Properties

Label 144.2.x.a.61.1
Level $144$
Weight $2$
Character 144.61
Analytic conductor $1.150$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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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: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 61.1
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 144.61
Dual form 144.2.x.a.85.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 + 1.00000i) q^{2} +1.73205 q^{3} -2.00000i q^{4} +(-1.86603 - 0.500000i) q^{5} +(-1.73205 + 1.73205i) q^{6} +(3.86603 + 2.23205i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000 q^{9} +O(q^{10})\) \(q+(-1.00000 + 1.00000i) q^{2} +1.73205 q^{3} -2.00000i q^{4} +(-1.86603 - 0.500000i) q^{5} +(-1.73205 + 1.73205i) q^{6} +(3.86603 + 2.23205i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000 q^{9} +(2.36603 - 1.36603i) q^{10} +(-0.500000 - 1.86603i) q^{11} -3.46410i q^{12} +(-0.598076 + 2.23205i) q^{13} +(-6.09808 + 1.63397i) q^{14} +(-3.23205 - 0.866025i) q^{15} -4.00000 q^{16} +4.00000 q^{17} +(-3.00000 + 3.00000i) q^{18} +(-3.00000 - 3.00000i) q^{19} +(-1.00000 + 3.73205i) q^{20} +(6.69615 + 3.86603i) q^{21} +(2.36603 + 1.36603i) q^{22} +(-5.59808 + 3.23205i) q^{23} +(3.46410 + 3.46410i) q^{24} +(-1.09808 - 0.633975i) q^{25} +(-1.63397 - 2.83013i) q^{26} +5.19615 q^{27} +(4.46410 - 7.73205i) q^{28} +(-0.866025 + 0.232051i) q^{29} +(4.09808 - 2.36603i) q^{30} +(-4.59808 - 7.96410i) q^{31} +(4.00000 - 4.00000i) q^{32} +(-0.866025 - 3.23205i) q^{33} +(-4.00000 + 4.00000i) q^{34} +(-6.09808 - 6.09808i) q^{35} -6.00000i q^{36} +(-4.26795 + 4.26795i) q^{37} +6.00000 q^{38} +(-1.03590 + 3.86603i) q^{39} +(-2.73205 - 4.73205i) q^{40} +(0.696152 - 0.401924i) q^{41} +(-10.5622 + 2.83013i) q^{42} +(-1.69615 - 6.33013i) q^{43} +(-3.73205 + 1.00000i) q^{44} +(-5.59808 - 1.50000i) q^{45} +(2.36603 - 8.83013i) q^{46} +(-0.598076 + 1.03590i) q^{47} -6.92820 q^{48} +(6.46410 + 11.1962i) q^{49} +(1.73205 - 0.464102i) q^{50} +6.92820 q^{51} +(4.46410 + 1.19615i) q^{52} +(5.73205 - 5.73205i) q^{53} +(-5.19615 + 5.19615i) q^{54} +3.73205i q^{55} +(3.26795 + 12.1962i) q^{56} +(-5.19615 - 5.19615i) q^{57} +(0.633975 - 1.09808i) q^{58} +(-1.50000 - 0.401924i) q^{59} +(-1.73205 + 6.46410i) q^{60} +(-2.13397 + 0.571797i) q^{61} +(12.5622 + 3.36603i) q^{62} +(11.5981 + 6.69615i) q^{63} +8.00000i q^{64} +(2.23205 - 3.86603i) q^{65} +(4.09808 + 2.36603i) q^{66} +(-2.23205 + 8.33013i) q^{67} -8.00000i q^{68} +(-9.69615 + 5.59808i) q^{69} +12.1962 q^{70} -2.92820i q^{71} +(6.00000 + 6.00000i) q^{72} +7.46410i q^{73} -8.53590i q^{74} +(-1.90192 - 1.09808i) q^{75} +(-6.00000 + 6.00000i) q^{76} +(2.23205 - 8.33013i) q^{77} +(-2.83013 - 4.90192i) q^{78} +(-0.866025 + 1.50000i) q^{79} +(7.46410 + 2.00000i) q^{80} +9.00000 q^{81} +(-0.294229 + 1.09808i) q^{82} +(-14.1603 + 3.79423i) q^{83} +(7.73205 - 13.3923i) q^{84} +(-7.46410 - 2.00000i) q^{85} +(8.02628 + 4.63397i) q^{86} +(-1.50000 + 0.401924i) q^{87} +(2.73205 - 4.73205i) q^{88} +15.8564i q^{89} +(7.09808 - 4.09808i) q^{90} +(-7.29423 + 7.29423i) q^{91} +(6.46410 + 11.1962i) q^{92} +(-7.96410 - 13.7942i) q^{93} +(-0.437822 - 1.63397i) q^{94} +(4.09808 + 7.09808i) q^{95} +(6.92820 - 6.92820i) q^{96} +(-0.500000 + 0.866025i) q^{97} +(-17.6603 - 4.73205i) q^{98} +(-1.50000 - 5.59808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{2} - 4 q^{5} + 12 q^{7} + 8 q^{8} + 12 q^{9} + O(q^{10}) \) \( 4 q - 4 q^{2} - 4 q^{5} + 12 q^{7} + 8 q^{8} + 12 q^{9} + 6 q^{10} - 2 q^{11} + 8 q^{13} - 14 q^{14} - 6 q^{15} - 16 q^{16} + 16 q^{17} - 12 q^{18} - 12 q^{19} - 4 q^{20} + 6 q^{21} + 6 q^{22} - 12 q^{23} + 6 q^{25} - 10 q^{26} + 4 q^{28} + 6 q^{30} - 8 q^{31} + 16 q^{32} - 16 q^{34} - 14 q^{35} - 24 q^{37} + 24 q^{38} - 18 q^{39} - 4 q^{40} - 18 q^{41} - 18 q^{42} + 14 q^{43} - 8 q^{44} - 12 q^{45} + 6 q^{46} + 8 q^{47} + 12 q^{49} + 4 q^{52} + 16 q^{53} + 20 q^{56} + 6 q^{58} - 6 q^{59} - 12 q^{61} + 26 q^{62} + 36 q^{63} + 2 q^{65} + 6 q^{66} - 2 q^{67} - 18 q^{69} + 28 q^{70} + 24 q^{72} - 18 q^{75} - 24 q^{76} + 2 q^{77} + 6 q^{78} + 16 q^{80} + 36 q^{81} + 30 q^{82} - 22 q^{83} + 24 q^{84} - 16 q^{85} - 6 q^{86} - 6 q^{87} + 4 q^{88} + 18 q^{90} + 2 q^{91} + 12 q^{92} - 18 q^{93} - 26 q^{94} + 6 q^{95} - 2 q^{97} - 36 q^{98} - 6 q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 + 1.00000i −0.707107 + 0.707107i
\(3\) 1.73205 1.00000
\(4\) 2.00000i 1.00000i
\(5\) −1.86603 0.500000i −0.834512 0.223607i −0.183831 0.982958i \(-0.558850\pi\)
−0.650681 + 0.759351i \(0.725517\pi\)
\(6\) −1.73205 + 1.73205i −0.707107 + 0.707107i
\(7\) 3.86603 + 2.23205i 1.46122 + 0.843636i 0.999068 0.0431647i \(-0.0137440\pi\)
0.462152 + 0.886801i \(0.347077\pi\)
\(8\) 2.00000 + 2.00000i 0.707107 + 0.707107i
\(9\) 3.00000 1.00000
\(10\) 2.36603 1.36603i 0.748203 0.431975i
\(11\) −0.500000 1.86603i −0.150756 0.562628i −0.999432 0.0337145i \(-0.989266\pi\)
0.848676 0.528913i \(-0.177400\pi\)
\(12\) 3.46410i 1.00000i
\(13\) −0.598076 + 2.23205i −0.165876 + 0.619060i 0.832050 + 0.554700i \(0.187167\pi\)
−0.997927 + 0.0643593i \(0.979500\pi\)
\(14\) −6.09808 + 1.63397i −1.62978 + 0.436698i
\(15\) −3.23205 0.866025i −0.834512 0.223607i
\(16\) −4.00000 −1.00000
\(17\) 4.00000 0.970143 0.485071 0.874475i \(-0.338794\pi\)
0.485071 + 0.874475i \(0.338794\pi\)
\(18\) −3.00000 + 3.00000i −0.707107 + 0.707107i
\(19\) −3.00000 3.00000i −0.688247 0.688247i 0.273597 0.961844i \(-0.411786\pi\)
−0.961844 + 0.273597i \(0.911786\pi\)
\(20\) −1.00000 + 3.73205i −0.223607 + 0.834512i
\(21\) 6.69615 + 3.86603i 1.46122 + 0.843636i
\(22\) 2.36603 + 1.36603i 0.504438 + 0.291238i
\(23\) −5.59808 + 3.23205i −1.16728 + 0.673929i −0.953038 0.302851i \(-0.902061\pi\)
−0.214242 + 0.976781i \(0.568728\pi\)
\(24\) 3.46410 + 3.46410i 0.707107 + 0.707107i
\(25\) −1.09808 0.633975i −0.219615 0.126795i
\(26\) −1.63397 2.83013i −0.320449 0.555034i
\(27\) 5.19615 1.00000
\(28\) 4.46410 7.73205i 0.843636 1.46122i
