Properties

Label 735.2.v.a.472.2
Level 735
Weight 2
Character 735.472
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 472.2
Character \(\chi\) \(=\) 735.472
Dual form 735.2.v.a.313.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.681344 + 2.54281i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-4.26961 - 2.46506i) q^{4} +(2.18437 + 0.478051i) q^{5} +2.63251i q^{6} +(5.45433 - 5.45433i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})\) \(q+(-0.681344 + 2.54281i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-4.26961 - 2.46506i) q^{4} +(2.18437 + 0.478051i) q^{5} +2.63251i q^{6} +(5.45433 - 5.45433i) q^{8} +(0.866025 - 0.500000i) q^{9} +(-2.70390 + 5.22872i) q^{10} +(0.731395 - 1.26681i) q^{11} +(-4.76213 - 1.27601i) q^{12} +(0.887844 + 0.887844i) q^{13} +(2.23367 - 0.103594i) q^{15} +(5.22294 + 9.04639i) q^{16} +(-0.770902 - 2.87705i) q^{17} +(0.681344 + 2.54281i) q^{18} +(1.97993 + 3.42935i) q^{19} +(-8.14798 - 7.42570i) q^{20} +(2.72294 + 2.72294i) q^{22} +(5.64178 + 1.51171i) q^{23} +(3.85679 - 6.68016i) q^{24} +(4.54293 + 2.08848i) q^{25} +(-2.86255 + 1.65269i) q^{26} +(0.707107 - 0.707107i) q^{27} +5.18572i q^{29} +(-1.25848 + 5.75038i) q^{30} +(5.28575 + 3.05173i) q^{31} +(-11.6604 + 3.12439i) q^{32} +(0.378598 - 1.41295i) q^{33} +7.84104 q^{34} -4.93012 q^{36} +(0.825607 - 3.08121i) q^{37} +(-10.0692 + 2.69804i) q^{38} +(1.08738 + 0.627801i) q^{39} +(14.5217 - 9.30682i) q^{40} +0.769968i q^{41} +(-5.18572 + 5.18572i) q^{43} +(-6.24554 + 3.60587i) q^{44} +(2.13074 - 0.678180i) q^{45} +(-7.68800 + 13.3160i) q^{46} +(-11.7074 - 3.13699i) q^{47} +(7.38635 + 7.38635i) q^{48} +(-8.40592 + 10.1289i) q^{50} +(-1.48927 - 2.57949i) q^{51} +(-1.60216 - 5.97934i) q^{52} +(-0.199282 - 0.743732i) q^{53} +(1.31626 + 2.27982i) q^{54} +(2.20324 - 2.41754i) q^{55} +(2.80005 + 2.80005i) q^{57} +(-13.1863 - 3.53326i) q^{58} +(1.59816 - 2.76810i) q^{59} +(-9.79226 - 5.06382i) q^{60} +(1.23031 - 0.710320i) q^{61} +(-11.3614 + 11.3614i) q^{62} -10.8872i q^{64} +(1.51494 + 2.36381i) q^{65} +(3.33490 + 1.92541i) q^{66} +(8.10070 - 2.17058i) q^{67} +(-3.80064 + 14.1842i) q^{68} +5.84081 q^{69} +7.62611 q^{71} +(1.99642 - 7.45075i) q^{72} +(-9.30780 + 2.49402i) q^{73} +(7.27241 + 4.19873i) q^{74} +(4.92868 + 0.841520i) q^{75} -19.5226i q^{76} +(-2.33726 + 2.33726i) q^{78} +(3.91469 - 2.26015i) q^{79} +(7.08418 + 22.2575i) q^{80} +(0.500000 - 0.866025i) q^{81} +(-1.95788 - 0.524613i) q^{82} +(-6.75794 - 6.75794i) q^{83} +(-0.308559 - 6.65306i) q^{85} +(-9.65306 - 16.7196i) q^{86} +(1.34216 + 5.00903i) q^{87} +(-2.92035 - 10.8989i) q^{88} +(-0.599954 - 1.03915i) q^{89} +(0.272713 + 5.88016i) q^{90} +(-20.3618 - 20.3618i) q^{92} +(5.89549 + 1.57969i) q^{93} +(15.9535 - 27.6323i) q^{94} +(2.68550 + 8.43747i) 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 \(\left(\mathbb{Z}/735\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.681344 + 2.54281i −0.481783 + 1.79804i 0.112345 + 0.993669i \(0.464164\pi\)
−0.594128 + 0.804370i \(0.702503\pi\)
\(3\) 0.965926 0.258819i 0.557678 0.149429i
\(4\) −4.26961 2.46506i −2.13481 1.23253i
\(5\) 2.18437 + 0.478051i 0.976879 + 0.213791i
\(6\) 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
\(10\) −2.70390 + 5.22872i −0.855049 + 1.65347i
\(11\) 0.731395 1.26681i 0.220524 0.381958i −0.734443 0.678670i \(-0.762557\pi\)
0.954967 + 0.296712i \(0.0958900\pi\)
\(12\) −4.76213 1.27601i −1.37471 0.368352i
\(13\) 0.887844 + 0.887844i 0.246244 + 0.246244i 0.819427 0.573183i \(-0.194292\pi\)
−0.573183 + 0.819427i \(0.694292\pi\)
\(14\) 0 0
\(15\) 2.23367 0.103594i 0.576730 0.0267479i
\(16\) 5.22294 + 9.04639i 1.30573 + 2.26160i
\(17\) −0.770902 2.87705i −0.186971 0.697786i −0.994200 0.107547i \(-0.965700\pi\)
0.807229 0.590239i \(-0.200966\pi\)
\(18\) 0.681344 + 2.54281i 0.160594 + 0.599347i
\(19\) 1.97993 + 3.42935i 0.454228 + 0.786746i 0.998643 0.0520695i \(-0.0165817\pi\)
−0.544415 + 0.838816i \(0.683248\pi\)
\(20\) −8.14798 7.42570i −1.82194 1.66044i
\(21\) 0 0
\(22\) 2.72294 + 2.72294i 0.580532 + 0.580532i
\(23\) 5.64178 + 1.51171i 1.17639 + 0.315214i 0.793495 0.608577i \(-0.208259\pi\)
0.382898 + 0.923790i \(0.374926\pi\)
\(24\) 3.85679 6.68016i 0.787265 1.36358i
\(25\) 4.54293 + 2.08848i 0.908587 + 0.417696i
\(26\) −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 \(0.159901\pi\)
−0.876456 + 0.481482i \(0.840099\pi\)
\(30\) −1.25848 + 5.75038i −0.229765 + 1.04987i
\(31\) 5.28575 + 3.05173i 0.949349 + 0.548107i 0.892879 0.450297i \(-0.148682\pi\)
0.0564703 + 0.998404i \(0.482015\pi\)
\(32\) −11.6604 + 3.12439i −2.06128 + 0.552319i
\(33\) 0.378598 1.41295i 0.0659054 0.245962i
