Properties

Label 91.2.f.c.22.3
Level $91$
Weight $2$
Character 91.22
Analytic conductor $0.727$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 91 = 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 91.f (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.726638658394\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Defining polynomial: \(x^{8} - x^{7} + 7 x^{6} + 38 x^{4} - 16 x^{3} + 15 x^{2} + 3 x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 22.3
Root \(0.355143 - 0.615126i\) of defining polynomial
Character \(\chi\) \(=\) 91.22
Dual form 91.2.f.c.29.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.355143 - 0.615126i) q^{2} +(-1.20394 + 2.08529i) q^{3} +(0.747746 + 1.29513i) q^{4} -1.28971 q^{5} +(0.855143 + 1.48115i) q^{6} +(0.500000 + 0.866025i) q^{7} +2.48280 q^{8} +(-1.39895 - 2.42305i) q^{9} +O(q^{10})\) \(q+(0.355143 - 0.615126i) q^{2} +(-1.20394 + 2.08529i) q^{3} +(0.747746 + 1.29513i) q^{4} -1.28971 q^{5} +(0.855143 + 1.48115i) q^{6} +(0.500000 + 0.866025i) q^{7} +2.48280 q^{8} +(-1.39895 - 2.42305i) q^{9} +(-0.458033 + 0.793337i) q^{10} +(1.20394 - 2.08529i) q^{11} -3.60097 q^{12} +(1.25409 - 3.38042i) q^{13} +0.710287 q^{14} +(1.55274 - 2.68942i) q^{15} +(-0.613742 + 1.06303i) q^{16} +(-1.95169 - 3.38042i) q^{17} -1.98731 q^{18} +(2.94534 + 5.10148i) q^{19} +(-0.964379 - 1.67035i) q^{20} -2.40788 q^{21} +(-0.855143 - 1.48115i) q^{22} +(3.16197 - 5.47670i) q^{23} +(-2.98915 + 5.17736i) q^{24} -3.33664 q^{25} +(-1.63400 - 1.97196i) q^{26} -0.486640 q^{27} +(-0.747746 + 1.29513i) q^{28} +(-2.80683 + 4.86157i) q^{29} +(-1.10289 - 1.91026i) q^{30} +2.20578 q^{31} +(2.91873 + 5.05540i) q^{32} +(2.89895 + 5.02113i) q^{33} -2.77252 q^{34} +(-0.644857 - 1.11692i) q^{35} +(2.09212 - 3.62365i) q^{36} +(2.55908 - 4.43246i) q^{37} +4.18407 q^{38} +(5.53930 + 6.68497i) q^{39} -3.20210 q^{40} +(3.89260 - 6.74219i) q^{41} +(-0.855143 + 1.48115i) q^{42} +(-0.144857 - 0.250899i) q^{43} +3.60097 q^{44} +(1.80424 + 3.12504i) q^{45} +(-2.24591 - 3.89003i) q^{46} +1.27702 q^{47} +(-1.47782 - 2.55966i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-1.18499 + 2.05245i) q^{50} +9.39887 q^{51} +(5.31585 - 0.903480i) q^{52} -13.6225 q^{53} +(-0.172827 + 0.299345i) q^{54} +(-1.55274 + 2.68942i) q^{55} +(1.24140 + 2.15017i) q^{56} -14.1841 q^{57} +(1.99365 + 3.45311i) q^{58} +(2.01528 + 3.49057i) q^{59} +4.64422 q^{60} +(2.30049 + 3.98456i) q^{61} +(0.783368 - 1.35683i) q^{62} +(1.39895 - 2.42305i) q^{63} +1.69131 q^{64} +(-1.61742 + 4.35978i) q^{65} +4.11817 q^{66} +(-3.78779 + 6.56065i) q^{67} +(2.91873 - 5.05540i) q^{68} +(7.61366 + 13.1872i) q^{69} -0.916066 q^{70} +(-3.61366 - 6.25905i) q^{71} +(-3.47331 - 6.01595i) q^{72} -15.0125 q^{73} +(-1.81768 - 3.14832i) q^{74} +(4.01712 - 6.95785i) q^{75} +(-4.40474 + 7.62923i) q^{76} +2.40788 q^{77} +(6.07935 - 1.03324i) q^{78} -9.30758 q^{79} +(0.791552 - 1.37101i) q^{80} +(4.78273 - 8.28393i) q^{81} +(-2.76486 - 4.78888i) q^{82} -1.36463 q^{83} +(-1.80049 - 3.11853i) q^{84} +(2.51712 + 4.35978i) q^{85} -0.205780 q^{86} +(-6.75852 - 11.7061i) q^{87} +(2.98915 - 5.17736i) q^{88} +(0.449849 - 0.779162i) q^{89} +2.56306 q^{90} +(3.55458 - 0.604136i) q^{91} +9.45742 q^{92} +(-2.65563 + 4.59968i) q^{93} +(0.453526 - 0.785530i) q^{94} +(-3.79865 - 6.57945i) q^{95} -14.0559 q^{96} +(-7.83288 - 13.5669i) q^{97} +(0.355143 + 0.615126i) q^{98} -6.73701 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + q^{2} - q^{3} - 5q^{4} - 14q^{5} + 5q^{6} + 4q^{7} - 12q^{8} - 7q^{9} + O(q^{10}) \) \( 8q + q^{2} - q^{3} - 5q^{4} - 14q^{5} + 5q^{6} + 4q^{7} - 12q^{8} - 7q^{9} + 11q^{10} + q^{11} + 24q^{12} + 4q^{13} + 2q^{14} - 3q^{15} - 19q^{16} + 4q^{17} - 6q^{18} - q^{19} + 2q^{20} - 2q^{21} - 5q^{22} + 2q^{23} + 3q^{24} + 10q^{25} + 12q^{26} - 52q^{27} + 5q^{28} - q^{29} + 4q^{30} - 8q^{31} + 33q^{32} + 19q^{33} + 6q^{34} - 7q^{35} + 34q^{36} + 10q^{37} - 46q^{38} + 20q^{39} - 34q^{40} + 22q^{41} - 5q^{42} - 3q^{43} - 24q^{44} + 11q^{45} - 24q^{46} + 4q^{47} - 11q^{48} - 4q^{49} - 43q^{50} + 14q^{51} + 65q^{52} + 4q^{53} - 5q^{54} + 3q^{55} - 6q^{56} - 34q^{57} + 11q^{58} + 8q^{59} - 22q^{60} - 8q^{61} + 5q^{62} + 7q^{63} + 28q^{64} + 7q^{65} + 12q^{66} + 6q^{67} + 33q^{68} + 18q^{69} + 22q^{70} + 14q^{71} - 5q^{72} - 16q^{73} - 20q^{74} + 7q^{75} - 32q^{76} + 2q^{77} - q^{78} - 52q^{79} - 7q^{80} - 24q^{81} + 14q^{82} + 12q^{84} - 5q^{85} + 24q^{86} - 13q^{87} - 3q^{88} + q^{89} + 52q^{90} - 4q^{91} + 24q^{92} + 7q^{93} - 33q^{94} - 21q^{95} - 116q^{96} - 3q^{97} + q^{98} + 46q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/91\mathbb{Z}\right)^\times\).

