Properties

Label 77.2.e.b.23.3
Level $77$
Weight $2$
Character 77.23
Analytic conductor $0.615$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 77 = 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 77.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.614848095564\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.1783323.2
Defining polynomial: \(x^{6} - x^{5} + 5 x^{4} - 2 x^{3} + 19 x^{2} - 12 x + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 23.3
Root \(0.356769 + 0.617942i\) of defining polynomial
Character \(\chi\) \(=\) 77.23
Dual form 77.2.e.b.67.3

$q$-expansion

\(f(q)\) \(=\) \(q+(1.24543 - 2.15715i) q^{2} +(0.356769 + 0.617942i) q^{3} +(-2.10220 - 3.64112i) q^{4} +(-1.10220 + 1.90907i) q^{5} +1.77733 q^{6} +(-1.10220 + 2.40523i) q^{7} -5.49086 q^{8} +(1.24543 - 2.15715i) q^{9} +O(q^{10})\) \(q+(1.24543 - 2.15715i) q^{2} +(0.356769 + 0.617942i) q^{3} +(-2.10220 - 3.64112i) q^{4} +(-1.10220 + 1.90907i) q^{5} +1.77733 q^{6} +(-1.10220 + 2.40523i) q^{7} -5.49086 q^{8} +(1.24543 - 2.15715i) q^{9} +(2.74543 + 4.75523i) q^{10} +(0.500000 + 0.866025i) q^{11} +(1.50000 - 2.59808i) q^{12} -3.28646 q^{13} +(3.81574 + 5.37317i) q^{14} -1.57292 q^{15} +(-2.63409 + 4.56239i) q^{16} +(-0.745432 - 1.29113i) q^{17} +(-3.10220 - 5.37317i) q^{18} +(3.45897 - 5.99111i) q^{19} +9.26819 q^{20} +(-1.87953 + 0.177017i) q^{21} +2.49086 q^{22} +(-3.24543 + 5.62125i) q^{23} +(-1.95897 - 3.39304i) q^{24} +(0.0703069 + 0.121775i) q^{25} +(-4.09306 + 7.08940i) q^{26} +3.91794 q^{27} +(11.0748 - 1.04304i) q^{28} -1.64975 q^{29} +(-1.95897 + 3.39304i) q^{30} +(1.17512 + 2.03538i) q^{31} +(1.07031 + 1.85383i) q^{32} +(-0.356769 + 0.617942i) q^{33} -3.71354 q^{34} +(-3.37691 - 4.75523i) q^{35} -10.4726 q^{36} +(2.77733 - 4.81047i) q^{37} +(-8.61582 - 14.9230i) q^{38} +(-1.17251 - 2.03084i) q^{39} +(6.05203 - 10.4824i) q^{40} -11.2499 q^{41} +(-1.95897 + 4.27489i) q^{42} +5.26819 q^{43} +(2.10220 - 3.64112i) q^{44} +(2.74543 + 4.75523i) q^{45} +(8.08393 + 14.0018i) q^{46} +(-0.745432 + 1.29113i) q^{47} -3.75905 q^{48} +(-4.57031 - 5.30210i) q^{49} +0.350250 q^{50} +(0.531894 - 0.921267i) q^{51} +(6.90880 + 11.9664i) q^{52} +(-0.152367 - 0.263908i) q^{53} +(4.87953 - 8.45159i) q^{54} -2.20440 q^{55} +(6.05203 - 13.2068i) q^{56} +4.93621 q^{57} +(-2.05465 + 3.55876i) q^{58} +(6.32936 + 10.9628i) q^{59} +(3.30660 + 5.72720i) q^{60} +(6.49086 - 11.2425i) q^{61} +5.85415 q^{62} +(3.81574 + 5.37317i) q^{63} -5.20440 q^{64} +(3.62234 - 6.27408i) q^{65} +(0.888663 + 1.53921i) q^{66} +(2.28646 + 3.96027i) q^{67} +(-3.13409 + 5.42841i) q^{68} -4.63148 q^{69} +(-14.4635 + 1.36219i) q^{70} +11.3267 q^{71} +(-6.83850 + 11.8446i) q^{72} +(4.28384 + 7.41984i) q^{73} +(-6.91794 - 11.9822i) q^{74} +(-0.0501666 + 0.0868912i) q^{75} -29.0858 q^{76} +(-2.63409 + 0.248083i) q^{77} -5.84111 q^{78} +(-2.31574 + 4.01098i) q^{79} +(-5.80660 - 10.0573i) q^{80} +(-2.33850 - 4.05039i) q^{81} +(-14.0110 + 24.2678i) q^{82} -1.93621 q^{83} +(4.59568 + 6.47145i) q^{84} +3.28646 q^{85} +(6.56117 - 11.3643i) q^{86} +(-0.588580 - 1.01945i) q^{87} +(-2.74543 - 4.75523i) q^{88} +(-1.60220 + 2.77509i) q^{89} +13.6770 q^{90} +(3.62234 - 7.90471i) q^{91} +27.2902 q^{92} +(-0.838496 + 1.45232i) q^{93} +(1.85677 + 3.21602i) q^{94} +(7.62496 + 13.2068i) q^{95} +(-0.763705 + 1.32278i) q^{96} +1.85939 q^{97} +(-17.1294 + 3.25544i) q^{98} +2.49086 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + q^{3} - 4q^{4} + 2q^{5} - 2q^{6} + 2q^{7} - 18q^{8} + O(q^{10}) \) \( 6q + q^{3} - 4q^{4} + 2q^{5} - 2q^{6} + 2q^{7} - 18q^{8} + 9q^{10} + 3q^{11} + 9q^{12} - 22q^{13} + 12q^{14} - 14q^{15} - 2q^{16} + 3q^{17} - 10q^{18} + 11q^{19} + 28q^{20} + 10q^{21} - 12q^{23} - 2q^{24} - 3q^{25} - q^{26} + 4q^{27} + 13q^{28} - 18q^{29} - 2q^{30} + 3q^{31} + 3q^{32} - q^{33} - 20q^{34} + 9q^{35} - 18q^{36} + 4q^{37} - 8q^{38} + 5q^{39} + 3q^{40} - 10q^{41} - 2q^{42} + 4q^{43} + 4q^{44} + 9q^{45} + 10q^{46} + 3q^{47} + 20q^{48} - 24q^{49} - 6q^{50} - 2q^{51} + 7q^{52} - 17q^{53} + 8q^{54} + 4q^{55} + 3q^{56} + 40q^{57} + 13q^{58} - 8q^{59} - 6q^{60} + 24q^{61} + 26q^{62} + 12q^{63} - 14q^{64} - 15q^{65} - q^{66} + 16q^{67} - 5q^{68} - 6q^{69} - 27q^{70} + 14q^{71} - 10q^{72} + 20q^{73} - 22q^{74} - 25q^{75} - 78q^{76} - 2q^{77} - 12q^{78} - 3q^{79} - 9q^{80} + 17q^{81} - 41q^{82} - 22q^{83} + 12q^{84} + 22q^{85} + 21q^{86} - 30q^{87} - 9q^{88} - q^{89} + 20q^{90} - 15q^{91} + 50q^{92} + 26q^{93} + 10q^{94} + 17q^{95} - 27q^{96} + 18q^{97} - 24q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/77\mathbb{Z}\right)^\times\).

