Properties

Label 48.3.i.b.5.4
Level $48$
Weight $3$
Character 48.5
Analytic conductor $1.308$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 48.i (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.30790526893\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
Defining polynomial: \(x^{20} - 2 x^{18} + 6 x^{16} - 24 x^{14} - 24 x^{12} + 1216 x^{10} - 384 x^{8} - 6144 x^{6} + 24576 x^{4} - 131072 x^{2} + 1048576\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{13} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 5.4
Root \(-1.21144 - 1.59136i\) of defining polynomial
Character \(\chi\) \(=\) 48.5
Dual form 48.3.i.b.29.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.21144 + 1.59136i) q^{2} +(1.14944 - 2.77106i) q^{3} +(-1.06484 - 3.85566i) q^{4} +(4.80434 - 4.80434i) q^{5} +(3.01728 + 5.18614i) q^{6} +7.36187i q^{7} +(7.42573 + 2.97634i) q^{8} +(-6.35757 - 6.37035i) q^{9} +O(q^{10})\) \(q+(-1.21144 + 1.59136i) q^{2} +(1.14944 - 2.77106i) q^{3} +(-1.06484 - 3.85566i) q^{4} +(4.80434 - 4.80434i) q^{5} +(3.01728 + 5.18614i) q^{6} +7.36187i q^{7} +(7.42573 + 2.97634i) q^{8} +(-6.35757 - 6.37035i) q^{9} +(1.82527 + 13.4656i) q^{10} +(-0.514693 + 0.514693i) q^{11} +(-11.9082 - 1.48110i) q^{12} +(7.12969 - 7.12969i) q^{13} +(-11.7154 - 8.91843i) q^{14} +(-7.79081 - 18.8354i) q^{15} +(-13.7322 + 8.21135i) q^{16} +11.1126i q^{17} +(17.8393 - 2.39991i) q^{18} +(-21.1403 + 21.1403i) q^{19} +(-23.6398 - 13.4080i) q^{20} +(20.4002 + 8.46203i) q^{21} +(-0.195543 - 1.44258i) q^{22} -7.80231 q^{23} +(16.7830 - 17.1560i) q^{24} -21.1633i q^{25} +(2.70873 + 19.9831i) q^{26} +(-24.9603 + 10.2949i) q^{27} +(28.3849 - 7.83924i) q^{28} +(34.6058 + 34.6058i) q^{29} +(39.4120 + 10.4199i) q^{30} +24.8644 q^{31} +(3.56850 - 31.8004i) q^{32} +(0.834637 + 2.01786i) q^{33} +(-17.6842 - 13.4623i) q^{34} +(35.3689 + 35.3689i) q^{35} +(-17.7921 + 31.2960i) q^{36} +(-18.2760 - 18.2760i) q^{37} +(-8.03168 - 59.2520i) q^{38} +(-11.5617 - 27.9520i) q^{39} +(49.9750 - 21.3764i) q^{40} -64.2448 q^{41} +(-38.1797 + 22.2128i) q^{42} +(7.24058 + 7.24058i) q^{43} +(2.53255 + 1.43641i) q^{44} +(-61.1492 - 0.0613789i) q^{45} +(9.45200 - 12.4163i) q^{46} -23.0508i q^{47} +(6.96979 + 47.4913i) q^{48} -5.19710 q^{49} +(33.6784 + 25.6380i) q^{50} +(30.7938 + 12.7733i) q^{51} +(-35.0817 - 19.8976i) q^{52} +(31.9199 - 31.9199i) q^{53} +(13.8549 - 52.1923i) q^{54} +4.94552i q^{55} +(-21.9114 + 54.6672i) q^{56} +(34.2816 + 82.8807i) q^{57} +(-96.9929 + 13.1475i) q^{58} +(17.6272 - 17.6272i) q^{59} +(-64.3270 + 50.0955i) q^{60} +(-12.3933 + 12.3933i) q^{61} +(-30.1216 + 39.5682i) q^{62} +(46.8976 - 46.8036i) q^{63} +(46.2828 + 44.2029i) q^{64} -68.5069i q^{65} +(-4.22224 - 1.11630i) q^{66} +(41.1425 - 41.1425i) q^{67} +(42.8465 - 11.8332i) q^{68} +(-8.96830 + 21.6207i) q^{69} +(-99.1318 + 13.4374i) q^{70} -25.6785 q^{71} +(-28.2493 - 66.2267i) q^{72} -56.1845i q^{73} +(51.2239 - 6.94346i) q^{74} +(-58.6449 - 24.3260i) q^{75} +(104.021 + 58.9988i) q^{76} +(-3.78910 - 3.78910i) q^{77} +(58.4878 + 15.4633i) q^{78} -35.7013 q^{79} +(-26.5241 + 105.424i) q^{80} +(-0.162608 + 80.9998i) q^{81} +(77.8285 - 102.236i) q^{82} +(-94.9424 - 94.9424i) q^{83} +(10.9037 - 87.6669i) q^{84} +(53.3889 + 53.3889i) q^{85} +(-20.2939 + 2.75086i) q^{86} +(135.672 - 56.1175i) q^{87} +(-5.35387 + 2.29007i) q^{88} -44.8713 q^{89} +(74.1760 - 97.2360i) q^{90} +(52.4878 + 52.4878i) q^{91} +(8.30824 + 30.0830i) q^{92} +(28.5802 - 68.9008i) q^{93} +(36.6821 + 27.9246i) q^{94} +203.131i q^{95} +(-84.0191 - 46.4412i) q^{96} -82.3636 q^{97} +(6.29596 - 8.27045i) q^{98} +(6.55097 + 0.00657558i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 6q^{3} + 4q^{4} - 12q^{6} + O(q^{10}) \) \( 20q - 6q^{3} + 4q^{4} - 12q^{6} + 32q^{10} - 88q^{12} + 92q^{13} - 116q^{15} - 16q^{16} + 4q^{18} - 52q^{19} + 48q^{21} + 24q^{22} - 8q^{24} + 18q^{27} + 56q^{28} + 28q^{30} - 80q^{31} + 60q^{33} + 104q^{34} + 92q^{36} - 116q^{37} + 88q^{40} + 304q^{42} + 172q^{43} + 60q^{45} - 424q^{46} + 176q^{48} - 364q^{49} + 128q^{51} - 208q^{52} + 40q^{54} - 512q^{58} - 240q^{60} - 244q^{61} + 296q^{63} + 88q^{64} - 492q^{66} + 356q^{67} - 20q^{69} + 200q^{70} - 472q^{72} - 146q^{75} + 328q^{76} + 84q^{78} + 384q^{79} - 188q^{81} + 560q^{82} + 816q^{84} + 48q^{85} + 416q^{88} + 616q^{90} + 136q^{91} - 132q^{93} + 32q^{94} - 24q^{96} + 472q^{97} - 452q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/48\mathbb{Z}\right)^\times\).

