Properties

Label 74.2.c.c.63.2
Level $74$
Weight $2$
Character 74.63
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 63.2
Root \(1.43310 - 2.48220i\) of defining polynomial
Character \(\chi\) \(=\) 74.63
Dual form 74.2.c.c.47.2

$q$-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 \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).

\(n\) \(39\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) −0.258652 + 0.447998i −0.149333 + 0.258652i −0.930981 0.365067i \(-0.881046\pi\)
0.781648 + 0.623720i \(0.214379\pi\)
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 2.10755 3.65038i 0.942523 1.63250i 0.181888 0.983319i \(-0.441779\pi\)
0.760636 0.649179i \(-0.224887\pi\)
\(6\) 0.517304 0.211188
\(7\) 0.258652 0.447998i 0.0977613 0.169327i −0.812996 0.582269i \(-0.802165\pi\)
0.910758 + 0.412941i \(0.135499\pi\)
\(8\) 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 −0.970725 0.240192i \(-0.922790\pi\)
0.693375 + 0.720577i \(0.256123\pi\)
\(14\) −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 0.962617 0.270865i \(-0.0873098\pi\)
−0.715885 + 0.698218i \(0.753976\pi\)
\(18\) 1.36620 2.36632i 0.322016 0.557748i
\(19\) −3.34889 + 5.80045i −0.768289 + 1.33072i 0.170201 + 0.985409i \(0.445558\pi\)
−0.938490 + 0.345306i \(0.887775\pi\)
\(20\) 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 −0.924668 0.380773i \(-0.875658\pi\)
0.792093 + 0.610400i \(0.208991\pi\)
\(42\) 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 0.777588 0.628774i \(-0.216443\pi\)
−0.933328 + 0.359025i \(0.883109\pi\)
\(54\) 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 −0.910299 0.413951i \(-0.864148\pi\)
0.0966574 0.995318i \(-0.469185\pi\)
\(60\) −2.18048 −0.281499
\(61\) −1.24135 + 2.15008i −0.158938 + 0.275289i −0.934486 0.356000i \(-0.884140\pi\)
0.775548 + 0.631289i \(0.217474\pi\)
\(62\) 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 −0.857736 0.514090i \(-0.828130\pi\)
0.874083 + 0.485777i \(0.161463\pi\)
\(68\) −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 −0.744000 0.668179i \(-0.767074\pi\)
0.950660 + 0.310234i \(0.100407\pi\)
\(72\) 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 −0.968388 0.249449i \(-0.919751\pi\)
0.700223 + 0.713924i \(0.253084\pi\)
\(80\) −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 −0.992697 0.120635i \(-0.961507\pi\)
0.391875 0.920018i \(-0.371826\pi\)
\(84\) −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 −0.876848 0.480767i \(-0.840358\pi\)
0.0220673 0.999756i \(-0.492975\pi\)
\(90\) −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 −0.401836 0.915712i \(-0.631628\pi\)
0.993948 0.109856i \(-0.0350389\pi\)
\(108\) 1.48270 2.56810i 0.142672 0.247116i
\(109\) 3.45644 + 5.98673i 0.331067 + 0.573425i 0.982721 0.185091i \(-0.0592581\pi\)
−0.651654 + 0.758516i \(0.725925\pi\)
\(110\) 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 0.998843 0.0480910i \(-0.0153138\pi\)
−0.541070 + 0.840978i \(0.681980\pi\)
\(114\) −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 −0.969427 0.245379i \(-0.921088\pi\)
0.272209 0.962238i \(-0.412246\pi\)
\(128\) −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 0.994949 + 0.100380i \(0.0320059\pi\)
−0.410543 + 0.911841i \(0.634661\pi\)
\(132\) 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 −0.991036 0.133598i \(-0.957347\pi\)
0.379819 0.925061i \(-0.375986\pi\)
\(140\) 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 0.243824 + 0.969819i \(0.421598\pi\)
−0.961800 + 0.273752i \(0.911735\pi\)
\(152\) −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 0.993690 0.112162i \(-0.0357775\pi\)
−0.593980 + 0.804480i \(0.702444\pi\)
\(158\) 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 0.961297 0.275514i \(-0.0888480\pi\)
−0.719251 + 0.694751i \(0.755515\pi\)
\(164\) −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 −0.534875 0.844931i \(-0.679641\pi\)
0.999169 + 0.0407502i \(0.0129748\pi\)
\(168\) 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 0.916065 0.401029i \(-0.131347\pi\)
−0.805334 + 0.592821i \(0.798014\pi\)
\(174\) −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 −0.725297 0.688436i \(-0.758298\pi\)
0.958852 + 0.283908i \(0.0916309\pi\)
\(182\) 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 0.947406 0.320034i \(-0.103694\pi\)
−0.750860 + 0.660461i \(0.770361\pi\)
\(198\) −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 0.282927 + 0.959141i \(0.408695\pi\)
