Properties

Label 690.2.i.d.47.1
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 47.1
Root \(1.14412 + 1.14412i\) of defining polynomial
Character \(\chi\) \(=\) 690.47
Dual form 690.2.i.d.323.2

$q$-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} +(-2.16228 + 2.16228i) q^{13} +(0.654929 + 3.81721i) q^{15} -1.00000 q^{16} +(0.821854 - 0.821854i) q^{17} +(-1.29289 + 2.70711i) q^{18} +1.16228i 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} -3.05792i q^{26} +(-4.53553 + 2.53553i) q^{27} -4.47214 q^{29} +(-3.16228 - 2.23607i) q^{30} -2.32456 q^{31} +(0.707107 - 0.707107i) q^{32} +(0.828427 + 4.82843i) q^{33} +1.16228i q^{34} +(-1.00000 - 2.82843i) q^{36} +(-1.16228 - 1.16228i) q^{37} +(-0.821854 - 0.821854i) q^{38} +(3.05792 - 4.32456i) q^{39} +(1.58114 - 1.58114i) q^{40} -11.7727i q^{41} +(-9.16228 + 9.16228i) q^{43} -2.82843 q^{44} +(-2.23607 - 6.32456i) q^{45} -1.00000 q^{46} +(-0.229495 + 0.229495i) q^{47} +(1.70711 - 0.292893i) q^{48} -7.00000i q^{49} +(3.53553 - 3.53553i) q^{50} +(-1.16228 + 1.64371i) q^{51} +(2.16228 + 2.16228i) q^{52} +(-6.70820 - 6.70820i) q^{53} +(1.41421 - 5.00000i) q^{54} -6.32456 q^{55} +(-0.340423 - 1.98413i) q^{57} +(3.16228 - 3.16228i) q^{58} -9.89949 q^{59} +(3.81721 - 0.654929i) q^{60} +8.00000 q^{61} +(1.64371 - 1.64371i) q^{62} +1.00000i q^{64} +(4.83500 + 4.83500i) q^{65} +(-4.00000 - 2.82843i) q^{66} +(-1.16228 - 1.16228i) q^{67} +(-0.821854 - 0.821854i) q^{68} +(-1.41421 - 1.00000i) q^{69} +5.88635i q^{71} +(2.70711 + 1.29289i) q^{72} +(5.32456 - 5.32456i) q^{73} +1.64371 q^{74} +(8.53553 - 1.46447i) q^{75} +1.16228 q^{76} +(0.895645 + 5.22020i) q^{78} +3.16228i q^{79} +2.23607i q^{80} +(7.00000 - 5.65685i) q^{81} +(8.32456 + 8.32456i) q^{82} +(-3.05792 - 3.05792i) q^{83} +(-1.83772 - 1.83772i) q^{85} -12.9574i q^{86} +(7.63441 - 1.30986i) q^{87} +(2.00000 - 2.00000i) q^{88} -17.4296 q^{89} +(6.05327 + 2.89100i) q^{90} +(0.707107 - 0.707107i) q^{92} +(3.96826 - 0.680846i) q^{93} -0.324555i q^{94} +2.59893 q^{95} +(-1.00000 + 1.41421i) q^{96} +(-5.16228 - 5.16228i) 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
\(3\) −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
\(13\) −2.16228 + 2.16228i −0.599708 + 0.599708i −0.940235 0.340527i \(-0.889395\pi\)
0.340527 + 0.940235i \(0.389395\pi\)
\(14\) 0 0
\(15\) 0.654929 + 3.81721i 0.169102 + 0.985599i
\(16\) −1.00000 −0.250000
\(17\) 0.821854 0.821854i 0.199329 0.199329i −0.600383 0.799712i \(-0.704985\pi\)
0.799712 + 0.600383i \(0.204985\pi\)
\(18\) −1.29289 + 2.70711i −0.304738 + 0.638071i
\(19\) 1.16228i 0.266645i 0.991073 + 0.133322i \(0.0425646\pi\)
−0.991073 + 0.133322i \(0.957435\pi\)
\(20\) −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
\(26\) 3.05792i 0.599708i
\(27\) −4.53553 + 2.53553i −0.872864 + 0.487964i
\(28\) 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
\(31\) −2.32456 −0.417502 −0.208751 0.977969i \(-0.566940\pi\)
−0.208751 + 0.977969i \(0.566940\pi\)
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) 0.828427 + 4.82843i 0.144211 + 0.840521i
\(34\) 1.16228i 0.199329i
\(35\) 0 0
\(36\) −1.00000 2.82843i −0.166667 0.471405i
\(37\) −1.16228 1.16228i −0.191077 0.191077i 0.605084 0.796161i \(-0.293139\pi\)
−0.796161 + 0.605084i \(0.793139\pi\)
\(38\) −0.821854 0.821854i −0.133322 0.133322i
\(39\) 3.05792 4.32456i 0.489659 0.692483i
\(40\) 1.58114 1.58114i 0.250000 0.250000i
\(41\) 11.7727i 1.83859i −0.393573 0.919293i \(-0.628761\pi\)
0.393573 0.919293i \(-0.371239\pi\)
\(42\) 0 0
\(43\) −9.16228 + 9.16228i −1.39723 + 1.39723i −0.589374 + 0.807861i \(0.700625\pi\)
−0.807861 + 0.589374i \(0.799375\pi\)
\(44\) −2.82843 −0.426401
\(45\) −2.23607 6.32456i −0.333333 0.942809i
\(46\) −1.00000 −0.147442
\(47\) −0.229495 + 0.229495i −0.0334753 + 0.0334753i −0.723646 0.690171i \(-0.757535\pi\)
0.690171 + 0.723646i \(0.257535\pi\)
\(48\) 1.70711 0.292893i 0.246400 0.0422755i
\(49\) 7.00000i 1.00000i
\(50\) 3.53553 3.53553i 0.500000 0.500000i
\(51\) −1.16228 + 1.64371i −0.162751 + 0.230165i
\(52\) 2.16228 + 2.16228i 0.299854 + 0.299854i
\(53\) −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
\(57\) −0.340423 1.98413i −0.0450902 0.262805i
\(58\) 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 \(0.328850\pi\)
\(62\) 1.64371 1.64371i 0.208751 0.208751i
\(63\) 0 0
\(64\) 1.00000i 0.125000i
\(65\) 4.83500 + 4.83500i 0.599708 + 0.599708i
\(66\) −4.00000 2.82843i −0.492366 0.348155i
\(67\) −1.16228 1.16228i −0.141995 0.141995i 0.632536 0.774531i \(-0.282014\pi\)
−0.774531 + 0.632536i \(0.782014\pi\)
\(68\) −0.821854 0.821854i −0.0996645 0.0996645i
\(69\) −1.41421 1.00000i −0.170251 0.120386i
\(70\) 0 0
\(71\) 5.88635i 0.698581i 0.937014 + 0.349291i \(0.113577\pi\)
−0.937014 + 0.349291i \(0.886423\pi\)
\(72\) 2.70711 + 1.29289i 0.319036 + 0.152369i