\(29\) −0.866025 + 0.232051i −0.160817 + 0.0430908i −0.338329 0.941028i \(-0.609862\pi\)
0.177512 + 0.984119i \(0.443195\pi\)
\(30\) 4.09808 2.36603i 0.748203 0.431975i
\(31\) −4.59808 7.96410i −0.825839 1.43039i −0.901277 0.433244i \(-0.857369\pi\)
0.0754376 0.997151i \(-0.475965\pi\)
\(32\) 4.00000 4.00000i 0.707107 0.707107i
\(33\) −0.866025 3.23205i −0.150756 0.562628i
\(34\) −4.00000 + 4.00000i −0.685994 + 0.685994i
\(35\) −6.09808 6.09808i −1.03076 1.03076i
\(36\) 6.00000i 1.00000i
\(37\) −4.26795 + 4.26795i −0.701647 + 0.701647i −0.964764 0.263117i \(-0.915249\pi\)
0.263117 + 0.964764i \(0.415249\pi\)
\(38\) 6.00000 0.973329
\(39\) −1.03590 + 3.86603i −0.165876 + 0.619060i
\(40\) −2.73205 4.73205i −0.431975 0.748203i
\(41\) 0.696152 0.401924i 0.108721 0.0627700i −0.444654 0.895703i \(-0.646673\pi\)
0.553374 + 0.832933i \(0.313340\pi\)
\(42\) −10.5622 + 2.83013i −1.62978 + 0.436698i
\(43\) −1.69615 6.33013i −0.258661 0.965335i −0.966017 0.258478i \(-0.916779\pi\)
0.707356 0.706857i \(-0.249888\pi\)
\(44\) −3.73205 + 1.00000i −0.562628 + 0.150756i
\(45\) −5.59808 1.50000i −0.834512 0.223607i
\(46\) 2.36603 8.83013i 0.348851 1.30193i
\(47\) −0.598076 + 1.03590i −0.0872384 + 0.151101i −0.906343 0.422543i \(-0.861138\pi\)
0.819104 + 0.573644i \(0.194471\pi\)
\(48\) −6.92820 −1.00000
\(49\) 6.46410 + 11.1962i 0.923443 + 1.59945i
\(50\) 1.73205 0.464102i 0.244949 0.0656339i
\(51\) 6.92820 0.970143
\(52\) 4.46410 + 1.19615i 0.619060 + 0.165876i
\(53\) 5.73205 5.73205i 0.787358 0.787358i −0.193703 0.981060i \(-0.562050\pi\)
0.981060 + 0.193703i \(0.0620497\pi\)
\(54\) −5.19615 + 5.19615i −0.707107 + 0.707107i
\(55\) 3.73205i 0.503230i
\(56\) 3.26795 + 12.1962i 0.436698 + 1.62978i
\(57\) −5.19615 5.19615i −0.688247 0.688247i
\(58\) 0.633975 1.09808i 0.0832449 0.144184i
\(59\) −1.50000 0.401924i −0.195283 0.0523260i 0.159852 0.987141i \(-0.448898\pi\)
−0.355135 + 0.934815i \(0.615565\pi\)
\(60\) −1.73205 + 6.46410i −0.223607 + 0.834512i
\(61\) −2.13397 + 0.571797i −0.273227 + 0.0732111i −0.392831 0.919611i \(-0.628504\pi\)
0.119604 + 0.992822i \(0.461838\pi\)
\(62\) 12.5622 + 3.36603i 1.59540 + 0.427486i
\(63\) 11.5981 + 6.69615i 1.46122 + 0.843636i
\(64\) 8.00000i 1.00000i
\(65\) 2.23205 3.86603i 0.276852 0.479521i
\(66\) 4.09808 + 2.36603i 0.504438 + 0.291238i
\(67\) −2.23205 + 8.33013i −0.272688 + 1.01769i 0.684686 + 0.728838i \(0.259939\pi\)
−0.957375 + 0.288849i \(0.906727\pi\)
\(68\) 8.00000i 0.970143i
\(69\) −9.69615 + 5.59808i −1.16728 + 0.673929i
\(70\) 12.1962 1.45772
\(71\) 2.92820i 0.347514i −0.984789 0.173757i \(-0.944409\pi\)
0.984789 0.173757i \(-0.0555907\pi\)
\(72\) 6.00000 + 6.00000i 0.707107 + 0.707107i
\(73\) 7.46410i 0.873607i 0.899557 + 0.436804i \(0.143889\pi\)
−0.899557 + 0.436804i \(0.856111\pi\)
\(74\) 8.53590i 0.992278i
\(75\) −1.90192 1.09808i −0.219615 0.126795i
\(76\) −6.00000 + 6.00000i −0.688247 + 0.688247i
\(77\) 2.23205 8.33013i 0.254366 0.949306i
\(78\) −2.83013 4.90192i −0.320449 0.555034i
\(79\) −0.866025 + 1.50000i −0.0974355 + 0.168763i −0.910622 0.413239i \(-0.864397\pi\)
0.813187 + 0.582003i \(0.197731\pi\)
\(80\) 7.46410 + 2.00000i 0.834512 + 0.223607i
\(81\) 9.00000 1.00000
\(82\) −0.294229 + 1.09808i −0.0324921 + 0.121262i
\(83\) −14.1603 + 3.79423i −1.55429 + 0.416471i −0.930850 0.365401i \(-0.880932\pi\)
−0.623440 + 0.781872i \(0.714265\pi\)
\(84\) 7.73205 13.3923i 0.843636 1.46122i
\(85\) −7.46410 2.00000i −0.809595 0.216930i
\(86\) 8.02628 + 4.63397i 0.865496 + 0.499694i
\(87\) −1.50000 + 0.401924i −0.160817 + 0.0430908i
\(88\) 2.73205 4.73205i 0.291238 0.504438i
\(89\) 15.8564i 1.68078i 0.541985 + 0.840388i \(0.317673\pi\)
−0.541985 + 0.840388i \(0.682327\pi\)
\(90\) 7.09808 4.09808i 0.748203 0.431975i
\(91\) −7.29423 + 7.29423i −0.764643 + 0.764643i
\(92\) 6.46410 + 11.1962i 0.673929 + 1.16728i
\(93\) −7.96410 13.7942i −0.825839 1.43039i
\(94\) −0.437822 1.63397i −0.0451579 0.168532i
\(95\) 4.09808 + 7.09808i 0.420454 + 0.728247i
\(96\) 6.92820 6.92820i 0.707107 0.707107i
\(97\) −0.500000 + 0.866025i −0.0507673 + 0.0879316i −0.890292 0.455389i \(-0.849500\pi\)
0.839525 + 0.543321i \(0.182833\pi\)
\(98\) −17.6603 4.73205i −1.78396 0.478009i
\(99\) −1.50000 5.59808i −0.150756 0.562628i
\(100\) −1.26795 + 2.19615i −0.126795 + 0.219615i
\(101\) −0.133975 0.500000i −0.0133310 0.0497519i 0.958940 0.283609i \(-0.0915318\pi\)
−0.972271 + 0.233857i \(0.924865\pi\)
\(102\) −6.92820 + 6.92820i −0.685994 + 0.685994i
\(103\) 13.7942 7.96410i 1.35919 0.784726i 0.369672 0.929162i \(-0.379470\pi\)
0.989514 + 0.144436i \(0.0461369\pi\)
\(104\) −5.66025 + 3.26795i −0.555034 + 0.320449i
\(105\) −10.5622 10.5622i −1.03076 1.03076i
\(106\) 11.4641i 1.11349i
\(107\) 9.39230 9.39230i 0.907988 0.907988i −0.0881214 0.996110i \(-0.528086\pi\)
0.996110 + 0.0881214i \(0.0280863\pi\)
\(108\) 10.3923i 1.00000i
\(109\) −1.73205 1.73205i −0.165900 0.165900i 0.619274 0.785175i \(-0.287427\pi\)
−0.785175 + 0.619274i \(0.787427\pi\)
\(110\) −3.73205 3.73205i −0.355837 0.355837i
\(111\) −7.39230 + 7.39230i −0.701647 + 0.701647i
\(112\) −15.4641 8.92820i −1.46122 0.843636i
\(113\) −6.23205 10.7942i −0.586262 1.01544i −0.994717 0.102657i \(-0.967266\pi\)
0.408455 0.912779i \(-0.366068\pi\)
\(114\) 10.3923 0.973329
\(115\) 12.0622 3.23205i 1.12480 0.301390i
\(116\) 0.464102 + 1.73205i 0.0430908 + 0.160817i
\(117\) −1.79423 + 6.69615i −0.165876 + 0.619060i
\(118\) 1.90192 1.09808i 0.175086 0.101086i
\(119\) 15.4641 + 8.92820i 1.41759 + 0.818447i
\(120\) −4.73205 8.19615i −0.431975 0.748203i
\(121\) 6.29423 3.63397i 0.572203 0.330361i
\(122\) 1.56218 2.70577i 0.141433 0.244969i
\(123\) 1.20577 0.696152i 0.108721 0.0627700i
\(124\) −15.9282 + 9.19615i −1.43039 + 0.825839i
\(125\) 8.56218 + 8.56218i 0.765824 + 0.765824i
\(126\) −18.2942 + 4.90192i −1.62978 + 0.436698i
\(127\) 0.392305 0.0348114 0.0174057 0.999849i \(-0.494459\pi\)
0.0174057 + 0.999849i \(0.494459\pi\)
\(128\) −8.00000 8.00000i −0.707107 0.707107i
\(129\) −2.93782 10.9641i −0.258661 0.965335i
\(130\) 1.63397 + 6.09808i 0.143309 + 0.534837i
