Properties

Label 690.2.i.d.47.3
Level $690$
Weight $2$
Character 690.47
Analytic conductor $5.510$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 690.i (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.50967773947\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: 8.0.40960000.1
Defining polynomial: \(x^{8} + 7 x^{4} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 47.3
Root \(-1.14412 - 1.14412i\) of defining polynomial
Character \(\chi\) \(=\) 690.47
Dual form 690.2.i.d.323.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 - 0.707107i) q^{2} +(-0.292893 + 1.70711i) q^{3} -1.00000i q^{4} -2.23607i q^{5} +(1.00000 + 1.41421i) q^{6} +(-0.707107 - 0.707107i) q^{8} +(-2.82843 - 1.00000i) q^{9} +O(q^{10})\) \(q+(0.707107 - 0.707107i) q^{2} +(-0.292893 + 1.70711i) q^{3} -1.00000i q^{4} -2.23607i q^{5} +(1.00000 + 1.41421i) q^{6} +(-0.707107 - 0.707107i) q^{8} +(-2.82843 - 1.00000i) q^{9} +(-1.58114 - 1.58114i) q^{10} +2.82843i q^{11} +(1.70711 + 0.292893i) q^{12} +(4.16228 - 4.16228i) q^{13} +(3.81721 + 0.654929i) q^{15} -1.00000 q^{16} +(3.65028 - 3.65028i) q^{17} +(-2.70711 + 1.29289i) q^{18} -5.16228i q^{19} -2.23607 q^{20} +(2.00000 + 2.00000i) q^{22} +(-0.707107 - 0.707107i) q^{23} +(1.41421 - 1.00000i) q^{24} -5.00000 q^{25} -5.88635i q^{26} +(2.53553 - 4.53553i) q^{27} -4.47214 q^{29} +(3.16228 - 2.23607i) q^{30} +10.3246 q^{31} +(-0.707107 + 0.707107i) q^{32} +(-4.82843 - 0.828427i) q^{33} -5.16228i q^{34} +(-1.00000 + 2.82843i) q^{36} +(5.16228 + 5.16228i) q^{37} +(-3.65028 - 3.65028i) q^{38} +(5.88635 + 8.32456i) q^{39} +(-1.58114 + 1.58114i) q^{40} -6.11584i q^{41} +(-2.83772 + 2.83772i) q^{43} +2.82843 q^{44} +(-2.23607 + 6.32456i) q^{45} -1.00000 q^{46} +(-8.71478 + 8.71478i) q^{47} +(0.292893 - 1.70711i) q^{48} -7.00000i q^{49} +(-3.53553 + 3.53553i) q^{50} +(5.16228 + 7.30056i) q^{51} +(-4.16228 - 4.16228i) q^{52} +(-6.70820 - 6.70820i) q^{53} +(-1.41421 - 5.00000i) q^{54} +6.32456 q^{55} +(8.81256 + 1.51200i) q^{57} +(-3.16228 + 3.16228i) q^{58} +9.89949 q^{59} +(0.654929 - 3.81721i) q^{60} +8.00000 q^{61} +(7.30056 - 7.30056i) q^{62} +1.00000i q^{64} +(-9.30714 - 9.30714i) q^{65} +(-4.00000 + 2.82843i) q^{66} +(5.16228 + 5.16228i) q^{67} +(-3.65028 - 3.65028i) q^{68} +(1.41421 - 1.00000i) q^{69} +3.05792i q^{71} +(1.29289 + 2.70711i) q^{72} +(-7.32456 + 7.32456i) q^{73} +7.30056 q^{74} +(1.46447 - 8.53553i) q^{75} -5.16228 q^{76} +(10.0486 + 1.72407i) q^{78} -3.16228i q^{79} +2.23607i q^{80} +(7.00000 + 5.65685i) q^{81} +(-4.32456 - 4.32456i) q^{82} +(-5.88635 - 5.88635i) q^{83} +(-8.16228 - 8.16228i) q^{85} +4.01315i q^{86} +(1.30986 - 7.63441i) q^{87} +(2.00000 - 2.00000i) q^{88} -0.458991 q^{89} +(2.89100 + 6.05327i) q^{90} +(-0.707107 + 0.707107i) q^{92} +(-3.02399 + 17.6251i) q^{93} +12.3246i q^{94} -11.5432 q^{95} +(-1.00000 - 1.41421i) q^{96} +(1.16228 + 1.16228i) q^{97} +(-4.94975 - 4.94975i) q^{98} +(2.82843 - 8.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 8q^{3} + 8q^{6} + O(q^{10}) \) \( 8q - 8q^{3} + 8q^{6} + 8q^{12} + 8q^{13} - 8q^{16} - 16q^{18} + 16q^{22} - 40q^{25} - 8q^{27} + 32q^{31} - 16q^{33} - 8q^{36} + 16q^{37} - 48q^{43} - 8q^{46} + 8q^{48} + 16q^{51} - 8q^{52} + 16q^{57} + 64q^{61} - 32q^{66} + 16q^{67} + 16q^{72} - 8q^{73} + 40q^{75} - 16q^{76} + 8q^{78} + 56q^{81} + 16q^{82} - 40q^{85} + 16q^{88} - 32q^{93} - 8q^{96} - 16q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 0.707107i 0.500000 0.500000i
\(3\) −0.292893 + 1.70711i −0.169102 + 0.985599i
\(4\) 1.00000i 0.500000i
\(5\) 2.23607i 1.00000i
\(6\) 1.00000 + 1.41421i 0.408248 + 0.577350i
\(7\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(8\) −0.707107 0.707107i −0.250000 0.250000i
\(9\) −2.82843 1.00000i −0.942809 0.333333i
\(10\) −1.58114 1.58114i −0.500000 0.500000i
\(11\) 2.82843i 0.852803i 0.904534 + 0.426401i \(0.140219\pi\)
−0.904534 + 0.426401i \(0.859781\pi\)
\(12\) 1.70711 + 0.292893i 0.492799 + 0.0845510i
\(13\) 4.16228 4.16228i 1.15441 1.15441i 0.168749 0.985659i \(-0.446027\pi\)
0.985659 0.168749i \(-0.0539728\pi\)
\(14\) 0 0
\(15\) 3.81721 + 0.654929i 0.985599 + 0.169102i
\(16\) −1.00000 −0.250000
\(17\) 3.65028 3.65028i 0.885323 0.885323i −0.108746 0.994070i \(-0.534684\pi\)
0.994070 + 0.108746i \(0.0346836\pi\)
\(18\) −2.70711 + 1.29289i −0.638071 + 0.304738i
\(19\) 5.16228i 1.18431i −0.805825 0.592154i \(-0.798278\pi\)
0.805825 0.592154i \(-0.201722\pi\)
\(20\) −2.23607 −0.500000
\(21\) 0 0
\(22\) 2.00000 + 2.00000i 0.426401 + 0.426401i
\(23\) −0.707107 0.707107i −0.147442 0.147442i
\(24\) 1.41421 1.00000i 0.288675 0.204124i
\(25\) −5.00000 −1.00000
\(26\) 5.88635i 1.15441i
\(27\) 2.53553 4.53553i 0.487964 0.872864i
\(28\) 0 0
\(29\) −4.47214 −0.830455 −0.415227 0.909718i \(-0.636298\pi\)
−0.415227 + 0.909718i \(0.636298\pi\)
\(30\) 3.16228 2.23607i 0.577350 0.408248i
\(31\) 10.3246 1.85434 0.927172 0.374635i \(-0.122232\pi\)
0.927172 + 0.374635i \(0.122232\pi\)
\(32\) −0.707107 + 0.707107i −0.125000 + 0.125000i
\(33\) −4.82843 0.828427i −0.840521 0.144211i
\(34\) 5.16228i 0.885323i
\(35\) 0 0
\(36\) −1.00000 + 2.82843i −0.166667 + 0.471405i
\(37\) 5.16228 + 5.16228i 0.848673 + 0.848673i 0.989968 0.141294i \(-0.0451264\pi\)
−0.141294 + 0.989968i \(0.545126\pi\)
