Properties

Label 966.2.i.n.415.4
Level $966$
Weight $2$
Character 966.415
Analytic conductor $7.714$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 966.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.71354883526\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.173309020416.2
Defining polynomial: \( x^{8} - 5x^{6} - 28x^{5} - 4x^{4} + 70x^{3} + 51x^{2} + 406x + 841 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 415.4
Root \(-1.75834 + 0.512349i\) of defining polynomial
Character \(\chi\) \(=\) 966.415
Dual form 966.2.i.n.277.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.44864 - 2.50912i) q^{5} +1.00000 q^{6} +(-1.32288 - 2.29129i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.44864 - 2.50912i) q^{5} +1.00000 q^{6} +(-1.32288 - 2.29129i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.44864 - 2.50912i) q^{10} +(-0.809697 - 1.40244i) q^{11} +(0.500000 - 0.866025i) q^{12} -3.02636 q^{13} -2.64575 q^{14} +2.89728 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.77152 - 4.80040i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-1.38410 + 2.39733i) q^{19} -2.89728 q^{20} +(1.32288 - 2.29129i) q^{21} -1.61939 q^{22} +(-0.500000 + 0.866025i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-1.69711 - 2.93948i) q^{25} +(-1.51318 + 2.62090i) q^{26} -1.00000 q^{27} +(-1.32288 + 2.29129i) q^{28} +1.76820 q^{29} +(1.44864 - 2.50912i) q^{30} +(0.802888 + 1.39064i) q^{31} +(0.500000 + 0.866025i) q^{32} +(0.809697 - 1.40244i) q^{33} -5.54303 q^{34} -7.66548 q^{35} +1.00000 q^{36} +(0.513179 - 0.888851i) q^{37} +(1.38410 + 2.39733i) q^{38} +(-1.51318 - 2.62090i) q^{39} +(-1.44864 + 2.50912i) q^{40} +6.76820 q^{41} +(-1.32288 - 2.29129i) q^{42} +2.00000 q^{43} +(-0.809697 + 1.40244i) q^{44} +(1.44864 + 2.50912i) q^{45} +(0.500000 + 0.866025i) q^{46} +(2.07772 - 3.59871i) q^{47} -1.00000 q^{48} +(-3.50000 + 6.06218i) q^{49} -3.39422 q^{50} +(2.77152 - 4.80040i) q^{51} +(1.51318 + 2.62090i) q^{52} +(-2.44864 - 4.24117i) q^{53} +(-0.500000 + 0.866025i) q^{54} -4.69184 q^{55} +(1.32288 + 2.29129i) q^{56} -2.76820 q^{57} +(0.884100 - 1.53131i) q^{58} +(3.47849 + 6.02492i) q^{59} +(-1.44864 - 2.50912i) q^{60} +(6.89728 - 11.9464i) q^{61} +1.60578 q^{62} +2.64575 q^{63} +1.00000 q^{64} +(-4.38410 + 7.59348i) q^{65} +(-0.809697 - 1.40244i) q^{66} +(-3.61939 - 6.26897i) q^{67} +(-2.77152 + 4.80040i) q^{68} -1.00000 q^{69} +(-3.83274 + 6.63850i) q^{70} +4.87092 q^{71} +(0.500000 - 0.866025i) q^{72} +(-2.56803 - 4.44796i) q^{73} +(-0.513179 - 0.888851i) q^{74} +(1.69711 - 2.93948i) q^{75} +2.76820 q^{76} +(-2.14226 + 3.71050i) q^{77} -3.02636 q^{78} +(3.44532 - 5.96748i) q^{79} +(1.44864 + 2.50912i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(3.38410 - 5.86143i) q^{82} +5.15544 q^{83} -2.64575 q^{84} -16.0597 q^{85} +(1.00000 - 1.73205i) q^{86} +(0.884100 + 1.53131i) q^{87} +(0.809697 + 1.40244i) q^{88} +(7.28138 - 12.6117i) q^{89} +2.89728 q^{90} +(4.00349 + 6.93426i) q^{91} +1.00000 q^{92} +(-0.802888 + 1.39064i) q^{93} +(-2.07772 - 3.59871i) q^{94} +(4.01012 + 6.94574i) q^{95} +(-0.500000 + 0.866025i) q^{96} -14.6988 q^{97} +(3.50000 + 6.06218i) q^{98} +1.61939 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{2} + 4 q^{3} - 4 q^{4} - 2 q^{5} + 8 q^{6} - 8 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 4 q^{2} + 4 q^{3} - 4 q^{4} - 2 q^{5} + 8 q^{6} - 8 q^{8} - 4 q^{9} + 2 q^{10} - 6 q^{11} + 4 q^{12} - 4 q^{13} - 4 q^{15} - 4 q^{16} + 2 q^{17} + 4 q^{18} + 6 q^{19} + 4 q^{20} - 12 q^{22} - 4 q^{23} - 4 q^{24} - 6 q^{25} - 2 q^{26} - 8 q^{27} - 20 q^{29} - 2 q^{30} + 14 q^{31} + 4 q^{32} + 6 q^{33} + 4 q^{34} + 8 q^{36} - 6 q^{37} - 6 q^{38} - 2 q^{39} + 2 q^{40} + 20 q^{41} + 16 q^{43} - 6 q^{44} - 2 q^{45} + 4 q^{46} + 10 q^{47} - 8 q^{48} - 28 q^{49} - 12 q^{50} - 2 q^{51} + 2 q^{52} - 6 q^{53} - 4 q^{54} + 44 q^{55} + 12 q^{57} - 10 q^{58} - 24 q^{59} + 2 q^{60} + 28 q^{61} + 28 q^{62} + 8 q^{64} - 18 q^{65} - 6 q^{66} - 28 q^{67} + 2 q^{68} - 8 q^{69} + 32 q^{71} + 4 q^{72} - 6 q^{73} + 6 q^{74} + 6 q^{75} - 12 q^{76} - 14 q^{77} - 4 q^{78} + 4 q^{79} - 2 q^{80} - 4 q^{81} + 10 q^{82} + 28 q^{83} - 52 q^{85} + 8 q^{86} - 10 q^{87} + 6 q^{88} + 14 q^{89} - 4 q^{90} + 14 q^{91} + 8 q^{92} - 14 q^{93} - 10 q^{94} + 34 q^{95} - 4 q^{96} + 28 q^{98} + 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/966\mathbb{Z}\right)^\times\).

