Properties

Label 1110.2.bb.d.1009.12
Level $1110$
Weight $2$
Character 1110.1009
Analytic conductor $8.863$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.bb (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.86339462436\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(14\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1009.12
Character \(\chi\) \(=\) 1110.1009
Dual form 1110.2.bb.d.1099.12

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.56722 - 1.59494i) q^{5} +1.00000 q^{6} +(2.76595 - 1.59692i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.56722 - 1.59494i) q^{5} +1.00000 q^{6} +(2.76595 - 1.59692i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(2.15472 - 0.597644i) q^{10} -4.26721 q^{11} +(0.866025 + 0.500000i) q^{12} +(2.86606 - 1.65472i) q^{13} +3.19385 q^{14} +(0.559786 - 2.16486i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.167875 - 0.0969230i) q^{17} +(0.866025 - 0.500000i) q^{18} +(0.557077 + 0.964886i) q^{19} +(2.16486 + 0.559786i) q^{20} +(1.59692 - 2.76595i) q^{21} +(-3.69551 - 2.13361i) q^{22} +3.44373i q^{23} +(0.500000 + 0.866025i) q^{24} +(-0.0876353 - 4.99923i) q^{25} +3.30944 q^{26} -1.00000i q^{27} +(2.76595 + 1.59692i) q^{28} -4.19385 q^{29} +(1.56722 - 1.59494i) q^{30} +1.04223 q^{31} +(-0.866025 + 0.500000i) q^{32} +(-3.69551 + 2.13361i) q^{33} +(-0.0969230 - 0.167875i) q^{34} +(1.78787 - 6.91424i) q^{35} +1.00000 q^{36} +(-1.46220 - 5.90440i) q^{37} +1.11415i q^{38} +(1.65472 - 2.86606i) q^{39} +(1.59494 + 1.56722i) q^{40} +(2.83824 + 4.91597i) q^{41} +(2.76595 - 1.59692i) q^{42} -0.530223i q^{43} +(-2.13361 - 3.69551i) q^{44} +(-0.597644 - 2.15472i) q^{45} +(-1.72186 + 2.98235i) q^{46} +12.6135i q^{47} +1.00000i q^{48} +(1.60033 - 2.77185i) q^{49} +(2.42372 - 4.37328i) q^{50} -0.193846 q^{51} +(2.86606 + 1.65472i) q^{52} +(-6.53942 - 3.77554i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-6.68766 + 6.80592i) q^{55} +(1.59692 + 2.76595i) q^{56} +(0.964886 + 0.557077i) q^{57} +(-3.63198 - 2.09692i) q^{58} +(3.27626 - 5.67465i) q^{59} +(2.15472 - 0.597644i) q^{60} +(2.65132 + 4.59222i) q^{61} +(0.902598 + 0.521115i) q^{62} -3.19385i q^{63} -1.00000 q^{64} +(1.85258 - 7.16449i) q^{65} -4.26721 q^{66} +(-4.40816 + 2.54505i) q^{67} -0.193846i q^{68} +(1.72186 + 2.98235i) q^{69} +(5.00546 - 5.09398i) q^{70} +(1.82817 + 3.16649i) q^{71} +(0.866025 + 0.500000i) q^{72} -1.24307i q^{73} +(1.68590 - 5.84446i) q^{74} +(-2.57551 - 4.28564i) q^{75} +(-0.557077 + 0.964886i) q^{76} +(-11.8029 + 6.81441i) q^{77} +(2.86606 - 1.65472i) q^{78} +(2.12738 + 3.68473i) q^{79} +(0.597644 + 2.15472i) q^{80} +(-0.500000 - 0.866025i) q^{81} +5.67647i q^{82} +(14.4122 + 8.32089i) q^{83} +3.19385 q^{84} +(-0.417684 + 0.115851i) q^{85} +(0.265111 - 0.459186i) q^{86} +(-3.63198 + 2.09692i) q^{87} -4.26721i q^{88} +(6.09036 - 10.5488i) q^{89} +(0.559786 - 2.16486i) q^{90} +(5.28492 - 9.15376i) q^{91} +(-2.98235 + 1.72186i) q^{92} +(0.902598 - 0.521115i) q^{93} +(-6.30676 + 10.9236i) q^{94} +(2.41199 + 0.623688i) q^{95} +(-0.500000 + 0.866025i) q^{96} +17.1015i q^{97} +(2.77185 - 1.60033i) q^{98} +(-2.13361 + 3.69551i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q + 14q^{4} + 2q^{5} + 28q^{6} + 14q^{9} + O(q^{10}) \) \( 28q + 14q^{4} + 2q^{5} + 28q^{6} + 14q^{9} + 4q^{10} - 12q^{11} + 8q^{14} + 2q^{15} - 14q^{16} - 20q^{19} - 2q^{20} + 4q^{21} + 14q^{24} - 8q^{25} - 20q^{26} - 36q^{29} + 2q^{30} + 24q^{31} + 38q^{34} - 2q^{35} + 28q^{36} - 10q^{39} + 2q^{40} - 6q^{44} + 4q^{45} + 8q^{46} + 50q^{49} - 4q^{50} + 76q^{51} + 14q^{54} - 28q^{55} + 4q^{56} - 26q^{59} + 4q^{60} - 28q^{61} - 28q^{64} + 60q^{65} - 12q^{66} - 8q^{69} - 10q^{70} - 64q^{71} + 24q^{74} - 8q^{75} + 20q^{76} + 32q^{79} - 4q^{80} - 14q^{81} + 8q^{84} + 16q^{85} - 8q^{86} + 76q^{89} + 2q^{90} - 8q^{91} - 38q^{94} - 70q^{95} - 14q^{96} - 6q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 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
\(5\) 1.56722 1.59494i 0.700883 0.713277i
\(6\) 1.00000 0.408248
\(7\) 2.76595 1.59692i 1.04543 0.603580i 0.124065 0.992274i \(-0.460407\pi\)
0.921367 + 0.388694i \(0.127074\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 0.500000 0.866025i 0.166667 0.288675i
\(10\) 2.15472 0.597644i 0.681383 0.188992i
\(11\) −4.26721 −1.28661 −0.643306 0.765609i \(-0.722438\pi\)
−0.643306 + 0.765609i \(0.722438\pi\)
\(12\) 0.866025 + 0.500000i 0.250000 + 0.144338i
\(13\) 2.86606 1.65472i 0.794902 0.458937i −0.0467833 0.998905i \(-0.514897\pi\)
0.841686 + 0.539968i \(0.181564\pi\)
\(14\) 3.19385 0.853591
\(15\) 0.559786 2.16486i 0.144536 0.558966i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −0.167875 0.0969230i −0.0407158 0.0235073i 0.479504 0.877540i \(-0.340817\pi\)
−0.520220 + 0.854032i \(0.674150\pi\)
\(18\) 0.866025 0.500000i 0.204124 0.117851i
\(19\) 0.557077 + 0.964886i 0.127802 + 0.221360i 0.922825 0.385220i \(-0.125874\pi\)
−0.795023 + 0.606580i \(0.792541\pi\)
\(20\) 2.16486 + 0.559786i 0.484078 + 0.125172i
\(21\) 1.59692 2.76595i 0.348477 0.603580i
\(22\) −3.69551 2.13361i −0.787886 0.454886i
\(23\) 3.44373i 0.718066i 0.933325 + 0.359033i \(0.116894\pi\)
−0.933325 + 0.359033i \(0.883106\pi\)
\(24\) 0.500000 + 0.866025i 0.102062 + 0.176777i
\(25\) −0.0876353 4.99923i −0.0175271 0.999846i
\(26\) 3.30944 0.649035
\(27\) 1.00000i 0.192450i
\(28\) 2.76595 + 1.59692i 0.522716 + 0.301790i
\(29\) −4.19385 −0.778778 −0.389389 0.921073i \(-0.627314\pi\)
−0.389389 + 0.921073i \(0.627314\pi\)
\(30\) 1.56722 1.59494i 0.286134 0.291194i
\(31\) 1.04223 0.187190 0.0935951 0.995610i \(-0.470164\pi\)
0.0935951 + 0.995610i \(0.470164\pi\)
\(32\) −0.866025 + 0.500000i −0.153093 + 0.0883883i
\(33\) −3.69551 + 2.13361i −0.643306 + 0.371413i
\(34\) −0.0969230 0.167875i −0.0166221 0.0287904i
\(35\) 1.78787 6.91424i 0.302205 1.16872i
\(36\) 1.00000 0.166667
