Properties

Label 825.2.k.f.782.1
Level $825$
Weight $2$
Character 825.782
Analytic conductor $6.588$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 825.k (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.58765816676\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(\zeta_{8})\)
Defining polynomial: \(x^{4} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 165)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 782.1
Root \(-0.707107 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 825.782
Dual form 825.2.k.f.518.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.292893 - 0.292893i) q^{2} +(1.00000 + 1.41421i) q^{3} +1.82843i q^{4} +(0.707107 + 0.121320i) q^{6} +(3.41421 + 3.41421i) q^{7} +(1.12132 + 1.12132i) q^{8} +(-1.00000 + 2.82843i) q^{9} +O(q^{10})\) \(q+(0.292893 - 0.292893i) q^{2} +(1.00000 + 1.41421i) q^{3} +1.82843i q^{4} +(0.707107 + 0.121320i) q^{6} +(3.41421 + 3.41421i) q^{7} +(1.12132 + 1.12132i) q^{8} +(-1.00000 + 2.82843i) q^{9} -1.00000i q^{11} +(-2.58579 + 1.82843i) q^{12} +(2.00000 - 2.00000i) q^{13} +2.00000 q^{14} -3.00000 q^{16} +(2.82843 - 2.82843i) q^{17} +(0.535534 + 1.12132i) q^{18} -2.82843i q^{19} +(-1.41421 + 8.24264i) q^{21} +(-0.292893 - 0.292893i) q^{22} +(-3.24264 - 3.24264i) q^{23} +(-0.464466 + 2.70711i) q^{24} -1.17157i q^{26} +(-5.00000 + 1.41421i) q^{27} +(-6.24264 + 6.24264i) q^{28} +0.828427 q^{29} -3.17157 q^{31} +(-3.12132 + 3.12132i) q^{32} +(1.41421 - 1.00000i) q^{33} -1.65685i q^{34} +(-5.17157 - 1.82843i) q^{36} +(0.171573 + 0.171573i) q^{37} +(-0.828427 - 0.828427i) q^{38} +(4.82843 + 0.828427i) q^{39} -7.65685i q^{41} +(2.00000 + 2.82843i) q^{42} +(-0.242641 + 0.242641i) q^{43} +1.82843 q^{44} -1.89949 q^{46} +(7.24264 - 7.24264i) q^{47} +(-3.00000 - 4.24264i) q^{48} +16.3137i q^{49} +(6.82843 + 1.17157i) q^{51} +(3.65685 + 3.65685i) q^{52} +(-1.00000 - 1.00000i) q^{53} +(-1.05025 + 1.87868i) q^{54} +7.65685i q^{56} +(4.00000 - 2.82843i) q^{57} +(0.242641 - 0.242641i) q^{58} -4.00000 q^{59} -6.48528 q^{61} +(-0.928932 + 0.928932i) q^{62} +(-13.0711 + 6.24264i) q^{63} -4.17157i q^{64} +(0.121320 - 0.707107i) q^{66} +(6.41421 + 6.41421i) q^{67} +(5.17157 + 5.17157i) q^{68} +(1.34315 - 7.82843i) q^{69} -2.48528i q^{71} +(-4.29289 + 2.05025i) q^{72} +0.100505 q^{74} +5.17157 q^{76} +(3.41421 - 3.41421i) q^{77} +(1.65685 - 1.17157i) q^{78} +10.8284i q^{79} +(-7.00000 - 5.65685i) q^{81} +(-2.24264 - 2.24264i) q^{82} +(9.07107 + 9.07107i) q^{83} +(-15.0711 - 2.58579i) q^{84} +0.142136i q^{86} +(0.828427 + 1.17157i) q^{87} +(1.12132 - 1.12132i) q^{88} -9.65685 q^{89} +13.6569 q^{91} +(5.92893 - 5.92893i) q^{92} +(-3.17157 - 4.48528i) q^{93} -4.24264i q^{94} +(-7.53553 - 1.29289i) q^{96} +(-10.6569 - 10.6569i) q^{97} +(4.77817 + 4.77817i) q^{98} +(2.82843 + 1.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 4 q^{2} + 4 q^{3} + 8 q^{7} - 4 q^{8} - 4 q^{9} + O(q^{10}) \) \( 4 q + 4 q^{2} + 4 q^{3} + 8 q^{7} - 4 q^{8} - 4 q^{9} - 16 q^{12} + 8 q^{13} + 8 q^{14} - 12 q^{16} - 12 q^{18} - 4 q^{22} + 4 q^{23} - 16 q^{24} - 20 q^{27} - 8 q^{28} - 8 q^{29} - 24 q^{31} - 4 q^{32} - 32 q^{36} + 12 q^{37} + 8 q^{38} + 8 q^{39} + 8 q^{42} + 16 q^{43} - 4 q^{44} + 32 q^{46} + 12 q^{47} - 12 q^{48} + 16 q^{51} - 8 q^{52} - 4 q^{53} - 24 q^{54} + 16 q^{57} - 16 q^{58} - 16 q^{59} + 8 q^{61} - 32 q^{62} - 24 q^{63} - 8 q^{66} + 20 q^{67} + 32 q^{68} + 28 q^{69} - 20 q^{72} + 40 q^{74} + 32 q^{76} + 8 q^{77} - 16 q^{78} - 28 q^{81} + 8 q^{82} + 8 q^{83} - 32 q^{84} - 8 q^{87} - 4 q^{88} - 16 q^{89} + 32 q^{91} + 52 q^{92} - 24 q^{93} - 16 q^{96} - 20 q^{97} - 12 q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).

\(n\) \(376\) \(551\) \(727\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{1}{4}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.292893 0.292893i 0.207107 0.207107i −0.595930 0.803037i \(-0.703216\pi\)
0.803037 + 0.595930i \(0.203216\pi\)
\(3\) 1.00000 + 1.41421i 0.577350 + 0.816497i
\(4\) 1.82843i 0.914214i
\(5\) 0 0
\(6\) 0.707107 + 0.121320i 0.288675 + 0.0495288i
\(7\) 3.41421 + 3.41421i 1.29045 + 1.29045i 0.934507 + 0.355944i \(0.115841\pi\)
0.355944 + 0.934507i \(0.384159\pi\)
\(8\) 1.12132 + 1.12132i 0.396447 + 0.396447i
\(9\) −1.00000 + 2.82843i −0.333333 + 0.942809i
\(10\) 0 0
\(11\) 1.00000i 0.301511i
\(12\) −2.58579 + 1.82843i −0.746452 + 0.527821i
\(13\) 2.00000 2.00000i 0.554700 0.554700i −0.373094 0.927794i \(-0.621703\pi\)
0.927794 + 0.373094i \(0.121703\pi\)
\(14\) 2.00000 0.534522
\(15\) 0 0
\(16\) −3.00000 −0.750000
\(17\) 2.82843 2.82843i 0.685994 0.685994i −0.275350 0.961344i \(-0.588794\pi\)
0.961344 + 0.275350i \(0.0887937\pi\)
\(18\) 0.535534 + 1.12132i 0.126227 + 0.264298i
\(19\) 2.82843i 0.648886i −0.945905 0.324443i \(-0.894823\pi\)
0.945905 0.324443i \(-0.105177\pi\)
\(20\) 0 0
\(21\) −1.41421 + 8.24264i −0.308607 + 1.79869i
\(22\) −0.292893 0.292893i −0.0624450 0.0624450i
\(23\) −3.24264 3.24264i −0.676137 0.676137i 0.282987 0.959124i \(-0.408675\pi\)
−0.959124 + 0.282987i \(0.908675\pi\)
\(24\) −0.464466 + 2.70711i −0.0948087 + 0.552586i
\(25\) 0 0
\(26\) 1.17157i 0.229764i