\(34\) 7.84104 1.34473
\(35\) 0 0
\(36\) −4.93012 −0.821687
\(37\) 0.825607 3.08121i 0.135729 0.506548i −0.864265 0.503037i \(-0.832216\pi\)
0.999994 0.00351049i \(-0.00111743\pi\)
\(38\) −10.0692 + 2.69804i −1.63344 + 0.437679i
\(39\) 1.08738 + 0.627801i 0.174121 + 0.100529i
\(40\) 14.5217 9.30682i 2.29609 1.47154i
\(41\) 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 −0.981627 0.190811i \(-0.938888\pi\)
0.190811 + 0.981627i \(0.438888\pi\)
\(44\) −6.24554 + 3.60587i −0.941551 + 0.543605i
\(45\) 2.13074 0.678180i 0.317633 0.101097i
\(46\) −7.68800 + 13.3160i −1.13353 + 1.96334i
\(47\) −11.7074 3.13699i −1.70770 0.457577i −0.732841 0.680400i \(-0.761806\pi\)
−0.974859 + 0.222823i \(0.928473\pi\)
\(48\) 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
\(52\) −1.60216 5.97934i −0.222180 0.829185i
\(53\) −0.199282 0.743732i −0.0273735 0.102159i 0.950888 0.309537i \(-0.100174\pi\)
−0.978261 + 0.207377i \(0.933507\pi\)
\(54\) 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
\(58\) −13.1863 3.53326i −1.73145 0.463940i
\(59\) 1.59816 2.76810i 0.208063 0.360376i −0.743041 0.669246i \(-0.766617\pi\)
0.951104 + 0.308870i \(0.0999507\pi\)
\(60\) −9.79226 5.06382i −1.26418 0.653736i
\(61\) 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
\(65\) 1.51494 + 2.36381i 0.187906 + 0.293195i
\(66\) 3.33490 + 1.92541i 0.410498 + 0.237001i
\(67\) 8.10070 2.17058i 0.989658 0.265178i 0.272551 0.962141i \(-0.412133\pi\)
0.717107 + 0.696963i \(0.245466\pi\)
\(68\) −3.80064 + 14.1842i −0.460896 + 1.72009i
\(69\) 5.84081 0.703150
\(70\) 0 0
\(71\) 7.62611 0.905053 0.452526 0.891751i \(-0.350523\pi\)
0.452526 + 0.891751i \(0.350523\pi\)
\(72\) 1.99642 7.45075i 0.235281 0.878080i
\(73\) −9.30780 + 2.49402i −1.08940 + 0.291903i −0.758439 0.651744i \(-0.774038\pi\)
−0.330956 + 0.943646i \(0.607371\pi\)
\(74\) 7.27241 + 4.19873i 0.845401 + 0.488092i
\(75\) 4.92868 + 0.841520i 0.569114 + 0.0971703i
\(76\) 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 −0.263346 0.964701i \(-0.584826\pi\)
0.703783 + 0.710415i \(0.251493\pi\)
\(80\) 7.08418 + 22.2575i 0.792035 + 2.48846i
\(81\) 0.500000 0.866025i 0.0555556 0.0962250i
\(82\) −1.95788 0.524613i −0.216212 0.0579338i
\(83\) −6.75794 6.75794i −0.741781 0.741781i 0.231140 0.972921i \(-0.425754\pi\)
−0.972921 + 0.231140i \(0.925754\pi\)
\(84\) 0 0
\(85\) −0.308559 6.65306i −0.0334679 0.721626i
\(86\) −9.65306 16.7196i −1.04092 1.80292i
\(87\) 1.34216 + 5.00903i 0.143895 + 0.537024i
\(88\) −2.92035 10.8989i −0.311310 1.16182i
\(89\) −0.599954 1.03915i −0.0635950 0.110150i 0.832475 0.554063i \(-0.186923\pi\)
−0.896070 + 0.443913i \(0.853590\pi\)
\(90\) 0.272713 + 5.88016i 0.0287465 + 0.619823i
\(91\) 0 0
\(92\) −20.3618 20.3618i −2.12286 2.12286i
\(93\) 5.89549 + 1.57969i 0.611334 + 0.163806i
\(94\) 15.9535 27.6323i 1.64548 2.85006i
\(95\) 2.68550 + 8.43747i 0.275527 + 0.865666i
\(96\) −10.4544 + 6.03586i −1.06700 + 0.616032i
\(97\) −8.68829 + 8.68829i −0.882162 + 0.882162i −0.993754 0.111592i \(-0.964405\pi\)
0.111592 + 0.993754i \(0.464405\pi\)
\(98\) 0 0
\(99\) 1.46279i 0.147016i
\(100\) −14.2483 20.1156i −1.42483 2.01156i
\(101\) −13.2866 7.67102i −1.32207 0.763295i −0.338008 0.941143i \(-0.609753\pi\)
−0.984058 + 0.177848i \(0.943086\pi\)
\(102\) 7.57386 2.02941i 0.749924 0.200941i
\(103\) 3.04085 11.3486i 0.299624 1.11821i −0.637851 0.770160i \(-0.720177\pi\)
0.937475 0.348052i \(-0.113157\pi\)
\(104\) 9.68519 0.949711
\(105\) 0 0
\(106\) 2.02695 0.196875
\(107\) 1.60693 5.99715i 0.155348 0.579766i −0.843727 0.536772i \(-0.819644\pi\)
0.999075 0.0429945i \(-0.0136898\pi\)
\(108\) −4.76213 + 1.27601i −0.458237 + 0.122784i
\(109\) −6.44831 3.72294i −0.617636 0.356593i 0.158312 0.987389i \(-0.449395\pi\)
−0.775948 + 0.630797i \(0.782728\pi\)
\(110\) 4.64619 + 7.24960i 0.442997 + 0.691222i
\(111\) 3.18990i 0.302772i
\(112\) 0 0
\(113\) 2.54445 2.54445i 0.239362 0.239362i −0.577224 0.816586i \(-0.695864\pi\)
0.816586 + 0.577224i \(0.195864\pi\)
\(114\) −9.02780 + 5.21220i −0.845531 + 0.488168i
\(115\) 11.6011 + 5.99920i 1.08180 + 0.559428i
\(116\) 12.7831 22.1410i 1.18688 2.05574i
\(117\) 1.21282 + 0.324974i 0.112125 + 0.0300438i
\(118\) 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
\(122\) 0.967945 + 3.61242i 0.0876337 + 0.327053i
\(123\) 0.199282 + 0.743732i 0.0179687 + 0.0670600i
\(124\) −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 0.963867 0.266383i \(-0.0858286\pi\)
−0.266383 + 0.963867i \(0.585829\pi\)
\(128\) 4.36334 + 1.16915i 0.385668 + 0.103339i
\(129\) −3.66686 + 6.35119i −0.322849 + 0.559191i
\(130\) −7.04293 + 2.24165i −0.617706 + 0.196605i