\(73\) 5.32456 5.32456i 0.623192 0.623192i −0.323154 0.946346i \(-0.604743\pi\)
0.946346 + 0.323154i \(0.104743\pi\)
\(74\) 1.64371 0.191077
\(75\) 8.53553 1.46447i 0.985599 0.169102i
\(76\) 1.16228 0.133322
\(77\) 0 0
\(78\) 0.895645 + 5.22020i 0.101412 + 0.591071i
\(79\) 3.16228i 0.355784i 0.984050 + 0.177892i \(0.0569278\pi\)
−0.984050 + 0.177892i \(0.943072\pi\)
\(80\) 2.23607i 0.250000i
\(81\) 7.00000 5.65685i 0.777778 0.628539i
\(82\) 8.32456 + 8.32456i 0.919293 + 0.919293i
\(83\) −3.05792 3.05792i −0.335651 0.335651i 0.519077 0.854728i \(-0.326276\pi\)
−0.854728 + 0.519077i \(0.826276\pi\)
\(84\) 0 0
\(85\) −1.83772 1.83772i −0.199329 0.199329i
\(86\) 12.9574i 1.39723i
\(87\) 7.63441 1.30986i 0.818495 0.140432i
\(88\) 2.00000 2.00000i 0.213201 0.213201i
\(89\) −17.4296 −1.84753 −0.923764 0.382961i \(-0.874904\pi\)
−0.923764 + 0.382961i \(0.874904\pi\)
\(90\) 6.05327 + 2.89100i 0.638071 + 0.304738i
\(91\) 0 0
\(92\) 0.707107 0.707107i 0.0737210 0.0737210i
\(93\) 3.96826 0.680846i 0.411490 0.0706005i
\(94\) 0.324555i 0.0334753i
\(95\) 2.59893 0.266645
\(96\) −1.00000 + 1.41421i −0.102062 + 0.144338i
\(97\) −5.16228 5.16228i −0.524150 0.524150i 0.394672 0.918822i \(-0.370858\pi\)
−0.918822 + 0.394672i \(0.870858\pi\)
\(98\) 4.94975 + 4.94975i 0.500000 + 0.500000i
\(99\) −2.82843 8.00000i −0.284268 0.804030i
\(100\) 5.00000i 0.500000i
\(101\) 7.30056i 0.726433i 0.931705 + 0.363217i \(0.118321\pi\)
−0.931705 + 0.363217i \(0.881679\pi\)
\(102\) −0.340423 1.98413i −0.0337069 0.196458i
\(103\) −4.83772 + 4.83772i −0.476675 + 0.476675i −0.904067 0.427392i \(-0.859433\pi\)
0.427392 + 0.904067i \(0.359433\pi\)
\(104\) −3.05792 −0.299854
\(105\) 0 0
\(106\) 9.48683 0.921443
\(107\) −7.53006 + 7.53006i −0.727958 + 0.727958i −0.970213 0.242255i \(-0.922113\pi\)
0.242255 + 0.970213i \(0.422113\pi\)
\(108\) 2.53553 + 4.53553i 0.243982 + 0.436432i
\(109\) 1.67544i 0.160478i 0.996776 + 0.0802392i \(0.0255684\pi\)
−0.996776 + 0.0802392i \(0.974432\pi\)
\(110\) 4.47214 4.47214i 0.426401 0.426401i
\(111\) 2.32456 + 1.64371i 0.220637 + 0.156014i
\(112\) 0 0
\(113\) −0.362864 0.362864i −0.0341354 0.0341354i 0.689833 0.723968i \(-0.257684\pi\)
−0.723968 + 0.689833i \(0.757684\pi\)
\(114\) 1.64371 + 1.16228i 0.153947 + 0.108857i
\(115\) 1.58114 1.58114i 0.147442 0.147442i
\(116\) 4.47214i 0.415227i
\(117\) −3.95357 + 8.27812i −0.365507 + 0.765313i
\(118\) 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
\(123\) 3.44814 + 20.0973i 0.310909 + 1.81211i
\(124\) 2.32456i 0.208751i
\(125\) 11.1803i 1.00000i
\(126\) 0 0
\(127\) 1.16228 + 1.16228i 0.103135 + 0.103135i 0.756792 0.653656i \(-0.226766\pi\)
−0.653656 + 0.756792i \(0.726766\pi\)
\(128\) −0.707107 0.707107i −0.0625000 0.0625000i
\(129\) 12.9574 18.3246i 1.14084 1.61339i
\(130\) −6.83772 −0.599708
\(131\) 10.3585i 0.905025i 0.891758 + 0.452513i \(0.149472\pi\)
−0.891758 + 0.452513i \(0.850528\pi\)
\(132\) 4.82843 0.828427i 0.420261 0.0721053i
\(133\) 0 0
\(134\) 1.64371 0.141995
\(135\) 5.66963 + 10.1418i 0.487964 + 0.872864i
\(136\) 1.16228 0.0996645
\(137\) −0.821854 + 0.821854i −0.0702158 + 0.0702158i −0.741343 0.671127i \(-0.765811\pi\)
0.671127 + 0.741343i \(0.265811\pi\)
\(138\) 1.70711 0.292893i 0.145319 0.0249327i
\(139\) 10.3246i 0.875717i −0.899044 0.437859i \(-0.855737\pi\)
0.899044 0.437859i \(-0.144263\pi\)
\(140\) 0 0
\(141\) 0.324555 0.458991i 0.0273325 0.0386540i
\(142\) −4.16228 4.16228i −0.349291 0.349291i
\(143\) 6.11584 + 6.11584i 0.511433 + 0.511433i
\(144\) −2.82843 + 1.00000i −0.235702 + 0.0833333i
\(145\) 10.0000i 0.830455i
\(146\) 7.53006i 0.623192i
\(147\) 2.05025 + 11.9497i 0.169102 + 0.985599i
\(148\) −1.16228 + 1.16228i −0.0955386 + 0.0955386i
\(149\) −7.75955 −0.635687 −0.317844 0.948143i \(-0.602959\pi\)
−0.317844 + 0.948143i \(0.602959\pi\)
\(150\) −5.00000 + 7.07107i −0.408248 + 0.577350i
\(151\) −10.3246 −0.840200 −0.420100 0.907478i \(-0.638005\pi\)
−0.420100 + 0.907478i \(0.638005\pi\)
\(152\) −0.821854 + 0.821854i −0.0666612 + 0.0666612i
\(153\) 1.50270 3.14641i 0.121486 0.254372i
\(154\) 0 0
\(155\) 5.19786i 0.417502i
\(156\) −4.32456 3.05792i −0.346242 0.244830i
\(157\) 9.48683 + 9.48683i 0.757132 + 0.757132i 0.975799 0.218668i \(-0.0701711\pi\)
−0.218668 + 0.975799i \(0.570171\pi\)
\(158\) −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
\(163\) −8.64911 + 8.64911i −0.677451 + 0.677451i −0.959423 0.281972i \(-0.909011\pi\)
0.281972 + 0.959423i \(0.409011\pi\)
\(164\) −11.7727 −0.919293
\(165\) 10.7967 1.85242i 0.840521 0.144211i
\(166\) 4.32456 0.335651
\(167\) 14.6011 14.6011i 1.12987 1.12987i 0.139671 0.990198i \(-0.455395\pi\)
0.990198 0.139671i \(-0.0446045\pi\)
\(168\) 0 0
\(169\) 3.64911i 0.280701i
\(170\) 2.59893 0.199329
\(171\) 1.16228 + 3.28742i 0.0888816 + 0.251395i
\(172\) 9.16228 + 9.16228i 0.698617 + 0.698617i