\(n\) \(323\) \(829\) \(925\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 1.44864 2.50912i 0.647851 1.12211i −0.335784 0.941939i \(-0.609001\pi\)
0.983635 0.180172i \(-0.0576655\pi\)
\(6\) 1.00000 0.408248
\(7\) −1.32288 2.29129i −0.500000 0.866025i
\(8\) −1.00000 −0.353553
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) −1.44864 2.50912i −0.458100 0.793452i
\(11\) −0.809697 1.40244i −0.244133 0.422851i 0.717755 0.696296i \(-0.245170\pi\)
−0.961887 + 0.273446i \(0.911837\pi\)
\(12\) 0.500000 0.866025i 0.144338 0.250000i
\(13\) −3.02636 −0.839360 −0.419680 0.907672i \(-0.637858\pi\)
−0.419680 + 0.907672i \(0.637858\pi\)
\(14\) −2.64575 −0.707107
\(15\) 2.89728 0.748074
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −2.77152 4.80040i −0.672191 1.16427i −0.977281 0.211946i \(-0.932020\pi\)
0.305090 0.952323i \(-0.401313\pi\)
\(18\) 0.500000 + 0.866025i 0.117851 + 0.204124i
\(19\) −1.38410 + 2.39733i −0.317534 + 0.549986i −0.979973 0.199131i \(-0.936188\pi\)
0.662439 + 0.749116i \(0.269522\pi\)
\(20\) −2.89728 −0.647851
\(21\) 1.32288 2.29129i 0.288675 0.500000i
\(22\) −1.61939 −0.345256
\(23\) −0.500000 + 0.866025i −0.104257 + 0.180579i
\(24\) −0.500000 0.866025i −0.102062 0.176777i
\(25\) −1.69711 2.93948i −0.339422 0.587897i
\(26\) −1.51318 + 2.62090i −0.296759 + 0.514001i
\(27\) −1.00000 −0.192450
\(28\) −1.32288 + 2.29129i −0.250000 + 0.433013i
\(29\) 1.76820 0.328347 0.164173 0.986432i \(-0.447504\pi\)
0.164173 + 0.986432i \(0.447504\pi\)
\(30\) 1.44864 2.50912i 0.264484 0.458100i
\(31\) 0.802888 + 1.39064i 0.144203 + 0.249767i 0.929075 0.369891i \(-0.120605\pi\)
−0.784872 + 0.619657i \(0.787272\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 0.809697 1.40244i 0.140950 0.244133i
\(34\) −5.54303 −0.950622
\(35\) −7.66548 −1.29570
\(36\) 1.00000 0.166667
\(37\) 0.513179 0.888851i 0.0843660 0.146126i −0.820755 0.571281i \(-0.806447\pi\)
0.905121 + 0.425154i \(0.139780\pi\)
\(38\) 1.38410 + 2.39733i 0.224531 + 0.388899i
\(39\) −1.51318 2.62090i −0.242302 0.419680i
\(40\) −1.44864 + 2.50912i −0.229050 + 0.396726i
\(41\) 6.76820 1.05702 0.528508 0.848929i \(-0.322752\pi\)
0.528508 + 0.848929i \(0.322752\pi\)
\(42\) −1.32288 2.29129i −0.204124 0.353553i
\(43\) 2.00000 0.304997 0.152499 0.988304i \(-0.451268\pi\)
0.152499 + 0.988304i \(0.451268\pi\)
\(44\) −0.809697 + 1.40244i −0.122066 + 0.211425i
\(45\) 1.44864 + 2.50912i 0.215950 + 0.374037i
\(46\) 0.500000 + 0.866025i 0.0737210 + 0.127688i
\(47\) 2.07772 3.59871i 0.303066 0.524926i −0.673763 0.738948i \(-0.735323\pi\)
0.976829 + 0.214022i \(0.0686563\pi\)
\(48\) −1.00000 −0.144338
\(49\) −3.50000 + 6.06218i −0.500000 + 0.866025i
\(50\) −3.39422 −0.480016
\(51\) 2.77152 4.80040i 0.388090 0.672191i
\(52\) 1.51318 + 2.62090i 0.209840 + 0.363454i
\(53\) −2.44864 4.24117i −0.336346 0.582569i 0.647396 0.762154i \(-0.275858\pi\)
−0.983743 + 0.179585i \(0.942525\pi\)
\(54\) −0.500000 + 0.866025i −0.0680414 + 0.117851i
\(55\) −4.69184 −0.632647
\(56\) 1.32288 + 2.29129i 0.176777 + 0.306186i
\(57\) −2.76820 −0.366657
\(58\) 0.884100 1.53131i 0.116088 0.201070i
\(59\) 3.47849 + 6.02492i 0.452861 + 0.784378i 0.998562 0.0536015i \(-0.0170701\pi\)
−0.545701 + 0.837980i \(0.683737\pi\)
\(60\) −1.44864 2.50912i −0.187019 0.323926i
\(61\) 6.89728 11.9464i 0.883106 1.52958i 0.0352369 0.999379i \(-0.488781\pi\)
0.847869 0.530206i \(-0.177885\pi\)
\(62\) 1.60578 0.203934
\(63\) 2.64575 0.333333
\(64\) 1.00000 0.125000
\(65\) −4.38410 + 7.59348i −0.543781 + 0.941856i
\(66\) −0.809697 1.40244i −0.0996668 0.172628i
\(67\) −3.61939 6.26897i −0.442179 0.765877i 0.555672 0.831402i \(-0.312461\pi\)
−0.997851 + 0.0655248i \(0.979128\pi\)
\(68\) −2.77152 + 4.80040i −0.336096 + 0.582135i
\(69\) −1.00000 −0.120386
\(70\) −3.83274 + 6.63850i −0.458100 + 0.793452i
\(71\) 4.87092 0.578072 0.289036 0.957318i \(-0.406665\pi\)
0.289036 + 0.957318i \(0.406665\pi\)
\(72\) 0.500000 0.866025i 0.0589256 0.102062i
\(73\) −2.56803 4.44796i −0.300566 0.520595i 0.675699 0.737178i \(-0.263842\pi\)
−0.976264 + 0.216583i \(0.930509\pi\)
\(74\) −0.513179 0.888851i −0.0596558 0.103327i
\(75\) 1.69711 2.93948i 0.195966 0.339422i
\(76\) 2.76820 0.317534
\(77\) −2.14226 + 3.71050i −0.244133 + 0.422851i
\(78\) −3.02636 −0.342667
\(79\) 3.44532 5.96748i 0.387629 0.671394i −0.604501 0.796604i \(-0.706627\pi\)
0.992130 + 0.125211i \(0.0399607\pi\)
\(80\) 1.44864 + 2.50912i 0.161963 + 0.280528i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 3.38410 5.86143i 0.373711 0.647287i
\(83\) 5.15544 0.565883 0.282941 0.959137i \(-0.408690\pi\)
0.282941 + 0.959137i \(0.408690\pi\)
\(84\) −2.64575 −0.288675
\(85\) −16.0597 −1.74192
\(86\) 1.00000 1.73205i 0.107833 0.186772i
\(87\) 0.884100 + 1.53131i 0.0947855 + 0.164173i
\(88\) 0.809697 + 1.40244i 0.0863140 + 0.149500i
\(89\) 7.28138 12.6117i 0.771825 1.33684i −0.164737 0.986337i \(-0.552678\pi\)
0.936562 0.350502i \(-0.113989\pi\)
\(90\) 2.89728 0.305400
\(91\) 4.00349 + 6.93426i 0.419680 + 0.726907i
\(92\) 1.00000 0.104257
\(93\) −0.802888 + 1.39064i −0.0832556 + 0.144203i
\(94\) −2.07772 3.59871i −0.214300 0.371179i
\(95\) 4.01012 + 6.94574i 0.411430 + 0.712618i
\(96\) −0.500000 + 0.866025i −0.0510310 + 0.0883883i
\(97\) −14.6988 −1.49244 −0.746220 0.665700i \(-0.768133\pi\)
−0.746220 + 0.665700i \(0.768133\pi\)
\(98\) 3.50000 + 6.06218i 0.353553 + 0.612372i
\(99\) 1.61939 0.162755
\(100\) −1.69711 + 2.93948i −0.169711 + 0.293948i
\(101\) 1.69711 + 2.93948i 0.168869 + 0.292490i 0.938022 0.346574i \(-0.112655\pi\)
−0.769154 + 0.639064i \(0.779322\pi\)
\(102\) −2.77152 4.80040i −0.274421 0.475311i
\(103\) 5.50986 9.54336i 0.542903 0.940336i −0.455833 0.890066i \(-0.650658\pi\)
0.998736 0.0502701i \(-0.0160082\pi\)
\(104\) 3.02636 0.296759
\(105\) −3.83274 6.63850i −0.374037 0.647851i
\(106\) −4.89728 −0.475666
\(107\) −4.57772 + 7.92884i −0.442545 + 0.766510i −0.997878 0.0651183i \(-0.979258\pi\)