\(n\) \(17\) \(31\) \(37\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.21144 + 1.59136i −0.605718 + 0.795679i
\(3\) 1.14944 2.77106i 0.383147 0.923687i
\(4\) −1.06484 3.85566i −0.266211 0.963915i
\(5\) 4.80434 4.80434i 0.960868 0.960868i −0.0383950 0.999263i \(-0.512225\pi\)
0.999263 + 0.0383950i \(0.0122245\pi\)
\(6\) 3.01728 + 5.18614i 0.502880 + 0.864356i
\(7\) 7.36187i 1.05170i 0.850579 + 0.525848i \(0.176252\pi\)
−0.850579 + 0.525848i \(0.823748\pi\)
\(8\) 7.42573 + 2.97634i 0.928216 + 0.372042i
\(9\) −6.35757 6.37035i −0.706397 0.707816i
\(10\) 1.82527 + 13.4656i 0.182527 + 1.34656i
\(11\) −0.514693 + 0.514693i −0.0467903 + 0.0467903i −0.730115 0.683325i \(-0.760533\pi\)
0.683325 + 0.730115i \(0.260533\pi\)
\(12\) −11.9082 1.48110i −0.992354 0.123425i
\(13\) 7.12969 7.12969i 0.548438 0.548438i −0.377551 0.925989i \(-0.623234\pi\)
0.925989 + 0.377551i \(0.123234\pi\)
\(14\) −11.7154 8.91843i −0.836812 0.637031i
\(15\) −7.79081 18.8354i −0.519388 1.25569i
\(16\) −13.7322 + 8.21135i −0.858263 + 0.513210i
\(17\) 11.1126i 0.653684i 0.945079 + 0.326842i \(0.105985\pi\)
−0.945079 + 0.326842i \(0.894015\pi\)
\(18\) 17.8393 2.39991i 0.991072 0.133328i
\(19\) −21.1403 + 21.1403i −1.11265 + 1.11265i −0.119858 + 0.992791i \(0.538244\pi\)
−0.992791 + 0.119858i \(0.961756\pi\)
\(20\) −23.6398 13.4080i −1.18199 0.670401i
\(21\) 20.4002 + 8.46203i 0.971438 + 0.402954i
\(22\) −0.195543 1.44258i −0.00888834 0.0655718i
\(23\) −7.80231 −0.339231 −0.169615 0.985510i \(-0.554253\pi\)
−0.169615 + 0.985510i \(0.554253\pi\)
\(24\) 16.7830 17.1560i 0.699294 0.714834i
\(25\) 21.1633i 0.846533i
\(26\) 2.70873 + 19.9831i 0.104182 + 0.768579i
\(27\) −24.9603 + 10.2949i −0.924455 + 0.381292i
\(28\) 28.3849 7.83924i 1.01374 0.279973i
\(29\) 34.6058 + 34.6058i 1.19330 + 1.19330i 0.976134 + 0.217169i \(0.0696823\pi\)
0.217169 + 0.976134i \(0.430318\pi\)
\(30\) 39.4120 + 10.4199i 1.31373 + 0.347331i
\(31\) 24.8644 0.802078 0.401039 0.916061i \(-0.368649\pi\)
0.401039 + 0.916061i \(0.368649\pi\)
\(32\) 3.56850 31.8004i 0.111516 0.993763i
\(33\) 0.834637 + 2.01786i 0.0252920 + 0.0611472i
\(34\) −17.6842 13.4623i −0.520123 0.395949i
\(35\) 35.3689 + 35.3689i 1.01054 + 1.01054i
\(36\) −17.7921 + 31.2960i −0.494224 + 0.869335i
\(37\) −18.2760 18.2760i −0.493946 0.493946i 0.415601 0.909547i \(-0.363571\pi\)
−0.909547 + 0.415601i \(0.863571\pi\)
\(38\) −8.03168 59.2520i −0.211360 1.55926i
\(39\) −11.5617 27.9520i −0.296453 0.716717i
\(40\) 49.9750 21.3764i 1.24938 0.534409i
\(41\) −64.2448 −1.56695 −0.783473 0.621426i \(-0.786554\pi\)
−0.783473 + 0.621426i \(0.786554\pi\)
\(42\) −38.1797 + 22.2128i −0.909040 + 0.528876i
\(43\) 7.24058 + 7.24058i 0.168386 + 0.168386i 0.786269 0.617884i \(-0.212010\pi\)
−0.617884 + 0.786269i \(0.712010\pi\)
\(44\) 2.53255 + 1.43641i 0.0575579 + 0.0326458i
\(45\) −61.1492 0.0613789i −1.35887 0.00136398i
\(46\) 9.45200 12.4163i 0.205478 0.269919i
\(47\) 23.0508i 0.490442i −0.969467 0.245221i \(-0.921139\pi\)
0.969467 0.245221i \(-0.0788606\pi\)
\(48\) 6.96979 + 47.4913i 0.145204 + 0.989402i
\(49\) −5.19710 −0.106063
\(50\) 33.6784 + 25.6380i 0.673569 + 0.512760i
\(51\) 30.7938 + 12.7733i 0.603800 + 0.250457i
\(52\) −35.0817 19.8976i −0.674647 0.382647i
\(53\) 31.9199 31.9199i 0.602263 0.602263i −0.338650 0.940913i \(-0.609970\pi\)
0.940913 + 0.338650i \(0.109970\pi\)
\(54\) 13.8549 52.1923i 0.256573 0.966525i
\(55\) 4.94552i 0.0899185i
\(56\) −21.9114 + 54.6672i −0.391275 + 0.976200i
\(57\) 34.2816 + 82.8807i 0.601432 + 1.45405i
\(58\) −96.9929 + 13.1475i −1.67229 + 0.226681i
\(59\) 17.6272 17.6272i 0.298766 0.298766i −0.541764 0.840530i \(-0.682244\pi\)
0.840530 + 0.541764i \(0.182244\pi\)
\(60\) −64.3270 + 50.0955i −1.07212 + 0.834925i
\(61\) −12.3933 + 12.3933i −0.203170 + 0.203170i −0.801357 0.598187i \(-0.795888\pi\)
0.598187 + 0.801357i \(0.295888\pi\)
\(62\) −30.1216 + 39.5682i −0.485833 + 0.638196i
\(63\) 46.8976 46.8036i 0.744407 0.742914i
\(64\) 46.2828 + 44.2029i 0.723169 + 0.690671i
\(65\) 68.5069i 1.05395i
\(66\) −4.22224 1.11630i −0.0639734 0.0169136i
\(67\) 41.1425 41.1425i 0.614067 0.614067i −0.329936 0.944003i \(-0.607027\pi\)
0.944003 + 0.329936i \(0.107027\pi\)
\(68\) 42.8465 11.8332i 0.630096 0.174018i
\(69\) −8.96830 + 21.6207i −0.129975 + 0.313343i
\(70\) −99.1318 + 13.4374i −1.41617 + 0.191963i
\(71\) −25.6785 −0.361669 −0.180834 0.983514i \(-0.557880\pi\)
−0.180834 + 0.983514i \(0.557880\pi\)
\(72\) −28.2493 66.2267i −0.392351 0.919815i
\(73\) 56.1845i 0.769650i −0.922990 0.384825i \(-0.874262\pi\)
0.922990 0.384825i \(-0.125738\pi\)
\(74\) 51.2239 6.94346i 0.692214 0.0938305i
\(75\) −58.6449 24.3260i −0.781932 0.324347i
\(76\) 104.021 + 58.9988i 1.36870 + 0.776299i
\(77\) −3.78910 3.78910i −0.0492091 0.0492091i
\(78\) 58.4878 + 15.4633i 0.749844 + 0.198247i
\(79\) −35.7013 −0.451915 −0.225957 0.974137i \(-0.572551\pi\)
−0.225957 + 0.974137i \(0.572551\pi\)
\(80\) −26.5241 + 105.424i −0.331551 + 1.31780i
\(81\) −0.162608 + 80.9998i −0.00200751 + 0.999998i
\(82\) 77.8285 102.236i 0.949128 1.24679i
\(83\) −94.9424 94.9424i −1.14388 1.14388i −0.987733 0.156151i \(-0.950091\pi\)
−0.156151 0.987733i \(-0.549909\pi\)
\(84\) 10.9037 87.6669i 0.129806 1.04365i
\(85\) 53.3889 + 53.3889i 0.628104 + 0.628104i
\(86\) −20.2939 + 2.75086i −0.235975 + 0.0319867i
\(87\) 135.672 56.1175i 1.55945 0.645028i
\(88\) −5.35387 + 2.29007i −0.0608394 + 0.0260235i
\(89\) −44.8713 −0.504172 −0.252086 0.967705i \(-0.581117\pi\)
−0.252086 + 0.967705i \(0.581117\pi\)
\(90\) 74.1760 97.2360i 0.824178 1.08040i
\(91\) 52.4878 + 52.4878i 0.576789 + 0.576789i
\(92\) 8.30824 + 30.0830i 0.0903070 + 0.326990i
\(93\) 28.5802 68.9008i 0.307314 0.740869i
\(94\) 36.6821 + 27.9246i 0.390235 + 0.297070i
\(95\) 203.131i 2.13822i
\(96\) −84.0191 46.4412i −0.875199 0.483763i
\(97\) −82.3636 −0.849109 −0.424554 0.905402i \(-0.639569\pi\)
−0.424554 + 0.905402i \(0.639569\pi\)
\(98\) 6.29596 8.27045i 0.0642445 0.0843924i
\(99\) 6.55097 + 0.00657558i 0.0661714 + 6.64200e-5i
\(100\) −81.5986 + 22.5356i −0.815986 + 0.225356i
\(101\) −36.3420 + 36.3420i −0.359822 + 0.359822i −0.863747 0.503925i \(-0.831889\pi\)
0.503925 + 0.863747i \(0.331889\pi\)
\(102\) −57.6317 + 33.5299i −0.565016 + 0.328725i
\(103\) 87.5176i 0.849685i 0.905267 + 0.424843i \(0.139671\pi\)