\(n\) \(45\) \(57\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.24543 2.15715i 0.880653 1.52534i 0.0300373 0.999549i \(-0.490437\pi\)
0.850616 0.525787i \(-0.176229\pi\)
\(3\) 0.356769 + 0.617942i 0.205981 + 0.356769i 0.950445 0.310894i \(-0.100628\pi\)
−0.744464 + 0.667663i \(0.767295\pi\)
\(4\) −2.10220 3.64112i −1.05110 1.82056i
\(5\) −1.10220 + 1.90907i −0.492919 + 0.853761i −0.999967 0.00815703i \(-0.997404\pi\)
0.507048 + 0.861918i \(0.330737\pi\)
\(6\) 1.77733 0.725590
\(7\) −1.10220 + 2.40523i −0.416593 + 0.909093i
\(8\) −5.49086 −1.94131
\(9\) 1.24543 2.15715i 0.415144 0.719050i
\(10\) 2.74543 + 4.75523i 0.868182 + 1.50373i
\(11\) 0.500000 + 0.866025i 0.150756 + 0.261116i
\(12\) 1.50000 2.59808i 0.433013 0.750000i
\(13\) −3.28646 −0.911501 −0.455750 0.890108i \(-0.650629\pi\)
−0.455750 + 0.890108i \(0.650629\pi\)
\(14\) 3.81574 + 5.37317i 1.01980 + 1.43604i
\(15\) −1.57292 −0.406127
\(16\) −2.63409 + 4.56239i −0.658524 + 1.14060i
\(17\) −0.745432 1.29113i −0.180794 0.313144i 0.761357 0.648333i \(-0.224533\pi\)
−0.942151 + 0.335189i \(0.891200\pi\)
\(18\) −3.10220 5.37317i −0.731196 1.26647i
\(19\) 3.45897 5.99111i 0.793542 1.37446i −0.130219 0.991485i \(-0.541568\pi\)
0.923761 0.382970i \(-0.125099\pi\)
\(20\) 9.26819 2.07243
\(21\) −1.87953 + 0.177017i −0.410146 + 0.0386283i
\(22\) 2.49086 0.531054
\(23\) −3.24543 + 5.62125i −0.676719 + 1.17211i 0.299244 + 0.954177i \(0.403266\pi\)
−0.975963 + 0.217936i \(0.930068\pi\)
\(24\) −1.95897 3.39304i −0.399873 0.692600i
\(25\) 0.0703069 + 0.121775i 0.0140614 + 0.0243550i
\(26\) −4.09306 + 7.08940i −0.802716 + 1.39034i
\(27\) 3.91794 0.754008
\(28\) 11.0748 1.04304i 2.09294 0.197116i
\(29\) −1.64975 −0.306351 −0.153175 0.988199i \(-0.548950\pi\)
−0.153175 + 0.988199i \(0.548950\pi\)
\(30\) −1.95897 + 3.39304i −0.357657 + 0.619481i
\(31\) 1.17512 + 2.03538i 0.211059 + 0.365564i 0.952046 0.305955i \(-0.0989756\pi\)
−0.740987 + 0.671519i \(0.765642\pi\)
\(32\) 1.07031 + 1.85383i 0.189205 + 0.327713i
\(33\) −0.356769 + 0.617942i −0.0621055 + 0.107570i
\(34\) −3.71354 −0.636867
\(35\) −3.37691 4.75523i −0.570802 0.803780i
\(36\) −10.4726 −1.74543
\(37\) 2.77733 4.81047i 0.456590 0.790836i −0.542189 0.840257i \(-0.682404\pi\)
0.998778 + 0.0494206i \(0.0157375\pi\)
\(38\) −8.61582 14.9230i −1.39767 2.42084i
\(39\) −1.17251 2.03084i −0.187751 0.325195i
\(40\) 6.05203 10.4824i 0.956911 1.65742i
\(41\) −11.2499 −1.75694 −0.878471 0.477796i \(-0.841436\pi\)
−0.878471 + 0.477796i \(0.841436\pi\)
\(42\) −1.95897 + 4.27489i −0.302276 + 0.659629i
\(43\) 5.26819 0.803391 0.401696 0.915773i \(-0.368421\pi\)
0.401696 + 0.915773i \(0.368421\pi\)
\(44\) 2.10220 3.64112i 0.316919 0.548919i
\(45\) 2.74543 + 4.75523i 0.409265 + 0.708867i
\(46\) 8.08393 + 14.0018i 1.19191 + 2.06445i
\(47\) −0.745432 + 1.29113i −0.108732 + 0.188330i −0.915257 0.402871i \(-0.868012\pi\)
0.806525 + 0.591201i \(0.201346\pi\)
\(48\) −3.75905 −0.542573
\(49\) −4.57031 5.30210i −0.652901 0.757443i
\(50\) 0.350250 0.0495328
\(51\) 0.531894 0.921267i 0.0744800 0.129003i
\(52\) 6.90880 + 11.9664i 0.958079 + 1.65944i
\(53\) −0.152367 0.263908i −0.0209293 0.0362506i 0.855371 0.518016i \(-0.173329\pi\)
−0.876300 + 0.481765i \(0.839996\pi\)
\(54\) 4.87953 8.45159i 0.664019 1.15012i
\(55\) −2.20440 −0.297241
\(56\) 6.05203 13.2068i 0.808737 1.76483i
\(57\) 4.93621 0.653817
\(58\) −2.05465 + 3.55876i −0.269789 + 0.467288i
\(59\) 6.32936 + 10.9628i 0.824012 + 1.42723i 0.902672 + 0.430330i \(0.141603\pi\)
−0.0786592 + 0.996902i \(0.525064\pi\)
\(60\) 3.30660 + 5.72720i 0.426881 + 0.739379i
\(61\) 6.49086 11.2425i 0.831070 1.43946i −0.0661206 0.997812i \(-0.521062\pi\)
0.897191 0.441644i \(-0.145604\pi\)
\(62\) 5.85415 0.743478
\(63\) 3.81574 + 5.37317i 0.480738 + 0.676956i
\(64\) −5.20440 −0.650550
\(65\) 3.62234 6.27408i 0.449296 0.778204i
\(66\) 0.888663 + 1.53921i 0.109387 + 0.189464i
\(67\) 2.28646 + 3.96027i 0.279336 + 0.483824i 0.971220 0.238185i \(-0.0765524\pi\)
−0.691884 + 0.722009i \(0.743219\pi\)
\(68\) −3.13409 + 5.42841i −0.380065 + 0.658292i
\(69\) −4.63148 −0.557564
\(70\) −14.4635 + 1.36219i −1.72871 + 0.162813i
\(71\) 11.3267 1.34424 0.672119 0.740444i \(-0.265385\pi\)
0.672119 + 0.740444i \(0.265385\pi\)
\(72\) −6.83850 + 11.8446i −0.805925 + 1.39590i
\(73\) 4.28384 + 7.41984i 0.501386 + 0.868426i 0.999999 + 0.00160129i \(0.000509706\pi\)
−0.498613 + 0.866825i \(0.666157\pi\)
\(74\) −6.91794 11.9822i −0.804194 1.39291i
\(75\) −0.0501666 + 0.0868912i −0.00579274 + 0.0100333i
\(76\) −29.0858 −3.33637
\(77\) −2.63409 + 0.248083i −0.300183 + 0.0282717i
\(78\) −5.84111 −0.661376
\(79\) −2.31574 + 4.01098i −0.260541 + 0.451270i −0.966386 0.257096i \(-0.917234\pi\)
0.705845 + 0.708366i \(0.250568\pi\)
\(80\) −5.80660 10.0573i −0.649198 1.12444i
\(81\) −2.33850 4.05039i −0.259833 0.450044i
\(82\) −14.0110 + 24.2678i −1.54726 + 2.67993i
\(83\) −1.93621 −0.212527 −0.106263 0.994338i \(-0.533889\pi\)
−0.106263 + 0.994338i \(0.533889\pi\)
\(84\) 4.59568 + 6.47145i 0.501430 + 0.706093i
\(85\) 3.28646 0.356467
\(86\) 6.56117 11.3643i 0.707509 1.22544i
\(87\) −0.588580 1.01945i −0.0631024 0.109297i
\(88\) −2.74543 4.75523i −0.292664 0.506909i
\(89\) −1.60220 + 2.77509i −0.169833 + 0.294159i −0.938361 0.345657i \(-0.887656\pi\)
0.768528 + 0.639816i \(0.220989\pi\)
\(90\) 13.6770 1.44168
\(91\) 3.62234 7.90471i 0.379725 0.828639i
\(92\) 27.2902 2.84520
\(93\) −0.838496 + 1.45232i −0.0869480 + 0.150598i
\(94\) 1.85677 + 3.21602i 0.191511 + 0.331707i
\(95\) 7.62496 + 13.2068i 0.782304 + 1.35499i
\(96\) −0.763705 + 1.32278i −0.0779453 + 0.135005i
\(97\) 1.85939 0.188792 0.0943960 0.995535i \(-0.469908\pi\)
0.0943960 + 0.995535i \(0.469908\pi\)
\(98\) −17.1294 + 3.25544i −1.73034 + 0.328849i
\(99\) 2.49086 0.250341
\(100\) 0.295598 0.511992i 0.0295598 0.0511992i
\(101\) −3.02276 5.23557i −0.300776 0.520959i 0.675536 0.737327i \(-0.263912\pi\)
−0.976312 + 0.216368i \(0.930579\pi\)
\(102\) −1.32488 2.29475i −0.131182 0.227214i
