Properties

Label 32.2.g.a.21.1
Level $32$
Weight $2$
Character 32.21
Analytic conductor $0.256$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 32 = 2^{5} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 32.g (of order \(8\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.255521286468\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{8})\)
Defining polynomial: \( x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 21.1
Root \(-0.707107 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 32.21
Dual form 32.2.g.a.29.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.41421i q^{2} +(-0.707107 + 0.292893i) q^{3} -2.00000 q^{4} +(1.12132 - 2.70711i) q^{5} +(-0.414214 - 1.00000i) q^{6} +(1.00000 + 1.00000i) q^{7} -2.82843i q^{8} +(-1.70711 + 1.70711i) q^{9} +O(q^{10})\) \(q+1.41421i q^{2} +(-0.707107 + 0.292893i) q^{3} -2.00000 q^{4} +(1.12132 - 2.70711i) q^{5} +(-0.414214 - 1.00000i) q^{6} +(1.00000 + 1.00000i) q^{7} -2.82843i q^{8} +(-1.70711 + 1.70711i) q^{9} +(3.82843 + 1.58579i) q^{10} +(-4.12132 - 1.70711i) q^{11} +(1.41421 - 0.585786i) q^{12} +(0.292893 + 0.707107i) q^{13} +(-1.41421 + 1.41421i) q^{14} +2.24264i q^{15} +4.00000 q^{16} +2.82843i q^{17} +(-2.41421 - 2.41421i) q^{18} +(1.53553 + 3.70711i) q^{19} +(-2.24264 + 5.41421i) q^{20} +(-1.00000 - 0.414214i) q^{21} +(2.41421 - 5.82843i) q^{22} +(5.82843 - 5.82843i) q^{23} +(0.828427 + 2.00000i) q^{24} +(-2.53553 - 2.53553i) q^{25} +(-1.00000 + 0.414214i) q^{26} +(1.58579 - 3.82843i) q^{27} +(-2.00000 - 2.00000i) q^{28} +(-3.12132 + 1.29289i) q^{29} -3.17157 q^{30} -4.00000 q^{31} +5.65685i q^{32} +3.41421 q^{33} -4.00000 q^{34} +(3.82843 - 1.58579i) q^{35} +(3.41421 - 3.41421i) q^{36} +(0.292893 - 0.707107i) q^{37} +(-5.24264 + 2.17157i) q^{38} +(-0.414214 - 0.414214i) q^{39} +(-7.65685 - 3.17157i) q^{40} +(-0.171573 + 0.171573i) q^{41} +(0.585786 - 1.41421i) q^{42} +(4.70711 + 1.94975i) q^{43} +(8.24264 + 3.41421i) q^{44} +(2.70711 + 6.53553i) q^{45} +(8.24264 + 8.24264i) q^{46} +0.343146i q^{47} +(-2.82843 + 1.17157i) q^{48} -5.00000i q^{49} +(3.58579 - 3.58579i) q^{50} +(-0.828427 - 2.00000i) q^{51} +(-0.585786 - 1.41421i) q^{52} +(-1.12132 - 0.464466i) q^{53} +(5.41421 + 2.24264i) q^{54} +(-9.24264 + 9.24264i) q^{55} +(2.82843 - 2.82843i) q^{56} +(-2.17157 - 2.17157i) q^{57} +(-1.82843 - 4.41421i) q^{58} +(-1.87868 + 4.53553i) q^{59} -4.48528i q^{60} +(1.70711 - 0.707107i) q^{61} -5.65685i q^{62} -3.41421 q^{63} -8.00000 q^{64} +2.24264 q^{65} +4.82843i q^{66} +(-5.53553 + 2.29289i) q^{67} -5.65685i q^{68} +(-2.41421 + 5.82843i) q^{69} +(2.24264 + 5.41421i) q^{70} +(-5.82843 - 5.82843i) q^{71} +(4.82843 + 4.82843i) q^{72} +(7.00000 - 7.00000i) q^{73} +(1.00000 + 0.414214i) q^{74} +(2.53553 + 1.05025i) q^{75} +(-3.07107 - 7.41421i) q^{76} +(-2.41421 - 5.82843i) q^{77} +(0.585786 - 0.585786i) q^{78} -6.00000i q^{79} +(4.48528 - 10.8284i) q^{80} -4.07107i q^{81} +(-0.242641 - 0.242641i) q^{82} +(1.87868 + 4.53553i) q^{83} +(2.00000 + 0.828427i) q^{84} +(7.65685 + 3.17157i) q^{85} +(-2.75736 + 6.65685i) q^{86} +(1.82843 - 1.82843i) q^{87} +(-4.82843 + 11.6569i) q^{88} +(8.65685 + 8.65685i) q^{89} +(-9.24264 + 3.82843i) q^{90} +(-0.414214 + 1.00000i) q^{91} +(-11.6569 + 11.6569i) q^{92} +(2.82843 - 1.17157i) q^{93} -0.485281 q^{94} +11.7574 q^{95} +(-1.65685 - 4.00000i) q^{96} -18.4853 q^{97} +7.07107 q^{98} +(9.94975 - 4.12132i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 8 q^{4} - 4 q^{5} + 4 q^{6} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 8 q^{4} - 4 q^{5} + 4 q^{6} + 4 q^{7} - 4 q^{9} + 4 q^{10} - 8 q^{11} + 4 q^{13} + 16 q^{16} - 4 q^{18} - 8 q^{19} + 8 q^{20} - 4 q^{21} + 4 q^{22} + 12 q^{23} - 8 q^{24} + 4 q^{25} - 4 q^{26} + 12 q^{27} - 8 q^{28} - 4 q^{29} - 24 q^{30} - 16 q^{31} + 8 q^{33} - 16 q^{34} + 4 q^{35} + 8 q^{36} + 4 q^{37} - 4 q^{38} + 4 q^{39} - 8 q^{40} - 12 q^{41} + 8 q^{42} + 16 q^{43} + 16 q^{44} + 8 q^{45} + 16 q^{46} + 20 q^{50} + 8 q^{51} - 8 q^{52} + 4 q^{53} + 16 q^{54} - 20 q^{55} - 20 q^{57} + 4 q^{58} - 16 q^{59} + 4 q^{61} - 8 q^{63} - 32 q^{64} - 8 q^{65} - 8 q^{67} - 4 q^{69} - 8 q^{70} - 12 q^{71} + 8 q^{72} + 28 q^{73} + 4 q^{74} - 4 q^{75} + 16 q^{76} - 4 q^{77} + 8 q^{78} - 16 q^{80} + 16 q^{82} + 16 q^{83} + 8 q^{84} + 8 q^{85} - 28 q^{86} - 4 q^{87} - 8 q^{88} + 12 q^{89} - 20 q^{90} + 4 q^{91} - 24 q^{92} + 32 q^{94} + 64 q^{95} + 16 q^{96} - 40 q^{97} + 20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/32\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(31\)
\(\chi(n)\) \(e\left(\frac{5}{8}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.41421i 1.00000i
\(3\) −0.707107 + 0.292893i −0.408248 + 0.169102i −0.577350 0.816497i \(-0.695913\pi\)
0.169102 + 0.985599i \(0.445913\pi\)
\(4\) −2.00000 −1.00000
\(5\) 1.12132 2.70711i 0.501470 1.21065i −0.447214 0.894427i \(-0.647584\pi\)
0.948683 0.316228i \(-0.102416\pi\)
\(6\) −0.414214 1.00000i −0.169102 0.408248i
\(7\) 1.00000 + 1.00000i 0.377964 + 0.377964i 0.870367 0.492403i \(-0.163881\pi\)
−0.492403 + 0.870367i \(0.663881\pi\)
\(8\) 2.82843i 1.00000i
\(9\) −1.70711 + 1.70711i −0.569036 + 0.569036i
\(10\) 3.82843 + 1.58579i 1.21065 + 0.501470i
\(11\) −4.12132 1.70711i −1.24262 0.514712i −0.338091 0.941113i \(-0.609781\pi\)
−0.904534 + 0.426401i \(0.859781\pi\)
\(12\) 1.41421 0.585786i 0.408248 0.169102i
\(13\) 0.292893 + 0.707107i 0.0812340 + 0.196116i 0.959278 0.282464i \(-0.0911517\pi\)
−0.878044 + 0.478580i \(0.841152\pi\)
\(14\) −1.41421 + 1.41421i −0.377964 + 0.377964i
\(15\) 2.24264i 0.579047i
\(16\) 4.00000 1.00000
\(17\) 2.82843i 0.685994i 0.939336 + 0.342997i \(0.111442\pi\)
−0.939336 + 0.342997i \(0.888558\pi\)
\(18\) −2.41421 2.41421i −0.569036 0.569036i
\(19\) 1.53553 + 3.70711i 0.352276 + 0.850469i 0.996339 + 0.0854961i \(0.0272475\pi\)
−0.644063 + 0.764973i \(0.722752\pi\)
\(20\) −2.24264 + 5.41421i −0.501470 + 1.21065i