−0.972104 + 0.234549i \(0.924639\pi\)
\(228\) 3.46479 0.229462
\(229\) 0.939136 1.62663i 0.0620599 0.107491i −0.833326 0.552782i \(-0.813566\pi\)
0.895386 + 0.445291i \(0.146900\pi\)
\(230\) −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 0.851473 0.524398i \(-0.175710\pi\)
−0.879879 + 0.475198i \(0.842376\pi\)
\(240\) 1.09024 1.88835i 0.0703748 0.121893i
\(241\) −7.90081 + 13.6846i −0.508936 + 0.881502i 0.491011 + 0.871154i \(0.336628\pi\)
−0.999946 + 0.0103489i \(0.996706\pi\)
\(242\) −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 0.727111 0.686520i \(-0.240862\pi\)
−0.958099 + 0.286437i \(0.907529\pi\)
\(258\) 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 −0.977278 0.211961i \(-0.932015\pi\)
0.672203 + 0.740367i \(0.265348\pi\)
\(264\) 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 0.859793 0.510642i \(-0.170592\pi\)
−0.872126 + 0.489282i \(0.837259\pi\)
\(272\) 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 −0.454601 0.890695i \(-0.650218\pi\)
0.998665 0.0516518i \(-0.0164486\pi\)
\(278\) −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 0.996686 + 0.0813416i \(0.0259205\pi\)
−0.427899 + 0.903826i \(0.640746\pi\)
\(282\) −0.673639 −0.0401146
\(283\) −8.57294 + 14.8488i −0.509608 + 0.882667i 0.490330 + 0.871537i \(0.336876\pi\)
−0.999938 + 0.0111304i \(0.996457\pi\)
\(284\) 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 0.459024 + 0.888424i \(0.348199\pi\)
−0.998910 + 0.0466851i \(0.985134\pi\)
\(294\) 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 0.999958 + 0.00911511i \(0.00290147\pi\)
−0.492085 + 0.870547i \(0.663765\pi\)
\(312\) −0.517304 0.895997i −0.0292866 0.0507258i
\(313\) −2.41871 4.18933i −0.136714 0.236795i 0.789537 0.613703i \(-0.210321\pi\)
−0.926251 + 0.376908i \(0.876987\pi\)
\(314\) 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 −0.958953 0.283564i \(-0.908483\pi\)
0.233903 0.972260i \(-0.424850\pi\)
\(318\) −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 −0.999340 0.0363345i \(-0.988432\pi\)
0.468203 0.883621i \(-0.344902\pi\)
\(332\) 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 −0.867763 0.496978i \(-0.834443\pi\)
0.864277 + 0.503016i \(0.167776\pi\)
\(338\) 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 0.717310 0.696754i \(-0.245373\pi\)
−0.962062 + 0.272832i \(0.912040\pi\)
\(350\) 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 0.714628 0.699504i \(-0.246596\pi\)
−0.963103 + 0.269134i \(0.913263\pi\)
\(354\) −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 −0.809093 0.587680i \(-0.800041\pi\)
0.913493 + 0.406855i \(0.133375\pi\)
\(368\) −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 −0.866122 0.499833i \(-0.833395\pi\)
0.865929 + 0.500167i \(0.166728\pi\)
\(374\) −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 0.999083 0.0428187i \(-0.0136338\pi\)
−0.536623 + 0.843822i \(0.680300\pi\)
\(380\) −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 −0.590318 0.807171i \(-0.700997\pi\)
0.994189 + 0.107644i \(0.0343308\pi\)
\(384\) 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 −0.882259 0.470764i \(-0.843978\pi\)
0.848823 + 0.528677i \(0.177312\pi\)
\(390\) 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 0.994820 0.101655i \(-0.0324138\pi\)
−0.585446 + 0.810712i \(0.699080\pi\)
\(410\) 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 −0.998596 0.0529745i \(-0.983130\pi\)
0.453421 0.891297i \(-0.350204\pi\)
\(420\) −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 −0.451844 0.892097i \(-0.649233\pi\)
0.998501 0.0547405i \(-0.0174332\pi\)
\(432\) 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 −0.944165 0.329472i \(-0.893129\pi\)
0.757414 + 0.652935i \(0.226463\pi\)
\(440\) −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 −0.987999 0.154460i \(-0.950636\pi\)
0.627766 + 0.778402i \(0.283970\pi\)
\(450\) −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 −0.588388 0.808579i \(-0.700237\pi\)
0.994444 + 0.105269i \(0.0335705\pi\)
\(458\) −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 0.758784 0.651342i \(-0.225794\pi\)
−0.943471 + 0.331455i \(0.892460\pi\)
\(462\) −0.499401 + 0.864988i −0.0232342 + 0.0402429i
\(463\) 5.20614 9.01730i 0.241950 0.419070i −0.719320 0.694679i \(-0.755546\pi\)
0.961270 + 0.275610i \(0.0888797\pi\)
\(464\) 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 0.999468 0.0326209i \(-0.0103854\pi\)
−0.527984 + 0.849254i \(0.677052\pi\)