\(103\) 0.531894 0.921267i 0.0524091 0.0907752i −0.838631 0.544700i \(-0.816643\pi\)
0.891040 + 0.453925i \(0.149977\pi\)
\(104\) 18.0455 1.76951
\(105\) 1.73368 3.78325i 0.169190 0.369208i
\(106\) −0.759053 −0.0737257
\(107\) 3.16599 5.48365i 0.306068 0.530125i −0.671431 0.741067i \(-0.734320\pi\)
0.977498 + 0.210943i \(0.0676533\pi\)
\(108\) −8.23630 14.2657i −0.792538 1.37272i
\(109\) 1.40694 + 2.43688i 0.134760 + 0.233411i 0.925506 0.378734i \(-0.123640\pi\)
−0.790746 + 0.612145i \(0.790307\pi\)
\(110\) −2.74543 + 4.75523i −0.261767 + 0.453393i
\(111\) 3.96345 0.376194
\(112\) −8.07031 11.3643i −0.762572 1.07382i
\(113\) −12.7538 −1.19978 −0.599889 0.800083i \(-0.704789\pi\)
−0.599889 + 0.800083i \(0.704789\pi\)
\(114\) 6.14772 10.6482i 0.575786 0.997291i
\(115\) −7.15423 12.3915i −0.667136 1.15551i
\(116\) 3.46811 + 6.00694i 0.322006 + 0.557730i
\(117\) −4.09306 + 7.08940i −0.378404 + 0.655415i
\(118\) 31.5311 2.90268
\(119\) 3.92708 0.369859i 0.359994 0.0339049i
\(120\) 8.63671 0.788420
\(121\) −0.500000 + 0.866025i −0.0454545 + 0.0787296i
\(122\) −16.1679 28.0035i −1.46377 2.53532i
\(123\) −4.01362 6.95180i −0.361896 0.626822i
\(124\) 4.94070 8.55754i 0.443688 0.768490i
\(125\) −11.3320 −1.01356
\(126\) 16.3430 1.53921i 1.45595 0.137124i
\(127\) −12.3775 −1.09832 −0.549162 0.835716i \(-0.685053\pi\)
−0.549162 + 0.835716i \(0.685053\pi\)
\(128\) −8.62234 + 14.9343i −0.762114 + 1.32002i
\(129\) 1.87953 + 3.25544i 0.165483 + 0.286625i
\(130\) −9.02276 15.6279i −0.791348 1.37066i
\(131\) −0.379526 + 0.657359i −0.0331594 + 0.0574337i −0.882129 0.471008i \(-0.843890\pi\)
0.848969 + 0.528442i \(0.177224\pi\)
\(132\) 3.00000 0.261116
\(133\) 10.5975 + 14.9230i 0.918924 + 1.29399i
\(134\) 11.3905 0.983992
\(135\) −4.31836 + 7.47961i −0.371665 + 0.643742i
\(136\) 4.09306 + 7.08940i 0.350977 + 0.607911i
\(137\) 2.92056 + 5.05855i 0.249520 + 0.432181i 0.963393 0.268094i \(-0.0863938\pi\)
−0.713873 + 0.700275i \(0.753060\pi\)
\(138\) −5.76819 + 9.99080i −0.491021 + 0.850473i
\(139\) −5.57292 −0.472689 −0.236345 0.971669i \(-0.575949\pi\)
−0.236345 + 0.971669i \(0.575949\pi\)
\(140\) −10.2154 + 22.2922i −0.863359 + 1.88403i
\(141\) −1.06379 −0.0895871
\(142\) 14.1067 24.4335i 1.18381 2.05041i
\(143\) −1.64323 2.84616i −0.137414 0.238008i
\(144\) 6.56117 + 11.3643i 0.546764 + 0.947023i
\(145\) 1.81836 3.14948i 0.151006 0.261550i
\(146\) 21.3409 1.76619
\(147\) 1.64585 4.71581i 0.135747 0.388953i
\(148\) −23.3540 −1.91969
\(149\) 0.500000 0.866025i 0.0409616 0.0709476i −0.844818 0.535054i \(-0.820291\pi\)
0.885779 + 0.464107i \(0.153625\pi\)
\(150\) 0.124958 + 0.216434i 0.0102028 + 0.0176718i
\(151\) −7.42056 12.8528i −0.603876 1.04594i −0.992228 0.124433i \(-0.960289\pi\)
0.388352 0.921511i \(-0.373045\pi\)
\(152\) −18.9927 + 32.8964i −1.54051 + 2.66825i
\(153\) −3.71354 −0.300222
\(154\) −2.74543 + 5.99111i −0.221233 + 0.482778i
\(155\) −5.18089 −0.416139
\(156\) −4.92969 + 8.53848i −0.394691 + 0.683625i
\(157\) −3.19527 5.53436i −0.255010 0.441690i 0.709888 0.704314i \(-0.248745\pi\)
−0.964898 + 0.262624i \(0.915412\pi\)
\(158\) 5.76819 + 9.99080i 0.458893 + 0.794825i
\(159\) 0.108720 0.188308i 0.00862205 0.0149338i
\(160\) −4.71877 −0.373052
\(161\) −9.94331 14.0018i −0.783643 1.10349i
\(162\) −11.6498 −0.915291
\(163\) −4.97259 + 8.61278i −0.389483 + 0.674605i −0.992380 0.123214i \(-0.960680\pi\)
0.602897 + 0.797819i \(0.294013\pi\)
\(164\) 23.6496 + 40.9623i 1.84672 + 3.19862i
\(165\) −0.786462 1.36219i −0.0612260 0.106047i
\(166\) −2.41142 + 4.17670i −0.187163 + 0.324175i
\(167\) −1.94145 −0.150234 −0.0751168 0.997175i \(-0.523933\pi\)
−0.0751168 + 0.997175i \(0.523933\pi\)
\(168\) 10.3202 0.971976i 0.796223 0.0749896i
\(169\) −2.19917 −0.169167
\(170\) 4.09306 7.08940i 0.313924 0.543732i
\(171\) −8.61582 14.9230i −0.658868 1.14119i
\(172\) −11.0748 19.1821i −0.844445 1.46262i
\(173\) −3.21616 + 5.57054i −0.244520 + 0.423521i −0.961996 0.273062i \(-0.911964\pi\)
0.717477 + 0.696582i \(0.245297\pi\)
\(174\) −2.93214 −0.222285
\(175\) −0.370390 + 0.0348840i −0.0279989 + 0.00263698i
\(176\) −5.26819 −0.397105
\(177\) −4.51624 + 7.82235i −0.339461 + 0.587964i
\(178\) 3.99086 + 6.91238i 0.299128 + 0.518105i
\(179\) 1.79298 + 3.10553i 0.134014 + 0.232119i 0.925220 0.379430i \(-0.123880\pi\)
−0.791207 + 0.611549i \(0.790547\pi\)
\(180\) 11.5429 19.9929i 0.860357 1.49018i
\(181\) 12.2134 0.907813 0.453906 0.891049i \(-0.350030\pi\)
0.453906 + 0.891049i \(0.350030\pi\)
\(182\) −12.5403 17.6587i −0.929547 1.30895i
\(183\) 9.26295 0.684737
\(184\) 17.8202 30.8655i 1.31372 2.27544i
\(185\) 6.12234 + 10.6042i 0.450123 + 0.779637i
\(186\) 2.08858 + 3.61753i 0.153142 + 0.265250i
\(187\) 0.745432 1.29113i 0.0545114 0.0944165i
\(188\) 6.26819 0.457155
\(189\) −4.31836 + 9.42356i −0.314114 + 0.685463i
\(190\) 37.9855 2.75576
\(191\) −6.05465 + 10.4870i −0.438099 + 0.758810i −0.997543 0.0700583i \(-0.977681\pi\)
0.559444 + 0.828868i \(0.311015\pi\)
\(192\) −1.85677 3.21602i −0.134001 0.232096i
\(193\) 5.96997 + 10.3403i 0.429728 + 0.744311i 0.996849 0.0793237i \(-0.0252761\pi\)
−0.567121 + 0.823635i \(0.691943\pi\)
\(194\) 2.31574 4.01098i 0.166260 0.287971i
\(195\) 5.16936 0.370185
\(196\) −9.69788 + 27.7871i −0.692706 + 1.98479i
\(197\) 12.1626 0.866551 0.433275 0.901262i \(-0.357358\pi\)
0.433275 + 0.901262i \(0.357358\pi\)
\(198\) 3.10220 5.37317i 0.220464 0.381855i
\(199\) −0.952451 1.64969i −0.0675174 0.116944i 0.830290 0.557331i \(-0.188174\pi\)
−0.897808 + 0.440387i \(0.854841\pi\)
\(200\) −0.386046 0.668651i −0.0272975 0.0472807i
\(201\) −1.63148 + 2.82580i −0.115076 + 0.199317i
\(202\) −15.0586 −1.05952
\(203\) 1.81836 3.96804i 0.127624 0.278502i
\(204\) −4.47259 −0.313144
\(205\) 12.3997 21.4769i 0.866030 1.50001i
\(206\) −1.32488 2.29475i −0.0923084 0.159883i
\(207\) 8.08393 + 14.0018i 0.561872 + 0.973191i
\(208\) 8.65685 14.9941i 0.600245 1.03965i
\(209\) 6.91794 0.478524
\(210\) −6.00187 8.45159i −0.414168 0.583215i
\(211\) −16.2447 −1.11833 −0.559165 0.829056i \(-0.688878\pi\)
−0.559165 + 0.829056i \(0.688878\pi\)
