Properties

Label 74.2.c.c.47.2
Level $74$
Weight $2$
Character 74.47
Analytic conductor $0.591$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 74 = 2 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 74.c (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.590892974957\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.4406832.1
Defining polynomial: \( x^{6} - x^{5} + 6x^{4} + 7x^{3} + 24x^{2} + 5x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 47.2
Root \(1.43310 + 2.48220i\) of defining polynomial
Character \(\chi\) \(=\) 74.47
Dual form 74.2.c.c.63.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.258652 - 0.447998i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.10755 + 3.65038i) q^{5} +0.517304 q^{6} +(0.258652 + 0.447998i) q^{7} +1.00000 q^{8} +(1.36620 - 2.36632i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.258652 - 0.447998i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.10755 + 3.65038i) q^{5} +0.517304 q^{6} +(0.258652 + 0.447998i) q^{7} +1.00000 q^{8} +(1.36620 - 2.36632i) q^{9} -4.21509 q^{10} -3.73240 q^{11} +(-0.258652 + 0.447998i) q^{12} +(-1.00000 - 1.73205i) q^{13} -0.517304 q^{14} +(1.09024 - 1.88835i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.01730 - 1.76202i) q^{17} +(1.36620 + 2.36632i) q^{18} +(-3.34889 - 5.80045i) q^{19} +(2.10755 - 3.65038i) q^{20} +(0.133802 - 0.231751i) q^{21} +(1.86620 - 3.23235i) q^{22} +7.21509 q^{23} +(-0.258652 - 0.447998i) q^{24} +(-6.38350 + 11.0566i) q^{25} +2.00000 q^{26} -2.96539 q^{27} +(0.258652 - 0.447998i) q^{28} -0.482696 q^{29} +(1.09024 + 1.88835i) q^{30} -2.69779 q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.965392 + 1.67211i) q^{33} +(1.01730 + 1.76202i) q^{34} +(-1.09024 + 1.88835i) q^{35} -2.73240 q^{36} +(-4.10755 + 4.48643i) q^{37} +6.69779 q^{38} +(-0.517304 + 0.895997i) q^{39} +(2.10755 + 3.65038i) q^{40} +(-0.848894 - 1.47033i) q^{41} +(0.133802 + 0.231751i) q^{42} +8.24970 q^{43} +(1.86620 + 3.23235i) q^{44} +11.5173 q^{45} +(-3.60755 + 6.24845i) q^{46} -1.30221 q^{47} +0.517304 q^{48} +(3.36620 - 5.83043i) q^{49} +(-6.38350 - 11.0566i) q^{50} -1.05251 q^{51} +(-1.00000 + 1.73205i) q^{52} +(-1.13380 + 1.96380i) q^{53} +(1.48270 - 2.56810i) q^{54} +(-7.86620 - 13.6247i) q^{55} +(0.258652 + 0.447998i) q^{56} +(-1.73240 + 3.00060i) q^{57} +(0.241348 - 0.418027i) q^{58} +(-6.24970 + 10.8248i) q^{59} -2.18048 q^{60} +(-1.24135 - 2.15008i) q^{61} +(1.34889 - 2.33635i) q^{62} +1.41348 q^{63} +1.00000 q^{64} +(4.21509 - 7.30075i) q^{65} -1.93078 q^{66} +(0.133802 + 0.231751i) q^{67} -2.03461 q^{68} +(-1.86620 - 3.23235i) q^{69} +(-1.09024 - 1.88835i) q^{70} +(1.74135 + 3.01610i) q^{71} +(1.36620 - 2.36632i) q^{72} +5.73240 q^{73} +(-1.83159 - 5.80045i) q^{74} +6.60442 q^{75} +(-3.34889 + 5.80045i) q^{76} +(-0.965392 - 1.67211i) q^{77} +(-0.517304 - 0.895997i) q^{78} +(-2.38350 - 4.12835i) q^{79} -4.21509 q^{80} +(-3.33159 - 5.77048i) q^{81} +1.69779 q^{82} +(-5.47374 + 9.48080i) q^{83} -0.267603 q^{84} +8.57606 q^{85} +(-4.12485 + 7.14445i) q^{86} +(0.124850 + 0.216247i) q^{87} -3.73240 q^{88} +(-8.06399 + 13.9672i) q^{89} +(-5.75865 + 9.97428i) q^{90} +(0.517304 - 0.895997i) q^{91} +(-3.60755 - 6.24845i) q^{92} +(0.697788 + 1.20861i) q^{93} +(0.651106 - 1.12775i) q^{94} +(14.1159 - 24.4495i) q^{95} +(-0.258652 + 0.447998i) q^{96} +0.302212 q^{97} +(3.36620 + 5.83043i) q^{98} +(-5.09919 + 8.83206i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 3 q^{2} - 3 q^{4} - q^{5} + 6 q^{8} - 7 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 3 q^{2} - 3 q^{4} - q^{5} + 6 q^{8} - 7 q^{9} + 2 q^{10} + 8 q^{11} - 6 q^{13} - 4 q^{15} - 3 q^{16} + 3 q^{17} - 7 q^{18} - 8 q^{19} - q^{20} + 16 q^{21} - 4 q^{22} + 16 q^{23} - 20 q^{25} + 12 q^{26} - 24 q^{27} - 6 q^{29} - 4 q^{30} + 8 q^{31} - 3 q^{32} + 12 q^{33} + 3 q^{34} + 4 q^{35} + 14 q^{36} - 11 q^{37} + 16 q^{38} - q^{40} + 7 q^{41} + 16 q^{42} + 16 q^{43} - 4 q^{44} + 66 q^{45} - 8 q^{46} - 32 q^{47} + 5 q^{49} - 20 q^{50} - 64 q^{51} - 6 q^{52} - 22 q^{53} + 12 q^{54} - 32 q^{55} + 20 q^{57} + 3 q^{58} - 4 q^{59} + 8 q^{60} - 9 q^{61} - 4 q^{62} + 24 q^{63} + 6 q^{64} - 2 q^{65} - 24 q^{66} + 16 q^{67} - 6 q^{68} + 4 q^{69} + 4 q^{70} + 12 q^{71} - 7 q^{72} + 4 q^{73} - 2 q^{74} + 88 q^{75} - 8 q^{76} - 12 q^{77} + 4 q^{79} + 2 q^{80} - 11 q^{81} - 14 q^{82} - 4 q^{83} - 32 q^{84} - 18 q^{85} - 8 q^{86} - 16 q^{87} + 8 q^{88} - 9 q^{89} - 33 q^{90} - 8 q^{92} - 20 q^{93} + 16 q^{94} + 36 q^{95} + 26 q^{97} + 5 q^{98} - 52 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).

