Properties

Label 450.2.p.e.443.2
Level 450
Weight 2
Character 450.443
Analytic conductor 3.593
Analytic rank 0
Dimension 8
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 450.p (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.59326809096\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\Q(\zeta_{24})\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 443.2
Root \(-0.258819 - 0.965926i\) of \(x^{8} - x^{4} + 1\)
Character \(\chi\) \(=\) 450.443
Dual form 450.2.p.e.257.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.965926 - 0.258819i) q^{2} +(1.22474 - 1.22474i) q^{3} +(0.866025 - 0.500000i) q^{4} +(0.866025 - 1.50000i) q^{6} +(0.328169 + 1.22474i) q^{7} +(0.707107 - 0.707107i) q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+(0.965926 - 0.258819i) q^{2} +(1.22474 - 1.22474i) q^{3} +(0.866025 - 0.500000i) q^{4} +(0.866025 - 1.50000i) q^{6} +(0.328169 + 1.22474i) q^{7} +(0.707107 - 0.707107i) q^{8} -3.00000i q^{9} +(3.00000 + 1.73205i) q^{11} +(0.448288 - 1.67303i) q^{12} +(-0.328169 + 1.22474i) q^{13} +(0.633975 + 1.09808i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-0.776457 - 2.89778i) q^{18} -7.19615i q^{19} +(1.90192 + 1.09808i) q^{21} +(3.34607 + 0.896575i) q^{22} +(-7.91688 - 2.12132i) q^{23} -1.73205i q^{24} +1.26795i q^{26} +(-3.67423 - 3.67423i) q^{27} +(0.896575 + 0.896575i) q^{28} +(-3.63397 + 6.29423i) q^{29} +(5.09808 + 8.83013i) q^{31} +(0.258819 - 0.965926i) q^{32} +(5.79555 - 1.55291i) q^{33} +(-1.50000 - 2.59808i) q^{36} +(-1.55291 + 1.55291i) q^{37} +(-1.86250 - 6.95095i) q^{38} +(1.09808 + 1.90192i) q^{39} +(-1.50000 + 0.866025i) q^{41} +(2.12132 + 0.568406i) q^{42} +(-6.24384 + 1.67303i) q^{43} +3.46410 q^{44} -8.19615 q^{46} +(-5.79555 + 1.55291i) q^{47} +(-0.448288 - 1.67303i) q^{48} +(4.66987 - 2.69615i) q^{49} +(0.328169 + 1.22474i) q^{52} +(-1.55291 + 1.55291i) q^{53} +(-4.50000 - 2.59808i) q^{54} +(1.09808 + 0.633975i) q^{56} +(-8.81345 - 8.81345i) q^{57} +(-1.88108 + 7.02030i) q^{58} +(6.23205 + 10.7942i) q^{59} +(2.00000 - 3.46410i) q^{61} +(7.20977 + 7.20977i) q^{62} +(3.67423 - 0.984508i) q^{63} -1.00000i q^{64} +(5.19615 - 3.00000i) q^{66} +(12.0394 + 3.22595i) q^{67} +(-12.2942 + 7.09808i) q^{69} -10.7321i q^{71} +(-2.12132 - 2.12132i) q^{72} +(3.67423 + 3.67423i) q^{73} +(-1.09808 + 1.90192i) q^{74} +(-3.59808 - 6.23205i) q^{76} +(-1.13681 + 4.24264i) q^{77} +(1.55291 + 1.55291i) q^{78} +(8.66025 + 5.00000i) q^{79} -9.00000 q^{81} +(-1.22474 + 1.22474i) q^{82} +(1.76097 + 6.57201i) q^{83} +2.19615 q^{84} +(-5.59808 + 3.23205i) q^{86} +(3.25813 + 12.1595i) q^{87} +(3.34607 - 0.896575i) q^{88} -8.66025 q^{89} -1.60770 q^{91} +(-7.91688 + 2.12132i) q^{92} +(17.0585 + 4.57081i) q^{93} +(-5.19615 + 3.00000i) q^{94} +(-0.866025 - 1.50000i) q^{96} +(-3.79435 - 14.1607i) q^{97} +(3.81294 - 3.81294i) q^{98} +(5.19615 - 9.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + O(q^{10}) \) \( 8q + 24q^{11} + 12q^{14} + 4q^{16} + 36q^{21} - 36q^{29} + 20q^{31} - 12q^{36} - 12q^{39} - 12q^{41} - 24q^{46} + 72q^{49} - 36q^{54} - 12q^{56} + 36q^{59} + 16q^{61} - 36q^{69} + 12q^{74} - 8q^{76} - 72q^{81} - 24q^{84} - 24q^{86} - 96q^{91} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.965926 0.258819i 0.683013 0.183013i
\(3\) 1.22474 1.22474i 0.707107 0.707107i
\(4\) 0.866025 0.500000i 0.433013 0.250000i
\(5\) 0 0
\(6\) 0.866025 1.50000i 0.353553 0.612372i
\(7\) 0.328169 + 1.22474i 0.124036 + 0.462910i 0.999803 0.0198238i \(-0.00631052\pi\)
−0.875767 + 0.482734i \(0.839644\pi\)
\(8\) 0.707107 0.707107i 0.250000 0.250000i
\(9\) 3.00000i 1.00000i
\(10\) 0 0
\(11\) 3.00000 + 1.73205i 0.904534 + 0.522233i 0.878668 0.477432i \(-0.158432\pi\)
0.0258656 + 0.999665i \(0.491766\pi\)
\(12\) 0.448288 1.67303i 0.129410 0.482963i
\(13\) −0.328169 + 1.22474i −0.0910178 + 0.339683i −0.996386 0.0849451i \(-0.972929\pi\)
0.905368 + 0.424628i \(0.139595\pi\)
\(14\) 0.633975 + 1.09808i 0.169437 + 0.293473i
\(15\) 0 0
\(16\) 0.500000 0.866025i 0.125000 0.216506i
\(17\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(18\) −0.776457 2.89778i −0.183013 0.683013i
\(19\) 7.19615i 1.65091i −0.564467 0.825455i \(-0.690918\pi\)
0.564467 0.825455i \(-0.309082\pi\)
\(20\) 0 0
\(21\) 1.90192 + 1.09808i 0.415034 + 0.239620i
\(22\) 3.34607 + 0.896575i 0.713384 + 0.191151i
\(23\) −7.91688 2.12132i −1.65078 0.442326i −0.690951 0.722902i \(-0.742808\pi\)
−0.959832 + 0.280576i \(0.909475\pi\)
\(24\) 1.73205i 0.353553i
\(25\) 0 0
\(26\) 1.26795i 0.248665i
\(27\) −3.67423 3.67423i −0.707107 0.707107i
\(28\) 0.896575 + 0.896575i 0.169437 + 0.169437i
\(29\) −3.63397 + 6.29423i −0.674812 + 1.16881i 0.301712 + 0.953399i \(0.402442\pi\)
−0.976524 + 0.215410i \(0.930891\pi\)
\(30\) 0 0
\(31\) 5.09808 + 8.83013i 0.915642 + 1.58594i 0.805959 + 0.591971i \(0.201650\pi\)
0.109682 + 0.993967i \(0.465017\pi\)
\(32\) 0.258819 0.965926i 0.0457532 0.170753i
\(33\) 5.79555 1.55291i 1.00888 0.270328i
\(34\) 0 0
\(35\) 0 0
\(36\) −1.50000 2.59808i −0.250000 0.433013i
\(37\) −1.55291 + 1.55291i −0.255298 + 0.255298i −0.823138 0.567841i \(-0.807779\pi\)
0.567841 + 0.823138i \(0.307779\pi\)
\(38\) −1.86250 6.95095i −0.302138 1.12759i
\(39\) 1.09808 + 1.90192i 0.175833 + 0.304552i
