Properties

Label 690.2.i.d.47.2
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 47.2
Root \(-0.437016 - 0.437016i\) of defining polynomial
Character \(\chi\) \(=\) 690.47
Dual form 690.2.i.d.323.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(-1.70711 + 0.292893i) q^{3} -1.00000i q^{4} +2.23607i q^{5} +(1.00000 - 1.41421i) q^{6} +(0.707107 + 0.707107i) q^{8} +(2.82843 - 1.00000i) q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(-1.70711 + 0.292893i) 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} +(0.292893 + 1.70711i) q^{12} +(4.16228 - 4.16228i) q^{13} +(-0.654929 - 3.81721i) q^{15} -1.00000 q^{16} +(-3.65028 + 3.65028i) q^{17} +(-1.29289 + 2.70711i) 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} +(-4.53553 + 2.53553i) q^{27} +4.47214 q^{29} +(3.16228 + 2.23607i) q^{30} +10.3246 q^{31} +(0.707107 - 0.707107i) q^{32} +(0.828427 + 4.82843i) 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} +(1.70711 - 0.292893i) 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} +(1.51200 + 8.81256i) q^{57} +(-3.16228 + 3.16228i) q^{58} -9.89949 q^{59} +(-3.81721 + 0.654929i) 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} +(2.70711 + 1.29289i) q^{72} +(-7.32456 + 7.32456i) q^{73} -7.30056 q^{74} +(8.53553 - 1.46447i) q^{75} -5.16228 q^{76} +(-1.72407 - 10.0486i) 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} +(-7.63441 + 1.30986i) q^{87} +(2.00000 - 2.00000i) q^{88} +0.458991 q^{89} +(-6.05327 - 2.89100i) q^{90} +(0.707107 - 0.707107i) q^{92} +(-17.6251 + 3.02399i) 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})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 8 q^{3} + 8 q^{6} + O(q^{10}) \) \( 8 q - 8 q^{3} + 8 q^{6} + 8 q^{12} + 8 q^{13} - 8 q^{16} - 16 q^{18} + 16 q^{22} - 40 q^{25} - 8 q^{27} + 32 q^{31} - 16 q^{33} - 8 q^{36} + 16 q^{37} - 48 q^{43} - 8 q^{46} + 8 q^{48} + 16 q^{51} - 8 q^{52} + 16 q^{57} + 64 q^{61} - 32 q^{66} + 16 q^{67} + 16 q^{72} - 8 q^{73} + 40 q^{75} - 16 q^{76} + 8 q^{78} + 56 q^{81} + 16 q^{82} - 40 q^{85} + 16 q^{88} - 32 q^{93} - 8 q^{96} - 16 q^{97} + O(q^{100}) \)

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
\(3\) −1.70711 + 0.292893i −0.985599 + 0.169102i
\(4\) 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 \(-0.859781\pi\)
0.904534 0.426401i \(-0.140219\pi\)
\(12\) 0.292893 + 1.70711i 0.0845510 + 0.492799i
\(13\) 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
\(15\) −0.654929 3.81721i −0.169102 0.985599i
\(16\) −1.00000 −0.250000
\(17\) −3.65028 + 3.65028i −0.885323 + 0.885323i −0.994070 0.108746i \(-0.965316\pi\)
0.108746 + 0.994070i \(0.465316\pi\)
\(18\) −1.29289 + 2.70711i −0.304738 + 0.638071i
\(19\) 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
\(27\) −4.53553 + 2.53553i −0.872864 + 0.487964i
\(28\) 0 0
\(29\) 4.47214 0.830455 0.415227 0.909718i \(-0.363702\pi\)
0.415227 + 0.909718i \(0.363702\pi\)
\(30\) 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
\(33\) 0.828427 + 4.82843i 0.144211 + 0.840521i
\(34\) 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 \(0.158481\pi\)
−0.878595 + 0.477567i \(0.841519\pi\)