\(131\) 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
\(135\) 1.88262 1.20655i 0.162030 0.103843i
\(136\) −19.8971 11.4876i −1.70616 0.985054i
\(137\) −12.3703 + 3.31460i −1.05686 + 0.283185i −0.745085 0.666970i \(-0.767591\pi\)
−0.311777 + 0.950155i \(0.600924\pi\)
\(138\) −3.97960 + 14.8521i −0.338766 + 1.26429i
\(139\) −11.9913 −1.01709 −0.508544 0.861036i \(-0.669816\pi\)
−0.508544 + 0.861036i \(0.669816\pi\)
\(140\) 0 0
\(141\) −12.1204 −1.02072
\(142\) −5.19601 + 19.3918i −0.436039 + 1.62732i
\(143\) 1.77410 0.475368i 0.148357 0.0397523i
\(144\) 9.04639 + 5.22294i 0.753866 + 0.435245i
\(145\) −2.47904 + 11.3275i −0.205873 + 0.940701i
\(146\) 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 −0.503431 0.864036i \(-0.667929\pi\)
0.496561 + 0.868002i \(0.334596\pi\)
\(150\) −5.49795 + 11.9593i −0.448906 + 0.976475i
\(151\) 6.72748 11.6523i 0.547475 0.948254i −0.450972 0.892538i \(-0.648923\pi\)
0.998447 0.0557157i \(-0.0177440\pi\)
\(152\) 29.5040 + 7.90558i 2.39309 + 0.641227i
\(153\) −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
\(157\) 0.603054 + 2.25063i 0.0481290 + 0.179620i 0.985806 0.167888i \(-0.0536947\pi\)
−0.937677 + 0.347508i \(0.887028\pi\)
\(158\) 3.07988 + 11.4943i 0.245022 + 0.914434i
\(159\) −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
\(163\) 14.0354 + 3.76077i 1.09934 + 0.294566i 0.762495 0.646995i \(-0.223974\pi\)
0.336842 + 0.941561i \(0.390641\pi\)
\(164\) 1.89802 3.28746i 0.148210 0.256708i
\(165\) 1.50246 2.90541i 0.116966 0.226186i
\(166\) 21.7887 12.5797i 1.69113 0.976373i
\(167\) 0.293008 0.293008i 0.0226737 0.0226737i −0.695679 0.718353i \(-0.744896\pi\)
0.718353 + 0.695679i \(0.244896\pi\)
\(168\) 0 0
\(169\) 11.4235i 0.878728i
\(170\) 17.1277 + 3.74842i 1.31364 + 0.287490i
\(171\) 3.42935 + 1.97993i 0.262249 + 0.151409i
\(172\) 34.9242 9.35790i 2.66294 0.713533i
\(173\) −1.26348 + 4.71537i −0.0960606 + 0.358503i −0.997178 0.0750719i \(-0.976081\pi\)
0.901118 + 0.433575i \(0.142748\pi\)
\(174\) −13.6515 −1.03492
\(175\) 0 0
\(176\) 15.2801 1.15178
\(177\) 0.827271 3.08742i 0.0621815 0.232064i
\(178\) 3.05114 0.817551i 0.228693 0.0612781i
\(179\) 1.72994 + 0.998779i 0.129302 + 0.0746523i 0.563256 0.826283i \(-0.309549\pi\)
−0.433954 + 0.900935i \(0.642882\pi\)
\(180\) −10.7692 2.35685i −0.802689 0.175669i
\(181\) 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
\(185\) 3.27641 6.33581i 0.240886 0.465818i
\(186\) −8.03372 + 13.9148i −0.589061 + 1.02028i
\(187\) −4.20851 1.12767i −0.307757 0.0824632i
\(188\) 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 \(0.741860\pi\)
\(192\) −2.81781 10.5162i −0.203358 0.758943i
\(193\) 4.96393 + 18.5257i 0.357312 + 1.33351i 0.877550 + 0.479485i \(0.159176\pi\)
−0.520239 + 0.854021i \(0.674157\pi\)
\(194\) −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 0.167943 0.985797i \(-0.446287\pi\)
−0.985797 + 0.167943i \(0.946287\pi\)
\(198\) 3.71960 + 0.996663i 0.264340 + 0.0708298i
\(199\) −10.0734 + 17.4476i −0.714084 + 1.23683i 0.249228 + 0.968445i \(0.419823\pi\)
−0.963312 + 0.268384i \(0.913510\pi\)
\(200\) 36.1699 13.3874i 2.55760 0.946632i
\(201\) 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
\(205\) −0.368084 + 1.68189i −0.0257081 + 0.117469i
\(206\) 26.7855 + 15.4646i 1.86623 + 1.07747i
\(207\) 5.64178 1.51171i 0.392131 0.105071i
\(208\) −3.39463 + 12.6689i −0.235375 + 0.878433i
\(209\) 5.79246 0.400673
\(210\) 0 0
\(211\) 11.9662 0.823785 0.411892 0.911233i \(-0.364868\pi\)
0.411892 + 0.911233i \(0.364868\pi\)
\(212\) −0.982486 + 3.66669i −0.0674774 + 0.251829i
\(213\) 7.36626 1.97378i 0.504728 0.135241i
\(214\) 14.1548 + 8.17225i 0.967599 + 0.558644i
\(215\) −13.8066 + 8.84849i −0.941601 + 0.603462i
\(216\) 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
\(220\) −15.3664 + 4.89085i −1.03600 + 0.329741i
\(221\) 1.86993 3.23881i 0.125785 0.217866i
\(222\) 8.11132 + 2.17342i 0.544396 + 0.145871i
\(223\) −0.660910 0.660910i −0.0442578 0.0442578i 0.684632 0.728889i \(-0.259963\pi\)
−0.728889 + 0.684632i \(0.759963\pi\)
\(224\) 0 0
\(225\) 4.97854 0.462789i 0.331902 0.0308526i
\(226\) 4.73641 + 8.20370i 0.315061 + 0.545702i
\(227\) −6.35007 23.6988i −0.421469 1.57294i −0.771516 0.636210i \(-0.780501\pi\)
0.350047 0.936732i \(-0.386166\pi\)
\(228\) −5.05283 18.8574i −0.334632 1.24886i
\(229\) 12.5391 + 21.7184i 0.828607 + 1.43519i 0.899131 + 0.437679i \(0.144200\pi\)
−0.0705240 + 0.997510i \(0.522467\pi\)
\(230\) −23.1592 + 25.4118i −1.52707 + 1.67560i
\(231\) 0 0
\(232\) 28.2847 + 28.2847i 1.85698 + 1.85698i
\(233\) −3.06178 0.820401i −0.200584 0.0537462i 0.157128 0.987578i \(-0.449776\pi\)