\(40\) 0 0
\(41\) −1.50000 + 0.866025i −0.234261 + 0.135250i −0.612536 0.790443i \(-0.709851\pi\)
0.378275 + 0.925693i \(0.376517\pi\)
\(42\) 2.12132 + 0.568406i 0.327327 + 0.0877070i
\(43\) −6.24384 + 1.67303i −0.952177 + 0.255135i −0.701286 0.712880i \(-0.747390\pi\)
−0.250891 + 0.968015i \(0.580724\pi\)
\(44\) 3.46410 0.522233
\(45\) 0 0
\(46\) −8.19615 −1.20846
\(47\) −5.79555 + 1.55291i −0.845369 + 0.226516i −0.655407 0.755276i \(-0.727503\pi\)
−0.189961 + 0.981792i \(0.560836\pi\)
\(48\) −0.448288 1.67303i −0.0647048 0.241481i
\(49\) 4.66987 2.69615i 0.667125 0.385165i
\(50\) 0 0
\(51\) 0 0
\(52\) 0.328169 + 1.22474i 0.0455089 + 0.169842i
\(53\) −1.55291 + 1.55291i −0.213309 + 0.213309i −0.805672 0.592362i \(-0.798195\pi\)
0.592362 + 0.805672i \(0.298195\pi\)
\(54\) −4.50000 2.59808i −0.612372 0.353553i
\(55\) 0 0
\(56\) 1.09808 + 0.633975i 0.146737 + 0.0847184i
\(57\) −8.81345 8.81345i −1.16737 1.16737i
\(58\) −1.88108 + 7.02030i −0.246998 + 0.921811i
\(59\) 6.23205 + 10.7942i 0.811344 + 1.40529i 0.911924 + 0.410360i \(0.134597\pi\)
−0.100580 + 0.994929i \(0.532070\pi\)
\(60\) 0 0
\(61\) 2.00000 3.46410i 0.256074 0.443533i −0.709113 0.705095i \(-0.750904\pi\)
0.965187 + 0.261562i \(0.0842377\pi\)
\(62\) 7.20977 + 7.20977i 0.915642 + 0.915642i
\(63\) 3.67423 0.984508i 0.462910 0.124036i
\(64\) 1.00000i 0.125000i
\(65\) 0 0
\(66\) 5.19615 3.00000i 0.639602 0.369274i
\(67\) 12.0394 + 3.22595i 1.47085 + 0.394112i 0.903221 0.429175i \(-0.141196\pi\)
0.567625 + 0.823287i \(0.307862\pi\)
\(68\) 0 0
\(69\) −12.2942 + 7.09808i −1.48005 + 0.854508i
\(70\) 0 0
\(71\) 10.7321i 1.27366i −0.771004 0.636830i \(-0.780245\pi\)
0.771004 0.636830i \(-0.219755\pi\)
\(72\) −2.12132 2.12132i −0.250000 0.250000i
\(73\) 3.67423 + 3.67423i 0.430037 + 0.430037i 0.888641 0.458604i \(-0.151650\pi\)
−0.458604 + 0.888641i \(0.651650\pi\)
\(74\) −1.09808 + 1.90192i −0.127649 + 0.221094i
\(75\) 0 0
\(76\) −3.59808 6.23205i −0.412728 0.714865i
\(77\) −1.13681 + 4.24264i −0.129552 + 0.483494i
\(78\) 1.55291 + 1.55291i 0.175833 + 0.175833i
\(79\) 8.66025 + 5.00000i 0.974355 + 0.562544i 0.900561 0.434730i \(-0.143156\pi\)
0.0737937 + 0.997274i \(0.476489\pi\)
\(80\) 0 0
\(81\) −9.00000 −1.00000
\(82\) −1.22474 + 1.22474i −0.135250 + 0.135250i
\(83\) 1.76097 + 6.57201i 0.193291 + 0.721372i 0.992703 + 0.120588i \(0.0384781\pi\)
−0.799412 + 0.600784i \(0.794855\pi\)
\(84\) 2.19615 0.239620
\(85\) 0 0
\(86\) −5.59808 + 3.23205i −0.603656 + 0.348521i
\(87\) 3.25813 + 12.1595i 0.349308 + 1.30364i
\(88\) 3.34607 0.896575i 0.356692 0.0955753i
\(89\) −8.66025 −0.917985 −0.458993 0.888440i \(-0.651790\pi\)
−0.458993 + 0.888440i \(0.651790\pi\)
\(90\) 0 0
\(91\) −1.60770 −0.168532
\(92\) −7.91688 + 2.12132i −0.825391 + 0.221163i
\(93\) 17.0585 + 4.57081i 1.76888 + 0.473971i
\(94\) −5.19615 + 3.00000i −0.535942 + 0.309426i
\(95\) 0 0
\(96\) −0.866025 1.50000i −0.0883883 0.153093i
\(97\) −3.79435 14.1607i −0.385258 1.43780i −0.837760 0.546039i \(-0.816135\pi\)
0.452501 0.891764i \(-0.350532\pi\)
\(98\) 3.81294 3.81294i 0.385165 0.385165i
\(99\) 5.19615 9.00000i 0.522233 0.904534i
\(100\) 0 0
\(101\) −9.29423 5.36603i −0.924810 0.533939i −0.0396438 0.999214i \(-0.512622\pi\)
−0.885167 + 0.465274i \(0.845956\pi\)
\(102\) 0 0
\(103\) −2.68973 + 10.0382i −0.265027 + 0.989093i 0.697207 + 0.716869i \(0.254426\pi\)
−0.962234 + 0.272223i \(0.912241\pi\)
\(104\) 0.633975 + 1.09808i 0.0621663 + 0.107675i
\(105\) 0 0
\(106\) −1.09808 + 1.90192i −0.106655 + 0.184731i
\(107\) 0.568406 + 0.568406i 0.0549499 + 0.0549499i 0.734048 0.679098i \(-0.237629\pi\)
−0.679098 + 0.734048i \(0.737629\pi\)
\(108\) −5.01910 1.34486i −0.482963 0.129410i
\(109\) 12.1962i 1.16818i −0.811689 0.584090i \(-0.801452\pi\)
0.811689 0.584090i \(-0.198548\pi\)
\(110\) 0 0
\(111\) 3.80385i 0.361045i
\(112\) 1.22474 + 0.328169i 0.115728 + 0.0310091i
\(113\) −7.14042 1.91327i −0.671714 0.179985i −0.0931872 0.995649i \(-0.529706\pi\)
−0.578527 + 0.815663i \(0.696372\pi\)
\(114\) −10.7942 6.23205i −1.01097 0.583685i
\(115\) 0 0
\(116\) 7.26795i 0.674812i
\(117\) 3.67423 + 0.984508i 0.339683 + 0.0910178i
\(118\) 8.81345 + 8.81345i 0.811344 + 0.811344i
\(119\) 0 0
\(120\) 0 0
\(121\) 0.500000 + 0.866025i 0.0454545 + 0.0787296i
\(122\) 1.03528 3.86370i 0.0937295 0.349803i
\(123\) −0.776457 + 2.89778i −0.0700108 + 0.261284i
\(124\) 8.83013 + 5.09808i 0.792969 + 0.457821i
\(125\) 0 0
\(126\) 3.29423 1.90192i 0.293473 0.169437i
\(127\) −1.55291 + 1.55291i −0.137799 + 0.137799i −0.772641 0.634843i \(-0.781065\pi\)
0.634843 + 0.772641i \(0.281065\pi\)
\(128\) −0.258819 0.965926i −0.0228766 0.0853766i
\(129\) −5.59808 + 9.69615i −0.492883 + 0.853699i
\(130\) 0 0
\(131\) −6.00000 + 3.46410i −0.524222 + 0.302660i −0.738661 0.674078i \(-0.764541\pi\)
0.214438 + 0.976738i \(0.431208\pi\)
\(132\) 4.24264 4.24264i 0.369274 0.369274i
\(133\) 8.81345 2.36156i 0.764223 0.204773i
\(134\) 12.4641 1.07673
\(135\) 0 0
\(136\) 0 0
\(137\) −7.14042 + 1.91327i −0.610047 + 0.163462i −0.550599 0.834770i \(-0.685601\pi\)
−0.0594480 + 0.998231i \(0.518934\pi\)
\(138\) −10.0382 + 10.0382i −0.854508 + 0.854508i
\(139\) −6.92820 + 4.00000i −0.587643 + 0.339276i −0.764165 0.645021i \(-0.776849\pi\)
