Properties

Label 825.2.k.c.518.2
Level $825$
Weight $2$
Character 825.518
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: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 165)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 518.2
Root \(0.707107 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 825.518
Dual form 825.2.k.c.782.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.292893 - 0.292893i) q^{2} +(-1.41421 + 1.00000i) q^{3} -1.82843i q^{4} +(0.707107 + 0.121320i) q^{6} +(3.41421 - 3.41421i) q^{7} +(-1.12132 + 1.12132i) q^{8} +(1.00000 - 2.82843i) q^{9} +O(q^{10})\) \(q+(-0.292893 - 0.292893i) q^{2} +(-1.41421 + 1.00000i) 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} +(1.82843 + 2.58579i) q^{12} +(2.00000 + 2.00000i) q^{13} -2.00000 q^{14} -3.00000 q^{16} +(-2.82843 - 2.82843i) q^{17} +(-1.12132 + 0.535534i) 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} +(1.41421 + 5.00000i) q^{27} +(-6.24264 - 6.24264i) q^{28} -0.828427 q^{29} -3.17157 q^{31} +(3.12132 + 3.12132i) q^{32} +(1.00000 + 1.41421i) 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} +(2.82843 - 2.00000i) q^{42} +(-0.242641 - 0.242641i) q^{43} -1.82843 q^{44} -1.89949 q^{46} +(-7.24264 - 7.24264i) q^{47} +(4.24264 - 3.00000i) 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} +(-2.82843 - 4.00000i) q^{57} +(0.242641 + 0.242641i) q^{58} +4.00000 q^{59} -6.48528 q^{61} +(0.928932 + 0.928932i) q^{62} +(-6.24264 - 13.0711i) 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} +(2.05025 + 4.29289i) q^{72} -0.100505 q^{74} +5.17157 q^{76} +(-3.41421 - 3.41421i) q^{77} +(1.17157 + 1.65685i) 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} +(1.17157 - 0.828427i) q^{87} +(1.12132 + 1.12132i) q^{88} +9.65685 q^{89} +13.6569 q^{91} +(-5.92893 - 5.92893i) q^{92} +(4.48528 - 3.17157i) 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})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{2} + 8 q^{7} + 4 q^{8} + 4 q^{9} + O(q^{10}) \) \( 4 q - 4 q^{2} + 8 q^{7} + 4 q^{8} + 4 q^{9} - 4 q^{12} + 8 q^{13} - 8 q^{14} - 12 q^{16} + 4 q^{18} - 4 q^{22} - 4 q^{23} + 16 q^{24} - 8 q^{28} + 8 q^{29} - 24 q^{31} + 4 q^{32} + 4 q^{33} - 32 q^{36} + 12 q^{37} - 8 q^{38} - 8 q^{39} + 16 q^{43} + 4 q^{44} + 32 q^{46} - 12 q^{47} + 16 q^{51} - 8 q^{52} + 4 q^{53} + 24 q^{54} - 16 q^{58} + 16 q^{59} + 8 q^{61} + 32 q^{62} - 8 q^{63} - 8 q^{66} + 20 q^{67} - 32 q^{68} - 28 q^{69} + 28 q^{72} - 40 q^{74} + 32 q^{76} - 8 q^{77} + 16 q^{78} - 28 q^{81} + 8 q^{82} - 8 q^{83} + 32 q^{84} + 16 q^{87} - 4 q^{88} + 16 q^{89} + 32 q^{91} - 52 q^{92} - 16 q^{93} - 16 q^{96} - 20 q^{97} + 12 q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(376\) \(551\) \(727\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{3}{4}\right)\)

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 \(-0.296784\pi\)
−0.803037 + 0.595930i \(0.796784\pi\)
\(3\) −1.41421 + 1.00000i −0.816497 + 0.577350i
\(4\) 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 0.355944 0.934507i \(-0.384159\pi\)
0.934507 0.355944i \(-0.115841\pi\)
\(8\) −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
\(12\) 1.82843 + 2.58579i 0.527821 + 0.746452i
\(13\) 2.00000 + 2.00000i 0.554700 + 0.554700i 0.927794 0.373094i \(-0.121703\pi\)
−0.373094 + 0.927794i \(0.621703\pi\)
\(14\) −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 \(-0.411206\pi\)