\(42\) 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 \(-0.394396\pi\)
0.945469 0.325712i \(-0.105604\pi\)
\(48\) 1.70711 0.292893i 0.246400 0.0422755i
\(49\) 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 0.997131 0.0756888i \(-0.0241156\pi\)
−0.0756888 + 0.997131i \(0.524116\pi\)
\(54\) 1.41421 5.00000i 0.192450 0.680414i
\(55\) 6.32456 0.852803
\(56\) 0 0
\(57\) 1.51200 + 8.81256i 0.200269 + 1.16725i
\(58\) −3.16228 + 3.16228i −0.415227 + 0.415227i
\(59\) −9.89949 −1.28880 −0.644402 0.764687i \(-0.722894\pi\)
−0.644402 + 0.764687i \(0.722894\pi\)
\(60\) −3.81721 + 0.654929i −0.492799 + 0.0845510i
\(61\) 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 \(-0.941920\pi\)
0.983399 0.181454i \(-0.0580804\pi\)
\(72\) 2.70711 + 1.29289i 0.319036 + 0.152369i
\(73\) −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
\(75\) 8.53553 1.46447i 0.985599 0.169102i
\(76\) −5.16228 −0.592154
\(77\) 0 0
\(78\) −1.72407 10.0486i −0.195213 1.13778i
\(79\) 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 0.952051 0.305940i \(-0.0989707\pi\)
−0.305940 + 0.952051i \(0.598971\pi\)
\(84\) 0 0
\(85\) −8.16228 8.16228i −0.885323 0.885323i
\(86\) 4.01315i 0.432749i
\(87\) −7.63441 + 1.30986i −0.818495 + 0.140432i
\(88\) 2.00000 2.00000i 0.213201 0.213201i
\(89\) 0.458991 0.0486529 0.0243264 0.999704i \(-0.492256\pi\)
0.0243264 + 0.999704i \(0.492256\pi\)
\(90\) −6.05327 2.89100i −0.638071 0.304738i
\(91\) 0 0
\(92\) 0.707107 0.707107i 0.0737210 0.0737210i
\(93\) −17.6251 + 3.02399i −1.82764 + 0.313573i
\(94\) 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 \(-0.973940\pi\)
0.996651 0.0817776i \(-0.0260597\pi\)
\(102\) 1.51200 + 8.81256i 0.149710 + 0.872573i
\(103\) −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 \(-0.499556\pi\)
0.999999 0.00139356i \(-0.000443584\pi\)
\(108\) 2.53553 + 4.53553i 0.243982 + 0.436432i
\(109\) 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 \(-0.880935\pi\)
−0.365391 0.930854i \(-0.619065\pi\)
\(114\) −7.30056 5.16228i −0.683760 0.483492i
\(115\) −1.58114 + 1.58114i −0.147442 + 0.147442i
\(116\) 4.47214i 0.415227i
\(117\) 7.61042 15.9350i 0.703584 1.47319i
\(118\) 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
\(123\) −1.79129 10.4404i −0.161515 0.941379i
\(124\) 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 \(-0.893305\pi\)
0.944347 0.328952i \(-0.106695\pi\)
\(132\) 4.82843 0.828427i 0.420261 0.0721053i
\(133\) 0 0
\(134\) −7.30056 −0.630673
\(135\) −5.66963 10.1418i −0.487964 0.872864i
\(136\) −5.16228 −0.442662
\(137\) 3.65028 3.65028i 0.311865 0.311865i −0.533767 0.845632i \(-0.679224\pi\)
0.845632 + 0.533767i \(0.179224\pi\)
\(138\) 1.70711 0.292893i 0.145319 0.0249327i
\(139\) 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
\(147\) 2.05025 + 11.9497i 0.169102 + 0.985599i
\(148\) 5.16228 5.16228i 0.424337 0.424337i
\(149\) 19.0733 1.56254 0.781271 0.624192i \(-0.214572\pi\)
0.781271 + 0.624192i \(0.214572\pi\)
\(150\) −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
\(153\) −6.67427 + 13.9748i −0.539583 + 1.12980i
\(154\) 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