\(131\) 1.30385 4.86603i 0.113918 0.425147i −0.885286 0.465047i \(-0.846037\pi\)
0.999204 + 0.0399004i \(0.0127041\pi\)
\(132\) −6.46410 + 1.73205i −0.562628 + 0.150756i
\(133\) −4.90192 18.2942i −0.425051 1.58631i
\(134\) −6.09808 10.5622i −0.526794 0.912433i
\(135\) −9.69615 2.59808i −0.834512 0.223607i
\(136\) 8.00000 + 8.00000i 0.685994 + 0.685994i
\(137\) −0.571797 0.330127i −0.0488519 0.0282047i 0.475375 0.879783i \(-0.342312\pi\)
−0.524227 + 0.851579i \(0.675646\pi\)
\(138\) 4.09808 15.2942i 0.348851 1.30193i
\(139\) 16.1603 + 4.33013i 1.37069 + 0.367277i 0.867732 0.497032i \(-0.165577\pi\)
0.502962 + 0.864308i \(0.332243\pi\)
\(140\) −12.1962 + 12.1962i −1.03076 + 1.03076i
\(141\) −1.03590 + 1.79423i −0.0872384 + 0.151101i
\(142\) 2.92820 + 2.92820i 0.245729 + 0.245729i
\(143\) 4.46410 0.373307
\(144\) −12.0000 −1.00000
\(145\) 1.73205 0.143839
\(146\) −7.46410 7.46410i −0.617733 0.617733i
\(147\) 11.1962 + 19.3923i 0.923443 + 1.59945i
\(148\) 8.53590 + 8.53590i 0.701647 + 0.701647i
\(149\) 16.0622 + 4.30385i 1.31586 + 0.352585i 0.847427 0.530912i \(-0.178150\pi\)
0.468438 + 0.883497i \(0.344817\pi\)
\(150\) 3.00000 0.803848i 0.244949 0.0656339i
\(151\) −6.06218 3.50000i −0.493333 0.284826i 0.232623 0.972567i \(-0.425269\pi\)
−0.725956 + 0.687741i \(0.758602\pi\)
\(152\) 12.0000i 0.973329i
\(153\) 12.0000 0.970143
\(154\) 6.09808 + 10.5622i 0.491397 + 0.851125i
\(155\) 4.59808 + 17.1603i 0.369326 + 1.37834i
\(156\) 7.73205 + 2.07180i 0.619060 + 0.165876i
\(157\) −0.866025 + 3.23205i −0.0691164 + 0.257946i −0.991835 0.127529i \(-0.959296\pi\)
0.922719 + 0.385474i \(0.125962\pi\)
\(158\) −0.633975 2.36603i −0.0504363 0.188231i
\(159\) 9.92820 9.92820i 0.787358 0.787358i
\(160\) −9.46410 + 5.46410i −0.748203 + 0.431975i
\(161\) −28.8564 −2.27420
\(162\) −9.00000 + 9.00000i −0.707107 + 0.707107i
\(163\) −1.92820 1.92820i −0.151029 0.151029i 0.627549 0.778577i \(-0.284058\pi\)
−0.778577 + 0.627549i \(0.784058\pi\)
\(164\) −0.803848 1.39230i −0.0627700 0.108721i
\(165\) 6.46410i 0.503230i
\(166\) 10.3660 17.9545i 0.804560 1.39354i
\(167\) −14.2583 + 8.23205i −1.10334 + 0.637015i −0.937097 0.349069i \(-0.886498\pi\)
−0.166246 + 0.986084i \(0.553165\pi\)
\(168\) 5.66025 + 21.1244i 0.436698 + 1.62978i
\(169\) 6.63397 + 3.83013i 0.510306 + 0.294625i
\(170\) 9.46410 5.46410i 0.725863 0.419077i
\(171\) −9.00000 9.00000i −0.688247 0.688247i
\(172\) −12.6603 + 3.39230i −0.965335 + 0.258661i
\(173\) 7.59808 2.03590i 0.577671 0.154786i 0.0418586 0.999124i \(-0.486672\pi\)
0.535812 + 0.844337i \(0.320005\pi\)
\(174\) 1.09808 1.90192i 0.0832449 0.144184i
\(175\) −2.83013 4.90192i −0.213937 0.370551i
\(176\) 2.00000 + 7.46410i 0.150756 + 0.562628i
\(177\) −2.59808 0.696152i −0.195283 0.0523260i
\(178\) −15.8564 15.8564i −1.18849 1.18849i
\(179\) −5.92820 5.92820i −0.443095 0.443095i 0.449956 0.893051i \(-0.351440\pi\)
−0.893051 + 0.449956i \(0.851440\pi\)
\(180\) −3.00000 + 11.1962i −0.223607 + 0.834512i
\(181\) −7.73205 + 7.73205i −0.574719 + 0.574719i −0.933443 0.358725i \(-0.883212\pi\)
0.358725 + 0.933443i \(0.383212\pi\)
\(182\) 14.5885i 1.08137i
\(183\) −3.69615 + 0.990381i −0.273227 + 0.0732111i
\(184\) −17.6603 4.73205i −1.30193 0.348851i
\(185\) 10.0981 5.83013i 0.742425 0.428639i
\(186\) 21.7583 + 5.83013i 1.59540 + 0.427486i
\(187\) −2.00000 7.46410i −0.146254 0.545829i
\(188\) 2.07180 + 1.19615i 0.151101 + 0.0872384i
\(189\) 20.0885 + 11.5981i 1.46122 + 0.843636i
\(190\) −11.1962 3.00000i −0.812254 0.217643i
\(191\) 1.40192 2.42820i 0.101440 0.175699i −0.810838 0.585270i \(-0.800988\pi\)
0.912278 + 0.409572i \(0.134322\pi\)
\(192\) 13.8564i 1.00000i
\(193\) 2.23205 + 3.86603i 0.160667 + 0.278283i 0.935108 0.354363i \(-0.115302\pi\)
−0.774441 + 0.632646i \(0.781969\pi\)
\(194\) −0.366025 1.36603i −0.0262791 0.0980749i
\(195\) 3.86603 6.69615i 0.276852 0.479521i
\(196\) 22.3923 12.9282i 1.59945 0.923443i
\(197\) 3.53590 3.53590i 0.251922 0.251922i −0.569836 0.821758i \(-0.692993\pi\)
0.821758 + 0.569836i \(0.192993\pi\)
\(198\) 7.09808 + 4.09808i 0.504438 + 0.291238i
\(199\) 21.8564i 1.54936i −0.632354 0.774680i \(-0.717911\pi\)
0.632354 0.774680i \(-0.282089\pi\)
\(200\) −0.928203 3.46410i −0.0656339 0.244949i
\(201\) −3.86603 + 14.4282i −0.272688 + 1.01769i
\(202\) 0.633975 + 0.366025i 0.0446063 + 0.0257535i
\(203\) −3.86603 1.03590i −0.271342 0.0727058i
\(204\) 13.8564i 0.970143i
\(205\) −1.50000 + 0.401924i −0.104765 + 0.0280716i
\(206\) −5.83013 + 21.7583i −0.406204 + 1.51597i
\(207\) −16.7942 + 9.69615i −1.16728 + 0.673929i
\(208\) 2.39230 8.92820i 0.165876 0.619060i
\(209\) −4.09808 + 7.09808i −0.283470 + 0.490984i
\(210\) 21.1244 1.45772
\(211\) −4.96410 + 18.5263i −0.341743 + 1.27540i 0.554629 + 0.832098i \(0.312860\pi\)
−0.896371 + 0.443304i \(0.853806\pi\)
\(212\) −11.4641 11.4641i −0.787358 0.787358i
\(213\) 5.07180i 0.347514i
\(214\) 18.7846i 1.28409i
\(215\) 12.6603i 0.863422i
\(216\) 10.3923 + 10.3923i 0.707107 + 0.707107i
\(217\) 41.0526i 2.78683i
\(218\) 3.46410 0.234619
\(219\) 12.9282i 0.873607i
\(220\) 7.46410 0.503230
\(221\) −2.39230 + 8.92820i −0.160924 + 0.600576i
\(222\) 14.7846i 0.992278i
\(223\) 7.79423 13.5000i 0.521940 0.904027i −0.477734 0.878504i \(-0.658542\pi\)
0.999674 0.0255224i \(-0.00812491\pi\)
\(224\) 24.3923 6.53590i 1.62978 0.436698i
\(225\) −3.29423 1.90192i −0.219615 0.126795i
\(226\) 17.0263 + 4.56218i 1.13257 + 0.303472i
\(227\) 19.6244 5.25833i 1.30251 0.349008i 0.460114 0.887860i \(-0.347809\pi\)
0.842400 + 0.538852i \(0.181142\pi\)
\(228\) −10.3923 + 10.3923i −0.688247 + 0.688247i
\(229\) 16.5263 + 4.42820i 1.09209 + 0.292624i 0.759539 0.650462i \(-0.225425\pi\)
0.332549 + 0.943086i \(0.392091\pi\)
\(230\) −8.83013 + 15.2942i −0.582241 + 1.00847i
\(231\) 3.86603 14.4282i 0.254366 0.949306i
\(232\) −2.19615 1.26795i −0.144184 0.0832449i
\(233\) 9.07180i 0.594313i 0.954829 + 0.297157i \(0.0960383\pi\)
−0.954829 + 0.297157i \(0.903962\pi\)
\(234\) −4.90192 8.49038i −0.320449 0.555034i
