Properties

Label 322.2.e.a.277.1
Level $322$
Weight $2$
Character 322.277
Analytic conductor $2.571$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 322 = 2 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 322.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.57118294509\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.310217769.2
Defining polynomial: \(x^{8} + 4 x^{6} - 2 x^{5} + 15 x^{4} - 4 x^{3} + 5 x^{2} + x + 1\)
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 277.1
Root \(-1.03075 + 1.78531i\) of defining polynomial
Character \(\chi\) \(=\) 322.277
Dual form 322.2.e.a.93.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-1.28821 + 2.23124i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.663319 - 1.14890i) q^{5} +2.57641 q^{6} +(-1.46157 - 2.20541i) q^{7} +1.00000 q^{8} +(-1.81896 - 3.15053i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-1.28821 + 2.23124i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.663319 - 1.14890i) q^{5} +2.57641 q^{6} +(-1.46157 - 2.20541i) q^{7} +1.00000 q^{8} +(-1.81896 - 3.15053i) q^{9} +(-0.663319 + 1.14890i) q^{10} +(-1.04567 + 1.81115i) q^{11} +(-1.28821 - 2.23124i) q^{12} +3.11142 q^{13} +(-1.17915 + 2.36846i) q^{14} +3.41797 q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.47460 - 6.01818i) q^{17} +(-1.81896 + 3.15053i) q^{18} +(-3.88326 - 6.72601i) q^{19} +1.32664 q^{20} +(6.80360 - 0.420095i) q^{21} +2.09133 q^{22} +(0.500000 + 0.866025i) q^{23} +(-1.28821 + 2.23124i) q^{24} +(1.62002 - 2.80595i) q^{25} +(-1.55571 - 2.69457i) q^{26} +1.64353 q^{27} +(2.64072 - 0.163054i) q^{28} +1.15845 q^{29} +(-1.70898 - 2.96005i) q^{30} +(4.35694 - 7.54644i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.69407 - 4.66626i) q^{33} -6.94919 q^{34} +(-1.56431 + 3.14209i) q^{35} +3.63791 q^{36} +(1.65472 + 2.86606i) q^{37} +(-3.88326 + 6.72601i) q^{38} +(-4.00815 + 6.94232i) q^{39} +(-0.663319 - 1.14890i) q^{40} -4.26425 q^{41} +(-3.76561 - 5.68204i) q^{42} -8.36716 q^{43} +(-1.04567 - 1.81115i) q^{44} +(-2.41310 + 4.17961i) q^{45} +(0.500000 - 0.866025i) q^{46} +(1.74065 + 3.01490i) q^{47} +2.57641 q^{48} +(-2.72763 + 6.44671i) q^{49} -3.24003 q^{50} +(8.95200 + 15.5053i) q^{51} +(-1.55571 + 2.69457i) q^{52} +(-2.12002 + 3.67198i) q^{53} +(-0.821765 - 1.42334i) q^{54} +2.77444 q^{55} +(-1.46157 - 2.20541i) q^{56} +20.0098 q^{57} +(-0.579223 - 1.00324i) q^{58} +(-4.59225 + 7.95401i) q^{59} +(-1.70898 + 2.96005i) q^{60} +(-6.01934 - 10.4258i) q^{61} -8.71388 q^{62} +(-4.28965 + 8.61625i) q^{63} +1.00000 q^{64} +(-2.06386 - 3.57471i) q^{65} +(-2.69407 + 4.66626i) q^{66} +(3.63160 - 6.29011i) q^{67} +(3.47460 + 6.01818i) q^{68} -2.57641 q^{69} +(3.50328 - 0.216314i) q^{70} -7.41708 q^{71} +(-1.81896 - 3.15053i) q^{72} +(2.18402 - 3.78284i) q^{73} +(1.65472 - 2.86606i) q^{74} +(4.17383 + 7.22929i) q^{75} +7.76653 q^{76} +(5.52262 - 0.341000i) q^{77} +8.01631 q^{78} +(0.398625 + 0.690439i) q^{79} +(-0.663319 + 1.14890i) q^{80} +(3.33966 - 5.78446i) q^{81} +(2.13212 + 3.69295i) q^{82} +10.3746 q^{83} +(-3.03798 + 6.10213i) q^{84} -9.21906 q^{85} +(4.18358 + 7.24617i) q^{86} +(-1.49232 + 2.58477i) q^{87} +(-1.04567 + 1.81115i) q^{88} +(-8.32132 - 14.4129i) q^{89} +4.82619 q^{90} +(-4.54756 - 6.86194i) q^{91} -1.00000 q^{92} +(11.2253 + 19.4428i) q^{93} +(1.74065 - 3.01490i) q^{94} +(-5.15168 + 8.92298i) q^{95} +(-1.28821 - 2.23124i) q^{96} +6.65800 q^{97} +(6.94683 - 0.861161i) q^{98} +7.60808 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 4 q^{2} - 3 q^{3} - 4 q^{4} - 7 q^{5} + 6 q^{6} - q^{7} + 8 q^{8} + q^{9} + O(q^{10}) \) \( 8 q - 4 q^{2} - 3 q^{3} - 4 q^{4} - 7 q^{5} + 6 q^{6} - q^{7} + 8 q^{8} + q^{9} - 7 q^{10} - 2 q^{11} - 3 q^{12} + 2 q^{13} - q^{14} + 18 q^{15} - 4 q^{16} - 5 q^{17} + q^{18} - 11 q^{19} + 14 q^{20} + q^{21} + 4 q^{22} + 4 q^{23} - 3 q^{24} - 3 q^{25} - q^{26} + 6 q^{27} + 2 q^{28} + 4 q^{29} - 9 q^{30} - 6 q^{31} - 4 q^{32} - 15 q^{33} + 10 q^{34} - 8 q^{35} - 2 q^{36} + 8 q^{37} - 11 q^{38} - 3 q^{39} - 7 q^{40} + 18 q^{41} - 2 q^{42} + 8 q^{43} - 2 q^{44} - 3 q^{45} + 4 q^{46} - 11 q^{47} + 6 q^{48} - 19 q^{49} + 6 q^{50} + 18 q^{51} - q^{52} - q^{53} - 3 q^{54} + 20 q^{55} - q^{56} + 6 q^{57} - 2 q^{58} - 12 q^{59} - 9 q^{60} - 21 q^{61} + 12 q^{62} - 15 q^{63} + 8 q^{64} + 24 q^{65} - 15 q^{66} + 3 q^{67} - 5 q^{68} - 6 q^{69} - 8 q^{70} + 22 q^{71} + q^{72} + 16 q^{73} + 8 q^{74} - 18 q^{75} + 22 q^{76} - 19 q^{77} + 6 q^{78} + 21 q^{79} - 7 q^{80} + 8 q^{81} - 9 q^{82} + 8 q^{83} + q^{84} + 20 q^{85} - 4 q^{86} + 7 q^{87} - 2 q^{88} - 27 q^{89} + 6 q^{90} - 54 q^{91} - 8 q^{92} + 27 q^{93} - 11 q^{94} - 5 q^{95} - 3 q^{96} + 12 q^{97} + 14 q^{98} + 26 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/322\mathbb{Z}\right)^\times\).

