Properties

Label 144.2.x.c.13.1
Level $144$
Weight $2$
Character 144.13
Analytic conductor $1.150$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 144.x (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.14984578911\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 13.1
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 144.13
Dual form 144.2.x.c.133.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.36603 - 0.366025i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(1.73205 + 1.00000i) q^{4} +(1.00000 + 3.73205i) q^{5} +(0.633975 + 2.36603i) q^{6} +(0.633975 - 0.366025i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(-1.36603 - 0.366025i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(1.73205 + 1.00000i) q^{4} +(1.00000 + 3.73205i) q^{5} +(0.633975 + 2.36603i) q^{6} +(0.633975 - 0.366025i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-1.50000 + 2.59808i) q^{9} -5.46410i q^{10} +(2.86603 + 0.767949i) q^{11} -3.46410i q^{12} +(6.09808 - 1.63397i) q^{13} +(-1.00000 + 0.267949i) q^{14} +(4.73205 - 4.73205i) q^{15} +(2.00000 + 3.46410i) q^{16} -2.26795 q^{17} +(3.00000 - 3.00000i) q^{18} +(-0.633975 - 0.633975i) q^{19} +(-2.00000 + 7.46410i) q^{20} +(-1.09808 - 0.633975i) q^{21} +(-3.63397 - 2.09808i) q^{22} +(1.09808 + 0.633975i) q^{23} +(-1.26795 + 4.73205i) q^{24} +(-8.59808 + 4.96410i) q^{25} -8.92820 q^{26} +5.19615 q^{27} +1.46410 q^{28} +(0.633975 - 2.36603i) q^{29} +(-8.19615 + 4.73205i) q^{30} +(-3.73205 + 6.46410i) q^{31} +(-1.46410 - 5.46410i) q^{32} +(-1.33013 - 4.96410i) q^{33} +(3.09808 + 0.830127i) q^{34} +(2.00000 + 2.00000i) q^{35} +(-5.19615 + 3.00000i) q^{36} +(1.26795 - 1.26795i) q^{37} +(0.633975 + 1.09808i) q^{38} +(-7.73205 - 7.73205i) q^{39} +(5.46410 - 9.46410i) q^{40} +(2.59808 + 1.50000i) q^{41} +(1.26795 + 1.26795i) q^{42} +(-1.23205 - 0.330127i) q^{43} +(4.19615 + 4.19615i) q^{44} +(-11.1962 - 3.00000i) q^{45} +(-1.26795 - 1.26795i) q^{46} +(-4.83013 - 8.36603i) q^{47} +(3.46410 - 6.00000i) q^{48} +(-3.23205 + 5.59808i) q^{49} +(13.5622 - 3.63397i) q^{50} +(1.96410 + 3.40192i) q^{51} +(12.1962 + 3.26795i) q^{52} +(-0.535898 + 0.535898i) q^{53} +(-7.09808 - 1.90192i) q^{54} +11.4641i q^{55} +(-2.00000 - 0.535898i) q^{56} +(-0.401924 + 1.50000i) q^{57} +(-1.73205 + 3.00000i) q^{58} +(-1.33013 - 4.96410i) q^{59} +(12.9282 - 3.46410i) q^{60} +(0.803848 - 3.00000i) q^{61} +(7.46410 - 7.46410i) q^{62} +2.19615i q^{63} +8.00000i q^{64} +(12.1962 + 21.1244i) q^{65} +7.26795i q^{66} +(-5.23205 + 1.40192i) q^{67} +(-3.92820 - 2.26795i) q^{68} -2.19615i q^{69} +(-2.00000 - 3.46410i) q^{70} -10.9282i q^{71} +(8.19615 - 2.19615i) q^{72} -9.73205i q^{73} +(-2.19615 + 1.26795i) q^{74} +(14.8923 + 8.59808i) q^{75} +(-0.464102 - 1.73205i) q^{76} +(2.09808 - 0.562178i) q^{77} +(7.73205 + 13.3923i) q^{78} +(-6.00000 - 10.3923i) q^{79} +(-10.9282 + 10.9282i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-3.00000 - 3.00000i) q^{82} +(0.366025 - 1.36603i) q^{83} +(-1.26795 - 2.19615i) q^{84} +(-2.26795 - 8.46410i) q^{85} +(1.56218 + 0.901924i) q^{86} +(-4.09808 + 1.09808i) q^{87} +(-4.19615 - 7.26795i) q^{88} -2.00000i q^{89} +(14.1962 + 8.19615i) q^{90} +(3.26795 - 3.26795i) q^{91} +(1.26795 + 2.19615i) q^{92} +12.9282 q^{93} +(3.53590 + 13.1962i) q^{94} +(1.73205 - 3.00000i) q^{95} +(-6.92820 + 6.92820i) q^{96} +(-4.13397 - 7.16025i) q^{97} +(6.46410 - 6.46410i) q^{98} +(-6.29423 + 6.29423i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{2} + 4q^{5} + 6q^{6} + 6q^{7} - 8q^{8} - 6q^{9} + O(q^{10}) \) \( 4q - 2q^{2} + 4q^{5} + 6q^{6} + 6q^{7} - 8q^{8} - 6q^{9} + 8q^{11} + 14q^{13} - 4q^{14} + 12q^{15} + 8q^{16} - 16q^{17} + 12q^{18} - 6q^{19} - 8q^{20} + 6q^{21} - 18q^{22} - 6q^{23} - 12q^{24} - 24q^{25} - 8q^{26} - 8q^{28} + 6q^{29} - 12q^{30} - 8q^{31} + 8q^{32} + 12q^{33} + 2q^{34} + 8q^{35} + 12q^{37} + 6q^{38} - 24q^{39} + 8q^{40} + 12q^{42} + 2q^{43} - 4q^{44} - 24q^{45} - 12q^{46} - 2q^{47} - 6q^{49} + 30q^{50} - 6q^{51} + 28q^{52} - 16q^{53} - 18q^{54} - 8q^{56} - 12q^{57} + 12q^{59} + 24q^{60} + 24q^{61} + 16q^{62} + 28q^{65} - 14q^{67} + 12q^{68} - 8q^{70} + 12q^{72} + 12q^{74} + 18q^{75} + 12q^{76} - 2q^{77} + 24q^{78} - 24q^{79} - 16q^{80} - 18q^{81} - 12q^{82} - 2q^{83} - 12q^{84} - 16q^{85} - 18q^{86} - 6q^{87} + 4q^{88} + 36q^{90} + 20q^{91} + 12q^{92} + 24q^{93} + 28q^{94} - 20q^{97} + 12q^{98} + 6q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.36603 0.366025i −0.965926 0.258819i
\(3\) −0.866025 1.50000i −0.500000 0.866025i
\(4\) 1.73205 + 1.00000i 0.866025 + 0.500000i
\(5\) 1.00000 + 3.73205i 0.447214 + 1.66902i 0.710025 + 0.704177i \(0.248684\pi\)
−0.262811 + 0.964847i \(0.584650\pi\)
\(6\) 0.633975 + 2.36603i 0.258819 + 0.965926i
\(7\) 0.633975 0.366025i 0.239620 0.138345i −0.375382 0.926870i \(-0.622489\pi\)
0.615002 + 0.788526i \(0.289155\pi\)
\(8\) −2.00000 2.00000i −0.707107 0.707107i
\(9\) −1.50000 + 2.59808i −0.500000 + 0.866025i
\(10\) 5.46410i 1.72790i
\(11\) 2.86603 + 0.767949i 0.864139 + 0.231545i 0.663552 0.748130i \(-0.269048\pi\)
0.200587 + 0.979676i \(0.435715\pi\)
\(12\) 3.46410i 1.00000i
\(13\) 6.09808 1.63397i 1.69130 0.453183i 0.720577 0.693375i \(-0.243877\pi\)
0.970725 + 0.240192i \(0.0772105\pi\)
\(14\) −1.00000 + 0.267949i −0.267261 + 0.0716124i
\(15\) 4.73205 4.73205i 1.22181 1.22181i
\(16\) 2.00000 + 3.46410i 0.500000 + 0.866025i
\(17\) −2.26795 −0.550058 −0.275029 0.961436i \(-0.588688\pi\)
−0.275029 + 0.961436i \(0.588688\pi\)
\(18\) 3.00000 3.00000i 0.707107 0.707107i
\(19\) −0.633975 0.633975i −0.145444 0.145444i 0.630635 0.776079i \(-0.282794\pi\)
−0.776079 + 0.630635i \(0.782794\pi\)
\(20\) −2.00000 + 7.46410i −0.447214 + 1.66902i
\(21\) −1.09808 0.633975i −0.239620 0.138345i
\(22\) −3.63397 2.09808i −0.774766 0.447311i
\(23\) 1.09808 + 0.633975i 0.228965 + 0.132193i 0.610094 0.792329i \(-0.291132\pi\)
−0.381130 + 0.924522i \(0.624465\pi\)
\(24\) −1.26795 + 4.73205i −0.258819 + 0.965926i
\(25\) −8.59808 + 4.96410i −1.71962 + 0.992820i
\(26\) −8.92820 −1.75096