\(21\) −1.00000 0.414214i −0.218218 0.0903888i
\(22\) 2.41421 5.82843i 0.514712 1.24262i
\(23\) 5.82843 5.82843i 1.21531 1.21531i 0.246055 0.969256i \(-0.420866\pi\)
0.969256 0.246055i \(-0.0791345\pi\)
\(24\) 0.828427 + 2.00000i 0.169102 + 0.408248i
\(25\) −2.53553 2.53553i −0.507107 0.507107i
\(26\) −1.00000 + 0.414214i −0.196116 + 0.0812340i
\(27\) 1.58579 3.82843i 0.305185 0.736781i
\(28\) −2.00000 2.00000i −0.377964 0.377964i
\(29\) −3.12132 + 1.29289i −0.579615 + 0.240084i −0.653176 0.757206i \(-0.726564\pi\)
0.0735609 + 0.997291i \(0.476564\pi\)
\(30\) −3.17157 −0.579047
\(31\) −4.00000 −0.718421 −0.359211 0.933257i \(-0.616954\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) 5.65685i 1.00000i
\(33\) 3.41421 0.594338
\(34\) −4.00000 −0.685994
\(35\) 3.82843 1.58579i 0.647122 0.268047i
\(36\) 3.41421 3.41421i 0.569036 0.569036i
\(37\) 0.292893 0.707107i 0.0481513 0.116248i −0.897974 0.440049i \(-0.854961\pi\)
0.946125 + 0.323802i \(0.104961\pi\)
\(38\) −5.24264 + 2.17157i −0.850469 + 0.352276i
\(39\) −0.414214 0.414214i −0.0663273 0.0663273i
\(40\) −7.65685 3.17157i −1.21065 0.501470i
\(41\) −0.171573 + 0.171573i −0.0267952 + 0.0267952i −0.720377 0.693582i \(-0.756031\pi\)
0.693582 + 0.720377i \(0.256031\pi\)
\(42\) 0.585786 1.41421i 0.0903888 0.218218i
\(43\) 4.70711 + 1.94975i 0.717827 + 0.297334i 0.711539 0.702647i \(-0.247998\pi\)
0.00628798 + 0.999980i \(0.497998\pi\)
\(44\) 8.24264 + 3.41421i 1.24262 + 0.514712i
\(45\) 2.70711 + 6.53553i 0.403552 + 0.974260i
\(46\) 8.24264 + 8.24264i 1.21531 + 1.21531i
\(47\) 0.343146i 0.0500530i 0.999687 + 0.0250265i \(0.00796701\pi\)
−0.999687 + 0.0250265i \(0.992033\pi\)
\(48\) −2.82843 + 1.17157i −0.408248 + 0.169102i
\(49\) 5.00000i 0.714286i
\(50\) 3.58579 3.58579i 0.507107 0.507107i
\(51\) −0.828427 2.00000i −0.116003 0.280056i
\(52\) −0.585786 1.41421i −0.0812340 0.196116i
\(53\) −1.12132 0.464466i −0.154025 0.0637993i 0.304339 0.952564i \(-0.401564\pi\)
−0.458364 + 0.888764i \(0.651564\pi\)
\(54\) 5.41421 + 2.24264i 0.736781 + 0.305185i
\(55\) −9.24264 + 9.24264i −1.24628 + 1.24628i
\(56\) 2.82843 2.82843i 0.377964 0.377964i
\(57\) −2.17157 2.17157i −0.287632 0.287632i
\(58\) −1.82843 4.41421i −0.240084 0.579615i
\(59\) −1.87868 + 4.53553i −0.244583 + 0.590476i −0.997727 0.0673793i \(-0.978536\pi\)
0.753144 + 0.657855i \(0.228536\pi\)
\(60\) 4.48528i 0.579047i
\(61\) 1.70711 0.707107i 0.218573 0.0905357i −0.270710 0.962661i \(-0.587259\pi\)
0.489283 + 0.872125i \(0.337259\pi\)
\(62\) 5.65685i 0.718421i
\(63\) −3.41421 −0.430150
\(64\) −8.00000 −1.00000
\(65\) 2.24264 0.278165
\(66\) 4.82843i 0.594338i
\(67\) −5.53553 + 2.29289i −0.676273 + 0.280121i −0.694268 0.719717i \(-0.744272\pi\)
0.0179949 + 0.999838i \(0.494272\pi\)
\(68\) 5.65685i 0.685994i
\(69\) −2.41421 + 5.82843i −0.290637 + 0.701660i
\(70\) 2.24264 + 5.41421i 0.268047 + 0.647122i
\(71\) −5.82843 5.82843i −0.691707 0.691707i 0.270900 0.962607i \(-0.412679\pi\)
−0.962607 + 0.270900i \(0.912679\pi\)
\(72\) 4.82843 + 4.82843i 0.569036 + 0.569036i
\(73\) 7.00000 7.00000i 0.819288 0.819288i −0.166717 0.986005i \(-0.553317\pi\)
0.986005 + 0.166717i \(0.0533166\pi\)
\(74\) 1.00000 + 0.414214i 0.116248 + 0.0481513i
\(75\) 2.53553 + 1.05025i 0.292778 + 0.121273i
\(76\) −3.07107 7.41421i −0.352276 0.850469i
\(77\) −2.41421 5.82843i −0.275125 0.664211i
\(78\) 0.585786 0.585786i 0.0663273 0.0663273i
\(79\) 6.00000i 0.675053i −0.941316 0.337526i \(-0.890410\pi\)
0.941316 0.337526i \(-0.109590\pi\)
\(80\) 4.48528 10.8284i 0.501470 1.21065i
\(81\) 4.07107i 0.452341i
\(82\) −0.242641 0.242641i −0.0267952 0.0267952i
\(83\) 1.87868 + 4.53553i 0.206212 + 0.497840i 0.992821 0.119612i \(-0.0381651\pi\)
−0.786609 + 0.617452i \(0.788165\pi\)
\(84\) 2.00000 + 0.828427i 0.218218 + 0.0903888i
\(85\) 7.65685 + 3.17157i 0.830502 + 0.344005i
\(86\) −2.75736 + 6.65685i −0.297334 + 0.717827i
\(87\) 1.82843 1.82843i 0.196028 0.196028i
\(88\) −4.82843 + 11.6569i −0.514712 + 1.24262i
\(89\) 8.65685 + 8.65685i 0.917625 + 0.917625i 0.996856 0.0792315i \(-0.0252466\pi\)
−0.0792315 + 0.996856i \(0.525247\pi\)
\(90\) −9.24264 + 3.82843i −0.974260 + 0.403552i
\(91\) −0.414214 + 1.00000i −0.0434214 + 0.104828i
\(92\) −11.6569 + 11.6569i −1.21531 + 1.21531i
\(93\) 2.82843 1.17157i 0.293294 0.121486i
\(94\) −0.485281 −0.0500530
\(95\) 11.7574 1.20628
\(96\) −1.65685 4.00000i −0.169102 0.408248i
\(97\) −18.4853 −1.87690 −0.938448 0.345421i \(-0.887736\pi\)
−0.938448 + 0.345421i \(0.887736\pi\)
\(98\) 7.07107 0.714286
\(99\) 9.94975 4.12132i 0.999987 0.414208i
\(100\) 5.07107 + 5.07107i 0.507107 + 0.507107i
\(101\) −1.36396 + 3.29289i −0.135719 + 0.327655i −0.977098 0.212791i \(-0.931745\pi\)
0.841379 + 0.540446i \(0.181745\pi\)
\(102\) 2.82843 1.17157i 0.280056 0.116003i
\(103\) 9.48528 + 9.48528i 0.934613 + 0.934613i 0.997990 0.0633771i \(-0.0201871\pi\)
−0.0633771 + 0.997990i \(0.520187\pi\)
\(104\) 2.00000 0.828427i 0.196116 0.0812340i
\(105\) −2.24264 + 2.24264i −0.218859 + 0.218859i
\(106\) 0.656854 1.58579i 0.0637993 0.154025i
\(107\) −4.12132 1.70711i −0.398423 0.165032i 0.174470 0.984663i \(-0.444179\pi\)
−0.572893 + 0.819630i \(0.694179\pi\)
\(108\) −3.17157 + 7.65685i −0.305185 + 0.736781i
\(109\) −5.70711 13.7782i −0.546642 1.31971i −0.919962 0.392007i \(-0.871781\pi\)
0.373320 0.927702i \(-0.378219\pi\)
\(110\) −13.0711 13.0711i −1.24628 1.24628i
\(111\) 0.585786i 0.0556004i
\(112\) 4.00000 + 4.00000i 0.377964 + 0.377964i
\(113\) 6.34315i 0.596713i 0.954455 + 0.298356i \(0.0964384\pi\)
−0.954455 + 0.298356i \(0.903562\pi\)
\(114\) 3.07107 3.07107i 0.287632 0.287632i
\(115\) −9.24264 22.3137i −0.861881 2.08076i
\(116\) 6.24264 2.58579i 0.579615 0.240084i
\(117\) −1.70711 0.707107i −0.157822 0.0653720i
\(118\) −6.41421 2.65685i −0.590476 0.244583i
\(119\) −2.82843 + 2.82843i −0.259281 + 0.259281i
\(120\) 6.34315 0.579047
\(121\) 6.29289 + 6.29289i 0.572081 + 0.572081i