\(173\) −8.71478 8.71478i −0.662572 0.662572i 0.293413 0.955986i \(-0.405209\pi\)
−0.955986 + 0.293413i \(0.905209\pi\)
\(174\) −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
\(178\) 12.3246 12.3246i 0.923764 0.923764i
\(179\) 13.1869 0.985636 0.492818 0.870132i \(-0.335967\pi\)
0.492818 + 0.870132i \(0.335967\pi\)
\(180\) −6.32456 + 2.23607i −0.471405 + 0.166667i
\(181\) 22.3246 1.65937 0.829686 0.558231i \(-0.188520\pi\)
0.829686 + 0.558231i \(0.188520\pi\)
\(182\) 0 0
\(183\) −13.6569 + 2.34315i −1.00954 + 0.173210i
\(184\) 1.00000i 0.0737210i
\(185\) −2.59893 + 2.59893i −0.191077 + 0.191077i
\(186\) −2.32456 + 3.28742i −0.170445 + 0.241045i
\(187\) −2.32456 2.32456i −0.169988 0.169988i
\(188\) 0.229495 + 0.229495i 0.0167377 + 0.0167377i
\(189\) 0 0
\(190\) −1.83772 + 1.83772i −0.133322 + 0.133322i
\(191\) 17.4296i 1.26116i −0.776125 0.630579i \(-0.782817\pi\)
0.776125 0.630579i \(-0.217183\pi\)
\(192\) −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 \(0.201204\pi\)
\(194\) 7.30056 0.524150
\(195\) −9.67000 6.83772i −0.692483 0.489659i
\(196\) −7.00000 −0.500000
\(197\) 2.59893 2.59893i 0.185166 0.185166i −0.608436 0.793603i \(-0.708203\pi\)
0.793603 + 0.608436i \(0.208203\pi\)
\(198\) 7.65685 + 3.65685i 0.544149 + 0.259881i
\(199\) 15.1623i 1.07483i −0.843319 0.537413i \(-0.819402\pi\)
0.843319 0.537413i \(-0.180598\pi\)
\(200\) −3.53553 3.53553i −0.250000 0.250000i
\(201\) 2.32456 + 1.64371i 0.163961 + 0.115938i
\(202\) −5.16228 5.16228i −0.363217 0.363217i
\(203\) 0 0
\(204\) 1.64371 + 1.16228i 0.115083 + 0.0813757i
\(205\) −26.3246 −1.83859
\(206\) 6.84157i 0.476675i
\(207\) 2.70711 + 1.29289i 0.188157 + 0.0898623i
\(208\) 2.16228 2.16228i 0.149927 0.149927i
\(209\) 3.28742 0.227395
\(210\) 0 0
\(211\) 1.67544 0.115342 0.0576712 0.998336i \(-0.481633\pi\)
0.0576712 + 0.998336i \(0.481633\pi\)
\(212\) −6.70820 + 6.70820i −0.460721 + 0.460721i
\(213\) −1.72407 10.0486i −0.118131 0.688521i
\(214\) 10.6491i 0.727958i
\(215\) 20.4875 + 20.4875i 1.39723 + 1.39723i
\(216\) −5.00000 1.41421i −0.340207 0.0962250i
\(217\) 0 0
\(218\) −1.18472 1.18472i −0.0802392 0.0802392i
\(219\) −7.53006 + 10.6491i −0.508834 + 0.719600i
\(220\) 6.32456i 0.426401i
\(221\) 3.55415i 0.239078i
\(222\) −2.80599 + 0.481431i −0.188325 + 0.0323115i
\(223\) 6.83772 6.83772i 0.457888 0.457888i −0.440074 0.897962i \(-0.645048\pi\)
0.897962 + 0.440074i \(0.145048\pi\)
\(224\) 0 0
\(225\) −14.1421 + 5.00000i −0.942809 + 0.333333i
\(226\) 0.513167 0.0341354
\(227\) 4.24264 4.24264i 0.281594 0.281594i −0.552151 0.833744i \(-0.686193\pi\)
0.833744 + 0.552151i \(0.186193\pi\)
\(228\) −1.98413 + 0.340423i −0.131402 + 0.0225451i
\(229\) 25.2982i 1.67175i −0.548917 0.835877i \(-0.684960\pi\)
0.548917 0.835877i \(-0.315040\pi\)
\(230\) 2.23607i 0.147442i
\(231\) 0 0
\(232\) −3.16228 3.16228i −0.207614 0.207614i
\(233\) −3.05792 3.05792i −0.200331 0.200331i 0.599811 0.800142i \(-0.295243\pi\)
−0.800142 + 0.599811i \(0.795243\pi\)
\(234\) −3.05792 8.64911i −0.199903 0.565410i
\(235\) 0.513167 + 0.513167i 0.0334753 + 0.0334753i
\(236\) 9.89949i 0.644402i
\(237\) −0.926210 5.39835i −0.0601638 0.350660i
\(238\) 0 0
\(239\) 20.4875 1.32522 0.662612 0.748963i \(-0.269448\pi\)
0.662612 + 0.748963i \(0.269448\pi\)
\(240\) −0.654929 3.81721i −0.0422755 0.246400i
\(241\) −4.32456 −0.278569 −0.139285 0.990252i \(-0.544480\pi\)
−0.139285 + 0.990252i \(0.544480\pi\)
\(242\) −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
\(246\) −16.6491 11.7727i −1.06151 0.750600i
\(247\) −2.51317 2.51317i −0.159909 0.159909i
\(248\) −1.64371 1.64371i −0.104376 0.104376i
\(249\) 6.11584 + 4.32456i 0.387576 + 0.274058i
\(250\) −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
\(254\) −1.64371 −0.103135
\(255\) 3.67544 + 2.59893i 0.230165 + 0.162751i
\(256\) 1.00000 0.0625000
\(257\) 19.3028 19.3028i 1.20407 1.20407i 0.231156 0.972917i \(-0.425749\pi\)
0.972917 0.231156i \(-0.0742509\pi\)
\(258\) 3.79514 + 22.1197i 0.236275 + 1.37711i
\(259\) 0 0
\(260\) 4.83500 4.83500i 0.299854 0.299854i
\(261\) −12.6491 + 4.47214i −0.782960 + 0.276818i
\(262\) −7.32456 7.32456i −0.452513 0.452513i
\(263\) 0.458991 + 0.458991i 0.0283026 + 0.0283026i 0.721116 0.692814i \(-0.243629\pi\)
−0.692814 + 0.721116i \(0.743629\pi\)
\(264\) −2.82843 + 4.00000i −0.174078 + 0.246183i
\(265\) −15.0000 + 15.0000i −0.921443 + 0.921443i
\(266\) 0 0
\(267\) 29.7541 5.10500i 1.82092 0.312421i
\(268\) −1.16228 + 1.16228i −0.0709974 + 0.0709974i
\(269\) −9.67000 −0.589590 −0.294795 0.955560i \(-0.595251\pi\)
−0.294795 + 0.955560i \(0.595251\pi\)
\(270\) −11.1803 3.16228i −0.680414 0.192450i
\(271\) 30.9737 1.88152 0.940758 0.339078i \(-0.110115\pi\)
0.940758 + 0.339078i \(0.110115\pi\)
\(272\) −0.821854 + 0.821854i −0.0498322 + 0.0498322i
\(273\) 0 0