\(27\) −5.00000 + 1.41421i −0.962250 + 0.272166i
\(28\) −6.24264 + 6.24264i −1.17975 + 1.17975i
\(29\) 0.828427 0.153835 0.0769175 0.997037i \(-0.475492\pi\)
0.0769175 + 0.997037i \(0.475492\pi\)
\(30\) 0 0
\(31\) −3.17157 −0.569631 −0.284816 0.958582i \(-0.591932\pi\)
−0.284816 + 0.958582i \(0.591932\pi\)
\(32\) −3.12132 + 3.12132i −0.551777 + 0.551777i
\(33\) 1.41421 1.00000i 0.246183 0.174078i
\(34\) 1.65685i 0.284148i
\(35\) 0 0
\(36\) −5.17157 1.82843i −0.861929 0.304738i
\(37\) 0.171573 + 0.171573i 0.0282064 + 0.0282064i 0.721069 0.692863i \(-0.243651\pi\)
−0.692863 + 0.721069i \(0.743651\pi\)
\(38\) −0.828427 0.828427i −0.134389 0.134389i
\(39\) 4.82843 + 0.828427i 0.773167 + 0.132655i
\(40\) 0 0
\(41\) 7.65685i 1.19580i −0.801571 0.597900i \(-0.796002\pi\)
0.801571 0.597900i \(-0.203998\pi\)
\(42\) 2.00000 + 2.82843i 0.308607 + 0.436436i
\(43\) −0.242641 + 0.242641i −0.0370024 + 0.0370024i −0.725366 0.688364i \(-0.758329\pi\)
0.688364 + 0.725366i \(0.258329\pi\)
\(44\) 1.82843 0.275646
\(45\) 0 0
\(46\) −1.89949 −0.280065
\(47\) 7.24264 7.24264i 1.05645 1.05645i 0.0581392 0.998308i \(-0.481483\pi\)
0.998308 0.0581392i \(-0.0185167\pi\)
\(48\) −3.00000 4.24264i −0.433013 0.612372i
\(49\) 16.3137i 2.33053i
\(50\) 0 0
\(51\) 6.82843 + 1.17157i 0.956171 + 0.164053i
\(52\) 3.65685 + 3.65685i 0.507114 + 0.507114i
\(53\) −1.00000 1.00000i −0.137361 0.137361i 0.635083 0.772444i \(-0.280966\pi\)
−0.772444 + 0.635083i \(0.780966\pi\)
\(54\) −1.05025 + 1.87868i −0.142921 + 0.255656i
\(55\) 0 0
\(56\) 7.65685i 1.02319i
\(57\) 4.00000 2.82843i 0.529813 0.374634i
\(58\) 0.242641 0.242641i 0.0318603 0.0318603i
\(59\) −4.00000 −0.520756 −0.260378 0.965507i \(-0.583847\pi\)
−0.260378 + 0.965507i \(0.583847\pi\)
\(60\) 0 0
\(61\) −6.48528 −0.830355 −0.415178 0.909740i \(-0.636281\pi\)
−0.415178 + 0.909740i \(0.636281\pi\)
\(62\) −0.928932 + 0.928932i −0.117975 + 0.117975i
\(63\) −13.0711 + 6.24264i −1.64680 + 0.786499i
\(64\) 4.17157i 0.521447i
\(65\) 0 0
\(66\) 0.121320 0.707107i 0.0149335 0.0870388i
\(67\) 6.41421 + 6.41421i 0.783621 + 0.783621i 0.980440 0.196819i \(-0.0630611\pi\)
−0.196819 + 0.980440i \(0.563061\pi\)
\(68\) 5.17157 + 5.17157i 0.627145 + 0.627145i
\(69\) 1.34315 7.82843i 0.161696 0.942432i
\(70\) 0 0
\(71\) 2.48528i 0.294949i −0.989066 0.147474i \(-0.952886\pi\)
0.989066 0.147474i \(-0.0471144\pi\)
\(72\) −4.29289 + 2.05025i −0.505922 + 0.241625i
\(73\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(74\) 0.100505 0.0116835
\(75\) 0 0
\(76\) 5.17157 0.593220
\(77\) 3.41421 3.41421i 0.389086 0.389086i
\(78\) 1.65685 1.17157i 0.187602 0.132655i
\(79\) 10.8284i 1.21829i 0.793058 + 0.609147i \(0.208488\pi\)
−0.793058 + 0.609147i \(0.791512\pi\)
\(80\) 0 0
\(81\) −7.00000 5.65685i −0.777778 0.628539i
\(82\) −2.24264 2.24264i −0.247658 0.247658i
\(83\) 9.07107 + 9.07107i 0.995679 + 0.995679i 0.999991 0.00431166i \(-0.00137245\pi\)
−0.00431166 + 0.999991i \(0.501372\pi\)
\(84\) −15.0711 2.58579i −1.64439 0.282132i
\(85\) 0 0
\(86\) 0.142136i 0.0153269i
\(87\) 0.828427 + 1.17157i 0.0888167 + 0.125606i
\(88\) 1.12132 1.12132i 0.119533 0.119533i
\(89\) −9.65685 −1.02362 −0.511812 0.859097i \(-0.671026\pi\)
−0.511812 + 0.859097i \(0.671026\pi\)
\(90\) 0 0
\(91\) 13.6569 1.43163
\(92\) 5.92893 5.92893i 0.618134 0.618134i
\(93\) −3.17157 4.48528i −0.328877 0.465102i
\(94\) 4.24264i 0.437595i
\(95\) 0 0
\(96\) −7.53553 1.29289i −0.769092 0.131955i
\(97\) −10.6569 10.6569i −1.08204 1.08204i −0.996319 0.0857204i \(-0.972681\pi\)
−0.0857204 0.996319i \(-0.527319\pi\)
\(98\) 4.77817 + 4.77817i 0.482669 + 0.482669i
\(99\) 2.82843 + 1.00000i 0.284268 + 0.100504i
\(100\) 0 0
\(101\) 7.17157i 0.713598i −0.934181 0.356799i \(-0.883868\pi\)
0.934181 0.356799i \(-0.116132\pi\)
\(102\) 2.34315 1.65685i 0.232006 0.164053i
\(103\) 6.41421 6.41421i 0.632011 0.632011i −0.316561 0.948572i \(-0.602528\pi\)
0.948572 + 0.316561i \(0.102528\pi\)
\(104\) 4.48528 0.439818
\(105\) 0 0
\(106\) −0.585786 −0.0568966
\(107\) −0.242641 + 0.242641i −0.0234570 + 0.0234570i −0.718738 0.695281i \(-0.755280\pi\)
0.695281 + 0.718738i \(0.255280\pi\)
\(108\) −2.58579 9.14214i −0.248817 0.879702i
\(109\) 3.17157i 0.303782i 0.988397 + 0.151891i \(0.0485362\pi\)
−0.988397 + 0.151891i \(0.951464\pi\)
\(110\) 0 0
\(111\) −0.0710678 + 0.414214i −0.00674546 + 0.0393154i
\(112\) −10.2426 10.2426i −0.967839 0.967839i
\(113\) 5.82843 + 5.82843i 0.548292 + 0.548292i 0.925947 0.377654i \(-0.123269\pi\)
−0.377654 + 0.925947i \(0.623269\pi\)
\(114\) 0.343146 2.00000i 0.0321385 0.187317i
\(115\) 0 0
\(116\) 1.51472i 0.140638i
\(117\) 3.65685 + 7.65685i 0.338076 + 0.707876i
\(118\) −1.17157 + 1.17157i −0.107852 + 0.107852i
\(119\) 19.3137 1.77048
\(120\) 0 0
\(121\) −1.00000 −0.0909091
\(122\) −1.89949 + 1.89949i −0.171972 + 0.171972i
\(123\) 10.8284 7.65685i 0.976366 0.690395i
\(124\) 5.79899i 0.520765i
\(125\) 0 0
\(126\) −2.00000 + 5.65685i −0.178174 + 0.503953i
\(127\) −1.41421 1.41421i −0.125491 0.125491i 0.641572 0.767063i \(-0.278283\pi\)
−0.767063 + 0.641572i \(0.778283\pi\)
\(128\) −7.46447 7.46447i −0.659772 0.659772i
\(129\) −0.585786 0.100505i −0.0515756 0.00884898i