\(122\) 1.00000 + 2.41421i 0.0905357 + 0.218573i
\(123\) 0.0710678 0.171573i 0.00640797 0.0154702i
\(124\) 8.00000 0.718421
\(125\) 3.82843 1.58579i 0.342425 0.141837i
\(126\) 4.82843i 0.430150i
\(127\) 12.9706 1.15095 0.575476 0.817819i \(-0.304817\pi\)
0.575476 + 0.817819i \(0.304817\pi\)
\(128\) 11.3137i 1.00000i
\(129\) −3.89949 −0.343331
\(130\) 3.17157i 0.278165i
\(131\) −16.3640 + 6.77817i −1.42973 + 0.592212i −0.957284 0.289150i \(-0.906627\pi\)
−0.472442 + 0.881362i \(0.656627\pi\)
\(132\) −6.82843 −0.594338
\(133\) −2.17157 + 5.24264i −0.188299 + 0.454595i
\(134\) −3.24264 7.82843i −0.280121 0.676273i
\(135\) −8.58579 8.58579i −0.738947 0.738947i
\(136\) 8.00000 0.685994
\(137\) −8.65685 + 8.65685i −0.739605 + 0.739605i −0.972502 0.232897i \(-0.925180\pi\)
0.232897 + 0.972502i \(0.425180\pi\)
\(138\) −8.24264 3.41421i −0.701660 0.290637i
\(139\) 13.1924 + 5.46447i 1.11896 + 0.463490i 0.864016 0.503465i \(-0.167942\pi\)
0.254948 + 0.966955i \(0.417942\pi\)
\(140\) −7.65685 + 3.17157i −0.647122 + 0.268047i
\(141\) −0.100505 0.242641i −0.00846405 0.0204340i
\(142\) 8.24264 8.24264i 0.691707 0.691707i
\(143\) 3.41421i 0.285511i
\(144\) −6.82843 + 6.82843i −0.569036 + 0.569036i
\(145\) 9.89949i 0.822108i
\(146\) 9.89949 + 9.89949i 0.819288 + 0.819288i
\(147\) 1.46447 + 3.53553i 0.120787 + 0.291606i
\(148\) −0.585786 + 1.41421i −0.0481513 + 0.116248i
\(149\) −15.6066 6.46447i −1.27854 0.529590i −0.362992 0.931792i \(-0.618245\pi\)
−0.915551 + 0.402203i \(0.868245\pi\)
\(150\) −1.48528 + 3.58579i −0.121273 + 0.292778i
\(151\) −1.48528 + 1.48528i −0.120870 + 0.120870i −0.764955 0.644084i \(-0.777239\pi\)
0.644084 + 0.764955i \(0.277239\pi\)
\(152\) 10.4853 4.34315i 0.850469 0.352276i
\(153\) −4.82843 4.82843i −0.390355 0.390355i
\(154\) 8.24264 3.41421i 0.664211 0.275125i
\(155\) −4.48528 + 10.8284i −0.360266 + 0.869760i
\(156\) 0.828427 + 0.828427i 0.0663273 + 0.0663273i
\(157\) 1.70711 0.707107i 0.136242 0.0564333i −0.313521 0.949581i \(-0.601509\pi\)
0.449763 + 0.893148i \(0.351509\pi\)
\(158\) 8.48528 0.675053
\(159\) 0.928932 0.0736691
\(160\) 15.3137 + 6.34315i 1.21065 + 0.501470i
\(161\) 11.6569 0.918689
\(162\) 5.75736 0.452341
\(163\) 0.464466 0.192388i 0.0363798 0.0150690i −0.364419 0.931235i \(-0.618733\pi\)
0.400799 + 0.916166i \(0.368733\pi\)
\(164\) 0.343146 0.343146i 0.0267952 0.0267952i
\(165\) 3.82843 9.24264i 0.298043 0.719539i
\(166\) −6.41421 + 2.65685i −0.497840 + 0.206212i
\(167\) 14.6569 + 14.6569i 1.13418 + 1.13418i 0.989475 + 0.144707i \(0.0462239\pi\)
0.144707 + 0.989475i \(0.453776\pi\)
\(168\) −1.17157 + 2.82843i −0.0903888 + 0.218218i
\(169\) 8.77817 8.77817i 0.675244 0.675244i
\(170\) −4.48528 + 10.8284i −0.344005 + 0.830502i
\(171\) −8.94975 3.70711i −0.684404 0.283490i
\(172\) −9.41421 3.89949i −0.717827 0.297334i
\(173\) 3.12132 + 7.53553i 0.237310 + 0.572916i 0.997003 0.0773656i \(-0.0246509\pi\)
−0.759693 + 0.650282i \(0.774651\pi\)
\(174\) 2.58579 + 2.58579i 0.196028 + 0.196028i
\(175\) 5.07107i 0.383337i
\(176\) −16.4853 6.82843i −1.24262 0.514712i
\(177\) 3.75736i 0.282420i
\(178\) −12.2426 + 12.2426i −0.917625 + 0.917625i
\(179\) −1.63604 3.94975i −0.122283 0.295218i 0.850870 0.525377i \(-0.176076\pi\)
−0.973153 + 0.230159i \(0.926076\pi\)
\(180\) −5.41421 13.0711i −0.403552 0.974260i
\(181\) 16.1924 + 6.70711i 1.20357 + 0.498535i 0.892151 0.451737i \(-0.149196\pi\)
0.311420 + 0.950272i \(0.399196\pi\)
\(182\) −1.41421 0.585786i −0.104828 0.0434214i
\(183\) −1.00000 + 1.00000i −0.0739221 + 0.0739221i
\(184\) −16.4853 16.4853i −1.21531 1.21531i
\(185\) −1.58579 1.58579i −0.116589 0.116589i
\(186\) 1.65685 + 4.00000i 0.121486 + 0.293294i
\(187\) 4.82843 11.6569i 0.353090 0.852434i
\(188\) 0.686292i 0.0500530i
\(189\) 5.41421 2.24264i 0.393826 0.163128i
\(190\) 16.6274i 1.20628i
\(191\) −12.0000 −0.868290 −0.434145 0.900843i \(-0.642949\pi\)
−0.434145 + 0.900843i \(0.642949\pi\)
\(192\) 5.65685 2.34315i 0.408248 0.169102i
\(193\) −1.51472 −0.109032 −0.0545159 0.998513i \(-0.517362\pi\)
−0.0545159 + 0.998513i \(0.517362\pi\)
\(194\) 26.1421i 1.87690i
\(195\) −1.58579 + 0.656854i −0.113561 + 0.0470383i
\(196\) 10.0000i 0.714286i
\(197\) 4.63604 11.1924i 0.330304 0.797425i −0.668264 0.743924i \(-0.732962\pi\)
0.998568 0.0535002i \(-0.0170378\pi\)
\(198\) 5.82843 + 14.0711i 0.414208 + 0.999987i
\(199\) −15.9706 15.9706i −1.13212 1.13212i −0.989824 0.142300i \(-0.954550\pi\)
−0.142300 0.989824i \(-0.545450\pi\)
\(200\) −7.17157 + 7.17157i −0.507107 + 0.507107i
\(201\) 3.24264 3.24264i 0.228718 0.228718i
\(202\) −4.65685 1.92893i −0.327655 0.135719i
\(203\) −4.41421 1.82843i −0.309817 0.128330i
\(204\) 1.65685 + 4.00000i 0.116003 + 0.280056i
\(205\) 0.272078 + 0.656854i 0.0190027 + 0.0458767i
\(206\) −13.4142 + 13.4142i −0.934613 + 0.934613i
\(207\) 19.8995i 1.38311i
\(208\) 1.17157 + 2.82843i 0.0812340 + 0.196116i
\(209\) 17.8995i 1.23813i
\(210\) −3.17157 3.17157i −0.218859 0.218859i
\(211\) 7.53553 + 18.1924i 0.518768 + 1.25242i 0.938661 + 0.344842i \(0.112068\pi\)
−0.419893 + 0.907574i \(0.637932\pi\)
\(212\) 2.24264 + 0.928932i 0.154025 + 0.0637993i
\(213\) 5.82843 + 2.41421i 0.399357 + 0.165419i
\(214\) 2.41421 5.82843i 0.165032 0.398423i
\(215\) 10.5563 10.5563i 0.719937 0.719937i
\(216\) −10.8284 4.48528i −0.736781 0.305185i
\(217\) −4.00000 4.00000i −0.271538 0.271538i
\(218\) 19.4853 8.07107i 1.31971 0.546642i
\(219\) −2.89949 + 7.00000i −0.195930 + 0.473016i
\(220\) 18.4853 18.4853i 1.24628 1.24628i
\(221\) −2.00000 + 0.828427i −0.134535 + 0.0557260i
\(222\) −0.828427 −0.0556004
\(223\) −20.9706 −1.40429 −0.702146 0.712033i \(-0.747775\pi\)
−0.702146 + 0.712033i \(0.747775\pi\)
\(224\) −5.65685 + 5.65685i −0.377964 + 0.377964i
\(225\) 8.65685 0.577124
\(226\) −8.97056 −0.596713
\(227\) 18.6066 7.70711i 1.23496 0.511539i 0.332826 0.942988i \(-0.391998\pi\)
0.902137 + 0.431449i \(0.141998\pi\)
\(228\) 4.34315 + 4.34315i 0.287632 + 0.287632i