\(38\) −3.65028 3.65028i −0.592154 0.592154i
\(39\) 5.88635 + 8.32456i 0.942570 + 1.33300i
\(40\) −1.58114 + 1.58114i −0.250000 + 0.250000i
\(41\) 6.11584i 0.955134i −0.878595 0.477567i \(-0.841519\pi\)
0.878595 0.477567i \(-0.158481\pi\)
\(42\) 0 0
\(43\) −2.83772 + 2.83772i −0.432749 + 0.432749i −0.889562 0.456814i \(-0.848991\pi\)
0.456814 + 0.889562i \(0.348991\pi\)
\(44\) 2.82843 0.426401
\(45\) −2.23607 + 6.32456i −0.333333 + 0.942809i
\(46\) −1.00000 −0.147442
\(47\) −8.71478 + 8.71478i −1.27118 + 1.27118i −0.325712 + 0.945469i \(0.605604\pi\)
−0.945469 + 0.325712i \(0.894396\pi\)
\(48\) 0.292893 1.70711i 0.0422755 0.246400i
\(49\) 7.00000i 1.00000i
\(50\) −3.53553 + 3.53553i −0.500000 + 0.500000i
\(51\) 5.16228 + 7.30056i 0.722863 + 1.02228i
\(52\) −4.16228 4.16228i −0.577204 0.577204i
\(53\) −6.70820 6.70820i −0.921443 0.921443i 0.0756888 0.997131i \(-0.475884\pi\)
−0.997131 + 0.0756888i \(0.975884\pi\)
\(54\) −1.41421 5.00000i −0.192450 0.680414i
\(55\) 6.32456 0.852803
\(56\) 0 0
\(57\) 8.81256 + 1.51200i 1.16725 + 0.200269i
\(58\) −3.16228 + 3.16228i −0.415227 + 0.415227i
\(59\) 9.89949 1.28880 0.644402 0.764687i \(-0.277106\pi\)
0.644402 + 0.764687i \(0.277106\pi\)
\(60\) 0.654929 3.81721i 0.0845510 0.492799i
\(61\) 8.00000 1.02430 0.512148 0.858898i \(-0.328850\pi\)
0.512148 + 0.858898i \(0.328850\pi\)
\(62\) 7.30056 7.30056i 0.927172 0.927172i
\(63\) 0 0
\(64\) 1.00000i 0.125000i
\(65\) −9.30714 9.30714i −1.15441 1.15441i
\(66\) −4.00000 + 2.82843i −0.492366 + 0.348155i
\(67\) 5.16228 + 5.16228i 0.630673 + 0.630673i 0.948237 0.317564i \(-0.102865\pi\)
−0.317564 + 0.948237i \(0.602865\pi\)
\(68\) −3.65028 3.65028i −0.442662 0.442662i
\(69\) 1.41421 1.00000i 0.170251 0.120386i
\(70\) 0 0
\(71\) 3.05792i 0.362909i 0.983399 + 0.181454i \(0.0580804\pi\)
−0.983399 + 0.181454i \(0.941920\pi\)
\(72\) 1.29289 + 2.70711i 0.152369 + 0.319036i
\(73\) −7.32456 + 7.32456i −0.857274 + 0.857274i −0.991016 0.133742i \(-0.957301\pi\)
0.133742 + 0.991016i \(0.457301\pi\)
\(74\) 7.30056 0.848673
\(75\) 1.46447 8.53553i 0.169102 0.985599i
\(76\) −5.16228 −0.592154
\(77\) 0 0
\(78\) 10.0486 + 1.72407i 1.13778 + 0.195213i
\(79\) 3.16228i 0.355784i −0.984050 0.177892i \(-0.943072\pi\)
0.984050 0.177892i \(-0.0569278\pi\)
\(80\) 2.23607i 0.250000i
\(81\) 7.00000 + 5.65685i 0.777778 + 0.628539i
\(82\) −4.32456 4.32456i −0.477567 0.477567i
\(83\) −5.88635 5.88635i −0.646111 0.646111i 0.305940 0.952051i \(-0.401029\pi\)
−0.952051 + 0.305940i \(0.901029\pi\)
\(84\) 0 0
\(85\) −8.16228 8.16228i −0.885323 0.885323i
\(86\) 4.01315i 0.432749i
\(87\) 1.30986 7.63441i 0.140432 0.818495i
\(88\) 2.00000 2.00000i 0.213201 0.213201i
\(89\) −0.458991 −0.0486529 −0.0243264 0.999704i \(-0.507744\pi\)
−0.0243264 + 0.999704i \(0.507744\pi\)
\(90\) 2.89100 + 6.05327i 0.304738 + 0.638071i
\(91\) 0 0
\(92\) −0.707107 + 0.707107i −0.0737210 + 0.0737210i
\(93\) −3.02399 + 17.6251i −0.313573 + 1.82764i
\(94\) 12.3246i 1.27118i
\(95\) −11.5432 −1.18431
\(96\) −1.00000 1.41421i −0.102062 0.144338i
\(97\) 1.16228 + 1.16228i 0.118011 + 0.118011i 0.763646 0.645635i \(-0.223407\pi\)
−0.645635 + 0.763646i \(0.723407\pi\)
\(98\) −4.94975 4.94975i −0.500000 0.500000i
\(99\) 2.82843 8.00000i 0.284268 0.804030i
\(100\) 5.00000i 0.500000i
\(101\) 1.64371i 0.163555i 0.996651 + 0.0817776i \(0.0260597\pi\)
−0.996651 + 0.0817776i \(0.973940\pi\)
\(102\) 8.81256 + 1.51200i 0.872573 + 0.149710i
\(103\) −11.1623 + 11.1623i −1.09985 + 1.09985i −0.105425 + 0.994427i \(0.533620\pi\)
−0.994427 + 0.105425i \(0.966380\pi\)
\(104\) −5.88635 −0.577204
\(105\) 0 0
\(106\) −9.48683 −0.921443
\(107\) −10.3585 + 10.3585i −1.00139 + 1.00139i −0.00139356 + 0.999999i \(0.500444\pi\)
−0.999999 + 0.00139356i \(0.999556\pi\)
\(108\) −4.53553 2.53553i −0.436432 0.243982i
\(109\) 14.3246i 1.37204i 0.727581 + 0.686022i \(0.240645\pi\)
−0.727581 + 0.686022i \(0.759355\pi\)
\(110\) 4.47214 4.47214i 0.426401 0.426401i
\(111\) −10.3246 + 7.30056i −0.979963 + 0.692939i
\(112\) 0 0
\(113\) 13.7793 + 13.7793i 1.29624 + 1.29624i 0.930854 + 0.365391i \(0.119065\pi\)
0.365391 + 0.930854i \(0.380935\pi\)
\(114\) 7.30056 5.16228i 0.683760 0.483492i
\(115\) −1.58114 + 1.58114i −0.147442 + 0.147442i
\(116\) 4.47214i 0.415227i
\(117\) −15.9350 + 7.61042i −1.47319 + 0.703584i
\(118\) 7.00000 7.00000i 0.644402 0.644402i
\(119\) 0 0
\(120\) −2.23607 3.16228i −0.204124 0.288675i
\(121\) 3.00000 0.272727
\(122\) 5.65685 5.65685i 0.512148 0.512148i
\(123\) 10.4404 + 1.79129i 0.941379 + 0.161515i
\(124\) 10.3246i 0.927172i
\(125\) 11.1803i 1.00000i
\(126\) 0 0
\(127\) −5.16228 5.16228i −0.458078 0.458078i 0.439946 0.898024i \(-0.354998\pi\)
−0.898024 + 0.439946i \(0.854998\pi\)
\(128\) 0.707107 + 0.707107i 0.0625000 + 0.0625000i
\(129\) −4.01315 5.67544i −0.353338 0.499695i
\(130\) −13.1623 −1.15441
\(131\) 7.53006i 0.657904i 0.944347 + 0.328952i \(0.106695\pi\)
−0.944347 + 0.328952i \(0.893305\pi\)
\(132\) −0.828427 + 4.82843i −0.0721053 + 0.420261i
\(133\) 0 0
\(134\) 7.30056 0.630673
\(135\) −10.1418 5.66963i −0.872864 0.487964i
\(136\) −5.16228 −0.442662
\(137\) −3.65028 + 3.65028i −0.311865 + 0.311865i −0.845632 0.533767i \(-0.820776\pi\)
0.533767 + 0.845632i \(0.320776\pi\)
\(138\) 0.292893 1.70711i 0.0249327 0.145319i