\(27\) 5.19615 1.00000
\(28\) 1.46410 0.276689
\(29\) 0.633975 2.36603i 0.117726 0.439360i −0.881750 0.471717i \(-0.843635\pi\)
0.999476 + 0.0323566i \(0.0103012\pi\)
\(30\) −8.19615 + 4.73205i −1.49641 + 0.863950i
\(31\) −3.73205 + 6.46410i −0.670296 + 1.16099i 0.307524 + 0.951540i \(0.400500\pi\)
−0.977820 + 0.209447i \(0.932834\pi\)
\(32\) −1.46410 5.46410i −0.258819 0.965926i
\(33\) −1.33013 4.96410i −0.231545 0.864139i
\(34\) 3.09808 + 0.830127i 0.531316 + 0.142366i
\(35\) 2.00000 + 2.00000i 0.338062 + 0.338062i
\(36\) −5.19615 + 3.00000i −0.866025 + 0.500000i
\(37\) 1.26795 1.26795i 0.208450 0.208450i −0.595159 0.803608i \(-0.702911\pi\)
0.803608 + 0.595159i \(0.202911\pi\)
\(38\) 0.633975 + 1.09808i 0.102844 + 0.178131i
\(39\) −7.73205 7.73205i −1.23812 1.23812i
\(40\) 5.46410 9.46410i 0.863950 1.49641i
\(41\) 2.59808 + 1.50000i 0.405751 + 0.234261i 0.688963 0.724797i \(-0.258066\pi\)
−0.283211 + 0.959058i \(0.591400\pi\)
\(42\) 1.26795 + 1.26795i 0.195649 + 0.195649i
\(43\) −1.23205 0.330127i −0.187886 0.0503439i 0.163649 0.986519i \(-0.447674\pi\)
−0.351535 + 0.936175i \(0.614340\pi\)
\(44\) 4.19615 + 4.19615i 0.632594 + 0.632594i
\(45\) −11.1962 3.00000i −1.66902 0.447214i
\(46\) −1.26795 1.26795i −0.186949 0.186949i
\(47\) −4.83013 8.36603i −0.704546 1.22031i −0.966855 0.255326i \(-0.917817\pi\)
0.262309 0.964984i \(-0.415516\pi\)
\(48\) 3.46410 6.00000i 0.500000 0.866025i
\(49\) −3.23205 + 5.59808i −0.461722 + 0.799725i
\(50\) 13.5622 3.63397i 1.91798 0.513922i
\(51\) 1.96410 + 3.40192i 0.275029 + 0.476365i
\(52\) 12.1962 + 3.26795i 1.69130 + 0.453183i
\(53\) −0.535898 + 0.535898i −0.0736113 + 0.0736113i −0.742954 0.669343i \(-0.766576\pi\)
0.669343 + 0.742954i \(0.266576\pi\)
\(54\) −7.09808 1.90192i −0.965926 0.258819i
\(55\) 11.4641i 1.54582i
\(56\) −2.00000 0.535898i −0.267261 0.0716124i
\(57\) −0.401924 + 1.50000i −0.0532361 + 0.198680i
\(58\) −1.73205 + 3.00000i −0.227429 + 0.393919i
\(59\) −1.33013 4.96410i −0.173168 0.646271i −0.996856 0.0792287i \(-0.974754\pi\)
0.823689 0.567042i \(-0.191912\pi\)
\(60\) 12.9282 3.46410i 1.66902 0.447214i
\(61\) 0.803848 3.00000i 0.102922 0.384111i −0.895179 0.445707i \(-0.852952\pi\)
0.998101 + 0.0615961i \(0.0196191\pi\)
\(62\) 7.46410 7.46410i 0.947942 0.947942i
\(63\) 2.19615i 0.276689i
\(64\) 8.00000i 1.00000i
\(65\) 12.1962 + 21.1244i 1.51275 + 2.62015i
\(66\) 7.26795i 0.894623i
\(67\) −5.23205 + 1.40192i −0.639197 + 0.171272i −0.563840 0.825884i \(-0.690676\pi\)
−0.0753572 + 0.997157i \(0.524010\pi\)
\(68\) −3.92820 2.26795i −0.476365 0.275029i
\(69\) 2.19615i 0.264386i
\(70\) −2.00000 3.46410i −0.239046 0.414039i
\(71\) 10.9282i 1.29694i −0.761241 0.648470i \(-0.775409\pi\)
0.761241 0.648470i \(-0.224591\pi\)
\(72\) 8.19615 2.19615i 0.965926 0.258819i
\(73\) 9.73205i 1.13905i −0.821974 0.569525i \(-0.807127\pi\)
0.821974 0.569525i \(-0.192873\pi\)
\(74\) −2.19615 + 1.26795i −0.255298 + 0.147396i
\(75\) 14.8923 + 8.59808i 1.71962 + 0.992820i
\(76\) −0.464102 1.73205i −0.0532361 0.198680i
\(77\) 2.09808 0.562178i 0.239098 0.0640661i
\(78\) 7.73205 + 13.3923i 0.875482 + 1.51638i
\(79\) −6.00000 10.3923i −0.675053 1.16923i −0.976453 0.215728i \(-0.930788\pi\)
0.301401 0.953498i \(-0.402546\pi\)
\(80\) −10.9282 + 10.9282i −1.22181 + 1.22181i
\(81\) −4.50000 7.79423i −0.500000 0.866025i
\(82\) −3.00000 3.00000i −0.331295 0.331295i
\(83\) 0.366025 1.36603i 0.0401765 0.149941i −0.942924 0.333009i \(-0.891936\pi\)
0.983100 + 0.183068i \(0.0586028\pi\)
\(84\) −1.26795 2.19615i −0.138345 0.239620i
\(85\) −2.26795 8.46410i −0.245994 0.918061i
\(86\) 1.56218 + 0.901924i 0.168454 + 0.0972569i
\(87\) −4.09808 + 1.09808i −0.439360 + 0.117726i
\(88\) −4.19615 7.26795i −0.447311 0.774766i
\(89\) 2.00000i 0.212000i −0.994366 0.106000i \(-0.966196\pi\)
0.994366 0.106000i \(-0.0338043\pi\)
\(90\) 14.1962 + 8.19615i 1.49641 + 0.863950i
\(91\) 3.26795 3.26795i 0.342574 0.342574i
\(92\) 1.26795 + 2.19615i 0.132193 + 0.228965i
\(93\) 12.9282 1.34059
\(94\) 3.53590 + 13.1962i 0.364700 + 1.36108i
\(95\) 1.73205 3.00000i 0.177705 0.307794i
\(96\) −6.92820 + 6.92820i −0.707107 + 0.707107i
\(97\) −4.13397 7.16025i −0.419742 0.727014i 0.576172 0.817329i \(-0.304546\pi\)
−0.995913 + 0.0903150i \(0.971213\pi\)
\(98\) 6.46410 6.46410i 0.652973 0.652973i
\(99\) −6.29423 + 6.29423i −0.632594 + 0.632594i
\(100\) −19.8564 −1.98564
\(101\) 7.46410 + 2.00000i 0.742706 + 0.199007i 0.610280 0.792186i \(-0.291057\pi\)
0.132426 + 0.991193i \(0.457723\pi\)
\(102\) −1.43782 5.36603i −0.142366 0.531316i
\(103\) 7.90192 + 4.56218i 0.778600 + 0.449525i 0.835934 0.548830i \(-0.184927\pi\)
−0.0573341 + 0.998355i \(0.518260\pi\)
\(104\) −15.4641 8.92820i −1.51638 0.875482i
\(105\) 1.26795 4.73205i 0.123739 0.461801i
\(106\) 0.928203 0.535898i 0.0901551 0.0520511i
\(107\) −13.4904 + 13.4904i −1.30416 + 1.30416i −0.378607 + 0.925558i \(0.623597\pi\)
−0.925558 + 0.378607i \(0.876403\pi\)
\(108\) 9.00000 + 5.19615i 0.866025 + 0.500000i
\(109\) 7.26795 + 7.26795i 0.696143 + 0.696143i 0.963576 0.267433i \(-0.0861754\pi\)
−0.267433 + 0.963576i \(0.586175\pi\)
\(110\) 4.19615 15.6603i 0.400087 1.49315i
\(111\) −3.00000 0.803848i −0.284747 0.0762978i
\(112\) 2.53590 + 1.46410i 0.239620 + 0.138345i
\(113\) 6.92820 12.0000i 0.651751 1.12887i −0.330947 0.943649i \(-0.607368\pi\)
0.982698 0.185216i \(-0.0592984\pi\)
\(114\) 1.09808 1.90192i 0.102844 0.178131i
\(115\) −1.26795 + 4.73205i −0.118237 + 0.441266i
\(116\) 3.46410 3.46410i 0.321634 0.321634i
\(117\) −4.90192 + 18.2942i −0.453183 + 1.69130i
\(118\) 7.26795i 0.669069i
\(119\) −1.43782 + 0.830127i −0.131805 + 0.0760976i
\(120\) −18.9282 −1.72790
\(121\) −1.90192 1.09808i −0.172902 0.0998251i
\(122\) −2.19615 + 3.80385i −0.198830 + 0.344384i
\(123\) 5.19615i 0.468521i
\(124\) −12.9282 + 7.46410i −1.16099 + 0.670296i
\(125\) −13.4641 13.4641i −1.20427 1.20427i
\(126\) 0.803848 3.00000i 0.0716124 0.267261i
\(127\) −6.19615 −0.549820 −0.274910 0.961470i \(-0.588648\pi\)
−0.274910 + 0.961470i \(0.588648\pi\)
