Properties

Label 735.2.v.a.178.8
Level 735
Weight 2
Character 735.178
Analytic conductor 5.869
Analytic rank 0
Dimension 32
CM no
Inner twists 8

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Newspace parameters

Level: \( N \) \(=\) \( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 735.v (of order \(12\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.86900454856\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 178.8
Character \(\chi\) \(=\) 735.178
Dual form 735.2.v.a.607.8

$q$-expansion

\(f(q)\) \(=\) \(q+(2.54281 + 0.681344i) q^{2} +(0.258819 + 0.965926i) q^{3} +(4.26961 + 2.46506i) q^{4} +(0.678180 - 2.13074i) q^{5} +2.63251i q^{6} +(5.45433 + 5.45433i) q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})\) \(q+(2.54281 + 0.681344i) q^{2} +(0.258819 + 0.965926i) q^{3} +(4.26961 + 2.46506i) q^{4} +(0.678180 - 2.13074i) q^{5} +2.63251i q^{6} +(5.45433 + 5.45433i) q^{8} +(-0.866025 + 0.500000i) q^{9} +(3.17625 - 4.95601i) q^{10} +(0.731395 - 1.26681i) q^{11} +(-1.27601 + 4.76213i) q^{12} +(-0.887844 + 0.887844i) q^{13} +(2.23367 + 0.103594i) q^{15} +(5.22294 + 9.04639i) q^{16} +(-2.87705 + 0.770902i) q^{17} +(-2.54281 + 0.681344i) q^{18} +(-1.97993 - 3.42935i) q^{19} +(8.14798 - 7.42570i) q^{20} +(2.72294 - 2.72294i) q^{22} +(-1.51171 + 5.64178i) q^{23} +(-3.85679 + 6.68016i) q^{24} +(-4.08014 - 2.89006i) q^{25} +(-2.86255 + 1.65269i) q^{26} +(-0.707107 - 0.707107i) q^{27} -5.18572i q^{29} +(5.60921 + 1.78532i) q^{30} +(5.28575 + 3.05173i) q^{31} +(3.12439 + 11.6604i) q^{32} +(1.41295 + 0.378598i) q^{33} -7.84104 q^{34} -4.93012 q^{36} +(-3.08121 - 0.825607i) q^{37} +(-2.69804 - 10.0692i) q^{38} +(-1.08738 - 0.627801i) q^{39} +(15.3208 - 7.92277i) q^{40} +0.769968i q^{41} +(-5.18572 - 5.18572i) q^{43} +(6.24554 - 3.60587i) q^{44} +(0.478051 + 2.18437i) q^{45} +(-7.68800 + 13.3160i) q^{46} +(-3.13699 + 11.7074i) q^{47} +(-7.38635 + 7.38635i) q^{48} +(-8.40592 - 10.1289i) q^{50} +(-1.48927 - 2.57949i) q^{51} +(-5.97934 + 1.60216i) q^{52} +(0.743732 - 0.199282i) q^{53} +(-1.31626 - 2.27982i) q^{54} +(-2.20324 - 2.41754i) q^{55} +(2.80005 - 2.80005i) q^{57} +(3.53326 - 13.1863i) q^{58} +(-1.59816 + 2.76810i) q^{59} +(9.28153 + 5.94843i) q^{60} +(1.23031 - 0.710320i) q^{61} +(11.3614 + 11.3614i) q^{62} +10.8872i q^{64} +(1.28965 + 2.49389i) q^{65} +(3.33490 + 1.92541i) q^{66} +(-2.17058 - 8.10070i) q^{67} +(-14.1842 - 3.80064i) q^{68} -5.84081 q^{69} +7.62611 q^{71} +(-7.45075 - 1.99642i) q^{72} +(-2.49402 - 9.30780i) q^{73} +(-7.27241 - 4.19873i) q^{74} +(1.73556 - 4.68912i) q^{75} -19.5226i q^{76} +(-2.33726 - 2.33726i) q^{78} +(-3.91469 + 2.26015i) q^{79} +(22.8176 - 4.99366i) q^{80} +(0.500000 - 0.866025i) q^{81} +(-0.524613 + 1.95788i) q^{82} +(6.75794 - 6.75794i) q^{83} +(-0.308559 + 6.65306i) q^{85} +(-9.65306 - 16.7196i) q^{86} +(5.00903 - 1.34216i) q^{87} +(10.8989 - 2.92035i) q^{88} +(0.599954 + 1.03915i) q^{89} +(-0.272713 + 5.88016i) q^{90} +(-20.3618 + 20.3618i) q^{92} +(-1.57969 + 5.89549i) q^{93} +(-15.9535 + 27.6323i) q^{94} +(-8.64982 + 1.89302i) q^{95} +(-10.4544 + 6.03586i) q^{96} +(8.68829 + 8.68829i) q^{97} +1.46279i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 48q^{8} + O(q^{10}) \) \( 32q + 48q^{8} + 16q^{11} + 16q^{15} + 48q^{16} - 32q^{22} + 40q^{23} + 8q^{30} - 48q^{32} - 32q^{36} - 32q^{37} - 32q^{43} - 64q^{46} - 144q^{50} + 16q^{51} - 24q^{53} + 16q^{57} - 32q^{58} - 40q^{60} - 40q^{65} + 32q^{67} + 128q^{71} - 24q^{72} - 16q^{78} + 16q^{81} + 96q^{85} - 64q^{86} + 64q^{88} - 80q^{92} - 24q^{93} + 72q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/735\mathbb{Z}\right)^\times\).

\(n\) \(346\) \(442\) \(491\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{3}{4}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.54281 + 0.681344i 1.79804 + 0.481783i 0.993669 0.112345i \(-0.0358361\pi\)
0.804370 + 0.594128i \(0.202503\pi\)
\(3\) 0.258819 + 0.965926i 0.149429 + 0.557678i
\(4\) 4.26961 + 2.46506i 2.13481 + 1.23253i
\(5\) 0.678180 2.13074i 0.303291 0.952898i
\(6\) 2.63251i 1.07472i
\(7\) 0 0
\(8\) 5.45433 + 5.45433i 1.92840 + 1.92840i
\(9\) −0.866025 + 0.500000i −0.288675 + 0.166667i
\(10\) 3.17625 4.95601i 1.00442 1.56723i
\(11\) 0.731395 1.26681i 0.220524 0.381958i −0.734443 0.678670i \(-0.762557\pi\)
0.954967 + 0.296712i \(0.0958900\pi\)
\(12\) −1.27601 + 4.76213i −0.368352 + 1.37471i
\(13\) −0.887844 + 0.887844i −0.246244 + 0.246244i −0.819427 0.573183i \(-0.805708\pi\)
0.573183 + 0.819427i \(0.305708\pi\)
\(14\) 0 0
\(15\) 2.23367 + 0.103594i 0.576730 + 0.0267479i
\(16\) 5.22294 + 9.04639i 1.30573 + 2.26160i
\(17\) −2.87705 + 0.770902i −0.697786 + 0.186971i −0.590239 0.807229i \(-0.700966\pi\)
−0.107547 + 0.994200i \(0.534300\pi\)
\(18\) −2.54281 + 0.681344i −0.599347 + 0.160594i
\(19\) −1.97993 3.42935i −0.454228 0.786746i 0.544415 0.838816i \(-0.316752\pi\)
−0.998643 + 0.0520695i \(0.983418\pi\)
\(20\) 8.14798 7.42570i 1.82194 1.66044i
\(21\) 0 0
\(22\) 2.72294 2.72294i 0.580532 0.580532i
\(23\) −1.51171 + 5.64178i −0.315214 + 1.17639i 0.608577 + 0.793495i \(0.291741\pi\)
−0.923790 + 0.382898i \(0.874926\pi\)
\(24\) −3.85679 + 6.68016i −0.787265 + 1.36358i
\(25\) −4.08014 2.89006i −0.816029 0.578011i
\(26\) −2.86255 + 1.65269i −0.561392 + 0.324120i
\(27\) −0.707107 0.707107i −0.136083 0.136083i
\(28\) 0 0
\(29\) 5.18572i 0.962965i −0.876456 0.481482i \(-0.840099\pi\)
0.876456 0.481482i \(-0.159901\pi\)
\(30\) 5.60921 + 1.78532i 1.02410 + 0.325953i
\(31\) 5.28575 + 3.05173i 0.949349 + 0.548107i 0.892879 0.450297i \(-0.148682\pi\)