\(229\) −9.22183 + 22.2635i −0.609395 + 1.47121i 0.254264 + 0.967135i \(0.418167\pi\)
−0.863659 + 0.504076i \(0.831833\pi\)
\(230\) 31.5563 13.0711i 2.08076 0.861881i
\(231\) 3.41421 + 3.41421i 0.224639 + 0.224639i
\(232\) 3.65685 + 8.82843i 0.240084 + 0.579615i
\(233\) −2.65685 + 2.65685i −0.174056 + 0.174056i −0.788759 0.614703i \(-0.789276\pi\)
0.614703 + 0.788759i \(0.289276\pi\)
\(234\) 1.00000 2.41421i 0.0653720 0.157822i
\(235\) 0.928932 + 0.384776i 0.0605969 + 0.0251000i
\(236\) 3.75736 9.07107i 0.244583 0.590476i
\(237\) 1.75736 + 4.24264i 0.114153 + 0.275589i
\(238\) −4.00000 4.00000i −0.259281 0.259281i
\(239\) 5.31371i 0.343715i 0.985122 + 0.171858i \(0.0549769\pi\)
−0.985122 + 0.171858i \(0.945023\pi\)
\(240\) 8.97056i 0.579047i
\(241\) 8.48528i 0.546585i 0.961931 + 0.273293i \(0.0881127\pi\)
−0.961931 + 0.273293i \(0.911887\pi\)
\(242\) −8.89949 + 8.89949i −0.572081 + 0.572081i
\(243\) 5.94975 + 14.3640i 0.381676 + 0.921449i
\(244\) −3.41421 + 1.41421i −0.218573 + 0.0905357i
\(245\) −13.5355 5.60660i −0.864754 0.358193i
\(246\) 0.242641 + 0.100505i 0.0154702 + 0.00640797i
\(247\) −2.17157 + 2.17157i −0.138174 + 0.138174i
\(248\) 11.3137i 0.718421i
\(249\) −2.65685 2.65685i −0.168371 0.168371i
\(250\) 2.24264 + 5.41421i 0.141837 + 0.342425i
\(251\) 6.60660 15.9497i 0.417005 1.00674i −0.566205 0.824264i \(-0.691589\pi\)
0.983210 0.182475i \(-0.0584109\pi\)
\(252\) 6.82843 0.430150
\(253\) −33.9706 + 14.0711i −2.13571 + 0.884640i
\(254\) 18.3431i 1.15095i
\(255\) −6.34315 −0.397223
\(256\) 16.0000 1.00000
\(257\) 6.00000 0.374270 0.187135 0.982334i \(-0.440080\pi\)
0.187135 + 0.982334i \(0.440080\pi\)
\(258\) 5.51472i 0.343331i
\(259\) 1.00000 0.414214i 0.0621370 0.0257380i
\(260\) −4.48528 −0.278165
\(261\) 3.12132 7.53553i 0.193205 0.466438i
\(262\) −9.58579 23.1421i −0.592212 1.42973i
\(263\) −5.82843 5.82843i −0.359396 0.359396i 0.504194 0.863590i \(-0.331790\pi\)
−0.863590 + 0.504194i \(0.831790\pi\)
\(264\) 9.65685i 0.594338i
\(265\) −2.51472 + 2.51472i −0.154478 + 0.154478i
\(266\) −7.41421 3.07107i −0.454595 0.188299i
\(267\) −8.65685 3.58579i −0.529791 0.219447i
\(268\) 11.0711 4.58579i 0.676273 0.280121i
\(269\) 9.12132 + 22.0208i 0.556137 + 1.34263i 0.912803 + 0.408401i \(0.133913\pi\)
−0.356666 + 0.934232i \(0.616087\pi\)
\(270\) 12.1421 12.1421i 0.738947 0.738947i
\(271\) 18.0000i 1.09342i −0.837321 0.546711i \(-0.815880\pi\)
0.837321 0.546711i \(-0.184120\pi\)
\(272\) 11.3137i 0.685994i
\(273\) 0.828427i 0.0501387i
\(274\) −12.2426 12.2426i −0.739605 0.739605i
\(275\) 6.12132 + 14.7782i 0.369130 + 0.891157i
\(276\) 4.82843 11.6569i 0.290637 0.701660i
\(277\) 1.70711 + 0.707107i 0.102570 + 0.0424859i 0.433378 0.901212i \(-0.357321\pi\)
−0.330808 + 0.943698i \(0.607321\pi\)
\(278\) −7.72792 + 18.6569i −0.463490 + 1.11896i
\(279\) 6.82843 6.82843i 0.408807 0.408807i
\(280\) −4.48528 10.8284i −0.268047 0.647122i
\(281\) −11.8284 11.8284i −0.705625 0.705625i 0.259987 0.965612i \(-0.416282\pi\)
−0.965612 + 0.259987i \(0.916282\pi\)
\(282\) 0.343146 0.142136i 0.0204340 0.00846405i
\(283\) 5.77817 13.9497i 0.343477 0.829226i −0.653882 0.756596i \(-0.726861\pi\)
0.997359 0.0726300i \(-0.0231392\pi\)
\(284\) 11.6569 + 11.6569i 0.691707 + 0.691707i
\(285\) −8.31371 + 3.44365i −0.492462 + 0.203984i
\(286\) 4.82843 0.285511
\(287\) −0.343146 −0.0202553
\(288\) −9.65685 9.65685i −0.569036 0.569036i
\(289\) 9.00000 0.529412
\(290\) −14.0000 −0.822108
\(291\) 13.0711 5.41421i 0.766240 0.317387i
\(292\) −14.0000 + 14.0000i −0.819288 + 0.819288i
\(293\) 9.60660 23.1924i 0.561224 1.35491i −0.347565 0.937656i \(-0.612991\pi\)
0.908788 0.417258i \(-0.137009\pi\)
\(294\) −5.00000 + 2.07107i −0.291606 + 0.120787i
\(295\) 10.1716 + 10.1716i 0.592212 + 0.592212i
\(296\) −2.00000 0.828427i −0.116248 0.0481513i
\(297\) −13.0711 + 13.0711i −0.758460 + 0.758460i
\(298\) 9.14214 22.0711i 0.529590 1.27854i
\(299\) 5.82843 + 2.41421i 0.337067 + 0.139618i
\(300\) −5.07107 2.10051i −0.292778 0.121273i
\(301\) 2.75736 + 6.65685i 0.158932 + 0.383695i
\(302\) −2.10051 2.10051i −0.120870 0.120870i
\(303\) 2.72792i 0.156715i
\(304\) 6.14214 + 14.8284i 0.352276 + 0.850469i
\(305\) 5.41421i 0.310017i
\(306\) 6.82843 6.82843i 0.390355 0.390355i
\(307\) −6.94975 16.7782i −0.396643 0.957581i −0.988456 0.151506i \(-0.951588\pi\)
0.591813 0.806075i \(-0.298412\pi\)
\(308\) 4.82843 + 11.6569i 0.275125 + 0.664211i
\(309\) −9.48528 3.92893i −0.539599 0.223509i
\(310\) −15.3137 6.34315i −0.869760 0.360266i
\(311\) −2.65685 + 2.65685i −0.150656 + 0.150656i −0.778411 0.627755i \(-0.783974\pi\)
0.627755 + 0.778411i \(0.283974\pi\)
\(312\) −1.17157 + 1.17157i −0.0663273 + 0.0663273i
\(313\) −7.48528 7.48528i −0.423093 0.423093i 0.463174 0.886267i \(-0.346710\pi\)
−0.886267 + 0.463174i \(0.846710\pi\)
\(314\) 1.00000 + 2.41421i 0.0564333 + 0.136242i
\(315\) −3.82843 + 9.24264i −0.215707 + 0.520764i
\(316\) 12.0000i 0.675053i
\(317\) 17.3640 7.19239i 0.975257 0.403965i 0.162591 0.986694i \(-0.448015\pi\)
0.812667 + 0.582729i \(0.198015\pi\)
\(318\) 1.31371i 0.0736691i
\(319\) 15.0711 0.843818
\(320\) −8.97056 + 21.6569i −0.501470 + 1.21065i
\(321\) 3.41421 0.190563
\(322\) 16.4853i 0.918689i
\(323\) −10.4853 + 4.34315i −0.583417 + 0.241659i
\(324\) 8.14214i 0.452341i
\(325\) 1.05025 2.53553i 0.0582575 0.140646i
\(326\) 0.272078 + 0.656854i 0.0150690 + 0.0363798i
\(327\) 8.07107 + 8.07107i 0.446331 + 0.446331i
\(328\) 0.485281 + 0.485281i 0.0267952 + 0.0267952i
\(329\) −0.343146 + 0.343146i −0.0189182 + 0.0189182i
\(330\) 13.0711 + 5.41421i 0.719539 + 0.298043i
\(331\) −1.29289 0.535534i −0.0710638 0.0294356i 0.346868 0.937914i \(-0.387245\pi\)
−0.417932 + 0.908478i \(0.637245\pi\)
\(332\) −3.75736 9.07107i −0.206212 0.497840i
\(333\) 0.707107 + 1.70711i 0.0387492 + 0.0935489i
\(334\) −20.7279 + 20.7279i −1.13418 + 1.13418i
\(335\) 17.5563i 0.959206i
\(336\) −4.00000 1.65685i −0.218218 0.0903888i