−0.961344 + 0.275350i \(0.911206\pi\)
\(18\) −1.12132 + 0.535534i −0.264298 + 0.126227i
\(19\) 2.82843i 0.648886i 0.945905 + 0.324443i \(0.105177\pi\)
−0.945905 + 0.324443i \(0.894823\pi\)
\(20\) 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 \(-0.591325\pi\)
0.959124 + 0.282987i \(0.0913252\pi\)
\(24\) 0.464466 2.70711i 0.0948087 0.552586i
\(25\) 0 0
\(26\) 1.17157i 0.229764i
\(27\) 1.41421 + 5.00000i 0.272166 + 0.962250i
\(28\) −6.24264 6.24264i −1.17975 1.17975i
\(29\) −0.828427 −0.153835 −0.0769175 0.997037i \(-0.524508\pi\)
−0.0769175 + 0.997037i \(0.524508\pi\)
\(30\) 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
\(33\) 1.00000 + 1.41421i 0.174078 + 0.246183i
\(34\) 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 −0.692863 0.721069i \(-0.743651\pi\)
0.721069 + 0.692863i \(0.243651\pi\)
\(38\) 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 \(-0.203998\pi\)
\(42\) 2.82843 2.00000i 0.436436 0.308607i
\(43\) −0.242641 0.242641i −0.0370024 0.0370024i 0.688364 0.725366i \(-0.258329\pi\)
−0.725366 + 0.688364i \(0.758329\pi\)
\(44\) −1.82843 −0.275646
\(45\) 0 0
\(46\) −1.89949 −0.280065
\(47\) −7.24264 7.24264i −1.05645 1.05645i −0.998308 0.0581392i \(-0.981483\pi\)
−0.0581392 0.998308i \(-0.518517\pi\)
\(48\) 4.24264 3.00000i 0.612372 0.433013i
\(49\) 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 \(-0.719034\pi\)
0.772444 + 0.635083i \(0.219034\pi\)
\(54\) 1.05025 1.87868i 0.142921 0.255656i
\(55\) 0 0
\(56\) 7.65685i 1.02319i
\(57\) −2.82843 4.00000i −0.374634 0.529813i
\(58\) 0.242641 + 0.242641i 0.0318603 + 0.0318603i
\(59\) 4.00000 0.520756 0.260378 0.965507i \(-0.416153\pi\)
0.260378 + 0.965507i \(0.416153\pi\)
\(60\) 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
\(63\) −6.24264 13.0711i −0.786499 1.64680i
\(64\) 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 −0.196819 0.980440i \(-0.563061\pi\)
0.980440 + 0.196819i \(0.0630611\pi\)
\(68\) −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 \(-0.0471144\pi\)
\(72\) 2.05025 + 4.29289i 0.241625 + 0.505922i
\(73\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(74\) −0.100505 −0.0116835
\(75\) 0 0
\(76\) 5.17157 0.593220
\(77\) −3.41421 3.41421i −0.389086 0.389086i
\(78\) 1.17157 + 1.65685i 0.132655 + 0.187602i
\(79\) 10.8284i 1.21829i −0.793058 0.609147i \(-0.791512\pi\)
0.793058 0.609147i \(-0.208488\pi\)
\(80\) 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 \(-0.998628\pi\)
0.00431166 + 0.999991i \(0.498628\pi\)
\(84\) 15.0711 + 2.58579i 1.64439 + 0.282132i
\(85\) 0 0
\(86\) 0.142136i 0.0153269i
\(87\) 1.17157 0.828427i 0.125606 0.0888167i
\(88\) 1.12132 + 1.12132i 0.119533 + 0.119533i
\(89\) 9.65685 1.02362 0.511812 0.859097i \(-0.328974\pi\)
0.511812 + 0.859097i \(0.328974\pi\)
\(90\) 0 0
\(91\) 13.6569 1.43163
\(92\) −5.92893 5.92893i −0.618134 0.618134i
\(93\) 4.48528 3.17157i 0.465102 0.328877i
\(94\) 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 −0.0857204 + 0.996319i \(0.527319\pi\)
−0.996319 + 0.0857204i \(0.972681\pi\)
\(98\) −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 \(-0.116132\pi\)
\(102\) −1.65685 2.34315i −0.164053 0.232006i
\(103\) 6.41421 + 6.41421i 0.632011 + 0.632011i 0.948572 0.316561i \(-0.102528\pi\)
−0.316561 + 0.948572i \(0.602528\pi\)
\(104\) −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 \(-0.244720\pi\)
−0.695281 + 0.718738i \(0.744720\pi\)