−0.905267 + 0.424843i \(0.860329\pi\)
\(104\) 74.1635 31.7228i 0.713110 0.305027i
\(105\) 138.664 57.3550i 1.32061 0.546238i
\(106\) 12.1271 + 89.4650i 0.114407 + 0.844010i
\(107\) 104.866 104.866i 0.980058 0.980058i −0.0197471 0.999805i \(-0.506286\pi\)
0.999805 + 0.0197471i \(0.00628610\pi\)
\(108\) 66.2724 + 85.2759i 0.613633 + 0.789591i
\(109\) 7.64006 7.64006i 0.0700923 0.0700923i −0.671192 0.741284i \(-0.734217\pi\)
0.741284 + 0.671192i \(0.234217\pi\)
\(110\) −7.87010 5.99118i −0.0715463 0.0544653i
\(111\) −71.6511 + 29.6367i −0.645505 + 0.266998i
\(112\) −60.4509 101.095i −0.539740 0.902632i
\(113\) 13.1273i 0.116171i −0.998312 0.0580853i \(-0.981500\pi\)
0.998312 0.0580853i \(-0.0184995\pi\)
\(114\) −173.423 45.8504i −1.52125 0.402197i
\(115\) −37.4849 + 37.4849i −0.325956 + 0.325956i
\(116\) 96.5784 170.278i 0.832572 1.46791i
\(117\) −90.7461 0.0910869i −0.775607 0.000778521i
\(118\) 6.69696 + 49.4054i 0.0567539 + 0.418690i
\(119\) −81.8098 −0.687477
\(120\) −1.79191 163.055i −0.0149326 1.35879i
\(121\) 120.470i 0.995621i
\(122\) −4.70851 34.7360i −0.0385943 0.284721i
\(123\) −73.8456 + 178.026i −0.600371 + 1.44737i
\(124\) −26.4767 95.8687i −0.213522 0.773134i
\(125\) 18.4327 + 18.4327i 0.147461 + 0.147461i
\(126\) 17.6678 + 131.331i 0.140221 + 1.04231i
\(127\) −88.2707 −0.695045 −0.347523 0.937672i \(-0.612977\pi\)
−0.347523 + 0.937672i \(0.612977\pi\)
\(128\) −126.411 + 20.1036i −0.987589 + 0.157059i
\(129\) 28.3867 11.7415i 0.220052 0.0910192i
\(130\) 109.019 + 82.9917i 0.838608 + 0.638398i
\(131\) −57.0518 57.0518i −0.435510 0.435510i 0.454988 0.890498i \(-0.349644\pi\)
−0.890498 + 0.454988i \(0.849644\pi\)
\(132\) 6.89141 5.36678i 0.0522076 0.0406574i
\(133\) −155.632 155.632i −1.17017 1.17017i
\(134\) 15.6310 + 115.314i 0.116649 + 0.860552i
\(135\) −70.4575 + 169.378i −0.521907 + 1.25465i
\(136\) −33.0749 + 82.5194i −0.243198 + 0.606760i
\(137\) 165.112 1.20520 0.602599 0.798045i \(-0.294132\pi\)
0.602599 + 0.798045i \(0.294132\pi\)
\(138\) −23.5417 40.4639i −0.170592 0.293216i
\(139\) −95.0802 95.0802i −0.684030 0.684030i 0.276875 0.960906i \(-0.410701\pi\)
−0.960906 + 0.276875i \(0.910701\pi\)
\(140\) 98.7081 174.033i 0.705058 1.24309i
\(141\) −63.8752 26.4955i −0.453015 0.187912i
\(142\) 31.1078 40.8637i 0.219069 0.287772i
\(143\) 7.33920i 0.0513231i
\(144\) 139.613 + 35.2747i 0.969532 + 0.244963i
\(145\) 332.516 2.29321
\(146\) 89.4096 + 68.0639i 0.612395 + 0.466191i
\(147\) −5.97376 + 14.4015i −0.0406378 + 0.0979693i
\(148\) −51.0049 + 89.9271i −0.344628 + 0.607615i
\(149\) −131.077 + 131.077i −0.879709 + 0.879709i −0.993504 0.113795i \(-0.963699\pi\)
0.113795 + 0.993504i \(0.463699\pi\)
\(150\) 109.756 63.8557i 0.731706 0.425704i
\(151\) 123.070i 0.815031i −0.913198 0.407515i \(-0.866395\pi\)
0.913198 0.407515i \(-0.133605\pi\)
\(152\) −219.903 + 94.0616i −1.44673 + 0.618826i
\(153\) 70.7913 70.6494i 0.462688 0.461761i
\(154\) 10.6201 1.43956i 0.0689615 0.00934782i
\(155\) 119.457 119.457i 0.770690 0.770690i
\(156\) −95.4619 + 74.3423i −0.611935 + 0.476553i
\(157\) 139.181 139.181i 0.886503 0.886503i −0.107683 0.994185i \(-0.534343\pi\)
0.994185 + 0.107683i \(0.0343430\pi\)
\(158\) 43.2498 56.8135i 0.273733 0.359579i
\(159\) −51.7620 125.142i −0.325547 0.787058i
\(160\) −135.636 169.924i −0.847723 1.06203i
\(161\) 57.4396i 0.356768i
\(162\) −128.703 98.3849i −0.794462 0.607314i
\(163\) −19.9311 + 19.9311i −0.122277 + 0.122277i −0.765597 0.643320i \(-0.777556\pi\)
0.643320 + 0.765597i \(0.277556\pi\)
\(164\) 68.4107 + 247.706i 0.417138 + 1.51040i
\(165\) 13.7043 + 5.68458i 0.0830566 + 0.0344520i
\(166\) 266.104 36.0707i 1.60304 0.217294i
\(167\) 60.3220 0.361210 0.180605 0.983556i \(-0.442194\pi\)
0.180605 + 0.983556i \(0.442194\pi\)
\(168\) 126.300 + 123.555i 0.751788 + 0.735444i
\(169\) 67.3351i 0.398432i
\(170\) −149.638 + 20.2836i −0.880224 + 0.119315i
\(171\) 269.072 + 0.270083i 1.57352 + 0.00157943i
\(172\) 20.2071 35.6273i 0.117483 0.207135i
\(173\) 74.8292 + 74.8292i 0.432539 + 0.432539i 0.889491 0.456952i \(-0.151059\pi\)
−0.456952 + 0.889491i \(0.651059\pi\)
\(174\) −75.0551 + 283.886i −0.431351 + 1.63153i
\(175\) 155.802 0.890295
\(176\) 2.84155 11.2942i 0.0161452 0.0641716i
\(177\) −28.5846 69.1074i −0.161495 0.390438i
\(178\) 54.3587 71.4063i 0.305386 0.401159i
\(179\) 3.96558 + 3.96558i 0.0221541 + 0.0221541i 0.718097 0.695943i \(-0.245013\pi\)
−0.695943 + 0.718097i \(0.745013\pi\)
\(180\) 64.8777 + 235.836i 0.360432 + 1.31020i
\(181\) 158.820 + 158.820i 0.877457 + 0.877457i 0.993271 0.115814i \(-0.0369475\pi\)
−0.115814 + 0.993271i \(0.536948\pi\)
\(182\) −147.113 + 19.9413i −0.808311 + 0.109568i
\(183\) 20.0973 + 48.5882i 0.109821 + 0.265509i
\(184\) −57.9378 23.2223i −0.314879 0.126208i
\(185\) −175.608 −0.949233
\(186\) 75.0228 + 128.950i 0.403349 + 0.693281i
\(187\) −5.71960 5.71960i −0.0305861 0.0305861i
\(188\) −88.8760 + 24.5455i −0.472745 + 0.130561i
\(189\) −75.7896 183.754i −0.401003 0.972245i
\(190\) −323.254 246.080i −1.70133 1.29516i
\(191\) 68.8639i 0.360544i 0.983617 + 0.180272i \(0.0576978\pi\)
−0.983617 + 0.180272i \(0.942302\pi\)
\(192\) 175.688 77.4440i 0.915044 0.403354i
\(193\) −366.645 −1.89971 −0.949856 0.312686i \(-0.898771\pi\)
−0.949856 + 0.312686i \(0.898771\pi\)
\(194\) 99.7782 131.070i 0.514321 0.675618i
\(195\) −189.837 78.7446i −0.973522 0.403819i
\(196\) 5.53410 + 20.0383i 0.0282352 + 0.102236i
\(197\) 246.744 246.744i 1.25251 1.25251i 0.297912 0.954593i \(-0.403710\pi\)
0.954593 0.297912i \(-0.0962901\pi\)
\(198\) −7.94655 + 10.4170i −0.0401341 + 0.0526110i
\(199\) 287.802i 1.44624i −0.690722 0.723120i \(-0.742707\pi\)
0.690722 0.723120i \(-0.257293\pi\)
\(200\) 62.9892 157.153i 0.314946 0.785765i
\(201\) −66.7176 161.299i −0.331928 0.802484i
\(202\) −13.8071 101.859i −0.0683521 0.504253i
\(203\) −254.763 + 254.763i −1.25499 + 1.25499i
\(204\) 16.4590 132.332i 0.0806812 0.648686i
\(205\) −308.654 + 308.654i −1.50563 + 1.50563i
\(206\) −139.272 106.022i −0.676077 0.514670i
\(207\) 49.6037 + 49.7034i 0.239632 + 0.240113i
\(208\) −39.3620 + 156.451i −0.189240 + 0.752167i
\(209\) 21.7616i 0.104122i
\(210\) −76.7102 + 290.146i −0.365287 + 1.38165i
\(211\) 156.146 156.146i 0.740027 0.740027i −0.232556 0.972583i \(-0.574709\pi\)