\(130\) 0 0
\(131\) 6.82843i 0.596602i 0.954472 + 0.298301i \(0.0964200\pi\)
−0.954472 + 0.298301i \(0.903580\pi\)
\(132\) 1.82843 + 2.58579i 0.159144 + 0.225064i
\(133\) 9.65685 9.65685i 0.837355 0.837355i
\(134\) 3.75736 0.324586
\(135\) 0 0
\(136\) 6.34315 0.543920
\(137\) −0.171573 + 0.171573i −0.0146585 + 0.0146585i −0.714398 0.699740i \(-0.753299\pi\)
0.699740 + 0.714398i \(0.253299\pi\)
\(138\) −1.89949 2.68629i −0.161696 0.228672i
\(139\) 17.6569i 1.49763i −0.662776 0.748817i \(-0.730622\pi\)
0.662776 0.748817i \(-0.269378\pi\)
\(140\) 0 0
\(141\) 17.4853 + 3.00000i 1.47253 + 0.252646i
\(142\) −0.727922 0.727922i −0.0610859 0.0610859i
\(143\) −2.00000 2.00000i −0.167248 0.167248i
\(144\) 3.00000 8.48528i 0.250000 0.707107i
\(145\) 0 0
\(146\) 0 0
\(147\) −23.0711 + 16.3137i −1.90287 + 1.34553i
\(148\) −0.313708 + 0.313708i −0.0257867 + 0.0257867i
\(149\) −10.0000 −0.819232 −0.409616 0.912258i \(-0.634337\pi\)
−0.409616 + 0.912258i \(0.634337\pi\)
\(150\) 0 0
\(151\) 10.1421 0.825355 0.412678 0.910877i \(-0.364594\pi\)
0.412678 + 0.910877i \(0.364594\pi\)
\(152\) 3.17157 3.17157i 0.257249 0.257249i
\(153\) 5.17157 + 10.8284i 0.418097 + 0.875426i
\(154\) 2.00000i 0.161165i
\(155\) 0 0
\(156\) −1.51472 + 8.82843i −0.121275 + 0.706840i
\(157\) 9.48528 + 9.48528i 0.757008 + 0.757008i 0.975777 0.218769i \(-0.0702041\pi\)
−0.218769 + 0.975777i \(0.570204\pi\)
\(158\) 3.17157 + 3.17157i 0.252317 + 0.252317i
\(159\) 0.414214 2.41421i 0.0328493 0.191460i
\(160\) 0 0
\(161\) 22.1421i 1.74504i
\(162\) −3.70711 + 0.393398i −0.291258 + 0.0309083i
\(163\) −3.58579 + 3.58579i −0.280860 + 0.280860i −0.833452 0.552592i \(-0.813639\pi\)
0.552592 + 0.833452i \(0.313639\pi\)
\(164\) 14.0000 1.09322
\(165\) 0 0
\(166\) 5.31371 0.412424
\(167\) −14.7279 + 14.7279i −1.13968 + 1.13968i −0.151174 + 0.988507i \(0.548305\pi\)
−0.988507 + 0.151174i \(0.951695\pi\)
\(168\) −10.8284 + 7.65685i −0.835431 + 0.590739i
\(169\) 5.00000i 0.384615i
\(170\) 0 0
\(171\) 8.00000 + 2.82843i 0.611775 + 0.216295i
\(172\) −0.443651 0.443651i −0.0338281 0.0338281i
\(173\) −8.48528 8.48528i −0.645124 0.645124i 0.306687 0.951811i \(-0.400780\pi\)
−0.951811 + 0.306687i \(0.900780\pi\)
\(174\) 0.585786 + 0.100505i 0.0444084 + 0.00761927i
\(175\) 0 0
\(176\) 3.00000i 0.226134i
\(177\) −4.00000 5.65685i −0.300658 0.425195i
\(178\) −2.82843 + 2.82843i −0.212000 + 0.212000i
\(179\) 24.1421 1.80447 0.902234 0.431247i \(-0.141926\pi\)
0.902234 + 0.431247i \(0.141926\pi\)
\(180\) 0 0
\(181\) 5.65685 0.420471 0.210235 0.977651i \(-0.432577\pi\)
0.210235 + 0.977651i \(0.432577\pi\)
\(182\) 4.00000 4.00000i 0.296500 0.296500i
\(183\) −6.48528 9.17157i −0.479406 0.677982i
\(184\) 7.27208i 0.536105i
\(185\) 0 0
\(186\) −2.24264 0.384776i −0.164438 0.0282132i
\(187\) −2.82843 2.82843i −0.206835 0.206835i
\(188\) 13.2426 + 13.2426i 0.965819 + 0.965819i
\(189\) −21.8995 12.2426i −1.59295 0.890521i
\(190\) 0 0
\(191\) 11.3137i 0.818631i 0.912393 + 0.409316i \(0.134232\pi\)
−0.912393 + 0.409316i \(0.865768\pi\)
\(192\) 5.89949 4.17157i 0.425759 0.301057i
\(193\) −8.00000 + 8.00000i −0.575853 + 0.575853i −0.933758 0.357905i \(-0.883491\pi\)
0.357905 + 0.933758i \(0.383491\pi\)
\(194\) −6.24264 −0.448195
\(195\) 0 0
\(196\) −29.8284 −2.13060
\(197\) 14.1421 14.1421i 1.00759 1.00759i 0.00761443 0.999971i \(-0.497576\pi\)
0.999971 0.00761443i \(-0.00242377\pi\)
\(198\) 1.12132 0.535534i 0.0796888 0.0380587i
\(199\) 14.4853i 1.02683i −0.858139 0.513417i \(-0.828379\pi\)
0.858139 0.513417i \(-0.171621\pi\)
\(200\) 0 0
\(201\) −2.65685 + 15.4853i −0.187400 + 1.09225i
\(202\) −2.10051 2.10051i −0.147791 0.147791i
\(203\) 2.82843 + 2.82843i 0.198517 + 0.198517i
\(204\) −2.14214 + 12.4853i −0.149979 + 0.874145i
\(205\) 0 0
\(206\) 3.75736i 0.261788i
\(207\) 12.4142 5.92893i 0.862847 0.412089i
\(208\) −6.00000 + 6.00000i −0.416025 + 0.416025i
\(209\) −2.82843 −0.195646
\(210\) 0 0
\(211\) −4.48528 −0.308780 −0.154390 0.988010i \(-0.549341\pi\)
−0.154390 + 0.988010i \(0.549341\pi\)
\(212\) 1.82843 1.82843i 0.125577 0.125577i
\(213\) 3.51472 2.48528i 0.240825 0.170289i
\(214\) 0.142136i 0.00971619i
\(215\) 0 0
\(216\) −7.19239 4.02082i −0.489380 0.273582i
\(217\) −10.8284 10.8284i −0.735082 0.735082i
\(218\) 0.928932 + 0.928932i 0.0629152 + 0.0629152i
\(219\) 0 0
\(220\) 0 0
\(221\) 11.3137i 0.761042i
\(222\) 0.100505 + 0.142136i 0.00674546 + 0.00953952i
\(223\) 16.5563 16.5563i 1.10870 1.10870i 0.115373 0.993322i \(-0.463194\pi\)
0.993322 0.115373i \(-0.0368063\pi\)
\(224\) −21.3137 −1.42408
\(225\) 0 0
\(226\) 3.41421 0.227110
\(227\) −10.2426 + 10.2426i −0.679828 + 0.679828i −0.959961 0.280133i \(-0.909621\pi\)
0.280133 + 0.959961i \(0.409621\pi\)
\(228\) 5.17157 + 7.31371i 0.342496 + 0.484362i
\(229\) 9.65685i 0.638143i −0.947731 0.319071i \(-0.896629\pi\)
0.947731 0.319071i \(-0.103371\pi\)
\(230\) 0 0
\(231\) 8.24264 + 1.41421i 0.542326 + 0.0930484i
\(232\) 0.928932 + 0.928932i 0.0609874 + 0.0609874i
\(233\) −19.6569 19.6569i −1.28776 1.28776i −0.936143 0.351621i \(-0.885631\pi\)
−0.351621 0.936143i \(-0.614369\pi\)
\(234\) 3.31371 + 1.17157i 0.216624 + 0.0765881i