\(212\) −0.640614 + 1.10958i −0.0439975 + 0.0762060i
\(213\) 4.04103 + 6.99927i 0.276887 + 0.479582i
\(214\) −7.88605 13.6590i −0.539079 0.933712i
\(215\) −5.80660 + 10.0573i −0.396007 + 0.685904i
\(216\) −21.5129 −1.46377
\(217\) −6.19078 + 0.583058i −0.420258 + 0.0395806i
\(218\) 7.00897 0.474707
\(219\) −3.05669 + 5.29434i −0.206552 + 0.357758i
\(220\) 4.63409 + 8.02649i 0.312431 + 0.541146i
\(221\) 2.44983 + 4.24324i 0.164794 + 0.285431i
\(222\) 4.93621 8.54977i 0.331297 0.573823i
\(223\) 3.03655 0.203342 0.101671 0.994818i \(-0.467581\pi\)
0.101671 + 0.994818i \(0.467581\pi\)
\(224\) −5.63858 + 0.531051i −0.376743 + 0.0354823i
\(225\) 0.350250 0.0233500
\(226\) −15.8840 + 27.5119i −1.05659 + 1.83007i
\(227\) −9.22454 15.9774i −0.612254 1.06046i −0.990860 0.134897i \(-0.956930\pi\)
0.378605 0.925558i \(-0.376404\pi\)
\(228\) −10.3769 17.9733i −0.687228 1.19031i
\(229\) 12.7499 22.0835i 0.842538 1.45932i −0.0452039 0.998978i \(-0.514394\pi\)
0.887742 0.460341i \(-0.152273\pi\)
\(230\) −35.6404 −2.35006
\(231\) −1.09306 1.53921i −0.0719184 0.101273i
\(232\) 9.05855 0.594723
\(233\) −1.90880 + 3.30614i −0.125050 + 0.216593i −0.921752 0.387779i \(-0.873242\pi\)
0.796703 + 0.604372i \(0.206576\pi\)
\(234\) 10.1953 + 17.6587i 0.666485 + 1.15439i
\(235\) −1.64323 2.84616i −0.107193 0.185663i
\(236\) 26.6112 46.0919i 1.73224 3.00033i
\(237\) −3.30473 −0.214666
\(238\) 4.09306 8.93193i 0.265314 0.578971i
\(239\) 13.0037 0.841142 0.420571 0.907260i \(-0.361830\pi\)
0.420571 + 0.907260i \(0.361830\pi\)
\(240\) 4.14323 7.17629i 0.267444 0.463227i
\(241\) 0.225292 + 0.390216i 0.0145123 + 0.0251360i 0.873190 0.487379i \(-0.162047\pi\)
−0.858678 + 0.512515i \(0.828714\pi\)
\(242\) 1.24543 + 2.15715i 0.0800594 + 0.138667i
\(243\) 7.54551 13.0692i 0.484045 0.838391i
\(244\) −54.5804 −3.49415
\(245\) 15.1595 2.88104i 0.968503 0.184063i
\(246\) −19.9948 −1.27482
\(247\) −11.3678 + 19.6896i −0.723314 + 1.25282i
\(248\) −6.45245 11.1760i −0.409731 0.709675i
\(249\) −0.690780 1.19647i −0.0437764 0.0758230i
\(250\) −14.1132 + 24.4448i −0.892597 + 1.54602i
\(251\) 1.11861 0.0706058 0.0353029 0.999377i \(-0.488760\pi\)
0.0353029 + 0.999377i \(0.488760\pi\)
\(252\) 11.5429 25.1890i 0.727134 1.58676i
\(253\) −6.49086 −0.408077
\(254\) −15.4153 + 26.7001i −0.967243 + 1.67531i
\(255\) 1.17251 + 2.03084i 0.0734253 + 0.127176i
\(256\) 16.2727 + 28.1851i 1.01704 + 1.76157i
\(257\) 11.4198 19.7797i 0.712348 1.23382i −0.251626 0.967825i \(-0.580965\pi\)
0.963974 0.265998i \(-0.0857015\pi\)
\(258\) 9.36329 0.582933
\(259\) 8.50914 + 11.9822i 0.528732 + 0.744539i
\(260\) −30.4596 −1.88902
\(261\) −2.05465 + 3.55876i −0.127180 + 0.220282i
\(262\) 0.945349 + 1.63739i 0.0584038 + 0.101158i
\(263\) 4.59568 + 7.95995i 0.283382 + 0.490832i 0.972215 0.234088i \(-0.0752103\pi\)
−0.688834 + 0.724919i \(0.741877\pi\)
\(264\) 1.95897 3.39304i 0.120566 0.208827i
\(265\) 0.671758 0.0412658
\(266\) 45.3898 4.27489i 2.78303 0.262110i
\(267\) −2.28646 −0.139929
\(268\) 9.61320 16.6506i 0.587220 1.01709i
\(269\) 7.80660 + 13.5214i 0.475977 + 0.824416i 0.999621 0.0275208i \(-0.00876123\pi\)
−0.523644 + 0.851937i \(0.675428\pi\)
\(270\) 10.7564 + 18.6307i 0.654616 + 1.13383i
\(271\) −13.8723 + 24.0275i −0.842680 + 1.45956i 0.0449415 + 0.998990i \(0.485690\pi\)
−0.887621 + 0.460574i \(0.847643\pi\)
\(272\) 7.85415 0.476228
\(273\) 6.17699 0.581759i 0.373849 0.0352097i
\(274\) 14.5494 0.878962
\(275\) −0.0703069 + 0.121775i −0.00423967 + 0.00734332i
\(276\) 9.73630 + 16.8638i 0.586056 + 1.01508i
\(277\) −7.40619 12.8279i −0.444995 0.770753i 0.553057 0.833143i \(-0.313461\pi\)
−0.998052 + 0.0623900i \(0.980128\pi\)
\(278\) −6.94070 + 12.0216i −0.416275 + 0.721010i
\(279\) 5.85415 0.350479
\(280\) 18.5421 + 26.1103i 1.10811 + 1.56039i
\(281\) 15.2227 0.908109 0.454054 0.890974i \(-0.349977\pi\)
0.454054 + 0.890974i \(0.349977\pi\)
\(282\) −1.32488 + 2.29475i −0.0788952 + 0.136650i
\(283\) −10.8586 18.8077i −0.645479 1.11800i −0.984191 0.177112i \(-0.943324\pi\)
0.338712 0.940890i \(-0.390009\pi\)
\(284\) −23.8111 41.2420i −1.41293 2.44726i
\(285\) −5.44070 + 9.42356i −0.322279 + 0.558204i
\(286\) −8.18613 −0.484056
\(287\) 12.3997 27.0587i 0.731929 1.59722i
\(288\) 5.33198 0.314190
\(289\) 7.38866 12.7975i 0.434627 0.752796i
\(290\) −4.52928 7.84494i −0.265968 0.460671i
\(291\) 0.663371 + 1.14899i 0.0388875 + 0.0673551i
\(292\) 18.0110 31.1960i 1.05401 1.82561i
\(293\) 11.1276 0.650080 0.325040 0.945700i \(-0.394622\pi\)
0.325040 + 0.945700i \(0.394622\pi\)
\(294\) −8.12292 9.42356i −0.473739 0.549593i
\(295\) −27.9049 −1.62469
\(296\) −15.2499 + 26.4136i −0.886383 + 1.53526i
\(297\) 1.95897 + 3.39304i 0.113671 + 0.196884i
\(298\) −1.24543 2.15715i −0.0721459 0.124960i
\(299\) 10.6660 18.4740i 0.616830 1.06838i
\(300\) 0.421841 0.0243550
\(301\) −5.80660 + 12.6712i −0.334687 + 0.730358i
\(302\) −36.9672 −2.12722
\(303\) 2.15685 3.73578i 0.123908 0.214615i
\(304\) 18.2225 + 31.5623i 1.04513 + 1.81022i
\(305\) 14.3085 + 24.7830i 0.819301 + 1.41907i
\(306\) −4.62496 + 8.01066i −0.264391 + 0.457939i
\(307\) 24.9855 1.42600 0.712998 0.701166i \(-0.247337\pi\)
0.712998 + 0.701166i \(0.247337\pi\)
\(308\) 6.44070 + 9.06953i 0.366993 + 0.516784i
\(309\) 0.759053 0.0431810
\(310\) −6.45245 + 11.1760i −0.366475 + 0.634753i
\(311\) −17.3704 30.0864i −0.984984 1.70604i −0.642005 0.766700i \(-0.721897\pi\)
−0.342979 0.939343i \(-0.611436\pi\)
\(312\) 6.43808 + 11.1511i 0.364484 + 0.631306i
\(313\) −11.8547 + 20.5330i −0.670069 + 1.16059i 0.307815 + 0.951446i \(0.400402\pi\)
−0.977884 + 0.209148i \(0.932931\pi\)
\(314\) −15.9179 −0.898301
\(315\) −14.4635 + 1.36219i −0.814923 + 0.0767508i
\(316\) 19.4726 1.09542
\(317\) −9.83850 + 17.0408i −0.552585 + 0.957105i 0.445502 + 0.895281i \(0.353025\pi\)
−0.998087 + 0.0618244i \(0.980308\pi\)
\(318\) −0.270807 0.469051i −0.0151861 0.0263031i
\(319\) −0.824875 1.42873i −0.0461841 0.0799933i
\(320\) 5.73630 9.93556i 0.320669 0.555414i
\(321\) 4.51811 0.252176
\(322\) −42.5877 + 4.01098i −2.37332 + 0.223523i