0.0564703 + 0.998404i \(0.482015\pi\)
\(32\) 3.12439 + 11.6604i 0.552319 + 2.06128i
\(33\) 1.41295 + 0.378598i 0.245962 + 0.0659054i
\(34\) −7.84104 −1.34473
\(35\) 0 0
\(36\) −4.93012 −0.821687
\(37\) −3.08121 0.825607i −0.506548 0.135729i −0.00351049 0.999994i \(-0.501117\pi\)
−0.503037 + 0.864265i \(0.667784\pi\)
\(38\) −2.69804 10.0692i −0.437679 1.63344i
\(39\) −1.08738 0.627801i −0.174121 0.100529i
\(40\) 15.3208 7.92277i 2.42243 1.25270i
\(41\) 0.769968i 0.120249i 0.998191 + 0.0601244i \(0.0191497\pi\)
−0.998191 + 0.0601244i \(0.980850\pi\)
\(42\) 0 0
\(43\) −5.18572 5.18572i −0.790816 0.790816i 0.190811 0.981627i \(-0.438888\pi\)
−0.981627 + 0.190811i \(0.938888\pi\)
\(44\) 6.24554 3.60587i 0.941551 0.543605i
\(45\) 0.478051 + 2.18437i 0.0712637 + 0.325626i
\(46\) −7.68800 + 13.3160i −1.13353 + 1.96334i
\(47\) −3.13699 + 11.7074i −0.457577 + 1.70770i 0.222823 + 0.974859i \(0.428473\pi\)
−0.680400 + 0.732841i \(0.738194\pi\)
\(48\) −7.38635 + 7.38635i −1.06613 + 1.06613i
\(49\) 0 0
\(50\) −8.40592 10.1289i −1.18878 1.43244i
\(51\) −1.48927 2.57949i −0.208539 0.361201i
\(52\) −5.97934 + 1.60216i −0.829185 + 0.222180i
\(53\) 0.743732 0.199282i 0.102159 0.0273735i −0.207377 0.978261i \(-0.566493\pi\)
0.309537 + 0.950888i \(0.399826\pi\)
\(54\) −1.31626 2.27982i −0.179120 0.310245i
\(55\) −2.20324 2.41754i −0.297084 0.325981i
\(56\) 0 0
\(57\) 2.80005 2.80005i 0.370876 0.370876i
\(58\) 3.53326 13.1863i 0.463940 1.73145i
\(59\) −1.59816 + 2.76810i −0.208063 + 0.360376i −0.951104 0.308870i \(-0.900049\pi\)
0.743041 + 0.669246i \(0.233383\pi\)
\(60\) 9.28153 + 5.94843i 1.19824 + 0.767939i
\(61\) 1.23031 0.710320i 0.157525 0.0909472i −0.419165 0.907910i \(-0.637677\pi\)
0.576690 + 0.816963i \(0.304344\pi\)
\(62\) 11.3614 + 11.3614i 1.44290 + 1.44290i
\(63\) 0 0
\(64\) 10.8872i 1.36090i
\(65\) 1.28965 + 2.49389i 0.159962 + 0.309329i
\(66\) 3.33490 + 1.92541i 0.410498 + 0.237001i
\(67\) −2.17058 8.10070i −0.265178 0.989658i −0.962141 0.272551i \(-0.912133\pi\)
0.696963 0.717107i \(-0.254534\pi\)
\(68\) −14.1842 3.80064i −1.72009 0.460896i
\(69\) −5.84081 −0.703150
\(70\) 0 0
\(71\) 7.62611 0.905053 0.452526 0.891751i \(-0.350523\pi\)
0.452526 + 0.891751i \(0.350523\pi\)
\(72\) −7.45075 1.99642i −0.878080 0.235281i
\(73\) −2.49402 9.30780i −0.291903 1.08940i −0.943646 0.330956i \(-0.892629\pi\)
0.651744 0.758439i \(-0.274038\pi\)
\(74\) −7.27241 4.19873i −0.845401 0.488092i
\(75\) 1.73556 4.68912i 0.200405 0.541453i
\(76\) 19.5226i 2.23940i
\(77\) 0 0
\(78\) −2.33726 2.33726i −0.264643 0.264643i
\(79\) −3.91469 + 2.26015i −0.440437 + 0.254286i −0.703783 0.710415i \(-0.748507\pi\)
0.263346 + 0.964701i \(0.415174\pi\)
\(80\) 22.8176 4.99366i 2.55109 0.558308i
\(81\) 0.500000 0.866025i 0.0555556 0.0962250i
\(82\) −0.524613 + 1.95788i −0.0579338 + 0.216212i
\(83\) 6.75794 6.75794i 0.741781 0.741781i −0.231140 0.972921i \(-0.574246\pi\)
0.972921 + 0.231140i \(0.0742455\pi\)
\(84\) 0 0
\(85\) −0.308559 + 6.65306i −0.0334679 + 0.721626i
\(86\) −9.65306 16.7196i −1.04092 1.80292i
\(87\) 5.00903 1.34216i 0.537024 0.143895i
\(88\) 10.8989 2.92035i 1.16182 0.311310i
\(89\) 0.599954 + 1.03915i 0.0635950 + 0.110150i 0.896070 0.443913i \(-0.146410\pi\)
−0.832475 + 0.554063i \(0.813077\pi\)
\(90\) −0.272713 + 5.88016i −0.0287465 + 0.619823i
\(91\) 0 0
\(92\) −20.3618 + 20.3618i −2.12286 + 2.12286i
\(93\) −1.57969 + 5.89549i −0.163806 + 0.611334i
\(94\) −15.9535 + 27.6323i −1.64548 + 2.85006i
\(95\) −8.64982 + 1.89302i −0.887452 + 0.194220i
\(96\) −10.4544 + 6.03586i −1.06700 + 0.616032i
\(97\) 8.68829 + 8.68829i 0.882162 + 0.882162i 0.993754 0.111592i \(-0.0355950\pi\)
−0.111592 + 0.993754i \(0.535595\pi\)
\(98\) 0 0
\(99\) 1.46279i 0.147016i
\(100\) −10.2965 22.3972i −1.02965 2.23972i
\(101\) −13.2866 7.67102i −1.32207 0.763295i −0.338008 0.941143i \(-0.609753\pi\)
−0.984058 + 0.177848i \(0.943086\pi\)
\(102\) −2.02941 7.57386i −0.200941 0.749924i
\(103\) 11.3486 + 3.04085i 1.11821 + 0.299624i 0.770160 0.637851i \(-0.220177\pi\)
0.348052 + 0.937475i \(0.386843\pi\)
\(104\) −9.68519 −0.949711
\(105\) 0 0
\(106\) 2.02695 0.196875
\(107\) −5.99715 1.60693i −0.579766 0.155348i −0.0429945 0.999075i \(-0.513690\pi\)
−0.536772 + 0.843727i \(0.680356\pi\)
\(108\) −1.27601 4.76213i −0.122784 0.458237i
\(109\) 6.44831 + 3.72294i 0.617636 + 0.356593i 0.775948 0.630797i \(-0.217272\pi\)
−0.158312 + 0.987389i \(0.550605\pi\)
\(110\) −3.95524 7.64852i −0.377117 0.729258i
\(111\) 3.18990i 0.302772i
\(112\) 0 0
\(113\) 2.54445 + 2.54445i 0.239362 + 0.239362i 0.816586 0.577224i \(-0.195864\pi\)
−0.577224 + 0.816586i \(0.695864\pi\)
\(114\) 9.02780 5.21220i 0.845531 0.488168i
\(115\) 10.9960 + 7.04722i 1.02538 + 0.657156i
\(116\) 12.7831 22.1410i 1.18688 2.05574i
\(117\) 0.324974 1.21282i 0.0300438 0.112125i
\(118\) −5.94986 + 5.94986i −0.547729 + 0.547729i
\(119\) 0 0
\(120\) 11.6181 + 12.7482i 1.06058 + 1.16375i
\(121\) 4.43012 + 7.67320i 0.402738 + 0.697564i
\(122\) 3.61242 0.967945i 0.327053 0.0876337i
\(123\) −0.743732 + 0.199282i −0.0670600 + 0.0179687i
\(124\) 15.0454 + 26.0594i 1.35112 + 2.34020i
\(125\) −8.92504 + 6.73377i −0.798280 + 0.602287i
\(126\) 0 0
\(127\) 7.86025 7.86025i 0.697484 0.697484i −0.266383 0.963867i \(-0.585829\pi\)
0.963867 + 0.266383i \(0.0858286\pi\)
\(128\) −1.16915 + 4.36334i −0.103339 + 0.385668i
\(129\) 3.66686 6.35119i 0.322849 0.559191i
\(130\) 1.58014 + 7.22018i 0.138588 + 0.633252i
\(131\) 5.35391 3.09108i 0.467773 0.270069i −0.247534 0.968879i \(-0.579620\pi\)
0.715307 + 0.698810i \(0.246287\pi\)