\(128\) 2.92820 10.9282i 0.258819 0.965926i
\(129\) 0.571797 + 2.13397i 0.0503439 + 0.187886i
\(130\) −8.92820 33.3205i −0.783055 2.92240i
\(131\) −3.09808 + 0.830127i −0.270680 + 0.0725285i −0.391606 0.920133i \(-0.628080\pi\)
0.120926 + 0.992662i \(0.461414\pi\)
\(132\) 2.66025 9.92820i 0.231545 0.864139i
\(133\) −0.633975 0.169873i −0.0549726 0.0147299i
\(134\) 7.66025 0.661745
\(135\) 5.19615 + 19.3923i 0.447214 + 1.66902i
\(136\) 4.53590 + 4.53590i 0.388950 + 0.388950i
\(137\) −14.2583 + 8.23205i −1.21817 + 0.703312i −0.964527 0.263986i \(-0.914963\pi\)
−0.253645 + 0.967297i \(0.581629\pi\)
\(138\) −0.803848 + 3.00000i −0.0684280 + 0.255377i
\(139\) 2.42820 + 9.06218i 0.205958 + 0.768644i 0.989156 + 0.146872i \(0.0469204\pi\)
−0.783198 + 0.621772i \(0.786413\pi\)
\(140\) 1.46410 + 5.46410i 0.123739 + 0.461801i
\(141\) −8.36603 + 14.4904i −0.704546 + 1.22031i
\(142\) −4.00000 + 14.9282i −0.335673 + 1.25275i
\(143\) 18.7321 1.56645
\(144\) −12.0000 −1.00000
\(145\) 9.46410 0.785951
\(146\) −3.56218 + 13.2942i −0.294808 + 1.10024i
\(147\) 11.1962 0.923443
\(148\) 3.46410 0.928203i 0.284747 0.0762978i
\(149\) −0.830127 3.09808i −0.0680067 0.253804i 0.923550 0.383478i \(-0.125274\pi\)
−0.991557 + 0.129674i \(0.958607\pi\)
\(150\) −17.1962 17.1962i −1.40406 1.40406i
\(151\) 2.36603 1.36603i 0.192544 0.111166i −0.400629 0.916240i \(-0.631208\pi\)
0.593173 + 0.805075i \(0.297875\pi\)
\(152\) 2.53590i 0.205689i
\(153\) 3.40192 5.89230i 0.275029 0.476365i
\(154\) −3.07180 −0.247532
\(155\) −27.8564 7.46410i −2.23748 0.599531i
\(156\) −5.66025 21.1244i −0.453183 1.69130i
\(157\) 4.73205 1.26795i 0.377659 0.101193i −0.0649959 0.997886i \(-0.520703\pi\)
0.442655 + 0.896692i \(0.354037\pi\)
\(158\) 4.39230 + 16.3923i 0.349433 + 1.30410i
\(159\) 1.26795 + 0.339746i 0.100555 + 0.0269436i
\(160\) 18.9282 10.9282i 1.49641 0.863950i
\(161\) 0.928203 0.0731527
\(162\) 3.29423 + 12.2942i 0.258819 + 0.965926i
\(163\) −7.00000 7.00000i −0.548282 0.548282i 0.377661 0.925944i \(-0.376728\pi\)
−0.925944 + 0.377661i \(0.876728\pi\)
\(164\) 3.00000 + 5.19615i 0.234261 + 0.405751i
\(165\) 17.1962 9.92820i 1.33872 0.772910i
\(166\) −1.00000 + 1.73205i −0.0776151 + 0.134433i
\(167\) −0.464102 0.267949i −0.0359133 0.0207345i 0.481936 0.876206i \(-0.339934\pi\)
−0.517849 + 0.855472i \(0.673267\pi\)
\(168\) 0.928203 + 3.46410i 0.0716124 + 0.267261i
\(169\) 23.2583 13.4282i 1.78910 1.03294i
\(170\) 12.3923i 0.950446i
\(171\) 2.59808 0.696152i 0.198680 0.0532361i
\(172\) −1.80385 1.80385i −0.137542 0.137542i
\(173\) 3.36603 12.5622i 0.255914 0.955085i −0.711665 0.702519i \(-0.752059\pi\)
0.967580 0.252566i \(-0.0812745\pi\)
\(174\) 6.00000 0.454859
\(175\) −3.63397 + 6.29423i −0.274703 + 0.475799i
\(176\) 3.07180 + 11.4641i 0.231545 + 0.864139i
\(177\) −6.29423 + 6.29423i −0.473103 + 0.473103i
\(178\) −0.732051 + 2.73205i −0.0548695 + 0.204776i
\(179\) 11.9282 + 11.9282i 0.891556 + 0.891556i 0.994670 0.103114i \(-0.0328806\pi\)
−0.103114 + 0.994670i \(0.532881\pi\)
\(180\) −16.3923 16.3923i −1.22181 1.22181i
\(181\) 13.3923 13.3923i 0.995442 0.995442i −0.00454748 0.999990i \(-0.501448\pi\)
0.999990 + 0.00454748i \(0.00144751\pi\)
\(182\) −5.66025 + 3.26795i −0.419566 + 0.242237i
\(183\) −5.19615 + 1.39230i −0.384111 + 0.102922i
\(184\) −0.928203 3.46410i −0.0684280 0.255377i
\(185\) 6.00000 + 3.46410i 0.441129 + 0.254686i
\(186\) −17.6603 4.73205i −1.29491 0.346971i
\(187\) −6.50000 1.74167i −0.475327 0.127364i
\(188\) 19.3205i 1.40909i
\(189\) 3.29423 1.90192i 0.239620 0.138345i
\(190\) −3.46410 + 3.46410i −0.251312 + 0.251312i
\(191\) 7.02628 + 12.1699i 0.508404 + 0.880581i 0.999953 + 0.00973114i \(0.00309757\pi\)
−0.491549 + 0.870850i \(0.663569\pi\)
\(192\) 12.0000 6.92820i 0.866025 0.500000i
\(193\) −9.13397 + 15.8205i −0.657478 + 1.13879i 0.323789 + 0.946129i \(0.395043\pi\)
−0.981266 + 0.192656i \(0.938290\pi\)
\(194\) 3.02628 + 11.2942i 0.217274 + 0.810878i
\(195\) 21.1244 36.5885i 1.51275 2.62015i
\(196\) −11.1962 + 6.46410i −0.799725 + 0.461722i
\(197\) −3.66025 + 3.66025i −0.260782 + 0.260782i −0.825372 0.564590i \(-0.809034\pi\)
0.564590 + 0.825372i \(0.309034\pi\)
\(198\) 10.9019 6.29423i 0.774766 0.447311i
\(199\) 0.875644i 0.0620728i 0.999518 + 0.0310364i \(0.00988078\pi\)
−0.999518 + 0.0310364i \(0.990119\pi\)
\(200\) 27.1244 + 7.26795i 1.91798 + 0.513922i
\(201\) 6.63397 + 6.63397i 0.467924 + 0.467924i
\(202\) −9.46410 5.46410i −0.665892 0.384453i
\(203\) −0.464102 1.73205i −0.0325735 0.121566i
\(204\) 7.85641i 0.550058i
\(205\) −3.00000 + 11.1962i −0.209529 + 0.781973i
\(206\) −9.12436 9.12436i −0.635724 0.635724i
\(207\) −3.29423 + 1.90192i −0.228965 + 0.132193i
\(208\) 17.8564 + 17.8564i 1.23812 + 1.23812i
\(209\) −1.33013 2.30385i −0.0920068 0.159360i
\(210\) −3.46410 + 6.00000i −0.239046 + 0.414039i
\(211\) 4.09808 1.09808i 0.282123 0.0755947i −0.114983 0.993367i \(-0.536681\pi\)
0.397106 + 0.917773i \(0.370015\pi\)
\(212\) −1.46410 + 0.392305i −0.100555 + 0.0269436i
\(213\) −16.3923 + 9.46410i −1.12318 + 0.648470i
\(214\) 23.3660 13.4904i 1.59727 0.922183i
\(215\) 4.92820i 0.336101i
\(216\) −10.3923 10.3923i −0.707107 0.707107i
\(217\) 5.46410i 0.370927i
\(218\) −7.26795 12.5885i −0.492248 0.852598i
\(219\) −14.5981 + 8.42820i −0.986447 + 0.569525i
\(220\) −11.4641 + 19.8564i −0.772910 + 1.33872i
\(221\) −13.8301 + 3.70577i −0.930315 + 0.249277i
\(222\) 3.80385 + 2.19615i 0.255298 + 0.147396i
\(223\) 11.0263 + 19.0981i 0.738374 + 1.27890i 0.953227 + 0.302255i \(0.0977395\pi\)
−0.214853 + 0.976646i \(0.568927\pi\)
\(224\) −2.92820 2.92820i −0.195649 0.195649i
\(225\) 29.7846i 1.98564i
\(226\) −13.8564 + 13.8564i −0.921714 + 0.921714i
\(227\) 3.86603 14.4282i 0.256597 0.957633i −0.710598 0.703598i \(-0.751575\pi\)
0.967195 0.254035i \(-0.0817579\pi\)
\(228\) −2.19615 + 2.19615i −0.145444 + 0.145444i
\(229\) −1.83013 6.83013i −0.120938 0.451347i 0.878724 0.477330i \(-0.158395\pi\)
−0.999662 + 0.0259823i \(0.991729\pi\)
\(230\) 3.46410 6.00000i 0.228416 0.395628i
