Properties

Label 169.2.c.c.146.3
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 146.3
Root \(0.900969 + 1.56052i\) of defining polynomial
Character \(\chi\) \(=\) 169.146
Dual form 169.2.c.c.22.3

$q$-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 \(0.125562\pi\)
−0.128775 + 0.991674i \(0.541104\pi\)
\(3\) 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 \(-0.604732\pi\)
−0.323121 + 0.946358i \(0.604732\pi\)
\(6\) −0.623490 + 1.07992i −0.254539 + 0.440874i
\(7\) −1.02446 + 1.77441i −0.387209 + 0.670666i −0.992073 0.125663i \(-0.959894\pi\)
0.604864 + 0.796329i \(0.293227\pi\)
\(8\) −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 0.991793 0.127851i \(-0.0408079\pi\)
−0.606619 + 0.794993i \(0.707475\pi\)
\(12\) −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 \(-0.599139\pi\)
0.977581 0.210558i \(-0.0675280\pi\)
\(20\) 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 \(-0.625228\pi\)
−0.383345 + 0.923605i \(0.625228\pi\)
\(32\) −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 0.557380 0.830258i \(-0.311807\pi\)
−0.997714 + 0.0675764i \(0.978473\pi\)
\(38\) 13.1468 2.13268
\(39\) 0 0
\(40\) 3.40581 0.538506
\(41\) −0.637063 1.10343i −0.0994926 0.172326i 0.811982 0.583682i \(-0.198389\pi\)
−0.911475 + 0.411356i \(0.865055\pi\)
\(42\) −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 \(-0.569050\pi\)
−0.215230 + 0.976563i \(0.569050\pi\)
\(48\) −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 \(-0.540984\pi\)
0.923057 0.384664i \(-0.125683\pi\)
\(60\) 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 0.847873 0.530199i \(-0.177883\pi\)
−0.883102 + 0.469180i \(0.844549\pi\)
\(68\) 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 −0.696916 0.717153i \(-0.745445\pi\)
0.969531 + 0.244970i \(0.0787782\pi\)
\(72\) −3.17241 + 5.49477i −0.373872 + 0.647565i
\(73\) −10.5526 −1.23508 −0.617542 0.786538i \(-0.711872\pi\)
−0.617542 + 0.786538i \(0.711872\pi\)
\(74\) 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 \(-0.360667\pi\)
0.423881 + 0.905718i \(0.360667\pi\)
\(84\) 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 0.635822 0.771836i \(-0.280661\pi\)
−0.986340 + 0.164720i \(0.947328\pi\)
\(90\) −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 \(0.373693\pi\)
−0.991973 + 0.126453i \(0.959641\pi\)
\(98\) −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 \(-0.498140\pi\)
0.00584264 + 0.999983i \(0.498140\pi\)
\(110\) 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 −0.882451 0.470405i \(-0.844108\pi\)
0.848608 + 0.529023i \(0.177441\pi\)
\(138\) −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 −0.985229 0.171241i \(-0.945222\pi\)
0.640914 + 0.767613i \(0.278556\pi\)
\(150\) 1.81551 3.14456i 0.148236 0.256752i
\(151\) 14.1293 1.14983 0.574913 0.818215i \(-0.305036\pi\)
0.574913 + 0.818215i \(0.305036\pi\)
\(152\) −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 −0.984596 0.174844i \(-0.944058\pi\)
0.643717 + 0.765263i \(0.277391\pi\)
\(164\) 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 \(0.207548\pi\)
0.128080 + 0.991764i \(0.459119\pi\)
\(168\) 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 0.736267 0.676692i \(-0.236587\pi\)
−0.954165 + 0.299280i \(0.903254\pi\)
\(194\) −26.7995 −1.92410
\(195\) 0 0
\(196\) −8.54288 −0.610205
\(197\) 5.70775 + 9.88611i 0.406660 + 0.704357i 0.994513 0.104611i \(-0.0333599\pi\)
−0.587853 + 0.808968i \(0.700027\pi\)
\(198\) 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 0.962300 0.271992i \(-0.0876823\pi\)
−0.716701 + 0.697380i \(0.754349\pi\)
\(224\) −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 −0.685427 0.728141i \(-0.740384\pi\)
0.973302 + 0.229526i \(0.0737177\pi\)
\(228\) −4.94989 + 8.57345i −0.327814 + 0.567791i
\(229\) −13.6866 −0.904439 −0.452219 0.891907i \(-0.649368\pi\)
−0.452219 + 0.891907i \(0.649368\pi\)
\(230\) 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 \(-0.614942\pi\)
−0.353305 + 0.935508i \(0.614942\pi\)
\(240\) 0.321552 0.556945i 0.0207561 0.0359506i
\(241\) −5.95742 + 10.3186i −0.383751 + 0.664676i −0.991595 0.129380i \(-0.958701\pi\)
0.607844 + 0.794056i \(0.292035\pi\)
\(242\) 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 0.894740 0.446587i \(-0.147361\pi\)
−0.834126 + 0.551574i \(0.814027\pi\)
\(272\) 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 \(-0.561838\pi\)
−0.193049 + 0.981189i \(0.561838\pi\)
\(282\) 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 \(-0.581610\pi\)
0.964511 0.264044i \(-0.0850563\pi\)
\(294\) −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 \(-0.631550\pi\)
−0.401613 + 0.915809i \(0.631550\pi\)
\(308\) 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 \(-0.180592\pi\)
0.843330 + 0.537396i \(0.180592\pi\)
\(318\) −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 −0.565104 0.825020i \(-0.691164\pi\)
0.997040 + 0.0768845i \(0.0244973\pi\)
\(332\) −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 0.971418 0.237373i \(-0.0762865\pi\)