\(n\) \(185\) \(281\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) −1.28821 + 2.23124i −0.743747 + 1.28821i 0.207031 + 0.978334i \(0.433620\pi\)
−0.950778 + 0.309873i \(0.899713\pi\)
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −0.663319 1.14890i −0.296645 0.513804i 0.678721 0.734396i \(-0.262535\pi\)
−0.975366 + 0.220592i \(0.929201\pi\)
\(6\) 2.57641 1.05182
\(7\) −1.46157 2.20541i −0.552422 0.833565i
\(8\) 1.00000 0.353553
\(9\) −1.81896 3.15053i −0.606319 1.05018i
\(10\) −0.663319 + 1.14890i −0.209760 + 0.363315i
\(11\) −1.04567 + 1.81115i −0.315280 + 0.546081i −0.979497 0.201459i \(-0.935432\pi\)
0.664217 + 0.747540i \(0.268765\pi\)
\(12\) −1.28821 2.23124i −0.371873 0.644104i
\(13\) 3.11142 0.862952 0.431476 0.902124i \(-0.357993\pi\)
0.431476 + 0.902124i \(0.357993\pi\)
\(14\) −1.17915 + 2.36846i −0.315142 + 0.632997i
\(15\) 3.41797 0.882516
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 3.47460 6.01818i 0.842713 1.45962i −0.0448794 0.998992i \(-0.514290\pi\)
0.887593 0.460629i \(-0.152376\pi\)
\(18\) −1.81896 + 3.15053i −0.428732 + 0.742586i
\(19\) −3.88326 6.72601i −0.890882 1.54305i −0.838820 0.544409i \(-0.816754\pi\)
−0.0520619 0.998644i \(-0.516579\pi\)
\(20\) 1.32664 0.296645
\(21\) 6.80360 0.420095i 1.48467 0.0916722i
\(22\) 2.09133 0.445873
\(23\) 0.500000 + 0.866025i 0.104257 + 0.180579i
\(24\) −1.28821 + 2.23124i −0.262954 + 0.455450i
\(25\) 1.62002 2.80595i 0.324003 0.561190i
\(26\) −1.55571 2.69457i −0.305100 0.528448i
\(27\) 1.64353 0.316298
\(28\) 2.64072 0.163054i 0.499050 0.0308143i
\(29\) 1.15845 0.215118 0.107559 0.994199i \(-0.465697\pi\)
0.107559 + 0.994199i \(0.465697\pi\)
\(30\) −1.70898 2.96005i −0.312016 0.540428i
\(31\) 4.35694 7.54644i 0.782530 1.35538i −0.147934 0.988997i \(-0.547262\pi\)
0.930464 0.366384i \(-0.119404\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) −2.69407 4.66626i −0.468977 0.812292i
\(34\) −6.94919 −1.19178
\(35\) −1.56431 + 3.14209i −0.264416 + 0.531110i
\(36\) 3.63791 0.606319
\(37\) 1.65472 + 2.86606i 0.272034 + 0.471177i 0.969383 0.245555i \(-0.0789702\pi\)
−0.697348 + 0.716732i \(0.745637\pi\)
\(38\) −3.88326 + 6.72601i −0.629949 + 1.09110i
\(39\) −4.00815 + 6.94232i −0.641818 + 1.11166i
\(40\) −0.663319 1.14890i −0.104880 0.181657i
\(41\) −4.26425 −0.665964 −0.332982 0.942933i \(-0.608055\pi\)
−0.332982 + 0.942933i \(0.608055\pi\)
\(42\) −3.76561 5.68204i −0.581046 0.876758i
\(43\) −8.36716 −1.27598 −0.637990 0.770045i \(-0.720234\pi\)
−0.637990 + 0.770045i \(0.720234\pi\)
\(44\) −1.04567 1.81115i −0.157640 0.273040i
\(45\) −2.41310 + 4.17961i −0.359723 + 0.623059i
\(46\) 0.500000 0.866025i 0.0737210 0.127688i
\(47\) 1.74065 + 3.01490i 0.253900 + 0.439768i 0.964596 0.263731i \(-0.0849532\pi\)
−0.710696 + 0.703499i \(0.751620\pi\)
\(48\) 2.57641 0.371873
\(49\) −2.72763 + 6.44671i −0.389661 + 0.920958i
\(50\) −3.24003 −0.458210
\(51\) 8.95200 + 15.5053i 1.25353 + 2.17118i
\(52\) −1.55571 + 2.69457i −0.215738 + 0.373669i
\(53\) −2.12002 + 3.67198i −0.291207 + 0.504385i −0.974095 0.226138i \(-0.927390\pi\)
0.682889 + 0.730522i \(0.260723\pi\)
\(54\) −0.821765 1.42334i −0.111828 0.193692i
\(55\) 2.77444 0.374105
\(56\) −1.46157 2.20541i −0.195311 0.294710i
\(57\) 20.0098 2.65036
\(58\) −0.579223 1.00324i −0.0760557 0.131732i
\(59\) −4.59225 + 7.95401i −0.597860 + 1.03552i 0.395277 + 0.918562i \(0.370649\pi\)
−0.993136 + 0.116961i \(0.962685\pi\)
\(60\) −1.70898 + 2.96005i −0.220629 + 0.382140i
\(61\) −6.01934 10.4258i −0.770698 1.33489i −0.937181 0.348844i \(-0.886574\pi\)
0.166483 0.986044i \(-0.446759\pi\)
\(62\) −8.71388 −1.10666
\(63\) −4.28965 + 8.61625i −0.540446 + 1.08555i
\(64\) 1.00000 0.125000
\(65\) −2.06386 3.57471i −0.255991 0.443389i
\(66\) −2.69407 + 4.66626i −0.331617 + 0.574377i
\(67\) 3.63160 6.29011i 0.443670 0.768459i −0.554288 0.832325i \(-0.687010\pi\)
0.997959 + 0.0638656i \(0.0203429\pi\)
\(68\) 3.47460 + 6.01818i 0.421357 + 0.729811i
\(69\) −2.57641 −0.310164
\(70\) 3.50328 0.216314i 0.418722 0.0258544i
\(71\) −7.41708 −0.880245 −0.440123 0.897938i \(-0.645065\pi\)
−0.440123 + 0.897938i \(0.645065\pi\)
\(72\) −1.81896 3.15053i −0.214366 0.371293i
\(73\) 2.18402 3.78284i 0.255621 0.442748i −0.709443 0.704763i \(-0.751054\pi\)
0.965064 + 0.262015i \(0.0843868\pi\)
\(74\) 1.65472 2.86606i 0.192357 0.333173i
\(75\) 4.17383 + 7.22929i 0.481953 + 0.834767i
\(76\) 7.76653 0.890882
\(77\) 5.52262 0.341000i 0.629361 0.0388606i
\(78\) 8.01631 0.907668
\(79\) 0.398625 + 0.690439i 0.0448488 + 0.0776805i 0.887578 0.460657i \(-0.152386\pi\)
−0.842730 + 0.538337i \(0.819053\pi\)
\(80\) −0.663319 + 1.14890i −0.0741613 + 0.128451i
\(81\) 3.33966 5.78446i 0.371074 0.642718i
\(82\) 2.13212 + 3.69295i 0.235454 + 0.407818i
\(83\) 10.3746 1.13876 0.569381 0.822074i \(-0.307183\pi\)
0.569381 + 0.822074i \(0.307183\pi\)
\(84\) −3.03798 + 6.10213i −0.331471 + 0.665797i
\(85\) −9.21906 −0.999947
\(86\) 4.18358 + 7.24617i 0.451127 + 0.781375i
\(87\) −1.49232 + 2.58477i −0.159993 + 0.277117i
\(88\) −1.04567 + 1.81115i −0.111468 + 0.193069i
\(89\) −8.32132 14.4129i −0.882058 1.52777i −0.849049 0.528315i \(-0.822824\pi\)
−0.0330095 0.999455i \(-0.510509\pi\)
\(90\) 4.82619 0.508725
\(91\) −4.54756 6.86194i −0.476713 0.719327i
\(92\) −1.00000 −0.104257
\(93\) 11.2253 + 19.4428i 1.16401 + 2.01612i
\(94\) 1.74065 3.01490i 0.179534 0.310963i
\(95\) −5.15168 + 8.92298i −0.528552 + 0.915478i
\(96\) −1.28821 2.23124i −0.131477 0.227725i
\(97\) 6.65800 0.676018 0.338009 0.941143i \(-0.390247\pi\)
0.338009 + 0.941143i \(0.390247\pi\)
\(98\) 6.94683 0.861161i 0.701735 0.0869904i
\(99\) 7.60808 0.764641
\(100\) 1.62002 + 2.80595i 0.162002 + 0.280595i
\(101\) −4.57940 + 7.93175i −0.455667 + 0.789238i −0.998726 0.0504560i \(-0.983933\pi\)
0.543059 + 0.839694i \(0.317266\pi\)
\(102\) 8.95200 15.5053i 0.886380 1.53526i
\(103\) −2.26606 3.92492i −0.223281 0.386734i 0.732521 0.680744i \(-0.238343\pi\)
−0.955802 + 0.294010i \(0.905010\pi\)
\(104\) 3.11142 0.305100
