309i
\(536\) 0.679644 + 1.17718i 0.0293562 + 0.0508464i
\(537\) 1.67092 2.89411i 0.0721053 0.124890i
\(538\) 1.46681 0.0632388
\(539\) 3.57942 6.19973i 0.154176 0.267041i
\(540\) −6.95862 + 12.0527i −0.299451 + 0.518665i
\(541\) −34.4819 −1.48249 −0.741246 0.671234i \(-0.765765\pi\)
−0.741246 + 0.671234i \(0.765765\pi\)
\(542\) −2.24214 + 3.88349i −0.0963080 + 0.166810i
\(543\) −1.32573 2.29624i −0.0568926 0.0985409i
\(544\) −17.2533 29.8836i −0.739730 1.28125i
\(545\) −0.176292 −0.00755152
\(546\) 0 0
\(547\) 36.8582 1.57594 0.787970 0.615713i \(-0.211132\pi\)
0.787970 + 0.615713i \(0.211132\pi\)
\(548\) 1.20775 + 2.09189i 0.0515926 + 0.0893609i
\(549\) 11.5281 + 19.9673i 0.492008 + 0.852182i
\(550\) 8.35839 14.4772i 0.356403 0.617308i
\(551\) 13.2741 0.565497
\(552\) −1.23609 + 2.14098i −0.0526117 + 0.0911261i
\(553\) −16.1637 + 27.9963i −0.687350 + 1.19052i
\(554\) 26.4795 1.12501
\(555\) −2.14795 + 3.72036i −0.0911753 + 0.157920i
\(556\) 17.2865 + 29.9411i 0.733111 + 1.26979i
\(557\) 0.638260 + 1.10550i 0.0270439 + 0.0468415i 0.879231 0.476396i \(-0.158057\pi\)
−0.852187 + 0.523238i \(0.824724\pi\)
\(558\) −25.8213 −1.09310
\(559\) 0 0
\(560\) 2.37435 0.100335
\(561\) −3.75451 6.50301i −0.158516 0.274557i
\(562\) −7.27144 12.5945i −0.306727 0.531267i
\(563\) 4.56369 7.90454i 0.192336 0.333137i −0.753688 0.657233i \(-0.771727\pi\)
0.946024 + 0.324096i \(0.105060\pi\)
\(564\) −4.99330 −0.210256
\(565\) −5.28017 + 9.14552i −0.222138 + 0.384755i
\(566\) −7.39373 + 12.8063i −0.310782 + 0.538290i
\(567\) −12.9554 −0.544075
\(568\) −5.41401 + 9.37734i −0.227167 + 0.393464i
\(569\) 2.86078 + 4.95502i 0.119930 + 0.207725i 0.919740 0.392529i \(-0.128400\pi\)
−0.799810 + 0.600254i \(0.795066\pi\)
\(570\) 5.27144 + 9.13040i 0.220796 + 0.382430i
\(571\) 7.60148 0.318112 0.159056 0.987270i \(-0.449155\pi\)
0.159056 + 0.987270i \(0.449155\pi\)
\(572\) 0 0
\(573\) −10.2282 −0.427289
\(574\) −2.93296 5.08004i −0.122419 0.212037i
\(575\) −2.75182 4.76630i −0.114759 0.198768i
\(576\) −17.5477 + 30.3935i −0.731155 + 1.26640i
\(577\) −45.1564 −1.87989 −0.939944 0.341330i \(-0.889123\pi\)
−0.939944 + 0.341330i \(0.889123\pi\)
\(578\) −12.4107 + 21.4959i −0.516215 + 0.894111i
\(579\) −1.67994 + 2.90974i −0.0698159 + 0.120925i
\(580\) 9.99569 0.415048
\(581\) −7.91239 + 13.7047i −0.328261 + 0.568565i
\(582\) −7.43631 12.8801i −0.308245 0.533896i
\(583\) −7.05310 12.2163i −0.292109 0.505948i
\(584\) 24.8713 1.02918
\(585\) 0 0
\(586\) 54.6872 2.25911
\(587\) −16.2020 28.0627i −0.668728 1.15827i −0.978260 0.207382i \(-0.933506\pi\)
0.309532 0.950889i \(-0.399828\pi\)
\(588\) −2.37047 4.10577i −0.0977565 0.169319i
\(589\) −12.4879 + 21.6297i −0.514556 + 0.891237i
\(590\) 39.6383 1.63188
\(591\) 3.16756 5.48638i 0.130296 0.225680i
\(592\) −2.14795 + 3.72036i −0.0882801 + 0.152906i
\(593\) −36.6848 −1.50647 −0.753233 0.657754i \(-0.771507\pi\)