\(274\) 1.16228i 0.0702158i
\(275\) 14.1421i 0.852803i
\(276\) −1.00000 + 1.41421i −0.0601929 + 0.0851257i
\(277\) −2.16228 2.16228i −0.129919 0.129919i 0.639157 0.769076i \(-0.279283\pi\)
−0.769076 + 0.639157i \(0.779283\pi\)
\(278\) 7.30056 + 7.30056i 0.437859 + 0.437859i
\(279\) −6.57484 + 2.32456i −0.393625 + 0.139167i
\(280\) 0 0
\(281\) 24.7301i 1.47528i 0.675197 + 0.737638i \(0.264059\pi\)
−0.675197 + 0.737638i \(0.735941\pi\)
\(282\) 0.0950601 + 0.554051i 0.00566074 + 0.0329932i
\(283\) 8.64911 8.64911i 0.514136 0.514136i −0.401655 0.915791i \(-0.631565\pi\)
0.915791 + 0.401655i \(0.131565\pi\)
\(284\) 5.88635 0.349291
\(285\) −4.43665 + 0.761210i −0.262805 + 0.0450902i
\(286\) −8.64911 −0.511433
\(287\) 0 0
\(288\) 1.29289 2.70711i 0.0761845 0.159518i
\(289\) 15.6491i 0.920536i
\(290\) −7.07107 7.07107i −0.415227 0.415227i
\(291\) 10.3246 + 7.30056i 0.605236 + 0.427967i
\(292\) −5.32456 5.32456i −0.311596 0.311596i
\(293\) −22.4940 22.4940i −1.31412 1.31412i −0.918352 0.395764i \(-0.870480\pi\)
−0.395764 0.918352i \(-0.629520\pi\)
\(294\) −9.89949 7.00000i −0.577350 0.408248i
\(295\) 22.1359i 1.28880i
\(296\) 1.64371i 0.0955386i
\(297\) 7.17157 + 12.8284i 0.416137 + 0.744381i
\(298\) 5.48683 5.48683i 0.317844 0.317844i
\(299\) −3.05792 −0.176844
\(300\) −1.46447 8.53553i −0.0845510 0.492799i
\(301\) 0 0
\(302\) 7.30056 7.30056i 0.420100 0.420100i
\(303\) −2.13829 12.4628i −0.122841 0.715971i
\(304\) 1.16228i 0.0666612i
\(305\) 17.8885i 1.02430i
\(306\) 1.16228 + 3.28742i 0.0664430 + 0.187929i
\(307\) −10.3246 10.3246i −0.589253 0.589253i 0.348176 0.937429i \(-0.386801\pi\)
−0.937429 + 0.348176i \(0.886801\pi\)
\(308\) 0 0
\(309\) 6.84157 9.67544i 0.389203 0.550417i
\(310\) −3.67544 3.67544i −0.208751 0.208751i
\(311\) 18.1180i 1.02738i −0.857976 0.513690i \(-0.828278\pi\)
0.857976 0.513690i \(-0.171722\pi\)
\(312\) 5.22020 0.895645i 0.295536 0.0507059i
\(313\) −2.83772 + 2.83772i −0.160398 + 0.160398i −0.782743 0.622345i \(-0.786180\pi\)
0.622345 + 0.782743i \(0.286180\pi\)
\(314\) −13.4164 −0.757132
\(315\) 0 0
\(316\) 3.16228 0.177892
\(317\) 11.5432 11.5432i 0.648331 0.648331i −0.304259 0.952589i \(-0.598409\pi\)
0.952589 + 0.304259i \(0.0984087\pi\)
\(318\) −16.1950 + 2.77863i −0.908173 + 0.155818i
\(319\) 12.6491i 0.708214i
\(320\) 2.23607 0.125000
\(321\) 10.6491 15.0601i 0.594375 0.840574i
\(322\) 0 0
\(323\) 0.955223 + 0.955223i 0.0531500 + 0.0531500i
\(324\) −5.65685 7.00000i −0.314270 0.388889i
\(325\) 10.8114 10.8114i 0.599708 0.599708i
\(326\) 12.2317i 0.677451i
\(327\) −0.490726 2.86016i −0.0271372 0.158167i
\(328\) 8.32456 8.32456i 0.459647 0.459647i
\(329\) 0 0
\(330\) −6.32456 + 8.94427i −0.348155 + 0.492366i
\(331\) −34.9737 −1.92233 −0.961163 0.275980i \(-0.910998\pi\)
−0.961163 + 0.275980i \(0.910998\pi\)
\(332\) −3.05792 + 3.05792i −0.167825 + 0.167825i
\(333\) −4.44970 2.12514i −0.243842 0.116457i
\(334\) 20.6491i 1.12987i
\(335\) −2.59893 + 2.59893i −0.141995 + 0.141995i
\(336\) 0 0
\(337\) 9.48683 + 9.48683i 0.516781 + 0.516781i 0.916596 0.399815i \(-0.130926\pi\)
−0.399815 + 0.916596i \(0.630926\pi\)
\(338\) −2.58031 2.58031i −0.140350 0.140350i
\(339\) 0.725728 + 0.513167i 0.0394161 + 0.0278714i
\(340\) −1.83772 + 1.83772i −0.0996645 + 0.0996645i
\(341\) 6.57484i 0.356047i
\(342\) −3.14641 1.50270i −0.170138 0.0812568i
\(343\) 0 0
\(344\) −12.9574 −0.698617
\(345\) −2.23607 + 3.16228i −0.120386 + 0.170251i
\(346\) 12.3246 0.662572
\(347\) 18.8438 18.8438i 1.01159 1.01159i 0.0116543 0.999932i \(-0.496290\pi\)
0.999932 0.0116543i \(-0.00370977\pi\)
\(348\) −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
\(351\) 4.32456 15.2896i 0.230828 0.816099i
\(352\) −2.00000 2.00000i −0.106600 0.106600i
\(353\) 9.17377 + 9.17377i 0.488270 + 0.488270i 0.907760 0.419490i \(-0.137791\pi\)
−0.419490 + 0.907760i \(0.637791\pi\)
\(354\) −9.89949 + 14.0000i −0.526152 + 0.744092i
\(355\) 13.1623 0.698581
\(356\) 17.4296i 0.923764i
\(357\) 0 0
\(358\) −9.32456 + 9.32456i −0.492818 + 0.492818i
\(359\) −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
\(361\) 17.6491 0.928901
\(362\) −15.7858 + 15.7858i −0.829686 + 0.829686i
\(363\) −5.12132 + 0.878680i −0.268800 + 0.0461187i
\(364\) 0 0
\(365\) −11.9061 11.9061i −0.623192 0.623192i
\(366\) 8.00000 11.3137i 0.418167 0.591377i
\(367\) −17.4868 17.4868i −0.912805 0.912805i 0.0836869 0.996492i \(-0.473330\pi\)
−0.996492 + 0.0836869i \(0.973330\pi\)
\(368\) −0.707107 0.707107i −0.0368605 0.0368605i
\(369\) −11.7727 33.2982i −0.612862 1.73344i
\(370\) 3.67544i 0.191077i
\(371\) 0 0
\(372\) −0.680846 3.96826i −0.0353002 0.205745i
\(373\) −5.48683 + 5.48683i −0.284097 + 0.284097i −0.834741 0.550643i \(-0.814382\pi\)
0.550643 + 0.834741i \(0.314382\pi\)
\(374\) 3.28742 0.169988
\(375\) −3.27465 19.0860i −0.169102 0.985599i
\(376\) −0.324555 −0.0167377
