Properties

Label 462.2.p.a.241.2
Level $462$
Weight $2$
Character 462.241
Analytic conductor $3.689$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 462.p (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.68908857338\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 8 x^{15} + 74 x^{14} - 378 x^{13} + 1878 x^{12} - 6718 x^{11} + 22086 x^{10} - 56904 x^{9} + 130215 x^{8} - 239606 x^{7} + 378750 x^{6} - 477124 x^{5} + 493030 x^{4} - 386266 x^{3} + 223844 x^{2} - 82874 x + 13417\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 241.2
Root \(0.500000 + 1.56688i\) of defining polynomial
Character \(\chi\) \(=\) 462.241
Dual form 462.2.p.a.439.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.606961 + 0.350429i) q^{5} -1.00000 q^{6} +(-1.82993 + 1.91085i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.606961 + 0.350429i) q^{5} -1.00000 q^{6} +(-1.82993 + 1.91085i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(0.350429 - 0.606961i) q^{10} +(2.78007 + 1.80865i) q^{11} +(0.866025 - 0.500000i) q^{12} -7.03562 q^{13} +(0.629345 - 2.56981i) q^{14} -0.700858 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.308893 + 0.535018i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(0.391696 + 0.678438i) q^{19} +0.700858i q^{20} +(-2.54019 + 0.739877i) q^{21} +(-3.31194 - 0.176300i) q^{22} +(2.63592 + 4.56555i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-2.25440 + 3.90473i) q^{25} +(6.09302 - 3.51781i) q^{26} +1.00000i q^{27} +(0.739877 + 2.54019i) q^{28} +2.09176i q^{29} +(0.606961 - 0.350429i) q^{30} +(-5.35024 - 3.08896i) q^{31} +(0.866025 + 0.500000i) q^{32} +(1.50329 + 2.95637i) q^{33} -0.617785i q^{34} +(0.441081 - 1.80107i) q^{35} +1.00000 q^{36} +(1.99709 + 3.45907i) q^{37} +(-0.678438 - 0.391696i) q^{38} +(-6.09302 - 3.51781i) q^{39} +(-0.350429 - 0.606961i) q^{40} +5.85343 q^{41} +(1.82993 - 1.91085i) q^{42} -3.62441i q^{43} +(2.95637 - 1.50329i) q^{44} +(-0.606961 - 0.350429i) q^{45} +(-4.56555 - 2.63592i) q^{46} +(-2.03495 + 1.17488i) q^{47} -1.00000i q^{48} +(-0.302687 - 6.99345i) q^{49} -4.50880i q^{50} +(-0.535018 + 0.308893i) q^{51} +(-3.51781 + 6.09302i) q^{52} +(-3.95068 + 6.84278i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(-2.32120 - 0.123562i) q^{55} +(-1.91085 - 1.82993i) q^{56} +0.783393i q^{57} +(-1.04588 - 1.81152i) q^{58} +(-3.25961 - 1.88193i) q^{59} +(-0.350429 + 0.606961i) q^{60} +(4.18286 + 7.24493i) q^{61} +6.17793 q^{62} +(-2.56981 - 0.629345i) q^{63} -1.00000 q^{64} +(4.27034 - 2.46548i) q^{65} +(-2.78007 - 1.80865i) q^{66} +(-1.07040 + 1.85399i) q^{67} +(0.308893 + 0.535018i) q^{68} +5.27184i q^{69} +(0.518548 + 1.78031i) q^{70} -4.48503 q^{71} +(-0.866025 + 0.500000i) q^{72} +(2.64471 - 4.58078i) q^{73} +(-3.45907 - 1.99709i) q^{74} +(-3.90473 + 2.25440i) q^{75} +0.783393 q^{76} +(-8.54340 + 2.00259i) q^{77} +7.03562 q^{78} +(3.75818 - 2.16979i) q^{79} +(0.606961 + 0.350429i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-5.06922 + 2.92671i) q^{82} +4.03988 q^{83} +(-0.629345 + 2.56981i) q^{84} -0.432980i q^{85} +(1.81220 + 3.13883i) q^{86} +(-1.04588 + 1.81152i) q^{87} +(-1.80865 + 2.78007i) q^{88} +(14.0396 - 8.10574i) q^{89} +0.700858 q^{90} +(12.8747 - 13.4440i) q^{91} +5.27184 q^{92} +(-3.08896 - 5.35024i) q^{93} +(1.17488 - 2.03495i) q^{94} +(-0.475489 - 0.274523i) q^{95} +(0.500000 + 0.866025i) q^{96} +10.4926i q^{97} +(3.75886 + 5.90516i) q^{98} +(-0.176300 + 3.31194i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 8q^{4} + 12q^{5} - 16q^{6} - 6q^{7} + 8q^{9} + O(q^{10}) \) \( 16q + 8q^{4} + 12q^{5} - 16q^{6} - 6q^{7} + 8q^{9} + 2q^{10} - 4q^{11} + 8q^{14} - 4q^{15} - 8q^{16} - 10q^{19} - 4q^{21} + 2q^{22} - 4q^{23} - 8q^{24} + 10q^{25} + 12q^{26} - 12q^{30} + 6q^{31} + 2q^{33} - 8q^{35} + 16q^{36} + 14q^{37} - 12q^{38} - 12q^{39} - 2q^{40} + 32q^{41} + 6q^{42} + 4q^{44} + 12q^{45} + 18q^{46} - 24q^{47} - 6q^{49} + 6q^{51} - 8q^{54} - 14q^{55} + 4q^{56} - 2q^{60} + 28q^{61} - 8q^{62} - 6q^{63} - 16q^{64} + 72q^{65} + 4q^{66} - 16q^{67} - 30q^{70} - 56q^{71} - 44q^{73} + 24q^{74} - 12q^{75} - 20q^{76} + 32q^{77} - 30q^{79} - 12q^{80} - 8q^{81} - 12q^{82} + 8q^{83} - 8q^{84} - 12q^{86} + 4q^{88} - 36q^{89} + 4q^{90} - 8q^{91} - 8q^{92} + 4q^{93} + 14q^{94} + 72q^{95} + 8q^{96} - 40q^{98} - 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(211\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 0.500000i −0.612372 + 0.353553i
\(3\) 0.866025 + 0.500000i 0.500000 + 0.288675i
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) −0.606961 + 0.350429i −0.271441 + 0.156717i −0.629542 0.776966i \(-0.716758\pi\)
0.358101 + 0.933683i \(0.383424\pi\)
\(6\) −1.00000 −0.408248
\(7\) −1.82993 + 1.91085i −0.691650 + 0.722233i
\(8\) 1.00000i 0.353553i
\(9\) 0.500000 + 0.866025i 0.166667 + 0.288675i
\(10\) 0.350429 0.606961i 0.110815 0.191938i
\(11\) 2.78007 + 1.80865i 0.838223 + 0.545328i
\(12\) 0.866025 0.500000i 0.250000 0.144338i
\(13\) −7.03562 −1.95133 −0.975665 0.219267i \(-0.929633\pi\)
−0.975665 + 0.219267i \(0.929633\pi\)
\(14\) 0.629345 2.56981i 0.168199 0.686811i
\(15\) −0.700858 −0.180961
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −0.308893 + 0.535018i −0.0749175 + 0.129761i −0.901050 0.433714i \(-0.857203\pi\)
0.826133 + 0.563475i \(0.190536\pi\)
\(18\) −0.866025 0.500000i −0.204124 0.117851i
\(19\) 0.391696 + 0.678438i 0.0898613 + 0.155644i 0.907452 0.420155i \(-0.138024\pi\)
−0.817591 + 0.575799i \(0.804691\pi\)
\(20\) 0.700858i 0.156717i
\(21\) −2.54019 + 0.739877i −0.554316 + 0.161454i
\(22\) −3.31194 0.176300i −0.706107 0.0375874i
\(23\) 2.63592 + 4.56555i 0.549627 + 0.951982i 0.998300 + 0.0582859i \(0.0185635\pi\)
−0.448673 + 0.893696i \(0.648103\pi\)
\(24\) −0.500000 + 0.866025i −0.102062 + 0.176777i
\(25\) −2.25440 + 3.90473i −0.450880 + 0.780947i
\(26\) 6.09302 3.51781i 1.19494 0.689899i
\(27\) 1.00000i 0.192450i
\(28\) 0.739877 + 2.54019i 0.139824 + 0.480051i