\(139\) 2.32456i 0.197166i 0.995129 + 0.0985831i \(0.0314310\pi\)
−0.995129 + 0.0985831i \(0.968569\pi\)
\(140\) 0 0
\(141\) −12.3246 17.4296i −1.03791 1.46783i
\(142\) 2.16228 + 2.16228i 0.181454 + 0.181454i
\(143\) 11.7727 + 11.7727i 0.984483 + 0.984483i
\(144\) 2.82843 + 1.00000i 0.235702 + 0.0833333i
\(145\) 10.0000i 0.830455i
\(146\) 10.3585i 0.857274i
\(147\) 11.9497 + 2.05025i 0.985599 + 0.169102i
\(148\) 5.16228 5.16228i 0.424337 0.424337i
\(149\) −19.0733 −1.56254 −0.781271 0.624192i \(-0.785428\pi\)
−0.781271 + 0.624192i \(0.785428\pi\)
\(150\) −5.00000 7.07107i −0.408248 0.577350i
\(151\) 2.32456 0.189170 0.0945848 0.995517i \(-0.469848\pi\)
0.0945848 + 0.995517i \(0.469848\pi\)
\(152\) −3.65028 + 3.65028i −0.296077 + 0.296077i
\(153\) −13.9748 + 6.67427i −1.12980 + 0.539583i
\(154\) 0 0
\(155\) 23.0864i 1.85434i
\(156\) 8.32456 5.88635i 0.666498 0.471285i
\(157\) −9.48683 9.48683i −0.757132 0.757132i 0.218668 0.975799i \(-0.429829\pi\)
−0.975799 + 0.218668i \(0.929829\pi\)
\(158\) −2.23607 2.23607i −0.177892 0.177892i
\(159\) 13.4164 9.48683i 1.06399 0.752355i
\(160\) 1.58114 + 1.58114i 0.125000 + 0.125000i
\(161\) 0 0
\(162\) 8.94975 0.949747i 0.703159 0.0746192i
\(163\) 16.6491 16.6491i 1.30406 1.30406i 0.378428 0.925631i \(-0.376465\pi\)
0.925631 0.378428i \(-0.123535\pi\)
\(164\) −6.11584 −0.477567
\(165\) −1.85242 + 10.7967i −0.144211 + 0.840521i
\(166\) −8.32456 −0.646111
\(167\) 3.28742 3.28742i 0.254388 0.254388i −0.568379 0.822767i \(-0.692429\pi\)
0.822767 + 0.568379i \(0.192429\pi\)
\(168\) 0 0
\(169\) 21.6491i 1.66532i
\(170\) −11.5432 −0.885323
\(171\) −5.16228 + 14.6011i −0.394769 + 1.11658i
\(172\) 2.83772 + 2.83772i 0.216374 + 0.216374i
\(173\) −0.229495 0.229495i −0.0174482 0.0174482i 0.698329 0.715777i \(-0.253927\pi\)
−0.715777 + 0.698329i \(0.753927\pi\)
\(174\) −4.47214 6.32456i −0.339032 0.479463i
\(175\) 0 0
\(176\) 2.82843i 0.213201i
\(177\) −2.89949 + 16.8995i −0.217939 + 1.27024i
\(178\) −0.324555 + 0.324555i −0.0243264 + 0.0243264i
\(179\) 4.70163 0.351416 0.175708 0.984442i \(-0.443778\pi\)
0.175708 + 0.984442i \(0.443778\pi\)
\(180\) 6.32456 + 2.23607i 0.471405 + 0.166667i
\(181\) 9.67544 0.719170 0.359585 0.933112i \(-0.382918\pi\)
0.359585 + 0.933112i \(0.382918\pi\)
\(182\) 0 0
\(183\) −2.34315 + 13.6569i −0.173210 + 1.00954i
\(184\) 1.00000i 0.0737210i
\(185\) 11.5432 11.5432i 0.848673 0.848673i
\(186\) 10.3246 + 14.6011i 0.757033 + 1.07061i
\(187\) 10.3246 + 10.3246i 0.755006 + 0.755006i
\(188\) 8.71478 + 8.71478i 0.635590 + 0.635590i
\(189\) 0 0
\(190\) −8.16228 + 8.16228i −0.592154 + 0.592154i
\(191\) 0.458991i 0.0332114i −0.999862 0.0166057i \(-0.994714\pi\)
0.999862 0.0166057i \(-0.00528600\pi\)
\(192\) −1.70711 0.292893i −0.123200 0.0211377i
\(193\) 3.00000 3.00000i 0.215945 0.215945i −0.590842 0.806787i \(-0.701204\pi\)
0.806787 + 0.590842i \(0.201204\pi\)
\(194\) 1.64371 0.118011
\(195\) 18.6143 13.1623i 1.33300 0.942570i
\(196\) −7.00000 −0.500000
\(197\) −11.5432 + 11.5432i −0.822419 + 0.822419i −0.986454 0.164035i \(-0.947549\pi\)
0.164035 + 0.986454i \(0.447549\pi\)
\(198\) −3.65685 7.65685i −0.259881 0.544149i
\(199\) 8.83772i 0.626490i −0.949672 0.313245i \(-0.898584\pi\)
0.949672 0.313245i \(-0.101416\pi\)
\(200\) 3.53553 + 3.53553i 0.250000 + 0.250000i
\(201\) −10.3246 + 7.30056i −0.728238 + 0.514942i
\(202\) 1.16228 + 1.16228i 0.0817776 + 0.0817776i
\(203\) 0 0
\(204\) 7.30056 5.16228i 0.511142 0.361432i
\(205\) −13.6754 −0.955134
\(206\) 15.7858i 1.09985i
\(207\) 1.29289 + 2.70711i 0.0898623 + 0.188157i
\(208\) −4.16228 + 4.16228i −0.288602 + 0.288602i
\(209\) 14.6011 1.00998
\(210\) 0 0
\(211\) 14.3246 0.986143 0.493072 0.869989i \(-0.335874\pi\)
0.493072 + 0.869989i \(0.335874\pi\)
\(212\) −6.70820 + 6.70820i −0.460721 + 0.460721i
\(213\) −5.22020 0.895645i −0.357682 0.0613686i
\(214\) 14.6491i 1.00139i
\(215\) 6.34534 + 6.34534i 0.432749 + 0.432749i
\(216\) −5.00000 + 1.41421i −0.340207 + 0.0962250i
\(217\) 0 0
\(218\) 10.1290 + 10.1290i 0.686022 + 0.686022i
\(219\) −10.3585 14.6491i −0.699962 0.989895i
\(220\) 6.32456i 0.426401i
\(221\) 30.3870i 2.04405i
\(222\) −2.13829 + 12.4628i −0.143512 + 0.836451i
\(223\) 13.1623 13.1623i 0.881411 0.881411i −0.112267 0.993678i \(-0.535811\pi\)
0.993678 + 0.112267i \(0.0358111\pi\)
\(224\) 0 0
\(225\) 14.1421 + 5.00000i 0.942809 + 0.333333i
\(226\) 19.4868 1.29624
\(227\) −4.24264 + 4.24264i −0.281594 + 0.281594i −0.833744 0.552151i \(-0.813807\pi\)
0.552151 + 0.833744i \(0.313807\pi\)
\(228\) 1.51200 8.81256i 0.100134 0.583626i
\(229\) 25.2982i 1.67175i 0.548917 + 0.835877i \(0.315040\pi\)
−0.548917 + 0.835877i \(0.684960\pi\)
\(230\) 2.23607i 0.147442i
\(231\) 0 0
\(232\) 3.16228 + 3.16228i 0.207614 + 0.207614i
\(233\) −5.88635 5.88635i −0.385628 0.385628i 0.487497 0.873125i \(-0.337910\pi\)
−0.873125 + 0.487497i \(0.837910\pi\)
\(234\) −5.88635 + 16.6491i −0.384803 + 1.08839i
\(235\) 19.4868 + 19.4868i 1.27118 + 1.27118i
\(236\) 9.89949i 0.644402i
\(237\) 5.39835 + 0.926210i 0.350660 + 0.0601638i
\(238\) 0 0
\(239\) 6.34534 0.410446 0.205223 0.978715i \(-0.434208\pi\)
0.205223 + 0.978715i \(0.434208\pi\)
\(240\) −3.81721 0.654929i −0.246400 0.0422755i
\(241\) 8.32456 0.536232 0.268116 0.963387i \(-0.413599\pi\)