\(235\) 1.63397 1.63397i 0.106589 0.106589i
\(236\) −0.803848 + 3.00000i −0.0523260 + 0.195283i
\(237\) −1.50000 + 2.59808i −0.0974355 + 0.168763i
\(238\) −24.3923 + 6.53590i −1.58112 + 0.423659i
\(239\) −0.401924 0.696152i −0.0259983 0.0450304i 0.852734 0.522346i \(-0.174943\pi\)
−0.878732 + 0.477316i \(0.841610\pi\)
\(240\) 12.9282 + 3.46410i 0.834512 + 0.223607i
\(241\) −2.76795 + 4.79423i −0.178299 + 0.308823i −0.941298 0.337576i \(-0.890393\pi\)
0.762999 + 0.646400i \(0.223726\pi\)
\(242\) −2.66025 + 9.92820i −0.171008 + 0.638209i
\(243\) 15.5885 1.00000
\(244\) 1.14359 + 4.26795i 0.0732111 + 0.273227i
\(245\) −6.46410 24.1244i −0.412976 1.54125i
\(246\) −0.509619 + 1.90192i −0.0324921 + 0.121262i
\(247\) 8.49038 4.90192i 0.540230 0.311902i
\(248\) 6.73205 25.1244i 0.427486 1.59540i
\(249\) −24.5263 + 6.57180i −1.55429 + 0.416471i
\(250\) −17.1244 −1.08304
\(251\) −13.3923 + 13.3923i −0.845315 + 0.845315i −0.989544 0.144229i \(-0.953930\pi\)
0.144229 + 0.989544i \(0.453930\pi\)
\(252\) 13.3923 23.1962i 0.843636 1.46122i
\(253\) 8.83013 + 8.83013i 0.555145 + 0.555145i
\(254\) −0.392305 + 0.392305i −0.0246154 + 0.0246154i
\(255\) −12.9282 3.46410i −0.809595 0.216930i
\(256\) 16.0000 1.00000
\(257\) 12.1603 + 21.0622i 0.758536 + 1.31382i 0.943597 + 0.331096i \(0.107418\pi\)
−0.185061 + 0.982727i \(0.559248\pi\)
\(258\) 13.9019 + 8.02628i 0.865496 + 0.499694i
\(259\) −26.0263 + 6.97372i −1.61719 + 0.433326i
\(260\) −7.73205 4.46410i −0.479521 0.276852i
\(261\) −2.59808 + 0.696152i −0.160817 + 0.0430908i
\(262\) 3.56218 + 6.16987i 0.220072 + 0.381176i
\(263\) −8.59808 4.96410i −0.530180 0.306100i 0.210910 0.977506i \(-0.432357\pi\)
−0.741090 + 0.671406i \(0.765691\pi\)
\(264\) 4.73205 8.19615i 0.291238 0.504438i
\(265\) −13.5622 + 7.83013i −0.833118 + 0.481001i
\(266\) 23.1962 + 13.3923i 1.42225 + 0.821135i
\(267\) 27.4641i 1.68078i
\(268\) 16.6603 + 4.46410i 1.01769 + 0.272688i
\(269\) 4.26795 + 4.26795i 0.260221 + 0.260221i 0.825144 0.564923i \(-0.191094\pi\)
−0.564923 + 0.825144i \(0.691094\pi\)
\(270\) 12.2942 7.09808i 0.748203 0.431975i
\(271\) −1.07180 −0.0651070 −0.0325535 0.999470i \(-0.510364\pi\)
−0.0325535 + 0.999470i \(0.510364\pi\)
\(272\) −16.0000 −0.970143
\(273\) −12.6340 + 12.6340i −0.764643 + 0.764643i
\(274\) 0.901924 0.241670i 0.0544872 0.0145998i
\(275\) −0.633975 + 2.36603i −0.0382301 + 0.142677i
\(276\) 11.1962 + 19.3923i 0.673929 + 1.16728i
\(277\) −1.79423 6.69615i −0.107805 0.402333i 0.890844 0.454310i \(-0.150114\pi\)
−0.998648 + 0.0519775i \(0.983448\pi\)
\(278\) −20.4904 + 11.8301i −1.22893 + 0.709524i
\(279\) −13.7942 23.8923i −0.825839 1.43039i
\(280\) 24.3923i 1.45772i
\(281\) −10.0359 5.79423i −0.598692 0.345655i 0.169835 0.985472i \(-0.445676\pi\)
−0.768527 + 0.639818i \(0.779010\pi\)
\(282\) −0.758330 2.83013i −0.0451579 0.168532i
\(283\) −13.1603 3.52628i −0.782296 0.209616i −0.154499 0.987993i \(-0.549376\pi\)
−0.627797 + 0.778377i \(0.716043\pi\)
\(284\) −5.85641 −0.347514
\(285\) 7.09808 + 12.2942i 0.420454 + 0.728247i
\(286\) −4.46410 + 4.46410i −0.263968 + 0.263968i
\(287\) 3.58846 0.211820
\(288\) 12.0000 12.0000i 0.707107 0.707107i
\(289\) −1.00000 −0.0588235
\(290\) −1.73205 + 1.73205i −0.101710 + 0.101710i
\(291\) −0.866025 + 1.50000i −0.0507673 + 0.0879316i
\(292\) 14.9282 0.873607
\(293\) 2.13397 + 0.571797i 0.124668 + 0.0334047i 0.320614 0.947210i \(-0.396111\pi\)
−0.195945 + 0.980615i \(0.562778\pi\)
\(294\) −30.5885 8.19615i −1.78396 0.478009i
\(295\) 2.59808 + 1.50000i 0.151266 + 0.0873334i
\(296\) −17.0718 −0.992278
\(297\) −2.59808 9.69615i −0.150756 0.562628i
\(298\) −20.3660 + 11.7583i −1.17977 + 0.681142i
\(299\) −3.86603 14.4282i −0.223578 0.834405i
\(300\) −2.19615 + 3.80385i −0.126795 + 0.219615i
\(301\) 7.57180 28.2583i 0.436431 1.62878i
\(302\) 9.56218 2.56218i 0.550242 0.147437i
\(303\) −0.232051 0.866025i −0.0133310 0.0497519i
\(304\) 12.0000 + 12.0000i 0.688247 + 0.688247i
\(305\) 4.26795 0.244382
\(306\) −12.0000 + 12.0000i −0.685994 + 0.685994i
\(307\) 7.92820 + 7.92820i 0.452486 + 0.452486i 0.896179 0.443693i \(-0.146332\pi\)
−0.443693 + 0.896179i \(0.646332\pi\)
\(308\) −16.6603 4.46410i −0.949306 0.254366i
\(309\) 23.8923 13.7942i 1.35919 0.784726i
\(310\) −21.7583 12.5622i −1.23579 0.713484i
\(311\) 9.18653 5.30385i 0.520921 0.300754i −0.216391 0.976307i \(-0.569428\pi\)
0.737311 + 0.675553i \(0.236095\pi\)
\(312\) −9.80385 + 5.66025i −0.555034 + 0.320449i
\(313\) 25.1603 + 14.5263i 1.42214 + 0.821074i 0.996482 0.0838094i \(-0.0267087\pi\)
0.425660 + 0.904883i \(0.360042\pi\)
\(314\) −2.36603 4.09808i −0.133523 0.231268i
\(315\) −18.2942 18.2942i −1.03076 1.03076i
\(316\) 3.00000 + 1.73205i 0.168763 + 0.0974355i
\(317\) −33.4545 + 8.96410i −1.87899 + 0.503474i −0.879364 + 0.476150i \(0.842032\pi\)
−0.999627 + 0.0273246i \(0.991301\pi\)
\(318\) 19.8564i 1.11349i
\(319\) 0.866025 + 1.50000i 0.0484881 + 0.0839839i
\(320\) 4.00000 14.9282i 0.223607 0.834512i
\(321\) 16.2679 16.2679i 0.907988 0.907988i
\(322\) 28.8564 28.8564i 1.60810 1.60810i
\(323\) −12.0000 12.0000i −0.667698 0.667698i
\(324\) 18.0000i 1.00000i
\(325\) 2.07180 2.07180i 0.114923 0.114923i
\(326\) 3.85641 0.213587
\(327\) −3.00000 3.00000i −0.165900 0.165900i
\(328\) 2.19615 + 0.588457i 0.121262 + 0.0324921i
\(329\) −4.62436 + 2.66987i −0.254949 + 0.147195i
\(330\) −6.46410 6.46410i −0.355837 0.355837i
\(331\) 1.35641 + 5.06218i 0.0745548 + 0.278242i 0.993132 0.116999i \(-0.0373275\pi\)
−0.918577 + 0.395242i \(0.870661\pi\)
\(332\) 7.58846 + 28.3205i 0.416471 + 1.55429i
\(333\) −12.8038 + 12.8038i −0.701647 + 0.701647i
\(334\) 6.02628 22.4904i 0.329743 1.23062i
\(335\) 8.33013 14.4282i 0.455123 0.788297i
\(336\) −26.7846 15.4641i −1.46122 0.843636i
\(337\) −9.69615 16.7942i −0.528183 0.914840i −0.999460 0.0328547i \(-0.989540\pi\)
0.471277 0.881985i \(-0.343793\pi\)
\(338\) −10.4641 + 2.80385i −0.569172 + 0.152509i
\(339\) −10.7942 18.6962i −0.586262 1.01544i
\(340\) −4.00000 + 14.9282i −0.216930 + 0.809595i
\(341\) −12.5622 + 12.5622i −0.680280 + 0.680280i