\(n\) \(15\) \(66\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.355143 0.615126i 0.251124 0.434960i −0.712711 0.701457i \(-0.752533\pi\)
0.963836 + 0.266497i \(0.0858664\pi\)
\(3\) −1.20394 + 2.08529i −0.695096 + 1.20394i 0.275053 + 0.961429i \(0.411305\pi\)
−0.970148 + 0.242512i \(0.922029\pi\)
\(4\) 0.747746 + 1.29513i 0.373873 + 0.647567i
\(5\) −1.28971 −0.576777 −0.288389 0.957513i \(-0.593120\pi\)
−0.288389 + 0.957513i \(0.593120\pi\)
\(6\) 0.855143 + 1.48115i 0.349111 + 0.604678i
\(7\) 0.500000 + 0.866025i 0.188982 + 0.327327i
\(8\) 2.48280 0.877803
\(9\) −1.39895 2.42305i −0.466316 0.807683i
\(10\) −0.458033 + 0.793337i −0.144843 + 0.250875i
\(11\) 1.20394 2.08529i 0.363002 0.628738i −0.625451 0.780263i \(-0.715085\pi\)
0.988453 + 0.151525i \(0.0484185\pi\)
\(12\) −3.60097 −1.03951
\(13\) 1.25409 3.38042i 0.347823 0.937560i
\(14\) 0.710287 0.189832
\(15\) 1.55274 2.68942i 0.400915 0.694406i
\(16\) −0.613742 + 1.06303i −0.153436 + 0.265758i
\(17\) −1.95169 3.38042i −0.473354 0.819873i 0.526181 0.850373i \(-0.323623\pi\)
−0.999535 + 0.0304998i \(0.990290\pi\)
\(18\) −1.98731 −0.468413
\(19\) 2.94534 + 5.10148i 0.675708 + 1.17036i 0.976261 + 0.216595i \(0.0694952\pi\)
−0.300554 + 0.953765i \(0.597171\pi\)
\(20\) −0.964379 1.67035i −0.215642 0.373502i
\(21\) −2.40788 −0.525443
\(22\) −0.855143 1.48115i −0.182317 0.315783i
\(23\) 3.16197 5.47670i 0.659317 1.14197i −0.321475 0.946918i \(-0.604179\pi\)
0.980793 0.195053i \(-0.0624879\pi\)
\(24\) −2.98915 + 5.17736i −0.610157 + 1.05682i
\(25\) −3.33664 −0.667328
\(26\) −1.63400 1.97196i −0.320455 0.386733i
\(27\) −0.486640 −0.0936539
\(28\) −0.747746 + 1.29513i −0.141311 + 0.244757i
\(29\) −2.80683 + 4.86157i −0.521215 + 0.902772i 0.478480 + 0.878098i \(0.341188\pi\)
−0.999696 + 0.0246732i \(0.992145\pi\)
\(30\) −1.10289 1.91026i −0.201359 0.348764i
\(31\) 2.20578 0.396170 0.198085 0.980185i \(-0.436528\pi\)
0.198085 + 0.980185i \(0.436528\pi\)
\(32\) 2.91873 + 5.05540i 0.515964 + 0.893676i
\(33\) 2.89895 + 5.02113i 0.504642 + 0.874066i
\(34\) −2.77252 −0.475482
\(35\) −0.644857 1.11692i −0.109001 0.188795i
\(36\) 2.09212 3.62365i 0.348686 0.603942i
\(37\) 2.55908 4.43246i 0.420711 0.728693i −0.575298 0.817944i \(-0.695114\pi\)
0.996009 + 0.0892511i \(0.0284473\pi\)
\(38\) 4.18407 0.678746
\(39\) 5.53930 + 6.68497i 0.886998 + 1.07045i
\(40\) −3.20210 −0.506297
\(41\) 3.89260 6.74219i 0.607922 1.05295i −0.383660 0.923474i \(-0.625336\pi\)
0.991582 0.129478i \(-0.0413302\pi\)
\(42\) −0.855143 + 1.48115i −0.131951 + 0.228547i
\(43\) −0.144857 0.250899i −0.0220904 0.0382618i 0.854769 0.519009i \(-0.173699\pi\)
−0.876859 + 0.480747i \(0.840366\pi\)
\(44\) 3.60097 0.542867
\(45\) 1.80424 + 3.12504i 0.268961 + 0.465853i
\(46\) −2.24591 3.89003i −0.331141 0.573553i
\(47\) 1.27702 0.186273 0.0931364 0.995653i \(-0.470311\pi\)
0.0931364 + 0.995653i \(0.470311\pi\)
\(48\) −1.47782 2.55966i −0.213305 0.369455i
\(49\) −0.500000 + 0.866025i −0.0714286 + 0.123718i
\(50\) −1.18499 + 2.05245i −0.167582 + 0.290261i
\(51\) 9.39887 1.31610
\(52\) 5.31585 0.903480i 0.737175 0.125290i
\(53\) −13.6225 −1.87120 −0.935598 0.353067i \(-0.885139\pi\)
−0.935598 + 0.353067i \(0.885139\pi\)
\(54\) −0.172827 + 0.299345i −0.0235188 + 0.0407357i
\(55\) −1.55274 + 2.68942i −0.209371 + 0.362642i
\(56\) 1.24140 + 2.15017i 0.165889 + 0.287328i
\(57\) −14.1841 −1.87873
\(58\) 1.99365 + 3.45311i 0.261780 + 0.453416i
\(59\) 2.01528 + 3.49057i 0.262367 + 0.454433i 0.966870 0.255268i \(-0.0821636\pi\)
−0.704503 + 0.709701i \(0.748830\pi\)
\(60\) 4.64422 0.599566
\(61\) 2.30049 + 3.98456i 0.294547 + 0.510170i 0.974879 0.222733i \(-0.0714979\pi\)
−0.680332 + 0.732904i \(0.738165\pi\)
\(62\) 0.783368 1.35683i 0.0994878 0.172318i
\(63\) 1.39895 2.42305i 0.176251 0.305276i
\(64\) 1.69131 0.211413
\(65\) −1.61742 + 4.35978i −0.200616 + 0.540764i
\(66\) 4.11817 0.506912
\(67\) −3.78779 + 6.56065i −0.462753 + 0.801511i −0.999097 0.0424881i \(-0.986472\pi\)
0.536344 + 0.843999i \(0.319805\pi\)
\(68\) 2.91873 5.05540i 0.353949 0.613057i
\(69\) 7.61366 + 13.1872i 0.916577 + 1.58756i
\(70\) −0.916066 −0.109491
\(71\) −3.61366 6.25905i −0.428863 0.742812i 0.567910 0.823091i \(-0.307752\pi\)
−0.996772 + 0.0802788i \(0.974419\pi\)
\(72\) −3.47331 6.01595i −0.409334 0.708987i
\(73\) −15.0125 −1.75708 −0.878542 0.477665i \(-0.841483\pi\)
−0.878542 + 0.477665i \(0.841483\pi\)
\(74\) −1.81768 3.14832i −0.211301 0.365985i
\(75\) 4.01712 6.95785i 0.463857 0.803424i
\(76\) −4.40474 + 7.62923i −0.505258 + 0.875133i
\(77\) 2.40788 0.274404
\(78\) 6.07935 1.03324i 0.688350 0.116992i
\(79\) −9.30758 −1.04718 −0.523592 0.851969i \(-0.675408\pi\)
−0.523592 + 0.851969i \(0.675408\pi\)
\(80\) 0.791552 1.37101i 0.0884982 0.153283i
\(81\) 4.78273 8.28393i 0.531415 0.920437i
\(82\) −2.76486 4.78888i −0.305328 0.528844i
\(83\) −1.36463 −0.149788 −0.0748940 0.997192i \(-0.523862\pi\)
−0.0748940 + 0.997192i \(0.523862\pi\)
\(84\) −1.80049 3.11853i −0.196449 0.340260i
\(85\) 2.51712 + 4.35978i 0.273020 + 0.472884i
\(86\) −0.205780 −0.0221898
\(87\) −6.75852 11.7061i −0.724589 1.25503i
\(88\) 2.98915 5.17736i 0.318644 0.551908i
\(89\) 0.449849 0.779162i 0.0476839 0.0825910i −0.841198 0.540727i \(-0.818149\pi\)
0.888882 + 0.458136i \(0.151483\pi\)
\(90\) 2.56306 0.270170
\(91\) 3.55458 0.604136i 0.372621 0.0633306i
\(92\) 9.45742 0.986004
\(93\) −2.65563 + 4.59968i −0.275376 + 0.476965i
\(94\) 0.453526 0.785530i 0.0467776 0.0810212i
\(95\) −3.79865 6.57945i −0.389733 0.675037i
\(96\) −14.0559 −1.43458
\(97\) −7.83288 13.5669i −0.795309 1.37752i −0.922643 0.385655i \(-0.873975\pi\)
0.127334 0.991860i \(-0.459358\pi\)
\(98\) 0.355143 + 0.615126i 0.0358749 + 0.0621371i
\(99\) −6.73701 −0.677095
\(100\) −2.49496 4.32140i −0.249496 0.432140i
\(101\) −0.342452 + 0.593145i −0.0340753 + 0.0590201i −0.882560 0.470200i \(-0.844182\pi\)
0.848485 + 0.529220i \(0.177515\pi\)
\(102\) 3.33795 5.78149i 0.330506 0.572453i
\(103\) 17.9249 1.76619 0.883097 0.469190i \(-0.155454\pi\)