\(108\) 9.14214 2.58579i 0.879702 0.248817i
\(109\) 3.17157i 0.303782i −0.988397 0.151891i \(-0.951464\pi\)
0.988397 0.151891i \(-0.0485362\pi\)
\(110\) 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 \(-0.876731\pi\)
0.377654 + 0.925947i \(0.376731\pi\)
\(114\) −0.343146 + 2.00000i −0.0321385 + 0.187317i
\(115\) 0 0
\(116\) 1.51472i 0.140638i
\(117\) 7.65685 3.65685i 0.707876 0.338076i
\(118\) −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
\(123\) 7.65685 + 10.8284i 0.690395 + 0.976366i
\(124\) 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 −0.767063 0.641572i \(-0.778283\pi\)
0.641572 + 0.767063i \(0.278283\pi\)
\(128\) 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 \(0.903580\pi\)
\(132\) 2.58579 1.82843i 0.225064 0.159144i
\(133\) 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 \(-0.246701\pi\)
−0.699740 + 0.714398i \(0.746701\pi\)
\(138\) 2.68629 1.89949i 0.228672 0.161696i
\(139\) 17.6569i 1.49763i 0.662776 + 0.748817i \(0.269378\pi\)
−0.662776 + 0.748817i \(0.730622\pi\)
\(140\) 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
\(147\) 16.3137 + 23.0711i 1.34553 + 1.90287i
\(148\) −0.313708 0.313708i −0.0257867 0.0257867i
\(149\) 10.0000 0.819232 0.409616 0.912258i \(-0.365663\pi\)
0.409616 + 0.912258i \(0.365663\pi\)
\(150\) 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
\(153\) −10.8284 + 5.17157i −0.875426 + 0.418097i
\(154\) 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 −0.218769 0.975777i \(-0.570204\pi\)
0.975777 + 0.218769i \(0.0702041\pi\)
\(158\) −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
\(162\) 0.393398 + 3.70711i 0.0309083 + 0.291258i
\(163\) −3.58579 3.58579i −0.280860 0.280860i 0.552592 0.833452i \(-0.313639\pi\)
−0.833452 + 0.552592i \(0.813639\pi\)
\(164\) −14.0000 −1.09322
\(165\) 0 0
\(166\) 5.31371 0.412424
\(167\) 14.7279 + 14.7279i 1.13968 + 1.13968i 0.988507 + 0.151174i \(0.0483052\pi\)
0.151174 + 0.988507i \(0.451695\pi\)
\(168\) −7.65685 10.8284i −0.590739 0.835431i
\(169\) 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 \(-0.599220\pi\)
0.951811 + 0.306687i \(0.0992203\pi\)
\(174\) −0.585786 0.100505i −0.0444084 0.00761927i
\(175\) 0 0
\(176\) 3.00000i 0.226134i
\(177\) −5.65685 + 4.00000i −0.425195 + 0.300658i
\(178\) −2.82843 2.82843i −0.212000 0.212000i
\(179\) −24.1421 −1.80447 −0.902234 0.431247i \(-0.858074\pi\)
−0.902234 + 0.431247i \(0.858074\pi\)
\(180\) 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
\(183\) 9.17157 6.48528i 0.677982 0.479406i
\(184\) 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 \(0.865768\pi\)
\(192\) −4.17157 5.89949i −0.301057 0.425759i
\(193\) −8.00000 8.00000i −0.575853 0.575853i 0.357905 0.933758i \(-0.383491\pi\)
−0.933758 + 0.357905i \(0.883491\pi\)
\(194\) 6.24264 0.448195
\(195\) 0 0
\(196\) −29.8284 −2.13060
\(197\) −14.1421 14.1421i −1.00759 1.00759i −0.999971 0.00761443i \(-0.997576\pi\)
−0.00761443 0.999971i \(-0.502424\pi\)
\(198\) 0.535534 + 1.12132i 0.0380587 + 0.0796888i
\(199\) 14.4853i 1.02683i 0.858139 + 0.513417i \(0.171621\pi\)
−0.858139 + 0.513417i \(0.828379\pi\)
\(200\) 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
\(207\) −5.92893 12.4142i −0.412089 0.862847i
\(208\) −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
\(213\) 2.48528 + 3.51472i 0.170289 + 0.240825i
\(214\) 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