\(337\) 16.9706i 0.924445i 0.886764 + 0.462223i \(0.152948\pi\)
−0.886764 + 0.462223i \(0.847052\pi\)
\(338\) 12.4142 + 12.4142i 0.675244 + 0.675244i
\(339\) −1.85786 4.48528i −0.100905 0.243607i
\(340\) −15.3137 6.34315i −0.830502 0.344005i
\(341\) 16.4853 + 6.82843i 0.892728 + 0.369780i
\(342\) 5.24264 12.6569i 0.283490 0.684404i
\(343\) 12.0000 12.0000i 0.647939 0.647939i
\(344\) 5.51472 13.3137i 0.297334 0.717827i
\(345\) 13.0711 + 13.0711i 0.703723 + 0.703723i
\(346\) −10.6569 + 4.41421i −0.572916 + 0.237310i
\(347\) 1.63604 3.94975i 0.0878272 0.212034i −0.873863 0.486172i \(-0.838393\pi\)
0.961690 + 0.274139i \(0.0883927\pi\)
\(348\) −3.65685 + 3.65685i −0.196028 + 0.196028i
\(349\) 24.6777 10.2218i 1.32097 0.547162i 0.392901 0.919581i \(-0.371472\pi\)
0.928065 + 0.372419i \(0.121472\pi\)
\(350\) 7.17157 0.383337
\(351\) 3.17157 0.169286
\(352\) 9.65685 23.3137i 0.514712 1.24262i
\(353\) 6.00000 0.319348 0.159674 0.987170i \(-0.448956\pi\)
0.159674 + 0.987170i \(0.448956\pi\)
\(354\) 5.31371 0.282420
\(355\) −22.3137 + 9.24264i −1.18429 + 0.490548i
\(356\) −17.3137 17.3137i −0.917625 0.917625i
\(357\) 1.17157 2.82843i 0.0620062 0.149696i
\(358\) 5.58579 2.31371i 0.295218 0.122283i
\(359\) −17.8284 17.8284i −0.940948 0.940948i 0.0574027 0.998351i \(-0.481718\pi\)
−0.998351 + 0.0574027i \(0.981718\pi\)
\(360\) 18.4853 7.65685i 0.974260 0.403552i
\(361\) 2.05025 2.05025i 0.107908 0.107908i
\(362\) −9.48528 + 22.8995i −0.498535 + 1.20357i
\(363\) −6.29289 2.60660i −0.330291 0.136811i
\(364\) 0.828427 2.00000i 0.0434214 0.104828i
\(365\) −11.1005 26.7990i −0.581027 1.40272i
\(366\) −1.41421 1.41421i −0.0739221 0.0739221i
\(367\) 6.00000i 0.313197i 0.987662 + 0.156599i \(0.0500529\pi\)
−0.987662 + 0.156599i \(0.949947\pi\)
\(368\) 23.3137 23.3137i 1.21531 1.21531i
\(369\) 0.585786i 0.0304948i
\(370\) 2.24264 2.24264i 0.116589 0.116589i
\(371\) −0.656854 1.58579i −0.0341022 0.0823299i
\(372\) −5.65685 + 2.34315i −0.293294 + 0.121486i
\(373\) −10.2929 4.26346i −0.532946 0.220753i 0.0999471 0.994993i \(-0.468133\pi\)
−0.632893 + 0.774239i \(0.718133\pi\)
\(374\) 16.4853 + 6.82843i 0.852434 + 0.353090i
\(375\) −2.24264 + 2.24264i −0.115809 + 0.115809i
\(376\) 0.970563 0.0500530
\(377\) −1.82843 1.82843i −0.0941688 0.0941688i
\(378\) 3.17157 + 7.65685i 0.163128 + 0.393826i
\(379\) −13.6777 + 33.0208i −0.702575 + 1.69617i 0.0151948 + 0.999885i \(0.495163\pi\)
−0.717769 + 0.696281i \(0.754837\pi\)
\(380\) −23.5147 −1.20628
\(381\) −9.17157 + 3.79899i −0.469874 + 0.194628i
\(382\) 16.9706i 0.868290i
\(383\) −16.9706 −0.867155 −0.433578 0.901116i \(-0.642749\pi\)
−0.433578 + 0.901116i \(0.642749\pi\)
\(384\) 3.31371 + 8.00000i 0.169102 + 0.408248i
\(385\) −18.4853 −0.942097
\(386\) 2.14214i 0.109032i
\(387\) −11.3640 + 4.70711i −0.577663 + 0.239276i
\(388\) 36.9706 1.87690
\(389\) −8.39340 + 20.2635i −0.425562 + 1.02740i 0.555117 + 0.831773i \(0.312674\pi\)
−0.980679 + 0.195625i \(0.937326\pi\)
\(390\) −0.928932 2.24264i −0.0470383 0.113561i
\(391\) 16.4853 + 16.4853i 0.833697 + 0.833697i
\(392\) −14.1421 −0.714286
\(393\) 9.58579 9.58579i 0.483539 0.483539i
\(394\) 15.8284 + 6.55635i 0.797425 + 0.330304i
\(395\) −16.2426 6.72792i −0.817256 0.338518i
\(396\) −19.8995 + 8.24264i −0.999987 + 0.414208i
\(397\) −9.22183 22.2635i −0.462830 1.11737i −0.967230 0.253901i \(-0.918286\pi\)
0.504400 0.863470i \(-0.331714\pi\)
\(398\) 22.5858 22.5858i 1.13212 1.13212i
\(399\) 4.34315i 0.217429i
\(400\) −10.1421 10.1421i −0.507107 0.507107i
\(401\) 2.82843i 0.141245i 0.997503 + 0.0706225i \(0.0224986\pi\)
−0.997503 + 0.0706225i \(0.977501\pi\)
\(402\) 4.58579 + 4.58579i 0.228718 + 0.228718i
\(403\) −1.17157 2.82843i −0.0583602 0.140894i
\(404\) 2.72792 6.58579i 0.135719 0.327655i
\(405\) −11.0208 4.56497i −0.547629 0.226835i
\(406\) 2.58579 6.24264i 0.128330 0.309817i
\(407\) −2.41421 + 2.41421i −0.119668 + 0.119668i
\(408\) −5.65685 + 2.34315i −0.280056 + 0.116003i
\(409\) 21.4853 + 21.4853i 1.06238 + 1.06238i 0.997920 + 0.0644584i \(0.0205320\pi\)
0.0644584 + 0.997920i \(0.479468\pi\)
\(410\) −0.928932 + 0.384776i −0.0458767 + 0.0190027i
\(411\) 3.58579 8.65685i 0.176874 0.427011i
\(412\) −18.9706 18.9706i −0.934613 0.934613i
\(413\) −6.41421 + 2.65685i −0.315623 + 0.130735i
\(414\) −28.1421 −1.38311
\(415\) 14.3848 0.706121
\(416\) −4.00000 + 1.65685i −0.196116 + 0.0812340i
\(417\) −10.9289 −0.535192
\(418\) 25.3137 1.23813
\(419\) 12.6066 5.22183i 0.615873 0.255103i −0.0528644 0.998602i \(-0.516835\pi\)
0.668737 + 0.743499i \(0.266835\pi\)
\(420\) 4.48528 4.48528i 0.218859 0.218859i
\(421\) 6.29289 15.1924i 0.306697 0.740432i −0.693111 0.720831i \(-0.743760\pi\)
0.999808 0.0196009i \(-0.00623955\pi\)
\(422\) −25.7279 + 10.6569i −1.25242 + 0.518768i
\(423\) −0.585786 0.585786i −0.0284819 0.0284819i
\(424\) −1.31371 + 3.17157i −0.0637993 + 0.154025i
\(425\) 7.17157 7.17157i 0.347872 0.347872i
\(426\) −3.41421 + 8.24264i −0.165419 + 0.399357i
\(427\) 2.41421 + 1.00000i 0.116832 + 0.0483934i
\(428\) 8.24264 + 3.41421i 0.398423 + 0.165032i
\(429\) 1.00000 + 2.41421i 0.0482805 + 0.116559i
\(430\) 14.9289 + 14.9289i 0.719937 + 0.719937i
\(431\) 12.3431i 0.594548i 0.954792 + 0.297274i \(0.0960775\pi\)
−0.954792 + 0.297274i \(0.903922\pi\)
\(432\) 6.34315 15.3137i 0.305185 0.736781i
\(433\) 15.5147i 0.745590i 0.927914 + 0.372795i \(0.121600\pi\)
−0.927914 + 0.372795i \(0.878400\pi\)
\(434\) 5.65685 5.65685i 0.271538 0.271538i
\(435\) −2.89949 7.00000i −0.139020 0.335624i
\(436\) 11.4142 + 27.5563i 0.546642 + 1.31971i
\(437\) 30.5563 + 12.6569i 1.46171 + 0.605459i
\(438\) −9.89949 4.10051i −0.473016 0.195930i
\(439\) −17.0000 + 17.0000i −0.811366 + 0.811366i −0.984839 0.173473i \(-0.944501\pi\)
0.173473 + 0.984839i \(0.444501\pi\)
\(440\) 26.1421 + 26.1421i 1.24628 + 1.24628i
\(441\) 8.53553 + 8.53553i 0.406454 + 0.406454i
\(442\) −1.17157 2.82843i −0.0557260 0.134535i