−0.357712 + 0.933832i \(0.616443\pi\)
\(234\) −1.65269 + 2.86255i −0.108040 + 0.187131i
\(235\) −24.0736 12.4491i −1.57039 0.812088i
\(236\) −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 \(-0.757003\pi\)
0.722492 0.691380i \(-0.242997\pi\)
\(240\) 12.6035 + 19.6656i 0.813549 + 1.26941i
\(241\) 0.540512 + 0.312065i 0.0348174 + 0.0201018i 0.517308 0.855799i \(-0.326934\pi\)
−0.482490 + 0.875901i \(0.660268\pi\)
\(242\) −22.5299 + 6.03688i −1.44828 + 0.388065i
\(243\) 0.258819 0.965926i 0.0166032 0.0619642i
\(244\) −7.00393 −0.448381
\(245\) 0 0
\(246\) −2.02695 −0.129234
\(247\) −1.28685 + 4.80260i −0.0818805 + 0.305582i
\(248\) 45.4754 12.1851i 2.88769 0.773754i
\(249\) −8.27676 4.77859i −0.524518 0.302831i
\(250\) −23.2037 + 18.1067i −1.46753 + 1.14517i
\(251\) 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
\(255\) −2.01998 6.34650i −0.126496 0.397433i
\(256\) 4.94133 8.55863i 0.308833 0.534914i
\(257\) −29.1038 7.79833i −1.81544 0.486446i −0.819235 0.573458i \(-0.805602\pi\)
−0.996207 + 0.0870116i \(0.972268\pi\)
\(258\) −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
\(262\) 4.21218 + 15.7201i 0.260230 + 0.971190i
\(263\) −5.98263 22.3275i −0.368905 1.37677i −0.862049 0.506824i \(-0.830819\pi\)
0.493145 0.869947i \(-0.335847\pi\)
\(264\) −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
\(268\) −39.9374 10.7012i −2.43957 0.653680i
\(269\) 8.29515 14.3676i 0.505764 0.876009i −0.494213 0.869341i \(-0.664544\pi\)
0.999978 0.00666889i \(-0.00212279\pi\)
\(270\) 1.78532 + 5.60921i 0.108651 + 0.341366i
\(271\) 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
\(275\) 5.96839 4.22754i 0.359908 0.254930i
\(276\) −24.9380 14.3979i −1.50109 0.866654i
\(277\) −29.1109 + 7.80024i −1.74910 + 0.468671i −0.984435 0.175751i \(-0.943765\pi\)
−0.764670 + 0.644422i \(0.777098\pi\)
\(278\) 8.17019 30.4916i 0.490016 1.82876i
\(279\) 6.10346 0.365405
\(280\) 0 0
\(281\) −21.1519 −1.26182 −0.630908 0.775858i \(-0.717317\pi\)
−0.630908 + 0.775858i \(0.717317\pi\)
\(282\) 8.25816 30.8199i 0.491766 1.83530i
\(283\) −3.62641 + 0.971693i −0.215567 + 0.0577611i −0.364986 0.931013i \(-0.618926\pi\)
0.149419 + 0.988774i \(0.452260\pi\)
\(284\) −32.5605 18.7988i −1.93211 1.11551i
\(285\) 4.77778 + 7.45491i 0.283011 + 0.441591i
\(286\) 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
\(290\) −27.1147 14.0217i −1.59223 0.823382i
\(291\) −6.14355 + 10.6409i −0.360141 + 0.623783i
\(292\) 45.8886 + 12.2958i 2.68543 + 0.719558i
\(293\) −1.56714 1.56714i −0.0915536 0.0915536i 0.659847 0.751400i \(-0.270621\pi\)
−0.751400 + 0.659847i \(0.770621\pi\)
\(294\) 0 0
\(295\) 4.81428 5.28255i 0.280298 0.307562i
\(296\) −12.3028 21.3091i −0.715085 1.23856i
\(297\) −0.378598 1.41295i −0.0219685 0.0819875i
\(298\) −0.0659719 0.246211i −0.00382165 0.0142626i
\(299\) 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
\(303\) −14.8193 3.97081i −0.851345 0.228117i
\(304\) −20.6821 + 35.8225i −1.18620 + 2.05456i
\(305\) 3.02702 0.963450i 0.173327 0.0551670i
\(306\) 6.79054 3.92052i 0.388189 0.224121i
\(307\) −17.3551 + 17.3551i −0.990510 + 0.990510i −0.999955 0.00944588i \(-0.996993\pi\)
0.00944588 + 0.999955i \(0.496993\pi\)
\(308\) 0 0
\(309\) 11.7489i 0.668374i
\(310\) −30.2488 + 19.3861i −1.71802 + 1.10106i
\(311\) −26.9029 15.5324i −1.52553 0.880763i −0.999542 0.0302685i \(-0.990364\pi\)
−0.525984 0.850494i \(-0.676303\pi\)
\(312\) 9.35518 2.50671i 0.529633 0.141915i
\(313\) 2.09522 7.81948i 0.118429 0.441983i −0.881091 0.472946i \(-0.843191\pi\)
0.999521 + 0.0309625i \(0.00985725\pi\)
\(314\) −6.13381 −0.346151
\(315\) 0 0
\(316\) −22.2856 −1.25366
\(317\) 0.275463 1.02804i 0.0154715 0.0577406i −0.957759 0.287574i \(-0.907151\pi\)
0.973230 + 0.229833i \(0.0738180\pi\)
\(318\) 1.95788 0.524613i 0.109793 0.0294188i
\(319\) 6.56934 + 3.79281i 0.367813 + 0.212357i
\(320\) 5.20464 23.7817i 0.290948 1.32943i
\(321\) 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
\(325\) 2.17917 + 5.88766i 0.120879 + 0.326589i
\(326\) −19.1259 + 33.1270i −1.05928 + 1.83473i
\(327\) −7.19216 1.92713i −0.397727 0.106571i
\(328\) 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 \(0.976390\pi\)
\(332\) 12.1950 + 45.5125i 0.669290 + 2.49783i
\(333\) −0.825607 3.08121i −0.0452430 0.168849i
\(334\) 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 −0.995318 0.0966558i \(-0.969185\pi\)
−0.0966558 0.995318i \(-0.530815\pi\)
\(338\) 29.0477 + 7.78331i 1.57999 + 0.423357i
\(339\) 1.79920 3.11630i 0.0977190 0.169254i
\(340\) −15.0828 + 29.1666i −0.817978 + 1.58178i
\(341\) 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