\(222\) 0.142136 0.100505i 0.00953952 0.00674546i
\(223\) 16.5563 + 16.5563i 1.10870 + 1.10870i 0.993322 + 0.115373i \(0.0368063\pi\)
0.115373 + 0.993322i \(0.463194\pi\)
\(224\) 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 \(-0.0903786\pi\)
−0.280133 + 0.959961i \(0.590379\pi\)
\(228\) −7.31371 + 5.17157i −0.484362 + 0.342496i
\(229\) 9.65685i 0.638143i 0.947731 + 0.319071i \(0.103371\pi\)
−0.947731 + 0.319071i \(0.896629\pi\)
\(230\) 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 0.351621 0.936143i \(-0.385631\pi\)
0.936143 0.351621i \(-0.114369\pi\)
\(234\) −3.31371 1.17157i −0.216624 0.0765881i
\(235\) 0 0
\(236\) 7.31371i 0.476082i
\(237\) 10.8284 + 15.3137i 0.703382 + 0.994732i
\(238\) 5.65685 + 5.65685i 0.366679 + 0.366679i
\(239\) 23.7990 1.53943 0.769714 0.638388i \(-0.220399\pi\)
0.769714 + 0.638388i \(0.220399\pi\)
\(240\) 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
\(243\) 15.5563 + 1.00000i 0.997940 + 0.0641500i
\(244\) 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 \(-0.170148\pi\)
\(252\) −23.8995 + 11.4142i −1.50553 + 0.719028i
\(253\) −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 \(-0.275699\pi\)
−0.761831 + 0.647776i \(0.775699\pi\)
\(258\) −0.142136 0.201010i −0.00884898 0.0125143i
\(259\) 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 \(-0.774414\pi\)
0.650846 + 0.759210i \(0.274414\pi\)
\(264\) −2.70711 0.464466i −0.166611 0.0285859i
\(265\) 0 0
\(266\) 5.65685i 0.346844i
\(267\) −13.6569 + 9.65685i −0.835786 + 0.590990i
\(268\) −11.7279 11.7279i −0.716397 0.716397i
\(269\) 14.0000 0.853595 0.426798 0.904347i \(-0.359642\pi\)
0.426798 + 0.904347i \(0.359642\pi\)
\(270\) 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
\(273\) −19.3137 + 13.6569i −1.16892 + 0.826550i
\(274\) 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 0.117613 0.993059i \(-0.462476\pi\)
0.993059 0.117613i \(-0.0375244\pi\)
\(278\) 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 \(0.674241\pi\)
\(282\) −4.24264 6.00000i −0.252646 0.357295i
\(283\) 15.0711 + 15.0711i 0.895882 + 0.895882i 0.995069 0.0991868i \(-0.0316241\pi\)
−0.0991868 + 0.995069i \(0.531624\pi\)
\(284\) −4.54416 −0.269646
\(285\) 0 0
\(286\) −1.17157 −0.0692766
\(287\) −26.1421 26.1421i −1.54312 1.54312i
\(288\) 11.9497 5.70711i 0.704146 0.336294i
\(289\) 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 \(-0.798270\pi\)
0.592174 + 0.805810i \(0.298270\pi\)
\(294\) 1.97918 11.5355i 0.115428 0.672766i
\(295\) 0 0
\(296\) 0.384776i 0.0223647i
\(297\) 5.00000 1.41421i 0.290129 0.0820610i
\(298\) −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
\(303\) 7.17157 + 10.1421i 0.411996 + 0.582650i
\(304\) 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 −0.280666 0.959806i \(-0.590555\pi\)
0.959806 + 0.280666i \(0.0905552\pi\)
\(308\) −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 \(0.705946\pi\)
\(312\) 6.34315 4.48528i 0.359110 0.253929i
\(313\) −12.6569 12.6569i −0.715408 0.715408i 0.252253 0.967661i \(-0.418828\pi\)
−0.967661 + 0.252253i \(0.918828\pi\)
\(314\) −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 \(-0.220709\pi\)
−0.639140 + 0.769091i \(0.720709\pi\)
\(318\) 0.828427 0.585786i 0.0464559 0.0328493i
\(319\) 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
\(327\) 3.17157 + 4.48528i 0.175388 + 0.248037i