\(29\) 2.09176i 0.388431i 0.980959 + 0.194215i \(0.0622161\pi\)
−0.980959 + 0.194215i \(0.937784\pi\)
\(30\) 0.606961 0.350429i 0.110815 0.0639793i
\(31\) −5.35024 3.08896i −0.960932 0.554794i −0.0644719 0.997920i \(-0.520536\pi\)
−0.896460 + 0.443125i \(0.853870\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) 1.50329 + 2.95637i 0.261689 + 0.514638i
\(34\) 0.617785i 0.105949i
\(35\) 0.441081 1.80107i 0.0745563 0.304437i
\(36\) 1.00000 0.166667
\(37\) 1.99709 + 3.45907i 0.328320 + 0.568667i 0.982179 0.187950i \(-0.0601842\pi\)
−0.653859 + 0.756617i \(0.726851\pi\)
\(38\) −0.678438 0.391696i −0.110057 0.0635416i
\(39\) −6.09302 3.51781i −0.975665 0.563300i
\(40\) −0.350429 0.606961i −0.0554077 0.0959689i
\(41\) 5.85343 0.914152 0.457076 0.889428i \(-0.348897\pi\)
0.457076 + 0.889428i \(0.348897\pi\)
\(42\) 1.82993 1.91085i 0.282365 0.294850i
\(43\) 3.62441i 0.552717i −0.961055 0.276359i \(-0.910872\pi\)
0.961055 0.276359i \(-0.0891277\pi\)
\(44\) 2.95637 1.50329i 0.445690 0.226629i
\(45\) −0.606961 0.350429i −0.0904803 0.0522389i
\(46\) −4.56555 2.63592i −0.673153 0.388645i
\(47\) −2.03495 + 1.17488i −0.296828 + 0.171374i −0.641017 0.767527i \(-0.721487\pi\)
0.344189 + 0.938900i \(0.388154\pi\)
\(48\) 1.00000i 0.144338i
\(49\) −0.302687 6.99345i −0.0432409 0.999065i
\(50\) 4.50880i 0.637640i
\(51\) −0.535018 + 0.308893i −0.0749175 + 0.0432536i
\(52\) −3.51781 + 6.09302i −0.487832 + 0.844951i
\(53\) −3.95068 + 6.84278i −0.542668 + 0.939928i 0.456082 + 0.889938i \(0.349252\pi\)
−0.998750 + 0.0499906i \(0.984081\pi\)
\(54\) −0.500000 0.866025i −0.0680414 0.117851i
\(55\) −2.32120 0.123562i −0.312990 0.0166610i
\(56\) −1.91085 1.82993i −0.255348 0.244535i
\(57\) 0.783393i 0.103763i
\(58\) −1.04588 1.81152i −0.137331 0.237864i
\(59\) −3.25961 1.88193i −0.424365 0.245007i 0.272578 0.962134i \(-0.412124\pi\)
−0.696943 + 0.717127i \(0.745457\pi\)
\(60\) −0.350429 + 0.606961i −0.0452402 + 0.0783583i
\(61\) 4.18286 + 7.24493i 0.535560 + 0.927618i 0.999136 + 0.0415604i \(0.0132329\pi\)
−0.463576 + 0.886057i \(0.653434\pi\)
\(62\) 6.17793 0.784597
\(63\) −2.56981 0.629345i −0.323766 0.0792900i
\(64\) −1.00000 −0.125000
\(65\) 4.27034 2.46548i 0.529671 0.305806i
\(66\) −2.78007 1.80865i −0.342203 0.222629i
\(67\) −1.07040 + 1.85399i −0.130771 + 0.226501i −0.923974 0.382456i \(-0.875078\pi\)
0.793203 + 0.608957i \(0.208412\pi\)
\(68\) 0.308893 + 0.535018i 0.0374587 + 0.0648804i
\(69\) 5.27184i 0.634655i
\(70\) 0.518548 + 1.78031i 0.0619784 + 0.212788i
\(71\) −4.48503 −0.532275 −0.266138 0.963935i \(-0.585748\pi\)
−0.266138 + 0.963935i \(0.585748\pi\)
\(72\) −0.866025 + 0.500000i −0.102062 + 0.0589256i
\(73\) 2.64471 4.58078i 0.309540 0.536139i −0.668722 0.743513i \(-0.733158\pi\)
0.978262 + 0.207373i \(0.0664915\pi\)
\(74\) −3.45907 1.99709i −0.402108 0.232157i
\(75\) −3.90473 + 2.25440i −0.450880 + 0.260316i
\(76\) 0.783393 0.0898613
\(77\) −8.54340 + 2.00259i −0.973611 + 0.228216i
\(78\) 7.03562 0.796627
\(79\) 3.75818 2.16979i 0.422828 0.244120i −0.273458 0.961884i \(-0.588168\pi\)
0.696287 + 0.717764i \(0.254834\pi\)
\(80\) 0.606961 + 0.350429i 0.0678603 + 0.0391791i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −5.06922 + 2.92671i −0.559801 + 0.323202i
\(83\) 4.03988 0.443435 0.221717 0.975111i \(-0.428834\pi\)
0.221717 + 0.975111i \(0.428834\pi\)
\(84\) −0.629345 + 2.56981i −0.0686671 + 0.280389i
\(85\) 0.432980i 0.0469632i
\(86\) 1.81220 + 3.13883i 0.195415 + 0.338469i
\(87\) −1.04588 + 1.81152i −0.112130 + 0.194215i
\(88\) −1.80865 + 2.78007i −0.192803 + 0.296356i
\(89\) 14.0396 8.10574i 1.48819 0.859207i 0.488281 0.872687i \(-0.337624\pi\)
0.999909 + 0.0134796i \(0.00429082\pi\)
\(90\) 0.700858 0.0738769
\(91\) 12.8747 13.4440i 1.34964 1.40931i
\(92\) 5.27184 0.549627
\(93\) −3.08896 5.35024i −0.320311 0.554794i
\(94\) 1.17488 2.03495i 0.121179 0.209889i
\(95\) −0.475489 0.274523i −0.0487841 0.0281655i
\(96\) 0.500000 + 0.866025i 0.0510310 + 0.0883883i
\(97\) 10.4926i 1.06536i 0.846317 + 0.532680i \(0.178815\pi\)
−0.846317 + 0.532680i \(0.821185\pi\)
\(98\) 3.75886 + 5.90516i 0.379702 + 0.596512i
\(99\) −0.176300 + 3.31194i −0.0177189 + 0.332862i
\(100\) 2.25440 + 3.90473i 0.225440 + 0.390473i
\(101\) 7.49737 12.9858i 0.746016 1.29214i −0.203702 0.979033i \(-0.565297\pi\)
0.949718 0.313105i \(-0.101369\pi\)
\(102\) 0.308893 0.535018i 0.0305849 0.0529746i
\(103\) 12.4289 7.17585i 1.22466 0.707057i 0.258752 0.965944i \(-0.416689\pi\)
0.965908 + 0.258887i \(0.0833556\pi\)
\(104\) 7.03562i 0.689899i
\(105\) 1.28252 1.33923i 0.125161 0.130696i
\(106\) 7.90136i 0.767448i
\(107\) 9.93081 5.73356i 0.960048 0.554284i 0.0638601 0.997959i \(-0.479659\pi\)
0.896188 + 0.443675i \(0.146326\pi\)
\(108\) 0.866025 + 0.500000i 0.0833333 + 0.0481125i
\(109\) −1.25820 0.726424i −0.120514 0.0695788i 0.438531 0.898716i \(-0.355499\pi\)
−0.559045 + 0.829137i \(0.688832\pi\)
\(110\) 2.07200 1.05359i 0.197557 0.100456i
\(111\) 3.99419i 0.379111i
\(112\) 2.56981 + 0.629345i 0.242824 + 0.0594675i
\(113\) 12.0074 1.12956 0.564781 0.825241i \(-0.308961\pi\)
0.564781 + 0.825241i \(0.308961\pi\)
\(114\) −0.391696 0.678438i −0.0366857 0.0635416i
\(115\) −3.19980 1.84740i −0.298383 0.172271i
\(116\) 1.81152 + 1.04588i 0.168195 + 0.0971077i
\(117\) −3.51781 6.09302i −0.325222 0.563300i
\(118\) 3.76387 0.346492
\(119\) −0.457085 1.56929i −0.0419009 0.143857i
\(120\) 0.700858i 0.0639793i
\(121\) 4.45758 + 10.0563i 0.405235 + 0.914213i
\(122\) −7.24493 4.18286i −0.655925 0.378698i
\(123\) 5.06922 + 2.92671i 0.457076 + 0.263893i
\(124\) −5.35024 + 3.08896i −0.480466 + 0.277397i
\(125\) 6.66432i 0.596074i
\(126\) 2.54019 0.739877i 0.226298 0.0659135i
\(127\) 3.43188i 0.304530i −0.988340 0.152265i \(-0.951343\pi\)
0.988340 0.152265i \(-0.0486568\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) 1.81220 3.13883i 0.159556 0.276359i
\(130\) −2.46548 + 4.27034i −0.216237 + 0.374534i