\(37\) −1.46220 5.90440i −0.240384 0.970678i
\(38\) 1.11415i 0.180740i
\(39\) 1.65472 2.86606i 0.264967 0.458937i
\(40\) 1.59494 + 1.56722i 0.252181 + 0.247799i
\(41\) 2.83824 + 4.91597i 0.443258 + 0.767746i 0.997929 0.0643242i \(-0.0204892\pi\)
−0.554671 + 0.832070i \(0.687156\pi\)
\(42\) 2.76595 1.59692i 0.426796 0.246411i
\(43\) 0.530223i 0.0808582i −0.999182 0.0404291i \(-0.987128\pi\)
0.999182 0.0404291i \(-0.0128725\pi\)
\(44\) −2.13361 3.69551i −0.321653 0.557120i
\(45\) −0.597644 2.15472i −0.0890915 0.321207i
\(46\) −1.72186 + 2.98235i −0.253875 + 0.439724i
\(47\) 12.6135i 1.83987i 0.392070 + 0.919935i \(0.371759\pi\)
−0.392070 + 0.919935i \(0.628241\pi\)
\(48\) 1.00000i 0.144338i
\(49\) 1.60033 2.77185i 0.228618 0.395978i
\(50\) 2.42372 4.37328i 0.342766 0.618475i
\(51\) −0.193846 −0.0271439
\(52\) 2.86606 + 1.65472i 0.397451 + 0.229469i
\(53\) −6.53942 3.77554i −0.898259 0.518610i −0.0216239 0.999766i \(-0.506884\pi\)
−0.876635 + 0.481156i \(0.840217\pi\)
\(54\) 0.500000 0.866025i 0.0680414 0.117851i
\(55\) −6.68766 + 6.80592i −0.901764 + 0.917711i
\(56\) 1.59692 + 2.76595i 0.213398 + 0.369616i
\(57\) 0.964886 + 0.557077i 0.127802 + 0.0737867i
\(58\) −3.63198 2.09692i −0.476902 0.275339i
\(59\) 3.27626 5.67465i 0.426532 0.738776i −0.570030 0.821624i \(-0.693068\pi\)
0.996562 + 0.0828482i \(0.0264017\pi\)
\(60\) 2.15472 0.597644i 0.278173 0.0771555i
\(61\) 2.65132 + 4.59222i 0.339466 + 0.587973i 0.984332 0.176322i \(-0.0564202\pi\)
−0.644866 + 0.764296i \(0.723087\pi\)
\(62\) 0.902598 + 0.521115i 0.114630 + 0.0661817i
\(63\) 3.19385i 0.402387i
\(64\) −1.00000 −0.125000
\(65\) 1.85258 7.16449i 0.229784 0.888646i
\(66\) −4.26721 −0.525257
\(67\) −4.40816 + 2.54505i −0.538542 + 0.310927i −0.744488 0.667636i \(-0.767306\pi\)
0.205946 + 0.978563i \(0.433973\pi\)
\(68\) 0.193846i 0.0235073i
\(69\) 1.72186 + 2.98235i 0.207288 + 0.359033i
\(70\) 5.00546 5.09398i 0.598267 0.608847i
\(71\) 1.82817 + 3.16649i 0.216964 + 0.375793i 0.953878 0.300193i \(-0.0970512\pi\)
−0.736914 + 0.675986i \(0.763718\pi\)
\(72\) 0.866025 + 0.500000i 0.102062 + 0.0589256i
\(73\) 1.24307i 0.145491i −0.997351 0.0727454i \(-0.976824\pi\)
0.997351 0.0727454i \(-0.0231761\pi\)
\(74\) 1.68590 5.84446i 0.195982 0.679405i
\(75\) −2.57551 4.28564i −0.297394 0.494864i
\(76\) −0.557077 + 0.964886i −0.0639011 + 0.110680i
\(77\) −11.8029 + 6.81441i −1.34507 + 0.776574i
\(78\) 2.86606 1.65472i 0.324517 0.187360i
\(79\) 2.12738 + 3.68473i 0.239349 + 0.414565i 0.960528 0.278184i \(-0.0897326\pi\)
−0.721179 + 0.692749i \(0.756399\pi\)
\(80\) 0.597644 + 2.15472i 0.0668186 + 0.240905i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 5.67647i 0.626862i
\(83\) 14.4122 + 8.32089i 1.58194 + 0.913336i 0.994576 + 0.104016i \(0.0331694\pi\)
0.587368 + 0.809320i \(0.300164\pi\)
\(84\) 3.19385 0.348477
\(85\) −0.417684 + 0.115851i −0.0453042 + 0.0125658i
\(86\) 0.265111 0.459186i 0.0285877 0.0495153i
\(87\) −3.63198 + 2.09692i −0.389389 + 0.224814i
\(88\) 4.26721i 0.454886i
\(89\) 6.09036 10.5488i 0.645577 1.11817i −0.338591 0.940933i \(-0.609950\pi\)
0.984168 0.177238i \(-0.0567162\pi\)
\(90\) 0.559786 2.16486i 0.0590066 0.228197i
\(91\) 5.28492 9.15376i 0.554011 0.959574i
\(92\) −2.98235 + 1.72186i −0.310932 + 0.179517i
\(93\) 0.902598 0.521115i 0.0935951 0.0540371i
\(94\) −6.30676 + 10.9236i −0.650493 + 1.12669i
\(95\) 2.41199 + 0.623688i 0.247465 + 0.0639890i
\(96\) −0.500000 + 0.866025i −0.0510310 + 0.0883883i
\(97\) 17.1015i 1.73640i 0.496218 + 0.868198i \(0.334722\pi\)
−0.496218 + 0.868198i \(0.665278\pi\)
\(98\) 2.77185 1.60033i 0.279999 0.161657i
\(99\) −2.13361 + 3.69551i −0.214435 + 0.371413i
\(100\) 4.28564 2.57551i 0.428564 0.257551i
\(101\) 5.59331 0.556555 0.278277 0.960501i \(-0.410237\pi\)
0.278277 + 0.960501i \(0.410237\pi\)
\(102\) −0.167875 0.0969230i −0.0166221 0.00959680i
\(103\) 6.48119i 0.638610i −0.947652 0.319305i \(-0.896551\pi\)
0.947652 0.319305i \(-0.103449\pi\)
\(104\) 1.65472 + 2.86606i 0.162259 + 0.281040i
\(105\) −1.90878 6.88185i −0.186278 0.671599i
\(106\) −3.77554 6.53942i −0.366713 0.635165i
\(107\) −2.59468 + 1.49804i −0.250837 + 0.144821i −0.620147 0.784485i \(-0.712927\pi\)
0.369310 + 0.929306i \(0.379594\pi\)
\(108\) 0.866025 0.500000i 0.0833333 0.0481125i
\(109\) −2.49564 + 4.32258i −0.239039 + 0.414028i −0.960439 0.278491i \(-0.910166\pi\)
0.721400 + 0.692519i \(0.243499\pi\)
\(110\) −9.19465 + 2.55027i −0.876675 + 0.243159i
\(111\) −4.21850 4.38226i −0.400403 0.415946i
\(112\) 3.19385i 0.301790i
\(113\) 1.57329 + 0.908340i 0.148003 + 0.0854494i 0.572173 0.820133i \(-0.306101\pi\)
−0.424170 + 0.905583i \(0.639434\pi\)
\(114\) 0.557077 + 0.964886i 0.0521751 + 0.0903699i
\(115\) 5.49252 + 5.39708i 0.512180 + 0.503280i
\(116\) −2.09692 3.63198i −0.194694 0.337221i
\(117\) 3.30944i 0.305958i
\(118\) 5.67465 3.27626i 0.522393 0.301604i
\(119\) −0.619114 −0.0567541
\(120\) 2.16486 + 0.559786i 0.197624 + 0.0511012i
\(121\) 7.20909 0.655372
\(122\) 5.30264i 0.480078i
\(123\) 4.91597 + 2.83824i 0.443258 + 0.255915i
\(124\) 0.521115 + 0.902598i 0.0467975 + 0.0810557i
\(125\) −8.11079 7.69513i −0.725451 0.688273i
\(126\) 1.59692 2.76595i 0.142265 0.246411i
\(127\) −0.0665183 0.0384044i −0.00590254 0.00340784i 0.497046 0.867724i \(-0.334418\pi\)
−0.502948 + 0.864316i \(0.667751\pi\)
\(128\) −0.866025 0.500000i −0.0765466 0.0441942i
\(129\) −0.265111 0.459186i −0.0233418 0.0404291i
\(130\) 5.18663 5.27834i 0.454897 0.462941i
\(131\) −7.40018 + 12.8175i −0.646557 + 1.11987i 0.337382 + 0.941368i \(0.390458\pi\)
−0.983940 + 0.178502i \(0.942875\pi\)
\(132\) −3.69551 2.13361i −0.321653 0.185707i
\(133\) 3.08170 + 1.77922i 0.267217 + 0.154278i
\(134\) −5.09010 −0.439718
\(135\) −1.59494 1.56722i −0.137270 0.134885i
\(136\) 0.0969230 0.167875i 0.00831107 0.0143952i
\(137\) 17.5496i 1.49936i 0.661798 + 0.749682i \(0.269794\pi\)