\(n\) \(39\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) −0.258652 0.447998i −0.149333 0.258652i 0.781648 0.623720i \(-0.214379\pi\)
−0.930981 + 0.365067i \(0.881046\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 2.10755 + 3.65038i 0.942523 + 1.63250i 0.760636 + 0.649179i \(0.224887\pi\)
0.181888 + 0.983319i \(0.441779\pi\)
\(6\) 0.517304 0.211188
\(7\) 0.258652 + 0.447998i 0.0977613 + 0.169327i 0.910758 0.412941i \(-0.135499\pi\)
−0.812996 + 0.582269i \(0.802165\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.36620 2.36632i 0.455399 0.788775i
\(10\) −4.21509 −1.33293
\(11\) −3.73240 −1.12536 −0.562680 0.826675i \(-0.690230\pi\)
−0.562680 + 0.826675i \(0.690230\pi\)
\(12\) −0.258652 + 0.447998i −0.0746664 + 0.129326i
\(13\) −1.00000 1.73205i −0.277350 0.480384i 0.693375 0.720577i \(-0.256123\pi\)
−0.970725 + 0.240192i \(0.922790\pi\)
\(14\) −0.517304 −0.138255
\(15\) 1.09024 1.88835i 0.281499 0.487571i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 1.01730 1.76202i 0.246732 0.427353i −0.715885 0.698218i \(-0.753976\pi\)
0.962617 + 0.270865i \(0.0873098\pi\)
\(18\) 1.36620 + 2.36632i 0.322016 + 0.557748i
\(19\) −3.34889 5.80045i −0.768289 1.33072i −0.938490 0.345306i \(-0.887775\pi\)
0.170201 0.985409i \(-0.445558\pi\)
\(20\) 2.10755 3.65038i 0.471262 0.816249i
\(21\) 0.133802 0.231751i 0.0291979 0.0505723i
\(22\) 1.86620 3.23235i 0.397875 0.689139i
\(23\) 7.21509 1.50445 0.752225 0.658906i \(-0.228980\pi\)
0.752225 + 0.658906i \(0.228980\pi\)
\(24\) −0.258652 0.447998i −0.0527971 0.0914473i
\(25\) −6.38350 + 11.0566i −1.27670 + 2.21131i
\(26\) 2.00000 0.392232
\(27\) −2.96539 −0.570690
\(28\) 0.258652 0.447998i 0.0488806 0.0846637i
\(29\) −0.482696 −0.0896344 −0.0448172 0.998995i \(-0.514271\pi\)
−0.0448172 + 0.998995i \(0.514271\pi\)
\(30\) 1.09024 + 1.88835i 0.199050 + 0.344765i
\(31\) −2.69779 −0.484537 −0.242269 0.970209i \(-0.577892\pi\)
−0.242269 + 0.970209i \(0.577892\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 0.965392 + 1.67211i 0.168053 + 0.291077i
\(34\) 1.01730 + 1.76202i 0.174466 + 0.302184i
\(35\) −1.09024 + 1.88835i −0.184285 + 0.319190i
\(36\) −2.73240 −0.455399
\(37\) −4.10755 + 4.48643i −0.675276 + 0.737565i
\(38\) 6.69779 1.08652
\(39\) −0.517304 + 0.895997i −0.0828349 + 0.143474i
\(40\) 2.10755 + 3.65038i 0.333232 + 0.577175i
\(41\) −0.848894 1.47033i −0.132575 0.229627i 0.792093 0.610400i \(-0.208991\pi\)
−0.924668 + 0.380773i \(0.875658\pi\)
\(42\) 0.133802 + 0.231751i 0.0206461 + 0.0357600i
\(43\) 8.24970 1.25807 0.629034 0.777378i \(-0.283451\pi\)
0.629034 + 0.777378i \(0.283451\pi\)
\(44\) 1.86620 + 3.23235i 0.281340 + 0.487295i
\(45\) 11.5173 1.71690
\(46\) −3.60755 + 6.24845i −0.531904 + 0.921284i
\(47\) −1.30221 −0.189947 −0.0949735 0.995480i \(-0.530277\pi\)
−0.0949735 + 0.995480i \(0.530277\pi\)
\(48\) 0.517304 0.0746664
\(49\) 3.36620 5.83043i 0.480885 0.832918i
\(50\) −6.38350 11.0566i −0.902764 1.56363i
\(51\) −1.05251 −0.147381
\(52\) −1.00000 + 1.73205i −0.138675 + 0.240192i
\(53\) −1.13380 + 1.96380i −0.155740 + 0.269749i −0.933328 0.359025i \(-0.883109\pi\)
0.777588 + 0.628774i \(0.216443\pi\)
\(54\) 1.48270 2.56810i 0.201769 0.349475i
\(55\) −7.86620 13.6247i −1.06068 1.83715i
\(56\) 0.258652 + 0.447998i 0.0345638 + 0.0598663i
\(57\) −1.73240 + 3.00060i −0.229462 + 0.397439i
\(58\) 0.241348 0.418027i 0.0316905 0.0548896i
\(59\) −6.24970 + 10.8248i −0.813642 + 1.40927i 0.0966574 + 0.995318i \(0.469185\pi\)
−0.910299 + 0.413951i \(0.864148\pi\)
\(60\) −2.18048 −0.281499
\(61\) −1.24135 2.15008i −0.158938 0.275289i 0.775548 0.631289i \(-0.217474\pi\)
−0.934486 + 0.356000i \(0.884140\pi\)
\(62\) 1.34889 2.33635i 0.171310 0.296717i
\(63\) 1.41348 0.178082
\(64\) 1.00000 0.125000
\(65\) 4.21509 7.30075i 0.522818 0.905547i
\(66\) −1.93078 −0.237663
\(67\) 0.133802 + 0.231751i 0.0163465 + 0.0283129i 0.874083 0.485777i \(-0.161463\pi\)
−0.857736 + 0.514090i \(0.828130\pi\)
\(68\) −2.03461 −0.246732
\(69\) −1.86620 3.23235i −0.224664 0.389129i
\(70\) −1.09024 1.88835i −0.130309 0.225702i
\(71\) 1.74135 + 3.01610i 0.206660 + 0.357946i 0.950660 0.310234i \(-0.100407\pi\)
−0.744000 + 0.668179i \(0.767074\pi\)
\(72\) 1.36620 2.36632i 0.161008 0.278874i
\(73\) 5.73240 0.670926 0.335463 0.942053i \(-0.391107\pi\)
0.335463 + 0.942053i \(0.391107\pi\)
\(74\) −1.83159 5.80045i −0.212918 0.674289i
\(75\) 6.60442 0.762613
\(76\) −3.34889 + 5.80045i −0.384145 + 0.665358i
\(77\) −0.965392 1.67211i −0.110017 0.190554i
\(78\) −0.517304 0.895997i −0.0585731 0.101452i
\(79\) −2.38350 4.12835i −0.268165 0.464475i 0.700223 0.713924i \(-0.253084\pi\)
−0.968388 + 0.249449i \(0.919751\pi\)
\(80\) −4.21509 −0.471262
\(81\) −3.33159 5.77048i −0.370177 0.641165i
\(82\) 1.69779 0.187489
\(83\) −5.47374 + 9.48080i −0.600822 + 1.04065i 0.391875 + 0.920018i \(0.371826\pi\)
−0.992697 + 0.120635i \(0.961507\pi\)
\(84\) −0.267603 −0.0291979
\(85\) 8.57606 0.930204
\(86\) −4.12485 + 7.14445i −0.444794 + 0.770406i
\(87\) 0.124850 + 0.216247i 0.0133854 + 0.0231841i
\(88\) −3.73240 −0.397875
\(89\) −8.06399 + 13.9672i −0.854781 + 1.48052i 0.0220673 + 0.999756i \(0.492975\pi\)
−0.876848 + 0.480767i \(0.840358\pi\)
\(90\) −5.75865 + 9.97428i −0.607015 + 1.05138i
\(91\) 0.517304 0.895997i 0.0542282 0.0939260i
\(92\) −3.60755 6.24845i −0.376113 0.651446i
\(93\) 0.697788 + 1.20861i 0.0723573 + 0.125327i
\(94\) 0.651106 1.12775i 0.0671564 0.116318i
\(95\) 14.1159 24.4495i 1.44826 2.50846i
\(96\) −0.258652 + 0.447998i −0.0263986 + 0.0457236i
\(97\) 0.302212 0.0306849 0.0153425 0.999882i \(-0.495116\pi\)
0.0153425 + 0.999882i \(0.495116\pi\)
\(98\) 3.36620 + 5.83043i 0.340037 + 0.588962i
\(99\) −5.09919 + 8.83206i −0.512488 + 0.887656i
\(100\) 12.7670 1.27670
\(101\) −9.24970 −0.920380 −0.460190 0.887821i \(-0.652219\pi\)
−0.460190 + 0.887821i \(0.652219\pi\)
\(102\) 0.526255 0.911501i 0.0521071 0.0902521i
\(103\) 6.44809 0.635349 0.317674 0.948200i \(-0.397098\pi\)
0.317674 + 0.948200i \(0.397098\pi\)