\(131\) 7.30288 + 12.6490i 0.638056 + 1.10515i 0.985859 + 0.167578i \(0.0535945\pi\)
−0.347803 + 0.937568i \(0.613072\pi\)
\(132\) 3.31194 + 0.176300i 0.288267 + 0.0153450i
\(133\) −2.01317 0.493024i −0.174564 0.0427506i
\(134\) 2.14081i 0.184938i
\(135\) −0.350429 0.606961i −0.0301601 0.0522389i
\(136\) −0.535018 0.308893i −0.0458774 0.0264873i
\(137\) −8.35804 + 14.4765i −0.714075 + 1.23681i 0.249240 + 0.968442i \(0.419819\pi\)
−0.963315 + 0.268373i \(0.913514\pi\)
\(138\) −2.63592 4.56555i −0.224384 0.388645i
\(139\) −12.9399 −1.09755 −0.548775 0.835970i \(-0.684906\pi\)
−0.548775 + 0.835970i \(0.684906\pi\)
\(140\) −1.33923 1.28252i −0.113186 0.108393i
\(141\) −2.34976 −0.197885
\(142\) 3.88415 2.24252i 0.325951 0.188188i
\(143\) −19.5595 12.7250i −1.63565 1.06411i
\(144\) 0.500000 0.866025i 0.0416667 0.0721688i
\(145\) −0.733014 1.26962i −0.0608735 0.105436i
\(146\) 5.28943i 0.437756i
\(147\) 3.23459 6.20785i 0.266785 0.512015i
\(148\) 3.99419 0.328320
\(149\) 8.42523 4.86431i 0.690221 0.398500i −0.113474 0.993541i \(-0.536198\pi\)
0.803695 + 0.595041i \(0.202864\pi\)
\(150\) 2.25440 3.90473i 0.184071 0.318820i
\(151\) 17.1367 + 9.89387i 1.39456 + 0.805151i 0.993816 0.111037i \(-0.0354173\pi\)
0.400747 + 0.916189i \(0.368751\pi\)
\(152\) −0.678438 + 0.391696i −0.0550286 + 0.0317708i
\(153\) −0.617785 −0.0499450
\(154\) 6.39751 6.00599i 0.515526 0.483976i
\(155\) 4.32985 0.347782
\(156\) −6.09302 + 3.51781i −0.487832 + 0.281650i
\(157\) 10.4014 + 6.00523i 0.830119 + 0.479269i 0.853893 0.520448i \(-0.174235\pi\)
−0.0237745 + 0.999717i \(0.507568\pi\)
\(158\) −2.16979 + 3.75818i −0.172619 + 0.298985i
\(159\) −6.84278 + 3.95068i −0.542668 + 0.313309i
\(160\) −0.700858 −0.0554077
\(161\) −13.5476 3.31780i −1.06770 0.261479i
\(162\) 1.00000i 0.0785674i
\(163\) −11.1980 19.3955i −0.877094 1.51917i −0.854515 0.519426i \(-0.826146\pi\)
−0.0225784 0.999745i \(-0.507188\pi\)
\(164\) 2.92671 5.06922i 0.228538 0.395839i
\(165\) −1.94843 1.26761i −0.151685 0.0986829i
\(166\) −3.49864 + 2.01994i −0.271547 + 0.156778i
\(167\) −17.9924 −1.39229 −0.696145 0.717901i \(-0.745103\pi\)
−0.696145 + 0.717901i \(0.745103\pi\)
\(168\) −0.739877 2.54019i −0.0570827 0.195980i
\(169\) 36.4999 2.80769
\(170\) 0.216490 + 0.374971i 0.0166040 + 0.0287590i
\(171\) −0.391696 + 0.678438i −0.0299538 + 0.0518815i
\(172\) −3.13883 1.81220i −0.239334 0.138179i
\(173\) −0.189191 0.327689i −0.0143839 0.0249137i 0.858744 0.512405i \(-0.171245\pi\)
−0.873128 + 0.487491i \(0.837912\pi\)
\(174\) 2.09176i 0.158576i
\(175\) −3.33596 11.4532i −0.252175 0.865782i
\(176\) 0.176300 3.31194i 0.0132891 0.249647i
\(177\) −1.88193 3.25961i −0.141455 0.245007i
\(178\) −8.10574 + 14.0396i −0.607551 + 1.05231i
\(179\) 2.15547 3.73338i 0.161107 0.279046i −0.774159 0.632991i \(-0.781827\pi\)
0.935266 + 0.353946i \(0.115160\pi\)
\(180\) −0.606961 + 0.350429i −0.0452402 + 0.0261194i
\(181\) 6.96276i 0.517538i 0.965939 + 0.258769i \(0.0833169\pi\)
−0.965939 + 0.258769i \(0.916683\pi\)
\(182\) −4.42783 + 18.0802i −0.328212 + 1.34019i
\(183\) 8.36572i 0.618412i
\(184\) −4.56555 + 2.63592i −0.336576 + 0.194323i
\(185\) −2.42431 1.39968i −0.178239 0.102906i
\(186\) 5.35024 + 3.08896i 0.392299 + 0.226494i
\(187\) −1.82640 + 0.928709i −0.133560 + 0.0679139i
\(188\) 2.34976i 0.171374i
\(189\) −1.91085 1.82993i −0.138994 0.133108i
\(190\) 0.549047 0.0398321
\(191\) 9.27949 + 16.0725i 0.671440 + 1.16297i 0.977496 + 0.210955i \(0.0676574\pi\)
−0.306055 + 0.952014i \(0.599009\pi\)
\(192\) −0.866025 0.500000i −0.0625000 0.0360844i
\(193\) −15.1738 8.76059i −1.09223 0.630601i −0.158063 0.987429i \(-0.550525\pi\)
−0.934170 + 0.356828i \(0.883858\pi\)
\(194\) −5.24629 9.08684i −0.376662 0.652397i
\(195\) 4.93097 0.353114
\(196\) −6.20785 3.23459i −0.443418 0.231042i
\(197\) 18.8663i 1.34417i 0.740474 + 0.672086i \(0.234601\pi\)
−0.740474 + 0.672086i \(0.765399\pi\)
\(198\) −1.50329 2.95637i −0.106834 0.210100i
\(199\) −11.7194 6.76618i −0.830764 0.479642i 0.0233504 0.999727i \(-0.492567\pi\)
−0.854114 + 0.520086i \(0.825900\pi\)
\(200\) −3.90473 2.25440i −0.276106 0.159410i
\(201\) −1.85399 + 1.07040i −0.130771 + 0.0755004i
\(202\) 14.9947i 1.05503i
\(203\) −3.99704 3.82779i −0.280537 0.268658i
\(204\) 0.617785i 0.0432536i
\(205\) −3.55280 + 2.05121i −0.248138 + 0.143263i
\(206\) −7.17585 + 12.4289i −0.499965 + 0.865965i
\(207\) −2.63592 + 4.56555i −0.183209 + 0.317327i
\(208\) 3.51781 + 6.09302i 0.243916 + 0.422475i
\(209\) −0.138113 + 2.59455i −0.00955344 + 0.179469i
\(210\) −0.441081 + 1.80107i −0.0304375 + 0.124286i
\(211\) 4.94368i 0.340337i −0.985415 0.170168i \(-0.945569\pi\)
0.985415 0.170168i \(-0.0544312\pi\)
\(212\) 3.95068 + 6.84278i 0.271334 + 0.469964i
\(213\) −3.88415 2.24252i −0.266138 0.153655i
\(214\) −5.73356 + 9.93081i −0.391938 + 0.678856i
\(215\) 1.27010 + 2.19987i 0.0866199 + 0.150030i
\(216\) −1.00000 −0.0680414
\(217\) 15.6931 4.57090i 1.06532 0.310293i
\(218\) 1.45285 0.0983993
\(219\) 4.58078 2.64471i 0.309540 0.178713i
\(220\) −1.26761 + 1.94843i −0.0854619 + 0.131363i
\(221\) 2.17325 3.76418i 0.146189 0.253206i
\(222\) −1.99709 3.45907i −0.134036 0.232157i
\(223\) 22.9194i 1.53480i −0.641169 0.767400i \(-0.721550\pi\)
0.641169 0.767400i \(-0.278450\pi\)
\(224\) −2.54019 + 0.739877i −0.169724 + 0.0494351i
\(225\) −4.50880 −0.300587
\(226\) −10.3987 + 6.00371i −0.691713 + 0.399361i
\(227\) −12.1141 + 20.9823i −0.804042 + 1.39264i 0.112894 + 0.993607i \(0.463988\pi\)
−0.916936 + 0.399034i \(0.869345\pi\)
\(228\) 0.678438 + 0.391696i 0.0449307 + 0.0259407i
\(229\) −11.5855 + 6.68891i −0.765594 + 0.442016i −0.831300 0.555823i \(-0.812403\pi\)
0.0657068 + 0.997839i \(0.479070\pi\)
\(230\) 3.69481 0.243628
\(231\) −8.40009 2.53741i −0.552686 0.166949i
\(232\) −2.09176 −0.137331
\(233\) −24.1664 + 13.9525i −1.58319 + 0.914057i −0.588805 + 0.808275i \(0.700401\pi\)
−0.994389 + 0.105782i \(0.966265\pi\)