\(105\) −4.99560 7.53801i −0.487521 0.735634i
\(106\) 4.24003 0.411828
\(107\) 6.16722 + 10.6819i 0.596207 + 1.03266i 0.993375 + 0.114916i \(0.0366597\pi\)
−0.397168 + 0.917746i \(0.630007\pi\)
\(108\) −0.821765 + 1.42334i −0.0790744 + 0.136961i
\(109\) 0.549920 0.952489i 0.0526728 0.0912319i −0.838487 0.544922i \(-0.816559\pi\)
0.891160 + 0.453690i \(0.149893\pi\)
\(110\) −1.38722 2.40273i −0.132266 0.229092i
\(111\) −8.52649 −0.809299
\(112\) −1.17915 + 2.36846i −0.111419 + 0.223798i
\(113\) 4.44278 0.417942 0.208971 0.977922i \(-0.432989\pi\)
0.208971 + 0.977922i \(0.432989\pi\)
\(114\) −10.0049 17.3290i −0.937045 1.62301i
\(115\) 0.663319 1.14890i 0.0618548 0.107136i
\(116\) −0.579223 + 1.00324i −0.0537795 + 0.0931489i
\(117\) −5.65954 9.80260i −0.523224 0.906251i
\(118\) 9.18450 0.845501
\(119\) −18.3509 + 1.13309i −1.68222 + 0.103871i
\(120\) 3.41797 0.312016
\(121\) 3.31317 + 5.73857i 0.301197 + 0.521689i
\(122\) −6.01934 + 10.4258i −0.544966 + 0.943908i
\(123\) 5.49324 9.51457i 0.495308 0.857899i
\(124\) 4.35694 + 7.54644i 0.391265 + 0.677691i
\(125\) −10.9315 −0.977746
\(126\) 9.60672 0.593177i 0.855835 0.0528444i
\(127\) 2.41201 0.214031 0.107015 0.994257i \(-0.465871\pi\)
0.107015 + 0.994257i \(0.465871\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 10.7786 18.6691i 0.949006 1.64373i
\(130\) −2.06386 + 3.57471i −0.181013 + 0.313523i
\(131\) −0.761712 1.31932i −0.0665511 0.115270i 0.830830 0.556526i \(-0.187866\pi\)
−0.897381 + 0.441257i \(0.854533\pi\)
\(132\) 5.38814 0.468977
\(133\) −9.15792 + 18.3947i −0.794092 + 1.59502i
\(134\) −7.26319 −0.627444
\(135\) −1.09018 1.88825i −0.0938281 0.162515i
\(136\) 3.47460 6.01818i 0.297944 0.516054i
\(137\) −4.81334 + 8.33695i −0.411231 + 0.712274i −0.995025 0.0996287i \(-0.968235\pi\)
0.583793 + 0.811902i \(0.301568\pi\)
\(138\) 1.28821 + 2.23124i 0.109660 + 0.189936i
\(139\) 8.57676 0.727471 0.363736 0.931502i \(-0.381501\pi\)
0.363736 + 0.931502i \(0.381501\pi\)
\(140\) −1.93897 2.92577i −0.163873 0.247273i
\(141\) −8.96928 −0.755349
\(142\) 3.70854 + 6.42338i 0.311214 + 0.539038i
\(143\) −3.25350 + 5.63523i −0.272072 + 0.471242i
\(144\) −1.81896 + 3.15053i −0.151580 + 0.262544i
\(145\) −0.768419 1.33094i −0.0638137 0.110529i
\(146\) −4.36805 −0.361502
\(147\) −10.8704 14.3907i −0.896576 1.18692i
\(148\) −3.30944 −0.272034
\(149\) −8.01069 13.8749i −0.656261 1.13668i −0.981576 0.191072i \(-0.938804\pi\)
0.325315 0.945606i \(-0.394530\pi\)
\(150\) 4.17383 7.22929i 0.340792 0.590269i
\(151\) 6.96789 12.0687i 0.567039 0.982140i −0.429818 0.902915i \(-0.641422\pi\)
0.996857 0.0792244i \(-0.0252443\pi\)
\(152\) −3.88326 6.72601i −0.314974 0.545552i
\(153\) −25.2806 −2.04381
\(154\) −3.05663 4.61223i −0.246310 0.371664i
\(155\) −11.5602 −0.928535
\(156\) −4.00815 6.94232i −0.320909 0.555831i
\(157\) 7.71135 13.3564i 0.615433 1.06596i −0.374876 0.927075i \(-0.622315\pi\)
0.990308 0.138885i \(-0.0443520\pi\)
\(158\) 0.398625 0.690439i 0.0317129 0.0549284i
\(159\) −5.46204 9.46053i −0.433168 0.750269i
\(160\) 1.32664 0.104880
\(161\) 1.17915 2.36846i 0.0929302 0.186661i
\(162\) −6.67932 −0.524777
\(163\) 4.30693 + 7.45983i 0.337345 + 0.584299i 0.983932 0.178541i \(-0.0571378\pi\)
−0.646587 + 0.762840i \(0.723804\pi\)
\(164\) 2.13212 3.69295i 0.166491 0.288371i
\(165\) −3.57405 + 6.19044i −0.278240 + 0.481925i
\(166\) −5.18730 8.98468i −0.402613 0.697346i
\(167\) 11.9693 0.926211 0.463105 0.886303i \(-0.346735\pi\)
0.463105 + 0.886303i \(0.346735\pi\)
\(168\) 6.80360 0.420095i 0.524909 0.0324110i
\(169\) −3.31907 −0.255313
\(170\) 4.60953 + 7.98394i 0.353535 + 0.612340i
\(171\) −14.1270 + 24.4686i −1.08032 + 1.87116i
\(172\) 4.18358 7.24617i 0.318995 0.552515i
\(173\) 9.90984 + 17.1644i 0.753431 + 1.30498i 0.946150 + 0.323727i \(0.104936\pi\)
−0.192719 + 0.981254i \(0.561731\pi\)
\(174\) 2.98464 0.226265
\(175\) −8.55603 + 0.528301i −0.646775 + 0.0399358i
\(176\) 2.09133 0.157640
\(177\) −11.8315 20.4928i −0.889313 1.54033i
\(178\) −8.32132 + 14.4129i −0.623709 + 1.08030i
\(179\) 8.20481 14.2112i 0.613257 1.06219i −0.377431 0.926038i \(-0.623193\pi\)
0.990688 0.136154i \(-0.0434742\pi\)
\(180\) −2.41310 4.17961i −0.179862 0.311529i
\(181\) −11.2306 −0.834766 −0.417383 0.908731i \(-0.637053\pi\)
−0.417383 + 0.908731i \(0.637053\pi\)
\(182\) −3.66884 + 7.36927i −0.271952 + 0.546247i
\(183\) 31.0167 2.29282
\(184\) 0.500000 + 0.866025i 0.0368605 + 0.0638442i
\(185\) 2.19521 3.80222i 0.161395 0.279545i
\(186\) 11.2253 19.4428i 0.823078 1.42561i
\(187\) 7.26653 + 12.5860i 0.531381 + 0.920379i
\(188\) −3.48130 −0.253900
\(189\) −2.40213 3.62465i −0.174730 0.263655i
\(190\) 10.3034 0.747485
\(191\) −3.18402 5.51489i −0.230388 0.399044i 0.727534 0.686071i \(-0.240666\pi\)
−0.957922 + 0.287028i \(0.907333\pi\)
\(192\) −1.28821 + 2.23124i −0.0929684 + 0.161026i
\(193\) 7.02750 12.1720i 0.505850 0.876158i −0.494127 0.869390i \(-0.664512\pi\)
0.999977 0.00676850i \(-0.00215450\pi\)
\(194\) −3.32900 5.76600i −0.239008 0.413975i
\(195\) 10.6347 0.761569
\(196\) −4.21920 5.58555i −0.301371 0.398968i
\(197\) −6.95570 −0.495573 −0.247786 0.968815i \(-0.579703\pi\)
−0.247786 + 0.968815i \(0.579703\pi\)
\(198\) −3.80404 6.58879i −0.270341 0.468245i
\(199\) −10.5449 + 18.2642i −0.747506 + 1.29472i 0.201509 + 0.979487i \(0.435415\pi\)
−0.949015 + 0.315231i \(0.897918\pi\)
\(200\) 1.62002 2.80595i 0.114552 0.198411i
\(201\) 9.35650 + 16.2059i 0.659956 + 1.14308i
\(202\) 9.15879 0.644410
\(203\) −1.69315 2.55484i −0.118836 0.179315i
\(204\) −17.9040 −1.25353
\(205\) 2.82856 + 4.89920i 0.197555 + 0.342175i
\(206\) −2.26606 + 3.92492i −0.157884 + 0.273462i
\(207\) 1.81896 3.15053i 0.126426 0.218977i
\(208\) −1.55571 2.69457i −0.107869 0.186835i
\(209\) 16.2424 1.12351
\(210\) −4.03030 + 8.09532i −0.278117 + 0.558630i
\(211\) 26.5036 1.82458 0.912290 0.409544i \(-0.134312\pi\)
0.912290 + 0.409544i \(0.134312\pi\)
\(212\) −2.12002 3.67198i −0.145603 0.252192i
\(213\) 9.55474 16.5493i 0.654680 1.13394i
\(214\) 6.16722 10.6819i 0.421582 0.730202i