\(342\) 18.0000 0.973329
\(343\) 26.4641i 1.42893i
\(344\) 9.26795 16.0526i 0.499694 0.865496i
\(345\) 20.8923 5.59808i 1.12480 0.301390i
\(346\) −5.56218 + 9.63397i −0.299025 + 0.517926i
\(347\) −1.76795 0.473721i −0.0949085 0.0254307i 0.211052 0.977475i \(-0.432311\pi\)
−0.305961 + 0.952044i \(0.598978\pi\)
\(348\) 0.803848 + 3.00000i 0.0430908 + 0.160817i
\(349\) −3.86603 + 1.03590i −0.206944 + 0.0554504i −0.360802 0.932643i \(-0.617497\pi\)
0.153858 + 0.988093i \(0.450830\pi\)
\(350\) 7.73205 + 2.07180i 0.413296 + 0.110742i
\(351\) −3.10770 + 11.5981i −0.165876 + 0.619060i
\(352\) −9.46410 5.46410i −0.504438 0.291238i
\(353\) −11.7679 + 20.3827i −0.626345 + 1.08486i 0.361934 + 0.932204i \(0.382116\pi\)
−0.988279 + 0.152657i \(0.951217\pi\)
\(354\) 3.29423 1.90192i 0.175086 0.101086i
\(355\) −1.46410 + 5.46410i −0.0777064 + 0.290004i
\(356\) 31.7128 1.68078
\(357\) 26.7846 + 15.4641i 1.41759 + 0.818447i
\(358\) 11.8564 0.626631
\(359\) 28.9282i 1.52677i −0.645942 0.763386i \(-0.723535\pi\)
0.645942 0.763386i \(-0.276465\pi\)
\(360\) −8.19615 14.1962i −0.431975 0.748203i
\(361\) 1.00000i 0.0526316i
\(362\) 15.4641i 0.812775i
\(363\) 10.9019 6.29423i 0.572203 0.330361i
\(364\) 14.5885 + 14.5885i 0.764643 + 0.764643i
\(365\) 3.73205 13.9282i 0.195344 0.729035i
\(366\) 2.70577 4.68653i 0.141433 0.244969i
\(367\) −17.4545 + 30.2321i −0.911117 + 1.57810i −0.0986270 + 0.995124i \(0.531445\pi\)
−0.812490 + 0.582976i \(0.801888\pi\)
\(368\) 22.3923 12.9282i 1.16728 0.673929i
\(369\) 2.08846 1.20577i 0.108721 0.0627700i
\(370\) −4.26795 + 15.9282i −0.221880 + 0.828068i
\(371\) 34.9545 9.36603i 1.81475 0.486260i
\(372\) −27.5885 + 15.9282i −1.43039 + 0.825839i
\(373\) −1.59808 0.428203i −0.0827452 0.0221715i 0.217209 0.976125i \(-0.430305\pi\)
−0.299954 + 0.953954i \(0.596971\pi\)
\(374\) 9.46410 + 5.46410i 0.489377 + 0.282542i
\(375\) 14.8301 + 14.8301i 0.765824 + 0.765824i
\(376\) −3.26795 + 0.875644i −0.168532 + 0.0451579i
\(377\) 2.07180i 0.106703i
\(378\) −31.6865 + 8.49038i −1.62978 + 0.436698i
\(379\) −15.5885 + 15.5885i −0.800725 + 0.800725i −0.983209 0.182484i \(-0.941586\pi\)
0.182484 + 0.983209i \(0.441586\pi\)
\(380\) 14.1962 8.19615i 0.728247 0.420454i
\(381\) 0.679492 0.0348114
\(382\) 1.02628 + 3.83013i 0.0525090 + 0.195966i
\(383\) 3.66987 + 6.35641i 0.187522 + 0.324797i 0.944423 0.328732i \(-0.106621\pi\)
−0.756902 + 0.653529i \(0.773288\pi\)
\(384\) −13.8564 13.8564i −0.707107 0.707107i
\(385\) −8.33013 + 14.4282i −0.424543 + 0.735329i
\(386\) −6.09808 1.63397i −0.310384 0.0831671i
\(387\) −5.08846 18.9904i −0.258661 0.965335i
\(388\) 1.73205 + 1.00000i 0.0879316 + 0.0507673i
\(389\) 2.40192 + 8.96410i 0.121782 + 0.454498i 0.999705 0.0243053i \(-0.00773738\pi\)
−0.877922 + 0.478803i \(0.841071\pi\)
\(390\) 2.83013 + 10.5622i 0.143309 + 0.534837i
\(391\) −22.3923 + 12.9282i −1.13243 + 0.653807i
\(392\) −9.46410 + 35.3205i −0.478009 + 1.78396i
\(393\) 2.25833 8.42820i 0.113918 0.425147i
\(394\) 7.07180i 0.356272i
\(395\) 2.36603 2.36603i 0.119048 0.119048i
\(396\) −11.1962 + 3.00000i −0.562628 + 0.150756i
\(397\) 17.0526 + 17.0526i 0.855843 + 0.855843i 0.990845 0.135002i \(-0.0431041\pi\)
−0.135002 + 0.990845i \(0.543104\pi\)
\(398\) 21.8564 + 21.8564i 1.09556 + 1.09556i
\(399\) −8.49038 31.6865i −0.425051 1.58631i
\(400\) 4.39230 + 2.53590i 0.219615 + 0.126795i
\(401\) −16.1603 27.9904i −0.807005 1.39777i −0.914929 0.403614i \(-0.867754\pi\)
0.107925 0.994159i \(-0.465579\pi\)
\(402\) −10.5622 18.2942i −0.526794 0.912433i
\(403\) 20.5263 5.50000i 1.02249 0.273975i
\(404\) −1.00000 + 0.267949i −0.0497519 + 0.0133310i
\(405\) −16.7942 4.50000i −0.834512 0.223607i
\(406\) 4.90192 2.83013i 0.243278 0.140457i
\(407\) 10.0981 + 5.83013i 0.500543 + 0.288989i
\(408\) 13.8564 + 13.8564i 0.685994 + 0.685994i
\(409\) −19.6244 + 11.3301i −0.970362 + 0.560239i −0.899347 0.437236i \(-0.855957\pi\)
−0.0710154 + 0.997475i \(0.522624\pi\)
\(410\) 1.09808 1.90192i 0.0542301 0.0939293i
\(411\) −0.990381 0.571797i −0.0488519 0.0282047i
\(412\) −15.9282 27.5885i −0.784726 1.35919i
\(413\) −4.90192 4.90192i −0.241208 0.241208i
\(414\) 7.09808 26.4904i 0.348851 1.30193i
\(415\) 28.3205 1.39020
\(416\) 6.53590 + 11.3205i 0.320449 + 0.555034i
\(417\) 27.9904 + 7.50000i 1.37069 + 0.367277i
\(418\) −3.00000 11.1962i −0.146735 0.547622i
\(419\) −4.96410 + 18.5263i −0.242512 + 0.905068i 0.732105 + 0.681191i \(0.238538\pi\)
−0.974618 + 0.223876i \(0.928129\pi\)
\(420\) −21.1244 + 21.1244i −1.03076 + 1.03076i
\(421\) −4.79423 17.8923i −0.233656 0.872018i −0.978750 0.205058i \(-0.934262\pi\)
0.745094 0.666960i \(-0.232405\pi\)
\(422\) −13.5622 23.4904i −0.660196 1.14349i
\(423\) −1.79423 + 3.10770i −0.0872384 + 0.151101i
\(424\) 22.9282 1.11349
\(425\) −4.39230 2.53590i −0.213058 0.123009i
\(426\) 5.07180 + 5.07180i 0.245729 + 0.245729i
\(427\) −9.52628 2.55256i −0.461009 0.123527i
\(428\) −18.7846 18.7846i −0.907988 0.907988i
\(429\) 7.73205 0.373307
\(430\) −12.6603 12.6603i −0.610532 0.610532i
\(431\) −3.32051 −0.159943 −0.0799716 0.996797i \(-0.525483\pi\)
−0.0799716 + 0.996797i \(0.525483\pi\)
\(432\) −20.7846 −1.00000
\(433\) 3.60770 0.173375 0.0866874 0.996236i \(-0.472372\pi\)
0.0866874 + 0.996236i \(0.472372\pi\)
\(434\) 41.0526 + 41.0526i 1.97059 + 1.97059i
\(435\) 3.00000 0.143839
\(436\) −3.46410 + 3.46410i −0.165900 + 0.165900i
\(437\) 26.4904 + 7.09808i 1.26721 + 0.339547i
\(438\) −12.9282 12.9282i −0.617733 0.617733i
\(439\) 5.93782 + 3.42820i 0.283397 + 0.163619i 0.634960 0.772545i \(-0.281016\pi\)
−0.351563 + 0.936164i \(0.614350\pi\)
\(440\) −7.46410 + 7.46410i −0.355837 + 0.355837i
\(441\) 19.3923 + 33.5885i 0.923443 + 1.59945i
\(442\) −6.53590 11.3205i −0.310881 0.538462i
\(443\) −1.16025 4.33013i −0.0551253 0.205731i 0.932870 0.360213i \(-0.117296\pi\)
−0.987996 + 0.154482i \(0.950629\pi\)
\(444\) 14.7846 + 14.7846i 0.701647 + 0.701647i
\(445\) 7.92820 29.5885i 0.375833 1.40263i
\(446\) 5.70577 + 21.2942i 0.270176 + 1.00831i
\(447\) 27.8205 + 7.45448i 1.31586 + 0.352585i