0.883097 + 0.469190i \(0.155454\pi\)
\(104\) 3.11366 8.39292i 0.305320 0.822993i
\(105\) 3.10548 0.303064
\(106\) −4.83795 + 8.37957i −0.469903 + 0.813895i
\(107\) −4.24775 + 7.35731i −0.410645 + 0.711258i −0.994960 0.100268i \(-0.968030\pi\)
0.584315 + 0.811527i \(0.301363\pi\)
\(108\) −0.363883 0.630264i −0.0350147 0.0606472i
\(109\) 12.0928 1.15828 0.579139 0.815228i \(-0.303389\pi\)
0.579139 + 0.815228i \(0.303389\pi\)
\(110\) 1.10289 + 1.91026i 0.105156 + 0.182136i
\(111\) 6.16197 + 10.6729i 0.584869 + 1.01302i
\(112\) −1.22748 −0.115986
\(113\) 7.12635 + 12.3432i 0.670391 + 1.16115i 0.977793 + 0.209571i \(0.0672069\pi\)
−0.307402 + 0.951580i \(0.599460\pi\)
\(114\) −5.03738 + 8.72500i −0.471794 + 0.817171i
\(115\) −4.07804 + 7.06337i −0.380279 + 0.658663i
\(116\) −8.39519 −0.779474
\(117\) −9.94534 + 1.69031i −0.919447 + 0.156269i
\(118\) 2.86285 0.263547
\(119\) 1.95169 3.38042i 0.178911 0.309883i
\(120\) 3.85514 6.67730i 0.351925 0.609552i
\(121\) 2.60105 + 4.50515i 0.236459 + 0.409559i
\(122\) 3.26801 0.295872
\(123\) 9.37293 + 16.2344i 0.845129 + 1.46381i
\(124\) 1.64936 + 2.85678i 0.148117 + 0.256547i
\(125\) 10.7519 0.961677
\(126\) −0.993655 1.72106i −0.0885218 0.153324i
\(127\) 4.41231 7.64234i 0.391529 0.678148i −0.601122 0.799157i \(-0.705280\pi\)
0.992651 + 0.121009i \(0.0386129\pi\)
\(128\) −5.23681 + 9.07043i −0.462873 + 0.801720i
\(129\) 0.697596 0.0614199
\(130\) 2.10740 + 2.54326i 0.184831 + 0.223059i
\(131\) −19.4294 −1.69756 −0.848778 0.528749i \(-0.822661\pi\)
−0.848778 + 0.528749i \(0.822661\pi\)
\(132\) −4.33536 + 7.50906i −0.377344 + 0.653580i
\(133\) −2.94534 + 5.10148i −0.255394 + 0.442355i
\(134\) 2.69042 + 4.65994i 0.232417 + 0.402558i
\(135\) 0.627626 0.0540174
\(136\) −4.84565 8.39292i −0.415511 0.719687i
\(137\) −5.11809 8.86479i −0.437268 0.757370i 0.560210 0.828351i \(-0.310720\pi\)
−0.997478 + 0.0709806i \(0.977387\pi\)
\(138\) 10.8158 0.920699
\(139\) −4.07361 7.05571i −0.345519 0.598457i 0.639929 0.768434i \(-0.278964\pi\)
−0.985448 + 0.169977i \(0.945631\pi\)
\(140\) 0.964379 1.67035i 0.0815049 0.141171i
\(141\) −1.53746 + 2.66296i −0.129477 + 0.224262i
\(142\) −5.13347 −0.430791
\(143\) −5.53930 6.68497i −0.463219 0.559025i
\(144\) 3.43438 0.286198
\(145\) 3.62001 6.27004i 0.300625 0.520698i
\(146\) −5.33160 + 9.23460i −0.441246 + 0.764261i
\(147\) −1.20394 2.08529i −0.0992994 0.171992i
\(148\) 7.65419 0.629170
\(149\) 4.89444 + 8.47742i 0.400968 + 0.694497i 0.993843 0.110797i \(-0.0353404\pi\)
−0.592875 + 0.805295i \(0.702007\pi\)
\(150\) −2.85330 4.94207i −0.232971 0.403518i
\(151\) 14.7407 1.19958 0.599790 0.800158i \(-0.295251\pi\)
0.599790 + 0.800158i \(0.295251\pi\)
\(152\) 7.31270 + 12.6660i 0.593138 + 1.02735i
\(153\) −5.46062 + 9.45807i −0.441465 + 0.764640i
\(154\) 0.855143 1.48115i 0.0689094 0.119355i
\(155\) −2.84482 −0.228502
\(156\) −4.51595 + 12.1728i −0.361565 + 0.974604i
\(157\) 20.5844 1.64282 0.821409 0.570340i \(-0.193189\pi\)
0.821409 + 0.570340i \(0.193189\pi\)
\(158\) −3.30553 + 5.72534i −0.262973 + 0.455483i
\(159\) 16.4007 28.4069i 1.30066 2.25281i
\(160\) −3.76433 6.52001i −0.297597 0.515452i
\(161\) 6.32395 0.498397
\(162\) −3.39711 5.88397i −0.266902 0.462288i
\(163\) 1.99043 + 3.44753i 0.155902 + 0.270031i 0.933387 0.358871i \(-0.116838\pi\)
−0.777485 + 0.628902i \(0.783505\pi\)
\(164\) 11.6427 0.909144
\(165\) −3.73881 6.47581i −0.291066 0.504141i
\(166\) −0.484640 + 0.839422i −0.0376154 + 0.0651518i
\(167\) −4.33923 + 7.51576i −0.335780 + 0.581587i −0.983634 0.180177i \(-0.942333\pi\)
0.647855 + 0.761764i \(0.275666\pi\)
\(168\) −5.97829 −0.461235
\(169\) −9.85451 8.47872i −0.758039 0.652209i
\(170\) 3.57575 0.274248
\(171\) 8.24076 14.2734i 0.630187 1.09152i
\(172\) 0.216632 0.375218i 0.0165180 0.0286101i
\(173\) −0.466967 0.808810i −0.0355028 0.0614927i 0.847728 0.530431i \(-0.177970\pi\)
−0.883231 + 0.468938i \(0.844637\pi\)
\(174\) −9.60097 −0.727848
\(175\) −1.66832 2.88961i −0.126113 0.218434i
\(176\) 1.47782 + 2.55966i 0.111395 + 0.192942i
\(177\) −9.70511 −0.729481
\(178\) −0.319522 0.553428i −0.0239492 0.0414812i
\(179\) −6.77305 + 11.7313i −0.506241 + 0.876836i 0.493733 + 0.869614i \(0.335632\pi\)
−0.999974 + 0.00722197i \(0.997701\pi\)
\(180\) −2.69823 + 4.67348i −0.201114 + 0.348340i
\(181\) −8.86269 −0.658759 −0.329379 0.944198i \(-0.606839\pi\)
−0.329379 + 0.944198i \(0.606839\pi\)
\(182\) 0.890765 2.40107i 0.0660279 0.177979i
\(183\) −11.0786 −0.818953
\(184\) 7.85056 13.5976i 0.578751 1.00243i
\(185\) −3.30049 + 5.71661i −0.242657 + 0.420293i
\(186\) 1.88626 + 3.26709i 0.138307 + 0.239555i
\(187\) −9.39887 −0.687313
\(188\) 0.954889 + 1.65392i 0.0696424 + 0.120624i
\(189\) −0.243320 0.421442i −0.0176989 0.0306554i
\(190\) −5.39626 −0.391486
\(191\) 7.68674 + 13.3138i 0.556193 + 0.963355i 0.997810 + 0.0661509i \(0.0210719\pi\)
−0.441616 + 0.897204i \(0.645595\pi\)
\(192\) −2.03623 + 3.52686i −0.146953 + 0.254529i
\(193\) 12.2477 21.2136i 0.881606 1.52699i 0.0320517 0.999486i \(-0.489796\pi\)
0.849555 0.527501i \(-0.176871\pi\)
\(194\) −11.1272 −0.798885
\(195\) −7.14411 8.62170i −0.511600 0.617413i
\(196\) −1.49549 −0.106821
\(197\) 3.35706 5.81460i 0.239181 0.414273i −0.721299 0.692624i \(-0.756454\pi\)
0.960479 + 0.278351i \(0.0897878\pi\)
\(198\) −2.39260 + 4.14411i −0.170035 + 0.294509i
\(199\) 2.43641 + 4.21998i 0.172712 + 0.299147i 0.939367 0.342913i \(-0.111414\pi\)
−0.766655 + 0.642059i \(0.778080\pi\)
\(200\) −8.28421 −0.585782
\(201\) −9.12056 15.7973i −0.643315 1.11425i
\(202\) 0.243239 + 0.421303i 0.0171143 + 0.0296428i
\(203\) −5.61366 −0.394002
\(204\) 7.02797 + 12.1728i 0.492056 + 0.852267i
\(205\) −5.02034 + 8.69549i −0.350636 + 0.607319i
\(206\) 6.36592 11.0261i 0.443534 0.768224i
\(207\) −17.6938 −1.22980
\(208\) 2.82381 + 3.40785i 0.195796 + 0.236292i
\(209\) 14.1841 0.981133
\(210\) 1.10289 1.91026i 0.0761066 0.131821i
\(211\) −1.84373 + 3.19344i −0.126928 + 0.219846i −0.922485 0.386033i \(-0.873845\pi\)
0.795557 + 0.605879i \(0.207178\pi\)