−0.753233 + 0.657754i \(0.771507\pi\)
\(594\) −9.06734 + 15.7051i −0.372037 + 0.644387i
\(595\) −7.83997 13.5792i −0.321407 0.556694i
\(596\) 12.8143 + 22.1950i 0.524895 + 0.909144i
\(597\) 7.71678 0.315827
\(598\) 0 0
\(599\) −9.99223 −0.408271 −0.204136 0.978943i \(-0.565438\pi\)
−0.204136 + 0.978943i \(0.565438\pi\)
\(600\) −1.90432 3.29838i −0.0777436 0.134656i
\(601\) 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
\(603\) 1.55257 0.0632253
\(604\) 21.5395 37.3076i 0.876431 1.51802i
\(605\) 3.23125 5.59669i 0.131369 0.227538i
\(606\) −16.2905 −0.661757
\(607\) −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
\(609\) −1.28986 2.23410i −0.0522676 0.0905302i
\(610\) 27.8092 1.12596
\(611\) 0 0
\(612\) 43.4674 1.75707
\(613\) −10.4472 18.0951i −0.421958 0.730853i 0.574173 0.818734i \(-0.305324\pi\)
−0.996131 + 0.0878810i \(0.971990\pi\)
\(614\) −15.8116 27.3865i −0.638105 1.10523i
\(615\) −0.510885 + 0.884879i −0.0206009 + 0.0356818i
\(616\) −12.3381 −0.497117
\(617\) 6.04958 10.4782i 0.243547 0.421836i −0.718175 0.695862i \(-0.755022\pi\)
0.961722 + 0.274027i \(0.0883557\pi\)
\(618\) 5.71648 9.90123i 0.229951 0.398286i
\(619\) 10.5526 0.424143 0.212072 0.977254i \(-0.431979\pi\)
0.212072 + 0.977254i \(0.431979\pi\)
\(620\) −9.40366 + 16.2876i −0.377660 + 0.654126i
\(621\) 2.98523 + 5.17057i 0.119793 + 0.207488i
\(622\) 33.4463 + 57.9307i 1.34107 + 2.32281i
\(623\) 13.5506 0.542895
\(624\) 0 0
\(625\) −1.96184 −0.0784735
\(626\) 8.40246 + 14.5535i 0.335830 + 0.581674i
\(627\) 4.14795 + 7.18446i 0.165653 + 0.286920i
\(628\) 14.3802 24.9072i 0.573831 0.993904i
\(629\) 28.3696 1.13117
\(630\) −8.95473 + 15.5100i −0.356765 + 0.617935i
\(631\) −6.92572 + 11.9957i −0.275709 + 0.477541i −0.970314 0.241850i \(-0.922246\pi\)
0.694605 + 0.719391i \(0.255579\pi\)
\(632\) −37.1866 −1.47920
\(633\) −3.67510 + 6.36545i −0.146072 + 0.253004i
\(634\) 33.7385 + 58.4369i 1.33993 + 2.32082i
\(635\) 13.7066 + 23.7404i 0.543928 + 0.942111i
\(636\) −9.34183 −0.370428
\(637\) 0 0
\(638\) 13.0248 0.515655
\(639\) 6.18382 + 10.7107i 0.244628 + 0.423709i
\(640\) 11.7497 + 20.3510i 0.464446 + 0.804445i
\(641\) −17.4804 + 30.2769i −0.690434 + 1.19587i 0.281262 + 0.959631i \(0.409247\pi\)
−0.971696 + 0.236235i \(0.924086\pi\)
\(642\) 8.60388 0.339568
\(643\) 16.6990 28.9236i 0.658545 1.14063i −0.322447 0.946587i \(-0.604505\pi\)
0.980992 0.194046i \(-0.0621612\pi\)
\(644\) −5.90366 + 10.2254i −0.232637 + 0.402939i
\(645\) −4.92154 −0.193786
\(646\) 34.8119 60.2960i 1.36966 2.37232i
\(647\) −1.16421 2.01647i −0.0457698 0.0792757i 0.842233 0.539114i \(-0.181241\pi\)
−0.888003 + 0.459838i \(0.847907\pi\)
\(648\) −7.45138 12.9062i −0.292718 0.507002i
\(649\) 31.1903 1.22433
\(650\) 0 0
\(651\) 4.85384 0.190237
\(652\) 13.2690 + 22.9827i 0.519656 + 0.900070i
\(653\) −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