0.555333 + 0.831628i \(0.312591\pi\)
\(108\) 0.500000 + 0.866025i 0.0481125 + 0.0833333i
\(109\) −5.28469 9.15336i −0.506182 0.876733i −0.999974 0.00715295i \(-0.997723\pi\)
0.493793 0.869580i \(-0.335610\pi\)
\(110\) −2.34592 + 4.06325i −0.223675 + 0.387416i
\(111\) 1.02636 0.0974175
\(112\) 2.64575 0.250000
\(113\) 3.76209 0.353908 0.176954 0.984219i \(-0.443376\pi\)
0.176954 + 0.984219i \(0.443376\pi\)
\(114\) −1.38410 + 2.39733i −0.129633 + 0.224531i
\(115\) 1.44864 + 2.50912i 0.135086 + 0.233976i
\(116\) −0.884100 1.53131i −0.0820866 0.142178i
\(117\) 1.51318 2.62090i 0.139893 0.242302i
\(118\) 6.95698 0.640442
\(119\) −7.33274 + 12.7007i −0.672191 + 1.16427i
\(120\) −2.89728 −0.264484
\(121\) 4.18878 7.25518i 0.380798 0.659562i
\(122\) −6.89728 11.9464i −0.624450 1.08158i
\(123\) 3.38410 + 5.86143i 0.305134 + 0.528508i
\(124\) 0.802888 1.39064i 0.0721015 0.124883i
\(125\) 4.65238 0.416122
\(126\) 1.32288 2.29129i 0.117851 0.204124i
\(127\) 13.7252 1.21791 0.608956 0.793204i \(-0.291588\pi\)
0.608956 + 0.793204i \(0.291588\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 1.00000 + 1.73205i 0.0880451 + 0.152499i
\(130\) 4.38410 + 7.59348i 0.384511 + 0.665993i
\(131\) −1.45876 + 2.52665i −0.127453 + 0.220755i −0.922689 0.385545i \(-0.874013\pi\)
0.795236 + 0.606300i \(0.207347\pi\)
\(132\) −1.61939 −0.140950
\(133\) 7.32397 0.635069
\(134\) −7.23879 −0.625336
\(135\) −1.44864 + 2.50912i −0.124679 + 0.215950i
\(136\) 2.77152 + 4.80040i 0.237655 + 0.411631i
\(137\) 5.80137 + 10.0483i 0.495644 + 0.858481i 0.999987 0.00502238i \(-0.00159868\pi\)
−0.504343 + 0.863503i \(0.668265\pi\)
\(138\) −0.500000 + 0.866025i −0.0425628 + 0.0737210i
\(139\) −0.155436 −0.0131839 −0.00659194 0.999978i \(-0.502098\pi\)
−0.00659194 + 0.999978i \(0.502098\pi\)
\(140\) 3.83274 + 6.63850i 0.323926 + 0.561056i
\(141\) 4.15544 0.349951
\(142\) 2.43546 4.21834i 0.204379 0.353995i
\(143\) 2.45043 + 4.24427i 0.204915 + 0.354924i
\(144\) −0.500000 0.866025i −0.0416667 0.0721688i
\(145\) 2.56148 4.43662i 0.212720 0.368441i
\(146\) −5.13607 −0.425064
\(147\) −7.00000 −0.577350
\(148\) −1.02636 −0.0843660
\(149\) −8.31786 + 14.4070i −0.681426 + 1.18026i 0.293120 + 0.956076i \(0.405306\pi\)
−0.974546 + 0.224188i \(0.928027\pi\)
\(150\) −1.69711 2.93948i −0.138569 0.240008i
\(151\) 9.86259 + 17.0825i 0.802606 + 1.39015i 0.917895 + 0.396823i \(0.129887\pi\)
−0.115289 + 0.993332i \(0.536779\pi\)
\(152\) 1.38410 2.39733i 0.112265 0.194449i
\(153\) 5.54303 0.448127
\(154\) 2.14226 + 3.71050i 0.172628 + 0.299000i
\(155\) 4.65238 0.373688
\(156\) −1.51318 + 2.62090i −0.121151 + 0.209840i
\(157\) −0.900593 1.55987i −0.0718752 0.124491i 0.827848 0.560953i \(-0.189565\pi\)
−0.899723 + 0.436461i \(0.856232\pi\)
\(158\) −3.44532 5.96748i −0.274095 0.474747i
\(159\) 2.44864 4.24117i 0.194190 0.336346i
\(160\) 2.89728 0.229050
\(161\) 2.64575 0.208514
\(162\) −1.00000 −0.0785674
\(163\) −4.43546 + 7.68244i −0.347412 + 0.601735i −0.985789 0.167989i \(-0.946273\pi\)
0.638377 + 0.769724i \(0.279606\pi\)
\(164\) −3.38410 5.86143i −0.264254 0.457701i
\(165\) −2.34592 4.06325i −0.182629 0.316324i
\(166\) 2.57772 4.46474i 0.200070 0.346531i
\(167\) −1.26427 −0.0978319 −0.0489159 0.998803i \(-0.515577\pi\)
−0.0489159 + 0.998803i \(0.515577\pi\)
\(168\) −1.32288 + 2.29129i −0.102062 + 0.176777i
\(169\) −3.84116 −0.295474
\(170\) −8.02985 + 13.9081i −0.615861 + 1.06670i
\(171\) −1.38410 2.39733i −0.105845 0.183329i
\(172\) −1.00000 1.73205i −0.0762493 0.132068i
\(173\) 0.431967 0.748188i 0.0328418 0.0568837i −0.849137 0.528172i \(-0.822878\pi\)
0.881979 + 0.471288i \(0.156211\pi\)
\(174\) 1.76820 0.134047
\(175\) −4.49014 + 7.77714i −0.339422 + 0.587897i
\(176\) 1.61939 0.122066
\(177\) −3.47849 + 6.02492i −0.261459 + 0.452861i
\(178\) −7.28138 12.6117i −0.545762 0.945288i
\(179\) 8.93062 + 15.4683i 0.667506 + 1.15615i 0.978599 + 0.205775i \(0.0659716\pi\)
−0.311093 + 0.950379i \(0.600695\pi\)
\(180\) 1.44864 2.50912i 0.107975 0.187019i
\(181\) 5.30512 0.394327 0.197163 0.980371i \(-0.436827\pi\)
0.197163 + 0.980371i \(0.436827\pi\)
\(182\) 8.00699 0.593517
\(183\) 13.7946 1.01972
\(184\) 0.500000 0.866025i 0.0368605 0.0638442i
\(185\) −1.48682 2.57525i −0.109313 0.189336i
\(186\) 0.802888 + 1.39064i 0.0588706 + 0.101967i
\(187\) −4.48818 + 7.77375i −0.328208 + 0.568473i
\(188\) −4.15544 −0.303066
\(189\) 1.32288 + 2.29129i 0.0962250 + 0.166667i
\(190\) 8.02025 0.581850
\(191\) −9.15230 + 15.8522i −0.662237 + 1.14703i 0.317789 + 0.948161i \(0.397060\pi\)
−0.980026 + 0.198867i \(0.936274\pi\)
\(192\) 0.500000 + 0.866025i 0.0360844 + 0.0625000i
\(193\) −0.170755 0.295756i −0.0122912 0.0212890i 0.859814 0.510607i \(-0.170579\pi\)
−0.872106 + 0.489318i \(0.837246\pi\)
\(194\) −7.34941 + 12.7296i −0.527657 + 0.913929i
\(195\) −8.76820 −0.627904
\(196\) 7.00000 0.500000
\(197\) 20.2476 1.44258 0.721291 0.692632i \(-0.243549\pi\)
0.721291 + 0.692632i \(0.243549\pi\)
\(198\) 0.809697 1.40244i 0.0575427 0.0996668i
\(199\) 13.4471 + 23.2911i 0.953241 + 1.65106i 0.738343 + 0.674425i \(0.235608\pi\)
0.214898 + 0.976637i \(0.431058\pi\)
\(200\) 1.69711 + 2.93948i 0.120004 + 0.207853i
\(201\) 3.61939 6.26897i 0.255292 0.442179i
\(202\) 3.39422 0.238817
\(203\) −2.33911 4.05146i −0.164173 0.284356i
\(204\) −5.54303 −0.388090
\(205\) 9.80468 16.9822i 0.684789 1.18609i
\(206\) −5.50986 9.54336i −0.383890 0.664918i
\(207\) −0.500000 0.866025i −0.0347524 0.0601929i
\(208\) 1.51318 2.62090i 0.104920 0.181727i
\(209\) 4.48281 0.310082
\(210\) −7.66548 −0.528968
\(211\) 6.41359 0.441530 0.220765 0.975327i \(-0.429145\pi\)
0.220765 + 0.975327i \(0.429145\pi\)
\(212\) −2.44864 + 4.24117i −0.168173 + 0.291285i
\(213\) 2.43546 + 4.21834i 0.166875 + 0.289036i
\(214\) 4.57772 + 7.92884i 0.312926 + 0.542004i
\(215\) 2.89728 5.01823i 0.197593 0.342241i
\(216\) 1.00000 0.0680414
\(217\) 2.12424 3.67930i 0.144203 0.249767i