\(443\) 0.606602 1.46447i 0.0288205 0.0695789i −0.908814 0.417201i \(-0.863011\pi\)
0.937635 + 0.347623i \(0.113011\pi\)
\(444\) 1.17157i 0.0556004i
\(445\) 33.1421 13.7279i 1.57109 0.650766i
\(446\) 29.6569i 1.40429i
\(447\) 12.9289 0.611518
\(448\) −8.00000 8.00000i −0.377964 0.377964i
\(449\) −19.4558 −0.918178 −0.459089 0.888390i \(-0.651824\pi\)
−0.459089 + 0.888390i \(0.651824\pi\)
\(450\) 12.2426i 0.577124i
\(451\) 1.00000 0.414214i 0.0470882 0.0195046i
\(452\) 12.6863i 0.596713i
\(453\) 0.615224 1.48528i 0.0289057 0.0697846i
\(454\) 10.8995 + 26.3137i 0.511539 + 1.23496i
\(455\) 2.24264 + 2.24264i 0.105137 + 0.105137i
\(456\) −6.14214 + 6.14214i −0.287632 + 0.287632i
\(457\) −7.48528 + 7.48528i −0.350147 + 0.350147i −0.860164 0.510017i \(-0.829639\pi\)
0.510017 + 0.860164i \(0.329639\pi\)
\(458\) −31.4853 13.0416i −1.47121 0.609395i
\(459\) 10.8284 + 4.48528i 0.505428 + 0.209355i
\(460\) 18.4853 + 44.6274i 0.861881 + 2.08076i
\(461\) 0.636039 + 1.53553i 0.0296233 + 0.0715169i 0.937999 0.346638i \(-0.112677\pi\)
−0.908376 + 0.418155i \(0.862677\pi\)
\(462\) −4.82843 + 4.82843i −0.224639 + 0.224639i
\(463\) 22.9706i 1.06753i −0.845632 0.533766i \(-0.820776\pi\)
0.845632 0.533766i \(-0.179224\pi\)
\(464\) −12.4853 + 5.17157i −0.579615 + 0.240084i
\(465\) 8.97056i 0.416000i
\(466\) −3.75736 3.75736i −0.174056 0.174056i
\(467\) −9.09188 21.9497i −0.420722 1.01571i −0.982135 0.188177i \(-0.939742\pi\)
0.561413 0.827536i \(-0.310258\pi\)
\(468\) 3.41421 + 1.41421i 0.157822 + 0.0653720i
\(469\) −7.82843 3.24264i −0.361483 0.149731i
\(470\) −0.544156 + 1.31371i −0.0251000 + 0.0605969i
\(471\) −1.00000 + 1.00000i −0.0460776 + 0.0460776i
\(472\) 12.8284 + 5.31371i 0.590476 + 0.244583i
\(473\) −16.0711 16.0711i −0.738948 0.738948i
\(474\) −6.00000 + 2.48528i −0.275589 + 0.114153i
\(475\) 5.50610 13.2929i 0.252637 0.609920i
\(476\) 5.65685 5.65685i 0.259281 0.259281i
\(477\) 2.70711 1.12132i 0.123950 0.0513417i
\(478\) −7.51472 −0.343715
\(479\) 28.9706 1.32370 0.661849 0.749637i \(-0.269772\pi\)
0.661849 + 0.749637i \(0.269772\pi\)
\(480\) −12.6863 −0.579047
\(481\) 0.585786 0.0267096
\(482\) −12.0000 −0.546585
\(483\) −8.24264 + 3.41421i −0.375053 + 0.155352i
\(484\) −12.5858 12.5858i −0.572081 0.572081i
\(485\) −20.7279 + 50.0416i −0.941206 + 2.27227i
\(486\) −20.3137 + 8.41421i −0.921449 + 0.381676i
\(487\) −11.0000 11.0000i −0.498458 0.498458i 0.412500 0.910958i \(-0.364656\pi\)
−0.910958 + 0.412500i \(0.864656\pi\)
\(488\) −2.00000 4.82843i −0.0905357 0.218573i
\(489\) −0.272078 + 0.272078i −0.0123038 + 0.0123038i
\(490\) 7.92893 19.1421i 0.358193 0.864754i
\(491\) 39.3345 + 16.2929i 1.77514 + 0.735288i 0.993800 + 0.111186i \(0.0354648\pi\)
0.781343 + 0.624102i \(0.214535\pi\)
\(492\) −0.142136 + 0.343146i −0.00640797 + 0.0154702i
\(493\) −3.65685 8.82843i −0.164696 0.397612i
\(494\) −3.07107 3.07107i −0.138174 0.138174i
\(495\) 31.5563i 1.41835i
\(496\) −16.0000 −0.718421
\(497\) 11.6569i 0.522881i
\(498\) 3.75736 3.75736i 0.168371 0.168371i
\(499\) −0.949747 2.29289i −0.0425165 0.102644i 0.901195 0.433415i \(-0.142691\pi\)
−0.943711 + 0.330771i \(0.892691\pi\)
\(500\) −7.65685 + 3.17157i −0.342425 + 0.141837i
\(501\) −14.6569 6.07107i −0.654820 0.271235i
\(502\) 22.5563 + 9.34315i 1.00674 + 0.417005i
\(503\) −11.1421 + 11.1421i −0.496803 + 0.496803i −0.910441 0.413638i \(-0.864258\pi\)
0.413638 + 0.910441i \(0.364258\pi\)
\(504\) 9.65685i 0.430150i
\(505\) 7.38478 + 7.38478i 0.328618 + 0.328618i
\(506\) −19.8995 48.0416i −0.884640 2.13571i
\(507\) −3.63604 + 8.77817i −0.161482 + 0.389852i
\(508\) −25.9411 −1.15095
\(509\) −26.0919 + 10.8076i −1.15650 + 0.479039i −0.876709 0.481021i \(-0.840266\pi\)
−0.279793 + 0.960060i \(0.590266\pi\)
\(510\) 8.97056i 0.397223i
\(511\) 14.0000 0.619324
\(512\) 22.6274i 1.00000i
\(513\) 16.6274 0.734118
\(514\) 8.48528i 0.374270i
\(515\) 36.3137 15.0416i 1.60017 0.662813i
\(516\) 7.79899 0.343331
\(517\) 0.585786 1.41421i 0.0257629 0.0621970i
\(518\) 0.585786 + 1.41421i 0.0257380 + 0.0621370i
\(519\) −4.41421 4.41421i −0.193762 0.193762i
\(520\) 6.34315i 0.278165i
\(521\) 3.34315 3.34315i 0.146466 0.146466i −0.630071 0.776537i \(-0.716974\pi\)
0.776537 + 0.630071i \(0.216974\pi\)
\(522\) 10.6569 + 4.41421i 0.466438 + 0.193205i
\(523\) 19.1924 + 7.94975i 0.839225 + 0.347618i 0.760548 0.649282i \(-0.224930\pi\)
0.0786768 + 0.996900i \(0.474930\pi\)
\(524\) 32.7279 13.5563i 1.42973 0.592212i
\(525\) 1.48528 + 3.58579i 0.0648230 + 0.156497i
\(526\) 8.24264 8.24264i 0.359396 0.359396i
\(527\) 11.3137i 0.492833i
\(528\) 13.6569 0.594338
\(529\) 44.9411i 1.95396i
\(530\) −3.55635 3.55635i −0.154478 0.154478i
\(531\) −4.53553 10.9497i −0.196825 0.475179i
\(532\) 4.34315 10.4853i 0.188299 0.454595i
\(533\) −0.171573 0.0710678i −0.00743165 0.00307829i
\(534\) 5.07107 12.2426i 0.219447 0.529791i
\(535\) −9.24264 + 9.24264i −0.399594 + 0.399594i
\(536\) 6.48528 + 15.6569i 0.280121 + 0.676273i
\(537\) 2.31371 + 2.31371i 0.0998439 + 0.0998439i
\(538\) −31.1421 + 12.8995i −1.34263 + 0.556137i
\(539\) −8.53553 + 20.6066i −0.367651 + 0.887589i
\(540\) 17.1716 + 17.1716i 0.738947 + 0.738947i
\(541\) −27.2635 + 11.2929i −1.17215 + 0.485519i −0.881902 0.471433i \(-0.843737\pi\)
−0.290246 + 0.956952i \(0.593737\pi\)
\(542\) 25.4558 1.09342
\(543\) −13.4142 −0.575659
\(544\) −16.0000 −0.685994
\(545\) −43.6985 −1.87184
\(546\) 1.17157 0.0501387
\(547\) −17.5355 + 7.26346i −0.749765 + 0.310563i −0.724646 0.689122i \(-0.757997\pi\)
−0.0251195 + 0.999684i \(0.507997\pi\)
\(548\) 17.3137 17.3137i 0.739605 0.739605i
\(549\) −1.70711 + 4.12132i −0.0728575 + 0.175894i
\(550\) −20.8995 + 8.65685i −0.891157 + 0.369130i
\(551\) −9.58579 9.58579i −0.408368 0.408368i
\(552\) 16.4853 + 6.82843i 0.701660 + 0.290637i
\(553\) 6.00000 6.00000i 0.255146 0.255146i
\(554\) −1.00000 + 2.41421i −0.0424859 + 0.102570i
\(555\) 1.58579 + 0.656854i 0.0673129 + 0.0278819i