0.972583 + 0.232556i \(0.0747089\pi\)
\(212\) −157.062 89.0826i −0.740859 0.420201i
\(213\) −29.5159 + 71.1567i −0.138572 + 0.334069i
\(214\) 39.8410 + 293.918i 0.186173 + 1.37345i
\(215\) 69.5724 0.323593
\(216\) −215.989 + 2.15681i −0.999950 + 0.00998524i
\(217\) 183.048i 0.843541i
\(218\) 2.90263 + 21.4135i 0.0133148 + 0.0982271i
\(219\) −155.691 64.5807i −0.710916 0.294889i
\(220\) 19.0682 5.26621i 0.0866738 0.0239373i
\(221\) 79.2296 + 79.2296i 0.358505 + 0.358505i
\(222\) 39.6381 149.926i 0.178550 0.675340i
\(223\) 45.2998 0.203138 0.101569 0.994828i \(-0.467614\pi\)
0.101569 + 0.994828i \(0.467614\pi\)
\(224\) 234.110 + 26.2708i 1.04514 + 0.117280i
\(225\) −134.818 + 134.547i −0.599190 + 0.597988i
\(226\) 20.8902 + 15.9029i 0.0924345 + 0.0703666i
\(227\) 300.757 + 300.757i 1.32492 + 1.32492i 0.909737 + 0.415186i \(0.136283\pi\)
0.415186 + 0.909737i \(0.363717\pi\)
\(228\) 283.055 220.433i 1.24147 0.966813i
\(229\) 65.7088 + 65.7088i 0.286938 + 0.286938i 0.835868 0.548930i \(-0.184965\pi\)
−0.548930 + 0.835868i \(0.684965\pi\)
\(230\) −14.2414 105.063i −0.0619190 0.456794i
\(231\) −14.8552 + 6.14449i −0.0643082 + 0.0265995i
\(232\) 153.975 + 359.972i 0.663684 + 1.55160i
\(233\) −42.8218 −0.183785 −0.0918923 0.995769i \(-0.529292\pi\)
−0.0918923 + 0.995769i \(0.529292\pi\)
\(234\) 110.078 144.299i 0.470419 0.616663i
\(235\) −110.744 110.744i −0.471250 0.471250i
\(236\) −86.7346 49.1942i −0.367520 0.208450i
\(237\) −41.0365 + 98.9305i −0.173150 + 0.417428i
\(238\) 99.1073 130.189i 0.416417 0.547011i
\(239\) 100.598i 0.420913i −0.977603 0.210456i \(-0.932505\pi\)
0.977603 0.210456i \(-0.0674950\pi\)
\(240\) 261.649 + 194.679i 1.09021 + 0.811162i
\(241\) −5.23162 −0.0217080 −0.0108540 0.999941i \(-0.503455\pi\)
−0.0108540 + 0.999941i \(0.503455\pi\)
\(242\) −191.711 145.942i −0.792195 0.603066i
\(243\) 224.269 + 93.5551i 0.922916 + 0.385001i
\(244\) 60.9815 + 34.5875i 0.249924 + 0.141752i
\(245\) −24.9686 + 24.9686i −0.101913 + 0.101913i
\(246\) −193.844 333.182i −0.787985 1.35440i
\(247\) 301.448i 1.22044i
\(248\) 184.636 + 74.0048i 0.744501 + 0.298407i
\(249\) −372.222 + 153.961i −1.49487 + 0.618315i
\(250\) −51.6630 + 7.00298i −0.206652 + 0.0280119i
\(251\) 17.4381 17.4381i 0.0694747 0.0694747i −0.671516 0.740990i \(-0.734356\pi\)
0.740990 + 0.671516i \(0.234356\pi\)
\(252\) −230.397 130.983i −0.914275 0.519773i
\(253\) 4.01579 4.01579i 0.0158727 0.0158727i
\(254\) 106.934 140.470i 0.421001 0.553033i
\(255\) 209.311 86.5765i 0.820828 0.339516i
\(256\) 121.147 225.520i 0.473232 0.880938i
\(257\) 343.676i 1.33726i 0.743595 + 0.668630i \(0.233119\pi\)
−0.743595 + 0.668630i \(0.766881\pi\)
\(258\) −15.7038 + 59.3975i −0.0608674 + 0.230223i
\(259\) 134.545 134.545i 0.519480 0.519480i
\(260\) −264.139 + 72.9491i −1.01592 + 0.280574i
\(261\) 0.442114 440.460i 0.00169392 1.68758i
\(262\) 159.904 21.6752i 0.610322 0.0827299i
\(263\) 98.0863 0.372952 0.186476 0.982460i \(-0.440293\pi\)
0.186476 + 0.982460i \(0.440293\pi\)
\(264\) 0.191969 + 17.4682i 0.000727155 + 0.0661675i
\(265\) 306.708i 1.15739i
\(266\) 436.206 59.1282i 1.63987 0.222286i
\(267\) −51.5769 + 124.341i −0.193172 + 0.465697i
\(268\) −202.442 114.821i −0.755380 0.428437i
\(269\) −126.560 126.560i −0.470482 0.470482i 0.431589 0.902070i \(-0.357953\pi\)
−0.902070 + 0.431589i \(0.857953\pi\)
\(270\) −184.186 317.313i −0.682170 1.17523i
\(271\) −206.487 −0.761945 −0.380972 0.924586i \(-0.624411\pi\)
−0.380972 + 0.924586i \(0.624411\pi\)
\(272\) −91.2498 152.601i −0.335477 0.561033i
\(273\) 205.779 85.1154i 0.753768 0.311778i
\(274\) −200.023 + 262.752i −0.730010 + 0.958950i
\(275\) 10.8926 + 10.8926i 0.0396095 + 0.0396095i
\(276\) 92.9118 + 11.5560i 0.336637 + 0.0418697i
\(277\) 183.416 + 183.416i 0.662153 + 0.662153i 0.955887 0.293734i \(-0.0948980\pi\)
−0.293734 + 0.955887i \(0.594898\pi\)
\(278\) 266.490 36.1231i 0.958598 0.129939i
\(279\) −158.077 158.395i −0.566585 0.567723i
\(280\) 157.370 + 367.910i 0.562036 + 1.31396i
\(281\) −109.143 −0.388409 −0.194204 0.980961i \(-0.562213\pi\)
−0.194204 + 0.980961i \(0.562213\pi\)
\(282\) 119.545 69.5507i 0.423917 0.246634i
\(283\) 60.4623 + 60.4623i 0.213648 + 0.213648i 0.805815 0.592167i \(-0.201728\pi\)
−0.592167 + 0.805815i \(0.701728\pi\)
\(284\) 27.3436 + 99.0075i 0.0962802 + 0.348618i
\(285\) 562.888 + 233.487i 1.97504 + 0.819252i
\(286\) −11.6793 8.89098i −0.0408367 0.0310873i
\(287\) 472.962i 1.64795i
\(288\) −225.267 + 179.441i −0.782176 + 0.623058i
\(289\) 165.509 0.572697
\(290\) −402.822 + 529.152i −1.38904 + 1.82466i
\(291\) −94.6721 + 228.235i −0.325334 + 0.784311i
\(292\) −216.628 + 59.8277i −0.741877 + 0.204889i
\(293\) 19.4639 19.4639i 0.0664296 0.0664296i −0.673111 0.739541i \(-0.735043\pi\)
0.739541 + 0.673111i \(0.235043\pi\)
\(294\) −15.6811 26.9529i −0.0533371 0.0916765i
\(295\) 169.374i 0.574149i
\(296\) −81.3170 190.108i −0.274720 0.642257i
\(297\) 7.54818 18.1456i 0.0254147 0.0610963i
\(298\) −49.7990 367.381i −0.167111 1.23282i
\(299\) −55.6280 + 55.6280i −0.186047 + 0.186047i
\(300\) −31.3451 + 252.018i −0.104484 + 0.840060i
\(301\) −53.3042 + 53.3042i −0.177090 + 0.177090i
\(302\) 195.848 + 149.091i 0.648503 + 0.493679i
\(303\) 58.9329 + 142.479i 0.194498 + 0.470227i
\(304\) 116.713 463.894i 0.383924 1.52597i
\(305\) 119.084i 0.390438i
\(306\) 26.6693 + 198.242i 0.0871545 + 0.647848i
\(307\) −408.201 + 408.201i −1.32964 + 1.32964i −0.423967 + 0.905677i \(0.639363\pi\)
−0.905677 + 0.423967i \(0.860637\pi\)
\(308\) −10.5747 + 18.6443i −0.0343334 + 0.0605334i
\(309\) 242.517 + 100.596i 0.784844 + 0.325554i
\(310\) 45.3844 + 334.813i 0.146401 + 1.08004i
\(311\) −360.965 −1.16066 −0.580330 0.814381i \(-0.697076\pi\)
−0.580330 + 0.814381i \(0.697076\pi\)
\(312\) −2.65921 241.975i −0.00852311 0.775561i
\(313\) 73.9217i 0.236172i −0.993003 0.118086i \(-0.962324\pi\)
0.993003 0.118086i \(-0.0376758\pi\)
\(314\) 52.8779 + 390.096i 0.168401 + 1.24234i
\(315\) 0.451863 450.172i 0.00143449 1.42912i
\(316\) 38.0163 + 137.652i 0.120305 + 0.435607i
\(317\) −172.709 172.709i −0.544825 0.544825i 0.380115 0.924939i \(-0.375884\pi\)
−0.924939 + 0.380115i \(0.875884\pi\)
\(318\) 261.853 + 69.2299i 0.823436 + 0.217704i
\(319\) −35.6227 −0.111670
\(320\) 434.724 9.99263i 1.35851 0.0312270i
\(321\) −170.053 411.128i −0.529761 1.28077i