−0.691281 + 0.722586i \(0.742953\pi\)
\(350\) 13.4058 0.716571
\(351\) 0 0
\(352\) −16.6474 −0.887310
\(353\) −7.76540 13.4501i −0.413310 0.715875i 0.581939 0.813232i \(-0.302294\pi\)
−0.995249 + 0.0973578i \(0.968961\pi\)
\(354\) 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 \(-0.691285\pi\)
−0.565417 + 0.824805i \(0.691285\pi\)
\(360\) 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 0.571634 0.820509i \(-0.306310\pi\)
−0.996398 + 0.0847951i \(0.972976\pi\)
\(380\) −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 −0.946091 0.323900i \(-0.895006\pi\)
0.753551 + 0.657389i \(0.228339\pi\)
\(384\) 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 −0.882485 0.470341i \(-0.844131\pi\)
0.848569 + 0.529084i \(0.177464\pi\)
\(398\) 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 0.858705 0.512470i \(-0.171270\pi\)
−0.873165 + 0.487425i \(0.837936\pi\)
\(402\) 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 −0.615544 0.788103i \(-0.711064\pi\)
0.990289 + 0.139025i \(0.0443969\pi\)
\(410\) −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 \(-0.825849\pi\)
−0.854032 + 0.520221i \(0.825849\pi\)
\(422\) −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 \(0.142519\pi\)
−0.0757909 + 0.997124i \(0.524148\pi\)
\(432\) 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 −0.672638 0.739972i \(-0.734839\pi\)
0.977153 + 0.212535i \(0.0681720\pi\)
\(450\) −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 0.806410 0.591357i \(-0.201408\pi\)
−0.915335 + 0.402693i \(0.868074\pi\)
\(458\) −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 \(-0.570753\pi\)
0.954945 0.296782i \(-0.0959135\pi\)
\(462\) 3.26391 5.65325i 0.151851 0.263013i
\(463\) 17.6504 0.820284 0.410142 0.912022i \(-0.365479\pi\)
0.410142 + 0.912022i \(0.365479\pi\)
\(464\) 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 \(0.127075\pi\)
−0.124059 + 0.992275i \(0.539591\pi\)
\(480\) 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 \(0.563428\pi\)
−0.749914 + 0.661536i \(0.769905\pi\)
\(488\) 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 \(-0.323295\pi\)
0.527058 + 0.849829i \(0.323295\pi\)
\(500\) −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 0.769165 0.639051i \(-0.220673\pi\)
−0.938016 + 0.346591i \(0.887339\pi\)
\(510\) −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 \(-0.234235\pi\)
0.741246 + 0.671234i \(0.234235\pi\)
\(542\) −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 0.852187 0.523238i \(-0.175276\pi\)
−0.879231 + 0.476396i \(0.841943\pi\)
\(558\) −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 \(-0.110877\pi\)
0.939944 + 0.341330i \(0.110877\pi\)
\(578\) 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 \(0.0664944\pi\)
−0.309532 + 0.950889i \(0.600172\pi\)
\(588\) −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 \(-0.228493\pi\)
0.753233 + 0.657754i \(0.228493\pi\)
\(594\) −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 0.996131 0.0878810i \(-0.0280095\pi\)
−0.574173 + 0.818734i \(0.694676\pi\)
\(614\) −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 −0.961722 0.274027i \(-0.911644\pi\)
0.718175 + 0.695862i \(0.244978\pi\)
\(618\) −5.71648 + 9.90123i −0.229951 + 0.398286i
\(619\) −10.5526 −0.424143 −0.212072 0.977254i \(-0.568021\pi\)
−0.212072 + 0.977254i \(0.568021\pi\)
\(620\) −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 −0.694605 0.719391i \(-0.744421\pi\)
0.970314 + 0.241850i \(0.0777542\pi\)
\(632\) 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 \(0.395495\pi\)
−0.980992 + 0.194046i \(0.937839\pi\)
\(644\) 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 0.968693 0.248260i \(-0.0798587\pi\)
−0.699346 + 0.714783i \(0.746525\pi\)
\(662\) 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 −0.969189 0.246317i \(-0.920779\pi\)
0.697912 + 0.716184i \(0.254113\pi\)
\(684\) 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 \(-0.967466\pi\)
0.409028 0.912522i \(-0.365868\pi\)
\(692\) 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 \(-0.481007\pi\)
0.834668 0.550753i \(-0.185660\pi\)
\(710\) −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 \(-0.267989\pi\)
0.666038 + 0.745918i \(0.267989\pi\)
\(734\) 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 \(-0.997691\pi\)
0.493704 0.869630i \(-0.335643\pi\)
\(740\) −23.6015 −0.867608
\(741\) 0 0
\(742\) −25.4185 −0.933142
\(743\) 5.23460 + 9.06660i 0.192039 + 0.332621i 0.945926 0.324383i \(-0.105157\pi\)
−0.753887 + 0.657004i \(0.771823\pi\)
\(744\) 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 −0.510127 0.860099i \(-0.670402\pi\)
0.999931 + 0.0117336i \(0.00373501\pi\)
\(762\) −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 \(0.0731327\pi\)
−0.289635 + 0.957137i \(0.593534\pi\)
\(770\) 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 −0.680897 0.732379i \(-0.738410\pi\)
0.974707 + 0.223485i \(0.0717434\pi\)