\(556\) −26.3848 10.9289i −1.11896 0.463490i
\(557\) 15.1213 + 36.5061i 0.640711 + 1.54681i 0.825722 + 0.564077i \(0.190768\pi\)
−0.185012 + 0.982736i \(0.559232\pi\)
\(558\) 9.65685 + 9.65685i 0.408807 + 0.408807i
\(559\) 3.89949i 0.164931i
\(560\) 15.3137 6.34315i 0.647122 0.268047i
\(561\) 9.65685i 0.407713i
\(562\) 16.7279 16.7279i 0.705625 0.705625i
\(563\) 7.87868 + 19.0208i 0.332047 + 0.801632i 0.998430 + 0.0560220i \(0.0178417\pi\)
−0.666383 + 0.745610i \(0.732158\pi\)
\(564\) 0.201010 + 0.485281i 0.00846405 + 0.0204340i
\(565\) 17.1716 + 7.11270i 0.722414 + 0.299233i
\(566\) 19.7279 + 8.17157i 0.829226 + 0.343477i
\(567\) 4.07107 4.07107i 0.170969 0.170969i
\(568\) −16.4853 + 16.4853i −0.691707 + 0.691707i
\(569\) 14.6569 + 14.6569i 0.614447 + 0.614447i 0.944102 0.329654i \(-0.106932\pi\)
−0.329654 + 0.944102i \(0.606932\pi\)
\(570\) −4.87006 11.7574i −0.203984 0.492462i
\(571\) −2.70711 + 6.53553i −0.113289 + 0.273504i −0.970347 0.241716i \(-0.922290\pi\)
0.857058 + 0.515220i \(0.172290\pi\)
\(572\) 6.82843i 0.285511i
\(573\) 8.48528 3.51472i 0.354478 0.146829i
\(574\) 0.485281i 0.0202553i
\(575\) −29.5563 −1.23258
\(576\) 13.6569 13.6569i 0.569036 0.569036i
\(577\) 18.9706 0.789755 0.394877 0.918734i \(-0.370787\pi\)
0.394877 + 0.918734i \(0.370787\pi\)
\(578\) 12.7279i 0.529412i
\(579\) 1.07107 0.443651i 0.0445121 0.0184375i
\(580\) 19.7990i 0.822108i
\(581\) −2.65685 + 6.41421i −0.110225 + 0.266106i
\(582\) 7.65685 + 18.4853i 0.317387 + 0.766240i
\(583\) 3.82843 + 3.82843i 0.158557 + 0.158557i
\(584\) −19.7990 19.7990i −0.819288 0.819288i
\(585\) −3.82843 + 3.82843i −0.158286 + 0.158286i
\(586\) 32.7990 + 13.5858i 1.35491 + 0.561224i
\(587\) −12.6066 5.22183i −0.520330 0.215528i 0.107032 0.994256i \(-0.465865\pi\)
−0.627362 + 0.778728i \(0.715865\pi\)
\(588\) −2.92893 7.07107i −0.120787 0.291606i
\(589\) −6.14214 14.8284i −0.253082 0.610995i
\(590\) −14.3848 + 14.3848i −0.592212 + 0.592212i
\(591\) 9.27208i 0.381402i
\(592\) 1.17157 2.82843i 0.0481513 0.116248i
\(593\) 28.2843i 1.16150i 0.814083 + 0.580748i \(0.197240\pi\)
−0.814083 + 0.580748i \(0.802760\pi\)
\(594\) −18.4853 18.4853i −0.758460 0.758460i
\(595\) 4.48528 + 10.8284i 0.183879 + 0.443922i
\(596\) 31.2132 + 12.9289i 1.27854 + 0.529590i
\(597\) 15.9706 + 6.61522i 0.653632 + 0.270743i
\(598\) −3.41421 + 8.24264i −0.139618 + 0.337067i
\(599\) −26.6569 + 26.6569i −1.08917 + 1.08917i −0.0935555 + 0.995614i \(0.529823\pi\)
−0.995614 + 0.0935555i \(0.970177\pi\)
\(600\) 2.97056 7.17157i 0.121273 0.292778i
\(601\) −21.9706 21.9706i −0.896198 0.896198i 0.0988995 0.995097i \(-0.468468\pi\)
−0.995097 + 0.0988995i \(0.968468\pi\)
\(602\) −9.41421 + 3.89949i −0.383695 + 0.158932i
\(603\) 5.53553 13.3640i 0.225424 0.544223i
\(604\) 2.97056 2.97056i 0.120870 0.120870i
\(605\) 24.0919 9.97918i 0.979474 0.405712i
\(606\) 3.85786 0.156715
\(607\) −32.9706 −1.33823 −0.669117 0.743157i \(-0.733327\pi\)
−0.669117 + 0.743157i \(0.733327\pi\)
\(608\) −20.9706 + 8.68629i −0.850469 + 0.352276i
\(609\) 3.65685 0.148183
\(610\) 7.65685 0.310017
\(611\) −0.242641 + 0.100505i −0.00981619 + 0.00406600i
\(612\) 9.65685 + 9.65685i 0.390355 + 0.390355i
\(613\) 1.32233 3.19239i 0.0534084 0.128939i −0.894923 0.446220i \(-0.852770\pi\)
0.948332 + 0.317281i \(0.102770\pi\)
\(614\) 23.7279 9.82843i 0.957581 0.396643i
\(615\) −0.384776 0.384776i −0.0155157 0.0155157i
\(616\) −16.4853 + 6.82843i −0.664211 + 0.275125i
\(617\) 22.7990 22.7990i 0.917853 0.917853i −0.0790202 0.996873i \(-0.525179\pi\)
0.996873 + 0.0790202i \(0.0251792\pi\)
\(618\) 5.55635 13.4142i 0.223509 0.539599i
\(619\) −21.7782 9.02082i −0.875339 0.362577i −0.100651 0.994922i \(-0.532093\pi\)
−0.774687 + 0.632345i \(0.782093\pi\)
\(620\) 8.97056 21.6569i 0.360266 0.869760i
\(621\) −13.0711 31.5563i −0.524524 1.26631i
\(622\) −3.75736 3.75736i −0.150656 0.150656i
\(623\) 17.3137i 0.693659i
\(624\) −1.65685 1.65685i −0.0663273 0.0663273i
\(625\) 30.0711i 1.20284i
\(626\) 10.5858 10.5858i 0.423093 0.423093i
\(627\) 5.24264 + 12.6569i 0.209371 + 0.505466i
\(628\) −3.41421 + 1.41421i −0.136242 + 0.0564333i
\(629\) 2.00000 + 0.828427i 0.0797452 + 0.0330316i
\(630\) −13.0711 5.41421i −0.520764 0.215707i
\(631\) 32.4558 32.4558i 1.29205 1.29205i 0.358528 0.933519i \(-0.383279\pi\)
0.933519 0.358528i \(-0.116721\pi\)
\(632\) −16.9706 −0.675053
\(633\) −10.6569 10.6569i −0.423572 0.423572i
\(634\) 10.1716 + 24.5563i 0.403965 + 0.975257i
\(635\) 14.5442 35.1127i 0.577167 1.39340i
\(636\) −1.85786 −0.0736691
\(637\) 3.53553 1.46447i 0.140083 0.0580243i
\(638\) 21.3137i 0.843818i
\(639\) 19.8995 0.787212
\(640\) −30.6274 12.6863i −1.21065 0.501470i
\(641\) 7.45584 0.294488 0.147244 0.989100i \(-0.452960\pi\)
0.147244 + 0.989100i \(0.452960\pi\)
\(642\) 4.82843i 0.190563i
\(643\) 11.4350 4.73654i 0.450954 0.186791i −0.145635 0.989338i \(-0.546522\pi\)
0.596588 + 0.802547i \(0.296522\pi\)
\(644\) −23.3137 −0.918689
\(645\) −4.37258 + 10.5563i −0.172170 + 0.415656i
\(646\) −6.14214 14.8284i −0.241659 0.583417i
\(647\) 6.17157 + 6.17157i 0.242630 + 0.242630i 0.817937 0.575308i \(-0.195118\pi\)
−0.575308 + 0.817937i \(0.695118\pi\)
\(648\) −11.5147 −0.452341
\(649\) 15.4853 15.4853i 0.607850 0.607850i
\(650\) 3.58579 + 1.48528i 0.140646 + 0.0582575i
\(651\) 4.00000 + 1.65685i 0.156772 + 0.0649372i
\(652\) −0.928932 + 0.384776i −0.0363798 + 0.0150690i
\(653\) 2.09188 + 5.05025i 0.0818617 + 0.197632i 0.959511 0.281672i \(-0.0908891\pi\)
−0.877649 + 0.479304i \(0.840889\pi\)
\(654\) −11.4142 + 11.4142i −0.446331 + 0.446331i
\(655\) 51.8995i 2.02788i
\(656\) −0.686292 + 0.686292i −0.0267952 + 0.0267952i
\(657\) 23.8995i 0.932408i
\(658\) −0.485281 0.485281i −0.0189182 0.0189182i
\(659\) −10.1213 24.4350i −0.394271 0.951854i −0.988998 0.147926i \(-0.952740\pi\)
0.594728 0.803927i \(-0.297260\pi\)
\(660\) −7.65685 + 18.4853i −0.298043 + 0.719539i
