Properties

Label 690.2.j.b.367.11
Level $690$
Weight $2$
Character 690.367
Analytic conductor $5.510$
Analytic rank $0$
Dimension $24$
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.j (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.50967773947\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 367.11
Character \(\chi\) \(=\) 690.367
Dual form 690.2.j.b.643.11

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 + 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(1.52094 + 1.63913i) q^{5} +1.00000 q^{6} +(-2.68754 + 2.68754i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +O(q^{10})\) \(q+(0.707107 + 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(1.52094 + 1.63913i) q^{5} +1.00000 q^{6} +(-2.68754 + 2.68754i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +(-0.0835670 + 2.23451i) q^{10} +0.403497i q^{11} +(0.707107 + 0.707107i) q^{12} +(-2.12629 + 2.12629i) q^{13} -3.80076 q^{14} +(2.23451 + 0.0835670i) q^{15} -1.00000 q^{16} +(-4.95666 + 4.95666i) q^{17} +(0.707107 - 0.707107i) q^{18} +5.20795 q^{19} +(-1.63913 + 1.52094i) q^{20} +3.80076i q^{21} +(-0.285316 + 0.285316i) q^{22} +(4.10854 - 2.47384i) q^{23} +1.00000i q^{24} +(-0.373462 + 4.98603i) q^{25} -3.00703 q^{26} +(-0.707107 - 0.707107i) q^{27} +(-2.68754 - 2.68754i) q^{28} -9.42076i q^{29} +(1.52094 + 1.63913i) q^{30} +3.33683 q^{31} +(-0.707107 - 0.707107i) q^{32} +(0.285316 + 0.285316i) q^{33} -7.00978 q^{34} +(-8.49282 - 0.317618i) q^{35} +1.00000 q^{36} +(2.17130 - 2.17130i) q^{37} +(3.68258 + 3.68258i) q^{38} +3.00703i q^{39} +(-2.23451 - 0.0835670i) q^{40} +5.69885 q^{41} +(-2.68754 + 2.68754i) q^{42} +(-2.56936 - 2.56936i) q^{43} -0.403497 q^{44} +(1.63913 - 1.52094i) q^{45} +(4.65445 + 1.15590i) q^{46} +(8.64413 + 8.64413i) q^{47} +(-0.707107 + 0.707107i) q^{48} -7.44578i q^{49} +(-3.78974 + 3.26158i) q^{50} +7.00978i q^{51} +(-2.12629 - 2.12629i) q^{52} +(-1.47608 - 1.47608i) q^{53} -1.00000i q^{54} +(-0.661382 + 0.613696i) q^{55} -3.80076i q^{56} +(3.68258 - 3.68258i) q^{57} +(6.66148 - 6.66148i) q^{58} +13.4003i q^{59} +(-0.0835670 + 2.23451i) q^{60} -7.51118i q^{61} +(2.35950 + 2.35950i) q^{62} +(2.68754 + 2.68754i) q^{63} -1.00000i q^{64} +(-6.71923 - 0.251289i) q^{65} +0.403497i q^{66} +(4.60755 - 4.60755i) q^{67} +(-4.95666 - 4.95666i) q^{68} +(1.15590 - 4.65445i) q^{69} +(-5.78074 - 6.22992i) q^{70} -5.45281 q^{71} +(0.707107 + 0.707107i) q^{72} +(1.06175 - 1.06175i) q^{73} +3.07068 q^{74} +(3.26158 + 3.78974i) q^{75} +5.20795i q^{76} +(-1.08442 - 1.08442i) q^{77} +(-2.12629 + 2.12629i) q^{78} +0.383565 q^{79} +(-1.52094 - 1.63913i) q^{80} -1.00000 q^{81} +(4.02970 + 4.02970i) q^{82} +(12.3708 + 12.3708i) q^{83} -3.80076 q^{84} +(-15.6634 - 0.585786i) q^{85} -3.63363i q^{86} +(-6.66148 - 6.66148i) q^{87} +(-0.285316 - 0.285316i) q^{88} +6.23158 q^{89} +(2.23451 + 0.0835670i) q^{90} -11.4290i q^{91} +(2.47384 + 4.10854i) q^{92} +(2.35950 - 2.35950i) q^{93} +12.2247i q^{94} +(7.92100 + 8.53649i) q^{95} -1.00000 q^{96} +(8.25631 - 8.25631i) q^{97} +(5.26496 - 5.26496i) q^{98} +0.403497 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 24q^{6} + O(q^{10}) \) \( 24q + 24q^{6} + 16q^{13} - 24q^{16} + 16q^{23} - 16q^{25} + 16q^{31} + 24q^{36} + 8q^{46} + 40q^{47} - 8q^{50} + 16q^{52} - 56q^{55} - 16q^{58} - 8q^{62} + 32q^{70} + 64q^{71} - 16q^{73} + 32q^{75} + 16q^{77} + 16q^{78} - 24q^{81} + 24q^{82} - 48q^{85} + 16q^{87} + 16q^{92} - 8q^{93} + 24q^{95} - 24q^{96} + O(q^{100}) \)

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
\(3\) 0.707107 0.707107i 0.408248 0.408248i
\(4\) 1.00000i 0.500000i
\(5\) 1.52094 + 1.63913i 0.680187 + 0.733039i
\(6\) 1.00000 0.408248
\(7\) −2.68754 + 2.68754i −1.01580 + 1.01580i −0.0159226 + 0.999873i \(0.505069\pi\)
−0.999873 + 0.0159226i \(0.994931\pi\)
\(8\) −0.707107 + 0.707107i −0.250000 + 0.250000i
\(9\) 1.00000i 0.333333i
\(10\) −0.0835670 + 2.23451i −0.0264262 + 0.706613i
\(11\) 0.403497i 0.121659i 0.998148 + 0.0608295i \(0.0193746\pi\)
−0.998148 + 0.0608295i \(0.980625\pi\)
\(12\) 0.707107 + 0.707107i 0.204124 + 0.204124i
\(13\) −2.12629 + 2.12629i −0.589728 + 0.589728i −0.937558 0.347830i \(-0.886919\pi\)
0.347830 + 0.937558i \(0.386919\pi\)
\(14\) −3.80076 −1.01580
\(15\) 2.23451 + 0.0835670i 0.576947 + 0.0215769i
\(16\) −1.00000 −0.250000
\(17\) −4.95666 + 4.95666i −1.20217 + 1.20217i −0.228662 + 0.973506i \(0.573435\pi\)
−0.973506 + 0.228662i \(0.926565\pi\)
\(18\) 0.707107 0.707107i 0.166667 0.166667i
\(19\) 5.20795 1.19479 0.597393 0.801949i \(-0.296203\pi\)
0.597393 + 0.801949i \(0.296203\pi\)
\(20\) −1.63913 + 1.52094i −0.366520 + 0.340093i
\(21\) 3.80076i 0.829394i
\(22\) −0.285316 + 0.285316i −0.0608295 + 0.0608295i
\(23\) 4.10854 2.47384i 0.856690 0.515832i
\(24\) 1.00000i 0.204124i
\(25\) −0.373462 + 4.98603i −0.0746924 + 0.997207i
\(26\) −3.00703 −0.589728
\(27\) −0.707107 0.707107i −0.136083 0.136083i
\(28\) −2.68754 2.68754i −0.507898 0.507898i
\(29\) 9.42076i 1.74939i −0.484673 0.874695i \(-0.661061\pi\)
0.484673 0.874695i \(-0.338939\pi\)
\(30\) 1.52094 + 1.63913i 0.277685 + 0.299262i
\(31\) 3.33683 0.599312 0.299656 0.954047i \(-0.403128\pi\)
0.299656 + 0.954047i \(0.403128\pi\)
\(32\) −0.707107 0.707107i −0.125000 0.125000i
\(33\) 0.285316 + 0.285316i 0.0496671 + 0.0496671i
\(34\) −7.00978 −1.20217
\(35\) −8.49282 0.317618i −1.43555 0.0536873i
\(36\) 1.00000 0.166667
\(37\) 2.17130 2.17130i 0.356959 0.356959i −0.505732 0.862691i \(-0.668777\pi\)
0.862691 + 0.505732i \(0.168777\pi\)
\(38\) 3.68258 + 3.68258i 0.597393 + 0.597393i