0.176522 + 0.984297i \(0.443515\pi\)
\(140\) 0 0
\(141\) −5.19615 + 9.00000i −0.437595 + 0.757937i
\(142\) −2.77766 10.3664i −0.233096 0.869926i
\(143\) −3.10583 + 3.10583i −0.259722 + 0.259722i
\(144\) −2.59808 1.50000i −0.216506 0.125000i
\(145\) 0 0
\(146\) 4.50000 + 2.59808i 0.372423 + 0.215018i
\(147\) 2.41730 9.02150i 0.199376 0.744081i
\(148\) −0.568406 + 2.12132i −0.0467227 + 0.174371i
\(149\) −9.00000 15.5885i −0.737309 1.27706i −0.953703 0.300750i \(-0.902763\pi\)
0.216394 0.976306i \(-0.430570\pi\)
\(150\) 0 0
\(151\) 4.00000 6.92820i 0.325515 0.563809i −0.656101 0.754673i \(-0.727796\pi\)
0.981617 + 0.190864i \(0.0611289\pi\)
\(152\) −5.08845 5.08845i −0.412728 0.412728i
\(153\) 0 0
\(154\) 4.39230i 0.353942i
\(155\) 0 0
\(156\) 1.90192 + 1.09808i 0.152276 + 0.0879165i
\(157\) 7.58871 + 2.03339i 0.605645 + 0.162282i 0.548593 0.836089i \(-0.315163\pi\)
0.0570512 + 0.998371i \(0.481830\pi\)
\(158\) 9.65926 + 2.58819i 0.768449 + 0.205905i
\(159\) 3.80385i 0.301665i
\(160\) 0 0
\(161\) 10.3923i 0.819028i
\(162\) −8.69333 + 2.32937i −0.683013 + 0.183013i
\(163\) −14.3688 14.3688i −1.12545 1.12545i −0.990908 0.134541i \(-0.957044\pi\)
−0.134541 0.990908i \(-0.542956\pi\)
\(164\) −0.866025 + 1.50000i −0.0676252 + 0.117130i
\(165\) 0 0
\(166\) 3.40192 + 5.89230i 0.264040 + 0.457332i
\(167\) 1.13681 4.24264i 0.0879692 0.328305i −0.907891 0.419207i \(-0.862308\pi\)
0.995860 + 0.0909015i \(0.0289749\pi\)
\(168\) 2.12132 0.568406i 0.163663 0.0438535i
\(169\) 9.86603 + 5.69615i 0.758925 + 0.438166i
\(170\) 0 0
\(171\) −21.5885 −1.65091
\(172\) −4.57081 + 4.57081i −0.348521 + 0.348521i
\(173\) 1.13681 + 4.24264i 0.0864302 + 0.322562i 0.995581 0.0939047i \(-0.0299349\pi\)
−0.909151 + 0.416467i \(0.863268\pi\)
\(174\) 6.29423 + 10.9019i 0.477164 + 0.826473i
\(175\) 0 0
\(176\) 3.00000 1.73205i 0.226134 0.130558i
\(177\) 20.8528 + 5.58750i 1.56740 + 0.419983i
\(178\) −8.36516 + 2.24144i −0.626995 + 0.168003i
\(179\) 4.85641 0.362985 0.181492 0.983392i \(-0.441907\pi\)
0.181492 + 0.983392i \(0.441907\pi\)
\(180\) 0 0
\(181\) 8.39230 0.623795 0.311898 0.950116i \(-0.399035\pi\)
0.311898 + 0.950116i \(0.399035\pi\)
\(182\) −1.55291 + 0.416102i −0.115110 + 0.0308435i
\(183\) −1.79315 6.69213i −0.132554 0.494697i
\(184\) −7.09808 + 4.09808i −0.523277 + 0.302114i
\(185\) 0 0
\(186\) 17.6603 1.29491
\(187\) 0 0
\(188\) −4.24264 + 4.24264i −0.309426 + 0.309426i
\(189\) 3.29423 5.70577i 0.239620 0.415034i
\(190\) 0 0
\(191\) 3.00000 + 1.73205i 0.217072 + 0.125327i 0.604594 0.796534i \(-0.293335\pi\)
−0.387522 + 0.921861i \(0.626669\pi\)
\(192\) −1.22474 1.22474i −0.0883883 0.0883883i
\(193\) 6.45189 24.0788i 0.464417 1.73323i −0.194396 0.980923i \(-0.562275\pi\)
0.658813 0.752306i \(-0.271059\pi\)
\(194\) −7.33013 12.6962i −0.526272 0.911531i
\(195\) 0 0
\(196\) 2.69615 4.66987i 0.192582 0.333562i
\(197\) −2.68973 2.68973i −0.191635 0.191635i 0.604767 0.796402i \(-0.293266\pi\)
−0.796402 + 0.604767i \(0.793266\pi\)
\(198\) 2.68973 10.0382i 0.191151 0.713384i
\(199\) 0.392305i 0.0278098i 0.999903 + 0.0139049i \(0.00442620\pi\)
−0.999903 + 0.0139049i \(0.995574\pi\)
\(200\) 0 0
\(201\) 18.6962 10.7942i 1.31872 0.761366i
\(202\) −10.3664 2.77766i −0.729375 0.195435i
\(203\) −8.90138 2.38512i −0.624755 0.167403i
\(204\) 0 0
\(205\) 0 0
\(206\) 10.3923i 0.724066i
\(207\) −6.36396 + 23.7506i −0.442326 + 1.65078i
\(208\) 0.896575 + 0.896575i 0.0621663 + 0.0621663i
\(209\) 12.4641 21.5885i 0.862160 1.49330i
\(210\) 0 0
\(211\) 4.59808 + 7.96410i 0.316545 + 0.548271i 0.979765 0.200153i \(-0.0641440\pi\)
−0.663220 + 0.748424i \(0.730811\pi\)
\(212\) −0.568406 + 2.12132i −0.0390383 + 0.145693i
\(213\) −13.1440 13.1440i −0.900614 0.900614i
\(214\) 0.696152 + 0.401924i 0.0475880 + 0.0274749i
\(215\) 0 0
\(216\) −5.19615 −0.353553
\(217\) −9.14162 + 9.14162i −0.620574 + 0.620574i
\(218\) −3.15660 11.7806i −0.213792 0.797881i
\(219\) 9.00000 0.608164
\(220\) 0 0
\(221\) 0 0
\(222\) 0.984508 + 3.67423i 0.0660759 + 0.246598i
\(223\) 9.14162 2.44949i 0.612168 0.164030i 0.0606032 0.998162i \(-0.480698\pi\)
0.551565 + 0.834132i \(0.314031\pi\)
\(224\) 1.26795 0.0847184
\(225\) 0 0
\(226\) −7.39230 −0.491729
\(227\) 22.4058 6.00361i 1.48712 0.398473i 0.578358 0.815783i \(-0.303694\pi\)
0.908764 + 0.417310i \(0.137027\pi\)
\(228\) −12.0394 3.22595i −0.797329 0.213644i
\(229\) −14.0263 + 8.09808i −0.926883 + 0.535136i −0.885824 0.464021i \(-0.846406\pi\)
−0.0410583 + 0.999157i \(0.513073\pi\)
\(230\) 0 0
\(231\) 3.80385 + 6.58846i 0.250275 + 0.433489i
\(232\) 1.88108 + 7.02030i 0.123499 + 0.460905i
\(233\) 17.9551 17.9551i 1.17628 1.17628i 0.195590 0.980686i \(-0.437338\pi\)
0.980686 0.195590i \(-0.0626622\pi\)
\(234\) 3.80385 0.248665
\(235\) 0 0
\(236\) 10.7942 + 6.23205i 0.702644 + 0.405672i
\(237\) 16.7303 4.48288i 1.08675 0.291194i
\(238\) 0 0
\(239\) 7.09808 + 12.2942i 0.459136 + 0.795248i 0.998916 0.0465591i \(-0.0148256\pi\)
−0.539779 + 0.841807i \(0.681492\pi\)
\(240\) 0 0
\(241\) 5.69615 9.86603i 0.366921 0.635527i −0.622161 0.782889i \(-0.713745\pi\)
0.989083 + 0.147363i \(0.0470785\pi\)
\(242\) 0.707107 + 0.707107i 0.0454545 + 0.0454545i
\(243\) −11.0227 + 11.0227i −0.707107 + 0.707107i