\(377\) 9.67000 9.67000i 0.498030 0.498030i
\(378\) 0 0
\(379\) 15.4868i 0.795505i 0.917493 + 0.397753i \(0.130210\pi\)
−0.917493 + 0.397753i \(0.869790\pi\)
\(380\) 2.59893i 0.133322i
\(381\) −2.32456 1.64371i −0.119091 0.0842098i
\(382\) 12.3246 + 12.3246i 0.630579 + 0.630579i
\(383\) −15.7858 15.7858i −0.806619 0.806619i 0.177502 0.984121i \(-0.443199\pi\)
−0.984121 + 0.177502i \(0.943199\pi\)
\(384\) 1.41421 + 1.00000i 0.0721688 + 0.0510310i
\(385\) 0 0
\(386\) 4.24264i 0.215945i
\(387\) −16.7526 + 35.0771i −0.851580 + 1.78307i
\(388\) −5.16228 + 5.16228i −0.262075 + 0.262075i
\(389\) 21.4427 1.08719 0.543594 0.839348i \(-0.317063\pi\)
0.543594 + 0.839348i \(0.317063\pi\)
\(390\) 11.6727 2.00272i 0.591071 0.101412i
\(391\) 1.16228 0.0587789
\(392\) 4.94975 4.94975i 0.250000 0.250000i
\(393\) −3.03393 17.6830i −0.153042 0.891991i
\(394\) 3.67544i 0.185166i
\(395\) 7.07107 0.355784
\(396\) −8.00000 + 2.82843i −0.402015 + 0.142134i
\(397\) −24.8114 24.8114i −1.24525 1.24525i −0.957795 0.287453i \(-0.907191\pi\)
−0.287453 0.957795i \(-0.592809\pi\)
\(398\) 10.7213 + 10.7213i 0.537413 + 0.537413i
\(399\) 0 0
\(400\) 5.00000 0.250000
\(401\) 19.7990i 0.988714i 0.869259 + 0.494357i \(0.164597\pi\)
−0.869259 + 0.494357i \(0.835403\pi\)
\(402\) −2.80599 + 0.481431i −0.139950 + 0.0240116i
\(403\) 5.02633 5.02633i 0.250380 0.250380i
\(404\) 7.30056 0.363217
\(405\) −12.6491 15.6525i −0.628539 0.777778i
\(406\) 0 0
\(407\) −3.28742 + 3.28742i −0.162951 + 0.162951i
\(408\) −1.98413 + 0.340423i −0.0982292 + 0.0168535i
\(409\) 20.0000i 0.988936i −0.869196 0.494468i \(-0.835363\pi\)
0.869196 0.494468i \(-0.164637\pi\)
\(410\) 18.6143 18.6143i 0.919293 0.919293i
\(411\) 1.16228 1.64371i 0.0573309 0.0810782i
\(412\) 4.83772 + 4.83772i 0.238337 + 0.238337i
\(413\) 0 0
\(414\) −2.82843 + 1.00000i −0.139010 + 0.0491473i
\(415\) −6.83772 + 6.83772i −0.335651 + 0.335651i
\(416\) 3.05792i 0.149927i
\(417\) 3.02399 + 17.6251i 0.148086 + 0.863106i
\(418\) −2.32456 + 2.32456i −0.113698 + 0.113698i
\(419\) 9.40326 0.459379 0.229690 0.973264i \(-0.426229\pi\)
0.229690 + 0.973264i \(0.426229\pi\)
\(420\) 0 0
\(421\) 36.6491 1.78617 0.893084 0.449890i \(-0.148537\pi\)
0.893084 + 0.449890i \(0.148537\pi\)
\(422\) −1.18472 + 1.18472i −0.0576712 + 0.0576712i
\(423\) −0.419615 + 0.878606i −0.0204024 + 0.0427193i
\(424\) 9.48683i 0.460721i
\(425\) −4.10927 + 4.10927i −0.199329 + 0.199329i
\(426\) 8.32456 + 5.88635i 0.403326 + 0.285195i
\(427\) 0 0
\(428\) 7.53006 + 7.53006i 0.363979 + 0.363979i
\(429\) −12.2317 8.64911i −0.590552 0.417583i
\(430\) −28.9737 −1.39723
\(431\) 11.7727i 0.567071i −0.958962 0.283535i \(-0.908493\pi\)
0.958962 0.283535i \(-0.0915074\pi\)
\(432\) 4.53553 2.53553i 0.218216 0.121991i
\(433\) −28.1359 + 28.1359i −1.35213 + 1.35213i −0.468849 + 0.883279i \(0.655331\pi\)
−0.883279 + 0.468849i \(0.844669\pi\)
\(434\) 0 0
\(435\) −2.92893 17.0711i −0.140432 0.818495i
\(436\) 1.67544 0.0802392
\(437\) −0.821854 + 0.821854i −0.0393146 + 0.0393146i
\(438\) −2.20550 12.8546i −0.105383 0.614217i
\(439\) 36.6491i 1.74917i 0.484875 + 0.874583i \(0.338865\pi\)
−0.484875 + 0.874583i \(0.661135\pi\)
\(440\) −4.47214 4.47214i −0.213201 0.213201i
\(441\) −7.00000 19.7990i −0.333333 0.942809i
\(442\) −2.51317 2.51317i −0.119539 0.119539i
\(443\) −11.3137 11.3137i −0.537531 0.537531i 0.385272 0.922803i \(-0.374107\pi\)
−0.922803 + 0.385272i \(0.874107\pi\)
\(444\) 1.64371 2.32456i 0.0780070 0.110319i
\(445\) 38.9737i 1.84753i
\(446\) 9.67000i 0.457888i
\(447\) 13.2464 2.27272i 0.626533 0.107496i
\(448\) 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
\(451\) −33.2982 −1.56795
\(452\) −0.362864 + 0.362864i −0.0170677 + 0.0170677i
\(453\) 17.6251 3.02399i 0.828100 0.142080i
\(454\) 6.00000i 0.281594i
\(455\) 0 0
\(456\) 1.16228 1.64371i 0.0544286 0.0769737i
\(457\) −12.8377 12.8377i −0.600523 0.600523i 0.339928 0.940451i \(-0.389597\pi\)
−0.940451 + 0.339928i \(0.889597\pi\)
\(458\) 17.8885 + 17.8885i 0.835877 + 0.835877i
\(459\) −1.64371 + 5.81139i −0.0767218 + 0.271252i
\(460\) −1.58114 1.58114i −0.0737210 0.0737210i
\(461\) 12.9574i 0.603487i −0.953389 0.301744i \(-0.902431\pi\)
0.953389 0.301744i \(-0.0975686\pi\)
\(462\) 0 0
\(463\) 18.1359 18.1359i 0.842849 0.842849i −0.146380 0.989228i \(-0.546762\pi\)
0.989228 + 0.146380i \(0.0467621\pi\)
\(464\) 4.47214 0.207614
\(465\) −1.52242 8.87331i −0.0706005 0.411490i
\(466\) 4.32456 0.200331
\(467\) −13.1869 + 13.1869i −0.610218 + 0.610218i −0.943003 0.332785i \(-0.892012\pi\)
0.332785 + 0.943003i \(0.392012\pi\)
\(468\) 8.27812 + 3.95357i 0.382656 + 0.182754i
\(469\) 0 0
\(470\) −0.725728 −0.0334753
\(471\) −18.9737 13.4164i −0.874260 0.618195i
\(472\) −7.00000 7.00000i −0.322201 0.322201i
\(473\) 25.9148 + 25.9148i 1.19157 + 1.19157i