−0.661798 + 0.749682i \(0.730206\pi\)
\(138\) 3.44373i 0.293149i
\(139\) 7.79525 13.5018i 0.661185 1.14521i −0.319120 0.947714i \(-0.603387\pi\)
0.980305 0.197491i \(-0.0632794\pi\)
\(140\) 6.88185 1.90878i 0.581622 0.161321i
\(141\) 6.30676 + 10.9236i 0.531125 + 0.919935i
\(142\) 3.65634i 0.306834i
\(143\) −12.2301 + 7.06104i −1.02273 + 0.590474i
\(144\) 0.500000 + 0.866025i 0.0416667 + 0.0721688i
\(145\) −6.57268 + 6.68891i −0.545832 + 0.555484i
\(146\) 0.621537 1.07653i 0.0514388 0.0890946i
\(147\) 3.20065i 0.263985i
\(148\) 4.38226 4.21850i 0.360220 0.346759i
\(149\) −18.2871 −1.49814 −0.749069 0.662492i \(-0.769499\pi\)
−0.749069 + 0.662492i \(0.769499\pi\)
\(150\) −0.0876353 4.99923i −0.00715539 0.408186i
\(151\) −8.03136 13.9107i −0.653583 1.13204i −0.982247 0.187592i \(-0.939932\pi\)
0.328664 0.944447i \(-0.393402\pi\)
\(152\) −0.964886 + 0.557077i −0.0782626 + 0.0451849i
\(153\) −0.167875 + 0.0969230i −0.0135719 + 0.00783576i
\(154\) −13.6288 −1.09824
\(155\) 1.63341 1.66229i 0.131198 0.133518i
\(156\) 3.30944 0.264967
\(157\) −9.03871 5.21850i −0.721368 0.416482i 0.0938882 0.995583i \(-0.470070\pi\)
−0.815256 + 0.579101i \(0.803404\pi\)
\(158\) 4.25476i 0.338491i
\(159\) −7.55107 −0.598839
\(160\) −0.559786 + 2.16486i −0.0442550 + 0.171148i
\(161\) 5.49936 + 9.52518i 0.433411 + 0.750689i
\(162\) 1.00000i 0.0785674i
\(163\) 3.23228 + 1.86616i 0.253172 + 0.146169i 0.621216 0.783640i \(-0.286639\pi\)
−0.368044 + 0.929808i \(0.619972\pi\)
\(164\) −2.83824 + 4.91597i −0.221629 + 0.383873i
\(165\) −2.38872 + 9.23794i −0.185962 + 0.719172i
\(166\) 8.32089 + 14.4122i 0.645826 + 1.11860i
\(167\) −15.9918 + 9.23287i −1.23748 + 0.714461i −0.968579 0.248706i \(-0.919995\pi\)
−0.268904 + 0.963167i \(0.586661\pi\)
\(168\) 2.76595 + 1.59692i 0.213398 + 0.123205i
\(169\) −1.02380 + 1.77327i −0.0787537 + 0.136405i
\(170\) −0.419650 0.108512i −0.0321857 0.00832251i
\(171\) 1.11415 0.0852015
\(172\) 0.459186 0.265111i 0.0350126 0.0202146i
\(173\) −20.4312 11.7960i −1.55336 0.896831i −0.997865 0.0653097i \(-0.979196\pi\)
−0.555492 0.831522i \(-0.687470\pi\)
\(174\) −4.19385 −0.317935
\(175\) −8.22578 13.6877i −0.621811 1.03469i
\(176\) 2.13361 3.69551i 0.160827 0.278560i
\(177\) 6.55252i 0.492517i
\(178\) 10.5488 6.09036i 0.790667 0.456492i
\(179\) 1.79411 0.134098 0.0670489 0.997750i \(-0.478642\pi\)
0.0670489 + 0.997750i \(0.478642\pi\)
\(180\) 1.56722 1.59494i 0.116814 0.118879i
\(181\) 0.774014 + 1.34063i 0.0575320 + 0.0996483i 0.893357 0.449348i \(-0.148344\pi\)
−0.835825 + 0.548996i \(0.815010\pi\)
\(182\) 9.15376 5.28492i 0.678522 0.391745i
\(183\) 4.59222 + 2.65132i 0.339466 + 0.195991i
\(184\) −3.44373 −0.253875
\(185\) −11.7087 6.92140i −0.860843 0.508871i
\(186\) 1.04223 0.0764201
\(187\) 0.716360 + 0.413591i 0.0523854 + 0.0302447i
\(188\) −10.9236 + 6.30676i −0.796687 + 0.459968i
\(189\) −1.59692 2.76595i −0.116159 0.201193i
\(190\) 1.77700 + 1.74613i 0.128917 + 0.126677i
\(191\) −16.9881 −1.22921 −0.614607 0.788833i \(-0.710685\pi\)
−0.614607 + 0.788833i \(0.710685\pi\)
\(192\) −0.866025 + 0.500000i −0.0625000 + 0.0360844i
\(193\) 20.3587i 1.46545i −0.680523 0.732726i \(-0.738248\pi\)
0.680523 0.732726i \(-0.261752\pi\)
\(194\) −8.55076 + 14.8103i −0.613908 + 1.06332i
\(195\) −1.97787 7.13092i −0.141638 0.510656i
\(196\) 3.20065 0.228618
\(197\) 12.0297 + 6.94535i 0.857080 + 0.494836i 0.863034 0.505147i \(-0.168562\pi\)
−0.00595307 + 0.999982i \(0.501895\pi\)
\(198\) −3.69551 + 2.13361i −0.262629 + 0.151629i
\(199\) 4.57809 0.324532 0.162266 0.986747i \(-0.448120\pi\)
0.162266 + 0.986747i \(0.448120\pi\)
\(200\) 4.99923 0.0876353i 0.353499 0.00619675i
\(201\) −2.54505 + 4.40816i −0.179514 + 0.310927i
\(202\) 4.84394 + 2.79665i 0.340819 + 0.196772i
\(203\) −11.6000 + 6.69725i −0.814159 + 0.470055i
\(204\) −0.0969230 0.167875i −0.00678596 0.0117536i
\(205\) 12.2888 + 3.17761i 0.858287 + 0.221934i
\(206\) 3.24059 5.61287i 0.225783 0.391067i
\(207\) 2.98235 + 1.72186i 0.207288 + 0.119678i
\(208\) 3.30944i 0.229469i
\(209\) −2.37717 4.11737i −0.164432 0.284805i
\(210\) 1.78787 6.91424i 0.123375 0.477128i
\(211\) 15.6806 1.07950 0.539750 0.841825i \(-0.318519\pi\)
0.539750 + 0.841825i \(0.318519\pi\)
\(212\) 7.55107i 0.518610i
\(213\) 3.16649 + 1.82817i 0.216964 + 0.125264i
\(214\) −2.99608 −0.204808
\(215\) −0.845671 0.830976i −0.0576743 0.0566721i
\(216\) 1.00000 0.0680414
\(217\) 2.88276 1.66436i 0.195694 0.112984i
\(218\) −4.32258 + 2.49564i −0.292762 + 0.169026i
\(219\) −0.621537 1.07653i −0.0419996 0.0727454i
\(220\) −9.23794 2.38872i −0.622821 0.161048i
\(221\) −0.641522 −0.0431534
\(222\) −1.46220 5.90440i −0.0981363 0.396278i
\(223\) 18.1317i 1.21419i 0.794631 + 0.607093i \(0.207664\pi\)
−0.794631 + 0.607093i \(0.792336\pi\)
\(224\) −1.59692 + 2.76595i −0.106699 + 0.184808i
\(225\) −4.37328 2.42372i −0.291552 0.161581i
\(226\) 0.908340 + 1.57329i 0.0604219 + 0.104654i
\(227\) −0.866099 + 0.500042i −0.0574850 + 0.0331890i −0.528467 0.848954i \(-0.677233\pi\)
0.470982 + 0.882143i \(0.343900\pi\)
\(228\) 1.11415i 0.0737867i
\(229\) 6.09970 + 10.5650i 0.403080 + 0.698154i 0.994096 0.108505i \(-0.0346064\pi\)
−0.591016 + 0.806660i \(0.701273\pi\)
\(230\) 2.05812 + 7.42027i 0.135708 + 0.489278i
\(231\) −6.81441 + 11.8029i −0.448355 + 0.776574i
\(232\) 4.19385i 0.275339i
\(233\) 20.3003i 1.32992i −0.746880 0.664959i \(-0.768449\pi\)
0.746880 0.664959i \(-0.231551\pi\)
\(234\) 1.65472 2.86606i 0.108172 0.187360i
\(235\) 20.1177 + 19.7682i 1.31234 + 1.28953i
\(236\) 6.55252 0.426532
\(237\) 3.68473 + 2.12738i 0.239349 + 0.138188i
\(238\) −0.536168 0.309557i −0.0347546 0.0200656i
\(239\) −5.66979 + 9.82037i −0.366748 + 0.635227i −0.989055 0.147547i \(-0.952862\pi\)
0.622307 + 0.782773i \(0.286196\pi\)
\(240\) 1.59494 + 1.56722i 0.102953 + 0.101164i