\(244\) 4.00000i 0.256074i
\(245\) 0 0
\(246\) 3.00000i 0.191273i
\(247\) 8.81345 + 2.36156i 0.560786 + 0.150262i
\(248\) 9.84873 + 2.63896i 0.625395 + 0.167574i
\(249\) 10.2058 + 5.89230i 0.646764 + 0.373410i
\(250\) 0 0
\(251\) 9.00000i 0.568075i −0.958813 0.284037i \(-0.908326\pi\)
0.958813 0.284037i \(-0.0916740\pi\)
\(252\) 2.68973 2.68973i 0.169437 0.169437i
\(253\) −20.0764 20.0764i −1.26219 1.26219i
\(254\) −1.09808 + 1.90192i −0.0688994 + 0.119337i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −1.19256 + 4.45069i −0.0743898 + 0.277627i −0.993094 0.117319i \(-0.962570\pi\)
0.918704 + 0.394946i \(0.129237\pi\)
\(258\) −2.89778 + 10.8147i −0.180408 + 0.673291i
\(259\) −2.41154 1.39230i −0.149846 0.0865136i
\(260\) 0 0
\(261\) 18.8827 + 10.9019i 1.16881 + 0.674812i
\(262\) −4.89898 + 4.89898i −0.302660 + 0.302660i
\(263\) 4.81105 + 17.9551i 0.296662 + 1.10716i 0.939889 + 0.341481i \(0.110929\pi\)
−0.643227 + 0.765676i \(0.722405\pi\)
\(264\) 3.00000 5.19615i 0.184637 0.319801i
\(265\) 0 0
\(266\) 7.90192 4.56218i 0.484498 0.279725i
\(267\) −10.6066 + 10.6066i −0.649113 + 0.649113i
\(268\) 12.0394 3.22595i 0.735423 0.197056i
\(269\) −28.0526 −1.71039 −0.855197 0.518303i \(-0.826564\pi\)
−0.855197 + 0.518303i \(0.826564\pi\)
\(270\) 0 0
\(271\) −4.58846 −0.278729 −0.139364 0.990241i \(-0.544506\pi\)
−0.139364 + 0.990241i \(0.544506\pi\)
\(272\) 0 0
\(273\) −1.96902 + 1.96902i −0.119170 + 0.119170i
\(274\) −6.40192 + 3.69615i −0.386754 + 0.223293i
\(275\) 0 0
\(276\) −7.09808 + 12.2942i −0.427254 + 0.740026i
\(277\) −6.60420 24.6472i −0.396808 1.48091i −0.818679 0.574251i \(-0.805293\pi\)
0.421871 0.906656i \(-0.361373\pi\)
\(278\) −5.65685 + 5.65685i −0.339276 + 0.339276i
\(279\) 26.4904 15.2942i 1.58594 0.915642i
\(280\) 0 0
\(281\) 9.00000 + 5.19615i 0.536895 + 0.309976i 0.743820 0.668380i \(-0.233012\pi\)
−0.206925 + 0.978357i \(0.566345\pi\)
\(282\) −2.68973 + 10.0382i −0.160171 + 0.597766i
\(283\) 2.56961 9.58991i 0.152747 0.570061i −0.846540 0.532325i \(-0.821319\pi\)
0.999288 0.0377364i \(-0.0120147\pi\)
\(284\) −5.36603 9.29423i −0.318415 0.551511i
\(285\) 0 0
\(286\) −2.19615 + 3.80385i −0.129861 + 0.224926i
\(287\) −1.55291 1.55291i −0.0916656 0.0916656i
\(288\) −2.89778 0.776457i −0.170753 0.0457532i
\(289\) 17.0000i 1.00000i
\(290\) 0 0
\(291\) −21.9904 12.6962i −1.28910 0.744262i
\(292\) 5.01910 + 1.34486i 0.293720 + 0.0787022i
\(293\) 13.7124 + 3.67423i 0.801089 + 0.214651i 0.636062 0.771638i \(-0.280562\pi\)
0.165027 + 0.986289i \(0.447229\pi\)
\(294\) 9.33975i 0.544705i
\(295\) 0 0
\(296\) 2.19615i 0.127649i
\(297\) −4.65874 17.3867i −0.270328 1.00888i
\(298\) −12.7279 12.7279i −0.737309 0.737309i
\(299\) 5.19615 9.00000i 0.300501 0.520483i
\(300\) 0 0
\(301\) −4.09808 7.09808i −0.236209 0.409126i
\(302\) 2.07055 7.72741i 0.119147 0.444662i
\(303\) −17.9551 + 4.81105i −1.03149 + 0.276387i
\(304\) −6.23205 3.59808i −0.357433 0.206364i
\(305\) 0 0
\(306\) 0 0
\(307\) −2.44949 + 2.44949i −0.139800 + 0.139800i −0.773543 0.633743i \(-0.781517\pi\)
0.633743 + 0.773543i \(0.281517\pi\)
\(308\) 1.13681 + 4.24264i 0.0647759 + 0.241747i
\(309\) 9.00000 + 15.5885i 0.511992 + 0.886796i
\(310\) 0 0
\(311\) 21.5885 12.4641i 1.22417 0.706774i 0.258365 0.966047i \(-0.416816\pi\)
0.965804 + 0.259273i \(0.0834829\pi\)
\(312\) 2.12132 + 0.568406i 0.120096 + 0.0321797i
\(313\) 3.22595 0.864390i 0.182341 0.0488582i −0.166493 0.986043i \(-0.553244\pi\)
0.348834 + 0.937184i \(0.386578\pi\)
\(314\) 7.85641 0.443363
\(315\) 0 0
\(316\) 10.0000 0.562544
\(317\) 23.7506 6.36396i 1.33397 0.357436i 0.479775 0.877392i \(-0.340718\pi\)
0.854193 + 0.519956i \(0.174052\pi\)
\(318\) 0.984508 + 3.67423i 0.0552085 + 0.206041i
\(319\) −21.8038 + 12.5885i −1.22078 + 0.704818i
\(320\) 0 0
\(321\) 1.39230 0.0777109
\(322\) −2.68973 10.0382i −0.149893 0.559407i
\(323\) 0 0
\(324\) −7.79423 + 4.50000i −0.433013 + 0.250000i
\(325\) 0 0
\(326\) −17.5981 10.1603i −0.974667 0.562724i
\(327\) −14.9372 14.9372i −0.826028 0.826028i
\(328\) −0.448288 + 1.67303i −0.0247525 + 0.0923778i
\(329\) −3.80385 6.58846i −0.209713 0.363233i
\(330\) 0 0
\(331\) −8.79423 + 15.2321i −0.483375 + 0.837229i −0.999818 0.0190922i \(-0.993922\pi\)
0.516443 + 0.856321i \(0.327256\pi\)
\(332\) 4.81105 + 4.81105i 0.264040 + 0.264040i
\(333\) 4.65874 + 4.65874i 0.255298 + 0.255298i
\(334\) 4.39230i 0.240336i
\(335\) 0 0
\(336\) 1.90192 1.09808i 0.103758 0.0599050i
\(337\) −26.5283 7.10823i −1.44509 0.387210i −0.550775 0.834653i \(-0.685668\pi\)
−0.894312 + 0.447443i \(0.852335\pi\)
\(338\) 11.0041 + 2.94855i 0.598545 + 0.160380i
\(339\) −11.0885 + 6.40192i −0.602242 + 0.347705i
\(340\) 0 0
\(341\) 35.3205i 1.91271i
\(342\) −20.8528 + 5.58750i −1.12759 + 0.302138i
\(343\) 11.1106 + 11.1106i 0.599918 + 0.599918i
\(344\) −3.23205 + 5.59808i −0.174261 + 0.301828i
\(345\) 0 0
\(346\) 2.19615 + 3.80385i 0.118066 + 0.204496i
\(347\) 8.48528 31.6675i 0.455514 1.70000i −0.231059 0.972940i \(-0.574219\pi\)
0.686573 0.727061i \(-0.259114\pi\)
\(348\) 8.90138 + 8.90138i 0.477164 + 0.477164i
\(349\) 1.73205 + 1.00000i 0.0927146 + 0.0535288i 0.545640 0.838019i \(-0.316286\pi\)
−0.452926 + 0.891548i \(0.649620\pi\)