\(655\) 4.70602 0.183879
\(656\) −0.510885 + 0.884879i −0.0199467 + 0.0345487i
\(657\) 14.2039 24.6018i 0.554146 0.959808i
\(658\) −13.5864 −0.529654
\(659\) −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
\(661\) −6.92490 11.9943i −0.269347 0.466523i 0.699346 0.714783i \(-0.253475\pi\)
−0.968693 + 0.248260i \(0.920141\pi\)
\(662\) 35.3153 1.37257
\(663\) 0 0
\(664\) −18.2034 −0.706430
\(665\) 8.66152 + 15.0022i 0.335879 + 0.581760i
\(666\) −16.2017 28.0622i −0.627804 1.08739i
\(667\) 2.14406 3.71363i 0.0830185 0.143792i
\(668\) 72.7284 2.81395
\(669\) 2.03534 3.52532i 0.0786909 0.136297i
\(670\) 0.936313 1.62174i 0.0361729 0.0626533i
\(671\) 21.8823 0.844757
\(672\) 3.70440 6.41621i 0.142900 0.247511i
\(673\) 3.26487 + 5.65491i 0.125851 + 0.217981i 0.922065 0.387034i \(-0.126500\pi\)
−0.796214 + 0.605015i \(0.793167\pi\)
\(674\) −2.19537 3.80250i −0.0845626 0.146467i
\(675\) −9.19806 −0.354034
\(676\) 0 0
\(677\) −11.3104 −0.434693 −0.217346 0.976095i \(-0.569740\pi\)
−0.217346 + 0.976095i \(0.569740\pi\)
\(678\) 4.55645 + 7.89200i 0.174989 + 0.303091i
\(679\) −12.2186 21.1633i −0.468908 0.812173i
\(680\) 9.01842 15.6204i 0.345841 0.599013i
\(681\) −4.81402 −0.184474
\(682\) −12.2533 + 21.2234i −0.469204 + 0.812685i
\(683\) 7.08964 12.2796i 0.271277 0.469866i −0.697912 0.716184i \(-0.745887\pi\)
0.969189 + 0.246317i \(0.0792206\pi\)
\(684\) −48.0224 −1.83618
\(685\) 0.572417 0.991455i 0.0218709 0.0378815i
\(686\) −22.5635 39.0810i −0.861477 1.49212i
\(687\) 3.79776 + 6.57791i 0.144893 + 0.250963i
\(688\) −4.92154 −0.187632
\(689\) 0 0
\(690\) 3.40581 0.129657
\(691\) 15.3976 + 26.6695i 0.585753 + 1.01455i 0.994781 + 0.102032i \(0.0325344\pi\)
−0.409028 + 0.912522i \(0.634132\pi\)
\(692\) 28.7439 + 49.7859i 1.09268 + 1.89258i
\(693\) −7.04623 + 12.2044i −0.267664 + 0.463608i
\(694\) −38.4795 −1.46066
\(695\) 8.19298 14.1907i 0.310777 0.538282i
\(696\) 1.48374 2.56991i 0.0562409 0.0974122i
\(697\) 6.74764 0.255585
\(698\) −11.7594 + 20.3678i −0.445098 + 0.770933i
\(699\) −1.41185 2.44540i −0.0534012 0.0924936i
\(700\) −9.09515 15.7533i −0.343764 0.595417i
\(701\) 6.73184 0.254258 0.127129 0.991886i \(-0.459424\pi\)
0.127129 + 0.991886i \(0.459424\pi\)
\(702\) 0 0
\(703\) −31.3424 −1.18210
\(704\) 16.6543 + 28.8461i 0.627682 + 1.08718i
\(705\) 1.18329 + 2.04952i 0.0445654 + 0.0771895i
\(706\) 17.4487 30.2220i 0.656690 1.13742i
\(707\) −26.7670 −1.00668
\(708\) 10.3279 17.8884i 0.388146 0.672288i
\(709\) −23.8126 + 41.2446i −0.894300 + 1.54897i −0.0596324 + 0.998220i \(0.518993\pi\)
−0.834668 + 0.550753i \(0.814340\pi\)
\(710\) 14.9172 0.559834
\(711\) −21.2371 + 36.7837i −0.796452 + 1.37949i
\(712\) 7.79374 + 13.4992i 0.292083 + 0.505902i
\(713\) 4.03415 + 6.98735i 0.151080 + 0.261678i
\(714\) −13.5308 −0.506377
\(715\) 0 0
\(716\) 18.3599 0.686141
\(717\) 3.03116 + 5.25013i 0.113201 + 0.196070i