\(323\) −10.3137 −0.573870
\(324\) −9.83198 + 17.0295i −0.546221 + 0.946082i
\(325\) −0.231061 0.400209i −0.0128170 0.0221996i
\(326\) 12.3860 + 21.4533i 0.686000 + 1.18819i
\(327\) −1.00390 + 1.73881i −0.0555159 + 0.0961564i
\(328\) 61.7718 3.41077
\(329\) −2.28384 3.21602i −0.125912 0.177305i
\(330\) −3.91794 −0.215675
\(331\) 14.0949 24.4131i 0.774728 1.34187i −0.160220 0.987081i \(-0.551220\pi\)
0.934947 0.354786i \(-0.115446\pi\)
\(332\) 4.07031 + 7.04998i 0.223387 + 0.386918i
\(333\) −6.91794 11.9822i −0.379101 0.656622i
\(334\) −2.41794 + 4.18799i −0.132304 + 0.229157i
\(335\) −10.0806 −0.550760
\(336\) 4.14323 9.04140i 0.226032 0.493249i
\(337\) 21.7460 1.18458 0.592290 0.805725i \(-0.298224\pi\)
0.592290 + 0.805725i \(0.298224\pi\)
\(338\) −2.73891 + 4.74394i −0.148977 + 0.258036i
\(339\) −4.55017 7.88112i −0.247131 0.428044i
\(340\) −6.90880 11.9664i −0.374682 0.648969i
\(341\) −1.17512 + 2.03538i −0.0636366 + 0.110222i
\(342\) −42.9217 −2.32094
\(343\) 17.7902 5.14868i 0.960580 0.278003i
\(344\) −28.9269 −1.55963
\(345\) 5.10482 8.84180i 0.274834 0.476027i
\(346\) 8.01100 + 13.8755i 0.430674 + 0.745950i
\(347\) 1.97072 + 3.41339i 0.105794 + 0.183241i 0.914062 0.405574i \(-0.132928\pi\)
−0.808268 + 0.588814i \(0.799595\pi\)
\(348\) −2.47463 + 4.28618i −0.132654 + 0.229763i
\(349\) −14.1093 −0.755254 −0.377627 0.925958i \(-0.623260\pi\)
−0.377627 + 0.925958i \(0.623260\pi\)
\(350\) −0.386046 + 0.842433i −0.0206350 + 0.0450299i
\(351\) −12.8762 −0.687279
\(352\) −1.07031 + 1.85383i −0.0570475 + 0.0988093i
\(353\) 2.48434 + 4.30301i 0.132228 + 0.229026i 0.924535 0.381097i \(-0.124453\pi\)
−0.792307 + 0.610123i \(0.791120\pi\)
\(354\) 11.2493 + 19.4844i 0.597895 + 1.03559i
\(355\) −12.4843 + 21.6235i −0.662600 + 1.14766i
\(356\) 13.4726 0.714046
\(357\) 1.62961 + 2.29475i 0.0862481 + 0.121451i
\(358\) 8.93214 0.472078
\(359\) 2.03580 3.52610i 0.107445 0.186101i −0.807289 0.590156i \(-0.799066\pi\)
0.914735 + 0.404055i \(0.132400\pi\)
\(360\) −15.0748 26.1103i −0.794511 1.37613i
\(361\) −14.4289 24.9917i −0.759418 1.31535i
\(362\) 15.2109 26.3461i 0.799468 1.38472i
\(363\) −0.713538 −0.0374510
\(364\) −36.3969 + 3.42792i −1.90772 + 0.179672i
\(365\) −18.8866 −0.988571
\(366\) 11.5364 19.9816i 0.603016 1.04445i
\(367\) 9.01100 + 15.6075i 0.470371 + 0.814706i 0.999426 0.0338816i \(-0.0107869\pi\)
−0.529055 + 0.848587i \(0.677454\pi\)
\(368\) −17.0975 29.6138i −0.891271 1.54373i
\(369\) −14.0110 + 24.2678i −0.729384 + 1.26333i
\(370\) 30.4998 1.58561
\(371\) 0.802700 0.0755997i 0.0416741 0.00392494i
\(372\) 7.05075 0.365564
\(373\) −14.4582 + 25.0424i −0.748618 + 1.29664i 0.199867 + 0.979823i \(0.435949\pi\)
−0.948485 + 0.316822i \(0.897384\pi\)
\(374\) −1.85677 3.21602i −0.0960112 0.166296i
\(375\) −4.04290 7.00250i −0.208774 0.361608i
\(376\) 4.09306 7.08940i 0.211084 0.365608i
\(377\) 5.42184 0.279239
\(378\) 14.9498 + 21.0518i 0.768936 + 1.08279i
\(379\) 4.30847 0.221311 0.110656 0.993859i \(-0.464705\pi\)
0.110656 + 0.993859i \(0.464705\pi\)
\(380\) 32.0584 55.5268i 1.64456 2.84846i
\(381\) −4.41591 7.64857i −0.226234 0.391848i
\(382\) 15.0813 + 26.1216i 0.771627 + 1.33650i
\(383\) 6.17438 10.6943i 0.315496 0.546455i −0.664047 0.747691i \(-0.731163\pi\)
0.979543 + 0.201236i \(0.0644958\pi\)
\(384\) −12.3047 −0.627923
\(385\) 2.42969 5.30210i 0.123829 0.270220i
\(386\) 29.7408 1.51377
\(387\) 6.56117 11.3643i 0.333523 0.577679i
\(388\) −3.90880 6.77025i −0.198439 0.343707i
\(389\) −14.7115 25.4811i −0.745903 1.29194i −0.949772 0.312943i \(-0.898685\pi\)
0.203869 0.978998i \(-0.434648\pi\)
\(390\) 6.43808 11.1511i 0.326005 0.564657i
\(391\) 9.67699 0.489387
\(392\) 25.0949 + 29.1131i 1.26749 + 1.47043i
\(393\) −0.541613 −0.0273208
\(394\) 15.1477 26.2366i 0.763131 1.32178i
\(395\) −5.10482 8.84180i −0.256851 0.444879i
\(396\) −5.23630 9.06953i −0.263134 0.455761i
\(397\) 8.64975 14.9818i 0.434119 0.751915i −0.563105 0.826386i \(-0.690393\pi\)
0.997223 + 0.0744702i \(0.0237266\pi\)
\(398\) −4.74485 −0.237838
\(399\) −5.44070 + 11.8727i −0.272376 + 0.594381i
\(400\) −0.740780 −0.0370390
\(401\) 12.4752 21.6077i 0.622982 1.07904i −0.365945 0.930636i \(-0.619254\pi\)
0.988927 0.148400i \(-0.0474124\pi\)
\(402\) 4.06379 + 7.03869i 0.202683 + 0.351058i
\(403\) −3.86200 6.68919i −0.192380 0.333212i
\(404\) −12.7089 + 22.0124i −0.632291 + 1.09516i
\(405\) 10.3100 0.512306
\(406\) −6.29502 8.86439i −0.312416 0.439932i
\(407\) 5.55465 0.275334
\(408\) −2.92056 + 5.05855i −0.144589 + 0.250436i
\(409\) 19.2792 + 33.3925i 0.953295 + 1.65115i 0.738223 + 0.674557i \(0.235665\pi\)
0.215072 + 0.976598i \(0.431001\pi\)
\(410\) −30.8859 53.4959i −1.52534 2.64197i
\(411\) −2.08393 + 3.60947i −0.102793 + 0.178042i
\(412\) −4.47259 −0.220349
\(413\) −33.3443 + 3.14042i −1.64076 + 0.154530i
\(414\) 40.2719 1.97926
\(415\) 2.13409 3.69636i 0.104759 0.181447i
\(416\) −3.51752 6.09253i −0.172461 0.298711i
\(417\) −1.98825 3.44374i −0.0973648 0.168641i
\(418\) 8.61582 14.9230i 0.421414 0.729910i
\(419\) 0.908970 0.0444061 0.0222030 0.999753i \(-0.492932\pi\)
0.0222030 + 0.999753i \(0.492932\pi\)
\(420\) −17.4198 + 1.64063i −0.850000 + 0.0800544i
\(421\) 15.5532 0.758014 0.379007 0.925394i \(-0.376266\pi\)
0.379007 + 0.925394i \(0.376266\pi\)
\(422\) −20.2316 + 35.0422i −0.984861 + 1.70583i
\(423\) 1.85677 + 3.21602i 0.0902792 + 0.156368i
\(424\) 0.836629 + 1.44908i 0.0406303 + 0.0703737i
\(425\) 0.104818 0.181550i 0.00508442 0.00880647i
\(426\) 20.1313 0.975365
\(427\) 19.8866 + 28.0035i 0.962381 + 1.35519i
\(428\) −26.6222 −1.28683
\(429\) 1.17251 2.03084i 0.0566092 0.0980500i
\(430\) 14.4635 + 25.0514i 0.697490 + 1.20809i
\(431\) −1.76819 3.06259i −0.0851707 0.147520i 0.820293 0.571943i \(-0.193810\pi\)
−0.905464 + 0.424423i \(0.860477\pi\)
\(432\) −10.3202 + 17.8752i −0.496532 + 0.860019i
\(433\) 17.6457 0.847997 0.423999 0.905663i \(-0.360626\pi\)
0.423999 + 0.905663i \(0.360626\pi\)
\(434\) −6.45245 + 14.0806i −0.309728 + 0.675891i
\(435\) 2.59493 0.124417