\(162\) −0.949747 + 8.94975i −0.0746192 + 0.703159i
\(163\) 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
\(165\) −10.7967 + 1.85242i −0.840521 + 0.144211i
\(166\) −8.32456 −0.646111
\(167\) −3.28742 + 3.28742i −0.254388 + 0.254388i −0.822767 0.568379i \(-0.807571\pi\)
0.568379 + 0.822767i \(0.307571\pi\)
\(168\) 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 0.715777 0.698329i \(-0.246073\pi\)
−0.698329 + 0.715777i \(0.746073\pi\)
\(174\) 4.47214 6.32456i 0.339032 0.479463i
\(175\) 0 0
\(176\) 2.82843i 0.213201i
\(177\) 16.8995 2.89949i 1.27024 0.217939i
\(178\) −0.324555 + 0.324555i −0.0243264 + 0.0243264i
\(179\) −4.70163 −0.351416 −0.175708 0.984442i \(-0.556222\pi\)
−0.175708 + 0.984442i \(0.556222\pi\)
\(180\) 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
\(183\) −13.6569 + 2.34315i −1.00954 + 0.173210i
\(184\) 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 \(0.00528600\pi\)
−0.999862 + 0.0166057i \(0.994714\pi\)
\(192\) −0.292893 1.70711i −0.0211377 0.123200i
\(193\) 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 −0.164035 0.986454i \(-0.552451\pi\)
0.986454 + 0.164035i \(0.0524511\pi\)
\(198\) 7.65685 + 3.65685i 0.544149 + 0.259881i
\(199\) 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
\(207\) 2.70711 + 1.29289i 0.188157 + 0.0898623i
\(208\) −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
\(213\) 0.895645 + 5.22020i 0.0613686 + 0.357682i
\(214\) 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
\(222\) 12.4628 2.13829i 0.836451 0.143512i
\(223\) 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 −0.552151 0.833744i \(-0.686193\pi\)
0.833744 + 0.552151i \(0.186193\pi\)
\(228\) 8.81256 1.51200i 0.583626 0.100134i
\(229\) 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 0.873125 0.487497i \(-0.162090\pi\)
−0.487497 + 0.873125i \(0.662090\pi\)
\(234\) 5.88635 + 16.6491i 0.384803 + 1.08839i
\(235\) 19.4868 + 19.4868i 1.27118 + 1.27118i
\(236\) 9.89949i 0.644402i
\(237\) 0.926210 + 5.39835i 0.0601638 + 0.350660i
\(238\) 0 0
\(239\) −6.34534 −0.410446 −0.205223 0.978715i \(-0.565792\pi\)
−0.205223 + 0.978715i \(0.565792\pi\)
\(240\) 0.654929 + 3.81721i 0.0422755 + 0.246400i
\(241\) 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
\(243\) −10.2929 + 11.7071i −0.660289 + 0.751011i
\(244\) 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 \(0.0571337\pi\)
−0.983935 + 0.178529i \(0.942866\pi\)
\(252\) 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 \(0.508925\pi\)
−0.999607 + 0.0280335i \(0.991075\pi\)
\(258\) 1.17542 + 6.85087i 0.0731786 + 0.426516i
\(259\) 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 \(-0.975216\pi\)
−0.0777819 0.996970i \(-0.524784\pi\)
\(264\) −2.82843 + 4.00000i −0.174078 + 0.246183i
\(265\) −15.0000 + 15.0000i −0.921443 + 0.921443i
\(266\) 0 0
\(267\) −0.783546 + 0.134435i −0.0479522 + 0.00822730i
\(268\) 5.16228 5.16228i 0.315336 0.315336i
\(269\) −18.6143 −1.13493 −0.567466 0.823397i \(-0.692076\pi\)
−0.567466 + 0.823397i \(0.692076\pi\)
\(270\) 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 \(-0.980023\pi\)