\(328\) 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
\(333\) −0.313708 0.656854i −0.0171911 0.0359954i
\(334\) 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 −0.347732 0.937594i \(-0.613048\pi\)
0.937594 + 0.347732i \(0.113048\pi\)
\(338\) −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
\(342\) −1.51472 3.17157i −0.0819066 0.171499i
\(343\) −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 \(-0.227029\pi\)
−0.654281 + 0.756251i \(0.727029\pi\)
\(348\) −1.51472 2.14214i −0.0811974 0.114831i
\(349\) 30.0000i 1.60586i −0.596071 0.802932i \(-0.703272\pi\)
0.596071 0.802932i \(-0.296728\pi\)
\(350\) 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 \(-0.654805\pi\)
0.884053 + 0.467387i \(0.154805\pi\)
\(354\) 2.82843 + 0.485281i 0.150329 + 0.0257924i
\(355\) 0 0
\(356\) 17.6569i 0.935811i
\(357\) 27.3137 19.3137i 1.44559 1.02219i
\(358\) 7.07107 + 7.07107i 0.373718 + 0.373718i
\(359\) 22.1421 1.16862 0.584309 0.811532i \(-0.301366\pi\)
0.584309 + 0.811532i \(0.301366\pi\)
\(360\) 0 0
\(361\) 11.0000 0.578947
\(362\) −1.65685 1.65685i −0.0870823 0.0870823i
\(363\) 1.41421 1.00000i 0.0742270 0.0524864i
\(364\) 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 −0.677800 0.735246i \(-0.737067\pi\)
0.735246 + 0.677800i \(0.237067\pi\)
\(368\) −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
\(372\) −5.79899 8.20101i −0.300664 0.425203i
\(373\) −3.51472 3.51472i −0.181985 0.181985i 0.610235 0.792220i \(-0.291075\pi\)
−0.792220 + 0.610235i \(0.791075\pi\)
\(374\) 1.65685 0.0856739
\(375\) 0 0
\(376\) 16.2426 0.837650
\(377\) −1.65685 1.65685i −0.0853323 0.0853323i
\(378\) −2.82843 10.0000i −0.145479 0.514344i
\(379\) 28.1421i 1.44556i 0.691076 + 0.722782i \(0.257137\pi\)
−0.691076 + 0.722782i \(0.742863\pi\)
\(380\) 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 \(-0.820396\pi\)
0.534776 + 0.844994i \(0.320396\pi\)
\(384\) −3.09188 + 18.0208i −0.157782 + 0.919621i
\(385\) 0 0
\(386\) 4.68629i 0.238526i
\(387\) −0.928932 + 0.443651i −0.0472203 + 0.0225520i
\(388\) 19.4853 + 19.4853i 0.989215 + 0.989215i
\(389\) 17.3137 0.877840 0.438920 0.898526i \(-0.355361\pi\)
0.438920 + 0.898526i \(0.355361\pi\)
\(390\) 0 0
\(391\) −18.3431 −0.927653
\(392\) 18.2929 + 18.2929i 0.923931 + 0.923931i
\(393\) −6.82843 9.65685i −0.344449 0.487124i
\(394\) 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 −0.844810 0.535067i \(-0.820286\pi\)
0.535067 + 0.844810i \(0.320286\pi\)
\(398\) 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 \(0.650488\pi\)
\(402\) 5.31371 3.75736i 0.265024 0.187400i
\(403\) −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
\(408\) −8.97056 + 6.34315i −0.444109 + 0.314033i
\(409\) 18.4853i 0.914038i −0.889457 0.457019i \(-0.848917\pi\)
0.889457 0.457019i \(-0.151083\pi\)
\(410\) 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
\(417\) −17.6569 24.9706i −0.864660 1.22281i
\(418\) −0.828427 0.828427i −0.0405197 0.0405197i
\(419\) −15.4558 −0.755067 −0.377534 0.925996i \(-0.623228\pi\)
−0.377534 + 0.925996i \(0.623228\pi\)
\(420\) 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
\(423\) −27.7279 + 13.2426i −1.34818 + 0.643879i
\(424\) 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 \(-0.0488191\pi\)
\(432\) −4.24264 15.0000i −0.204124 0.721688i
\(433\) 0.313708 + 0.313708i 0.0150759 + 0.0150759i 0.714605 0.699529i \(-0.246607\pi\)
−0.699529 + 0.714605i \(0.746607\pi\)