\(474\) 4.47214 + 3.16228i 0.205412 + 0.145248i
\(475\) 5.81139i 0.266645i
\(476\) 0 0
\(477\) −25.6819 12.2655i −1.17589 0.561597i
\(478\) −14.4868 + 14.4868i −0.662612 + 0.662612i
\(479\) 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
\(481\) 5.02633 0.229181
\(482\) 3.05792 3.05792i 0.139285 0.139285i
\(483\) 0 0
\(484\) 3.00000i 0.136364i
\(485\) −11.5432 + 11.5432i −0.524150 + 0.524150i
\(486\) −1.00000 15.5563i −0.0453609 0.705650i
\(487\) −16.8377 16.8377i −0.762990 0.762990i 0.213872 0.976862i \(-0.431393\pi\)
−0.976862 + 0.213872i \(0.931393\pi\)
\(488\) 5.65685 + 5.65685i 0.256074 + 0.256074i
\(489\) 12.2317 17.2982i 0.553136 0.782253i
\(490\) 11.0680 11.0680i 0.500000 0.500000i
\(491\) 9.89949i 0.446758i −0.974732 0.223379i \(-0.928291\pi\)
0.974732 0.223379i \(-0.0717087\pi\)
\(492\) 20.0973 3.44814i 0.906054 0.155454i
\(493\) −3.67544 + 3.67544i −0.165534 + 0.165534i
\(494\) 3.55415 0.159909
\(495\) −17.8885 + 6.32456i −0.804030 + 0.284268i
\(496\) 2.32456 0.104376
\(497\) 0 0
\(498\) −7.38248 + 1.26663i −0.330817 + 0.0567592i
\(499\) 40.6491i 1.81970i 0.414933 + 0.909852i \(0.363805\pi\)
−0.414933 + 0.909852i \(0.636195\pi\)
\(500\) 11.1803 0.500000
\(501\) −20.6491 + 29.2023i −0.922534 + 1.30466i
\(502\) −4.00000 4.00000i −0.178529 0.178529i
\(503\) 6.84157 + 6.84157i 0.305051 + 0.305051i 0.842986 0.537935i \(-0.180796\pi\)
−0.537935 + 0.842986i \(0.680796\pi\)
\(504\) 0 0
\(505\) 16.3246 0.726433
\(506\) 2.82843i 0.125739i
\(507\) −1.06880 6.22942i −0.0474671 0.276658i
\(508\) 1.16228 1.16228i 0.0515677 0.0515677i
\(509\) −18.1553 −0.804719 −0.402359 0.915482i \(-0.631810\pi\)
−0.402359 + 0.915482i \(0.631810\pi\)
\(510\) −4.43665 + 0.761210i −0.196458 + 0.0337069i
\(511\) 0 0
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) −2.94699 5.27155i −0.130113 0.232745i
\(514\) 27.2982i 1.20407i
\(515\) 10.8175 + 10.8175i 0.476675 + 0.476675i
\(516\) −18.3246 12.9574i −0.806694 0.570418i
\(517\) 0.649111 + 0.649111i 0.0285479 + 0.0285479i
\(518\) 0 0
\(519\) 17.4296 + 12.3246i 0.765072 + 0.540988i
\(520\) 6.83772i 0.299854i
\(521\) 26.3738i 1.15546i 0.816229 + 0.577729i \(0.196061\pi\)
−0.816229 + 0.577729i \(0.803939\pi\)
\(522\) 5.78199 12.1065i 0.253071 0.529889i
\(523\) 29.2982 29.2982i 1.28112 1.28112i 0.341092 0.940030i \(-0.389203\pi\)
0.940030 0.341092i \(-0.110797\pi\)
\(524\) 10.3585 0.452513
\(525\) 0 0
\(526\) −0.649111 −0.0283026
\(527\) −1.91045 + 1.91045i −0.0832203 + 0.0832203i
\(528\) −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
\(534\) −17.4296 + 24.6491i −0.754251 + 1.06667i
\(535\) 16.8377 + 16.8377i 0.727958 + 0.727958i
\(536\) 1.64371i 0.0709974i
\(537\) −22.5115 + 3.86236i −0.971442 + 0.166673i
\(538\) 6.83772 6.83772i 0.294795 0.294795i
\(539\) −19.7990 −0.852803
\(540\) 10.1418 5.66963i 0.436432 0.243982i
\(541\) 13.6754 0.587953 0.293977 0.955813i \(-0.405021\pi\)
0.293977 + 0.955813i \(0.405021\pi\)
\(542\) −21.9017 + 21.9017i −0.940758 + 0.940758i
\(543\) −38.1104 + 6.53871i −1.63547 + 0.280603i
\(544\) 1.16228i 0.0498322i
\(545\) 3.74641 0.160478
\(546\) 0 0
\(547\) −6.32456 6.32456i −0.270418 0.270418i 0.558850 0.829269i \(-0.311243\pi\)
−0.829269 + 0.558850i \(0.811243\pi\)
\(548\) 0.821854 + 0.821854i 0.0351079 + 0.0351079i
\(549\) 22.6274 8.00000i 0.965715 0.341432i
\(550\) −10.0000 10.0000i −0.426401 0.426401i
\(551\) 5.19786i 0.221436i
\(552\) −0.292893 1.70711i −0.0124664 0.0726593i
\(553\) 0 0
\(554\) 3.05792 0.129919
\(555\) 3.67544 5.19786i 0.156014 0.220637i
\(556\) −10.3246 −0.437859
\(557\) 17.5629 17.5629i 0.744165 0.744165i −0.229212 0.973377i \(-0.573615\pi\)
0.973377 + 0.229212i \(0.0736148\pi\)
\(558\) 3.00540 6.29282i 0.127229 0.266396i
\(559\) 39.6228i 1.67586i
\(560\) 0 0
\(561\) 4.64911 + 3.28742i 0.196286 + 0.138795i
\(562\) −17.4868 17.4868i −0.737638 0.737638i
\(563\) 5.88635 + 5.88635i 0.248080 + 0.248080i 0.820182 0.572102i \(-0.193872\pi\)
−0.572102 + 0.820182i \(0.693872\pi\)
\(564\) −0.458991 0.324555i −0.0193270 0.0136662i
\(565\) −0.811388 + 0.811388i −0.0341354 + 0.0341354i
\(566\) 12.2317i 0.514136i
\(567\) 0 0
\(568\) −4.16228 + 4.16228i −0.174645 + 0.174645i
\(569\) −10.1290 −0.424629 −0.212315 0.977201i \(-0.568100\pi\)
−0.212315 + 0.977201i \(0.568100\pi\)
\(570\) 2.59893 3.67544i 0.108857 0.153947i
\(571\) −10.8377 −0.453545 −0.226772 0.973948i \(-0.572817\pi\)
−0.226772 + 0.973948i \(0.572817\pi\)
\(572\) 6.11584 6.11584i 0.255716 0.255716i
\(573\) 5.10500 + 29.7541i 0.213264 + 1.24300i
\(574\) 0 0
\(575\) −3.53553 3.53553i −0.147442 0.147442i
\(576\) 1.00000 + 2.82843i 0.0416667 + 0.117851i
\(577\) −6.67544 6.67544i −0.277902 0.277902i 0.554369 0.832271i \(-0.312960\pi\)
−0.832271 + 0.554369i \(0.812960\pi\)
\(578\) −11.0656 11.0656i −0.460268 0.460268i
\(579\) −4.24264 + 6.00000i −0.176318 + 0.249351i