\(241\) −6.90124 11.9533i −0.444548 0.769980i 0.553473 0.832867i \(-0.313302\pi\)
−0.998021 + 0.0628877i \(0.979969\pi\)
\(242\) 6.24326 + 3.60455i 0.401332 + 0.231709i
\(243\) −0.866025 0.500000i −0.0555556 0.0320750i
\(244\) −2.65132 + 4.59222i −0.169733 + 0.293987i
\(245\) −1.91285 6.89651i −0.122207 0.440602i
\(246\) 2.83824 + 4.91597i 0.180959 + 0.313431i
\(247\) 3.19323 + 1.84361i 0.203181 + 0.117306i
\(248\) 1.04223i 0.0661817i
\(249\) 16.6418 1.05463
\(250\) −3.17659 10.7196i −0.200905 0.677965i
\(251\) −20.4047 −1.28793 −0.643966 0.765054i \(-0.722712\pi\)
−0.643966 + 0.765054i \(0.722712\pi\)
\(252\) 2.76595 1.59692i 0.174239 0.100597i
\(253\) 14.6951i 0.923873i
\(254\) −0.0384044 0.0665183i −0.00240970 0.00417373i
\(255\) −0.303799 + 0.309172i −0.0190247 + 0.0193611i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −12.0465 6.95507i −0.751443 0.433846i 0.0747723 0.997201i \(-0.476177\pi\)
−0.826215 + 0.563355i \(0.809510\pi\)
\(258\) 0.530223i 0.0330102i
\(259\) −13.4732 13.9963i −0.837187 0.869686i
\(260\) 7.13092 1.97787i 0.442241 0.122662i
\(261\) −2.09692 + 3.63198i −0.129796 + 0.224814i
\(262\) −12.8175 + 7.40018i −0.791867 + 0.457185i
\(263\) 19.5696 11.2985i 1.20671 0.696696i 0.244674 0.969605i \(-0.421319\pi\)
0.962040 + 0.272909i \(0.0879859\pi\)
\(264\) −2.13361 3.69551i −0.131314 0.227443i
\(265\) −16.2705 + 4.51285i −0.999486 + 0.277222i
\(266\) 1.77922 + 3.08170i 0.109091 + 0.188951i
\(267\) 12.1807i 0.745448i
\(268\) −4.40816 2.54505i −0.269271 0.155464i
\(269\) 12.3810 0.754881 0.377441 0.926034i \(-0.376804\pi\)
0.377441 + 0.926034i \(0.376804\pi\)
\(270\) −0.597644 2.15472i −0.0363714 0.131132i
\(271\) −7.61718 + 13.1933i −0.462711 + 0.801438i −0.999095 0.0425356i \(-0.986456\pi\)
0.536384 + 0.843974i \(0.319790\pi\)
\(272\) 0.167875 0.0969230i 0.0101789 0.00587682i
\(273\) 10.5698i 0.639716i
\(274\) −8.77481 + 15.1984i −0.530105 + 0.918170i
\(275\) 0.373958 + 21.3328i 0.0225505 + 1.28641i
\(276\) −1.72186 + 2.98235i −0.103644 + 0.179517i
\(277\) 6.70591 3.87166i 0.402919 0.232625i −0.284824 0.958580i \(-0.591935\pi\)
0.687743 + 0.725955i \(0.258602\pi\)
\(278\) 13.5018 7.79525i 0.809783 0.467528i
\(279\) 0.521115 0.902598i 0.0311984 0.0540371i
\(280\) 6.91424 + 1.78787i 0.413205 + 0.106846i
\(281\) −7.79373 + 13.4991i −0.464935 + 0.805291i −0.999199 0.0400267i \(-0.987256\pi\)
0.534263 + 0.845318i \(0.320589\pi\)
\(282\) 12.6135i 0.751124i
\(283\) 2.34418 1.35341i 0.139347 0.0804519i −0.428706 0.903444i \(-0.641030\pi\)
0.568053 + 0.822992i \(0.307697\pi\)
\(284\) −1.82817 + 3.16649i −0.108482 + 0.187896i
\(285\) 2.40069 0.665867i 0.142205 0.0394426i
\(286\) −14.1221 −0.835056
\(287\) 15.7009 + 9.06489i 0.926792 + 0.535084i
\(288\) 1.00000i 0.0589256i
\(289\) −8.48121 14.6899i −0.498895 0.864111i
\(290\) −9.03657 + 2.50643i −0.530646 + 0.147182i
\(291\) 8.55076 + 14.8103i 0.501254 + 0.868198i
\(292\) 1.07653 0.621537i 0.0629994 0.0363727i
\(293\) −2.03490 + 1.17485i −0.118880 + 0.0686355i −0.558261 0.829665i \(-0.688531\pi\)
0.439381 + 0.898301i \(0.355198\pi\)
\(294\) 1.60033 2.77185i 0.0933329 0.161657i
\(295\) −3.91607 14.1188i −0.228002 0.822031i
\(296\) 5.90440 1.46220i 0.343186 0.0849885i
\(297\) 4.26721i 0.247609i
\(298\) −15.8371 9.14356i −0.917419 0.529672i
\(299\) 5.69840 + 9.86993i 0.329547 + 0.570793i
\(300\) 2.42372 4.37328i 0.139934 0.252491i
\(301\) −0.846725 1.46657i −0.0488044 0.0845317i
\(302\) 16.0627i 0.924306i
\(303\) 4.84394 2.79665i 0.278277 0.160663i
\(304\) −1.11415 −0.0639011
\(305\) 11.4795 + 2.96834i 0.657314 + 0.169967i
\(306\) −0.193846 −0.0110814
\(307\) 5.06023i 0.288803i −0.989519 0.144401i \(-0.953874\pi\)
0.989519 0.144401i \(-0.0461256\pi\)
\(308\) −11.8029 6.81441i −0.672533 0.388287i
\(309\) −3.24059 5.61287i −0.184351 0.319305i
\(310\) 2.24572 0.622883i 0.127548 0.0353774i
\(311\) −1.77350 + 3.07179i −0.100566 + 0.174185i −0.911918 0.410373i \(-0.865399\pi\)
0.811352 + 0.584558i \(0.198732\pi\)
\(312\) 2.86606 + 1.65472i 0.162259 + 0.0936801i
\(313\) 12.4632 + 7.19561i 0.704459 + 0.406720i 0.809006 0.587800i \(-0.200006\pi\)
−0.104547 + 0.994520i \(0.533339\pi\)
\(314\) −5.21850 9.03871i −0.294497 0.510084i
\(315\) −5.09398 5.00546i −0.287013 0.282026i
\(316\) −2.12738 + 3.68473i −0.119675 + 0.207282i
\(317\) −21.2706 12.2806i −1.19468 0.689748i −0.235314 0.971919i \(-0.575612\pi\)
−0.959364 + 0.282172i \(0.908945\pi\)
\(318\) −6.53942 3.77554i −0.366713 0.211722i
\(319\) 17.8960 1.00199
\(320\) −1.56722 + 1.59494i −0.0876103 + 0.0891596i
\(321\) −1.49804 + 2.59468i −0.0836124 + 0.144821i
\(322\) 10.9987i 0.612935i
\(323\) 0.215974i 0.0120171i
\(324\) 0.500000 0.866025i 0.0277778 0.0481125i
\(325\) −8.52350 14.1831i −0.472799 0.786736i
\(326\) 1.86616 + 3.23228i 0.103357 + 0.179019i
\(327\) 4.99128i 0.276018i
\(328\) −4.91597 + 2.83824i −0.271439 + 0.156715i
\(329\) 20.1428 + 34.8884i 1.11051 + 1.92346i
\(330\) −6.68766 + 6.80592i −0.368144 + 0.374654i
\(331\) 3.34593 5.79532i 0.183909 0.318539i −0.759299 0.650741i \(-0.774458\pi\)
0.943208 + 0.332202i \(0.107792\pi\)
\(332\) 16.6418i 0.913336i
\(333\) −5.84446 1.68590i −0.320275 0.0923868i
\(334\) −18.4657 −1.01040
\(335\) −2.84937 + 11.0194i −0.155678 + 0.602053i
\(336\) 1.59692 + 2.76595i 0.0871193 + 0.150895i
\(337\) −28.1935 + 16.2775i −1.53580 + 0.886694i −0.536722 + 0.843759i \(0.680337\pi\)
−0.999078 + 0.0429349i \(0.986329\pi\)
\(338\) −1.77327 + 1.02380i −0.0964531 + 0.0556872i
\(339\) 1.81668 0.0986685
\(340\) −0.309172 0.303799i −0.0167672 0.0164758i
\(341\) −4.44742 −0.240841
\(342\) 0.964886 + 0.557077i 0.0521751 + 0.0301233i
\(343\) 12.1345i 0.655203i
\(344\) 0.530223 0.0285877
\(345\) 7.45520 + 1.92775i 0.401375 + 0.103787i
\(346\) −11.7960 20.4312i −0.634156 1.09839i
\(347\) 15.1246i 0.811930i 0.913889 + 0.405965i \(0.133064\pi\)
−0.913889 + 0.405965i \(0.866936\pi\)