\(39\) 3.00703i 0.481511i
\(40\) −2.23451 0.0835670i −0.353306 0.0132131i
\(41\) 5.69885 0.890011 0.445006 0.895528i \(-0.353202\pi\)
0.445006 + 0.895528i \(0.353202\pi\)
\(42\) −2.68754 + 2.68754i −0.414697 + 0.414697i
\(43\) −2.56936 2.56936i −0.391824 0.391824i 0.483513 0.875337i \(-0.339361\pi\)
−0.875337 + 0.483513i \(0.839361\pi\)
\(44\) −0.403497 −0.0608295
\(45\) 1.63913 1.52094i 0.244346 0.226729i
\(46\) 4.65445 + 1.15590i 0.686261 + 0.170429i
\(47\) 8.64413 + 8.64413i 1.26088 + 1.26088i 0.950669 + 0.310208i \(0.100399\pi\)
0.310208 + 0.950669i \(0.399601\pi\)
\(48\) −0.707107 + 0.707107i −0.102062 + 0.102062i
\(49\) 7.44578i 1.06368i
\(50\) −3.78974 + 3.26158i −0.535950 + 0.461257i
\(51\) 7.00978i 0.981566i
\(52\) −2.12629 2.12629i −0.294864 0.294864i
\(53\) −1.47608 1.47608i −0.202755 0.202755i 0.598424 0.801179i \(-0.295794\pi\)
−0.801179 + 0.598424i \(0.795794\pi\)
\(54\) 1.00000i 0.136083i
\(55\) −0.661382 + 0.613696i −0.0891808 + 0.0827508i
\(56\) 3.80076i 0.507898i
\(57\) 3.68258 3.68258i 0.487769 0.487769i
\(58\) 6.66148 6.66148i 0.874695 0.874695i
\(59\) 13.4003i 1.74458i 0.488992 + 0.872288i \(0.337365\pi\)
−0.488992 + 0.872288i \(0.662635\pi\)
\(60\) −0.0835670 + 2.23451i −0.0107885 + 0.288473i
\(61\) 7.51118i 0.961708i −0.876801 0.480854i \(-0.840327\pi\)
0.876801 0.480854i \(-0.159673\pi\)
\(62\) 2.35950 + 2.35950i 0.299656 + 0.299656i
\(63\) 2.68754 + 2.68754i 0.338599 + 0.338599i
\(64\) 1.00000i 0.125000i
\(65\) −6.71923 0.251289i −0.833418 0.0311685i
\(66\) 0.403497i 0.0496671i
\(67\) 4.60755 4.60755i 0.562902 0.562902i −0.367229 0.930131i \(-0.619693\pi\)
0.930131 + 0.367229i \(0.119693\pi\)
\(68\) −4.95666 4.95666i −0.601084 0.601084i
\(69\) 1.15590 4.65445i 0.139154 0.560330i
\(70\) −5.78074 6.22992i −0.690931 0.744618i
\(71\) −5.45281 −0.647129 −0.323565 0.946206i \(-0.604881\pi\)
−0.323565 + 0.946206i \(0.604881\pi\)
\(72\) 0.707107 + 0.707107i 0.0833333 + 0.0833333i
\(73\) 1.06175 1.06175i 0.124269 0.124269i −0.642237 0.766506i \(-0.721994\pi\)
0.766506 + 0.642237i \(0.221994\pi\)
\(74\) 3.07068 0.356959
\(75\) 3.26158 + 3.78974i 0.376615 + 0.437601i
\(76\) 5.20795i 0.597393i
\(77\) −1.08442 1.08442i −0.123581 0.123581i
\(78\) −2.12629 + 2.12629i −0.240755 + 0.240755i
\(79\) 0.383565 0.0431544 0.0215772 0.999767i \(-0.493131\pi\)
0.0215772 + 0.999767i \(0.493131\pi\)
\(80\) −1.52094 1.63913i −0.170047 0.183260i
\(81\) −1.00000 −0.111111
\(82\) 4.02970 + 4.02970i 0.445006 + 0.445006i
\(83\) 12.3708 + 12.3708i 1.35787 + 1.35787i 0.876540 + 0.481328i \(0.159846\pi\)
0.481328 + 0.876540i \(0.340154\pi\)
\(84\) −3.80076 −0.414697
\(85\) −15.6634 0.585786i −1.69893 0.0635375i
\(86\) 3.63363i 0.391824i
\(87\) −6.66148 6.66148i −0.714186 0.714186i
\(88\) −0.285316 0.285316i −0.0304147 0.0304147i
\(89\) 6.23158 0.660546 0.330273 0.943885i \(-0.392859\pi\)
0.330273 + 0.943885i \(0.392859\pi\)
\(90\) 2.23451 + 0.0835670i 0.235538 + 0.00880874i
\(91\) 11.4290i 1.19809i
\(92\) 2.47384 + 4.10854i 0.257916 + 0.428345i
\(93\) 2.35950 2.35950i 0.244668 0.244668i
\(94\) 12.2247i 1.26088i
\(95\) 7.92100 + 8.53649i 0.812678 + 0.875825i
\(96\) −1.00000 −0.102062
\(97\) 8.25631 8.25631i 0.838301 0.838301i −0.150334 0.988635i \(-0.548035\pi\)
0.988635 + 0.150334i \(0.0480350\pi\)
\(98\) 5.26496 5.26496i 0.531841 0.531841i
\(99\) 0.403497 0.0405530
\(100\) −4.98603 0.373462i −0.498603 0.0373462i
\(101\) −7.08442 −0.704926 −0.352463 0.935826i \(-0.614656\pi\)
−0.352463 + 0.935826i \(0.614656\pi\)
\(102\) −4.95666 + 4.95666i −0.490783 + 0.490783i
\(103\) −6.87041 6.87041i −0.676961 0.676961i 0.282350 0.959311i \(-0.408886\pi\)
−0.959311 + 0.282350i \(0.908886\pi\)
\(104\) 3.00703i 0.294864i
\(105\) −6.22992 + 5.78074i −0.607978 + 0.564143i
\(106\) 2.08749i 0.202755i
\(107\) −3.14660 + 3.14660i −0.304194 + 0.304194i −0.842652 0.538458i \(-0.819007\pi\)
0.538458 + 0.842652i \(0.319007\pi\)
\(108\) 0.707107 0.707107i 0.0680414 0.0680414i
\(109\) −12.6901 −1.21549 −0.607744 0.794133i \(-0.707925\pi\)
−0.607744 + 0.794133i \(0.707925\pi\)
\(110\) −0.901617 0.0337191i −0.0859658 0.00321499i
\(111\) 3.07068i 0.291456i
\(112\) 2.68754 2.68754i 0.253949 0.253949i
\(113\) −8.96499 8.96499i −0.843356 0.843356i 0.145938 0.989294i \(-0.453380\pi\)
−0.989294 + 0.145938i \(0.953380\pi\)
\(114\) 5.20795 0.487769
\(115\) 10.3038 + 2.97183i 0.960834 + 0.277125i
\(116\) 9.42076 0.874695
\(117\) 2.12629 + 2.12629i 0.196576 + 0.196576i
\(118\) −9.47547 + 9.47547i −0.872288 + 0.872288i
\(119\) 26.6425i 2.44231i
\(120\) −1.63913 + 1.52094i −0.149631 + 0.138843i
\(121\) 10.8372 0.985199
\(122\) 5.31121 5.31121i 0.480854 0.480854i
\(123\) 4.02970 4.02970i 0.363346 0.363346i
\(124\) 3.33683i 0.299656i
\(125\) −8.74075 + 6.97132i −0.781796 + 0.623534i
\(126\) 3.80076i 0.338599i
\(127\) −9.84286 9.84286i −0.873413 0.873413i 0.119430 0.992843i \(-0.461893\pi\)
−0.992843 + 0.119430i \(0.961893\pi\)
\(128\) 0.707107 0.707107i 0.0625000 0.0625000i
\(129\) −3.63363 −0.319923
\(130\) −4.57353 4.92890i −0.401125 0.432293i
\(131\) −1.09419 −0.0955998 −0.0477999 0.998857i \(-0.515221\pi\)
−0.0477999 + 0.998857i \(0.515221\pi\)
\(132\) −0.285316 + 0.285316i −0.0248335 + 0.0248335i
\(133\) −13.9966 + 13.9966i −1.21366 + 1.21366i
\(134\) 6.51606 0.562902
\(135\) 0.0835670 2.23451i 0.00719230 0.192316i
\(136\) 7.00978i 0.601084i
\(137\) 13.9152 13.9152i 1.18885 1.18885i 0.211471 0.977384i \(-0.432175\pi\)
0.977384 0.211471i \(-0.0678253\pi\)
\(138\) 4.10854 2.47384i 0.349742 0.210588i
\(139\) 19.8141i 1.68061i −0.542116 0.840304i \(-0.682377\pi\)