\(580\) 10.0000 0.415227
\(581\) 0 0
\(582\) −12.4628 + 2.13829i −0.516601 + 0.0886348i
\(583\) −18.9737 + 18.9737i −0.785809 + 0.785809i
\(584\) 7.53006 0.311596
\(585\) 18.5104 + 8.84044i 0.765313 + 0.365507i
\(586\) 31.8114 1.31412
\(587\) −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
\(589\) 2.70178i 0.111325i
\(590\) −15.6525 15.6525i −0.644402 0.644402i
\(591\) −3.67544 + 5.19786i −0.151188 + 0.213812i
\(592\) 1.16228 + 1.16228i 0.0477693 + 0.0477693i
\(593\) 27.7880 + 27.7880i 1.14112 + 1.14112i 0.988246 + 0.152872i \(0.0488522\pi\)
0.152872 + 0.988246i \(0.451148\pi\)
\(594\) −14.1421 4.00000i −0.580259 0.164122i
\(595\) 0 0
\(596\) 7.75955i 0.317844i
\(597\) 4.44093 + 25.8836i 0.181755 + 1.05935i
\(598\) 2.16228 2.16228i 0.0884221 0.0884221i
\(599\) 17.2001 0.702775 0.351388 0.936230i \(-0.385710\pi\)
0.351388 + 0.936230i \(0.385710\pi\)
\(600\) 7.07107 + 5.00000i 0.288675 + 0.204124i
\(601\) −9.35089 −0.381431 −0.190715 0.981645i \(-0.561081\pi\)
−0.190715 + 0.981645i \(0.561081\pi\)
\(602\) 0 0
\(603\) −4.44970 2.12514i −0.181206 0.0865424i
\(604\) 10.3246i 0.420100i
\(605\) 6.70820i 0.272727i
\(606\) 10.3246 + 7.30056i 0.419406 + 0.296565i
\(607\) 7.16228 + 7.16228i 0.290708 + 0.290708i 0.837360 0.546652i \(-0.184098\pi\)
−0.546652 + 0.837360i \(0.684098\pi\)
\(608\) 0.821854 + 0.821854i 0.0333306 + 0.0333306i
\(609\) 0 0
\(610\) 12.6491 + 12.6491i 0.512148 + 0.512148i
\(611\) 0.992465i 0.0401508i
\(612\) −3.14641 1.50270i −0.127186 0.0607431i
\(613\) 30.4605 30.4605i 1.23029 1.23029i 0.266435 0.963853i \(-0.414154\pi\)
0.963853 0.266435i \(-0.0858458\pi\)
\(614\) 14.6011 0.589253
\(615\) 44.9388 7.71028i 1.81211 0.310909i
\(616\) 0 0
\(617\) −12.1356 + 12.1356i −0.488559 + 0.488559i −0.907851 0.419292i \(-0.862278\pi\)
0.419292 + 0.907851i \(0.362278\pi\)
\(618\) 2.00385 + 11.6793i 0.0806067 + 0.469810i
\(619\) 38.4605i 1.54586i −0.634493 0.772929i \(-0.718791\pi\)
0.634493 0.772929i \(-0.281209\pi\)
\(620\) 5.19786 0.208751
\(621\) −5.00000 1.41421i −0.200643 0.0567504i
\(622\) 12.8114 + 12.8114i 0.513690 + 0.513690i
\(623\) 0 0
\(624\) −3.05792 + 4.32456i −0.122415 + 0.173121i
\(625\) 25.0000 1.00000
\(626\) 4.01315i 0.160398i
\(627\) −5.61197 + 0.962862i −0.224121 + 0.0384530i
\(628\) 9.48683 9.48683i 0.378566 0.378566i
\(629\) −1.91045 −0.0761745
\(630\) 0 0
\(631\) 3.81139 0.151729 0.0758645 0.997118i \(-0.475828\pi\)
0.0758645 + 0.997118i \(0.475828\pi\)
\(632\) −2.23607 + 2.23607i −0.0889460 + 0.0889460i
\(633\) −2.86016 + 0.490726i −0.113681 + 0.0195046i
\(634\) 16.3246i 0.648331i
\(635\) 2.59893 2.59893i 0.103135 0.103135i
\(636\) 9.48683 13.4164i 0.376177 0.531995i
\(637\) 15.1359 + 15.1359i 0.599708 + 0.599708i
\(638\) −8.94427 8.94427i −0.354107 0.354107i
\(639\) 5.88635 + 16.6491i 0.232860 + 0.658629i
\(640\) −1.58114 + 1.58114i −0.0625000 + 0.0625000i
\(641\) 28.7433i 1.13529i 0.823273 + 0.567645i \(0.192145\pi\)
−0.823273 + 0.567645i \(0.807855\pi\)
\(642\) 3.11905 + 18.1792i 0.123099 + 0.717475i
\(643\) 1.16228 1.16228i 0.0458358 0.0458358i −0.683817 0.729653i \(-0.739682\pi\)
0.729653 + 0.683817i \(0.239682\pi\)
\(644\) 0 0
\(645\) −40.9750 28.9737i −1.61339 1.14084i
\(646\) −1.35089 −0.0531500
\(647\) −28.5138 + 28.5138i −1.12099 + 1.12099i −0.129399 + 0.991593i \(0.541305\pi\)
−0.991593 + 0.129399i \(0.958695\pi\)
\(648\) 8.94975 + 0.949747i 0.351579 + 0.0373096i
\(649\) 28.0000i 1.09910i
\(650\) 15.2896i 0.599708i
\(651\) 0 0
\(652\) 8.64911 + 8.64911i 0.338725 + 0.338725i
\(653\) 9.17377 + 9.17377i 0.358997 + 0.358997i 0.863443 0.504446i \(-0.168303\pi\)
−0.504446 + 0.863443i \(0.668303\pi\)
\(654\) 2.36944 + 1.67544i 0.0926523 + 0.0655151i
\(655\) 23.1623 0.905025
\(656\) 11.7727i 0.459647i
\(657\) 9.73556 20.3847i 0.379820 0.795282i
\(658\) 0 0
\(659\) −8.94427 −0.348419 −0.174210 0.984709i \(-0.555737\pi\)
−0.174210 + 0.984709i \(0.555737\pi\)
\(660\) −1.85242 10.7967i −0.0721053 0.420261i
\(661\) −7.35089 −0.285916 −0.142958 0.989729i \(-0.545661\pi\)
−0.142958 + 0.989729i \(0.545661\pi\)
\(662\) 24.7301 24.7301i 0.961163 0.961163i
\(663\) −1.04099 6.06732i −0.0404286 0.235635i
\(664\) 4.32456i 0.167825i
\(665\) 0 0
\(666\) 4.64911 1.64371i 0.180149 0.0636924i
\(667\) −3.16228 3.16228i −0.122444 0.122444i
\(668\) −14.6011 14.6011i −0.564935 0.564935i
\(669\) −9.67000 + 13.6754i −0.373864 + 0.528723i
\(670\) 3.67544i 0.141995i
\(671\) 22.6274i 0.873522i
\(672\) 0 0
\(673\) 18.6754 18.6754i 0.719885 0.719885i −0.248696 0.968582i \(-0.580002\pi\)
0.968582 + 0.248696i \(0.0800020\pi\)
\(674\) −13.4164 −0.516781
\(675\) 22.6777 12.6777i 0.872864 0.487964i
\(676\) 3.64911 0.140350
\(677\) −14.4678 + 14.4678i −0.556041 + 0.556041i −0.928178 0.372137i \(-0.878625\pi\)
0.372137 + 0.928178i \(0.378625\pi\)
\(678\) −0.876031 + 0.150303i −0.0336438 + 0.00577236i