\(348\) −3.63198 2.09692i −0.194694 0.112407i
\(349\) 8.37294 14.5024i 0.448193 0.776294i −0.550075 0.835115i \(-0.685401\pi\)
0.998269 + 0.0588214i \(0.0187342\pi\)
\(350\) −0.279894 15.9668i −0.0149609 0.853460i
\(351\) −1.65472 2.86606i −0.0883225 0.152979i
\(352\) 3.69551 2.13361i 0.196972 0.113722i
\(353\) −25.7954 14.8930i −1.37295 0.792674i −0.381654 0.924305i \(-0.624645\pi\)
−0.991299 + 0.131631i \(0.957979\pi\)
\(354\) 3.27626 5.67465i 0.174131 0.301604i
\(355\) 7.91549 + 2.04677i 0.420111 + 0.108631i
\(356\) 12.1807 0.645577
\(357\) −0.536168 + 0.309557i −0.0283770 + 0.0163835i
\(358\) 1.55374 + 0.897053i 0.0821177 + 0.0474107i
\(359\) 17.0677 0.900796 0.450398 0.892828i \(-0.351282\pi\)
0.450398 + 0.892828i \(0.351282\pi\)
\(360\) 2.15472 0.597644i 0.113564 0.0314986i
\(361\) 8.87933 15.3795i 0.467333 0.809445i
\(362\) 1.54803i 0.0813625i
\(363\) 6.24326 3.60455i 0.327686 0.189190i
\(364\) 10.5698 0.554011
\(365\) −1.98262 1.94817i −0.103775 0.101972i
\(366\) 2.65132 + 4.59222i 0.138587 + 0.240039i
\(367\) −2.69960 + 1.55861i −0.140918 + 0.0813590i −0.568801 0.822475i \(-0.692593\pi\)
0.427883 + 0.903834i \(0.359259\pi\)
\(368\) −2.98235 1.72186i −0.155466 0.0897583i
\(369\) 5.67647 0.295505
\(370\) −6.67936 11.8485i −0.347243 0.615972i
\(371\) −24.1170 −1.25209
\(372\) 0.902598 + 0.521115i 0.0467975 + 0.0270186i
\(373\) 13.1227 7.57637i 0.679466 0.392290i −0.120188 0.992751i \(-0.538350\pi\)
0.799654 + 0.600462i \(0.205016\pi\)
\(374\) 0.413591 + 0.716360i 0.0213863 + 0.0370421i
\(375\) −10.8717 2.60878i −0.561413 0.134717i
\(376\) −12.6135 −0.650493
\(377\) −12.0198 + 6.93964i −0.619052 + 0.357410i
\(378\) 3.19385i 0.164274i
\(379\) −1.85010 + 3.20447i −0.0950334 + 0.164603i −0.909623 0.415436i \(-0.863629\pi\)
0.814589 + 0.580038i \(0.196962\pi\)
\(380\) 0.665867 + 2.40069i 0.0341583 + 0.123153i
\(381\) −0.0768087 −0.00393503
\(382\) −14.7121 8.49404i −0.752737 0.434593i
\(383\) 27.2734 15.7463i 1.39360 0.804597i 0.399891 0.916563i \(-0.369048\pi\)
0.993712 + 0.111965i \(0.0357146\pi\)
\(384\) −1.00000 −0.0510310
\(385\) −7.62922 + 29.5045i −0.388821 + 1.50369i
\(386\) 10.1794 17.6312i 0.518116 0.897403i
\(387\) −0.459186 0.265111i −0.0233418 0.0134764i
\(388\) −14.8103 + 8.55076i −0.751881 + 0.434099i
\(389\) −7.99233 13.8431i −0.405227 0.701874i 0.589121 0.808045i \(-0.299474\pi\)
−0.994348 + 0.106171i \(0.966141\pi\)
\(390\) 1.85258 7.16449i 0.0938090 0.362788i
\(391\) 0.333776 0.578117i 0.0168798 0.0292366i
\(392\) 2.77185 + 1.60033i 0.139999 + 0.0808287i
\(393\) 14.8004i 0.746580i
\(394\) 6.94535 + 12.0297i 0.349902 + 0.606047i
\(395\) 9.21099 + 2.38176i 0.463455 + 0.119839i
\(396\) −4.26721 −0.214435
\(397\) 2.23054i 0.111947i 0.998432 + 0.0559737i \(0.0178263\pi\)
−0.998432 + 0.0559737i \(0.982174\pi\)
\(398\) 3.96475 + 2.28905i 0.198735 + 0.114740i
\(399\) 3.55844 0.178145
\(400\) 4.37328 + 2.42372i 0.218664 + 0.121186i
\(401\) 14.1146 0.704852 0.352426 0.935840i \(-0.385357\pi\)
0.352426 + 0.935840i \(0.385357\pi\)
\(402\) −4.40816 + 2.54505i −0.219859 + 0.126936i
\(403\) 2.98710 1.72460i 0.148798 0.0859085i
\(404\) 2.79665 + 4.84394i 0.139139 + 0.240995i
\(405\) −2.16486 0.559786i −0.107573 0.0278160i
\(406\) −13.3945 −0.664758
\(407\) 6.23951 + 25.1953i 0.309281 + 1.24889i
\(408\) 0.193846i 0.00959680i
\(409\) 16.3841 28.3780i 0.810140 1.40320i −0.102626 0.994720i \(-0.532725\pi\)
0.912766 0.408483i \(-0.133942\pi\)
\(410\) 9.05361 + 8.89629i 0.447126 + 0.439356i
\(411\) 8.77481 + 15.1984i 0.432829 + 0.749682i
\(412\) 5.61287 3.24059i 0.276526 0.159653i
\(413\) 20.9277i 1.02979i
\(414\) 1.72186 + 2.98235i 0.0846249 + 0.146575i
\(415\) 35.8584 9.94585i 1.76022 0.488222i
\(416\) −1.65472 + 2.86606i −0.0811294 + 0.140520i
\(417\) 15.5905i 0.763470i
\(418\) 4.75433i 0.232542i
\(419\) 18.9817 32.8773i 0.927317 1.60616i 0.139526 0.990218i \(-0.455442\pi\)
0.787791 0.615943i \(-0.211225\pi\)
\(420\) 5.00546 5.09398i 0.244242 0.248561i
\(421\) −20.4242 −0.995413 −0.497706 0.867346i \(-0.665824\pi\)
−0.497706 + 0.867346i \(0.665824\pi\)
\(422\) 13.5798 + 7.84032i 0.661056 + 0.381661i
\(423\) 10.9236 + 6.30676i 0.531125 + 0.306645i
\(424\) 3.77554 6.53942i 0.183356 0.317582i
\(425\) −0.469829 + 0.847742i −0.0227900 + 0.0411215i
\(426\) 1.82817 + 3.16649i 0.0885752 + 0.153417i
\(427\) 14.6668 + 8.46790i 0.709778 + 0.409790i
\(428\) −2.59468 1.49804i −0.125419 0.0724104i
\(429\) −7.06104 + 12.2301i −0.340910 + 0.590474i
\(430\) −0.316884 1.14248i −0.0152815 0.0550954i
\(431\) −6.60347 11.4376i −0.318078 0.550927i 0.662009 0.749496i \(-0.269704\pi\)
−0.980087 + 0.198569i \(0.936371\pi\)
\(432\) 0.866025 + 0.500000i 0.0416667 + 0.0240563i
\(433\) 20.4183i 0.981242i 0.871373 + 0.490621i \(0.163230\pi\)
−0.871373 + 0.490621i \(0.836770\pi\)
\(434\) 3.32872 0.159784
\(435\) −2.34766 + 9.07911i −0.112561 + 0.435310i
\(436\) −4.99128 −0.239039
\(437\) −3.32280 + 1.91842i −0.158951 + 0.0917705i
\(438\) 1.24307i 0.0593964i
\(439\) 9.05730 + 15.6877i 0.432281 + 0.748733i 0.997069 0.0765027i \(-0.0243754\pi\)
−0.564788 + 0.825236i \(0.691042\pi\)
\(440\) −6.80592 6.68766i −0.324460 0.318822i
\(441\) −1.60033 2.77185i −0.0762060 0.131993i
\(442\) −0.555574 0.320761i −0.0264260 0.0152570i
\(443\) 17.1304i 0.813891i −0.913452 0.406945i \(-0.866594\pi\)
0.913452 0.406945i \(-0.133406\pi\)
\(444\) 1.68590 5.84446i 0.0800093 0.277366i
\(445\) −7.27973 26.2460i −0.345092 1.24418i
\(446\) −9.06583 + 15.7025i −0.429279 + 0.743533i
\(447\) −15.8371 + 9.14356i −0.749069 + 0.432475i
\(448\) −2.76595 + 1.59692i −0.130679 + 0.0754475i
\(449\) −10.8011 18.7080i −0.509734 0.882885i −0.999936 0.0112766i \(-0.996410\pi\)
0.490202 0.871609i \(-0.336923\pi\)
\(450\) −2.57551 4.28564i −0.121411 0.202027i
\(451\) −12.1114 20.9775i −0.570301 0.987791i
\(452\) 1.81668i 0.0854494i
\(453\) −13.9107 8.03136i −0.653583 0.377346i