0.268116 + 0.963387i \(0.413599\pi\)
\(242\) 2.12132 2.12132i 0.136364 0.136364i
\(243\) −11.7071 + 10.2929i −0.751011 + 0.660289i
\(244\) 8.00000i 0.512148i
\(245\) −15.6525 −1.00000
\(246\) 8.64911 6.11584i 0.551447 0.389932i
\(247\) −21.4868 21.4868i −1.36717 1.36717i
\(248\) −7.30056 7.30056i −0.463586 0.463586i
\(249\) 11.7727 8.32456i 0.746064 0.527547i
\(250\) 7.90569 + 7.90569i 0.500000 + 0.500000i
\(251\) 5.65685i 0.357057i −0.983935 0.178529i \(-0.942866\pi\)
0.983935 0.178529i \(-0.0571337\pi\)
\(252\) 0 0
\(253\) 2.00000 2.00000i 0.125739 0.125739i
\(254\) −7.30056 −0.458078
\(255\) 16.3246 11.5432i 1.02228 0.722863i
\(256\) 1.00000 0.0625000
\(257\) 16.4743 16.4743i 1.02764 1.02764i 0.0280335 0.999607i \(-0.491075\pi\)
0.999607 0.0280335i \(-0.00892451\pi\)
\(258\) −6.85087 1.17542i −0.426516 0.0731786i
\(259\) 0 0
\(260\) −9.30714 + 9.30714i −0.577204 + 0.577204i
\(261\) 12.6491 + 4.47214i 0.782960 + 0.276818i
\(262\) 5.32456 + 5.32456i 0.328952 + 0.328952i
\(263\) 17.4296 + 17.4296i 1.07475 + 1.07475i 0.996970 + 0.0777819i \(0.0247838\pi\)
0.0777819 + 0.996970i \(0.475216\pi\)
\(264\) 2.82843 + 4.00000i 0.174078 + 0.246183i
\(265\) −15.0000 + 15.0000i −0.921443 + 0.921443i
\(266\) 0 0
\(267\) 0.134435 0.783546i 0.00822730 0.0479522i
\(268\) 5.16228 5.16228i 0.315336 0.315336i
\(269\) 18.6143 1.13493 0.567466 0.823397i \(-0.307924\pi\)
0.567466 + 0.823397i \(0.307924\pi\)
\(270\) −11.1803 + 3.16228i −0.680414 + 0.192450i
\(271\) −6.97367 −0.423620 −0.211810 0.977311i \(-0.567936\pi\)
−0.211810 + 0.977311i \(0.567936\pi\)
\(272\) −3.65028 + 3.65028i −0.221331 + 0.221331i
\(273\) 0 0
\(274\) 5.16228i 0.311865i
\(275\) 14.1421i 0.852803i
\(276\) −1.00000 1.41421i −0.0601929 0.0851257i
\(277\) 4.16228 + 4.16228i 0.250087 + 0.250087i 0.821006 0.570919i \(-0.193413\pi\)
−0.570919 + 0.821006i \(0.693413\pi\)
\(278\) 1.64371 + 1.64371i 0.0985831 + 0.0985831i
\(279\) −29.2023 10.3246i −1.74829 0.618115i
\(280\) 0 0
\(281\) 2.10270i 0.125437i 0.998031 + 0.0627183i \(0.0199770\pi\)
−0.998031 + 0.0627183i \(0.980023\pi\)
\(282\) −21.0393 3.60978i −1.25287 0.214959i
\(283\) −16.6491 + 16.6491i −0.989687 + 0.989687i −0.999947 0.0102605i \(-0.996734\pi\)
0.0102605 + 0.999947i \(0.496734\pi\)
\(284\) 3.05792 0.181454
\(285\) 3.38093 19.7055i 0.200269 1.16725i
\(286\) 16.6491 0.984483
\(287\) 0 0
\(288\) 2.70711 1.29289i 0.159518 0.0761845i
\(289\) 9.64911i 0.567595i
\(290\) 7.07107 + 7.07107i 0.415227 + 0.415227i
\(291\) −2.32456 + 1.64371i −0.136268 + 0.0963559i
\(292\) 7.32456 + 7.32456i 0.428637 + 0.428637i
\(293\) 0.133369 + 0.133369i 0.00779148 + 0.00779148i 0.710992 0.703200i \(-0.248246\pi\)
−0.703200 + 0.710992i \(0.748246\pi\)
\(294\) 9.89949 7.00000i 0.577350 0.408248i
\(295\) 22.1359i 1.28880i
\(296\) 7.30056i 0.424337i
\(297\) 12.8284 + 7.17157i 0.744381 + 0.416137i
\(298\) −13.4868 + 13.4868i −0.781271 + 0.781271i
\(299\) −5.88635 −0.340416
\(300\) −8.53553 1.46447i −0.492799 0.0845510i
\(301\) 0 0
\(302\) 1.64371 1.64371i 0.0945848 0.0945848i
\(303\) −2.80599 0.481431i −0.161200 0.0276575i
\(304\) 5.16228i 0.296077i
\(305\) 17.8885i 1.02430i
\(306\) −5.16228 + 14.6011i −0.295108 + 0.834691i
\(307\) 2.32456 + 2.32456i 0.132669 + 0.132669i 0.770323 0.637654i \(-0.220095\pi\)
−0.637654 + 0.770323i \(0.720095\pi\)
\(308\) 0 0
\(309\) −15.7858 22.3246i −0.898025 1.27000i
\(310\) −16.3246 16.3246i −0.927172 0.927172i
\(311\) 26.6033i 1.50854i −0.656567 0.754268i \(-0.727992\pi\)
0.656567 0.754268i \(-0.272008\pi\)
\(312\) 1.72407 10.0486i 0.0976063 0.568891i
\(313\) −9.16228 + 9.16228i −0.517883 + 0.517883i −0.916930 0.399048i \(-0.869341\pi\)
0.399048 + 0.916930i \(0.369341\pi\)
\(314\) −13.4164 −0.757132
\(315\) 0 0
\(316\) −3.16228 −0.177892
\(317\) −2.59893 + 2.59893i −0.145971 + 0.145971i −0.776315 0.630345i \(-0.782914\pi\)
0.630345 + 0.776315i \(0.282914\pi\)
\(318\) 2.77863 16.1950i 0.155818 0.908173i
\(319\) 12.6491i 0.708214i
\(320\) 2.23607 0.125000
\(321\) −14.6491 20.7170i −0.817634 1.15631i
\(322\) 0 0
\(323\) −18.8438 18.8438i −1.04850 1.04850i
\(324\) 5.65685 7.00000i 0.314270 0.388889i
\(325\) −20.8114 + 20.8114i −1.15441 + 1.15441i
\(326\) 23.5454i 1.30406i
\(327\) −24.4535 4.19557i −1.35228 0.232015i
\(328\) −4.32456 + 4.32456i −0.238784 + 0.238784i
\(329\) 0 0
\(330\) 6.32456 + 8.94427i 0.348155 + 0.492366i
\(331\) 2.97367 0.163447 0.0817237 0.996655i \(-0.473957\pi\)
0.0817237 + 0.996655i \(0.473957\pi\)
\(332\) −5.88635 + 5.88635i −0.323055 + 0.323055i
\(333\) −9.43885 19.7634i −0.517246 1.08303i
\(334\) 4.64911i 0.254388i
\(335\) 11.5432 11.5432i 0.630673 0.630673i
\(336\) 0 0
\(337\) −9.48683 9.48683i −0.516781 0.516781i 0.399815 0.916596i \(-0.369074\pi\)
−0.916596 + 0.399815i \(0.869074\pi\)
\(338\) −15.3082 15.3082i −0.832658 0.832658i
\(339\) −27.5585 + 19.4868i −1.49677 + 1.05838i
\(340\) −8.16228 + 8.16228i −0.442662 + 0.442662i
\(341\) 29.2023i 1.58139i
\(342\) 6.67427 + 13.9748i 0.360903 + 0.755673i
\(343\) 0 0
\(344\) 4.01315 0.216374
\(345\) −2.23607 3.16228i −0.120386 0.170251i
\(346\) −0.324555 −0.0174482
\(347\) −0.955223 + 0.955223i −0.0512791 + 0.0512791i −0.732281 0.681002i \(-0.761544\pi\)
0.681002 + 0.732281i \(0.261544\pi\)
\(348\) −7.63441 1.30986i −0.409248 0.0702158i