\(434\) 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 \(-0.944159\pi\)
0.984651 0.174532i \(-0.0558413\pi\)
\(440\) 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 \(-0.995641\pi\)
0.0136943 + 0.999906i \(0.495641\pi\)
\(444\) 0.757359 + 0.129942i 0.0359427 + 0.00616679i
\(445\) 0 0
\(446\) 9.69848i 0.459237i
\(447\) −14.1421 + 10.0000i −0.668900 + 0.472984i
\(448\) 14.2426 + 14.2426i 0.672902 + 0.672902i
\(449\) 3.02944 0.142968 0.0714840 0.997442i \(-0.477227\pi\)
0.0714840 + 0.997442i \(0.477227\pi\)
\(450\) 0 0
\(451\) −7.65685 −0.360547
\(452\) 10.6569 + 10.6569i 0.501256 + 0.501256i
\(453\) −14.3431 + 10.1421i −0.673900 + 0.476519i
\(454\) 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 −0.538962 0.842330i \(-0.681183\pi\)
0.842330 + 0.538962i \(0.181183\pi\)
\(458\) 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 \(-0.101911\pi\)
\(462\) −2.00000 2.82843i −0.0930484 0.131590i
\(463\) −11.7279 11.7279i −0.545043 0.545043i 0.379960 0.925003i \(-0.375938\pi\)
−0.925003 + 0.379960i \(0.875938\pi\)
\(464\) 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 \(-0.254314\pi\)
−0.716626 + 0.697458i \(0.754314\pi\)
\(468\) −6.68629 14.0000i −0.309074 0.647150i
\(469\) 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
\(477\) −1.82843 3.82843i −0.0837179 0.175292i
\(478\) −6.97056 6.97056i −0.318826 0.318826i
\(479\) 30.1421 1.37723 0.688615 0.725127i \(-0.258219\pi\)
0.688615 + 0.725127i \(0.258219\pi\)
\(480\) 0 0
\(481\) 0.686292 0.0312922
\(482\) −0.0416306 0.0416306i −0.00189622 0.00189622i
\(483\) 22.1421 + 31.3137i 1.00750 + 1.42482i
\(484\) 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 −0.921002 0.389559i \(-0.872628\pi\)
0.389559 + 0.921002i \(0.372628\pi\)
\(488\) 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 \(-0.149037\pi\)
\(492\) 19.7990 14.0000i 0.892607 0.631169i
\(493\) 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
\(498\) −7.51472 + 5.31371i −0.336743 + 0.238113i
\(499\) 24.8284i 1.11147i 0.831358 + 0.555737i \(0.187564\pi\)
−0.831358 + 0.555737i \(0.812436\pi\)
\(500\) 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 \(-0.740676\pi\)
0.727513 + 0.686094i \(0.240676\pi\)
\(504\) 21.6569 + 7.65685i 0.964673 + 0.341063i
\(505\) 0 0
\(506\) 1.89949i 0.0844428i
\(507\) 5.00000 + 7.07107i 0.222058 + 0.314037i
\(508\) 2.58579 + 2.58579i 0.114726 + 0.114726i
\(509\) −35.6569 −1.58046 −0.790231 0.612809i \(-0.790040\pi\)
−0.790231 + 0.612809i \(0.790040\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −16.0919 16.0919i −0.711167 0.711167i
\(513\) −14.1421 + 4.00000i −0.624391 + 0.176604i
\(514\) 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 \(-0.207161\pi\)
\(522\) 0.928932 0.443651i 0.0406583 0.0194181i
\(523\) 27.2132 + 27.2132i 1.18995 + 1.18995i 0.977081 + 0.212870i \(0.0682810\pi\)
0.212870 + 0.977081i \(0.431719\pi\)
\(524\) 12.4853 0.545422
\(525\) 0 0
\(526\) 1.02944 0.0448856
\(527\) 8.97056 + 8.97056i 0.390764 + 0.390764i
\(528\) −3.00000 4.24264i −0.130558 0.184637i
\(529\) 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
\(537\) 34.1421 24.1421i 1.47334 1.04181i
\(538\) −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
\(543\) −8.00000 + 5.65685i −0.343313 + 0.242759i
\(544\) 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 −0.750585 0.660774i \(-0.770228\pi\)