\(231\) −2.66025 2.66025i −0.175032 0.175032i
\(232\) −6.00000 + 3.46410i −0.393919 + 0.227429i
\(233\) 7.19615i 0.471436i 0.971822 + 0.235718i \(0.0757441\pi\)
−0.971822 + 0.235718i \(0.924256\pi\)
\(234\) 13.3923 23.1962i 0.875482 1.51638i
\(235\) 26.3923 26.3923i 1.72164 1.72164i
\(236\) 2.66025 9.92820i 0.173168 0.646271i
\(237\) −10.3923 + 18.0000i −0.675053 + 1.16923i
\(238\) 2.26795 0.607695i 0.147009 0.0393910i
\(239\) −13.0981 + 22.6865i −0.847244 + 1.46747i 0.0364139 + 0.999337i \(0.488407\pi\)
−0.883658 + 0.468133i \(0.844927\pi\)
\(240\) 25.8564 + 6.92820i 1.66902 + 0.447214i
\(241\) −6.40192 11.0885i −0.412384 0.714270i 0.582766 0.812640i \(-0.301971\pi\)
−0.995150 + 0.0983699i \(0.968637\pi\)
\(242\) 2.19615 + 2.19615i 0.141174 + 0.141174i
\(243\) −7.79423 + 13.5000i −0.500000 + 0.866025i
\(244\) 4.39230 4.39230i 0.281189 0.281189i
\(245\) −24.1244 6.46410i −1.54125 0.412976i
\(246\) −1.90192 + 7.09808i −0.121262 + 0.452557i
\(247\) −4.90192 2.83013i −0.311902 0.180077i
\(248\) 20.3923 5.46410i 1.29491 0.346971i
\(249\) −2.36603 + 0.633975i −0.149941 + 0.0401765i
\(250\) 13.4641 + 23.3205i 0.851545 + 1.47492i
\(251\) 2.83013 2.83013i 0.178636 0.178636i −0.612125 0.790761i \(-0.709685\pi\)
0.790761 + 0.612125i \(0.209685\pi\)
\(252\) −2.19615 + 3.80385i −0.138345 + 0.239620i
\(253\) 2.66025 + 2.66025i 0.167249 + 0.167249i
\(254\) 8.46410 + 2.26795i 0.531085 + 0.142304i
\(255\) −10.7321 + 10.7321i −0.672067 + 0.672067i
\(256\) −8.00000 + 13.8564i −0.500000 + 0.866025i
\(257\) −4.42820 + 7.66987i −0.276224 + 0.478434i −0.970443 0.241330i \(-0.922416\pi\)
0.694219 + 0.719763i \(0.255750\pi\)
\(258\) 3.12436i 0.194514i
\(259\) 0.339746 1.26795i 0.0211108 0.0787865i
\(260\) 48.7846i 3.02549i
\(261\) 5.19615 + 5.19615i 0.321634 + 0.321634i
\(262\) 4.53590 0.280229
\(263\) 23.4904 13.5622i 1.44848 0.836280i 0.450088 0.892984i \(-0.351393\pi\)
0.998391 + 0.0567045i \(0.0180593\pi\)
\(264\) −7.26795 + 12.5885i −0.447311 + 0.774766i
\(265\) −2.53590 1.46410i −0.155779 0.0899390i
\(266\) 0.803848 + 0.464102i 0.0492871 + 0.0284559i
\(267\) −3.00000 + 1.73205i −0.183597 + 0.106000i
\(268\) −10.4641 2.80385i −0.639197 0.171272i
\(269\) 4.73205 + 4.73205i 0.288518 + 0.288518i 0.836494 0.547976i \(-0.184601\pi\)
−0.547976 + 0.836494i \(0.684601\pi\)
\(270\) 28.3923i 1.72790i
\(271\) 20.3923 1.23874 0.619372 0.785098i \(-0.287387\pi\)
0.619372 + 0.785098i \(0.287387\pi\)
\(272\) −4.53590 7.85641i −0.275029 0.476365i
\(273\) −7.73205 2.07180i −0.467965 0.125391i
\(274\) 22.4904 6.02628i 1.35869 0.364061i
\(275\) −28.4545 + 7.62436i −1.71587 + 0.459766i
\(276\) 2.19615 3.80385i 0.132193 0.228965i
\(277\) 15.7583 + 4.22243i 0.946826 + 0.253701i 0.699015 0.715107i \(-0.253622\pi\)
0.247811 + 0.968808i \(0.420289\pi\)
\(278\) 13.2679i 0.795759i
\(279\) −11.1962 19.3923i −0.670296 1.16099i
\(280\) 8.00000i 0.478091i
\(281\) 8.66025 5.00000i 0.516627 0.298275i −0.218926 0.975741i \(-0.570255\pi\)
0.735554 + 0.677466i \(0.236922\pi\)
\(282\) 16.7321 16.7321i 0.996379 0.996379i
\(283\) −7.43782 27.7583i −0.442133 1.65006i −0.723398 0.690431i \(-0.757421\pi\)
0.281265 0.959630i \(-0.409246\pi\)
\(284\) 10.9282 18.9282i 0.648470 1.12318i
\(285\) −6.00000 −0.355409
\(286\) −25.5885 6.85641i −1.51308 0.405428i
\(287\) 2.19615 0.129635
\(288\) 16.3923 + 4.39230i 0.965926 + 0.258819i
\(289\) −11.8564 −0.697436
\(290\) −12.9282 3.46410i −0.759170 0.203419i
\(291\) −7.16025 + 12.4019i −0.419742 + 0.727014i
\(292\) 9.73205 16.8564i 0.569525 0.986447i
\(293\) −3.63397 13.5622i −0.212299 0.792311i −0.987100 0.160106i \(-0.948817\pi\)
0.774801 0.632205i \(-0.217850\pi\)
\(294\) −15.2942 4.09808i −0.891978 0.239005i
\(295\) 17.1962 9.92820i 1.00120 0.578042i
\(296\) −5.07180 −0.294792
\(297\) 14.8923 + 3.99038i 0.864139 + 0.231545i
\(298\) 4.53590i 0.262758i
\(299\) 7.73205 + 2.07180i 0.447156 + 0.119815i
\(300\) 17.1962 + 29.7846i 0.992820 + 1.71962i
\(301\) −0.901924 + 0.241670i −0.0519860 + 0.0139296i
\(302\) −3.73205 + 1.00000i −0.214755 + 0.0575435i
\(303\) −3.46410 12.9282i −0.199007 0.742706i
\(304\) 0.928203 3.46410i 0.0532361 0.198680i
\(305\) 12.0000 0.687118
\(306\) −6.80385 + 6.80385i −0.388950 + 0.388950i
\(307\) −16.0263 16.0263i −0.914668 0.914668i 0.0819670 0.996635i \(-0.473880\pi\)
−0.996635 + 0.0819670i \(0.973880\pi\)
\(308\) 4.19615 + 1.12436i 0.239098 + 0.0640661i
\(309\) 15.8038i 0.899049i
\(310\) 35.3205 + 20.3923i 2.00607 + 1.15821i
\(311\) −13.9019 8.02628i −0.788306 0.455129i 0.0510600 0.998696i \(-0.483740\pi\)
−0.839366 + 0.543567i \(0.817073\pi\)
\(312\) 30.9282i 1.75096i
\(313\) −24.6506 + 14.2321i −1.39334 + 0.804443i −0.993683 0.112223i \(-0.964203\pi\)
−0.399653 + 0.916666i \(0.630869\pi\)
\(314\) −6.92820 −0.390981
\(315\) −8.19615 + 2.19615i −0.461801 + 0.123739i
\(316\) 24.0000i 1.35011i
\(317\) −8.43782 + 31.4904i −0.473915 + 1.76868i 0.151577 + 0.988445i \(0.451565\pi\)
−0.625492 + 0.780231i \(0.715102\pi\)
\(318\) −1.60770 0.928203i −0.0901551 0.0520511i
\(319\) 3.63397 6.29423i 0.203464 0.352409i
\(320\) −29.8564 + 8.00000i −1.66902 + 0.447214i
\(321\) 31.9186 + 8.55256i 1.78152 + 0.477357i
\(322\) −1.26795 0.339746i −0.0706600 0.0189333i
\(323\) 1.43782 + 1.43782i 0.0800026 + 0.0800026i
\(324\) 18.0000i 1.00000i
\(325\) −44.3205 + 44.3205i −2.45846 + 2.45846i
\(326\) 7.00000 + 12.1244i 0.387694 + 0.671506i
\(327\) 4.60770 17.1962i 0.254806 0.950949i
\(328\) −2.19615 8.19615i −0.121262 0.452557i
\(329\) −6.12436 3.53590i −0.337647 0.194940i
\(330\) −27.1244 + 7.26795i −1.49315 + 0.400087i
\(331\) −19.0263 5.09808i −1.04578 0.280216i −0.305273 0.952265i \(-0.598748\pi\)
−0.740506 + 0.672049i \(0.765414\pi\)
\(332\) 2.00000 2.00000i 0.109764 0.109764i
\(333\) 1.39230 + 5.19615i 0.0762978 + 0.284747i
\(334\) 0.535898 + 0.535898i 0.0293231 + 0.0293231i
\(335\) −10.4641 18.1244i −0.571715 0.990239i
\(336\) 5.07180i 0.276689i
\(337\) −11.8923 + 20.5981i −0.647815 + 1.12205i 0.335829 + 0.941923i \(0.390984\pi\)
−0.983644 + 0.180126i \(0.942350\pi\)
\(338\) −36.6865 + 9.83013i −1.99548 + 0.534688i