\(350\) 0 0
\(351\) 5.70577 3.29423i 0.304552 0.175833i
\(352\) 2.44949 2.44949i 0.130558 0.130558i
\(353\) 3.88229 + 14.4889i 0.206633 + 0.771166i 0.988946 + 0.148279i \(0.0473735\pi\)
−0.782312 + 0.622886i \(0.785960\pi\)
\(354\) 21.5885 1.14741
\(355\) 0 0
\(356\) −7.50000 + 4.33013i −0.397499 + 0.229496i
\(357\) 0 0
\(358\) 4.69093 1.25693i 0.247923 0.0664308i
\(359\) 0.679492 0.0358622 0.0179311 0.999839i \(-0.494292\pi\)
0.0179311 + 0.999839i \(0.494292\pi\)
\(360\) 0 0
\(361\) −32.7846 −1.72551
\(362\) 8.10634 2.17209i 0.426060 0.114162i
\(363\) 1.67303 + 0.448288i 0.0878114 + 0.0235290i
\(364\) −1.39230 + 0.803848i −0.0729766 + 0.0421331i
\(365\) 0 0
\(366\) −3.46410 6.00000i −0.181071 0.313625i
\(367\) 8.24504 + 30.7709i 0.430388 + 1.60623i 0.751868 + 0.659313i \(0.229153\pi\)
−0.321481 + 0.946916i \(0.604181\pi\)
\(368\) −5.79555 + 5.79555i −0.302114 + 0.302114i
\(369\) 2.59808 + 4.50000i 0.135250 + 0.234261i
\(370\) 0 0
\(371\) −2.41154 1.39230i −0.125201 0.0722849i
\(372\) 17.0585 4.57081i 0.884442 0.236985i
\(373\) −2.92996 + 10.9348i −0.151708 + 0.566181i 0.847657 + 0.530545i \(0.178013\pi\)
−0.999365 + 0.0356365i \(0.988654\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −3.00000 + 5.19615i −0.154713 + 0.267971i
\(377\) −6.51626 6.51626i −0.335605 0.335605i
\(378\) 1.70522 6.36396i 0.0877070 0.327327i
\(379\) 20.3923i 1.04748i 0.851877 + 0.523741i \(0.175464\pi\)
−0.851877 + 0.523741i \(0.824536\pi\)
\(380\) 0 0
\(381\) 3.80385i 0.194877i
\(382\) 3.34607 + 0.896575i 0.171200 + 0.0458728i
\(383\) 35.3417 + 9.46979i 1.80588 + 0.483884i 0.994871 0.101152i \(-0.0322529\pi\)
0.811007 + 0.585036i \(0.198920\pi\)
\(384\) −1.50000 0.866025i −0.0765466 0.0441942i
\(385\) 0 0
\(386\) 24.9282i 1.26881i
\(387\) 5.01910 + 18.7315i 0.255135 + 0.952177i
\(388\) −10.3664 10.3664i −0.526272 0.526272i
\(389\) 5.19615 9.00000i 0.263455 0.456318i −0.703702 0.710495i \(-0.748471\pi\)
0.967158 + 0.254177i \(0.0818045\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 1.39563 5.20857i 0.0704900 0.263072i
\(393\) −3.10583 + 11.5911i −0.156668 + 0.584694i
\(394\) −3.29423 1.90192i −0.165961 0.0958175i
\(395\) 0 0
\(396\) 10.3923i 0.522233i
\(397\) −6.03579 + 6.03579i −0.302928 + 0.302928i −0.842158 0.539231i \(-0.818715\pi\)
0.539231 + 0.842158i \(0.318715\pi\)
\(398\) 0.101536 + 0.378937i 0.00508954 + 0.0189944i
\(399\) 7.90192 13.6865i 0.395591 0.685184i
\(400\) 0 0
\(401\) 9.00000 5.19615i 0.449439 0.259483i −0.258154 0.966104i \(-0.583114\pi\)
0.707593 + 0.706620i \(0.249781\pi\)
\(402\) 15.2653 15.2653i 0.761366 0.761366i
\(403\) −12.4877 + 3.34607i −0.622056 + 0.166679i
\(404\) −10.7321 −0.533939
\(405\) 0 0
\(406\) −9.21539 −0.457352
\(407\) −7.34847 + 1.96902i −0.364250 + 0.0976005i
\(408\) 0 0
\(409\) −0.526279 + 0.303848i −0.0260228 + 0.0150243i −0.512955 0.858416i \(-0.671449\pi\)
0.486932 + 0.873440i \(0.338116\pi\)
\(410\) 0 0
\(411\) −6.40192 + 11.0885i −0.315784 + 0.546953i
\(412\) 2.68973 + 10.0382i 0.132513 + 0.494546i
\(413\) −11.1750 + 11.1750i −0.549886 + 0.549886i
\(414\) 24.5885i 1.20846i
\(415\) 0 0
\(416\) 1.09808 + 0.633975i 0.0538376 + 0.0310832i
\(417\) −3.58630 + 13.3843i −0.175622 + 0.655430i
\(418\) 6.45189 24.0788i 0.315572 1.17773i
\(419\) 4.50000 + 7.79423i 0.219839 + 0.380773i 0.954759 0.297382i \(-0.0961133\pi\)
−0.734919 + 0.678155i \(0.762780\pi\)
\(420\) 0 0
\(421\) 4.29423 7.43782i 0.209288 0.362497i −0.742203 0.670176i \(-0.766219\pi\)
0.951490 + 0.307678i \(0.0995521\pi\)
\(422\) 6.50266 + 6.50266i 0.316545 + 0.316545i
\(423\) 4.65874 + 17.3867i 0.226516 + 0.845369i
\(424\) 2.19615i 0.106655i
\(425\) 0 0
\(426\) −16.0981 9.29423i −0.779954 0.450307i
\(427\) 4.89898 + 1.31268i 0.237078 + 0.0635249i
\(428\) 0.776457 + 0.208051i 0.0375315 + 0.0100565i
\(429\) 7.60770i 0.367303i
\(430\) 0 0
\(431\) 3.12436i 0.150495i −0.997165 0.0752475i \(-0.976025\pi\)
0.997165 0.0752475i \(-0.0239747\pi\)
\(432\) −5.01910 + 1.34486i −0.241481 + 0.0647048i
\(433\) 21.8695 + 21.8695i 1.05098 + 1.05098i 0.998629 + 0.0523546i \(0.0166726\pi\)
0.0523546 + 0.998629i \(0.483327\pi\)
\(434\) −6.46410 + 11.1962i −0.310287 + 0.537433i
\(435\) 0 0
\(436\) −6.09808 10.5622i −0.292045 0.505837i
\(437\) −15.2653 + 56.9710i −0.730240 + 2.72529i
\(438\) 8.69333 2.32937i 0.415383 0.111302i
\(439\) −28.2224 16.2942i −1.34698 0.777681i −0.359162 0.933275i \(-0.616937\pi\)
−0.987821 + 0.155594i \(0.950271\pi\)
\(440\) 0 0
\(441\) −8.08846 14.0096i −0.385165 0.667125i
\(442\) 0 0
\(443\) −2.68973 10.0382i −0.127793 0.476929i 0.872131 0.489272i \(-0.162738\pi\)
−0.999924 + 0.0123433i \(0.996071\pi\)
\(444\) 1.90192 + 3.29423i 0.0902613 + 0.156337i
\(445\) 0 0
\(446\) 8.19615 4.73205i 0.388099 0.224069i
\(447\) −30.1146 8.06918i −1.42437 0.381659i
\(448\) 1.22474 0.328169i 0.0578638 0.0155045i
\(449\) −5.87564 −0.277289 −0.138644 0.990342i \(-0.544275\pi\)
−0.138644 + 0.990342i \(0.544275\pi\)
\(450\) 0 0
\(451\) −6.00000 −0.282529
\(452\) −7.14042 + 1.91327i −0.335857 + 0.0899926i
\(453\) −3.58630 13.3843i −0.168499 0.628847i
\(454\) 20.0885 11.5981i 0.942798 0.544325i
\(455\) 0 0
\(456\) −12.4641 −0.583685
\(457\) 0.928761 + 3.46618i 0.0434456 + 0.162141i 0.984240 0.176835i \(-0.0565860\pi\)