0.998031 0.0627183i \(-0.0199770\pi\)
\(282\) −3.60978 21.0393i −0.214959 1.25287i
\(283\) −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
\(285\) −19.7055 + 3.38093i −1.16725 + 0.200269i
\(286\) 16.6491 0.984483
\(287\) 0 0
\(288\) 1.29289 2.70711i 0.0761845 0.159518i
\(289\) 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 0.703200 0.710992i \(-0.251754\pi\)
−0.710992 + 0.703200i \(0.751754\pi\)
\(294\) −9.89949 7.00000i −0.577350 0.408248i
\(295\) 22.1359i 1.28880i
\(296\) 7.30056i 0.424337i
\(297\) 7.17157 + 12.8284i 0.416137 + 0.744381i
\(298\) −13.4868 + 13.4868i −0.781271 + 0.781271i
\(299\) 5.88635 0.340416
\(300\) −1.46447 8.53553i −0.0845510 0.492799i
\(301\) 0 0
\(302\) −1.64371 + 1.64371i −0.0945848 + 0.0945848i
\(303\) 0.481431 + 2.80599i 0.0276575 + 0.161200i
\(304\) 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 \(0.272008\pi\)
−0.656567 + 0.754268i \(0.727992\pi\)
\(312\) −10.0486 + 1.72407i −0.568891 + 0.0976063i
\(313\) −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 −0.630345 0.776315i \(-0.717086\pi\)
0.776315 + 0.630345i \(0.217086\pi\)
\(318\) 16.1950 2.77863i 0.908173 0.155818i
\(319\) 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
\(327\) −4.19557 24.4535i −0.232015 1.35228i
\(328\) −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
\(333\) 19.7634 + 9.43885i 1.08303 + 0.517246i
\(334\) 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
\(342\) 13.9748 + 6.67427i 0.755673 + 0.360903i
\(343\) 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 −0.681002 0.732281i \(-0.738456\pi\)
0.732281 + 0.681002i \(0.238456\pi\)
\(348\) 1.30986 + 7.63441i 0.0702158 + 0.409248i
\(349\) 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 0.0583971 0.998293i \(-0.481401\pi\)
−0.998293 + 0.0583971i \(0.981401\pi\)
\(354\) −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 \(-0.674991\pi\)
−0.522475 + 0.852654i \(0.674991\pi\)
\(360\) −2.89100 + 6.05327i −0.152369 + 0.319036i
\(361\) −7.64911 −0.402585
\(362\) −6.84157 + 6.84157i −0.359585 + 0.359585i
\(363\) −5.12132 + 0.878680i −0.268800 + 0.0461187i
\(364\) 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
\(372\) 3.02399 + 17.6251i 0.156787 + 0.913820i
\(373\) 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
\(375\) 3.27465 + 19.0860i 0.169102 + 0.985599i
\(376\) 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 0.510368 0.859956i \(-0.329509\pi\)
−0.859956 + 0.510368i \(0.829509\pi\)
\(384\) 1.41421 + 1.00000i 0.0721688 + 0.0510310i
\(385\) 0 0
\(386\) 4.24264i 0.215945i
\(387\) −5.18857 + 10.8640i −0.263750 + 0.552249i
\(388\) 1.16228 1.16228i 0.0590057 0.0590057i
\(389\) 12.4984 0.633695 0.316848 0.948476i \(-0.397376\pi\)
0.316848 + 0.948476i \(0.397376\pi\)
\(390\) 22.4694 3.85514i 1.13778 0.195213i
\(391\) −5.16228 −0.261068
\(392\) 4.94975 4.94975i 0.250000 0.250000i
\(393\) 2.20550 + 12.8546i 0.111253 + 0.648429i
\(394\) 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 \(0.164597\pi\)
−0.869259 + 0.494357i \(0.835403\pi\)
\(402\) 12.4628 2.13829i 0.621590 0.106648i
\(403\) 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