\(339\) −24.0000 −1.30350
\(340\) 4.53590 16.9282i 0.245994 0.918061i
\(341\) −15.6603 + 15.6603i −0.848050 + 0.848050i
\(342\) −3.80385 −0.205689
\(343\) 9.85641i 0.532196i
\(344\) 1.80385 + 3.12436i 0.0972569 + 0.168454i
\(345\) 8.19615 2.19615i 0.441266 0.118237i
\(346\) −9.19615 + 15.9282i −0.494388 + 0.856306i
\(347\) 6.62436 + 24.7224i 0.355614 + 1.32717i 0.879710 + 0.475510i \(0.157737\pi\)
−0.524096 + 0.851659i \(0.675597\pi\)
\(348\) −8.19615 2.19615i −0.439360 0.117726i
\(349\) 2.07180 7.73205i 0.110901 0.413887i −0.888047 0.459753i \(-0.847938\pi\)
0.998948 + 0.0458657i \(0.0146046\pi\)
\(350\) 7.26795 7.26795i 0.388488 0.388488i
\(351\) 31.6865 8.49038i 1.69130 0.453183i
\(352\) 16.7846i 0.894623i
\(353\) −10.1603 17.5981i −0.540776 0.936651i −0.998860 0.0477421i \(-0.984797\pi\)
0.458084 0.888909i \(-0.348536\pi\)
\(354\) 10.9019 6.29423i 0.579431 0.334534i
\(355\) 40.7846 10.9282i 2.16462 0.580009i
\(356\) 2.00000 3.46410i 0.106000 0.183597i
\(357\) 2.49038 + 1.43782i 0.131805 + 0.0760976i
\(358\) −11.9282 20.6603i −0.630425 1.09193i
\(359\) 14.7321i 0.777528i 0.921337 + 0.388764i \(0.127098\pi\)
−0.921337 + 0.388764i \(0.872902\pi\)
\(360\) 16.3923 + 28.3923i 0.863950 + 1.49641i
\(361\) 18.1962i 0.957692i
\(362\) −23.1962 + 13.3923i −1.21916 + 0.703884i
\(363\) 3.80385i 0.199650i
\(364\) 8.92820 2.39230i 0.467965 0.125391i
\(365\) 36.3205 9.73205i 1.90110 0.509399i
\(366\) 7.60770 0.397661
\(367\) −10.1244 17.5359i −0.528487 0.915366i −0.999448 0.0332125i \(-0.989426\pi\)
0.470961 0.882154i \(-0.343907\pi\)
\(368\) 5.07180i 0.264386i
\(369\) −7.79423 + 4.50000i −0.405751 + 0.234261i
\(370\) −6.92820 6.92820i −0.360180 0.360180i
\(371\) −0.143594 + 0.535898i −0.00745501 + 0.0278225i
\(372\) 22.3923 + 12.9282i 1.16099 + 0.670296i
\(373\) 1.50962 + 5.63397i 0.0781651 + 0.291716i 0.993932 0.109993i \(-0.0350829\pi\)
−0.915767 + 0.401709i \(0.868416\pi\)
\(374\) 8.24167 + 4.75833i 0.426167 + 0.246047i
\(375\) −8.53590 + 31.8564i −0.440792 + 1.64506i
\(376\) −7.07180 + 26.3923i −0.364700 + 1.36108i
\(377\) 15.4641i 0.796442i
\(378\) −5.19615 + 1.39230i −0.267261 + 0.0716124i
\(379\) −18.7583 + 18.7583i −0.963551 + 0.963551i −0.999359 0.0358080i \(-0.988600\pi\)
0.0358080 + 0.999359i \(0.488600\pi\)
\(380\) 6.00000 3.46410i 0.307794 0.177705i
\(381\) 5.36603 + 9.29423i 0.274910 + 0.476158i
\(382\) −5.14359 19.1962i −0.263169 0.982161i
\(383\) −3.26795 + 5.66025i −0.166984 + 0.289225i −0.937358 0.348367i \(-0.886736\pi\)
0.770374 + 0.637593i \(0.220070\pi\)
\(384\) −18.9282 + 5.07180i −0.965926 + 0.258819i
\(385\) 4.19615 + 7.26795i 0.213856 + 0.370409i
\(386\) 18.2679 18.2679i 0.929814 0.929814i
\(387\) 2.70577 2.70577i 0.137542 0.137542i
\(388\) 16.5359i 0.839483i
\(389\) 10.2942 + 2.75833i 0.521938 + 0.139853i 0.510163 0.860078i \(-0.329585\pi\)
0.0117752 + 0.999931i \(0.496252\pi\)
\(390\) −42.2487 + 42.2487i −2.13935 + 2.13935i
\(391\) −2.49038 1.43782i −0.125944 0.0727138i
\(392\) 17.6603 4.73205i 0.891978 0.239005i
\(393\) 3.92820 + 3.92820i 0.198152 + 0.198152i
\(394\) 6.33975 3.66025i 0.319392 0.184401i
\(395\) 32.7846 32.7846i 1.64957 1.64957i
\(396\) −17.1962 + 4.60770i −0.864139 + 0.231545i
\(397\) −12.7321 12.7321i −0.639003 0.639003i 0.311306 0.950310i \(-0.399233\pi\)
−0.950310 + 0.311306i \(0.899233\pi\)
\(398\) 0.320508 1.19615i 0.0160656 0.0599577i
\(399\) 0.294229 + 1.09808i 0.0147299 + 0.0549726i
\(400\) −34.3923 19.8564i −1.71962 0.992820i
\(401\) 13.7942 23.8923i 0.688851 1.19312i −0.283359 0.959014i \(-0.591449\pi\)
0.972210 0.234111i \(-0.0752179\pi\)
\(402\) −6.63397 11.4904i −0.330873 0.573088i
\(403\) −12.1962 + 45.5167i −0.607534 + 2.26735i
\(404\) 10.9282 + 10.9282i 0.543698 + 0.543698i
\(405\) 24.5885 24.5885i 1.22181 1.22181i
\(406\) 2.53590i 0.125855i
\(407\) 4.60770 2.66025i 0.228395 0.131864i
\(408\) 2.87564 10.7321i 0.142366 0.531316i
\(409\) 26.1340 + 15.0885i 1.29224 + 0.746076i 0.979051 0.203614i \(-0.0652688\pi\)
0.313191 + 0.949690i \(0.398602\pi\)
\(410\) 8.19615 14.1962i 0.404779 0.701098i
\(411\) 24.6962 + 14.2583i 1.21817 + 0.703312i
\(412\) 9.12436 + 15.8038i 0.449525 + 0.778600i
\(413\) −2.66025 2.66025i −0.130903 0.130903i
\(414\) 5.19615 1.39230i 0.255377 0.0684280i
\(415\) 5.46410 0.268222
\(416\) −17.8564 30.9282i −0.875482 1.51638i
\(417\) 11.4904 11.4904i 0.562686 0.562686i
\(418\) 0.973721 + 3.63397i 0.0476262 + 0.177744i
\(419\) 31.2224 8.36603i 1.52532 0.408707i 0.603828 0.797115i \(-0.293641\pi\)
0.921488 + 0.388408i \(0.126975\pi\)
\(420\) 6.92820 6.92820i 0.338062 0.338062i
\(421\) −2.19615 0.588457i −0.107034 0.0286797i 0.204905 0.978782i \(-0.434312\pi\)
−0.311938 + 0.950102i \(0.600978\pi\)
\(422\) −6.00000 −0.292075
\(423\) 28.9808 1.40909
\(424\) 2.14359 0.104102
\(425\) 19.5000 11.2583i 0.945889 0.546109i
\(426\) 25.8564 6.92820i 1.25275 0.335673i
\(427\) −0.588457 2.19615i −0.0284774 0.106279i
\(428\) −36.8564 + 9.87564i −1.78152 + 0.477357i
\(429\) −16.2224 28.0981i −0.783226 1.35659i
\(430\) −1.80385 + 6.73205i −0.0869893 + 0.324648i
\(431\) −5.80385 −0.279562 −0.139781 0.990182i \(-0.544640\pi\)
−0.139781 + 0.990182i \(0.544640\pi\)
\(432\) 10.3923 + 18.0000i 0.500000 + 0.866025i
\(433\) −2.26795 −0.108991 −0.0544953 0.998514i \(-0.517355\pi\)
−0.0544953 + 0.998514i \(0.517355\pi\)
\(434\) 2.00000 7.46410i 0.0960031 0.358288i
\(435\) −8.19615 14.1962i −0.392975 0.680653i
\(436\) 5.32051 + 19.8564i 0.254806 + 0.950949i
\(437\) −0.294229 1.09808i −0.0140749 0.0525281i
\(438\) 23.0263 6.16987i 1.10024 0.294808i
\(439\) 4.85641 2.80385i 0.231784 0.133820i −0.379611 0.925146i \(-0.623942\pi\)
0.611395 + 0.791326i \(0.290609\pi\)
\(440\) 22.9282 22.9282i 1.09306 1.09306i
\(441\) −9.69615 16.7942i −0.461722 0.799725i
\(442\) 20.2487 0.963133
\(443\) 19.6244 + 5.25833i 0.932381 + 0.249831i 0.692870 0.721063i \(-0.256346\pi\)
0.239511 + 0.970894i \(0.423013\pi\)
\(444\) −4.39230 4.39230i −0.208450 0.208450i
\(445\) 7.46410 2.00000i 0.353832 0.0948091i
\(446\) −8.07180 30.1244i −0.382211 1.42643i