−0.940795 + 0.338976i \(0.889919\pi\)
\(458\) −11.4524 + 11.4524i −0.535136 + 0.535136i
\(459\) 0 0
\(460\) 0 0
\(461\) −24.2942 14.0263i −1.13150 0.653269i −0.187185 0.982325i \(-0.559936\pi\)
−0.944310 + 0.329056i \(0.893270\pi\)
\(462\) 5.37945 + 5.37945i 0.250275 + 0.250275i
\(463\) −2.12132 + 7.91688i −0.0985861 + 0.367928i −0.997539 0.0701175i \(-0.977663\pi\)
0.898953 + 0.438046i \(0.144329\pi\)
\(464\) 3.63397 + 6.29423i 0.168703 + 0.292202i
\(465\) 0 0
\(466\) 12.6962 21.9904i 0.588138 1.01868i
\(467\) −15.2653 15.2653i −0.706396 0.706396i 0.259380 0.965775i \(-0.416482\pi\)
−0.965775 + 0.259380i \(0.916482\pi\)
\(468\) 3.67423 0.984508i 0.169842 0.0455089i
\(469\) 15.8038i 0.729754i
\(470\) 0 0
\(471\) 11.7846 6.80385i 0.543006 0.313505i
\(472\) 12.0394 + 3.22595i 0.554158 + 0.148486i
\(473\) −21.6293 5.79555i −0.994517 0.266480i
\(474\) 15.0000 8.66025i 0.688973 0.397779i
\(475\) 0 0
\(476\) 0 0
\(477\) 4.65874 + 4.65874i 0.213309 + 0.213309i
\(478\) 10.0382 + 10.0382i 0.459136 + 0.459136i
\(479\) −10.5622 + 18.2942i −0.482598 + 0.835885i −0.999800 0.0199786i \(-0.993640\pi\)
0.517202 + 0.855863i \(0.326974\pi\)
\(480\) 0 0
\(481\) −1.39230 2.41154i −0.0634836 0.109957i
\(482\) 2.94855 11.0041i 0.134303 0.501224i
\(483\) −12.7279 12.7279i −0.579141 0.579141i
\(484\) 0.866025 + 0.500000i 0.0393648 + 0.0227273i
\(485\) 0 0
\(486\) −7.79423 + 13.5000i −0.353553 + 0.612372i
\(487\) −15.5935 + 15.5935i −0.706610 + 0.706610i −0.965821 0.259211i \(-0.916537\pi\)
0.259211 + 0.965821i \(0.416537\pi\)
\(488\) −1.03528 3.86370i −0.0468648 0.174902i
\(489\) −35.1962 −1.59163
\(490\) 0 0
\(491\) −31.7942 + 18.3564i −1.43485 + 0.828413i −0.997486 0.0708697i \(-0.977423\pi\)
−0.437368 + 0.899283i \(0.644089\pi\)
\(492\) 0.776457 + 2.89778i 0.0350054 + 0.130642i
\(493\) 0 0
\(494\) 9.12436 0.410524
\(495\) 0 0
\(496\) 10.1962 0.457821
\(497\) 13.1440 3.52193i 0.589590 0.157980i
\(498\) 11.3831 + 3.05008i 0.510087 + 0.136677i
\(499\) −16.9641 + 9.79423i −0.759417 + 0.438450i −0.829087 0.559120i \(-0.811139\pi\)
0.0696691 + 0.997570i \(0.477806\pi\)
\(500\) 0 0
\(501\) −3.80385 6.58846i −0.169943 0.294351i
\(502\) −2.32937 8.69333i −0.103965 0.388002i
\(503\) 25.8719 25.8719i 1.15357 1.15357i 0.167742 0.985831i \(-0.446352\pi\)
0.985831 0.167742i \(-0.0536476\pi\)
\(504\) 1.90192 3.29423i 0.0847184 0.146737i
\(505\) 0 0
\(506\) −24.5885 14.1962i −1.09309 0.631096i
\(507\) 19.0597 5.10703i 0.846471 0.226811i
\(508\) −0.568406 + 2.12132i −0.0252189 + 0.0941184i
\(509\) 10.3923 + 18.0000i 0.460631 + 0.797836i 0.998992 0.0448779i \(-0.0142899\pi\)
−0.538362 + 0.842714i \(0.680957\pi\)
\(510\) 0 0
\(511\) −3.29423 + 5.70577i −0.145728 + 0.252408i
\(512\) −0.707107 0.707107i −0.0312500 0.0312500i
\(513\) −26.4404 + 26.4404i −1.16737 + 1.16737i
\(514\) 4.60770i 0.203237i
\(515\) 0 0
\(516\) 11.1962i 0.492883i
\(517\) −20.0764 5.37945i −0.882959 0.236588i
\(518\) −2.68973 0.720710i −0.118180 0.0316662i
\(519\) 6.58846 + 3.80385i 0.289201 + 0.166970i
\(520\) 0 0
\(521\) 38.7846i 1.69918i 0.527440 + 0.849592i \(0.323152\pi\)
−0.527440 + 0.849592i \(0.676848\pi\)
\(522\) 21.0609 + 5.64325i 0.921811 + 0.246998i
\(523\) 14.1929 + 14.1929i 0.620612 + 0.620612i 0.945688 0.325076i \(-0.105390\pi\)
−0.325076 + 0.945688i \(0.605390\pi\)
\(524\) −3.46410 + 6.00000i −0.151330 + 0.262111i
\(525\) 0 0
\(526\) 9.29423 + 16.0981i 0.405248 + 0.701909i
\(527\) 0 0
\(528\) 1.55291 5.79555i 0.0675819 0.252219i
\(529\) 38.2583 + 22.0885i 1.66341 + 0.960368i
\(530\) 0 0
\(531\) 32.3827 18.6962i 1.40529 0.811344i
\(532\) 6.45189 6.45189i 0.279725 0.279725i
\(533\) −0.568406 2.12132i −0.0246204 0.0918846i
\(534\) −7.50000 + 12.9904i −0.324557 + 0.562149i
\(535\) 0 0
\(536\) 10.7942 6.23205i 0.466240 0.269184i
\(537\) 5.94786 5.94786i 0.256669 0.256669i
\(538\) −27.0967 + 7.26054i −1.16822 + 0.313024i
\(539\) 18.6795 0.804583
\(540\) 0 0
\(541\) 12.3923 0.532787 0.266393 0.963864i \(-0.414168\pi\)
0.266393 + 0.963864i \(0.414168\pi\)
\(542\) −4.43211 + 1.18758i −0.190375 + 0.0510109i
\(543\) 10.2784 10.2784i 0.441090 0.441090i
\(544\) 0 0
\(545\) 0 0
\(546\) −1.39230 + 2.41154i −0.0595851 + 0.103205i
\(547\) −5.73981 21.4213i −0.245416 0.915907i −0.973174 0.230072i \(-0.926104\pi\)
0.727757 0.685835i \(-0.240563\pi\)
\(548\) −5.22715 + 5.22715i −0.223293 + 0.223293i
\(549\) −10.3923 6.00000i −0.443533 0.256074i
\(550\) 0 0
\(551\) 45.2942 + 26.1506i 1.92960 + 1.11405i
\(552\) −3.67423 + 13.7124i −0.156386 + 0.583640i
\(553\) −3.28169 + 12.2474i −0.139552 + 0.520814i
\(554\) −12.7583 22.0981i −0.542050 0.938857i
\(555\) 0 0
\(556\) −4.00000 + 6.92820i −0.169638 + 0.293821i
\(557\) −11.5911 11.5911i −0.491131 0.491131i 0.417531 0.908662i \(-0.362895\pi\)
−0.908662 + 0.417531i \(0.862895\pi\)
\(558\) 21.6293 21.6293i 0.915642 0.915642i
\(559\) 8.19615i 0.346660i
\(560\) 0 0
\(561\) 0 0
\(562\) 10.0382 + 2.68973i 0.423436 + 0.113459i
\(563\) −32.4440 8.69333i −1.36735 0.366380i −0.500840 0.865540i \(-0.666975\pi\)
−0.866510 + 0.499160i \(0.833642\pi\)
\(564\) 10.3923i 0.437595i
\(565\) 0 0
\(566\) 9.92820i 0.417314i
\(567\) −2.95352 11.0227i −0.124036 0.462910i