\(345\) 12.7585 + 2.79220i 0.686893 + 0.150327i
\(346\) −11.1294 6.42558i −0.598322 0.345441i
\(347\) 27.4362 7.35151i 1.47285 0.394650i 0.568945 0.822376i \(-0.307352\pi\)
0.903908 + 0.427726i \(0.140685\pi\)
\(348\) 6.61704 24.6951i 0.354710 1.32380i
\(349\) 14.7663 0.790420 0.395210 0.918591i \(-0.370672\pi\)
0.395210 + 0.918591i \(0.370672\pi\)
\(350\) 0 0
\(351\) 1.25560 0.0670190
\(352\) −4.57032 + 17.0567i −0.243599 + 0.909124i
\(353\) 17.0603 4.57130i 0.908029 0.243306i 0.225568 0.974227i \(-0.427576\pi\)
0.682461 + 0.730922i \(0.260910\pi\)
\(354\) 7.28706 + 4.20719i 0.387303 + 0.223610i
\(355\) 16.6582 + 3.64567i 0.884127 + 0.193492i
\(356\) 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 −0.721093 0.692838i \(-0.756360\pi\)
0.239468 + 0.970904i \(0.423027\pi\)
\(360\) 7.92277 15.3208i 0.417567 0.807477i
\(361\) 1.65972 2.87471i 0.0873535 0.151301i
\(362\) 21.5765 + 5.78140i 1.13403 + 0.303864i
\(363\) 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
\(367\) 4.09618 + 15.2871i 0.213819 + 0.797982i 0.986579 + 0.163284i \(0.0522088\pi\)
−0.772760 + 0.634698i \(0.781125\pi\)
\(368\) 15.7911 + 58.9334i 0.823170 + 3.07211i
\(369\) 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
\(373\) −23.5976 6.32295i −1.22184 0.327390i −0.410440 0.911887i \(-0.634625\pi\)
−0.811396 + 0.584497i \(0.801292\pi\)
\(374\) 5.73489 9.93312i 0.296544 0.513630i
\(375\) 10.3638 + 4.19435i 0.535182 + 0.216595i
\(376\) −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 \(0.149515\pi\)
−0.891697 + 0.452634i \(0.850485\pi\)
\(380\) 9.33283 42.6447i 0.478764 2.18762i
\(381\) 9.62680 + 5.55803i 0.493196 + 0.284747i
\(382\) −19.9210 + 5.33782i −1.01925 + 0.273106i
\(383\) 5.90211 22.0270i 0.301584 1.12553i −0.634263 0.773118i \(-0.718696\pi\)
0.935846 0.352408i \(-0.114637\pi\)
\(384\) 4.51726 0.230520
\(385\) 0 0
\(386\) −50.4894 −2.56984
\(387\) −1.89811 + 7.08383i −0.0964862 + 0.360091i
\(388\) 58.5128 15.6785i 2.97054 0.795953i
\(389\) −13.3377 7.70053i −0.676249 0.390432i 0.122191 0.992507i \(-0.461008\pi\)
−0.798440 + 0.602074i \(0.794341\pi\)
\(390\) −6.22277 + 3.98811i −0.315102 + 0.201946i
\(391\) 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
\(395\) 9.63159 3.06557i 0.484618 0.154246i
\(396\) −3.60587 + 6.24554i −0.181202 + 0.313850i
\(397\) −22.0997 5.92159i −1.10915 0.297196i −0.342665 0.939458i \(-0.611330\pi\)
−0.766486 + 0.642261i \(0.777996\pi\)
\(398\) −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 \(0.825563\pi\)
\(402\) 5.71407 + 21.3252i 0.284992 + 1.06360i
\(403\) 1.98346 + 7.40238i 0.0988033 + 0.368739i
\(404\) 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
\(408\) −22.1923 5.94642i −1.09868 0.294392i
\(409\) −12.1586 + 21.0593i −0.601203 + 1.04131i 0.391437 + 0.920205i \(0.371978\pi\)
−0.992639 + 0.121108i \(0.961355\pi\)
\(410\) −4.02595 2.08192i −0.198827 0.102819i
\(411\) −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
\(415\) −11.5312 17.9925i −0.566044 0.883216i
\(416\) −13.1266 7.57863i −0.643583 0.371573i
\(417\) −11.5827 + 3.10357i −0.567207 + 0.151983i
\(418\) −3.94666 + 14.7291i −0.193037 + 0.720425i
\(419\) 15.9893 0.781127 0.390563 0.920576i \(-0.372280\pi\)
0.390563 + 0.920576i \(0.372280\pi\)
\(420\) 0 0
\(421\) 14.7000 0.716433 0.358216 0.933639i \(-0.383385\pi\)
0.358216 + 0.933639i \(0.383385\pi\)
\(422\) −8.15308 + 30.4277i −0.396886 + 1.48120i
\(423\) −11.7074 + 3.13699i −0.569233 + 0.152526i
\(424\) −5.14351 2.96961i −0.249791 0.144217i
\(425\) 2.50650 14.6802i 0.121583 0.712096i
\(426\) 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
\(430\) −13.0930 41.1364i −0.631401 1.98377i
\(431\) −11.1361 + 19.2883i −0.536407 + 0.929084i 0.462687 + 0.886522i \(0.346885\pi\)
−0.999094 + 0.0425619i \(0.986448\pi\)
\(432\) 10.0899 + 2.70359i 0.485452 + 0.130077i
\(433\) −28.0171 28.0171i −1.34642 1.34642i −0.889520 0.456896i \(-0.848961\pi\)
−0.456896 0.889520i \(-0.651039\pi\)
\(434\) 0 0
\(435\) 0.537211 + 11.5832i 0.0257573 + 0.555371i
\(436\) 18.3545 + 31.7910i 0.879023 + 1.52251i
\(437\) 5.98618 + 22.3407i 0.286358 + 1.06870i
\(438\) −6.56553 24.5029i −0.313713 1.17079i
\(439\) 1.17828 + 2.04084i 0.0562363 + 0.0974042i 0.892773 0.450507i \(-0.148757\pi\)
−0.836537 + 0.547911i \(0.815423\pi\)
\(440\) −1.16889 25.2033i −0.0557246 1.20152i
\(441\) 0 0
\(442\) 6.96162 + 6.96162i 0.331130 + 0.331130i
\(443\) 7.47553 + 2.00306i 0.355173 + 0.0951684i 0.431994 0.901877i \(-0.357810\pi\)
−0.0768206 + 0.997045i \(0.524477\pi\)
\(444\) −7.86331 + 13.6196i −0.373176 + 0.646360i
\(445\) −0.813754 2.55670i −0.0385756 0.121199i
\(446\) 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 \(-0.990984\pi\)