\(322\) 91.4070 + 69.5844i 0.283873 + 0.216101i
\(323\) −234.925 234.925i −0.727321 0.727321i
\(324\) 312.481 85.6252i 0.964447 0.264275i
\(325\) −150.888 150.888i −0.464271 0.464271i
\(326\) −7.57226 55.8627i −0.0232278 0.171358i
\(327\) −12.3893 29.9529i −0.0378877 0.0915990i
\(328\) −477.064 191.214i −1.45446 0.582970i
\(329\) 169.697 0.515796
\(330\) −25.6481 + 14.9220i −0.0777217 + 0.0452182i
\(331\) 261.507 + 261.507i 0.790051 + 0.790051i 0.981502 0.191451i \(-0.0613194\pi\)
−0.191451 + 0.981502i \(0.561319\pi\)
\(332\) −264.967 + 467.164i −0.798092 + 1.40712i
\(333\) −0.233489 + 232.615i −0.000701168 + 0.698544i
\(334\) −73.0763 + 95.9940i −0.218791 + 0.287407i
\(335\) 395.325i 1.18007i
\(336\) −349.625 + 51.3107i −1.04055 + 0.152710i
\(337\) 18.2211 0.0540684 0.0270342 0.999635i \(-0.491394\pi\)
0.0270342 + 0.999635i \(0.491394\pi\)
\(338\) −107.154 81.5722i −0.317024 0.241338i
\(339\) −36.3765 15.0890i −0.107305 0.0445104i
\(340\) 148.998 262.700i 0.438231 0.772647i
\(341\) −12.7975 + 12.7975i −0.0375294 + 0.0375294i
\(342\) −326.394 + 427.863i −0.954368 + 1.25106i
\(343\) 322.471i 0.940149i
\(344\) 32.2162 + 75.3170i 0.0936517 + 0.218945i
\(345\) 60.7863 + 146.960i 0.176192 + 0.425970i
\(346\) −209.731 + 28.4293i −0.606159 + 0.0821656i
\(347\) −173.710 + 173.710i −0.500605 + 0.500605i −0.911626 0.411021i \(-0.865172\pi\)
0.411021 + 0.911626i \(0.365172\pi\)
\(348\) −360.839 463.349i −1.03690 1.33146i
\(349\) 387.899 387.899i 1.11146 1.11146i 0.118506 0.992953i \(-0.462189\pi\)
0.992953 0.118506i \(-0.0378106\pi\)
\(350\) −188.744 + 247.936i −0.539268 + 0.708389i
\(351\) −104.560 + 251.358i −0.297891 + 0.716121i
\(352\) 14.5308 + 18.2041i 0.0412806 + 0.0517163i
\(353\) 676.812i 1.91732i −0.284561 0.958658i \(-0.591848\pi\)
0.284561 0.958658i \(-0.408152\pi\)
\(354\) 144.603 + 38.2309i 0.408484 + 0.107997i
\(355\) −123.368 + 123.368i −0.347516 + 0.347516i
\(356\) 47.7809 + 173.008i 0.134216 + 0.485979i
\(357\) −94.0355 + 226.700i −0.263405 + 0.635014i
\(358\) −11.1147 + 1.50661i −0.0310467 + 0.00420842i
\(359\) 240.896 0.671020 0.335510 0.942037i \(-0.391091\pi\)
0.335510 + 0.942037i \(0.391091\pi\)
\(360\) −453.895 182.456i −1.26082 0.506823i
\(361\) 532.827i 1.47598i
\(362\) −445.139 + 60.3392i −1.22967 + 0.166683i
\(363\) 333.830 + 138.473i 0.919643 + 0.381469i
\(364\) 146.484 258.267i 0.402428 0.709523i
\(365\) −269.929 269.929i −0.739532 0.739532i
\(366\) −101.668 26.8794i −0.277781 0.0734411i
\(367\) 666.702 1.81663 0.908313 0.418291i \(-0.137371\pi\)
0.908313 + 0.418291i \(0.137371\pi\)
\(368\) 107.143 64.0675i 0.291149 0.174096i
\(369\) 408.441 + 409.261i 1.10689 + 1.10911i
\(370\) 212.738 279.455i 0.574968 0.755285i
\(371\) 234.990 + 234.990i 0.633397 + 0.633397i
\(372\) −296.091 36.8268i −0.795945 0.0989967i
\(373\) −358.513 358.513i −0.961160 0.961160i 0.0381137 0.999273i \(-0.487865\pi\)
−0.999273 + 0.0381137i \(0.987865\pi\)
\(374\) 16.0309 2.17300i 0.0428633 0.00581017i
\(375\) 72.2653 29.8908i 0.192708 0.0797088i
\(376\) 68.6069 171.169i 0.182465 0.455236i
\(377\) 493.457 1.30890
\(378\) 384.233 + 101.998i 1.01649 + 0.269836i
\(379\) −140.959 140.959i −0.371925 0.371925i 0.496253 0.868178i \(-0.334709\pi\)
−0.868178 + 0.496253i \(0.834709\pi\)
\(380\) 783.202 216.302i 2.06106 0.569217i
\(381\) −101.462 + 244.604i −0.266305 + 0.642004i
\(382\) −109.587 83.4242i −0.286877 0.218388i
\(383\) 69.4683i 0.181379i 0.995879 + 0.0906897i \(0.0289071\pi\)
−0.995879 + 0.0906897i \(0.971093\pi\)
\(384\) −89.5942 + 373.402i −0.233318 + 0.972400i
\(385\) −36.4083 −0.0945669
\(386\) 444.167 583.463i 1.15069 1.51156i
\(387\) 0.0925037 92.1575i 0.000239028 0.238133i
\(388\) 87.7043 + 317.566i 0.226042 + 0.818468i
\(389\) −265.362 + 265.362i −0.682165 + 0.682165i −0.960488 0.278322i \(-0.910222\pi\)
0.278322 + 0.960488i \(0.410222\pi\)
\(390\) 355.286 206.704i 0.910990 0.530011i
\(391\) 86.7042i 0.221750i
\(392\) −38.5923 15.4683i −0.0984496 0.0394600i
\(393\) −223.672 + 92.5164i −0.569139 + 0.235411i
\(394\) 93.7434 + 691.571i 0.237927 + 1.75526i
\(395\) −171.521 + 171.521i −0.434230 + 0.434230i
\(396\) −6.95041 25.2653i −0.0175515 0.0638013i
\(397\) 259.123 259.123i 0.652703 0.652703i −0.300940 0.953643i \(-0.597300\pi\)
0.953643 + 0.300940i \(0.0973004\pi\)
\(398\) 457.996 + 348.654i 1.15074 + 0.876014i
\(399\) −610.157 + 252.377i −1.52922 + 0.632523i
\(400\) 173.780 + 290.619i 0.434449 + 0.726548i
\(401\) 664.163i 1.65627i 0.560531 + 0.828133i \(0.310597\pi\)
−0.560531 + 0.828133i \(0.689403\pi\)
\(402\) 337.509 + 89.2323i 0.839575 + 0.221971i
\(403\) 177.275 177.275i 0.439889 0.439889i
\(404\) 178.821 + 101.424i 0.442626 + 0.251049i
\(405\) 388.369 + 389.932i 0.958937 + 0.962795i
\(406\) −96.7902 714.049i −0.238400 1.75874i
\(407\) 18.8131 0.0462237
\(408\) 190.649 + 186.504i 0.467276 + 0.457117i
\(409\) 530.421i 1.29687i 0.761269 + 0.648437i \(0.224577\pi\)
−0.761269 + 0.648437i \(0.775423\pi\)
\(410\) −117.264 865.093i −0.286011 2.10998i
\(411\) 189.787 457.536i 0.461768 1.11323i
\(412\) 337.438 93.1926i 0.819024 0.226196i
\(413\) 129.769 + 129.769i 0.314211 + 0.314211i
\(414\) −139.188 + 18.7248i −0.336202 + 0.0452290i
\(415\) −912.271 −2.19824
\(416\) −201.285 252.169i −0.483857 0.606176i
\(417\) −372.762 + 154.184i −0.893914 + 0.369746i
\(418\) 34.6305 + 26.3628i 0.0828480 + 0.0630688i
\(419\) −404.149 404.149i −0.964556 0.964556i 0.0348367 0.999393i \(-0.488909\pi\)
−0.999393 + 0.0348367i \(0.988909\pi\)
\(420\) −368.797 473.567i −0.878087 1.12754i
\(421\) −264.630 264.630i −0.628575 0.628575i 0.319134 0.947710i \(-0.396608\pi\)
−0.947710 + 0.319134i \(0.896608\pi\)
\(422\) 59.3232 + 437.644i 0.140576 + 1.03707i
\(423\) −146.842 + 146.547i −0.347143 + 0.346447i
\(424\) 332.033 142.024i 0.783097 0.334963i
\(425\) 235.180 0.553366
\(426\) −77.4791 133.172i −0.181876 0.312611i
\(427\) −91.2382 91.2382i −0.213673 0.213673i
\(428\) −515.994 292.662i −1.20559 0.683790i
\(429\) 20.3374 + 8.43598i 0.0474065 + 0.0196643i
\(430\) −84.2825 + 110.715i −0.196006 + 0.257476i
\(431\) 766.652i 1.77877i 0.457155 + 0.889387i \(0.348868\pi\)
−0.457155 + 0.889387i \(0.651132\pi\)
\(432\) 258.225 346.329i 0.597743 0.801688i
\(433\) 151.222 0.349243 0.174622 0.984636i \(-0.444130\pi\)
0.174622 + 0.984636i \(0.444130\pi\)