\(349\) 14.0000i 0.749403i 0.927146 + 0.374701i \(0.122255\pi\)
−0.927146 + 0.374701i \(0.877745\pi\)
\(350\) 0 0
\(351\) −8.32456 29.4317i −0.444332 1.57095i
\(352\) −2.00000 2.00000i −0.106600 0.106600i
\(353\) 17.6590 + 17.6590i 0.939896 + 0.939896i 0.998293 0.0583971i \(-0.0185990\pi\)
−0.0583971 + 0.998293i \(0.518599\pi\)
\(354\) 9.89949 + 14.0000i 0.526152 + 0.744092i
\(355\) 6.83772 0.362909
\(356\) 0.458991i 0.0243264i
\(357\) 0 0
\(358\) 3.32456 3.32456i 0.175708 0.175708i
\(359\) 19.7990 1.04495 0.522475 0.852654i \(-0.325009\pi\)
0.522475 + 0.852654i \(0.325009\pi\)
\(360\) 6.05327 2.89100i 0.319036 0.152369i
\(361\) −7.64911 −0.402585
\(362\) 6.84157 6.84157i 0.359585 0.359585i
\(363\) −0.878680 + 5.12132i −0.0461187 + 0.268800i
\(364\) 0 0
\(365\) 16.3782 + 16.3782i 0.857274 + 0.857274i
\(366\) 8.00000 + 11.3137i 0.418167 + 0.591377i
\(367\) 1.48683 + 1.48683i 0.0776120 + 0.0776120i 0.744847 0.667235i \(-0.232522\pi\)
−0.667235 + 0.744847i \(0.732522\pi\)
\(368\) 0.707107 + 0.707107i 0.0368605 + 0.0368605i
\(369\) −6.11584 + 17.2982i −0.318378 + 0.900509i
\(370\) 16.3246i 0.848673i
\(371\) 0 0
\(372\) 17.6251 + 3.02399i 0.913820 + 0.156787i
\(373\) 13.4868 13.4868i 0.698322 0.698322i −0.265727 0.964048i \(-0.585612\pi\)
0.964048 + 0.265727i \(0.0856119\pi\)
\(374\) 14.6011 0.755006
\(375\) −19.0860 3.27465i −0.985599 0.169102i
\(376\) 12.3246 0.635590
\(377\) −18.6143 + 18.6143i −0.958684 + 0.958684i
\(378\) 0 0
\(379\) 3.48683i 0.179107i −0.995982 0.0895533i \(-0.971456\pi\)
0.995982 0.0895533i \(-0.0285439\pi\)
\(380\) 11.5432i 0.592154i
\(381\) 10.3246 7.30056i 0.528943 0.374019i
\(382\) −0.324555 0.324555i −0.0166057 0.0166057i
\(383\) 6.84157 + 6.84157i 0.349588 + 0.349588i 0.859956 0.510368i \(-0.170491\pi\)
−0.510368 + 0.859956i \(0.670491\pi\)
\(384\) −1.41421 + 1.00000i −0.0721688 + 0.0510310i
\(385\) 0 0
\(386\) 4.24264i 0.215945i
\(387\) 10.8640 5.18857i 0.552249 0.263750i
\(388\) 1.16228 1.16228i 0.0590057 0.0590057i
\(389\) −12.4984 −0.633695 −0.316848 0.948476i \(-0.602624\pi\)
−0.316848 + 0.948476i \(0.602624\pi\)
\(390\) 3.85514 22.4694i 0.195213 1.13778i
\(391\) −5.16228 −0.261068
\(392\) −4.94975 + 4.94975i −0.250000 + 0.250000i
\(393\) −12.8546 2.20550i −0.648429 0.111253i
\(394\) 16.3246i 0.822419i
\(395\) −7.07107 −0.355784
\(396\) −8.00000 2.82843i −0.402015 0.142134i
\(397\) 6.81139 + 6.81139i 0.341854 + 0.341854i 0.857064 0.515210i \(-0.172286\pi\)
−0.515210 + 0.857064i \(0.672286\pi\)
\(398\) −6.24921 6.24921i −0.313245 0.313245i
\(399\) 0 0
\(400\) 5.00000 0.250000
\(401\) 19.7990i 0.988714i −0.869259 0.494357i \(-0.835403\pi\)
0.869259 0.494357i \(-0.164597\pi\)
\(402\) −2.13829 + 12.4628i −0.106648 + 0.621590i
\(403\) 42.9737 42.9737i 2.14067 2.14067i
\(404\) 1.64371 0.0817776
\(405\) 12.6491 15.6525i 0.628539 0.777778i
\(406\) 0 0
\(407\) −14.6011 + 14.6011i −0.723751 + 0.723751i
\(408\) 1.51200 8.81256i 0.0748550 0.436287i
\(409\) 20.0000i 0.988936i −0.869196 0.494468i \(-0.835363\pi\)
0.869196 0.494468i \(-0.164637\pi\)
\(410\) −9.67000 + 9.67000i −0.477567 + 0.477567i
\(411\) −5.16228 7.30056i −0.254636 0.360110i
\(412\) 11.1623 + 11.1623i 0.549926 + 0.549926i
\(413\) 0 0
\(414\) 2.82843 + 1.00000i 0.139010 + 0.0491473i
\(415\) −13.1623 + 13.1623i −0.646111 + 0.646111i
\(416\) 5.88635i 0.288602i
\(417\) −3.96826 0.680846i −0.194327 0.0333412i
\(418\) 10.3246 10.3246i 0.504991 0.504991i
\(419\) 26.3738 1.28845 0.644223 0.764838i \(-0.277181\pi\)
0.644223 + 0.764838i \(0.277181\pi\)
\(420\) 0 0
\(421\) 11.3509 0.553208 0.276604 0.960984i \(-0.410791\pi\)
0.276604 + 0.960984i \(0.410791\pi\)
\(422\) 10.1290 10.1290i 0.493072 0.493072i
\(423\) 33.3639 15.9343i 1.62221 0.774754i
\(424\) 9.48683i 0.460721i
\(425\) −18.2514 + 18.2514i −0.885323 + 0.885323i
\(426\) −4.32456 + 3.05792i −0.209525 + 0.148157i
\(427\) 0 0
\(428\) 10.3585 + 10.3585i 0.500696 + 0.500696i
\(429\) −23.5454 + 16.6491i −1.13678 + 0.803827i
\(430\) 8.97367 0.432749
\(431\) 6.11584i 0.294590i −0.989093 0.147295i \(-0.952943\pi\)
0.989093 0.147295i \(-0.0470566\pi\)
\(432\) −2.53553 + 4.53553i −0.121991 + 0.218216i
\(433\) 16.1359 16.1359i 0.775444 0.775444i −0.203608 0.979052i \(-0.565267\pi\)
0.979052 + 0.203608i \(0.0652669\pi\)
\(434\) 0 0
\(435\) −17.0711 2.92893i −0.818495 0.140432i
\(436\) 14.3246 0.686022
\(437\) −3.65028 + 3.65028i −0.174617 + 0.174617i
\(438\) −17.6830 3.03393i −0.844928 0.144967i
\(439\) 11.3509i 0.541748i 0.962615 + 0.270874i \(0.0873127\pi\)
−0.962615 + 0.270874i \(0.912687\pi\)
\(440\) −4.47214 4.47214i −0.213201 0.213201i
\(441\) −7.00000 + 19.7990i −0.333333 + 0.942809i
\(442\) −21.4868 21.4868i −1.02202 1.02202i
\(443\) 11.3137 + 11.3137i 0.537531 + 0.537531i 0.922803 0.385272i \(-0.125893\pi\)
−0.385272 + 0.922803i \(0.625893\pi\)
\(444\) 7.30056 + 10.3246i 0.346469 + 0.489982i
\(445\) 1.02633i 0.0486529i
\(446\) 18.6143i 0.881411i
\(447\) 5.58643 32.5601i 0.264229 1.54004i
\(448\) 0 0
\(449\) −5.65685 −0.266963 −0.133482 0.991051i \(-0.542616\pi\)
−0.133482 + 0.991051i \(0.542616\pi\)
\(450\) 13.5355 6.46447i 0.638071 0.304738i
\(451\) 17.2982 0.814541
\(452\) 13.7793 13.7793i 0.648122 0.648122i
\(453\) −0.680846 + 3.96826i −0.0319890 + 0.186445i
\(454\) 6.00000i 0.281594i
\(455\) 0 0