\(212\) −10.1862 17.6430i −0.699590 1.21173i
\(213\) 17.4025 1.19240
\(214\) 3.01712 + 5.22580i 0.206246 + 0.357228i
\(215\) 0.186824 + 0.323588i 0.0127413 + 0.0220685i
\(216\) −1.20823 −0.0822096
\(217\) 1.10289 + 1.91026i 0.0748690 + 0.129677i
\(218\) 4.29467 7.43859i 0.290872 0.503805i
\(219\) 18.0742 31.3054i 1.22134 2.11543i
\(220\) −4.64422 −0.313113
\(221\) −13.8748 + 2.35817i −0.933323 + 0.158628i
\(222\) 8.75354 0.587499
\(223\) −4.40713 + 7.63338i −0.295123 + 0.511169i −0.975014 0.222145i \(-0.928694\pi\)
0.679890 + 0.733314i \(0.262027\pi\)
\(224\) −2.91873 + 5.05540i −0.195016 + 0.337778i
\(225\) 4.66779 + 8.08484i 0.311186 + 0.538990i
\(226\) 10.1235 0.673406
\(227\) 6.72557 + 11.6490i 0.446391 + 0.773173i 0.998148 0.0608325i \(-0.0193756\pi\)
−0.551757 + 0.834005i \(0.686042\pi\)
\(228\) −10.6061 18.3703i −0.702406 1.21660i
\(229\) 6.81576 0.450398 0.225199 0.974313i \(-0.427697\pi\)
0.225199 + 0.974313i \(0.427697\pi\)
\(230\) 2.89658 + 5.01702i 0.190995 + 0.330812i
\(231\) −2.89895 + 5.02113i −0.190737 + 0.330366i
\(232\) −6.96881 + 12.0703i −0.457524 + 0.792456i
\(233\) −25.0672 −1.64221 −0.821105 0.570777i \(-0.806642\pi\)
−0.821105 + 0.570777i \(0.806642\pi\)
\(234\) −2.49227 + 6.71794i −0.162925 + 0.439166i
\(235\) −1.64699 −0.107438
\(236\) −3.01384 + 5.22012i −0.196184 + 0.339801i
\(237\) 11.2058 19.4090i 0.727894 1.26075i
\(238\) −1.38626 2.40107i −0.0898577 0.155638i
\(239\) −2.78521 −0.180160 −0.0900800 0.995935i \(-0.528712\pi\)
−0.0900800 + 0.995935i \(0.528712\pi\)
\(240\) 1.90596 + 3.30123i 0.123029 + 0.213093i
\(241\) −3.48915 6.04338i −0.224756 0.389288i 0.731490 0.681852i \(-0.238825\pi\)
−0.956246 + 0.292563i \(0.905492\pi\)
\(242\) 3.69498 0.237523
\(243\) 10.7863 + 18.6824i 0.691941 + 1.19848i
\(244\) −3.44036 + 5.95888i −0.220246 + 0.381478i
\(245\) 0.644857 1.11692i 0.0411984 0.0713577i
\(246\) 13.3149 0.848929
\(247\) 20.9389 3.55877i 1.33231 0.226439i
\(248\) 5.47651 0.347759
\(249\) 1.64294 2.84565i 0.104117 0.180336i
\(250\) 3.81846 6.61376i 0.241500 0.418291i
\(251\) 0.391515 + 0.678123i 0.0247122 + 0.0428028i 0.878117 0.478446i \(-0.158800\pi\)
−0.853405 + 0.521249i \(0.825466\pi\)
\(252\) 4.18424 0.263582
\(253\) −7.61366 13.1872i −0.478667 0.829075i
\(254\) −3.13400 5.42825i −0.196645 0.340599i
\(255\) −12.1218 −0.759099
\(256\) 5.41095 + 9.37203i 0.338184 + 0.585752i
\(257\) −1.62902 + 2.82155i −0.101616 + 0.176003i −0.912350 0.409410i \(-0.865734\pi\)
0.810735 + 0.585414i \(0.199068\pi\)
\(258\) 0.247746 0.429109i 0.0154240 0.0267152i
\(259\) 5.11817 0.318028
\(260\) −6.85592 + 1.16523i −0.425186 + 0.0722645i
\(261\) 15.7064 0.972205
\(262\) −6.90023 + 11.9516i −0.426298 + 0.738369i
\(263\) −14.7915 + 25.6196i −0.912081 + 1.57977i −0.100962 + 0.994890i \(0.532192\pi\)
−0.811119 + 0.584881i \(0.801141\pi\)
\(264\) 7.19752 + 12.4665i 0.442976 + 0.767258i
\(265\) 17.5691 1.07926
\(266\) 2.09204 + 3.62351i 0.128271 + 0.222172i
\(267\) 1.08318 + 1.87613i 0.0662898 + 0.114817i
\(268\) −11.3292 −0.692043
\(269\) −0.618249 1.07084i −0.0376953 0.0652902i 0.846562 0.532290i \(-0.178668\pi\)
−0.884258 + 0.467000i \(0.845335\pi\)
\(270\) 0.222897 0.386069i 0.0135651 0.0234954i
\(271\) −12.6036 + 21.8300i −0.765612 + 1.32608i 0.174311 + 0.984691i \(0.444230\pi\)
−0.939923 + 0.341388i \(0.889103\pi\)
\(272\) 4.79133 0.290517
\(273\) −3.01971 + 8.13966i −0.182761 + 0.492635i
\(274\) −7.27062 −0.439234
\(275\) −4.01712 + 6.95785i −0.242241 + 0.419574i
\(276\) −11.3862 + 19.7214i −0.685367 + 1.18709i
\(277\) −4.76801 8.25843i −0.286482 0.496201i 0.686486 0.727143i \(-0.259152\pi\)
−0.972967 + 0.230942i \(0.925819\pi\)
\(278\) −5.78687 −0.347073
\(279\) −3.08577 5.34471i −0.184740 0.319980i
\(280\) −1.60105 2.77310i −0.0956811 0.165725i
\(281\) 9.56546 0.570628 0.285314 0.958434i \(-0.407902\pi\)
0.285314 + 0.958434i \(0.407902\pi\)
\(282\) 1.09204 + 1.89146i 0.0650299 + 0.112635i
\(283\) −5.71602 + 9.90044i −0.339782 + 0.588520i −0.984392 0.175992i \(-0.943687\pi\)
0.644609 + 0.764512i \(0.277020\pi\)
\(284\) 5.40421 9.36036i 0.320681 0.555435i
\(285\) 18.2934 1.08361
\(286\) −6.07935 + 1.03324i −0.359479 + 0.0610971i
\(287\) 7.78521 0.459546
\(288\) 8.16632 14.1445i 0.481205 0.833472i
\(289\) 0.881831 1.52738i 0.0518724 0.0898457i
\(290\) −2.57124 4.45352i −0.150989 0.261520i
\(291\) 37.7213 2.21126
\(292\) −11.2256 19.4433i −0.656927 1.13783i
\(293\) 4.67781 + 8.10220i 0.273281 + 0.473336i 0.969700 0.244299i \(-0.0785579\pi\)
−0.696419 + 0.717635i \(0.745225\pi\)
\(294\) −1.71029 −0.0997459
\(295\) −2.59913 4.50183i −0.151327 0.262107i
\(296\) 6.35370 11.0049i 0.369301 0.639649i
\(297\) −0.585886 + 1.01478i −0.0339965 + 0.0588837i
\(298\) 6.95291 0.402771
\(299\) −14.5482 17.5571i −0.841341 1.01535i
\(300\) 12.0151 0.693695
\(301\) 0.144857 0.250899i 0.00834940 0.0144616i
\(302\) 5.23506 9.06738i 0.301244 0.521769i
\(303\) −0.824585 1.42822i −0.0473712 0.0820493i
\(304\) −7.23072 −0.414711
\(305\) −2.96697 5.13894i −0.169888 0.294255i
\(306\) 3.87861 + 6.71794i 0.221725 + 0.384039i
\(307\) 8.11449 0.463119 0.231559 0.972821i \(-0.425617\pi\)
0.231559 + 0.972821i \(0.425617\pi\)
\(308\) 1.80049 + 3.11853i 0.102592 + 0.177695i
\(309\) −21.5805 + 37.3786i −1.22767 + 2.12639i
\(310\) −1.01032 + 1.74993i −0.0573823 + 0.0993891i
\(311\) −8.64016 −0.489938 −0.244969 0.969531i \(-0.578778\pi\)
−0.244969 + 0.969531i \(0.578778\pi\)
\(312\) 13.7530 + 16.5975i 0.778609 + 0.939646i
\(313\) −5.22732 −0.295466 −0.147733 0.989027i \(-0.547198\pi\)
−0.147733 + 0.989027i \(0.547198\pi\)
\(314\) 7.31043 12.6620i 0.412551 0.714560i
\(315\) −1.80424 + 3.12504i −0.101658 + 0.176076i
\(316\) −6.95971 12.0546i −0.391514 0.678123i
\(317\) 11.1929 0.628657 0.314329 0.949314i \(-0.398221\pi\)
0.314329 + 0.949314i \(0.398221\pi\)
\(318\) −11.6492 20.1770i −0.653255 1.13147i
\(319\) 6.75852 + 11.7061i 0.378404 + 0.655416i
\(320\) −2.18130 −0.121938
\(321\) −10.2281 17.7155i −0.570875 0.988785i
\(322\) 2.24591 3.89003i 0.125160 0.216783i