\(454\) −1.00008 −0.0469363
\(455\) −6.31700 22.7751i −0.296146 1.06771i
\(456\) −0.557077 + 0.964886i −0.0260875 + 0.0451849i
\(457\) −1.91953 + 1.10824i −0.0897919 + 0.0518414i −0.544224 0.838940i \(-0.683176\pi\)
0.454432 + 0.890782i \(0.349842\pi\)
\(458\) 12.1994i 0.570041i
\(459\) −0.0969230 + 0.167875i −0.00452398 + 0.00783576i
\(460\) −1.92775 + 7.45520i −0.0898818 + 0.347601i
\(461\) 11.2124 19.4205i 0.522215 0.904502i −0.477451 0.878658i \(-0.658439\pi\)
0.999666 0.0258440i \(-0.00822732\pi\)
\(462\) −11.8029 + 6.81441i −0.549121 + 0.317035i
\(463\) 11.6407 6.72077i 0.540990 0.312341i −0.204490 0.978869i \(-0.565554\pi\)
0.745480 + 0.666528i \(0.232220\pi\)
\(464\) 2.09692 3.63198i 0.0973472 0.168610i
\(465\) 0.583426 2.25629i 0.0270557 0.104633i
\(466\) 10.1502 17.5806i 0.470197 0.814405i
\(467\) 36.1934i 1.67483i 0.546569 + 0.837414i \(0.315934\pi\)
−0.546569 + 0.837414i \(0.684066\pi\)
\(468\) 2.86606 1.65472i 0.132484 0.0764895i
\(469\) −8.12850 + 14.0790i −0.375339 + 0.650107i
\(470\) 7.53839 + 27.1786i 0.347720 + 1.25366i
\(471\) −10.4370 −0.480912
\(472\) 5.67465 + 3.27626i 0.261197 + 0.150802i
\(473\) 2.26257i 0.104033i
\(474\) 2.12738 + 3.68473i 0.0977139 + 0.169245i
\(475\) 4.77487 2.86952i 0.219086 0.131662i
\(476\) −0.309557 0.536168i −0.0141885 0.0245752i
\(477\) −6.53942 + 3.77554i −0.299420 + 0.172870i
\(478\) −9.82037 + 5.66979i −0.449173 + 0.259330i
\(479\) 2.55176 4.41978i 0.116593 0.201945i −0.801822 0.597562i \(-0.796136\pi\)
0.918415 + 0.395617i \(0.129469\pi\)
\(480\) 0.597644 + 2.15472i 0.0272786 + 0.0983491i
\(481\) −13.9609 14.5028i −0.636562 0.661273i
\(482\) 13.8025i 0.628686i
\(483\) 9.52518 + 5.49936i 0.433411 + 0.250230i
\(484\) 3.60455 + 6.24326i 0.163843 + 0.283784i
\(485\) 27.2758 + 26.8019i 1.23853 + 1.21701i
\(486\) −0.500000 0.866025i −0.0226805 0.0392837i
\(487\) 18.9209i 0.857389i 0.903450 + 0.428694i \(0.141026\pi\)
−0.903450 + 0.428694i \(0.858974\pi\)
\(488\) −4.59222 + 2.65132i −0.207880 + 0.120020i
\(489\) 3.73232 0.168781
\(490\) 1.79168 6.92898i 0.0809398 0.313019i
\(491\) −27.2584 −1.23015 −0.615077 0.788467i \(-0.710875\pi\)
−0.615077 + 0.788467i \(0.710875\pi\)
\(492\) 5.67647i 0.255915i
\(493\) 0.704044 + 0.406480i 0.0317085 + 0.0183069i
\(494\) 1.84361 + 3.19323i 0.0829482 + 0.143670i
\(495\) 2.55027 + 9.19465i 0.114626 + 0.413269i
\(496\) −0.521115 + 0.902598i −0.0233988 + 0.0405279i
\(497\) 10.1133 + 5.83890i 0.453642 + 0.261910i
\(498\) 14.4122 + 8.32089i 0.645826 + 0.372868i
\(499\) −0.594301 1.02936i −0.0266046 0.0460805i 0.852417 0.522863i \(-0.175136\pi\)
−0.879021 + 0.476783i \(0.841803\pi\)
\(500\) 2.60878 10.8717i 0.116668 0.486198i
\(501\) −9.23287 + 15.9918i −0.412494 + 0.714461i
\(502\) −17.6710 10.2023i −0.788694 0.455353i
\(503\) 9.98003 + 5.76197i 0.444988 + 0.256914i 0.705711 0.708500i \(-0.250628\pi\)
−0.260723 + 0.965414i \(0.583961\pi\)
\(504\) 3.19385 0.142265
\(505\) 8.76595 8.92096i 0.390079 0.396977i
\(506\) 7.34755 12.7263i 0.326639 0.565755i
\(507\) 2.04760i 0.0909369i
\(508\) 0.0768087i 0.00340784i
\(509\) 16.7089 28.9406i 0.740608 1.28277i −0.211610 0.977354i \(-0.567871\pi\)
0.952219 0.305417i \(-0.0987960\pi\)
\(510\) −0.417684 + 0.115851i −0.0184954 + 0.00512996i
\(511\) −1.98509 3.43828i −0.0878154 0.152101i
\(512\) 1.00000i 0.0441942i
\(513\) 0.964886 0.557077i 0.0426008 0.0245956i
\(514\) −6.95507 12.0465i −0.306775 0.531350i
\(515\) −10.3371 10.1575i −0.455506 0.447591i
\(516\) 0.265111 0.459186i 0.0116709 0.0202146i
\(517\) 53.8245i 2.36720i
\(518\) −4.67004 18.8578i −0.205190 0.828562i
\(519\) −23.5919 −1.03557
\(520\) 7.16449 + 1.85258i 0.314184 + 0.0812410i
\(521\) 21.6358 + 37.4743i 0.947882 + 1.64178i 0.749875 + 0.661580i \(0.230114\pi\)
0.198008 + 0.980200i \(0.436553\pi\)
\(522\) −3.63198 + 2.09692i −0.158967 + 0.0917798i
\(523\) −26.1999 + 15.1265i −1.14564 + 0.661436i −0.947821 0.318802i \(-0.896719\pi\)
−0.197820 + 0.980238i \(0.563386\pi\)
\(524\) −14.8004 −0.646557
\(525\) −13.9676 7.74099i −0.609595 0.337845i
\(526\) 22.5970 0.985277
\(527\) −0.174965 0.101016i −0.00762159 0.00440033i
\(528\) 4.26721i 0.185707i
\(529\) 11.1408 0.484381
\(530\) −16.3471 4.22698i −0.710071 0.183608i
\(531\) −3.27626 5.67465i −0.142177 0.246259i
\(532\) 3.55844i 0.154278i
\(533\) 16.2691 + 9.39298i 0.704694 + 0.406855i
\(534\) 6.09036 10.5488i 0.263556 0.456492i
\(535\) −1.67716 + 6.48610i −0.0725100 + 0.280419i
\(536\) −2.54505 4.40816i −0.109929 0.190403i
\(537\) 1.55374 0.897053i 0.0670489 0.0387107i
\(538\) 10.7222 + 6.19049i 0.462268 + 0.266891i
\(539\) −6.82893 + 11.8281i −0.294143 + 0.509470i
\(540\) 0.559786 2.16486i 0.0240893 0.0931609i
\(541\) 22.5497 0.969488 0.484744 0.874656i \(-0.338913\pi\)
0.484744 + 0.874656i \(0.338913\pi\)
\(542\) −13.1933 + 7.61718i −0.566702 + 0.327186i
\(543\) 1.34063 + 0.774014i 0.0575320 + 0.0332161i
\(544\) 0.193846 0.00831107
\(545\) 2.98301 + 10.7548i 0.127778 + 0.460686i
\(546\) 5.28492 9.15376i 0.226174 0.391745i
\(547\) 43.7821i 1.87199i 0.352017 + 0.935993i \(0.385496\pi\)
−0.352017 + 0.935993i \(0.614504\pi\)
\(548\) −15.1984 + 8.77481i −0.649244 + 0.374841i
\(549\) 5.30264 0.226311
\(550\) −10.3425 + 18.6617i −0.441007 + 0.795738i
\(551\) −2.33630 4.04658i −0.0995296 0.172390i
\(552\) −2.98235 + 1.72186i −0.126937 + 0.0732873i
\(553\) 11.7685 + 6.79453i 0.500446 + 0.288933i
\(554\) 7.74331 0.328982
\(555\) −13.6008 0.139740i −0.577320 0.00593165i
\(556\) 15.5905 0.661185
\(557\) 22.6846 + 13.0970i 0.961178 + 0.554936i 0.896535 0.442972i \(-0.146076\pi\)
0.0646424 + 0.997908i \(0.479409\pi\)
\(558\) 0.902598 0.521115i 0.0382100 0.0220606i
\(559\) −0.877371 1.51965i −0.0371088 0.0642744i
\(560\) 5.09398 + 5.00546i 0.215260 + 0.211519i
\(561\) 0.827181 0.0349236
\(562\) −13.4991 + 7.79373i −0.569427 + 0.328759i