\(215\) 5.55009 + 9.61304i 0.378513 + 0.655604i
\(216\) 1.64353 0.111828
\(217\) −23.0109 + 1.42083i −1.56208 + 0.0964525i
\(218\) −1.09984 −0.0744906
\(219\) 5.62695 + 9.74617i 0.380234 + 0.658585i
\(220\) −1.38722 + 2.40273i −0.0935263 + 0.161992i
\(221\) 10.8109 18.7251i 0.727221 1.25958i
\(222\) 4.26325 + 7.38416i 0.286130 + 0.495592i
\(223\) −9.80109 −0.656329 −0.328165 0.944621i \(-0.606430\pi\)
−0.328165 + 0.944621i \(0.606430\pi\)
\(224\) 2.64072 0.163054i 0.176441 0.0108945i
\(225\) −11.7870 −0.785797
\(226\) −2.22139 3.84756i −0.147765 0.255936i
\(227\) 14.2481 24.6784i 0.945679 1.63796i 0.191292 0.981533i \(-0.438732\pi\)
0.754387 0.656430i \(-0.227934\pi\)
\(228\) −10.0049 + 17.3290i −0.662591 + 1.14764i
\(229\) 12.5957 + 21.8164i 0.832347 + 1.44167i 0.896172 + 0.443707i \(0.146337\pi\)
−0.0638246 + 0.997961i \(0.520330\pi\)
\(230\) −1.32664 −0.0874759
\(231\) −6.35343 + 12.7616i −0.418025 + 0.839650i
\(232\) 1.15845 0.0760557
\(233\) 6.58123 + 11.3990i 0.431151 + 0.746775i 0.996973 0.0777524i \(-0.0247744\pi\)
−0.565822 + 0.824527i \(0.691441\pi\)
\(234\) −5.65954 + 9.80260i −0.369975 + 0.640816i
\(235\) 2.30921 3.99967i 0.150636 0.260910i
\(236\) −4.59225 7.95401i −0.298930 0.517762i
\(237\) −2.05405 −0.133425
\(238\) 10.1567 + 15.3258i 0.658363 + 0.993423i
\(239\) −8.78283 −0.568114 −0.284057 0.958807i \(-0.591681\pi\)
−0.284057 + 0.958807i \(0.591681\pi\)
\(240\) −1.70898 2.96005i −0.110314 0.191070i
\(241\) −0.763776 + 1.32290i −0.0491992 + 0.0852154i −0.889576 0.456787i \(-0.849000\pi\)
0.840377 + 0.542002i \(0.182334\pi\)
\(242\) 3.31317 5.73857i 0.212978 0.368890i
\(243\) 11.0697 + 19.1732i 0.710118 + 1.22996i
\(244\) 12.0387 0.770698
\(245\) 9.21592 1.14245i 0.588784 0.0729884i
\(246\) −10.9865 −0.700472
\(247\) −12.0825 20.9274i −0.768789 1.33158i
\(248\) 4.35694 7.54644i 0.276666 0.479200i
\(249\) −13.3646 + 23.1483i −0.846950 + 1.46696i
\(250\) 5.46577 + 9.46699i 0.345686 + 0.598745i
\(251\) 1.04230 0.0657895 0.0328947 0.999459i \(-0.489527\pi\)
0.0328947 + 0.999459i \(0.489527\pi\)
\(252\) −5.31707 8.02307i −0.334944 0.505406i
\(253\) −2.09133 −0.131481
\(254\) −1.20600 2.08886i −0.0756714 0.131067i
\(255\) 11.8761 20.5699i 0.743707 1.28814i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 3.38705 + 5.86654i 0.211278 + 0.365944i 0.952115 0.305741i \(-0.0989041\pi\)
−0.740837 + 0.671685i \(0.765571\pi\)
\(258\) −21.5573 −1.34210
\(259\) 3.90234 7.83828i 0.242479 0.487047i
\(260\) 4.12772 0.255991
\(261\) −2.10716 3.64972i −0.130430 0.225912i
\(262\) −0.761712 + 1.31932i −0.0470588 + 0.0815082i
\(263\) −0.228543 + 0.395849i −0.0140926 + 0.0244091i −0.872986 0.487746i \(-0.837819\pi\)
0.858893 + 0.512155i \(0.171153\pi\)
\(264\) −2.69407 4.66626i −0.165808 0.287189i
\(265\) 5.62499 0.345540
\(266\) 20.5092 1.26636i 1.25750 0.0776458i
\(267\) 42.8783 2.62411
\(268\) 3.63160 + 6.29011i 0.221835 + 0.384229i
\(269\) −9.27674 + 16.0678i −0.565613 + 0.979671i 0.431379 + 0.902171i \(0.358027\pi\)
−0.996992 + 0.0775000i \(0.975306\pi\)
\(270\) −1.09018 + 1.88825i −0.0663465 + 0.114916i
\(271\) −9.14545 15.8404i −0.555546 0.962235i −0.997861 0.0653746i \(-0.979176\pi\)
0.442314 0.896860i \(-0.354158\pi\)
\(272\) −6.94919 −0.421357
\(273\) 21.1688 1.30709i 1.28120 0.0791088i
\(274\) 9.62668 0.581569
\(275\) 3.38799 + 5.86817i 0.204304 + 0.353864i
\(276\) 1.28821 2.23124i 0.0775410 0.134305i
\(277\) −10.0783 + 17.4562i −0.605548 + 1.04884i 0.386416 + 0.922325i \(0.373713\pi\)
−0.991965 + 0.126516i \(0.959620\pi\)
\(278\) −4.28838 7.42769i −0.257200 0.445483i
\(279\) −31.7004 −1.89785
\(280\) −1.56431 + 3.14209i −0.0934852 + 0.187776i
\(281\) −7.27365 −0.433909 −0.216955 0.976182i \(-0.569612\pi\)
−0.216955 + 0.976182i \(0.569612\pi\)
\(282\) 4.48464 + 7.76762i 0.267056 + 0.462555i
\(283\) 1.38120 2.39231i 0.0821038 0.142208i −0.822050 0.569416i \(-0.807169\pi\)
0.904153 + 0.427208i \(0.140503\pi\)
\(284\) 3.70854 6.42338i 0.220061 0.381157i
\(285\) −13.2729 22.9893i −0.786217 1.36177i
\(286\) 6.50701 0.384767
\(287\) 6.23250 + 9.40440i 0.367893 + 0.555124i
\(288\) 3.63791 0.214366
\(289\) −15.6456 27.0990i −0.920331 1.59406i
\(290\) −0.768419 + 1.33094i −0.0451231 + 0.0781556i
\(291\) −8.57689 + 14.8556i −0.502786 + 0.870851i
\(292\) 2.18402 + 3.78284i 0.127810 + 0.221374i
\(293\) 25.3756 1.48246 0.741228 0.671253i \(-0.234244\pi\)
0.741228 + 0.671253i \(0.234244\pi\)
\(294\) −7.02750 + 16.6094i −0.409852 + 0.968680i
\(295\) 12.1845 0.709409
\(296\) 1.65472 + 2.86606i 0.0961787 + 0.166586i
\(297\) −1.71858 + 2.97667i −0.0997223 + 0.172724i
\(298\) −8.01069 + 13.8749i −0.464047 + 0.803753i
\(299\) 1.55571 + 2.69457i 0.0899690 + 0.155831i
\(300\) −8.34767 −0.481953
\(301\) 12.2292 + 18.4530i 0.704879 + 1.06361i
\(302\) −13.9358 −0.801914
\(303\) −11.7984 20.4355i −0.677802 1.17399i
\(304\) −3.88326 + 6.72601i −0.222720 + 0.385763i
\(305\) −7.98549 + 13.8313i −0.457248 + 0.791976i
\(306\) 12.6403 + 21.8936i 0.722597 + 1.25157i
\(307\) −29.2469 −1.66921 −0.834606 0.550848i \(-0.814304\pi\)
−0.834606 + 0.550848i \(0.814304\pi\)
\(308\) −2.46600 + 4.95323i −0.140513 + 0.282237i
\(309\) 11.6766 0.664259
\(310\) 5.78008 + 10.0114i 0.328287 + 0.568609i
\(311\) −13.6414 + 23.6276i −0.773534 + 1.33980i 0.162081 + 0.986778i \(0.448180\pi\)
−0.935615 + 0.353023i \(0.885154\pi\)
\(312\) −4.00815 + 6.94232i −0.226917 + 0.393032i
\(313\) −1.28838 2.23154i −0.0728236 0.126134i 0.827314 0.561739i \(-0.189868\pi\)
−0.900138 + 0.435605i \(0.856534\pi\)
\(314\) −15.4227 −0.870353
\(315\) 12.7446 0.786930i 0.718079 0.0443385i
\(316\) −0.797250 −0.0448488
\(317\) 6.25323 + 10.8309i 0.351216 + 0.608325i 0.986463 0.163985i \(-0.0524348\pi\)
−0.635246 + 0.772310i \(0.719101\pi\)
\(318\) −5.46204 + 9.46053i −0.306296 + 0.530520i
\(319\) −1.21135 + 2.09812i −0.0678224 + 0.117472i
\(320\) −0.663319 1.14890i −0.0370806 0.0642256i
\(321\) −31.7786 −1.77371
\(322\) −2.64072 + 0.163054i −0.147162 + 0.00908665i
\(323\) −53.9711 −3.00303
\(324\) 3.33966 + 5.78446i 0.185537 + 0.321359i