0.542116 0.840304i \(-0.317623\pi\)
\(140\) 0.317618 8.49282i 0.0268436 0.717774i
\(141\) 12.2247 1.02950
\(142\) −3.85572 3.85572i −0.323565 0.323565i
\(143\) −0.857953 0.857953i −0.0717457 0.0717457i
\(144\) 1.00000i 0.0833333i
\(145\) 15.4418 14.3284i 1.28237 1.18991i
\(146\) 1.50154 0.124269
\(147\) −5.26496 5.26496i −0.434247 0.434247i
\(148\) 2.17130 + 2.17130i 0.178480 + 0.178480i
\(149\) −11.1431 −0.912875 −0.456438 0.889755i \(-0.650875\pi\)
−0.456438 + 0.889755i \(0.650875\pi\)
\(150\) −0.373462 + 4.98603i −0.0304930 + 0.407108i
\(151\) 19.9653 1.62475 0.812375 0.583135i \(-0.198174\pi\)
0.812375 + 0.583135i \(0.198174\pi\)
\(152\) −3.68258 + 3.68258i −0.298697 + 0.298697i
\(153\) 4.95666 + 4.95666i 0.400723 + 0.400723i
\(154\) 1.53360i 0.123581i
\(155\) 5.07513 + 5.46948i 0.407644 + 0.439319i
\(156\) −3.00703 −0.240755
\(157\) −2.44491 + 2.44491i −0.195125 + 0.195125i −0.797907 0.602781i \(-0.794059\pi\)
0.602781 + 0.797907i \(0.294059\pi\)
\(158\) 0.271221 + 0.271221i 0.0215772 + 0.0215772i
\(159\) −2.08749 −0.165549
\(160\) 0.0835670 2.23451i 0.00660655 0.176653i
\(161\) −4.39331 + 17.6904i −0.346242 + 1.39420i
\(162\) −0.707107 0.707107i −0.0555556 0.0555556i
\(163\) 0.238521 0.238521i 0.0186824 0.0186824i −0.697704 0.716386i \(-0.745795\pi\)
0.716386 + 0.697704i \(0.245795\pi\)
\(164\) 5.69885i 0.445006i
\(165\) −0.0337191 + 0.901617i −0.00262502 + 0.0701908i
\(166\) 17.4949i 1.35787i
\(167\) 6.43688 + 6.43688i 0.498101 + 0.498101i 0.910846 0.412746i \(-0.135430\pi\)
−0.412746 + 0.910846i \(0.635430\pi\)
\(168\) −2.68754 2.68754i −0.207348 0.207348i
\(169\) 3.95776i 0.304443i
\(170\) −10.6615 11.4899i −0.817698 0.881236i
\(171\) 5.20795i 0.398262i
\(172\) 2.56936 2.56936i 0.195912 0.195912i
\(173\) −5.89468 + 5.89468i −0.448164 + 0.448164i −0.894744 0.446580i \(-0.852642\pi\)
0.446580 + 0.894744i \(0.352642\pi\)
\(174\) 9.42076i 0.714186i
\(175\) −12.3965 14.4039i −0.937086 1.08883i
\(176\) 0.403497i 0.0304147i
\(177\) 9.47547 + 9.47547i 0.712220 + 0.712220i
\(178\) 4.40639 + 4.40639i 0.330273 + 0.330273i
\(179\) 2.77575i 0.207469i 0.994605 + 0.103735i \(0.0330792\pi\)
−0.994605 + 0.103735i \(0.966921\pi\)
\(180\) 1.52094 + 1.63913i 0.113364 + 0.122173i
\(181\) 21.2640i 1.58054i −0.612760 0.790269i \(-0.709941\pi\)
0.612760 0.790269i \(-0.290059\pi\)
\(182\) 8.08153 8.08153i 0.599043 0.599043i
\(183\) −5.31121 5.31121i −0.392616 0.392616i
\(184\) −1.15590 + 4.65445i −0.0852143 + 0.343130i
\(185\) 6.86145 + 0.256608i 0.504464 + 0.0188662i
\(186\) 3.33683 0.244668
\(187\) −2.00000 2.00000i −0.146254 0.146254i
\(188\) −8.64413 + 8.64413i −0.630438 + 0.630438i
\(189\) 3.80076 0.276465
\(190\) −0.435213 + 11.6372i −0.0315737 + 0.844251i
\(191\) 15.5937i 1.12832i 0.825666 + 0.564160i \(0.190800\pi\)
−0.825666 + 0.564160i \(0.809200\pi\)
\(192\) −0.707107 0.707107i −0.0510310 0.0510310i
\(193\) −6.99660 + 6.99660i −0.503626 + 0.503626i −0.912563 0.408937i \(-0.865900\pi\)
0.408937 + 0.912563i \(0.365900\pi\)
\(194\) 11.6762 0.838301
\(195\) −4.92890 + 4.57353i −0.352966 + 0.327517i
\(196\) 7.44578 0.531841
\(197\) 4.96503 + 4.96503i 0.353744 + 0.353744i 0.861501 0.507757i \(-0.169525\pi\)
−0.507757 + 0.861501i \(0.669525\pi\)
\(198\) 0.285316 + 0.285316i 0.0202765 + 0.0202765i
\(199\) 13.2209 0.937202 0.468601 0.883410i \(-0.344758\pi\)
0.468601 + 0.883410i \(0.344758\pi\)
\(200\) −3.26158 3.78974i −0.230629 0.267975i
\(201\) 6.51606i 0.459608i
\(202\) −5.00944 5.00944i −0.352463 0.352463i
\(203\) 25.3187 + 25.3187i 1.77702 + 1.77702i
\(204\) −7.00978 −0.490783
\(205\) 8.66763 + 9.34113i 0.605374 + 0.652413i
\(206\) 9.71622i 0.676961i
\(207\) −2.47384 4.10854i −0.171944 0.285563i
\(208\) 2.12629 2.12629i 0.147432 0.147432i
\(209\) 2.10139i 0.145356i
\(210\) −8.49282 0.317618i −0.586060 0.0219177i
\(211\) 14.3412 0.987286 0.493643 0.869665i \(-0.335665\pi\)
0.493643 + 0.869665i \(0.335665\pi\)
\(212\) 1.47608 1.47608i 0.101377 0.101377i
\(213\) −3.85572 + 3.85572i −0.264189 + 0.264189i
\(214\) −4.44997 −0.304194
\(215\) 0.303651 8.11936i 0.0207088 0.553736i
\(216\) 1.00000 0.0680414
\(217\) −8.96787 + 8.96787i −0.608779 + 0.608779i
\(218\) −8.97323 8.97323i −0.607744 0.607744i
\(219\) 1.50154i 0.101465i
\(220\) −0.613696 0.661382i −0.0413754 0.0445904i
\(221\) 21.0786i 1.41790i
\(222\) 2.17130 2.17130i 0.145728 0.145728i
\(223\) −10.4795 + 10.4795i −0.701757 + 0.701757i −0.964788 0.263030i \(-0.915278\pi\)
0.263030 + 0.964788i \(0.415278\pi\)
\(224\) 3.80076 0.253949
\(225\) 4.98603 + 0.373462i 0.332402 + 0.0248975i
\(226\) 12.6784i 0.843356i
\(227\) −0.390578 + 0.390578i −0.0259236 + 0.0259236i −0.719950 0.694026i \(-0.755835\pi\)
0.694026 + 0.719950i \(0.255835\pi\)
\(228\) 3.68258 + 3.68258i 0.243885 + 0.243885i
\(229\) −16.0170 −1.05844 −0.529218 0.848486i \(-0.677515\pi\)
−0.529218 + 0.848486i \(0.677515\pi\)
\(230\) 5.18448 + 9.38729i 0.341855 + 0.618979i
\(231\) −1.53360 −0.100903
\(232\) 6.66148 + 6.66148i 0.437348 + 0.437348i
\(233\) −13.0826 + 13.0826i −0.857070 + 0.857070i −0.990992 0.133922i \(-0.957243\pi\)
0.133922 + 0.990992i \(0.457243\pi\)
\(234\) 3.00703i 0.196576i
\(235\) −1.02158 + 27.3161i −0.0666404 + 1.78190i
\(236\) −13.4003 −0.872288
\(237\) 0.271221 0.271221i 0.0176177 0.0176177i
\(238\) 18.8391 18.8391i 1.22116 1.22116i
\(239\) 14.8384i 0.959816i −0.877319 0.479908i \(-0.840670\pi\)
0.877319 0.479908i \(-0.159330\pi\)
\(240\) −2.23451 0.0835670i −0.144237 0.00539423i
\(241\) 9.52147i 0.613332i −0.951817 0.306666i \(-0.900787\pi\)
0.951817 0.306666i \(-0.0992135\pi\)