\(235\) 0 0
\(236\) 7.31371i 0.476082i
\(237\) −15.3137 + 10.8284i −0.994732 + 0.703382i
\(238\) 5.65685 5.65685i 0.366679 0.366679i
\(239\) −23.7990 −1.53943 −0.769714 0.638388i \(-0.779601\pi\)
−0.769714 + 0.638388i \(0.779601\pi\)
\(240\) 0 0
\(241\) 0.142136 0.00915576 0.00457788 0.999990i \(-0.498543\pi\)
0.00457788 + 0.999990i \(0.498543\pi\)
\(242\) −0.292893 + 0.292893i −0.0188279 + 0.0188279i
\(243\) 1.00000 15.5563i 0.0641500 0.997940i
\(244\) 11.8579i 0.759122i
\(245\) 0 0
\(246\) 0.928932 5.41421i 0.0592266 0.345198i
\(247\) −5.65685 5.65685i −0.359937 0.359937i
\(248\) −3.55635 3.55635i −0.225828 0.225828i
\(249\) −3.75736 + 21.8995i −0.238113 + 1.38782i
\(250\) 0 0
\(251\) 16.1421i 1.01888i −0.860505 0.509441i \(-0.829852\pi\)
0.860505 0.509441i \(-0.170148\pi\)
\(252\) −11.4142 23.8995i −0.719028 1.50553i
\(253\) −3.24264 + 3.24264i −0.203863 + 0.203863i
\(254\) −0.828427 −0.0519801
\(255\) 0 0
\(256\) 3.97056 0.248160
\(257\) 1.82843 1.82843i 0.114054 0.114054i −0.647776 0.761831i \(-0.724301\pi\)
0.761831 + 0.647776i \(0.224301\pi\)
\(258\) −0.201010 + 0.142136i −0.0125143 + 0.00884898i
\(259\) 1.17157i 0.0727980i
\(260\) 0 0
\(261\) −0.828427 + 2.34315i −0.0512784 + 0.145037i
\(262\) 2.00000 + 2.00000i 0.123560 + 0.123560i
\(263\) 1.75736 + 1.75736i 0.108363 + 0.108363i 0.759210 0.650846i \(-0.225586\pi\)
−0.650846 + 0.759210i \(0.725586\pi\)
\(264\) 2.70711 + 0.464466i 0.166611 + 0.0285859i
\(265\) 0 0
\(266\) 5.65685i 0.346844i
\(267\) −9.65685 13.6569i −0.590990 0.835786i
\(268\) −11.7279 + 11.7279i −0.716397 + 0.716397i
\(269\) −14.0000 −0.853595 −0.426798 0.904347i \(-0.640358\pi\)
−0.426798 + 0.904347i \(0.640358\pi\)
\(270\) 0 0
\(271\) 8.48528 0.515444 0.257722 0.966219i \(-0.417028\pi\)
0.257722 + 0.966219i \(0.417028\pi\)
\(272\) −8.48528 + 8.48528i −0.514496 + 0.514496i
\(273\) 13.6569 + 19.3137i 0.826550 + 1.16892i
\(274\) 0.100505i 0.00607173i
\(275\) 0 0
\(276\) 14.3137 + 2.45584i 0.861584 + 0.147824i
\(277\) 18.4853 + 18.4853i 1.11067 + 1.11067i 0.993059 + 0.117613i \(0.0375244\pi\)
0.117613 + 0.993059i \(0.462476\pi\)
\(278\) −5.17157 5.17157i −0.310170 0.310170i
\(279\) 3.17157 8.97056i 0.189877 0.537054i
\(280\) 0 0
\(281\) 28.6274i 1.70777i 0.520463 + 0.853884i \(0.325759\pi\)
−0.520463 + 0.853884i \(0.674241\pi\)
\(282\) 6.00000 4.24264i 0.357295 0.252646i
\(283\) 15.0711 15.0711i 0.895882 0.895882i −0.0991868 0.995069i \(-0.531624\pi\)
0.995069 + 0.0991868i \(0.0316241\pi\)
\(284\) 4.54416 0.269646
\(285\) 0 0
\(286\) −1.17157 −0.0692766
\(287\) 26.1421 26.1421i 1.54312 1.54312i
\(288\) −5.70711 11.9497i −0.336294 0.704146i
\(289\) 1.00000i 0.0588235i
\(290\) 0 0
\(291\) 4.41421 25.7279i 0.258766 1.50820i
\(292\) 0 0
\(293\) 3.65685 + 3.65685i 0.213636 + 0.213636i 0.805810 0.592174i \(-0.201730\pi\)
−0.592174 + 0.805810i \(0.701730\pi\)
\(294\) −1.97918 + 11.5355i −0.115428 + 0.672766i
\(295\) 0 0
\(296\) 0.384776i 0.0223647i
\(297\) 1.41421 + 5.00000i 0.0820610 + 0.290129i
\(298\) −2.92893 + 2.92893i −0.169668 + 0.169668i
\(299\) −12.9706 −0.750107
\(300\) 0 0
\(301\) −1.65685 −0.0954995
\(302\) 2.97056 2.97056i 0.170937 0.170937i
\(303\) 10.1421 7.17157i 0.582650 0.411996i
\(304\) 8.48528i 0.486664i
\(305\) 0 0
\(306\) 4.68629 + 1.65685i 0.267897 + 0.0947161i
\(307\) 11.8995 + 11.8995i 0.679140 + 0.679140i 0.959806 0.280666i \(-0.0905552\pi\)
−0.280666 + 0.959806i \(0.590555\pi\)
\(308\) 6.24264 + 6.24264i 0.355707 + 0.355707i
\(309\) 15.4853 + 2.65685i 0.880927 + 0.151143i
\(310\) 0 0
\(311\) 28.1421i 1.59579i 0.602794 + 0.797897i \(0.294054\pi\)
−0.602794 + 0.797897i \(0.705946\pi\)
\(312\) 4.48528 + 6.34315i 0.253929 + 0.359110i
\(313\) −12.6569 + 12.6569i −0.715408 + 0.715408i −0.967661 0.252253i \(-0.918828\pi\)
0.252253 + 0.967661i \(0.418828\pi\)
\(314\) 5.55635 0.313563
\(315\) 0 0
\(316\) −19.7990 −1.11378
\(317\) −2.31371 + 2.31371i −0.129951 + 0.129951i −0.769091 0.639140i \(-0.779291\pi\)
0.639140 + 0.769091i \(0.279291\pi\)
\(318\) −0.585786 0.828427i −0.0328493 0.0464559i
\(319\) 0.828427i 0.0463830i
\(320\) 0 0
\(321\) −0.585786 0.100505i −0.0326954 0.00560965i
\(322\) −6.48528 6.48528i −0.361411 0.361411i
\(323\) −8.00000 8.00000i −0.445132 0.445132i
\(324\) 10.3431 12.7990i 0.574619 0.711055i
\(325\) 0 0
\(326\) 2.10051i 0.116336i
\(327\) −4.48528 + 3.17157i −0.248037 + 0.175388i
\(328\) 8.58579 8.58579i 0.474071 0.474071i
\(329\) 49.4558 2.72659
\(330\) 0 0
\(331\) −6.48528 −0.356463 −0.178232 0.983989i \(-0.557038\pi\)
−0.178232 + 0.983989i \(0.557038\pi\)
\(332\) −16.5858 + 16.5858i −0.910263 + 0.910263i
\(333\) −0.656854 + 0.313708i −0.0359954 + 0.0171911i
\(334\) 8.62742i 0.472071i
\(335\) 0 0
\(336\) 4.24264 24.7279i 0.231455 1.34902i
\(337\) 10.8284 + 10.8284i 0.589862 + 0.589862i 0.937594 0.347732i \(-0.113048\pi\)
−0.347732 + 0.937594i \(0.613048\pi\)
\(338\) 1.46447 + 1.46447i 0.0796565 + 0.0796565i
\(339\) −2.41421 + 14.0711i −0.131122 + 0.764235i
\(340\) 0 0
\(341\) 3.17157i 0.171750i
\(342\) 3.17157 1.51472i 0.171499 0.0819066i
\(343\) −31.7990 + 31.7990i −1.71698 + 1.71698i
\(344\) −0.544156 −0.0293389