0.999599 0.0283205i \(-0.00901591\pi\)
\(450\) −2.21531 + 12.9748i −0.104431 + 0.611638i
\(451\) 0.975405 + 0.563150i 0.0459300 + 0.0265177i
\(452\) −17.1360 + 4.59159i −0.806011 + 0.215970i
\(453\) 3.48240 12.9965i 0.163617 0.610629i
\(454\) 64.5881 3.03127
\(455\) 0 0
\(456\) 30.5448 1.43039
\(457\) −7.71489 + 28.7924i −0.360887 + 1.34685i 0.512024 + 0.858971i \(0.328896\pi\)
−0.872912 + 0.487879i \(0.837771\pi\)
\(458\) −63.7692 + 17.0869i −2.97974 + 0.798418i
\(459\) −2.57949 1.48927i −0.120400 0.0695131i
\(460\) −34.7436 54.2116i −1.61993 2.52763i
\(461\) 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 −0.00746987 + 0.999972i \(0.502378\pi\)
−0.999972 + 0.00746987i \(0.997622\pi\)
\(464\) −46.9121 + 27.0847i −2.17784 + 1.25738i
\(465\) 12.1227 + 6.26898i 0.562179 + 0.290717i
\(466\) 4.17225 7.22655i 0.193276 0.334763i
\(467\) −9.71653 2.60354i −0.449627 0.120477i 0.0268978 0.999638i \(-0.491437\pi\)
−0.476525 + 0.879161i \(0.658104\pi\)
\(468\) −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
\(472\) −6.38123 23.8151i −0.293720 1.09618i
\(473\) 2.77653 + 10.3622i 0.127665 + 0.476452i
\(474\) 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
\(478\) 54.3575 + 14.5651i 2.48626 + 0.666190i
\(479\) −15.8875 + 27.5179i −0.725917 + 1.25733i 0.232678 + 0.972554i \(0.425251\pi\)
−0.958595 + 0.284771i \(0.908082\pi\)
\(480\) −25.7217 + 8.18679i −1.17403 + 0.373674i
\(481\) 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
\(485\) −23.1319 + 14.8250i −1.05036 + 0.673168i
\(486\) 2.27982 + 1.31626i 0.103415 + 0.0597066i
\(487\) 6.57642 1.76215i 0.298006 0.0798505i −0.106718 0.994289i \(-0.534034\pi\)
0.404724 + 0.914439i \(0.367368\pi\)
\(488\) 2.83620 10.5848i 0.128389 0.479153i
\(489\) 14.5305 0.657092
\(490\) 0 0
\(491\) 28.3401 1.27897 0.639484 0.768804i \(-0.279148\pi\)
0.639484 + 0.768804i \(0.279148\pi\)
\(492\) 0.982486 3.66669i 0.0442939 0.165307i
\(493\) 14.9196 3.99769i 0.671943 0.180047i
\(494\) −11.3353 6.54445i −0.510000 0.294449i
\(495\) 0.699288 3.19527i 0.0314307 0.143617i
\(496\) 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 −0.432806 0.901487i \(-0.642476\pi\)
0.564308 + 0.825564i \(0.309143\pi\)
\(500\) −21.5073 50.7514i −0.961836 2.26967i
\(501\) 0.207188 0.358861i 0.00925649 0.0160327i
\(502\) −41.5605 11.1361i −1.85494 0.497029i
\(503\) −8.32921 8.32921i −0.371381 0.371381i 0.496599 0.867980i \(-0.334582\pi\)
−0.867980 + 0.496599i \(0.834582\pi\)
\(504\) 0 0
\(505\) −25.3557 23.1080i −1.12831 1.02829i
\(506\) 11.2459 + 19.4785i 0.499942 + 0.865925i
\(507\) −2.95661 11.0342i −0.131308 0.490047i
\(508\) −14.1842 52.9362i −0.629323 2.34866i
\(509\) 19.4726 + 33.7275i 0.863108 + 1.49495i 0.868914 + 0.494963i \(0.164818\pi\)
−0.00580659 + 0.999983i \(0.501848\pi\)
\(510\) 17.5143 0.812285i 0.775545 0.0359686i
\(511\) 0 0
\(512\) 24.7846 + 24.7846i 1.09534 + 1.09534i
\(513\) 3.82494 + 1.02489i 0.168875 + 0.0452500i
\(514\) 39.6594 68.6920i 1.74930 3.02988i
\(515\) 12.0676 23.3359i 0.531760 1.02830i
\(516\) 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
\(520\) 21.1560 + 4.63002i 0.927753 + 0.203040i
\(521\) 6.12042 + 3.53363i 0.268141 + 0.154811i 0.628042 0.778179i \(-0.283856\pi\)
−0.359902 + 0.932990i \(0.617190\pi\)
\(522\) −13.1863 + 3.53326i −0.577150 + 0.154647i
\(523\) 5.33985 19.9286i 0.233495 0.871416i −0.745326 0.666700i \(-0.767706\pi\)
0.978821 0.204716i \(-0.0656272\pi\)
\(524\) −30.4788 −1.33147
\(525\) 0 0
\(526\) 60.8508 2.65322
\(527\) 4.70517 17.5599i 0.204960 0.764923i
\(528\) 14.7595 3.95478i 0.642323 0.172110i
\(529\) 9.62588 + 5.55750i 0.418516 + 0.241631i
\(530\) 4.42761 + 0.968986i 0.192323 + 0.0420901i
\(531\) 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
\(535\) 6.37708 12.3318i 0.275705 0.533150i
\(536\) 32.3449 56.0229i 1.39708 2.41982i
\(537\) 1.92949 + 0.517006i 0.0832638 + 0.0223105i
\(538\) 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 \(0.964276\pi\)
\(542\) 5.30108 + 19.7839i 0.227701 + 0.849792i
\(543\) −2.19615 8.19615i −0.0942459 0.351731i
\(544\) 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 0.535515 0.844526i \(-0.320118\pi\)
−0.844526 + 0.535515i \(0.820118\pi\)
\(548\) 60.9869 + 16.3414i 2.60523 + 0.698069i
\(549\) 0.710320 1.23031i 0.0303157 0.0525084i
\(550\) 6.68332 + 18.0569i 0.284978 + 0.769949i
\(551\) −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
\(555\) 1.52494 6.96792i 0.0647300 0.295772i
\(556\) 51.1981 + 29.5593i 2.17128 + 1.25359i
\(557\) 0.763508 0.204581i 0.0323509 0.00866839i −0.242607 0.970125i \(-0.578003\pi\)
0.274958 + 0.961456i \(0.411336\pi\)