\(242\) 7.66305 + 7.66305i 0.492600 + 0.492600i
\(243\) −0.707107 + 0.707107i −0.0453609 + 0.0453609i
\(244\) 7.51118 0.480854
\(245\) 12.2046 11.3246i 0.779721 0.723503i
\(246\) 5.69885 0.363346
\(247\) −11.0736 + 11.0736i −0.704598 + 0.704598i
\(248\) −2.35950 + 2.35950i −0.149828 + 0.149828i
\(249\) 17.4949 1.10870
\(250\) −11.1101 1.25117i −0.702665 0.0791310i
\(251\) 2.75797i 0.174082i −0.996205 0.0870409i \(-0.972259\pi\)
0.996205 0.0870409i \(-0.0277411\pi\)
\(252\) −2.68754 + 2.68754i −0.169299 + 0.169299i
\(253\) 0.998189 + 1.65778i 0.0627556 + 0.104224i
\(254\) 13.9199i 0.873413i
\(255\) −11.4899 + 10.6615i −0.719526 + 0.667648i
\(256\) 1.00000 0.0625000
\(257\) 4.31593 + 4.31593i 0.269220 + 0.269220i 0.828786 0.559566i \(-0.189032\pi\)
−0.559566 + 0.828786i \(0.689032\pi\)
\(258\) −2.56936 2.56936i −0.159961 0.159961i
\(259\) 11.6709i 0.725196i
\(260\) 0.251289 6.71923i 0.0155843 0.416709i
\(261\) −9.42076 −0.583130
\(262\) −0.773709 0.773709i −0.0477999 0.0477999i
\(263\) 4.09411 + 4.09411i 0.252453 + 0.252453i 0.821976 0.569522i \(-0.192872\pi\)
−0.569522 + 0.821976i \(0.692872\pi\)
\(264\) −0.403497 −0.0248335
\(265\) 0.174445 4.66451i 0.0107161 0.286538i
\(266\) −19.7942 −1.21366
\(267\) 4.40639 4.40639i 0.269667 0.269667i
\(268\) 4.60755 + 4.60755i 0.281451 + 0.281451i
\(269\) 30.5379i 1.86193i −0.365111 0.930964i \(-0.618969\pi\)
0.365111 0.930964i \(-0.381031\pi\)
\(270\) 1.63913 1.52094i 0.0997540 0.0925617i
\(271\) −14.3414 −0.871178 −0.435589 0.900146i \(-0.643460\pi\)
−0.435589 + 0.900146i \(0.643460\pi\)
\(272\) 4.95666 4.95666i 0.300542 0.300542i
\(273\) −8.08153 8.08153i −0.489116 0.489116i
\(274\) 19.6791 1.18885
\(275\) −2.01185 0.150691i −0.121319 0.00908700i
\(276\) 4.65445 + 1.15590i 0.280165 + 0.0695772i
\(277\) 2.49148 + 2.49148i 0.149698 + 0.149698i 0.777983 0.628285i \(-0.216243\pi\)
−0.628285 + 0.777983i \(0.716243\pi\)
\(278\) 14.0107 14.0107i 0.840304 0.840304i
\(279\) 3.33683i 0.199771i
\(280\) 6.22992 5.78074i 0.372309 0.345465i
\(281\) 24.3745i 1.45406i 0.686604 + 0.727031i \(0.259100\pi\)
−0.686604 + 0.727031i \(0.740900\pi\)
\(282\) 8.64413 + 8.64413i 0.514751 + 0.514751i
\(283\) 1.55632 + 1.55632i 0.0925135 + 0.0925135i 0.751849 0.659335i \(-0.229162\pi\)
−0.659335 + 0.751849i \(0.729162\pi\)
\(284\) 5.45281i 0.323565i
\(285\) 11.6372 + 0.435213i 0.689328 + 0.0257798i
\(286\) 1.21333i 0.0717457i
\(287\) −15.3159 + 15.3159i −0.904070 + 0.904070i
\(288\) −0.707107 + 0.707107i −0.0416667 + 0.0416667i
\(289\) 32.1370i 1.89041i
\(290\) 21.0507 + 0.787264i 1.23614 + 0.0462298i
\(291\) 11.6762i 0.684470i
\(292\) 1.06175 + 1.06175i 0.0621343 + 0.0621343i
\(293\) −16.6999 16.6999i −0.975619 0.975619i 0.0240909 0.999710i \(-0.492331\pi\)
−0.999710 + 0.0240909i \(0.992331\pi\)
\(294\) 7.44578i 0.434247i
\(295\) −21.9648 + 20.3812i −1.27884 + 1.18664i
\(296\) 3.07068i 0.178480i
\(297\) 0.285316 0.285316i 0.0165557 0.0165557i
\(298\) −7.87934 7.87934i −0.456438 0.456438i
\(299\) −3.47584 + 13.9961i −0.201013 + 0.809414i
\(300\) −3.78974 + 3.26158i −0.218800 + 0.188307i
\(301\) 13.8105 0.796026
\(302\) 14.1176 + 14.1176i 0.812375 + 0.812375i
\(303\) −5.00944 + 5.00944i −0.287785 + 0.287785i
\(304\) −5.20795 −0.298697
\(305\) 12.3118 11.4241i 0.704970 0.654141i
\(306\) 7.00978i 0.400723i
\(307\) 2.34796 + 2.34796i 0.134005 + 0.134005i 0.770928 0.636923i \(-0.219793\pi\)
−0.636923 + 0.770928i \(0.719793\pi\)
\(308\) 1.08442 1.08442i 0.0617903 0.0617903i
\(309\) −9.71622 −0.552737
\(310\) −0.278849 + 7.45617i −0.0158376 + 0.423482i
\(311\) 12.8558 0.728988 0.364494 0.931206i \(-0.381242\pi\)
0.364494 + 0.931206i \(0.381242\pi\)
\(312\) −2.12629 2.12629i −0.120378 0.120378i
\(313\) −3.38173 3.38173i −0.191147 0.191147i 0.605045 0.796192i \(-0.293155\pi\)
−0.796192 + 0.605045i \(0.793155\pi\)
\(314\) −3.45763 −0.195125
\(315\) −0.317618 + 8.49282i −0.0178958 + 0.478516i
\(316\) 0.383565i 0.0215772i
\(317\) 16.1019 + 16.1019i 0.904375 + 0.904375i 0.995811 0.0914360i \(-0.0291457\pi\)
−0.0914360 + 0.995811i \(0.529146\pi\)
\(318\) −1.47608 1.47608i −0.0827743 0.0827743i
\(319\) 3.80125 0.212829
\(320\) 1.63913 1.52094i 0.0916299 0.0850233i
\(321\) 4.44997i 0.248373i
\(322\) −15.6156 + 9.40249i −0.870222 + 0.523980i
\(323\) −25.8141 + 25.8141i −1.43633 + 1.43633i
\(324\) 1.00000i 0.0555556i
\(325\) −9.80768 11.3959i −0.544032 0.632128i
\(326\) 0.337320 0.0186824
\(327\) −8.97323 + 8.97323i −0.496221 + 0.496221i
\(328\) −4.02970 + 4.02970i −0.222503 + 0.222503i
\(329\) −46.4630 −2.56159
\(330\) −0.661382 + 0.613696i −0.0364079 + 0.0337829i
\(331\) 11.6757 0.641756 0.320878 0.947120i \(-0.396022\pi\)
0.320878 + 0.947120i \(0.396022\pi\)
\(332\) −12.3708 + 12.3708i −0.678934 + 0.678934i
\(333\) −2.17130 2.17130i −0.118986 0.118986i
\(334\) 9.10312i 0.498101i
\(335\) 14.5602 + 0.544528i 0.795508 + 0.0297507i
\(336\) 3.80076i 0.207348i
\(337\) −10.5109 + 10.5109i −0.572567 + 0.572567i −0.932845 0.360278i \(-0.882682\pi\)
0.360278 + 0.932845i \(0.382682\pi\)
\(338\) −2.79856 + 2.79856i −0.152221 + 0.152221i
\(339\) −12.6784 −0.688597
\(340\) 0.585786 15.6634i 0.0317687 0.849467i
\(341\) 1.34640i 0.0729117i
\(342\) 3.68258 3.68258i 0.199131 0.199131i
\(343\) 1.19805 + 1.19805i 0.0646884 + 0.0646884i
\(344\) 3.63363 0.195912
\(345\) 9.38729 5.18448i 0.505395 0.279123i
\(346\) −8.33634 −0.448164
\(347\) −17.9614 17.9614i −0.964218 0.964218i 0.0351639 0.999382i \(-0.488805\pi\)
−0.999382 + 0.0351639i \(0.988805\pi\)
\(348\) 6.66148 6.66148i 0.357093 0.357093i
\(349\) 18.2166i 0.975113i 0.873092 + 0.487556i \(0.162112\pi\)