\(661\) −41.7487 17.2929i −1.62384 0.672616i −0.629316 0.777149i \(-0.716665\pi\)
−0.994521 + 0.104534i \(0.966665\pi\)
\(662\) 0.757359 1.82843i 0.0294356 0.0710638i
\(663\) 1.17157 1.17157i 0.0455001 0.0455001i
\(664\) 12.8284 5.31371i 0.497840 0.206212i
\(665\) 11.7574 + 11.7574i 0.455931 + 0.455931i
\(666\) −2.41421 + 1.00000i −0.0935489 + 0.0387492i
\(667\) −10.6569 + 25.7279i −0.412635 + 0.996189i
\(668\) −29.3137 29.3137i −1.13418 1.13418i
\(669\) 14.8284 6.14214i 0.573300 0.237469i
\(670\) −24.8284 −0.959206
\(671\) −8.24264 −0.318204
\(672\) 2.34315 5.65685i 0.0903888 0.218218i
\(673\) 22.4853 0.866744 0.433372 0.901215i \(-0.357324\pi\)
0.433372 + 0.901215i \(0.357324\pi\)
\(674\) −24.0000 −0.924445
\(675\) −13.7279 + 5.68629i −0.528388 + 0.218865i
\(676\) −17.5563 + 17.5563i −0.675244 + 0.675244i
\(677\) 15.6066 37.6777i 0.599810 1.44807i −0.273964 0.961740i \(-0.588335\pi\)
0.873775 0.486331i \(-0.161665\pi\)
\(678\) 6.34315 2.62742i 0.243607 0.100905i
\(679\) −18.4853 18.4853i −0.709400 0.709400i
\(680\) 8.97056 21.6569i 0.344005 0.830502i
\(681\) −10.8995 + 10.8995i −0.417670 + 0.417670i
\(682\) −9.65685 + 23.3137i −0.369780 + 0.892728i
\(683\) −10.1213 4.19239i −0.387282 0.160417i 0.180543 0.983567i \(-0.442215\pi\)
−0.567824 + 0.823150i \(0.692215\pi\)
\(684\) 17.8995 + 7.41421i 0.684404 + 0.283490i
\(685\) 13.7279 + 33.1421i 0.524517 + 1.26630i
\(686\) 16.9706 + 16.9706i 0.647939 + 0.647939i
\(687\) 18.4437i 0.703669i
\(688\) 18.8284 + 7.79899i 0.717827 + 0.297334i
\(689\) 0.928932i 0.0353895i
\(690\) −18.4853 + 18.4853i −0.703723 + 0.703723i
\(691\) 12.5061 + 30.1924i 0.475754 + 1.14857i 0.961582 + 0.274518i \(0.0885183\pi\)
−0.485828 + 0.874055i \(0.661482\pi\)
\(692\) −6.24264 15.0711i −0.237310 0.572916i
\(693\) 14.0711 + 5.82843i 0.534516 + 0.221404i
\(694\) 5.58579 + 2.31371i 0.212034 + 0.0878272i
\(695\) 29.5858 29.5858i 1.12225 1.12225i
\(696\) −5.17157 5.17157i −0.196028 0.196028i
\(697\) −0.485281 0.485281i −0.0183813 0.0183813i
\(698\) 14.4558 + 34.8995i 0.547162 + 1.32097i
\(699\) 1.10051 2.65685i 0.0416249 0.100491i
\(700\) 10.1421i 0.383337i
\(701\) 2.87868 1.19239i 0.108726 0.0450359i −0.327657 0.944797i \(-0.606259\pi\)
0.436383 + 0.899761i \(0.356259\pi\)
\(702\) 4.48528i 0.169286i
\(703\) 3.07107 0.115828
\(704\) 32.9706 + 13.6569i 1.24262 + 0.514712i
\(705\) −0.769553 −0.0289830
\(706\) 8.48528i 0.319348i
\(707\) −4.65685 + 1.92893i −0.175139 + 0.0725450i
\(708\) 7.51472i 0.282420i
\(709\) 8.77817 21.1924i 0.329671 0.795897i −0.668945 0.743312i \(-0.733254\pi\)
0.998616 0.0525851i \(-0.0167461\pi\)
\(710\) −13.0711 31.5563i −0.490548 1.18429i
\(711\) 10.2426 + 10.2426i 0.384129 + 0.384129i
\(712\) 24.4853 24.4853i 0.917625 0.917625i
\(713\) −23.3137 + 23.3137i −0.873105 + 0.873105i
\(714\) 4.00000 + 1.65685i 0.149696 + 0.0620062i
\(715\) −9.24264 3.82843i −0.345655 0.143175i
\(716\) 3.27208 + 7.89949i 0.122283 + 0.295218i
\(717\) −1.55635 3.75736i −0.0581229 0.140321i
\(718\) 25.2132 25.2132i 0.940948 0.940948i
\(719\) 35.6569i 1.32978i −0.746943 0.664888i \(-0.768479\pi\)
0.746943 0.664888i \(-0.231521\pi\)
\(720\) 10.8284 + 26.1421i 0.403552 + 0.974260i
\(721\) 18.9706i 0.706501i
\(722\) 2.89949 + 2.89949i 0.107908 + 0.107908i
\(723\) −2.48528 6.00000i −0.0924286 0.223142i
\(724\) −32.3848 13.4142i −1.20357 0.498535i
\(725\) 11.1924 + 4.63604i 0.415675 + 0.172178i
\(726\) 3.68629 8.89949i 0.136811 0.330291i
\(727\) −9.97056 + 9.97056i −0.369788 + 0.369788i −0.867400 0.497612i \(-0.834210\pi\)
0.497612 + 0.867400i \(0.334210\pi\)
\(728\) 2.82843 + 1.17157i 0.104828 + 0.0434214i
\(729\) 0.221825 + 0.221825i 0.00821576 + 0.00821576i
\(730\) 37.8995 15.6985i 1.40272 0.581027i
\(731\) −5.51472 + 13.3137i −0.203969 + 0.492425i
\(732\) 2.00000 2.00000i 0.0739221 0.0739221i
\(733\) −33.2635 + 13.7782i −1.22861 + 0.508908i −0.900138 0.435604i \(-0.856535\pi\)
−0.328475 + 0.944513i \(0.606535\pi\)
\(734\) −8.48528 −0.313197
\(735\) 11.2132 0.413605
\(736\) 32.9706 + 32.9706i 1.21531 + 1.21531i
\(737\) 26.7279 0.984536
\(738\) 0.828427 0.0304948
\(739\) 0.464466 0.192388i 0.0170857 0.00707711i −0.374124 0.927379i \(-0.622057\pi\)
0.391210 + 0.920301i \(0.372057\pi\)
\(740\) 3.17157 + 3.17157i 0.116589 + 0.116589i
\(741\) 0.899495 2.17157i 0.0330438 0.0797747i
\(742\) 2.24264 0.928932i 0.0823299 0.0341022i
\(743\) 31.6274 + 31.6274i 1.16030 + 1.16030i 0.984410 + 0.175887i \(0.0562793\pi\)
0.175887 + 0.984410i \(0.443721\pi\)
\(744\) −3.31371 8.00000i −0.121486 0.293294i
\(745\) −35.0000 + 35.0000i −1.28230 + 1.28230i
\(746\) 6.02944 14.5563i 0.220753 0.532946i
\(747\) −10.9497 4.53553i −0.400630 0.165947i
\(748\) −9.65685 + 23.3137i −0.353090 + 0.852434i
\(749\) −2.41421 5.82843i −0.0882134 0.212966i
\(750\) −3.17157 3.17157i −0.115809 0.115809i
\(751\) 10.9706i 0.400322i 0.979763 + 0.200161i \(0.0641464\pi\)
−0.979763 + 0.200161i \(0.935854\pi\)
\(752\) 1.37258i 0.0500530i
\(753\) 13.2132i 0.481516i
\(754\) 2.58579 2.58579i 0.0941688 0.0941688i
\(755\) 2.35534 + 5.68629i 0.0857196 + 0.206945i
\(756\) −10.8284 + 4.48528i −0.393826 + 0.163128i
\(757\) −33.2635 13.7782i −1.20898 0.500776i −0.315090 0.949062i \(-0.602035\pi\)
−0.893890 + 0.448285i \(0.852035\pi\)
\(758\) −46.6985 19.3431i −1.69617 0.702575i
\(759\) 19.8995 19.8995i 0.722306 0.722306i
\(760\) 33.2548i 1.20628i
\(761\) −29.8284 29.8284i −1.08128 1.08128i −0.996390 0.0848892i \(-0.972946\pi\)
−0.0848892 0.996390i \(-0.527054\pi\)
\(762\) −5.37258 12.9706i −0.194628 0.469874i
\(763\) 8.07107 19.4853i 0.292192 0.705415i
\(764\) 24.0000 0.868290
\(765\) −18.4853 + 7.65685i −0.668337 + 0.276834i
\(766\) 24.0000i 0.867155i
\(767\) −3.75736 −0.135670
\(768\) −11.3137 + 4.68629i −0.408248 + 0.169102i
\(769\) 5.51472 0.198866 0.0994329 0.995044i \(-0.468297\pi\)
0.0994329 + 0.995044i \(0.468297\pi\)
\(770\) 26.1421i 0.942097i
\(771\) −4.24264 + 1.75736i −0.152795 + 0.0632897i
\(772\) 3.02944 0.109032