\(563\) 26.6763i 1.12427i 0.827045 + 0.562135i \(0.190020\pi\)
−0.827045 + 0.562135i \(0.809980\pi\)
\(564\) −6.30676 + 10.9236i −0.265562 + 0.459968i
\(565\) 3.91444 1.08573i 0.164682 0.0456769i
\(566\) 2.70682 0.113776
\(567\) −2.76595 1.59692i −0.116159 0.0670645i
\(568\) −3.16649 + 1.82817i −0.132863 + 0.0767084i
\(569\) 25.5075 1.06933 0.534665 0.845064i \(-0.320438\pi\)
0.534665 + 0.845064i \(0.320438\pi\)
\(570\) 2.41199 + 0.623688i 0.101027 + 0.0261234i
\(571\) 9.79873 16.9719i 0.410064 0.710252i −0.584832 0.811154i \(-0.698840\pi\)
0.994896 + 0.100902i \(0.0321730\pi\)
\(572\) −12.2301 7.06104i −0.511366 0.295237i
\(573\) −14.7121 + 8.49404i −0.614607 + 0.354844i
\(574\) 9.06489 + 15.7009i 0.378361 + 0.655341i
\(575\) 17.2160 0.301792i 0.717956 0.0125856i
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) 25.3021 + 14.6082i 1.05334 + 0.608147i 0.923583 0.383399i \(-0.125246\pi\)
0.129759 + 0.991546i \(0.458580\pi\)
\(578\) 16.9624i 0.705544i
\(579\) −10.1794 17.6312i −0.423040 0.732726i
\(580\) −9.07911 2.34766i −0.376990 0.0974811i
\(581\) 53.1513 2.20509
\(582\) 17.1015i 0.708880i
\(583\) 27.9051 + 16.1110i 1.15571 + 0.667250i
\(584\) 1.24307 0.0514388
\(585\) −5.27834 5.18663i −0.218233 0.214441i
\(586\) −2.34970 −0.0970652
\(587\) 38.9840 22.5074i 1.60904 0.928981i 0.619457 0.785031i \(-0.287353\pi\)
0.989585 0.143950i \(-0.0459804\pi\)
\(588\) 2.77185 1.60033i 0.114309 0.0659963i
\(589\) 0.580603 + 1.00563i 0.0239233 + 0.0414364i
\(590\) 3.66801 14.1853i 0.151009 0.584000i
\(591\) 13.8907 0.571387
\(592\) 5.84446 + 1.68590i 0.240206 + 0.0692901i
\(593\) 3.44657i 0.141534i −0.997493 0.0707669i \(-0.977455\pi\)
0.997493 0.0707669i \(-0.0225447\pi\)
\(594\) −2.13361 + 3.69551i −0.0875429 + 0.151629i
\(595\) −0.970289 + 0.987447i −0.0397780 + 0.0404814i
\(596\) −9.14356 15.8371i −0.374535 0.648713i
\(597\) 3.96475 2.28905i 0.162266 0.0936845i
\(598\) 11.3968i 0.466050i
\(599\) −4.13216 7.15712i −0.168836 0.292432i 0.769175 0.639038i \(-0.220667\pi\)
−0.938011 + 0.346606i \(0.887334\pi\)
\(600\) 4.28564 2.57551i 0.174961 0.105145i
\(601\) 18.1366 31.4135i 0.739806 1.28138i −0.212776 0.977101i \(-0.568250\pi\)
0.952582 0.304281i \(-0.0984163\pi\)
\(602\) 1.69345i 0.0690199i
\(603\) 5.09010i 0.207285i
\(604\) 8.03136 13.9107i 0.326791 0.566019i
\(605\) 11.2982 11.4980i 0.459339 0.467461i
\(606\) 5.59331 0.227212
\(607\) 19.5670 + 11.2970i 0.794202 + 0.458533i 0.841440 0.540351i \(-0.181709\pi\)
−0.0472380 + 0.998884i \(0.515042\pi\)
\(608\) −0.964886 0.557077i −0.0391313 0.0225925i
\(609\) −6.69725 + 11.6000i −0.271386 + 0.470055i
\(610\) 8.45736 + 8.31040i 0.342428 + 0.336478i
\(611\) 20.8719 + 36.1511i 0.844385 + 1.46252i
\(612\) −0.167875 0.0969230i −0.00678596 0.00391788i
\(613\) 0.835756 + 0.482524i 0.0337559 + 0.0194890i 0.516783 0.856116i \(-0.327129\pi\)
−0.483027 + 0.875605i \(0.660463\pi\)
\(614\) 2.53012 4.38229i 0.102107 0.176855i
\(615\) 12.2312 3.39251i 0.493210 0.136799i
\(616\) −6.81441 11.8029i −0.274560 0.475552i
\(617\) −32.4902 18.7582i −1.30801 0.755177i −0.326243 0.945286i \(-0.605783\pi\)
−0.981763 + 0.190109i \(0.939116\pi\)
\(618\) 6.48119i 0.260712i
\(619\) 17.9959 0.723315 0.361658 0.932311i \(-0.382211\pi\)
0.361658 + 0.932311i \(0.382211\pi\)
\(620\) 2.25629 + 0.583426i 0.0906147 + 0.0234310i
\(621\) 3.44373 0.138192
\(622\) −3.07179 + 1.77350i −0.123167 + 0.0711107i
\(623\) 38.9033i 1.55863i
\(624\) 1.65472 + 2.86606i 0.0662419 + 0.114734i
\(625\) −24.9846 + 0.876219i −0.999386 + 0.0350487i
\(626\) 7.19561 + 12.4632i 0.287594 + 0.498128i
\(627\) −4.11737 2.37717i −0.164432 0.0949349i
\(628\) 10.4370i 0.416482i
\(629\) −0.326805 + 1.13293i −0.0130306 + 0.0451727i
\(630\) −1.90878 6.88185i −0.0760477 0.274179i
\(631\) 15.6815 27.1611i 0.624269 1.08127i −0.364412 0.931238i \(-0.618730\pi\)
0.988682 0.150028i \(-0.0479365\pi\)
\(632\) −3.68473 + 2.12738i −0.146571 + 0.0846227i
\(633\) 13.5798 7.84032i 0.539750 0.311625i
\(634\) −12.2806 21.2706i −0.487725 0.844765i
\(635\) −0.165501 + 0.0459042i −0.00656772 + 0.00182165i
\(636\) −3.77554 6.53942i −0.149710 0.259305i
\(637\) 10.5924i 0.419685i
\(638\) 15.4984 + 8.94801i 0.613588 + 0.354255i
\(639\) 3.65634 0.144643
\(640\) −2.15472 + 0.597644i −0.0851728 + 0.0236239i
\(641\) −11.3794 + 19.7098i −0.449461 + 0.778489i −0.998351 0.0574058i \(-0.981717\pi\)
0.548890 + 0.835894i \(0.315050\pi\)
\(642\) −2.59468 + 1.49804i −0.102404 + 0.0591229i
\(643\) 26.7296i 1.05411i 0.849831 + 0.527055i \(0.176704\pi\)
−0.849831 + 0.527055i \(0.823296\pi\)
\(644\) −5.49936 + 9.52518i −0.216705 + 0.375345i
\(645\) −1.14786 0.296811i −0.0451970 0.0116869i
\(646\) 0.107987 0.187039i 0.00424870 0.00735896i
\(647\) 6.72466 3.88249i 0.264374 0.152636i −0.361954 0.932196i \(-0.617890\pi\)
0.626328 + 0.779560i \(0.284557\pi\)
\(648\) 0.866025 0.500000i 0.0340207 0.0196419i
\(649\) −13.9805 + 24.2149i −0.548782 + 0.950518i
\(650\) −0.290024 16.5447i −0.0113757 0.648935i
\(651\) 1.66436 2.88276i 0.0652315 0.112984i
\(652\) 3.73232i 0.146169i
\(653\) 14.3288 8.27272i 0.560728 0.323737i −0.192710 0.981256i \(-0.561728\pi\)
0.753438 + 0.657519i \(0.228394\pi\)
\(654\) −2.49564 + 4.32258i −0.0975872 + 0.169026i
\(655\) 8.84535 + 31.8907i 0.345616 + 1.24607i
\(656\) −5.67647 −0.221629
\(657\) −1.07653 0.621537i −0.0419996 0.0242485i
\(658\) 40.2856i 1.57050i
\(659\) 1.40114 + 2.42684i 0.0545805 + 0.0945362i 0.892025 0.451987i \(-0.149285\pi\)
−0.837444 + 0.546523i \(0.815951\pi\)
\(660\) −9.19465 + 2.55027i −0.357901 + 0.0992692i
\(661\) −21.3281 36.9414i −0.829569 1.43686i −0.898377 0.439225i \(-0.855253\pi\)
0.0688084 0.997630i \(-0.478080\pi\)
\(662\) 5.79532 3.34593i 0.225241 0.130043i
\(663\) −0.555574 + 0.320761i −0.0215767 + 0.0124573i
\(664\) −8.32089 + 14.4122i −0.322913 + 0.559302i
\(665\) 7.66744 2.12668i 0.297331 0.0824690i
\(666\) −4.21850 4.38226i −0.163464 0.169809i