\(325\) 5.04055 8.73049i 0.279599 0.484280i
\(326\) 4.30693 7.45983i 0.238539 0.413162i
\(327\) 1.41682 + 2.45401i 0.0783504 + 0.135707i
\(328\) −4.26425 −0.235454
\(329\) 4.10498 8.24532i 0.226315 0.454579i
\(330\) 7.14810 0.393490
\(331\) −1.36699 2.36769i −0.0751363 0.130140i 0.826009 0.563657i \(-0.190606\pi\)
−0.901146 + 0.433517i \(0.857273\pi\)
\(332\) −5.18730 + 8.98468i −0.284690 + 0.493098i
\(333\) 6.01973 10.4265i 0.329879 0.571368i
\(334\) −5.98464 10.3657i −0.327465 0.567186i
\(335\) −9.63562 −0.526450
\(336\) −3.76561 5.68204i −0.205431 0.309981i
\(337\) 12.4355 0.677405 0.338703 0.940893i \(-0.390012\pi\)
0.338703 + 0.940893i \(0.390012\pi\)
\(338\) 1.65954 + 2.87440i 0.0902669 + 0.156347i
\(339\) −5.72323 + 9.91292i −0.310843 + 0.538396i
\(340\) 4.60953 7.98394i 0.249987 0.432990i
\(341\) 9.11181 + 15.7821i 0.493432 + 0.854649i
\(342\) 28.2540 1.52780
\(343\) 18.2042 3.40680i 0.982936 0.183950i
\(344\) −8.36716 −0.451127
\(345\) 1.70898 + 2.96005i 0.0920086 + 0.159364i
\(346\) 9.90984 17.1644i 0.532756 0.922761i
\(347\) −1.10374 + 1.91173i −0.0592518 + 0.102627i −0.894130 0.447808i \(-0.852205\pi\)
0.834878 + 0.550435i \(0.185538\pi\)
\(348\) −1.49232 2.58477i −0.0799967 0.138558i
\(349\) 10.7710 0.576558 0.288279 0.957546i \(-0.406917\pi\)
0.288279 + 0.957546i \(0.406917\pi\)
\(350\) 4.73554 + 7.14559i 0.253125 + 0.381948i
\(351\) 5.11371 0.272950
\(352\) −1.04567 1.81115i −0.0557342 0.0965344i
\(353\) 6.94849 12.0351i 0.369831 0.640566i −0.619708 0.784832i \(-0.712749\pi\)
0.989539 + 0.144267i \(0.0460823\pi\)
\(354\) −11.8315 + 20.4928i −0.628839 + 1.08918i
\(355\) 4.91989 + 8.52149i 0.261120 + 0.452274i
\(356\) 16.6426 0.882058
\(357\) 21.1115 42.4049i 1.11734 2.24430i
\(358\) −16.4096 −0.867276
\(359\) 9.73350 + 16.8589i 0.513714 + 0.889780i 0.999873 + 0.0159091i \(0.00506425\pi\)
−0.486159 + 0.873870i \(0.661602\pi\)
\(360\) −2.41310 + 4.17961i −0.127181 + 0.220285i
\(361\) −20.6595 + 35.7833i −1.08734 + 1.88333i
\(362\) 5.61532 + 9.72601i 0.295135 + 0.511188i
\(363\) −17.0722 −0.896057
\(364\) 8.21639 0.507330i 0.430656 0.0265913i
\(365\) −5.79482 −0.303315
\(366\) −15.5083 26.8612i −0.810633 1.40406i
\(367\) −8.59369 + 14.8847i −0.448587 + 0.776976i −0.998294 0.0583816i \(-0.981406\pi\)
0.549707 + 0.835357i \(0.314739\pi\)
\(368\) 0.500000 0.866025i 0.0260643 0.0451447i
\(369\) 7.75648 + 13.4346i 0.403786 + 0.699379i
\(370\) −4.39043 −0.228248
\(371\) 11.1967 0.691355i 0.581306 0.0358934i
\(372\) −22.4506 −1.16401
\(373\) 4.71828 + 8.17231i 0.244303 + 0.423146i 0.961936 0.273276i \(-0.0881074\pi\)
−0.717632 + 0.696422i \(0.754774\pi\)
\(374\) 7.26653 12.5860i 0.375743 0.650806i
\(375\) 14.0821 24.3909i 0.727196 1.25954i
\(376\) 1.74065 + 3.01490i 0.0897672 + 0.155481i
\(377\) 3.60441 0.185637
\(378\) −1.93797 + 3.89264i −0.0996785 + 0.200216i
\(379\) 6.99131 0.359120 0.179560 0.983747i \(-0.442533\pi\)
0.179560 + 0.983747i \(0.442533\pi\)
\(380\) −5.15168 8.92298i −0.264276 0.457739i
\(381\) −3.10716 + 5.38177i −0.159185 + 0.275716i
\(382\) −3.18402 + 5.51489i −0.162909 + 0.282166i
\(383\) −13.7705 23.8512i −0.703640 1.21874i −0.967180 0.254092i \(-0.918223\pi\)
0.263540 0.964649i \(-0.415110\pi\)
\(384\) 2.57641 0.131477
\(385\) −4.05504 6.11876i −0.206664 0.311841i
\(386\) −14.0550 −0.715380
\(387\) 15.2195 + 26.3609i 0.773651 + 1.34000i
\(388\) −3.32900 + 5.76600i −0.169004 + 0.292724i
\(389\) −3.35222 + 5.80621i −0.169964 + 0.294386i −0.938407 0.345532i \(-0.887698\pi\)
0.768443 + 0.639918i \(0.221032\pi\)
\(390\) −5.31737 9.20995i −0.269255 0.466364i
\(391\) 6.94919 0.351436
\(392\) −2.72763 + 6.44671i −0.137766 + 0.325608i
\(393\) 3.92497 0.197989
\(394\) 3.47785 + 6.02381i 0.175211 + 0.303475i
\(395\) 0.528831 0.915962i 0.0266084 0.0460871i
\(396\) −3.80404 + 6.58879i −0.191160 + 0.331099i
\(397\) −11.3026 19.5767i −0.567262 0.982527i −0.996835 0.0794950i \(-0.974669\pi\)
0.429573 0.903032i \(-0.358664\pi\)
\(398\) 21.0897 1.05713
\(399\) −29.2457 44.1297i −1.46412 2.20925i
\(400\) −3.24003 −0.162002
\(401\) 4.85413 + 8.40761i 0.242404 + 0.419856i 0.961398 0.275160i \(-0.0887308\pi\)
−0.718995 + 0.695016i \(0.755397\pi\)
\(402\) 9.35650 16.2059i 0.466660 0.808278i
\(403\) 13.5563 23.4801i 0.675286 1.16963i
\(404\) −4.57940 7.93175i −0.227833 0.394619i
\(405\) −8.86104 −0.440309
\(406\) −1.36598 + 2.74373i −0.0677927 + 0.136169i
\(407\) −6.92114 −0.343068
\(408\) 8.95200 + 15.5053i 0.443190 + 0.767628i
\(409\) 18.1680 31.4679i 0.898350 1.55599i 0.0687468 0.997634i \(-0.478100\pi\)
0.829603 0.558354i \(-0.188567\pi\)
\(410\) 2.82856 4.89920i 0.139692 0.241954i
\(411\) −12.4012 21.4794i −0.611704 1.05950i
\(412\) 4.53211 0.223281
\(413\) 24.2537 1.49757i 1.19345 0.0736906i
\(414\) −3.63791 −0.178794
\(415\) −6.88167 11.9194i −0.337808 0.585101i
\(416\) −1.55571 + 2.69457i −0.0762749 + 0.132112i
\(417\) −11.0486 + 19.1368i −0.541055 + 0.937134i
\(418\) −8.12119 14.0663i −0.397220 0.688006i
\(419\) 9.98642 0.487868 0.243934 0.969792i \(-0.421562\pi\)
0.243934 + 0.969792i \(0.421562\pi\)
\(420\) 9.02590 0.557314i 0.440419 0.0271941i
\(421\) 14.1053 0.687448 0.343724 0.939071i \(-0.388312\pi\)
0.343724 + 0.939071i \(0.388312\pi\)
\(422\) −13.2518 22.9528i −0.645087 1.11732i
\(423\) 6.33234 10.9679i 0.307889 0.533279i
\(424\) −2.12002 + 3.67198i −0.102957 + 0.178327i
\(425\) −11.2578 19.4991i −0.546084 0.945845i
\(426\) −19.1095 −0.925857
\(427\) −14.1954 + 28.5131i −0.686966 + 1.37985i
\(428\) −12.3344 −0.596207
\(429\) −8.38237 14.5187i −0.404705 0.700969i
\(430\) 5.55009 9.61304i 0.267649 0.463582i
\(431\) 1.77185 3.06893i 0.0853468 0.147825i −0.820192 0.572088i \(-0.806134\pi\)
0.905539 + 0.424263i \(0.139467\pi\)
\(432\) −0.821765 1.42334i −0.0395372 0.0684804i
\(433\) −16.2680 −0.781792 −0.390896 0.920435i \(-0.627835\pi\)
−0.390896 + 0.920435i \(0.627835\pi\)
\(434\) 12.7360 + 19.2176i 0.611345 + 0.922477i
\(435\) 3.95953 0.189845
\(436\) 0.549920 + 0.952489i 0.0263364 + 0.0456160i