\(104\) −1.00000 1.73205i −0.0980581 0.169842i
\(105\) 1.12797 0.110079
\(106\) −1.13380 1.96380i −0.110125 0.190741i
\(107\) 6.12485 + 10.6086i 0.592112 + 1.02557i 0.993948 + 0.109856i \(0.0350389\pi\)
−0.401836 + 0.915712i \(0.631628\pi\)
\(108\) 1.48270 + 2.56810i 0.142672 + 0.247116i
\(109\) 3.45644 5.98673i 0.331067 0.573425i −0.651654 0.758516i \(-0.725925\pi\)
0.982721 + 0.185091i \(0.0592581\pi\)
\(110\) 15.7324 1.50003
\(111\) 3.07234 + 0.679750i 0.291614 + 0.0645190i
\(112\) −0.517304 −0.0488806
\(113\) 4.86620 8.42850i 0.457773 0.792887i −0.541070 0.840978i \(-0.681980\pi\)
0.998843 + 0.0480910i \(0.0153138\pi\)
\(114\) −1.73240 3.00060i −0.162254 0.281032i
\(115\) 15.2061 + 26.3378i 1.41798 + 2.45601i
\(116\) 0.241348 + 0.418027i 0.0224086 + 0.0388128i
\(117\) −5.46479 −0.505220
\(118\) −6.24970 10.8248i −0.575332 0.996504i
\(119\) 1.05251 0.0964835
\(120\) 1.09024 1.88835i 0.0995250 0.172382i
\(121\) 2.93078 0.266435
\(122\) 2.48270 0.224773
\(123\) −0.439136 + 0.760607i −0.0395956 + 0.0685816i
\(124\) 1.34889 + 2.33635i 0.121134 + 0.209811i
\(125\) −32.7386 −2.92823
\(126\) −0.706740 + 1.22411i −0.0629614 + 0.109052i
\(127\) −7.85725 + 13.6092i −0.697218 + 1.20762i 0.272209 + 0.962238i \(0.412246\pi\)
−0.969427 + 0.245379i \(0.921088\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) −2.13380 3.69585i −0.187871 0.325402i
\(130\) 4.21509 + 7.30075i 0.369688 + 0.640319i
\(131\) 6.68884 11.5854i 0.584406 1.01222i −0.410543 0.911841i \(-0.634661\pi\)
0.994949 0.100380i \(-0.0320059\pi\)
\(132\) 0.965392 1.67211i 0.0840266 0.145538i
\(133\) 1.73240 3.00060i 0.150218 0.260185i
\(134\) −0.267603 −0.0231174
\(135\) −6.24970 10.8248i −0.537889 0.931650i
\(136\) 1.01730 1.76202i 0.0872331 0.151092i
\(137\) −13.3610 −1.14150 −0.570752 0.821122i \(-0.693348\pi\)
−0.570752 + 0.821122i \(0.693348\pi\)
\(138\) 3.73240 0.317723
\(139\) −7.20614 + 12.4814i −0.611217 + 1.05866i 0.379819 + 0.925061i \(0.375986\pi\)
−0.991036 + 0.133598i \(0.957347\pi\)
\(140\) 2.18048 0.184285
\(141\) 0.336820 + 0.583389i 0.0283653 + 0.0491302i
\(142\) −3.48270 −0.292261
\(143\) 3.73240 + 6.46470i 0.312119 + 0.540605i
\(144\) 1.36620 + 2.36632i 0.113850 + 0.197194i
\(145\) −1.01730 1.76202i −0.0844825 0.146328i
\(146\) −2.86620 + 4.96440i −0.237208 + 0.410857i
\(147\) −3.48270 −0.287248
\(148\) 5.93914 + 1.31402i 0.488194 + 0.108012i
\(149\) 20.9129 1.71325 0.856625 0.515940i \(-0.172557\pi\)
0.856625 + 0.515940i \(0.172557\pi\)
\(150\) −3.30221 + 5.71960i −0.269624 + 0.467003i
\(151\) −8.82264 15.2813i −0.717976 1.24357i −0.961800 0.273752i \(-0.911735\pi\)
0.243824 0.969819i \(-0.421598\pi\)
\(152\) −3.34889 5.80045i −0.271631 0.470479i
\(153\) −2.77968 4.81454i −0.224724 0.389233i
\(154\) 1.93078 0.155587
\(155\) −5.68571 9.84795i −0.456688 0.791006i
\(156\) 1.03461 0.0828349
\(157\) 5.00835 8.67472i 0.399710 0.692318i −0.593980 0.804480i \(-0.702444\pi\)
0.993690 + 0.112162i \(0.0357775\pi\)
\(158\) 4.76700 0.379243
\(159\) 1.17304 0.0930282
\(160\) 2.10755 3.65038i 0.166616 0.288588i
\(161\) 1.86620 + 3.23235i 0.147077 + 0.254745i
\(162\) 6.66318 0.523509
\(163\) 3.09024 5.35246i 0.242046 0.419237i −0.719251 0.694751i \(-0.755515\pi\)
0.961297 + 0.275514i \(0.0888480\pi\)
\(164\) −0.848894 + 1.47033i −0.0662875 + 0.114813i
\(165\) −4.06922 + 7.04809i −0.316788 + 0.548693i
\(166\) −5.47374 9.48080i −0.424845 0.735853i
\(167\) 6.00000 + 10.3923i 0.464294 + 0.804181i 0.999169 0.0407502i \(-0.0129748\pi\)
−0.534875 + 0.844931i \(0.679641\pi\)
\(168\) 0.133802 0.231751i 0.0103230 0.0178800i
\(169\) 4.50000 7.79423i 0.346154 0.599556i
\(170\) −4.28803 + 7.42709i −0.328877 + 0.569632i
\(171\) −18.3010 −1.39951
\(172\) −4.12485 7.14445i −0.314517 0.544759i
\(173\) 1.45644 2.52263i 0.110731 0.191792i −0.805334 0.592821i \(-0.798014\pi\)
0.916065 + 0.401029i \(0.131347\pi\)
\(174\) −0.249701 −0.0189298
\(175\) −6.60442 −0.499247
\(176\) 1.86620 3.23235i 0.140670 0.243648i
\(177\) 6.46599 0.486014
\(178\) −8.06399 13.9672i −0.604421 1.04689i
\(179\) −6.96539 −0.520618 −0.260309 0.965525i \(-0.583824\pi\)
−0.260309 + 0.965525i \(0.583824\pi\)
\(180\) −5.75865 9.97428i −0.429225 0.743439i
\(181\) 3.14215 + 5.44237i 0.233554 + 0.404528i 0.958852 0.283908i \(-0.0916309\pi\)
−0.725297 + 0.688436i \(0.758298\pi\)
\(182\) 0.517304 + 0.895997i 0.0383451 + 0.0664157i
\(183\) −0.642154 + 1.11224i −0.0474694 + 0.0822194i
\(184\) 7.21509 0.531904
\(185\) −25.0340 5.53873i −1.84054 0.407216i
\(186\) −1.39558 −0.102329
\(187\) −3.79698 + 6.57657i −0.277663 + 0.480926i
\(188\) 0.651106 + 1.12775i 0.0474868 + 0.0822495i
\(189\) −0.767005 1.32849i −0.0557914 0.0966335i
\(190\) 14.1159 + 24.4495i 1.02407 + 1.77375i
\(191\) 11.5761 0.837614 0.418807 0.908075i \(-0.362448\pi\)
0.418807 + 0.908075i \(0.362448\pi\)
\(192\) −0.258652 0.447998i −0.0186666 0.0323315i
\(193\) 13.4302 0.966726 0.483363 0.875420i \(-0.339415\pi\)
0.483363 + 0.875420i \(0.339415\pi\)
\(194\) −0.151106 + 0.261723i −0.0108488 + 0.0187906i
\(195\) −4.36097 −0.312295
\(196\) −6.73240 −0.480885
\(197\) 2.75865 4.77813i 0.196546 0.340427i −0.750860 0.660461i \(-0.770361\pi\)
0.947406 + 0.320034i \(0.103694\pi\)
\(198\) −5.09919 8.83206i −0.362384 0.627667i
\(199\) 16.3431 1.15853 0.579265 0.815140i \(-0.303340\pi\)
0.579265 + 0.815140i \(0.303340\pi\)
\(200\) −6.38350 + 11.0566i −0.451382 + 0.781816i
\(201\) 0.0692162 0.119886i 0.00488213 0.00845610i
\(202\) 4.62485 8.01048i 0.325403 0.563615i
\(203\) −0.124850 0.216247i −0.00876277 0.0151776i
\(204\) 0.526255 + 0.911501i 0.0368453 + 0.0638179i
\(205\) 3.57817 6.19757i 0.249910 0.432857i
\(206\) −3.22404 + 5.58421i −0.224630 + 0.389070i
\(207\) 9.85725 17.0733i 0.685126 1.18667i
\(208\) 2.00000 0.138675
\(209\) 12.4994 + 21.6496i 0.864602 + 1.49753i
\(210\) −0.563987 + 0.976854i −0.0389188 + 0.0674093i
\(211\) 20.7491 1.42843 0.714214 0.699928i \(-0.246785\pi\)
0.714214 + 0.699928i \(0.246785\pi\)
\(212\) 2.26760 0.155740
\(213\) 0.900806 1.56024i 0.0617222 0.106906i