\(679\) 0 0
\(680\) 2.59893i 0.0996645i
\(681\) −6.00000 + 8.48528i −0.229920 + 0.325157i
\(682\) −4.64911 4.64911i −0.178024 0.178024i
\(683\) 22.5902 + 22.5902i 0.864389 + 0.864389i 0.991844 0.127455i \(-0.0406809\pi\)
−0.127455 + 0.991844i \(0.540681\pi\)
\(684\) 3.28742 1.16228i 0.125698 0.0444408i
\(685\) 1.83772 + 1.83772i 0.0702158 + 0.0702158i
\(686\) 0 0
\(687\) 7.40968 + 43.1868i 0.282697 + 1.64768i
\(688\) 9.16228 9.16228i 0.349309 0.349309i
\(689\) 29.0100 1.10519
\(690\) −0.654929 3.81721i −0.0249327 0.145319i
\(691\) 12.6491 0.481195 0.240597 0.970625i \(-0.422657\pi\)
0.240597 + 0.970625i \(0.422657\pi\)
\(692\) −8.71478 + 8.71478i −0.331286 + 0.331286i
\(693\) 0 0
\(694\) 26.6491i 1.01159i
\(695\) −23.0864 −0.875717
\(696\) 6.32456 + 4.47214i 0.239732 + 0.169516i
\(697\) −9.67544 9.67544i −0.366484 0.366484i
\(698\) −9.89949 9.89949i −0.374701 0.374701i
\(699\) 6.11584 + 4.32456i 0.231322 + 0.163570i
\(700\) 0 0
\(701\) 8.02629i 0.303149i 0.988446 + 0.151574i \(0.0484343\pi\)
−0.988446 + 0.151574i \(0.951566\pi\)
\(702\) 7.75347 + 13.8693i 0.292636 + 0.523463i
\(703\) 1.35089 1.35089i 0.0509498 0.0509498i
\(704\) 2.82843 0.106600
\(705\) −1.02633 0.725728i −0.0386540 0.0273325i
\(706\) −12.9737 −0.488270
\(707\) 0 0
\(708\) −2.89949 16.8995i −0.108970 0.635122i
\(709\) 49.9473i 1.87581i 0.346890 + 0.937906i \(0.387238\pi\)
−0.346890 + 0.937906i \(0.612762\pi\)
\(710\) −9.30714 + 9.30714i −0.349291 + 0.349291i
\(711\) 3.16228 + 8.94427i 0.118595 + 0.335436i
\(712\) −12.3246 12.3246i −0.461882 0.461882i
\(713\) −1.64371 1.64371i −0.0615574 0.0615574i
\(714\) 0 0
\(715\) 13.6754 13.6754i 0.511433 0.511433i
\(716\) 13.1869i 0.492818i
\(717\) −34.9743 + 6.00064i −1.30614 + 0.224098i
\(718\) 14.0000 14.0000i 0.522475 0.522475i
\(719\) −50.1487 −1.87023 −0.935116 0.354342i \(-0.884705\pi\)
−0.935116 + 0.354342i \(0.884705\pi\)
\(720\) 2.23607 + 6.32456i 0.0833333 + 0.235702i
\(721\) 0 0
\(722\) −12.4798 + 12.4798i −0.464450 + 0.464450i
\(723\) 7.38248 1.26663i 0.274557 0.0471066i
\(724\) 22.3246i 0.829686i
\(725\) 22.3607 0.830455
\(726\) 3.00000 4.24264i 0.111340 0.157459i
\(727\) 26.3246 + 26.3246i 0.976324 + 0.976324i 0.999726 0.0234024i \(-0.00744990\pi\)
−0.0234024 + 0.999726i \(0.507450\pi\)
\(728\) 0 0
\(729\) 14.1421 23.0000i 0.523783 0.851852i
\(730\) 16.8377 0.623192
\(731\) 15.0601i 0.557019i
\(732\) 2.34315 + 13.6569i 0.0866052 + 0.504772i
\(733\) −2.18861 + 2.18861i −0.0808382 + 0.0808382i −0.746370 0.665532i \(-0.768205\pi\)
0.665532 + 0.746370i \(0.268205\pi\)
\(734\) 24.7301 0.912805
\(735\) 26.7204 4.58450i 0.985599 0.169102i
\(736\) 1.00000 0.0368605
\(737\) −3.28742 + 3.28742i −0.121094 + 0.121094i
\(738\) 31.8700 + 15.2208i 1.17315 + 0.560287i
\(739\) 36.2719i 1.33428i −0.744931 0.667141i \(-0.767518\pi\)
0.744931 0.667141i \(-0.232482\pi\)
\(740\) 2.59893 + 2.59893i 0.0955386 + 0.0955386i
\(741\) 5.02633 + 3.55415i 0.184647 + 0.130565i
\(742\) 0 0
\(743\) −10.5880 10.5880i −0.388435 0.388435i 0.485694 0.874129i \(-0.338567\pi\)
−0.874129 + 0.485694i \(0.838567\pi\)
\(744\) 3.28742 + 2.32456i 0.120523 + 0.0852223i
\(745\) 17.3509i 0.635687i
\(746\) 7.75955i 0.284097i
\(747\) −11.7070 5.59119i −0.428338 0.204571i
\(748\) −2.32456 + 2.32456i −0.0849942 + 0.0849942i
\(749\) 0 0
\(750\) 15.8114 + 11.1803i 0.577350 + 0.408248i
\(751\) 28.4605 1.03854 0.519269 0.854611i \(-0.326204\pi\)
0.519269 + 0.854611i \(0.326204\pi\)
\(752\) 0.229495 0.229495i 0.00836883 0.00836883i
\(753\) −1.65685 9.65685i −0.0603791 0.351915i
\(754\) 13.6754i 0.498030i
\(755\) 23.0864i 0.840200i
\(756\) 0 0
\(757\) −9.48683 9.48683i −0.344805 0.344805i 0.513365 0.858170i \(-0.328399\pi\)
−0.858170 + 0.513365i \(0.828399\pi\)
\(758\) −10.9508 10.9508i −0.397753 0.397753i
\(759\) −2.82843 + 4.00000i −0.102665 + 0.145191i
\(760\) 1.83772 + 1.83772i 0.0666612 + 0.0666612i
\(761\) 32.4897i 1.17775i −0.808224 0.588875i \(-0.799571\pi\)
0.808224 0.588875i \(-0.200429\pi\)
\(762\) 2.80599 0.481431i 0.101650 0.0174404i
\(763\) 0 0
\(764\) −17.4296 −0.630579
\(765\) −7.03559 3.36014i −0.254372 0.121486i
\(766\) 22.3246 0.806619
\(767\) 21.4055 21.4055i 0.772906 0.772906i
\(768\) −1.70711 + 0.292893i −0.0615999 + 0.0105689i
\(769\) 16.3246i 0.588679i 0.955701 + 0.294339i \(0.0950996\pi\)
−0.955701 + 0.294339i \(0.904900\pi\)
\(770\) 0 0
\(771\) −27.2982 + 38.6055i −0.983121 + 1.39034i
\(772\) −3.00000 3.00000i −0.107972 0.107972i
\(773\) −22.0351 22.0351i −0.792546 0.792546i 0.189361 0.981907i \(-0.439358\pi\)
−0.981907 + 0.189361i \(0.939358\pi\)
\(774\) −12.9574 36.6491i −0.465745 1.31733i
\(775\) 11.6228 0.417502
\(776\) 7.30056i 0.262075i
\(777\) 0 0
\(778\) −15.1623 + 15.1623i −0.543594 + 0.543594i
\(779\) 13.6831 0.490250
\(780\) −6.83772 + 9.67000i −0.244830 + 0.346242i
\(781\) 16.6491 0.595752
\(782\)