\(448\) −17.8564 + 30.9282i −0.843636 + 1.46122i
\(449\) 35.3205 1.66688 0.833439 0.552612i \(-0.186369\pi\)
0.833439 + 0.552612i \(0.186369\pi\)
\(450\) 5.19615 1.39230i 0.244949 0.0656339i
\(451\) −1.09808 1.09808i −0.0517064 0.0517064i
\(452\) −21.5885 + 12.4641i −1.01544 + 0.586262i
\(453\) −10.5000 6.06218i −0.493333 0.284826i
\(454\) −14.3660 + 24.8827i −0.674231 + 1.16780i
\(455\) 17.2583 9.96410i 0.809083 0.467124i
\(456\) 20.7846i 0.973329i
\(457\) 25.9641 + 14.9904i 1.21455 + 0.701220i 0.963747 0.266818i \(-0.0859722\pi\)
0.250802 + 0.968038i \(0.419306\pi\)
\(458\) −20.9545 + 12.0981i −0.979139 + 0.565306i
\(459\) 20.7846 0.970143
\(460\) −6.46410 24.1244i −0.301390 1.12480i
\(461\) 4.59808 1.23205i 0.214154 0.0573823i −0.150147 0.988664i \(-0.547975\pi\)
0.364301 + 0.931281i \(0.381308\pi\)
\(462\) 10.5622 + 18.2942i 0.491397 + 0.851125i
\(463\) −5.33013 9.23205i −0.247712 0.429050i 0.715179 0.698942i \(-0.246345\pi\)
−0.962891 + 0.269892i \(0.913012\pi\)
\(464\) 3.46410 0.928203i 0.160817 0.0430908i
\(465\) 7.96410 + 29.7224i 0.369326 + 1.37834i
\(466\) −9.07180 9.07180i −0.420243 0.420243i
\(467\) 21.7846 + 21.7846i 1.00807 + 1.00807i 0.999967 + 0.00810436i \(0.00257972\pi\)
0.00810436 + 0.999967i \(0.497420\pi\)
\(468\) 13.3923 + 3.58846i 0.619060 + 0.165876i
\(469\) −27.2224 + 27.2224i −1.25702 + 1.25702i
\(470\) 3.26795i 0.150739i
\(471\) −1.50000 + 5.59808i −0.0691164 + 0.257946i
\(472\) −2.19615 3.80385i −0.101086 0.175086i
\(473\) −10.9641 + 6.33013i −0.504130 + 0.291060i
\(474\) −1.09808 4.09808i −0.0504363 0.188231i
\(475\) 1.39230 + 5.19615i 0.0638833 + 0.238416i
\(476\) 17.8564 30.9282i 0.818447 1.41759i
\(477\) 17.1962 17.1962i 0.787358 0.787358i
\(478\) 1.09808 + 0.294229i 0.0502248 + 0.0134577i
\(479\) 9.33013 16.1603i 0.426304 0.738381i −0.570237 0.821480i \(-0.693149\pi\)
0.996541 + 0.0830995i \(0.0264819\pi\)
\(480\) −16.3923 + 9.46410i −0.748203 + 0.431975i
\(481\) −6.97372 12.0788i −0.317974 0.550748i
\(482\) −2.02628 7.56218i −0.0922945 0.344448i
\(483\) −49.9808 −2.27420
\(484\) −7.26795 12.5885i −0.330361 0.572203i
\(485\) 1.36603 1.36603i 0.0620280 0.0620280i
\(486\) −15.5885 + 15.5885i −0.707107 + 0.707107i
\(487\) 6.78461i 0.307440i −0.988114 0.153720i \(-0.950875\pi\)
0.988114 0.153720i \(-0.0491254\pi\)
\(488\) −5.41154 3.12436i −0.244969 0.141433i
\(489\) −3.33975 3.33975i −0.151029 0.151029i
\(490\) 30.5885 + 17.6603i 1.38185 + 0.797809i
\(491\) 0.500000 + 0.133975i 0.0225647 + 0.00604619i 0.270084 0.962837i \(-0.412949\pi\)
−0.247519 + 0.968883i \(0.579615\pi\)
\(492\) −1.39230 2.41154i −0.0627700 0.108721i
\(493\) −3.46410 + 0.928203i −0.156015 + 0.0418042i
\(494\) −3.58846 + 13.3923i −0.161452 + 0.602548i
\(495\) 11.1962i 0.503230i
\(496\) 18.3923 + 31.8564i 0.825839 + 1.43039i
\(497\) 6.53590 11.3205i 0.293175 0.507794i
\(498\) 17.9545 31.0981i 0.804560 1.39354i
\(499\) −2.50000 + 9.33013i −0.111915 + 0.417674i −0.999038 0.0438606i \(-0.986034\pi\)
0.887122 + 0.461534i \(0.152701\pi\)
\(500\) 17.1244 17.1244i 0.765824 0.765824i
\(501\) −24.6962 + 14.2583i −1.10334 + 0.637015i
\(502\) 26.7846i 1.19546i
\(503\) 13.8564i 0.617827i 0.951090 + 0.308913i \(0.0999653\pi\)
−0.951090 + 0.308913i \(0.900035\pi\)
\(504\) 9.80385 + 36.5885i 0.436698 + 1.62978i
\(505\) 1.00000i 0.0444994i
\(506\) −17.6603 −0.785094
\(507\) 11.4904 + 6.63397i 0.510306 + 0.294625i
\(508\) 0.784610i 0.0348114i
\(509\) 1.25833 4.69615i 0.0557745 0.208153i −0.932415 0.361389i \(-0.882303\pi\)
0.988190 + 0.153236i \(0.0489693\pi\)
\(510\) 16.3923 9.46410i 0.725863 0.419077i
\(511\) −16.6603 + 28.8564i −0.737006 + 1.27653i
\(512\) −16.0000 + 16.0000i −0.707107 + 0.707107i
\(513\) −15.5885 15.5885i −0.688247 0.688247i
\(514\) −33.2224 8.90192i −1.46538 0.392647i
\(515\) −29.7224 + 7.96410i −1.30973 + 0.350940i
\(516\) −21.9282 + 5.87564i −0.965335 + 0.258661i
\(517\) 2.23205 + 0.598076i 0.0981655 + 0.0263034i
\(518\) 19.0526 33.0000i 0.837121 1.44994i
\(519\) 13.1603 3.52628i 0.577671 0.154786i
\(520\) 12.1962 3.26795i 0.534837 0.143309i
\(521\) 41.8564i 1.83376i −0.399160 0.916881i \(-0.630698\pi\)
0.399160 0.916881i \(-0.369302\pi\)
\(522\) 1.90192 3.29423i 0.0832449 0.144184i
\(523\) 22.1244 22.1244i 0.967431 0.967431i −0.0320556 0.999486i \(-0.510205\pi\)
0.999486 + 0.0320556i \(0.0102054\pi\)
\(524\) −9.73205 2.60770i −0.425147 0.113918i
\(525\) −4.90192 8.49038i −0.213937 0.370551i
\(526\) 13.5622 3.63397i 0.591339 0.158449i
\(527\) −18.3923 31.8564i −0.801181 1.38769i
\(528\) 3.46410 + 12.9282i 0.150756 + 0.562628i
\(529\) 9.39230 16.2679i 0.408361 0.707302i
\(530\) 5.73205 21.3923i 0.248984 0.929222i
\(531\) −4.50000 1.20577i −0.195283 0.0523260i
\(532\) −36.5885 + 9.80385i −1.58631 + 0.425051i
\(533\) 0.480762 + 1.79423i 0.0208241 + 0.0777167i
\(534\) −27.4641 27.4641i −1.18849 1.18849i
\(535\) −22.2224 + 12.8301i −0.960760 + 0.554695i
\(536\) −21.1244 + 12.1962i −0.912433 + 0.526794i
\(537\) −10.2679 10.2679i −0.443095 0.443095i
\(538\) −8.53590 −0.368009
\(539\) 17.6603 17.6603i 0.760681 0.760681i
\(540\) −5.19615 + 19.3923i −0.223607 + 0.834512i
\(541\) −15.0000 15.0000i −0.644900 0.644900i 0.306856 0.951756i \(-0.400723\pi\)
−0.951756 + 0.306856i \(0.900723\pi\)
\(542\) 1.07180 1.07180i 0.0460376 0.0460376i
\(543\) −13.3923 + 13.3923i −0.574719 + 0.574719i
\(544\) 16.0000 16.0000i 0.685994 0.685994i
\(545\) 2.36603 + 4.09808i 0.101349 + 0.175542i
\(546\) 25.2679i 1.08137i
\(547\) 21.4282 5.74167i 0.916204 0.245496i 0.230242 0.973133i \(-0.426048\pi\)
0.685962 + 0.727637i \(0.259382\pi\)
\(548\) −0.660254 + 1.14359i −0.0282047 + 0.0488519i
\(549\) −6.40192 + 1.71539i −0.273227 + 0.0732111i
\(550\) −1.73205 3.00000i −0.0738549 0.127920i
\(551\) 3.29423 + 1.90192i 0.140339 + 0.0810247i
\(552\) −30.5885 8.19615i −1.30193 0.348851i
\(553\) −6.69615 + 3.86603i −0.284749 + 0.164400i
\(554\) 8.49038 + 4.90192i 0.360722 + 0.208263i
\(555\) 17.4904 10.0981i 0.742425 0.428639i
\(556\) 8.66025 32.3205i 0.367277 1.37069i