\(345\) 0 0
\(346\) −4.97056 −0.267219
\(347\) −1.89949 + 1.89949i −0.101970 + 0.101970i −0.756251 0.654281i \(-0.772971\pi\)
0.654281 + 0.756251i \(0.272971\pi\)
\(348\) −2.14214 + 1.51472i −0.114831 + 0.0811974i
\(349\) 30.0000i 1.60586i 0.596071 + 0.802932i \(0.296728\pi\)
−0.596071 + 0.802932i \(0.703272\pi\)
\(350\) 0 0
\(351\) −7.17157 + 12.8284i −0.382790 + 0.684731i
\(352\) 3.12132 + 3.12132i 0.166367 + 0.166367i
\(353\) −7.82843 7.82843i −0.416665 0.416665i 0.467387 0.884053i \(-0.345195\pi\)
−0.884053 + 0.467387i \(0.845195\pi\)
\(354\) −2.82843 0.485281i −0.150329 0.0257924i
\(355\) 0 0
\(356\) 17.6569i 0.935811i
\(357\) 19.3137 + 27.3137i 1.02219 + 1.44559i
\(358\) 7.07107 7.07107i 0.373718 0.373718i
\(359\) −22.1421 −1.16862 −0.584309 0.811532i \(-0.698634\pi\)
−0.584309 + 0.811532i \(0.698634\pi\)
\(360\) 0 0
\(361\) 11.0000 0.578947
\(362\) 1.65685 1.65685i 0.0870823 0.0870823i
\(363\) −1.00000 1.41421i −0.0524864 0.0742270i
\(364\) 24.9706i 1.30881i
\(365\) 0 0
\(366\) −4.58579 0.786797i −0.239703 0.0411265i
\(367\) 1.10051 + 1.10051i 0.0574459 + 0.0574459i 0.735246 0.677800i \(-0.237067\pi\)
−0.677800 + 0.735246i \(0.737067\pi\)
\(368\) 9.72792 + 9.72792i 0.507103 + 0.507103i
\(369\) 21.6569 + 7.65685i 1.12741 + 0.398600i
\(370\) 0 0
\(371\) 6.82843i 0.354514i
\(372\) 8.20101 5.79899i 0.425203 0.300664i
\(373\) −3.51472 + 3.51472i −0.181985 + 0.181985i −0.792220 0.610235i \(-0.791075\pi\)
0.610235 + 0.792220i \(0.291075\pi\)
\(374\) −1.65685 −0.0856739
\(375\) 0 0
\(376\) 16.2426 0.837650
\(377\) 1.65685 1.65685i 0.0853323 0.0853323i
\(378\) −10.0000 + 2.82843i −0.514344 + 0.145479i
\(379\) 28.1421i 1.44556i −0.691076 0.722782i \(-0.742863\pi\)
0.691076 0.722782i \(-0.257137\pi\)
\(380\) 0 0
\(381\) 0.585786 3.41421i 0.0300107 0.174915i
\(382\) 3.31371 + 3.31371i 0.169544 + 0.169544i
\(383\) 6.07107 + 6.07107i 0.310217 + 0.310217i 0.844994 0.534776i \(-0.179604\pi\)
−0.534776 + 0.844994i \(0.679604\pi\)
\(384\) 3.09188 18.0208i 0.157782 0.919621i
\(385\) 0 0
\(386\) 4.68629i 0.238526i
\(387\) −0.443651 0.928932i −0.0225520 0.0472203i
\(388\) 19.4853 19.4853i 0.989215 0.989215i
\(389\) −17.3137 −0.877840 −0.438920 0.898526i \(-0.644639\pi\)
−0.438920 + 0.898526i \(0.644639\pi\)
\(390\) 0 0
\(391\) −18.3431 −0.927653
\(392\) −18.2929 + 18.2929i −0.923931 + 0.923931i
\(393\) −9.65685 + 6.82843i −0.487124 + 0.344449i
\(394\) 8.28427i 0.417356i
\(395\) 0 0
\(396\) −1.82843 + 5.17157i −0.0918819 + 0.259881i
\(397\) −6.17157 6.17157i −0.309742 0.309742i 0.535067 0.844810i \(-0.320286\pi\)
−0.844810 + 0.535067i \(0.820286\pi\)
\(398\) −4.24264 4.24264i −0.212664 0.212664i
\(399\) 23.3137 + 4.00000i 1.16715 + 0.200250i
\(400\) 0 0
\(401\) 35.6569i 1.78062i 0.455357 + 0.890309i \(0.349512\pi\)
−0.455357 + 0.890309i \(0.650488\pi\)
\(402\) 3.75736 + 5.31371i 0.187400 + 0.265024i
\(403\) −6.34315 + 6.34315i −0.315975 + 0.315975i
\(404\) 13.1127 0.652381
\(405\) 0 0
\(406\) 1.65685 0.0822283
\(407\) 0.171573 0.171573i 0.00850455 0.00850455i
\(408\) 6.34315 + 8.97056i 0.314033 + 0.444109i
\(409\) 18.4853i 0.914038i 0.889457 + 0.457019i \(0.151083\pi\)
−0.889457 + 0.457019i \(0.848917\pi\)
\(410\) 0 0
\(411\) −0.414214 0.0710678i −0.0204316 0.00350552i
\(412\) 11.7279 + 11.7279i 0.577793 + 0.577793i
\(413\) −13.6569 13.6569i −0.672010 0.672010i
\(414\) 1.89949 5.37258i 0.0933551 0.264048i
\(415\) 0 0
\(416\) 12.4853i 0.612141i
\(417\) 24.9706 17.6569i 1.22281 0.864660i
\(418\) −0.828427 + 0.828427i −0.0405197 + 0.0405197i
\(419\) 15.4558 0.755067 0.377534 0.925996i \(-0.376772\pi\)
0.377534 + 0.925996i \(0.376772\pi\)
\(420\) 0 0
\(421\) −4.00000 −0.194948 −0.0974740 0.995238i \(-0.531076\pi\)
−0.0974740 + 0.995238i \(0.531076\pi\)
\(422\) −1.31371 + 1.31371i −0.0639503 + 0.0639503i
\(423\) 13.2426 + 27.7279i 0.643879 + 1.34818i
\(424\) 2.24264i 0.108912i
\(425\) 0 0
\(426\) 0.301515 1.75736i 0.0146085 0.0851443i
\(427\) −22.1421 22.1421i −1.07153 1.07153i
\(428\) −0.443651 0.443651i −0.0214447 0.0214447i
\(429\) 0.828427 4.82843i 0.0399968 0.233119i
\(430\) 0 0
\(431\) 6.34315i 0.305539i −0.988262 0.152769i \(-0.951181\pi\)
0.988262 0.152769i \(-0.0488191\pi\)
\(432\) 15.0000 4.24264i 0.721688 0.204124i
\(433\) 0.313708 0.313708i 0.0150759 0.0150759i −0.699529 0.714605i \(-0.746607\pi\)
0.714605 + 0.699529i \(0.246607\pi\)
\(434\) −6.34315 −0.304481
\(435\) 0 0
\(436\) −5.79899 −0.277721
\(437\) −9.17157 + 9.17157i −0.438736 + 0.438736i
\(438\) 0 0
\(439\) 7.31371i 0.349064i 0.984651 + 0.174532i \(0.0558413\pi\)
−0.984651 + 0.174532i \(0.944159\pi\)
\(440\) 0 0
\(441\) −46.1421 16.3137i −2.19724 0.776843i
\(442\) −3.31371 3.31371i −0.157617 0.157617i
\(443\) 20.7574 + 20.7574i 0.986212 + 0.986212i 0.999906 0.0136943i \(-0.00435918\pi\)
−0.0136943 + 0.999906i \(0.504359\pi\)
\(444\) −0.757359 0.129942i −0.0359427 0.00616679i
\(445\) 0 0
\(446\) 9.69848i 0.459237i
\(447\) −10.0000 14.1421i −0.472984 0.668900i
\(448\) 14.2426 14.2426i 0.672902 0.672902i
\(449\) −3.02944 −0.142968 −0.0714840 0.997442i \(-0.522773\pi\)
−0.0714840 + 0.997442i \(0.522773\pi\)
\(450\) 0 0
\(451\) −7.65685 −0.360547