−0.873092 + 0.487556i \(0.837888\pi\)
\(350\) 1.41944 18.9507i 0.0758722 1.01296i
\(351\) 3.00703 0.160504
\(352\) 0.285316 0.285316i 0.0152074 0.0152074i
\(353\) −13.3386 + 13.3386i −0.709942 + 0.709942i −0.966523 0.256581i \(-0.917404\pi\)
0.256581 + 0.966523i \(0.417404\pi\)
\(354\) 13.4003i 0.712220i
\(355\) −8.29342 8.93784i −0.440169 0.474371i
\(356\) 6.23158i 0.330273i
\(357\) −18.8391 18.8391i −0.997070 0.997070i
\(358\) −1.96275 + 1.96275i −0.103735 + 0.103735i
\(359\) −23.6679 −1.24915 −0.624573 0.780967i \(-0.714727\pi\)
−0.624573 + 0.780967i \(0.714727\pi\)
\(360\) −0.0835670 + 2.23451i −0.00440437 + 0.117769i
\(361\) 8.12277 0.427514
\(362\) 15.0359 15.0359i 0.790269 0.790269i
\(363\) 7.66305 7.66305i 0.402206 0.402206i
\(364\) 11.4290 0.599043
\(365\) 3.35521 + 0.125479i 0.175620 + 0.00656789i
\(366\) 7.51118i 0.392616i
\(367\) −1.82999 + 1.82999i −0.0955248 + 0.0955248i −0.753254 0.657729i \(-0.771517\pi\)
0.657729 + 0.753254i \(0.271517\pi\)
\(368\) −4.10854 + 2.47384i −0.214172 + 0.128958i
\(369\) 5.69885i 0.296670i
\(370\) 4.67033 + 5.03323i 0.242799 + 0.261665i
\(371\) 7.93404 0.411915
\(372\) 2.35950 + 2.35950i 0.122334 + 0.122334i
\(373\) 4.97536 + 4.97536i 0.257615 + 0.257615i 0.824083 0.566469i \(-0.191691\pi\)
−0.566469 + 0.824083i \(0.691691\pi\)
\(374\) 2.82843i 0.146254i
\(375\) −1.25117 + 11.1101i −0.0646102 + 0.573724i
\(376\) −12.2247 −0.630438
\(377\) 20.0313 + 20.0313i 1.03166 + 1.03166i
\(378\) 2.68754 + 2.68754i 0.138232 + 0.138232i
\(379\) −3.53426 −0.181543 −0.0907714 0.995872i \(-0.528933\pi\)
−0.0907714 + 0.995872i \(0.528933\pi\)
\(380\) −8.53649 + 7.92100i −0.437912 + 0.406339i
\(381\) −13.9199 −0.713138
\(382\) −11.0264 + 11.0264i −0.564160 + 0.564160i
\(383\) 13.8129 + 13.8129i 0.705805 + 0.705805i 0.965650 0.259845i \(-0.0836715\pi\)
−0.259845 + 0.965650i \(0.583671\pi\)
\(384\) 1.00000i 0.0510310i
\(385\) 0.128158 3.42683i 0.00653154 0.174647i
\(386\) −9.89468 −0.503626
\(387\) −2.56936 + 2.56936i −0.130608 + 0.130608i
\(388\) 8.25631 + 8.25631i 0.419150 + 0.419150i
\(389\) −6.63285 −0.336299 −0.168149 0.985762i \(-0.553779\pi\)
−0.168149 + 0.985762i \(0.553779\pi\)
\(390\) −6.71923 0.251289i −0.340242 0.0127245i
\(391\) −8.10263 + 32.6267i −0.409768 + 1.65000i
\(392\) 5.26496 + 5.26496i 0.265921 + 0.265921i
\(393\) −0.773709 + 0.773709i −0.0390284 + 0.0390284i
\(394\) 7.02162i 0.353744i
\(395\) 0.583380 + 0.628711i 0.0293530 + 0.0316339i
\(396\) 0.403497i 0.0202765i
\(397\) −6.61498 6.61498i −0.331996 0.331996i 0.521348 0.853344i \(-0.325429\pi\)
−0.853344 + 0.521348i \(0.825429\pi\)
\(398\) 9.34856 + 9.34856i 0.468601 + 0.468601i
\(399\) 19.7942i 0.990948i
\(400\) 0.373462 4.98603i 0.0186731 0.249302i
\(401\) 9.81654i 0.490215i 0.969496 + 0.245107i \(0.0788232\pi\)
−0.969496 + 0.245107i \(0.921177\pi\)
\(402\) 4.60755 4.60755i 0.229804 0.229804i
\(403\) −7.09508 + 7.09508i −0.353431 + 0.353431i
\(404\) 7.08442i 0.352463i
\(405\) −1.52094 1.63913i −0.0755763 0.0814488i
\(406\) 35.8060i 1.77702i
\(407\) 0.876113 + 0.876113i 0.0434273 + 0.0434273i
\(408\) −4.95666 4.95666i −0.245391 0.245391i
\(409\) 1.62998i 0.0805974i −0.999188 0.0402987i \(-0.987169\pi\)
0.999188 0.0402987i \(-0.0128309\pi\)
\(410\) −0.476236 + 12.7341i −0.0235196 + 0.628893i
\(411\) 19.6791i 0.970696i
\(412\) 6.87041 6.87041i 0.338481 0.338481i
\(413\) −36.0140 36.0140i −1.77213 1.77213i
\(414\) 1.15590 4.65445i 0.0568096 0.228754i
\(415\) −1.46200 + 39.0925i −0.0717666 + 1.91897i
\(416\) 3.00703 0.147432
\(417\) −14.0107 14.0107i −0.686105 0.686105i
\(418\) −1.48591 + 1.48591i −0.0726782 + 0.0726782i
\(419\) 11.2744 0.550791 0.275395 0.961331i \(-0.411191\pi\)
0.275395 + 0.961331i \(0.411191\pi\)
\(420\) −5.78074 6.22992i −0.282071 0.303989i
\(421\) 16.1033i 0.784825i 0.919789 + 0.392412i \(0.128359\pi\)
−0.919789 + 0.392412i \(0.871641\pi\)
\(422\) 10.1407 + 10.1407i 0.493643 + 0.493643i
\(423\) 8.64413 8.64413i 0.420292 0.420292i
\(424\) 2.08749 0.101377
\(425\) −22.8630 26.5652i −1.10902 1.28860i
\(426\) −5.45281 −0.264189
\(427\) 20.1866 + 20.1866i 0.976899 + 0.976899i
\(428\) −3.14660 3.14660i −0.152097 0.152097i
\(429\) −1.21333 −0.0585801
\(430\) 5.95597 5.52654i 0.287222 0.266513i
\(431\) 37.5672i 1.80955i 0.425894 + 0.904773i \(0.359960\pi\)
−0.425894 + 0.904773i \(0.640040\pi\)
\(432\) 0.707107 + 0.707107i 0.0340207 + 0.0340207i
\(433\) 19.4771 + 19.4771i 0.936012 + 0.936012i 0.998072 0.0620607i \(-0.0197672\pi\)
−0.0620607 + 0.998072i \(0.519767\pi\)
\(434\) −12.6825 −0.608779
\(435\) 0.787264 21.0507i 0.0377464 1.00931i
\(436\) 12.6901i 0.607744i
\(437\) 21.3971 12.8837i 1.02356 0.616309i
\(438\) 1.06175 1.06175i 0.0507324 0.0507324i
\(439\) 27.5197i 1.31344i −0.754133 0.656721i \(-0.771943\pi\)
0.754133 0.656721i \(-0.228057\pi\)
\(440\) 0.0337191 0.901617i 0.00160749 0.0429829i
\(441\) −7.44578 −0.354561
\(442\) 14.9048 14.9048i 0.708951 0.708951i
\(443\) 21.8369 21.8369i 1.03750 1.03750i 0.0382321 0.999269i \(-0.487827\pi\)
0.999269 0.0382321i \(-0.0121726\pi\)
\(444\) 3.07068 0.145728
\(445\) 9.47788 + 10.2143i 0.449295 + 0.484206i
\(446\) −14.8202 −0.701757
\(447\) −7.87934 + 7.87934i −0.372680 + 0.372680i
\(448\) 2.68754 + 2.68754i 0.126974 + 0.126974i
\(449\) 3.81966i 0.180261i 0.995930 + 0.0901306i \(0.0287284\pi\)
−0.995930 + 0.0901306i \(0.971272\pi\)
\(450\) 3.26158 + 3.78974i 0.153752 + 0.178650i
\(451\) 2.29947i 0.108278i
\(452\) 8.96499 8.96499i 0.421678 0.421678i
\(453\) 14.1176 14.1176i 0.663301 0.663301i
\(454\) −0.552361 −0.0259236