\(434\) −291.296 221.752i −0.671188 0.510948i
\(435\) 382.207 921.422i 0.878638 2.11821i
\(436\) −37.5929 21.3220i −0.0862223 0.0489036i
\(437\) 164.943 164.943i 0.377445 0.377445i
\(438\) 291.380 169.524i 0.665252 0.387041i
\(439\) 565.007i 1.28703i 0.765433 + 0.643516i \(0.222525\pi\)
−0.765433 + 0.643516i \(0.777475\pi\)
\(440\) −14.7195 + 36.7241i −0.0334535 + 0.0834638i
\(441\) 33.0409 + 33.1073i 0.0749228 + 0.0750733i
\(442\) −222.064 + 30.1011i −0.502408 + 0.0681020i
\(443\) −100.963 + 100.963i −0.227907 + 0.227907i −0.811818 0.583911i \(-0.801522\pi\)
0.583911 + 0.811818i \(0.301522\pi\)
\(444\) 190.566 + 244.704i 0.429204 + 0.551134i
\(445\) −215.577 + 215.577i −0.484442 + 0.484442i
\(446\) −54.8779 + 72.0883i −0.123045 + 0.161633i
\(447\) 212.557 + 513.887i 0.475518 + 1.14963i
\(448\) −325.416 + 340.728i −0.726375 + 0.760554i
\(449\) 131.725i 0.293375i 0.989183 + 0.146687i \(0.0468611\pi\)
−0.989183 + 0.146687i \(0.953139\pi\)
\(450\) −50.7900 377.539i −0.112867 0.838975i
\(451\) 33.0663 33.0663i 0.0733178 0.0733178i
\(452\) −50.6143 + 13.9785i −0.111979 + 0.0309259i
\(453\) −341.034 141.461i −0.752833 0.312277i
\(454\) −842.961 + 114.264i −1.85674 + 0.251684i
\(455\) 504.339 1.10844
\(456\) 7.88486 + 717.483i 0.0172914 + 1.57343i
\(457\) 137.963i 0.301888i 0.988542 + 0.150944i \(0.0482313\pi\)
−0.988542 + 0.150944i \(0.951769\pi\)
\(458\) −184.168 + 24.9642i −0.402114 + 0.0545071i
\(459\) −114.403 277.374i −0.249245 0.604302i
\(460\) 184.445 + 104.613i 0.400967 + 0.227421i
\(461\) −303.536 303.536i −0.658430 0.658430i 0.296579 0.955008i \(-0.404154\pi\)
−0.955008 + 0.296579i \(0.904154\pi\)
\(462\) 8.21803 31.0836i 0.0177879 0.0672805i
\(463\) 280.379 0.605570 0.302785 0.953059i \(-0.402084\pi\)
0.302785 + 0.953059i \(0.402084\pi\)
\(464\) −759.374 191.054i −1.63658 0.411754i
\(465\) −193.714 468.332i −0.416589 1.00716i
\(466\) 51.8759 68.1449i 0.111322 0.146234i
\(467\) −65.6355 65.6355i −0.140547 0.140547i 0.633333 0.773880i \(-0.281687\pi\)
−0.773880 + 0.633333i \(0.781687\pi\)
\(468\) 96.2792 + 349.983i 0.205725 + 0.747827i
\(469\) 302.886 + 302.886i 0.645812 + 0.645812i
\(470\) 310.392 42.0740i 0.660409 0.0895192i
\(471\) −225.699 545.659i −0.479190 1.15851i
\(472\) 183.359 78.4302i 0.388473 0.166166i
\(473\) −7.45335 −0.0157576
\(474\) −107.721 185.152i −0.227259 0.390616i
\(475\) 447.400 + 447.400i 0.941894 + 0.941894i
\(476\) 87.1147 + 315.431i 0.183014 + 0.662669i
\(477\) −406.274 0.407800i −0.851728 0.000854927i
\(478\) 160.088 + 121.868i 0.334912 + 0.254955i
\(479\) 373.272i 0.779273i −0.920969 0.389636i \(-0.872601\pi\)
0.920969 0.389636i \(-0.127399\pi\)
\(480\) −626.776 + 180.537i −1.30578 + 0.376119i
\(481\) −260.604 −0.541797
\(482\) 6.33778 8.32539i 0.0131489 0.0172726i
\(483\) −159.169 66.0234i −0.329542 0.136694i
\(484\) 464.492 128.282i 0.959694 0.265045i
\(485\) −395.702 + 395.702i −0.815881 + 0.815881i
\(486\) −420.567 + 243.556i −0.865364 + 0.501144i
\(487\) 0.0470526i 9.66171e-5i 1.00000 4.83086e-5i \(1.53771e-5\pi\)
−1.00000 4.83086e-5i \(0.999985\pi\)
\(488\) −128.916 + 55.1429i −0.264173 + 0.112998i
\(489\) 32.3206 + 78.1398i 0.0660954 + 0.159795i
\(490\) −9.48614 69.9820i −0.0193595 0.142820i
\(491\) 273.442 273.442i 0.556908 0.556908i −0.371518 0.928426i \(-0.621163\pi\)
0.928426 + 0.371518i \(0.121163\pi\)
\(492\) 765.043 + 95.1532i 1.55496 + 0.193401i
\(493\) −384.562 + 384.562i −0.780044 + 0.780044i
\(494\) −479.712 365.185i −0.971077 0.739241i
\(495\) 31.5047 31.4415i 0.0636458 0.0635182i
\(496\) −341.443 + 204.170i −0.688394 + 0.411634i
\(497\) 189.042i 0.380365i
\(498\) 205.917 778.852i 0.413487 1.56396i
\(499\) −46.2637 + 46.2637i −0.0927129 + 0.0927129i −0.751942 0.659229i \(-0.770883\pi\)
0.659229 + 0.751942i \(0.270883\pi\)
\(500\) 51.4422 90.6980i 0.102884 0.181396i
\(501\) 69.3366 167.156i 0.138396 0.333645i
\(502\) 6.62514 + 48.8755i 0.0131975 + 0.0973616i
\(503\) 864.426 1.71854 0.859270 0.511522i \(-0.170918\pi\)
0.859270 + 0.511522i \(0.170918\pi\)
\(504\) 487.552 207.968i 0.967366 0.412634i
\(505\) 349.198i 0.691482i
\(506\) 1.52569 + 11.2554i 0.00301520 + 0.0222440i
\(507\) 186.590 + 77.3977i 0.368027 + 0.152658i
\(508\) 93.9946 + 340.342i 0.185029 + 0.669964i
\(509\) −171.041 171.041i −0.336033 0.336033i 0.518839 0.854872i \(-0.326365\pi\)
−0.854872 + 0.518839i \(0.826365\pi\)
\(510\) −115.793 + 437.971i −0.227045 + 0.858767i
\(511\) 413.623 0.809438
\(512\) 212.121 + 465.992i 0.414299 + 0.910141i
\(513\) 310.031 745.306i 0.604349 1.45284i
\(514\) −546.911 416.341i −1.06403 0.810002i
\(515\) 420.464 + 420.464i 0.816435 + 0.816435i
\(516\) −75.4986 96.9467i −0.146315 0.187881i
\(517\) 11.8641 + 11.8641i 0.0229479 + 0.0229479i
\(518\) 51.1168 + 377.103i 0.0986811 + 0.727999i
\(519\) 293.368 121.345i 0.565257 0.233805i
\(520\) 203.899 508.713i 0.392114 0.978295i
\(521\) 351.572 0.674802 0.337401 0.941361i \(-0.390452\pi\)
0.337401 + 0.941361i \(0.390452\pi\)
\(522\) 700.394 + 534.292i 1.34175 + 1.02355i
\(523\) −287.638 287.638i −0.549977 0.549977i 0.376457 0.926434i \(-0.377142\pi\)
−0.926434 + 0.376457i \(0.877142\pi\)
\(524\) −159.221 + 280.724i −0.303857 + 0.535732i
\(525\) 179.085 431.736i 0.341114 0.822354i
\(526\) −118.825 + 156.090i −0.225904 + 0.296750i
\(527\) 276.309i 0.524306i
\(528\) −28.0307 20.8561i −0.0530885 0.0395003i
\(529\) −468.124 −0.884922
\(530\) 488.083 + 371.558i 0.920911 + 0.701052i
\(531\) −224.357 0.225200i −0.422519 0.000424106i
\(532\) −434.341 + 765.789i −0.816431 + 1.43945i
\(533\) −458.045 + 458.045i −0.859372 + 0.859372i
\(534\) −135.389 232.709i −0.253538 0.435784i
\(535\) 1007.63i 1.88341i
\(536\) 427.967 183.059i 0.798446 0.341528i
\(537\) 15.5471 6.43067i 0.0289517 0.0119752i
\(538\) 354.721 48.0828i 0.659332 0.0893732i
\(539\) 2.67491 2.67491i 0.00496273 0.00496273i
\(540\) 728.089 + 91.2993i 1.34831 + 0.169073i
\(541\) 419.846 419.846i 0.776056 0.776056i −0.203102 0.979158i \(-0.565102\pi\)
0.979158 + 0.203102i \(0.0651021\pi\)
\(542\) 250.146 328.595i 0.461524 0.606264i
\(543\) 622.654 257.545i 1.14669 0.474301i
\(544\) 353.386 + 39.6554i 0.649607 + 0.0728960i
\(545\) 73.4108i 0.134699i
\(546\) −113.839 + 430.580i −0.208496 + 0.788607i
\(547\) 517.346 517.346i 0.945789 0.945789i −0.0528155 0.998604i \(-0.516820\pi\)