\(568\) −7.58871 7.58871i −0.318415 0.318415i
\(569\) 5.53590 9.58846i 0.232077 0.401969i −0.726342 0.687333i \(-0.758781\pi\)
0.958419 + 0.285364i \(0.0921146\pi\)
\(570\) 0 0
\(571\) −4.40192 7.62436i −0.184215 0.319069i 0.759097 0.650978i \(-0.225641\pi\)
−0.943312 + 0.331908i \(0.892308\pi\)
\(572\) −1.13681 + 4.24264i −0.0475325 + 0.177394i
\(573\) 5.79555 1.55291i 0.242113 0.0648739i
\(574\) −1.90192 1.09808i −0.0793848 0.0458328i
\(575\) 0 0
\(576\) −3.00000 −0.125000
\(577\) 15.9217 15.9217i 0.662828 0.662828i −0.293217 0.956046i \(-0.594726\pi\)
0.956046 + 0.293217i \(0.0947260\pi\)
\(578\) −4.39992 16.4207i −0.183013 0.683013i
\(579\) −21.5885 37.3923i −0.897186 1.55397i
\(580\) 0 0
\(581\) −7.47114 + 4.31347i −0.309955 + 0.178953i
\(582\) −24.5271 6.57201i −1.01668 0.272419i
\(583\) −7.34847 + 1.96902i −0.304342 + 0.0815483i
\(584\) 5.19615 0.215018
\(585\) 0 0
\(586\) 14.1962 0.586438
\(587\) −15.8338 + 4.24264i −0.653529 + 0.175113i −0.570324 0.821420i \(-0.693182\pi\)
−0.0832050 + 0.996532i \(0.526516\pi\)
\(588\) −2.41730 9.02150i −0.0996879 0.372040i
\(589\) 63.5429 36.6865i 2.61824 1.51164i
\(590\) 0 0
\(591\) −6.58846 −0.271013
\(592\) 0.568406 + 2.12132i 0.0233613 + 0.0871857i
\(593\) −14.8492 + 14.8492i −0.609785 + 0.609785i −0.942890 0.333105i \(-0.891904\pi\)
0.333105 + 0.942890i \(0.391904\pi\)
\(594\) −9.00000 15.5885i −0.369274 0.639602i
\(595\) 0 0
\(596\) −15.5885 9.00000i −0.638528 0.368654i
\(597\) 0.480473 + 0.480473i 0.0196645 + 0.0196645i
\(598\) 2.68973 10.0382i 0.109991 0.410492i
\(599\) 5.36603 + 9.29423i 0.219250 + 0.379752i 0.954579 0.297958i \(-0.0963057\pi\)
−0.735329 + 0.677710i \(0.762972\pi\)
\(600\) 0 0
\(601\) −6.39230 + 11.0718i −0.260748 + 0.451628i −0.966441 0.256890i \(-0.917302\pi\)
0.705693 + 0.708518i \(0.250636\pi\)
\(602\) −5.79555 5.79555i −0.236209 0.236209i
\(603\) 9.67784 36.1182i 0.394112 1.47085i
\(604\) 8.00000i 0.325515i
\(605\) 0 0
\(606\) −16.0981 + 9.29423i −0.653940 + 0.377552i
\(607\) 16.8183 + 4.50644i 0.682632 + 0.182911i 0.583438 0.812157i \(-0.301707\pi\)
0.0991937 + 0.995068i \(0.468374\pi\)
\(608\) −6.95095 1.86250i −0.281898 0.0755344i
\(609\) −13.8231 + 7.98076i −0.560140 + 0.323397i
\(610\) 0 0
\(611\) 7.60770i 0.307774i
\(612\) 0 0
\(613\) 2.68973 + 2.68973i 0.108637 + 0.108637i 0.759336 0.650699i \(-0.225524\pi\)
−0.650699 + 0.759336i \(0.725524\pi\)
\(614\) −1.73205 + 3.00000i −0.0698999 + 0.121070i
\(615\) 0 0
\(616\) 2.19615 + 3.80385i 0.0884855 + 0.153261i
\(617\) −7.70882 + 28.7697i −0.310346 + 1.15823i 0.617900 + 0.786257i \(0.287984\pi\)
−0.928245 + 0.371969i \(0.878683\pi\)
\(618\) 12.7279 + 12.7279i 0.511992 + 0.511992i
\(619\) −14.2128 8.20577i −0.571261 0.329818i 0.186392 0.982476i \(-0.440321\pi\)
−0.757653 + 0.652658i \(0.773654\pi\)
\(620\) 0 0
\(621\) 21.2942 + 36.8827i 0.854508 + 1.48005i
\(622\) 17.6269 17.6269i 0.706774 0.706774i
\(623\) −2.84203 10.6066i −0.113864 0.424945i
\(624\) 2.19615 0.0879165
\(625\) 0 0
\(626\) 2.89230 1.66987i 0.115600 0.0667415i
\(627\) −11.1750 41.7057i −0.446287 1.66557i
\(628\) 7.58871 2.03339i 0.302822 0.0811410i
\(629\) 0 0
\(630\) 0 0
\(631\) 40.7846 1.62361 0.811805 0.583929i \(-0.198485\pi\)
0.811805 + 0.583929i \(0.198485\pi\)
\(632\) 9.65926 2.58819i 0.384225 0.102953i
\(633\) 15.3855 + 4.12252i 0.611517 + 0.163856i
\(634\) 21.2942 12.2942i 0.845702 0.488266i
\(635\) 0 0
\(636\) 1.90192 + 3.29423i 0.0754162 + 0.130625i
\(637\) 1.76959 + 6.60420i 0.0701137 + 0.261668i
\(638\) −17.8028 + 17.8028i −0.704818 + 0.704818i
\(639\) −32.1962 −1.27366
\(640\) 0 0
\(641\) −0.911543 0.526279i −0.0360038 0.0207868i 0.481890 0.876232i \(-0.339950\pi\)
−0.517894 + 0.855445i \(0.673284\pi\)
\(642\) 1.34486 0.360355i 0.0530775 0.0142221i
\(643\) −4.29839 + 16.0418i −0.169512 + 0.632627i 0.827910 + 0.560861i \(0.189530\pi\)
−0.997422 + 0.0717654i \(0.977137\pi\)
\(644\) −5.19615 9.00000i −0.204757 0.354650i
\(645\) 0 0
\(646\) 0 0
\(647\) 2.68973 + 2.68973i 0.105744 + 0.105744i 0.757999 0.652255i \(-0.226177\pi\)
−0.652255 + 0.757999i \(0.726177\pi\)
\(648\) −6.36396 + 6.36396i −0.250000 + 0.250000i
\(649\) 43.1769i 1.69484i
\(650\) 0 0
\(651\) 22.3923i 0.877624i
\(652\) −19.6281 5.25933i −0.768696 0.205971i
\(653\) 2.12132 + 0.568406i 0.0830137 + 0.0222434i 0.300087 0.953912i \(-0.402984\pi\)
−0.217073 + 0.976155i \(0.569651\pi\)
\(654\) −18.2942 10.5622i −0.715361 0.413014i
\(655\) 0 0
\(656\) 1.73205i 0.0676252i
\(657\) 11.0227 11.0227i 0.430037 0.430037i
\(658\) −5.37945 5.37945i −0.209713 0.209713i
\(659\) 11.0885 19.2058i 0.431945 0.748151i −0.565096 0.825025i \(-0.691161\pi\)
0.997041 + 0.0768747i \(0.0244941\pi\)
\(660\) 0 0
\(661\) −11.5885 20.0718i −0.450739 0.780702i 0.547693 0.836679i \(-0.315506\pi\)
−0.998432 + 0.0559768i \(0.982173\pi\)
\(662\) −4.55223 + 16.9891i −0.176927 + 0.660302i
\(663\) 0 0
\(664\) 5.89230 + 3.40192i 0.228666 + 0.132020i
\(665\) 0 0
\(666\) 5.70577 + 3.29423i 0.221094 + 0.127649i
\(667\) 42.1218 42.1218i 1.63096 1.63096i
\(668\) −1.13681 4.24264i −0.0439846 0.164153i
\(669\) 8.19615 14.1962i 0.316882 0.548855i
\(670\) 0 0
\(671\) 12.0000 6.92820i 0.463255 0.267460i
\(672\) 1.55291 1.55291i 0.0599050 0.0599050i