\(455\) 18.7336 17.3829i 0.878244 0.814922i
\(456\) 5.20795i 0.243885i
\(457\) 19.1698 19.1698i 0.896726 0.896726i −0.0984194 0.995145i \(-0.531379\pi\)
0.995145 + 0.0984194i \(0.0313787\pi\)
\(458\) −11.3258 11.3258i −0.529218 0.529218i
\(459\) 7.00978 0.327189
\(460\) −2.97183 + 10.3038i −0.138562 + 0.480417i
\(461\) −23.5334 −1.09606 −0.548029 0.836459i \(-0.684622\pi\)
−0.548029 + 0.836459i \(0.684622\pi\)
\(462\) −1.08442 1.08442i −0.0504516 0.0504516i
\(463\) 20.0945 20.0945i 0.933869 0.933869i −0.0640760 0.997945i \(-0.520410\pi\)
0.997945 + 0.0640760i \(0.0204100\pi\)
\(464\) 9.42076i 0.437348i
\(465\) 7.45617 + 0.278849i 0.345771 + 0.0129313i
\(466\) −18.5016 −0.857070
\(467\) 8.34291 8.34291i 0.386064 0.386064i −0.487217 0.873281i \(-0.661988\pi\)
0.873281 + 0.487217i \(0.161988\pi\)
\(468\) −2.12629 + 2.12629i −0.0982879 + 0.0982879i
\(469\) 24.7660i 1.14359i
\(470\) −20.0377 + 18.5930i −0.924272 + 0.857631i
\(471\) 3.45763i 0.159319i
\(472\) −9.47547 9.47547i −0.436144 0.436144i
\(473\) 1.03673 1.03673i 0.0476689 0.0476689i
\(474\) 0.383565 0.0176177
\(475\) −1.94497 + 25.9670i −0.0892414 + 1.19145i
\(476\) 26.6425 1.22116
\(477\) −1.47608 + 1.47608i −0.0675849 + 0.0675849i
\(478\) 10.4923 10.4923i 0.479908 0.479908i
\(479\) 21.0887 0.963565 0.481783 0.876291i \(-0.339989\pi\)
0.481783 + 0.876291i \(0.339989\pi\)
\(480\) −1.52094 1.63913i −0.0694213 0.0748155i
\(481\) 9.23364i 0.421018i
\(482\) 6.73270 6.73270i 0.306666 0.306666i
\(483\) 9.40249 + 15.6156i 0.427828 + 0.710533i
\(484\) 10.8372i 0.492600i
\(485\) 26.0905 + 0.975743i 1.18471 + 0.0443062i
\(486\) −1.00000 −0.0453609
\(487\) −0.859666 0.859666i −0.0389552 0.0389552i 0.687361 0.726316i \(-0.258769\pi\)
−0.726316 + 0.687361i \(0.758769\pi\)
\(488\) 5.31121 + 5.31121i 0.240427 + 0.240427i
\(489\) 0.337320i 0.0152541i
\(490\) 16.6376 + 0.622221i 0.751612 + 0.0281091i
\(491\) −27.6182 −1.24639 −0.623197 0.782065i \(-0.714166\pi\)
−0.623197 + 0.782065i \(0.714166\pi\)
\(492\) 4.02970 + 4.02970i 0.181673 + 0.181673i
\(493\) 46.6955 + 46.6955i 2.10306 + 2.10306i
\(494\) −15.6605 −0.704598
\(495\) 0.613696 + 0.661382i 0.0275836 + 0.0297269i
\(496\) −3.33683 −0.149828
\(497\) 14.6547 14.6547i 0.657351 0.657351i
\(498\) 12.3708 + 12.3708i 0.554348 + 0.554348i
\(499\) 18.6771i 0.836101i 0.908424 + 0.418051i \(0.137287\pi\)
−0.908424 + 0.418051i \(0.862713\pi\)
\(500\) −6.97132 8.74075i −0.311767 0.390898i
\(501\) 9.10312 0.406697
\(502\) 1.95018 1.95018i 0.0870409 0.0870409i
\(503\) −2.24840 2.24840i −0.100251 0.100251i 0.655202 0.755453i \(-0.272583\pi\)
−0.755453 + 0.655202i \(0.772583\pi\)
\(504\) −3.80076 −0.169299
\(505\) −10.7750 11.6122i −0.479481 0.516738i
\(506\) −0.466404 + 1.87806i −0.0207342 + 0.0834898i
\(507\) 2.79856 + 2.79856i 0.124288 + 0.124288i
\(508\) 9.84286 9.84286i 0.436706 0.436706i
\(509\) 10.9101i 0.483582i −0.970328 0.241791i \(-0.922265\pi\)
0.970328 0.241791i \(-0.0777348\pi\)
\(510\) −15.6634 0.585786i −0.693587 0.0259391i
\(511\) 5.70700i 0.252463i
\(512\) 0.707107 + 0.707107i 0.0312500 + 0.0312500i
\(513\) −3.68258 3.68258i −0.162590 0.162590i
\(514\) 6.10364i 0.269220i
\(515\) 0.811956 21.7110i 0.0357790 0.956699i
\(516\) 3.63363i 0.159961i
\(517\) −3.48788 + 3.48788i −0.153397 + 0.153397i
\(518\) −8.25259 + 8.25259i −0.362598 + 0.362598i
\(519\) 8.33634i 0.365925i
\(520\) 4.92890 4.57353i 0.216147 0.200562i
\(521\) 31.7519i 1.39108i −0.718489 0.695539i \(-0.755166\pi\)
0.718489 0.695539i \(-0.244834\pi\)
\(522\) −6.66148 6.66148i −0.291565 0.291565i
\(523\) −17.6479 17.6479i −0.771687 0.771687i 0.206714 0.978401i \(-0.433723\pi\)
−0.978401 + 0.206714i \(0.933723\pi\)
\(524\) 1.09419i 0.0477999i
\(525\) −18.9507 1.41944i −0.827077 0.0619494i
\(526\) 5.78994i 0.252453i
\(527\) −16.5395 + 16.5395i −0.720474 + 0.720474i
\(528\) −0.285316 0.285316i −0.0124168 0.0124168i
\(529\) 10.7602 20.3278i 0.467834 0.883816i
\(530\) 3.42165 3.17495i 0.148627 0.137911i
\(531\) 13.4003 0.581525
\(532\) −13.9966 13.9966i −0.606829 0.606829i
\(533\) −12.1174 + 12.1174i −0.524864 + 0.524864i
\(534\) 6.23158 0.269667
\(535\) −9.94348 0.371871i −0.429894 0.0160774i
\(536\) 6.51606i 0.281451i
\(537\) 1.96275 + 1.96275i 0.0846989 + 0.0846989i
\(538\) 21.5936 21.5936i 0.930964 0.930964i
\(539\) 3.00435 0.129407
\(540\) 2.23451 + 0.0835670i 0.0961578 + 0.00359615i
\(541\) 33.4617 1.43863 0.719315 0.694684i \(-0.244456\pi\)
0.719315 + 0.694684i \(0.244456\pi\)
\(542\) −10.1409 10.1409i −0.435589 0.435589i
\(543\) −15.0359 15.0359i −0.645252 0.645252i
\(544\) 7.00978 0.300542
\(545\) −19.3009 20.8006i −0.826758 0.890999i
\(546\) 11.4290i 0.489116i
\(547\) −12.8216 12.8216i −0.548213 0.548213i 0.377711 0.925924i \(-0.376711\pi\)
−0.925924 + 0.377711i \(0.876711\pi\)
\(548\) 13.9152 + 13.9152i 0.594427 + 0.594427i
\(549\) −7.51118 −0.320569
\(550\) −1.31604 1.52915i −0.0561161 0.0652031i
\(551\) 49.0629i 2.09015i
\(552\) 2.47384 + 4.10854i 0.105294 + 0.174871i
\(553\) −1.03085 + 1.03085i −0.0438361 + 0.0438361i
\(554\) 3.52348i 0.149698i
\(555\) 5.03323 4.67033i 0.213649 0.198245i
\(556\) 19.8141 0.840304
\(557\) −14.8590 + 14.8590i −0.629594 + 0.629594i −0.947966 0.318372i \(-0.896864\pi\)
0.318372 + 0.947966i \(0.396864\pi\)
\(558\) 2.35950 2.35950i 0.0998854 0.0998854i
\(559\) 10.9264 0.462139
\(560\) 8.49282 + 0.317618i 0.358887 + 0.0134218i
\(561\) −2.82843 −0.119416
\(562\) −17.2354 + 17.2354i −0.727031 + 0.727031i
\(563\) −2.14137 2.14137i −0.0902478 0.0902478i 0.660542 0.750789i \(-0.270327\pi\)
−0.750789 + 0.660542i \(0.770327\pi\)
\(564\) 12.2247i 0.514751i