\(456\) −5.16228 7.30056i −0.241746 0.341880i
\(457\) −19.1623 19.1623i −0.896374 0.896374i 0.0987397 0.995113i \(-0.468519\pi\)
−0.995113 + 0.0987397i \(0.968519\pi\)
\(458\) 17.8885 + 17.8885i 0.835877 + 0.835877i
\(459\) −7.30056 25.8114i −0.340761 1.20477i
\(460\) 1.58114 + 1.58114i 0.0737210 + 0.0737210i
\(461\) 4.01315i 0.186911i 0.995623 + 0.0934554i \(0.0297913\pi\)
−0.995623 + 0.0934554i \(0.970209\pi\)
\(462\) 0 0
\(463\) −26.1359 + 26.1359i −1.21464 + 1.21464i −0.245157 + 0.969483i \(0.578839\pi\)
−0.969483 + 0.245157i \(0.921161\pi\)
\(464\) 4.47214 0.207614
\(465\) 39.4110 + 6.76185i 1.82764 + 0.313573i
\(466\) −8.32456 −0.385628
\(467\) −4.70163 + 4.70163i −0.217566 + 0.217566i −0.807472 0.589906i \(-0.799165\pi\)
0.589906 + 0.807472i \(0.299165\pi\)
\(468\) 7.61042 + 15.9350i 0.351792 + 0.736595i
\(469\) 0 0
\(470\) 27.5585 1.27118
\(471\) 18.9737 13.4164i 0.874260 0.618195i
\(472\) −7.00000 7.00000i −0.322201 0.322201i
\(473\) −8.02629 8.02629i −0.369049 0.369049i
\(474\) 4.47214 3.16228i 0.205412 0.145248i
\(475\) 25.8114i 1.18431i
\(476\) 0 0
\(477\) 12.2655 + 25.6819i 0.561597 + 1.17589i
\(478\) 4.48683 4.48683i 0.205223 0.205223i
\(479\) −28.2843 −1.29234 −0.646171 0.763193i \(-0.723631\pi\)
−0.646171 + 0.763193i \(0.723631\pi\)
\(480\) −3.16228 + 2.23607i −0.144338 + 0.102062i
\(481\) 42.9737 1.95943
\(482\) 5.88635 5.88635i 0.268116 0.268116i
\(483\) 0 0
\(484\) 3.00000i 0.136364i
\(485\) 2.59893 2.59893i 0.118011 0.118011i
\(486\) −1.00000 + 15.5563i −0.0453609 + 0.705650i
\(487\) −23.1623 23.1623i −1.04958 1.04958i −0.998705 0.0508781i \(-0.983798\pi\)
−0.0508781 0.998705i \(-0.516202\pi\)
\(488\) −5.65685 5.65685i −0.256074 0.256074i
\(489\) 23.5454 + 33.2982i 1.06476 + 1.50580i
\(490\) −11.0680 + 11.0680i −0.500000 + 0.500000i
\(491\) 9.89949i 0.446758i 0.974732 + 0.223379i \(0.0717087\pi\)
−0.974732 + 0.223379i \(0.928291\pi\)
\(492\) 1.79129 10.4404i 0.0807576 0.470690i
\(493\) −16.3246 + 16.3246i −0.735221 + 0.735221i
\(494\) −30.3870 −1.36717
\(495\) −17.8885 6.32456i −0.804030 0.284268i
\(496\) −10.3246 −0.463586
\(497\) 0 0
\(498\) 2.43821 14.2109i 0.109259 0.636806i
\(499\) 15.3509i 0.687200i 0.939116 + 0.343600i \(0.111646\pi\)
−0.939116 + 0.343600i \(0.888354\pi\)
\(500\) 11.1803 0.500000
\(501\) 4.64911 + 6.57484i 0.207707 + 0.293742i
\(502\) −4.00000 4.00000i −0.178529 0.178529i
\(503\) −15.7858 15.7858i −0.703856 0.703856i 0.261380 0.965236i \(-0.415822\pi\)
−0.965236 + 0.261380i \(0.915822\pi\)
\(504\) 0 0
\(505\) 3.67544 0.163555
\(506\) 2.82843i 0.125739i
\(507\) 36.9573 + 6.34088i 1.64133 + 0.281608i
\(508\) −5.16228 + 5.16228i −0.229039 + 0.229039i
\(509\) 27.0996 1.20117 0.600583 0.799562i \(-0.294935\pi\)
0.600583 + 0.799562i \(0.294935\pi\)
\(510\) 3.38093 19.7055i 0.149710 0.872573i
\(511\) 0 0
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) −23.4137 13.0891i −1.03374 0.577899i
\(514\) 23.2982i 1.02764i
\(515\) 24.9596 + 24.9596i 1.09985 + 1.09985i
\(516\) −5.67544 + 4.01315i −0.249848 + 0.176669i
\(517\) −24.6491 24.6491i −1.08407 1.08407i
\(518\) 0 0
\(519\) 0.458991 0.324555i 0.0201474 0.0142464i
\(520\) 13.1623i 0.577204i
\(521\) 9.40326i 0.411964i 0.978556 + 0.205982i \(0.0660389\pi\)
−0.978556 + 0.205982i \(0.933961\pi\)
\(522\) 12.1065 5.78199i 0.529889 0.253071i
\(523\) −21.2982 + 21.2982i −0.931306 + 0.931306i −0.997788 0.0664815i \(-0.978823\pi\)
0.0664815 + 0.997788i \(0.478823\pi\)
\(524\) 7.53006 0.328952
\(525\) 0 0
\(526\) 24.6491 1.07475
\(527\) 37.6875 37.6875i 1.64169 1.64169i
\(528\) 4.82843 + 0.828427i 0.210130 + 0.0360527i
\(529\) 1.00000i 0.0434783i
\(530\) 21.2132i 0.921443i
\(531\) −28.0000 9.89949i −1.21510 0.429601i
\(532\) 0 0
\(533\) −25.4558 25.4558i −1.10262 1.10262i
\(534\) −0.458991 0.649111i −0.0198625 0.0280898i
\(535\) 23.1623 + 23.1623i 1.00139 + 1.00139i
\(536\) 7.30056i 0.315336i
\(537\) −1.37708 + 8.02619i −0.0594252 + 0.346356i
\(538\) 13.1623 13.1623i 0.567466 0.567466i
\(539\) 19.7990 0.852803
\(540\) −5.66963 + 10.1418i −0.243982 + 0.436432i
\(541\) 26.3246 1.13178 0.565891 0.824480i \(-0.308532\pi\)
0.565891 + 0.824480i \(0.308532\pi\)
\(542\) −4.93113 + 4.93113i −0.211810 + 0.211810i
\(543\) −2.83387 + 16.5170i −0.121613 + 0.708813i
\(544\) 5.16228i 0.221331i
\(545\) 32.0307 1.37204
\(546\) 0 0
\(547\) 6.32456 + 6.32456i 0.270418 + 0.270418i 0.829269 0.558850i \(-0.188757\pi\)
−0.558850 + 0.829269i \(0.688757\pi\)
\(548\) 3.65028 + 3.65028i 0.155932 + 0.155932i
\(549\) −22.6274 8.00000i −0.965715 0.341432i
\(550\) −10.0000 10.0000i −0.426401 0.426401i
\(551\) 23.0864i 0.983514i
\(552\) −1.70711 0.292893i −0.0726593 0.0124664i
\(553\) 0 0
\(554\) 5.88635 0.250087
\(555\) 16.3246 + 23.0864i 0.692939 + 0.979963i
\(556\) 2.32456 0.0985831
\(557\) −22.0351 + 22.0351i −0.933655 + 0.933655i −0.997932 0.0642767i \(-0.979526\pi\)
0.0642767 + 0.997932i \(0.479526\pi\)
\(558\) −27.9497 + 13.3485i −1.18320 + 0.565089i
\(559\) 23.6228i 0.999137i
\(560\) 0 0
\(561\) −20.6491 + 14.6011i −0.871806 + 0.616460i
\(562\) 1.48683 + 1.48683i 0.0627183 + 0.0627183i
\(563\) 3.05792 + 3.05792i 0.128876 + 0.128876i 0.768603 0.639727i \(-0.220952\pi\)
−0.639727 + 0.768603i \(0.720952\pi\)
\(564\) −17.4296 + 12.3246i −0.733917 + 0.518957i