0.660774 + 0.750585i \(0.270228\pi\)
\(548\) 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
\(552\) −7.27208 10.2843i −0.309520 0.437728i
\(553\) −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 \(-0.163384\pi\)
−0.491041 + 0.871136i \(0.663384\pi\)
\(558\) 3.55635 1.69848i 0.150552 0.0719026i
\(559\) 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 \(-0.845325\pi\)
0.467028 + 0.884242i \(0.345325\pi\)
\(564\) 5.48528 31.9706i 0.230972 1.34620i
\(565\) 0 0
\(566\) 8.82843i 0.371086i
\(567\) −43.2132 + 4.58579i −1.81478 + 0.192585i
\(568\) 2.78680 + 2.78680i 0.116931 + 0.116931i
\(569\) 28.3431 1.18821 0.594103 0.804389i \(-0.297507\pi\)
0.594103 + 0.804389i \(0.297507\pi\)
\(570\) 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
\(573\) −11.3137 16.0000i −0.472637 0.668410i
\(574\) 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 −0.966055 0.258336i \(-0.916826\pi\)
0.258336 + 0.966055i \(0.416826\pi\)
\(578\) −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
\(582\) −8.82843 + 6.24264i −0.365950 + 0.258766i
\(583\) −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 \(-0.253848\pi\)
−0.715603 + 0.698507i \(0.753848\pi\)
\(588\) 42.1838 29.8284i 1.73963 1.23010i
\(589\) 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 \(-0.695592\pi\)
0.817079 + 0.576525i \(0.195592\pi\)
\(594\) −1.87868 1.05025i −0.0770832 0.0430924i
\(595\) 0 0
\(596\) 18.2843i 0.748953i
\(597\) −14.4853 20.4853i −0.592843 0.838407i
\(598\) −3.79899 3.79899i −0.155352 0.155352i
\(599\) 3.45584 0.141202 0.0706010 0.997505i \(-0.477508\pi\)
0.0706010 + 0.997505i \(0.477508\pi\)
\(600\) 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
\(603\) −11.7279 24.5563i −0.477598 1.00001i
\(604\) 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 −0.105542 0.994415i \(-0.533658\pi\)
0.994415 + 0.105542i \(0.0336577\pi\)
\(608\) −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
\(612\) 9.45584 + 19.7990i 0.382230 + 0.800327i
\(613\) 16.0000 + 16.0000i 0.646234 + 0.646234i 0.952081 0.305847i \(-0.0989395\pi\)
−0.305847 + 0.952081i \(0.598940\pi\)
\(614\) −6.97056 −0.281309
\(615\) 0 0
\(616\) 7.65685 0.308503
\(617\) 29.8284 + 29.8284i 1.20085 + 1.20085i 0.973909 + 0.226938i \(0.0728715\pi\)
0.226938 + 0.973909i \(0.427129\pi\)
\(618\) 3.75736 + 5.31371i 0.151143 + 0.213749i
\(619\) 0.686292i 0.0275844i −0.999905 0.0137922i \(-0.995610\pi\)
0.999905 0.0137922i \(-0.00439033\pi\)
\(620\) 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
\(627\) −4.00000 + 2.82843i −0.159745 + 0.112956i
\(628\) −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
\(633\) 6.34315 4.48528i 0.252117 0.178274i
\(634\) 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 \(-0.222873\pi\)
\(642\) 0.142136 + 0.201010i 0.00560965 + 0.00793324i
\(643\) 9.24264 + 9.24264i 0.364494 + 0.364494i 0.865464 0.500970i \(-0.167023\pi\)
−0.500970 + 0.865464i \(0.667023\pi\)
\(644\) −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 \(-0.144290\pi\)
−0.437935 + 0.899007i \(0.644290\pi\)
\(648\) 14.1924 1.50610i 0.557530 0.0591651i
\(649\) 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 \(-0.673001\pi\)
0.855904 + 0.517135i \(0.173001\pi\)
\(654\) 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 \(-0.338325\pi\)
0.486358 + 0.873760i \(0.338325\pi\)
\(660\) 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