\(132\) 5.09947 + 5.09947i 0.443851 + 0.443851i
\(133\) 0 0
\(134\) 22.0775i 1.90720i
\(135\) −1.98621 + 1.02712i −0.170946 + 0.0884003i
\(136\) −19.8971 11.4876i −1.70616 0.985054i
\(137\) 3.31460 + 12.3703i 0.283185 + 1.05686i 0.950155 + 0.311777i \(0.100924\pi\)
−0.666970 + 0.745085i \(0.732409\pi\)
\(138\) −14.8521 3.97960i −1.26429 0.338766i
\(139\) 11.9913 1.01709 0.508544 0.861036i \(-0.330184\pi\)
0.508544 + 0.861036i \(0.330184\pi\)
\(140\) 0 0
\(141\) −12.1204 −1.02072
\(142\) 19.3918 + 5.19601i 1.62732 + 0.436039i
\(143\) 0.475368 + 1.77410i 0.0397523 + 0.148357i
\(144\) −9.04639 5.22294i −0.753866 0.435245i
\(145\) −11.0495 3.51685i −0.917607 0.292059i
\(146\) 25.3673i 2.09941i
\(147\) 0 0
\(148\) −11.1204 11.1204i −0.914091 0.914091i
\(149\) 0.0838539 0.0484130i 0.00686958 0.00396615i −0.496561 0.868002i \(-0.665404\pi\)
0.503431 + 0.864036i \(0.332071\pi\)
\(150\) 7.60811 10.7410i 0.621199 0.877002i
\(151\) 6.72748 11.6523i 0.547475 0.948254i −0.450972 0.892538i \(-0.648923\pi\)
0.998447 0.0557157i \(-0.0177440\pi\)
\(152\) 7.90558 29.5040i 0.641227 2.39309i
\(153\) 2.10614 2.10614i 0.170272 0.170272i
\(154\) 0 0
\(155\) 10.0871 9.19296i 0.810219 0.738397i
\(156\) −3.09513 5.36093i −0.247809 0.429218i
\(157\) 2.25063 0.603054i 0.179620 0.0481290i −0.167888 0.985806i \(-0.553695\pi\)
0.347508 + 0.937677i \(0.387028\pi\)
\(158\) −11.4943 + 3.07988i −0.914434 + 0.245022i
\(159\) 0.384984 + 0.666812i 0.0305312 + 0.0528816i
\(160\) 26.9642 + 1.25056i 2.13171 + 0.0988653i
\(161\) 0 0
\(162\) 1.86147 1.86147i 0.146251 0.146251i
\(163\) −3.76077 + 14.0354i −0.294566 + 1.09934i 0.646995 + 0.762495i \(0.276026\pi\)
−0.941561 + 0.336842i \(0.890641\pi\)
\(164\) −1.89802 + 3.28746i −0.148210 + 0.256708i
\(165\) 1.76493 2.75387i 0.137399 0.214388i
\(166\) 21.7887 12.5797i 1.69113 0.976373i
\(167\) −0.293008 0.293008i −0.0226737 0.0226737i 0.695679 0.718353i \(-0.255104\pi\)
−0.718353 + 0.695679i \(0.755104\pi\)
\(168\) 0 0
\(169\) 11.4235i 0.878728i
\(170\) −5.31763 + 16.7072i −0.407844 + 1.28139i
\(171\) 3.42935 + 1.97993i 0.262249 + 0.151409i
\(172\) −9.35790 34.9242i −0.713533 2.66294i
\(173\) −4.71537 1.26348i −0.358503 0.0960606i 0.0750719 0.997178i \(-0.476081\pi\)
−0.433575 + 0.901118i \(0.642748\pi\)
\(174\) 13.6515 1.03492
\(175\) 0 0
\(176\) 15.2801 1.15178
\(177\) −3.08742 0.827271i −0.232064 0.0621815i
\(178\) 0.817551 + 3.05114i 0.0612781 + 0.228693i
\(179\) −1.72994 0.998779i −0.129302 0.0746523i 0.433954 0.900935i \(-0.357118\pi\)
−0.563256 + 0.826283i \(0.690451\pi\)
\(180\) −3.34351 + 10.5048i −0.249211 + 0.782984i
\(181\) 8.48528i 0.630706i −0.948974 0.315353i \(-0.897877\pi\)
0.948974 0.315353i \(-0.102123\pi\)
\(182\) 0 0
\(183\) 1.00454 + 1.00454i 0.0742581 + 0.0742581i
\(184\) −39.0175 + 22.5268i −2.87641 + 1.66070i
\(185\) −3.84877 + 6.00536i −0.282967 + 0.441523i
\(186\) −8.03372 + 13.9148i −0.589061 + 1.02028i
\(187\) −1.12767 + 4.20851i −0.0824632 + 0.307757i
\(188\) −42.2532 + 42.2532i −3.08163 + 3.08163i
\(189\) 0 0
\(190\) −23.2847 1.07991i −1.68925 0.0783447i
\(191\) 3.91712 + 6.78465i 0.283433 + 0.490920i 0.972228 0.234036i \(-0.0751934\pi\)
−0.688795 + 0.724956i \(0.741860\pi\)
\(192\) −10.5162 + 2.81781i −0.758943 + 0.203358i
\(193\) −18.5257 + 4.96393i −1.33351 + 0.357312i −0.854021 0.520239i \(-0.825843\pi\)
−0.479485 + 0.877550i \(0.659176\pi\)
\(194\) 16.1730 + 28.0124i 1.16115 + 2.01117i
\(195\) −2.07512 + 1.89117i −0.148603 + 0.135430i
\(196\) 0 0
\(197\) −11.4791 + 11.4791i −0.817853 + 0.817853i −0.985797 0.167943i \(-0.946287\pi\)
0.167943 + 0.985797i \(0.446287\pi\)
\(198\) −0.996663 + 3.71960i −0.0708298 + 0.264340i
\(199\) 10.0734 17.4476i 0.714084 1.23683i −0.249228 0.968445i \(-0.580177\pi\)
0.963312 0.268384i \(-0.0864897\pi\)
\(200\) −6.49114 38.0178i −0.458993 2.68826i
\(201\) 7.26289 4.19323i 0.512285 0.295768i
\(202\) −28.5587 28.5587i −2.00938 2.00938i
\(203\) 0 0
\(204\) 14.6846i 1.02812i
\(205\) 1.64060 + 0.522176i 0.114585 + 0.0364704i
\(206\) 26.7855 + 15.4646i 1.86623 + 1.07747i
\(207\) −1.51171 5.64178i −0.105071 0.392131i
\(208\) −12.6689 3.39463i −0.878433 0.235375i
\(209\) −5.79246 −0.400673
\(210\) 0 0
\(211\) 11.9662 0.823785 0.411892 0.911233i \(-0.364868\pi\)
0.411892 + 0.911233i \(0.364868\pi\)
\(212\) 3.66669 + 0.982486i 0.251829 + 0.0674774i
\(213\) 1.97378 + 7.36626i 0.135241 + 0.504728i
\(214\) −14.1548 8.17225i −0.967599 0.558644i
\(215\) −14.5663 + 7.53260i −0.993414 + 0.513719i
\(216\) 7.71359i 0.524843i
\(217\) 0 0
\(218\) 13.8602 + 13.8602i 0.938734 + 0.938734i
\(219\) 8.34514 4.81807i 0.563912 0.325575i
\(220\) −3.44758 15.7531i −0.232436 1.06207i
\(221\) 1.86993 3.23881i 0.125785 0.217866i
\(222\) 2.17342 8.11132i 0.145871 0.544396i
\(223\) 0.660910 0.660910i 0.0442578 0.0442578i −0.684632 0.728889i \(-0.740037\pi\)
0.728889 + 0.684632i \(0.240037\pi\)
\(224\) 0 0
\(225\) 4.97854 + 0.462789i 0.331902 + 0.0308526i
\(226\) 4.73641 + 8.20370i 0.315061 + 0.545702i
\(227\) −23.6988 + 6.35007i −1.57294 + 0.421469i −0.936732 0.350047i \(-0.886166\pi\)
−0.636210 + 0.771516i \(0.719499\pi\)
\(228\) 18.8574 5.05283i 1.24886 0.334632i
\(229\) −12.5391 21.7184i −0.828607 1.43519i −0.899131 0.437679i \(-0.855800\pi\)
0.0705240 0.997510i \(-0.477533\pi\)
\(230\) 23.1592 + 25.4118i 1.52707 + 1.67560i
\(231\) 0 0
\(232\) 28.2847 28.2847i 1.85698 1.85698i
\(233\) 0.820401 3.06178i 0.0537462 0.200584i −0.933832 0.357712i \(-0.883557\pi\)
0.987578 + 0.157128i \(0.0502236\pi\)
\(234\) 1.65269 2.86255i 0.108040 0.187131i
\(235\) 22.8180 + 14.6238i 1.48848 + 0.953954i