\(447\) −3.92820 + 3.92820i −0.185798 + 0.185798i
\(448\) 2.92820 + 5.07180i 0.138345 + 0.239620i
\(449\) −20.6603 −0.975018 −0.487509 0.873118i \(-0.662094\pi\)
−0.487509 + 0.873118i \(0.662094\pi\)
\(450\) −10.9019 + 40.6865i −0.513922 + 1.91798i
\(451\) 6.29423 + 6.29423i 0.296384 + 0.296384i
\(452\) 24.0000 13.8564i 1.12887 0.651751i
\(453\) −4.09808 2.36603i −0.192544 0.111166i
\(454\) −10.5622 + 18.2942i −0.495708 + 0.858591i
\(455\) 15.4641 + 8.92820i 0.724968 + 0.418561i
\(456\) 3.80385 2.19615i 0.178131 0.102844i
\(457\) −20.2583 + 11.6962i −0.947645 + 0.547123i −0.892348 0.451347i \(-0.850944\pi\)
−0.0552962 + 0.998470i \(0.517610\pi\)
\(458\) 10.0000i 0.467269i
\(459\) −11.7846 −0.550058
\(460\) −6.92820 + 6.92820i −0.323029 + 0.323029i
\(461\) −0.686533 + 2.56218i −0.0319751 + 0.119333i −0.980069 0.198659i \(-0.936342\pi\)
0.948094 + 0.317991i \(0.103008\pi\)
\(462\) 2.66025 + 4.60770i 0.123766 + 0.214369i
\(463\) −9.19615 + 15.9282i −0.427381 + 0.740246i −0.996640 0.0819125i \(-0.973897\pi\)
0.569258 + 0.822159i \(0.307231\pi\)
\(464\) 9.46410 2.53590i 0.439360 0.117726i
\(465\) 12.9282 + 48.2487i 0.599531 + 2.23748i
\(466\) 2.63397 9.83013i 0.122017 0.455372i
\(467\) 4.36603 + 4.36603i 0.202036 + 0.202036i 0.800872 0.598836i \(-0.204370\pi\)
−0.598836 + 0.800872i \(0.704370\pi\)
\(468\) −26.7846 + 26.7846i −1.23812 + 1.23812i
\(469\) −2.80385 + 2.80385i −0.129470 + 0.129470i
\(470\) −45.7128 + 26.3923i −2.10857 + 1.21739i
\(471\) −6.00000 6.00000i −0.276465 0.276465i
\(472\) −7.26795 + 12.5885i −0.334534 + 0.579431i
\(473\) −3.27757 1.89230i −0.150703 0.0870083i
\(474\) 20.7846 20.7846i 0.954669 0.954669i
\(475\) 8.59808 + 2.30385i 0.394507 + 0.105708i
\(476\) −3.32051 −0.152195
\(477\) −0.588457 2.19615i −0.0269436 0.100555i
\(478\) 26.1962 26.1962i 1.19818 1.19818i
\(479\) 12.8301 + 22.2224i 0.586223 + 1.01537i 0.994722 + 0.102610i \(0.0327193\pi\)
−0.408498 + 0.912759i \(0.633947\pi\)
\(480\) −32.7846 18.9282i −1.49641 0.863950i
\(481\) 5.66025 9.80385i 0.258085 0.447017i
\(482\) 4.68653 + 17.4904i 0.213466 + 0.796665i
\(483\) −0.803848 1.39230i −0.0365763 0.0633521i
\(484\) −2.19615 3.80385i −0.0998251 0.172902i
\(485\) 22.5885 22.5885i 1.02569 1.02569i
\(486\) 15.5885 15.5885i 0.707107 0.707107i
\(487\) 16.1962i 0.733918i 0.930237 + 0.366959i \(0.119601\pi\)
−0.930237 + 0.366959i \(0.880399\pi\)
\(488\) −7.60770 + 4.39230i −0.344384 + 0.198830i
\(489\) −4.43782 + 16.5622i −0.200685 + 0.748968i
\(490\) 30.5885 + 17.6603i 1.38185 + 0.797809i
\(491\) 6.89230 + 25.7224i 0.311045 + 1.16084i 0.927615 + 0.373537i \(0.121855\pi\)
−0.616570 + 0.787300i \(0.711478\pi\)
\(492\) 5.19615 9.00000i 0.234261 0.405751i
\(493\) −1.43782 + 5.36603i −0.0647563 + 0.241674i
\(494\) 5.66025 + 5.66025i 0.254667 + 0.254667i
\(495\) −29.7846 17.1962i −1.33872 0.772910i
\(496\) −29.8564 −1.34059
\(497\) −4.00000 6.92820i −0.179425 0.310772i
\(498\) 3.46410 0.155230
\(499\) 6.33013 1.69615i 0.283375 0.0759302i −0.114332 0.993443i \(-0.536473\pi\)
0.397707 + 0.917512i \(0.369806\pi\)
\(500\) −9.85641 36.7846i −0.440792 1.64506i
\(501\) 0.928203i 0.0414691i
\(502\) −4.90192 + 2.83013i −0.218784 + 0.126315i
\(503\) 27.7128i 1.23565i 0.786314 + 0.617827i \(0.211987\pi\)
−0.786314 + 0.617827i \(0.788013\pi\)
\(504\) 4.39230 4.39230i 0.195649 0.195649i
\(505\) 29.8564i 1.32859i
\(506\) −2.66025 4.60770i −0.118263 0.204837i
\(507\) −40.2846 23.2583i −1.78910 1.03294i
\(508\) −10.7321 6.19615i −0.476158 0.274910i
\(509\) 16.9282 4.53590i 0.750329 0.201050i 0.136665 0.990617i \(-0.456362\pi\)
0.613664 + 0.789567i \(0.289695\pi\)
\(510\) 18.5885 10.7321i 0.823111 0.475223i
\(511\) −3.56218 6.16987i −0.157581 0.272939i
\(512\) 16.0000 16.0000i 0.707107 0.707107i
\(513\) −3.29423 3.29423i −0.145444 0.145444i
\(514\) 8.85641 8.85641i 0.390639 0.390639i
\(515\) −9.12436 + 34.0526i −0.402067 + 1.50054i
\(516\) −1.14359 + 4.26795i −0.0503439 + 0.187886i
\(517\) −7.41858 27.6865i −0.326269 1.21765i
\(518\) −0.928203 + 1.60770i −0.0407829 + 0.0706381i
\(519\) −21.7583 + 5.83013i −0.955085 + 0.255914i
\(520\) 17.8564 66.6410i 0.783055 2.92240i
\(521\) 13.0000i 0.569540i 0.958596 + 0.284770i \(0.0919173\pi\)
−0.958596 + 0.284770i \(0.908083\pi\)
\(522\) −5.19615 9.00000i −0.227429 0.393919i
\(523\) −14.4641 + 14.4641i −0.632471 + 0.632471i −0.948687 0.316216i \(-0.897588\pi\)
0.316216 + 0.948687i \(0.397588\pi\)
\(524\) −6.19615 1.66025i −0.270680 0.0725285i
\(525\) 12.5885 0.549405
\(526\) −37.0526 + 9.92820i −1.61557 + 0.432890i
\(527\) 8.46410 14.6603i 0.368702 0.638611i
\(528\) 14.5359 14.5359i 0.632594 0.632594i
\(529\) −10.6962 18.5263i −0.465050 0.805490i
\(530\) 2.92820 + 2.92820i 0.127193 + 0.127193i
\(531\) 14.8923 + 3.99038i 0.646271 + 0.173168i
\(532\) −0.928203 0.928203i −0.0402427 0.0402427i
\(533\) 18.2942 + 4.90192i 0.792411 + 0.212326i
\(534\) 4.73205 1.26795i 0.204776 0.0548695i
\(535\) −63.8372 36.8564i −2.75992 1.59344i
\(536\) 13.2679 + 7.66025i 0.573088 + 0.330873i
\(537\) 7.56218 28.2224i 0.326332 1.21789i
\(538\) −4.73205 8.19615i −0.204013 0.353361i
\(539\) −13.5622 + 13.5622i −0.584164 + 0.584164i
\(540\) −10.3923 + 38.7846i −0.447214 + 1.66902i
\(541\) −8.19615 8.19615i −0.352380 0.352380i 0.508614 0.860994i \(-0.330158\pi\)
−0.860994 + 0.508614i \(0.830158\pi\)
\(542\) −27.8564 7.46410i −1.19654 0.320611i
\(543\) −31.6865 8.49038i −1.35980 0.364357i
\(544\) 3.32051 + 12.3923i 0.142366 + 0.531316i
\(545\) −19.8564 + 34.3923i −0.850555 + 1.47320i
\(546\) 9.80385 + 5.66025i 0.419566 + 0.242237i
\(547\) 8.37564 31.2583i 0.358117 1.33651i −0.518400 0.855138i \(-0.673472\pi\)
0.876517 0.481371i \(-0.159861\pi\)
\(548\) −32.9282 −1.40662
\(549\) 6.58846 + 6.58846i 0.281189 + 0.281189i
\(550\) 41.6603 1.77640
\(551\) −1.90192 + 1.09808i −0.0810247 + 0.0467796i
\(552\) −4.39230 + 4.39230i −0.186949 + 0.186949i
\(553\) −7.60770 4.39230i −0.323512 0.186780i
\(554\) −19.9808 11.5359i −0.848901 0.490113i
\(555\) 12.0000i 0.509372i
\(556\) −4.85641 + 18.1244i −0.205958 + 0.768644i