\(565\) 30.8114 30.8114i 1.29624 1.29624i
\(566\) 23.5454i 0.989687i
\(567\) 0 0
\(568\) 2.16228 2.16228i 0.0907272 0.0907272i
\(569\) 1.18472 0.0496660 0.0248330 0.999692i \(-0.492095\pi\)
0.0248330 + 0.999692i \(0.492095\pi\)
\(570\) −11.5432 16.3246i −0.483492 0.683760i
\(571\) −17.1623 −0.718219 −0.359109 0.933295i \(-0.616920\pi\)
−0.359109 + 0.933295i \(0.616920\pi\)
\(572\) 11.7727 11.7727i 0.492241 0.492241i
\(573\) 0.783546 + 0.134435i 0.0327331 + 0.00561611i
\(574\) 0 0
\(575\) 3.53553 + 3.53553i 0.147442 + 0.147442i
\(576\) 1.00000 2.82843i 0.0416667 0.117851i
\(577\) −19.3246 19.3246i −0.804492 0.804492i 0.179302 0.983794i \(-0.442616\pi\)
−0.983794 + 0.179302i \(0.942616\pi\)
\(578\) −6.82295 6.82295i −0.283797 0.283797i
\(579\) 4.24264 + 6.00000i 0.176318 + 0.249351i
\(580\) 10.0000 0.415227
\(581\) 0 0
\(582\) −0.481431 + 2.80599i −0.0199560 + 0.116312i
\(583\) 18.9737 18.9737i 0.785809 0.785809i
\(584\) 10.3585 0.428637
\(585\) 17.0174 + 35.6317i 0.703584 + 1.47319i
\(586\) 0.188612 0.00779148
\(587\) 7.07107 7.07107i 0.291854 0.291854i −0.545958 0.837812i \(-0.683834\pi\)
0.837812 + 0.545958i \(0.183834\pi\)
\(588\) 2.05025 11.9497i 0.0845510 0.492799i
\(589\) 53.2982i 2.19611i
\(590\) −15.6525 15.6525i −0.644402 0.644402i
\(591\) −16.3246 23.0864i −0.671502 0.949648i
\(592\) −5.16228 5.16228i −0.212168 0.212168i
\(593\) 7.98905 + 7.98905i 0.328071 + 0.328071i 0.851853 0.523782i \(-0.175479\pi\)
−0.523782 + 0.851853i \(0.675479\pi\)
\(594\) 14.1421 4.00000i 0.580259 0.164122i
\(595\) 0 0
\(596\) 19.0733i 0.781271i
\(597\) 15.0869 + 2.58851i 0.617467 + 0.105941i
\(598\) −4.16228 + 4.16228i −0.170208 + 0.170208i
\(599\) −8.25579 −0.337322 −0.168661 0.985674i \(-0.553944\pi\)
−0.168661 + 0.985674i \(0.553944\pi\)
\(600\) −7.07107 + 5.00000i −0.288675 + 0.204124i
\(601\) −34.6491 −1.41337 −0.706683 0.707530i \(-0.749809\pi\)
−0.706683 + 0.707530i \(0.749809\pi\)
\(602\) 0 0
\(603\) −9.43885 19.7634i −0.384380 0.804828i
\(604\) 2.32456i 0.0945848i
\(605\) 6.70820i 0.272727i
\(606\) −2.32456 + 1.64371i −0.0944286 + 0.0667711i
\(607\) 0.837722 + 0.837722i 0.0340021 + 0.0340021i 0.723903 0.689901i \(-0.242346\pi\)
−0.689901 + 0.723903i \(0.742346\pi\)
\(608\) 3.65028 + 3.65028i 0.148038 + 0.148038i
\(609\) 0 0
\(610\) −12.6491 12.6491i −0.512148 0.512148i
\(611\) 72.5466i 2.93492i
\(612\) 6.67427 + 13.9748i 0.269792 + 0.564899i
\(613\) −26.4605 + 26.4605i −1.06873 + 1.06873i −0.0712726 + 0.997457i \(0.522706\pi\)
−0.997457 + 0.0712726i \(0.977294\pi\)
\(614\) 3.28742 0.132669
\(615\) 4.00545 23.3454i 0.161515 0.941379i
\(616\) 0 0
\(617\) 7.66343 7.66343i 0.308518 0.308518i −0.535817 0.844334i \(-0.679996\pi\)
0.844334 + 0.535817i \(0.179996\pi\)
\(618\) −26.9481 4.62357i −1.08401 0.185987i
\(619\) 18.4605i 0.741990i 0.928635 + 0.370995i \(0.120983\pi\)
−0.928635 + 0.370995i \(0.879017\pi\)
\(620\) −23.0864 −0.927172
\(621\) −5.00000 + 1.41421i −0.200643 + 0.0567504i
\(622\) −18.8114 18.8114i −0.754268 0.754268i
\(623\) 0 0
\(624\) −5.88635 8.32456i −0.235643 0.333249i
\(625\) 25.0000 1.00000
\(626\) 12.9574i 0.517883i
\(627\) −4.27657 + 24.9257i −0.170790 + 0.995436i
\(628\) −9.48683 + 9.48683i −0.378566 + 0.378566i
\(629\) 37.6875 1.50270
\(630\) 0 0
\(631\) −27.8114 −1.10715 −0.553577 0.832798i \(-0.686738\pi\)
−0.553577 + 0.832798i \(0.686738\pi\)
\(632\) −2.23607 + 2.23607i −0.0889460 + 0.0889460i
\(633\) −4.19557 + 24.4535i −0.166759 + 0.971941i
\(634\) 3.67544i 0.145971i
\(635\) −11.5432 + 11.5432i −0.458078 + 0.458078i
\(636\) −9.48683 13.4164i −0.376177 0.531995i
\(637\) −29.1359 29.1359i −1.15441 1.15441i
\(638\) −8.94427 8.94427i −0.354107 0.354107i
\(639\) 3.05792 8.64911i 0.120970 0.342154i
\(640\) 1.58114 1.58114i 0.0625000 0.0625000i
\(641\) 10.8547i 0.428736i −0.976753 0.214368i \(-0.931231\pi\)
0.976753 0.214368i \(-0.0687691\pi\)
\(642\) −25.0076 4.29063i −0.986971 0.169337i
\(643\) −5.16228 + 5.16228i −0.203580 + 0.203580i −0.801532 0.597952i \(-0.795981\pi\)
0.597952 + 0.801532i \(0.295981\pi\)
\(644\) 0 0
\(645\) −12.6907 + 8.97367i −0.499695 + 0.353338i
\(646\) −26.6491 −1.04850
\(647\) 19.5695 19.5695i 0.769356 0.769356i −0.208637 0.977993i \(-0.566903\pi\)
0.977993 + 0.208637i \(0.0669027\pi\)
\(648\) −0.949747 8.94975i −0.0373096 0.351579i
\(649\) 28.0000i 1.09910i
\(650\) 29.4317i 1.15441i
\(651\) 0 0
\(652\) −16.6491 16.6491i −0.652029 0.652029i
\(653\) 17.6590 + 17.6590i 0.691052 + 0.691052i 0.962463 0.271411i \(-0.0874904\pi\)
−0.271411 + 0.962463i \(0.587490\pi\)
\(654\) −20.2580 + 14.3246i −0.792150 + 0.560134i
\(655\) 16.8377 0.657904
\(656\) 6.11584i 0.238784i
\(657\) 28.0415 13.3924i 1.09400 0.522488i
\(658\) 0 0
\(659\) −8.94427 −0.348419 −0.174210 0.984709i \(-0.555737\pi\)
−0.174210 + 0.984709i \(0.555737\pi\)
\(660\) 10.7967 + 1.85242i 0.420261 + 0.0721053i
\(661\) −32.6491 −1.26990 −0.634952 0.772552i \(-0.718980\pi\)
−0.634952 + 0.772552i \(0.718980\pi\)
\(662\) 2.10270 2.10270i 0.0817237 0.0817237i
\(663\) 51.8738 + 8.90014i 2.01461 + 0.345653i
\(664\) 8.32456i 0.323055i
\(665\) 0 0
\(666\) −20.6491 7.30056i −0.800137 0.282891i
\(667\) 3.16228 + 3.16228i 0.122444 + 0.122444i
\(668\) −3.28742 3.28742i −0.127194 0.127194i
\(669\) 18.6143 + 26.3246i 0.719669 + 1.01777i
\(670\) 16.3246i 0.630673i