\(718\) −24.0722 41.6942i −0.898366 1.55602i
\(719\) 2.99665 5.19035i 0.111756 0.193567i −0.804722 0.593651i \(-0.797686\pi\)
0.916478 + 0.400084i \(0.131019\pi\)
\(720\) 3.11960 0.116261
\(721\) 9.39277 16.2688i 0.349805 0.605880i
\(722\) −17.1136 + 29.6416i −0.636901 + 1.10314i
\(723\) 6.61224 0.245912
\(724\) 7.28352 12.6154i 0.270690 0.468849i
\(725\) 3.30313 + 5.72120i 0.122675 + 0.212480i
\(726\) −2.78836 4.82959i −0.103486 0.179243i
\(727\) −24.1226 −0.894657 −0.447329 0.894370i \(-0.647625\pi\)
−0.447329 + 0.894370i \(0.647625\pi\)
\(728\) 0 0
\(729\) −11.7627 −0.435656
\(730\) −17.1320 29.6735i −0.634083 1.09826i
\(731\) 16.2506 + 28.1469i 0.601051 + 1.04105i
\(732\) 7.24578 12.5501i 0.267812 0.463864i
\(733\) −36.0646 −1.33208 −0.666038 0.745918i \(-0.732011\pi\)
−0.666038 + 0.745918i \(0.732011\pi\)
\(734\) −38.5393 + 66.7520i −1.42251 + 2.46386i
\(735\) −1.12349 + 1.94594i −0.0414405 + 0.0717771i
\(736\) 12.3153 0.453947
\(737\) 0.736758 1.27610i 0.0271388 0.0470059i
\(738\) −3.85354 6.67453i −0.141851 0.245693i
\(739\) 13.7627 + 23.8377i 0.506269 + 0.876884i 0.999974 + 0.00725452i \(0.00230920\pi\)
−0.493704 + 0.869630i \(0.664357\pi\)
\(740\) −23.6015 −0.867608
\(741\) 0 0
\(742\) −25.4185 −0.933142
\(743\) −5.23460 9.06660i −0.192039 0.332621i 0.753887 0.657004i \(-0.228177\pi\)
−0.945926 + 0.324383i \(0.894843\pi\)
\(744\) 2.79172 + 4.83539i 0.102349 + 0.177274i
\(745\) 6.07338 10.5194i 0.222511 0.385401i
\(746\) −28.3032 −1.03625
\(747\) −10.3959 + 18.0062i −0.380366 + 0.658813i
\(748\) 20.6271 35.7273i 0.754203 1.30632i
\(749\) 14.1371 0.516557
\(750\) −7.12833 + 12.3466i −0.260290 + 0.450835i
\(751\) −2.03385 3.52273i −0.0742163 0.128546i 0.826529 0.562894i \(-0.190312\pi\)
−0.900745 + 0.434348i \(0.856979\pi\)
\(752\) 1.18329 + 2.04952i 0.0431502 + 0.0747384i
\(753\) −12.4021 −0.451957
\(754\) 0 0
\(755\) −20.4174 −0.743066
\(756\) 9.86658 + 17.0894i 0.358844 + 0.621536i
\(757\) −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
\(759\) 2.67994 0.0972757
\(760\) −9.96346 + 17.2572i −0.361413 + 0.625985i
\(761\) −13.5118 + 23.4032i −0.489804 + 0.848365i −0.999931 0.0117336i \(-0.996265\pi\)
0.510127 + 0.860099i \(0.329598\pi\)
\(762\) 23.6558 0.856958
\(763\) −0.124982 + 0.216475i −0.00452464 + 0.00783691i
\(764\) −28.0966 48.6648i −1.01650 1.76063i
\(765\) −10.3007 17.8414i −0.372424 0.645057i
\(766\) −16.9336 −0.611837
\(767\) 0 0
\(768\) 5.80864 0.209601
\(769\) −18.9703 32.8576i −0.684088 1.18487i −0.973723 0.227737i \(-0.926867\pi\)
0.289635 0.957137i \(-0.406466\pi\)
\(770\) 8.49880 + 14.7204i 0.306276 + 0.530485i
\(771\) −5.17778 + 8.96818i −0.186473 + 0.322981i
\(772\) −18.4590 −0.664355
\(773\) −8.16876 + 14.1487i −0.293810 + 0.508894i −0.974707 0.223485i \(-0.928257\pi\)
0.680897 + 0.732379i \(0.261590\pi\)
\(774\) 18.5613 32.1491i 0.667172 1.15558i