\(667\) 14.4425i 0.559214i
\(668\) −15.9918 9.23287i −0.618741 0.357231i
\(669\) 9.06583 + 15.7025i 0.350505 + 0.607093i
\(670\) −7.97732 + 8.11838i −0.308191 + 0.313640i
\(671\) −11.3137 19.5960i −0.436762 0.756494i
\(672\) 3.19385i 0.123205i
\(673\) −21.8380 + 12.6082i −0.841794 + 0.486010i −0.857874 0.513861i \(-0.828215\pi\)
0.0160794 + 0.999871i \(0.494882\pi\)
\(674\) −32.5551 −1.25398
\(675\) −4.99923 + 0.0876353i −0.192421 + 0.00337309i
\(676\) −2.04760 −0.0787537
\(677\) 51.5166i 1.97994i −0.141269 0.989971i \(-0.545118\pi\)
0.141269 0.989971i \(-0.454882\pi\)
\(678\) 1.57329 + 0.908340i 0.0604219 + 0.0348846i
\(679\) 27.3098 + 47.3020i 1.04805 + 1.81528i
\(680\) −0.115851 0.417684i −0.00444267 0.0160174i
\(681\) −0.500042 + 0.866099i −0.0191617 + 0.0331890i
\(682\) −3.85158 2.22371i −0.147485 0.0851502i
\(683\) −33.6241 19.4129i −1.28659 0.742814i −0.308547 0.951209i \(-0.599843\pi\)
−0.978045 + 0.208395i \(0.933176\pi\)
\(684\) 0.557077 + 0.964886i 0.0213004 + 0.0368933i
\(685\) 27.9905 + 27.5041i 1.06946 + 1.05088i
\(686\) −6.06727 + 10.5088i −0.231649 + 0.401228i
\(687\) 10.5650 + 6.09970i 0.403080 + 0.232718i
\(688\) 0.459186 + 0.265111i 0.0175063 + 0.0101073i
\(689\) −24.9898 −0.952037
\(690\) 5.49252 + 5.39708i 0.209097 + 0.205463i
\(691\) −10.4387 + 18.0804i −0.397109 + 0.687812i −0.993368 0.114980i \(-0.963320\pi\)
0.596259 + 0.802792i \(0.296653\pi\)
\(692\) 23.5919i 0.896831i
\(693\) 13.6288i 0.517716i
\(694\) −7.56229 + 13.0983i −0.287060 + 0.497203i
\(695\) −9.31757 33.5932i −0.353435 1.27426i
\(696\) −2.09692 3.63198i −0.0794837 0.137670i
\(697\) 1.10036i 0.0416792i
\(698\) 14.5024 8.37294i 0.548923 0.316921i
\(699\) −10.1502 17.5806i −0.383914 0.664959i
\(700\) 7.74099 13.9676i 0.292582 0.527925i
\(701\) −8.57769 + 14.8570i −0.323975 + 0.561141i −0.981304 0.192462i \(-0.938353\pi\)
0.657330 + 0.753603i \(0.271686\pi\)
\(702\) 3.30944i 0.124907i
\(703\) 4.88252 4.70006i 0.184148 0.177266i
\(704\) 4.26721 0.160827
\(705\) 27.3066 + 7.06087i 1.02842 + 0.265928i
\(706\) −14.8930 25.7954i −0.560505 0.970824i
\(707\) 15.4708 8.93208i 0.581840 0.335925i
\(708\) 5.67465 3.27626i 0.213266 0.123129i
\(709\) 13.4264 0.504239 0.252120 0.967696i \(-0.418872\pi\)
0.252120 + 0.967696i \(0.418872\pi\)
\(710\) 5.83163 + 5.73030i 0.218857 + 0.215054i
\(711\) 4.25476 0.159566
\(712\) 10.5488 + 6.09036i 0.395333 + 0.228246i
\(713\) 3.58916i 0.134415i
\(714\) −0.619114 −0.0231698
\(715\) −7.90534 + 30.5724i −0.295643 + 1.14334i
\(716\) 0.897053 + 1.55374i 0.0335244 + 0.0580660i
\(717\) 11.3396i 0.423484i
\(718\) 14.7810 + 8.53383i 0.551623 + 0.318480i
\(719\) 1.99668 3.45835i 0.0744636 0.128975i −0.826389 0.563099i \(-0.809609\pi\)
0.900853 + 0.434125i \(0.142942\pi\)
\(720\) 2.16486 + 0.559786i 0.0806797 + 0.0208620i
\(721\) −10.3500 17.9266i −0.385452 0.667623i
\(722\) 15.3795 8.87933i 0.572364 0.330454i
\(723\) −11.9533 6.90124i −0.444548 0.256660i
\(724\) −0.774014 + 1.34063i −0.0287660 + 0.0498242i
\(725\) 0.367529 + 20.9660i 0.0136497 + 0.778658i
\(726\) 7.20909 0.267554
\(727\) −14.5632 + 8.40804i −0.540117 + 0.311837i −0.745127 0.666923i \(-0.767611\pi\)
0.205009 + 0.978760i \(0.434278\pi\)
\(728\) 9.15376 + 5.28492i 0.339261 + 0.195872i
\(729\) −1.00000 −0.0370370
\(730\) −0.742915 2.67848i −0.0274965 0.0991349i
\(731\) −0.0513908 + 0.0890114i −0.00190076 + 0.00329221i
\(732\) 5.30264i 0.195991i
\(733\) −36.5875 + 21.1238i −1.35139 + 0.780225i −0.988444 0.151585i \(-0.951562\pi\)
−0.362945 + 0.931810i \(0.618229\pi\)
\(734\) −3.11723 −0.115059
\(735\) −5.10483 5.01613i −0.188295 0.185023i
\(736\) −1.72186 2.98235i −0.0634687 0.109931i
\(737\) 18.8105 10.8603i 0.692895 0.400043i
\(738\) 4.91597 + 2.83824i 0.180959 + 0.104477i
\(739\) 34.5965 1.27265 0.636326 0.771420i \(-0.280453\pi\)
0.636326 + 0.771420i \(0.280453\pi\)
\(740\) 0.139740 13.6008i 0.00513696 0.499974i
\(741\) 3.68723 0.135454
\(742\) −20.8859 12.0585i −0.766746 0.442681i
\(743\) 7.63173 4.40618i 0.279981 0.161647i −0.353434 0.935460i \(-0.614986\pi\)
0.633415 + 0.773812i \(0.281653\pi\)
\(744\) 0.521115 + 0.902598i 0.0191050 + 0.0330909i
\(745\) −28.6599 + 29.1668i −1.05002 + 1.06859i
\(746\) 15.1527 0.554781
\(747\) 14.4122 8.32089i 0.527315 0.304445i
\(748\) 0.827181i 0.0302447i
\(749\) −4.78450 + 8.28700i −0.174822 + 0.302801i
\(750\) −8.11079 7.69513i −0.296164 0.280986i
\(751\) 31.7368 1.15809 0.579045 0.815295i \(-0.303425\pi\)
0.579045 + 0.815295i \(0.303425\pi\)
\(752\) −10.9236 6.30676i −0.398344 0.229984i
\(753\) −17.6710 + 10.2023i −0.643966 + 0.371794i
\(754\) −13.8793 −0.505454
\(755\) −34.7736 8.99169i −1.26554 0.327241i
\(756\) 1.59692 2.76595i 0.0580795 0.100597i
\(757\) −21.2066 12.2436i −0.770767 0.445003i 0.0623810 0.998052i \(-0.480131\pi\)
−0.833148 + 0.553050i \(0.813464\pi\)
\(758\) −3.20447 + 1.85010i −0.116392 + 0.0671988i
\(759\) −7.34755 12.7263i −0.266699 0.461937i
\(760\) −0.623688 + 2.41199i −0.0226235 + 0.0874922i
\(761\) 16.7286 28.9747i 0.606410 1.05033i −0.385417 0.922743i \(-0.625942\pi\)
0.991827 0.127591i \(-0.0407244\pi\)
\(762\) −0.0665183 0.0384044i −0.00240970 0.00139124i
\(763\) 15.9414i 0.577117i
\(764\) −8.49404 14.7121i −0.307304 0.532265i
\(765\) −0.108512 + 0.419650i −0.00392327 + 0.0151725i
\(766\) 31.4926 1.13787
\(767\) 21.6852i 0.783006i
\(768\) −0.866025 0.500000i −0.0312500 0.0180422i
\(769\) −13.2958 −0.479458 −0.239729 0.970840i \(-0.577059\pi\)
−0.239729 + 0.970840i \(0.577059\pi\)
\(770\) −21.3594 + 21.7371i −0.769738 + 0.783350i
\(771\) −13.9101 −0.500962
\(772\) 17.6312 10.1794i 0.634560 0.366363i
\(773\) 38.3025 22.1139i 1.37764 0.795383i 0.385769 0.922596i \(-0.373936\pi\)
0.991876 + 0.127212i \(0.0406030\pi\)
\(774\) −0.265111 0.459186i −0.00952923 0.0165051i
\(775\) −0.0913362 5.21035i −0.00328089 0.187161i
\(776\) −17.1015 −0.613908