\(218\) −10.5694 −0.715849
\(219\) 2.56803 4.44796i 0.173532 0.300566i
\(220\) 2.34592 + 4.06325i 0.158162 + 0.273944i
\(221\) 8.38759 + 14.5277i 0.564211 + 0.977242i
\(222\) 0.513179 0.888851i 0.0344423 0.0596558i
\(223\) −16.1888 −1.08408 −0.542040 0.840352i \(-0.682348\pi\)
−0.542040 + 0.840352i \(0.682348\pi\)
\(224\) 1.32288 2.29129i 0.0883883 0.153093i
\(225\) 3.39422 0.226282
\(226\) 1.88105 3.25807i 0.125125 0.216723i
\(227\) −11.4554 19.8414i −0.760325 1.31692i −0.942683 0.333689i \(-0.891706\pi\)
0.182358 0.983232i \(-0.441627\pi\)
\(228\) 1.38410 + 2.39733i 0.0916643 + 0.158767i
\(229\) 2.58273 4.47343i 0.170672 0.295612i −0.767983 0.640470i \(-0.778740\pi\)
0.938655 + 0.344858i \(0.112073\pi\)
\(230\) 2.89728 0.191041
\(231\) −4.28451 −0.281900
\(232\) −1.76820 −0.116088
\(233\) −5.54652 + 9.60686i −0.363365 + 0.629366i −0.988512 0.151140i \(-0.951705\pi\)
0.625147 + 0.780507i \(0.285039\pi\)
\(234\) −1.51318 2.62090i −0.0989196 0.171334i
\(235\) −6.01973 10.4265i −0.392684 0.680148i
\(236\) 3.47849 6.02492i 0.226430 0.392189i
\(237\) 6.89065 0.447596
\(238\) 7.33274 + 12.7007i 0.475311 + 0.823263i
\(239\) −5.63912 −0.364764 −0.182382 0.983228i \(-0.558381\pi\)
−0.182382 + 0.983228i \(0.558381\pi\)
\(240\) −1.44864 + 2.50912i −0.0935093 + 0.161963i
\(241\) −12.0479 20.8675i −0.776072 1.34420i −0.934190 0.356776i \(-0.883876\pi\)
0.158118 0.987420i \(-0.449457\pi\)
\(242\) −4.18878 7.25518i −0.269265 0.466381i
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) −13.7946 −0.883106
\(245\) 10.1405 + 17.5638i 0.647851 + 1.12211i
\(246\) 6.76820 0.431525
\(247\) 4.18878 7.25518i 0.266526 0.461636i
\(248\) −0.802888 1.39064i −0.0509834 0.0883059i
\(249\) 2.57772 + 4.46474i 0.163356 + 0.282941i
\(250\) 2.32619 4.02908i 0.147121 0.254821i
\(251\) 17.9970 1.13596 0.567979 0.823043i \(-0.307726\pi\)
0.567979 + 0.823043i \(0.307726\pi\)
\(252\) −1.32288 2.29129i −0.0833333 0.144338i
\(253\) 1.61939 0.101810
\(254\) 6.86259 11.8864i 0.430597 0.745816i
\(255\) −8.02985 13.9081i −0.502849 0.870960i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −0.635628 + 1.10094i −0.0396494 + 0.0686747i −0.885169 0.465269i \(-0.845957\pi\)
0.845520 + 0.533944i \(0.179291\pi\)
\(258\) 2.00000 0.124515
\(259\) −2.71549 −0.168732
\(260\) 8.76820 0.543781
\(261\) −0.884100 + 1.53131i −0.0547244 + 0.0947855i
\(262\) 1.45876 + 2.52665i 0.0901227 + 0.156097i
\(263\) 13.3639 + 23.1470i 0.824056 + 1.42731i 0.902639 + 0.430399i \(0.141627\pi\)
−0.0785824 + 0.996908i \(0.525039\pi\)
\(264\) −0.809697 + 1.40244i −0.0498334 + 0.0863140i
\(265\) −14.1888 −0.871610
\(266\) 3.66198 6.34274i 0.224531 0.388899i
\(267\) 14.5628 0.891226
\(268\) −3.61939 + 6.26897i −0.221090 + 0.382939i
\(269\) −12.5759 21.7822i −0.766768 1.32808i −0.939307 0.343079i \(-0.888530\pi\)
0.172538 0.985003i \(-0.444803\pi\)
\(270\) 1.44864 + 2.50912i 0.0881614 + 0.152700i
\(271\) 10.8429 18.7804i 0.658657 1.14083i −0.322306 0.946635i \(-0.604458\pi\)
0.980964 0.194192i \(-0.0622085\pi\)
\(272\) 5.54303 0.336096
\(273\) −4.00349 + 6.93426i −0.242302 + 0.419680i
\(274\) 11.6027 0.700947
\(275\) −2.74829 + 4.76018i −0.165728 + 0.287050i
\(276\) 0.500000 + 0.866025i 0.0300965 + 0.0521286i
\(277\) −4.88454 8.46027i −0.293484 0.508328i 0.681147 0.732146i \(-0.261481\pi\)
−0.974631 + 0.223818i \(0.928148\pi\)
\(278\) −0.0777178 + 0.134611i −0.00466121 + 0.00807345i
\(279\) −1.60578 −0.0961353
\(280\) 7.66548 0.458100
\(281\) −2.80730 −0.167469 −0.0837346 0.996488i \(-0.526685\pi\)
−0.0837346 + 0.996488i \(0.526685\pi\)
\(282\) 2.07772 3.59871i 0.123726 0.214300i
\(283\) −12.9570 22.4422i −0.770213 1.33405i −0.937446 0.348130i \(-0.886817\pi\)
0.167234 0.985917i \(-0.446517\pi\)
\(284\) −2.43546 4.21834i −0.144518 0.250313i
\(285\) −4.01012 + 6.94574i −0.237539 + 0.411430i
\(286\) 4.90087 0.289794
\(287\) −8.95349 15.5079i −0.528508 0.915402i
\(288\) −1.00000 −0.0589256
\(289\) −6.86259 + 11.8864i −0.403682 + 0.699197i
\(290\) −2.56148 4.43662i −0.150416 0.260527i
\(291\) −7.34941 12.7296i −0.430830 0.746220i
\(292\) −2.56803 + 4.44796i −0.150283 + 0.260297i
\(293\) 31.3143 1.82940 0.914700 0.404133i \(-0.132427\pi\)
0.914700 + 0.404133i \(0.132427\pi\)
\(294\) −3.50000 + 6.06218i −0.204124 + 0.353553i
\(295\) 20.1563 1.17355
\(296\) −0.513179 + 0.888851i −0.0298279 + 0.0516634i
\(297\) 0.809697 + 1.40244i 0.0469834 + 0.0813776i
\(298\) 8.31786 + 14.4070i 0.481841 + 0.834573i
\(299\) 1.51318 2.62090i 0.0875094 0.151571i
\(300\) −3.39422 −0.195966
\(301\) −2.64575 4.58258i −0.152499 0.264135i
\(302\) 19.7252 1.13506
\(303\) −1.69711 + 2.93948i −0.0974965 + 0.168869i
\(304\) −1.38410 2.39733i −0.0793836 0.137496i
\(305\) −19.9833 34.6122i −1.14424 1.98189i
\(306\) 2.77152 4.80040i 0.158437 0.274421i
\(307\) −13.6067 −0.776573 −0.388286 0.921539i \(-0.626933\pi\)
−0.388286 + 0.921539i \(0.626933\pi\)
\(308\) 4.28451 0.244133
\(309\) 11.0197 0.626890
\(310\) 2.32619 4.02908i 0.132119 0.228836i
\(311\) 7.38545 + 12.7920i 0.418791 + 0.725367i 0.995818 0.0913580i \(-0.0291208\pi\)
−0.577027 + 0.816725i \(0.695787\pi\)
\(312\) 1.51318 + 2.62090i 0.0856669 + 0.148379i
\(313\) −1.34242 + 2.32515i −0.0758783 + 0.131425i −0.901468 0.432846i \(-0.857509\pi\)
0.825590 + 0.564271i \(0.190843\pi\)
\(314\) −1.80119 −0.101647
\(315\) 3.83274 6.63850i 0.215950 0.374037i
\(316\) −6.89065 −0.387629
\(317\) −5.52151 + 9.56353i −0.310119 + 0.537142i −0.978388 0.206778i \(-0.933702\pi\)
0.668269 + 0.743920i \(0.267036\pi\)
\(318\) −2.44864 4.24117i −0.137313 0.237833i
\(319\) −1.43171 2.47979i −0.0801602 0.138841i
\(320\) 1.44864 2.50912i 0.0809814 0.140264i
\(321\) −9.15544 −0.511007
\(322\) 1.32288 2.29129i 0.0737210 0.127688i
\(323\) 15.3442 0.853775
\(324\) −0.500000 + 0.866025i −0.0277778 + 0.0481125i
\(325\) 5.13607 + 8.89593i 0.284898 + 0.493457i
\(326\) 4.43546 + 7.68244i 0.245657 + 0.425491i