\(663\) 11.3137 + 16.0000i 0.439388 + 0.621389i
\(664\) 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
\(672\) −30.1421 + 21.3137i −1.16276 + 0.822194i
\(673\) 22.3431 + 22.3431i 0.861265 + 0.861265i 0.991485 0.130220i \(-0.0415684\pi\)
−0.130220 + 0.991485i \(0.541568\pi\)
\(674\) −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 \(-0.0706126\pi\)
−0.220021 + 0.975495i \(0.570613\pi\)
\(678\) −4.82843 + 3.41421i −0.185435 + 0.131122i
\(679\) 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 \(-0.682949\pi\)
0.839327 + 0.543627i \(0.182949\pi\)
\(684\) 5.17157 14.6274i 0.197740 0.559293i
\(685\) 0 0
\(686\) 18.6274i 0.711198i
\(687\) −9.65685 13.6569i −0.368432 0.521041i
\(688\) 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
\(693\) −13.0711 + 6.24264i −0.496529 + 0.237138i
\(694\) 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 \(0.992102\pi\)
\(702\) 5.85786 1.65685i 0.221091 0.0625339i
\(703\) 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
\(708\) 7.31371 + 10.3431i 0.274866 + 0.388719i
\(709\) 29.3137i 1.10090i 0.834868 + 0.550450i \(0.185544\pi\)
−0.834868 + 0.550450i \(0.814456\pi\)
\(710\) 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
\(717\) −33.6569 + 23.7990i −1.25694 + 0.888790i
\(718\) −6.48528 6.48528i −0.242029 0.242029i
\(719\) 22.7696 0.849161 0.424581 0.905390i \(-0.360422\pi\)
0.424581 + 0.905390i \(0.360422\pi\)
\(720\) 0 0
\(721\) 43.7990 1.63116
\(722\) −3.22183 3.22183i −0.119904 0.119904i
\(723\) −0.201010 + 0.142136i −0.00747565 + 0.00528608i
\(724\) 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 −0.974416 0.224750i \(-0.927843\pi\)
0.224750 + 0.974416i \(0.427843\pi\)
\(728\) −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
\(732\) −11.8579 16.7696i −0.438279 0.619821i
\(733\) −3.79899 3.79899i −0.140319 0.140319i 0.633458 0.773777i \(-0.281635\pi\)
−0.773777 + 0.633458i \(0.781635\pi\)
\(734\) −0.644661 −0.0237949
\(735\) 0 0
\(736\) 20.2426 0.746154
\(737\) −6.41421 6.41421i −0.236271 0.236271i
\(738\) 4.10051 + 8.58579i 0.150942 + 0.316047i
\(739\) 14.6274i 0.538078i −0.963129 0.269039i \(-0.913294\pi\)
0.963129 0.269039i \(-0.0867061\pi\)
\(740\) 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 \(-0.986095\pi\)
0.0436712 + 0.999046i \(0.486095\pi\)
\(744\) −1.47309 + 8.58579i −0.0540060 + 0.314770i
\(745\) 0 0
\(746\) 2.05887i 0.0753808i
\(747\) 16.5858 + 34.7279i 0.606842 + 1.27063i
\(748\) 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
\(753\) 16.1421 + 22.8284i 0.588252 + 0.831914i
\(754\) 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 −0.710218 0.703982i \(-0.751404\pi\)
0.703982 + 0.710218i \(0.251404\pi\)
\(758\) 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 \(0.991260\pi\)
\(762\) −1.17157 + 0.828427i −0.0424416 + 0.0300107i
\(763\) −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
\(768\) −5.61522 + 3.97056i −0.202622 + 0.143275i
\(769\) 52.6274i 1.89779i 0.315587 + 0.948897i \(0.397799\pi\)
−0.315587 + 0.948897i \(0.602201\pi\)
\(770\) 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 \(-0.662634\pi\)
0.872290 + 0.488989i \(0.162634\pi\)
\(774\) 0.402020 + 0.142136i 0.0144503 + 0.00510896i
\(775\) 0 0
\(776\) 23.8995i 0.857942i
\(777\) 1.17157 + 1.65685i 0.0420299 + 0.0594393i
\(778\) −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
\(783\) −1.17157 4.14214i −0.0418686 0.148028i
\(784\)