\(436\) 5.91532 10.2456i 0.283293 0.490677i
\(437\) 22.4517 + 38.8875i 1.07401 + 1.86024i
\(438\) 7.61379 + 13.1875i 0.363801 + 0.630122i
\(439\) −7.51362 + 13.0140i −0.358606 + 0.621123i −0.987728 0.156183i \(-0.950081\pi\)
0.629123 + 0.777306i \(0.283414\pi\)
\(440\) 12.1041 0.577039
\(441\) −17.1294 + 3.25544i −0.815688 + 0.155021i
\(442\) 12.2044 0.580504
\(443\) −6.61134 + 11.4512i −0.314114 + 0.544062i −0.979249 0.202662i \(-0.935041\pi\)
0.665135 + 0.746723i \(0.268374\pi\)
\(444\) −8.33198 14.4314i −0.395418 0.684884i
\(445\) −3.53189 6.11742i −0.167428 0.289994i
\(446\) 3.78181 6.55029i 0.179074 0.310165i
\(447\) 0.713538 0.0337492
\(448\) 5.73630 12.5178i 0.271014 0.591411i
\(449\) −9.90864 −0.467617 −0.233809 0.972283i \(-0.575119\pi\)
−0.233809 + 0.972283i \(0.575119\pi\)
\(450\) 0.436212 0.755542i 0.0205632 0.0356166i
\(451\) −5.62496 9.74271i −0.264869 0.458766i
\(452\) 26.8111 + 46.4382i 1.26109 + 2.18427i
\(453\) 5.29485 9.17095i 0.248774 0.430889i
\(454\) −45.9542 −2.15674
\(455\) 11.0981 + 15.6279i 0.520286 + 0.732646i
\(456\) −27.1041 −1.26926
\(457\) −5.17251 + 8.95905i −0.241960 + 0.419087i −0.961272 0.275600i \(-0.911124\pi\)
0.719313 + 0.694686i \(0.244457\pi\)
\(458\) −31.7583 55.0070i −1.48397 2.57031i
\(459\) −2.92056 5.05855i −0.136320 0.236113i
\(460\) −30.0793 + 52.0988i −1.40245 + 2.42912i
\(461\) −15.3372 −0.714325 −0.357163 0.934042i \(-0.616256\pi\)
−0.357163 + 0.934042i \(0.616256\pi\)
\(462\) −4.68164 + 0.440925i −0.217810 + 0.0205137i
\(463\) −25.1313 −1.16795 −0.583976 0.811771i \(-0.698504\pi\)
−0.583976 + 0.811771i \(0.698504\pi\)
\(464\) 4.34560 7.52680i 0.201739 0.349423i
\(465\) −1.84838 3.20149i −0.0857167 0.148466i
\(466\) 4.75457 + 8.23515i 0.220251 + 0.381486i
\(467\) 0.373007 0.646068i 0.0172607 0.0298964i −0.857266 0.514874i \(-0.827839\pi\)
0.874527 + 0.484977i \(0.161172\pi\)
\(468\) 34.4178 1.59096
\(469\) −12.0455 + 1.13447i −0.556210 + 0.0523848i
\(470\) −8.18613 −0.377598
\(471\) 2.27994 3.94898i 0.105054 0.181959i
\(472\) −34.7537 60.1951i −1.59967 2.77070i
\(473\) 2.63409 + 4.56239i 0.121116 + 0.209779i
\(474\) −4.11582 + 7.12881i −0.189046 + 0.327437i
\(475\) 0.972758 0.0446332
\(476\) −9.60220 13.5214i −0.440116 0.619754i
\(477\) −0.759053 −0.0347546
\(478\) 16.1953 28.0510i 0.740754 1.28302i
\(479\) 10.0565 + 17.4184i 0.459494 + 0.795867i 0.998934 0.0461569i \(-0.0146974\pi\)
−0.539440 + 0.842024i \(0.681364\pi\)
\(480\) −1.68351 2.91593i −0.0768414 0.133093i
\(481\) −9.12758 + 15.8094i −0.416182 + 0.720848i
\(482\) 1.12234 0.0511212
\(483\) 5.10482 11.1398i 0.232277 0.506878i
\(484\) 4.20440 0.191109
\(485\) −2.04942 + 3.54969i −0.0930592 + 0.161183i
\(486\) −18.7948 32.5536i −0.852552 1.47666i
\(487\) 2.12496 + 3.68054i 0.0962911 + 0.166781i 0.910147 0.414286i \(-0.135969\pi\)
−0.813856 + 0.581067i \(0.802635\pi\)
\(488\) −35.6404 + 61.7311i −1.61337 + 2.79443i
\(489\) −7.09626 −0.320904
\(490\) 12.6652 36.2894i 0.572157 1.63939i
\(491\) 30.3279 1.36868 0.684340 0.729163i \(-0.260091\pi\)
0.684340 + 0.729163i \(0.260091\pi\)
\(492\) −16.8749 + 29.2281i −0.760778 + 1.31771i
\(493\) 1.22978 + 2.13003i 0.0553863 + 0.0959320i
\(494\) 28.3156 + 49.0440i 1.27398 + 2.20659i
\(495\) −2.74543 + 4.75523i −0.123398 + 0.213732i
\(496\) −12.3816 −0.555948
\(497\) −12.4843 + 27.2435i −0.559999 + 1.22204i
\(498\) −3.44128 −0.154207
\(499\) −7.22064 + 12.5065i −0.323240 + 0.559869i −0.981155 0.193224i \(-0.938106\pi\)
0.657914 + 0.753093i \(0.271439\pi\)
\(500\) 23.8221 + 41.2611i 1.06536 + 1.84525i
\(501\) −0.692648 1.19970i −0.0309452 0.0535987i
\(502\) 1.39315 2.41300i 0.0621792 0.107698i
\(503\) −2.95822 −0.131901 −0.0659503 0.997823i \(-0.521008\pi\)
−0.0659503 + 0.997823i \(0.521008\pi\)
\(504\) −20.9517 29.5033i −0.933263 1.31418i
\(505\) 13.3267 0.593032
\(506\) −8.08393 + 14.0018i −0.359374 + 0.622455i
\(507\) −0.784595 1.35896i −0.0348451 0.0603534i
\(508\) 26.0200 + 45.0679i 1.15445 + 1.99957i
\(509\) 12.4953 21.6426i 0.553847 0.959290i −0.444146 0.895955i \(-0.646493\pi\)
0.997992 0.0633358i \(-0.0201739\pi\)
\(510\) 5.84111 0.258649
\(511\) −22.5681 + 2.12550i −0.998354 + 0.0940267i
\(512\) 46.5767 2.05842
\(513\) 13.5520 23.4728i 0.598337 1.03635i
\(514\) −28.4452 49.2685i −1.25466 2.17314i
\(515\) 1.17251 + 2.03084i 0.0516669 + 0.0894896i
\(516\) 7.90228 13.6872i 0.347879 0.602544i
\(517\) −1.49086 −0.0655681
\(518\) 36.4450 3.43245i 1.60130 0.150813i
\(519\) −4.58970 −0.201465
\(520\) −19.8898 + 34.4501i −0.872225 + 1.51074i
\(521\) −14.4316 24.9962i −0.632258 1.09510i −0.987089 0.160173i \(-0.948795\pi\)
0.354831 0.934931i \(-0.384538\pi\)
\(522\) 5.11786 + 8.86439i 0.224002 + 0.387984i
\(523\) −0.236295 + 0.409276i −0.0103325 + 0.0178964i −0.871145 0.491025i \(-0.836622\pi\)
0.860813 + 0.508921i \(0.169956\pi\)
\(524\) 3.19136 0.139415
\(525\) −0.153700 0.216434i −0.00670802 0.00944596i
\(526\) 22.8944 0.998245
\(527\) 1.75195 3.03447i 0.0763162 0.132184i
\(528\) −1.87953 3.25544i −0.0817959 0.141675i
\(529\) −9.56566 16.5682i −0.415898 0.720357i
\(530\) 0.836629 1.44908i 0.0363408 0.0629442i
\(531\) 31.5311 1.36834
\(532\) 32.0584 69.9582i 1.38991 3.03307i
\(533\) 36.9724 1.60145
\(534\) −2.84763 + 4.93224i −0.123229 + 0.213439i
\(535\) 6.97911 + 12.0882i 0.301733 + 0.522617i
\(536\) −12.5547 21.7453i −0.542278 0.939254i
\(537\) −1.27936 + 2.21592i −0.0552085 + 0.0956239i
\(538\) 38.8904 1.67668
\(539\) 2.30660 6.60905i 0.0993524 0.284672i
\(540\) 36.3122 1.56263
\(541\) −7.72978 + 13.3884i −0.332329 + 0.575611i −0.982968 0.183776i \(-0.941168\pi\)
0.650639 + 0.759387i \(0.274501\pi\)
\(542\) 34.5539 + 59.8491i 1.48422 + 2.57074i
\(543\) 4.35735 + 7.54715i 0.186992 + 0.323879i
\(544\) 1.59568 2.76380i 0.0684143 0.118497i
\(545\) −6.20290 −0.265703
\(546\) 6.43808 14.0492i 0.275524 0.601252i
\(547\) −35.0440 −1.49837 −0.749187 0.662359i \(-0.769556\pi\)
−0.749187 + 0.662359i \(0.769556\pi\)
\(548\) 12.2792 21.2682i 0.524541 0.908532i
\(549\) −16.1679 28.0035i −0.690027 1.19516i
\(550\) 0.175125 + 0.303325i 0.00746735 + 0.0129338i