\(327\) 5.28469 9.15336i 0.292244 0.506182i
\(328\) −6.76820 −0.373711
\(329\) −10.9942 −0.606133
\(330\) −4.69184 −0.258277
\(331\) −4.14619 + 7.18141i −0.227895 + 0.394726i −0.957184 0.289480i \(-0.906518\pi\)
0.729289 + 0.684206i \(0.239851\pi\)
\(332\) −2.57772 4.46474i −0.141471 0.245034i
\(333\) 0.513179 + 0.888851i 0.0281220 + 0.0487088i
\(334\) −0.632133 + 1.09489i −0.0345888 + 0.0599095i
\(335\) −20.9728 −1.14587
\(336\) 1.32288 + 2.29129i 0.0721688 + 0.125000i
\(337\) −25.0624 −1.36524 −0.682618 0.730775i \(-0.739159\pi\)
−0.682618 + 0.730775i \(0.739159\pi\)
\(338\) −1.92058 + 3.32654i −0.104466 + 0.180940i
\(339\) 1.88105 + 3.25807i 0.102164 + 0.176954i
\(340\) 8.02985 + 13.9081i 0.435480 + 0.754273i
\(341\) 1.30019 2.25200i 0.0704094 0.121953i
\(342\) −2.76820 −0.149687
\(343\) 18.5203 1.00000
\(344\) −2.00000 −0.107833
\(345\) −1.44864 + 2.50912i −0.0779921 + 0.135086i
\(346\) −0.431967 0.748188i −0.0232227 0.0402228i
\(347\) −3.39422 5.87897i −0.182211 0.315600i 0.760422 0.649429i \(-0.224992\pi\)
−0.942633 + 0.333830i \(0.891659\pi\)
\(348\) 0.884100 1.53131i 0.0473927 0.0820866i
\(349\) 12.0070 0.642719 0.321360 0.946957i \(-0.395860\pi\)
0.321360 + 0.946957i \(0.395860\pi\)
\(350\) 4.49014 + 7.77714i 0.240008 + 0.415706i
\(351\) 3.02636 0.161535
\(352\) 0.809697 1.40244i 0.0431570 0.0747501i
\(353\) −10.4632 18.1227i −0.556898 0.964576i −0.997753 0.0669979i \(-0.978658\pi\)
0.440855 0.897578i \(-0.354675\pi\)
\(354\) 3.47849 + 6.02492i 0.184880 + 0.320221i
\(355\) 7.05621 12.2217i 0.374505 0.648661i
\(356\) −14.5628 −0.771825
\(357\) −14.6655 −0.776179
\(358\) 17.8612 0.943996
\(359\) 5.01362 8.68384i 0.264609 0.458316i −0.702852 0.711336i \(-0.748091\pi\)
0.967461 + 0.253020i \(0.0814239\pi\)
\(360\) −1.44864 2.50912i −0.0763500 0.132242i
\(361\) 5.66853 + 9.81819i 0.298344 + 0.516747i
\(362\) 2.65256 4.59437i 0.139415 0.241475i
\(363\) 8.37756 0.439708
\(364\) 4.00349 6.93426i 0.209840 0.363454i
\(365\) −14.8806 −0.778887
\(366\) 6.89728 11.9464i 0.360527 0.624450i
\(367\) 12.1242 + 20.9998i 0.632880 + 1.09618i 0.986960 + 0.160966i \(0.0514608\pi\)
−0.354080 + 0.935215i \(0.615206\pi\)
\(368\) −0.500000 0.866025i −0.0260643 0.0451447i
\(369\) −3.38410 + 5.86143i −0.176169 + 0.305134i
\(370\) −2.97364 −0.154592
\(371\) −6.47849 + 11.2211i −0.336346 + 0.582569i
\(372\) 1.60578 0.0832556
\(373\) −17.4599 + 30.2414i −0.904037 + 1.56584i −0.0818326 + 0.996646i \(0.526077\pi\)
−0.822205 + 0.569192i \(0.807256\pi\)
\(374\) 4.48818 + 7.77375i 0.232078 + 0.401971i
\(375\) 2.32619 + 4.02908i 0.120124 + 0.208061i
\(376\) −2.07772 + 3.59871i −0.107150 + 0.185589i
\(377\) −5.35121 −0.275601
\(378\) 2.64575 0.136083
\(379\) 3.76732 0.193514 0.0967571 0.995308i \(-0.469153\pi\)
0.0967571 + 0.995308i \(0.469153\pi\)
\(380\) 4.01012 6.94574i 0.205715 0.356309i
\(381\) 6.86259 + 11.8864i 0.351581 + 0.608956i
\(382\) 9.15230 + 15.8522i 0.468272 + 0.811072i
\(383\) −16.6826 + 28.8951i −0.852441 + 1.47647i 0.0265587 + 0.999647i \(0.491545\pi\)
−0.878999 + 0.476823i \(0.841788\pi\)
\(384\) 1.00000 0.0510310
\(385\) 6.20672 + 10.7503i 0.316324 + 0.547888i
\(386\) −0.341510 −0.0173824
\(387\) −1.00000 + 1.73205i −0.0508329 + 0.0880451i
\(388\) 7.34941 + 12.7296i 0.373110 + 0.646245i
\(389\) 13.1752 + 22.8201i 0.668007 + 1.15702i 0.978461 + 0.206434i \(0.0661858\pi\)
−0.310453 + 0.950589i \(0.600481\pi\)
\(390\) −4.38410 + 7.59348i −0.221998 + 0.384511i
\(391\) 5.54303 0.280323
\(392\) 3.50000 6.06218i 0.176777 0.306186i
\(393\) −2.91753 −0.147170
\(394\) 10.1238 17.5349i 0.510030 0.883398i
\(395\) −9.98207 17.2894i −0.502252 0.869926i
\(396\) −0.809697 1.40244i −0.0406888 0.0704751i
\(397\) 6.39073 11.0691i 0.320742 0.555541i −0.659900 0.751354i \(-0.729401\pi\)
0.980641 + 0.195813i \(0.0627346\pi\)
\(398\) 26.8942 1.34809
\(399\) 3.66198 + 6.34274i 0.183329 + 0.317534i
\(400\) 3.39422 0.169711
\(401\) −3.61957 + 6.26929i −0.180753 + 0.313073i −0.942137 0.335228i \(-0.891187\pi\)
0.761384 + 0.648301i \(0.224520\pi\)
\(402\) −3.61939 6.26897i −0.180519 0.312668i
\(403\) −2.42983 4.20858i −0.121038 0.209644i
\(404\) 1.69711 2.93948i 0.0844345 0.146245i
\(405\) −2.89728 −0.143967
\(406\) −4.67822 −0.232176
\(407\) −1.66208 −0.0823861
\(408\) −2.77152 + 4.80040i −0.137210 + 0.237655i
\(409\) −14.1988 24.5931i −0.702087 1.21605i −0.967733 0.251979i \(-0.918919\pi\)
0.265646 0.964071i \(-0.414415\pi\)
\(410\) −9.80468 16.9822i −0.484219 0.838691i
\(411\) −5.80137 + 10.0483i −0.286160 + 0.495644i
\(412\) −11.0197 −0.542903
\(413\) 9.20322 15.9404i 0.452861 0.784378i
\(414\) −1.00000 −0.0491473
\(415\) 7.46837 12.9356i 0.366608 0.634983i
\(416\) −1.51318 2.62090i −0.0741897 0.128500i
\(417\) −0.0777178 0.134611i −0.00380586 0.00659194i
\(418\) 2.24140 3.88222i 0.109631 0.189886i
\(419\) 16.3112 0.796856 0.398428 0.917200i \(-0.369556\pi\)
0.398428 + 0.917200i \(0.369556\pi\)
\(420\) −3.83274 + 6.63850i −0.187019 + 0.323926i
\(421\) −35.7221 −1.74099 −0.870495 0.492177i \(-0.836201\pi\)
−0.870495 + 0.492177i \(0.836201\pi\)
\(422\) 3.20680 5.55433i 0.156104 0.270381i
\(423\) 2.07772 + 3.59871i 0.101022 + 0.174975i
\(424\) 2.44864 + 4.24117i 0.118916 + 0.205969i
\(425\) −9.40714 + 16.2936i −0.456313 + 0.790358i
\(426\) 4.87092 0.235997
\(427\) −36.4970 −1.76621
\(428\) 9.15544 0.442545
\(429\) −2.45043 + 4.24427i −0.118308 + 0.204915i
\(430\) −2.89728 5.01823i −0.139719 0.242001i
\(431\) −12.7252 22.0407i −0.612950 1.06166i −0.990740 0.135770i \(-0.956649\pi\)
0.377790 0.925891i \(-0.376684\pi\)
\(432\) 0.500000 0.866025i 0.0240563 0.0416667i
\(433\) 35.4496 1.70360 0.851801 0.523866i \(-0.175511\pi\)
0.851801 + 0.523866i \(0.175511\pi\)
\(434\) −2.12424 3.67930i −0.101967 0.176612i
\(435\) 5.12297 0.245628
\(436\) −5.28469 + 9.15336i −0.253091 + 0.438366i
\(437\) −1.38410 2.39733i −0.0662105 0.114680i
\(438\) −2.56803 4.44796i −0.122705 0.212532i