\(452\) −10.6569 + 10.6569i −0.501256 + 0.501256i
\(453\) 10.1421 + 14.3431i 0.476519 + 0.673900i
\(454\) 6.00000i 0.281594i
\(455\) 0 0
\(456\) 7.65685 + 1.31371i 0.358565 + 0.0615200i
\(457\) 6.48528 + 6.48528i 0.303369 + 0.303369i 0.842330 0.538962i \(-0.181183\pi\)
−0.538962 + 0.842330i \(0.681183\pi\)
\(458\) −2.82843 2.82843i −0.132164 0.132164i
\(459\) −10.1421 + 18.1421i −0.473394 + 0.846802i
\(460\) 0 0
\(461\) 13.5147i 0.629443i −0.949184 0.314722i \(-0.898089\pi\)
0.949184 0.314722i \(-0.101911\pi\)
\(462\) 2.82843 2.00000i 0.131590 0.0930484i
\(463\) −11.7279 + 11.7279i −0.545043 + 0.545043i −0.925003 0.379960i \(-0.875938\pi\)
0.379960 + 0.925003i \(0.375938\pi\)
\(464\) −2.48528 −0.115376
\(465\) 0 0
\(466\) −11.5147 −0.533409
\(467\) 0.414214 0.414214i 0.0191675 0.0191675i −0.697458 0.716626i \(-0.745686\pi\)
0.716626 + 0.697458i \(0.245686\pi\)
\(468\) −14.0000 + 6.68629i −0.647150 + 0.309074i
\(469\) 43.7990i 2.02245i
\(470\) 0 0
\(471\) −3.92893 + 22.8995i −0.181036 + 1.05515i
\(472\) −4.48528 4.48528i −0.206452 0.206452i
\(473\) 0.242641 + 0.242641i 0.0111566 + 0.0111566i
\(474\) −1.31371 + 7.65685i −0.0603406 + 0.351691i
\(475\) 0 0
\(476\) 35.3137i 1.61860i
\(477\) 3.82843 1.82843i 0.175292 0.0837179i
\(478\) −6.97056 + 6.97056i −0.318826 + 0.318826i
\(479\) −30.1421 −1.37723 −0.688615 0.725127i \(-0.741781\pi\)
−0.688615 + 0.725127i \(0.741781\pi\)
\(480\) 0 0
\(481\) 0.686292 0.0312922
\(482\) 0.0416306 0.0416306i 0.00189622 0.00189622i
\(483\) 31.3137 22.1421i 1.42482 1.00750i
\(484\) 1.82843i 0.0831103i
\(485\) 0 0
\(486\) −4.26346 4.84924i −0.193394 0.219966i
\(487\) −11.7279 11.7279i −0.531443 0.531443i 0.389559 0.921002i \(-0.372628\pi\)
−0.921002 + 0.389559i \(0.872628\pi\)
\(488\) −7.27208 7.27208i −0.329192 0.329192i
\(489\) −8.65685 1.48528i −0.391476 0.0671667i
\(490\) 0 0
\(491\) 20.0000i 0.902587i −0.892375 0.451294i \(-0.850963\pi\)
0.892375 0.451294i \(-0.149037\pi\)
\(492\) 14.0000 + 19.7990i 0.631169 + 0.892607i
\(493\) 2.34315 2.34315i 0.105530 0.105530i
\(494\) −3.31371 −0.149091
\(495\) 0 0
\(496\) 9.51472 0.427223
\(497\) 8.48528 8.48528i 0.380617 0.380617i
\(498\) 5.31371 + 7.51472i 0.238113 + 0.336743i
\(499\) 24.8284i 1.11147i −0.831358 0.555737i \(-0.812436\pi\)
0.831358 0.555737i \(-0.187564\pi\)
\(500\) 0 0
\(501\) −35.5563 6.10051i −1.58854 0.272550i
\(502\) −4.72792 4.72792i −0.211017 0.211017i
\(503\) −0.928932 0.928932i −0.0414190 0.0414190i 0.686094 0.727513i \(-0.259324\pi\)
−0.727513 + 0.686094i \(0.759324\pi\)
\(504\) −21.6569 7.65685i −0.964673 0.341063i
\(505\) 0 0
\(506\) 1.89949i 0.0844428i
\(507\) −7.07107 + 5.00000i −0.314037 + 0.222058i
\(508\) 2.58579 2.58579i 0.114726 0.114726i
\(509\) 35.6569 1.58046 0.790231 0.612809i \(-0.209960\pi\)
0.790231 + 0.612809i \(0.209960\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 16.0919 16.0919i 0.711167 0.711167i
\(513\) 4.00000 + 14.1421i 0.176604 + 0.624391i
\(514\) 1.07107i 0.0472428i
\(515\) 0 0
\(516\) 0.183766 1.07107i 0.00808986 0.0471511i
\(517\) −7.24264 7.24264i −0.318531 0.318531i
\(518\) 0.343146 + 0.343146i 0.0150770 + 0.0150770i
\(519\) 3.51472 20.4853i 0.154279 0.899204i
\(520\) 0 0
\(521\) 27.6569i 1.21167i −0.795591 0.605834i \(-0.792839\pi\)
0.795591 0.605834i \(-0.207161\pi\)
\(522\) 0.443651 + 0.928932i 0.0194181 + 0.0406583i
\(523\) 27.2132 27.2132i 1.18995 1.18995i 0.212870 0.977081i \(-0.431719\pi\)
0.977081 0.212870i \(-0.0682810\pi\)
\(524\) −12.4853 −0.545422
\(525\) 0 0
\(526\) 1.02944 0.0448856
\(527\) −8.97056 + 8.97056i −0.390764 + 0.390764i
\(528\) −4.24264 + 3.00000i −0.184637 + 0.130558i
\(529\) 1.97056i 0.0856766i
\(530\) 0 0
\(531\) 4.00000 11.3137i 0.173585 0.490973i
\(532\) 17.6569 + 17.6569i 0.765522 + 0.765522i
\(533\) −15.3137 15.3137i −0.663310 0.663310i
\(534\) −6.82843 1.17157i −0.295495 0.0506989i
\(535\) 0 0
\(536\) 14.3848i 0.621328i
\(537\) 24.1421 + 34.1421i 1.04181 + 1.47334i
\(538\) −4.10051 + 4.10051i −0.176785 + 0.176785i
\(539\) 16.3137 0.702681
\(540\) 0 0
\(541\) −10.6863 −0.459440 −0.229720 0.973257i \(-0.573781\pi\)
−0.229720 + 0.973257i \(0.573781\pi\)
\(542\) 2.48528 2.48528i 0.106752 0.106752i
\(543\) 5.65685 + 8.00000i 0.242759 + 0.343313i
\(544\) 17.6569i 0.757031i
\(545\) 0 0
\(546\) 9.65685 + 1.65685i 0.413275 + 0.0709068i
\(547\) −2.10051 2.10051i −0.0898111 0.0898111i 0.660774 0.750585i \(-0.270228\pi\)
−0.750585 + 0.660774i \(0.770228\pi\)
\(548\) −0.313708 0.313708i −0.0134010 0.0134010i
\(549\) 6.48528 18.3431i 0.276785 0.782866i
\(550\) 0 0
\(551\) 2.34315i 0.0998214i
\(552\) 10.2843 7.27208i 0.437728 0.309520i
\(553\) −36.9706 + 36.9706i −1.57215 + 1.57215i
\(554\) 10.8284 0.460056
\(555\) 0 0
\(556\) 32.2843 1.36916
\(557\) −8.97056 + 8.97056i −0.380095 + 0.380095i −0.871136 0.491041i \(-0.836616\pi\)
0.491041 + 0.871136i \(0.336616\pi\)
\(558\) −1.69848 3.55635i −0.0719026 0.150552i
\(559\) 0.970563i 0.0410504i
\(560\) 0 0
\(561\) 1.17157 6.82843i 0.0494638 0.288296i
\(562\) 8.38478 + 8.38478i 0.353690 + 0.353690i
\(563\) 9.89949 + 9.89949i 0.417214 + 0.417214i 0.884242 0.467028i \(-0.154675\pi\)
−0.467028 + 0.884242i \(0.654675\pi\)