\(234\) 6.09302 + 3.51781i 0.398313 + 0.229966i
\(235\) 0.823423 1.42621i 0.0537142 0.0930357i
\(236\) −3.25961 + 1.88193i −0.212182 + 0.122503i
\(237\) 4.33957 0.281886
\(238\) 1.18049 + 1.13051i 0.0765201 + 0.0732798i
\(239\) 9.27514i 0.599959i −0.953946 0.299979i \(-0.903020\pi\)
0.953946 0.299979i \(-0.0969798\pi\)
\(240\) 0.350429 + 0.606961i 0.0226201 + 0.0391791i
\(241\) −9.54851 + 16.5385i −0.615074 + 1.06534i 0.375298 + 0.926904i \(0.377540\pi\)
−0.990372 + 0.138434i \(0.955793\pi\)
\(242\) −8.88855 6.48026i −0.571378 0.416567i
\(243\) −0.866025 + 0.500000i −0.0555556 + 0.0320750i
\(244\) 8.36572 0.535560
\(245\) 2.63443 + 4.13868i 0.168307 + 0.264411i
\(246\) −5.85343 −0.373201
\(247\) −2.75583 4.77323i −0.175349 0.303713i
\(248\) 3.08896 5.35024i 0.196149 0.339741i
\(249\) 3.49864 + 2.01994i 0.221717 + 0.128009i
\(250\) 3.33216 + 5.77147i 0.210744 + 0.365020i
\(251\) 12.1328i 0.765818i −0.923786 0.382909i \(-0.874922\pi\)
0.923786 0.382909i \(-0.125078\pi\)
\(252\) −1.82993 + 1.91085i −0.115275 + 0.120372i
\(253\) −0.929428 + 17.4600i −0.0584326 + 1.09770i
\(254\) 1.71594 + 2.97210i 0.107668 + 0.186486i
\(255\) 0.216490 0.374971i 0.0135571 0.0234816i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 17.2747 9.97355i 1.07757 0.622133i 0.147327 0.989088i \(-0.452933\pi\)
0.930239 + 0.366955i \(0.119600\pi\)
\(258\) 3.62441i 0.225646i
\(259\) −10.2643 2.51372i −0.637793 0.156195i
\(260\) 4.93097i 0.305806i
\(261\) −1.81152 + 1.04588i −0.112130 + 0.0647385i
\(262\) −12.6490 7.30288i −0.781456 0.451174i
\(263\) −14.5377 8.39335i −0.896433 0.517556i −0.0203919 0.999792i \(-0.506491\pi\)
−0.876041 + 0.482236i \(0.839825\pi\)
\(264\) −2.95637 + 1.50329i −0.181952 + 0.0925209i
\(265\) 5.53773i 0.340180i
\(266\) 1.98997 0.579614i 0.122013 0.0355384i
\(267\) 16.2115 0.992127
\(268\) 1.07040 + 1.85399i 0.0653853 + 0.113251i
\(269\) −16.8835 9.74767i −1.02940 0.594326i −0.112589 0.993642i \(-0.535914\pi\)
−0.916813 + 0.399316i \(0.869248\pi\)
\(270\) 0.606961 + 0.350429i 0.0369384 + 0.0213264i
\(271\) 5.34130 + 9.25140i 0.324461 + 0.561983i 0.981403 0.191958i \(-0.0614838\pi\)
−0.656942 + 0.753941i \(0.728150\pi\)
\(272\) 0.617785 0.0374587
\(273\) 17.8718 5.20549i 1.08165 0.315051i
\(274\) 16.7161i 1.00986i
\(275\) −13.3297 + 6.77802i −0.803810 + 0.408730i
\(276\) 4.56555 + 2.63592i 0.274814 + 0.158664i
\(277\) 26.6632 + 15.3940i 1.60203 + 0.924934i 0.991080 + 0.133268i \(0.0425471\pi\)
0.610954 + 0.791666i \(0.290786\pi\)
\(278\) 11.2063 6.46997i 0.672110 0.388043i
\(279\) 6.17793i 0.369863i
\(280\) 1.80107 + 0.441081i 0.107635 + 0.0263596i
\(281\) 21.3381i 1.27292i 0.771308 + 0.636462i \(0.219603\pi\)
−0.771308 + 0.636462i \(0.780397\pi\)
\(282\) 2.03495 1.17488i 0.121179 0.0699630i
\(283\) 1.26154 2.18504i 0.0749905 0.129887i −0.826092 0.563536i \(-0.809441\pi\)
0.901082 + 0.433648i \(0.142774\pi\)
\(284\) −2.24252 + 3.88415i −0.133069 + 0.230482i
\(285\) −0.274523 0.475489i −0.0162614 0.0281655i
\(286\) 23.3015 + 1.24038i 1.37785 + 0.0733454i
\(287\) −10.7114 + 11.1850i −0.632273 + 0.660231i
\(288\) 1.00000i 0.0589256i
\(289\) 8.30917 + 14.3919i 0.488775 + 0.846583i
\(290\) 1.26962 + 0.733014i 0.0745545 + 0.0430441i
\(291\) −5.24629 + 9.08684i −0.307543 + 0.532680i
\(292\) −2.64471 4.58078i −0.154770 0.268070i
\(293\) −5.71831 −0.334067 −0.167034 0.985951i \(-0.553419\pi\)
−0.167034 + 0.985951i \(0.553419\pi\)
\(294\) 0.302687 + 6.99345i 0.0176530 + 0.407866i
\(295\) 2.63794 0.153587
\(296\) −3.45907 + 1.99709i −0.201054 + 0.116079i
\(297\) −1.80865 + 2.78007i −0.104948 + 0.161316i
\(298\) −4.86431 + 8.42523i −0.281782 + 0.488060i
\(299\) −18.5453 32.1214i −1.07250 1.85763i
\(300\) 4.50880i 0.260316i
\(301\) 6.92570 + 6.63243i 0.399191 + 0.382287i
\(302\) −19.7877 −1.13866
\(303\) 12.9858 7.49737i 0.746016 0.430713i
\(304\) 0.391696 0.678438i 0.0224653 0.0389111i
\(305\) −5.07766 2.93159i −0.290746 0.167862i
\(306\) 0.535018 0.308893i 0.0305849 0.0176582i
\(307\) −20.7839 −1.18620 −0.593099 0.805130i \(-0.702096\pi\)
−0.593099 + 0.805130i \(0.702096\pi\)
\(308\) −2.53741 + 8.40009i −0.144582 + 0.478640i
\(309\) 14.3517 0.816439
\(310\) −3.74976 + 2.16492i −0.212972 + 0.122959i
\(311\) −6.38045 3.68376i −0.361802 0.208887i 0.308069 0.951364i \(-0.400317\pi\)
−0.669871 + 0.742477i \(0.733651\pi\)
\(312\) 3.51781 6.09302i 0.199157 0.344950i
\(313\) −6.36871 + 3.67697i −0.359981 + 0.207835i −0.669072 0.743197i \(-0.733308\pi\)
0.309092 + 0.951032i \(0.399975\pi\)
\(314\) −12.0105 −0.677789
\(315\) 1.78031 0.518548i 0.100309 0.0292169i
\(316\) 4.33957i 0.244120i
\(317\) 7.39030 + 12.8004i 0.415080 + 0.718940i 0.995437 0.0954222i \(-0.0304201\pi\)
−0.580356 + 0.814363i \(0.697087\pi\)
\(318\) 3.95068 6.84278i 0.221543 0.383724i
\(319\) −3.78327 + 5.81525i −0.211822 + 0.325591i
\(320\) 0.606961 0.350429i 0.0339301 0.0195896i
\(321\) 11.4671 0.640032
\(322\) 13.3915 3.90051i 0.746278 0.217367i
\(323\) −0.483969 −0.0269287
\(324\) 0.500000 + 0.866025i 0.0277778 + 0.0481125i
\(325\) 15.8611 27.4722i 0.879815 1.52388i
\(326\) 19.3955 + 11.1980i 1.07422 + 0.620199i
\(327\) −0.726424 1.25820i −0.0401714 0.0695788i
\(328\) 5.85343i 0.323202i
\(329\) 1.47881 6.03843i 0.0815292 0.332909i
\(330\) 2.32120 + 0.123562i 0.127778 + 0.00680184i
\(331\) −13.6449 23.6336i −0.749991 1.29902i −0.947826 0.318787i \(-0.896725\pi\)
0.197836 0.980235i \(-0.436609\pi\)
\(332\) 2.01994 3.49864i 0.110859 0.192013i
\(333\) −1.99709 + 3.45907i −0.109440 + 0.189556i
\(334\) 15.5818 8.99618i 0.852600 0.492249i
\(335\) 1.50040i 0.0819757i
\(336\) 1.91085 + 1.82993i 0.104245 + 0.0998311i
\(337\) 13.0929i 0.713215i −0.934254 0.356607i \(-0.883933\pi\)
0.934254 0.356607i \(-0.116067\pi\)
\(338\) −31.6099 + 18.2500i −1.71935 + 0.992667i
\(339\) 10.3987 + 6.00371i 0.564781 + 0.326077i
\(340\) −0.374971 0.216490i −0.0203357 0.0117408i
\(341\) −9.28720 18.2642i −0.502930 0.989064i