\(323\) 11.4968 19.9130i 0.639698 1.10799i
\(324\) 14.3051 0.794727
\(325\) −4.18445 + 11.2792i −0.232112 + 0.625660i
\(326\) 2.82755 0.156604
\(327\) −14.5590 + 25.2169i −0.805115 + 1.39450i
\(328\) 9.66456 16.7395i 0.533636 0.924285i
\(329\) 0.638511 + 1.10593i 0.0352023 + 0.0609721i
\(330\) −5.31126 −0.292375
\(331\) −10.0234 17.3610i −0.550935 0.954247i −0.998207 0.0598495i \(-0.980938\pi\)
0.447272 0.894398i \(-0.352395\pi\)
\(332\) −1.02040 1.76738i −0.0560017 0.0969978i
\(333\) −14.3201 −0.784737
\(334\) 3.08210 + 5.33835i 0.168645 + 0.292101i
\(335\) 4.88517 8.46136i 0.266905 0.462294i
\(336\) 1.47782 2.55966i 0.0806217 0.139641i
\(337\) 18.5866 1.01248 0.506239 0.862393i \(-0.331035\pi\)
0.506239 + 0.862393i \(0.331035\pi\)
\(338\) −8.71525 + 3.05061i −0.474047 + 0.165931i
\(339\) −34.3188 −1.86394
\(340\) −3.76433 + 6.52001i −0.204150 + 0.353597i
\(341\) 2.65563 4.59968i 0.143810 0.249087i
\(342\) −5.85330 10.1382i −0.316510 0.548212i
\(343\) −1.00000 −0.0539949
\(344\) −0.359650 0.622933i −0.0193911 0.0335863i
\(345\) −9.81944 17.0078i −0.528661 0.915668i
\(346\) −0.663361 −0.0356625
\(347\) −11.1708 19.3484i −0.599681 1.03868i −0.992868 0.119220i \(-0.961961\pi\)
0.393186 0.919459i \(-0.371373\pi\)
\(348\) 10.1073 17.5064i 0.541809 0.938441i
\(349\) −4.39316 + 7.60917i −0.235160 + 0.407310i −0.959319 0.282323i \(-0.908895\pi\)
0.724159 + 0.689633i \(0.242228\pi\)
\(350\) −2.36997 −0.126680
\(351\) −0.610291 + 1.64505i −0.0325749 + 0.0878061i
\(352\) 14.0559 0.749184
\(353\) −3.85949 + 6.68483i −0.205420 + 0.355798i −0.950266 0.311438i \(-0.899189\pi\)
0.744847 + 0.667236i \(0.232523\pi\)
\(354\) −3.44671 + 5.96987i −0.183190 + 0.317295i
\(355\) 4.66059 + 8.07238i 0.247358 + 0.428437i
\(356\) 1.34549 0.0713110
\(357\) 4.69943 + 8.13966i 0.248720 + 0.430796i
\(358\) 4.81081 + 8.33256i 0.254259 + 0.440389i
\(359\) −10.5956 −0.559216 −0.279608 0.960114i \(-0.590205\pi\)
−0.279608 + 0.960114i \(0.590205\pi\)
\(360\) 4.47958 + 7.75886i 0.236094 + 0.408928i
\(361\) −7.85008 + 13.5967i −0.413162 + 0.715618i
\(362\) −3.14753 + 5.45167i −0.165430 + 0.286534i
\(363\) −12.5261 −0.657447
\(364\) 3.44036 + 4.15192i 0.180324 + 0.217620i
\(365\) 19.3619 1.01345
\(366\) −3.93449 + 6.81474i −0.205659 + 0.356212i
\(367\) −2.91033 + 5.04085i −0.151918 + 0.263130i −0.931933 0.362632i \(-0.881878\pi\)
0.780014 + 0.625762i \(0.215212\pi\)
\(368\) 3.88128 + 6.72257i 0.202325 + 0.350438i
\(369\) −21.7822 −1.13394
\(370\) 2.34429 + 4.06043i 0.121874 + 0.211092i
\(371\) −6.81126 11.7974i −0.353623 0.612493i
\(372\) −7.94295 −0.411823
\(373\) −13.0284 22.5659i −0.674587 1.16842i −0.976589 0.215112i \(-0.930988\pi\)
0.302002 0.953307i \(-0.402345\pi\)
\(374\) −3.33795 + 5.78149i −0.172601 + 0.298954i
\(375\) −12.9446 + 22.4207i −0.668458 + 1.15780i
\(376\) 3.17059 0.163511
\(377\) 12.9141 + 15.5851i 0.665112 + 0.802675i
\(378\) −0.345654 −0.0177785
\(379\) −7.82662 + 13.5561i −0.402026 + 0.696330i −0.993970 0.109649i \(-0.965027\pi\)
0.591944 + 0.805979i \(0.298361\pi\)
\(380\) 5.68085 9.83952i 0.291421 0.504757i
\(381\) 10.6243 + 18.4019i 0.544300 + 0.942756i
\(382\) 10.9196 0.558694
\(383\) 6.27939 + 10.8762i 0.320862 + 0.555749i 0.980666 0.195688i \(-0.0626941\pi\)
−0.659804 + 0.751438i \(0.729361\pi\)
\(384\) −12.6096 21.8405i −0.643482 1.11454i
\(385\) −3.10548 −0.158270
\(386\) −8.69935 15.0677i −0.442785 0.766927i
\(387\) −0.405294 + 0.701990i −0.0206023 + 0.0356842i
\(388\) 11.7140 20.2893i 0.594689 1.03003i
\(389\) −0.503007 −0.0255035 −0.0127517 0.999919i \(-0.504059\pi\)
−0.0127517 + 0.999919i \(0.504059\pi\)
\(390\) −7.84061 + 1.33259i −0.397025 + 0.0674783i
\(391\) −24.6847 −1.24836
\(392\) −1.24140 + 2.15017i −0.0627002 + 0.108600i
\(393\) 23.3919 40.5159i 1.17996 2.04376i
\(394\) −2.38448 4.13003i −0.120128 0.208068i
\(395\) 12.0041 0.603992
\(396\) −5.03757 8.72533i −0.253148 0.438464i
\(397\) 1.17522 + 2.03554i 0.0589827 + 0.102161i 0.894009 0.448049i \(-0.147881\pi\)
−0.835026 + 0.550210i \(0.814548\pi\)
\(398\) 3.46110 0.173489
\(399\) −7.09204 12.2838i −0.355046 0.614958i
\(400\) 2.04784 3.54696i 0.102392 0.177348i
\(401\) 17.3023 29.9685i 0.864037 1.49656i −0.00396357 0.999992i \(-0.501262\pi\)
0.868000 0.496564i \(-0.165405\pi\)
\(402\) −12.9564 −0.646208
\(403\) 2.76625 7.45647i 0.137797 0.371433i
\(404\) −1.02427 −0.0509593
\(405\) −6.16835 + 10.6839i −0.306508 + 0.530887i
\(406\) −1.99365 + 3.45311i −0.0989434 + 0.171375i
\(407\) −6.16197 10.6729i −0.305438 0.529034i
\(408\) 23.3355 1.15528
\(409\) 4.01205 + 6.94908i 0.198383 + 0.343610i 0.948004 0.318257i \(-0.103098\pi\)
−0.749621 + 0.661867i \(0.769764\pi\)
\(410\) 3.56588 + 6.17629i 0.176106 + 0.305025i
\(411\) 24.6475 1.21577
\(412\) 13.4033 + 23.2152i 0.660333 + 1.14373i
\(413\) −2.01528 + 3.49057i −0.0991654 + 0.171760i
\(414\) −6.28382 + 10.8839i −0.308833 + 0.534914i
\(415\) 1.75999 0.0863943
\(416\) 20.7497 3.52662i 1.01734 0.172907i
\(417\) 19.6176 0.960676
\(418\) 5.03738 8.72500i 0.246386 0.426754i
\(419\) 5.83472 10.1060i 0.285045 0.493712i −0.687575 0.726113i \(-0.741325\pi\)
0.972620 + 0.232401i \(0.0746582\pi\)
\(420\) 2.32211 + 4.02201i 0.113307 + 0.196254i
\(421\) −18.3381 −0.893746 −0.446873 0.894597i \(-0.647462\pi\)
−0.446873 + 0.894597i \(0.647462\pi\)
\(422\) 1.30958 + 2.26826i 0.0637494 + 0.110417i
\(423\) −1.78649 3.09429i −0.0868621 0.150449i
\(424\) −33.8220 −1.64254
\(425\) 6.51208 + 11.2792i 0.315882 + 0.547124i
\(426\) 6.18040 10.7048i 0.299441 0.518647i
\(427\) −2.30049 + 3.98456i −0.111328 + 0.192826i
\(428\) −12.7049 −0.614117
\(429\) 20.6091 3.50272i 0.995015 0.169113i
\(430\) 0.265397 0.0127986
\(431\) 15.6218 27.0577i 0.752474 1.30332i −0.194146 0.980973i \(-0.562194\pi\)
0.946620 0.322351i \(-0.104473\pi\)
\(432\) 0.298671 0.517314i 0.0143698 0.0248893i
\(433\) 15.2756 + 26.4582i 0.734100 + 1.27150i 0.955117 + 0.296229i \(0.0957291\pi\)
−0.221017 + 0.975270i \(0.570938\pi\)
\(434\) 1.56674 0.0752057
\(435\) 8.71655 + 15.0975i 0.417927 + 0.723870i