\(564\) −5.48528 + 31.9706i −0.230972 + 1.34620i
\(565\) 0 0
\(566\) 8.82843i 0.371086i
\(567\) −4.58579 43.2132i −0.192585 1.81478i
\(568\) 2.78680 2.78680i 0.116931 0.116931i
\(569\) −28.3431 −1.18821 −0.594103 0.804389i \(-0.702493\pi\)
−0.594103 + 0.804389i \(0.702493\pi\)
\(570\) 0 0
\(571\) 29.6569 1.24110 0.620550 0.784167i \(-0.286909\pi\)
0.620550 + 0.784167i \(0.286909\pi\)
\(572\) 3.65685 3.65685i 0.152901 0.152901i
\(573\) −16.0000 + 11.3137i −0.668410 + 0.472637i
\(574\) 15.3137i 0.639182i
\(575\) 0 0
\(576\) 11.7990 + 4.17157i 0.491625 + 0.173816i
\(577\) −17.0000 17.0000i −0.707719 0.707719i 0.258336 0.966055i \(-0.416826\pi\)
−0.966055 + 0.258336i \(0.916826\pi\)
\(578\) 0.292893 + 0.292893i 0.0121828 + 0.0121828i
\(579\) −19.3137 3.31371i −0.802650 0.137713i
\(580\) 0 0
\(581\) 61.9411i 2.56975i
\(582\) −6.24264 8.82843i −0.258766 0.365950i
\(583\) −1.00000 + 1.00000i −0.0414158 + 0.0414158i
\(584\) 0 0
\(585\) 0 0
\(586\) 2.14214 0.0884908
\(587\) 0.414214 0.414214i 0.0170964 0.0170964i −0.698507 0.715603i \(-0.746152\pi\)
0.715603 + 0.698507i \(0.246152\pi\)
\(588\) −29.8284 42.1838i −1.23010 1.73963i
\(589\) 8.97056i 0.369626i
\(590\) 0 0
\(591\) 34.1421 + 5.85786i 1.40442 + 0.240960i
\(592\) −0.514719 0.514719i −0.0211548 0.0211548i
\(593\) −5.85786 5.85786i −0.240554 0.240554i 0.576525 0.817079i \(-0.304408\pi\)
−0.817079 + 0.576525i \(0.804408\pi\)
\(594\) 1.87868 + 1.05025i 0.0770832 + 0.0430924i
\(595\) 0 0
\(596\) 18.2843i 0.748953i
\(597\) 20.4853 14.4853i 0.838407 0.592843i
\(598\) −3.79899 + 3.79899i −0.155352 + 0.155352i
\(599\) −3.45584 −0.141202 −0.0706010 0.997505i \(-0.522492\pi\)
−0.0706010 + 0.997505i \(0.522492\pi\)
\(600\) 0 0
\(601\) −27.4558 −1.11995 −0.559974 0.828510i \(-0.689189\pi\)
−0.559974 + 0.828510i \(0.689189\pi\)
\(602\) −0.485281 + 0.485281i −0.0197786 + 0.0197786i
\(603\) −24.5563 + 11.7279i −1.00001 + 0.477598i
\(604\) 18.5442i 0.754551i
\(605\) 0 0
\(606\) 0.870058 5.07107i 0.0353437 0.205998i
\(607\) 21.8995 + 21.8995i 0.888873 + 0.888873i 0.994415 0.105542i \(-0.0336577\pi\)
−0.105542 + 0.994415i \(0.533658\pi\)
\(608\) 8.82843 + 8.82843i 0.358040 + 0.358040i
\(609\) −1.17157 + 6.82843i −0.0474745 + 0.276702i
\(610\) 0 0
\(611\) 28.9706i 1.17202i
\(612\) −19.7990 + 9.45584i −0.800327 + 0.382230i
\(613\) 16.0000 16.0000i 0.646234 0.646234i −0.305847 0.952081i \(-0.598940\pi\)
0.952081 + 0.305847i \(0.0989395\pi\)
\(614\) 6.97056 0.281309
\(615\) 0 0
\(616\) 7.65685 0.308503
\(617\) −29.8284 + 29.8284i −1.20085 + 1.20085i −0.226938 + 0.973909i \(0.572871\pi\)
−0.973909 + 0.226938i \(0.927129\pi\)
\(618\) 5.31371 3.75736i 0.213749 0.151143i
\(619\) 0.686292i 0.0275844i 0.999905 + 0.0137922i \(0.00439033\pi\)
−0.999905 + 0.0137922i \(0.995610\pi\)
\(620\) 0 0
\(621\) 20.7990 + 11.6274i 0.834635 + 0.466592i
\(622\) 8.24264 + 8.24264i 0.330500 + 0.330500i
\(623\) −32.9706 32.9706i −1.32094 1.32094i
\(624\) −14.4853 2.48528i −0.579875 0.0994909i
\(625\) 0 0
\(626\) 7.41421i 0.296332i
\(627\) −2.82843 4.00000i −0.112956 0.159745i
\(628\) −17.3431 + 17.3431i −0.692067 + 0.692067i
\(629\) 0.970563 0.0386989
\(630\) 0 0
\(631\) −16.9706 −0.675587 −0.337794 0.941220i \(-0.609681\pi\)
−0.337794 + 0.941220i \(0.609681\pi\)
\(632\) −12.1421 + 12.1421i −0.482988 + 0.482988i
\(633\) −4.48528 6.34315i −0.178274 0.252117i
\(634\) 1.35534i 0.0538274i
\(635\) 0 0
\(636\) 4.41421 + 0.757359i 0.175035 + 0.0300313i
\(637\) 32.6274 + 32.6274i 1.29275 + 1.29275i
\(638\) −0.242641 0.242641i −0.00960624 0.00960624i
\(639\) 7.02944 + 2.48528i 0.278080 + 0.0983162i
\(640\) 0 0
\(641\) 32.6274i 1.28871i −0.764728 0.644353i \(-0.777127\pi\)
0.764728 0.644353i \(-0.222873\pi\)
\(642\) −0.201010 + 0.142136i −0.00793324 + 0.00560965i
\(643\) 9.24264 9.24264i 0.364494 0.364494i −0.500970 0.865464i \(-0.667023\pi\)
0.865464 + 0.500970i \(0.167023\pi\)
\(644\) 40.4853 1.59534
\(645\) 0 0
\(646\) −4.68629 −0.184380
\(647\) −11.7279 + 11.7279i −0.461072 + 0.461072i −0.899007 0.437935i \(-0.855710\pi\)
0.437935 + 0.899007i \(0.355710\pi\)
\(648\) −1.50610 14.1924i −0.0591651 0.557530i
\(649\) 4.00000i 0.157014i
\(650\) 0 0
\(651\) 4.48528 26.1421i 0.175792 1.02459i
\(652\) −6.55635 6.55635i −0.256766 0.256766i
\(653\) −8.65685 8.65685i −0.338769 0.338769i 0.517135 0.855904i \(-0.326999\pi\)
−0.855904 + 0.517135i \(0.826999\pi\)
\(654\) −0.384776 + 2.24264i −0.0150459 + 0.0876942i
\(655\) 0 0
\(656\) 22.9706i 0.896850i
\(657\) 0 0
\(658\) 14.4853 14.4853i 0.564695 0.564695i
\(659\) −24.9706 −0.972715 −0.486358 0.873760i \(-0.661675\pi\)
−0.486358 + 0.873760i \(0.661675\pi\)
\(660\) 0 0
\(661\) 14.0000 0.544537 0.272268 0.962221i \(-0.412226\pi\)
0.272268 + 0.962221i \(0.412226\pi\)
\(662\) −1.89949 + 1.89949i −0.0738260 + 0.0738260i
\(663\) 16.0000 11.3137i 0.621389 0.439388i
\(664\) 20.3431i 0.789467i
\(665\) 0 0
\(666\) −0.100505 + 0.284271i −0.00389449 + 0.0110153i
\(667\) −2.68629 2.68629i −0.104014 0.104014i
\(668\) −26.9289 26.9289i −1.04191 1.04191i
\(669\) 39.9706 + 6.85786i 1.54535 + 0.265140i
\(670\) 0 0
\(671\) 6.48528i 0.250362i
\(672\) −21.3137 30.1421i −0.822194 1.16276i