\(236\) −13.6471 + 7.87915i −0.888350 + 0.512889i
\(237\) −3.19633 3.19633i −0.207624 0.207624i
\(238\) 0 0
\(239\) 21.3769i 1.38276i 0.722492 + 0.691380i \(0.242997\pi\)
−0.722492 + 0.691380i \(0.757003\pi\)
\(240\) 10.7291 + 20.7477i 0.692563 + 1.33926i
\(241\) 0.540512 + 0.312065i 0.0348174 + 0.0201018i 0.517308 0.855799i \(-0.326934\pi\)
−0.482490 + 0.875901i \(0.660268\pi\)
\(242\) 6.03688 + 22.5299i 0.388065 + 1.44828i
\(243\) 0.965926 + 0.258819i 0.0619642 + 0.0166032i
\(244\) 7.00393 0.448381
\(245\) 0 0
\(246\) −2.02695 −0.129234
\(247\) 4.80260 + 1.28685i 0.305582 + 0.0818805i
\(248\) 12.1851 + 45.4754i 0.773754 + 2.88769i
\(249\) 8.27676 + 4.77859i 0.524518 + 0.302831i
\(250\) −27.2827 + 11.0417i −1.72551 + 0.698337i
\(251\) 16.3443i 1.03164i 0.856696 + 0.515822i \(0.172513\pi\)
−0.856696 + 0.515822i \(0.827487\pi\)
\(252\) 0 0
\(253\) 6.04143 + 6.04143i 0.379821 + 0.379821i
\(254\) 25.3427 14.6316i 1.59014 0.918068i
\(255\) −6.50622 + 1.42389i −0.407435 + 0.0891677i
\(256\) 4.94133 8.55863i 0.308833 0.534914i
\(257\) −7.79833 + 29.1038i −0.486446 + 1.81544i 0.0870116 + 0.996207i \(0.472268\pi\)
−0.573458 + 0.819235i \(0.694398\pi\)
\(258\) 13.6515 13.6515i 0.849904 0.849904i
\(259\) 0 0
\(260\) −0.641275 + 13.8270i −0.0397702 + 0.857514i
\(261\) 2.59286 + 4.49097i 0.160494 + 0.277984i
\(262\) 15.7201 4.21218i 0.971190 0.260230i
\(263\) 22.3275 5.98263i 1.37677 0.368905i 0.506824 0.862049i \(-0.330819\pi\)
0.869947 + 0.493145i \(0.164153\pi\)
\(264\) 5.64168 + 9.77167i 0.347221 + 0.601405i
\(265\) 0.0797641 1.71985i 0.00489987 0.105650i
\(266\) 0 0
\(267\) −0.848464 + 0.848464i −0.0519251 + 0.0519251i
\(268\) 10.7012 39.9374i 0.653680 2.43957i
\(269\) −8.29515 + 14.3676i −0.505764 + 0.876009i 0.494213 + 0.869341i \(0.335456\pi\)
−0.999978 + 0.00666889i \(0.997877\pi\)
\(270\) −5.75038 + 1.25848i −0.349957 + 0.0765884i
\(271\) 6.73796 3.89016i 0.409302 0.236311i −0.281188 0.959653i \(-0.590728\pi\)
0.690490 + 0.723342i \(0.257395\pi\)
\(272\) −22.0005 22.0005i −1.33398 1.33398i
\(273\) 0 0
\(274\) 33.7136i 2.03671i
\(275\) −6.64536 + 3.05501i −0.400730 + 0.184224i
\(276\) −24.9380 14.3979i −1.50109 0.866654i
\(277\) 7.80024 + 29.1109i 0.468671 + 1.74910i 0.644422 + 0.764670i \(0.277098\pi\)
−0.175751 + 0.984435i \(0.556235\pi\)
\(278\) 30.4916 + 8.17019i 1.82876 + 0.490016i
\(279\) −6.10346 −0.365405
\(280\) 0 0
\(281\) −21.1519 −1.26182 −0.630908 0.775858i \(-0.717317\pi\)
−0.630908 + 0.775858i \(0.717317\pi\)
\(282\) −30.8199 8.25816i −1.83530 0.491766i
\(283\) −0.971693 3.62641i −0.0577611 0.215567i 0.931013 0.364986i \(-0.118926\pi\)
−0.988774 + 0.149419i \(0.952260\pi\)
\(284\) 32.5605 + 18.7988i 1.93211 + 1.11551i
\(285\) −4.06725 7.86513i −0.240923 0.465890i
\(286\) 4.83508i 0.285905i
\(287\) 0 0
\(288\) −8.53599 8.53599i −0.502988 0.502988i
\(289\) −7.03933 + 4.06416i −0.414078 + 0.239068i
\(290\) −25.7005 16.4712i −1.50919 0.967221i
\(291\) −6.14355 + 10.6409i −0.360141 + 0.623783i
\(292\) 12.2958 45.8886i 0.719558 2.68543i
\(293\) 1.56714 1.56714i 0.0915536 0.0915536i −0.659847 0.751400i \(-0.729379\pi\)
0.751400 + 0.659847i \(0.229379\pi\)
\(294\) 0 0
\(295\) 4.81428 + 5.28255i 0.280298 + 0.307562i
\(296\) −12.3028 21.3091i −0.715085 1.23856i
\(297\) −1.41295 + 0.378598i −0.0819875 + 0.0219685i
\(298\) 0.246211 0.0659719i 0.0142626 0.00382165i
\(299\) −3.66686 6.35119i −0.212060 0.367299i
\(300\) 18.9691 15.7425i 1.09518 0.908891i
\(301\) 0 0
\(302\) 25.0460 25.0460i 1.44123 1.44123i
\(303\) 3.97081 14.8193i 0.228117 0.851345i
\(304\) 20.6821 35.8225i 1.18620 2.05456i
\(305\) −0.679139 3.10320i −0.0388874 0.177689i
\(306\) 6.79054 3.92052i 0.388189 0.224121i
\(307\) 17.3551 + 17.3551i 0.990510 + 0.990510i 0.999955 0.00944588i \(-0.00300676\pi\)
−0.00944588 + 0.999955i \(0.503007\pi\)
\(308\) 0 0
\(309\) 11.7489i 0.668374i
\(310\) 31.9133 16.5032i 1.81255 0.937316i
\(311\) −26.9029 15.5324i −1.52553 0.880763i −0.999542 0.0302685i \(-0.990364\pi\)
−0.525984 0.850494i \(-0.676303\pi\)
\(312\) −2.50671 9.35518i −0.141915 0.529633i
\(313\) 7.81948 + 2.09522i 0.441983 + 0.118429i 0.472946 0.881091i \(-0.343191\pi\)
−0.0309625 + 0.999521i \(0.509857\pi\)
\(314\) 6.13381 0.346151
\(315\) 0 0
\(316\) −22.2856 −1.25366
\(317\) −1.02804 0.275463i −0.0577406 0.0154715i 0.229833 0.973230i \(-0.426182\pi\)
−0.287574 + 0.957759i \(0.592849\pi\)
\(318\) 0.524613 + 1.95788i 0.0294188 + 0.109793i
\(319\) −6.56934 3.79281i −0.367813 0.212357i
\(320\) 23.1978 + 7.38348i 1.29680 + 0.412749i
\(321\) 6.20871i 0.346536i
\(322\) 0 0
\(323\) 8.34005 + 8.34005i 0.464053 + 0.464053i
\(324\) 4.26961 2.46506i 0.237201 0.136948i
\(325\) 6.18845 1.05661i 0.343274 0.0586104i
\(326\) −19.1259 + 33.1270i −1.05928 + 1.83473i
\(327\) −1.92713 + 7.19216i −0.106571 + 0.397727i
\(328\) −4.19966 + 4.19966i −0.231887 + 0.231887i
\(329\) 0 0
\(330\) 6.36421 5.80005i 0.350338 0.319282i
\(331\) −7.90412 13.6903i −0.434449 0.752489i 0.562801 0.826592i \(-0.309724\pi\)
−0.997251 + 0.0741038i \(0.976390\pi\)
\(332\) 45.5125 12.1950i 2.49783 0.669290i
\(333\) 3.08121 0.825607i 0.168849 0.0452430i
\(334\) −0.545426 0.944705i −0.0298444 0.0516920i
\(335\) −18.7326 0.868788i −1.02347 0.0474670i
\(336\) 0 0
\(337\) −20.0460 + 20.0460i −1.09197 + 1.09197i −0.0966558 + 0.995318i \(0.530815\pi\)
−0.995318 + 0.0966558i \(0.969185\pi\)
\(338\) −7.78331 + 29.0477i −0.423357 + 1.57999i
\(339\) −1.79920 + 3.11630i −0.0977190 + 0.169254i
\(340\) −17.7176 + 27.6454i −0.960873 + 1.49928i
\(341\) 7.73194 4.46404i 0.418708 0.241741i