\(408\) 8.81256 1.51200i 0.436287 0.0748550i
\(409\) 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
\(417\) −0.680846 3.96826i −0.0333412 0.194327i
\(418\) 10.3246 10.3246i 0.504991 0.504991i
\(419\) −26.3738 −1.28845 −0.644223 0.764838i \(-0.722819\pi\)
−0.644223 + 0.764838i \(0.722819\pi\)
\(420\) 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
\(423\) 15.9343 33.3639i 0.774754 1.62221i
\(424\) 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 \(0.0470566\pi\)
−0.989093 + 0.147295i \(0.952943\pi\)
\(432\) 4.53553 2.53553i 0.218216 0.121991i
\(433\) 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
\(435\) −2.92893 17.0711i −0.140432 0.818495i
\(436\) 14.3246 0.686022
\(437\) 3.65028 3.65028i 0.174617 0.174617i
\(438\) 3.03393 + 17.6830i 0.144967 + 0.844928i
\(439\) 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 0.385272 0.922803i \(-0.374107\pi\)
−0.922803 + 0.385272i \(0.874107\pi\)
\(444\) −7.30056 + 10.3246i −0.346469 + 0.489982i
\(445\) 1.02633i 0.0486529i
\(446\) 18.6143i 0.881411i
\(447\) −32.5601 + 5.58643i −1.54004 + 0.264229i
\(448\) 0 0
\(449\) 5.65685 0.266963 0.133482 0.991051i \(-0.457384\pi\)
0.133482 + 0.991051i \(0.457384\pi\)
\(450\) 6.46447 13.5355i 0.304738 0.638071i
\(451\) 17.2982 0.814541
\(452\) −13.7793 + 13.7793i −0.648122 + 0.648122i
\(453\) −3.96826 + 0.680846i −0.186445 + 0.0319890i
\(454\) 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 \(-0.970209\pi\)
0.995623 0.0934554i \(-0.0297913\pi\)
\(462\) 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
\(465\) −6.76185 39.4110i −0.313573 1.82764i
\(466\) −8.32456 −0.385628
\(467\) 4.70163 4.70163i 0.217566 0.217566i −0.589906 0.807472i \(-0.700835\pi\)
0.807472 + 0.589906i \(0.200835\pi\)
\(468\) −15.9350 7.61042i −0.736595 0.351792i
\(469\) 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
\(477\) 25.6819 + 12.2655i 1.17589 + 0.561597i
\(478\) 4.48683 4.48683i 0.205223 0.205223i
\(479\) 28.2843 1.29234 0.646171 0.763193i \(-0.276369\pi\)
0.646171 + 0.763193i \(0.276369\pi\)
\(480\) −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 \(-0.928291\pi\)
0.974732 0.223379i \(-0.0717087\pi\)
\(492\) −10.4404 + 1.79129i −0.470690 + 0.0807576i
\(493\) −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
\(498\) 14.2109 2.43821i 0.636806 0.109259i
\(499\) 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 0.965236 0.261380i \(-0.0841776\pi\)
−0.261380 + 0.965236i \(0.584178\pi\)
\(504\) 0 0
\(505\) 3.67544 0.163555
\(506\) 2.82843i 0.125739i
\(507\) 6.34088 + 36.9573i 0.281608 + 1.64133i
\(508\) −5.16228 + 5.16228i −0.229039 + 0.229039i
\(509\) −27.0996 −1.20117 −0.600583 0.799562i \(-0.705065\pi\)
−0.600583 + 0.799562i \(0.705065\pi\)
\(510\) −19.7055 + 3.38093i −0.872573 + 0.149710i
\(511\) 0 0
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) 13.0891 + 23.4137i 0.577899 + 1.03374i
\(514\) 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 \(-0.933961\pi\)
0.978556 0.205982i \(-0.0660389\pi\)
\(522\) −5.78199 + 12.1065i −0.253071 + 0.529889i
\(523\) −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