\(673\) 22.3431 22.3431i 0.861265 0.861265i −0.130220 0.991485i \(-0.541568\pi\)
0.991485 + 0.130220i \(0.0415684\pi\)
\(674\) 6.34315 0.244329
\(675\) 0 0
\(676\) −9.14214 −0.351621
\(677\) −19.6569 + 19.6569i −0.755474 + 0.755474i −0.975495 0.220021i \(-0.929387\pi\)
0.220021 + 0.975495i \(0.429387\pi\)
\(678\) 3.41421 + 4.82843i 0.131122 + 0.185435i
\(679\) 72.7696i 2.79264i
\(680\) 0 0
\(681\) −24.7279 4.24264i −0.947576 0.162578i
\(682\) 0.928932 + 0.928932i 0.0355707 + 0.0355707i
\(683\) −7.72792 7.72792i −0.295701 0.295701i 0.543627 0.839327i \(-0.317051\pi\)
−0.839327 + 0.543627i \(0.817051\pi\)
\(684\) −5.17157 + 14.6274i −0.197740 + 0.559293i
\(685\) 0 0
\(686\) 18.6274i 0.711198i
\(687\) 13.6569 9.65685i 0.521041 0.368432i
\(688\) 0.727922 0.727922i 0.0277518 0.0277518i
\(689\) −4.00000 −0.152388
\(690\) 0 0
\(691\) 20.0000 0.760836 0.380418 0.924815i \(-0.375780\pi\)
0.380418 + 0.924815i \(0.375780\pi\)
\(692\) 15.5147 15.5147i 0.589781 0.589781i
\(693\) 6.24264 + 13.0711i 0.237138 + 0.496529i
\(694\) 1.11270i 0.0422375i
\(695\) 0 0
\(696\) −0.384776 + 2.24264i −0.0145849 + 0.0850071i
\(697\) −21.6569 21.6569i −0.820312 0.820312i
\(698\) 8.78680 + 8.78680i 0.332585 + 0.332585i
\(699\) 8.14214 47.4558i 0.307964 1.79494i
\(700\) 0 0
\(701\) 1.31371i 0.0496181i 0.999692 + 0.0248090i \(0.00789777\pi\)
−0.999692 + 0.0248090i \(0.992102\pi\)
\(702\) 1.65685 + 5.85786i 0.0625339 + 0.221091i
\(703\) 0.485281 0.485281i 0.0183027 0.0183027i
\(704\) −4.17157 −0.157222
\(705\) 0 0
\(706\) −4.58579 −0.172588
\(707\) 24.4853 24.4853i 0.920864 0.920864i
\(708\) 10.3431 7.31371i 0.388719 0.274866i
\(709\) 29.3137i 1.10090i −0.834868 0.550450i \(-0.814456\pi\)
0.834868 0.550450i \(-0.185544\pi\)
\(710\) 0 0
\(711\) −30.6274 10.8284i −1.14862 0.406098i
\(712\) −10.8284 10.8284i −0.405812 0.405812i
\(713\) 10.2843 + 10.2843i 0.385149 + 0.385149i
\(714\) 13.6569 + 2.34315i 0.511095 + 0.0876900i
\(715\) 0 0
\(716\) 44.1421i 1.64967i
\(717\) −23.7990 33.6569i −0.888790 1.25694i
\(718\) −6.48528 + 6.48528i −0.242029 + 0.242029i
\(719\) −22.7696 −0.849161 −0.424581 0.905390i \(-0.639578\pi\)
−0.424581 + 0.905390i \(0.639578\pi\)
\(720\) 0 0
\(721\) 43.7990 1.63116
\(722\) 3.22183 3.22183i 0.119904 0.119904i
\(723\) 0.142136 + 0.201010i 0.00528608 + 0.00747565i
\(724\) 10.3431i 0.384400i
\(725\) 0 0
\(726\) −0.707107 0.121320i −0.0262432 0.00450262i
\(727\) −20.2132 20.2132i −0.749666 0.749666i 0.224750 0.974416i \(-0.427843\pi\)
−0.974416 + 0.224750i \(0.927843\pi\)
\(728\) 15.3137 + 15.3137i 0.567564 + 0.567564i
\(729\) 23.0000 14.1421i 0.851852 0.523783i
\(730\) 0 0
\(731\) 1.37258i 0.0507668i
\(732\) 16.7696 11.8579i 0.619821 0.438279i
\(733\) −3.79899 + 3.79899i −0.140319 + 0.140319i −0.773777 0.633458i \(-0.781635\pi\)
0.633458 + 0.773777i \(0.281635\pi\)
\(734\) 0.644661 0.0237949
\(735\) 0 0
\(736\) 20.2426 0.746154
\(737\) 6.41421 6.41421i 0.236271 0.236271i
\(738\) 8.58579 4.10051i 0.316047 0.150942i
\(739\) 14.6274i 0.538078i 0.963129 + 0.269039i \(0.0867061\pi\)
−0.963129 + 0.269039i \(0.913294\pi\)
\(740\) 0 0
\(741\) 2.34315 13.6569i 0.0860776 0.501697i
\(742\) −2.00000 2.00000i −0.0734223 0.0734223i
\(743\) 26.0416 + 26.0416i 0.955375 + 0.955375i 0.999046 0.0436712i \(-0.0139054\pi\)
−0.0436712 + 0.999046i \(0.513905\pi\)
\(744\) 1.47309 8.58579i 0.0540060 0.314770i
\(745\) 0 0
\(746\) 2.05887i 0.0753808i
\(747\) −34.7279 + 16.5858i −1.27063 + 0.606842i
\(748\) 5.17157 5.17157i 0.189091 0.189091i
\(749\) −1.65685 −0.0605401
\(750\) 0 0
\(751\) −46.6274 −1.70146 −0.850729 0.525604i \(-0.823839\pi\)
−0.850729 + 0.525604i \(0.823839\pi\)
\(752\) −21.7279 + 21.7279i −0.792336 + 0.792336i
\(753\) 22.8284 16.1421i 0.831914 0.588252i
\(754\) 0.970563i 0.0353458i
\(755\) 0 0
\(756\) 22.3848 40.0416i 0.814126 1.45630i
\(757\) −0.171573 0.171573i −0.00623592 0.00623592i 0.703982 0.710218i \(-0.251404\pi\)
−0.710218 + 0.703982i \(0.751404\pi\)
\(758\) −8.24264 8.24264i −0.299386 0.299386i
\(759\) −7.82843 1.34315i −0.284154 0.0487531i
\(760\) 0 0
\(761\) 1.51472i 0.0549085i 0.999623 + 0.0274543i \(0.00874006\pi\)
−0.999623 + 0.0274543i \(0.991260\pi\)
\(762\) −0.828427 1.17157i −0.0300107 0.0424416i
\(763\) −10.8284 + 10.8284i −0.392015 + 0.392015i
\(764\) −20.6863 −0.748404
\(765\) 0 0
\(766\) 3.55635 0.128496
\(767\) −8.00000 + 8.00000i −0.288863 + 0.288863i
\(768\) 3.97056 + 5.61522i 0.143275 + 0.202622i
\(769\) 52.6274i 1.89779i −0.315587 0.948897i \(-0.602201\pi\)
0.315587 0.948897i \(-0.397799\pi\)
\(770\) 0 0
\(771\) 4.41421 + 0.757359i 0.158974 + 0.0272756i
\(772\) −14.6274 14.6274i −0.526452 0.526452i
\(773\) −10.6569 10.6569i −0.383300 0.383300i 0.488989 0.872290i \(-0.337366\pi\)
−0.872290 + 0.488989i \(0.837366\pi\)
\(774\) −0.402020 0.142136i −0.0144503 0.00510896i
\(775\) 0 0
\(776\) 23.8995i 0.857942i
\(777\) −1.65685 + 1.17157i −0.0594393 + 0.0420299i
\(778\) −5.07107 + 5.07107i −0.181807 + 0.181807i
\(779\) −21.6569 −0.775937
\(780\) 0 0
\(781\) −2.48528 −0.0889304
\(782\) −5.37258 + 5.37258i −0.192123 + 0.192123i
\(783\) −4.14214 + 1.17157i −0.148028 + 0.0418686i
\(784\) 48.9411i