\(437\) 3.88326 6.72601i 0.185762 0.321749i
\(438\) 5.62695 9.74617i 0.268866 0.465690i
\(439\) −0.585013 1.01327i −0.0279211 0.0483608i 0.851727 0.523985i \(-0.175555\pi\)
−0.879648 + 0.475625i \(0.842222\pi\)
\(440\) 2.77444 0.132266
\(441\) 25.2720 3.13283i 1.20343 0.149182i
\(442\) −21.6218 −1.02845
\(443\) −19.5037 33.7813i −0.926647 1.60500i −0.788891 0.614533i \(-0.789345\pi\)
−0.137755 0.990466i \(-0.543989\pi\)
\(444\) 4.26325 7.38416i 0.202325 0.350437i
\(445\) −11.0394 + 19.1208i −0.523317 + 0.906411i
\(446\) 4.90054 + 8.48799i 0.232047 + 0.401918i
\(447\) 41.2777 1.95237
\(448\) −1.46157 2.20541i −0.0690527 0.104196i
\(449\) 32.1714 1.51826 0.759130 0.650939i \(-0.225624\pi\)
0.759130 + 0.650939i \(0.225624\pi\)
\(450\) 5.89348 + 10.2078i 0.277821 + 0.481201i
\(451\) 4.45898 7.72318i 0.209965 0.363670i
\(452\) −2.22139 + 3.84756i −0.104485 + 0.180974i
\(453\) 17.9522 + 31.0941i 0.843467 + 1.46093i
\(454\) −28.4962 −1.33739
\(455\) −4.86721 + 9.77635i −0.228179 + 0.458322i
\(456\) 20.0098 0.937045
\(457\) 17.1774 + 29.7521i 0.803524 + 1.39174i 0.917283 + 0.398236i \(0.130377\pi\)
−0.113759 + 0.993508i \(0.536289\pi\)
\(458\) 12.5957 21.8164i 0.588558 1.01941i
\(459\) 5.71060 9.89105i 0.266548 0.461675i
\(460\) 0.663319 + 1.14890i 0.0309274 + 0.0535678i
\(461\) 10.5155 0.489756 0.244878 0.969554i \(-0.421252\pi\)
0.244878 + 0.969554i \(0.421252\pi\)
\(462\) 14.2286 0.878558i 0.661973 0.0408742i
\(463\) −19.9943 −0.929213 −0.464606 0.885517i \(-0.653804\pi\)
−0.464606 + 0.885517i \(0.653804\pi\)
\(464\) −0.579223 1.00324i −0.0268898 0.0465744i
\(465\) 14.8919 25.7935i 0.690595 1.19615i
\(466\) 6.58123 11.3990i 0.304870 0.528050i
\(467\) 13.7321 + 23.7848i 0.635448 + 1.10063i 0.986420 + 0.164242i \(0.0525177\pi\)
−0.350973 + 0.936386i \(0.614149\pi\)
\(468\) 11.3191 0.523224
\(469\) −19.1801 + 1.18429i −0.885653 + 0.0546856i
\(470\) −4.61843 −0.213032
\(471\) 19.8676 + 34.4117i 0.915452 + 1.58561i
\(472\) −4.59225 + 7.95401i −0.211375 + 0.366113i
\(473\) 8.74925 15.1541i 0.402291 0.696788i
\(474\) 1.02702 + 1.77886i 0.0471728 + 0.0817056i
\(475\) −25.1638 −1.15459
\(476\) 8.19415 16.4589i 0.375578 0.754391i
\(477\) 15.4249 0.706257
\(478\) 4.39142 + 7.60616i 0.200859 + 0.347898i
\(479\) 4.22275 7.31402i 0.192943 0.334186i −0.753282 0.657698i \(-0.771530\pi\)
0.946224 + 0.323512i \(0.104864\pi\)
\(480\) −1.70898 + 2.96005i −0.0780041 + 0.135107i
\(481\) 5.14853 + 8.91751i 0.234753 + 0.406604i
\(482\) 1.52755 0.0695781
\(483\) 3.76561 + 5.68204i 0.171341 + 0.258542i
\(484\) −6.62633 −0.301197
\(485\) −4.41638 7.64939i −0.200537 0.347341i
\(486\) 11.0697 19.1732i 0.502130 0.869714i
\(487\) −16.6395 + 28.8205i −0.754009 + 1.30598i 0.191856 + 0.981423i \(0.438549\pi\)
−0.945865 + 0.324559i \(0.894784\pi\)
\(488\) −6.01934 10.4258i −0.272483 0.471954i
\(489\) −22.1929 −1.00360
\(490\) −5.59735 7.41000i −0.252862 0.334750i
\(491\) 15.8532 0.715444 0.357722 0.933828i \(-0.383553\pi\)
0.357722 + 0.933828i \(0.383553\pi\)
\(492\) 5.49324 + 9.51457i 0.247654 + 0.428950i
\(493\) 4.02513 6.97173i 0.181283 0.313991i
\(494\) −12.0825 + 20.9274i −0.543616 + 0.941570i
\(495\) −5.04658 8.74094i −0.226827 0.392876i
\(496\) −8.71388 −0.391265
\(497\) 10.8406 + 16.3577i 0.486266 + 0.733742i
\(498\) 26.7293 1.19777
\(499\) 9.66615 + 16.7423i 0.432717 + 0.749487i 0.997106 0.0760215i \(-0.0242218\pi\)
−0.564390 + 0.825509i \(0.690888\pi\)
\(500\) 5.46577 9.46699i 0.244437 0.423377i
\(501\) −15.4189 + 26.7063i −0.688866 + 1.19315i
\(502\) −0.521150 0.902659i −0.0232601 0.0402876i
\(503\) 40.9220 1.82462 0.912310 0.409500i \(-0.134297\pi\)
0.912310 + 0.409500i \(0.134297\pi\)
\(504\) −4.28965 + 8.61625i −0.191076 + 0.383798i
\(505\) 12.1504 0.540686
\(506\) 1.04567 + 1.81115i 0.0464855 + 0.0805152i
\(507\) 4.27565 7.40565i 0.189888 0.328897i
\(508\) −1.20600 + 2.08886i −0.0535077 + 0.0926781i
\(509\) −0.260911 0.451912i −0.0115647 0.0200306i 0.860185 0.509982i \(-0.170348\pi\)
−0.871750 + 0.489951i \(0.837015\pi\)
\(510\) −23.7521 −1.05176
\(511\) −11.5348 + 0.712228i −0.510270 + 0.0315071i
\(512\) 1.00000 0.0441942
\(513\) −6.38226 11.0544i −0.281784 0.488064i
\(514\) 3.38705 5.86654i 0.149396 0.258762i
\(515\) −3.00623 + 5.20695i −0.132471 + 0.229446i
\(516\) 10.7786 + 18.6691i 0.474503 + 0.821863i
\(517\) −7.28055 −0.320198
\(518\) −8.73932 + 0.539618i −0.383983 + 0.0237095i
\(519\) −51.0637 −2.24145
\(520\) −2.06386 3.57471i −0.0905063 0.156762i
\(521\) −6.14887 + 10.6502i −0.269387 + 0.466592i −0.968704 0.248220i \(-0.920154\pi\)
0.699317 + 0.714812i \(0.253488\pi\)
\(522\) −2.10716 + 3.64972i −0.0922281 + 0.159744i
\(523\) −15.6891 27.1742i −0.686034 1.18825i −0.973111 0.230339i \(-0.926017\pi\)
0.287076 0.957908i \(-0.407317\pi\)
\(524\) 1.52342 0.0665511
\(525\) 9.84317 19.7711i 0.429591 0.862882i
\(526\) 0.457086 0.0199299
\(527\) −30.2772 52.4417i −1.31890 2.28440i
\(528\) −2.69407 + 4.66626i −0.117244 + 0.203073i
\(529\) −0.500000 + 0.866025i −0.0217391 + 0.0376533i
\(530\) −2.81249 4.87138i −0.122167 0.211599i
\(531\) 33.4124 1.44997
\(532\) −11.3513 17.1283i −0.492142 0.742608i
\(533\) −13.2679 −0.574695
\(534\) −21.4392 37.1337i −0.927764 1.60693i
\(535\) 8.18166 14.1711i 0.353724 0.612668i
\(536\) 3.63160 6.29011i 0.156861 0.271691i
\(537\) 21.1390 + 36.6138i 0.912215 + 1.58000i
\(538\) 18.5535 0.799898
\(539\) −8.82375 11.6812i −0.380066 0.503146i
\(540\) 2.18037 0.0938281
\(541\) −0.375985 0.651226i −0.0161649 0.0279984i 0.857830 0.513934i \(-0.171812\pi\)
−0.873995 + 0.485935i \(0.838479\pi\)
\(542\) −9.14545 + 15.8404i −0.392831 + 0.680403i
\(543\) 14.4674 25.0582i 0.620855 1.07535i
\(544\) 3.47460 + 6.01818i 0.148972 + 0.258027i
\(545\) −1.45909 −0.0625005
\(546\) −11.7164 17.6792i −0.501415 0.756600i
\(547\) −27.3113 −1.16775 −0.583874 0.811844i \(-0.698464\pi\)
−0.583874 + 0.811844i \(0.698464\pi\)
\(548\) −4.81334 8.33695i −0.205616 0.356137i
\(549\) −21.8979 + 37.9282i −0.934578 + 1.61874i
\(550\) 3.38799 5.86817i 0.144464 0.250220i
\(551\) −4.49855 7.79172i −0.191645 0.331939i