\(528\) −0.828427 4.82843i −0.0360527 0.210130i
\(529\) 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
\(537\) 8.02619 1.37708i 0.346356 0.0594252i
\(538\) 13.1623 13.1623i 0.567466 0.567466i
\(539\) −19.7990 −0.852803
\(540\) −10.1418 + 5.66963i −0.436432 + 0.243982i
\(541\) 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
\(543\) −16.5170 + 2.83387i −0.708813 + 0.121613i
\(544\) 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
\(552\) −0.292893 1.70711i −0.0124664 0.0726593i
\(553\) 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 −0.0642767 0.997932i \(-0.520474\pi\)
0.997932 + 0.0642767i \(0.0204740\pi\)
\(558\) −13.3485 + 27.9497i −0.565089 + 1.18320i
\(559\) 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 0.639727 0.768603i \(-0.279048\pi\)
−0.768603 + 0.639727i \(0.779048\pi\)
\(564\) 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 \(-0.507905\pi\)
−0.0248330 + 0.999692i \(0.507905\pi\)
\(570\) 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
\(573\) −0.134435 0.783546i −0.00561611 0.0327331i
\(574\) 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
\(582\) 2.80599 0.481431i 0.116312 0.0199560i
\(583\) 18.9737 18.9737i 0.785809 0.785809i
\(584\) −10.3585 −0.428637
\(585\) 35.6317 + 17.0174i 1.47319 + 0.703584i
\(586\) 0.188612 0.00779148
\(587\) −7.07107 + 7.07107i −0.291854 + 0.291854i −0.837812 0.545958i \(-0.816166\pi\)
0.545958 + 0.837812i \(0.316166\pi\)
\(588\) 11.9497 2.05025i 0.492799 0.0845510i
\(589\) 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 0.523782 0.851853i \(-0.324521\pi\)
−0.851853 + 0.523782i \(0.824521\pi\)
\(594\) −14.1421 4.00000i −0.580259 0.164122i
\(595\) 0 0
\(596\) 19.0733i 0.781271i
\(597\) 2.58851 + 15.0869i 0.105941 + 0.617467i
\(598\) −4.16228 + 4.16228i −0.170208 + 0.170208i
\(599\) 8.25579 0.337322 0.168661 0.985674i \(-0.446056\pi\)
0.168661 + 0.985674i \(0.446056\pi\)
\(600\) 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
\(603\) 19.7634 + 9.43885i 0.804828 + 0.384380i
\(604\) 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
\(612\) 13.9748 + 6.67427i 0.564899 + 0.269792i
\(613\) −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
\(615\) 23.3454 4.00545i 0.941379 0.161515i
\(616\) 0 0
\(617\) −7.66343 + 7.66343i −0.308518 + 0.308518i −0.844334 0.535817i \(-0.820004\pi\)
0.535817 + 0.844334i \(0.320004\pi\)
\(618\) 4.62357 + 26.9481i 0.185987 + 1.08401i
\(619\) 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
\(627\) 24.9257 4.27657i 0.995436 0.170790i
\(628\) −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
\(633\) −24.4535 + 4.19557i −0.971941 + 0.166759i
\(634\) 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 \(0.0687691\pi\)
−0.976753 + 0.214368i \(0.931231\pi\)
\(642\) −4.29063 25.0076i −0.169337 0.986971i
\(643\) −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 −0.977993 0.208637i \(-0.933097\pi\)
0.208637 + 0.977993i \(0.433097\pi\)
\(648\) 8.94975 + 0.949747i 0.351579 + 0.0373096i
\(649\) 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 0.271411 0.962463i \(-0.412510\pi\)
−0.962463 + 0.271411i \(0.912510\pi\)