\(558\) −4.15856 + 15.5200i −0.176046 + 0.657012i
\(559\) −9.20823 −0.389467
\(560\) 0 0
\(561\) −4.35697 −0.183951
\(562\) 14.4117 53.7853i 0.607922 2.26879i
\(563\) −0.959599 + 0.257124i −0.0404423 + 0.0108365i −0.278983 0.960296i \(-0.589997\pi\)
0.238541 + 0.971132i \(0.423331\pi\)
\(564\) 51.7494 + 29.8775i 2.17904 + 1.25807i
\(565\) 6.77439 4.34164i 0.285001 0.182654i
\(566\) 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 −0.313057 0.949734i \(-0.601353\pi\)
0.665966 + 0.745982i \(0.268020\pi\)
\(570\) −22.2117 + 7.06962i −0.930348 + 0.296114i
\(571\) 0.493342 0.854493i 0.0206457 0.0357594i −0.855518 0.517773i \(-0.826761\pi\)
0.876164 + 0.482014i \(0.160094\pi\)
\(572\) −8.74652 2.34362i −0.365710 0.0979918i
\(573\) 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
\(577\) −3.78872 14.1397i −0.157726 0.588643i −0.998856 0.0478100i \(-0.984776\pi\)
0.841130 0.540833i \(-0.181891\pi\)
\(578\) 5.53819 + 20.6688i 0.230358 + 0.859708i
\(579\) 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
\(583\) −1.08792 0.291508i −0.0450572 0.0120730i
\(584\) −37.1646 + 64.3710i −1.53788 + 2.66369i
\(585\) 2.49389 + 1.28965i 0.103110 + 0.0533205i
\(586\) 5.05272 2.91719i 0.208726 0.120508i
\(587\) −21.1413 + 21.1413i −0.872594 + 0.872594i −0.992755 0.120160i \(-0.961659\pi\)
0.120160 + 0.992755i \(0.461659\pi\)
\(588\) 0 0
\(589\) 24.1689i 0.995862i
\(590\) 10.1524 + 15.8410i 0.417966 + 0.652165i
\(591\) −14.0590 8.11696i −0.578310 0.333887i
\(592\) 32.1859 8.62419i 1.32283 0.354452i
\(593\) 2.59079 9.66895i 0.106391 0.397056i −0.892108 0.451821i \(-0.850774\pi\)
0.998499 + 0.0547654i \(0.0174411\pi\)
\(594\) 3.85081 0.158001
\(595\) 0 0
\(596\) 0.477365 0.0195536
\(597\) −5.21437 + 19.4603i −0.213410 + 0.796457i
\(598\) −18.6483 + 4.99679i −0.762585 + 0.204334i
\(599\) 6.18210 + 3.56924i 0.252594 + 0.145835i 0.620951 0.783849i \(-0.286746\pi\)
−0.368358 + 0.929684i \(0.620080\pi\)
\(600\) 31.4726 22.2927i 1.28486 0.910096i
\(601\) 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
\(605\) 6.00884 + 18.8789i 0.244294 + 0.767537i
\(606\) 20.1941 34.9771i 0.820328 1.42085i
\(607\) 7.32715 + 1.96330i 0.297400 + 0.0796880i 0.404434 0.914567i \(-0.367469\pi\)
−0.107034 + 0.994255i \(0.534135\pi\)
\(608\) −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
\(612\) 3.80064 + 14.1842i 0.153632 + 0.573362i
\(613\) −3.83917 14.3280i −0.155062 0.578701i −0.999100 0.0424169i \(-0.986494\pi\)
0.844038 0.536284i \(-0.180172\pi\)
\(614\) −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 0.982631 0.185571i \(-0.0594135\pi\)
−0.185571 + 0.982631i \(0.559414\pi\)
\(618\) 29.8754 + 8.00508i 1.20176 + 0.322011i
\(619\) 6.03375 10.4508i 0.242517 0.420052i −0.718914 0.695099i \(-0.755360\pi\)
0.961431 + 0.275048i \(0.0886936\pi\)
\(620\) −20.4070 64.1158i −0.819564 2.57495i
\(621\) 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
\(625\) 16.2765 + 18.9757i 0.651060 + 0.759026i
\(626\) 18.4559 + 10.6555i 0.737647 + 0.425880i
\(627\) 5.59508 1.49920i 0.223446 0.0598722i
\(628\) 2.97313 11.0959i 0.118641 0.442774i
\(629\) −9.50124 −0.378839
\(630\) 0 0
\(631\) 30.4435 1.21194 0.605969 0.795488i \(-0.292786\pi\)
0.605969 + 0.795488i \(0.292786\pi\)
\(632\) 9.02442 33.6796i 0.358972 1.33970i
\(633\) 11.5584 3.09707i 0.459406 0.123098i
\(634\) 2.42643 + 1.40090i 0.0963660 + 0.0556369i
\(635\) 13.4121 + 20.9273i 0.532242 + 0.830474i
\(636\) 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
\(640\) 8.97222 + 4.63976i 0.354658 + 0.183403i
\(641\) −18.2964 + 31.6904i −0.722666 + 1.25169i 0.237262 + 0.971446i \(0.423750\pi\)
−0.959928 + 0.280248i \(0.909583\pi\)
\(642\) 15.7876 + 4.23027i 0.623086 + 0.166955i
\(643\) −12.1140 12.1140i −0.477731 0.477731i 0.426675 0.904405i \(-0.359685\pi\)
−0.904405 + 0.426675i \(0.859685\pi\)
\(644\) 0 0
\(645\) −11.0460 + 12.1204i −0.434935 + 0.477240i
\(646\) 15.5247 + 26.8896i 0.610813 + 1.05796i
\(647\) −6.99030 26.0881i −0.274817 1.02563i −0.955964 0.293484i \(-0.905185\pi\)
0.681147 0.732147i \(-0.261481\pi\)
\(648\) −1.99642 7.45075i −0.0784269 0.292693i
\(649\) −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
\(653\) −27.8271 7.45625i −1.08896 0.291786i −0.330698 0.943737i \(-0.607284\pi\)
−0.758261 + 0.651951i \(0.773951\pi\)
\(654\) 9.80067 16.9753i 0.383237 0.663785i
\(655\) 13.1726 4.19262i 0.514696 0.163819i
\(656\) −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 \(0.210160\pi\)
−0.789847 + 0.613304i \(0.789840\pi\)
\(660\) −13.5769 + 8.70131i −0.528481 + 0.338698i
\(661\) −41.7321 24.0940i −1.62319 0.937149i −0.986060 0.166392i \(-0.946788\pi\)