\(214\) −12.2497 −0.837372
\(215\) 17.3866 + 30.1145i 1.18576 + 2.05379i
\(216\) −2.96539 −0.201769
\(217\) −0.697788 1.20861i −0.0473690 0.0820455i
\(218\) 3.45644 + 5.98673i 0.234100 + 0.405473i
\(219\) −1.48270 2.56810i −0.100191 0.173536i
\(220\) −7.86620 + 13.6247i −0.530339 + 0.918574i
\(221\) −4.06922 −0.273725
\(222\) −2.12485 + 2.32085i −0.142611 + 0.155765i
\(223\) −6.85412 −0.458986 −0.229493 0.973310i \(-0.573707\pi\)
−0.229493 + 0.973310i \(0.573707\pi\)
\(224\) 0.258652 0.447998i 0.0172819 0.0299332i
\(225\) 17.4423 + 30.2109i 1.16282 + 2.01406i
\(226\) 4.86620 + 8.42850i 0.323695 + 0.560656i
\(227\) −10.3835 17.9848i −0.689177 1.19369i −0.972104 0.234549i \(-0.924639\pi\)
0.282927 0.959141i \(-0.408695\pi\)
\(228\) 3.46479 0.229462
\(229\) 0.939136 + 1.62663i 0.0620599 + 0.107491i 0.895386 0.445291i \(-0.146900\pi\)
−0.833326 + 0.552782i \(0.813566\pi\)
\(230\) −30.4123 −2.00533
\(231\) −0.499401 + 0.864988i −0.0328582 + 0.0569120i
\(232\) −0.482696 −0.0316905
\(233\) −13.8604 −0.908023 −0.454012 0.890996i \(-0.650008\pi\)
−0.454012 + 0.890996i \(0.650008\pi\)
\(234\) 2.73240 4.73265i 0.178622 0.309383i
\(235\) −2.74447 4.75356i −0.179030 0.310088i
\(236\) 12.4994 0.813642
\(237\) −1.23300 + 2.13561i −0.0800917 + 0.138723i
\(238\) −0.526255 + 0.911501i −0.0341121 + 0.0590839i
\(239\) −0.439136 + 0.760607i −0.0284054 + 0.0491995i −0.879879 0.475198i \(-0.842376\pi\)
0.851473 + 0.524398i \(0.175710\pi\)
\(240\) 1.09024 + 1.88835i 0.0703748 + 0.121893i
\(241\) −7.90081 13.6846i −0.508936 0.881502i −0.999946 0.0103489i \(-0.996706\pi\)
0.491011 0.871154i \(-0.336628\pi\)
\(242\) −1.46539 + 2.53813i −0.0941990 + 0.163157i
\(243\) −6.17153 + 10.6894i −0.395904 + 0.685726i
\(244\) −1.24135 + 2.15008i −0.0794692 + 0.137645i
\(245\) 28.3777 1.81298
\(246\) −0.439136 0.760607i −0.0279983 0.0484945i
\(247\) −6.69779 + 11.6009i −0.426170 + 0.738148i
\(248\) −2.69779 −0.171310
\(249\) 5.66318 0.358889
\(250\) 16.3693 28.3525i 1.03529 1.79317i
\(251\) 14.6799 0.926586 0.463293 0.886205i \(-0.346668\pi\)
0.463293 + 0.886205i \(0.346668\pi\)
\(252\) −0.706740 1.22411i −0.0445204 0.0771116i
\(253\) −26.9296 −1.69305
\(254\) −7.85725 13.6092i −0.493008 0.853914i
\(255\) −2.21822 3.84206i −0.138910 0.240599i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −3.70302 + 6.41382i −0.230988 + 0.400083i −0.958099 0.286437i \(-0.907529\pi\)
0.727111 + 0.686520i \(0.240862\pi\)
\(258\) 4.26760 0.265689
\(259\) −3.07234 0.679750i −0.190906 0.0422376i
\(260\) −8.43018 −0.522818
\(261\) −0.659458 + 1.14222i −0.0408194 + 0.0707014i
\(262\) 6.68884 + 11.5854i 0.413238 + 0.715749i
\(263\) −4.94749 8.56930i −0.305075 0.528406i 0.672203 0.740367i \(-0.265348\pi\)
−0.977278 + 0.211961i \(0.932015\pi\)
\(264\) 0.965392 + 1.67211i 0.0594158 + 0.102911i
\(265\) −9.55816 −0.587153
\(266\) 1.73240 + 3.00060i 0.106220 + 0.183979i
\(267\) 8.34307 0.510587
\(268\) 0.133802 0.231751i 0.00817324 0.0141565i
\(269\) −5.32636 −0.324754 −0.162377 0.986729i \(-0.551916\pi\)
−0.162377 + 0.986729i \(0.551916\pi\)
\(270\) 12.4994 0.760689
\(271\) −0.203018 + 0.351637i −0.0123325 + 0.0213604i −0.872126 0.489282i \(-0.837259\pi\)
0.859793 + 0.510642i \(0.170592\pi\)
\(272\) 1.01730 + 1.76202i 0.0616831 + 0.106838i
\(273\) −0.535207 −0.0323922
\(274\) 6.68048 11.5709i 0.403583 0.699026i
\(275\) 23.8258 41.2674i 1.43675 2.48852i
\(276\) −1.86620 + 3.23235i −0.112332 + 0.194565i
\(277\) 9.05504 + 15.6838i 0.544064 + 0.942347i 0.998665 + 0.0516518i \(0.0164486\pi\)
−0.454601 + 0.890695i \(0.650218\pi\)
\(278\) −7.20614 12.4814i −0.432196 0.748585i
\(279\) −3.68571 + 6.38384i −0.220658 + 0.382191i
\(280\) −1.09024 + 1.88835i −0.0651544 + 0.112851i
\(281\) 9.53461 16.5144i 0.568787 0.985168i −0.427899 0.903826i \(-0.640746\pi\)
0.996686 0.0813416i \(-0.0259205\pi\)
\(282\) −0.673639 −0.0401146
\(283\) −8.57294 14.8488i −0.509608 0.882667i −0.999938 0.0111304i \(-0.996457\pi\)
0.490330 0.871537i \(-0.336876\pi\)
\(284\) 1.74135 3.01610i 0.103330 0.178973i
\(285\) −14.6044 −0.865091
\(286\) −7.46479 −0.441402
\(287\) 0.439136 0.760607i 0.0259214 0.0448972i
\(288\) −2.73240 −0.161008
\(289\) 6.43018 + 11.1374i 0.378246 + 0.655142i
\(290\) 2.03461 0.119476
\(291\) −0.0781676 0.135390i −0.00458227 0.00793672i
\(292\) −2.86620 4.96440i −0.167732 0.290520i
\(293\) −9.24135 16.0065i −0.539885 0.935109i −0.998910 0.0466851i \(-0.985134\pi\)
0.459024 0.888424i \(-0.348199\pi\)
\(294\) 1.74135 3.01610i 0.101557 0.175903i
\(295\) −52.6861 −3.06751
\(296\) −4.10755 + 4.48643i −0.238746 + 0.260769i
\(297\) 11.0680 0.642232
\(298\) −10.4564 + 18.1111i −0.605725 + 1.04915i
\(299\) −7.21509 12.4969i −0.417260 0.722715i
\(300\) −3.30221 5.71960i −0.190653 0.330221i
\(301\) 2.13380 + 3.69585i 0.122990 + 0.213025i
\(302\) 17.6453 1.01537
\(303\) 2.39245 + 4.14385i 0.137443 + 0.238058i
\(304\) 6.69779 0.384145
\(305\) 5.23240 9.06278i 0.299606 0.518933i
\(306\) 5.55936 0.317807
\(307\) −11.2151 −0.640079 −0.320040 0.947404i \(-0.603696\pi\)
−0.320040 + 0.947404i \(0.603696\pi\)
\(308\) −0.965392 + 1.67211i −0.0550083 + 0.0952772i
\(309\) −1.66781 2.88873i −0.0948785 0.164334i
\(310\) 11.3714 0.645854
\(311\) 8.95644 15.5130i 0.507873 0.879662i −0.492085 0.870547i \(-0.663765\pi\)
0.999958 0.00911511i \(-0.00290147\pi\)
\(312\) −0.517304 + 0.895997i −0.0292866 + 0.0507258i
\(313\) −2.41871 + 4.18933i −0.136714 + 0.236795i −0.926251 0.376908i \(-0.876987\pi\)
0.789537 + 0.613703i \(0.210321\pi\)
\(314\) 5.00835 + 8.67472i 0.282638 + 0.489543i
\(315\) 2.97897 + 5.15973i 0.167846 + 0.290718i
\(316\) −2.38350 + 4.12835i −0.134082 + 0.232238i
\(317\) −12.9092 + 22.3593i −0.725051 + 1.25582i 0.233903 + 0.972260i \(0.424850\pi\)
−0.958953 + 0.283564i \(0.908483\pi\)
\(318\) −0.586520 + 1.01588i −0.0328904 + 0.0569679i
\(319\) 1.80161 0.100871
\(320\) 2.10755 + 3.65038i 0.117815 + 0.204062i
\(321\) 3.16841 5.48785i 0.176843 0.306302i
\(322\) −3.73240 −0.207998
\(323\) −13.6274 −0.758247