\(552\) −2.57641 −0.109660
\(553\) 0.940079 1.88825i 0.0399762 0.0802968i
\(554\) 20.1567 0.856375
\(555\) 5.65578 + 9.79610i 0.240075 + 0.415821i
\(556\) −4.28838 + 7.42769i −0.181868 + 0.315004i
\(557\) −14.6243 + 25.3300i −0.619650 + 1.07327i 0.369899 + 0.929072i \(0.379392\pi\)
−0.989549 + 0.144194i \(0.953941\pi\)
\(558\) 15.8502 + 27.4533i 0.670992 + 1.16219i
\(559\) −26.0337 −1.10111
\(560\) 3.50328 0.216314i 0.148041 0.00914092i
\(561\) −37.4432 −1.58085
\(562\) 3.63682 + 6.29916i 0.153410 + 0.265714i
\(563\) −0.257258 + 0.445584i −0.0108421 + 0.0187791i −0.871396 0.490581i \(-0.836785\pi\)
0.860553 + 0.509360i \(0.170118\pi\)
\(564\) 4.48464 7.76762i 0.188837 0.327076i
\(565\) −2.94698 5.10432i −0.123980 0.214740i
\(566\) −2.76240 −0.116112
\(567\) −17.6382 + 1.08909i −0.740736 + 0.0457375i
\(568\) −7.41708 −0.311214
\(569\) −16.9002 29.2720i −0.708493 1.22715i −0.965416 0.260714i \(-0.916042\pi\)
0.256923 0.966432i \(-0.417291\pi\)
\(570\) −13.2729 + 22.9893i −0.555940 + 0.962915i
\(571\) 6.69143 11.5899i 0.280028 0.485022i −0.691364 0.722507i \(-0.742990\pi\)
0.971391 + 0.237485i \(0.0763230\pi\)
\(572\) −3.25350 5.63523i −0.136036 0.235621i
\(573\) 16.4067 0.685401
\(574\) 5.02820 10.0997i 0.209873 0.421553i
\(575\) 3.24003 0.135119
\(576\) −1.81896 3.15053i −0.0757899 0.131272i
\(577\) 18.3241 31.7382i 0.762842 1.32128i −0.178538 0.983933i \(-0.557137\pi\)
0.941380 0.337348i \(-0.109530\pi\)
\(578\) −15.6456 + 27.0990i −0.650772 + 1.12717i
\(579\) 18.1057 + 31.3601i 0.752449 + 1.30328i
\(580\) 1.53684 0.0638137
\(581\) −15.1632 22.8802i −0.629076 0.949231i
\(582\) 17.1538 0.711047
\(583\) −4.43366 7.67932i −0.183623 0.318045i
\(584\) 2.18402 3.78284i 0.0903756 0.156535i
\(585\) −7.50815 + 13.0045i −0.310424 + 0.537670i
\(586\) −12.6878 21.9759i −0.524127 0.907815i
\(587\) −10.8300 −0.447003 −0.223502 0.974704i \(-0.571749\pi\)
−0.223502 + 0.974704i \(0.571749\pi\)
\(588\) 17.8979 2.21871i 0.738097 0.0914980i
\(589\) −67.6766 −2.78857
\(590\) −6.09225 10.5521i −0.250814 0.434422i
\(591\) 8.96038 15.5198i 0.368581 0.638401i
\(592\) 1.65472 2.86606i 0.0680086 0.117794i
\(593\) 3.90397 + 6.76187i 0.160317 + 0.277677i 0.934982 0.354694i \(-0.115415\pi\)
−0.774665 + 0.632371i \(0.782082\pi\)
\(594\) 3.43717 0.141029
\(595\) 13.4743 + 20.3318i 0.552392 + 0.833521i
\(596\) 16.0214 0.656261
\(597\) −27.1679 47.0563i −1.11191 1.92588i
\(598\) 1.55571 2.69457i 0.0636177 0.110189i
\(599\) 17.3699 30.0856i 0.709715 1.22926i −0.255248 0.966876i \(-0.582157\pi\)
0.964963 0.262387i \(-0.0845097\pi\)
\(600\) 4.17383 + 7.22929i 0.170396 + 0.295135i
\(601\) −33.4939 −1.36625 −0.683123 0.730303i \(-0.739379\pi\)
−0.683123 + 0.730303i \(0.739379\pi\)
\(602\) 9.86615 19.8173i 0.402114 0.807692i
\(603\) −26.4229 −1.07602
\(604\) 6.96789 + 12.0687i 0.283519 + 0.491070i
\(605\) 4.39537 7.61301i 0.178697 0.309513i
\(606\) −11.7984 + 20.4355i −0.479278 + 0.830134i
\(607\) 16.5199 + 28.6134i 0.670523 + 1.16138i 0.977756 + 0.209746i \(0.0672637\pi\)
−0.307233 + 0.951634i \(0.599403\pi\)
\(608\) 7.76653 0.314974
\(609\) 7.88160 0.486658i 0.319379 0.0197204i
\(610\) 15.9710 0.646646
\(611\) 5.41589 + 9.38060i 0.219104 + 0.379499i
\(612\) 12.6403 21.8936i 0.510953 0.884996i
\(613\) −0.172305 + 0.298441i −0.00695934 + 0.0120539i −0.869484 0.493961i \(-0.835549\pi\)
0.862525 + 0.506015i \(0.168882\pi\)
\(614\) 14.6235 + 25.3286i 0.590155 + 1.02218i
\(615\) −14.5751 −0.587723
\(616\) 5.52262 0.341000i 0.222513 0.0137393i
\(617\) 18.8997 0.760872 0.380436 0.924807i \(-0.375774\pi\)
0.380436 + 0.924807i \(0.375774\pi\)
\(618\) −5.83830 10.1122i −0.234851 0.406774i
\(619\) −11.2136 + 19.4225i −0.450712 + 0.780656i −0.998430 0.0560067i \(-0.982163\pi\)
0.547718 + 0.836663i \(0.315497\pi\)
\(620\) 5.78008 10.0114i 0.232134 0.402067i
\(621\) 0.821765 + 1.42334i 0.0329763 + 0.0571166i
\(622\) 27.2828 1.09394
\(623\) −19.6242 + 39.4174i −0.786227 + 1.57923i
\(624\) 8.01631 0.320909
\(625\) −0.848991 1.47050i −0.0339596 0.0588198i
\(626\) −1.28838 + 2.23154i −0.0514940 + 0.0891903i
\(627\) −20.9236 + 36.2407i −0.835606 + 1.44731i
\(628\) 7.71135 + 13.3564i 0.307716 + 0.532980i
\(629\) 22.9979 0.916988
\(630\) −7.05382 10.6437i −0.281031 0.424056i
\(631\) 45.9749 1.83023 0.915117 0.403189i \(-0.132098\pi\)
0.915117 + 0.403189i \(0.132098\pi\)
\(632\) 0.398625 + 0.690439i 0.0158565 + 0.0274642i
\(633\) −34.1421 + 59.1358i −1.35703 + 2.35044i
\(634\) 6.25323 10.8309i 0.248348 0.430151i
\(635\) −1.59993 2.77116i −0.0634912 0.109970i
\(636\) 10.9241 0.433168
\(637\) −8.48679 + 20.0584i −0.336259 + 0.794743i
\(638\) 2.42270 0.0959154
\(639\) 13.4913 + 23.3677i 0.533709 + 0.924412i
\(640\) −0.663319 + 1.14890i −0.0262200 + 0.0454143i
\(641\) 5.92284 10.2587i 0.233938 0.405193i −0.725025 0.688722i \(-0.758172\pi\)
0.958964 + 0.283529i \(0.0915053\pi\)
\(642\) 15.8893 + 27.5211i 0.627101 + 1.08617i
\(643\) 40.7199 1.60584 0.802918 0.596089i \(-0.203280\pi\)
0.802918 + 0.596089i \(0.203280\pi\)
\(644\) 1.46157 + 2.20541i 0.0575939 + 0.0869051i
\(645\) −28.5987 −1.12607
\(646\) 26.9855 + 46.7403i 1.06173 + 1.83897i
\(647\) −0.360840 + 0.624994i −0.0141861 + 0.0245710i −0.873031 0.487664i \(-0.837849\pi\)
0.858845 + 0.512235i \(0.171182\pi\)
\(648\) 3.33966 5.78446i 0.131194 0.227235i
\(649\) −9.60391 16.6345i −0.376986 0.652960i
\(650\) −10.0811 −0.395413
\(651\) 26.4726 53.1733i 1.03754 2.08403i
\(652\) −8.61387 −0.337345
\(653\) 0.373131 + 0.646282i 0.0146018 + 0.0252910i 0.873234 0.487301i \(-0.162019\pi\)
−0.858632 + 0.512592i \(0.828685\pi\)
\(654\) 1.41682 2.45401i 0.0554021 0.0959593i
\(655\) −1.01052 + 1.75027i −0.0394841 + 0.0683885i
\(656\) 2.13212 + 3.69295i 0.0832455 + 0.144185i
\(657\) −15.8906 −0.619951
\(658\) −9.19315 + 0.567641i −0.358386 + 0.0221289i
\(659\) 6.85325 0.266965 0.133482 0.991051i \(-0.457384\pi\)
0.133482 + 0.991051i \(0.457384\pi\)
\(660\) −3.57405 6.19044i −0.139120 0.240963i
\(661\) −16.8918 + 29.2575i −0.657016 + 1.13798i 0.324369 + 0.945931i \(0.394848\pi\)