\(565\) 1.05950 28.3300i 0.0445734 1.19185i
\(566\) 2.20097i 0.0925135i
\(567\) 2.68754 2.68754i 0.112866 0.112866i
\(568\) 3.85572 3.85572i 0.161782 0.161782i
\(569\) 44.6987 1.87387 0.936934 0.349506i \(-0.113650\pi\)
0.936934 + 0.349506i \(0.113650\pi\)
\(570\) 7.92100 + 8.53649i 0.331774 + 0.357554i
\(571\) 26.7672i 1.12017i 0.828435 + 0.560085i \(0.189232\pi\)
−0.828435 + 0.560085i \(0.810768\pi\)
\(572\) 0.857953 0.857953i 0.0358728 0.0358728i
\(573\) 11.0264 + 11.0264i 0.460635 + 0.460635i
\(574\) −21.6600 −0.904070
\(575\) 10.8003 + 21.4092i 0.450403 + 0.892825i
\(576\) −1.00000 −0.0416667
\(577\) −14.2226 14.2226i −0.592095 0.592095i 0.346102 0.938197i \(-0.387505\pi\)
−0.938197 + 0.346102i \(0.887505\pi\)
\(578\) 22.7243 22.7243i 0.945207 0.945207i
\(579\) 9.89468i 0.411209i
\(580\) 14.3284 + 15.4418i 0.594956 + 0.641186i
\(581\) −66.4940 −2.75863
\(582\) 8.25631 8.25631i 0.342235 0.342235i
\(583\) 0.595593 0.595593i 0.0246669 0.0246669i
\(584\) 1.50154i 0.0621343i
\(585\) −0.251289 + 6.71923i −0.0103895 + 0.277806i
\(586\) 23.6172i 0.975619i
\(587\) −7.01819 7.01819i −0.289672 0.289672i 0.547279 0.836950i \(-0.315664\pi\)
−0.836950 + 0.547279i \(0.815664\pi\)
\(588\) 5.26496 5.26496i 0.217123 0.217123i
\(589\) 17.3781 0.716050
\(590\) −29.9431 1.11983i −1.23274 0.0461025i
\(591\) 7.02162 0.288831
\(592\) −2.17130 + 2.17130i −0.0892398 + 0.0892398i
\(593\) −22.3974 + 22.3974i −0.919752 + 0.919752i −0.997011 0.0772588i \(-0.975383\pi\)
0.0772588 + 0.997011i \(0.475383\pi\)
\(594\) 0.403497 0.0165557
\(595\) 43.6704 40.5217i 1.79031 1.66123i
\(596\) 11.1431i 0.456438i
\(597\) 9.34856 9.34856i 0.382611 0.382611i
\(598\) −12.3545 + 7.43893i −0.505214 + 0.304201i
\(599\) 2.54190i 0.103859i 0.998651 + 0.0519296i \(0.0165371\pi\)
−0.998651 + 0.0519296i \(0.983463\pi\)
\(600\) −4.98603 0.373462i −0.203554 0.0152465i
\(601\) −15.8155 −0.645130 −0.322565 0.946547i \(-0.604545\pi\)
−0.322565 + 0.946547i \(0.604545\pi\)
\(602\) 9.76553 + 9.76553i 0.398013 + 0.398013i
\(603\) −4.60755 4.60755i −0.187634 0.187634i
\(604\) 19.9653i 0.812375i
\(605\) 16.4828 + 17.7635i 0.670119 + 0.722189i
\(606\) −7.08442 −0.287785
\(607\) −3.60929 3.60929i −0.146497 0.146497i 0.630054 0.776551i \(-0.283033\pi\)
−0.776551 + 0.630054i \(0.783033\pi\)
\(608\) −3.68258 3.68258i −0.149348 0.149348i
\(609\) 35.8060 1.45093
\(610\) 16.7838 + 0.627687i 0.679556 + 0.0254143i
\(611\) −36.7599 −1.48715
\(612\) −4.95666 + 4.95666i −0.200361 + 0.200361i
\(613\) −14.0673 14.0673i −0.568173 0.568173i 0.363444 0.931616i \(-0.381601\pi\)
−0.931616 + 0.363444i \(0.881601\pi\)
\(614\) 3.32051i 0.134005i
\(615\) 12.7341 + 0.476236i 0.513489 + 0.0192037i
\(616\) 1.53360 0.0617903
\(617\) −31.3443 + 31.3443i −1.26187 + 1.26187i −0.311688 + 0.950185i \(0.600894\pi\)
−0.950185 + 0.311688i \(0.899106\pi\)
\(618\) −6.87041 6.87041i −0.276368 0.276368i
\(619\) 20.0495 0.805857 0.402928 0.915232i \(-0.367992\pi\)
0.402928 + 0.915232i \(0.367992\pi\)
\(620\) −5.46948 + 5.07513i −0.219660 + 0.203822i
\(621\) −4.65445 1.15590i −0.186777 0.0463848i
\(622\) 9.09045 + 9.09045i 0.364494 + 0.364494i
\(623\) −16.7476 + 16.7476i −0.670980 + 0.670980i
\(624\) 3.00703i 0.120378i
\(625\) −24.7211 3.72419i −0.988842 0.148967i
\(626\) 4.78249i 0.191147i
\(627\) 1.48591 + 1.48591i 0.0593415 + 0.0593415i
\(628\) −2.44491 2.44491i −0.0975627 0.0975627i
\(629\) 21.5248i 0.858250i
\(630\) −6.22992 + 5.78074i −0.248206 + 0.230310i
\(631\) 13.0006i 0.517544i −0.965938 0.258772i \(-0.916682\pi\)
0.965938 0.258772i \(-0.0833178\pi\)
\(632\) −0.271221 + 0.271221i −0.0107886 + 0.0107886i
\(633\) 10.1407 10.1407i 0.403058 0.403058i
\(634\) 22.7716i 0.904375i
\(635\) 1.16324 31.1041i 0.0461620 1.23433i
\(636\) 2.08749i 0.0827743i
\(637\) 15.8319 + 15.8319i 0.627283 + 0.627283i
\(638\) 2.68789 + 2.68789i 0.106415 + 0.106415i
\(639\) 5.45281i 0.215710i
\(640\) 2.23451 + 0.0835670i 0.0883266 + 0.00330328i
\(641\) 14.0108i 0.553393i −0.960957 0.276696i \(-0.910760\pi\)
0.960957 0.276696i \(-0.0892396\pi\)
\(642\) −3.14660 + 3.14660i −0.124187 + 0.124187i
\(643\) 10.2908 + 10.2908i 0.405829 + 0.405829i 0.880281 0.474452i \(-0.157354\pi\)
−0.474452 + 0.880281i \(0.657354\pi\)
\(644\) −17.6904 4.39331i −0.697101 0.173121i
\(645\) −5.52654 5.95597i −0.217607 0.234516i
\(646\) −36.5066 −1.43633
\(647\) −11.8108 11.8108i −0.464329 0.464329i 0.435743 0.900071i \(-0.356486\pi\)
−0.900071 + 0.435743i \(0.856486\pi\)
\(648\) 0.707107 0.707107i 0.0277778 0.0277778i
\(649\) −5.40700 −0.212243
\(650\) 1.12301 14.9932i 0.0440482 0.588080i
\(651\) 12.6825i 0.497066i
\(652\) 0.238521 + 0.238521i 0.00934121 + 0.00934121i
\(653\) −7.33870 + 7.33870i −0.287185 + 0.287185i −0.835966 0.548781i \(-0.815092\pi\)
0.548781 + 0.835966i \(0.315092\pi\)
\(654\) −12.6901 −0.496221
\(655\) −1.66420 1.79351i −0.0650257 0.0700784i
\(656\) −5.69885 −0.222503
\(657\) −1.06175 1.06175i −0.0414229 0.0414229i
\(658\) −32.8543 32.8543i −1.28079 1.28079i
\(659\) 29.6115 1.15350 0.576750 0.816921i \(-0.304321\pi\)
0.576750 + 0.816921i \(0.304321\pi\)
\(660\) −0.901617 0.0337191i −0.0350954 0.00131251i
\(661\) 0.177775i 0.00691465i 0.999994 + 0.00345732i \(0.00110050\pi\)
−0.999994 + 0.00345732i \(0.998899\pi\)
\(662\) 8.25599 + 8.25599i 0.320878 + 0.320878i
\(663\) −14.9048 14.9048i −0.578856 0.578856i
\(664\) −17.4949 −0.678934
\(665\) −44.2302 1.65414i −1.71517 0.0641448i
\(666\) 3.07068i 0.118986i
\(667\) −23.3055 38.7055i −0.902392 1.49868i
\(668\) −6.43688 + 6.43688i −0.249050 + 0.249050i
\(669\) 14.8202i 0.572982i