\(324\) −3.33159 + 5.77048i −0.185088 + 0.320582i
\(325\) 25.5340 1.41637
\(326\) 3.09024 + 5.35246i 0.171153 + 0.296445i
\(327\) −3.57606 −0.197757
\(328\) −0.848894 1.47033i −0.0468723 0.0811853i
\(329\) −0.336820 0.583389i −0.0185695 0.0321633i
\(330\) −4.06922 7.04809i −0.224003 0.387985i
\(331\) −9.66318 + 16.7371i −0.531136 + 0.919955i 0.468203 + 0.883621i \(0.344902\pi\)
−0.999340 + 0.0363345i \(0.988432\pi\)
\(332\) 10.9475 0.600822
\(333\) 5.00463 + 15.8491i 0.274252 + 0.868528i
\(334\) −12.0000 −0.656611
\(335\) −0.563987 + 0.976854i −0.0308139 + 0.0533712i
\(336\) 0.133802 + 0.231751i 0.00729948 + 0.0126431i
\(337\) −0.0639867 0.110828i −0.00348558 0.00603720i 0.864277 0.503016i \(-0.167776\pi\)
−0.867763 + 0.496978i \(0.834443\pi\)
\(338\) 4.50000 + 7.79423i 0.244768 + 0.423950i
\(339\) −5.03461 −0.273442
\(340\) −4.28803 7.42709i −0.232551 0.402790i
\(341\) 10.0692 0.545279
\(342\) 9.15051 15.8491i 0.494803 0.857023i
\(343\) 7.10382 0.383570
\(344\) 8.24970 0.444794
\(345\) 7.86620 13.6247i 0.423502 0.733527i
\(346\) 1.45644 + 2.52263i 0.0782987 + 0.135617i
\(347\) −9.69034 −0.520205 −0.260102 0.965581i \(-0.583756\pi\)
−0.260102 + 0.965581i \(0.583756\pi\)
\(348\) 0.124850 0.216247i 0.00669268 0.0115921i
\(349\) −4.57234 + 7.91952i −0.244752 + 0.423922i −0.962062 0.272832i \(-0.912040\pi\)
0.717310 + 0.696754i \(0.245373\pi\)
\(350\) 3.30221 5.71960i 0.176511 0.305725i
\(351\) 2.96539 + 5.13621i 0.158281 + 0.274151i
\(352\) 1.86620 + 3.23235i 0.0994687 + 0.172285i
\(353\) −4.66841 + 8.08592i −0.248474 + 0.430370i −0.963103 0.269134i \(-0.913263\pi\)
0.714628 + 0.699504i \(0.246596\pi\)
\(354\) −3.23300 + 5.59971i −0.171832 + 0.297621i
\(355\) −7.33994 + 12.7132i −0.389564 + 0.674744i
\(356\) 16.1280 0.854781
\(357\) −0.272234 0.471523i −0.0144082 0.0249557i
\(358\) 3.48270 6.03221i 0.184066 0.318812i
\(359\) −13.9308 −0.735239 −0.367619 0.929976i \(-0.619827\pi\)
−0.367619 + 0.929976i \(0.619827\pi\)
\(360\) 11.5173 0.607015
\(361\) −12.9302 + 22.3957i −0.680536 + 1.17872i
\(362\) −6.28431 −0.330296
\(363\) −0.758053 1.31299i −0.0397875 0.0689139i
\(364\) −1.03461 −0.0542282
\(365\) 12.0813 + 20.9254i 0.632364 + 1.09529i
\(366\) −0.642154 1.11224i −0.0335659 0.0581379i
\(367\) 2.00000 + 3.46410i 0.104399 + 0.180825i 0.913493 0.406855i \(-0.133375\pi\)
−0.809093 + 0.587680i \(0.800041\pi\)
\(368\) −3.60755 + 6.24845i −0.188056 + 0.325723i
\(369\) −4.63903 −0.241498
\(370\) 17.3137 18.9107i 0.900096 0.983122i
\(371\) −1.17304 −0.0609012
\(372\) 0.697788 1.20861i 0.0361786 0.0626633i
\(373\) −0.00372197 0.00644664i −0.000192716 0.000333794i 0.865929 0.500167i \(-0.166728\pi\)
−0.866122 + 0.499833i \(0.833395\pi\)
\(374\) −3.79698 6.57657i −0.196337 0.340066i
\(375\) 8.46792 + 14.6669i 0.437281 + 0.757393i
\(376\) −1.30221 −0.0671564
\(377\) 0.482696 + 0.836054i 0.0248601 + 0.0430590i
\(378\) 1.53401 0.0789009
\(379\) 9.00312 15.5939i 0.462459 0.801003i −0.536623 0.843822i \(-0.680300\pi\)
0.999083 + 0.0428187i \(0.0136338\pi\)
\(380\) −28.2318 −1.44826
\(381\) 8.12917 0.416470
\(382\) −5.78803 + 10.0252i −0.296141 + 0.512932i
\(383\) 7.90393 + 13.6900i 0.403872 + 0.699527i 0.994189 0.107644i \(-0.0343308\pi\)
−0.590318 + 0.807171i \(0.700997\pi\)
\(384\) 0.517304 0.0263986
\(385\) 4.06922 7.04809i 0.207386 0.359204i
\(386\) −6.71509 + 11.6309i −0.341789 + 0.591996i
\(387\) 11.2707 19.5215i 0.572923 0.992332i
\(388\) −0.151106 0.261723i −0.00767123 0.0132870i
\(389\) −0.659458 1.14222i −0.0334359 0.0579126i 0.848823 0.528677i \(-0.177312\pi\)
−0.882259 + 0.470764i \(0.843978\pi\)
\(390\) 2.18048 3.77671i 0.110413 0.191241i
\(391\) 7.33994 12.7132i 0.371197 0.642932i
\(392\) 3.36620 5.83043i 0.170019 0.294481i
\(393\) −6.92032 −0.349084
\(394\) 2.75865 + 4.77813i 0.138979 + 0.240718i
\(395\) 10.0467 17.4014i 0.505503 0.875558i
\(396\) 10.1984 0.512488
\(397\) 21.8183 1.09503 0.547515 0.836796i \(-0.315574\pi\)
0.547515 + 0.836796i \(0.315574\pi\)
\(398\) −8.17153 + 14.1535i −0.409602 + 0.709451i
\(399\) −1.79235 −0.0897298
\(400\) −6.38350 11.0566i −0.319175 0.552828i
\(401\) 4.19839 0.209657 0.104829 0.994490i \(-0.466571\pi\)
0.104829 + 0.994490i \(0.466571\pi\)
\(402\) 0.0692162 + 0.119886i 0.00345219 + 0.00597937i
\(403\) 2.69779 + 4.67271i 0.134386 + 0.232764i
\(404\) 4.62485 + 8.01048i 0.230095 + 0.398536i
\(405\) 14.0430 24.3231i 0.697800 1.20863i
\(406\) 0.249701 0.0123924
\(407\) 15.3310 16.7451i 0.759929 0.830026i
\(408\) −1.05251 −0.0521071
\(409\) 8.27908 14.3398i 0.409374 0.709057i −0.585446 0.810712i \(-0.699080\pi\)
0.994820 + 0.101655i \(0.0324138\pi\)
\(410\) 3.57817 + 6.19757i 0.176713 + 0.306076i
\(411\) 3.45584 + 5.98569i 0.170464 + 0.295252i
\(412\) −3.22404 5.58421i −0.158837 0.275114i
\(413\) −6.46599 −0.318171
\(414\) 9.85725 + 17.0733i 0.484457 + 0.839105i
\(415\) −46.1447 −2.26515
\(416\) −1.00000 + 1.73205i −0.0490290 + 0.0849208i
\(417\) 7.45553 0.365099
\(418\) −24.9988 −1.22273
\(419\) −11.1595 + 19.3287i −0.545175 + 0.944271i 0.453421 + 0.891297i \(0.350204\pi\)
−0.998596 + 0.0529745i \(0.983130\pi\)
\(420\) −0.563987 0.976854i −0.0275197 0.0476656i
\(421\) 25.1805 1.22722 0.613611 0.789609i \(-0.289716\pi\)
0.613611 + 0.789609i \(0.289716\pi\)
\(422\) −10.3746 + 17.9692i −0.505025 + 0.874729i
\(423\) −1.77908 + 3.08146i −0.0865018 + 0.149825i
\(424\) −1.13380 + 1.96380i −0.0550623 + 0.0953707i
\(425\) 12.9879 + 22.4957i 0.630007 + 1.09120i
\(426\) 0.900806 + 1.56024i 0.0436442 + 0.0755940i
\(427\) 0.642154 1.11224i 0.0310760 0.0538253i
\(428\) 6.12485 10.6086i 0.296056 0.512784i
\(429\) 1.93078 3.34422i 0.0932191 0.161460i
\(430\) −34.7733 −1.67692
\(431\) 11.3489 + 19.6569i 0.546657 + 0.946838i 0.998501 + 0.0547405i \(0.0174332\pi\)
−0.451844 + 0.892097i \(0.649233\pi\)
\(432\) 1.48270 2.56810i 0.0713362 0.123558i
\(433\) −24.6966 −1.18684 −0.593421 0.804892i \(-0.702223\pi\)
−0.593421 + 0.804892i \(0.702223\pi\)
\(434\) 1.39558 0.0669898
\(435\) −0.526255 + 0.911501i −0.0252320 + 0.0437031i