\(439\) −8.66378 + 15.0061i −0.413500 + 0.716202i −0.995270 0.0971510i \(-0.969027\pi\)
0.581770 + 0.813353i \(0.302360\pi\)
\(440\) 4.69184 0.223675
\(441\) −3.50000 6.06218i −0.166667 0.288675i
\(442\) 16.7752 0.797914
\(443\) 11.8924 20.5983i 0.565027 0.978655i −0.432020 0.901864i \(-0.642199\pi\)
0.997047 0.0767915i \(-0.0244676\pi\)
\(444\) −0.513179 0.888851i −0.0243544 0.0421830i
\(445\) −21.0962 36.5397i −1.00006 1.73215i
\(446\) −8.09439 + 14.0199i −0.383281 + 0.663861i
\(447\) −16.6357 −0.786843
\(448\) −1.32288 2.29129i −0.0625000 0.108253i
\(449\) −30.3846 −1.43394 −0.716968 0.697106i \(-0.754471\pi\)
−0.716968 + 0.697106i \(0.754471\pi\)
\(450\) 1.69711 2.93948i 0.0800026 0.138569i
\(451\) −5.48019 9.49197i −0.258052 0.446959i
\(452\) −1.88105 3.25807i −0.0884769 0.153247i
\(453\) −9.86259 + 17.0825i −0.463385 + 0.802606i
\(454\) −22.9109 −1.07526
\(455\) 23.1985 1.08756
\(456\) 2.76820 0.129633
\(457\) −10.7103 + 18.5508i −0.501006 + 0.867768i 0.498993 + 0.866606i \(0.333703\pi\)
−0.999999 + 0.00116232i \(0.999630\pi\)
\(458\) −2.58273 4.47343i −0.120683 0.209029i
\(459\) 2.77152 + 4.80040i 0.129363 + 0.224064i
\(460\) 1.44864 2.50912i 0.0675432 0.116988i
\(461\) −19.1660 −0.892650 −0.446325 0.894871i \(-0.647267\pi\)
−0.446325 + 0.894871i \(0.647267\pi\)
\(462\) −2.14226 + 3.71050i −0.0996668 + 0.172628i
\(463\) 7.72787 0.359144 0.179572 0.983745i \(-0.442529\pi\)
0.179572 + 0.983745i \(0.442529\pi\)
\(464\) −0.884100 + 1.53131i −0.0410433 + 0.0710891i
\(465\) 2.32619 + 4.02908i 0.107874 + 0.186844i
\(466\) 5.54652 + 9.60686i 0.256938 + 0.445029i
\(467\) −2.61259 + 4.52513i −0.120896 + 0.209398i −0.920121 0.391634i \(-0.871910\pi\)
0.799225 + 0.601032i \(0.205243\pi\)
\(468\) −3.02636 −0.139893
\(469\) −9.57602 + 16.5861i −0.442179 + 0.765877i
\(470\) −12.0395 −0.555339
\(471\) 0.900593 1.55987i 0.0414972 0.0718752i
\(472\) −3.47849 6.02492i −0.160111 0.277320i
\(473\) −1.61939 2.80487i −0.0744598 0.128968i
\(474\) 3.44532 5.96748i 0.158249 0.274095i
\(475\) 9.39589 0.431113
\(476\) 14.6655 0.672191
\(477\) 4.89728 0.224231
\(478\) −2.81956 + 4.88362i −0.128964 + 0.223372i
\(479\) −7.38410 12.7896i −0.337388 0.584373i 0.646552 0.762870i \(-0.276210\pi\)
−0.983941 + 0.178496i \(0.942877\pi\)
\(480\) 1.44864 + 2.50912i 0.0661210 + 0.114525i
\(481\) −1.55306 + 2.68998i −0.0708135 + 0.122653i
\(482\) −24.0958 −1.09753
\(483\) 1.32288 + 2.29129i 0.0601929 + 0.104257i
\(484\) −8.37756 −0.380798
\(485\) −21.2933 + 36.8811i −0.966879 + 1.67468i
\(486\) −0.500000 0.866025i −0.0226805 0.0392837i
\(487\) −5.08077 8.80016i −0.230232 0.398773i 0.727644 0.685954i \(-0.240615\pi\)
−0.957876 + 0.287181i \(0.907282\pi\)
\(488\) −6.89728 + 11.9464i −0.312225 + 0.540790i
\(489\) −8.87092 −0.401157
\(490\) 20.2810 0.916200
\(491\) 7.02976 0.317249 0.158624 0.987339i \(-0.449294\pi\)
0.158624 + 0.987339i \(0.449294\pi\)
\(492\) 3.38410 5.86143i 0.152567 0.264254i
\(493\) −4.90059 8.48808i −0.220712 0.382284i
\(494\) −4.18878 7.25518i −0.188462 0.326426i
\(495\) 2.34592 4.06325i 0.105441 0.182629i
\(496\) −1.60578 −0.0721015
\(497\) −6.44362 11.1607i −0.289036 0.500625i
\(498\) 5.15544 0.231021
\(499\) −19.8293 + 34.3453i −0.887679 + 1.53751i −0.0450680 + 0.998984i \(0.514350\pi\)
−0.842611 + 0.538522i \(0.818983\pi\)
\(500\) −2.32619 4.02908i −0.104030 0.180186i
\(501\) −0.632133 1.09489i −0.0282416 0.0489159i
\(502\) 8.99848 15.5858i 0.401622 0.695629i
\(503\) 26.6752 1.18939 0.594694 0.803952i \(-0.297273\pi\)
0.594694 + 0.803952i \(0.297273\pi\)
\(504\) −2.64575 −0.117851
\(505\) 9.83401 0.437608
\(506\) 0.809697 1.40244i 0.0359954 0.0623459i
\(507\) −1.92058 3.32654i −0.0852960 0.147737i
\(508\) −6.86259 11.8864i −0.304478 0.527372i
\(509\) −18.3644 + 31.8080i −0.813987 + 1.40987i 0.0960660 + 0.995375i \(0.469374\pi\)
−0.910053 + 0.414492i \(0.863959\pi\)
\(510\) −16.0597 −0.711136
\(511\) −6.79438 + 11.7682i −0.300566 + 0.520595i
\(512\) −1.00000 −0.0441942
\(513\) 1.38410 2.39733i 0.0611095 0.105845i
\(514\) 0.635628 + 1.10094i 0.0280363 + 0.0485603i
\(515\) −15.9636 27.6498i −0.703441 1.21840i
\(516\) 1.00000 1.73205i 0.0440225 0.0762493i
\(517\) −6.72929 −0.295954
\(518\) −1.35774 + 2.35168i −0.0596558 + 0.103327i
\(519\) 0.863933 0.0379225
\(520\) 4.38410 7.59348i 0.192256 0.332996i
\(521\) −4.39422 7.61102i −0.192514 0.333445i 0.753568 0.657369i \(-0.228331\pi\)
−0.946083 + 0.323925i \(0.894998\pi\)
\(522\) 0.884100 + 1.53131i 0.0386960 + 0.0670235i
\(523\) −19.2415 + 33.3272i −0.841372 + 1.45730i 0.0473633 + 0.998878i \(0.484918\pi\)
−0.888735 + 0.458421i \(0.848415\pi\)
\(524\) 2.91753 0.127453
\(525\) −8.98027 −0.391931
\(526\) 26.7279 1.16539
\(527\) 4.45043 7.70838i 0.193864 0.335782i
\(528\) 0.809697 + 1.40244i 0.0352375 + 0.0610332i
\(529\) −0.500000 0.866025i −0.0217391 0.0376533i
\(530\) −7.09439 + 12.2878i −0.308161 + 0.533750i
\(531\) −6.95698 −0.301907
\(532\) −3.66198 6.34274i −0.158767 0.274993i
\(533\) −20.4830 −0.887217
\(534\) 7.28138 12.6117i 0.315096 0.545762i
\(535\) 13.2629 + 22.9721i 0.573406 + 0.993169i
\(536\) 3.61939 + 6.26897i 0.156334 + 0.270778i
\(537\) −8.93062 + 15.4683i −0.385385 + 0.667506i
\(538\) −25.1519 −1.08437
\(539\) 11.3358 0.488266
\(540\) 2.89728 0.124679
\(541\) 9.98988 17.3030i 0.429498 0.743913i −0.567330 0.823490i \(-0.692024\pi\)
0.996829 + 0.0795774i \(0.0253571\pi\)
\(542\) −10.8429 18.7804i −0.465741 0.806687i
\(543\) 2.65256 + 4.59437i 0.113832 + 0.197163i
\(544\) 2.77152 4.80040i 0.118828 0.205816i
\(545\) −30.6225 −1.31172
\(546\) 4.00349 + 6.93426i 0.171334 + 0.296759i
\(547\) 15.3485 0.656254 0.328127 0.944634i \(-0.393583\pi\)
0.328127 + 0.944634i \(0.393583\pi\)
\(548\) 5.80137 10.0483i 0.247822 0.429240i
\(549\) 6.89728 + 11.9464i 0.294369 + 0.509862i
\(550\) 2.74829 + 4.76018i 0.117188 + 0.202975i
\(551\) −2.44737 + 4.23896i −0.104261 + 0.180586i
\(552\) 1.00000 0.0425628
\(553\) −18.2309 −0.775259