\(342\) 7.37117 + 7.37117i 0.398587 + 0.398587i
\(343\) 0 0
\(344\) 56.5693i 3.05001i
\(345\) −3.96112 + 12.4453i −0.213259 + 0.670030i
\(346\) −11.1294 6.42558i −0.598322 0.345441i
\(347\) −7.35151 27.4362i −0.394650 1.47285i −0.822376 0.568945i \(-0.807352\pi\)
0.427726 0.903908i \(-0.359315\pi\)
\(348\) 24.6951 + 6.61704i 1.32380 + 0.354710i
\(349\) −14.7663 −0.790420 −0.395210 0.918591i \(-0.629328\pi\)
−0.395210 + 0.918591i \(0.629328\pi\)
\(350\) 0 0
\(351\) 1.25560 0.0670190
\(352\) 17.0567 + 4.57032i 0.909124 + 0.243599i
\(353\) 4.57130 + 17.0603i 0.243306 + 0.908029i 0.974227 + 0.225568i \(0.0724238\pi\)
−0.730922 + 0.682461i \(0.760910\pi\)
\(354\) −7.28706 4.20719i −0.387303 0.223610i
\(355\) 5.17187 16.2493i 0.274495 0.862423i
\(356\) 5.91570i 0.313531i
\(357\) 0 0
\(358\) −3.71839 3.71839i −0.196523 0.196523i
\(359\) 9.12549 5.26861i 0.481625 0.278066i −0.239468 0.970904i \(-0.576973\pi\)
0.721093 + 0.692838i \(0.243640\pi\)
\(360\) −9.30682 + 14.5217i −0.490512 + 0.765362i
\(361\) 1.65972 2.87471i 0.0873535 0.151301i
\(362\) 5.78140 21.5765i 0.303864 1.13403i
\(363\) −6.26514 + 6.26514i −0.328835 + 0.328835i
\(364\) 0 0
\(365\) −21.5239 0.998247i −1.12661 0.0522507i
\(366\) 1.86993 + 3.23881i 0.0977427 + 0.169295i
\(367\) 15.2871 4.09618i 0.797982 0.213819i 0.163284 0.986579i \(-0.447791\pi\)
0.634698 + 0.772760i \(0.281125\pi\)
\(368\) −58.9334 + 15.7911i −3.07211 + 0.823170i
\(369\) −0.384984 0.666812i −0.0200415 0.0347128i
\(370\) −13.8784 + 12.6482i −0.721505 + 0.657546i
\(371\) 0 0
\(372\) −21.2774 + 21.2774i −1.10318 + 1.10318i
\(373\) 6.32295 23.5976i 0.327390 1.22184i −0.584497 0.811396i \(-0.698708\pi\)
0.911887 0.410440i \(-0.134625\pi\)
\(374\) −5.73489 + 9.93312i −0.296544 + 0.513630i
\(375\) −8.81429 6.87810i −0.455168 0.355184i
\(376\) −80.9662 + 46.7459i −4.17551 + 2.41073i
\(377\) 4.60412 + 4.60412i 0.237124 + 0.237124i
\(378\) 0 0
\(379\) 17.6237i 0.905267i −0.891697 0.452634i \(-0.850485\pi\)
0.891697 0.452634i \(-0.149515\pi\)
\(380\) −41.5978 13.2399i −2.13392 0.679191i
\(381\) 9.62680 + 5.55803i 0.493196 + 0.284747i
\(382\) 5.33782 + 19.9210i 0.273106 + 1.01925i
\(383\) 22.0270 + 5.90211i 1.12553 + 0.301584i 0.773118 0.634263i \(-0.218696\pi\)
0.352408 + 0.935846i \(0.385363\pi\)
\(384\) −4.51726 −0.230520
\(385\) 0 0
\(386\) −50.4894 −2.56984
\(387\) 7.08383 + 1.89811i 0.360091 + 0.0964862i
\(388\) 15.6785 + 58.5128i 0.795953 + 2.97054i
\(389\) 13.3377 + 7.70053i 0.676249 + 0.390432i 0.798440 0.602074i \(-0.205659\pi\)
−0.122191 + 0.992507i \(0.538992\pi\)
\(390\) −6.56519 + 3.39502i −0.332441 + 0.171914i
\(391\) 17.3971i 0.879807i
\(392\) 0 0
\(393\) 4.37145 + 4.37145i 0.220510 + 0.220510i
\(394\) −37.0105 + 21.3680i −1.86456 + 1.07650i
\(395\) 2.16093 + 9.87398i 0.108728 + 0.496814i
\(396\) −3.60587 + 6.24554i −0.181202 + 0.313850i
\(397\) −5.92159 + 22.0997i −0.297196 + 1.10915i 0.642261 + 0.766486i \(0.277996\pi\)
−0.939458 + 0.342665i \(0.888670\pi\)
\(398\) 37.5026 37.5026i 1.87983 1.87983i
\(399\) 0 0
\(400\) 4.83424 52.0051i 0.241712 2.60026i
\(401\) 0.488797 + 0.846622i 0.0244094 + 0.0422783i 0.877972 0.478712i \(-0.158896\pi\)
−0.853563 + 0.520990i \(0.825563\pi\)
\(402\) 21.3252 5.71407i 1.06360 0.284992i
\(403\) −7.40238 + 1.98346i −0.368739 + 0.0988033i
\(404\) −37.8191 65.5046i −1.88157 3.25897i
\(405\) −1.50619 1.65269i −0.0748431 0.0821230i
\(406\) 0 0
\(407\) −3.29947 + 3.29947i −0.163549 + 0.163549i
\(408\) 5.94642 22.1923i 0.294392 1.09868i
\(409\) 12.1586 21.0593i 0.601203 1.04131i −0.391437 0.920205i \(-0.628022\pi\)
0.992639 0.121108i \(-0.0386449\pi\)
\(410\) 3.81597 + 2.44561i 0.188457 + 0.120780i
\(411\) −11.0909 + 6.40331i −0.547072 + 0.315852i
\(412\) 40.9583 + 40.9583i 2.01787 + 2.01787i
\(413\) 0 0
\(414\) 15.3760i 0.755689i
\(415\) −9.81635 18.9825i −0.481866 0.931817i
\(416\) −13.1266 7.57863i −0.643583 0.371573i
\(417\) 3.10357 + 11.5827i 0.151983 + 0.567207i
\(418\) −14.7291 3.94666i −0.720425 0.193037i
\(419\) −15.9893 −0.781127 −0.390563 0.920576i \(-0.627720\pi\)
−0.390563 + 0.920576i \(0.627720\pi\)
\(420\) 0 0
\(421\) 14.7000 0.716433 0.358216 0.933639i \(-0.383385\pi\)
0.358216 + 0.933639i \(0.383385\pi\)
\(422\) 30.4277 + 8.15308i 1.48120 + 0.396886i
\(423\) −3.13699 11.7074i −0.152526 0.569233i
\(424\) 5.14351 + 2.96961i 0.249791 + 0.144217i
\(425\) 13.9667 + 5.16943i 0.677485 + 0.250754i
\(426\) 20.0758i 0.972677i
\(427\) 0 0
\(428\) −21.6443 21.6443i −1.04622 1.04622i
\(429\) −1.59061 + 0.918340i −0.0767955 + 0.0443379i
\(430\) −42.1717 + 9.22932i −2.03370 + 0.445077i
\(431\) −11.1361 + 19.2883i −0.536407 + 0.929084i 0.462687 + 0.886522i \(0.346885\pi\)
−0.999094 + 0.0425619i \(0.986448\pi\)
\(432\) 2.70359 10.0899i 0.130077 0.485452i
\(433\) 28.0171 28.0171i 1.34642 1.34642i 0.456896 0.889520i \(-0.348961\pi\)
0.889520 0.456896i \(-0.151039\pi\)
\(434\) 0 0
\(435\) 0.537211 11.5832i 0.0257573 0.555371i
\(436\) 18.3545 + 31.7910i 0.879023 + 1.52251i
\(437\) 22.3407 5.98618i 1.06870 0.286358i
\(438\) 24.5029 6.56553i 1.17079 0.313713i
\(439\) −1.17828 2.04084i −0.0562363 0.0974042i 0.836537 0.547911i \(-0.184577\pi\)
−0.892773 + 0.450507i \(0.851243\pi\)
\(440\) 1.16889 25.2033i 0.0557246 1.20152i
\(441\) 0 0
\(442\) 6.96162 6.96162i 0.331130 0.331130i
\(443\) −2.00306 + 7.47553i −0.0951684 + 0.355173i −0.997045 0.0768206i \(-0.975523\pi\)
0.901877 + 0.431994i \(0.142190\pi\)
\(444\) 7.86331 13.6196i 0.373176 0.646360i
\(445\) 2.62104 0.573618i 0.124249 0.0271921i
\(446\) 2.13088 1.23026i 0.100900 0.0582546i
\(447\) 0.0684664 + 0.0684664i 0.00323835 + 0.00323835i