\(342\) 0.783393i 0.0423610i
\(343\) 13.9173 + 12.2192i 0.751465 + 0.659773i
\(344\) 3.62441 0.195415
\(345\) −1.84740 3.19980i −0.0994609 0.172271i
\(346\) 0.327689 + 0.189191i 0.0176167 + 0.0101710i
\(347\) 9.82708 + 5.67367i 0.527545 + 0.304578i 0.740016 0.672589i \(-0.234818\pi\)
−0.212471 + 0.977167i \(0.568151\pi\)
\(348\) 1.04588 + 1.81152i 0.0560651 + 0.0971077i
\(349\) −12.4060 −0.664076 −0.332038 0.943266i \(-0.607736\pi\)
−0.332038 + 0.943266i \(0.607736\pi\)
\(350\) 8.61563 + 8.25080i 0.460525 + 0.441024i
\(351\) 7.03562i 0.375534i
\(352\) 1.50329 + 2.95637i 0.0801255 + 0.157575i
\(353\) 5.90974 + 3.41199i 0.314544 + 0.181602i 0.648958 0.760824i \(-0.275205\pi\)
−0.334414 + 0.942426i \(0.608538\pi\)
\(354\) 3.25961 + 1.88193i 0.173246 + 0.100024i
\(355\) 2.72224 1.57168i 0.144481 0.0834163i
\(356\) 16.2115i 0.859207i
\(357\) 0.388800 1.58759i 0.0205775 0.0840242i
\(358\) 4.31093i 0.227840i
\(359\) 17.6942 10.2157i 0.933862 0.539166i 0.0458314 0.998949i \(-0.485406\pi\)
0.888031 + 0.459783i \(0.152073\pi\)
\(360\) 0.350429 0.606961i 0.0184692 0.0319896i
\(361\) 9.19315 15.9230i 0.483850 0.838053i
\(362\) −3.48138 6.02993i −0.182977 0.316926i
\(363\) −1.16779 + 10.9378i −0.0612932 + 0.574088i
\(364\) −5.20549 17.8718i −0.272842 0.936739i
\(365\) 3.70714i 0.194040i
\(366\) −4.18286 7.24493i −0.218642 0.378698i
\(367\) 17.4563 + 10.0784i 0.911212 + 0.526088i 0.880821 0.473450i \(-0.156991\pi\)
0.0303908 + 0.999538i \(0.490325\pi\)
\(368\) 2.63592 4.56555i 0.137407 0.237995i
\(369\) 2.92671 + 5.06922i 0.152359 + 0.263893i
\(370\) 2.79936 0.145532
\(371\) −5.84604 20.0710i −0.303511 1.04203i
\(372\) −6.17793 −0.320311
\(373\) 7.22139 4.16927i 0.373909 0.215877i −0.301256 0.953543i \(-0.597406\pi\)
0.675165 + 0.737667i \(0.264072\pi\)
\(374\) 1.11736 1.71749i 0.0577771 0.0888091i
\(375\) 3.33216 5.77147i 0.172072 0.298037i
\(376\) −1.17488 2.03495i −0.0605897 0.104944i
\(377\) 14.7169i 0.757956i
\(378\) 2.56981 + 0.629345i 0.132177 + 0.0323700i
\(379\) −12.2093 −0.627151 −0.313575 0.949563i \(-0.601527\pi\)
−0.313575 + 0.949563i \(0.601527\pi\)
\(380\) −0.475489 + 0.274523i −0.0243921 + 0.0140828i
\(381\) 1.71594 2.97210i 0.0879103 0.152265i
\(382\) −16.0725 9.27949i −0.822343 0.474780i
\(383\) 16.1528 9.32585i 0.825372 0.476529i −0.0268936 0.999638i \(-0.508562\pi\)
0.852265 + 0.523110i \(0.175228\pi\)
\(384\) 1.00000 0.0510310
\(385\) 4.48374 4.20934i 0.228513 0.214528i
\(386\) 17.5212 0.891805
\(387\) 3.13883 1.81220i 0.159556 0.0921195i
\(388\) 9.08684 + 5.24629i 0.461314 + 0.266340i
\(389\) 4.75722 8.23974i 0.241201 0.417772i −0.719856 0.694123i \(-0.755792\pi\)
0.961057 + 0.276352i \(0.0891255\pi\)
\(390\) −4.27034 + 2.46548i −0.216237 + 0.124845i
\(391\) −3.25686 −0.164707
\(392\) 6.99345 0.302687i 0.353223 0.0152880i
\(393\) 14.6058i 0.736764i
\(394\) −9.43317 16.3387i −0.475236 0.823133i
\(395\) −1.52071 + 2.63395i −0.0765153 + 0.132528i
\(396\) 2.78007 + 1.80865i 0.139704 + 0.0908880i
\(397\) −29.5051 + 17.0348i −1.48082 + 0.854952i −0.999764 0.0217370i \(-0.993080\pi\)
−0.481057 + 0.876689i \(0.659747\pi\)
\(398\) 13.5324 0.678316
\(399\) −1.49695 1.43356i −0.0749410 0.0717676i
\(400\) 4.50880 0.225440
\(401\) 14.8179 + 25.6653i 0.739969 + 1.28166i 0.952508 + 0.304512i \(0.0984934\pi\)
−0.212539 + 0.977153i \(0.568173\pi\)
\(402\) 1.07040 1.85399i 0.0533869 0.0924688i
\(403\) 37.6423 + 21.7328i 1.87509 + 1.08259i
\(404\) −7.49737 12.9858i −0.373008 0.646069i
\(405\) 0.700858i 0.0348259i
\(406\) 5.37544 + 1.31644i 0.266778 + 0.0653338i
\(407\) −0.704177 + 13.2285i −0.0349048 + 0.655712i
\(408\) −0.308893 0.535018i −0.0152925 0.0264873i
\(409\) 13.6644 23.6675i 0.675662 1.17028i −0.300613 0.953746i \(-0.597191\pi\)
0.976275 0.216534i \(-0.0694753\pi\)
\(410\) 2.05121 3.55280i 0.101302 0.175460i
\(411\) −14.4765 + 8.35804i −0.714075 + 0.412272i
\(412\) 14.3517i 0.707057i
\(413\) 9.56095 2.78480i 0.470464 0.137031i
\(414\) 5.27184i 0.259097i
\(415\) −2.45205 + 1.41569i −0.120366 + 0.0694936i
\(416\) −6.09302 3.51781i −0.298735 0.172475i
\(417\) −11.2063 6.46997i −0.548775 0.316836i
\(418\) −1.17766 2.31600i −0.0576014 0.113279i
\(419\) 25.6972i 1.25539i 0.778459 + 0.627696i \(0.216002\pi\)
−0.778459 + 0.627696i \(0.783998\pi\)
\(420\) −0.518548 1.78031i −0.0253026 0.0868704i
\(421\) −36.9246 −1.79959 −0.899797 0.436309i \(-0.856285\pi\)
−0.899797 + 0.436309i \(0.856285\pi\)
\(422\) 2.47184 + 4.28135i 0.120327 + 0.208413i
\(423\) −2.03495 1.17488i −0.0989426 0.0571245i
\(424\) −6.84278 3.95068i −0.332315 0.191862i
\(425\) −1.39273 2.41229i −0.0675575 0.117013i
\(426\) 4.48503 0.217300
\(427\) −21.4983 5.26492i −1.04038 0.254787i
\(428\) 11.4671i 0.554284i
\(429\) −10.5766 20.7999i −0.510641 1.00423i
\(430\) −2.19987 1.27010i −0.106087 0.0612495i
\(431\) 17.4320 + 10.0644i 0.839668 + 0.484783i 0.857152 0.515064i \(-0.172232\pi\)
−0.0174831 + 0.999847i \(0.505565\pi\)
\(432\) 0.866025 0.500000i 0.0416667 0.0240563i
\(433\) 38.1992i 1.83574i 0.396884 + 0.917869i \(0.370092\pi\)
−0.396884 + 0.917869i \(0.629908\pi\)
\(434\) −11.3052 + 11.8051i −0.542667 + 0.566662i
\(435\) 1.46603i 0.0702907i
\(436\) −1.25820 + 0.726424i −0.0602570 + 0.0347894i
\(437\) −2.06496 + 3.57662i −0.0987804 + 0.171093i
\(438\) −2.64471 + 4.58078i −0.126369 + 0.218878i
\(439\) 3.66099 + 6.34102i 0.174729 + 0.302640i 0.940068 0.340988i \(-0.110762\pi\)
−0.765338 + 0.643628i \(0.777428\pi\)
\(440\) 0.123562 2.32120i 0.00589057 0.110659i
\(441\) 5.90516 3.75886i 0.281198 0.178993i
\(442\) 4.34650i 0.206742i
\(443\) 16.5124 + 28.6003i 0.784527 + 1.35884i 0.929281 + 0.369373i \(0.120428\pi\)
−0.144754 + 0.989468i \(0.546239\pi\)
\(444\) 3.45907 + 1.99709i 0.164160 + 0.0947778i
\(445\) −5.68097 + 9.83973i −0.269304 + 0.466448i
\(446\) 11.4597 + 19.8488i 0.542633 + 0.939869i
\(447\) 9.72861 0.460148
\(448\) 1.82993 1.91085i 0.0864562 0.0902791i