\(557\) −25.1962 25.1962i −1.06760 1.06760i −0.997543 0.0700519i \(-0.977684\pi\)
−0.0700519 0.997543i \(-0.522316\pi\)
\(558\) 8.19615 + 30.5885i 0.346971 + 1.29491i
\(559\) −8.05256 −0.340587
\(560\) −2.92820 + 10.9282i −0.123739 + 0.461801i
\(561\) 3.01666 + 11.2583i 0.127364 + 0.475327i
\(562\) −13.6603 + 3.66025i −0.576223 + 0.154398i
\(563\) −3.76795 + 1.00962i −0.158800 + 0.0425504i −0.337343 0.941382i \(-0.609528\pi\)
0.178543 + 0.983932i \(0.442862\pi\)
\(564\) −28.9808 + 16.7321i −1.22031 + 0.704546i
\(565\) 51.7128 + 13.8564i 2.17557 + 0.582943i
\(566\) 40.6410i 1.70827i
\(567\) −5.70577 3.29423i −0.239620 0.138345i
\(568\) −21.8564 + 21.8564i −0.917074 + 0.917074i
\(569\) −23.5981 + 13.6244i −0.989283 + 0.571163i −0.905060 0.425284i \(-0.860174\pi\)
−0.0842230 + 0.996447i \(0.526841\pi\)
\(570\) 8.19615 + 2.19615i 0.343299 + 0.0919867i
\(571\) 5.33013 + 19.8923i 0.223059 + 0.832467i 0.983173 + 0.182677i \(0.0584764\pi\)
−0.760114 + 0.649790i \(0.774857\pi\)
\(572\) 32.4449 + 18.7321i 1.35659 + 0.783226i
\(573\) 12.1699 21.0788i 0.508404 0.880581i
\(574\) −3.00000 0.803848i −0.125218 0.0335519i
\(575\) −12.5885 −0.524975
\(576\) −20.7846 12.0000i −0.866025 0.500000i
\(577\) 35.7846 1.48973 0.744866 0.667214i \(-0.232513\pi\)
0.744866 + 0.667214i \(0.232513\pi\)
\(578\) 16.1962 + 4.33975i 0.673671 + 0.180510i
\(579\) 31.6410 1.31496
\(580\) 16.3923 + 9.46410i 0.680653 + 0.392975i
\(581\) −0.267949 1.00000i −0.0111164 0.0414870i
\(582\) 14.3205 14.3205i 0.593604 0.593604i
\(583\) −1.94744 + 1.12436i −0.0806548 + 0.0465661i
\(584\) −19.4641 + 19.4641i −0.805430 + 0.805430i
\(585\) −73.1769 −3.02549
\(586\) 19.8564i 0.820261i
\(587\) 3.76795 + 1.00962i 0.155520 + 0.0416714i 0.335739 0.941955i \(-0.391014\pi\)
−0.180219 + 0.983626i \(0.557681\pi\)
\(588\) 19.3923 + 11.1962i 0.799725 + 0.461722i
\(589\) 6.46410 1.73205i 0.266349 0.0713679i
\(590\) −27.1244 + 7.26795i −1.11669 + 0.299217i
\(591\) 8.66025 + 2.32051i 0.356235 + 0.0954529i
\(592\) 6.92820 + 1.85641i 0.284747 + 0.0762978i
\(593\) 10.5359 0.432657 0.216329 0.976321i \(-0.430592\pi\)
0.216329 + 0.976321i \(0.430592\pi\)
\(594\) −18.8827 10.9019i −0.774766 0.447311i
\(595\) −4.53590 4.53590i −0.185954 0.185954i
\(596\) 1.66025 6.19615i 0.0680067 0.253804i
\(597\) 1.31347 0.758330i 0.0537566 0.0310364i
\(598\) −9.80385 5.66025i −0.400909 0.231465i
\(599\) −23.3205 13.4641i −0.952850 0.550128i −0.0588850 0.998265i \(-0.518755\pi\)
−0.893965 + 0.448136i \(0.852088\pi\)
\(600\) −12.5885 46.9808i −0.513922 1.91798i
\(601\) 17.5526 10.1340i 0.715984 0.413373i −0.0972889 0.995256i \(-0.531017\pi\)
0.813273 + 0.581883i \(0.197684\pi\)
\(602\) 1.32051 0.0538199
\(603\) 4.20577 15.6962i 0.171272 0.639197i
\(604\) 5.46410 0.222331
\(605\) 2.19615 8.19615i 0.0892863 0.333221i
\(606\) 18.9282i 0.768906i
\(607\) 22.5885 39.1244i 0.916837 1.58801i 0.112648 0.993635i \(-0.464067\pi\)
0.804189 0.594374i \(-0.202600\pi\)
\(608\) −2.53590 + 4.39230i −0.102844 + 0.178131i
\(609\) −2.19615 + 2.19615i −0.0889926 + 0.0889926i
\(610\) −16.3923 4.39230i −0.663705 0.177839i
\(611\) −43.1244 43.1244i −1.74462 1.74462i
\(612\) 11.7846 6.80385i 0.476365 0.275029i
\(613\) 1.66025 1.66025i 0.0670570 0.0670570i −0.672783 0.739840i \(-0.734901\pi\)
0.739840 + 0.672783i \(0.234901\pi\)
\(614\) 16.0263 + 27.7583i 0.646768 + 1.12024i
\(615\) 19.3923 5.19615i 0.781973 0.209529i
\(616\) −5.32051 3.07180i −0.214369 0.123766i
\(617\) −3.91154 2.25833i −0.157473 0.0909170i 0.419193 0.907897i \(-0.362313\pi\)
−0.576666 + 0.816980i \(0.695646\pi\)
\(618\) −5.78461 + 21.5885i −0.232691 + 0.868415i
\(619\) 38.8205 + 10.4019i 1.56033 + 0.418089i 0.932767 0.360479i \(-0.117387\pi\)
0.627561 + 0.778568i \(0.284053\pi\)
\(620\) −40.7846 40.7846i −1.63795 1.63795i
\(621\) 5.70577 + 3.29423i 0.228965 + 0.132193i
\(622\) 16.0526 + 16.0526i 0.643649 + 0.643649i
\(623\) −0.732051 1.26795i −0.0293290 0.0507993i
\(624\) 11.3205 42.2487i 0.453183 1.69130i
\(625\) 11.9641 20.7224i 0.478564 0.828897i
\(626\) 38.8827 10.4186i 1.55406 0.416410i
\(627\) −2.30385 + 3.99038i −0.0920068 + 0.159360i
\(628\) 9.46410 + 2.53590i 0.377659 + 0.101193i
\(629\) −2.87564 + 2.87564i −0.114659 + 0.114659i
\(630\) 12.0000 0.478091
\(631\) 38.3923i 1.52837i 0.644995 + 0.764187i \(0.276859\pi\)
−0.644995 + 0.764187i \(0.723141\pi\)
\(632\) −8.78461 + 32.7846i −0.349433 + 1.30410i
\(633\) −5.19615 5.19615i −0.206529 0.206529i
\(634\) 23.0526 39.9282i 0.915534 1.58575i
\(635\) −6.19615 23.1244i −0.245887 0.917662i
\(636\) 1.85641 + 1.85641i 0.0736113 + 0.0736113i
\(637\) −10.5622 + 39.4186i −0.418489 + 1.56182i
\(638\) −7.26795 + 7.26795i −0.287741 + 0.287741i
\(639\) 28.3923 + 16.3923i 1.12318 + 0.648470i
\(640\) 43.7128 1.72790
\(641\) −4.20577 7.28461i −0.166118 0.287725i 0.770934 0.636915i \(-0.219790\pi\)
−0.937052 + 0.349191i \(0.886457\pi\)
\(642\) −40.4711 23.3660i −1.59727 0.922183i
\(643\) −45.6506 + 12.2321i −1.80029 + 0.482385i −0.994023 0.109173i \(-0.965180\pi\)
−0.806263 + 0.591558i \(0.798513\pi\)
\(644\) 1.60770 + 0.928203i 0.0633521 + 0.0365763i
\(645\) −7.39230 + 4.26795i −0.291072 + 0.168050i
\(646\) −1.43782 2.49038i −0.0565704 0.0979827i
\(647\) 13.2679i 0.521617i 0.965391 + 0.260808i \(0.0839891\pi\)
−0.965391 + 0.260808i \(0.916011\pi\)
\(648\) −6.58846 + 24.5885i −0.258819 + 0.965926i
\(649\) 15.2487i 0.598564i
\(650\) 76.7654 44.3205i 3.01099 1.73839i
\(651\) 8.19615 4.73205i 0.321233 0.185464i
\(652\) −5.12436 19.1244i −0.200685 0.748968i
\(653\) 5.63397 1.50962i 0.220474 0.0590760i −0.146891 0.989153i \(-0.546927\pi\)
0.367365 + 0.930077i \(0.380260\pi\)
\(654\) −12.5885 + 21.8038i −0.492248 + 0.852598i
\(655\) −6.19615 10.7321i −0.242104 0.419336i
\(656\) 12.0000i 0.468521i
\(657\) 25.2846 + 14.5981i 0.986447 + 0.569525i
\(658\) 7.07180 + 7.07180i 0.275687 + 0.275687i
\(659\) 4.02628 15.0263i 0.156842 0.585341i −0.842099 0.539323i \(-0.818680\pi\)
0.998941 0.0460178i \(-0.0146531\pi\)
\(660\) 39.7128 1.54582