\(480\) −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 0.358974 + 0.933348i \(0.383127\pi\)
−0.987790 + 0.155793i \(0.950207\pi\)
\(500\) 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 0.719012 0.694998i \(-0.244595\pi\)
−0.961392 + 0.275184i \(0.911261\pi\)
\(504\) 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 0.885126 0.465351i \(-0.154072\pi\)
−0.845569 + 0.533866i \(0.820739\pi\)
\(510\) 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 0.345950 + 0.938253i \(0.387557\pi\)
−0.985526 + 0.169525i \(0.945777\pi\)
\(522\) −0.659458 + 1.14222i −0.0288637 + 0.0499934i
\(523\) −21.0078 + 36.3865i −0.918605 + 1.59107i −0.117069 + 0.993124i \(0.537350\pi\)
−0.801536 + 0.597947i \(0.795983\pi\)
\(524\) −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 0.993152 + 0.116833i \(0.0372741\pi\)
−0.395396 + 0.918511i \(0.629393\pi\)
\(558\) −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 0.999215 + 0.0396065i \(0.0126104\pi\)
−0.465307 + 0.885149i \(0.654056\pi\)
\(572\) 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 −0.902745 0.430177i \(-0.858451\pi\)
0.0788280 0.996888i \(-0.474882\pi\)
\(578\) −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 −0.985438 0.170036i \(-0.945612\pi\)
0.639974 + 0.768396i \(0.278945\pi\)
\(588\) 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 −0.742847 0.669462i \(-0.766525\pi\)
0.951194 + 0.308593i \(0.0998582\pi\)
\(600\) 6.60442 0.269624
\(601\) −20.2670 35.1035i −0.826708 1.43190i −0.900607 0.434635i \(-0.856877\pi\)
0.0738983 0.997266i \(-0.476456\pi\)
\(602\) −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 0.837749 0.546055i \(-0.183871\pi\)
−0.891772 + 0.452484i \(0.850538\pi\)
\(608\) −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 0.960333 0.278857i \(-0.0899557\pi\)
−0.721664 + 0.692244i \(0.756622\pi\)
\(614\) 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 0.881622 0.471956i \(-0.156452\pi\)
−0.849537 + 0.527529i \(0.823119\pi\)
\(618\) 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 0.954323 + 0.298775i \(0.0965782\pi\)
−0.218415 + 0.975856i \(0.570089\pi\)
\(632\) −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 0.886600 0.462536i \(-0.153060\pi\)
−0.843868 + 0.536550i \(0.819727\pi\)
\(642\) 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 0.0113669 0.999935i \(-0.496382\pi\)
0.860286 0.509812i \(-0.170285\pi\)
\(648\) −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 −0.848035 0.529940i \(-0.822214\pi\)
0.882959 + 0.469450i \(0.155548\pi\)
\(654\) 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 0.275992 + 0.961160i \(0.410994\pi\)
−0.970385 + 0.241564i \(0.922340\pi\)
\(660\) 8.13843 0.316788
\(661\) 5.16006 8.93748i 0.200703 0.347628i −0.748052 0.663640i \(-0.769011\pi\)
0.948755 + 0.316012i \(0.102344\pi\)
\(662\) −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 −0.376721 0.926327i \(-0.622948\pi\)
0.990583 0.136913i \(-0.0437182\pi\)
\(674\) 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 0.818360 + 0.574706i \(0.194884\pi\)
0.0885305 + 0.996073i \(0.471783\pi\)
\(684\) 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 0.896307 0.443435i \(-0.146240\pi\)
−0.832179 + 0.554507i \(0.812907\pi\)
\(692\) −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 −0.859690 0.510815i \(-0.829344\pi\)
−0.0125340 0.999921i \(-0.503990\pi\)
\(702\) −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 0.770174 0.637833i \(-0.220169\pi\)
−0.937467 + 0.348074i \(0.886836\pi\)
\(720\) −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 −0.363955 0.931416i \(-0.618574\pi\)
0.988608 0.150514i \(-0.0480927\pi\)
\(728\) 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 −0.352830 0.935688i \(-0.614780\pi\)
0.986744 0.162284i \(-0.0518862\pi\)
\(734\) −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 −0.342454 0.939535i \(-0.611258\pi\)
0.984888 0.173193i \(-0.0554085\pi\)
\(744\) 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 −0.999187 0.0403108i \(-0.987165\pi\)
0.464683 0.885477i \(-0.346168\pi\)
\(758\) 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 −0.999946 0.0104263i \(-0.996681\pi\)
0.490943 0.871191i \(-0.336652\pi\)
\(762\) −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 0.466315 + 0.884619i \(0.345581\pi\)
−0.999260 + 0.0384692i \(0.987752\pi\)
\(774\) 11.2707 19.5215i 0.405118 0.701685i
\(775\) 17.2213 + 29.8282i 0.618609 + 1.07146i