\(449\) −22.5285 −1.06319 −0.531594 0.846999i \(-0.678407\pi\)
−0.531594 + 0.846999i \(0.678407\pi\)
\(450\) 3.90473 2.25440i 0.184071 0.106273i
\(451\) 16.2729 + 10.5868i 0.766263 + 0.498513i
\(452\) 6.00371 10.3987i 0.282391 0.489115i
\(453\) 9.89387 + 17.1367i 0.464854 + 0.805151i
\(454\) 24.2282i 1.13709i
\(455\) −3.10328 + 12.6717i −0.145484 + 0.594056i
\(456\) −0.783393 −0.0366857
\(457\) 28.7305 16.5876i 1.34396 0.775934i 0.356572 0.934268i \(-0.383946\pi\)
0.987386 + 0.158334i \(0.0506122\pi\)
\(458\) 6.68891 11.5855i 0.312552 0.541356i
\(459\) −0.535018 0.308893i −0.0249725 0.0144179i
\(460\) −3.19980 + 1.84740i −0.149191 + 0.0861357i
\(461\) −7.42955 −0.346029 −0.173014 0.984919i \(-0.555351\pi\)
−0.173014 + 0.984919i \(0.555351\pi\)
\(462\) 8.54340 2.00259i 0.397475 0.0931688i
\(463\) −15.7504 −0.731984 −0.365992 0.930618i \(-0.619270\pi\)
−0.365992 + 0.930618i \(0.619270\pi\)
\(464\) 1.81152 1.04588i 0.0840977 0.0485538i
\(465\) 3.74976 + 2.16492i 0.173891 + 0.100396i
\(466\) 13.9525 24.1664i 0.646336 1.11949i
\(467\) 11.5815 6.68657i 0.535927 0.309418i −0.207500 0.978235i \(-0.566533\pi\)
0.743427 + 0.668817i \(0.233199\pi\)
\(468\) −7.03562 −0.325222
\(469\) −1.58393 5.43806i −0.0731392 0.251106i
\(470\) 1.64685i 0.0759633i
\(471\) 6.00523 + 10.4014i 0.276706 + 0.479269i
\(472\) 1.88193 3.25961i 0.0866231 0.150036i
\(473\) 6.55528 10.0761i 0.301412 0.463300i
\(474\) −3.75818 + 2.16979i −0.172619 + 0.0996616i
\(475\) −3.53216 −0.162067
\(476\) −1.58759 0.388800i −0.0727671 0.0178206i
\(477\) −7.90136 −0.361779
\(478\) 4.63757 + 8.03251i 0.212117 + 0.367398i
\(479\) −5.63050 + 9.75230i −0.257264 + 0.445594i −0.965508 0.260374i \(-0.916154\pi\)
0.708244 + 0.705968i \(0.249488\pi\)
\(480\) −0.606961 0.350429i −0.0277038 0.0159948i
\(481\) −14.0508 24.3367i −0.640661 1.10966i
\(482\) 19.0970i 0.869845i
\(483\) −10.0737 9.64711i −0.458369 0.438959i
\(484\) 10.9378 + 1.16779i 0.497174 + 0.0530814i
\(485\) −3.67690 6.36858i −0.166960 0.289182i
\(486\) 0.500000 0.866025i 0.0226805 0.0392837i
\(487\) −1.33482 + 2.31197i −0.0604862 + 0.104765i −0.894683 0.446702i \(-0.852598\pi\)
0.834197 + 0.551467i \(0.185932\pi\)
\(488\) −7.24493 + 4.18286i −0.327962 + 0.189349i
\(489\) 22.3960i 1.01278i
\(490\) −4.35082 2.26699i −0.196550 0.102412i
\(491\) 11.3063i 0.510245i 0.966909 + 0.255123i \(0.0821158\pi\)
−0.966909 + 0.255123i \(0.917884\pi\)
\(492\) 5.06922 2.92671i 0.228538 0.131946i
\(493\) −1.11913 0.646130i −0.0504031 0.0291002i
\(494\) 4.77323 + 2.75583i 0.214758 + 0.123991i
\(495\) −1.05359 2.07200i −0.0473554 0.0931293i
\(496\) 6.17793i 0.277397i
\(497\) 8.20731 8.57022i 0.368148 0.384427i
\(498\) −4.03988 −0.181032
\(499\) −10.7200 18.5676i −0.479894 0.831200i 0.519840 0.854263i \(-0.325991\pi\)
−0.999734 + 0.0230633i \(0.992658\pi\)
\(500\) −5.77147 3.33216i −0.258108 0.149019i
\(501\) −15.5818 8.99618i −0.696145 0.401920i
\(502\) 6.06642 + 10.5073i 0.270757 + 0.468966i
\(503\) 30.0822 1.34130 0.670649 0.741775i \(-0.266016\pi\)
0.670649 + 0.741775i \(0.266016\pi\)
\(504\) 0.629345 2.56981i 0.0280332 0.114468i
\(505\) 10.5092i 0.467652i
\(506\) −7.92509 15.5855i −0.352313 0.692860i
\(507\) 31.6099 + 18.2500i 1.40384 + 0.810509i
\(508\) −2.97210 1.71594i −0.131866 0.0761326i
\(509\) 11.6751 6.74064i 0.517491 0.298774i −0.218416 0.975856i \(-0.570089\pi\)
0.735908 + 0.677082i \(0.236756\pi\)
\(510\) 0.432980i 0.0191727i
\(511\) 3.91352 + 13.4362i 0.173124 + 0.594381i
\(512\) 1.00000i 0.0441942i
\(513\) −0.678438 + 0.391696i −0.0299538 + 0.0172938i
\(514\) −9.97355 + 17.2747i −0.439914 + 0.761954i
\(515\) −5.02925 + 8.71091i −0.221615 + 0.383849i
\(516\) −1.81220 3.13883i −0.0797779 0.138179i
\(517\) −7.78224 0.414263i −0.342263 0.0182193i
\(518\) 10.1460 2.95521i 0.445790 0.129844i
\(519\) 0.378382i 0.0166091i
\(520\) 2.46548 + 4.27034i 0.108119 + 0.187267i
\(521\) −9.63608 5.56339i −0.422164 0.243737i 0.273839 0.961776i \(-0.411707\pi\)
−0.696003 + 0.718039i \(0.745040\pi\)
\(522\) 1.04588 1.81152i 0.0457770 0.0792881i
\(523\) 7.45440 + 12.9114i 0.325958 + 0.564576i 0.981706 0.190404i \(-0.0609798\pi\)
−0.655748 + 0.754980i \(0.727646\pi\)
\(524\) 14.6058 0.638056
\(525\) 2.83759 11.5868i 0.123842 0.505688i
\(526\) 16.7867 0.731935
\(527\) 3.30530 1.90832i 0.143981 0.0831275i
\(528\) 1.80865 2.78007i 0.0787113 0.120987i
\(529\) −2.39614 + 4.15023i −0.104180 + 0.180445i
\(530\) 2.76887 + 4.79582i 0.120272 + 0.208317i
\(531\) 3.76387i 0.163338i
\(532\) −1.43356 + 1.49695i −0.0621526 + 0.0649008i
\(533\) −41.1825 −1.78381
\(534\) −14.0396 + 8.10574i −0.607551 + 0.350770i
\(535\) −4.01841 + 6.96009i −0.173731 + 0.300911i
\(536\) −1.85399 1.07040i −0.0800803 0.0462344i
\(537\) 3.73338 2.15547i 0.161107 0.0930152i
\(538\) 19.4953 0.840504
\(539\) 11.8072 19.9897i 0.508572 0.861019i
\(540\) −0.700858 −0.0301601
\(541\) −23.0202 + 13.2907i −0.989717 + 0.571413i −0.905190 0.425008i \(-0.860271\pi\)
−0.0845270 + 0.996421i \(0.526938\pi\)
\(542\) −9.25140 5.34130i −0.397382 0.229428i
\(543\) −3.48138 + 6.02993i −0.149400 + 0.258769i
\(544\) −0.535018 + 0.308893i −0.0229387 + 0.0132437i
\(545\) 1.01824 0.0436166
\(546\) −12.8747 + 13.4440i −0.550987 + 0.575350i
\(547\) 18.2285i 0.779393i −0.920943 0.389696i \(-0.872580\pi\)
0.920943 0.389696i \(-0.127420\pi\)
\(548\) 8.35804 + 14.4765i 0.357038 + 0.618407i
\(549\) −4.18286 + 7.24493i −0.178520 + 0.309206i
\(550\) 8.15483 12.5348i 0.347723 0.534485i
\(551\) −1.41913 + 0.819336i −0.0604571 + 0.0349049i
\(552\) −5.27184 −0.224384
\(553\) −2.73109 + 11.1519i −0.116138 + 0.474226i
\(554\) −30.7880 −1.30805
\(555\) −1.39968 2.42431i −0.0594130 0.102906i
\(556\) −6.46997 + 11.2063i −0.274388 + 0.475253i
\(557\) −27.2666 15.7424i −1.15532 0.667025i −0.205143 0.978732i \(-0.565766\pi\)
−0.950178 + 0.311707i \(0.899099\pi\)
\(558\) 3.08896 + 5.35024i 0.130766 + 0.226494i
\(559\) 25.5000i 1.07853i
\(560\) −1.78031 + 0.518548i −0.0752320 + 0.0219127i