\(661\) 2.19615 + 8.19615i 0.0854204 + 0.318793i 0.995393 0.0958740i \(-0.0305646\pi\)
−0.909973 + 0.414667i \(0.863898\pi\)
\(662\) 24.1244 + 13.9282i 0.937620 + 0.541335i
\(663\) 17.5359 + 17.5359i 0.681038 + 0.681038i
\(664\) −3.46410 + 2.00000i −0.134433 + 0.0776151i
\(665\) 2.53590i 0.0983379i
\(666\) 7.60770i 0.294792i
\(667\) 2.19615 2.19615i 0.0850354 0.0850354i
\(668\) −0.535898 0.928203i −0.0207345 0.0359133i
\(669\) 19.0981 33.0788i 0.738374 1.27890i
\(670\) 7.66025 + 28.5885i 0.295941 + 1.10447i
\(671\) 4.60770 7.98076i 0.177878 0.308094i
\(672\) −1.85641 + 6.92820i −0.0716124 + 0.267261i
\(673\) 8.80385 + 15.2487i 0.339363 + 0.587795i 0.984313 0.176430i \(-0.0564550\pi\)
−0.644950 + 0.764225i \(0.723122\pi\)
\(674\) 23.7846 23.7846i 0.916149 0.916149i
\(675\) −44.6769 + 25.7942i −1.71962 + 0.992820i
\(676\) 53.7128 2.06588
\(677\) 4.73205 + 1.26795i 0.181867 + 0.0487312i 0.348603 0.937270i \(-0.386656\pi\)
−0.166736 + 0.986002i \(0.553323\pi\)
\(678\) 32.7846 + 8.78461i 1.25909 + 0.337371i
\(679\) −5.24167 3.02628i −0.201157 0.116138i
\(680\) −12.3923 + 21.4641i −0.475223 + 0.823111i
\(681\) −24.9904 + 6.69615i −0.957633 + 0.256597i
\(682\) 27.1244 15.6603i 1.03865 0.599662i
\(683\) −4.70577 + 4.70577i −0.180061 + 0.180061i −0.791383 0.611321i \(-0.790638\pi\)
0.611321 + 0.791383i \(0.290638\pi\)
\(684\) 5.19615 + 1.39230i 0.198680 + 0.0532361i
\(685\) −44.9808 44.9808i −1.71863 1.71863i
\(686\) 3.60770 13.4641i 0.137742 0.514062i
\(687\) −8.66025 + 8.66025i −0.330409 + 0.330409i
\(688\) −1.32051 4.92820i −0.0503439 0.187886i
\(689\) −2.39230 + 4.14359i −0.0911396 + 0.157858i
\(690\) −12.0000 −0.456832
\(691\) −6.29423 + 23.4904i −0.239444 + 0.893616i 0.736651 + 0.676273i \(0.236406\pi\)
−0.976095 + 0.217344i \(0.930261\pi\)
\(692\) 18.3923 18.3923i 0.699171 0.699171i
\(693\) −1.68653 + 6.29423i −0.0640661 + 0.239098i
\(694\) 36.1962i 1.37399i
\(695\) −31.3923 + 18.1244i −1.19078 + 0.687496i
\(696\) 10.3923 + 6.00000i 0.393919 + 0.227429i
\(697\) −5.89230 3.40192i −0.223187 0.128857i
\(698\) −5.66025 + 9.80385i −0.214244 + 0.371081i
\(699\) 10.7942 6.23205i 0.408275 0.235718i
\(700\) −12.5885 + 7.26795i −0.475799 + 0.274703i
\(701\) 10.6603 + 10.6603i 0.402632 + 0.402632i 0.879160 0.476527i \(-0.158105\pi\)
−0.476527 + 0.879160i \(0.658105\pi\)
\(702\) −46.3923 −1.75096
\(703\) −1.60770 −0.0606354
\(704\) −6.14359 + 22.9282i −0.231545 + 0.864139i
\(705\) −62.4449 16.7321i −2.35181 0.630165i
\(706\) 7.43782 + 27.7583i 0.279926 + 1.04470i
\(707\) 5.46410 1.46410i 0.205499 0.0550632i
\(708\) −17.1962 + 4.60770i −0.646271 + 0.173168i
\(709\) −20.1962 5.41154i −0.758482 0.203235i −0.141205 0.989980i \(-0.545098\pi\)
−0.617277 + 0.786746i \(0.711764\pi\)
\(710\) −59.7128 −2.24098
\(711\) 36.0000 1.35011
\(712\) −4.00000 + 4.00000i −0.149906 + 0.149906i
\(713\) −8.19615 + 4.73205i −0.306948 + 0.177217i
\(714\) −2.87564 2.87564i −0.107618 0.107618i
\(715\) 18.7321 + 69.9090i 0.700539 + 2.61445i
\(716\) 8.73205 + 32.5885i 0.326332 + 1.21789i
\(717\) 45.3731 1.69449
\(718\) 5.39230 20.1244i 0.201239 0.751034i
\(719\) −16.3923 −0.611330 −0.305665 0.952139i \(-0.598879\pi\)
−0.305665 + 0.952139i \(0.598879\pi\)
\(720\) −12.0000 44.7846i −0.447214 1.66902i
\(721\) 6.67949 0.248757
\(722\) −6.66025 + 24.8564i −0.247869 + 0.925060i
\(723\) −11.0885 + 19.2058i −0.412384 + 0.714270i
\(724\) 36.5885 9.80385i 1.35980 0.364357i
\(725\) 6.29423 + 23.4904i 0.233762 + 0.872411i
\(726\) 1.39230 5.19615i 0.0516733 0.192847i
\(727\) 31.8109 18.3660i 1.17980 0.681158i 0.223832 0.974628i \(-0.428143\pi\)
0.955968 + 0.293470i \(0.0948099\pi\)
\(728\) −13.0718 −0.484473
\(729\) 27.0000 1.00000
\(730\) −53.1769 −1.96817
\(731\) 2.79423 + 0.748711i 0.103348 + 0.0276921i
\(732\) −10.3923 2.78461i −0.384111 0.102922i
\(733\) −29.9545 + 8.02628i −1.10639 + 0.296457i −0.765366 0.643596i \(-0.777442\pi\)
−0.341028 + 0.940053i \(0.610775\pi\)
\(734\) 7.41154 + 27.6603i 0.273565 + 1.02096i
\(735\) 11.1962 + 41.7846i 0.412976 + 1.54125i
\(736\) 1.85641 6.92820i 0.0684280 0.255377i
\(737\) −16.0718 −0.592012
\(738\) 12.2942 3.29423i 0.452557 0.121262i
\(739\) 21.2224 + 21.2224i 0.780680 + 0.780680i 0.979945 0.199266i \(-0.0638557\pi\)
−0.199266 + 0.979945i \(0.563856\pi\)
\(740\) 6.92820 + 12.0000i 0.254686 + 0.441129i
\(741\) 9.80385i 0.360153i
\(742\) 0.392305 0.679492i 0.0144020 0.0249449i
\(743\) 2.24167 + 1.29423i 0.0822389 + 0.0474806i 0.540556 0.841308i \(-0.318214\pi\)
−0.458317 + 0.888789i \(0.651547\pi\)
\(744\) −25.8564 25.8564i −0.947942 0.947942i
\(745\) 10.7321 6.19615i 0.393192 0.227009i
\(746\) 8.24871i 0.302007i
\(747\) 3.00000 + 3.00000i 0.109764 + 0.109764i
\(748\) −9.51666 9.51666i −0.347964 0.347964i
\(749\) −3.61474 + 13.4904i −0.132080 + 0.492928i
\(750\) 23.3205 40.3923i 0.851545 1.47492i
\(751\) 18.8564 32.6603i 0.688080 1.19179i −0.284378 0.958712i \(-0.591787\pi\)
0.972458 0.233077i \(-0.0748796\pi\)
\(752\) 19.3205 33.4641i 0.704546 1.22031i
\(753\) −6.69615 1.79423i −0.244021 0.0653853i
\(754\) −5.66025 + 21.1244i −0.206134 + 0.769304i
\(755\) 7.46410 + 7.46410i 0.271646 + 0.271646i
\(756\) 7.60770 0.276689
\(757\) −6.07180 + 6.07180i −0.220683 + 0.220683i −0.808786 0.588103i \(-0.799875\pi\)
0.588103 + 0.808786i \(0.299875\pi\)
\(758\) 32.4904 18.7583i 1.18010 0.681333i
\(759\) 1.68653 6.29423i 0.0612173 0.228466i
\(760\) −9.46410 + 2.53590i −0.343299 + 0.0919867i
\(761\) −27.3731 15.8038i −0.992273 0.572889i −0.0863200 0.996267i \(-0.527511\pi\)
−0.905953 + 0.423378i \(0.860844\pi\)
\(762\) −3.92820 14.6603i −0.142304 0.531085i
\(763\) 7.26795 + 1.94744i 0.263117 + 0.0705021i
\(764\) 28.1051i 1.01681i
\(765\) 25.3923 + 6.80385i 0.918061 + 0.245994i
\(766\) 6.53590 6.53590i 0.236152 0.236152i
\(767\) −16.2224 28.0981i −0.585758 1.01456i
\(768\) 27.7128 1.00000
\(769\) 10.1244 17.5359i 0.365094 0.632361i −0.623698 0.781666i \(-0.714370\pi\)
0.988791 + 0.149305i \(0.0477036\pi\)
\(770\) −3.07180 11.4641i −0.110700 0.413138i
\(771\) 15.3397 0.552447
\(772\) −31.6410 + 18.2679i −1.13879 + 0.657478i