0.998604 + 0.0528155i \(0.0168195\pi\)
\(548\) −175.819 636.616i −0.320837 1.16171i
\(549\) 157.742 + 0.158334i 0.287325 + 0.000288404i
\(550\) −30.5298 + 4.13835i −0.0555087 + 0.00752427i
\(551\) −1463.16 −2.65546
\(552\) −130.947 + 133.857i −0.237222 + 0.242494i
\(553\) 262.828i 0.475277i
\(554\) −514.079 + 69.6840i −0.927940 + 0.125783i
\(555\) −201.851 + 486.621i −0.363696 + 0.876794i
\(556\) −265.351 + 467.843i −0.477251 + 0.841443i
\(557\) 31.8976 + 31.8976i 0.0572667 + 0.0572667i 0.735160 0.677893i \(-0.237107\pi\)
−0.677893 + 0.735160i \(0.737107\pi\)
\(558\) 443.563 59.6722i 0.794917 0.106939i
\(559\) 103.246 0.184698
\(560\) −776.120 195.267i −1.38593 0.348691i
\(561\) −22.4237 + 9.27502i −0.0399709 + 0.0165330i
\(562\) 132.220 173.685i 0.235266 0.309049i
\(563\) −32.9214 32.9214i −0.0584750 0.0584750i 0.677265 0.735740i \(-0.263165\pi\)
−0.735740 + 0.677265i \(0.763165\pi\)
\(564\) −34.1406 + 274.495i −0.0605330 + 0.486692i
\(565\) −63.0679 63.0679i −0.111625 0.111625i
\(566\) −169.464 + 22.9710i −0.299406 + 0.0405848i
\(567\) −596.310 1.19710i −1.05169 0.00211129i
\(568\) −190.681 76.4278i −0.335707 0.134556i
\(569\) 647.095 1.13725 0.568624 0.822597i \(-0.307476\pi\)
0.568624 + 0.822597i \(0.307476\pi\)
\(570\) −1053.46 + 612.902i −1.84818 + 1.07527i
\(571\) 451.861 + 451.861i 0.791350 + 0.791350i 0.981714 0.190363i \(-0.0609666\pi\)
−0.190363 + 0.981714i \(0.560967\pi\)
\(572\) 28.2975 7.81511i 0.0494711 0.0136628i
\(573\) 190.826 + 79.1550i 0.333030 + 0.138141i
\(574\) 752.652 + 572.963i 1.31124 + 0.998193i
\(575\) 165.123i 0.287170i
\(576\) −12.6585 575.861i −0.0219766 0.999758i
\(577\) 532.176 0.922315 0.461157 0.887318i \(-0.347434\pi\)
0.461157 + 0.887318i \(0.347434\pi\)
\(578\) −200.504 + 263.385i −0.346893 + 0.455683i
\(579\) −421.436 + 1015.99i −0.727869 + 1.75474i
\(580\) −354.078 1282.07i −0.610478 2.21046i
\(581\) 698.953 698.953i 1.20302 1.20302i
\(582\) −248.514 427.149i −0.427000 0.733933i
\(583\) 32.8579i 0.0563601i
\(584\) 167.224 417.210i 0.286342 0.714402i
\(585\) −436.412 + 435.537i −0.746004 + 0.744508i
\(586\) 7.39475 + 54.5532i 0.0126190 + 0.0930942i
\(587\) 532.393 532.393i 0.906973 0.906973i −0.0890534 0.996027i \(-0.528384\pi\)
0.996027 + 0.0890534i \(0.0283842\pi\)
\(588\) 61.8884 + 7.69745i 0.105252 + 0.0130909i
\(589\) −525.642 + 525.642i −0.892431 + 0.892431i
\(590\) 269.535 + 205.186i 0.456838 + 0.347772i
\(591\) −400.124 967.359i −0.677029 1.63682i
\(592\) 401.040 + 100.899i 0.677433 + 0.170438i
\(593\) 254.750i 0.429595i −0.976659 0.214798i \(-0.931091\pi\)
0.976659 0.214798i \(-0.0689092\pi\)
\(594\) 19.7320 + 33.9941i 0.0332189 + 0.0572291i
\(595\) −393.042 + 393.042i −0.660574 + 0.660574i
\(596\) 644.963 + 365.811i 1.08215 + 0.613777i
\(597\) −797.517 330.811i −1.33587 0.554123i
\(598\) −21.1343 155.914i −0.0353417 0.260726i
\(599\) 624.772 1.04303 0.521513 0.853244i \(-0.325368\pi\)
0.521513 + 0.853244i \(0.325368\pi\)
\(600\) −363.079 355.185i −0.605131 0.591975i
\(601\) 386.910i 0.643777i −0.946778 0.321889i \(-0.895682\pi\)
0.946778 0.321889i \(-0.104318\pi\)
\(602\) −20.2515 149.401i −0.0336403 0.248174i
\(603\) −523.658 0.525625i −0.868422 0.000871684i
\(604\) −474.514 + 131.050i −0.785620 + 0.216970i
\(605\) 578.779 + 578.779i 0.956660 + 0.956660i
\(606\) −298.128 78.8207i −0.491961 0.130067i
\(607\) −951.141 −1.56695 −0.783477 0.621421i \(-0.786556\pi\)
−0.783477 + 0.621421i \(0.786556\pi\)
\(608\) 596.832 + 747.710i 0.981632 + 1.22979i
\(609\) 413.129 + 998.800i 0.678373 + 1.64007i
\(610\) −189.505 144.262i −0.310664 0.236496i
\(611\) −164.345 164.345i −0.268977 0.268977i
\(612\) −347.782 197.717i −0.568271 0.323066i
\(613\) 387.896 + 387.896i 0.632783 + 0.632783i 0.948765 0.315982i \(-0.102334\pi\)
−0.315982 + 0.948765i \(0.602334\pi\)
\(614\) −155.085 1144.10i −0.252581 1.86336i
\(615\) 500.519 + 1210.08i 0.813852 + 1.96761i
\(616\) −16.8592 39.4145i −0.0273688 0.0639846i
\(617\) −882.945 −1.43103 −0.715514 0.698598i \(-0.753808\pi\)
−0.715514 + 0.698598i \(0.753808\pi\)
\(618\) −453.878 + 264.065i −0.734431 + 0.427290i
\(619\) −694.731 694.731i −1.12234 1.12234i −0.991388 0.130955i \(-0.958196\pi\)
−0.130955 0.991388i \(-0.541804\pi\)
\(620\) −587.789 333.382i −0.948046 0.537714i
\(621\) 194.748 80.3239i 0.313604 0.129346i
\(622\) 437.286 574.425i 0.703033 0.923513i
\(623\) 330.337i 0.530235i
\(624\) 388.291 + 288.906i 0.622260 + 0.462990i
\(625\) 706.197 1.12991
\(626\) 117.636 + 89.5515i 0.187917 + 0.143053i
\(627\) −60.3027 25.0136i −0.0961765 0.0398942i
\(628\) −684.840 388.428i −1.09051 0.618516i
\(629\) 203.094 203.094i 0.322885 0.322885i
\(630\) 715.838 + 546.074i 1.13625 + 0.866785i
\(631\) 927.845i 1.47044i 0.677831 + 0.735218i \(0.262920\pi\)
−0.677831 + 0.735218i \(0.737080\pi\)
\(632\) −265.108 106.259i −0.419475 0.168131i
\(633\) −253.209 612.170i −0.400014 0.967093i
\(634\) 484.069 65.6161i 0.763516 0.103495i
\(635\) −424.082 + 424.082i −0.667846 + 0.667846i
\(636\) −427.387 + 332.834i −0.671992 + 0.523323i
\(637\) −37.0537 + 37.0537i −0.0581691 + 0.0581691i
\(638\) 43.1547 56.6885i 0.0676405 0.0888535i
\(639\) 163.253 + 163.581i 0.255482 + 0.255995i
\(640\) −510.739 + 703.908i −0.798029 + 1.09986i
\(641\) 759.287i 1.18453i 0.805741 + 0.592267i \(0.201767\pi\)
−0.805741 + 0.592267i \(0.798233\pi\)
\(642\) 860.261 + 227.440i 1.33997 + 0.354268i
\(643\) 274.424 274.424i 0.426787 0.426787i −0.460746 0.887532i \(-0.652418\pi\)
0.887532 + 0.460746i \(0.152418\pi\)
\(644\) −221.467 + 61.1642i −0.343893 + 0.0949755i
\(645\) 79.9694 192.789i 0.123984 0.298898i
\(646\) 658.446 89.2532i 1.01927 0.138163i
\(647\) −747.683 −1.15561 −0.577807 0.816173i \(-0.696092\pi\)
−0.577807 + 0.816173i \(0.696092\pi\)
\(648\) −242.290 + 600.999i −0.373905 + 0.927467i
\(649\) 18.1452i 0.0279587i
\(650\) 422.908 57.3257i 0.650628 0.0881934i
\(651\) 507.239 + 210.403i 0.779168 + 0.323200i
\(652\) 98.0709 + 55.6239i 0.150416 + 0.0853128i
\(653\) 605.127 + 605.127i 0.926688 + 0.926688i 0.997490 0.0708022i \(-0.0225559\pi\)
−0.0708022 + 0.997490i \(0.522556\pi\)
\(654\) 62.6746 + 16.5702i 0.0958327 + 0.0253367i
\(655\) −548.192 −0.836935
\(656\) 882.223 527.537i 1.34485 0.804172i
\(657\) −357.914 + 357.197i −0.544771 + 0.543678i
\(658\) −205.577 + 270.049i −0.312427 + 0.410408i