\(448\) 0 0
\(449\) 1.20020i 0.0566410i 0.999599 + 0.0283205i \(0.00901591\pi\)
−0.999599 + 0.0283205i \(0.990984\pi\)
\(450\) 12.3442 + 4.56888i 0.581909 + 0.215379i
\(451\) 0.975405 + 0.563150i 0.0459300 + 0.0265177i
\(452\) 4.59159 + 17.1360i 0.215970 + 0.806011i
\(453\) 12.9965 + 3.48240i 0.610629 + 0.163617i
\(454\) −64.5881 −3.03127
\(455\) 0 0
\(456\) 30.5448 1.43039
\(457\) 28.7924 + 7.71489i 1.34685 + 0.360887i 0.858971 0.512024i \(-0.171104\pi\)
0.487879 + 0.872912i \(0.337771\pi\)
\(458\) −17.0869 63.7692i −0.798418 2.97974i
\(459\) 2.57949 + 1.48927i 0.120400 + 0.0695131i
\(460\) 29.5768 + 57.1947i 1.37902 + 2.66672i
\(461\) 21.9670i 1.02311i −0.859252 0.511553i \(-0.829071\pi\)
0.859252 0.511553i \(-0.170929\pi\)
\(462\) 0 0
\(463\) −21.6776 21.6776i −1.00744 1.00744i −0.999972 0.00746987i \(-0.997622\pi\)
−0.00746987 0.999972i \(-0.502378\pi\)
\(464\) 46.9121 27.0847i 2.17784 1.25738i
\(465\) 11.4905 + 7.36412i 0.532858 + 0.341503i
\(466\) 4.17225 7.22655i 0.193276 0.334763i
\(467\) −2.60354 + 9.71653i −0.120477 + 0.449627i −0.999638 0.0268978i \(-0.991437\pi\)
0.879161 + 0.476525i \(0.158104\pi\)
\(468\) 4.37718 4.37718i 0.202335 0.202335i
\(469\) 0 0
\(470\) 48.0581 + 52.7326i 2.21676 + 2.43237i
\(471\) 1.16501 + 2.01786i 0.0536809 + 0.0929780i
\(472\) −23.8151 + 6.38123i −1.09618 + 0.293720i
\(473\) −10.3622 + 2.77653i −0.476452 + 0.127665i
\(474\) −5.94986 10.3055i −0.273286 0.473346i
\(475\) −1.83259 + 19.7144i −0.0840848 + 0.904557i
\(476\) 0 0
\(477\) −0.544449 + 0.544449i −0.0249286 + 0.0249286i
\(478\) −14.5651 + 54.3575i −0.666190 + 2.48626i
\(479\) 15.8875 27.5179i 0.725917 1.25733i −0.232678 0.972554i \(-0.574749\pi\)
0.958595 0.284771i \(-0.0919177\pi\)
\(480\) 5.77090 + 26.3691i 0.263404 + 1.20358i
\(481\) 3.46864 2.00262i 0.158157 0.0913117i
\(482\) 1.16180 + 1.16180i 0.0529184 + 0.0529184i
\(483\) 0 0
\(484\) 43.6821i 1.98555i
\(485\) 24.4047 12.6203i 1.10816 0.573058i
\(486\) 2.27982 + 1.31626i 0.103415 + 0.0597066i
\(487\) −1.76215 6.57642i −0.0798505 0.298006i 0.914439 0.404724i \(-0.132632\pi\)
−0.994289 + 0.106718i \(0.965966\pi\)
\(488\) 10.5848 + 2.83620i 0.479153 + 0.128389i
\(489\) −14.5305 −0.657092
\(490\) 0 0
\(491\) 28.3401 1.27897 0.639484 0.768804i \(-0.279148\pi\)
0.639484 + 0.768804i \(0.279148\pi\)
\(492\) −3.66669 0.982486i −0.165307 0.0442939i
\(493\) 3.99769 + 14.9196i 0.180047 + 0.671943i
\(494\) 11.3353 + 6.54445i 0.510000 + 0.294449i
\(495\) 3.11683 + 0.992034i 0.140091 + 0.0445886i
\(496\) 63.7559i 2.86273i
\(497\) 0 0
\(498\) 17.7904 + 17.7904i 0.797206 + 0.797206i
\(499\) −2.93753 + 1.69599i −0.131502 + 0.0759227i −0.564308 0.825564i \(-0.690857\pi\)
0.432806 + 0.901487i \(0.357524\pi\)
\(500\) −54.7056 + 6.74980i −2.44651 + 0.301860i
\(501\) 0.207188 0.358861i 0.00925649 0.0160327i
\(502\) −11.1361 + 41.5605i −0.497029 + 1.85494i
\(503\) 8.32921 8.32921i 0.371381 0.371381i −0.496599 0.867980i \(-0.665418\pi\)
0.867980 + 0.496599i \(0.165418\pi\)
\(504\) 0 0
\(505\) −25.3557 + 23.1080i −1.12831 + 1.02829i
\(506\) 11.2459 + 19.4785i 0.499942 + 0.865925i
\(507\) −11.0342 + 2.95661i −0.490047 + 0.131308i
\(508\) 52.9362 14.1842i 2.34866 0.629323i
\(509\) −19.4726 33.7275i −0.863108 1.49495i −0.868914 0.494963i \(-0.835182\pi\)
0.00580659 0.999983i \(-0.498152\pi\)
\(510\) −17.5143 0.812285i −0.775545 0.0359686i
\(511\) 0 0
\(512\) 24.7846 24.7846i 1.09534 1.09534i
\(513\) −1.02489 + 3.82494i −0.0452500 + 0.168875i
\(514\) −39.6594 + 68.6920i −1.74930 + 3.02988i
\(515\) 14.1757 22.1187i 0.624655 0.974668i
\(516\) 31.3121 18.0781i 1.37844 0.795843i
\(517\) 12.5367 + 12.5367i 0.551364 + 0.551364i
\(518\) 0 0
\(519\) 4.88171i 0.214283i
\(520\) −6.56830 + 20.6367i −0.288039 + 0.904978i
\(521\) 6.12042 + 3.53363i 0.268141 + 0.154811i 0.628042 0.778179i \(-0.283856\pi\)
−0.359902 + 0.932990i \(0.617190\pi\)
\(522\) 3.53326 + 13.1863i 0.154647 + 0.577150i
\(523\) 19.9286 + 5.33985i 0.871416 + 0.233495i 0.666700 0.745326i \(-0.267706\pi\)
0.204716 + 0.978821i \(0.434373\pi\)
\(524\) 30.4788 1.33147
\(525\) 0 0
\(526\) 60.8508 2.65322
\(527\) −17.5599 4.70517i −0.764923 0.204960i
\(528\) 3.95478 + 14.7595i 0.172110 + 0.642323i
\(529\) −9.62588 5.55750i −0.418516 0.241631i
\(530\) 1.37464 4.31891i 0.0597104 0.187602i
\(531\) 3.19633i 0.138709i
\(532\) 0 0
\(533\) −0.683611 0.683611i −0.0296105 0.0296105i
\(534\) −2.73558 + 1.57939i −0.118380 + 0.0683468i
\(535\) −7.49111 + 11.6886i −0.323869 + 0.505343i
\(536\) 32.3449 56.0229i 1.39708 2.41982i
\(537\) 0.517006 1.92949i 0.0223105 0.0832638i
\(538\) −30.8823 + 30.8823i −1.33143 + 1.33143i
\(539\) 0 0
\(540\) −11.0123 0.510732i −0.473892 0.0219784i
\(541\) −9.30063 16.1092i −0.399865 0.692587i 0.593844 0.804581i \(-0.297610\pi\)
−0.993709 + 0.111993i \(0.964276\pi\)
\(542\) 19.7839 5.30108i 0.849792 0.227701i
\(543\) 8.19615 2.19615i 0.351731 0.0942459i
\(544\) −17.9780 31.1388i −0.770801 1.33507i
\(545\) 12.3057 11.2149i 0.527120 0.480393i
\(546\) 0 0
\(547\) −7.22715 + 7.22715i −0.309011 + 0.309011i −0.844526 0.535515i \(-0.820118\pi\)
0.535515 + 0.844526i \(0.320118\pi\)
\(548\) −16.3414 + 60.9869i −0.698069 + 2.60523i
\(549\) −0.710320 + 1.23031i −0.0303157 + 0.0525084i
\(550\) −18.9794 + 3.24053i −0.809284 + 0.138177i
\(551\) −17.7837 + 10.2674i −0.757609 + 0.437406i
\(552\) −31.8577 31.8577i −1.35595 1.35595i
\(553\) 0 0
\(554\) 79.3382i 3.37076i
\(555\) −6.79687 2.16333i −0.288511 0.0918281i
\(556\) 51.1981 + 29.5593i 2.17128 + 1.25359i
\(557\) −0.204581 0.763508i −0.00866839 0.0323509i 0.961456 0.274958i \(-0.0886640\pi\)