\(554\) −9.76908 −0.415048
\(555\) 1.48682 2.57525i 0.0631121 0.109313i
\(556\) 0.0777178 + 0.134611i 0.00329597 + 0.00570879i
\(557\) 10.4320 + 18.0687i 0.442017 + 0.765596i 0.997839 0.0657053i \(-0.0209297\pi\)
−0.555822 + 0.831301i \(0.687596\pi\)
\(558\) −0.802888 + 1.39064i −0.0339890 + 0.0588706i
\(559\) −6.05271 −0.256003
\(560\) 3.83274 6.63850i 0.161963 0.280528i
\(561\) −8.97635 −0.378982
\(562\) −1.40365 + 2.43119i −0.0592093 + 0.102554i
\(563\) −7.31938 12.6775i −0.308475 0.534295i 0.669554 0.742764i \(-0.266485\pi\)
−0.978029 + 0.208469i \(0.933152\pi\)
\(564\) −2.07772 3.59871i −0.0874877 0.151533i
\(565\) 5.44991 9.43953i 0.229280 0.397124i
\(566\) −25.9140 −1.08925
\(567\) −1.32288 + 2.29129i −0.0555556 + 0.0962250i
\(568\) −4.87092 −0.204379
\(569\) 19.3512 33.5173i 0.811245 1.40512i −0.100749 0.994912i \(-0.532124\pi\)
0.911993 0.410205i \(-0.134543\pi\)
\(570\) 4.01012 + 6.94574i 0.167966 + 0.290925i
\(571\) −6.47320 11.2119i −0.270895 0.469204i 0.698196 0.715906i \(-0.253986\pi\)
−0.969091 + 0.246702i \(0.920653\pi\)
\(572\) 2.45043 4.24427i 0.102458 0.177462i
\(573\) −18.3046 −0.764686
\(574\) −17.9070 −0.747423
\(575\) 3.39422 0.141549
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) −3.92757 6.80275i −0.163507 0.283202i 0.772617 0.634872i \(-0.218947\pi\)
−0.936124 + 0.351670i \(0.885614\pi\)
\(578\) 6.86259 + 11.8864i 0.285446 + 0.494407i
\(579\) 0.170755 0.295756i 0.00709633 0.0122912i
\(580\) −5.12297 −0.212720
\(581\) −6.82000 11.8126i −0.282941 0.490069i
\(582\) −14.6988 −0.609286
\(583\) −3.96531 + 6.86812i −0.164226 + 0.284449i
\(584\) 2.56803 + 4.44796i 0.106266 + 0.184058i
\(585\) −4.38410 7.59348i −0.181260 0.313952i
\(586\) 15.6571 27.1190i 0.646791 1.12027i
\(587\) 39.8243 1.64373 0.821863 0.569685i \(-0.192935\pi\)
0.821863 + 0.569685i \(0.192935\pi\)
\(588\) 3.50000 + 6.06218i 0.144338 + 0.250000i
\(589\) −4.44511 −0.183158
\(590\) 10.0782 17.4559i 0.414911 0.718647i
\(591\) 10.1238 + 17.5349i 0.416438 + 0.721291i
\(592\) 0.513179 + 0.888851i 0.0210915 + 0.0365316i
\(593\) 13.0470 22.5980i 0.535775 0.927989i −0.463351 0.886175i \(-0.653353\pi\)
0.999125 0.0418139i \(-0.0133137\pi\)
\(594\) 1.61939 0.0664445
\(595\) 21.2450 + 36.7974i 0.870960 + 1.50855i
\(596\) 16.6357 0.681426
\(597\) −13.4471 + 23.2911i −0.550354 + 0.953241i
\(598\) −1.51318 2.62090i −0.0618785 0.107177i
\(599\) −18.9482 32.8193i −0.774203 1.34096i −0.935241 0.354011i \(-0.884818\pi\)
0.161038 0.986948i \(-0.448516\pi\)
\(600\) −1.69711 + 2.93948i −0.0692843 + 0.120004i
\(601\) 3.65849 0.149233 0.0746165 0.997212i \(-0.476227\pi\)
0.0746165 + 0.997212i \(0.476227\pi\)
\(602\) −5.29150 −0.215666
\(603\) 7.23879 0.294786
\(604\) 9.86259 17.0825i 0.401303 0.695077i
\(605\) −12.1361 21.0203i −0.493401 0.854596i
\(606\) 1.69711 + 2.93948i 0.0689405 + 0.119408i
\(607\) 10.3323 17.8961i 0.419375 0.726379i −0.576502 0.817096i \(-0.695583\pi\)
0.995877 + 0.0907170i \(0.0289159\pi\)
\(608\) −2.76820 −0.112265
\(609\) 2.33911 4.05146i 0.0947855 0.164173i
\(610\) −39.9667 −1.61820
\(611\) −6.28792 + 10.8910i −0.254382 + 0.440602i
\(612\) −2.77152 4.80040i −0.112032 0.194045i
\(613\) −14.4269 24.9881i −0.582696 1.00926i −0.995158 0.0982842i \(-0.968665\pi\)
0.412463 0.910975i \(-0.364669\pi\)
\(614\) −6.80333 + 11.7837i −0.274560 + 0.475552i
\(615\) 19.6094 0.790726
\(616\) 2.14226 3.71050i 0.0863140 0.149500i
\(617\) 21.1524 0.851563 0.425782 0.904826i \(-0.359999\pi\)
0.425782 + 0.904826i \(0.359999\pi\)
\(618\) 5.50986 9.54336i 0.221639 0.383890i
\(619\) 10.6492 + 18.4450i 0.428029 + 0.741369i 0.996698 0.0811982i \(-0.0258747\pi\)
−0.568669 + 0.822567i \(0.692541\pi\)
\(620\) −2.32619 4.02908i −0.0934221 0.161812i
\(621\) 0.500000 0.866025i 0.0200643 0.0347524i
\(622\) 14.7709 0.592259
\(623\) −38.5294 −1.54365
\(624\) 3.02636 0.121151
\(625\) 15.2252 26.3708i 0.609007 1.05483i
\(626\) 1.34242 + 2.32515i 0.0536540 + 0.0929315i
\(627\) 2.24140 + 3.88222i 0.0895130 + 0.155041i
\(628\) −0.900593 + 1.55987i −0.0359376 + 0.0622457i
\(629\) −5.68913 −0.226840
\(630\) −3.83274 6.63850i −0.152700 0.264484i
\(631\) 41.4808 1.65133 0.825663 0.564164i \(-0.190801\pi\)
0.825663 + 0.564164i \(0.190801\pi\)
\(632\) −3.44532 + 5.96748i −0.137048 + 0.237373i
\(633\) 3.20680 + 5.55433i 0.127459 + 0.220765i
\(634\) 5.52151 + 9.56353i 0.219287 + 0.379816i
\(635\) 19.8828 34.4381i 0.789026 1.36663i
\(636\) −4.89728 −0.194190
\(637\) 10.5923 18.3463i 0.419680 0.726907i
\(638\) −2.86341 −0.113364
\(639\) −2.43546 + 4.21834i −0.0963453 + 0.166875i
\(640\) −1.44864 2.50912i −0.0572625 0.0991816i
\(641\) 1.60246 + 2.77554i 0.0632934 + 0.109627i 0.895936 0.444184i \(-0.146506\pi\)
−0.832642 + 0.553811i \(0.813173\pi\)
\(642\) −4.57772 + 7.92884i −0.180668 + 0.312926i
\(643\) −34.0131 −1.34135 −0.670673 0.741753i \(-0.733995\pi\)
−0.670673 + 0.741753i \(0.733995\pi\)
\(644\) −1.32288 2.29129i −0.0521286 0.0902894i
\(645\) 5.79456 0.228160
\(646\) 7.67211 13.2885i 0.301855 0.522828i
\(647\) −5.75986 9.97637i −0.226443 0.392211i 0.730308 0.683118i \(-0.239376\pi\)
−0.956752 + 0.290906i \(0.906043\pi\)
\(648\) 0.500000 + 0.866025i 0.0196419 + 0.0340207i
\(649\) 5.63305 9.75672i 0.221116 0.382985i
\(650\) 10.2721 0.402906
\(651\) 4.24848 0.166511
\(652\) 8.87092 0.347412
\(653\) 6.17560 10.6965i 0.241670 0.418585i −0.719520 0.694472i \(-0.755638\pi\)
0.961190 + 0.275887i \(0.0889715\pi\)
\(654\) −5.28469 9.15336i −0.206648 0.357925i
\(655\) 4.22644 + 7.32041i 0.165141 + 0.286032i
\(656\) −3.38410 + 5.86143i −0.132127 + 0.228851i
\(657\) 5.13607 0.200377
\(658\) −5.49712 + 9.52130i −0.214300 + 0.371179i
\(659\) −4.82754 −0.188054 −0.0940272 0.995570i \(-0.529974\pi\)
−0.0940272 + 0.995570i \(0.529974\pi\)
\(660\) −2.34592 + 4.06325i −0.0913147 + 0.158162i
\(661\) 7.73503 + 13.3975i 0.300858 + 0.521101i 0.976331 0.216284i \(-0.0693937\pi\)
−0.675473 + 0.737385i \(0.736060\pi\)