\(561\) −2.04606 0.108916i −0.0863849 0.00459843i
\(562\) −10.6691 18.4793i −0.450047 0.779504i
\(563\) −10.9701 + 19.0008i −0.462335 + 0.800787i −0.999077 0.0429591i \(-0.986321\pi\)
0.536742 + 0.843746i \(0.319655\pi\)
\(564\) −1.17488 + 2.03495i −0.0494713 + 0.0856868i
\(565\) −7.28803 + 4.20774i −0.306610 + 0.177021i
\(566\) 2.52307i 0.106053i
\(567\) −0.739877 2.54019i −0.0310719 0.106678i
\(568\) 4.48503i 0.188188i
\(569\) 26.8999 15.5307i 1.12770 0.651080i 0.184347 0.982861i \(-0.440983\pi\)
0.943356 + 0.331781i \(0.107650\pi\)
\(570\) 0.475489 + 0.274523i 0.0199160 + 0.0114985i
\(571\) −8.45951 4.88410i −0.354020 0.204393i 0.312435 0.949939i \(-0.398855\pi\)
−0.666454 + 0.745546i \(0.732189\pi\)
\(572\) −20.7999 + 10.5766i −0.869687 + 0.442228i
\(573\) 18.5590i 0.775313i
\(574\) 3.68382 15.0422i 0.153760 0.627849i
\(575\) −23.7697 −0.991263
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) 16.7912 + 9.69442i 0.699028 + 0.403584i 0.806985 0.590571i \(-0.201098\pi\)
−0.107957 + 0.994156i \(0.534431\pi\)
\(578\) −14.3919 8.30917i −0.598624 0.345616i
\(579\) −8.76059 15.1738i −0.364078 0.630601i
\(580\) −1.46603 −0.0608735
\(581\) −7.39272 + 7.71961i −0.306702 + 0.320263i
\(582\) 10.4926i 0.434931i
\(583\) −23.3594 + 11.8780i −0.967446 + 0.491937i
\(584\) 4.58078 + 2.64471i 0.189554 + 0.109439i
\(585\) 4.27034 + 2.46548i 0.176557 + 0.101935i
\(586\) 4.95220 2.85916i 0.204574 0.118111i
\(587\) 14.0625i 0.580421i −0.956963 0.290210i \(-0.906275\pi\)
0.956963 0.290210i \(-0.0937253\pi\)
\(588\) −3.75886 5.90516i −0.155013 0.243525i
\(589\) 4.83974i 0.199418i
\(590\) −2.28452 + 1.31897i −0.0940522 + 0.0543011i
\(591\) −9.43317 + 16.3387i −0.388029 + 0.672086i
\(592\) 1.99709 3.45907i 0.0820800 0.142167i
\(593\) 19.0546 + 33.0036i 0.782480 + 1.35530i 0.930493 + 0.366310i \(0.119379\pi\)
−0.148013 + 0.988985i \(0.547288\pi\)
\(594\) 0.176300 3.31194i 0.00723370 0.135890i
\(595\) 0.827358 + 0.792324i 0.0339184 + 0.0324821i
\(596\) 9.72861i 0.398500i
\(597\) −6.76618 11.7194i −0.276921 0.479642i
\(598\) 32.1214 + 18.5453i 1.31354 + 0.758375i
\(599\) 12.2662 21.2456i 0.501183 0.868074i −0.498817 0.866708i \(-0.666232\pi\)
0.999999 0.00136605i \(-0.000434826\pi\)
\(600\) −2.25440 3.90473i −0.0920355 0.159410i
\(601\) −3.08091 −0.125673 −0.0628365 0.998024i \(-0.520015\pi\)
−0.0628365 + 0.998024i \(0.520015\pi\)
\(602\) −9.31404 2.28100i −0.379612 0.0929667i
\(603\) −2.14081 −0.0871804
\(604\) 17.1367 9.89387i 0.697282 0.402576i
\(605\) −6.22961 4.54174i −0.253270 0.184648i
\(606\) −7.49737 + 12.9858i −0.304560 + 0.527513i
\(607\) −20.3839 35.3059i −0.827356 1.43302i −0.900105 0.435673i \(-0.856510\pi\)
0.0727485 0.997350i \(-0.476823\pi\)
\(608\) 0.783393i 0.0317708i
\(609\) −1.54765 5.31348i −0.0627138 0.215313i
\(610\) 5.86318 0.237393
\(611\) 14.3171 8.26600i 0.579209 0.334406i
\(612\) −0.308893 + 0.535018i −0.0124862 + 0.0216268i
\(613\) −7.75535 4.47755i −0.313236 0.180847i 0.335138 0.942169i \(-0.391217\pi\)
−0.648373 + 0.761322i \(0.724550\pi\)
\(614\) 17.9993 10.3919i 0.726394 0.419384i
\(615\) −4.10242 −0.165426
\(616\) −2.00259 8.54340i −0.0806865 0.344223i
\(617\) 19.1914 0.772618 0.386309 0.922369i \(-0.373750\pi\)
0.386309 + 0.922369i \(0.373750\pi\)
\(618\) −12.4289 + 7.17585i −0.499965 + 0.288655i
\(619\) 2.91921 + 1.68541i 0.117333 + 0.0677422i 0.557518 0.830165i \(-0.311754\pi\)
−0.440185 + 0.897907i \(0.645087\pi\)
\(620\) 2.16492 3.74976i 0.0869454 0.150594i
\(621\) −4.56555 + 2.63592i −0.183209 + 0.105776i
\(622\) 7.36751 0.295410
\(623\) −10.2026 + 41.6604i −0.408759 + 1.66909i
\(624\) 7.03562i 0.281650i
\(625\) −8.93663 15.4787i −0.357465 0.619148i
\(626\) 3.67697 6.36871i 0.146961 0.254545i
\(627\) −1.41688 + 2.17789i −0.0565848 + 0.0869764i
\(628\) 10.4014 6.00523i 0.415059 0.239635i
\(629\) −2.46755 −0.0983876
\(630\) −1.28252 + 1.33923i −0.0510969 + 0.0533563i
\(631\) 33.1910 1.32131 0.660657 0.750688i \(-0.270278\pi\)
0.660657 + 0.750688i \(0.270278\pi\)
\(632\) 2.16979 + 3.75818i 0.0863095 + 0.149492i
\(633\) 2.47184 4.28135i 0.0982468 0.170168i
\(634\) −12.8004 7.39030i −0.508368 0.293506i
\(635\) 1.20263 + 2.08302i 0.0477250 + 0.0826620i
\(636\) 7.90136i 0.313309i
\(637\) 2.12959 + 49.2033i 0.0843773 + 1.94950i
\(638\) 0.368779 6.92779i 0.0146001 0.274274i
\(639\) −2.24252 3.88415i −0.0887125 0.153655i
\(640\) −0.350429 + 0.606961i −0.0138519 + 0.0239922i
\(641\) 17.2306 29.8442i 0.680566 1.17878i −0.294242 0.955731i \(-0.595067\pi\)
0.974808 0.223045i \(-0.0715995\pi\)
\(642\) −9.93081 + 5.73356i −0.391938 + 0.226285i
\(643\) 2.69205i 0.106164i −0.998590 0.0530821i \(-0.983095\pi\)
0.998590 0.0530821i \(-0.0169045\pi\)
\(644\) −9.64711 + 10.0737i −0.380149 + 0.396959i
\(645\) 2.54020i 0.100020i
\(646\) 0.419129 0.241984i 0.0164904 0.00952074i
\(647\) 40.4270 + 23.3405i 1.58935 + 0.917611i 0.993414 + 0.114577i \(0.0365514\pi\)
0.595934 + 0.803033i \(0.296782\pi\)
\(648\) −0.866025 0.500000i −0.0340207 0.0196419i
\(649\) −5.65818 11.1274i −0.222103 0.436788i
\(650\) 31.7222i 1.24425i
\(651\) 15.8761 + 3.88804i 0.622233 + 0.152384i
\(652\) −22.3960 −0.877094
\(653\) −19.9929 34.6287i −0.782383 1.35513i −0.930550 0.366165i \(-0.880671\pi\)
0.148167 0.988962i \(-0.452663\pi\)
\(654\) 1.25820 + 0.726424i 0.0491997 + 0.0284054i
\(655\) −8.86513 5.11828i −0.346389 0.199988i
\(656\) −2.92671 5.06922i −0.114269 0.197920i
\(657\) 5.28943 0.206360
\(658\) 1.73853 + 5.96884i 0.0677750 + 0.232689i
\(659\) 24.9930i 0.973590i −0.873516 0.486795i \(-0.838166\pi\)
0.873516 0.486795i \(-0.161834\pi\)
\(660\) −2.07200 + 1.05359i −0.0806523 + 0.0410110i
\(661\) 12.7267 + 7.34774i 0.495010 + 0.285794i 0.726650 0.687007i \(-0.241076\pi\)
−0.231641 + 0.972801i \(0.574409\pi\)
\(662\) 23.6336 + 13.6449i 0.918547 + 0.530323i
\(663\) 3.76418 2.17325i 0.146189 0.0844021i
\(664\) 4.03988i 0.156778i
\(665\) 1.39469 0.406227i 0.0540836 0.0157528i