\(670\) 9.91057 + 10.6806i 0.382879 + 0.412629i
\(671\) 3.03074 0.117000
\(672\) 2.68754 2.68754i 0.103674 0.103674i
\(673\) 3.91098 3.91098i 0.150757 0.150757i −0.627699 0.778456i \(-0.716003\pi\)
0.778456 + 0.627699i \(0.216003\pi\)
\(674\) −14.8647 −0.572567
\(675\) 3.78974 3.26158i 0.145867 0.125538i
\(676\) −3.95776 −0.152221
\(677\) 31.1105 31.1105i 1.19567 1.19567i 0.220223 0.975450i \(-0.429322\pi\)
0.975450 0.220223i \(-0.0706784\pi\)
\(678\) −8.96499 8.96499i −0.344299 0.344299i
\(679\) 44.3784i 1.70309i
\(680\) 11.4899 10.6615i 0.440618 0.408849i
\(681\) 0.552361i 0.0211665i
\(682\) −0.952050 + 0.952050i −0.0364559 + 0.0364559i
\(683\) 27.1997 27.1997i 1.04077 1.04077i 0.0416348 0.999133i \(-0.486743\pi\)
0.999133 0.0416348i \(-0.0132566\pi\)
\(684\) 5.20795 0.199131
\(685\) 43.9730 + 1.64452i 1.68012 + 0.0628339i
\(686\) 1.69429i 0.0646884i
\(687\) −11.3258 + 11.3258i −0.432104 + 0.432104i
\(688\) 2.56936 + 2.56936i 0.0979560 + 0.0979560i
\(689\) 6.27715 0.239140
\(690\) 10.3038 + 2.97183i 0.392259 + 0.113136i
\(691\) 31.8947 1.21333 0.606666 0.794957i \(-0.292507\pi\)
0.606666 + 0.794957i \(0.292507\pi\)
\(692\) −5.89468 5.89468i −0.224082 0.224082i
\(693\) −1.08442 + 1.08442i −0.0411936 + 0.0411936i
\(694\) 25.4012i 0.964218i
\(695\) 32.4777 30.1361i 1.23195 1.14313i
\(696\) 9.42076 0.357093
\(697\) −28.2473 + 28.2473i −1.06994 + 1.06994i
\(698\) −12.8811 + 12.8811i −0.487556 + 0.487556i
\(699\) 18.5016i 0.699795i
\(700\) 14.4039 12.3965i 0.544415 0.468543i
\(701\) 39.2405i 1.48209i −0.671454 0.741046i \(-0.734330\pi\)
0.671454 0.741046i \(-0.265670\pi\)
\(702\) 2.12629 + 2.12629i 0.0802518 + 0.0802518i
\(703\) 11.3080 11.3080i 0.426490 0.426490i
\(704\) 0.403497 0.0152074
\(705\) 18.5930 + 20.0377i 0.700253 + 0.754665i
\(706\) −18.8636 −0.709942
\(707\) 19.0397 19.0397i 0.716061 0.716061i
\(708\) −9.47547 + 9.47547i −0.356110 + 0.356110i
\(709\) −19.6493 −0.737944 −0.368972 0.929440i \(-0.620290\pi\)
−0.368972 + 0.929440i \(0.620290\pi\)
\(710\) 0.455675 12.1843i 0.0171012 0.457270i
\(711\) 0.383565i 0.0143848i
\(712\) −4.40639 + 4.40639i −0.165137 + 0.165137i
\(713\) 13.7095 8.25480i 0.513425 0.309145i
\(714\) 26.6425i 0.997070i
\(715\) 0.101394 2.71119i 0.00379193 0.101393i
\(716\) −2.77575 −0.103735
\(717\) −10.4923 10.4923i −0.391843 0.391843i
\(718\) −16.7358 16.7358i −0.624573 0.624573i
\(719\) 42.4908i 1.58464i 0.610105 + 0.792321i \(0.291127\pi\)
−0.610105 + 0.792321i \(0.708873\pi\)
\(720\) −1.63913 + 1.52094i −0.0610866 + 0.0566822i
\(721\) 36.9290 1.37531
\(722\) 5.74366 + 5.74366i 0.213757 + 0.213757i
\(723\) −6.73270 6.73270i −0.250392 0.250392i
\(724\) 21.2640 0.790269
\(725\) 46.9722 + 3.51829i 1.74450 + 0.130666i
\(726\) 10.8372 0.402206
\(727\) 28.3443 28.3443i 1.05123 1.05123i 0.0526167 0.998615i \(-0.483244\pi\)
0.998615 0.0526167i \(-0.0167562\pi\)
\(728\) 8.08153 + 8.08153i 0.299521 + 0.299521i
\(729\) 1.00000i 0.0370370i
\(730\) 2.28376 + 2.46122i 0.0845258 + 0.0910937i
\(731\) 25.4709 0.942076
\(732\) 5.31121 5.31121i 0.196308 0.196308i
\(733\) −35.1881 35.1881i −1.29970 1.29970i −0.928587 0.371114i \(-0.878976\pi\)
−0.371114 0.928587i \(-0.621024\pi\)
\(734\) −2.58800 −0.0955248
\(735\) 0.622221 16.6376i 0.0229510 0.613688i
\(736\) −4.65445 1.15590i −0.171565 0.0426072i
\(737\) 1.85913 + 1.85913i 0.0684821 + 0.0684821i
\(738\) 4.02970 4.02970i 0.148335 0.148335i
\(739\) 7.24476i 0.266503i −0.991082 0.133251i \(-0.957458\pi\)
0.991082 0.133251i \(-0.0425417\pi\)
\(740\) −0.256608 + 6.86145i −0.00943308 + 0.252232i
\(741\) 15.6605i 0.575302i
\(742\) 5.61022 + 5.61022i 0.205957 + 0.205957i
\(743\) −38.2888 38.2888i −1.40468 1.40468i −0.784309 0.620370i \(-0.786983\pi\)
−0.620370 0.784309i \(-0.713017\pi\)
\(744\) 3.33683i 0.122334i
\(745\) −16.9480 18.2649i −0.620926 0.669173i
\(746\) 7.03623i 0.257615i
\(747\) 12.3708 12.3708i 0.452623 0.452623i
\(748\) 2.00000 2.00000i 0.0731272 0.0731272i
\(749\) 16.9133i 0.617997i
\(750\) −8.74075 + 6.97132i −0.319167 + 0.254557i
\(751\) 24.3210i 0.887484i −0.896155 0.443742i \(-0.853651\pi\)
0.896155 0.443742i \(-0.146349\pi\)
\(752\) −8.64413 8.64413i −0.315219 0.315219i
\(753\) −1.95018 1.95018i −0.0710686 0.0710686i
\(754\) 28.3285i 1.03166i
\(755\) 30.3660 + 32.7256i 1.10513 + 1.19101i
\(756\) 3.80076i 0.138232i
\(757\) 26.9257 26.9257i 0.978630 0.978630i −0.0211465 0.999776i \(-0.506732\pi\)
0.999776 + 0.0211465i \(0.00673165\pi\)
\(758\) −2.49910 2.49910i −0.0907714 0.0907714i
\(759\) 1.87806 + 0.466404i 0.0681691 + 0.0169294i
\(760\) −11.6372 0.435213i −0.422126 0.0157868i
\(761\) −6.15795 −0.223226 −0.111613 0.993752i \(-0.535602\pi\)
−0.111613 + 0.993752i \(0.535602\pi\)
\(762\) −9.84286 9.84286i −0.356569 0.356569i
\(763\) 34.1051 34.1051i 1.23469 1.23469i
\(764\) −15.5937 −0.564160
\(765\) −0.585786 + 15.6634i −0.0211792 + 0.566311i
\(766\) 19.5344i 0.705805i
\(767\) −28.4931 28.4931i −1.02882 1.02882i
\(768\) 0.707107 0.707107i 0.0255155 0.0255155i
\(769\) 23.1519 0.834877 0.417439 0.908705i \(-0.362928\pi\)
0.417439 + 0.908705i \(0.362928\pi\)
\(770\) 2.51376 2.33251i 0.0905895 0.0840579i
\(771\) 6.10364 0.219817
\(772\) −6.99660 6.99660i −0.251813 0.251813i
\(773\) 7.51233 + 7.51233i 0.270200 + 0.270200i 0.829181 0.558981i \(-0.188807\pi\)
−0.558981 + 0.829181i \(0.688807\pi\)
\(774\) −3.63363 −0.130608
\(775\) −1.24618 + 16.6375i −0.0447641 + 0.597638i
\(776\) 11.6762i 0.419150i
\(777\) 8.25259 + 8.25259i 0.296060 + 0.296060i
\(778\) −4.69013 4.69013i −0.168149 0.168149i
\(779\) 29.6794 1.06337
\(780\) −4.57353