\(557\) −23.9808 23.9808i −1.01610 1.01610i −0.999868 0.0162292i \(-0.994834\pi\)
−0.0162292 0.999868i \(-0.505166\pi\)
\(558\) 37.6865 + 10.0981i 1.59540 + 0.427486i
\(559\) 15.1436 0.640506
\(560\) 24.3923 + 24.3923i 1.03076 + 1.03076i
\(561\) −3.46410 12.9282i −0.146254 0.545829i
\(562\) 15.8301 4.24167i 0.667754 0.178924i
\(563\) −1.64359 + 6.13397i −0.0692692 + 0.258516i −0.991873 0.127233i \(-0.959390\pi\)
0.922604 + 0.385749i \(0.126057\pi\)
\(564\) 3.58846 + 2.07180i 0.151101 + 0.0872384i
\(565\) 6.23205 + 23.2583i 0.262184 + 0.978485i
\(566\) 16.6865 9.63397i 0.701387 0.404946i
\(567\) 34.7942 + 20.0885i 1.46122 + 0.843636i
\(568\) 5.85641 5.85641i 0.245729 0.245729i
\(569\) −27.4808 15.8660i −1.15205 0.665138i −0.202667 0.979248i \(-0.564961\pi\)
−0.949387 + 0.314109i \(0.898294\pi\)
\(570\) −19.3923 5.19615i −0.812254 0.217643i
\(571\) 39.5526 + 10.5981i 1.65522 + 0.443516i 0.961068 0.276310i \(-0.0891117\pi\)
0.694155 + 0.719826i \(0.255778\pi\)
\(572\) 8.92820i 0.373307i
\(573\) 2.42820 4.20577i 0.101440 0.175699i
\(574\) −3.58846 + 3.58846i −0.149779 + 0.149779i
\(575\) 8.19615 0.341803
\(576\) 24.0000i 1.00000i
\(577\) −25.1769 −1.04813 −0.524064 0.851679i \(-0.675585\pi\)
−0.524064 + 0.851679i \(0.675585\pi\)
\(578\) 1.00000 1.00000i 0.0415945 0.0415945i
\(579\) 3.86603 + 6.69615i 0.160667 + 0.278283i
\(580\) 3.46410i 0.143839i
\(581\) −63.2128 16.9378i −2.62251 0.702699i
\(582\) −0.633975 2.36603i −0.0262791 0.0980749i
\(583\) −13.5622 7.83013i −0.561688 0.324291i
\(584\) −14.9282 + 14.9282i −0.617733 + 0.617733i
\(585\) 6.69615 11.5981i 0.276852 0.479521i
\(586\) −2.70577 + 1.56218i −0.111774 + 0.0645330i
\(587\) 3.96410 + 14.7942i 0.163616 + 0.610623i 0.998213 + 0.0597617i \(0.0190341\pi\)
−0.834597 + 0.550861i \(0.814299\pi\)
\(588\) 38.7846 22.3923i 1.59945 0.923443i
\(589\) −10.0981 + 37.6865i −0.416084 + 1.55285i
\(590\) −4.09808 + 1.09808i −0.168715 + 0.0452071i
\(591\) 6.12436 6.12436i 0.251922 0.251922i
\(592\) 17.0718 17.0718i 0.701647 0.701647i
\(593\) −5.46410 −0.224384 −0.112192 0.993687i \(-0.535787\pi\)
−0.112192 + 0.993687i \(0.535787\pi\)
\(594\) 12.2942 + 7.09808i 0.504438 + 0.291238i
\(595\) −24.3923 24.3923i −0.999987 0.999987i
\(596\) 8.60770 32.1244i 0.352585 1.31586i
\(597\) 37.8564i 1.54936i
\(598\) 18.2942 + 10.5622i 0.748107 + 0.431920i
\(599\) −30.3109 + 17.5000i −1.23847 + 0.715031i −0.968781 0.247917i \(-0.920254\pi\)
−0.269688 + 0.962948i \(0.586921\pi\)
\(600\) −1.60770 6.00000i −0.0656339 0.244949i
\(601\) −26.7679 15.4545i −1.09189 0.630401i −0.157809 0.987470i \(-0.550443\pi\)
−0.934078 + 0.357068i \(0.883776\pi\)
\(602\) 20.6865 + 35.8301i 0.843120 + 1.46033i
\(603\) −6.69615 + 24.9904i −0.272688 + 1.01769i
\(604\) −7.00000 + 12.1244i −0.284826 + 0.493333i
\(605\) −13.5622 + 3.63397i −0.551381 + 0.147742i
\(606\) 1.09808 + 0.633975i 0.0446063 + 0.0257535i
\(607\) 0.598076 + 1.03590i 0.0242752 + 0.0420458i 0.877908 0.478830i \(-0.158939\pi\)
−0.853633 + 0.520876i \(0.825606\pi\)
\(608\) −24.0000 −0.973329
\(609\) −6.69615 1.79423i −0.271342 0.0727058i
\(610\) −4.26795 + 4.26795i −0.172804 + 0.172804i
\(611\) −1.95448 1.95448i −0.0790699 0.0790699i
\(612\) 24.0000i 0.970143i
\(613\) 23.5885 23.5885i 0.952729 0.952729i −0.0462032 0.998932i \(-0.514712\pi\)
0.998932 + 0.0462032i \(0.0147122\pi\)
\(614\) −15.8564 −0.639912
\(615\) −2.59808 + 0.696152i −0.104765 + 0.0280716i
\(616\) 21.1244 12.1962i 0.851125 0.491397i
\(617\) 23.0885 13.3301i 0.929506 0.536651i 0.0428509 0.999081i \(-0.486356\pi\)
0.886655 + 0.462431i \(0.153023\pi\)
\(618\) −10.0981 + 37.6865i −0.406204 + 1.51597i
\(619\) −1.91154 7.13397i −0.0768314 0.286739i 0.916811 0.399322i \(-0.130754\pi\)
−0.993642 + 0.112583i \(0.964088\pi\)
\(620\) 34.3205 9.19615i 1.37834 0.369326i
\(621\) −29.0885 + 16.7942i −1.16728 + 0.673929i
\(622\) −3.88269 + 14.4904i −0.155682 + 0.581011i
\(623\) −35.3923 + 61.3013i −1.41796 + 2.45598i
\(624\) 4.14359 15.4641i 0.165876 0.619060i
\(625\) −8.52628 14.7679i −0.341051 0.590718i
\(626\) −39.6865 + 10.6340i −1.58619 + 0.425019i
\(627\) −7.09808 + 12.2942i −0.283470 + 0.490984i
\(628\) 6.46410 + 1.73205i 0.257946 + 0.0691164i
\(629\) −17.0718 + 17.0718i −0.680697 + 0.680697i
\(630\) 36.5885 1.45772
\(631\) 16.2487i 0.646851i 0.946254 + 0.323425i \(0.104835\pi\)
−0.946254 + 0.323425i \(0.895165\pi\)
\(632\) −4.73205 + 1.26795i −0.188231 + 0.0504363i
\(633\) −8.59808 + 32.0885i −0.341743 + 1.27540i
\(634\) 24.4904 42.4186i 0.972637 1.68466i
\(635\) −0.732051 0.196152i −0.0290506 0.00778407i
\(636\) −19.8564 19.8564i −0.787358 0.787358i
\(637\) −28.8564 + 7.73205i −1.14333 + 0.306355i
\(638\) −2.36603 0.633975i −0.0936718 0.0250993i
\(639\) 8.78461i 0.347514i
\(640\) 10.9282 + 18.9282i 0.431975 + 0.748203i
\(641\) 9.23205 15.9904i 0.364644 0.631582i −0.624075 0.781365i \(-0.714524\pi\)
0.988719 + 0.149782i \(0.0478573\pi\)
\(642\) 32.5359i 1.28409i
\(643\) 7.96410 29.7224i 0.314074 1.17214i −0.610776 0.791804i \(-0.709142\pi\)
0.924849 0.380334i \(-0.124191\pi\)
\(644\) 57.7128i 2.27420i
\(645\) 21.9282i 0.863422i
\(646\) 24.0000 0.944267
\(647\) 25.6077i 1.00674i 0.864070 + 0.503371i \(0.167907\pi\)
−0.864070 + 0.503371i \(0.832093\pi\)
\(648\) 18.0000 + 18.0000i 0.707107 + 0.707107i
\(649\) 3.00000i 0.117760i
\(650\) 4.14359i 0.162525i
\(651\) 71.1051i 2.78683i
\(652\) −3.85641 + 3.85641i −0.151029 + 0.151029i
\(653\) −12.6699 + 47.2846i −0.495810 + 1.85039i 0.0296324 + 0.999561i \(0.490566\pi\)
−0.525443 + 0.850829i \(0.676100\pi\)
\(654\) 6.00000 0.234619
\(655\) −4.86603 + 8.42820i −0.190131 + 0.329317i
\(656\) −2.78461 + 1.60770i −0.108721 + 0.0627700i
\(657\) 22.3923i 0.873607i
\(658\) 1.95448 7.29423i 0.0761937 0.284359i
\(659\) 1.23205 0.330127i 0.0479939 0.0128599i −0.234742 0.972058i \(-0.575425\pi\)
0.282736 + 0.959198i \(0.408758\pi\)
\(660\) 12.9282 0.503230
\(661\) 19.7942 + 5.30385i 0.769906 + 0.206296i 0.622330 0.782755i \(-0.286186\pi\)
0.147576 + 0.989051i \(0.452853\pi\)
\(662\) −6.41858 3.70577i −0.249465 0.144029i