\(551\) −5.70644 + 9.88384i −0.243102 + 0.421066i
\(552\) 25.4308 1.08241
\(553\) −7.09493 9.99080i −0.301707 0.424852i
\(554\) −36.8956 −1.56754
\(555\) −4.36852 + 7.56650i −0.185433 + 0.321180i
\(556\) 11.7154 + 20.2917i 0.496844 + 0.860559i
\(557\) −5.26632 9.12154i −0.223141 0.386492i 0.732619 0.680639i \(-0.238298\pi\)
−0.955760 + 0.294147i \(0.904964\pi\)
\(558\) 7.29095 12.6283i 0.308650 0.534598i
\(559\) −17.3137 −0.732292
\(560\) 30.5903 2.88104i 1.29268 0.121746i
\(561\) 1.06379 0.0449132
\(562\) 18.9588 32.8376i 0.799729 1.38517i
\(563\) 15.3574 + 26.5997i 0.647235 + 1.12104i 0.983780 + 0.179377i \(0.0574082\pi\)
−0.336545 + 0.941667i \(0.609258\pi\)
\(564\) 2.23630 + 3.87338i 0.0941650 + 0.163099i
\(565\) 14.0573 24.3479i 0.591394 1.02432i
\(566\) −54.0948 −2.27377
\(567\) 12.3196 1.16028i 0.517376 0.0487274i
\(568\) −62.1936 −2.60959
\(569\) 15.3860 26.6494i 0.645017 1.11720i −0.339281 0.940685i \(-0.610184\pi\)
0.984298 0.176516i \(-0.0564829\pi\)
\(570\) 13.5520 + 23.4728i 0.567632 + 0.983168i
\(571\) 3.75847 + 6.50986i 0.157287 + 0.272429i 0.933889 0.357562i \(-0.116392\pi\)
−0.776602 + 0.629991i \(0.783059\pi\)
\(572\) −6.90880 + 11.9664i −0.288872 + 0.500340i
\(573\) −8.64045 −0.360960
\(574\) −42.9267 60.4477i −1.79173 2.52304i
\(575\) −0.912705 −0.0380624
\(576\) −6.48173 + 11.2267i −0.270072 + 0.467778i
\(577\) −13.8092 23.9183i −0.574885 0.995731i −0.996054 0.0887483i \(-0.971713\pi\)
0.421169 0.906982i \(-0.361620\pi\)
\(578\) −18.4042 31.8769i −0.765512 1.32591i
\(579\) −4.25980 + 7.37819i −0.177031 + 0.306627i
\(580\) −15.2902 −0.634891
\(581\) 2.13409 4.65704i 0.0885372 0.193207i
\(582\) 3.30473 0.136986
\(583\) 0.152367 0.263908i 0.00631041 0.0109300i
\(584\) −23.5220 40.7413i −0.973348 1.68589i
\(585\) −9.02276 15.6279i −0.373045 0.646133i
\(586\) 13.8586 24.0039i 0.572495 0.991590i
\(587\) −29.9582 −1.23651 −0.618254 0.785978i \(-0.712160\pi\)
−0.618254 + 0.785978i \(0.712160\pi\)
\(588\) −20.6307 + 3.92085i −0.850797 + 0.161693i
\(589\) 16.2589 0.669936
\(590\) −34.7537 + 60.1951i −1.43079 + 2.47819i
\(591\) 4.33925 + 7.51579i 0.178493 + 0.309158i
\(592\) 14.6315 + 25.3425i 0.601350 + 1.04157i
\(593\) −6.33401 + 10.9708i −0.260107 + 0.450518i −0.966270 0.257531i \(-0.917091\pi\)
0.706163 + 0.708049i \(0.250424\pi\)
\(594\) 9.75905 0.400419
\(595\) −3.62234 + 7.90471i −0.148502 + 0.324062i
\(596\) −4.20440 −0.172219
\(597\) 0.679610 1.17712i 0.0278146 0.0481762i
\(598\) −26.5675 46.0163i −1.08643 1.88175i
\(599\) −0.647133 1.12087i −0.0264411 0.0457974i 0.852502 0.522724i \(-0.175084\pi\)
−0.878943 + 0.476926i \(0.841751\pi\)
\(600\) 0.275458 0.477108i 0.0112455 0.0194778i
\(601\) −41.0220 −1.67332 −0.836661 0.547721i \(-0.815496\pi\)
−0.836661 + 0.547721i \(0.815496\pi\)
\(602\) 20.1020 + 28.3069i 0.819298 + 1.15370i
\(603\) 11.3905 0.463858
\(604\) −31.1990 + 54.0383i −1.26947 + 2.19879i
\(605\) −1.10220 1.90907i −0.0448108 0.0776146i
\(606\) −5.37242 9.30531i −0.218240 0.378002i
\(607\) 10.5884 18.3397i 0.429770 0.744384i −0.567082 0.823661i \(-0.691928\pi\)
0.996853 + 0.0792770i \(0.0252612\pi\)
\(608\) 14.8086 0.600570
\(609\) 3.10075 0.292034i 0.125649 0.0118338i
\(610\) 71.2809 2.88608
\(611\) 2.44983 4.24324i 0.0991096 0.171663i
\(612\) 7.80660 + 13.5214i 0.315563 + 0.546571i
\(613\) −3.38156 5.85704i −0.136580 0.236563i 0.789620 0.613596i \(-0.210278\pi\)
−0.926200 + 0.377033i \(0.876944\pi\)
\(614\) 31.1177 53.8974i 1.25581 2.17512i
\(615\) 17.6953 0.713542
\(616\) 14.4635 1.36219i 0.582749 0.0548843i
\(617\) −41.0728 −1.65353 −0.826763 0.562550i \(-0.809820\pi\)
−0.826763 + 0.562550i \(0.809820\pi\)
\(618\) 0.945349 1.63739i 0.0380275 0.0658656i
\(619\) 15.2134 + 26.3503i 0.611477 + 1.05911i 0.990992 + 0.133924i \(0.0427577\pi\)
−0.379515 + 0.925186i \(0.623909\pi\)
\(620\) 10.8913 + 18.8643i 0.437404 + 0.757607i
\(621\) −12.7154 + 22.0237i −0.510252 + 0.883782i
\(622\) −86.5345 −3.46972
\(623\) −4.90880 6.91238i −0.196667 0.276939i
\(624\) 12.3540 0.494555
\(625\) 12.1386 21.0246i 0.485543 0.840985i
\(626\) 29.5285 + 51.1449i 1.18020 + 2.04416i
\(627\) 2.46811 + 4.27489i 0.0985667 + 0.170722i
\(628\) −13.4342 + 23.2687i −0.536082 + 0.928521i
\(629\) −8.28123 −0.330194
\(630\) −15.0748 + 32.8964i −0.600594 + 1.31062i
\(631\) 12.3670 0.492323 0.246162 0.969229i \(-0.420831\pi\)
0.246162 + 0.969229i \(0.420831\pi\)
\(632\) 12.7154 22.0237i 0.505792 0.876057i
\(633\) −5.79560 10.0383i −0.230354 0.398985i
\(634\) 24.5064 + 42.4462i 0.973272 + 1.68576i
\(635\) 13.6425 23.6295i 0.541385 0.937707i
\(636\) −0.914205 −0.0362506
\(637\) 15.0201 + 17.4252i 0.595120 + 0.690410i
\(638\) −4.10930 −0.162689
\(639\) 14.1067 24.4335i 0.558052 0.966574i
\(640\) −19.0071 32.9213i −0.751322 1.30133i
\(641\) 23.5657 + 40.8169i 0.930787 + 1.61217i 0.781979 + 0.623305i \(0.214211\pi\)
0.148809 + 0.988866i \(0.452456\pi\)
\(642\) 5.62699 9.74624i 0.222080 0.384653i
\(643\) 1.87242 0.0738412 0.0369206 0.999318i \(-0.488245\pi\)
0.0369206 + 0.999318i \(0.488245\pi\)
\(644\) −30.0793 + 65.6393i −1.18529 + 2.58655i
\(645\) −8.28646 −0.326279
\(646\) −12.8450 + 22.2482i −0.505380 + 0.875344i
\(647\) 0.917939 + 1.58992i 0.0360879 + 0.0625061i 0.883505 0.468421i \(-0.155177\pi\)
−0.847417 + 0.530927i \(0.821844\pi\)
\(648\) 12.8404 + 22.2402i 0.504417 + 0.873676i
\(649\) −6.32936 + 10.9628i −0.248449 + 0.430326i
\(650\) −1.15108 −0.0451492
\(651\) −2.56897 3.61753i −0.100686 0.141782i
\(652\) 41.8135 1.63754
\(653\) 9.08858 15.7419i 0.355664 0.616027i −0.631568 0.775321i \(-0.717588\pi\)
0.987231 + 0.159293i \(0.0509216\pi\)
\(654\) 2.50058 + 4.33114i 0.0977805 + 0.169361i
\(655\) −0.836629 1.44908i −0.0326898 0.0566204i
\(656\) 29.6333 51.3265i 1.15699 2.00396i
\(657\) 21.3409 0.832590
\(658\) −9.78181 + 0.921267i −0.381335 + 0.0359147i
\(659\) −16.8997 −0.658318 −0.329159 0.944275i \(-0.606765\pi\)
−0.329159 + 0.944275i \(0.606765\pi\)
\(660\) −3.30660 + 5.72720i −0.128709 + 0.222931i
\(661\) 22.6516 + 39.2338i 0.881046 + 1.52602i 0.850180 + 0.526493i \(0.176493\pi\)