\(662\) 4.14619 + 7.18141i 0.161146 + 0.279114i
\(663\) −8.38759 + 14.5277i −0.325747 + 0.564211i
\(664\) −5.15544 −0.200070
\(665\) 10.6098 18.3767i 0.411430 0.712618i
\(666\) 1.02636 0.0397705
\(667\) −0.884100 + 1.53131i −0.0342325 + 0.0592924i
\(668\) 0.632133 + 1.09489i 0.0244580 + 0.0423624i
\(669\) −8.09439 14.0199i −0.312947 0.542040i
\(670\) −10.4864 + 18.1630i −0.405125 + 0.701697i
\(671\) −22.3388 −0.862381
\(672\) 2.64575 0.102062
\(673\) 15.3248 0.590729 0.295365 0.955385i \(-0.404559\pi\)
0.295365 + 0.955385i \(0.404559\pi\)
\(674\) −12.5312 + 21.7047i −0.482684 + 0.836033i
\(675\) 1.69711 + 2.93948i 0.0653219 + 0.113141i
\(676\) 1.92058 + 3.32654i 0.0738685 + 0.127944i
\(677\) 23.8126 41.2446i 0.915192 1.58516i 0.108572 0.994089i \(-0.465372\pi\)
0.806620 0.591070i \(-0.201294\pi\)
\(678\) 3.76209 0.144482
\(679\) 19.4447 + 33.6792i 0.746220 + 1.29249i
\(680\) 16.0597 0.615861
\(681\) 11.4554 19.8414i 0.438974 0.760325i
\(682\) −1.30019 2.25200i −0.0497869 0.0862335i
\(683\) 13.8091 + 23.9180i 0.528390 + 0.915199i 0.999452 + 0.0330984i \(0.0105375\pi\)
−0.471062 + 0.882100i \(0.656129\pi\)
\(684\) −1.38410 + 2.39733i −0.0529224 + 0.0916643i
\(685\) 33.6164 1.28441
\(686\) 9.26013 16.0390i 0.353553 0.612372i
\(687\) 5.16547 0.197075
\(688\) −1.00000 + 1.73205i −0.0381246 + 0.0660338i
\(689\) 7.41046 + 12.8353i 0.282316 + 0.488986i
\(690\) 1.44864 + 2.50912i 0.0551488 + 0.0955205i
\(691\) −1.96487 + 3.40326i −0.0747473 + 0.129466i −0.900976 0.433868i \(-0.857148\pi\)
0.826229 + 0.563334i \(0.190482\pi\)
\(692\) −0.863933 −0.0328418
\(693\) −2.14226 3.71050i −0.0813776 0.140950i
\(694\) −6.78845 −0.257686
\(695\) −0.225170 + 0.390006i −0.00854119 + 0.0147938i
\(696\) −0.884100 1.53131i −0.0335117 0.0580440i
\(697\) −18.7582 32.4901i −0.710516 1.23065i
\(698\) 6.00349 10.3984i 0.227236 0.393584i
\(699\) −11.0930 −0.419578
\(700\) 8.98027 0.339422
\(701\) 13.5725 0.512624 0.256312 0.966594i \(-0.417492\pi\)
0.256312 + 0.966594i \(0.417492\pi\)
\(702\) 1.51318 2.62090i 0.0571112 0.0989196i
\(703\) 1.42058 + 2.46052i 0.0535782 + 0.0928002i
\(704\) −0.809697 1.40244i −0.0305166 0.0528563i
\(705\) 6.01973 10.4265i 0.226716 0.392684i
\(706\) −20.9263 −0.787573
\(707\) 4.49014 7.77714i 0.168869 0.292490i
\(708\) 6.95698 0.261459
\(709\) −6.24821 + 10.8222i −0.234657 + 0.406437i −0.959173 0.282821i \(-0.908730\pi\)
0.724516 + 0.689258i \(0.242063\pi\)
\(710\) −7.05621 12.2217i −0.264815 0.458673i
\(711\) 3.44532 + 5.96748i 0.129210 + 0.223798i
\(712\) −7.28138 + 12.6117i −0.272881 + 0.472644i
\(713\) −1.60578 −0.0601368
\(714\) −7.33274 + 12.7007i −0.274421 + 0.475311i
\(715\) 14.1992 0.531019
\(716\) 8.93062 15.4683i 0.333753 0.578077i
\(717\) −2.81956 4.88362i −0.105298 0.182382i
\(718\) −5.01362 8.68384i −0.187107 0.324078i
\(719\) 25.7981 44.6837i 0.962108 1.66642i 0.244917 0.969544i \(-0.421239\pi\)
0.717191 0.696877i \(-0.245428\pi\)
\(720\) −2.89728 −0.107975
\(721\) −29.1555 −1.08581
\(722\) 11.3371 0.421922
\(723\) 12.0479 20.8675i 0.448065 0.776072i
\(724\) −2.65256 4.59437i −0.0985816 0.170748i
\(725\) −3.00083 5.19760i −0.111448 0.193034i
\(726\) 4.18878 7.25518i 0.155460 0.269265i
\(727\) −41.3991 −1.53541 −0.767704 0.640804i \(-0.778601\pi\)
−0.767704 + 0.640804i \(0.778601\pi\)
\(728\) −4.00349 6.93426i −0.148379 0.257001i
\(729\) 1.00000 0.0370370
\(730\) −7.44031 + 12.8870i −0.275378 + 0.476969i
\(731\) −5.54303 9.60081i −0.205016 0.355099i
\(732\) −6.89728 11.9464i −0.254931 0.441553i
\(733\) −12.0494 + 20.8702i −0.445055 + 0.770857i −0.998056 0.0623230i \(-0.980149\pi\)
0.553001 + 0.833180i \(0.313482\pi\)
\(734\) 24.2485 0.895028
\(735\) −10.1405 + 17.5638i −0.374037 + 0.647851i
\(736\) −1.00000 −0.0368605
\(737\) −5.86123 + 10.1519i −0.215901 + 0.373952i
\(738\) 3.38410 + 5.86143i 0.124570 + 0.215762i
\(739\) −7.79931 13.5088i −0.286902 0.496929i 0.686166 0.727445i \(-0.259292\pi\)
−0.973069 + 0.230515i \(0.925959\pi\)
\(740\) −1.48682 + 2.57525i −0.0546566 + 0.0946681i
\(741\) 8.37756 0.307757
\(742\) 6.47849 + 11.2211i 0.237833 + 0.411939i
\(743\) 25.7488 0.944633 0.472317 0.881429i \(-0.343418\pi\)
0.472317 + 0.881429i \(0.343418\pi\)
\(744\) 0.802888 1.39064i 0.0294353 0.0509834i
\(745\) 24.0992 + 41.7410i 0.882925 + 1.52927i
\(746\) 17.4599 + 30.2414i 0.639251 + 1.10721i
\(747\) −2.57772 + 4.46474i −0.0943138 + 0.163356i
\(748\) 8.97635 0.328208
\(749\) 24.2230 0.885089
\(750\) 4.65238 0.169881
\(751\) −11.2867 + 19.5491i −0.411856 + 0.713356i −0.995093 0.0989464i \(-0.968453\pi\)
0.583236 + 0.812302i \(0.301786\pi\)
\(752\) 2.07772 + 3.59871i 0.0757666 + 0.131232i
\(753\) 8.99848 + 15.5858i 0.327923 + 0.567979i
\(754\) −2.67560 + 4.63428i −0.0974397 + 0.168771i
\(755\) 57.1493 2.07988
\(756\) 1.32288 2.29129i 0.0481125 0.0833333i
\(757\) 15.4706 0.562289 0.281144 0.959665i \(-0.409286\pi\)
0.281144 + 0.959665i \(0.409286\pi\)
\(758\) 1.88366 3.26260i 0.0684176 0.118503i
\(759\) 0.809697 + 1.40244i 0.0293901 + 0.0509052i
\(760\) −4.01012 6.94574i −0.145462 0.251948i
\(761\) −19.2520 + 33.3454i −0.697884 + 1.20877i 0.271315 + 0.962491i \(0.412541\pi\)
−0.969199 + 0.246279i \(0.920792\pi\)
\(762\) 13.7252 0.497211
\(763\) −13.9820 + 24.2175i −0.506182 + 0.876733i
\(764\) 18.3046 0.662237
\(765\) 8.02985 13.9081i 0.290320 0.502849i
\(766\) 16.6826 + 28.8951i 0.602767 + 1.04402i
\(767\) −10.5272 18.2336i −0.380114 0.658376i
\(768\) 0.500000 0.866025i 0.0180422 0.0312500i
\(769\) 10.9842 0.396101 0.198051 0.980192i \(-0.436539\pi\)
0.198051 + 0.980192i \(0.436539\pi\)
\(770\) 12.4134 0.447349
\(771\) −1.27126 −0.0457831
\(772\) −0.170755 + 0.295756i −0.00614560 + 0.0106445i
\(773\) 9.53640 + 16.5175i 0.343000 + 0.594094i 0.984988 0.172620i \(-0.0552234\pi\)
−0.641988 + 0.766715i \(0.721890\pi\)
\(774\) 1.00000 + 1.73205i 0.0359443 + 0.0622573i
\(775\) 2.72518 4.72015i 0.0978914 0.169553i
\(776\) 14.6988 0.527657