\(436\) 9.04234 + 15.6618i 0.433049 + 0.750064i
\(437\) 37.2524 1.78202
\(438\) −12.8379 22.2358i −0.613417 1.06247i
\(439\) 6.07361 10.5198i 0.289878 0.502083i −0.683903 0.729573i \(-0.739719\pi\)
0.973780 + 0.227490i \(0.0730520\pi\)
\(440\) −3.85514 + 6.67730i −0.183787 + 0.318328i
\(441\) 2.79790 0.133233
\(442\) −3.47699 + 9.37227i −0.165384 + 0.445794i
\(443\) −8.46532 −0.402200 −0.201100 0.979571i \(-0.564452\pi\)
−0.201100 + 0.979571i \(0.564452\pi\)
\(444\) −9.21519 + 15.9612i −0.437333 + 0.757484i
\(445\) −0.580177 + 1.00490i −0.0275030 + 0.0476366i
\(446\) 3.13033 + 5.42189i 0.148225 + 0.256734i
\(447\) −23.5705 −1.11485
\(448\) 0.845654 + 1.46472i 0.0399534 + 0.0692013i
\(449\) 11.6632 + 20.2013i 0.550420 + 0.953356i 0.998244 + 0.0592342i \(0.0188659\pi\)
−0.447824 + 0.894122i \(0.647801\pi\)
\(450\) 6.63093 0.312585
\(451\) −9.37293 16.2344i −0.441354 0.764448i
\(452\) −10.6574 + 18.4592i −0.501282 + 0.868247i
\(453\) −17.7469 + 30.7386i −0.833823 + 1.44422i
\(454\) 9.55416 0.448399
\(455\) −4.58439 + 0.779162i −0.214919 + 0.0365277i
\(456\) −35.2162 −1.64915
\(457\) −7.74332 + 13.4118i −0.362217 + 0.627379i −0.988325 0.152358i \(-0.951313\pi\)
0.626108 + 0.779736i \(0.284647\pi\)
\(458\) 2.42057 4.19256i 0.113106 0.195905i
\(459\) 0.949769 + 1.64505i 0.0443314 + 0.0767842i
\(460\) −12.1974 −0.568705
\(461\) 4.64102 + 8.03848i 0.216154 + 0.374389i 0.953629 0.300985i \(-0.0973154\pi\)
−0.737475 + 0.675374i \(0.763982\pi\)
\(462\) 2.05908 + 3.56644i 0.0957973 + 0.165926i
\(463\) 28.8283 1.33976 0.669882 0.742467i \(-0.266345\pi\)
0.669882 + 0.742467i \(0.266345\pi\)
\(464\) −3.44534 5.96751i −0.159946 0.277035i
\(465\) 3.42500 5.93227i 0.158831 0.275103i
\(466\) −8.90246 + 15.4195i −0.412399 + 0.714295i
\(467\) −2.87393 −0.132990 −0.0664948 0.997787i \(-0.521182\pi\)
−0.0664948 + 0.997787i \(0.521182\pi\)
\(468\) −9.62577 11.6166i −0.444951 0.536979i
\(469\) −7.57559 −0.349808
\(470\) −0.584919 + 1.01311i −0.0269803 + 0.0467312i
\(471\) −24.7825 + 42.9245i −1.14192 + 1.97786i
\(472\) 5.00354 + 8.66638i 0.230307 + 0.398903i
\(473\) −0.697596 −0.0320755
\(474\) −7.95932 13.7859i −0.365583 0.633209i
\(475\) −9.82754 17.0218i −0.450919 0.781014i
\(476\) 5.83747 0.267560
\(477\) 19.0572 + 33.0080i 0.872569 + 1.51133i
\(478\) −0.989147 + 1.71325i −0.0452425 + 0.0783624i
\(479\) 11.3041 19.5792i 0.516497 0.894598i −0.483320 0.875444i \(-0.660569\pi\)
0.999817 0.0191546i \(-0.00609749\pi\)
\(480\) 18.1281 0.827432
\(481\) −11.7743 14.2095i −0.536861 0.647898i
\(482\) −4.95659 −0.225766
\(483\) −7.61366 + 13.1872i −0.346434 + 0.600041i
\(484\) −3.88985 + 6.73742i −0.176812 + 0.306247i
\(485\) 10.1022 + 17.4975i 0.458716 + 0.794519i
\(486\) 15.3227 0.695053
\(487\) −1.43401 2.48379i −0.0649814 0.112551i 0.831704 0.555219i \(-0.187365\pi\)
−0.896686 + 0.442668i \(0.854032\pi\)
\(488\) 5.71165 + 9.89287i 0.258554 + 0.447829i
\(489\) −9.58544 −0.433469
\(490\) −0.458033 0.793337i −0.0206918 0.0358393i
\(491\) 11.3600 19.6762i 0.512672 0.887973i −0.487220 0.873279i \(-0.661989\pi\)
0.999892 0.0146943i \(-0.00467751\pi\)
\(492\) −14.0172 + 24.2784i −0.631942 + 1.09456i
\(493\) 21.9122 0.986877
\(494\) 5.24721 14.1439i 0.236083 0.636366i
\(495\) 8.68881 0.390533
\(496\) −1.35378 + 2.34482i −0.0607865 + 0.105285i
\(497\) 3.61366 6.25905i 0.162095 0.280757i
\(498\) −1.16696 2.02123i −0.0522926 0.0905734i
\(499\) −18.0151 −0.806466 −0.403233 0.915097i \(-0.632114\pi\)
−0.403233 + 0.915097i \(0.632114\pi\)
\(500\) 8.03968 + 13.9251i 0.359545 + 0.622751i
\(501\) −10.4483 18.0971i −0.466798 0.808518i
\(502\) 0.556175 0.0248233
\(503\) 15.5748 + 26.9764i 0.694447 + 1.20282i 0.970367 + 0.241636i \(0.0776841\pi\)
−0.275920 + 0.961181i \(0.588983\pi\)
\(504\) 3.47331 6.01595i 0.154714 0.267972i
\(505\) 0.441665 0.764987i 0.0196539 0.0340415i
\(506\) −10.8158 −0.480819
\(507\) 29.5448 10.3416i 1.31213 0.459286i
\(508\) 13.1972 0.585529
\(509\) 19.7509 34.2096i 0.875444 1.51631i 0.0191556 0.999817i \(-0.493902\pi\)
0.856289 0.516497i \(-0.172764\pi\)
\(510\) −4.30499 + 7.45647i −0.190628 + 0.330178i
\(511\) −7.50626 13.0012i −0.332058 0.575141i
\(512\) −13.2606 −0.586042
\(513\) −1.43332 2.48258i −0.0632826 0.109609i
\(514\) 1.15707 + 2.00411i 0.0510363 + 0.0883974i
\(515\) −23.1180 −1.01870
\(516\) 0.521625 + 0.903480i 0.0229632 + 0.0397735i
\(517\) 1.53746 2.66296i 0.0676174 0.117117i
\(518\) 1.81768 3.14832i 0.0798644 0.138329i
\(519\) 2.24880 0.0987115
\(520\) −4.01573 + 10.8245i −0.176101 + 0.474684i
\(521\) −17.7672 −0.778394 −0.389197 0.921155i \(-0.627247\pi\)
−0.389197 + 0.921155i \(0.627247\pi\)
\(522\) 5.57804 9.66145i 0.244144 0.422870i
\(523\) 0.894522 1.54936i 0.0391147 0.0677487i −0.845805 0.533492i \(-0.820880\pi\)
0.884920 + 0.465743i \(0.154213\pi\)
\(524\) −14.5283 25.1637i −0.634671 1.09928i
\(525\) 8.03424 0.350643
\(526\) 10.5062 + 18.1972i 0.458091 + 0.793438i
\(527\) −4.30499 7.45647i −0.187528 0.324809i
\(528\) −7.11683 −0.309720
\(529\) −8.49616 14.7158i −0.369398 0.639817i
\(530\) 6.23956 10.8072i 0.271029 0.469436i
\(531\) 5.63854 9.76624i 0.244692 0.423819i
\(532\) −8.80948 −0.381939
\(533\) −17.9098 21.6140i −0.775758 0.936205i
\(534\) 1.53874 0.0665879
\(535\) 5.47838 9.48882i 0.236851 0.410238i
\(536\) −9.40434 + 16.2888i −0.406206 + 0.703569i
\(537\) −16.3087 28.2475i −0.703772 1.21897i
\(538\) −0.878269 −0.0378649
\(539\) 1.20394 + 2.08529i 0.0518574 + 0.0898197i
\(540\) 0.469305 + 0.812860i 0.0201957 + 0.0349799i
\(541\) 15.4027 0.662214 0.331107 0.943593i \(-0.392578\pi\)
0.331107 + 0.943593i \(0.392578\pi\)
\(542\) 8.95214 + 15.5056i 0.384527 + 0.666021i
\(543\) 10.6702 18.4813i 0.457900 0.793107i
\(544\) 11.3929 19.7331i 0.488467 0.846050i
\(545\) −15.5962 −0.668069
\(546\) 3.93449 + 4.74825i 0.168381 + 0.203206i
\(547\) −3.96944 −0.169721 −0.0848605 0.996393i \(-0.527044\pi\)
−0.0848605 + 0.996393i \(0.527044\pi\)
\(548\) 7.65406 13.2572i 0.326965 0.566321i
\(549\) 6.43652 11.1484i 0.274704 0.475801i