\(666\) 3.99419i 0.154772i
\(667\) −9.55004 + 5.51372i −0.369779 + 0.213492i
\(668\) −8.99618 + 15.5818i −0.348073 + 0.602879i
\(669\) 11.4597 19.8488i 0.443058 0.767400i
\(670\) 0.750200 + 1.29939i 0.0289828 + 0.0501996i
\(671\) −1.47488 + 27.7067i −0.0569371 + 1.06961i
\(672\) −2.56981 0.629345i −0.0991326 0.0242775i
\(673\) 51.7415i 1.99449i 0.0741830 + 0.997245i \(0.476365\pi\)
−0.0741830 + 0.997245i \(0.523635\pi\)
\(674\) 6.54644 + 11.3388i 0.252159 + 0.436753i
\(675\) −3.90473 2.25440i −0.150293 0.0867719i
\(676\) 18.2500 31.6099i 0.701922 1.21576i
\(677\) 18.7265 + 32.4353i 0.719718 + 1.24659i 0.961111 + 0.276161i \(0.0890624\pi\)
−0.241393 + 0.970427i \(0.577604\pi\)
\(678\) −12.0074 −0.461142
\(679\) −20.0497 19.2007i −0.769438 0.736856i
\(680\) 0.432980 0.0166040
\(681\) −20.9823 + 12.1141i −0.804042 + 0.464214i
\(682\) 17.1751 + 11.1737i 0.657667 + 0.427863i
\(683\) 21.0079 36.3868i 0.803845 1.39230i −0.113223 0.993570i \(-0.536117\pi\)
0.917068 0.398731i \(-0.130549\pi\)
\(684\) 0.391696 + 0.678438i 0.0149769 + 0.0259407i
\(685\) 11.7156i 0.447630i
\(686\) −18.1623 3.62344i −0.693441 0.138344i
\(687\) −13.3778 −0.510396
\(688\) −3.13883 + 1.81220i −0.119667 + 0.0690896i
\(689\) 27.7955 48.1432i 1.05892 1.83411i
\(690\) 3.19980 + 1.84740i 0.121814 + 0.0703295i
\(691\) −23.9459 + 13.8252i −0.910945 + 0.525934i −0.880735 0.473610i \(-0.842951\pi\)
−0.0302096 + 0.999544i \(0.509617\pi\)
\(692\) −0.378382 −0.0143839
\(693\) −6.00599 6.39751i −0.228149 0.243021i
\(694\) −11.3473 −0.430739
\(695\) 7.85403 4.53453i 0.297920 0.172004i
\(696\) −1.81152 1.04588i −0.0686655 0.0396440i
\(697\) −1.80808 + 3.13169i −0.0684859 + 0.118621i
\(698\) 10.7439 6.20298i 0.406662 0.234786i
\(699\) −27.9050 −1.05546
\(700\) −11.5868 2.83759i −0.437938 0.107251i
\(701\) 8.73779i 0.330022i 0.986292 + 0.165011i \(0.0527659\pi\)
−0.986292 + 0.165011i \(0.947234\pi\)
\(702\) 3.51781 + 6.09302i 0.132771 + 0.229966i
\(703\) −1.56451 + 2.70981i −0.0590065 + 0.102202i
\(704\) −2.78007 1.80865i −0.104778 0.0681660i
\(705\) 1.42621 0.823423i 0.0537142 0.0310119i
\(706\) −6.82398 −0.256824
\(707\) 11.0943 + 38.0895i 0.417243 + 1.43250i
\(708\) −3.76387 −0.141455
\(709\) 16.6683 + 28.8703i 0.625990 + 1.08425i 0.988349 + 0.152208i \(0.0486382\pi\)
−0.362359 + 0.932039i \(0.618028\pi\)
\(710\) −1.57168 + 2.72224i −0.0589843 + 0.102164i
\(711\) 3.75818 + 2.16979i 0.140943 + 0.0813734i
\(712\) 8.10574 + 14.0396i 0.303776 + 0.526155i
\(713\) 32.5690i 1.21972i
\(714\) 0.457085 + 1.56929i 0.0171060 + 0.0587293i
\(715\) 16.3310 + 0.869332i 0.610747 + 0.0325112i
\(716\) −2.15547 3.73338i −0.0805536 0.139523i
\(717\) 4.63757 8.03251i 0.173193 0.299979i
\(718\) −10.2157 + 17.6942i −0.381248 + 0.660340i
\(719\) −9.08278 + 5.24394i −0.338730 + 0.195566i −0.659711 0.751520i \(-0.729321\pi\)
0.320980 + 0.947086i \(0.395988\pi\)
\(720\) 0.700858i 0.0261194i
\(721\) −9.03216 + 36.8811i −0.336375 + 1.37353i
\(722\) 18.3863i 0.684267i
\(723\) −16.5385 + 9.54851i −0.615074 + 0.355113i
\(724\) 6.02993 + 3.48138i 0.224101 + 0.129385i
\(725\) −8.16778 4.71567i −0.303344 0.175136i
\(726\) −4.45758 10.0563i −0.165436 0.373226i
\(727\) 9.73041i 0.360881i −0.983586 0.180440i \(-0.942248\pi\)
0.983586 0.180440i \(-0.0577523\pi\)
\(728\) 13.4440 + 12.8747i 0.498268 + 0.477169i
\(729\) −1.00000 −0.0370370
\(730\) −1.85357 3.21047i −0.0686036 0.118825i
\(731\) 1.93912 + 1.11955i 0.0717210 + 0.0414082i
\(732\) 7.24493 + 4.18286i 0.267780 + 0.154603i
\(733\) −0.800499 1.38650i −0.0295671 0.0512117i 0.850863 0.525387i \(-0.176080\pi\)
−0.880430 + 0.474176i \(0.842746\pi\)
\(734\) −20.1568 −0.744001
\(735\) 0.212140 + 4.90142i 0.00782491 + 0.180791i
\(736\) 5.27184i 0.194323i
\(737\) −6.32902 + 3.21825i −0.233132 + 0.118546i
\(738\) −5.06922 2.92671i −0.186600 0.107734i
\(739\) 23.6755 + 13.6691i 0.870918 + 0.502825i 0.867653 0.497170i \(-0.165627\pi\)
0.00326478 + 0.999995i \(0.498961\pi\)
\(740\) −2.42431 + 1.39968i −0.0891195 + 0.0514532i
\(741\) 5.51165i 0.202476i
\(742\) 15.0983 + 14.4590i 0.554277 + 0.530806i
\(743\) 49.7705i 1.82590i −0.408067 0.912952i \(-0.633797\pi\)
0.408067 0.912952i \(-0.366203\pi\)
\(744\) 5.35024 3.08896i 0.196149 0.113247i
\(745\) −3.40919 + 5.90489i −0.124903 + 0.216338i
\(746\) −4.16927 + 7.22139i −0.152648 + 0.264394i
\(747\) 2.01994 + 3.49864i 0.0739058 + 0.128009i
\(748\) −0.108916 + 2.04606i −0.00398236 + 0.0748115i
\(749\) −7.21677 + 29.4683i −0.263695 + 1.07675i
\(750\) 6.66432i 0.243346i
\(751\) 11.5318 + 19.9737i 0.420803 + 0.728852i 0.996018 0.0891499i \(-0.0284150\pi\)
−0.575215 + 0.818002i \(0.695082\pi\)
\(752\) 2.03495 + 1.17488i 0.0742070 + 0.0428434i
\(753\) 6.06642 10.5073i 0.221073 0.382909i
\(754\) 7.35843 + 12.7452i 0.267978 + 0.464152i
\(755\) −13.8684 −0.504722
\(756\) −2.54019 + 0.739877i −0.0923859 + 0.0269091i
\(757\) −35.4691 −1.28915 −0.644574 0.764542i \(-0.722965\pi\)
−0.644574 + 0.764542i \(0.722965\pi\)
\(758\) 10.5736 6.10466i 0.384050 0.221731i
\(759\) −9.53490 + 14.6561i −0.346095 + 0.531982i
\(760\) 0.274523 0.475489i 0.00995801 0.0172478i
\(761\) 8.13485 + 14.0900i 0.294888 + 0.510761i 0.974959 0.222385i \(-0.0713843\pi\)
−0.680071 + 0.733146i \(0.738051\pi\)
\(762\) 3.43188i 0.124324i
\(763\) 3.69052 1.07493i 0.133606 0.0389151i
\(764\) 18.5590 0.671440
\(765\) 0.374971 0.216490i 0.0135571 0.00782720i
\(766\) −9.32585 + 16.1528i −0.336957 + 0.583626i
\(767\) 22.9333 + 13.2406i 0.828075 + 0.478089i
\(768\) −0.866025 + 0.500000i −0.0312500 + 0.0180422i
\(769\) −31.2492 −1.12687 −0.563437 0.826159i \(-0.690521\pi\)
−0.563437 + 0.826159i \(0.690521\pi\)
\(770\) −1.77836 + 5.88727i −0.0640877 + 0.212163i
\(771\) 19.9471 0.718377
\(772\) −15.1738 + 8.76059i −0.546117 + 0.315301i
\(773\) −14.3081 8.26079i −0.514627 0.297120i 0.220107 0.975476i \(-0.429359\pi\)
−0.734733 + 0.678356i \(0.762693\pi\)
\(774\) −1.81220 + 3.13883i −0.0651383 + 0.112823i