\(673\) 1.55291 0.416102i 0.0598604 0.0160396i −0.228765 0.973482i \(-0.573469\pi\)
0.288625 + 0.957442i \(0.406802\pi\)
\(674\) −27.4641 −1.05788
\(675\) 0 0
\(676\) 11.3923 0.438166
\(677\) −6.36396 + 1.70522i −0.244587 + 0.0655369i −0.379030 0.925384i \(-0.623742\pi\)
0.134443 + 0.990921i \(0.457076\pi\)
\(678\) −9.05369 + 9.05369i −0.347705 + 0.347705i
\(679\) 16.0981 9.29423i 0.617787 0.356680i
\(680\) 0 0
\(681\) 20.0885 34.7942i 0.769791 1.33332i
\(682\) 9.14162 + 34.1170i 0.350051 + 1.30641i
\(683\) 27.9933 27.9933i 1.07113 1.07113i 0.0738643 0.997268i \(-0.476467\pi\)
0.997268 0.0738643i \(-0.0235332\pi\)
\(684\) −18.6962 + 10.7942i −0.714865 + 0.412728i
\(685\) 0 0
\(686\) 13.6077 + 7.85641i 0.519544 + 0.299959i
\(687\) −7.26054 + 27.0967i −0.277007 + 1.03380i
\(688\) −1.67303 + 6.24384i −0.0637838 + 0.238044i
\(689\) −1.39230 2.41154i −0.0530426 0.0918725i
\(690\) 0 0
\(691\) −6.20577 + 10.7487i −0.236079 + 0.408900i −0.959586 0.281417i \(-0.909196\pi\)
0.723507 + 0.690317i \(0.242529\pi\)
\(692\) 3.10583 + 3.10583i 0.118066 + 0.118066i
\(693\) 12.7279 + 3.41044i 0.483494 + 0.129552i
\(694\) 32.7846i 1.24449i
\(695\) 0 0
\(696\) 10.9019 + 6.29423i 0.413236 + 0.238582i
\(697\) 0 0
\(698\) 1.93185 + 0.517638i 0.0731217 + 0.0195929i
\(699\) 43.9808i 1.66351i
\(700\) 0 0
\(701\) 21.4641i 0.810688i −0.914164 0.405344i \(-0.867152\pi\)
0.914164 0.405344i \(-0.132848\pi\)
\(702\) 4.65874 4.65874i 0.175833 0.175833i
\(703\) 11.1750 + 11.1750i 0.421473 + 0.421473i
\(704\) 1.73205 3.00000i 0.0652791 0.113067i
\(705\) 0 0
\(706\) 7.50000 + 12.9904i 0.282266 + 0.488899i
\(707\) 3.52193 13.1440i 0.132456 0.494332i
\(708\) 20.8528 5.58750i 0.783698 0.209991i
\(709\) −22.3468 12.9019i −0.839251 0.484542i 0.0177584 0.999842i \(-0.494347\pi\)
−0.857010 + 0.515300i \(0.827680\pi\)
\(710\) 0 0
\(711\) 15.0000 25.9808i 0.562544 0.974355i
\(712\) −6.12372 + 6.12372i −0.229496 + 0.229496i
\(713\) −21.6293 80.7217i −0.810024 3.02305i
\(714\) 0 0
\(715\) 0 0
\(716\) 4.20577 2.42820i 0.157177 0.0907462i
\(717\) 23.7506 + 6.36396i 0.886983 + 0.237666i
\(718\) 0.656339 0.175865i 0.0244943 0.00656324i
\(719\) 39.1244 1.45909 0.729546 0.683932i \(-0.239731\pi\)
0.729546 + 0.683932i \(0.239731\pi\)
\(720\) 0 0
\(721\) −13.1769 −0.490734
\(722\) −31.6675 + 8.48528i −1.17854 + 0.315789i
\(723\) −5.10703 19.0597i −0.189933 0.708838i
\(724\) 7.26795 4.19615i 0.270111 0.155949i
\(725\) 0 0
\(726\) 1.73205 0.0642824
\(727\) 1.79315 + 6.69213i 0.0665043 + 0.248197i 0.991173 0.132575i \(-0.0423247\pi\)
−0.924669 + 0.380773i \(0.875658\pi\)
\(728\) −1.13681 + 1.13681i −0.0421331 + 0.0421331i
\(729\) 27.0000i 1.00000i
\(730\) 0 0
\(731\) 0 0
\(732\) −4.89898 4.89898i −0.181071 0.181071i
\(733\) −8.90138 + 33.2204i −0.328780 + 1.22702i 0.581677 + 0.813420i \(0.302397\pi\)
−0.910457 + 0.413604i \(0.864270\pi\)
\(734\) 15.9282 + 27.5885i 0.587921 + 1.01831i
\(735\) 0 0
\(736\) −4.09808 + 7.09808i −0.151057 + 0.261639i
\(737\) 30.5307 + 30.5307i 1.12461 + 1.12461i
\(738\) 3.67423 + 3.67423i 0.135250 + 0.135250i
\(739\) 11.5885i 0.426288i −0.977021 0.213144i \(-0.931630\pi\)
0.977021 0.213144i \(-0.0683704\pi\)
\(740\) 0 0
\(741\) 13.6865 7.90192i 0.502787 0.290284i
\(742\) −2.68973 0.720710i −0.0987430 0.0264581i
\(743\) −38.0315 10.1905i −1.39524 0.373853i −0.518606 0.855013i \(-0.673549\pi\)
−0.876633 + 0.481160i \(0.840216\pi\)
\(744\) 15.2942 8.83013i 0.560714 0.323728i
\(745\) 0 0
\(746\) 11.3205i 0.414473i
\(747\) 19.7160 5.28290i 0.721372 0.193291i
\(748\) 0 0
\(749\) −0.509619 + 0.882686i −0.0186211 + 0.0322526i
\(750\) 0 0
\(751\) 10.2942 + 17.8301i 0.375642 + 0.650631i 0.990423 0.138067i \(-0.0440890\pi\)
−0.614781 + 0.788698i \(0.710756\pi\)
\(752\) −1.55291 + 5.79555i −0.0566290 + 0.211342i
\(753\) −11.0227 11.0227i −0.401690 0.401690i
\(754\) −7.98076 4.60770i −0.290642 0.167802i
\(755\) 0 0
\(756\) 6.58846i 0.239620i
\(757\) 10.5187 10.5187i 0.382308 0.382308i −0.489625 0.871933i \(-0.662866\pi\)
0.871933 + 0.489625i \(0.162866\pi\)
\(758\) 5.27792 + 19.6975i 0.191703 + 0.715444i
\(759\) −49.1769 −1.78501
\(760\) 0 0
\(761\) −9.91154 + 5.72243i −0.359293 + 0.207438i −0.668771 0.743469i \(-0.733179\pi\)
0.309478 + 0.950907i \(0.399846\pi\)
\(762\) 0.984508 + 3.67423i 0.0356650 + 0.133103i
\(763\) 14.9372 4.00240i 0.540762 0.144897i
\(764\) 3.46410 0.125327
\(765\) 0 0
\(766\) 36.5885 1.32199
\(767\) −15.2653 + 4.09034i −0.551200 + 0.147693i
\(768\) −1.67303 0.448288i −0.0603704 0.0161762i
\(769\) 28.9186 16.6962i 1.04283 0.602079i 0.122197 0.992506i \(-0.461006\pi\)
0.920634 + 0.390427i \(0.127673\pi\)
\(770\) 0 0
\(771\) 3.99038 + 6.91154i 0.143710 + 0.248913i
\(772\) −6.45189 24.0788i −0.232209 0.866615i
\(773\) 6.51626 6.51626i 0.234374 0.234374i −0.580142 0.814516i \(-0.697003\pi\)
0.814516 + 0.580142i \(0.197003\pi\)
\(774\) 9.69615 + 16.7942i 0.348521 + 0.603656i
\(775\) 0 0
\(776\) −12.6962 7.33013i −0.455765 0.263136i
\(777\) −4.65874 + 1.24831i −0.167131 + 0.0447827i
\(778\) 2.68973 10.0382i 0.0964314 0.359887i
\(779\) 6.23205 + 10.7942i 0.223286 + 0.386743i
\(780\) 0 0
\(781\) 18.5885 32.1962i 0.665147 1.15207i
\(782\) 0 0
\(783\) 36.4785 9.77440i 1.30364 0.349308i
\(784\) 5.39230i 0.192582i
\(785\) 0 0