\(671\) 22.6274i 0.873522i
\(672\) 0 0
\(673\) 31.3246 31.3246i 1.20747 1.20747i 0.235630 0.971843i \(-0.424285\pi\)
0.971843 0.235630i \(-0.0757154\pi\)
\(674\) −13.4164 −0.516781
\(675\) −12.6777 + 22.6777i −0.487964 + 0.872864i
\(676\) −21.6491 −0.832658
\(677\) −25.7815 + 25.7815i −0.990862 + 0.990862i −0.999959 0.00909639i \(-0.997104\pi\)
0.00909639 + 0.999959i \(0.497104\pi\)
\(678\) −5.70756 + 33.2661i −0.219198 + 1.27758i
\(679\) 0 0
\(680\) 11.5432i 0.442662i
\(681\) −6.00000 8.48528i −0.229920 0.325157i
\(682\) 20.6491 + 20.6491i 0.790695 + 0.790695i
\(683\) 31.0755 + 31.0755i 1.18907 + 1.18907i 0.977325 + 0.211744i \(0.0679144\pi\)
0.211744 + 0.977325i \(0.432086\pi\)
\(684\) 14.6011 + 5.16228i 0.558288 + 0.197385i
\(685\) 8.16228 + 8.16228i 0.311865 + 0.311865i
\(686\) 0 0
\(687\) −43.1868 7.40968i −1.64768 0.282697i
\(688\) 2.83772 2.83772i 0.108187 0.108187i
\(689\) −55.8428 −2.12744
\(690\) −3.81721 0.654929i −0.145319 0.0249327i
\(691\) −12.6491 −0.481195 −0.240597 0.970625i \(-0.577343\pi\)
−0.240597 + 0.970625i \(0.577343\pi\)
\(692\) −0.229495 + 0.229495i −0.00872410 + 0.00872410i
\(693\) 0 0
\(694\) 1.35089i 0.0512791i
\(695\) 5.19786 0.197166
\(696\) −6.32456 + 4.47214i −0.239732 + 0.169516i
\(697\) −22.3246 22.3246i −0.845603 0.845603i
\(698\) 9.89949 + 9.89949i 0.374701 + 0.374701i
\(699\) 11.7727 8.32456i 0.445284 0.314864i
\(700\) 0 0
\(701\) 25.9148i 0.978790i −0.872062 0.489395i \(-0.837218\pi\)
0.872062 0.489395i \(-0.162782\pi\)
\(702\) −26.6977 14.9250i −1.00764 0.563309i
\(703\) 26.6491 26.6491i 1.00509 1.00509i
\(704\) −2.82843 −0.106600
\(705\) −38.9737 + 27.5585i −1.46783 + 1.03791i
\(706\) 24.9737 0.939896
\(707\) 0 0
\(708\) 16.8995 + 2.89949i 0.635122 + 0.108970i
\(709\) 25.9473i 0.974473i −0.873270 0.487236i \(-0.838005\pi\)
0.873270 0.487236i \(-0.161995\pi\)
\(710\) 4.83500 4.83500i 0.181454 0.181454i
\(711\) −3.16228 + 8.94427i −0.118595 + 0.335436i
\(712\) 0.324555 + 0.324555i 0.0121632 + 0.0121632i
\(713\) −7.30056 7.30056i −0.273408 0.273408i
\(714\) 0 0
\(715\) 26.3246 26.3246i 0.984483 0.984483i
\(716\) 4.70163i 0.175708i
\(717\) −1.85851 + 10.8322i −0.0694072 + 0.404535i
\(718\) 14.0000 14.0000i 0.522475 0.522475i
\(719\) −30.3497 −1.13185 −0.565927 0.824455i \(-0.691482\pi\)
−0.565927 + 0.824455i \(0.691482\pi\)
\(720\) 2.23607 6.32456i 0.0833333 0.235702i
\(721\) 0 0
\(722\) −5.40874 + 5.40874i −0.201292 + 0.201292i
\(723\) −2.43821 + 14.2109i −0.0906778 + 0.528509i
\(724\) 9.67544i 0.359585i
\(725\) 22.3607 0.830455
\(726\) 3.00000 + 4.24264i 0.111340 + 0.157459i
\(727\) 13.6754 + 13.6754i 0.507194 + 0.507194i 0.913664 0.406470i \(-0.133240\pi\)
−0.406470 + 0.913664i \(0.633240\pi\)
\(728\) 0 0
\(729\) −14.1421 23.0000i −0.523783 0.851852i
\(730\) 23.1623 0.857274
\(731\) 20.7170i 0.766245i
\(732\) 13.6569 + 2.34315i 0.504772 + 0.0866052i
\(733\) −33.8114 + 33.8114i −1.24885 + 1.24885i −0.292625 + 0.956227i \(0.594529\pi\)
−0.956227 + 0.292625i \(0.905471\pi\)
\(734\) 2.10270 0.0776120
\(735\) 4.58450 26.7204i 0.169102 0.985599i
\(736\) 1.00000 0.0368605
\(737\) −14.6011 + 14.6011i −0.537839 + 0.537839i
\(738\) 7.90713 + 16.5562i 0.291066 + 0.609444i
\(739\) 52.2719i 1.92285i 0.275063 + 0.961426i \(0.411301\pi\)
−0.275063 + 0.961426i \(0.588699\pi\)
\(740\) −11.5432 11.5432i −0.424337 0.424337i
\(741\) 42.9737 30.3870i 1.57868 1.11629i
\(742\) 0 0
\(743\) −16.2448 16.2448i −0.595965 0.595965i 0.343271 0.939236i \(-0.388465\pi\)
−0.939236 + 0.343271i \(0.888465\pi\)
\(744\) 14.6011 10.3246i 0.535303 0.378517i
\(745\) 42.6491i 1.56254i
\(746\) 19.0733i 0.698322i
\(747\) 10.7628 + 22.5355i 0.393789 + 0.824529i
\(748\) 10.3246 10.3246i 0.377503 0.377503i
\(749\) 0 0
\(750\) −15.8114 + 11.1803i −0.577350 + 0.408248i
\(751\) −28.4605 −1.03854 −0.519269 0.854611i \(-0.673796\pi\)
−0.519269 + 0.854611i \(0.673796\pi\)
\(752\) 8.71478 8.71478i 0.317795 0.317795i
\(753\) 9.65685 + 1.65685i 0.351915 + 0.0603791i
\(754\) 26.3246i 0.958684i
\(755\) 5.19786i 0.189170i
\(756\) 0 0
\(757\) 9.48683 + 9.48683i 0.344805 + 0.344805i 0.858170 0.513365i \(-0.171601\pi\)
−0.513365 + 0.858170i \(0.671601\pi\)
\(758\) −2.46556 2.46556i −0.0895533 0.0895533i
\(759\) 2.82843 + 4.00000i 0.102665 + 0.145191i
\(760\) 8.16228 + 8.16228i 0.296077 + 0.296077i
\(761\) 21.1760i 0.767628i −0.923410 0.383814i \(-0.874610\pi\)
0.923410 0.383814i \(-0.125390\pi\)
\(762\) 2.13829 12.4628i 0.0774619 0.451481i
\(763\) 0 0
\(764\) −0.458991 −0.0166057
\(765\) 14.9241 + 31.2487i 0.539583 + 1.12980i
\(766\) 9.67544 0.349588
\(767\) 41.2044 41.2044i 1.48781 1.48781i
\(768\) −0.292893 + 1.70711i −0.0105689 + 0.0615999i
\(769\) 3.67544i 0.132540i 0.997802 + 0.0662700i \(0.0211099\pi\)
−0.997802 + 0.0662700i \(0.978890\pi\)
\(770\) 0 0
\(771\) 23.2982 + 32.9487i 0.839065 + 1.18662i
\(772\) −3.00000 3.00000i −0.107972 0.107972i
\(773\) 17.5629 + 17.5629i 0.631694 + 0.631694i 0.948493 0.316798i \(-0.102608\pi\)
−0.316798 + 0.948493i \(0.602608\pi\)
\(774\) 4.01315 11.3509i 0.144250 0.407999i
\(775\) −51.6228 −1.85434
\(776\) 1.64371i 0.0590057i
\(777\) 0 0
\(778\) −8.83772 + 8.83772i −0.316848 + 0.316848i
\(779\) −31.5717 −1.13117
\(780\) −13.1623 18.6143i −0.471285 0.666498i
\(781\) −8.64911 −0.309490
\(782\) −3.65028 +