\(550\) 2.85330 + 4.94207i 0.121665 + 0.210731i
\(551\) −33.0683 −1.40876
\(552\) 18.9032 + 32.7413i 0.804574 + 1.39356i
\(553\) −4.65379 8.06060i −0.197899 0.342772i
\(554\) −6.77331 −0.287770
\(555\) −7.94718 13.7649i −0.337339 0.584288i
\(556\) 6.09206 10.5518i 0.258361 0.447494i
\(557\) −9.34504 + 16.1861i −0.395962 + 0.685826i −0.993223 0.116220i \(-0.962922\pi\)
0.597261 + 0.802047i \(0.296255\pi\)
\(558\) −4.38357 −0.185571
\(559\) −1.02981 + 0.175026i −0.0435563 + 0.00740282i
\(560\) 1.58310 0.0668983
\(561\) 11.3157 19.5993i 0.477749 0.827485i
\(562\) 3.39711 5.88397i 0.143298 0.248200i
\(563\) −18.1530 31.4418i −0.765056 1.32512i −0.940217 0.340576i \(-0.889378\pi\)
0.175161 0.984540i \(-0.443955\pi\)
\(564\) −4.59852 −0.193633
\(565\) −9.19095 15.9192i −0.386666 0.669726i
\(566\) 4.06001 + 7.03215i 0.170655 + 0.295583i
\(567\) 9.56546 0.401712
\(568\) −8.97201 15.5400i −0.376457 0.652043i
\(569\) −5.48798 + 9.50546i −0.230068 + 0.398489i −0.957828 0.287343i \(-0.907228\pi\)
0.727760 + 0.685832i \(0.240562\pi\)
\(570\) 6.49678 11.2527i 0.272120 0.471326i
\(571\) 31.3363 1.31138 0.655692 0.755028i \(-0.272377\pi\)
0.655692 + 0.755028i \(0.272377\pi\)
\(572\) 4.51595 12.1728i 0.188821 0.508970i
\(573\) −37.0175 −1.54643
\(574\) 2.76486 4.78888i 0.115403 0.199884i
\(575\) −10.5504 + 18.2738i −0.439981 + 0.762069i
\(576\) −2.36605 4.09812i −0.0985855 0.170755i
\(577\) −42.7876 −1.78127 −0.890636 0.454717i \(-0.849740\pi\)
−0.890636 + 0.454717i \(0.849740\pi\)
\(578\) −0.626353 1.08487i −0.0260528 0.0451248i
\(579\) 29.4909 + 51.0798i 1.22560 + 2.12280i
\(580\) 10.8274 0.449583
\(581\) −0.682316 1.18181i −0.0283073 0.0490296i
\(582\) 13.3965 23.2034i 0.555302 0.961811i
\(583\) −16.4007 + 28.4069i −0.679248 + 1.17649i
\(584\) −37.2731 −1.54237
\(585\) 12.8266 2.18001i 0.530316 0.0901325i
\(586\) 6.64517 0.274509
\(587\) 19.3943 33.5919i 0.800488 1.38649i −0.118808 0.992917i \(-0.537907\pi\)
0.919296 0.393568i \(-0.128759\pi\)
\(588\) 1.80049 3.11853i 0.0742508 0.128606i
\(589\) 6.49678 + 11.2527i 0.267695 + 0.463661i
\(590\) −3.69226 −0.152008
\(591\) 8.08341 + 14.0009i 0.332507 + 0.575919i
\(592\) 3.14124 + 5.44078i 0.129104 + 0.223615i
\(593\) −29.9564 −1.23016 −0.615081 0.788464i \(-0.710877\pi\)
−0.615081 + 0.788464i \(0.710877\pi\)
\(594\) 0.416147 + 0.720787i 0.0170747 + 0.0295743i
\(595\) −2.51712 + 4.35978i −0.103192 + 0.178733i
\(596\) −7.31960 + 12.6779i −0.299823 + 0.519308i
\(597\) −11.7332 −0.480207
\(598\) −15.9665 + 2.71367i −0.652919 + 0.110970i
\(599\) 41.2539 1.68559 0.842794 0.538236i \(-0.180909\pi\)
0.842794 + 0.538236i \(0.180909\pi\)
\(600\) 9.97371 17.2750i 0.407175 0.705248i
\(601\) −3.30544 + 5.72520i −0.134832 + 0.233536i −0.925533 0.378666i \(-0.876383\pi\)
0.790701 + 0.612202i \(0.209716\pi\)
\(602\) −0.102890 0.178210i −0.00419347 0.00726331i
\(603\) 21.1957 0.863156
\(604\) 11.0223 + 19.0912i 0.448491 + 0.776809i
\(605\) −3.35461 5.81036i −0.136384 0.236225i
\(606\) −1.17138 −0.0475842
\(607\) 10.4416 + 18.0854i 0.423811 + 0.734062i 0.996309 0.0858444i \(-0.0273588\pi\)
−0.572498 + 0.819906i \(0.694025\pi\)
\(608\) −17.1933 + 29.7797i −0.697282 + 1.20773i
\(609\) 6.75852 11.7061i 0.273869 0.474355i
\(610\) −4.21479 −0.170652
\(611\) 1.60150 4.31687i 0.0647899 0.174642i
\(612\) −16.3326 −0.660208
\(613\) 2.14828 3.72092i 0.0867680 0.150287i −0.819375 0.573258i \(-0.805679\pi\)
0.906143 + 0.422971i \(0.139013\pi\)
\(614\) 2.88181 4.99144i 0.116300 0.201438i
\(615\) −12.0884 20.9377i −0.487451 0.844290i
\(616\) 5.97829 0.240872
\(617\) 15.3690 + 26.6199i 0.618732 + 1.07167i 0.989717 + 0.143036i \(0.0456866\pi\)
−0.370986 + 0.928639i \(0.620980\pi\)
\(618\) 15.3284 + 26.5495i 0.616598 + 1.06798i
\(619\) −20.6417 −0.829658 −0.414829 0.909899i \(-0.636159\pi\)
−0.414829 + 0.909899i \(0.636159\pi\)
\(620\) −2.12721 3.68443i −0.0854307 0.147970i
\(621\) −1.53874 + 2.66518i −0.0617476 + 0.106950i
\(622\) −3.06849 + 5.31479i −0.123035 + 0.213104i
\(623\) 0.899698 0.0360457
\(624\) −10.5060 + 1.78561i −0.420578 + 0.0714815i
\(625\) 2.81636 0.112654
\(626\) −1.85645 + 3.21546i −0.0741986 + 0.128516i
\(627\) −17.0768 + 29.5779i −0.681981 + 1.18123i
\(628\) 15.3919 + 26.6596i 0.614205 + 1.06383i
\(629\) −19.9781 −0.796580
\(630\) 1.28153 + 2.21967i 0.0510574 + 0.0884339i
\(631\) −14.6683 25.4063i −0.583937 1.01141i −0.995007 0.0998043i \(-0.968178\pi\)
0.411070 0.911604i \(-0.365155\pi\)
\(632\) −23.1089 −0.919222
\(633\) −4.43950 7.68943i −0.176454 0.305628i
\(634\) 3.97509 6.88506i 0.157871 0.273441i
\(635\) −5.69061 + 9.85643i −0.225825 + 0.391141i
\(636\) 49.0543 1.94513
\(637\) 2.30049 + 2.77629i 0.0911486 + 0.110000i
\(638\) 9.60097 0.380106
\(639\) −10.1107 + 17.5122i −0.399971 + 0.692771i
\(640\) 6.75399 11.6983i 0.266975 0.462414i
\(641\) 2.00840 + 3.47865i 0.0793271 + 0.137399i 0.902960 0.429725i \(-0.141390\pi\)
−0.823633 + 0.567124i \(0.808056\pi\)
\(642\) −14.5297 −0.573443
\(643\) 3.43641 + 5.95203i 0.135519 + 0.234725i 0.925795 0.378025i \(-0.123397\pi\)
−0.790277 + 0.612750i \(0.790063\pi\)
\(644\) 4.72871 + 8.19037i 0.186337 + 0.322746i
\(645\) −0.899698 −0.0354256
\(646\) −8.16601 14.1439i −0.321287 0.556486i
\(647\) 16.8715 29.2224i 0.663289 1.14885i −0.316457 0.948607i \(-0.602493\pi\)
0.979746 0.200243i \(-0.0641732\pi\)
\(648\) 11.8746 20.5674i 0.466477 0.807962i
\(649\) 9.70511 0.380959
\(650\) 5.45208 + 6.57972i 0.213848 + 0.258078i
\(651\) −5.31126 −0.208165
\(652\) −2.97667 + 5.15575i −0.116576 + 0.201915i
\(653\) −16.2001 + 28.0594i −0.633958 + 1.09805i 0.352777 + 0.935708i \(0.385238\pi\)
−0.986735 + 0.162340i \(0.948096\pi\)
\(654\) 10.3411 + 17.9113i 0.404368 + 0.700385i
\(655\) 25.0584 0.979112
\(656\) 4.77811 + 8.27593i 0.186554 + 0.323121i
\(657\) 21.0018 + 36.3761i 0.819357 + 1.41917i
\(658\) 0.907052 0.0353606
\(659\) −2.00518 3.47307i −0.0781106 0.135291i 0.824324 0.566118i \(-0.191555\pi\)
−0.902435 + 0.430827i \(0.858222\pi\)
\(660\) 5.59137 9.68453i 0.217644 0.376970i