−0.637129 0.770757i \(-0.719878\pi\)
\(662\) 40.1974 10.7709i 1.56231 0.418621i
\(663\) 0.967945 3.61242i 0.0375919 0.140295i
\(664\) −73.7201 −2.86089
\(665\) 0 0
\(666\) 8.39746 0.325395
\(667\) −7.83932 + 29.2567i −0.303540 + 1.13283i
\(668\) −1.97332 + 0.528748i −0.0763499 + 0.0204579i
\(669\) −0.809446 0.467334i −0.0312950 0.0180682i
\(670\) −10.5542 + 48.2253i −0.407743 + 1.86311i
\(671\) 2.07810i 0.0802241i
\(672\) 0 0
\(673\) −30.6900 + 30.6900i −1.18301 + 1.18301i −0.204055 + 0.978960i \(0.565412\pi\)
−0.978960 + 0.204055i \(0.934588\pi\)
\(674\) 64.6314 37.3149i 2.48951 1.43732i
\(675\) 4.68912 1.73556i 0.180484 0.0668018i
\(676\) −28.1595 + 48.7738i −1.08306 + 1.87591i
\(677\) 2.10450 + 0.563899i 0.0808825 + 0.0216724i 0.299033 0.954243i \(-0.403336\pi\)
−0.218151 + 0.975915i \(0.570002\pi\)
\(678\) 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
\(682\) 6.08310 + 22.7024i 0.232934 + 0.869321i
\(683\) 5.20319 + 19.4186i 0.199094 + 0.743030i 0.991169 + 0.132606i \(0.0423345\pi\)
−0.792074 + 0.610424i \(0.790999\pi\)
\(684\) −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
\(688\) −73.9968 19.8274i −2.82110 0.755912i
\(689\) 0.483386 0.837249i 0.0184155 0.0318967i
\(690\) −15.7930 + 30.5399i −0.601228 + 1.16264i
\(691\) −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
\(695\) −26.1934 5.73245i −0.993572 0.217444i
\(696\) 34.6415 + 20.0003i 1.31308 + 0.758108i
\(697\) 2.21523 0.593570i 0.0839079 0.0224831i
\(698\) −10.0609 + 37.5478i −0.380811 + 1.42121i
\(699\) −3.16979 −0.119892
\(700\) 0 0
\(701\) −44.3183 −1.67388 −0.836939 0.547297i \(-0.815657\pi\)
−0.836939 + 0.547297i \(0.815657\pi\)
\(702\) −0.855497 + 3.19276i −0.0322887 + 0.120503i
\(703\) 12.2012 3.26930i 0.460176 0.123304i
\(704\) −13.7920 7.96284i −0.519807 0.300111i
\(705\) −26.4754 5.79417i −0.997122 0.218221i
\(706\) 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 −0.513243 0.858243i \(-0.671556\pi\)
0.486639 + 0.873603i \(0.338223\pi\)
\(710\) −20.6203 + 39.8748i −0.773864 + 1.49647i
\(711\) 2.26015 3.91469i 0.0847621 0.146812i
\(712\) −8.94022 2.39553i −0.335049 0.0897761i
\(713\) 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
\(717\) −5.53276 20.6485i −0.206625 0.771134i
\(718\) −7.17947 26.7941i −0.267935 0.999949i
\(719\) −0.00381028 0.00659960i −0.000142099 0.000246124i 0.865954 0.500123i \(-0.166712\pi\)
−0.866096 + 0.499877i \(0.833379\pi\)
\(720\) 17.2638 + 15.7335i 0.643385 + 0.586351i
\(721\) 0 0
\(722\) 6.17902 + 6.17902i 0.229959 + 0.229959i
\(723\) 0.602863 + 0.161537i 0.0224207 + 0.00600761i
\(724\) −20.9167 + 36.2289i −0.777365 + 1.34644i
\(725\) −10.8303 + 23.5584i −0.402227 + 0.874937i
\(726\) −20.1998 + 11.6624i −0.749685 + 0.432831i
\(727\) 28.5738 28.5738i 1.05974 1.05974i 0.0616465 0.998098i \(-0.480365\pi\)
0.998098 0.0616465i \(-0.0196352\pi\)
\(728\) 0 0
\(729\) 1.00000i 0.0370370i
\(730\) 12.1269 55.4115i 0.448835 2.05087i
\(731\) 18.9173 + 10.9219i 0.699680 + 0.403960i
\(732\) −6.76528 + 1.81275i −0.250052 + 0.0670012i
\(733\) −8.84033 + 32.9926i −0.326525 + 1.21861i 0.586244 + 0.810134i \(0.300606\pi\)
−0.912770 + 0.408475i \(0.866061\pi\)
\(734\) −41.6632 −1.53782
\(735\) 0 0
\(736\) −70.5085 −2.59898
\(737\) 3.17510 11.8496i 0.116956 0.436486i
\(738\) −1.95788 + 0.524613i −0.0720707 + 0.0193113i
\(739\) 32.8676 + 18.9761i 1.20905 + 0.698047i 0.962552 0.271096i \(-0.0873860\pi\)
0.246500 + 0.969143i \(0.420719\pi\)
\(740\) −29.6072 + 18.9749i −1.08838 + 0.697532i
\(741\) 4.97202i 0.182652i
\(742\) 0 0
\(743\) −18.8022 + 18.8022i −0.689784 + 0.689784i −0.962184 0.272400i \(-0.912183\pi\)
0.272400 + 0.962184i \(0.412183\pi\)
\(744\) 40.7721 23.5398i 1.49478 0.863010i
\(745\) −0.206312 + 0.0656655i −0.00755867 + 0.00240580i
\(746\) 32.1562 55.6961i 1.17732 2.03918i
\(747\) −9.23152 2.47358i −0.337764 0.0905035i
\(748\) 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 \(0.833948\pi\)
\(752\) −32.7686 122.294i −1.19495 4.45960i
\(753\) 4.23022 + 15.7874i 0.154158 + 0.575325i
\(754\) −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 0.761949 0.647637i \(-0.224243\pi\)
−0.647637 + 0.761949i \(0.724243\pi\)
\(758\) −44.8137 12.0078i −1.62771 0.436143i
\(759\) 4.27193 7.39921i 0.155061 0.268574i
\(760\) 60.6684 + 31.3731i 2.20067 + 1.13802i
\(761\) 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
\(765\) −3.59375 5.60744i −0.129932 0.202737i
\(766\) 51.9891 + 30.0159i 1.87844 + 1.08452i
\(767\) 3.87656 1.03872i 0.139975 0.0375061i
\(768\) 2.55782 9.54591i 0.0922973 0.344458i
\(769\) 8.16835 0.294558 0.147279 0.989095i \(-0.452948\pi\)
0.147279 + 0.989095i \(0.452948\pi\)
\(770\) 0 0