\(654\) 20.2580 + 14.3246i 0.792150 + 0.560134i
\(655\) 16.8377 0.657904
\(656\) 6.11584i 0.238784i
\(657\) −13.3924 + 28.0415i −0.522488 + 1.09400i
\(658\) 0 0
\(659\) 8.94427 0.348419 0.174210 0.984709i \(-0.444263\pi\)
0.174210 + 0.984709i \(0.444263\pi\)
\(660\) 1.85242 + 10.7967i 0.0721053 + 0.420261i
\(661\) −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
\(663\) −8.90014 51.8738i −0.345653 2.01461i
\(664\) 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
\(675\) 22.6777 12.6777i 0.872864 0.487964i
\(676\) −21.6491 −0.832658
\(677\) 25.7815 25.7815i 0.990862 0.990862i −0.00909639 0.999959i \(-0.502896\pi\)
0.999959 + 0.00909639i \(0.00289551\pi\)
\(678\) −33.2661 + 5.70756i −1.27758 + 0.219198i
\(679\) 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 \(-0.932086\pi\)
−0.211744 0.977325i \(-0.567914\pi\)
\(684\) −14.6011 + 5.16228i −0.558288 + 0.197385i
\(685\) 8.16228 + 8.16228i 0.311865 + 0.311865i
\(686\) 0 0
\(687\) −7.40968 43.1868i −0.282697 1.64768i
\(688\) 2.83772 2.83772i 0.108187 0.108187i
\(689\) 55.8428 2.12744
\(690\) 0.654929 + 3.81721i 0.0249327 + 0.145319i
\(691\) −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 \(0.162782\pi\)
−0.872062 + 0.489395i \(0.837218\pi\)
\(702\) −14.9250 26.6977i −0.563309 1.00764i
\(703\) 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
\(708\) −2.89949 16.8995i −0.108970 0.635122i
\(709\) 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
\(717\) 10.8322 1.85851i 0.404535 0.0694072i
\(718\) 14.0000 14.0000i 0.522475 0.522475i
\(719\) 30.3497 1.13185 0.565927 0.824455i \(-0.308518\pi\)
0.565927 + 0.824455i \(0.308518\pi\)
\(720\) −2.23607 6.32456i −0.0833333 0.235702i
\(721\) 0 0
\(722\) 5.40874 5.40874i 0.201292 0.201292i
\(723\) −14.2109 + 2.43821i −0.528509 + 0.0906778i
\(724\) 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
\(732\) 2.34315 + 13.6569i 0.0866052 + 0.504772i
\(733\) −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
\(735\) −26.7204 + 4.58450i −0.985599 + 0.169102i
\(736\) 1.00000 0.0368605
\(737\) 14.6011 14.6011i 0.537839 0.537839i
\(738\) −16.5562 7.90713i −0.609444 0.291066i
\(739\) 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 0.939236 0.343271i \(-0.111535\pi\)
−0.343271 + 0.939236i \(0.611535\pi\)
\(744\) −14.6011 10.3246i −0.535303 0.378517i
\(745\) 42.6491i 1.56254i
\(746\) 19.0733i 0.698322i
\(747\) 22.5355 + 10.7628i 0.824529 + 0.393789i
\(748\) 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
\(753\) −1.65685 9.65685i −0.0603791 0.351915i
\(754\) 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 \(0.125390\pi\)
−0.923410 + 0.383814i \(0.874610\pi\)
\(762\) −12.4628 + 2.13829i −0.451481 + 0.0774619i
\(763\) 0 0
\(764\) 0.458991 0.0166057
\(765\) −31.2487 14.9241i −1.12980 0.539583i
\(766\) 9.67544 0.349588
\(767\) −41.2044 + 41.2044i −1.48781 + 1.48781i
\(768\) −1.70711 + 0.292893i −0.0615999 + 0.0105689i
\(769\) 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 0.316798 0.948493i \(-0.397392\pi\)
−0.948493 + 0.316798i \(0.897392\pi\)
\(774\) −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