\(661\) 0.908971 1.57438i 0.0353549 0.0612364i −0.847807 0.530306i \(-0.822077\pi\)
0.883161 + 0.469069i \(0.155411\pi\)
\(662\) −14.2389 −0.553412
\(663\) 11.7870 31.7721i 0.457771 1.23393i
\(664\) −3.38811 −0.131484
\(665\) 3.79865 6.57945i 0.147305 0.255140i
\(666\) −5.08569 + 8.80868i −0.197067 + 0.341329i
\(667\) 17.7503 + 30.7443i 0.687293 + 1.19043i
\(668\) −12.9786 −0.502156
\(669\) −10.6119 18.3803i −0.410278 0.710622i
\(670\) −3.46987 6.00999i −0.134053 0.232186i
\(671\) 11.0786 0.427684
\(672\) −7.02797 12.1728i −0.271110 0.469576i
\(673\) 11.4871 19.8963i 0.442797 0.766947i −0.555099 0.831784i \(-0.687320\pi\)
0.997896 + 0.0648375i \(0.0206529\pi\)
\(674\) 6.60091 11.4331i 0.254258 0.440387i
\(675\) 1.62374 0.0624978
\(676\) 3.61241 19.1028i 0.138939 0.734725i
\(677\) 38.0276 1.46152 0.730760 0.682634i \(-0.239166\pi\)
0.730760 + 0.682634i \(0.239166\pi\)
\(678\) −12.1881 + 21.1104i −0.468081 + 0.810741i
\(679\) 7.83288 13.5669i 0.300598 0.520652i
\(680\) 6.24950 + 10.8245i 0.239658 + 0.415099i
\(681\) −32.3887 −1.24114
\(682\) −1.88626 3.26709i −0.0722285 0.125103i
\(683\) 20.3893 + 35.3153i 0.780176 + 1.35130i 0.931839 + 0.362872i \(0.118204\pi\)
−0.151663 + 0.988432i \(0.548463\pi\)
\(684\) 24.6480 0.942440
\(685\) 6.60087 + 11.4330i 0.252206 + 0.436834i
\(686\) −0.355143 + 0.615126i −0.0135594 + 0.0234856i
\(687\) −8.20578 + 14.2128i −0.313070 + 0.542253i
\(688\) 0.355619 0.0135578
\(689\) −17.0839 + 46.0499i −0.650844 + 1.75436i
\(690\) −13.9492 −0.531038
\(691\) 1.56434 2.70952i 0.0595104 0.103075i −0.834735 0.550651i \(-0.814379\pi\)
0.894246 + 0.447576i \(0.147713\pi\)
\(692\) 0.698346 1.20957i 0.0265471 0.0459809i
\(693\) −3.36850 5.83442i −0.127959 0.221631i
\(694\) −15.8690 −0.602378
\(695\) 5.25379 + 9.09984i 0.199288 + 0.345177i
\(696\) −16.7801 29.0639i −0.636047 1.10167i
\(697\) −30.3886 −1.15105
\(698\) 3.12040 + 5.40470i 0.118109 + 0.204571i
\(699\) 30.1795 52.2724i 1.14149 1.97712i
\(700\) 2.49496 4.32140i 0.0943006 0.163333i
\(701\) 9.61382 0.363109 0.181555 0.983381i \(-0.441887\pi\)
0.181555 + 0.983381i \(0.441887\pi\)
\(702\) 0.795171 + 0.959634i 0.0300118 + 0.0362190i
\(703\) 30.1495 1.13711
\(704\) 2.03623 3.52686i 0.0767435 0.132924i
\(705\) 1.98288 3.43445i 0.0746797 0.129349i
\(706\) 2.74134 + 4.74815i 0.103172 + 0.178699i
\(707\) −0.684905 −0.0257585
\(708\) −7.25696 12.5694i −0.272733 0.472388i
\(709\) −14.0647 24.3608i −0.528211 0.914889i −0.999459 0.0328880i \(-0.989530\pi\)
0.471248 0.882001i \(-0.343804\pi\)
\(710\) 6.62071 0.248471
\(711\) 13.0208 + 22.5527i 0.488319 + 0.845794i
\(712\) 1.11689 1.93450i 0.0418571 0.0724986i
\(713\) 6.97462 12.0804i 0.261201 0.452414i
\(714\) 6.67589 0.249839
\(715\) 7.14411 + 8.62170i 0.267174 + 0.322433i
\(716\) −20.2581 −0.757080
\(717\) 3.35322 5.80796i 0.125228 0.216902i
\(718\) −3.76297 + 6.51765i −0.140433 + 0.243237i
\(719\) −12.4522 21.5679i −0.464389 0.804346i 0.534784 0.844989i \(-0.320393\pi\)
−0.999174 + 0.0406425i \(0.987060\pi\)
\(720\) −4.42936 −0.165073
\(721\) 8.96246 + 15.5234i 0.333779 + 0.578123i
\(722\) 5.57581 + 9.65758i 0.207510 + 0.359418i
\(723\) 16.8029 0.624907
\(724\) −6.62705 11.4784i −0.246292 0.426591i
\(725\) 9.36538 16.2213i 0.347822 0.602445i
\(726\) −4.44854 + 7.70510i −0.165101 + 0.285963i
\(727\) −24.2120 −0.897974 −0.448987 0.893538i \(-0.648215\pi\)
−0.448987 + 0.893538i \(0.648215\pi\)
\(728\) 8.82531 1.49995i 0.327088 0.0555918i
\(729\) −23.2479 −0.861032
\(730\) 6.87624 11.9100i 0.254501 0.440808i
\(731\) −0.565430 + 0.979353i −0.0209132 + 0.0362227i
\(732\) −8.28398 14.3483i −0.306185 0.530328i
\(733\) −12.3989 −0.457963 −0.228981 0.973431i \(-0.573539\pi\)
−0.228981 + 0.973431i \(0.573539\pi\)
\(734\) 2.06717 + 3.58045i 0.0763007 + 0.132157i
\(735\) 1.55274 + 2.68942i 0.0572736 + 0.0992009i
\(736\) 36.9159 1.36074
\(737\) 9.12056 + 15.7973i 0.335960 + 0.581900i
\(738\) −7.73581 + 13.3988i −0.284759 + 0.493217i
\(739\) 5.48019 9.49197i 0.201592 0.349168i −0.747450 0.664319i \(-0.768722\pi\)
0.949042 + 0.315151i \(0.102055\pi\)
\(740\) −9.87170 −0.362891
\(741\) −17.7881 + 47.9482i −0.653463 + 1.76142i
\(742\) −9.67589 −0.355213
\(743\) −20.3462 + 35.2407i −0.746431 + 1.29286i 0.203092 + 0.979160i \(0.434901\pi\)
−0.949523 + 0.313697i \(0.898432\pi\)
\(744\) −6.59340 + 11.4201i −0.241726 + 0.418681i
\(745\) −6.31243 10.9334i −0.231269 0.400570i
\(746\) −18.5079 −0.677621
\(747\) 1.90905 + 3.30657i 0.0698485 + 0.120981i
\(748\) −7.02797 12.1728i −0.256968 0.445082i
\(749\) −8.49549 −0.310419
\(750\) 9.19439 + 15.9252i 0.335732 + 0.581505i
\(751\) −4.70236 + 8.14473i −0.171592 + 0.297205i −0.938976 0.343981i \(-0.888224\pi\)
0.767385 + 0.641187i \(0.221558\pi\)
\(752\) −0.783763 + 1.35752i −0.0285809 + 0.0495035i
\(753\) −1.88544 −0.0687093
\(754\) 14.1732 2.40888i 0.516157 0.0877261i
\(755\) −19.0113 −0.691890
\(756\) 0.363883 0.630264i 0.0132343 0.0229225i
\(757\) 14.7904 25.6177i 0.537566 0.931091i −0.461469 0.887156i \(-0.652677\pi\)
0.999034 0.0439345i \(-0.0139893\pi\)
\(758\) 5.55914 + 9.62872i 0.201917 + 0.349731i
\(759\) 36.6656 1.33088
\(760\) −9.43129 16.3355i −0.342109 0.592550i
\(761\) −8.47086 14.6720i −0.307068 0.531858i 0.670651 0.741773i \(-0.266015\pi\)
−0.977720 + 0.209915i \(0.932681\pi\)
\(762\) 15.0926 0.546748
\(763\) 6.04639 + 10.4727i 0.218894 + 0.379136i
\(764\) −11.4955 + 19.9107i −0.415891 + 0.720345i
\(765\) 7.04264 12.1982i 0.254627 0.441027i
\(766\) 8.92034 0.322305
\(767\) 14.3269 2.43500i 0.517316 0.0879229i
\(768\) −26.0578 −0.940281
\(769\) −3.68287 + 6.37892i −0.132808 + 0.230030i −0.924758 0.380556i \(-0.875733\pi\)
0.791950 + 0.610586i \(0.209066\pi\)
\(770\) −1.10289 + 1.91026i −0.0397454 + 0.0688410i
\(771\) −3.92249 6.79396i −0.141265 0.244678i
\(772\) 36.6326 1.31844
\(773\) 22.3867 + 38.7749i 0.805194 + 1.39464i 0.916160 + 0.400813i \(0.131272\pi\)
−0.110966 + 0.993824i \(0.535394\pi\)
\(774\) 0.287875 + 0.498614i 0.0103475 + 0.0179223i
\(775\) −7.35989 −0.264375
\(776\) −19.4475 33.6840i