−0.970125 + 0.242607i \(0.921997\pi\)
\(558\) −15.5200 4.15856i −0.657012 0.176046i
\(559\) 9.20823 0.389467
\(560\) 0 0
\(561\) −4.35697 −0.183951
\(562\) −53.7853 14.4117i −2.26879 0.607922i
\(563\) −0.257124 0.959599i −0.0108365 0.0404423i 0.960296 0.278983i \(-0.0899975\pi\)
−0.971132 + 0.238541i \(0.923331\pi\)
\(564\) −51.7494 29.8775i −2.17904 1.25807i
\(565\) 7.14717 3.69598i 0.300684 0.155491i
\(566\) 9.88333i 0.415427i
\(567\) 0 0
\(568\) 41.5953 + 41.5953i 1.74530 + 1.74530i
\(569\) −8.41819 + 4.86025i −0.352909 + 0.203752i −0.665966 0.745982i \(-0.731980\pi\)
0.313057 + 0.949734i \(0.398647\pi\)
\(570\) −4.98340 22.7707i −0.208732 0.953762i
\(571\) 0.493342 0.854493i 0.0206457 0.0357594i −0.855518 0.517773i \(-0.826761\pi\)
0.876164 + 0.482014i \(0.160094\pi\)
\(572\) −2.34362 + 8.74652i −0.0979918 + 0.365710i
\(573\) −5.53964 + 5.53964i −0.231422 + 0.231422i
\(574\) 0 0
\(575\) 22.4731 18.6504i 0.937192 0.777774i
\(576\) −5.44360 9.42859i −0.226817 0.392858i
\(577\) −14.1397 + 3.78872i −0.588643 + 0.157726i −0.540833 0.841130i \(-0.681891\pi\)
−0.0478100 + 0.998856i \(0.515224\pi\)
\(578\) −20.6688 + 5.53819i −0.859708 + 0.230358i
\(579\) −9.58958 16.6096i −0.398529 0.690273i
\(580\) −38.5076 42.2532i −1.59894 1.75447i
\(581\) 0 0
\(582\) −22.8720 + 22.8720i −0.948076 + 0.948076i
\(583\) 0.291508 1.08792i 0.0120730 0.0450572i
\(584\) 37.1646 64.3710i 1.53788 2.66369i
\(585\) −2.36381 1.51494i −0.0977317 0.0626352i
\(586\) 5.05272 2.91719i 0.208726 0.120508i
\(587\) 21.1413 + 21.1413i 0.872594 + 0.872594i 0.992755 0.120160i \(-0.0383409\pi\)
−0.120160 + 0.992755i \(0.538341\pi\)
\(588\) 0 0
\(589\) 24.1689i 0.995862i
\(590\) 8.64256 + 16.7127i 0.355809 + 0.688052i
\(591\) −14.0590 8.11696i −0.578310 0.333887i
\(592\) −8.62419 32.1859i −0.354452 1.32283i
\(593\) 9.66895 + 2.59079i 0.397056 + 0.106391i 0.451821 0.892108i \(-0.350774\pi\)
−0.0547654 + 0.998499i \(0.517441\pi\)
\(594\) −3.85081 −0.158001
\(595\) 0 0
\(596\) 0.477365 0.0195536
\(597\) 19.4603 + 5.21437i 0.796457 + 0.213410i
\(598\) −4.99679 18.6483i −0.204334 0.762585i
\(599\) −6.18210 3.56924i −0.252594 0.145835i 0.368358 0.929684i \(-0.379920\pi\)
−0.620951 + 0.783849i \(0.713254\pi\)
\(600\) 35.0423 16.1097i 1.43060 0.657675i
\(601\) 35.0829i 1.43106i 0.698580 + 0.715532i \(0.253815\pi\)
−0.698580 + 0.715532i \(0.746185\pi\)
\(602\) 0 0
\(603\) 5.93012 + 5.93012i 0.241493 + 0.241493i
\(604\) 57.4475 33.1673i 2.33750 1.34956i
\(605\) 19.3540 4.23565i 0.786854 0.172204i
\(606\) 20.1941 34.9771i 0.820328 1.42085i
\(607\) 1.96330 7.32715i 0.0796880 0.297400i −0.914567 0.404434i \(-0.867469\pi\)
0.994255 + 0.107034i \(0.0341353\pi\)
\(608\) 33.8014 33.8014i 1.37083 1.37083i
\(609\) 0 0
\(610\) 0.387427 8.35359i 0.0156865 0.338227i
\(611\) −7.60919 13.1795i −0.307835 0.533186i
\(612\) 14.1842 3.80064i 0.573362 0.153632i
\(613\) 14.3280 3.83917i 0.578701 0.155062i 0.0424169 0.999100i \(-0.486494\pi\)
0.536284 + 0.844038i \(0.319828\pi\)
\(614\) 32.3060 + 55.9557i 1.30376 + 2.25819i
\(615\) −0.0797641 + 1.71985i −0.00321640 + 0.0693511i
\(616\) 0 0
\(617\) 19.7986 19.7986i 0.797060 0.797060i −0.185571 0.982631i \(-0.559414\pi\)
0.982631 + 0.185571i \(0.0594135\pi\)
\(618\) −8.00508 + 29.8754i −0.322011 + 1.20176i
\(619\) −6.03375 + 10.4508i −0.242517 + 0.420052i −0.961431 0.275048i \(-0.911306\pi\)
0.718914 + 0.695099i \(0.244640\pi\)
\(620\) 65.7294 14.3850i 2.63976 0.577714i
\(621\) 5.05829 2.92040i 0.202982 0.117192i
\(622\) −57.8262 57.8262i −2.31862 2.31862i
\(623\) 0 0
\(624\) 13.1158i 0.525054i
\(625\) 8.29516 + 23.5837i 0.331806 + 0.943348i
\(626\) 18.4559 + 10.6555i 0.737647 + 0.425880i
\(627\) −1.49920 5.59508i −0.0598722 0.223446i
\(628\) 11.0959 + 2.97313i 0.442774 + 0.118641i
\(629\) 9.50124 0.378839
\(630\) 0 0
\(631\) 30.4435 1.21194 0.605969 0.795488i \(-0.292786\pi\)
0.605969 + 0.795488i \(0.292786\pi\)
\(632\) −33.6796 9.02442i −1.33970 0.358972i
\(633\) 3.09707 + 11.5584i 0.123098 + 0.459406i
\(634\) −2.42643 1.40090i −0.0963660 0.0556369i
\(635\) −11.4175 22.0788i −0.453090 0.876172i
\(636\) 3.79604i 0.150523i
\(637\) 0 0
\(638\) −14.1204 14.1204i −0.559032 0.559032i
\(639\) −6.60440 + 3.81305i −0.261266 + 0.150842i
\(640\) 8.50426 + 5.45029i 0.336160 + 0.215442i
\(641\) −18.2964 + 31.6904i −0.722666 + 1.25169i 0.237262 + 0.971446i \(0.423750\pi\)
−0.959928 + 0.280248i \(0.909583\pi\)
\(642\) 4.23027 15.7876i 0.166955 0.623086i
\(643\) 12.1140 12.1140i 0.477731 0.477731i −0.426675 0.904405i \(-0.640315\pi\)
0.904405 + 0.426675i \(0.140315\pi\)
\(644\) 0 0
\(645\) −11.0460 12.1204i −0.434935 0.477240i
\(646\) 15.5247 + 26.8896i 0.610813 + 1.05796i
\(647\) −26.0881 + 6.99030i −1.02563 + 0.274817i −0.732147 0.681147i \(-0.761481\pi\)
−0.293484 + 0.955964i \(0.594815\pi\)
\(648\) 7.45075 1.99642i 0.292693 0.0784269i
\(649\) 2.33778 + 4.04915i 0.0917658 + 0.158943i
\(650\) 16.4560 + 1.52970i 0.645457 + 0.0599997i
\(651\) 0 0
\(652\) −50.6552 + 50.6552i −1.98381 + 1.98381i
\(653\) 7.45625 27.8271i 0.291786 1.08896i −0.651951 0.758261i \(-0.726049\pi\)
0.943737 0.330698i \(-0.107284\pi\)
\(654\) −9.80067 + 16.9753i −0.383237 + 0.663785i
\(655\) −2.95539 13.5041i −0.115477 0.527650i
\(656\) −6.96543 + 4.02149i −0.271954 + 0.157013i
\(657\) 6.81378 + 6.81378i 0.265831 + 0.265831i
\(658\) 0 0
\(659\) 31.4882i 1.22661i −0.789847 0.613304i \(-0.789840\pi\)
0.789847 0.613304i \(-0.210160\pi\)
\(660\) 14.3240 7.40730i 0.557561 0.288329i
\(661\) −41.7321 24.0940i −1.62319 0.937149i −0.986060 0.166392i \(-0.946788\pi\)