\(436\) −6.91288 −0.331067
\(437\) −24.1626 41.8508i −1.15585 2.00200i
\(438\) 2.96539 0.141692
\(439\) −3.91288 6.77731i −0.186752 0.323463i 0.757414 0.652935i \(-0.226463\pi\)
−0.944165 + 0.329472i \(0.893129\pi\)
\(440\) −7.86620 13.6247i −0.375006 0.649530i
\(441\) −9.19779 15.9310i −0.437990 0.758621i
\(442\) 2.03461 3.52404i 0.0967764 0.167622i
\(443\) 34.3944 1.63413 0.817063 0.576548i \(-0.195601\pi\)
0.817063 + 0.576548i \(0.195601\pi\)
\(444\) −0.947489 3.00060i −0.0449658 0.142402i
\(445\) −67.9809 −3.22260
\(446\) 3.42706 5.93585i 0.162276 0.281070i
\(447\) −5.40916 9.36894i −0.255844 0.443136i
\(448\) 0.258652 + 0.447998i 0.0122202 + 0.0211659i
\(449\) −7.63320 13.2211i −0.360233 0.623942i 0.627766 0.778402i \(-0.283970\pi\)
−0.987999 + 0.154460i \(0.950636\pi\)
\(450\) −34.8845 −1.64447
\(451\) 3.16841 + 5.48785i 0.149195 + 0.258413i
\(452\) −9.73240 −0.457773
\(453\) −4.56399 + 7.90506i −0.214435 + 0.371412i
\(454\) 20.7670 0.974644
\(455\) 4.36097 0.204445
\(456\) −1.73240 + 3.00060i −0.0811269 + 0.140516i
\(457\) 8.68048 + 15.0350i 0.406056 + 0.703310i 0.994444 0.105269i \(-0.0335705\pi\)
−0.588388 + 0.808579i \(0.700237\pi\)
\(458\) −1.87827 −0.0877659
\(459\) −3.01671 + 5.22509i −0.140808 + 0.243886i
\(460\) 15.2061 26.3378i 0.708990 1.22801i
\(461\) −3.96539 + 6.86826i −0.184687 + 0.319887i −0.943471 0.331455i \(-0.892460\pi\)
0.758784 + 0.651342i \(0.225794\pi\)
\(462\) −0.499401 0.864988i −0.0232342 0.0402429i
\(463\) 5.20614 + 9.01730i 0.241950 + 0.419070i 0.961270 0.275610i \(-0.0888797\pi\)
−0.719320 + 0.694679i \(0.755546\pi\)
\(464\) 0.241348 0.418027i 0.0112043 0.0194064i
\(465\) −2.94124 + 5.09438i −0.136397 + 0.236246i
\(466\) 6.93018 12.0034i 0.321035 0.556048i
\(467\) 5.70825 0.264146 0.132073 0.991240i \(-0.457837\pi\)
0.132073 + 0.991240i \(0.457837\pi\)
\(468\) 2.73240 + 4.73265i 0.126305 + 0.218767i
\(469\) −0.0692162 + 0.119886i −0.00319611 + 0.00553582i
\(470\) 5.48894 0.253186
\(471\) −5.18168 −0.238759
\(472\) −6.24970 + 10.8248i −0.287666 + 0.498252i
\(473\) −30.7912 −1.41578
\(474\) −1.23300 2.13561i −0.0566334 0.0980918i
\(475\) 85.5107 3.92350
\(476\) −0.526255 0.911501i −0.0241209 0.0417786i
\(477\) 3.09800 + 5.36589i 0.141847 + 0.245687i
\(478\) −0.439136 0.760607i −0.0200856 0.0347893i
\(479\) 10.3189 17.8729i 0.471483 0.816633i −0.527984 0.849254i \(-0.677052\pi\)
0.999468 + 0.0326209i \(0.0103854\pi\)
\(480\) −2.18048 −0.0995250
\(481\) 11.8783 + 2.62805i 0.541603 + 0.119829i
\(482\) 15.8016 0.719744
\(483\) 0.965392 1.67211i 0.0439269 0.0760835i
\(484\) −1.46539 2.53813i −0.0666087 0.115370i
\(485\) 0.636925 + 1.10319i 0.0289213 + 0.0500931i
\(486\) −6.17153 10.6894i −0.279946 0.484881i
\(487\) 32.2497 1.46137 0.730687 0.682713i \(-0.239200\pi\)
0.730687 + 0.682713i \(0.239200\pi\)
\(488\) −1.24135 2.15008i −0.0561932 0.0973294i
\(489\) −3.19719 −0.144582
\(490\) −14.1888 + 24.5758i −0.640986 + 1.11022i
\(491\) 3.73240 0.168441 0.0842203 0.996447i \(-0.473160\pi\)
0.0842203 + 0.996447i \(0.473160\pi\)
\(492\) 0.878273 0.0395956
\(493\) −0.491049 + 0.850521i −0.0221157 + 0.0383055i
\(494\) −6.69779 11.6009i −0.301348 0.521950i
\(495\) −42.9871 −1.93213
\(496\) 1.34889 2.33635i 0.0605671 0.104905i
\(497\) −0.900806 + 1.56024i −0.0404067 + 0.0699864i
\(498\) −2.83159 + 4.90446i −0.126887 + 0.219774i
\(499\) −14.0467 24.3296i −0.628816 1.08914i −0.987790 0.155793i \(-0.950207\pi\)
0.358974 0.933348i \(-0.383127\pi\)
\(500\) 16.3693 + 28.3525i 0.732058 + 1.26796i
\(501\) 3.10382 5.37598i 0.138669 0.240181i
\(502\) −7.33994 + 12.7132i −0.327598 + 0.567416i
\(503\) −5.43601 + 9.41545i −0.242380 + 0.419814i −0.961392 0.275184i \(-0.911261\pi\)
0.719012 + 0.694998i \(0.244595\pi\)
\(504\) 1.41348 0.0629614
\(505\) −19.4942 33.7649i −0.867479 1.50252i
\(506\) 13.4648 23.3217i 0.598583 1.03678i
\(507\) −4.65574 −0.206769
\(508\) 15.7145 0.697218
\(509\) 0.892454 1.54578i 0.0395573 0.0685153i −0.845569 0.533866i \(-0.820739\pi\)
0.885126 + 0.465351i \(0.154072\pi\)
\(510\) 4.43643 0.196448
\(511\) 1.48270 + 2.56810i 0.0655906 + 0.113606i
\(512\) 1.00000 0.0441942
\(513\) 9.93078 + 17.2006i 0.438455 + 0.759426i
\(514\) −3.70302 6.41382i −0.163333 0.282901i
\(515\) 13.5896 + 23.5380i 0.598831 + 1.03721i
\(516\) −2.13380 + 3.69585i −0.0939354 + 0.162701i
\(517\) 4.86037 0.213759
\(518\) 2.12485 2.32085i 0.0933606 0.101972i
\(519\) −1.50685 −0.0661432
\(520\) 4.21509 7.30075i 0.184844 0.320159i
\(521\) −14.5986 25.2855i −0.639576 1.10778i −0.985526 0.169525i \(-0.945777\pi\)
0.345950 0.938253i \(-0.387557\pi\)
\(522\) −0.659458 1.14222i −0.0288637 0.0499934i
\(523\) −21.0078 36.3865i −0.918605 1.59107i −0.801536 0.597947i \(-0.795983\pi\)
−0.117069 0.993124i \(-0.537350\pi\)
\(524\) −13.3777 −0.584406
\(525\) 1.70825 + 2.95877i 0.0745540 + 0.129131i
\(526\) 9.89498 0.431442
\(527\) −2.74447 + 4.75356i −0.119551 + 0.207068i
\(528\) −1.93078 −0.0840266
\(529\) 29.0576 1.26337
\(530\) 4.77908 8.27761i 0.207590 0.359556i
\(531\) 17.0767 + 29.5776i 0.741064 + 1.28356i
\(532\) −3.46479 −0.150218
\(533\) −1.69779 + 2.94066i −0.0735394 + 0.127374i
\(534\) −4.17153 + 7.22531i −0.180520 + 0.312670i
\(535\) −25.8168 + 44.7160i −1.11616 + 1.93324i
\(536\) 0.133802 + 0.231751i 0.00577935 + 0.0100101i
\(537\) 1.80161 + 3.12048i 0.0777453 + 0.134659i
\(538\) 2.66318 4.61276i 0.114818 0.198870i
\(539\) −12.5640 + 21.7615i −0.541169 + 0.937333i
\(540\) −6.24970 + 10.8248i −0.268944 + 0.465825i
\(541\) −19.5865 −0.842090 −0.421045 0.907040i \(-0.638337\pi\)
−0.421045 + 0.907040i \(0.638337\pi\)
\(542\) −0.203018 0.351637i −0.00872037 0.0151041i
\(543\) 1.62545 2.81536i 0.0697547 0.120819i
\(544\) −2.03461 −0.0872331
\(545\) 29.1384 1.24815
\(546\) 0.267603 0.463503i 0.0114524 0.0198361i
\(547\) 1.16378 0.0497596 0.0248798 0.999690i \(-0.492080\pi\)
0.0248798 + 0.999690i \(0.492080\pi\)
\(548\) 6.68048 + 11.5709i 0.285376 + 0.494286i
\(549\) −6.78371 −0.289522
\(550\) 23.8258 + 41.2674i 1.01593 + 1.75965i