−0.981384 + 0.192054i \(0.938485\pi\)
\(662\) −1.36699 + 2.36769i −0.0531294 + 0.0920228i
\(663\) 27.8534 + 48.2435i 1.08174 + 1.87362i
\(664\) 10.3746 0.402613
\(665\) 27.2083 1.68001i 1.05509 0.0651478i
\(666\) −12.0395 −0.466520
\(667\) 0.579223 + 1.00324i 0.0224276 + 0.0388458i
\(668\) −5.98464 + 10.3657i −0.231553 + 0.401061i
\(669\) 12.6258 21.8686i 0.488143 0.845488i
\(670\) 4.81781 + 8.34469i 0.186128 + 0.322384i
\(671\) 25.1769 0.971943
\(672\) −3.03798 + 6.10213i −0.117193 + 0.235395i
\(673\) 32.6054 1.25684 0.628422 0.777873i \(-0.283701\pi\)
0.628422 + 0.777873i \(0.283701\pi\)
\(674\) −6.21775 10.7695i −0.239499 0.414824i
\(675\) 2.66255 4.61167i 0.102481 0.177503i
\(676\) 1.65954 2.87440i 0.0638283 0.110554i
\(677\) −12.5764 21.7829i −0.483349 0.837184i 0.516469 0.856306i \(-0.327246\pi\)
−0.999817 + 0.0191219i \(0.993913\pi\)
\(678\) 11.4465 0.439598
\(679\) −9.73114 14.6836i −0.373447 0.563505i
\(680\) −9.21906 −0.353535
\(681\) 36.7090 + 63.5818i 1.40669 + 2.43646i
\(682\) 9.11181 15.7821i 0.348909 0.604328i
\(683\) 16.8507 29.1863i 0.644776 1.11678i −0.339578 0.940578i \(-0.610284\pi\)
0.984353 0.176206i \(-0.0563825\pi\)
\(684\) −14.1270 24.4686i −0.540159 0.935582i
\(685\) 12.7711 0.487959
\(686\) −12.0525 14.0619i −0.460166 0.536887i
\(687\) −64.9035 −2.47622
\(688\) 4.18358 + 7.24617i 0.159497 + 0.276258i
\(689\) −6.59626 + 11.4251i −0.251297 + 0.435260i
\(690\) 1.70898 2.96005i 0.0650599 0.112687i
\(691\) −12.5502 21.7376i −0.477431 0.826935i 0.522234 0.852802i \(-0.325099\pi\)
−0.999665 + 0.0258668i \(0.991765\pi\)
\(692\) −19.8197 −0.753431
\(693\) −11.1197 16.7789i −0.422404 0.637378i
\(694\) 2.20748 0.0837947
\(695\) −5.68913 9.85385i −0.215801 0.373778i
\(696\) −1.49232 + 2.58477i −0.0565662 + 0.0979756i
\(697\) −14.8165 + 25.6630i −0.561216 + 0.972055i
\(698\) −5.38550 9.32796i −0.203844 0.353069i
\(699\) −33.9120 −1.28267
\(700\) 3.82049 7.67389i 0.144401 0.290046i
\(701\) −32.8099 −1.23921 −0.619607 0.784912i \(-0.712708\pi\)
−0.619607 + 0.784912i \(0.712708\pi\)
\(702\) −2.55686 4.42860i −0.0965023 0.167147i
\(703\) 12.8514 22.2593i 0.484701 0.839527i
\(704\) −1.04567 + 1.81115i −0.0394100 + 0.0682601i
\(705\) 5.94949 + 10.3048i 0.224071 + 0.388102i
\(706\) −13.8970 −0.523020
\(707\) 24.1858 1.49338i 0.909602 0.0561643i
\(708\) 23.6631 0.889313
\(709\) 9.54605 + 16.5343i 0.358510 + 0.620957i 0.987712 0.156285i \(-0.0499517\pi\)
−0.629202 + 0.777241i \(0.716618\pi\)
\(710\) 4.91989 8.52149i 0.184640 0.319806i
\(711\) 1.45016 2.51176i 0.0543854 0.0941983i
\(712\) −8.32132 14.4129i −0.311855 0.540148i
\(713\) 8.71388 0.326338
\(714\) −47.2795 + 2.91932i −1.76939 + 0.109253i
\(715\) 8.63244 0.322835
\(716\) 8.20481 + 14.2112i 0.306628 + 0.531096i
\(717\) 11.3141 19.5966i 0.422533 0.731849i
\(718\) 9.73350 16.8589i 0.363251 0.629169i
\(719\) −10.5225 18.2254i −0.392421 0.679693i 0.600347 0.799740i \(-0.295029\pi\)
−0.992768 + 0.120046i \(0.961696\pi\)
\(720\) 4.82619 0.179862
\(721\) −5.34405 + 10.7341i −0.199023 + 0.399760i
\(722\) 41.3190 1.53773
\(723\) −1.96780 3.40834i −0.0731834 0.126757i
\(724\) 5.61532 9.72601i 0.208692 0.361464i
\(725\) 1.87670 3.25054i 0.0696990 0.120722i
\(726\) 8.53609 + 14.7849i 0.316804 + 0.548721i
\(727\) 11.6826 0.433282 0.216641 0.976251i \(-0.430490\pi\)
0.216641 + 0.976251i \(0.430490\pi\)
\(728\) −4.54756 6.86194i −0.168544 0.254320i
\(729\) −37.0021 −1.37045
\(730\) 2.89741 + 5.01846i 0.107238 + 0.185741i
\(731\) −29.0725 + 50.3550i −1.07528 + 1.86245i
\(732\) −15.5083 + 26.8612i −0.573204 + 0.992819i
\(733\) 12.1238 + 20.9990i 0.447802 + 0.775615i 0.998243 0.0592589i \(-0.0188737\pi\)
−0.550441 + 0.834874i \(0.685540\pi\)
\(734\) 17.1874 0.634398
\(735\) −9.32294 + 22.0346i −0.343882 + 0.812760i
\(736\) −1.00000 −0.0368605
\(737\) 7.59487 + 13.1547i 0.279761 + 0.484560i
\(738\) 7.75648 13.4346i 0.285520 0.494535i
\(739\) 13.5595 23.4857i 0.498793 0.863935i −0.501206 0.865328i \(-0.667110\pi\)
0.999999 + 0.00139329i \(0.000443498\pi\)
\(740\) 2.19521 + 3.80222i 0.0806977 + 0.139773i
\(741\) 62.2589 2.28714
\(742\) −6.19711 9.35099i −0.227503 0.343286i
\(743\) −10.3281 −0.378902 −0.189451 0.981890i \(-0.560671\pi\)
−0.189451 + 0.981890i \(0.560671\pi\)
\(744\) 11.2253 + 19.4428i 0.411539 + 0.712807i
\(745\) −10.6273 + 18.4070i −0.389353 + 0.674380i
\(746\) 4.71828 8.17231i 0.172749 0.299209i
\(747\) −18.8710 32.6855i −0.690453 1.19590i
\(748\) −14.5331 −0.531381
\(749\) 14.5442 29.2136i 0.531433 1.06744i
\(750\) −28.1642 −1.02841
\(751\) 5.15333 + 8.92583i 0.188048 + 0.325708i 0.944599 0.328226i \(-0.106451\pi\)
−0.756552 + 0.653934i \(0.773117\pi\)
\(752\) 1.74065 3.01490i 0.0634750 0.109942i
\(753\) −1.34270 + 2.32562i −0.0489307 + 0.0847505i
\(754\) −1.80221 3.12151i −0.0656325 0.113679i
\(755\) −18.4877 −0.672837
\(756\) 4.34011 0.267984i 0.157848 0.00974650i
\(757\) −39.6243 −1.44017 −0.720084 0.693887i \(-0.755897\pi\)
−0.720084 + 0.693887i \(0.755897\pi\)
\(758\) −3.49566 6.05465i −0.126968 0.219915i
\(759\) 2.69407 4.66626i 0.0977885 0.169375i
\(760\) −5.15168 + 8.92298i −0.186871 + 0.323670i
\(761\) 26.7319 + 46.3010i 0.969031 + 1.67841i 0.698372 + 0.715735i \(0.253908\pi\)
0.270658 + 0.962676i \(0.412759\pi\)
\(762\) 6.21433 0.225121
\(763\) −2.90437 + 0.179333i −0.105145 + 0.00649231i
\(764\) 6.36805 0.230388
\(765\) 16.7691 + 29.0449i 0.606287 + 1.05012i
\(766\) −13.7705 + 23.8512i −0.497549 + 0.861780i
\(767\) −14.2884 + 24.7482i −0.515924 + 0.893607i
\(768\) −1.28821 2.23124i −0.0464842 0.0805130i
\(769\) 8.56383 0.308820 0.154410 0.988007i \(-0.450652\pi\)
0.154410 + 0.988007i \(0.450652\pi\)
\(770\) −3.27148 + 6.57114i −0.117896 + 0.236808i
\(771\) −17.4529 −0.628550
\(772\) 7.02750 + 12.1720i 0.252925 + 0.438079i
\(773\) 15.8946 27.5302i 0.571688 0.990193i −0.424705 0.905332i \(-0.639622\pi\)
0.996393 0.0848607i \(-0.0270445\pi\)
\(774\) 15.2195 26.3609i 0.547054 0.947525i
\(775\) −14.1166 24.4507i −0.507085 0.878296i
\(776\) 6.65800 0.239008