\(659\) 588.767 + 588.767i 0.893425 + 0.893425i 0.994844 0.101418i \(-0.0323381\pi\)
−0.101418 + 0.994844i \(0.532338\pi\)
\(660\) 7.32483 58.8925i 0.0110982 0.0892310i
\(661\) 3.60334 + 3.60334i 0.00545135 + 0.00545135i 0.709827 0.704376i \(-0.248773\pi\)
−0.704376 + 0.709827i \(0.748773\pi\)
\(662\) −732.950 + 99.3523i −1.10718 + 0.150079i
\(663\) 310.620 128.480i 0.468507 0.193786i
\(664\) −422.436 987.597i −0.636198 1.48734i
\(665\) −1495.42 −2.24875
\(666\) −369.891 282.170i −0.555393 0.423679i
\(667\) −270.005 270.005i −0.404805 0.404805i
\(668\) −64.2336 232.581i −0.0961581 0.348176i
\(669\) 52.0695 125.529i 0.0778319 0.187636i
\(670\) 629.104 + 478.911i 0.938961 + 0.714793i
\(671\) 12.7575i 0.0190127i
\(672\) 341.894 618.538i 0.508771 0.920443i
\(673\) −460.445 −0.684167 −0.342084 0.939670i \(-0.611133\pi\)
−0.342084 + 0.939670i \(0.611133\pi\)
\(674\) −22.0737 + 28.9963i −0.0327502 + 0.0430211i
\(675\) 217.874 + 528.242i 0.322776 + 0.782581i
\(676\) 259.621 71.7014i 0.384055 0.106067i
\(677\) 150.713 150.713i 0.222618 0.222618i −0.586982 0.809600i \(-0.699684\pi\)
0.809600 + 0.586982i \(0.199684\pi\)
\(678\) 68.0799 39.6086i 0.100413 0.0584198i
\(679\) 606.350i 0.893004i
\(680\) 237.548 + 555.354i 0.349335 + 0.816698i
\(681\) 1179.12 487.714i 1.73145 0.716174i
\(682\) −4.86207 35.8689i −0.00712913 0.0525937i
\(683\) −577.893 + 577.893i −0.846109 + 0.846109i −0.989645 0.143536i \(-0.954153\pi\)
0.143536 + 0.989645i \(0.454153\pi\)
\(684\) −285.479 1037.74i −0.417367 1.51716i
\(685\) 793.254 793.254i 1.15803 1.15803i
\(686\) −513.167 390.653i −0.748057 0.569465i
\(687\) 257.612 106.555i 0.374981 0.155102i
\(688\) −158.884 39.9742i −0.230936 0.0581021i
\(689\) 455.158i 0.660607i
\(690\) −307.505 81.2996i −0.445659 0.117825i
\(691\) −545.023 + 545.023i −0.788745 + 0.788745i −0.981288 0.192544i \(-0.938326\pi\)
0.192544 + 0.981288i \(0.438326\pi\)
\(692\) 208.834 368.197i 0.301784 0.532077i
\(693\) −0.0484085 + 48.2274i −6.98536e−5 + 0.0695922i
\(694\) −65.9963 486.874i −0.0950956 0.701547i
\(695\) −913.595 −1.31453
\(696\) 1174.49 12.9072i 1.68748 0.0185448i
\(697\) 713.929i 1.02429i
\(698\) 147.372 + 1087.20i 0.211134 + 1.55760i
\(699\) −49.2212 + 118.662i −0.0704165 + 0.169760i
\(700\) −165.904 600.718i −0.237006 0.858169i
\(701\) −413.745 413.745i −0.590221 0.590221i 0.347470 0.937691i \(-0.387041\pi\)
−0.937691 + 0.347470i \(0.887041\pi\)
\(702\) −273.334 470.897i −0.389364 0.670793i
\(703\) 772.721 1.09918
\(704\) −46.5724 + 1.07052i −0.0661540 + 0.00152062i
\(705\) −434.171 + 179.584i −0.615846 + 0.254730i
\(706\) 1077.05 + 819.915i 1.52557 + 1.16135i
\(707\) −267.545 267.545i −0.378423 0.378423i
\(708\) −236.017 + 183.801i −0.333357 + 0.259606i
\(709\) 521.959 + 521.959i 0.736191 + 0.736191i 0.971839 0.235648i \(-0.0757212\pi\)
−0.235648 + 0.971839i \(0.575721\pi\)
\(710\) −46.8703 345.776i −0.0660145 0.487008i
\(711\) 226.973 + 227.429i 0.319231 + 0.319873i
\(712\) −333.202 133.552i −0.467980 0.187573i
\(713\) −194.000 −0.272089
\(714\) −246.843 424.277i −0.345718 0.594225i
\(715\) 35.2600 + 35.2600i 0.0493147 + 0.0493147i
\(716\) 11.0672 19.5127i 0.0154570 0.0272523i
\(717\) −278.764 115.632i −0.388792 0.161272i
\(718\) −291.830 + 383.352i −0.406449 + 0.533917i
\(719\) 567.983i 0.789963i −0.918689 0.394981i \(-0.870751\pi\)
0.918689 0.394981i \(-0.129249\pi\)
\(720\) 840.218 501.275i 1.16697 0.696215i
\(721\) −644.293 −0.893610
\(722\) 847.919 + 645.486i 1.17440 + 0.894025i
\(723\) −6.01344 + 14.4972i −0.00831735 + 0.0200514i
\(724\) 443.237 781.473i 0.612205 1.07938i
\(725\) 732.374 732.374i 1.01017 1.01017i
\(726\) −624.775 + 363.492i −0.860572 + 0.500678i
\(727\) 635.396i 0.873998i −0.899462 0.436999i \(-0.856041\pi\)
0.899462 0.436999i \(-0.143959\pi\)
\(728\) 233.539 + 545.982i 0.320795 + 0.749975i
\(729\) 517.031 513.926i 0.709233 0.704974i
\(730\) 756.556 102.552i 1.03638 0.140482i
\(731\) −80.4619 + 80.4619i −0.110071 + 0.110071i
\(732\) 165.939 129.227i 0.226692 0.176540i
\(733\) −637.378 + 637.378i −0.869547 + 0.869547i −0.992422 0.122875i \(-0.960788\pi\)
0.122875 + 0.992422i \(0.460788\pi\)
\(734\) −807.667 + 1060.96i −1.10036 + 1.44545i
\(735\) 40.4897 + 97.8896i 0.0550880 + 0.133183i
\(736\) −27.8425 + 248.117i −0.0378295 + 0.337115i
\(737\) 42.3515i 0.0574648i
\(738\) −1146.08 + 154.181i −1.55296 + 0.208918i
\(739\) 397.296 397.296i 0.537613 0.537613i −0.385214 0.922827i \(-0.625872\pi\)
0.922827 + 0.385214i \(0.125872\pi\)
\(740\) 186.995 + 677.085i 0.252696 + 0.914980i
\(741\) 835.331 + 346.497i 1.12730 + 0.467607i
\(742\) −658.630 + 89.2781i −0.887641 + 0.120321i
\(743\) 1160.78 1.56229 0.781145 0.624349i \(-0.214636\pi\)
0.781145 + 0.624349i \(0.214636\pi\)
\(744\) 417.301 426.574i 0.560888 0.573353i
\(745\) 1259.47i 1.69057i
\(746\) 1004.84 136.207i 1.34697 0.182583i
\(747\) −1.21296 + 1208.42i −0.00162377 + 1.61770i
\(748\) −15.9623 + 28.1433i −0.0213400 + 0.0376247i
\(749\) 772.011 + 772.011i 1.03072 + 1.03072i
\(750\) −39.9779 + 151.211i −0.0533038 + 0.201615i
\(751\) 1220.14 1.62469 0.812343 0.583181i \(-0.198192\pi\)
0.812343 + 0.583181i \(0.198192\pi\)
\(752\) 189.278 + 316.538i 0.251700 + 0.420929i
\(753\) −28.2781 68.3663i −0.0375539 0.0907919i
\(754\) −597.792 + 785.267i −0.792827 + 1.04147i
\(755\) −591.268 591.268i −0.783136 0.783136i
\(756\) −627.790 + 487.888i −0.830410 + 0.645355i
\(757\) 202.623 + 202.623i 0.267666 + 0.267666i 0.828159 0.560493i \(-0.189388\pi\)
−0.560493 + 0.828159i \(0.689388\pi\)
\(758\) 395.080 53.5536i 0.521214 0.0706512i
\(759\) −6.51210 15.7439i −0.00857984 0.0207430i
\(760\) −604.585 + 1508.39i −0.795507 + 1.98473i
\(761\) −694.461 −0.912563 −0.456282 0.889835i \(-0.650819\pi\)
−0.456282 + 0.889835i \(0.650819\pi\)
\(762\) −266.337 457.784i −0.349524 0.600767i
\(763\) 56.2451 + 56.2451i 0.0737157 + 0.0737157i
\(764\) 265.516 73.3293i 0.347534 0.0959808i
\(765\) 0.682081 679.529i 0.000891610 0.888273i
\(766\) −110.549 84.1564i −0.144320 0.109865i
\(767\) 251.353i 0.327709i
\(768\) −485.678 594.929i −0.632394 0.774647i
\(769\) 405.268 0.527007 0.263503 0.964658i \(-0.415122\pi\)
0.263503 + 0.964658i \(0.415122\pi\)
\(770\) 44.1063 57.9386i 0.0572809 0.0752449i
\(771\) 952.347 + 395.035i 1.23521 + 0.512367i
\(772\) 390.419 + 1413.66i