\(551\) 1.61650 + 2.79986i 0.0688651 + 0.119278i
\(552\) −1.86620 3.23235i −0.0794307 0.137578i
\(553\) 1.23300 2.13561i 0.0524323 0.0908154i
\(554\) −18.1101 −0.769423
\(555\) 3.99375 + 12.6478i 0.169525 + 0.536869i
\(556\) 14.4123 0.611217
\(557\) 14.1075 24.4350i 0.597756 1.03534i −0.395396 0.918511i \(-0.629393\pi\)
0.993152 0.116833i \(-0.0372741\pi\)
\(558\) −3.68571 6.38384i −0.156029 0.270250i
\(559\) −8.24970 14.2889i −0.348925 0.604356i
\(560\) −1.09024 1.88835i −0.0460711 0.0797976i
\(561\) 3.92839 0.165857
\(562\) 9.53461 + 16.5144i 0.402193 + 0.696619i
\(563\) −6.08712 −0.256541 −0.128271 0.991739i \(-0.540943\pi\)
−0.128271 + 0.991739i \(0.540943\pi\)
\(564\) 0.336820 0.583389i 0.0141827 0.0245651i
\(565\) 41.0230 1.72585
\(566\) 17.1459 0.720695
\(567\) 1.72345 2.98509i 0.0723779 0.125362i
\(568\) 1.74135 + 3.01610i 0.0730653 + 0.126553i
\(569\) 24.7658 1.03824 0.519118 0.854702i \(-0.326260\pi\)
0.519118 + 0.854702i \(0.326260\pi\)
\(570\) 7.30221 12.6478i 0.305856 0.529758i
\(571\) 12.7581 22.0976i 0.533908 0.924756i −0.465307 0.885149i \(-0.654056\pi\)
0.999215 0.0396065i \(-0.0126104\pi\)
\(572\) 3.73240 6.46470i 0.156059 0.270303i
\(573\) −2.99417 5.18606i −0.125083 0.216651i
\(574\) 0.439136 + 0.760607i 0.0183292 + 0.0317471i
\(575\) −46.0576 + 79.7740i −1.92073 + 3.32681i
\(576\) 1.36620 2.36632i 0.0569249 0.0985969i
\(577\) −19.7912 + 34.2793i −0.823917 + 1.42707i 0.0788280 + 0.996888i \(0.474882\pi\)
−0.902745 + 0.430177i \(0.858451\pi\)
\(578\) −12.8604 −0.534921
\(579\) −3.47374 6.01670i −0.144364 0.250046i
\(580\) −1.01730 + 1.76202i −0.0422413 + 0.0731640i
\(581\) −5.66318 −0.234948
\(582\) 0.156335 0.00648031
\(583\) 4.23180 7.32969i 0.175263 0.303565i
\(584\) 5.73240 0.237208
\(585\) −11.5173 19.9486i −0.476182 0.824771i
\(586\) 18.4827 0.763513
\(587\) −8.36992 14.4971i −0.345464 0.598360i 0.639974 0.768396i \(-0.278945\pi\)
−0.985438 + 0.170036i \(0.945612\pi\)
\(588\) 1.74135 + 3.01610i 0.0718120 + 0.124382i
\(589\) 9.03461 + 15.6484i 0.372265 + 0.644781i
\(590\) 26.3431 45.6275i 1.08453 1.87846i
\(591\) −2.85412 −0.117403
\(592\) −1.83159 5.80045i −0.0752779 0.238397i
\(593\) −20.1972 −0.829399 −0.414700 0.909958i \(-0.636113\pi\)
−0.414700 + 0.909958i \(0.636113\pi\)
\(594\) −5.53401 + 9.58519i −0.227063 + 0.393285i
\(595\) 2.21822 + 3.84206i 0.0909380 + 0.157509i
\(596\) −10.4564 18.1111i −0.428312 0.741859i
\(597\) −4.22717 7.32167i −0.173006 0.299656i
\(598\) 14.4302 0.590094
\(599\) 5.09919 + 8.83206i 0.208347 + 0.360868i 0.951194 0.308593i \(-0.0998582\pi\)
−0.742847 + 0.669462i \(0.766525\pi\)
\(600\) 6.60442 0.269624
\(601\) −20.2670 + 35.1035i −0.826708 + 1.43190i 0.0738983 + 0.997266i \(0.476456\pi\)
−0.900607 + 0.434635i \(0.856877\pi\)
\(602\) −4.26760 −0.173935
\(603\) 0.731199 0.0297767
\(604\) −8.82264 + 15.2813i −0.358988 + 0.621786i
\(605\) 6.17676 + 10.6985i 0.251121 + 0.434955i
\(606\) −4.78491 −0.194374
\(607\) −1.33099 + 2.30534i −0.0540233 + 0.0935710i −0.891772 0.452484i \(-0.850538\pi\)
0.837749 + 0.546055i \(0.183871\pi\)
\(608\) −3.34889 + 5.80045i −0.135816 + 0.235240i
\(609\) −0.0645856 + 0.111865i −0.00261714 + 0.00453302i
\(610\) 5.23240 + 9.06278i 0.211854 + 0.366941i
\(611\) 1.30221 + 2.25550i 0.0526818 + 0.0912476i
\(612\) −2.77968 + 4.81454i −0.112362 + 0.194616i
\(613\) 5.90916 10.2350i 0.238669 0.413386i −0.721664 0.692244i \(-0.756622\pi\)
0.960333 + 0.278857i \(0.0899557\pi\)
\(614\) 5.60755 9.71255i 0.226302 0.391967i
\(615\) −3.70200 −0.149279
\(616\) −0.965392 1.67211i −0.0388967 0.0673711i
\(617\) 0.796982 1.38041i 0.0320853 0.0555734i −0.849537 0.527529i \(-0.823119\pi\)
0.881622 + 0.471956i \(0.156452\pi\)
\(618\) 3.33562 0.134178
\(619\) −22.2831 −0.895634 −0.447817 0.894125i \(-0.647798\pi\)
−0.447817 + 0.894125i \(0.647798\pi\)
\(620\) −5.68571 + 9.84795i −0.228344 + 0.395503i
\(621\) −21.3956 −0.858575
\(622\) 8.95644 + 15.5130i 0.359121 + 0.622015i
\(623\) −8.34307 −0.334258
\(624\) −0.517304 0.895997i −0.0207087 0.0358686i
\(625\) −37.0807 64.2256i −1.48323 2.56903i
\(626\) −2.41871 4.18933i −0.0966711 0.167439i
\(627\) 6.46599 11.1994i 0.258227 0.447262i
\(628\) −10.0167 −0.399710
\(629\) 3.72657 + 11.8017i 0.148588 + 0.470563i
\(630\) −5.95795 −0.237370
\(631\) 18.4858 32.0184i 0.735909 1.27463i −0.218415 0.975856i \(-0.570089\pi\)
0.954323 0.298775i \(-0.0965782\pi\)
\(632\) −2.38350 4.12835i −0.0948106 0.164217i
\(633\) −5.36680 9.29557i −0.213311 0.369466i
\(634\) −12.9092 22.3593i −0.512688 0.888002i
\(635\) −66.2380 −2.62858
\(636\) −0.586520 1.01588i −0.0232570 0.0402824i
\(637\) −13.4648 −0.533495
\(638\) −0.900806 + 1.56024i −0.0356633 + 0.0617706i
\(639\) 9.51611 0.376451
\(640\) −4.21509 −0.166616
\(641\) 1.08189 1.87389i 0.0427321 0.0740141i −0.843868 0.536550i \(-0.819727\pi\)
0.886600 + 0.462536i \(0.153060\pi\)
\(642\) 3.16841 + 5.48785i 0.125047 + 0.216588i
\(643\) 38.1626 1.50499 0.752493 0.658601i \(-0.228851\pi\)
0.752493 + 0.658601i \(0.228851\pi\)
\(644\) 1.86620 3.23235i 0.0735385 0.127372i
\(645\) 8.99417 15.5784i 0.354145 0.613397i
\(646\) 6.81369 11.8017i 0.268081 0.464330i
\(647\) 22.1715 + 38.4022i 0.871653 + 1.50975i 0.860286 + 0.509812i \(0.170285\pi\)
0.0113669 + 0.999935i \(0.496382\pi\)
\(648\) −3.33159 5.77048i −0.130877 0.226686i
\(649\) 23.3264 40.4024i 0.915640 1.58593i
\(650\) −12.7670 + 22.1131i −0.500763 + 0.867347i
\(651\) −0.360969 + 0.625216i −0.0141475 + 0.0245042i
\(652\) −6.18048 −0.242046
\(653\) 0.892454 + 1.54578i 0.0349244 + 0.0604909i 0.882959 0.469450i \(-0.155548\pi\)
−0.848035 + 0.529940i \(0.822214\pi\)
\(654\) 1.78803 3.09696i 0.0699175 0.121101i
\(655\) 56.3881 2.20327
\(656\) 1.69779 0.0662875
\(657\) 7.83159 13.5647i 0.305539 0.529210i
\(658\) 0.673639 0.0262612
\(659\) −17.8258 30.8751i −0.694393 1.20272i −0.970385 0.241564i \(-0.922340\pi\)
0.275992 0.961160i \(-0.410994\pi\)
\(660\) 8.13843 0.316788
\(661\) 5.16006 + 8.93748i 0.200703 + 0.347628i 0.948755 0.316012i \(-0.102344\pi\)