0.0308661 + 0.999524i \(0.490173\pi\)
\(662\) −35.1086 60.8098i −1.36453 2.36344i
\(663\) −1.74805 + 3.02771i −0.0678886 + 0.117587i
\(664\) 10.6315 0.412581
\(665\) −40.1697 + 3.78325i −1.55772 + 0.146708i
\(666\) −34.4633 −1.33543
\(667\) 5.35415 9.27366i 0.207314 0.359078i
\(668\) 4.08131 + 7.06904i 0.157911 + 0.273509i
\(669\) 1.08335 + 1.87641i 0.0418845 + 0.0725462i
\(670\) −12.5547 + 21.7453i −0.485028 + 0.840094i
\(671\) 12.9817 0.501154
\(672\) −2.33983 3.29485i −0.0902609 0.127102i
\(673\) 39.5076 1.52291 0.761454 0.648219i \(-0.224486\pi\)
0.761454 + 0.648219i \(0.224486\pi\)
\(674\) 27.0832 46.9094i 1.04321 1.80688i
\(675\) 0.275458 + 0.477108i 0.0106024 + 0.0183639i
\(676\) 4.62309 + 8.00743i 0.177811 + 0.307978i
\(677\) 17.0669 29.5608i 0.655936 1.13611i −0.325723 0.945465i \(-0.605608\pi\)
0.981658 0.190649i \(-0.0610591\pi\)
\(678\) −22.6677 −0.870547
\(679\) −2.04942 + 4.47226i −0.0786494 + 0.171630i
\(680\) −18.0455 −0.692014
\(681\) 6.58206 11.4005i 0.252225 0.436867i
\(682\) 2.92708 + 5.06984i 0.112084 + 0.194134i
\(683\) −11.8931 20.5995i −0.455079 0.788219i 0.543614 0.839335i \(-0.317056\pi\)
−0.998693 + 0.0511160i \(0.983722\pi\)
\(684\) −36.2244 + 62.7425i −1.38507 + 2.39902i
\(685\) −12.8762 −0.491973
\(686\) 11.0500 44.7885i 0.421891 1.71003i
\(687\) 18.1951 0.694186
\(688\) −13.8769 + 24.0355i −0.529052 + 0.916345i
\(689\) 0.500750 + 0.867324i 0.0190770 + 0.0330424i
\(690\) −12.7154 22.0237i −0.484067 0.838429i
\(691\) 10.2812 17.8076i 0.391116 0.677433i −0.601481 0.798887i \(-0.705422\pi\)
0.992597 + 0.121454i \(0.0387557\pi\)
\(692\) 27.0440 1.02806
\(693\) −2.74543 + 5.99111i −0.104290 + 0.227584i
\(694\) 9.81761 0.372671
\(695\) 6.14248 10.6391i 0.232998 0.403564i
\(696\) 3.23181 + 5.59766i 0.122501 + 0.212179i
\(697\) 8.38605 + 14.5251i 0.317644 + 0.550176i
\(698\) −17.5722 + 30.4359i −0.665117 + 1.15202i
\(699\) −2.72401 −0.103031
\(700\) 0.905651 + 1.27530i 0.0342304 + 0.0482019i
\(701\) −23.9907 −0.906116 −0.453058 0.891481i \(-0.649667\pi\)
−0.453058 + 0.891481i \(0.649667\pi\)
\(702\) −16.0364 + 27.7758i −0.605254 + 1.04833i
\(703\) −19.2134 33.2785i −0.724646 1.25512i
\(704\) −2.60220 4.50714i −0.0980741 0.169869i
\(705\) 1.17251 2.03084i 0.0441592 0.0764860i
\(706\) 12.3763 0.465789
\(707\) 15.9245 1.49979i 0.598901 0.0564055i
\(708\) 37.9762 1.42723
\(709\) 25.8559 44.7836i 0.971037 1.68189i 0.278599 0.960407i \(-0.410130\pi\)
0.692437 0.721478i \(-0.256537\pi\)
\(710\) 31.0968 + 53.8612i 1.16704 + 2.02138i
\(711\) 5.76819 + 9.99080i 0.216324 + 0.374684i
\(712\) 8.79747 15.2377i 0.329699 0.571055i
\(713\) −15.2552 −0.571310
\(714\) 6.97969 0.657359i 0.261208 0.0246010i
\(715\) 7.24468 0.270936
\(716\) 7.53841 13.0569i 0.281724 0.487960i
\(717\) 4.63933 + 8.03555i 0.173259 + 0.300093i
\(718\) −5.07089 8.78304i −0.189244 0.327780i
\(719\) −12.8926 + 22.3306i −0.480812 + 0.832790i −0.999758 0.0220170i \(-0.992991\pi\)
0.518946 + 0.854807i \(0.326325\pi\)
\(720\) −28.9269 −1.07804
\(721\) 1.62961 + 2.29475i 0.0606898 + 0.0854610i
\(722\) −71.8811 −2.67514
\(723\) −0.160754 + 0.278434i −0.00597851 + 0.0103551i
\(724\) −25.6750 44.4703i −0.954202 1.65273i
\(725\) −0.115989 0.200899i −0.00430772 0.00746118i
\(726\) −0.888663 + 1.53921i −0.0329814 + 0.0571254i
\(727\) 32.7330 1.21400 0.606999 0.794702i \(-0.292373\pi\)
0.606999 + 0.794702i \(0.292373\pi\)
\(728\) −19.8898 + 43.4037i −0.737164 + 1.60865i
\(729\) −3.26295 −0.120850
\(730\) −23.5220 + 40.7413i −0.870589 + 1.50790i
\(731\) −3.92708 6.80189i −0.145248 0.251577i
\(732\) −19.4726 33.7275i −0.719728 1.24660i
\(733\) 4.64136 8.03908i 0.171433 0.296930i −0.767488 0.641063i \(-0.778494\pi\)
0.938921 + 0.344133i \(0.111827\pi\)
\(734\) 44.8904 1.65693
\(735\) 7.18875 + 8.33981i 0.265161 + 0.307618i
\(736\) −13.8944 −0.512156
\(737\) −2.28646 + 3.96027i −0.0842229 + 0.145878i
\(738\) 34.8995 + 60.4477i 1.28467 + 2.22511i
\(739\) 25.0466 + 43.3820i 0.921355 + 1.59583i 0.797320 + 0.603556i \(0.206250\pi\)
0.124035 + 0.992278i \(0.460417\pi\)
\(740\) 25.7408 44.5843i 0.946250 1.63895i
\(741\) −16.2227 −0.595955
\(742\) 0.836629 1.82570i 0.0307136 0.0670236i
\(743\) 13.1679 0.483082 0.241541 0.970391i \(-0.422347\pi\)
0.241541 + 0.970391i \(0.422347\pi\)
\(744\) 4.60407 7.97448i 0.168793 0.292359i
\(745\) 1.10220 + 1.90907i 0.0403815 + 0.0699428i
\(746\) 36.0135 + 62.3771i 1.31855 + 2.28379i
\(747\) −2.41142 + 4.17670i −0.0882293 + 0.152818i
\(748\) −6.26819 −0.229188
\(749\) 9.69992 + 13.6590i 0.354427 + 0.499090i
\(750\) −20.1406 −0.735431
\(751\) −20.6569 + 35.7787i −0.753779 + 1.30558i 0.192200 + 0.981356i \(0.438438\pi\)
−0.945979 + 0.324228i \(0.894895\pi\)
\(752\) −3.92708 6.80189i −0.143206 0.248040i
\(753\) 0.399084 + 0.691234i 0.0145434 + 0.0251900i
\(754\) 6.75253 11.6957i 0.245913 0.425933i
\(755\) 32.7158 1.19065
\(756\) 43.3904 4.08658i 1.57809 0.148627i
\(757\) −45.5114 −1.65414 −0.827069 0.562100i \(-0.809994\pi\)
−0.827069 + 0.562100i \(0.809994\pi\)
\(758\) 5.36591 9.29402i 0.194898 0.337574i
\(759\) −2.31574 4.01098i −0.0840560 0.145589i
\(760\) −41.8676 72.5168i −1.51870 2.63046i
\(761\) −15.6360 + 27.0823i −0.566803 + 0.981732i 0.430076 + 0.902793i \(0.358487\pi\)
−0.996879 + 0.0789393i \(0.974847\pi\)
\(762\) −21.9988 −0.796934
\(763\) −7.41200 + 0.698075i −0.268333 + 0.0252720i
\(764\) 50.9124 1.84194
\(765\) 4.09306 7.08940i 0.147985 0.256318i
\(766\) −15.3795 26.6381i −0.555685 0.962474i
\(767\) −20.8012 36.0287i −0.751088 1.30092i
\(768\) −11.6112 + 20.1111i −0.418982 + 0.725698i
\(769\) 42.0467 1.51624 0.758121 0.652114i \(-0.226118\pi\)
0.758121 + 0.652114i \(0.226118\pi\)
\(770\) −8.41142 11.8446i −0.303127 0.426851i
\(771\) 16.2969 0.586920
\(772\) 25.1002 43.4748i 0.903375 1.56469i
\(773\) −3.82226 6.62034i −0.137477 0.238117i 0.789064 0.614311i \(-0.210566\pi\)
−0.926541 + 0.376194i \(0.877233\pi\)
\(774\) −16.3430 28.3069i −0.587436 1.01747i
\(775\) −0.165239 + 0.286202i −0.00593555 + 0.0102807i
\(776\) −10.2096 −0.366505