\(663\) −4.14359 + 15.4641i −0.160924 + 0.600576i
\(664\) −35.9090 20.7321i −1.39354 0.804560i
\(665\) 36.5885i 1.41884i
\(666\) 25.6077i 0.992278i
\(667\) 4.09808 4.09808i 0.158678 0.158678i
\(668\) 16.4641 + 28.5167i 0.637015 + 1.10334i
\(669\) 13.5000 23.3827i 0.521940 0.904027i
\(670\) 6.09808 + 22.7583i 0.235589 + 0.879231i
\(671\) 2.13397 + 3.69615i 0.0823812 + 0.142688i
\(672\) 42.2487 11.3205i 1.62978 0.436698i
\(673\) 21.1603 36.6506i 0.815668 1.41278i −0.0931795 0.995649i \(-0.529703\pi\)
0.908847 0.417129i \(-0.136964\pi\)
\(674\) 26.4904 + 7.09808i 1.02037 + 0.273408i
\(675\) −5.70577 3.29423i −0.219615 0.126795i
\(676\) 7.66025 13.2679i 0.294625 0.510306i
\(677\) 2.34936 + 8.76795i 0.0902934 + 0.336980i 0.996264 0.0863612i \(-0.0275239\pi\)
−0.905970 + 0.423341i \(0.860857\pi\)
\(678\) 29.4904 + 7.90192i 1.13257 + 0.303472i
\(679\) −3.86603 + 2.23205i −0.148364 + 0.0856582i
\(680\) −10.9282 18.9282i −0.419077 0.725863i
\(681\) 33.9904 9.10770i 1.30251 0.349008i
\(682\) 25.1244i 0.962061i
\(683\) 15.3923 15.3923i 0.588970 0.588970i −0.348382 0.937353i \(-0.613269\pi\)
0.937353 + 0.348382i \(0.113269\pi\)
\(684\) −18.0000 + 18.0000i −0.688247 + 0.688247i
\(685\) 0.901924 + 0.901924i 0.0344607 + 0.0344607i
\(686\) −26.4641 26.4641i −1.01040 1.01040i
\(687\) 28.6244 + 7.66987i 1.09209 + 0.292624i
\(688\) 6.78461 + 25.3205i 0.258661 + 0.965335i
\(689\) 9.36603 + 16.2224i 0.356817 + 0.618025i
\(690\) −15.2942 + 26.4904i −0.582241 + 1.00847i
\(691\) −1.96410 + 0.526279i −0.0747179 + 0.0200206i −0.295984 0.955193i \(-0.595648\pi\)
0.221266 + 0.975213i \(0.428981\pi\)
\(692\) −4.07180 15.1962i −0.154786 0.577671i
\(693\) 6.69615 24.9904i 0.254366 0.949306i
\(694\) 2.24167 1.29423i 0.0850926 0.0491282i
\(695\) −27.9904 16.1603i −1.06174 0.612993i
\(696\) −3.80385 2.19615i −0.144184 0.0832449i
\(697\) 2.78461 1.60770i 0.105475 0.0608958i
\(698\) 2.83013 4.90192i 0.107122 0.185541i
\(699\) 15.7128i 0.594313i
\(700\) −9.80385 + 5.66025i −0.370551 + 0.213937i
\(701\) 17.0526 + 17.0526i 0.644066 + 0.644066i 0.951553 0.307486i \(-0.0994878\pi\)
−0.307486 + 0.951553i \(0.599488\pi\)
\(702\) −8.49038 14.7058i −0.320449 0.555034i
\(703\) 25.6077 0.965813
\(704\) 14.9282 4.00000i 0.562628 0.150756i
\(705\) 2.83013 2.83013i 0.106589 0.106589i
\(706\) −8.61474 32.1506i −0.324220 1.21001i
\(707\) 0.598076 2.23205i 0.0224930 0.0839449i
\(708\) −1.39230 + 5.19615i −0.0523260 + 0.195283i
\(709\) 10.1147 + 37.7487i 0.379867 + 1.41768i 0.846102 + 0.533022i \(0.178944\pi\)
−0.466235 + 0.884661i \(0.654390\pi\)
\(710\) −4.00000 6.92820i −0.150117 0.260011i
\(711\) −2.59808 + 4.50000i −0.0974355 + 0.168763i
\(712\) −31.7128 + 31.7128i −1.18849 + 1.18849i
\(713\) 51.4808 + 29.7224i 1.92797 + 1.11311i
\(714\) −42.2487 + 11.3205i −1.58112 + 0.423659i
\(715\) −8.33013 2.23205i −0.311529 0.0834740i
\(716\) −11.8564 + 11.8564i −0.443095 + 0.443095i
\(717\) −0.696152 1.20577i −0.0259983 0.0450304i
\(718\) 28.9282 + 28.9282i 1.07959 + 1.07959i
\(719\) −11.3205 −0.422184 −0.211092 0.977466i \(-0.567702\pi\)
−0.211092 + 0.977466i \(0.567702\pi\)
\(720\) 22.3923 + 6.00000i 0.834512 + 0.223607i
\(721\) 71.1051 2.64809
\(722\) 1.00000 + 1.00000i 0.0372161 + 0.0372161i
\(723\) −4.79423 + 8.30385i −0.178299 + 0.308823i
\(724\) 15.4641 + 15.4641i 0.574719 + 0.574719i
\(725\) 1.09808 + 0.294229i 0.0407815 + 0.0109274i
\(726\) −4.60770 + 17.1962i −0.171008 + 0.638209i
\(727\) 3.06218 + 1.76795i 0.113570 + 0.0655696i 0.555709 0.831377i \(-0.312447\pi\)
−0.442139 + 0.896947i \(0.645780\pi\)
\(728\) −29.1769 −1.08137
\(729\) 27.0000 1.00000
\(730\) 10.1962 + 17.6603i 0.377377 + 0.653635i
\(731\) −6.78461 25.3205i −0.250938 0.936513i
\(732\) 1.98076 + 7.39230i 0.0732111 + 0.273227i
\(733\) 8.47372 31.6244i 0.312984 1.16807i −0.612868 0.790185i \(-0.709984\pi\)
0.925852 0.377887i \(-0.123349\pi\)
\(734\) −12.7776 47.6865i −0.471629 1.76014i
\(735\) −11.1962 41.7846i −0.412976 1.54125i
\(736\) −9.46410 + 35.3205i −0.348851 + 1.30193i
\(737\) 16.6603 0.613688
\(738\) −0.882686 + 3.29423i −0.0324921 + 0.121262i
\(739\) −26.2679 26.2679i −0.966282 0.966282i 0.0331677 0.999450i \(-0.489440\pi\)
−0.999450 + 0.0331677i \(0.989440\pi\)
\(740\) −11.6603 20.1962i −0.428639 0.742425i
\(741\) 14.7058 8.49038i 0.540230 0.311902i
\(742\) −25.5885 + 44.3205i −0.939382 + 1.62706i
\(743\) 25.1147 14.5000i 0.921370 0.531953i 0.0372984 0.999304i \(-0.488125\pi\)
0.884072 + 0.467351i \(0.154791\pi\)
\(744\) 11.6603 43.5167i 0.427486 1.59540i
\(745\) −27.8205 16.0622i −1.01926 0.588473i
\(746\) 2.02628 1.16987i 0.0741874 0.0428321i
\(747\) −42.4808 + 11.3827i −1.55429 + 0.416471i
\(748\) −14.9282 + 4.00000i −0.545829 + 0.146254i
\(749\) 57.2750 15.3468i 2.09278 0.560759i
\(750\) −29.6603 −1.08304
\(751\) −24.7224 42.8205i −0.902134 1.56254i −0.824718 0.565544i \(-0.808666\pi\)
−0.0774160 0.996999i \(-0.524667\pi\)
\(752\) 2.39230 4.14359i 0.0872384 0.151101i
\(753\) −23.1962 + 23.1962i −0.845315 + 0.845315i
\(754\) 2.07180 + 2.07180i 0.0754504 + 0.0754504i
\(755\) 9.56218 + 9.56218i 0.348003 + 0.348003i
\(756\) 23.1962 40.1769i 0.843636 1.46122i
\(757\) 1.53590 1.53590i 0.0558232 0.0558232i −0.678644 0.734467i \(-0.737432\pi\)
0.734467 + 0.678644i \(0.237432\pi\)
\(758\) 31.1769i 1.13240i
\(759\) 15.2942 + 15.2942i 0.555145 + 0.555145i
\(760\) −6.00000 + 22.3923i −0.217643 + 0.812254i
\(761\) −16.2846 + 9.40192i −0.590317 + 0.340819i −0.765223 0.643766i \(-0.777371\pi\)
0.174906 + 0.984585i \(0.444038\pi\)
\(762\) −0.679492 + 0.679492i −0.0246154 + 0.0246154i
\(763\) −2.83013 10.5622i −0.102457 0.382377i
\(764\) −4.85641 2.80385i −0.175699 0.101440i
\(765\) −22.3923 6.00000i −0.809595 0.216930i
\(766\) −10.0263 2.68653i −0.362264 0.0970684i
\(767\) 1.79423 3.10770i 0.0647858 0.112212i
\(768\) 27.7128 1.00000
\(769\) −3.50000 6.06218i −0.126213 0.218608i 0.795993 0.605305i \(-0.206949\pi\)
−0.922207 + 0.386698i \(0.873616\pi\)
\(770\) −6.09808 22.7583i −0.219759 0.820153i
\(771\) 21.0622 + 36.4808i 0.758536 + 1.31382i