−0.637129 0.770757i \(-0.719878\pi\)
\(662\) −10.7709 40.1974i −0.418621 1.56231i
\(663\) 3.61242 + 0.967945i 0.140295 + 0.0375919i
\(664\) 73.7201 2.86089
\(665\) 0 0
\(666\) 8.39746 0.325395
\(667\) 29.2567 + 7.83932i 1.13283 + 0.303540i
\(668\) −0.528748 1.97332i −0.0204579 0.0763499i
\(669\) 0.809446 + 0.467334i 0.0312950 + 0.0180682i
\(670\) −47.0414 14.9725i −1.81737 0.578438i
\(671\) 2.07810i 0.0802241i
\(672\) 0 0
\(673\) −30.6900 30.6900i −1.18301 1.18301i −0.978960 0.204055i \(-0.934588\pi\)
−0.204055 0.978960i \(-0.565412\pi\)
\(674\) −64.6314 + 37.3149i −2.48951 + 1.43732i
\(675\) 0.841520 + 4.92868i 0.0323901 + 0.189705i
\(676\) −28.1595 + 48.7738i −1.08306 + 1.87591i
\(677\) 0.563899 2.10450i 0.0216724 0.0808825i −0.954243 0.299033i \(-0.903336\pi\)
0.975915 + 0.218151i \(0.0700025\pi\)
\(678\) −6.69830 + 6.69830i −0.257246 + 0.257246i
\(679\) 0 0
\(680\) −37.9710 + 34.6050i −1.45612 + 1.32704i
\(681\) −12.2674 21.2477i −0.470087 0.814215i
\(682\) 22.7024 6.08310i 0.869321 0.232934i
\(683\) −19.4186 + 5.20319i −0.743030 + 0.199094i −0.610424 0.792074i \(-0.709001\pi\)
−0.132606 + 0.991169i \(0.542334\pi\)
\(684\) 9.76132 + 16.9071i 0.373234 + 0.646459i
\(685\) 28.6057 + 1.32669i 1.09297 + 0.0506903i
\(686\) 0 0
\(687\) 17.7330 17.7330i 0.676555 0.676555i
\(688\) 19.8274 73.9968i 0.755912 2.82110i
\(689\) −0.483386 + 0.837249i −0.0184155 + 0.0318967i
\(690\) −18.5519 + 28.9471i −0.706258 + 1.10200i
\(691\) −8.91028 + 5.14435i −0.338963 + 0.195700i −0.659813 0.751429i \(-0.729365\pi\)
0.320850 + 0.947130i \(0.396031\pi\)
\(692\) −17.0182 17.0182i −0.646937 0.646937i
\(693\) 0 0
\(694\) 74.7741i 2.83838i
\(695\) 8.13225 25.5504i 0.308474 0.969180i
\(696\) 34.6415 + 20.0003i 1.31308 + 0.758108i
\(697\) −0.593570 2.21523i −0.0224831 0.0839079i
\(698\) −37.5478 10.0609i −1.42121 0.380811i
\(699\) 3.16979 0.119892
\(700\) 0 0
\(701\) −44.3183 −1.67388 −0.836939 0.547297i \(-0.815657\pi\)
−0.836939 + 0.547297i \(0.815657\pi\)
\(702\) 3.19276 + 0.855497i 0.120503 + 0.0322887i
\(703\) 3.26930 + 12.2012i 0.123304 + 0.460176i
\(704\) 13.7920 + 7.96284i 0.519807 + 0.300111i
\(705\) −8.21981 + 25.8255i −0.309576 + 0.972643i
\(706\) 46.4958i 1.74989i
\(707\) 0 0
\(708\) −11.1428 11.1428i −0.418772 0.418772i
\(709\) 0.708388 0.408988i 0.0266041 0.0153599i −0.486639 0.873603i \(-0.661777\pi\)
0.513243 + 0.858243i \(0.328444\pi\)
\(710\) 24.2225 37.7951i 0.909053 1.41842i
\(711\) 2.26015 3.91469i 0.0847621 0.146812i
\(712\) −2.39553 + 8.94022i −0.0897761 + 0.335049i
\(713\) −25.2077 + 25.2077i −0.944037 + 0.944037i
\(714\) 0 0
\(715\) 4.10253 + 0.190269i 0.153426 + 0.00711567i
\(716\) −4.92411 8.52880i −0.184022 0.318736i
\(717\) −20.6485 + 5.53276i −0.771134 + 0.206625i
\(718\) 26.7941 7.17947i 0.999949 0.267935i
\(719\) 0.00381028 + 0.00659960i 0.000142099 + 0.000246124i 0.866096 0.499877i \(-0.166621\pi\)
−0.865954 + 0.500123i \(0.833288\pi\)
\(720\) −17.2638 + 15.7335i −0.643385 + 0.586351i
\(721\) 0 0
\(722\) 6.17902 6.17902i 0.229959 0.229959i
\(723\) −0.161537 + 0.602863i −0.00600761 + 0.0224207i
\(724\) 20.9167 36.2289i 0.777365 1.34644i
\(725\) −14.9870 + 21.1585i −0.556604 + 0.785807i
\(726\) −20.1998 + 11.6624i −0.749685 + 0.432831i
\(727\) −28.5738 28.5738i −1.05974 1.05974i −0.998098 0.0616465i \(-0.980365\pi\)
−0.0616465 0.998098i \(-0.519635\pi\)
\(728\) 0 0
\(729\) 1.00000i 0.0370370i
\(730\) −54.0512 17.2036i −2.00052 0.636732i
\(731\) 18.9173 + 10.9219i 0.699680 + 0.403960i
\(732\) 1.81275 + 6.76528i 0.0670012 + 0.250052i
\(733\) −32.9926 8.84033i −1.21861 0.326525i −0.408475 0.912770i \(-0.633939\pi\)
−0.810134 + 0.586244i \(0.800606\pi\)
\(734\) 41.6632 1.53782
\(735\) 0 0
\(736\) −70.5085 −2.59898
\(737\) −11.8496 3.17510i −0.436486 0.116956i
\(738\) −0.524613 1.95788i −0.0193113 0.0720707i
\(739\) −32.8676 18.9761i −1.20905 0.698047i −0.246500 0.969143i \(-0.579281\pi\)
−0.962552 + 0.271096i \(0.912614\pi\)
\(740\) −31.2363 + 16.1531i −1.14827 + 0.593799i
\(741\) 4.97202i 0.182652i
\(742\) 0 0
\(743\) −18.8022 18.8022i −0.689784 0.689784i 0.272400 0.962184i \(-0.412183\pi\)
−0.962184 + 0.272400i \(0.912183\pi\)
\(744\) −40.7721 + 23.5398i −1.49478 + 0.863010i
\(745\) −0.0462878 0.211504i −0.00169586 0.00774890i
\(746\) 32.1562 55.6961i 1.17732 2.03918i
\(747\) −2.47358 + 9.23152i −0.0905035 + 0.337764i
\(748\) −15.1889 + 15.1889i −0.555363 + 0.555363i
\(749\) 0 0
\(750\) −17.7267 23.4953i −0.647289 0.857927i
\(751\) −0.0529576 0.0917252i −0.00193245 0.00334710i 0.865058 0.501673i \(-0.167282\pi\)
−0.866990 + 0.498326i \(0.833948\pi\)
\(752\) −122.294 + 32.7686i −4.45960 + 1.19495i
\(753\) −15.7874 + 4.23022i −0.575325 + 0.154158i
\(754\) 8.57041 + 14.8444i 0.312116 + 0.540601i
\(755\) −20.2657 22.2369i −0.737545 0.809284i
\(756\) 0 0
\(757\) 3.14514 3.14514i 0.114312 0.114312i −0.647637 0.761949i \(-0.724243\pi\)
0.761949 + 0.647637i \(0.224243\pi\)
\(758\) 12.0078 44.8137i 0.436143 1.62771i
\(759\) −4.27193 + 7.39921i −0.155061 + 0.268574i
\(760\) −57.5041 36.8538i −2.08589 1.33683i
\(761\) 30.4082 17.5562i 1.10230 0.636410i 0.165472 0.986214i \(-0.447085\pi\)
0.936823 + 0.349804i \(0.113752\pi\)
\(762\) 20.6922 + 20.6922i 0.749599 + 0.749599i
\(763\) 0 0
\(764\) 38.6238i 1.39736i
\(765\) −3.05931 5.91600i −0.110610 0.213893i
\(766\) 51.9891 + 30.0159i 1.87844 + 1.08452i
\(767\) −1.03872 3.87656i −0.0375061 0.139975i
\(768\) 9.54591 + 2.55782i 0.344458 + 0.0922973i
\(769\) −8.16835 −0.294558 −0.147279 0.989095i \(-0.547052\pi\)
−0.147279 + 0.989095i \(0.547052\pi\)
\(770\) 0