−0.748052 + 0.663640i \(0.769011\pi\)
\(662\) −9.66318 16.7371i −0.375570 0.650507i
\(663\) 1.05251 + 1.82300i 0.0408761 + 0.0707996i
\(664\) −5.47374 + 9.48080i −0.212422 + 0.367927i
\(665\) 14.6044 0.566335
\(666\) −16.2281 3.59043i −0.628825 0.139126i
\(667\) −3.48270 −0.134851
\(668\) 6.00000 10.3923i 0.232147 0.402090i
\(669\) 1.77283 + 3.07064i 0.0685417 + 0.118718i
\(670\) −0.563987 0.976854i −0.0217887 0.0377391i
\(671\) 4.63320 + 8.02494i 0.178863 + 0.309799i
\(672\) −0.267603 −0.0103230
\(673\) 15.9250 + 27.5828i 0.613862 + 1.06324i 0.990583 + 0.136913i \(0.0437182\pi\)
−0.376721 + 0.926327i \(0.622948\pi\)
\(674\) 0.127973 0.00492935
\(675\) 18.9296 32.7870i 0.728600 1.26197i
\(676\) −9.00000 −0.346154
\(677\) −18.0167 −0.692438 −0.346219 0.938154i \(-0.612535\pi\)
−0.346219 + 0.938154i \(0.612535\pi\)
\(678\) 2.51730 4.36010i 0.0966765 0.167449i
\(679\) 0.0781676 + 0.135390i 0.00299980 + 0.00519580i
\(680\) 8.57606 0.328877
\(681\) −5.37143 + 9.30359i −0.205834 + 0.356514i
\(682\) −5.03461 + 8.72020i −0.192785 + 0.333914i
\(683\) 23.7009 41.0512i 0.906890 1.57078i 0.0885305 0.996073i \(-0.471783\pi\)
0.818360 0.574706i \(-0.194884\pi\)
\(684\) 9.15051 + 15.8491i 0.349878 + 0.606007i
\(685\) −28.1589 48.7726i −1.07589 1.86350i
\(686\) −3.55191 + 6.15209i −0.135613 + 0.234888i
\(687\) 0.485819 0.841463i 0.0185352 0.0321038i
\(688\) −4.12485 + 7.14445i −0.157258 + 0.272380i
\(689\) 4.53521 0.172778
\(690\) 7.86620 + 13.6247i 0.299461 + 0.518682i
\(691\) 1.68571 2.91974i 0.0641276 0.111072i −0.832179 0.554507i \(-0.812907\pi\)
0.896307 + 0.443435i \(0.146240\pi\)
\(692\) −2.91288 −0.110731
\(693\) −5.27567 −0.200406
\(694\) 4.84517 8.39208i 0.183920 0.318559i
\(695\) −60.7491 −2.30434
\(696\) 0.124850 + 0.216247i 0.00473244 + 0.00819682i
\(697\) −3.45433 −0.130842
\(698\) −4.57234 7.91952i −0.173066 0.299758i
\(699\) 3.58501 + 6.20942i 0.135598 + 0.234862i
\(700\) 3.30221 + 5.71960i 0.124812 + 0.216180i
\(701\) −23.0934 + 39.9989i −0.872224 + 1.51074i −0.0125340 + 0.999921i \(0.503990\pi\)
−0.859690 + 0.510815i \(0.829344\pi\)
\(702\) −5.93078 −0.223843
\(703\) 39.7791 + 8.80105i 1.50030 + 0.331938i
\(704\) −3.73240 −0.140670
\(705\) −1.41973 + 2.45904i −0.0534700 + 0.0926127i
\(706\) −4.66841 8.08592i −0.175698 0.304318i
\(707\) −2.39245 4.14385i −0.0899775 0.155846i
\(708\) −3.23300 5.59971i −0.121503 0.210450i
\(709\) 15.2571 0.572994 0.286497 0.958081i \(-0.407509\pi\)
0.286497 + 0.958081i \(0.407509\pi\)
\(710\) −7.33994 12.7132i −0.275463 0.477116i
\(711\) −13.0253 −0.488489
\(712\) −8.06399 + 13.9672i −0.302211 + 0.523444i
\(713\) −19.4648 −0.728962
\(714\) 0.544468 0.0203762
\(715\) −15.7324 + 27.2493i −0.588358 + 1.01907i
\(716\) 3.48270 + 6.03221i 0.130154 + 0.225434i
\(717\) 0.454334 0.0169674
\(718\) 6.96539 12.0644i 0.259946 0.450240i
\(719\) −4.48582 + 7.76967i −0.167293 + 0.289760i −0.937467 0.348074i \(-0.886836\pi\)
0.770174 + 0.637833i \(0.220169\pi\)
\(720\) −5.75865 + 9.97428i −0.214612 + 0.371719i
\(721\) 1.66781 + 2.88873i 0.0621125 + 0.107582i
\(722\) −12.9302 22.3957i −0.481212 0.833483i
\(723\) −4.08712 + 7.07910i −0.152002 + 0.263274i
\(724\) 3.14215 5.44237i 0.116777 0.202264i
\(725\) 3.08129 5.33695i 0.114436 0.198209i
\(726\) 1.51611 0.0562680
\(727\) 16.8425 + 29.1720i 0.624653 + 1.08193i 0.988608 + 0.150514i \(0.0480927\pi\)
−0.363955 + 0.931416i \(0.618574\pi\)
\(728\) 0.517304 0.895997i 0.0191726 0.0332079i
\(729\) −13.6044 −0.503868
\(730\) −24.1626 −0.894297
\(731\) 8.39245 14.5362i 0.310406 0.537639i
\(732\) 1.28431 0.0474694
\(733\) 17.1626 + 29.7265i 0.633914 + 1.09797i 0.986744 + 0.162284i \(0.0518862\pi\)
−0.352830 + 0.935688i \(0.614780\pi\)
\(734\) −4.00000 −0.147643
\(735\) −7.33994 12.7132i −0.270738 0.468932i
\(736\) −3.60755 6.24845i −0.132976 0.230321i
\(737\) −0.499401 0.864988i −0.0183957 0.0318622i
\(738\) 2.31952 4.01752i 0.0853825 0.147887i
\(739\) 6.27385 0.230787 0.115394 0.993320i \(-0.463187\pi\)
0.115394 + 0.993320i \(0.463187\pi\)
\(740\) 7.72032 + 24.4495i 0.283805 + 0.898780i
\(741\) 6.92959 0.254565
\(742\) 0.586520 1.01588i 0.0215318 0.0372942i
\(743\) 17.5115 + 30.3308i 0.642434 + 1.11273i 0.984888 + 0.173193i \(0.0554085\pi\)
−0.342454 + 0.939535i \(0.611258\pi\)
\(744\) 0.697788 + 1.20861i 0.0255822 + 0.0443096i
\(745\) 44.0749 + 76.3399i 1.61478 + 2.79688i
\(746\) 0.00744394 0.000272542
\(747\) 14.9564 + 25.9053i 0.547228 + 0.947826i
\(748\) 7.59396 0.277663
\(749\) −3.16841 + 5.48785i −0.115771 + 0.200522i
\(750\) −16.9358 −0.618409
\(751\) −11.6694 −0.425823 −0.212912 0.977071i \(-0.568295\pi\)
−0.212912 + 0.977071i \(0.568295\pi\)
\(752\) 0.651106 1.12775i 0.0237434 0.0411247i
\(753\) −3.79698 6.57657i −0.138370 0.239663i
\(754\) −0.965392 −0.0351575
\(755\) 37.1882 64.4119i 1.35342 2.34419i
\(756\) −0.767005 + 1.32849i −0.0278957 + 0.0483167i
\(757\) −14.7061 + 25.4718i −0.534504 + 0.925788i 0.464683 + 0.885477i \(0.346168\pi\)
−0.999187 + 0.0403108i \(0.987165\pi\)
\(758\) 9.00312 + 15.5939i 0.327008 + 0.566395i
\(759\) 6.96539 + 12.0644i 0.252828 + 0.437910i
\(760\) 14.1159 24.4495i 0.512037 0.886875i
\(761\) −14.0415 + 24.3205i −0.509002 + 0.881618i 0.490943 + 0.871191i \(0.336652\pi\)
−0.999946 + 0.0104263i \(0.996681\pi\)
\(762\) −4.06459 + 7.04007i −0.147244 + 0.255035i
\(763\) 3.57606 0.129462
\(764\) −5.78803 10.0252i −0.209404 0.362698i
\(765\) 11.7166 20.2937i 0.423615 0.733722i
\(766\) −15.8079 −0.571161
\(767\) 24.9988 0.902654
\(768\) −0.258652 + 0.447998i −0.00933330 + 0.0161658i
\(769\) 31.9883 1.15353 0.576765 0.816910i \(-0.304315\pi\)
0.576765 + 0.816910i \(0.304315\pi\)
\(770\) 4.06922 + 7.04809i 0.146644 + 0.253996i
\(771\) 3.83117 0.137976
\(772\) −6.71509 11.6309i −0.241681 0.418605i
\(773\) −14.8174 25.6645i −0.532945 0.923088i −0.999260 0.0384692i \(-0.987752\pi\)
0.466315 0.884619i \(-0.345581\pi\)
\(774\) 11.2707 + 19.5215i 0.405118 + 0.701685i
\(775\) 17.2213 29.8282i 0.618609 1.07146i
\(776\) 0.302212